LMFDB - Embedded newform 608.2.s.c.335.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [608,2,Mod(335,608)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(608, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("608.335");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 608 = 2^{5} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	608.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.85490444289$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			335.14
Character	$\chi$	$=$	608.335
Dual form			608.2.s.c.559.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.65547 - 1.53314i) q^{3} +(2.25688 - 1.30301i) q^{5} +4.30088i q^{7} +(3.20101 - 5.54431i) q^{9} +O(q^{10})$	\(q+(2.65547 - 1.53314i) q^{3} +(2.25688 - 1.30301i) q^{5} +4.30088i q^{7} +(3.20101 - 5.54431i) q^{9} +0.349633 q^{11} +(-0.839767 + 1.45452i) q^{13} +(3.99538 - 6.92020i) q^{15} +(0.357047 + 0.618424i) q^{17} +(-4.35063 + 0.268300i) q^{19} +(6.59384 + 11.4209i) q^{21} +(-1.38083 - 0.797223i) q^{23} +(0.895662 - 1.55133i) q^{25} -10.4315i q^{27} +(-0.463655 + 0.803074i) q^{29} -2.80517 q^{31} +(0.928441 - 0.536035i) q^{33} +(5.60409 + 9.70656i) q^{35} -10.2099 q^{37} +5.14991i q^{39} +(4.87850 - 2.81660i) q^{41} +(-4.32286 - 7.48741i) q^{43} -16.6838i q^{45} +(-6.26395 - 3.61649i) q^{47} -11.4976 q^{49} +(1.89626 + 1.09480i) q^{51} +(4.73541 - 8.20196i) q^{53} +(0.789079 - 0.455575i) q^{55} +(-11.1416 + 7.38258i) q^{57} +(-6.62664 + 3.82589i) q^{59} +(3.46531 + 2.00070i) q^{61} +(23.8454 + 13.7672i) q^{63} +4.37690i q^{65} +(10.6067 + 6.12378i) q^{67} -4.88901 q^{69} +(-5.09365 - 8.82246i) q^{71} +(2.54260 + 4.40392i) q^{73} -5.49268i q^{75} +1.50373i q^{77} +(-1.31170 - 2.27193i) q^{79} +(-6.38991 - 11.0677i) q^{81} +4.69293 q^{83} +(1.61162 + 0.930471i) q^{85} +2.84338i q^{87} +(7.37293 + 4.25676i) q^{89} +(-6.25572 - 3.61174i) q^{91} +(-7.44905 + 4.30071i) q^{93} +(-9.46925 + 6.27443i) q^{95} +(6.30190 - 3.63841i) q^{97} +(1.11918 - 1.93848i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 6 q^{3} + 8 q^{9}+O(q^{10}) $ 28 * q + 6 * q^3 + 8 * q^9	$ 28 q + 6 q^{3} + 8 q^{9} + 16 q^{11} - 22 q^{17} - 4 q^{19} + 16 q^{25} + 36 q^{33} + 28 q^{35} + 6 q^{41} - 30 q^{43} - 68 q^{49} + 42 q^{51} - 26 q^{57} + 18 q^{59} - 78 q^{67} + 14 q^{73} + 6 q^{81} + 32 q^{83} - 18 q^{89} + 12 q^{91} + 30 q^{97} + 28 q^{99}+O(q^{100}) $ 28 * q + 6 * q^3 + 8 * q^9 + 16 * q^11 - 22 * q^17 - 4 * q^19 + 16 * q^25 + 36 * q^33 + 28 * q^35 + 6 * q^41 - 30 * q^43 - 68 * q^49 + 42 * q^51 - 26 * q^57 + 18 * q^59 - 78 * q^67 + 14 * q^73 + 6 * q^81 + 32 * q^83 - 18 * q^89 + 12 * q^91 + 30 * q^97 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/608\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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			0
$2$		0			0
$3$	2.65547	−	1.53314i	1.53314	−	0.885156i	0.533921	−	0.845534i	$-0.320718\pi$
$3$	2.65547	−	1.53314i	1.53314	−	0.885156i	0.999215	−	0.0396221i	$-0.0126154\pi$
$4$		0			0
$5$	2.25688	−	1.30301i	1.00931	−	0.582723i	0.0983176	−	0.995155i	$-0.468654\pi$
$5$	2.25688	−	1.30301i	1.00931	−	0.582723i	0.910988	+	0.412432i	$0.135321\pi$
$6$		0			0
$7$			4.30088i			1.62558i	0.582556	+	0.812791i	$0.302053\pi$
$7$			4.30088i			1.62558i	−0.582556	+	0.812791i	$0.697947\pi$
$8$		0			0
$9$	3.20101	−	5.54431i	1.06700	−	1.84810i
$10$		0			0
$11$	0.349633			0.105418			0.0527092	−	0.998610i	$-0.483214\pi$
$11$	0.349633			0.105418			0.0527092	+	0.998610i	$0.483214\pi$
$12$		0			0
$13$	−0.839767	+	1.45452i	−0.232910	+	0.403411i	−0.958663	−	0.284544i	$-0.908158\pi$
$13$	−0.839767	+	1.45452i	−0.232910	+	0.403411i	0.725754	+	0.687955i	$0.241491\pi$
$14$		0			0
$15$	3.99538	−	6.92020i	1.03160	−	1.78679i
$16$		0			0
$17$	0.357047	+	0.618424i	0.0865967	+	0.149990i	0.906070	−	0.423127i	$-0.139068\pi$
$17$	0.357047	+	0.618424i	0.0865967	+	0.149990i	−0.819474	+	0.573117i	$0.805734\pi$
$18$		0			0
$19$	−4.35063	+	0.268300i	−0.998104	+	0.0615522i
$19$	−4.35063	+	0.268300i	−0.998104	+	0.0615522i
$20$		0			0
$21$	6.59384	+	11.4209i	1.43889	+	2.49224i
$22$		0			0
$23$	−1.38083	−	0.797223i	−0.287923	−	0.166233i	0.349082	−	0.937092i	$-0.386494\pi$
$23$	−1.38083	−	0.797223i	−0.287923	−	0.166233i	−0.637005	+	0.770860i	$0.719827\pi$
$24$		0			0
$25$	0.895662	−	1.55133i	0.179132	−	0.310266i
$26$		0			0
$27$		−	10.4315i		−	2.00755i
$28$		0			0
$29$	−0.463655	+	0.803074i	−0.0860985	+	0.149127i	−0.905859	−	0.423580i	$-0.860773\pi$
$29$	−0.463655	+	0.803074i	−0.0860985	+	0.149127i	0.819760	+	0.572707i	$0.194107\pi$
$30$		0			0
$31$	−2.80517			−0.503824			−0.251912	−	0.967750i	$-0.581059\pi$
$31$	−2.80517			−0.503824			−0.251912	+	0.967750i	$0.581059\pi$
$32$		0			0
$33$	0.928441	−	0.536035i	0.161621	−	0.0933118i
$34$		0			0
$35$	5.60409	+	9.70656i	0.947264	+	1.64071i
$36$		0			0
$37$	−10.2099			−1.67849			−0.839245	−	0.543753i	$-0.817003\pi$
$37$	−10.2099			−1.67849			−0.839245	+	0.543753i	$0.817003\pi$
$38$		0			0
$39$			5.14991i			0.824645i
$40$		0			0
$41$	4.87850	−	2.81660i	0.761893	−	0.439879i	−0.0680819	−	0.997680i	$-0.521688\pi$
$41$	4.87850	−	2.81660i	0.761893	−	0.439879i	0.829975	+	0.557801i	$0.188355\pi$
$42$		0			0
$43$	−4.32286	−	7.48741i	−0.659230	−	1.14182i	−0.980815	−	0.194939i	$-0.937549\pi$
$43$	−4.32286	−	7.48741i	−0.659230	−	1.14182i	0.321586	−	0.946880i	$-0.395784\pi$
$44$		0			0
$45$		−	16.6838i		−	2.48707i
$46$		0			0
$47$	−6.26395	−	3.61649i	−0.913691	−	0.527520i	−0.0320740	−	0.999485i	$-0.510211\pi$
$47$	−6.26395	−	3.61649i	−0.913691	−	0.527520i	−0.881617	+	0.471966i	$0.843545\pi$
$48$		0			0
$49$	−11.4976			−1.64251
$50$		0			0
$51$	1.89626	+	1.09480i	0.265529	+	0.153303i
$52$		0			0
$53$	4.73541	−	8.20196i	0.650458	−	1.12663i	−0.332554	−	0.943084i	$-0.607910\pi$
$53$	4.73541	−	8.20196i	0.650458	−	1.12663i	0.983012	−	0.183542i	$-0.0587563\pi$
$54$		0			0
$55$	0.789079	−	0.455575i	0.106399	−	0.0614297i
$56$		0			0
$57$	−11.1416	+	7.38258i	−1.47575	+	0.977846i
$58$		0			0
$59$	−6.62664	+	3.82589i	−0.862715	+	0.498089i	−0.864921	−	0.501909i	$-0.832631\pi$
$59$	−6.62664	+	3.82589i	−0.862715	+	0.498089i	0.00220531	+	0.999998i	$0.499298\pi$
$60$		0			0
$61$	3.46531	+	2.00070i	0.443687	+	0.256163i	0.705160	−	0.709048i	$-0.250875\pi$
$61$	3.46531	+	2.00070i	0.443687	+	0.256163i	−0.261473	+	0.965211i	$0.584208\pi$
$62$		0			0
$63$	23.8454	+	13.7672i	3.00424	+	1.73450i
$64$		0			0
$65$			4.37690i			0.542887i
$66$		0			0
$67$	10.6067	+	6.12378i	1.29581	+	0.748139i	0.979678	−	0.200575i	$-0.0642810\pi$
