LMFDB - Embedded newform 308.2.y.b.9.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(9,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 10, 18]))

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

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

chi := DirichletCharacter("308.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.y (of order $15$, degree $8$, 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:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.6
Character	$\chi$	$=$	308.9
Dual form			308.2.y.b.137.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.61762 + 1.16544i) q^{3} +(1.05782 + 0.224846i) q^{5} +(-2.30739 - 1.29459i) q^{7} +(3.48627 + 3.87190i) q^{9} +(2.91378 - 1.58426i) q^{11} +(-0.192953 + 0.593849i) q^{13} +(2.50691 + 1.82138i) q^{15} +(-1.85116 + 2.05593i) q^{17} +(-0.231015 - 2.19796i) q^{19} +(-4.53108 - 6.07786i) q^{21} +(-3.41468 + 5.91439i) q^{23} +(-3.49931 - 1.55799i) q^{25} +(1.95696 + 6.02289i) q^{27} +(-5.64552 - 4.10171i) q^{29} +(3.26747 - 0.694522i) q^{31} +(9.47352 - 0.751145i) q^{33} +(-2.14971 - 1.88825i) q^{35} +(-6.91813 + 3.08015i) q^{37} +(-1.19717 + 1.32959i) q^{39} +(3.27666 - 2.38063i) q^{41} +7.35350 q^{43} +(2.81726 + 4.87963i) q^{45} +(-0.982812 - 9.35083i) q^{47} +(3.64805 + 5.97425i) q^{49} +(-7.24169 + 3.22421i) q^{51} +(7.85012 - 1.66859i) q^{53} +(3.43846 - 1.02070i) q^{55} +(1.95688 - 6.02265i) q^{57} +(0.875795 - 8.33264i) q^{59} +(-14.0206 - 2.98017i) q^{61} +(-3.03164 - 13.4473i) q^{63} +(-0.337633 + 0.584798i) q^{65} +(3.06689 + 5.31200i) q^{67} +(-15.8312 + 11.5020i) q^{69} +(-1.03776 - 3.19390i) q^{71} +(-1.44942 + 13.7903i) q^{73} +(-7.34410 - 8.15645i) q^{75} +(-8.77419 - 0.116675i) q^{77} +(2.66452 + 2.95925i) q^{79} +(-0.262916 + 2.50148i) q^{81} +(-0.270229 - 0.831680i) q^{83} +(-2.42046 + 1.75857i) q^{85} +(-9.99752 - 17.3162i) q^{87} +(0.189410 - 0.328068i) q^{89} +(1.21401 - 1.12044i) q^{91} +(9.36240 + 1.99004i) q^{93} +(0.249831 - 2.37698i) q^{95} +(-1.69834 + 5.22696i) q^{97} +(16.2923 + 5.75872i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{3} + 7 q^{5} - 7 q^{7} + 13 q^{9} - 5 q^{11} - 8 q^{13} - 48 q^{15} + 19 q^{17} + 13 q^{19} - 22 q^{21} - 30 q^{23} - 7 q^{25} + 26 q^{27} - 12 q^{29} + 3 q^{31} - 28 q^{33} + 37 q^{35} + 19 q^{37}+ \cdots + 140 q^{99}+O(q^{100}) $ 48 * q - q^3 + 7 * q^5 - 7 * q^7 + 13 * q^9 - 5 * q^11 - 8 * q^13 - 48 * q^15 + 19 * q^17 + 13 * q^19 - 22 * q^21 - 30 * q^23 - 7 * q^25 + 26 * q^27 - 12 * q^29 + 3 * q^31 - 28 * q^33 + 37 * q^35 + 19 * q^37 + 3 * q^39 - 10 * q^41 + 84 * q^43 - 24 * q^45 + 11 * q^47 + 51 * q^49 - 21 * q^51 + 33 * q^53 + 48 * q^55 - 108 * q^57 + 23 * q^59 + 46 * q^61 - 90 * q^63 - 54 * q^65 - 8 * q^67 - 82 * q^69 - 64 * q^71 + 4 * q^73 - 15 * q^75 + 6 * q^77 - 14 * q^79 + 7 * q^81 - 28 * q^83 + 50 * q^85 - 66 * q^87 - 58 * q^89 + 70 * q^91 - 42 * q^93 + 4 * q^95 - 100 * q^97 + 140 * q^99

Character values

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

$n$	$45$	$57$	$155$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$	$1$

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
$3$	2.61762	+	1.16544i	1.51128	+	0.672866i	0.984218	−	0.176960i	$-0.0566265\pi$
$3$	2.61762	+	1.16544i	1.51128	+	0.672866i	0.527063	+	0.849826i	$0.323293\pi$
$4$		0			0
$5$	1.05782	+	0.224846i	0.473070	+	0.100554i	0.438276	−	0.898840i	$-0.355589\pi$
$5$	1.05782	+	0.224846i	0.473070	+	0.100554i	0.0347938	+	0.999395i	$0.488923\pi$
$6$		0			0
$7$	−2.30739	−	1.29459i	−0.872110	−	0.489311i
$7$	−2.30739	−	1.29459i	−0.872110	−	0.489311i
$8$		0			0
$9$	3.48627	+	3.87190i	1.16209	+	1.29063i
$10$		0			0
$11$	2.91378	−	1.58426i	0.878539	−	0.477672i
$11$	2.91378	−	1.58426i	0.878539	−	0.477672i
$12$		0			0
$13$	−0.192953	+	0.593849i	−0.0535156	+	0.164704i	−0.974242	−	0.225504i	$-0.927597\pi$
$13$	−0.192953	+	0.593849i	−0.0535156	+	0.164704i	0.920727	+	0.390208i	$0.127597\pi$
$14$		0			0
$15$	2.50691	+	1.82138i	0.647282	+	0.470278i
$16$		0			0
$17$	−1.85116	+	2.05593i	−0.448973	+	0.498636i	−0.924562	−	0.381033i	$-0.875569\pi$
$17$	−1.85116	+	2.05593i	−0.448973	+	0.498636i	0.475588	+	0.879668i	$0.342235\pi$
$18$		0			0
$19$	−0.231015	−	2.19796i	−0.0529985	−	0.504247i	−0.988532	−	0.151010i	$-0.951748\pi$
$19$	−0.231015	−	2.19796i	−0.0529985	−	0.504247i	0.935534	−	0.353237i	$-0.114919\pi$
$20$		0			0
$21$	−4.53108	−	6.07786i	−0.988762	−	1.32630i
$22$		0			0
$23$	−3.41468	+	5.91439i	−0.712009	+	1.23324i	0.252092	+	0.967703i	$0.418881\pi$
$23$	−3.41468	+	5.91439i	−0.712009	+	1.23324i	−0.964102	+	0.265533i	$0.914452\pi$
$24$		0			0
$25$	−3.49931	−	1.55799i	−0.699862	−	0.311598i
$26$		0			0
$27$	1.95696	+	6.02289i	0.376616	+	1.15911i
$28$		0			0
$29$	−5.64552	−	4.10171i	−1.04835	−	0.761669i	−0.0764495	−	0.997073i	$-0.524358\pi$
$29$	−5.64552	−	4.10171i	−1.04835	−	0.761669i	−0.971897	+	0.235405i	$0.924358\pi$
$30$		0			0
$31$	3.26747	−	0.694522i	0.586855	−	0.124740i	0.0950911	−	0.995469i	$-0.469686\pi$
$31$	3.26747	−	0.694522i	0.586855	−	0.124740i	0.491764	+	0.870729i	$0.336352\pi$
$32$		0			0
$33$	9.47352	−	0.751145i	1.64913	−	0.130758i
$34$		0			0
$35$	−2.14971	−	1.88825i	−0.363367	−	0.319172i
$36$		0			0
$37$	−6.91813	+	3.08015i	−1.13733	+	0.506373i	−0.886992	−	0.461784i	$-0.847209\pi$
$37$	−6.91813	+	3.08015i	−1.13733	+	0.506373i	−0.250341	+	0.968158i	$0.580543\pi$
$38$		0			0
$39$	−1.19717	+	1.32959i	−0.191701	+	0.212905i
$40$		0			0
$41$	3.27666	−	2.38063i	0.511729	−	0.371793i	−0.301750	−	0.953387i	$-0.597571\pi$
$41$	3.27666	−	2.38063i	0.511729	−	0.371793i	0.813479	+	0.581594i	$0.197571\pi$
$42$		0			0
$43$	7.35350			1.12140			0.560699	−	0.828019i	$-0.310532\pi$
$43$	7.35350			1.12140			0.560699	+	0.828019i	$0.310532\pi$
$44$		0			0
$45$	2.81726	+	4.87963i	0.419972	+	0.727413i
$46$		0			0
$47$	−0.982812	−	9.35083i	−0.143358	−	1.36396i	−0.795542	−	0.605899i	$-0.792814\pi$
$47$	−0.982812	−	9.35083i	−0.143358	−	1.36396i	0.652184	−	0.758061i	$-0.273853\pi$
$48$		0			0
$49$	3.64805	+	5.97425i	0.521150	+	0.853465i
$50$		0			0
$51$	−7.24169	+	3.22421i	−1.01404	+	0.451480i
$52$		0			0
$53$	7.85012	−	1.66859i	1.07830	−	0.229199i	0.365671	−	0.930744i	$-0.380839\pi$
$53$	7.85012	−	1.66859i	1.07830	−	0.229199i	0.712625	+	0.701545i	$0.247506\pi$
$54$		0			0
$55$	3.43846	−	1.02070i	0.463642	−	0.137631i
$56$		0			0
$57$	1.95688	−	6.02265i	0.259195	−	0.797720i
$58$		0			0
$59$	0.875795	−	8.33264i	0.114019	−	1.08482i	−0.776577	−	0.630022i	$-0.783046\pi$
$59$	0.875795	−	8.33264i	0.114019	−	1.08482i	0.890596	−	0.454795i	$-0.150287\pi$
$60$		0			0
$61$	−14.0206	−	2.98017i	−1.79515	−	0.381572i	−0.814945	−	0.579539i	$-0.803233\pi$
$61$	−14.0206	−	2.98017i	−1.79515	−	0.381572i	−0.980209	+	0.197967i	$0.936566\pi$
$62$		0			0
$63$	−3.03164	−	13.4473i	−0.381951	−	1.69420i
$64$		0			0
$65$	−0.337633	+	0.584798i	−0.0418783	+	0.0725353i
$66$		0			0
$67$	3.06689	+	5.31200i	0.374680	+	0.648964i	0.990279	−	0.139095i	$-0.0444193\pi$
