LMFDB - Embedded newform 640.2.q.e.289.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [640,2,Mod(289,640)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("640.289"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,8,0,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.534694406811304329216.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			289.7
Root			$-1.40501 - 0.161069i$ of defining polynomial
Character	$\chi$	$=$	640.289
Dual form			640.2.q.e.609.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.86033 - 1.86033i) q^{3} +(1.17216 + 1.90421i) q^{5} +3.61392 q^{7} -3.92163i q^{9} +(0.0947876 - 0.0947876i) q^{11} +(-2.59462 + 2.59462i) q^{13} +(5.72307 + 1.36185i) q^{15} -1.89939i q^{17} +(2.16418 + 2.16418i) q^{19} +(6.72307 - 6.72307i) q^{21} -5.08251 q^{23} +(-2.25207 + 4.46410i) q^{25} +(-1.71452 - 1.71452i) q^{27} +(-1.25896 - 1.25896i) q^{29} -1.27453 q^{31} -0.352672i q^{33} +(4.23610 + 6.88168i) q^{35} +(-2.25207 - 2.25207i) q^{37} +9.65368i q^{39} -8.52451i q^{41} +(-1.61439 - 1.61439i) q^{43} +(7.46762 - 4.59679i) q^{45} +2.53884i q^{47} +6.06040 q^{49} +(-3.53349 - 3.53349i) q^{51} +(-5.67100 - 5.67100i) q^{53} +(0.291602 + 0.0693893i) q^{55} +8.05215 q^{57} +(7.81785 - 7.81785i) q^{59} +(-3.46410 - 3.46410i) q^{61} -14.1724i q^{63} +(-7.98203 - 1.89939i) q^{65} +(-6.29856 + 6.29856i) q^{67} +(-9.45512 + 9.45512i) q^{69} -11.3074i q^{71} -16.1786 q^{73} +(4.11511 + 12.4943i) q^{75} +(0.342555 - 0.342555i) q^{77} +1.13575 q^{79} +5.38573 q^{81} +(3.75489 - 3.75489i) q^{83} +(3.61685 - 2.22640i) q^{85} -4.68417 q^{87} +3.98203i q^{89} +(-9.37674 + 9.37674i) q^{91} +(-2.37103 + 2.37103i) q^{93} +(-1.58429 + 6.65783i) q^{95} +10.3042i q^{97} +(-0.371721 - 0.371721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{5} - 8 q^{11} + 8 q^{19} + 16 q^{21} + 16 q^{29} + 16 q^{31} + 24 q^{35} - 8 q^{45} + 16 q^{49} + 16 q^{51} + 24 q^{59} - 32 q^{69} - 48 q^{75} + 16 q^{79} - 16 q^{81} + 16 q^{91} + 32 q^{95}+ \cdots - 88 q^{99}+O(q^{100}) $ 16 * q + 8 * q^5 - 8 * q^11 + 8 * q^19 + 16 * q^21 + 16 * q^29 + 16 * q^31 + 24 * q^35 - 8 * q^45 + 16 * q^49 + 16 * q^51 + 24 * q^59 - 32 * q^69 - 48 * q^75 + 16 * q^79 - 16 * q^81 + 16 * q^91 + 32 * q^95 - 88 * q^99

Character values

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

$n$	$257$	$261$	$511$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.86033	−	1.86033i	1.07406	−	1.07406i	0.0770310	−	0.997029i	$-0.475456\pi$
$3$	1.86033	−	1.86033i	1.07406	−	1.07406i	0.997029	−	0.0770310i	$-0.0245441\pi$
$4$		0			0
$5$	1.17216	+	1.90421i	0.524207	+	0.851591i
$5$	1.17216	+	1.90421i	0.524207	+	0.851591i
$6$		0			0
$7$	3.61392			1.36593			0.682966	−	0.730450i	$-0.260690\pi$
$7$	3.61392			1.36593			0.682966	+	0.730450i	$0.260690\pi$
$8$		0			0
$9$		−	3.92163i		−	1.30721i
$10$		0			0
$11$	0.0947876	−	0.0947876i	0.0285795	−	0.0285795i	−0.692673	−	0.721252i	$-0.743567\pi$
$11$	0.0947876	−	0.0947876i	0.0285795	−	0.0285795i	0.721252	+	0.692673i	$0.243567\pi$
$12$		0			0
$13$	−2.59462	+	2.59462i	−0.719618	+	0.719618i	−0.968527	−	0.248909i	$-0.919928\pi$
$13$	−2.59462	+	2.59462i	−0.719618	+	0.719618i	0.248909	+	0.968527i	$0.419928\pi$
$14$		0			0
$15$	5.72307	+	1.36185i	1.47769	+	0.351629i
$16$		0			0
$17$		−	1.89939i		−	0.460671i	−0.973111	−	0.230335i	$-0.926018\pi$
$17$		−	1.89939i		−	0.460671i	0.973111	−	0.230335i	$-0.0739823\pi$
$18$		0			0
$19$	2.16418	+	2.16418i	0.496496	+	0.496496i	0.910345	−	0.413849i	$-0.135816\pi$
$19$	2.16418	+	2.16418i	0.496496	+	0.496496i	−0.413849	+	0.910345i	$0.635816\pi$
$20$		0			0
$21$	6.72307	−	6.72307i	1.46709	−	1.46709i
$22$		0			0
$23$	−5.08251			−1.05978			−0.529888	−	0.848068i	$-0.677766\pi$
$23$	−5.08251			−1.05978			−0.529888	+	0.848068i	$0.677766\pi$
$24$		0			0
$25$	−2.25207	+	4.46410i	−0.450413	+	0.892820i
$26$		0			0
$27$	−1.71452	−	1.71452i	−0.329960	−	0.329960i
$28$		0			0
$29$	−1.25896	−	1.25896i	−0.233784	−	0.233784i	0.580486	−	0.814270i	$-0.302863\pi$
$29$	−1.25896	−	1.25896i	−0.233784	−	0.233784i	−0.814270	+	0.580486i	$0.802863\pi$
$30$		0			0
$31$	−1.27453			−0.228912			−0.114456	−	0.993428i	$-0.536512\pi$
$31$	−1.27453			−0.228912			−0.114456	+	0.993428i	$0.536512\pi$
$32$		0			0
$33$		−	0.352672i		−	0.0613923i
$34$		0			0
$35$	4.23610	+	6.88168i	0.716032	+	1.16322i
$36$		0			0
$37$	−2.25207	−	2.25207i	−0.370237	−	0.370237i	0.497326	−	0.867564i	$-0.334315\pi$
$37$	−2.25207	−	2.25207i	−0.370237	−	0.370237i	−0.867564	+	0.497326i	$0.834315\pi$
$38$		0			0
$39$			9.65368i			1.54583i
$40$		0			0
$41$		−	8.52451i		−	1.33130i	−0.746262	−	0.665652i	$-0.768153\pi$
$41$		−	8.52451i		−	1.33130i	0.746262	−	0.665652i	$-0.231847\pi$
$42$		0			0
$43$	−1.61439	−	1.61439i	−0.246192	−	0.246192i	0.573214	−	0.819406i	$-0.305696\pi$
$43$	−1.61439	−	1.61439i	−0.246192	−	0.246192i	−0.819406	+	0.573214i	$0.805696\pi$
$44$		0			0
$45$	7.46762	−	4.59679i	1.11321	−	0.685249i
$46$		0			0
$47$			2.53884i			0.370328i	0.982708	+	0.185164i	$0.0592816\pi$
$47$			2.53884i			0.370328i	−0.982708	+	0.185164i	$0.940718\pi$
$48$		0			0
$49$	6.06040			0.865772
$50$		0			0
$51$	−3.53349	−	3.53349i	−0.494788	−	0.494788i
$52$		0			0
$53$	−5.67100	−	5.67100i	−0.778971	−	0.778971i	0.200684	−	0.979656i	$-0.435683\pi$
$53$	−5.67100	−	5.67100i	−0.778971	−	0.778971i	−0.979656	+	0.200684i	$0.935683\pi$
$54$		0			0
$55$	0.291602	+	0.0693893i	0.0393197	+	0.00935646i
$56$		0			0
$57$	8.05215			1.06653
$58$		0			0
$59$	7.81785	−	7.81785i	1.01780	−	1.01780i	0.0179591	−	0.999839i	$-0.494283\pi$
$59$	7.81785	−	7.81785i	1.01780	−	1.01780i	0.999839	−	0.0179591i	$-0.00571688\pi$
$60$		0			0
$61$	−3.46410	−	3.46410i	−0.443533	−	0.443533i	0.449665	−	0.893197i	$-0.351543\pi$
$61$	−3.46410	−	3.46410i	−0.443533	−	0.443533i	−0.893197	+	0.449665i	$0.851543\pi$
$62$		0			0
$63$		−	14.1724i		−	1.78556i
$64$		0			0
$65$	−7.98203	−	1.89939i	−0.990049	−	0.235591i
$66$		0			0
$67$	−6.29856	+	6.29856i	−0.769491	+	0.769491i	−0.978017	−	0.208526i	$-0.933134\pi$
$67$	−6.29856	+	6.29856i	−0.769491	+	0.769491i	0.208526	+	0.978017i	$0.433134\pi$
$68$		0			0
$69$	−9.45512	+	9.45512i	−1.13826	+	1.13826i
$70$		0			0
$71$		−	11.3074i		−	1.34194i	−0.741486	−	0.670968i	$-0.765879\pi$
$71$		−	11.3074i		−	1.34194i	0.741486	−	0.670968i	$-0.234121\pi$
$72$		0			0
$73$	−16.1786			−1.89356			−0.946779	−	0.321885i	$-0.895684\pi$
$73$	−16.1786			−1.89356			−0.946779	+	0.321885i	$0.895684\pi$
