LMFDB - Embedded newform 1920.2.y.i.223.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(223,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("1920.223");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.y (of order $4$, degree $2$, 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:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 $ x^16 - 6x^15 + 14x^14 - 10x^13 - 26x^12 + 78x^11 - 66x^10 - 74x^9 + 233x^8 - 148x^7 - 264x^6 + 624x^5 - 416x^4 - 320x^3 + 896x^2 - 768*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			223.8
Root			$1.40838 + 0.128355i$ of defining polynomial
Character	$\chi$	$=$	1920.223
Dual form			1920.2.y.i.1567.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} +(2.17005 + 0.539352i) q^{5} +(3.00806 - 3.00806i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} +(2.17005 + 0.539352i) q^{5} +(3.00806 - 3.00806i) q^{7} +1.00000 q^{9} +(2.91811 + 2.91811i) q^{11} +4.96870i q^{13} +(-2.17005 - 0.539352i) q^{15} +(-2.56773 + 2.56773i) q^{17} +(0.174647 + 0.174647i) q^{19} +(-3.00806 + 3.00806i) q^{21} +(2.93410 + 2.93410i) q^{23} +(4.41820 + 2.34084i) q^{25} -1.00000 q^{27} +(-4.90621 + 4.90621i) q^{29} +5.24365i q^{31} +(-2.91811 - 2.91811i) q^{33} +(8.15002 - 4.90522i) q^{35} +2.27540i q^{37} -4.96870i q^{39} +0.187334i q^{41} -12.2767i q^{43} +(2.17005 + 0.539352i) q^{45} +(0.0810813 + 0.0810813i) q^{47} -11.0968i q^{49} +(2.56773 - 2.56773i) q^{51} -10.3383 q^{53} +(4.75854 + 7.90632i) q^{55} +(-0.174647 - 0.174647i) q^{57} +(-3.33519 + 3.33519i) q^{59} +(1.32102 + 1.32102i) q^{61} +(3.00806 - 3.00806i) q^{63} +(-2.67988 + 10.7823i) q^{65} -9.03323i q^{67} +(-2.93410 - 2.93410i) q^{69} +4.47057 q^{71} +(-3.50820 + 3.50820i) q^{73} +(-4.41820 - 2.34084i) q^{75} +17.5557 q^{77} -6.75271 q^{79} +1.00000 q^{81} -0.203861 q^{83} +(-6.95702 + 4.18719i) q^{85} +(4.90621 - 4.90621i) q^{87} +2.76590 q^{89} +(14.9461 + 14.9461i) q^{91} -5.24365i q^{93} +(0.284797 + 0.473190i) q^{95} +(9.90816 - 9.90816i) q^{97} +(2.91811 + 2.91811i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{3} + 4 q^{5} - 4 q^{7} + 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^3 + 4 * q^5 - 4 * q^7 + 16 * q^9	$ 16 q - 16 q^{3} + 4 q^{5} - 4 q^{7} + 16 q^{9} - 4 q^{15} - 8 q^{17} - 8 q^{19} + 4 q^{21} + 32 q^{25} - 16 q^{27} - 12 q^{29} + 20 q^{35} + 4 q^{45} - 32 q^{47} + 8 q^{51} - 16 q^{53} - 4 q^{55} + 8 q^{57} + 24 q^{59} - 40 q^{61} - 4 q^{63} - 4 q^{65} + 8 q^{73} - 32 q^{75} + 72 q^{77} - 48 q^{79} + 16 q^{81} + 8 q^{83} + 8 q^{85} + 12 q^{87} + 40 q^{91} + 8 q^{95} + 48 q^{97}+O(q^{100}) $ 16 * q - 16 * q^3 + 4 * q^5 - 4 * q^7 + 16 * q^9 - 4 * q^15 - 8 * q^17 - 8 * q^19 + 4 * q^21 + 32 * q^25 - 16 * q^27 - 12 * q^29 + 20 * q^35 + 4 * q^45 - 32 * q^47 + 8 * q^51 - 16 * q^53 - 4 * q^55 + 8 * q^57 + 24 * q^59 - 40 * q^61 - 4 * q^63 - 4 * q^65 + 8 * q^73 - 32 * q^75 + 72 * q^77 - 48 * q^79 + 16 * q^81 + 8 * q^83 + 8 * q^85 + 12 * q^87 + 40 * q^91 + 8 * q^95 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	2.17005	+	0.539352i	0.970474	+	0.241206i
$5$	2.17005	+	0.539352i	0.970474	+	0.241206i
$6$		0			0
$7$	3.00806	−	3.00806i	1.13694	−	1.13694i	0.147942	−	0.988996i	$-0.452735\pi$
$7$	3.00806	−	3.00806i	1.13694	−	1.13694i	0.988996	−	0.147942i	$-0.0472649\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	2.91811	+	2.91811i	0.879844	+	0.879844i	0.993518	−	0.113675i	$-0.0362621\pi$
$11$	2.91811	+	2.91811i	0.879844	+	0.879844i	−0.113675	+	0.993518i	$0.536262\pi$
$12$		0			0
$13$			4.96870i			1.37807i	0.724728	+	0.689035i	$0.241966\pi$
$13$			4.96870i			1.37807i	−0.724728	+	0.689035i	$0.758034\pi$
$14$		0			0
$15$	−2.17005	−	0.539352i	−0.560303	−	0.139260i
$16$		0			0
$17$	−2.56773	+	2.56773i	−0.622767	+	0.622767i	−0.946238	−	0.323471i	$-0.895150\pi$
$17$	−2.56773	+	2.56773i	−0.622767	+	0.622767i	0.323471	+	0.946238i	$0.395150\pi$
$18$		0			0
$19$	0.174647	+	0.174647i	0.0400669	+	0.0400669i	0.726856	−	0.686789i	$-0.240981\pi$
$19$	0.174647	+	0.174647i	0.0400669	+	0.0400669i	−0.686789	+	0.726856i	$0.740981\pi$
$20$		0			0
$21$	−3.00806	+	3.00806i	−0.656412	+	0.656412i
$22$		0			0
$23$	2.93410	+	2.93410i	0.611802	+	0.611802i	0.943415	−	0.331613i	$-0.107593\pi$
$23$	2.93410	+	2.93410i	0.611802	+	0.611802i	−0.331613	+	0.943415i	$0.607593\pi$
$24$		0			0
$25$	4.41820	+	2.34084i	0.883640	+	0.468168i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−4.90621	+	4.90621i	−0.911060	+	0.911060i	−0.996356	−	0.0852961i	$-0.972816\pi$
$29$	−4.90621	+	4.90621i	−0.911060	+	0.911060i	0.0852961	+	0.996356i	$0.472816\pi$
$30$		0			0
$31$			5.24365i			0.941788i	0.882190	+	0.470894i	$0.156069\pi$
$31$			5.24365i			0.941788i	−0.882190	+	0.470894i	$0.843931\pi$
$32$		0			0
$33$	−2.91811	−	2.91811i	−0.507978	−	0.507978i
$34$		0			0
$35$	8.15002	−	4.90522i	1.37760	−	0.829133i
$36$		0			0
$37$			2.27540i			0.374073i	0.982353	+	0.187036i	$0.0598883\pi$
$37$			2.27540i			0.374073i	−0.982353	+	0.187036i	$0.940112\pi$
$38$		0			0
$39$		−	4.96870i		−	0.795630i
$40$		0			0
$41$			0.187334i			0.0292566i	0.999893	+	0.0146283i	$0.00465651\pi$
$41$			0.187334i			0.0292566i	−0.999893	+	0.0146283i	$0.995343\pi$
$42$		0			0
$43$		−	12.2767i		−	1.87218i	−0.351764	−	0.936089i	$-0.614418\pi$
$43$		−	12.2767i		−	1.87218i	0.351764	−	0.936089i	$-0.385582\pi$
$44$		0			0
$45$	2.17005	+	0.539352i	0.323491	+	0.0804019i
$46$		0			0
$47$	0.0810813	+	0.0810813i	0.0118269	+	0.0118269i	0.712996	−	0.701169i	$-0.247338\pi$
$47$	0.0810813	+	0.0810813i	0.0118269	+	0.0118269i	−0.701169	+	0.712996i	$0.747338\pi$
$48$		0			0
$49$		−	11.0968i		−	1.58526i
$50$		0			0
$51$	2.56773	−	2.56773i	0.359555	−	0.359555i
$52$		0			0
$53$	−10.3383			−1.42007			−0.710036	−	0.704166i	$-0.751321\pi$
$53$	−10.3383			−1.42007			−0.710036	+	0.704166i	$0.751321\pi$
$54$		0			0
$55$	4.75854	+	7.90632i	0.641642	+	1.06609i
$56$		0			0
$57$	−0.174647	−	0.174647i	−0.0231326	−	0.0231326i
$58$		0			0
$59$	−3.33519	+	3.33519i	−0.434204	+	0.434204i	−0.890056	−	0.455852i	$-0.849335\pi$
$59$	−3.33519	+	3.33519i	−0.434204	+	0.434204i	0.455852	+	0.890056i	$0.349335\pi$
$60$		0			0
$61$	1.32102	+	1.32102i	0.169139	+	0.169139i	0.786601	−	0.617462i	$-0.211839\pi$
$61$	1.32102	+	1.32102i	0.169139	+	0.169139i	−0.617462	+	0.786601i	$0.711839\pi$
$62$		0			0
$63$	3.00806	−	3.00806i	0.378979	−	0.378979i
$64$		0			0
$65$	−2.67988	+	10.7823i	−0.332399	+	1.33738i
$66$		0			0
$67$		−	9.03323i		−	1.10358i	−0.833982	−	0.551792i	$-0.813944\pi$
