LMFDB - Embedded newform 460.2.m.b.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(41,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("460.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.m (of order $11$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			101.1
Character	$\chi$	$=$	460.101
Dual form			460.2.m.b.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.08327 - 2.40422i) q^{3} +(0.142315 + 0.989821i) q^{5} +(-0.796185 + 1.74340i) q^{7} +(-1.01332 + 7.04777i) q^{9} +O(q^{10})$	\(q+(-2.08327 - 2.40422i) q^{3} +(0.142315 + 0.989821i) q^{5} +(-0.796185 + 1.74340i) q^{7} +(-1.01332 + 7.04777i) q^{9} +(4.46646 + 1.31147i) q^{11} +(0.742699 + 1.62629i) q^{13} +(2.08327 - 2.40422i) q^{15} +(0.0167394 + 0.0107578i) q^{17} +(2.95095 - 1.89646i) q^{19} +(5.85018 - 1.71777i) q^{21} +(-3.63032 - 3.13381i) q^{23} +(-0.959493 + 0.281733i) q^{25} +(11.0267 - 7.08643i) q^{27} +(2.28049 + 1.46558i) q^{29} +(3.56257 - 4.11142i) q^{31} +(-6.15176 - 13.4705i) q^{33} +(-1.83896 - 0.539969i) q^{35} +(-1.23016 + 8.55595i) q^{37} +(2.36270 - 5.17359i) q^{39} +(1.45469 + 10.1176i) q^{41} +(1.39107 + 1.60538i) q^{43} -7.12025 q^{45} +11.9279 q^{47} +(2.17849 + 2.51411i) q^{49} +(-0.00900865 - 0.0626565i) q^{51} +(1.66049 - 3.63597i) q^{53} +(-0.662478 + 4.60764i) q^{55} +(-10.7071 - 3.14389i) q^{57} +(3.06524 + 6.71193i) q^{59} +(0.257922 - 0.297658i) q^{61} +(-11.4803 - 7.37795i) q^{63} +(-1.50403 + 0.966584i) q^{65} +(2.16593 - 0.635975i) q^{67} +(0.0285629 + 15.2566i) q^{69} +(-15.2262 + 4.47082i) q^{71} +(11.3008 - 7.26261i) q^{73} +(2.67622 + 1.71990i) q^{75} +(-5.84254 + 6.74266i) q^{77} +(-5.04461 - 11.0461i) q^{79} +(-19.5134 - 5.72965i) q^{81} +(-2.21540 + 15.4084i) q^{83} +(-0.00826601 + 0.0181000i) q^{85} +(-1.22729 - 8.53597i) q^{87} +(2.47778 + 2.85951i) q^{89} -3.42659 q^{91} -17.3065 q^{93} +(2.29712 + 2.65102i) q^{95} +(-1.14610 - 7.97132i) q^{97} +(-13.7689 + 30.1497i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) $ 50 * q + 5 * q^5 - q^7 - 25 * q^9	$ 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) $ 50 * q + 5 * q^5 - q^7 - 25 * q^9 - 6 * q^13 + 12 * q^17 + 19 * q^19 + 39 * q^21 - 16 * q^23 - 5 * q^25 + 21 * q^27 - 6 * q^29 + 34 * q^31 + 50 * q^33 - 10 * q^35 + 7 * q^37 - 70 * q^39 - 51 * q^41 - 18 * q^43 - 74 * q^45 + 30 * q^47 - 16 * q^49 - 80 * q^51 - 23 * q^53 - 33 * q^55 + 27 * q^57 - 18 * q^59 + 76 * q^61 + 138 * q^63 + 6 * q^65 + 25 * q^67 - 30 * q^69 - 37 * q^71 + 20 * q^73 + 92 * q^77 + 18 * q^79 + 25 * q^81 - 22 * q^83 - 12 * q^85 - 109 * q^87 + 8 * q^89 + 110 * q^91 + 64 * q^93 + 3 * q^95 - 38 * q^97 - 126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{11}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.08327	−	2.40422i	−1.20277	−	1.38807i	−0.900501	−	0.434853i	$-0.856800\pi$
$3$	−2.08327	−	2.40422i	−1.20277	−	1.38807i	−0.302272	−	0.953222i	$-0.597745\pi$
$4$		0			0
$5$	0.142315	+	0.989821i	0.0636451	+	0.442662i
$5$	0.142315	+	0.989821i	0.0636451	+	0.442662i
$6$		0			0
$7$	−0.796185	+	1.74340i	−0.300930	+	0.658944i	−0.998332	−	0.0577361i	$-0.981612\pi$
$7$	−0.796185	+	1.74340i	−0.300930	+	0.658944i	0.697402	+	0.716680i	$0.254339\pi$
$8$		0			0
$9$	−1.01332	+	7.04777i	−0.337772	+	2.34926i
$10$		0			0
$11$	4.46646	+	1.31147i	1.34669	+	0.395423i	0.874051	−	0.485834i	$-0.161484\pi$
$11$	4.46646	+	1.31147i	1.34669	+	0.395423i	0.472637	+	0.881257i	$0.343302\pi$
$12$		0			0
$13$	0.742699	+	1.62629i	0.205988	+	0.451050i	0.984225	−	0.176920i	$-0.0566133\pi$
$13$	0.742699	+	1.62629i	0.205988	+	0.451050i	−0.778238	+	0.627970i	$0.783886\pi$
$14$		0			0
$15$	2.08327	−	2.40422i	0.537897	−	0.620766i
$16$		0			0
$17$	0.0167394	+	0.0107578i	0.00405991	+	0.00260915i	0.542669	−	0.839947i	$-0.317414\pi$
$17$	0.0167394	+	0.0107578i	0.00405991	+	0.00260915i	−0.538609	+	0.842556i	$0.681050\pi$
$18$		0			0
$19$	2.95095	−	1.89646i	0.676994	−	0.435078i	−0.156447	−	0.987686i	$-0.550004\pi$
$19$	2.95095	−	1.89646i	0.676994	−	0.435078i	0.833441	+	0.552609i	$0.186368\pi$
$20$		0			0
$21$	5.85018	−	1.71777i	1.27661	−	0.374847i
$22$		0			0
$23$	−3.63032	−	3.13381i	−0.756974	−	0.653445i
$23$	−3.63032	−	3.13381i	−0.756974	−	0.653445i
$24$		0			0
$25$	−0.959493	+	0.281733i	−0.191899	+	0.0563465i
$26$		0			0
$27$	11.0267	−	7.08643i	2.12209	−	1.36379i
$28$		0			0
$29$	2.28049	+	1.46558i	0.423475	+	0.272151i	0.734974	−	0.678096i	$-0.237194\pi$
$29$	2.28049	+	1.46558i	0.423475	+	0.272151i	−0.311498	+	0.950247i	$0.600831\pi$
$30$		0			0
$31$	3.56257	−	4.11142i	0.639856	−	0.738433i	−0.339493	−	0.940608i	$-0.610256\pi$
$31$	3.56257	−	4.11142i	0.639856	−	0.738433i	0.979349	+	0.202175i	$0.0648011\pi$
$32$		0			0
$33$	−6.15176	−	13.4705i	−1.07088	−	2.34491i
$34$		0			0
$35$	−1.83896	−	0.539969i	−0.310842	−	0.0912714i
$36$		0			0
$37$	−1.23016	+	8.55595i	−0.202237	+	1.40659i	0.595389	+	0.803437i	$0.296998\pi$
$37$	−1.23016	+	8.55595i	−0.202237	+	1.40659i	−0.797626	+	0.603152i	$0.793911\pi$
$38$		0			0
$39$	2.36270	−	5.17359i	0.378335	−	0.828438i
$40$		0			0
$41$	1.45469	+	10.1176i	0.227185	+	1.58011i	0.709883	+	0.704320i	$0.248748\pi$
$41$	1.45469	+	10.1176i	0.227185	+	1.58011i	−0.482698	+	0.875787i	$0.660343\pi$
$42$		0			0
$43$	1.39107	+	1.60538i	0.212136	+	0.244818i	0.851839	−	0.523804i	$-0.175488\pi$
$43$	1.39107	+	1.60538i	0.212136	+	0.244818i	−0.639702	+	0.768623i	$0.720942\pi$
$44$		0			0
$45$	−7.12025			−1.06142
$46$		0			0
$47$	11.9279			1.73986			0.869931	−	0.493174i	$-0.164163\pi$
$47$	11.9279			1.73986			0.869931	+	0.493174i	$0.164163\pi$
$48$		0			0
$49$	2.17849	+	2.51411i	0.311213	+	0.359158i
$50$		0			0
$51$	−0.00900865	−	0.0626565i	−0.00126146	−	0.00877367i
$52$		0			0
$53$	1.66049	−	3.63597i	0.228086	−	0.499439i	−0.760640	−	0.649174i	$-0.775115\pi$
$53$	1.66049	−	3.63597i	0.228086	−	0.499439i	0.988726	+	0.149735i	$0.0478420\pi$
$54$		0			0
$55$	−0.662478	+	4.60764i	−0.0893286	+	0.621294i
$56$		0			0
$57$	−10.7071	−	3.14389i	−1.41819	−	0.416418i
$58$		0			0
$59$	3.06524	+	6.71193i	0.399060	+	0.873819i	0.997365	+	0.0725508i	$0.0231139\pi$
$59$	3.06524	+	6.71193i	0.399060	+	0.873819i	−0.598305	+	0.801269i	$0.704159\pi$
$60$		0			0
$61$	0.257922	−	0.297658i	0.0330235	−	0.0381112i	−0.738998	−	0.673708i	$-0.764701\pi$
$61$	0.257922	−	0.297658i	0.0330235	−	0.0381112i	0.772021	+	0.635597i	$0.219246\pi$
$62$		0			0
$63$	−11.4803	−	7.37795i	−1.44638	−	0.929534i
$64$		0			0
$65$	−1.50403	+	0.966584i	−0.186553	+	0.119890i
$66$		0			0
$67$	2.16593	−	0.635975i	0.264611	−	0.0776967i	−0.146736	−	0.989176i	$-0.546877\pi$
$67$	2.16593	−	0.635975i	0.264611	−	0.0776967i	0.411347	+	0.911479i	$0.365059\pi$
$68$		0			0
$69$	0.0285629	+	15.2566i	0.00343857	+	1.83668i
$70$		0			0
$71$	−15.2262	+	4.47082i	−1.80702	+	0.530589i	−0.998337	−	0.0576548i	$-0.981638\pi$
$71$	−15.2262	+	4.47082i	−1.80702	+	0.530589i	−0.808684	+	0.588244i	$0.799820\pi$
