LMFDB - Embedded newform 256.4.g.b.33.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,4,Mod(33,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("256.33");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	256.g (of order $8$, degree $4$, 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:	$15.1044889615$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			33.4
Character	$\chi$	$=$	256.33
Dual form			256.4.g.b.225.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64064 + 3.96085i) q^{3} +(11.8087 - 4.89132i) q^{5} +(-5.11236 + 5.11236i) q^{7} +(6.09524 + 6.09524i) q^{9} +O(q^{10})$	\(q+(-1.64064 + 3.96085i) q^{3} +(11.8087 - 4.89132i) q^{5} +(-5.11236 + 5.11236i) q^{7} +(6.09524 + 6.09524i) q^{9} +(-15.2446 - 36.8038i) q^{11} +(73.4903 + 30.4407i) q^{13} +54.7973i q^{15} -66.8708i q^{17} +(37.0353 + 15.3405i) q^{19} +(-11.8618 - 28.6368i) q^{21} +(30.1143 + 30.1143i) q^{23} +(27.1316 - 27.1316i) q^{25} +(-141.085 + 58.4395i) q^{27} +(-64.4434 + 155.580i) q^{29} +219.132 q^{31} +170.785 q^{33} +(-35.3641 + 85.3765i) q^{35} +(286.081 - 118.499i) q^{37} +(-241.142 + 241.142i) q^{39} +(64.2737 + 64.2737i) q^{41} +(200.870 + 484.942i) q^{43} +(101.791 + 42.1630i) q^{45} +392.444i q^{47} +290.727i q^{49} +(264.865 + 109.711i) q^{51} +(-107.214 - 258.838i) q^{53} +(-360.038 - 360.038i) q^{55} +(-121.523 + 121.523i) q^{57} +(-237.764 + 98.4852i) q^{59} +(43.9101 - 106.008i) q^{61} -62.3222 q^{63} +1016.72 q^{65} +(333.028 - 804.000i) q^{67} +(-168.685 + 69.8717i) q^{69} +(387.445 - 387.445i) q^{71} +(-518.132 - 518.132i) q^{73} +(62.9512 + 151.978i) q^{75} +(266.091 + 110.218i) q^{77} -214.985i q^{79} -421.957i q^{81} +(-436.657 - 180.869i) q^{83} +(-327.086 - 789.656i) q^{85} +(-510.501 - 510.501i) q^{87} +(-877.926 + 877.926i) q^{89} +(-531.333 + 220.085i) q^{91} +(-359.517 + 867.951i) q^{93} +512.374 q^{95} +43.7563 q^{97} +(131.408 - 317.248i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9	$ 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9} + 4 q^{11} + 4 q^{13} + 4 q^{19} + 4 q^{21} + 324 q^{23} - 4 q^{25} + 268 q^{27} + 4 q^{29} - 752 q^{31} - 8 q^{33} + 460 q^{35} + 4 q^{37} + 596 q^{39} - 4 q^{41} - 804 q^{43} - 104 q^{45} + 1384 q^{51} - 748 q^{53} - 292 q^{55} - 4 q^{57} - 1372 q^{59} + 1828 q^{61} + 2512 q^{63} - 8 q^{65} - 2036 q^{67} + 1060 q^{69} + 220 q^{71} - 4 q^{73} + 1712 q^{75} - 1900 q^{77} - 2436 q^{83} - 496 q^{85} - 1292 q^{87} - 4 q^{89} + 3604 q^{91} + 112 q^{93} - 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9 + 4 * q^11 + 4 * q^13 + 4 * q^19 + 4 * q^21 + 324 * q^23 - 4 * q^25 + 268 * q^27 + 4 * q^29 - 752 * q^31 - 8 * q^33 + 460 * q^35 + 4 * q^37 + 596 * q^39 - 4 * q^41 - 804 * q^43 - 104 * q^45 + 1384 * q^51 - 748 * q^53 - 292 * q^55 - 4 * q^57 - 1372 * q^59 + 1828 * q^61 + 2512 * q^63 - 8 * q^65 - 2036 * q^67 + 1060 * q^69 + 220 * q^71 - 4 * q^73 + 1712 * q^75 - 1900 * q^77 - 2436 * q^83 - 496 * q^85 - 1292 * q^87 - 4 * q^89 + 3604 * q^91 + 112 * q^93 - 6088 * q^95 - 8 * q^97 + 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.64064	+	3.96085i	−0.315741	+	0.762266i	0.683730	+	0.729735i	$0.260357\pi$
$3$	−1.64064	+	3.96085i	−0.315741	+	0.762266i	−0.999471	+	0.0325307i	$0.989643\pi$
$4$		0			0
$5$	11.8087	−	4.89132i	1.05620	−	0.437493i	0.214099	−	0.976812i	$-0.431318\pi$
$5$	11.8087	−	4.89132i	1.05620	−	0.437493i	0.842101	+	0.539319i	$0.181318\pi$
$6$		0			0
$7$	−5.11236	+	5.11236i	−0.276042	+	0.276042i	−0.831527	−	0.555485i	$-0.812533\pi$
$7$	−5.11236	+	5.11236i	−0.276042	+	0.276042i	0.555485	+	0.831527i	$0.312533\pi$
$8$		0			0
$9$	6.09524	+	6.09524i	0.225750	+	0.225750i
$10$		0			0
$11$	−15.2446	−	36.8038i	−0.417858	−	1.00880i	−0.982967	−	0.183781i	$-0.941166\pi$
$11$	−15.2446	−	36.8038i	−0.417858	−	1.00880i	0.565110	−	0.825016i	$-0.308834\pi$
$12$		0			0
$13$	73.4903	+	30.4407i	1.56789	+	0.649440i	0.986437	−	0.164142i	$-0.0524854\pi$
$13$	73.4903	+	30.4407i	1.56789	+	0.649440i	0.581450	+	0.813582i	$0.302485\pi$
$14$		0			0
$15$			54.7973i			0.943240i
$16$		0			0
$17$		−	66.8708i		−	0.954033i	−0.878894	−	0.477016i	$-0.841718\pi$
$17$		−	66.8708i		−	0.954033i	0.878894	−	0.477016i	$-0.158282\pi$
$18$		0			0
$19$	37.0353	+	15.3405i	0.447184	+	0.185230i	0.594899	−	0.803800i	$-0.297192\pi$
$19$	37.0353	+	15.3405i	0.447184	+	0.185230i	−0.147715	+	0.989030i	$0.547192\pi$
$20$		0			0
$21$	−11.8618	−	28.6368i	−0.123260	−	0.297575i
$22$		0			0
$23$	30.1143	+	30.1143i	0.273012	+	0.273012i	0.830311	−	0.557300i	$-0.188163\pi$
$23$	30.1143	+	30.1143i	0.273012	+	0.273012i	−0.557300	+	0.830311i	$0.688163\pi$
$24$		0			0
$25$	27.1316	−	27.1316i	0.217053	−	0.217053i
$26$		0			0
$27$	−141.085	+	58.4395i	−1.00563	+	0.416544i
$28$		0			0
$29$	−64.4434	+	155.580i	−0.412649	+	0.996224i	0.571774	+	0.820411i	$0.306255\pi$
$29$	−64.4434	+	155.580i	−0.412649	+	0.996224i	−0.984424	+	0.175813i	$0.943745\pi$
$30$		0			0
$31$	219.132			1.26959			0.634796	−	0.772680i	$-0.281084\pi$
$31$	219.132			1.26959			0.634796	+	0.772680i	$0.281084\pi$
$32$		0			0
$33$	170.785			0.900907
$34$		0			0
$35$	−35.3641	+	85.3765i	−0.170789	+	0.412322i
$36$		0			0
$37$	286.081	−	118.499i	1.27112	−	0.526515i	0.357816	−	0.933792i	$-0.383522\pi$
$37$	286.081	−	118.499i	1.27112	−	0.526515i	0.913305	+	0.407277i	$0.133522\pi$
$38$		0			0
$39$	−241.142	+	241.142i	−0.990092	+	0.990092i
$40$		0			0
$41$	64.2737	+	64.2737i	0.244826	+	0.244826i	0.818843	−	0.574017i	$-0.194616\pi$
$41$	64.2737	+	64.2737i	0.244826	+	0.244826i	−0.574017	+	0.818843i	$0.694616\pi$
$42$		0			0
$43$	200.870	+	484.942i	0.712380	+	1.71984i	0.693967	+	0.720006i	$0.255861\pi$
$43$	200.870	+	484.942i	0.712380	+	1.71984i	0.0184123	+	0.999830i	$0.494139\pi$
$44$		0			0
$45$	101.791	+	42.1630i	0.337201	+	0.139673i
$46$		0			0
$47$			392.444i			1.21795i	0.793188	+	0.608977i	$0.208420\pi$
$47$			392.444i			1.21795i	−0.793188	+	0.608977i	$0.791580\pi$
$48$		0			0
$49$			290.727i			0.847602i
$50$		0			0
$51$	264.865	+	109.711i	0.727227	+	0.301227i
$52$		0			0
$53$	−107.214	−	258.838i	−0.277868	−	0.670833i	0.721908	−	0.691989i	$-0.243265\pi$
$53$	−107.214	−	258.838i	−0.277868	−	0.670833i	−0.999776	+	0.0211562i	$0.993265\pi$
$54$		0			0
$55$	−360.038	−	360.038i	−0.882683	−	0.882683i
$56$		0			0
$57$	−121.523	+	121.523i	−0.282388	+	0.282388i
$58$		0			0
$59$	−237.764	+	98.4852i	−0.524649	+	0.217317i	−0.629258	−	0.777197i	$-0.716641\pi$
$59$	−237.764	+	98.4852i	−0.524649	+	0.217317i	0.104609	+	0.994513i	$0.466641\pi$
$60$		0			0
$61$	43.9101	−	106.008i	0.0921658	−	0.222508i	−0.871074	−	0.491153i	$-0.836576\pi$
$61$	43.9101	−	106.008i	0.0921658	−	0.222508i	0.963239	+	0.268645i	$0.0865757\pi$
$62$		0			0
$63$	−62.3222			−0.124633
$64$		0			0
