LMFDB - Embedded newform 2548.2.bq.c.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,2,Mod(361,2548)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2548, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 5]))

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

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

chi := DirichletCharacter("2548.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.bq (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 38x^{14} + 587x^{12} + 4762x^{10} + 21849x^{8} + 56552x^{6} + 76456x^{4} + 42624x^{2} + 2704 $ x^16 + 38x^14 + 587x^12 + 4762x^10 + 21849x^8 + 56552x^6 + 76456x^4 + 42624*x^2 + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.2
Root			$-1.77673i$ of defining polynomial
Character	$\chi$	$=$	2548.361
Dual form			2548.2.bq.c.1941.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.77673 q^{3} +(3.31518 - 1.91402i) q^{5} +0.156761 q^{9} -4.32707i q^{11} +(0.930395 - 3.48344i) q^{13} +(-5.89018 + 3.40069i) q^{15} +(-1.45744 - 2.52436i) q^{17} +5.45810i q^{19} +(-0.307112 + 0.531934i) q^{23} +(4.82696 - 8.36053i) q^{25} +5.05166 q^{27} +(-4.62872 - 8.01717i) q^{29} +(-4.59646 - 2.65377i) q^{31} +7.68802i q^{33} +(0.974022 + 0.562352i) q^{37} +(-1.65306 + 6.18913i) q^{39} +(-10.4130 + 6.01195i) q^{41} +(0.641552 - 1.11120i) q^{43} +(0.519691 - 0.300044i) q^{45} +(-4.91966 + 2.84037i) q^{47} +(2.58947 + 4.48510i) q^{51} +(1.98007 - 3.42958i) q^{53} +(-8.28210 - 14.3450i) q^{55} -9.69757i q^{57} +(-6.68359 + 3.85877i) q^{59} +14.3462 q^{61} +(-3.58295 - 13.3290i) q^{65} +0.541525i q^{67} +(0.545654 - 0.945101i) q^{69} +(7.96918 + 4.60101i) q^{71} +(6.38086 + 3.68399i) q^{73} +(-8.57618 + 14.8544i) q^{75} +(-0.165843 - 0.287249i) q^{79} -9.44571 q^{81} +16.6777i q^{83} +(-9.66335 - 5.57914i) q^{85} +(8.22397 + 14.2443i) q^{87} +(2.55836 + 1.47707i) q^{89} +(8.16665 + 4.71502i) q^{93} +(10.4469 + 18.0946i) q^{95} +(-8.36220 - 4.82792i) q^{97} -0.678314i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 28 q^{9} - 10 q^{13} + 6 q^{15} - 2 q^{17} + 22 q^{25} + 12 q^{27} - 22 q^{29} + 30 q^{31} - 12 q^{37} - 6 q^{39} - 36 q^{41} + 6 q^{43} - 30 q^{45} - 18 q^{47} + 2 q^{51} - 4 q^{53} - 2 q^{55} - 18 q^{59}+ \cdots + 42 q^{97}+O(q^{100}) $ 16 * q + 28 * q^9 - 10 * q^13 + 6 * q^15 - 2 * q^17 + 22 * q^25 + 12 * q^27 - 22 * q^29 + 30 * q^31 - 12 * q^37 - 6 * q^39 - 36 * q^41 + 6 * q^43 - 30 * q^45 - 18 * q^47 + 2 * q^51 - 4 * q^53 - 2 * q^55 - 18 * q^59 + 8 * q^61 + 52 * q^69 + 36 * q^71 - 12 * q^73 + 10 * q^75 - 4 * q^79 + 42 * q^85 - 26 * q^87 - 36 * q^89 + 42 * q^93 - 30 * q^95 + 42 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.77673			−1.02579			−0.512897	−	0.858450i	$-0.671428\pi$
$3$	−1.77673			−1.02579			−0.512897	+	0.858450i	$0.671428\pi$
$4$		0			0
$5$	3.31518	−	1.91402i	1.48259	−	0.855976i	0.482790	−	0.875736i	$-0.339624\pi$