$67$	10.6067	+	6.12378i	1.29581	+	0.748139i	0.316136	+	0.948714i	$0.397614\pi$
$68$		0			0
$69$	−4.88901			−0.588567
$70$		0			0
$71$	−5.09365	−	8.82246i	−0.604505	−	1.04703i	−0.992129	−	0.125216i	$-0.960038\pi$
$71$	−5.09365	−	8.82246i	−0.604505	−	1.04703i	0.387624	−	0.921817i	$-0.373296\pi$
$72$		0			0
$73$	2.54260	+	4.40392i	0.297589	+	0.515439i	0.975584	−	0.219627i	$-0.0704842\pi$
$73$	2.54260	+	4.40392i	0.297589	+	0.515439i	−0.677995	+	0.735067i	$0.737151\pi$
$74$		0			0
$75$		−	5.49268i		−	0.634241i
$76$		0			0
$77$			1.50373i			0.171366i
$78$		0			0
$79$	−1.31170	−	2.27193i	−0.147578	−	0.255612i	0.782754	−	0.622331i	$-0.213814\pi$
$79$	−1.31170	−	2.27193i	−0.147578	−	0.255612i	−0.930332	+	0.366719i	$0.880481\pi$
$80$		0			0
$81$	−6.38991	−	11.0677i	−0.709990	−	1.22974i
$82$		0			0
$83$	4.69293			0.515116			0.257558	−	0.966263i	$-0.417082\pi$
$83$	4.69293			0.515116			0.257558	+	0.966263i	$0.417082\pi$
$84$		0			0
$85$	1.61162	+	0.930471i	0.174805	+	0.100924i
$86$		0			0
$87$			2.84338i			0.304843i
$88$		0			0
$89$	7.37293	+	4.25676i	0.781529	+	0.451216i	0.836972	−	0.547246i	$-0.184324\pi$
$89$	7.37293	+	4.25676i	0.781529	+	0.451216i	−0.0554428	+	0.998462i	$0.517657\pi$
$90$		0			0
$91$	−6.25572	−	3.61174i	−0.655778	−	0.378613i
$92$		0			0
$93$	−7.44905	+	4.30071i	−0.772430	+	0.445963i
$94$		0			0
$95$	−9.46925	+	6.27443i	−0.971524	+	0.643743i
$96$		0			0
$97$	6.30190	−	3.63841i	0.639861	−	0.369424i	−0.144700	−	0.989476i	$-0.546222\pi$
$97$	6.30190	−	3.63841i	0.639861	−	0.369424i	0.784561	+	0.620051i	$0.212888\pi$
$98$		0			0
$99$	1.11918	−	1.93848i	0.112482	−	0.194824i
$100$		0			0
$101$	3.66074	+	2.11353i	0.364257	+	0.210304i	0.670947	−	0.741506i	$-0.265888\pi$
$101$	3.66074	+	2.11353i	0.364257	+	0.210304i	−0.306689	+	0.951810i	$0.599221\pi$
$102$		0			0
$103$	18.3567			1.80874			0.904370	−	0.426750i	$-0.140341\pi$
$103$	18.3567			1.80874			0.904370	+	0.426750i	$0.140341\pi$
$104$		0			0
$105$	29.7630	+	17.1837i	2.90457	+	1.67695i
$106$		0			0
$107$			11.6010i			1.12151i	0.827982	+	0.560754i	$0.189489\pi$
$107$			11.6010i			1.12151i	−0.827982	+	0.560754i	$0.810511\pi$
$108$		0			0
$109$	0.253698	+	0.439417i	0.0242998	+	0.0420886i	0.877920	−	0.478808i	$-0.158931\pi$
$109$	0.253698	+	0.439417i	0.0242998	+	0.0420886i	−0.853620	+	0.520897i	$0.825598\pi$
$110$		0			0
$111$	−27.1120	+	15.6531i	−2.57335	+	1.48573i
$112$		0			0
$113$		−	7.70645i		−	0.724961i	−0.931991	−	0.362481i	$-0.881930\pi$
$113$		−	7.70645i		−	0.724961i	0.931991	−	0.362481i	$-0.118070\pi$
$114$		0			0
$115$	−4.15515			−0.387470
$116$		0			0
$117$	5.37621	+	9.31187i	0.497031	+	0.860882i
$118$		0			0
$119$	−2.65977	+	1.53562i	−0.243821	+	0.140770i
$120$		0			0
$121$	−10.8778			−0.988887
$122$		0			0
$123$	8.63647	−	14.9588i	0.778724	−	1.34879i
$124$		0			0
$125$			8.36186i			0.747908i
$126$		0			0
$127$	6.90707	−	11.9634i	0.612903	−	1.06158i	−0.377846	−	0.925869i	$-0.623335\pi$
$127$	6.90707	−	11.9634i	0.612903	−	1.06158i	0.990749	−	0.135710i	$-0.0433317\pi$
$128$		0			0
$129$	−22.9584	−	13.2551i	−2.02138	−	1.16704i
$130$		0			0
$131$	7.66432	+	13.2750i	0.669635	+	1.15984i	0.978006	+	0.208575i	$0.0668826\pi$
$131$	7.66432	+	13.2750i	0.669635	+	1.15984i	−0.308372	+	0.951266i	$0.599784\pi$
$132$		0			0
$133$	−1.15393	−	18.7116i	−0.100058	−	1.62250i
$134$		0			0
$135$	−13.5924	−	23.5427i	−1.16984	−	2.02623i
$136$		0			0
$137$	−4.73230	+	8.19659i	−0.404308	+	0.700282i	−0.994241	−	0.107171i	$-0.965821\pi$
$137$	−4.73230	+	8.19659i	−0.404308	+	0.700282i	0.589933	+	0.807452i	$0.299154\pi$
$138$		0			0
$139$	2.16855	−	3.75604i	0.183934	−	0.318583i	−0.759283	−	0.650761i	$-0.774450\pi$
$139$	2.16855	−	3.75604i	0.183934	−	0.318583i	0.943217	+	0.332178i	$0.107783\pi$
$140$		0			0
$141$	−22.1783			−1.86775
$142$		0			0
$143$	−0.293611	+	0.508549i	−0.0245530	+	0.0425270i
$144$		0			0
$145$			2.41658i			0.200686i
$146$		0			0
$147$	−30.5315	+	17.6274i	−2.51820	+	1.45388i
$148$		0			0
$149$	−4.50515	+	2.60105i	−0.369076	+	0.213086i	−0.673055	−	0.739592i	$-0.735018\pi$
$149$	−4.50515	+	2.60105i	−0.369076	+	0.213086i	0.303978	+	0.952679i	$0.401685\pi$
$150$		0			0
$151$	−4.14034			−0.336936			−0.168468	−	0.985707i	$-0.553882\pi$
$151$	−4.14034			−0.336936			−0.168468	+	0.985707i	$0.553882\pi$
$152$		0			0
$153$	4.57165			0.369596
$154$		0			0
$155$	−6.33093	+	3.65516i	−0.508512	+	0.293590i
$156$		0			0
$157$	−2.57943	+	1.48923i	−0.205861	+	0.118854i	−0.599386	−	0.800460i	$-0.704589\pi$
$157$	−2.57943	+	1.48923i	−0.205861	+	0.118854i	0.393525	+	0.919314i	$0.371255\pi$
$158$		0			0
$159$		−	29.0401i		−	2.30303i
$160$		0			0
$161$	3.42876	−	5.93879i	0.270224	−	0.468042i
$162$		0			0
$163$	0.299245			0.0234387			0.0117194	−	0.999931i	$-0.496270\pi$
$163$	0.299245			0.0234387			0.0117194	+	0.999931i	$0.496270\pi$
$164$		0			0
$165$	1.39692	−	2.41953i	0.108750	−	0.188360i
$166$		0			0
$167$	−3.94944	+	6.84063i	−0.305617	+	0.529344i	−0.977398	−	0.211405i	$-0.932196\pi$
$167$	−3.94944	+	6.84063i	−0.305617	+	0.529344i	0.671782	+	0.740749i	$0.265529\pi$
$168$		0			0
$169$	5.08958	+	8.81541i	0.391506	+	0.678109i
$170$		0			0
$171$	−12.4389	+	24.9801i	−0.951226	+	1.91028i
$172$		0			0
$173$	8.01754	+	13.8868i	0.609562	+	1.05579i	0.991313	+	0.131527i	$0.0419880\pi$
$173$	8.01754	+	13.8868i	0.609562	+	1.05579i	−0.381751	+	0.924265i	$0.624679\pi$
$174$		0			0
$175$	6.67210	+	3.85214i	0.504363	+	0.291194i
$176$		0			0
$177$	−11.7312	+	20.3191i	−0.881773	+	1.52728i
$178$		0			0
$179$		−	15.5488i		−	1.16218i	−0.813841	−	0.581088i	$-0.802627\pi$
$179$		−	15.5488i		−	1.16218i	0.813841	−	0.581088i	$-0.197373\pi$
$180$		0			0
$181$	0.129430	−	0.224180i	0.00962046	−	0.0166631i	−0.861175	−	0.508308i	$-0.830271\pi$
$181$	0.129430	−	0.224180i	0.00962046	−	0.0166631i	0.870796	+	0.491645i	$0.163604\pi$
$182$		0			0
$183$	12.2694			0.906977
$184$		0			0
$185$	−23.0424	+	13.3035i	−1.69411	+	0.978095i
$186$		0			0
$187$	0.124836	+	0.216222i	0.00912889	+	0.0158117i
$188$		0			0
$189$	44.8648			3.26343
$190$		0			0
$191$			6.00136i			0.434244i	0.976145	+	0.217122i	$0.0696669\pi$
$191$			6.00136i			0.434244i	−0.976145	+	0.217122i	$0.930333\pi$
$192$		0			0
$193$	−6.63936	+	3.83324i	−0.477912	+	0.275922i	−0.719546	−	0.694445i	$-0.755650\pi$
$193$	−6.63936	+	3.83324i	−0.477912	+	0.275922i	0.241634	+	0.970367i	$0.422317\pi$
$194$		0			0
$195$	6.71037	+	11.6227i	0.480540	+	0.832320i
$196$		0			0
$197$		−	5.38374i		−	0.383576i	−0.981436	−	0.191788i	$-0.938571\pi$
$197$		−	5.38374i		−	0.383576i	0.981436	−	0.191788i	$-0.0614286\pi$
