LMFDB - Embedded newform 1120.2.bz.e.271.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1120,2,Mod(271,1120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1120, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("1120.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bz (of order $6$, 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:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.12
Character	$\chi$	$=$	1120.271
Dual form			1120.2.bz.e.591.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.66758 - 1.54013i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.53597 + 0.754231i) q^{7} +(3.24397 - 5.61873i) q^{9} +O(q^{10})$	\(q+(2.66758 - 1.54013i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.53597 + 0.754231i) q^{7} +(3.24397 - 5.61873i) q^{9} +(1.64217 + 2.84433i) q^{11} +6.72078 q^{13} +3.08025i q^{15} +(3.32426 - 1.91926i) q^{17} +(0.618548 + 0.357119i) q^{19} +(-5.60328 + 5.91768i) q^{21} +(-1.09312 - 0.631110i) q^{23} +(-0.500000 - 0.866025i) q^{25} -10.7438i q^{27} -3.04491i q^{29} +(-0.0335679 - 0.0581414i) q^{31} +(8.76124 + 5.05831i) q^{33} +(0.614801 - 2.57333i) q^{35} +(-0.498735 - 0.287945i) q^{37} +(17.9282 - 10.3508i) q^{39} +0.230821i q^{41} -10.0631 q^{43} +(3.24397 + 5.61873i) q^{45} +(4.23402 - 7.33354i) q^{47} +(5.86227 - 3.82541i) q^{49} +(5.91181 - 10.2396i) q^{51} +(2.16915 - 1.25236i) q^{53} -3.28435 q^{55} +2.20003 q^{57} +(-0.986424 + 0.569512i) q^{59} +(-0.0888960 + 0.153972i) q^{61} +(-3.98880 + 16.6956i) q^{63} +(-3.36039 + 5.82037i) q^{65} +(6.92927 + 12.0019i) q^{67} -3.88796 q^{69} +12.0720i q^{71} +(-3.89739 + 2.25016i) q^{73} +(-2.66758 - 1.54013i) q^{75} +(-6.30978 - 5.97455i) q^{77} +(-9.66655 - 5.58099i) q^{79} +(-6.81481 - 11.8036i) q^{81} -3.24478i q^{83} +3.83853i q^{85} +(-4.68955 - 8.12253i) q^{87} +(-13.3148 - 7.68732i) q^{89} +(-17.0437 + 5.06902i) q^{91} +(-0.179090 - 0.103398i) q^{93} +(-0.618548 + 0.357119i) q^{95} +5.76555i q^{97} +21.3087 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9}+O(q^{10}) $ 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9	$ 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9} - 8 q^{11} + 20 q^{13} + 6 q^{17} - 18 q^{19} - 26 q^{21} - 18 q^{23} - 12 q^{25} + 6 q^{31} + 12 q^{33} + 8 q^{35} + 18 q^{39} - 32 q^{43} + 12 q^{45} + 8 q^{49} + 22 q^{51} + 30 q^{53} + 16 q^{55} - 44 q^{57} + 18 q^{59} + 22 q^{61} + 12 q^{63} - 10 q^{65} + 8 q^{67} - 12 q^{69} + 30 q^{73} + 12 q^{75} - 32 q^{77} - 6 q^{79} - 4 q^{81} - 14 q^{87} - 60 q^{89} - 18 q^{91} - 18 q^{93} + 18 q^{95} + 56 q^{99}+O(q^{100}) $ 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9 - 8 * q^11 + 20 * q^13 + 6 * q^17 - 18 * q^19 - 26 * q^21 - 18 * q^23 - 12 * q^25 + 6 * q^31 + 12 * q^33 + 8 * q^35 + 18 * q^39 - 32 * q^43 + 12 * q^45 + 8 * q^49 + 22 * q^51 + 30 * q^53 + 16 * q^55 - 44 * q^57 + 18 * q^59 + 22 * q^61 + 12 * q^63 - 10 * q^65 + 8 * q^67 - 12 * q^69 + 30 * q^73 + 12 * q^75 - 32 * q^77 - 6 * q^79 - 4 * q^81 - 14 * q^87 - 60 * q^89 - 18 * q^91 - 18 * q^93 + 18 * q^95 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.66758	−	1.54013i	1.54013	−	0.889192i	0.541296	−	0.840832i	$-0.317934\pi$
$3$	2.66758	−	1.54013i	1.54013	−	0.889192i	0.998830	−	0.0483596i	$-0.0153994\pi$
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−2.53597	+	0.754231i	−0.958506	+	0.285072i
$7$	−2.53597	+	0.754231i	−0.958506	+	0.285072i
$8$		0			0
$9$	3.24397	−	5.61873i	1.08132	−	1.87291i
$10$		0			0
$11$	1.64217	+	2.84433i	0.495134	+	0.857597i	0.999984	−	0.00560987i	$-0.00178569\pi$
$11$	1.64217	+	2.84433i	0.495134	+	0.857597i	−0.504850	+	0.863207i	$0.668452\pi$
$12$		0			0
$13$	6.72078			1.86401			0.932005	−	0.362446i	$-0.118058\pi$
$13$	6.72078			1.86401			0.932005	+	0.362446i	$0.118058\pi$
$14$		0			0
$15$			3.08025i			0.795317i
$16$		0			0
$17$	3.32426	−	1.91926i	0.806252	−	0.465490i	−0.0394009	−	0.999223i	$-0.512545\pi$
$17$	3.32426	−	1.91926i	0.806252	−	0.465490i	0.845652	+	0.533734i	$0.179212\pi$
$18$		0			0
$19$	0.618548	+	0.357119i	0.141905	+	0.0819287i	0.569271	−	0.822150i	$-0.307225\pi$
$19$	0.618548	+	0.357119i	0.141905	+	0.0819287i	−0.427367	+	0.904078i	$0.640559\pi$
$20$		0			0
$21$	−5.60328	+	5.91768i	−1.22274	+	1.29134i
$22$		0			0
$23$	−1.09312	−	0.631110i	−0.227930	−	0.131596i	0.381687	−	0.924292i	$-0.375343\pi$
$23$	−1.09312	−	0.631110i	−0.227930	−	0.131596i	−0.609617	+	0.792696i	$0.708677\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		−	10.7438i		−	2.06764i
$28$		0			0
$29$		−	3.04491i		−	0.565426i	−0.959205	−	0.282713i	$-0.908766\pi$
$29$		−	3.04491i		−	0.565426i	0.959205	−	0.282713i	$-0.0912344\pi$
$30$		0			0
$31$	−0.0335679	−	0.0581414i	−0.00602898	−	0.0104425i	0.862995	−	0.505212i	$-0.168586\pi$
$31$	−0.0335679	−	0.0581414i	−0.00602898	−	0.0104425i	−0.869024	+	0.494770i	$0.835252\pi$
$32$		0			0
$33$	8.76124	+	5.05831i	1.52514	+	0.880538i
$34$		0			0
$35$	0.614801	−	2.57333i	0.103920	−	0.434972i
$36$		0			0
$37$	−0.498735	−	0.287945i	−0.0819916	−	0.0473379i	0.458444	−	0.888723i	$-0.348407\pi$
$37$	−0.498735	−	0.287945i	−0.0819916	−	0.0473379i	−0.540435	+	0.841386i	$0.681740\pi$
$38$		0			0
$39$	17.9282	−	10.3508i	2.87081	−	1.65746i
$40$		0			0
$41$			0.230821i			0.0360483i	0.999838	+	0.0180241i	$0.00573757\pi$
$41$			0.230821i			0.0360483i	−0.999838	+	0.0180241i	$0.994262\pi$
$42$		0			0
$43$	−10.0631			−1.53462			−0.767308	−	0.641279i	$-0.778404\pi$
$43$	−10.0631			−1.53462			−0.767308	+	0.641279i	$0.778404\pi$
$44$		0			0
$45$	3.24397	+	5.61873i	0.483583	+	0.837591i
$46$		0			0
$47$	4.23402	−	7.33354i	0.617595	−	1.06971i	−0.372328	−	0.928101i	$-0.621440\pi$
$47$	4.23402	−	7.33354i	0.617595	−	1.06971i	0.989923	−	0.141605i	$-0.0452263\pi$
$48$		0			0
$49$	5.86227	−	3.82541i	0.837467	−	0.546487i
$50$		0			0
$51$	5.91181	−	10.2396i	0.827819	−	1.43382i
$52$		0			0
$53$	2.16915	−	1.25236i	0.297955	−	0.172024i	−0.343569	−	0.939128i	$-0.611636\pi$
$53$	2.16915	−	1.25236i	0.297955	−	0.172024i	0.641524	+	0.767103i	$0.278303\pi$
$54$		0			0
$55$	−3.28435			−0.442861
$56$		0			0
$57$	2.20003			0.291401
$58$		0			0
$59$	−0.986424	+	0.569512i	−0.128422	+	0.0741442i	−0.562835	−	0.826570i	$-0.690289\pi$
$59$	−0.986424	+	0.569512i	−0.128422	+	0.0741442i	0.434413	+	0.900714i	$0.356956\pi$
$60$		0			0
$61$	−0.0888960	+	0.153972i	−0.0113820	+	0.0197141i	−0.871660	−	0.490111i	$-0.836956\pi$
$61$	−0.0888960	+	0.153972i	−0.0113820	+	0.0197141i	0.860278	+	0.509825i	$0.170290\pi$
$62$		0			0
$63$	−3.98880	+	16.6956i	−0.502541	+	2.10345i
$64$		0			0
$65$	−3.36039	+	5.82037i	−0.416805	+	0.721928i
$66$		0			0
$67$	6.92927	+	12.0019i	0.846545	+	1.46626i	0.884272	+	0.466971i	$0.154655\pi$