$72$		0			0
$73$	11.3008	−	7.26261i	1.32266	−	0.850025i	0.327181	−	0.944962i	$-0.393901\pi$
$73$	11.3008	−	7.26261i	1.32266	−	0.850025i	0.995483	+	0.0949372i	$0.0302650\pi$
$74$		0			0
$75$	2.67622	+	1.71990i	0.309024	+	0.198598i
$76$		0			0
$77$	−5.84254	+	6.74266i	−0.665820	+	0.768397i
$78$		0			0
$79$	−5.04461	−	11.0461i	−0.567562	−	1.24279i	−0.948085	−	0.318017i	$-0.896983\pi$
$79$	−5.04461	−	11.0461i	−0.567562	−	1.24279i	0.380523	−	0.924772i	$-0.375744\pi$
$80$		0			0
$81$	−19.5134	−	5.72965i	−2.16815	−	0.636628i
$82$		0			0
$83$	−2.21540	+	15.4084i	−0.243171	+	1.69129i	0.392834	+	0.919609i	$0.371495\pi$
$83$	−2.21540	+	15.4084i	−0.243171	+	1.69129i	−0.636006	+	0.771684i	$0.719414\pi$
$84$		0			0
$85$	−0.00826601	+	0.0181000i	−0.000896575	+	0.00196323i
$86$		0			0
$87$	−1.22729	−	8.53597i	−0.131579	−	0.915152i
$88$		0			0
$89$	2.47778	+	2.85951i	0.262644	+	0.303108i	0.871720	−	0.490004i	$-0.163005\pi$
$89$	2.47778	+	2.85951i	0.262644	+	0.303108i	−0.609076	+	0.793112i	$0.708459\pi$
$90$		0			0
$91$	−3.42659			−0.359205
$92$		0			0
$93$	−17.3065			−1.79460
$94$		0			0
$95$	2.29712	+	2.65102i	0.235680	+	0.271989i
$96$		0			0
$97$	−1.14610	−	7.97132i	−0.116369	−	0.809365i	−0.961500	−	0.274805i	$-0.911387\pi$
$97$	−1.14610	−	7.97132i	−0.116369	−	0.809365i	0.845131	−	0.534560i	$-0.179523\pi$
$98$		0			0
$99$	−13.7689	+	30.1497i	−1.38383	+	3.03015i
$100$		0			0
$101$	0.809278	−	5.62865i	0.0805261	−	0.560072i	−0.909119	−	0.416536i	$-0.863244\pi$
$101$	0.809278	−	5.62865i	0.0805261	−	0.560072i	0.989645	−	0.143535i	$-0.0458470\pi$
$102$		0			0
$103$	−11.7082	−	3.43783i	−1.15364	−	0.338739i	−0.351682	−	0.936119i	$-0.614390\pi$
$103$	−11.7082	−	3.43783i	−1.15364	−	0.338739i	−0.801958	+	0.597380i	$0.796208\pi$
$104$		0			0
$105$	2.53285	+	5.54617i	0.247181	+	0.541250i
$106$		0			0
$107$	−13.1346	+	15.1581i	−1.26977	+	1.46539i	−0.449644	+	0.893208i	$0.648449\pi$
$107$	−13.1346	+	15.1581i	−1.26977	+	1.46539i	−0.820125	+	0.572184i	$0.806096\pi$
$108$		0			0
$109$	2.40435	+	1.54518i	0.230295	+	0.148002i	0.650700	−	0.759335i	$-0.274476\pi$
$109$	2.40435	+	1.54518i	0.230295	+	0.148002i	−0.420405	+	0.907337i	$0.638112\pi$
$110$		0			0
$111$	23.1331	−	14.8667i	2.19570	−	1.41109i
$112$		0			0
$113$	13.4666	−	3.95416i	1.26684	−	0.371976i	0.421801	−	0.906689i	$-0.361398\pi$
$113$	13.4666	−	3.95416i	1.26684	−	0.371976i	0.845034	+	0.534712i	$0.179580\pi$
$114$		0			0
$115$	2.58526	−	4.03936i	0.241077	−	0.376672i
$116$		0			0
$117$	−12.2143	+	3.58644i	−1.12921	+	0.331566i
$118$		0			0
$119$	−0.0320828	+	0.0206184i	−0.00294103	+	0.00189008i
$120$		0			0
$121$	8.97551	+	5.76821i	0.815955	+	0.524383i
$122$		0			0
$123$	21.2944	−	24.5751i	1.92005	−	2.21586i
$124$		0			0
$125$	−0.415415	−	0.909632i	−0.0371558	−	0.0813600i
$126$		0			0
$127$	−10.4945	−	3.08147i	−0.931238	−	0.273436i	−0.219283	−	0.975661i	$-0.570372\pi$
$127$	−10.4945	−	3.08147i	−0.931238	−	0.273436i	−0.711955	+	0.702225i	$0.752190\pi$
$128$		0			0
$129$	0.961715	−	6.68887i	0.0846742	−	0.588922i
$130$		0			0
$131$	1.82071	−	3.98679i	0.159076	−	0.348327i	−0.813265	−	0.581893i	$-0.802312\pi$
$131$	1.82071	−	3.98679i	0.159076	−	0.348327i	0.972341	+	0.233566i	$0.0750394\pi$
$132$		0			0
$133$	0.956790	+	6.65462i	0.0829642	+	0.577029i
$134$		0			0
$135$	8.58357	+	9.90597i	0.738756	+	0.852570i
$136$		0			0
$137$	−1.39957			−0.119573			−0.0597867	−	0.998211i	$-0.519042\pi$
$137$	−1.39957			−0.119573			−0.0597867	+	0.998211i	$0.519042\pi$
$138$		0			0
$139$	8.38432			0.711149			0.355574	−	0.934648i	$-0.384285\pi$
$139$	8.38432			0.711149			0.355574	+	0.934648i	$0.384285\pi$
$140$		0			0
$141$	−24.8490	−	28.6772i	−2.09266	−	2.41506i
$142$		0			0
$143$	1.18441	+	8.23776i	0.0990455	+	0.688876i
$144$		0			0
$145$	−1.12611	+	2.46585i	−0.0935187	+	0.204777i
$146$		0			0
$147$	1.50609	−	10.4751i	0.124220	−	0.863972i
$148$		0			0
$149$	−7.00175	−	2.05590i	−0.573606	−	0.168426i	−0.0179509	−	0.999839i	$-0.505714\pi$
$149$	−7.00175	−	2.05590i	−0.573606	−	0.168426i	−0.555655	+	0.831413i	$0.687532\pi$
$150$		0			0
$151$	−5.38008	−	11.7807i	−0.437824	−	0.958702i	−0.991992	−	0.126297i	$-0.959691\pi$
$151$	−5.38008	−	11.7807i	−0.437824	−	0.958702i	0.554168	−	0.832405i	$-0.313036\pi$
$152$		0			0
$153$	−0.0927808	+	0.107075i	−0.00750088	+	0.00865648i
$154$		0			0
$155$	4.57658	+	2.94119i	0.367600	+	0.236242i
$156$		0			0
$157$	4.45591	−	2.86364i	0.355620	−	0.228543i	−0.350616	−	0.936519i	$-0.614028\pi$
$157$	4.45591	−	2.86364i	0.355620	−	0.228543i	0.706237	+	0.707976i	$0.250392\pi$
$158$		0			0
$159$	−12.2009	+	3.58251i	−0.967595	+	0.284111i
$160$		0			0
$161$	8.35389	−	3.83401i	0.658379	−	0.302163i
$162$		0			0
$163$	18.4725	−	5.42402i	1.44688	−	0.424842i	0.538371	−	0.842708i	$-0.319040\pi$
$163$	18.4725	−	5.42402i	1.44688	−	0.424842i	0.908509	+	0.417866i	$0.137222\pi$
$164$		0			0
$165$	12.4579	−	8.00619i	0.969844	−	0.623281i
$166$		0			0
$167$	1.91310	+	1.22947i	0.148040	+	0.0951396i	0.612564	−	0.790421i	$-0.290138\pi$
$167$	1.91310	+	1.22947i	0.148040	+	0.0951396i	−0.464524	+	0.885561i	$0.653775\pi$
$168$		0			0
$169$	6.41999	−	7.40906i	0.493845	−	0.569928i
$170$		0			0
$171$	10.3756	+	22.7193i	0.793440	+	1.73739i
$172$		0			0
$173$	−4.03578	−	1.18501i	−0.306835	−	0.0900949i	0.124690	−	0.992196i	$-0.460206\pi$
$173$	−4.03578	−	1.18501i	−0.306835	−	0.0900949i	−0.431525	+	0.902101i	$0.642024\pi$
$174$		0			0
$175$	0.272761	−	1.89709i	0.0206188	−	0.143407i
$176$		0			0
$177$	9.75124	−	21.3522i	0.732948	−	1.60493i
$178$		0			0
$179$	0.943970	+	6.56545i	0.0705556	+	0.490725i	0.994206	+	0.107489i	$0.0342812\pi$
$179$	0.943970	+	6.56545i	0.0705556	+	0.490725i	−0.923651	+	0.383236i	$0.874810\pi$
$180$		0			0
$181$	−11.0132	−	12.7099i	−0.818601	−	0.944716i	0.180644	−	0.983548i	$-0.442182\pi$
$181$	−11.0132	−	12.7099i	−0.818601	−	0.944716i	−0.999246	+	0.0388322i	$0.987636\pi$
$182$		0			0
$183$	−1.25295			−0.0926210
$184$		0			0
$185$	−8.64393			−0.635514
$186$		0			0
$187$	0.0606575	+	0.0700025i	0.00443571	+	0.00511909i
$188$		0			0
$189$	3.57520	+	24.8661i	0.260058	+	1.80874i
$190$		0			0
$191$	−9.39566	+	20.5736i	−0.679846	+	1.48866i	0.182960	+	0.983120i	$0.441432\pi$
$191$	−9.39566	+	20.5736i	−0.679846	+	1.48866i	−0.862806	+	0.505535i	$0.831295\pi$
$192$		0			0
$193$	−3.10525	+	21.5975i	−0.223521	+	1.55462i	0.501049	+	0.865419i	$0.332947\pi$
$193$	−3.10525	+	21.5975i	−0.223521	+	1.55462i	−0.724570	+	0.689201i	$0.757962\pi$
$194$		0			0
$195$	5.45718	+	1.60237i	0.390797	+	0.114748i
$196$		0			0
$197$	1.28461	+	2.81290i	0.0915247	+	0.200411i	0.949858	−	0.312681i	$-0.101227\pi$
$197$	1.28461	+	2.81290i	0.0915247	+	0.200411i	−0.858333	+	0.513092i	$0.828500\pi$
$198$		0			0
$199$	−6.00080	+	6.92530i	−0.425386	+	0.490921i	−0.927470	−	0.373897i	$-0.878021\pi$
