LMFDB - Embedded newform 1368.2.e.g.379.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1368,2,Mod(379,1368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1368, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1368.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1368 = 2^{3} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1368.e (of order $2$, degree $1$, 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:	$10.9235349965$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.15
Character	$\chi$	$=$	1368.379
Dual form			1368.2.e.g.379.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.558288 - 1.29935i) q^{2} +(-1.37663 + 1.45082i) q^{4} -1.71991i q^{5} +0.342554i q^{7} +(2.65369 + 0.978748i) q^{8} +O(q^{10})$	\(q+(-0.558288 - 1.29935i) q^{2} +(-1.37663 + 1.45082i) q^{4} -1.71991i q^{5} +0.342554i q^{7} +(2.65369 + 0.978748i) q^{8} +(-2.23477 + 0.960208i) q^{10} +1.65811 q^{11} -4.72788 q^{13} +(0.445098 - 0.191244i) q^{14} +(-0.209784 - 3.99450i) q^{16} -5.61427 q^{17} +(2.42611 + 3.62133i) q^{19} +(2.49529 + 2.36769i) q^{20} +(-0.925701 - 2.15446i) q^{22} -3.13552i q^{23} +2.04189 q^{25} +(2.63952 + 6.14317i) q^{26} +(-0.496986 - 0.471570i) q^{28} -1.36187 q^{29} -6.03963 q^{31} +(-5.07313 + 2.50266i) q^{32} +(3.13438 + 7.29491i) q^{34} +0.589164 q^{35} -4.87686 q^{37} +(3.35091 - 5.17411i) q^{38} +(1.68336 - 4.56412i) q^{40} -0.258720i q^{41} -9.29057 q^{43} +(-2.28260 + 2.40562i) q^{44} +(-4.07414 + 1.75052i) q^{46} -1.67000i q^{47} +6.88266 q^{49} +(-1.13996 - 2.65314i) q^{50} +(6.50853 - 6.85932i) q^{52} -13.5751 q^{53} -2.85180i q^{55} +(-0.335274 + 0.909032i) q^{56} +(0.760315 + 1.76955i) q^{58} -6.84913i q^{59} +14.1874i q^{61} +(3.37185 + 7.84760i) q^{62} +(6.08411 + 5.19458i) q^{64} +8.13155i q^{65} +5.78635i q^{67} +(7.72877 - 8.14532i) q^{68} +(-0.328923 - 0.765531i) q^{70} -3.71913 q^{71} +9.05440 q^{73} +(2.72269 + 6.33675i) q^{74} +(-8.59376 - 1.46537i) q^{76} +0.567991i q^{77} -6.46470 q^{79} +(-6.87019 + 0.360810i) q^{80} +(-0.336169 + 0.144440i) q^{82} -10.3405 q^{83} +9.65607i q^{85} +(5.18682 + 12.0717i) q^{86} +(4.40010 + 1.62287i) q^{88} +9.18327i q^{89} -1.61955i q^{91} +(4.54909 + 4.31645i) q^{92} +(-2.16992 + 0.932340i) q^{94} +(6.22837 - 4.17270i) q^{95} +7.65610i q^{97} +(-3.84250 - 8.94299i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{4}+O(q^{10}) $ 40 * q - 4 * q^4	$ 40 q - 4 q^{4} + 4 q^{16} + 8 q^{19} - 32 q^{20} - 40 q^{25} - 40 q^{26} - 8 q^{28} + 48 q^{35} + 8 q^{44} - 56 q^{49} + 16 q^{58} - 40 q^{62} + 68 q^{64} + 88 q^{68} - 16 q^{73} + 40 q^{74} - 12 q^{76} + 32 q^{80} - 64 q^{82} - 80 q^{83} + 48 q^{92}+O(q^{100}) $ 40 * q - 4 * q^4 + 4 * q^16 + 8 * q^19 - 32 * q^20 - 40 * q^25 - 40 * q^26 - 8 * q^28 + 48 * q^35 + 8 * q^44 - 56 * q^49 + 16 * q^58 - 40 * q^62 + 68 * q^64 + 88 * q^68 - 16 * q^73 + 40 * q^74 - 12 * q^76 + 32 * q^80 - 64 * q^82 - 80 * q^83 + 48 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times$.

$n$	$343$	$685$	$1009$	$1217$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−0.558288	−	1.29935i	−0.394769	−	0.918780i
$2$	−0.558288	−	1.29935i	−0.394769	−	0.918780i
$3$		0			0
$3$		0			0
$4$	−1.37663	+	1.45082i	−0.688315	+	0.725412i
$5$		−	1.71991i		−	0.769169i	−0.923090	−	0.384585i	$-0.874345\pi$
$5$		−	1.71991i		−	0.769169i	0.923090	−	0.384585i	$-0.125655\pi$
$6$		0			0
$7$			0.342554i			0.129473i	0.997902	+	0.0647367i	$0.0206207\pi$
$7$			0.342554i			0.129473i	−0.997902	+	0.0647367i	$0.979379\pi$
$8$	2.65369	+	0.978748i	0.938220	+	0.346040i
$9$		0			0
$10$	−2.23477	+	0.960208i	−0.706698	+	0.303644i
$11$	1.65811			0.499938			0.249969	−	0.968254i	$-0.419580\pi$
$11$	1.65811			0.499938			0.249969	+	0.968254i	$0.419580\pi$
$12$		0			0
$13$	−4.72788			−1.31128			−0.655639	−	0.755075i	$-0.727600\pi$
$13$	−4.72788			−1.31128			−0.655639	+	0.755075i	$0.727600\pi$
$14$	0.445098	−	0.191244i	0.118958	−	0.0511121i
$15$		0			0
$16$	−0.209784	−	3.99450i	−0.0524460	−	0.998624i
$17$	−5.61427			−1.36166			−0.680830	−	0.732441i	$-0.738381\pi$
$17$	−5.61427			−1.36166			−0.680830	+	0.732441i	$0.738381\pi$
$18$		0			0
$19$	2.42611	+	3.62133i	0.556587	+	0.830789i
$19$	2.42611	+	3.62133i	0.556587	+	0.830789i
$20$	2.49529	+	2.36769i	0.557965	+	0.529430i
$21$		0			0
$22$	−0.925701	−	2.15446i	−0.197360	−	0.459333i
$23$		−	3.13552i		−	0.653801i	−0.945059	−	0.326901i	$-0.893996\pi$
$23$		−	3.13552i		−	0.653801i	0.945059	−	0.326901i	$-0.106004\pi$
$24$		0			0
$25$	2.04189			0.408379
$26$	2.63952	+	6.14317i	0.517652	+	1.20478i
$27$		0			0
$28$	−0.496986	−	0.471570i	−0.0939215	−	0.0891184i
$29$	−1.36187			−0.252893			−0.126446	−	0.991973i	$-0.540357\pi$
$29$	−1.36187			−0.252893			−0.126446	+	0.991973i	$0.540357\pi$
$30$		0			0
$31$	−6.03963			−1.08475			−0.542374	−	0.840137i	$-0.682475\pi$
$31$	−6.03963			−1.08475			−0.542374	+	0.840137i	$0.682475\pi$
$32$	−5.07313	+	2.50266i	−0.896812	+	0.442412i
$33$		0			0
$34$	3.13438	+	7.29491i	0.537542	+	1.25107i
$35$	0.589164			0.0995869
$36$		0			0
$37$	−4.87686			−0.801750			−0.400875	−	0.916133i	$-0.631294\pi$
$37$	−4.87686			−0.801750			−0.400875	+	0.916133i	$0.631294\pi$
$38$	3.35091	−	5.17411i	0.543590	−	0.839351i
$39$		0			0
$40$	1.68336	−	4.56412i	0.266163	−	0.721650i
$41$		−	0.258720i		−	0.0404053i	−0.999796	−	0.0202027i	$-0.993569\pi$
$41$		−	0.258720i		−	0.0404053i	0.999796	−	0.0202027i	$-0.00643114\pi$
$42$		0			0
$43$	−9.29057			−1.41680			−0.708400	−	0.705812i	$-0.750583\pi$
$43$	−9.29057			−1.41680			−0.708400	+	0.705812i	$0.750583\pi$
$44$	−2.28260	+	2.40562i	−0.344115	+	0.362661i
$45$		0			0
$46$	−4.07414	+	1.75052i	−0.600700	+	0.258101i
$47$		−	1.67000i		−	0.243594i	−0.992555	−	0.121797i	$-0.961134\pi$
$47$		−	1.67000i		−	0.243594i	0.992555	−	0.121797i	$-0.0388658\pi$
$48$		0			0
$49$	6.88266			0.983237
$50$	−1.13996	−	2.65314i	−0.161215	−	0.375210i
$51$		0			0
$52$	6.50853	−	6.85932i	0.902571	−	0.951217i
$53$	−13.5751			−1.86469			−0.932343	−	0.361576i	$-0.882239\pi$
$53$	−13.5751			−1.86469			−0.932343	+	0.361576i	$0.882239\pi$
$54$		0			0
$55$		−	2.85180i		−	0.384537i
$56$	−0.335274	+	0.909032i	−0.0448029	+	0.121474i
$57$		0			0
$58$	0.760315	+	1.76955i	0.0998343	+	0.232353i
$59$		−	6.84913i		−	0.891681i	−0.895112	−	0.445840i	$-0.852905\pi$
$59$		−	6.84913i		−	0.891681i	0.895112	−	0.445840i	$-0.147095\pi$
$60$		0			0
$61$			14.1874i			1.81651i	0.418414	+	0.908256i	$0.362586\pi$
$61$			14.1874i			1.81651i	−0.418414	+	0.908256i	$0.637414\pi$
$62$	3.37185	+	7.84760i	0.428225	+	0.996646i
$63$		0			0
$64$	6.08411	+	5.19458i	0.760513	+	0.649322i
$65$			8.13155i			1.00859i
$66$		0			0
$67$			5.78635i			0.706915i	0.935450	+	0.353458i	$0.114994\pi$
$67$			5.78635i			0.706915i	−0.935450	+	0.353458i	$0.885006\pi$
