LMFDB - Embedded newform 640.3.i.b.33.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,3,Mod(33,640)]

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, 3]))

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

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

chi := DirichletCharacter("640.33");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	640.i (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:	$17.4387369191$
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			33.17
Character	$\chi$	$=$	640.33
Dual form			640.3.i.b.97.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.50699i q^{3} +(-2.43881 - 4.36488i) q^{5} +(-7.18571 - 7.18571i) q^{7} +2.71500 q^{9} +O(q^{10})$	\(q+2.50699i q^{3} +(-2.43881 - 4.36488i) q^{5} +(-7.18571 - 7.18571i) q^{7} +2.71500 q^{9} +(8.38398 - 8.38398i) q^{11} +12.9652i q^{13} +(10.9427 - 6.11407i) q^{15} +(-22.8157 + 22.8157i) q^{17} +(3.16584 - 3.16584i) q^{19} +(18.0145 - 18.0145i) q^{21} +(-3.81600 + 3.81600i) q^{23} +(-13.1044 + 21.2902i) q^{25} +29.3694i q^{27} +(-18.3544 + 18.3544i) q^{29} -8.78531 q^{31} +(21.0186 + 21.0186i) q^{33} +(-13.8402 + 48.8893i) q^{35} +32.4039i q^{37} -32.5036 q^{39} +0.937574i q^{41} -57.8364 q^{43} +(-6.62136 - 11.8506i) q^{45} +(27.9276 - 27.9276i) q^{47} +54.2688i q^{49} +(-57.1987 - 57.1987i) q^{51} -20.6425 q^{53} +(-57.0420 - 16.1482i) q^{55} +(7.93674 + 7.93674i) q^{57} +(-40.1490 - 40.1490i) q^{59} +(25.3893 + 25.3893i) q^{61} +(-19.5092 - 19.5092i) q^{63} +(56.5915 - 31.6196i) q^{65} +29.3419 q^{67} +(-9.56668 - 9.56668i) q^{69} +34.7686i q^{71} +(76.2777 - 76.2777i) q^{73} +(-53.3744 - 32.8527i) q^{75} -120.490 q^{77} +17.2292i q^{79} -49.1938 q^{81} +73.3919i q^{83} +(155.231 + 43.9447i) q^{85} +(-46.0144 - 46.0144i) q^{87} -96.9216 q^{89} +(93.1639 - 93.1639i) q^{91} -22.0247i q^{93} +(-21.5394 - 6.09765i) q^{95} +(-53.4378 + 53.4378i) q^{97} +(22.7625 - 22.7625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{5} - 108 q^{9}+O(q^{10}) $ 44 * q + 2 * q^5 - 108 * q^9	$ 44 q + 2 q^{5} - 108 q^{9} + 4 q^{11} - 4 q^{15} - 4 q^{17} - 32 q^{19} + 4 q^{21} - 8 q^{31} - 4 q^{33} - 96 q^{35} + 72 q^{39} - 124 q^{43} + 34 q^{45} - 4 q^{47} + 100 q^{51} + 4 q^{53} + 36 q^{57} - 64 q^{59} + 36 q^{61} - 200 q^{63} - 4 q^{65} + 292 q^{67} + 60 q^{69} + 48 q^{73} - 96 q^{75} - 192 q^{77} + 100 q^{81} - 48 q^{85} + 36 q^{87} - 188 q^{91} + 380 q^{95} - 4 q^{97} + 92 q^{99}+O(q^{100}) $ 44 * q + 2 * q^5 - 108 * q^9 + 4 * q^11 - 4 * q^15 - 4 * q^17 - 32 * q^19 + 4 * q^21 - 8 * q^31 - 4 * q^33 - 96 * q^35 + 72 * q^39 - 124 * q^43 + 34 * q^45 - 4 * q^47 + 100 * q^51 + 4 * q^53 + 36 * q^57 - 64 * q^59 + 36 * q^61 - 200 * q^63 - 4 * q^65 + 292 * q^67 + 60 * q^69 + 48 * q^73 - 96 * q^75 - 192 * q^77 + 100 * q^81 - 48 * q^85 + 36 * q^87 - 188 * q^91 + 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 $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$			2.50699i			0.835664i	0.908524	+	0.417832i	$0.137210\pi$
$3$			2.50699i			0.835664i	−0.908524	+	0.417832i	$0.862790\pi$
$4$		0			0
$5$	−2.43881	−	4.36488i	−0.487762	−	0.872977i
$5$	−2.43881	−	4.36488i	−0.487762	−	0.872977i
$6$		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	−0.214536	−	0.976716i	$-0.568824\pi$
$11$	8.38398	−	8.38398i	0.762180	−	0.762180i	0.976716	+	0.214536i	$0.0688239\pi$
$12$		0			0
$13$			12.9652i			0.997321i	0.866797	+	0.498660i	$0.166175\pi$
$13$			12.9652i			0.997321i	−0.866797	+	0.498660i	$0.833825\pi$
$14$		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	$-0.712409\pi$
$19$	3.16584	−	3.16584i	0.166623	−	0.166623i	0.785493	+	0.618870i	$0.212409\pi$
$20$		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
$27$			29.3694i			1.08776i
$28$		0			0
$29$	−18.3544	+	18.3544i	−0.632911	+	0.632911i	−0.948797	−	0.315886i	$-0.897698\pi$
$29$	−18.3544	+	18.3544i	−0.632911	+	0.632911i	0.315886	+	0.948797i	$0.397698\pi$
$30$		0			0
$31$	−8.78531			−0.283397			−0.141698	−	0.989910i	$-0.545256\pi$
$31$	−8.78531			−0.283397			−0.141698	+	0.989910i	$0.545256\pi$
$32$		0			0
$33$	21.0186	+	21.0186i	0.636926	+	0.636926i
$34$		0			0
$35$	−13.8402	+	48.8893i	−0.395434	+	1.39684i
$36$		0			0
$37$			32.4039i			0.875781i	0.899028	+	0.437891i	$0.144274\pi$
$37$			32.4039i			0.875781i	−0.899028	+	0.437891i	$0.855726\pi$
$38$		0			0
$39$	−32.5036			−0.833425
$40$		0			0
$41$			0.937574i			0.0228677i	0.999935	+	0.0114338i	$0.00363958\pi$
$41$			0.937574i			0.0228677i	−0.999935	+	0.0114338i	$0.996360\pi$
$42$		0			0
$43$	−57.8364			−1.34503			−0.672516	−	0.740083i	$-0.734786\pi$