$198$		0			0
$199$	16.1469	+	9.32240i	1.14462	+	0.660847i	0.947571	−	0.319546i	$-0.103530\pi$
$199$	16.1469	+	9.32240i	1.14462	+	0.660847i	0.197050	+	0.980393i	$0.436864\pi$
$200$		0			0
$201$	37.5544			2.64888
$202$		0			0
$203$	−3.45393	−	1.99413i	−0.242418	−	0.139960i
$204$		0			0
$205$	7.34011	−	12.7134i	0.512656	−	0.887945i
$206$		0			0
$207$	−8.84011	+	5.10384i	−0.614430	+	0.354741i
$208$		0			0
$209$	−1.52113	+	0.0938066i	−0.105219	+	0.00648874i
$210$		0			0
$211$	−0.807263	+	0.466073i	−0.0555743	+	0.0320858i	−0.527530	−	0.849537i	$-0.676882\pi$
$211$	−0.807263	+	0.466073i	−0.0555743	+	0.0320858i	0.471955	+	0.881622i	$0.343548\pi$
$212$		0			0
$213$	−27.0521	−	15.6185i	−1.85358	−	1.07016i
$214$		0			0
$215$	−19.5123	−	11.2654i	−1.33073	−	0.768297i
$216$		0			0
$217$		−	12.0647i		−	0.819006i
$218$		0			0
$219$	13.5036	+	7.79631i	0.912489	+	0.526826i
$220$		0			0
$221$	−1.19935			−0.0806768
$222$		0			0
$223$	−7.62648	−	13.2095i	−0.510707	−	0.884571i	−0.999923	−	0.0124080i	$-0.996050\pi$
$223$	−7.62648	−	13.2095i	−0.510707	−	0.884571i	0.489216	−	0.872163i	$-0.337283\pi$
$224$		0			0
$225$	−5.73405	−	9.93166i	−0.382270	−	0.662111i
$226$		0			0
$227$		−	5.51895i		−	0.366306i	−0.983084	−	0.183153i	$-0.941370\pi$
$227$		−	5.51895i		−	0.366306i	0.983084	−	0.183153i	$-0.0586303\pi$
$228$		0			0
$229$			12.8139i			0.846768i	0.905950	+	0.423384i	$0.139158\pi$
$229$			12.8139i			0.846768i	−0.905950	+	0.423384i	$0.860842\pi$
$230$		0			0
$231$	2.30543	+	3.99311i	0.151686	+	0.262728i
$232$		0			0
$233$	0.958205	+	1.65966i	0.0627741	+	0.108728i	0.895704	−	0.444650i	$-0.146672\pi$
$233$	0.958205	+	1.65966i	0.0627741	+	0.108728i	−0.832930	+	0.553378i	$0.813339\pi$
$234$		0			0
$235$	−18.8493			−1.22959
$236$		0			0
$237$	−6.96636	−	4.02203i	−0.452514	−	0.261259i
$238$		0			0
$239$			26.1872i			1.69391i	0.531665	+	0.846955i	$0.321566\pi$
$239$			26.1872i			1.69391i	−0.531665	+	0.846955i	$0.678434\pi$
$240$		0			0
$241$	−13.2053	−	7.62406i	−0.850625	−	0.491109i	0.0102365	−	0.999948i	$-0.496742\pi$
$241$	−13.2053	−	7.62406i	−0.850625	−	0.491109i	−0.860862	+	0.508839i	$0.830075\pi$
$242$		0			0
$243$	−6.83453	−	3.94592i	−0.438435	−	0.253131i
$244$		0			0
$245$	−25.9487	+	14.9815i	−1.65780	+	0.957131i
$246$		0			0
$247$	3.26327	−	6.55339i	0.207637	−	0.416982i
$248$		0			0
$249$	12.4619	−	7.19490i	0.789743	−	0.455958i
$250$		0			0
$251$	3.40850	−	5.90370i	0.215143	−	0.372638i	−0.738174	−	0.674610i	$-0.764312\pi$
$251$	3.40850	−	5.90370i	0.215143	−	0.372638i	0.953317	+	0.301972i	$0.0976450\pi$
$252$		0			0
$253$	−0.482785	−	0.278736i	−0.0303524	−	0.0175240i
$254$		0			0
$255$	5.70616			0.357333
$256$		0			0
$257$	9.99669	+	5.77159i	0.623576	+	0.360022i	0.778260	−	0.627942i	$-0.216103\pi$
$257$	9.99669	+	5.77159i	0.623576	+	0.360022i	−0.154684	+	0.987964i	$0.549436\pi$
$258$		0			0
$259$		−	43.9114i		−	2.72852i
$260$		0			0
$261$	2.96833	+	5.14130i	0.183735	+	0.318238i
$262$		0			0
$263$	11.8061	−	6.81625i	0.727994	−	0.420308i	−0.0896937	−	0.995969i	$-0.528589\pi$
$263$	11.8061	−	6.81625i	0.727994	−	0.420308i	0.817688	+	0.575662i	$0.195255\pi$
$264$		0			0
$265$		−	24.6811i		−	1.51615i
$266$		0			0
$267$	26.1048			1.59759
$268$		0			0
$269$	−14.0715	−	24.3725i	−0.857953	−	1.48602i	−0.873878	−	0.486144i	$-0.838403\pi$
$269$	−14.0715	−	24.3725i	−0.857953	−	1.48602i	0.0159257	−	0.999873i	$-0.494930\pi$
$270$		0			0
$271$	3.45517	−	1.99485i	0.209887	−	0.121178i	−0.391372	−	0.920233i	$-0.627999\pi$
$271$	3.45517	−	1.99485i	0.209887	−	0.121178i	0.601259	+	0.799054i	$0.294666\pi$
$272$		0			0
$273$	−22.1492			−1.34053
$274$		0			0
$275$	0.313153	−	0.542397i	0.0188838	−	0.0327078i
$276$		0			0
$277$		−	12.1974i		−	0.732869i	−0.930444	−	0.366435i	$-0.880578\pi$
$277$		−	12.1974i		−	0.732869i	0.930444	−	0.366435i	$-0.119422\pi$
$278$		0			0
$279$	−8.97939	+	15.5528i	−0.537582	+	0.931119i
$280$		0			0
$281$	−0.459532	−	0.265311i	−0.0274134	−	0.0158271i	0.486231	−	0.873830i	$-0.338371\pi$
$281$	−0.459532	−	0.265311i	−0.0274134	−	0.0158271i	−0.513644	+	0.858003i	$0.671705\pi$
$282$		0			0
$283$	−1.48484	−	2.57181i	−0.0882644	−	0.152878i	0.818513	−	0.574488i	$-0.194799\pi$
$283$	−1.48484	−	2.57181i	−0.0882644	−	0.152878i	−0.906778	+	0.421609i	$0.861465\pi$
$284$		0			0
$285$	−15.5257	+	31.1792i	−0.919665	+	1.84690i
$286$		0			0
$287$	12.1139	+	20.9818i	0.715059	+	1.23852i
$288$		0			0
$289$	8.24503	−	14.2808i	0.485002	−	0.840048i
$290$		0			0
$291$	11.1563	−	19.3233i	0.653996	−	1.13275i
$292$		0			0
$293$	15.8714			0.927216			0.463608	−	0.886040i	$-0.346555\pi$
$293$	15.8714			0.927216			0.463608	+	0.886040i	$0.346555\pi$
$294$		0			0
$295$	−9.97034	+	17.2691i	−0.580496	+	1.00545i
$296$		0			0
$297$		−	3.64721i		−	0.211633i
$298$		0			0
$299$	2.31915	−	1.33896i	0.134120	−	0.0774343i
$300$		0			0
$301$	32.2025	−	18.5921i	1.85612	−	1.07163i
$302$		0			0
$303$	12.9613			0.744608
$304$		0			0
$305$	10.4277			0.597088
$306$		0			0
$307$	19.5928	−	11.3119i	1.11822	−	0.645605i	0.177274	−	0.984161i	$-0.443272\pi$
$307$	19.5928	−	11.3119i	1.11822	−	0.645605i	0.940946	+	0.338557i	$0.109939\pi$
$308$		0			0
$309$	48.7457	−	28.1433i	2.77304	−	1.60102i
$310$		0			0
$311$			15.1802i			0.860792i	0.902640	+	0.430396i	$0.141626\pi$
$311$			15.1802i			0.860792i	−0.902640	+	0.430396i	$0.858374\pi$
$312$		0			0
$313$	2.14838	−	3.72111i	0.121434	−	0.210330i	−0.798899	−	0.601465i	$-0.794584\pi$
$313$	2.14838	−	3.72111i	0.121434	−	0.210330i	0.920333	+	0.391135i	$0.127917\pi$
$314$		0			0
$315$	71.7550			4.04294
$316$		0			0
$317$	−0.160202	+	0.277479i	−0.00899787	+	0.0155848i	−0.870489	−	0.492187i	$-0.836197\pi$
$317$	−0.160202	+	0.277479i	−0.00899787	+	0.0155848i	0.861491	+	0.507772i	$0.169531\pi$
$318$		0			0
$319$	−0.162109	+	0.280781i	−0.00907637	+	0.0157207i
$320$		0			0
$321$	17.7859	+	30.8060i	0.992710	+	1.71942i
$322$		0			0
$323$	−1.71931	−	2.59474i	−0.0956647	−	0.144375i
$324$		0			0
$325$	1.50429	+	2.60552i	0.0834433	+	0.144528i
$326$		0			0
$327$	1.34737	+	0.777906i	0.0745099	+	0.0430183i
$328$		0			0
$329$	15.5541	−	26.9405i	0.857526	−	1.48528i
$330$		0			0
$331$			15.7503i			0.865713i	0.901463	+	0.432856i	$0.142494\pi$
$331$			15.7503i			0.865713i	−0.901463	+	0.432856i	$0.857506\pi$
$332$		0			0
$333$	−32.6819	+	56.6067i	−1.79096	+	3.10203i
$334$		0			0
$335$	31.9174			1.74383
$336$		0			0
$337$	−3.84020	+	2.21714i	−0.209189	+	0.120775i	−0.600934	−	0.799298i	$-0.705205\pi$
$337$	−3.84020	+	2.21714i	−0.209189	+	0.120775i	0.391746	+	0.920074i	$0.371871\pi$