$67$	3.06689	+	5.31200i	0.374680	+	0.648964i	−0.615599	+	0.788059i	$0.711086\pi$
$68$		0			0
$69$	−15.8312	+	11.5020i	−1.90585	+	1.38468i
$70$		0			0
$71$	−1.03776	−	3.19390i	−0.123160	−	0.379046i	0.870402	−	0.492342i	$-0.163859\pi$
$71$	−1.03776	−	3.19390i	−0.123160	−	0.379046i	−0.993561	+	0.113296i	$0.963859\pi$
$72$		0			0
$73$	−1.44942	+	13.7903i	−0.169641	+	1.61403i	0.496387	+	0.868101i	$0.334660\pi$
$73$	−1.44942	+	13.7903i	−0.169641	+	1.61403i	−0.666028	+	0.745927i	$0.732007\pi$
$74$		0			0
$75$	−7.34410	−	8.15645i	−0.848024	−	0.941826i
$76$		0			0
$77$	−8.77419	−	0.116675i	−0.999912	−	0.0132963i
$78$		0			0
$79$	2.66452	+	2.95925i	0.299782	+	0.332942i	0.874150	−	0.485655i	$-0.161419\pi$
$79$	2.66452	+	2.95925i	0.299782	+	0.332942i	−0.574368	+	0.818597i	$0.694752\pi$
$80$		0			0
$81$	−0.262916	+	2.50148i	−0.0292129	+	0.277942i
$82$		0			0
$83$	−0.270229	−	0.831680i	−0.0296615	−	0.0912887i	0.935130	−	0.354305i	$-0.115283\pi$
$83$	−0.270229	−	0.831680i	−0.0296615	−	0.0912887i	−0.964791	+	0.263017i	$0.915283\pi$
$84$		0			0
$85$	−2.42046	+	1.75857i	−0.262536	+	0.190743i
$86$		0			0
$87$	−9.99752	−	17.3162i	−1.07185	−	1.85649i
$88$		0			0
$89$	0.189410	−	0.328068i	0.0200774	−	0.0347751i	−0.855812	−	0.517287i	$-0.826942\pi$
$89$	0.189410	−	0.328068i	0.0200774	−	0.0347751i	0.875890	+	0.482512i	$0.160275\pi$
$90$		0			0
$91$	1.21401	−	1.12044i	0.127263	−	0.117454i
$92$		0			0
$93$	9.36240	+	1.99004i	0.970836	+	0.206357i
$94$		0			0
$95$	0.249831	−	2.37698i	0.0256321	−	0.243873i
$96$		0			0
$97$	−1.69834	+	5.22696i	−0.172440	+	0.530717i	−0.999507	−	0.0313863i	$-0.990008\pi$
$97$	−1.69834	+	5.22696i	−0.172440	+	0.530717i	0.827067	+	0.562104i	$0.190008\pi$
$98$		0			0
$99$	16.2923	+	5.75872i	1.63744	+	0.578773i
$100$		0			0
$101$	−2.80661	+	0.596564i	−0.279268	+	0.0593603i	−0.345417	−	0.938449i	$-0.612262\pi$
$101$	−2.80661	+	0.596564i	−0.279268	+	0.0593603i	0.0661481	+	0.997810i	$0.478929\pi$
$102$		0			0
$103$	10.1639	−	4.52528i	1.00148	−	0.445889i	0.160550	−	0.987028i	$-0.448673\pi$
$103$	10.1639	−	4.52528i	1.00148	−	0.445889i	0.840933	+	0.541139i	$0.182007\pi$
$104$		0			0
$105$	−3.42647	−	7.44806i	−0.334389	−	0.726856i
$106$		0			0
$107$	−1.65570	−	15.7530i	−0.160063	−	1.52290i	−0.719773	−	0.694209i	$-0.755754\pi$
$107$	−1.65570	−	15.7530i	−0.160063	−	1.52290i	0.559710	−	0.828688i	$-0.310912\pi$
$108$		0			0
$109$	5.48591	+	9.50187i	0.525455	+	0.910114i	0.999560	+	0.0296463i	$0.00943810\pi$
$109$	5.48591	+	9.50187i	0.525455	+	0.910114i	−0.474106	+	0.880468i	$0.657229\pi$
$110$		0			0
$111$	−21.6987			−2.05955
$112$		0			0
$113$	−16.0077	+	11.6303i	−1.50588	+	1.09409i	−0.537918	+	0.842997i	$0.680789\pi$
$113$	−16.0077	+	11.6303i	−1.50588	+	1.09409i	−0.967964	+	0.251090i	$0.919211\pi$
$114$		0			0
$115$	−4.94193	+	5.48857i	−0.460837	+	0.511812i
$116$		0			0
$117$	−2.97201	+	1.32322i	−0.274763	+	0.122332i
$118$		0			0
$119$	6.93294	−	2.34731i	0.635542	−	0.215177i
$120$		0			0
$121$	5.98026	−	9.23236i	0.543660	−	0.839306i
$122$		0			0
$123$	11.3515	−	2.41284i	1.02353	−	0.217559i
$124$		0			0
$125$	−7.72587	−	5.61317i	−0.691023	−	0.502057i
$126$		0			0
$127$	3.50835	+	10.7976i	0.311316	+	0.958132i	0.977244	+	0.212116i	$0.0680356\pi$
$127$	3.50835	+	10.7976i	0.311316	+	0.958132i	−0.665928	+	0.746016i	$0.731964\pi$
$128$		0			0
$129$	19.2486	+	8.57005i	1.69475	+	0.754551i
$130$		0			0
$131$	−7.06364	+	12.2346i	−0.617153	+	1.06894i	0.372850	+	0.927892i	$0.378381\pi$
$131$	−7.06364	+	12.2346i	−0.617153	+	1.06894i	−0.990003	+	0.141048i	$0.954953\pi$
$132$		0			0
$133$	−2.31243	+	5.37062i	−0.200513	+	0.465691i
$134$		0			0
$135$	0.715878	+	6.81113i	0.0616130	+	0.586208i
$136$		0			0
$137$	0.193381	−	0.214771i	0.0165216	−	0.0183491i	−0.734827	−	0.678254i	$-0.762737\pi$
$137$	0.193381	−	0.214771i	0.0165216	−	0.0183491i	0.751349	+	0.659905i	$0.229404\pi$
$138$		0			0
$139$	−5.68353	−	4.12933i	−0.482071	−	0.350245i	0.320056	−	0.947399i	$-0.396298\pi$
$139$	−5.68353	−	4.12933i	−0.482071	−	0.350245i	−0.802127	+	0.597154i	$0.796298\pi$
$140$		0			0
$141$	8.32519	−	25.6223i	0.701107	−	2.15779i
$142$		0			0
$143$	0.378586	+	2.03603i	0.0316589	+	0.170262i
$144$		0			0
$145$	−5.04967	−	5.60823i	−0.419352	−	0.465738i
$146$		0			0
$147$	2.58658	+	19.8899i	0.213337	+	1.64049i
$148$		0			0
$149$	21.5988	+	4.59097i	1.76944	+	0.376107i	0.973397	−	0.229126i	$-0.0735869\pi$
$149$	21.5988	+	4.59097i	1.76944	+	0.376107i	0.796048	+	0.605233i	$0.206920\pi$
$150$		0			0
$151$	18.6690	+	8.31197i	1.51926	+	0.676418i	0.985571	−	0.169262i	$-0.0541384\pi$
$151$	18.6690	+	8.31197i	1.51926	+	0.676418i	0.533690	+	0.845680i	$0.320805\pi$
$152$		0			0
$153$	−14.4140			−1.16530
$154$		0			0
$155$	3.61254			0.290166
$156$		0			0
$157$	7.50995	+	3.34364i	0.599359	+	0.266852i	0.683909	−	0.729567i	$-0.260279\pi$
$157$	7.50995	+	3.34364i	0.599359	+	0.266852i	−0.0845500	+	0.996419i	$0.526945\pi$
$158$		0			0
$159$	22.4932	+	4.78108i	1.78383	+	0.379165i
$160$		0			0
$161$	15.5357	−	9.22616i	1.22439	−	0.727124i
$162$		0			0
$163$	2.55077	+	2.83291i	0.199791	+	0.221891i	0.834712	−	0.550686i	$-0.185634\pi$
$163$	2.55077	+	2.83291i	0.199791	+	0.221891i	−0.634921	+	0.772577i	$0.718967\pi$
$164$		0			0
$165$	10.1901	+	1.33551i	0.793301	+	0.103969i
$166$		0			0
$167$	−2.19769	+	6.76380i	−0.170063	+	0.523399i	−0.999374	−	0.0353886i	$-0.988733\pi$
$167$	−2.19769	+	6.76380i	−0.170063	+	0.523399i	0.829311	+	0.558787i	$0.188733\pi$
$168$		0			0
$169$	10.2018	+	7.41204i	0.784753	+	0.570157i
$170$		0			0
$171$	7.70491	−	8.55717i	0.589209	−	0.654383i
$172$		0			0
$173$	−0.435280	−	4.14141i	−0.0330937	−	0.314866i	−0.998529	−	0.0542223i	$-0.982732\pi$
$173$	−0.435280	−	4.14141i	−0.0330937	−	0.314866i	0.965435	−	0.260643i	$-0.0839346\pi$
$174$		0			0
$175$	6.05728	+	8.12507i	0.457888	+	0.614198i
$176$		0			0
$177$	12.0037	−	20.7910i	0.902251	−	1.56274i
$178$		0			0
$179$	17.6638	+	7.86443i	1.32025	+	0.587815i	0.941291	−	0.337597i	$-0.109614\pi$
$179$	17.6638	+	7.86443i	1.32025	+	0.587815i	0.378963	+	0.925412i	$0.376281\pi$
$180$		0			0
$181$	4.89387	+	15.0618i	0.363759	+	1.11953i	0.950755	+	0.309944i	$0.100310\pi$
$181$	4.89387	+	15.0618i	0.363759	+	1.11953i	−0.586996	+	0.809590i	$0.699690\pi$
$182$		0			0
$183$	−33.2273	−	24.1411i	−2.45624	−	1.78456i
$184$		0			0
$185$	−8.01067	+	1.70272i	−0.588956	+	0.125186i
$186$		0			0
$187$	−2.13678	+	8.92325i	−0.156256	+	0.652532i
$188$		0			0
$189$	3.28175	−	16.4306i	0.238712	−	1.19515i
$190$		0			0
$191$	−7.17410	+	3.19412i	−0.519100	+	0.231118i	−0.649525	−	0.760340i	$-0.725032\pi$
$191$	−7.17410	+	3.19412i	−0.519100	+	0.231118i	0.130425	+	0.991458i	$0.458366\pi$
$192$		0			0
$193$	−7.54687	+	8.38165i	−0.543235	+	0.603324i	−0.950782	−	0.309860i	$-0.899718\pi$
$193$	−7.54687	+	8.38165i	−0.543235	+	0.603324i	0.407547	+	0.913184i	$0.366384\pi$
$194$		0			0
$195$	−1.56534	+	1.13729i	−0.112096	+	0.0814428i
$196$		0			0
$197$	8.44137			0.601423			0.300711	−	0.953715i	$-0.402776\pi$
