LMFDB - Embedded newform 640.2.q.f.609.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(289,640)]

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

lf = mfeigenbasis(mf)

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")

//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: 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:	$16$
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			609.2
Root			$1.40501 - 0.161069i$ of defining polynomial
Character	$\chi$	$=$	640.609
Dual form			640.2.q.f.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86033 - 1.86033i) q^{3} +(1.17216 - 1.90421i) q^{5} -3.61392 q^{7} +3.92163i q^{9} +O(q^{10})$	\(q+(-1.86033 - 1.86033i) q^{3} +(1.17216 - 1.90421i) q^{5} -3.61392 q^{7} +3.92163i q^{9} +(-0.0947876 - 0.0947876i) q^{11} +(-2.59462 - 2.59462i) q^{13} +(-5.72307 + 1.36185i) q^{15} +1.89939i q^{17} +(-2.16418 + 2.16418i) q^{19} +(6.72307 + 6.72307i) q^{21} +5.08251 q^{23} +(-2.25207 - 4.46410i) q^{25} +(1.71452 - 1.71452i) q^{27} +(-1.25896 + 1.25896i) q^{29} +1.27453 q^{31} +0.352672i q^{33} +(-4.23610 + 6.88168i) q^{35} +(-2.25207 + 2.25207i) q^{37} +9.65368i q^{39} +8.52451i q^{41} +(1.61439 - 1.61439i) q^{43} +(7.46762 + 4.59679i) q^{45} +2.53884i q^{47} +6.06040 q^{49} +(3.53349 - 3.53349i) q^{51} +(-5.67100 + 5.67100i) q^{53} +(-0.291602 + 0.0693893i) q^{55} +8.05215 q^{57} +(-7.81785 - 7.81785i) q^{59} +(-3.46410 + 3.46410i) q^{61} -14.1724i q^{63} +(-7.98203 + 1.89939i) q^{65} +(6.29856 + 6.29856i) q^{67} +(-9.45512 - 9.45512i) q^{69} -11.3074i q^{71} -16.1786 q^{73} +(-4.11511 + 12.4943i) q^{75} +(0.342555 + 0.342555i) q^{77} -1.13575 q^{79} +5.38573 q^{81} +(-3.75489 - 3.75489i) q^{83} +(3.61685 + 2.22640i) q^{85} +4.68417 q^{87} -3.98203i q^{89} +(9.37674 + 9.37674i) q^{91} +(-2.37103 - 2.37103i) q^{93} +(1.58429 + 6.65783i) q^{95} -10.3042i q^{97} +(0.371721 - 0.371721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{5}+O(q^{10}) $ 16 * q + 8 * q^5	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.997029	−	0.0770310i	$-0.975456\pi$
$3$	−1.86033	−	1.86033i	−1.07406	−	1.07406i	−0.0770310	−	0.997029i	$-0.524544\pi$
$4$		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	$-0.739310\pi$
$7$	−3.61392			−1.36593			−0.682966	+	0.730450i	$0.739310\pi$
$8$		0			0
$9$			3.92163i			1.30721i
$10$		0			0
$11$	−0.0947876	−	0.0947876i	−0.0285795	−	0.0285795i	0.692673	−	0.721252i	$-0.256433\pi$
$11$	−0.0947876	−	0.0947876i	−0.0285795	−	0.0285795i	−0.721252	+	0.692673i	$0.756433\pi$
$12$		0			0
$13$	−2.59462	−	2.59462i	−0.719618	−	0.719618i	0.248909	−	0.968527i	$-0.419928\pi$
$13$	−2.59462	−	2.59462i	−0.719618	−	0.719618i	−0.968527	+	0.248909i	$0.919928\pi$
$14$		0			0
$15$	−5.72307	+	1.36185i	−1.47769	+	0.351629i
$16$		0			0
$17$			1.89939i			0.460671i	0.973111	+	0.230335i	$0.0739823\pi$
$17$			1.89939i			0.460671i	−0.973111	+	0.230335i	$0.926018\pi$
$18$		0			0
$19$	−2.16418	+	2.16418i	−0.496496	+	0.496496i	−0.910345	−	0.413849i	$-0.864184\pi$
$19$	−2.16418	+	2.16418i	−0.496496	+	0.496496i	0.413849	+	0.910345i	$0.364184\pi$
$20$		0			0
$21$	6.72307	+	6.72307i	1.46709	+	1.46709i
$22$		0			0
$23$	5.08251			1.05978			0.529888	−	0.848068i	$-0.322234\pi$
$23$	5.08251			1.05978			0.529888	+	0.848068i	$0.322234\pi$
$24$		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	−0.814270	−	0.580486i	$-0.802863\pi$
$29$	−1.25896	+	1.25896i	−0.233784	+	0.233784i	0.580486	+	0.814270i	$0.302863\pi$
$30$		0			0
$31$	1.27453			0.228912			0.114456	−	0.993428i	$-0.463488\pi$