$199$	−6.00080	+	6.92530i	−0.425386	+	0.490921i	0.502084	+	0.864819i	$0.332567\pi$
$200$		0			0
$201$	−6.04123	−	3.88246i	−0.426115	−	0.273848i
$202$		0			0
$203$	−4.37078	+	2.80893i	−0.306769	+	0.197148i
$204$		0			0
$205$	−9.80761	+	2.87978i	−0.684993	+	0.201132i
$206$		0			0
$207$	25.7651	−	22.4101i	1.79080	−	1.55761i
$208$		0			0
$209$	15.6674	−	4.60038i	1.08374	−	0.318215i
$210$		0			0
$211$	−17.2750	+	11.1020i	−1.18926	+	0.764292i	−0.977066	−	0.212935i	$-0.931698\pi$
$211$	−17.2750	+	11.1020i	−1.18926	+	0.764292i	−0.212196	+	0.977227i	$0.568061\pi$
$212$		0			0
$213$	42.4691	+	27.2932i	2.90993	+	1.87010i
$214$		0			0
$215$	−1.39107	+	1.60538i	−0.0948703	+	0.109486i
$216$		0			0
$217$	4.33140	+	9.48443i	0.294034	+	0.643845i
$218$		0			0
$219$	−41.0035	−	12.0397i	−2.77076	−	0.813569i
$220$		0			0
$221$	−0.00506285	+	0.0352129i	−0.000340564	+	0.00236868i
$222$		0			0
$223$	2.00710	−	4.39493i	0.134405	−	0.294306i	−0.830448	−	0.557096i	$-0.811915\pi$
$223$	2.00710	−	4.39493i	0.134405	−	0.294306i	0.964853	+	0.262790i	$0.0846426\pi$
$224$		0			0
$225$	−1.01332	−	7.04777i	−0.0675545	−	0.469852i
$226$		0			0
$227$	3.03238	+	3.49955i	0.201266	+	0.232273i	0.847406	−	0.530946i	$-0.178163\pi$
$227$	3.03238	+	3.49955i	0.201266	+	0.232273i	−0.646140	+	0.763219i	$0.723618\pi$
$228$		0			0
$229$	17.4943			1.15606			0.578028	−	0.816017i	$-0.303822\pi$
$229$	17.4943			1.15606			0.578028	+	0.816017i	$0.303822\pi$
$230$		0			0
$231$	28.3824			1.86742
$232$		0			0
$233$	−1.88427	−	2.17457i	−0.123443	−	0.142461i	0.690664	−	0.723176i	$-0.257318\pi$
$233$	−1.88427	−	2.17457i	−0.123443	−	0.142461i	−0.814107	+	0.580715i	$0.802773\pi$
$234$		0			0
$235$	1.69752	+	11.8065i	0.110734	+	0.770170i
$236$		0			0
$237$	−16.0481	+	35.1404i	−1.04243	+	2.28261i
$238$		0			0
$239$	1.86559	−	12.9754i	0.120675	−	0.839311i	−0.836120	−	0.548547i	$-0.815181\pi$
$239$	1.86559	−	12.9754i	0.120675	−	0.839311i	0.956795	−	0.290764i	$-0.0939095\pi$
$240$		0			0
$241$	−28.3683	−	8.32968i	−1.82736	−	0.536562i	−0.827667	−	0.561220i	$-0.810332\pi$
$241$	−28.3683	−	8.32968i	−1.82736	−	0.536562i	−0.999696	+	0.0246577i	$0.992150\pi$
$242$		0			0
$243$	10.5411	+	23.0819i	0.676214	+	1.48070i
$244$		0			0
$245$	−2.17849	+	2.51411i	−0.139178	+	0.160621i
$246$		0			0
$247$	5.27585	+	3.39058i	0.335694	+	0.215738i
$248$		0			0
$249$	41.6604	−	26.7735i	2.64012	−	1.69670i
$250$		0			0
$251$	2.65636	−	0.779978i	0.167668	−	0.0492318i	−0.196821	−	0.980439i	$-0.563062\pi$
$251$	2.65636	−	0.779978i	0.167668	−	0.0492318i	0.364489	+	0.931208i	$0.381244\pi$
$252$		0			0
$253$	−12.1048	−	18.7581i	−0.761021	−	1.17931i
$254$		0			0
$255$	0.0607367	−	0.0178339i	0.00380348	−	0.00111680i
$256$		0			0
$257$	−20.4608	+	13.1493i	−1.27631	+	0.820233i	−0.990428	−	0.138032i	$-0.955922\pi$
$257$	−20.4608	+	13.1493i	−1.27631	+	0.820233i	−0.285880	+	0.958265i	$0.592286\pi$
$258$		0			0
$259$	−13.9370	−	8.95677i	−0.866004	−	0.556547i
$260$		0			0
$261$	−12.6399	+	14.5872i	−0.782392	+	0.902928i
$262$		0			0
$263$	−9.69892	−	21.2377i	−0.598061	−	1.30957i	−0.930447	−	0.366428i	$-0.880581\pi$
$263$	−9.69892	−	21.2377i	−0.598061	−	1.30957i	0.332385	−	0.943144i	$-0.392147\pi$
$264$		0			0
$265$	3.83527	+	1.12614i	0.235599	+	0.0691781i
$266$		0			0
$267$	1.71301	−	11.9142i	0.104834	−	0.729140i
$268$		0			0
$269$	1.13268	−	2.48022i	0.0690605	−	0.151221i	−0.871954	−	0.489588i	$-0.837147\pi$
$269$	1.13268	−	2.48022i	0.0690605	−	0.151221i	0.941014	+	0.338367i	$0.109874\pi$
$270$		0			0
$271$	−2.74783	−	19.1115i	−0.166919	−	1.16094i	−0.885207	−	0.465198i	$-0.845983\pi$
$271$	−2.74783	−	19.1115i	−0.166919	−	1.16094i	0.718288	−	0.695746i	$-0.244926\pi$
$272$		0			0
$273$	7.13850	+	8.23827i	0.432042	+	0.498603i
$274$		0			0
$275$	−4.65502			−0.280708
$276$		0			0
$277$	6.12319			0.367907			0.183953	−	0.982935i	$-0.441110\pi$
$277$	6.12319			0.367907			0.183953	+	0.982935i	$0.441110\pi$
$278$		0			0
$279$	25.3664	+	29.2743i	1.51864	+	1.75261i
$280$		0			0
$281$	0.104665	+	0.727959i	0.00624377	+	0.0434264i	0.992705	−	0.120567i	$-0.0384714\pi$
$281$	0.104665	+	0.727959i	0.00624377	+	0.0434264i	−0.986461	+	0.163994i	$0.947562\pi$
$282$		0			0
$283$	12.6345	−	27.6656i	0.751041	−	1.64455i	−0.0134437	−	0.999910i	$-0.504279\pi$
$283$	12.6345	−	27.6656i	0.751041	−	1.64455i	0.764485	−	0.644641i	$-0.222993\pi$
$284$		0			0
$285$	1.58811	−	11.0455i	0.0940715	−	0.654282i
$286$		0			0
$287$	−18.7973	−	5.51938i	−1.10957	−	0.325799i
$288$		0			0
$289$	−7.06189	−	15.4634i	−0.415405	−	0.909611i
$290$		0			0
$291$	−16.7771	+	19.3619i	−0.983494	+	1.13501i
$292$		0			0
$293$	11.6126	+	7.46294i	0.678413	+	0.435990i	0.833950	−	0.551841i	$-0.186074\pi$
$293$	11.6126	+	7.46294i	0.678413	+	0.435990i	−0.155537	+	0.987830i	$0.549711\pi$
$294$		0			0
$295$	−6.20739	+	3.98925i	−0.361408	+	0.232263i
$296$		0			0
$297$	58.5440	−	17.1901i	3.39707	−	0.997469i
$298$		0			0
$299$	2.40023	−	8.23142i	0.138809	−	0.476035i
$300$		0			0
$301$	−3.90637	+	1.14701i	−0.225160	+	0.0661128i
$302$		0			0
$303$	−15.2184	+	9.78029i	−0.874276	+	0.561863i
$304$		0			0
$305$	0.331334	+	0.212936i	0.0189721	+	0.0121927i
$306$		0			0
$307$	7.01807	−	8.09928i	0.400542	−	0.462250i	−0.519269	−	0.854611i	$-0.673796\pi$
$307$	7.01807	−	8.09928i	0.400542	−	0.462250i	0.919812	+	0.392360i	$0.128341\pi$
$308$		0			0
$309$	16.1259	+	35.3109i	0.917373	+	2.00877i
$310$		0			0
$311$	20.7572	+	6.09486i	1.17703	+	0.345608i	0.811029	−	0.585006i	$-0.198908\pi$
$311$	20.7572	+	6.09486i	1.17703	+	0.345608i	0.366003	+	0.930614i	$0.380726\pi$
$312$		0			0
$313$	−0.354888	+	2.46830i	−0.0200595	+	0.139517i	−0.997390	−	0.0722027i	$-0.976997\pi$
$313$	−0.354888	+	2.46830i	−0.0200595	+	0.139517i	0.977331	+	0.211719i	$0.0679063\pi$
$314$		0			0
$315$	5.66903	−	12.4134i	0.319414	−	0.699419i
$316$		0			0
$317$	1.63634	+	11.3810i	0.0919061	+	0.639221i	0.982754	+	0.184919i	$0.0592023\pi$
$317$	1.63634	+	11.3810i	0.0919061	+	0.639221i	−0.890848	+	0.454302i	$0.849889\pi$
$318$		0			0
$319$	8.26363	+	9.53674i	0.462674	+	0.533955i
$320$		0			0
$321$	63.8063			3.56132
$322$		0			0
$323$	0.0697989			0.00388372
$324$		0			0
$325$	−1.17079	−	1.35117i	−0.0649439	−	0.0749492i
$326$		0			0
$327$	−1.29395	−	8.99962i	−0.0715556	−	0.497680i
$328$		0			0
$329$	−9.49680	+	20.7951i	−0.523576	+	1.14647i
$330$		0			0
$331$	2.75655	−	19.1722i	0.151514	−	1.05380i	−0.762171	−	0.647376i	$-0.775866\pi$
$331$	2.75655	−	19.1722i	0.151514	−	1.05380i	0.913684	−	0.406424i	$-0.133225\pi$
$332$		0			0
$333$	−59.0538	−	17.3398i	−3.23613	−	0.950214i
$334$		0			0
$335$	0.937745	+	2.05338i	0.0512345	+	0.112188i
$336$		0			0
$337$	−4.02616	+	4.64644i	−0.219319	+	0.253108i	−0.854738	−	0.519060i	$-0.826282\pi$
$337$	−4.02616	+	4.64644i	−0.219319	+	0.253108i	0.635419	+	0.772168i	$0.280828\pi$
$338$		0			0
$339$	−37.5612	−	24.1391i	−2.04005	−	1.31106i
$340$		0			0