$67$		−	9.03323i		−	1.10358i	0.833982	−	0.551792i	$-0.186056\pi$
$68$		0			0
$69$	−2.93410	−	2.93410i	−0.353224	−	0.353224i
$70$		0			0
$71$	4.47057			0.530560			0.265280	−	0.964171i	$-0.414536\pi$
$71$	4.47057			0.530560			0.265280	+	0.964171i	$0.414536\pi$
$72$		0			0
$73$	−3.50820	+	3.50820i	−0.410604	+	0.410604i	−0.881949	−	0.471345i	$-0.843769\pi$
$73$	−3.50820	+	3.50820i	−0.410604	+	0.410604i	0.471345	+	0.881949i	$0.343769\pi$
$74$		0			0
$75$	−4.41820	−	2.34084i	−0.510170	−	0.270297i
$76$		0			0
$77$	17.5557			2.00066
$78$		0			0
$79$	−6.75271			−0.759740			−0.379870	−	0.925040i	$-0.624031\pi$
$79$	−6.75271			−0.759740			−0.379870	+	0.925040i	$0.624031\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−0.203861			−0.0223766			−0.0111883	−	0.999937i	$-0.503561\pi$
$83$	−0.203861			−0.0223766			−0.0111883	+	0.999937i	$0.503561\pi$
$84$		0			0
$85$	−6.95702	+	4.18719i	−0.754594	+	0.454164i
$86$		0			0
$87$	4.90621	−	4.90621i	0.526000	−	0.526000i
$88$		0			0
$89$	2.76590			0.293184			0.146592	−	0.989197i	$-0.453169\pi$
$89$	2.76590			0.293184			0.146592	+	0.989197i	$0.453169\pi$
$90$		0			0
$91$	14.9461	+	14.9461i	1.56678	+	1.56678i
$92$		0			0
$93$		−	5.24365i		−	0.543741i
$94$		0			0
$95$	0.284797	+	0.473190i	0.0292195	+	0.0485482i
$96$		0			0
$97$	9.90816	−	9.90816i	1.00602	−	1.00602i	0.00603974	−	0.999982i	$-0.498077\pi$
$97$	9.90816	−	9.90816i	1.00602	−	1.00602i	0.999982	−	0.00603974i	$-0.00192252\pi$
$98$		0			0
$99$	2.91811	+	2.91811i	0.293281	+	0.293281i
$100$		0			0
$101$	9.51134	−	9.51134i	0.946414	−	0.946414i	−0.0522219	−	0.998636i	$-0.516630\pi$
$101$	9.51134	−	9.51134i	0.946414	−	0.946414i	0.998636	+	0.0522219i	$0.0166303\pi$
$102$		0			0
$103$	5.17090	+	5.17090i	0.509504	+	0.509504i	0.914374	−	0.404870i	$-0.132683\pi$
$103$	5.17090	+	5.17090i	0.509504	+	0.509504i	−0.404870	+	0.914374i	$0.632683\pi$
$104$		0			0
$105$	−8.15002	+	4.90522i	−0.795361	+	0.478700i
$106$		0			0
$107$	5.04996			0.488198			0.244099	−	0.969750i	$-0.421508\pi$
$107$	5.04996			0.488198			0.244099	+	0.969750i	$0.421508\pi$
$108$		0			0
$109$	−6.77367	+	6.77367i	−0.648800	+	0.648800i	−0.952703	−	0.303903i	$-0.901710\pi$
$109$	−6.77367	+	6.77367i	−0.648800	+	0.648800i	0.303903	+	0.952703i	$0.401710\pi$
$110$		0			0
$111$		−	2.27540i		−	0.215971i
$112$		0			0
$113$	2.59004	+	2.59004i	0.243651	+	0.243651i	0.818359	−	0.574708i	$-0.194884\pi$
$113$	2.59004	+	2.59004i	0.243651	+	0.243651i	−0.574708	+	0.818359i	$0.694884\pi$
$114$		0			0
$115$	4.78462	+	7.94965i	0.446168	+	0.741308i
$116$		0			0
$117$			4.96870i			0.459357i
$118$		0			0
$119$			15.4478i			1.41610i
$120$		0			0
$121$			6.03074i			0.548249i
$122$		0			0
$123$		−	0.187334i		−	0.0168913i
$124$		0			0
$125$	8.32516	+	7.46269i	0.744625	+	0.667484i
$126$		0			0
$127$	−5.95445	−	5.95445i	−0.528372	−	0.528372i	0.391715	−	0.920087i	$-0.371882\pi$
$127$	−5.95445	−	5.95445i	−0.528372	−	0.528372i	−0.920087	+	0.391715i	$0.871882\pi$
$128$		0			0
$129$			12.2767i			1.08090i
$130$		0			0
$131$	−1.07093	+	1.07093i	−0.0935679	+	0.0935679i	−0.752341	−	0.658773i	$-0.771076\pi$
$131$	−1.07093	+	1.07093i	−0.0935679	+	0.0935679i	0.658773	+	0.752341i	$0.271076\pi$
$132$		0			0
$133$	1.05070			0.0911071
$134$		0			0
$135$	−2.17005	−	0.539352i	−0.186768	−	0.0464201i
$136$		0			0
$137$	6.57542	+	6.57542i	0.561776	+	0.561776i	0.929812	−	0.368036i	$-0.119970\pi$
$137$	6.57542	+	6.57542i	0.561776	+	0.561776i	−0.368036	+	0.929812i	$0.619970\pi$
$138$		0			0
$139$	10.0808	−	10.0808i	0.855039	−	0.855039i	−0.135710	−	0.990749i	$-0.543331\pi$
$139$	10.0808	−	10.0808i	0.855039	−	0.855039i	0.990749	+	0.135710i	$0.0433315\pi$
$140$		0			0
$141$	−0.0810813	−	0.0810813i	−0.00682828	−	0.00682828i
$142$		0			0
$143$	−14.4992	+	14.4992i	−1.21249	+	1.21249i
$144$		0			0
$145$	−13.2929	+	8.00052i	−1.10391	+	0.664407i
$146$		0			0
$147$			11.0968i			0.915248i
$148$		0			0
$149$	15.1118	+	15.1118i	1.23800	+	1.23800i	0.960816	+	0.277187i	$0.0894023\pi$
$149$	15.1118	+	15.1118i	1.23800	+	1.23800i	0.277187	+	0.960816i	$0.410598\pi$
$150$		0			0
$151$	−13.6260			−1.10886			−0.554432	−	0.832229i	$-0.687065\pi$
$151$	−13.6260			−1.10886			−0.554432	+	0.832229i	$0.687065\pi$
$152$		0			0
$153$	−2.56773	+	2.56773i	−0.207589	+	0.207589i
$154$		0			0
$155$	−2.82818	+	11.3790i	−0.227165	+	0.913980i
$156$		0			0
$157$	7.13379			0.569338			0.284669	−	0.958626i	$-0.408116\pi$
$157$	7.13379			0.569338			0.284669	+	0.958626i	$0.408116\pi$
$158$		0			0
$159$	10.3383			0.819878
$160$		0			0
$161$	17.6519			1.39116
$162$		0			0
$163$	−15.7963			−1.23727			−0.618633	−	0.785680i	$-0.712313\pi$
$163$	−15.7963			−1.23727			−0.618633	+	0.785680i	$0.712313\pi$
$164$		0			0
$165$	−4.75854	−	7.90632i	−0.370452	−	0.615507i
$166$		0			0
$167$	11.1560	−	11.1560i	0.863278	−	0.863278i	−0.128439	−	0.991717i	$-0.540997\pi$
$167$	11.1560	−	11.1560i	0.863278	−	0.863278i	0.991717	+	0.128439i	$0.0409968\pi$
$168$		0			0
$169$	−11.6880			−0.899079
$170$		0			0
$171$	0.174647	+	0.174647i	0.0133556	+	0.0133556i
$172$		0			0
$173$		−	24.3506i		−	1.85134i	−0.378334	−	0.925669i	$-0.623503\pi$
$173$		−	24.3506i		−	1.85134i	0.378334	−	0.925669i	$-0.376497\pi$
$174$		0			0
$175$	20.3316	−	6.24881i	1.53692	−	0.472366i
$176$		0			0
$177$	3.33519	−	3.33519i	0.250688	−	0.250688i
$178$		0			0
$179$	−6.13094	−	6.13094i	−0.458248	−	0.458248i	0.439832	−	0.898080i	$-0.355038\pi$
$179$	−6.13094	−	6.13094i	−0.458248	−	0.458248i	−0.898080	+	0.439832i	$0.855038\pi$
$180$		0			0
$181$	−8.99477	+	8.99477i	−0.668576	+	0.668576i	−0.957386	−	0.288810i	$-0.906740\pi$
$181$	−8.99477	+	8.99477i	−0.668576	+	0.668576i	0.288810	+	0.957386i	$0.406740\pi$
$182$		0			0
$183$	−1.32102	−	1.32102i	−0.0976524	−	0.0976524i
$184$		0			0
$185$	−1.22724	+	4.93772i	−0.0902285	+	0.363028i
$186$		0			0
$187$	−14.9859			−1.09588
$188$		0			0
$189$	−3.00806	+	3.00806i	−0.218804	+	0.218804i
$190$		0			0
$191$			0.148691i			0.0107589i	0.999986	+	0.00537945i	$0.00171234\pi$
$191$			0.148691i			0.0107589i	−0.999986	+	0.00537945i	$0.998288\pi$
$192$		0			0
$193$	−4.33825	−	4.33825i	−0.312274	−	0.312274i	0.533516	−	0.845790i	$-0.320870\pi$
$193$	−4.33825	−	4.33825i	−0.312274	−	0.312274i	−0.845790	+	0.533516i	$0.820870\pi$
$194$		0			0
$195$	2.67988	−	10.7823i	0.191910	−	0.772138i
$196$		0			0
$197$			5.86883i			0.418137i	0.977901	+	0.209068i	$0.0670431\pi$
$197$			5.86883i			0.418137i	−0.977901	+	0.209068i	$0.932957\pi$
$198$		0			0
$199$		−	5.93363i		−	0.420624i	−0.977634	−	0.210312i	$-0.932552\pi$