$74$		0			0
$75$	4.11511	+	12.4943i	0.475172	+	1.44271i
$76$		0			0
$77$	0.342555	−	0.342555i	0.0390377	−	0.0390377i
$78$		0			0
$79$	1.13575			0.127782			0.0638908	−	0.997957i	$-0.479649\pi$
$79$	1.13575			0.127782			0.0638908	+	0.997957i	$0.479649\pi$
$80$		0			0
$81$	5.38573			0.598414
$82$		0			0
$83$	3.75489	−	3.75489i	0.412153	−	0.412153i	−0.470335	−	0.882488i	$-0.655867\pi$
$83$	3.75489	−	3.75489i	0.412153	−	0.412153i	0.882488	+	0.470335i	$0.155867\pi$
$84$		0			0
$85$	3.61685	−	2.22640i	0.392303	−	0.241487i
$86$		0			0
$87$	−4.68417			−0.502196
$88$		0			0
$89$			3.98203i			0.422094i	0.977476	+	0.211047i	$0.0676874\pi$
$89$			3.98203i			0.422094i	−0.977476	+	0.211047i	$0.932313\pi$
$90$		0			0
$91$	−9.37674	+	9.37674i	−0.982950	+	0.982950i
$92$		0			0
$93$	−2.37103	+	2.37103i	−0.245865	+	0.245865i
$94$		0			0
$95$	−1.58429	+	6.65783i	−0.162544	+	0.683079i
$96$		0			0
$97$			10.3042i			1.04623i	0.852261	+	0.523117i	$0.175231\pi$
$97$			10.3042i			1.04623i	−0.852261	+	0.523117i	$0.824769\pi$
$98$		0			0
$99$	−0.371721	−	0.371721i	−0.0373594	−	0.0373594i
$100$		0			0
$101$	−1.25896	+	1.25896i	−0.125272	+	0.125272i	−0.766963	−	0.641691i	$-0.778233\pi$
$101$	−1.25896	+	1.25896i	−0.125272	+	0.125272i	0.641691	+	0.766963i	$0.278233\pi$
$102$		0			0
$103$	10.8655			1.07061			0.535306	−	0.844658i	$-0.320196\pi$
$103$	10.8655			1.07061			0.535306	+	0.844658i	$0.320196\pi$
$104$		0			0
$105$	20.6827	+	4.92163i	2.01842	+	0.480302i
$106$		0			0
$107$	9.48167	+	9.48167i	0.916628	+	0.916628i	0.996782	−	0.0801549i	$-0.0255415\pi$
$107$	9.48167	+	9.48167i	0.916628	+	0.916628i	−0.0801549	+	0.996782i	$0.525541\pi$
$108$		0			0
$109$	8.57530	+	8.57530i	0.821365	+	0.821365i	0.986304	−	0.164939i	$-0.0527427\pi$
$109$	8.57530	+	8.57530i	0.821365	+	0.821365i	−0.164939	+	0.986304i	$0.552743\pi$
$110$		0			0
$111$	−8.37915			−0.795314
$112$		0			0
$113$			12.5286i			1.17860i	0.807916	+	0.589298i	$0.200595\pi$
$113$			12.5286i			1.17860i	−0.807916	+	0.589298i	$0.799405\pi$
$114$		0			0
$115$	−5.95753	−	9.67818i	−0.555542	−	0.902495i
$116$		0			0
$117$	10.1751	+	10.1751i	0.940691	+	0.940691i
$118$		0			0
$119$		−	6.86425i		−	0.629245i
$120$		0			0
$121$			10.9820i			0.998366i
$122$		0			0
$123$	−15.8584	−	15.8584i	−1.42990	−	1.42990i
$124$		0			0
$125$	−11.1404	+	0.944243i	−0.996427	+	0.0844556i
$126$		0			0
$127$			2.94200i			0.261061i	0.991444	+	0.130530i	$0.0416680\pi$
$127$			2.94200i			0.261061i	−0.991444	+	0.130530i	$0.958332\pi$
$128$		0			0
$129$	−6.00658			−0.528850
$130$		0			0
$131$	−6.54333	−	6.54333i	−0.571693	−	0.571693i	0.360908	−	0.932601i	$-0.382467\pi$
$131$	−6.54333	−	6.54333i	−0.571693	−	0.571693i	−0.932601	+	0.360908i	$0.882467\pi$
$132$		0			0
$133$	7.82116	+	7.82116i	0.678180	+	0.678180i
$134$		0			0
$135$	1.25512	−	5.27453i	0.108023	−	0.453959i
$136$		0			0
$137$	−1.82513			−0.155931			−0.0779657	−	0.996956i	$-0.524842\pi$
$137$	−1.82513			−0.155931			−0.0779657	+	0.996956i	$0.524842\pi$
$138$		0			0
$139$	5.36931	−	5.36931i	0.455419	−	0.455419i	−0.441729	−	0.897148i	$-0.645635\pi$
$139$	5.36931	−	5.36931i	0.455419	−	0.455419i	0.897148	+	0.441729i	$0.145635\pi$
$140$		0			0
$141$	4.72307	+	4.72307i	0.397754	+	0.397754i
$142$		0			0
$143$			0.491875i			0.0411327i
$144$		0			0
$145$	0.921626	−	3.87305i	0.0765369	−	0.321639i
$146$		0			0
$147$	11.2743	−	11.2743i	0.929891	−	0.929891i
$148$		0			0
$149$	−4.37915	+	4.37915i	−0.358754	+	0.358754i	−0.863354	−	0.504600i	$-0.831640\pi$
$149$	−4.37915	+	4.37915i	−0.358754	+	0.358754i	0.504600	+	0.863354i	$0.331640\pi$
$150$		0			0
$151$			12.9610i			1.05475i	0.849631	+	0.527377i	$0.176824\pi$
$151$			12.9610i			1.05475i	−0.849631	+	0.527377i	$0.823176\pi$
$152$		0			0
$153$	−7.44871			−0.602193
$154$		0			0
$155$	−1.49395	−	2.42697i	−0.119997	−	0.194939i
$156$		0			0
$157$	9.12723	−	9.12723i	0.728432	−	0.728432i	−0.241875	−	0.970307i	$-0.577762\pi$
$157$	9.12723	−	9.12723i	0.728432	−	0.728432i	0.970307	+	0.241875i	$0.0777624\pi$
$158$		0			0
$159$	−21.0998			−1.67332
$160$		0			0
$161$	−18.3678			−1.44758
$162$		0			0
$163$	−6.15099	+	6.15099i	−0.481783	+	0.481783i	−0.905701	−	0.423918i	$-0.860654\pi$
$163$	−6.15099	+	6.15099i	−0.481783	+	0.481783i	0.423918	+	0.905701i	$0.360654\pi$
$164$		0			0
$165$	0.671562	−	0.413389i	0.0522811	−	0.0321823i
$166$		0			0
$167$	−0.710173			−0.0549548			−0.0274774	−	0.999622i	$-0.508747\pi$
$167$	−0.710173			−0.0549548			−0.0274774	+	0.999622i	$0.508747\pi$
$168$		0			0
$169$		−	0.464102i		−	0.0357001i
$170$		0			0
$171$	8.48709	−	8.48709i	0.649024	−	0.649024i
$172$		0			0
$173$	−14.1773	+	14.1773i	−1.07788	+	1.07788i	−0.0811779	+	0.996700i	$0.525868\pi$
$173$	−14.1773	+	14.1773i	−1.07788	+	1.07788i	−0.996700	+	0.0811779i	$0.974132\pi$
$174$		0			0
$175$	−8.13878	+	16.1329i	−0.615234	+	1.21953i
$176$		0			0
$177$		−	29.0875i		−	2.18635i
$178$		0			0
$179$	−9.00502	−	9.00502i	−0.673067	−	0.673067i	0.285355	−	0.958422i	$-0.407889\pi$
$179$	−9.00502	−	9.00502i	−0.673067	−	0.673067i	−0.958422	+	0.285355i	$0.907889\pi$
$180$		0			0
$181$	−14.1872	+	14.1872i	−1.05452	+	1.05452i	−0.0560986	+	0.998425i	$0.517866\pi$
$181$	−14.1872	+	14.1872i	−1.05452	+	1.05452i	−0.998425	+	0.0560986i	$0.982134\pi$
$182$		0			0
$183$	−12.8887			−0.952761
$184$		0			0
$185$	1.64863	−	6.92820i	0.121209	−	0.509372i
$186$		0			0
$187$	−0.180039	−	0.180039i	−0.0131657	−	0.0131657i
$188$		0			0
$189$	−6.19615	−	6.19615i	−0.450704	−	0.450704i
$190$		0			0
$191$	18.9282			1.36960			0.684798	−	0.728733i	$-0.259890\pi$
$191$	18.9282			1.36960			0.684798	+	0.728733i	$0.259890\pi$
$192$		0			0
$193$		−	21.3880i		−	1.53954i	−0.638319	−	0.769772i	$-0.720370\pi$
$193$		−	21.3880i		−	1.53954i	0.638319	−	0.769772i	$-0.279630\pi$
$194$		0			0
$195$	−18.3827	+	11.3157i	−1.31641	+	0.810333i
$196$		0			0
$197$	−6.39341	−	6.39341i	−0.455511	−	0.455511i	0.441667	−	0.897179i	$-0.354387\pi$
$197$	−6.39341	−	6.39341i	−0.455511	−	0.455511i	−0.897179	+	0.441667i	$0.854387\pi$
$198$		0			0
$199$		−	5.85641i		−	0.415150i	−0.978219	−	0.207575i	$-0.933443\pi$
$199$		−	5.85641i		−	0.415150i	0.978219	−	0.207575i	$-0.0665570\pi$
$200$		0			0
$201$			23.4347i			1.65296i
$202$		0			0
$203$	−4.54979	−	4.54979i	−0.319333	−	0.319333i
$204$		0			0
$205$	16.2325	−	9.99212i	1.13373	−	0.697880i
$206$		0			0
$207$			19.9317i			1.38535i
$208$		0			0
$209$	0.410274			0.0283793