$341$	21.3041	−	13.6913i	1.15368	−	0.741425i
$342$		0			0
$343$	−18.9903	+	5.57606i	−1.02538	+	0.301079i
$344$		0			0
$345$	−15.0973	+	2.19952i	−0.812810	+	0.118418i
$346$		0			0
$347$	−23.4473	+	6.88476i	−1.25872	+	0.369593i	−0.842017	−	0.539450i	$-0.818632\pi$
$347$	−23.4473	+	6.88476i	−1.25872	+	0.369593i	−0.416701	+	0.909043i	$0.636814\pi$
$348$		0			0
$349$	30.9187	−	19.8702i	1.65504	−	1.06363i	0.730226	−	0.683206i	$-0.239415\pi$
$349$	30.9187	−	19.8702i	1.65504	−	1.06363i	0.924813	−	0.380422i	$-0.124221\pi$
$350$		0			0
$351$	19.7141	+	12.6695i	1.05226	+	0.676247i
$352$		0			0
$353$	15.4929	−	17.8798i	0.824604	−	0.951643i	−0.174853	−	0.984594i	$-0.555945\pi$
$353$	15.4929	−	17.8798i	0.824604	−	0.951643i	0.999457	+	0.0329513i	$0.0104906\pi$
$354$		0			0
$355$	−6.59223	−	14.4350i	−0.349879	−	0.766129i
$356$		0			0
$357$	0.116408	+	0.0341805i	0.00616097	+	0.00180902i
$358$		0			0
$359$	4.89714	−	34.0603i	0.258461	−	1.79764i	−0.285345	−	0.958425i	$-0.592108\pi$
$359$	4.89714	−	34.0603i	0.258461	−	1.79764i	0.543806	−	0.839211i	$-0.316983\pi$
$360$		0			0
$361$	−2.78135	+	6.09030i	−0.146387	+	0.320542i
$362$		0			0
$363$	−4.83034	−	33.5958i	−0.253527	−	1.76332i
$364$		0			0
$365$	8.79697	+	10.1522i	0.460454	+	0.531393i
$366$		0			0
$367$	−17.4550			−0.911143			−0.455571	−	0.890199i	$-0.650565\pi$
$367$	−17.4550			−0.911143			−0.455571	+	0.890199i	$0.650565\pi$
$368$		0			0
$369$	−72.7808			−3.78882
$370$		0			0
$371$	5.01690	+	5.78981i	0.260464	+	0.300592i
$372$		0			0
$373$	0.435222	+	3.02703i	0.0225349	+	0.156734i	0.997982	−	0.0635012i	$-0.0202267\pi$
$373$	0.435222	+	3.02703i	0.0225349	+	0.156734i	−0.975447	+	0.220235i	$0.929318\pi$
$374$		0			0
$375$	−1.32153	+	2.89375i	−0.0682436	+	0.149433i
$376$		0			0
$377$	−0.689734	+	4.79720i	−0.0355231	+	0.247069i
$378$		0			0
$379$	34.1669	+	10.0323i	1.75503	+	0.515325i	0.991462	−	0.130398i	$-0.0416254\pi$
$379$	34.1669	+	10.0323i	1.75503	+	0.515325i	0.763572	+	0.645722i	$0.223444\pi$
$380$		0			0
$381$	14.4543	+	31.6506i	0.740519	+	1.62151i
$382$		0			0
$383$	−7.99001	+	9.22096i	−0.408270	+	0.471169i	−0.922228	−	0.386646i	$-0.873633\pi$
$383$	−7.99001	+	9.22096i	−0.408270	+	0.471169i	0.513958	+	0.857816i	$0.328179\pi$
$384$		0			0
$385$	−7.50551	−	4.82350i	−0.382516	−	0.245828i
$386$		0			0
$387$	−12.7240	+	8.17720i	−0.646795	+	0.415670i
$388$		0			0
$389$	−21.1594	+	6.21295i	−1.07282	+	0.315009i	−0.770004	−	0.638039i	$-0.779746\pi$
$389$	−21.1594	+	6.21295i	−1.07282	+	0.315009i	−0.302818	+	0.953048i	$0.597928\pi$
$390$		0			0
$391$	−0.0270567	−	0.0915124i	−0.00136831	−	0.00462798i
$392$		0			0
$393$	−13.3781	+	3.92817i	−0.674837	+	0.198150i
$394$		0			0
$395$	10.2158	−	6.56529i	0.514012	−	0.330336i
$396$		0			0
$397$	9.47217	+	6.08739i	0.475394	+	0.305517i	0.756308	−	0.654216i	$-0.227001\pi$
$397$	9.47217	+	6.08739i	0.475394	+	0.305517i	−0.280914	+	0.959733i	$0.590637\pi$
$398$		0			0
$399$	14.0059	−	16.1637i	0.701172	−	0.809195i
$400$		0			0
$401$	−6.78783	−	14.8633i	−0.338968	−	0.742237i	0.660999	−	0.750387i	$-0.270133\pi$
$401$	−6.78783	−	14.8633i	−0.338968	−	0.742237i	−0.999967	+	0.00815049i	$0.997406\pi$
$402$		0			0
$403$	9.33226	+	2.74020i	0.464873	+	0.136499i
$404$		0			0
$405$	2.89428	−	20.1302i	0.143818	−	1.00028i
$406$		0			0
$407$	−16.7153	+	36.6015i	−0.828548	+	1.81427i
$408$		0			0
$409$	−4.10251	−	28.5336i	−0.202856	−	1.41090i	−0.795755	−	0.605619i	$-0.792926\pi$
$409$	−4.10251	−	28.5336i	−0.202856	−	1.41090i	0.592899	−	0.805277i	$-0.297983\pi$
$410$		0			0
$411$	2.91568	+	3.36487i	0.143820	+	0.165977i
$412$		0			0
$413$	−14.1421			−0.695887
$414$		0			0
$415$	−15.5669			−0.764148
$416$		0			0
$417$	−17.4668	−	20.1577i	−0.855351	−	0.987128i
$418$		0			0
$419$	−1.22504	−	8.52033i	−0.0598471	−	0.416245i	−0.997617	−	0.0689894i	$-0.978023\pi$
$419$	−1.22504	−	8.52033i	−0.0598471	−	0.416245i	0.937770	−	0.347256i	$-0.112887\pi$
$420$		0			0
$421$	−1.35908	+	2.97597i	−0.0662376	+	0.145040i	−0.939855	−	0.341573i	$-0.889040\pi$
$421$	−1.35908	+	2.97597i	−0.0662376	+	0.145040i	0.873618	+	0.486613i	$0.161768\pi$
$422$		0			0
$423$	−12.0867	+	84.0651i	−0.587677	+	4.08738i
$424$		0			0
$425$	−0.0190922	−	0.00560597i	−0.000926107	−	0.000271930i
$426$		0			0
$427$	0.313583	+	0.686652i	0.0151754	+	0.0332294i
$428$		0			0
$429$	17.3379	−	20.0090i	0.837083	−	0.966045i
$430$		0			0
$431$	16.0632	+	10.3232i	0.773739	+	0.497252i	0.866950	−	0.498395i	$-0.166077\pi$
$431$	16.0632	+	10.3232i	0.773739	+	0.497252i	−0.0932116	+	0.995646i	$0.529713\pi$
$432$		0			0
$433$	−3.56603	+	2.29175i	−0.171373	+	0.110134i	−0.623515	−	0.781811i	$-0.714296\pi$
$433$	−3.56603	+	2.29175i	−0.171373	+	0.110134i	0.452143	+	0.891946i	$0.350660\pi$
$434$		0			0
$435$	8.27442	−	2.42959i	0.396728	−	0.116490i
$436$		0			0
$437$	−16.6560	−	2.36296i	−0.796766	−	0.113036i
$438$		0			0
$439$	−26.2489	+	7.70738i	−1.25279	+	0.367853i	−0.839807	−	0.542885i	$-0.817332\pi$
$439$	−26.2489	+	7.70738i	−1.25279	+	0.367853i	−0.412985	+	0.910738i	$0.635514\pi$
$440$		0			0
$441$	−19.9264	+	12.8059i	−0.948875	+	0.609805i
$442$		0			0
$443$	−7.92336	−	5.09203i	−0.376450	−	0.241930i	0.338709	−	0.940891i	$-0.390010\pi$
$443$	−7.92336	−	5.09203i	−0.376450	−	0.241930i	−0.715160	+	0.698961i	$0.753646\pi$
$444$		0			0
$445$	−2.47778	+	2.85951i	−0.117458	+	0.135554i
$446$		0			0
$447$	9.64368	+	21.1167i	0.456130	+	0.998786i
$448$		0			0
$449$	−18.2011	−	5.34433i	−0.858963	−	0.252214i	−0.177549	−	0.984112i	$-0.556817\pi$
$449$	−18.2011	−	5.34433i	−0.858963	−	0.252214i	−0.681415	+	0.731898i	$0.738635\pi$
$450$		0			0
$451$	−6.77163	+	47.0977i	−0.318864	+	2.21775i
$452$		0			0
$453$	−17.1153	+	37.4772i	−0.804146	+	1.76083i
$454$		0			0
$455$	−0.487655	−	3.39172i	−0.0228616	−	0.159006i
$456$		0			0
$457$	12.1985	+	14.0778i	0.570623	+	0.658534i	0.965562	−	0.260174i	$-0.0837798\pi$
$457$	12.1985	+	14.0778i	0.570623	+	0.658534i	−0.394939	+	0.918707i	$0.629234\pi$
$458$		0			0
$459$	0.260815			0.0121738
$460$		0			0
$461$	18.9181			0.881104			0.440552	−	0.897727i	$-0.354783\pi$
$461$	18.9181			0.881104			0.440552	+	0.897727i	$0.354783\pi$
$462$		0			0
$463$	−1.53317	−	1.76937i	−0.0712523	−	0.0822295i	0.719004	−	0.695006i	$-0.244598\pi$
$463$	−1.53317	−	1.76937i	−0.0712523	−	0.0822295i	−0.790256	+	0.612776i	$0.790053\pi$
$464$		0			0
$465$	−2.46297	−	17.1304i	−0.114218	−	0.794401i
$466$		0			0
$467$	−0.709183	+	1.55290i	−0.0328171	+	0.0718594i	−0.925331	−	0.379161i	$-0.876213\pi$
$467$	−0.709183	+	1.55290i	−0.0328171	+	0.0718594i	0.892514	+	0.451021i	$0.148940\pi$
$468$		0			0
$469$	−0.615722	+	4.28244i	−0.0284314	+	0.197745i
$470$		0			0
$471$	−16.1676	−	4.74725i	−0.744966	−	0.218742i
$472$		0			0
$473$	4.10775	+	8.99472i	0.188875	+	0.413578i
$474$		0			0
$475$	−2.29712	+	2.65102i	−0.105399	+	0.121637i
$476$		0			0
$477$	23.9429	+	15.3872i	1.09627	+	0.704530i
