LMFDB - Embedded newform 304.2.u.b.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(17,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("304.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.u (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			161.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	304.161
Dual form			304.2.u.b.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.20574 - 1.85083i) q^{3} +(-0.826352 - 0.300767i) q^{5} +(0.173648 - 0.300767i) q^{7} +(0.918748 - 5.21048i) q^{9} +O(q^{10})$	\(q+(2.20574 - 1.85083i) q^{3} +(-0.826352 - 0.300767i) q^{5} +(0.173648 - 0.300767i) q^{7} +(0.918748 - 5.21048i) q^{9} +(-1.11334 - 1.92836i) q^{11} +(1.97178 + 1.65452i) q^{13} +(-2.37939 + 0.866025i) q^{15} +(0.0812519 + 0.460802i) q^{17} +(4.29813 + 0.725293i) q^{19} +(-0.173648 - 0.984808i) q^{21} +(-2.53209 + 0.921605i) q^{23} +(-3.23783 - 2.71686i) q^{25} +(-3.29813 - 5.71253i) q^{27} +(-1.19459 + 6.77487i) q^{29} +(-3.55303 + 6.15403i) q^{31} +(-6.02481 - 2.19285i) q^{33} +(-0.233956 + 0.196312i) q^{35} +4.94356 q^{37} +7.41147 q^{39} +(1.89646 - 1.59132i) q^{41} +(3.66637 + 1.33445i) q^{43} +(-2.32635 + 4.02936i) q^{45} +(1.26604 - 7.18009i) q^{47} +(3.43969 + 5.95772i) q^{49} +(1.03209 + 0.866025i) q^{51} +(2.66637 - 0.970481i) q^{53} +(0.340022 + 1.92836i) q^{55} +(10.8229 - 6.35532i) q^{57} +(1.09492 + 6.20961i) q^{59} +(-8.57785 + 3.12208i) q^{61} +(-1.40760 - 1.18112i) q^{63} +(-1.13176 - 1.96026i) q^{65} +(-1.33275 + 7.55839i) q^{67} +(-3.87939 + 6.71929i) q^{69} +(-8.74422 - 3.18264i) q^{71} +(1.06418 - 0.892951i) q^{73} -12.1702 q^{75} -0.773318 q^{77} +(9.07398 - 7.61397i) q^{79} +(-2.93242 - 1.06731i) q^{81} +(-7.41534 + 12.8438i) q^{83} +(0.0714517 - 0.405223i) q^{85} +(9.90420 + 17.1546i) q^{87} +(-7.88326 - 6.61484i) q^{89} +(0.840022 - 0.305743i) q^{91} +(3.55303 + 20.1503i) q^{93} +(-3.33363 - 1.89209i) q^{95} +(1.64156 + 9.30975i) q^{97} +(-11.0706 + 4.02936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 6 q^{5} + 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 6 * q^5 + 3 * q^9	$ 6 q + 3 q^{3} - 6 q^{5} + 3 q^{9} - 3 q^{13} - 3 q^{15} + 3 q^{17} + 12 q^{19} - 6 q^{23} - 6 q^{27} - 3 q^{29} - 9 q^{31} - 9 q^{33} - 6 q^{35} + 24 q^{39} + 21 q^{41} + 3 q^{43} - 15 q^{45} + 3 q^{47} + 15 q^{49} - 3 q^{51} - 3 q^{53} - 18 q^{55} + 24 q^{57} - 12 q^{59} - 12 q^{61} - 12 q^{63} - 12 q^{65} + 30 q^{67} - 12 q^{69} + 6 q^{71} - 12 q^{73} - 30 q^{75} - 18 q^{77} + 39 q^{79} + 6 q^{81} + 21 q^{87} - 12 q^{89} - 15 q^{91} + 9 q^{93} - 39 q^{95} + 18 q^{97} - 9 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 - 6 * q^5 + 3 * q^9 - 3 * q^13 - 3 * q^15 + 3 * q^17 + 12 * q^19 - 6 * q^23 - 6 * q^27 - 3 * q^29 - 9 * q^31 - 9 * q^33 - 6 * q^35 + 24 * q^39 + 21 * q^41 + 3 * q^43 - 15 * q^45 + 3 * q^47 + 15 * q^49 - 3 * q^51 - 3 * q^53 - 18 * q^55 + 24 * q^57 - 12 * q^59 - 12 * q^61 - 12 * q^63 - 12 * q^65 + 30 * q^67 - 12 * q^69 + 6 * q^71 - 12 * q^73 - 30 * q^75 - 18 * q^77 + 39 * q^79 + 6 * q^81 + 21 * q^87 - 12 * q^89 - 15 * q^91 + 9 * q^93 - 39 * q^95 + 18 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.20574	−	1.85083i	1.27348	−	1.06858i	0.279375	−	0.960182i	$-0.409873\pi$
$3$	2.20574	−	1.85083i	1.27348	−	1.06858i	0.994108	−	0.108397i	$-0.0345718\pi$
$4$		0			0
$5$	−0.826352	−	0.300767i	−0.369556	−	0.134507i	0.150565	−	0.988600i	$-0.451891\pi$
$5$	−0.826352	−	0.300767i	−0.369556	−	0.134507i	−0.520121	+	0.854093i	$0.674113\pi$
$6$		0			0
$7$	0.173648	−	0.300767i	0.0656328	−	0.113679i	−0.831342	−	0.555762i	$-0.812427\pi$
$7$	0.173648	−	0.300767i	0.0656328	−	0.113679i	0.896975	+	0.442082i	$0.145760\pi$
$8$		0			0
$9$	0.918748	−	5.21048i	0.306249	−	1.73683i
$10$		0			0
$11$	−1.11334	−	1.92836i	−0.335685	−	0.581423i	0.647931	−	0.761699i	$-0.275634\pi$
$11$	−1.11334	−	1.92836i	−0.335685	−	0.581423i	−0.983616	+	0.180276i	$0.942301\pi$
$12$		0			0
$13$	1.97178	+	1.65452i	0.546874	+	0.458882i	0.873881	−	0.486140i	$-0.161596\pi$
$13$	1.97178	+	1.65452i	0.546874	+	0.458882i	−0.327007	+	0.945022i	$0.606040\pi$
$14$		0			0
$15$	−2.37939	+	0.866025i	−0.614355	+	0.223607i
$16$		0			0
$17$	0.0812519	+	0.460802i	0.0197065	+	0.111761i	0.993074	−	0.117488i	$-0.0374841\pi$
$17$	0.0812519	+	0.460802i	0.0197065	+	0.111761i	−0.973368	+	0.229249i	$0.926373\pi$
$18$		0			0
$19$	4.29813	+	0.725293i	0.986059	+	0.166394i
$19$	4.29813	+	0.725293i	0.986059	+	0.166394i
$20$		0			0
$21$	−0.173648	−	0.984808i	−0.0378931	−	0.214903i
$22$		0			0
$23$	−2.53209	+	0.921605i	−0.527977	+	0.192168i	−0.592235	−	0.805765i	$-0.701754\pi$
$23$	−2.53209	+	0.921605i	−0.527977	+	0.192168i	0.0642578	+	0.997933i	$0.479532\pi$
$24$		0			0
$25$	−3.23783	−	2.71686i	−0.647565	−	0.543372i
$26$		0			0
$27$	−3.29813	−	5.71253i	−0.634726	−	1.09938i
$28$		0			0
$29$	−1.19459	+	6.77487i	−0.221830	+	1.25806i	0.646822	+	0.762641i	$0.276097\pi$
$29$	−1.19459	+	6.77487i	−0.221830	+	1.25806i	−0.868653	+	0.495421i	$0.835014\pi$
$30$		0			0
$31$	−3.55303	+	6.15403i	−0.638144	+	1.10530i	0.347696	+	0.937607i	$0.386964\pi$
$31$	−3.55303	+	6.15403i	−0.638144	+	1.10530i	−0.985840	+	0.167690i	$0.946369\pi$
$32$		0			0
$33$	−6.02481	−	2.19285i	−1.04879	−	0.381727i
$34$		0			0
$35$	−0.233956	+	0.196312i	−0.0395457	+	0.0331828i
$36$		0			0
$37$	4.94356			0.812717			0.406358	−	0.913714i	$-0.366798\pi$
$37$	4.94356			0.812717			0.406358	+	0.913714i	$0.366798\pi$
$38$		0			0
$39$	7.41147			1.18679
$40$		0			0
$41$	1.89646	−	1.59132i	0.296177	−	0.248522i	−0.482574	−	0.875855i	$-0.660298\pi$
$41$	1.89646	−	1.59132i	0.296177	−	0.248522i	0.778751	+	0.627333i	$0.215854\pi$
$42$		0			0
$43$	3.66637	+	1.33445i	0.559117	+	0.203502i	0.606093	−	0.795394i	$-0.292736\pi$
$43$	3.66637	+	1.33445i	0.559117	+	0.203502i	−0.0469757	+	0.998896i	$0.514958\pi$
$44$		0			0
$45$	−2.32635	+	4.02936i	−0.346792	+	0.600661i
$46$		0			0
$47$	1.26604	−	7.18009i	0.184672	−	1.04732i	−0.741705	−	0.670726i	$-0.765983\pi$
$47$	1.26604	−	7.18009i	0.184672	−	1.04732i	0.926377	−	0.376598i	$-0.122906\pi$
$48$		0			0
$49$	3.43969	+	5.95772i	0.491385	+	0.851103i
$50$		0			0
$51$	1.03209	+	0.866025i	0.144521	+	0.121268i
$52$		0			0
$53$	2.66637	−	0.970481i	0.366255	−	0.133306i	−0.152335	−	0.988329i	$-0.548679\pi$
$53$	2.66637	−	0.970481i	0.366255	−	0.133306i	0.518590	+	0.855023i	$0.326457\pi$
$54$		0			0
$55$	0.340022	+	1.92836i	0.0458486	+	0.260020i
$56$		0			0
$57$	10.8229	−	6.35532i	1.43353	−	0.841783i
$58$		0			0
$59$	1.09492	+	6.20961i	0.142547	+	0.808423i	0.969304	+	0.245864i	$0.0790718\pi$
$59$	1.09492	+	6.20961i	0.142547	+	0.808423i	−0.826757	+	0.562559i	$0.809817\pi$
$60$		0			0
$61$	−8.57785	+	3.12208i	−1.09828	+	0.399742i	−0.826682	−	0.562669i	$-0.809775\pi$
$61$	−8.57785	+	3.12208i	−1.09828	+	0.399742i	−0.271599	+	0.962411i	$0.587552\pi$
$62$		0			0
$63$	−1.40760	−	1.18112i	−0.177341	−	0.148807i
$64$		0			0
$65$	−1.13176	−	1.96026i	−0.140377	−	0.243141i
$66$		0			0
$67$	−1.33275	+	7.55839i	−0.162821	+	0.923405i	0.788461	+	0.615084i	$0.210878\pi$
$67$	−1.33275	+	7.55839i	−0.162821	+	0.923405i	−0.951283	+	0.308320i	$0.900233\pi$
$68$		0			0
$69$	−3.87939	+	6.71929i	−0.467023	+	0.808908i
$70$		0			0
$71$	−8.74422	−	3.18264i	−1.03775	−	0.377709i	−0.233722	−	0.972303i	$-0.575091\pi$