$197$	8.44137			0.601423			0.300711	+	0.953715i	$0.402776\pi$
$198$		0			0
$199$	−12.9222	−	22.3819i	−0.916028	−	1.58661i	−0.805389	−	0.592747i	$-0.798043\pi$
$199$	−12.9222	−	22.3819i	−0.916028	−	1.58661i	−0.110640	−	0.993861i	$-0.535290\pi$
$200$		0			0
$201$	1.83712	+	17.4790i	0.129581	+	1.23288i
$202$		0			0
$203$	7.71634	+	16.7729i	0.541581	+	1.17723i
$204$		0			0
$205$	4.00138	−	1.78153i	0.279469	−	0.124427i
$206$		0			0
$207$	−34.8045	+	7.39791i	−2.41908	+	0.514191i
$208$		0			0
$209$	−4.15526	−	6.03840i	−0.287426	−	0.417685i
$210$		0			0
$211$	−7.12826	+	21.9385i	−0.490730	+	1.51031i	0.332777	+	0.943005i	$0.392014\pi$
$211$	−7.12826	+	21.9385i	−0.490730	+	1.51031i	−0.823507	+	0.567306i	$0.807986\pi$
$212$		0			0
$213$	1.00583	−	9.56985i	0.0689185	−	0.655715i
$214$		0			0
$215$	7.77866	+	1.65340i	0.530500	+	0.112761i
$216$		0			0
$217$	−8.43843	−	2.62752i	−0.572838	−	0.178367i
$218$		0			0
$219$	−19.8657	+	34.4084i	−1.34240	+	2.32510i
$220$		0			0
$221$	−0.863722	−	1.49601i	−0.0581002	−	0.100633i
$222$		0			0
$223$	0.109862	−	0.0798192i	0.00735689	−	0.00534509i	−0.584101	−	0.811681i	$-0.698553\pi$
$223$	0.109862	−	0.0798192i	0.00735689	−	0.00534509i	0.591458	+	0.806336i	$0.298553\pi$
$224$		0			0
$225$	−6.16716	−	18.9806i	−0.411144	−	1.26537i
$226$		0			0
$227$	0.184923	−	1.75942i	0.0122738	−	0.116777i	−0.986670	−	0.162737i	$-0.947968\pi$
$227$	0.184923	−	1.75942i	0.0122738	−	0.116777i	0.998943	+	0.0459597i	$0.0146346\pi$
$228$		0			0
$229$	−18.6209	−	20.6807i	−1.23051	−	1.36662i	−0.907408	−	0.420251i	$-0.861942\pi$
$229$	−18.6209	−	20.6807i	−1.23051	−	1.36662i	−0.323099	−	0.946365i	$-0.604725\pi$
$230$		0			0
$231$	−22.8315	−	10.5312i	−1.50220	−	0.692901i
$232$		0			0
$233$	−10.1703	−	11.2952i	−0.666275	−	0.739974i	0.311357	−	0.950293i	$-0.399216\pi$
$233$	−10.1703	−	11.2952i	−0.666275	−	0.739974i	−0.977633	+	0.210319i	$0.932550\pi$
$234$		0			0
$235$	1.06286	−	10.1124i	0.0693334	−	0.659663i
$236$		0			0
$237$	3.52587	+	10.8515i	0.229030	+	0.704881i
$238$		0			0
$239$	0.203662	−	0.147969i	0.0131738	−	0.00957133i	−0.581179	−	0.813776i	$-0.697408\pi$
$239$	0.203662	−	0.147969i	0.0131738	−	0.00957133i	0.594353	+	0.804205i	$0.297408\pi$
$240$		0			0
$241$	−7.50249	−	12.9947i	−0.483278	−	0.837062i	0.516538	−	0.856265i	$-0.327221\pi$
$241$	−7.50249	−	12.9947i	−0.483278	−	0.837062i	−0.999816	+	0.0192024i	$0.993887\pi$
$242$		0			0
$243$	5.89573	−	10.2117i	0.378211	−	0.655081i
$244$		0			0
$245$	2.51568	+	7.13991i	0.160721	+	0.456152i
$246$		0			0
$247$	1.34983	+	0.286916i	0.0858878	+	0.0182560i
$248$		0			0
$249$	0.261915	−	2.49195i	0.0165982	−	0.157921i
$250$		0			0
$251$	4.24511	−	13.0651i	0.267949	−	0.824662i	−0.723050	−	0.690795i	$-0.757261\pi$
$251$	4.24511	−	13.0651i	0.267949	−	0.824662i	0.990999	−	0.133867i	$-0.0427395\pi$
$252$		0			0
$253$	−0.579705	+	22.6430i	−0.0364458	+	1.42355i
$254$		0			0
$255$	−8.38533	+	1.78236i	−0.525110	+	0.111616i
$256$		0			0
$257$	6.96286	−	3.10007i	0.434332	−	0.193377i	−0.177911	−	0.984046i	$-0.556934\pi$
$257$	6.96286	−	3.10007i	0.434332	−	0.193377i	0.612243	+	0.790670i	$0.290267\pi$
$258$		0			0
$259$	19.9503	+	1.84908i	1.23965	+	0.114896i
$260$		0			0
$261$	−3.80042	−	36.1586i	−0.235240	−	2.23816i
$262$		0			0
$263$	0.0803943	+	0.139247i	0.00495732	+	0.00858634i	0.868493	−	0.495701i	$-0.165089\pi$
$263$	0.0803943	+	0.139247i	0.00495732	+	0.00858634i	−0.863536	+	0.504287i	$0.831755\pi$
$264$		0			0
$265$	8.67916			0.533156
$266$		0			0
$267$	0.878144	−	0.638009i	0.0537416	−	0.0390455i
$268$		0			0
$269$	−6.90790	+	7.67200i	−0.421182	+	0.467770i	−0.915972	−	0.401243i	$-0.868578\pi$
$269$	−6.90790	+	7.67200i	−0.421182	+	0.467770i	0.494790	+	0.869013i	$0.335245\pi$
$270$		0			0
$271$	−15.9244	+	7.09000i	−0.967339	+	0.430687i	−0.828723	−	0.559659i	$-0.810932\pi$
$271$	−15.9244	+	7.09000i	−0.967339	+	0.430687i	−0.138616	+	0.990346i	$0.544265\pi$
$272$		0			0
$273$	4.48362	−	1.51803i	0.271361	−	0.0918755i
$274$		0			0
$275$	−12.6645	+	1.00415i	−0.763697	+	0.0605527i
$276$		0			0
$277$	4.25426	−	0.904270i	0.255613	−	0.0543323i	−0.0783225	−	0.996928i	$-0.524956\pi$
$277$	4.25426	−	0.904270i	0.255613	−	0.0543323i	0.333936	+	0.942596i	$0.391623\pi$
$278$		0			0
$279$	14.0804	+	10.2300i	0.842972	+	0.612455i
$280$		0			0
$281$	−3.74325	−	11.5206i	−0.223304	−	0.687259i	−0.998459	−	0.0554880i	$-0.982329\pi$
$281$	−3.74325	−	11.5206i	−0.223304	−	0.687259i	0.775156	−	0.631770i	$-0.217671\pi$
$282$		0			0
$283$	28.2298	+	12.5687i	1.67809	+	0.747133i	0.999925	+	0.0122218i	$0.00389043\pi$
$283$	28.2298	+	12.5687i	1.67809	+	0.747133i	0.678163	+	0.734911i	$0.262776\pi$
$284$		0			0
$285$	3.42419	−	5.93087i	0.202831	−	0.351314i
$286$		0			0
$287$	−10.6425	+	1.25109i	−0.628206	+	0.0738496i
$288$		0			0
$289$	0.976960	+	9.29515i	0.0574682	+	0.546774i
$290$		0			0
$291$	−10.5373	+	11.7029i	−0.617708	+	0.686034i
$292$		0			0
$293$	4.20555	+	3.05551i	0.245691	+	0.178505i	0.703815	−	0.710383i	$-0.251478\pi$
$293$	4.20555	+	3.05551i	0.245691	+	0.178505i	−0.458124	+	0.888888i	$0.651478\pi$
$294$		0			0
$295$	2.79999	−	8.61748i	0.163022	−	0.501729i
$296$		0			0
$297$	15.2440	+	14.4491i	0.884544	+	0.838420i
$298$		0			0
$299$	−2.85338	−	3.16900i	−0.165015	−	0.183268i
$300$		0			0
$301$	−16.9674	−	9.51980i	−0.977983	−	0.548712i
$302$		0			0
$303$	−8.04189	−	1.70936i	−0.461995	−	0.0982000i
$304$		0			0
$305$	−14.1611	−	6.30494i	−0.810864	−	0.361020i
$306$		0			0
$307$	17.9401			1.02389			0.511947	−	0.859017i	$-0.328924\pi$
$307$	17.9401			1.02389			0.511947	+	0.859017i	$0.328924\pi$
$308$		0			0
$309$	31.8792			1.81355
$310$		0			0
$311$	−1.98048	−	0.881768i	−0.112303	−	0.0500005i	0.349816	−	0.936818i	$-0.386244\pi$
$311$	−1.98048	−	0.881768i	−0.112303	−	0.0500005i	−0.462119	+	0.886818i	$0.652911\pi$
$312$		0			0
$313$	−18.8173	−	3.99975i	−1.06362	−	0.226079i	−0.357312	−	0.933985i	$-0.616307\pi$
$313$	−18.8173	−	3.99975i	−1.06362	−	0.226079i	−0.706307	+	0.707906i	$0.749640\pi$
$314$		0			0
$315$	−0.183353	−	14.9064i	−0.0103308	−	0.839881i
$316$		0			0
$317$	10.3050	+	11.4449i	0.578787	+	0.642808i	0.959441	−	0.281909i	$-0.0909678\pi$
$317$	10.3050	+	11.4449i	0.578787	+	0.642808i	−0.380654	+	0.924718i	$0.624301\pi$
$318$		0			0
$319$	−22.9480	−	3.00754i	−1.28484	−	0.168390i
$320$		0			0
$321$	14.0251	−	43.1649i	0.782805	−	2.40923i
$322$		0			0
$323$	4.94650	+	3.59384i	0.275230	+	0.199967i
$324$		0			0
$325$	1.60041	−	1.77744i	0.0887750	−	0.0985946i
$326$		0			0
$327$	3.28616	+	31.2657i	0.181725	+	1.72900i
$328$		0			0
$329$	−9.83781	+	22.8483i	−0.542376	+	1.25967i
$330$		0			0
$331$	2.96884	−	5.14219i	0.163182	−	0.282640i	−0.772826	−	0.634618i	$-0.781157\pi$
$331$	2.96884	−	5.14219i	0.163182	−	0.282640i	0.936008	+	0.351978i	$0.114491\pi$
$332$		0			0
$333$	−36.0445	−	16.0481i	−1.97523	−	0.879428i
$334$		0			0
$335$	2.04982	+	6.30870i	0.111994	+	0.344681i
$336$		0			0
$337$	4.17284	+	3.03174i	0.227309	+	0.165150i	0.695611	−	0.718419i	$-0.255134\pi$
