LMFDB - Embedded newform 208.4.w.e.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,4,Mod(17,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("208.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	208.w (of order $6$, 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:	$12.2723972812$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 340 x^{18} + 48278 x^{16} + 3724852 x^{14} + 170209937 x^{12} + 4703455168 x^{10} + \cdots + 549543481344 $ x^20 + 340x^18 + 48278x^16 + 3724852x^14 + 170209937x^12 + 4703455168x^10 + 76591569568x^8 + 674465272704x^6 + 2596745246976x^4 + 2244726908928*x^2 + 549543481344
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{40} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.5
Root			$-0.691753i$ of defining polynomial
Character	$\chi$	$=$	208.49
Dual form			208.4.w.e.17.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.154124 + 0.266950i) q^{3} +0.737582i q^{5} +(27.7822 + 16.0401i) q^{7} +(13.4525 - 23.3004i) q^{9} +O(q^{10})$	\(q+(0.154124 + 0.266950i) q^{3} +0.737582i q^{5} +(27.7822 + 16.0401i) q^{7} +(13.4525 - 23.3004i) q^{9} +(-28.2437 + 16.3065i) q^{11} +(-46.6227 + 4.82977i) q^{13} +(-0.196897 + 0.113679i) q^{15} +(20.0831 - 34.7849i) q^{17} +(93.5997 + 54.0398i) q^{19} +9.88860i q^{21} +(108.178 + 187.369i) q^{23} +124.456 q^{25} +16.6161 q^{27} +(107.736 + 186.605i) q^{29} -220.292i q^{31} +(-8.70603 - 5.02643i) q^{33} +(-11.8309 + 20.4916i) q^{35} +(192.423 - 111.095i) q^{37} +(-8.47496 - 11.7015i) q^{39} +(-316.561 + 182.766i) q^{41} +(-40.9836 + 70.9856i) q^{43} +(17.1860 + 9.92231i) q^{45} -92.6883i q^{47} +(343.067 + 594.209i) q^{49} +12.3811 q^{51} +72.5313 q^{53} +(-12.0274 - 20.8320i) q^{55} +33.3152i q^{57} +(-376.044 - 217.109i) q^{59} +(173.006 - 299.655i) q^{61} +(747.479 - 431.557i) q^{63} +(-3.56235 - 34.3880i) q^{65} +(-490.038 + 282.923i) q^{67} +(-33.3454 + 57.7560i) q^{69} +(221.073 + 127.637i) q^{71} -714.554i q^{73} +(19.1816 + 33.2235i) q^{75} -1046.23 q^{77} -365.290 q^{79} +(-360.656 - 624.675i) q^{81} +467.396i q^{83} +(25.6567 + 14.8129i) q^{85} +(-33.2094 + 57.5203i) q^{87} +(-367.132 + 211.964i) q^{89} +(-1372.75 - 613.649i) q^{91} +(58.8069 - 33.9522i) q^{93} +(-39.8588 + 69.0374i) q^{95} +(-513.919 - 296.711i) q^{97} +877.452i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{3} + 54 q^{7} - 72 q^{9}+O(q^{10}) $ 20 * q + 6 * q^3 + 54 * q^7 - 72 * q^9	$ 20 q + 6 q^{3} + 54 q^{7} - 72 q^{9} + 42 q^{11} + 24 q^{13} - 70 q^{17} + 102 q^{19} - 90 q^{23} - 628 q^{25} - 708 q^{27} + 170 q^{29} - 678 q^{33} + 544 q^{35} + 582 q^{37} - 1162 q^{39} + 438 q^{41} - 270 q^{43} + 540 q^{45} + 92 q^{49} + 444 q^{51} - 592 q^{53} + 288 q^{55} - 90 q^{59} + 746 q^{61} + 1068 q^{63} - 1412 q^{65} - 846 q^{67} + 682 q^{69} + 1038 q^{71} - 722 q^{75} + 2812 q^{77} + 1008 q^{79} + 694 q^{81} - 180 q^{85} + 338 q^{87} + 2466 q^{89} - 690 q^{91} - 4764 q^{93} + 2592 q^{95} - 846 q^{97}+O(q^{100}) $ 20 * q + 6 * q^3 + 54 * q^7 - 72 * q^9 + 42 * q^11 + 24 * q^13 - 70 * q^17 + 102 * q^19 - 90 * q^23 - 628 * q^25 - 708 * q^27 + 170 * q^29 - 678 * q^33 + 544 * q^35 + 582 * q^37 - 1162 * q^39 + 438 * q^41 - 270 * q^43 + 540 * q^45 + 92 * q^49 + 444 * q^51 - 592 * q^53 + 288 * q^55 - 90 * q^59 + 746 * q^61 + 1068 * q^63 - 1412 * q^65 - 846 * q^67 + 682 * q^69 + 1038 * q^71 - 722 * q^75 + 2812 * q^77 + 1008 * q^79 + 694 * q^81 - 180 * q^85 + 338 * q^87 + 2466 * q^89 - 690 * q^91 - 4764 * q^93 + 2592 * q^95 - 846 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	0.154124	+	0.266950i	0.0296611	+	0.0513745i	0.880475	−	0.474093i	$-0.157224\pi$
$3$	0.154124	+	0.266950i	0.0296611	+	0.0513745i	−0.850814	+	0.525467i	$0.823891\pi$
$4$		0			0
$5$			0.737582i			0.0659713i	0.999456	+	0.0329857i	$0.0105016\pi$
$5$			0.737582i			0.0659713i	−0.999456	+	0.0329857i	$0.989498\pi$
$6$		0			0
$7$	27.7822	+	16.0401i	1.50010	+	0.866082i	1.00000		0.000112369i	$3.57683e-5\pi$
$7$	27.7822	+	16.0401i	1.50010	+	0.866082i	0.500097	+	0.865969i	$0.333298\pi$
$8$		0			0
$9$	13.4525	−	23.3004i	0.498240	−	0.862978i
$10$		0			0
$11$	−28.2437	+	16.3065i	−0.774162	+	0.446963i	−0.834357	−	0.551224i	$-0.814161\pi$
$11$	−28.2437	+	16.3065i	−0.774162	+	0.446963i	0.0601950	+	0.998187i	$0.480828\pi$
$12$		0			0
$13$	−46.6227	+	4.82977i	−0.994677	+	0.103041i
$13$	−46.6227	+	4.82977i	−0.994677	+	0.103041i
$14$		0			0
$15$	−0.196897	+	0.113679i	−0.00338925	+	0.00195678i
$16$		0			0
$17$	20.0831	−	34.7849i	0.286521	−	0.496270i	−0.686456	−	0.727172i	$-0.740834\pi$
$17$	20.0831	−	34.7849i	0.286521	−	0.496270i	0.972977	+	0.230902i	$0.0741677\pi$
$18$		0			0
$19$	93.5997	+	54.0398i	1.13017	+	0.652504i	0.943978	−	0.330009i	$-0.107052\pi$
$19$	93.5997	+	54.0398i	1.13017	+	0.652504i	0.186193	+	0.982513i	$0.440385\pi$
$20$		0			0
$21$			9.88860i			0.102756i
$22$		0			0
$23$	108.178	+	187.369i	0.980721	+	1.69866i	0.659594	+	0.751622i	$0.270728\pi$
$23$	108.178	+	187.369i	0.980721	+	1.69866i	0.321127	+	0.947036i	$0.395939\pi$
$24$		0			0
$25$	124.456			0.995648
$26$		0			0
$27$	16.6161			0.118436
$28$		0			0
$29$	107.736	+	186.605i	0.689866	+	1.19488i	0.971881	+	0.235473i	$0.0756638\pi$
$29$	107.736	+	186.605i	0.689866	+	1.19488i	−0.282015	+	0.959410i	$0.591003\pi$
$30$		0			0
$31$		−	220.292i		−	1.27631i	−0.769908	−	0.638155i	$-0.779698\pi$
$31$		−	220.292i		−	1.27631i	0.769908	−	0.638155i	$-0.220302\pi$
$32$		0			0
$33$	−8.70603	−	5.02643i	−0.0459250	−	0.0265148i
$34$		0			0
$35$	−11.8309	+	20.4916i	−0.0571365	+	0.0989634i
$36$		0			0
$37$	192.423	−	111.095i	0.854976	−	0.493620i	−0.00735084	−	0.999973i	$-0.502340\pi$
$37$	192.423	−	111.095i	0.854976	−	0.493620i	0.862327	+	0.506353i	$0.169007\pi$
$38$		0			0
$39$	−8.47496	−	11.7015i	−0.0347969	−	0.0480448i
$40$		0			0
$41$	−316.561	+	182.766i	−1.20582	+	0.696179i	−0.961843	−	0.273603i	$-0.911785\pi$
$41$	−316.561	+	182.766i	−1.20582	+	0.696179i	−0.243974	+	0.969782i	$0.578451\pi$
$42$		0			0
$43$	−40.9836	+	70.9856i	−0.145347	+	0.251749i	−0.929502	−	0.368816i	$-0.879763\pi$
$43$	−40.9836	+	70.9856i	−0.145347	+	0.251749i	0.784155	+	0.620565i	$0.213097\pi$
$44$		0			0
$45$	17.1860	+	9.92231i	0.0569318	+	0.0328696i
$46$		0			0
$47$		−	92.6883i		−	0.287659i	−0.989602	−	0.143830i	$-0.954058\pi$
$47$		−	92.6883i		−	0.287659i	0.989602	−	0.143830i	$-0.0459417\pi$
$48$		0			0
$49$	343.067	+	594.209i	1.00019	+	1.73239i
$50$		0			0
$51$	12.3811			0.0339942
$52$		0			0
$53$	72.5313			0.187980			0.0939900	−	0.995573i	$-0.470038\pi$
$53$	72.5313			0.187980			0.0939900	+	0.995573i	$0.470038\pi$
$54$		0			0
$55$	−12.0274	−	20.8320i	−0.0294867	−	0.0510725i
$56$		0			0
$57$			33.3152i			0.0774160i
$58$		0			0
