LMFDB - Embedded newform 920.2.bv.a.17.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.14
Character	$\chi$	$=$	920.17
Dual form			920.2.bv.a.433.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.908585 + 0.496125i) q^{3} +(-1.66942 + 1.48763i) q^{5} +(-2.79645 - 3.73561i) q^{7} +(-1.04254 + 1.62222i) q^{9} +(2.29557 - 1.04835i) q^{11} +(-0.327078 - 0.244848i) q^{13} +(0.778756 - 2.17988i) q^{15} +(0.0784177 + 1.09642i) q^{17} +(4.96085 + 5.72512i) q^{19} +(4.39414 + 2.00674i) q^{21} +(-2.00167 - 4.35813i) q^{23} +(0.573901 - 4.96695i) q^{25} +(0.363964 - 5.08888i) q^{27} +(-2.43252 - 2.10779i) q^{29} +(9.47417 - 2.78187i) q^{31} +(-1.56561 + 2.09141i) q^{33} +(10.2257 + 2.07621i) q^{35} +(9.82620 - 2.13756i) q^{37} +(0.418654 + 0.0601933i) q^{39} +(-1.80123 + 1.15758i) q^{41} +(4.57456 + 8.37769i) q^{43} +(-0.672836 - 4.25906i) q^{45} +(3.49473 + 3.49473i) q^{47} +(-4.16257 + 14.1764i) q^{49} +(-0.615212 - 0.957289i) q^{51} +(-0.250815 + 0.187757i) q^{53} +(-2.27270 + 5.16511i) q^{55} +(-7.34773 - 2.74056i) q^{57} +(4.13198 - 0.594090i) q^{59} +(-2.77586 - 9.45372i) q^{61} +(8.97537 - 0.641931i) q^{63} +(0.910273 - 0.0778194i) q^{65} +(-1.01878 - 2.73145i) q^{67} +(3.98087 + 2.96666i) q^{69} +(-0.534163 + 1.16965i) q^{71} +(11.6654 + 0.834326i) q^{73} +(1.94279 + 4.79763i) q^{75} +(-10.3357 - 5.64371i) q^{77} +(0.810015 + 5.63378i) q^{79} +(-0.209146 - 0.457966i) q^{81} +(-3.04666 - 14.0053i) q^{83} +(-1.76199 - 1.71373i) q^{85} +(3.25587 + 0.708272i) q^{87} +(3.01589 + 0.885546i) q^{89} +1.90654i q^{91} +(-7.22794 + 7.22794i) q^{93} +(-16.7986 - 2.17770i) q^{95} +(-0.547518 + 2.51690i) q^{97} +(-0.692560 + 4.81686i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{7}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.908585	+	0.496125i	−0.524572	+	0.286438i	−0.719635	−	0.694353i	$-0.755691\pi$
$3$	−0.908585	+	0.496125i	−0.524572	+	0.286438i	0.195063	+	0.980791i	$0.437509\pi$
$4$		0			0
$5$	−1.66942	+	1.48763i	−0.746586	+	0.665289i
$5$	−1.66942	+	1.48763i	−0.746586	+	0.665289i
$6$		0			0
$7$	−2.79645	−	3.73561i	−1.05696	−	1.41193i	−0.905944	−	0.423397i	$-0.860837\pi$
$7$	−2.79645	−	3.73561i	−1.05696	−	1.41193i	−0.151013	−	0.988532i	$-0.548254\pi$
$8$		0			0
$9$	−1.04254	+	1.62222i	−0.347512	+	0.540739i
$10$		0			0
$11$	2.29557	−	1.04835i	0.692142	−	0.316090i	−0.0381054	−	0.999274i	$-0.512132\pi$
$11$	2.29557	−	1.04835i	0.692142	−	0.316090i	0.730247	+	0.683183i	$0.239405\pi$
$12$		0			0
$13$	−0.327078	−	0.244848i	−0.0907152	−	0.0679085i	0.552957	−	0.833210i	$-0.313499\pi$
$13$	−0.327078	−	0.244848i	−0.0907152	−	0.0679085i	−0.643673	+	0.765301i	$0.722590\pi$
$14$		0			0
$15$	0.778756	−	2.17988i	0.201074	−	0.562843i
$16$		0			0
$17$	0.0784177	+	1.09642i	0.0190191	+	0.265922i	0.998060	+	0.0622582i	$0.0198302\pi$
$17$	0.0784177	+	1.09642i	0.0190191	+	0.265922i	−0.979041	+	0.203663i	$0.934715\pi$
$18$		0			0
$19$	4.96085	+	5.72512i	1.13810	+	1.31343i	0.943055	+	0.332638i	$0.107939\pi$
$19$	4.96085	+	5.72512i	1.13810	+	1.31343i	0.195041	+	0.980795i	$0.437516\pi$
$20$		0			0
$21$	4.39414	+	2.00674i	0.958880	+	0.437906i
$22$		0			0
$23$	−2.00167	−	4.35813i	−0.417377	−	0.908733i
$23$	−2.00167	−	4.35813i	−0.417377	−	0.908733i
$24$		0			0
$25$	0.573901	−	4.96695i	0.114780	−	0.993391i
$26$		0			0
$27$	0.363964	−	5.08888i	0.0700449	−	0.979355i
$28$		0			0
$29$	−2.43252	−	2.10779i	−0.451707	−	0.391406i	0.399081	−	0.916916i	$-0.369329\pi$
$29$	−2.43252	−	2.10779i	−0.451707	−	0.391406i	−0.850788	+	0.525510i	$0.823875\pi$
$30$		0			0
$31$	9.47417	−	2.78187i	1.70161	−	0.499638i	0.720561	−	0.693391i	$-0.243884\pi$
$31$	9.47417	−	2.78187i	1.70161	−	0.499638i	0.981050	+	0.193753i	$0.0620660\pi$
$32$		0			0
$33$	−1.56561	+	2.09141i	−0.272538	+	0.364068i
$34$		0			0
$35$	10.2257	+	2.07621i	1.72845	+	0.350944i
$36$		0			0
$37$	9.82620	−	2.13756i	1.61542	−	0.351412i	0.688079	−	0.725636i	$-0.258454\pi$
$37$	9.82620	−	2.13756i	1.61542	−	0.351412i	0.927338	+	0.374224i	$0.122091\pi$
$38$		0			0
$39$	0.418654	+	0.0601933i	0.0670382	+	0.00963864i
$40$		0			0
$41$	−1.80123	+	1.15758i	−0.281304	+	0.180783i	−0.673683	−	0.739021i	$-0.735289\pi$
$41$	−1.80123	+	1.15758i	−0.281304	+	0.180783i	0.392379	+	0.919804i	$0.371652\pi$
$42$		0			0
$43$	4.57456	+	8.37769i	0.697614	+	1.27759i	0.950691	+	0.310139i	$0.100376\pi$
$43$	4.57456	+	8.37769i	0.697614	+	1.27759i	−0.253077	+	0.967446i	$0.581443\pi$
$44$		0			0
$45$	−0.672836	−	4.25906i	−0.100300	−	0.634904i
$46$		0			0
$47$	3.49473	+	3.49473i	0.509759	+	0.509759i	0.914453	−	0.404693i	$-0.132622\pi$
$47$	3.49473	+	3.49473i	0.509759	+	0.509759i	−0.404693	+	0.914453i	$0.632622\pi$
$48$		0			0
$49$	−4.16257	+	14.1764i	−0.594654	+	2.02520i
$50$		0			0
$51$	−0.615212	−	0.957289i	−0.0861469	−	0.134047i
$52$		0			0
$53$	−0.250815	+	0.187757i	−0.0344520	+	0.0257905i	−0.616365	−	0.787461i	$-0.711395\pi$
$53$	−0.250815	+	0.187757i	−0.0344520	+	0.0257905i	0.581913	+	0.813251i	$0.302304\pi$
$54$		0			0
$55$	−2.27270	+	5.16511i	−0.306451	+	0.696463i
$56$		0			0
$57$	−7.34773	−	2.74056i	−0.973230	−	0.362996i
$58$		0			0
$59$	4.13198	−	0.594090i	0.537939	−	0.0773439i	0.132009	−	0.991248i	$-0.457857\pi$
$59$	4.13198	−	0.594090i	0.537939	−	0.0773439i	0.405929	+	0.913905i	$0.366948\pi$
$60$		0			0
$61$	−2.77586	−	9.45372i	−0.355413	−	1.21042i	−0.922250	−	0.386594i	$-0.873651\pi$
$61$	−2.77586	−	9.45372i	−0.355413	−	1.21042i	0.566837	−	0.823830i	$-0.308167\pi$
$62$		0			0
$63$	8.97537	−	0.641931i	1.13079	−	0.0808757i
$64$		0			0
$65$	0.910273	−	0.0778194i	0.112905	−	0.00965230i
$66$		0			0
$67$	−1.01878	−	2.73145i	−0.124464	−	0.333700i	0.859742	−	0.510728i	$-0.170624\pi$
$67$	−1.01878	−	2.73145i	−0.124464	−	0.333700i	−0.984206	+	0.177029i	$0.943351\pi$
$68$		0			0
$69$	3.98087	+	2.96666i	0.479240	+	0.357143i
$70$		0			0
$71$	−0.534163	+	1.16965i	−0.0633935	+	0.138812i	−0.938677	−	0.344798i	$-0.887947\pi$
$71$	−0.534163	+	1.16965i	−0.0633935	+	0.138812i	0.875284	+	0.483610i	$0.160675\pi$
$72$		0			0
$73$	11.6654	+	0.834326i	1.36533	+	0.0976505i	0.734679	−	0.678414i	$-0.237333\pi$
$73$	11.6654	+	0.834326i	1.36533	+	0.0976505i	0.630653	+	0.776065i	$0.282787\pi$
$74$		0			0
$75$	1.94279	+	4.79763i	0.224334	+	0.553983i
$76$		0			0
$77$	−10.3357	−	5.64371i	−1.17786	−	0.643161i
$78$		0			0
$79$	0.810015	+	5.63378i	0.0911338	+	0.633849i	0.983280	+	0.182102i	$0.0582901\pi$
$79$	0.810015	+	5.63378i	0.0911338	+	0.633849i	−0.892146	+	0.451747i	$0.850801\pi$
$80$		0			0
$81$	−0.209146	−	0.457966i	−0.0232385	−	0.0508851i
$82$		0			0
$83$	−3.04666	−	14.0053i	−0.334415	−	1.53728i	−0.770539	−	0.637393i	$-0.780013\pi$
$83$	−3.04666	−	14.0053i	−0.334415	−	1.53728i	0.436124	−	0.899887i	$-0.356351\pi$
$84$		0			0
$85$	−1.76199	−	1.71373i	−0.191114	−	0.185880i