$71$	−8.74422	−	3.18264i	−1.03775	−	0.377709i	−0.804026	+	0.594594i	$0.797313\pi$
$72$		0			0
$73$	1.06418	−	0.892951i	0.124553	−	0.104512i	−0.578384	−	0.815765i	$-0.696316\pi$
$73$	1.06418	−	0.892951i	0.124553	−	0.104512i	0.702936	+	0.711253i	$0.251872\pi$
$74$		0			0
$75$	−12.1702			−1.40530
$76$		0			0
$77$	−0.773318			−0.0881278
$78$		0			0
$79$	9.07398	−	7.61397i	1.02090	−	0.856639i	0.0311616	−	0.999514i	$-0.490079\pi$
$79$	9.07398	−	7.61397i	1.02090	−	0.856639i	0.989741	+	0.142876i	$0.0456349\pi$
$80$		0			0
$81$	−2.93242	−	1.06731i	−0.325824	−	0.118590i
$82$		0			0
$83$	−7.41534	+	12.8438i	−0.813940	+	1.40979i	0.0961469	+	0.995367i	$0.469348\pi$
$83$	−7.41534	+	12.8438i	−0.813940	+	1.40979i	−0.910087	+	0.414418i	$0.863985\pi$
$84$		0			0
$85$	0.0714517	−	0.405223i	0.00775003	−	0.0439526i
$86$		0			0
$87$	9.90420	+	17.1546i	1.06184	+	1.83916i
$88$		0			0
$89$	−7.88326	−	6.61484i	−0.835623	−	0.701171i	0.120951	−	0.992658i	$-0.461406\pi$
$89$	−7.88326	−	6.61484i	−0.835623	−	0.701171i	−0.956575	+	0.291487i	$0.905850\pi$
$90$		0			0
$91$	0.840022	−	0.305743i	0.0880583	−	0.0320506i
$92$		0			0
$93$	3.55303	+	20.1503i	0.368432	+	2.08948i
$94$		0			0
$95$	−3.33363	−	1.89209i	−0.342023	−	0.194124i
$96$		0			0
$97$	1.64156	+	9.30975i	0.166675	+	0.945261i	0.947320	+	0.320287i	$0.103779\pi$
$97$	1.64156	+	9.30975i	0.166675	+	0.945261i	−0.780645	+	0.624974i	$0.785109\pi$
$98$		0			0
$99$	−11.0706	+	4.02936i	−1.11263	+	0.404966i
$100$		0			0
$101$	−7.08512	−	5.94512i	−0.704996	−	0.591562i	0.218194	−	0.975905i	$-0.429983\pi$
$101$	−7.08512	−	5.94512i	−0.704996	−	0.591562i	−0.923190	+	0.384343i	$0.874428\pi$
$102$		0			0
$103$	−2.75490	−	4.77163i	−0.271448	−	0.470162i	0.697785	−	0.716308i	$-0.254169\pi$
$103$	−2.75490	−	4.77163i	−0.271448	−	0.470162i	−0.969233	+	0.246145i	$0.920836\pi$
$104$		0			0
$105$	−0.152704	+	0.866025i	−0.0149023	+	0.0845154i
$106$		0			0
$107$	5.11721	−	8.86327i	0.494699	−	0.856845i	−0.505282	−	0.862954i	$-0.668611\pi$
$107$	5.11721	−	8.86327i	0.494699	−	0.856845i	0.999981	+	0.00610974i	$0.00194480\pi$
$108$		0			0
$109$	1.71301	+	0.623485i	0.164077	+	0.0597190i	0.422753	−	0.906245i	$-0.361064\pi$
$109$	1.71301	+	0.623485i	0.164077	+	0.0597190i	−0.258676	+	0.965964i	$0.583286\pi$
$110$		0			0
$111$	10.9042	−	9.14971i	1.03498	−	0.868452i
$112$		0			0
$113$	−17.6878			−1.66393			−0.831963	−	0.554830i	$-0.812783\pi$
$113$	−17.6878			−1.66393			−0.831963	+	0.554830i	$0.812783\pi$
$114$		0			0
$115$	2.36959			0.220965
$116$		0			0
$117$	10.4324	−	8.75384i	0.964477	−	0.809293i
$118$		0			0
$119$	0.152704	+	0.0555796i	0.0139983	+	0.00509497i
$120$		0			0
$121$	3.02094	−	5.23243i	0.274631	−	0.475675i
$122$		0			0
$123$	1.23783	−	7.02006i	0.111611	−	0.632977i
$124$		0			0
$125$	4.05690	+	7.02676i	0.362861	+	0.628493i
$126$		0			0
$127$	−8.88919	−	7.45891i	−0.788788	−	0.661871i	0.156657	−	0.987653i	$-0.449928\pi$
$127$	−8.88919	−	7.45891i	−0.788788	−	0.661871i	−0.945445	+	0.325782i	$0.894373\pi$
$128$		0			0
$129$	10.5569	−	3.84240i	0.929484	−	0.338304i
$130$		0			0
$131$	−0.320422	−	1.81720i	−0.0279954	−	0.158770i	0.967605	−	0.252468i	$-0.0812422\pi$
$131$	−0.320422	−	1.81720i	−0.0279954	−	0.158770i	−0.995601	+	0.0936982i	$0.970131\pi$
$132$		0			0
$133$	0.964508	−	1.16679i	0.0836334	−	0.101174i
$134$		0			0
$135$	1.00727	+	5.71253i	0.0866923	+	0.491657i
$136$		0			0
$137$	−0.240352	+	0.0874810i	−0.0205347	+	0.00747401i	−0.352267	−	0.935900i	$-0.614589\pi$
$137$	−0.240352	+	0.0874810i	−0.0205347	+	0.00747401i	0.331732	+	0.943374i	$0.392367\pi$
$138$		0			0
$139$	−3.26604	−	2.74054i	−0.277022	−	0.232449i	0.493682	−	0.869643i	$-0.335651\pi$
$139$	−3.26604	−	2.74054i	−0.277022	−	0.232449i	−0.770704	+	0.637193i	$0.780095\pi$
$140$		0			0
$141$	−10.4966	−	18.1806i	−0.883973	−	1.53109i
$142$		0			0
$143$	0.995252	−	5.64436i	0.0832272	−	0.472005i
$144$		0			0
$145$	3.02481	−	5.23913i	0.251197	−	0.435086i
$146$		0			0
$147$	18.6138	+	6.77487i	1.53524	+	0.558782i
$148$		0			0
$149$	12.6853	−	10.6442i	1.03922	−	0.872007i	0.0472981	−	0.998881i	$-0.484939\pi$
$149$	12.6853	−	10.6442i	1.03922	−	0.872007i	0.991919	+	0.126874i	$0.0404945\pi$
$150$		0			0
$151$	4.36184			0.354962			0.177481	−	0.984124i	$-0.443205\pi$
$151$	4.36184			0.354962			0.177481	+	0.984124i	$0.443205\pi$
$152$		0			0
$153$	2.47565			0.200145
$154$		0			0
$155$	4.78699	−	4.01676i	0.384500	−	0.322634i
$156$		0			0
$157$	9.03849	+	3.28974i	0.721350	+	0.262550i	0.676499	−	0.736444i	$-0.263496\pi$
$157$	9.03849	+	3.28974i	0.721350	+	0.262550i	0.0448510	+	0.998994i	$0.485719\pi$
$158$		0			0
$159$	4.08512	−	7.07564i	0.323971	−	0.561135i
$160$		0			0
$161$	−0.162504	+	0.921605i	−0.0128071	+	0.0726326i
$162$		0			0
$163$	4.17752	+	7.23567i	0.327209	+	0.566742i	0.981957	−	0.189105i	$-0.0605587\pi$
$163$	4.17752	+	7.23567i	0.327209	+	0.566742i	−0.654748	+	0.755847i	$0.727225\pi$
$164$		0			0
$165$	4.31908	+	3.62414i	0.336240	+	0.282139i
$166$		0			0
$167$	3.79174	−	1.38008i	0.293413	−	0.106794i	−0.191120	−	0.981567i	$-0.561212\pi$
$167$	3.79174	−	1.38008i	0.293413	−	0.106794i	0.484533	+	0.874773i	$0.338990\pi$
$168$		0			0
$169$	−1.10694	−	6.27779i	−0.0851496	−	0.482907i
$170$		0			0
$171$	7.72803	−	21.7290i	0.590977	−	1.66166i
$172$		0			0
$173$	−3.49794	−	19.8378i	−0.265943	−	1.50824i	−0.766335	−	0.642441i	$-0.777922\pi$
$173$	−3.49794	−	19.8378i	−0.265943	−	1.50824i	0.500391	−	0.865799i	$-0.333189\pi$
$174$		0			0
$175$	−1.37939	+	0.502055i	−0.104272	+	0.0379518i
$176$		0			0
$177$	13.9081	+	11.6703i	1.04539	+	0.877190i
$178$		0			0
$179$	−5.75624	−	9.97011i	−0.430242	−	0.745201i	0.566652	−	0.823957i	$-0.308238\pi$
$179$	−5.75624	−	9.97011i	−0.430242	−	0.745201i	−0.996894	+	0.0787564i	$0.974905\pi$
$180$		0			0
$181$	1.48246	−	8.40744i	0.110190	−	0.624920i	−0.878829	−	0.477136i	$-0.841675\pi$
$181$	1.48246	−	8.40744i	0.110190	−	0.624920i	0.989020	−	0.147784i	$-0.0472141\pi$
$182$		0			0
$183$	−13.1420	+	22.7627i	−0.971487	+	1.68266i
$184$		0			0
$185$	−4.08512	−	1.48686i	−0.300344	−	0.109316i
$186$		0			0
$187$	0.798133	−	0.669713i	0.0583653	−	0.0489743i
$188$		0			0
$189$	−2.29086			−0.166635
$190$		0			0
$191$	−18.3354			−1.32671			−0.663353	−	0.748307i	$-0.730867\pi$
$191$	−18.3354			−1.32671			−0.663353	+	0.748307i	$0.730867\pi$
$192$		0			0
$193$	0.228026	−	0.191336i	0.0164137	−	0.0137727i	−0.634544	−	0.772887i	$-0.718812\pi$
$193$	0.228026	−	0.191336i	0.0164137	−	0.0137727i	0.650958	+	0.759114i	$0.274368\pi$
$194$		0			0
$195$	−6.12449	−	2.22913i	−0.438583	−	0.159631i
$196$		0			0
$197$	−6.57057	+	11.3806i	−0.468134	+	0.810832i	−0.999337	−	0.0364128i	$-0.988407\pi$
$197$	−6.57057	+	11.3806i	−0.468134	+	0.810832i	0.531203	+	0.847245i	$0.321740\pi$
$198$		0			0
$199$	0.0445774	−	0.252811i	0.00316001	−	0.0179213i	−0.983187	−	0.182602i	$-0.941548\pi$
$199$	0.0445774	−	0.252811i	0.00316001	−	0.0179213i	0.986347	+	0.164680i	$0.0526593\pi$
$200$		0			0
$201$	11.0496	+	19.1385i	0.779381	+	1.34993i
$202$		0			0
$203$	1.83022	+	1.53574i	0.128456	+	0.107788i
$204$		0			0
$205$	−2.04576	+	0.744596i	−0.142882	+	0.0520048i
$206$		0			0
$207$	2.47565	+	14.0401i	0.172070	+	0.975856i
$208$		0			0
$209$	−3.38666	−	9.09586i	−0.234260	−	0.629174i
$210$		0			0
$211$	−0.425145	−	2.41112i	−0.0292682	−	0.165988i	0.966670	−	0.256024i	$-0.0824128\pi$
