LMFDB - Embedded newform 308.3.r.a.57.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,3,Mod(29,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("308.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	308.r (of order $10$, degree $4$, 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:	$8.39239214230$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			57.6
Character	$\chi$	$=$	308.57
Dual form			308.3.r.a.281.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0173009 + 0.0125698i) q^{3} +(-1.51166 - 4.65241i) q^{5} +(-1.55513 + 2.14046i) q^{7} +(-2.78101 + 8.55907i) q^{9} +O(q^{10})$	\(q+(-0.0173009 + 0.0125698i) q^{3} +(-1.51166 - 4.65241i) q^{5} +(-1.55513 + 2.14046i) q^{7} +(-2.78101 + 8.55907i) q^{9} +(-10.0566 - 4.45702i) q^{11} +(-7.67584 - 2.49403i) q^{13} +(0.0846332 + 0.0614896i) q^{15} +(-8.67490 + 2.81864i) q^{17} +(17.4905 + 24.0736i) q^{19} -0.0565797i q^{21} -28.7304 q^{23} +(0.865634 - 0.628920i) q^{25} +(-0.118947 - 0.366083i) q^{27} +(-18.0447 + 24.8365i) q^{29} +(-13.5454 + 41.6885i) q^{31} +(0.230012 - 0.0492994i) q^{33} +(12.3091 + 3.99947i) q^{35} +(-43.3337 - 31.4838i) q^{37} +(0.164149 - 0.0533351i) q^{39} +(-35.0923 - 48.3004i) q^{41} -58.4675i q^{43} +44.0242 q^{45} +(-14.9161 + 10.8372i) q^{47} +(-2.16312 - 6.65740i) q^{49} +(0.114654 - 0.157807i) q^{51} +(-11.5361 + 35.5044i) q^{53} +(-5.53372 + 53.5249i) q^{55} +(-0.605204 - 0.196643i) q^{57} +(20.7630 + 15.0852i) q^{59} +(17.8291 - 5.79302i) q^{61} +(-13.9955 - 19.2631i) q^{63} +39.4812i q^{65} +104.956 q^{67} +(0.497062 - 0.361137i) q^{69} +(-23.4203 - 72.0803i) q^{71} +(-53.2579 + 73.3032i) q^{73} +(-0.00707083 + 0.0217618i) q^{75} +(25.1794 - 14.5945i) q^{77} +(110.169 + 35.7960i) q^{79} +(-65.5204 - 47.6033i) q^{81} +(123.868 - 40.2470i) q^{83} +(26.2270 + 36.0983i) q^{85} -0.656513i q^{87} -94.4349 q^{89} +(17.2753 - 12.5513i) q^{91} +(-0.289670 - 0.891513i) q^{93} +(85.5607 - 117.764i) q^{95} +(-1.26363 + 3.88906i) q^{97} +(66.1154 - 73.6801i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9}+O(q^{10}) $ 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9	$ 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9} - 10 q^{11} + 30 q^{13} + 24 q^{15} + 60 q^{19} - 132 q^{23} - 186 q^{25} - 110 q^{27} - 90 q^{29} - 26 q^{31} + 46 q^{33} + 82 q^{37} + 290 q^{39} - 336 q^{45} + 84 q^{47} + 84 q^{49} - 20 q^{51} + 58 q^{53} + 370 q^{55} - 20 q^{57} + 436 q^{59} + 160 q^{61} + 276 q^{67} - 118 q^{69} - 150 q^{71} - 320 q^{73} - 692 q^{75} + 28 q^{77} - 560 q^{79} + 122 q^{81} - 630 q^{83} + 220 q^{85} - 444 q^{89} - 126 q^{91} + 500 q^{93} + 440 q^{95} - 80 q^{97} + 1034 q^{99}+O(q^{100}) $ 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9 - 10 * q^11 + 30 * q^13 + 24 * q^15 + 60 * q^19 - 132 * q^23 - 186 * q^25 - 110 * q^27 - 90 * q^29 - 26 * q^31 + 46 * q^33 + 82 * q^37 + 290 * q^39 - 336 * q^45 + 84 * q^47 + 84 * q^49 - 20 * q^51 + 58 * q^53 + 370 * q^55 - 20 * q^57 + 436 * q^59 + 160 * q^61 + 276 * q^67 - 118 * q^69 - 150 * q^71 - 320 * q^73 - 692 * q^75 + 28 * q^77 - 560 * q^79 + 122 * q^81 - 630 * q^83 + 220 * q^85 - 444 * q^89 - 126 * q^91 + 500 * q^93 + 440 * q^95 - 80 * q^97 + 1034 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0173009	+	0.0125698i	−0.00576697	+	0.00418995i	−0.590665	−	0.806917i	$-0.701135\pi$
$3$	−0.0173009	+	0.0125698i	−0.00576697	+	0.00418995i	0.584898	+	0.811107i	$0.301135\pi$
$4$		0			0
$5$	−1.51166	−	4.65241i	−0.302332	−	0.930482i	−0.980659	−	0.195722i	$-0.937295\pi$
$5$	−1.51166	−	4.65241i	−0.302332	−	0.930482i	0.678328	−	0.734760i	$-0.262705\pi$
$6$		0			0
$7$	−1.55513	+	2.14046i	−0.222162	+	0.305780i
$7$	−1.55513	+	2.14046i	−0.222162	+	0.305780i
$8$		0			0
$9$	−2.78101	+	8.55907i	−0.309001	+	0.951008i
$10$		0			0
$11$	−10.0566	−	4.45702i	−0.914236	−	0.405183i
$11$	−10.0566	−	4.45702i	−0.914236	−	0.405183i
$12$		0			0
$13$	−7.67584	−	2.49403i	−0.590449	−	0.191848i	−0.00147280	−	0.999999i	$-0.500469\pi$
$13$	−7.67584	−	2.49403i	−0.590449	−	0.191848i	−0.588976	+	0.808150i	$0.700469\pi$
$14$		0			0
$15$	0.0846332	+	0.0614896i	0.00564221	+	0.00409931i
$16$		0			0
$17$	−8.67490	+	2.81864i	−0.510288	+	0.165803i	−0.552833	−	0.833292i	$-0.686453\pi$
$17$	−8.67490	+	2.81864i	−0.510288	+	0.165803i	0.0425452	+	0.999095i	$0.486453\pi$
$18$		0			0
$19$	17.4905	+	24.0736i	0.920553	+	1.26703i	0.963432	+	0.267953i	$0.0863471\pi$
$19$	17.4905	+	24.0736i	0.920553	+	1.26703i	−0.0428786	+	0.999080i	$0.513653\pi$
$20$		0			0
$21$		−	0.0565797i		−	0.00269427i
$22$		0			0
$23$	−28.7304			−1.24915			−0.624574	−	0.780966i	$-0.714727\pi$
$23$	−28.7304			−1.24915			−0.624574	+	0.780966i	$0.714727\pi$
$24$		0			0
$25$	0.865634	−	0.628920i	0.0346254	−	0.0251568i
$26$		0			0
$27$	−0.118947	−	0.366083i	−0.00440546	−	0.0135586i
$28$		0			0
$29$	−18.0447	+	24.8365i	−0.622232	+	0.856429i	−0.997513	−	0.0704819i	$-0.977546\pi$
$29$	−18.0447	+	24.8365i	−0.622232	+	0.856429i	0.375281	+	0.926911i	$0.377546\pi$
$30$		0			0
$31$	−13.5454	+	41.6885i	−0.436949	+	1.34479i	0.454127	+	0.890937i	$0.349951\pi$
$31$	−13.5454	+	41.6885i	−0.436949	+	1.34479i	−0.891076	+	0.453854i	$0.850049\pi$
$32$		0			0
$33$	0.230012	−	0.0492994i	0.00697007	−	0.00149392i
$34$		0			0
$35$	12.3091	+	3.99947i	0.351689	+	0.114271i
$36$		0			0
$37$	−43.3337	−	31.4838i	−1.17118	−	0.850913i	−0.180031	−	0.983661i	$-0.557620\pi$
$37$	−43.3337	−	31.4838i	−1.17118	−	0.850913i	−0.991150	+	0.132748i	$0.957620\pi$
$38$		0			0
$39$	0.164149	−	0.0533351i	0.00420894	−	0.00136757i
$40$		0			0
$41$	−35.0923	−	48.3004i	−0.855910	−	1.17806i	−0.982529	−	0.186108i	$-0.940413\pi$
$41$	−35.0923	−	48.3004i	−0.855910	−	1.17806i	0.126619	−	0.991951i	$-0.459587\pi$
$42$		0			0
$43$		−	58.4675i		−	1.35971i	−0.733347	−	0.679854i	$-0.762043\pi$
$43$		−	58.4675i		−	1.35971i	0.733347	−	0.679854i	$-0.237957\pi$
$44$		0			0
$45$	44.0242			0.978317
$46$		0			0
$47$	−14.9161	+	10.8372i	−0.317363	+	0.230578i	−0.735050	−	0.678013i	$-0.762841\pi$
$47$	−14.9161	+	10.8372i	−0.317363	+	0.230578i	0.417686	+	0.908591i	$0.362841\pi$
$48$		0			0
$49$	−2.16312	−	6.65740i	−0.0441453	−	0.135865i
$50$		0			0
$51$	0.114654	−	0.157807i	0.00224811	−	0.00309426i
$52$		0			0
$53$	−11.5361	+	35.5044i	−0.217662	+	0.669893i	0.781292	+	0.624165i	$0.214561\pi$
$53$	−11.5361	+	35.5044i	−0.217662	+	0.669893i	−0.998954	+	0.0457282i	$0.985439\pi$
$54$		0			0
$55$	−5.53372	+	53.5249i	−0.100613	+	0.973179i
$56$		0			0
$57$	−0.605204	−	0.196643i	−0.0106176	−	0.00344987i
$58$		0			0
$59$	20.7630	+	15.0852i	0.351915	+	0.255681i	0.749672	−	0.661810i	$-0.230211\pi$
$59$	20.7630	+	15.0852i	0.351915	+	0.255681i	−0.397757	+	0.917491i	$0.630211\pi$
$60$		0			0
$61$	17.8291	−	5.79302i	0.292280	−	0.0949676i	−0.159207	−	0.987245i	$-0.550894\pi$
$61$	17.8291	−	5.79302i	0.292280	−	0.0949676i	0.451487	+	0.892278i	$0.350894\pi$
$62$		0			0