$43$	−57.8364			−1.34503			−0.672516	+	0.740083i	$0.734786\pi$
$44$		0			0
$45$	−6.62136	−	11.8506i	−0.147141	−	0.263348i
$46$		0			0
$47$	27.9276	−	27.9276i	0.594205	−	0.594205i	−0.344560	−	0.938764i	$-0.611972\pi$
$47$	27.9276	−	27.9276i	0.594205	−	0.594205i	0.938764	+	0.344560i	$0.111972\pi$
$48$		0			0
$49$			54.2688i			1.10753i
$50$		0			0
$51$	−57.1987	−	57.1987i	−1.12154	−	1.12154i
$52$		0			0
$53$	−20.6425			−0.389482			−0.194741	−	0.980855i	$-0.562387\pi$
$53$	−20.6425			−0.389482			−0.194741	+	0.980855i	$0.562387\pi$
$54$		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	$-0.409792\pi$
$59$	−40.1490	−	40.1490i	−0.680492	−	0.680492i	−0.960111	+	0.279619i	$0.909792\pi$
$60$		0			0
$61$	25.3893	+	25.3893i	0.416217	+	0.416217i	0.883898	−	0.467680i	$-0.154910\pi$
$61$	25.3893	+	25.3893i	0.416217	+	0.416217i	−0.467680	+	0.883898i	$0.654910\pi$
$62$		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
$67$	29.3419			0.437938			0.218969	−	0.975732i	$-0.429731\pi$
$67$	29.3419			0.437938			0.218969	+	0.975732i	$0.429731\pi$
$68$		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	$-0.485366\pi$
$73$	76.2777	−	76.2777i	1.04490	−	1.04490i	0.998943	−	0.0459567i	$-0.0146336\pi$
$74$		0			0
$75$	−53.3744	−	32.8527i	−0.711659	−	0.438035i
$76$		0			0
$77$	−120.490			−1.56480
$78$		0			0
$79$			17.2292i			0.218092i	0.994037	+	0.109046i	$0.0347795\pi$
$79$			17.2292i			0.218092i	−0.994037	+	0.109046i	$0.965220\pi$
$80$		0			0
$81$	−49.1938			−0.607331
$82$		0			0
$83$			73.3919i			0.884239i	0.896956	+	0.442120i	$0.145773\pi$
$83$			73.3919i			0.884239i	−0.896956	+	0.442120i	$0.854227\pi$
$84$		0			0
$85$	155.231	+	43.9447i	1.82625	+	0.516997i
$86$		0			0
$87$	−46.0144	−	46.0144i	−0.528901	−	0.528901i
$88$		0			0
$89$	−96.9216			−1.08901			−0.544503	−	0.838759i	$-0.683282\pi$
$89$	−96.9216			−1.08901			−0.544503	+	0.838759i	$0.683282\pi$
$90$		0			0
$91$	93.1639	−	93.1639i	1.02378	−	1.02378i
$92$		0			0
$93$		−	22.0247i		−	0.236825i
$94$		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	$-0.907800\pi$
$101$	−67.9450	+	67.9450i	−0.672723	+	0.672723i	0.285620	+	0.958343i	$0.407800\pi$
$102$		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
$107$		−	44.9125i		−	0.419743i	−0.977729	−	0.209872i	$-0.932695\pi$
$107$		−	44.9125i		−	0.419743i	0.977729	−	0.209872i	$-0.0673046\pi$
$108$		0			0
$109$	−31.7568	+	31.7568i	−0.291346	+	0.291346i	−0.837612	−	0.546266i	$-0.816049\pi$
$109$	−31.7568	+	31.7568i	−0.291346	+	0.291346i	0.546266	+	0.837612i	$0.316049\pi$
$110$		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
$115$	25.9629	+	7.34990i	0.225764	+	0.0639122i
$116$		0			0
$117$			35.2004i			0.300858i
$118$		0			0
$119$	327.894			2.75541
$120$		0			0
$121$		−	19.5823i		−	0.161837i
$122$		0			0
$123$	−2.35049			−0.0191097
$124$		0			0
$125$	124.889	+	5.27642i	0.999109	+	0.0422114i
$126$		0			0
$127$	−106.254	+	106.254i	−0.836645	+	0.836645i	−0.988416	−	0.151771i	$-0.951502\pi$
$127$	−106.254	+	106.254i	−0.836645	+	0.836645i	0.151771	+	0.988416i	$0.451502\pi$
$128$		0			0
$129$		−	144.995i		−	1.12399i
$130$		0			0
$131$	59.7795	+	59.7795i	0.456332	+	0.456332i	0.897449	−	0.441117i	$-0.145418\pi$
$131$	59.7795	+	59.7795i	0.456332	+	0.456332i	−0.441117	+	0.897449i	$0.645418\pi$
$132$		0			0
$133$	−45.4976			−0.342088
$134$		0			0
$135$	128.194	−	71.6263i	0.949585	−	0.530566i
$136$		0			0
$137$	126.441	+	126.441i	0.922925	+	0.922925i	0.997235	−	0.0743099i	$-0.0236754\pi$
$137$	126.441	+	126.441i	0.922925	+	0.922925i	−0.0743099	+	0.997235i	$0.523675\pi$
$138$		0			0
$139$	41.3857	+	41.3857i	0.297739	+	0.297739i	0.840128	−	0.542389i	$-0.182480\pi$
$139$	41.3857	+	41.3857i	0.297739	+	0.297739i	−0.542389	+	0.840128i	$0.682480\pi$
$140$		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
$147$	−136.051			−0.925519
$148$		0			0
$149$	−30.0503	−	30.0503i	−0.201680	−	0.201680i	0.599040	−	0.800719i	$-0.295549\pi$
$149$	−30.0503	−	30.0503i	−0.201680	−	0.201680i	−0.800719	+	0.599040i	$0.795549\pi$
$150$		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
$155$	21.4257	+	38.3468i	0.138230	+	0.247399i
$156$		0			0
$157$	2.64846			0.0168691			0.00843457	−	0.999964i	$-0.497315\pi$
$157$	2.64846			0.0168691			0.00843457	+	0.999964i	$0.497315\pi$
$158$		0			0
$159$		−	51.7507i		−	0.325476i
$160$		0			0
$161$	54.8413			0.340629
$162$		0			0
$163$		−	143.714i		−	0.881682i	−0.897585	−	0.440841i	$-0.854680\pi$
$163$		−	143.714i		−	0.881682i	0.897585	−	0.440841i	$-0.145320\pi$
$164$		0			0
$165$	40.4833	−	143.004i	0.245353	−	0.866690i