$65$	1016.72			1.94013
$66$		0			0
$67$	333.028	−	804.000i	0.607251	−	1.46603i	−0.258727	−	0.965951i	$-0.583303\pi$
$67$	333.028	−	804.000i	0.607251	−	1.46603i	0.865978	−	0.500083i	$-0.166697\pi$
$68$		0			0
$69$	−168.685	+	69.8717i	−0.294309	+	0.121907i
$70$		0			0
$71$	387.445	−	387.445i	0.647624	−	0.647624i	−0.304794	−	0.952418i	$-0.598588\pi$
$71$	387.445	−	387.445i	0.647624	−	0.647624i	0.952418	+	0.304794i	$0.0985877\pi$
$72$		0			0
$73$	−518.132	−	518.132i	−0.830723	−	0.830723i	0.156892	−	0.987616i	$-0.449852\pi$
$73$	−518.132	−	518.132i	−0.830723	−	0.830723i	−0.987616	+	0.156892i	$0.949852\pi$
$74$		0			0
$75$	62.9512	+	151.978i	0.0969197	+	0.233985i
$76$		0			0
$77$	266.091	+	110.218i	0.393816	+	0.163124i
$78$		0			0
$79$		−	214.985i		−	0.306173i	−0.988213	−	0.153086i	$-0.951079\pi$
$79$		−	214.985i		−	0.306173i	0.988213	−	0.153086i	$-0.0489213\pi$
$80$		0			0
$81$		−	421.957i		−	0.578816i
$82$		0			0
$83$	−436.657	−	180.869i	−0.577462	−	0.239193i	0.0747842	−	0.997200i	$-0.476173\pi$
$83$	−436.657	−	180.869i	−0.577462	−	0.239193i	−0.652246	+	0.758007i	$0.726173\pi$
$84$		0			0
$85$	−327.086	−	789.656i	−0.417382	−	1.00765i
$86$		0			0
$87$	−510.501	−	510.501i	−0.629097	−	0.629097i
$88$		0			0
$89$	−877.926	+	877.926i	−1.04562	+	1.04562i	−0.0467087	+	0.998909i	$0.514873\pi$
$89$	−877.926	+	877.926i	−1.04562	+	1.04562i	−0.998909	+	0.0467087i	$0.985127\pi$
$90$		0			0
$91$	−531.333	+	220.085i	−0.612075	+	0.253530i
$92$		0			0
$93$	−359.517	+	867.951i	−0.400862	+	0.967767i
$94$		0			0
$95$	512.374			0.553352
$96$		0			0
$97$	43.7563			0.0458019			0.0229009	−	0.999738i	$-0.492710\pi$
$97$	43.7563			0.0458019			0.0229009	+	0.999738i	$0.492710\pi$
$98$		0			0
$99$	131.408	−	317.248i	0.133404	−	0.322067i
$100$		0			0
$101$	−427.453	+	177.057i	−0.421120	+	0.174434i	−0.583172	−	0.812349i	$-0.698189\pi$
$101$	−427.453	+	177.057i	−0.421120	+	0.174434i	0.162052	+	0.986782i	$0.448189\pi$
$102$		0			0
$103$	570.431	−	570.431i	0.545691	−	0.545691i	−0.379500	−	0.925192i	$-0.623904\pi$
$103$	570.431	−	570.431i	0.545691	−	0.545691i	0.925192	+	0.379500i	$0.123904\pi$
$104$		0			0
$105$	−280.144	−	280.144i	−0.260374	−	0.260374i
$106$		0			0
$107$	−398.490	−	962.041i	−0.360033	−	0.869196i	−0.995294	−	0.0968989i	$-0.969108\pi$
$107$	−398.490	−	962.041i	−0.360033	−	0.869196i	0.635261	−	0.772297i	$-0.280892\pi$
$108$		0			0
$109$	129.224	+	53.5263i	0.113554	+	0.0470357i	0.438737	−	0.898615i	$-0.355426\pi$
$109$	129.224	+	53.5263i	0.113554	+	0.0470357i	−0.325183	+	0.945651i	$0.605426\pi$
$110$		0			0
$111$			1327.54i			1.13517i
$112$		0			0
$113$		−	772.521i		−	0.643121i	−0.946889	−	0.321561i	$-0.895793\pi$
$113$		−	772.521i		−	0.643121i	0.946889	−	0.321561i	$-0.104207\pi$
$114$		0			0
$115$	502.909	+	208.312i	0.407796	+	0.168915i
$116$		0			0
$117$	262.398	+	633.484i	0.207339	+	0.500561i
$118$		0			0
$119$	341.868	+	341.868i	0.263353	+	0.263353i
$120$		0			0
$121$	−180.963	+	180.963i	−0.135960	+	0.135960i
$122$		0			0
$123$	−360.028	+	149.129i	−0.263924	+	0.109321i
$124$		0			0
$125$	−423.735	+	1022.99i	−0.303200	+	0.731990i
$126$		0			0
$127$	485.865			0.339477			0.169738	−	0.985489i	$-0.445708\pi$
$127$	485.865			0.339477			0.169738	+	0.985489i	$0.445708\pi$
$128$		0			0
$129$	−2250.34			−1.53590
$130$		0			0
$131$	764.762	−	1846.30i	0.510058	−	1.23139i	−0.433792	−	0.901013i	$-0.642825\pi$
$131$	764.762	−	1846.30i	0.510058	−	1.23139i	0.943850	−	0.330375i	$-0.107175\pi$
$132$		0			0
$133$	−267.765	+	110.912i	−0.174572	+	0.0723103i
$134$		0			0
$135$	−1380.19	+	1380.19i	−0.879908	+	0.879908i
$136$		0			0
$137$	−1360.64	−	1360.64i	−0.848519	−	0.848519i	0.141430	−	0.989948i	$-0.454830\pi$
$137$	−1360.64	−	1360.64i	−0.848519	−	0.848519i	−0.989948	+	0.141430i	$0.954830\pi$
$138$		0			0
$139$	−76.8204	−	185.461i	−0.0468764	−	0.113170i	0.898707	−	0.438550i	$-0.144508\pi$
$139$	−76.8204	−	185.461i	−0.0468764	−	0.113170i	−0.945583	+	0.325380i	$0.894508\pi$
$140$		0			0
$141$	−1554.41	−	643.859i	−0.928405	−	0.384558i
$142$		0			0
$143$		−	3168.78i		−	1.85305i
$144$		0			0
$145$			2152.41i			1.23274i
$146$		0			0
$147$	−1151.53	−	476.978i	−0.646098	−	0.267623i
$148$		0			0
$149$	−687.916	−	1660.78i	−0.378230	−	0.913128i	−0.992298	−	0.123875i	$-0.960468\pi$
$149$	−687.916	−	1660.78i	−0.378230	−	0.913128i	0.614068	−	0.789253i	$-0.289532\pi$
$150$		0			0
$151$	−1133.92	−	1133.92i	−0.611107	−	0.611107i	0.332128	−	0.943235i	$-0.392234\pi$
$151$	−1133.92	−	1133.92i	−0.611107	−	0.611107i	−0.943235	+	0.332128i	$0.892234\pi$
$152$		0			0
$153$	407.594	−	407.594i	0.215373	−	0.215373i
$154$		0			0
$155$	2587.67	−	1071.85i	1.34094	−	0.555437i
$156$		0			0
$157$	368.347	−	889.267i	0.187244	−	0.452046i	−0.802183	−	0.597078i	$-0.796328\pi$
$157$	368.347	−	889.267i	0.187244	−	0.452046i	0.989427	+	0.145032i	$0.0463284\pi$
$158$		0			0
$159$	1201.12			0.599087
$160$		0			0
$161$	−307.911			−0.150725
$162$		0			0
$163$	−988.667	+	2386.85i	−0.475082	+	1.14695i	0.486807	+	0.873509i	$0.338161\pi$
$163$	−988.667	+	2386.85i	−0.475082	+	1.14695i	−0.961889	+	0.273440i	$0.911839\pi$
$164$		0			0
$165$	2016.75	−	835.365i	0.951538	−	0.394140i
$166$		0			0
$167$	373.791	−	373.791i	0.173202	−	0.173202i	−0.615182	−	0.788385i	$-0.710918\pi$
$167$	373.791	−	373.791i	0.173202	−	0.173202i	0.788385	+	0.615182i	$0.210918\pi$
$168$		0			0
$169$	2920.67	+	2920.67i	1.32939	+	1.32939i
$170$		0			0
$171$	132.235	+	319.244i	0.0591361	+	0.142767i
$172$		0			0
$173$	71.8748	+	29.7715i	0.0315870	+	0.0130837i	0.398421	−	0.917203i	$-0.369558\pi$
$173$	71.8748	+	29.7715i	0.0315870	+	0.0130837i	−0.366834	+	0.930286i	$0.619558\pi$
$174$		0			0
$175$			277.414i			0.119831i
$176$		0			0
$177$		−	1103.33i		−	0.468538i
$178$		0			0
$179$	1660.73	+	687.899i	0.693459	+	0.287240i	0.701440	−	0.712728i	$-0.252541\pi$
$179$	1660.73	+	687.899i	0.693459	+	0.287240i	−0.00798155	+	0.999968i	$0.502541\pi$
$180$		0			0
$181$	757.224	+	1828.10i	0.310962	+	0.750728i	0.999670	+	0.0256892i	$0.00817804\pi$
$181$	757.224	+	1828.10i	0.310962	+	0.750728i	−0.688708	+	0.725038i	$0.741822\pi$
$182$		0			0
$183$	347.843	+	347.843i	0.140510	+	0.140510i
$184$		0			0
$185$	2798.63	−	2798.63i	1.11221	−	1.11221i
$186$		0			0
$187$	−2461.10	+	1019.42i	−0.962426	+	0.398650i
$188$		0			0
$189$	422.516	−	1020.04i	0.162611	−	0.392578i
$190$		0			0
$191$	−3023.78			−1.14551			−0.572757	−	0.819725i	$-0.694126\pi$
$191$	−3023.78			−1.14551			−0.572757	+	0.819725i	$0.694126\pi$
$192$		0			0
$193$	2155.34			0.803860			0.401930	−	0.915670i	$-0.368339\pi$
$193$	2155.34			0.803860			0.401930	+	0.915670i	$0.368339\pi$
$194$		0			0
$195$	−1668.07	+	4027.07i	−0.612578	+	1.47889i
$196$		0			0
$197$	−2832.03	+	1173.07i	−1.02423	+	0.424251i	−0.830628	−	0.556828i	$-0.812018\pi$