$59$	−376.044	−	217.109i	−0.829776	−	0.479071i	0.0240000	−	0.999712i	$-0.492360\pi$
$59$	−376.044	−	217.109i	−0.829776	−	0.479071i	−0.853776	+	0.520641i	$0.825693\pi$
$60$		0			0
$61$	173.006	−	299.655i	0.363134	−	0.628966i	−0.625341	−	0.780352i	$-0.715040\pi$
$61$	173.006	−	299.655i	0.363134	−	0.628966i	0.988475	+	0.151386i	$0.0483735\pi$
$62$		0			0
$63$	747.479	−	431.557i	1.49482	−	0.863034i
$64$		0			0
$65$	−3.56235	−	34.3880i	−0.00679777	−	0.0656202i
$66$		0			0
$67$	−490.038	+	282.923i	−0.893547	+	0.515890i	−0.875101	−	0.483940i	$-0.839205\pi$
$67$	−490.038	+	282.923i	−0.893547	+	0.515890i	−0.0184460	+	0.999830i	$0.505872\pi$
$68$		0			0
$69$	−33.3454	+	57.7560i	−0.0581785	+	0.100768i
$70$		0			0
$71$	221.073	+	127.637i	0.369529	+	0.213347i	0.673252	−	0.739413i	$-0.264897\pi$
$71$	221.073	+	127.637i	0.369529	+	0.213347i	−0.303724	+	0.952760i	$0.598230\pi$
$72$		0			0
$73$		−	714.554i		−	1.14565i	−0.819679	−	0.572823i	$-0.805848\pi$
$73$		−	714.554i		−	1.14565i	0.819679	−	0.572823i	$-0.194152\pi$
$74$		0			0
$75$	19.1816	+	33.2235i	0.0295320	+	0.0511509i
$76$		0			0
$77$	−1046.23			−1.54843
$78$		0			0
$79$	−365.290			−0.520232			−0.260116	−	0.965577i	$-0.583761\pi$
$79$	−365.290			−0.520232			−0.260116	+	0.965577i	$0.583761\pi$
$80$		0			0
$81$	−360.656	−	624.675i	−0.494728	−	0.856893i
$82$		0			0
$83$			467.396i			0.618113i	0.951044	+	0.309057i	$0.100013\pi$
$83$			467.396i			0.618113i	−0.951044	+	0.309057i	$0.899987\pi$
$84$		0			0
$85$	25.6567	+	14.8129i	0.0327396	+	0.0189022i
$86$		0			0
$87$	−33.2094	+	57.5203i	−0.0409244	+	0.0708831i
$88$		0			0
$89$	−367.132	+	211.964i	−0.437257	+	0.252450i	−0.702433	−	0.711749i	$-0.747903\pi$
$89$	−367.132	+	211.964i	−0.437257	+	0.252450i	0.265176	+	0.964200i	$0.414570\pi$
$90$		0			0
$91$	−1372.75	−	613.649i	−1.58135	−	0.706899i
$92$		0			0
$93$	58.8069	−	33.9522i	0.0655698	−	0.0378568i
$94$		0			0
$95$	−39.8588	+	69.0374i	−0.0430466	+	0.0745589i
$96$		0			0
$97$	−513.919	−	296.711i	−0.537944	−	0.310582i	0.206301	−	0.978489i	$-0.433857\pi$
$97$	−513.919	−	296.711i	−0.537944	−	0.310582i	−0.744245	+	0.667906i	$0.767191\pi$
$98$		0			0
$99$			877.452i			0.890780i
$100$		0			0
$101$	−553.501	−	958.691i	−0.545301	−	0.944489i	−0.998588	−	0.0531242i	$-0.983082\pi$
$101$	−553.501	−	958.691i	−0.545301	−	0.944489i	0.453287	−	0.891365i	$-0.350251\pi$
$102$		0			0
$103$	1164.96			1.11444			0.557219	−	0.830365i	$-0.311868\pi$
$103$	1164.96			1.11444			0.557219	+	0.830365i	$0.311868\pi$
$104$		0			0
$105$	−7.29365			−0.00677893
$106$		0			0
$107$	−175.040	−	303.178i	−0.158147	−	0.273919i	0.776053	−	0.630667i	$-0.217219\pi$
$107$	−175.040	−	303.178i	−0.158147	−	0.273919i	−0.934200	+	0.356749i	$0.883885\pi$
$108$		0			0
$109$		−	591.625i		−	0.519884i	−0.965624	−	0.259942i	$-0.916297\pi$
$109$		−	591.625i		−	0.519884i	0.965624	−	0.259942i	$-0.0837035\pi$
$110$		0			0
$111$	59.3138	+	34.2448i	0.0507190	+	0.0292827i
$112$		0			0
$113$	809.143	−	1401.48i	0.673609	−	1.16672i	−0.303265	−	0.952906i	$-0.598077\pi$
$113$	809.143	−	1401.48i	0.673609	−	1.16672i	0.976873	−	0.213818i	$-0.0685901\pi$
$114$		0			0
$115$	−138.200	+	79.7898i	−0.112063	+	0.0646994i
$116$		0			0
$117$	−514.655	+	1151.30i	−0.406666	+	0.909724i
$118$		0			0
$119$	1115.90	−	644.267i	0.859620	−	0.496302i
$120$		0			0
$121$	−133.697	+	231.569i	−0.100448	+	0.173982i
$122$		0			0
$123$	−97.5790	−	56.3372i	−0.0715317	−	0.0412988i
$124$		0			0
$125$			183.994i			0.131656i
$126$		0			0
$127$	−949.364	−	1644.35i	−0.663326	−	1.14891i	−0.979736	−	0.200292i	$-0.935811\pi$
$127$	−949.364	−	1644.35i	−0.663326	−	1.14891i	0.316410	−	0.948623i	$-0.397522\pi$
$128$		0			0
$129$	−25.2661			−0.0172446
$130$		0			0
$131$	−1481.34			−0.987981			−0.493990	−	0.869467i	$-0.664462\pi$
$131$	−1481.34			−0.987981			−0.493990	+	0.869467i	$0.664462\pi$
$132$		0			0
$133$	1733.60	+	3002.69i	1.13024	+	1.95764i
$134$		0			0
$135$			12.2557i			0.00781336i
$136$		0			0
$137$	726.755	+	419.592i	0.453218	+	0.261665i	0.709188	−	0.705019i	$-0.249062\pi$
$137$	726.755	+	419.592i	0.453218	+	0.261665i	−0.255970	+	0.966685i	$0.582395\pi$
$138$		0			0
$139$	−976.097	+	1690.65i	−0.595622	+	1.03165i	0.397837	+	0.917456i	$0.369761\pi$
$139$	−976.097	+	1690.65i	−0.595622	+	1.03165i	−0.993459	+	0.114191i	$0.963572\pi$
$140$		0			0
$141$	24.7431	−	14.2855i	0.0147783	−	0.00853228i
$142$		0			0
$143$	1238.04	−	896.663i	0.723986	−	0.524355i
$144$		0			0
$145$	−137.636	+	79.4643i	−0.0788280	+	0.0455114i
$146$		0			0
$147$	−105.749	+	183.163i	−0.0593337	+	0.102769i
$148$		0			0
$149$	−2865.97	−	1654.67i	−1.57577	−	0.909771i	−0.995440	−	0.0953883i	$-0.969591\pi$
$149$	−2865.97	−	1654.67i	−1.57577	−	0.909771i	−0.580329	−	0.814382i	$-0.697076\pi$
$150$		0			0
$151$		−	629.237i		−	0.339116i	−0.985520	−	0.169558i	$-0.945766\pi$
$151$		−	629.237i		−	0.339116i	0.985520	−	0.169558i	$-0.0542341\pi$
$152$		0			0
$153$	−540.335	−	935.888i	−0.285513	−	0.494523i
$154$		0			0
$155$	162.483			0.0841999
$156$		0			0
$157$	2430.53			1.23552			0.617761	−	0.786366i	$-0.288040\pi$
$157$	2430.53			1.23552			0.617761	+	0.786366i	$0.288040\pi$
$158$		0			0
$159$	11.1788	+	19.3622i	0.00557569	+	0.00965738i
$160$		0			0
$161$			6940.70i			3.39754i
$162$		0			0
$163$	−1130.75	−	652.838i	−0.543356	−	0.313707i	0.203082	−	0.979162i	$-0.434904\pi$
$163$	−1130.75	−	652.838i	−0.543356	−	0.313707i	−0.746438	+	0.665455i	$0.768238\pi$
$164$		0			0
$165$	3.70740	−	6.42141i	0.00174922	−	0.00302973i
$166$		0			0
$167$	552.127	−	318.771i	0.255838	−	0.147708i	−0.366597	−	0.930380i	$-0.619477\pi$
$167$	552.127	−	318.771i	0.255838	−	0.147708i	0.622434	+	0.782672i	$0.286144\pi$
$168$		0			0
$169$	2150.35	−	450.354i	0.978765	−	0.204986i
$170$		0			0
$171$	2518.30	−	1453.94i	1.12619	−	0.650208i
$172$		0			0
$173$	1768.46	−	3063.05i	0.777186	−	1.34613i	−0.156372	−	0.987698i	$-0.549980\pi$
$173$	1768.46	−	3063.05i	0.777186	−	1.34613i	0.933558	−	0.358427i	$-0.116687\pi$
$174$		0			0
$175$	3457.66	+	1996.28i	1.49357	+	0.862312i
$176$		0			0
$177$		−	133.847i		−	0.0568391i
$178$		0			0
$179$	−559.525	−	969.125i	−0.233636	−	0.404669i	0.725239	−	0.688497i	$-0.241729\pi$
$179$	−559.525	−	969.125i	−0.233636	−	0.404669i	−0.958875	+	0.283827i	$0.908396\pi$
$180$		0			0
$181$	3887.83			1.59658			0.798288	−	0.602276i	$-0.205739\pi$
$181$	3887.83			1.59658			0.798288	+	0.602276i	$0.205739\pi$
$182$		0			0
$183$	106.657			0.0430838
$184$		0			0
$185$	81.9419	+	141.928i	0.0325648	+	0.0564039i
$186$		0			0
$187$			1309.94i			0.512258i
$188$		0			0
$189$	461.631	+	266.523i	0.177665	+	0.102575i
$190$		0			0
$191$	−1925.75	+	3335.49i	−0.729540	+	1.26360i	0.227538	+	0.973769i	$0.426932\pi$
$191$	−1925.75	+	3335.49i	−0.729540	+	1.26360i	−0.957078	+	0.289831i	$0.906401\pi$