$166$		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
$173$			2.04705i			0.0118326i	0.999982	+	0.00591632i	$0.00188323\pi$
$173$			2.04705i			0.0118326i	−0.999982	+	0.00591632i	$0.998117\pi$
$174$		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	$-0.619079\pi$
$179$	101.208	−	101.208i	0.565405	−	0.565405i	0.930838	+	0.365432i	$0.119079\pi$
$180$		0			0
$181$	−154.013	+	154.013i	−0.850901	+	0.850901i	−0.990244	−	0.139343i	$-0.955501\pi$
$181$	−154.013	+	154.013i	−0.850901	+	0.850901i	0.139343	+	0.990244i	$0.455501\pi$
$182$		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
$187$			382.573i			2.04584i
$188$		0			0
$189$	211.040	−	211.040i	1.11661	−	1.11661i
$190$		0			0
$191$	45.3049			0.237198			0.118599	−	0.992942i	$-0.462160\pi$
$191$	45.3049			0.237198			0.118599	+	0.992942i	$0.462160\pi$
$192$		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
$195$	79.2700	+	141.874i	0.406513	+	0.727560i
$196$		0			0
$197$		−	308.173i		−	1.56433i	−0.623072	−	0.782164i	$-0.714116\pi$
$197$		−	308.173i		−	1.56433i	0.623072	−	0.782164i	$-0.285884\pi$
$198$		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
$203$	263.779			1.29940
$204$		0			0
$205$	4.09240	−	2.28656i	0.0199629	−	0.0111540i
$206$		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	−0.995011	−	0.0997692i	$-0.968190\pi$
$211$	−230.999	−	230.999i	−1.09478	−	1.09478i	−0.0997692	−	0.995011i	$-0.531810\pi$
$212$		0			0
$213$	−87.1645			−0.409223
$214$		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	0.557861	−	0.829934i	$-0.311622\pi$
$223$	−60.6724	−	60.6724i	−0.272073	−	0.272073i	−0.829934	+	0.557861i	$0.811622\pi$
$224$		0			0
$225$	−35.5785	+	57.8030i	−0.158127	+	0.256902i
$226$		0			0
$227$	202.529			0.892199			0.446099	−	0.894983i	$-0.352813\pi$
$227$	202.529			0.892199			0.446099	+	0.894983i	$0.352813\pi$
$228$		0			0
$229$	−137.361	−	137.361i	−0.599829	−	0.599829i	0.340438	−	0.940267i	$-0.389425\pi$
$229$	−137.361	−	137.361i	−0.599829	−	0.599829i	−0.940267	+	0.340438i	$0.889425\pi$
$230$		0			0
$231$		−	302.067i		−	1.30765i
$232$		0			0
$233$	197.272	−	197.272i	0.846660	−	0.846660i	−0.143055	−	0.989715i	$-0.545692\pi$
$233$	197.272	−	197.272i	0.846660	−	0.846660i	0.989715	+	0.143055i	$0.0456925\pi$
$234$		0			0
$235$	−190.011	−	53.7907i	−0.808557	−	0.228896i
$236$		0			0
$237$	−43.1935			−0.182251
$238$		0			0
$239$		−	411.923i		−	1.72353i	−0.507310	−	0.861763i	$-0.669360\pi$
$239$		−	411.923i		−	1.72353i	0.507310	−	0.861763i	$-0.330640\pi$
$240$		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
$243$			140.996i			0.580231i
$244$		0			0
$245$	236.877	−	132.351i	0.966844	−	0.540209i
$246$		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	−0.981542	−	0.191244i	$-0.938748\pi$
$251$	−198.365	+	198.365i	−0.790298	+	0.790298i	0.191244	+	0.981542i	$0.438748\pi$
$252$		0			0
$253$			63.9866i			0.252911i
$254$		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
$267$		−	242.981i		−	0.910043i
$268$		0			0
$269$	269.805	−	269.805i	1.00299	−	1.00299i	0.00299625	−	0.999996i	$-0.499046\pi$
$269$	269.805	−	269.805i	1.00299	−	1.00299i	0.999996	−	0.00299625i	$-0.000953737\pi$
$270$		0			0
$271$	71.4599			0.263690			0.131845	−	0.991270i	$-0.457910\pi$
$271$	71.4599			0.263690			0.131845	+	0.991270i	$0.457910\pi$
$272$		0			0
$273$	233.561	+	233.561i	0.855535	+	0.855535i
$274$		0			0
$275$	68.6298	+	288.364i	0.249563	+	1.04860i
$276$		0			0
$277$			256.078i			0.924470i	0.886758	+	0.462235i	$0.152952\pi$
$277$			256.078i			0.924470i	−0.886758	+	0.462235i	$0.847048\pi$
$278$		0			0
$279$	−23.8521			−0.0854914
$280$		0			0
$281$		−	315.882i		−	1.12413i	−0.827092	−	0.562067i	$-0.810006\pi$
$281$		−	315.882i		−	1.12413i	0.827092	−	0.562067i	$-0.189994\pi$
$282$		0			0
$283$	8.65428			0.0305805			0.0152903	−	0.999883i	$-0.495133\pi$
$283$	8.65428			0.0305805			0.0152903	+	0.999883i	$0.495133\pi$
$284$		0			0
$285$	15.2867	−	53.9991i	0.0536377	−	0.189471i
$286$		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
$293$	533.382			1.82042			0.910208	−	0.414151i	$-0.135921\pi$
$293$	533.382			1.82042			0.910208	+	0.414151i	$0.135921\pi$
$294$		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
$307$	−322.054			−1.04903			−0.524517	−	0.851400i	$-0.675754\pi$
$307$	−322.054			−1.04903			−0.524517	+	0.851400i	$0.675754\pi$
$308$		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	−0.728243	−	0.685319i	$-0.759663\pi$
$313$	−13.4351	+	13.4351i	−0.0429237	+	0.0429237i	0.685319	+	0.728243i	$0.259663\pi$
$314$		0			0
$315$	−37.5761	+	132.734i	−0.119289	+	0.421379i
$316$		0			0