$197$	−2832.03	+	1173.07i	−1.02423	+	0.424251i	−0.193606	+	0.981079i	$0.562018\pi$
$198$		0			0
$199$	751.482	−	751.482i	0.267694	−	0.267694i	−0.560476	−	0.828171i	$-0.689382\pi$
$199$	751.482	−	751.482i	0.267694	−	0.267694i	0.828171	+	0.560476i	$0.189382\pi$
$200$		0			0
$201$	2638.15	+	2638.15i	0.925774	+	0.925774i
$202$		0			0
$203$	−465.924	−	1124.84i	−0.161091	−	0.388908i
$204$		0			0
$205$	1073.37	+	444.605i	0.365695	+	0.151476i
$206$		0			0
$207$			367.108i			0.123265i
$208$		0			0
$209$		−	1596.90i		−	0.528517i
$210$		0			0
$211$	469.343	+	194.408i	0.153132	+	0.0634295i	0.457933	−	0.888987i	$-0.348590\pi$
$211$	469.343	+	194.408i	0.153132	+	0.0634295i	−0.304801	+	0.952416i	$0.598590\pi$
$212$		0			0
$213$	898.956	+	2170.27i	0.289180	+	0.698143i
$214$		0			0
$215$	4744.01	+	4744.01i	1.50483	+	1.50483i
$216$		0			0
$217$	−1120.29	+	1120.29i	−0.350460	+	0.350460i
$218$		0			0
$219$	2902.31	−	1202.18i	0.895525	−	0.370939i
$220$		0			0
$221$	2035.59	−	4914.35i	0.619587	−	1.49582i
$222$		0			0
$223$	−6411.24			−1.92524			−0.962619	−	0.270857i	$-0.912693\pi$
$223$	−6411.24			−1.92524			−0.962619	+	0.270857i	$0.912693\pi$
$224$		0			0
$225$	330.748			0.0979993
$226$		0			0
$227$	−139.729	+	337.336i	−0.0408553	+	0.0986334i	−0.942990	−	0.332821i	$-0.891999\pi$
$227$	−139.729	+	337.336i	−0.0408553	+	0.0986334i	0.902135	+	0.431455i	$0.141999\pi$
$228$		0			0
$229$	2169.11	−	898.477i	0.625935	−	0.259271i	−0.0470898	−	0.998891i	$-0.514995\pi$
$229$	2169.11	−	898.477i	0.625935	−	0.259271i	0.673025	+	0.739620i	$0.264995\pi$
$230$		0			0
$231$	−873.117	+	873.117i	−0.248688	+	0.248688i
$232$		0			0
$233$	−1442.89	−	1442.89i	−0.405696	−	0.405696i	0.474539	−	0.880235i	$-0.342615\pi$
$233$	−1442.89	−	1442.89i	−0.405696	−	0.405696i	−0.880235	+	0.474539i	$0.842615\pi$
$234$		0			0
$235$	1919.57	+	4634.25i	0.532846	+	1.28640i
$236$		0			0
$237$	851.522	+	352.712i	0.233385	+	0.0966713i
$238$		0			0
$239$			2049.94i			0.554811i	0.960753	+	0.277406i	$0.0894746\pi$
$239$			2049.94i			0.554811i	−0.960753	+	0.277406i	$0.910525\pi$
$240$		0			0
$241$			3964.18i			1.05956i	0.848134	+	0.529782i	$0.177726\pi$
$241$			3964.18i			1.05956i	−0.848134	+	0.529782i	$0.822274\pi$
$242$		0			0
$243$	−2138.00	−	885.588i	−0.564414	−	0.233788i
$244$		0			0
$245$	1422.04	+	3433.11i	0.370820	+	0.895238i
$246$		0			0
$247$	2254.76	+	2254.76i	0.580838	+	0.580838i
$248$		0			0
$249$	1432.79	−	1432.79i	0.364657	−	0.364657i
$250$		0			0
$251$	3653.50	−	1513.33i	0.918754	−	0.380560i	0.127353	−	0.991858i	$-0.459352\pi$
$251$	3653.50	−	1513.33i	0.918754	−	0.380560i	0.791401	+	0.611297i	$0.209352\pi$
$252$		0			0
$253$	649.240	−	1567.41i	0.161334	−	0.389494i
$254$		0			0
$255$	3664.34			0.899882
$256$		0			0
$257$	−6137.79			−1.48975			−0.744873	−	0.667206i	$-0.767490\pi$
$257$	−6137.79			−1.48975			−0.744873	+	0.667206i	$0.767490\pi$
$258$		0			0
$259$	−856.743	+	2068.36i	−0.205542	+	0.496223i
$260$		0			0
$261$	−1341.10	+	555.500i	−0.318053	+	0.131742i
$262$		0			0
$263$	1379.24	−	1379.24i	0.323374	−	0.323374i	−0.526686	−	0.850060i	$-0.676566\pi$
$263$	1379.24	−	1379.24i	0.323374	−	0.323374i	0.850060	+	0.526686i	$0.176566\pi$
$264$		0			0
$265$	−2532.12	−	2532.12i	−0.586969	−	0.586969i
$266$		0			0
$267$	−2036.97	−	4917.69i	−0.466894	−	1.12718i
$268$		0			0
$269$	−136.201	−	56.4164i	−0.0308711	−	0.0127872i	0.367194	−	0.930144i	$-0.380318\pi$
$269$	−136.201	−	56.4164i	−0.0308711	−	0.0127872i	−0.398066	+	0.917357i	$0.630318\pi$
$270$		0			0
$271$			1576.16i			0.353302i	0.984274	+	0.176651i	$0.0565264\pi$
$271$			1576.16i			0.353302i	−0.984274	+	0.176651i	$0.943474\pi$
$272$		0			0
$273$		−	2465.61i		−	0.546614i
$274$		0			0
$275$	−1412.16	−	584.936i	−0.309660	−	0.128265i
$276$		0			0
$277$	1137.39	+	2745.89i	0.246711	+	0.595613i	0.997921	−	0.0644505i	$-0.0205294\pi$
$277$	1137.39	+	2745.89i	0.246711	+	0.595613i	−0.751210	+	0.660063i	$0.770529\pi$
$278$		0			0
$279$	1335.67	+	1335.67i	0.286610	+	0.286610i
$280$		0			0
$281$	346.910	−	346.910i	0.0736474	−	0.0736474i	−0.669324	−	0.742971i	$-0.733416\pi$
$281$	346.910	−	346.910i	0.0736474	−	0.0736474i	0.742971	+	0.669324i	$0.233416\pi$
$282$		0			0
$283$	−2926.90	+	1212.36i	−0.614791	+	0.254655i	−0.668275	−	0.743914i	$-0.732967\pi$
$283$	−2926.90	+	1212.36i	−0.614791	+	0.254655i	0.0534844	+	0.998569i	$0.482967\pi$
$284$		0			0
$285$	−840.620	+	2029.44i	−0.174716	+	0.421802i
$286$		0			0
$287$	−657.181			−0.135164
$288$		0			0
$289$	441.294			0.0898217
$290$		0			0
$291$	−71.7883	+	173.312i	−0.0144615	+	0.0349132i
$292$		0			0
$293$	−551.934	+	228.618i	−0.110049	+	0.0455837i	−0.437029	−	0.899448i	$-0.643969\pi$
$293$	−551.934	+	228.618i	−0.110049	+	0.0455837i	0.326980	+	0.945031i	$0.393969\pi$
$294$		0			0
$295$	−2325.96	+	2325.96i	−0.459060	+	0.459060i
$296$		0			0
$297$	4301.59	+	4301.59i	0.840416	+	0.840416i
$298$		0			0
$299$	1296.41	+	3129.81i	0.250747	+	0.605357i
$300$		0			0
$301$	−3506.12	−	1452.28i	−0.671393	−	0.278100i
$302$		0			0
$303$		−	1983.56i		−	0.376081i
$304$		0			0
$305$		−	1466.60i		−	0.275335i
$306$		0			0
$307$	−3795.75	−	1572.25i	−0.705651	−	0.292290i	0.000852873	−	1.00000i	$-0.499729\pi$
$307$	−3795.75	−	1572.25i	−0.705651	−	0.292290i	−0.706503	+	0.707710i	$0.749729\pi$
$308$		0			0
$309$	1323.52	+	3195.26i	0.243665	+	0.588259i
$310$		0			0
$311$	−2922.48	−	2922.48i	−0.532857	−	0.532857i	0.388565	−	0.921421i	$-0.372971\pi$
$311$	−2922.48	−	2922.48i	−0.532857	−	0.532857i	−0.921421	+	0.388565i	$0.872971\pi$
$312$		0			0
$313$	4410.61	−	4410.61i	0.796493	−	0.796493i	−0.186048	−	0.982541i	$-0.559568\pi$
$313$	4410.61	−	4410.61i	0.796493	−	0.796493i	0.982541	+	0.186048i	$0.0595678\pi$
$314$		0			0
$315$	−735.943	+	304.838i	−0.131637	+	0.0545259i
$316$		0			0
$317$	823.383	−	1987.82i	0.145886	−	0.352199i	−0.833998	−	0.551767i	$-0.813954\pi$
$317$	823.383	−	1987.82i	0.145886	−	0.352199i	0.979884	+	0.199568i	$0.0639538\pi$
$318$		0			0
$319$	6708.36			1.17742
$320$		0			0
$321$	4464.28			0.776236
$322$		0			0
$323$	1025.83	−	2476.58i	0.176715	−	0.426628i
$324$		0			0
$325$	2819.82	−	1168.01i	0.481278	−	0.199352i
$326$		0			0
$327$	−424.019	+	424.019i	−0.0717074	+	0.0717074i
$328$		0			0
$329$	−2006.32	−	2006.32i	−0.336206	−	0.336206i
$330$		0			0
$331$	−2294.33	−	5539.00i	−0.380990	−	0.919791i	−0.991775	−	0.127995i	$-0.959146\pi$
$331$	−2294.33	−	5539.00i	−0.380990	−	0.919791i	0.610785	−	0.791797i	$-0.290854\pi$
$332$		0			0
$333$	2466.01	+	1021.46i	0.405816	+	0.168094i
$334$		0			0
$335$		−	11123.1i		−	1.81409i
$336$		0			0
$337$			4177.18i			0.675209i	0.941288	+	0.337604i	$0.109617\pi$
$337$			4177.18i			0.675209i	−0.941288	+	0.337604i	$0.890383\pi$
$338$		0			0
