LMFDB - Embedded newform 1320.2.bw.b.1081.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1320,2,Mod(361,1320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1320, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 6]))

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

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

chi := DirichletCharacter("1320.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1320.bw (of order $5$, degree $4$, 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:	$10.5402530668$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1081.1
Root			$1.69513 + 1.23158i$ of defining polynomial
Character	$\chi$	$=$	1320.1081
Dual form			1320.2.bw.b.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.591149 + 1.81937i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.591149 + 1.81937i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(0.105203 - 3.31496i) q^{11} +(-2.22004 + 1.61295i) q^{13} +(0.309017 - 0.951057i) q^{15} +(-2.58124 - 1.87538i) q^{17} +(-0.756830 - 2.32928i) q^{19} -1.91300 q^{21} -7.03640 q^{23} +(0.309017 + 0.951057i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(0.0488697 - 0.150406i) q^{29} +(3.62218 - 2.63167i) q^{31} +(3.18522 - 0.924324i) q^{33} +(1.54765 - 1.12443i) q^{35} +(0.179491 - 0.552416i) q^{37} +(-2.22004 - 1.61295i) q^{39} +(0.608520 + 1.87283i) q^{41} -6.80467 q^{43} +1.00000 q^{45} +(-3.69473 - 11.3712i) q^{47} +(2.70248 + 1.96346i) q^{49} +(0.985946 - 3.03443i) q^{51} +(-2.89282 + 2.10176i) q^{53} +(-2.03359 + 2.62002i) q^{55} +(1.98141 - 1.43958i) q^{57} +(3.49143 - 10.7455i) q^{59} +(-6.77164 - 4.91988i) q^{61} +(-0.591149 - 1.81937i) q^{63} +2.74411 q^{65} -10.9347 q^{67} +(-2.17437 - 6.69201i) q^{69} +(2.55499 + 1.85631i) q^{71} +(1.00256 - 3.08557i) q^{73} +(-0.809017 + 0.587785i) q^{75} +(5.96893 + 2.15103i) q^{77} +(-10.8899 + 7.91195i) q^{79} +(0.309017 - 0.951057i) q^{81} +(5.76295 + 4.18703i) q^{83} +(0.985946 + 3.03443i) q^{85} +0.158146 q^{87} -0.802777 q^{89} +(-1.62218 - 4.99255i) q^{91} +(3.62218 + 2.63167i) q^{93} +(-0.756830 + 2.32928i) q^{95} +(2.74259 - 1.99261i) q^{97} +(1.86337 + 2.74369i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 2 q^{5} - 5 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 - 2 * q^5 - 5 * q^7 - 2 * q^9	$ 8 q - 2 q^{3} - 2 q^{5} - 5 q^{7} - 2 q^{9} + 3 q^{11} + 6 q^{13} - 2 q^{15} - 4 q^{17} + 10 q^{19} - 30 q^{23} - 2 q^{25} - 2 q^{27} + 6 q^{29} + 5 q^{31} - 2 q^{33} + 5 q^{35} + 19 q^{37} + 6 q^{39} + 13 q^{41} - 8 q^{43} + 8 q^{45} + 15 q^{47} + 13 q^{49} + 6 q^{51} - 17 q^{53} - 7 q^{55} - 5 q^{57} + 13 q^{59} - 31 q^{61} - 5 q^{63} + 6 q^{65} - 42 q^{67} - 5 q^{69} + 15 q^{71} + 23 q^{73} - 2 q^{75} - 5 q^{77} - 32 q^{79} - 2 q^{81} + 19 q^{83} + 6 q^{85} + 6 q^{87} - 24 q^{89} + 11 q^{91} + 5 q^{93} + 10 q^{95} + 27 q^{97} + 3 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 - 2 * q^5 - 5 * q^7 - 2 * q^9 + 3 * q^11 + 6 * q^13 - 2 * q^15 - 4 * q^17 + 10 * q^19 - 30 * q^23 - 2 * q^25 - 2 * q^27 + 6 * q^29 + 5 * q^31 - 2 * q^33 + 5 * q^35 + 19 * q^37 + 6 * q^39 + 13 * q^41 - 8 * q^43 + 8 * q^45 + 15 * q^47 + 13 * q^49 + 6 * q^51 - 17 * q^53 - 7 * q^55 - 5 * q^57 + 13 * q^59 - 31 * q^61 - 5 * q^63 + 6 * q^65 - 42 * q^67 - 5 * q^69 + 15 * q^71 + 23 * q^73 - 2 * q^75 - 5 * q^77 - 32 * q^79 - 2 * q^81 + 19 * q^83 + 6 * q^85 + 6 * q^87 - 24 * q^89 + 11 * q^91 + 5 * q^93 + 10 * q^95 + 27 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$		0			0
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	−0.591149	+	1.81937i	−0.223433	+	0.687657i	0.775014	+	0.631944i	$0.217743\pi$
$7$	−0.591149	+	1.81937i	−0.223433	+	0.687657i	−0.998447	+	0.0557121i	$0.982257\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	0.105203	−	3.31496i	0.0317198	−	0.999497i
$11$	0.105203	−	3.31496i	0.0317198	−	0.999497i
$12$		0			0
$13$	−2.22004	+	1.61295i	−0.615727	+	0.447352i	−0.851426	−	0.524474i	$-0.824262\pi$
$13$	−2.22004	+	1.61295i	−0.615727	+	0.447352i	0.235699	+	0.971826i	$0.424262\pi$
$14$		0			0
$15$	0.309017	−	0.951057i	0.0797878	−	0.245562i
$16$		0			0
$17$	−2.58124	−	1.87538i	−0.626043	−	0.454847i	0.228984	−	0.973430i	$-0.426460\pi$
$17$	−2.58124	−	1.87538i	−0.626043	−	0.454847i	−0.855027	+	0.518584i	$0.826460\pi$
$18$		0			0
$19$	−0.756830	−	2.32928i	−0.173629	−	0.534374i	0.825940	−	0.563759i	$-0.190645\pi$
$19$	−0.756830	−	2.32928i	−0.173629	−	0.534374i	−0.999568	+	0.0293848i	$0.990645\pi$
$20$		0			0
$21$	−1.91300			−0.417450
$22$		0			0
$23$	−7.03640			−1.46719			−0.733595	−	0.679587i	$-0.762159\pi$
$23$	−7.03640			−1.46719			−0.733595	+	0.679587i	$0.762159\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$		0			0
$29$	0.0488697	−	0.150406i	0.00907488	−	0.0279296i	−0.946417	−	0.322948i	$-0.895326\pi$
$29$	0.0488697	−	0.150406i	0.00907488	−	0.0279296i	0.955491	+	0.295019i	$0.0953259\pi$
$30$		0			0
$31$	3.62218	−	2.63167i	0.650563	−	0.472661i	−0.212900	−	0.977074i	$-0.568291\pi$
$31$	3.62218	−	2.63167i	0.650563	−	0.472661i	0.863463	+	0.504413i	$0.168291\pi$
$32$		0			0
$33$	3.18522	−	0.924324i	0.554476	−	0.160904i
$34$		0			0
$35$	1.54765	−	1.12443i	0.261600	−	0.190064i
$36$		0			0
$37$	0.179491	−	0.552416i	0.0295081	−	0.0908167i	−0.935218	−	0.354073i	$-0.884796\pi$
$37$	0.179491	−	0.552416i	0.0295081	−	0.0908167i	0.964726	+	0.263256i	$0.0847965\pi$
$38$		0			0
$39$	−2.22004	−	1.61295i	−0.355490	−	0.258279i
$40$		0			0
$41$	0.608520	+	1.87283i	0.0950349	+	0.292487i	0.987263	−	0.159098i	$-0.0508586\pi$
$41$	0.608520	+	1.87283i	0.0950349	+	0.292487i	−0.892228	+	0.451585i	$0.850859\pi$
$42$		0			0
$43$	−6.80467			−1.03770			−0.518851	−	0.854865i	$-0.673640\pi$
$43$	−6.80467			−1.03770			−0.518851	+	0.854865i	$0.673640\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	−3.69473	−	11.3712i	−0.538932	−	1.65866i	−0.734996	−	0.678072i	$-0.762816\pi$
$47$	−3.69473	−	11.3712i	−0.538932	−	1.65866i	0.196063	−	0.980591i	$-0.437184\pi$
$48$		0			0
$49$	2.70248	+	1.96346i	0.386068	+	0.280495i
$50$		0			0
$51$	0.985946	−	3.03443i	0.138060	−	0.424905i
$52$		0			0
$53$	−2.89282	+	2.10176i	−0.397359	+	0.288698i	−0.768465	−	0.639892i	$-0.778979\pi$
$53$	−2.89282	+	2.10176i	−0.397359	+	0.288698i	0.371105	+	0.928591i	$0.378979\pi$
$54$		0			0
$55$	−2.03359	+	2.62002i	−0.274210	+	0.353283i
$56$		0			0
$57$	1.98141	−	1.43958i	0.262444	−	0.190676i
$58$		0			0
$59$	3.49143	−	10.7455i	0.454546	−	1.39895i	−0.417122	−	0.908850i	$-0.636961\pi$
$59$	3.49143	−	10.7455i	0.454546	−	1.39895i	0.871668	−	0.490097i	$-0.163039\pi$
$60$		0			0
$61$	−6.77164	−	4.91988i	−0.867020	−	0.629927i	0.0627660	−	0.998028i	$-0.480008\pi$
$61$	−6.77164	−	4.91988i	−0.867020	−	0.629927i	−0.929786	+	0.368102i	$0.880008\pi$
$62$		0			0
$63$	−0.591149	−	1.81937i	−0.0744777	−	0.229219i