$337$	4.17284	+	3.03174i	0.227309	+	0.165150i	−0.468302	+	0.883569i	$0.655134\pi$
$338$		0			0
$339$	−55.4565	+	11.7876i	−3.01198	+	0.640217i
$340$		0			0
$341$	8.42039	−	7.20020i	0.455990	−	0.389913i
$342$		0			0
$343$	−0.683225	−	18.5077i	−0.0368907	−	0.999319i
$344$		0			0
$345$	−19.3327	+	8.60745i	−1.04083	+	0.463410i
$346$		0			0
$347$	17.8855	−	19.8639i	0.960145	−	1.06635i	−0.0376040	−	0.999293i	$-0.511973\pi$
$347$	17.8855	−	19.8639i	0.960145	−	1.06635i	0.997749	−	0.0670565i	$-0.0213608\pi$
$348$		0			0
$349$	10.6247	−	7.71930i	0.568728	−	0.413205i	−0.265915	−	0.963996i	$-0.585674\pi$
$349$	10.6247	−	7.71930i	0.568728	−	0.413205i	0.834643	+	0.550792i	$0.185674\pi$
$350$		0			0
$351$	−3.95429			−0.211064
$352$		0			0
$353$	16.2404	+	28.1292i	0.864390	+	1.49717i	0.867652	+	0.497172i	$0.165628\pi$
$353$	16.2404	+	28.1292i	0.864390	+	1.49717i	−0.00326199	+	0.999995i	$0.501038\pi$
$354$		0			0
$355$	−0.379626	−	3.61190i	−0.0201484	−	0.191700i
$356$		0			0
$357$	20.8834	+	1.93556i	1.10527	+	0.102441i
$358$		0			0
$359$	9.25795	−	4.12190i	0.488616	−	0.217546i	−0.147615	−	0.989045i	$-0.547160\pi$
$359$	9.25795	−	4.12190i	0.488616	−	0.217546i	0.636230	+	0.771499i	$0.280493\pi$
$360$		0			0
$361$	13.8071	−	2.93480i	0.726691	−	0.154463i
$362$		0			0
$363$	26.4138	−	17.1972i	1.38636	−	0.902617i
$364$		0			0
$365$	−4.63390	+	14.2617i	−0.242549	+	0.746490i
$366$		0			0
$367$	2.24832	−	21.3913i	0.117361	−	1.11662i	−0.764341	−	0.644812i	$-0.776936\pi$
$367$	2.24832	−	21.3913i	0.117361	−	1.11662i	0.881703	−	0.471806i	$-0.156398\pi$
$368$		0			0
$369$	20.6409	+	4.38736i	1.07452	+	0.228397i
$370$		0			0
$371$	−20.2734	−	6.31263i	−1.05254	−	0.327735i
$372$		0			0
$373$	−3.85835	+	6.68285i	−0.199778	+	0.346025i	−0.948456	−	0.316908i	$-0.897355\pi$
$373$	−3.85835	+	6.68285i	−0.199778	+	0.346025i	0.748679	+	0.662933i	$0.230689\pi$
$374$		0			0
$375$	−13.6816	−	23.6971i	−0.706512	−	1.22372i
$376$		0			0
$377$	3.52512	−	2.56115i	0.181553	−	0.131906i
$378$		0			0
$379$	2.43418	+	7.49164i	0.125035	+	0.384820i	0.993908	−	0.110217i	$-0.0351546\pi$
$379$	2.43418	+	7.49164i	0.125035	+	0.384820i	−0.868872	+	0.495037i	$0.835155\pi$
$380$		0			0
$381$	−3.40041	+	32.3527i	−0.174208	+	1.65748i
$382$		0			0
$383$	−1.91749	−	2.12959i	−0.0979794	−	0.108817i	0.692161	−	0.721743i	$-0.256659\pi$
$383$	−1.91749	−	2.12959i	−0.0979794	−	0.108817i	−0.790140	+	0.612926i	$0.789992\pi$
$384$		0			0
$385$	−9.25525	−	2.09626i	−0.471691	−	0.106835i
$386$		0			0
$387$	25.6363	+	28.4720i	1.30317	+	1.44731i
$388$		0			0
$389$	1.86307	−	17.7259i	0.0944612	−	0.898738i	−0.839979	−	0.542619i	$-0.817433\pi$
$389$	1.86307	−	17.7259i	0.0944612	−	0.898738i	0.934440	−	0.356120i	$-0.115900\pi$
$390$		0			0
$391$	−5.83843	−	17.9688i	−0.295262	−	0.908724i
$392$		0			0
$393$	−32.7485	+	23.7932i	−1.65194	+	1.20021i
$394$		0			0
$395$	2.15320	+	3.72945i	0.108339	+	0.187649i
$396$		0			0
$397$	−2.80186	+	4.85296i	−0.140621	+	0.243563i	−0.927731	−	0.373250i	$-0.878243\pi$
$397$	−2.80186	+	4.85296i	−0.140621	+	0.243563i	0.787109	+	0.616813i	$0.211577\pi$
$398$		0			0
$399$	−12.3122	+	11.3632i	−0.616379	+	0.568872i
$400$		0			0
$401$	−21.1008	−	4.48512i	−1.05373	−	0.223976i	−0.351689	−	0.936117i	$-0.614392\pi$
$401$	−21.1008	−	4.48512i	−1.05373	−	0.223976i	−0.702037	+	0.712141i	$0.747726\pi$
$402$		0			0
$403$	−0.218027	+	2.07439i	−0.0108607	+	0.103333i
$404$		0			0
$405$	−0.840564	+	2.58699i	−0.0417680	+	0.128549i
$406$		0			0
$407$	−15.2782	+	19.9350i	−0.757311	+	0.988140i
$408$		0			0
$409$	−27.3816	+	5.82014i	−1.35393	+	0.287787i	−0.827039	−	0.562144i	$-0.809977\pi$
$409$	−27.3816	+	5.82014i	−1.35393	+	0.287787i	−0.526893	+	0.849931i	$0.676643\pi$
$410$		0			0
$411$	0.756498	−	0.336815i	0.0373153	−	0.0166138i
$412$		0			0
$413$	−12.8082	+	18.0928i	−0.630249	+	0.890289i
$414$		0			0
$415$	−0.0988531	−	0.940524i	−0.00485251	−	0.0461685i
$416$		0			0
$417$	−10.0648	−	17.4328i	−0.492877	−	0.853688i
$418$		0			0
$419$	−13.2229			−0.645981			−0.322990	−	0.946402i	$-0.604688\pi$
$419$	−13.2229			−0.645981			−0.322990	+	0.946402i	$0.604688\pi$
$420$		0			0
$421$	8.84984	−	6.42979i	0.431315	−	0.313369i	−0.350860	−	0.936428i	$-0.614111\pi$
$421$	8.84984	−	6.42979i	0.431315	−	0.313369i	0.782174	+	0.623059i	$0.214111\pi$
$422$		0			0
$423$	32.7791	−	36.4049i	1.59378	−	1.77007i
$424$		0			0
$425$	9.68091	−	4.31022i	0.469593	−	0.209076i
$426$		0			0
$427$	28.4928	+	25.0274i	1.37886	+	1.21116i
$428$		0			0
$429$	−1.38188	+	5.77077i	−0.0667177	+	0.278616i
$430$		0			0
$431$	−3.28136	+	0.697475i	−0.158058	+	0.0335962i	−0.286261	−	0.958152i	$-0.592412\pi$
$431$	−3.28136	+	0.697475i	−0.158058	+	0.0335962i	0.128203	+	0.991748i	$0.459079\pi$
$432$		0			0
$433$	−8.56499	−	6.22283i	−0.411607	−	0.299050i	0.362645	−	0.931927i	$-0.381874\pi$
$433$	−8.56499	−	6.22283i	−0.411607	−	0.299050i	−0.774252	+	0.632877i	$0.781874\pi$
$434$		0			0
$435$	−6.68206	−	20.5653i	−0.320380	−	0.986029i
$436$		0			0
$437$	13.7885	+	6.13902i	0.659591	+	0.293669i
$438$		0			0
$439$	5.41795	−	9.38416i	0.258584	−	0.447881i	−0.707278	−	0.706935i	$-0.750077\pi$
$439$	5.41795	−	9.38416i	0.258584	−	0.447881i	0.965863	+	0.259054i	$0.0834106\pi$
$440$		0			0
$441$	−10.4136	+	34.9528i	−0.495886	+	1.66442i
$442$		0			0
$443$	−1.94808	−	18.5348i	−0.0925563	−	0.880614i	−0.938020	−	0.346581i	$-0.887343\pi$
$443$	−1.94808	−	18.5348i	−0.0925563	−	0.880614i	0.845464	−	0.534033i	$-0.179324\pi$
$444$		0			0
$445$	0.274125	−	0.304447i	0.0129948	−	0.0144322i
$446$		0			0
$447$	51.1869	+	37.1895i	2.42106	+	1.75900i
$448$		0			0
$449$	11.0012	−	33.8582i	0.519179	−	1.59787i	−0.256370	−	0.966579i	$-0.582526\pi$
$449$	11.0012	−	33.8582i	0.519179	−	1.59787i	0.775548	−	0.631288i	$-0.217474\pi$
$450$		0			0
$451$	5.77594	−	12.1277i	0.271979	−	0.571072i
$452$		0			0
$453$	39.1812	+	43.5151i	1.84089	+	2.04452i
$454$		0			0
$455$	1.53613	−	0.912257i	0.0720147	−	0.0427672i
$456$		0			0
$457$	−16.9287	−	3.59830i	−0.791890	−	0.168321i	−0.205828	−	0.978588i	$-0.565989\pi$
$457$	−16.9287	−	3.59830i	−0.791890	−	0.168321i	−0.586061	+	0.810267i	$0.699322\pi$
$458$		0			0
$459$	−16.0053	−	7.12601i	−0.747062	−	0.332613i
$460$		0			0
$461$	18.2705			0.850942			0.425471	−	0.904972i	$-0.360108\pi$
$461$	18.2705			0.850942			0.425471	+	0.904972i	$0.360108\pi$
$462$		0			0
$463$	−11.1967			−0.520357			−0.260178	−	0.965561i	$-0.583781\pi$
$463$	−11.1967			−0.520357			−0.260178	+	0.965561i	$0.583781\pi$
$464$		0			0
$465$	9.45625	+	4.21019i	0.438523	+	0.195243i
$466$		0			0
$467$	−35.8944	−	7.62960i	−1.66100	−	0.353056i	−0.720656	−	0.693293i	$-0.756159\pi$
$467$	−35.8944	−	7.62960i	−1.66100	−	0.353056i	−0.940340	+	0.340237i	$0.889493\pi$
$468$		0			0
$469$	−0.199600	−	16.2272i	−0.00921665	−	0.749303i
$470$		0			0
$471$	15.7613	+	17.5047i	0.726244	+	0.806576i
$472$		0			0
$473$	21.4265	−	11.6498i	0.985192	−	0.535660i
$474$		0			0
$475$	−2.61601	+	8.05126i	−0.120031	+	0.369417i
