LMFDB - Embedded newform 1372.2.e.d.1353.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1372,2,Mod(361,1372)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1372.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1372, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1372 = 2^{2} \cdot 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1372.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,7,0,7,0,0,0,-9,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$10.9554751573$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 10 x^{10} - 7 x^{9} + 68 x^{8} - 44 x^{7} + 225 x^{6} - 77 x^{5} + 490 x^{4} + \cdots + 49 $ x^12 - x^11 + 10x^10 - 7x^9 + 68x^8 - 44x^7 + 225x^6 - 77x^5 + 490x^4 - 182x^3 + 343x^2 + 98x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1353.5
Root			$-0.174968 + 0.303054i$ of defining polynomial
Character	$\chi$	$=$	1372.1353
Dual form			1372.2.e.d.361.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.57594 + 2.72960i) q^{3} +(2.01664 - 3.49292i) q^{5} +(-3.46716 + 6.00529i) q^{9} +(1.36090 + 2.35715i) q^{11} +3.56957 q^{13} +12.7124 q^{15} +(-0.845598 - 1.46462i) q^{17} +(-2.17393 + 3.76535i) q^{19} +(-0.891403 + 1.54396i) q^{23} +(-5.63368 - 9.75781i) q^{25} -12.4005 q^{27} +0.407899 q^{29} +(3.29367 + 5.70481i) q^{31} +(-4.28940 + 7.42946i) q^{33} +(4.99236 - 8.64701i) q^{37} +(5.62541 + 9.74350i) q^{39} +7.86636 q^{41} +6.09932 q^{43} +(13.9840 + 24.2210i) q^{45} +(0.856390 - 1.48331i) q^{47} +(2.66522 - 4.61630i) q^{51} +(2.96127 + 5.12907i) q^{53} +10.9778 q^{55} -13.7039 q^{57} +(3.84093 + 6.65269i) q^{59} +(-2.26027 + 3.91491i) q^{61} +(7.19853 - 12.4682i) q^{65} +(-2.08050 - 3.60354i) q^{67} -5.61918 q^{69} -7.93900 q^{71} +(-6.09087 - 10.5497i) q^{73} +(17.7566 - 30.7554i) q^{75} +(0.142640 - 0.247060i) q^{79} +(-9.14088 - 15.8325i) q^{81} -9.36705 q^{83} -6.82107 q^{85} +(0.642824 + 1.11340i) q^{87} +(-4.47487 + 7.75071i) q^{89} +(-10.3812 + 17.9808i) q^{93} +(8.76805 + 15.1867i) q^{95} -7.00302 q^{97} -18.8739 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 7 q^{3} + 7 q^{5} - 9 q^{9} - 3 q^{11} - 14 q^{13} + 22 q^{15} + 7 q^{19} - 11 q^{23} - 3 q^{25} - 56 q^{27} + 12 q^{29} + 14 q^{31} + 6 q^{37} - 5 q^{39} - 6 q^{43} + 21 q^{45} + 42 q^{47} + 17 q^{51}+ \cdots - 68 q^{99}+O(q^{100}) $ 12 * q + 7 * q^3 + 7 * q^5 - 9 * q^9 - 3 * q^11 - 14 * q^13 + 22 * q^15 + 7 * q^19 - 11 * q^23 - 3 * q^25 - 56 * q^27 + 12 * q^29 + 14 * q^31 + 6 * q^37 - 5 * q^39 - 6 * q^43 + 21 * q^45 + 42 * q^47 + 17 * q^51 + 17 * q^53 - 28 * q^55 - 12 * q^57 + 35 * q^59 + 7 * q^61 + 6 * q^65 + 14 * q^67 - 28 * q^69 - 56 * q^71 + 35 * q^75 - 6 * q^79 - 34 * q^81 - 98 * q^83 - 46 * q^85 + 21 * q^87 - 7 * q^89 + 14 * q^93 + 25 * q^95 + 42 * q^97 - 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1372\mathbb{Z}\right)^\times$.

$n$	$687$	$689$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.57594	+	2.72960i	0.909868	+	1.57594i	0.814246	+	0.580520i	$0.197151\pi$
$3$	1.57594	+	2.72960i	0.909868	+	1.57594i	0.0956215	+	0.995418i	$0.469516\pi$
$4$		0			0
$5$	2.01664	−	3.49292i	0.901869	−	1.56208i	0.0768032	−	0.997046i	$-0.475529\pi$
$5$	2.01664	−	3.49292i	0.901869	−	1.56208i	0.825066	−	0.565037i	$-0.191138\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−3.46716	+	6.00529i	−1.15572	+	2.00176i
$10$		0			0
$11$	1.36090	+	2.35715i	0.410328	+	0.710709i	0.994925	−	0.100615i	$-0.0320809\pi$
$11$	1.36090	+	2.35715i	0.410328	+	0.710709i	−0.584598	+	0.811323i	$0.698748\pi$
$12$		0			0
$13$	3.56957			0.990019			0.495010	−	0.868887i	$-0.335165\pi$
$13$	3.56957			0.990019			0.495010	+	0.868887i	$0.335165\pi$
$14$		0			0
$15$	12.7124			3.28233
$16$		0			0
$17$	−0.845598	−	1.46462i	−0.205088	−	0.355222i	0.745073	−	0.666983i	$-0.232415\pi$
$17$	−0.845598	−	1.46462i	−0.205088	−	0.355222i	−0.950161	+	0.311761i	$0.899081\pi$
$18$		0			0
$19$	−2.17393	+	3.76535i	−0.498733	+	0.863830i	−0.999999	−	0.00146273i	$-0.999534\pi$
$19$	−2.17393	+	3.76535i	−0.498733	+	0.863830i	0.501266	+	0.865293i	$0.332868\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.891403	+	1.54396i	−0.185870	+	0.321937i	−0.943869	−	0.330319i	$-0.892844\pi$
$23$	−0.891403	+	1.54396i	−0.185870	+	0.321937i	0.757999	+	0.652256i	$0.226177\pi$
$24$		0			0
$25$	−5.63368	−	9.75781i	−1.12674	−	1.95156i
$26$		0			0
$27$	−12.4005			−2.38647
$28$		0			0
$29$	0.407899			0.0757450			0.0378725	−	0.999283i	$-0.487942\pi$
$29$	0.407899			0.0757450			0.0378725	+	0.999283i	$0.487942\pi$
$30$		0			0
$31$	3.29367	+	5.70481i	0.591561	+	1.02461i	0.994022	+	0.109177i	$0.0348215\pi$
$31$	3.29367	+	5.70481i	0.591561	+	1.02461i	−0.402461	+	0.915437i	$0.631845\pi$
$32$		0			0
$33$	−4.28940	+	7.42946i	−0.746688	+	1.29330i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.99236	−	8.64701i	0.820738	−	1.42156i	−0.0843949	−	0.996432i	$-0.526896\pi$
$37$	4.99236	−	8.64701i	0.820738	−	1.42156i	0.905133	−	0.425128i	$-0.139771\pi$
$38$		0			0
$39$	5.62541	+	9.74350i	0.900787	+	1.56021i
$40$		0			0
$41$	7.86636			1.22852			0.614259	−	0.789104i	$-0.289455\pi$
$41$	7.86636			1.22852			0.614259	+	0.789104i	$0.289455\pi$
$42$		0			0
$43$	6.09932			0.930137			0.465068	−	0.885275i	$-0.346030\pi$
$43$	6.09932			0.930137			0.465068	+	0.885275i	$0.346030\pi$
$44$		0			0
$45$	13.9840	+	24.2210i	2.08461	+	3.61066i
$46$		0			0
$47$	0.856390	−	1.48331i	0.124917	−	0.216363i	−0.796783	−	0.604265i	$-0.793467\pi$
$47$	0.856390	−	1.48331i	0.124917	−	0.216363i	0.921701	+	0.387902i	$0.126800\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	2.66522	−	4.61630i	0.373205	−	0.646411i
$52$		0			0
$53$	2.96127	+	5.12907i	0.406762	+	0.704532i	0.994525	−	0.104501i	$-0.0333246\pi$
$53$	2.96127	+	5.12907i	0.406762	+	0.704532i	−0.587763	+	0.809033i	$0.699991\pi$
$54$		0			0
$55$	10.9778			1.48025
$56$		0			0
$57$	−13.7039			−1.81512
$58$		0			0
$59$	3.84093	+	6.65269i	0.500047	+	0.866106i	1.00000		5.38702e-5i	$1.71474e-5\pi$
$59$	3.84093	+	6.65269i	0.500047	+	0.866106i	−0.499953	+	0.866052i	$0.666650\pi$
$60$		0			0
$61$	−2.26027	+	3.91491i	−0.289398	+	0.501252i	−0.973666	−	0.227978i	$-0.926789\pi$
$61$	−2.26027	+	3.91491i	−0.289398	+	0.501252i	0.684268	+	0.729231i	$0.260122\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.19853	−	12.4682i	0.892868	−	1.54649i
