LMFDB - Embedded newform 152.2.q.c.9.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(9,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.9"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.q (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 21 x^{16} - 34 x^{15} + 204 x^{14} - 267 x^{13} + 1304 x^{12} - 972 x^{11} + \cdots + 1 $ x^18 - 3x^17 + 21x^16 - 34x^15 + 204x^14 - 267x^13 + 1304x^12 - 972x^11 + 4890x^10 - 2547x^9 + 12945x^8 - 2403x^7 + 14457x^6 - 6729x^5 + 8769x^4 - 686x^3 + 132x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			9.3
Root			$1.18094 + 2.04545i$ of defining polynomial
Character	$\chi$	$=$	152.9
Dual form			152.2.q.c.17.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.80930 - 1.51819i) q^{3} +(2.20161 + 0.801320i) q^{5} +(-2.07787 + 3.59897i) q^{7} +(0.447746 - 2.53930i) q^{9} +(-2.68364 - 4.64821i) q^{11} +(-2.26353 - 1.89933i) q^{13} +(5.19993 - 1.89262i) q^{15} +(0.962770 + 5.46014i) q^{17} +(-2.01029 - 3.86765i) q^{19} +(1.70442 + 9.66622i) q^{21} +(-1.68566 + 0.613531i) q^{23} +(0.374747 + 0.314450i) q^{25} +(0.497804 + 0.862221i) q^{27} +(-0.0374386 + 0.212325i) q^{29} +(1.20325 - 2.08410i) q^{31} +(-11.9124 - 4.33575i) q^{33} +(-7.45858 + 6.25849i) q^{35} +6.54964 q^{37} -6.97896 q^{39} +(-1.33930 + 1.12381i) q^{41} +(1.55003 + 0.564166i) q^{43} +(3.02055 - 5.23175i) q^{45} +(-1.19032 + 6.75067i) q^{47} +(-5.13507 - 8.89419i) q^{49} +(10.0315 + 8.41739i) q^{51} +(5.94835 - 2.16502i) q^{53} +(-2.18363 - 12.3840i) q^{55} +(-9.50904 - 3.94576i) q^{57} +(1.77838 + 10.0857i) q^{59} +(-9.39192 + 3.41838i) q^{61} +(8.20849 + 6.88774i) q^{63} +(-3.46145 - 5.99540i) q^{65} +(1.55400 - 8.81316i) q^{67} +(-2.11842 + 3.66921i) q^{69} +(10.0956 + 3.67449i) q^{71} +(9.55268 - 8.01565i) q^{73} +1.15542 q^{75} +22.3050 q^{77} +(-4.29216 + 3.60155i) q^{79} +(9.47859 + 3.44993i) q^{81} +(3.65613 - 6.33261i) q^{83} +(-2.25568 + 12.7926i) q^{85} +(0.254611 + 0.440999i) q^{87} +(4.15664 + 3.48783i) q^{89} +(11.5390 - 4.19984i) q^{91} +(-0.986995 - 5.59753i) q^{93} +(-1.32665 - 10.1259i) q^{95} +(-3.09867 - 17.5734i) q^{97} +(-13.0048 + 4.73334i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{7} - 6 q^{9} - 3 q^{11} + 3 q^{13} + 33 q^{15} + 9 q^{17} - 24 q^{19} - 15 q^{21} + 6 q^{23} + 6 q^{25} - 12 q^{27} - 3 q^{29} - 6 q^{31} - 45 q^{33} - 15 q^{35} + 48 q^{37} + 12 q^{39} - 18 q^{41}+ \cdots + 15 q^{99}+O(q^{100}) $ 18 * q - 9 * q^7 - 6 * q^9 - 3 * q^11 + 3 * q^13 + 33 * q^15 + 9 * q^17 - 24 * q^19 - 15 * q^21 + 6 * q^23 + 6 * q^25 - 12 * q^27 - 3 * q^29 - 6 * q^31 - 45 * q^33 - 15 * q^35 + 48 * q^37 + 12 * q^39 - 18 * q^41 - 39 * q^43 - 42 * q^45 - 27 * q^47 - 18 * q^49 + 48 * q^51 + 39 * q^53 - 27 * q^55 - 6 * q^57 + 9 * q^59 - 24 * q^61 + 3 * q^63 + 27 * q^65 + 39 * q^67 - 3 * q^69 + 12 * q^73 + 90 * q^75 + 60 * q^77 + 63 * q^79 - 6 * q^81 - 27 * q^83 - 30 * q^85 + 18 * q^87 + 66 * q^89 + 108 * q^91 + 60 * q^93 - 75 * q^95 - 81 * q^97 + 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{9}\right)$

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
$3$	1.80930	−	1.51819i	1.04460	−	0.876525i	0.0520863	−	0.998643i	$-0.483413\pi$
$3$	1.80930	−	1.51819i	1.04460	−	0.876525i	0.992516	+	0.122118i	$0.0389685\pi$
$4$		0			0
$5$	2.20161	+	0.801320i	0.984590	+	0.358361i	0.783623	−	0.621237i	$-0.213369\pi$
$5$	2.20161	+	0.801320i	0.984590	+	0.358361i	0.200967	+	0.979598i	$0.435592\pi$
$6$		0			0
$7$	−2.07787	+	3.59897i	−0.785360	+	1.36028i	0.143424	+	0.989661i	$0.454189\pi$
$7$	−2.07787	+	3.59897i	−0.785360	+	1.36028i	−0.928784	+	0.370622i	$0.879145\pi$
$8$		0			0
$9$	0.447746	−	2.53930i	0.149249	−	0.846432i
$10$		0			0
$11$	−2.68364	−	4.64821i	−0.809149	−	1.40149i	−0.913454	−	0.406942i	$-0.866595\pi$
$11$	−2.68364	−	4.64821i	−0.809149	−	1.40149i	0.104305	−	0.994545i	$-0.466738\pi$
$12$		0			0
$13$	−2.26353	−	1.89933i	−0.627792	−	0.526780i	0.272450	−	0.962170i	$-0.412166\pi$
$13$	−2.26353	−	1.89933i	−0.627792	−	0.526780i	−0.900242	+	0.435390i	$0.856610\pi$
$14$		0			0
$15$	5.19993	−	1.89262i	1.34262	−	0.488673i
$16$		0			0
$17$	0.962770	+	5.46014i	0.233506	+	1.32428i	0.845737	+	0.533600i	$0.179161\pi$
$17$	0.962770	+	5.46014i	0.233506	+	1.32428i	−0.612231	+	0.790679i	$0.709728\pi$
$18$		0			0
$19$	−2.01029	−	3.86765i	−0.461193	−	0.887300i
$19$	−2.01029	−	3.86765i	−0.461193	−	0.887300i
$20$		0			0
$21$	1.70442	+	9.66622i	0.371934	+	2.10934i
$22$		0			0
$23$	−1.68566	+	0.613531i	−0.351485	+	0.127930i	−0.511728	−	0.859148i	$-0.670994\pi$
$23$	−1.68566	+	0.613531i	−0.351485	+	0.127930i	0.160243	+	0.987078i	$0.448772\pi$
$24$		0			0
$25$	0.374747	+	0.314450i	0.0749494	+	0.0628900i
$26$		0			0
$27$	0.497804	+	0.862221i	0.0958024	+	0.165935i
$28$		0			0
$29$	−0.0374386	+	0.212325i	−0.00695217	+	0.0394277i	−0.988087	−	0.153900i	$-0.950817\pi$
$29$	−0.0374386	+	0.212325i	−0.00695217	+	0.0394277i	0.981134	+	0.193327i	$0.0619279\pi$
$30$		0			0
$31$	1.20325	−	2.08410i	0.216111	−	0.374315i	−0.737505	−	0.675342i	$-0.763996\pi$
$31$	1.20325	−	2.08410i	0.216111	−	0.374315i	0.953616	+	0.301027i	$0.0973294\pi$
$32$		0			0
$33$	−11.9124	−	4.33575i	−2.07368	−	0.754757i
$34$		0			0
$35$	−7.45858	+	6.25849i	−1.26073	+	1.05788i
$36$		0			0
$37$	6.54964			1.07676			0.538378	−	0.842704i	$-0.319037\pi$
$37$	6.54964			1.07676			0.538378	+	0.842704i	$0.319037\pi$
$38$		0			0
$39$	−6.97896			−1.11753
$40$		0			0
$41$	−1.33930	+	1.12381i	−0.209164	+	0.175509i	−0.741351	−	0.671117i	$-0.765815\pi$
$41$	−1.33930	+	1.12381i	−0.209164	+	0.175509i	0.532187	+	0.846627i	$0.321370\pi$
$42$		0			0
$43$	1.55003	+	0.564166i	0.236378	+	0.0860346i	0.457493	−	0.889213i	$-0.348747\pi$
$43$	1.55003	+	0.564166i	0.236378	+	0.0860346i	−0.221115	+	0.975248i	$0.570970\pi$
$44$		0			0
$45$	3.02055	−	5.23175i	0.450277	−	0.779903i
$46$		0			0
$47$	−1.19032	+	6.75067i	−0.173627	+	0.984686i	0.766090	+	0.642733i	$0.222199\pi$
$47$	−1.19032	+	6.75067i	−0.173627	+	0.984686i	−0.939717	+	0.341953i	$0.888912\pi$
$48$		0			0
$49$	−5.13507	−	8.89419i	−0.733581	−	1.27060i
$50$		0			0
$51$	10.0315	+	8.41739i	1.40468	+	1.17867i
$52$		0			0
$53$	5.94835	−	2.16502i	0.817068	−	0.297388i	0.100528	−	0.994934i	$-0.467947\pi$
$53$	5.94835	−	2.16502i	0.817068	−	0.297388i	0.716540	+	0.697546i	$0.245725\pi$
$54$		0			0
$55$	−2.18363	−	12.3840i	−0.294441	−	1.66986i
$56$		0			0
$57$	−9.50904	−	3.94576i	−1.25950	−	0.522628i
$58$		0			0
$59$	1.77838	+	10.0857i	0.231525	+	1.31304i	0.849810	+	0.527089i	$0.176717\pi$
$59$	1.77838	+	10.0857i	0.231525	+	1.31304i	−0.618285	+	0.785954i	$0.712172\pi$
$60$		0			0
$61$	−9.39192	+	3.41838i	−1.20251	+	0.437679i	−0.864100	−	0.503319i	$-0.832112\pi$
$61$	−9.39192	+	3.41838i	−1.20251	+	0.437679i	−0.338412	+	0.940998i	$0.609890\pi$
$62$		0			0
$63$	8.20849	+	6.88774i	1.03417	+	0.867774i
$64$		0			0
$65$	−3.46145	−	5.99540i	−0.429340	−	0.743638i
$66$		0			0