$67$	6.92927	+	12.0019i	0.846545	+	1.46626i	−0.0377270	+	0.999288i	$0.512012\pi$
$68$		0			0
$69$	−3.88796			−0.468055
$70$		0			0
$71$			12.0720i			1.43268i	0.697749	+	0.716342i	$0.254185\pi$
$71$			12.0720i			1.43268i	−0.697749	+	0.716342i	$0.745815\pi$
$72$		0			0
$73$	−3.89739	+	2.25016i	−0.456155	+	0.263361i	−0.710426	−	0.703772i	$-0.751498\pi$
$73$	−3.89739	+	2.25016i	−0.456155	+	0.263361i	0.254271	+	0.967133i	$0.418164\pi$
$74$		0			0
$75$	−2.66758	−	1.54013i	−0.308025	−	0.177838i
$76$		0			0
$77$	−6.30978	−	5.97455i	−0.719066	−	0.680863i
$78$		0			0
$79$	−9.66655	−	5.58099i	−1.08757	−	0.627910i	−0.154643	−	0.987970i	$-0.549423\pi$
$79$	−9.66655	−	5.58099i	−1.08757	−	0.627910i	−0.932929	+	0.360061i	$0.882756\pi$
$80$		0			0
$81$	−6.81481	−	11.8036i	−0.757202	−	1.31151i
$82$		0			0
$83$		−	3.24478i		−	0.356161i	−0.984016	−	0.178081i	$-0.943011\pi$
$83$		−	3.24478i		−	0.356161i	0.984016	−	0.178081i	$-0.0569888\pi$
$84$		0			0
$85$			3.83853i			0.416347i
$86$		0			0
$87$	−4.68955	−	8.12253i	−0.502772	−	0.870827i
$88$		0			0
$89$	−13.3148	−	7.68732i	−1.41137	−	0.814854i	−0.415852	−	0.909433i	$-0.636516\pi$
$89$	−13.3148	−	7.68732i	−1.41137	−	0.814854i	−0.995517	+	0.0945783i	$0.969850\pi$
$90$		0			0
$91$	−17.0437	+	5.06902i	−1.78666	+	0.531378i
$92$		0			0
$93$	−0.179090	−	0.103398i	−0.0185708	−	0.0107218i
$94$		0			0
$95$	−0.618548	+	0.357119i	−0.0634617	+	0.0366396i
$96$		0			0
$97$			5.76555i			0.585403i	0.956204	+	0.292701i	$0.0945542\pi$
$97$			5.76555i			0.585403i	−0.956204	+	0.292701i	$0.905446\pi$
$98$		0			0
$99$	21.3087			2.14160
$100$		0			0
$101$	5.65852	+	9.80085i	0.563044	+	0.975221i	0.997229	+	0.0743970i	$0.0237032\pi$
$101$	5.65852	+	9.80085i	0.563044	+	0.975221i	−0.434185	+	0.900824i	$0.642963\pi$
$102$		0			0
$103$	−0.346486	+	0.600132i	−0.0341403	+	0.0591327i	−0.882591	−	0.470142i	$-0.844203\pi$
$103$	−0.346486	+	0.600132i	−0.0341403	+	0.0591327i	0.848450	+	0.529275i	$0.177536\pi$
$104$		0			0
$105$	−2.32322	−	7.81142i	−0.226723	−	0.762317i
$106$		0			0
$107$	−2.55924	+	4.43274i	−0.247411	+	0.428529i	−0.962807	−	0.270191i	$-0.912913\pi$
$107$	−2.55924	+	4.43274i	−0.247411	+	0.428529i	0.715396	+	0.698720i	$0.246247\pi$
$108$		0			0
$109$	−10.6122	+	6.12698i	−1.01647	+	0.586858i	−0.913079	−	0.407783i	$-0.866302\pi$
$109$	−10.6122	+	6.12698i	−1.01647	+	0.586858i	−0.103389	+	0.994641i	$0.532969\pi$
$110$		0			0
$111$	−1.77389			−0.168370
$112$		0			0
$113$	−6.58353			−0.619326			−0.309663	−	0.950846i	$-0.600216\pi$
$113$	−6.58353			−0.619326			−0.309663	+	0.950846i	$0.600216\pi$
$114$		0			0
$115$	1.09312	−	0.631110i	0.101934	−	0.0588514i
$116$		0			0
$117$	21.8020	−	37.7622i	2.01560	−	3.49112i
$118$		0			0
$119$	−6.98265	+	7.37445i	−0.640099	+	0.676015i
$120$		0			0
$121$	0.106534	−	0.184523i	0.00968495	−	0.0167748i
$122$		0			0
$123$	0.355494	+	0.615734i	0.0320538	+	0.0555188i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$		−	16.4627i		−	1.46083i	−0.683004	−	0.730415i	$-0.739327\pi$
$127$		−	16.4627i		−	1.46083i	0.683004	−	0.730415i	$-0.260673\pi$
$128$		0			0
$129$	−26.8442	+	15.4985i	−2.36350	+	1.36457i
$130$		0			0
$131$	0.446341	+	0.257695i	0.0389970	+	0.0225149i	0.519372	−	0.854548i	$-0.326166\pi$
$131$	0.446341	+	0.257695i	0.0389970	+	0.0225149i	−0.480375	+	0.877063i	$0.659499\pi$
$132$		0			0
$133$	−1.83797	−	0.439114i	−0.159372	−	0.0380760i
$134$		0			0
$135$	9.30437	+	5.37188i	0.800792	+	0.462338i
$136$		0			0
$137$	4.22144	+	7.31175i	0.360662	+	0.624685i	0.988070	−	0.154006i	$-0.0492175\pi$
$137$	4.22144	+	7.31175i	0.360662	+	0.624685i	−0.627408	+	0.778691i	$0.715884\pi$
$138$		0			0
$139$			19.1037i			1.62036i	0.586182	+	0.810179i	$0.300630\pi$
$139$			19.1037i			1.62036i	−0.586182	+	0.810179i	$0.699370\pi$
$140$		0			0
$141$		−	26.0837i		−	2.19664i
$142$		0			0
$143$	11.0367	+	19.1161i	0.922934	+	1.59857i
$144$		0			0
$145$	2.63697	+	1.52246i	0.218988	+	0.126433i
$146$		0			0
$147$	9.74644	−	19.2332i	0.803873	−	1.58633i
$148$		0			0
$149$	−5.64120	−	3.25695i	−0.462145	−	0.266820i	0.250801	−	0.968039i	$-0.419306\pi$
$149$	−5.64120	−	3.25695i	−0.462145	−	0.266820i	−0.712946	+	0.701219i	$0.752639\pi$
$150$		0			0
$151$	−6.19052	+	3.57410i	−0.503777	+	0.290856i	−0.730272	−	0.683156i	$-0.760607\pi$
$151$	−6.19052	+	3.57410i	−0.503777	+	0.290856i	0.226495	+	0.974012i	$0.427273\pi$
$152$		0			0
$153$		−	24.9042i		−	2.01338i
$154$		0			0
$155$	0.0671359			0.00539248
$156$		0			0
$157$	11.5674	+	20.0353i	0.923176	+	1.59899i	0.794469	+	0.607304i	$0.207749\pi$
$157$	11.5674	+	20.0353i	0.923176	+	1.59899i	0.128706	+	0.991683i	$0.458918\pi$
$158$		0			0
$159$	3.85757	−	6.68151i	0.305926	−	0.529879i
$160$		0			0
$161$	3.24811	+	0.776015i	0.255987	+	0.0611585i
$162$		0			0
$163$	0.415413	−	0.719516i	0.0325376	−	0.0563568i	−0.849298	−	0.527914i	$-0.822974\pi$
$163$	0.415413	−	0.719516i	0.0325376	−	0.0563568i	0.881836	+	0.471557i	$0.156308\pi$
$164$		0			0
$165$	−8.76124	+	5.05831i	−0.682062	+	0.393789i
$166$		0			0
$167$	3.59980			0.278561			0.139280	−	0.990253i	$-0.455521\pi$
$167$	3.59980			0.278561			0.139280	+	0.990253i	$0.455521\pi$
$168$		0			0
$169$	32.1689			2.47453
$170$		0			0
$171$	4.01311	−	2.31697i	0.306890	−	0.177183i
$172$		0			0
$173$	−5.28828	+	9.15958i	−0.402061	+	0.696390i	−0.993974	−	0.109612i	$-0.965039\pi$
$173$	−5.28828	+	9.15958i	−0.402061	+	0.696390i	0.591914	+	0.806001i	$0.298373\pi$
$174$		0			0
$175$	1.92117	+	1.81910i	0.145227	+	0.137511i
$176$		0			0
$177$	−1.75424	+	3.03844i	−0.131857	+	0.228383i
$178$		0			0
$179$	−9.34059	−	16.1784i	−0.698149	−	1.20923i	−0.969108	−	0.246638i	$-0.920674\pi$
$179$	−9.34059	−	16.1784i	−0.698149	−	1.20923i	0.270959	−	0.962591i	$-0.412659\pi$
$180$		0			0
$181$	−17.3231			−1.28761			−0.643807	−	0.765188i	$-0.722646\pi$
$181$	−17.3231			−1.28761			−0.643807	+	0.765188i	$0.722646\pi$
$182$		0			0
$183$			0.547644i			0.0404830i
$184$		0			0
$185$	0.498735	−	0.287945i	0.0366677	−	0.0211701i
$186$		0			0
$187$	10.9180	+	6.30352i	0.798405	+	0.460959i
$188$		0			0
$189$	8.10327	+	27.2458i	0.589426	+	1.98184i
$190$		0			0
$191$	−7.26161	−	4.19249i	−0.525432	−	0.303358i	0.213722	−	0.976894i	$-0.431441\pi$
$191$	−7.26161	−	4.19249i	−0.525432	−	0.303358i	−0.739154	+	0.673536i	$0.764775\pi$
$192$		0			0
$193$	4.32438	+	7.49005i	0.311276	+	0.539146i	0.978639	−	0.205587i	$-0.0659103\pi$
$193$	4.32438	+	7.49005i	0.311276	+	0.539146i	−0.667363	+	0.744733i	$0.732577\pi$
$194$		0			0
$195$			20.7017i			1.48248i
$196$		0			0
$197$		−	9.70322i		−	0.691326i	−0.938359	−	0.345663i	$-0.887654\pi$
$197$		−	9.70322i		−	0.691326i	0.938359	−	0.345663i	$-0.112346\pi$
