LMFDB - Embedded newform 320.3.t.a.113.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(17,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("320.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.t (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:	$8.71936845953$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			113.17
Character	$\chi$	$=$	320.113
Dual form			320.3.t.a.17.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.50699 q^{3} +(-4.36488 + 2.43881i) q^{5} +(-7.18571 - 7.18571i) q^{7} -2.71500 q^{9} +O(q^{10})$	\(q+2.50699 q^{3} +(-4.36488 + 2.43881i) q^{5} +(-7.18571 - 7.18571i) q^{7} -2.71500 q^{9} +(8.38398 + 8.38398i) q^{11} -12.9652 q^{13} +(-10.9427 + 6.11407i) q^{15} +(-22.8157 + 22.8157i) q^{17} +(-3.16584 - 3.16584i) q^{19} +(-18.0145 - 18.0145i) q^{21} +(-3.81600 + 3.81600i) q^{23} +(13.1044 - 21.2902i) q^{25} -29.3694 q^{27} +(-18.3544 - 18.3544i) q^{29} +8.78531 q^{31} +(21.0186 + 21.0186i) q^{33} +(48.8893 + 13.8402i) q^{35} +32.4039 q^{37} -32.5036 q^{39} -0.937574i q^{41} -57.8364i q^{43} +(11.8506 - 6.62136i) q^{45} +(-27.9276 + 27.9276i) q^{47} +54.2688i q^{49} +(-57.1987 + 57.1987i) q^{51} +20.6425i q^{53} +(-57.0420 - 16.1482i) q^{55} +(-7.93674 - 7.93674i) q^{57} +(40.1490 - 40.1490i) q^{59} +(-25.3893 + 25.3893i) q^{61} +(19.5092 + 19.5092i) q^{63} +(56.5915 - 31.6196i) q^{65} -29.3419i q^{67} +(-9.56668 + 9.56668i) q^{69} +34.7686i q^{71} +(-76.2777 + 76.2777i) q^{73} +(32.8527 - 53.3744i) q^{75} -120.490i q^{77} -17.2292i q^{79} -49.1938 q^{81} +73.3919 q^{83} +(43.9447 - 155.231i) q^{85} +(-46.0144 - 46.0144i) q^{87} +96.9216 q^{89} +(93.1639 + 93.1639i) q^{91} +22.0247 q^{93} +(21.5394 + 6.09765i) q^{95} +(-53.4378 + 53.4378i) q^{97} +(-22.7625 - 22.7625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9	$ 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{15} - 4 q^{17} + 32 q^{19} - 4 q^{21} + 40 q^{27} + 8 q^{31} - 4 q^{33} + 4 q^{35} - 4 q^{37} + 72 q^{39} - 70 q^{45} + 4 q^{47} + 100 q^{51} - 36 q^{57} + 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 60 q^{69} - 48 q^{73} + 324 q^{75} + 100 q^{81} - 156 q^{83} - 52 q^{85} + 36 q^{87} - 188 q^{91} - 40 q^{93} - 380 q^{95} - 4 q^{97} - 92 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^15 - 4 * q^17 + 32 * q^19 - 4 * q^21 + 40 * q^27 + 8 * q^31 - 4 * q^33 + 4 * q^35 - 4 * q^37 + 72 * q^39 - 70 * q^45 + 4 * q^47 + 100 * q^51 - 36 * q^57 + 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 60 * q^69 - 48 * q^73 + 324 * q^75 + 100 * q^81 - 156 * q^83 - 52 * q^85 + 36 * q^87 - 188 * q^91 - 40 * q^93 - 380 * q^95 - 4 * q^97 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.50699			0.835664			0.417832	−	0.908524i	$-0.362790\pi$
$3$	2.50699			0.835664			0.417832	+	0.908524i	$0.362790\pi$
$4$		0			0
$5$	−4.36488	+	2.43881i	−0.872977	+	0.487762i
$5$	−4.36488	+	2.43881i	−0.872977	+	0.487762i
$6$		0			0
$7$	−7.18571	−	7.18571i	−1.02653	−	1.02653i	−0.999638	−	0.0268912i	$-0.991439\pi$
$7$	−7.18571	−	7.18571i	−1.02653	−	1.02653i	−0.0268912	−	0.999638i	$-0.508561\pi$
$8$		0			0
$9$	−2.71500			−0.301666
$10$		0			0
$11$	8.38398	+	8.38398i	0.762180	+	0.762180i	0.976716	−	0.214536i	$-0.0688239\pi$
$11$	8.38398	+	8.38398i	0.762180	+	0.762180i	−0.214536	+	0.976716i	$0.568824\pi$
$12$		0			0
$13$	−12.9652			−0.997321			−0.498660	−	0.866797i	$-0.666175\pi$
$13$	−12.9652			−0.997321			−0.498660	+	0.866797i	$0.666175\pi$
$14$		0			0
$15$	−10.9427	+	6.11407i	−0.729515	+	0.407605i
$16$		0			0
$17$	−22.8157	+	22.8157i	−1.34210	+	1.34210i	−0.448132	+	0.893967i	$0.647911\pi$
$17$	−22.8157	+	22.8157i	−1.34210	+	1.34210i	−0.893967	+	0.448132i	$0.852089\pi$
$18$		0			0
$19$	−3.16584	−	3.16584i	−0.166623	−	0.166623i	0.618870	−	0.785493i	$-0.287591\pi$
$19$	−3.16584	−	3.16584i	−0.166623	−	0.166623i	−0.785493	+	0.618870i	$0.787591\pi$
$20$		0			0
$21$	−18.0145	−	18.0145i	−0.857833	−	0.857833i
$22$		0			0
$23$	−3.81600	+	3.81600i	−0.165913	+	0.165913i	−0.785180	−	0.619267i	$-0.787430\pi$
$23$	−3.81600	+	3.81600i	−0.165913	+	0.165913i	0.619267	+	0.785180i	$0.287430\pi$
$24$		0			0
$25$	13.1044	−	21.2902i	0.524177	−	0.851610i
$26$		0			0
$27$	−29.3694			−1.08776
$28$		0			0
$29$	−18.3544	−	18.3544i	−0.632911	−	0.632911i	0.315886	−	0.948797i	$-0.397698\pi$
$29$	−18.3544	−	18.3544i	−0.632911	−	0.632911i	−0.948797	+	0.315886i	$0.897698\pi$
$30$		0			0
$31$	8.78531			0.283397			0.141698	−	0.989910i	$-0.454744\pi$
$31$	8.78531			0.283397			0.141698	+	0.989910i	$0.454744\pi$
$32$		0			0
$33$	21.0186	+	21.0186i	0.636926	+	0.636926i
$34$		0			0
$35$	48.8893	+	13.8402i	1.39684	+	0.395434i
$36$		0			0
$37$	32.4039			0.875781			0.437891	−	0.899028i	$-0.355726\pi$
$37$	32.4039			0.875781			0.437891	+	0.899028i	$0.355726\pi$
$38$		0			0
$39$	−32.5036			−0.833425
$40$		0			0
$41$		−	0.937574i		−	0.0228677i	−0.999935	−	0.0114338i	$-0.996360\pi$
$41$		−	0.937574i		−	0.0228677i	0.999935	−	0.0114338i	$-0.00363958\pi$
$42$		0			0
$43$		−	57.8364i		−	1.34503i	−0.740083	−	0.672516i	$-0.765214\pi$
$43$		−	57.8364i		−	1.34503i	0.740083	−	0.672516i	$-0.234786\pi$
$44$		0			0
$45$	11.8506	−	6.62136i	0.263348	−	0.147141i
$46$		0			0
$47$	−27.9276	+	27.9276i	−0.594205	+	0.594205i	−0.938764	−	0.344560i	$-0.888028\pi$
$47$	−27.9276	+	27.9276i	−0.594205	+	0.594205i	0.344560	+	0.938764i	$0.388028\pi$
$48$		0			0
$49$			54.2688i			1.10753i
$50$		0			0
$51$	−57.1987	+	57.1987i	−1.12154	+	1.12154i
$52$		0			0
$53$			20.6425i			0.389482i	0.980855	+	0.194741i	$0.0623866\pi$
$53$			20.6425i			0.389482i	−0.980855	+	0.194741i	$0.937613\pi$
$54$		0			0
$55$	−57.0420	−	16.1482i	−1.03713	−	0.293603i
$56$		0			0
$57$	−7.93674	−	7.93674i	−0.139241	−	0.139241i
$58$		0			0
$59$	40.1490	−	40.1490i	0.680492	−	0.680492i	−0.279619	−	0.960111i	$-0.590208\pi$
$59$	40.1490	−	40.1490i	0.680492	−	0.680492i	0.960111	+	0.279619i	$0.0902081\pi$
$60$		0			0
$61$	−25.3893	+	25.3893i	−0.416217	+	0.416217i	−0.883898	−	0.467680i	$-0.845090\pi$
$61$	−25.3893	+	25.3893i	−0.416217	+	0.416217i	0.467680	+	0.883898i	$0.345090\pi$
$62$		0			0
$63$	19.5092	+	19.5092i	0.309669	+	0.309669i
$64$		0			0
$65$	56.5915	−	31.6196i	0.870638	−	0.486455i
$66$		0			0
$67$		−	29.3419i		−	0.437938i	−0.975732	−	0.218969i	$-0.929731\pi$
$67$		−	29.3419i		−	0.437938i	0.975732	−	0.218969i	$-0.0702694\pi$
$68$		0			0
$69$	−9.56668	+	9.56668i	−0.138648	+	0.138648i
$70$		0			0
$71$			34.7686i			0.489698i	0.969561	+	0.244849i	$0.0787385\pi$