$476$		0			0
$477$	33.8283	+	24.5777i	1.54889	+	1.12534i
$478$		0			0
$479$	−14.5731	+	16.1850i	−0.665860	+	0.739513i	−0.977557	−	0.210669i	$-0.932436\pi$
$479$	−14.5731	+	16.1850i	−0.665860	+	0.739513i	0.311697	+	0.950181i	$0.399102\pi$
$480$		0			0
$481$	−0.494268	−	4.70265i	−0.0225367	−	0.214422i
$482$		0			0
$483$	51.4191	−	6.04464i	2.33965	−	0.275041i
$484$		0			0
$485$	−2.97179	+	5.14730i	−0.134942	+	0.233727i
$486$		0			0
$487$	18.2284	+	8.11579i	0.826006	+	0.367762i	0.775801	−	0.630977i	$-0.217346\pi$
$487$	18.2284	+	8.11579i	0.826006	+	0.367762i	0.0502050	+	0.998739i	$0.484013\pi$
$488$		0			0
$489$	3.37534	+	10.3882i	0.152638	+	0.469772i
$490$		0			0
$491$	−15.1747	−	11.0251i	−0.684826	−	0.497555i	0.190129	−	0.981759i	$-0.439109\pi$
$491$	−15.1747	−	11.0251i	−0.684826	−	0.497555i	−0.874955	+	0.484204i	$0.839109\pi$
$492$		0			0
$493$	18.8836	−	4.01383i	0.850475	−	0.180774i
$494$		0			0
$495$	15.9395	+	9.75493i	0.716426	+	0.438452i
$496$		0			0
$497$	−1.74029	+	8.71304i	−0.0780627	+	0.390833i
$498$		0			0
$499$	−12.5181	+	5.57341i	−0.560386	+	0.249500i	−0.667326	−	0.744765i	$-0.732561\pi$
$499$	−12.5181	+	5.57341i	−0.560386	+	0.249500i	0.106940	+	0.994265i	$0.465895\pi$
$500$		0			0
$501$	−13.6355	+	15.1438i	−0.609189	+	0.676573i
$502$		0			0
$503$	30.2095	−	21.9485i	1.34697	−	0.978633i	0.347817	−	0.937563i	$-0.386923\pi$
$503$	30.2095	−	21.9485i	1.34697	−	0.978633i	0.999156	−	0.0410704i	$-0.0130768\pi$
$504$		0			0
$505$	−3.10302			−0.138082
$506$		0			0
$507$	18.0661	+	31.2914i	0.802344	+	1.38970i
$508$		0			0
$509$	2.35307	+	22.3880i	0.104298	+	0.992330i	0.914062	+	0.405575i	$0.132929\pi$
$509$	2.35307	+	22.3880i	0.104298	+	0.992330i	−0.809764	+	0.586756i	$0.800405\pi$
$510$		0			0
$511$	21.1972	−	29.9430i	0.937707	−	1.32460i
$512$		0			0
$513$	12.7860	−	5.69269i	0.564516	−	0.251339i
$514$		0			0
$515$	11.7691	−	2.50159i	0.518607	−	0.110233i
$516$		0			0
$517$	−17.6778	−	25.6893i	−0.777470	−	1.12981i
$518$		0			0
$519$	3.68716	−	11.3479i	0.161848	−	0.498118i
$520$		0			0
$521$	2.97144	−	28.2713i	0.130181	−	1.23859i	−0.713079	−	0.701084i	$-0.752700\pi$
$521$	2.97144	−	28.2713i	0.130181	−	1.23859i	0.843260	−	0.537506i	$-0.180634\pi$
$522$		0			0
$523$	−29.2253	−	6.21204i	−1.27794	−	0.271633i	−0.481547	−	0.876420i	$-0.659925\pi$
$523$	−29.2253	−	6.21204i	−1.27794	−	0.271633i	−0.796388	+	0.604787i	$0.793258\pi$
$524$		0			0
$525$	6.38637	+	28.3277i	0.278724	+	1.23632i
$526$		0			0
$527$	−4.62074	+	8.00335i	−0.201282	+	0.348631i
$528$		0			0
$529$	−11.8200	−	20.4729i	−0.513915	−	0.890127i
$530$		0			0
$531$	35.3164	−	25.6589i	1.53260	−	1.11350i
$532$		0			0
$533$	0.781495	+	2.40519i	0.0338503	+	0.104180i
$534$		0			0
$535$	1.79056	−	17.0360i	0.0774126	−	0.736532i
$536$		0			0
$537$	37.0715	+	41.1721i	1.59975	+	1.77671i
$538$		0			0
$539$	20.0944	+	11.6282i	0.865526	+	0.500863i
$540$		0			0
$541$	4.19838	+	4.66277i	0.180502	+	0.200468i	0.826605	−	0.562782i	$-0.190269\pi$
$541$	4.19838	+	4.66277i	0.180502	+	0.200468i	−0.646103	+	0.763250i	$0.723602\pi$
$542$		0			0
$543$	−4.74330	+	45.1295i	−0.203554	+	1.93669i
$544$		0			0
$545$	3.66663	+	11.2847i	0.157061	+	0.483384i
$546$		0			0
$547$	−29.0569	+	21.1110i	−1.24238	+	0.902643i	−0.997755	−	0.0669745i	$-0.978665\pi$
$547$	−29.0569	+	21.1110i	−1.24238	+	0.902643i	−0.244627	+	0.969617i	$0.578665\pi$
$548$		0			0
$549$	−37.3407	−	64.6760i	−1.59366	−	2.76031i
$550$		0			0
$551$	−7.71120	+	13.3562i	−0.328508	+	0.568993i
$552$		0			0
$553$	−2.31705	−	10.2776i	−0.0985308	−	0.437048i
$554$		0			0
$555$	−22.9533	−	4.87887i	−0.974312	−	0.207096i
$556$		0			0
$557$	−2.31337	+	22.0102i	−0.0980206	+	0.932604i	0.829418	+	0.558629i	$0.188672\pi$
$557$	−2.31337	+	22.0102i	−0.0980206	+	0.932604i	−0.927439	+	0.373975i	$0.877994\pi$
$558$		0			0
$559$	−1.41888	+	4.36687i	−0.0600123	+	0.184699i
$560$		0			0
$561$	−15.9927	+	20.8673i	−0.675214	+	0.881020i
$562$		0			0
$563$	−43.3867	+	9.22212i	−1.82853	+	0.388666i	−0.988170	−	0.153363i	$-0.950990\pi$
$563$	−43.3867	+	9.22212i	−1.82853	+	0.388666i	−0.840360	+	0.542029i	$0.817656\pi$
$564$		0			0
$565$	−19.5483	+	8.70345i	−0.822402	+	0.366157i
$566$		0			0
$567$	3.84505	−	5.43151i	0.161477	−	0.228102i
$568$		0			0
$569$	−2.03990	−	19.4083i	−0.0855170	−	0.813640i	−0.950267	−	0.311437i	$-0.899190\pi$
$569$	−2.03990	−	19.4083i	−0.0855170	−	0.813640i	0.864750	−	0.502203i	$-0.167477\pi$
$570$		0			0
$571$	−9.23702	−	15.9990i	−0.386557	−	0.669537i	0.605427	−	0.795901i	$-0.293002\pi$
$571$	−9.23702	−	15.9990i	−0.386557	−	0.669537i	−0.991984	+	0.126364i	$0.959669\pi$
$572$		0			0
$573$	−22.5016			−0.940017
$574$		0			0
$575$	21.1636	−	15.3762i	0.882583	−	0.641234i
$576$		0			0
$577$	24.4557	−	27.1608i	1.01810	−	1.13072i	0.0267312	−	0.999643i	$-0.491490\pi$
$577$	24.4557	−	27.1608i	1.01810	−	1.13072i	0.991372	−	0.131076i	$-0.0418431\pi$
$578$		0			0
$579$	−29.5231	+	13.1445i	−1.22694	+	0.546268i
$580$		0			0
$581$	−0.453165	+	2.26884i	−0.0188005	+	0.0941274i
$582$		0			0
$583$	20.2300	−	17.2985i	0.837843	−	0.716432i
$584$		0			0
$585$	−3.44136	+	0.731485i	−0.142283	+	0.0302432i
$586$		0			0
$587$	−4.41680	−	3.20899i	−0.182301	−	0.132449i	0.492892	−	0.870090i	$-0.335940\pi$
$587$	−4.41680	−	3.20899i	−0.182301	−	0.132449i	−0.675193	+	0.737641i	$0.735940\pi$
$588$		0			0
$589$	−2.28137	−	7.02133i	−0.0940021	−	0.289309i
$590$		0			0
$591$	22.0963	+	9.83789i	0.908919	+	0.404677i
$592$		0			0
$593$	21.1055	−	36.5557i	0.866697	−	1.50116i	0.00134483	−	0.999999i	$-0.499572\pi$
$593$	21.1055	−	36.5557i	0.866697	−	1.50116i	0.865352	−	0.501164i	$-0.167095\pi$
$594$		0			0
$595$	7.86156	−	0.924178i	0.322293	−	0.0378876i
$596$		0			0
$597$	−7.74062	−	73.6471i	−0.316803	−	3.01417i
$598$		0			0
$599$	−29.4761	+	32.7365i	−1.20436	+	1.33758i	−0.278167	+	0.960533i	$0.589727\pi$
$599$	−29.4761	+	32.7365i	−1.20436	+	1.33758i	−0.926195	+	0.377046i	$0.876940\pi$
$600$		0			0
$601$	−18.8729	−	13.7120i	−0.769841	−	0.559322i	0.132072	−	0.991240i	$-0.457837\pi$
$601$	−18.8729	−	13.7120i	−0.769841	−	0.559322i	−0.901913	+	0.431918i	$0.857837\pi$
$602$		0			0
$603$	−9.87554	+	30.3938i	−0.402163	+	1.23773i
$604$		0			0
$605$	8.40187	−	8.42151i	0.341585	−	0.342383i
$606$		0			0
$607$	1.97877	+	2.19764i	0.0803156	+	0.0891995i	0.781963	−	0.623325i	$-0.214219\pi$
$607$	1.97877	+	2.19764i	0.0803156	+	0.0891995i	−0.701647	+	0.712524i	$0.747552\pi$
$608$		0			0
$609$	0.650660	+	52.8979i	0.0263661	+	2.14353i
$610$		0			0
$611$	5.74262	+	1.22063i	0.232322	+	0.0493815i
$612$		0			0
$613$	−18.3618	−	8.17522i	−0.741628	−	0.330194i	0.000908552	−	1.00000i	$-0.499711\pi$
$613$	−18.3618	−	8.17522i	−0.741628	−	0.330194i	−0.742537	+	0.669806i	$0.766377\pi$
$614$		0			0
$615$	12.5503			0.506079
$616$		0			0
$617$	0.715487			0.0288044			0.0144022	−	0.999896i	$-0.495415\pi$
$617$	0.715487			0.0288044			0.0144022	+	0.999896i	$0.495415\pi$
$618$		0			0
$619$	−28.2158	−	12.5625i	−1.13409	−	0.504929i	−0.248146	−	0.968723i	$-0.579821\pi$