$66$		0			0
$67$	−2.08050	−	3.60354i	−0.254174	−	0.440242i	0.710497	−	0.703700i	$-0.248470\pi$
$67$	−2.08050	−	3.60354i	−0.254174	−	0.440242i	−0.964671	+	0.263458i	$0.915137\pi$
$68$		0			0
$69$	−5.61918			−0.676470
$70$		0			0
$71$	−7.93900			−0.942186			−0.471093	−	0.882084i	$-0.656140\pi$
$71$	−7.93900			−0.942186			−0.471093	+	0.882084i	$0.656140\pi$
$72$		0			0
$73$	−6.09087	−	10.5497i	−0.712883	−	1.23475i	−0.963770	−	0.266733i	$-0.914056\pi$
$73$	−6.09087	−	10.5497i	−0.712883	−	1.23475i	0.250888	−	0.968016i	$-0.419278\pi$
$74$		0			0
$75$	17.7566	−	30.7554i	2.05036	−	3.55133i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.142640	−	0.247060i	0.0160482	−	0.0277964i	−0.857890	−	0.513834i	$-0.828225\pi$
$79$	0.142640	−	0.247060i	0.0160482	−	0.0277964i	0.873938	+	0.486037i	$0.161558\pi$
$80$		0			0
$81$	−9.14088	−	15.8325i	−1.01565	−	1.75916i
$82$		0			0
$83$	−9.36705			−1.02817			−0.514084	−	0.857740i	$-0.671868\pi$
$83$	−9.36705			−1.02817			−0.514084	+	0.857740i	$0.671868\pi$
$84$		0			0
$85$	−6.82107			−0.739849
$86$		0			0
$87$	0.642824	+	1.11340i	0.0689179	+	0.119369i
$88$		0			0
$89$	−4.47487	+	7.75071i	−0.474336	+	0.821574i	−0.999568	−	0.0293852i	$-0.990645\pi$
$89$	−4.47487	+	7.75071i	−0.474336	+	0.821574i	0.525232	+	0.850959i	$0.323978\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−10.3812	+	17.9808i	−1.07648	+	1.86453i
$94$		0			0
$95$	8.76805	+	15.1867i	0.899583	+	1.55812i
$96$		0			0
$97$	−7.00302			−0.711049			−0.355524	−	0.934667i	$-0.615698\pi$
$97$	−7.00302			−0.711049			−0.355524	+	0.934667i	$0.615698\pi$
$98$		0			0
$99$	−18.8739			−1.89690
$100$		0			0
$101$	0.572723	+	0.991986i	0.0569881	+	0.0987063i	0.893112	−	0.449834i	$-0.148517\pi$
$101$	0.572723	+	0.991986i	0.0569881	+	0.0987063i	−0.836124	+	0.548541i	$0.815184\pi$
$102$		0			0
$103$	4.13721	−	7.16586i	0.407651	−	0.706073i	−0.586975	−	0.809605i	$-0.699681\pi$
$103$	4.13721	−	7.16586i	0.407651	−	0.706073i	0.994626	+	0.103532i	$0.0330145\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.93666	−	13.7467i	0.767266	−	1.32894i	−0.171775	−	0.985136i	$-0.554950\pi$
$107$	7.93666	−	13.7467i	0.767266	−	1.32894i	0.939040	−	0.343807i	$-0.111717\pi$
$108$		0			0
$109$	−6.68804	−	11.5840i	−0.640598	−	1.10955i	−0.985299	−	0.170836i	$-0.945353\pi$
$109$	−6.68804	−	11.5840i	−0.640598	−	1.10955i	0.344701	−	0.938712i	$-0.387980\pi$
$110$		0			0
$111$	31.4706			2.98705
$112$		0			0
$113$	−16.5314			−1.55514			−0.777572	−	0.628793i	$-0.783549\pi$
$113$	−16.5314			−1.55514			−0.777572	+	0.628793i	$0.783549\pi$
$114$		0			0
$115$	3.59528	+	6.22721i	0.335262	+	0.580690i
$116$		0			0
$117$	−12.3762	+	21.4363i	−1.14418	+	1.98179i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.79588	−	3.11056i	0.163262	−	0.282778i
$122$		0			0
$123$	12.3969	+	21.4720i	1.11779	+	1.93607i
$124$		0			0
$125$	−25.2780			−2.26093
$126$		0			0
$127$	−9.32693			−0.827631			−0.413815	−	0.910361i	$-0.635804\pi$
$127$	−9.32693			−0.827631			−0.413815	+	0.910361i	$0.635804\pi$
$128$		0			0
$129$	9.61214	+	16.6487i	0.846302	+	1.46584i
$130$		0			0
$131$	−5.64849	+	9.78347i	−0.493511	+	0.854785i	−0.999972	−	0.00747720i	$-0.997620\pi$
$131$	−5.64849	+	9.78347i	−0.493511	+	0.854785i	0.506461	+	0.862263i	$0.330953\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−25.0073	+	43.3139i	−2.15228	+	3.72786i
$136$		0			0
$137$	−8.61292	−	14.9180i	−0.735852	−	1.27453i	−0.954349	−	0.298695i	$-0.903449\pi$
$137$	−8.61292	−	14.9180i	−0.735852	−	1.27453i	0.218497	−	0.975838i	$-0.429885\pi$
$138$		0			0
$139$	−3.46595			−0.293978			−0.146989	−	0.989138i	$-0.546958\pi$
$139$	−3.46595			−0.293978			−0.146989	+	0.989138i	$0.546958\pi$
$140$		0			0
$141$	5.39847			0.454633
$142$		0			0
$143$	4.85784	+	8.41402i	0.406233	+	0.703616i
$144$		0			0
$145$	0.822586	−	1.42476i	0.0683121	−	0.118320i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.69452	+	4.66705i	−0.220744	+	0.382340i	−0.955034	−	0.296496i	$-0.904182\pi$
$149$	−2.69452	+	4.66705i	−0.220744	+	0.382340i	0.734290	+	0.678836i	$0.237515\pi$
$150$		0			0
$151$	−11.0994	−	19.2248i	−0.903260	−	1.56449i	−0.823236	−	0.567699i	$-0.807834\pi$
$151$	−11.0994	−	19.2248i	−0.903260	−	1.56449i	−0.0800242	−	0.996793i	$-0.525500\pi$
$152$		0			0
$153$	11.7273			0.948095
$154$		0			0
$155$	26.5686			2.13404
$156$		0			0
$157$	5.56757	+	9.64331i	0.444340	+	0.769620i	0.998006	−	0.0631190i	$-0.0201048\pi$
$157$	5.56757	+	9.64331i	0.444340	+	0.769620i	−0.553666	+	0.832739i	$0.686771\pi$
$158$		0			0
$159$	−9.33355	+	16.1662i	−0.740199	+	1.28206i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	3.80380	−	6.58837i	0.297936	−	0.516041i	−0.677727	−	0.735313i	$-0.737035\pi$
$163$	3.80380	−	6.58837i	0.297936	−	0.516041i	0.975664	+	0.219272i	$0.0703683\pi$
$164$		0			0
$165$	17.3003	+	29.9651i	1.34683	+	2.33278i
$166$		0			0
$167$	−22.4957			−1.74077			−0.870383	−	0.492375i	$-0.836129\pi$
$167$	−22.4957			−1.74077			−0.870383	+	0.492375i	$0.836129\pi$
$168$		0			0
$169$	−0.258201			−0.0198616
$170$		0			0
$171$	−15.0747	−	26.1101i	−1.15279	−	1.99669i
$172$		0			0
$173$	2.05794	−	3.56446i	0.156463	−	0.271001i	−0.777128	−	0.629342i	$-0.783324\pi$
$173$	2.05794	−	3.56446i	0.156463	−	0.271001i	0.933591	+	0.358341i	$0.116658\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−12.1061	+	20.9684i	−0.909953	+	1.57608i
$178$		0			0
$179$	0.667927	+	1.15688i	0.0499232	+	0.0864695i	0.889907	−	0.456142i	$-0.150769\pi$
$179$	0.667927	+	1.15688i	0.0499232	+	0.0864695i	−0.839984	+	0.542611i	$0.817436\pi$
$180$		0			0
$181$	7.17301			0.533166			0.266583	−	0.963812i	$-0.414105\pi$
$181$	7.17301			0.533166			0.266583	+	0.963812i	$0.414105\pi$
$182$		0			0
$183$	−14.2482			−1.05326
$184$		0			0
$185$	−20.1356	−	34.8758i	−1.48040	−	2.56412i
$186$		0			0
$187$	2.30156	−	3.98641i	0.168306	−	0.291515i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.86476	−	3.22986i	0.134930	−	0.233705i	−0.790641	−	0.612280i	$-0.790253\pi$
$191$	1.86476	−	3.22986i	0.134930	−	0.233705i	0.925571	+	0.378575i	$0.123586\pi$
$192$		0			0
$193$	3.64170	+	6.30761i	0.262135	+	0.454032i	0.966809	−	0.255500i	$-0.0822400\pi$