$68$	7.72877	−	8.14532i	0.937251	−	0.987765i
$69$		0			0
$70$	−0.328923	−	0.765531i	−0.0393138	−	0.0914985i
$71$	−3.71913			−0.441379			−0.220689	−	0.975344i	$-0.570831\pi$
$71$	−3.71913			−0.441379			−0.220689	+	0.975344i	$0.570831\pi$
$72$		0			0
$73$	9.05440			1.05974			0.529869	−	0.848080i	$-0.322241\pi$
$73$	9.05440			1.05974			0.529869	+	0.848080i	$0.322241\pi$
$74$	2.72269	+	6.33675i	0.316506	+	0.736632i
$75$		0			0
$76$	−8.59376	−	1.46537i	−0.985772	−	0.168089i
$77$			0.567991i			0.0647286i
$78$		0			0
$79$	−6.46470			−0.727336			−0.363668	−	0.931529i	$-0.618476\pi$
$79$	−6.46470			−0.727336			−0.363668	+	0.931529i	$0.618476\pi$
$80$	−6.87019	+	0.360810i	−0.768111	+	0.0403398i
$81$		0			0
$82$	−0.336169	+	0.144440i	−0.0371236	+	0.0159508i
$83$	−10.3405			−1.13502			−0.567509	−	0.823367i	$-0.692093\pi$
$83$	−10.3405			−1.13502			−0.567509	+	0.823367i	$0.692093\pi$
$84$		0			0
$85$			9.65607i			1.04735i
$86$	5.18682	+	12.0717i	0.559309	+	1.30173i
$87$		0			0
$88$	4.40010	+	1.62287i	0.469052	+	0.172998i
$89$			9.18327i			0.973425i	0.873562	+	0.486712i	$0.161804\pi$
$89$			9.18327i			0.973425i	−0.873562	+	0.486712i	$0.838196\pi$
$90$		0			0
$91$		−	1.61955i		−	0.169775i
$92$	4.54909	+	4.31645i	0.474276	+	0.450021i
$93$		0			0
$94$	−2.16992	+	0.932340i	−0.223810	+	0.0961636i
$95$	6.22837	−	4.17270i	0.639018	−	0.428110i
$96$		0			0
$97$			7.65610i			0.777359i	0.921373	+	0.388679i	$0.127069\pi$
$97$			7.65610i			0.777359i	−0.921373	+	0.388679i	$0.872931\pi$
$98$	−3.84250	−	8.94299i	−0.388152	−	0.903379i
$99$		0			0
$100$	−2.81093	+	2.96243i	−0.281093	+	0.296243i
$101$			7.42911i			0.739224i	0.929186	+	0.369612i	$0.120509\pi$
$101$			7.42911i			0.739224i	−0.929186	+	0.369612i	$0.879491\pi$
$102$		0			0
$103$	0.00914495			0.000901079			0.000450539	−	1.00000i	$-0.499857\pi$
$103$	0.00914495			0.000901079			0.000450539		1.00000i	$0.499857\pi$
$104$	−12.5463	−	4.62740i	−1.23027	−	0.453754i
$105$		0			0
$106$	7.57882	+	17.6388i	0.736120	+	1.71324i
$107$			1.51249i			0.146218i	0.997324	+	0.0731092i	$0.0232922\pi$
$107$			1.51249i			0.146218i	−0.997324	+	0.0731092i	$0.976708\pi$
$108$		0			0
$109$	14.4449			1.38357			0.691785	−	0.722104i	$-0.256825\pi$
$109$	14.4449			1.38357			0.691785	+	0.722104i	$0.256825\pi$
$110$	−3.70549	+	1.59213i	−0.353305	+	0.151803i
$111$		0			0
$112$	1.36833	−	0.0718623i	0.129295	−	0.00679035i
$113$			12.0648i			1.13496i	0.823388	+	0.567478i	$0.192081\pi$
$113$			12.0648i			1.13496i	−0.823388	+	0.567478i	$0.807919\pi$
$114$		0			0
$115$	−5.39283			−0.502884
$116$	1.87479	−	1.97583i	0.174070	−	0.183451i
$117$		0			0
$118$	−8.89943	+	3.82379i	−0.819259	+	0.352008i
$119$		−	1.92319i		−	0.176299i
$120$		0			0
$121$	−8.25068			−0.750062
$122$	18.4344	−	7.92066i	1.66898	−	0.717103i
$123$		0			0
$124$	8.31433	−	8.76244i	0.746649	−	0.786890i
$125$		−	12.1115i		−	1.08328i
$126$		0			0
$127$	−1.86283			−0.165300			−0.0826498	−	0.996579i	$-0.526338\pi$
$127$	−1.86283			−0.165300			−0.0826498	+	0.996579i	$0.526338\pi$
$128$	3.35290	−	10.8055i	0.296357	−	0.955077i
$129$		0			0
$130$	10.5657	−	4.53974i	0.926676	−	0.398162i
$131$	−1.20224			−0.105040			−0.0525202	−	0.998620i	$-0.516725\pi$
$131$	−1.20224			−0.105040			−0.0525202	+	0.998620i	$0.516725\pi$
$132$		0			0
$133$	−1.24050	+	0.831073i	−0.107565	+	0.0720632i
$134$	7.51851	−	3.23045i	0.649500	−	0.279068i
$135$		0			0
$136$	−14.8985	−	5.49495i	−1.27754	−	0.471188i
$137$	−0.491024			−0.0419510			−0.0209755	−	0.999780i	$-0.506677\pi$
$137$	−0.491024			−0.0419510			−0.0209755	+	0.999780i	$0.506677\pi$
$138$		0			0
$139$	−10.2434			−0.868834			−0.434417	−	0.900712i	$-0.643046\pi$
$139$	−10.2434			−0.868834			−0.434417	+	0.900712i	$0.643046\pi$
$140$	−0.811061	+	0.854774i	−0.0685471	+	0.0722416i
$141$		0			0
$142$	2.07634	+	4.83245i	0.174243	+	0.405530i
$143$	−7.83933			−0.655557
$144$		0			0
$145$			2.34230i			0.194517i
$146$	−5.05496	−	11.7649i	−0.418352	−	0.973666i
$147$		0			0
$148$	6.71362	−	7.07546i	0.551856	−	0.581599i
$149$		−	3.22235i		−	0.263985i	−0.991251	−	0.131993i	$-0.957863\pi$
$149$		−	3.22235i		−	0.263985i	0.991251	−	0.131993i	$-0.0421375\pi$
$150$		0			0
$151$	12.8206			1.04332			0.521662	−	0.853152i	$-0.325312\pi$
$151$	12.8206			1.04332			0.521662	+	0.853152i	$0.325312\pi$
$152$	2.89376	+	11.9844i	0.234715	+	0.972064i
$153$		0			0
$154$	0.738021	−	0.317103i	0.0594714	−	0.0255529i
$155$			10.3876i			0.834356i
$156$		0			0
$157$		−	22.4852i		−	1.79452i	−0.441506	−	0.897258i	$-0.645556\pi$
$157$		−	22.4852i		−	1.79452i	0.441506	−	0.897258i	$-0.354444\pi$
$158$	3.60916	+	8.39992i	0.287130	+	0.668262i
$159$		0			0
$160$	4.30436	+	8.72536i	0.340290	+	0.689800i
$161$	1.07409			0.0846498
$162$		0			0
$163$	−5.38711			−0.421951			−0.210976	−	0.977491i	$-0.567664\pi$
$163$	−5.38711			−0.421951			−0.210976	+	0.977491i	$0.567664\pi$
$164$	0.375358	+	0.356162i	0.0293105	+	0.0278116i
$165$		0			0
$166$	5.77298	+	13.4360i	0.448070	+	1.04283i
$167$	−2.45682			−0.190115			−0.0950574	−	0.995472i	$-0.530303\pi$
$167$	−2.45682			−0.190115			−0.0950574	+	0.995472i	$0.530303\pi$
$168$		0			0
$169$	9.35282			0.719448
$170$	12.5466	−	5.39087i	0.962282	−	0.413460i
$171$		0			0
$172$	12.7897	−	13.4790i	0.975204	−	1.02776i
$173$	−15.9885			−1.21558			−0.607790	−	0.794097i	$-0.707944\pi$
$173$	−15.9885			−1.21558			−0.607790	+	0.794097i	$0.707944\pi$
$174$		0			0
$175$			0.699459i			0.0528741i
$176$	−0.347844	−	6.62330i	−0.0262197	−	0.499250i
$177$		0			0
$178$	11.9323	−	5.12691i	0.894363	−	0.384278i
$179$		−	14.4228i		−	1.07801i	−0.842301	−	0.539007i	$-0.818800\pi$
$179$		−	14.4228i		−	1.07801i	0.842301	−	0.539007i	$-0.181200\pi$
$180$		0			0
$181$	−12.4912			−0.928461			−0.464231	−	0.885714i	$-0.653669\pi$
$181$	−12.4912			−0.928461			−0.464231	+	0.885714i	$0.653669\pi$
$182$	−2.10437	+	0.904178i	−0.155986	+	0.0670221i
$183$		0			0
$184$	3.06888	−	8.32069i	0.226241	−	0.613409i
$185$			8.38778i			0.616682i
$186$		0			0
$187$	−9.30906			−0.680746
$188$	2.42288	+	2.29897i	0.176706	+	0.167670i
$189$		0			0
$190$	−8.89903	−	5.76328i	−0.645603	−	0.418112i
$191$			14.1792i			1.02597i	0.858396	+	0.512987i	$0.171461\pi$
$191$			14.1792i			1.02597i	−0.858396	+	0.512987i	$0.828539\pi$
$192$		0			0
$193$		−	8.62850i		−	0.621093i	−0.950558	−	0.310547i	$-0.899488\pi$
$193$		−	8.62850i		−	0.621093i	0.950558	−	0.310547i	$-0.100512\pi$
$194$	9.94796	−	4.27431i	0.714222	−	0.306877i
$195$		0			0
$196$	−9.47487	+	9.98553i	−0.676776	+	0.713252i
$197$			19.7211i			1.40507i	0.711648	+	0.702536i	$0.247949\pi$
$197$			19.7211i			1.40507i	−0.711648	+	0.702536i	$0.752051\pi$
$198$		0			0
$199$		−	13.3718i		−	0.947901i	−0.880551	−	0.473950i	$-0.842828\pi$
$199$		−	13.3718i		−	0.947901i	0.880551	−	0.473950i	$-0.157172\pi$
$200$	5.41854	+	1.99850i	0.383149	+	0.141315i