$619$	−28.2158	−	12.5625i	−1.13409	−	0.504929i	−0.885943	+	0.463794i	$0.846488\pi$
$620$		0			0
$621$	−42.3041	−	8.99202i	−1.69761	−	0.360837i
$622$		0			0
$623$	−0.861756	+	0.511769i	−0.0345255	+	0.0205036i
$624$		0			0
$625$	5.90497	+	6.55813i	0.236199	+	0.262325i
$626$		0			0
$627$	−3.83951	−	20.6489i	−0.153335	−	0.824638i
$628$		0			0
$629$	6.47403	−	19.9250i	0.258137	−	0.794463i
$630$		0			0
$631$	−17.2828	−	12.5567i	−0.688016	−	0.499873i	0.187991	−	0.982171i	$-0.439802\pi$
$631$	−17.2828	−	12.5567i	−0.688016	−	0.499873i	−0.876007	+	0.482298i	$0.839802\pi$
$632$		0			0
$633$	−44.2271	+	49.1191i	−1.75787	+	1.95231i
$634$		0			0
$635$	1.28340	+	12.2107i	0.0509301	+	0.484568i
$636$		0			0
$637$	−4.25171	+	1.01364i	−0.168459	+	0.0401619i
$638$		0			0
$639$	8.74855	−	15.1529i	0.346087	−	0.599440i
$640$		0			0
$641$	−10.1661	−	4.52624i	−0.401537	−	0.178776i	0.196024	−	0.980599i	$-0.437197\pi$
$641$	−10.1661	−	4.52624i	−0.401537	−	0.178776i	−0.597561	+	0.801823i	$0.703863\pi$
$642$		0			0
$643$	1.54329	+	4.74975i	0.0608613	+	0.187312i	0.976865	−	0.213859i	$-0.0686033\pi$
$643$	1.54329	+	4.74975i	0.0608613	+	0.187312i	−0.916003	+	0.401171i	$0.868603\pi$
$644$		0			0
$645$	18.4346	+	13.3935i	0.725861	+	0.527369i
$646$		0			0
$647$	−7.14680	+	1.51910i	−0.280970	+	0.0597220i	−0.346241	−	0.938146i	$-0.612542\pi$
$647$	−7.14680	+	1.51910i	−0.280970	+	0.0597220i	0.0652712	+	0.997868i	$0.479209\pi$
$648$		0			0
$649$	−10.6492	−	25.6670i	−0.418016	−	1.00752i
$650$		0			0
$651$	−19.0264	−	16.7123i	−0.745702	−	0.655007i
$652$		0			0
$653$	7.15803	−	3.18696i	0.280116	−	0.124715i	−0.261870	−	0.965103i	$-0.584339\pi$
$653$	7.15803	−	3.18696i	0.280116	−	0.124715i	0.541986	+	0.840388i	$0.317673\pi$
$654$		0			0
$655$	−10.2229	+	11.3537i	−0.399443	+	0.443626i
$656$		0			0
$657$	−58.4476	+	42.4647i	−2.28026	+	1.65670i
$658$		0			0
$659$	0.307551			0.0119805			0.00599025	−	0.999982i	$-0.498093\pi$
$659$	0.307551			0.0119805			0.00599025	+	0.999982i	$0.498093\pi$
$660$		0			0
$661$	0.967431	+	1.67564i	0.0376287	+	0.0651748i	0.884226	−	0.467058i	$-0.154686\pi$
$661$	0.967431	+	1.67564i	0.0376287	+	0.0651748i	−0.846598	+	0.532233i	$0.821353\pi$
$662$		0			0
$663$	−0.517385	−	4.92259i	−0.0200936	−	0.191178i
$664$		0			0
$665$	−3.65368	+	5.16119i	−0.141684	+	0.200142i
$666$		0			0
$667$	43.5368	−	19.3838i	1.68575	−	0.750544i
$668$		0			0
$669$	0.380600	−	0.0808991i	0.0147149	−	0.00312774i
$670$		0			0
$671$	−45.5743	+	13.5287i	−1.75938	+	0.522268i
$672$		0			0
$673$	−5.58936	+	17.2023i	−0.215454	+	0.663099i	0.783667	+	0.621181i	$0.213347\pi$
$673$	−5.58936	+	17.2023i	−0.215454	+	0.663099i	−0.999121	+	0.0419181i	$0.986653\pi$
$674$		0			0
$675$	2.53563	−	24.1249i	0.0975963	−	0.928567i
$676$		0			0
$677$	26.8330	+	5.70352i	1.03127	+	0.219204i	0.692314	−	0.721597i	$-0.256591\pi$
$677$	26.8330	+	5.70352i	1.03127	+	0.219204i	0.338960	+	0.940801i	$0.389925\pi$
$678$		0			0
$679$	10.6855	−	9.86194i	0.410073	−	0.378467i
$680$		0			0
$681$	2.53455	−	4.38998i	0.0971243	−	0.168224i
$682$		0			0
$683$	11.3231	+	19.6121i	0.433265	+	0.750437i	0.997152	−	0.0754148i	$-0.0240281\pi$
$683$	11.3231	+	19.6121i	0.433265	+	0.750437i	−0.563887	+	0.825852i	$0.690695\pi$
$684$		0			0
$685$	0.252851	−	0.183707i	0.00966096	−	0.00701910i
$686$		0			0
$687$	−24.6405	−	75.8356i	−0.940092	−	2.89331i
$688$		0			0
$689$	−0.523812	+	4.98374i	−0.0199557	+	0.189865i
$690$		0			0
$691$	10.3283	+	11.4707i	0.392906	+	0.436366i	0.906847	−	0.421459i	$-0.138482\pi$
$691$	10.3283	+	11.4707i	0.392906	+	0.436366i	−0.513942	+	0.857825i	$0.671815\pi$
$692$		0			0
$693$	−30.1375	−	34.3795i	−1.14483	−	1.30597i
$694$		0			0
$695$	−5.08367	−	5.64599i	−0.192835	−	0.214165i
$696$		0			0
$697$	−1.17123	+	11.1435i	−0.0443636	+	0.422091i
$698$		0			0
$699$	−13.4580	−	41.4193i	−0.509026	−	1.56662i
$700$		0			0
$701$	−5.95134	+	4.32390i	−0.224779	+	0.163312i	−0.694475	−	0.719517i	$-0.744363\pi$
$701$	−5.95134	+	4.32390i	−0.224779	+	0.163312i	0.469696	+	0.882828i	$0.344363\pi$
$702$		0			0
$703$	8.36824	+	14.4942i	0.315614	+	0.546660i
$704$		0			0
$705$	14.5676	−	25.2318i	0.548647	−	0.950285i
$706$		0			0
$707$	7.24824	+	2.25692i	0.272598	+	0.0848803i
$708$		0			0
$709$	21.5521	+	4.58105i	0.809408	+	0.172045i	0.593985	−	0.804476i	$-0.297554\pi$
$709$	21.5521	+	4.58105i	0.809408	+	0.172045i	0.215422	+	0.976521i	$0.430887\pi$
$710$		0			0
$711$	−2.16867	+	20.6335i	−0.0813315	+	0.773817i
$712$		0			0
$713$	−7.04968	+	21.6967i	−0.264012	+	0.812547i
$714$		0			0
$715$	−0.0573196	+	2.23887i	−0.00214363	+	0.0837291i
$716$		0			0
$717$	0.705558	−	0.149971i	0.0263495	−	0.00560077i
$718$		0			0
$719$	13.3285	−	5.93421i	0.497067	−	0.221309i	−0.142862	−	0.989743i	$-0.545630\pi$
$719$	13.3285	−	5.93421i	0.497067	−	0.221309i	0.639929	+	0.768434i	$0.278964\pi$
$720$		0			0
$721$	−29.3105	−	2.71662i	−1.09158	−	0.101172i
$722$		0			0
$723$	−4.49413	−	42.7588i	−0.167139	−	1.59022i
$724$		0			0
$725$	13.3650	+	23.1488i	0.496363	+	0.859726i
$726$		0			0
$727$	−1.06804			−0.0396116			−0.0198058	−	0.999804i	$-0.506305\pi$
$727$	−1.06804			−0.0396116			−0.0198058	+	0.999804i	$0.506305\pi$
$728$		0			0
$729$	33.4385	−	24.2945i	1.23846	−	0.899797i
$730$		0			0
$731$	−13.6125	+	15.1183i	−0.503478	+	0.559169i
$732$		0			0
$733$	−37.6755	+	16.7742i	−1.39158	+	0.619570i	−0.959356	−	0.282198i	$-0.908937\pi$
$733$	−37.6755	+	16.7742i	−1.39158	+	0.619570i	−0.432221	+	0.901768i	$0.642270\pi$
$734$		0			0
$735$	−1.73603	+	21.6214i	−0.0640345	+	0.797518i
$736$		0			0
$737$	17.3518	+	10.6193i	0.639162	+	0.391166i
$738$		0			0
$739$	34.2805	−	7.28654i	1.26103	−	0.268040i	0.471561	−	0.881833i	$-0.343691\pi$
$739$	34.2805	−	7.28654i	1.26103	−	0.268040i	0.789467	+	0.613794i	$0.210357\pi$
$740$		0			0
$741$	3.19896	+	2.32418i	0.117517	+	0.0853809i
$742$		0			0
$743$	2.26608	+	6.97427i	0.0831343	+	0.255861i	0.983980	−	0.178278i	$-0.0570526\pi$
$743$	2.26608	+	6.97427i	0.0831343	+	0.255861i	−0.900846	+	0.434139i	$0.857053\pi$
$744$		0			0
$745$	21.8153	+	9.71281i	0.799252	+	0.355850i
$746$		0			0
$747$	2.27809	−	3.94576i	0.0833509	−	0.144368i
$748$		0			0
$749$	−16.5734	+	38.4917i	−0.605578	+	1.40645i
$750$		0			0
$751$	−2.57657	−	24.5145i	−0.0940205	−	0.894546i	−0.935279	−	0.353912i	$-0.884851\pi$
$751$	−2.57657	−	24.5145i	−0.0940205	−	0.894546i	0.841258	−	0.540634i	$-0.181815\pi$
$752$		0			0
$753$	26.3386	−	29.2520i	0.959833	−	1.06600i
$754$		0			0
$755$	17.8794	+	12.9902i	0.650700	+	0.472761i
$756$		0			0
$757$	−1.90247	+	5.85521i	−0.0691466	+	0.212811i	−0.979659	−	0.200671i	$-0.935688\pi$
$757$	−1.90247	+	5.85521i	−0.0691466	+	0.212811i	0.910512	+	0.413483i	$0.135688\pi$
$758$		0			0
$759$	−27.9064	+	58.5950i	−1.01294	+	2.12686i
$760$		0			0
$761$	−1.64073	−	1.82222i	−0.0594766	−	0.0660554i	0.712672	−	0.701497i	$-0.247485\pi$
$761$	−1.64073	−	1.82222i	−0.0594766	−	0.0660554i	−0.772149	+	0.635442i	$0.780818\pi$
$762$		0			0
