LMFDB - Embedded newform 1232.2.q.i.177.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(177,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1232.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.q (of order $3$, 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:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 616)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.3
Root			$0.222521 - 0.385418i$ of defining polynomial
Character	$\chi$	$=$	1232.177
Dual form			1232.2.q.i.529.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0990311 - 0.171527i) q^{3} +(1.96950 - 3.41127i) q^{5} +(-0.167563 - 2.64044i) q^{7} +(1.48039 - 2.56410i) q^{9} +O(q^{10})$	\(q+(-0.0990311 - 0.171527i) q^{3} +(1.96950 - 3.41127i) q^{5} +(-0.167563 - 2.64044i) q^{7} +(1.48039 - 2.56410i) q^{9} +(0.500000 + 0.866025i) q^{11} +0.692021 q^{13} -0.780167 q^{15} +(-0.425428 - 0.736862i) q^{17} +(0.376510 - 0.652135i) q^{19} +(-0.436313 + 0.290227i) q^{21} +(-0.321552 + 0.556945i) q^{23} +(-5.25786 - 9.10689i) q^{25} -1.18060 q^{27} +5.43296 q^{29} +(3.22252 + 5.58157i) q^{31} +(0.0990311 - 0.171527i) q^{33} +(-9.33728 - 4.62874i) q^{35} +(-5.04892 + 8.74498i) q^{37} +(-0.0685317 - 0.118700i) q^{39} +1.89977 q^{41} -2.97823 q^{43} +(-5.83124 - 10.1000i) q^{45} +(-6.33728 + 10.9765i) q^{47} +(-6.94385 + 0.884879i) q^{49} +(-0.0842611 + 0.145945i) q^{51} +(1.01089 + 1.75090i) q^{53} +3.93900 q^{55} -0.149145 q^{57} +(-3.86778 - 6.69919i) q^{59} +(4.74094 - 8.21155i) q^{61} +(-7.01842 - 3.47922i) q^{63} +(1.36294 - 2.36068i) q^{65} +(-4.40581 - 7.63109i) q^{67} +0.127375 q^{69} +0.313355 q^{71} +(8.00484 + 13.8648i) q^{73} +(-1.04138 + 1.80373i) q^{75} +(2.20291 - 1.46533i) q^{77} +(3.77748 - 6.54279i) q^{79} +(-4.32424 - 7.48980i) q^{81} +13.1685 q^{83} -3.35152 q^{85} +(-0.538032 - 0.931899i) q^{87} +(-0.530499 + 0.918852i) q^{89} +(-0.115957 - 1.82724i) q^{91} +(0.638260 - 1.10550i) q^{93} +(-1.48307 - 2.56876i) q^{95} +5.85623 q^{97} +2.96077 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 5 q^{3} + 2 q^{5} - 4 q^{9}+O(q^{10}) $ 6 * q - 5 * q^3 + 2 * q^5 - 4 * q^9	$ 6 q - 5 q^{3} + 2 q^{5} - 4 q^{9} + 3 q^{11} - 6 q^{13} - 2 q^{15} + 11 q^{17} + 7 q^{19} + 14 q^{21} - 6 q^{23} - 19 q^{25} + 16 q^{27} - 6 q^{29} + 19 q^{31} + 5 q^{33} - 35 q^{35} - 12 q^{37} + 5 q^{39} - 34 q^{41} - 24 q^{43} + 5 q^{45} - 17 q^{47} + 30 q^{51} + 3 q^{53} + 4 q^{55} - 28 q^{57} - 12 q^{59} - 14 q^{63} + 19 q^{65} + 34 q^{69} + 6 q^{71} + 26 q^{73} - 13 q^{75} + 23 q^{79} - 27 q^{81} + 18 q^{83} - 18 q^{85} + 12 q^{87} - 13 q^{89} - 21 q^{91} + 34 q^{93} + 7 q^{95} + 2 q^{97} - 8 q^{99}+O(q^{100}) $ 6 * q - 5 * q^3 + 2 * q^5 - 4 * q^9 + 3 * q^11 - 6 * q^13 - 2 * q^15 + 11 * q^17 + 7 * q^19 + 14 * q^21 - 6 * q^23 - 19 * q^25 + 16 * q^27 - 6 * q^29 + 19 * q^31 + 5 * q^33 - 35 * q^35 - 12 * q^37 + 5 * q^39 - 34 * q^41 - 24 * q^43 + 5 * q^45 - 17 * q^47 + 30 * q^51 + 3 * q^53 + 4 * q^55 - 28 * q^57 - 12 * q^59 - 14 * q^63 + 19 * q^65 + 34 * q^69 + 6 * q^71 + 26 * q^73 - 13 * q^75 + 23 * q^79 - 27 * q^81 + 18 * q^83 - 18 * q^85 + 12 * q^87 - 13 * q^89 - 21 * q^91 + 34 * q^93 + 7 * q^95 + 2 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0990311	−	0.171527i	−0.0571757	−	0.0990311i	0.836021	−	0.548698i	$-0.184876\pi$
$3$	−0.0990311	−	0.171527i	−0.0571757	−	0.0990311i	−0.893197	+	0.449667i	$0.851543\pi$
$4$		0			0
$5$	1.96950	−	3.41127i	0.880787	−	1.52557i	0.0303204	−	0.999540i	$-0.490347\pi$
$5$	1.96950	−	3.41127i	0.880787	−	1.52557i	0.850467	−	0.526028i	$-0.176319\pi$
$6$		0			0
$7$	−0.167563	−	2.64044i	−0.0633328	−	0.997992i
$7$	−0.167563	−	2.64044i	−0.0633328	−	0.997992i
$8$		0			0
$9$	1.48039	−	2.56410i	0.493462	−	0.854701i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	0.692021			0.191932			0.0959661	−	0.995385i	$-0.469406\pi$
$13$	0.692021			0.191932			0.0959661	+	0.995385i	$0.469406\pi$
$14$		0			0
$15$	−0.780167			−0.201438
$16$		0			0
$17$	−0.425428	−	0.736862i	−0.103181	−	0.178715i	0.809812	−	0.586689i	$-0.199569\pi$
$17$	−0.425428	−	0.736862i	−0.103181	−	0.178715i	−0.912994	+	0.407974i	$0.866236\pi$
$18$		0			0
$19$	0.376510	−	0.652135i	0.0863774	−	0.149610i	−0.819600	−	0.572936i	$-0.805804\pi$
$19$	0.376510	−	0.652135i	0.0863774	−	0.149610i	0.905977	+	0.423326i	$0.139138\pi$
$20$		0			0
$21$	−0.436313	+	0.290227i	−0.0952112	+	0.0633328i
$22$		0			0
$23$	−0.321552	+	0.556945i	−0.0670482	+	0.116131i	−0.897601	−	0.440809i	$-0.854691\pi$
$23$	−0.321552	+	0.556945i	−0.0670482	+	0.116131i	0.830552	+	0.556940i	$0.188025\pi$
$24$		0			0
$25$	−5.25786	−	9.10689i	−1.05157	−	1.82138i
$26$		0			0
$27$	−1.18060			−0.227207
$28$		0			0
$29$	5.43296			1.00888			0.504438	−	0.863448i	$-0.331700\pi$
$29$	5.43296			1.00888			0.504438	+	0.863448i	$0.331700\pi$
$30$		0			0
$31$	3.22252	+	5.58157i	0.578782	+	1.00248i	0.995619	+	0.0934986i	$0.0298051\pi$
$31$	3.22252	+	5.58157i	0.578782	+	1.00248i	−0.416838	+	0.908981i	$0.636862\pi$
$32$		0			0
$33$	0.0990311	−	0.171527i	0.0172391	−	0.0298590i
$34$		0			0
$35$	−9.33728	−	4.62874i	−1.57829	−	0.782401i
$36$		0			0
$37$	−5.04892	+	8.74498i	−0.830037	+	1.43767i	0.0679713	+	0.997687i	$0.478347\pi$
$37$	−5.04892	+	8.74498i	−0.830037	+	1.43767i	−0.898008	+	0.439979i	$0.854986\pi$
$38$		0			0
$39$	−0.0685317	−	0.118700i	−0.0109738	−	0.0190073i
$40$		0			0
$41$	1.89977			0.296695			0.148347	−	0.988935i	$-0.452605\pi$
$41$	1.89977			0.296695			0.148347	+	0.988935i	$0.452605\pi$
$42$		0			0
$43$	−2.97823			−0.454176			−0.227088	−	0.973874i	$-0.572920\pi$
$43$	−2.97823			−0.454176			−0.227088	+	0.973874i	$0.572920\pi$
$44$		0			0
$45$	−5.83124	−	10.1000i	−0.869270	−	1.50562i
$46$		0			0
$47$	−6.33728	+	10.9765i	−0.924388	+	1.60109i	−0.131844	+	0.991270i	$0.542090\pi$
$47$	−6.33728	+	10.9765i	−0.924388	+	1.60109i	−0.792543	+	0.609816i	$0.791243\pi$
$48$		0			0
$49$	−6.94385	+	0.884879i	−0.991978	+	0.126411i
$50$		0			0
$51$	−0.0842611	+	0.145945i	−0.0117989	+	0.0204363i
$52$		0			0
$53$	1.01089	+	1.75090i	0.138856	+	0.240505i	0.927064	−	0.374904i	$-0.122324\pi$
$53$	1.01089	+	1.75090i	0.138856	+	0.240505i	−0.788208	+	0.615409i	$0.788991\pi$
$54$		0			0
$55$	3.93900			0.531135
$56$		0			0
$57$	−0.149145			−0.0197547
$58$		0			0
$59$	−3.86778	−	6.69919i	−0.503542	−	0.872161i	−0.999992	−	0.00409502i	$-0.998697\pi$
$59$	−3.86778	−	6.69919i	−0.503542	−	0.872161i	0.496449	−	0.868066i	$-0.334637\pi$
$60$		0			0
$61$	4.74094	−	8.21155i	0.607015	−	1.05138i	−0.384715	−	0.923036i	$-0.625700\pi$
$61$	4.74094	−	8.21155i	0.607015	−	1.05138i	0.991730	−	0.128345i	$-0.0409666\pi$
$62$		0			0
$63$	−7.01842	−	3.47922i	−0.884238	−	0.438341i
$64$		0			0