$210$		0			0
$211$	19.2640	+	19.2640i	1.32619	+	1.32619i	0.908668	+	0.417520i	$0.137100\pi$
$211$	19.2640	+	19.2640i	1.32619	+	1.32619i	0.417520	+	0.908668i	$0.362900\pi$
$212$		0			0
$213$	−21.0354	−	21.0354i	−1.44132	−	1.44132i
$214$		0			0
$215$	1.18181	−	4.96647i	0.0805991	−	0.338710i
$216$		0			0
$217$	−4.60603			−0.312678
$218$		0			0
$219$	−30.0974	+	30.0974i	−2.03379	+	2.03379i
$220$		0			0
$221$	4.92820	+	4.92820i	0.331507	+	0.331507i
$222$		0			0
$223$		−	20.1117i		−	1.34678i	−0.739287	−	0.673390i	$-0.764837\pi$
$223$		−	20.1117i		−	1.34678i	0.739287	−	0.673390i	$-0.235163\pi$
$224$		0			0
$225$	17.5065	+	8.83176i	1.16710	+	0.588784i
$226$		0			0
$227$	−4.21430	+	4.21430i	−0.279713	+	0.279713i	−0.832994	−	0.553282i	$-0.813375\pi$
$227$	−4.21430	+	4.21430i	−0.279713	+	0.279713i	0.553282	+	0.832994i	$0.313375\pi$
$228$		0			0
$229$	18.0304	−	18.0304i	1.19148	−	1.19148i	0.214833	−	0.976651i	$-0.431079\pi$
$229$	18.0304	−	18.0304i	1.19148	−	1.19148i	0.976651	−	0.214833i	$-0.0689207\pi$
$230$		0			0
$231$		−	1.27453i		−	0.0838577i
$232$		0			0
$233$	−4.57839			−0.299941			−0.149970	−	0.988691i	$-0.547918\pi$
$233$	−4.57839			−0.299941			−0.149970	+	0.988691i	$0.547918\pi$
$234$		0			0
$235$	−4.83449	+	2.97593i	−0.315367	+	0.194128i
$236$		0			0
$237$	2.11286	−	2.11286i	0.137245	−	0.137245i
$238$		0			0
$239$	18.3104			1.18440			0.592200	−	0.805791i	$-0.298259\pi$
$239$	18.3104			1.18440			0.592200	+	0.805791i	$0.298259\pi$
$240$		0			0
$241$	−9.31393			−0.599963			−0.299982	−	0.953945i	$-0.596981\pi$
$241$	−9.31393			−0.599963			−0.299982	+	0.953945i	$0.596981\pi$
$242$		0			0
$243$	15.1628	−	15.1628i	0.972693	−	0.972693i
$244$		0			0
$245$	7.10379	+	11.5403i	0.453844	+	0.737283i
$246$		0			0
$247$	−11.2304			−0.714575
$248$		0			0
$249$		−	13.9706i		−	0.885353i
$250$		0			0
$251$	14.2156	−	14.2156i	0.897281	−	0.897281i	−0.0979143	−	0.995195i	$-0.531217\pi$
$251$	14.2156	−	14.2156i	0.897281	−	0.897281i	0.995195	+	0.0979143i	$0.0312171\pi$
$252$		0			0
$253$	−0.481758	+	0.481758i	−0.0302879	+	0.0302879i
$254$		0			0
$255$	2.58669	−	10.8704i	0.161985	−	0.680728i
$256$		0			0
$257$			17.1347i			1.06883i	0.845222	+	0.534416i	$0.179468\pi$
$257$			17.1347i			1.06883i	−0.845222	+	0.534416i	$0.820532\pi$
$258$		0			0
$259$	−8.13878	−	8.13878i	−0.505719	−	0.505719i
$260$		0			0
$261$	−4.93719	+	4.93719i	−0.305604	+	0.305604i
$262$		0			0
$263$	−5.11593			−0.315462			−0.157731	−	0.987482i	$-0.550418\pi$
$263$	−5.11593			−0.315462			−0.157731	+	0.987482i	$0.550418\pi$
$264$		0			0
$265$	4.15146	−	17.4461i	0.255022	−	1.07171i
$266$		0			0
$267$	7.40788	+	7.40788i	0.453355	+	0.453355i
$268$		0			0
$269$	−19.1506	−	19.1506i	−1.16763	−	1.16763i	−0.982763	−	0.184870i	$-0.940814\pi$
$269$	−19.1506	−	19.1506i	−1.16763	−	1.16763i	−0.184870	−	0.982763i	$-0.559186\pi$
$270$		0			0
$271$	4.72066			0.286760			0.143380	−	0.989668i	$-0.454203\pi$
$271$	4.72066			0.286760			0.143380	+	0.989668i	$0.454203\pi$
$272$		0			0
$273$			34.8876i			2.11149i
$274$		0			0
$275$	0.209674	+	0.636609i	0.0126438	+	0.0383890i
$276$		0			0
$277$	12.8887	+	12.8887i	0.774408	+	0.774408i	0.978874	−	0.204466i	$-0.0655457\pi$
$277$	12.8887	+	12.8887i	0.774408	+	0.774408i	−0.204466	+	0.978874i	$0.565546\pi$
$278$		0			0
$279$			4.99822i			0.299235i
$280$		0			0
$281$		−	16.4934i		−	0.983913i	−0.870620	−	0.491956i	$-0.836282\pi$
$281$		−	16.4934i		−	0.983913i	0.870620	−	0.491956i	$-0.163718\pi$
$282$		0			0
$283$	7.69771	+	7.69771i	0.457581	+	0.457581i	0.897861	−	0.440279i	$-0.145121\pi$
$283$	7.69771	+	7.69771i	0.457581	+	0.457581i	−0.440279	+	0.897861i	$0.645121\pi$
$284$		0			0
$285$	9.43844	+	15.3330i	0.559085	+	0.908250i
$286$		0			0
$287$		−	30.8069i		−	1.81847i
$288$		0			0
$289$	13.3923			0.787783
$290$		0			0
$291$	19.1692	+	19.1692i	1.12372	+	1.12372i
$292$		0			0
$293$	5.75538	+	5.75538i	0.336233	+	0.336233i	0.854947	−	0.518715i	$-0.173589\pi$
$293$	5.75538	+	5.75538i	0.336233	+	0.336233i	−0.518715	+	0.854947i	$0.673589\pi$
$294$		0			0
$295$	24.0507	+	5.72307i	1.40028	+	0.333210i
$296$		0			0
$297$	−0.325031			−0.0188602
$298$		0			0
$299$	13.1872	−	13.1872i	0.762634	−	0.762634i
$300$		0			0
$301$	−5.83427	−	5.83427i	−0.336282	−	0.336282i
$302$		0			0
$303$			4.68417i			0.269098i
$304$		0			0
$305$	2.53590	−	10.6569i	0.145205	−	0.610212i
$306$		0			0
$307$	−9.60547	+	9.60547i	−0.548213	+	0.548213i	−0.925924	−	0.377711i	$-0.876711\pi$
$307$	−9.60547	+	9.60547i	−0.548213	+	0.548213i	0.377711	+	0.925924i	$0.376711\pi$
$308$		0			0
$309$	20.2134	−	20.2134i	1.14990	−	1.14990i
$310$		0			0
$311$			20.3415i			1.15346i	0.816934	+	0.576731i	$0.195672\pi$
$311$			20.3415i			1.15346i	−0.816934	+	0.576731i	$0.804328\pi$
$312$		0			0
$313$	25.6414			1.44934			0.724669	−	0.689097i	$-0.241993\pi$
$313$	25.6414			1.44934			0.724669	+	0.689097i	$0.241993\pi$
$314$		0			0
$315$	26.9874	−	16.6124i	1.52057	−	0.936003i
$316$		0			0
$317$	−0.945994	+	0.945994i	−0.0531323	+	0.0531323i	−0.733174	−	0.680041i	$-0.761962\pi$
$317$	−0.945994	+	0.945994i	−0.0531323	+	0.0531323i	0.680041	+	0.733174i	$0.261962\pi$
$318$		0			0
$319$	−0.238668			−0.0133629
$320$		0			0
$321$	35.2780			1.96903
$322$		0			0
$323$	4.11062	−	4.11062i	0.228721	−	0.228721i
$324$		0			0
$325$	−5.73939	−	17.4259i	−0.318364	−	0.966615i
$326$		0			0
$327$	31.9057			1.76439
$328$		0			0
$329$			9.17515i			0.505843i
$330$		0			0
$331$	−6.16418	+	6.16418i	−0.338814	+	0.338814i	−0.855921	−	0.517107i	$-0.827009\pi$
$331$	−6.16418	+	6.16418i	−0.338814	+	0.338814i	0.517107	+	0.855921i	$0.327009\pi$
$332$		0			0
$333$	−8.83176	+	8.83176i	−0.483977	+	0.483977i
$334$		0			0
$335$	−19.3767	−	4.61086i	−1.05866	−	0.251918i
$336$		0			0
$337$			28.2333i			1.53797i	0.639269	+	0.768983i	$0.279237\pi$
$337$			28.2333i			1.53797i	−0.639269	+	0.768983i	$0.720763\pi$
$338$		0			0
$339$	23.3074	+	23.3074i	1.26588	+	1.26588i
$340$		0			0
$341$	−0.120809	+	0.120809i	−0.00654219	+	0.00654219i
$342$		0			0
$343$	−3.39562			−0.183346
$344$		0			0
$345$	−29.0875	−	6.92163i	−1.56602	−	0.372648i
$346$		0			0
$347$	−13.0548	−	13.0548i	−0.700816	−	0.700816i	0.263770	−	0.964586i	$-0.415034\pi$
$347$	−13.0548	−	13.0548i	−0.700816	−	0.700816i	−0.964586	+	0.263770i	$0.915034\pi$
$348$		0			0
$349$	20.3080	+	20.3080i	1.08706	+	1.08706i	0.995830	+	0.0912314i	$0.0290803\pi$
$349$	20.3080	+	20.3080i	1.08706	+	1.08706i	0.0912314	+	0.995830i	$0.470920\pi$