$201$		0			0
$202$	9.65302	−	4.14758i	0.679184	−	0.291823i
$203$		−	0.466514i		−	0.0327429i
$204$		0			0
$205$	−0.444977			−0.0310785
$206$	−0.00510552	−	0.0118825i	−0.000355718	−	0.000827893i
$207$		0			0
$208$	0.991832	+	18.8855i	0.0687712	+	1.30947i
$209$	4.02274	+	6.00455i	0.278259	+	0.415343i
$210$		0			0
$211$		−	13.5526i		−	0.932999i	−0.884521	−	0.466500i	$-0.845515\pi$
$211$		−	13.5526i		−	0.932999i	0.884521	−	0.466500i	$-0.154485\pi$
$212$	18.6879	−	19.6951i	1.28349	−	1.35267i
$213$		0			0
$214$	1.96526	−	0.844407i	0.134343	−	0.0577225i
$215$			15.9790i			1.08976i
$216$		0			0
$217$		−	2.06890i		−	0.140446i
$218$	−8.06441	−	18.7690i	−0.546191	−	1.27120i
$219$		0			0
$220$	4.13747	+	3.92587i	0.278948	+	0.264682i
$221$	26.5436			1.78551
$222$		0			0
$223$	28.6194			1.91650			0.958248	−	0.285940i	$-0.0923057\pi$
$223$	28.6194			1.91650			0.958248	+	0.285940i	$0.0923057\pi$
$224$	−0.857297	−	1.73782i	−0.0572806	−	0.116113i
$225$		0			0
$226$	15.6764	−	6.73561i	1.04278	−	0.448046i
$227$			11.2369i			0.745820i	0.927868	+	0.372910i	$0.121640\pi$
$227$			11.2369i			0.745820i	−0.927868	+	0.372910i	$0.878360\pi$
$228$		0			0
$229$		−	6.71479i		−	0.443726i	−0.975078	−	0.221863i	$-0.928786\pi$
$229$		−	6.71479i		−	0.443726i	0.975078	−	0.221863i	$-0.0712137\pi$
$230$	3.01075	+	7.00718i	0.198523	+	0.462040i
$231$		0			0
$232$	−3.61397	−	1.33293i	−0.237269	−	0.0875109i
$233$	11.1262			0.728901			0.364451	−	0.931223i	$-0.381257\pi$
$233$	11.1262			0.728901			0.364451	+	0.931223i	$0.381257\pi$
$234$		0			0
$235$	−2.87226			−0.187365
$236$	9.93689	+	9.42871i	0.646836	+	0.613757i
$237$		0			0
$238$	−2.49890	+	1.07369i	−0.161980	+	0.0695973i
$239$		−	28.8075i		−	1.86340i	−0.363223	−	0.931702i	$-0.618324\pi$
$239$		−	28.8075i		−	1.86340i	0.363223	−	0.931702i	$-0.381676\pi$
$240$		0			0
$241$			4.33620i			0.279319i	0.990200	+	0.139660i	$0.0446008\pi$
$241$			4.33620i			0.279319i	−0.990200	+	0.139660i	$0.955399\pi$
$242$	4.60626	+	10.7205i	0.296101	+	0.689142i
$243$		0			0
$244$	−20.5835	−	19.5308i	−1.31772	−	1.25033i
$245$		−	11.8376i		−	0.756275i
$246$		0			0
$247$	−11.4703	−	17.1212i	−0.729840	−	1.08940i
$248$	−16.0273	−	5.91127i	−1.01773	−	0.375366i
$249$		0			0
$250$	−15.7370	+	6.76168i	−0.995298	+	0.427646i
$251$	−9.54753			−0.602635			−0.301318	−	0.953524i	$-0.597426\pi$
$251$	−9.54753			−0.602635			−0.301318	+	0.953524i	$0.597426\pi$
$252$		0			0
$253$		−	5.19903i		−	0.326860i
$254$	1.04000	+	2.42047i	0.0652552	+	0.151874i
$255$		0			0
$256$	−15.9120	+	1.67596i	−0.994499	+	0.104748i
$257$		−	10.8840i		−	0.678924i	−0.940620	−	0.339462i	$-0.889755\pi$
$257$		−	10.8840i		−	0.678924i	0.940620	−	0.339462i	$-0.110245\pi$
$258$		0			0
$259$		−	1.67059i		−	0.103805i
$260$	−11.7974	−	11.1941i	−0.731647	−	0.694230i
$261$		0			0
$262$	0.671197	+	1.56213i	0.0414667	+	0.0965090i
$263$			19.6870i			1.21395i	0.794720	+	0.606976i	$0.207618\pi$
$263$			19.6870i			1.21395i	−0.794720	+	0.606976i	$0.792382\pi$
$264$		0			0
$265$			23.3480i			1.43426i
$266$	1.77241	+	1.14787i	0.108674	+	0.0703803i
$267$		0			0
$268$	−8.39498	−	7.96566i	−0.512805	−	0.486580i
$269$	1.96852			0.120023			0.0600113	−	0.998198i	$-0.480886\pi$
$269$	1.96852			0.120023			0.0600113	+	0.998198i	$0.480886\pi$
$270$		0			0
$271$		−	5.02022i		−	0.304957i	−0.988307	−	0.152478i	$-0.951275\pi$
$271$		−	5.02022i		−	0.304957i	0.988307	−	0.152478i	$-0.0487254\pi$
$272$	1.17778	+	22.4262i	0.0714136	+	1.35979i
$273$		0			0
$274$	0.274133	+	0.638012i	0.0165610	+	0.0385437i
$275$	3.38568			0.204164
$276$		0			0
$277$		−	14.7763i		−	0.887824i	−0.896070	−	0.443912i	$-0.853590\pi$
$277$		−	14.7763i		−	0.887824i	0.896070	−	0.443912i	$-0.146410\pi$
$278$	5.71876	+	13.3098i	0.342989	+	0.798267i
$279$		0			0
$280$	1.56346	+	0.576643i	0.0934344	+	0.0344610i
$281$		−	17.0536i		−	1.01733i	−0.860964	−	0.508666i	$-0.830139\pi$
$281$		−	17.0536i		−	1.01733i	0.860964	−	0.508666i	$-0.169861\pi$
$282$		0			0
$283$	−25.3478			−1.50677			−0.753386	−	0.657579i	$-0.771581\pi$
$283$	−25.3478			−1.50677			−0.753386	+	0.657579i	$0.771581\pi$
$284$	5.11986	−	5.39580i	0.303808	−	0.320182i
$285$		0			0
$286$	4.37660	+	10.1860i	0.258794	+	0.602313i
$287$	0.0886257			0.00523141
$288$		0			0
$289$	14.5200			0.854119
$290$	3.04347	−	1.30768i	0.178719	−	0.0767894i
$291$		0			0
$292$	−12.4646	+	13.1363i	−0.729433	+	0.768747i
$293$	−9.37744			−0.547836			−0.273918	−	0.961753i	$-0.588320\pi$
$293$	−9.37744			−0.547836			−0.273918	+	0.961753i	$0.588320\pi$
$294$		0			0
$295$	−11.7799			−0.685854
$296$	−12.9416	−	4.77321i	−0.752218	−	0.277437i
$297$		0			0
$298$	−4.18696	+	1.79900i	−0.242544	+	0.104213i
$299$			14.8244i			0.857315i
$300$		0			0
$301$		−	3.18253i		−	0.183438i
$302$	−7.15758	−	16.6585i	−0.411872	−	0.958586i
$303$		0			0
$304$	13.9564	−	10.4508i	0.800455	−	0.599393i
$305$	24.4012			1.39721
$306$		0			0
$307$		−	18.9434i		−	1.08116i	−0.841293	−	0.540579i	$-0.818205\pi$
$307$		−	18.9434i		−	1.08116i	0.841293	−	0.540579i	$-0.181795\pi$
$308$	−0.824056	−	0.781914i	−0.0469549	−	0.0445537i
$309$		0			0
$310$	13.4972	−	5.79930i	0.766589	−	0.329378i
$311$		−	14.2323i		−	0.807039i	−0.914971	−	0.403520i	$-0.867787\pi$
$311$		−	14.2323i		−	0.807039i	0.914971	−	0.403520i	$-0.132213\pi$
$312$		0			0
$313$	8.33434			0.471085			0.235542	−	0.971864i	$-0.424313\pi$
$313$	8.33434			0.471085			0.235542	+	0.971864i	$0.424313\pi$
$314$	−29.2162	+	12.5532i	−1.64877	+	0.708420i
$315$		0			0
$316$	8.89950	−	9.37915i	0.500636	−	0.527618i
$317$	5.92607			0.332841			0.166421	−	0.986055i	$-0.446779\pi$
$317$	5.92607			0.332841			0.166421	+	0.986055i	$0.446779\pi$
$318$		0			0
$319$	−2.25812			−0.126431
$320$	8.93423	−	10.4641i	0.499439	−	0.584963i
$321$		0			0
$322$	−0.599649	−	1.39562i	−0.0334171	−	0.0777746i
$323$	−13.6208	−	20.3311i	−0.757883	−	1.13125i
$324$		0			0
$325$	−9.65382			−0.535498
$326$	3.00756	+	6.99975i	0.166573	+	0.387680i
$327$		0			0
$328$	0.253222	−	0.686562i	0.0139818	−	0.0379091i
$329$	0.572065			0.0315390
$330$		0			0
$331$		−	24.4626i		−	1.34458i	−0.740286	−	0.672292i	$-0.765310\pi$
$331$		−	24.4626i		−	1.34458i	0.740286	−	0.672292i	$-0.234690\pi$
$332$	14.2350	−	15.0023i	0.781250	−	0.823356i
$333$		0			0
$334$	1.37161	+	3.19228i	0.0750514	+	0.174674i
$335$	9.95203			0.543738
$336$		0			0
$337$			6.58037i			0.358456i	0.983808	+	0.179228i	$0.0573600\pi$
$337$			6.58037i			0.358456i	−0.983808	+	0.179228i	$0.942640\pi$
$338$	−5.22157	−	12.1526i	−0.284016	−	0.661015i
$339$		0			0
$340$	−14.0093	−	13.2928i	−0.759759	−	0.720905i
$341$	−10.0143			−0.542307
$342$		0			0
$343$			4.75556i			0.256776i
$344$	−24.6543	−	9.09313i	−1.32927	−	0.490269i
$345$		0			0
$346$	8.92617	+	20.7746i	0.479874	+	1.11685i