$31$	1.27453			0.228912			0.114456	+	0.993428i	$0.463488\pi$
$32$		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	−0.867564	−	0.497326i	$-0.834315\pi$
$37$	−2.25207	+	2.25207i	−0.370237	+	0.370237i	0.497326	+	0.867564i	$0.334315\pi$
$38$		0			0
$39$			9.65368i			1.54583i
$40$		0			0
$41$			8.52451i			1.33130i	0.746262	+	0.665652i	$0.231847\pi$
$41$			8.52451i			1.33130i	−0.746262	+	0.665652i	$0.768153\pi$
$42$		0			0
$43$	1.61439	−	1.61439i	0.246192	−	0.246192i	−0.573214	−	0.819406i	$-0.694304\pi$
$43$	1.61439	−	1.61439i	0.246192	−	0.246192i	0.819406	+	0.573214i	$0.194304\pi$
$44$		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	−0.979656	−	0.200684i	$-0.935683\pi$
$53$	−5.67100	+	5.67100i	−0.778971	+	0.778971i	0.200684	+	0.979656i	$0.435683\pi$
$54$		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	−0.999839	−	0.0179591i	$-0.994283\pi$
$59$	−7.81785	−	7.81785i	−1.01780	−	1.01780i	−0.0179591	−	0.999839i	$-0.505717\pi$
$60$		0			0
$61$	−3.46410	+	3.46410i	−0.443533	+	0.443533i	−0.893197	−	0.449665i	$-0.851543\pi$
$61$	−3.46410	+	3.46410i	−0.443533	+	0.443533i	0.449665	+	0.893197i	$0.351543\pi$
$62$		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	$-0.0668665\pi$
$67$	6.29856	+	6.29856i	0.769491	+	0.769491i	−0.208526	+	0.978017i	$0.566866\pi$
$68$		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	$-0.520351\pi$
$79$	−1.13575			−0.127782			−0.0638908	+	0.997957i	$0.520351\pi$
$80$		0			0
$81$	5.38573			0.598414
$82$		0			0
$83$	−3.75489	−	3.75489i	−0.412153	−	0.412153i	0.470335	−	0.882488i	$-0.344133\pi$
$83$	−3.75489	−	3.75489i	−0.412153	−	0.412153i	−0.882488	+	0.470335i	$0.844133\pi$
$84$		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	$-0.932313\pi$
$89$		−	3.98203i		−	0.422094i	0.977476	−	0.211047i	$-0.0676874\pi$
$90$		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	$-0.824769\pi$
$97$		−	10.3042i		−	1.04623i	0.852261	−	0.523117i	$-0.175231\pi$
$98$		0			0
$99$	0.371721	−	0.371721i	0.0373594	−	0.0373594i
$100$		0			0
$101$	−1.25896	−	1.25896i	−0.125272	−	0.125272i	0.641691	−	0.766963i	$-0.278233\pi$
$101$	−1.25896	−	1.25896i	−0.125272	−	0.125272i	−0.766963	+	0.641691i	$0.778233\pi$
$102$		0			0
$103$	−10.8655			−1.07061			−0.535306	−	0.844658i	$-0.679804\pi$
$103$	−10.8655			−1.07061			−0.535306	+	0.844658i	$0.679804\pi$
$104$		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	$-0.974459\pi$
$107$	−9.48167	+	9.48167i	−0.916628	+	0.916628i	0.0801549	+	0.996782i	$0.474459\pi$
$108$		0			0
$109$	8.57530	−	8.57530i	0.821365	−	0.821365i	−0.164939	−	0.986304i	$-0.552743\pi$
$109$	8.57530	−	8.57530i	0.821365	−	0.821365i	0.986304	+	0.164939i	$0.0527427\pi$
$110$		0			0
$111$	8.37915			0.795314
$112$		0			0
$113$		−	12.5286i		−	1.17860i	−0.807916	−	0.589298i	$-0.799405\pi$
$113$		−	12.5286i		−	1.17860i	0.807916	−	0.589298i	$-0.200595\pi$
$114$		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	$-0.617533\pi$
$131$	6.54333	−	6.54333i	0.571693	−	0.571693i	0.932601	+	0.360908i	$0.117533\pi$
$132$		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	$-0.354365\pi$
$139$	−5.36931	−	5.36931i	−0.455419	−	0.455419i	−0.897148	+	0.441729i	$0.854365\pi$
$140$		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	0.504600	−	0.863354i	$-0.331640\pi$
$149$	−4.37915	−	4.37915i	−0.358754	−	0.358754i	−0.863354	+	0.504600i	$0.831640\pi$
$150$		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	0.970307	−	0.241875i	$-0.0777624\pi$
$157$	9.12723	+	9.12723i	0.728432	+	0.728432i	−0.241875	+	0.970307i	$0.577762\pi$