$64$		0			0
$65$	2.74411			0.340366
$66$		0			0
$67$	−10.9347			−1.33589			−0.667943	−	0.744212i	$-0.732825\pi$
$67$	−10.9347			−1.33589			−0.667943	+	0.744212i	$0.732825\pi$
$68$		0			0
$69$	−2.17437	−	6.69201i	−0.261763	−	0.805624i
$70$		0			0
$71$	2.55499	+	1.85631i	0.303222	+	0.220304i	0.728983	−	0.684532i	$-0.239993\pi$
$71$	2.55499	+	1.85631i	0.303222	+	0.220304i	−0.425761	+	0.904836i	$0.639993\pi$
$72$		0			0
$73$	1.00256	−	3.08557i	0.117341	−	0.361138i	−0.875087	−	0.483965i	$-0.839196\pi$
$73$	1.00256	−	3.08557i	0.117341	−	0.361138i	0.992428	+	0.122827i	$0.0391960\pi$
$74$		0			0
$75$	−0.809017	+	0.587785i	−0.0934172	+	0.0678716i
$76$		0			0
$77$	5.96893	+	2.15103i	0.680223	+	0.245133i
$78$		0			0
$79$	−10.8899	+	7.91195i	−1.22521	+	0.890164i	−0.996521	−	0.0833371i	$-0.973442\pi$
$79$	−10.8899	+	7.91195i	−1.22521	+	0.890164i	−0.228684	+	0.973501i	$0.573442\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	5.76295	+	4.18703i	0.632566	+	0.459586i	0.857288	−	0.514837i	$-0.172147\pi$
$83$	5.76295	+	4.18703i	0.632566	+	0.459586i	−0.224722	+	0.974423i	$0.572147\pi$
$84$		0			0
$85$	0.985946	+	3.03443i	0.106941	+	0.329130i
$86$		0			0
$87$	0.158146			0.0169550
$88$		0			0
$89$	−0.802777			−0.0850941			−0.0425471	−	0.999094i	$-0.513547\pi$
$89$	−0.802777			−0.0850941			−0.0425471	+	0.999094i	$0.513547\pi$
$90$		0			0
$91$	−1.62218	−	4.99255i	−0.170051	−	0.523362i
$92$		0			0
$93$	3.62218	+	2.63167i	0.375603	+	0.272891i
$94$		0			0
$95$	−0.756830	+	2.32928i	−0.0776491	+	0.238979i
$96$		0			0
$97$	2.74259	−	1.99261i	0.278468	−	0.202318i	−0.439781	−	0.898105i	$-0.644944\pi$
$97$	2.74259	−	1.99261i	0.278468	−	0.202318i	0.718249	+	0.695786i	$0.244944\pi$
$98$		0			0
$99$	1.86337	+	2.74369i	0.187276	+	0.275751i
$100$		0			0
$101$	6.60965	−	4.80219i	0.657685	−	0.477836i	−0.208195	−	0.978087i	$-0.566759\pi$
$101$	6.60965	−	4.80219i	0.657685	−	0.477836i	0.865880	+	0.500251i	$0.166759\pi$
$102$		0			0
$103$	−4.54808	+	13.9975i	−0.448136	+	1.37922i	0.430873	+	0.902413i	$0.358206\pi$
$103$	−4.54808	+	13.9975i	−0.448136	+	1.37922i	−0.879008	+	0.476807i	$0.841794\pi$
$104$		0			0
$105$	1.54765	+	1.12443i	0.151035	+	0.109733i
$106$		0			0
$107$	−5.51832	−	16.9836i	−0.533476	−	1.64187i	−0.746920	−	0.664914i	$-0.768468\pi$
$107$	−5.51832	−	16.9836i	−0.533476	−	1.64187i	0.213444	−	0.976955i	$-0.431532\pi$
$108$		0			0
$109$	0.104375			0.00999731			0.00499865	−	0.999988i	$-0.498409\pi$
$109$	0.104375			0.00999731			0.00499865	+	0.999988i	$0.498409\pi$
$110$		0			0
$111$	0.580845			0.0551314
$112$		0			0
$113$	−1.49866	−	4.61240i	−0.140982	−	0.433898i	0.855490	−	0.517819i	$-0.173256\pi$
$113$	−1.49866	−	4.61240i	−0.140982	−	0.433898i	−0.996472	+	0.0839204i	$0.973256\pi$
$114$		0			0
$115$	5.69257	+	4.13589i	0.530835	+	0.385674i
$116$		0			0
$117$	0.847978	−	2.60981i	0.0783956	−	0.241277i
$118$		0			0
$119$	4.93790	−	3.58760i	0.452657	−	0.328874i
$120$		0			0
$121$	−10.9779	−	0.697484i	−0.997988	−	0.0634077i
$122$		0			0
$123$	−1.59313	+	1.15747i	−0.143647	+	0.104366i
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	−5.56359	−	4.04218i	−0.493689	−	0.358686i	0.312912	−	0.949782i	$-0.398695\pi$
$127$	−5.56359	−	4.04218i	−0.493689	−	0.358686i	−0.806601	+	0.591096i	$0.798695\pi$
$128$		0			0
$129$	−2.10276	−	6.47162i	−0.185137	−	0.569794i
$130$		0			0
$131$	−11.8217			−1.03286			−0.516432	−	0.856328i	$-0.672740\pi$
$131$	−11.8217			−1.03286			−0.516432	+	0.856328i	$0.672740\pi$
$132$		0			0
$133$	4.68522			0.406260
$134$		0			0
$135$	0.309017	+	0.951057i	0.0265959	+	0.0818539i
$136$		0			0
$137$	5.58218	+	4.05569i	0.476918	+	0.346501i	0.800131	−	0.599825i	$-0.204763\pi$
$137$	5.58218	+	4.05569i	0.476918	+	0.346501i	−0.323213	+	0.946326i	$0.604763\pi$
$138$		0			0
$139$	0.287500	−	0.884833i	0.0243854	−	0.0750506i	−0.938123	−	0.346302i	$-0.887437\pi$
$139$	0.287500	−	0.884833i	0.0243854	−	0.0750506i	0.962509	+	0.271251i	$0.0874374\pi$
$140$		0			0
$141$	9.67294	−	7.02780i	0.814608	−	0.591848i
$142$		0			0
$143$	5.11330	+	7.52901i	0.427596	+	0.629607i
$144$		0			0
$145$	−0.127943	+	0.0929558i	−0.0106251	+	0.00771956i
$146$		0			0
$147$	−1.03225	+	3.17695i	−0.0851388	+	0.262030i
$148$		0			0
$149$	13.6413	+	9.91100i	1.11754	+	0.811941i	0.983834	−	0.179080i	$-0.0573121\pi$
$149$	13.6413	+	9.91100i	1.11754	+	0.811941i	0.133706	+	0.991021i	$0.457312\pi$
$150$		0			0
$151$	2.77774	+	8.54901i	0.226049	+	0.695709i	0.998183	+	0.0602488i	$0.0191894\pi$
$151$	2.77774	+	8.54901i	0.226049	+	0.695709i	−0.772134	+	0.635460i	$0.780811\pi$
$152$		0			0
$153$	3.19059			0.257944
$154$		0			0
$155$	−4.47726			−0.359622
$156$		0			0
$157$	0.393647	+	1.21152i	0.0314164	+	0.0966898i	0.965535	−	0.260273i	$-0.0838124\pi$
$157$	0.393647	+	1.21152i	0.0314164	+	0.0966898i	−0.934119	+	0.356962i	$0.883812\pi$
$158$		0			0
$159$	−2.89282	−	2.10176i	−0.229415	−	0.166680i
$160$		0			0
$161$	4.15956	−	12.8018i	0.327819	−	1.00892i
$162$		0			0
$163$	9.45808	−	6.87170i	0.740814	−	0.538233i	−0.152152	−	0.988357i	$-0.548620\pi$
$163$	9.45808	−	6.87170i	0.740814	−	0.538233i	0.892966	+	0.450124i	$0.148620\pi$
$164$		0			0
$165$	−3.12020	−	1.12443i	−0.242907	−	0.0875369i
$166$		0			0
$167$	−20.2372	+	14.7032i	−1.56600	+	1.13776i	−0.635134	+	0.772402i	$0.719055\pi$
$167$	−20.2372	+	14.7032i	−1.56600	+	1.13776i	−0.930865	+	0.365363i	$0.880945\pi$
$168$		0			0
$169$	−1.69027	+	5.20212i	−0.130021	+	0.400163i
$170$		0			0
$171$	1.98141	+	1.43958i	0.151522	+	0.110087i
$172$		0			0
$173$	7.52451	+	23.1581i	0.572078	+	1.76068i	0.645920	+	0.763405i	$0.276474\pi$
$173$	7.52451	+	23.1581i	0.572078	+	1.76068i	−0.0738418	+	0.997270i	$0.523526\pi$
$174$		0			0
$175$	−1.91300			−0.144609
$176$		0			0
$177$	11.2985			0.849248
$178$		0			0
$179$	−4.55399	−	14.0158i	−0.340381	−	1.04759i	−0.964010	−	0.265866i	$-0.914342\pi$
$179$	−4.55399	−	14.0158i	−0.340381	−	1.04759i	0.623629	−	0.781721i	$-0.285658\pi$
$180$		0			0
$181$	6.55563	+	4.76295i	0.487276	+	0.354027i	0.804136	−	0.594445i	$-0.202628\pi$
$181$	6.55563	+	4.76295i	0.487276	+	0.354027i	−0.316860	+	0.948472i	$0.602628\pi$
$182$		0			0
$183$	2.58654	−	7.96054i	0.191202	−	0.588460i
$184$		0			0
$185$	−0.469913	+	0.341412i	−0.0345487	+	0.0251011i
$186$		0			0
$187$	−6.48836	+	8.35940i	−0.474476	+	0.611300i
$188$		0			0
$189$	1.54765	−	1.12443i	0.112575	−	0.0817903i
$190$		0			0
$191$	4.95523	−	15.2506i	0.358548	−	1.10350i	−0.595376	−	0.803447i	$-0.702997\pi$
$191$	4.95523	−	15.2506i	0.358548	−	1.10350i	0.953924	−	0.300050i	$-0.0970032\pi$
$192$		0			0
$193$	7.81731	+	5.67961i	0.562702	+	0.408827i	0.832447	−	0.554105i	$-0.186939\pi$
$193$	7.81731	+	5.67961i	0.562702	+	0.408827i	−0.269745	+	0.962932i	$0.586939\pi$
$194$		0			0
$195$	0.847978	+	2.60981i	0.0607250	+	0.186892i
$196$		0			0