$198$		0			0
$199$	0.189423	+	0.328090i	0.0134278	+	0.0232577i	0.872661	−	0.488326i	$-0.162392\pi$
$199$	0.189423	+	0.328090i	0.0134278	+	0.0232577i	−0.859233	+	0.511584i	$0.829059\pi$
$200$		0			0
$201$	36.9687	+	21.3439i	2.60757	+	1.50548i
$202$		0			0
$203$	2.29657	+	7.72180i	0.161187	+	0.541964i
$204$		0			0
$205$	−0.199897	−	0.115411i	−0.0139614	−	0.00806064i
$206$		0			0
$207$	−7.09208	+	4.09461i	−0.492933	+	0.284595i
$208$		0			0
$209$			2.34580i			0.162263i
$210$		0			0
$211$	−1.17567			−0.0809367			−0.0404684	−	0.999181i	$-0.512885\pi$
$211$	−1.17567			−0.0809367			−0.0404684	+	0.999181i	$0.512885\pi$
$212$		0			0
$213$	18.5924	+	32.2030i	1.27393	+	2.20651i
$214$		0			0
$215$	5.03157	−	8.71494i	0.343150	−	0.594354i
$216$		0			0
$217$	0.128979	+	0.122127i	0.00875568	+	0.00829050i
$218$		0			0
$219$	−6.93105	+	12.0049i	−0.468357	+	0.811218i
$220$		0			0
$221$	22.3416	−	12.8989i	1.50286	−	0.867677i
$222$		0			0
$223$	−7.97945			−0.534343			−0.267172	−	0.963649i	$-0.586089\pi$
$223$	−7.97945			−0.534343			−0.267172	+	0.963649i	$0.586089\pi$
$224$		0			0
$225$	−6.48795			−0.432530
$226$		0			0
$227$	5.41980	−	3.12912i	0.359725	−	0.207687i	−0.309235	−	0.950986i	$-0.600073\pi$
$227$	5.41980	−	3.12912i	0.359725	−	0.207687i	0.668960	+	0.743298i	$0.266740\pi$
$228$		0			0
$229$	6.97388	−	12.0791i	0.460847	−	0.798211i	−0.538156	−	0.842845i	$-0.680879\pi$
$229$	6.97388	−	12.0791i	0.460847	−	0.798211i	0.999003	+	0.0446343i	$0.0142123\pi$
$230$		0			0
$231$	−26.0334	−	6.21971i	−1.71287	−	0.409227i
$232$		0			0
$233$	−0.0277929	+	0.0481388i	−0.00182077	+	0.00315367i	−0.866934	−	0.498422i	$-0.833913\pi$
$233$	−0.0277929	+	0.0481388i	−0.00182077	+	0.00315367i	0.865114	+	0.501576i	$0.167246\pi$
$234$		0			0
$235$	4.23402	+	7.33354i	0.276197	+	0.478387i
$236$		0			0
$237$	−34.3817			−2.23333
$238$		0			0
$239$		−	7.90839i		−	0.511552i	−0.966736	−	0.255776i	$-0.917669\pi$
$239$		−	7.90839i		−	0.511552i	0.966736	−	0.255776i	$-0.0823309\pi$
$240$		0			0
$241$	−11.6219	+	6.70993i	−0.748635	+	0.432225i	−0.825201	−	0.564840i	$-0.808938\pi$
$241$	−11.6219	+	6.70993i	−0.748635	+	0.432225i	0.0765652	+	0.997065i	$0.475605\pi$
$242$		0			0
$243$	−8.44497	−	4.87570i	−0.541745	−	0.312777i
$244$		0			0
$245$	0.381767	+	6.98958i	0.0243902	+	0.446548i
$246$		0			0
$247$	4.15713	+	2.40012i	0.264512	+	0.152716i
$248$		0			0
$249$	−4.99737	−	8.65570i	−0.316696	−	0.548533i
$250$		0			0
$251$		−	18.3987i		−	1.16132i	−0.814148	−	0.580658i	$-0.802795\pi$
$251$		−	18.3987i		−	1.16132i	0.814148	−	0.580658i	$-0.197205\pi$
$252$		0			0
$253$		−	4.14557i		−	0.260630i
$254$		0			0
$255$	5.91181	+	10.2396i	0.370212	+	0.641226i
$256$		0			0
$257$	−25.9092	−	14.9587i	−1.61617	−	0.933096i	−0.987899	−	0.155101i	$-0.950430\pi$
$257$	−25.9092	−	14.9587i	−1.61617	−	0.933096i	−0.628271	−	0.777995i	$-0.716237\pi$
$258$		0			0
$259$	1.48195	+	0.354058i	0.0920841	+	0.0220001i
$260$		0			0
$261$	−17.1085	−	9.87761i	−1.05899	−	0.611409i
$262$		0			0
$263$	17.3117	−	9.99491i	1.06748	−	0.616313i	0.139992	−	0.990153i	$-0.455292\pi$
$263$	17.3117	−	9.99491i	1.06748	−	0.616313i	0.927493	+	0.373840i	$0.121959\pi$
$264$		0			0
$265$			2.50471i			0.153863i
$266$		0			0
$267$	−47.3578			−2.89825
$268$		0			0
$269$	−11.9143	−	20.6361i	−0.726426	−	1.25821i	−0.958384	−	0.285481i	$-0.907847\pi$
$269$	−11.9143	−	20.6361i	−0.726426	−	1.25821i	0.231958	−	0.972726i	$-0.425487\pi$
$270$		0			0
$271$	9.94307	−	17.2219i	0.603999	−	1.04616i	−0.388210	−	0.921571i	$-0.626907\pi$
$271$	9.94307	−	17.2219i	0.603999	−	1.04616i	0.992209	−	0.124585i	$-0.0397601\pi$
$272$		0			0
$273$	−37.6584	+	39.7714i	−2.27919	+	2.40708i
$274$		0			0
$275$	1.64217	−	2.84433i	0.0990268	−	0.171519i
$276$		0			0
$277$	−17.1311	+	9.89062i	−1.02931	+	0.594270i	−0.916786	−	0.399380i	$-0.869226\pi$
$277$	−17.1311	+	9.89062i	−1.02931	+	0.594270i	−0.112520	+	0.993649i	$0.535892\pi$
$278$		0			0
$279$	−0.435574			−0.0260771
$280$		0			0
$281$	−9.91394			−0.591416			−0.295708	−	0.955278i	$-0.595556\pi$
$281$	−9.91394			−0.591416			−0.295708	+	0.955278i	$0.595556\pi$
$282$		0			0
$283$	−23.3509	+	13.4816i	−1.38806	+	0.801399i	−0.993097	−	0.117296i	$-0.962577\pi$
$283$	−23.3509	+	13.4816i	−1.38806	+	0.801399i	−0.394967	+	0.918695i	$0.629244\pi$
$284$		0			0
$285$	−1.10002	+	1.90528i	−0.0651593	+	0.112859i
$286$		0			0
$287$	−0.174093	−	0.585356i	−0.0102764	−	0.0345525i
$288$		0			0
$289$	−1.13286	+	1.96217i	−0.0666389	+	0.115422i
$290$		0			0
$291$	8.87967	+	15.3800i	0.520535	+	0.901594i
$292$		0			0
$293$	−2.04836			−0.119666			−0.0598332	−	0.998208i	$-0.519057\pi$
$293$	−2.04836			−0.119666			−0.0598332	+	0.998208i	$0.519057\pi$
$294$		0			0
$295$		−	1.13902i		−	0.0663166i
$296$		0			0
$297$	30.5588	−	17.6431i	1.77320	−	1.02376i
$298$		0			0
$299$	−7.34659	−	4.24156i	−0.424864	−	0.245295i
$300$		0			0
$301$	25.5198	−	7.58993i	1.47094	−	0.437477i
$302$		0			0
$303$	30.1891	+	17.4297i	1.73432	+	1.00131i
$304$		0			0
$305$	−0.0888960	−	0.153972i	−0.00509017	−	0.00881644i
$306$		0			0
$307$			7.59189i			0.433292i	0.976250	+	0.216646i	$0.0695118\pi$
$307$			7.59189i			0.433292i	−0.976250	+	0.216646i	$0.930488\pi$
$308$		0			0
$309$			2.13453i			0.121429i
$310$		0			0
$311$	−8.84137	−	15.3137i	−0.501348	−	0.868360i	−0.999999	−	0.00155721i	$-0.999504\pi$
$311$	−8.84137	−	15.3137i	−0.501348	−	0.868360i	0.498651	−	0.866803i	$-0.333829\pi$
$312$		0			0
$313$	11.5543	+	6.67087i	0.653087	+	0.377060i	0.789638	−	0.613573i	$-0.210268\pi$
$313$	11.5543	+	6.67087i	0.653087	+	0.377060i	−0.136551	+	0.990633i	$0.543602\pi$
$314$		0			0
$315$	−12.4644	−	11.8022i	−0.702291	−	0.664979i
$316$		0			0
$317$	1.03929	+	0.600036i	0.0583725	+	0.0337014i	0.528902	−	0.848683i	$-0.322604\pi$
$317$	1.03929	+	0.600036i	0.0583725	+	0.0337014i	−0.470530	+	0.882384i	$0.655937\pi$
$318$		0			0
$319$	8.66072	−	5.00027i	0.484907	−	0.279961i
$320$		0			0
$321$			15.7662i			0.879984i
$322$		0			0
$323$	2.74162			0.152548
$324$		0			0
$325$	−3.36039	−	5.82037i	−0.186401	−	0.322856i
$326$		0			0
$327$	−18.8726	+	32.6884i	−1.04366	+	1.80767i
$328$		0			0
$329$	−5.20616	+	21.7910i	−0.287025	+	1.20138i
$330$		0			0
$331$	3.01312	−	5.21888i	0.165616	−	0.286856i	−0.771258	−	0.636523i	$-0.780372\pi$
$331$	3.01312	−	5.21888i	0.165616	−	0.286856i	0.936874	+	0.349667i	$0.113705\pi$
$332$		0			0
$333$	−3.23577	+	1.86817i	−0.177319	+	0.102375i
$334$		0			0
$335$	−13.8585			−0.757173
$336$		0			0
$337$	−17.3124			−0.943069			−0.471534	−	0.881848i	$-0.656300\pi$
$337$	−17.3124			−0.943069			−0.471534	+	0.881848i	$0.656300\pi$
$338$		0			0
$339$	−17.5621	+	10.1395i	−0.953840	+	0.550700i