$158$		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	$-0.139346\pi$
$163$	6.15099	+	6.15099i	0.481783	+	0.481783i	−0.423918	+	0.905701i	$0.639346\pi$
$164$		0			0
$165$	0.671562	+	0.413389i	0.0522811	+	0.0321823i
$166$		0			0
$167$	0.710173			0.0549548			0.0274774	−	0.999622i	$-0.491253\pi$
$167$	0.710173			0.0549548			0.0274774	+	0.999622i	$0.491253\pi$
$168$		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	−0.996700	−	0.0811779i	$-0.974132\pi$
$173$	−14.1773	−	14.1773i	−1.07788	−	1.07788i	−0.0811779	−	0.996700i	$-0.525868\pi$
$174$		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	$-0.592111\pi$
$179$	9.00502	−	9.00502i	0.673067	−	0.673067i	0.958422	+	0.285355i	$0.0921115\pi$
$180$		0			0
$181$	−14.1872	−	14.1872i	−1.05452	−	1.05452i	−0.998425	−	0.0560986i	$-0.982134\pi$
$181$	−14.1872	−	14.1872i	−1.05452	−	1.05452i	−0.0560986	−	0.998425i	$-0.517866\pi$
$182$		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	$-0.740110\pi$
$191$	−18.9282			−1.36960			−0.684798	+	0.728733i	$0.740110\pi$
$192$		0			0
$193$			21.3880i			1.53954i	0.638319	+	0.769772i	$0.279630\pi$
$193$			21.3880i			1.53954i	−0.638319	+	0.769772i	$0.720370\pi$
$194$		0			0
$195$	18.3827	+	11.3157i	1.31641	+	0.810333i
$196$		0			0
$197$	−6.39341	+	6.39341i	−0.455511	+	0.455511i	−0.897179	−	0.441667i	$-0.854387\pi$
$197$	−6.39341	+	6.39341i	−0.455511	+	0.455511i	0.441667	+	0.897179i	$0.354387\pi$
$198$		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	−0.417520	+	0.908668i	$0.637100\pi$
$211$	−19.2640	+	19.2640i	−1.32619	+	1.32619i	−0.908668	+	0.417520i	$0.862900\pi$
$212$		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	$-0.186625\pi$
$227$	4.21430	+	4.21430i	0.279713	+	0.279713i	−0.553282	+	0.832994i	$0.686625\pi$
$228$		0			0
$229$	18.0304	+	18.0304i	1.19148	+	1.19148i	0.976651	+	0.214833i	$0.0689207\pi$
$229$	18.0304	+	18.0304i	1.19148	+	1.19148i	0.214833	+	0.976651i	$0.431079\pi$
$230$		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	$-0.701741\pi$
$239$	−18.3104			−1.18440			−0.592200	+	0.805791i	$0.701741\pi$
$240$		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	$-0.468783\pi$
$251$	−14.2156	−	14.2156i	−0.897281	−	0.897281i	−0.995195	+	0.0979143i	$0.968783\pi$
$252$		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	$-0.820532\pi$
$257$		−	17.1347i		−	1.06883i	0.845222	−	0.534416i	$-0.179468\pi$
$258$		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	$-0.449582\pi$
$263$	5.11593			0.315462			0.157731	+	0.987482i	$0.449582\pi$
$264$		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	−0.184870	+	0.982763i	$0.559186\pi$
$269$	−19.1506	+	19.1506i	−1.16763	+	1.16763i	−0.982763	+	0.184870i	$0.940814\pi$
$270$		0			0
$271$	−4.72066			−0.286760			−0.143380	−	0.989668i	$-0.545797\pi$
$271$	−4.72066			−0.286760			−0.143380	+	0.989668i	$0.545797\pi$
$272$		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	−0.204466	−	0.978874i	$-0.565546\pi$
$277$	12.8887	−	12.8887i	0.774408	−	0.774408i	0.978874	+	0.204466i	$0.0655457\pi$
$278$		0			0
$279$			4.99822i			0.299235i
$280$		0			0
$281$			16.4934i			0.983913i	0.870620	+	0.491956i	$0.163718\pi$
$281$			16.4934i			0.983913i	−0.870620	+	0.491956i	$0.836282\pi$
$282$		0			0
$283$	−7.69771	+	7.69771i	−0.457581	+	0.457581i	−0.897861	−	0.440279i	$-0.854879\pi$
$283$	−7.69771	+	7.69771i	−0.457581	+	0.457581i	0.440279	+	0.897861i	$0.354879\pi$
$284$		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	−0.518715	−	0.854947i	$-0.673589\pi$
$293$	5.75538	−	5.75538i	0.336233	−	0.336233i	0.854947	+	0.518715i	$0.173589\pi$