$63$	−13.9955	−	19.2631i	−0.222151	−	0.305764i
$64$		0			0
$65$			39.4812i			0.607404i
$66$		0			0
$67$	104.956			1.56650			0.783251	−	0.621706i	$-0.213560\pi$
$67$	104.956			1.56650			0.783251	+	0.621706i	$0.213560\pi$
$68$		0			0
$69$	0.497062	−	0.361137i	0.00720380	−	0.00523387i
$70$		0			0
$71$	−23.4203	−	72.0803i	−0.329863	−	1.01521i	−0.969197	−	0.246286i	$-0.920790\pi$
$71$	−23.4203	−	72.0803i	−0.329863	−	1.01521i	0.639334	−	0.768929i	$-0.279210\pi$
$72$		0			0
$73$	−53.2579	+	73.3032i	−0.729561	+	1.00415i	0.269591	+	0.962975i	$0.413111\pi$
$73$	−53.2579	+	73.3032i	−0.729561	+	1.00415i	−0.999152	+	0.0411791i	$0.986889\pi$
$74$		0			0
$75$	−0.00707083	+	0.0217618i	−9.42778e−5	+	0.000290157i
$76$		0			0
$77$	25.1794	−	14.5945i	0.327005	−	0.189538i
$78$		0			0
$79$	110.169	+	35.7960i	1.39454	+	0.453114i	0.907422	−	0.420221i	$-0.138048\pi$
$79$	110.169	+	35.7960i	1.39454	+	0.453114i	0.487120	+	0.873335i	$0.338048\pi$
$80$		0			0
$81$	−65.5204	−	47.6033i	−0.808894	−	0.587696i
$82$		0			0
$83$	123.868	−	40.2470i	1.49238	−	0.484904i	0.554596	−	0.832120i	$-0.312873\pi$
$83$	123.868	−	40.2470i	1.49238	−	0.484904i	0.937785	+	0.347216i	$0.112873\pi$
$84$		0			0
$85$	26.2270	+	36.0983i	0.308553	+	0.424686i
$86$		0			0
$87$		−	0.656513i		−	0.00754613i
$88$		0			0
$89$	−94.4349			−1.06107			−0.530533	−	0.847664i	$-0.678008\pi$
$89$	−94.4349			−1.06107			−0.530533	+	0.847664i	$0.678008\pi$
$90$		0			0
$91$	17.2753	−	12.5513i	0.189839	−	0.137926i
$92$		0			0
$93$	−0.289670	−	0.891513i	−0.00311473	−	0.00958616i
$94$		0			0
$95$	85.5607	−	117.764i	0.900638	−	1.23962i
$96$		0			0
$97$	−1.26363	+	3.88906i	−0.0130271	+	0.0400934i	−0.957359	−	0.288902i	$-0.906710\pi$
$97$	−1.26363	+	3.88906i	−0.0130271	+	0.0400934i	0.944332	+	0.328995i	$0.106710\pi$
$98$		0			0
$99$	66.1154	−	73.6801i	0.667832	−	0.744243i
$100$		0			0
$101$	−6.98313	−	2.26896i	−0.0691399	−	0.0224649i	0.274243	−	0.961660i	$-0.411573\pi$
$101$	−6.98313	−	2.26896i	−0.0691399	−	0.0224649i	−0.343383	+	0.939196i	$0.611573\pi$
$102$		0			0
$103$	−3.07561	−	2.23456i	−0.0298603	−	0.0216948i	0.572755	−	0.819727i	$-0.305875\pi$
$103$	−3.07561	−	2.23456i	−0.0298603	−	0.0216948i	−0.602615	+	0.798032i	$0.705875\pi$
$104$		0			0
$105$	−0.263232	+	0.0855292i	−0.00250697	+	0.000814564i
$106$		0			0
$107$	1.36113	+	1.87344i	0.0127208	+	0.0175087i	0.815330	−	0.578996i	$-0.196556\pi$
$107$	1.36113	+	1.87344i	0.0127208	+	0.0175087i	−0.802609	+	0.596505i	$0.796556\pi$
$108$		0			0
$109$		−	108.440i		−	0.994861i	−0.867504	−	0.497430i	$-0.834277\pi$
$109$		−	108.440i		−	0.994861i	0.867504	−	0.497430i	$-0.165723\pi$
$110$		0			0
$111$	1.14546			0.0103194
$112$		0			0
$113$	121.977	−	88.6218i	1.07945	−	0.784264i	0.101860	−	0.994799i	$-0.467521\pi$
$113$	121.977	−	88.6218i	1.07945	−	0.784264i	0.977586	+	0.210535i	$0.0675206\pi$
$114$		0			0
$115$	43.4306	+	133.666i	0.377657	+	1.16231i
$116$		0			0
$117$	42.6932	−	58.7621i	0.364899	−	0.502240i
$118$		0			0
$119$	7.45743	−	22.9516i	0.0626675	−	0.192871i
$120$		0			0
$121$	81.2700	+	89.6448i	0.671653	+	0.740866i
$122$		0			0
$123$	1.21426	+	0.394536i	0.00987202	+	0.00320761i
$124$		0			0
$125$	−103.174	−	74.9602i	−0.825391	−	0.599682i
$126$		0			0
$127$	−136.416	+	44.3242i	−1.07414	+	0.349009i	−0.792099	−	0.610393i	$-0.791011\pi$
$127$	−136.416	+	44.3242i	−1.07414	+	0.349009i	−0.282041	+	0.959402i	$0.591011\pi$
$128$		0			0
$129$	0.734927	+	1.01154i	0.00569711	+	0.00784140i
$130$		0			0
$131$			173.465i			1.32416i	0.749432	+	0.662081i	$0.230326\pi$
$131$			173.465i			1.32416i	−0.749432	+	0.662081i	$0.769674\pi$
$132$		0			0
$133$	−78.7287			−0.591945
$134$		0			0
$135$	−1.52336	+	1.10678i	−0.0112841	+	0.00819840i
$136$		0			0
$137$	−7.17028	−	22.0678i	−0.0523378	−	0.161079i	0.921471	−	0.388447i	$-0.126988\pi$
$137$	−7.17028	−	22.0678i	−0.0523378	−	0.161079i	−0.973809	+	0.227367i	$0.926988\pi$
$138$		0			0
$139$	114.149	−	157.112i	0.821213	−	1.13030i	−0.168282	−	0.985739i	$-0.553822\pi$
$139$	114.149	−	157.112i	0.821213	−	1.13030i	0.989495	−	0.144564i	$-0.0461781\pi$
$140$		0			0
$141$	0.121840	−	0.374986i	0.000864115	−	0.00265947i
$142$		0			0
$143$	66.0768	+	59.2928i	0.462076	+	0.414635i
$144$		0			0
$145$	142.827	+	46.4072i	0.985012	+	0.320050i
$146$		0			0
$147$	0.121106	+	0.0879889i	0.000823853	+	0.000598564i
$148$		0			0
$149$	−13.7103	+	4.45474i	−0.0920154	+	0.0298976i	−0.354663	−	0.934994i	$-0.615404\pi$
$149$	−13.7103	+	4.45474i	−0.0920154	+	0.0298976i	0.262648	+	0.964892i	$0.415404\pi$
$150$		0			0
$151$	−83.6632	−	115.153i	−0.554061	−	0.762599i	0.436495	−	0.899707i	$-0.356220\pi$
$151$	−83.6632	−	115.153i	−0.554061	−	0.762599i	−0.990556	+	0.137107i	$0.956220\pi$
$152$		0			0
$153$		−	82.0878i		−	0.536521i
$154$		0			0
$155$	214.428			1.38341
$156$		0			0
$157$	−208.423	+	151.428i	−1.32754	+	0.964513i	−0.327733	+	0.944770i	$0.606285\pi$
$157$	−208.423	+	151.428i	−1.32754	+	0.964513i	−0.999805	+	0.0197422i	$0.993715\pi$
$158$		0			0
$159$	−0.246700	−	0.759264i	−0.00155157	−	0.00477525i
$160$		0			0
$161$	44.6796	−	61.4962i	0.277513	−	0.381964i
$162$		0			0
$163$	−82.6160	+	254.266i	−0.506847	+	1.55991i	0.290797	+	0.956785i	$0.406080\pi$
$163$	−82.6160	+	254.266i	−0.506847	+	1.55991i	−0.797644	+	0.603129i	$0.793920\pi$
$164$		0			0
$165$	−0.577061	−	0.995587i	−0.00349734	−	0.00603386i
$166$		0			0
$167$	86.0681	+	27.9652i	0.515378	+	0.167456i	0.555147	−	0.831753i	$-0.312662\pi$
$167$	86.0681	+	27.9652i	0.515378	+	0.167456i	−0.0397688	+	0.999209i	$0.512662\pi$
$168$		0			0
$169$	−84.0256	−	61.0482i	−0.497193	−	0.361232i
$170$		0			0
$171$	−254.689	+	82.7536i	−1.48941	+	0.483939i
$172$		0			0
$173$	−148.708	−	204.679i	−0.859585	−	1.18312i	−0.981668	−	0.190598i	$-0.938957\pi$
$173$	−148.708	−	204.679i	−0.859585	−	1.18312i	0.122083	−	0.992520i	$-0.461043\pi$
$174$		0			0
$175$			2.83091i			0.0161766i
$176$		0			0
$177$	−0.548837			−0.00310077
$178$		0			0
$179$	−166.040	+	120.635i	−0.927597	+	0.673938i	−0.945403	−	0.325903i	$-0.894332\pi$
$179$	−166.040	+	120.635i	−0.927597	+	0.673938i	0.0178065	+	0.999841i	$0.494332\pi$
$180$		0			0
$181$	61.1891	+	188.321i	0.338062	+	1.04045i	0.965194	+	0.261534i	$0.0842284\pi$
$181$	61.1891	+	188.321i	0.338062	+	1.04045i	−0.627133	+	0.778912i	$0.715772\pi$
$182$		0			0
$183$	−0.235642	+	0.324333i	−0.00128766	+	0.00177231i
$184$		0			0
$185$	−80.9696	+	249.199i	−0.437673	+	1.34702i
$186$		0			0
$187$	99.8026	+	10.3182i	0.533704	+	0.0551775i
$188$		0			0
$189$	0.968564	+	0.314705i	0.00512468	+	0.00166511i
$190$		0			0
$191$	115.282	+	83.7575i	0.603572	+	0.438521i	0.847145	−	0.531362i	$-0.178320\pi$
$191$	115.282	+	83.7575i	0.603572	+	0.438521i	−0.243573	+	0.969883i	$0.578320\pi$
$192$		0			0
$193$	−60.2224	+	19.5674i	−0.312033	+	0.101386i	−0.460847	−	0.887480i	$-0.652454\pi$
$193$	−60.2224	+	19.5674i	−0.312033	+	0.101386i	0.148814	+	0.988865i	$0.452454\pi$
$194$		0			0