$86$		0			0
$87$	3.25587	+	0.708272i	0.349066	+	0.0759347i
$88$		0			0
$89$	3.01589	+	0.885546i	0.319684	+	0.0938677i	0.437638	−	0.899151i	$-0.355815\pi$
$89$	3.01589	+	0.885546i	0.319684	+	0.0938677i	−0.117954	+	0.993019i	$0.537633\pi$
$90$		0			0
$91$			1.90654i			0.199860i
$92$		0			0
$93$	−7.22794	+	7.22794i	−0.749503	+	0.749503i
$94$		0			0
$95$	−16.7986	−	2.17770i	−1.72350	−	0.223427i
$96$		0			0
$97$	−0.547518	+	2.51690i	−0.0555920	+	0.255552i	−0.996553	−	0.0829640i	$-0.973561\pi$
$97$	−0.547518	+	2.51690i	−0.0555920	+	0.255552i	0.940961	+	0.338516i	$0.109925\pi$
$98$		0			0
$99$	−0.692560	+	4.81686i	−0.0696049	+	0.484113i
$100$		0			0
$101$	11.7181	+	7.53074i	1.16599	+	0.749336i	0.972759	−	0.231817i	$-0.0744670\pi$
$101$	11.7181	+	7.53074i	1.16599	+	0.749336i	0.193231	+	0.981153i	$0.438103\pi$
$102$		0			0
$103$	5.06784	−	13.5874i	0.499349	−	1.33881i	−0.405897	−	0.913919i	$-0.633041\pi$
$103$	5.06784	−	13.5874i	0.499349	−	1.33881i	0.905246	−	0.424887i	$-0.139686\pi$
$104$		0			0
$105$	−10.3209	+	3.18679i	−1.00722	+	0.310998i
$106$		0			0
$107$	1.75531	−	3.21461i	0.169692	−	0.310768i	−0.778969	−	0.627063i	$-0.784257\pi$
$107$	1.75531	−	3.21461i	0.169692	−	0.310768i	0.948661	+	0.316295i	$0.102439\pi$
$108$		0			0
$109$	−0.538206	+	0.621123i	−0.0515508	+	0.0594928i	−0.780939	−	0.624607i	$-0.785259\pi$
$109$	−0.538206	+	0.621123i	−0.0515508	+	0.0594928i	0.729389	+	0.684100i	$0.239805\pi$
$110$		0			0
$111$	−7.86744	+	6.81718i	−0.746745	+	0.647058i
$112$		0			0
$113$	−11.9275	+	4.44872i	−1.12204	+	0.418500i	−0.840914	−	0.541169i	$-0.817982\pi$
$113$	−11.9275	+	4.44872i	−1.12204	+	0.418500i	−0.281130	+	0.959670i	$0.590709\pi$
$114$		0			0
$115$	9.82492	+	4.29779i	0.916178	+	0.400771i
$116$		0			0
$117$	0.738187	−	0.275329i	0.0682454	−	0.0254542i
$118$		0			0
$119$	3.87652	−	3.35902i	0.355360	−	0.307921i
$120$		0			0
$121$	−3.03285	+	3.50010i	−0.275714	+	0.318191i
$122$		0			0
$123$	1.06226	−	1.94539i	0.0957811	−	0.175410i
$124$		0			0
$125$	6.43092	+	9.14567i	0.575199	+	0.818013i
$126$		0			0
$127$	4.29224	−	11.5080i	0.380875	−	1.02117i	−0.595170	−	0.803600i	$-0.702915\pi$
$127$	4.29224	−	11.5080i	0.380875	−	1.02117i	0.976046	−	0.217566i	$-0.0698118\pi$
$128$		0			0
$129$	−8.31276	−	5.34229i	−0.731898	−	0.470362i
$130$		0			0
$131$	3.10553	−	21.5994i	0.271331	−	1.88715i	−0.163351	−	0.986568i	$-0.552230\pi$
$131$	3.10553	−	21.5994i	0.271331	−	1.88715i	0.434682	−	0.900584i	$-0.356861\pi$
$132$		0			0
$133$	7.51411	−	34.5418i	0.651556	−	2.99515i
$134$		0			0
$135$	6.96277	+	9.03690i	0.599260	+	0.777773i
$136$		0			0
$137$	−10.0994	+	10.0994i	−0.862848	+	0.862848i	−0.991668	−	0.128820i	$-0.958881\pi$
$137$	−10.0994	+	10.0994i	−0.862848	+	0.862848i	0.128820	+	0.991668i	$0.458881\pi$
$138$		0			0
$139$		−	17.7144i		−	1.50251i	−0.660010	−	0.751257i	$-0.729448\pi$
$139$		−	17.7144i		−	1.50251i	0.660010	−	0.751257i	$-0.270552\pi$
$140$		0			0
$141$	−4.90909	−	1.44144i	−0.413420	−	0.121391i
$142$		0			0
$143$	−1.00752	−	0.219172i	−0.0842530	−	0.0183281i
$144$		0			0
$145$	7.19649	−	0.0999148i	0.597636	−	0.00829747i
$146$		0			0
$147$	−3.25123	−	14.9457i	−0.268157	−	1.23270i
$148$		0			0
$149$	1.01259	+	2.21726i	0.0829543	+	0.181645i	0.946564	−	0.322517i	$-0.104529\pi$
$149$	1.01259	+	2.21726i	0.0829543	+	0.181645i	−0.863609	+	0.504161i	$0.831802\pi$
$150$		0			0
$151$	1.26068	+	8.76823i	0.102593	+	0.713548i	0.974583	+	0.224025i	$0.0719199\pi$
$151$	1.26068	+	8.76823i	0.102593	+	0.713548i	−0.871991	+	0.489523i	$0.837171\pi$
$152$		0			0
$153$	−1.86039	−	1.01585i	−0.150403	−	0.0821265i
$154$		0			0
$155$	−11.6779	+	18.7382i	−0.937995	+	1.50509i
$156$		0			0
$157$	−3.87655	−	0.277256i	−0.309382	−	0.0221274i	−0.0842150	−	0.996448i	$-0.526838\pi$
$157$	−3.87655	−	0.277256i	−0.309382	−	0.0221274i	−0.225167	+	0.974320i	$0.572293\pi$
$158$		0			0
$159$	0.134735	−	0.295029i	0.0106852	−	0.0233973i
$160$		0			0
$161$	−10.6827	+	19.6647i	−0.841918	+	1.54980i
$162$		0			0
$163$	1.47977	+	3.96741i	0.115904	+	0.310751i	0.981929	−	0.189250i	$-0.0606056\pi$
$163$	1.47977	+	3.96741i	0.115904	+	0.310751i	−0.866025	+	0.500001i	$0.833333\pi$
$164$		0			0
$165$	−0.497594	−	5.82049i	−0.0387377	−	0.453124i
$166$		0			0
$167$	−23.0561	+	1.64901i	−1.78414	+	0.127604i	−0.923983	−	0.382432i	$-0.875086\pi$
$167$	−23.0561	+	1.64901i	−1.78414	+	0.127604i	−0.860153	+	0.510036i	$0.829632\pi$
$168$		0			0
$169$	−3.61549	−	12.3132i	−0.278115	−	0.947172i
$170$		0			0
$171$	−14.4592	+	2.07893i	−1.10573	+	0.158979i
$172$		0			0
$173$	23.2171	+	8.65954i	1.76517	+	0.658373i	0.999892	+	0.0146662i	$0.00466858\pi$
$173$	23.2171	+	8.65954i	1.76517	+	0.658373i	0.765273	+	0.643706i	$0.222604\pi$
$174$		0			0
$175$	−20.1595	+	11.7459i	−1.52392	+	0.887910i
$176$		0			0
$177$	−3.45952	+	2.58976i	−0.260033	+	0.194658i
$178$		0			0
$179$	−6.34238	−	9.86893i	−0.474051	−	0.737638i	0.519069	−	0.854732i	$-0.326279\pi$
$179$	−6.34238	−	9.86893i	−0.474051	−	0.737638i	−0.993121	+	0.117094i	$0.962642\pi$
$180$		0			0
$181$	−1.47105	+	5.00995i	−0.109343	+	0.372387i	−0.995925	−	0.0901837i	$-0.971255\pi$
$181$	−1.47105	+	5.00995i	−0.109343	+	0.372387i	0.886583	+	0.462570i	$0.153073\pi$
$182$		0			0
$183$	7.21233	+	7.21233i	0.533151	+	0.533151i
$184$		0			0
$185$	−13.2241	+	18.1862i	−0.972256	+	1.33708i
$186$		0			0
$187$	1.32945	+	2.43471i	0.0972192	+	0.178044i
$188$		0			0
$189$	−20.0279	+	12.8711i	−1.45681	+	0.936238i
$190$		0			0
$191$	−0.995170	−	0.143084i	−0.0720080	−	0.0103532i	0.106217	−	0.994343i	$-0.466126\pi$
$191$	−0.995170	−	0.143084i	−0.0720080	−	0.0103532i	−0.178225	+	0.983990i	$0.557035\pi$
$192$		0			0
$193$	14.6657	−	3.19033i	1.05566	−	0.229645i	0.348946	−	0.937143i	$-0.386540\pi$
$193$	14.6657	−	3.19033i	1.05566	−	0.229645i	0.706716	+	0.707498i	$0.250176\pi$
$194$		0			0
$195$	−0.788453	+	0.522315i	−0.0564623	+	0.0374037i
$196$		0			0
$197$	−1.88542	+	2.51863i	−0.134331	+	0.179445i	−0.862663	−	0.505780i	$-0.831205\pi$
$197$	−1.88542	+	2.51863i	−0.134331	+	0.179445i	0.728332	+	0.685224i	$0.240296\pi$
$198$		0			0
$199$	−4.56898	+	1.34157i	−0.323886	+	0.0951015i	−0.439634	−	0.898177i	$-0.644892\pi$
$199$	−4.56898	+	1.34157i	−0.323886	+	0.0951015i	0.115748	+	0.993279i	$0.463074\pi$
$200$		0			0
$201$	2.28079	+	1.97631i	0.160874	+	0.139398i
$202$		0			0
$203$	−1.07148	+	14.9812i	−0.0752032	+	1.05148i
$204$		0			0
$205$	1.28495	−	4.61204i	0.0897445	−	0.322119i
$206$		0			0
$207$	9.15665	+	1.29636i	0.636431	+	0.0901035i
$208$		0			0
$209$	17.3899	+	7.94172i	1.20289	+	0.549340i
$210$		0			0
$211$	3.89959	+	4.50036i	0.268459	+	0.309818i	0.873932	−	0.486048i	$-0.161562\pi$
$211$	3.89959	+	4.50036i	0.268459	+	0.309818i	−0.605474	+	0.795865i	$0.707016\pi$
$212$		0			0