$199$		−	5.93363i		−	0.420624i	0.977634	−	0.210312i	$-0.0674479\pi$
$200$		0			0
$201$			9.03323i			0.637155i
$202$		0			0
$203$			29.5163i			2.07164i
$204$		0			0
$205$	−0.101039	+	0.406523i	−0.00705687	+	0.0283928i
$206$		0			0
$207$	2.93410	+	2.93410i	0.203934	+	0.203934i
$208$		0			0
$209$			1.01928i			0.0705052i
$210$		0			0
$211$	7.09893	−	7.09893i	0.488710	−	0.488710i	−0.419189	−	0.907899i	$-0.637685\pi$
$211$	7.09893	−	7.09893i	0.488710	−	0.488710i	0.907899	+	0.419189i	$0.137685\pi$
$212$		0			0
$213$	−4.47057			−0.306319
$214$		0			0
$215$	6.62146	−	26.6410i	0.451580	−	1.81690i
$216$		0			0
$217$	15.7732	+	15.7732i	1.07075	+	1.07075i
$218$		0			0
$219$	3.50820	−	3.50820i	0.237062	−	0.237062i
$220$		0			0
$221$	−12.7583	−	12.7583i	−0.858217	−	0.858217i
$222$		0			0
$223$	19.9362	−	19.9362i	1.33503	−	1.33503i	0.434217	−	0.900808i	$-0.357025\pi$
$223$	19.9362	−	19.9362i	1.33503	−	1.33503i	0.900808	−	0.434217i	$-0.142975\pi$
$224$		0			0
$225$	4.41820	+	2.34084i	0.294547	+	0.156056i
$226$		0			0
$227$		−	6.50202i		−	0.431554i	−0.976443	−	0.215777i	$-0.930772\pi$
$227$		−	6.50202i		−	0.431554i	0.976443	−	0.215777i	$-0.0692284\pi$
$228$		0			0
$229$	6.53144	+	6.53144i	0.431610	+	0.431610i	0.889176	−	0.457566i	$-0.151279\pi$
$229$	6.53144	+	6.53144i	0.431610	+	0.431610i	−0.457566	+	0.889176i	$0.651279\pi$
$230$		0			0
$231$	−17.5557			−1.15508
$232$		0			0
$233$	14.3657	−	14.3657i	0.941130	−	0.941130i	−0.0572311	−	0.998361i	$-0.518227\pi$
$233$	14.3657	−	14.3657i	0.941130	−	0.941130i	0.998361	+	0.0572311i	$0.0182272\pi$
$234$		0			0
$235$	0.132219	+	0.219682i	0.00862500	+	0.0143304i
$236$		0			0
$237$	6.75271			0.438636
$238$		0			0
$239$	6.65388			0.430404			0.215202	−	0.976570i	$-0.430959\pi$
$239$	6.65388			0.430404			0.215202	+	0.976570i	$0.430959\pi$
$240$		0			0
$241$	−15.6797			−1.01002			−0.505009	−	0.863114i	$-0.668511\pi$
$241$	−15.6797			−1.01002			−0.505009	+	0.863114i	$0.668511\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	5.98508	−	24.0806i	0.382373	−	1.53845i
$246$		0			0
$247$	−0.867772	+	0.867772i	−0.0552150	+	0.0552150i
$248$		0			0
$249$	0.203861			0.0129192
$250$		0			0
$251$	2.31676	+	2.31676i	0.146233	+	0.146233i	0.776433	−	0.630200i	$-0.217027\pi$
$251$	2.31676	+	2.31676i	0.146233	+	0.146233i	−0.630200	+	0.776433i	$0.717027\pi$
$252$		0			0
$253$			17.1241i			1.07658i
$254$		0			0
$255$	6.95702	−	4.18719i	0.435665	−	0.262212i
$256$		0			0
$257$	10.9722	−	10.9722i	0.684430	−	0.684430i	−0.276565	−	0.960995i	$-0.589196\pi$
$257$	10.9722	−	10.9722i	0.684430	−	0.684430i	0.960995	+	0.276565i	$0.0891962\pi$
$258$		0			0
$259$	6.84452	+	6.84452i	0.425298	+	0.425298i
$260$		0			0
$261$	−4.90621	+	4.90621i	−0.303687	+	0.303687i
$262$		0			0
$263$	9.46655	+	9.46655i	0.583733	+	0.583733i	0.935927	−	0.352194i	$-0.114564\pi$
$263$	9.46655	+	9.46655i	0.583733	+	0.583733i	−0.352194	+	0.935927i	$0.614564\pi$
$264$		0			0
$265$	−22.4345	−	5.57597i	−1.37814	−	0.342529i
$266$		0			0
$267$	−2.76590			−0.169270
$268$		0			0
$269$	−2.77544	+	2.77544i	−0.169222	+	0.169222i	−0.786637	−	0.617416i	$-0.788180\pi$
$269$	−2.77544	+	2.77544i	−0.169222	+	0.169222i	0.617416	+	0.786637i	$0.288180\pi$
$270$		0			0
$271$			3.86079i			0.234526i	0.993101	+	0.117263i	$0.0374121\pi$
$271$			3.86079i			0.234526i	−0.993101	+	0.117263i	$0.962588\pi$
$272$		0			0
$273$	−14.9461	−	14.9461i	−0.904582	−	0.904582i
$274$		0			0
$275$	6.06196	+	19.7236i	0.365550	+	1.18938i
$276$		0			0
$277$		−	28.9073i		−	1.73687i	−0.495803	−	0.868435i	$-0.665126\pi$
$277$		−	28.9073i		−	1.73687i	0.495803	−	0.868435i	$-0.334874\pi$
$278$		0			0
$279$			5.24365i			0.313929i
$280$		0			0
$281$		−	16.2395i		−	0.968770i	−0.874855	−	0.484385i	$-0.839043\pi$
$281$		−	16.2395i		−	0.968770i	0.874855	−	0.484385i	$-0.160957\pi$
$282$		0			0
$283$		−	22.8092i		−	1.35587i	−0.735122	−	0.677934i	$-0.762875\pi$
$283$		−	22.8092i		−	1.35587i	0.735122	−	0.677934i	$-0.237125\pi$
$284$		0			0
$285$	−0.284797	−	0.473190i	−0.0168699	−	0.0280293i
$286$		0			0
$287$	0.563511	+	0.563511i	0.0332630	+	0.0332630i
$288$		0			0
$289$			3.81348i			0.224322i
$290$		0			0
$291$	−9.90816	+	9.90816i	−0.580827	+	0.580827i
$292$		0			0
$293$	30.6990			1.79346			0.896728	−	0.442582i	$-0.145937\pi$
$293$	30.6990			1.79346			0.896728	+	0.442582i	$0.145937\pi$
$294$		0			0
$295$	−9.03635	+	5.43867i	−0.526116	+	0.316651i
$296$		0			0
$297$	−2.91811	−	2.91811i	−0.169326	−	0.169326i
$298$		0			0
$299$	−14.5787	+	14.5787i	−0.843107	+	0.843107i
$300$		0			0
$301$	−36.9290	−	36.9290i	−2.12855	−	2.12855i
$302$		0			0
$303$	−9.51134	+	9.51134i	−0.546412	+	0.546412i
$304$		0			0
$305$	2.15417	+	3.57916i	0.123348	+	0.204942i
$306$		0			0
$307$		−	17.3607i		−	0.990829i	−0.868657	−	0.495415i	$-0.835016\pi$
$307$		−	17.3607i		−	0.990829i	0.868657	−	0.495415i	$-0.164984\pi$
$308$		0			0
$309$	−5.17090	−	5.17090i	−0.294162	−	0.294162i
$310$		0			0
$311$	−20.0448			−1.13664			−0.568318	−	0.822809i	$-0.692406\pi$
$311$	−20.0448			−1.13664			−0.568318	+	0.822809i	$0.692406\pi$
$312$		0			0
$313$	10.7674	−	10.7674i	0.608610	−	0.608610i	−0.333973	−	0.942583i	$-0.608389\pi$
$313$	10.7674	−	10.7674i	0.608610	−	0.608610i	0.942583	+	0.333973i	$0.108389\pi$
$314$		0			0
$315$	8.15002	−	4.90522i	0.459202	−	0.276378i
$316$		0			0
$317$	−11.6799			−0.656006			−0.328003	−	0.944677i	$-0.606376\pi$
$317$	−11.6799			−0.656006			−0.328003	+	0.944677i	$0.606376\pi$
$318$		0			0
$319$	−28.6337			−1.60318
$320$		0			0
$321$	−5.04996			−0.281861
$322$		0			0
$323$	−0.896897			−0.0499047
$324$		0			0
$325$	−11.6309	+	21.9527i	−0.645168	+	1.21772i
$326$		0			0
$327$	6.77367	−	6.77367i	0.374585	−	0.374585i
$328$		0			0
$329$	0.487794			0.0268930
$330$		0			0
$331$	−18.7327	−	18.7327i	−1.02964	−	1.02964i	−0.999547	−	0.0300961i	$-0.990419\pi$
$331$	−18.7327	−	18.7327i	−1.02964	−	1.02964i	−0.0300961	−	0.999547i	$-0.509581\pi$
$332$		0			0
$333$			2.27540i			0.124691i
$334$		0			0
$335$	4.87209	−	19.6025i	0.266191	−	1.07100i
$336$		0			0
$337$	−6.18087	+	6.18087i	−0.336694	+	0.336694i	−0.855121	−	0.518428i	$-0.826518\pi$
$337$	−6.18087	+	6.18087i	−0.336694	+	0.336694i	0.518428	+	0.855121i	$0.326518\pi$
$338$		0			0
$339$	−2.59004	−	2.59004i	−0.140672	−	0.140672i
$340$		0			0
$341$	−15.3016	+	15.3016i	−0.828626	+	0.828626i
$342$		0			0
$343$	−12.3234	−	12.3234i	−0.665401	−	0.665401i
$344$		0			0
$345$	−4.78462	−	7.94965i	−0.257595	−	0.427995i
$346$		0			0
$347$	3.87988			0.208283			0.104142	−	0.994562i	$-0.466791\pi$