$67$	1.55400	−	8.81316i	0.189851	−	1.07670i	−0.729712	−	0.683755i	$-0.760346\pi$
$67$	1.55400	−	8.81316i	0.189851	−	1.07670i	0.919563	−	0.392944i	$-0.128543\pi$
$68$		0			0
$69$	−2.11842	+	3.66921i	−0.255028	+	0.441721i
$70$		0			0
$71$	10.0956	+	3.67449i	1.19812	+	0.436082i	0.862569	−	0.505939i	$-0.168854\pi$
$71$	10.0956	+	3.67449i	1.19812	+	0.436082i	0.335555	+	0.942020i	$0.391076\pi$
$72$		0			0
$73$	9.55268	−	8.01565i	1.11806	−	0.938161i	0.119552	−	0.992828i	$-0.461854\pi$
$73$	9.55268	−	8.01565i	1.11806	−	0.938161i	0.998505	+	0.0546667i	$0.0174096\pi$
$74$		0			0
$75$	1.15542			0.133417
$76$		0			0
$77$	22.3050			2.54189
$78$		0			0
$79$	−4.29216	+	3.60155i	−0.482906	+	0.405206i	−0.851476	−	0.524394i	$-0.824292\pi$
$79$	−4.29216	+	3.60155i	−0.482906	+	0.405206i	0.368570	+	0.929600i	$0.379847\pi$
$80$		0			0
$81$	9.47859	+	3.44993i	1.05318	+	0.383325i
$82$		0			0
$83$	3.65613	−	6.33261i	0.401313	−	0.695094i	−0.592572	−	0.805518i	$-0.701887\pi$
$83$	3.65613	−	6.33261i	0.401313	−	0.695094i	0.993885	+	0.110423i	$0.0352207\pi$
$84$		0			0
$85$	−2.25568	+	12.7926i	−0.244663	+	1.38755i
$86$		0			0
$87$	0.254611	+	0.440999i	0.0272971	+	0.0472800i
$88$		0			0
$89$	4.15664	+	3.48783i	0.440603	+	0.369710i	0.835935	−	0.548829i	$-0.184926\pi$
$89$	4.15664	+	3.48783i	0.440603	+	0.369710i	−0.395332	+	0.918538i	$0.629371\pi$
$90$		0			0
$91$	11.5390	−	4.19984i	1.20961	−	0.440263i
$92$		0			0
$93$	−0.986995	−	5.59753i	−0.102347	−	0.580436i
$94$		0			0
$95$	−1.32665	−	10.1259i	−0.136112	−	1.03890i
$96$		0			0
$97$	−3.09867	−	17.5734i	−0.314622	−	1.78431i	−0.574329	−	0.818625i	$-0.694737\pi$
$97$	−3.09867	−	17.5734i	−0.314622	−	1.78431i	0.259706	−	0.965688i	$-0.416374\pi$
$98$		0			0
$99$	−13.0048	+	4.73334i	−1.30703	+	0.475719i
$100$		0			0
$101$	−7.75287	−	6.50543i	−0.771439	−	0.647314i	0.169638	−	0.985506i	$-0.445740\pi$
$101$	−7.75287	−	6.50543i	−0.771439	−	0.647314i	−0.941077	+	0.338192i	$0.890185\pi$
$102$		0			0
$103$	−2.36474	−	4.09586i	−0.233005	−	0.403577i	0.725686	−	0.688026i	$-0.241523\pi$
$103$	−2.36474	−	4.09586i	−0.233005	−	0.403577i	−0.958691	+	0.284449i	$0.908189\pi$
$104$		0			0
$105$	−3.99328	+	22.6470i	−0.389704	+	2.21012i
$106$		0			0
$107$	−4.52267	+	7.83349i	−0.437223	+	0.757292i	−0.997474	−	0.0710306i	$-0.977371\pi$
$107$	−4.52267	+	7.83349i	−0.437223	+	0.757292i	0.560251	+	0.828323i	$0.310705\pi$
$108$		0			0
$109$	−7.55953	−	2.75144i	−0.724072	−	0.263541i	−0.0464184	−	0.998922i	$-0.514781\pi$
$109$	−7.55953	−	2.75144i	−0.724072	−	0.263541i	−0.677653	+	0.735382i	$0.737003\pi$
$110$		0			0
$111$	11.8503	−	9.94358i	1.12478	−	0.943803i
$112$		0			0
$113$	−4.20523			−0.395595			−0.197797	−	0.980243i	$-0.563379\pi$
$113$	−4.20523			−0.395595			−0.197797	+	0.980243i	$0.563379\pi$
$114$		0			0
$115$	−4.20280			−0.391913
$116$		0			0
$117$	−5.83645	+	4.89736i	−0.539580	+	0.452762i
$118$		0			0
$119$	−21.6514	−	7.88046i	−1.98478	−	0.722401i
$120$		0			0
$121$	−8.90388	+	15.4220i	−0.809444	+	1.40200i
$122$		0			0
$123$	−0.717055	+	4.06662i	−0.0646547	+	0.366675i
$124$		0			0
$125$	−5.28419	−	9.15248i	−0.472632	−	0.818623i
$126$		0			0
$127$	4.06439	+	3.41043i	0.360657	+	0.302627i	0.805052	−	0.593204i	$-0.202137\pi$
$127$	4.06439	+	3.41043i	0.360657	+	0.302627i	−0.444396	+	0.895831i	$0.646582\pi$
$128$		0			0
$129$	3.66099	−	1.33249i	0.322332	−	0.117319i
$130$		0			0
$131$	−0.428531	−	2.43032i	−0.0374409	−	0.212338i	0.960348	−	0.278805i	$-0.0899383\pi$
$131$	−0.428531	−	2.43032i	−0.0374409	−	0.212338i	−0.997789	+	0.0664672i	$0.978827\pi$
$132$		0			0
$133$	18.0967	+	0.801477i	1.56918	+	0.0694969i
$134$		0			0
$135$	0.405054	+	2.29717i	0.0348615	+	0.197709i
$136$		0			0
$137$	−1.07126	+	0.389905i	−0.0915235	+	0.0333118i	−0.387376	−	0.921922i	$-0.626619\pi$
$137$	−1.07126	+	0.389905i	−0.0915235	+	0.0333118i	0.295853	+	0.955234i	$0.404396\pi$
$138$		0			0
$139$	12.8475	+	10.7804i	1.08971	+	0.914378i	0.996691	−	0.0812861i	$-0.0259028\pi$
$139$	12.8475	+	10.7804i	1.08971	+	0.914378i	0.0930223	+	0.995664i	$0.470347\pi$
$140$		0			0
$141$	8.09511	+	14.0211i	0.681731	+	1.18079i
$142$		0			0
$143$	−2.75396	+	15.6185i	−0.230298	+	1.30608i
$144$		0			0
$145$	−0.252565	+	0.437456i	−0.0209744	+	0.0363287i
$146$		0			0
$147$	−22.7939	−	8.29631i	−1.88001	−	0.684268i
$148$		0			0
$149$	4.93511	−	4.14105i	0.404300	−	0.339248i	−0.417853	−	0.908515i	$-0.637217\pi$
$149$	4.93511	−	4.14105i	0.404300	−	0.339248i	0.822153	+	0.569267i	$0.192773\pi$
$150$		0			0
$151$	−9.15755			−0.745231			−0.372616	−	0.927986i	$-0.621539\pi$
$151$	−9.15755			−0.745231			−0.372616	+	0.927986i	$0.621539\pi$
$152$		0			0
$153$	14.2960			1.15576
$154$		0			0
$155$	4.31912	−	3.62417i	0.346920	−	0.291101i
$156$		0			0
$157$	−17.0488	−	6.20525i	−1.36064	−	0.495233i	−0.444389	−	0.895834i	$-0.646579\pi$
$157$	−17.0488	−	6.20525i	−1.36064	−	0.495233i	−0.916253	+	0.400601i	$0.868801\pi$
$158$		0			0
$159$	7.47546	−	12.9479i	0.592842	−	1.02683i
$160$		0			0
$161$	1.29450	−	7.34149i	0.102021	−	0.578590i
$162$		0			0
$163$	3.87556	+	6.71266i	0.303557	+	0.525776i	0.976939	−	0.213519i	$-0.0684924\pi$
$163$	3.87556	+	6.71266i	0.303557	+	0.525776i	−0.673382	+	0.739295i	$0.735159\pi$
$164$		0			0
$165$	−22.7521	−	19.0912i	−1.77124	−	1.48625i
$166$		0			0
$167$	4.42208	−	1.60950i	0.342191	−	0.124547i	−0.165208	−	0.986259i	$-0.552829\pi$
$167$	4.42208	−	1.60950i	0.342191	−	0.124547i	0.507398	+	0.861712i	$0.330607\pi$
$168$		0			0
$169$	−0.741296	−	4.20410i	−0.0570227	−	0.323392i
$170$		0			0
$171$	−10.7212	+	3.37300i	−0.819871	+	0.257940i
$172$		0			0
$173$	3.73835	+	21.2012i	0.284221	+	1.61190i	0.708053	+	0.706159i	$0.249574\pi$
$173$	3.73835	+	21.2012i	0.284221	+	1.61190i	−0.423832	+	0.905741i	$0.639315\pi$
$174$		0			0
$175$	−1.91037	+	0.695318i	−0.144410	+	0.0525611i
$176$		0			0
$177$	18.5296	+	15.5481i	1.39277	+	1.16867i
$178$		0			0
$179$	−5.56774	−	9.64362i	−0.416153	−	0.720798i	0.579396	−	0.815046i	$-0.303288\pi$
$179$	−5.56774	−	9.64362i	−0.416153	−	0.720798i	−0.995549	+	0.0942486i	$0.969955\pi$
$180$		0			0
$181$	−3.39994	+	19.2820i	−0.252716	+	1.43322i	0.549152	+	0.835722i	$0.314951\pi$
$181$	−3.39994	+	19.2820i	−0.252716	+	1.43322i	−0.801868	+	0.597501i	$0.796160\pi$
$182$		0			0
$183$	−11.8031	+	20.4436i	−0.872510	+	1.51123i
$184$		0			0
$185$	14.4198	+	5.24836i	1.06016	+	0.385867i
$186$		0			0
$187$	22.7961	−	19.1282i	1.66702	−	1.39879i
$188$		0			0
$189$	−4.13748			−0.300957
$190$		0			0
$191$	−14.0015			−1.01312			−0.506558	−	0.862206i	$-0.669082\pi$
$191$	−14.0015			−1.01312			−0.506558	+	0.862206i	$0.669082\pi$
$192$		0			0
$193$	−0.100174	+	0.0840556i	−0.00721065	+	0.00605046i	−0.646386	−	0.763011i	$-0.723720\pi$
$193$	−0.100174	+	0.0840556i	−0.00721065	+	0.00605046i	0.639175	+	0.769061i	$0.279276\pi$
$194$		0			0
$195$	−15.3649	−	5.59238i	−1.10031	−	0.400479i
$196$		0			0
$197$	6.05232	−	10.4829i	0.431210	−	0.746878i	−0.565768	−	0.824565i	$-0.691420\pi$