$213$	−0.0949619	−	1.32774i	−0.00650668	−	0.0909753i
$214$		0			0
$215$	−20.0998	−	7.18058i	−1.37079	−	0.489711i
$216$		0			0
$217$	−36.8860	−	27.6125i	−2.50398	−	1.87446i
$218$		0			0
$219$	−11.0129	+	5.02944i	−0.744186	+	0.339858i
$220$		0			0
$221$	0.242808	−	0.377816i	0.0163330	−	0.0254147i
$222$		0			0
$223$	−0.822245	−	1.09839i	−0.0550616	−	0.0735537i	0.772165	−	0.635422i	$-0.219174\pi$
$223$	−0.822245	−	1.09839i	−0.0550616	−	0.0735537i	−0.827227	+	0.561868i	$0.810083\pi$
$224$		0			0
$225$	7.45916	+	6.10922i	0.497278	+	0.407281i
$226$		0			0
$227$	7.43176	−	4.05805i	0.493263	−	0.269342i	−0.213307	−	0.976985i	$-0.568423\pi$
$227$	7.43176	−	4.05805i	0.493263	−	0.269342i	0.706570	+	0.707643i	$0.250242\pi$
$228$		0			0
$229$	3.36156			0.222138			0.111069	−	0.993813i	$-0.464572\pi$
$229$	3.36156			0.222138			0.111069	+	0.993813i	$0.464572\pi$
$230$		0			0
$231$	12.1908			0.802099
$232$		0			0
$233$	13.1660	−	7.18917i	0.862533	−	0.470978i	0.0138643	−	0.999904i	$-0.495587\pi$
$233$	13.1660	−	7.18917i	0.862533	−	0.470978i	0.848668	+	0.528925i	$0.177405\pi$
$234$		0			0
$235$	−11.0330	−	0.635287i	−0.719717	−	0.0414416i
$236$		0			0
$237$	−3.53103	−	4.71690i	−0.229365	−	0.306395i
$238$		0			0
$239$	−4.84076	+	7.53238i	−0.313123	+	0.487229i	−0.961769	−	0.273861i	$-0.911699\pi$
$239$	−4.84076	+	7.53238i	−0.313123	+	0.487229i	0.648646	+	0.761090i	$0.275335\pi$
$240$		0			0
$241$	−2.76023	+	1.26055i	−0.177802	+	0.0811994i	−0.502327	−	0.864678i	$-0.667523\pi$
$241$	−2.76023	+	1.26055i	−0.177802	+	0.0811994i	0.324525	+	0.945877i	$0.394795\pi$
$242$		0			0
$243$	12.6700	+	9.48466i	0.812783	+	0.608441i
$244$		0			0
$245$	−14.1402	−	29.8587i	−0.903387	−	1.90760i
$246$		0			0
$247$	−0.220802	−	3.08721i	−0.0140493	−	0.196435i
$248$		0			0
$249$	9.71653	+	11.2135i	0.615760	+	0.710625i
$250$		0			0
$251$	25.8793	+	11.8187i	1.63349	+	0.745988i	0.999623	−	0.0274564i	$-0.00874076\pi$
$251$	25.8793	+	11.8187i	1.63349	+	0.745988i	0.633864	+	0.773445i	$0.281468\pi$
$252$		0			0
$253$	−9.16385	−	7.90596i	−0.576126	−	0.497043i
$254$		0			0
$255$	2.45114	+	0.682904i	0.153496	+	0.0427651i
$256$		0			0
$257$	−0.488538	+	6.83065i	−0.0304742	+	0.426084i	0.959198	+	0.282735i	$0.0912417\pi$
$257$	−0.488538	+	6.83065i	−0.0304742	+	0.426084i	−0.989672	+	0.143349i	$0.954213\pi$
$258$		0			0
$259$	−35.4635	−	30.7293i	−2.20360	−	1.90943i
$260$		0			0
$261$	5.95527	−	1.74862i	0.368622	−	0.108237i
$262$		0			0
$263$	−3.94607	+	5.27134i	−0.243325	+	0.325045i	−0.905533	−	0.424276i	$-0.860529\pi$
$263$	−3.94607	+	5.27134i	−0.243325	+	0.325045i	0.662208	+	0.749320i	$0.269620\pi$
$264$		0			0
$265$	0.139400	−	0.686565i	0.00856327	−	0.0421754i
$266$		0			0
$267$	−3.17954	+	0.691666i	−0.194585	+	0.0423293i
$268$		0			0
$269$	14.8287	+	2.13205i	0.904124	+	0.129993i	0.578667	−	0.815564i	$-0.303573\pi$
$269$	14.8287	+	2.13205i	0.904124	+	0.129993i	0.325456	+	0.945557i	$0.394482\pi$
$270$		0			0
$271$	17.0531	−	10.9594i	1.03590	−	0.665735i	0.0919334	−	0.995765i	$-0.470695\pi$
$271$	17.0531	−	10.9594i	1.03590	−	0.665735i	0.943970	+	0.330030i	$0.107059\pi$
$272$		0			0
$273$	−0.945883	−	1.73226i	−0.0572474	−	0.104841i
$274$		0			0
$275$	−3.88969	−	12.0037i	−0.234557	−	0.723848i
$276$		0			0
$277$	−7.90757	−	7.90757i	−0.475120	−	0.475120i	0.428447	−	0.903567i	$-0.359061\pi$
$277$	−7.90757	−	7.90757i	−0.475120	−	0.475120i	−0.903567	+	0.428447i	$0.859061\pi$
$278$		0			0
$279$	−5.36437	+	18.2694i	−0.321156	+	1.09376i
$280$		0			0
$281$	5.93709	+	9.23829i	0.354177	+	0.551110i	0.971932	−	0.235260i	$-0.0755942\pi$
$281$	5.93709	+	9.23829i	0.354177	+	0.551110i	−0.617756	+	0.786370i	$0.711958\pi$
$282$		0			0
$283$	−13.7973	+	10.3285i	−0.820164	+	0.613967i	−0.924761	−	0.380548i	$-0.875736\pi$
$283$	−13.7973	+	10.3285i	−0.820164	+	0.613967i	0.104597	+	0.994515i	$0.466645\pi$
$284$		0			0
$285$	16.3434	−	6.35558i	0.968097	−	0.376472i
$286$		0			0
$287$	9.36129	+	3.49158i	0.552580	+	0.206101i
$288$		0			0
$289$	15.6310	−	2.24739i	0.919469	−	0.132200i
$290$		0			0
$291$	−0.751230	−	2.55845i	−0.0440379	−	0.149979i
$292$		0			0
$293$	−30.7770	+	2.20122i	−1.79801	+	0.128596i	−0.929910	−	0.367788i	$-0.880115\pi$
$293$	−30.7770	+	2.20122i	−1.79801	+	0.128596i	−0.868103	+	0.496384i	$0.834661\pi$
$294$		0			0
$295$	−6.01422	+	7.13866i	−0.350161	+	0.415629i
$296$		0			0
$297$	−4.49944	−	12.0635i	−0.261084	−	0.699993i
$298$		0			0
$299$	−0.412376	+	1.91555i	−0.0238483	+	0.110779i
$300$		0			0
$301$	18.5033	−	40.5165i	1.06651	−	2.33533i
$302$		0			0
$303$	−14.3830	−	1.02870i	−0.826284	−	0.0590970i
$304$		0			0
$305$	18.6977	+	11.6527i	1.07063	+	0.667233i
$306$		0			0
$307$	0.390980	+	0.213491i	0.0223144	+	0.0121846i	0.490367	−	0.871516i	$-0.336863\pi$
$307$	0.390980	+	0.213491i	0.0223144	+	0.0121846i	−0.468053	+	0.883700i	$0.655044\pi$
$308$		0			0
$309$	2.13649	+	14.8596i	0.121540	+	0.845333i
$310$		0			0
$311$	−0.181415	−	0.397244i	−0.0102871	−	0.0225257i	0.904419	−	0.426646i	$-0.140305\pi$
$311$	−0.181415	−	0.397244i	−0.0102871	−	0.0225257i	−0.914706	+	0.404120i	$0.867578\pi$
$312$		0			0
$313$	−4.08378	−	18.7728i	−0.230829	−	1.06110i	−0.935982	−	0.352049i	$-0.885485\pi$
$313$	−4.08378	−	18.7728i	−0.230829	−	1.06110i	0.705153	−	0.709056i	$-0.250878\pi$
$314$		0			0
$315$	−14.0287	+	14.4237i	−0.790426	+	0.812683i
$316$		0			0
$317$	−8.82084	−	1.91886i	−0.495428	−	0.107774i	−0.0420923	−	0.999114i	$-0.513402\pi$
$317$	−8.82084	−	1.91886i	−0.495428	−	0.107774i	−0.453335	+	0.891340i	$0.649766\pi$
$318$		0			0
$319$	−7.79373	−	2.28844i	−0.436365	−	0.128128i
$320$		0			0
$321$			3.79160i			0.211626i
$322$		0			0
$323$	−5.88813	+	5.88813i	−0.327625	+	0.327625i
$324$		0			0
$325$	−1.40386	+	1.48406i	−0.0778720	+	0.0823211i
$326$		0			0
$327$	0.180851	−	0.831360i	0.0100011	−	0.0459743i
$328$		0			0
$329$	3.28214	−	22.8278i	0.180950	−	1.25854i
$330$		0			0
$331$	10.2991	+	6.61882i	0.566089	+	0.363803i	0.792166	−	0.610306i	$-0.208954\pi$
$331$	10.2991	+	6.61882i	0.566089	+	0.363803i	−0.226077	+	0.974110i	$0.572590\pi$
$332$		0			0
$333$	−6.77657	+	18.1687i	−0.371354	+	0.995639i
$334$		0			0
$335$	5.76416	+	3.04436i	0.314930	+	0.166331i
$336$		0			0
$337$	−3.82562	+	7.00610i	−0.208395	+	0.381647i	−0.960881	−	0.276961i	$-0.910673\pi$
$337$	−3.82562	+	7.00610i	−0.208395	+	0.381647i	0.752486	+	0.658608i	$0.228854\pi$
$338$		0			0
$339$	8.63001	−	9.95957i	0.468718	−	0.540929i
$340$		0			0
$341$	18.8323	−	16.3183i	1.01983	−	0.883684i
$342$		0			0
$343$	33.9931	−	12.6788i	1.83545	−	0.684588i
$344$		0			0
$345$	−11.0590	+	0.969482i	−0.595398	+	0.0521952i
$346$		0			0
$347$	30.6040	−	11.4147i	1.64291	−	0.612772i	0.653368	−	0.757040i	$-0.273355\pi$
$347$	30.6040	−	11.4147i	1.64291	−	0.612772i	0.989539	+	0.144268i	$0.0460827\pi$