$339$	3059.84	+	1267.43i	0.490229	+	0.203060i
$340$		0			0
$341$	−3340.60	−	8064.91i	−0.530509	−	1.28076i
$342$		0			0
$343$	−3239.85	−	3239.85i	−0.510015	−	0.510015i
$344$		0			0
$345$	−1650.18	+	1650.18i	−0.257516	+	0.257516i
$346$		0			0
$347$	6068.09	−	2513.48i	0.938767	−	0.388850i	0.139769	−	0.990184i	$-0.455364\pi$
$347$	6068.09	−	2513.48i	0.938767	−	0.388850i	0.798998	+	0.601334i	$0.205364\pi$
$348$		0			0
$349$	−3219.82	+	7773.32i	−0.493848	+	1.19225i	0.458899	+	0.888488i	$0.348244\pi$
$349$	−3219.82	+	7773.32i	−0.493848	+	1.19225i	−0.952747	+	0.303765i	$0.901756\pi$
$350$		0			0
$351$	−12147.3			−1.84723
$352$		0			0
$353$	−10007.7			−1.50895			−0.754473	−	0.656331i	$-0.772107\pi$
$353$	−10007.7			−1.50895			−0.754473	+	0.656331i	$0.772107\pi$
$354$		0			0
$355$	2680.10	−	6470.34i	0.400690	−	0.967352i
$356$		0			0
$357$	−1914.97	+	793.206i	−0.283896	+	0.117594i
$358$		0			0
$359$	3853.86	−	3853.86i	0.566572	−	0.566572i	−0.364595	−	0.931166i	$-0.618792\pi$
$359$	3853.86	−	3853.86i	0.566572	−	0.566572i	0.931166	+	0.364595i	$0.118792\pi$
$360$		0			0
$361$	−3713.76	−	3713.76i	−0.541443	−	0.541443i
$362$		0			0
$363$	−419.873	−	1013.66i	−0.0607097	−	0.146566i
$364$		0			0
$365$	−8652.81	−	3584.11i	−1.24085	−	0.513975i
$366$		0			0
$367$			2274.12i			0.323456i	0.986835	+	0.161728i	$0.0517067\pi$
$367$			2274.12i			0.323456i	−0.986835	+	0.161728i	$0.948293\pi$
$368$		0			0
$369$			783.528i			0.110539i
$370$		0			0
$371$	1871.39	+	775.156i	0.261881	+	0.108475i
$372$		0			0
$373$	−4974.80	−	12010.2i	−0.690577	−	1.66720i	−0.743615	−	0.668608i	$-0.766891\pi$
$373$	−4974.80	−	12010.2i	−0.690577	−	1.66720i	0.0530384	−	0.998592i	$-0.483109\pi$
$374$		0			0
$375$	−3356.70	−	3356.70i	−0.462238	−	0.462238i
$376$		0			0
$377$	−9471.92	+	9471.92i	−1.29398	+	1.29398i
$378$		0			0
$379$	−10078.6	+	4174.70i	−1.36597	+	0.565805i	−0.940694	−	0.339257i	$-0.889824\pi$
$379$	−10078.6	+	4174.70i	−1.36597	+	0.565805i	−0.425280	+	0.905062i	$0.639824\pi$
$380$		0			0
$381$	−797.128	+	1924.44i	−0.107187	+	0.258771i
$382$		0			0
$383$	14593.3			1.94695			0.973477	−	0.228784i	$-0.0734751\pi$
$383$	14593.3			1.94695			0.973477	+	0.228784i	$0.0734751\pi$
$384$		0			0
$385$	3681.29			0.487314
$386$		0			0
$387$	−1731.49	+	4180.19i	−0.227433	+	0.549072i
$388$		0			0
$389$	−5607.97	+	2322.90i	−0.730939	+	0.302765i	−0.716938	−	0.697137i	$-0.754457\pi$
$389$	−5607.97	+	2322.90i	−0.730939	+	0.302765i	−0.0140014	+	0.999902i	$0.504457\pi$
$390$		0			0
$391$	2013.77	−	2013.77i	0.260462	−	0.260462i
$392$		0			0
$393$	6058.21	+	6058.21i	0.777599	+	0.777599i
$394$		0			0
$395$	−1051.56	−	2538.69i	−0.133948	−	0.323380i
$396$		0			0
$397$	1428.80	+	591.828i	0.180628	+	0.0748187i	0.471165	−	0.882045i	$-0.343834\pi$
$397$	1428.80	+	591.828i	0.180628	+	0.0748187i	−0.290536	+	0.956864i	$0.593834\pi$
$398$		0			0
$399$		−	1242.54i		−	0.155902i
$400$		0			0
$401$		−	7265.44i		−	0.904786i	−0.891819	−	0.452393i	$-0.850571\pi$
$401$		−	7265.44i		−	0.904786i	0.891819	−	0.452393i	$-0.149429\pi$
$402$		0			0
$403$	16104.1	+	6670.54i	1.99058	+	0.824524i
$404$		0			0
$405$	−2063.92	−	4982.75i	−0.253228	−	0.611346i
$406$		0			0
$407$	−8722.41	−	8722.41i	−1.06229	−	1.06229i
$408$		0			0
$409$	−7223.12	+	7223.12i	−0.873252	+	0.873252i	−0.992825	−	0.119573i	$-0.961847\pi$
$409$	−7223.12	+	7223.12i	−0.873252	+	0.873252i	0.119573	+	0.992825i	$0.461847\pi$
$410$		0			0
$411$	7621.59	−	3156.97i	0.914709	−	0.378885i
$412$		0			0
$413$	712.046	−	1719.03i	0.0848365	−	0.204813i
$414$		0			0
$415$	−6041.03			−0.714561
$416$		0			0
$417$	860.618			0.101066
$418$		0			0
$419$	3225.87	−	7787.95i	0.376120	−	0.908034i	−0.616566	−	0.787304i	$-0.711476\pi$
$419$	3225.87	−	7787.95i	0.376120	−	0.908034i	0.992685	−	0.120730i	$-0.0385235\pi$
$420$		0			0
$421$	−1956.30	+	810.327i	−0.226471	+	0.0938074i	−0.493034	−	0.870010i	$-0.664112\pi$
$421$	−1956.30	+	810.327i	−0.226471	+	0.0938074i	0.266563	+	0.963818i	$0.414112\pi$
$422$		0			0
$423$	−2392.04	+	2392.04i	−0.274953	+	0.274953i
$424$		0			0
$425$	−1814.31	−	1814.31i	−0.207076	−	0.207076i
$426$		0			0
$427$	317.469	+	766.438i	0.0359799	+	0.0868631i
$428$		0			0
$429$	12551.1	+	5198.82i	1.41252	+	0.585085i
$430$		0			0
$431$			10185.7i			1.13835i	0.822216	+	0.569175i	$0.192737\pi$
$431$			10185.7i			1.13835i	−0.822216	+	0.569175i	$0.807263\pi$
$432$		0			0
$433$		−	4456.20i		−	0.494576i	−0.968942	−	0.247288i	$-0.920461\pi$
$433$		−	4456.20i		−	0.494576i	0.968942	−	0.247288i	$-0.0795394\pi$
$434$		0			0
$435$	−8525.37	−	3531.32i	−0.939678	−	0.389227i
$436$		0			0
$437$	653.325	+	1577.27i	0.0715166	+	0.172656i
$438$		0			0
$439$	2494.47	+	2494.47i	0.271195	+	0.271195i	0.829581	−	0.558386i	$-0.188579\pi$
$439$	2494.47	+	2494.47i	0.271195	+	0.271195i	−0.558386	+	0.829581i	$0.688579\pi$
$440$		0			0
$441$	−1772.05	+	1772.05i	−0.191346	+	0.191346i
$442$		0			0
$443$	−13843.2	+	5734.06i	−1.48468	+	0.614974i	−0.970151	−	0.242501i	$-0.922032\pi$
$443$	−13843.2	+	5734.06i	−1.48468	+	0.614974i	−0.514526	+	0.857475i	$0.672032\pi$
$444$		0			0
$445$	−6072.93	+	14661.4i	−0.646932	+	1.56183i
$446$		0			0
$447$	7706.71			0.815469
$448$		0			0
$449$	6724.60			0.706801			0.353400	−	0.935472i	$-0.385025\pi$
$449$	6724.60			0.706801			0.353400	+	0.935472i	$0.385025\pi$
$450$		0			0
$451$	1385.69	−	3345.35i	0.144677	−	0.349282i
$452$		0			0
$453$	6351.64	−	2630.94i	0.658778	−	0.272875i
$454$		0			0
$455$	−5197.83	+	5197.83i	−0.535556	+	0.535556i
$456$		0			0
$457$	−12569.7	−	12569.7i	−1.28662	−	1.28662i	−0.936826	−	0.349795i	$-0.886251\pi$
$457$	−12569.7	−	12569.7i	−1.28662	−	1.28662i	−0.349795	−	0.936826i	$-0.613749\pi$
$458$		0			0
$459$	3907.90	+	9434.49i	0.397396	+	0.959400i
$460$		0			0
$461$	−5822.39	−	2411.71i	−0.588234	−	0.243654i	0.0686568	−	0.997640i	$-0.478129\pi$
$461$	−5822.39	−	2411.71i	−0.588234	−	0.243654i	−0.656891	+	0.753986i	$0.728129\pi$
$462$		0			0
$463$			15045.1i			1.51016i	0.655634	+	0.755079i	$0.272402\pi$
$463$			15045.1i			1.51016i	−0.655634	+	0.755079i	$0.727598\pi$
$464$		0			0
$465$			12007.9i			1.19753i
$466$		0			0
$467$	−12797.5	−	5300.90i	−1.26809	−	0.525260i	−0.355708	−	0.934597i	$-0.615760\pi$
$467$	−12797.5	−	5300.90i	−1.26809	−	0.525260i	−0.912383	+	0.409337i	$0.865760\pi$
$468$		0			0
$469$	2407.78	+	5812.90i	0.237060	+	0.572313i
$470$		0			0
$471$	2917.93	+	2917.93i	0.285459	+	0.285459i
$472$		0			0
$473$	14785.5	−	14785.5i	1.43729	−	1.43729i
$474$		0			0
$475$	1421.04	−	588.616i	0.137267	−	0.0568580i
$476$		0			0
$477$	924.184	−	2231.18i	0.0887117	−	0.214169i
$478$		0			0
$479$	5991.54			0.571525			0.285762	−	0.958301i	$-0.407753\pi$
$479$	5991.54			0.571525			0.285762	+	0.958301i	$0.407753\pi$
$480$		0			0