$317$	182.394			0.575377			0.287688	−	0.957724i	$-0.407113\pi$
$317$	182.394			0.575377			0.287688	+	0.957724i	$0.407113\pi$
$318$		0			0
$319$			307.766i			0.964785i
$320$		0			0
$321$	112.595			0.350764
$322$		0			0
$323$			144.462i			0.447250i
$324$		0			0
$325$	−276.032	−	169.901i	−0.849328	−	0.522772i
$326$		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	−0.306621	−	0.951832i	$-0.599198\pi$
$331$	213.565	−	213.565i	0.645211	−	0.645211i	0.951832	+	0.306621i	$0.0991983\pi$
$332$		0			0
$333$			87.9766i			0.264194i
$334$		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
$347$		−	481.819i		−	1.38853i	−0.719721	−	0.694264i	$-0.755730\pi$
$347$		−	481.819i		−	1.38853i	0.719721	−	0.694264i	$-0.244270\pi$
$348$		0			0
$349$	−398.473	+	398.473i	−1.14176	+	1.14176i	−0.153628	+	0.988129i	$0.549096\pi$
$349$	−398.473	+	398.473i	−1.14176	+	1.14176i	−0.988129	+	0.153628i	$0.950904\pi$
$350$		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
$355$	151.761	−	84.7940i	0.427495	−	0.238856i
$356$		0			0
$357$			822.027i			2.30260i
$358$		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
$363$	49.0927			0.135242
$364$		0			0
$365$	−518.970	−	146.917i	−1.42184	−	0.402511i
$366$		0			0
$367$	−109.049	+	109.049i	−0.297136	+	0.297136i	−0.839891	−	0.542755i	$-0.817381\pi$
$367$	−109.049	+	109.049i	−0.297136	+	0.297136i	0.542755	+	0.839891i	$0.317381\pi$
$368$		0			0
$369$			2.54551i			0.00689841i
$370$		0			0
$371$	148.331	+	148.331i	0.399815	+	0.399815i
$372$		0			0
$373$	308.832			0.827968			0.413984	−	0.910284i	$-0.364137\pi$
$373$	308.832			0.827968			0.413984	+	0.910284i	$0.364137\pi$
$374$		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	$-0.233145\pi$
$379$	28.3677	+	28.3677i	0.0748489	+	0.0748489i	−0.668691	+	0.743540i	$0.733145\pi$
$380$		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	$0.0352237\pi$
$383$	422.953	+	422.953i	1.10432	+	1.10432i	0.110433	+	0.993884i	$0.464776\pi$
$384$		0			0
$385$	293.851	+	525.923i	0.763250	+	1.36603i
$386$		0			0
$387$	−157.026			−0.405751
$388$		0			0
$389$	178.975	+	178.975i	0.460089	+	0.460089i	0.898685	−	0.438595i	$-0.144524\pi$
$389$	178.975	+	178.975i	0.460089	+	0.460089i	−0.438595	+	0.898685i	$0.644524\pi$
$390$		0			0
$391$		−	174.129i		−	0.445344i
$392$		0			0
$393$	−149.867	+	149.867i	−0.381340	+	0.381340i
$394$		0			0
$395$	75.2036	−	42.0188i	0.190389	−	0.106377i
$396$		0			0
$397$	−20.4646			−0.0515480			−0.0257740	−	0.999668i	$-0.508205\pi$
$397$	−20.4646			−0.0515480			−0.0257740	+	0.999668i	$0.508205\pi$
$398$		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
$403$		−	113.903i		−	0.282638i
$404$		0			0
$405$	119.974	+	214.725i	0.296233	+	0.530186i
$406$		0			0
$407$	271.674	+	271.674i	0.667503	+	0.667503i
$408$		0			0
$409$	346.930			0.848239			0.424120	−	0.905606i	$-0.360584\pi$
$409$	346.930			0.848239			0.424120	+	0.905606i	$0.360584\pi$
$410$		0			0
$411$	−316.986	+	316.986i	−0.771255	+	0.771255i
$412$		0			0
$413$			576.998i			1.39709i
$414$		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	$-0.698935\pi$
$419$	94.6547	−	94.6547i	0.225906	−	0.225906i	0.810980	+	0.585074i	$0.198935\pi$
$420$		0			0
$421$	−303.154	+	303.154i	−0.720080	+	0.720080i	−0.968621	−	0.248541i	$-0.920049\pi$
$421$	−303.154	+	303.154i	−0.720080	+	0.720080i	0.248541	+	0.968621i	$0.420049\pi$
$422$		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
$427$		−	364.880i		−	0.854519i
$428$		0			0
$429$	−272.509	+	272.509i	−0.635220	+	0.635220i
$430$		0			0
$431$	505.491			1.17283			0.586416	−	0.810010i	$-0.300538\pi$
$431$	505.491			1.17283			0.586416	+	0.810010i	$0.300538\pi$
$432$		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
$435$	−88.6271	+	313.068i	−0.203740	+	0.719696i
$436$		0			0
$437$			24.1617i			0.0552900i
$438$		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
$443$	−401.681			−0.906729			−0.453365	−	0.891325i	$-0.649776\pi$
$443$	−401.681			−0.906729			−0.453365	+	0.891325i	$0.649776\pi$
$444$		0			0
$445$	236.373	+	423.051i	0.531176	+	0.950677i
$446$		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
$453$	−65.4052			−0.144382
$454$		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	$-0.976997\pi$
$457$	−488.804	−	488.804i	−1.06959	−	1.06959i	−0.0722037	−	0.997390i	$-0.523003\pi$
$458$		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	$-0.455516\pi$
$461$	−392.290	−	392.290i	−0.850954	−	0.850954i	−0.990251	+	0.139297i	$0.955516\pi$
$462$		0			0
$463$	−70.7053	−	70.7053i	−0.152711	−	0.152711i	0.626616	−	0.779328i	$-0.284439\pi$