$5$	3.31518	−	1.91402i	1.48259	−	0.855976i	0.999805	+	0.0197599i	$0.00629017\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	0.156761			0.0522536
$10$		0			0
$11$		−	4.32707i		−	1.30466i	−0.757935	−	0.652330i	$-0.773792\pi$
$11$		−	4.32707i		−	1.30466i	0.757935	−	0.652330i	$-0.226208\pi$
$12$		0			0
$13$	0.930395	−	3.48344i	0.258045	−	0.966133i
$13$	0.930395	−	3.48344i	0.258045	−	0.966133i
$14$		0			0
$15$	−5.89018	+	3.40069i	−1.52084	+	0.878056i
$16$		0			0
$17$	−1.45744	−	2.52436i	−0.353481	−	0.612247i	0.633376	−	0.773844i	$-0.281669\pi$
$17$	−1.45744	−	2.52436i	−0.353481	−	0.612247i	−0.986857	+	0.161597i	$0.948335\pi$
$18$		0			0
$19$			5.45810i			1.25218i	0.779753	+	0.626088i	$0.215345\pi$
$19$			5.45810i			1.25218i	−0.779753	+	0.626088i	$0.784655\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.307112	+	0.531934i	−0.0640373	+	0.110916i	−0.896267	−	0.443516i	$-0.853731\pi$
$23$	−0.307112	+	0.531934i	−0.0640373	+	0.110916i	0.832229	+	0.554432i	$0.187064\pi$
$24$		0			0
$25$	4.82696	−	8.36053i	0.965391	−	1.67211i
$26$		0			0
$27$	5.05166			0.972193
$28$		0			0
$29$	−4.62872	−	8.01717i	−0.859531	−	1.48875i	−0.872377	−	0.488834i	$-0.837422\pi$
$29$	−4.62872	−	8.01717i	−0.859531	−	1.48875i	0.0128452	−	0.999917i	$-0.495911\pi$
$30$		0			0
$31$	−4.59646	−	2.65377i	−0.825548	−	0.476630i	0.0267778	−	0.999641i	$-0.491475\pi$
$31$	−4.59646	−	2.65377i	−0.825548	−	0.476630i	−0.852326	+	0.523011i	$0.824809\pi$
$32$		0			0
$33$			7.68802i			1.33831i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.974022	+	0.562352i	0.160128	+	0.0924501i	0.577923	−	0.816091i	$-0.303863\pi$
$37$	0.974022	+	0.562352i	0.160128	+	0.0924501i	−0.417795	+	0.908542i	$0.637197\pi$
$38$		0			0
$39$	−1.65306	+	6.18913i	−0.264701	+	0.991053i
$40$		0			0
$41$	−10.4130	+	6.01195i	−1.62624	+	0.938909i	−0.641037	+	0.767510i	$0.721495\pi$
$41$	−10.4130	+	6.01195i	−1.62624	+	0.938909i	−0.985202	+	0.171399i	$0.945171\pi$
$42$		0			0
$43$	0.641552	−	1.11120i	0.0978358	−	0.169457i	−0.812953	−	0.582330i	$-0.802141\pi$
$43$	0.641552	−	1.11120i	0.0978358	−	0.169457i	0.910789	+	0.412873i	$0.135475\pi$
$44$		0			0
$45$	0.519691	−	0.300044i	0.0774709	−	0.0447278i
$46$		0			0
$47$	−4.91966	+	2.84037i	−0.717606	+	0.414310i	−0.813871	−	0.581046i	$-0.802644\pi$
$47$	−4.91966	+	2.84037i	−0.717606	+	0.414310i	0.0962647	+	0.995356i	$0.469310\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	2.58947	+	4.48510i	0.362599	+	0.628039i
$52$		0			0
$53$	1.98007	−	3.42958i	0.271983	−	0.471088i	−0.697386	−	0.716695i	$-0.745654\pi$
$53$	1.98007	−	3.42958i	0.271983	−	0.471088i	0.969370	+	0.245607i	$0.0789872\pi$
$54$		0			0
$55$	−8.28210	−	14.3450i	−1.11676	−	1.93428i
$56$		0			0
$57$		−	9.69757i		−	1.28447i
$58$		0			0
$59$	−6.68359	+	3.85877i	−0.870129	+	0.502369i	−0.867391	−	0.497627i	$-0.834205\pi$
$59$	−6.68359	+	3.85877i	−0.870129	+	0.502369i	−0.00273800	+	0.999996i	$0.500872\pi$
$60$		0			0
$61$	14.3462			1.83684			0.918419	−	0.395610i	$-0.129467\pi$