$193$	3.64170	+	6.30761i	0.262135	+	0.454032i	−0.704674	+	0.709531i	$0.748907\pi$
$194$		0			0
$195$	45.3777			3.24957
$196$		0			0
$197$	24.3500			1.73487			0.867433	−	0.497554i	$-0.165768\pi$
$197$	24.3500			1.73487			0.867433	+	0.497554i	$0.165768\pi$
$198$		0			0
$199$	−8.87473	−	15.3715i	−0.629113	−	1.08966i	−0.987730	−	0.156171i	$-0.950085\pi$
$199$	−8.87473	−	15.3715i	−0.629113	−	1.08966i	0.358617	−	0.933485i	$-0.383249\pi$
$200$		0			0
$201$	6.55748	−	11.3579i	0.462529	−	0.801124i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	15.8636	−	27.4766i	1.10796	−	1.91905i
$206$		0			0
$207$	−6.18127	−	10.7063i	−0.429628	−	0.744137i
$208$		0			0
$209$	−11.8340			−0.818576
$210$		0			0
$211$	6.53230			0.449702			0.224851	−	0.974393i	$-0.427810\pi$
$211$	6.53230			0.449702			0.224851	+	0.974393i	$0.427810\pi$
$212$		0			0
$213$	−12.5114	−	21.6703i	−0.857265	−	1.48483i
$214$		0			0
$215$	12.3001	−	21.3044i	0.838862	−	1.45295i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	19.1977	−	33.2513i	1.29726	−	2.24692i
$220$		0			0
$221$	−3.01842	−	5.22805i	−0.203041	−	0.351677i
$222$		0			0
$223$	−17.2181			−1.15301			−0.576503	−	0.817095i	$-0.695583\pi$
$223$	−17.2181			−1.15301			−0.576503	+	0.817095i	$0.695583\pi$
$224$		0			0
$225$	78.1314			5.20876
$226$		0			0
$227$	3.89868	+	6.75271i	0.258764	+	0.448193i	0.965911	−	0.258874i	$-0.0833514\pi$
$227$	3.89868	+	6.75271i	0.258764	+	0.448193i	−0.707147	+	0.707067i	$0.750018\pi$
$228$		0			0
$229$	3.18162	−	5.51073i	0.210247	−	0.364159i	−0.741544	−	0.670904i	$-0.765906\pi$
$229$	3.18162	−	5.51073i	0.210247	−	0.364159i	0.951792	+	0.306744i	$0.0992397\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.97775	−	5.15761i	0.195079	−	0.337886i	−0.751848	−	0.659337i	$-0.770837\pi$
$233$	2.97775	−	5.15761i	0.195079	−	0.337886i	0.946926	+	0.321451i	$0.104170\pi$
$234$		0			0
$235$	−3.45406	−	5.98261i	−0.225318	−	0.390263i
$236$		0			0
$237$	0.899167			0.0584071
$238$		0			0
$239$	−2.45790			−0.158988			−0.0794941	−	0.996835i	$-0.525330\pi$
$239$	−2.45790			−0.158988			−0.0794941	+	0.996835i	$0.525330\pi$
$240$		0			0
$241$	2.50265	+	4.33471i	0.161210	+	0.279223i	0.935303	−	0.353848i	$-0.115127\pi$
$241$	2.50265	+	4.33471i	0.161210	+	0.279223i	−0.774093	+	0.633072i	$0.781794\pi$
$242$		0			0
$243$	10.2102	−	17.6846i	0.654986	−	1.13447i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−7.75997	+	13.4407i	−0.493755	+	0.855209i
$248$		0			0
$249$	−14.7619	−	25.5683i	−0.935497	−	1.62033i
$250$		0			0
$251$	−5.82496			−0.367668			−0.183834	−	0.982957i	$-0.558851\pi$
$251$	−5.82496			−0.367668			−0.183834	+	0.982957i	$0.558851\pi$
$252$		0			0
$253$	−4.85246			−0.305071
$254$		0			0
$255$	−10.7496	−	18.6188i	−0.673165	−	1.16596i
$256$		0			0
$257$	−0.216636	+	0.375224i	−0.0135134	+	0.0234059i	−0.872703	−	0.488251i	$-0.837635\pi$
$257$	−0.216636	+	0.375224i	−0.0135134	+	0.0234059i	0.859190	+	0.511657i	$0.170968\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.41425	+	2.44955i	−0.0875399	+	0.151624i
$262$		0			0
$263$	10.7239	+	18.5744i	0.661267	+	1.14535i	0.980283	+	0.197598i	$0.0633142\pi$
$263$	10.7239	+	18.5744i	0.661267	+	1.14535i	−0.319016	+	0.947749i	$0.603352\pi$
$264$		0			0
$265$	23.8873			1.46738
$266$		0			0
$267$	−28.2085			−1.72633
$268$		0			0
$269$	9.96373	+	17.2577i	0.607500	+	1.05222i	0.991651	+	0.128950i	$0.0411607\pi$
$269$	9.96373	+	17.2577i	0.607500	+	1.05222i	−0.384152	+	0.923270i	$0.625506\pi$
$270$		0			0
$271$	4.48673	−	7.77125i	0.272549	−	0.472070i	−0.696964	−	0.717106i	$-0.745466\pi$
$271$	4.48673	−	7.77125i	0.272549	−	0.472070i	0.969514	+	0.245036i	$0.0787998\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	15.3338	−	26.5589i	0.924662	−	1.60156i
$276$		0			0
$277$	8.90965	+	15.4320i	0.535329	+	0.927217i	0.999147	+	0.0412866i	$0.0131457\pi$
$277$	8.90965	+	15.4320i	0.535329	+	0.927217i	−0.463818	+	0.885930i	$0.653521\pi$
$278$		0			0
$279$	−45.6787			−2.73471
$280$		0			0
$281$	−2.18474			−0.130331			−0.0651653	−	0.997874i	$-0.520757\pi$
$281$	−2.18474			−0.130331			−0.0651653	+	0.997874i	$0.520757\pi$
$282$		0			0
$283$	6.93718	+	12.0155i	0.412372	+	0.714250i	0.995149	−	0.0983826i	$-0.0313669\pi$
$283$	6.93718	+	12.0155i	0.412372	+	0.714250i	−0.582776	+	0.812633i	$0.698034\pi$
$284$		0			0
$285$	−27.6358	+	47.8666i	−1.63700	+	2.83537i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.06993	−	12.2455i	0.415878	−	0.720322i
$290$		0			0
$291$	−11.0363	−	19.1155i	−0.646960	−	1.12057i
$292$		0			0
$293$	−21.3205			−1.24556			−0.622779	−	0.782398i	$-0.713996\pi$
$293$	−21.3205			−1.24556			−0.622779	+	0.782398i	$0.713996\pi$
$294$		0			0
$295$	30.9831			1.80391
$296$		0			0
$297$	−16.8758	−	29.2298i	−0.979235	−	1.69609i
$298$		0			0
$299$	−3.18192	+	5.51125i	−0.184015	+	0.318724i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−1.80515	+	3.12661i	−0.103703	+	0.179619i
$304$		0			0
$305$	9.11631	+	15.7899i	0.521999	+	0.904128i
$306$		0			0
$307$	0.702447			0.0400908			0.0200454	−	0.999799i	$-0.493619\pi$
$307$	0.702447			0.0400908			0.0200454	+	0.999799i	$0.493619\pi$
$308$		0			0
$309$	26.0799			1.48364
$310$		0			0
$311$	4.59396	+	7.95698i	0.260500	+	0.451199i	0.966375	−	0.257138i	$-0.0827793\pi$
$311$	4.59396	+	7.95698i	0.260500	+	0.451199i	−0.705875	+	0.708336i	$0.749446\pi$
$312$		0			0
$313$	−9.94766	+	17.2298i	−0.562275	+	0.973889i	0.435023	+	0.900420i	$0.356740\pi$
$313$	−9.94766	+	17.2298i	−0.562275	+	0.973889i	−0.997297	+	0.0734692i	$0.976593\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.56416	+	4.44126i	−0.144018	+	0.249446i	−0.929006	−	0.370065i	$-0.879336\pi$
$317$	−2.56416	+	4.44126i	−0.144018	+	0.249446i	0.784988	+	0.619510i	$0.212669\pi$
$318$		0			0
$319$	0.555112	+	0.961481i	0.0310803	+	0.0538326i
$320$		0			0
$321$	50.0307			2.79244
$322$		0			0
$323$	7.35307			0.409136
$324$		0			0
$325$	−20.1098	−	34.8312i	−1.11549	−	1.93209i
$326$		0			0
$327$	21.0799	−	36.5114i	1.16572	−	2.01909i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	3.12296	−	5.40912i	0.171653	−	0.297312i	−0.767345	−	0.641235i	$-0.778422\pi$
$331$	3.12296	−	5.40912i	0.171653	−	0.297312i	0.938998	+	0.343923i	$0.111756\pi$
$332$		0			0