$294$		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	$-0.123289\pi$
$307$	9.60547	+	9.60547i	0.548213	+	0.548213i	−0.377711	+	0.925924i	$0.623289\pi$
$308$		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	0.680041	−	0.733174i	$-0.261962\pi$
$317$	−0.945994	−	0.945994i	−0.0531323	−	0.0531323i	−0.733174	+	0.680041i	$0.761962\pi$
$318$		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	$-0.172991\pi$
$331$	6.16418	+	6.16418i	0.338814	+	0.338814i	−0.517107	+	0.855921i	$0.672991\pi$
$332$		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	$-0.720763\pi$
$337$		−	28.2333i		−	1.53797i	0.639269	−	0.768983i	$-0.279237\pi$
$338$		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	$-0.584966\pi$
$347$	13.0548	−	13.0548i	0.700816	−	0.700816i	0.964586	+	0.263770i	$0.0849659\pi$
$348$		0			0
$349$	20.3080	−	20.3080i	1.08706	−	1.08706i	0.0912314	−	0.995830i	$-0.470920\pi$
$349$	20.3080	−	20.3080i	1.08706	−	1.08706i	0.995830	−	0.0912314i	$-0.0290803\pi$
$350$		0			0
$351$	−8.89708			−0.474891
$352$		0			0
$353$			18.6814i			0.994310i	0.867662	+	0.497155i	$0.165622\pi$
$353$			18.6814i			0.994310i	−0.867662	+	0.497155i	$0.834378\pi$
$354$		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	−0.896023	−	0.444008i	$-0.853556\pi$
$373$	−8.72985	+	8.72985i	−0.452015	+	0.452015i	0.444008	+	0.896023i	$0.353556\pi$
$374$		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	$-0.178733\pi$
$379$	6.11276	+	6.11276i	0.313991	+	0.313991i	−0.532462	+	0.846454i	$0.678733\pi$
$380$		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	0.909539	−	0.415618i	$-0.136435\pi$
$389$	9.74166	+	9.74166i	0.493922	+	0.493922i	−0.415618	+	0.909539i	$0.636435\pi$
$390$		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	0.475888	−	0.879506i	$-0.342127\pi$
$397$	−8.04203	−	8.04203i	−0.403618	−	0.403618i	−0.879506	+	0.475888i	$0.842127\pi$
$398$		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	$-0.868313\pi$
$409$		−	16.2601i		−	0.804010i	0.915637	−	0.402005i	$-0.131687\pi$
$410$		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	$-0.863923\pi$
$419$	−10.1408	+	10.1408i	−0.495409	+	0.495409i	0.414596	+	0.910005i	$0.363923\pi$
$420$		0			0
$421$	13.5849	+	13.5849i	0.662088	+	0.662088i	0.955872	−	0.293784i	$-0.0949146\pi$
$421$	13.5849	+	13.5849i	0.662088	+	0.662088i	−0.293784	+	0.955872i	$0.594915\pi$
$422$		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	$-0.510552\pi$
$431$	−1.37612			−0.0662853			−0.0331427	+	0.999451i	$0.510552\pi$
$432$		0			0
$433$			19.9307i			0.957810i	0.877867	+	0.478905i	$0.158966\pi$
$433$			19.9307i			0.957810i	−0.877867	+	0.478905i	$0.841034\pi$
$434$		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	0.193402	−	0.981120i	$-0.438048\pi$
$443$	24.7208	−	24.7208i	1.17452	−	1.17452i	0.981120	−	0.193402i	$-0.0619522\pi$
$444$		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	−0.928286	−	0.371868i	$-0.878717\pi$
$461$	−11.9468	+	11.9468i	−0.556418	+	0.556418i	0.371868	+	0.928286i	$0.378717\pi$
$462$		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	$-0.371923\pi$
$467$	−11.4219	−	11.4219i	−0.528542	−	0.528542i	−0.920138	+	0.391595i	$0.871923\pi$
$468$		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	$-0.546519\pi$
$479$	−6.37434			−0.291251			−0.145625	+	0.989340i	$0.546519\pi$
$480$		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	$-0.248862\pi$
$487$	31.3203			1.41926			0.709629	+	0.704575i	$0.248862\pi$
$488$		0			0
$489$		−	22.8857i		−	1.03493i
$490$		0			0