$197$	2.21474			0.157794			0.0788968	−	0.996883i	$-0.474860\pi$
$197$	2.21474			0.157794			0.0788968	+	0.996883i	$0.474860\pi$
$198$		0			0
$199$	−17.8737			−1.26704			−0.633518	−	0.773728i	$-0.718390\pi$
$199$	−17.8737			−1.26704			−0.633518	+	0.773728i	$0.718390\pi$
$200$		0			0
$201$	−3.37901	−	10.3995i	−0.238337	−	0.733526i
$202$		0			0
$203$	0.244754	+	0.177824i	0.0171784	+	0.0124808i
$204$		0			0
$205$	0.608520	−	1.87283i	0.0425009	−	0.130804i
$206$		0			0
$207$	5.69257	−	4.13589i	0.395661	−	0.287464i
$208$		0			0
$209$	−7.80109	+	2.26381i	−0.539612	+	0.156591i
$210$		0			0
$211$	12.9154	−	9.38359i	0.889133	−	0.645993i	−0.0465185	−	0.998917i	$-0.514813\pi$
$211$	12.9154	−	9.38359i	0.889133	−	0.645993i	0.935652	+	0.352924i	$0.114813\pi$
$212$		0			0
$213$	−0.975921	+	3.00358i	−0.0668690	+	0.205802i
$214$		0			0
$215$	5.50509	+	3.99968i	0.375444	+	0.272776i
$216$		0			0
$217$	2.64673	+	8.14578i	0.179671	+	0.552972i
$218$		0			0
$219$	3.24436			0.219233
$220$		0			0
$221$	8.75534			0.588948
$222$		0			0
$223$	5.29212	+	16.2875i	0.354387	+	1.09069i	0.956364	+	0.292177i	$0.0943797\pi$
$223$	5.29212	+	16.2875i	0.354387	+	1.09069i	−0.601977	+	0.798513i	$0.705620\pi$
$224$		0			0
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$		0			0
$227$	6.36968	−	19.6039i	0.422771	−	1.30115i	−0.482342	−	0.875983i	$-0.660214\pi$
$227$	6.36968	−	19.6039i	0.422771	−	1.30115i	0.905113	−	0.425172i	$-0.139786\pi$
$228$		0			0
$229$	−11.0729	+	8.04494i	−0.731719	+	0.531625i	−0.890107	−	0.455752i	$-0.849370\pi$
$229$	−11.0729	+	8.04494i	−0.731719	+	0.531625i	0.158388	+	0.987377i	$0.449370\pi$
$230$		0			0
$231$	−0.201252	+	6.34150i	−0.0132414	+	0.417240i
$232$		0			0
$233$	−7.32590	+	5.32258i	−0.479936	+	0.348694i	−0.801301	−	0.598262i	$-0.795858\pi$
$233$	−7.32590	+	5.32258i	−0.479936	+	0.348694i	0.321365	+	0.946955i	$0.395858\pi$
$234$		0			0
$235$	−3.69473	+	11.3712i	−0.241018	+	0.741777i
$236$		0			0
$237$	−10.8899	−	7.91195i	−0.707373	−	0.513936i
$238$		0			0
$239$	3.29374	+	10.1371i	0.213054	+	0.655714i	0.999286	+	0.0377820i	$0.0120292\pi$
$239$	3.29374	+	10.1371i	0.213054	+	0.655714i	−0.786232	+	0.617932i	$0.787971\pi$
$240$		0			0
$241$	−16.5958			−1.06903			−0.534514	−	0.845160i	$-0.679505\pi$
$241$	−16.5958			−1.06903			−0.534514	+	0.845160i	$0.679505\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−1.03225	−	3.17695i	−0.0659483	−	0.202968i
$246$		0			0
$247$	5.43720	+	3.95036i	0.345961	+	0.251355i
$248$		0			0
$249$	−2.20125	+	6.77476i	−0.139499	+	0.429333i
$250$		0			0
$251$	−3.35742	+	2.43931i	−0.211918	+	0.153968i	−0.688681	−	0.725064i	$-0.741810\pi$
$251$	−3.35742	+	2.43931i	−0.211918	+	0.153968i	0.476763	+	0.879032i	$0.341810\pi$
$252$		0			0
$253$	−0.740248	+	23.3254i	−0.0465390	+	1.46645i
$254$		0			0
$255$	−2.58124	+	1.87538i	−0.161644	+	0.117441i
$256$		0			0
$257$	−1.88023	+	5.78676i	−0.117286	+	0.360968i	−0.992417	−	0.122918i	$-0.960775\pi$
$257$	−1.88023	+	5.78676i	−0.117286	+	0.360968i	0.875131	+	0.483886i	$0.160775\pi$
$258$		0			0
$259$	0.898943	+	0.653120i	0.0558576	+	0.0405829i
$260$		0			0
$261$	0.0488697	+	0.150406i	0.00302496	+	0.00930987i
$262$		0			0
$263$	−13.5369			−0.834720			−0.417360	−	0.908741i	$-0.637045\pi$
$263$	−13.5369			−0.834720			−0.417360	+	0.908741i	$0.637045\pi$
$264$		0			0
$265$	3.57572			0.219655
$266$		0			0
$267$	−0.248072	−	0.763486i	−0.0151817	−	0.0467246i
$268$		0			0
$269$	13.3939	+	9.73125i	0.816642	+	0.593325i	0.915749	−	0.401752i	$-0.131599\pi$
$269$	13.3939	+	9.73125i	0.816642	+	0.593325i	−0.0991070	+	0.995077i	$0.531599\pi$
$270$		0			0
$271$	−4.41200	+	13.5787i	−0.268010	+	0.824849i	0.722975	+	0.690874i	$0.242774\pi$
$271$	−4.41200	+	13.5787i	−0.268010	+	0.824849i	−0.990985	+	0.133975i	$0.957226\pi$
$272$		0			0
$273$	4.24692	−	3.08557i	0.257035	−	0.186747i
$274$		0			0
$275$	3.18522	−	0.924324i	0.192076	−	0.0557388i
$276$		0			0
$277$	4.92227	−	3.57624i	0.295750	−	0.214875i	−0.430008	−	0.902825i	$-0.641489\pi$
$277$	4.92227	−	3.57624i	0.295750	−	0.214875i	0.725758	+	0.687950i	$0.241489\pi$
$278$		0			0
$279$	−1.38355	+	4.25813i	−0.0828309	+	0.254927i
$280$		0			0
$281$	−0.0411281	−	0.0298813i	−0.00245349	−	0.00178257i	0.586558	−	0.809907i	$-0.300483\pi$
$281$	−0.0411281	−	0.0298813i	−0.00245349	−	0.00178257i	−0.589011	+	0.808125i	$0.700483\pi$
$282$		0			0
$283$	5.56423	+	17.1249i	0.330759	+	1.01797i	0.968774	+	0.247947i	$0.0797560\pi$
$283$	5.56423	+	17.1249i	0.330759	+	1.01797i	−0.638014	+	0.770024i	$0.720244\pi$
$284$		0			0
$285$	−2.44915			−0.145075
$286$		0			0
$287$	−3.76710			−0.222365
$288$		0			0
$289$	−2.10754	−	6.48635i	−0.123973	−	0.381550i
$290$		0			0
$291$	2.74259	+	1.99261i	0.160773	+	0.116809i
$292$		0			0
$293$	−8.23511	+	25.3450i	−0.481100	+	1.48067i	0.356451	+	0.934314i	$0.383987\pi$
$293$	−8.23511	+	25.3450i	−0.481100	+	1.48067i	−0.837551	+	0.546359i	$0.816013\pi$
$294$		0			0
$295$	−9.14068	+	6.64110i	−0.532191	+	0.386660i
$296$		0			0
$297$	−2.03359	+	2.62002i	−0.118001	+	0.152029i
$298$		0			0
$299$	15.6211	−	11.3494i	0.903389	−	0.656350i
$300$		0			0
$301$	4.02257	−	12.3802i	0.231857	−	0.713582i
$302$		0			0
$303$	6.60965	+	4.80219i	0.379715	+	0.275879i
$304$		0			0
$305$	2.58654	+	7.96054i	0.148105	+	0.455819i
$306$		0			0
$307$	3.54633			0.202400			0.101200	−	0.994866i	$-0.467732\pi$
$307$	3.54633			0.202400			0.101200	+	0.994866i	$0.467732\pi$
$308$		0			0
$309$	−14.7179			−0.837272
$310$		0			0
$311$	0.362499	+	1.11566i	0.0205554	+	0.0632632i	0.960808	−	0.277214i	$-0.0894112\pi$
$311$	0.362499	+	1.11566i	0.0205554	+	0.0632632i	−0.940253	+	0.340478i	$0.889411\pi$
$312$		0			0
$313$	−7.66849	−	5.57148i	−0.433449	−	0.314919i	0.349578	−	0.936907i	$-0.386325\pi$
$313$	−7.66849	−	5.57148i	−0.433449	−	0.314919i	−0.783026	+	0.621989i	$0.786325\pi$
$314$		0			0
$315$	−0.591149	+	1.81937i	−0.0333074	+	0.102510i
$316$		0			0
$317$	15.4029	−	11.1908i	0.865112	−	0.628541i	−0.0641589	−	0.997940i	$-0.520436\pi$
$317$	15.4029	−	11.1908i	0.865112	−	0.628541i	0.929271	+	0.369399i	$0.120436\pi$
$318$		0			0
$319$	−0.493447	−	0.177824i	−0.0276277	−	0.00995624i
$320$		0			0
$321$	14.4471	−	10.4965i	0.806361	−	0.585855i
$322$		0			0
$323$	−2.41473	+	7.43178i	−0.134359	+	0.413515i
$324$		0			0
$325$	−2.22004	−	1.61295i	−0.123145	−	0.0894704i
$326$		0			0
$327$	0.0322536	+	0.0992665i	0.00178363	+	0.00548945i
$328$		0			0
$329$	22.8726			1.26101
$330$		0			0
$331$	10.9490			0.601811			0.300905	−	0.953654i	$-0.402711\pi$
$331$	10.9490			0.601811			0.300905	+	0.953654i	$0.402711\pi$
$332$		0			0
$333$	0.179491	+	0.552416i	0.00983604	+	0.0302722i
$334$		0			0
$335$	8.84636	+	6.42726i	0.483328	+	0.351159i
$336$		0			0
$337$	−1.05014	+	3.23199i	−0.0572046	+	0.176058i	−0.975576	−	0.219662i	$-0.929505\pi$