$71$			34.7686i			0.489698i	−0.969561	+	0.244849i	$0.921262\pi$
$72$		0			0
$73$	−76.2777	+	76.2777i	−1.04490	+	1.04490i	−0.0459567	+	0.998943i	$0.514634\pi$
$73$	−76.2777	+	76.2777i	−1.04490	+	1.04490i	−0.998943	+	0.0459567i	$0.985366\pi$
$74$		0			0
$75$	32.8527	−	53.3744i	0.438035	−	0.711659i
$76$		0			0
$77$		−	120.490i		−	1.56480i
$78$		0			0
$79$		−	17.2292i		−	0.218092i	−0.994037	−	0.109046i	$-0.965220\pi$
$79$		−	17.2292i		−	0.218092i	0.994037	−	0.109046i	$-0.0347795\pi$
$80$		0			0
$81$	−49.1938			−0.607331
$82$		0			0
$83$	73.3919			0.884239			0.442120	−	0.896956i	$-0.354227\pi$
$83$	73.3919			0.884239			0.442120	+	0.896956i	$0.354227\pi$
$84$		0			0
$85$	43.9447	−	155.231i	0.516997	−	1.82625i
$86$		0			0
$87$	−46.0144	−	46.0144i	−0.528901	−	0.528901i
$88$		0			0
$89$	96.9216			1.08901			0.544503	−	0.838759i	$-0.316718\pi$
$89$	96.9216			1.08901			0.544503	+	0.838759i	$0.316718\pi$
$90$		0			0
$91$	93.1639	+	93.1639i	1.02378	+	1.02378i
$92$		0			0
$93$	22.0247			0.236825
$94$		0			0
$95$	21.5394	+	6.09765i	0.226731	+	0.0641858i
$96$		0			0
$97$	−53.4378	+	53.4378i	−0.550905	+	0.550905i	−0.926702	−	0.375797i	$-0.877369\pi$
$97$	−53.4378	+	53.4378i	−0.550905	+	0.550905i	0.375797	+	0.926702i	$0.377369\pi$
$98$		0			0
$99$	−22.7625	−	22.7625i	−0.229924	−	0.229924i
$100$		0			0
$101$	67.9450	+	67.9450i	0.672723	+	0.672723i	0.958343	−	0.285620i	$-0.0921995\pi$
$101$	67.9450	+	67.9450i	0.672723	+	0.672723i	−0.285620	+	0.958343i	$0.592200\pi$
$102$		0			0
$103$	−132.887	+	132.887i	−1.29017	+	1.29017i	−0.355486	+	0.934681i	$0.615685\pi$
$103$	−132.887	+	132.887i	−1.29017	+	1.29017i	−0.934681	+	0.355486i	$0.884315\pi$
$104$		0			0
$105$	122.565	+	34.6973i	1.16729	+	0.330450i
$106$		0			0
$107$	44.9125			0.419743			0.209872	−	0.977729i	$-0.432695\pi$
$107$	44.9125			0.419743			0.209872	+	0.977729i	$0.432695\pi$
$108$		0			0
$109$	−31.7568	−	31.7568i	−0.291346	−	0.291346i	0.546266	−	0.837612i	$-0.316049\pi$
$109$	−31.7568	−	31.7568i	−0.291346	−	0.291346i	−0.837612	+	0.546266i	$0.816049\pi$
$110$		0			0
$111$	81.2363			0.731859
$112$		0			0
$113$	5.56976	+	5.56976i	0.0492899	+	0.0492899i	0.731322	−	0.682032i	$-0.238904\pi$
$113$	5.56976	+	5.56976i	0.0492899	+	0.0492899i	−0.682032	+	0.731322i	$0.738904\pi$
$114$		0			0
$115$	7.34990	−	25.9629i	0.0639122	−	0.225764i
$116$		0			0
$117$	35.2004			0.300858
$118$		0			0
$119$	327.894			2.75541
$120$		0			0
$121$			19.5823i			0.161837i
$122$		0			0
$123$		−	2.35049i		−	0.0191097i
$124$		0			0
$125$	−5.27642	+	124.889i	−0.0422114	+	0.999109i
$126$		0			0
$127$	106.254	−	106.254i	0.836645	−	0.836645i	−0.151771	−	0.988416i	$-0.548498\pi$
$127$	106.254	−	106.254i	0.836645	−	0.836645i	0.988416	+	0.151771i	$0.0484977\pi$
$128$		0			0
$129$		−	144.995i		−	1.12399i
$130$		0			0
$131$	59.7795	−	59.7795i	0.456332	−	0.456332i	−0.441117	−	0.897449i	$-0.645418\pi$
$131$	59.7795	−	59.7795i	0.456332	−	0.456332i	0.897449	+	0.441117i	$0.145418\pi$
$132$		0			0
$133$			45.4976i			0.342088i
$134$		0			0
$135$	128.194	−	71.6263i	0.949585	−	0.530566i
$136$		0			0
$137$	−126.441	−	126.441i	−0.922925	−	0.922925i	0.0743099	−	0.997235i	$-0.476325\pi$
$137$	−126.441	−	126.441i	−0.922925	−	0.922925i	−0.997235	+	0.0743099i	$0.976325\pi$
$138$		0			0
$139$	−41.3857	+	41.3857i	−0.297739	+	0.297739i	−0.840128	−	0.542389i	$-0.817520\pi$
$139$	−41.3857	+	41.3857i	−0.297739	+	0.297739i	0.542389	+	0.840128i	$0.317520\pi$
$140$		0			0
$141$	−70.0143	+	70.0143i	−0.496555	+	0.496555i
$142$		0			0
$143$	−108.700	−	108.700i	−0.760138	−	0.760138i
$144$		0			0
$145$	124.878	+	35.3520i	0.861227	+	0.243807i
$146$		0			0
$147$			136.051i			0.925519i
$148$		0			0
$149$	−30.0503	+	30.0503i	−0.201680	+	0.201680i	−0.800719	−	0.599040i	$-0.795549\pi$
$149$	−30.0503	+	30.0503i	−0.201680	+	0.201680i	0.599040	+	0.800719i	$0.295549\pi$
$150$		0			0
$151$			26.0891i			0.172776i	0.996262	+	0.0863878i	$0.0275324\pi$
$151$			26.0891i			0.172776i	−0.996262	+	0.0863878i	$0.972468\pi$
$152$		0			0
$153$	61.9445	−	61.9445i	0.404866	−	0.404866i
$154$		0			0
$155$	−38.3468	+	21.4257i	−0.247399	+	0.138230i
$156$		0			0
$157$			2.64846i			0.0168691i	0.999964	+	0.00843457i	$0.00268484\pi$
$157$			2.64846i			0.0168691i	−0.999964	+	0.00843457i	$0.997315\pi$
$158$		0			0
$159$			51.7507i			0.325476i
$160$		0			0
$161$	54.8413			0.340629
$162$		0			0
$163$	−143.714			−0.881682			−0.440841	−	0.897585i	$-0.645320\pi$
$163$	−143.714			−0.881682			−0.440841	+	0.897585i	$0.645320\pi$
$164$		0			0
$165$	−143.004	−	40.4833i	−0.866690	−	0.245353i
$166$		0			0
$167$	−192.906	−	192.906i	−1.15513	−	1.15513i	−0.985510	−	0.169619i	$-0.945746\pi$
$167$	−192.906	−	192.906i	−1.15513	−	1.15513i	−0.169619	−	0.985510i	$-0.554254\pi$
$168$		0			0
$169$	−0.904324			−0.00535103
$170$		0			0
$171$	8.59526	+	8.59526i	0.0502647	+	0.0502647i
$172$		0			0
$173$	−2.04705			−0.0118326			−0.00591632	−	0.999982i	$-0.501883\pi$
$173$	−2.04705			−0.0118326			−0.00591632	+	0.999982i	$0.501883\pi$
$174$		0			0
$175$	−247.150	+	58.8209i	−1.41229	+	0.336119i
$176$		0			0
$177$	100.653	−	100.653i	0.568663	−	0.568663i
$178$		0			0
$179$	−101.208	−	101.208i	−0.565405	−	0.565405i	0.365432	−	0.930838i	$-0.380921\pi$
$179$	−101.208	−	101.208i	−0.565405	−	0.565405i	−0.930838	+	0.365432i	$0.880921\pi$
$180$		0			0
$181$	154.013	+	154.013i	0.850901	+	0.850901i	0.990244	−	0.139343i	$-0.0444991\pi$
$181$	154.013	+	154.013i	0.850901	+	0.850901i	−0.139343	+	0.990244i	$0.544499\pi$
$182$		0			0
$183$	−63.6506	+	63.6506i	−0.347818	+	0.347818i
$184$		0			0
$185$	−141.439	+	79.0270i	−0.764537	+	0.427173i
$186$		0			0
$187$	−382.573			−2.04584
$188$		0			0
$189$	211.040	+	211.040i	1.11661	+	1.11661i
$190$		0			0
$191$	−45.3049			−0.237198			−0.118599	−	0.992942i	$-0.537840\pi$
$191$	−45.3049			−0.237198			−0.118599	+	0.992942i	$0.537840\pi$
$192$		0			0
$193$	−176.113	−	176.113i	−0.912503	−	0.912503i	0.0839658	−	0.996469i	$-0.473241\pi$
$193$	−176.113	−	176.113i	−0.912503	−	0.912503i	−0.996469	+	0.0839658i	$0.973241\pi$
$194$		0			0
$195$	141.874	−	79.2700i	0.727560	−	0.406513i
$196$		0			0
$197$	−308.173			−1.56433			−0.782164	−	0.623072i	$-0.785884\pi$
$197$	−308.173			−1.56433			−0.782164	+	0.623072i	$0.785884\pi$
$198$		0			0
$199$	190.912			0.959358			0.479679	−	0.877444i	$-0.340753\pi$
$199$	190.912			0.959358			0.479679	+	0.877444i	$0.340753\pi$
$200$		0			0
$201$		−	73.5598i		−	0.365969i
$202$		0			0