$491$	14.0893	+	14.0893i	0.635843	+	0.635843i	0.949527	−	0.313684i	$-0.101563\pi$
$491$	14.0893	+	14.0893i	0.635843	+	0.635843i	−0.313684	+	0.949527i	$0.601563\pi$
$492$		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	$-0.773219\pi$
$499$	−2.30233	+	2.30233i	−0.103067	+	0.103067i	0.653693	+	0.756760i	$0.273219\pi$
$500$		0			0
$501$	−1.32115	−	1.32115i	−0.0590248	−	0.0590248i
$502$		0			0
$503$	−14.7556			−0.657921			−0.328961	−	0.944344i	$-0.606698\pi$
$503$	−14.7556			−0.657921			−0.328961	+	0.944344i	$0.606698\pi$
$504$		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	−0.506373	−	0.862315i	$-0.669014\pi$
$509$	8.03042	−	8.03042i	0.355942	−	0.355942i	0.862315	+	0.506373i	$0.169014\pi$
$510$		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	$0.0973259\pi$
$521$			13.7417i			0.602033i	−0.953619	+	0.301017i	$0.902674\pi$
$522$		0			0
$523$	−6.77116	+	6.77116i	−0.296082	+	0.296082i	−0.839477	−	0.543395i	$-0.817139\pi$
$523$	−6.77116	+	6.77116i	−0.296082	+	0.296082i	0.543395	+	0.839477i	$0.317139\pi$
$524$		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	−0.855035	−	0.518570i	$-0.826465\pi$
$541$	−7.82599	+	7.82599i	−0.336465	+	0.336465i	0.518570	+	0.855035i	$0.326465\pi$
$542$		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	$-0.412112\pi$
$547$	−16.1263	−	16.1263i	−0.689511	−	0.689511i	−0.962124	+	0.272613i	$0.912112\pi$
$548$		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	0.935424	−	0.353527i	$-0.115018\pi$
$557$	13.7333	+	13.7333i	0.581897	+	0.581897i	−0.353527	+	0.935424i	$0.615018\pi$
$558$		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	$-0.121284\pi$
$563$	13.2023	+	13.2023i	0.556412	+	0.556412i	−0.371872	+	0.928284i	$0.621284\pi$
$564$		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	$-0.950934\pi$
$569$		−	7.32481i		−	0.307072i	0.988143	−	0.153536i	$-0.0490661\pi$
$570$		0			0
$571$	−22.1916	−	22.1916i	−0.928688	−	0.928688i	0.0689332	−	0.997621i	$-0.478040\pi$
$571$	−22.1916	−	22.1916i	−0.928688	−	0.928688i	−0.997621	+	0.0689332i	$0.978040\pi$
$572$		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	$-0.937350\pi$
$577$		−	9.39473i		−	0.391108i	0.980693	−	0.195554i	$-0.0626504\pi$
$578$		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	$-0.851334\pi$
$587$	−10.7246	+	10.7246i	−0.442650	+	0.442650i	0.450252	+	0.892902i	$0.351334\pi$
$588$		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	$-0.712733\pi$
$593$		−	38.2253i		−	1.56973i	0.619670	−	0.784863i	$-0.287267\pi$
$594$		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	$-0.843785\pi$
$601$		−	23.1081i		−	0.942599i	0.881973	−	0.471299i	$-0.156215\pi$
$602$		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	−0.682727	−	0.730674i	$-0.739206\pi$
$613$	1.18710	−	1.18710i	0.0479466	−	0.0479466i	0.730674	+	0.682727i	$0.239206\pi$
$614$		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	$-0.309405\pi$
$619$	−6.52847	−	6.52847i	−0.262401	−	0.262401i	−0.826029	+	0.563628i	$0.809405\pi$
$620$		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	$-0.444139\pi$
$643$	−20.5408	−	20.5408i	−0.810049	−	0.810049i	−0.984641	+	0.174592i	$0.944139\pi$
$644$		0			0
$645$	−7.04069	+	11.4378i	−0.277227	+	0.450363i
$646$		0			0
$647$	−31.7472			−1.24811			−0.624056	−	0.781379i	$-0.714516\pi$
$647$	−31.7472			−1.24811			−0.624056	+	0.781379i	$0.714516\pi$
$648$		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	0.617930	−	0.786233i	$-0.287971\pi$
$653$	−4.30078	−	4.30078i	−0.168302	−	0.168302i	−0.786233	+	0.617930i	$0.787971\pi$
$654$		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	$-0.917310\pi$