$478$		0			0
$479$	−16.3304	+	10.4949i	−0.746154	+	0.479524i	−0.857645	−	0.514242i	$-0.828073\pi$
$479$	−16.3304	+	10.4949i	−0.746154	+	0.479524i	0.111492	+	0.993765i	$0.464437\pi$
$480$		0			0
$481$	−14.8280	+	4.35391i	−0.676101	+	0.198521i
$482$		0			0
$483$	−26.6212	−	12.0973i	−1.21131	−	0.550446i
$484$		0			0
$485$	7.72708	−	2.26887i	0.350869	−	0.103024i
$486$		0			0
$487$	10.5683	−	6.79183i	0.478895	−	0.307767i	−0.278831	−	0.960340i	$-0.589947\pi$
$487$	10.5683	−	6.79183i	0.478895	−	0.307767i	0.757726	+	0.652573i	$0.226310\pi$
$488$		0			0
$489$	−51.5237	−	33.1123i	−2.32998	−	1.49739i
$490$		0			0
$491$	−1.47631	+	1.70375i	−0.0666250	+	0.0768893i	−0.788084	−	0.615568i	$-0.788927\pi$
$491$	−1.47631	+	1.70375i	−0.0666250	+	0.0768893i	0.721459	+	0.692458i	$0.243472\pi$
$492$		0			0
$493$	0.0224077	+	0.0490659i	0.00100919	+	0.00220982i
$494$		0			0
$495$	−31.8023	−	9.33800i	−1.42941	−	0.419712i
$496$		0			0
$497$	4.32845	−	30.1050i	0.194157	−	1.35039i
$498$		0			0
$499$	12.7428	−	27.9028i	0.570446	−	1.24910i	−0.376114	−	0.926573i	$-0.622740\pi$
$499$	12.7428	−	27.9028i	0.570446	−	1.24910i	0.946560	−	0.322529i	$-0.104533\pi$
$500$		0			0
$501$	−1.02957	−	7.16082i	−0.0459978	−	0.319922i
$502$		0			0
$503$	−2.53285	−	2.92306i	−0.112934	−	0.130333i	0.696468	−	0.717588i	$-0.254754\pi$
$503$	−2.53285	−	2.92306i	−0.112934	−	0.130333i	−0.809402	+	0.587255i	$0.800208\pi$
$504$		0			0
$505$	5.68653			0.253047
$506$		0			0
$507$	−31.1875			−1.38509
$508$		0			0
$509$	−6.64077	−	7.66386i	−0.294347	−	0.339695i	0.589243	−	0.807956i	$-0.299426\pi$
$509$	−6.64077	−	7.66386i	−0.294347	−	0.339695i	−0.883590	+	0.468261i	$0.844881\pi$
$510$		0			0
$511$	3.66409	+	25.4843i	0.162090	+	1.12736i
$512$		0			0
$513$	19.1001	−	41.8234i	0.843290	−	1.84655i
$514$		0			0
$515$	1.73659	−	12.0783i	0.0765233	−	0.532231i
$516$		0			0
$517$	53.2754	+	15.6431i	2.34305	+	0.687982i
$518$		0			0
$519$	5.55858	+	12.1716i	0.243995	+	0.534274i
$520$		0			0
$521$	26.3821	−	30.4465i	1.15582	−	1.33389i	0.222461	−	0.974942i	$-0.428591\pi$
$521$	26.3821	−	30.4465i	1.15582	−	1.33389i	0.933359	−	0.358945i	$-0.116864\pi$
$522$		0			0
$523$	−22.0124	−	14.1465i	−0.962534	−	0.618583i	−0.0378357	−	0.999284i	$-0.512046\pi$
$523$	−22.0124	−	14.1465i	−0.962534	−	0.618583i	−0.924698	+	0.380701i	$0.875683\pi$
$524$		0			0
$525$	−5.12925	+	3.29637i	−0.223859	+	0.143865i
$526$		0			0
$527$	0.103865	−	0.0304976i	0.00452444	−	0.00132849i
$528$		0			0
$529$	3.35846	+	22.7535i	0.146020	+	0.989282i
$530$		0			0
$531$	−50.4103	+	14.8018i	−2.18762	+	0.642343i
$532$		0			0
$533$	−15.3737	+	9.88010i	−0.665910	+	0.427955i
$534$		0			0
$535$	−16.8731	−	10.8437i	−0.729487	−	0.468813i
$536$		0			0
$537$	13.8182	−	15.9471i	0.596301	−	0.688167i
$538$		0			0
$539$	6.43294	+	14.0862i	0.277087	+	0.606735i
$540$		0			0
$541$	−11.2326	−	3.29819i	−0.482927	−	0.141800i	0.0312016	−	0.999513i	$-0.490067\pi$
$541$	−11.2326	−	3.29819i	−0.482927	−	0.141800i	−0.514129	+	0.857713i	$0.671885\pi$
$542$		0			0
$543$	−7.61392	+	52.9560i	−0.326745	+	2.27256i
$544$		0			0
$545$	−1.18728	+	2.59978i	−0.0508576	+	0.111363i
$546$		0			0
$547$	−2.28099	−	15.8646i	−0.0975281	−	0.678323i	−0.978665	−	0.205462i	$-0.934130\pi$
$547$	−2.28099	−	15.8646i	−0.0975281	−	0.678323i	0.881137	−	0.472861i	$-0.156779\pi$
$548$		0			0
$549$	1.83647	+	2.11940i	0.0783785	+	0.0904537i
$550$		0			0
$551$	9.50901			0.405097
$552$		0			0
$553$	23.2743			0.989724
$554$		0			0
$555$	18.0076	+	20.7819i	0.764380	+	0.882141i
$556$		0			0
$557$	−4.70244	−	32.7062i	−0.199249	−	1.38580i	−0.806471	−	0.591273i	$-0.798626\pi$
$557$	−4.70244	−	32.7062i	−0.199249	−	1.38580i	0.607223	−	0.794532i	$-0.292284\pi$
$558$		0			0
$559$	−1.57766	+	3.45459i	−0.0667279	+	0.146114i
$560$		0			0
$561$	0.0419354	−	0.291667i	0.00177052	−	0.0123142i
$562$		0			0
$563$	27.3500	+	8.03068i	1.15266	+	0.338453i	0.801578	−	0.597890i	$-0.203994\pi$
$563$	27.3500	+	8.03068i	1.15266	+	0.338453i	0.351087	+	0.936343i	$0.385812\pi$
$564$		0			0
$565$	5.83042	+	12.7668i	0.245288	+	0.537105i
$566$		0			0
$567$	25.5253	−	29.4578i	1.07196	−	1.23711i
$568$		0			0
$569$	19.6283	+	12.6143i	0.822859	+	0.528819i	0.883001	−	0.469370i	$-0.155519\pi$
$569$	19.6283	+	12.6143i	0.822859	+	0.528819i	−0.0601423	+	0.998190i	$0.519155\pi$
$570$		0			0
$571$	−8.86246	+	5.69556i	−0.370882	+	0.238352i	−0.712783	−	0.701384i	$-0.752566\pi$
$571$	−8.86246	+	5.69556i	−0.370882	+	0.238352i	0.341901	+	0.939736i	$0.388929\pi$
$572$		0			0
$573$	69.0371	−	20.2711i	2.88407	−	0.846838i
$574$		0			0
$575$	4.36616	+	1.98409i	0.182082	+	0.0827423i
$576$		0			0
$577$	3.27173	−	0.960666i	0.136204	−	0.0399930i	−0.212920	−	0.977070i	$-0.568297\pi$
$577$	3.27173	−	0.960666i	0.136204	−	0.0399930i	0.349124	+	0.937077i	$0.386479\pi$
$578$		0			0
$579$	58.3940	−	37.5276i	2.42677	−	1.55959i
$580$		0			0
$581$	−25.0992	−	16.1303i	−1.04129	−	0.669196i
$582$		0			0
$583$	12.1850	−	14.0622i	0.504651	−	0.582398i
$584$		0			0
$585$	−5.28820	−	11.5796i	−0.218640	−	0.478756i
$586$		0			0
$587$	−12.0838	−	3.54811i	−0.498750	−	0.146446i	0.0226756	−	0.999743i	$-0.492782\pi$
$587$	−12.0838	−	3.54811i	−0.498750	−	0.146446i	−0.521426	+	0.853297i	$0.674600\pi$
$588$		0			0
$589$	2.71581	−	18.8889i	0.111903	−	0.778302i
$590$		0			0
$591$	4.08664	−	8.94850i	0.168102	−	0.368092i
$592$		0			0
$593$	2.40198	+	16.7061i	0.0986375	+	0.686039i	0.977804	+	0.209523i	$0.0671913\pi$
$593$	2.40198	+	16.7061i	0.0986375	+	0.686039i	−0.879166	+	0.476515i	$0.841900\pi$
$594$		0			0
$595$	−0.0249744	−	0.0288220i	−0.00102385	−	0.00118159i
$596$		0			0
$597$	29.1512			1.19308
$598$		0			0
$599$	29.9269			1.22278			0.611391	−	0.791329i	$-0.290610\pi$
$599$	29.9269			1.22278			0.611391	+	0.791329i	$0.290610\pi$
$600$		0			0
$601$	−0.986112	−	1.13803i	−0.0402243	−	0.0464214i	0.735281	−	0.677762i	$-0.237050\pi$
$601$	−0.986112	−	1.13803i	−0.0402243	−	0.0464214i	−0.775505	+	0.631341i	$0.782505\pi$
$602$		0			0
$603$	2.28743	+	15.9094i	0.0931514	+	0.647882i
$604$		0			0
$605$	−4.43215	+	9.70505i	−0.180192	+	0.394566i
$606$		0			0
$607$	−4.03173	+	28.0413i	−0.163643	+	1.13816i	0.728052	+	0.685522i	$0.240426\pi$
$607$	−4.03173	+	28.0413i	−0.163643	+	1.13816i	−0.891694	+	0.452638i	$0.850483\pi$
$608$		0			0
$609$	15.8588	+	4.65655i	0.642630	+	0.188693i
$610$		0			0
$611$	8.85884	+	19.3982i	0.358390	+	0.784765i
$612$		0			0
$613$	−8.53380	+	9.84853i	−0.344677	+	0.397778i	−0.901448	−	0.432888i	$-0.857495\pi$
$613$	−8.53380	+	9.84853i	−0.344677	+	0.397778i	0.556771	+	0.830666i	$0.312040\pi$
$614$		0			0
$615$	27.3555	+	17.5803i	1.10308	+	0.708906i
$616$		0			0
$617$	−2.93874	+	1.88862i	−0.118309	+	0.0760328i	−0.598457	−	0.801155i	$-0.704219\pi$
$617$	−2.93874	+	1.88862i	−0.118309	+	0.0760328i	0.480148	+	0.877188i	$0.340583\pi$
$618$		0			0