$463$	−70.7053	−	70.7053i	−0.152711	−	0.152711i	−0.779328	+	0.626616i	$0.784439\pi$
$464$		0			0
$465$	−96.1352	+	53.7140i	−0.206742	+	0.115514i
$466$		0			0
$467$	−918.293			−1.96637			−0.983183	−	0.182623i	$-0.941541\pi$
$467$	−918.293			−1.96637			−0.983183	+	0.182623i	$0.941541\pi$
$468$		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
$475$	25.9150	+	108.888i	0.0545579	+	0.229238i
$476$		0			0
$477$	−56.0445			−0.117494
$478$		0			0
$479$			49.5880i			0.103524i	0.998659	+	0.0517620i	$0.0164837\pi$
$479$			49.5880i			0.103524i	−0.998659	+	0.0517620i	$0.983516\pi$
$480$		0			0
$481$	−420.122			−0.873435
$482$		0			0
$483$			137.487i			0.284652i
$484$		0			0
$485$	363.575	+	102.925i	0.749638	+	0.212217i
$486$		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	0.108130	−	0.994137i	$-0.465514\pi$
$491$	541.213	−	541.213i	1.10227	−	1.10227i	0.994137	−	0.108130i	$-0.0344861\pi$
$492$		0			0
$493$		−	837.538i		−	1.69886i
$494$		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	$-0.814713\pi$
$499$	−142.483	+	142.483i	−0.285537	+	0.285537i	0.549775	+	0.835313i	$0.314713\pi$
$500$		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
$507$			2.26713i			0.00447166i
$508$		0			0
$509$	268.080	−	268.080i	0.526681	−	0.526681i	−0.392900	−	0.919581i	$-0.628528\pi$
$509$	268.080	−	268.080i	0.526681	−	0.526681i	0.919581	+	0.392900i	$0.128528\pi$
$510$		0			0
$511$	−1096.22			−2.14524
$512$		0			0
$513$	92.9789	+	92.9789i	0.181245	+	0.181245i
$514$		0			0
$515$	904.124	+	255.951i	1.75558	+	0.496992i
$516$		0			0
$517$		−	468.289i		−	0.905782i
$518$		0			0
$519$	−5.13193			−0.00988811
$520$		0			0
$521$			364.737i			0.700071i	0.936736	+	0.350036i	$0.113831\pi$
$521$			364.737i			0.700071i	−0.936736	+	0.350036i	$0.886169\pi$
$522$		0			0
$523$	−434.085			−0.829991			−0.414996	−	0.909823i	$-0.636217\pi$
$523$	−434.085			−0.829991			−0.414996	+	0.909823i	$0.636217\pi$
$524$		0			0
$525$	147.463	+	619.603i	0.280883	+	1.18020i
$526$		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
$533$	−12.1558			−0.0228064
$534$		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	$-0.121938\pi$
$541$	299.573	+	299.573i	0.553739	+	0.553739i	−0.373779	+	0.927518i	$0.621938\pi$
$542$		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
$547$	9.98799			0.0182596			0.00912979	−	0.999958i	$-0.497094\pi$
$547$	9.98799			0.0182596			0.00912979	+	0.999958i	$0.497094\pi$
$548$		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
$555$	198.120	+	354.587i	0.356973	+	0.638896i
$556$		0			0
$557$	360.011			0.646339			0.323170	−	0.946341i	$-0.395252\pi$
$557$	360.011			0.646339			0.323170	+	0.946341i	$0.395252\pi$
$558$		0			0
$559$		−	749.859i		−	1.34143i
$560$		0			0
$561$	−959.106			−1.70964
$562$		0			0
$563$			524.373i			0.931392i	0.884945	+	0.465696i	$0.154196\pi$
$563$			524.373i			0.931392i	−0.884945	+	0.465696i	$0.845804\pi$
$564$		0			0
$565$	10.7278	−	37.8949i	0.0189872	−	0.0670707i
$566$		0			0
$567$	353.492	+	353.492i	0.623443	+	0.623443i
$568$		0			0
$569$	606.955			1.06670			0.533352	−	0.845893i	$-0.320932\pi$
$569$	606.955			1.06670			0.533352	+	0.845893i	$0.320932\pi$
$570$		0			0
$571$	−763.721	+	763.721i	−1.33752	+	1.33752i	−0.439056	+	0.898460i	$0.644687\pi$
$571$	−763.721	+	763.721i	−1.33752	+	1.33752i	−0.898460	+	0.439056i	$0.855313\pi$
$572$		0			0
$573$			113.579i			0.198218i
$574$		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
$587$			445.447i			0.758853i	0.925222	+	0.379427i	$0.123879\pi$
$587$			445.447i			0.758853i	−0.925222	+	0.379427i	$0.876121\pi$
$588$		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
$595$	−799.670	−	1431.22i	−1.34398	−	2.40541i
$596$		0			0
$597$			478.615i			0.801700i
$598$		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	$0.140304\pi$
$601$			512.825i			0.853287i	−0.904420	+	0.426643i	$0.859696\pi$
$602$		0			0
$603$	79.6631			0.132111
$604$		0			0
$605$	−85.4746	+	47.7576i	−0.141280	+	0.0789381i
$606$		0			0
$607$	−700.017	+	700.017i	−1.15324	+	1.15324i	−0.167341	+	0.985899i	$0.553518\pi$
$607$	−700.017	+	700.017i	−1.15324	+	1.15324i	−0.985899	+	0.167341i	$0.946482\pi$
$608$		0			0
$609$			661.292i			1.08586i
$610$		0			0
$611$	362.086	+	362.086i	0.592613	+	0.592613i
$612$		0			0
$613$	−402.030			−0.655840			−0.327920	−	0.944705i	$-0.606348\pi$
$613$	−402.030			−0.655840			−0.327920	+	0.944705i	$0.606348\pi$
$614$		0			0
$615$	5.73240	+	10.2596i	0.00932097	+	0.0166823i
$616$		0			0
$617$	−451.281	−	451.281i	−0.731412	−	0.731412i	0.239488	−	0.970899i	$-0.423021\pi$
$617$	−451.281	−	451.281i	−0.731412	−	0.731412i	−0.970899	+	0.239488i	$0.923021\pi$