$197$	6.05232	−	10.4829i	0.431210	−	0.746878i	0.996978	+	0.0776867i	$0.0247534\pi$
$198$		0			0
$199$	2.02946	−	11.5096i	0.143864	−	0.815895i	−0.824408	−	0.565997i	$-0.808492\pi$
$199$	2.02946	−	11.5096i	0.143864	−	0.815895i	0.968272	−	0.249899i	$-0.0803973\pi$
$200$		0			0
$201$	−10.5684	−	18.3049i	−0.745435	−	1.29113i
$202$		0			0
$203$	−0.686359	−	0.575923i	−0.0481729	−	0.0404219i
$204$		0			0
$205$	−3.84915	+	1.40098i	−0.268836	+	0.0978484i
$206$		0			0
$207$	0.803187	+	4.55510i	0.0558254	+	0.316601i
$208$		0			0
$209$	−12.5827	+	19.7236i	−0.870365	+	1.36431i
$210$		0			0
$211$	−0.286105	−	1.62258i	−0.0196963	−	0.111703i	0.973375	−	0.229220i	$-0.0736176\pi$
$211$	−0.286105	−	1.62258i	−0.0196963	−	0.111703i	−0.993071	+	0.117517i	$0.962507\pi$
$212$		0			0
$213$	23.8445	−	8.67870i	1.63380	−	0.594655i
$214$		0			0
$215$	2.96049	+	2.48415i	0.201904	+	0.169417i
$216$		0			0
$217$	5.00040	+	8.66095i	0.339449	+	0.587944i
$218$		0			0
$219$	5.11445	−	29.0055i	0.345603	−	1.96001i
$220$		0			0
$221$	8.19135	−	14.1878i	0.551010	−	0.954377i
$222$		0			0
$223$	17.3431	+	6.31237i	1.16138	+	0.422707i	0.849590	−	0.527444i	$-0.176850\pi$
$223$	17.3431	+	6.31237i	1.16138	+	0.422707i	0.311789	+	0.950151i	$0.399072\pi$
$224$		0			0
$225$	0.966273	−	0.810799i	0.0644182	−	0.0540533i
$226$		0			0
$227$	3.16564			0.210111			0.105055	−	0.994466i	$-0.466498\pi$
$227$	3.16564			0.210111			0.105055	+	0.994466i	$0.466498\pi$
$228$		0			0
$229$	−12.8379			−0.848353			−0.424177	−	0.905580i	$-0.639436\pi$
$229$	−12.8379			−0.848353			−0.424177	+	0.905580i	$0.639436\pi$
$230$		0			0
$231$	40.3565	−	33.8632i	2.65527	−	2.22803i
$232$		0			0
$233$	−5.43406	−	1.97784i	−0.355997	−	0.129572i	0.157830	−	0.987466i	$-0.449550\pi$
$233$	−5.43406	−	1.97784i	−0.355997	−	0.129572i	−0.513827	+	0.857894i	$0.671773\pi$
$234$		0			0
$235$	−8.03008	+	13.9085i	−0.523824	+	0.907290i
$236$		0			0
$237$	−2.29800	+	13.0326i	−0.149271	+	0.846558i
$238$		0			0
$239$	6.52635	+	11.3040i	0.422154	+	0.731193i	0.996150	−	0.0876657i	$-0.0279407\pi$
$239$	6.52635	+	11.3040i	0.422154	+	0.731193i	−0.573996	+	0.818858i	$0.694607\pi$
$240$		0			0
$241$	8.31220	+	6.97476i	0.535436	+	0.449284i	0.869974	−	0.493098i	$-0.164136\pi$
$241$	8.31220	+	6.97476i	0.535436	+	0.449284i	−0.334538	+	0.942382i	$0.608580\pi$
$242$		0			0
$243$	19.5806	−	7.12675i	1.25610	−	0.457181i
$244$		0			0
$245$	−4.17831	−	23.6964i	−0.266942	−	1.51391i
$246$		0			0
$247$	−2.79558	+	12.5728i	−0.177879	+	0.799986i
$248$		0			0
$249$	−2.99902	−	17.0083i	−0.190055	−	1.07786i
$250$		0			0
$251$	10.5707	−	3.84743i	0.667219	−	0.242848i	0.0138689	−	0.999904i	$-0.495585\pi$
$251$	10.5707	−	3.84743i	0.667219	−	0.242848i	0.653350	+	0.757056i	$0.273363\pi$
$252$		0			0
$253$	7.37553	+	6.18881i	0.463696	+	0.389087i
$254$		0			0
$255$	15.3403	+	26.5702i	0.960648	+	1.66389i
$256$		0			0
$257$	−3.55535	+	20.1634i	−0.221776	+	1.25776i	0.646976	+	0.762510i	$0.276033\pi$
$257$	−3.55535	+	20.1634i	−0.221776	+	1.25776i	−0.868753	+	0.495246i	$0.835078\pi$
$258$		0			0
$259$	−13.6093	+	23.5720i	−0.845640	+	1.46469i
$260$		0			0
$261$	0.522392	+	0.190135i	0.0323353	+	0.0117691i
$262$		0			0
$263$	−21.3665	+	17.9286i	−1.31751	+	1.10552i	−0.330687	+	0.943741i	$0.607280\pi$
$263$	−21.3665	+	17.9286i	−1.31751	+	1.10552i	−0.986826	+	0.161784i	$0.948275\pi$
$264$		0			0
$265$	14.8308			0.911049
$266$		0			0
$267$	12.8158			0.784314
$268$		0			0
$269$	−4.01106	+	3.36568i	−0.244559	+	0.205209i	−0.756825	−	0.653617i	$-0.773251\pi$
$269$	−4.01106	+	3.36568i	−0.244559	+	0.205209i	0.512266	+	0.858827i	$0.328806\pi$
$270$		0			0
$271$	−5.06671	−	1.84413i	−0.307781	−	0.112023i	0.183512	−	0.983017i	$-0.441253\pi$
$271$	−5.06671	−	1.84413i	−0.307781	−	0.112023i	−0.491293	+	0.870994i	$0.663476\pi$
$272$		0			0
$273$	14.5014	−	25.1171i	0.877662	−	1.52015i
$274$		0			0
$275$	0.455941	−	2.58577i	0.0274943	−	0.155928i
$276$		0			0
$277$	−12.7451	−	22.0752i	−0.765781	−	1.32637i	−0.939833	−	0.341635i	$-0.889019\pi$
$277$	−12.7451	−	22.0752i	−0.765781	−	1.32637i	0.174052	−	0.984736i	$-0.444314\pi$
$278$		0			0
$279$	−4.75338	−	3.98856i	−0.284578	−	0.238789i
$280$		0			0
$281$	17.2976	−	6.29580i	1.03189	−	0.375576i	0.230088	−	0.973170i	$-0.426099\pi$
$281$	17.2976	−	6.29580i	1.03189	−	0.375576i	0.801799	+	0.597594i	$0.203876\pi$
$282$		0			0
$283$	3.43385	+	19.4743i	0.204121	+	1.15763i	0.898817	+	0.438325i	$0.144428\pi$
$283$	3.43385	+	19.4743i	0.204121	+	1.15763i	−0.694696	+	0.719304i	$0.744461\pi$
$284$		0			0
$285$	−17.7734	−	16.3068i	−1.05280	−	0.965931i
$286$		0			0
$287$	−1.26166	−	7.15524i	−0.0744735	−	0.422360i
$288$		0			0
$289$	−12.9114	+	4.69938i	−0.759496	+	0.276434i
$290$		0			0
$291$	−32.2862	−	27.0913i	−1.89265	−	1.58812i
$292$		0			0
$293$	0.848104	+	1.46896i	0.0495468	+	0.0858175i	0.889735	−	0.456477i	$-0.150889\pi$
$293$	0.848104	+	1.46896i	0.0495468	+	0.0858175i	−0.840188	+	0.542295i	$0.817556\pi$
$294$		0			0
$295$	−4.16657	+	23.6298i	−0.242587	+	1.37578i
$296$		0			0
$297$	2.67185	−	4.62779i	0.155037	−	0.268531i
$298$		0			0
$299$	4.98085	+	1.81288i	0.288050	+	0.104842i
$300$		0			0
$301$	−5.25118	+	4.40627i	−0.302673	+	0.253973i
$302$		0			0
$303$	−23.9037			−1.37323
$304$		0			0
$305$	−23.4166			−1.34083
$306$		0			0
$307$	−17.3246	+	14.5371i	−0.988769	+	0.829676i	−0.985389	−	0.170319i	$-0.945520\pi$
$307$	−17.3246	+	14.5371i	−0.988769	+	0.829676i	−0.00337987	+	0.999994i	$0.501076\pi$
$308$		0			0
$309$	−10.4968	−	3.82053i	−0.597143	−	0.217342i
$310$		0			0
$311$	−0.649314	+	1.12464i	−0.0368192	+	0.0637727i	−0.883848	−	0.467775i	$-0.845056\pi$
$311$	−0.649314	+	1.12464i	−0.0368192	+	0.0637727i	0.847029	+	0.531547i	$0.178389\pi$
$312$		0			0
$313$	−1.40380	+	7.96137i	−0.0793477	+	0.450003i	0.919086	+	0.394057i	$0.128929\pi$
$313$	−1.40380	+	7.96137i	−0.0793477	+	0.450003i	−0.998434	+	0.0559462i	$0.982182\pi$
$314$		0			0
$315$	12.5526	+	21.7418i	0.707259	+	1.22501i
$316$		0			0
$317$	−5.47537	−	4.59438i	−0.307527	−	0.258046i	0.475942	−	0.879477i	$-0.342107\pi$
$317$	−5.47537	−	4.59438i	−0.307527	−	0.258046i	−0.783469	+	0.621431i	$0.786552\pi$
$318$		0			0
$319$	1.08740	−	0.395782i	0.0608828	−	0.0221595i
$320$		0			0
$321$	3.70982	+	21.0394i	0.207062	+	1.17431i
$322$		0			0
$323$	19.1825	−	14.7001i	1.06734	−	0.817938i
$324$		0			0
$325$	−0.251008	−	1.42354i	−0.0139234	−	0.0789636i
$326$		0			0
$327$	−17.8547	+	6.49858i	−0.987367	+	0.359372i
$328$		0			0
$329$	−21.8221	−	18.3109i	−1.20309	−	1.00951i
$330$		0			0
$331$	−13.6322	−	23.6116i	−0.749292	−	1.29781i	−0.948162	−	0.317786i	$-0.897060\pi$
$331$	−13.6322	−	23.6116i	−0.749292	−	1.29781i	0.198870	−	0.980026i	$-0.436273\pi$
$332$		0			0
$333$	2.93258	−	16.6315i	0.160704	−	0.911400i
$334$		0			0
$335$	10.4835	−	18.1579i	0.572772	−	0.992071i
$336$		0			0
$337$	23.0029	+	8.37237i	1.25305	+	0.456072i	0.881430	−	0.472314i	$-0.156581\pi$