$203$			263.779i			1.29940i
$204$		0			0
$205$	2.28656	+	4.09240i	0.0111540	+	0.0199629i
$206$		0			0
$207$	10.3604	−	10.3604i	0.0500504	−	0.0500504i
$208$		0			0
$209$		−	53.0847i		−	0.253994i
$210$		0			0
$211$	−230.999	+	230.999i	−1.09478	+	1.09478i	−0.0997692	+	0.995011i	$0.531810\pi$
$211$	−230.999	+	230.999i	−1.09478	+	1.09478i	−0.995011	+	0.0997692i	$0.968190\pi$
$212$		0			0
$213$			87.1645i			0.409223i
$214$		0			0
$215$	141.052	+	252.449i	0.656055	+	1.17418i
$216$		0			0
$217$	−63.1286	−	63.1286i	−0.290915	−	0.290915i
$218$		0			0
$219$	−191.228	+	191.228i	−0.873185	+	0.873185i
$220$		0			0
$221$	295.809	−	295.809i	1.33850	−	1.33850i
$222$		0			0
$223$	60.6724	+	60.6724i	0.272073	+	0.272073i	0.829934	−	0.557861i	$-0.188378\pi$
$223$	60.6724	+	60.6724i	0.272073	+	0.272073i	−0.557861	+	0.829934i	$0.688378\pi$
$224$		0			0
$225$	−35.5785	+	57.8030i	−0.158127	+	0.256902i
$226$		0			0
$227$		−	202.529i		−	0.892199i	−0.894983	−	0.446099i	$-0.852813\pi$
$227$		−	202.529i		−	0.892199i	0.894983	−	0.446099i	$-0.147187\pi$
$228$		0			0
$229$	−137.361	+	137.361i	−0.599829	+	0.599829i	−0.940267	−	0.340438i	$-0.889425\pi$
$229$	−137.361	+	137.361i	−0.599829	+	0.599829i	0.340438	+	0.940267i	$0.389425\pi$
$230$		0			0
$231$		−	302.067i		−	1.30765i
$232$		0			0
$233$	−197.272	+	197.272i	−0.846660	+	0.846660i	−0.989715	−	0.143055i	$-0.954308\pi$
$233$	−197.272	+	197.272i	−0.846660	+	0.846660i	0.143055	+	0.989715i	$0.454308\pi$
$234$		0			0
$235$	53.7907	−	190.011i	0.228896	−	0.808557i
$236$		0			0
$237$		−	43.1935i		−	0.182251i
$238$		0			0
$239$			411.923i			1.72353i	0.507310	+	0.861763i	$0.330640\pi$
$239$			411.923i			1.72353i	−0.507310	+	0.861763i	$0.669360\pi$
$240$		0			0
$241$	−293.936			−1.21965			−0.609826	−	0.792535i	$-0.708761\pi$
$241$	−293.936			−1.21965			−0.609826	+	0.792535i	$0.708761\pi$
$242$		0			0
$243$	140.996			0.580231
$244$		0			0
$245$	−132.351	−	236.877i	−0.540209	−	0.966844i
$246$		0			0
$247$	41.0457	+	41.0457i	0.166177	+	0.166177i
$248$		0			0
$249$	183.993			0.738926
$250$		0			0
$251$	−198.365	−	198.365i	−0.790298	−	0.790298i	0.191244	−	0.981542i	$-0.438748\pi$
$251$	−198.365	−	198.365i	−0.790298	−	0.790298i	−0.981542	+	0.191244i	$0.938748\pi$
$252$		0			0
$253$	−63.9866			−0.252911
$254$		0			0
$255$	110.169	−	389.163i	0.432035	−	1.52613i
$256$		0			0
$257$	−239.646	+	239.646i	−0.932473	+	0.932473i	−0.997860	−	0.0653871i	$-0.979172\pi$
$257$	−239.646	+	239.646i	−0.932473	+	0.932473i	0.0653871	+	0.997860i	$0.479172\pi$
$258$		0			0
$259$	−232.845	−	232.845i	−0.899015	−	0.899015i
$260$		0			0
$261$	49.8322	+	49.8322i	0.190928	+	0.190928i
$262$		0			0
$263$	142.437	−	142.437i	0.541585	−	0.541585i	−0.382408	−	0.923993i	$-0.624905\pi$
$263$	142.437	−	142.437i	0.541585	−	0.541585i	0.923993	+	0.382408i	$0.124905\pi$
$264$		0			0
$265$	−50.3432	−	90.1023i	−0.189974	−	0.340009i
$266$		0			0
$267$	242.981			0.910043
$268$		0			0
$269$	269.805	+	269.805i	1.00299	+	1.00299i	0.999996	+	0.00299625i	$0.000953737\pi$
$269$	269.805	+	269.805i	1.00299	+	1.00299i	0.00299625	+	0.999996i	$0.499046\pi$
$270$		0			0
$271$	−71.4599			−0.263690			−0.131845	−	0.991270i	$-0.542090\pi$
$271$	−71.4599			−0.263690			−0.131845	+	0.991270i	$0.542090\pi$
$272$		0			0
$273$	233.561	+	233.561i	0.855535	+	0.855535i
$274$		0			0
$275$	288.364	−	68.6298i	1.04860	−	0.249563i
$276$		0			0
$277$	256.078			0.924470			0.462235	−	0.886758i	$-0.347048\pi$
$277$	256.078			0.924470			0.462235	+	0.886758i	$0.347048\pi$
$278$		0			0
$279$	−23.8521			−0.0854914
$280$		0			0
$281$			315.882i			1.12413i	0.827092	+	0.562067i	$0.189994\pi$
$281$			315.882i			1.12413i	−0.827092	+	0.562067i	$0.810006\pi$
$282$		0			0
$283$			8.65428i			0.0305805i	0.999883	+	0.0152903i	$0.00486723\pi$
$283$			8.65428i			0.0305805i	−0.999883	+	0.0152903i	$0.995133\pi$
$284$		0			0
$285$	53.9991	+	15.2867i	0.189471	+	0.0536377i
$286$		0			0
$287$	−6.73713	+	6.73713i	−0.0234743	+	0.0234743i
$288$		0			0
$289$		−	752.111i		−	2.60246i
$290$		0			0
$291$	−133.968	+	133.968i	−0.460372	+	0.460372i
$292$		0			0
$293$		−	533.382i		−	1.82042i	−0.414151	−	0.910208i	$-0.635921\pi$
$293$		−	533.382i		−	1.82042i	0.414151	−	0.910208i	$-0.364079\pi$
$294$		0			0
$295$	−77.3300	+	273.162i	−0.262136	+	0.925972i
$296$		0			0
$297$	−246.232	−	246.232i	−0.829066	−	0.829066i
$298$		0			0
$299$	49.4751	−	49.4751i	0.165469	−	0.165469i
$300$		0			0
$301$	−415.595	+	415.595i	−1.38072	+	1.38072i
$302$		0			0
$303$	170.338	+	170.338i	0.562170	+	0.562170i
$304$		0			0
$305$	48.9016	−	172.741i	0.160333	−	0.566363i
$306$		0			0
$307$			322.054i			1.04903i	0.851400	+	0.524517i	$0.175754\pi$
$307$			322.054i			1.04903i	−0.851400	+	0.524517i	$0.824246\pi$
$308$		0			0
$309$	−333.147	+	333.147i	−1.07815	+	1.07815i
$310$		0			0
$311$			10.0499i			0.0323149i	0.999869	+	0.0161575i	$0.00514331\pi$
$311$			10.0499i			0.0323149i	−0.999869	+	0.0161575i	$0.994857\pi$
$312$		0			0
$313$	13.4351	−	13.4351i	0.0429237	−	0.0429237i	−0.685319	−	0.728243i	$-0.740337\pi$
$313$	13.4351	−	13.4351i	0.0429237	−	0.0429237i	0.728243	+	0.685319i	$0.240337\pi$
$314$		0			0
$315$	−132.734	−	37.5761i	−0.421379	−	0.119289i
$316$		0			0
$317$			182.394i			0.575377i	0.957724	+	0.287688i	$0.0928867\pi$
$317$			182.394i			0.575377i	−0.957724	+	0.287688i	$0.907113\pi$
$318$		0			0
$319$		−	307.766i		−	0.964785i
$320$		0			0
$321$	112.595			0.350764
$322$		0			0
$323$	144.462			0.447250
$324$		0			0
$325$	−169.901	+	276.032i	−0.522772	+	0.849328i
$326$		0			0
$327$	−79.6139	−	79.6139i	−0.243468	−	0.243468i
$328$		0			0
$329$	401.359			1.21994
$330$		0			0
$331$	213.565	+	213.565i	0.645211	+	0.645211i	0.951832	−	0.306621i	$-0.0991983\pi$
$331$	213.565	+	213.565i	0.645211	+	0.645211i	−0.306621	+	0.951832i	$0.599198\pi$
$332$		0			0
$333$	−87.9766			−0.264194
$334$		0			0
$335$	71.5592	+	128.074i	0.213610	+	0.382310i
$336$		0			0
$337$	−99.5263	+	99.5263i	−0.295330	+	0.295330i	−0.839182	−	0.543851i	$-0.816966\pi$
$337$	−99.5263	+	99.5263i	−0.295330	+	0.295330i	0.543851	+	0.839182i	$0.316966\pi$
$338$		0			0
$339$	13.9633	+	13.9633i	0.0411898	+	0.0411898i
$340$		0			0
$341$	73.6559	+	73.6559i	0.216000	+	0.216000i
$342$		0			0
$343$	37.8598	−	37.8598i	0.110378	−	0.110378i
$344$		0			0
$345$	18.4261	−	65.0888i	0.0534091	−	0.188663i
$346$		0			0
$347$	481.819			1.38853			0.694264	−	0.719721i	$-0.255730\pi$
$347$	481.819			1.38853			0.694264	+	0.719721i	$0.255730\pi$