$61$	14.3462			1.83684			0.918419	+	0.395610i	$0.129467\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.58295	−	13.3290i	−0.444411	−	1.65326i
$66$		0			0
$67$			0.541525i			0.0661578i	0.999453	+	0.0330789i	$0.0105313\pi$
$67$			0.541525i			0.0661578i	−0.999453	+	0.0330789i	$0.989469\pi$
$68$		0			0
$69$	0.545654	−	0.945101i	0.0656891	−	0.113777i
$70$		0			0
$71$	7.96918	+	4.60101i	0.945768	+	0.546040i	0.891764	−	0.452501i	$-0.149468\pi$
$71$	7.96918	+	4.60101i	0.945768	+	0.546040i	0.0540044	+	0.998541i	$0.482801\pi$
$72$		0			0
$73$	6.38086	+	3.68399i	0.746823	+	0.431179i	0.824545	−	0.565797i	$-0.191431\pi$
$73$	6.38086	+	3.68399i	0.746823	+	0.431179i	−0.0777217	+	0.996975i	$0.524765\pi$
$74$		0			0
$75$	−8.57618	+	14.8544i	−0.990293	+	1.71524i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.165843	−	0.287249i	−0.0186588	−	0.0323180i	0.856545	−	0.516072i	$-0.172606\pi$
$79$	−0.165843	−	0.287249i	−0.0186588	−	0.0323180i	−0.875204	+	0.483754i	$0.839273\pi$
$80$		0			0
$81$	−9.44571			−1.04952
$82$		0			0
$83$			16.6777i			1.83061i	0.402758	+	0.915306i	$0.368052\pi$
$83$			16.6777i			1.83061i	−0.402758	+	0.915306i	$0.631948\pi$
$84$		0			0
$85$	−9.66335	−	5.57914i	−1.04814	−	0.605143i
$86$		0			0
$87$	8.22397	+	14.2443i	0.881702	+	1.52715i
$88$		0			0
$89$	2.55836	+	1.47707i	0.271185	+	0.156569i	0.629426	−	0.777060i	$-0.283290\pi$
$89$	2.55836	+	1.47707i	0.271185	+	0.156569i	−0.358241	+	0.933629i	$0.616623\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	8.16665	+	4.71502i	0.846842	+	0.488925i
$94$		0			0
$95$	10.4469	+	18.0946i	1.07183	+	1.85647i
$96$		0			0
$97$	−8.36220	−	4.82792i	−0.849052	−	0.490201i	0.0112787	−	0.999936i	$-0.496410\pi$
$97$	−8.36220	−	4.82792i	−0.849052	−	0.490201i	−0.860331	+	0.509736i	$0.829743\pi$
$98$		0			0
$99$		−	0.678314i		−	0.0681731i
$100$		0			0
$101$	−6.35056			−0.631905			−0.315952	−	0.948775i	$-0.602324\pi$
$101$	−6.35056			−0.631905			−0.315952	+	0.948775i	$0.602324\pi$
$102$		0			0
$103$	−2.53559	−	4.39176i	−0.249839	−	0.432733i	0.713642	−	0.700510i	$-0.247044\pi$
$103$	−2.53559	−	4.39176i	−0.249839	−	0.432733i	−0.963481	+	0.267777i	$0.913711\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.74289	−	4.75083i	0.265166	−	0.459280i	−0.702441	−	0.711742i	$-0.747907\pi$
$107$	2.74289	−	4.75083i	0.265166	−	0.459280i	0.967607	+	0.252461i	$0.0812401\pi$
$108$		0			0
$109$	−5.89490	−	3.40342i	−0.564629	−	0.325989i	0.190372	−	0.981712i	$-0.439031\pi$
$109$	−5.89490	−	3.40342i	−0.564629	−	0.325989i	−0.755002	+	0.655723i	$0.772364\pi$
$110$		0			0
$111$	−1.73057	−	0.999146i	−0.164259	−	0.0948347i
$112$		0			0
$113$	3.28384	−	5.68778i	0.308918	−	0.535061i	−0.669208	−	0.743075i	$-0.733367\pi$
$113$	3.28384	−	5.68778i	0.308918	−	0.535061i	0.978126	+	0.208014i	$0.0666999\pi$
$114$		0			0
$115$			2.35128i			0.219258i
$116$		0			0
$117$	0.145849	−	0.546067i	0.0134838	−	0.0504839i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−7.72349			−0.702136