$338$		0			0
$339$	−11.8150	−	20.4642i	−0.641704	−	1.11146i
$340$		0			0
$341$	−0.980782			−0.0531123
$342$		0			0
$343$		−	19.3436i		−	1.04446i
$344$		0			0
$345$	−11.0339	+	6.37042i	−0.594044	+	0.342972i
$346$		0			0
$347$	4.37820	+	7.58327i	0.235034	+	0.407091i	0.959283	−	0.282448i	$-0.0911465\pi$
$347$	4.37820	+	7.58327i	0.235034	+	0.407091i	−0.724248	+	0.689539i	$0.757813\pi$
$348$		0			0
$349$			31.3794i			1.67970i	0.542819	+	0.839850i	$0.317357\pi$
$349$			31.3794i			1.67970i	−0.542819	+	0.839850i	$0.682643\pi$
$350$		0			0
$351$	15.1729	+	8.76005i	0.809867	+	0.467577i
$352$		0			0
$353$	−3.85737			−0.205307			−0.102653	−	0.994717i	$-0.532733\pi$
$353$	−3.85737			−0.205307			−0.102653	+	0.994717i	$0.532733\pi$
$354$		0			0
$355$	−22.9915	−	13.2741i	−1.22026	−	0.704518i
$356$		0			0
$357$	−4.70862	+	8.15558i	−0.249207	+	0.431639i
$358$		0			0
$359$	25.0177	−	14.4440i	1.32039	−	0.762325i	0.336596	−	0.941649i	$-0.390724\pi$
$359$	25.0177	−	14.4440i	1.32039	−	0.762325i	0.983790	+	0.179324i	$0.0573910\pi$
$360$		0			0
$361$	18.8560	−	2.33455i	0.992423	−	0.122871i
$362$		0			0
$363$	−28.8855	+	16.6771i	−1.51610	+	0.875320i
$364$		0			0
$365$	11.4767	+	6.62606i	0.600717	+	0.346824i
$366$		0			0
$367$	−30.0071	−	17.3246i	−1.56636	−	0.904336i	−0.996589	−	0.0825294i	$-0.973700\pi$
$367$	−30.0071	−	17.3246i	−1.56636	−	0.904336i	−0.569767	−	0.821806i	$-0.692966\pi$
$368$		0			0
$369$		−	36.0639i		−	1.87741i
$370$		0			0
$371$	35.2757	+	20.3664i	1.83142	+	1.05737i
$372$		0			0
$373$	6.50847			0.336996			0.168498	−	0.985702i	$-0.446108\pi$
$373$	6.50847			0.336996			0.168498	+	0.985702i	$0.446108\pi$
$374$		0			0
$375$	12.8199	+	22.2047i	0.662015	+	1.14664i
$376$		0			0
$377$	−0.778724	−	1.34879i	−0.0401063	−	0.0694662i
$378$		0			0
$379$		−	22.8576i		−	1.17412i	−0.809544	−	0.587059i	$-0.800286\pi$
$379$		−	22.8576i		−	1.17412i	0.809544	−	0.587059i	$-0.199714\pi$
$380$		0			0
$381$		−	42.3579i		−	2.17006i
$382$		0			0
$383$	−3.86012	−	6.68592i	−0.197243	−	0.341634i	0.750391	−	0.660995i	$-0.229865\pi$
$383$	−3.86012	−	6.68592i	−0.197243	−	0.341634i	−0.947633	+	0.319360i	$0.896532\pi$
$384$		0			0
$385$	1.95938	+	3.39374i	0.0998590	+	0.172961i
$386$		0			0
$387$	−55.3501			−2.81360
$388$		0			0
$389$	13.5074	+	7.79852i	0.684854	+	0.395401i	0.801681	−	0.597752i	$-0.203939\pi$
$389$	13.5074	+	7.79852i	0.684854	+	0.395401i	−0.116827	+	0.993152i	$0.537272\pi$
$390$		0			0
$391$		−	1.13859i		−	0.0575807i
$392$		0			0
$393$	40.7047	+	23.5009i	2.05328	+	1.18546i
$394$		0			0
$395$	−5.92069	−	3.41831i	−0.297902	−	0.171994i
$396$		0			0
$397$	17.5633	−	10.1402i	0.881478	−	0.508922i	0.0103327	−	0.999947i	$-0.496711\pi$
$397$	17.5633	−	10.1402i	0.881478	−	0.508922i	0.871146	+	0.491025i	$0.163378\pi$
$398$		0			0
$399$	−31.7516	−	47.9189i	−1.58957	−	2.39894i
$400$		0			0
$401$	−17.7743	+	10.2620i	−0.887608	+	0.512461i	−0.873159	−	0.487435i	$-0.837933\pi$
$401$	−17.7743	+	10.2620i	−0.887608	+	0.512461i	−0.0144489	+	0.999896i	$0.504599\pi$
$402$		0			0
$403$	2.35569	−	4.08018i	0.117345	−	0.203248i
$404$		0			0
$405$	−28.8425	−	16.6522i	−1.43319	−	0.827455i
$406$		0			0
$407$	−3.56971			−0.176944
$408$		0			0
$409$	−9.46841	−	5.46659i	−0.468183	−	0.270306i	0.247296	−	0.968940i	$-0.420458\pi$
$409$	−9.46841	−	5.46659i	−0.468183	−	0.270306i	−0.715479	+	0.698634i	$0.753791\pi$
$410$		0			0
$411$			29.0210i			1.43150i
$412$		0			0
$413$	−16.4547	−	28.5004i	−0.809684	−	1.40241i
$414$		0			0
$415$	10.5914	−	6.11493i	0.519910	−	0.300170i
$416$		0			0
$417$		−	13.2987i		−	0.651242i
$418$		0			0
$419$	−25.2865			−1.23532			−0.617662	−	0.786443i	$-0.711920\pi$
$419$	−25.2865			−1.23532			−0.617662	+	0.786443i	$0.711920\pi$
$420$		0			0
$421$	7.89762	+	13.6791i	0.384906	+	0.666677i	0.991756	−	0.128139i	$-0.0409004\pi$
$421$	7.89762	+	13.6791i	0.384906	+	0.666677i	−0.606850	+	0.794816i	$0.707567\pi$
$422$		0			0
$423$	−40.1019	+	23.1529i	−1.94982	+	1.12573i
$424$		0			0
$425$	1.27917			0.0620491
$426$		0			0
$427$	−8.60476	+	14.9039i	−0.416414	+	0.721249i
$428$		0			0
$429$			1.80058i			0.0869328i
$430$		0			0
$431$	18.9346	−	32.7957i	0.912048	−	1.57971i	0.100882	−	0.994898i	$-0.467834\pi$
$431$	18.9346	−	32.7957i	0.912048	−	1.57971i	0.811166	−	0.584816i	$-0.198833\pi$
$432$		0			0
$433$	−32.1519	−	18.5629i	−1.54512	−	0.892077i	−0.998503	−	0.0546959i	$-0.982581\pi$
$433$	−32.1519	−	18.5629i	−1.54512	−	0.892077i	−0.546620	−	0.837381i	$-0.684086\pi$
$434$		0			0
$435$	3.70495	+	6.41717i	0.177639	+	0.307680i
$436$		0			0
$437$	6.22138	+	3.09795i	0.297609	+	0.148195i
$438$		0			0
$439$	−8.17633	−	14.1618i	−0.390235	−	0.675907i	0.602245	−	0.798311i	$-0.294273\pi$
$439$	−8.17633	−	14.1618i	−0.390235	−	0.675907i	−0.992480	+	0.122404i	$0.960940\pi$
$440$		0			0
$441$	−36.8039	+	63.7463i	−1.75257	+	3.03554i
$442$		0			0
$443$	−1.30941	+	2.26796i	−0.0622119	+	0.107754i	−0.895454	−	0.445154i	$-0.853149\pi$
$443$	−1.30941	+	2.26796i	−0.0622119	+	0.107754i	0.833242	+	0.552909i	$0.186482\pi$
$444$		0			0
$445$	22.1864			1.05174
$446$		0			0
$447$	−7.97553	+	13.8140i	−0.377230	+	0.653381i
$448$		0			0
$449$		−	17.9548i		−	0.847342i	−0.905816	−	0.423671i	$-0.860741\pi$
$449$		−	17.9548i		−	0.847342i	0.905816	−	0.423671i	$-0.139259\pi$
$450$		0			0
$451$	1.70569	−	0.984778i	0.0803176	−	0.0463714i
$452$		0			0
$453$	−10.9945	+	6.34770i	−0.516569	+	0.298241i
$454$		0			0
$455$	−18.8245			−0.882507
$456$		0			0
$457$	−15.9102			−0.744246			−0.372123	−	0.928183i	$-0.621370\pi$
$457$	−15.9102			−0.744246			−0.372123	+	0.928183i	$0.621370\pi$
$458$		0			0
$459$	6.45111	−	3.72455i	0.301112	−	0.173847i
$460$		0			0
$461$	−15.3144	+	8.84177i	−0.713262	+	0.411802i	−0.812268	−	0.583285i	$-0.801767\pi$
$461$	−15.3144	+	8.84177i	−0.713262	+	0.411802i	0.0990055	+	0.995087i	$0.468434\pi$
$462$		0			0
$463$			22.4205i			1.04197i	0.853566	+	0.520985i	$0.174435\pi$
$463$			22.4205i			1.04197i	−0.853566	+	0.520985i	$0.825565\pi$
$464$		0			0
$465$	−11.2077	+	19.4123i	−0.519746	+	0.900226i
$466$		0			0
$467$	−36.8007			−1.70293			−0.851467	−	0.524408i	$-0.824287\pi$
$467$	−36.8007			−1.70293			−0.851467	+	0.524408i	$0.824287\pi$
$468$		0			0
$469$	−26.3377	+	45.6182i	−1.21616	+	2.10645i
$470$		0			0
$471$	−4.56639	+	7.90923i	−0.210408	+	0.364438i
$472$		0			0
$473$	−1.51142	−	2.61785i	−0.0694949	−	0.120369i
$474$		0			0
$475$	−3.48047	+	6.98958i	−0.159695	+	0.320704i
$476$		0			0
$477$	−30.3162	−	52.5091i	−1.38808	−	2.40423i
$478$		0			0