$65$	1.36294	−	2.36068i	0.169051	−	0.292806i
$66$		0			0
$67$	−4.40581	−	7.63109i	−0.538256	−	0.932286i	−0.998998	−	0.0447524i	$-0.985750\pi$
$67$	−4.40581	−	7.63109i	−0.538256	−	0.932286i	0.460742	−	0.887534i	$-0.347583\pi$
$68$		0			0
$69$	0.127375			0.0153341
$70$		0			0
$71$	0.313355			0.0371884			0.0185942	−	0.999827i	$-0.494081\pi$
$71$	0.313355			0.0371884			0.0185942	+	0.999827i	$0.494081\pi$
$72$		0			0
$73$	8.00484	+	13.8648i	0.936896	+	1.62275i	0.771217	+	0.636572i	$0.219648\pi$
$73$	8.00484	+	13.8648i	0.936896	+	1.62275i	0.165679	+	0.986180i	$0.447018\pi$
$74$		0			0
$75$	−1.04138	+	1.80373i	−0.120249	+	0.208277i
$76$		0			0
$77$	2.20291	−	1.46533i	0.251045	−	0.166990i
$78$		0			0
$79$	3.77748	−	6.54279i	0.425000	−	0.736121i	−0.571421	−	0.820657i	$-0.693608\pi$
$79$	3.77748	−	6.54279i	0.425000	−	0.736121i	0.996420	+	0.0845363i	$0.0269409\pi$
$80$		0			0
$81$	−4.32424	−	7.48980i	−0.480471	−	0.832200i
$82$		0			0
$83$	13.1685			1.44543			0.722717	−	0.691145i	$-0.242893\pi$
$83$	13.1685			1.44543			0.722717	+	0.691145i	$0.242893\pi$
$84$		0			0
$85$	−3.35152			−0.363523
$86$		0			0
$87$	−0.538032	−	0.931899i	−0.0576831	−	0.0999101i
$88$		0			0
$89$	−0.530499	+	0.918852i	−0.0562328	+	0.0973981i	−0.892771	−	0.450510i	$-0.851242\pi$
$89$	−0.530499	+	0.918852i	−0.0562328	+	0.0973981i	0.836539	+	0.547908i	$0.184576\pi$
$90$		0			0
$91$	−0.115957	−	1.82724i	−0.0121556	−	0.191547i
$92$		0			0
$93$	0.638260	−	1.10550i	0.0661845	−	0.114635i
$94$		0			0
$95$	−1.48307	−	2.56876i	−0.152160	−	0.263549i
$96$		0			0
$97$	5.85623			0.594610			0.297305	−	0.954783i	$-0.403912\pi$
$97$	5.85623			0.594610			0.297305	+	0.954783i	$0.403912\pi$
$98$		0			0
$99$	2.96077			0.297569
$100$		0			0
$101$	5.78836	+	10.0257i	0.575964	+	0.997599i	0.995936	+	0.0900616i	$0.0287064\pi$
$101$	5.78836	+	10.0257i	0.575964	+	0.997599i	−0.419972	+	0.907537i	$0.637960\pi$
$102$		0			0
$103$	2.83728	−	4.91432i	0.279566	−	0.484222i	−0.691711	−	0.722174i	$-0.743143\pi$
$103$	2.83728	−	4.91432i	0.279566	−	0.484222i	0.971277	+	0.237952i	$0.0764762\pi$
$104$		0			0
$105$	0.130727	+	2.05999i	0.0127577	+	0.201034i
$106$		0			0
$107$	5.73221	−	9.92848i	0.554154	−	0.959822i	−0.443815	−	0.896118i	$-0.646375\pi$
$107$	5.73221	−	9.92848i	0.554154	−	0.959822i	0.997969	−	0.0637039i	$-0.0202913\pi$
$108$		0			0
$109$	−8.01842	−	13.8883i	−0.768025	−	1.33026i	−0.938632	−	0.344919i	$-0.887906\pi$
$109$	−8.01842	−	13.8883i	−0.768025	−	1.33026i	0.170607	−	0.985339i	$-0.445427\pi$
$110$		0			0
$111$	2.00000			0.189832
$112$		0			0
$113$	−15.6189			−1.46931			−0.734653	−	0.678443i	$-0.762655\pi$
$113$	−15.6189			−1.46931			−0.734653	+	0.678443i	$0.762655\pi$
$114$		0			0
$115$	1.26659	+	2.19381i	0.118110	+	0.204573i
$116$		0			0
$117$	1.02446	−	1.77441i	0.0947112	−	0.164045i
$118$		0			0
$119$	−1.87435	+	1.24679i	−0.171822	+	0.114293i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−0.188137	−	0.325862i	−0.0169637	−	0.0293820i
$124$		0			0
$125$	−21.7265			−1.94327
$126$		0			0
$127$	19.1739			1.70141			0.850704	−	0.525645i	$-0.176176\pi$
$127$	19.1739			1.70141			0.850704	+	0.525645i	$0.176176\pi$
$128$		0			0
$129$	0.294937	+	0.510847i	0.0259678	+	0.0449775i
$130$		0			0
$131$	6.40850	−	11.0999i	0.559913	−	0.969798i	−0.437590	−	0.899175i	$-0.644168\pi$
$131$	6.40850	−	11.0999i	0.559913	−	0.969798i	0.997503	−	0.0706236i	$-0.0224989\pi$
$132$		0			0
$133$	−1.78501	−	0.884879i	−0.154780	−	0.0767287i
$134$		0			0
$135$	−2.32520	+	4.02736i	−0.200121	+	0.346620i
$136$		0			0
$137$	7.38889	+	12.7979i	0.631275	+	1.09340i	0.987291	+	0.158921i	$0.0508015\pi$
$137$	7.38889	+	12.7979i	0.631275	+	1.09340i	−0.356016	+	0.934480i	$0.615865\pi$
$138$		0			0
$139$	−2.10992			−0.178961			−0.0894804	−	0.995989i	$-0.528521\pi$
$139$	−2.10992			−0.178961			−0.0894804	+	0.995989i	$0.528521\pi$
$140$		0			0
$141$	2.51035			0.211410
$142$		0			0
$143$	0.346011	+	0.599308i	0.0289349	+	0.0501167i
$144$		0			0
$145$	10.7002	−	18.5333i	0.888605	−	1.53911i
$146$		0			0
$147$	0.839437	+	1.10343i	0.0692356	+	0.0910090i
$148$		0			0
$149$	−6.65883	+	11.5334i	−0.545513	+	0.944856i	0.453062	+	0.891479i	$0.350332\pi$
$149$	−6.65883	+	11.5334i	−0.545513	+	0.944856i	−0.998574	+	0.0533768i	$0.983002\pi$
$150$		0			0
$151$	0.928116	+	1.60754i	0.0755290	+	0.130820i	0.901316	−	0.433162i	$-0.142602\pi$
$151$	0.928116	+	1.60754i	0.0755290	+	0.130820i	−0.825787	+	0.563982i	$0.809269\pi$
$152$		0			0
$153$	−2.51919			−0.203664
$154$		0			0
$155$	25.3870			2.03914
$156$		0			0
$157$	6.08211	+	10.5345i	0.485405	+	0.840746i	0.999859	−	0.0167718i	$-0.00533889\pi$
$157$	6.08211	+	10.5345i	0.485405	+	0.840746i	−0.514455	+	0.857518i	$0.672006\pi$
$158$		0			0
$159$	0.200218	−	0.346788i	0.0158783	−	0.0275021i
$160$		0			0
$161$	1.52446	+	0.755716i	0.120144	+	0.0595587i
$162$		0			0
$163$	3.65883	−	6.33729i	0.286582	−	0.496375i	−0.686410	−	0.727215i	$-0.740814\pi$
$163$	3.65883	−	6.33729i	0.286582	−	0.496375i	0.972992	+	0.230841i	$0.0741476\pi$
$164$		0			0
$165$	−0.390084	−	0.675645i	−0.0303680	−	0.0525989i
$166$		0			0
$167$	−22.5623			−1.74592			−0.872960	−	0.487792i	$-0.837802\pi$
$167$	−22.5623			−1.74592			−0.872960	+	0.487792i	$0.837802\pi$
$168$		0			0
$169$	−12.5211			−0.963162
$170$		0			0
$171$	−1.11476	−	1.93082i	−0.0852479	−	0.147654i
$172$		0			0
$173$	−2.53199	+	4.38554i	−0.192504	+	0.333426i	−0.946079	−	0.323935i	$-0.894994\pi$
$173$	−2.53199	+	4.38554i	−0.192504	+	0.333426i	0.753576	+	0.657361i	$0.228327\pi$
$174$		0			0
$175$	−23.1652	+	15.4091i	−1.75112	+	1.16481i
$176$		0			0
$177$	−0.766061	+	1.32686i	−0.0575807	+	0.0997327i
$178$		0			0
$179$	−9.12983	−	15.8133i	−0.682395	−	1.18194i	−0.974248	−	0.225480i	$-0.927605\pi$
$179$	−9.12983	−	15.8133i	−0.682395	−	1.18194i	0.291853	−	0.956463i	$-0.405728\pi$
$180$		0			0
$181$	−1.73556			−0.129003			−0.0645017	−	0.997918i	$-0.520546\pi$
$181$	−1.73556			−0.129003			−0.0645017	+	0.997918i	$0.520546\pi$
$182$		0			0
$183$	−1.87800			−0.138826
$184$		0			0
$185$	19.8877	+	34.4465i	1.46217	+	2.53256i
$186$		0			0
$187$	0.425428	−	0.736862i	0.0311103	−	0.0538847i
$188$		0			0
$189$	0.197825	+	3.11731i	0.0143897	+	0.226751i
$190$		0			0
$191$	−10.0036	+	17.3268i	−0.723839	+	1.25373i	0.235612	+	0.971847i	$0.424291\pi$
$191$	−10.0036	+	17.3268i	−0.723839	+	1.25373i	−0.959450	+	0.281878i	$0.909043\pi$
$192$		0			0
$193$	0.693218	+	1.20069i	0.0498989	+	0.0864275i	0.889896	−	0.456163i	$-0.150777\pi$
$193$	0.693218	+	1.20069i	0.0498989	+	0.0864275i	−0.839997	+	0.542591i	$0.817443\pi$
$194$		0			0
$195$	−0.539893			−0.0386625
$196$		0			0
$197$	18.3642			1.30839			0.654197	−	0.756324i	$-0.273007\pi$