$347$	3.87988			0.208283			0.104142	+	0.994562i	$0.466791\pi$
$348$		0			0
$349$	−1.56009	+	1.56009i	−0.0835098	+	0.0835098i	−0.747628	−	0.664118i	$-0.768807\pi$
$349$	−1.56009	+	1.56009i	−0.0835098	+	0.0835098i	0.664118	+	0.747628i	$0.268807\pi$
$350$		0			0
$351$		−	4.96870i		−	0.265210i
$352$		0			0
$353$	5.74300	+	5.74300i	0.305669	+	0.305669i	0.843227	−	0.537558i	$-0.180653\pi$
$353$	5.74300	+	5.74300i	0.305669	+	0.305669i	−0.537558	+	0.843227i	$0.680653\pi$
$354$		0			0
$355$	9.70135	+	2.41121i	0.514894	+	0.127974i
$356$		0			0
$357$		−	15.4478i		−	0.817583i
$358$		0			0
$359$			18.0862i			0.954552i	0.878753	+	0.477276i	$0.158376\pi$
$359$			18.0862i			0.954552i	−0.878753	+	0.477276i	$0.841624\pi$
$360$		0			0
$361$		−	18.9390i		−	0.996789i
$362$		0			0
$363$		−	6.03074i		−	0.316532i
$364$		0			0
$365$	−9.50512	+	5.72080i	−0.497521	+	0.299440i
$366$		0			0
$367$	−1.00068	−	1.00068i	−0.0522350	−	0.0522350i	0.680507	−	0.732742i	$-0.261760\pi$
$367$	−1.00068	−	1.00068i	−0.0522350	−	0.0522350i	−0.732742	+	0.680507i	$0.761760\pi$
$368$		0			0
$369$			0.187334i			0.00975222i
$370$		0			0
$371$	−31.0981	+	31.0981i	−1.61453	+	1.61453i
$372$		0			0
$373$	2.25365			0.116689			0.0583447	−	0.998296i	$-0.481418\pi$
$373$	2.25365			0.116689			0.0583447	+	0.998296i	$0.481418\pi$
$374$		0			0
$375$	−8.32516	−	7.46269i	−0.429909	−	0.385372i
$376$		0			0
$377$	−24.3775	−	24.3775i	−1.25550	−	1.25550i
$378$		0			0
$379$	−7.91100	+	7.91100i	−0.406361	+	0.406361i	−0.880467	−	0.474107i	$-0.842771\pi$
$379$	−7.91100	+	7.91100i	−0.406361	+	0.406361i	0.474107	+	0.880467i	$0.342771\pi$
$380$		0			0
$381$	5.95445	+	5.95445i	0.305056	+	0.305056i
$382$		0			0
$383$	−19.7391	+	19.7391i	−1.00862	+	1.00862i	−0.00865943	+	0.999963i	$0.502756\pi$
$383$	−19.7391	+	19.7391i	−1.00862	+	1.00862i	−0.999963	+	0.00865943i	$0.997244\pi$
$384$		0			0
$385$	38.0966	+	9.46870i	1.94158	+	0.482570i
$386$		0			0
$387$		−	12.2767i		−	0.624059i
$388$		0			0
$389$	5.49649	+	5.49649i	0.278683	+	0.278683i	0.832583	−	0.553900i	$-0.186861\pi$
$389$	5.49649	+	5.49649i	0.278683	+	0.278683i	−0.553900	+	0.832583i	$0.686861\pi$
$390$		0			0
$391$	−15.0680			−0.762021
$392$		0			0
$393$	1.07093	−	1.07093i	0.0540214	−	0.0540214i
$394$		0			0
$395$	−14.6537	−	3.64209i	−0.737308	−	0.183254i
$396$		0			0
$397$	25.4492			1.27726			0.638630	−	0.769514i	$-0.279501\pi$
$397$	25.4492			1.27726			0.638630	+	0.769514i	$0.279501\pi$
$398$		0			0
$399$	−1.05070			−0.0526007
$400$		0			0
$401$	−1.45606			−0.0727124			−0.0363562	−	0.999339i	$-0.511575\pi$
$401$	−1.45606			−0.0727124			−0.0363562	+	0.999339i	$0.511575\pi$
$402$		0			0
$403$	−26.0542			−1.29785
$404$		0			0
$405$	2.17005	+	0.539352i	0.107830	+	0.0268006i
$406$		0			0
$407$	−6.63986	+	6.63986i	−0.329126	+	0.329126i
$408$		0			0
$409$	−14.9174			−0.737620			−0.368810	−	0.929505i	$-0.620235\pi$
$409$	−14.9174			−0.737620			−0.368810	+	0.929505i	$0.620235\pi$
$410$		0			0
$411$	−6.57542	−	6.57542i	−0.324341	−	0.324341i
$412$		0			0
$413$			20.0649i			0.987327i
$414$		0			0
$415$	−0.442387	−	0.109953i	−0.0217159	−	0.00539737i
$416$		0			0
$417$	−10.0808	+	10.0808i	−0.493657	+	0.493657i
$418$		0			0
$419$	12.3766	+	12.3766i	0.604638	+	0.604638i	0.941540	−	0.336902i	$-0.109379\pi$
$419$	12.3766	+	12.3766i	0.604638	+	0.604638i	−0.336902	+	0.941540i	$0.609379\pi$
$420$		0			0
$421$	23.1411	−	23.1411i	1.12783	−	1.12783i	0.137299	−	0.990530i	$-0.456158\pi$
$421$	23.1411	−	23.1411i	1.12783	−	1.12783i	0.990530	−	0.137299i	$-0.0438421\pi$
$422$		0			0
$423$	0.0810813	+	0.0810813i	0.00394231	+	0.00394231i
$424$		0			0
$425$	−17.3554	+	5.33411i	−0.841861	+	0.258742i
$426$		0			0
$427$	7.94739			0.384601
$428$		0			0
$429$	14.4992	−	14.4992i	0.700030	−	0.700030i
$430$		0			0
$431$			16.0042i			0.770896i	0.922730	+	0.385448i	$0.125953\pi$
$431$			16.0042i			0.770896i	−0.922730	+	0.385448i	$0.874047\pi$
$432$		0			0
$433$	−21.6931	−	21.6931i	−1.04250	−	1.04250i	−0.999056	−	0.0434459i	$-0.986166\pi$
$433$	−21.6931	−	21.6931i	−1.04250	−	1.04250i	−0.0434459	−	0.999056i	$-0.513834\pi$
$434$		0			0
$435$	13.2929	−	8.00052i	0.637344	−	0.383595i
$436$		0			0
$437$			1.02487i			0.0490260i
$438$		0			0
$439$			4.04860i			0.193229i	0.995322	+	0.0966145i	$0.0308014\pi$
$439$			4.04860i			0.193229i	−0.995322	+	0.0966145i	$0.969199\pi$
$440$		0			0
$441$		−	11.0968i		−	0.528419i
$442$		0			0
$443$		−	24.3284i		−	1.15588i	−0.816081	−	0.577938i	$-0.803858\pi$
$443$		−	24.3284i		−	1.15588i	0.816081	−	0.577938i	$-0.196142\pi$
$444$		0			0
$445$	6.00212	+	1.49179i	0.284528	+	0.0707178i
$446$		0			0
$447$	−15.1118	−	15.1118i	−0.714761	−	0.714761i
$448$		0			0
$449$			26.9577i			1.27221i	0.771602	+	0.636106i	$0.219456\pi$
$449$			26.9577i			1.27221i	−0.771602	+	0.636106i	$0.780544\pi$
$450$		0			0
$451$	−0.546661	+	0.546661i	−0.0257413	+	0.0257413i
$452$		0			0
$453$	13.6260			0.640203
$454$		0			0
$455$	24.3726	+	40.4950i	1.14260	+	1.89844i
$456$		0			0
$457$	10.7623	+	10.7623i	0.503440	+	0.503440i	0.912505	−	0.409065i	$-0.134145\pi$
$457$	10.7623	+	10.7623i	0.503440	+	0.503440i	−0.409065	+	0.912505i	$0.634145\pi$
$458$		0			0
$459$	2.56773	−	2.56773i	0.119852	−	0.119852i
$460$		0			0
$461$	4.26657	+	4.26657i	0.198714	+	0.198714i	0.799449	−	0.600734i	$-0.205125\pi$
$461$	4.26657	+	4.26657i	0.198714	+	0.198714i	−0.600734	+	0.799449i	$0.705125\pi$
$462$		0			0
$463$	−23.4907	+	23.4907i	−1.09170	+	1.09170i	−0.0963571	+	0.995347i	$0.530719\pi$
$463$	−23.4907	+	23.4907i	−1.09170	+	1.09170i	−0.995347	+	0.0963571i	$0.969281\pi$
$464$		0			0
$465$	2.82818	−	11.3790i	0.131154	−	0.527687i
$466$		0			0
$467$		−	28.5742i		−	1.32226i	−0.750273	−	0.661128i	$-0.770078\pi$
$467$		−	28.5742i		−	1.32226i	0.750273	−	0.661128i	$-0.229922\pi$
$468$		0			0
$469$	−27.1725	−	27.1725i	−1.25471	−	1.25471i
$470$		0			0
$471$	−7.13379			−0.328708
$472$		0			0
$473$	35.8247	−	35.8247i	1.64722	−	1.64722i
$474$		0			0
$475$	0.362806	+	1.18045i	0.0166467	+	0.0541627i
$476$		0			0
$477$	−10.3383			−0.473357
$478$		0			0
$479$	−3.27525			−0.149650			−0.0748250	−	0.997197i	$-0.523840\pi$
$479$	−3.27525			−0.149650			−0.0748250	+	0.997197i	$0.523840\pi$
$480$		0			0
$481$	−11.3058			−0.515499
$482$		0			0
$483$	−17.6519			−0.803188
$484$		0			0
$485$	26.8452	−	16.1572i	1.21898	−	0.733660i
$486$		0			0
$487$	6.15496	−	6.15496i	0.278908	−	0.278908i	−0.553765	−	0.832673i	$-0.686809\pi$
$487$	6.15496	−	6.15496i	0.278908	−	0.278908i	0.832673	+	0.553765i	$0.186809\pi$