$659$	−18.2156	+	18.2156i	−0.709579	+	0.709579i	0.256868	+	0.966447i	$0.417310\pi$
$660$		0			0
$661$	19.7679	+	19.7679i	0.768883	+	0.768883i	0.977910	−	0.209027i	$-0.0670297\pi$
$661$	19.7679	+	19.7679i	0.768883	+	0.768883i	−0.209027	+	0.977910i	$0.567030\pi$
$662$		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	$-0.948037\pi$
$673$		−	8.43246i		−	0.325047i	0.986705	−	0.162524i	$-0.0519634\pi$
$674$		0			0
$675$	−11.5150	−	3.79259i	−0.443214	−	0.145977i
$676$		0			0
$677$	20.8693	−	20.8693i	0.802073	−	0.802073i	−0.181346	−	0.983419i	$-0.558046\pi$
$677$	20.8693	−	20.8693i	0.802073	−	0.802073i	0.983419	+	0.181346i	$0.0580455\pi$
$678$		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	$-0.896728\pi$
$683$	−16.4398	+	16.4398i	−0.629051	+	0.629051i	0.318778	+	0.947829i	$0.396728\pi$
$684$		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	$-0.594882\pi$
$691$	17.4076	−	17.4076i	0.662216	−	0.662216i	0.955902	+	0.293686i	$0.0948821\pi$
$692$		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	−0.0402687	−	0.999189i	$-0.512821\pi$
$701$	25.3888	−	25.3888i	0.958920	−	0.958920i	0.999189	+	0.0402687i	$0.0128214\pi$
$702$		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	0.294051	−	0.955790i	$-0.404996\pi$
$709$	−17.6201	−	17.6201i	−0.661738	−	0.661738i	−0.955790	+	0.294051i	$0.904996\pi$
$710$		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	$-0.207742\pi$
$719$	42.6068			1.58896			0.794482	+	0.607287i	$0.207742\pi$
$720$		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	$-0.112667\pi$
$727$	50.5830			1.87602			0.938010	+	0.346609i	$0.112667\pi$
$728$		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	0.583854	−	0.811859i	$-0.301544\pi$
$733$	−6.17299	−	6.17299i	−0.228005	−	0.228005i	−0.811859	+	0.583854i	$0.801544\pi$
$734$		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	$-0.546918\pi$
$739$	22.8974	−	22.8974i	0.842293	−	0.842293i	0.989157	+	0.146864i	$0.0469178\pi$
$740$		0			0
$741$	−20.8923	−	20.8923i	−0.767497	−	0.767497i
$742$		0			0
$743$	11.8975			0.436478			0.218239	−	0.975895i	$-0.429969\pi$
$743$	11.8975			0.436478			0.218239	+	0.975895i	$0.429969\pi$
$744$		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	$-0.640474\pi$
$751$	−23.4102			−0.854250			−0.427125	+	0.904193i	$0.640474\pi$
$752$		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	−0.470763	−	0.882260i	$-0.656021\pi$
$757$	11.3218	−	11.3218i	0.411496	−	0.411496i	0.882260	+	0.470763i	$0.156021\pi$
$758$		0			0
$759$			1.79246i			0.0650620i
$760$		0			0
$761$		−	8.53590i		−	0.309426i	−0.987959	−	0.154713i	$-0.950555\pi$
$761$		−	8.53590i		−	0.309426i	0.987959	−	0.154713i	$-0.0494453\pi$
$762$		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	−0.991485	−	0.130219i	$-0.958432\pi$
$773$	−23.9457	+	23.9457i	−0.861267	+	0.861267i	0.130219	+	0.991485i	$0.458432\pi$
$774$		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	0.985614	+	0.169014i	$0.0540582\pi$
$787$	32.3914	+	32.3914i	1.15463	+	1.15463i	0.169014	+	0.985614i	$0.445942\pi$
$788$		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	0.672162	−	0.740404i	$-0.265366\pi$
$797$	−1.92658	−	1.92658i	−0.0682428	−	0.0682428i	−0.740404	+	0.672162i	$0.765366\pi$
$798$		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	$0.340580\pi$
$809$			49.8993i			1.75437i	−0.480157	+	0.877183i	$0.659420\pi$
$810$		0			0
$811$	22.9363	+	22.9363i	0.805401	+	0.805401i	0.983934	−	0.178533i	$-0.0571351\pi$
$811$	22.9363	+	22.9363i	0.805401	+	0.805401i	−0.178533	+	0.983934i	$0.557135\pi$