$195$	−0.496273	−	0.683062i	−0.00254499	−	0.00350288i
$196$		0			0
$197$		−	307.475i		−	1.56079i	−0.625289	−	0.780393i	$-0.715019\pi$
$197$		−	307.475i		−	1.56079i	0.625289	−	0.780393i	$-0.284981\pi$
$198$		0			0
$199$	12.4463			0.0625441			0.0312721	−	0.999511i	$-0.490044\pi$
$199$	12.4463			0.0625441			0.0312721	+	0.999511i	$0.490044\pi$
$200$		0			0
$201$	−1.81583	+	1.31928i	−0.00903397	+	0.00656356i
$202$		0			0
$203$	−25.0994	−	77.2480i	−0.123642	−	0.380532i
$204$		0			0
$205$	−171.666	+	236.278i	−0.837394	+	1.15257i
$206$		0			0
$207$	79.8996	−	245.906i	0.385988	−	1.18795i
$208$		0			0
$209$	−68.5984	−	320.054i	−0.328222	−	1.53136i
$210$		0			0
$211$	−93.7249	−	30.4531i	−0.444194	−	0.144327i	0.0783760	−	0.996924i	$-0.475027\pi$
$211$	−93.7249	−	30.4531i	−0.444194	−	0.144327i	−0.522570	+	0.852597i	$0.675027\pi$
$212$		0			0
$213$	1.31123	+	0.952665i	0.00615601	+	0.00447260i
$214$		0			0
$215$	−272.015	+	88.3829i	−1.26518	+	0.411083i
$216$		0			0
$217$	−68.1676	−	93.8246i	−0.314136	−	0.432371i
$218$		0			0
$219$		−	1.93766i		−	0.00884775i
$220$		0			0
$221$	73.6169			0.333108
$222$		0			0
$223$	−198.510	+	144.226i	−0.890178	+	0.646752i	−0.935924	−	0.352201i	$-0.885433\pi$
$223$	−198.510	+	144.226i	−0.890178	+	0.646752i	0.0457467	+	0.998953i	$0.485433\pi$
$224$		0			0
$225$	2.97563	+	9.15806i	0.0132250	+	0.0407025i
$226$		0			0
$227$	77.4534	−	106.605i	0.341204	−	0.469627i	−0.603588	−	0.797296i	$-0.706263\pi$
$227$	77.4534	−	106.605i	0.341204	−	0.469627i	0.944793	+	0.327669i	$0.106263\pi$
$228$		0			0
$229$	−107.248	+	330.077i	−0.468334	+	1.44138i	0.386407	+	0.922328i	$0.373716\pi$
$229$	−107.248	+	330.077i	−0.468334	+	1.44138i	−0.854741	+	0.519055i	$0.826284\pi$
$230$		0			0
$231$	−0.252176	+	0.568999i	−0.00109167	+	0.00246320i
$232$		0			0
$233$	−32.3664	−	10.5165i	−0.138912	−	0.0451352i	0.238736	−	0.971085i	$-0.423267\pi$
$233$	−32.3664	−	10.5165i	−0.138912	−	0.0451352i	−0.377648	+	0.925949i	$0.623267\pi$
$234$		0			0
$235$	72.9669	+	53.0136i	0.310498	+	0.225590i
$236$		0			0
$237$	−2.35597	+	0.765501i	−0.00994080	+	0.00322996i
$238$		0			0
$239$	−180.356	−	248.239i	−0.754627	−	1.03866i	−0.997642	−	0.0686330i	$-0.978136\pi$
$239$	−180.356	−	248.239i	−0.754627	−	1.03866i	0.243014	−	0.970023i	$-0.421864\pi$
$240$		0			0
$241$			267.798i			1.11120i	0.831451	+	0.555598i	$0.187511\pi$
$241$			267.798i			1.11120i	−0.831451	+	0.555598i	$0.812489\pi$
$242$		0			0
$243$	5.19623			0.0213837
$244$		0			0
$245$	−27.7030	+	20.1274i	−0.113074	+	0.0821528i
$246$		0			0
$247$	−74.2140	−	228.407i	−0.300461	−	0.924725i
$248$		0			0
$249$	−1.63712	+	2.25331i	−0.00657479	+	0.00904943i
$250$		0			0
$251$	−128.943	+	396.847i	−0.513719	+	1.58106i	0.271882	+	0.962331i	$0.412354\pi$
$251$	−128.943	+	396.847i	−0.513719	+	1.58106i	−0.785601	+	0.618734i	$0.787646\pi$
$252$		0			0
$253$	288.930	+	128.052i	1.14202	+	0.506134i
$254$		0			0
$255$	−0.907501	−	0.294865i	−0.00355883	−	0.00115633i
$256$		0			0
$257$	97.5529	+	70.8763i	0.379583	+	0.275783i	0.761174	−	0.648548i	$-0.224624\pi$
$257$	97.5529	+	70.8763i	0.379583	+	0.275783i	−0.381590	+	0.924332i	$0.624624\pi$
$258$		0			0
$259$	134.779	−	43.7925i	0.520384	−	0.169083i
$260$		0			0
$261$	−162.394	−	223.517i	−0.622201	−	0.856386i
$262$		0			0
$263$		−	123.732i		−	0.470463i	−0.971939	−	0.235232i	$-0.924415\pi$
$263$		−	123.732i		−	0.470463i	0.971939	−	0.235232i	$-0.0755849\pi$
$264$		0			0
$265$	182.619			0.689130
$266$		0			0
$267$	1.63381	−	1.18703i	0.00611914	−	0.00444581i
$268$		0			0
$269$	144.081	+	443.436i	0.535617	+	1.64846i	0.742312	+	0.670055i	$0.233729\pi$
$269$	144.081	+	443.436i	0.535617	+	1.64846i	−0.206694	+	0.978406i	$0.566271\pi$
$270$		0			0
$271$	−37.5722	+	51.7137i	−0.138643	+	0.190825i	−0.872692	−	0.488270i	$-0.837628\pi$
$271$	−37.5722	+	51.7137i	−0.138643	+	0.190825i	0.734050	+	0.679096i	$0.237628\pi$
$272$		0			0
$273$	−0.141111	+	0.434296i	−0.000516892	+	0.00159083i
$274$		0			0
$275$	−11.5084	+	2.46665i	−0.0418489	+	0.00896962i
$276$		0			0
$277$	130.595	+	42.4328i	0.471461	+	0.153187i	0.535105	−	0.844786i	$-0.320272\pi$
$277$	130.595	+	42.4328i	0.471461	+	0.153187i	−0.0636438	+	0.997973i	$0.520272\pi$
$278$		0			0
$279$	−319.145	−	231.872i	−1.14389	−	0.831084i
$280$		0			0
$281$	−373.777	+	121.448i	−1.33017	+	0.432198i	−0.885975	−	0.463733i	$-0.846510\pi$
$281$	−373.777	+	121.448i	−1.33017	+	0.432198i	−0.444193	+	0.895931i	$0.646510\pi$
$282$		0			0
$283$	191.572	+	263.677i	0.676934	+	0.931720i	0.999892	−	0.0146935i	$-0.00467725\pi$
$283$	191.572	+	263.677i	0.676934	+	0.931720i	−0.322958	+	0.946413i	$0.604677\pi$
$284$		0			0
$285$			3.11291i			0.0109225i
$286$		0			0
$287$	157.958			0.550377
$288$		0			0
$289$	−166.497	+	120.967i	−0.576114	+	0.418571i
$290$		0			0
$291$	−0.0270229	−	0.0831679i	−9.28622e−5	−	0.000285801i
$292$		0			0
$293$	269.147	−	370.449i	0.918590	−	1.26433i	−0.0455563	−	0.998962i	$-0.514506\pi$
$293$	269.147	−	370.449i	0.918590	−	1.26433i	0.964147	−	0.265370i	$-0.0854939\pi$
$294$		0			0
$295$	38.7959	−	119.401i	0.131511	−	0.404751i
$296$		0			0
$297$	−0.435430	+	4.21169i	−0.00146609	+	0.0141808i
$298$		0			0
$299$	220.530	+	71.6545i	0.737558	+	0.239647i
$300$		0			0
$301$	125.147	+	90.9247i	0.415771	+	0.302075i
$302$		0			0
$303$	0.149335	−	0.0485219i	0.000492854	−	0.000160138i
$304$		0			0
$305$	−53.9030	−	74.1911i	−0.176731	−	0.243250i
$306$		0			0
$307$		−	5.18556i		−	0.0168911i	−0.999964	−	0.00844554i	$-0.997312\pi$
$307$		−	5.18556i		−	0.0168911i	0.999964	−	0.00844554i	$-0.00268833\pi$
$308$		0			0
$309$	0.0812989			0.000263103
$310$		0			0
$311$	−17.0845	+	12.4126i	−0.0549340	+	0.0399119i	−0.614913	−	0.788595i	$-0.710809\pi$
$311$	−17.0845	+	12.4126i	−0.0549340	+	0.0399119i	0.559979	+	0.828507i	$0.310809\pi$
$312$		0			0
$313$	−94.1683	−	289.820i	−0.300857	−	0.925944i	−0.981191	−	0.193041i	$-0.938165\pi$
$313$	−94.1683	−	289.820i	−0.300857	−	0.925944i	0.680333	−	0.732903i	$-0.261835\pi$
$314$		0			0
$315$	−68.4636	+	94.2320i	−0.217345	+	0.299149i
$316$		0			0
$317$	−12.7387	+	39.2057i	−0.0401851	+	0.123677i	−0.969137	−	0.246525i	$-0.920711\pi$
$317$	−12.7387	+	39.2057i	−0.0401851	+	0.123677i	0.928951	+	0.370202i	$0.120711\pi$
$318$		0			0
$319$	292.165	−	169.344i	0.915878	−	0.530860i
$320$		0			0
$321$	−0.0470976	−	0.0153029i	−0.000146721	−	4.76727e-5i
$322$		0			0
$323$	−219.583	−	159.537i	−0.679825	−	0.493922i
$324$		0			0
$325$	−8.21301	+	2.66857i	−0.0252708	+	0.00821098i
$326$		0			0
$327$	1.36307	+	1.87611i	0.00416842	+	0.00573733i
$328$		0			0
$329$		−	48.7805i		−	0.148269i
$330$		0			0
$331$	148.464			0.448531			0.224266	−	0.974528i	$-0.428002\pi$
$331$	148.464			0.448531			0.224266	+	0.974528i	$0.428002\pi$
$332$		0			0
$333$	389.983	−	283.339i	1.17112	−	0.850869i
$334$		0			0
$335$	−158.657	−	488.296i	−0.473603	−	1.45760i
$336$		0			0