$350$		0			0
$351$	8.89708			0.474891
$352$		0			0
$353$		−	18.6814i		−	0.994310i	−0.867662	−	0.497155i	$-0.834378\pi$
$353$		−	18.6814i		−	0.994310i	0.867662	−	0.497155i	$-0.165622\pi$
$354$		0			0
$355$	21.5316	−	13.2541i	1.14278	−	0.703453i
$356$		0			0
$357$	−12.7697	−	12.7697i	−0.675847	−	0.675847i
$358$		0			0
$359$		−	16.4072i		−	0.865937i	−0.901409	−	0.432968i	$-0.857466\pi$
$359$		−	16.4072i		−	0.865937i	0.901409	−	0.432968i	$-0.142534\pi$
$360$		0			0
$361$		−	9.63268i		−	0.506983i
$362$		0			0
$363$	20.4302	+	20.4302i	1.07231	+	1.07231i
$364$		0			0
$365$	−18.9639	−	30.8075i	−0.992617	−	1.61254i
$366$		0			0
$367$			3.58049i			0.186900i	0.995624	+	0.0934500i	$0.0297895\pi$
$367$			3.58049i			0.186900i	−0.995624	+	0.0934500i	$0.970210\pi$
$368$		0			0
$369$	−33.4299			−1.74029
$370$		0			0
$371$	−20.4945	−	20.4945i	−1.06402	−	1.06402i
$372$		0			0
$373$	−8.72985	−	8.72985i	−0.452015	−	0.452015i	0.444008	−	0.896023i	$-0.353556\pi$
$373$	−8.72985	−	8.72985i	−0.452015	−	0.452015i	−0.896023	+	0.444008i	$0.853556\pi$
$374$		0			0
$375$	−18.9682	+	22.4814i	−0.979512	+	1.16093i
$376$		0			0
$377$	6.53307			0.336470
$378$		0			0
$379$	−6.11276	+	6.11276i	−0.313991	+	0.313991i	−0.846454	−	0.532462i	$-0.821267\pi$
$379$	−6.11276	+	6.11276i	−0.313991	+	0.313991i	0.532462	+	0.846454i	$0.321267\pi$
$380$		0			0
$381$	5.47309	+	5.47309i	0.280395	+	0.280395i
$382$		0			0
$383$			7.31434i			0.373745i	0.982384	+	0.186873i	$0.0598351\pi$
$383$			7.31434i			0.373745i	−0.982384	+	0.186873i	$0.940165\pi$
$384$		0			0
$385$	1.05383	+	0.250767i	0.0537080	+	0.0127803i
$386$		0			0
$387$	−6.33103	+	6.33103i	−0.321824	+	0.321824i
$388$		0			0
$389$	9.74166	−	9.74166i	0.493922	−	0.493922i	−0.415618	−	0.909539i	$-0.636435\pi$
$389$	9.74166	−	9.74166i	0.493922	−	0.493922i	0.909539	+	0.415618i	$0.136435\pi$
$390$		0			0
$391$			9.65368i			0.488207i
$392$		0			0
$393$	−24.3454			−1.22807
$394$		0			0
$395$	1.33128	+	2.16271i	0.0669841	+	0.108818i
$396$		0			0
$397$	−8.04203	+	8.04203i	−0.403618	+	0.403618i	−0.879506	−	0.475888i	$-0.842127\pi$
$397$	−8.04203	+	8.04203i	−0.403618	+	0.403618i	0.475888	+	0.879506i	$0.342127\pi$
$398$		0			0
$399$	29.0998			1.45681
$400$		0			0
$401$	−6.77627			−0.338391			−0.169195	−	0.985583i	$-0.554117\pi$
$401$	−6.77627			−0.338391			−0.169195	+	0.985583i	$0.554117\pi$
$402$		0			0
$403$	3.30691	−	3.30691i	0.164729	−	0.164729i
$404$		0			0
$405$	6.31295	+	10.2556i	0.313693	+	0.509604i
$406$		0			0
$407$	−0.426936			−0.0211624
$408$		0			0
$409$			16.2601i			0.804010i	0.915637	+	0.402005i	$0.131687\pi$
$409$			16.2601i			0.804010i	−0.915637	+	0.402005i	$0.868313\pi$
$410$		0			0
$411$	−3.39534	+	3.39534i	−0.167480	+	0.167480i
$412$		0			0
$413$	28.2531	−	28.2531i	1.39024	−	1.39024i
$414$		0			0
$415$	11.5515	+	2.74877i	0.567039	+	0.134932i
$416$		0			0
$417$		−	19.9773i		−	0.978295i
$418$		0			0
$419$	10.1408	+	10.1408i	0.495409	+	0.495409i	0.910005	−	0.414596i	$-0.136077\pi$
$419$	10.1408	+	10.1408i	0.495409	+	0.495409i	−0.414596	+	0.910005i	$0.636077\pi$
$420$		0			0
$421$	13.5849	−	13.5849i	0.662088	−	0.662088i	−0.293784	−	0.955872i	$-0.594915\pi$
$421$	13.5849	−	13.5849i	0.662088	−	0.662088i	0.955872	+	0.293784i	$0.0949146\pi$
$422$		0			0
$423$	9.95637			0.484095
$424$		0			0
$425$	8.47908	+	4.27756i	0.411296	+	0.207492i
$426$		0			0
$427$	−12.5190	−	12.5190i	−0.605836	−	0.605836i
$428$		0			0
$429$	0.915049	+	0.915049i	0.0441790	+	0.0441790i
$430$		0			0
$431$	1.37612			0.0662853			0.0331427	−	0.999451i	$-0.489448\pi$
$431$	1.37612			0.0662853			0.0331427	+	0.999451i	$0.489448\pi$
$432$		0			0
$433$		−	19.9307i		−	0.957810i	−0.877867	−	0.478905i	$-0.841034\pi$
$433$		−	19.9307i		−	0.957810i	0.877867	−	0.478905i	$-0.158966\pi$
$434$		0			0
$435$	−5.49061	−	8.91966i	−0.263255	−	0.427665i
$436$		0			0
$437$	−10.9994	−	10.9994i	−0.526175	−	0.526175i
$438$		0			0
$439$		−	25.4133i		−	1.21291i	−0.795117	−	0.606455i	$-0.792591\pi$
$439$		−	25.4133i		−	1.21291i	0.795117	−	0.606455i	$-0.207409\pi$
$440$		0			0
$441$		−	23.7666i		−	1.13174i
$442$		0			0
$443$	−24.7208	−	24.7208i	−1.17452	−	1.17452i	−0.981120	−	0.193402i	$-0.938048\pi$
$443$	−24.7208	−	24.7208i	−1.17452	−	1.17452i	−0.193402	−	0.981120i	$-0.561952\pi$
$444$		0			0
$445$	−7.58264	+	4.66759i	−0.359452	+	0.221265i
$446$		0			0
$447$			16.2933i			0.770646i
$448$		0			0
$449$	5.62743			0.265575			0.132787	−	0.991145i	$-0.457607\pi$
$449$	5.62743			0.265575			0.132787	+	0.991145i	$0.457607\pi$
$450$		0			0
$451$	−0.808017	−	0.808017i	−0.0380481	−	0.0380481i
$452$		0			0
$453$	24.1117	+	24.1117i	1.13287	+	1.13287i
$454$		0			0
$455$	−28.8464	−	6.86425i	−1.35234	−	0.321801i
$456$		0			0
$457$	26.6040			1.24448			0.622241	−	0.782825i	$-0.286222\pi$
$457$	26.6040			1.24448			0.622241	+	0.782825i	$0.286222\pi$
$458$		0			0
$459$	−3.25656	+	3.25656i	−0.152003	+	0.152003i
$460$		0			0
$461$	−11.9468	−	11.9468i	−0.556418	−	0.556418i	0.371868	−	0.928286i	$-0.378717\pi$
$461$	−11.9468	−	11.9468i	−0.556418	−	0.556418i	−0.928286	+	0.371868i	$0.878717\pi$
$462$		0			0
$463$		−	0.530134i		−	0.0246374i	−0.999924	−	0.0123187i	$-0.996079\pi$
$463$		−	0.530134i		−	0.0246374i	0.999924	−	0.0123187i	$-0.00392127\pi$
$464$		0			0
$465$	−7.29420	−	1.73572i	−0.338260	−	0.0804920i
$466$		0			0
$467$	11.4219	−	11.4219i	0.528542	−	0.528542i	−0.391595	−	0.920138i	$-0.628077\pi$
$467$	11.4219	−	11.4219i	0.528542	−	0.528542i	0.920138	+	0.391595i	$0.128077\pi$
$468$		0			0
$469$	−22.7625	+	22.7625i	−1.05107	+	1.05107i
$470$		0			0
$471$		−	33.9592i		−	1.56476i
$472$		0			0
$473$	−0.306048			−0.0140721
$474$		0			0
$475$	−14.5350	+	4.78724i	−0.666910	+	0.219654i
$476$		0			0
$477$	−22.2395	+	22.2395i	−1.01828	+	1.01828i
$478$		0			0
$479$	6.37434			0.291251			0.145625	−	0.989340i	$-0.453481\pi$
$479$	6.37434			0.291251			0.145625	+	0.989340i	$0.453481\pi$
$480$		0			0
$481$	11.6865			0.532859
$482$		0			0
$483$	−34.1700	+	34.1700i	−1.55479	+	1.55479i
$484$		0			0
$485$	−19.6214	+	12.0782i	−0.890963	+	0.548444i
$486$		0			0
$487$	−31.3203			−1.41926			−0.709629	−	0.704575i	$-0.751138\pi$
$487$	−31.3203			−1.41926			−0.709629	+	0.704575i	$0.751138\pi$
$488$		0			0
$489$			22.8857i			1.03493i
$490$		0			0
$491$	−14.0893	+	14.0893i	−0.635843	+	0.635843i	−0.949527	−	0.313684i	$-0.898437\pi$
$491$	−14.0893	+	14.0893i	−0.635843	+	0.635843i	0.313684	+	0.949527i	$0.398437\pi$