$197$	18.3642			1.30839			0.654197	+	0.756324i	$0.273007\pi$
$198$		0			0
$199$	−0.777479	−	1.34663i	−0.0551140	−	0.0954603i	0.837152	−	0.546970i	$-0.184219\pi$
$199$	−0.777479	−	1.34663i	−0.0551140	−	0.0954603i	−0.892266	+	0.451510i	$0.850886\pi$
$200$		0			0
$201$	−0.872625	+	1.51143i	−0.0615502	+	0.106608i
$202$		0			0
$203$	−0.910362	−	14.3454i	−0.0638949	−	1.00685i
$204$		0			0
$205$	3.74160	−	6.48065i	0.261325	−	0.452628i
$206$		0			0
$207$	0.952042	+	1.64899i	0.0661715	+	0.114612i
$208$		0			0
$209$	0.753020			0.0520875
$210$		0			0
$211$	15.5797			1.07255			0.536276	−	0.844043i	$-0.319831\pi$
$211$	15.5797			1.07255			0.536276	+	0.844043i	$0.319831\pi$
$212$		0			0
$213$	−0.0310319	−	0.0537489i	−0.00212627	−	0.00368281i
$214$		0			0
$215$	−5.86563	+	10.1596i	−0.400032	+	0.692876i
$216$		0			0
$217$	14.1978	−	9.44414i	0.963811	−	0.641110i
$218$		0			0
$219$	1.58546	−	2.74609i	0.107135	−	0.185564i
$220$		0			0
$221$	−0.294405	−	0.509924i	−0.0198038	−	0.0343012i
$222$		0			0
$223$	−15.9444			−1.06771			−0.533857	−	0.845575i	$-0.679258\pi$
$223$	−15.9444			−1.06771			−0.533857	+	0.845575i	$0.679258\pi$
$224$		0			0
$225$	−31.1347			−2.07564
$226$		0			0
$227$	4.85421	+	8.40773i	0.322185	+	0.558041i	0.980939	−	0.194318i	$-0.0622493\pi$
$227$	4.85421	+	8.40773i	0.322185	+	0.558041i	−0.658754	+	0.752359i	$0.728916\pi$
$228$		0			0
$229$	4.41185	−	7.64156i	0.291544	−	0.504968i	−0.682631	−	0.730763i	$-0.739165\pi$
$229$	4.41185	−	7.64156i	0.291544	−	0.504968i	0.974175	+	0.225795i	$0.0724979\pi$
$230$		0			0
$231$	−0.469501	−	0.232744i	−0.0308909	−	0.0153134i
$232$		0			0
$233$	5.65883	−	9.80139i	0.370723	−	0.642110i	−0.618954	−	0.785427i	$-0.712443\pi$
$233$	5.65883	−	9.80139i	0.370723	−	0.642110i	0.989677	+	0.143317i	$0.0457768\pi$
$234$		0			0
$235$	24.9626	+	43.2364i	1.62838	+	2.82043i
$236$		0			0
$237$	−1.49635			−0.0971985
$238$		0			0
$239$	5.77479			0.373540			0.186770	−	0.982404i	$-0.440198\pi$
$239$	5.77479			0.373540			0.186770	+	0.982404i	$0.440198\pi$
$240$		0			0
$241$	11.8339	+	20.4970i	0.762290	+	1.32033i	0.941667	+	0.336545i	$0.109259\pi$
$241$	11.8339	+	20.4970i	0.762290	+	1.32033i	−0.179377	+	0.983780i	$0.557408\pi$
$242$		0			0
$243$	−2.62737	+	4.55075i	−0.168546	+	0.291931i
$244$		0			0
$245$	−10.6573	+	25.4301i	−0.680873	+	1.62467i
$246$		0			0
$247$	0.260553	−	0.451291i	0.0165786	−	0.0287150i
$248$		0			0
$249$	−1.30409	−	2.25876i	−0.0826436	−	0.143143i
$250$		0			0
$251$	3.94139			0.248779			0.124389	−	0.992233i	$-0.460303\pi$
$251$	3.94139			0.248779			0.124389	+	0.992233i	$0.460303\pi$
$252$		0			0
$253$	−0.643104			−0.0404316
$254$		0			0
$255$	0.331905	+	0.574876i	0.0207847	+	0.0360001i
$256$		0			0
$257$	−9.23759	+	16.0000i	−0.576225	+	0.998051i	0.419683	+	0.907671i	$0.362141\pi$
$257$	−9.23759	+	16.0000i	−0.576225	+	0.998051i	−0.995907	+	0.0903797i	$0.971192\pi$
$258$		0			0
$259$	23.9366	+	11.8660i	1.48735	+	0.737319i
$260$		0			0
$261$	8.04288	−	13.9307i	0.497842	−	0.862287i
$262$		0			0
$263$	5.35839	+	9.28100i	0.330412	+	0.572291i	0.982593	−	0.185773i	$-0.0594789\pi$
$263$	5.35839	+	9.28100i	0.330412	+	0.572291i	−0.652180	+	0.758064i	$0.726146\pi$
$264$		0			0
$265$	7.96376			0.489210
$266$		0			0
$267$	0.210144			0.0128606
$268$		0			0
$269$	−0.518418	−	0.897926i	−0.0316085	−	0.0547475i	0.849788	−	0.527124i	$-0.176730\pi$
$269$	−0.518418	−	0.897926i	−0.0316085	−	0.0547475i	−0.881397	+	0.472376i	$0.843396\pi$
$270$		0			0
$271$	−14.2409	+	24.6660i	−0.865075	+	1.49835i	0.00189684	+	0.999998i	$0.499396\pi$
$271$	−14.2409	+	24.6660i	−0.865075	+	1.49835i	−0.866972	+	0.498356i	$0.833937\pi$
$272$		0			0
$273$	−0.301938	+	0.200844i	−0.0182741	+	0.0121556i
$274$		0			0
$275$	5.25786	−	9.10689i	0.317061	−	0.549166i
$276$		0			0
$277$	7.27897	+	12.6075i	0.437351	+	0.757514i	0.997484	−	0.0708884i	$-0.0225834\pi$
$277$	7.27897	+	12.6075i	0.437351	+	0.757514i	−0.560133	+	0.828403i	$0.689250\pi$
$278$		0			0
$279$	19.0823			1.14243
$280$		0			0
$281$	−17.7821			−1.06079			−0.530395	−	0.847751i	$-0.677956\pi$
$281$	−17.7821			−1.06079			−0.530395	+	0.847751i	$0.677956\pi$
$282$		0			0
$283$	8.82520	+	15.2857i	0.524604	+	0.908640i	0.999590	+	0.0286468i	$0.00911982\pi$
$283$	8.82520	+	15.2857i	0.524604	+	0.908640i	−0.474986	+	0.879993i	$0.657547\pi$
$284$		0			0
$285$	−0.293741	+	0.508774i	−0.0173997	+	0.0301372i
$286$		0			0
$287$	−0.318331	−	5.01623i	−0.0187905	−	0.296099i
$288$		0			0
$289$	8.13802	−	14.0955i	0.478707	−	0.829145i
$290$		0			0
$291$	−0.579949	−	1.00450i	−0.0339972	−	0.0588849i
$292$		0			0
$293$	−11.9444			−0.697798			−0.348899	−	0.937160i	$-0.613444\pi$
$293$	−11.9444			−0.697798			−0.348899	+	0.937160i	$0.613444\pi$
$294$		0			0
$295$	−30.4704			−1.77405
$296$		0			0
$297$	−0.590302	−	1.02243i	−0.0342528	−	0.0593276i
$298$		0			0
$299$	−0.222521	+	0.385418i	−0.0128687	+	0.0222893i
$300$		0			0
$301$	0.499041	+	7.86384i	0.0287642	+	0.453264i
$302$		0			0
$303$	1.14646	−	1.98572i	0.0658622	−	0.114077i
$304$		0			0
$305$	−18.6746	−	32.3453i	−1.06930	−	1.85209i
$306$		0			0
$307$	−9.99330			−0.570347			−0.285174	−	0.958476i	$-0.592051\pi$
$307$	−9.99330			−0.570347			−0.285174	+	0.958476i	$0.592051\pi$
$308$		0			0
$309$	−1.12392			−0.0639374
$310$		0			0
$311$	−1.15010	−	1.99204i	−0.0652164	−	0.112958i	0.831574	−	0.555415i	$-0.187440\pi$
$311$	−1.15010	−	1.99204i	−0.0652164	−	0.112958i	−0.896790	+	0.442456i	$0.854107\pi$
$312$		0			0
$313$	12.1054	−	20.9671i	0.684236	−	1.18513i	−0.289440	−	0.957196i	$-0.593469\pi$
$313$	12.1054	−	20.9671i	0.684236	−	1.18513i	0.973676	−	0.227935i	$-0.0731974\pi$
$314$		0			0
$315$	−25.6914	+	17.0894i	−1.44754	+	0.962880i
$316$		0			0
$317$	9.95593	−	17.2442i	0.559181	−	0.968529i	−0.438385	−	0.898788i	$-0.644449\pi$
$317$	9.95593	−	17.2442i	0.559181	−	0.968529i	0.997565	−	0.0697416i	$-0.0222175\pi$
$318$		0			0
$319$	2.71648	+	4.70508i	0.152094	+	0.263434i
$320$		0			0
$321$	−2.27067			−0.126736
$322$		0			0
$323$	−0.640711			−0.0356501
$324$		0			0
$325$	−3.63856	−	6.30216i	−0.201831	−	0.349581i
$326$		0			0
$327$	−1.58815	+	2.75075i	−0.0878247	+	0.152117i
$328$		0			0
$329$	30.0447	+	14.8940i	1.65642	+	0.821131i
$330$		0			0
$331$	14.1625	−	24.5301i	0.778440	−	1.34830i	−0.154400	−	0.988008i	$-0.549344\pi$
$331$	14.1625	−	24.5301i	0.778440	−	1.34830i	0.932840	−	0.360290i	$-0.117322\pi$
$332$		0			0
$333$	14.9487	+	25.8919i	0.819183	+	1.41887i
$334$		0			0
$335$	−34.7090			−1.89636
$336$		0			0
$337$	4.49827			0.245036			0.122518	−	0.992466i	$-0.460903\pi$
$337$	4.49827			0.245036			0.122518	+	0.992466i	$0.460903\pi$
$338$		0			0
$339$	1.54676	+	2.67907i	0.0840085	+	0.145507i