$337$	23.0029	+	8.37237i	1.25305	+	0.456072i	0.371617	+	0.928386i	$0.378803\pi$
$338$		0			0
$339$	−7.60853	+	6.38432i	−0.413239	+	0.346749i
$340$		0			0
$341$	−12.9164			−0.699463
$342$		0			0
$343$	13.5898			0.733780
$344$		0			0
$345$	−7.60415	+	6.38064i	−0.409394	+	0.343522i
$346$		0			0
$347$	21.4518	+	7.80782i	1.15159	+	0.419146i	0.846087	−	0.533045i	$-0.178952\pi$
$347$	21.4518	+	7.80782i	1.15159	+	0.419146i	0.305506	+	0.952190i	$0.401174\pi$
$348$		0			0
$349$	−1.29358	+	2.24054i	−0.0692435	+	0.119933i	−0.898569	−	0.438833i	$-0.855392\pi$
$349$	−1.29358	+	2.24054i	−0.0692435	+	0.119933i	0.829325	+	0.558767i	$0.188725\pi$
$350$		0			0
$351$	0.510848	−	2.89716i	0.0272670	−	0.154639i
$352$		0			0
$353$	5.48049	+	9.49249i	0.291697	+	0.505234i	0.974211	−	0.225638i	$-0.0724467\pi$
$353$	5.48049	+	9.49249i	0.291697	+	0.505234i	−0.682514	+	0.730872i	$0.739113\pi$
$354$		0			0
$355$	19.2821	+	16.1796i	1.02339	+	0.858723i
$356$		0			0
$357$	−51.1380	+	18.6127i	−2.70651	+	0.985088i
$358$		0			0
$359$	−4.08393	−	23.1611i	−0.215542	−	1.22240i	−0.879964	−	0.475040i	$-0.842433\pi$
$359$	−4.08393	−	23.1611i	−0.215542	−	1.22240i	0.664422	−	0.747357i	$-0.268678\pi$
$360$		0			0
$361$	−10.9174	+	15.5502i	−0.574602	+	0.818433i
$362$		0			0
$363$	7.30360	+	41.4208i	0.383340	+	2.17403i
$364$		0			0
$365$	27.4544	−	9.99258i	1.43703	−	0.523035i
$366$		0			0
$367$	−6.14137	−	5.15322i	−0.320577	−	0.268996i	0.468270	−	0.883585i	$-0.344877\pi$
$367$	−6.14137	−	5.15322i	−0.320577	−	0.268996i	−0.788847	+	0.614589i	$0.789322\pi$
$368$		0			0
$369$	2.25401	+	3.90407i	0.117339	+	0.203238i
$370$		0			0
$371$	−4.56802	+	25.9066i	−0.237160	+	1.34500i
$372$		0			0
$373$	8.48051	−	14.6887i	0.439104	−	0.760551i	−0.558516	−	0.829493i	$-0.688629\pi$
$373$	8.48051	−	14.6887i	0.439104	−	0.760551i	0.997621	+	0.0689426i	$0.0219625\pi$
$374$		0			0
$375$	−23.4559	−	8.53724i	−1.21126	−	0.440861i
$376$		0			0
$377$	0.488019	−	0.409496i	0.0251342	−	0.0210901i
$378$		0			0
$379$	−22.6828			−1.16513			−0.582567	−	0.812782i	$-0.697952\pi$
$379$	−22.6828			−1.16513			−0.582567	+	0.812782i	$0.697952\pi$
$380$		0			0
$381$	12.5314			0.642002
$382$		0			0
$383$	9.46785	−	7.94447i	0.483784	−	0.405943i	−0.368008	−	0.929823i	$-0.619960\pi$
$383$	9.46785	−	7.94447i	0.483784	−	0.405943i	0.851792	+	0.523879i	$0.175516\pi$
$384$		0			0
$385$	49.1069	+	17.8735i	2.50272	+	0.910916i
$386$		0			0
$387$	2.12661	−	3.68339i	0.108102	−	0.187237i
$388$		0			0
$389$	−3.36690	+	19.0947i	−0.170709	+	0.968138i	0.772272	+	0.635292i	$0.219120\pi$
$389$	−3.36690	+	19.0947i	−0.170709	+	0.968138i	−0.942981	+	0.332846i	$0.891991\pi$
$390$		0			0
$391$	−4.97287	−	8.61326i	−0.251489	−	0.435591i
$392$		0			0
$393$	−4.46502	−	3.74660i	−0.225230	−	0.188991i
$394$		0			0
$395$	−12.3357	+	4.48981i	−0.620674	+	0.225907i
$396$		0			0
$397$	0.956093	+	5.42227i	0.0479849	+	0.272136i	0.999355	−	0.0359147i	$-0.0114345\pi$
$397$	0.956093	+	5.42227i	0.0479849	+	0.272136i	−0.951370	+	0.308051i	$0.900323\pi$
$398$		0			0
$399$	33.9592	−	26.0240i	1.70009	−	1.30283i
$400$		0			0
$401$	−1.22303	−	6.93616i	−0.0610753	−	0.346375i	−0.999997	−	0.00224576i	$-0.999285\pi$
$401$	−1.22303	−	6.93616i	−0.0610753	−	0.346375i	0.938922	−	0.344130i	$-0.111826\pi$
$402$		0			0
$403$	−6.68200	+	2.43205i	−0.332854	+	0.121149i
$404$		0			0
$405$	18.1037	+	15.1908i	0.899578	+	0.754836i
$406$		0			0
$407$	−17.5769	−	30.4441i	−0.871255	−	1.50906i
$408$		0			0
$409$	6.62579	−	37.5767i	0.327624	−	1.85805i	−0.162929	−	0.986638i	$-0.552094\pi$
$409$	6.62579	−	37.5767i	0.327624	−	1.85805i	0.490553	−	0.871411i	$-0.336795\pi$
$410$		0			0
$411$	−1.34628	+	2.33182i	−0.0664070	+	0.115020i
$412$		0			0
$413$	−39.9933	−	14.5564i	−1.96794	−	0.716272i
$414$		0			0
$415$	13.1238	−	11.0122i	0.644223	−	0.540568i
$416$		0			0
$417$	39.6117			1.93979
$418$		0			0
$419$	8.28410			0.404705			0.202352	−	0.979313i	$-0.435141\pi$
$419$	8.28410			0.404705			0.202352	+	0.979313i	$0.435141\pi$
$420$		0			0
$421$	−0.0605690	+	0.0508234i	−0.00295195	+	0.00247698i	−0.644262	−	0.764805i	$-0.722836\pi$
$421$	−0.0605690	+	0.0508234i	−0.00295195	+	0.00247698i	0.641310	+	0.767282i	$0.278391\pi$
$422$		0			0
$423$	16.6090	+	6.04517i	0.807556	+	0.293926i
$424$		0			0
$425$	−1.35615	+	2.34891i	−0.0657827	+	0.113939i
$426$		0			0
$427$	7.21251	−	40.9042i	0.349038	−	1.97949i
$428$		0			0
$429$	18.7290	+	32.4396i	0.904246	+	1.56620i
$430$		0			0
$431$	0.679798	+	0.570418i	0.0327447	+	0.0274761i	0.659013	−	0.752131i	$-0.270974\pi$
$431$	0.679798	+	0.570418i	0.0327447	+	0.0274761i	−0.626268	+	0.779607i	$0.715419\pi$
$432$		0			0
$433$	−13.6455	+	4.96655i	−0.655760	+	0.238677i	−0.648405	−	0.761296i	$-0.724563\pi$
$433$	−13.6455	+	4.96655i	−0.655760	+	0.238677i	−0.00735516	+	0.999973i	$0.502341\pi$
$434$		0			0
$435$	0.207172	+	1.17493i	0.00993315	+	0.0563337i
$436$		0			0
$437$	5.76160	+	5.28617i	0.275615	+	0.252872i
$438$		0			0
$439$	−2.02637	−	11.4921i	−0.0967134	−	0.548489i	−0.994209	−	0.107465i	$-0.965727\pi$
$439$	−2.02637	−	11.4921i	−0.0967134	−	0.548489i	0.897495	−	0.441024i	$-0.145385\pi$
$440$		0			0
$441$	−24.8842	+	9.05710i	−1.18496	+	0.431291i
$442$		0			0
$443$	−8.35367	−	7.00956i	−0.396895	−	0.333034i	0.422397	−	0.906411i	$-0.361189\pi$
$443$	−8.35367	−	7.00956i	−0.396895	−	0.333034i	−0.819292	+	0.573377i	$0.805633\pi$
$444$		0			0
$445$	6.35642	+	11.0096i	0.301323	+	0.521907i
$446$		0			0
$447$	2.64223	−	14.9848i	0.124973	−	0.708758i
$448$		0			0
$449$	−1.40626	+	2.43571i	−0.0663655	+	0.114948i	−0.897299	−	0.441424i	$-0.854474\pi$
$449$	−1.40626	+	2.43571i	−0.0663655	+	0.114948i	0.830933	+	0.556372i	$0.187807\pi$
$450$		0			0
$451$	8.81790	+	3.20945i	0.415219	+	0.151127i
$452$		0			0
$453$	−16.5688	+	13.9029i	−0.778470	+	0.653214i
$454$		0			0
$455$	28.7697			1.34874
$456$		0			0
$457$	4.19534			0.196250			0.0981248	−	0.995174i	$-0.468716\pi$
$457$	4.19534			0.196250			0.0981248	+	0.995174i	$0.468716\pi$
$458$		0			0
$459$	−4.22858	+	3.54820i	−0.197373	+	0.165616i
$460$		0			0
$461$	30.4257	+	11.0741i	1.41707	+	0.515771i	0.933196	−	0.359368i	$-0.117008\pi$
$461$	30.4257	+	11.0741i	1.41707	+	0.515771i	0.483872	+	0.875139i	$0.339230\pi$
$462$		0			0
$463$	−11.0196	+	19.0865i	−0.512124	+	0.887025i	0.487777	+	0.872968i	$0.337808\pi$
$463$	−11.0196	+	19.0865i	−0.512124	+	0.887025i	−0.999901	+	0.0140569i	$0.995525\pi$
$464$		0			0
$465$	2.31243	−	13.1145i	0.107237	−	0.608169i
$466$		0			0
$467$	−7.67905	−	13.3005i	−0.355344	−	0.615474i	0.631833	−	0.775105i	$-0.282303\pi$
$467$	−7.67905	−	13.3005i	−0.355344	−	0.615474i	−0.987177	+	0.159631i	$0.948970\pi$
$468$		0			0
$469$	28.4893	+	23.9054i	1.31551	+	1.10385i
$470$		0			0
$471$	−40.2672	+	14.6561i	−1.85541	+	0.675315i
$472$		0			0
$473$	−1.53738	−	8.71890i	−0.0706887	−	0.400895i
$474$		0			0
$475$	0.462832	−	2.08153i	0.0212362	−	0.0955070i