$192$		0			0
$193$	−939.979	+	542.697i	−0.350576	+	0.202405i	−0.664939	−	0.746898i	$-0.731542\pi$
$193$	−939.979	+	542.697i	−0.350576	+	0.202405i	0.314363	+	0.949303i	$0.398209\pi$
$194$		0			0
$195$	8.63084	−	6.25098i	0.00316958	−	0.00229560i
$196$		0			0
$197$	−3686.66	+	2128.49i	−1.33332	+	0.769791i	−0.985807	−	0.167885i	$-0.946306\pi$
$197$	−3686.66	+	2128.49i	−1.33332	+	0.769791i	−0.347511	+	0.937676i	$0.612973\pi$
$198$		0			0
$199$	888.559	−	1539.03i	0.316524	−	0.548236i	−0.663236	−	0.748410i	$-0.730818\pi$
$199$	888.559	−	1539.03i	0.316524	−	0.548236i	0.979760	+	0.200174i	$0.0641509\pi$
$200$		0			0
$201$	−151.053	−	87.2104i	−0.0530072	−	0.0306037i
$202$		0			0
$203$			6912.38i			2.38992i
$204$		0			0
$205$	−134.805	−	233.489i	−0.0459278	−	0.0795493i
$206$		0			0
$207$	5821.03			1.95454
$208$		0			0
$209$	−3524.80			−1.16658
$210$		0			0
$211$	−890.710	−	1542.75i	−0.290611	−	0.503354i	0.683343	−	0.730097i	$-0.260525\pi$
$211$	−890.710	−	1542.75i	−0.290611	−	0.503354i	−0.973954	+	0.226744i	$0.927192\pi$
$212$		0			0
$213$			78.6872i			0.0253125i
$214$		0			0
$215$	−52.3577	−	30.2287i	−0.0166082	−	0.00958876i
$216$		0			0
$217$	3533.50	−	6120.20i	1.10539	−	1.91459i
$218$		0			0
$219$	190.750	−	110.130i	0.0588570	−	0.0339811i
$220$		0			0
$221$	−768.324	+	1718.76i	−0.233860	+	0.523151i
$222$		0			0
$223$	−3073.74	+	1774.62i	−0.923017	+	0.532904i	−0.884596	−	0.466358i	$-0.845566\pi$
$223$	−3073.74	+	1774.62i	−0.923017	+	0.532904i	−0.0384205	+	0.999262i	$0.512233\pi$
$224$		0			0
$225$	1674.24	−	2899.87i	0.496072	−	0.859222i
$226$		0			0
$227$	−850.502	−	491.038i	−0.248678	−	0.143574i	0.370481	−	0.928840i	$-0.379193\pi$
$227$	−850.502	−	491.038i	−0.248678	−	0.143574i	−0.619159	+	0.785266i	$0.712526\pi$
$228$		0			0
$229$		−	252.400i		−	0.0728344i	−0.999337	−	0.0364172i	$-0.988405\pi$
$229$		−	252.400i		−	0.0728344i	0.999337	−	0.0364172i	$-0.0115945\pi$
$230$		0			0
$231$	−161.248	−	279.290i	−0.0459280	−	0.0795496i
$232$		0			0
$233$	−3333.08			−0.937155			−0.468577	−	0.883422i	$-0.655233\pi$
$233$	−3333.08			−0.937155			−0.468577	+	0.883422i	$0.655233\pi$
$234$		0			0
$235$	68.3652			0.0189772
$236$		0			0
$237$	−56.2998	−	97.5141i	−0.0154307	−	0.0267267i
$238$		0			0
$239$			1011.52i			0.273766i	0.990587	+	0.136883i	$0.0437084\pi$
$239$			1011.52i			0.273766i	−0.990587	+	0.136883i	$0.956292\pi$
$240$		0			0
$241$	1457.91	+	841.724i	0.389677	+	0.224980i	0.682020	−	0.731333i	$-0.261102\pi$
$241$	1457.91	+	841.724i	0.389677	+	0.224980i	−0.292343	+	0.956314i	$0.594435\pi$
$242$		0			0
$243$	335.488	−	581.082i	0.0885661	−	0.153401i
$244$		0			0
$245$	−438.278	+	253.040i	−0.114288	+	0.0659842i
$246$		0			0
$247$	−4624.87	−	2067.42i	−1.19139	−	0.532577i
$248$		0			0
$249$	−124.771	+	72.0368i	−0.0317553	+	0.0183339i
$250$		0			0
$251$	808.620	−	1400.57i	0.203345	−	0.352204i	−0.746259	−	0.665656i	$-0.768152\pi$
$251$	808.620	−	1400.57i	0.203345	−	0.352204i	0.949604	+	0.313452i	$0.101485\pi$
$252$		0			0
$253$	−6110.66	−	3527.99i	−1.51847	−	0.876692i
$254$		0			0
$255$			9.13208i			0.00224264i
$256$		0			0
$257$	923.279	+	1599.17i	0.224095	+	0.388145i	0.956048	−	0.293211i	$-0.0947239\pi$
$257$	923.279	+	1599.17i	0.224095	+	0.388145i	−0.731952	+	0.681356i	$0.761391\pi$
$258$		0			0
$259$	7127.90			1.71006
$260$		0			0
$261$	5797.28			1.37488
$262$		0			0
$263$	1151.79	+	1994.97i	0.270048	+	0.467737i	0.968874	−	0.247555i	$-0.0796270\pi$
$263$	1151.79	+	1994.97i	0.270048	+	0.467737i	−0.698826	+	0.715292i	$0.746294\pi$
$264$		0			0
$265$			53.4977i			0.0124013i
$266$		0			0
$267$	−113.167	−	65.3372i	−0.0259390	−	0.0149759i
$268$		0			0
$269$	25.8338	−	44.7454i	0.00585543	−	0.0101419i	−0.863083	−	0.505062i	$-0.831469\pi$
$269$	25.8338	−	44.7454i	0.00585543	−	0.0101419i	0.868938	+	0.494920i	$0.164803\pi$
$270$		0			0
$271$	5820.25	−	3360.32i	1.30463	−	0.753229i	0.323437	−	0.946250i	$-0.395162\pi$
$271$	5820.25	−	3360.32i	1.30463	−	0.753229i	0.981195	+	0.193021i	$0.0618284\pi$
$272$		0			0
$273$	−47.7597	−	461.033i	−0.0105881	−	0.102209i
$274$		0			0
$275$	−3515.09	+	2029.44i	−0.770793	+	0.445018i
$276$		0			0
$277$	−2276.49	+	3942.99i	−0.493794	+	0.855277i	−0.999974	−	0.00715116i	$-0.997724\pi$
$277$	−2276.49	+	3942.99i	−0.493794	+	0.855277i	0.506180	+	0.862428i	$0.331057\pi$
$278$		0			0
$279$	−5132.89	−	2963.48i	−1.10143	−	0.635909i
$280$		0			0
$281$		−	1411.11i		−	0.299571i	−0.988719	−	0.149786i	$-0.952142\pi$
$281$		−	1411.11i		−	0.299571i	0.988719	−	0.149786i	$-0.0478583\pi$
$282$		0			0
$283$	−46.1004	−	79.8483i	−0.00968334	−	0.0167720i	0.861143	−	0.508363i	$-0.169749\pi$
$283$	−46.1004	−	79.8483i	−0.00968334	−	0.0167720i	−0.870826	+	0.491591i	$0.836416\pi$
$284$		0			0
$285$	−24.5727			−0.00510724
$286$		0			0
$287$	−11726.3			−2.41179
$288$		0			0
$289$	1649.84	+	2857.61i	0.335811	+	0.581642i
$290$		0			0
$291$		−	182.921i		−	0.0368488i
$292$		0			0
$293$	−1404.55	−	810.917i	−0.280050	−	0.161687i	0.353396	−	0.935474i	$-0.385027\pi$
$293$	−1404.55	−	810.917i	−0.280050	−	0.161687i	−0.633446	+	0.773787i	$0.718360\pi$
$294$		0			0
$295$	160.136	−	277.363i	0.0316050	−	0.0547414i
$296$		0			0
$297$	−469.299	+	270.950i	−0.0916884	+	0.0529363i
$298$		0			0
$299$	−5948.48	−	8213.17i	−1.15053	−	1.58856i
$300$		0			0
$301$	−2277.23	+	1314.76i	−0.436070	+	0.251765i
$302$		0			0
$303$	170.615	−	295.514i	0.0323484	−	0.0560292i
$304$		0			0
$305$	221.020	+	127.606i	0.0414937	+	0.0239564i
$306$		0			0
$307$		−	7127.30i		−	1.32501i	−0.749060	−	0.662503i	$-0.769494\pi$
$307$		−	7127.30i		−	1.32501i	0.749060	−	0.662503i	$-0.230506\pi$
$308$		0			0
$309$	179.548	+	310.987i	0.0330555	+	0.0572538i
$310$		0			0
$311$	−3158.71			−0.575930			−0.287965	−	0.957641i	$-0.592979\pi$
$311$	−3158.71			−0.575930			−0.287965	+	0.957641i	$0.592979\pi$
$312$		0			0
$313$	−5966.01			−1.07738			−0.538688	−	0.842505i	$-0.681080\pi$
$313$	−5966.01			−1.07738			−0.538688	+	0.842505i	$0.681080\pi$
$314$		0			0
$315$	318.309	+	551.327i	0.0569355	+	0.0986151i
$316$		0			0
$317$		−	470.217i		−	0.0833124i	−0.999132	−	0.0416562i	$-0.986737\pi$
$317$		−	470.217i		−	0.0833124i	0.999132	−	0.0416562i	$-0.0132634\pi$
$318$		0			0
$319$	−6085.73	−	3513.60i	−1.06814	−	0.616689i
$320$		0			0
$321$	53.9555	−	93.4537i	0.00938163	−	0.0162495i
$322$		0			0
$323$	3759.54	−	2170.57i	0.647636	−	0.373913i
$324$		0			0
$325$	−5802.47	+	601.094i	−0.990348	+	0.102593i
$326$		0			0
$327$	157.934	−	91.1833i	0.0267088	−	0.0154203i
$328$		0			0
$329$	1486.73	−	2575.08i	0.249136	−	0.431517i
$330$		0			0
$331$	5825.74	+	3363.49i	0.967406	+	0.558532i	0.898445	−	0.439087i	$-0.144698\pi$
$331$	5825.74	+	3363.49i	0.967406	+	0.558532i	0.0689619	+	0.997619i	$0.478031\pi$