$211$	−0.425145	−	2.41112i	−0.0292682	−	0.165988i	−0.995938	+	0.0900364i	$0.971302\pi$
$212$		0			0
$213$	−25.1780	+	9.16404i	−1.72517	+	0.627909i
$214$		0			0
$215$	−2.62836	−	2.20545i	−0.179252	−	0.150411i
$216$		0			0
$217$	1.23396	+	2.13727i	0.0837664	+	0.145088i
$218$		0			0
$219$	0.694593	−	3.93923i	0.0469362	−	0.266189i
$220$		0			0
$221$	−0.602196	+	1.04303i	−0.0405081	+	0.0701621i
$222$		0			0
$223$	−7.99660	−	2.91052i	−0.535492	−	0.194903i	0.0600971	−	0.998193i	$-0.480859\pi$
$223$	−7.99660	−	2.91052i	−0.535492	−	0.194903i	−0.595589	+	0.803289i	$0.703081\pi$
$224$		0			0
$225$	−17.1309	+	14.3745i	−1.14206	+	0.958301i
$226$		0			0
$227$	14.1506			0.939211			0.469606	−	0.882876i	$-0.344396\pi$
$227$	14.1506			0.939211			0.469606	+	0.882876i	$0.344396\pi$
$228$		0			0
$229$	−20.5330			−1.35686			−0.678430	−	0.734665i	$-0.737339\pi$
$229$	−20.5330			−1.35686			−0.678430	+	0.734665i	$0.737339\pi$
$230$		0			0
$231$	−1.70574	+	1.43128i	−0.112229	+	0.0941715i
$232$		0			0
$233$	−16.5865	−	6.03698i	−1.08662	−	0.395496i	−0.264249	−	0.964454i	$-0.585124\pi$
$233$	−16.5865	−	6.03698i	−1.08662	−	0.395496i	−0.822366	+	0.568959i	$0.807346\pi$
$234$		0			0
$235$	−3.20574	+	5.55250i	−0.209119	+	0.362205i
$236$		0			0
$237$	5.92262	−	33.5888i	0.384715	−	2.18183i
$238$		0			0
$239$	1.17617	+	2.03719i	0.0760804	+	0.131775i	0.901556	−	0.432663i	$-0.142426\pi$
$239$	1.17617	+	2.03719i	0.0760804	+	0.131775i	−0.825475	+	0.564438i	$0.809093\pi$
$240$		0			0
$241$	10.5719	+	8.87089i	0.680997	+	0.571424i	0.916298	−	0.400498i	$-0.131163\pi$
$241$	10.5719	+	8.87089i	0.680997	+	0.571424i	−0.235300	+	0.971923i	$0.575607\pi$
$242$		0			0
$243$	10.1518	−	3.69496i	0.651240	−	0.237032i
$244$		0			0
$245$	−1.05051	−	5.95772i	−0.0671144	−	0.380625i
$246$		0			0
$247$	7.27497	+	8.54147i	0.462895	+	0.543481i
$248$		0			0
$249$	7.41534	+	42.0545i	0.469928	+	2.66510i
$250$		0			0
$251$	−3.91400	+	1.42458i	−0.247050	+	0.0899187i	−0.462577	−	0.886579i	$-0.653075\pi$
$251$	−3.91400	+	1.42458i	−0.247050	+	0.0899187i	0.215528	+	0.976498i	$0.430853\pi$
$252$		0			0
$253$	4.59627	+	3.85673i	0.288965	+	0.242470i
$254$		0			0
$255$	−0.592396	−	1.02606i	−0.0370973	−	0.0642544i
$256$		0			0
$257$	0.115867	−	0.657115i	0.00722759	−	0.0409897i	−0.980981	−	0.194105i	$-0.937820\pi$
$257$	0.115867	−	0.657115i	0.00722759	−	0.0409897i	0.988208	+	0.153116i	$0.0489307\pi$
$258$		0			0
$259$	0.858441	−	1.48686i	0.0533409	−	0.0923892i
$260$		0			0
$261$	34.2028	+	12.4488i	2.11710	+	0.770561i
$262$		0			0
$263$	−8.73261	+	7.32753i	−0.538476	+	0.451835i	−0.871016	−	0.491254i	$-0.836539\pi$
$263$	−8.73261	+	7.32753i	−0.538476	+	0.451835i	0.332540	+	0.943089i	$0.392094\pi$
$264$		0			0
$265$	−2.49525			−0.153282
$266$		0			0
$267$	−29.6313			−1.81341
$268$		0			0
$269$	14.8537	−	12.4637i	0.905646	−	0.759927i	−0.0656400	−	0.997843i	$-0.520909\pi$
$269$	14.8537	−	12.4637i	0.905646	−	0.759927i	0.971286	+	0.237916i	$0.0764644\pi$
$270$		0			0
$271$	−12.5865	−	4.58110i	−0.764573	−	0.278282i	−0.0698486	−	0.997558i	$-0.522252\pi$
$271$	−12.5865	−	4.58110i	−0.764573	−	0.278282i	−0.694725	+	0.719276i	$0.744474\pi$
$272$		0			0
$273$	1.28699	−	2.22913i	0.0778921	−	0.134913i
$274$		0			0
$275$	−1.63429	+	9.26849i	−0.0985511	+	0.558911i
$276$		0			0
$277$	−8.87346	−	15.3693i	−0.533154	−	0.923450i	−0.999250	−	0.0387161i	$-0.987673\pi$
$277$	−8.87346	−	15.3693i	−0.533154	−	0.923450i	0.466096	−	0.884734i	$-0.345660\pi$
$278$		0			0
$279$	28.8011	+	24.1670i	1.72428	+	1.44684i
$280$		0			0
$281$	−17.1766	+	6.25179i	−1.02467	+	0.372950i	−0.799050	−	0.601265i	$-0.794664\pi$
$281$	−17.1766	+	6.25179i	−1.02467	+	0.372950i	−0.225622	+	0.974215i	$0.572442\pi$
$282$		0			0
$283$	−1.33497	−	7.57099i	−0.0793557	−	0.450049i	−0.998432	−	0.0559700i	$-0.982175\pi$
$283$	−1.33497	−	7.57099i	−0.0793557	−	0.450049i	0.919077	−	0.394079i	$-0.128936\pi$
$284$		0			0
$285$	−10.8550	+	1.99654i	−0.642997	+	0.118265i
$286$		0			0
$287$	−0.149300	−	0.846723i	−0.00881290	−	0.0499805i
$288$		0			0
$289$	15.7690	−	5.73946i	0.927590	−	0.337615i
$290$		0			0
$291$	20.8516	+	17.4966i	1.22234	+	1.02567i
$292$		0			0
$293$	5.25150	+	9.09586i	0.306796	+	0.531386i	0.977660	−	0.210195i	$-0.0674098\pi$
$293$	5.25150	+	9.09586i	0.306796	+	0.531386i	−0.670864	+	0.741581i	$0.734076\pi$
$294$		0			0
$295$	0.962859	−	5.46064i	0.0560598	−	0.317931i
$296$		0			0
$297$	−7.34389	+	12.7200i	−0.426136	+	0.738089i
$298$		0			0
$299$	−6.51754	−	2.37219i	−0.376919	−	0.137187i
$300$		0			0
$301$	1.03802	−	0.871001i	0.0598304	−	0.0502037i
$302$		0			0
$303$	−26.6313			−1.52993
$304$		0			0
$305$	8.02734			0.459644
$306$		0			0
$307$	8.95929	−	7.51774i	0.511334	−	0.429060i	−0.350264	−	0.936651i	$-0.613908\pi$
$307$	8.95929	−	7.51774i	0.511334	−	0.429060i	0.861598	+	0.507591i	$0.169464\pi$
$308$		0			0
$309$	−14.9081	−	5.42609i	−0.848091	−	0.308680i
$310$		0			0
$311$	7.98293	−	13.8268i	0.452670	−	0.784048i	−0.545881	−	0.837863i	$-0.683805\pi$
$311$	7.98293	−	13.8268i	0.452670	−	0.784048i	0.998551	+	0.0538151i	$0.0171382\pi$
$312$		0			0
$313$	−4.62402	+	26.2241i	−0.261365	+	1.48227i	0.517825	+	0.855487i	$0.326742\pi$
$313$	−4.62402	+	26.2241i	−0.261365	+	1.48227i	−0.779190	+	0.626788i	$0.784369\pi$
$314$		0			0
$315$	0.807934	+	1.39938i	0.0455219	+	0.0788462i
$316$		0			0
$317$	22.6229	+	18.9829i	1.27063	+	1.06618i	0.994465	+	0.105073i	$0.0335077\pi$
$317$	22.6229	+	18.9829i	1.27063	+	1.06618i	0.276164	+	0.961111i	$0.410937\pi$
$318$		0			0
$319$	14.3944	−	5.23913i	0.805932	−	0.293335i
$320$		0			0
$321$	−5.11721	−	29.0211i	−0.285615	−	1.61980i
$322$		0			0
$323$	0.0150147	+	2.03952i	0.000835443	+	0.113482i
$324$		0			0
$325$	−1.88919	−	10.7141i	−0.104793	−	0.594311i
$326$		0			0
$327$	4.93242	−	1.79525i	0.272763	−	0.0992777i
$328$		0			0
$329$	−1.93969	−	1.62760i	−0.106939	−	0.0897322i
$330$		0			0
$331$	13.8327	+	23.9590i	0.760317	+	1.31691i	0.942687	+	0.333677i	$0.108290\pi$
$331$	13.8327	+	23.9590i	0.760317	+	1.31691i	−0.182371	+	0.983230i	$0.558377\pi$
$332$		0			0
$333$	4.54189	−	25.7583i	0.248894	−	1.41155i
$334$		0			0
$335$	3.37464	−	5.84504i	0.184376	−	0.319349i
$336$		0			0
$337$	−16.7827	−	6.10841i	−0.914212	−	0.332746i	−0.158279	−	0.987394i	$-0.550594\pi$
$337$	−16.7827	−	6.10841i	−0.914212	−	0.332746i	−0.755934	+	0.654648i	$0.772817\pi$
$338$		0			0
$339$	−39.0146	+	32.7371i	−2.11898	+	1.77804i
$340$		0			0
$341$	15.8229			0.856861
$342$		0			0
$343$	4.82026			0.260270
$344$		0			0
$345$	5.22668	−	4.38571i	0.281395	−	0.236119i
$346$		0			0
$347$	−5.45084	−	1.98394i	−0.292616	−	0.106504i	0.191541	−	0.981485i	$-0.438652\pi$
$347$	−5.45084	−	1.98394i	−0.292616	−	0.106504i	−0.484157	+	0.874981i	$0.660874\pi$
$348$		0			0
$349$	−2.68614	+	4.65253i	−0.143786	+	0.249044i	−0.928919	−	0.370282i	$-0.879261\pi$
$349$	−2.68614	+	4.65253i	−0.143786	+	0.249044i	0.785134	+	0.619326i	$0.212594\pi$
$350$		0			0
$351$	2.94831	−	16.7207i	0.157369	−	0.892485i
$352$		0			0
$353$	12.6172	+	21.8537i	0.671546	+	1.16315i	0.977466	+	0.211095i	$0.0677029\pi$
$353$	12.6172	+	21.8537i	0.671546	+	1.16315i	−0.305919	+	0.952057i	$0.598964\pi$
$354$		0			0
$355$	6.26857	+	5.25996i	0.332701	+	0.279169i
$356$		0			0
$357$	0.439693	−	0.160035i	0.0232710	−	0.00846995i