$340$		0			0
$341$	−3.22252	+	5.58157i	−0.174509	+	0.302259i
$342$		0			0
$343$	3.50000	+	18.1865i	0.188982	+	0.981981i
$344$		0			0
$345$	0.250864	−	0.434510i	0.0135061	−	0.0233932i
$346$		0			0
$347$	−12.2322	−	21.1868i	−0.656659	−	1.13737i	−0.981475	−	0.191590i	$-0.938636\pi$
$347$	−12.2322	−	21.1868i	−0.656659	−	1.13737i	0.324816	−	0.945777i	$-0.394698\pi$
$348$		0			0
$349$	18.5254			0.991643			0.495821	−	0.868424i	$-0.334867\pi$
$349$	18.5254			0.991643			0.495821	+	0.868424i	$0.334867\pi$
$350$		0			0
$351$	−0.817003			−0.0436084
$352$		0			0
$353$	−0.730054	−	1.26449i	−0.0388568	−	0.0673020i	0.845943	−	0.533273i	$-0.179038\pi$
$353$	−0.730054	−	1.26449i	−0.0388568	−	0.0673020i	−0.884800	+	0.465971i	$0.845705\pi$
$354$		0			0
$355$	0.617154	−	1.06894i	0.0327551	−	0.0567335i
$356$		0			0
$357$	0.399477	+	0.198032i	0.0211426	+	0.0104809i
$358$		0			0
$359$	2.17241	−	3.76272i	0.114655	−	0.198589i	−0.802987	−	0.595997i	$-0.796757\pi$
$359$	2.17241	−	3.76272i	0.114655	−	0.198589i	0.917642	+	0.397408i	$0.130090\pi$
$360$		0			0
$361$	9.21648	+	15.9634i	0.485078	+	0.840180i
$362$		0			0
$363$	0.198062			0.0103956
$364$		0			0
$365$	63.0622			3.30083
$366$		0			0
$367$	7.76002	+	13.4408i	0.405070	+	0.701601i	0.994330	−	0.106342i	$-0.0339139\pi$
$367$	7.76002	+	13.4408i	0.405070	+	0.701601i	−0.589260	+	0.807944i	$0.700581\pi$
$368$		0			0
$369$	2.81240	−	4.87121i	0.146407	−	0.253585i
$370$		0			0
$371$	4.45377	−	2.96257i	0.231228	−	0.153809i
$372$		0			0
$373$	−9.44869	+	16.3656i	−0.489235	+	0.847379i	−0.999923	−	0.0123865i	$-0.996057\pi$
$373$	−9.44869	+	16.3656i	−0.489235	+	0.847379i	0.510689	+	0.859766i	$0.329390\pi$
$374$		0			0
$375$	2.15160	+	3.72667i	0.111108	+	0.192445i
$376$		0			0
$377$	3.75973			0.193636
$378$		0			0
$379$	22.3220			1.14660			0.573302	−	0.819344i	$-0.305662\pi$
$379$	22.3220			1.14660			0.573302	+	0.819344i	$0.305662\pi$
$380$		0			0
$381$	−1.89881	−	3.28884i	−0.0972791	−	0.168492i
$382$		0			0
$383$	−14.5025	+	25.1190i	−0.741041	+	1.28352i	0.210981	+	0.977490i	$0.432334\pi$
$383$	−14.5025	+	25.1190i	−0.741041	+	1.28352i	−0.952022	+	0.306030i	$0.900999\pi$
$384$		0			0
$385$	−0.660030	−	10.4007i	−0.0336382	−	0.530069i
$386$		0			0
$387$	−4.40893	+	7.63649i	−0.224118	+	0.388185i
$388$		0			0
$389$	−15.1766	−	26.2866i	−0.769484	−	1.33278i	−0.937843	−	0.347059i	$-0.887180\pi$
$389$	−15.1766	−	26.2866i	−0.769484	−	1.33278i	0.168360	−	0.985726i	$-0.446153\pi$
$390$		0			0
$391$	0.547188			0.0276725
$392$		0			0
$393$	−2.53856			−0.128054
$394$		0			0
$395$	−14.8795	−	25.7720i	−0.748669	−	1.29673i
$396$		0			0
$397$	19.5187	−	33.8074i	0.979616	−	1.69674i	0.315842	−	0.948812i	$-0.397713\pi$
$397$	19.5187	−	33.8074i	0.979616	−	1.69674i	0.663774	−	0.747933i	$-0.268954\pi$
$398$		0			0
$399$	0.0249911	+	0.393808i	0.00125112	+	0.0197151i
$400$		0			0
$401$	4.77293	−	8.26696i	0.238349	−	0.412832i	−0.721892	−	0.692006i	$-0.756727\pi$
$401$	4.77293	−	8.26696i	0.238349	−	0.412832i	0.960241	+	0.279174i	$0.0900605\pi$
$402$		0			0
$403$	2.23005	+	3.86257i	0.111087	+	0.192408i
$404$		0			0
$405$	−34.0664			−1.69277
$406$		0			0
$407$	−10.0978			−0.500531
$408$		0			0
$409$	−10.1169	−	17.5230i	−0.500249	−	0.866457i	−1.00000		0.000287922i	$-0.999908\pi$
$409$	−10.1169	−	17.5230i	−0.500249	−	0.866457i	0.499751	−	0.866169i	$-0.333425\pi$
$410$		0			0
$411$	1.46346	−	2.53479i	0.0721871	−	0.125032i
$412$		0			0
$413$	−17.0407	+	11.3352i	−0.838519	+	0.557768i
$414$		0			0
$415$	25.9354	−	44.9215i	1.27312	−	2.20511i
$416$		0			0
$417$	0.208947	+	0.361908i	0.0102322	+	0.0177227i
$418$		0			0
$419$	2.24267			0.109561			0.0547807	−	0.998498i	$-0.482554\pi$
$419$	2.24267			0.109561			0.0547807	+	0.998498i	$0.482554\pi$
$420$		0			0
$421$	14.4319			0.703368			0.351684	−	0.936119i	$-0.385609\pi$
$421$	14.4319			0.703368			0.351684	+	0.936119i	$0.385609\pi$
$422$		0			0
$423$	18.7632	+	32.4989i	0.912300	+	1.58015i
$424$		0			0
$425$	−4.47368	+	7.74864i	−0.217005	+	0.375864i
$426$		0			0
$427$	−22.4765	−	11.1422i	−1.08771	−	0.539210i
$428$		0			0
$429$	0.0685317	−	0.118700i	0.00330874	−	0.00573091i
$430$		0			0
$431$	−11.6032	−	20.0974i	−0.558907	−	0.968055i	−0.997588	−	0.0694125i	$-0.977888\pi$
$431$	−11.6032	−	20.0974i	−0.558907	−	0.968055i	0.438681	−	0.898643i	$-0.355446\pi$
$432$		0			0
$433$	−18.1521			−0.872336			−0.436168	−	0.899865i	$-0.643665\pi$
$433$	−18.1521			−0.872336			−0.436168	+	0.899865i	$0.643665\pi$
$434$		0			0
$435$	−4.23862			−0.203226
$436$		0			0
$437$	0.242135	+	0.419391i	0.0115829	+	0.0200622i
$438$		0			0
$439$	10.3148	−	17.8658i	0.492301	−	0.852690i	−0.507660	−	0.861558i	$-0.669489\pi$
$439$	10.3148	−	17.8658i	0.492301	−	0.852690i	0.999961	+	0.00886757i	$0.00282267\pi$
$440$		0			0
$441$	−8.01065	+	19.1147i	−0.381459	+	0.910224i
$442$		0			0
$443$	2.60052	−	4.50424i	0.123555	−	0.214003i	−0.797612	−	0.603170i	$-0.793904\pi$
$443$	2.60052	−	4.50424i	0.123555	−	0.214003i	0.921167	+	0.389167i	$0.127237\pi$
$444$		0			0
$445$	2.08964	+	3.61936i	0.0990583	+	0.171574i
$446$		0			0
$447$	2.63773			0.124760
$448$		0			0
$449$	−26.2379			−1.23824			−0.619121	−	0.785296i	$-0.712511\pi$
$449$	−26.2379			−1.23824			−0.619121	+	0.785296i	$0.712511\pi$
$450$		0			0
$451$	0.949886	+	1.64525i	0.0447284	+	0.0774719i
$452$		0			0
$453$	0.183825	−	0.318394i	0.00863684	−	0.0149594i
$454$		0			0
$455$	−6.46160	−	3.20319i	−0.302924	−	0.150168i
$456$		0			0
$457$	1.28836	−	2.23151i	0.0602671	−	0.104386i	−0.834318	−	0.551284i	$-0.814138\pi$
$457$	1.28836	−	2.23151i	0.0602671	−	0.104386i	0.894585	+	0.446898i	$0.147471\pi$
$458$		0			0
$459$	0.502261	+	0.869942i	0.0234436	+	0.0406054i
$460$		0			0
$461$	−23.5599			−1.09729			−0.548646	−	0.836055i	$-0.684857\pi$
$461$	−23.5599			−1.09729			−0.548646	+	0.836055i	$0.684857\pi$
$462$		0			0
$463$	38.5429			1.79124			0.895620	−	0.444821i	$-0.146733\pi$
$463$	38.5429			1.79124			0.895620	+	0.444821i	$0.146733\pi$
$464$		0			0
$465$	−2.51411	−	4.35456i	−0.116589	−	0.201938i
$466$		0			0
$467$	−16.2582	+	28.1600i	−0.752338	+	1.30309i	0.194349	+	0.980932i	$0.437741\pi$
$467$	−16.2582	+	28.1600i	−0.752338	+	1.30309i	−0.946687	+	0.322155i	$0.895593\pi$
$468$		0			0
$469$	−19.4112	+	12.9120i	−0.896325	+	0.596219i
$470$		0			0
$471$	1.20464	−	2.08649i	0.0555067	−	0.0961404i
$472$		0			0
$473$	−1.48911	−	2.57922i	−0.0684696	−	0.118593i
$474$		0			0
$475$	−7.91856			−0.363328
$476$		0			0
$477$	5.98600			0.274080
$478$		0			0
$479$	13.3572	+	23.1353i	0.610306	+	1.05708i	0.991189	+	0.132457i	$0.0422867\pi$
$479$	13.3572	+	23.1353i	0.610306	+	1.05708i	−0.380883	+	0.924623i	$0.624380\pi$
$480$		0			0