$476$		0			0
$477$	−2.83428	−	16.0740i	−0.129773	−	0.735977i
$478$		0			0
$479$	−19.0736	+	6.94223i	−0.871497	+	0.317199i	−0.738773	−	0.673954i	$-0.764594\pi$
$479$	−19.0736	+	6.94223i	−0.871497	+	0.317199i	−0.132723	+	0.991153i	$0.542372\pi$
$480$		0			0
$481$	−14.8253	−	12.4399i	−0.675978	−	0.567213i
$482$		0			0
$483$	−8.80359	−	15.2483i	−0.400577	−	0.693820i
$484$		0			0
$485$	7.25989	−	41.1729i	0.329655	−	1.86956i
$486$		0			0
$487$	14.9451	−	25.8857i	0.677227	−	1.17299i	−0.298586	−	0.954383i	$-0.596515\pi$
$487$	14.9451	−	25.8857i	0.677227	−	1.17299i	0.975813	−	0.218609i	$-0.0701518\pi$
$488$		0			0
$489$	17.2031	+	6.26143i	0.777952	+	0.283152i
$490$		0			0
$491$	5.73209	−	4.80980i	0.258686	−	0.217063i	−0.504216	−	0.863578i	$-0.668218\pi$
$491$	5.73209	−	4.80980i	0.258686	−	0.217063i	0.762902	+	0.646515i	$0.223774\pi$
$492$		0			0
$493$	−1.19537			−0.0538367
$494$		0			0
$495$	−32.4243			−1.45736
$496$		0			0
$497$	−34.2017	+	28.6986i	−1.53415	+	1.28731i
$498$		0			0
$499$	9.36579	+	3.40887i	0.419270	+	0.152602i	0.543036	−	0.839710i	$-0.317275\pi$
$499$	9.36579	+	3.40887i	0.419270	+	0.152602i	−0.123765	+	0.992312i	$0.539497\pi$
$500$		0			0
$501$	5.55735	−	9.62562i	0.248284	−	0.430041i
$502$		0			0
$503$	−1.28858	+	7.30788i	−0.0574548	+	0.325842i	−0.999965	−	0.00833436i	$-0.997347\pi$
$503$	−1.28858	+	7.30788i	−0.0574548	+	0.325842i	0.942511	+	0.334177i	$0.108458\pi$
$504$		0			0
$505$	−11.8559	−	20.5349i	−0.527579	−	0.913793i
$506$		0			0
$507$	−7.72383	−	6.48106i	−0.343027	−	0.287834i
$508$		0			0
$509$	39.2336	−	14.2799i	1.73900	−	0.632943i	0.739794	−	0.672834i	$-0.234923\pi$
$509$	39.2336	−	14.2799i	1.73900	−	0.632943i	0.999204	+	0.0398901i	$0.0127008\pi$
$510$		0			0
$511$	8.99890	+	51.0353i	0.398088	+	2.25767i
$512$		0			0
$513$	2.33404	−	3.65865i	0.103050	−	0.161533i
$514$		0			0
$515$	−1.92415	−	10.9124i	−0.0847882	−	0.480858i
$516$		0			0
$517$	34.5729	−	12.5835i	1.52051	−	0.553422i
$518$		0			0
$519$	38.9512	+	32.6840i	1.70977	+	1.43467i
$520$		0			0
$521$	16.6434	+	28.8272i	0.729160	+	1.26294i	0.957239	+	0.289299i	$0.0934223\pi$
$521$	16.6434	+	28.8272i	0.729160	+	1.26294i	−0.228079	+	0.973643i	$0.573244\pi$
$522$		0			0
$523$	5.29947	−	30.0548i	0.231730	−	1.31421i	−0.617663	−	0.786443i	$-0.711920\pi$
$523$	5.29947	−	30.0548i	0.231730	−	1.31421i	0.849392	−	0.527762i	$-0.176969\pi$
$524$		0			0
$525$	−2.40082	+	4.15834i	−0.104780	+	0.181485i
$526$		0			0
$527$	12.5379	+	4.56343i	0.546160	+	0.198786i
$528$		0			0
$529$	−15.1540	+	12.7157i	−0.658869	+	0.552857i
$530$		0			0
$531$	26.4068			1.14596
$532$		0			0
$533$	5.16604			0.223766
$534$		0			0
$535$	−16.2343	+	13.6222i	−0.701869	+	0.588938i
$536$		0			0
$537$	−24.7145	−	8.99536i	−1.06651	−	0.388178i
$538$		0			0
$539$	−27.5614	+	47.7377i	−1.18715	+	2.05621i
$540$		0			0
$541$	0.432458	−	2.45259i	0.0185928	−	0.105445i	−0.974099	−	0.226122i	$-0.927395\pi$
$541$	0.432458	−	2.45259i	0.0185928	−	0.105445i	0.992692	+	0.120677i	$0.0385064\pi$
$542$		0			0
$543$	23.1222	+	40.0488i	0.992268	+	1.71866i
$544$		0			0
$545$	−14.4383	−	12.1152i	−0.618471	−	0.518959i
$546$		0			0
$547$	13.3326	−	4.85266i	0.570059	−	0.207485i	−0.0408772	−	0.999164i	$-0.513015\pi$
$547$	13.3326	−	4.85266i	0.570059	−	0.207485i	0.610937	+	0.791680i	$0.290793\pi$
$548$		0			0
$549$	4.47508	+	25.3794i	0.190992	+	1.08317i
$550$		0			0
$551$	0.896461	−	0.282036i	0.0381905	−	0.0120151i
$552$		0			0
$553$	−4.04334	−	22.9309i	−0.171940	−	0.975121i
$554$		0			0
$555$	34.0577	−	12.3960i	1.44567	−	0.526181i
$556$		0			0
$557$	4.90694	+	4.11741i	0.207914	+	0.174460i	0.740798	−	0.671728i	$-0.234447\pi$
$557$	4.90694	+	4.11741i	0.207914	+	0.174460i	−0.532884	+	0.846188i	$0.678892\pi$
$558$		0			0
$559$	−2.43702	−	4.22104i	−0.103075	−	0.178531i
$560$		0			0
$561$	12.2049	−	69.2175i	0.515292	−	2.92237i
$562$		0			0
$563$	14.1747	−	24.5513i	0.597393	−	1.03471i	−0.395812	−	0.918332i	$-0.629537\pi$
$563$	14.1747	−	24.5513i	0.597393	−	1.03471i	0.993204	−	0.116383i	$-0.0371299\pi$
$564$		0			0
$565$	−9.25827	−	3.36973i	−0.389498	−	0.141766i
$566$		0			0
$567$	−32.1114	+	26.9447i	−1.34855	+	1.13157i
$568$		0			0
$569$	−16.4200			−0.688362			−0.344181	−	0.938903i	$-0.611843\pi$
$569$	−16.4200			−0.688362			−0.344181	+	0.938903i	$0.611843\pi$
$570$		0			0
$571$	−36.9283			−1.54540			−0.772701	−	0.634771i	$-0.781095\pi$
$571$	−36.9283			−1.54540			−0.772701	+	0.634771i	$0.781095\pi$
$572$		0			0
$573$	−25.3331	+	21.2570i	−1.05830	+	0.888022i
$574$		0			0
$575$	−0.824621	−	0.300138i	−0.0343891	−	0.0125166i
$576$		0			0
$577$	−20.5819	+	35.6489i	−0.856835	+	1.48408i	0.0180977	+	0.999836i	$0.494239\pi$
$577$	−20.5819	+	35.6489i	−0.856835	+	1.48408i	−0.874932	+	0.484245i	$0.839094\pi$
$578$		0			0
$579$	−0.0536324	+	0.304164i	−0.00222889	+	0.0126406i
$580$		0			0
$581$	15.1939	+	26.3166i	0.630350	+	1.09180i
$582$		0			0
$583$	−26.0267	−	21.8390i	−1.07792	−	0.904479i
$584$		0			0
$585$	−16.7739	+	6.10522i	−0.693517	+	0.252420i
$586$		0			0
$587$	1.26956	+	7.20005i	0.0524005	+	0.297178i	0.999734	−	0.0230713i	$-0.00734449\pi$
$587$	1.26956	+	7.20005i	0.0524005	+	0.297178i	−0.947333	+	0.320249i	$0.896233\pi$
$588$		0			0
$589$	−10.4794	−	0.464120i	−0.431798	−	0.0191237i
$590$		0			0
$591$	−4.96455	−	28.1554i	−0.204214	−	1.15816i
$592$		0			0
$593$	−0.174214	+	0.0634086i	−0.00715410	+	0.00260388i	−0.345595	−	0.938384i	$-0.612323\pi$
$593$	−0.174214	+	0.0634086i	−0.00715410	+	0.00260388i	0.338441	+	0.940988i	$0.390101\pi$
$594$		0			0
$595$	−41.3531	−	34.6994i	−1.69531	−	1.42254i
$596$		0			0
$597$	−13.8018	−	23.9055i	−0.564872	−	0.978386i
$598$		0			0
$599$	4.06132	−	23.0329i	0.165941	−	0.941099i	−0.782147	−	0.623093i	$-0.785876\pi$
$599$	4.06132	−	23.0329i	0.165941	−	0.941099i	0.948089	−	0.318006i	$-0.103013\pi$
$600$		0			0
$601$	−13.3289	+	23.0863i	−0.543697	+	0.941710i	0.454991	+	0.890496i	$0.349643\pi$
$601$	−13.3289	+	23.0863i	−0.543697	+	0.941710i	−0.998688	+	0.0512144i	$0.983691\pi$
$602$		0			0
$603$	−21.6834	−	7.89212i	−0.883017	−	0.321392i
$604$		0			0
$605$	−31.9608	+	26.8183i	−1.29939	+	1.09032i
$606$		0			0
$607$	20.2286			0.821052			0.410526	−	0.911849i	$-0.365345\pi$
$607$	20.2286			0.821052			0.410526	+	0.911849i	$0.365345\pi$
$608$		0			0
$609$	−2.11619			−0.0857523
$610$		0			0
$611$	15.5161	−	13.0195i	0.627714	−	0.526715i
$612$		0			0
$613$	−22.7806	−	8.29147i	−0.920101	−	0.334889i	−0.161822	−	0.986820i	$-0.551737\pi$
$613$	−22.7806	−	8.29147i	−0.920101	−	0.334889i	−0.758279	+	0.651931i	$0.773959\pi$
$614$		0			0
$615$	−4.83734	+	8.37852i	−0.195060	+	0.337854i
$616$		0			0
$617$	−3.84962	+	21.8323i	−0.154980	+	0.878934i	0.803825	+	0.594866i	$0.202795\pi$
$617$	−3.84962	+	21.8323i	−0.154980	+	0.878934i	−0.958804	+	0.284067i	$0.908316\pi$
$618$		0			0
$619$	−5.33292	−	9.23690i	−0.214348	−	0.371262i	0.738722	−	0.674010i	$-0.235429\pi$