$492$		0			0
$493$	−2.39127	+	2.39127i	−0.107697	+	0.107697i
$494$		0			0
$495$	0.272119	−	1.14356i	0.0122308	−	0.0513990i
$496$		0			0
$497$		−	40.8639i		−	1.83299i
$498$		0			0
$499$	2.30233	+	2.30233i	0.103067	+	0.103067i	0.756760	−	0.653693i	$-0.226781\pi$
$499$	2.30233	+	2.30233i	0.103067	+	0.103067i	−0.653693	+	0.756760i	$0.726781\pi$
$500$		0			0
$501$	−1.32115	+	1.32115i	−0.0590248	+	0.0590248i
$502$		0			0
$503$	14.7556			0.657921			0.328961	−	0.944344i	$-0.393302\pi$
$503$	14.7556			0.657921			0.328961	+	0.944344i	$0.393302\pi$
$504$		0			0
$505$	−3.87305	−	0.921626i	−0.172348	−	0.0410118i
$506$		0			0
$507$	−0.863380	−	0.863380i	−0.0383441	−	0.0383441i
$508$		0			0
$509$	8.03042	+	8.03042i	0.355942	+	0.355942i	0.862315	−	0.506373i	$-0.169014\pi$
$509$	8.03042	+	8.03042i	0.355942	+	0.355942i	−0.506373	+	0.862315i	$0.669014\pi$
$510$		0			0
$511$	−58.4680			−2.58647
$512$		0			0
$513$		−	7.42107i		−	0.327648i
$514$		0			0
$515$	12.7362	+	20.6903i	0.561223	+	0.911723i
$516$		0			0
$517$	0.240650	+	0.240650i	0.0105838	+	0.0105838i
$518$		0			0
$519$			52.7487i			2.31541i
$520$		0			0
$521$		−	13.7417i		−	0.602033i	−0.953619	−	0.301017i	$-0.902674\pi$
$521$		−	13.7417i		−	0.602033i	0.953619	−	0.301017i	$-0.0973259\pi$
$522$		0			0
$523$	6.77116	+	6.77116i	0.296082	+	0.296082i	0.839477	−	0.543395i	$-0.182861\pi$
$523$	6.77116	+	6.77116i	0.296082	+	0.296082i	−0.543395	+	0.839477i	$0.682861\pi$
$524$		0			0
$525$	14.8717	+	45.1532i	0.649053	+	1.97065i
$526$		0			0
$527$			2.42083i			0.105453i
$528$		0			0
$529$	2.83186			0.123124
$530$		0			0
$531$	−30.6587	−	30.6587i	−1.33047	−	1.33047i
$532$		0			0
$533$	22.1179	+	22.1179i	0.958030	+	0.958030i
$534$		0			0
$535$	−6.94106	+	29.1692i	−0.300088	+	1.26109i
$536$		0			0
$537$	−33.5046			−1.44583
$538$		0			0
$539$	0.574451	−	0.574451i	0.0247434	−	0.0247434i
$540$		0			0
$541$	−7.82599	−	7.82599i	−0.336465	−	0.336465i	0.518570	−	0.855035i	$-0.326465\pi$
$541$	−7.82599	−	7.82599i	−0.336465	−	0.336465i	−0.855035	+	0.518570i	$0.826465\pi$
$542$		0			0
$543$			52.7855i			2.26524i
$544$		0			0
$545$	−6.27756	+	26.3809i	−0.268901	+	1.13003i
$546$		0			0
$547$	16.1263	−	16.1263i	0.689511	−	0.689511i	−0.272613	−	0.962124i	$-0.587888\pi$
$547$	16.1263	−	16.1263i	0.689511	−	0.689511i	0.962124	+	0.272613i	$0.0878878\pi$
$548$		0			0
$549$	−13.5849	+	13.5849i	−0.579790	+	0.579790i
$550$		0			0
$551$		−	5.44924i		−	0.232146i
$552$		0			0
$553$	4.10450			0.174541
$554$		0			0
$555$	−9.82174	−	15.9557i	−0.416909	−	0.677282i
$556$		0			0
$557$	13.7333	−	13.7333i	0.581897	−	0.581897i	−0.353527	−	0.935424i	$-0.615018\pi$
$557$	13.7333	−	13.7333i	0.581897	−	0.581897i	0.935424	+	0.353527i	$0.115018\pi$
$558$		0			0
$559$	8.37745			0.354328
$560$		0			0
$561$	−0.669862			−0.0282816
$562$		0			0
$563$	−13.2023	+	13.2023i	−0.556412	+	0.556412i	−0.928284	−	0.371872i	$-0.878716\pi$
$563$	−13.2023	+	13.2023i	−0.556412	+	0.556412i	0.371872	+	0.928284i	$0.378716\pi$
$564$		0			0
$565$	−23.8572	+	14.6856i	−1.00368	+	0.617828i
$566$		0			0
$567$	19.4636			0.817393
$568$		0			0
$569$			7.32481i			0.307072i	0.988143	+	0.153536i	$0.0490661\pi$
$569$			7.32481i			0.307072i	−0.988143	+	0.153536i	$0.950934\pi$
$570$		0			0
$571$	22.1916	−	22.1916i	0.928688	−	0.928688i	−0.0689332	−	0.997621i	$-0.521960\pi$
$571$	22.1916	−	22.1916i	0.928688	−	0.928688i	0.997621	+	0.0689332i	$0.0219595\pi$
$572$		0			0
$573$	35.2126	−	35.2126i	1.47103	−	1.47103i
$574$		0			0
$575$	11.4461	−	22.6888i	0.477337	−	0.946189i
$576$		0			0
$577$			9.39473i			0.391108i	0.980693	+	0.195554i	$0.0626504\pi$
$577$			9.39473i			0.391108i	−0.980693	+	0.195554i	$0.937350\pi$
$578$		0			0
$579$	−39.7887	−	39.7887i	−1.65356	−	1.65356i
$580$		0			0
$581$	13.5699	−	13.5699i	0.562973	−	0.562973i
$582$		0			0
$583$	−1.07508			−0.0445253
$584$		0			0
$585$	−7.44871	+	31.3025i	−0.307966	+	1.29420i
$586$		0			0
$587$	10.7246	+	10.7246i	0.442650	+	0.442650i	0.892902	−	0.450252i	$-0.148666\pi$
$587$	10.7246	+	10.7246i	0.442650	+	0.442650i	−0.450252	+	0.892902i	$0.648666\pi$
$588$		0			0
$589$	−2.75830	−	2.75830i	−0.113654	−	0.113654i
$590$		0			0
$591$	−23.7876			−0.978493
$592$		0			0
$593$			38.2253i			1.56973i	0.619670	+	0.784863i	$0.287267\pi$
$593$			38.2253i			1.56973i	−0.619670	+	0.784863i	$0.712733\pi$
$594$		0			0
$595$	13.0710	−	8.04603i	0.535859	−	0.329855i
$596$		0			0
$597$	−10.8948	−	10.8948i	−0.445896	−	0.445896i
$598$		0			0
$599$		−	41.5801i		−	1.69892i	−0.527656	−	0.849458i	$-0.676929\pi$
$599$		−	41.5801i		−	1.69892i	0.527656	−	0.849458i	$-0.323071\pi$
$600$		0			0
$601$			23.1081i			0.942599i	0.881973	+	0.471299i	$0.156215\pi$
$601$			23.1081i			0.942599i	−0.881973	+	0.471299i	$0.843785\pi$
$602$		0			0
$603$	24.7006	+	24.7006i	1.00589	+	1.00589i
$604$		0			0
$605$	−20.9121	+	12.8727i	−0.850199	+	0.523351i
$606$		0			0
$607$		−	15.1150i		−	0.613500i	−0.951790	−	0.306750i	$-0.900759\pi$
$607$		−	15.1150i		−	0.613500i	0.951790	−	0.306750i	$-0.0992415\pi$
$608$		0			0
$609$	−16.9282			−0.685965
$610$		0			0
$611$	−6.58732	−	6.58732i	−0.266494	−	0.266494i
$612$		0			0
$613$	1.18710	+	1.18710i	0.0479466	+	0.0479466i	0.730674	−	0.682727i	$-0.239206\pi$
$613$	1.18710	+	1.18710i	0.0479466	+	0.0479466i	−0.682727	+	0.730674i	$0.739206\pi$
$614$		0			0
$615$	11.6091	−	48.7863i	0.468125	−	1.96725i
$616$		0			0
$617$	5.23711			0.210838			0.105419	−	0.994428i	$-0.466382\pi$
$617$	5.23711			0.210838			0.105419	+	0.994428i	$0.466382\pi$
$618$		0			0
$619$	6.52847	−	6.52847i	0.262401	−	0.262401i	−0.563628	−	0.826029i	$-0.690595\pi$
$619$	6.52847	−	6.52847i	0.262401	−	0.262401i	0.826029	+	0.563628i	$0.190595\pi$
$620$		0			0
$621$	8.71408	+	8.71408i	0.349684	+	0.349684i
$622$		0			0
$623$			14.3907i			0.576553i
$624$		0			0
$625$	−14.8564	−	20.1069i	−0.594256	−	0.804276i
$626$		0			0
$627$	0.763244	−	0.763244i	0.0304810	−	0.0304810i
$628$		0			0
$629$	−4.27756	+	4.27756i	−0.170557	+	0.170557i
$630$		0			0
$631$		−	21.7193i		−	0.864633i	−0.901722	−	0.432316i	$-0.857696\pi$
$631$		−	21.7193i		−	0.864633i	0.901722	−	0.432316i	$-0.142304\pi$
$632$		0			0
$633$	71.6746			2.84881
$634$		0			0
$635$	−5.60221	+	3.44851i	−0.222317	+	0.136850i
$636$		0			0
$637$	−15.7244	+	15.7244i	−0.623025	+	0.623025i
$638$		0			0
$639$	−44.3432			−1.75419
$640$		0			0
$641$	−45.3927			−1.79291			−0.896453	−	0.443139i	$-0.853865\pi$