$332$		0			0
$333$		−	5978.04i		−	0.983767i
$334$		0			0
$335$	−208.679	−	361.443i	−0.0340339	−	0.0589485i
$336$		0			0
$337$	1456.63			0.235454			0.117727	−	0.993046i	$-0.462439\pi$
$337$	1456.63			0.235454			0.117727	+	0.993046i	$0.462439\pi$
$338$		0			0
$339$	498.832			0.0799199
$340$		0			0
$341$	3592.19	+	6221.86i	0.570463	+	0.988072i
$342$		0			0
$343$			11007.8i			1.73284i
$344$		0			0
$345$	−42.5998	−	24.5950i	−0.00664781	−	0.00383811i
$346$		0			0
$347$	2674.30	−	4632.03i	0.413730	−	0.716601i	−0.581564	−	0.813500i	$-0.697559\pi$
$347$	2674.30	−	4632.03i	0.413730	−	0.716601i	0.995294	+	0.0968995i	$0.0308925\pi$
$348$		0			0
$349$	10895.1	−	6290.30i	1.67107	−	0.964791i	0.704023	−	0.710177i	$-0.251385\pi$
$349$	10895.1	−	6290.30i	1.67107	−	0.964791i	0.967043	−	0.254614i	$-0.0819483\pi$
$350$		0			0
$351$	−774.685	+	80.2518i	−0.117805	+	0.0122038i
$352$		0			0
$353$	−7836.42	+	4524.36i	−1.18156	+	0.682174i	−0.956375	−	0.292143i	$-0.905632\pi$
$353$	−7836.42	+	4524.36i	−1.18156	+	0.682174i	−0.225184	+	0.974316i	$0.572298\pi$
$354$		0			0
$355$	−94.1424	+	163.059i	−0.0140748	+	0.0243783i
$356$		0			0
$357$	343.974	+	198.594i	0.0509945	+	0.0294417i
$358$		0			0
$359$			4356.05i			0.640399i	0.947350	+	0.320200i	$0.103750\pi$
$359$			4356.05i			0.640399i	−0.947350	+	0.320200i	$0.896250\pi$
$360$		0			0
$361$	2411.10	+	4176.15i	0.351524	+	0.608857i
$362$		0			0
$363$	−82.4232			−0.0119176
$364$		0			0
$365$	527.042			0.0755798
$366$		0			0
$367$	752.519	+	1303.40i	0.107033	+	0.185387i	0.914567	−	0.404434i	$-0.132532\pi$
$367$	752.519	+	1303.40i	0.107033	+	0.185387i	−0.807534	+	0.589821i	$0.799198\pi$
$368$		0			0
$369$			9834.66i			1.38746i
$370$		0			0
$371$	2015.08	+	1163.41i	0.281988	+	0.162806i
$372$		0			0
$373$	3903.51	−	6761.09i	0.541867	−	0.938541i	−0.456930	−	0.889503i	$-0.651051\pi$
$373$	3903.51	−	6761.09i	0.541867	−	0.938541i	0.998797	−	0.0490383i	$-0.0156156\pi$
$374$		0			0
$375$	−49.1172	+	28.3578i	−0.00676374	+	0.00390505i
$376$		0			0
$377$	−5924.21	−	8179.66i	−0.809316	−	1.11744i
$378$		0			0
$379$	2483.03	−	1433.58i	0.336529	−	0.194295i	−0.322207	−	0.946669i	$-0.604425\pi$
$379$	2483.03	−	1433.58i	0.336529	−	0.194295i	0.658736	+	0.752374i	$0.271091\pi$
$380$		0			0
$381$	292.639	−	506.865i	0.0393500	−	0.0681562i
$382$		0			0
$383$	−848.922	−	490.125i	−0.113258	−	0.0653896i	0.442301	−	0.896867i	$-0.354162\pi$
$383$	−848.922	−	490.125i	−0.113258	−	0.0653896i	−0.555559	+	0.831477i	$0.687496\pi$
$384$		0			0
$385$		−	771.679i		−	0.102152i
$386$		0			0
$387$	1102.66	+	1909.87i	0.144836	+	0.250863i
$388$		0			0
$389$	2880.85			0.375488			0.187744	−	0.982218i	$-0.439882\pi$
$389$	2880.85			0.375488			0.187744	+	0.982218i	$0.439882\pi$
$390$		0			0
$391$	8690.15			1.12399
$392$		0			0
$393$	−228.310	−	395.444i	−0.0293046	−	0.0507570i
$394$		0			0
$395$		−	269.431i		−	0.0343204i
$396$		0			0
$397$	−6993.51	−	4037.70i	−0.884116	−	0.510445i	−0.0121027	−	0.999927i	$-0.503853\pi$
$397$	−6993.51	−	4037.70i	−0.884116	−	0.510445i	−0.872013	+	0.489482i	$0.837186\pi$
$398$		0			0
$399$	−534.378	+	925.570i	−0.0670486	+	0.116132i
$400$		0			0
$401$	5994.02	−	3460.65i	0.746451	−	0.430964i	−0.0779589	−	0.996957i	$-0.524840\pi$
$401$	5994.02	−	3460.65i	0.746451	−	0.430964i	0.824410	+	0.565993i	$0.191507\pi$
$402$		0			0
$403$	1063.96	+	10270.6i	0.131513	+	1.26952i
$404$		0			0
$405$	460.749	−	266.014i	0.0565304	−	0.0326378i
$406$		0			0
$407$	−3623.15	+	6275.48i	−0.441260	+	0.764285i
$408$		0			0
$409$	−6611.17	−	3816.96i	−0.799270	−	0.461459i	0.0439456	−	0.999034i	$-0.486007\pi$
$409$	−6611.17	−	3816.96i	−0.799270	−	0.461459i	−0.843216	+	0.537575i	$0.819340\pi$
$410$		0			0
$411$			258.676i			0.0310451i
$412$		0			0
$413$	−6964.89	−	12063.5i	−0.829830	−	1.43731i
$414$		0			0
$415$	−344.743			−0.0407778
$416$		0			0
$417$	−601.758			−0.0706672
$418$		0			0
$419$	4848.23	+	8397.37i	0.565278	+	0.979090i	0.997024	+	0.0770945i	$0.0245643\pi$
$419$	4848.23	+	8397.37i	0.565278	+	0.979090i	−0.431746	+	0.901995i	$0.642102\pi$
$420$		0			0
$421$			15426.4i			1.78584i	0.450214	+	0.892921i	$0.351348\pi$
$421$			15426.4i			1.78584i	−0.450214	+	0.892921i	$0.648652\pi$
$422$		0			0
$423$	−2159.67	−	1246.89i	−0.248243	−	0.143323i
$424$		0			0
$425$	2499.46	−	4329.19i	0.285274	−	0.494110i
$426$		0			0
$427$	9612.97	−	5550.05i	1.08947	−	0.629007i
$428$		0			0
$429$	430.175	+	192.297i	0.0484127	+	0.0216415i
$430$		0			0
$431$	−6646.72	+	3837.48i	−0.742833	+	0.428875i	−0.823098	−	0.567899i	$-0.807757\pi$
$431$	−6646.72	+	3837.48i	−0.742833	+	0.428875i	0.0802654	+	0.996774i	$0.474423\pi$
$432$		0			0
$433$	1125.29	−	1949.05i	0.124891	−	0.216317i	−0.796799	−	0.604244i	$-0.793475\pi$
$433$	1125.29	−	1949.05i	0.124891	−	0.216317i	0.921690	+	0.387927i	$0.126809\pi$
$434$		0			0
$435$	−42.4260	−	24.4946i	−0.00467625	−	0.00269983i
$436$		0			0
$437$			23383.6i			2.55970i
$438$		0			0
$439$	1926.47	+	3336.74i	0.209442	+	0.362765i	0.951539	−	0.307528i	$-0.0995018\pi$
$439$	1926.47	+	3336.74i	0.209442	+	0.362765i	−0.742097	+	0.670293i	$0.766168\pi$
$440$		0			0
$441$	18460.4			1.99335
$442$		0			0
$443$	1051.06			0.112725			0.0563626	−	0.998410i	$-0.482050\pi$
$443$	1051.06			0.112725			0.0563626	+	0.998410i	$0.482050\pi$
$444$		0			0
$445$	−156.340	−	270.790i	−0.0166545	−	0.0288464i
$446$		0			0
$447$		−	1020.09i		−	0.107939i
$448$		0			0
$449$	4815.35	+	2780.14i	0.506125	+	0.292212i	0.731240	−	0.682121i	$-0.238942\pi$
$449$	4815.35	+	2780.14i	0.506125	+	0.292212i	−0.225114	+	0.974332i	$0.572275\pi$
$450$		0			0
$451$	5960.56	−	10324.0i	0.622332	−	1.07791i
$452$		0			0
$453$	167.975	−	96.9802i	0.0174219	−	0.0100586i
$454$		0			0
$455$	452.616	−	1012.52i	0.0466351	−	0.104324i
$456$		0			0
$457$	11246.4	−	6493.09i	1.15116	−	0.664625i	0.201994	−	0.979387i	$-0.435258\pi$
$457$	11246.4	−	6493.09i	1.15116	−	0.664625i	0.949171	+	0.314762i	$0.101925\pi$
$458$		0			0
$459$	333.702	−	577.988i	0.0339343	−	0.0587760i
$460$		0			0
$461$	11932.7	+	6889.36i	1.20556	+	0.696029i	0.961786	−	0.273803i	$-0.0882817\pi$
$461$	11932.7	+	6889.36i	1.20556	+	0.696029i	0.243772	+	0.969832i	$0.421615\pi$
$462$		0			0
$463$			7777.18i			0.780640i	0.920679	+	0.390320i	$0.127636\pi$
$463$			7777.18i			0.780640i	−0.920679	+	0.390320i	$0.872364\pi$
$464$		0			0
$465$	25.0425	+	43.3749i	0.00249746	+	0.00432573i
$466$		0			0
$467$	11585.5			1.14800			0.573999	−	0.818856i	$-0.305391\pi$
$467$	11585.5			1.14800			0.573999	+	0.818856i	$0.305391\pi$
$468$		0			0
$469$	−18152.4			−1.78721
$470$		0			0
$471$	374.601	+	648.829i	0.0366470	+	0.0634744i
$472$		0			0
$473$		−	2673.19i		−	0.259859i
$474$		0			0