$481$	24631.4			2.33491
$482$		0			0
$483$	505.170	−	1219.59i	0.0475902	−	0.114893i
$484$		0			0
$485$	516.705	−	214.026i	0.0483760	−	0.0200380i
$486$		0			0
$487$	6120.86	−	6120.86i	0.569534	−	0.569534i	−0.362464	−	0.931998i	$-0.618064\pi$
$487$	6120.86	−	6120.86i	0.569534	−	0.569534i	0.931998	+	0.362464i	$0.118064\pi$
$488$		0			0
$489$	−7831.92	−	7831.92i	−0.724278	−	0.724278i
$490$		0			0
$491$	7107.17	+	17158.2i	0.653242	+	1.57707i	0.808045	+	0.589121i	$0.200526\pi$
$491$	7107.17	+	17158.2i	0.653242	+	1.57707i	−0.154803	+	0.987945i	$0.549474\pi$
$492$		0			0
$493$	10403.8	+	4309.38i	0.950430	+	0.393681i
$494$		0			0
$495$		−	4389.04i		−	0.398531i
$496$		0			0
$497$			3961.52i			0.357543i
$498$		0			0
$499$	−276.250	−	114.426i	−0.0247828	−	0.0102654i	0.370258	−	0.928929i	$-0.379269\pi$
$499$	−276.250	−	114.426i	−0.0247828	−	0.0102654i	−0.395040	+	0.918664i	$0.629269\pi$
$500$		0			0
$501$	867.274	+	2093.78i	0.0773392	+	0.186713i
$502$		0			0
$503$	3966.95	+	3966.95i	0.351645	+	0.351645i	0.860721	−	0.509076i	$-0.170013\pi$
$503$	3966.95	+	3966.95i	0.351645	+	0.351645i	−0.509076	+	0.860721i	$0.670013\pi$
$504$		0			0
$505$	−4181.61	+	4181.61i	−0.368474	+	0.368474i
$506$		0			0
$507$	−16360.1	+	6776.58i	−1.43309	+	0.593606i
$508$		0			0
$509$	4067.11	−	9818.87i	0.354168	−	0.855037i	−0.641928	−	0.766765i	$-0.721865\pi$
$509$	4067.11	−	9818.87i	0.354168	−	0.855037i	0.996096	−	0.0882726i	$-0.0281347\pi$
$510$		0			0
$511$	5297.76			0.458629
$512$		0			0
$513$	−6121.64			−0.526856
$514$		0			0
$515$	3945.88	−	9526.19i	0.337624	−	0.815095i
$516$		0			0
$517$	14443.4	−	5982.67i	1.22867	−	0.508931i
$518$		0			0
$519$	−235.841	+	235.841i	−0.0199466	+	0.0199466i
$520$		0			0
$521$	9171.85	+	9171.85i	0.771259	+	0.771259i	0.978327	−	0.207067i	$-0.0663919\pi$
$521$	9171.85	+	9171.85i	0.771259	+	0.771259i	−0.207067	+	0.978327i	$0.566392\pi$
$522$		0			0
$523$	−6048.17	−	14601.6i	−0.505675	−	1.22081i	−0.946351	−	0.323140i	$-0.895261\pi$
$523$	−6048.17	−	14601.6i	−0.505675	−	1.22081i	0.440676	−	0.897666i	$-0.354739\pi$
$524$		0			0
$525$	−1098.79	−	455.135i	−0.0913434	−	0.0378357i
$526$		0			0
$527$		−	14653.6i		−	1.21123i
$528$		0			0
$529$		−	10353.3i		−	0.850929i
$530$		0			0
$531$	−2049.52	−	848.940i	−0.167499	−	0.0693802i
$532$		0			0
$533$	2766.96	+	6680.03i	0.224860	+	0.542860i
$534$		0			0
$535$	−9411.29	−	9411.29i	−0.760534	−	0.760534i
$536$		0			0
$537$	−5449.33	+	5449.33i	−0.437907	+	0.437907i
$538$		0			0
$539$	10699.9	−	4432.04i	0.855059	−	0.354177i
$540$		0			0
$541$	−1872.33	+	4520.21i	−0.148795	+	0.359222i	−0.980650	−	0.195771i	$-0.937279\pi$
$541$	−1872.33	+	4520.21i	−0.148795	+	0.359222i	0.831855	+	0.554993i	$0.187279\pi$
$542$		0			0
$543$	−8483.17			−0.670437
$544$		0			0
$545$	1787.78			0.140514
$546$		0			0
$547$	1131.56	−	2731.83i	0.0884499	−	0.213537i	−0.873464	−	0.486888i	$-0.838132\pi$
$547$	1131.56	−	2731.83i	0.0884499	−	0.213537i	0.961914	+	0.273351i	$0.0881320\pi$
$548$		0			0
$549$	913.789	−	378.504i	0.0710375	−	0.0294247i
$550$		0			0
$551$	−4773.36	+	4773.36i	−0.369060	+	0.369060i
$552$		0			0
$553$	1099.08	+	1099.08i	0.0845165	+	0.0845165i
$554$		0			0
$555$	6493.41	+	15676.5i	0.496630	+	1.19897i
$556$		0			0
$557$	4125.91	+	1709.01i	0.313861	+	0.130005i	0.534053	−	0.845451i	$-0.320668\pi$
$557$	4125.91	+	1709.01i	0.313861	+	0.130005i	−0.220192	+	0.975457i	$0.570668\pi$
$558$		0			0
$559$			41753.1i			3.15916i
$560$		0			0
$561$		−	11420.6i		−	0.859494i
$562$		0			0
$563$	13629.3	+	5645.44i	1.02026	+	0.422605i	0.829187	−	0.558971i	$-0.188804\pi$
$563$	13629.3	+	5645.44i	1.02026	+	0.422605i	0.191072	+	0.981576i	$0.438804\pi$
$564$		0			0
$565$	−3778.65	−	9122.46i	−0.281361	−	0.679265i
$566$		0			0
$567$	2157.20	+	2157.20i	0.159777	+	0.159777i
$568$		0			0
$569$	−1198.17	+	1198.17i	−0.0882777	+	0.0882777i	−0.749867	−	0.661589i	$-0.769882\pi$
$569$	−1198.17	+	1198.17i	−0.0882777	+	0.0882777i	0.661589	+	0.749867i	$0.269882\pi$
$570$		0			0
$571$	−1981.86	+	820.913i	−0.145251	+	0.0601649i	−0.454125	−	0.890938i	$-0.650048\pi$
$571$	−1981.86	+	820.913i	−0.145251	+	0.0601649i	0.308874	+	0.951103i	$0.400048\pi$
$572$		0			0
$573$	4960.93	−	11976.7i	0.361685	−	0.873186i
$574$		0			0
$575$	1634.10			0.118516
$576$		0			0
$577$	1653.54			0.119303			0.0596515	−	0.998219i	$-0.481001\pi$
$577$	1653.54			0.119303			0.0596515	+	0.998219i	$0.481001\pi$
$578$		0			0
$579$	−3536.14	+	8536.99i	−0.253812	+	0.612755i
$580$		0			0
$581$	3157.02	−	1307.68i	0.225431	−	0.0933765i
$582$		0			0
$583$	−7891.78	+	7891.78i	−0.560625	+	0.560625i
$584$		0			0
$585$	6197.14	+	6197.14i	0.437983	+	0.437983i
$586$		0			0
$587$	−5748.28	−	13877.6i	−0.404186	−	0.975790i	−0.986638	−	0.162926i	$-0.947907\pi$
$587$	−5748.28	−	13877.6i	−0.404186	−	0.975790i	0.582453	−	0.812865i	$-0.302093\pi$
$588$		0			0
$589$	8115.65	+	3361.61i	0.567741	+	0.235166i
$590$		0			0
$591$		−	13141.8i		−	0.914692i
$592$		0			0
$593$			10098.5i			0.699322i	0.936876	+	0.349661i	$0.113703\pi$
$593$			10098.5i			0.699322i	−0.936876	+	0.349661i	$0.886297\pi$
$594$		0			0
$595$	5709.19	+	2364.83i	0.393368	+	0.162938i
$596$		0			0
$597$	1743.60	+	4209.42i	0.119532	+	0.288576i
$598$		0			0
$599$	15005.1	+	15005.1i	1.02353	+	1.02353i	0.999716	+	0.0238107i	$0.00757989\pi$
$599$	15005.1	+	15005.1i	1.02353	+	1.02353i	0.0238107	+	0.999716i	$0.492420\pi$
$600$		0			0
$601$	11177.5	−	11177.5i	0.758632	−	0.758632i	−0.217442	−	0.976073i	$-0.569771\pi$
$601$	11177.5	−	11177.5i	0.758632	−	0.758632i	0.976073	+	0.217442i	$0.0697712\pi$
$602$		0			0
$603$	6930.46	−	2870.69i	0.468043	−	0.193870i
$604$		0			0
$605$	−1251.79	+	3022.08i	−0.0841197	+	0.203083i
$606$		0			0
$607$	−16418.5			−1.09787			−0.548935	−	0.835865i	$-0.684967\pi$
$607$	−16418.5			−1.09787			−0.548935	+	0.835865i	$0.684967\pi$
$608$		0			0
$609$	5219.73			0.347314
$610$		0			0
$611$	−11946.3	+	28840.8i	−0.790989	+	1.90962i
$612$		0			0
$613$	954.545	−	395.385i	0.0628935	−	0.0260513i	−0.351015	−	0.936370i	$-0.614163\pi$
$613$	954.545	−	395.385i	0.0628935	−	0.0260513i	0.413908	+	0.910319i	$0.364163\pi$
$614$		0			0
$615$	−3522.03	+	3522.03i	−0.230930	+	0.230930i
$616$		0			0
$617$	7933.23	+	7933.23i	0.517633	+	0.517633i	0.916855	−	0.399221i	$-0.130719\pi$
$617$	7933.23	+	7933.23i	0.517633	+	0.517633i	−0.399221	+	0.916855i	$0.630719\pi$
$618$		0			0
$619$	5475.77	+	13219.7i	0.355557	+	0.858391i	0.995913	+	0.0903128i	$0.0287867\pi$
$619$	5475.77	+	13219.7i	0.355557	+	0.858391i	−0.640356	+	0.768078i	$0.721213\pi$
$620$		0			0
$621$	−6008.56	−	2488.83i	−0.388269	−	0.160826i
$622$		0			0
$623$		−	8976.55i		−	0.577268i
$624$		0			0
$625$			18949.0i			1.21274i
$626$		0			0
$627$	6325.10	+	2619.94i	0.402871	+	0.166875i