$641$	−45.3927			−1.79291			−0.896453	+	0.443139i	$0.853865\pi$
$642$		0			0
$643$	20.5408	−	20.5408i	0.810049	−	0.810049i	−0.174592	−	0.984641i	$-0.555861\pi$
$643$	20.5408	−	20.5408i	0.810049	−	0.810049i	0.984641	+	0.174592i	$0.0558607\pi$
$644$		0			0
$645$	−7.04069	−	11.4378i	−0.277227	−	0.450363i
$646$		0			0
$647$	31.7472			1.24811			0.624056	−	0.781379i	$-0.285484\pi$
$647$	31.7472			1.24811			0.624056	+	0.781379i	$0.285484\pi$
$648$		0			0
$649$		−	1.48207i		−	0.0581764i
$650$		0			0
$651$	−8.56873	+	8.56873i	−0.335835	+	0.335835i
$652$		0			0
$653$	−4.30078	+	4.30078i	−0.168302	+	0.168302i	−0.786233	−	0.617930i	$-0.787971\pi$
$653$	−4.30078	+	4.30078i	−0.168302	+	0.168302i	0.617930	+	0.786233i	$0.287971\pi$
$654$		0			0
$655$	4.79005	−	20.1297i	0.187163	−	0.786534i
$656$		0			0
$657$			63.4463i			2.47527i
$658$		0			0
$659$	18.2156	+	18.2156i	0.709579	+	0.709579i	0.966447	−	0.256868i	$-0.0826905\pi$
$659$	18.2156	+	18.2156i	0.709579	+	0.709579i	−0.256868	+	0.966447i	$0.582690\pi$
$660$		0			0
$661$	19.7679	−	19.7679i	0.768883	−	0.768883i	−0.209027	−	0.977910i	$-0.567030\pi$
$661$	19.7679	−	19.7679i	0.768883	−	0.768883i	0.977910	+	0.209027i	$0.0670297\pi$
$662$		0			0
$663$	18.3361			0.712116
$664$		0			0
$665$	−5.72549	+	24.0608i	−0.222025	+	0.933039i
$666$		0			0
$667$	6.39869	+	6.39869i	0.247758	+	0.247758i
$668$		0			0
$669$	−37.4144	−	37.4144i	−1.44652	−	1.44652i
$670$		0			0
$671$	−0.656708			−0.0253519
$672$		0			0
$673$			8.43246i			0.325047i	0.986705	+	0.162524i	$0.0519634\pi$
$673$			8.43246i			0.325047i	−0.986705	+	0.162524i	$0.948037\pi$
$674$		0			0
$675$	11.5150	−	3.79259i	0.443214	−	0.145977i
$676$		0			0
$677$	20.8693	+	20.8693i	0.802073	+	0.802073i	0.983419	−	0.181346i	$-0.0580455\pi$
$677$	20.8693	+	20.8693i	0.802073	+	0.802073i	−0.181346	+	0.983419i	$0.558046\pi$
$678$		0			0
$679$			37.2386i			1.42909i
$680$		0			0
$681$			15.6799i			0.600856i
$682$		0			0
$683$	16.4398	+	16.4398i	0.629051	+	0.629051i	0.947829	−	0.318778i	$-0.103272\pi$
$683$	16.4398	+	16.4398i	0.629051	+	0.629051i	−0.318778	+	0.947829i	$0.603272\pi$
$684$		0			0
$685$	−2.13935	−	3.47544i	−0.0817404	−	0.132790i
$686$		0			0
$687$		−	67.0849i		−	2.55945i
$688$		0			0
$689$	29.4282			1.12112
$690$		0			0
$691$	−17.4076	−	17.4076i	−0.662216	−	0.662216i	0.293686	−	0.955902i	$-0.405118\pi$
$691$	−17.4076	−	17.4076i	−0.662216	−	0.662216i	−0.955902	+	0.293686i	$0.905118\pi$
$692$		0			0
$693$	−1.34337	−	1.34337i	−0.0510304	−	0.0510304i
$694$		0			0
$695$	16.5180	+	3.93061i	0.626565	+	0.149097i
$696$		0			0
$697$	−16.1914			−0.613293
$698$		0			0
$699$	−8.51731	+	8.51731i	−0.322154	+	0.322154i
$700$		0			0
$701$	25.3888	+	25.3888i	0.958920	+	0.958920i	0.999189	−	0.0402687i	$-0.0128214\pi$
$701$	25.3888	+	25.3888i	0.958920	+	0.958920i	−0.0402687	+	0.999189i	$0.512821\pi$
$702$		0			0
$703$		−	9.74773i		−	0.367643i
$704$		0			0
$705$	−3.45752	+	14.5299i	−0.130218	+	0.547229i
$706$		0			0
$707$	−4.54979	+	4.54979i	−0.171113	+	0.171113i
$708$		0			0
$709$	−17.6201	+	17.6201i	−0.661738	+	0.661738i	−0.955790	−	0.294051i	$-0.904996\pi$
$709$	−17.6201	+	17.6201i	−0.661738	+	0.661738i	0.294051	+	0.955790i	$0.404996\pi$
$710$		0			0
$711$		−	4.45398i		−	0.167037i
$712$		0			0
$713$	6.47779			0.242595
$714$		0			0
$715$	−0.936636	+	0.576559i	−0.0350282	+	0.0215621i
$716$		0			0
$717$	34.0633	−	34.0633i	1.27212	−	1.27212i
$718$		0			0
$719$	−42.6068			−1.58896			−0.794482	−	0.607287i	$-0.792258\pi$
$719$	−42.6068			−1.58896			−0.794482	+	0.607287i	$0.792258\pi$
$720$		0			0
$721$	39.2671			1.46238
$722$		0			0
$723$	−17.3269	+	17.3269i	−0.644396	+	0.644396i
$724$		0			0
$725$	8.45542	−	2.78488i	0.314026	−	0.103428i
$726$		0			0
$727$	−50.5830			−1.87602			−0.938010	−	0.346609i	$-0.887333\pi$
$727$	−50.5830			−1.87602			−0.938010	+	0.346609i	$0.887333\pi$
$728$		0			0
$729$		−	40.2583i		−	1.49105i
$730$		0			0
$731$	−3.06636	+	3.06636i	−0.113413	+	0.113413i
$732$		0			0
$733$	−6.17299	+	6.17299i	−0.228005	+	0.228005i	−0.811859	−	0.583854i	$-0.801544\pi$
$733$	−6.17299	+	6.17299i	−0.228005	+	0.228005i	0.583854	+	0.811859i	$0.301544\pi$
$734$		0			0
$735$	34.6841	+	8.25338i	1.27934	+	0.304431i
$736$		0			0
$737$			1.19405i			0.0439834i
$738$		0			0
$739$	−22.8974	−	22.8974i	−0.842293	−	0.842293i	0.146864	−	0.989157i	$-0.453082\pi$
$739$	−22.8974	−	22.8974i	−0.842293	−	0.842293i	−0.989157	+	0.146864i	$0.953082\pi$
$740$		0			0
$741$	−20.8923	+	20.8923i	−0.767497	+	0.767497i
$742$		0			0
$743$	−11.8975			−0.436478			−0.218239	−	0.975895i	$-0.570031\pi$
$743$	−11.8975			−0.436478			−0.218239	+	0.975895i	$0.570031\pi$
$744$		0			0
$745$	−13.4719	−	3.20576i	−0.493573	−	0.117450i
$746$		0			0
$747$	−14.7253	−	14.7253i	−0.538770	−	0.538770i
$748$		0			0
$749$	34.2660	+	34.2660i	1.25205	+	1.25205i
$750$		0			0
$751$	23.4102			0.854250			0.427125	−	0.904193i	$-0.359526\pi$
$751$	23.4102			0.854250			0.427125	+	0.904193i	$0.359526\pi$
$752$		0			0
$753$		−	52.8913i		−	1.92747i
$754$		0			0
$755$	−24.6806	+	15.1924i	−0.898218	+	0.552910i
$756$		0			0
$757$	11.3218	+	11.3218i	0.411496	+	0.411496i	0.882260	−	0.470763i	$-0.156021\pi$
$757$	11.3218	+	11.3218i	0.411496	+	0.411496i	−0.470763	+	0.882260i	$0.656021\pi$
$758$		0			0
$759$			1.79246i			0.0650620i
$760$		0			0
$761$			8.53590i			0.309426i	0.987959	+	0.154713i	$0.0494453\pi$
$761$			8.53590i			0.309426i	−0.987959	+	0.154713i	$0.950555\pi$
$762$		0			0
$763$	30.9904	+	30.9904i	1.12193	+	1.12193i
$764$		0			0
$765$	−8.73111	−	14.1839i	−0.315674	−	0.512821i
$766$		0			0
$767$			40.5687i			1.46485i
$768$		0			0
$769$	−17.8384			−0.643270			−0.321635	−	0.946864i	$-0.604232\pi$
$769$	−17.8384			−0.643270			−0.321635	+	0.946864i	$0.604232\pi$
$770$		0			0
$771$	31.8761	+	31.8761i	1.14799	+	1.14799i
$772$		0			0
$773$	−23.9457	−	23.9457i	−0.861267	−	0.861267i	0.130219	−	0.991485i	$-0.458432\pi$
$773$	−23.9457	−	23.9457i	−0.861267	−	0.861267i	−0.991485	+	0.130219i	$0.958432\pi$
$774$		0			0
$775$	2.87032	−	5.68962i	0.103105	−	0.204377i
$776$		0			0
$777$	−30.2816			−1.08635
$778$		0			0
$779$	18.4485	−	18.4485i	0.660988	−	0.660988i
$780$		0			0
$781$	−1.07180	−	1.07180i	−0.0383519	−	0.0383519i
$782$		0			0
$783$			4.31705i			0.154279i
$784$		0			0
$785$	28.0788	+	6.68160i	1.00218	+	0.238476i
$786$		0			0
$787$	−32.3914	+	32.3914i	−1.15463	+	1.15463i	−0.169014	+	0.985614i	$0.554058\pi$