$340$		0			0
$341$	0.110249	−	0.190956i	0.00597030	−	0.0103409i
$342$		0			0
$343$	−11.9813	+	14.1226i	−0.646929	+	0.762550i
$344$		0			0
$345$	1.94398	−	3.36707i	0.104660	−	0.181277i
$346$		0			0
$347$	2.07692	+	3.59734i	0.111495	+	0.193115i	0.916373	−	0.400325i	$-0.131103\pi$
$347$	2.07692	+	3.59734i	0.111495	+	0.193115i	−0.804878	+	0.593440i	$0.797769\pi$
$348$		0			0
$349$	−12.1023			−0.647823			−0.323912	−	0.946087i	$-0.604998\pi$
$349$	−12.1023			−0.647823			−0.323912	+	0.946087i	$0.604998\pi$
$350$		0			0
$351$		−	72.2064i		−	3.85409i
$352$		0			0
$353$	10.4647	−	6.04182i	0.556982	−	0.321573i	−0.194952	−	0.980813i	$-0.562455\pi$
$353$	10.4647	−	6.04182i	0.556982	−	0.321573i	0.751933	+	0.659239i	$0.229122\pi$
$354$		0			0
$355$	−10.4547	−	6.03601i	−0.554876	−	0.320358i
$356$		0			0
$357$	−7.26918	+	30.4261i	−0.384726	+	1.61032i
$358$		0			0
$359$	−8.88907	−	5.13211i	−0.469147	−	0.270862i	0.246735	−	0.969083i	$-0.420642\pi$
$359$	−8.88907	−	5.13211i	−0.469147	−	0.270862i	−0.715883	+	0.698221i	$0.753975\pi$
$360$		0			0
$361$	−9.24493	−	16.0127i	−0.486575	−	0.842773i
$362$		0			0
$363$		−	0.656306i		−	0.0344471i
$364$		0			0
$365$		−	4.50031i		−	0.235557i
$366$		0			0
$367$	9.27079	+	16.0575i	0.483931	+	0.838194i	0.999830	−	0.0184562i	$-0.00587511\pi$
$367$	9.27079	+	16.0575i	0.483931	+	0.838194i	−0.515898	+	0.856650i	$0.672542\pi$
$368$		0			0
$369$	1.29692	+	0.748779i	0.0675151	+	0.0389799i
$370$		0			0
$371$	−4.55632	+	4.81197i	−0.236552	+	0.249825i
$372$		0			0
$373$	23.0707	+	13.3199i	1.19456	+	0.689677i	0.959336	−	0.282266i	$-0.0910860\pi$
$373$	23.0707	+	13.3199i	1.19456	+	0.689677i	0.235219	+	0.971942i	$0.424419\pi$
$374$		0			0
$375$	2.66758	−	1.54013i	0.137753	−	0.0795317i
$376$		0			0
$377$		−	20.4642i		−	1.05396i
$378$		0			0
$379$	24.7032			1.26892			0.634459	−	0.772956i	$-0.281223\pi$
$379$	24.7032			1.26892			0.634459	+	0.772956i	$0.281223\pi$
$380$		0			0
$381$	−25.3546	−	43.9155i	−1.29896	−	2.24986i
$382$		0			0
$383$	−9.52490	+	16.4976i	−0.486700	+	0.842989i	−0.999883	−	0.0152904i	$-0.995133\pi$
$383$	−9.52490	+	16.4976i	−0.486700	+	0.842989i	0.513183	+	0.858279i	$0.328466\pi$
$384$		0			0
$385$	8.32900	−	2.47716i	0.424485	−	0.126248i
$386$		0			0
$387$	−32.6446	+	56.5421i	−1.65942	+	2.87420i
$388$		0			0
$389$	26.6121	−	15.3645i	1.34929	−	0.779010i	0.361137	−	0.932513i	$-0.382389\pi$
$389$	26.6121	−	15.3645i	1.34929	−	0.779010i	0.988148	+	0.153502i	$0.0490553\pi$
$390$		0			0
$391$	−4.84507			−0.245026
$392$		0			0
$393$	1.58753			0.0800803
$394$		0			0
$395$	9.66655	−	5.58099i	0.486377	−	0.280810i
$396$		0			0
$397$	−14.3388	+	24.8356i	−0.719646	+	1.24646i	0.241494	+	0.970402i	$0.422363\pi$
$397$	−14.3388	+	24.8356i	−0.719646	+	1.24646i	−0.961140	+	0.276061i	$0.910971\pi$
$398$		0			0
$399$	−5.57921	+	1.65933i	−0.279310	+	0.0830705i
$400$		0			0
$401$	−3.59148	+	6.22063i	−0.179350	+	0.310643i	−0.941658	−	0.336571i	$-0.890733\pi$
$401$	−3.59148	+	6.22063i	−0.179350	+	0.310643i	0.762308	+	0.647214i	$0.224066\pi$
$402$		0			0
$403$	−0.225603	−	0.390755i	−0.0112381	−	0.0194649i
$404$		0			0
$405$	13.6296			0.677262
$406$		0			0
$407$		−	1.89142i		−	0.0937543i
$408$		0			0
$409$	−13.5732	+	7.83652i	−0.671154	+	0.387491i	−0.796514	−	0.604620i	$-0.793325\pi$
$409$	−13.5732	+	7.83652i	−0.671154	+	0.387491i	0.125360	+	0.992111i	$0.459991\pi$
$410$		0			0
$411$	22.5220	+	13.0031i	1.11093	+	0.641395i
$412$		0			0
$413$	2.07200	−	2.18826i	0.101956	−	0.107677i
$414$		0			0
$415$	2.81006	+	1.62239i	0.137941	+	0.0796401i
$416$		0			0
$417$	29.4222	+	50.9607i	1.44081	+	2.49556i
$418$		0			0
$419$		−	36.8405i		−	1.79978i	−0.436122	−	0.899888i	$-0.643648\pi$
$419$		−	36.8405i		−	1.79978i	0.436122	−	0.899888i	$-0.356352\pi$
$420$		0			0
$421$		−	8.37624i		−	0.408233i	−0.978947	−	0.204116i	$-0.934568\pi$
$421$		−	8.37624i		−	0.408233i	0.978947	−	0.204116i	$-0.0654321\pi$
$422$		0			0
$423$	−27.4701	−	47.5796i	−1.33564	−	2.31340i
$424$		0			0
$425$	−3.32426	−	1.91926i	−0.161250	−	0.0930979i
$426$		0			0
$427$	0.109307	−	0.457517i	0.00528972	−	0.0221408i
$428$		0			0
$429$	58.8824	+	33.9958i	2.84287	+	1.64133i
$430$		0			0
$431$	20.5648	−	11.8731i	0.990570	−	0.571906i	0.0851256	−	0.996370i	$-0.472871\pi$
$431$	20.5648	−	11.8731i	0.990570	−	0.571906i	0.905445	+	0.424464i	$0.139538\pi$
$432$		0			0
$433$			6.49599i			0.312177i	0.987743	+	0.156089i	$0.0498885\pi$
$433$			6.49599i			0.312177i	−0.987743	+	0.156089i	$0.950111\pi$
$434$		0			0
$435$	9.37909			0.449693
$436$		0			0
$437$	−0.450763	−	0.780744i	−0.0215629	−	0.0373481i
$438$		0			0
$439$	−11.0256	+	19.0969i	−0.526223	+	0.911444i	0.473311	+	0.880896i	$0.343059\pi$
$439$	−11.0256	+	19.0969i	−0.526223	+	0.911444i	−0.999533	+	0.0305486i	$0.990275\pi$
$440$		0			0
$441$	−2.47689	−	45.3480i	−0.117947	−	2.15943i
$442$		0			0
$443$	2.81959	−	4.88367i	0.133963	−	0.232030i	−0.791238	−	0.611508i	$-0.790563\pi$
$443$	2.81959	−	4.88367i	0.133963	−	0.232030i	0.925201	+	0.379478i	$0.123896\pi$
$444$		0			0
$445$	13.3148	−	7.68732i	0.631183	−	0.364414i
$446$		0			0
$447$	−20.0644			−0.949015
$448$		0			0
$449$	16.7623			0.791063			0.395531	−	0.918452i	$-0.370560\pi$
$449$	16.7623			0.791063			0.395531	+	0.918452i	$0.370560\pi$
$450$		0			0
$451$	−0.656532	+	0.379049i	−0.0309149	+	0.0178487i
$452$		0			0
$453$	−11.0091	+	19.0684i	−0.517254	+	0.895910i
$454$		0			0
$455$	4.13194	−	17.2948i	0.193709	−	0.810792i
$456$		0			0
$457$	−7.58737	+	13.1417i	−0.354922	+	0.614744i	−0.987105	−	0.160076i	$-0.948826\pi$
$457$	−7.58737	+	13.1417i	−0.354922	+	0.614744i	0.632182	+	0.774820i	$0.282159\pi$
$458$		0			0
$459$	−20.6201	−	35.7150i	−0.962463	−	1.66704i
$460$		0			0
$461$	−28.7740			−1.34014			−0.670070	−	0.742298i	$-0.733736\pi$
$461$	−28.7740			−1.34014			−0.670070	+	0.742298i	$0.733736\pi$
$462$		0			0
$463$			34.4369i			1.60042i	0.599720	+	0.800210i	$0.295279\pi$
$463$			34.4369i			1.60042i	−0.599720	+	0.800210i	$0.704721\pi$
$464$		0			0
$465$	0.179090	−	0.103398i	0.00830510	−	0.00479495i
$466$		0			0
$467$	−15.9360	−	9.20065i	−0.737430	−	0.425755i	0.0837042	−	0.996491i	$-0.473325\pi$
$467$	−15.9360	−	9.20065i	−0.737430	−	0.425755i	−0.821134	+	0.570735i	$0.806658\pi$
$468$		0			0
$469$	−26.6246	−	25.2100i	−1.22941	−	1.16409i
$470$		0			0
$471$	61.7136	+	35.6304i	2.84361	+	1.64176i
$472$		0			0
$473$	−16.5254	−	28.6229i	−0.759840	−	1.31608i
$474$		0			0
$475$		−	0.714238i		−	0.0327715i
$476$		0			0
$477$		−	16.2505i		−	0.744057i
$478$		0			0
$479$	11.9755	+	20.7422i	0.547175	+	0.947735i	0.998467	+	0.0553583i	$0.0176301\pi$
$479$	11.9755	+	20.7422i	0.547175	+	0.947735i	−0.451292	+	0.892377i	$0.649037\pi$