$475$	11649.0	+	6725.58i	1.12525	+	0.649665i
$476$		0			0
$477$	975.726	−	1690.01i	0.0936592	−	0.162222i
$478$		0			0
$479$	−6216.77	+	3589.25i	−0.593009	+	0.342374i	−0.766286	−	0.642499i	$-0.777898\pi$
$479$	−6216.77	+	3589.25i	−0.593009	+	0.342374i	0.173277	+	0.984873i	$0.444564\pi$
$480$		0			0
$481$	−8434.70	+	6108.92i	−0.799561	+	0.579091i
$482$		0			0
$483$	−1852.82	+	1069.72i	−0.174547	+	0.100775i
$484$		0			0
$485$	218.849	−	379.057i	0.0204895	−	0.0354889i
$486$		0			0
$487$	−13093.5	−	7559.56i	−1.21833	−	0.703401i	−0.253767	−	0.967265i	$-0.581670\pi$
$487$	−13093.5	−	7559.56i	−1.21833	−	0.703401i	−0.964560	+	0.263864i	$0.915003\pi$
$488$		0			0
$489$		−	402.471i		−	0.0372195i
$490$		0			0
$491$	−10060.6	−	17425.5i	−0.924704	−	1.60163i	−0.792037	−	0.610474i	$-0.790979\pi$
$491$	−10060.6	−	17425.5i	−0.924704	−	1.60163i	−0.132667	−	0.991161i	$-0.542354\pi$
$492$		0			0
$493$	8654.70			0.790645
$494$		0			0
$495$	−647.192			−0.0587659
$496$		0			0
$497$	4094.59	+	7092.04i	0.369553	+	0.640084i
$498$		0			0
$499$			10711.2i			0.960923i	0.877016	+	0.480462i	$0.159531\pi$
$499$			10711.2i			0.960923i	−0.877016	+	0.480462i	$0.840469\pi$
$500$		0			0
$501$	170.192	+	98.2602i	0.0151768	+	0.00876236i
$502$		0			0
$503$	3472.96	−	6015.34i	0.307856	−	0.533222i	−0.670037	−	0.742328i	$-0.733722\pi$
$503$	3472.96	−	6015.34i	0.307856	−	0.533222i	0.977893	+	0.209105i	$0.0670551\pi$
$504$		0			0
$505$	707.113	−	408.252i	0.0623092	−	0.0359742i
$506$		0			0
$507$	451.641	+	504.625i	0.0395623	+	0.0442035i
$508$		0			0
$509$	−1808.20	+	1043.96i	−0.157460	+	0.0909093i	−0.576659	−	0.816985i	$-0.695644\pi$
$509$	−1808.20	+	1043.96i	−0.157460	+	0.0909093i	0.419200	+	0.907894i	$0.362311\pi$
$510$		0			0
$511$	11461.5	−	19851.9i	0.992223	−	1.71858i
$512$		0			0
$513$	1555.26	+	897.929i	0.133852	+	0.0772798i
$514$		0			0
$515$			859.255i			0.0735210i
$516$		0			0
$517$	1511.42	+	2617.86i	0.128573	+	0.222695i
$518$		0			0
$519$	1090.24			0.0922088
$520$		0			0
$521$	1510.31			0.127002			0.0635009	−	0.997982i	$-0.479773\pi$
$521$	1510.31			0.127002			0.0635009	+	0.997982i	$0.479773\pi$
$522$		0			0
$523$	−820.842	−	1421.74i	−0.0686289	−	0.118869i	0.829669	−	0.558255i	$-0.188529\pi$
$523$	−820.842	−	1421.74i	−0.0686289	−	0.118869i	−0.898298	+	0.439387i	$0.855196\pi$
$524$		0			0
$525$			1230.70i			0.102309i
$526$		0			0
$527$	−7662.84	−	4424.14i	−0.633394	−	0.365690i
$528$		0			0
$529$	−17321.3	+	30001.3i	−1.42363	+	2.46579i
$530$		0			0
$531$	−10117.5	+	5841.32i	−0.826856	+	0.477385i
$532$		0			0
$533$	13876.2	−	10050.0i	1.12766	−	0.816722i
$534$		0			0
$535$	223.618	−	129.106i	0.0180708	−	0.0104332i
$536$		0			0
$537$	172.472	−	298.730i	0.0138598	−	0.0240059i
$538$		0			0
$539$	−19378.9	−	11188.4i	−1.54863	−	0.894100i
$540$		0			0
$541$		−	7124.73i		−	0.566204i	−0.959090	−	0.283102i	$-0.908637\pi$
$541$		−	7124.73i		−	0.566204i	0.959090	−	0.283102i	$-0.0913634\pi$
$542$		0			0
$543$	599.207	+	1037.86i	0.0473562	+	0.0820233i
$544$		0			0
$545$	436.372			0.0342974
$546$		0			0
$547$	−19252.4			−1.50488			−0.752442	−	0.658659i	$-0.771124\pi$
$547$	−19252.4			−1.50488			−0.752442	+	0.658659i	$0.771124\pi$
$548$		0			0
$549$	−4654.72	−	8062.22i	−0.361856	−	0.626753i
$550$		0			0
$551$			23288.2i			1.80056i
$552$		0			0
$553$	−10148.6	−	5859.27i	−0.780399	−	0.450563i
$554$		0			0
$555$	−25.2584	+	43.7488i	−0.00193182	+	0.00334600i
$556$		0			0
$557$	−4704.14	+	2715.94i	−0.357847	+	0.206603i	−0.668136	−	0.744039i	$-0.732908\pi$
$557$	−4704.14	+	2715.94i	−0.357847	+	0.206603i	0.310289	+	0.950642i	$0.399574\pi$
$558$		0			0
$559$	1567.92	−	3507.48i	0.118633	−	0.265386i
$560$		0			0
$561$	−349.688	+	201.892i	−0.0263170	+	0.0151941i
$562$		0			0
$563$	11651.1	−	20180.3i	0.872177	−	1.51065i	0.0124369	−	0.999923i	$-0.496041\pi$
$563$	11651.1	−	20180.3i	0.872177	−	1.51065i	0.859740	−	0.510732i	$-0.170626\pi$
$564$		0			0
$565$	1033.70	+	596.809i	0.0769704	+	0.0444389i
$566$		0			0
$567$		−	23139.8i		−	1.71390i
$568$		0			0
$569$	−10745.6	−	18611.9i	−0.791702	−	1.37127i	−0.924913	−	0.380180i	$-0.875862\pi$
$569$	−10745.6	−	18611.9i	−0.791702	−	1.37127i	0.133211	−	0.991088i	$-0.457471\pi$
$570$		0			0
$571$	7960.29			0.583411			0.291706	−	0.956508i	$-0.405777\pi$
$571$	7960.29			0.583411			0.291706	+	0.956508i	$0.405777\pi$
$572$		0			0
$573$	−1187.21			−0.0865558
$574$		0			0
$575$	13463.3	+	23319.2i	0.976452	+	1.69127i
$576$		0			0
$577$		−	11828.5i		−	0.853428i	−0.904387	−	0.426714i	$-0.859671\pi$
$577$		−	11828.5i		−	0.853428i	0.904387	−	0.426714i	$-0.140329\pi$
$578$		0			0
$579$	−289.746	−	167.285i	−0.0207970	−	0.0120071i
$580$		0			0
$581$	−7497.06	+	12985.3i	−0.535337	+	0.927230i
$582$		0			0
$583$	−2048.55	+	1182.73i	−0.145527	+	0.0840200i
$584$		0			0
$585$	−849.177	−	379.601i	−0.0600157	−	0.0268283i
$586$		0			0
$587$	−18939.4	+	10934.7i	−1.33171	+	0.768864i	−0.985562	−	0.169316i	$-0.945844\pi$
$587$	−18939.4	+	10934.7i	−1.33171	+	0.768864i	−0.346149	+	0.938179i	$0.612511\pi$
$588$		0			0
$589$	11904.5	−	20619.3i	0.832798	−	1.44245i
$590$		0			0
$591$	−1136.40	−	656.102i	−0.0790953	−	0.0456657i
$592$		0			0
$593$			13550.2i			0.938346i	0.883106	+	0.469173i	$0.155448\pi$
$593$			13550.2i			0.938346i	−0.883106	+	0.469173i	$0.844552\pi$
$594$		0			0
$595$	475.200	+	823.071i	0.0327417	+	0.0567103i
$596$		0			0
$597$	547.792			0.0375538
$598$		0			0
$599$	17375.9			1.18524			0.592620	−	0.805482i	$-0.298094\pi$
$599$	17375.9			1.18524			0.592620	+	0.805482i	$0.298094\pi$
$600$		0			0
$601$	−3110.59	−	5387.69i	−0.211121	−	0.365672i	0.740945	−	0.671566i	$-0.234378\pi$
$601$	−3110.59	−	5387.69i	−0.211121	−	0.365672i	−0.952066	+	0.305894i	$0.901045\pi$
$602$		0			0
$603$			15224.1i			1.02815i
$604$		0			0
$605$	−170.801	−	98.6122i	−0.0114778	−	0.00662671i
$606$		0			0
$607$	5691.52	−	9858.00i	0.380579	−	0.659182i	−0.610566	−	0.791965i	$-0.709058\pi$
$607$	5691.52	−	9858.00i	0.380579	−	0.659182i	0.991145	+	0.132783i	$0.0423913\pi$
$608$		0			0
$609$	−1845.26	+	1065.36i	−0.122781	+	0.0708877i
$610$		0			0
$611$	447.663	+	4321.37i	0.0296408	+	0.286128i
$612$		0			0
$613$	−612.483	+	353.617i	−0.0403555	+	0.0232993i	−0.520042	−	0.854141i	$-0.674084\pi$
$613$	−612.483	+	353.617i	−0.0403555	+	0.0232993i	0.479687	+	0.877440i	$0.340750\pi$
$614$		0			0
$615$	41.5533	−	71.9725i	0.00272454	−	0.00471904i
$616$		0			0
$617$	−12739.8	−	7355.33i	−0.831257	−	0.479926i	0.0230261	−	0.999735i	$-0.492670\pi$
$617$	−12739.8	−	7355.33i	−0.831257	−	0.479926i	−0.854283	+	0.519809i	$0.826003\pi$
$618$		0			0
$619$			2155.84i			0.139985i	0.997548	+	0.0699925i	$0.0222975\pi$
$619$			2155.84i			0.139985i	−0.997548	+	0.0699925i	$0.977702\pi$
$620$		0			0