$348$		0			0
$349$	−398.473	−	398.473i	−1.14176	−	1.14176i	−0.988129	−	0.153628i	$-0.950904\pi$
$349$	−398.473	−	398.473i	−1.14176	−	1.14176i	−0.153628	−	0.988129i	$-0.549096\pi$
$350$		0			0
$351$	380.779			1.08484
$352$		0			0
$353$	356.849	+	356.849i	1.01090	+	1.01090i	0.999940	+	0.0109648i	$0.00349027\pi$
$353$	356.849	+	356.849i	1.01090	+	1.01090i	0.0109648	+	0.999940i	$0.496510\pi$
$354$		0			0
$355$	−84.7940	−	151.761i	−0.238856	−	0.427495i
$356$		0			0
$357$	822.027			2.30260
$358$		0			0
$359$	−417.857			−1.16395			−0.581974	−	0.813207i	$-0.697719\pi$
$359$	−417.857			−1.16395			−0.581974	+	0.813207i	$0.697719\pi$
$360$		0			0
$361$		−	340.955i		−	0.944473i
$362$		0			0
$363$			49.0927i			0.135242i
$364$		0			0
$365$	146.917	−	518.970i	0.402511	−	1.42184i
$366$		0			0
$367$	109.049	−	109.049i	0.297136	−	0.297136i	−0.542755	−	0.839891i	$-0.682619\pi$
$367$	109.049	−	109.049i	0.297136	−	0.297136i	0.839891	+	0.542755i	$0.182619\pi$
$368$		0			0
$369$			2.54551i			0.00689841i
$370$		0			0
$371$	148.331	−	148.331i	0.399815	−	0.399815i
$372$		0			0
$373$		−	308.832i		−	0.827968i	−0.910284	−	0.413984i	$-0.864137\pi$
$373$		−	308.832i		−	0.827968i	0.910284	−	0.413984i	$-0.135863\pi$
$374$		0			0
$375$	−13.2279	+	313.095i	−0.0352745	+	0.834919i
$376$		0			0
$377$	237.968	+	237.968i	0.631216	+	0.631216i
$378$		0			0
$379$	−28.3677	+	28.3677i	−0.0748489	+	0.0748489i	−0.743540	−	0.668691i	$-0.766855\pi$
$379$	−28.3677	+	28.3677i	−0.0748489	+	0.0748489i	0.668691	+	0.743540i	$0.266855\pi$
$380$		0			0
$381$	266.377	−	266.377i	0.699153	−	0.699153i
$382$		0			0
$383$	−422.953	−	422.953i	−1.10432	−	1.10432i	−0.993884	−	0.110433i	$-0.964776\pi$
$383$	−422.953	−	422.953i	−1.10432	−	1.10432i	−0.110433	−	0.993884i	$-0.535224\pi$
$384$		0			0
$385$	293.851	+	525.923i	0.763250	+	1.36603i
$386$		0			0
$387$			157.026i			0.405751i
$388$		0			0
$389$	178.975	−	178.975i	0.460089	−	0.460089i	−0.438595	−	0.898685i	$-0.644524\pi$
$389$	178.975	−	178.975i	0.460089	−	0.460089i	0.898685	+	0.438595i	$0.144524\pi$
$390$		0			0
$391$		−	174.129i		−	0.445344i
$392$		0			0
$393$	149.867	−	149.867i	0.381340	−	0.381340i
$394$		0			0
$395$	42.0188	+	75.2036i	0.106377	+	0.190389i
$396$		0			0
$397$		−	20.4646i		−	0.0515480i	−0.999668	−	0.0257740i	$-0.991795\pi$
$397$		−	20.4646i		−	0.0515480i	0.999668	−	0.0257740i	$-0.00820503\pi$
$398$		0			0
$399$			114.062i			0.285870i
$400$		0			0
$401$	97.7306			0.243717			0.121859	−	0.992547i	$-0.461115\pi$
$401$	97.7306			0.243717			0.121859	+	0.992547i	$0.461115\pi$
$402$		0			0
$403$	−113.903			−0.282638
$404$		0			0
$405$	214.725	−	119.974i	0.530186	−	0.296233i
$406$		0			0
$407$	271.674	+	271.674i	0.667503	+	0.667503i
$408$		0			0
$409$	−346.930			−0.848239			−0.424120	−	0.905606i	$-0.639416\pi$
$409$	−346.930			−0.848239			−0.424120	+	0.905606i	$0.639416\pi$
$410$		0			0
$411$	−316.986	−	316.986i	−0.771255	−	0.771255i
$412$		0			0
$413$	−576.998			−1.39709
$414$		0			0
$415$	−320.347	+	178.989i	−0.771920	+	0.431298i
$416$		0			0
$417$	−103.753	+	103.753i	−0.248809	+	0.248809i
$418$		0			0
$419$	−94.6547	−	94.6547i	−0.225906	−	0.225906i	0.585074	−	0.810980i	$-0.301065\pi$
$419$	−94.6547	−	94.6547i	−0.225906	−	0.225906i	−0.810980	+	0.585074i	$0.801065\pi$
$420$		0			0
$421$	303.154	+	303.154i	0.720080	+	0.720080i	0.968621	−	0.248541i	$-0.0799512\pi$
$421$	303.154	+	303.154i	0.720080	+	0.720080i	−0.248541	+	0.968621i	$0.579951\pi$
$422$		0			0
$423$	75.8234	−	75.8234i	0.179252	−	0.179252i
$424$		0			0
$425$	186.765	+	784.738i	0.439447	+	1.84644i
$426$		0			0
$427$	364.880			0.854519
$428$		0			0
$429$	−272.509	−	272.509i	−0.635220	−	0.635220i
$430$		0			0
$431$	−505.491			−1.17283			−0.586416	−	0.810010i	$-0.699462\pi$
$431$	−505.491			−1.17283			−0.586416	+	0.810010i	$0.699462\pi$
$432$		0			0
$433$	8.23935	+	8.23935i	0.0190285	+	0.0190285i	0.716557	−	0.697529i	$-0.245717\pi$
$433$	8.23935	+	8.23935i	0.0190285	+	0.0190285i	−0.697529	+	0.716557i	$0.745717\pi$
$434$		0			0
$435$	313.068	+	88.6271i	0.719696	+	0.203740i
$436$		0			0
$437$	24.1617			0.0552900
$438$		0			0
$439$	195.298			0.444870			0.222435	−	0.974948i	$-0.428600\pi$
$439$	195.298			0.444870			0.222435	+	0.974948i	$0.428600\pi$
$440$		0			0
$441$		−	147.340i		−	0.334103i
$442$		0			0
$443$		−	401.681i		−	0.906729i	−0.891325	−	0.453365i	$-0.850224\pi$
$443$		−	401.681i		−	0.906729i	0.891325	−	0.453365i	$-0.149776\pi$
$444$		0			0
$445$	−423.051	+	236.373i	−0.950677	+	0.531176i
$446$		0			0
$447$	−75.3357	+	75.3357i	−0.168536	+	0.168536i
$448$		0			0
$449$			189.448i			0.421934i	0.977493	+	0.210967i	$0.0676613\pi$
$449$			189.448i			0.421934i	−0.977493	+	0.210967i	$0.932339\pi$
$450$		0			0
$451$	7.86061	−	7.86061i	0.0174293	−	0.0174293i
$452$		0			0
$453$			65.4052i			0.144382i
$454$		0			0
$455$	−633.859	−	179.441i	−1.39310	−	0.394375i
$456$		0			0
$457$	488.804	+	488.804i	1.06959	+	1.06959i	0.997390	+	0.0722037i	$0.0230032\pi$
$457$	488.804	+	488.804i	1.06959	+	1.06959i	0.0722037	+	0.997390i	$0.476997\pi$
$458$		0			0
$459$	670.083	−	670.083i	1.45988	−	1.45988i
$460$		0			0
$461$	392.290	−	392.290i	0.850954	−	0.850954i	−0.139297	−	0.990251i	$-0.544484\pi$
$461$	392.290	−	392.290i	0.850954	−	0.850954i	0.990251	+	0.139297i	$0.0444842\pi$
$462$		0			0
$463$	70.7053	+	70.7053i	0.152711	+	0.152711i	0.779328	−	0.626616i	$-0.215561\pi$
$463$	70.7053	+	70.7053i	0.152711	+	0.152711i	−0.626616	+	0.779328i	$0.715561\pi$
$464$		0			0
$465$	−96.1352	+	53.7140i	−0.206742	+	0.115514i
$466$		0			0
$467$			918.293i			1.96637i	0.182623	+	0.983183i	$0.441541\pi$
$467$			918.293i			1.96637i	−0.182623	+	0.983183i	$0.558459\pi$
$468$		0			0
$469$	−210.842	+	210.842i	−0.449557	+	0.449557i
$470$		0			0
$471$			6.63965i			0.0140969i
$472$		0			0
$473$	484.899	−	484.899i	1.02516	−	1.02516i
$474$		0			0
$475$	−108.888	+	25.9150i	−0.229238	+	0.0545579i
$476$		0			0
$477$		−	56.0445i		−	0.117494i
$478$		0			0
$479$		−	49.5880i		−	0.103524i	−0.998659	−	0.0517620i	$-0.983516\pi$
$479$		−	49.5880i		−	0.103524i	0.998659	−	0.0517620i	$-0.0164837\pi$
$480$		0			0
$481$	−420.122			−0.873435
$482$		0			0
$483$	137.487			0.284652
$484$		0			0
$485$	102.925	−	363.575i	0.212217	−	0.749638i
$486$		0			0
$487$	−644.145	−	644.145i	−1.32268	−	1.32268i	−0.911599	−	0.411081i	$-0.865151\pi$
$487$	−644.145	−	644.145i	−1.32268	−	1.32268i	−0.411081	−	0.911599i	$-0.634849\pi$
$488$		0			0