$619$	−21.6405	+	6.35422i	−0.869805	+	0.255398i	−0.686032	−	0.727571i	$-0.740649\pi$
$619$	−21.6405	+	6.35422i	−0.869805	+	0.255398i	−0.183773	+	0.982969i	$0.558831\pi$
$620$		0			0
$621$	−62.2380	−	8.82958i	−2.49753	−	0.354319i
$622$		0			0
$623$	−6.95805	+	2.04307i	−0.278768	+	0.0818538i
$624$		0			0
$625$	0.841254	−	0.540641i	0.0336501	−	0.0216256i
$626$		0			0
$627$	−43.6997	−	28.0841i	−1.74520	−	1.12157i
$628$		0			0
$629$	−0.112635	+	0.129988i	−0.00449106	+	0.00518296i
$630$		0			0
$631$	3.88773	+	8.51295i	0.154768	+	0.338895i	0.971094	−	0.238696i	$-0.0767200\pi$
$631$	3.88773	+	8.51295i	0.154768	+	0.338895i	−0.816326	+	0.577591i	$0.803993\pi$
$632$		0			0
$633$	62.6800	+	18.4045i	2.49131	+	0.731514i
$634$		0			0
$635$	1.55658	−	10.8262i	0.0617709	−	0.429626i
$636$		0			0
$637$	−2.47070	+	5.41007i	−0.0978925	+	0.214355i
$638$		0			0
$639$	−16.0804	−	111.841i	−0.636129	−	4.42438i
$640$		0			0
$641$	−14.9799	−	17.2877i	−0.591670	−	0.682823i	0.378402	−	0.925641i	$-0.376474\pi$
$641$	−14.9799	−	17.2877i	−0.591670	−	0.682823i	−0.970072	+	0.242818i	$0.921928\pi$
$642$		0			0
$643$	41.8986			1.65232			0.826159	−	0.563437i	$-0.190521\pi$
$643$	41.8986			1.65232			0.826159	+	0.563437i	$0.190521\pi$
$644$		0			0
$645$	6.75765			0.266082
$646$		0			0
$647$	20.2264	+	23.3425i	0.795181	+	0.917688i	0.998107	−	0.0615062i	$-0.0195904\pi$
$647$	20.2264	+	23.3425i	0.795181	+	0.917688i	−0.202926	+	0.979194i	$0.565045\pi$
$648$		0			0
$649$	4.88825	+	33.9985i	0.191881	+	1.33456i
$650$		0			0
$651$	13.7792	−	30.1722i	0.540049	−	1.18254i
$652$		0			0
$653$	1.01030	−	7.02678i	0.0395360	−	0.274979i	−0.960458	−	0.278425i	$-0.910188\pi$
$653$	1.01030	−	7.02678i	0.0395360	−	0.274979i	0.999994	+	0.00344570i	$0.00109680\pi$
$654$		0			0
$655$	4.20532	+	1.23479i	0.164316	+	0.0482474i
$656$		0			0
$657$	39.7339	+	87.0051i	1.55017	+	3.39439i
$658$		0			0
$659$	6.32978	−	7.30496i	0.246573	−	0.284561i	−0.618949	−	0.785431i	$-0.712441\pi$
$659$	6.32978	−	7.30496i	0.246573	−	0.284561i	0.865522	+	0.500870i	$0.166987\pi$
$660$		0			0
$661$	36.7548	+	23.6208i	1.42959	+	0.918744i	0.999875	+	0.0157815i	$0.00502362\pi$
$661$	36.7548	+	23.6208i	1.42959	+	0.918744i	0.429719	+	0.902963i	$0.358613\pi$
$662$		0			0
$663$	0.0952067	−	0.0611856i	0.00369752	−	0.00237625i
$664$		0			0
$665$	−6.45072	+	1.89410i	−0.250148	+	0.0734501i
$666$		0			0
$667$	−3.68605	−	12.4671i	−0.142724	−	0.482729i
$668$		0			0
$669$	−14.7477	+	4.33031i	−0.570179	+	0.167420i
$670$		0			0
$671$	1.54237	−	0.991219i	0.0595424	−	0.0382656i
$672$		0			0
$673$	−5.24271	−	3.36928i	−0.202092	−	0.129876i	0.435681	−	0.900101i	$-0.356508\pi$
$673$	−5.24271	−	3.36928i	−0.202092	−	0.129876i	−0.637772	+	0.770225i	$0.720144\pi$
$674$		0			0
$675$	−8.58357	+	9.90597i	−0.330382	+	0.381281i
$676$		0			0
$677$	−15.6591	−	34.2887i	−0.601828	−	1.31782i	−0.928025	−	0.372518i	$-0.878494\pi$
$677$	−15.6591	−	34.2887i	−0.601828	−	1.31782i	0.326197	−	0.945302i	$-0.394233\pi$
$678$		0			0
$679$	14.8097	+	4.34853i	0.568345	+	0.166881i
$680$		0			0
$681$	2.09643	−	14.5810i	0.0803354	−	0.558745i
$682$		0			0
$683$	0.191913	−	0.420231i	0.00734334	−	0.0160797i	−0.905925	−	0.423439i	$-0.860823\pi$
$683$	0.191913	−	0.420231i	0.00734334	−	0.0160797i	0.913268	+	0.407359i	$0.133550\pi$
$684$		0			0
$685$	−0.199180	−	1.38533i	−0.00761026	−	0.0529306i
$686$		0			0
$687$	−36.4453	−	42.0601i	−1.39047	−	1.60469i
$688$		0			0
$689$	7.14637			0.272255
$690$		0			0
$691$	−31.6507			−1.20405			−0.602024	−	0.798478i	$-0.705639\pi$
$691$	−31.6507			−1.20405			−0.602024	+	0.798478i	$0.705639\pi$
$692$		0			0
$693$	−41.6004	−	48.0094i	−1.58027	−	1.82373i
$694$		0			0
$695$	1.19321	+	8.29898i	0.0452612	+	0.314798i
$696$		0			0
$697$	−0.0844924	+	0.185013i	−0.00320038	+	0.00700785i
$698$		0			0
$699$	−1.30269	+	9.06040i	−0.0492722	+	0.342696i
$700$		0			0
$701$	−8.98930	−	2.63950i	−0.339521	−	0.0996924i	0.107527	−	0.994202i	$-0.465707\pi$
$701$	−8.98930	−	2.63950i	−0.339521	−	0.0996924i	−0.447049	+	0.894510i	$0.647525\pi$
$702$		0			0
$703$	12.5959	+	27.5811i	0.475062	+	1.04024i
$704$		0			0
$705$	24.8490	−	28.6772i	0.935866	−	1.08005i
$706$		0			0
$707$	9.16866	+	5.89234i	0.344823	+	0.221604i
$708$		0			0
$709$	−3.27953	+	2.10762i	−0.123165	+	0.0791535i	−0.600773	−	0.799420i	$-0.705140\pi$
$709$	−3.27953	+	2.10762i	−0.123165	+	0.0791535i	0.477608	+	0.878573i	$0.341504\pi$
$710$		0			0
$711$	82.9625	−	24.3600i	3.11134	−	0.913571i
$712$		0			0
$713$	−25.8177	+	3.76137i	−0.966880	+	0.140864i
$714$		0			0
$715$	−7.98536	+	2.34471i	−0.298635	+	0.0876872i
$716$		0			0
$717$	−35.0822	+	22.5460i	−1.31017	+	0.841995i
$718$		0			0
$719$	−28.2352	−	18.1457i	−1.05300	−	0.676719i	−0.104828	−	0.994490i	$-0.533429\pi$
$719$	−28.2352	−	18.1457i	−1.05300	−	0.676719i	−0.948167	+	0.317772i	$0.897065\pi$
$720$		0			0
$721$	15.3154	−	17.6749i	0.570375	−	0.658247i
$722$		0			0
$723$	39.0723	+	85.5565i	1.45312	+	3.18188i
$724$		0			0
$725$	−2.60101	−	0.763726i	−0.0965991	−	0.0283641i
$726$		0			0
$727$	−0.312081	+	2.17057i	−0.0115744	+	0.0805021i	−0.994790	−	0.101946i	$-0.967493\pi$
$727$	−0.312081	+	2.17057i	−0.0115744	+	0.0805021i	0.983215	+	0.182448i	$0.0584022\pi$
$728$		0			0
$729$	8.18868	−	17.9307i	0.303284	−	0.664100i
$730$		0			0
$731$	0.00601540	+	0.0418380i	0.000222488	+	0.00154744i
$732$		0			0
$733$	18.8961	+	21.8073i	0.697944	+	0.805470i	0.988473	−	0.151396i	$-0.0483769\pi$
$733$	18.8961	+	21.8073i	0.697944	+	0.805470i	−0.290529	+	0.956866i	$0.593831\pi$
$734$		0			0
$735$	10.5828			0.390353
$736$		0			0
$737$	10.5081			0.387071
$738$		0			0
$739$	21.4967	+	24.8085i	0.790767	+	0.912594i	0.997837	−	0.0657319i	$-0.0209382\pi$
$739$	21.4967	+	24.8085i	0.790767	+	0.912594i	−0.207070	+	0.978326i	$0.566393\pi$
$740$		0			0
$741$	−2.83930	−	19.7478i	−0.104304	−	0.725453i
$742$		0			0
$743$	5.80180	−	12.7042i	0.212847	−	0.466071i	−0.772852	−	0.634587i	$-0.781170\pi$
$743$	5.80180	−	12.7042i	0.212847	−	0.466071i	0.985699	+	0.168516i	$0.0538975\pi$
$744$		0			0
$745$	1.03852	−	7.22307i	0.0380484	−	0.264633i
$746$		0			0
$747$	−106.350	−	31.2272i	−3.89115	−	1.14254i
$748$		0			0
$749$	−15.9691	−	34.9675i	−0.583500	−	1.27769i
$750$		0			0
$751$	0.759354	−	0.876341i	0.0277092	−	0.0319782i	−0.741726	−	0.670703i	$-0.765992\pi$
$751$	0.759354	−	0.876341i	0.0277092	−	0.0319782i	0.769435	+	0.638725i	$0.220538\pi$
$752$		0			0
$753$	−7.40914	−	4.76157i	−0.270004	−	0.173521i
$754$		0			0
$755$	10.8951	−	7.00189i	0.396515	−	0.254825i
$756$		0			0
$757$	13.9104	−	4.08447i	0.505583	−	0.148452i	−0.0189874	−	0.999820i	$-0.506044\pi$
$757$	13.9104	−	4.08447i	0.505583	−	0.148452i	0.524570	+	0.851367i	$0.324226\pi$
$758$		0			0
$759$	−19.8811	+	68.1806i	−0.721636	+	2.47480i
$760$		0			0
$761$	26.6203	−	7.81642i	0.964985	−	0.283345i	0.238972	−	0.971026i	$-0.423190\pi$