$358$		0			0
$359$	−1.16116	−	6.58526i	−0.0612837	−	0.347557i	−0.999996	−	0.00285518i	$-0.999091\pi$
$359$	−1.16116	−	6.58526i	−0.0612837	−	0.347557i	0.938712	−	0.344702i	$-0.112020\pi$
$360$		0			0
$361$	17.9479	+	6.23481i	0.944626	+	0.328148i
$362$		0			0
$363$	−3.02094	−	17.1326i	−0.158558	−	0.899230i
$364$		0			0
$365$	−1.14796	+	0.417822i	−0.0600868	+	0.0218698i
$366$		0			0
$367$	−6.21941	−	5.21870i	−0.324650	−	0.272414i	0.465865	−	0.884856i	$-0.345743\pi$
$367$	−6.21941	−	5.21870i	−0.324650	−	0.272414i	−0.790516	+	0.612441i	$0.790188\pi$
$368$		0			0
$369$	−6.54916	−	11.3435i	−0.340936	−	0.590518i
$370$		0			0
$371$	0.171122	−	0.970481i	0.00888421	−	0.0503849i
$372$		0			0
$373$	−17.4488	+	30.2222i	−0.903463	+	1.56484i	−0.0804968	+	0.996755i	$0.525651\pi$
$373$	−17.4488	+	30.2222i	−0.903463	+	1.56484i	−0.822967	+	0.568090i	$0.807683\pi$
$374$		0			0
$375$	21.9538	+	7.99054i	1.13369	+	0.412630i
$376$		0			0
$377$	−13.5646	+	11.3821i	−0.698615	+	0.586207i
$378$		0			0
$379$	−1.70140			−0.0873950			−0.0436975	−	0.999045i	$-0.513914\pi$
$379$	−1.70140			−0.0873950			−0.0436975	+	0.999045i	$0.513914\pi$
$380$		0			0
$381$	−33.4124			−1.71177
$382$		0			0
$383$	−2.24969	+	1.88771i	−0.114954	+	0.0964575i	−0.698453	−	0.715656i	$-0.746128\pi$
$383$	−2.24969	+	1.88771i	−0.114954	+	0.0964575i	0.583499	+	0.812114i	$0.301683\pi$
$384$		0			0
$385$	0.639033	+	0.232589i	0.0325681	+	0.0118538i
$386$		0			0
$387$	10.3216	−	17.8775i	0.524677	−	0.908767i
$388$		0			0
$389$	−4.26604	+	24.1939i	−0.216297	+	1.22668i	0.662344	+	0.749199i	$0.269562\pi$
$389$	−4.26604	+	24.1939i	−0.216297	+	1.22668i	−0.878642	+	0.477482i	$0.841550\pi$
$390$		0			0
$391$	−0.630415	−	1.09191i	−0.0318815	−	0.0552203i
$392$		0			0
$393$	−4.07011	−	3.41523i	−0.205310	−	0.172275i
$394$		0			0
$395$	−9.78833	+	3.56266i	−0.492504	+	0.179257i
$396$		0			0
$397$	−5.52822	−	31.3521i	−0.277453	−	1.57352i	−0.731059	−	0.682314i	$-0.760974\pi$
$397$	−5.52822	−	31.3521i	−0.277453	−	1.57352i	0.453606	−	0.891202i	$-0.350137\pi$
$398$		0			0
$399$	−0.0320889	−	4.35878i	−0.00160645	−	0.218212i
$400$		0			0
$401$	−0.0150147	−	0.0851529i	−0.000749801	−	0.00425233i	0.984431	−	0.175774i	$-0.0562428\pi$
$401$	−0.0150147	−	0.0851529i	−0.000749801	−	0.00425233i	−0.985180	+	0.171522i	$0.945132\pi$
$402$		0			0
$403$	−17.1878	+	6.25584i	−0.856185	+	0.311626i
$404$		0			0
$405$	2.10220	+	1.76395i	0.104459	+	0.0876515i
$406$		0			0
$407$	−5.50387	−	9.53298i	−0.272817	−	0.472532i
$408$		0			0
$409$	3.47400	−	19.7021i	0.171778	−	0.974204i	−0.770019	−	0.638021i	$-0.779753\pi$
$409$	3.47400	−	19.7021i	0.171778	−	0.974204i	0.941797	−	0.336182i	$-0.109136\pi$
$410$		0			0
$411$	−0.368241	+	0.637812i	−0.0181640	+	0.0314609i
$412$		0			0
$413$	2.05778	+	0.748971i	0.101257	+	0.0368545i
$414$		0			0
$415$	9.99067	−	8.38316i	0.490423	−	0.411513i
$416$		0			0
$417$	−12.2763			−0.601174
$418$		0			0
$419$	−25.4097			−1.24135			−0.620673	−	0.784070i	$-0.713141\pi$
$419$	−25.4097			−1.24135			−0.620673	+	0.784070i	$0.713141\pi$
$420$		0			0
$421$	3.34730	−	2.80872i	0.163137	−	0.136888i	−0.557565	−	0.830134i	$-0.688264\pi$
$421$	3.34730	−	2.80872i	0.163137	−	0.136888i	0.720702	+	0.693245i	$0.243820\pi$
$422$		0			0
$423$	−36.2486	−	13.1934i	−1.76247	−	0.641485i
$424$		0			0
$425$	0.988856	−	1.71275i	0.0479665	−	0.0830805i
$426$		0			0
$427$	−0.550507	+	3.12208i	−0.0266409	+	0.151088i
$428$		0			0
$429$	−8.25150	−	14.2920i	−0.398386	−	0.690025i
$430$		0			0
$431$	29.3444	+	24.6228i	1.41347	+	1.18604i	0.954732	+	0.297468i	$0.0961422\pi$
$431$	29.3444	+	24.6228i	1.41347	+	1.18604i	0.458736	+	0.888572i	$0.348302\pi$
$432$		0			0
$433$	17.0376	−	6.20118i	0.818775	−	0.298010i	0.101532	−	0.994832i	$-0.467626\pi$
$433$	17.0376	−	6.20118i	0.818775	−	0.298010i	0.717244	+	0.696823i	$0.245403\pi$
$434$		0			0
$435$	−3.02481	−	17.1546i	−0.145029	−	0.822499i
$436$		0			0
$437$	−11.5517	+	2.12467i	−0.552592	+	0.101637i
$438$		0			0
$439$	1.05762	+	5.99806i	0.0504774	+	0.286272i	0.999589	−	0.0286685i	$-0.00912670\pi$
$439$	1.05762	+	5.99806i	0.0504774	+	0.286272i	−0.949112	+	0.314940i	$0.898016\pi$
$440$		0			0
$441$	34.2028	−	12.4488i	1.62870	−	0.592800i
$442$		0			0
$443$	22.8995	+	19.2149i	1.08799	+	0.912928i	0.996559	−	0.0828833i	$-0.0264129\pi$
$443$	22.8995	+	19.2149i	1.08799	+	0.912928i	0.0914266	+	0.995812i	$0.470857\pi$
$444$		0			0
$445$	4.52481	+	7.83721i	0.214497	+	0.371519i
$446$		0			0
$447$	8.27972	−	46.9566i	0.391617	−	2.22097i
$448$		0			0
$449$	5.62495	−	9.74270i	0.265458	−	0.459787i	−0.702226	−	0.711955i	$-0.747810\pi$
$449$	5.62495	−	9.74270i	0.265458	−	0.459787i	0.967683	+	0.252168i	$0.0811435\pi$
$450$		0			0
$451$	−5.18004	−	1.88538i	−0.243919	−	0.0887792i
$452$		0			0
$453$	9.62108	−	8.07305i	0.452038	−	0.379305i
$454$		0			0
$455$	−0.786112			−0.0368535
$456$		0			0
$457$	−23.3901			−1.09414			−0.547072	−	0.837086i	$-0.684258\pi$
$457$	−23.3901			−1.09414			−0.547072	+	0.837086i	$0.684258\pi$
$458$		0			0
$459$	2.36437	−	1.98394i	0.110359	−	0.0926025i
$460$		0			0
$461$	34.4149	+	12.5260i	1.60286	+	0.583395i	0.980011	−	0.198945i	$-0.0637514\pi$
$461$	34.4149	+	12.5260i	1.60286	+	0.583395i	0.622853	+	0.782339i	$0.285974\pi$
$462$		0			0
$463$	−21.4932	+	37.2273i	−0.998873	+	1.73010i	−0.458340	+	0.888777i	$0.651556\pi$
$463$	−21.4932	+	37.2273i	−0.998873	+	1.73010i	−0.540534	+	0.841322i	$0.681778\pi$
$464$		0			0
$465$	3.12449	−	17.7198i	0.144895	−	0.821738i
$466$		0			0
$467$	12.7981	+	22.1670i	0.592227	+	1.02577i	0.993932	+	0.109998i	$0.0350845\pi$
$467$	12.7981	+	22.1670i	0.592227	+	1.02577i	−0.401705	+	0.915769i	$0.631582\pi$
$468$		0			0
$469$	2.04189	+	1.71335i	0.0942857	+	0.0791151i
$470$		0			0
$471$	26.0253	−	9.47243i	1.19918	−	0.436466i
$472$		0			0
$473$	−1.50862	−	8.55580i	−0.0693663	−	0.393396i
$474$		0			0
$475$	−11.9461	−	14.0258i	−0.548124	−	0.643548i
$476$		0			0
$477$	−2.60694	−	14.7847i	−0.119364	−	0.676946i
$478$		0			0
$479$	35.8739	−	13.0570i	1.63912	−	0.596591i	0.652236	−	0.758016i	$-0.273831\pi$
$479$	35.8739	−	13.0570i	1.63912	−	0.596591i	0.986885	+	0.161424i	$0.0516088\pi$
$480$		0			0
$481$	9.74763	+	8.17923i	0.444453	+	0.372941i
$482$		0			0
$483$	1.34730	+	2.33359i	0.0613041	+	0.106182i
$484$		0			0
$485$	1.44356	−	8.18685i	0.0655488	−	0.371746i
$486$		0			0
$487$	3.88191	−	6.72367i	0.175906	−	0.304678i	−0.764568	−	0.644543i	$-0.777048\pi$
$487$	3.88191	−	6.72367i	0.175906	−	0.304678i	0.940475	+	0.339864i	$0.110381\pi$
$488$		0			0
$489$	22.6065	+	8.22811i	1.02230	+	0.372088i
$490$		0			0
$491$	28.1313	−	23.6050i	1.26955	−	1.06528i	0.274954	−	0.961457i	$-0.411337\pi$
$491$	28.1313	−	23.6050i	1.26955	−	1.06528i	0.994596	−	0.103822i	$-0.0331071\pi$
$492$		0			0
$493$	−3.21894			−0.144974
$494$		0			0
$495$	10.3601			0.465651
$496$		0			0
$497$	−2.47565	+	2.07732i	−0.111048	+	0.0931805i
$498$		0			0
$499$	4.62923	+	1.68490i	0.207233	+	0.0754266i	0.443551	−	0.896249i	$-0.353719\pi$
$499$	4.62923	+	1.68490i	0.207233	+	0.0754266i	−0.236318	+	0.971676i	$0.575941\pi$
$500$		0			0
$501$	5.80928	−	10.0620i	0.259539	−	0.449535i
$502$		0			0
$503$	−5.72163	+	32.4490i	−0.255115	+	1.44683i	0.540663	+	0.841239i	$0.318173\pi$
$503$	−5.72163	+	32.4490i	−0.255115	+	1.44683i	−0.795778	+	0.605589i	$0.792938\pi$