$619$	−5.33292	−	9.23690i	−0.214348	−	0.371262i	−0.953071	+	0.302748i	$0.902096\pi$
$620$		0			0
$621$	−1.36813	−	1.14800i	−0.0549011	−	0.0460675i
$622$		0			0
$623$	−21.1896	+	7.71237i	−0.848942	+	0.308989i
$624$		0			0
$625$	−4.72439	−	26.7933i	−0.188976	−	1.07173i
$626$		0			0
$627$	7.17819	+	54.7890i	0.286669	+	2.18806i
$628$		0			0
$629$	6.30580	+	35.7620i	0.251429	+	1.42592i
$630$		0			0
$631$	−36.6833	+	13.3516i	−1.46034	+	0.531520i	−0.945459	−	0.325742i	$-0.894386\pi$
$631$	−36.6833	+	13.3516i	−1.46034	+	0.531520i	−0.514881	+	0.857262i	$0.672164\pi$
$632$		0			0
$633$	−2.98104	−	2.50139i	−0.118486	−	0.0994212i
$634$		0			0
$635$	6.21536	+	10.7653i	0.246649	+	0.427208i
$636$		0			0
$637$	−5.26962	+	29.8855i	−0.208790	+	1.18411i
$638$		0			0
$639$	13.8509	−	23.9904i	0.547932	−	0.949046i
$640$		0			0
$641$	−14.9266	−	5.43283i	−0.589564	−	0.214584i	0.0299734	−	0.999551i	$-0.490458\pi$
$641$	−14.9266	−	5.43283i	−0.589564	−	0.214584i	−0.619538	+	0.784967i	$0.712680\pi$
$642$		0			0
$643$	−20.1664	+	16.9216i	−0.795285	+	0.667324i	−0.947048	−	0.321093i	$-0.895950\pi$
$643$	−20.1664	+	16.9216i	−0.795285	+	0.667324i	0.151762	+	0.988417i	$0.451505\pi$
$644$		0			0
$645$	9.12783			0.359408
$646$		0			0
$647$	27.2044			1.06952			0.534758	−	0.845005i	$-0.320403\pi$
$647$	27.2044			1.06952			0.534758	+	0.845005i	$0.320403\pi$
$648$		0			0
$649$	42.1078	−	35.3326i	1.65287	−	1.38693i
$650$		0			0
$651$	22.1962	+	8.07875i	0.869937	+	0.316631i
$652$		0			0
$653$	−15.2033	+	26.3329i	−0.594952	+	1.03049i	0.398601	+	0.917124i	$0.369496\pi$
$653$	−15.2033	+	26.3329i	−0.594952	+	1.03049i	−0.993554	+	0.113363i	$0.963838\pi$
$654$		0			0
$655$	1.00401	−	5.69400i	0.0392298	−	0.222483i
$656$		0			0
$657$	−16.0769	−	27.8461i	−0.627221	−	1.08638i
$658$		0			0
$659$	11.6154	+	9.74647i	0.452471	+	0.379668i	0.840352	−	0.542041i	$-0.182348\pi$
$659$	11.6154	+	9.74647i	0.452471	+	0.379668i	−0.387881	+	0.921710i	$0.626793\pi$
$660$		0			0
$661$	8.83885	−	3.21708i	0.343791	−	0.125130i	−0.164353	−	0.986402i	$-0.552554\pi$
$661$	8.83885	−	3.21708i	0.343791	−	0.125130i	0.508145	+	0.861272i	$0.330331\pi$
$662$		0			0
$663$	−6.71913	−	38.1061i	−0.260949	−	1.47992i
$664$		0			0
$665$	39.1996	+	16.2658i	1.52010	+	0.630760i
$666$		0			0
$667$	−0.0671590	−	0.380878i	−0.00260041	−	0.0147476i
$668$		0			0
$669$	40.9623	−	14.9090i	1.58369	−	0.576417i
$670$		0			0
$671$	41.0939	+	34.4819i	1.58641	+	1.33116i
$672$		0			0
$673$	−20.8035	−	36.0328i	−0.801917	−	1.38896i	−0.918353	−	0.395763i	$-0.870480\pi$
$673$	−20.8035	−	36.0328i	−0.801917	−	1.38896i	0.116436	−	0.993198i	$-0.462853\pi$
$674$		0			0
$675$	−0.0845751	+	0.479649i	−0.00325530	+	0.0184617i
$676$		0			0
$677$	16.4951	−	28.5704i	0.633959	−	1.09805i	−0.352776	−	0.935708i	$-0.614762\pi$
$677$	16.4951	−	28.5704i	0.633959	−	1.09805i	0.986735	−	0.162341i	$-0.0519044\pi$
$678$		0			0
$679$	69.6849	+	25.3632i	2.67426	+	0.973352i
$680$		0			0
$681$	5.72760	−	4.80603i	0.219482	−	0.184168i
$682$		0			0
$683$	−42.6980			−1.63379			−0.816896	−	0.576785i	$-0.804307\pi$
$683$	−42.6980			−1.63379			−0.816896	+	0.576785i	$0.804307\pi$
$684$		0			0
$685$	−2.67093			−0.102051
$686$		0			0
$687$	−23.2277	+	19.4903i	−0.886191	+	0.743603i
$688$		0			0
$689$	−17.5764	−	6.39728i	−0.669607	−	0.243717i
$690$		0			0
$691$	17.3407	−	30.0350i	0.659671	−	1.14258i	−0.321030	−	0.947069i	$-0.604029\pi$
$691$	17.3407	−	30.0350i	0.659671	−	1.14258i	0.980701	−	0.195515i	$-0.0626377\pi$
$692$		0			0
$693$	9.98699	−	56.6390i	0.379374	−	2.15154i
$694$		0			0
$695$	19.6467	+	34.0291i	0.745243	+	1.29080i
$696$		0			0
$697$	−7.42559	−	6.23081i	−0.281264	−	0.236009i
$698$		0			0
$699$	−12.8346	+	4.67141i	−0.485448	+	0.176689i
$700$		0			0
$701$	−2.22493	−	12.6182i	−0.0840345	−	0.476584i	−0.997561	−	0.0698037i	$-0.977763\pi$
$701$	−2.22493	−	12.6182i	−0.0840345	−	0.476584i	0.913526	−	0.406780i	$-0.133348\pi$
$702$		0			0
$703$	−13.1667	−	25.3317i	−0.496592	−	0.955405i
$704$		0			0
$705$	6.58684	+	37.3558i	0.248075	+	1.40690i
$706$		0			0
$707$	39.5223	−	14.3849i	1.48639	−	0.541001i
$708$		0			0
$709$	−22.0852	−	18.5317i	−0.829427	−	0.695972i	0.125732	−	0.992064i	$-0.459872\pi$
$709$	−22.0852	−	18.5317i	−0.829427	−	0.695972i	−0.955159	+	0.296092i	$0.904316\pi$
$710$		0			0
$711$	7.22360	+	12.5116i	0.270906	+	0.469223i
$712$		0			0
$713$	−0.749622	+	4.25132i	−0.0280735	+	0.159213i
$714$		0			0
$715$	−18.5786	+	32.1790i	−0.694799	+	1.20343i
$716$		0			0
$717$	28.9697	+	10.5441i	1.08189	+	0.393776i
$718$		0			0
$719$	−1.75518	+	1.47277i	−0.0654570	+	0.0549249i	−0.674929	−	0.737883i	$-0.735826\pi$
$719$	−1.75518	+	1.47277i	−0.0654570	+	0.0549249i	0.609472	+	0.792807i	$0.291381\pi$
$720$		0			0
$721$	19.6545			0.731972
$722$		0			0
$723$	25.6283			0.953126
$724$		0			0
$725$	−0.0807955	+	0.0677955i	−0.00300067	+	0.00251786i
$726$		0			0
$727$	36.8332	+	13.4062i	1.36607	+	0.497208i	0.917925	−	0.396754i	$-0.129863\pi$
$727$	36.8332	+	13.4062i	1.36607	+	0.497208i	0.448143	+	0.893962i	$0.352086\pi$
$728$		0			0
$729$	9.47713	−	16.4149i	0.351005	−	0.607958i
$730$		0			0
$731$	−1.58810	+	9.00657i	−0.0587380	+	0.333120i
$732$		0			0
$733$	8.76216	+	15.1765i	0.323638	+	0.560557i	0.981236	−	0.192812i	$-0.0617608\pi$
$733$	8.76216	+	15.1765i	0.323638	+	0.560557i	−0.657598	+	0.753369i	$0.728427\pi$
$734$		0			0
$735$	−43.5353	−	36.5305i	−1.60582	−	1.34745i
$736$		0			0
$737$	−45.1357	+	16.4281i	−1.66260	+	0.605136i
$738$		0			0
$739$	5.84262	+	33.1352i	0.214924	+	1.21890i	0.881038	+	0.473046i	$0.156846\pi$
$739$	5.84262	+	33.1352i	0.214924	+	1.21890i	−0.666113	+	0.745851i	$0.732043\pi$
$740$		0			0
$741$	14.0298	+	26.9922i	0.515396	+	0.991582i
$742$		0			0
$743$	1.08832	+	6.17214i	0.0399264	+	0.226434i	0.998241	−	0.0592799i	$-0.0188804\pi$
$743$	1.08832	+	6.17214i	0.0399264	+	0.226434i	−0.958315	+	0.285714i	$0.907769\pi$
$744$		0			0
$745$	14.1835	−	5.16236i	0.519643	−	0.189134i
$746$		0			0
$747$	−14.4433	−	12.1194i	−0.528454	−	0.443426i
$748$		0			0
$749$	−18.7950	−	32.5539i	−0.686755	−	1.18949i
$750$		0			0
$751$	−0.608536	+	3.45118i	−0.0222058	+	0.125935i	−0.993896	−	0.110325i	$-0.964811\pi$
$751$	−0.608536	+	3.45118i	−0.0222058	+	0.125935i	0.971690	+	0.236261i	$0.0759219\pi$
$752$		0			0
$753$	13.2845	−	23.0095i	0.484116	−	0.838513i
$754$		0			0
$755$	−20.1614	−	7.33813i	−0.733747	−	0.267062i
$756$		0			0
$757$	13.9306	−	11.6892i	0.506316	−	0.424850i	−0.353515	−	0.935429i	$-0.615014\pi$
$757$	13.9306	−	11.6892i	0.506316	−	0.424850i	0.859831	+	0.510579i	$0.170569\pi$
$758$		0			0
$759$	22.7403			0.825422
$760$		0			0
$761$	−30.9777			−1.12294			−0.561469	−	0.827497i	$-0.689764\pi$
$761$	−30.9777			−1.12294			−0.561469	+	0.827497i	$0.689764\pi$
$762$		0			0
$763$	25.6101	−	21.4894i	0.927147	−	0.777969i
$764$		0			0
$765$	31.4742	+	11.4557i	1.13795	+	0.414180i
$766$		0			0