$489$	−360.290			−0.736790
$490$		0			0
$491$	541.213	+	541.213i	1.10227	+	1.10227i	0.994137	+	0.108130i	$0.0344861\pi$
$491$	541.213	+	541.213i	1.10227	+	1.10227i	0.108130	+	0.994137i	$0.465514\pi$
$492$		0			0
$493$	837.538			1.69886
$494$		0			0
$495$	154.869	+	43.8423i	0.312867	+	0.0885702i
$496$		0			0
$497$	249.837	−	249.837i	0.502690	−	0.502690i
$498$		0			0
$499$	142.483	+	142.483i	0.285537	+	0.285537i	0.835313	−	0.549775i	$-0.185287\pi$
$499$	142.483	+	142.483i	0.285537	+	0.285537i	−0.549775	+	0.835313i	$0.685287\pi$
$500$		0			0
$501$	−483.615	−	483.615i	−0.965299	−	0.965299i
$502$		0			0
$503$	−307.222	+	307.222i	−0.610780	+	0.610780i	−0.943149	−	0.332370i	$-0.892152\pi$
$503$	−307.222	+	307.222i	−0.610780	+	0.610780i	0.332370	+	0.943149i	$0.392152\pi$
$504$		0			0
$505$	−462.277	−	130.867i	−0.915400	−	0.259143i
$506$		0			0
$507$	−2.26713			−0.00447166
$508$		0			0
$509$	268.080	+	268.080i	0.526681	+	0.526681i	0.919581	−	0.392900i	$-0.128528\pi$
$509$	268.080	+	268.080i	0.526681	+	0.526681i	−0.392900	+	0.919581i	$0.628528\pi$
$510$		0			0
$511$	1096.22			2.14524
$512$		0			0
$513$	92.9789	+	92.9789i	0.181245	+	0.181245i
$514$		0			0
$515$	255.951	−	904.124i	0.496992	−	1.75558i
$516$		0			0
$517$	−468.289			−0.905782
$518$		0			0
$519$	−5.13193			−0.00988811
$520$		0			0
$521$		−	364.737i		−	0.700071i	−0.936736	−	0.350036i	$-0.886169\pi$
$521$		−	364.737i		−	0.700071i	0.936736	−	0.350036i	$-0.113831\pi$
$522$		0			0
$523$		−	434.085i		−	0.829991i	−0.909823	−	0.414996i	$-0.863783\pi$
$523$		−	434.085i		−	0.829991i	0.909823	−	0.414996i	$-0.136217\pi$
$524$		0			0
$525$	−619.603	+	147.463i	−1.18020	+	0.280883i
$526$		0			0
$527$	−200.443	+	200.443i	−0.380347	+	0.380347i
$528$		0			0
$529$			499.876i			0.944946i
$530$		0			0
$531$	−109.005	+	109.005i	−0.205282	+	0.205282i
$532$		0			0
$533$			12.1558i			0.0228064i
$534$		0			0
$535$	−196.038	+	109.533i	−0.366426	+	0.204735i
$536$		0			0
$537$	−253.726	−	253.726i	−0.472489	−	0.472489i
$538$		0			0
$539$	−454.988	+	454.988i	−0.844134	+	0.844134i
$540$		0			0
$541$	−299.573	+	299.573i	−0.553739	+	0.553739i	−0.927518	−	0.373779i	$-0.878062\pi$
$541$	−299.573	+	299.573i	−0.553739	+	0.553739i	0.373779	+	0.927518i	$0.378062\pi$
$542$		0			0
$543$	386.109	+	386.109i	0.711067	+	0.711067i
$544$		0			0
$545$	216.063	+	61.1659i	0.396446	+	0.112231i
$546$		0			0
$547$		−	9.98799i		−	0.0182596i	−0.999958	−	0.00912979i	$-0.997094\pi$
$547$		−	9.98799i		−	0.0182596i	0.999958	−	0.00912979i	$-0.00290614\pi$
$548$		0			0
$549$	68.9318	−	68.9318i	0.125559	−	0.125559i
$550$		0			0
$551$			116.214i			0.210916i
$552$		0			0
$553$	−123.804	+	123.804i	−0.223877	+	0.223877i
$554$		0			0
$555$	−354.587	+	198.120i	−0.638896	+	0.356973i
$556$		0			0
$557$			360.011i			0.646339i	0.946341	+	0.323170i	$0.104748\pi$
$557$			360.011i			0.646339i	−0.946341	+	0.323170i	$0.895252\pi$
$558$		0			0
$559$			749.859i			1.34143i
$560$		0			0
$561$	−959.106			−1.70964
$562$		0			0
$563$	524.373			0.931392			0.465696	−	0.884945i	$-0.345804\pi$
$563$	524.373			0.931392			0.465696	+	0.884945i	$0.345804\pi$
$564$		0			0
$565$	−37.8949	−	10.7278i	−0.0670707	−	0.0189872i
$566$		0			0
$567$	353.492	+	353.492i	0.623443	+	0.623443i
$568$		0			0
$569$	−606.955			−1.06670			−0.533352	−	0.845893i	$-0.679068\pi$
$569$	−606.955			−1.06670			−0.533352	+	0.845893i	$0.679068\pi$
$570$		0			0
$571$	−763.721	−	763.721i	−1.33752	−	1.33752i	−0.898460	−	0.439056i	$-0.855313\pi$
$571$	−763.721	−	763.721i	−1.33752	−	1.33752i	−0.439056	−	0.898460i	$-0.644687\pi$
$572$		0			0
$573$	−113.579			−0.198218
$574$		0			0
$575$	31.2371	+	131.250i	0.0543254	+	0.228261i
$576$		0			0
$577$	−95.1565	+	95.1565i	−0.164916	+	0.164916i	−0.784740	−	0.619824i	$-0.787204\pi$
$577$	−95.1565	+	95.1565i	−0.164916	+	0.164916i	0.619824	+	0.784740i	$0.287204\pi$
$578$		0			0
$579$	−441.514	−	441.514i	−0.762545	−	0.762545i
$580$		0			0
$581$	−527.372	−	527.372i	−0.907698	−	0.907698i
$582$		0			0
$583$	−173.067	+	173.067i	−0.296855	+	0.296855i
$584$		0			0
$585$	−153.646	+	85.8471i	−0.262642	+	0.146747i
$586$		0			0
$587$	−445.447			−0.758853			−0.379427	−	0.925222i	$-0.623879\pi$
$587$	−445.447			−0.758853			−0.379427	+	0.925222i	$0.623879\pi$
$588$		0			0
$589$	−27.8129	−	27.8129i	−0.0472205	−	0.0472205i
$590$		0			0
$591$	−772.586			−1.30725
$592$		0			0
$593$	−359.016	−	359.016i	−0.605424	−	0.605424i	0.336323	−	0.941747i	$-0.390817\pi$
$593$	−359.016	−	359.016i	−0.605424	−	0.605424i	−0.941747	+	0.336323i	$0.890817\pi$
$594$		0			0
$595$	−1431.22	+	799.670i	−2.40541	+	1.34398i
$596$		0			0
$597$	478.615			0.801700
$598$		0			0
$599$	−66.3175			−0.110714			−0.0553568	−	0.998467i	$-0.517630\pi$
$599$	−66.3175			−0.110714			−0.0553568	+	0.998467i	$0.517630\pi$
$600$		0			0
$601$		−	512.825i		−	0.853287i	−0.904420	−	0.426643i	$-0.859696\pi$
$601$		−	512.825i		−	0.853287i	0.904420	−	0.426643i	$-0.140304\pi$
$602$		0			0
$603$			79.6631i			0.132111i
$604$		0			0
$605$	−47.7576	−	85.4746i	−0.0789381	−	0.141280i
$606$		0			0
$607$	700.017	−	700.017i	1.15324	−	1.15324i	0.167341	−	0.985899i	$-0.446482\pi$
$607$	700.017	−	700.017i	1.15324	−	1.15324i	0.985899	−	0.167341i	$-0.0535182\pi$
$608$		0			0
$609$			661.292i			1.08586i
$610$		0			0
$611$	362.086	−	362.086i	0.592613	−	0.592613i
$612$		0			0
$613$			402.030i			0.655840i	0.944705	+	0.327920i	$0.106348\pi$
$613$			402.030i			0.655840i	−0.944705	+	0.327920i	$0.893652\pi$
$614$		0			0
$615$	5.73240	+	10.2596i	0.00932097	+	0.0166823i
$616$		0			0
$617$	451.281	+	451.281i	0.731412	+	0.731412i	0.970899	−	0.239488i	$-0.0769794\pi$
$617$	451.281	+	451.281i	0.731412	+	0.731412i	−0.239488	+	0.970899i	$0.576979\pi$
$618$		0			0
$619$	−141.521	+	141.521i	−0.228629	+	0.228629i	−0.812120	−	0.583491i	$-0.801686\pi$
$619$	−141.521	+	141.521i	−0.228629	+	0.228629i	0.583491	+	0.812120i	$0.301686\pi$
$620$		0			0
$621$	112.074	−	112.074i	0.180473	−	0.180473i
$622$		0			0
$623$	−696.450	−	696.450i	−1.11790	−	1.11790i
$624$		0			0
$625$	−281.549	−	557.992i	−0.450478	−	0.892788i
$626$		0			0
$627$		−	133.083i		−	0.212254i
$628$		0			0
$629$	−739.318	+	739.318i	−1.17539	+	1.17539i
$630$		0			0
$631$		−	430.554i		−	0.682335i	−0.940002	−	0.341168i	$-0.889178\pi$
$631$		−	430.554i		−	0.682335i	0.940002	−	0.341168i	$-0.110822\pi$
$632$		0			0
$633$	−579.111	+	579.111i	−0.914868	+	0.914868i
$634$		0			0
$635$	−204.653	+	722.919i	−0.322288	+	1.13845i
$636$		0			0