$122$		0			0
$123$	18.5011	−	10.6816i	1.66819	−	0.963128i
$124$		0			0
$125$		−	17.8154i		−	1.59346i
$126$		0			0
$127$	−10.1425	−	17.5674i	−0.900003	−	1.55885i	−0.827488	−	0.561483i	$-0.810231\pi$
$127$	−10.1425	−	17.5674i	−0.900003	−	1.55885i	−0.0725145	−	0.997367i	$-0.523102\pi$
$128$		0			0
$129$	−1.13986	+	1.97430i	−0.100359	+	0.173828i
$130$		0			0
$131$	2.46221	+	4.26467i	0.215124	+	0.372606i	0.953311	−	0.301990i	$-0.0976510\pi$
$131$	2.46221	+	4.26467i	0.215124	+	0.372606i	−0.738187	+	0.674596i	$0.764318\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	16.7472	−	9.66899i	1.44137	−	0.832174i
$136$		0			0
$137$	−11.1993	+	6.46589i	−0.956817	+	0.552419i	−0.895192	−	0.445681i	$-0.852962\pi$
$137$	−11.1993	+	6.46589i	−0.956817	+	0.552419i	−0.0616251	+	0.998099i	$0.519628\pi$
$138$		0			0
$139$	7.90466	−	13.6913i	0.670464	−	1.16128i	−0.307308	−	0.951610i	$-0.599428\pi$
$139$	7.90466	−	13.6913i	0.670464	−	1.16128i	0.977773	−	0.209668i	$-0.0672384\pi$
$140$		0			0
$141$	8.74090	−	5.04656i	0.736116	−	0.424997i
$142$		0			0
$143$	−15.0731	−	4.02588i	−1.26047	−	0.336661i
$144$		0			0
$145$	−30.6901	−	17.7189i	−2.54867	−	1.47148i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	15.9310i		−	1.30512i	−0.757737	−	0.652561i	$-0.773695\pi$
$149$		−	15.9310i		−	1.30512i	0.757737	−	0.652561i	$-0.226305\pi$
$150$		0			0
$151$	5.51968	+	3.18679i	0.449185	+	0.259337i	0.707486	−	0.706727i	$-0.249829\pi$
$151$	5.51968	+	3.18679i	0.449185	+	0.259337i	−0.258301	+	0.966065i	$0.583163\pi$
$152$		0			0
$153$	−0.228469	−	0.395721i	−0.0184707	−	0.0319921i
$154$		0			0
$155$	−20.3175			−1.63194
$156$		0			0
$157$	−3.69400	+	6.39820i	−0.294813	+	0.510632i	−0.974941	−	0.222462i	$-0.928591\pi$
$157$	−3.69400	+	6.39820i	−0.294813	+	0.510632i	0.680128	+	0.733093i	$0.261924\pi$
$158$		0			0
$159$	−3.51804	+	6.09342i	−0.278999	+	0.483240i
$160$		0			0
$161$		0			0
$162$		0			0
$163$			0.0875638i			0.00685852i	0.999994	+	0.00342926i	$0.00109157\pi$
$163$			0.0875638i			0.00685852i	−0.999994	+	0.00342926i	$0.998908\pi$
$164$		0			0
$165$	14.7150	+	25.4872i	1.14556	+	1.98417i
$166$		0			0
$167$	−16.0309	+	9.25542i	−1.24050	+	0.716206i	−0.969197	−	0.246287i	$-0.920789\pi$
$167$	−16.0309	+	9.25542i	−1.24050	+	0.716206i	−0.271308	+	0.962493i	$0.587456\pi$
$168$		0			0
$169$	−11.2687	−	6.48195i	−0.866826	−	0.498612i
$170$		0			0
$171$			0.855617i			0.0654307i
$172$		0			0
$173$	0.410903			0.0312404			0.0156202	−	0.999878i	$-0.495028\pi$
$173$	0.410903			0.0312404			0.0156202	+	0.999878i	$0.495028\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	11.8749	−	6.85599i	0.892573	−	0.515327i
$178$		0			0
$179$	−2.15475			−0.161054			−0.0805268	−	0.996752i	$-0.525660\pi$
$179$	−2.15475			−0.161054			−0.0805268	+	0.996752i	$0.525660\pi$
$180$		0			0
$181$	−6.50124			−0.483233			−0.241617	−	0.970372i	$-0.577678\pi$