$628$		0			0
$629$	−7924.11	−	19130.5i	−0.502313	−	1.21269i
$630$		0			0
$631$	−14339.1	−	14339.1i	−0.904647	−	0.904647i	0.0911870	−	0.995834i	$-0.470934\pi$
$631$	−14339.1	−	14339.1i	−0.904647	−	0.904647i	−0.995834	+	0.0911870i	$0.970934\pi$
$632$		0			0
$633$	−1540.04	+	1540.04i	−0.0967002	+	0.0967002i
$634$		0			0
$635$	5737.42	−	2376.52i	0.358555	−	0.148519i
$636$		0			0
$637$	−8849.94	+	21365.6i	−0.550467	+	1.32894i
$638$		0			0
$639$	4723.15			0.292402
$640$		0			0
$641$	−8662.28			−0.533759			−0.266879	−	0.963730i	$-0.585993\pi$
$641$	−8662.28			−0.533759			−0.266879	+	0.963730i	$0.585993\pi$
$642$		0			0
$643$	−3070.12	+	7411.92i	−0.188295	+	0.454584i	−0.989632	−	0.143630i	$-0.954123\pi$
$643$	−3070.12	+	7411.92i	−0.188295	+	0.454584i	0.801337	+	0.598214i	$0.204123\pi$
$644$		0			0
$645$	−26573.5	+	11007.1i	−1.62222	+	0.671945i
$646$		0			0
$647$	16839.6	−	16839.6i	1.02323	−	1.02323i	0.0235089	−	0.999724i	$-0.492516\pi$
$647$	16839.6	−	16839.6i	1.02323	−	1.02323i	0.999724	−	0.0235089i	$-0.00748380\pi$
$648$		0			0
$649$	7249.27	+	7249.27i	0.438457	+	0.438457i
$650$		0			0
$651$	−2599.30	−	6275.26i	−0.156489	−	0.377799i
$652$		0			0
$653$	−5431.53	−	2249.81i	−0.325501	−	0.134827i	0.213948	−	0.976845i	$-0.431368\pi$
$653$	−5431.53	−	2249.81i	−0.325501	−	0.134827i	−0.539449	+	0.842018i	$0.681368\pi$
$654$		0			0
$655$		−	25543.0i		−	1.52374i
$656$		0			0
$657$		−	6316.28i		−	0.375071i
$658$		0			0
$659$	−6283.92	−	2602.88i	−0.371452	−	0.153860i	0.189145	−	0.981949i	$-0.439428\pi$
$659$	−6283.92	−	2602.88i	−0.371452	−	0.153860i	−0.560597	+	0.828089i	$0.689428\pi$
$660$		0			0
$661$	6288.29	+	15181.3i	0.370024	+	0.893318i	0.993745	+	0.111671i	$0.0356202\pi$
$661$	6288.29	+	15181.3i	0.370024	+	0.893318i	−0.623721	+	0.781647i	$0.714380\pi$
$662$		0			0
$663$	16125.4	+	16125.4i	0.944580	+	0.944580i
$664$		0			0
$665$	−2619.44	+	2619.44i	−0.152748	+	0.152748i
$666$		0			0
$667$	−6625.86	+	2744.52i	−0.384639	+	0.159323i
$668$		0			0
$669$	10518.5	−	25394.0i	0.607877	−	1.46754i
$670$		0			0
$671$	−4570.91			−0.262978
$672$		0			0
$673$	−22750.9			−1.30309			−0.651546	−	0.758609i	$-0.725879\pi$
$673$	−22750.9			−1.30309			−0.651546	+	0.758609i	$0.725879\pi$
$674$		0			0
$675$	−2242.32	+	5413.44i	−0.127862	+	0.308686i
$676$		0			0
$677$	−18090.7	+	7493.42i	−1.02701	+	0.425400i	−0.831631	−	0.555329i	$-0.812592\pi$
$677$	−18090.7	+	7493.42i	−1.02701	+	0.425400i	−0.195375	+	0.980729i	$0.562592\pi$
$678$		0			0
$679$	−223.698	+	223.698i	−0.0126432	+	0.0126432i
$680$		0			0
$681$	−1106.89	−	1106.89i	−0.0622852	−	0.0622852i
$682$		0			0
$683$	−4949.33	−	11948.7i	−0.277278	−	0.669408i	0.722481	−	0.691391i	$-0.243002\pi$
$683$	−4949.33	−	11948.7i	−0.277278	−	0.669408i	−0.999758	+	0.0219835i	$0.993002\pi$
$684$		0			0
$685$	−22722.6	−	9412.02i	−1.26743	−	0.524985i
$686$		0			0
$687$			10065.6i			0.558991i
$688$		0			0
$689$		−	22285.7i		−	1.23225i
$690$		0			0
$691$	8985.78	+	3722.03i	0.494696	+	0.204910i	0.616062	−	0.787698i	$-0.288727\pi$
$691$	8985.78	+	3722.03i	0.494696	+	0.204910i	−0.121365	+	0.992608i	$0.538727\pi$
$692$		0			0
$693$	950.080	+	2293.69i	0.0520787	+	0.125729i
$694$		0			0
$695$	−1814.30	−	1814.30i	−0.0990218	−	0.0990218i
$696$		0			0
$697$	4298.04	−	4298.04i	0.233572	−	0.233572i
$698$		0			0
$699$	8082.35	−	3347.82i	0.437343	−	0.181153i
$700$		0			0
$701$	5041.79	−	12172.0i	0.271649	−	0.655818i	−0.727905	−	0.685678i	$-0.759506\pi$
$701$	5041.79	−	12172.0i	0.271649	−	0.655818i	0.999554	+	0.0298593i	$0.00950593\pi$
$702$		0			0
$703$	12413.0			0.665951
$704$		0			0
$705$	−21504.9			−1.14882
$706$		0			0
$707$	1280.12	−	3090.47i	0.0680958	−	0.164398i
$708$		0			0
$709$	29815.3	−	12349.9i	1.57932	−	0.654176i	0.591014	−	0.806661i	$-0.298728\pi$
$709$	29815.3	−	12349.9i	1.57932	−	0.654176i	0.988306	+	0.152486i	$0.0487277\pi$
$710$		0			0
$711$	1310.38	−	1310.38i	0.0691185	−	0.0691185i
$712$		0			0
$713$	6599.03	+	6599.03i	0.346614	+	0.346614i
$714$		0			0
$715$	−15499.5	−	37419.1i	−0.810697	−	1.95720i
$716$		0			0
$717$	−8119.52	−	3363.22i	−0.422914	−	0.175177i
$718$		0			0
$719$		−	35519.5i		−	1.84236i	−0.389141	−	0.921178i	$-0.627228\pi$
$719$		−	35519.5i		−	1.84236i	0.389141	−	0.921178i	$-0.372772\pi$
$720$		0			0
$721$			5832.50i			0.301267i
$722$		0			0
$723$	−15701.5	−	6503.78i	−0.807670	−	0.334548i
$724$		0			0
$725$	2472.69	+	5969.60i	0.126667	+	0.305800i
$726$		0			0
$727$	−6873.52	−	6873.52i	−0.350653	−	0.350653i	0.509699	−	0.860353i	$-0.329757\pi$
$727$	−6873.52	−	6873.52i	−0.350653	−	0.350653i	−0.860353	+	0.509699i	$0.829757\pi$
$728$		0			0
$729$	15071.3	−	15071.3i	0.765702	−	0.765702i
$730$		0			0
$731$	32428.5	−	13432.3i	1.64078	−	0.679634i
$732$		0			0
$733$	−6189.58	+	14943.0i	−0.311893	+	0.752975i	0.687742	+	0.725955i	$0.258602\pi$
$733$	−6189.58	+	14943.0i	−0.311893	+	0.752975i	−0.999635	+	0.0270204i	$0.991398\pi$
$734$		0			0
$735$	−15931.1			−0.799492
$736$		0			0
$737$	−34667.2			−1.73268
$738$		0			0
$739$	8349.16	−	20156.7i	0.415601	−	1.00335i	−0.568007	−	0.823024i	$-0.692285\pi$
$739$	8349.16	−	20156.7i	0.415601	−	1.00335i	0.983607	−	0.180325i	$-0.0577148\pi$
$740$		0			0
$741$	−12630.0	+	5231.53i	−0.626148	+	0.259359i
$742$		0			0
$743$	−6318.96	+	6318.96i	−0.312006	+	0.312006i	−0.845686	−	0.533680i	$-0.820809\pi$
$743$	−6318.96	+	6318.96i	−0.312006	+	0.312006i	0.533680	+	0.845686i	$0.320809\pi$
$744$		0			0
$745$	−16246.8	−	16246.8i	−0.798974	−	0.798974i
$746$		0			0
$747$	−1559.09	−	3763.97i	−0.0763642	−	0.184360i
$748$		0			0
$749$	6955.53	+	2881.07i	0.339318	+	0.140550i
$750$		0			0
$751$			4475.99i			0.217485i	0.994070	+	0.108742i	$0.0346824\pi$
$751$			4475.99i			0.217485i	−0.994070	+	0.108742i	$0.965318\pi$
$752$		0			0
$753$			16953.8i			0.820493i
$754$		0			0
$755$	−18936.5	−	7843.74i	−0.912806	−	0.378097i
$756$		0			0
$757$	8674.08	+	20941.1i	0.416466	+	1.00544i	0.983363	+	0.181650i	$0.0581436\pi$
$757$	8674.08	+	20941.1i	0.416466	+	1.00544i	−0.566897	+	0.823788i	$0.691856\pi$
$758$		0			0
$759$	5143.09	+	5143.09i	0.245958	+	0.245958i
$760$		0			0
$761$	−6136.35	+	6136.35i	−0.292303	+	0.292303i	−0.837989	−	0.545686i	$-0.816269\pi$
$761$	−6136.35	+	6136.35i	−0.292303	+	0.292303i	0.545686	+	0.837989i	$0.316269\pi$
$762$		0			0
$763$	−934.286	+	386.994i	−0.0443295	+	0.0183619i
$764$		0			0
$765$	2819.48	−	6806.82i	0.133253	−	0.321701i
$766$		0			0
$767$	−20471.3			−0.963725
$768$		0			0
$769$	13154.1			0.616838			0.308419	−	0.951251i	$-0.400200\pi$
$769$	13154.1			0.616838			0.308419	+	0.951251i	$0.400200\pi$
$770$		0			0
$771$	10069.9	−	24310.9i	0.470374	−	1.13558i
$772$		0			0
$773$	14475.7	−	5996.05i	0.673552	−	0.278995i	−0.0195763	−	0.999808i	$-0.506232\pi$