$504$		0			0
$505$	4.06670	+	7.04374i	0.180966	+	0.313442i
$506$		0			0
$507$	−14.0608	−	11.7984i	−0.624461	−	0.523985i
$508$		0			0
$509$	34.7075	−	12.6325i	1.53839	−	0.559926i	0.572728	−	0.819746i	$-0.305885\pi$
$509$	34.7075	−	12.6325i	1.53839	−	0.559926i	0.965657	+	0.259819i	$0.0836630\pi$
$510$		0			0
$511$	−0.0837781	−	0.475129i	−0.00370613	−	0.0210185i
$512$		0			0
$513$	−10.0326	−	26.9453i	−0.442948	−	1.18967i
$514$		0			0
$515$	0.841367	+	4.77163i	0.0370750	+	0.210263i
$516$		0			0
$517$	−15.2554	+	5.55250i	−0.670930	+	0.244199i
$518$		0			0
$519$	−44.4320	−	37.2829i	−1.95035	−	1.63654i
$520$		0			0
$521$	−4.64590	−	8.04693i	−0.203540	−	0.352542i	0.746126	−	0.665804i	$-0.231912\pi$
$521$	−4.64590	−	8.04693i	−0.203540	−	0.352542i	−0.949667	+	0.313262i	$0.898578\pi$
$522$		0			0
$523$	4.93423	−	27.9834i	0.215759	−	1.22363i	−0.663826	−	0.747887i	$-0.731068\pi$
$523$	4.93423	−	27.9834i	0.215759	−	1.22363i	0.879585	−	0.475742i	$-0.157820\pi$
$524$		0			0
$525$	−2.11334	+	3.66041i	−0.0922338	+	0.159754i
$526$		0			0
$527$	−3.12449	−	1.13722i	−0.136105	−	0.0495381i
$528$		0			0
$529$	−12.0569	+	10.1169i	−0.524213	+	0.439867i
$530$		0			0
$531$	33.3610			1.44775
$532$		0			0
$533$	6.37227			0.276014
$534$		0			0
$535$	−6.89440	+	5.78509i	−0.298071	+	0.250111i
$536$		0			0
$537$	−31.1498	−	11.3376i	−1.34421	−	0.489253i
$538$		0			0
$539$	7.65910	−	13.2660i	0.329901	−	0.571405i
$540$		0			0
$541$	2.60220	−	14.7578i	0.111877	−	0.634487i	−0.876372	−	0.481635i	$-0.840043\pi$
$541$	2.60220	−	14.7578i	0.111877	−	0.634487i	0.988249	−	0.152852i	$-0.0488458\pi$
$542$		0			0
$543$	−12.2909	−	21.2884i	−0.527451	−	0.913572i
$544$		0			0
$545$	−1.22803	−	1.03044i	−0.0526028	−	0.0441390i
$546$		0			0
$547$	−3.65270	+	1.32948i	−0.156178	+	0.0568443i	−0.418926	−	0.908020i	$-0.637593\pi$
$547$	−3.65270	+	1.32948i	−0.156178	+	0.0568443i	0.262748	+	0.964864i	$0.415371\pi$
$548$		0			0
$549$	8.38666	+	47.5631i	0.357934	+	2.02994i
$550$		0			0
$551$	−10.0483	+	28.2529i	−0.428071	+	1.20361i
$552$		0			0
$553$	−0.714355	−	4.05131i	−0.0303775	−	0.172279i
$554$		0			0
$555$	−11.7626	+	4.28125i	−0.499296	+	0.181729i
$556$		0			0
$557$	10.1152	+	8.48762i	0.428593	+	0.359632i	0.831420	−	0.555644i	$-0.187528\pi$
$557$	10.1152	+	8.48762i	0.428593	+	0.359632i	−0.402828	+	0.915276i	$0.631973\pi$
$558$		0			0
$559$	5.02141	+	8.69734i	0.212383	+	0.367858i
$560$		0			0
$561$	0.520945	−	2.95442i	0.0219943	−	0.124736i
$562$		0			0
$563$	5.35638	−	9.27752i	0.225745	−	0.391001i	−0.730798	−	0.682594i	$-0.760852\pi$
$563$	5.35638	−	9.27752i	0.225745	−	0.391001i	0.956543	+	0.291593i	$0.0941852\pi$
$564$		0			0
$565$	14.6163	+	5.31991i	0.614914	+	0.223810i
$566$		0			0
$567$	−0.830222	+	0.696639i	−0.0348661	+	0.0292561i
$568$		0			0
$569$	−13.4706			−0.564717			−0.282358	−	0.959309i	$-0.591117\pi$
$569$	−13.4706			−0.564717			−0.282358	+	0.959309i	$0.591117\pi$
$570$		0			0
$571$	−12.6655			−0.530035			−0.265017	−	0.964244i	$-0.585378\pi$
$571$	−12.6655			−0.530035			−0.265017	+	0.964244i	$0.585378\pi$
$572$		0			0
$573$	−40.4432	+	33.9358i	−1.68954	+	1.41769i
$574$		0			0
$575$	10.7023	+	3.89533i	0.446318	+	0.162447i
$576$		0			0
$577$	5.27719	−	9.14036i	0.219692	−	0.380518i	−0.735022	−	0.678044i	$-0.762828\pi$
$577$	5.27719	−	9.14036i	0.219692	−	0.380518i	0.954714	+	0.297526i	$0.0961613\pi$
$578$		0			0
$579$	0.148833	−	0.844075i	0.00618530	−	0.0350786i
$580$		0			0
$581$	2.57532	+	4.46059i	0.106842	+	0.185056i
$582$		0			0
$583$	−4.84002	−	4.06126i	−0.200453	−	0.168200i
$584$		0			0
$585$	−11.2537	+	4.09602i	−0.465284	+	0.169350i
$586$		0			0
$587$	3.32619	+	18.8638i	0.137287	+	0.778591i	0.973240	+	0.229791i	$0.0738041\pi$
$587$	3.32619	+	18.8638i	0.137287	+	0.778591i	−0.835954	+	0.548800i	$0.815085\pi$
$588$		0			0
$589$	−19.7349	+	23.8739i	−0.813162	+	0.983706i
$590$		0			0
$591$	6.57057	+	37.2636i	0.270277	+	1.53282i
$592$		0			0
$593$	8.17024	−	2.97373i	0.335512	−	0.122116i	−0.168770	−	0.985655i	$-0.553980\pi$
$593$	8.17024	−	2.97373i	0.335512	−	0.122116i	0.504282	+	0.863539i	$0.331757\pi$
$594$		0			0
$595$	−0.109470	−	0.0918566i	−0.00448785	−	0.00376575i
$596$		0			0
$597$	−0.369585	−	0.640140i	−0.0151261	−	0.0261992i
$598$		0			0
$599$	−3.44373	+	19.5303i	−0.140707	+	0.797988i	0.830008	+	0.557752i	$0.188336\pi$
$599$	−3.44373	+	19.5303i	−0.140707	+	0.797988i	−0.970715	+	0.240236i	$0.922775\pi$
$600$		0			0
$601$	16.8807	−	29.2383i	0.688579	−	1.19265i	−0.283718	−	0.958908i	$-0.591568\pi$
$601$	16.8807	−	29.2383i	0.688579	−	1.19265i	0.972298	−	0.233747i	$-0.0750986\pi$
$602$		0			0
$603$	38.1584	+	13.8885i	1.55393	+	0.565584i
$604$		0			0
$605$	−4.07011	+	3.41523i	−0.165473	+	0.138849i
$606$		0			0
$607$	−35.2850			−1.43217			−0.716087	−	0.698011i	$-0.754068\pi$
$607$	−35.2850			−1.43217			−0.716087	+	0.698011i	$0.754068\pi$
$608$		0			0
$609$	6.87939			0.278767
$610$		0			0
$611$	14.3760	−	12.0629i	0.581590	−	0.488012i
$612$		0			0
$613$	−17.3405	−	6.31142i	−0.700376	−	0.254916i	−0.0328044	−	0.999462i	$-0.510444\pi$
$613$	−17.3405	−	6.31142i	−0.700376	−	0.254916i	−0.667571	+	0.744546i	$0.732666\pi$
$614$		0			0
$615$	−3.13429	+	5.42874i	−0.126387	+	0.218908i
$616$		0			0
$617$	−6.19671	+	35.1433i	−0.249470	+	1.41482i	0.560408	+	0.828217i	$0.310644\pi$
$617$	−6.19671	+	35.1433i	−0.249470	+	1.41482i	−0.809878	+	0.586598i	$0.800467\pi$
$618$		0			0
$619$	1.82976	+	3.16923i	0.0735441	+	0.127382i	0.900452	−	0.434955i	$-0.143236\pi$
$619$	1.82976	+	3.16923i	0.0735441	+	0.127382i	−0.826908	+	0.562337i	$0.809902\pi$
$620$		0			0
$621$	13.6159	+	11.4251i	0.546386	+	0.458472i
$622$		0			0
$623$	−3.35844	+	1.22237i	−0.134553	+	0.0489733i
$624$		0			0
$625$	2.43077	+	13.7856i	0.0972308	+	0.551423i
$626$		0			0
$627$	−24.3050	−	13.7949i	−0.970648	−	0.550917i
$628$		0			0
$629$	0.401674	+	2.27801i	0.0160158	+	0.0908301i
$630$		0			0
$631$	−0.745977	+	0.271514i	−0.0296969	+	0.0108088i	−0.356826	−	0.934171i	$-0.616141\pi$
$631$	−0.745977	+	0.271514i	−0.0296969	+	0.0108088i	0.327129	+	0.944980i	$0.393919\pi$
$632$		0			0
$633$	−5.40033	−	4.53141i	−0.214644	−	0.180108i
$634$		0			0
$635$	5.10220	+	8.83726i	0.202474	+	0.350696i
$636$		0			0
$637$	−3.07486	+	17.4384i	−0.121830	+	0.690933i
$638$		0			0
$639$	−24.6168	+	42.6375i	−0.973826	+	1.68672i
$640$		0			0
$641$	−27.6104	−	10.0494i	−1.09055	−	0.396926i	−0.266723	−	0.963773i	$-0.585941\pi$
$641$	−27.6104	−	10.0494i	−1.09055	−	0.396926i	−0.823823	+	0.566847i	$0.808163\pi$
$642$		0			0
$643$	−17.0168	+	14.2788i	−0.671078	+	0.563101i	−0.913384	−	0.407098i	$-0.866541\pi$
$643$	−17.0168	+	14.2788i	−0.671078	+	0.563101i	0.242306	+	0.970200i	$0.422096\pi$
$644$		0			0
$645$	−9.87939			−0.389000
$646$		0			0
$647$	−11.2591			−0.442640			−0.221320	−	0.975201i	$-0.571037\pi$
$647$	−11.2591			−0.442640			−0.221320	+	0.975201i	$0.571037\pi$
$648$		0			0
$649$	10.7554	−	9.02482i	0.422185	−	0.354255i
$650$		0			0
$651$	6.67752	+	2.43042i	0.261713	+	0.0952556i
$652$		0			0
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	0.471160	+	0.882048i	$0.343835\pi$
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	−0.999456	+	0.0329874i	$0.989498\pi$
$654$		0			0
$655$	−0.281774	+	1.59802i	−0.0110098	+	0.0624399i
$656$		0			0