$481$	−3.49396	+	6.05171i	−0.159311	+	0.275934i
$482$		0			0
$483$	−0.0213433	−	0.336325i	−0.000971152	−	0.0153033i
$484$		0			0
$485$	11.5339	−	19.9772i	0.523725	−	0.907119i
$486$		0			0
$487$	19.8949	+	34.4590i	0.901525	+	1.56149i	0.825515	+	0.564381i	$0.190885\pi$
$487$	19.8949	+	34.4590i	0.901525	+	1.56149i	0.0760105	+	0.997107i	$0.475782\pi$
$488$		0			0
$489$	−1.44935			−0.0655420
$490$		0			0
$491$	−26.1051			−1.17811			−0.589054	−	0.808094i	$-0.700499\pi$
$491$	−26.1051			−1.17811			−0.589054	+	0.808094i	$0.700499\pi$
$492$		0			0
$493$	−2.31133	−	4.00334i	−0.104097	−	0.180301i
$494$		0			0
$495$	5.83124	−	10.1000i	0.262095	−	0.453961i
$496$		0			0
$497$	−0.0525067	−	0.827396i	−0.00235525	−	0.0371138i
$498$		0			0
$499$	12.3300	−	21.3563i	0.551969	−	0.956038i	−0.446164	−	0.894951i	$-0.647210\pi$
$499$	12.3300	−	21.3563i	0.551969	−	0.956038i	0.998132	−	0.0610864i	$-0.0194565\pi$
$500$		0			0
$501$	2.23437	+	3.87003i	0.0998241	+	0.172900i
$502$		0			0
$503$	21.7972			0.971887			0.485943	−	0.873990i	$-0.338476\pi$
$503$	21.7972			0.971887			0.485943	+	0.873990i	$0.338476\pi$
$504$		0			0
$505$	45.6007			2.02921
$506$		0			0
$507$	1.23998	+	2.14771i	0.0550694	+	0.0953830i
$508$		0			0
$509$	−7.96897	+	13.8027i	−0.353218	+	0.611792i	−0.986811	−	0.161874i	$-0.948246\pi$
$509$	−7.96897	+	13.8027i	−0.353218	+	0.611792i	0.633593	+	0.773666i	$0.281579\pi$
$510$		0			0
$511$	35.2678	−	23.4595i	1.56016	−	1.03779i
$512$		0			0
$513$	−0.444509	+	0.769913i	−0.0196256	+	0.0339925i
$514$		0			0
$515$	−11.1761	−	19.3575i	−0.492476	−	0.852993i
$516$		0			0
$517$	−12.6746			−0.557427
$518$		0			0
$519$	1.00298			0.0440261
$520$		0			0
$521$	13.0746	+	22.6458i	0.572807	+	0.992132i	0.996276	+	0.0862208i	$0.0274790\pi$
$521$	13.0746	+	22.6458i	0.572807	+	0.992132i	−0.423469	+	0.905911i	$0.639188\pi$
$522$		0			0
$523$	−2.80947	+	4.86615i	−0.122850	+	0.212782i	−0.920890	−	0.389822i	$-0.872537\pi$
$523$	−2.80947	+	4.86615i	−0.122850	+	0.212782i	0.798041	+	0.602603i	$0.205870\pi$
$524$		0			0
$525$	4.93714	+	2.44748i	0.215474	+	0.106817i
$526$		0			0
$527$	2.74190	−	4.74911i	0.119439	−	0.206874i
$528$		0			0
$529$	11.2932	+	19.5604i	0.491009	+	0.850453i
$530$		0			0
$531$	−22.9032			−0.993916
$532$		0			0
$533$	1.31468			0.0569453
$534$		0			0
$535$	−22.5792	−	39.1083i	−0.976183	−	1.69080i
$536$		0			0
$537$	−1.80827	+	3.13202i	−0.0780328	+	0.135157i
$538$		0			0
$539$	−4.23825	−	5.57111i	−0.182554	−	0.239965i
$540$		0			0
$541$	−12.5087	+	21.6658i	−0.537792	+	0.931484i	0.461230	+	0.887280i	$0.347408\pi$
$541$	−12.5087	+	21.6658i	−0.537792	+	0.931484i	−0.999023	+	0.0442031i	$0.985925\pi$
$542$		0			0
$543$	0.171875	+	0.297696i	0.00737585	+	0.0127753i
$544$		0			0
$545$	−63.1691			−2.70587
$546$		0			0
$547$	−33.0194			−1.41181			−0.705903	−	0.708308i	$-0.749459\pi$
$547$	−33.0194			−1.41181			−0.705903	+	0.708308i	$0.749459\pi$
$548$		0			0
$549$	−14.0368	−	24.3125i	−0.599078	−	1.03763i
$550$		0			0
$551$	2.04556	−	3.54302i	0.0871440	−	0.150938i
$552$		0			0
$553$	−17.9088	−	8.87788i	−0.761560	−	0.377526i
$554$		0			0
$555$	3.93900	−	6.82255i	0.167201	−	0.289601i
$556$		0			0
$557$	7.54623	+	13.0705i	0.319744	+	0.553813i	0.980435	−	0.196846i	$-0.0630698\pi$
$557$	7.54623	+	13.0705i	0.319744	+	0.553813i	−0.660691	+	0.750658i	$0.729736\pi$
$558$		0			0
$559$	−2.06100			−0.0871710
$560$		0			0
$561$	−0.168522			−0.00711502
$562$		0			0
$563$	−12.0523	−	20.8751i	−0.507943	−	0.879782i	−0.999958	−	0.00919575i	$-0.997073\pi$
$563$	−12.0523	−	20.8751i	−0.507943	−	0.879782i	0.492015	−	0.870587i	$-0.336260\pi$
$564$		0			0
$565$	−30.7615	+	53.2805i	−1.29415	+	2.24153i
$566$		0			0
$567$	−19.0518	+	12.6729i	−0.800100	+	0.532212i
$568$		0			0
$569$	20.0383	−	34.7074i	0.840050	−	1.45501i	−0.0498008	−	0.998759i	$-0.515859\pi$
$569$	20.0383	−	34.7074i	0.840050	−	1.45501i	0.889851	−	0.456251i	$-0.150808\pi$
$570$		0			0
$571$	11.0782	+	19.1880i	0.463609	+	0.802995i	0.999138	−	0.0415227i	$-0.0132209\pi$
$571$	11.0782	+	19.1880i	0.463609	+	0.802995i	−0.535528	+	0.844517i	$0.679888\pi$
$572$		0			0
$573$	3.96269			0.165544
$574$		0			0
$575$	6.76271			0.282024
$576$		0			0
$577$	13.0903	+	22.6731i	0.544956	+	0.943892i	0.998610	+	0.0527139i	$0.0167871\pi$
$577$	13.0903	+	22.6731i	0.544956	+	0.943892i	−0.453653	+	0.891178i	$0.649880\pi$
$578$		0			0
$579$	0.137300	−	0.237811i	0.00570601	−	0.00988309i
$580$		0			0
$581$	−2.20655	−	34.7707i	−0.0915433	−	1.44253i
$582$		0			0
$583$	−1.01089	+	1.75090i	−0.0418666	+	0.0725151i
$584$		0			0
$585$	−4.03534	−	6.98942i	−0.166841	−	0.288977i
$586$		0			0
$587$	−18.6450			−0.769562			−0.384781	−	0.923008i	$-0.625723\pi$
$587$	−18.6450			−0.769562			−0.384781	+	0.923008i	$0.625723\pi$
$588$		0			0
$589$	4.85325			0.199975
$590$		0			0
$591$	−1.81863	−	3.14995i	−0.0748083	−	0.129572i
$592$		0			0
$593$	3.97554	−	6.88584i	0.163256	−	0.282768i	−0.772779	−	0.634676i	$-0.781134\pi$
$593$	3.97554	−	6.88584i	0.163256	−	0.282768i	0.936035	+	0.351908i	$0.114467\pi$
$594$		0			0
$595$	0.561590	+	8.84948i	0.0230229	+	0.362793i
$596$		0			0
$597$	−0.153989	+	0.266717i	−0.00630236	+	0.0109160i
$598$		0			0
$599$	−9.63826	−	16.6940i	−0.393809	−	0.682097i	0.599140	−	0.800644i	$-0.295509\pi$
$599$	−9.63826	−	16.6940i	−0.393809	−	0.682097i	−0.992948	+	0.118548i	$0.962176\pi$
$600$		0			0
$601$	2.18896			0.0892897			0.0446449	−	0.999003i	$-0.485784\pi$
$601$	2.18896			0.0892897			0.0446449	+	0.999003i	$0.485784\pi$
$602$		0			0
$603$	−26.0892			−1.06243
$604$		0			0
$605$	1.96950	+	3.41127i	0.0800716	+	0.138688i
$606$		0			0
$607$	16.6027	−	28.7567i	0.673882	−	1.16720i	−0.302912	−	0.953018i	$-0.597959\pi$
$607$	16.6027	−	28.7567i	0.673882	−	1.16720i	0.976794	−	0.214179i	$-0.0687077\pi$
$608$		0			0
$609$	−2.37047	+	1.57679i	−0.0960563	+	0.0638949i
$610$		0			0
$611$	−4.38553	+	7.59597i	−0.177420	+	0.307300i
$612$		0			0
$613$	−2.34481	−	4.06134i	−0.0947062	−	0.164036i	0.814780	−	0.579771i	$-0.196858\pi$
$613$	−2.34481	−	4.06134i	−0.0947062	−	0.164036i	−0.909486	+	0.415735i	$0.863524\pi$
$614$		0			0
$615$	−1.48214			−0.0597657
$616$		0			0
$617$	−4.00000			−0.161034			−0.0805170	−	0.996753i	$-0.525657\pi$
$617$	−4.00000			−0.161034			−0.0805170	+	0.996753i	$0.525657\pi$
$618$		0			0
$619$	22.7114	+	39.3373i	0.912848	+	1.58110i	0.810022	+	0.586400i	$0.199455\pi$
$619$	22.7114	+	39.3373i	0.912848	+	1.58110i	0.102827	+	0.994699i	$0.467211\pi$
$620$		0			0
$621$	0.379626	−	0.657531i	0.0152339	−	0.0263858i
$622$		0			0
$623$	2.51507	+	1.24679i	0.100764	+	0.0499514i
$624$		0			0
$625$	−16.5010	+	28.5805i	−0.660038	+	1.14322i
$626$		0			0
$627$	−0.0745725	−	0.129163i	−0.00297814	−	0.00515829i