$333$	34.6186	+	59.9611i	1.89709	+	3.28585i
$334$		0			0
$335$	−16.7825			−0.916926
$336$		0			0
$337$	0.644555			0.0351112			0.0175556	−	0.999846i	$-0.494412\pi$
$337$	0.644555			0.0351112			0.0175556	+	0.999846i	$0.494412\pi$
$338$		0			0
$339$	−26.0525	−	45.1242i	−1.41498	−	2.45081i
$340$		0			0
$341$	−8.96474	+	15.5274i	−0.485468	+	0.840855i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−11.3319	+	19.6274i	−0.610087	+	1.05670i
$346$		0			0
$347$	−15.6899	−	27.1757i	−0.842278	−	1.45887i	−0.887964	−	0.459913i	$-0.847881\pi$
$347$	−15.6899	−	27.1757i	−0.842278	−	1.45887i	0.0456858	−	0.998956i	$-0.485453\pi$
$348$		0			0
$349$	37.2595			1.99445			0.997226	−	0.0744289i	$-0.0237134\pi$
$349$	37.2595			1.99445			0.997226	+	0.0744289i	$0.0237134\pi$
$350$		0			0
$351$	−44.2643			−2.36265
$352$		0			0
$353$	−7.89314	−	13.6713i	−0.420110	−	0.727651i	0.575840	−	0.817562i	$-0.304675\pi$
$353$	−7.89314	−	13.6713i	−0.420110	−	0.727651i	−0.995950	+	0.0899110i	$0.971342\pi$
$354$		0			0
$355$	−16.0101	+	27.7303i	−0.849728	+	1.47177i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−4.83855	+	8.38062i	−0.255369	+	0.442312i	−0.964996	−	0.262266i	$-0.915530\pi$
$359$	−4.83855	+	8.38062i	−0.255369	+	0.442312i	0.709627	+	0.704578i	$0.248864\pi$
$360$		0			0
$361$	0.0480962	+	0.0833051i	0.00253138	+	0.00438448i
$362$		0			0
$363$	11.3208			0.594187
$364$		0			0
$365$	−49.1324			−2.57171
$366$		0			0
$367$	−5.12314	−	8.87355i	−0.267426	−	0.463195i	0.700770	−	0.713387i	$-0.252840\pi$
$367$	−5.12314	−	8.87355i	−0.267426	−	0.463195i	−0.968196	+	0.250192i	$0.919506\pi$
$368$		0			0
$369$	−27.2739	+	47.2398i	−1.41982	+	2.45920i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	2.00915	−	3.47995i	0.104030	−	0.180185i	−0.809312	−	0.587380i	$-0.800160\pi$
$373$	2.00915	−	3.47995i	0.104030	−	0.180185i	0.913341	+	0.407195i	$0.133493\pi$
$374$		0			0
$375$	−39.8365	−	68.9989i	−2.05715	−	3.56309i
$376$		0			0
$377$	1.45602			0.0749890
$378$		0			0
$379$	−28.4114			−1.45939			−0.729697	−	0.683771i	$-0.760339\pi$
$379$	−28.4114			−1.45939			−0.729697	+	0.683771i	$0.760339\pi$
$380$		0			0
$381$	−14.6987	−	25.4588i	−0.753035	−	1.30429i
$382$		0			0
$383$	9.81142	−	16.9939i	0.501340	−	0.868347i	−0.498659	−	0.866798i	$-0.666174\pi$
$383$	9.81142	−	16.9939i	0.501340	−	0.868347i	0.999999	−	0.00154825i	$-0.000492824\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−21.1473	+	36.6282i	−1.07498	+	1.86191i
$388$		0			0
$389$	1.17070	+	2.02771i	0.0593569	+	0.102809i	0.894177	−	0.447714i	$-0.147762\pi$
$389$	1.17070	+	2.02771i	0.0593569	+	0.102809i	−0.834820	+	0.550523i	$0.814428\pi$
$390$		0			0
$391$	3.01508			0.152479
$392$		0			0
$393$	−35.6066			−1.79612
$394$		0			0
$395$	−0.575307	−	0.996461i	−0.0289468	−	0.0501374i
$396$		0			0
$397$	12.1026	−	20.9624i	0.607414	−	1.05207i	−0.384251	−	0.923229i	$-0.625540\pi$
$397$	12.1026	−	20.9624i	0.607414	−	1.05207i	0.991665	−	0.128844i	$-0.0411266\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.38574	+	2.40017i	−0.0692006	+	0.119859i	−0.898550	−	0.438872i	$-0.855378\pi$
$401$	−1.38574	+	2.40017i	−0.0692006	+	0.119859i	0.829349	+	0.558731i	$0.188712\pi$
$402$		0			0
$403$	11.7570	+	20.3637i	0.585657	+	1.01439i
$404$		0			0
$405$	−73.7355			−3.66395
$406$		0			0
$407$	27.1765			1.34709
$408$		0			0
$409$	19.1815	+	33.2233i	0.948463	+	1.64279i	0.748663	+	0.662950i	$0.230696\pi$
$409$	19.1815	+	33.2233i	0.948463	+	1.64279i	0.199800	+	0.979837i	$0.435971\pi$
$410$		0			0
$411$	27.1469	−	47.0197i	1.33906	−	2.31931i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−18.8900	+	32.7184i	−0.927273	+	1.60608i
$416$		0			0
$417$	−5.46211	−	9.46066i	−0.267481	−	0.463290i
$418$		0			0
$419$	11.1510			0.544762			0.272381	−	0.962189i	$-0.412189\pi$
$419$	11.1510			0.544762			0.272381	+	0.962189i	$0.412189\pi$
$420$		0			0
$421$	−23.9079			−1.16520			−0.582600	−	0.812759i	$-0.697964\pi$
$421$	−23.9079			−1.16520			−0.582600	+	0.812759i	$0.697964\pi$
$422$		0			0
$423$	5.93848	+	10.2857i	0.288739	+	0.500110i
$424$		0			0
$425$	−9.52765	+	16.5024i	−0.462159	+	0.800483i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−15.3113	+	26.5199i	−0.739236	+	1.28039i
$430$		0			0
$431$	−9.04663	−	15.6692i	−0.435761	−	0.754760i	0.561597	−	0.827411i	$-0.310187\pi$
$431$	−9.04663	−	15.6692i	−0.435761	−	0.754760i	−0.997357	+	0.0726515i	$0.976854\pi$
$432$		0			0
$433$	19.2070			0.923028			0.461514	−	0.887133i	$-0.347306\pi$
$433$	19.2070			0.923028			0.461514	+	0.887133i	$0.347306\pi$
$434$		0			0
$435$	5.18538			0.248620
$436$		0			0
$437$	−3.87569	−	6.71289i	−0.185399	−	0.321121i
$438$		0			0
$439$	12.8728	−	22.2963i	0.614383	−	1.06414i	−0.376109	−	0.926575i	$-0.622738\pi$
$439$	12.8728	−	22.2963i	0.614383	−	1.06414i	0.990492	−	0.137568i	$-0.0439284\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.2727	−	17.7928i	0.488071	−	0.845364i	−0.511835	−	0.859084i	$-0.671034\pi$
$443$	10.2727	−	17.7928i	0.488071	−	0.845364i	0.999906	+	0.0137201i	$0.00436737\pi$
$444$		0			0
$445$	18.0484	+	31.2608i	0.855577	+	1.48190i
$446$		0			0
$447$	−16.9856			−0.803391
$448$		0			0
$449$	−27.5024			−1.29792			−0.648960	−	0.760823i	$-0.724796\pi$
$449$	−27.5024			−1.29792			−0.648960	+	0.760823i	$0.724796\pi$
$450$		0			0
$451$	10.7054	+	18.5422i	0.504095	+	0.873119i
$452$		0			0
$453$	34.9841	−	60.5942i	1.64369	−	2.84696i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	19.9566	−	34.5659i	0.933531	−	1.61692i	0.156299	−	0.987710i	$-0.450044\pi$
$457$	19.9566	−	34.5659i	0.933531	−	1.61692i	0.777232	−	0.629214i	$-0.216623\pi$
$458$		0			0
$459$	10.4858	+	18.1620i	0.489436	+	0.847727i
$460$		0			0
$461$	−27.7528			−1.29258			−0.646289	−	0.763093i	$-0.723680\pi$
$461$	−27.7528			−1.29258			−0.646289	+	0.763093i	$0.723680\pi$
$462$		0			0
$463$	5.25880			0.244397			0.122199	−	0.992506i	$-0.461006\pi$
$463$	5.25880			0.244397			0.122199	+	0.992506i	$0.461006\pi$
$464$		0			0
$465$	41.8705	+	72.5218i	1.94170	+	3.36312i
$466$		0			0
$467$	−9.01918	+	15.6217i	−0.417358	+	0.722885i	−0.995673	−	0.0929287i	$-0.970377\pi$
$467$	−9.01918	+	15.6217i	−0.417358	+	0.722885i	0.578315	+	0.815814i	$0.303710\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−17.5483	+	30.3945i	−0.808582	+	1.40050i