$337$	−1.05014	+	3.23199i	−0.0572046	+	0.176058i	0.918372	+	0.395719i	$0.129505\pi$
$338$		0			0
$339$	3.92354	−	2.85062i	0.213098	−	0.154825i
$340$		0			0
$341$	−8.34280	−	12.2842i	−0.451788	−	0.665228i
$342$		0			0
$343$	−16.0034	+	11.6271i	−0.864100	+	0.627805i
$344$		0			0
$345$	−2.17437	+	6.69201i	−0.117064	+	0.360286i
$346$		0			0
$347$	17.3470	+	12.6033i	0.931236	+	0.676582i	0.946295	−	0.323304i	$-0.104794\pi$
$347$	17.3470	+	12.6033i	0.931236	+	0.676582i	−0.0150593	+	0.999887i	$0.504794\pi$
$348$		0			0
$349$	5.36618	+	16.5154i	0.287245	+	0.884049i	0.985717	+	0.168411i	$0.0538637\pi$
$349$	5.36618	+	16.5154i	0.287245	+	0.884049i	−0.698472	+	0.715637i	$0.746136\pi$
$350$		0			0
$351$	2.74411			0.146470
$352$		0			0
$353$	−16.2782			−0.866401			−0.433201	−	0.901298i	$-0.642616\pi$
$353$	−16.2782			−0.866401			−0.433201	+	0.901298i	$0.642616\pi$
$354$		0			0
$355$	−0.975921	−	3.00358i	−0.0517965	−	0.159413i
$356$		0			0
$357$	4.93790	+	3.58760i	0.261342	+	0.189876i
$358$		0			0
$359$	1.90197	−	5.85367i	0.100382	−	0.308945i	−0.888237	−	0.459386i	$-0.848069\pi$
$359$	1.90197	−	5.85367i	0.100382	−	0.308945i	0.988619	+	0.150441i	$0.0480695\pi$
$360$		0			0
$361$	10.5186	−	7.64218i	0.553608	−	0.402220i
$362$		0			0
$363$	−2.72900	−	10.6561i	−0.143235	−	0.559300i
$364$		0			0
$365$	−2.62474	+	1.90699i	−0.137385	+	0.0998162i
$366$		0			0
$367$	6.73705	−	20.7345i	0.351671	−	1.08233i	−0.606244	−	0.795279i	$-0.707324\pi$
$367$	6.73705	−	20.7345i	0.351671	−	1.08233i	0.957915	−	0.287053i	$-0.0926756\pi$
$368$		0			0
$369$	−1.59313	−	1.15747i	−0.0829349	−	0.0602557i
$370$		0			0
$371$	−2.11378	−	6.50555i	−0.109742	−	0.337751i
$372$		0			0
$373$	20.3877			1.05564			0.527819	−	0.849357i	$-0.323010\pi$
$373$	20.3877			1.05564			0.527819	+	0.849357i	$0.323010\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	0.134104	+	0.412730i	0.00690672	+	0.0212567i
$378$		0			0
$379$	13.5632	+	9.85424i	0.696695	+	0.506178i	0.878854	−	0.477091i	$-0.158309\pi$
$379$	13.5632	+	9.85424i	0.696695	+	0.506178i	−0.182159	+	0.983269i	$0.558309\pi$
$380$		0			0
$381$	2.12510	−	6.54039i	0.108872	−	0.335074i
$382$		0			0
$383$	13.2147	−	9.60106i	0.675241	−	0.490591i	−0.196535	−	0.980497i	$-0.562969\pi$
$383$	13.2147	−	9.60106i	0.675241	−	0.490591i	0.871775	+	0.489906i	$0.162969\pi$
$384$		0			0
$385$	−3.56462	−	5.24867i	−0.181670	−	0.267497i
$386$		0			0
$387$	5.50509	−	3.99968i	0.279839	−	0.203315i
$388$		0			0
$389$	5.67073	−	17.4527i	0.287518	−	0.884888i	−0.698115	−	0.715985i	$-0.745978\pi$
$389$	5.67073	−	17.4527i	0.287518	−	0.884888i	0.985633	−	0.168903i	$-0.0540223\pi$
$390$		0			0
$391$	18.1626	+	13.1959i	0.918524	+	0.667347i
$392$		0			0
$393$	−3.65309	−	11.2431i	−0.184274	−	0.567138i
$394$		0			0
$395$	13.4606			0.677277
$396$		0			0
$397$	20.6715			1.03747			0.518737	−	0.854934i	$-0.326403\pi$
$397$	20.6715			1.03747			0.518737	+	0.854934i	$0.326403\pi$
$398$		0			0
$399$	1.44781	+	4.45591i	0.0724813	+	0.223074i
$400$		0			0
$401$	−22.1341	−	16.0814i	−1.10533	−	0.803066i	−0.123405	−	0.992356i	$-0.539381\pi$
$401$	−22.1341	−	16.0814i	−1.10533	−	0.803066i	−0.981921	+	0.189290i	$0.939381\pi$
$402$		0			0
$403$	−3.79662	+	11.6848i	−0.189123	+	0.582061i
$404$		0			0
$405$	−0.809017	+	0.587785i	−0.0402004	+	0.0292073i
$406$		0			0
$407$	−1.81235	−	0.653120i	−0.0898350	−	0.0323740i
$408$		0			0
$409$	−13.2225	+	9.60669i	−0.653809	+	0.475020i	−0.864567	−	0.502518i	$-0.832407\pi$
$409$	−13.2225	+	9.60669i	−0.653809	+	0.475020i	0.210757	+	0.977538i	$0.432407\pi$
$410$		0			0
$411$	−2.13220	+	6.56225i	−0.105174	+	0.323692i
$412$		0			0
$413$	17.4861	+	12.7044i	0.860435	+	0.625142i
$414$		0			0
$415$	−2.20125	−	6.77476i	−0.108055	−	0.332560i
$416$		0			0
$417$	0.930369			0.0455604
$418$		0			0
$419$	24.3595			1.19004			0.595020	−	0.803711i	$-0.297144\pi$
$419$	24.3595			1.19004			0.595020	+	0.803711i	$0.297144\pi$
$420$		0			0
$421$	−12.3363	−	37.9672i	−0.601233	−	1.85041i	−0.520861	−	0.853641i	$-0.674389\pi$
$421$	−12.3363	−	37.9672i	−0.601233	−	1.85041i	−0.0803724	−	0.996765i	$-0.525611\pi$
$422$		0			0
$423$	9.67294	+	7.02780i	0.470314	+	0.341703i
$424$		0			0
$425$	0.985946	−	3.03443i	0.0478254	−	0.147191i
$426$		0			0
$427$	12.9541	−	9.41172i	0.626894	−	0.455465i
$428$		0			0
$429$	−5.58041	+	7.18963i	−0.269425	+	0.347119i
$430$		0			0
$431$	−8.39217	+	6.09727i	−0.404237	+	0.293695i	−0.771265	−	0.636515i	$-0.780375\pi$
$431$	−8.39217	+	6.09727i	−0.404237	+	0.293695i	0.367028	+	0.930210i	$0.380375\pi$
$432$		0			0
$433$	−8.35197	+	25.7047i	−0.401370	+	1.23529i	0.522518	+	0.852628i	$0.324993\pi$
$433$	−8.35197	+	25.7047i	−0.401370	+	1.23529i	−0.923888	+	0.382662i	$0.875007\pi$
$434$		0			0
$435$	−0.127943	−	0.0929558i	−0.00613438	−	0.00445689i
$436$		0			0
$437$	5.32535	+	16.3898i	0.254746	+	0.784028i
$438$		0			0
$439$	−23.6669			−1.12956			−0.564780	−	0.825241i	$-0.691039\pi$
$439$	−23.6669			−1.12956			−0.564780	+	0.825241i	$0.691039\pi$
$440$		0			0
$441$	−3.34044			−0.159069
$442$		0			0
$443$	−3.48414	−	10.7231i	−0.165536	−	0.509469i	0.833539	−	0.552461i	$-0.186311\pi$
$443$	−3.48414	−	10.7231i	−0.165536	−	0.509469i	−0.999075	+	0.0429918i	$0.986311\pi$
$444$		0			0
$445$	0.649460	+	0.471860i	0.0307874	+	0.0223683i
$446$		0			0
$447$	−5.21052	+	16.0363i	−0.246449	+	0.758493i
$448$		0			0
$449$	−4.38675	+	3.18716i	−0.207024	+	0.150411i	−0.686466	−	0.727162i	$-0.740839\pi$
$449$	−4.38675	+	3.18716i	−0.207024	+	0.150411i	0.479442	+	0.877573i	$0.340839\pi$
$450$		0			0
$451$	6.27238	−	1.82019i	0.295355	−	0.0857095i
$452$		0			0
$453$	−7.27222	+	5.28358i	−0.341679	+	0.248244i
$454$		0			0
$455$	−1.62218	+	4.99255i	−0.0760489	+	0.234055i
$456$		0			0
$457$	16.2017	+	11.7713i	0.757886	+	0.550636i	0.898261	−	0.439462i	$-0.144831\pi$
$457$	16.2017	+	11.7713i	0.757886	+	0.550636i	−0.140375	+	0.990098i	$0.544831\pi$
$458$		0			0
$459$	0.985946	+	3.03443i	0.0460200	+	0.141635i
$460$		0			0
$461$	−42.4654			−1.97781			−0.988905	−	0.148552i	$-0.952539\pi$
$461$	−42.4654			−1.97781			−0.988905	+	0.148552i	$0.952539\pi$
$462$		0			0
$463$	17.7128			0.823182			0.411591	−	0.911369i	$-0.364973\pi$
$463$	17.7128			0.823182			0.411591	+	0.911369i	$0.364973\pi$
$464$		0			0
$465$	−1.38355	−	4.25813i	−0.0641606	−	0.197466i
$466$		0			0
$467$	−17.1577	−	12.4658i	−0.793962	−	0.576847i	0.115175	−	0.993345i	$-0.463257\pi$
$467$	−17.1577	−	12.4658i	−0.793962	−	0.576847i	−0.909137	+	0.416498i	$0.863257\pi$
$468$		0			0
$469$	6.46403	−	19.8942i	0.298481	−	0.918631i
$470$		0			0
$471$	−1.03058	+	0.748760i	−0.0474866	+	0.0345011i
$472$		0			0
$473$	−0.715869	+	22.5572i	−0.0329157	+	1.03718i
$474$		0			0
$475$	1.98141	−	1.43958i	0.0909131	−	0.0660522i
$476$		0			0
$477$	1.10496	−	3.40071i	0.0505926	−	0.155708i
$478$		0			0