$348$		0			0
$349$	4.11194	−	3.56302i	0.220107	−	0.190724i	−0.537826	−	0.843056i	$-0.680754\pi$
$349$	4.11194	−	3.56302i	0.220107	−	0.190724i	0.757934	+	0.652331i	$0.226209\pi$
$350$		0			0
$351$	−1.36504	+	1.57535i	−0.0728607	+	0.0840857i
$352$		0			0
$353$	−5.59997	+	10.2556i	−0.298056	+	0.545849i	−0.983194	−	0.182564i	$-0.941560\pi$
$353$	−5.59997	+	10.2556i	−0.298056	+	0.545849i	0.685138	+	0.728414i	$0.259742\pi$
$354$		0			0
$355$	−0.848274	−	2.74728i	−0.0450217	−	0.145810i
$356$		0			0
$357$	−1.85565	+	4.97520i	−0.0982116	+	0.263315i
$358$		0			0
$359$	16.0422	+	10.3097i	0.846677	+	0.544126i	0.890537	−	0.454912i	$-0.150329\pi$
$359$	16.0422	+	10.3097i	0.846677	+	0.544126i	−0.0438599	+	0.999038i	$0.513966\pi$
$360$		0			0
$361$	−5.46304	+	37.9963i	−0.287528	+	1.99980i
$362$		0			0
$363$	1.01912	−	4.68481i	0.0534899	−	0.245889i
$364$		0			0
$365$	−20.7156	+	15.9610i	−1.08430	+	0.835437i
$366$		0			0
$367$	5.33139	−	5.33139i	0.278296	−	0.278296i	−0.554132	−	0.832429i	$-0.686950\pi$
$367$	5.33139	−	5.33139i	0.278296	−	0.278296i	0.832429	+	0.554132i	$0.186950\pi$
$368$		0			0
$369$		−	4.12879i		−	0.214936i
$370$		0			0
$371$	1.40278	+	0.411893i	0.0728286	+	0.0213844i
$372$		0			0
$373$	8.70268	+	1.89315i	0.450608	+	0.0980237i	0.432141	−	0.901806i	$-0.357758\pi$
$373$	8.70268	+	1.89315i	0.450608	+	0.0980237i	0.0184660	+	0.999829i	$0.494122\pi$
$374$		0			0
$375$	−10.3804	−	5.11908i	−0.536043	−	0.264348i
$376$		0			0
$377$	0.279536	+	1.28501i	0.0143968	+	0.0661812i
$378$		0			0
$379$	−3.91207	−	8.56624i	−0.200950	−	0.440018i	0.782150	−	0.623090i	$-0.214123\pi$
$379$	−3.91207	−	8.56624i	−0.200950	−	0.440018i	−0.983099	+	0.183072i	$0.941396\pi$
$380$		0			0
$381$	1.80951	+	12.5854i	0.0927042	+	0.644772i
$382$		0			0
$383$	−6.39673	−	3.49288i	−0.326858	−	0.178478i	0.307439	−	0.951568i	$-0.400528\pi$
$383$	−6.39673	−	3.49288i	−0.326858	−	0.178478i	−0.634296	+	0.773090i	$0.718710\pi$
$384$		0			0
$385$	25.6503	−	5.95400i	1.30726	−	0.303444i
$386$		0			0
$387$	−18.3596	−	1.31310i	−0.933269	−	0.0667487i
$388$		0			0
$389$	0.235617	−	0.515930i	0.0119463	−	0.0261587i	−0.903565	−	0.428451i	$-0.859059\pi$
$389$	0.235617	−	0.515930i	0.0119463	−	0.0261587i	0.915511	+	0.402293i	$0.131787\pi$
$390$		0			0
$391$	4.62139	−	2.53643i	0.233714	−	0.128273i
$392$		0			0
$393$	7.89439	+	21.1657i	0.398219	+	1.06767i
$394$		0			0
$395$	−9.73324	−	8.20011i	−0.489732	−	0.412593i
$396$		0			0
$397$	6.94846	−	0.496964i	0.348733	−	0.0249419i	0.104126	−	0.994564i	$-0.466796\pi$
$397$	6.94846	−	0.496964i	0.348733	−	0.0249419i	0.244607	+	0.969622i	$0.421341\pi$
$398$		0			0
$399$	10.3098	+	35.1121i	0.516138	+	1.75780i
$400$		0			0
$401$	−27.5340	+	3.95879i	−1.37498	+	0.197693i	−0.789877	−	0.613265i	$-0.789856\pi$
$401$	−27.5340	+	3.95879i	−1.37498	+	0.197693i	−0.585105	+	0.810957i	$0.698947\pi$
$402$		0			0
$403$	−3.77993	−	1.40984i	−0.188292	−	0.0702292i
$404$		0			0
$405$	1.03044	+	0.453404i	0.0512028	+	0.0225298i
$406$		0			0
$407$	20.3158	−	15.2083i	1.00702	−	0.753845i
$408$		0			0
$409$	20.2927	+	31.5761i	1.00341	+	1.56134i	0.815174	+	0.579215i	$0.196641\pi$
$409$	20.2927	+	31.5761i	1.00341	+	1.56134i	0.188237	+	0.982124i	$0.439723\pi$
$410$		0			0
$411$	4.16559	−	14.1867i	0.205473	−	0.699778i
$412$		0			0
$413$	−13.7742	−	13.7742i	−0.677782	−	0.677782i
$414$		0			0
$415$	25.9209	+	18.8483i	1.27241	+	0.925228i
$416$		0			0
$417$	8.78854	+	16.0950i	0.430377	+	0.788176i
$418$		0			0
$419$	2.04143	−	1.31195i	0.0997304	−	0.0640929i	−0.489825	−	0.871821i	$-0.662939\pi$
$419$	2.04143	−	1.31195i	0.0997304	−	0.0640929i	0.589555	+	0.807728i	$0.299303\pi$
$420$		0			0
$421$	30.5447	+	4.39166i	1.48866	+	0.214037i	0.838140	−	0.545455i	$-0.183643\pi$
$421$	30.5447	+	4.39166i	1.48866	+	0.214037i	0.650517	+	0.759492i	$0.274552\pi$
$422$		0			0
$423$	−9.31260	+	2.02583i	−0.452794	+	0.0984993i
$424$		0			0
$425$	5.49089	+	0.239741i	0.266347	+	0.0116292i
$426$		0			0
$427$	−27.5529	+	36.8063i	−1.33338	+	1.78118i
$428$		0			0
$429$	1.02415	−	0.300719i	0.0494466	−	0.0145188i
$430$		0			0
$431$	13.7314	+	11.8984i	0.661420	+	0.573123i	0.919543	−	0.392988i	$-0.128559\pi$
$431$	13.7314	+	11.8984i	0.661420	+	0.573123i	−0.258124	+	0.966112i	$0.583104\pi$
$432$		0			0
$433$	0.547340	−	7.65281i	0.0263035	−	0.367771i	−0.967204	−	0.254002i	$-0.918253\pi$
$433$	0.547340	−	7.65281i	0.0263035	−	0.367771i	0.993507	−	0.113769i	$-0.0362923\pi$
$434$		0			0
$435$	−6.48906	+	3.66114i	−0.311127	+	0.175538i
$436$		0			0
$437$	15.0209	−	33.0798i	0.718545	−	1.58242i
$438$		0			0
$439$	−29.4630	−	13.4553i	−1.40619	−	0.642185i	−0.439525	−	0.898230i	$-0.644853\pi$
$439$	−29.4630	−	13.4553i	−1.40619	−	0.642185i	−0.966665	+	0.256045i	$0.917580\pi$
$440$		0			0
$441$	−18.6576	−	21.5320i	−0.888457	−	1.02533i
$442$		0			0
$443$	2.55779	+	35.7626i	0.121524	+	1.69913i	0.583396	+	0.812188i	$0.301723\pi$
$443$	2.55779	+	35.7626i	0.121524	+	1.69913i	−0.461872	+	0.886947i	$0.652822\pi$
$444$		0			0
$445$	−6.35215	+	3.00820i	−0.301121	+	0.142602i
$446$		0			0
$447$	−2.02006	−	1.51220i	−0.0955454	−	0.0715244i
$448$		0			0
$449$	12.0812	−	5.51730i	0.570147	−	0.260378i	−0.109414	−	0.993996i	$-0.534897\pi$
$449$	12.0812	−	5.51730i	0.570147	−	0.260378i	0.679561	+	0.733619i	$0.262170\pi$
$450$		0			0
$451$	−2.92130	+	4.54563i	−0.137558	+	0.214045i
$452$		0			0
$453$	−5.49557	−	7.34123i	−0.258205	−	0.344921i
$454$		0			0
$455$	−2.83623	−	3.18281i	−0.132965	−	0.149212i
$456$		0			0
$457$	21.1981	−	11.5750i	0.991603	−	0.541456i	0.100345	−	0.994953i	$-0.468005\pi$
$457$	21.1981	−	11.5750i	0.991603	−	0.541456i	0.891258	+	0.453496i	$0.149824\pi$
$458$		0			0
$459$	5.60810			0.261764
$460$		0			0
$461$	31.4875			1.46652			0.733260	−	0.679948i	$-0.237998\pi$
$461$	31.4875			1.46652			0.733260	+	0.679948i	$0.237998\pi$
$462$		0			0
$463$	21.6165	−	11.8035i	1.00461	−	0.548557i	0.109301	−	0.994009i	$-0.465139\pi$
$463$	21.6165	−	11.8035i	1.00461	−	0.548557i	0.895306	+	0.445452i	$0.146957\pi$
$464$		0			0
$465$	1.31393	−	22.8190i	0.0609318	−	1.05820i
$466$		0			0
$467$	11.3731	+	15.1927i	0.526284	+	0.703034i	0.982379	−	0.186897i	$-0.0598432\pi$
$467$	11.3731	+	15.1927i	0.526284	+	0.703034i	−0.456095	+	0.889931i	$0.650752\pi$
$468$		0			0
$469$	−7.35468	+	11.4441i	−0.339608	+	0.528440i
$470$		0			0
$471$	3.65973	−	1.67134i	0.168631	−	0.0770113i
$472$		0			0
$473$	19.2840	+	14.4358i	0.886680	+	0.663761i
$474$		0			0
$475$	31.2835	−	21.3546i	1.43538	−	0.979818i
$476$		0			0
$477$	−0.0431002	−	0.602619i	−0.00197342	−	0.0275920i
$478$		0			0
$479$	−18.1339	−	20.9276i	−0.828559	−	0.956208i	0.171019	−	0.985268i	$-0.445294\pi$
$479$	−18.1339	−	20.9276i	−0.828559	−	0.956208i	−0.999578	+	0.0290599i	$0.990749\pi$
$480$		0			0