$479$	1.17380	+	0.677696i	0.0536324	+	0.0309647i	0.526576	−	0.850128i	$-0.323475\pi$
$479$	1.17380	+	0.677696i	0.0536324	+	0.0309647i	−0.472944	+	0.881092i	$0.656809\pi$
$480$		0			0
$481$	8.57390	−	14.8504i	0.390936	−	0.677122i
$482$		0			0
$483$		−	21.0270i		−	0.956764i
$484$		0			0
$485$	9.48175	−	16.4229i	0.430544	−	0.745724i
$486$		0			0
$487$	−16.1529			−0.731957			−0.365979	−	0.930623i	$-0.619266\pi$
$487$	−16.1529			−0.731957			−0.365979	+	0.930623i	$0.619266\pi$
$488$		0			0
$489$	0.794637	−	0.458784i	0.0359347	−	0.0207469i
$490$		0			0
$491$	0.839069	+	1.45331i	0.0378666	+	0.0655870i	0.884338	−	0.466848i	$-0.154610\pi$
$491$	0.839069	+	1.45331i	0.0378666	+	0.0655870i	−0.846471	+	0.532435i	$0.821277\pi$
$492$		0			0
$493$	−0.662187			−0.0298234
$494$		0			0
$495$		−	5.83321i		−	0.262183i
$496$		0			0
$497$	37.9444	−	21.9072i	1.70204	−	0.982672i
$498$		0			0
$499$	11.6119	+	20.1124i	0.519819	+	0.900354i	0.999735	+	0.0230387i	$0.00733410\pi$
$499$	11.6119	+	20.1124i	0.519819	+	0.900354i	−0.479915	+	0.877315i	$0.659333\pi$
$500$		0			0
$501$			24.2201i			1.08207i
$502$		0			0
$503$	−25.5941	−	14.7768i	−1.14118	−	0.658863i	−0.194460	−	0.980910i	$-0.562296\pi$
$503$	−25.5941	−	14.7768i	−1.14118	−	0.658863i	−0.946724	+	0.322047i	$0.895629\pi$
$504$		0			0
$505$	11.0158			0.490196
$506$		0			0
$507$	27.0305	+	15.6060i	1.20046	+	0.693089i
$508$		0			0
$509$	1.27450	−	2.20750i	0.0564913	−	0.0978459i	−0.836397	−	0.548124i	$-0.815342\pi$
$509$	1.27450	−	2.20750i	0.0564913	−	0.0978459i	0.892888	+	0.450279i	$0.148675\pi$
$510$		0			0
$511$	−18.9407	+	10.9354i	−0.837888	+	0.483755i
$512$		0			0
$513$	2.79878	+	45.3837i	0.123569	+	2.00374i
$514$		0			0
$515$	41.4288	−	23.9189i	1.82557	−	1.05399i
$516$		0			0
$517$	−2.19009	−	1.26445i	−0.0963199	−	0.0556103i
$518$		0			0
$519$	42.5806	+	24.5839i	1.86908	+	1.07912i
$520$		0			0
$521$			36.4489i			1.59686i	0.602091	+	0.798428i	$0.294335\pi$
$521$			36.4489i			1.59686i	−0.602091	+	0.798428i	$0.705665\pi$
$522$		0			0
$523$	−22.0155	−	12.7107i	−0.962673	−	0.555799i	−0.0656782	−	0.997841i	$-0.520921\pi$
$523$	−22.0155	−	12.7107i	−0.962673	−	0.555799i	−0.896995	+	0.442041i	$0.854254\pi$
$524$		0			0
$525$	23.6234			1.03101
$526$		0			0
$527$	−1.00158	−	1.73479i	−0.0436295	−	0.0755685i
$528$		0			0
$529$	−10.2289	−	17.7169i	−0.444734	−	0.770301i
$530$		0			0
$531$			48.9869i			2.12585i
$532$		0			0
$533$			9.46116i			0.409808i
$534$		0			0
$535$	15.1162	+	26.1820i	0.653529	+	1.13194i
$536$		0			0
$537$	−23.8385	−	41.2895i	−1.02871	−	1.78177i
$538$		0			0
$539$	−4.01994			−0.173151
$540$		0			0
$541$	−19.1779	−	11.0724i	−0.824524	−	0.476039i	0.0274503	−	0.999623i	$-0.491261\pi$
$541$	−19.1779	−	11.0724i	−0.824524	−	0.476039i	−0.851974	+	0.523584i	$0.824595\pi$
$542$		0			0
$543$		−	0.793736i		−	0.0340625i
$544$		0			0
$545$	1.14513	+	0.661141i	0.0490519	+	0.0283202i
$546$		0			0
$547$	7.87144	+	4.54458i	0.336559	+	0.194312i	0.658749	−	0.752363i	$-0.271086\pi$
$547$	7.87144	+	4.54458i	0.336559	+	0.194312i	−0.322191	+	0.946675i	$0.604419\pi$
$548$		0			0
$549$	22.1850	−	12.8085i	0.946832	−	0.546654i
$550$		0			0
$551$	1.80173	−	3.61828i	0.0767562	−	0.154144i
$552$		0			0
$553$	9.77132	−	5.64147i	0.415519	−	0.239900i
$554$		0			0
$555$	−40.7922	+	70.6542i	−1.73153	+	2.99911i
$556$		0			0
$557$	8.28385	+	4.78268i	0.350998	+	0.202649i	0.665125	−	0.746732i	$-0.268378\pi$
$557$	8.28385	+	4.78268i	0.350998	+	0.202649i	−0.314127	+	0.949381i	$0.601712\pi$
$558$		0			0
$559$	14.5208			0.614163
$560$		0			0
$561$	0.662994	+	0.382780i	0.0279916	+	0.0161610i
$562$		0			0
$563$		−	28.0350i		−	1.18153i	−0.806842	−	0.590767i	$-0.798825\pi$
$563$		−	28.0350i		−	1.18153i	0.806842	−	0.590767i	$-0.201175\pi$
$564$		0			0
$565$	−10.0416	−	17.3925i	−0.422452	−	0.731708i
$566$		0			0
$567$	47.6007	−	27.4823i	1.99904	−	1.15415i
$568$		0			0
$569$			37.1158i			1.55597i	0.628280	+	0.777987i	$0.283759\pi$
$569$			37.1158i			1.55597i	−0.628280	+	0.777987i	$0.716241\pi$
$570$		0			0
$571$	−7.10876			−0.297492			−0.148746	−	0.988875i	$-0.547524\pi$
$571$	−7.10876			−0.297492			−0.148746	+	0.988875i	$0.547524\pi$
$572$		0			0
$573$	9.20091	+	15.9364i	0.384373	+	0.665754i
$574$		0			0
$575$	−2.47351	+	1.42808i	−0.103153	+	0.0595552i
$576$		0			0
$577$	−6.48963			−0.270167			−0.135083	−	0.990834i	$-0.543130\pi$
$577$	−6.48963			−0.270167			−0.135083	+	0.990834i	$0.543130\pi$
$578$		0			0
$579$	−11.7537	+	20.3581i	−0.488469	+	0.846053i
$580$		0			0
$581$			20.1838i			0.837363i
$582$		0			0
$583$	1.65566	−	2.86768i	0.0685702	−	0.118767i
$584$		0			0
$585$	24.2669	+	14.0105i	1.00331	+	0.579262i
$586$		0			0
$587$	−17.8311	−	30.8843i	−0.735966	−	1.27473i	−0.954298	−	0.298856i	$-0.903395\pi$
$587$	−17.8311	−	30.8843i	−0.735966	−	1.27473i	0.218332	−	0.975875i	$-0.429939\pi$
$588$		0			0
$589$	12.2043	−	0.752628i	0.502868	−	0.0310115i
$590$		0			0
$591$	−8.25401	−	14.2964i	−0.339525	−	0.588074i
$592$		0			0
$593$	−11.0443	+	19.1293i	−0.453536	+	0.785547i	−0.998603	−	0.0528454i	$-0.983171\pi$
$593$	−11.0443	+	19.1293i	−0.453536	+	0.785547i	0.545067	+	0.838393i	$0.316504\pi$
$594$		0			0
$595$	−4.00185	+	6.93140i	−0.164060	+	0.284160i
$596$		0			0
$597$	57.1700			2.33981
$598$		0			0
$599$	4.63842	−	8.03398i	0.189521	−	0.328260i	−0.755570	−	0.655068i	$-0.772640\pi$
$599$	4.63842	−	8.03398i	0.189521	−	0.328260i	0.945091	+	0.326809i	$0.105973\pi$
$600$		0			0
$601$		−	20.5743i		−	0.839245i	−0.907699	−	0.419622i	$-0.862163\pi$
$601$		−	20.5743i		−	0.839245i	0.907699	−	0.419622i	$-0.137837\pi$
$602$		0			0
$603$	67.9043	−	39.2046i	2.76528	−	1.59653i
$604$		0			0
$605$	−24.5498	+	14.1738i	−0.998090	+	0.576247i
$606$		0			0
$607$	0.329758			0.0133845			0.00669223	−	0.999978i	$-0.497870\pi$
$607$	0.329758			0.0133845			0.00669223	+	0.999978i	$0.497870\pi$
$608$		0			0
$609$	−12.2291			−0.495546
$610$		0			0
$611$	10.5205	−	6.07402i	0.425615	−	0.245729i
$612$		0			0
$613$	−22.6430	+	13.0730i	−0.914544	+	0.528012i	−0.881890	−	0.471455i	$-0.843729\pi$
$613$	−22.6430	+	13.0730i	−0.914544	+	0.528012i	−0.0326533	+	0.999467i	$0.510396\pi$
$614$		0			0
$615$		−	45.0135i		−	1.81512i
$616$		0			0
$617$	−17.8159	+	30.8580i	−0.717240	+	1.24230i	0.244849	+	0.969561i	$0.421262\pi$
$617$	−17.8159	+	30.8580i	−0.717240	+	1.24230i	−0.962089	+	0.272735i	$0.912072\pi$
$618$		0			0
$619$	−9.09549			−0.365579			−0.182789	−	0.983152i	$-0.558513\pi$
$619$	−9.09549			−0.365579			−0.182789	+	0.983152i	$0.558513\pi$
$620$		0			0
$621$	−8.31625	+	14.4042i	−0.333720	+	0.578020i