$347$	−4.16884			−0.223795			−0.111898	−	0.993720i	$-0.535693\pi$
$347$	−4.16884			−0.223795			−0.111898	+	0.993720i	$0.535693\pi$
$348$		0			0
$349$			28.4770i			1.52434i	0.647377	+	0.762170i	$0.275866\pi$
$349$			28.4770i			1.52434i	−0.647377	+	0.762170i	$0.724134\pi$
$350$	0.908843	−	0.390500i	0.0485797	−	0.0208731i
$351$		0			0
$352$	−8.41180	+	4.14968i	−0.448350	+	0.221179i
$353$	−1.98669			−0.105741			−0.0528704	−	0.998601i	$-0.516837\pi$
$353$	−1.98669			−0.105741			−0.0528704	+	0.998601i	$0.516837\pi$
$354$		0			0
$355$			6.39658i			0.339495i
$356$	−13.3233	−	12.6420i	−0.706134	−	0.670022i
$357$		0			0
$358$	−18.7403	+	8.05210i	−0.990458	+	0.425567i
$359$		−	30.4330i		−	1.60619i	−0.595850	−	0.803096i	$-0.703185\pi$
$359$		−	30.4330i		−	1.60619i	0.595850	−	0.803096i	$-0.296815\pi$
$360$		0			0
$361$	−7.22801	+	17.5714i	−0.380422	+	0.924813i
$362$	6.97367	+	16.2304i	0.366528	+	0.853052i
$363$		0			0
$364$	2.34969	+	2.22953i	0.123157	+	0.116859i
$365$		−	15.5728i		−	0.815118i
$366$		0			0
$367$		−	32.8643i		−	1.71550i	−0.514063	−	0.857752i	$-0.671860\pi$
$367$		−	32.8643i		−	1.71550i	0.514063	−	0.857752i	$-0.328140\pi$
$368$	−12.5248	+	0.657782i	−0.652902	+	0.0342892i
$369$		0			0
$370$	10.8987	−	4.68279i	0.566595	−	0.243447i
$371$		−	4.65021i		−	0.241427i
$372$		0			0
$373$	−4.97097			−0.257387			−0.128694	−	0.991684i	$-0.541078\pi$
$373$	−4.97097			−0.257387			−0.128694	+	0.991684i	$0.541078\pi$
$374$	5.19714	+	12.0957i	0.268737	+	0.625456i
$375$		0			0
$376$	1.63451	−	4.43165i	0.0842933	−	0.228545i
$377$	6.43875			0.331612
$378$		0			0
$379$		−	28.5095i		−	1.46443i	−0.681072	−	0.732216i	$-0.738486\pi$
$379$		−	28.5095i		−	1.46443i	0.681072	−	0.732216i	$-0.261514\pi$
$380$	−2.52031	+	14.7805i	−0.129289	+	0.758225i
$381$		0			0
$382$	18.4238	−	7.91610i	0.942645	−	0.405023i
$383$	−32.7071			−1.67125			−0.835627	−	0.549297i	$-0.814895\pi$
$383$	−32.7071			−1.67125			−0.835627	+	0.549297i	$0.814895\pi$
$384$		0			0
$385$	0.976897			0.0497873
$386$	−11.2115	+	4.81719i	−0.570648	+	0.245188i
$387$		0			0
$388$	−11.1077	−	10.5396i	−0.563906	−	0.535067i
$389$		−	12.1616i		−	0.616616i	−0.951287	−	0.308308i	$-0.900237\pi$
$389$		−	12.1616i		−	0.616616i	0.951287	−	0.308308i	$-0.0997628\pi$
$390$		0			0
$391$			17.6037i			0.890256i
$392$	18.2644	+	6.73638i	0.922492	+	0.340239i
$393$		0			0
$394$	25.6247	−	11.0101i	1.29095	−	0.554679i
$395$			11.1187i			0.559444i
$396$		0			0
$397$			16.3134i			0.818749i	0.912367	+	0.409374i	$0.134253\pi$
$397$			16.3134i			0.818749i	−0.912367	+	0.409374i	$0.865747\pi$
$398$	−17.3747	+	7.46531i	−0.870913	+	0.374202i
$399$		0			0
$400$	−0.428356	−	8.15633i	−0.0214178	−	0.407817i
$401$		−	9.02475i		−	0.450675i	−0.974281	−	0.225337i	$-0.927652\pi$
$401$		−	9.02475i		−	0.450675i	0.974281	−	0.225337i	$-0.0723484\pi$
$402$		0			0
$403$	28.5546			1.42241
$404$	−10.7783	−	10.2271i	−0.536242	−	0.508818i
$405$		0			0
$406$	−0.606166	+	0.260449i	−0.0300835	+	0.0129259i
$407$	−8.08635			−0.400825
$408$		0			0
$409$			28.6728i			1.41778i	0.705320	+	0.708889i	$0.250803\pi$
$409$			28.6728i			1.41778i	−0.705320	+	0.708889i	$0.749197\pi$
$410$	0.248425	+	0.578181i	0.0122688	+	0.0285543i
$411$		0			0
$412$	−0.0125892	+	0.0132677i	−0.000620226	+	0.000653654i
$413$	2.34620			0.115449
$414$		0			0
$415$			17.7848i			0.873021i
$416$	23.9852	−	11.8323i	1.17597	−	0.580125i
$417$		0			0
$418$	5.55617	−	8.57922i	0.271761	−	0.419624i
$419$	−39.2518			−1.91758			−0.958788	−	0.284122i	$-0.908298\pi$
$419$	−39.2518			−1.91758			−0.958788	+	0.284122i	$0.908298\pi$
$420$		0			0
$421$	−0.0934950			−0.00455667			−0.00227833	−	0.999997i	$-0.500725\pi$
$421$	−0.0934950			−0.00455667			−0.00227833	+	0.999997i	$0.500725\pi$
$422$	−17.6096	+	7.56625i	−0.857221	+	0.368319i
$423$		0			0
$424$	−36.0241	−	13.2866i	−1.74948	−	0.645255i
$425$	−11.4637			−0.556073
$426$		0			0
$427$	−4.85996			−0.235190
$428$	−2.19436	−	2.08214i	−0.106069	−	0.100644i
$429$		0			0
$430$	20.7623	−	8.92088i	1.00125	−	0.430203i
$431$	23.8027			1.14654			0.573268	−	0.819368i	$-0.305675\pi$
$431$	23.8027			1.14654			0.573268	+	0.819368i	$0.305675\pi$
$432$		0			0
$433$		−	27.8029i		−	1.33612i	−0.744107	−	0.668060i	$-0.767125\pi$
$433$		−	27.8029i		−	1.33612i	0.744107	−	0.668060i	$-0.232875\pi$
$434$	−2.68823	+	1.15504i	−0.129039	+	0.0554438i
$435$		0			0
$436$	−19.8853	+	20.9570i	−0.952331	+	1.00366i
$437$	11.3547	−	7.60711i	0.543171	−	0.363897i
$438$		0			0
$439$	23.3509			1.11448			0.557238	−	0.830353i	$-0.311861\pi$
$439$	23.3509			1.11448			0.557238	+	0.830353i	$0.311861\pi$
$440$	2.79119	−	7.56779i	0.133065	−	0.360780i
$441$		0			0
$442$	−14.8190	−	34.4894i	−0.704866	−	1.64050i
$443$	35.5048			1.68688			0.843441	−	0.537222i	$-0.180526\pi$
$443$	35.5048			1.68688			0.843441	+	0.537222i	$0.180526\pi$
$444$		0			0
$445$	15.7944			0.748728
$446$	−15.9779	−	37.1866i	−0.756573	−	1.76084i
$447$		0			0
$448$	−1.77943	+	2.08414i	−0.0840699	+	0.0984662i
$449$		−	41.5275i		−	1.95981i	−0.199476	−	0.979903i	$-0.563924\pi$
$449$		−	41.5275i		−	1.95981i	0.199476	−	0.979903i	$-0.436076\pi$
$450$		0			0
$451$		−	0.428986i		−	0.0202002i
$452$	−17.5038	−	16.6087i	−0.823312	−	0.781207i
$453$		0			0
$454$	14.6007	−	6.27343i	0.685244	−	0.294427i
$455$	−2.78550			−0.130586
$456$		0			0
$457$	−36.9416			−1.72806			−0.864028	−	0.503443i	$-0.832066\pi$
$457$	−36.9416			−1.72806			−0.864028	+	0.503443i	$0.832066\pi$
$458$	−8.72487	+	3.74879i	−0.407687	+	0.175169i
$459$		0			0
$460$	7.42393	−	7.82405i	0.346142	−	0.364798i
$461$			41.0812i			1.91334i	0.291167	+	0.956672i	$0.405957\pi$
$461$			41.0812i			1.91334i	−0.291167	+	0.956672i	$0.594043\pi$
$462$		0			0
$463$			18.7481i			0.871299i	0.900116	+	0.435649i	$0.143481\pi$
$463$			18.7481i			0.871299i	−0.900116	+	0.435649i	$0.856519\pi$
$464$	0.285698	+	5.43998i	0.0132632	+	0.252545i
$465$		0			0
$466$	−6.21162	−	14.4568i	−0.287748	−	0.669700i
$467$	−24.3348			−1.12608			−0.563040	−	0.826430i	$-0.690368\pi$
$467$	−24.3348			−1.12608			−0.563040	+	0.826430i	$0.690368\pi$
$468$		0			0
$469$	−1.98214			−0.0915267
$470$	1.60355	+	3.73207i	0.0739661	+	0.172148i
$471$		0			0
$472$	6.70357	−	18.1754i	0.308557	−	0.836593i
$473$	−15.4048			−0.708312
$474$		0			0
$475$	4.95385	+	7.39436i	0.227298	+	0.339277i
$476$	2.79021	+	2.64752i	0.127889	+	0.121349i
$477$		0			0
$478$	−37.4311	+	16.0829i	−1.71206	+	0.735615i
$479$			8.97471i			0.410065i	0.978755	+	0.205033i	$0.0657300\pi$
$479$			8.97471i			0.410065i	−0.978755	+	0.205033i	$0.934270\pi$
$480$		0			0
$481$	23.0572			1.05132
$482$	5.63425	−	2.42085i	0.256633	−	0.110267i
$483$		0			0
$484$	11.3581	−	11.9703i	0.516279	−	0.544104i
$485$	13.1678			0.597921
$486$		0			0
$487$	15.0545			0.682183			0.341092	−	0.940030i	$-0.389203\pi$