$481$	−3.73731	−	1.70677i	−0.170407	−	0.0778222i
$482$		0			0
$483$	−0.0499973	−	23.1671i	−0.00227495	−	1.05414i
$484$		0			0
$485$	−2.83018	−	5.01625i	−0.128512	−	0.227776i
$486$		0			0
$487$	0.171613	−	2.39946i	0.00777651	−	0.108730i	−0.992081	−	0.125598i	$-0.959915\pi$
$487$	0.171613	−	2.39946i	0.00777651	−	0.108730i	0.999858	+	0.0168683i	$0.00536959\pi$
$488$		0			0
$489$	−3.31282	−	2.87058i	−0.149811	−	0.129812i
$490$		0			0
$491$	−7.18583	+	2.10995i	−0.324292	+	0.0952207i	−0.439827	−	0.898083i	$-0.644960\pi$
$491$	−7.18583	+	2.10995i	−0.324292	+	0.0952207i	0.115535	+	0.993303i	$0.463142\pi$
$492$		0			0
$493$	2.12027	−	2.83235i	0.0954923	−	0.127563i
$494$		0			0
$495$	−6.00955	−	9.07163i	−0.270109	−	0.407739i
$496$		0			0
$497$	5.86313	−	1.27545i	0.262997	−	0.0572116i
$498$		0			0
$499$	−12.5114	−	1.79886i	−0.560085	−	0.0805281i	−0.143542	−	0.989644i	$-0.545849\pi$
$499$	−12.5114	−	1.79886i	−0.560085	−	0.0805281i	−0.416543	+	0.909116i	$0.636758\pi$
$500$		0			0
$501$	20.1303	−	12.9370i	0.899357	−	0.577982i
$502$		0			0
$503$	−13.2785	−	24.3178i	−0.592060	−	1.08428i	−0.986252	−	0.165249i	$-0.947157\pi$
$503$	−13.2785	−	24.3178i	−0.592060	−	1.08428i	0.394191	−	0.919028i	$-0.371025\pi$
$504$		0			0
$505$	−30.7653	+	4.86022i	−1.36904	+	0.216277i
$506$		0			0
$507$	9.39389	+	9.39389i	0.417197	+	0.417197i
$508$		0			0
$509$	7.68252	−	26.1643i	0.340522	−	1.15971i	−0.594196	−	0.804320i	$-0.702530\pi$
$509$	7.68252	−	26.1643i	0.340522	−	1.15971i	0.934718	−	0.355390i	$-0.115652\pi$
$510$		0			0
$511$	−29.5050	−	45.9106i	−1.30522	−	2.03097i
$512$		0			0
$513$	30.9400	−	23.1614i	1.36604	−	1.02260i
$514$		0			0
$515$	11.7527	+	30.2221i	0.517887	+	1.33174i
$516$		0			0
$517$	11.6861	+	4.35871i	0.513956	+	0.191696i
$518$		0			0
$519$	−25.3910	+	3.65067i	−1.11454	+	0.160247i
$520$		0			0
$521$	−5.23328	−	17.8229i	−0.229274	−	0.780837i	−0.991108	−	0.133063i	$-0.957519\pi$
$521$	−5.23328	−	17.8229i	−0.229274	−	0.780837i	0.761833	−	0.647773i	$-0.224300\pi$
$522$		0			0
$523$	−35.9161	+	2.56877i	−1.57050	+	0.112325i	−0.829241	−	0.558892i	$-0.811227\pi$
$523$	−35.9161	+	2.56877i	−1.57050	+	0.112325i	−0.741261	+	0.671216i	$0.765772\pi$
$524$		0			0
$525$	12.4892	−	20.6738i	0.545072	−	0.902280i
$526$		0			0
$527$	3.79305	+	10.1696i	0.165228	+	0.442993i
$528$		0			0
$529$	−14.9866	+	17.4471i	−0.651593	+	0.758569i
$530$		0			0
$531$	−3.34400	+	7.32233i	−0.145117	+	0.317762i
$532$		0			0
$533$	0.872572	+	0.0624076i	0.0377953	+	0.00270317i
$534$		0			0
$535$	1.85181	+	7.97777i	0.0800609	+	0.344909i
$536$		0			0
$537$	10.6588	+	5.82015i	0.459962	+	0.251158i
$538$		0			0
$539$	5.30641	+	36.9069i	0.228563	+	1.58969i
$540$		0			0
$541$	−15.1112	−	33.0890i	−0.649683	−	1.42261i	−0.891831	−	0.452368i	$-0.850579\pi$
$541$	−15.1112	−	33.0890i	−0.649683	−	1.42261i	0.242148	−	0.970239i	$-0.422148\pi$
$542$		0			0
$543$	−1.14898	−	5.28179i	−0.0493076	−	0.226663i
$544$		0			0
$545$	−0.0255124	−	1.83756i	−0.00109283	−	0.0787126i
$546$		0			0
$547$	33.8155	+	7.35610i	1.44584	+	0.314524i	0.865935	−	0.500157i	$-0.166724\pi$
$547$	33.8155	+	7.35610i	1.44584	+	0.314524i	0.579909	+	0.814681i	$0.303088\pi$
$548$		0			0
$549$	18.2299	+	5.35278i	0.778033	+	0.228451i
$550$		0			0
$551$		−	24.3829i		−	1.03874i
$552$		0			0
$553$	18.7805	−	18.7805i	0.798626	−	0.798626i
$554$		0			0
$555$	2.99258	−	23.0846i	0.127028	−	0.979885i
$556$		0			0
$557$	−6.29030	+	28.9161i	−0.266529	+	1.22521i	0.628004	+	0.778210i	$0.283872\pi$
$557$	−6.29030	+	28.9161i	−0.266529	+	1.22521i	−0.894533	+	0.447003i	$0.852491\pi$
$558$		0			0
$559$	0.555017	−	3.86023i	0.0234747	−	0.163270i
$560$		0			0
$561$	−2.41584	−	1.55257i	−0.101997	−	0.0655494i
$562$		0			0
$563$	−6.59967	+	17.6944i	−0.278143	+	0.745730i	0.720490	+	0.693465i	$0.243917\pi$
$563$	−6.59967	+	17.6944i	−0.278143	+	0.745730i	−0.998633	+	0.0522650i	$0.983356\pi$
$564$		0			0
$565$	13.2939	−	25.1705i	0.559277	−	1.05893i
$566$		0			0
$567$	−1.12592	+	2.06197i	−0.0472842	+	0.0865945i
$568$		0			0
$569$	14.4449	−	16.6703i	0.605562	−	0.698856i	−0.367337	−	0.930088i	$-0.619730\pi$
$569$	14.4449	−	16.6703i	0.605562	−	0.698856i	0.972899	+	0.231232i	$0.0742757\pi$
$570$		0			0
$571$	−15.4271	+	13.3676i	−0.645603	+	0.559418i	−0.914921	−	0.403633i	$-0.867747\pi$
$571$	−15.4271	+	13.3676i	−0.645603	+	0.559418i	0.269318	+	0.963051i	$0.413202\pi$
$572$		0			0
$573$	0.975184	−	0.363725i	0.0407389	−	0.0151948i
$574$		0			0
$575$	−22.7954	+	7.44107i	−0.950634	+	0.310314i
$576$		0			0
$577$	6.49398	−	2.42213i	0.270348	−	0.100834i	−0.210634	−	0.977565i	$-0.567553\pi$
$577$	6.49398	−	2.42213i	0.270348	−	0.100834i	0.480982	+	0.876730i	$0.340280\pi$
$578$		0			0
$579$	−11.7423	+	10.1747i	−0.487991	+	0.422847i
$580$		0			0
$581$	−43.7985	+	50.5462i	−1.81707	+	2.09701i
$582$		0			0
$583$	−0.378927	+	0.693953i	−0.0156936	+	0.0287406i
$584$		0			0
$585$	−0.822752	+	1.55779i	−0.0340166	+	0.0644067i
$586$		0			0
$587$	1.30231	−	3.49162i	0.0537520	−	0.144115i	−0.907299	−	0.420487i	$-0.861859\pi$
$587$	1.30231	−	3.49162i	0.0537520	−	0.144115i	0.961051	+	0.276372i	$0.0891321\pi$
$588$		0			0
$589$	62.9264	+	40.4404i	2.59284	+	1.66632i
$590$		0			0
$591$	0.463511	−	3.22379i	0.0190663	−	0.132609i
$592$		0			0
$593$	−2.37207	+	10.9042i	−0.0974093	+	0.447783i	0.902447	+	0.430802i	$0.141769\pi$
$593$	−2.37207	+	10.9042i	−0.0974093	+	0.447783i	−0.999856	+	0.0169813i	$0.994594\pi$
$594$		0			0
$595$	−1.47453	+	11.3744i	−0.0604500	+	0.466307i
$596$		0			0
$597$	3.48572	−	3.48572i	0.142661	−	0.142661i
$598$		0			0
$599$		−	37.6571i		−	1.53863i	−0.638871	−	0.769314i	$-0.720598\pi$
$599$		−	37.6571i		−	1.53863i	0.638871	−	0.769314i	$-0.279402\pi$
$600$		0			0
$601$	16.3859	+	4.81132i	0.668393	+	0.196258i	0.598287	−	0.801282i	$-0.295848\pi$
$601$	16.3859	+	4.81132i	0.668393	+	0.196258i	0.0701058	+	0.997540i	$0.477666\pi$
$602$		0			0
$603$	5.49311	+	1.19495i	0.223697	+	0.0486623i
$604$		0			0
$605$	−0.143765	−	10.3549i	−0.00584489	−	0.420986i
$606$		0			0
$607$	3.41348	+	15.6915i	0.138549	+	0.636900i	0.993074	+	0.117490i	$0.0374846\pi$
$607$	3.41348	+	15.6915i	0.138549	+	0.636900i	−0.854525	+	0.519410i	$0.826152\pi$
$608$		0			0
$609$	−6.45904	−	14.1433i	−0.261734	−	0.573117i
$610$		0			0
$611$	−0.287374	−	1.99873i	−0.0116259	−	0.0808599i
$612$		0			0
$613$	4.95664	+	2.70653i	0.200197	+	0.109316i	0.576220	−	0.817294i	$-0.304527\pi$
$613$	4.95664	+	2.70653i	0.200197	+	0.109316i	−0.376024	+	0.926610i	$0.622709\pi$
$614$		0			0
$615$	1.12067	+	4.82793i	0.0451896	+	0.194681i
$616$		0			0
$617$	−0.750821	−	0.0536998i	−0.0302269	−	0.00216187i	0.0562175	−	0.998419i	$-0.482096\pi$
$617$	−0.750821	−	0.0536998i	−0.0302269	−	0.00216187i	−0.0864444	+	0.996257i	$0.527551\pi$
$618$		0			0