$637$		−	703.604i		−	1.10456i
$638$		0			0
$639$		−	94.3966i		−	0.147726i
$640$		0			0
$641$	244.316			0.381147			0.190574	−	0.981673i	$-0.438965\pi$
$641$	244.316			0.381147			0.190574	+	0.981673i	$0.438965\pi$
$642$		0			0
$643$	521.720			0.811384			0.405692	−	0.914010i	$-0.367031\pi$
$643$	521.720			0.811384			0.405692	+	0.914010i	$0.367031\pi$
$644$		0			0
$645$	353.616	+	632.887i	0.548242	+	0.981221i
$646$		0			0
$647$	7.36567	+	7.36567i	0.0113843	+	0.0113843i	0.712776	−	0.701392i	$-0.247438\pi$
$647$	7.36567	+	7.36567i	0.0113843	+	0.0113843i	−0.701392	+	0.712776i	$0.747438\pi$
$648$		0			0
$649$	673.218			1.03732
$650$		0			0
$651$	−158.263	−	158.263i	−0.243107	−	0.243107i
$652$		0			0
$653$	171.839			0.263154			0.131577	−	0.991306i	$-0.457996\pi$
$653$	171.839			0.263154			0.131577	+	0.991306i	$0.457996\pi$
$654$		0			0
$655$	−115.140	+	406.721i	−0.175786	+	0.620949i
$656$		0			0
$657$	207.094	−	207.094i	0.315211	−	0.315211i
$658$		0			0
$659$	66.3827	+	66.3827i	0.100732	+	0.100732i	0.755677	−	0.654945i	$-0.227308\pi$
$659$	66.3827	+	66.3827i	0.100732	+	0.100732i	−0.654945	+	0.755677i	$0.727308\pi$
$660$		0			0
$661$	−38.9121	−	38.9121i	−0.0588685	−	0.0588685i	0.677060	−	0.735928i	$-0.263254\pi$
$661$	−38.9121	−	38.9121i	−0.0588685	−	0.0588685i	−0.735928	+	0.677060i	$0.763254\pi$
$662$		0			0
$663$	741.591	−	741.591i	1.11854	−	1.11854i
$664$		0			0
$665$	−110.960	−	198.592i	−0.166857	−	0.298634i
$666$		0			0
$667$	140.081			0.210017
$668$		0			0
$669$	152.105	+	152.105i	0.227362	+	0.227362i
$670$		0			0
$671$	−425.726			−0.634465
$672$		0			0
$673$	58.7394	+	58.7394i	0.0872799	+	0.0872799i	0.749399	−	0.662119i	$-0.230343\pi$
$673$	58.7394	+	58.7394i	0.0872799	+	0.0872799i	−0.662119	+	0.749399i	$0.730343\pi$
$674$		0			0
$675$	−384.869	+	625.281i	−0.570176	+	0.926343i
$676$		0			0
$677$	−408.523			−0.603431			−0.301716	−	0.953398i	$-0.597559\pi$
$677$	−408.523			−0.603431			−0.301716	+	0.953398i	$0.597559\pi$
$678$		0			0
$679$	767.977			1.13104
$680$		0			0
$681$		−	507.738i		−	0.745578i
$682$		0			0
$683$		−	611.720i		−	0.895636i	−0.894125	−	0.447818i	$-0.852201\pi$
$683$		−	611.720i		−	0.895636i	0.894125	−	0.447818i	$-0.147799\pi$
$684$		0			0
$685$	860.264	+	243.534i	1.25586	+	0.355524i
$686$		0			0
$687$	−344.363	+	344.363i	−0.501256	+	0.501256i
$688$		0			0
$689$		−	267.634i		−	0.388438i
$690$		0			0
$691$	528.007	−	528.007i	0.764120	−	0.764120i	−0.212944	−	0.977064i	$-0.568305\pi$
$691$	528.007	−	528.007i	0.764120	−	0.764120i	0.977064	+	0.212944i	$0.0683053\pi$
$692$		0			0
$693$			327.129i			0.472048i
$694$		0			0
$695$	79.7119	−	281.575i	0.114693	−	0.405144i
$696$		0			0
$697$	21.3914	+	21.3914i	0.0306907	+	0.0306907i
$698$		0			0
$699$	−494.559	+	494.559i	−0.707523	+	0.707523i
$700$		0			0
$701$	163.932	−	163.932i	0.233855	−	0.233855i	−0.580445	−	0.814300i	$-0.697121\pi$
$701$	163.932	−	163.932i	0.233855	−	0.233855i	0.814300	+	0.580445i	$0.197121\pi$
$702$		0			0
$703$	−102.586	−	102.586i	−0.145926	−	0.145926i
$704$		0			0
$705$	134.853	−	476.356i	0.191280	−	0.675682i
$706$		0			0
$707$		−	976.466i		−	1.38114i
$708$		0			0
$709$	820.614	−	820.614i	1.15742	−	1.15742i	0.172397	−	0.985027i	$-0.444849\pi$
$709$	820.614	−	820.614i	1.15742	−	1.15742i	0.985027	−	0.172397i	$-0.0551513\pi$
$710$		0			0
$711$			46.7773i			0.0657909i
$712$		0			0
$713$	−33.5248	+	33.5248i	−0.0470193	+	0.0470193i
$714$		0			0
$715$	739.560	+	209.364i	1.03435	+	0.292817i
$716$		0			0
$717$			1032.69i			1.44029i
$718$		0			0
$719$		−	578.830i		−	0.805048i	−0.915409	−	0.402524i	$-0.868133\pi$
$719$		−	578.830i		−	0.805048i	0.915409	−	0.402524i	$-0.131867\pi$
$720$		0			0
$721$	1909.78			2.64879
$722$		0			0
$723$	−736.896			−1.01922
$724$		0			0
$725$	−631.294	+	150.246i	−0.870751	+	0.207236i
$726$		0			0
$727$	771.845	+	771.845i	1.06168	+	1.06168i	0.997968	+	0.0637163i	$0.0202953\pi$
$727$	771.845	+	771.845i	1.06168	+	1.06168i	0.0637163	+	0.997968i	$0.479705\pi$
$728$		0			0
$729$	796.220			1.09221
$730$		0			0
$731$	1319.58	+	1319.58i	1.80517	+	1.80517i
$732$		0			0
$733$	455.036			0.620785			0.310393	−	0.950608i	$-0.399539\pi$
$733$	455.036			0.620785			0.310393	+	0.950608i	$0.399539\pi$
$734$		0			0
$735$	−331.803	−	593.848i	−0.451433	−	0.807957i
$736$		0			0
$737$	246.002	−	246.002i	0.333788	−	0.333788i
$738$		0			0
$739$	723.106	+	723.106i	0.978493	+	0.978493i	0.999774	−	0.0212803i	$-0.00677425\pi$
$739$	723.106	+	723.106i	0.978493	+	0.978493i	−0.0212803	+	0.999774i	$0.506774\pi$
$740$		0			0
$741$	102.901	+	102.901i	0.138868	+	0.138868i
$742$		0			0
$743$	134.068	−	134.068i	0.180442	−	0.180442i	−0.611107	−	0.791548i	$-0.709275\pi$
$743$	134.068	−	134.068i	0.180442	−	0.180442i	0.791548	+	0.611107i	$0.209275\pi$
$744$		0			0
$745$	57.8790	−	204.453i	0.0776900	−	0.274433i
$746$		0			0
$747$	−199.259			−0.266745
$748$		0			0
$749$	−322.728	−	322.728i	−0.430879	−	0.430879i
$750$		0			0
$751$	216.822			0.288711			0.144356	−	0.989526i	$-0.453889\pi$
$751$	216.822			0.288711			0.144356	+	0.989526i	$0.453889\pi$
$752$		0			0
$753$	−497.299	−	497.299i	−0.660423	−	0.660423i
$754$		0			0
$755$	−63.6264	−	113.876i	−0.0842733	−	0.150829i
$756$		0			0
$757$	747.764			0.987800			0.493900	−	0.869519i	$-0.335571\pi$
$757$	747.764			0.987800			0.493900	+	0.869519i	$0.335571\pi$
$758$		0			0
$759$	−160.414			−0.211349
$760$		0			0
$761$			1410.33i			1.85326i	0.375978	+	0.926629i	$0.377307\pi$
$761$			1410.33i			1.85326i	−0.375978	+	0.926629i	$0.622693\pi$
$762$		0			0
$763$			456.390i			0.598152i
$764$		0			0
$765$	−119.310	+	421.452i	−0.155961	+	0.550917i
$766$		0			0
$767$	−520.539	+	520.539i	−0.678669	+	0.678669i
$768$		0			0
$769$		−	925.036i		−	1.20291i	−0.798907	−	0.601454i	$-0.794588\pi$
$769$		−	925.036i		−	1.20291i	0.798907	−	0.601454i	$-0.205412\pi$
$770$		0			0
$771$	−600.789	+	600.789i	−0.779234	+	0.779234i
$772$		0			0
$773$			146.591i			0.189639i	0.995494	+	0.0948196i	$0.0302274\pi$
$773$			146.591i			0.189639i	−0.995494	+	0.0948196i	$0.969773\pi$
$774$		0			0
$775$	115.126	−	187.041i	0.148550	−	0.241344i
$776$		0			0
$777$	−583.740	−	583.740i	−0.751274	−	0.751274i
$778$		0			0
$779$	−2.96821	+	2.96821i	−0.00381029	+	0.00381029i
$780$		0			0
$781$	−291.499	+	291.499i	−0.373238	+	0.373238i
$782$		0			0
$783$	539.058	+	539.058i	0.688453	+	0.688453i
$784$		0			0
$785$	−6.45908	−	11.5602i	−0.00822813	−	0.0147264i
$786$		0			0