$767$	15.1306	−	26.2070i	0.546335	−	0.946280i
$768$		0			0
$769$	7.65535	−	43.4156i	0.276059	−	1.56561i	−0.459519	−	0.888168i	$-0.651978\pi$
$769$	7.65535	−	43.4156i	0.276059	−	1.56561i	0.735578	−	0.677440i	$-0.236911\pi$
$770$		0			0
$771$	24.1790	+	41.8793i	0.870787	+	1.50825i
$772$		0			0
$773$	5.60200	+	4.70064i	0.201490	+	0.169070i	0.737950	−	0.674856i	$-0.235794\pi$
$773$	5.60200	+	4.70064i	0.201490	+	0.169070i	−0.536460	+	0.843926i	$0.680239\pi$
$774$		0			0
$775$	1.10626	−	0.402646i	0.0397380	−	0.0144635i
$776$		0			0
$777$	11.1633	+	63.3103i	0.400482	+	2.27125i
$778$		0			0
$779$	7.03889	+	2.92077i	0.252194	+	0.104647i
$780$		0			0
$781$	−10.0131	−	56.7874i	−0.358298	−	2.03201i
$782$		0			0
$783$	−0.201708	+	0.0734157i	−0.00720846	+	0.00262366i
$784$		0			0
$785$	−32.5624	−	27.3231i	−1.16220	−	0.975203i
$786$		0			0
$787$	19.4063	+	33.6127i	0.691760	+	1.19816i	0.971261	+	0.238018i	$0.0764976\pi$
$787$	19.4063	+	33.6127i	0.691760	+	1.19816i	−0.279501	+	0.960145i	$0.590169\pi$
$788$		0			0
$789$	−11.4395	+	64.8766i	−0.407256	+	2.30967i
$790$		0			0
$791$	8.73791	−	15.1345i	0.310684	−	0.538121i
$792$		0			0
$793$	27.7516	+	10.1007i	0.985488	+	0.358688i
$794$		0			0
$795$	26.8334	−	22.5159i	0.951684	−	0.798558i
$796$		0			0
$797$	−29.8075			−1.05583			−0.527917	−	0.849296i	$-0.677027\pi$
$797$	−29.8075			−1.05583			−0.527917	+	0.849296i	$0.677027\pi$
$798$		0			0
$799$	−38.0056			−1.34454
$800$		0			0
$801$	10.7178	−	8.99327i	0.378693	−	0.317761i
$802$		0			0
$803$	−62.8944	−	22.8917i	−2.21949	−	0.807830i
$804$		0			0
$805$	8.73287	−	15.1258i	0.307793	−	0.533113i
$806$		0			0
$807$	−2.14750	+	12.1791i	−0.0755956	+	0.428724i
$808$		0			0
$809$	16.9308	+	29.3251i	0.595257	+	1.03101i	0.993511	+	0.113740i	$0.0362830\pi$
$809$	16.9308	+	29.3251i	0.595257	+	1.03101i	−0.398254	+	0.917275i	$0.630384\pi$
$810$		0			0
$811$	2.54668	+	2.13691i	0.0894259	+	0.0750372i	0.686405	−	0.727220i	$-0.259188\pi$
$811$	2.54668	+	2.13691i	0.0894259	+	0.0750372i	−0.596979	+	0.802257i	$0.703632\pi$
$812$		0			0
$813$	−11.9669	+	4.35561i	−0.419699	+	0.152758i
$814$		0			0
$815$	3.15347	+	17.8842i	0.110461	+	0.626457i
$816$		0			0
$817$	−0.934025	−	7.12913i	−0.0326774	−	0.249417i
$818$		0			0
$819$	−5.49810	−	31.1813i	−0.192119	−	1.08956i
$820$		0			0
$821$	−51.9452	+	18.9065i	−1.81290	+	0.659842i	−0.816284	+	0.577650i	$0.803970\pi$
$821$	−51.9452	+	18.9065i	−1.81290	+	0.659842i	−0.996617	+	0.0821917i	$0.973808\pi$
$822$		0			0
$823$	−29.3090	−	24.5932i	−1.02165	−	0.857264i	−0.0318139	−	0.999494i	$-0.510128\pi$
$823$	−29.3090	−	24.5932i	−1.02165	−	0.857264i	−0.989834	+	0.142230i	$0.954573\pi$
$824$		0			0
$825$	−3.10075	−	5.37065i	−0.107954	−	0.186982i
$826$		0			0
$827$	0.106962	−	0.606611i	0.00371943	−	0.0210939i	−0.982892	−	0.184185i	$-0.941035\pi$
$827$	0.106962	−	0.606611i	0.00371943	−	0.0210939i	0.986611	+	0.163091i	$0.0521465\pi$
$828$		0			0
$829$	−0.151334	+	0.262118i	−0.00525604	+	0.00910372i	−0.868641	−	0.495441i	$-0.835006\pi$
$829$	−0.151334	+	0.262118i	−0.00525604	+	0.00910372i	0.863385	+	0.504545i	$0.168340\pi$
$830$		0			0
$831$	−56.5741	−	20.5913i	−1.96253	−	0.714304i
$832$		0			0
$833$	43.6197	−	36.6012i	1.51133	−	1.26816i
$834$		0			0
$835$	11.0254			0.381550
$836$		0			0
$837$	2.39594			0.0828157
$838$		0			0
$839$	14.8062	−	12.4238i	0.511166	−	0.428919i	−0.350374	−	0.936610i	$-0.613945\pi$
$839$	14.8062	−	12.4238i	0.511166	−	0.428919i	0.861539	+	0.507691i	$0.169501\pi$
$840$		0			0
$841$	27.2074	+	9.90269i	0.938186	+	0.341472i
$842$		0			0
$843$	21.7384	−	37.6520i	0.748709	−	1.29680i
$844$		0			0
$845$	1.73678	−	9.84979i	0.0597472	−	0.338843i
$846$		0			0
$847$	−37.0022	−	64.0896i	−1.27141	−	2.20215i
$848$		0			0
$849$	35.7785	+	30.0217i	1.22792	+	1.03034i
$850$		0			0
$851$	−11.0405	+	4.01841i	−0.378463	+	0.137749i
$852$		0			0
$853$	2.45154	+	13.9034i	0.0839392	+	0.476043i	0.997580	+	0.0695214i	$0.0221472\pi$
$853$	2.45154	+	13.9034i	0.0839392	+	0.476043i	−0.913641	+	0.406521i	$0.866742\pi$
$854$		0			0
$855$	−26.3068	−	1.16509i	−0.899672	−	0.0398452i
$856$		0			0
$857$	−3.03064	−	17.1876i	−0.103525	−	0.587118i	−0.991799	−	0.127805i	$-0.959207\pi$
$857$	−3.03064	−	17.1876i	−0.103525	−	0.587118i	0.888275	−	0.459313i	$-0.151904\pi$
$858$		0			0
$859$	−2.93068	+	1.06668i	−0.0999935	+	0.0363947i	−0.391532	−	0.920164i	$-0.628055\pi$
$859$	−2.93068	+	1.06668i	−0.0999935	+	0.0363947i	0.291539	+	0.956559i	$0.405833\pi$
$860$		0			0
$861$	−13.1457	−	11.0306i	−0.448004	−	0.375920i
$862$		0			0
$863$	26.6218	+	46.1104i	0.906217	+	1.56961i	0.819275	+	0.573401i	$0.194376\pi$
$863$	26.6218	+	46.1104i	0.906217	+	1.56961i	0.0869427	+	0.996213i	$0.472290\pi$
$864$		0			0
$865$	−8.75859	+	49.6725i	−0.297801	+	1.68891i
$866$		0			0
$867$	−16.2262	+	28.1045i	−0.551070	+	0.954480i
$868$		0			0
$869$	28.2594	+	10.2856i	0.958634	+	0.348914i
$870$		0			0
$871$	−20.2566	+	16.9973i	−0.686370	+	0.575933i
$872$		0			0
$873$	−46.0116			−1.55726
$874$		0			0
$875$	43.9194			1.48475
$876$		0			0
$877$	21.9957	−	18.4566i	0.742743	−	0.623235i	−0.190830	−	0.981623i	$-0.561118\pi$
$877$	21.9957	−	18.4566i	0.742743	−	0.623235i	0.933573	+	0.358388i	$0.116673\pi$
$878$		0			0
$879$	3.76463	+	1.37021i	0.126978	+	0.0462162i
$880$		0			0
$881$	−3.32686	+	5.76228i	−0.112085	+	0.194136i	−0.916611	−	0.399781i	$-0.869086\pi$
$881$	−3.32686	+	5.76228i	−0.112085	+	0.194136i	0.804526	+	0.593917i	$0.202419\pi$
$882$		0			0
$883$	−2.27954	+	12.9279i	−0.0767126	+	0.435058i	0.922127	+	0.386888i	$0.126450\pi$
$883$	−2.27954	+	12.9279i	−0.0767126	+	0.435058i	−0.998839	+	0.0481702i	$0.984661\pi$
$884$		0			0
$885$	28.3358	+	49.0790i	0.952497	+	1.64977i
$886$		0			0
$887$	8.11349	+	6.80803i	0.272424	+	0.228591i	0.768757	−	0.639542i	$-0.220876\pi$
$887$	8.11349	+	6.80803i	0.272424	+	0.228591i	−0.496332	+	0.868133i	$0.665320\pi$
$888$		0			0
$889$	−20.7193	+	7.54121i	−0.694903	+	0.252924i
$890$		0			0
$891$	−9.40119	−	53.3168i	−0.314952	−	1.78618i
$892$		0			0
$893$	28.5021	−	8.96706i	0.953787	−	0.300071i
$894$		0			0
$895$	−4.53037	−	25.6930i	−0.151434	−	0.858823i
$896$		0			0
$897$	11.7642	−	4.28181i	0.392794	−	0.142965i
$898$		0			0
$899$	0.397457	+	0.333506i	0.0132559	+	0.0111231i
$900$		0			0
$901$	17.5482	+	30.3944i	0.584615	+	1.01258i
$902$		0			0
$903$	−2.81145	+	15.9445i	−0.0935593	+	0.530601i
$904$		0			0
$905$	−22.9364	+	39.7271i	−0.762433	+	1.32057i
$906$		0			0
$907$	34.8416	+	12.6813i	1.15690	+	0.421076i	0.847988	−	0.530015i	$-0.177814\pi$
$907$	34.8416	+	12.6813i	1.15690	+	0.421076i	0.308909	+	0.951092i	$0.400036\pi$
$908$		0			0
$909$	−19.9905	+	16.7740i	−0.663044	+	0.556360i
$910$		0			0
$911$	−29.8600			−0.989307			−0.494653	−	0.869090i	$-0.664705\pi$
$911$	−29.8600			−0.989307			−0.494653	+	0.869090i	$0.664705\pi$
$912$		0			0
$913$	−39.2470			−1.29889
$914$		0			0
$915$	−42.3677	+	35.5507i	−1.40063	+	1.17527i
$916$		0			0