$761$	26.6203	−	7.81642i	0.964985	−	0.283345i	0.726013	+	0.687681i	$0.241371\pi$
$762$		0			0
$763$	−4.60819	+	2.96150i	−0.166828	+	0.107214i
$764$		0			0
$765$	−0.119189	−	0.0765981i	−0.00430929	−	0.00276941i
$766$		0			0
$767$	−8.63897	+	9.96990i	−0.311935	+	0.359992i
$768$		0			0
$769$	−4.20764	−	9.21345i	−0.151731	−	0.332245i	0.818468	−	0.574551i	$-0.194823\pi$
$769$	−4.20764	−	9.21345i	−0.151731	−	0.332245i	−0.970200	+	0.242306i	$0.922096\pi$
$770$		0			0
$771$	74.2391	+	21.7986i	2.67365	+	0.785056i
$772$		0			0
$773$	−0.987215	+	6.86623i	−0.0355077	+	0.246961i	−0.999843	−	0.0177225i	$-0.994358\pi$
$773$	−0.987215	+	6.86623i	−0.0355077	+	0.246961i	0.964335	+	0.264684i	$0.0852676\pi$
$774$		0			0
$775$	−2.25994	+	4.94857i	−0.0811793	+	0.177758i
$776$		0			0
$777$	7.50047	+	52.1669i	0.269078	+	1.87148i
$778$		0			0
$779$	23.4804	+	27.0978i	0.841272	+	0.970880i
$780$		0			0
$781$	−73.8706			−2.64330
$782$		0			0
$783$	35.5320			1.26981
$784$		0			0
$785$	3.46863	+	4.00302i	0.123801	+	0.142874i
$786$		0			0
$787$	3.61833	+	25.1660i	0.128979	+	0.897071i	0.946851	+	0.321671i	$0.104245\pi$
$787$	3.61833	+	25.1660i	0.128979	+	0.897071i	−0.817872	+	0.575400i	$0.804846\pi$
$788$		0			0
$789$	−30.8545	+	67.5620i	−1.09845	+	2.40527i
$790$		0			0
$791$	−3.82824	+	26.6260i	−0.136117	+	0.946712i
$792$		0			0
$793$	0.675635	+	0.198384i	0.0239925	+	0.00704483i
$794$		0			0
$795$	−5.28241	−	11.5669i	−0.187348	−	0.410235i
$796$		0			0
$797$	2.20446	−	2.54408i	0.0780858	−	0.0901158i	−0.715362	−	0.698754i	$-0.753738\pi$
$797$	2.20446	−	2.54408i	0.0780858	−	0.0901158i	0.793448	+	0.608638i	$0.208284\pi$
$798$		0			0
$799$	0.199666	+	0.128318i	0.00706368	+	0.00453955i
$800$		0			0
$801$	−22.6640	+	14.5653i	−0.800792	+	0.514638i
$802$		0			0
$803$	59.9995	−	17.6174i	2.11734	−	0.621706i
$804$		0			0
$805$	4.98387	+	7.72323i	0.175658	+	0.272208i
$806$		0			0
$807$	−8.32264	+	2.44375i	−0.292971	+	0.0860240i
$808$		0			0
$809$	−5.13722	+	3.30149i	−0.180615	+	0.116074i	−0.627824	−	0.778355i	$-0.716054\pi$
$809$	−5.13722	+	3.30149i	−0.180615	+	0.116074i	0.447209	+	0.894429i	$0.352418\pi$
$810$		0			0
$811$	−37.6190	−	24.1762i	−1.32098	−	0.848942i	−0.325652	−	0.945490i	$-0.605584\pi$
$811$	−37.6190	−	24.1762i	−1.32098	−	0.848942i	−0.995328	+	0.0965474i	$0.969220\pi$
$812$		0			0
$813$	−40.2238	+	46.4208i	−1.41071	+	1.62805i
$814$		0			0
$815$	7.99773	+	17.5126i	0.280148	+	0.613439i
$816$		0			0
$817$	7.14952	+	2.09929i	0.250130	+	0.0734448i
$818$		0			0
$819$	3.47222	−	24.1499i	0.121329	−	0.843864i
$820$		0			0
$821$	−19.4358	+	42.5585i	−0.678314	+	1.48530i	0.186106	+	0.982530i	$0.440413\pi$
$821$	−19.4358	+	42.5585i	−0.678314	+	1.48530i	−0.864420	+	0.502771i	$0.832314\pi$
$822$		0			0
$823$	−0.431050	−	2.99802i	−0.0150254	−	0.104504i	0.980929	−	0.194369i	$-0.0622658\pi$
$823$	−0.431050	−	2.99802i	−0.0150254	−	0.104504i	−0.995954	+	0.0898643i	$0.971357\pi$
$824$		0			0
$825$	9.69764	+	11.1917i	0.337628	+	0.389644i
$826$		0			0
$827$	34.6693			1.20557			0.602784	−	0.797904i	$-0.294058\pi$
$827$	34.6693			1.20557			0.602784	+	0.797904i	$0.294058\pi$
$828$		0			0
$829$	−2.87454			−0.0998369			−0.0499185	−	0.998753i	$-0.515896\pi$
$829$	−2.87454			−0.0998369			−0.0499185	+	0.998753i	$0.515896\pi$
$830$		0			0
$831$	−12.7562	−	14.7215i	−0.442508	−	0.510682i
$832$		0			0
$833$	0.00942042	+	0.0655205i	0.000326398	+	0.00227015i
$834$		0			0
$835$	−0.944697	+	2.06860i	−0.0326926	+	0.0715868i
$836$		0			0
$837$	10.1481	−	70.5813i	0.350768	−	2.43965i
$838$		0			0
$839$	28.2779	+	8.30315i	0.976262	+	0.286656i	0.730681	−	0.682719i	$-0.239203\pi$
$839$	28.2779	+	8.30315i	0.976262	+	0.286656i	0.245582	+	0.969376i	$0.421021\pi$
$840$		0			0
$841$	−8.99434	−	19.6949i	−0.310150	−	0.679133i
$842$		0			0
$843$	1.53213	−	1.76817i	0.0527693	−	0.0608990i
$844$		0			0
$845$	8.24731	+	5.30022i	0.283716	+	0.182333i
$846$		0			0
$847$	−17.2025	+	11.0554i	−0.591084	+	0.379866i
$848$		0			0
$849$	−92.8351	+	27.2588i	−3.18609	+	0.935521i
$850$		0			0
$851$	31.2786	−	27.2057i	1.07222	−	0.932601i
$852$		0			0
$853$	−40.0907	+	11.7717i	−1.37268	+	0.403055i	−0.883215	−	0.468968i	$-0.844626\pi$
$853$	−40.0907	+	11.7717i	−1.37268	+	0.403055i	−0.489465	+	0.872023i	$0.662808\pi$
$854$		0			0
$855$	−21.0115	+	13.5033i	−0.718578	+	0.461802i
$856$		0			0
$857$	−23.6402	−	15.1926i	−0.807534	−	0.518971i	0.0705321	−	0.997510i	$-0.477530\pi$
$857$	−23.6402	−	15.1926i	−0.807534	−	0.518971i	−0.878066	+	0.478539i	$0.841167\pi$
$858$		0			0
$859$	17.5022	−	20.1986i	0.597167	−	0.689168i	−0.374038	−	0.927414i	$-0.622027\pi$
$859$	17.5022	−	20.1986i	0.597167	−	0.689168i	0.971205	+	0.238246i	$0.0765723\pi$
$860$		0			0
$861$	25.8899	+	56.6910i	0.882327	+	1.93203i
$862$		0			0
$863$	14.7635	+	4.33496i	0.502556	+	0.147564i	0.523178	−	0.852224i	$-0.324746\pi$
$863$	14.7635	+	4.33496i	0.502556	+	0.147564i	−0.0206220	+	0.999787i	$0.506565\pi$
$864$		0			0
$865$	0.598599	−	4.16335i	0.0203530	−	0.141558i
$866$		0			0
$867$	−22.4655	+	49.1926i	−0.762969	+	1.67067i
$868$		0			0
$869$	−8.04483	−	55.9530i	−0.272902	−	1.89808i
$870$		0			0
$871$	2.64291	+	3.05008i	0.0895516	+	0.103348i
$872$		0			0
$873$	57.3414			1.94071
$874$		0			0
$875$	1.91660			0.0647929
$876$		0			0
$877$	9.15189	+	10.5618i	0.309037	+	0.356648i	0.888929	−	0.458046i	$-0.151450\pi$
$877$	9.15189	+	10.5618i	0.309037	+	0.356648i	−0.579891	+	0.814694i	$0.696905\pi$
$878$		0			0
$879$	−6.24952	−	43.4664i	−0.210791	−	1.46608i
$880$		0			0
$881$	13.6021	−	29.7845i	0.458267	−	1.00346i	−0.529612	−	0.848240i	$-0.677663\pi$
$881$	13.6021	−	29.7845i	0.458267	−	1.00346i	0.987879	−	0.155225i	$-0.0496102\pi$
$882$		0			0
$883$	7.65047	−	53.2102i	0.257459	−	1.79066i	−0.293321	−	0.956014i	$-0.594760\pi$
$883$	7.65047	−	53.2102i	0.257459	−	1.79066i	0.550779	−	0.834651i	$-0.314331\pi$
$884$		0			0
$885$	22.5226	+	6.61324i	0.757090	+	0.222302i
$886$		0			0
$887$	−8.50191	−	18.6166i	−0.285466	−	0.625084i	0.711520	−	0.702666i	$-0.248007\pi$
$887$	−8.50191	−	18.6166i	−0.285466	−	0.625084i	−0.996986	+	0.0775824i	$0.975280\pi$
$888$		0			0
$889$	13.7278	−	15.8427i	0.460416	−	0.531348i
$890$		0			0
$891$	−79.6415	−	51.1825i	−2.66809	−	1.71468i
$892$		0			0
$893$	35.1986	−	22.6208i	1.17788	−	0.756975i
$894$		0			0
$895$	−6.36428	+	1.86872i	−0.212735	+	0.0624645i
$896$		0			0
$897$	−24.7904	+	11.3775i	−0.827728	+	0.379885i
$898$		0			0
$899$	14.1500	−	4.15481i	0.471929	−	0.138571i
$900$		0			0
$901$	0.0669107	−	0.0430009i	0.00222912	−	0.00143257i
$902$		0			0
$903$	10.8957	+	7.00223i	0.362586	+	0.233020i
$904$		0			0
$905$	11.0132	−	12.7099i	0.366090	−	0.422490i
$906$		0			0
$907$	−5.16702	−	11.3142i	−0.171568	−	0.375682i	0.804242	−	0.594302i	$-0.202572\pi$
$907$	−5.16702	−	11.3142i	−0.171568	−	0.375682i	−0.975810	+	0.218620i	$0.929844\pi$
$908$		0			0
$909$	38.8494	+	11.4072i	1.28855	+	0.378353i