$479$	19.9953	+	14.5274i	0.913609	+	0.663776i	0.941925	−	0.335823i	$-0.109014\pi$
$479$	19.9953	+	14.5274i	0.913609	+	0.663776i	−0.0283161	+	0.999599i	$0.509014\pi$
$480$		0			0
$481$	0.492544	+	1.51589i	0.0224581	+	0.0691188i
$482$		0			0
$483$	13.4606			0.612479
$484$		0			0
$485$	−3.39002			−0.153933
$486$		0			0
$487$	−6.57129	−	20.2243i	−0.297773	−	0.916452i	−0.982276	−	0.187442i	$-0.939980\pi$
$487$	−6.57129	−	20.2243i	−0.297773	−	0.916452i	0.684502	−	0.729011i	$-0.260020\pi$
$488$		0			0
$489$	9.45808	+	6.87170i	0.427709	+	0.310749i
$490$		0			0
$491$	5.59471	−	17.2187i	0.252486	−	0.777071i	−0.741829	−	0.670589i	$-0.766041\pi$
$491$	5.59471	−	17.2187i	0.252486	−	0.777071i	0.994315	−	0.106482i	$-0.0339587\pi$
$492$		0			0
$493$	−0.408212	+	0.296584i	−0.0183850	+	0.0133575i
$494$		0			0
$495$	0.105203	−	3.31496i	0.00472851	−	0.148996i
$496$		0			0
$497$	−4.88769	+	3.55112i	−0.219243	+	0.159289i
$498$		0			0
$499$	7.22311	−	22.2304i	0.323351	−	0.995171i	−0.648829	−	0.760934i	$-0.724741\pi$
$499$	7.22311	−	22.2304i	0.323351	−	0.995171i	0.972180	−	0.234237i	$-0.0752591\pi$
$500$		0			0
$501$	−20.2372	−	14.7032i	−0.904130	−	0.656889i
$502$		0			0
$503$	−6.00497	−	18.4814i	−0.267749	−	0.824045i	−0.991047	−	0.133510i	$-0.957375\pi$
$503$	−6.00497	−	18.4814i	−0.267749	−	0.824045i	0.723299	−	0.690535i	$-0.242625\pi$
$504$		0			0
$505$	−8.16998			−0.363559
$506$		0			0
$507$	−5.46983			−0.242924
$508$		0			0
$509$	−7.35018	−	22.6215i	−0.325791	−	1.00268i	−0.971082	−	0.238745i	$-0.923264\pi$
$509$	−7.35018	−	22.6215i	−0.325791	−	1.00268i	0.645291	−	0.763937i	$-0.276736\pi$
$510$		0			0
$511$	5.02112	+	3.64806i	0.222121	+	0.161381i
$512$		0			0
$513$	−0.756830	+	2.32928i	−0.0334148	+	0.102840i
$514$		0			0
$515$	11.9070	−	8.65096i	0.524686	−	0.381207i
$516$		0			0
$517$	−38.0838	+	11.0516i	−1.67492	+	0.486049i
$518$		0			0
$519$	−19.6994	+	14.3125i	−0.864709	+	0.628248i
$520$		0			0
$521$	−11.5776	+	35.6321i	−0.507222	+	1.56107i	0.289780	+	0.957093i	$0.406418\pi$
$521$	−11.5776	+	35.6321i	−0.507222	+	1.56107i	−0.797002	+	0.603976i	$0.793582\pi$
$522$		0			0
$523$	−4.01905	−	2.92001i	−0.175741	−	0.127683i	0.496437	−	0.868072i	$-0.334641\pi$
$523$	−4.01905	−	2.92001i	−0.175741	−	0.127683i	−0.672178	+	0.740389i	$0.734641\pi$
$524$		0			0
$525$	−0.591149	−	1.81937i	−0.0257998	−	0.0794037i
$526$		0			0
$527$	−14.2851			−0.622268
$528$		0			0
$529$	26.5109			1.15265
$530$		0			0
$531$	3.49143	+	10.7455i	0.151515	+	0.466316i
$532$		0			0
$533$	−4.37172	−	3.17624i	−0.189360	−	0.137578i
$534$		0			0
$535$	−5.51832	+	16.9836i	−0.238578	+	0.734266i
$536$		0			0
$537$	11.9225	−	8.66221i	0.514494	−	0.373802i
$538$		0			0
$539$	6.79310	−	8.75202i	0.292600	−	0.376976i
$540$		0			0
$541$	−13.1513	+	9.55497i	−0.565418	+	0.410800i	−0.833438	−	0.552613i	$-0.813631\pi$
$541$	−13.1513	+	9.55497i	−0.565418	+	0.410800i	0.268020	+	0.963413i	$0.413631\pi$
$542$		0			0
$543$	−2.50403	+	7.70661i	−0.107458	+	0.330722i
$544$		0			0
$545$	−0.0844411	−	0.0613500i	−0.00361706	−	0.00262795i
$546$		0			0
$547$	−4.66233	−	14.3492i	−0.199347	−	0.613526i	−0.999898	−	0.0142624i	$-0.995460\pi$
$547$	−4.66233	−	14.3492i	−0.199347	−	0.613526i	0.800551	−	0.599264i	$-0.204540\pi$
$548$		0			0
$549$	8.37021			0.357232
$550$		0			0
$551$	−0.387323			−0.0165005
$552$		0			0
$553$	−7.95722	−	24.4898i	−0.338375	−	1.04141i
$554$		0			0
$555$	−0.469913	−	0.341412i	−0.0199467	−	0.0144921i
$556$		0			0
$557$	−3.19253	+	9.82560i	−0.135272	+	0.416324i	−0.995632	−	0.0933622i	$-0.970239\pi$
$557$	−3.19253	+	9.82560i	−0.135272	+	0.416324i	0.860360	+	0.509686i	$0.170239\pi$
$558$		0			0
$559$	15.1066	−	10.9756i	0.638941	−	0.464218i
$560$		0			0
$561$	−9.95528	−	3.58760i	−0.420312	−	0.151468i
$562$		0			0
$563$	−11.5622	+	8.40041i	−0.487288	+	0.354035i	−0.804140	−	0.594440i	$-0.797374\pi$
$563$	−11.5622	+	8.40041i	−0.487288	+	0.354035i	0.316853	+	0.948475i	$0.397374\pi$
$564$		0			0
$565$	−1.49866	+	4.61240i	−0.0630491	+	0.194045i
$566$		0			0
$567$	1.54765	+	1.12443i	0.0649951	+	0.0472217i
$568$		0			0
$569$	−0.711350	−	2.18931i	−0.0298213	−	0.0917806i	0.935038	−	0.354547i	$-0.115365\pi$
$569$	−0.711350	−	2.18931i	−0.0298213	−	0.0917806i	−0.964859	+	0.262767i	$0.915365\pi$
$570$		0			0
$571$	−33.0904			−1.38479			−0.692395	−	0.721519i	$-0.743444\pi$
$571$	−33.0904			−1.38479			−0.692395	+	0.721519i	$0.743444\pi$
$572$		0			0
$573$	16.0355			0.669891
$574$		0			0
$575$	−2.17437	−	6.69201i	−0.0906774	−	0.279076i
$576$		0			0
$577$	−2.06140	−	1.49769i	−0.0858170	−	0.0623497i	0.544049	−	0.839053i	$-0.316890\pi$
$577$	−2.06140	−	1.49769i	−0.0858170	−	0.0623497i	−0.629866	+	0.776703i	$0.716890\pi$
$578$		0			0
$579$	−2.98595	+	9.18980i	−0.124092	+	0.381915i
$580$		0			0
$581$	−11.0245	+	8.00978i	−0.457374	+	0.332302i
$582$		0			0
$583$	6.66290	+	9.81068i	0.275949	+	0.406317i
$584$		0			0
$585$	−2.22004	+	1.61295i	−0.0917872	+	0.0666873i
$586$		0			0
$587$	14.0112	−	43.1219i	0.578303	−	1.77983i	−0.0463438	−	0.998926i	$-0.514757\pi$
$587$	14.0112	−	43.1219i	0.578303	−	1.77983i	0.624647	−	0.780908i	$-0.285243\pi$
$588$		0			0
$589$	−8.87127	−	6.44535i	−0.365534	−	0.265576i
$590$		0			0
$591$	0.684392	+	2.10634i	0.0281521	+	0.0866433i
$592$		0			0
$593$	−33.3826			−1.37086			−0.685429	−	0.728139i	$-0.740385\pi$
$593$	−33.3826			−1.37086			−0.685429	+	0.728139i	$0.740385\pi$
$594$		0			0
$595$	−6.10358			−0.250223
$596$		0			0
$597$	−5.52329	−	16.9989i	−0.226053	−	0.695720i
$598$		0			0
$599$	−19.1978	−	13.9481i	−0.784403	−	0.569902i	0.121894	−	0.992543i	$-0.461103\pi$
$599$	−19.1978	−	13.9481i	−0.784403	−	0.569902i	−0.906297	+	0.422641i	$0.861103\pi$
$600$		0			0
$601$	4.79611	−	14.7609i	0.195638	−	0.602110i	−0.804331	−	0.594181i	$-0.797476\pi$
$601$	4.79611	−	14.7609i	0.195638	−	0.602110i	0.999969	−	0.00792901i	$-0.00252391\pi$
$602$		0			0
$603$	8.84636	−	6.42726i	0.360252	−	0.261738i
$604$		0			0
$605$	8.47131	+	7.01690i	0.344408	+	0.285278i
$606$		0			0
$607$	−9.46394	+	6.87595i	−0.384129	+	0.279086i	−0.763046	−	0.646345i	$-0.776297\pi$
$607$	−9.46394	+	6.87595i	−0.384129	+	0.279086i	0.378916	+	0.925431i	$0.376297\pi$
$608$		0			0
$609$	−0.0934877	+	0.287725i	−0.00378831	+	0.0116592i
$610$		0			0
$611$	26.5437	+	19.2851i	1.07384	+	0.780191i
$612$		0			0
$613$	−14.4373	−	44.4333i	−0.583116	−	1.79465i	−0.606709	−	0.794924i	$-0.707511\pi$
$613$	−14.4373	−	44.4333i	−0.583116	−	1.79465i	0.0235937	−	0.999722i	$-0.492489\pi$
$614$		0			0
$615$	1.96921			0.0794063
$616$		0			0
$617$	28.1650			1.13388			0.566939	−	0.823759i	$-0.308127\pi$
$617$	28.1650			1.13388			0.566939	+	0.823759i	$0.308127\pi$
$618$		0			0
$619$	−6.51966	−	20.0654i	−0.262047	−	0.806498i	−0.992359	−	0.123384i	$-0.960625\pi$
$619$	−6.51966	−	20.0654i	−0.262047	−	0.806498i	0.730312	−	0.683114i	$-0.239375\pi$