$480$		0			0
$481$	−3.35189	−	1.93521i	−0.152833	−	0.0882382i
$482$		0			0
$483$	9.85974	−	2.93242i	0.448634	−	0.133430i
$484$		0			0
$485$	−4.99311	−	2.88277i	−0.226726	−	0.130900i
$486$		0			0
$487$	21.5404	−	12.4364i	0.976089	−	0.563545i	0.0750017	−	0.997183i	$-0.476104\pi$
$487$	21.5404	−	12.4364i	0.976089	−	0.563545i	0.901087	+	0.433638i	$0.142770\pi$
$488$		0			0
$489$		−	2.55915i		−	0.115729i
$490$		0			0
$491$	14.2945			0.645102			0.322551	−	0.946552i	$-0.395460\pi$
$491$	14.2945			0.645102			0.322551	+	0.946552i	$0.395460\pi$
$492$		0			0
$493$	−5.84398	−	10.1221i	−0.263200	−	0.455875i
$494$		0			0
$495$	−10.6543	+	18.4538i	−0.478877	+	0.829439i
$496$		0			0
$497$	−9.10508	−	30.6142i	−0.408419	−	1.37324i
$498$		0			0
$499$	−0.248745	+	0.430838i	−0.0111353	+	0.0192870i	−0.871539	−	0.490326i	$-0.836878\pi$
$499$	−0.248745	+	0.430838i	−0.0111353	+	0.0192870i	0.860404	+	0.509612i	$0.170211\pi$
$500$		0			0
$501$	9.60274	−	5.54414i	0.429019	−	0.247694i
$502$		0			0
$503$	14.1052			0.628918			0.314459	−	0.949271i	$-0.398177\pi$
$503$	14.1052			0.628918			0.314459	+	0.949271i	$0.398177\pi$
$504$		0			0
$505$	−11.3170			−0.503602
$506$		0			0
$507$	85.8130	−	49.5441i	3.81109	−	2.20033i
$508$		0			0
$509$	−13.9373	+	24.1401i	−0.617760	+	1.06999i	0.372133	+	0.928179i	$0.378626\pi$
$509$	−13.9373	+	24.1401i	−0.617760	+	1.06999i	−0.989894	+	0.141813i	$0.954707\pi$
$510$		0			0
$511$	8.18651	−	8.64586i	0.362150	−	0.382470i
$512$		0			0
$513$	3.83680	−	6.64553i	0.169399	−	0.293407i
$514$		0			0
$515$	−0.346486	−	0.600132i	−0.0152680	−	0.0264450i
$516$		0			0
$517$	27.8120			1.22317
$518$		0			0
$519$			32.5785i			1.43004i
$520$		0			0
$521$	14.0644	−	8.12006i	0.616171	−	0.355746i	−0.159206	−	0.987245i	$-0.550893\pi$
$521$	14.0644	−	8.12006i	0.616171	−	0.355746i	0.775377	+	0.631499i	$0.217560\pi$
$522$		0			0
$523$	3.56646	+	2.05910i	0.155950	+	0.0900380i	0.575944	−	0.817489i	$-0.304634\pi$
$523$	3.56646	+	2.05910i	0.155950	+	0.0900380i	−0.419994	+	0.907527i	$0.637968\pi$
$524$		0			0
$525$	7.92650	+	1.89374i	0.345941	+	0.0826497i
$526$		0			0
$527$	−0.223177	−	0.128851i	−0.00972175	−	0.00561285i
$528$		0			0
$529$	−10.7034	−	18.5388i	−0.465365	−	0.806036i
$530$		0			0
$531$			7.38993i			0.320696i
$532$		0			0
$533$			1.55130i			0.0671943i
$534$		0			0
$535$	−2.55924	−	4.43274i	−0.110646	−	0.191644i
$536$		0			0
$537$	−49.8335	−	28.7714i	−2.15047	−	1.24158i
$538$		0			0
$539$	20.5076	+	10.3922i	0.883324	+	0.447625i
$540$		0			0
$541$	5.94834	+	3.43428i	0.255739	+	0.147651i	0.622389	−	0.782708i	$-0.286162\pi$
$541$	5.94834	+	3.43428i	0.255739	+	0.147651i	−0.366650	+	0.930359i	$0.619495\pi$
$542$		0			0
$543$	−46.2106	+	26.6797i	−1.98309	+	1.14494i
$544$		0			0
$545$		−	12.2540i		−	0.524902i
$546$		0			0
$547$	25.9783			1.11075			0.555376	−	0.831599i	$-0.312574\pi$
$547$	25.9783			1.11075			0.555376	+	0.831599i	$0.312574\pi$
$548$		0			0
$549$	0.576753	+	0.998965i	0.0246152	+	0.0426348i
$550$		0			0
$551$	1.08740	−	1.88342i	0.0463246	−	0.0802365i
$552$		0			0
$553$	28.7234	+	6.86239i	1.22144	+	0.291819i
$554$		0			0
$555$	0.886943	−	1.53623i	0.0376486	−	0.0652093i
$556$		0			0
$557$	6.50339	−	3.75473i	0.275557	−	0.159093i	−0.355853	−	0.934542i	$-0.615810\pi$
$557$	6.50339	−	3.75473i	0.275557	−	0.159093i	0.631410	+	0.775449i	$0.282476\pi$
$558$		0			0
$559$	−67.6322			−2.86054
$560$		0			0
$561$	38.8329			1.63953
$562$		0			0
$563$	−25.3072	+	14.6111i	−1.06657	+	0.615786i	−0.927243	−	0.374460i	$-0.877828\pi$
$563$	−25.3072	+	14.6111i	−1.06657	+	0.615786i	−0.139329	+	0.990246i	$0.544495\pi$
$564$		0			0
$565$	3.29176	−	5.70150i	0.138486	−	0.239864i
$566$		0			0
$567$	26.1848	+	24.7936i	1.09966	+	1.04123i
$568$		0			0
$569$	21.0499	−	36.4596i	0.882460	−	1.52847i	0.0338620	−	0.999427i	$-0.489219\pi$
$569$	21.0499	−	36.4596i	0.882460	−	1.52847i	0.848598	−	0.529039i	$-0.177447\pi$
$570$		0			0
$571$	13.3062	+	23.0470i	0.556846	+	0.964485i	0.997757	+	0.0669348i	$0.0213219\pi$
$571$	13.3062	+	23.0470i	0.556846	+	0.964485i	−0.440911	+	0.897551i	$0.645345\pi$
$572$		0			0
$573$	−25.8279			−1.07897
$574$		0			0
$575$			1.26222i			0.0526382i
$576$		0			0
$577$	25.7918	−	14.8909i	1.07373	−	0.619916i	0.144528	−	0.989501i	$-0.453833\pi$
$577$	25.7918	−	14.8909i	1.07373	−	0.619916i	0.929197	+	0.369585i	$0.120500\pi$
$578$		0			0
$579$	23.0712	+	13.3202i	0.958808	+	0.553568i
$580$		0			0
$581$	2.44732	+	8.22867i	0.101532	+	0.341383i
$582$		0			0
$583$	7.12423	+	4.11317i	0.295055	+	0.170350i
$584$		0			0
$585$	21.8020	+	37.7622i	0.901403	+	1.56128i
$586$		0			0
$587$		−	25.4403i		−	1.05003i	−0.851092	−	0.525017i	$-0.824059\pi$
$587$		−	25.4403i		−	1.05003i	0.851092	−	0.525017i	$-0.175941\pi$
$588$		0			0
$589$		−	0.0479510i		−	0.00197579i
$590$		0			0
$591$	−14.9442	−	25.8841i	−0.614721	−	1.06473i
$592$		0			0
$593$	−12.1719	−	7.02748i	−0.499842	−	0.288584i	0.228806	−	0.973472i	$-0.426518\pi$
$593$	−12.1719	−	7.02748i	−0.499842	−	0.288584i	−0.728648	+	0.684888i	$0.759851\pi$
$594$		0			0
$595$	−2.89513	−	9.73438i	−0.118689	−	0.399071i
$596$		0			0
$597$	1.01060	+	0.583471i	0.0413612	+	0.0238799i
$598$		0			0
$599$	−5.81502	+	3.35730i	−0.237595	+	0.137176i	−0.614071	−	0.789251i	$-0.710469\pi$
$599$	−5.81502	+	3.35730i	−0.237595	+	0.137176i	0.376476	+	0.926426i	$0.377136\pi$
$600$		0			0
$601$			2.72540i			0.111171i	0.998454	+	0.0555856i	$0.0177026\pi$
$601$			2.72540i			0.111171i	−0.998454	+	0.0555856i	$0.982297\pi$
$602$		0			0
$603$	89.9135			3.66156
$604$		0			0
$605$	0.106534	+	0.184523i	0.00433124	+	0.00750193i
$606$		0			0
$607$	16.0138	−	27.7367i	0.649979	−	1.12580i	−0.333148	−	0.942875i	$-0.608111\pi$
$607$	16.0138	−	27.7367i	0.649979	−	1.12580i	0.983127	−	0.182923i	$-0.0585559\pi$
$608$		0			0
$609$	18.0188	+	17.0615i	0.730159	+	0.691366i
$610$		0			0
$611$	28.4559	−	49.2871i	1.15120	−	1.99394i
$612$		0			0
$613$	26.3757	−	15.2280i	1.06530	−	0.615054i	0.138410	−	0.990375i	$-0.455801\pi$
$613$	26.3757	−	15.2280i	1.06530	−	0.615054i	0.926895	+	0.375321i	$0.122468\pi$
$614$		0			0
$615$	−0.710988			−0.0286698
$616$		0			0
$617$	25.2200			1.01532			0.507660	−	0.861557i	$-0.330511\pi$
$617$	25.2200			1.01532			0.507660	+	0.861557i	$0.330511\pi$
$618$		0			0
$619$	−1.07430	+	0.620250i	−0.0431800	+	0.0249300i	−0.521435	−	0.853291i	$-0.674603\pi$
$619$	−1.07430	+	0.620250i	−0.0431800	+	0.0249300i	0.478255	+	0.878221i	$0.341270\pi$
$620$		0			0
$621$	−6.78050	+	11.7442i	−0.272092	+	0.471277i
$622$		0			0
$623$	39.5640	+	9.45235i	1.58510	+	0.378700i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	3.61283	+	6.25761i	0.144283	+	0.249905i