$621$	1797.48	+	3113.33i	0.116152	+	0.201182i
$622$		0			0
$623$	−13599.6			−0.874571
$624$		0			0
$625$	15421.3			0.986962
$626$		0			0
$627$	−543.255	−	940.945i	−0.0346021	−	0.0599326i
$628$		0			0
$629$		−	8924.55i		−	0.565731i
$630$		0			0
$631$	−965.813	−	557.613i	−0.0609325	−	0.0351794i	0.469224	−	0.883079i	$-0.344534\pi$
$631$	−965.813	−	557.613i	−0.0609325	−	0.0351794i	−0.530157	+	0.847900i	$0.677867\pi$
$632$		0			0
$633$	274.559	−	475.550i	0.0172397	−	0.0298600i
$634$		0			0
$635$	1212.84	−	700.234i	0.0757954	−	0.0437605i
$636$		0			0
$637$	−18864.6	−	26046.7i	−1.17338	−	1.62011i
$638$		0			0
$639$	5947.96	−	3434.06i	0.368228	−	0.212597i
$640$		0			0
$641$	−4847.34	+	8395.84i	−0.298687	+	0.517341i	−0.975836	−	0.218505i	$-0.929882\pi$
$641$	−4847.34	+	8395.84i	−0.298687	+	0.517341i	0.677149	+	0.735846i	$0.263215\pi$
$642$		0			0
$643$	−17749.4	−	10247.6i	−1.08860	−	0.628503i	−0.155396	−	0.987852i	$-0.549665\pi$
$643$	−17749.4	−	10247.6i	−1.08860	−	0.628503i	−0.933203	+	0.359349i	$0.882999\pi$
$644$		0			0
$645$		−	18.6358i		−	0.00113765i
$646$		0			0
$647$	−2743.28	−	4751.51i	−0.166692	−	0.288719i	0.770563	−	0.637364i	$-0.219975\pi$
$647$	−2743.28	−	4751.51i	−0.166692	−	0.288719i	−0.937255	+	0.348645i	$0.886642\pi$
$648$		0			0
$649$	14161.2			0.856509
$650$		0			0
$651$	2178.38			0.131148
$652$		0			0
$653$	−9669.19	−	16747.5i	−0.579456	−	1.00365i	−0.995542	−	0.0943219i	$-0.969932\pi$
$653$	−9669.19	−	16747.5i	−0.579456	−	1.00365i	0.416086	−	0.909325i	$-0.363402\pi$
$654$		0			0
$655$		−	1092.61i		−	0.0651784i
$656$		0			0
$657$	−16649.4	−	9612.53i	−0.988667	−	0.570807i
$658$		0			0
$659$	7871.01	−	13633.0i	0.465267	−	0.805866i	−0.533947	−	0.845518i	$-0.679292\pi$
$659$	7871.01	−	13633.0i	0.465267	−	0.805866i	0.999214	+	0.0396523i	$0.0126250\pi$
$660$		0			0
$661$	−5677.62	+	3277.98i	−0.334091	+	0.192887i	−0.657656	−	0.753319i	$-0.728452\pi$
$661$	−5677.62	+	3277.98i	−0.334091	+	0.192887i	0.323565	+	0.946206i	$0.395118\pi$
$662$		0			0
$663$	−577.240	+	59.7979i	−0.0338132	+	0.00350280i
$664$		0			0
$665$	−2214.73	+	1278.67i	−0.129148	+	0.0745637i
$666$		0			0
$667$	−23309.3	+	40372.8i	−1.35313	+	2.34369i
$668$		0			0
$669$	−947.471	−	547.023i	−0.0547554	−	0.0316130i
$670$		0			0
$671$			11284.5i			0.649229i
$672$		0			0
$673$	−7594.70	−	13154.4i	−0.434999	−	0.753440i	0.562297	−	0.826936i	$-0.309918\pi$
$673$	−7594.70	−	13154.4i	−0.434999	−	0.753440i	−0.997296	+	0.0734954i	$0.976585\pi$
$674$		0			0
$675$	2067.97			0.117920
$676$		0			0
$677$	−20225.1			−1.14817			−0.574087	−	0.818794i	$-0.694643\pi$
$677$	−20225.1			−1.14817			−0.574087	+	0.818794i	$0.694643\pi$
$678$		0			0
$679$	−9518.53	−	16486.6i	−0.537979	−	0.931807i
$680$		0			0
$681$		−	302.722i		−	0.0170343i
$682$		0			0
$683$	27528.8	+	15893.8i	1.54225	+	0.890421i	0.998696	+	0.0510497i	$0.0162567\pi$
$683$	27528.8	+	15893.8i	1.54225	+	0.890421i	0.543558	+	0.839371i	$0.317077\pi$
$684$		0			0
$685$	−309.483	+	536.041i	−0.0172624	+	0.0298994i
$686$		0			0
$687$	67.3782	−	38.9008i	0.00374183	−	0.00216035i
$688$		0			0
$689$	−3381.60	+	350.309i	−0.186979	+	0.0193697i
$690$		0			0
$691$	−18513.2	+	10688.6i	−1.01921	+	0.588441i	−0.913875	−	0.405996i	$-0.866925\pi$
$691$	−18513.2	+	10688.6i	−1.01921	+	0.588441i	−0.105335	+	0.994437i	$0.533592\pi$
$692$		0			0
$693$	−14074.4	+	24377.5i	−0.771488	+	1.33626i
$694$		0			0
$695$	−1246.99	−	719.951i	−0.0680591	−	0.0392940i
$696$		0			0
$697$			14682.1i			0.797880i
$698$		0			0
$699$	−513.706	−	889.764i	−0.0277970	−	0.0481459i
$700$		0			0
$701$	16159.9			0.870688			0.435344	−	0.900264i	$-0.356627\pi$
$701$	16159.9			0.870688			0.435344	+	0.900264i	$0.356627\pi$
$702$		0			0
$703$	24014.3			1.28836
$704$		0			0
$705$	10.5367	+	18.2501i	0.000562886	+	0.000974947i
$706$		0			0
$707$		−	35512.7i		−	1.88910i
$708$		0			0
$709$	23410.3	+	13515.9i	1.24004	+	0.715939i	0.969103	−	0.246657i	$-0.0793321\pi$
$709$	23410.3	+	13515.9i	1.24004	+	0.715939i	0.270940	+	0.962596i	$0.412665\pi$
$710$		0			0
$711$	−4914.06	+	8511.40i	−0.259201	+	0.448949i
$712$		0			0
$713$	41275.9	−	23830.7i	2.16801	−	1.25170i
$714$		0			0
$715$	661.362	+	913.155i	0.0345924	+	0.0477623i
$716$		0			0
$717$	−270.026	+	155.900i	−0.0140646	+	0.00812019i
$718$		0			0
$719$	15580.2	−	26985.7i	0.808126	−	1.39971i	−0.106035	−	0.994362i	$-0.533815\pi$
$719$	15580.2	−	26985.7i	0.808126	−	1.39971i	0.914160	−	0.405353i	$-0.132851\pi$
$720$		0			0
$721$	32365.2	+	18686.1i	1.67177	+	0.965195i
$722$		0			0
$723$			518.918i			0.0266926i
$724$		0			0
$725$	13408.4	+	23224.1i	0.686863	+	1.18968i
$726$		0			0
$727$	−5870.86			−0.299502			−0.149751	−	0.988724i	$-0.547847\pi$
$727$	−5870.86			−0.299502			−0.149751	+	0.988724i	$0.547847\pi$
$728$		0			0
$729$	−19268.6			−0.978947
$730$		0			0
$731$	1646.15	+	2851.22i	0.0832902	+	0.144263i
$732$		0			0
$733$			38396.1i			1.93478i	0.253299	+	0.967388i	$0.418484\pi$
$733$			38396.1i			1.93478i	−0.253299	+	0.967388i	$0.581516\pi$
$734$		0			0
$735$	−135.098	−	77.9988i	−0.00677981	−	0.00391433i
$736$		0			0
$737$	9226.98	−	15981.6i	0.461167	−	0.798765i
$738$		0			0
$739$	−25387.3	+	14657.4i	−1.26372	+	0.729609i	−0.973792	−	0.227440i	$-0.926964\pi$
$739$	−25387.3	+	14657.4i	−1.26372	+	0.729609i	−0.289927	+	0.957049i	$0.593631\pi$
$740$		0			0
$741$	−160.905	−	1553.25i	−0.00797705	−	0.0770039i
$742$		0			0
$743$	13045.0	−	7531.55i	0.644112	−	0.371878i	−0.142085	−	0.989855i	$-0.545380\pi$
$743$	13045.0	−	7531.55i	0.644112	−	0.371878i	0.786197	+	0.617976i	$0.212047\pi$
$744$		0			0
$745$	1220.45	−	2113.89i	0.0600188	−	0.103956i
$746$		0			0
$747$	10890.5	+	6287.64i	0.533418	+	0.307969i
$748$		0			0
$749$		−	11230.6i		−	0.547873i
$750$		0			0
$751$	13884.3	+	24048.3i	0.674628	+	1.16849i	0.976578	+	0.215166i	$0.0690291\pi$
$751$	13884.3	+	24048.3i	0.674628	+	1.16849i	−0.301950	+	0.953324i	$0.597638\pi$
$752$		0			0
$753$	498.509			0.0241258
$754$		0			0
$755$	464.114			0.0223720
$756$		0			0
$757$	3919.53	+	6788.83i	0.188187	+	0.325950i	0.944646	−	0.328092i	$-0.106405\pi$
$757$	3919.53	+	6788.83i	0.188187	+	0.325950i	−0.756459	+	0.654042i	$0.773072\pi$
$758$		0			0
$759$		−	2174.99i		−	0.104015i
$760$		0			0
$761$	−3241.72	−	1871.61i	−0.154418	−	0.0891535i	0.420800	−	0.907154i	$-0.361749\pi$
$761$	−3241.72	−	1871.61i	−0.154418	−	0.0891535i	−0.575218	+	0.818000i	$0.695083\pi$
$762$		0			0
$763$	9489.69	−	16436.6i	0.450262	−	0.779877i
$764$		0			0
$765$	690.294	−	398.541i	0.0326243	−	0.0188357i
$766$		0			0
$767$	18580.8	+	8306.00i	0.874723	+	0.391020i
$768$		0			0
$769$	−5934.01	+	3426.00i	−0.278265	+	0.160656i	−0.632638	−	0.774448i	$-0.718028\pi$
$769$	−5934.01	+	3426.00i	−0.278265	+	0.160656i	0.354373	+	0.935104i	$0.384694\pi$