$337$	254.819	−	350.729i	0.756140	−	1.04074i	−0.241385	−	0.970429i	$-0.577602\pi$
$337$	254.819	−	350.729i	0.756140	−	1.04074i	0.997525	−	0.0703086i	$-0.0223984\pi$
$338$		0			0
$339$	−0.996359	+	3.06648i	−0.00293911	+	0.00904565i
$340$		0			0
$341$	322.027	−	358.872i	0.944361	−	1.05241i
$342$		0			0
$343$	17.6138	+	5.72307i	0.0513522	+	0.0166853i
$344$		0			0
$345$	−2.43154	−	1.76662i	−0.00704795	−	0.00512064i
$346$		0			0
$347$	−53.2058	+	17.2876i	−0.153331	+	0.0498202i	−0.384677	−	0.923051i	$-0.625687\pi$
$347$	−53.2058	+	17.2876i	−0.153331	+	0.0498202i	0.231346	+	0.972872i	$0.425687\pi$
$348$		0			0
$349$	87.0430	+	119.804i	0.249407	+	0.343279i	0.915303	−	0.402765i	$-0.131951\pi$
$349$	87.0430	+	119.804i	0.249407	+	0.343279i	−0.665897	+	0.746044i	$0.731951\pi$
$350$		0			0
$351$			3.10665i			0.00885085i
$352$		0			0
$353$	296.244			0.839217			0.419608	−	0.907705i	$-0.362167\pi$
$353$	296.244			0.839217			0.419608	+	0.907705i	$0.362167\pi$
$354$		0			0
$355$	−299.943	+	217.922i	−0.844911	+	0.613864i
$356$		0			0
$357$	0.159478	+	0.490823i	0.000446717	+	0.00137485i
$358$		0			0
$359$	8.99606	−	12.3820i	0.0250587	−	0.0344903i	−0.796304	−	0.604897i	$-0.793214\pi$
$359$	8.99606	−	12.3820i	0.0250587	−	0.0344903i	0.821363	+	0.570407i	$0.193214\pi$
$360$		0			0
$361$	−162.066	+	498.789i	−0.448937	+	1.38169i
$362$		0			0
$363$	−2.53287	−	0.529384i	−0.00697759	−	0.00145836i
$364$		0			0
$365$	421.544	+	136.968i	1.15492	+	0.375255i
$366$		0			0
$367$	−202.083	−	146.822i	−0.550636	−	0.400061i	0.277384	−	0.960759i	$-0.410533\pi$
$367$	−202.083	−	146.822i	−0.550636	−	0.400061i	−0.828020	+	0.560699i	$0.810533\pi$
$368$		0			0
$369$	510.999	−	166.034i	1.38482	−	0.449956i
$370$		0			0
$371$	−58.0554	−	79.9065i	−0.156484	−	0.215381i
$372$		0			0
$373$			58.9580i			0.158064i	0.996872	+	0.0790322i	$0.0251830\pi$
$373$			58.9580i			0.158064i	−0.996872	+	0.0790322i	$0.974817\pi$
$374$		0			0
$375$	2.72724			0.00727264
$376$		0			0
$377$	200.451	−	145.636i	0.531701	−	0.386303i
$378$		0			0
$379$	89.1512	+	274.379i	0.235227	+	0.723956i	0.997091	+	0.0762183i	$0.0242846\pi$
$379$	89.1512	+	274.379i	0.235227	+	0.723956i	−0.761864	+	0.647737i	$0.775715\pi$
$380$		0			0
$381$	1.80297	−	2.48157i	0.00473220	−	0.00651332i
$382$		0			0
$383$	−213.043	+	655.678i	−0.556247	+	1.71195i	0.136381	+	0.990656i	$0.456453\pi$
$383$	−213.043	+	655.678i	−0.556247	+	1.71195i	−0.692628	+	0.721295i	$0.743547\pi$
$384$		0			0
$385$	−105.962	−	95.0830i	−0.275226	−	0.246969i
$386$		0			0
$387$	500.427	+	162.599i	1.29309	+	0.420152i
$388$		0			0
$389$	−461.429	−	335.248i	−1.18619	−	0.861819i	−0.193335	−	0.981133i	$-0.561931\pi$
$389$	−461.429	−	335.248i	−1.18619	−	0.861819i	−0.992857	+	0.119314i	$0.961931\pi$
$390$		0			0
$391$	249.233	−	80.9808i	0.637425	−	0.207112i
$392$		0			0
$393$	−2.18043	−	3.00111i	−0.00554817	−	0.00763640i
$394$		0			0
$395$		−	566.661i		−	1.43459i
$396$		0			0
$397$	188.320			0.474357			0.237178	−	0.971466i	$-0.423777\pi$
$397$	188.320			0.474357			0.237178	+	0.971466i	$0.423777\pi$
$398$		0			0
$399$	1.36208	−	0.989608i	0.00341373	−	0.00248022i
$400$		0			0
$401$	115.060	+	354.119i	0.286933	+	0.883090i	0.985812	+	0.167851i	$0.0536826\pi$
$401$	115.060	+	354.119i	0.286933	+	0.883090i	−0.698879	+	0.715240i	$0.746317\pi$
$402$		0			0
$403$	207.945	−	286.211i	0.515992	−	0.710202i
$404$		0			0
$405$	−122.426	+	376.788i	−0.302286	+	0.930340i
$406$		0			0
$407$	295.466	+	509.758i	0.725960	+	1.25248i
$408$		0			0
$409$	252.299	+	81.9770i	0.616869	+	0.200433i	0.600750	−	0.799437i	$-0.294869\pi$
$409$	252.299	+	81.9770i	0.616869	+	0.200433i	0.0161192	+	0.999870i	$0.494869\pi$
$410$		0			0
$411$	0.401442	+	0.291665i	0.000976744	+	0.000709646i
$412$		0			0
$413$	−64.5784	+	20.9828i	−0.156364	+	0.0508058i
$414$		0			0
$415$	−374.491	−	515.443i	−0.902388	−	1.24203i
$416$		0			0
$417$			4.15302i			0.00995927i
$418$		0			0
$419$	−153.966			−0.367462			−0.183731	−	0.982977i	$-0.558817\pi$
$419$	−153.966			−0.367462			−0.183731	+	0.982977i	$0.558817\pi$
$420$		0			0
$421$	25.0783	−	18.2205i	0.0595685	−	0.0432790i	−0.557603	−	0.830108i	$-0.688279\pi$
$421$	25.0783	−	18.2205i	0.0595685	−	0.0432790i	0.617171	+	0.786829i	$0.288279\pi$
$422$		0			0
$423$	−51.2743	−	157.806i	−0.121216	−	0.373064i
$424$		0			0
$425$	−5.73658	+	7.89573i	−0.0134978	+	0.0185782i
$426$		0			0
$427$	−15.3269	+	47.1713i	−0.0358944	+	0.110471i
$428$		0			0
$429$	−1.88849	−	0.195243i	−0.00440208	−	0.000455113i
$430$		0			0
$431$	−144.999	−	47.1132i	−0.336426	−	0.109311i	0.135932	−	0.990718i	$-0.456597\pi$
$431$	−144.999	−	47.1132i	−0.336426	−	0.109311i	−0.472358	+	0.881407i	$0.656597\pi$
$432$		0			0
$433$	277.657	+	201.730i	0.641241	+	0.465889i	0.860276	−	0.509828i	$-0.170291\pi$
$433$	277.657	+	201.730i	0.641241	+	0.465889i	−0.219035	+	0.975717i	$0.570291\pi$
$434$		0			0
$435$	−3.05437	+	0.992424i	−0.00702153	+	0.00228143i
$436$		0			0
$437$	−502.509	−	691.645i	−1.14991	−	1.58271i
$438$		0			0
$439$		−	316.830i		−	0.721709i	−0.932622	−	0.360854i	$-0.882485\pi$
$439$		−	316.830i		−	0.721709i	0.932622	−	0.360854i	$-0.117515\pi$
$440$		0			0
$441$	62.9968			0.142850
$442$		0			0
$443$	−145.891	+	105.996i	−0.329325	+	0.239268i	−0.740144	−	0.672448i	$-0.765243\pi$
$443$	−145.891	+	105.996i	−0.329325	+	0.239268i	0.410819	+	0.911717i	$0.365243\pi$
$444$		0			0
$445$	142.753	+	439.350i	0.320794	+	0.987302i
$446$		0			0
$447$	0.181205	−	0.249407i	0.000405381	−	0.000557958i
$448$		0			0
$449$	223.957	−	689.270i	0.498792	−	1.53512i	−0.312172	−	0.950026i	$-0.601056\pi$
$449$	223.957	−	689.270i	0.498792	−	1.53512i	0.810963	−	0.585097i	$-0.198944\pi$
$450$		0			0
$451$	137.633	+	642.145i	0.305174	+	1.42382i
$452$		0			0
$453$	2.89490	+	0.940610i	0.00639051	+	0.00207640i
$454$		0			0
$455$	−84.5079	−	61.3986i	−0.185732	−	0.134942i
$456$		0			0
$457$	340.737	−	110.712i	0.745595	−	0.242258i	0.0885102	−	0.996075i	$-0.471789\pi$
$457$	340.737	−	110.712i	0.745595	−	0.242258i	0.657085	+	0.753817i	$0.271789\pi$
$458$		0			0
$459$	2.06371	+	2.84046i	0.00449611	+	0.00618836i
$460$		0			0
$461$			391.405i			0.849035i	0.905420	+	0.424518i	$0.139556\pi$
$461$			391.405i			0.849035i	−0.905420	+	0.424518i	$0.860444\pi$
$462$		0			0
$463$	−611.982			−1.32178			−0.660888	−	0.750485i	$-0.729820\pi$
$463$	−611.982			−1.32178			−0.660888	+	0.750485i	$0.729820\pi$
$464$		0			0
$465$	−3.70980	+	2.69533i	−0.00797807	+	0.00579640i
$466$		0			0
$467$	−126.406	−	389.038i	−0.270677	−	0.833058i	−0.990331	−	0.138725i	$-0.955699\pi$
$467$	−126.406	−	389.038i	−0.270677	−	0.833058i	0.719654	−	0.694333i	$-0.244301\pi$
$468$		0			0
$469$	−163.220	+	224.653i	−0.348017	+	0.479004i
$470$		0			0
$471$	1.70248	−	5.23970i	0.00361461	−	0.0111246i
$472$		0			0
$473$	−260.590	+	587.983i	−0.550931	+	1.24309i
$474$		0			0
$475$	30.2808	+	9.83882i	0.0637490	+	0.0207133i
$476$		0			0
$477$	−271.802	−	197.476i	−0.569816	−	0.413996i