$487$	15.0545			0.682183			0.341092	+	0.940030i	$0.389203\pi$
$488$	−13.8859	+	37.6490i	−0.628585	+	1.70429i
$489$		0			0
$490$	−15.3812	+	6.60878i	−0.694851	+	0.298554i
$491$	10.7570			0.485455			0.242727	−	0.970095i	$-0.421958\pi$
$491$	10.7570			0.485455			0.242727	+	0.970095i	$0.421958\pi$
$492$		0			0
$493$	7.64590			0.344354
$494$	−15.8427	+	24.4625i	−0.712797	+	1.10062i
$495$		0			0
$496$	1.26702	+	24.1253i	0.0568907	+	1.08326i
$497$		−	1.27400i		−	0.0571468i
$498$		0			0
$499$	39.7650			1.78012			0.890062	−	0.455839i	$-0.150661\pi$
$499$	39.7650			1.78012			0.890062	+	0.455839i	$0.150661\pi$
$500$	17.5716	+	16.6730i	0.785826	+	0.745639i
$501$		0			0
$502$	5.33027	+	12.4056i	0.237902	+	0.553689i
$503$		−	7.72567i		−	0.344471i	−0.985056	−	0.172235i	$-0.944901\pi$
$503$		−	7.72567i		−	0.344471i	0.985056	−	0.172235i	$-0.0550990\pi$
$504$		0			0
$505$	12.7774			0.568588
$506$	−6.75537	+	2.90256i	−0.300313	+	0.129034i
$507$		0			0
$508$	2.56443	−	2.70264i	0.113778	−	0.119910i
$509$	2.88527			0.127887			0.0639437	−	0.997954i	$-0.479632\pi$
$509$	2.88527			0.127887			0.0639437	+	0.997954i	$0.479632\pi$
$510$		0			0
$511$			3.10162i			0.137208i
$512$	11.0611	+	19.7396i	0.488837	+	0.872375i
$513$		0			0
$514$	−14.1421	+	6.07639i	−0.623782	+	0.268018i
$515$		−	0.0157285i		−	0.000693082i
$516$		0			0
$517$		−	2.76904i		−	0.121782i
$518$	−2.17068	+	0.932669i	−0.0953742	+	0.0409791i
$519$		0			0
$520$	−7.95873	+	21.5786i	−0.349013	+	0.946283i
$521$			40.5771i			1.77772i	0.458182	+	0.888858i	$0.348501\pi$
$521$			40.5771i			1.77772i	−0.458182	+	0.888858i	$0.651499\pi$
$522$		0			0
$523$		−	17.2054i		−	0.752340i	−0.926551	−	0.376170i	$-0.877241\pi$
$523$		−	17.2054i		−	0.752340i	0.926551	−	0.376170i	$-0.122759\pi$
$524$	1.65504	−	1.74424i	0.0723008	−	0.0761976i
$525$		0			0
$526$	25.5803	−	10.9910i	1.11536	−	0.479231i
$527$	33.9081			1.47706
$528$		0			0
$529$	13.1685			0.572544
$530$	30.3373	−	13.0349i	1.31777	−	0.566201i
$531$		0			0
$532$	0.501968	−	2.94383i	0.0217631	−	0.127631i
$533$			1.22320i			0.0529826i
$534$		0			0
$535$	2.60136			0.112467
$536$	−5.66338	+	15.3552i	−0.244621	+	0.663242i
$537$		0			0
$538$	−1.09900	−	2.55780i	−0.0473812	−	0.110274i
$539$	11.4122			0.491557
$540$		0			0
$541$			31.3154i			1.34635i	0.739481	+	0.673177i	$0.235071\pi$
$541$			31.3154i			1.34635i	−0.739481	+	0.673177i	$0.764929\pi$
$542$	−6.52303	+	2.80273i	−0.280188	+	0.120388i
$543$		0			0
$544$	28.4819	−	14.0506i	1.22115	−	0.602415i
$545$		−	24.8440i		−	1.06420i
$546$		0			0
$547$			44.5494i			1.90479i	0.304860	+	0.952397i	$0.401390\pi$
$547$			44.5494i			1.90479i	−0.304860	+	0.952397i	$0.598610\pi$
$548$	0.675958	−	0.712389i	0.0288755	−	0.0304318i
$549$		0			0
$550$	−1.89018	−	4.39918i	−0.0805976	−	0.187582i
$551$	−3.30404	−	4.93177i	−0.140757	−	0.210101i
$552$		0			0
$553$		−	2.21451i		−	0.0941706i
$554$	−19.1997	+	8.24945i	−0.815715	+	0.350485i
$555$		0			0
$556$	14.1014	−	14.8614i	0.598031	−	0.630263i
$557$			33.6142i			1.42428i	0.702039	+	0.712139i	$0.252273\pi$
$557$			33.6142i			1.42428i	−0.702039	+	0.712139i	$0.747727\pi$
$558$		0			0
$559$	43.9247			1.85782
$560$	−0.123597	−	2.35341i	−0.00522293	−	0.0994499i
$561$		0			0
$562$	−22.1586	+	9.52082i	−0.934705	+	0.401612i
$563$		−	21.8796i		−	0.922116i	−0.887370	−	0.461058i	$-0.847470\pi$
$563$		−	21.8796i		−	0.922116i	0.887370	−	0.461058i	$-0.152530\pi$
$564$		0			0
$565$	20.7504			0.872974
$566$	14.1514	+	32.9357i	0.594827	+	1.38439i
$567$		0			0
$568$	−9.86939	−	3.64009i	−0.414111	−	0.152735i
$569$		−	0.658619i		−	0.0276108i	−0.999905	−	0.0138054i	$-0.995605\pi$
$569$		−	0.658619i		−	0.0276108i	0.999905	−	0.0138054i	$-0.00439453\pi$
$570$		0			0
$571$	−1.41099			−0.0590480			−0.0295240	−	0.999564i	$-0.509399\pi$
$571$	−1.41099			−0.0590480			−0.0295240	+	0.999564i	$0.509399\pi$
$572$	10.7918	−	11.3735i	0.451230	−	0.475549i
$573$		0			0
$574$	−0.0494787	−	0.115156i	−0.00206520	−	0.00480652i
$575$		−	6.40240i		−	0.266998i
$576$		0			0
$577$	4.60220			0.191592			0.0957960	−	0.995401i	$-0.469460\pi$
$577$	4.60220			0.191592			0.0957960	+	0.995401i	$0.469460\pi$
$578$	−8.10636	−	18.8666i	−0.337180	−	0.784748i
$579$		0			0
$580$	−3.39826	−	3.22448i	−0.141105	−	0.133889i
$581$		−	3.54219i		−	0.146955i
$582$		0			0
$583$	−22.5090			−0.932227
$584$	24.0275	+	8.86197i	0.994267	+	0.366711i
$585$		0			0
$586$	5.23531	+	12.1846i	0.216269	+	0.503341i
$587$	1.17857			0.0486446			0.0243223	−	0.999704i	$-0.492257\pi$
$587$	1.17857			0.0486446			0.0243223	+	0.999704i	$0.492257\pi$
$588$		0			0
$589$	−14.6528	−	21.8715i	−0.603757	−	0.901198i
$590$	6.57659	+	15.3063i	0.270754	+	0.630149i
$591$		0			0
$592$	1.02309	+	19.4806i	0.0420486	+	0.800647i
$593$	26.5488			1.09023			0.545115	−	0.838361i	$-0.316486\pi$
$593$	26.5488			1.09023			0.545115	+	0.838361i	$0.316486\pi$
$594$		0			0
$595$	−3.30773			−0.135604
$596$	4.67506	+	4.43598i	0.191498	+	0.181705i
$597$		0			0
$598$	19.2621	−	8.27626i	0.787684	−	0.338441i
$599$	45.1222			1.84364			0.921822	−	0.387614i	$-0.126701\pi$
$599$	45.1222			1.84364			0.921822	+	0.387614i	$0.126701\pi$
$600$		0			0
$601$			21.6889i			0.884708i	0.896841	+	0.442354i	$0.145857\pi$
$601$			21.6889i			0.884708i	−0.896841	+	0.442354i	$0.854143\pi$
$602$	−4.13522	+	1.77677i	−0.168539	+	0.0724156i
$603$		0			0
$604$	−17.6492	+	18.6004i	−0.718136	+	0.756841i
$605$			14.1905i			0.576925i
$606$		0			0
$607$	−17.2626			−0.700667			−0.350334	−	0.936625i	$-0.613932\pi$
$607$	−17.2626			−0.700667			−0.350334	+	0.936625i	$0.613932\pi$
$608$	−21.3709	−	12.2998i	−0.866705	−	0.498821i
$609$		0			0
$610$	−13.6229	−	31.7057i	−0.551574	−	1.28373i
$611$			7.89555i			0.319420i
$612$		0			0
$613$		−	3.52341i		−	0.142309i	−0.997465	−	0.0711546i	$-0.977332\pi$
$613$		−	3.52341i		−	0.142309i	0.997465	−	0.0711546i	$-0.0226684\pi$
$614$	−24.6142	+	10.5759i	−0.993347	+	0.426808i
$615$		0			0
$616$	−0.555920	+	1.50727i	−0.0223987	+	0.0607297i
$617$	5.79963			0.233484			0.116742	−	0.993162i	$-0.462755\pi$
$617$	5.79963			0.233484			0.116742	+	0.993162i	$0.462755\pi$
$618$		0			0
$619$	6.19689			0.249074			0.124537	−	0.992215i	$-0.460255\pi$
$619$	6.19689			0.249074			0.124537	+	0.992215i	$0.460255\pi$
$620$	−15.0706	−	14.2999i	−0.605252	−	0.574299i
$621$		0			0
$622$	−18.4928	+	7.94572i	−0.741492	+	0.318594i
$623$	−3.14577			−0.126033
$624$		0			0
$625$	−10.6212			−0.424848
$626$	−4.65296	−	10.8292i	−0.185970	−	0.432824i
$627$		0			0
$628$	32.6221	+	30.9538i	1.30176	+	1.23519i
$629$	27.3800			1.09171
$630$		0			0
$631$			29.6886i			1.18188i	0.806714	+	0.590942i	$0.201244\pi$
$631$			29.6886i			1.18188i	−0.806714	+	0.590942i	$0.798756\pi$
$632$	−17.1553	−	6.32731i	−0.682401	−	0.251687i
$633$		0			0
$634$	−3.30845	−	7.70005i	−0.131395	−	0.305808i