$773$	14475.7	−	5996.05i	0.673552	−	0.278995i	0.693129	+	0.720814i	$0.256232\pi$
$774$		0			0
$775$	5945.42	−	5945.42i	0.275569	−	0.275569i
$776$		0			0
$777$	−6786.86	−	6786.86i	−0.313356	−	0.313356i
$778$		0			0
$779$	1394.41	+	3366.39i	0.0641332	+	0.154831i
$780$		0			0
$781$	−20165.9	−	8353.00i	−0.923936	−	0.382707i
$782$		0			0
$783$		−	25716.1i		−	1.17371i
$784$		0			0
$785$		−	12302.8i		−	0.559369i
$786$		0			0
$787$	−29783.0	−	12336.5i	−1.34898	−	0.558768i	−0.412975	−	0.910742i	$-0.635510\pi$
$787$	−29783.0	−	12336.5i	−1.34898	−	0.558768i	−0.936010	+	0.351975i	$0.885510\pi$
$788$		0			0
$789$	3200.12	+	7725.78i	0.144395	+	0.348599i
$790$		0			0
$791$	3949.41	+	3949.41i	0.177528	+	0.177528i
$792$		0			0
$793$	6453.93	−	6453.93i	0.289011	−	0.289011i
$794$		0			0
$795$	14183.6	−	5875.05i	0.632756	−	0.262096i
$796$		0			0
$797$	179.018	−	432.187i	0.00795626	−	0.0192081i	−0.919851	−	0.392267i	$-0.871691\pi$
$797$	179.018	−	432.187i	0.00795626	−	0.0192081i	0.927808	+	0.373059i	$0.121691\pi$
$798$		0			0
$799$	26243.1			1.16197
$800$		0			0
$801$	−10702.3			−0.472096
$802$		0			0
$803$	−11170.5	+	26968.0i	−0.490907	+	1.18516i
$804$		0			0
$805$	−3636.02	+	1506.09i	−0.159196	+	0.0659412i
$806$		0			0
$807$	446.914	−	446.914i	0.0194946	−	0.0194946i
$808$		0			0
$809$	−1696.33	−	1696.33i	−0.0737205	−	0.0737205i	0.669285	−	0.743006i	$-0.266600\pi$
$809$	−1696.33	−	1696.33i	−0.0737205	−	0.0737205i	−0.743006	+	0.669285i	$0.766600\pi$
$810$		0			0
$811$	9036.86	+	21816.9i	0.391279	+	0.944631i	0.989662	+	0.143421i	$0.0458102\pi$
$811$	9036.86	+	21816.9i	0.391279	+	0.944631i	−0.598383	+	0.801210i	$0.704190\pi$
$812$		0			0
$813$	−6242.93	−	2585.91i	−0.269310	−	0.111552i
$814$		0			0
$815$			33021.5i			1.41925i
$816$		0			0
$817$			21041.5i			0.901037i
$818$		0			0
$819$	−4580.07	−	1897.13i	−0.195410	−	0.0809415i
$820$		0			0
$821$	14759.0	+	35631.4i	0.627397	+	1.51467i	0.842846	+	0.538155i	$0.180878\pi$
$821$	14759.0	+	35631.4i	0.627397	+	1.51467i	−0.215450	+	0.976515i	$0.569122\pi$
$822$		0			0
$823$	26350.3	+	26350.3i	1.11606	+	1.11606i	0.992314	+	0.123742i	$0.0394894\pi$
$823$	26350.3	+	26350.3i	1.11606	+	1.11606i	0.123742	+	0.992314i	$0.460511\pi$
$824$		0			0
$825$	4633.69	−	4633.69i	0.195545	−	0.195545i
$826$		0			0
$827$	−15258.6	+	6320.31i	−0.641587	+	0.265754i	−0.679667	−	0.733521i	$-0.737876\pi$
$827$	−15258.6	+	6320.31i	−0.641587	+	0.265754i	0.0380800	+	0.999275i	$0.487876\pi$
$828$		0			0
$829$	12319.9	−	29742.8i	0.516148	−	1.24609i	−0.424104	−	0.905614i	$-0.639411\pi$
$829$	12319.9	−	29742.8i	0.516148	−	1.24609i	0.940252	−	0.340479i	$-0.110589\pi$
$830$		0			0
$831$	−12742.1			−0.531912
$832$		0			0
$833$	19441.2			0.808640
$834$		0			0
$835$	2585.65	−	6242.31i	0.107162	−	0.258711i
$836$		0			0
$837$	−30916.4	+	12806.0i	−1.27673	+	0.528841i
$838$		0			0
$839$	−17943.3	+	17943.3i	−0.738347	+	0.738347i	−0.972258	−	0.233911i	$-0.924848\pi$
$839$	−17943.3	+	17943.3i	−0.738347	+	0.738347i	0.233911	+	0.972258i	$0.424848\pi$
$840$		0			0
$841$	−2806.57	−	2806.57i	−0.115075	−	0.115075i
$842$		0			0
$843$	804.905	+	1943.21i	0.0328854	+	0.0793924i
$844$		0			0
$845$	48775.2	+	20203.4i	1.98570	+	0.822505i
$846$		0			0
$847$		−	1850.30i		−	0.0750614i
$848$		0			0
$849$		−	13582.0i		−	0.549039i
$850$		0			0
$851$	12183.7	+	5046.64i	0.490776	+	0.203286i
$852$		0			0
$853$	−12194.4	−	29439.9i	−0.489482	−	1.18171i	−0.954981	−	0.296666i	$-0.904125\pi$
$853$	−12194.4	−	29439.9i	−0.489482	−	1.18171i	0.465500	−	0.885048i	$-0.345875\pi$
$854$		0			0
$855$	3123.04	+	3123.04i	0.124919	+	0.124919i
$856$		0			0
$857$	−26988.2	+	26988.2i	−1.07573	+	1.07573i	−0.0788412	+	0.996887i	$0.525122\pi$
$857$	−26988.2	+	26988.2i	−1.07573	+	1.07573i	−0.996887	+	0.0788412i	$0.974878\pi$
$858$		0			0
$859$	−9332.38	+	3865.60i	−0.370683	+	0.153542i	−0.560245	−	0.828327i	$-0.689293\pi$
$859$	−9332.38	+	3865.60i	−0.370683	+	0.153542i	0.189562	+	0.981869i	$0.439293\pi$
$860$		0			0
$861$	1078.20	−	2603.00i	0.0426769	−	0.103031i
$862$		0			0
$863$	−42549.4			−1.67833			−0.839164	−	0.543878i	$-0.816956\pi$
$863$	−42549.4			−1.67833			−0.839164	+	0.543878i	$0.816956\pi$
$864$		0			0
$865$	994.369			0.0390862
$866$		0			0
$867$	−724.003	+	1747.90i	−0.0283604	+	0.0684680i
$868$		0			0
$869$	−7912.26	+	3277.36i	−0.308866	+	0.127937i
$870$		0			0
$871$	48948.6	−	48948.6i	1.90420	−	1.90420i
$872$		0			0
$873$	266.705	+	266.705i	0.0103398	+	0.0103398i
$874$		0			0
$875$	−3063.59	−	7396.17i	−0.118364	−	0.285756i
$876$		0			0
$877$	−29966.3	−	12412.4i	−1.15381	−	0.477923i	−0.277999	−	0.960581i	$-0.589671\pi$
$877$	−29966.3	−	12412.4i	−1.15381	−	0.477923i	−0.875809	+	0.482659i	$0.839671\pi$
$878$		0			0
$879$		−	2561.21i		−	0.0982792i
$880$		0			0
$881$		−	14567.6i		−	0.557088i	−0.960423	−	0.278544i	$-0.910148\pi$
$881$		−	14567.6i		−	0.557088i	0.960423	−	0.278544i	$-0.0898519\pi$
$882$		0			0
$883$	43111.8	+	17857.5i	1.64306	+	0.680580i	0.996602	−	0.0823661i	$-0.0262477\pi$
$883$	43111.8	+	17857.5i	1.64306	+	0.680580i	0.646462	+	0.762946i	$0.276248\pi$
$884$		0			0
$885$	−5396.72	−	13028.8i	−0.204982	−	0.494870i
$886$		0			0
$887$	−3731.29	−	3731.29i	−0.141245	−	0.141245i	0.632949	−	0.774194i	$-0.281844\pi$
$887$	−3731.29	−	3731.29i	−0.141245	−	0.141245i	−0.774194	+	0.632949i	$0.781844\pi$
$888$		0			0
$889$	−2483.92	+	2483.92i	−0.0937097	+	0.0937097i
$890$		0			0
$891$	−15529.6	+	6432.58i	−0.583908	+	0.241863i
$892$		0			0
$893$	−6020.31	+	14534.3i	−0.225601	+	0.544649i
$894$		0			0
$895$	22975.8			0.858097
$896$		0			0
$897$	−14523.7			−0.540614
$898$		0			0
$899$	−14121.6	+	34092.6i	−0.523896	+	1.26480i
$900$		0			0
$901$	−17308.7	+	7169.50i	−0.639996	+	0.265095i
$902$		0			0
$903$	11504.5	−	11504.5i	0.423973	−	0.423973i
$904$		0			0
$905$	17883.6	+	17883.6i	0.656876	+	0.656876i
$906$		0			0
$907$	−2716.64	−	6558.56i	−0.0994538	−	0.240103i	0.866320	−	0.499490i	$-0.166479\pi$
$907$	−2716.64	−	6558.56i	−0.0994538	−	0.240103i	−0.965773	+	0.259387i	$0.916479\pi$
$908$		0			0
$909$	−3684.63	−	1526.22i	−0.134446	−	0.0556894i
$910$		0			0
$911$			26795.2i			0.974496i	0.873264	+	0.487248i	$0.161999\pi$
$911$			26795.2i			0.974496i	−0.873264	+	0.487248i	$0.838001\pi$
$912$		0			0
$913$			18827.9i			0.682491i
$914$		0			0
$915$	5808.97	+	2406.15i	0.209878	+	0.0869345i
$916$		0			0
$917$	5529.21	+	13348.7i	0.199117	+	0.480712i
$918$		0			0
$919$	−39104.1	−	39104.1i	−1.40362	−	1.40362i	−0.788197	−	0.615423i	$-0.788985\pi$
$919$	−39104.1	−	39104.1i	−1.40362	−	1.40362i	−0.615423	−	0.788197i	$-0.711015\pi$
$920$		0			0
$921$	12454.9	−	12454.9i	0.445605	−	0.445605i
$922$		0			0
$923$	40267.6	−	16679.4i	1.43599	−	0.594808i
$924$		0			0
$925$	4546.79	−	10976.9i	0.161619	−	0.390183i
$926$		0			0