$478$		0			0
$479$	−178.314	+	57.9378i	−0.372264	+	0.120956i	−0.489173	−	0.872187i	$-0.662701\pi$
$479$	−178.314	+	57.9378i	−0.372264	+	0.120956i	0.116909	+	0.993143i	$0.462701\pi$
$480$		0			0
$481$	254.101	+	349.740i	0.528276	+	0.727110i
$482$		0			0
$483$			1.62556i			0.00336554i
$484$		0			0
$485$	20.0037			0.0412447
$486$		0			0
$487$	−433.284	+	314.799i	−0.889699	+	0.646404i	−0.935800	−	0.352532i	$-0.885321\pi$
$487$	−433.284	+	314.799i	−0.889699	+	0.646404i	0.0461003	+	0.998937i	$0.485321\pi$
$488$		0			0
$489$	−1.76675	−	5.43750i	−0.00361299	−	0.0111196i
$490$		0			0
$491$	−187.118	+	257.546i	−0.381096	+	0.524534i	−0.955875	−	0.293775i	$-0.905088\pi$
$491$	−187.118	+	257.546i	−0.381096	+	0.524534i	0.574778	+	0.818309i	$0.305088\pi$
$492$		0			0
$493$	86.5311	−	266.315i	0.175519	−	0.540193i
$494$		0			0
$495$	−442.734	−	196.217i	−0.894412	−	0.396397i
$496$		0			0
$497$	190.706	+	61.9643i	0.383715	+	0.124677i
$498$		0			0
$499$	−116.404	−	84.5726i	−0.233275	−	0.169484i	0.465007	−	0.885307i	$-0.346052\pi$
$499$	−116.404	−	84.5726i	−0.233275	−	0.169484i	−0.698282	+	0.715823i	$0.746052\pi$
$500$		0			0
$501$	−1.84058	+	0.598039i	−0.00367380	+	0.00119369i
$502$		0			0
$503$	6.24347	+	8.59340i	0.0124125	+	0.0170843i	0.815178	−	0.579210i	$-0.196639\pi$
$503$	6.24347	+	8.59340i	0.0124125	+	0.0170843i	−0.802766	+	0.596295i	$0.796639\pi$
$504$		0			0
$505$			35.9182i			0.0711252i
$506$		0			0
$507$	2.22109			0.00438084
$508$		0			0
$509$	698.186	−	507.262i	1.37168	−	0.996585i	0.374079	−	0.927397i	$-0.377959\pi$
$509$	698.186	−	507.262i	1.37168	−	0.996585i	0.997604	−	0.0691885i	$-0.0220410\pi$
$510$		0			0
$511$	−74.0793	−	227.993i	−0.144969	−	0.446170i
$512$		0			0
$513$	6.73249	−	9.26647i	0.0131238	−	0.0180633i
$514$		0			0
$515$	−5.74682	+	17.6869i	−0.0111589	+	0.0343435i
$516$		0			0
$517$	198.306	−	42.5037i	0.383571	−	0.0822122i
$518$		0			0
$519$	5.14558	+	1.67190i	0.00991441	+	0.00322139i
$520$		0			0
$521$	−389.415	−	282.926i	−0.747437	−	0.543045i	0.147595	−	0.989048i	$-0.452847\pi$
$521$	−389.415	−	282.926i	−0.747437	−	0.543045i	−0.895031	+	0.446003i	$0.852847\pi$
$522$		0			0
$523$	−335.043	+	108.862i	−0.640617	+	0.208149i	−0.611272	−	0.791420i	$-0.709342\pi$
$523$	−335.043	+	108.862i	−0.640617	+	0.208149i	−0.0293446	+	0.999569i	$0.509342\pi$
$524$		0			0
$525$	−0.0355841	−	0.0489773i	−6.77792e−5	−	9.32901e-5i
$526$		0			0
$527$		−	399.823i		−	0.758678i
$528$		0			0
$529$	296.436			0.560370
$530$		0			0
$531$	−186.857	+	135.760i	−0.351897	+	0.255668i
$532$		0			0
$533$	148.900	+	458.268i	0.279362	+	0.859789i
$534$		0			0
$535$	6.65842	−	9.16453i	0.0124456	−	0.0171300i
$536$		0			0
$537$	1.35628	−	4.17419i	0.00252566	−	0.00777317i
$538$		0			0
$539$	−7.91851	+	76.5918i	−0.0146911	+	0.142100i
$540$		0			0
$541$	−102.933	−	33.4449i	−0.190264	−	0.0618206i	0.212335	−	0.977197i	$-0.431893\pi$
$541$	−102.933	−	33.4449i	−0.190264	−	0.0618206i	−0.402599	+	0.915376i	$0.631893\pi$
$542$		0			0
$543$	−3.42579	−	2.48898i	−0.00630901	−	0.00458376i
$544$		0			0
$545$	−504.506	+	163.924i	−0.925700	+	0.300778i
$546$		0			0
$547$	495.898	+	682.545i	0.906578	+	1.24780i	0.968322	+	0.249706i	$0.0803339\pi$
$547$	495.898	+	682.545i	0.906578	+	1.24780i	−0.0617437	+	0.998092i	$0.519666\pi$
$548$		0			0
$549$			168.711i			0.307306i
$550$		0			0
$551$	−913.515			−1.65792
$552$		0			0
$553$	−247.947	+	180.144i	−0.448367	+	0.325758i
$554$		0			0
$555$	−1.73154	−	5.32914i	−0.00311990	−	0.00960206i
$556$		0			0
$557$	−196.566	+	270.550i	−0.352901	+	0.485727i	−0.948154	−	0.317812i	$-0.897052\pi$
$557$	−196.566	+	270.550i	−0.352901	+	0.485727i	0.595252	+	0.803539i	$0.297052\pi$
$558$		0			0
$559$	−145.820	+	448.787i	−0.260858	+	0.802838i
$560$		0			0
$561$	−1.85637	+	1.07599i	−0.00330905	+	0.00191799i
$562$		0			0
$563$	−91.5902	−	29.7595i	−0.162682	−	0.0528587i	0.226544	−	0.974001i	$-0.427257\pi$
$563$	−91.5902	−	29.7595i	−0.162682	−	0.0528587i	−0.389226	+	0.921142i	$0.627257\pi$
$564$		0			0
$565$	−596.693	−	433.523i	−1.05609	−	0.767297i
$566$		0			0
$567$	203.786	−	66.2141i	0.359411	−	0.116780i
$568$		0			0
$569$	108.984	+	150.004i	0.191536	+	0.263627i	0.893975	−	0.448117i	$-0.147905\pi$
$569$	108.984	+	150.004i	0.191536	+	0.263627i	−0.702438	+	0.711745i	$0.747905\pi$
$570$		0			0
$571$		−	305.886i		−	0.535703i	−0.963460	−	0.267851i	$-0.913686\pi$
$571$		−	305.886i		−	0.535703i	0.963460	−	0.267851i	$-0.0863136\pi$
$572$		0			0
$573$	−3.04731			−0.00531816
$574$		0			0
$575$	−24.8700	+	18.0691i	−0.0432522	+	0.0314246i
$576$		0			0
$577$	−278.651	−	857.599i	−0.482931	−	1.48631i	−0.834956	−	0.550317i	$-0.814507\pi$
$577$	−278.651	−	857.599i	−0.482931	−	1.48631i	0.352025	−	0.935991i	$-0.385493\pi$
$578$		0			0
$579$	0.795942	−	1.09552i	0.00137468	−	0.00189209i
$580$		0			0
$581$	−106.484	+	327.723i	−0.183276	+	0.564067i
$582$		0			0
$583$	274.257	−	305.636i	0.470424	−	0.524248i
$584$		0			0
$585$	−337.923	−	109.798i	−0.577646	−	0.187689i
$586$		0			0
$587$	443.662	+	322.340i	0.755813	+	0.549131i	0.897623	−	0.440763i	$-0.145292\pi$
$587$	443.662	+	322.340i	0.755813	+	0.549131i	−0.141810	+	0.989894i	$0.545292\pi$
$588$		0			0
$589$	−1240.51	+	403.066i	−2.10613	+	0.684323i
$590$		0			0
$591$	3.86491	+	5.31960i	0.00653962	+	0.00900101i
$592$		0			0
$593$			448.881i			0.756966i	0.925608	+	0.378483i	$0.123554\pi$
$593$			448.881i			0.756966i	−0.925608	+	0.378483i	$0.876446\pi$
$594$		0			0
$595$	−118.053			−0.198409
$596$		0			0
$597$	−0.215332	+	0.156448i	−0.000360690	+	0.000262057i
$598$		0			0
$599$	187.517	+	577.117i	0.313050	+	0.963468i	0.976550	+	0.215291i	$0.0690702\pi$
$599$	187.517	+	577.117i	0.313050	+	0.963468i	−0.663500	+	0.748176i	$0.730930\pi$
$600$		0			0
$601$	−475.686	+	654.726i	−0.791491	+	1.08939i	0.202429	+	0.979297i	$0.435116\pi$
$601$	−475.686	+	654.726i	−0.791491	+	1.08939i	−0.993921	+	0.110097i	$0.964884\pi$
$602$		0			0
$603$	−291.883	+	898.323i	−0.484051	+	1.48976i
$604$		0			0
$605$	294.211	−	513.614i	0.486300	−	0.848948i
$606$		0			0
$607$	−425.849	−	138.367i	−0.701564	−	0.227952i	−0.0635521	−	0.997979i	$-0.520243\pi$
$607$	−425.849	−	138.367i	−0.701564	−	0.227952i	−0.638012	+	0.770027i	$0.720243\pi$
$608$		0			0
$609$	1.40524	+	1.02097i	0.00230745	+	0.00167646i
$610$		0			0
$611$	141.522	−	45.9831i	0.231623	−	0.0752588i
$612$		0			0
$613$	−325.002	−	447.327i	−0.530183	−	0.729734i	0.456976	−	0.889479i	$-0.348933\pi$
$613$	−325.002	−	447.327i	−0.530183	−	0.729734i	−0.987158	+	0.159745i	$0.948933\pi$
$614$		0			0
$615$		−	6.24563i		−	0.0101555i
$616$		0			0
$617$	680.061			1.10221			0.551103	−	0.834437i	$-0.314207\pi$
$617$	680.061			1.10221			0.551103	+	0.834437i	$0.314207\pi$
$618$		0			0
$619$	666.583	−	484.301i	1.07687	−	0.782393i	0.0997367	−	0.995014i	$-0.468200\pi$
$619$	666.583	−	484.301i	1.07687	−	0.782393i	0.977135	+	0.212621i	$0.0682000\pi$
$620$		0			0