$488$		0			0
$489$	15.7963			0.714335
$490$		0			0
$491$	−11.4090	−	11.4090i	−0.514883	−	0.514883i	0.401136	−	0.916019i	$-0.368616\pi$
$491$	−11.4090	−	11.4090i	−0.514883	−	0.514883i	−0.916019	+	0.401136i	$0.868616\pi$
$492$		0			0
$493$		−	25.1957i		−	1.13476i
$494$		0			0
$495$	4.75854	+	7.90632i	0.213881	+	0.355363i
$496$		0			0
$497$	13.4477	−	13.4477i	0.603213	−	0.603213i
$498$		0			0
$499$	−10.8395	−	10.8395i	−0.485242	−	0.485242i	0.421559	−	0.906801i	$-0.361483\pi$
$499$	−10.8395	−	10.8395i	−0.485242	−	0.485242i	−0.906801	+	0.421559i	$0.861483\pi$
$500$		0			0
$501$	−11.1560	+	11.1560i	−0.498414	+	0.498414i
$502$		0			0
$503$	−25.2060	−	25.2060i	−1.12388	−	1.12388i	−0.991153	−	0.132726i	$-0.957627\pi$
$503$	−25.2060	−	25.2060i	−1.12388	−	1.12388i	−0.132726	−	0.991153i	$-0.542373\pi$
$504$		0			0
$505$	25.7700	−	15.5101i	1.14675	−	0.690189i
$506$		0			0
$507$	11.6880			0.519084
$508$		0			0
$509$	−11.1087	+	11.1087i	−0.492385	+	0.492385i	−0.909057	−	0.416672i	$-0.863196\pi$
$509$	−11.1087	+	11.1087i	−0.492385	+	0.492385i	0.416672	+	0.909057i	$0.363196\pi$
$510$		0			0
$511$			21.1057i			0.933663i
$512$		0			0
$513$	−0.174647	−	0.174647i	−0.00771088	−	0.00771088i
$514$		0			0
$515$	8.43215	+	14.0100i	0.371565	+	0.617355i
$516$		0			0
$517$			0.473208i			0.0208117i
$518$		0			0
$519$			24.3506i			1.06887i
$520$		0			0
$521$			15.9757i			0.699908i	0.936767	+	0.349954i	$0.113803\pi$
$521$			15.9757i			0.699908i	−0.936767	+	0.349954i	$0.886197\pi$
$522$		0			0
$523$			7.67260i			0.335499i	0.985830	+	0.167750i	$0.0536500\pi$
$523$			7.67260i			0.335499i	−0.985830	+	0.167750i	$0.946350\pi$
$524$		0			0
$525$	−20.3316	+	6.24881i	−0.887342	+	0.272721i
$526$		0			0
$527$	−13.4643	−	13.4643i	−0.586514	−	0.586514i
$528$		0			0
$529$		−	5.78211i		−	0.251396i
$530$		0			0
$531$	−3.33519	+	3.33519i	−0.144735	+	0.144735i
$532$		0			0
$533$	−0.930807			−0.0403177
$534$		0			0
$535$	10.9586	+	2.72371i	0.473784	+	0.117756i
$536$		0			0
$537$	6.13094	+	6.13094i	0.264569	+	0.264569i
$538$		0			0
$539$	32.3817	−	32.3817i	1.39478	−	1.39478i
$540$		0			0
$541$	−6.37490	−	6.37490i	−0.274078	−	0.274078i	0.556661	−	0.830740i	$-0.312082\pi$
$541$	−6.37490	−	6.37490i	−0.274078	−	0.274078i	−0.830740	+	0.556661i	$0.812082\pi$
$542$		0			0
$543$	8.99477	−	8.99477i	0.386002	−	0.386002i
$544$		0			0
$545$	−18.3526	+	11.0458i	−0.786138	+	0.473149i
$546$		0			0
$547$			44.7865i			1.91493i	0.288542	+	0.957467i	$0.406829\pi$
$547$			44.7865i			1.91493i	−0.288542	+	0.957467i	$0.593171\pi$
$548$		0			0
$549$	1.32102	+	1.32102i	0.0563796	+	0.0563796i
$550$		0			0
$551$	−1.71371			−0.0730066
$552$		0			0
$553$	−20.3125	+	20.3125i	−0.863777	+	0.863777i
$554$		0			0
$555$	1.22724	−	4.93772i	0.0520935	−	0.209594i
$556$		0			0
$557$	−10.4866			−0.444331			−0.222165	−	0.975009i	$-0.571313\pi$
$557$	−10.4866			−0.444331			−0.222165	+	0.975009i	$0.571313\pi$
$558$		0			0
$559$	60.9992			2.57999
$560$		0			0
$561$	14.9859			0.632704
$562$		0			0
$563$	31.5903			1.33137			0.665687	−	0.746231i	$-0.268139\pi$
$563$	31.5903			1.33137			0.665687	+	0.746231i	$0.268139\pi$
$564$		0			0
$565$	4.22357	+	7.01746i	0.177687	+	0.295227i
$566$		0			0
$567$	3.00806	−	3.00806i	0.126326	−	0.126326i
$568$		0			0
$569$	28.9118			1.21205			0.606023	−	0.795447i	$-0.292764\pi$
$569$	28.9118			1.21205			0.606023	+	0.795447i	$0.292764\pi$
$570$		0			0
$571$	5.84635	+	5.84635i	0.244662	+	0.244662i	0.818776	−	0.574113i	$-0.194653\pi$
$571$	5.84635	+	5.84635i	0.244662	+	0.244662i	−0.574113	+	0.818776i	$0.694653\pi$
$572$		0			0
$573$		−	0.148691i		−	0.00621165i
$574$		0			0
$575$	6.09518	+	19.8317i	0.254187	+	0.827039i
$576$		0			0
$577$	−10.0202	+	10.0202i	−0.417147	+	0.417147i	−0.884219	−	0.467072i	$-0.845309\pi$
$577$	−10.0202	+	10.0202i	−0.417147	+	0.417147i	0.467072	+	0.884219i	$0.345309\pi$
$578$		0			0
$579$	4.33825	+	4.33825i	0.180291	+	0.180291i
$580$		0			0
$581$	−0.613225	+	0.613225i	−0.0254408	+	0.0254408i
$582$		0			0
$583$	−30.1682	−	30.1682i	−1.24944	−	1.24944i
$584$		0			0
$585$	−2.67988	+	10.7823i	−0.110800	+	0.445794i
$586$		0			0
$587$	3.79915			0.156808			0.0784039	−	0.996922i	$-0.475018\pi$
$587$	3.79915			0.156808			0.0784039	+	0.996922i	$0.475018\pi$
$588$		0			0
$589$	−0.915791	+	0.915791i	−0.0377345	+	0.0377345i
$590$		0			0
$591$		−	5.86883i		−	0.241411i
$592$		0			0
$593$	−11.5151	−	11.5151i	−0.472869	−	0.472869i	0.429973	−	0.902842i	$-0.358523\pi$
$593$	−11.5151	−	11.5151i	−0.472869	−	0.472869i	−0.902842	+	0.429973i	$0.858523\pi$
$594$		0			0
$595$	−8.33180	+	33.5224i	−0.341570	+	1.37428i
$596$		0			0
$597$			5.93363i			0.242847i
$598$		0			0
$599$			21.2875i			0.869783i	0.900483	+	0.434891i	$0.143213\pi$
$599$			21.2875i			0.869783i	−0.900483	+	0.434891i	$0.856787\pi$
$600$		0			0
$601$		−	44.8560i		−	1.82971i	−0.403779	−	0.914856i	$-0.632304\pi$
$601$		−	44.8560i		−	1.82971i	0.403779	−	0.914856i	$-0.367696\pi$
$602$		0			0
$603$		−	9.03323i		−	0.367862i
$604$		0			0
$605$	−3.25270	+	13.0870i	−0.132241	+	0.532062i
$606$		0			0
$607$	−7.48042	−	7.48042i	−0.303621	−	0.303621i	0.538808	−	0.842429i	$-0.318875\pi$
$607$	−7.48042	−	7.48042i	−0.303621	−	0.303621i	−0.842429	+	0.538808i	$0.818875\pi$
$608$		0			0
$609$		−	29.5163i		−	1.19606i
$610$		0			0
$611$	−0.402869	+	0.402869i	−0.0162983	+	0.0162983i
$612$		0			0
$613$	−23.9275			−0.966423			−0.483211	−	0.875504i	$-0.660530\pi$
$613$	−23.9275			−0.966423			−0.483211	+	0.875504i	$0.660530\pi$
$614$		0			0
$615$	0.101039	−	0.406523i	0.00407429	−	0.0163926i
$616$		0			0
$617$	6.14250	+	6.14250i	0.247288	+	0.247288i	0.819857	−	0.572569i	$-0.194053\pi$
$617$	6.14250	+	6.14250i	0.247288	+	0.247288i	−0.572569	+	0.819857i	$0.694053\pi$
$618$		0			0
$619$	15.3689	−	15.3689i	0.617729	−	0.617729i	−0.327220	−	0.944948i	$-0.606112\pi$
$619$	15.3689	−	15.3689i	0.617729	−	0.617729i	0.944948	+	0.327220i	$0.106112\pi$
$620$		0			0
$621$	−2.93410	−	2.93410i	−0.117741	−	0.117741i
$622$		0			0
$623$	8.31997	−	8.31997i	0.333333	−	0.333333i
$624$		0			0
$625$	14.0409	+	20.6846i	0.561638	+	0.827383i
$626$		0			0
$627$		−	1.01928i		−	0.0407062i
$628$		0			0
$629$	−5.84262	−	5.84262i	−0.232960	−	0.232960i
$630$		0			0
$631$	36.1280			1.43823			0.719116	−	0.694891i	$-0.244547\pi$
$631$	36.1280			1.43823			0.719116	+	0.694891i	$0.244547\pi$
$632$		0			0
$633$	−7.09893	+	7.09893i	−0.282157	+	0.282157i
$634$		0			0
$635$	−9.70988	−	16.1330i	−0.385325	−	0.640218i
$636$		0			0
$637$	55.1367			2.18460