$472$		0			0
$473$	8.30058	+	14.3770i	0.381661	+	0.661057i
$474$		0			0
$475$	48.9888			2.24776
$476$		0			0
$477$	−41.0687			−1.88041
$478$		0			0
$479$	−5.60992	−	9.71667i	−0.256324	−	0.443966i	0.708930	−	0.705278i	$-0.249178\pi$
$479$	−5.60992	−	9.71667i	−0.256324	−	0.443966i	−0.965254	+	0.261312i	$0.915845\pi$
$480$		0			0
$481$	17.8205	−	30.8661i	0.812547	−	1.40737i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−14.1226	+	24.4610i	−0.641273	+	1.11072i
$486$		0			0
$487$	19.5749	+	33.9048i	0.887025	+	1.53637i	0.843375	+	0.537326i	$0.180565\pi$
$487$	19.5749	+	33.9048i	0.887025	+	1.53637i	0.0436502	+	0.999047i	$0.486101\pi$
$488$		0			0
$489$	23.9782			1.08433
$490$		0			0
$491$	−33.6735			−1.51966			−0.759831	−	0.650120i	$-0.774718\pi$
$491$	−33.6735			−1.51966			−0.759831	+	0.650120i	$0.774718\pi$
$492$		0			0
$493$	−0.344919	−	0.597417i	−0.0155344	−	0.0269063i
$494$		0			0
$495$	−38.0618	+	65.9250i	−1.71075	+	2.96311i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−10.2653	+	17.7800i	−0.459537	+	0.795942i	−0.998936	−	0.0461082i	$-0.985318\pi$
$499$	−10.2653	+	17.7800i	−0.459537	+	0.795942i	0.539399	+	0.842050i	$0.318651\pi$
$500$		0			0
$501$	−35.4518	−	61.4042i	−1.58387	−	2.74334i
$502$		0			0
$503$	14.7480			0.657582			0.328791	−	0.944403i	$-0.393359\pi$
$503$	14.7480			0.657582			0.328791	+	0.944403i	$0.393359\pi$
$504$		0			0
$505$	4.61991			0.205583
$506$		0			0
$507$	−0.406909	−	0.704787i	−0.0180715	−	0.0313007i
$508$		0			0
$509$	4.83687	−	8.37771i	0.214391	−	0.371335i	−0.738693	−	0.674042i	$-0.764557\pi$
$509$	4.83687	−	8.37771i	0.214391	−	0.371335i	0.953084	+	0.302706i	$0.0978901\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	26.9577	−	46.6921i	1.19021	−	2.06151i
$514$		0			0
$515$	−16.6865	−	28.9019i	−0.735296	−	1.27357i
$516$		0			0
$517$	4.66186			0.205028
$518$		0			0
$519$	12.9728			0.569441
$520$		0			0
$521$	3.45775	+	5.98901i	0.151487	+	0.262383i	0.931774	−	0.363038i	$-0.118261\pi$
$521$	3.45775	+	5.98901i	0.151487	+	0.262383i	−0.780287	+	0.625421i	$0.784927\pi$
$522$		0			0
$523$	4.46100	−	7.72668i	0.195066	−	0.337864i	−0.751856	−	0.659327i	$-0.770841\pi$
$523$	4.46100	−	7.72668i	0.195066	−	0.337864i	0.946922	+	0.321463i	$0.104175\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.57025	−	9.64795i	0.242644	−	0.420271i
$528$		0			0
$529$	9.91080	+	17.1660i	0.430904	+	0.746348i
$530$		0			0
$531$	−53.2684			−2.31165
$532$		0			0
$533$	28.0795			1.21626
$534$		0			0
$535$	−32.0108	−	55.4443i	−1.38395	−	2.39707i
$536$		0			0
$537$	−2.10522	+	3.64635i	−0.0908470	+	0.157352i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4.73834	−	8.20705i	0.203717	−	0.352849i	−0.746006	−	0.665939i	$-0.768031\pi$
$541$	4.73834	−	8.20705i	0.203717	−	0.352849i	0.949723	+	0.313091i	$0.101364\pi$
$542$		0			0
$543$	11.3042	+	19.5795i	0.485110	+	0.840236i
$544$		0			0
$545$	−53.9495			−2.31094
$546$		0			0
$547$	22.8869			0.978573			0.489287	−	0.872123i	$-0.337257\pi$
$547$	22.8869			0.978573			0.489287	+	0.872123i	$0.337257\pi$
$548$		0			0
$549$	−15.6734	−	27.1472i	−0.668926	−	1.15861i
$550$		0			0
$551$	−0.886742	+	1.53588i	−0.0377765	+	0.0654308i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	63.4648	−	109.924i	2.69393	−	4.66603i
$556$		0			0
$557$	−11.8415	−	20.5101i	−0.501742	−	0.869043i	−0.999998	−	0.00201276i	$-0.999359\pi$
$557$	−11.8415	−	20.5101i	−0.501742	−	0.869043i	0.498256	−	0.867030i	$-0.333974\pi$
$558$		0			0
$559$	21.7719			0.920854
$560$		0			0
$561$	14.5084			0.612546
$562$		0			0
$563$	2.10139	+	3.63972i	0.0885632	+	0.153396i	0.906904	−	0.421337i	$-0.138439\pi$
$563$	2.10139	+	3.63972i	0.0885632	+	0.153396i	−0.818341	+	0.574733i	$0.805106\pi$
$564$		0			0
$565$	−33.3379	+	57.7430i	−1.40254	+	2.42927i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−20.0905	+	34.7978i	−0.842237	+	1.45880i	0.0457613	+	0.998952i	$0.485429\pi$
$569$	−20.0905	+	34.7978i	−0.842237	+	1.45880i	−0.887999	+	0.459846i	$0.847905\pi$
$570$		0			0
$571$	−13.3821	−	23.1785i	−0.560024	−	0.969989i	−0.997494	−	0.0707565i	$-0.977459\pi$
$571$	−13.3821	−	23.1785i	−0.560024	−	0.969989i	0.437470	−	0.899233i	$-0.355875\pi$
$572$		0			0
$573$	11.7550			0.491072
$574$		0			0
$575$	20.0875			0.837707
$576$		0			0
$577$	17.8754	+	30.9610i	0.744161	+	1.28892i	0.950586	+	0.310462i	$0.100484\pi$
$577$	17.8754	+	30.9610i	0.744161	+	1.28892i	−0.206425	+	0.978462i	$0.566183\pi$
$578$		0			0
$579$	−11.4782	+	19.8808i	−0.477017	+	0.826218i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−8.06001	+	13.9603i	−0.333811	+	0.578178i
$584$		0			0
$585$	49.9169	+	86.4586i	2.06381	+	3.57462i
$586$		0			0
$587$	−13.3219			−0.549852			−0.274926	−	0.961465i	$-0.588653\pi$
$587$	−13.3219			−0.549852			−0.274926	+	0.961465i	$0.588653\pi$
$588$		0			0
$589$	−28.6408			−1.18012
$590$		0			0
$591$	38.3741	+	66.4659i	1.57850	+	2.73404i
$592$		0			0
$593$	13.5164	−	23.4111i	0.555052	−	0.961378i	−0.442848	−	0.896597i	$-0.646032\pi$
$593$	13.5164	−	23.4111i	0.555052	−	0.961378i	0.997899	−	0.0647812i	$-0.0206349\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	27.9721	−	48.4490i	1.14482	−	1.98289i
$598$		0			0
$599$	−10.7714	−	18.6567i	−0.440109	−	0.762292i	0.557588	−	0.830118i	$-0.311727\pi$
$599$	−10.7714	−	18.6567i	−0.440109	−	0.762292i	−0.997697	+	0.0678262i	$0.978394\pi$
$600$		0			0
$601$	−21.5781			−0.880190			−0.440095	−	0.897951i	$-0.645055\pi$
$601$	−21.5781			−0.880190			−0.440095	+	0.897951i	$0.645055\pi$
$602$		0			0
$603$	28.8537			1.17501
$604$		0			0
$605$	−7.24330	−	12.5458i	−0.294482	−	0.510057i
$606$		0			0
$607$	−14.7102	+	25.4788i	−0.597067	+	1.03415i	0.396184	+	0.918171i	$0.370334\pi$
$607$	−14.7102	+	25.4788i	−0.597067	+	1.03415i	−0.993252	+	0.115980i	$0.962999\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.05694	−	5.29478i	0.123671	−	0.214204i
$612$		0			0
$613$	9.52392	+	16.4959i	0.384668	+	0.666264i	0.991723	−	0.128396i	$-0.0409827\pi$
$613$	9.52392	+	16.4959i	0.384668	+	0.666264i	−0.607055	+	0.794659i	$0.707649\pi$
$614$		0			0
$615$	100.000			4.03240
$616$		0			0
$617$	−42.6375			−1.71652			−0.858261	−	0.513213i	$-0.828455\pi$