$812$		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	0.494581	−	0.869132i	$-0.335322\pi$
$821$	−10.7321	−	10.7321i	−0.374551	−	0.374551i	−0.869132	+	0.494581i	$0.835322\pi$
$822$		0			0
$823$	8.56875			0.298688			0.149344	−	0.988785i	$-0.452284\pi$
$823$	8.56875			0.298688			0.149344	+	0.988785i	$0.452284\pi$
$824$		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	$-0.829758\pi$
$827$	−10.0841	+	10.0841i	−0.350660	+	0.350660i	0.509695	+	0.860355i	$0.329758\pi$
$828$		0			0
$829$	−0.656708	+	0.656708i	−0.0228084	+	0.0228084i	−0.718419	−	0.695611i	$-0.755134\pi$
$829$	−0.656708	+	0.656708i	−0.0228084	+	0.0228084i	0.695611	+	0.718419i	$0.255134\pi$
$830$		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	−0.935753	−	0.352655i	$-0.885279\pi$
$853$	−17.0301	+	17.0301i	−0.583098	+	0.583098i	0.352655	+	0.935753i	$0.385279\pi$
$854$		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	$-0.333597\pi$
$859$	−10.7609	−	10.7609i	−0.367158	−	0.367158i	−0.866440	+	0.499282i	$0.833597\pi$
$860$		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	0.127278	−	0.991867i	$-0.459376\pi$
$877$	−25.6041	−	25.6041i	−0.864589	−	0.864589i	−0.991867	+	0.127278i	$0.959376\pi$
$878$		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	$-0.156275\pi$
$883$	12.1957	+	12.1957i	0.410419	+	0.410419i	−0.471466	+	0.881884i	$0.656275\pi$
$884$		0			0
$885$	55.3889	+	34.0953i	1.86188	+	1.14610i
$886$		0			0
$887$	−36.3716			−1.22124			−0.610619	−	0.791924i	$-0.709079\pi$
$887$	−36.3716			−1.22124			−0.610619	+	0.791924i	$0.709079\pi$
$888$		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	0.197996	−	0.980203i	$-0.436557\pi$
$907$	35.4831	−	35.4831i	1.17820	−	1.17820i	0.980203	−	0.197996i	$-0.0634432\pi$
$908$		0			0
$909$	4.93719	−	4.93719i	0.163756	−	0.163756i
$910$		0			0
$911$	−22.6536			−0.750547			−0.375274	−	0.926914i	$-0.622451\pi$
$911$	−22.6536			−0.750547			−0.375274	+	0.926914i	$0.622451\pi$
$912$		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	−0.117412	−	0.993083i	$-0.537460\pi$
$941$	26.8618	−	26.8618i	0.875671	−	0.875671i	0.993083	+	0.117412i	$0.0374599\pi$
$942$		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	−0.863451	−	0.504433i	$-0.831701\pi$
$947$	−42.0944	−	42.0944i	−1.36788	−	1.36788i	−0.504433	−	0.863451i	$-0.668299\pi$
$948$		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	$-0.660029\pi$
$967$	−29.9668			−0.963667			−0.481833	+	0.876263i	$0.660029\pi$
$968$		0			0
$969$			15.2942i			0.491320i
$970$		0			0
$971$	0.750872	+	0.750872i	0.0240966	+	0.0240966i	0.719052	−	0.694956i	$-0.244576\pi$
$971$	0.750872	+	0.750872i	0.0240966	+	0.0240966i	−0.694956	+	0.719052i	$0.744576\pi$
$972$		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	$0.137944\pi$
$977$			26.2513i			0.839854i	−0.907558	+	0.419927i	$0.862056\pi$
$978$		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	$-0.566591\pi$
$983$	−13.0227			−0.415360			−0.207680	+	0.978197i	$0.566591\pi$
$984$		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	$-0.751642\pi$
$991$	−44.7487			−1.42149			−0.710744	+	0.703451i	$0.751642\pi$
$992$		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	−0.285686	−	0.958323i	$-0.592222\pi$
$997$	21.2387	−	21.2387i	0.672637	−	0.672637i	0.958323	+	0.285686i	$0.0922215\pi$
$998$		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.f.609.2		16
4.3	odd	2		640.2.q.e.609.7		16
5.4	even	2	inner	640.2.q.f.609.7		16
8.3	odd	2		80.2.q.c.69.7	yes	16
8.5	even	2		320.2.q.c.49.7		16
16.3	odd	4		640.2.q.e.289.2		16