$787$		−	389.164i		−	0.494491i	−0.968953	−	0.247245i	$-0.920475\pi$
$787$		−	389.164i		−	0.494491i	0.968953	−	0.247245i	$-0.0795254\pi$
$788$		0			0
$789$	357.088	−	357.088i	0.452583	−	0.452583i
$790$		0			0
$791$		−	80.0453i		−	0.101195i
$792$		0			0
$793$	329.176	−	329.176i	0.415102	−	0.415102i
$794$		0			0
$795$	−126.210	−	225.886i	−0.158755	−	0.284133i
$796$		0			0
$797$		−	225.230i		−	0.282597i	−0.989967	−	0.141298i	$-0.954872\pi$
$797$		−	225.230i		−	0.282597i	0.989967	−	0.141298i	$-0.0451277\pi$
$798$		0			0
$799$		−	1274.38i		−	1.59496i
$800$		0			0
$801$	−263.142			−0.328517
$802$		0			0
$803$	−1279.02			−1.59280
$804$		0			0
$805$	−239.376	+	133.748i	−0.297362	+	0.166146i
$806$		0			0
$807$	676.398	+	676.398i	0.838164	+	0.838164i
$808$		0			0
$809$	−389.024			−0.480870			−0.240435	−	0.970665i	$-0.577290\pi$
$809$	−389.024			−0.480870			−0.240435	+	0.970665i	$0.577290\pi$
$810$		0			0
$811$	−235.660	−	235.660i	−0.290580	−	0.290580i	0.546730	−	0.837309i	$-0.315873\pi$
$811$	−235.660	−	235.660i	−0.290580	−	0.290580i	−0.837309	+	0.546730i	$0.815873\pi$
$812$		0			0
$813$	−179.149			−0.220356
$814$		0			0
$815$	627.296	−	350.492i	0.769688	−	0.430051i
$816$		0			0
$817$	−183.101	+	183.101i	−0.224114	+	0.224114i
$818$		0			0
$819$	−252.940	−	252.940i	−0.308840	−	0.308840i
$820$		0			0
$821$	423.452	+	423.452i	0.515775	+	0.515775i	0.916290	−	0.400515i	$-0.131169\pi$
$821$	423.452	+	423.452i	0.515775	+	0.515775i	−0.400515	+	0.916290i	$0.631169\pi$
$822$		0			0
$823$	543.405	−	543.405i	0.660274	−	0.660274i	−0.295171	−	0.955445i	$-0.595377\pi$
$823$	543.405	−	543.405i	0.660274	−	0.660274i	0.955445	+	0.295171i	$0.0953765\pi$
$824$		0			0
$825$	722.926	−	172.054i	0.876274	−	0.208551i
$826$		0			0
$827$	−912.383			−1.10324			−0.551622	−	0.834094i	$-0.685991\pi$
$827$	−912.383			−1.10324			−0.551622	+	0.834094i	$0.685991\pi$
$828$		0			0
$829$	401.447	+	401.447i	0.484254	+	0.484254i	0.906487	−	0.422233i	$-0.138754\pi$
$829$	401.447	+	401.447i	0.484254	+	0.484254i	−0.422233	+	0.906487i	$0.638754\pi$
$830$		0			0
$831$	641.985			0.772546
$832$		0			0
$833$	−1238.18	−	1238.18i	−1.48641	−	1.48641i
$834$		0			0
$835$	1312.48	+	371.552i	1.57183	+	0.444973i
$836$		0			0
$837$	−258.019			−0.308267
$838$		0			0
$839$	−355.908			−0.424205			−0.212102	−	0.977247i	$-0.568031\pi$
$839$	−355.908			−0.424205			−0.212102	+	0.977247i	$0.568031\pi$
$840$		0			0
$841$		−	167.230i		−	0.198847i
$842$		0			0
$843$			791.912i			0.939398i
$844$		0			0
$845$	3.94727	−	2.20547i	0.00467133	−	0.00261003i
$846$		0			0
$847$	140.713	−	140.713i	0.166131	−	0.166131i
$848$		0			0
$849$			21.6962i			0.0255550i
$850$		0			0
$851$	−123.653	+	123.653i	−0.145304	+	0.145304i
$852$		0			0
$853$			184.144i			0.215878i	0.994158	+	0.107939i	$0.0344252\pi$
$853$			184.144i			0.215878i	−0.994158	+	0.107939i	$0.965575\pi$
$854$		0			0
$855$	−58.4795	−	16.5551i	−0.0683971	−	0.0193627i
$856$		0			0
$857$	503.631	+	503.631i	0.587667	+	0.587667i	0.936999	−	0.349332i	$-0.113591\pi$
$857$	503.631	+	503.631i	0.587667	+	0.587667i	−0.349332	+	0.936999i	$0.613591\pi$
$858$		0			0
$859$	−136.193	+	136.193i	−0.158548	+	0.158548i	−0.781923	−	0.623375i	$-0.785761\pi$
$859$	−136.193	+	136.193i	−0.158548	+	0.158548i	0.623375	+	0.781923i	$0.285761\pi$
$860$		0			0
$861$	−16.8899	+	16.8899i	−0.0196166	+	0.0196166i
$862$		0			0
$863$	778.037	+	778.037i	0.901550	+	0.901550i	0.995570	−	0.0940206i	$-0.0299720\pi$
$863$	778.037	+	778.037i	0.901550	+	0.901550i	−0.0940206	+	0.995570i	$0.529972\pi$
$864$		0			0
$865$	8.93512	−	4.99236i	0.0103296	−	0.00577151i
$866$		0			0
$867$		−	1885.54i		−	2.17478i
$868$		0			0
$869$	144.450	−	144.450i	0.166225	−	0.166225i
$870$		0			0
$871$			380.422i			0.436765i
$872$		0			0
$873$	145.084	−	145.084i	0.166190	−	0.166190i
$874$		0			0
$875$	935.328	−	859.498i	1.06895	−	0.982283i
$876$		0			0
$877$			450.954i			0.514201i	0.966385	+	0.257101i	$0.0827672\pi$
$877$			450.954i			0.514201i	−0.966385	+	0.257101i	$0.917233\pi$
$878$		0			0
$879$		−	1337.18i		−	1.52126i
$880$		0			0
$881$	929.171			1.05468			0.527339	−	0.849655i	$-0.323190\pi$
$881$	929.171			1.05468			0.527339	+	0.849655i	$0.323190\pi$
$882$		0			0
$883$	244.738			0.277166			0.138583	−	0.990351i	$-0.455745\pi$
$883$	244.738			0.277166			0.138583	+	0.990351i	$0.455745\pi$
$884$		0			0
$885$	−193.866	+	684.814i	−0.219057	+	0.773801i
$886$		0			0
$887$	987.070	+	987.070i	1.11282	+	1.11282i	0.992768	+	0.120050i	$0.0383056\pi$
$887$	987.070	+	987.070i	1.11282	+	1.11282i	0.120050	+	0.992768i	$0.461694\pi$
$888$		0			0
$889$	−1527.02			−1.71768
$890$		0			0
$891$	−412.440	−	412.440i	−0.462896	−	0.462896i
$892$		0			0
$893$	176.829			0.198017
$894$		0			0
$895$	688.585	+	194.933i	0.769369	+	0.217803i
$896$		0			0
$897$	124.034	−	124.034i	0.138276	−	0.138276i
$898$		0			0
$899$	−161.249	−	161.249i	−0.179365	−	0.179365i
$900$		0			0
$901$	−470.974	−	470.974i	−0.522723	−	0.522723i
$902$		0			0
$903$	−1041.89	+	1041.89i	−1.15381	+	1.15381i
$904$		0			0
$905$	−1047.86	−	296.641i	−1.15785	−	0.327780i
$906$		0			0
$907$	−160.752			−0.177235			−0.0886177	−	0.996066i	$-0.528245\pi$
$907$	−160.752			−0.177235			−0.0886177	+	0.996066i	$0.528245\pi$
$908$		0			0
$909$	−184.471	−	184.471i	−0.202938	−	0.202938i
$910$		0			0
$911$	−36.8062			−0.0404020			−0.0202010	−	0.999796i	$-0.506431\pi$
$911$	−36.8062			−0.0404020			−0.0202010	+	0.999796i	$0.506431\pi$
$912$		0			0
$913$	615.316	+	615.316i	0.673950	+	0.673950i
$914$		0			0
$915$	122.596	−	433.059i	0.133985	−	0.473289i
$916$		0			0
$917$	−859.116			−0.936877
$918$		0			0
$919$	−502.632			−0.546934			−0.273467	−	0.961881i	$-0.588170\pi$
$919$	−502.632			−0.546934			−0.273467	+	0.961881i	$0.588170\pi$
$920$		0			0
$921$			807.386i			0.876640i
$922$		0			0
$923$		−	450.781i		−	0.488386i
$924$		0			0
$925$	424.634	−	689.887i	0.459064	−	0.745824i
$926$		0			0
$927$	360.789	−	360.789i	0.389200	−	0.389200i
$928$		0			0
$929$			1098.03i			1.18195i	0.806690	+	0.590975i	$0.201257\pi$
$929$			1098.03i			1.18195i	−0.806690	+	0.590975i	$0.798743\pi$
$930$		0			0
$931$	171.806	−	171.806i	0.184540	−	0.184540i
$932$		0			0
$933$			25.1951i			0.0270044i
$934$		0			0
$935$	1669.89	−	933.022i	1.78597	−	0.997884i
$936$		0			0
$937$	−68.4855	−	68.4855i	−0.0730902	−	0.0730902i	0.669617	−	0.742707i	$-0.266458\pi$
$937$	−68.4855	−	68.4855i	−0.0730902	−	0.0730902i	−0.742707	+	0.669617i	$0.766458\pi$
$938$		0			0