$617$	−42.6375			−1.71652			−0.858261	+	0.513213i	$0.828455\pi$
$618$		0			0
$619$	−9.88519	−	17.1217i	−0.397319	−	0.688177i	0.596075	−	0.802929i	$-0.296726\pi$
$619$	−9.88519	−	17.1217i	−0.397319	−	0.688177i	−0.993394	+	0.114752i	$0.963393\pi$
$620$		0			0
$621$	11.0538	−	19.1458i	0.443574	−	0.768293i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−22.8082	+	39.5050i	−0.912330	+	1.58020i
$626$		0			0
$627$	−18.6497	−	32.3022i	−0.744796	−	1.29002i
$628$		0			0
$629$	−16.8861			−0.673293
$630$		0			0
$631$	40.3578			1.60662			0.803310	−	0.595562i	$-0.203070\pi$
$631$	40.3578			1.60662			0.803310	+	0.595562i	$0.203070\pi$
$632$		0			0
$633$	10.2945	+	17.8306i	0.409169	+	0.708702i
$634$		0			0
$635$	−18.8091	+	32.5782i	−0.746415	+	1.29283i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	27.5258	−	47.6760i	1.08890	−	1.88603i
$640$		0			0
$641$	−16.6565	−	28.8498i	−0.657891	−	1.13950i	−0.981161	−	0.193193i	$-0.938116\pi$
$641$	−16.6565	−	28.8498i	−0.657891	−	1.13950i	0.323270	−	0.946307i	$-0.395218\pi$
$642$		0			0
$643$	−15.1943			−0.599204			−0.299602	−	0.954064i	$-0.596854\pi$
$643$	−15.1943			−0.599204			−0.299602	+	0.954064i	$0.596854\pi$
$644$		0			0
$645$	77.5369			3.05301
$646$		0			0
$647$	18.6961	+	32.3826i	0.735019	+	1.27309i	0.954715	+	0.297522i	$0.0961601\pi$
$647$	18.6961	+	32.3826i	0.735019	+	1.27309i	−0.219696	+	0.975568i	$0.570507\pi$
$648$		0			0
$649$	−10.4543	+	18.1073i	−0.410366	+	0.710775i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−12.2111	+	21.1502i	−0.477856	+	0.827670i	−0.999678	−	0.0253840i	$-0.991919\pi$
$653$	−12.2111	+	21.1502i	−0.477856	+	0.827670i	0.521822	+	0.853054i	$0.325252\pi$
$654$		0			0
$655$	22.7819	+	39.4595i	0.890164	+	1.54181i
$656$		0			0
$657$	84.4720			3.29557
$658$		0			0
$659$	45.0721			1.75576			0.877880	−	0.478881i	$-0.158957\pi$
$659$	45.0721			1.75576			0.877880	+	0.478881i	$0.158957\pi$
$660$		0			0
$661$	3.55597	+	6.15912i	0.138311	+	0.239562i	0.926857	−	0.375413i	$-0.122499\pi$
$661$	3.55597	+	6.15912i	0.138311	+	0.239562i	−0.788546	+	0.614975i	$0.789166\pi$
$662$		0			0
$663$	9.51367	−	16.4782i	0.369481	−	0.639959i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.363603	+	0.629778i	−0.0140788	+	0.0243851i
$668$		0			0
$669$	−27.1346	−	46.9985i	−1.04908	−	1.81707i
$670$		0			0
$671$	−12.3041			−0.474993
$672$		0			0
$673$	17.1198			0.659922			0.329961	−	0.943995i	$-0.392964\pi$
$673$	17.1198			0.659922			0.329961	+	0.943995i	$0.392964\pi$
$674$		0			0
$675$	69.8602	+	121.001i	2.68892	+	4.65735i
$676$		0			0
$677$	16.1703	−	28.0078i	0.621475	−	1.07643i	−0.367737	−	0.929930i	$-0.619867\pi$
$677$	16.1703	−	28.0078i	0.621475	−	1.07643i	0.989211	−	0.146496i	$-0.0467995\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−12.2881	+	21.2837i	−0.470883	+	0.815593i
$682$		0			0
$683$	−4.11255	−	7.12315i	−0.157362	−	0.272560i	0.776554	−	0.630050i	$-0.216966\pi$
$683$	−4.11255	−	7.12315i	−0.157362	−	0.272560i	−0.933917	+	0.357491i	$0.883632\pi$
$684$		0			0
$685$	−69.4767			−2.65457
$686$		0			0
$687$	20.0561			0.765190
$688$		0			0
$689$	10.5704	+	18.3085i	0.402702	+	0.697500i
$690$		0			0
$691$	−9.39992	+	16.2811i	−0.357590	+	0.619364i	−0.987558	−	0.157258i	$-0.949735\pi$
$691$	−9.39992	+	16.2811i	−0.357590	+	0.619364i	0.629968	+	0.776621i	$0.283068\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6.98957	+	12.1063i	−0.265129	+	0.459218i
$696$		0			0
$697$	−6.65178	−	11.5212i	−0.251954	−	0.436397i
$698$		0			0
$699$	18.7710			0.709983
$700$		0			0
$701$	3.70843			0.140065			0.0700327	−	0.997545i	$-0.477690\pi$
$701$	3.70843			0.140065			0.0700327	+	0.997545i	$0.477690\pi$
$702$		0			0
$703$	21.7060	+	37.5959i	0.818658	+	1.41796i
$704$		0			0
$705$	10.8868	−	18.8564i	0.410020	−	0.710175i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	9.25899	−	16.0370i	0.347729	−	0.602283i	−0.638117	−	0.769939i	$-0.720286\pi$
$709$	9.25899	−	16.0370i	0.347729	−	0.602283i	0.985846	+	0.167656i	$0.0536198\pi$
$710$		0			0
$711$	0.989110	+	1.71319i	0.0370945	+	0.0642496i
$712$		0			0
$713$	−11.7440			−0.439815
$714$		0			0
$715$	39.1860			1.46547
$716$		0			0
$717$	−3.87349	−	6.70909i	−0.144658	−	0.250555i
$718$		0			0
$719$	8.93697	−	15.4793i	0.333293	−	0.577280i	−0.649863	−	0.760052i	$-0.725174\pi$
$719$	8.93697	−	15.4793i	0.333293	−	0.577280i	0.983155	+	0.182772i	$0.0585069\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−7.88803	+	13.6625i	−0.293359	+	0.508113i
$724$		0			0
$725$	−2.29797	−	3.98020i	−0.0853445	−	0.147821i
$726$		0			0
$727$	40.0663			1.48598			0.742988	−	0.669305i	$-0.233408\pi$
$727$	40.0663			1.48598			0.742988	+	0.669305i	$0.233408\pi$
$728$		0			0
$729$	9.51739			0.352496
$730$		0			0
$731$	−5.15757	−	8.93317i	−0.190760	−	0.330405i
$732$		0			0
$733$	1.12538	−	1.94921i	0.0415667	−	0.0719956i	−0.844494	−	0.535566i	$-0.820098\pi$
$733$	1.12538	−	1.94921i	0.0415667	−	0.0719956i	0.886060	+	0.463570i	$0.153432\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.66273	−	9.80813i	0.208589	−	0.361287i
$738$		0			0
$739$	16.0545	+	27.8072i	0.590575	+	1.02291i	0.994155	+	0.107962i	$0.0344324\pi$
$739$	16.0545	+	27.8072i	0.590575	+	1.02291i	−0.403580	+	0.914944i	$0.632234\pi$
$740$		0			0
$741$	−48.9169			−1.79701
$742$		0			0
$743$	−49.2743			−1.80770			−0.903849	−	0.427851i	$-0.859271\pi$
$743$	−49.2743			−1.80770			−0.903849	+	0.427851i	$0.859271\pi$
$744$		0			0
$745$	10.8678	+	18.8235i	0.398164	+	0.689640i
$746$		0			0
$747$	32.4770	−	56.2519i	1.18827	−	2.05815i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−10.7672	+	18.6494i	−0.392902	+	0.680525i	−0.992831	−	0.119528i	$-0.961862\pi$
$751$	−10.7672	+	18.6494i	−0.392902	+	0.680525i	0.599929	+	0.800053i	$0.295195\pi$
$752$		0			0
$753$	−9.17978	−	15.8998i	−0.334530	−	0.579423i
$754$		0			0
$755$	−89.5344			−3.25849
$756$		0			0
$757$	−8.03758			−0.292131			−0.146065	−	0.989275i	$-0.546661\pi$
$757$	−8.03758			−0.292131			−0.146065	+	0.989275i	$0.546661\pi$
$758$		0			0
$759$	−7.64717	−	13.2453i	−0.277575	−	0.480773i
$760$		0			0
$761$	15.5913	−	27.0048i	0.565182	−	0.978925i	−0.431850	−	0.901945i	$-0.642139\pi$
$761$	15.5913	−	27.0048i	0.565182	−	0.978925i	0.997033	−	0.0769793i	$-0.0245275\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	23.6497	−	40.9625i	0.855057	−	1.48100i