$618$		0			0
$619$	141.521	+	141.521i	0.228629	+	0.228629i	0.812120	−	0.583491i	$-0.198314\pi$
$619$	141.521	+	141.521i	0.228629	+	0.228629i	−0.583491	+	0.812120i	$0.698314\pi$
$620$		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
$627$	133.083			0.212254
$628$		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
$635$	722.919	+	204.653i	1.13845	+	0.322288i
$636$		0			0
$637$	−703.604			−1.10456
$638$		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
$643$			521.720i			0.811384i	0.914010	+	0.405692i	$0.132969\pi$
$643$			521.720i			0.811384i	−0.914010	+	0.405692i	$0.867031\pi$
$644$		0			0
$645$	−632.887	+	353.616i	−0.981221	+	0.548242i
$646$		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
$653$		−	171.839i		−	0.263154i	−0.991306	−	0.131577i	$-0.957996\pi$
$653$		−	171.839i		−	0.263154i	0.991306	−	0.131577i	$-0.0420040\pi$
$654$		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	$-0.772692\pi$
$659$	−66.3827	+	66.3827i	−0.100732	+	0.100732i	0.654945	+	0.755677i	$0.272692\pi$
$660$		0			0
$661$	38.9121	−	38.9121i	0.0588685	−	0.0588685i	−0.677060	−	0.735928i	$-0.736746\pi$
$661$	38.9121	−	38.9121i	0.0588685	−	0.0588685i	0.735928	+	0.677060i	$0.236746\pi$
$662$		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
$667$		−	140.081i		−	0.210017i
$668$		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
$675$	−625.281	−	384.869i	−0.926343	−	0.570176i
$676$		0			0
$677$		−	408.523i		−	0.603431i	−0.953398	−	0.301716i	$-0.902441\pi$
$677$		−	408.523i		−	0.603431i	0.953398	−	0.301716i	$-0.0975593\pi$
$678$		0			0
$679$	767.977			1.13104
$680$		0			0
$681$			507.738i			0.745578i
$682$		0			0
$683$	−611.720			−0.895636			−0.447818	−	0.894125i	$-0.647799\pi$
$683$	−611.720			−0.895636			−0.447818	+	0.894125i	$0.647799\pi$
$684$		0			0
$685$	243.534	−	860.264i	0.355524	−	1.25586i
$686$		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	0.977064	−	0.212944i	$-0.0683053\pi$
$691$	528.007	+	528.007i	0.764120	+	0.764120i	−0.212944	+	0.977064i	$0.568305\pi$
$692$		0			0
$693$	−327.129			−0.472048
$694$		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	$-0.302879\pi$
$701$	−163.932	−	163.932i	−0.233855	−	0.233855i	−0.814300	+	0.580445i	$0.802879\pi$
$702$		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
$707$	976.466			1.38114
$708$		0			0
$709$	820.614	+	820.614i	1.15742	+	1.15742i	0.985027	+	0.172397i	$0.0551513\pi$
$709$	820.614	+	820.614i	1.15742	+	1.15742i	0.172397	+	0.985027i	$0.444849\pi$
$710$		0			0
$711$			46.7773i			0.0657909i
$712$		0			0
$713$	33.5248	−	33.5248i	0.0470193	−	0.0470193i
$714$		0			0
$715$	209.364	−	739.560i	0.292817	−	1.03435i
$716$		0			0
$717$	1032.69			1.44029
$718$		0			0
$719$			578.830i			0.805048i	0.915409	+	0.402524i	$0.131867\pi$
$719$			578.830i			0.805048i	−0.915409	+	0.402524i	$0.868133\pi$
$720$		0			0
$721$	1909.78			2.64879
$722$		0			0
$723$		−	736.896i		−	1.01922i
$724$		0			0
$725$	−150.246	−	631.294i	−0.207236	−	0.870751i
$726$		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
$733$		−	455.036i		−	0.620785i	−0.950608	−	0.310393i	$-0.899539\pi$
$733$		−	455.036i		−	0.620785i	0.950608	−	0.310393i	$-0.100461\pi$
$734$		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	$-0.993226\pi$
$739$	−723.106	+	723.106i	−0.978493	+	0.978493i	0.0212803	+	0.999774i	$0.493226\pi$
$740$		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
$747$			199.259i			0.266745i
$748$		0			0
$749$	−322.728	+	322.728i	−0.430879	+	0.430879i
$750$		0			0
$751$	−216.822			−0.288711			−0.144356	−	0.989526i	$-0.546111\pi$
$751$	−216.822			−0.288711			−0.144356	+	0.989526i	$0.546111\pi$
$752$		0			0
$753$	−497.299	−	497.299i	−0.660423	−	0.660423i
$754$		0			0
$755$	113.876	−	63.6264i	0.150829	−	0.0842733i
$756$		0			0
$757$			747.764i			0.987800i	0.869519	+	0.493900i	$0.164429\pi$
$757$			747.764i			0.987800i	−0.869519	+	0.493900i	$0.835571\pi$
$758$		0			0
$759$	−160.414			−0.211349
$760$		0			0
$761$		−	1410.33i		−	1.85326i	−0.375978	−	0.926629i	$-0.622693\pi$
$761$		−	1410.33i		−	1.85326i	0.375978	−	0.926629i	$-0.377307\pi$
$762$		0			0
$763$	456.390			0.598152
$764$		0			0
$765$	421.452	+	119.310i	0.550917	+	0.155961i
$766$		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
$773$	−146.591			−0.189639			−0.0948196	−	0.995494i	$-0.530227\pi$
$773$	−146.591			−0.189639			−0.0948196	+	0.995494i	$0.530227\pi$
$774$		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
$787$	389.164			0.494491			0.247245	−	0.968953i	$-0.420475\pi$
$787$	389.164			0.494491			0.247245	+	0.968953i	$0.420475\pi$