$622$		0			0
$623$	−18.3078	+	31.7101i	−0.733488	+	1.27044i
$624$		0			0
$625$	15.3739	+	26.6284i	0.614956	+	1.06513i
$626$		0			0
$627$	−3.89549	+	2.58119i	−0.155571	+	0.103083i
$628$		0			0
$629$	−3.64540	−	6.31402i	−0.145352	−	0.251757i
$630$		0			0
$631$	−34.9863	−	20.1993i	−1.39278	−	0.804123i	−0.399160	−	0.916881i	$-0.630698\pi$
$631$	−34.9863	−	20.1993i	−1.39278	−	0.804123i	−0.993622	+	0.112758i	$0.964032\pi$
$632$		0			0
$633$	−1.42911	+	2.47529i	−0.0568019	+	0.0983838i
$634$		0			0
$635$		−	35.9999i		−	1.42861i
$636$		0			0
$637$	9.65530	−	16.7235i	0.382557	−	0.662608i
$638$		0			0
$639$	−65.2193			−2.58004
$640$		0			0
$641$	42.3374	−	24.4435i	1.67223	−	0.965461i	0.705839	−	0.708373i	$-0.250570\pi$
$641$	42.3374	−	24.4435i	1.67223	−	0.965461i	0.966388	−	0.257088i	$-0.0827630\pi$
$642$		0			0
$643$	8.70125	+	15.0710i	0.343144	+	0.594343i	0.985015	−	0.172470i	$-0.0551748\pi$
$643$	8.70125	+	15.0710i	0.343144	+	0.594343i	−0.641871	+	0.766813i	$0.721842\pi$
$644$		0			0
$645$	−69.0858			−2.72025
$646$		0			0
$647$		−	17.5279i		−	0.689094i	−0.938769	−	0.344547i	$-0.888033\pi$
$647$		−	17.5279i		−	0.689094i	0.938769	−	0.344547i	$-0.111967\pi$
$648$		0			0
$649$	−2.31690	+	1.33766i	−0.0909461	+	0.0525077i
$650$		0			0
$651$	−18.4969	−	32.0375i	−0.724949	−	1.25565i
$652$		0			0
$653$		−	43.4983i		−	1.70222i	−0.524987	−	0.851111i	$-0.675930\pi$
$653$		−	43.4983i		−	1.70222i	0.524987	−	0.851111i	$-0.324070\pi$
$654$		0			0
$655$	34.5948	+	19.9733i	1.35173	+	0.780423i
$656$		0			0
$657$	32.5556			1.27011
$658$		0			0
$659$	36.1331	+	20.8615i	1.40755	+	0.812648i	0.995151	−	0.0983571i	$-0.0313587\pi$
$659$	36.1331	+	20.8615i	1.40755	+	0.812648i	0.412396	+	0.911005i	$0.364692\pi$
$660$		0			0
$661$	9.52479	−	16.4974i	0.370471	−	0.641675i	−0.619167	−	0.785259i	$-0.712530\pi$
$661$	9.52479	−	16.4974i	0.370471	−	0.641675i	0.989638	+	0.143584i	$0.0458629\pi$
$662$		0			0
$663$	−3.18483	+	1.83876i	−0.123688	+	0.0714116i
$664$		0			0
$665$	−26.9856	−	40.7261i	−1.04646	−	1.57929i
$666$		0			0
$667$	1.28046	−	0.739273i	0.0495795	−	0.0286248i
$668$		0			0
$669$	−40.5038	−	23.3849i	−1.56597	−	0.904111i
$670$		0			0
$671$	1.21159	+	0.699510i	0.0467728	+	0.0270043i
$672$		0			0
$673$		−	47.4291i		−	1.82826i	−0.405424	−	0.914129i	$-0.632876\pi$
$673$		−	47.4291i		−	1.82826i	0.405424	−	0.914129i	$-0.367124\pi$
$674$		0			0
$675$	−16.1828	−	9.34312i	−0.622875	−	0.359617i
$676$		0			0
$677$	28.6229			1.10007			0.550034	−	0.835142i	$-0.314615\pi$
$677$	28.6229			1.10007			0.550034	+	0.835142i	$0.314615\pi$
$678$		0			0
$679$	15.6484	+	27.1038i	0.600529	+	1.04015i
$680$		0			0
$681$	−8.46131	−	14.6554i	−0.324238	−	0.561597i
$682$		0			0
$683$			31.8971i			1.22051i	0.792206	+	0.610254i	$0.208933\pi$
$683$			31.8971i			1.22051i	−0.792206	+	0.610254i	$0.791067\pi$
$684$		0			0
$685$			24.6649i			0.942398i
$686$		0			0
$687$	19.6455	+	34.0270i	0.749522	+	1.29821i
$688$		0			0
$689$	7.95328	+	13.7755i	0.302996	+	0.524804i
$690$		0			0
$691$	37.7829			1.43733			0.718664	−	0.695358i	$-0.244754\pi$
$691$	37.7829			1.43733			0.718664	+	0.695358i	$0.244754\pi$
$692$		0			0
$693$	8.33716	+	4.81346i	0.316703	+	0.182848i
$694$		0			0
$695$		−	11.3026i		−	0.428731i
$696$		0			0
$697$	3.48371	+	2.01132i	0.131955	+	0.0761842i
$698$		0			0
$699$	5.08897	+	2.93812i	0.192483	+	0.111130i
$700$		0			0
$701$	−27.5119	+	15.8840i	−1.03911	+	0.599930i	−0.919581	−	0.392900i	$-0.871472\pi$
$701$	−27.5119	+	15.8840i	−1.03911	+	0.599930i	−0.119529	+	0.992831i	$0.538138\pi$
$702$		0			0
$703$	44.4194	−	2.73931i	1.67531	−	0.103315i
$704$		0			0
$705$	−50.0537	+	28.8985i	−1.88513	+	1.08838i
$706$		0			0
$707$	−9.09004	+	15.7444i	−0.341866	+	0.592130i
$708$		0			0
$709$	−19.9172	−	11.4992i	−0.748007	−	0.431862i	0.0769660	−	0.997034i	$-0.475477\pi$
$709$	−19.9172	−	11.4992i	−0.748007	−	0.431862i	−0.824974	+	0.565171i	$0.808810\pi$
$710$		0			0
$711$	−16.7951			−0.629865
$712$		0			0
$713$	3.87347	+	2.23635i	0.145063	+	0.0837519i
$714$		0			0
$715$			1.53031i			0.0572303i
$716$		0			0
$717$	40.1485	+	69.5393i	1.49937	+	2.59699i
$718$		0			0
$719$	21.7769	−	12.5729i	0.812142	−	0.468890i	−0.0355572	−	0.999368i	$-0.511321\pi$
$719$	21.7769	−	12.5729i	0.812142	−	0.468890i	0.847699	+	0.530477i	$0.177987\pi$
$720$		0			0
$721$			78.9500i			2.94025i
$722$		0			0
$723$	−46.7549			−1.73883
$724$		0			0
$725$	0.830556	+	1.43856i	0.0308461	+	0.0534270i
$726$		0			0
$727$	36.5628	−	21.1095i	1.35604	−	0.782909i	0.366951	−	0.930240i	$-0.380402\pi$
$727$	36.5628	−	21.1095i	1.35604	−	0.782909i	0.989087	+	0.147331i	$0.0470684\pi$
$728$		0			0
$729$	14.1410			0.523739
$730$		0			0
$731$	3.08693	−	5.34672i	0.114174	−	0.197756i
$732$		0			0
$733$		−	39.5644i		−	1.46134i	−0.682729	−	0.730671i	$-0.739207\pi$
$733$		−	39.5644i		−	1.46134i	0.682729	−	0.730671i	$-0.260793\pi$
$734$		0			0
$735$	−45.9372	+	79.5656i	−1.69442	+	2.93482i
$736$		0			0
$737$	3.70846	+	2.14108i	0.136603	+	0.0788676i
$738$		0			0
$739$	21.0534	+	36.4655i	0.774461	+	1.34141i	0.935097	+	0.354392i	$0.115312\pi$
$739$	21.0534	+	36.4655i	0.774461	+	1.34141i	−0.160636	+	0.987014i	$0.551355\pi$
$740$		0			0
$741$	−1.38172	−	22.4054i	−0.0507588	−	0.823082i
$742$		0			0
$743$	8.26746	+	14.3197i	0.303304	+	0.525338i	0.976882	−	0.213778i	$-0.0685770\pi$
$743$	8.26746	+	14.3197i	0.303304	+	0.525338i	−0.673578	+	0.739116i	$0.735244\pi$
$744$		0			0
$745$	−6.77838	+	11.7405i	−0.248341	+	0.430139i
$746$		0			0
$747$	15.0221	−	26.0191i	0.549631	−	0.951989i
$748$		0			0
$749$	−49.8944			−1.82310
$750$		0			0
$751$	−26.7472	+	46.3274i	−0.976018	+	1.69051i	−0.299483	+	0.954102i	$0.596814\pi$
$751$	−26.7472	+	46.3274i	−0.976018	+	1.69051i	−0.676535	+	0.736411i	$0.736519\pi$
$752$		0			0
$753$		−	20.9028i		−	0.761740i
$754$		0			0
$755$	−9.34424	+	5.39490i	−0.340072	+	0.196340i
$756$		0			0
$757$	26.9142	−	15.5389i	0.978212	−	0.564771i	0.0764821	−	0.997071i	$-0.475631\pi$
$757$	26.9142	−	15.5389i	0.978212	−	0.564771i	0.901730	+	0.432300i	$0.142298\pi$
$758$		0			0
$759$	−1.70936			−0.0620458
$760$		0			0
$761$	−24.1446			−0.875242			−0.437621	−	0.899160i	$-0.644179\pi$
$761$	−24.1446			−0.875242			−0.437621	+	0.899160i	$0.644179\pi$
$762$		0			0
$763$	−1.88988	+	1.09112i	−0.0684184	+	0.0395014i
$764$		0			0
$765$	10.3177	−	5.95690i	0.373035	−	0.215372i
$766$		0			0
$767$		−	12.8514i		−	0.464039i
$768$		0			0
$769$	−27.1275	+	46.9862i	−0.978242	+	1.69437i	−0.309450	+	0.950916i	$0.600145\pi$