$766$		0			0
$767$	13.7105	+	23.7472i	0.495056	+	0.857462i
$768$		0			0
$769$	28.4420			1.02565			0.512823	−	0.858494i	$-0.328600\pi$
$769$	28.4420			1.02565			0.512823	+	0.858494i	$0.328600\pi$
$770$		0			0
$771$	−1.36562			−0.0491815
$772$		0			0
$773$	8.93296	+	15.4723i	0.321296	+	0.556501i	0.980756	−	0.195239i	$-0.0625482\pi$
$773$	8.93296	+	15.4723i	0.321296	+	0.556501i	−0.659460	+	0.751740i	$0.729215\pi$
$774$		0			0
$775$	37.1110	−	64.2781i	1.33307	−	2.30894i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−17.1009	+	29.6196i	−0.612702	+	1.06123i
$780$		0			0
$781$	−10.8042	−	18.7135i	−0.386605	−	0.669620i
$782$		0			0
$783$	−5.05814			−0.180763
$784$		0			0
$785$	44.9111			1.60295
$786$		0			0
$787$	−23.1168	−	40.0395i	−0.824025	−	1.42725i	−0.902662	−	0.430350i	$-0.858390\pi$
$787$	−23.1168	−	40.0395i	−0.824025	−	1.42725i	0.0786370	−	0.996903i	$-0.474943\pi$
$788$		0			0
$789$	−33.8005	+	58.5442i	−1.20333	+	2.08423i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−8.06819	+	13.9745i	−0.286510	+	0.496250i
$794$		0			0
$795$	37.6448	+	65.2028i	1.33512	+	2.31250i
$796$		0			0
$797$	9.70433			0.343745			0.171873	−	0.985119i	$-0.445018\pi$
$797$	9.70433			0.343745			0.171873	+	0.985119i	$0.445018\pi$
$798$		0			0
$799$	−2.89665			−0.102476
$800$		0			0
$801$	−31.0302	−	53.7459i	−1.09640	−	1.89902i
$802$		0			0
$803$	16.5782	−	28.7143i	0.585031	−	1.01330i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−31.4044	+	54.3941i	−1.10549	+	1.91476i
$808$		0			0
$809$	23.0115	+	39.8571i	0.809041	+	1.40130i	0.913529	+	0.406773i	$0.133346\pi$
$809$	23.0115	+	39.8571i	0.809041	+	1.40130i	−0.104489	+	0.994526i	$0.533321\pi$
$810$		0			0
$811$	−39.0194			−1.37016			−0.685078	−	0.728470i	$-0.740232\pi$
$811$	−39.0194			−1.37016			−0.685078	+	0.728470i	$0.740232\pi$
$812$		0			0
$813$	28.2832			0.991936
$814$		0			0
$815$	−15.3418	−	26.5728i	−0.537399	−	0.930803i
$816$		0			0
$817$	−13.2595	+	22.9661i	−0.463890	+	0.803481i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10.3066	+	17.8515i	−0.359702	+	0.623022i	−0.987911	−	0.155022i	$-0.950455\pi$
$821$	−10.3066	+	17.8515i	−0.359702	+	0.623022i	0.628209	+	0.778045i	$0.283788\pi$
$822$		0			0
$823$	17.3427	+	30.0384i	0.604528	+	1.04707i	0.992126	+	0.125245i	$0.0399716\pi$
$823$	17.3427	+	30.0384i	0.604528	+	1.04707i	−0.387598	+	0.921829i	$0.626695\pi$
$824$		0			0
$825$	96.6603			3.36528
$826$		0			0
$827$	51.7310			1.79886			0.899432	−	0.437061i	$-0.143981\pi$
$827$	51.7310			1.79886			0.899432	+	0.437061i	$0.143981\pi$
$828$		0			0
$829$	20.8069	+	36.0386i	0.722652	+	1.25167i	0.959933	+	0.280230i	$0.0904106\pi$
$829$	20.8069	+	36.0386i	0.722652	+	1.25167i	−0.237281	+	0.971441i	$0.576256\pi$
$830$		0			0
$831$	−28.0821	+	48.6396i	−0.974157	+	1.68729i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−45.3657	+	78.5756i	−1.56994	+	2.71922i
$836$		0			0
$837$	−40.8431	−	70.7423i	−1.41174	−	2.44521i
$838$		0			0
$839$	−32.2174			−1.11227			−0.556133	−	0.831093i	$-0.687716\pi$
$839$	−32.2174			−1.11227			−0.556133	+	0.831093i	$0.687716\pi$
$840$		0			0
$841$	−28.8336			−0.994263
$842$		0			0
$843$	−3.44301	−	5.96347i	−0.118584	−	0.205393i
$844$		0			0
$845$	−0.520699	+	0.901877i	−0.0179126	+	0.0310255i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−21.8651	+	37.8715i	−0.750409	+	1.29975i
$850$		0			0
$851$	8.90041	+	15.4160i	0.305102	+	0.528452i
$852$		0			0
$853$	20.8951			0.715434			0.357717	−	0.933830i	$-0.383555\pi$
$853$	20.8951			0.715434			0.357717	+	0.933830i	$0.383555\pi$
$854$		0			0
$855$	−121.601			−4.15866
$856$		0			0
$857$	9.97712	+	17.2809i	0.340812	+	0.590304i	0.984584	−	0.174914i	$-0.0559647\pi$
$857$	9.97712	+	17.2809i	0.340812	+	0.590304i	−0.643772	+	0.765218i	$0.722631\pi$
$858$		0			0
$859$	−13.9738	+	24.2034i	−0.476782	+	0.825810i	−0.999646	−	0.0266059i	$-0.991530\pi$
$859$	−13.9738	+	24.2034i	−0.476782	+	0.825810i	0.522864	+	0.852416i	$0.324863\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	8.30931	−	14.3922i	0.282852	−	0.489915i	−0.689234	−	0.724539i	$-0.742053\pi$
$863$	8.30931	−	14.3922i	0.282852	−	0.489915i	0.972086	+	0.234624i	$0.0753860\pi$
$864$		0			0
$865$	−8.30026	−	14.3765i	−0.282217	−	0.488815i
$866$		0			0
$867$	44.5671			1.51358
$868$		0			0
$869$	0.776477			0.0263402
$870$		0			0
$871$	−7.42649	−	12.8631i	−0.251637	−	0.435848i
$872$		0			0
$873$	24.2806	−	42.0552i	0.821773	−	1.42335i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	5.80421	−	10.0532i	0.195994	−	0.339472i	−0.751232	−	0.660038i	$-0.770540\pi$
$877$	5.80421	−	10.0532i	0.195994	−	0.339472i	0.947226	+	0.320567i	$0.103873\pi$
$878$		0			0
$879$	−33.5998	−	58.1966i	−1.13329	−	1.96292i
$880$		0			0
$881$	−21.1358			−0.712084			−0.356042	−	0.934470i	$-0.615874\pi$
$881$	−21.1358			−0.712084			−0.356042	+	0.934470i	$0.615874\pi$
$882$		0			0
$883$	−36.5352			−1.22951			−0.614753	−	0.788720i	$-0.710744\pi$
$883$	−36.5352			−1.22951			−0.614753	+	0.788720i	$0.710744\pi$
$884$		0			0
$885$	48.8274	+	84.5716i	1.64132	+	2.84284i
$886$		0			0
$887$	−10.9644	+	18.9908i	−0.368147	+	0.637649i	−0.989276	−	0.146059i	$-0.953341\pi$
$887$	−10.9644	+	18.9908i	−0.368147	+	0.637649i	0.621129	+	0.783708i	$0.286674\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	24.8797	−	43.0929i	0.833502	−	1.44367i
$892$		0			0
$893$	3.72346	+	6.44922i	0.124601	+	0.215815i
$894$		0			0
$895$	5.38787			0.180097
$896$		0			0
$897$	−20.0580			−0.669718
$898$		0			0
$899$	1.34349	+	2.32699i	0.0448078	+	0.0776094i
$900$		0			0
$901$	5.00809	−	8.67426i	0.166844	−	0.288982i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	14.4654	−	25.0548i	0.480846	−	0.832849i
$906$		0			0
$907$	−15.7479	−	27.2761i	−0.522900	−	0.905689i	−0.999645	−	0.0266474i	$-0.991517\pi$
$907$	−15.7479	−	27.2761i	−0.522900	−	0.905689i	0.476745	−	0.879042i	$-0.341816\pi$
$908$		0			0
$909$	−7.94289			−0.263449
$910$		0			0
$911$	42.3039			1.40159			0.700796	−	0.713362i	$-0.252828\pi$
$911$	42.3039			1.40159			0.700796	+	0.713362i	$0.252828\pi$
$912$		0			0
$913$	−12.7477	−	22.0796i	−0.421886	−	0.730728i
$914$		0			0