$788$		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
$795$	−225.886	+	126.210i	−0.284133	+	0.158755i
$796$		0			0
$797$	−225.230			−0.282597			−0.141298	−	0.989967i	$-0.545128\pi$
$797$	−225.230			−0.282597			−0.141298	+	0.989967i	$0.545128\pi$
$798$		0			0
$799$			1274.38i			1.59496i
$800$		0			0
$801$	−263.142			−0.328517
$802$		0			0
$803$		−	1279.02i		−	1.59280i
$804$		0			0
$805$	−133.748	−	239.376i	−0.166146	−	0.297362i
$806$		0			0
$807$	676.398	+	676.398i	0.838164	+	0.838164i
$808$		0			0
$809$	389.024			0.480870			0.240435	−	0.970665i	$-0.422710\pi$
$809$	389.024			0.480870			0.240435	+	0.970665i	$0.422710\pi$
$810$		0			0
$811$	−235.660	+	235.660i	−0.290580	+	0.290580i	−0.837309	−	0.546730i	$-0.815873\pi$
$811$	−235.660	+	235.660i	−0.290580	+	0.290580i	0.546730	+	0.837309i	$0.315873\pi$
$812$		0			0
$813$			179.149i			0.220356i
$814$		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	$-0.868831\pi$
$821$	−423.452	+	423.452i	−0.515775	+	0.515775i	0.400515	+	0.916290i	$0.368831\pi$
$822$		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
$827$			912.383i			1.10324i	0.834094	+	0.551622i	$0.185991\pi$
$827$			912.383i			1.10324i	−0.834094	+	0.551622i	$0.814009\pi$
$828$		0			0
$829$	401.447	−	401.447i	0.484254	−	0.484254i	−0.422233	−	0.906487i	$-0.638754\pi$
$829$	401.447	−	401.447i	0.484254	−	0.484254i	0.906487	+	0.422233i	$0.138754\pi$
$830$		0			0
$831$	−641.985			−0.772546
$832$		0			0
$833$	−1238.18	−	1238.18i	−1.48641	−	1.48641i
$834$		0			0
$835$	−371.552	+	1312.48i	−0.444973	+	1.57183i
$836$		0			0
$837$		−	258.019i		−	0.308267i
$838$		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
$843$	791.912			0.939398
$844$		0			0
$845$	−2.20547	−	3.94727i	−0.00261003	−	0.00467133i
$846$		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
$853$	−184.144			−0.215878			−0.107939	−	0.994158i	$-0.534425\pi$
$853$	−184.144			−0.215878			−0.107939	+	0.994158i	$0.534425\pi$
$854$		0			0
$855$	−58.4795	−	16.5551i	−0.0683971	−	0.0193627i
$856$		0			0
$857$	−503.631	−	503.631i	−0.587667	−	0.587667i	0.349332	−	0.936999i	$-0.386409\pi$
$857$	−503.631	−	503.631i	−0.587667	−	0.587667i	−0.936999	+	0.349332i	$0.886409\pi$
$858$		0			0
$859$	136.193	+	136.193i	0.158548	+	0.158548i	0.781923	−	0.623375i	$-0.214239\pi$
$859$	136.193	+	136.193i	0.158548	+	0.158548i	−0.623375	+	0.781923i	$0.714239\pi$
$860$		0			0
$861$	16.8899	+	16.8899i	0.0196166	+	0.0196166i
$862$		0			0
$863$	−778.037	−	778.037i	−0.901550	−	0.901550i	0.0940206	−	0.995570i	$-0.470028\pi$
$863$	−778.037	−	778.037i	−0.901550	−	0.901550i	−0.995570	+	0.0940206i	$0.970028\pi$
$864$		0			0
$865$	8.93512	−	4.99236i	0.0103296	−	0.00577151i
$866$		0			0
$867$	1885.54			2.17478
$868$		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
$875$	−859.498	−	935.328i	−0.982283	−	1.06895i
$876$		0			0
$877$	450.954			0.514201			0.257101	−	0.966385i	$-0.417233\pi$
$877$	450.954			0.514201			0.257101	+	0.966385i	$0.417233\pi$
$878$		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
$883$			244.738i			0.277166i	0.990351	+	0.138583i	$0.0442548\pi$
$883$			244.738i			0.277166i	−0.990351	+	0.138583i	$0.955745\pi$
$884$		0			0
$885$	−684.814	−	193.866i	−0.773801	−	0.219057i
$886$		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
$893$		−	176.829i		−	0.198017i
$894$		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
$907$			160.752i			0.177235i	0.996066	+	0.0886177i	$0.0282449\pi$
$907$			160.752i			0.177235i	−0.996066	+	0.0886177i	$0.971755\pi$
$908$		0			0
$909$	−184.471	+	184.471i	−0.202938	+	0.202938i
$910$		0			0
$911$	36.8062			0.0404020			0.0202010	−	0.999796i	$-0.493569\pi$
$911$	36.8062			0.0404020			0.0202010	+	0.999796i	$0.493569\pi$
$912$		0			0
$913$	615.316	+	615.316i	0.673950	+	0.673950i
$914$		0			0
$915$	433.059	+	122.596i	0.473289	+	0.133985i
$916$		0			0
$917$		−	859.116i		−	0.936877i
$918$		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
$923$	−450.781			−0.488386
$924$		0			0
$925$	−689.887	−	424.634i	−0.745824	−	0.459064i
$926$		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
$933$	−25.1951			−0.0270044
$934$		0			0
$935$	1669.89	−	933.022i	1.78597	−	0.997884i
$936$		0			0
$937$	68.4855	+	68.4855i	0.0730902	+	0.0730902i	0.742707	−	0.669617i	$-0.233542\pi$
$937$	68.4855	+	68.4855i	0.0730902	+	0.0730902i	−0.669617	+	0.742707i	$0.733542\pi$
$938$		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	$-0.122881\pi$
$941$	517.439	+	517.439i	0.549882	+	0.549882i	−0.376525	+	0.926407i	$0.622881\pi$