16.5	even	4		320.2.q.c.209.2		16
16.11	odd	4		80.2.q.c.29.2	✓	16
16.13	even	4	inner	640.2.q.f.289.7		16
20.19	odd	2		640.2.q.e.609.2		16
24.11	even	2		720.2.bm.f.469.2		16
40.3	even	4		400.2.l.i.101.3		16
40.13	odd	4		1600.2.l.h.1201.2		16
40.19	odd	2		80.2.q.c.69.2	yes	16
40.27	even	4		400.2.l.i.101.6		16
40.29	even	2		320.2.q.c.49.2		16
40.37	odd	4		1600.2.l.h.1201.7		16
48.11	even	4		720.2.bm.f.109.7		16
80.19	odd	4		640.2.q.e.289.7		16
80.27	even	4		400.2.l.i.301.6		16
80.29	even	4	inner	640.2.q.f.289.2		16
80.37	odd	4		1600.2.l.h.401.7		16
80.43	even	4		400.2.l.i.301.3		16
80.53	odd	4		1600.2.l.h.401.2		16
80.59	odd	4		80.2.q.c.29.7	yes	16
80.69	even	4		320.2.q.c.209.7		16
120.59	even	2		720.2.bm.f.469.7		16
240.59	even	4		720.2.bm.f.109.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.2	✓	16	16.11	odd	4
80.2.q.c.29.7	yes	16	80.59	odd	4
80.2.q.c.69.2	yes	16	40.19	odd	2
80.2.q.c.69.7	yes	16	8.3	odd	2
320.2.q.c.49.2		16	40.29	even	2
320.2.q.c.49.7		16	8.5	even	2
320.2.q.c.209.2		16	16.5	even	4
320.2.q.c.209.7		16	80.69	even	4
400.2.l.i.101.3		16	40.3	even	4
400.2.l.i.101.6		16	40.27	even	4
400.2.l.i.301.3		16	80.43	even	4
400.2.l.i.301.6		16	80.27	even	4
640.2.q.e.289.2		16	16.3	odd	4
640.2.q.e.289.7		16	80.19	odd	4
640.2.q.e.609.2		16	20.19	odd	2
640.2.q.e.609.7		16	4.3	odd	2
640.2.q.f.289.2		16	80.29	even	4	inner
640.2.q.f.289.7		16	16.13	even	4	inner
640.2.q.f.609.2		16	1.1	even	1	trivial
640.2.q.f.609.7		16	5.4	even	2	inner
720.2.bm.f.109.2		16	240.59	even	4
720.2.bm.f.109.7		16	48.11	even	4
720.2.bm.f.469.2		16	24.11	even	2
720.2.bm.f.469.7		16	120.59	even	2
1600.2.l.h.401.2		16	80.53	odd	4
1600.2.l.h.401.7		16	80.37	odd	4
1600.2.l.h.1201.2		16	40.13	odd	4
1600.2.l.h.1201.7		16	40.37	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.86033 - 1.86033i) q^{3} +(1.17216 - 1.90421i) q^{5} -3.61392 q^{7} +3.92163i q^{9} +O(q^{10})\)	\(q+(-1.86033 - 1.86033i) q^{3} +(1.17216 - 1.90421i) q^{5} -3.61392 q^{7} +3.92163i q^{9} +(-0.0947876 - 0.0947876i) q^{11} +(-2.59462 - 2.59462i) q^{13} +(-5.72307 + 1.36185i) q^{15} +1.89939i q^{17} +(-2.16418 + 2.16418i) q^{19} +(6.72307 + 6.72307i) q^{21} +5.08251 q^{23} +(-2.25207 - 4.46410i) q^{25} +(1.71452 - 1.71452i) q^{27} +(-1.25896 + 1.25896i) q^{29} +1.27453 q^{31} +0.352672i q^{33} +(-4.23610 + 6.88168i) q^{35} +(-2.25207 + 2.25207i) q^{37} +9.65368i q^{39} +8.52451i q^{41} +(1.61439 - 1.61439i) q^{43} +(7.46762 + 4.59679i) q^{45} +2.53884i q^{47} +6.06040 q^{49} +(3.53349 - 3.53349i) q^{51} +(-5.67100 + 5.67100i) q^{53} +(-0.291602 + 0.0693893i) q^{55} +8.05215 q^{57} +(-7.81785 - 7.81785i) q^{59} +(-3.46410 + 3.46410i) q^{61} -14.1724i q^{63} +(-7.98203 + 1.89939i) q^{65} +(6.29856 + 6.29856i) q^{67} +(-9.45512 - 9.45512i) q^{69} -11.3074i q^{71} -16.1786 q^{73} +(-4.11511 + 12.4943i) q^{75} +(0.342555 + 0.342555i) q^{77} -1.13575 q^{79} +5.38573 q^{81} +(-3.75489 - 3.75489i) q^{83} +(3.61685 + 2.22640i) q^{85} +4.68417 q^{87} -3.98203i q^{89} +(9.37674 + 9.37674i) q^{91} +(-2.37103 - 2.37103i) q^{93} +(1.58429 + 6.65783i) q^{95} -10.3042i q^{97} +(0.371721 - 0.371721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{5}+O(q^{10}) \) 16 * q + 8 * q^5	\( 16 q + 8 q^{5} + 8 q^{11} - 8 q^{19} + 16 q^{21} + 16 q^{29} - 16 q^{31} - 24 q^{35} - 8 q^{45} + 16 q^{49} - 16 q^{51} - 24 q^{59} - 32 q^{69} + 48 q^{75} - 16 q^{79} - 16 q^{81} - 16 q^{91} - 32 q^{95} + 88 q^{99}+O(q^{100}) \) 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

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