$910$		0			0
$911$	3.96290	−	27.5626i	0.131297	−	0.913189i	−0.812570	−	0.582863i	$-0.801932\pi$
$911$	3.96290	−	27.5626i	0.131297	−	0.913189i	0.943867	−	0.330326i	$-0.107159\pi$
$912$		0			0
$913$	−30.1027	+	65.9156i	−0.996253	+	2.18149i
$914$		0			0
$915$	−0.178314	−	1.24020i	−0.00589487	−	0.0409997i
$916$		0			0
$917$	5.50096	+	6.34844i	0.181658	+	0.209644i
$918$		0			0
$919$	−32.1767			−1.06141			−0.530706	−	0.847556i	$-0.678073\pi$
$919$	−32.1767			−1.06141			−0.530706	+	0.847556i	$0.678073\pi$
$920$		0			0
$921$	−34.0929			−1.12340
$922$		0			0
$923$	−18.5793	−	21.4417i	−0.611546	−	0.705762i
$924$		0			0
$925$	−1.23016	−	8.55595i	−0.0404474	−	0.281318i
$926$		0			0
$927$	36.0931	−	79.0329i	1.18545	−	2.59578i
$928$		0			0
$929$	1.05517	−	7.33883i	0.0346188	−	0.240779i	−0.965163	−	0.261648i	$-0.915734\pi$
$929$	1.05517	−	7.33883i	0.0346188	−	0.240779i	0.999782	+	0.0208686i	$0.00664316\pi$
$930$		0			0
$931$	11.1965	+	3.28759i	0.366951	+	0.107746i
$932$		0			0
$933$	−28.5894	−	62.6020i	−0.935974	−	2.04950i
$934$		0			0
$935$	−0.0606575	+	0.0700025i	−0.00198371	+	0.00228933i
$936$		0			0
$937$	10.3614	+	6.65885i	0.338491	+	0.217535i	0.698832	−	0.715286i	$-0.253703\pi$
$937$	10.3614	+	6.65885i	0.338491	+	0.217535i	−0.360341	+	0.932821i	$0.617340\pi$
$938$		0			0
$939$	6.67365	−	4.28890i	0.217786	−	0.139963i
$940$		0			0
$941$	−22.6917	+	6.66289i	−0.739729	+	0.217204i	−0.629824	−	0.776738i	$-0.716873\pi$
$941$	−22.6917	+	6.66289i	−0.739729	+	0.217204i	−0.109905	+	0.993942i	$0.535055\pi$
$942$		0			0
$943$	26.4257	−	41.2889i	0.860539	−	1.34455i
$944$		0			0
$945$	−24.1042	+	7.07763i	−0.784109	+	0.230235i
$946$		0			0
$947$	1.46691	−	0.942726i	0.0476682	−	0.0306345i	−0.516590	−	0.856233i	$-0.672799\pi$
$947$	1.46691	−	0.942726i	0.0476682	−	0.0306345i	0.564258	+	0.825599i	$0.309162\pi$
$948$		0			0
$949$	20.2042	+	12.9845i	0.655856	+	0.421493i
$950$		0			0
$951$	23.9535	−	27.6438i	0.776744	−	0.896411i
$952$		0			0
$953$	7.21646	+	15.8018i	0.233764	+	0.511872i	0.989766	−	0.142697i	$-0.0455775\pi$
$953$	7.21646	+	15.8018i	0.233764	+	0.511872i	−0.756002	+	0.654569i	$0.772850\pi$
$954$		0			0
$955$	−21.7014	−	6.37210i	−0.702240	−	0.206196i
$956$		0			0
$957$	5.71304	−	39.7351i	0.184677	−	1.28445i
$958$		0			0
$959$	1.11432	−	2.44001i	0.0359832	−	0.0787921i
$960$		0			0
$961$	0.199857	+	1.39004i	0.00644701	+	0.0448399i
$962$		0			0
$963$	−93.5216	−	107.930i	−3.01369	−	3.47798i
$964$		0			0
$965$	−21.8196			−0.702396
$966$		0			0
$967$	61.2781			1.97057			0.985286	−	0.170914i	$-0.0546722\pi$
$967$	61.2781			1.97057			0.985286	+	0.170914i	$0.0546722\pi$
$968$		0			0
$969$	−0.145410	−	0.167812i	−0.00467123	−	0.00539089i
$970$		0			0
$971$	4.69735	+	32.6708i	0.150745	+	1.04845i	0.914975	+	0.403511i	$0.132210\pi$
$971$	4.69735	+	32.6708i	0.150745	+	1.04845i	−0.764230	+	0.644944i	$0.776881\pi$
$972$		0			0
$973$	−6.67547	+	14.6172i	−0.214006	+	0.468607i
$974$		0			0
$975$	−0.809425	+	5.62968i	−0.0259224	+	0.180294i
$976$		0			0
$977$	22.6853	+	6.66101i	0.725768	+	0.213105i	0.623690	−	0.781672i	$-0.285633\pi$
$977$	22.6853	+	6.66101i	0.725768	+	0.213105i	0.102078	+	0.994776i	$0.467451\pi$
$978$		0			0
$979$	7.31674	+	16.0214i	0.233844	+	0.512047i
$980$		0			0
$981$	−13.3265	+	15.3796i	−0.425482	+	0.491032i
$982$		0			0
$983$	−13.3014	−	8.54830i	−0.424249	−	0.272648i	0.311047	−	0.950395i	$-0.399320\pi$
$983$	−13.3014	−	8.54830i	−0.424249	−	0.272648i	−0.735296	+	0.677746i	$0.762957\pi$
$984$		0			0
$985$	−2.60145	+	1.67185i	−0.0828892	+	0.0532696i
$986$		0			0
$987$	69.7803	−	20.4893i	2.22113	−	0.652183i
$988$		0			0
$989$	−0.0190725	−	10.1874i	−0.000606469	−	0.323941i
$990$		0			0
$991$	−11.9180	+	3.49945i	−0.378588	+	0.111164i	−0.465490	−	0.885053i	$-0.654122\pi$
$991$	−11.9180	+	3.49945i	−0.378588	+	0.111164i	0.0869013	+	0.996217i	$0.472304\pi$
$992$		0			0
$993$	−51.8368	+	33.3135i	−1.64499	+	1.05717i
$994$		0			0
$995$	−7.70881	−	4.95415i	−0.244386	−	0.157057i
$996$		0			0
$997$	15.3235	−	17.6843i	0.485301	−	0.560067i	−0.459303	−	0.888280i	$-0.651901\pi$
$997$	15.3235	−	17.6843i	0.485301	−	0.560067i	0.944604	+	0.328213i	$0.106446\pi$
$998$		0			0
$999$	47.0666	+	103.061i	1.48912	+	3.26072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.b.101.1	yes	50
23.18	even	11	inner	460.2.m.b.41.1	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.b.41.1	✓	50	23.18	even	11	inner
460.2.m.b.101.1	yes	50	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.08327 - 2.40422i) q^{3} +(0.142315 + 0.989821i) q^{5} +(-0.796185 + 1.74340i) q^{7} +(-1.01332 + 7.04777i) q^{9} +O(q^{10})\)	\(q+(-2.08327 - 2.40422i) q^{3} +(0.142315 + 0.989821i) q^{5} +(-0.796185 + 1.74340i) q^{7} +(-1.01332 + 7.04777i) q^{9} +(4.46646 + 1.31147i) q^{11} +(0.742699 + 1.62629i) q^{13} +(2.08327 - 2.40422i) q^{15} +(0.0167394 + 0.0107578i) q^{17} +(2.95095 - 1.89646i) q^{19} +(5.85018 - 1.71777i) q^{21} +(-3.63032 - 3.13381i) q^{23} +(-0.959493 + 0.281733i) q^{25} +(11.0267 - 7.08643i) q^{27} +(2.28049 + 1.46558i) q^{29} +(3.56257 - 4.11142i) q^{31} +(-6.15176 - 13.4705i) q^{33} +(-1.83896 - 0.539969i) q^{35} +(-1.23016 + 8.55595i) q^{37} +(2.36270 - 5.17359i) q^{39} +(1.45469 + 10.1176i) q^{41} +(1.39107 + 1.60538i) q^{43} -7.12025 q^{45} +11.9279 q^{47} +(2.17849 + 2.51411i) q^{49} +(-0.00900865 - 0.0626565i) q^{51} +(1.66049 - 3.63597i) q^{53} +(-0.662478 + 4.60764i) q^{55} +(-10.7071 - 3.14389i) q^{57} +(3.06524 + 6.71193i) q^{59} +(0.257922 - 0.297658i) q^{61} +(-11.4803 - 7.37795i) q^{63} +(-1.50403 + 0.966584i) q^{65} +(2.16593 - 0.635975i) q^{67} +(0.0285629 + 15.2566i) q^{69} +(-15.2262 + 4.47082i) q^{71} +(11.3008 - 7.26261i) q^{73} +(2.67622 + 1.71990i) q^{75} +(-5.84254 + 6.74266i) q^{77} +(-5.04461 - 11.0461i) q^{79} +(-19.5134 - 5.72965i) q^{81} +(-2.21540 + 15.4084i) q^{83} +(-0.00826601 + 0.0181000i) q^{85} +(-1.22729 - 8.53597i) q^{87} +(2.47778 + 2.85951i) q^{89} -3.42659 q^{91} -17.3065 q^{93} +(2.29712 + 2.65102i) q^{95} +(-1.14610 - 7.97132i) q^{97} +(-13.7689 + 30.1497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) \) 50 * q + 5 * q^5 - q^7 - 25 * q^9	\( 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) \) 50 * q + 5 * q^5 - q^7 - 25 * q^9 - 6 * q^13 + 12 * q^17 + 19 * q^19 + 39 * q^21 - 16 * q^23 - 5 * q^25 + 21 * q^27 - 6 * q^29 + 34 * q^31 + 50 * q^33 - 10 * q^35 + 7 * q^37 - 70 * q^39 - 51 * q^41 - 18 * q^43 - 74 * q^45 + 30 * q^47 - 16 * q^49 - 80 * q^51 - 23 * q^53 - 33 * q^55 + 27 * q^57 - 18 * q^59 + 76 * q^61 + 138 * q^63 + 6 * q^65 + 25 * q^67 - 30 * q^69 - 37 * q^71 + 20 * q^73 + 92 * q^77 + 18 * q^79 + 25 * q^81 - 22 * q^83 - 12 * q^85 - 109 * q^87 + 8 * q^89 + 110 * q^91 + 64 * q^93 + 3 * q^95 - 38 * q^97 - 126 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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