$621$	3.41741	+	10.5177i	0.00550307	+	0.0169367i
$622$		0			0
$623$	146.859	−	202.134i	0.235728	−	0.324452i
$624$		0			0
$625$	−184.516	+	567.881i	−0.295225	+	0.908610i
$626$		0			0
$627$	5.20985	+	4.67496i	0.00830917	+	0.00745607i
$628$		0			0
$629$	464.657	+	150.976i	0.738723	+	0.240026i
$630$		0			0
$631$	−232.276	−	168.758i	−0.368108	−	0.267446i	0.388318	−	0.921525i	$-0.373056\pi$
$631$	−232.276	−	168.758i	−0.368108	−	0.267446i	−0.756426	+	0.654079i	$0.773056\pi$
$632$		0			0
$633$	2.00432	−	0.651242i	0.00316638	−	0.00102882i
$634$		0			0
$635$	412.428	+	567.659i	0.649493	+	0.893951i
$636$		0			0
$637$			56.4960i			0.0886907i
$638$		0			0
$639$	682.072			1.06741
$640$		0			0
$641$	−655.359	+	476.146i	−1.02240	+	0.742817i	−0.966774	−	0.255634i	$-0.917716\pi$
$641$	−655.359	+	476.146i	−1.02240	+	0.742817i	−0.0556268	+	0.998452i	$0.517716\pi$
$642$		0			0
$643$	−86.0697	−	264.895i	−0.133856	−	0.411968i	0.861554	−	0.507666i	$-0.169492\pi$
$643$	−86.0697	−	264.895i	−0.133856	−	0.411968i	−0.995410	+	0.0956983i	$0.969492\pi$
$644$		0			0
$645$	3.59514	−	4.94829i	0.00557386	−	0.00767176i
$646$		0			0
$647$	209.379	−	644.403i	0.323615	−	0.995986i	−0.648446	−	0.761260i	$-0.724581\pi$
$647$	209.379	−	644.403i	0.323615	−	0.995986i	0.972062	−	0.234725i	$-0.0754191\pi$
$648$		0			0
$649$	−141.570	−	244.246i	−0.218135	−	0.376343i
$650$		0			0
$651$	2.35872	+	0.766395i	0.00362323	+	0.00117726i
$652$		0			0
$653$	530.559	+	385.474i	0.812495	+	0.590312i	0.914553	−	0.404466i	$-0.132543\pi$
$653$	530.559	+	385.474i	0.812495	+	0.590312i	−0.102058	+	0.994778i	$0.532543\pi$
$654$		0			0
$655$	807.031	−	262.220i	1.23211	−	0.400336i
$656$		0			0
$657$	−479.297	−	659.696i	−0.729523	−	1.00410i
$658$		0			0
$659$			534.031i			0.810365i	0.914236	+	0.405183i	$0.132792\pi$
$659$			534.031i			0.810365i	−0.914236	+	0.405183i	$0.867208\pi$
$660$		0			0
$661$	−164.075			−0.248223			−0.124111	−	0.992268i	$-0.539608\pi$
$661$	−164.075			−0.248223			−0.124111	+	0.992268i	$0.539608\pi$
$662$		0			0
$663$	−1.27364	+	0.925353i	−0.00192102	+	0.00139571i
$664$		0			0
$665$	119.011	+	366.278i	0.178964	+	0.550794i
$666$		0			0
$667$	518.432	−	713.561i	0.777260	−	1.06981i
$668$		0			0
$669$	1.62150	−	4.99047i	0.00242377	−	0.00745960i
$670$		0			0
$671$	−205.119	−	21.2065i	−0.305692	−	0.0316043i
$672$		0			0
$673$	−732.973	−	238.157i	−1.08911	−	0.353874i	−0.291209	−	0.956659i	$-0.594058\pi$
$673$	−732.973	−	238.157i	−1.08911	−	0.353874i	−0.797903	+	0.602785i	$0.794058\pi$
$674$		0			0
$675$	−0.333202	−	0.242085i	−0.000493632	−	0.000358645i
$676$		0			0
$677$	294.475	−	95.6808i	0.434971	−	0.141331i	−0.0833434	−	0.996521i	$-0.526560\pi$
$677$	294.475	−	95.6808i	0.434971	−	0.141331i	0.518314	+	0.855190i	$0.326560\pi$
$678$		0			0
$679$	−6.35925	−	8.75276i	−0.00936561	−	0.0128907i
$680$		0			0
$681$			2.81795i			0.00413796i
$682$		0			0
$683$	454.159			0.664947			0.332473	−	0.943113i	$-0.392117\pi$
$683$	454.159			0.664947			0.332473	+	0.943113i	$0.392117\pi$
$684$		0			0
$685$	−91.8296	+	66.7181i	−0.134058	+	0.0973987i
$686$		0			0
$687$	−2.29352	−	7.05873i	−0.00333846	−	0.0102747i
$688$		0			0
$689$	177.098	−	243.754i	0.257036	−	0.353780i
$690$		0			0
$691$	111.747	−	343.922i	0.161718	−	0.497716i	−0.837062	−	0.547109i	$-0.815728\pi$
$691$	111.747	−	343.922i	0.161718	−	0.497716i	0.998779	+	0.0493922i	$0.0157284\pi$
$692$		0			0
$693$	54.8908	+	256.100i	0.0792075	+	0.369552i
$694$		0			0
$695$	−903.504	−	293.566i	−1.30001	−	0.422397i
$696$		0			0
$697$	440.564	+	320.089i	0.632086	+	0.459237i
$698$		0			0
$699$	0.692160	−	0.224896i	0.000990214	−	0.000321740i
$700$		0			0
$701$	419.633	+	577.575i	0.598620	+	0.823930i	0.995581	−	0.0939053i	$-0.0299351\pi$
$701$	419.633	+	577.575i	0.598620	+	0.823930i	−0.396961	+	0.917836i	$0.629935\pi$
$702$		0			0
$703$		−	1593.87i		−	2.26724i
$704$		0			0
$705$	−1.92877			−0.00273584
$706$		0			0
$707$	15.7163	−	11.4186i	0.0222296	−	0.0161507i
$708$		0			0
$709$	−271.037	−	834.165i	−0.382280	−	1.17654i	−0.938434	−	0.345458i	$-0.887724\pi$
$709$	−271.037	−	834.165i	−0.382280	−	1.17654i	0.556154	−	0.831079i	$-0.312276\pi$
$710$		0			0
$711$	−612.761	+	843.393i	−0.861830	+	1.18621i
$712$		0			0
$713$	389.165	−	1197.73i	0.545814	−	1.67984i
$714$		0			0
$715$	175.969	−	397.047i	0.246110	−	0.555310i
$716$		0			0
$717$	6.24065	+	2.02771i	0.00870383	+	0.00282805i
$718$		0			0
$719$	193.899	+	140.876i	0.269679	+	0.195933i	0.714403	−	0.699735i	$-0.246698\pi$
$719$	193.899	+	140.876i	0.269679	+	0.195933i	−0.444724	+	0.895667i	$0.646698\pi$
$720$		0			0
$721$	9.56597	−	3.10817i	0.0132676	−	0.00431092i
$722$		0			0
$723$	−3.36618	−	4.63315i	−0.00465585	−	0.00640823i
$724$		0			0
$725$			32.8480i			0.0453076i
$726$		0			0
$727$	54.6726			0.0752030			0.0376015	−	0.999293i	$-0.488028\pi$
$727$	54.6726			0.0752030			0.0376015	+	0.999293i	$0.488028\pi$
$728$		0			0
$729$	589.594	−	428.365i	0.808770	−	0.587606i
$730$		0			0
$731$	164.799	+	507.199i	0.225443	+	0.693843i
$732$		0			0
$733$	766.485	−	1054.98i	1.04568	−	1.43926i	0.153190	−	0.988197i	$-0.451045\pi$
$733$	766.485	−	1054.98i	1.04568	−	1.43926i	0.892493	−	0.451062i	$-0.148955\pi$
$734$		0			0
$735$	0.226289	−	0.696446i	0.000307876	−	0.000947545i
$736$		0			0
$737$	−1055.50	−	467.789i	−1.43215	−	0.634720i
$738$		0			0
$739$	991.274	+	322.085i	1.34137	+	0.435838i	0.889782	−	0.456387i	$-0.150857\pi$
$739$	991.274	+	322.085i	1.34137	+	0.435838i	0.451591	+	0.892225i	$0.350857\pi$
$740$		0			0
$741$	4.15501	+	3.01879i	0.00560730	+	0.00407394i
$742$		0			0
$743$	−91.6963	+	29.7939i	−0.123414	+	0.0400995i	−0.370073	−	0.929003i	$-0.620667\pi$
$743$	−91.6963	+	29.7939i	−0.123414	+	0.0400995i	0.246659	+	0.969102i	$0.420667\pi$
$744$		0			0
$745$	41.4506	+	57.0518i	0.0556384	+	0.0765796i
$746$		0			0
$747$			1172.12i			1.56910i
$748$		0			0
$749$	−6.12675			−0.00817990
$750$		0			0
$751$	−648.247	+	470.979i	−0.863179	+	0.627136i	−0.928748	−	0.370712i	$-0.879114\pi$
$751$	−648.247	+	470.979i	−0.863179	+	0.627136i	0.0655690	+	0.997848i	$0.479114\pi$
$752$		0			0
$753$	−2.75747	−	8.48662i	−0.00366198	−	0.0112704i
$754$		0			0
$755$	−409.266	+	563.307i	−0.542075	+	0.746102i
$756$		0			0
$757$	16.2614	−	50.0475i	0.0214814	−	0.0661130i	−0.939741	−	0.341887i	$-0.888934\pi$
$757$	16.2614	−	50.0475i	0.0214814	−	0.0661130i	0.961223	+	0.275774i	$0.0889341\pi$
$758$		0			0
$759$	−6.60834	+	1.41639i	−0.00870664	+	0.00186613i
$760$		0			0
$761$	740.143	+	240.487i	0.972593	+	0.316015i	0.751862	−	0.659320i	$-0.229156\pi$
$761$	740.143	+	240.487i	0.972593	+	0.316015i	0.220731	+	0.975335i	$0.429156\pi$
$762$		0			0
$763$	232.111	+	168.638i	0.304208	+	0.221020i
$764$		0			0
$765$	−381.906	+	124.089i	−0.499223	+	0.162207i
$766$		0			0
$767$	−121.750	−	167.575i	−0.158736	−	0.218481i
$768$		0			0
$769$			286.598i			0.372689i	0.982484	+	0.186345i	$0.0596641\pi$