$942$		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
$947$	−1065.70			−1.12534			−0.562672	−	0.826680i	$-0.690227\pi$
$947$	−1065.70			−1.12534			−0.562672	+	0.826680i	$0.690227\pi$
$948$		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	−0.302001	−	0.953307i	$-0.597655\pi$
$953$	620.695	−	620.695i	0.651306	−	0.651306i	0.953307	+	0.302001i	$0.0976547\pi$
$954$		0			0
$955$	−110.490	−	197.751i	−0.115696	−	0.207069i
$956$		0			0
$957$	−771.567			−0.806236
$958$		0			0
$959$		−	1817.13i		−	1.89482i
$960$		0			0
$961$	−883.818			−0.919686
$962$		0			0
$963$		−	121.937i		−	0.126622i
$964$		0			0
$965$	−339.207	+	1198.22i	−0.351510	+	1.24168i
$966$		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	−0.906628	−	0.421931i	$-0.861352\pi$
$971$	−470.641	+	470.641i	−0.484697	+	0.484697i	0.421931	+	0.906628i	$0.361352\pi$
$972$		0			0
$973$		−	594.771i		−	0.611275i
$974$		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
$987$		−	1006.20i		−	1.01946i
$988$		0			0
$989$	220.704	−	220.704i	0.223158	−	0.223158i
$990$		0			0
$991$	1697.53			1.71295			0.856474	−	0.516190i	$-0.172650\pi$
$991$	1697.53			1.71295			0.856474	+	0.516190i	$0.172650\pi$
$992$		0			0
$993$	535.405	+	535.405i	0.539179	+	0.539179i
$994$		0			0
$995$	−465.598	−	833.309i	−0.467938	−	0.837497i
$996$		0			0
$997$		−	1315.01i		−	1.31897i	−0.751720	−	0.659483i	$-0.770775\pi$
$997$		−	1315.01i		−	1.31897i	0.751720	−	0.659483i	$-0.229225\pi$
$998$		0			0
$999$	−951.683			−0.952636

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.22	✓	44	8.5	even	2
80.3.i.a.37.22	yes	44	80.77	odd	4
80.3.t.a.53.11	yes	44	16.13	even	4
80.3.t.a.77.11	yes	44	40.37	odd	4
320.3.i.a.177.6		44	80.67	even	4
320.3.i.a.273.17		44	8.3	odd	2
320.3.t.a.17.17		44	40.27	even	4
320.3.t.a.113.17		44	16.3	odd	4
400.3.i.b.93.1		44	40.29	even	2
400.3.i.b.357.1		44	80.13	odd	4
400.3.t.b.157.12		44	40.13	odd	4
400.3.t.b.293.12		44	80.29	even	4
640.3.i.a.33.6		44	4.3	odd	2
640.3.i.a.97.17		44	80.27	even	4
640.3.i.b.33.17		44	1.1	even	1	trivial
640.3.i.b.97.6		44	80.37	odd	4	inner
640.3.t.a.353.6		44	16.11	odd	4
640.3.t.a.417.6		44	20.7	even	4
640.3.t.b.353.17		44	16.5	even	4
640.3.t.b.417.17		44	5.2	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	640.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.50699i q^{3} +(-2.43881 - 4.36488i) q^{5} +(-7.18571 - 7.18571i) q^{7} +2.71500 q^{9} +O(q^{10})\)	\(q+2.50699i q^{3} +(-2.43881 - 4.36488i) q^{5} +(-7.18571 - 7.18571i) q^{7} +2.71500 q^{9} +(8.38398 - 8.38398i) q^{11} +12.9652i q^{13} +(10.9427 - 6.11407i) q^{15} +(-22.8157 + 22.8157i) q^{17} +(3.16584 - 3.16584i) q^{19} +(18.0145 - 18.0145i) q^{21} +(-3.81600 + 3.81600i) q^{23} +(-13.1044 + 21.2902i) q^{25} +29.3694i q^{27} +(-18.3544 + 18.3544i) q^{29} -8.78531 q^{31} +(21.0186 + 21.0186i) q^{33} +(-13.8402 + 48.8893i) q^{35} +32.4039i q^{37} -32.5036 q^{39} +0.937574i q^{41} -57.8364 q^{43} +(-6.62136 - 11.8506i) q^{45} +(27.9276 - 27.9276i) q^{47} +54.2688i q^{49} +(-57.1987 - 57.1987i) q^{51} -20.6425 q^{53} +(-57.0420 - 16.1482i) q^{55} +(7.93674 + 7.93674i) q^{57} +(-40.1490 - 40.1490i) q^{59} +(25.3893 + 25.3893i) q^{61} +(-19.5092 - 19.5092i) q^{63} +(56.5915 - 31.6196i) q^{65} +29.3419 q^{67} +(-9.56668 - 9.56668i) q^{69} +34.7686i q^{71} +(76.2777 - 76.2777i) q^{73} +(-53.3744 - 32.8527i) q^{75} -120.490 q^{77} +17.2292i q^{79} -49.1938 q^{81} +73.3919i q^{83} +(155.231 + 43.9447i) q^{85} +(-46.0144 - 46.0144i) q^{87} -96.9216 q^{89} +(93.1639 - 93.1639i) q^{91} -22.0247i q^{93} +(-21.5394 - 6.09765i) q^{95} +(-53.4378 + 53.4378i) q^{97} +(22.7625 - 22.7625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{5} - 108 q^{9}+O(q^{10}) \) 44 * q + 2 * q^5 - 108 * q^9	\( 44 q + 2 q^{5} - 108 q^{9} + 4 q^{11} - 4 q^{15} - 4 q^{17} - 32 q^{19} + 4 q^{21} - 8 q^{31} - 4 q^{33} - 96 q^{35} + 72 q^{39} - 124 q^{43} + 34 q^{45} - 4 q^{47} + 100 q^{51} + 4 q^{53} + 36 q^{57} - 64 q^{59} + 36 q^{61} - 200 q^{63} - 4 q^{65} + 292 q^{67} + 60 q^{69} + 48 q^{73} - 96 q^{75} - 192 q^{77} + 100 q^{81} - 48 q^{85} + 36 q^{87} - 188 q^{91} + 380 q^{95} - 4 q^{97} + 92 q^{99}+O(q^{100}) \) 44 * q + 2 * q^5 - 108 * q^9 + 4 * q^11 - 4 * q^15 - 4 * q^17 - 32 * q^19 + 4 * q^21 - 8 * q^31 - 4 * q^33 - 96 * q^35 + 72 * q^39 - 124 * q^43 + 34 * q^45 - 4 * q^47 + 100 * q^51 + 4 * q^53 + 36 * q^57 - 64 * q^59 + 36 * q^61 - 200 * q^63 - 4 * q^65 + 292 * q^67 + 60 * q^69 + 48 * q^73 - 96 * q^75 - 192 * q^77 + 100 * q^81 - 48 * q^85 + 36 * q^87 - 188 * q^91 + 380 * q^95 - 4 * q^97 + 92 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more