$657$	−3.67499	−	6.36527i	−0.143375	−	0.248333i
$658$		0			0
$659$	−21.4691	−	18.0147i	−0.836317	−	0.701753i	0.120415	−	0.992724i	$-0.461577\pi$
$659$	−21.4691	−	18.0147i	−0.836317	−	0.701753i	−0.956732	+	0.290970i	$0.906022\pi$
$660$		0			0
$661$	−10.6823	+	3.88803i	−0.415492	+	0.151227i	−0.541303	−	0.840827i	$-0.682069\pi$
$661$	−10.6823	+	3.88803i	−0.415492	+	0.151227i	0.125811	+	0.992054i	$0.459847\pi$
$662$		0			0
$663$	0.602196	+	3.41523i	0.0233874	+	0.132636i
$664$		0			0
$665$	−1.14796	+	0.674089i	−0.0445158	+	0.0261400i
$666$		0			0
$667$	−3.21894	−	18.2555i	−0.124638	−	0.706857i
$668$		0			0
$669$	−23.0253	+	8.38052i	−0.890209	+	0.324010i
$670$		0			0
$671$	15.5706	+	13.0653i	0.601095	+	0.504379i
$672$		0			0
$673$	8.28359	+	14.3476i	0.319309	+	0.553059i	0.980344	−	0.197296i	$-0.0632160\pi$
$673$	8.28359	+	14.3476i	0.319309	+	0.553059i	−0.661035	+	0.750355i	$0.729883\pi$
$674$		0			0
$675$	−4.84137	+	27.4568i	−0.186344	+	1.05681i
$676$		0			0
$677$	4.52481	−	7.83721i	0.173903	−	0.301208i	−0.765878	−	0.642986i	$-0.777695\pi$
$677$	4.52481	−	7.83721i	0.173903	−	0.301208i	0.939781	+	0.341777i	$0.111029\pi$
$678$		0			0
$679$	3.08512	+	1.12289i	0.118396	+	0.0430927i
$680$		0			0
$681$	31.2126	−	26.1905i	1.19607	−	1.00362i
$682$		0			0
$683$	−8.73143			−0.334099			−0.167049	−	0.985949i	$-0.553424\pi$
$683$	−8.73143			−0.334099			−0.167049	+	0.985949i	$0.553424\pi$
$684$		0			0
$685$	0.224927			0.00859402
$686$		0			0
$687$	−45.2904	+	38.0032i	−1.72794	+	1.44991i
$688$		0			0
$689$	6.86319	+	2.49800i	0.261467	+	0.0951661i
$690$		0			0
$691$	17.3601	−	30.0686i	0.660409	−	1.14386i	−0.320099	−	0.947384i	$-0.603716\pi$
$691$	17.3601	−	30.0686i	0.660409	−	1.14386i	0.980508	−	0.196478i	$-0.0629504\pi$
$692$		0			0
$693$	−0.710485	+	4.02936i	−0.0269891	+	0.153063i
$694$		0			0
$695$	1.87464	+	3.24697i	0.0711091	+	0.123164i
$696$		0			0
$697$	0.887374	+	0.744596i	0.0336117	+	0.0282036i
$698$		0			0
$699$	−47.7588	+	17.3828i	−1.80640	+	0.657478i
$700$		0			0
$701$	6.84436	+	38.8163i	0.258508	+	1.46607i	0.786905	+	0.617074i	$0.211682\pi$
$701$	6.84436	+	38.8163i	0.258508	+	1.46607i	−0.528397	+	0.848997i	$0.677207\pi$
$702$		0			0
$703$	21.2481	+	3.58553i	0.801387	+	0.135231i
$704$		0			0
$705$	3.20574	+	18.1806i	0.120735	+	0.684722i
$706$		0			0
$707$	−3.01842	+	1.09861i	−0.113519	+	0.0413176i
$708$		0			0
$709$	−31.5009	−	26.4324i	−1.18304	−	0.992690i	−0.999954	−	0.00959399i	$-0.996946\pi$
$709$	−31.5009	−	26.4324i	−1.18304	−	0.992690i	−0.183088	−	0.983096i	$-0.558609\pi$
$710$		0			0
$711$	−31.3357	−	54.2751i	−1.17518	−	2.03548i
$712$		0			0
$713$	3.32501	−	18.8571i	0.124523	−	0.706202i
$714$		0			0
$715$	−2.52007	+	4.36488i	−0.0942452	+	0.163237i
$716$		0			0
$717$	6.36484	+	2.31661i	0.237699	+	0.0865154i
$718$		0			0
$719$	32.4768	−	27.2513i	1.21118	−	1.01630i	0.211943	−	0.977282i	$-0.432021\pi$
$719$	32.4768	−	27.2513i	1.21118	−	1.01630i	0.999238	−	0.0390200i	$-0.0124236\pi$
$720$		0			0
$721$	−1.91353			−0.0712637
$722$		0			0
$723$	39.7374			1.47785
$724$		0			0
$725$	22.2743	−	18.6903i	0.827245	−	0.694141i
$726$		0			0
$727$	48.5411	+	17.6675i	1.80029	+	0.655251i	0.998324	+	0.0578805i	$0.0184342\pi$
$727$	48.5411	+	17.6675i	1.80029	+	0.655251i	0.801965	+	0.597371i	$0.203788\pi$
$728$		0			0
$729$	20.2344	−	35.0470i	0.749423	−	1.29804i
$730$		0			0
$731$	−0.317018	+	1.79790i	−0.0117254	+	0.0664978i
$732$		0			0
$733$	11.4581	+	19.8460i	0.423215	+	0.733030i	0.996252	−	0.0864997i	$-0.0275682\pi$
$733$	11.4581	+	19.8460i	0.423215	+	0.733030i	−0.573037	+	0.819530i	$0.694235\pi$
$734$		0			0
$735$	−13.3439	−	11.1969i	−0.492197	−	0.413002i
$736$		0			0
$737$	16.0591	−	5.84504i	0.591545	−	0.215305i
$738$		0			0
$739$	−4.88413	−	27.6993i	−0.179666	−	1.01894i	−0.932619	−	0.360862i	$-0.882483\pi$
$739$	−4.88413	−	27.6993i	−0.179666	−	1.01894i	0.752954	−	0.658074i	$-0.228628\pi$
$740$		0			0
$741$	31.8555	+	5.37549i	1.17024	+	0.197474i
$742$		0			0
$743$	−1.06489	−	6.03931i	−0.0390671	−	0.221561i	0.959024	−	0.283326i	$-0.0914380\pi$
$743$	−1.06489	−	6.03931i	−0.0390671	−	0.221561i	−0.998091	+	0.0617657i	$0.980327\pi$
$744$		0			0
$745$	−13.6839	+	4.98054i	−0.501340	+	0.182473i
$746$		0			0
$747$	60.1093	+	50.4377i	2.19928	+	1.84542i
$748$		0			0
$749$	−1.77719	−	3.07818i	−0.0649371	−	0.112474i
$750$		0			0
$751$	−0.979522	+	5.55515i	−0.0357433	+	0.202710i	−0.997450	−	0.0713710i	$-0.977263\pi$
$751$	−0.979522	+	5.55515i	−0.0357433	+	0.202710i	0.961707	+	0.274081i	$0.0883737\pi$
$752$		0			0
$753$	−5.99660	+	10.3864i	−0.218528	+	0.378502i
$754$		0			0
$755$	−3.60442	−	1.31190i	−0.131178	−	0.0477450i
$756$		0			0
$757$	12.0207	−	10.0866i	0.436900	−	0.366602i	−0.397648	−	0.917538i	$-0.630173\pi$
$757$	12.0207	−	10.0866i	0.436900	−	0.366602i	0.834548	+	0.550936i	$0.185729\pi$
$758$		0			0
$759$	17.2763			0.627090
$760$		0			0
$761$	4.86484			0.176350			0.0881751	−	0.996105i	$-0.471896\pi$
$761$	4.86484			0.176350			0.0881751	+	0.996105i	$0.471896\pi$
$762$		0			0
$763$	0.484985	−	0.406951i	0.0175576	−	0.0147326i
$764$		0			0
$765$	−2.04576	−	0.744596i	−0.0739646	−	0.0269209i
$766$		0			0
$767$	−8.11499	+	14.0556i	−0.293015	+	0.507517i
$768$		0			0
$769$	3.91266	−	22.1898i	0.141094	−	0.800184i	−0.829327	−	0.558764i	$-0.811276\pi$
$769$	3.91266	−	22.1898i	0.141094	−	0.800184i	0.970421	−	0.241420i	$-0.0776131\pi$
$770$		0			0
$771$	−0.960637	−	1.66387i	−0.0345965	−	0.0599229i
$772$		0			0
$773$	−20.2481	−	16.9902i	−0.728273	−	0.611094i	0.201387	−	0.979512i	$-0.435455\pi$
$773$	−20.2481	−	16.9902i	−0.728273	−	0.611094i	−0.929660	+	0.368418i	$0.879900\pi$
$774$		0			0
$775$	28.2237	−	10.2726i	1.01383	−	0.369003i
$776$		0			0
$777$	−0.858441	−	4.86846i	−0.0307964	−	0.174655i
$778$		0			0
$779$	9.30541	−	5.46421i	0.333401	−	0.195776i
$780$		0			0
$781$	3.59802	+	20.4054i	0.128747	+	0.730162i
$782$		0			0
$783$	42.6416	−	15.5203i	1.52389	−	0.554650i
$784$		0			0
$785$	−6.47952	−	5.43696i	−0.231264	−	0.194054i
$786$		0			0
$787$	−7.77884	−	13.4733i	−0.277286	−	0.480273i	0.693424	−	0.720530i	$-0.256101\pi$
$787$	−7.77884	−	13.4733i	−0.277286	−	0.480273i	−0.970709	+	0.240257i	$0.922768\pi$
$788$		0			0
$789$	−5.69981	+	32.3252i	−0.202919	+	1.15081i
$790$		0			0
$791$	−3.07145	+	5.31991i	−0.109208	+	0.189154i
$792$		0			0
$793$	−22.0792	−	8.03617i	−0.784055	−	0.285373i
$794$		0			0
$795$	−5.50387	+	4.61830i	−0.195202	+	0.163794i
$796$		0			0
$797$	33.4935			1.18640			0.593200	−	0.805055i	$-0.297864\pi$
$797$	33.4935			1.18640			0.593200	+	0.805055i	$0.297864\pi$
$798$		0			0
$799$	3.41147			0.120689
$800$		0			0
$801$	−41.7092	+	34.9982i	−1.47372	+	1.23660i
$802$		0			0
$803$	−2.90673	−	1.05796i	−0.102576	−	0.0373347i
$804$		0			0
$805$	0.411474	−	0.712694i	0.0145026	−	0.0251192i
$806$		0			0
$807$	9.69506	−	54.9834i	0.341282	−	1.93551i
$808$		0			0
$809$	−20.5581	−	35.6076i	−0.722784	−	1.25190i	−0.959880	−	0.280412i	$-0.909529\pi$
$809$	−20.5581	−	35.6076i	−0.722784	−	1.25190i	0.237096	−	0.971486i	$-0.423804\pi$
$810$		0			0
$811$	−12.7836	−	10.7267i	−0.448892	−	0.376665i	0.390132	−	0.920759i	$-0.372429\pi$
$811$	−12.7836	−	10.7267i	−0.448892	−	0.376665i	−0.839025	+	0.544093i	$0.816874\pi$
$812$		0			0
$813$	−36.2413	+	13.1907i	−1.27104	+	0.462620i
$814$		0			0