$769$	−27.1275	+	46.9862i	−0.978242	+	1.69437i	−0.668792	+	0.743450i	$0.733188\pi$
$770$		0			0
$771$	35.3945			1.27470
$772$		0			0
$773$	12.2153	−	21.1576i	0.439356	−	0.760986i	−0.558284	−	0.829650i	$-0.688540\pi$
$773$	12.2153	−	21.1576i	0.439356	−	0.760986i	0.997640	+	0.0686636i	$0.0218735\pi$
$774$		0			0
$775$	−2.51249	+	4.35175i	−0.0902511	+	0.156320i
$776$		0			0
$777$	−67.3222	−	116.605i	−2.41517	−	4.18320i
$778$		0			0
$779$	−20.4689	+	13.5629i	−0.733373	+	0.485941i
$780$		0			0
$781$	−1.78091	−	3.08463i	−0.0637260	−	0.110377i
$782$		0			0
$783$	8.37728	+	4.83663i	0.299380	+	0.172847i
$784$		0			0
$785$	−3.88097	+	6.72203i	−0.138518	+	0.239920i
$786$		0			0
$787$		−	7.34461i		−	0.261807i	−0.991395	−	0.130903i	$-0.958212\pi$
$787$		−	7.34461i		−	0.261807i	0.991395	−	0.130903i	$-0.0417878\pi$
$788$		0			0
$789$	20.9005	−	36.2007i	0.744076	−	1.28878i
$790$		0			0
$791$	33.1445			1.17848
$792$		0			0
$793$	−5.82010	+	3.36024i	−0.206678	+	0.119326i
$794$		0			0
$795$	−37.8395	−	65.5399i	−1.34203	−	2.32446i
$796$		0			0
$797$	31.5903			1.11899			0.559493	−	0.828835i	$-0.310996\pi$
$797$	31.5903			1.11899			0.559493	+	0.828835i	$0.310996\pi$
$798$		0			0
$799$		−	5.16504i		−	0.182726i
$800$		0			0
$801$	47.2017	−	27.2519i	1.66779	−	0.962898i
$802$		0			0
$803$	0.888978	+	1.53976i	0.0313714	+	0.0543368i
$804$		0			0
$805$		−	17.8708i		−	0.629864i
$806$		0			0
$807$	−74.7327	−	43.1470i	−2.63072	−	1.51884i
$808$		0			0
$809$	−50.1923			−1.76467			−0.882334	−	0.470624i	$-0.844029\pi$
$809$	−50.1923			−1.76467			−0.882334	+	0.470624i	$0.844029\pi$
$810$		0			0
$811$	−19.2290	−	11.1018i	−0.675220	−	0.389838i	0.122832	−	0.992428i	$-0.460802\pi$
$811$	−19.2290	−	11.1018i	−0.675220	−	0.389838i	−0.798052	+	0.602589i	$0.794136\pi$
$812$		0			0
$813$	6.11674	−	10.5945i	0.214523	−	0.371565i
$814$		0			0
$815$	0.675360	−	0.389919i	0.0236568	−	0.0136583i
$816$		0			0
$817$	20.8160	+	31.4152i	0.728261	+	1.09908i
$818$		0			0
$819$	−40.0493	+	23.1224i	−1.39943	+	0.807964i
$820$		0			0
$821$	−42.6691	−	24.6350i	−1.48916	−	0.859769i	−0.489239	−	0.872150i	$-0.662726\pi$
$821$	−42.6691	−	24.6350i	−1.48916	−	0.859769i	−0.999923	+	0.0123810i	$0.996059\pi$
$822$		0			0
$823$	−0.331446	−	0.191360i	−0.0115535	−	0.00667040i	0.494212	−	0.869341i	$-0.335457\pi$
$823$	−0.331446	−	0.191360i	−0.0115535	−	0.00667040i	−0.505766	+	0.862671i	$0.668790\pi$
$824$		0			0
$825$		−	1.92043i		−	0.0668606i
$826$		0			0
$827$	−1.33960	−	0.773418i	−0.0465824	−	0.0268944i	0.476528	−	0.879159i	$-0.341895\pi$
$827$	−1.33960	−	0.773418i	−0.0465824	−	0.0268944i	−0.523110	+	0.852265i	$0.675228\pi$
$828$		0			0
$829$	−32.7078			−1.13599			−0.567994	−	0.823033i	$-0.692280\pi$
$829$	−32.7078			−1.13599			−0.567994	+	0.823033i	$0.692280\pi$
$830$		0			0
$831$	−18.7002	−	32.3898i	−0.648704	−	1.12359i
$832$		0			0
$833$	−4.10519	−	7.11039i	−0.142236	−	0.246360i
$834$		0			0
$835$			20.5846i			0.712360i
$836$		0			0
$837$			29.2622i			1.01145i
$838$		0			0
$839$	3.97923	+	6.89223i	0.137378	+	0.237946i	0.926504	−	0.376286i	$-0.122799\pi$
$839$	3.97923	+	6.89223i	0.137378	+	0.237946i	−0.789125	+	0.614233i	$0.789466\pi$
$840$		0			0
$841$	14.0700	+	24.3700i	0.485174	+	0.840346i
$842$		0			0
$843$	−1.62703			−0.0560379
$844$		0			0
$845$	22.9731	+	13.2635i	0.790299	+	0.456280i
$846$		0			0
$847$		−	46.7840i		−	1.60752i
$848$		0			0
$849$	−7.88588	−	4.55291i	−0.270643	−	0.156256i
$850$		0			0
$851$	14.0981	+	8.13954i	0.483276	+	0.279020i
$852$		0			0
$853$	−5.06060	+	2.92174i	−0.173272	+	0.100039i	−0.584128	−	0.811662i	$-0.698563\pi$
$853$	−5.06060	+	2.92174i	−0.173272	+	0.100039i	0.410856	+	0.911700i	$0.365230\pi$
$854$		0			0
$855$	4.47626	+	72.5850i	0.153085	+	2.48235i
$856$		0			0
$857$	26.6433	−	15.3825i	0.910118	−	0.525457i	0.0296491	−	0.999560i	$-0.490561\pi$
$857$	26.6433	−	15.3825i	0.910118	−	0.525457i	0.880469	+	0.474103i	$0.157228\pi$
$858$		0			0
$859$	−4.27545	+	7.40529i	−0.145876	+	0.252665i	−0.929700	−	0.368319i	$-0.879933\pi$
$859$	−4.27545	+	7.40529i	−0.145876	+	0.252665i	0.783823	+	0.620984i	$0.213267\pi$
$860$		0			0
$861$	64.3360	+	37.1444i	2.19257	+	1.26588i
$862$		0			0
$863$	−14.5152			−0.494103			−0.247052	−	0.969002i	$-0.579462\pi$
$863$	−14.5152			−0.494103			−0.247052	+	0.969002i	$0.579462\pi$
$864$		0			0
$865$	36.1892	+	20.8938i	1.23047	+	0.710412i
$866$		0			0
$867$		−	50.5630i		−	1.71721i
$868$		0			0
$869$	−0.458614	−	0.794343i	−0.0155574	−	0.0269463i
$870$		0			0
$871$	−17.8143	+	10.2851i	−0.603615	+	0.348497i
$872$		0			0
$873$		−	46.5863i		−	1.57671i
$874$		0			0
$875$	−35.9634			−1.21578
$876$		0			0
$877$	10.8262	+	18.7515i	0.365575	+	0.633194i	0.988868	−	0.148794i	$-0.0475391\pi$
$877$	10.8262	+	18.7515i	0.365575	+	0.633194i	−0.623294	+	0.781988i	$0.714206\pi$
$878$		0			0
$879$	42.1460	−	24.3330i	1.42155	−	0.820731i
$880$		0			0
$881$	5.75645			0.193940			0.0969698	−	0.995287i	$-0.469085\pi$
$881$	5.75645			0.193940			0.0969698	+	0.995287i	$0.469085\pi$
$882$		0			0
$883$	−18.9840	+	32.8813i	−0.638863	+	1.10654i	0.346819	+	0.937932i	$0.387262\pi$
$883$	−18.9840	+	32.8813i	−0.638863	+	1.10654i	−0.985683	+	0.168612i	$0.946072\pi$
$884$		0			0
$885$			61.1436i			2.05532i
$886$		0			0
$887$	−10.8432	+	18.7809i	−0.364078	+	0.630602i	−0.988628	−	0.150383i	$-0.951949\pi$
$887$	−10.8432	+	18.7809i	−0.364078	+	0.630602i	0.624550	+	0.780985i	$0.285283\pi$
$888$		0			0
$889$	51.4531	+	29.7065i	1.72568	+	0.996323i
$890$		0			0
$891$	−2.23413	−	3.86962i	−0.0748460	−	0.129637i
$892$		0			0
$893$	28.2225	+	14.0534i	0.944428	+	0.470280i
$894$		0			0
$895$	−20.2603	−	35.0918i	−0.677226	−	1.17299i
$896$		0			0
$897$	4.10563	−	7.11115i	0.137083	−	0.237435i
$898$		0			0
$899$	1.30063	−	2.25276i	0.0433785	−	0.0751337i
$900$		0			0
$901$	6.76305			0.225310
$902$		0			0
$903$	57.0085	−	98.7415i	1.89712	−	3.28591i
$904$		0			0
$905$		−	0.674594i		−	0.0224243i
$906$		0			0
$907$	27.7864	−	16.0425i	0.922633	−	0.532683i	0.0381590	−	0.999272i	$-0.487851\pi$
$907$	27.7864	−	16.0425i	0.922633	−	0.532683i	0.884474	+	0.466589i	$0.154517\pi$
$908$		0			0
$909$	23.4361	−	13.5309i	0.777328	−	0.448790i
$910$		0			0
$911$	38.7962			1.28538			0.642688	−	0.766128i	$-0.277819\pi$
$911$	38.7962			1.28538			0.642688	+	0.766128i	$0.277819\pi$
$912$		0			0
$913$	1.64081			0.0543027
$914$		0			0
$915$	27.6904	−	15.9871i	0.915417	−	0.528516i
$916$		0			0
$917$	−57.0942	+	32.9633i	−1.88542	+	1.08855i
$918$		0			0
$919$		−	4.09055i		−	0.134935i	−0.997721	−	0.0674674i	$-0.978508\pi$