$620$		0			0
$621$	5.69257	+	4.13589i	0.228435	+	0.165968i
$622$		0			0
$623$	0.474560	−	1.46055i	0.0190129	−	0.0585155i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	−4.56368	−	6.71972i	−0.182256	−	0.268360i
$628$		0			0
$629$	−1.49930	+	1.08931i	−0.0597810	+	0.0434334i
$630$		0			0
$631$	8.56935	−	26.3738i	0.341141	−	1.04992i	−0.622477	−	0.782638i	$-0.713874\pi$
$631$	8.56935	−	26.3738i	0.341141	−	1.04992i	0.963618	−	0.267285i	$-0.0861264\pi$
$632$		0			0
$633$	12.9154	+	9.38359i	0.513341	+	0.372964i
$634$		0			0
$635$	2.12510	+	6.54039i	0.0843321	+	0.259548i
$636$		0			0
$637$	−9.16656			−0.363192
$638$		0			0
$639$	−3.15815			−0.124934
$640$		0			0
$641$	−14.2382	−	43.8207i	−0.562376	−	1.73081i	−0.675623	−	0.737247i	$-0.736125\pi$
$641$	−14.2382	−	43.8207i	−0.562376	−	1.73081i	0.113247	−	0.993567i	$-0.463875\pi$
$642$		0			0
$643$	29.8945	+	21.7196i	1.17892	+	0.856539i	0.992050	−	0.125845i	$-0.0401641\pi$
$643$	29.8945	+	21.7196i	1.17892	+	0.856539i	0.186875	+	0.982384i	$0.440164\pi$
$644$		0			0
$645$	−2.10276	+	6.47162i	−0.0827960	+	0.254820i
$646$		0			0
$647$	−3.41090	+	2.47817i	−0.134096	+	0.0974267i	−0.652811	−	0.757520i	$-0.726411\pi$
$647$	−3.41090	+	2.47817i	−0.134096	+	0.0974267i	0.518715	+	0.854947i	$0.326411\pi$
$648$		0			0
$649$	−35.2536	−	12.7044i	−1.38383	−	0.498691i
$650$		0			0
$651$	−6.92922	+	5.03437i	−0.271577	+	0.197313i
$652$		0			0
$653$	−11.0782	+	34.0953i	−0.433525	+	1.33425i	0.461065	+	0.887366i	$0.347468\pi$
$653$	−11.0782	+	34.0953i	−0.433525	+	1.33425i	−0.894590	+	0.446887i	$0.852532\pi$
$654$		0			0
$655$	9.56392	+	6.94860i	0.373693	+	0.271504i
$656$		0			0
$657$	1.00256	+	3.08557i	0.0391137	+	0.120379i
$658$		0			0
$659$	−18.7591			−0.730749			−0.365375	−	0.930861i	$-0.619059\pi$
$659$	−18.7591			−0.730749			−0.365375	+	0.930861i	$0.619059\pi$
$660$		0			0
$661$	−32.6346			−1.26934			−0.634669	−	0.772784i	$-0.718864\pi$
$661$	−32.6346			−1.26934			−0.634669	+	0.772784i	$0.718864\pi$
$662$		0			0
$663$	2.70555	+	8.32682i	0.105075	+	0.323387i
$664$		0			0
$665$	−3.79042	−	2.75390i	−0.146986	−	0.106792i
$666$		0			0
$667$	−0.343867	+	1.05831i	−0.0133146	+	0.0409781i
$668$		0			0
$669$	−13.8550	+	10.0662i	−0.535664	+	0.389182i
$670$		0			0
$671$	−17.0216	+	21.9301i	−0.657111	+	0.846602i
$672$		0			0
$673$	30.0697	−	21.8469i	1.15910	−	0.842137i	0.169438	−	0.985541i	$-0.445805\pi$
$673$	30.0697	−	21.8469i	1.15910	−	0.842137i	0.989664	+	0.143403i	$0.0458047\pi$
$674$		0			0
$675$	0.309017	−	0.951057i	0.0118941	−	0.0366062i
$676$		0			0
$677$	−20.5785	−	14.9512i	−0.790896	−	0.574620i	0.117333	−	0.993093i	$-0.462565\pi$
$677$	−20.5785	−	14.9512i	−0.790896	−	0.574620i	−0.908229	+	0.418473i	$0.862565\pi$
$678$		0			0
$679$	2.00401	+	6.16770i	0.0769068	+	0.236695i
$680$		0			0
$681$	20.6127			0.789882
$682$		0			0
$683$	−48.8432			−1.86893			−0.934467	−	0.356050i	$-0.884123\pi$
$683$	−48.8432			−1.86893			−0.934467	+	0.356050i	$0.884123\pi$
$684$		0			0
$685$	−2.13220	−	6.56225i	−0.0814674	−	0.250731i
$686$		0			0
$687$	−11.0729	−	8.04494i	−0.422458	−	0.306934i
$688$		0			0
$689$	3.03213	−	9.33195i	0.115515	−	0.355519i
$690$		0			0
$691$	28.8803	−	20.9828i	1.09866	−	0.798222i	0.117818	−	0.993035i	$-0.462410\pi$
$691$	28.8803	−	20.9828i	1.09866	−	0.798222i	0.980840	+	0.194813i	$0.0624101\pi$
$692$		0			0
$693$	−6.09332	+	1.76823i	−0.231466	+	0.0671695i
$694$		0			0
$695$	−0.752684	+	0.546857i	−0.0285509	+	0.0207435i
$696$		0			0
$697$	1.94154	−	5.97544i	0.0735410	−	0.226336i
$698$		0			0
$699$	−7.32590	−	5.32258i	−0.277091	−	0.201318i
$700$		0			0
$701$	−1.62629	−	5.00521i	−0.0614241	−	0.189044i	0.915636	−	0.402009i	$-0.131688\pi$
$701$	−1.62629	−	5.00521i	−0.0614241	−	0.189044i	−0.977060	+	0.212965i	$0.931688\pi$
$702$		0			0
$703$	−1.42258			−0.0536535
$704$		0			0
$705$	−11.9564			−0.450304
$706$		0			0
$707$	4.82967	+	14.8642i	0.181639	+	0.559026i
$708$		0			0
$709$	−16.4445	−	11.9476i	−0.617586	−	0.448702i	0.234492	−	0.972118i	$-0.424657\pi$
$709$	−16.4445	−	11.9476i	−0.617586	−	0.448702i	−0.852077	+	0.523416i	$0.824657\pi$
$710$		0			0
$711$	4.15956	−	12.8018i	0.155996	−	0.480105i
$712$		0			0
$713$	−25.4871	+	18.5175i	−0.954499	+	0.693484i
$714$		0			0
$715$	0.288688	−	9.09662i	0.0107963	−	0.340194i
$716$		0			0
$717$	−8.62312	+	6.26507i	−0.322036	+	0.233973i
$718$		0			0
$719$	9.01488	−	27.7450i	0.336198	−	1.03471i	−0.629930	−	0.776652i	$-0.716917\pi$
$719$	9.01488	−	27.7450i	0.336198	−	1.03471i	0.966129	−	0.258061i	$-0.0830834\pi$
$720$		0			0
$721$	−22.7781	−	16.5493i	−0.848301	−	0.616327i
$722$		0			0
$723$	−5.12838	−	15.7835i	−0.190726	−	0.586995i
$724$		0			0
$725$	0.158146			0.00587339
$726$		0			0
$727$	10.7821			0.399886			0.199943	−	0.979808i	$-0.435924\pi$
$727$	10.7821			0.399886			0.199943	+	0.979808i	$0.435924\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	17.5645	+	12.7613i	0.649645	+	0.471995i
$732$		0			0
$733$	13.2214	−	40.6912i	0.488343	−	1.50297i	−0.338737	−	0.940881i	$-0.610000\pi$
$733$	13.2214	−	40.6912i	0.488343	−	1.50297i	0.827080	−	0.562084i	$-0.190000\pi$
$734$		0			0
$735$	2.70248	−	1.96346i	0.0996823	−	0.0724234i
$736$		0			0
$737$	−1.15036	+	36.2481i	−0.0423740	+	1.33521i
$738$		0			0
$739$	−19.6355	+	14.2661i	−0.722305	+	0.524785i	−0.887120	−	0.461539i	$-0.847297\pi$
$739$	−19.6355	+	14.2661i	−0.722305	+	0.524785i	0.164815	+	0.986325i	$0.447297\pi$
$740$		0			0
$741$	−2.07683	+	6.39182i	−0.0762941	+	0.234809i
$742$		0			0
$743$	22.9862	+	16.7005i	0.843284	+	0.612681i	0.923286	−	0.384113i	$-0.125493\pi$
$743$	22.9862	+	16.7005i	0.843284	+	0.612681i	−0.0800024	+	0.996795i	$0.525493\pi$
$744$		0			0
$745$	−5.21052	−	16.0363i	−0.190899	−	0.587526i
$746$		0			0
$747$	−7.12340			−0.260632
$748$		0			0
$749$	34.1616			1.24824
$750$		0			0
$751$	3.25867	+	10.0292i	0.118911	+	0.365969i	0.992743	−	0.120259i	$-0.0383724\pi$
$751$	3.25867	+	10.0292i	0.118911	+	0.365969i	−0.873832	+	0.486228i	$0.838372\pi$
$752$		0			0
$753$	−3.35742	−	2.43931i	−0.122351	−	0.0888933i
$754$		0			0
$755$	2.77774	−	8.54901i	0.101092	−	0.311130i
$756$		0			0
$757$	2.30009	−	1.67111i	0.0835981	−	0.0607376i	−0.545201	−	0.838305i	$-0.683547\pi$
$757$	2.30009	−	1.67111i	0.0835981	−	0.0607376i	0.628799	+	0.777568i	$0.283547\pi$
$758$		0			0
$759$	−22.4125	+	6.50391i	−0.813521	+	0.236077i
$760$		0			0
$761$	−11.0712	+	8.04366i	−0.401329	+	0.291583i	−0.770082	−	0.637945i	$-0.779785\pi$
$761$	−11.0712	+	8.04366i	−0.401329	+	0.291583i	0.368753	+	0.929527i	$0.379785\pi$
$762$		0			0
$763$	−0.0617011	+	0.189896i	−0.00223373	+	0.00687471i
$764$		0			0
$765$	−2.58124	−	1.87538i	−0.0933249	−	0.0678045i
$766$		0			0
$767$	9.58089	+	29.4869i	0.345946	+	1.06471i
$768$		0			0
$769$	22.2375			0.801905			0.400953	−	0.916099i	$-0.368679\pi$