$635$			3.20391i			0.127143i
$636$		0			0
$637$	−32.5404			−1.28930
$638$	1.26068	+	2.93410i	0.0499109	+	0.116162i
$639$		0			0
$640$	−18.5845	−	5.76671i	−0.734616	−	0.227949i
$641$		−	33.4686i		−	1.32193i	−0.750417	−	0.660965i	$-0.770147\pi$
$641$		−	33.4686i		−	1.32193i	0.750417	−	0.660965i	$-0.229853\pi$
$642$		0			0
$643$	−33.0197			−1.30217			−0.651085	−	0.759005i	$-0.725686\pi$
$643$	−33.0197			−1.30217			−0.651085	+	0.759005i	$0.725686\pi$
$644$	−1.47862	+	1.55831i	−0.0582657	+	0.0614060i
$645$		0			0
$646$	−18.8129	+	29.0488i	−0.740184	+	1.14291i
$647$		−	6.86956i		−	0.270070i	−0.990841	−	0.135035i	$-0.956885\pi$
$647$		−	6.86956i		−	0.270070i	0.990841	−	0.135035i	$-0.0431147\pi$
$648$		0			0
$649$		−	11.3566i		−	0.445785i
$650$	5.38961	+	12.5437i	0.211398	+	0.492005i
$651$		0			0
$652$	7.41605	−	7.81575i	0.290435	−	0.306088i
$653$			22.2916i			0.872337i	0.899865	+	0.436168i	$0.143665\pi$
$653$			22.2916i			0.872337i	−0.899865	+	0.436168i	$0.856335\pi$
$654$		0			0
$655$			2.06775i			0.0807938i
$656$	−1.03346	+	0.0542753i	−0.0403497	+	0.00211910i
$657$		0			0
$658$	−0.319377	−	0.743314i	−0.0124506	−	0.0289774i
$659$		−	24.4798i		−	0.953599i	−0.879012	−	0.476800i	$-0.841797\pi$
$659$		−	24.4798i		−	0.953599i	0.879012	−	0.476800i	$-0.158203\pi$
$660$		0			0
$661$	−26.3768			−1.02594			−0.512969	−	0.858407i	$-0.671455\pi$
$661$	−26.3768			−1.02594			−0.512969	+	0.858407i	$0.671455\pi$
$662$	−31.7855	+	13.6572i	−1.23538	+	0.530800i
$663$		0			0
$664$	−27.4405	−	10.1207i	−1.06490	−	0.392761i
$665$	1.42937	+	2.13356i	0.0554288	+	0.0827357i
$666$		0			0
$667$			4.27017i			0.165342i
$668$	3.38214	−	3.56442i	0.130859	−	0.137912i
$669$		0			0
$670$	−5.55610	−	12.9312i	−0.214651	−	0.499576i
$671$			23.5243i			0.908144i
$672$		0			0
$673$		−	21.7878i		−	0.839859i	−0.907557	−	0.419929i	$-0.862055\pi$
$673$		−	21.7878i		−	0.839859i	0.907557	−	0.419929i	$-0.137945\pi$
$674$	8.55022	−	3.67374i	0.329342	−	0.141507i
$675$		0			0
$676$	−12.8754	+	13.5693i	−0.495206	+	0.521896i
$677$	33.6658			1.29388			0.646941	−	0.762540i	$-0.276048\pi$
$677$	33.6658			1.29388			0.646941	+	0.762540i	$0.276048\pi$
$678$		0			0
$679$	−2.62263			−0.100647
$680$	−9.45085	+	25.6242i	−0.362424	+	0.982642i
$681$		0			0
$682$	5.59089	+	13.0122i	0.214086	+	0.498261i
$683$			19.4062i			0.742557i	0.928522	+	0.371279i	$0.121081\pi$
$683$			19.4062i			0.742557i	−0.928522	+	0.371279i	$0.878919\pi$
$684$		0			0
$685$			0.844519i			0.0322674i
$686$	6.17915	−	2.65497i	0.235921	−	0.101367i
$687$		0			0
$688$	1.94901	+	37.1112i	0.0743054	+	1.41485i
$689$	64.1815			2.44512
$690$		0			0
$691$	20.2905			0.771887			0.385944	−	0.922522i	$-0.373876\pi$
$691$	20.2905			0.771887			0.385944	+	0.922522i	$0.373876\pi$
$692$	22.0102	−	23.1965i	0.836702	−	0.881797i
$693$		0			0
$694$	2.32741	+	5.41679i	0.0883474	+	0.205618i
$695$			17.6178i			0.668280i
$696$		0			0
$697$			1.45253i			0.0550183i
$698$	37.0017	−	15.8984i	1.40053	−	0.601762i
$699$		0			0
$700$	−1.01479	−	0.962896i	−0.0383555	−	0.0363940i
$701$		−	22.9181i		−	0.865606i	−0.901489	−	0.432803i	$-0.857525\pi$
$701$		−	22.9181i		−	0.865606i	0.901489	−	0.432803i	$-0.142475\pi$
$702$		0			0
$703$	−11.8318	−	17.6607i	−0.446244	−	0.666085i
$704$	10.0881	+	8.61317i	0.380209	+	0.324621i
$705$		0			0
$706$	1.10914	+	2.58141i	0.0417432	+	0.0971525i
$707$	−2.54487			−0.0957097
$708$		0			0
$709$			28.1662i			1.05780i	0.848683	+	0.528902i	$0.177396\pi$
$709$			28.1662i			1.05780i	−0.848683	+	0.528902i	$0.822604\pi$
$710$	8.31141	−	3.57113i	0.311921	−	0.134022i
$711$		0			0
$712$	−8.98810	+	24.3695i	−0.336843	+	0.913286i
$713$			18.9374i			0.709210i
$714$		0			0
$715$			13.4830i			0.504235i
$716$	20.9250	+	19.8549i	0.782004	+	0.742013i
$717$		0			0
$718$	−39.5431	+	16.9904i	−1.47574	+	0.634075i
$719$			35.7749i			1.33418i	0.744978	+	0.667089i	$0.232460\pi$
$719$			35.7749i			1.33418i	−0.744978	+	0.667089i	$0.767540\pi$
$720$		0			0
$721$			0.00313264i			0.000116666i
$722$	26.8668	−	0.418195i	0.999879	−	0.0155636i
$723$		0			0
$724$	17.1957	−	18.1225i	0.639074	−	0.673517i
$725$	−2.78079			−0.103276
$726$		0			0
$727$			33.9110i			1.25769i	0.777531	+	0.628845i	$0.216472\pi$
$727$			33.9110i			1.25769i	−0.777531	+	0.628845i	$0.783528\pi$
$728$	1.58513	−	4.29779i	0.0587490	−	0.159287i
$729$		0			0
$730$	−20.2345	+	8.69411i	−0.748914	+	0.321783i
$731$	52.1598			1.92920
$732$		0			0
$733$		−	2.07441i		−	0.0766202i	−0.999266	−	0.0383101i	$-0.987803\pi$
$733$		−	2.07441i		−	0.0766202i	0.999266	−	0.0383101i	$-0.0121975\pi$
$734$	−42.7023	+	18.3478i	−1.57617	+	0.677228i
$735$		0			0
$736$	7.84715	+	15.9069i	0.289250	+	0.586337i
$737$			9.59439i			0.353414i
$738$		0			0
$739$	2.88576			0.106154			0.0530772	−	0.998590i	$-0.483097\pi$
$739$	2.88576			0.106154			0.0530772	+	0.998590i	$0.483097\pi$
$740$	−12.1692	−	11.5469i	−0.447348	−	0.424471i
$741$		0			0
$742$	−6.04226	+	2.59616i	−0.221818	+	0.0953079i
$743$	39.8358			1.46143			0.730717	−	0.682680i	$-0.239186\pi$
$743$	39.8358			1.46143			0.730717	+	0.682680i	$0.239186\pi$
$744$		0			0
$745$	−5.54216			−0.203049
$746$	2.77523	+	6.45904i	0.101608	+	0.236482i
$747$		0			0
$748$	12.8151	−	13.5058i	0.468567	−	0.493821i
$749$	−0.518111			−0.0189314
$750$		0			0
$751$	−30.6201			−1.11734			−0.558672	−	0.829389i	$-0.688689\pi$
$751$	−30.6201			−1.11734			−0.558672	+	0.829389i	$0.688689\pi$
$752$	−6.67080	+	0.350339i	−0.243259	+	0.0127755i
$753$		0			0
$754$	−3.59468	−	8.36620i	−0.130910	−	0.304679i
$755$		−	22.0503i		−	0.802493i
$756$		0			0
$757$			19.7233i			0.716856i	0.933557	+	0.358428i	$0.116687\pi$
$757$			19.7233i			0.716856i	−0.933557	+	0.358428i	$0.883313\pi$
$758$	−37.0438	+	15.9165i	−1.34549	+	0.578113i
$759$		0			0
$760$	20.6122	−	4.97702i	0.747682	−	0.180536i
$761$	−28.7987			−1.04395			−0.521976	−	0.852960i	$-0.674805\pi$
$761$	−28.7987			−1.04395			−0.521976	+	0.852960i	$0.674805\pi$
$762$		0			0
$763$			4.94816i			0.179135i
$764$	−20.5716	−	19.5196i	−0.744254	−	0.706193i
$765$		0			0
$766$	18.2600	+	42.4980i	0.659759	+	1.53552i
$767$			32.3818i			1.16924i
$768$		0			0
$769$	13.8075			0.497913			0.248956	−	0.968515i	$-0.419912\pi$
$769$	13.8075			0.497913			0.248956	+	0.968515i	$0.419912\pi$
$770$	−0.545390	−	1.26933i	−0.0196545	−	0.0457436i
$771$		0			0
$772$	12.5184	+	11.8783i	0.450549	+	0.427508i
$773$	−34.3072			−1.23394			−0.616972	−	0.786985i	$-0.711641\pi$
$773$	−34.3072			−1.23394			−0.616972	+	0.786985i	$0.711641\pi$
$774$		0			0
$775$	−12.3323			−0.442988
$776$	−7.49339	+	20.3169i	−0.268997	+	0.729334i
$777$		0			0
$778$	−15.8022	+	6.78966i	−0.566535	+	0.243421i
$779$	0.936910	−	0.627683i	0.0335683	−	0.0224891i
$780$		0			0
$781$	−6.16671			−0.220662
$782$	22.8733	−	9.82791i	0.817949	−	0.351445i
$783$		0			0