$628$		0			0
$629$	8.59179			0.342577
$630$		0			0
$631$	16.9239			0.673731			0.336866	−	0.941553i	$-0.390633\pi$
$631$	16.9239			0.673731			0.336866	+	0.941553i	$0.390633\pi$
$632$		0			0
$633$	−1.54288	−	2.67234i	−0.0613238	−	0.106216i
$634$		0			0
$635$	37.7630	−	65.4074i	1.49858	−	2.59562i
$636$		0			0
$637$	−4.80529	+	0.612355i	−0.190393	+	0.0242624i
$638$		0			0
$639$	0.463887	−	0.803475i	0.0183511	−	0.0317850i
$640$		0			0
$641$	−15.4695	−	26.7940i	−0.611009	−	1.05830i	−0.991071	−	0.133337i	$-0.957431\pi$
$641$	−15.4695	−	26.7940i	−0.611009	−	1.05830i	0.380062	−	0.924961i	$-0.375903\pi$
$642$		0			0
$643$	−1.83446			−0.0723441			−0.0361721	−	0.999346i	$-0.511516\pi$
$643$	−1.83446			−0.0723441			−0.0361721	+	0.999346i	$0.511516\pi$
$644$		0			0
$645$	2.32352			0.0914884
$646$		0			0
$647$	0.0586060	+	0.101509i	0.00230404	+	0.00399071i	0.867175	−	0.498003i	$-0.165933\pi$
$647$	0.0586060	+	0.101509i	0.00230404	+	0.00399071i	−0.864871	+	0.501994i	$0.832600\pi$
$648$		0			0
$649$	3.86778	−	6.69919i	0.151824	−	0.262966i
$650$		0			0
$651$	−3.02595	−	1.50005i	−0.118596	−	0.0587914i
$652$		0			0
$653$	−3.92812	+	6.80370i	−0.153719	+	0.266249i	−0.932592	−	0.360933i	$-0.882458\pi$
$653$	−3.92812	+	6.80370i	−0.153719	+	0.266249i	0.778873	+	0.627182i	$0.215792\pi$
$654$		0			0
$655$	−25.2431	−	43.7223i	−0.986329	−	1.70837i
$656$		0			0
$657$	47.4010			1.84929
$658$		0			0
$659$	28.3314			1.10363			0.551817	−	0.833965i	$-0.313935\pi$
$659$	28.3314			1.10363			0.551817	+	0.833965i	$0.313935\pi$
$660$		0			0
$661$	−23.9792	−	41.5332i	−0.932682	−	1.61545i	−0.778715	−	0.627377i	$-0.784128\pi$
$661$	−23.9792	−	41.5332i	−0.932682	−	1.61545i	−0.153967	−	0.988076i	$-0.549205\pi$
$662$		0			0
$663$	−0.0583105	+	0.100997i	−0.00226459	+	0.00392239i
$664$		0			0
$665$	−6.53415	+	4.34640i	−0.253383	+	0.168546i
$666$		0			0
$667$	−1.74698	+	3.02586i	−0.0676433	+	0.117162i
$668$		0			0
$669$	1.57899	+	2.73489i	0.0610473	+	0.105737i
$670$		0			0
$671$	9.48188			0.366044
$672$		0			0
$673$	−18.4698			−0.711958			−0.355979	−	0.934494i	$-0.615853\pi$
$673$	−18.4698			−0.711958			−0.355979	+	0.934494i	$0.615853\pi$
$674$		0			0
$675$	6.20746	+	10.7516i	0.238925	+	0.413830i
$676$		0			0
$677$	8.98039	−	15.5545i	0.345144	−	0.597807i	−0.640236	−	0.768179i	$-0.721163\pi$
$677$	8.98039	−	15.5545i	0.345144	−	0.597807i	0.985380	+	0.170371i	$0.0544967\pi$
$678$		0			0
$679$	−0.981287	−	15.4630i	−0.0376583	−	0.593417i
$680$		0			0
$681$	0.961435	−	1.66525i	0.0368423	−	0.0638127i
$682$		0			0
$683$	−14.5591	−	25.2172i	−0.557090	−	0.964908i	−0.997738	−	0.0672280i	$-0.978585\pi$
$683$	−14.5591	−	25.2172i	−0.557090	−	0.964908i	0.440648	−	0.897680i	$-0.354749\pi$
$684$		0			0
$685$	58.2097			2.22408
$686$		0			0
$687$	−1.74764			−0.0666768
$688$		0			0
$689$	0.699554	+	1.21166i	0.0266509	+	0.0461607i
$690$		0			0
$691$	−11.0422	+	19.1257i	−0.420066	+	0.727575i	−0.995945	−	0.0899594i	$-0.971326\pi$
$691$	−11.0422	+	19.1257i	−0.420066	+	0.727575i	0.575880	+	0.817534i	$0.304660\pi$
$692$		0			0
$693$	−0.496115	−	7.81774i	−0.0188459	−	0.296971i
$694$		0			0
$695$	−4.15548	+	7.19750i	−0.157626	+	0.273017i
$696$		0			0
$697$	−0.808216	−	1.39987i	−0.0306133	−	0.0530239i
$698$		0			0
$699$	−2.24160			−0.0847852
$700$		0			0
$701$	−19.5056			−0.736715			−0.368358	−	0.929684i	$-0.620080\pi$
$701$	−19.5056			−0.736715			−0.368358	+	0.929684i	$0.620080\pi$
$702$		0			0
$703$	3.80194	+	6.58515i	0.143393	+	0.248364i
$704$		0			0
$705$	4.94414	−	8.56350i	0.186207	−	0.322520i
$706$		0			0
$707$	25.5025	−	16.9638i	0.959118	−	0.637988i
$708$		0			0
$709$	21.0516	−	36.4625i	0.790610	−	1.36938i	−0.134980	−	0.990848i	$-0.543097\pi$
$709$	21.0516	−	36.4625i	0.790610	−	1.36938i	0.925590	−	0.378528i	$-0.123570\pi$
$710$		0			0
$711$	−11.1843	−	19.3717i	−0.419442	−	0.726495i
$712$		0			0
$713$	−4.14483			−0.155225
$714$		0			0
$715$	2.72587			0.101942
$716$		0			0
$717$	−0.571884	−	0.990532i	−0.0213574	−	0.0369921i
$718$		0			0
$719$	2.27210	−	3.93540i	0.0847351	−	0.146766i	−0.820543	−	0.571585i	$-0.806329\pi$
$719$	2.27210	−	3.93540i	0.0847351	−	0.146766i	0.905278	+	0.424819i	$0.139662\pi$
$720$		0			0
$721$	−13.4514	−	6.66821i	−0.500956	−	0.248337i
$722$		0			0
$723$	2.34385	−	4.05968i	0.0871689	−	0.150981i
$724$		0			0
$725$	−28.5658	−	49.4774i	−1.06091	−	1.83754i
$726$		0			0
$727$	−4.46442			−0.165576			−0.0827881	−	0.996567i	$-0.526382\pi$
$727$	−4.46442			−0.165576			−0.0827881	+	0.996567i	$0.526382\pi$
$728$		0			0
$729$	−24.9047			−0.922395
$730$		0			0
$731$	1.26702	+	2.19454i	0.0468625	+	0.0811682i
$732$		0			0
$733$	−21.7136	+	37.6090i	−0.802008	+	1.38912i	0.116284	+	0.993216i	$0.462902\pi$
$733$	−21.7136	+	37.6090i	−0.802008	+	1.38912i	−0.918292	+	0.395903i	$0.870432\pi$
$734$		0			0
$735$	5.41736	−	0.690354i	0.199822	−	0.0254641i
$736$		0			0
$737$	4.40581	−	7.63109i	0.162290	−	0.281095i
$738$		0			0
$739$	0.650341	+	1.12642i	0.0239232	+	0.0414362i	0.877739	−	0.479139i	$-0.159051\pi$
$739$	0.650341	+	1.12642i	0.0239232	+	0.0414362i	−0.853816	+	0.520575i	$0.825718\pi$
$740$		0			0
$741$	−0.103211			−0.00379157
$742$		0			0
$743$	−1.37867			−0.0505784			−0.0252892	−	0.999680i	$-0.508051\pi$
$743$	−1.37867			−0.0505784			−0.0252892	+	0.999680i	$0.508051\pi$
$744$		0			0
$745$	26.2292	+	45.4302i	0.960962	+	1.66443i
$746$		0			0
$747$	19.4945	−	33.7655i	0.713266	−	1.23541i
$748$		0			0
$749$	−27.1761	−	13.4719i	−0.992991	−	0.492253i
$750$		0			0
$751$	−13.2262	+	22.9084i	−0.482630	+	0.835939i	−0.999801	−	0.0199426i	$-0.993652\pi$
$751$	−13.2262	+	22.9084i	−0.482630	+	0.835939i	0.517171	+	0.855882i	$0.326985\pi$
$752$		0			0
$753$	−0.390321	−	0.676055i	−0.0142241	−	0.0246368i
$754$		0			0
$755$	7.31170			0.266100
$756$		0			0
$757$	−22.2083			−0.807176			−0.403588	−	0.914941i	$-0.632237\pi$
$757$	−22.2083			−0.807176			−0.403588	+	0.914941i	$0.632237\pi$
$758$		0			0
$759$	0.0636873	+	0.110310i	0.00231170	+	0.00400399i
$760$		0			0
$761$	14.9351	−	25.8684i	0.541398	−	0.937728i	−0.457427	−	0.889247i	$-0.651229\pi$
$761$	14.9351	−	25.8684i	0.541398	−	0.937728i	0.998824	−	0.0484807i	$-0.0154379\pi$
$762$		0			0
$763$	−35.3277	+	23.4993i	−1.27895	+	0.850732i
$764$		0			0
$765$	−4.96154	+	8.59364i	−0.179385	+	0.310704i
$766$		0			0
$767$	−2.67659	−	4.63599i	−0.0966460	−	0.167396i
$768$		0			0
$769$	−5.16554			−0.186274			−0.0931370	−	0.995653i	$-0.529689\pi$
$769$	−5.16554			−0.186274			−0.0931370	+	0.995653i	$0.529689\pi$
$770$		0			0
$771$	3.65923			0.131784
$772$		0			0
$773$	−6.45689	−	11.1837i	−0.232238	−	0.402248i	0.726228	−	0.687454i	$-0.241272\pi$