$815$	−1.27584	−	7.23567i	−0.0446909	−	0.253455i
$816$		0			0
$817$	14.7907	+	8.39484i	0.517461	+	0.293698i
$818$		0			0
$819$	−0.821299	−	4.65782i	−0.0286985	−	0.162757i
$820$		0			0
$821$	29.4971	−	10.7361i	1.02945	−	0.374691i	0.228581	−	0.973525i	$-0.426591\pi$
$821$	29.4971	−	10.7361i	1.02945	−	0.374691i	0.800873	+	0.598834i	$0.204369\pi$
$822$		0			0
$823$	−35.4877	−	29.7777i	−1.23702	−	1.03799i	−0.997751	−	0.0670347i	$-0.978646\pi$
$823$	−35.4877	−	29.7777i	−1.23702	−	1.03799i	−0.239274	−	0.970952i	$-0.576909\pi$
$824$		0			0
$825$	13.5496	+	23.4686i	0.471738	+	0.817073i
$826$		0			0
$827$	−7.07769	+	40.1396i	−0.246115	+	1.39579i	0.571773	+	0.820412i	$0.306256\pi$
$827$	−7.07769	+	40.1396i	−0.246115	+	1.39579i	−0.817888	+	0.575377i	$0.804855\pi$
$828$		0			0
$829$	17.7417	−	30.7295i	0.616195	−	1.06728i	−0.373979	−	0.927437i	$-0.622007\pi$
$829$	17.7417	−	30.7295i	0.616195	−	1.06728i	0.990174	−	0.139843i	$-0.0446598\pi$
$830$		0			0
$831$	−48.0185	−	17.4773i	−1.66574	−	0.606281i
$832$		0			0
$833$	−2.46585	+	2.06910i	−0.0854367	+	0.0716899i
$834$		0			0
$835$	−3.54839			−0.122797
$836$		0			0
$837$	46.8735			1.62019
$838$		0			0
$839$	29.2649	−	24.5562i	1.01034	−	0.847774i	0.0219545	−	0.999759i	$-0.493011\pi$
$839$	29.2649	−	24.5562i	1.01034	−	0.847774i	0.988383	+	0.151985i	$0.0485667\pi$
$840$		0			0
$841$	−17.2208	−	6.26784i	−0.593819	−	0.216132i
$842$		0			0
$843$	−26.3161	+	45.5809i	−0.906376	+	1.56989i
$844$		0			0
$845$	−0.973430	+	5.52060i	−0.0334870	+	0.189914i
$846$		0			0
$847$	−1.04916	−	1.81720i	−0.0360497	−	0.0624399i
$848$		0			0
$849$	−16.9572	−	14.2288i	−0.581971	−	0.488331i
$850$		0			0
$851$	−12.5175	+	4.55601i	−0.429096	+	0.156178i
$852$		0			0
$853$	−4.44568	−	25.2127i	−0.152217	−	0.863266i	−0.961286	−	0.275552i	$-0.911139\pi$
$853$	−4.44568	−	25.2127i	−0.152217	−	0.863266i	0.809069	−	0.587714i	$-0.199972\pi$
$854$		0			0
$855$	−12.9214	+	15.6314i	−0.441904	+	0.534584i
$856$		0			0
$857$	−3.66163	−	20.7661i	−0.125079	−	0.709357i	−0.981261	−	0.192683i	$-0.938281\pi$
$857$	−3.66163	−	20.7661i	−0.125079	−	0.709357i	0.856182	−	0.516674i	$-0.172830\pi$
$858$		0			0
$859$	−18.3871	+	6.69237i	−0.627361	+	0.228341i	−0.636082	−	0.771621i	$-0.719446\pi$
$859$	−18.3871	+	6.69237i	−0.627361	+	0.228341i	0.00872148	+	0.999962i	$0.497224\pi$
$860$		0			0
$861$	−1.89646	−	1.59132i	−0.0646312	−	0.0542320i
$862$		0			0
$863$	2.47447	+	4.28591i	0.0842319	+	0.145894i	0.905064	−	0.425276i	$-0.139823\pi$
$863$	2.47447	+	4.28591i	0.0842319	+	0.145894i	−0.820832	+	0.571170i	$0.806490\pi$
$864$		0			0
$865$	−3.07604	+	17.4451i	−0.104588	+	0.593150i
$866$		0			0
$867$	24.1596	−	41.8456i	0.820502	−	1.42115i
$868$		0			0
$869$	−24.7849	−	9.02098i	−0.840771	−	0.306016i
$870$		0			0
$871$	−15.1334	+	12.6984i	−0.512776	+	0.430270i
$872$		0			0
$873$	50.0164			1.69280
$874$		0			0
$875$	2.81790			0.0952623
$876$		0			0
$877$	0.934478	−	0.784120i	0.0315551	−	0.0264779i	−0.626874	−	0.779121i	$-0.715666\pi$
$877$	0.934478	−	0.784120i	0.0315551	−	0.0264779i	0.658429	+	0.752643i	$0.271221\pi$
$878$		0			0
$879$	28.4183	+	10.3434i	0.958527	+	0.348875i
$880$		0			0
$881$	−23.2515	+	40.2728i	−0.783363	+	1.35682i	0.146609	+	0.989194i	$0.453164\pi$
$881$	−23.2515	+	40.2728i	−0.783363	+	1.35682i	−0.929972	+	0.367630i	$0.880169\pi$
$882$		0			0
$883$	−2.24438	+	12.7285i	−0.0755296	+	0.428349i	0.923472	+	0.383667i	$0.125339\pi$
$883$	−2.24438	+	12.7285i	−0.0755296	+	0.428349i	−0.999001	+	0.0446828i	$0.985772\pi$
$884$		0			0
$885$	−7.98293	−	13.8268i	−0.268343	−	0.464784i
$886$		0			0
$887$	17.7909	+	14.9283i	0.597359	+	0.501243i	0.890595	−	0.454796i	$-0.150288\pi$
$887$	17.7909	+	14.9283i	0.597359	+	0.501243i	−0.293237	+	0.956040i	$0.594732\pi$
$888$		0			0
$889$	−3.78699	+	1.37835i	−0.127012	+	0.0462284i
$890$		0			0
$891$	1.20661	+	6.84305i	0.0404231	+	0.229251i
$892$		0			0
$893$	10.6493	−	29.9428i	0.356365	−	1.00200i
$894$		0			0
$895$	1.75800	+	9.97011i	0.0587634	+	0.333264i
$896$		0			0
$897$	−18.7665	+	6.83045i	−0.626596	+	0.228062i
$898$		0			0
$899$	−37.4484	−	31.4229i	−1.24897	−	1.04801i
$900$		0			0
$901$	0.663848	+	1.14982i	0.0221160	+	0.0383060i
$902$		0			0
$903$	0.677519	−	3.84240i	0.0225464	−	0.127867i
$904$		0			0
$905$	−3.75372	+	6.50163i	−0.124778	+	0.216122i
$906$		0			0
$907$	−37.5847	−	13.6797i	−1.24798	−	0.454228i	−0.368261	−	0.929722i	$-0.620047\pi$
$907$	−37.5847	−	13.6797i	−1.24798	−	0.454228i	−0.879719	+	0.475495i	$0.842269\pi$
$908$		0			0
$909$	−37.4864	+	31.4548i	−1.24334	+	1.04329i
$910$		0			0
$911$	18.7997			0.622863			0.311431	−	0.950269i	$-0.399192\pi$
$911$	18.7997			0.622863			0.311431	+	0.950269i	$0.399192\pi$
$912$		0			0
$913$	33.0232			1.09291
$914$		0			0
$915$	17.7062	−	14.8573i	0.585349	−	0.491166i
$916$		0			0
$917$	−0.602196	−	0.219182i	−0.0198863	−	0.00723801i
$918$		0			0
$919$	19.9158	−	34.4952i	0.656962	−	1.13789i	−0.324436	−	0.945908i	$-0.605175\pi$
$919$	19.9158	−	34.4952i	0.656962	−	1.13789i	0.981398	−	0.191984i	$-0.0614921\pi$
$920$		0			0
$921$	5.84776	−	33.1643i	0.192690	−	1.09280i
$922$		0			0
$923$	−11.9760	−	20.7430i	−0.394193	−	0.682763i
$924$		0			0
$925$	−16.0064	−	13.4310i	−0.526287	−	0.441607i
$926$		0			0
$927$	−27.3935	+	9.97043i	−0.899721	+	0.327472i
$928$		0			0
$929$	4.68051	+	26.5445i	0.153563	+	0.870897i	0.960088	+	0.279698i	$0.0902342\pi$
$929$	4.68051	+	26.5445i	0.153563	+	0.870897i	−0.806526	+	0.591199i	$0.798655\pi$
$930$		0			0
$931$	10.4632	+	28.1019i	0.342916	+	0.921002i
$932$		0			0
$933$	−7.98293	−	45.2734i	−0.261349	−	1.48219i
$934$		0			0
$935$	−0.860967	+	0.313366i	−0.0281566	+	0.0102482i
$936$		0			0
$937$	2.00980	+	1.68642i	0.0656573	+	0.0550930i	0.675026	−	0.737794i	$-0.264133\pi$
$937$	2.00980	+	1.68642i	0.0656573	+	0.0550930i	−0.609368	+	0.792887i	$0.708577\pi$
$938$		0			0
$939$	38.3371	+	66.4018i	1.25108	+	2.16694i
$940$		0			0
$941$	−3.24194	+	18.3860i	−0.105684	+	0.599366i	0.885260	+	0.465096i	$0.153980\pi$
$941$	−3.24194	+	18.3860i	−0.105684	+	0.599366i	−0.990945	+	0.134270i	$0.957131\pi$
$942$		0			0
$943$	−3.33544	+	5.77715i	−0.108617	+	0.188130i
$944$		0			0
$945$	1.89306	+	0.689016i	0.0615811	+	0.0224137i
$946$		0			0
$947$	−6.43448	+	5.39917i	−0.209092	+	0.175449i	−0.741320	−	0.671152i	$-0.765800\pi$
$947$	−6.43448	+	5.39917i	−0.209092	+	0.175449i	0.532227	+	0.846602i	$0.321355\pi$
$948$		0			0
$949$	3.57573			0.116073
$950$		0			0
$951$	85.0343			2.75742
$952$		0			0
$953$	25.8102	−	21.6573i	0.836075	−	0.701550i	−0.120602	−	0.992701i	$-0.538483\pi$
$953$	25.8102	−	21.6573i	0.836075	−	0.701550i	0.956677	+	0.291151i	$0.0940382\pi$
$954$		0			0
$955$	15.1515	+	5.51470i	0.490292	+	0.178452i
$956$		0			0
$957$	22.0535	−	38.1978i	0.712888	−	1.23476i
$958$		0			0
$959$	−0.0154253	+	0.0874810i	−0.000498108	+	0.00282491i
$960$		0			0
$961$	−9.74809	−	16.8842i	−0.314455	−	0.544651i
$962$		0			0
$963$	−41.4805	−	34.8062i	−1.33669	−	1.12162i
$964$		0			0
$965$	−0.245977	+	0.0895284i	−0.00791829	+	0.00288202i
$966$		0			0
$967$	−2.03920	−	11.5649i	−0.0655763	−	0.371902i	−0.999881	−	0.0154262i	$-0.995089\pi$
$967$	−2.03920	−	11.5649i	−0.0655763	−	0.371902i	0.934305	−	0.356475i	$-0.116022\pi$
$968$		0			0
$969$	3.80793	+	4.47086i	0.122328	+	0.143625i
$970$		0			0