$628$		0			0
$629$	−2.21057			−0.0881411
$630$		0			0
$631$			8.73486i			0.347729i	0.984770	+	0.173865i	$0.0556255\pi$
$631$			8.73486i			0.347729i	−0.984770	+	0.173865i	$0.944374\pi$
$632$		0			0
$633$	−3.13620	+	1.81069i	−0.124653	+	0.0719683i
$634$		0			0
$635$	14.2571	+	8.23136i	0.565777	+	0.326651i
$636$		0			0
$637$	39.3990	−	25.7098i	1.56105	−	1.01866i
$638$		0			0
$639$	67.8293	+	39.1613i	2.68329	+	1.54920i
$640$		0			0
$641$	10.1834	+	17.6382i	0.402220	+	0.696665i	0.993994	−	0.109439i	$-0.0349054\pi$
$641$	10.1834	+	17.6382i	0.402220	+	0.696665i	−0.591774	+	0.806104i	$0.701572\pi$
$642$		0			0
$643$		−	20.9423i		−	0.825884i	−0.910757	−	0.412942i	$-0.864501\pi$
$643$		−	20.9423i		−	0.825884i	0.910757	−	0.412942i	$-0.135499\pi$
$644$		0			0
$645$		−	30.9970i		−	1.22051i
$646$		0			0
$647$	9.88308	+	17.1180i	0.388544	+	0.672978i	0.992254	−	0.124226i	$-0.0396448\pi$
$647$	9.88308	+	17.1180i	0.388544	+	0.672978i	−0.603710	+	0.797204i	$0.706311\pi$
$648$		0			0
$649$	−3.23976	−	1.87048i	−0.127172	−	0.0734226i
$650$		0			0
$651$	0.532152	+	0.127138i	0.0208567	+	0.00498293i
$652$		0			0
$653$	33.9904	+	19.6243i	1.33015	+	0.767960i	0.985322	−	0.170708i	$-0.0546054\pi$
$653$	33.9904	+	19.6243i	1.33015	+	0.767960i	0.344824	+	0.938667i	$0.387939\pi$
$654$		0			0
$655$	−0.446341	+	0.257695i	−0.0174400	+	0.0100690i
$656$		0			0
$657$			29.1978i			1.13911i
$658$		0			0
$659$	−43.0875			−1.67845			−0.839225	−	0.543785i	$-0.816991\pi$
$659$	−43.0875			−1.67845			−0.839225	+	0.543785i	$0.816991\pi$
$660$		0			0
$661$	4.37780	+	7.58258i	0.170277	+	0.294928i	0.938517	−	0.345234i	$-0.112200\pi$
$661$	4.37780	+	7.58258i	0.170277	+	0.294928i	−0.768240	+	0.640162i	$0.778867\pi$
$662$		0			0
$663$	39.7320	−	68.8178i	1.54306	−	2.67266i
$664$		0			0
$665$	1.29927	−	1.37217i	0.0503835	−	0.0532105i
$666$		0			0
$667$	−1.92167	+	3.32844i	−0.0744076	+	0.128878i
$668$		0			0
$669$	−21.2858	+	12.2894i	−0.822956	+	0.475134i
$670$		0			0
$671$	−0.583931			−0.0225424
$672$		0			0
$673$	−13.0780			−0.504121			−0.252060	−	0.967712i	$-0.581108\pi$
$673$	−13.0780			−0.504121			−0.252060	+	0.967712i	$0.581108\pi$
$674$		0			0
$675$	−9.30437	+	5.37188i	−0.358125	+	0.206764i
$676$		0			0
$677$	−13.8738	+	24.0302i	−0.533215	+	0.923555i	0.466033	+	0.884767i	$0.345683\pi$
$677$	−13.8738	+	24.0302i	−0.533215	+	0.923555i	−0.999247	+	0.0387876i	$0.987650\pi$
$678$		0			0
$679$	−4.34855	−	14.6212i	−0.166882	−	0.561112i
$680$		0			0
$681$	9.63849	−	16.6944i	0.369348	−	0.639729i
$682$		0			0
$683$	−23.1088	−	40.0257i	−0.884235	−	1.53154i	−0.846587	−	0.532250i	$-0.821347\pi$
$683$	−23.1088	−	40.0257i	−0.884235	−	1.53154i	−0.0376480	−	0.999291i	$-0.511987\pi$
$684$		0			0
$685$	−8.44288			−0.322586
$686$		0			0
$687$		−	42.9626i		−	1.63913i
$688$		0			0
$689$	14.5784	−	8.41682i	0.555391	−	0.320655i
$690$		0			0
$691$	13.6210	+	7.86409i	0.518167	+	0.299164i	0.736184	−	0.676781i	$-0.236626\pi$
$691$	13.6210	+	7.86409i	0.518167	+	0.299164i	−0.218017	+	0.975945i	$0.569959\pi$
$692$		0			0
$693$	−54.0381	+	16.0717i	−2.05274	+	0.610512i
$694$		0			0
$695$	−16.5443	−	9.55187i	−0.627562	−	0.362323i
$696$		0			0
$697$	0.443007	+	0.767311i	0.0167801	+	0.0290640i
$698$		0			0
$699$			0.171218i			0.00647607i
$700$		0			0
$701$			36.4270i			1.37583i	0.725792	+	0.687914i	$0.241474\pi$
$701$			36.4270i			1.37583i	−0.725792	+	0.687914i	$0.758526\pi$
$702$		0			0
$703$	−0.205661	−	0.356216i	−0.00775666	−	0.0134349i
$704$		0			0
$705$	22.5891	+	13.0418i	0.850756	+	0.491184i
$706$		0			0
$707$	−21.7419	−	20.5868i	−0.817690	−	0.774247i
$708$		0			0
$709$	−28.0338	−	16.1853i	−1.05283	−	0.607853i	−0.129391	−	0.991594i	$-0.541302\pi$
$709$	−28.0338	−	16.1853i	−1.05283	−	0.607853i	−0.923441	+	0.383741i	$0.874636\pi$
$710$		0			0
$711$	−62.7161	+	36.2091i	−2.35204	+	1.35795i
$712$		0			0
$713$			0.0847403i			0.00317355i
$714$		0			0
$715$	−22.0734			−0.825497
$716$		0			0
$717$	−12.1799	−	21.0962i	−0.454868	−	0.787854i
$718$		0			0
$719$	0.853166	−	1.47773i	0.0318177	−	0.0551099i	−0.849678	−	0.527302i	$-0.823204\pi$
$719$	0.853166	−	1.47773i	0.0318177	−	0.0551099i	0.881496	+	0.472192i	$0.156537\pi$
$720$		0			0
$721$	0.426040	−	1.78325i	0.0158666	−	0.0664116i
$722$		0			0
$723$	−20.6683	+	35.7985i	−0.768662	+	1.33136i
$724$		0			0
$725$	−2.63697	+	1.52246i	−0.0979346	+	0.0565426i
$726$		0			0
$727$	−13.8129			−0.512293			−0.256146	−	0.966638i	$-0.582453\pi$
$727$	−13.8129			−0.512293			−0.256146	+	0.966638i	$0.582453\pi$
$728$		0			0
$729$	10.8521			0.401930
$730$		0			0
$731$	−33.4525	+	19.3138i	−1.23729	+	0.714347i
$732$		0			0
$733$	−17.7219	+	30.6952i	−0.654574	+	1.13375i	0.327427	+	0.944876i	$0.393818\pi$
$733$	−17.7219	+	30.6952i	−0.654574	+	1.13375i	−0.982001	+	0.188878i	$0.939515\pi$
$734$		0			0
$735$	11.7832	+	18.0573i	0.434631	+	0.666052i
$736$		0			0
$737$	−22.7581	+	39.4182i	−0.838307	+	1.45199i
$738$		0			0
$739$	−14.3056	−	24.7780i	−0.526240	−	0.911474i	−0.999533	−	0.0305688i	$-0.990268\pi$
$739$	−14.3056	−	24.7780i	−0.526240	−	0.911474i	0.473293	−	0.880905i	$-0.343065\pi$
$740$		0			0
$741$	14.7859			0.543175
$742$		0			0
$743$		−	21.9551i		−	0.805456i	−0.915320	−	0.402728i	$-0.868062\pi$
$743$		−	21.9551i		−	0.805456i	0.915320	−	0.402728i	$-0.131938\pi$
$744$		0			0
$745$	5.64120	−	3.25695i	0.206678	−	0.119325i
$746$		0			0
$747$	−18.2316	−	10.5260i	−0.667058	−	0.385126i
$748$		0			0
$749$	3.14685	−	13.1715i	0.114983	−	0.481277i
$750$		0			0
$751$	−2.09527	−	1.20971i	−0.0764576	−	0.0441428i	0.461284	−	0.887253i	$-0.347389\pi$
$751$	−2.09527	−	1.20971i	−0.0764576	−	0.0441428i	−0.537741	+	0.843110i	$0.680722\pi$
$752$		0			0
$753$	−28.3363	−	49.0799i	−1.03263	−	1.78857i
$754$		0			0
$755$		−	7.14820i		−	0.260150i
$756$		0			0
$757$			12.1295i			0.440854i	0.975403	+	0.220427i	$0.0707451\pi$
$757$			12.1295i			0.440854i	−0.975403	+	0.220427i	$0.929255\pi$
$758$		0			0
$759$	−6.38470	−	11.0586i	−0.231750	−	0.401403i
$760$		0			0
$761$	−28.8033	−	16.6296i	−1.04412	−	0.602823i	−0.123122	−	0.992392i	$-0.539291\pi$
$761$	−28.8033	−	16.6296i	−1.04412	−	0.602823i	−0.920997	+	0.389569i	$0.872624\pi$
$762$		0			0
$763$	22.2911	−	23.5419i	0.806994	−	0.852274i
$764$		0			0
$765$	21.5676	+	12.4521i	0.779779	+	0.450206i
$766$		0			0
$767$	−6.62954	+	3.82757i	−0.239379	+	0.138205i
$768$		0			0
$769$		−	32.8673i		−	1.18523i	−0.805487	−	0.592613i	$-0.798096\pi$
$769$		−	32.8673i		−	1.18523i	0.805487	−	0.592613i	$-0.201904\pi$
$770$		0			0
$771$	−92.1529			−3.31881
$772$		0			0
$773$	13.9148	+	24.1011i	0.500480	+	0.866857i	1.00000		0.000554379i	$0.000176464\pi$