$638$		0			0
$639$	4.47057			0.176853
$640$		0			0
$641$	−43.5468			−1.72000			−0.859998	−	0.510297i	$-0.829536\pi$
$641$	−43.5468			−1.72000			−0.859998	+	0.510297i	$0.829536\pi$
$642$		0			0
$643$	8.84133			0.348668			0.174334	−	0.984687i	$-0.444223\pi$
$643$	8.84133			0.348668			0.174334	+	0.984687i	$0.444223\pi$
$644$		0			0
$645$	−6.62146	+	26.6410i	−0.260720	+	1.04899i
$646$		0			0
$647$	−16.9926	+	16.9926i	−0.668049	+	0.668049i	−0.957264	−	0.289215i	$-0.906606\pi$
$647$	−16.9926	+	16.9926i	−0.668049	+	0.668049i	0.289215	+	0.957264i	$0.406606\pi$
$648$		0			0
$649$	−19.4649			−0.764064
$650$		0			0
$651$	−15.7732	−	15.7732i	−0.618200	−	0.618200i
$652$		0			0
$653$		−	35.7891i		−	1.40053i	−0.713881	−	0.700267i	$-0.753064\pi$
$653$		−	35.7891i		−	1.40053i	0.713881	−	0.700267i	$-0.246936\pi$
$654$		0			0
$655$	−2.90159	+	1.74636i	−0.113374	+	0.0682361i
$656$		0			0
$657$	−3.50820	+	3.50820i	−0.136868	+	0.136868i
$658$		0			0
$659$	−11.8604	−	11.8604i	−0.462014	−	0.462014i	0.437301	−	0.899315i	$-0.355934\pi$
$659$	−11.8604	−	11.8604i	−0.462014	−	0.462014i	−0.899315	+	0.437301i	$0.855934\pi$
$660$		0			0
$661$	5.12628	−	5.12628i	0.199389	−	0.199389i	−0.600349	−	0.799738i	$-0.704972\pi$
$661$	5.12628	−	5.12628i	0.199389	−	0.199389i	0.799738	+	0.600349i	$0.204972\pi$
$662$		0			0
$663$	12.7583	+	12.7583i	0.495492	+	0.495492i
$664$		0			0
$665$	2.28006	+	0.566697i	0.0884171	+	0.0219756i
$666$		0			0
$667$	−28.7906			−1.11478
$668$		0			0
$669$	−19.9362	+	19.9362i	−0.770777	+	0.770777i
$670$		0			0
$671$			7.70975i			0.297632i
$672$		0			0
$673$	8.42753	+	8.42753i	0.324858	+	0.324858i	0.850627	−	0.525770i	$-0.176223\pi$
$673$	8.42753	+	8.42753i	0.324858	+	0.324858i	−0.525770	+	0.850627i	$0.676223\pi$
$674$		0			0
$675$	−4.41820	−	2.34084i	−0.170057	−	0.0900989i
$676$		0			0
$677$			13.1467i			0.505268i	0.967562	+	0.252634i	$0.0812969\pi$
$677$			13.1467i			0.505268i	−0.967562	+	0.252634i	$0.918703\pi$
$678$		0			0
$679$		−	59.6086i		−	2.28757i
$680$		0			0
$681$			6.50202i			0.249158i
$682$		0			0
$683$			15.9674i			0.610977i	0.952196	+	0.305489i	$0.0988198\pi$
$683$			15.9674i			0.610977i	−0.952196	+	0.305489i	$0.901180\pi$
$684$		0			0
$685$	10.7225	+	17.8154i	0.409685	+	0.680692i
$686$		0			0
$687$	−6.53144	−	6.53144i	−0.249190	−	0.249190i
$688$		0			0
$689$		−	51.3678i		−	1.95696i
$690$		0			0
$691$	14.4031	−	14.4031i	0.547919	−	0.547919i	−0.377919	−	0.925839i	$-0.623360\pi$
$691$	14.4031	−	14.4031i	0.547919	−	0.547919i	0.925839	+	0.377919i	$0.123360\pi$
$692$		0			0
$693$	17.5557			0.666885
$694$		0			0
$695$	27.3128	−	16.4386i	1.03603	−	0.623553i
$696$		0			0
$697$	−0.481024	−	0.481024i	−0.0182201	−	0.0182201i
$698$		0			0
$699$	−14.3657	+	14.3657i	−0.543362	+	0.543362i
$700$		0			0
$701$	9.70568	+	9.70568i	0.366579	+	0.366579i	0.866228	−	0.499649i	$-0.166538\pi$
$701$	9.70568	+	9.70568i	0.366579	+	0.366579i	−0.499649	+	0.866228i	$0.666538\pi$
$702$		0			0
$703$	−0.397392	+	0.397392i	−0.0149879	+	0.0149879i
$704$		0			0
$705$	−0.132219	−	0.219682i	−0.00497965	−	0.00827368i
$706$		0			0
$707$		−	57.2213i		−	2.15203i
$708$		0			0
$709$	9.01713	+	9.01713i	0.338645	+	0.338645i	0.855857	−	0.517212i	$-0.173030\pi$
$709$	9.01713	+	9.01713i	0.338645	+	0.338645i	−0.517212	+	0.855857i	$0.673030\pi$
$710$		0			0
$711$	−6.75271			−0.253247
$712$		0			0
$713$	−15.3854	+	15.3854i	−0.576188	+	0.576188i
$714$		0			0
$715$	−39.2842	+	23.6438i	−1.46915	+	0.884228i
$716$		0			0
$717$	−6.65388			−0.248494
$718$		0			0
$719$	24.3409			0.907762			0.453881	−	0.891062i	$-0.350039\pi$
$719$	24.3409			0.907762			0.453881	+	0.891062i	$0.350039\pi$
$720$		0			0
$721$	31.1087			1.15855
$722$		0			0
$723$	15.6797			0.583134
$724$		0			0
$725$	−33.1612	+	10.1920i	−1.23158	+	0.378520i
$726$		0			0
$727$	−23.7830	+	23.7830i	−0.882062	+	0.882062i	−0.993744	−	0.111682i	$-0.964376\pi$
$727$	−23.7830	+	23.7830i	−0.882062	+	0.882062i	0.111682	+	0.993744i	$0.464376\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	31.5233	+	31.5233i	1.16593	+	1.16593i
$732$		0			0
$733$			14.8205i			0.547406i	0.961814	+	0.273703i	$0.0882486\pi$
$733$			14.8205i			0.547406i	−0.961814	+	0.273703i	$0.911751\pi$
$734$		0			0
$735$	−5.98508	+	24.0806i	−0.220763	+	0.888225i
$736$		0			0
$737$	26.3600	−	26.3600i	0.970982	−	0.970982i
$738$		0			0
$739$	35.6500	+	35.6500i	1.31141	+	1.31141i	0.920378	+	0.391029i	$0.127881\pi$
$739$	35.6500	+	35.6500i	1.31141	+	1.31141i	0.391029	+	0.920378i	$0.372119\pi$
$740$		0			0
$741$	0.867772	−	0.867772i	0.0318784	−	0.0318784i
$742$		0			0
$743$	−24.3691	−	24.3691i	−0.894016	−	0.894016i	0.100883	−	0.994898i	$-0.467833\pi$
$743$	−24.3691	−	24.3691i	−0.894016	−	0.894016i	−0.994898	+	0.100883i	$0.967833\pi$
$744$		0			0
$745$	24.6426	+	40.9438i	0.902836	+	1.50006i
$746$		0			0
$747$	−0.203861			−0.00745888
$748$		0			0
$749$	15.1906	−	15.1906i	0.555051	−	0.555051i
$750$		0			0
$751$		−	25.6756i		−	0.936917i	−0.883486	−	0.468458i	$-0.844810\pi$
$751$		−	25.6756i		−	0.936917i	0.883486	−	0.468458i	$-0.155190\pi$
$752$		0			0
$753$	−2.31676	−	2.31676i	−0.0844275	−	0.0844275i
$754$		0			0
$755$	−29.5690	−	7.34919i	−1.07612	−	0.267465i
$756$		0			0
$757$			21.4132i			0.778274i	0.921180	+	0.389137i	$0.127227\pi$
$757$			21.4132i			0.778274i	−0.921180	+	0.389137i	$0.872773\pi$
$758$		0			0
$759$		−	17.1241i		−	0.621564i
$760$		0			0
$761$		−	15.6885i		−	0.568708i	−0.958719	−	0.284354i	$-0.908221\pi$
$761$		−	15.6885i		−	0.568708i	0.958719	−	0.284354i	$-0.0917791\pi$
$762$		0			0
$763$			40.7511i			1.47529i
$764$		0			0
$765$	−6.95702	+	4.18719i	−0.251531	+	0.151388i
$766$		0			0
$767$	−16.5716	−	16.5716i	−0.598364	−	0.598364i
$768$		0			0
$769$			51.0412i			1.84059i	0.391221	+	0.920297i	$0.372053\pi$
$769$			51.0412i			1.84059i	−0.391221	+	0.920297i	$0.627947\pi$
$770$		0			0
$771$	−10.9722	+	10.9722i	−0.395156	+	0.395156i
$772$		0			0
$773$	−15.9432			−0.573437			−0.286718	−	0.958015i	$-0.592564\pi$
$773$	−15.9432			−0.573437			−0.286718	+	0.958015i	$0.592564\pi$
$774$		0			0
$775$	−12.2745	+	23.1675i	−0.440915	+	0.832201i
$776$		0			0
$777$	−6.84452	−	6.84452i	−0.245546	−	0.245546i
$778$		0			0
$779$	−0.0327174	+	0.0327174i	−0.00117222	+	0.00117222i
$780$		0			0
$781$	13.0456	+	13.0456i	0.466809	+	0.466809i
$782$		0			0
$783$	4.90621	−	4.90621i	0.175333	−	0.175333i
$784$		0			0
$785$	15.4807	+	3.84763i	0.552528	+	0.137328i
$786$		0			0
$787$		−	26.1398i		−	0.931784i	−0.884841	−	0.465892i	$-0.845733\pi$