$763$	−0.357035	−	29.0265i	−0.0129255	−	1.05083i
$764$		0			0
$765$	−15.2474	−	3.24093i	−0.551270	−	0.117176i
$766$		0			0
$767$	4.77934	+	2.12790i	0.172572	+	0.0768340i
$768$		0			0
$769$	20.3699			0.734557			0.367279	−	0.930111i	$-0.380290\pi$
$769$	20.3699			0.734557			0.367279	+	0.930111i	$0.380290\pi$
$770$		0			0
$771$	21.8390			0.786514
$772$		0			0
$773$	0.500541	+	0.222855i	0.0180032	+	0.00801554i	0.415718	−	0.909493i	$-0.363530\pi$
$773$	0.500541	+	0.222855i	0.0180032	+	0.00801554i	−0.397715	+	0.917509i	$0.630197\pi$
$774$		0			0
$775$	−12.5159	−	2.66034i	−0.449586	−	0.0955624i
$776$		0			0
$777$	50.0673	+	28.0910i	1.79615	+	1.00776i
$778$		0			0
$779$	−5.98950	−	6.65202i	−0.214596	−	0.238333i
$780$		0			0
$781$	−8.08377	−	7.66225i	−0.289260	−	0.274177i
$782$		0			0
$783$	13.6561	−	42.0292i	0.488030	−	1.50200i
$784$		0			0
$785$	7.19234	+	5.22554i	0.256706	+	0.186508i
$786$		0			0
$787$	22.0796	−	24.5218i	0.787051	−	0.874109i	−0.207513	−	0.978232i	$-0.566537\pi$
$787$	22.0796	−	24.5218i	0.787051	−	0.874109i	0.994564	+	0.104123i	$0.0332036\pi$
$788$		0			0
$789$	0.0481577	+	0.458190i	0.00171446	+	0.0163120i
$790$		0			0
$791$	51.9926	−	6.11206i	1.84864	−	0.217320i
$792$		0			0
$793$	4.47509	−	7.75108i	0.158915	−	0.275249i
$794$		0			0
$795$	22.7187	+	10.1150i	0.805749	+	0.358743i
$796$		0			0
$797$	−12.8643	−	39.5924i	−0.455678	−	1.40243i	−0.870337	−	0.492456i	$-0.836099\pi$
$797$	−12.8643	−	39.5924i	−0.455678	−	1.40243i	0.414659	−	0.909977i	$-0.363901\pi$
$798$		0			0
$799$	21.0440	+	15.2893i	0.744482	+	0.540898i
$800$		0			0
$801$	1.93058	−	0.410357i	0.0682137	−	0.0144993i
$802$		0			0
$803$	17.6240	+	42.4781i	0.621939	+	1.49902i
$804$		0			0
$805$	18.5084	−	6.26645i	0.652335	−	0.220863i
$806$		0			0
$807$	−27.0235	+	12.0316i	−0.951271	+	0.423533i
$808$		0			0
$809$	5.12310	−	5.68978i	0.180119	−	0.200042i	−0.646324	−	0.763063i	$-0.723694\pi$
$809$	5.12310	−	5.68978i	0.180119	−	0.200042i	0.826442	+	0.563021i	$0.190361\pi$
$810$		0			0
$811$	−24.2505	+	17.6190i	−0.851550	+	0.618687i	−0.925573	−	0.378569i	$-0.876416\pi$
$811$	−24.2505	+	17.6190i	−0.851550	+	0.618687i	0.0740232	+	0.997257i	$0.476416\pi$
$812$		0			0
$813$	−49.9469			−1.75171
$814$		0			0
$815$	2.06127	+	3.57023i	0.0722033	+	0.125060i
$816$		0			0
$817$	−1.69877	−	16.1627i	−0.0594325	−	0.565462i
$818$		0			0
$819$	8.57061	+	0.794360i	0.299482	+	0.0277572i
$820$		0			0
$821$	−31.6455	+	14.0895i	−1.10444	+	0.491727i	−0.876234	−	0.481887i	$-0.839952\pi$
$821$	−31.6455	+	14.0895i	−1.10444	+	0.491727i	−0.228203	+	0.973614i	$0.573285\pi$
$822$		0			0
$823$	−1.84848	+	0.392906i	−0.0644338	+	0.0136958i	−0.240016	−	0.970769i	$-0.577153\pi$
$823$	−1.84848	+	0.392906i	−0.0644338	+	0.0136958i	0.175582	+	0.984465i	$0.443819\pi$
$824$		0			0
$825$	−34.3210	−	12.1312i	−1.19490	−	0.422353i
$826$		0			0
$827$	−0.0291606	+	0.0897472i	−0.00101401	+	0.00312082i	−0.951562	−	0.307456i	$-0.900522\pi$
$827$	−0.0291606	+	0.0897472i	−0.00101401	+	0.00312082i	0.950548	+	0.310577i	$0.100522\pi$
$828$		0			0
$829$	2.34473	−	22.3086i	0.0814360	−	0.774811i	−0.875246	−	0.483677i	$-0.839301\pi$
$829$	2.34473	−	22.3086i	0.0814360	−	0.774811i	0.956682	−	0.291134i	$-0.0940325\pi$
$830$		0			0
$831$	12.1899	+	2.59104i	0.422862	+	0.0898821i
$832$		0			0
$833$	−19.0358	−	3.55920i	−0.659551	−	0.123319i
$834$		0			0
$835$	−3.84557	+	6.66072i	−0.133081	+	0.230504i
$836$		0			0
$837$	10.5773	+	18.3205i	0.365606	+	0.633248i
$838$		0			0
$839$	−27.8840	+	20.2589i	−0.962664	+	0.699416i	−0.953768	−	0.300544i	$-0.902832\pi$
$839$	−27.8840	+	20.2589i	−0.962664	+	0.699416i	−0.00889603	+	0.999960i	$0.502832\pi$
$840$		0			0
$841$	6.08638	+	18.7320i	0.209875	+	0.645929i
$842$		0			0
$843$	3.62808	−	34.5189i	0.124958	−	1.18889i
$844$		0			0
$845$	9.12506	+	10.1344i	0.313912	+	0.348634i
$846$		0			0
$847$	−25.7509	+	13.5606i	−0.884812	+	0.465948i
$848$		0			0
$849$	59.2467	+	65.8002i	2.03334	+	2.25826i
$850$		0			0
$851$	5.40596	−	51.4343i	0.185314	−	1.76314i
$852$		0			0
$853$	10.6963	+	32.9197i	0.366233	+	1.12715i	0.949205	+	0.314657i	$0.101890\pi$
$853$	10.6963	+	32.9197i	0.366233	+	1.12715i	−0.582972	+	0.812492i	$0.698110\pi$
$854$		0			0
$855$	10.0744	−	7.31950i	0.344538	−	0.250321i
$856$		0			0
$857$	−5.24449	−	9.08372i	−0.179148	−	0.310294i	0.762441	−	0.647058i	$-0.224001\pi$
$857$	−5.24449	−	9.08372i	−0.179148	−	0.310294i	−0.941589	+	0.336764i	$0.890668\pi$
$858$		0			0
$859$	15.7529	−	27.2849i	0.537483	−	0.930948i	−0.461556	−	0.887111i	$-0.652709\pi$
$859$	15.7529	−	27.2849i	0.537483	−	0.930948i	0.999039	−	0.0438365i	$-0.0139581\pi$
$860$		0			0
$861$	−29.3160	−	9.12826i	−0.999086	−	0.311090i
$862$		0			0
$863$	−24.9347	−	5.30003i	−0.848787	−	0.180415i	−0.237071	−	0.971492i	$-0.576187\pi$
$863$	−24.9347	−	5.30003i	−0.848787	−	0.180415i	−0.611716	+	0.791077i	$0.709521\pi$
$864$		0			0
$865$	0.470733	−	4.47872i	0.0160054	−	0.152281i
$866$		0			0
$867$	−8.27561	+	25.4697i	−0.281055	+	0.864997i
$868$		0			0
$869$	12.4520	+	4.40132i	0.422407	+	0.149305i
$870$		0			0
$871$	−3.74629	+	0.796299i	−0.126938	+	0.0269816i
$872$		0			0
$873$	−26.1592	+	11.6468i	−0.885353	+	0.394185i
$874$		0			0
$875$	10.5598	+	22.9536i	0.356985	+	0.775974i
$876$		0			0
$877$	5.26481	+	50.0913i	0.177780	+	1.69146i	0.612159	+	0.790734i	$0.290301\pi$
$877$	5.26481	+	50.0913i	0.177780	+	1.69146i	−0.434379	+	0.900730i	$0.643032\pi$
$878$		0			0
$879$	7.44750	+	12.8995i	0.251198	+	0.435088i
$880$		0			0
$881$	35.1829			1.18534			0.592672	−	0.805444i	$-0.298073\pi$
$881$	35.1829			1.18534			0.592672	+	0.805444i	$0.298073\pi$
$882$		0			0
$883$	−20.1316	+	14.6265i	−0.677483	+	0.492220i	−0.872522	−	0.488575i	$-0.837517\pi$
$883$	−20.1316	+	14.6265i	−0.677483	+	0.492220i	0.195039	+	0.980796i	$0.437517\pi$
$884$		0			0
$885$	17.3724	−	19.2940i	0.583968	−	0.648562i
$886$		0			0
$887$	51.8290	−	23.0757i	1.74025	−	0.774808i	0.746216	−	0.665704i	$-0.231869\pi$
$887$	51.8290	−	23.0757i	1.74025	−	0.774808i	0.994030	−	0.109104i	$-0.0347980\pi$
$888$		0			0
$889$	5.88339	−	29.4561i	0.197323	−	0.987926i
$890$		0			0
$891$	3.19691	+	7.70530i	0.107100	+	0.258137i
$892$		0			0
$893$	−20.3257	+	4.32037i	−0.680175	+	0.144576i
$894$		0			0
$895$	16.9168	+	12.2908i	0.565465	+	0.410835i
$896$		0			0
$897$	−3.77579	−	11.6207i	−0.126070	−	0.388003i
$898$		0			0
$899$	−21.2953	−	9.48127i	−0.710238	−	0.316218i
$900$		0			0
$901$	−11.1014	+	19.2281i	−0.369840	+	0.640581i
$902$		0			0
$903$	−33.3193	−	44.6936i	−1.10880	−	1.48731i
$904$		0			0
$905$	1.79024	+	17.0330i	0.0595095	+	0.566195i
$906$		0			0
$907$	−25.8493	+	28.7086i	−0.858313	+	0.953253i	−0.999324	−	0.0367547i	$-0.988298\pi$
$907$	−25.8493	+	28.7086i	−0.858313	+	0.953253i	0.141011	+	0.990008i	$0.454965\pi$
$908$		0			0
$909$	−12.0945	−	8.78714i	−0.401148	−	0.291451i
$910$		0			0
$911$	−3.28333	+	10.1051i	−0.108782	+	0.334796i	−0.990599	−	0.136795i	$-0.956320\pi$
$911$	−3.28333	+	10.1051i	−0.108782	+	0.334796i	0.881818	+	0.471590i	$0.156320\pi$