$784$	−1.44387	−	27.4927i	−0.0515668	−	0.981883i
$785$	−38.6727			−1.38029
$786$		0			0
$787$		−	3.02131i		−	0.107698i	−0.998549	−	0.0538490i	$-0.982851\pi$
$787$		−	3.02131i		−	0.107698i	0.998549	−	0.0538490i	$-0.0171490\pi$
$788$	−28.6119	−	27.1487i	−1.01926	−	0.967131i
$789$		0			0
$790$	14.4471	−	6.20746i	0.514006	−	0.220851i
$791$	−4.13283			−0.146947
$792$		0			0
$793$		−	67.0764i		−	2.38195i
$794$	21.1969	−	9.10760i	0.752250	−	0.323217i
$795$		0			0
$796$	19.4001	+	18.4080i	0.687619	+	0.652454i
$797$	−37.7953			−1.33878			−0.669389	−	0.742912i	$-0.733444\pi$
$797$	−37.7953			−1.33878			−0.669389	+	0.742912i	$0.733444\pi$
$798$		0			0
$799$			9.37583i			0.331693i
$800$	−10.3588	+	5.11017i	−0.366239	+	0.180672i
$801$		0			0
$802$	−11.7263	+	5.03841i	−0.414071	+	0.177912i
$803$	15.0132			0.529803
$804$		0			0
$805$		−	1.84734i		−	0.0651101i
$806$	−15.9417	−	37.1025i	−0.561522	−	1.30688i
$807$		0			0
$808$	−7.27122	+	19.7145i	−0.255801	+	0.693554i
$809$	−27.5101			−0.967202			−0.483601	−	0.875289i	$-0.660671\pi$
$809$	−27.5101			−0.967202			−0.483601	+	0.875289i	$0.660671\pi$
$810$		0			0
$811$		−	4.67588i		−	0.164192i	−0.996624	−	0.0820962i	$-0.973839\pi$
$811$		−	4.67588i		−	0.164192i	0.996624	−	0.0820962i	$-0.0261615\pi$
$812$	0.676830	+	0.642217i	0.0237521	+	0.0225374i
$813$		0			0
$814$	4.51451	+	10.5070i	0.158233	+	0.368270i
$815$			9.26537i			0.324552i
$816$		0			0
$817$	−22.5399	−	33.6442i	−0.788572	−	1.17706i
$818$	37.2560	−	16.0077i	1.30263	−	0.559695i
$819$		0			0
$820$	0.612568	−	0.645583i	0.0213918	−	0.0225447i
$821$			30.8685i			1.07732i	0.842524	+	0.538659i	$0.181069\pi$
$821$			30.8685i			1.07732i	−0.842524	+	0.538659i	$0.818931\pi$
$822$		0			0
$823$		−	20.4942i		−	0.714382i	−0.934031	−	0.357191i	$-0.883734\pi$
$823$		−	20.4942i		−	0.714382i	0.934031	−	0.357191i	$-0.116266\pi$
$824$	0.0242678	+	0.00895060i	0.000845410	+	0.000311809i
$825$		0			0
$826$	−1.30985	−	3.04854i	−0.0455757	−	0.106072i
$827$		−	34.0902i		−	1.18543i	−0.805411	−	0.592716i	$-0.798056\pi$
$827$		−	34.0902i		−	1.18543i	0.805411	−	0.592716i	$-0.201944\pi$
$828$		0			0
$829$	48.7555			1.69335			0.846673	−	0.532113i	$-0.178602\pi$
$829$	48.7555			1.69335			0.846673	+	0.532113i	$0.178602\pi$
$830$	23.1087	−	9.92904i	0.802115	−	0.344642i
$831$		0			0
$832$	−28.7649	−	24.5593i	−0.997244	−	0.851442i
$833$	−38.6411			−1.33883
$834$		0			0
$835$			4.22553i			0.146230i
$836$	−14.2494	−	2.42974i	−0.492825	−	0.0840343i
$837$		0			0
$838$	21.9138	+	51.0019i	0.757000	+	1.76183i
$839$	−45.8390			−1.58254			−0.791268	−	0.611469i	$-0.790579\pi$
$839$	−45.8390			−1.58254			−0.791268	+	0.611469i	$0.790579\pi$
$840$		0			0
$841$	−27.1453			−0.936045
$842$	0.0521971	+	0.121483i	0.00179883	+	0.00418658i
$843$		0			0
$844$	19.6624	+	18.6569i	0.676809	+	0.642197i
$845$		−	16.0861i		−	0.553377i
$846$		0			0
$847$		−	2.82631i		−	0.0971130i
$848$	2.84784	+	54.2257i	0.0977952	+	1.86212i
$849$		0			0
$850$	6.40007	+	14.8954i	0.219520	+	0.510909i
$851$			15.2915i			0.524185i
$852$		0			0
$853$		−	31.7795i		−	1.08811i	−0.839050	−	0.544054i	$-0.816889\pi$
$853$		−	31.7795i		−	1.08811i	0.839050	−	0.544054i	$-0.183111\pi$
$854$	2.71326	+	6.31480i	0.0928457	+	0.216088i
$855$		0			0
$856$	−1.48035	+	4.01369i	−0.0505973	+	0.137185i
$857$		−	18.0812i		−	0.617641i	−0.951120	−	0.308820i	$-0.900066\pi$
$857$		−	18.0812i		−	0.617641i	0.951120	−	0.308820i	$-0.0999342\pi$
$858$		0			0
$859$	−28.9801			−0.988788			−0.494394	−	0.869238i	$-0.664610\pi$
$859$	−28.9801			−0.988788			−0.494394	+	0.869238i	$0.664610\pi$
$860$	−23.1827	−	21.9972i	−0.790524	−	0.750097i
$861$		0			0
$862$	−13.2888	−	30.9281i	−0.452617	−	1.05342i
$863$	9.09576			0.309623			0.154812	−	0.987944i	$-0.450523\pi$
$863$	9.09576			0.309623			0.154812	+	0.987944i	$0.450523\pi$
$864$		0			0
$865$			27.4988i			0.934988i
$866$	−36.1257	+	15.5220i	−1.22760	+	0.527459i
$867$		0			0
$868$	3.00161	+	2.84811i	0.101881	+	0.0966711i
$869$	−10.7192			−0.363623
$870$		0			0
$871$		−	27.3572i		−	0.926962i
$872$	38.3322	+	14.1379i	1.29809	+	0.478770i
$873$		0			0
$874$	−16.2235	−	10.5069i	−0.548769	−	0.355400i
$875$	4.14883			0.140256
$876$		0			0
$877$	48.0805			1.62356			0.811781	−	0.583962i	$-0.198498\pi$
$877$	48.0805			1.62356			0.811781	+	0.583962i	$0.198498\pi$
$878$	−13.0365	−	30.3410i	−0.439961	−	1.02396i
$879$		0			0
$880$	−11.3915	+	0.598262i	−0.384008	+	0.0201674i
$881$	52.1283			1.75625			0.878124	−	0.478434i	$-0.158795\pi$
$881$	52.1283			1.75625			0.878124	+	0.478434i	$0.158795\pi$
$882$		0			0
$883$	21.9449			0.738504			0.369252	−	0.929329i	$-0.379614\pi$
$883$	21.9449			0.738504			0.369252	+	0.929329i	$0.379614\pi$
$884$	−36.5407	+	38.5101i	−1.22900	+	1.29523i
$885$		0			0
$886$	−19.8219	−	46.1332i	−0.665929	−	1.54987i
$887$	−11.9209			−0.400263			−0.200132	−	0.979769i	$-0.564137\pi$
$887$	−11.9209			−0.400263			−0.200132	+	0.979769i	$0.564137\pi$
$888$		0			0
$889$		−	0.638121i		−	0.0214019i
$890$	−8.81785	−	20.5225i	−0.295575	−	0.687917i
$891$		0			0
$892$	−39.3983	+	41.5217i	−1.31915	+	1.39025i
$893$	6.04761	−	4.05160i	0.202376	−	0.135581i
$894$		0			0
$895$	−24.8061			−0.829175
$896$	3.70146	+	1.14855i	0.123657	+	0.0383704i
$897$		0			0
$898$	−53.9589	+	23.1843i	−1.80063	+	0.773671i
$899$	8.22518			0.274325
$900$		0			0
$901$	76.2144			2.53907
$902$	−0.557403	+	0.239498i	−0.0185595	+	0.00797440i
$903$		0			0
$904$	−11.8084	+	32.0161i	−0.392740	+	1.06484i
$905$			21.4838i			0.714144i
$906$		0			0
$907$		−	36.4292i		−	1.20961i	−0.796374	−	0.604805i	$-0.793251\pi$
$907$		−	36.4292i		−	1.20961i	0.796374	−	0.604805i	$-0.206749\pi$
$908$	−16.3028	−	15.4691i	−0.541027	−	0.513359i
$909$		0			0
$910$	1.55511	+	3.61934i	0.0515513	+	0.119980i
$911$	−52.7294			−1.74700			−0.873501	−	0.486822i	$-0.838156\pi$
$911$	−52.7294			−1.74700			−0.873501	+	0.486822i	$0.838156\pi$
$912$		0			0
$913$	−17.1457			−0.567439
$914$	20.6241	+	48.0002i	0.682183	+	1.58770i
$915$		0			0
$916$	9.74198	+	9.24378i	0.321884	+	0.305423i
$917$		−	0.411833i		−	0.0135999i
$918$		0			0
$919$			22.8376i			0.753342i	0.926347	+	0.376671i	$0.122931\pi$
$919$			22.8376i			0.753342i	−0.926347	+	0.376671i	$0.877069\pi$
$920$	−14.3109	−	5.27822i	−0.471816	−	0.174018i
$921$		0			0
$922$	53.3790	−	22.9352i	1.75794	−	0.755329i
$923$	17.5836			0.578770
$924$		0			0
$925$	−9.95802			−0.327418
$926$	24.3604	−	10.4668i	0.800532	−	0.343962i
$927$		0			0
$928$	6.90894	−	3.40830i	0.226797	−	0.111883i
$929$	−48.4718			−1.59031			−0.795154	−	0.606407i	$-0.792610\pi$
$929$	−48.4718			−1.59031			−0.795154	+	0.606407i	$0.792610\pi$
$930$		0			0
$931$	16.6981	+	24.9243i	0.547257	+	0.816863i
$932$	−15.3166	+	16.1422i	−0.501713	+	0.528754i
$933$		0			0
$934$	13.5858	+	31.6194i	0.444541	+	1.03462i