$619$	8.87716	−	19.4383i	0.356803	−	0.781290i	−0.643077	−	0.765802i	$-0.722342\pi$
$619$	8.87716	−	19.4383i	0.356803	−	0.781290i	0.999880	−	0.0154884i	$-0.00493032\pi$
$620$		0			0
$621$	−22.9065	+	8.60006i	−0.919208	+	0.345108i
$622$		0			0
$623$	−5.12572	−	13.7426i	−0.205358	−	0.550586i
$624$		0			0
$625$	−24.3413	−	5.70108i	−0.973651	−	0.228043i
$626$		0			0
$627$	−19.7403	+	1.41186i	−0.788353	+	0.0563841i
$628$		0			0
$629$	3.11422	+	10.6060i	0.124172	+	0.422891i
$630$		0			0
$631$	−16.4566	+	2.36610i	−0.655125	+	0.0941928i	−0.461859	−	0.886953i	$-0.652817\pi$
$631$	−16.4566	+	2.36610i	−0.655125	+	0.0941928i	−0.193267	+	0.981146i	$0.561908\pi$
$632$		0			0
$633$	−5.77585	−	2.15428i	−0.229569	−	0.0856250i
$634$		0			0
$635$	9.95406	+	25.5968i	0.395015	+	1.01578i
$636$		0			0
$637$	4.83255	−	3.61760i	0.191473	−	0.143335i
$638$		0			0
$639$	−1.34055	−	2.08593i	−0.0530312	−	0.0825182i
$640$		0			0
$641$	−6.98945	+	23.8039i	−0.276067	+	0.940197i	0.698408	+	0.715700i	$0.253892\pi$
$641$	−6.98945	+	23.8039i	−0.276067	+	0.940197i	−0.974475	+	0.224497i	$0.927926\pi$
$642$		0			0
$643$	19.4265	+	19.4265i	0.766106	+	0.766106i	0.977418	−	0.211313i	$-0.0677739\pi$
$643$	19.4265	+	19.4265i	0.766106	+	0.766106i	−0.211313	+	0.977418i	$0.567774\pi$
$644$		0			0
$645$	21.8248	−	3.44783i	0.859351	−	0.135758i
$646$		0			0
$647$	−9.56364	−	17.5145i	−0.375986	−	0.688566i	0.619342	−	0.785121i	$-0.287399\pi$
$647$	−9.56364	−	17.5145i	−0.375986	−	0.688566i	−0.995328	+	0.0965551i	$0.969218\pi$
$648$		0			0
$649$	8.86246	−	5.69556i	0.347882	−	0.223570i
$650$		0			0
$651$	47.2133	+	6.78825i	1.85044	+	0.266053i
$652$		0			0
$653$	−2.34642	+	0.510432i	−0.0918224	+	0.0199747i	−0.258242	−	0.966080i	$-0.583143\pi$
$653$	−2.34642	+	0.510432i	−0.0918224	+	0.0199747i	0.166419	+	0.986055i	$0.446779\pi$
$654$		0			0
$655$	26.9476	+	40.6783i	1.05293	+	1.58943i
$656$		0			0
$657$	−13.5151	+	18.0540i	−0.527273	+	0.704354i
$658$		0			0
$659$	13.8132	−	4.05592i	0.538085	−	0.157996i	−0.00138759	−	0.999999i	$-0.500442\pi$
$659$	13.8132	−	4.05592i	0.538085	−	0.157996i	0.539473	+	0.842003i	$0.318624\pi$
$660$		0			0
$661$	11.2080	+	9.71181i	0.435942	+	0.377746i	0.845003	−	0.534761i	$-0.179598\pi$
$661$	11.2080	+	9.71181i	0.435942	+	0.377746i	−0.409061	+	0.912507i	$0.634144\pi$
$662$		0			0
$663$	−0.0331674	+	0.463742i	−0.00128812	+	0.0180102i
$664$		0			0
$665$	38.8413	+	68.8429i	1.50620	+	2.66961i
$666$		0			0
$667$	−4.31692	+	14.8203i	−0.167152	+	0.573845i
$668$		0			0
$669$	1.29202	+	0.590045i	0.0499523	+	0.0228125i
$670$		0			0
$671$	−16.2830	−	18.7916i	−0.628599	−	0.725442i
$672$		0			0
$673$	2.58360	+	36.1234i	0.0995905	+	1.39246i	0.764062	+	0.645143i	$0.223202\pi$
$673$	2.58360	+	36.1234i	0.0995905	+	1.39246i	−0.664471	+	0.747314i	$0.731343\pi$
$674$		0			0
$675$	−25.0673	−	4.72831i	−0.964843	−	0.181993i
$676$		0			0
$677$	−14.5252	−	10.8734i	−0.558248	−	0.417899i	0.282546	−	0.959254i	$-0.408821\pi$
$677$	−14.5252	−	10.8734i	−0.558248	−	0.417899i	−0.840795	+	0.541354i	$0.817912\pi$
$678$		0			0
$679$	10.9333	−	4.99305i	0.419580	−	0.191616i
$680$		0			0
$681$	−4.73909	+	7.37416i	−0.181602	+	0.282579i
$682$		0			0
$683$	−15.2455	−	20.3656i	−0.583354	−	0.779269i	0.407645	−	0.913140i	$-0.366350\pi$
$683$	−15.2455	−	20.3656i	−0.583354	−	0.779269i	−0.990999	+	0.133871i	$0.957259\pi$
$684$		0			0
$685$	1.83591	−	31.8842i	0.0701464	−	1.21823i
$686$		0			0
$687$	−3.05427	+	1.66776i	−0.116528	+	0.0636288i
$688$		0			0
$689$	0.128008			0.00487671
$690$		0			0
$691$	1.91646			0.0729055			0.0364528	−	0.999335i	$-0.488394\pi$
$691$	1.91646			0.0729055			0.0364528	+	0.999335i	$0.488394\pi$
$692$		0			0
$693$	19.9306	−	10.8830i	0.757103	−	0.413409i
$694$		0			0
$695$	26.3525	+	29.5727i	0.999606	+	1.12175i
$696$		0			0
$697$	−1.41044	−	1.88413i	−0.0534243	−	0.0713665i
$698$		0			0
$699$	−8.39569	+	13.0640i	−0.317554	+	0.494124i
$700$		0			0
$701$	−28.0197	+	12.7962i	−1.05829	+	0.483305i	−0.867041	−	0.498236i	$-0.833981\pi$
$701$	−28.0197	+	12.7962i	−1.05829	+	0.483305i	−0.191249	+	0.981541i	$0.561254\pi$
$702$		0			0
$703$	60.9840	+	45.6521i	2.30006	+	1.72180i
$704$		0			0
$705$	10.3396	−	4.89656i	0.389414	−	0.184415i
$706$		0			0
$707$	−4.63698	−	64.8334i	−0.174392	−	2.43831i
$708$		0			0
$709$	−21.4177	−	24.7174i	−0.804359	−	0.928280i	0.194253	−	0.980951i	$-0.437772\pi$
$709$	−21.4177	−	24.7174i	−0.804359	−	0.928280i	−0.998612	+	0.0526718i	$0.983226\pi$
$710$		0			0
$711$	−9.98367	−	4.55939i	−0.374417	−	0.170991i
$712$		0			0
$713$	−31.0879	−	35.7213i	−1.16425	−	1.33777i
$714$		0			0
$715$	2.00802	−	1.13293i	0.0750956	−	0.0423691i
$716$		0			0
$717$	0.661246	−	9.24543i	0.0246947	−	0.345277i
$718$		0			0
$719$	4.50733	+	3.90562i	0.168095	+	0.145655i	0.734846	−	0.678234i	$-0.237254\pi$
$719$	4.50733	+	3.90562i	0.168095	+	0.145655i	−0.566751	+	0.823889i	$0.691800\pi$
$720$		0			0
$721$	−64.9292	+	19.0649i	−2.41809	+	0.710015i
$722$		0			0
$723$	1.88251	−	2.51474i	0.0700113	−	0.0935241i
$724$		0			0
$725$	−11.8653	+	10.8725i	−0.440666	+	0.403796i
$726$		0			0
$727$	−30.8905	+	6.71981i	−1.14566	+	0.249224i	−0.745041	−	0.667019i	$-0.767570\pi$
$727$	−30.8905	+	6.71981i	−1.14566	+	0.249224i	−0.400624	+	0.916243i	$0.631207\pi$
$728$		0			0
$729$	−14.7224	−	2.11676i	−0.545273	−	0.0783984i
$730$		0			0
$731$	−8.82676	+	5.67261i	−0.326469	+	0.209809i
$732$		0			0
$733$	−14.3815	−	26.3377i	−0.531193	−	0.972807i	−0.996166	−	0.0874821i	$-0.972118\pi$
$733$	−14.3815	−	26.3377i	−0.531193	−	0.972807i	0.464973	−	0.885325i	$-0.346064\pi$
$734$		0			0
$735$	27.6613	+	20.1139i	1.02030	+	0.741912i
$736$		0			0
$737$	−5.20220	−	5.20220i	−0.191626	−	0.191626i
$738$		0			0
$739$	6.23853	−	21.2465i	0.229488	−	0.781565i	−0.761564	−	0.648090i	$-0.775568\pi$
$739$	6.23853	−	21.2465i	0.229488	−	0.781565i	0.991052	−	0.133475i	$-0.0426137\pi$
$740$		0			0
$741$	1.73226	+	2.69545i	0.0636362	+	0.0990199i
$742$		0			0
$743$	−32.6497	+	24.4412i	−1.19780	+	0.896662i	−0.996560	−	0.0828800i	$-0.973588\pi$
$743$	−32.6497	+	24.4412i	−1.19780	+	0.896662i	−0.201240	+	0.979542i	$0.564497\pi$
$744$		0			0
$745$	−4.98889	−	2.19517i	−0.182779	−	0.0804247i
$746$		0			0
$747$	25.8959	+	9.65866i	0.947480	+	0.353392i
$748$		0			0
$749$	−16.9172	+	2.43232i	−0.618140	+	0.0888751i
$750$		0			0
$751$	−7.23427	−	24.6376i	−0.263982	−	0.899040i	−0.979669	−	0.200619i	$-0.935705\pi$
$751$	−7.23427	−	24.6376i	−0.263982	−	0.899040i	0.715687	−	0.698421i	$-0.246114\pi$
$752$		0			0
$753$	−29.3771	+	2.10109i	−1.07056	+	0.0765680i
$754$		0			0
$755$	−15.1485	−	12.7624i	−0.551310	−	0.464471i
$756$		0			0
$757$	3.29524	+	8.83489i	0.119768	+	0.321110i	0.982975	−	0.183740i	$-0.0588205\pi$
$757$	3.29524	+	8.83489i	0.119768	+	0.321110i	−0.863207	+	0.504850i	$0.831548\pi$