$769$			286.598i			0.372689i	−0.982484	+	0.186345i	$0.940336\pi$
$770$		0			0
$771$	−2.57866			−0.00334456
$772$		0			0
$773$	−371.798	+	270.127i	−0.480981	+	0.349453i	−0.801705	−	0.597720i	$-0.796074\pi$
$773$	−371.798	+	270.127i	−0.480981	+	0.349453i	0.320725	+	0.947172i	$0.396074\pi$
$774$		0			0
$775$	14.4934	+	44.6060i	0.0187011	+	0.0575561i
$776$		0			0
$777$	−1.78134	+	2.45181i	−0.00229259	+	0.00315548i
$778$		0			0
$779$	548.984	−	1689.60i	0.704729	−	2.16893i
$780$		0			0
$781$	−85.7345	+	829.266i	−0.109775	+	1.06180i
$782$		0			0
$783$	11.2386	+	3.65163i	0.0143532	+	0.00466364i
$784$		0			0
$785$	1019.57	+	740.763i	1.29882	+	0.943647i
$786$		0			0
$787$	1403.88	−	456.148i	1.78384	−	0.579604i	0.784652	−	0.619937i	$-0.212842\pi$
$787$	1403.88	−	456.148i	1.78384	−	0.579604i	0.999186	+	0.0403324i	$0.0128417\pi$
$788$		0			0
$789$	1.55529	+	2.14067i	0.00197122	+	0.00271315i
$790$		0			0
$791$			398.906i			0.504306i
$792$		0			0
$793$	−151.301			−0.190796
$794$		0			0
$795$	−3.15948	+	2.29550i	−0.00397419	+	0.00288742i
$796$		0			0
$797$	145.191	+	446.853i	0.182172	+	0.560669i	0.999888	−	0.0149534i	$-0.00475999\pi$
$797$	145.191	+	446.853i	0.182172	+	0.560669i	−0.817716	+	0.575622i	$0.804760\pi$
$798$		0			0
$799$	98.8493	−	136.054i	0.123716	−	0.170281i
$800$		0			0
$801$	262.624	−	808.275i	0.327871	−	1.00908i
$802$		0			0
$803$	862.307	−	499.809i	1.07386	−	0.622428i
$804$		0			0
$805$	−353.646	−	114.906i	−0.439312	−	0.142741i
$806$		0			0
$807$	−8.06665	−	5.86077i	−0.00999585	−	0.00726241i
$808$		0			0
$809$	−965.758	+	313.794i	−1.19377	+	0.387879i	−0.837464	−	0.546492i	$-0.815963\pi$
$809$	−965.758	+	313.794i	−1.19377	+	0.387879i	−0.356303	+	0.934370i	$0.615963\pi$
$810$		0			0
$811$	288.583	+	397.200i	0.355835	+	0.489765i	0.948983	−	0.315329i	$-0.102115\pi$
$811$	288.583	+	397.200i	0.355835	+	0.489765i	−0.593147	+	0.805094i	$0.702115\pi$
$812$		0			0
$813$		−	1.36697i		−	0.00168139i
$814$		0			0
$815$	1307.84			1.60471
$816$		0			0
$817$	1407.52	−	1022.63i	1.72280	−	1.25168i
$818$		0			0
$819$	59.3842	+	182.766i	0.0725082	+	0.223157i
$820$		0			0
$821$	196.280	−	270.156i	0.239074	−	0.329057i	−0.672573	−	0.740030i	$-0.734811\pi$
$821$	196.280	−	270.156i	0.239074	−	0.329057i	0.911647	+	0.410973i	$0.134811\pi$
$822$		0			0
$823$	276.825	−	851.978i	0.336360	−	1.03521i	−0.629688	−	0.776848i	$-0.716817\pi$
$823$	276.825	−	851.978i	0.336360	−	1.03521i	0.966048	−	0.258362i	$-0.0831829\pi$
$824$		0			0
$825$	0.168101	−	0.187335i	0.000203759	−	0.000227072i
$826$		0			0
$827$	−992.063	−	322.341i	−1.19959	−	0.389771i	−0.359982	−	0.932959i	$-0.617217\pi$
$827$	−992.063	−	322.341i	−1.19959	−	0.389771i	−0.839611	+	0.543188i	$0.817217\pi$
$828$		0			0
$829$	440.732	+	320.211i	0.531644	+	0.386262i	0.820972	−	0.570968i	$-0.193432\pi$
$829$	440.732	+	320.211i	0.531644	+	0.386262i	−0.289329	+	0.957230i	$0.593432\pi$
$830$		0			0
$831$	−2.79278	+	0.907429i	−0.00336075	+	0.00109197i
$832$		0			0
$833$	37.5297	+	51.6552i	0.0450536	+	0.0620110i
$834$		0			0
$835$		−	442.698i		−	0.530177i
$836$		0			0
$837$	16.8726			0.0201585
$838$		0			0
$839$	−9.98274	+	7.25288i	−0.0118984	+	0.00864468i	−0.593719	−	0.804673i	$-0.702341\pi$
$839$	−9.98274	+	7.25288i	−0.0118984	+	0.00864468i	0.581820	+	0.813317i	$0.302341\pi$
$840$		0			0
$841$	−31.3534	−	96.4960i	−0.0372811	−	0.114740i
$842$		0			0
$843$	4.94011	−	6.79948i	0.00586015	−	0.00806581i
$844$		0			0
$845$	−157.003	+	483.205i	−0.185802	+	0.571841i
$846$		0			0
$847$	−318.267	+	34.5455i	−0.375757	+	0.0407857i
$848$		0			0
$849$	−6.62875	−	2.15381i	−0.00780772	−	0.00253688i
$850$		0			0
$851$	1244.99	+	904.541i	1.46298	+	1.06292i
$852$		0			0
$853$	829.521	−	269.528i	0.972475	−	0.315976i	0.220660	−	0.975351i	$-0.429179\pi$
$853$	829.521	−	269.528i	0.972475	−	0.315976i	0.751815	+	0.659375i	$0.229179\pi$
$854$		0			0
$855$	770.007	+	1059.82i	0.900593	+	1.23956i
$856$		0			0
$857$			278.728i			0.325237i	0.986689	+	0.162618i	$0.0519939\pi$
$857$			278.728i			0.325237i	−0.986689	+	0.162618i	$0.948006\pi$
$858$		0			0
$859$	−1497.62			−1.74344			−0.871720	−	0.490004i	$-0.836995\pi$
$859$	−1497.62			−1.74344			−0.871720	+	0.490004i	$0.836995\pi$
$860$		0			0
$861$	−2.73282	+	1.98551i	−0.00317401	+	0.00230605i
$862$		0			0
$863$	302.550	+	931.153i	0.350579	+	1.07897i	0.958529	+	0.284996i	$0.0919924\pi$
$863$	302.550	+	931.153i	0.350579	+	1.07897i	−0.607949	+	0.793976i	$0.708008\pi$
$864$		0			0
$865$	−727.456	+	1001.26i	−0.840989	+	1.15752i
$866$		0			0
$867$	1.36001	−	4.18568i	0.00156864	−	0.00482777i
$868$		0			0
$869$	−948.379	−	851.009i	−1.09134	−	0.979297i
$870$		0			0
$871$	−805.622	−	261.763i	−0.924939	−	0.300531i
$872$		0			0
$873$	−29.7726	−	21.6310i	−0.0341037	−	0.0247778i
$874$		0			0
$875$	320.898	−	104.266i	0.366741	−	0.119161i
$876$		0			0
$877$	−806.843	−	1110.52i	−0.920003	−	1.26628i	−0.963633	−	0.267228i	$-0.913892\pi$
$877$	−806.843	−	1110.52i	−0.920003	−	1.26628i	0.0436302	−	0.999048i	$-0.486108\pi$
$878$		0			0
$879$			9.79224i			0.0111402i
$880$		0			0
$881$	−1667.11			−1.89230			−0.946149	−	0.323732i	$-0.895062\pi$
$881$	−1667.11			−1.89230			−0.946149	+	0.323732i	$0.895062\pi$
$882$		0			0
$883$	−337.680	+	245.339i	−0.382423	+	0.277847i	−0.762344	−	0.647172i	$-0.775951\pi$
$883$	−337.680	+	245.339i	−0.382423	+	0.277847i	0.379920	+	0.925019i	$0.375951\pi$
$884$		0			0
$885$	0.829654	+	2.55341i	0.000937462	+	0.00288521i
$886$		0			0
$887$	550.826	−	758.147i	0.620999	−	0.854732i	−0.376426	−	0.926447i	$-0.622847\pi$
$887$	550.826	−	758.147i	0.620999	−	0.854732i	0.997425	+	0.0717150i	$0.0228472\pi$
$888$		0			0
$889$	117.271	−	360.922i	0.131913	−	0.405987i
$890$		0			0
$891$	446.743	+	770.753i	0.501395	+	0.865042i
$892$		0			0
$893$	−521.780	−	169.536i	−0.584300	−	0.189850i
$894$		0			0
$895$	812.239	+	590.126i	0.907529	+	0.659359i
$896$		0			0
$897$	−4.71605	+	1.53234i	−0.00525758	+	0.00170829i
$898$		0			0
$899$	−790.971	−	1088.68i	−0.879834	−	1.21099i
$900$		0			0
$901$		−	340.513i		−	0.377928i
$902$		0			0
$903$	−3.30807			−0.00366342
$904$		0			0
$905$	783.648	−	569.354i	0.865910	−	0.629120i
$906$		0			0
$907$	−279.541	−	860.338i	−0.308204	−	0.948554i	−0.978462	−	0.206426i	$-0.933817\pi$
$907$	−279.541	−	860.338i	−0.308204	−	0.948554i	0.670258	−	0.742128i	$-0.266183\pi$
$908$		0			0
$909$	38.8403	−	53.4591i	0.0427286	−	0.0588109i
$910$		0			0
$911$	−349.771	+	1076.48i	−0.383941	+	1.18165i	0.553304	+	0.832979i	$0.313367\pi$
$911$	−349.771	+	1076.48i	−0.383941	+	1.18165i	−0.937245	+	0.348671i	$0.886633\pi$
$912$		0			0
$913$	−1425.07	−	147.332i	−1.56086	−	0.161371i
$914$		0			0
$915$	1.86514	+	0.606021i	0.00203841	+	0.000662319i
$916$		0			0
$917$	−371.295	−	269.762i	−0.404902	−	0.294178i
$918$		0			0
$919$	1092.31	−	354.913i	1.18858	−	0.386194i	0.353035	−	0.935610i	$-0.385150\pi$
$919$	1092.31	−	354.913i	1.18858	−	0.386194i	0.835549	+	0.549416i	$0.185150\pi$