$939$	33.6817	−	33.6817i	0.0358698	−	0.0358698i
$940$		0			0
$941$	−517.439	+	517.439i	−0.549882	+	0.549882i	−0.926407	−	0.376525i	$-0.877119\pi$
$941$	−517.439	+	517.439i	−0.549882	+	0.549882i	0.376525	+	0.926407i	$0.377119\pi$
$942$		0			0
$943$	3.57779	+	3.57779i	0.00379405	+	0.00379405i
$944$		0			0
$945$	−1435.85	−	406.478i	−1.51942	−	0.430136i
$946$		0			0
$947$			1065.70i			1.12534i	0.826680	+	0.562672i	$0.190227\pi$
$947$			1065.70i			1.12534i	−0.826680	+	0.562672i	$0.809773\pi$
$948$		0			0
$949$	988.954	−	988.954i	1.04210	−	1.04210i
$950$		0			0
$951$			457.261i			0.480821i
$952$		0			0
$953$	−620.695	+	620.695i	−0.651306	+	0.651306i	−0.953307	−	0.302001i	$-0.902345\pi$
$953$	−620.695	+	620.695i	−0.651306	+	0.651306i	0.302001	+	0.953307i	$0.402345\pi$
$954$		0			0
$955$	197.751	−	110.490i	0.207069	−	0.115696i
$956$		0			0
$957$		−	771.567i		−	0.806236i
$958$		0			0
$959$			1817.13i			1.89482i
$960$		0			0
$961$	−883.818			−0.919686
$962$		0			0
$963$	−121.937			−0.126622
$964$		0			0
$965$	1198.22	+	339.207i	1.24168	+	0.351510i
$966$		0			0
$967$	−1139.87	−	1139.87i	−1.17877	−	1.17877i	−0.980059	−	0.198709i	$-0.936325\pi$
$967$	−1139.87	−	1139.87i	−1.17877	−	1.17877i	−0.198709	−	0.980059i	$-0.563675\pi$
$968$		0			0
$969$	362.164			0.373751
$970$		0			0
$971$	−470.641	−	470.641i	−0.484697	−	0.484697i	0.421931	−	0.906628i	$-0.361352\pi$
$971$	−470.641	−	470.641i	−0.484697	−	0.484697i	−0.906628	+	0.421931i	$0.861352\pi$
$972$		0			0
$973$	594.771			0.611275
$974$		0			0
$975$	−425.940	+	692.009i	−0.436862	+	0.709752i
$976$		0			0
$977$	−2.84469	+	2.84469i	−0.00291165	+	0.00291165i	−0.708561	−	0.705649i	$-0.750655\pi$
$977$	−2.84469	+	2.84469i	−0.00291165	+	0.00291165i	0.705649	+	0.708561i	$0.250655\pi$
$978$		0			0
$979$	812.589	+	812.589i	0.830019	+	0.830019i
$980$		0			0
$981$	86.2195	+	86.2195i	0.0878894	+	0.0878894i
$982$		0			0
$983$	−177.652	+	177.652i	−0.180724	+	0.180724i	−0.791671	−	0.610947i	$-0.790789\pi$
$983$	−177.652	+	177.652i	−0.180724	+	0.180724i	0.610947	+	0.791671i	$0.290789\pi$
$984$		0			0
$985$	1345.14	−	751.575i	1.36562	−	0.763020i
$986$		0			0
$987$	1006.20			1.01946
$988$		0			0
$989$	220.704	+	220.704i	0.223158	+	0.223158i
$990$		0			0
$991$	−1697.53			−1.71295			−0.856474	−	0.516190i	$-0.827350\pi$
$991$	−1697.53			−1.71295			−0.856474	+	0.516190i	$0.827350\pi$
$992$		0			0
$993$	535.405	+	535.405i	0.539179	+	0.539179i
$994$		0			0
$995$	−833.309	+	465.598i	−0.837497	+	0.467938i
$996$		0			0
$997$	−1315.01			−1.31897			−0.659483	−	0.751720i	$-0.729225\pi$
$997$	−1315.01			−1.31897			−0.659483	+	0.751720i	$0.729225\pi$
$998$		0			0
$999$	−951.683			−0.952636

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.t.a.113.17		44
4.3	odd	2		80.3.t.a.53.11	yes	44
5.2	odd	4		320.3.i.a.177.6		44
8.3	odd	2		640.3.t.b.353.17		44
8.5	even	2		640.3.t.a.353.6		44
16.3	odd	4		80.3.i.a.13.22	✓	44
16.5	even	4		640.3.i.a.33.6		44
16.11	odd	4		640.3.i.b.33.17		44
16.13	even	4		320.3.i.a.273.17		44
20.3	even	4		400.3.i.b.357.1		44
20.7	even	4		80.3.i.a.37.22	yes	44
20.19	odd	2		400.3.t.b.293.12		44
40.27	even	4		640.3.i.b.97.6		44
40.37	odd	4		640.3.i.a.97.17		44
80.3	even	4		400.3.t.b.157.12		44
80.19	odd	4		400.3.i.b.93.1		44
80.27	even	4		640.3.t.b.417.17		44
80.37	odd	4		640.3.t.a.417.6		44
80.67	even	4		80.3.t.a.77.11	yes	44
80.77	odd	4	inner	320.3.t.a.17.17		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.22	✓	44	16.3	odd	4
80.3.i.a.37.22	yes	44	20.7	even	4
80.3.t.a.53.11	yes	44	4.3	odd	2
80.3.t.a.77.11	yes	44	80.67	even	4
320.3.i.a.177.6		44	5.2	odd	4
320.3.i.a.273.17		44	16.13	even	4
320.3.t.a.17.17		44	80.77	odd	4	inner
320.3.t.a.113.17		44	1.1	even	1	trivial
400.3.i.b.93.1		44	80.19	odd	4
400.3.i.b.357.1		44	20.3	even	4
400.3.t.b.157.12		44	80.3	even	4
400.3.t.b.293.12		44	20.19	odd	2
640.3.i.a.33.6		44	16.5	even	4
640.3.i.a.97.17		44	40.37	odd	4
640.3.i.b.33.17		44	16.11	odd	4
640.3.i.b.97.6		44	40.27	even	4
640.3.t.a.353.6		44	8.5	even	2
640.3.t.a.417.6		44	80.37	odd	4
640.3.t.b.353.17		44	8.3	odd	2
640.3.t.b.417.17		44	80.27	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	320.t (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.50699 q^{3} +(-4.36488 + 2.43881i) q^{5} +(-7.18571 - 7.18571i) q^{7} -2.71500 q^{9} +O(q^{10})\)	\(q+2.50699 q^{3} +(-4.36488 + 2.43881i) q^{5} +(-7.18571 - 7.18571i) q^{7} -2.71500 q^{9} +(8.38398 + 8.38398i) q^{11} -12.9652 q^{13} +(-10.9427 + 6.11407i) q^{15} +(-22.8157 + 22.8157i) q^{17} +(-3.16584 - 3.16584i) q^{19} +(-18.0145 - 18.0145i) q^{21} +(-3.81600 + 3.81600i) q^{23} +(13.1044 - 21.2902i) q^{25} -29.3694 q^{27} +(-18.3544 - 18.3544i) q^{29} +8.78531 q^{31} +(21.0186 + 21.0186i) q^{33} +(48.8893 + 13.8402i) q^{35} +32.4039 q^{37} -32.5036 q^{39} -0.937574i q^{41} -57.8364i q^{43} +(11.8506 - 6.62136i) q^{45} +(-27.9276 + 27.9276i) q^{47} +54.2688i q^{49} +(-57.1987 + 57.1987i) q^{51} +20.6425i q^{53} +(-57.0420 - 16.1482i) q^{55} +(-7.93674 - 7.93674i) q^{57} +(40.1490 - 40.1490i) q^{59} +(-25.3893 + 25.3893i) q^{61} +(19.5092 + 19.5092i) q^{63} +(56.5915 - 31.6196i) q^{65} -29.3419i q^{67} +(-9.56668 + 9.56668i) q^{69} +34.7686i q^{71} +(-76.2777 + 76.2777i) q^{73} +(32.8527 - 53.3744i) q^{75} -120.490i q^{77} -17.2292i q^{79} -49.1938 q^{81} +73.3919 q^{83} +(43.9447 - 155.231i) q^{85} +(-46.0144 - 46.0144i) q^{87} +96.9216 q^{89} +(93.1639 + 93.1639i) q^{91} +22.0247 q^{93} +(21.5394 + 6.09765i) q^{95} +(-53.4378 + 53.4378i) q^{97} +(-22.7625 - 22.7625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9	\( 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{15} - 4 q^{17} + 32 q^{19} - 4 q^{21} + 40 q^{27} + 8 q^{31} - 4 q^{33} + 4 q^{35} - 4 q^{37} + 72 q^{39} - 70 q^{45} + 4 q^{47} + 100 q^{51} - 36 q^{57} + 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 60 q^{69} - 48 q^{73} + 324 q^{75} + 100 q^{81} - 156 q^{83} - 52 q^{85} + 36 q^{87} - 188 q^{91} - 40 q^{93} - 380 q^{95} - 4 q^{97} - 92 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^15 - 4 * q^17 + 32 * q^19 - 4 * q^21 + 40 * q^27 + 8 * q^31 - 4 * q^33 + 4 * q^35 - 4 * q^37 + 72 * q^39 - 70 * q^45 + 4 * q^47 + 100 * q^51 - 36 * q^57 + 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 60 * q^69 - 48 * q^73 + 324 * q^75 + 100 * q^81 - 156 * q^83 - 52 * q^85 + 36 * q^87 - 188 * q^91 - 40 * q^93 - 380 * q^95 - 4 * q^97 - 92 * q^99

Introduction

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