$787$	−32.3914	+	32.3914i	−1.15463	+	1.15463i	−0.985614	+	0.169014i	$0.945942\pi$
$788$		0			0
$789$	−9.51731	+	9.51731i	−0.338825	+	0.338825i
$790$		0			0
$791$			45.2775i			1.60988i
$792$		0			0
$793$	17.9761			0.638348
$794$		0			0
$795$	−24.7324	−	40.1786i	−0.877169	−	1.42499i
$796$		0			0
$797$	−1.92658	+	1.92658i	−0.0682428	+	0.0682428i	−0.740404	−	0.672162i	$-0.765366\pi$
$797$	−1.92658	+	1.92658i	−0.0682428	+	0.0682428i	0.672162	+	0.740404i	$0.265366\pi$
$798$		0			0
$799$	4.82225			0.170599
$800$		0			0
$801$	15.6160			0.551765
$802$		0			0
$803$	−1.53353	+	1.53353i	−0.0541170	+	0.0541170i
$804$		0			0
$805$	−21.5300	−	34.9761i	−0.758833	−	1.23275i
$806$		0			0
$807$	−71.2527			−2.50822
$808$		0			0
$809$		−	49.8993i		−	1.75437i	−0.480157	−	0.877183i	$-0.659420\pi$
$809$		−	49.8993i		−	1.75437i	0.480157	−	0.877183i	$-0.340580\pi$
$810$		0			0
$811$	−22.9363	+	22.9363i	−0.805401	+	0.805401i	−0.983934	−	0.178533i	$-0.942865\pi$
$811$	−22.9363	+	22.9363i	−0.805401	+	0.805401i	0.178533	+	0.983934i	$0.442865\pi$
$812$		0			0
$813$	8.78196	−	8.78196i	0.307997	−	0.307997i
$814$		0			0
$815$	−18.9228	−	4.50284i	−0.662836	−	0.157727i
$816$		0			0
$817$		−	6.98764i		−	0.244467i
$818$		0			0
$819$	36.7721	+	36.7721i	1.28492	+	1.28492i
$820$		0			0
$821$	−10.7321	+	10.7321i	−0.374551	+	0.374551i	−0.869132	−	0.494581i	$-0.835322\pi$
$821$	−10.7321	+	10.7321i	−0.374551	+	0.374551i	0.494581	+	0.869132i	$0.335322\pi$
$822$		0			0
$823$	−8.56875			−0.298688			−0.149344	−	0.988785i	$-0.547716\pi$
$823$	−8.56875			−0.298688			−0.149344	+	0.988785i	$0.547716\pi$
$824$		0			0
$825$	1.57436	+	0.794239i	0.0548123	+	0.0276519i
$826$		0			0
$827$	10.0841	+	10.0841i	0.350660	+	0.350660i	0.860355	−	0.509695i	$-0.170242\pi$
$827$	10.0841	+	10.0841i	0.350660	+	0.350660i	−0.509695	+	0.860355i	$0.670242\pi$
$828$		0			0
$829$	−0.656708	−	0.656708i	−0.0228084	−	0.0228084i	0.695611	−	0.718419i	$-0.255134\pi$
$829$	−0.656708	−	0.656708i	−0.0228084	−	0.0228084i	−0.718419	+	0.695611i	$0.755134\pi$
$830$		0			0
$831$	47.9544			1.66352
$832$		0			0
$833$		−	11.5111i		−	0.398836i
$834$		0			0
$835$	−0.832439	−	1.35232i	−0.0288077	−	0.0467990i
$836$		0			0
$837$	2.18521	+	2.18521i	0.0755318	+	0.0755318i
$838$		0			0
$839$			5.41206i			0.186845i	0.995627	+	0.0934225i	$0.0297807\pi$
$839$			5.41206i			0.186845i	−0.995627	+	0.0934225i	$0.970219\pi$
$840$		0			0
$841$		−	25.8300i		−	0.890690i
$842$		0			0
$843$	−30.6831	−	30.6831i	−1.05678	−	1.05678i
$844$		0			0
$845$	0.883749	−	0.544003i	0.0304019	−	0.0187143i
$846$		0			0
$847$			39.6882i			1.36370i
$848$		0			0
$849$	28.6405			0.982939
$850$		0			0
$851$	11.4461	+	11.4461i	0.392368	+	0.392368i
$852$		0			0
$853$	−17.0301	−	17.0301i	−0.583098	−	0.583098i	0.352655	−	0.935753i	$-0.385279\pi$
$853$	−17.0301	−	17.0301i	−0.583098	−	0.583098i	−0.935753	+	0.352655i	$0.885279\pi$
$854$		0			0
$855$	26.1095	+	6.21298i	0.892926	+	0.212480i
$856$		0			0
$857$	−53.1079			−1.81413			−0.907066	−	0.420988i	$-0.861683\pi$
$857$	−53.1079			−1.81413			−0.907066	+	0.420988i	$0.861683\pi$
$858$		0			0
$859$	10.7609	−	10.7609i	0.367158	−	0.367158i	−0.499282	−	0.866440i	$-0.666403\pi$
$859$	10.7609	−	10.7609i	0.367158	−	0.367158i	0.866440	+	0.499282i	$0.166403\pi$
$860$		0			0
$861$	−57.3108	−	57.3108i	−1.95315	−	1.95315i
$862$		0			0
$863$			21.2106i			0.722016i	0.932563	+	0.361008i	$0.117567\pi$
$863$			21.2106i			0.722016i	−0.932563	+	0.361008i	$0.882433\pi$
$864$		0			0
$865$	−43.6146	−	10.3785i	−1.48294	−	0.352879i
$866$		0			0
$867$	24.9141	−	24.9141i	0.846126	−	0.846126i
$868$		0			0
$869$	0.107655	−	0.107655i	0.00365194	−	0.00365194i
$870$		0			0
$871$		−	32.6847i		−	1.10748i
$872$		0			0
$873$	40.4093			1.36765
$874$		0			0
$875$	−40.2605	+	3.41242i	−1.36105	+	0.115361i
$876$		0			0
$877$	−25.6041	+	25.6041i	−0.864589	+	0.864589i	−0.991867	−	0.127278i	$-0.959376\pi$
$877$	−25.6041	+	25.6041i	−0.864589	+	0.864589i	0.127278	+	0.991867i	$0.459376\pi$
$878$		0			0
$879$	21.4138			0.722268
$880$		0			0
$881$	−13.0675			−0.440255			−0.220128	−	0.975471i	$-0.570647\pi$
$881$	−13.0675			−0.440255			−0.220128	+	0.975471i	$0.570647\pi$
$882$		0			0
$883$	−12.1957	+	12.1957i	−0.410419	+	0.410419i	−0.881884	−	0.471466i	$-0.843725\pi$
$883$	−12.1957	+	12.1957i	−0.410419	+	0.410419i	0.471466	+	0.881884i	$0.343725\pi$
$884$		0			0
$885$	55.3889	−	34.0953i	1.86188	−	1.14610i
$886$		0			0
$887$	36.3716			1.22124			0.610619	−	0.791924i	$-0.290921\pi$
$887$	36.3716			1.22124			0.610619	+	0.791924i	$0.290921\pi$
$888$		0			0
$889$			10.6322i			0.356591i
$890$		0			0
$891$	0.510500	−	0.510500i	0.0171024	−	0.0171024i
$892$		0			0
$893$	−5.49449	+	5.49449i	−0.183866	+	0.183866i
$894$		0			0
$895$	6.59213	−	27.7028i	0.220351	−	0.926004i
$896$		0			0
$897$		−	49.0649i		−	1.63823i
$898$		0			0
$899$	1.60458	+	1.60458i	0.0535159	+	0.0535159i
$900$		0			0
$901$	−10.7715	+	10.7715i	−0.358849	+	0.358849i
$902$		0			0
$903$	−21.7073			−0.722373
$904$		0			0
$905$	−43.6451	−	10.3857i	−1.45081	−	0.345233i
$906$		0			0
$907$	−35.4831	−	35.4831i	−1.17820	−	1.17820i	−0.980203	−	0.197996i	$-0.936557\pi$
$907$	−35.4831	−	35.4831i	−1.17820	−	1.17820i	−0.197996	−	0.980203i	$-0.563443\pi$
$908$		0			0
$909$	4.93719	+	4.93719i	0.163756	+	0.163756i
$910$		0			0
$911$	22.6536			0.750547			0.375274	−	0.926914i	$-0.377549\pi$
$911$	22.6536			0.750547			0.375274	+	0.926914i	$0.377549\pi$
$912$		0			0
$913$		−	0.711834i		−	0.0235583i
$914$		0			0
$915$	−15.1077	−	24.5429i	−0.499445	−	0.811363i
$916$		0			0
$917$	−23.6470	−	23.6470i	−0.780894	−	0.780894i
$918$		0			0
$919$			19.9532i			0.658195i	0.944296	+	0.329097i	$0.106744\pi$
$919$			19.9532i			0.658195i	−0.944296	+	0.329097i	$0.893256\pi$
$920$		0			0
$921$			35.7386i			1.17763i
$922$		0			0
$923$	29.3383	+	29.3383i	0.965681	+	0.965681i
$924$		0			0
$925$	15.1252	−	4.98165i	0.497315	−	0.163796i
$926$		0			0
$927$		−	42.6105i		−	1.39951i
$928$		0			0
$929$	11.0293			0.361859			0.180929	−	0.983496i	$-0.442089\pi$
$929$	11.0293			0.361859			0.180929	+	0.983496i	$0.442089\pi$
$930$		0			0
$931$	13.1158	+	13.1158i	0.429853	+	0.429853i
$932$		0			0
$933$	37.8418	+	37.8418i	1.23889	+	1.23889i
$934$		0			0
$935$	0.131798	−	0.553868i	0.00431024	−	0.0181134i
$936$		0			0
$937$	36.6851			1.19845			0.599225	−	0.800581i	$-0.295476\pi$
$937$	36.6851			1.19845			0.599225	+	0.800581i	$0.295476\pi$
$938$		0			0