$971$	−2.22432	−	12.6147i	−0.0713817	−	0.404826i	−0.999473	−	0.0324723i	$-0.989662\pi$
$971$	−2.22432	−	12.6147i	−0.0713817	−	0.404826i	0.928091	−	0.372354i	$-0.121449\pi$
$972$		0			0
$973$	−1.39141	+	0.506431i	−0.0446065	+	0.0162354i
$974$		0			0
$975$	−23.9971	−	20.1359i	−0.768521	−	0.644866i
$976$		0			0
$977$	−7.26382	−	12.5813i	−0.232390	−	0.402512i	0.726121	−	0.687567i	$-0.241321\pi$
$977$	−7.26382	−	12.5813i	−0.232390	−	0.402512i	−0.958511	+	0.285055i	$0.907988\pi$
$978$		0			0
$979$	−3.97906	+	22.5663i	−0.127171	+	0.721224i
$980$		0			0
$981$	4.82248	−	8.35278i	0.153970	−	0.266684i
$982$		0			0
$983$	−34.8158	−	12.6719i	−1.11045	−	0.404172i	−0.279293	−	0.960206i	$-0.590100\pi$
$983$	−34.8158	−	12.6719i	−1.11045	−	0.404172i	−0.831159	+	0.556034i	$0.812322\pi$
$984$		0			0
$985$	8.85251	−	7.42814i	0.282064	−	0.236680i
$986$		0			0
$987$	−7.29086			−0.232071
$988$		0			0
$989$	−10.5134			−0.334307
$990$		0			0
$991$	−2.62860	+	2.20566i	−0.0835004	+	0.0700651i	−0.683582	−	0.729873i	$-0.739579\pi$
$991$	−2.62860	+	2.20566i	−0.0835004	+	0.0700651i	0.600082	+	0.799938i	$0.295135\pi$
$992$		0			0
$993$	74.8556	+	27.2452i	2.37547	+	0.864600i
$994$		0			0
$995$	−0.112874	+	0.195503i	−0.00357835	+	0.00619788i
$996$		0			0
$997$	2.21853	−	12.5819i	0.0702616	−	0.398473i	−0.929313	−	0.369294i	$-0.879600\pi$
$997$	2.21853	−	12.5819i	0.0702616	−	0.398473i	0.999574	−	0.0291792i	$-0.00928933\pi$
$998$		0			0
$999$	−16.3045	−	28.2403i	−0.515852	−	0.893483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.u.b.161.1		6
4.3	odd	2		19.2.e.a.9.1	✓	6
12.11	even	2		171.2.u.c.28.1		6
19.6	even	9		5776.2.a.br.1.3		3
19.13	odd	18		5776.2.a.bi.1.1		3
19.17	even	9	inner	304.2.u.b.17.1		6
20.3	even	4		475.2.u.a.199.1		12
20.7	even	4		475.2.u.a.199.2		12
20.19	odd	2		475.2.l.a.351.1		6
28.3	even	6		931.2.v.a.275.1		6
28.11	odd	6		931.2.v.b.275.1		6
28.19	even	6		931.2.x.b.655.1		6
28.23	odd	6		931.2.x.a.655.1		6
28.27	even	2		931.2.w.a.883.1		6
76.3	even	18		361.2.e.b.62.1		6
76.7	odd	6		361.2.e.f.99.1		6
76.11	odd	6		361.2.e.g.234.1		6
76.15	even	18		361.2.c.h.68.2		6
76.23	odd	18		361.2.c.i.68.2		6
76.27	even	6		361.2.e.a.234.1		6
76.31	even	6		361.2.e.b.99.1		6
76.35	odd	18		361.2.e.f.62.1		6
76.43	odd	18		361.2.e.g.54.1		6
76.47	odd	18		361.2.c.i.292.2		6
76.51	even	18		361.2.a.h.1.2		3
76.55	odd	18		19.2.e.a.17.1	yes	6
76.59	even	18		361.2.e.h.245.1		6
76.63	odd	18		361.2.a.g.1.2		3
76.67	even	18		361.2.c.h.292.2		6
76.71	even	18		361.2.e.a.54.1		6
76.75	even	2		361.2.e.h.28.1		6
228.131	even	18		171.2.u.c.55.1		6
228.203	odd	18		3249.2.a.s.1.2		3
228.215	even	18		3249.2.a.z.1.2		3
380.139	odd	18		9025.2.a.bd.1.2		3
380.207	even	36		475.2.u.a.74.1		12
380.279	even	18		9025.2.a.x.1.2		3
380.283	even	36		475.2.u.a.74.2		12
380.359	odd	18		475.2.l.a.226.1		6
532.55	even	18		931.2.w.a.834.1		6
532.131	even	18		931.2.v.a.606.1		6
532.207	odd	18		931.2.x.a.226.1		6
532.283	even	18		931.2.x.b.226.1		6
532.359	odd	18		931.2.v.b.606.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.9.1	✓	6	4.3	odd	2
19.2.e.a.17.1	yes	6	76.55	odd	18
171.2.u.c.28.1		6	12.11	even	2
171.2.u.c.55.1		6	228.131	even	18
304.2.u.b.17.1		6	19.17	even	9	inner
304.2.u.b.161.1		6	1.1	even	1	trivial
361.2.a.g.1.2		3	76.63	odd	18
361.2.a.h.1.2		3	76.51	even	18
361.2.c.h.68.2		6	76.15	even	18
361.2.c.h.292.2		6	76.67	even	18
361.2.c.i.68.2		6	76.23	odd	18
361.2.c.i.292.2		6	76.47	odd	18
361.2.e.a.54.1		6	76.71	even	18
361.2.e.a.234.1		6	76.27	even	6
361.2.e.b.62.1		6	76.3	even	18
361.2.e.b.99.1		6	76.31	even	6
361.2.e.f.62.1		6	76.35	odd	18
361.2.e.f.99.1		6	76.7	odd	6
361.2.e.g.54.1		6	76.43	odd	18
361.2.e.g.234.1		6	76.11	odd	6
361.2.e.h.28.1		6	76.75	even	2
361.2.e.h.245.1		6	76.59	even	18
475.2.l.a.226.1		6	380.359	odd	18
475.2.l.a.351.1		6	20.19	odd	2
475.2.u.a.74.1		12	380.207	even	36
475.2.u.a.74.2		12	380.283	even	36
475.2.u.a.199.1		12	20.3	even	4
475.2.u.a.199.2		12	20.7	even	4
931.2.v.a.275.1		6	28.3	even	6
931.2.v.a.606.1		6	532.131	even	18
931.2.v.b.275.1		6	28.11	odd	6
931.2.v.b.606.1		6	532.359	odd	18
931.2.w.a.834.1		6	532.55	even	18
931.2.w.a.883.1		6	28.27	even	2
931.2.x.a.226.1		6	532.207	odd	18
931.2.x.a.655.1		6	28.23	odd	6
931.2.x.b.226.1		6	532.283	even	18
931.2.x.b.655.1		6	28.19	even	6
3249.2.a.s.1.2		3	228.203	odd	18
3249.2.a.z.1.2		3	228.215	even	18
5776.2.a.bi.1.1		3	19.13	odd	18
5776.2.a.br.1.3		3	19.6	even	9
9025.2.a.x.1.2		3	380.279	even	18
9025.2.a.bd.1.2		3	380.139	odd	18

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.20574 - 1.85083i) q^{3} +(-0.826352 - 0.300767i) q^{5} +(0.173648 - 0.300767i) q^{7} +(0.918748 - 5.21048i) q^{9} +O(q^{10})\)	\(q+(2.20574 - 1.85083i) q^{3} +(-0.826352 - 0.300767i) q^{5} +(0.173648 - 0.300767i) q^{7} +(0.918748 - 5.21048i) q^{9} +(-1.11334 - 1.92836i) q^{11} +(1.97178 + 1.65452i) q^{13} +(-2.37939 + 0.866025i) q^{15} +(0.0812519 + 0.460802i) q^{17} +(4.29813 + 0.725293i) q^{19} +(-0.173648 - 0.984808i) q^{21} +(-2.53209 + 0.921605i) q^{23} +(-3.23783 - 2.71686i) q^{25} +(-3.29813 - 5.71253i) q^{27} +(-1.19459 + 6.77487i) q^{29} +(-3.55303 + 6.15403i) q^{31} +(-6.02481 - 2.19285i) q^{33} +(-0.233956 + 0.196312i) q^{35} +4.94356 q^{37} +7.41147 q^{39} +(1.89646 - 1.59132i) q^{41} +(3.66637 + 1.33445i) q^{43} +(-2.32635 + 4.02936i) q^{45} +(1.26604 - 7.18009i) q^{47} +(3.43969 + 5.95772i) q^{49} +(1.03209 + 0.866025i) q^{51} +(2.66637 - 0.970481i) q^{53} +(0.340022 + 1.92836i) q^{55} +(10.8229 - 6.35532i) q^{57} +(1.09492 + 6.20961i) q^{59} +(-8.57785 + 3.12208i) q^{61} +(-1.40760 - 1.18112i) q^{63} +(-1.13176 - 1.96026i) q^{65} +(-1.33275 + 7.55839i) q^{67} +(-3.87939 + 6.71929i) q^{69} +(-8.74422 - 3.18264i) q^{71} +(1.06418 - 0.892951i) q^{73} -12.1702 q^{75} -0.773318 q^{77} +(9.07398 - 7.61397i) q^{79} +(-2.93242 - 1.06731i) q^{81} +(-7.41534 + 12.8438i) q^{83} +(0.0714517 - 0.405223i) q^{85} +(9.90420 + 17.1546i) q^{87} +(-7.88326 - 6.61484i) q^{89} +(0.840022 - 0.305743i) q^{91} +(3.55303 + 20.1503i) q^{93} +(-3.33363 - 1.89209i) q^{95} +(1.64156 + 9.30975i) q^{97} +(-11.0706 + 4.02936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 6 q^{5} + 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 6 * q^5 + 3 * q^9	\( 6 q + 3 q^{3} - 6 q^{5} + 3 q^{9} - 3 q^{13} - 3 q^{15} + 3 q^{17} + 12 q^{19} - 6 q^{23} - 6 q^{27} - 3 q^{29} - 9 q^{31} - 9 q^{33} - 6 q^{35} + 24 q^{39} + 21 q^{41} + 3 q^{43} - 15 q^{45} + 3 q^{47} + 15 q^{49} - 3 q^{51} - 3 q^{53} - 18 q^{55} + 24 q^{57} - 12 q^{59} - 12 q^{61} - 12 q^{63} - 12 q^{65} + 30 q^{67} - 12 q^{69} + 6 q^{71} - 12 q^{73} - 30 q^{75} - 18 q^{77} + 39 q^{79} + 6 q^{81} + 21 q^{87} - 12 q^{89} - 15 q^{91} + 9 q^{93} - 39 q^{95} + 18 q^{97} - 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 6 * q^5 + 3 * q^9 - 3 * q^13 - 3 * q^15 + 3 * q^17 + 12 * q^19 - 6 * q^23 - 6 * q^27 - 3 * q^29 - 9 * q^31 - 9 * q^33 - 6 * q^35 + 24 * q^39 + 21 * q^41 + 3 * q^43 - 15 * q^45 + 3 * q^47 + 15 * q^49 - 3 * q^51 - 3 * q^53 - 18 * q^55 + 24 * q^57 - 12 * q^59 - 12 * q^61 - 12 * q^63 - 12 * q^65 + 30 * q^67 - 12 * q^69 + 6 * q^71 - 12 * q^73 - 30 * q^75 - 18 * q^77 + 39 * q^79 + 6 * q^81 + 21 * q^87 - 12 * q^89 - 15 * q^91 + 9 * q^93 - 39 * q^95 + 18 * q^97 - 9 * q^99

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