$769$	22.2375			0.801905			0.400953	+	0.916099i	$0.368679\pi$
$770$		0			0
$771$	−6.08456			−0.219130
$772$		0			0
$773$	−9.71862	−	29.9108i	−0.349555	−	1.07582i	−0.959100	−	0.283067i	$-0.908648\pi$
$773$	−9.71862	−	29.9108i	−0.349555	−	1.07582i	0.609545	−	0.792751i	$-0.291352\pi$
$774$		0			0
$775$	3.62218	+	2.63167i	0.130113	+	0.0945323i
$776$		0			0
$777$	−0.343366	+	1.05677i	−0.0123182	+	0.0379114i
$778$		0			0
$779$	3.90181	−	2.83483i	0.139797	−	0.101568i
$780$		0			0
$781$	6.42238	−	8.27440i	0.229811	−	0.296081i
$782$		0			0
$783$	−0.127943	+	0.0929558i	−0.00457230	+	0.00332197i
$784$		0			0
$785$	0.393647	−	1.21152i	0.0140499	−	0.0432410i
$786$		0			0
$787$	−7.03813	−	5.11350i	−0.250882	−	0.182277i	0.455236	−	0.890371i	$-0.349555\pi$
$787$	−7.03813	−	5.11350i	−0.250882	−	0.182277i	−0.706118	+	0.708094i	$0.749555\pi$
$788$		0			0
$789$	−4.18312	−	12.8743i	−0.148923	−	0.458338i
$790$		0			0
$791$	9.27759			0.329873
$792$		0			0
$793$	22.9688			0.815646
$794$		0			0
$795$	1.10496	+	3.40071i	0.0391888	+	0.120611i
$796$		0			0
$797$	12.5844	+	9.14307i	0.445761	+	0.323864i	0.787920	−	0.615778i	$-0.211158\pi$
$797$	12.5844	+	9.14307i	0.445761	+	0.323864i	−0.342159	+	0.939642i	$0.611158\pi$
$798$		0			0
$799$	−11.7884	+	36.2809i	−0.417043	+	1.28353i
$800$		0			0
$801$	0.649460	−	0.471860i	0.0229475	−	0.0166724i
$802$		0			0
$803$	−10.1231	−	3.64806i	−0.357235	−	0.128737i
$804$		0			0
$805$	−10.8899	+	7.91195i	−0.383817	+	0.278860i
$806$		0			0
$807$	−5.11602	+	15.7455i	−0.180092	+	0.554268i
$808$		0			0
$809$	9.93348	+	7.21710i	0.349243	+	0.253740i	0.748551	−	0.663077i	$-0.230750\pi$
$809$	9.93348	+	7.21710i	0.349243	+	0.253740i	−0.399309	+	0.916817i	$0.630750\pi$
$810$		0			0
$811$	−3.39994	−	10.4639i	−0.119388	−	0.367439i	0.873449	−	0.486916i	$-0.161878\pi$
$811$	−3.39994	−	10.4639i	−0.119388	−	0.367439i	−0.992837	+	0.119477i	$0.961878\pi$
$812$		0			0
$813$	−14.2775			−0.500735
$814$		0			0
$815$	−11.6908			−0.409512
$816$		0			0
$817$	5.14997	+	15.8500i	0.180175	+	0.554521i
$818$		0			0
$819$	4.24692	+	3.08557i	0.148399	+	0.107818i
$820$		0			0
$821$	12.8259	−	39.4739i	0.447626	−	1.37765i	−0.431953	−	0.901896i	$-0.642175\pi$
$821$	12.8259	−	39.4739i	0.447626	−	1.37765i	0.879579	−	0.475754i	$-0.157825\pi$
$822$		0			0
$823$	30.9273	−	22.4700i	1.07806	−	0.783255i	0.100715	−	0.994915i	$-0.467887\pi$
$823$	30.9273	−	22.4700i	1.07806	−	0.783255i	0.977343	+	0.211660i	$0.0678869\pi$
$824$		0			0
$825$	1.86337	+	2.74369i	0.0648743	+	0.0955231i
$826$		0			0
$827$	−10.0650	+	7.31262i	−0.349993	+	0.254285i	−0.748866	−	0.662721i	$-0.769401\pi$
$827$	−10.0650	+	7.31262i	−0.349993	+	0.254285i	0.398873	+	0.917006i	$0.369401\pi$
$828$		0			0
$829$	−9.29899	+	28.6194i	−0.322967	+	0.993991i	0.649382	+	0.760462i	$0.275027\pi$
$829$	−9.29899	+	28.6194i	−0.322967	+	0.993991i	−0.972350	+	0.233529i	$0.924973\pi$
$830$		0			0
$831$	4.92227	+	3.57624i	0.170752	+	0.124058i
$832$		0			0
$833$	−3.29350	−	10.1363i	−0.114113	−	0.351203i
$834$		0			0
$835$	25.0145			0.865663
$836$		0			0
$837$	−4.47726			−0.154757
$838$		0			0
$839$	−0.422617	−	1.30068i	−0.0145904	−	0.0449045i	0.943496	−	0.331383i	$-0.107515\pi$
$839$	−0.422617	−	1.30068i	−0.0145904	−	0.0449045i	−0.958087	+	0.286479i	$0.907515\pi$
$840$		0			0
$841$	23.4413	+	17.0311i	0.808319	+	0.587278i
$842$		0			0
$843$	0.0157095	−	0.0483489i	0.000541065	−	0.00166523i
$844$		0			0
$845$	4.42519	−	3.21509i	0.152231	−	0.110602i
$846$		0			0
$847$	7.75853	−	19.5605i	0.266586	−	0.672105i
$848$		0			0
$849$	−14.5673	+	10.5838i	−0.499950	+	0.363235i
$850$		0			0
$851$	−1.26297	+	3.88702i	−0.0432940	+	0.133245i
$852$		0			0
$853$	−4.46147	−	3.24145i	−0.152758	−	0.110985i	0.508781	−	0.860896i	$-0.330096\pi$
$853$	−4.46147	−	3.24145i	−0.152758	−	0.110985i	−0.661539	+	0.749911i	$0.730096\pi$
$854$		0			0
$855$	−0.756830	−	2.32928i	−0.0258830	−	0.0796598i
$856$		0			0
$857$	−29.0635			−0.992789			−0.496394	−	0.868097i	$-0.665343\pi$
$857$	−29.0635			−0.992789			−0.496394	+	0.868097i	$0.665343\pi$
$858$		0			0
$859$	39.3401			1.34227			0.671133	−	0.741337i	$-0.265808\pi$
$859$	39.3401			1.34227			0.671133	+	0.741337i	$0.265808\pi$
$860$		0			0
$861$	−1.16410	−	3.58272i	−0.0396723	−	0.122099i
$862$		0			0
$863$	−33.8044	−	24.5604i	−1.15072	−	0.836045i	−0.162141	−	0.986768i	$-0.551840\pi$
$863$	−33.8044	−	24.5604i	−1.15072	−	0.836045i	−0.988576	+	0.150723i	$0.951840\pi$
$864$		0			0
$865$	7.52451	−	23.1581i	0.255841	−	0.787398i
$866$		0			0
$867$	5.51762	−	4.00878i	0.187388	−	0.136145i
$868$		0			0
$869$	25.0821	+	36.9318i	0.850852	+	1.25282i
$870$		0			0
$871$	24.2754	−	17.6371i	0.822541	−	0.597611i
$872$		0			0
$873$	−1.04757	+	3.22410i	−0.0354550	+	0.109119i
$874$		0			0
$875$	1.54765	+	1.12443i	0.0523200	+	0.0380127i
$876$		0			0
$877$	−11.6767	−	35.9372i	−0.394294	−	1.21351i	−0.929510	−	0.368798i	$-0.879770\pi$
$877$	−11.6767	−	35.9372i	−0.394294	−	1.21351i	0.535215	−	0.844716i	$-0.320230\pi$
$878$		0			0
$879$	−26.6494			−0.898861
$880$		0			0
$881$	31.1195			1.04844			0.524221	−	0.851582i	$-0.324357\pi$
$881$	31.1195			1.04844			0.524221	+	0.851582i	$0.324357\pi$
$882$		0			0
$883$	−15.6490	−	48.1627i	−0.526631	−	1.62080i	−0.761069	−	0.648671i	$-0.775325\pi$
$883$	−15.6490	−	48.1627i	−0.526631	−	1.62080i	0.234438	−	0.972131i	$-0.424675\pi$
$884$		0			0
$885$	−9.14068	−	6.64110i	−0.307261	−	0.223238i
$886$		0			0
$887$	−2.39116	+	7.35922i	−0.0802872	+	0.247099i	−0.983141	−	0.182849i	$-0.941468\pi$
$887$	−2.39116	+	7.35922i	−0.0802872	+	0.247099i	0.902854	+	0.429948i	$0.141468\pi$
$888$		0			0
$889$	10.6431	−	7.73269i	0.356959	−	0.259346i
$890$		0			0
$891$	−3.12020	−	1.12443i	−0.104531	−	0.0376699i
$892$		0			0
$893$	−23.6905	+	17.2122i	−0.792772	+	0.575983i
$894$		0			0
$895$	−4.55399	+	14.0158i	−0.152223	+	0.468495i
$896$		0			0
$897$	15.6211	+	11.3494i	0.521572	+	0.378944i
$898$		0			0
$899$	−0.218803	−	0.673405i	−0.00729747	−	0.0224593i
$900$		0			0
$901$	11.4087			0.380077
$902$		0			0
$903$	13.0173			0.433189
$904$		0			0
$905$	−2.50403	−	7.70661i	−0.0832367	−	0.256176i
$906$		0			0
$907$	4.53666	+	3.29608i	0.150637	+	0.109444i	0.660551	−	0.750781i	$-0.270323\pi$
$907$	4.53666	+	3.29608i	0.150637	+	0.109444i	−0.509914	+	0.860226i	$0.670323\pi$
$908$		0			0
$909$	−2.52466	+	7.77011i	−0.0837378	+	0.257718i
$910$		0			0
$911$	−27.4261	+	19.9262i	−0.908668	+	0.660186i	−0.940678	−	0.339302i	$-0.889809\pi$
$911$	−27.4261	+	19.9262i	−0.908668	+	0.660186i	0.0320100	+	0.999488i	$0.489809\pi$
$912$		0			0
$913$	14.4861	−	18.6634i	0.479420	−	0.617670i
$914$		0			0
$915$	−6.77164	+	4.91988i	−0.223863	+	0.162646i
$916$		0			0
$917$	6.98836	−	21.5080i	0.230776	−	0.710255i
$918$		0			0
$919$	−18.1410	−	13.1802i	−0.598417	−	0.434776i	0.246899	−	0.969041i	$-0.420588\pi$