$787$		−	26.1398i		−	0.931784i	0.884841	−	0.465892i	$-0.154267\pi$
$788$		0			0
$789$	−9.46655	−	9.46655i	−0.337018	−	0.337018i
$790$		0			0
$791$	15.5820			0.554032
$792$		0			0
$793$	−6.56374	+	6.56374i	−0.233085	+	0.233085i
$794$		0			0
$795$	22.4345	+	5.57597i	0.795671	+	0.197759i
$796$		0			0
$797$	34.0127			1.20479			0.602396	−	0.798197i	$-0.294213\pi$
$797$	34.0127			1.20479			0.602396	+	0.798197i	$0.294213\pi$
$798$		0			0
$799$	−0.416390			−0.0147308
$800$		0			0
$801$	2.76590			0.0977282
$802$		0			0
$803$	−20.4746			−0.722534
$804$		0			0
$805$	38.3054	+	9.52058i	1.35009	+	0.335556i
$806$		0			0
$807$	2.77544	−	2.77544i	0.0977002	−	0.0977002i
$808$		0			0
$809$	−25.6058			−0.900253			−0.450127	−	0.892965i	$-0.648621\pi$
$809$	−25.6058			−0.900253			−0.450127	+	0.892965i	$0.648621\pi$
$810$		0			0
$811$	29.4467	+	29.4467i	1.03401	+	1.03401i	0.999401	+	0.0346118i	$0.0110195\pi$
$811$	29.4467	+	29.4467i	1.03401	+	1.03401i	0.0346118	+	0.999401i	$0.488981\pi$
$812$		0			0
$813$		−	3.86079i		−	0.135404i
$814$		0			0
$815$	−34.2788	−	8.51980i	−1.20073	−	0.298435i
$816$		0			0
$817$	2.14409	−	2.14409i	0.0750123	−	0.0750123i
$818$		0			0
$819$	14.9461	+	14.9461i	0.522260	+	0.522260i
$820$		0			0
$821$	22.3951	−	22.3951i	0.781595	−	0.781595i	−0.198505	−	0.980100i	$-0.563608\pi$
$821$	22.3951	−	22.3951i	0.781595	−	0.781595i	0.980100	+	0.198505i	$0.0636085\pi$
$822$		0			0
$823$	19.7666	+	19.7666i	0.689019	+	0.689019i	0.962015	−	0.272996i	$-0.0880146\pi$
$823$	19.7666	+	19.7666i	0.689019	+	0.689019i	−0.272996	+	0.962015i	$0.588015\pi$
$824$		0			0
$825$	−6.06196	−	19.7236i	−0.211051	−	0.686688i
$826$		0			0
$827$	−45.0540			−1.56668			−0.783341	−	0.621592i	$-0.786486\pi$
$827$	−45.0540			−1.56668			−0.783341	+	0.621592i	$0.786486\pi$
$828$		0			0
$829$	−20.1502	+	20.1502i	−0.699844	+	0.699844i	−0.964377	−	0.264533i	$-0.914782\pi$
$829$	−20.1502	+	20.1502i	−0.699844	+	0.699844i	0.264533	+	0.964377i	$0.414782\pi$
$830$		0			0
$831$			28.9073i			1.00278i
$832$		0			0
$833$	28.4936	+	28.4936i	0.987246	+	0.987246i
$834$		0			0
$835$	30.2261	−	18.1920i	1.04602	−	0.629561i
$836$		0			0
$837$		−	5.24365i		−	0.181247i
$838$		0			0
$839$			10.9329i			0.377445i	0.982030	+	0.188723i	$0.0604347\pi$
$839$			10.9329i			0.377445i	−0.982030	+	0.188723i	$0.939565\pi$
$840$		0			0
$841$		−	19.1417i		−	0.660059i
$842$		0			0
$843$			16.2395i			0.559319i
$844$		0			0
$845$	−25.3636	−	6.30397i	−0.872533	−	0.216863i
$846$		0			0
$847$	18.1408	+	18.1408i	0.623326	+	0.623326i
$848$		0			0
$849$			22.8092i			0.782811i
$850$		0			0
$851$	−6.67624	+	6.67624i	−0.228859	+	0.228859i
$852$		0			0
$853$	−18.1959			−0.623017			−0.311508	−	0.950243i	$-0.600834\pi$
$853$	−18.1959			−0.623017			−0.311508	+	0.950243i	$0.600834\pi$
$854$		0			0
$855$	0.284797	+	0.473190i	0.00973984	+	0.0161827i
$856$		0			0
$857$	40.4936	+	40.4936i	1.38324	+	1.38324i	0.838807	+	0.544430i	$0.183254\pi$
$857$	40.4936	+	40.4936i	1.38324	+	1.38324i	0.544430	+	0.838807i	$0.316746\pi$
$858$		0			0
$859$	−14.3628	+	14.3628i	−0.490053	+	0.490053i	−0.908323	−	0.418270i	$-0.862637\pi$
$859$	−14.3628	+	14.3628i	−0.490053	+	0.490053i	0.418270	+	0.908323i	$0.362637\pi$
$860$		0			0
$861$	−0.563511	−	0.563511i	−0.0192044	−	0.0192044i
$862$		0			0
$863$	10.5835	−	10.5835i	0.360268	−	0.360268i	−0.503644	−	0.863911i	$-0.668008\pi$
$863$	10.5835	−	10.5835i	0.360268	−	0.360268i	0.863911	+	0.503644i	$0.168008\pi$
$864$		0			0
$865$	13.1335	−	52.8418i	0.446553	−	1.79668i
$866$		0			0
$867$		−	3.81348i		−	0.129512i
$868$		0			0
$869$	−19.7052	−	19.7052i	−0.668452	−	0.668452i
$870$		0			0
$871$	44.8834			1.52082
$872$		0			0
$873$	9.90816	−	9.90816i	0.335341	−	0.335341i
$874$		0			0
$875$	47.4907	−	2.59433i	1.60548	−	0.0877045i
$876$		0			0
$877$	−55.3196			−1.86801			−0.934004	−	0.357262i	$-0.883710\pi$
$877$	−55.3196			−1.86801			−0.934004	+	0.357262i	$0.883710\pi$
$878$		0			0
$879$	−30.6990			−1.03545
$880$		0			0
$881$	−47.0634			−1.58561			−0.792804	−	0.609477i	$-0.791380\pi$
$881$	−47.0634			−1.58561			−0.792804	+	0.609477i	$0.791380\pi$
$882$		0			0
$883$	−42.7619			−1.43905			−0.719526	−	0.694465i	$-0.755641\pi$
$883$	−42.7619			−1.43905			−0.719526	+	0.694465i	$0.755641\pi$
$884$		0			0
$885$	9.03635	−	5.43867i	0.303753	−	0.182819i
$886$		0			0
$887$	14.8427	−	14.8427i	0.498370	−	0.498370i	−0.412560	−	0.910930i	$-0.635365\pi$
$887$	14.8427	−	14.8427i	0.498370	−	0.498370i	0.910930	+	0.412560i	$0.135365\pi$
$888$		0			0
$889$	−35.8226			−1.20145
$890$		0			0
$891$	2.91811	+	2.91811i	0.0977604	+	0.0977604i
$892$		0			0
$893$			0.0283213i			0.000947736i
$894$		0			0
$895$	−9.99768	−	16.6111i	−0.334185	−	0.555249i
$896$		0			0
$897$	14.5787	−	14.5787i	0.486768	−	0.486768i
$898$		0			0
$899$	−25.7264	−	25.7264i	−0.858025	−	0.858025i
$900$		0			0
$901$	26.5459	−	26.5459i	0.884374	−	0.884374i
$902$		0			0
$903$	36.9290	+	36.9290i	1.22892	+	1.22892i
$904$		0			0
$905$	−24.3704	+	14.6677i	−0.810100	+	0.487571i
$906$		0			0
$907$	31.3755			1.04181			0.520903	−	0.853616i	$-0.325595\pi$
$907$	31.3755			1.04181			0.520903	+	0.853616i	$0.325595\pi$
$908$		0			0
$909$	9.51134	−	9.51134i	0.315471	−	0.315471i
$910$		0			0
$911$		−	20.9112i		−	0.692818i	−0.938084	−	0.346409i	$-0.887401\pi$
$911$		−	20.9112i		−	0.692818i	0.938084	−	0.346409i	$-0.112599\pi$
$912$		0			0
$913$	−0.594888	−	0.594888i	−0.0196879	−	0.0196879i
$914$		0			0
$915$	−2.15417	−	3.57916i	−0.0712148	−	0.118323i
$916$		0			0
$917$			6.44286i			0.212762i
$918$		0			0
$919$		−	19.8382i		−	0.654403i	−0.944955	−	0.327201i	$-0.893894\pi$
$919$		−	19.8382i		−	0.654403i	0.944955	−	0.327201i	$-0.106106\pi$
$920$		0			0
$921$			17.3607i			0.572056i
$922$		0			0
$923$			22.2130i			0.731149i
$924$		0			0
$925$	−5.32634	+	10.0532i	−0.175129	+	0.330546i
$926$		0			0
$927$	5.17090	+	5.17090i	0.169835	+	0.169835i
$928$		0			0
$929$			20.2449i			0.664213i	0.943242	+	0.332106i	$0.107759\pi$
$929$			20.2449i			0.664213i	−0.943242	+	0.332106i	$0.892241\pi$
$930$		0			0
$931$	1.93803	−	1.93803i	0.0635163	−	0.0635163i
$932$		0			0
$933$	20.0448			0.656237
$934$		0			0
$935$	−32.5200	−	8.08266i	−1.06352	−	0.264331i
$936$		0			0
$937$	18.7073	+	18.7073i	0.611140	+	0.611140i	0.943243	−	0.332103i	$-0.107758\pi$
$937$	18.7073	+	18.7073i	0.611140	+	0.611140i	−0.332103	+	0.943243i	$0.607758\pi$
$938$		0			0
$939$	−10.7674	+	10.7674i	−0.351381	+	0.351381i
$940$		0			0
$941$	5.54352	+	5.54352i	0.180713	+	0.180713i	0.791667	−	0.610953i	$-0.209214\pi$