$773$	−6.45689	−	11.1837i	−0.232238	−	0.402248i	−0.958466	+	0.285205i	$0.907938\pi$
$774$		0			0
$775$	33.8872	−	58.6943i	1.21726	−	2.10836i
$776$		0			0
$777$	−0.335126	−	5.28088i	−0.0120226	−	0.189451i
$778$		0			0
$779$	0.715284	−	1.23891i	0.0256277	−	0.0443885i
$780$		0			0
$781$	0.156678	+	0.271374i	0.00560637	+	0.00971051i
$782$		0			0
$783$	−6.41417			−0.229224
$784$		0			0
$785$	47.9148			1.71015
$786$		0			0
$787$	−9.21193	−	15.9555i	−0.328370	−	0.568753i	0.653819	−	0.756651i	$-0.273166\pi$
$787$	−9.21193	−	15.9555i	−0.328370	−	0.568753i	−0.982189	+	0.187898i	$0.939833\pi$
$788$		0			0
$789$	1.06129	−	1.83822i	0.0377831	−	0.0654422i
$790$		0			0
$791$	2.61715	+	41.2409i	0.0930553	+	1.46636i
$792$		0			0
$793$	3.28083	−	5.68257i	0.116506	−	0.201794i
$794$		0			0
$795$	−0.788660	−	1.36600i	−0.0279709	−	0.0484470i
$796$		0			0
$797$	34.7469			1.23080			0.615399	−	0.788216i	$-0.288995\pi$
$797$	34.7469			1.23080			0.615399	+	0.788216i	$0.288995\pi$
$798$		0			0
$799$	10.7842			0.381518
$800$		0			0
$801$	1.57069	+	2.72051i	0.0554975	+	0.0961245i
$802$		0			0
$803$	−8.00484	+	13.8648i	−0.282485	+	0.489278i
$804$		0			0
$805$	5.58038	−	3.71197i	0.196682	−	0.130830i
$806$		0			0
$807$	−0.102679	+	0.177845i	−0.00361447	+	0.00626045i
$808$		0			0
$809$	−3.37502	−	5.84570i	−0.118659	−	0.205524i	0.800577	−	0.599230i	$-0.204526\pi$
$809$	−3.37502	−	5.84570i	−0.118659	−	0.205524i	−0.919237	+	0.393706i	$0.871193\pi$
$810$		0			0
$811$	26.3062			0.923735			0.461867	−	0.886949i	$-0.347180\pi$
$811$	26.3062			0.923735			0.461867	+	0.886949i	$0.347180\pi$
$812$		0			0
$813$	5.64119			0.197845
$814$		0			0
$815$	−14.4121	−	24.9626i	−0.504836	−	0.874401i
$816$		0			0
$817$	−1.12133	+	1.94221i	−0.0392305	+	0.0679492i
$818$		0			0
$819$	−4.85690	−	2.40770i	−0.169714	−	0.0841317i
$820$		0			0
$821$	−5.26002	+	9.11062i	−0.183576	+	0.317963i	−0.943096	−	0.332521i	$-0.892101\pi$
$821$	−5.26002	+	9.11062i	−0.183576	+	0.317963i	0.759520	+	0.650484i	$0.225434\pi$
$822$		0			0
$823$	1.66517	+	2.88416i	0.0580442	+	0.100535i	0.893587	−	0.448889i	$-0.148180\pi$
$823$	1.66517	+	2.88416i	0.0580442	+	0.100535i	−0.835543	+	0.549425i	$0.814847\pi$
$824$		0			0
$825$	−2.08277			−0.0725127
$826$		0			0
$827$	−2.25236			−0.0783221			−0.0391611	−	0.999233i	$-0.512469\pi$
$827$	−2.25236			−0.0783221			−0.0391611	+	0.999233i	$0.512469\pi$
$828$		0			0
$829$	−0.824240	−	1.42763i	−0.0286271	−	0.0495835i	0.851357	−	0.524587i	$-0.175780\pi$
$829$	−0.824240	−	1.42763i	−0.0286271	−	0.0495835i	−0.879984	+	0.475003i	$0.842447\pi$
$830$		0			0
$831$	1.44169	−	2.49708i	0.0500117	−	0.0866227i
$832$		0			0
$833$	3.60614	+	4.74020i	0.124945	+	0.164238i
$834$		0			0
$835$	−44.4364	+	76.9661i	−1.53778	+	2.66352i
$836$		0			0
$837$	−3.80452	−	6.58962i	−0.131503	−	0.227771i
$838$		0			0
$839$	19.7144			0.680616			0.340308	−	0.940314i	$-0.389469\pi$
$839$	19.7144			0.680616			0.340308	+	0.940314i	$0.389469\pi$
$840$		0			0
$841$	0.517057			0.0178296
$842$		0			0
$843$	1.76098	+	3.05011i	0.0606514	+	0.105051i
$844$		0			0
$845$	−24.6603	+	42.7129i	−0.848341	+	1.46937i
$846$		0			0
$847$	2.37047	+	1.17511i	0.0814503	+	0.0403771i
$848$		0			0
$849$	1.74794	−	3.02752i	0.0599891	−	0.103904i
$850$		0			0
$851$	−3.24698	−	5.62393i	−0.111305	−	0.192786i
$852$		0			0
$853$	2.77884			0.0951457			0.0475728	−	0.998868i	$-0.484851\pi$
$853$	2.77884			0.0951457			0.0475728	+	0.998868i	$0.484851\pi$
$854$		0			0
$855$	−8.78209			−0.300341
$856$		0			0
$857$	−6.23878	−	10.8059i	−0.213113	−	0.369122i	0.739574	−	0.673075i	$-0.235027\pi$
$857$	−6.23878	−	10.8059i	−0.213113	−	0.369122i	−0.952687	+	0.303953i	$0.901694\pi$
$858$		0			0
$859$	14.2753	−	24.7256i	0.487068	−	0.843626i	−0.512822	−	0.858495i	$-0.671400\pi$
$859$	14.2753	−	24.7256i	0.487068	−	0.843626i	0.999889	+	0.0148691i	$0.00473314\pi$
$860$		0			0
$861$	−0.828895	+	0.551366i	−0.0282487	+	0.0187905i
$862$		0			0
$863$	−19.3535	+	33.5213i	−0.658802	+	1.14108i	0.322124	+	0.946698i	$0.395603\pi$
$863$	−19.3535	+	33.5213i	−0.658802	+	1.14108i	−0.980926	+	0.194381i	$0.937730\pi$
$864$		0			0
$865$	9.97352	+	17.2746i	0.339110	+	0.587355i
$866$		0			0
$867$	−3.22367			−0.109482
$868$		0			0
$869$	7.55496			0.256284
$870$		0			0
$871$	−3.04892	−	5.28088i	−0.103309	−	0.178936i
$872$		0			0
$873$	8.66948	−	15.0160i	0.293418	−	0.508214i
$874$		0			0
$875$	3.64055	+	57.3674i	0.123073	+	1.93937i
$876$		0			0
$877$	21.6824	−	37.5550i	0.732162	−	1.26814i	−0.223795	−	0.974636i	$-0.571845\pi$
$877$	21.6824	−	37.5550i	0.732162	−	1.26814i	0.955957	−	0.293506i	$-0.0948221\pi$
$878$		0			0
$879$	1.18287	+	2.04878i	0.0398971	+	0.0691037i
$880$		0			0
$881$	−23.9675			−0.807485			−0.403742	−	0.914873i	$-0.632291\pi$
$881$	−23.9675			−0.807485			−0.403742	+	0.914873i	$0.632291\pi$
$882$		0			0
$883$	26.6571			0.897083			0.448541	−	0.893762i	$-0.351944\pi$
$883$	26.6571			0.897083			0.448541	+	0.893762i	$0.351944\pi$
$884$		0			0
$885$	3.01752	+	5.22649i	0.101433	+	0.175687i
$886$		0			0
$887$	−14.6821	+	25.4301i	−0.492977	+	0.853860i	−0.999967	−	0.00809111i	$-0.997424\pi$
$887$	−14.6821	+	25.4301i	−0.492977	+	0.853860i	0.506991	+	0.861952i	$0.330758\pi$
$888$		0			0
$889$	−3.21283	−	50.6275i	−0.107755	−	1.69799i
$890$		0			0
$891$	4.32424	−	7.48980i	0.144868	−	0.250918i
$892$		0			0
$893$	4.77210	+	8.26552i	0.159692	+	0.276595i
$894$		0			0
$895$	−71.9248			−2.40418
$896$		0			0
$897$	0.0881460			0.00294311
$898$		0			0
$899$	17.5078	+	30.3244i	0.583919	+	1.01138i
$900$		0			0
$901$	0.860117	−	1.48977i	0.0286546	−	0.0496313i
$902$		0			0
$903$	1.29944	−	0.864364i	0.0432426	−	0.0287642i
$904$		0			0
$905$	−3.41819	+	5.92048i	−0.113624	+	0.196803i
$906$		0			0
$907$	5.07673	+	8.79315i	0.168570	+	0.291972i	0.937917	−	0.346859i	$-0.112752\pi$
$907$	5.07673	+	8.79315i	0.168570	+	0.291972i	−0.769347	+	0.638831i	$0.779418\pi$
$908$		0			0
$909$	34.2760			1.13686
$910$		0			0
$911$	−54.4330			−1.80344			−0.901722	−	0.432316i	$-0.857697\pi$
$911$	−54.4330			−1.80344			−0.901722	+	0.432316i	$0.857697\pi$
$912$		0			0
$913$	6.58426	+	11.4043i	0.217907	+	0.377426i
$914$		0			0
$915$	−3.69873	+	6.40638i	−0.122276	+	0.211788i
$916$		0			0
$917$	−30.3823	−	15.0613i	−1.00331	−	0.497369i
$918$		0			0
$919$	11.9983	−	20.7816i	0.395786	−	0.685522i	−0.597415	−	0.801932i	$-0.703805\pi$
$919$	11.9983	−	20.7816i	0.395786	−	0.685522i	0.993201	+	0.116410i	$0.0371387\pi$
$920$		0			0
$921$	0.989647	+	1.71412i	0.0326100	+	0.0564822i
$922$		0			0
$923$	0.216849			0.00713766
$924$		0			0
$925$	106.186			3.49138
$926$		0			0
$927$	−8.40054	−	14.5502i	−0.275910	−	0.477890i
$928$		0			0