$935$			16.0108i			0.523609i
$936$		0			0
$937$	11.9982			0.391964			0.195982	−	0.980608i	$-0.437211\pi$
$937$	11.9982			0.391964			0.195982	+	0.980608i	$0.437211\pi$
$938$	1.10660	+	2.57550i	0.0361319	+	0.0840929i
$939$		0			0
$940$	3.95403	−	4.16714i	0.128966	−	0.135917i
$941$	7.36618			0.240131			0.120065	−	0.992766i	$-0.461690\pi$
$941$	7.36618			0.240131			0.120065	+	0.992766i	$0.461690\pi$
$942$		0			0
$943$	−0.811223			−0.0264170
$944$	−27.3588	+	1.43684i	−0.890454	+	0.0467651i
$945$		0			0
$946$	8.60029	+	20.0162i	0.279620	+	0.650783i
$947$	60.3309			1.96049			0.980246	−	0.197784i	$-0.0633744\pi$
$947$	60.3309			1.96049			0.980246	+	0.197784i	$0.0633744\pi$
$948$		0			0
$949$	−42.8081			−1.38961
$950$	6.84220	−	10.5650i	0.221990	−	0.342773i
$951$		0			0
$952$	1.88232	−	5.10355i	0.0610063	−	0.165407i
$953$			38.4438i			1.24532i	0.782493	+	0.622659i	$0.213948\pi$
$953$			38.4438i			1.24532i	−0.782493	+	0.622659i	$0.786052\pi$
$954$		0			0
$955$	24.3871			0.789148
$956$	41.7947	+	39.6573i	1.35174	+	1.28261i
$957$		0			0
$958$	11.6613	−	5.01047i	0.376760	−	0.161881i
$959$		−	0.168202i		−	0.00543153i
$960$		0			0
$961$	5.47709			0.176680
$962$	−12.8725	−	29.9594i	−0.415027	−	0.965929i
$963$		0			0
$964$	−6.29107	−	5.96934i	−0.202622	−	0.192259i
$965$	−14.8403			−0.477726
$966$		0			0
$967$		−	37.4228i		−	1.20344i	−0.798709	−	0.601718i	$-0.794483\pi$
$967$		−	37.4228i		−	1.20344i	0.798709	−	0.601718i	$-0.205517\pi$
$968$	−21.8947	−	8.07534i	−0.703723	−	0.259551i
$969$		0			0
$970$	−7.35144	−	17.1096i	−0.236041	−	0.549358i
$971$			40.6142i			1.30337i	0.758489	+	0.651686i	$0.225938\pi$
$971$			40.6142i			1.30337i	−0.758489	+	0.651686i	$0.774062\pi$
$972$		0			0
$973$		−	3.50892i		−	0.112491i
$974$	−8.40473	−	19.5611i	−0.269305	−	0.626776i
$975$		0			0
$976$	56.6716	−	2.97629i	1.81401	−	0.0952688i
$977$		−	8.86958i		−	0.283763i	−0.989884	−	0.141882i	$-0.954685\pi$
$977$		−	8.86958i		−	0.283763i	0.989884	−	0.141882i	$-0.0453152\pi$
$978$		0			0
$979$			15.2268i			0.486652i
$980$	17.1743	+	16.2960i	0.548612	+	0.520555i
$981$		0			0
$982$	−6.00548	−	13.9771i	−0.191643	−	0.446026i
$983$	−12.1285			−0.386838			−0.193419	−	0.981116i	$-0.561958\pi$
$983$	−12.1285			−0.386838			−0.193419	+	0.981116i	$0.561958\pi$
$984$		0			0
$985$	33.9187			1.08074
$986$	−4.26861	−	9.93471i	−0.135940	−	0.316386i
$987$		0			0
$988$	40.6302	+	6.92809i	1.29262	+	0.220412i
$989$			29.1308i			0.926305i
$990$		0			0
$991$	16.0627			0.510248			0.255124	−	0.966908i	$-0.417884\pi$
$991$	16.0627			0.510248			0.255124	+	0.966908i	$0.417884\pi$
$992$	30.6398	−	15.1151i	0.972816	−	0.479906i
$993$		0			0
$994$	−1.65538	+	0.711260i	−0.0525054	+	0.0225598i
$995$	−22.9983			−0.729096
$996$		0			0
$997$		−	44.3880i		−	1.40578i	−0.711298	−	0.702890i	$-0.751892\pi$
$997$		−	44.3880i		−	1.40578i	0.711298	−	0.702890i	$-0.248108\pi$
$998$	−22.2003	−	51.6687i	−0.702738	−	1.63554i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1368.2.e.g.379.15		40
3.2	odd	2		456.2.e.a.379.26	yes	40
4.3	odd	2		5472.2.e.g.5167.13		40
8.3	odd	2	inner	1368.2.e.g.379.25		40
8.5	even	2		5472.2.e.g.5167.8		40
12.11	even	2		1824.2.e.a.1519.33		40
19.18	odd	2	inner	1368.2.e.g.379.26		40
24.5	odd	2		1824.2.e.a.1519.27		40
24.11	even	2		456.2.e.a.379.16	yes	40
57.56	even	2		456.2.e.a.379.15	✓	40
76.75	even	2		5472.2.e.g.5167.7		40
152.37	odd	2		5472.2.e.g.5167.14		40
152.75	even	2	inner	1368.2.e.g.379.16		40
228.227	odd	2		1824.2.e.a.1519.28		40
456.227	odd	2		456.2.e.a.379.25	yes	40
456.341	even	2		1824.2.e.a.1519.34		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.e.a.379.15	✓	40	57.56	even	2
456.2.e.a.379.16	yes	40	24.11	even	2
456.2.e.a.379.25	yes	40	456.227	odd	2
456.2.e.a.379.26	yes	40	3.2	odd	2
1368.2.e.g.379.15		40	1.1	even	1	trivial
1368.2.e.g.379.16		40	152.75	even	2	inner
1368.2.e.g.379.25		40	8.3	odd	2	inner
1368.2.e.g.379.26		40	19.18	odd	2	inner
1824.2.e.a.1519.27		40	24.5	odd	2
1824.2.e.a.1519.28		40	228.227	odd	2
1824.2.e.a.1519.33		40	12.11	even	2
1824.2.e.a.1519.34		40	456.341	even	2
5472.2.e.g.5167.7		40	76.75	even	2
5472.2.e.g.5167.8		40	8.5	even	2
5472.2.e.g.5167.13		40	4.3	odd	2
5472.2.e.g.5167.14		40	152.37	odd	2

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:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1368.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.558288 - 1.29935i) q^{2} +(-1.37663 + 1.45082i) q^{4} -1.71991i q^{5} +0.342554i q^{7} +(2.65369 + 0.978748i) q^{8} +O(q^{10})\)	\(q+(-0.558288 - 1.29935i) q^{2} +(-1.37663 + 1.45082i) q^{4} -1.71991i q^{5} +0.342554i q^{7} +(2.65369 + 0.978748i) q^{8} +(-2.23477 + 0.960208i) q^{10} +1.65811 q^{11} -4.72788 q^{13} +(0.445098 - 0.191244i) q^{14} +(-0.209784 - 3.99450i) q^{16} -5.61427 q^{17} +(2.42611 + 3.62133i) q^{19} +(2.49529 + 2.36769i) q^{20} +(-0.925701 - 2.15446i) q^{22} -3.13552i q^{23} +2.04189 q^{25} +(2.63952 + 6.14317i) q^{26} +(-0.496986 - 0.471570i) q^{28} -1.36187 q^{29} -6.03963 q^{31} +(-5.07313 + 2.50266i) q^{32} +(3.13438 + 7.29491i) q^{34} +0.589164 q^{35} -4.87686 q^{37} +(3.35091 - 5.17411i) q^{38} +(1.68336 - 4.56412i) q^{40} -0.258720i q^{41} -9.29057 q^{43} +(-2.28260 + 2.40562i) q^{44} +(-4.07414 + 1.75052i) q^{46} -1.67000i q^{47} +6.88266 q^{49} +(-1.13996 - 2.65314i) q^{50} +(6.50853 - 6.85932i) q^{52} -13.5751 q^{53} -2.85180i q^{55} +(-0.335274 + 0.909032i) q^{56} +(0.760315 + 1.76955i) q^{58} -6.84913i q^{59} +14.1874i q^{61} +(3.37185 + 7.84760i) q^{62} +(6.08411 + 5.19458i) q^{64} +8.13155i q^{65} +5.78635i q^{67} +(7.72877 - 8.14532i) q^{68} +(-0.328923 - 0.765531i) q^{70} -3.71913 q^{71} +9.05440 q^{73} +(2.72269 + 6.33675i) q^{74} +(-8.59376 - 1.46537i) q^{76} +0.567991i q^{77} -6.46470 q^{79} +(-6.87019 + 0.360810i) q^{80} +(-0.336169 + 0.144440i) q^{82} -10.3405 q^{83} +9.65607i q^{85} +(5.18682 + 12.0717i) q^{86} +(4.40010 + 1.62287i) q^{88} +9.18327i q^{89} -1.61955i q^{91} +(4.54909 + 4.31645i) q^{92} +(-2.16992 + 0.932340i) q^{94} +(6.22837 - 4.17270i) q^{95} +7.65610i q^{97} +(-3.84250 - 8.94299i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{4}+O(q^{10}) \) 40 * q - 4 * q^4	\( 40 q - 4 q^{4} + 4 q^{16} + 8 q^{19} - 32 q^{20} - 40 q^{25} - 40 q^{26} - 8 q^{28} + 48 q^{35} + 8 q^{44} - 56 q^{49} + 16 q^{58} - 40 q^{62} + 68 q^{64} + 88 q^{68} - 16 q^{73} + 40 q^{74} - 12 q^{76} + 32 q^{80} - 64 q^{82} - 80 q^{83} + 48 q^{92}+O(q^{100}) \) 40 * q - 4 * q^4 + 4 * q^16 + 8 * q^19 - 32 * q^20 - 40 * q^25 - 40 * q^26 - 8 * q^28 + 48 * q^35 + 8 * q^44 - 56 * q^49 + 16 * q^58 - 40 * q^62 + 68 * q^64 + 88 * q^68 - 16 * q^73 + 40 * q^74 - 12 * q^76 + 32 * q^80 - 64 * q^82 - 80 * q^83 + 48 * q^92

Introduction

L-functions

Modular forms

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