$770$		0			0
$771$	−284.598	+	492.938i	−0.0132938	+	0.0230256i
$772$		0			0
$773$	9522.78	+	5497.98i	0.443093	+	0.255820i	0.704909	−	0.709298i	$-0.250988\pi$
$773$	9522.78	+	5497.98i	0.443093	+	0.255820i	−0.261816	+	0.965118i	$0.584321\pi$
$774$		0			0
$775$		−	27416.7i		−	1.27076i
$776$		0			0
$777$	1098.58	+	1902.79i	0.0507223	+	0.0878537i
$778$		0			0
$779$	−39506.7			−1.81704
$780$		0			0
$781$	−8325.21			−0.381434
$782$		0			0
$783$	1790.15	+	3100.63i	0.0817047	+	0.141517i
$784$		0			0
$785$			1792.71i			0.0815091i
$786$		0			0
$787$	−21068.9	−	12164.1i	−0.954288	−	0.550959i	−0.0598779	−	0.998206i	$-0.519071\pi$
$787$	−21068.9	−	12164.1i	−0.954288	−	0.550959i	−0.894410	+	0.447247i	$0.852404\pi$
$788$		0			0
$789$	−355.037	+	614.943i	−0.0160199	+	0.0277472i
$790$		0			0
$791$	44959.5	−	25957.4i	2.02096	−	1.16680i
$792$		0			0
$793$	−6618.74	+	14806.3i	−0.296391	+	0.663036i
$794$		0			0
$795$	−14.2812	+	8.24526i	−0.000637110	+	0.000367836i
$796$		0			0
$797$	2144.78	−	3714.87i	0.0953224	−	0.165103i	−0.814421	−	0.580275i	$-0.802945\pi$
$797$	2144.78	−	3714.87i	0.0953224	−	0.165103i	0.909743	+	0.415172i	$0.136278\pi$
$798$		0			0
$799$	−3224.15	−	1861.47i	−0.142756	−	0.0824205i
$800$		0			0
$801$			11405.7i			0.503124i
$802$		0			0
$803$	11651.9	+	20181.6i	0.512061	+	0.886916i
$804$		0			0
$805$	−5119.33			−0.224140
$806$		0			0
$807$	15.9264			0.000694715
$808$		0			0
$809$	13605.0	+	23564.6i	0.591257	+	1.02409i	0.994063	+	0.108802i	$0.0347014\pi$
$809$	13605.0	+	23564.6i	0.591257	+	1.02409i	−0.402806	+	0.915285i	$0.631965\pi$
$810$		0			0
$811$			3611.93i			0.156390i	0.996938	+	0.0781949i	$0.0249157\pi$
$811$			3611.93i			0.156390i	−0.996938	+	0.0781949i	$0.975084\pi$
$812$		0			0
$813$	1794.08	+	1035.81i	0.0773936	+	0.0446832i
$814$		0			0
$815$	481.521	−	834.019i	0.0206956	−	0.0358459i
$816$		0			0
$817$	−7672.10	+	4429.49i	−0.328535	+	0.189680i
$818$		0			0
$819$	−32765.2	+	23730.5i	−1.39793	+	1.01247i
$820$		0			0
$821$	27414.2	−	15827.6i	1.16536	−	0.672821i	0.212778	−	0.977101i	$-0.431749\pi$
$821$	27414.2	−	15827.6i	1.16536	−	0.672821i	0.952583	+	0.304280i	$0.0984157\pi$
$822$		0			0
$823$	−16513.5	+	28602.2i	−0.699421	+	1.21143i	0.269247	+	0.963071i	$0.413225\pi$
$823$	−16513.5	+	28602.2i	−0.699421	+	1.21143i	−0.968667	+	0.248361i	$0.920108\pi$
$824$		0			0
$825$	−1083.52	−	625.569i	−0.0457251	−	0.0263994i
$826$		0			0
$827$		−	27077.7i		−	1.13855i	−0.822146	−	0.569276i	$-0.807224\pi$
$827$		−	27077.7i		−	1.13855i	0.822146	−	0.569276i	$-0.192776\pi$
$828$		0			0
$829$	5659.74	+	9802.96i	0.237118	+	0.410701i	0.959886	−	0.280390i	$-0.0904638\pi$
$829$	5659.74	+	9802.96i	0.237118	+	0.410701i	−0.722768	+	0.691091i	$0.757130\pi$
$830$		0			0
$831$	−1403.44			−0.0585859
$832$		0			0
$833$	27559.4			1.14631
$834$		0			0
$835$	235.119	+	407.239i	0.00974448	+	0.0168779i
$836$		0			0
$837$		−	3660.39i		−	0.151161i
$838$		0			0
$839$	10897.4	+	6291.64i	0.448416	+	0.258893i	0.707161	−	0.707052i	$-0.249976\pi$
$839$	10897.4	+	6291.64i	0.448416	+	0.258893i	−0.258745	+	0.965946i	$0.583309\pi$
$840$		0			0
$841$	−11019.7	+	19086.6i	−0.451830	+	0.782592i
$842$		0			0
$843$	376.694	−	217.485i	0.0153903	−	0.00888561i
$844$		0			0
$845$	332.173	+	1586.06i	0.0135232	+	0.0645704i
$846$		0			0
$847$	−7428.77	+	4289.00i	−0.301364	+	0.173993i
$848$		0			0
$849$	14.2103	−	24.6130i	0.000574437	−	0.000994954i
$850$		0			0
$851$	41631.6	+	24036.0i	1.67698	+	0.968208i
$852$		0			0
$853$		−	28845.0i		−	1.15784i	−0.815385	−	0.578919i	$-0.803475\pi$
$853$		−	28845.0i		−	1.15784i	0.815385	−	0.578919i	$-0.196525\pi$
$854$		0			0
$855$	1072.40	+	1857.45i	0.0428951	+	0.0742965i
$856$		0			0
$857$	−27781.4			−1.10735			−0.553673	−	0.832734i	$-0.686774\pi$
$857$	−27781.4			−1.10735			−0.553673	+	0.832734i	$0.686774\pi$
$858$		0			0
$859$	−5935.79			−0.235770			−0.117885	−	0.993027i	$-0.537611\pi$
$859$	−5935.79			−0.235770			−0.117885	+	0.993027i	$0.537611\pi$
$860$		0			0
$861$	−1807.30	−	3130.34i	−0.0715363	−	0.123905i
$862$		0			0
$863$			10219.4i			0.403098i	0.979478	+	0.201549i	$0.0645975\pi$
$863$			10219.4i			0.403098i	−0.979478	+	0.201549i	$0.935403\pi$
$864$		0			0
$865$	2259.25	+	1304.38i	0.0888057	+	0.0512720i
$866$		0			0
$867$	−508.558	+	880.849i	−0.0199211	+	0.0345043i
$868$		0			0
$869$	10317.1	−	5956.60i	0.402744	−	0.232524i
$870$		0			0
$871$	21480.4	−	15557.4i	0.835633	−	0.605216i
$872$		0			0
$873$	−13827.0	+	7983.01i	−0.536051	+	0.309489i
$874$		0			0
$875$	−2951.28	+	5111.76i	−0.114024	+	0.197496i
$876$		0			0
$877$	18578.9	+	10726.6i	0.715355	+	0.413010i	0.813041	−	0.582207i	$-0.197811\pi$
$877$	18578.9	+	10726.6i	0.715355	+	0.413010i	−0.0976856	+	0.995217i	$0.531144\pi$
$878$		0			0
$879$		−	499.926i		−	0.0191833i
$880$		0			0
$881$	6744.63	+	11682.0i	0.257925	+	0.446740i	0.965686	−	0.259712i	$-0.0836278\pi$
$881$	6744.63	+	11682.0i	0.257925	+	0.446740i	−0.707761	+	0.706452i	$0.750294\pi$
$882$		0			0
$883$	17205.4			0.655728			0.327864	−	0.944725i	$-0.393671\pi$
$883$	17205.4			0.655728			0.327864	+	0.944725i	$0.393671\pi$
$884$		0			0
$885$	98.7228			0.00374975
$886$		0			0
$887$	16592.9	+	28739.8i	0.628112	+	1.08792i	0.987930	+	0.154900i	$0.0495056\pi$
$887$	16592.9	+	28739.8i	0.628112	+	1.08792i	−0.359818	+	0.933023i	$0.617161\pi$
$888$		0			0
$889$		−	60911.4i		−	2.29798i
$890$		0			0
$891$	20372.5	+	11762.1i	0.765999	+	0.442250i
$892$		0			0
$893$	5008.86	−	8675.60i	0.187699	−	0.325104i
$894$		0			0
$895$	714.809	−	412.695i	0.0266966	−	0.0154133i
$896$		0			0
$897$	1275.70	−	2853.79i	0.0474856	−	0.106227i
$898$		0			0
$899$	41107.5	−	23733.4i	1.52504	−	0.880483i
$900$		0			0
$901$	1456.65	−	2522.99i	0.0538603	−	0.0932887i
$902$		0			0
$903$	−701.949	−	405.270i	−0.0258686	−	0.0149353i
$904$		0			0
$905$			2867.59i			0.105328i
$906$		0			0
$907$	−17019.3	−	29478.3i	−0.623060	−	1.07917i	−0.988913	−	0.148499i	$-0.952556\pi$
$907$	−17019.3	−	29478.3i	−0.623060	−	1.07917i	0.365852	−	0.930673i	$-0.380778\pi$
$908$		0			0
$909$	−29783.9			−1.08676
$910$		0			0
$911$	−24459.5			−0.889550			−0.444775	−	0.895642i	$-0.646716\pi$
$911$	−24459.5			−0.889550			−0.444775	+	0.895642i	$0.646716\pi$
$912$		0			0
$913$	−7621.59	−	13201.0i	−0.276274	−	0.478520i
$914$		0			0
$915$			78.6685i			0.00284229i
$916$		0			0
$917$	−41154.9	−	23760.8i	−1.48207	−	0.855672i
$918$		0			0
$919$	−14134.6	+	24481.9i	−0.507354	+	0.878763i	0.492610	+	0.870250i	$0.336043\pi$
$919$	−14134.6	+	24481.9i	−0.507354	+	0.878763i	−0.999964	+	0.00851278i	$0.997290\pi$
$920$		0			0
$921$	1902.63	−	1098.49i	0.0680715	−	0.0393011i
$922$		0			0
$923$	−10923.5	−	4883.02i	−0.389545	−	0.174135i
$924$		0			0