$758$		0			0
$759$	12.2485	+	2.63682i	0.444592	+	0.0957106i
$760$		0			0
$761$	−4.23144	+	9.26556i	−0.153390	+	0.335876i	−0.970690	−	0.240336i	$-0.922742\pi$
$761$	−4.23144	+	9.26556i	−0.153390	+	0.335876i	0.817300	+	0.576212i	$0.195470\pi$
$762$		0			0
$763$	3.82534	+	0.273594i	0.138487	+	0.00990475i
$764$		0			0
$765$	4.61697	−	1.07170i	0.166927	−	0.0387473i
$766$		0			0
$767$	−1.49694	−	0.817393i	−0.0540515	−	0.0295144i
$768$		0			0
$769$	−6.23644	−	43.3754i	−0.224892	−	1.56416i	−0.719159	−	0.694846i	$-0.755473\pi$
$769$	−6.23644	−	43.3754i	−0.224892	−	1.56416i	0.494267	−	0.869310i	$-0.335437\pi$
$770$		0			0
$771$	−2.94498	−	6.44861i	−0.106061	−	0.232241i
$772$		0			0
$773$	3.24830	+	14.9322i	0.116833	+	0.537074i	0.997940	+	0.0641564i	$0.0204356\pi$
$773$	3.24830	+	14.9322i	0.116833	+	0.537074i	−0.881107	+	0.472918i	$0.843201\pi$
$774$		0			0
$775$	−8.38017	−	48.6543i	−0.301025	−	1.74771i
$776$		0			0
$777$	47.4672	+	10.3259i	1.70288	+	0.370438i
$778$		0			0
$779$	−15.5629	−	4.56967i	−0.557598	−	0.163725i
$780$		0			0
$781$			3.24502i			0.116116i
$782$		0			0
$783$	−11.6116	+	11.6116i	−0.414965	+	0.414965i
$784$		0			0
$785$	6.88402	−	5.30402i	0.245701	−	0.189309i
$786$		0			0
$787$	−1.65623	+	7.61359i	−0.0590384	+	0.271395i	−0.997198	−	0.0748081i	$-0.976166\pi$
$787$	−1.65623	+	7.61359i	−0.0590384	+	0.271395i	0.938160	+	0.346203i	$0.112529\pi$
$788$		0			0
$789$	0.970102	−	6.74721i	0.0345365	−	0.240207i
$790$		0			0
$791$	49.9733	+	32.1159i	1.77684	+	1.14191i
$792$		0			0
$793$	−1.40680	+	3.77177i	−0.0499568	+	0.133939i
$794$		0			0
$795$	0.213965	+	0.692963i	0.00758857	+	0.0245769i
$796$		0			0
$797$	8.03765	−	14.7198i	0.284708	−	0.521404i	−0.695712	−	0.718321i	$-0.744911\pi$
$797$	8.03765	−	14.7198i	0.284708	−	0.521404i	0.980420	+	0.196917i	$0.0630929\pi$
$798$		0			0
$799$	−3.55766	+	4.10576i	−0.125861	+	0.145251i
$800$		0			0
$801$	−4.58072	+	3.96922i	−0.161852	+	0.140245i
$802$		0			0
$803$	27.6535	−	10.3142i	0.975870	−	0.363981i
$804$		0			0
$805$	−11.4200	−	48.7206i	−0.402501	−	1.71718i
$806$		0			0
$807$	−14.5309	+	5.41976i	−0.511513	+	0.190784i
$808$		0			0
$809$	−38.7029	+	33.5362i	−1.36072	+	1.17907i	−0.395246	+	0.918575i	$0.629341\pi$
$809$	−38.7029	+	33.5362i	−1.36072	+	1.17907i	−0.965475	+	0.260496i	$0.916114\pi$
$810$		0			0
$811$	23.4211	−	27.0294i	0.822428	−	0.949132i	−0.176957	−	0.984219i	$-0.556625\pi$
$811$	23.4211	−	27.0294i	0.822428	−	0.949132i	0.999384	+	0.0350865i	$0.0111707\pi$
$812$		0			0
$813$	−10.0570	+	18.4180i	−0.352714	+	0.645948i
$814$		0			0
$815$	−8.37238	−	4.42190i	−0.293272	−	0.154893i
$816$		0			0
$817$	−25.2696	+	67.7503i	−0.884070	+	2.37028i
$818$		0			0
$819$	−3.09282	−	1.98764i	−0.108072	−	0.0694536i
$820$		0			0
$821$	1.10418	−	7.67976i	0.0385363	−	0.268026i	−0.961439	−	0.275017i	$-0.911316\pi$
$821$	1.10418	−	7.67976i	0.0385363	−	0.268026i	0.999976	+	0.00699163i	$0.00222552\pi$
$822$		0			0
$823$	1.93658	−	8.90234i	0.0675051	−	0.310316i	−0.930997	−	0.365026i	$-0.881060\pi$
$823$	1.93658	−	8.90234i	0.0675051	−	0.310316i	0.998502	+	0.0547105i	$0.0174236\pi$
$824$		0			0
$825$	9.48944	+	8.97658i	0.330380	+	0.312524i
$826$		0			0
$827$	1.87995	−	1.87995i	0.0653724	−	0.0653724i	−0.673665	−	0.739037i	$-0.735281\pi$
$827$	1.87995	−	1.87995i	0.0653724	−	0.0653724i	0.739037	+	0.673665i	$0.235281\pi$
$828$		0			0
$829$			40.0737i			1.39182i	0.718130	+	0.695909i	$0.244998\pi$
$829$			40.0737i			1.39182i	−0.718130	+	0.695909i	$0.755002\pi$
$830$		0			0
$831$	11.1078	+	3.26156i	0.385327	+	0.113142i
$832$		0			0
$833$	−15.8698	−	3.45226i	−0.549855	−	0.119614i
$834$		0			0
$835$	36.0372	−	37.0519i	1.24712	−	1.28223i
$836$		0			0
$837$	−10.7083	−	49.2254i	−0.370134	−	1.70148i
$838$		0			0
$839$	−15.3586	−	33.6307i	−0.530238	−	1.16106i	−0.965416	−	0.260715i	$-0.916042\pi$
$839$	−15.3586	−	33.6307i	−0.530238	−	1.16106i	0.435178	−	0.900344i	$-0.356685\pi$
$840$		0			0
$841$	−2.65276	−	18.4504i	−0.0914746	−	0.636220i
$842$		0			0
$843$	−9.97770	−	5.44823i	−0.343650	−	0.187647i
$844$		0			0
$845$	24.3533	+	15.1774i	0.837780	+	0.522118i
$846$		0			0
$847$	21.5562	+	1.54173i	0.740681	+	0.0529745i
$848$		0			0
$849$	7.41178	−	16.2295i	0.254372	−	0.556996i
$850$		0			0
$851$	−28.9846	−	38.5452i	−0.993578	−	1.32131i
$852$		0			0
$853$	−1.96610	−	5.27131i	−0.0673179	−	0.180486i	0.898935	−	0.438083i	$-0.144342\pi$
$853$	−1.96610	−	5.27131i	−0.0673179	−	0.180486i	−0.966253	+	0.257596i	$0.917070\pi$
$854$		0			0
$855$	21.0458	−	24.9806i	0.719752	−	0.854319i
$856$		0			0
$857$	−4.78393	+	0.342154i	−0.163416	+	0.0116878i	−0.152807	−	0.988256i	$-0.548831\pi$
$857$	−4.78393	+	0.342154i	−0.163416	+	0.0116878i	−0.0106086	+	0.999944i	$0.503377\pi$
$858$		0			0
$859$	3.21388	+	10.9455i	0.109656	+	0.373455i	0.995976	−	0.0896187i	$-0.0285648\pi$
$859$	3.21388	+	10.9455i	0.109656	+	0.373455i	−0.886320	+	0.463073i	$0.846747\pi$
$860$		0			0
$861$	−10.2378	+	1.47197i	−0.348903	+	0.0501647i
$862$		0			0
$863$	−36.2512	−	13.5210i	−1.23400	−	0.460260i	−0.354009	−	0.935242i	$-0.615182\pi$
$863$	−36.2512	−	13.5210i	−1.23400	−	0.460260i	−0.879996	+	0.474982i	$0.842455\pi$
$864$		0			0
$865$	−51.6412	+	20.0822i	−1.75586	+	0.682814i
$866$		0			0
$867$	−13.0871	+	9.79687i	−0.444461	+	0.332719i
$868$		0			0
$869$	7.76564	+	12.0836i	0.263431	+	0.409907i
$870$		0			0
$871$	−0.335569	+	1.14284i	−0.0113703	+	0.0387238i
$872$		0			0
$873$	−3.51215	−	3.51215i	−0.118868	−	0.118868i
$874$		0			0
$875$	16.1810	−	49.5988i	0.547017	−	1.67675i
$876$		0			0
$877$	22.4562	+	41.1254i	0.758291	+	1.38871i	0.915983	+	0.401217i	$0.131413\pi$
$877$	22.4562	+	41.1254i	0.758291	+	1.38871i	−0.157692	+	0.987488i	$0.550405\pi$
$878$		0			0
$879$	26.8715	−	17.2692i	0.906352	−	0.582477i
$880$		0			0
$881$	−52.2809	−	7.51685i	−1.76139	−	0.253249i	−0.815734	−	0.578427i	$-0.803667\pi$
$881$	−52.2809	−	7.51685i	−1.76139	−	0.253249i	−0.945653	+	0.325178i	$0.894576\pi$
$882$		0			0
$883$	5.11569	−	1.11285i	0.172157	−	0.0374504i	−0.125661	−	0.992073i	$-0.540105\pi$
$883$	5.11569	−	1.11285i	0.172157	−	0.0374504i	0.297817	+	0.954623i	$0.403741\pi$
$884$		0			0
$885$	1.92276	−	9.46988i	0.0646329	−	0.318327i
$886$		0			0
$887$	−16.2757	+	21.7418i	−0.546485	+	0.730018i	−0.985727	−	0.168350i	$-0.946156\pi$
$887$	−16.2757	+	21.7418i	−0.546485	+	0.730018i	0.439243	+	0.898369i	$0.355247\pi$
$888$		0			0
$889$	−54.9923	+	16.1472i	−1.84438	+	0.541560i
$890$		0			0
$891$	−0.960221	−	0.832036i	−0.0321686	−	0.0278743i
$892$		0			0
$893$	−2.67094	+	37.3446i	−0.0893796	+	1.24969i
$894$		0			0
$895$	25.2694	+	7.04023i	0.844663	+	0.235329i
$896$		0			0
$897$	−0.575676	−	1.94503i	−0.0192213	−	0.0649428i
$898$		0			0
$899$	−28.9097	−	13.2026i	−0.964191	−	0.440331i
$900$		0			0