$919$		−	4.09055i		−	0.134935i	0.997721	−	0.0674674i	$-0.0214919\pi$
$920$		0			0
$921$	34.6854	−	60.0769i	1.14292	−	1.97960i
$922$		0			0
$923$	17.1099			0.563180
$924$		0			0
$925$	−9.14458	+	15.8389i	−0.300672	+	0.520779i
$926$		0			0
$927$	58.7600	−	101.775i	1.92993	−	3.34274i
$928$		0			0
$929$	14.0628	+	24.3575i	0.461385	+	0.799143i	0.999030	−	0.0440285i	$-0.0140192\pi$
$929$	14.0628	+	24.3575i	0.461385	+	0.799143i	−0.537645	+	0.843171i	$0.680686\pi$
$930$		0			0
$931$	50.0218	−	3.08481i	1.63940	−	0.101100i
$932$		0			0
$933$	23.2734	+	40.3107i	0.761936	+	1.31971i
$934$		0			0
$935$	0.563477	+	0.325324i	0.0184277	+	0.0106392i
$936$		0			0
$937$	20.2150	−	35.0135i	0.660397	−	1.14384i	−0.320115	−	0.947379i	$-0.603721\pi$
$937$	20.2150	−	35.0135i	0.660397	−	1.14384i	0.980511	−	0.196462i	$-0.0629452\pi$
$938$		0			0
$939$		−	13.1751i		−	0.429952i
$940$		0			0
$941$	−13.0744	+	22.6456i	−0.426215	+	0.738226i	−0.996533	−	0.0831981i	$-0.973487\pi$
$941$	−13.0744	+	22.6456i	−0.426215	+	0.738226i	0.570318	+	0.821424i	$0.306820\pi$
$942$		0			0
$943$	−8.98184			−0.292489
$944$		0			0
$945$	101.254	−	58.4592i	3.29380	−	1.90168i
$946$		0			0
$947$	−16.0421	−	27.7858i	−0.521299	−	0.902917i	−0.999693	−	0.0247713i	$-0.992114\pi$
$947$	−16.0421	−	27.7858i	−0.521299	−	0.902917i	0.478394	−	0.878145i	$-0.341219\pi$
$948$		0			0
$949$	−8.54077			−0.277245
$950$		0			0
$951$			0.982449i			0.0318581i
$952$		0			0
$953$	−13.9593	+	8.05939i	−0.452185	+	0.261069i	−0.708753	−	0.705457i	$-0.750742\pi$
$953$	−13.9593	+	8.05939i	−0.452185	+	0.261069i	0.256567	+	0.966526i	$0.417408\pi$
$954$		0			0
$955$	7.81983	+	13.5443i	0.253044	+	0.438285i
$956$		0			0
$957$			0.994142i			0.0321360i
$958$		0			0
$959$	−35.2526	−	20.3531i	−1.13836	−	0.657235i
$960$		0			0
$961$	−23.1310			−0.746162
$962$		0			0
$963$	64.3194	+	37.1348i	2.07266	+	1.19665i
$964$		0			0
$965$	−9.98948	+	17.3023i	−0.321573	+	0.556980i
$966$		0			0
$967$	−33.9035	+	19.5742i	−1.09026	+	0.629464i	−0.933647	−	0.358195i	$-0.883392\pi$
$967$	−33.9035	+	19.5742i	−1.09026	+	0.629464i	−0.156617	+	0.987659i	$0.550059\pi$
$968$		0			0
$969$	−8.54365	−	4.25433i	−0.274462	−	0.136669i
$970$		0			0
$971$	−11.3501	+	6.55297i	−0.364241	+	0.210295i	−0.670940	−	0.741512i	$-0.734109\pi$
$971$	−11.3501	+	6.55297i	−0.364241	+	0.210295i	0.306698	+	0.951807i	$0.400776\pi$
$972$		0			0
$973$	16.1543	+	9.32669i	0.517883	+	0.299000i
$974$		0			0
$975$	7.98922	+	4.61258i	0.255860	+	0.147721i
$976$		0			0
$977$		−	36.1689i		−	1.15715i	−0.815631	−	0.578573i	$-0.803610\pi$
$977$		−	36.1689i		−	1.15715i	0.815631	−	0.578573i	$-0.196390\pi$
$978$		0			0
$979$	2.57782	+	1.48831i	0.0823876	+	0.0475665i
$980$		0			0
$981$	3.24836			0.103712
$982$		0			0
$983$	12.9126	+	22.3653i	0.411849	+	0.713343i	0.995092	−	0.0989546i	$-0.0315499\pi$
$983$	12.9126	+	22.3653i	0.411849	+	0.713343i	−0.583243	+	0.812298i	$0.698217\pi$
$984$		0			0
$985$	−7.01506	−	12.1504i	−0.223519	−	0.387145i
$986$		0			0
$987$		−	95.3863i		−	3.03618i
$988$		0			0
$989$			13.7851i			0.438342i
$990$		0			0
$991$	13.0397	+	22.5855i	0.414221	+	0.717452i	0.995346	−	0.0963621i	$-0.0307207\pi$
$991$	13.0397	+	22.5855i	0.414221	+	0.717452i	−0.581125	+	0.813814i	$0.697387\pi$
$992$		0			0
$993$	24.1473	+	41.8243i	0.766291	+	1.32726i
$994$		0			0
$995$	48.5886			1.54036
$996$		0			0
$997$	−28.5744	−	16.4974i	−0.904961	−	0.522479i	−0.0261544	−	0.999658i	$-0.508326\pi$
$997$	−28.5744	−	16.4974i	−0.904961	−	0.522479i	−0.878806	+	0.477179i	$0.841659\pi$
$998$		0			0
$999$			106.504i			3.36965i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	608.2.s.c.335.14		28
4.3	odd	2		152.2.o.c.107.11	yes	28
8.3	odd	2	inner	608.2.s.c.335.13		28
8.5	even	2		152.2.o.c.107.14	yes	28
19.8	odd	6	inner	608.2.s.c.559.13		28
76.27	even	6		152.2.o.c.27.14	yes	28
152.27	even	6	inner	608.2.s.c.559.14		28
152.141	odd	6		152.2.o.c.27.11	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.11	✓	28	152.141	odd	6
152.2.o.c.27.14	yes	28	76.27	even	6
152.2.o.c.107.11	yes	28	4.3	odd	2
152.2.o.c.107.14	yes	28	8.5	even	2
608.2.s.c.335.13		28	8.3	odd	2	inner
608.2.s.c.335.14		28	1.1	even	1	trivial
608.2.s.c.559.13		28	19.8	odd	6	inner
608.2.s.c.559.14		28	152.27	even	6	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:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	608.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.65547 - 1.53314i) q^{3} +(2.25688 - 1.30301i) q^{5} +4.30088i q^{7} +(3.20101 - 5.54431i) q^{9} +O(q^{10})\)	\(q+(2.65547 - 1.53314i) q^{3} +(2.25688 - 1.30301i) q^{5} +4.30088i q^{7} +(3.20101 - 5.54431i) q^{9} +0.349633 q^{11} +(-0.839767 + 1.45452i) q^{13} +(3.99538 - 6.92020i) q^{15} +(0.357047 + 0.618424i) q^{17} +(-4.35063 + 0.268300i) q^{19} +(6.59384 + 11.4209i) q^{21} +(-1.38083 - 0.797223i) q^{23} +(0.895662 - 1.55133i) q^{25} -10.4315i q^{27} +(-0.463655 + 0.803074i) q^{29} -2.80517 q^{31} +(0.928441 - 0.536035i) q^{33} +(5.60409 + 9.70656i) q^{35} -10.2099 q^{37} +5.14991i q^{39} +(4.87850 - 2.81660i) q^{41} +(-4.32286 - 7.48741i) q^{43} -16.6838i q^{45} +(-6.26395 - 3.61649i) q^{47} -11.4976 q^{49} +(1.89626 + 1.09480i) q^{51} +(4.73541 - 8.20196i) q^{53} +(0.789079 - 0.455575i) q^{55} +(-11.1416 + 7.38258i) q^{57} +(-6.62664 + 3.82589i) q^{59} +(3.46531 + 2.00070i) q^{61} +(23.8454 + 13.7672i) q^{63} +4.37690i q^{65} +(10.6067 + 6.12378i) q^{67} -4.88901 q^{69} +(-5.09365 - 8.82246i) q^{71} +(2.54260 + 4.40392i) q^{73} -5.49268i q^{75} +1.50373i q^{77} +(-1.31170 - 2.27193i) q^{79} +(-6.38991 - 11.0677i) q^{81} +4.69293 q^{83} +(1.61162 + 0.930471i) q^{85} +2.84338i q^{87} +(7.37293 + 4.25676i) q^{89} +(-6.25572 - 3.61174i) q^{91} +(-7.44905 + 4.30071i) q^{93} +(-9.46925 + 6.27443i) q^{95} +(6.30190 - 3.63841i) q^{97} +(1.11918 - 1.93848i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{3} + 8 q^{9}+O(q^{10}) \) 28 * q + 6 * q^3 + 8 * q^9	\( 28 q + 6 q^{3} + 8 q^{9} + 16 q^{11} - 22 q^{17} - 4 q^{19} + 16 q^{25} + 36 q^{33} + 28 q^{35} + 6 q^{41} - 30 q^{43} - 68 q^{49} + 42 q^{51} - 26 q^{57} + 18 q^{59} - 78 q^{67} + 14 q^{73} + 6 q^{81} + 32 q^{83} - 18 q^{89} + 12 q^{91} + 30 q^{97} + 28 q^{99}+O(q^{100}) \) 28 * q + 6 * q^3 + 8 * q^9 + 16 * q^11 - 22 * q^17 - 4 * q^19 + 16 * q^25 + 36 * q^33 + 28 * q^35 + 6 * q^41 - 30 * q^43 - 68 * q^49 + 42 * q^51 - 26 * q^57 + 18 * q^59 - 78 * q^67 + 14 * q^73 + 6 * q^81 + 32 * q^83 - 18 * q^89 + 12 * q^91 + 30 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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