$925$	23948.2	−	13826.5i	0.851255	−	0.491472i
$926$		0			0
$927$	15671.7	−	27144.1i	0.555258	−	0.961736i
$928$		0			0
$929$	−14792.6	−	8540.51i	−0.522422	−	0.301620i	0.215503	−	0.976503i	$-0.430861\pi$
$929$	−14792.6	−	8540.51i	−0.522422	−	0.301620i	−0.737925	+	0.674883i	$0.764194\pi$
$930$		0			0
$931$			74157.1i			2.61053i
$932$		0			0
$933$	−486.832	−	843.218i	−0.0170827	−	0.0295881i
$934$		0			0
$935$	−966.187			−0.0337943
$936$		0			0
$937$	31839.7			1.11009			0.555046	−	0.831819i	$-0.312701\pi$
$937$	31839.7			1.11009			0.555046	+	0.831819i	$0.312701\pi$
$938$		0			0
$939$	−919.503	−	1592.63i	−0.0319562	−	0.0553497i
$940$		0			0
$941$		−	42096.9i		−	1.45836i	−0.684320	−	0.729182i	$-0.739901\pi$
$941$		−	42096.9i		−	1.45836i	0.684320	−	0.729182i	$-0.260099\pi$
$942$		0			0
$943$	−68489.5	−	39542.4i	−2.36514	−	1.36551i
$944$		0			0
$945$	−196.582	+	340.490i	−0.00676700	+	0.0117208i
$946$		0			0
$947$	−25977.9	+	14998.4i	−0.891414	+	0.514658i	−0.874405	−	0.485197i	$-0.838748\pi$
$947$	−25977.9	+	14998.4i	−0.891414	+	0.514658i	−0.0170095	+	0.999855i	$0.505415\pi$
$948$		0			0
$949$	3451.13	+	33314.4i	0.118049	+	1.13955i
$950$		0			0
$951$	125.524	−	72.4716i	0.00428014	−	0.00247114i
$952$		0			0
$953$	−14853.8	+	25727.6i	−0.504892	+	0.874499i	0.495092	+	0.868841i	$0.335134\pi$
$953$	−14853.8	+	25727.6i	−0.504892	+	0.874499i	−0.999984	+	0.00565806i	$0.998199\pi$
$954$		0			0
$955$	−2460.20	−	1420.40i	−0.0833614	−	0.0481287i
$956$		0			0
$957$		−	2166.11i		−	0.0731667i
$958$		0			0
$959$	13460.6	+	23314.4i	0.453247	+	0.785047i
$960$		0			0
$961$	−18737.6			−0.628968
$962$		0			0
$963$	−9418.88			−0.315181
$964$		0			0
$965$	−400.284	−	693.312i	−0.0133529	−	0.0231280i
$966$		0			0
$967$			12040.2i			0.400400i	0.979755	+	0.200200i	$0.0641592\pi$
$967$			12040.2i			0.400400i	−0.979755	+	0.200200i	$0.935841\pi$
$968$		0			0
$969$	1158.87	+	669.073i	0.0384192	+	0.0221813i
$970$		0			0
$971$	9222.82	−	15974.4i	0.304814	−	0.527953i	−0.672406	−	0.740183i	$-0.734739\pi$
$971$	9222.82	−	15974.4i	0.304814	−	0.527953i	0.977220	+	0.212229i	$0.0680724\pi$
$972$		0			0
$973$	−54236.2	+	31313.3i	−1.78698	+	1.03171i
$974$		0			0
$975$	−1054.76	−	1456.33i	−0.0346455	−	0.0478356i
$976$		0			0
$977$	−15378.8	+	8878.98i	−0.503595	+	0.290751i	−0.730197	−	0.683237i	$-0.760572\pi$
$977$	−15378.8	+	8878.98i	−0.503595	+	0.290751i	0.226602	+	0.973988i	$0.427238\pi$
$978$		0			0
$979$	6912.76	−	11973.3i	0.225672	−	0.390875i
$980$		0			0
$981$	−13785.1	−	7958.83i	−0.448648	−	0.259027i
$982$		0			0
$983$		−	16776.6i		−	0.544345i	−0.962248	−	0.272173i	$-0.912258\pi$
$983$		−	16776.6i		−	0.544345i	0.962248	−	0.272173i	$-0.0877422\pi$
$984$		0			0
$985$	−1569.94	−	2719.21i	−0.0507841	−	0.0879607i
$986$		0			0
$987$	916.558			0.0295586
$988$		0			0
$989$	−17734.0			−0.570181
$990$		0			0
$991$	−7762.96	−	13445.8i	−0.248838	−	0.431000i	0.714366	−	0.699773i	$-0.246715\pi$
$991$	−7762.96	−	13445.8i	−0.248838	−	0.431000i	−0.963204	+	0.268773i	$0.913382\pi$
$992$		0			0
$993$			2073.57i			0.0662667i
$994$		0			0
$995$	1135.16	+	655.385i	0.0361678	+	0.0208815i
$996$		0			0
$997$	5621.68	−	9737.04i	0.178576	−	0.309303i	−0.762817	−	0.646615i	$-0.776184\pi$
$997$	5621.68	−	9737.04i	0.178576	−	0.309303i	0.941393	+	0.337312i	$0.109518\pi$
$998$		0			0
$999$	3197.31	−	1845.97i	0.101260	−	0.0584623i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.4.w.e.49.5		20
4.3	odd	2		104.4.o.a.49.6	yes	20
13.4	even	6	inner	208.4.w.e.17.5		20
52.11	even	12		1352.4.a.o.1.5		10
52.15	even	12		1352.4.a.p.1.5		10
52.43	odd	6		104.4.o.a.17.6	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.4.o.a.17.6	✓	20	52.43	odd	6
104.4.o.a.49.6	yes	20	4.3	odd	2
208.4.w.e.17.5		20	13.4	even	6	inner
208.4.w.e.49.5		20	1.1	even	1	trivial
1352.4.a.o.1.5		10	52.11	even	12
1352.4.a.p.1.5		10	52.15	even	12

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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	208.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.154124 + 0.266950i) q^{3} +0.737582i q^{5} +(27.7822 + 16.0401i) q^{7} +(13.4525 - 23.3004i) q^{9} +O(q^{10})\)	\(q+(0.154124 + 0.266950i) q^{3} +0.737582i q^{5} +(27.7822 + 16.0401i) q^{7} +(13.4525 - 23.3004i) q^{9} +(-28.2437 + 16.3065i) q^{11} +(-46.6227 + 4.82977i) q^{13} +(-0.196897 + 0.113679i) q^{15} +(20.0831 - 34.7849i) q^{17} +(93.5997 + 54.0398i) q^{19} +9.88860i q^{21} +(108.178 + 187.369i) q^{23} +124.456 q^{25} +16.6161 q^{27} +(107.736 + 186.605i) q^{29} -220.292i q^{31} +(-8.70603 - 5.02643i) q^{33} +(-11.8309 + 20.4916i) q^{35} +(192.423 - 111.095i) q^{37} +(-8.47496 - 11.7015i) q^{39} +(-316.561 + 182.766i) q^{41} +(-40.9836 + 70.9856i) q^{43} +(17.1860 + 9.92231i) q^{45} -92.6883i q^{47} +(343.067 + 594.209i) q^{49} +12.3811 q^{51} +72.5313 q^{53} +(-12.0274 - 20.8320i) q^{55} +33.3152i q^{57} +(-376.044 - 217.109i) q^{59} +(173.006 - 299.655i) q^{61} +(747.479 - 431.557i) q^{63} +(-3.56235 - 34.3880i) q^{65} +(-490.038 + 282.923i) q^{67} +(-33.3454 + 57.7560i) q^{69} +(221.073 + 127.637i) q^{71} -714.554i q^{73} +(19.1816 + 33.2235i) q^{75} -1046.23 q^{77} -365.290 q^{79} +(-360.656 - 624.675i) q^{81} +467.396i q^{83} +(25.6567 + 14.8129i) q^{85} +(-33.2094 + 57.5203i) q^{87} +(-367.132 + 211.964i) q^{89} +(-1372.75 - 613.649i) q^{91} +(58.8069 - 33.9522i) q^{93} +(-39.8588 + 69.0374i) q^{95} +(-513.919 - 296.711i) q^{97} +877.452i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{3} + 54 q^{7} - 72 q^{9}+O(q^{10}) \) 20 * q + 6 * q^3 + 54 * q^7 - 72 * q^9	\( 20 q + 6 q^{3} + 54 q^{7} - 72 q^{9} + 42 q^{11} + 24 q^{13} - 70 q^{17} + 102 q^{19} - 90 q^{23} - 628 q^{25} - 708 q^{27} + 170 q^{29} - 678 q^{33} + 544 q^{35} + 582 q^{37} - 1162 q^{39} + 438 q^{41} - 270 q^{43} + 540 q^{45} + 92 q^{49} + 444 q^{51} - 592 q^{53} + 288 q^{55} - 90 q^{59} + 746 q^{61} + 1068 q^{63} - 1412 q^{65} - 846 q^{67} + 682 q^{69} + 1038 q^{71} - 722 q^{75} + 2812 q^{77} + 1008 q^{79} + 694 q^{81} - 180 q^{85} + 338 q^{87} + 2466 q^{89} - 690 q^{91} - 4764 q^{93} + 2592 q^{95} - 846 q^{97}+O(q^{100}) \) 20 * q + 6 * q^3 + 54 * q^7 - 72 * q^9 + 42 * q^11 + 24 * q^13 - 70 * q^17 + 102 * q^19 - 90 * q^23 - 628 * q^25 - 708 * q^27 + 170 * q^29 - 678 * q^33 + 544 * q^35 + 582 * q^37 - 1162 * q^39 + 438 * q^41 - 270 * q^43 + 540 * q^45 + 92 * q^49 + 444 * q^51 - 592 * q^53 + 288 * q^55 - 90 * q^59 + 746 * q^61 + 1068 * q^63 - 1412 * q^65 - 846 * q^67 + 682 * q^69 + 1038 * q^71 - 722 * q^75 + 2812 * q^77 + 1008 * q^79 + 694 * q^81 - 180 * q^85 + 338 * q^87 + 2466 * q^89 - 690 * q^91 - 4764 * q^93 + 2592 * q^95 - 846 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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