$927$	6953.83			0.246379
$928$		0			0
$929$	48932.6			1.72812			0.864061	−	0.503386i	$-0.167913\pi$
$929$	48932.6			1.72812			0.864061	+	0.503386i	$0.167913\pi$
$930$		0			0
$931$	−4459.92	+	10767.2i	−0.157001	+	0.379034i
$932$		0			0
$933$	16370.2	−	6780.77i	0.574423	−	0.237934i
$934$		0			0
$935$	−24076.1	+	24076.1i	−0.842108	+	0.842108i
$936$		0			0
$937$	3286.41	+	3286.41i	0.114581	+	0.114581i	0.762072	−	0.647492i	$-0.224182\pi$
$937$	3286.41	+	3286.41i	0.114581	+	0.114581i	−0.647492	+	0.762072i	$0.724182\pi$
$938$		0			0
$939$	10233.5	+	24706.0i	0.355654	+	0.858625i
$940$		0			0
$941$	12857.9	+	5325.93i	0.445438	+	0.184506i	0.594116	−	0.804379i	$-0.297502\pi$
$941$	12857.9	+	5325.93i	0.445438	+	0.184506i	−0.148678	+	0.988886i	$0.547502\pi$
$942$		0			0
$943$			3871.12i			0.133681i
$944$		0			0
$945$		−	14112.0i		−	0.485782i
$946$		0			0
$947$	−24989.2	−	10350.8i	−0.857485	−	0.355182i	−0.0897616	−	0.995963i	$-0.528611\pi$
$947$	−24989.2	−	10350.8i	−0.857485	−	0.355182i	−0.767723	+	0.640781i	$0.778611\pi$
$948$		0			0
$949$	−22305.4	−	53850.0i	−0.762975	−	1.84199i
$950$		0			0
$951$	6522.59	+	6522.59i	0.222407	+	0.222407i
$952$		0			0
$953$	16871.9	−	16871.9i	0.573488	−	0.573488i	−0.359614	−	0.933101i	$-0.617092\pi$
$953$	16871.9	−	16871.9i	0.573488	−	0.573488i	0.933101	+	0.359614i	$0.117092\pi$
$954$		0			0
$955$	−35706.9	+	14790.3i	−1.20989	+	0.501154i
$956$		0			0
$957$	−11006.0	+	26570.8i	−0.371759	+	0.897504i
$958$		0			0
$959$	13912.1			0.468453
$960$		0			0
$961$	18228.0			0.611864
$962$		0			0
$963$	3434.98	−	8292.77i	0.114943	−	0.277498i
$964$		0			0
$965$	25451.8	−	10542.5i	0.849038	−	0.351683i
$966$		0			0
$967$	−20339.3	+	20339.3i	−0.676388	+	0.676388i	−0.959181	−	0.282793i	$-0.908739\pi$
$967$	−20339.3	+	20339.3i	−0.676388	+	0.676388i	0.282793	+	0.959181i	$0.408739\pi$
$968$		0			0
$969$	8126.35	+	8126.35i	0.269408	+	0.269408i
$970$		0			0
$971$	9157.64	+	22108.5i	0.302660	+	0.730685i	0.999904	+	0.0138517i	$0.00440928\pi$
$971$	9157.64	+	22108.5i	0.302660	+	0.730685i	−0.697244	+	0.716834i	$0.745591\pi$
$972$		0			0
$973$	1340.88	+	555.410i	0.0441794	+	0.0182997i
$974$		0			0
$975$			13085.1i			0.429805i
$976$		0			0
$977$			13599.6i			0.445334i	0.974895	+	0.222667i	$0.0714762\pi$
$977$			13599.6i			0.445334i	−0.974895	+	0.222667i	$0.928524\pi$
$978$		0			0
$979$	45694.7	+	18927.4i	1.49173	+	0.617897i
$980$		0			0
$981$	461.395	+	1113.91i	0.0150165	+	0.0362531i
$982$		0			0
$983$	19227.9	+	19227.9i	0.623882	+	0.623882i	0.946522	−	0.322640i	$-0.104570\pi$
$983$	19227.9	+	19227.9i	0.623882	+	0.623882i	−0.322640	+	0.946522i	$0.604570\pi$
$984$		0			0
$985$	−27704.7	+	27704.7i	−0.896189	+	0.896189i
$986$		0			0
$987$	11238.4	−	4655.08i	0.362433	−	0.150125i
$988$		0			0
$989$	−8554.66	+	20652.8i	−0.275048	+	0.664024i
$990$		0			0
$991$	−10267.1			−0.329106			−0.164553	−	0.986368i	$-0.552618\pi$
$991$	−10267.1			−0.329106			−0.164553	+	0.986368i	$0.552618\pi$
$992$		0			0
$993$	25703.3			0.821420
$994$		0			0
$995$	5198.28	−	12549.8i	0.165625	−	0.399853i
$996$		0			0
$997$	47357.4	−	19616.1i	1.50434	−	0.623117i	0.529957	−	0.848025i	$-0.322208\pi$
$997$	47357.4	−	19616.1i	1.50434	−	0.623117i	0.974380	+	0.224908i	$0.0722082\pi$
$998$		0			0
$999$	−33436.9	+	33436.9i	−1.05895	+	1.05895i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.4.g.b.33.4		44
4.3	odd	2		256.4.g.a.33.8		44
8.3	odd	2		128.4.g.a.17.4		44
8.5	even	2		32.4.g.a.13.11	yes	44
32.5	even	8	inner	256.4.g.b.225.4		44
32.11	odd	8		128.4.g.a.113.4		44
32.21	even	8		32.4.g.a.5.11	✓	44
32.27	odd	8		256.4.g.a.225.8		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.5.11	✓	44	32.21	even	8
32.4.g.a.13.11	yes	44	8.5	even	2
128.4.g.a.17.4		44	8.3	odd	2
128.4.g.a.113.4		44	32.11	odd	8
256.4.g.a.33.8		44	4.3	odd	2
256.4.g.a.225.8		44	32.27	odd	8
256.4.g.b.33.4		44	1.1	even	1	trivial
256.4.g.b.225.4		44	32.5	even	8	inner

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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	256.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.64064 + 3.96085i) q^{3} +(11.8087 - 4.89132i) q^{5} +(-5.11236 + 5.11236i) q^{7} +(6.09524 + 6.09524i) q^{9} +O(q^{10})\)	\(q+(-1.64064 + 3.96085i) q^{3} +(11.8087 - 4.89132i) q^{5} +(-5.11236 + 5.11236i) q^{7} +(6.09524 + 6.09524i) q^{9} +(-15.2446 - 36.8038i) q^{11} +(73.4903 + 30.4407i) q^{13} +54.7973i q^{15} -66.8708i q^{17} +(37.0353 + 15.3405i) q^{19} +(-11.8618 - 28.6368i) q^{21} +(30.1143 + 30.1143i) q^{23} +(27.1316 - 27.1316i) q^{25} +(-141.085 + 58.4395i) q^{27} +(-64.4434 + 155.580i) q^{29} +219.132 q^{31} +170.785 q^{33} +(-35.3641 + 85.3765i) q^{35} +(286.081 - 118.499i) q^{37} +(-241.142 + 241.142i) q^{39} +(64.2737 + 64.2737i) q^{41} +(200.870 + 484.942i) q^{43} +(101.791 + 42.1630i) q^{45} +392.444i q^{47} +290.727i q^{49} +(264.865 + 109.711i) q^{51} +(-107.214 - 258.838i) q^{53} +(-360.038 - 360.038i) q^{55} +(-121.523 + 121.523i) q^{57} +(-237.764 + 98.4852i) q^{59} +(43.9101 - 106.008i) q^{61} -62.3222 q^{63} +1016.72 q^{65} +(333.028 - 804.000i) q^{67} +(-168.685 + 69.8717i) q^{69} +(387.445 - 387.445i) q^{71} +(-518.132 - 518.132i) q^{73} +(62.9512 + 151.978i) q^{75} +(266.091 + 110.218i) q^{77} -214.985i q^{79} -421.957i q^{81} +(-436.657 - 180.869i) q^{83} +(-327.086 - 789.656i) q^{85} +(-510.501 - 510.501i) q^{87} +(-877.926 + 877.926i) q^{89} +(-531.333 + 220.085i) q^{91} +(-359.517 + 867.951i) q^{93} +512.374 q^{95} +43.7563 q^{97} +(131.408 - 317.248i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9	\( 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9} + 4 q^{11} + 4 q^{13} + 4 q^{19} + 4 q^{21} + 324 q^{23} - 4 q^{25} + 268 q^{27} + 4 q^{29} - 752 q^{31} - 8 q^{33} + 460 q^{35} + 4 q^{37} + 596 q^{39} - 4 q^{41} - 804 q^{43} - 104 q^{45} + 1384 q^{51} - 748 q^{53} - 292 q^{55} - 4 q^{57} - 1372 q^{59} + 1828 q^{61} + 2512 q^{63} - 8 q^{65} - 2036 q^{67} + 1060 q^{69} + 220 q^{71} - 4 q^{73} + 1712 q^{75} - 1900 q^{77} - 2436 q^{83} - 496 q^{85} - 1292 q^{87} - 4 q^{89} + 3604 q^{91} + 112 q^{93} - 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9 + 4 * q^11 + 4 * q^13 + 4 * q^19 + 4 * q^21 + 324 * q^23 - 4 * q^25 + 268 * q^27 + 4 * q^29 - 752 * q^31 - 8 * q^33 + 460 * q^35 + 4 * q^37 + 596 * q^39 - 4 * q^41 - 804 * q^43 - 104 * q^45 + 1384 * q^51 - 748 * q^53 - 292 * q^55 - 4 * q^57 - 1372 * q^59 + 1828 * q^61 + 2512 * q^63 - 8 * q^65 - 2036 * q^67 + 1060 * q^69 + 220 * q^71 - 4 * q^73 + 1712 * q^75 - 1900 * q^77 - 2436 * q^83 - 496 * q^85 - 1292 * q^87 - 4 * q^89 + 3604 * q^91 + 112 * q^93 - 6088 * q^95 - 8 * q^97 + 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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