$920$		0			0
$921$	0.0651817	+	0.0897150i	7.07728e−5	+	9.74104e-5i
$922$		0			0
$923$			611.687i			0.662716i
$924$		0			0
$925$	−57.3119			−0.0619588
$926$		0			0
$927$	27.6791	−	20.1100i	0.0298588	−	0.0216937i
$928$		0			0
$929$	−423.408	−	1303.12i	−0.455767	−	1.40271i	−0.870232	−	0.492642i	$-0.836031\pi$
$929$	−423.408	−	1303.12i	−0.455767	−	1.40271i	0.414465	−	0.910065i	$-0.363969\pi$
$930$		0			0
$931$	122.434	−	168.515i	0.131508	−	0.181005i
$932$		0			0
$933$	0.139552	−	0.429498i	0.000149574	−	0.000460341i
$934$		0			0
$935$	−102.863	−	479.920i	−0.110014	−	0.513284i
$936$		0			0
$937$	374.440	+	121.663i	0.399616	+	0.129843i	0.501928	−	0.864909i	$-0.332624\pi$
$937$	374.440	+	121.663i	0.399616	+	0.129843i	−0.102312	+	0.994752i	$0.532624\pi$
$938$		0			0
$939$	5.27220	+	3.83048i	0.00561469	+	0.00407931i
$940$		0			0
$941$	−306.198	+	99.4897i	−0.325396	+	0.105728i	−0.467160	−	0.884173i	$-0.654723\pi$
$941$	−306.198	+	99.4897i	−0.325396	+	0.105728i	0.141764	+	0.989901i	$0.454723\pi$
$942$		0			0
$943$	1008.22	+	1387.69i	1.06916	+	1.47157i
$944$		0			0
$945$		−	4.98188i		−	0.00527183i
$946$		0			0
$947$	−523.400			−0.552693			−0.276346	−	0.961058i	$-0.589124\pi$
$947$	−523.400			−0.552693			−0.276346	+	0.961058i	$0.589124\pi$
$948$		0			0
$949$	591.620	−	429.837i	0.623414	−	0.452937i
$950$		0			0
$951$	−0.272418	−	0.838417i	−0.000286454	−	0.000881616i
$952$		0			0
$953$	−35.5658	+	48.9521i	−0.0373198	+	0.0513663i	−0.827269	−	0.561806i	$-0.810107\pi$
$953$	−35.5658	+	48.9521i	−0.0373198	+	0.0513663i	0.789949	+	0.613172i	$0.210107\pi$
$954$		0			0
$955$	215.406	−	662.953i	0.225557	−	0.694192i
$956$		0			0
$957$	−2.92609	+	6.60228i	−0.00305756	+	0.00689894i
$958$		0			0
$959$	58.3860	+	18.9708i	0.0608822	+	0.0197818i
$960$		0			0
$961$	−776.988	−	564.515i	−0.808521	−	0.587425i
$962$		0			0
$963$	−19.8202	+	6.43997i	−0.0205817	+	0.00668740i
$964$		0			0
$965$	182.071	+	250.600i	0.188675	+	0.259689i
$966$		0			0
$967$		−	377.861i		−	0.390756i	−0.980728	−	0.195378i	$-0.937407\pi$
$967$		−	377.861i		−	0.390756i	0.980728	−	0.195378i	$-0.0625933\pi$
$968$		0			0
$969$	5.80435			0.00599004
$970$		0			0
$971$	−1240.21	+	901.068i	−1.27725	+	0.927979i	−0.999466	−	0.0326632i	$-0.989601\pi$
$971$	−1240.21	+	901.068i	−1.27725	+	0.927979i	−0.277788	+	0.960643i	$0.589601\pi$
$972$		0			0
$973$	158.776	+	488.661i	0.163181	+	0.502221i
$974$		0			0
$975$	0.108549	−	0.149405i	0.000111332	−	0.000153236i
$976$		0			0
$977$	329.001	−	1012.56i	0.336746	−	1.03640i	−0.629110	−	0.777316i	$-0.716580\pi$
$977$	329.001	−	1012.56i	0.336746	−	1.03640i	0.965856	−	0.259081i	$-0.0834195\pi$
$978$		0			0
$979$	949.693	+	420.898i	0.970064	+	0.429926i
$980$		0			0
$981$	928.144	+	301.572i	0.946121	+	0.307413i
$982$		0			0
$983$	723.838	+	525.899i	0.736356	+	0.534994i	0.891568	−	0.452887i	$-0.149606\pi$
$983$	723.838	+	525.899i	0.736356	+	0.534994i	−0.155212	+	0.987881i	$0.549606\pi$
$984$		0			0
$985$	−1430.50	+	464.797i	−1.45228	+	0.471876i
$986$		0			0
$987$	0.613163	+	0.843946i	0.000621239	+	0.000855062i
$988$		0			0
$989$			1679.79i			1.69848i
$990$		0			0
$991$	−887.578			−0.895639			−0.447820	−	0.894124i	$-0.647799\pi$
$991$	−887.578			−0.895639			−0.447820	+	0.894124i	$0.647799\pi$
$992$		0			0
$993$	−2.56856	+	1.86617i	−0.00258667	+	0.00187932i
$994$		0			0
$995$	−18.8145	−	57.9052i	−0.0189091	−	0.0581962i
$996$		0			0
$997$	−608.462	+	837.476i	−0.610293	+	0.839996i	−0.996602	−	0.0823735i	$-0.973750\pi$
$997$	−608.462	+	837.476i	−0.610293	+	0.839996i	0.386309	+	0.922370i	$0.373750\pi$
$998$		0			0
$999$	−6.37123	+	19.6086i	−0.00637761	+	0.0196283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.3.r.a.57.6	✓	48
11.6	odd	10	inner	308.3.r.a.281.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.3.r.a.57.6	✓	48	1.1	even	1	trivial
308.3.r.a.281.6	yes	48	11.6	odd	10	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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	308.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0173009 + 0.0125698i) q^{3} +(-1.51166 - 4.65241i) q^{5} +(-1.55513 + 2.14046i) q^{7} +(-2.78101 + 8.55907i) q^{9} +O(q^{10})\)	\(q+(-0.0173009 + 0.0125698i) q^{3} +(-1.51166 - 4.65241i) q^{5} +(-1.55513 + 2.14046i) q^{7} +(-2.78101 + 8.55907i) q^{9} +(-10.0566 - 4.45702i) q^{11} +(-7.67584 - 2.49403i) q^{13} +(0.0846332 + 0.0614896i) q^{15} +(-8.67490 + 2.81864i) q^{17} +(17.4905 + 24.0736i) q^{19} -0.0565797i q^{21} -28.7304 q^{23} +(0.865634 - 0.628920i) q^{25} +(-0.118947 - 0.366083i) q^{27} +(-18.0447 + 24.8365i) q^{29} +(-13.5454 + 41.6885i) q^{31} +(0.230012 - 0.0492994i) q^{33} +(12.3091 + 3.99947i) q^{35} +(-43.3337 - 31.4838i) q^{37} +(0.164149 - 0.0533351i) q^{39} +(-35.0923 - 48.3004i) q^{41} -58.4675i q^{43} +44.0242 q^{45} +(-14.9161 + 10.8372i) q^{47} +(-2.16312 - 6.65740i) q^{49} +(0.114654 - 0.157807i) q^{51} +(-11.5361 + 35.5044i) q^{53} +(-5.53372 + 53.5249i) q^{55} +(-0.605204 - 0.196643i) q^{57} +(20.7630 + 15.0852i) q^{59} +(17.8291 - 5.79302i) q^{61} +(-13.9955 - 19.2631i) q^{63} +39.4812i q^{65} +104.956 q^{67} +(0.497062 - 0.361137i) q^{69} +(-23.4203 - 72.0803i) q^{71} +(-53.2579 + 73.3032i) q^{73} +(-0.00707083 + 0.0217618i) q^{75} +(25.1794 - 14.5945i) q^{77} +(110.169 + 35.7960i) q^{79} +(-65.5204 - 47.6033i) q^{81} +(123.868 - 40.2470i) q^{83} +(26.2270 + 36.0983i) q^{85} -0.656513i q^{87} -94.4349 q^{89} +(17.2753 - 12.5513i) q^{91} +(-0.289670 - 0.891513i) q^{93} +(85.5607 - 117.764i) q^{95} +(-1.26363 + 3.88906i) q^{97} +(66.1154 - 73.6801i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9}+O(q^{10}) \) 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9	\( 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9} - 10 q^{11} + 30 q^{13} + 24 q^{15} + 60 q^{19} - 132 q^{23} - 186 q^{25} - 110 q^{27} - 90 q^{29} - 26 q^{31} + 46 q^{33} + 82 q^{37} + 290 q^{39} - 336 q^{45} + 84 q^{47} + 84 q^{49} - 20 q^{51} + 58 q^{53} + 370 q^{55} - 20 q^{57} + 436 q^{59} + 160 q^{61} + 276 q^{67} - 118 q^{69} - 150 q^{71} - 320 q^{73} - 692 q^{75} + 28 q^{77} - 560 q^{79} + 122 q^{81} - 630 q^{83} + 220 q^{85} - 444 q^{89} - 126 q^{91} + 500 q^{93} + 440 q^{95} - 80 q^{97} + 1034 q^{99}+O(q^{100}) \) 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9 - 10 * q^11 + 30 * q^13 + 24 * q^15 + 60 * q^19 - 132 * q^23 - 186 * q^25 - 110 * q^27 - 90 * q^29 - 26 * q^31 + 46 * q^33 + 82 * q^37 + 290 * q^39 - 336 * q^45 + 84 * q^47 + 84 * q^49 - 20 * q^51 + 58 * q^53 + 370 * q^55 - 20 * q^57 + 436 * q^59 + 160 * q^61 + 276 * q^67 - 118 * q^69 - 150 * q^71 - 320 * q^73 - 692 * q^75 + 28 * q^77 - 560 * q^79 + 122 * q^81 - 630 * q^83 + 220 * q^85 - 444 * q^89 - 126 * q^91 + 500 * q^93 + 440 * q^95 - 80 * q^97 + 1034 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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