$915$	−28.7335	+	49.7678i	−0.949900	+	1.64527i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	9.71438	−	16.8258i	0.320448	−	0.555032i	−0.660133	−	0.751149i	$-0.729500\pi$
$919$	9.71438	−	16.8258i	0.320448	−	0.555032i	0.980580	+	0.196117i	$0.0628333\pi$
$920$		0			0
$921$	1.10701	+	1.91740i	0.0364773	+	0.0631806i
$922$		0			0
$923$	−28.3388			−0.932782
$924$		0			0
$925$	−112.501			−3.69902
$926$		0			0
$927$	28.6887	+	49.6903i	0.942261	+	1.63204i
$928$		0			0
$929$	−28.1847	+	48.8173i	−0.924710	+	1.60165i	−0.132684	+	0.991158i	$0.542360\pi$
$929$	−28.1847	+	48.8173i	−0.924710	+	1.60165i	−0.792026	+	0.610487i	$0.790974\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−14.4796	+	25.0794i	−0.474041	+	0.821063i
$934$		0			0
$935$	−9.28282	−	16.0783i	−0.303581	−	0.525817i
$936$		0			0
$937$	54.4190			1.77779			0.888895	−	0.458111i	$-0.151474\pi$
$937$	54.4190			1.77779			0.888895	+	0.458111i	$0.151474\pi$
$938$		0			0
$939$	−62.7075			−2.04638
$940$		0			0
$941$	−12.6574	−	21.9233i	−0.412620	−	0.714679i	0.582555	−	0.812791i	$-0.302053\pi$
$941$	−12.6574	−	21.9233i	−0.412620	−	0.714679i	−0.995175	+	0.0981123i	$0.968720\pi$
$942$		0			0
$943$	−7.01210	+	12.1453i	−0.228345	+	0.395506i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−27.8684	+	48.2695i	−0.905601	+	1.56855i	−0.0854923	+	0.996339i	$0.527246\pi$
$947$	−27.8684	+	48.2695i	−0.905601	+	1.56855i	−0.820109	+	0.572208i	$0.806087\pi$
$948$		0			0
$949$	−21.7418	−	37.6579i	−0.705768	−	1.22243i
$950$		0			0
$951$	−16.1638			−0.524148
$952$		0			0
$953$	−14.4928			−0.469468			−0.234734	−	0.972060i	$-0.575422\pi$
$953$	−14.4928			−0.469468			−0.234734	+	0.972060i	$0.575422\pi$
$954$		0			0
$955$	−7.52111	−	13.0269i	−0.243377	−	0.421542i
$956$		0			0
$957$	−1.74964	+	3.03047i	−0.0565579	+	0.0979612i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−6.19656	+	10.7328i	−0.199889	+	0.346218i
$962$		0			0
$963$	55.0353	+	95.3239i	1.77349	+	3.07177i
$964$		0			0
$965$	29.3760			0.945647
$966$		0			0
$967$	0.662798			0.0213141			0.0106571	−	0.999943i	$-0.496608\pi$
$967$	0.662798			0.0213141			0.0106571	+	0.999943i	$0.496608\pi$
$968$		0			0
$969$	11.5880	+	20.0710i	0.372259	+	0.644772i
$970$		0			0
$971$	−15.3667	+	26.6158i	−0.493139	+	0.854143i	−0.999969	−	0.00790385i	$-0.997484\pi$
$971$	−15.3667	+	26.6158i	−0.493139	+	0.854143i	0.506829	+	0.862046i	$0.330817\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	63.3835	−	109.783i	2.02990	−	3.51588i
$976$		0			0
$977$	0.416537	+	0.721464i	0.0133262	+	0.0230817i	0.872612	−	0.488415i	$-0.162425\pi$
$977$	0.416537	+	0.721464i	0.0133262	+	0.0230817i	−0.859285	+	0.511496i	$0.829091\pi$
$978$		0			0
$979$	−24.3595			−0.778533
$980$		0			0
$981$	92.7539			2.96141
$982$		0			0
$983$	24.1163	+	41.7706i	0.769190	+	1.33228i	0.938003	+	0.346628i	$0.112673\pi$
$983$	24.1163	+	41.7706i	0.769190	+	1.33228i	−0.168812	+	0.985648i	$0.553993\pi$
$984$		0			0
$985$	49.1052	−	85.0527i	1.56462	−	2.71000i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−5.43695	+	9.41707i	−0.172885	+	0.299446i
$990$		0			0
$991$	−9.28566	−	16.0832i	−0.294969	−	0.510901i	0.680009	−	0.733204i	$-0.261976\pi$
$991$	−9.28566	−	16.0832i	−0.294969	−	0.510901i	−0.974978	+	0.222303i	$0.928643\pi$
$992$		0			0
$993$	19.6863			0.624727
$994$		0			0
$995$	−71.5886			−2.26951
$996$		0			0
$997$	17.9419	+	31.0762i	0.568225	+	0.984195i	0.996742	+	0.0806607i	$0.0257030\pi$
$997$	17.9419	+	31.0762i	0.568225	+	0.984195i	−0.428517	+	0.903534i	$0.640964\pi$
$998$		0			0
$999$	−61.9075	+	107.227i	−1.95867	+	3.39251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1372.2.e.d.1353.5		12
7.2	even	3		1372.2.a.a.1.2	✓	6
7.3	odd	6		1372.2.e.a.361.2		12
7.4	even	3	inner	1372.2.e.d.361.5		12
7.5	odd	6		1372.2.a.d.1.5	yes	6
7.6	odd	2		1372.2.e.a.1353.2		12
28.19	even	6		5488.2.a.g.1.2		6
28.23	odd	6		5488.2.a.q.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1372.2.a.a.1.2	✓	6	7.2	even	3
1372.2.a.d.1.5	yes	6	7.5	odd	6
1372.2.e.a.361.2		12	7.3	odd	6
1372.2.e.a.1353.2		12	7.6	odd	2
1372.2.e.d.361.5		12	7.4	even	3	inner
1372.2.e.d.1353.5		12	1.1	even	1	trivial
5488.2.a.g.1.2		6	28.19	even	6
5488.2.a.q.1.5		6	28.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1372 = 2^{2} \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1372.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.57594 + 2.72960i) q^{3} +(2.01664 - 3.49292i) q^{5} +(-3.46716 + 6.00529i) q^{9} +(1.36090 + 2.35715i) q^{11} +3.56957 q^{13} +12.7124 q^{15} +(-0.845598 - 1.46462i) q^{17} +(-2.17393 + 3.76535i) q^{19} +(-0.891403 + 1.54396i) q^{23} +(-5.63368 - 9.75781i) q^{25} -12.4005 q^{27} +0.407899 q^{29} +(3.29367 + 5.70481i) q^{31} +(-4.28940 + 7.42946i) q^{33} +(4.99236 - 8.64701i) q^{37} +(5.62541 + 9.74350i) q^{39} +7.86636 q^{41} +6.09932 q^{43} +(13.9840 + 24.2210i) q^{45} +(0.856390 - 1.48331i) q^{47} +(2.66522 - 4.61630i) q^{51} +(2.96127 + 5.12907i) q^{53} +10.9778 q^{55} -13.7039 q^{57} +(3.84093 + 6.65269i) q^{59} +(-2.26027 + 3.91491i) q^{61} +(7.19853 - 12.4682i) q^{65} +(-2.08050 - 3.60354i) q^{67} -5.61918 q^{69} -7.93900 q^{71} +(-6.09087 - 10.5497i) q^{73} +(17.7566 - 30.7554i) q^{75} +(0.142640 - 0.247060i) q^{79} +(-9.14088 - 15.8325i) q^{81} -9.36705 q^{83} -6.82107 q^{85} +(0.642824 + 1.11340i) q^{87} +(-4.47487 + 7.75071i) q^{89} +(-10.3812 + 17.9808i) q^{93} +(8.76805 + 15.1867i) q^{95} -7.00302 q^{97} -18.8739 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 7 q^{3} + 7 q^{5} - 9 q^{9} - 3 q^{11} - 14 q^{13} + 22 q^{15} + 7 q^{19} - 11 q^{23} - 3 q^{25} - 56 q^{27} + 12 q^{29} + 14 q^{31} + 6 q^{37} - 5 q^{39} - 6 q^{43} + 21 q^{45} + 42 q^{47} + 17 q^{51}+ \cdots - 68 q^{99}+O(q^{100}) \) 12 * q + 7 * q^3 + 7 * q^5 - 9 * q^9 - 3 * q^11 - 14 * q^13 + 22 * q^15 + 7 * q^19 - 11 * q^23 - 3 * q^25 - 56 * q^27 + 12 * q^29 + 14 * q^31 + 6 * q^37 - 5 * q^39 - 6 * q^43 + 21 * q^45 + 42 * q^47 + 17 * q^51 + 17 * q^53 - 28 * q^55 - 12 * q^57 + 35 * q^59 + 7 * q^61 + 6 * q^65 + 14 * q^67 - 28 * q^69 - 56 * q^71 + 35 * q^75 - 6 * q^79 - 34 * q^81 - 98 * q^83 - 46 * q^85 + 21 * q^87 - 7 * q^89 + 14 * q^93 + 25 * q^95 + 42 * q^97 - 68 * q^99

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