$912$		0			0
$913$	−2.10498	−	1.99522i	−0.0696648	−	0.0660322i
$914$		0			0
$915$	−29.7204	−	33.0078i	−0.982526	−	1.09121i
$916$		0			0
$917$	32.1373	−	19.0853i	1.06127	−	0.630253i
$918$		0			0
$919$	21.1400	+	4.49344i	0.697344	+	0.148225i	0.542926	−	0.839781i	$-0.317316\pi$
$919$	21.1400	+	4.49344i	0.697344	+	0.148225i	0.154418	+	0.988006i	$0.450650\pi$
$920$		0			0
$921$	46.9602	+	20.9080i	1.54739	+	0.688943i
$922$		0			0
$923$	2.09693			0.0690214
$924$		0			0
$925$	29.0075			0.953761
$926$		0			0
$927$	52.9557	+	23.5774i	1.73929	+	0.774384i
$928$		0			0
$929$	17.8382	+	3.79163i	0.585253	+	0.124399i	0.491016	−	0.871150i	$-0.336626\pi$
$929$	17.8382	+	3.79163i	0.585253	+	0.124399i	0.0942370	+	0.995550i	$0.469959\pi$
$930$		0			0
$931$	12.2884	−	9.39842i	0.402737	−	0.308021i
$932$		0			0
$933$	−4.15650	−	4.61626i	−0.136078	−	0.151130i
$934$		0			0
$935$	−4.26667	+	8.95871i	−0.139535	+	0.292981i
$936$		0			0
$937$	−11.7970	+	36.3075i	−0.385392	+	1.18611i	0.550803	+	0.834635i	$0.314321\pi$
$937$	−11.7970	+	36.3075i	−0.385392	+	1.18611i	−0.936195	+	0.351480i	$0.885679\pi$
$938$		0			0
$939$	−44.5951	−	32.4002i	−1.45531	−	1.05734i
$940$		0			0
$941$	27.4236	−	30.4570i	0.893984	−	0.992870i	−0.106015	−	0.994365i	$-0.533809\pi$
$941$	27.4236	−	30.4570i	0.893984	−	0.992870i	0.999999	+	0.00149461i	$0.000475749\pi$
$942$		0			0
$943$	2.89127	+	27.5086i	0.0941526	+	0.895802i
$944$		0			0
$945$	7.16584	−	16.6427i	0.233105	−	0.541386i
$946$		0			0
$947$	0.136090	−	0.235715i	0.00442233	−	0.00765970i	−0.863806	−	0.503825i	$-0.831926\pi$
$947$	0.136090	−	0.235715i	0.00442233	−	0.00765970i	0.868228	+	0.496165i	$0.165259\pi$
$948$		0			0
$949$	−7.90966	−	3.52161i	−0.256759	−	0.114316i
$950$		0			0
$951$	13.6363	+	41.9681i	0.442186	+	1.36091i
$952$		0			0
$953$	−5.11089	−	3.71328i	−0.165558	−	0.120285i	0.501921	−	0.864913i	$-0.332627\pi$
$953$	−5.11089	−	3.71328i	−0.165558	−	0.120285i	−0.667479	+	0.744628i	$0.732627\pi$
$954$		0			0
$955$	−8.30707	+	1.76572i	−0.268810	+	0.0571374i
$956$		0			0
$957$	−56.5639	−	34.6170i	−1.82845	−	1.11901i
$958$		0			0
$959$	−0.724245	+	0.245210i	−0.0233871	+	0.00791824i
$960$		0			0
$961$	−18.1259	+	8.07018i	−0.584707	+	0.260328i
$962$		0			0
$963$	55.2217	−	61.3299i	1.77950	−	1.97633i
$964$		0			0
$965$	−9.86778	+	7.16936i	−0.317655	+	0.230790i
$966$		0			0
$967$	18.9704			0.610046			0.305023	−	0.952345i	$-0.401336\pi$
$967$	18.9704			0.610046			0.305023	+	0.952345i	$0.401336\pi$
$968$		0			0
$969$	8.75963	+	15.1721i	0.281400	+	0.487399i
$970$		0			0
$971$	−2.39840	−	22.8192i	−0.0769682	−	0.732304i	−0.963150	−	0.268966i	$-0.913318\pi$
$971$	−2.39840	−	22.8192i	−0.0769682	−	0.732304i	0.886182	−	0.463338i	$-0.153348\pi$
$972$		0			0
$973$	7.76830	+	16.8858i	0.249040	+	0.541335i
$974$		0			0
$975$	6.26077	−	2.78747i	0.200505	−	0.0892706i
$976$		0			0
$977$	−16.6141	+	3.53143i	−0.531532	+	0.112981i	−0.465856	−	0.884860i	$-0.654254\pi$
$977$	−16.6141	+	3.53143i	−0.531532	+	0.112981i	−0.0656756	+	0.997841i	$0.520920\pi$
$978$		0			0
$979$	0.0321559	−	1.25599i	0.00102771	−	0.0401417i
$980$		0			0
$981$	−17.6649	+	54.3670i	−0.563997	+	1.73581i
$982$		0			0
$983$	−0.625618	+	5.95236i	−0.0199541	+	0.189851i	−0.999958	−	0.00912584i	$-0.997095\pi$
$983$	−0.625618	+	5.95236i	−0.0199541	+	0.189851i	0.980004	+	0.198977i	$0.0637618\pi$
$984$		0			0
$985$	8.92942	+	1.89801i	0.284515	+	0.0604755i
$986$		0			0
$987$	−52.3799	+	48.3428i	−1.66727	+	1.53877i
$988$		0			0
$989$	−25.1098	+	43.4915i	−0.798447	+	1.38295i
$990$		0			0
$991$	−15.6844	−	27.1662i	−0.498232	−	0.862963i	0.501766	−	0.865003i	$-0.332684\pi$
$991$	−15.6844	−	27.1662i	−0.498232	−	0.862963i	−0.999998	+	0.00204044i	$0.999351\pi$
$992$		0			0
$993$	13.7642	−	10.0003i	0.436793	−	0.317349i
$994$		0			0
$995$	−8.63682	−	26.5814i	−0.273806	−	0.842687i
$996$		0			0
$997$	−1.49816	+	14.2541i	−0.0474473	+	0.451431i	0.944846	+	0.327516i	$0.106212\pi$
$997$	−1.49816	+	14.2541i	−0.0474473	+	0.451431i	−0.992293	+	0.123915i	$0.960455\pi$
$998$		0			0
$999$	−32.0899	−	35.6394i	−1.01528	−	1.12758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.y.b.9.6	✓	48
7.4	even	3	inner	308.2.y.b.53.1	yes	48
11.5	even	5	inner	308.2.y.b.93.1	yes	48
77.60	even	15	inner	308.2.y.b.137.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.y.b.9.6	✓	48	1.1	even	1	trivial
308.2.y.b.53.1	yes	48	7.4	even	3	inner
308.2.y.b.93.1	yes	48	11.5	even	5	inner
308.2.y.b.137.6	yes	48	77.60	even	15	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.61762 + 1.16544i) q^{3} +(1.05782 + 0.224846i) q^{5} +(-2.30739 - 1.29459i) q^{7} +(3.48627 + 3.87190i) q^{9} +(2.91378 - 1.58426i) q^{11} +(-0.192953 + 0.593849i) q^{13} +(2.50691 + 1.82138i) q^{15} +(-1.85116 + 2.05593i) q^{17} +(-0.231015 - 2.19796i) q^{19} +(-4.53108 - 6.07786i) q^{21} +(-3.41468 + 5.91439i) q^{23} +(-3.49931 - 1.55799i) q^{25} +(1.95696 + 6.02289i) q^{27} +(-5.64552 - 4.10171i) q^{29} +(3.26747 - 0.694522i) q^{31} +(9.47352 - 0.751145i) q^{33} +(-2.14971 - 1.88825i) q^{35} +(-6.91813 + 3.08015i) q^{37} +(-1.19717 + 1.32959i) q^{39} +(3.27666 - 2.38063i) q^{41} +7.35350 q^{43} +(2.81726 + 4.87963i) q^{45} +(-0.982812 - 9.35083i) q^{47} +(3.64805 + 5.97425i) q^{49} +(-7.24169 + 3.22421i) q^{51} +(7.85012 - 1.66859i) q^{53} +(3.43846 - 1.02070i) q^{55} +(1.95688 - 6.02265i) q^{57} +(0.875795 - 8.33264i) q^{59} +(-14.0206 - 2.98017i) q^{61} +(-3.03164 - 13.4473i) q^{63} +(-0.337633 + 0.584798i) q^{65} +(3.06689 + 5.31200i) q^{67} +(-15.8312 + 11.5020i) q^{69} +(-1.03776 - 3.19390i) q^{71} +(-1.44942 + 13.7903i) q^{73} +(-7.34410 - 8.15645i) q^{75} +(-8.77419 - 0.116675i) q^{77} +(2.66452 + 2.95925i) q^{79} +(-0.262916 + 2.50148i) q^{81} +(-0.270229 - 0.831680i) q^{83} +(-2.42046 + 1.75857i) q^{85} +(-9.99752 - 17.3162i) q^{87} +(0.189410 - 0.328068i) q^{89} +(1.21401 - 1.12044i) q^{91} +(9.36240 + 1.99004i) q^{93} +(0.249831 - 2.37698i) q^{95} +(-1.69834 + 5.22696i) q^{97} +(16.2923 + 5.75872i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{3} + 7 q^{5} - 7 q^{7} + 13 q^{9} - 5 q^{11} - 8 q^{13} - 48 q^{15} + 19 q^{17} + 13 q^{19} - 22 q^{21} - 30 q^{23} - 7 q^{25} + 26 q^{27} - 12 q^{29} + 3 q^{31} - 28 q^{33} + 37 q^{35} + 19 q^{37}+ \cdots + 140 q^{99}+O(q^{100}) \) 48 * q - q^3 + 7 * q^5 - 7 * q^7 + 13 * q^9 - 5 * q^11 - 8 * q^13 - 48 * q^15 + 19 * q^17 + 13 * q^19 - 22 * q^21 - 30 * q^23 - 7 * q^25 + 26 * q^27 - 12 * q^29 + 3 * q^31 - 28 * q^33 + 37 * q^35 + 19 * q^37 + 3 * q^39 - 10 * q^41 + 84 * q^43 - 24 * q^45 + 11 * q^47 + 51 * q^49 - 21 * q^51 + 33 * q^53 + 48 * q^55 - 108 * q^57 + 23 * q^59 + 46 * q^61 - 90 * q^63 - 54 * q^65 - 8 * q^67 - 82 * q^69 - 64 * q^71 + 4 * q^73 - 15 * q^75 + 6 * q^77 - 14 * q^79 + 7 * q^81 - 28 * q^83 + 50 * q^85 - 66 * q^87 - 58 * q^89 + 70 * q^91 - 42 * q^93 + 4 * q^95 - 100 * q^97 + 140 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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