$939$	47.7014	−	47.7014i	1.55668	−	1.55668i
$940$		0			0
$941$	26.8618	+	26.8618i	0.875671	+	0.875671i	0.993083	−	0.117412i	$-0.0374599\pi$
$941$	26.8618	+	26.8618i	0.875671	+	0.875671i	−0.117412	+	0.993083i	$0.537460\pi$
$942$		0			0
$943$			43.3258i			1.41088i
$944$		0			0
$945$	4.53590	−	19.0617i	0.147553	−	0.620077i
$946$		0			0
$947$	42.0944	−	42.0944i	1.36788	−	1.36788i	0.504433	−	0.863451i	$-0.331701\pi$
$947$	42.0944	−	42.0944i	1.36788	−	1.36788i	0.863451	−	0.504433i	$-0.168299\pi$
$948$		0			0
$949$	41.9772	−	41.9772i	1.36264	−	1.36264i
$950$		0			0
$951$			3.51971i			0.114135i
$952$		0			0
$953$	5.32619			0.172532			0.0862661	−	0.996272i	$-0.472506\pi$
$953$	5.32619			0.172532			0.0862661	+	0.996272i	$0.472506\pi$
$954$		0			0
$955$	22.1870	+	36.0434i	0.717953	+	1.16634i
$956$		0			0
$957$	−0.444001	+	0.444001i	−0.0143525	+	0.0143525i
$958$		0			0
$959$	−6.59587			−0.212992
$960$		0			0
$961$	−29.3756			−0.947599
$962$		0			0
$963$	37.1836	−	37.1836i	1.19822	−	1.19822i
$964$		0			0
$965$	40.7274	−	25.0703i	1.31106	−	0.807041i
$966$		0			0
$967$	29.9668			0.963667			0.481833	−	0.876263i	$-0.339971\pi$
$967$	29.9668			0.963667			0.481833	+	0.876263i	$0.339971\pi$
$968$		0			0
$969$		−	15.2942i		−	0.491320i
$970$		0			0
$971$	−0.750872	+	0.750872i	−0.0240966	+	0.0240966i	−0.719052	−	0.694956i	$-0.755424\pi$
$971$	−0.750872	+	0.750872i	−0.0240966	+	0.0240966i	0.694956	+	0.719052i	$0.255424\pi$
$972$		0			0
$973$	19.4043	−	19.4043i	0.622072	−	0.622072i
$974$		0			0
$975$	−43.0950	−	21.7407i	−1.38014	−	0.696260i
$976$		0			0
$977$		−	26.2513i		−	0.839854i	−0.907558	−	0.419927i	$-0.862056\pi$
$977$		−	26.2513i		−	0.839854i	0.907558	−	0.419927i	$-0.137944\pi$
$978$		0			0
$979$	0.377447	+	0.377447i	0.0120633	+	0.0120633i
$980$		0			0
$981$	33.6291	−	33.6291i	1.07370	−	1.07370i
$982$		0			0
$983$	13.0227			0.415360			0.207680	−	0.978197i	$-0.433409\pi$
$983$	13.0227			0.415360			0.207680	+	0.978197i	$0.433409\pi$
$984$		0			0
$985$	4.68030	−	19.6685i	0.149127	−	0.626692i
$986$		0			0
$987$	17.0688	+	17.0688i	0.543305	+	0.543305i
$988$		0			0
$989$	8.20514	+	8.20514i	0.260908	+	0.260908i
$990$		0			0
$991$	44.7487			1.42149			0.710744	−	0.703451i	$-0.248358\pi$
$991$	44.7487			1.42149			0.710744	+	0.703451i	$0.248358\pi$
$992$		0			0
$993$			22.9348i			0.727813i
$994$		0			0
$995$	11.1519	−	6.86467i	0.353538	−	0.217625i
$996$		0			0
$997$	21.2387	+	21.2387i	0.672637	+	0.672637i	0.958323	−	0.285686i	$-0.0922215\pi$
$997$	21.2387	+	21.2387i	0.672637	+	0.672637i	−0.285686	+	0.958323i	$0.592222\pi$
$998$		0			0
$999$			7.72244i			0.244327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.q.e.289.7		16
4.3	odd	2		640.2.q.f.289.2		16
5.4	even	2	inner	640.2.q.e.289.2		16
8.3	odd	2		320.2.q.c.209.7		16
8.5	even	2		80.2.q.c.29.7	yes	16
16.3	odd	4		320.2.q.c.49.2		16
16.5	even	4	inner	640.2.q.e.609.2		16
16.11	odd	4		640.2.q.f.609.7		16
16.13	even	4		80.2.q.c.69.2	yes	16
20.19	odd	2		640.2.q.f.289.7		16
24.5	odd	2		720.2.bm.f.109.2		16
40.3	even	4		1600.2.l.h.401.7		16
40.13	odd	4		400.2.l.i.301.6		16
40.19	odd	2		320.2.q.c.209.2		16
40.27	even	4		1600.2.l.h.401.2		16
40.29	even	2		80.2.q.c.29.2	✓	16
40.37	odd	4		400.2.l.i.301.3		16
48.29	odd	4		720.2.bm.f.469.7		16
80.3	even	4		1600.2.l.h.1201.7		16
80.13	odd	4		400.2.l.i.101.6		16
80.19	odd	4		320.2.q.c.49.7		16
80.29	even	4		80.2.q.c.69.7	yes	16
80.59	odd	4		640.2.q.f.609.2		16
80.67	even	4		1600.2.l.h.1201.2		16
80.69	even	4	inner	640.2.q.e.609.7		16
80.77	odd	4		400.2.l.i.101.3		16
120.29	odd	2		720.2.bm.f.109.7		16
240.29	odd	4		720.2.bm.f.469.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.2	✓	16	40.29	even	2
80.2.q.c.29.7	yes	16	8.5	even	2
80.2.q.c.69.2	yes	16	16.13	even	4
80.2.q.c.69.7	yes	16	80.29	even	4
320.2.q.c.49.2		16	16.3	odd	4
320.2.q.c.49.7		16	80.19	odd	4
320.2.q.c.209.2		16	40.19	odd	2
320.2.q.c.209.7		16	8.3	odd	2
400.2.l.i.101.3		16	80.77	odd	4
400.2.l.i.101.6		16	80.13	odd	4
400.2.l.i.301.3		16	40.37	odd	4
400.2.l.i.301.6		16	40.13	odd	4
640.2.q.e.289.2		16	5.4	even	2	inner
640.2.q.e.289.7		16	1.1	even	1	trivial
640.2.q.e.609.2		16	16.5	even	4	inner
640.2.q.e.609.7		16	80.69	even	4	inner
640.2.q.f.289.2		16	4.3	odd	2
640.2.q.f.289.7		16	20.19	odd	2
640.2.q.f.609.2		16	80.59	odd	4
640.2.q.f.609.7		16	16.11	odd	4
720.2.bm.f.109.2		16	24.5	odd	2
720.2.bm.f.109.7		16	120.29	odd	2
720.2.bm.f.469.2		16	240.29	odd	4
720.2.bm.f.469.7		16	48.29	odd	4
1600.2.l.h.401.2		16	40.27	even	4
1600.2.l.h.401.7		16	40.3	even	4
1600.2.l.h.1201.2		16	80.67	even	4
1600.2.l.h.1201.7		16	80.3	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.86033 - 1.86033i) q^{3} +(1.17216 + 1.90421i) q^{5} +3.61392 q^{7} -3.92163i q^{9} +(0.0947876 - 0.0947876i) q^{11} +(-2.59462 + 2.59462i) q^{13} +(5.72307 + 1.36185i) q^{15} -1.89939i q^{17} +(2.16418 + 2.16418i) q^{19} +(6.72307 - 6.72307i) q^{21} -5.08251 q^{23} +(-2.25207 + 4.46410i) q^{25} +(-1.71452 - 1.71452i) q^{27} +(-1.25896 - 1.25896i) q^{29} -1.27453 q^{31} -0.352672i q^{33} +(4.23610 + 6.88168i) q^{35} +(-2.25207 - 2.25207i) q^{37} +9.65368i q^{39} -8.52451i q^{41} +(-1.61439 - 1.61439i) q^{43} +(7.46762 - 4.59679i) q^{45} +2.53884i q^{47} +6.06040 q^{49} +(-3.53349 - 3.53349i) q^{51} +(-5.67100 - 5.67100i) q^{53} +(0.291602 + 0.0693893i) q^{55} +8.05215 q^{57} +(7.81785 - 7.81785i) q^{59} +(-3.46410 - 3.46410i) q^{61} -14.1724i q^{63} +(-7.98203 - 1.89939i) q^{65} +(-6.29856 + 6.29856i) q^{67} +(-9.45512 + 9.45512i) q^{69} -11.3074i q^{71} -16.1786 q^{73} +(4.11511 + 12.4943i) q^{75} +(0.342555 - 0.342555i) q^{77} +1.13575 q^{79} +5.38573 q^{81} +(3.75489 - 3.75489i) q^{83} +(3.61685 - 2.22640i) q^{85} -4.68417 q^{87} +3.98203i q^{89} +(-9.37674 + 9.37674i) q^{91} +(-2.37103 + 2.37103i) q^{93} +(-1.58429 + 6.65783i) q^{95} +10.3042i q^{97} +(-0.371721 - 0.371721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{5} - 8 q^{11} + 8 q^{19} + 16 q^{21} + 16 q^{29} + 16 q^{31} + 24 q^{35} - 8 q^{45} + 16 q^{49} + 16 q^{51} + 24 q^{59} - 32 q^{69} - 48 q^{75} + 16 q^{79} - 16 q^{81} + 16 q^{91} + 32 q^{95}+ \cdots - 88 q^{99}+O(q^{100}) \) 16 * q + 8 * q^5 - 8 * q^11 + 8 * q^19 + 16 * q^21 + 16 * q^29 + 16 * q^31 + 24 * q^35 - 8 * q^45 + 16 * q^49 + 16 * q^51 + 24 * q^59 - 32 * q^69 - 48 * q^75 + 16 * q^79 - 16 * q^81 + 16 * q^91 + 32 * q^95 - 88 * q^99

Introduction

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