$773$	13.9148	+	24.1011i	0.500480	+	0.866857i	−0.499520	+	0.866302i	$0.666490\pi$
$774$		0			0
$775$	−0.0335679	+	0.0581414i	−0.00120580	+	0.00208850i
$776$		0			0
$777$	4.49852	−	1.33792i	0.161383	−	0.0479976i
$778$		0			0
$779$	−0.0824307	+	0.142774i	−0.00295339	+	0.00511542i
$780$		0			0
$781$	−34.3368	+	19.8243i	−1.22867	+	0.709370i
$782$		0			0
$783$	−32.7138			−1.16910
$784$		0			0
$785$	−23.1347			−0.825713
$786$		0			0
$787$	6.78734	−	3.91867i	0.241943	−	0.139686i	−0.374127	−	0.927378i	$-0.622057\pi$
$787$	6.78734	−	3.91867i	0.241943	−	0.139686i	0.616069	+	0.787692i	$0.288724\pi$
$788$		0			0
$789$	30.7868	−	53.3244i	1.09604	−	1.89840i
$790$		0			0
$791$	16.6956	−	4.96550i	0.593628	−	0.176553i
$792$		0			0
$793$	−0.597451	+	1.03482i	−0.0212161	+	0.0367474i
$794$		0			0
$795$	3.85757	+	6.68151i	0.136814	+	0.236969i
$796$		0			0
$797$	9.03418			0.320007			0.160004	−	0.987116i	$-0.448849\pi$
$797$	9.03418			0.320007			0.160004	+	0.987116i	$0.448849\pi$
$798$		0			0
$799$		−	32.5048i		−	1.14994i
$800$		0			0
$801$	−86.3859	+	49.8749i	−3.05230	+	1.76224i
$802$		0			0
$803$	−12.8004	−	7.39029i	−0.451715	−	0.260798i
$804$		0			0
$805$	−2.29610	+	2.42494i	−0.0809270	+	0.0854678i
$806$		0			0
$807$	−63.5644	−	36.6989i	−2.23757	−	1.29186i
$808$		0			0
$809$	4.13014	+	7.15361i	0.145208	+	0.251508i	0.929451	−	0.368947i	$-0.120282\pi$
$809$	4.13014	+	7.15361i	0.145208	+	0.251508i	−0.784243	+	0.620454i	$0.786948\pi$
$810$		0			0
$811$		−	4.89216i		−	0.171787i	−0.996304	−	0.0858936i	$-0.972626\pi$
$811$		−	4.89216i		−	0.171787i	0.996304	−	0.0858936i	$-0.0273745\pi$
$812$		0			0
$813$		−	61.2543i		−	2.14828i
$814$		0			0
$815$	0.415413	+	0.719516i	0.0145513	+	0.0252035i
$816$		0			0
$817$	−6.22454	−	3.59374i	−0.217769	−	0.125729i
$818$		0			0
$819$	−26.8078	+	112.208i	−0.936742	+	3.92085i
$820$		0			0
$821$	34.9611	+	20.1848i	1.22015	+	0.704455i	0.964950	−	0.262433i	$-0.0845248\pi$
$821$	34.9611	+	20.1848i	1.22015	+	0.704455i	0.255202	+	0.966888i	$0.417858\pi$
$822$		0			0
$823$	32.0112	−	18.4817i	1.11584	−	0.644231i	0.175505	−	0.984479i	$-0.443844\pi$
$823$	32.0112	−	18.4817i	1.11584	−	0.644231i	0.940336	+	0.340247i	$0.110511\pi$
$824$		0			0
$825$		−	10.1166i		−	0.352215i
$826$		0			0
$827$	−34.0217			−1.18305			−0.591526	−	0.806286i	$-0.701474\pi$
$827$	−34.0217			−1.18305			−0.591526	+	0.806286i	$0.701474\pi$
$828$		0			0
$829$	−5.83499	−	10.1065i	−0.202657	−	0.351013i	0.746726	−	0.665131i	$-0.231624\pi$
$829$	−5.83499	−	10.1065i	−0.202657	−	0.351013i	−0.949384	+	0.314118i	$0.898291\pi$
$830$		0			0
$831$	−30.4656	+	52.7680i	−1.05684	+	1.83050i
$832$		0			0
$833$	12.1457	−	23.9679i	0.420825	−	0.830439i
$834$		0			0
$835$	−1.79990	+	3.11752i	−0.0622881	+	0.107886i
$836$		0			0
$837$	−0.624657	+	0.360646i	−0.0215913	+	0.0124657i
$838$		0			0
$839$	29.7543			1.02723			0.513616	−	0.858020i	$-0.328306\pi$
$839$	29.7543			1.02723			0.513616	+	0.858020i	$0.328306\pi$
$840$		0			0
$841$	19.7285			0.680294
$842$		0			0
$843$	−26.4462	+	15.2687i	−0.910855	+	0.525883i
$844$		0			0
$845$	−16.0844	+	27.8591i	−0.553322	+	0.958382i
$846$		0			0
$847$	−0.130995	+	0.548296i	−0.00450104	+	0.0188397i
$848$		0			0
$849$	−41.5268	+	71.9265i	−1.42520	+	2.46851i
$850$		0			0
$851$	0.363450	+	0.629514i	0.0124589	+	0.0215795i
$852$		0			0
$853$	−11.5473			−0.395370			−0.197685	−	0.980266i	$-0.563342\pi$
$853$	−11.5473			−0.395370			−0.197685	+	0.980266i	$0.563342\pi$
$854$		0			0
$855$			4.63394i			0.158477i
$856$		0			0
$857$	29.7816	−	17.1944i	1.01732	−	0.587350i	0.103994	−	0.994578i	$-0.466838\pi$
$857$	29.7816	−	17.1944i	1.01732	−	0.587350i	0.913327	+	0.407228i	$0.133505\pi$
$858$		0			0
$859$	4.47750	+	2.58509i	0.152770	+	0.0882020i	0.574436	−	0.818549i	$-0.305221\pi$
$859$	4.47750	+	2.58509i	0.152770	+	0.0882020i	−0.421666	+	0.906751i	$0.638555\pi$
$860$		0			0
$861$	−1.36593	−	1.29336i	−0.0465507	−	0.0440775i
$862$		0			0
$863$	−24.4172	−	14.0973i	−0.831172	−	0.479878i	0.0230816	−	0.999734i	$-0.492652\pi$
$863$	−24.4172	−	14.0973i	−0.831172	−	0.479878i	−0.854254	+	0.519856i	$0.825986\pi$
$864$		0			0
$865$	−5.28828	−	9.15958i	−0.179807	−	0.311435i
$866$		0			0
$867$			6.97900i			0.237019i
$868$		0			0
$869$		−	36.6598i		−	1.24360i
$870$		0			0
$871$	46.5701	+	80.6618i	1.57797	+	2.73312i
$872$		0			0
$873$	32.3950	+	18.7033i	1.09641	+	0.633010i
$874$		0			0
$875$	−2.53597	+	0.754231i	−0.0857314	+	0.0254977i
$876$		0			0
$877$	3.75181	+	2.16611i	0.126690	+	0.0731443i	0.562005	−	0.827133i	$-0.310030\pi$
$877$	3.75181	+	2.16611i	0.126690	+	0.0731443i	−0.435316	+	0.900278i	$0.643363\pi$
$878$		0			0
$879$	−5.46415	+	3.15473i	−0.184301	+	0.106406i
$880$		0			0
$881$		−	4.70606i		−	0.158551i	−0.996853	−	0.0792757i	$-0.974739\pi$
$881$		−	4.70606i		−	0.158551i	0.996853	−	0.0792757i	$-0.0252607\pi$
$882$		0			0
$883$	18.9412			0.637424			0.318712	−	0.947852i	$-0.396750\pi$
$883$	18.9412			0.637424			0.318712	+	0.947852i	$0.396750\pi$
$884$		0			0
$885$	−1.75424	−	3.03844i	−0.0589682	−	0.102136i
$886$		0			0
$887$	−16.6634	+	28.8618i	−0.559501	+	0.969085i	0.438037	+	0.898957i	$0.355674\pi$
$887$	−16.6634	+	28.8618i	−0.559501	+	0.969085i	−0.997538	+	0.0701277i	$0.977659\pi$
$888$		0			0
$889$	12.4167	+	41.7489i	0.416442	+	1.40021i
$890$		0			0
$891$	22.3822	−	38.7671i	0.749832	−	1.29875i
$892$		0			0
$893$	5.23789	−	3.02410i	0.175279	−	0.101198i
$894$		0			0
$895$	18.6812			0.624443
$896$		0			0
$897$	−26.1301			−0.872459
$898$		0			0
$899$	−0.177035	+	0.102211i	−0.00590446	+	0.00340894i
$900$		0			0
$901$	4.80720	−	8.32632i	0.160151	−	0.277390i
$902$		0			0
$903$	56.3866	−	59.5505i	1.87643	−	1.98172i
$904$		0			0
$905$	8.66153	−	15.0022i	0.287919	−	0.498690i
$906$		0			0
$907$	22.7638	+	39.4281i	0.755861	+	1.30919i	0.944945	+	0.327228i	$0.106115\pi$
$907$	22.7638	+	39.4281i	0.755861	+	1.30919i	−0.189085	+	0.981961i	$0.560552\pi$
$908$		0			0
$909$	73.4244			2.43533
$910$		0			0
$911$		−	9.10038i		−	0.301509i	−0.988571	−	0.150755i	$-0.951830\pi$
$911$		−	9.10038i		−	0.301509i	0.988571	−	0.150755i	$-0.0481703\pi$
$912$		0			0
$913$	9.22922	−	5.32850i	0.305443	−	0.176347i
$914$		0			0
$915$	−0.474274	−	0.273822i	−0.0156790	−	0.00905228i
$916$		0			0
$917$	−1.32627	−	0.316862i	−0.0437972	−	0.0104637i
$918$		0			0
$919$	−21.5543	−	12.4444i	−0.711010	−	0.410502i	0.100425	−	0.994945i	$-0.467980\pi$
$919$	−21.5543	−	12.4444i	−0.711010	−	0.410502i	−0.811435	+	0.584443i	$0.801313\pi$
$920$		0			0
$921$	11.6925	+	20.2519i	0.385280	+	0.667324i
$922$		0			0
$923$			81.1333i			2.67054i
$924$		0			0
$925$			0.575890i			0.0189351i
$926$		0			0
$927$	2.24799	+	3.89362i	0.0738335	+	0.127883i
$928$		0			0