$929$	−13.1990	+	22.8614i	−0.433046	+	0.750057i	−0.997134	−	0.0756572i	$-0.975895\pi$
$929$	−13.1990	+	22.8614i	−0.433046	+	0.750057i	0.564088	+	0.825715i	$0.309228\pi$
$930$		0			0
$931$	−2.03737	+	4.86149i	−0.0667720	+	0.159329i
$932$		0			0
$933$	−0.227792	+	0.394548i	−0.00745758	+	0.0129169i
$934$		0			0
$935$	−1.67576	−	2.90250i	−0.0548032	−	0.0949219i
$936$		0			0
$937$	−15.2519			−0.498257			−0.249129	−	0.968470i	$-0.580144\pi$
$937$	−15.2519			−0.498257			−0.249129	+	0.968470i	$0.580144\pi$
$938$		0			0
$939$	−4.79523			−0.156487
$940$		0			0
$941$	17.8611	+	30.9363i	0.582254	+	1.00849i	0.995212	+	0.0977438i	$0.0311626\pi$
$941$	17.8611	+	30.9363i	0.582254	+	1.00849i	−0.412957	+	0.910750i	$0.635504\pi$
$942$		0			0
$943$	−0.610876	+	1.05807i	−0.0198929	+	0.0344554i
$944$		0			0
$945$	11.0236	+	5.46471i	0.358599	+	0.177767i
$946$		0			0
$947$	−22.8451	+	39.5689i	−0.742366	+	1.28582i	0.209049	+	0.977905i	$0.432963\pi$
$947$	−22.8451	+	39.5689i	−0.742366	+	1.28582i	−0.951415	+	0.307911i	$0.900370\pi$
$948$		0			0
$949$	5.53952	+	9.59474i	0.179821	+	0.311458i
$950$		0			0
$951$	−3.94379			−0.127886
$952$		0			0
$953$	2.55389			0.0827287			0.0413644	−	0.999144i	$-0.486830\pi$
$953$	2.55389			0.0827287			0.0413644	+	0.999144i	$0.486830\pi$
$954$		0			0
$955$	39.4044	+	68.2504i	1.27510	+	2.20853i
$956$		0			0
$957$	0.538032	−	0.931899i	0.0173921	−	0.0301240i
$958$		0			0
$959$	32.5541	−	21.6544i	1.05123	−	0.699256i
$960$		0			0
$961$	−5.26928	+	9.12666i	−0.169977	+	0.294409i
$962$		0			0
$963$	−16.9718	−	29.3960i	−0.546907	−	0.947271i
$964$		0			0
$965$	5.46117			0.175801
$966$		0			0
$967$	−30.4843			−0.980308			−0.490154	−	0.871636i	$-0.663059\pi$
$967$	−30.4843			−0.980308			−0.490154	+	0.871636i	$0.663059\pi$
$968$		0			0
$969$	0.0634504	+	0.109899i	0.00203832	+	0.00353047i
$970$		0			0
$971$	−21.4006	+	37.0669i	−0.686778	+	1.18953i	0.286097	+	0.958201i	$0.407642\pi$
$971$	−21.4006	+	37.0669i	−0.686778	+	1.18953i	−0.972875	+	0.231334i	$0.925691\pi$
$972$		0			0
$973$	0.353543	+	5.57111i	0.0113341	+	0.178601i
$974$		0			0
$975$	−0.720660	+	1.24822i	−0.0230796	+	0.0399751i
$976$		0			0
$977$	9.96897	+	17.2668i	0.318936	+	0.552413i	0.980266	−	0.197682i	$-0.0633413\pi$
$977$	9.96897	+	17.2668i	0.318936	+	0.552413i	−0.661331	+	0.750094i	$0.730008\pi$
$978$		0			0
$979$	−1.06100			−0.0339097
$980$		0			0
$981$	−47.4814			−1.51596
$982$		0			0
$983$	6.84063	+	11.8483i	0.218182	+	0.377903i	0.954252	−	0.299003i	$-0.0966539\pi$
$983$	6.84063	+	11.8483i	0.218182	+	0.377903i	−0.736070	+	0.676905i	$0.763321\pi$
$984$		0			0
$985$	36.1683	−	62.6453i	1.15242	−	1.99605i
$986$		0			0
$987$	−0.420642	−	6.62844i	−0.0133892	−	0.210985i
$988$		0			0
$989$	0.957656	−	1.65871i	0.0304517	−	0.0527439i
$990$		0			0
$991$	−11.1054	−	19.2351i	−0.352774	−	0.611022i	0.633961	−	0.773365i	$-0.281428\pi$
$991$	−11.1054	−	19.2351i	−0.352774	−	0.611022i	−0.986734	+	0.162343i	$0.948095\pi$
$992$		0			0
$993$	−5.61011			−0.178031
$994$		0			0
$995$	−6.12498			−0.194175
$996$		0			0
$997$	−12.0109	−	20.8035i	−0.380389	−	0.658852i	0.610729	−	0.791840i	$-0.290876\pi$
$997$	−12.0109	−	20.8035i	−0.380389	−	0.658852i	−0.991118	+	0.132987i	$0.957543\pi$
$998$		0			0
$999$	5.96077	−	10.3244i	0.188590	−	0.326648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.i.177.3		6
4.3	odd	2		616.2.q.c.177.1	✓	6
7.2	even	3		8624.2.a.cq.1.1		3
7.4	even	3	inner	1232.2.q.i.529.3		6
7.5	odd	6		8624.2.a.cf.1.3		3
28.11	odd	6		616.2.q.c.529.1	yes	6
28.19	even	6		4312.2.a.x.1.1		3
28.23	odd	6		4312.2.a.v.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.q.c.177.1	✓	6	4.3	odd	2
616.2.q.c.529.1	yes	6	28.11	odd	6
1232.2.q.i.177.3		6	1.1	even	1	trivial
1232.2.q.i.529.3		6	7.4	even	3	inner
4312.2.a.v.1.3		3	28.23	odd	6
4312.2.a.x.1.1		3	28.19	even	6
8624.2.a.cf.1.3		3	7.5	odd	6
8624.2.a.cq.1.1		3	7.2	even	3

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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0990311 - 0.171527i) q^{3} +(1.96950 - 3.41127i) q^{5} +(-0.167563 - 2.64044i) q^{7} +(1.48039 - 2.56410i) q^{9} +O(q^{10})\)	\(q+(-0.0990311 - 0.171527i) q^{3} +(1.96950 - 3.41127i) q^{5} +(-0.167563 - 2.64044i) q^{7} +(1.48039 - 2.56410i) q^{9} +(0.500000 + 0.866025i) q^{11} +0.692021 q^{13} -0.780167 q^{15} +(-0.425428 - 0.736862i) q^{17} +(0.376510 - 0.652135i) q^{19} +(-0.436313 + 0.290227i) q^{21} +(-0.321552 + 0.556945i) q^{23} +(-5.25786 - 9.10689i) q^{25} -1.18060 q^{27} +5.43296 q^{29} +(3.22252 + 5.58157i) q^{31} +(0.0990311 - 0.171527i) q^{33} +(-9.33728 - 4.62874i) q^{35} +(-5.04892 + 8.74498i) q^{37} +(-0.0685317 - 0.118700i) q^{39} +1.89977 q^{41} -2.97823 q^{43} +(-5.83124 - 10.1000i) q^{45} +(-6.33728 + 10.9765i) q^{47} +(-6.94385 + 0.884879i) q^{49} +(-0.0842611 + 0.145945i) q^{51} +(1.01089 + 1.75090i) q^{53} +3.93900 q^{55} -0.149145 q^{57} +(-3.86778 - 6.69919i) q^{59} +(4.74094 - 8.21155i) q^{61} +(-7.01842 - 3.47922i) q^{63} +(1.36294 - 2.36068i) q^{65} +(-4.40581 - 7.63109i) q^{67} +0.127375 q^{69} +0.313355 q^{71} +(8.00484 + 13.8648i) q^{73} +(-1.04138 + 1.80373i) q^{75} +(2.20291 - 1.46533i) q^{77} +(3.77748 - 6.54279i) q^{79} +(-4.32424 - 7.48980i) q^{81} +13.1685 q^{83} -3.35152 q^{85} +(-0.538032 - 0.931899i) q^{87} +(-0.530499 + 0.918852i) q^{89} +(-0.115957 - 1.82724i) q^{91} +(0.638260 - 1.10550i) q^{93} +(-1.48307 - 2.56876i) q^{95} +5.85623 q^{97} +2.96077 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 5 q^{3} + 2 q^{5} - 4 q^{9}+O(q^{10}) \) 6 * q - 5 * q^3 + 2 * q^5 - 4 * q^9	\( 6 q - 5 q^{3} + 2 q^{5} - 4 q^{9} + 3 q^{11} - 6 q^{13} - 2 q^{15} + 11 q^{17} + 7 q^{19} + 14 q^{21} - 6 q^{23} - 19 q^{25} + 16 q^{27} - 6 q^{29} + 19 q^{31} + 5 q^{33} - 35 q^{35} - 12 q^{37} + 5 q^{39} - 34 q^{41} - 24 q^{43} + 5 q^{45} - 17 q^{47} + 30 q^{51} + 3 q^{53} + 4 q^{55} - 28 q^{57} - 12 q^{59} - 14 q^{63} + 19 q^{65} + 34 q^{69} + 6 q^{71} + 26 q^{73} - 13 q^{75} + 23 q^{79} - 27 q^{81} + 18 q^{83} - 18 q^{85} + 12 q^{87} - 13 q^{89} - 21 q^{91} + 34 q^{93} + 7 q^{95} + 2 q^{97} - 8 q^{99}+O(q^{100}) \) 6 * q - 5 * q^3 + 2 * q^5 - 4 * q^9 + 3 * q^11 - 6 * q^13 - 2 * q^15 + 11 * q^17 + 7 * q^19 + 14 * q^21 - 6 * q^23 - 19 * q^25 + 16 * q^27 - 6 * q^29 + 19 * q^31 + 5 * q^33 - 35 * q^35 - 12 * q^37 + 5 * q^39 - 34 * q^41 - 24 * q^43 + 5 * q^45 - 17 * q^47 + 30 * q^51 + 3 * q^53 + 4 * q^55 - 28 * q^57 - 12 * q^59 - 14 * q^63 + 19 * q^65 + 34 * q^69 + 6 * q^71 + 26 * q^73 - 13 * q^75 + 23 * q^79 - 27 * q^81 + 18 * q^83 - 18 * q^85 + 12 * q^87 - 13 * q^89 - 21 * q^91 + 34 * q^93 + 7 * q^95 + 2 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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