$919$	−18.1410	−	13.1802i	−0.598417	−	0.434776i	−0.845317	+	0.534266i	$0.820588\pi$
$920$		0			0
$921$	1.09588	+	3.37276i	0.0361104	+	0.111136i
$922$		0			0
$923$	−8.66631			−0.285255
$924$		0			0
$925$	0.580845			0.0190981
$926$		0			0
$927$	−4.54808	−	13.9975i	−0.149379	−	0.459740i
$928$		0			0
$929$	−27.0814	−	19.6758i	−0.888511	−	0.645541i	0.0469787	−	0.998896i	$-0.485041\pi$
$929$	−27.0814	−	19.6758i	−0.888511	−	0.645541i	−0.935489	+	0.353355i	$0.885041\pi$
$930$		0			0
$931$	2.52815	−	7.78083i	0.0828566	−	0.255006i
$932$		0			0
$933$	−0.949035	+	0.689514i	−0.0310700	+	0.0225737i
$934$		0			0
$935$	10.1627	−	2.94914i	0.332357	−	0.0964471i
$936$		0			0
$937$	16.4406	−	11.9448i	0.537093	−	0.390221i	−0.285912	−	0.958256i	$-0.592296\pi$
$937$	16.4406	−	11.9448i	0.537093	−	0.390221i	0.823004	+	0.568035i	$0.192296\pi$
$938$		0			0
$939$	2.92910	−	9.01485i	0.0955876	−	0.294188i
$940$		0			0
$941$	−2.85016	−	2.07076i	−0.0929127	−	0.0675050i	0.540359	−	0.841435i	$-0.318288\pi$
$941$	−2.85016	−	2.07076i	−0.0929127	−	0.0675050i	−0.633272	+	0.773930i	$0.718288\pi$
$942$		0			0
$943$	−4.28179	−	13.1780i	−0.139434	−	0.429135i
$944$		0			0
$945$	−1.91300			−0.0622298
$946$		0			0
$947$	23.6414			0.768242			0.384121	−	0.923283i	$-0.374505\pi$
$947$	23.6414			0.768242			0.384121	+	0.923283i	$0.374505\pi$
$948$		0			0
$949$	2.75115	+	8.46715i	0.0893060	+	0.274855i
$950$		0			0
$951$	15.4029	+	11.1908i	0.499473	+	0.362888i
$952$		0			0
$953$	13.3289	−	41.0220i	0.431764	−	1.32883i	−0.464603	−	0.885519i	$-0.653803\pi$
$953$	13.3289	−	41.0220i	0.431764	−	1.32883i	0.896367	−	0.443313i	$-0.146197\pi$
$954$		0			0
$955$	−12.9730	+	9.42541i	−0.419795	+	0.304999i
$956$		0			0
$957$	0.0166374	−	0.524246i	0.000537809	−	0.0169465i
$958$		0			0
$959$	−10.6787	+	7.75853i	−0.344833	+	0.250536i
$960$		0			0
$961$	−3.38502	+	10.4180i	−0.109194	+	0.336065i
$962$		0			0
$963$	14.4471	+	10.4965i	0.465553	+	0.338244i
$964$		0			0
$965$	−2.98595	−	9.18980i	−0.0961210	−	0.295830i
$966$		0			0
$967$	4.21907			0.135676			0.0678381	−	0.997696i	$-0.478390\pi$
$967$	4.21907			0.135676			0.0678381	+	0.997696i	$0.478390\pi$
$968$		0			0
$969$	−7.81423			−0.251029
$970$		0			0
$971$	13.7450	+	42.3029i	0.441100	+	1.35756i	0.886705	+	0.462336i	$0.152988\pi$
$971$	13.7450	+	42.3029i	0.441100	+	1.35756i	−0.445605	+	0.895229i	$0.647012\pi$
$972$		0			0
$973$	1.43988	+	1.04614i	0.0461605	+	0.0335376i
$974$		0			0
$975$	0.847978	−	2.60981i	0.0271570	−	0.0835808i
$976$		0			0
$977$	−42.0210	+	30.5300i	−1.34437	+	0.976742i	−0.345099	+	0.938566i	$0.612155\pi$
$977$	−42.0210	+	30.5300i	−1.34437	+	0.976742i	−0.999271	+	0.0381754i	$0.987845\pi$
$978$		0			0
$979$	−0.0844542	+	2.66117i	−0.00269917	+	0.0850513i
$980$		0			0
$981$	−0.0844411	+	0.0613500i	−0.00269600	+	0.00195876i
$982$		0			0
$983$	−4.71334	+	14.5062i	−0.150332	+	0.462675i	−0.997658	−	0.0683983i	$-0.978211\pi$
$983$	−4.71334	+	14.5062i	−0.150332	+	0.462675i	0.847326	+	0.531073i	$0.178211\pi$
$984$		0			0
$985$	−1.79176	−	1.30179i	−0.0570903	−	0.0414785i
$986$		0			0
$987$	7.06801	+	21.7531i	0.224977	+	0.692409i
$988$		0			0
$989$	47.8803			1.52251
$990$		0			0
$991$	11.8553			0.376596			0.188298	−	0.982112i	$-0.439703\pi$
$991$	11.8553			0.376596			0.188298	+	0.982112i	$0.439703\pi$
$992$		0			0
$993$	3.38342	+	10.4131i	0.107370	+	0.330450i
$994$		0			0
$995$	14.4602	+	10.5059i	0.458418	+	0.333060i
$996$		0			0
$997$	−0.130182	+	0.400658i	−0.00412289	+	0.0126890i	−0.953097	−	0.302666i	$-0.902123\pi$
$997$	−0.130182	+	0.400658i	−0.00412289	+	0.0126890i	0.948974	+	0.315355i	$0.102123\pi$
$998$		0			0
$999$	−0.469913	+	0.341412i	−0.0148674	+	0.0108018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1320.2.bw.b.1081.1	yes	8
11.4	even	5	inner	1320.2.bw.b.961.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1320.2.bw.b.961.1	✓	8	11.4	even	5	inner
1320.2.bw.b.1081.1	yes	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.bw (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.591149 + 1.81937i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.591149 + 1.81937i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(0.105203 - 3.31496i) q^{11} +(-2.22004 + 1.61295i) q^{13} +(0.309017 - 0.951057i) q^{15} +(-2.58124 - 1.87538i) q^{17} +(-0.756830 - 2.32928i) q^{19} -1.91300 q^{21} -7.03640 q^{23} +(0.309017 + 0.951057i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(0.0488697 - 0.150406i) q^{29} +(3.62218 - 2.63167i) q^{31} +(3.18522 - 0.924324i) q^{33} +(1.54765 - 1.12443i) q^{35} +(0.179491 - 0.552416i) q^{37} +(-2.22004 - 1.61295i) q^{39} +(0.608520 + 1.87283i) q^{41} -6.80467 q^{43} +1.00000 q^{45} +(-3.69473 - 11.3712i) q^{47} +(2.70248 + 1.96346i) q^{49} +(0.985946 - 3.03443i) q^{51} +(-2.89282 + 2.10176i) q^{53} +(-2.03359 + 2.62002i) q^{55} +(1.98141 - 1.43958i) q^{57} +(3.49143 - 10.7455i) q^{59} +(-6.77164 - 4.91988i) q^{61} +(-0.591149 - 1.81937i) q^{63} +2.74411 q^{65} -10.9347 q^{67} +(-2.17437 - 6.69201i) q^{69} +(2.55499 + 1.85631i) q^{71} +(1.00256 - 3.08557i) q^{73} +(-0.809017 + 0.587785i) q^{75} +(5.96893 + 2.15103i) q^{77} +(-10.8899 + 7.91195i) q^{79} +(0.309017 - 0.951057i) q^{81} +(5.76295 + 4.18703i) q^{83} +(0.985946 + 3.03443i) q^{85} +0.158146 q^{87} -0.802777 q^{89} +(-1.62218 - 4.99255i) q^{91} +(3.62218 + 2.63167i) q^{93} +(-0.756830 + 2.32928i) q^{95} +(2.74259 - 1.99261i) q^{97} +(1.86337 + 2.74369i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 2 q^{5} - 5 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 - 2 * q^5 - 5 * q^7 - 2 * q^9	\( 8 q - 2 q^{3} - 2 q^{5} - 5 q^{7} - 2 q^{9} + 3 q^{11} + 6 q^{13} - 2 q^{15} - 4 q^{17} + 10 q^{19} - 30 q^{23} - 2 q^{25} - 2 q^{27} + 6 q^{29} + 5 q^{31} - 2 q^{33} + 5 q^{35} + 19 q^{37} + 6 q^{39} + 13 q^{41} - 8 q^{43} + 8 q^{45} + 15 q^{47} + 13 q^{49} + 6 q^{51} - 17 q^{53} - 7 q^{55} - 5 q^{57} + 13 q^{59} - 31 q^{61} - 5 q^{63} + 6 q^{65} - 42 q^{67} - 5 q^{69} + 15 q^{71} + 23 q^{73} - 2 q^{75} - 5 q^{77} - 32 q^{79} - 2 q^{81} + 19 q^{83} + 6 q^{85} + 6 q^{87} - 24 q^{89} + 11 q^{91} + 5 q^{93} + 10 q^{95} + 27 q^{97} + 3 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 - 2 * q^5 - 5 * q^7 - 2 * q^9 + 3 * q^11 + 6 * q^13 - 2 * q^15 - 4 * q^17 + 10 * q^19 - 30 * q^23 - 2 * q^25 - 2 * q^27 + 6 * q^29 + 5 * q^31 - 2 * q^33 + 5 * q^35 + 19 * q^37 + 6 * q^39 + 13 * q^41 - 8 * q^43 + 8 * q^45 + 15 * q^47 + 13 * q^49 + 6 * q^51 - 17 * q^53 - 7 * q^55 - 5 * q^57 + 13 * q^59 - 31 * q^61 - 5 * q^63 + 6 * q^65 - 42 * q^67 - 5 * q^69 + 15 * q^71 + 23 * q^73 - 2 * q^75 - 5 * q^77 - 32 * q^79 - 2 * q^81 + 19 * q^83 + 6 * q^85 + 6 * q^87 - 24 * q^89 + 11 * q^91 + 5 * q^93 + 10 * q^95 + 27 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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