$917$	9.63708	+	3.50761i	0.318244	+	0.115831i
$918$		0			0
$919$	14.6117	−	25.3082i	0.481996	−	0.834841i	−0.517791	−	0.855507i	$-0.673245\pi$
$919$	14.6117	−	25.3082i	0.481996	−	0.834841i	0.999786	+	0.0206665i	$0.00657882\pi$
$920$		0			0
$921$	−9.27551	+	52.6040i	−0.305638	+	1.73336i
$922$		0			0
$923$	−15.8726	−	27.4922i	−0.522454	−	0.904916i
$924$		0			0
$925$	2.45446	+	2.05954i	0.0807021	+	0.0677171i
$926$		0			0
$927$	−11.4594	+	4.17088i	−0.376376	+	0.136990i
$928$		0			0
$929$	1.74740	+	9.90999i	0.0573303	+	0.325136i	0.999962	−	0.00869779i	$-0.00276863\pi$
$929$	1.74740	+	9.90999i	0.0573303	+	0.325136i	−0.942632	+	0.333834i	$0.891658\pi$
$930$		0			0
$931$	−24.0766	+	37.7406i	−0.789080	+	1.23690i
$932$		0			0
$933$	0.532614	+	3.02060i	0.0174370	+	0.0988901i
$934$		0			0
$935$	65.5160	−	23.8459i	2.14260	−	0.779843i
$936$		0			0
$937$	−5.44819	−	4.57157i	−0.177985	−	0.149347i	0.549443	−	0.835531i	$-0.314840\pi$
$937$	−5.44819	−	4.57157i	−0.177985	−	0.149347i	−0.727428	+	0.686184i	$0.759284\pi$
$938$		0			0
$939$	9.54693	+	16.5358i	0.311552	+	0.539624i
$940$		0			0
$941$	5.66400	−	32.1221i	0.184641	−	1.04715i	−0.741775	−	0.670649i	$-0.766016\pi$
$941$	5.66400	−	32.1221i	0.184641	−	1.04715i	0.926416	−	0.376502i	$-0.122873\pi$
$942$		0			0
$943$	1.56812	−	2.71606i	0.0510650	−	0.0884472i
$944$		0			0
$945$	−9.10911	−	3.31545i	−0.296319	−	0.107851i
$946$		0			0
$947$	−1.60857	+	1.34975i	−0.0522716	+	0.0438611i	−0.668549	−	0.743668i	$-0.733084\pi$
$947$	−1.60857	+	1.34975i	−0.0522716	+	0.0438611i	0.616278	+	0.787529i	$0.288640\pi$
$948$		0			0
$949$	−36.8472			−1.19611
$950$		0			0
$951$	−16.8817			−0.547428
$952$		0			0
$953$	12.2947	−	10.3165i	0.398264	−	0.334183i	−0.421558	−	0.906801i	$-0.638517\pi$
$953$	12.2947	−	10.3165i	0.398264	−	0.334183i	0.819822	+	0.572618i	$0.194072\pi$
$954$		0			0
$955$	−30.8259	−	11.2197i	−0.997504	−	0.363062i
$956$		0			0
$957$	1.36657	−	2.36697i	0.0441749	−	0.0765132i
$958$		0			0
$959$	0.822669	−	4.66559i	0.0265654	−	0.150660i
$960$		0			0
$961$	12.6044	+	21.8314i	0.406592	+	0.704239i
$962$		0			0
$963$	17.8665	+	14.9918i	0.575741	+	0.483104i
$964$		0			0
$965$	−0.287899	+	0.104787i	−0.00926778	+	0.00337320i
$966$		0			0
$967$	−5.18726	−	29.4184i	−0.166811	−	0.946032i	−0.947178	−	0.320710i	$-0.896079\pi$
$967$	−5.18726	−	29.4184i	−0.166811	−	0.946032i	0.780367	−	0.625322i	$-0.215032\pi$
$968$		0			0
$969$	12.3894	−	55.7196i	0.398003	−	1.78997i
$970$		0			0
$971$	−3.38976	−	19.2243i	−0.108783	−	0.616937i	−0.989642	−	0.143559i	$-0.954145\pi$
$971$	−3.38976	−	19.2243i	−0.108783	−	0.616937i	0.880859	−	0.473379i	$-0.156966\pi$
$972$		0			0
$973$	−65.4937	+	23.8377i	−2.09963	+	0.764203i
$974$		0			0
$975$	−2.61534	−	2.19453i	−0.0837580	−	0.0702813i
$976$		0			0
$977$	27.0586	+	46.8668i	0.865681	+	1.49940i	0.866370	+	0.499403i	$0.166447\pi$
$977$	27.0586	+	46.8668i	0.865681	+	1.49940i	−0.000688697		1.00000i	$0.500219\pi$
$978$		0			0
$979$	5.05724	−	28.6810i	0.161630	−	0.916649i
$980$		0			0
$981$	−10.3715	+	17.9639i	−0.331136	+	0.573544i
$982$		0			0
$983$	24.5517	+	8.93610i	0.783079	+	0.285017i	0.702456	−	0.711727i	$-0.252087\pi$
$983$	24.5517	+	8.93610i	0.783079	+	0.285017i	0.0806230	+	0.996745i	$0.474309\pi$
$984$		0			0
$985$	21.7250	−	18.2295i	0.692217	−	0.580839i
$986$		0			0
$987$	−67.2822			−2.14162
$988$		0			0
$989$	−2.95897			−0.0940897
$990$		0			0
$991$	18.7980	−	15.7734i	0.597138	−	0.501059i	−0.293386	−	0.955994i	$-0.594782\pi$
$991$	18.7980	−	15.7734i	0.597138	−	0.501059i	0.890524	+	0.454935i	$0.150338\pi$
$992$		0			0
$993$	−60.5116	−	22.0244i	−1.92028	−	0.698924i
$994$		0			0
$995$	13.6910	−	23.7134i	0.434033	−	0.751767i
$996$		0			0
$997$	1.96904	−	11.1670i	0.0623602	−	0.353663i	−0.937622	−	0.347657i	$-0.886977\pi$
$997$	1.96904	−	11.1670i	0.0623602	−	0.353663i	0.999982	−	0.00600537i	$-0.00191158\pi$
$998$		0			0
$999$	3.26044	+	5.64724i	0.103156	+	0.178671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.q.c.9.3	✓	18
4.3	odd	2		304.2.u.f.161.1		18
19.6	even	9		2888.2.a.y.1.7		9
19.13	odd	18		2888.2.a.x.1.3		9
19.17	even	9	inner	152.2.q.c.17.3	yes	18
76.51	even	18		5776.2.a.ce.1.7		9
76.55	odd	18		304.2.u.f.17.1		18
76.63	odd	18		5776.2.a.cd.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.q.c.9.3	✓	18	1.1	even	1	trivial
152.2.q.c.17.3	yes	18	19.17	even	9	inner
304.2.u.f.17.1		18	76.55	odd	18
304.2.u.f.161.1		18	4.3	odd	2
2888.2.a.x.1.3		9	19.13	odd	18
2888.2.a.y.1.7		9	19.6	even	9
5776.2.a.cd.1.3		9	76.63	odd	18
5776.2.a.ce.1.7		9	76.51	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80930 - 1.51819i) q^{3} +(2.20161 + 0.801320i) q^{5} +(-2.07787 + 3.59897i) q^{7} +(0.447746 - 2.53930i) q^{9} +(-2.68364 - 4.64821i) q^{11} +(-2.26353 - 1.89933i) q^{13} +(5.19993 - 1.89262i) q^{15} +(0.962770 + 5.46014i) q^{17} +(-2.01029 - 3.86765i) q^{19} +(1.70442 + 9.66622i) q^{21} +(-1.68566 + 0.613531i) q^{23} +(0.374747 + 0.314450i) q^{25} +(0.497804 + 0.862221i) q^{27} +(-0.0374386 + 0.212325i) q^{29} +(1.20325 - 2.08410i) q^{31} +(-11.9124 - 4.33575i) q^{33} +(-7.45858 + 6.25849i) q^{35} +6.54964 q^{37} -6.97896 q^{39} +(-1.33930 + 1.12381i) q^{41} +(1.55003 + 0.564166i) q^{43} +(3.02055 - 5.23175i) q^{45} +(-1.19032 + 6.75067i) q^{47} +(-5.13507 - 8.89419i) q^{49} +(10.0315 + 8.41739i) q^{51} +(5.94835 - 2.16502i) q^{53} +(-2.18363 - 12.3840i) q^{55} +(-9.50904 - 3.94576i) q^{57} +(1.77838 + 10.0857i) q^{59} +(-9.39192 + 3.41838i) q^{61} +(8.20849 + 6.88774i) q^{63} +(-3.46145 - 5.99540i) q^{65} +(1.55400 - 8.81316i) q^{67} +(-2.11842 + 3.66921i) q^{69} +(10.0956 + 3.67449i) q^{71} +(9.55268 - 8.01565i) q^{73} +1.15542 q^{75} +22.3050 q^{77} +(-4.29216 + 3.60155i) q^{79} +(9.47859 + 3.44993i) q^{81} +(3.65613 - 6.33261i) q^{83} +(-2.25568 + 12.7926i) q^{85} +(0.254611 + 0.440999i) q^{87} +(4.15664 + 3.48783i) q^{89} +(11.5390 - 4.19984i) q^{91} +(-0.986995 - 5.59753i) q^{93} +(-1.32665 - 10.1259i) q^{95} +(-3.09867 - 17.5734i) q^{97} +(-13.0048 + 4.73334i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{7} - 6 q^{9} - 3 q^{11} + 3 q^{13} + 33 q^{15} + 9 q^{17} - 24 q^{19} - 15 q^{21} + 6 q^{23} + 6 q^{25} - 12 q^{27} - 3 q^{29} - 6 q^{31} - 45 q^{33} - 15 q^{35} + 48 q^{37} + 12 q^{39} - 18 q^{41}+ \cdots + 15 q^{99}+O(q^{100}) \) 18 * q - 9 * q^7 - 6 * q^9 - 3 * q^11 + 3 * q^13 + 33 * q^15 + 9 * q^17 - 24 * q^19 - 15 * q^21 + 6 * q^23 + 6 * q^25 - 12 * q^27 - 3 * q^29 - 6 * q^31 - 45 * q^33 - 15 * q^35 + 48 * q^37 + 12 * q^39 - 18 * q^41 - 39 * q^43 - 42 * q^45 - 27 * q^47 - 18 * q^49 + 48 * q^51 + 39 * q^53 - 27 * q^55 - 6 * q^57 + 9 * q^59 - 24 * q^61 + 3 * q^63 + 27 * q^65 + 39 * q^67 - 3 * q^69 + 12 * q^73 + 90 * q^75 + 60 * q^77 + 63 * q^79 - 6 * q^81 - 27 * q^83 - 30 * q^85 + 18 * q^87 + 66 * q^89 + 108 * q^91 + 60 * q^93 - 75 * q^95 - 81 * q^97 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more