$941$	5.54352	+	5.54352i	0.180713	+	0.180713i	−0.610953	+	0.791667i	$0.709214\pi$
$942$		0			0
$943$	−0.549657	+	0.549657i	−0.0178993	+	0.0178993i
$944$		0			0
$945$	−8.15002	+	4.90522i	−0.265120	+	0.159567i
$946$		0			0
$947$			18.6075i			0.604664i	0.953203	+	0.302332i	$0.0977651\pi$
$947$			18.6075i			0.604664i	−0.953203	+	0.302332i	$0.902235\pi$
$948$		0			0
$949$	−17.4312	−	17.4312i	−0.565841	−	0.565841i
$950$		0			0
$951$	11.6799			0.378745
$952$		0			0
$953$	−39.8932	+	39.8932i	−1.29227	+	1.29227i	−0.358888	+	0.933381i	$0.616844\pi$
$953$	−39.8932	+	39.8932i	−1.29227	+	1.29227i	−0.933381	+	0.358888i	$0.883156\pi$
$954$		0			0
$955$	−0.0801968	+	0.322666i	−0.00259511	+	0.0104412i
$956$		0			0
$957$	28.6337			0.925596
$958$		0			0
$959$	39.5584			1.27741
$960$		0			0
$961$	3.50411			0.113036
$962$		0			0
$963$	5.04996			0.162733
$964$		0			0
$965$	−7.07435	−	11.7540i	−0.227732	−	0.378376i
$966$		0			0
$967$	36.2541	−	36.2541i	1.16585	−	1.16585i	0.182682	−	0.983172i	$-0.441522\pi$
$967$	36.2541	−	36.2541i	1.16585	−	1.16585i	0.983172	−	0.182682i	$-0.0584778\pi$
$968$		0			0
$969$	0.896897			0.0288125
$970$		0			0
$971$	−25.3075	−	25.3075i	−0.812157	−	0.812157i	0.172800	−	0.984957i	$-0.444719\pi$
$971$	−25.3075	−	25.3075i	−0.812157	−	0.812157i	−0.984957	+	0.172800i	$0.944719\pi$
$972$		0			0
$973$		−	60.6470i		−	1.94425i
$974$		0			0
$975$	11.6309	−	21.9527i	0.372488	−	0.703050i
$976$		0			0
$977$	−23.4598	+	23.4598i	−0.750547	+	0.750547i	−0.974581	−	0.224035i	$-0.928077\pi$
$977$	−23.4598	+	23.4598i	−0.750547	+	0.750547i	0.224035	+	0.974581i	$0.428077\pi$
$978$		0			0
$979$	8.07119	+	8.07119i	0.257956	+	0.257956i
$980$		0			0
$981$	−6.77367	+	6.77367i	−0.216267	+	0.216267i
$982$		0			0
$983$	−15.8155	−	15.8155i	−0.504437	−	0.504437i	0.408377	−	0.912814i	$-0.366095\pi$
$983$	−15.8155	−	15.8155i	−0.504437	−	0.504437i	−0.912814	+	0.408377i	$0.866095\pi$
$984$		0			0
$985$	−3.16537	+	12.7356i	−0.100857	+	0.405791i
$986$		0			0
$987$	−0.487794			−0.0155267
$988$		0			0
$989$	36.0210	−	36.0210i	1.14540	−	1.14540i
$990$		0			0
$991$		−	30.1804i		−	0.958711i	−0.877621	−	0.479355i	$-0.840870\pi$
$991$		−	30.1804i		−	0.958711i	0.877621	−	0.479355i	$-0.159130\pi$
$992$		0			0
$993$	18.7327	+	18.7327i	0.594465	+	0.594465i
$994$		0			0
$995$	3.20032	−	12.8762i	0.101457	−	0.408204i
$996$		0			0
$997$			41.2092i			1.30511i	0.757741	+	0.652555i	$0.226303\pi$
$997$			41.2092i			1.30511i	−0.757741	+	0.652555i	$0.773697\pi$
$998$		0			0
$999$		−	2.27540i		−	0.0719904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.y.i.223.8		16
4.3	odd	2		1920.2.y.j.223.8		16
5.2	odd	4		1920.2.bc.i.607.2		16
8.3	odd	2		960.2.y.e.943.1		16
8.5	even	2		240.2.y.e.163.3	✓	16
16.3	odd	4		240.2.bc.e.43.7	yes	16
16.5	even	4		1920.2.bc.j.1183.2		16
16.11	odd	4		1920.2.bc.i.1183.2		16
16.13	even	4		960.2.bc.e.463.7		16
20.7	even	4		1920.2.bc.j.607.2		16
24.5	odd	2		720.2.z.f.163.6		16
40.27	even	4		960.2.bc.e.367.7		16
40.37	odd	4		240.2.bc.e.67.7	yes	16
48.35	even	4		720.2.bd.f.523.2		16
80.27	even	4	inner	1920.2.y.i.1567.8		16
80.37	odd	4		1920.2.y.j.1567.8		16
80.67	even	4		240.2.y.e.187.3	yes	16
80.77	odd	4		960.2.y.e.847.1		16
120.77	even	4		720.2.bd.f.307.2		16
240.227	odd	4		720.2.z.f.667.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.3	✓	16	8.5	even	2
240.2.y.e.187.3	yes	16	80.67	even	4
240.2.bc.e.43.7	yes	16	16.3	odd	4
240.2.bc.e.67.7	yes	16	40.37	odd	4
720.2.z.f.163.6		16	24.5	odd	2
720.2.z.f.667.6		16	240.227	odd	4
720.2.bd.f.307.2		16	120.77	even	4
720.2.bd.f.523.2		16	48.35	even	4
960.2.y.e.847.1		16	80.77	odd	4
960.2.y.e.943.1		16	8.3	odd	2
960.2.bc.e.367.7		16	40.27	even	4
960.2.bc.e.463.7		16	16.13	even	4
1920.2.y.i.223.8		16	1.1	even	1	trivial
1920.2.y.i.1567.8		16	80.27	even	4	inner
1920.2.y.j.223.8		16	4.3	odd	2
1920.2.y.j.1567.8		16	80.37	odd	4
1920.2.bc.i.607.2		16	5.2	odd	4
1920.2.bc.i.1183.2		16	16.11	odd	4
1920.2.bc.j.607.2		16	20.7	even	4
1920.2.bc.j.1183.2		16	16.5	even	4

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:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.y (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +(2.17005 + 0.539352i) q^{5} +(3.00806 - 3.00806i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} +(2.17005 + 0.539352i) q^{5} +(3.00806 - 3.00806i) q^{7} +1.00000 q^{9} +(2.91811 + 2.91811i) q^{11} +4.96870i q^{13} +(-2.17005 - 0.539352i) q^{15} +(-2.56773 + 2.56773i) q^{17} +(0.174647 + 0.174647i) q^{19} +(-3.00806 + 3.00806i) q^{21} +(2.93410 + 2.93410i) q^{23} +(4.41820 + 2.34084i) q^{25} -1.00000 q^{27} +(-4.90621 + 4.90621i) q^{29} +5.24365i q^{31} +(-2.91811 - 2.91811i) q^{33} +(8.15002 - 4.90522i) q^{35} +2.27540i q^{37} -4.96870i q^{39} +0.187334i q^{41} -12.2767i q^{43} +(2.17005 + 0.539352i) q^{45} +(0.0810813 + 0.0810813i) q^{47} -11.0968i q^{49} +(2.56773 - 2.56773i) q^{51} -10.3383 q^{53} +(4.75854 + 7.90632i) q^{55} +(-0.174647 - 0.174647i) q^{57} +(-3.33519 + 3.33519i) q^{59} +(1.32102 + 1.32102i) q^{61} +(3.00806 - 3.00806i) q^{63} +(-2.67988 + 10.7823i) q^{65} -9.03323i q^{67} +(-2.93410 - 2.93410i) q^{69} +4.47057 q^{71} +(-3.50820 + 3.50820i) q^{73} +(-4.41820 - 2.34084i) q^{75} +17.5557 q^{77} -6.75271 q^{79} +1.00000 q^{81} -0.203861 q^{83} +(-6.95702 + 4.18719i) q^{85} +(4.90621 - 4.90621i) q^{87} +2.76590 q^{89} +(14.9461 + 14.9461i) q^{91} -5.24365i q^{93} +(0.284797 + 0.473190i) q^{95} +(9.90816 - 9.90816i) q^{97} +(2.91811 + 2.91811i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} + 4 q^{5} - 4 q^{7} + 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^3 + 4 * q^5 - 4 * q^7 + 16 * q^9	\( 16 q - 16 q^{3} + 4 q^{5} - 4 q^{7} + 16 q^{9} - 4 q^{15} - 8 q^{17} - 8 q^{19} + 4 q^{21} + 32 q^{25} - 16 q^{27} - 12 q^{29} + 20 q^{35} + 4 q^{45} - 32 q^{47} + 8 q^{51} - 16 q^{53} - 4 q^{55} + 8 q^{57} + 24 q^{59} - 40 q^{61} - 4 q^{63} - 4 q^{65} + 8 q^{73} - 32 q^{75} + 72 q^{77} - 48 q^{79} + 16 q^{81} + 8 q^{83} + 8 q^{85} + 12 q^{87} + 40 q^{91} + 8 q^{95} + 48 q^{97}+O(q^{100}) \) 16 * q - 16 * q^3 + 4 * q^5 - 4 * q^7 + 16 * q^9 - 4 * q^15 - 8 * q^17 - 8 * q^19 + 4 * q^21 + 32 * q^25 - 16 * q^27 - 12 * q^29 + 20 * q^35 + 4 * q^45 - 32 * q^47 + 8 * q^51 - 16 * q^53 - 4 * q^55 + 8 * q^57 + 24 * q^59 - 40 * q^61 - 4 * q^63 - 4 * q^65 + 8 * q^73 - 32 * q^75 + 72 * q^77 - 48 * q^79 + 16 * q^81 + 8 * q^83 + 8 * q^85 + 12 * q^87 + 40 * q^91 + 8 * q^95 + 48 * q^97

Introduction

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