$901$	−0.225530	−	0.260275i	−0.00751349	−	0.00867102i
$902$		0			0
$903$	3.28946	+	45.9927i	0.109466	+	1.53054i
$904$		0			0
$905$	−4.99716	−	10.5521i	−0.166111	−	0.350763i
$906$		0			0
$907$	−1.42715	−	1.06835i	−0.0473878	−	0.0354740i	0.575321	−	0.817928i	$-0.304877\pi$
$907$	−1.42715	−	1.06835i	−0.0473878	−	0.0354740i	−0.622709	+	0.782454i	$0.713968\pi$
$908$		0			0
$909$	−24.4330	+	11.1582i	−0.810391	+	0.370093i
$910$		0			0
$911$	−15.1645	+	23.5964i	−0.502421	+	0.781783i	−0.996134	−	0.0878422i	$-0.972003\pi$
$911$	−15.1645	+	23.5964i	−0.502421	+	0.781783i	0.493713	+	0.869625i	$0.335639\pi$
$912$		0			0
$913$	−21.6763	−	28.9562i	−0.717382	−	0.958310i
$914$		0			0
$915$	−22.7697	−	1.31109i	−0.752743	−	0.0433432i
$916$		0			0
$917$	−89.3716	+	48.8006i	−2.95131	+	1.61154i
$918$		0			0
$919$	18.0327			0.594842			0.297421	−	0.954746i	$-0.403873\pi$
$919$	18.0327			0.594842			0.297421	+	0.954746i	$0.403873\pi$
$920$		0			0
$921$	−0.461157			−0.0151957
$922$		0			0
$923$	0.461100	−	0.251780i	0.0151773	−	0.00828743i
$924$		0			0
$925$	−4.97789	−	50.0330i	−0.163672	−	1.64508i
$926$		0			0
$927$	16.7583	+	22.3865i	0.550415	+	0.735268i
$928$		0			0
$929$	14.6298	−	22.7643i	0.479987	−	0.746874i	−0.513832	−	0.857891i	$-0.671774\pi$
$929$	14.6298	−	22.7643i	0.479987	−	0.746874i	0.993819	+	0.111017i	$0.0354108\pi$
$930$		0			0
$931$	−101.812	+	46.4958i	−3.33674	+	1.52384i
$932$		0			0
$933$	0.361914	+	0.270926i	0.0118485	+	0.00886971i
$934$		0			0
$935$	−5.84136	−	2.08681i	−0.191033	−	0.0682459i
$936$		0			0
$937$	1.95628	+	27.3524i	0.0639089	+	0.893564i	0.923749	+	0.383000i	$0.125109\pi$
$937$	1.95628	+	27.3524i	0.0639089	+	0.893564i	−0.859840	+	0.510564i	$0.829437\pi$
$938$		0			0
$939$	13.0241	+	15.0307i	0.425027	+	0.490507i
$940$		0			0
$941$	16.2510	+	7.42160i	0.529769	+	0.241937i	0.662296	−	0.749242i	$-0.269582\pi$
$941$	16.2510	+	7.42160i	0.529769	+	0.241937i	−0.132528	+	0.991179i	$0.542309\pi$
$942$		0			0
$943$	8.65033	+	5.53289i	0.281694	+	0.180176i
$944$		0			0
$945$	14.2874	−	51.2814i	0.464768	−	1.66818i
$946$		0			0
$947$	−2.73963	+	38.3050i	−0.0890259	+	1.24475i	0.734950	+	0.678121i	$0.237205\pi$
$947$	−2.73963	+	38.3050i	−0.0890259	+	1.24475i	−0.823976	+	0.566624i	$0.808249\pi$
$948$		0			0
$949$	−3.61122	−	3.12914i	−0.117225	−	0.101576i
$950$		0			0
$951$	8.96648	−	2.63280i	0.290758	−	0.0853743i
$952$		0			0
$953$	−6.81386	+	9.10225i	−0.220723	+	0.294851i	−0.897211	−	0.441603i	$-0.854410\pi$
$953$	−6.81386	+	9.10225i	−0.220723	+	0.294851i	0.676488	+	0.736454i	$0.263501\pi$
$954$		0			0
$955$	1.87421	−	1.24158i	0.0606480	−	0.0401766i
$956$		0			0
$957$	8.21662	−	1.78742i	0.265606	−	0.0577790i
$958$		0			0
$959$	65.9697	+	9.48501i	2.13027	+	0.306287i
$960$		0			0
$961$	55.9423	−	35.9519i	1.80459	−	1.15974i
$962$		0			0
$963$	3.38482	+	6.19883i	0.109074	+	0.199755i
$964$		0			0
$965$	−19.7371	+	27.1432i	−0.635361	+	0.873770i
$966$		0			0
$967$	−37.4013	−	37.4013i	−1.20275	−	1.20275i	−0.973328	−	0.229417i	$-0.926318\pi$
$967$	−37.4013	−	37.4013i	−1.20275	−	1.20275i	−0.229417	−	0.973328i	$-0.573682\pi$
$968$		0			0
$969$	2.42862	−	8.27112i	0.0780186	−	0.265707i
$970$		0			0
$971$	−16.8325	−	26.1919i	−0.540182	−	0.840539i	0.458662	−	0.888611i	$-0.348329\pi$
$971$	−16.8325	−	26.1919i	−0.540182	−	0.840539i	−0.998844	+	0.0480716i	$0.984692\pi$
$972$		0			0
$973$	−66.1740	+	49.5373i	−2.12144	+	1.58809i
$974$		0			0
$975$	0.539243	−	2.04489i	0.0172696	−	0.0654888i
$976$		0			0
$977$	−24.4922	−	9.13511i	−0.783574	−	0.292258i	−0.0743416	−	0.997233i	$-0.523686\pi$
$977$	−24.4922	−	9.13511i	−0.783574	−	0.292258i	−0.709232	+	0.704975i	$0.750958\pi$
$978$		0			0
$979$	7.85157	−	1.12889i	0.250937	−	0.0360793i
$980$		0			0
$981$	−0.446497	−	1.52063i	−0.0142555	−	0.0485499i
$982$		0			0
$983$	−8.71131	+	0.623045i	−0.277848	+	0.0198720i	−0.209568	−	0.977794i	$-0.567206\pi$
$983$	−8.71131	+	0.623045i	−0.277848	+	0.0198720i	−0.0682799	+	0.997666i	$0.521751\pi$
$984$		0			0
$985$	−0.599238	−	7.00945i	−0.0190933	−	0.223340i
$986$		0			0
$987$	8.34334	+	22.3694i	0.265572	+	0.712025i
$988$		0			0
$989$	27.3543	−	36.7059i	0.869816	−	1.16718i
$990$		0			0
$991$	−7.61859	+	16.6824i	−0.242013	+	0.529934i	−0.991192	−	0.132434i	$-0.957721\pi$
$991$	−7.61859	+	16.6824i	−0.242013	+	0.529934i	0.749179	+	0.662367i	$0.230448\pi$
$992$		0			0
$993$	−12.6414	−	0.904128i	−0.401161	−	0.0286916i
$994$		0			0
$995$	5.63176	−	9.03660i	0.178539	−	0.286479i
$996$		0			0
$997$	−0.342757	−	0.187160i	−0.0108552	−	0.00592740i	0.473812	−	0.880626i	$-0.342878\pi$
$997$	−0.342757	−	0.187160i	−0.0108552	−	0.00592740i	−0.484667	+	0.874699i	$0.661059\pi$
$998$		0			0
$999$	−7.30140	−	50.7823i	−0.231006	−	1.60668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.17.14	✓	720
5.3	odd	4	inner	920.2.bv.a.753.14	yes	720
23.19	odd	22	inner	920.2.bv.a.617.14	yes	720
115.88	even	44	inner	920.2.bv.a.433.14	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.14	✓	720	1.1	even	1	trivial
920.2.bv.a.433.14	yes	720	115.88	even	44	inner
920.2.bv.a.617.14	yes	720	23.19	odd	22	inner
920.2.bv.a.753.14	yes	720	5.3	odd	4	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.908585 + 0.496125i) q^{3} +(-1.66942 + 1.48763i) q^{5} +(-2.79645 - 3.73561i) q^{7} +(-1.04254 + 1.62222i) q^{9} +(2.29557 - 1.04835i) q^{11} +(-0.327078 - 0.244848i) q^{13} +(0.778756 - 2.17988i) q^{15} +(0.0784177 + 1.09642i) q^{17} +(4.96085 + 5.72512i) q^{19} +(4.39414 + 2.00674i) q^{21} +(-2.00167 - 4.35813i) q^{23} +(0.573901 - 4.96695i) q^{25} +(0.363964 - 5.08888i) q^{27} +(-2.43252 - 2.10779i) q^{29} +(9.47417 - 2.78187i) q^{31} +(-1.56561 + 2.09141i) q^{33} +(10.2257 + 2.07621i) q^{35} +(9.82620 - 2.13756i) q^{37} +(0.418654 + 0.0601933i) q^{39} +(-1.80123 + 1.15758i) q^{41} +(4.57456 + 8.37769i) q^{43} +(-0.672836 - 4.25906i) q^{45} +(3.49473 + 3.49473i) q^{47} +(-4.16257 + 14.1764i) q^{49} +(-0.615212 - 0.957289i) q^{51} +(-0.250815 + 0.187757i) q^{53} +(-2.27270 + 5.16511i) q^{55} +(-7.34773 - 2.74056i) q^{57} +(4.13198 - 0.594090i) q^{59} +(-2.77586 - 9.45372i) q^{61} +(8.97537 - 0.641931i) q^{63} +(0.910273 - 0.0778194i) q^{65} +(-1.01878 - 2.73145i) q^{67} +(3.98087 + 2.96666i) q^{69} +(-0.534163 + 1.16965i) q^{71} +(11.6654 + 0.834326i) q^{73} +(1.94279 + 4.79763i) q^{75} +(-10.3357 - 5.64371i) q^{77} +(0.810015 + 5.63378i) q^{79} +(-0.209146 - 0.457966i) q^{81} +(-3.04666 - 14.0053i) q^{83} +(-1.76199 - 1.71373i) q^{85} +(3.25587 + 0.708272i) q^{87} +(3.01589 + 0.885546i) q^{89} +1.90654i q^{91} +(-7.22794 + 7.22794i) q^{93} +(-16.7986 - 2.17770i) q^{95} +(-0.547518 + 2.51690i) q^{97} +(-0.692560 + 4.81686i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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