$929$	35.0593	+	20.2415i	1.15026	+	0.664102i	0.948950	−	0.315426i	$-0.102147\pi$
$929$	35.0593	+	20.2415i	1.15026	+	0.664102i	0.201308	+	0.979528i	$0.435481\pi$
$930$		0			0
$931$	4.99222	−	0.272673i	0.163614	−	0.00893648i
$932$		0			0
$933$	−47.1700	−	27.2336i	−1.54428	−	0.891589i
$934$		0			0
$935$	−10.9180	+	6.30352i	−0.357058	+	0.206147i
$936$		0			0
$937$			33.0886i			1.08096i	0.841358	+	0.540478i	$0.181757\pi$
$937$			33.0886i			1.08096i	−0.841358	+	0.540478i	$0.818243\pi$
$938$		0			0
$939$	41.0959			1.34111
$940$		0			0
$941$	12.0677	+	20.9019i	0.393396	+	0.681382i	0.992895	−	0.118994i	$-0.0379668\pi$
$941$	12.0677	+	20.9019i	0.393396	+	0.681382i	−0.599499	+	0.800375i	$0.704633\pi$
$942$		0			0
$943$	0.145674	−	0.252314i	0.00474379	−	0.00821649i
$944$		0			0
$945$	−27.6472	−	6.60527i	−0.899364	−	0.214870i
$946$		0			0
$947$	18.7287	−	32.4390i	0.608600	−	1.05413i	−0.382871	−	0.923802i	$-0.625065\pi$
$947$	18.7287	−	32.4390i	0.608600	−	1.05413i	0.991471	−	0.130325i	$-0.0416021\pi$
$948$		0			0
$949$	−26.1935	+	15.1228i	−0.850276	+	0.490907i
$950$		0			0
$951$	3.69652			0.119868
$952$		0			0
$953$	−13.4036			−0.434185			−0.217092	−	0.976151i	$-0.569657\pi$
$953$	−13.4036			−0.434185			−0.217092	+	0.976151i	$0.569657\pi$
$954$		0			0
$955$	7.26161	−	4.19249i	0.234980	−	0.135666i
$956$		0			0
$957$	15.4021	−	26.6772i	0.497879	−	0.862352i
$958$		0			0
$959$	−16.2202	−	15.3584i	−0.523777	−	0.495949i
$960$		0			0
$961$	15.4977	−	26.8429i	0.499927	−	0.865899i
$962$		0			0
$963$	16.6042	+	28.7594i	0.535064	+	0.926757i
$964$		0			0
$965$	−8.64877			−0.278414
$966$		0			0
$967$		−	16.1690i		−	0.519959i	−0.965614	−	0.259980i	$-0.916284\pi$
$967$		−	16.1690i		−	0.519959i	0.965614	−	0.259980i	$-0.0837158\pi$
$968$		0			0
$969$	7.31348	−	4.22244i	0.234943	−	0.135644i
$970$		0			0
$971$	−11.2868	−	6.51641i	−0.362209	−	0.209122i	0.307840	−	0.951438i	$-0.400394\pi$
$971$	−11.2868	−	6.51641i	−0.362209	−	0.209122i	−0.670049	+	0.742316i	$0.733727\pi$
$972$		0			0
$973$	−14.4086	−	48.4465i	−0.461920	−	1.55312i
$974$		0			0
$975$	−17.9282	−	10.3508i	−0.574162	−	0.331492i
$976$		0			0
$977$	5.75357	+	9.96548i	0.184073	+	0.318824i	0.943264	−	0.332044i	$-0.107738\pi$
$977$	5.75357	+	9.96548i	0.184073	+	0.318824i	−0.759191	+	0.650868i	$0.774405\pi$
$978$		0			0
$979$		−	50.4956i		−	1.61385i
$980$		0			0
$981$			79.5030i			2.53834i
$982$		0			0
$983$	6.41950	+	11.1189i	0.204750	+	0.354638i	0.950053	−	0.312088i	$-0.101028\pi$
$983$	6.41950	+	11.1189i	0.204750	+	0.354638i	−0.745303	+	0.666726i	$0.767695\pi$
$984$		0			0
$985$	8.40323	+	4.85161i	0.267749	+	0.154585i
$986$		0			0
$987$	19.6731	+	66.1474i	0.626202	+	2.10550i
$988$		0			0
$989$	11.0002	+	6.35096i	0.349785	+	0.201949i
$990$		0			0
$991$	21.2549	−	12.2715i	0.675183	−	0.389817i	−0.122854	−	0.992425i	$-0.539205\pi$
$991$	21.2549	−	12.2715i	0.675183	−	0.389817i	0.798038	+	0.602607i	$0.205871\pi$
$992$		0			0
$993$		−	18.5623i		−	0.589058i
$994$		0			0
$995$	−0.378846			−0.0120102
$996$		0			0
$997$	20.2325	+	35.0437i	0.640769	+	1.10984i	0.985262	+	0.171055i	$0.0547175\pi$
$997$	20.2325	+	35.0437i	0.640769	+	1.10984i	−0.344493	+	0.938789i	$0.611949\pi$
$998$		0			0
$999$	−3.09361	+	5.35829i	−0.0978775	+	0.169529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bz.e.271.12		24
4.3	odd	2		280.2.bj.f.131.6	yes	24
7.3	odd	6		1120.2.bz.f.591.12		24
8.3	odd	2		1120.2.bz.f.271.12		24
8.5	even	2		280.2.bj.e.131.10	✓	24
28.3	even	6		280.2.bj.e.171.10	yes	24
56.3	even	6	inner	1120.2.bz.e.591.12		24
56.45	odd	6		280.2.bj.f.171.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.10	✓	24	8.5	even	2
280.2.bj.e.171.10	yes	24	28.3	even	6
280.2.bj.f.131.6	yes	24	4.3	odd	2
280.2.bj.f.171.6	yes	24	56.45	odd	6
1120.2.bz.e.271.12		24	1.1	even	1	trivial
1120.2.bz.e.591.12		24	56.3	even	6	inner
1120.2.bz.f.271.12		24	8.3	odd	2
1120.2.bz.f.591.12		24	7.3	odd	6

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:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bz (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.66758 - 1.54013i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.53597 + 0.754231i) q^{7} +(3.24397 - 5.61873i) q^{9} +O(q^{10})\)	\(q+(2.66758 - 1.54013i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.53597 + 0.754231i) q^{7} +(3.24397 - 5.61873i) q^{9} +(1.64217 + 2.84433i) q^{11} +6.72078 q^{13} +3.08025i q^{15} +(3.32426 - 1.91926i) q^{17} +(0.618548 + 0.357119i) q^{19} +(-5.60328 + 5.91768i) q^{21} +(-1.09312 - 0.631110i) q^{23} +(-0.500000 - 0.866025i) q^{25} -10.7438i q^{27} -3.04491i q^{29} +(-0.0335679 - 0.0581414i) q^{31} +(8.76124 + 5.05831i) q^{33} +(0.614801 - 2.57333i) q^{35} +(-0.498735 - 0.287945i) q^{37} +(17.9282 - 10.3508i) q^{39} +0.230821i q^{41} -10.0631 q^{43} +(3.24397 + 5.61873i) q^{45} +(4.23402 - 7.33354i) q^{47} +(5.86227 - 3.82541i) q^{49} +(5.91181 - 10.2396i) q^{51} +(2.16915 - 1.25236i) q^{53} -3.28435 q^{55} +2.20003 q^{57} +(-0.986424 + 0.569512i) q^{59} +(-0.0888960 + 0.153972i) q^{61} +(-3.98880 + 16.6956i) q^{63} +(-3.36039 + 5.82037i) q^{65} +(6.92927 + 12.0019i) q^{67} -3.88796 q^{69} +12.0720i q^{71} +(-3.89739 + 2.25016i) q^{73} +(-2.66758 - 1.54013i) q^{75} +(-6.30978 - 5.97455i) q^{77} +(-9.66655 - 5.58099i) q^{79} +(-6.81481 - 11.8036i) q^{81} -3.24478i q^{83} +3.83853i q^{85} +(-4.68955 - 8.12253i) q^{87} +(-13.3148 - 7.68732i) q^{89} +(-17.0437 + 5.06902i) q^{91} +(-0.179090 - 0.103398i) q^{93} +(-0.618548 + 0.357119i) q^{95} +5.76555i q^{97} +21.3087 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9}+O(q^{10}) \) 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9	\( 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9} - 8 q^{11} + 20 q^{13} + 6 q^{17} - 18 q^{19} - 26 q^{21} - 18 q^{23} - 12 q^{25} + 6 q^{31} + 12 q^{33} + 8 q^{35} + 18 q^{39} - 32 q^{43} + 12 q^{45} + 8 q^{49} + 22 q^{51} + 30 q^{53} + 16 q^{55} - 44 q^{57} + 18 q^{59} + 22 q^{61} + 12 q^{63} - 10 q^{65} + 8 q^{67} - 12 q^{69} + 30 q^{73} + 12 q^{75} - 32 q^{77} - 6 q^{79} - 4 q^{81} - 14 q^{87} - 60 q^{89} - 18 q^{91} - 18 q^{93} + 18 q^{95} + 56 q^{99}+O(q^{100}) \) 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9 - 8 * q^11 + 20 * q^13 + 6 * q^17 - 18 * q^19 - 26 * q^21 - 18 * q^23 - 12 * q^25 + 6 * q^31 + 12 * q^33 + 8 * q^35 + 18 * q^39 - 32 * q^43 + 12 * q^45 + 8 * q^49 + 22 * q^51 + 30 * q^53 + 16 * q^55 - 44 * q^57 + 18 * q^59 + 22 * q^61 + 12 * q^63 - 10 * q^65 + 8 * q^67 - 12 * q^69 + 30 * q^73 + 12 * q^75 - 32 * q^77 - 6 * q^79 - 4 * q^81 - 14 * q^87 - 60 * q^89 - 18 * q^91 - 18 * q^93 + 18 * q^95 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more