$181$	−6.50124			−0.483233			−0.241617	+	0.970372i	$0.577678\pi$
$182$		0			0
$183$	−25.4892			−1.88422
$184$		0			0
$185$	4.30541			0.316540
$186$		0			0
$187$	−10.9231	+	6.30644i	−0.798774	+	0.461172i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−18.7750			−1.35851			−0.679256	−	0.733901i	$-0.737698\pi$
$191$	−18.7750			−1.35851			−0.679256	+	0.733901i	$0.737698\pi$
$192$		0			0
$193$		−	25.6173i		−	1.84397i	−0.387224	−	0.921986i	$-0.626566\pi$
$193$		−	25.6173i		−	1.84397i	0.387224	−	0.921986i	$-0.373434\pi$
$194$		0			0
$195$	6.36593	+	23.6821i	0.455874	+	1.69591i
$196$		0			0
$197$	−0.510570	+	0.294778i	−0.0363766	+	0.0210021i	−0.518078	−	0.855333i	$-0.673352\pi$
$197$	−0.510570	+	0.294778i	−0.0363766	+	0.0210021i	0.481701	+	0.876335i	$0.340019\pi$
$198$		0			0
$199$	−8.04513	−	13.9346i	−0.570304	−	0.987796i	−0.996534	−	0.0831814i	$-0.973492\pi$
$199$	−8.04513	−	13.9346i	−0.570304	−	0.987796i	0.426230	−	0.904615i	$-0.359841\pi$
$200$		0			0
$201$		−	0.962142i		−	0.0678643i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−23.0140	+	39.8614i	−1.60737	+	2.78404i
$206$		0			0
$207$	−0.0481431	+	0.0833863i	−0.00334618	+	0.00579575i
$208$		0			0
$209$	23.6176			1.63366
$210$		0			0
$211$	5.69247	+	9.85965i	0.391886	+	0.678766i	0.992698	−	0.120624i	$-0.0384895\pi$
$211$	5.69247	+	9.85965i	0.391886	+	0.678766i	−0.600812	+	0.799390i	$0.705156\pi$
$212$		0			0
$213$	−14.1591	−	8.17474i	−0.970164	−	0.560124i
$214$		0			0
$215$		−	4.91178i		−	0.334981i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−11.3370	−	6.54545i	−0.766087	−	0.442300i
$220$		0			0
$221$	−10.1495	+	2.72826i	−0.682726	+	0.183522i
$222$		0			0
$223$	2.03182	−	1.17307i	0.136060	−	0.0785545i	−0.430425	−	0.902626i	$-0.641636\pi$
$223$	2.03182	−	1.17307i	0.136060	−	0.0785545i	0.566485	+	0.824072i	$0.308303\pi$
$224$		0			0
$225$	0.756677	−	1.31060i	0.0504452	−	0.0873736i
$226$		0			0
$227$	−7.14587	+	4.12567i	−0.474288	+	0.273830i	−0.718033	−	0.696009i	$-0.754957\pi$
$227$	−7.14587	+	4.12567i	−0.474288	+	0.273830i	0.243745	+	0.969839i	$0.421624\pi$
$228$		0			0
$229$	14.9605	−	8.63748i	0.988621	−	0.570780i	0.0837590	−	0.996486i	$-0.473307\pi$
$229$	14.9605	−	8.63748i	0.988621	−	0.570780i	0.904862	+	0.425706i	$0.139974\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.06889	+	3.58342i	0.135537	+	0.234758i	0.925803	−	0.378007i	$-0.123391\pi$
$233$	2.06889	+	3.58342i	0.135537	+	0.234758i	−0.790265	+	0.612765i	$0.790057\pi$
$234$		0			0
$235$	−10.8730	+	18.8327i	−0.709280	+	1.22851i
$236$		0			0
$237$	0.294658	+	0.510363i	0.0191401	+	0.0331516i
$238$		0			0
$239$			5.83879i			0.377680i	0.982008	+	0.188840i	$0.0604727\pi$
$239$			5.83879i			0.377680i	−0.982008	+	0.188840i	$0.939527\pi$
$240$		0			0
$241$	24.6356	−	14.2234i	1.58692	−	0.916207i	0.593107	−	0.805124i	$-0.297901\pi$
$241$	24.6356	−	14.2234i	1.58692	−	0.916207i	0.993811	−	0.111084i	$-0.0354322\pi$
$242$		0			0
$243$	1.62747			0.104402
$244$		0			0
$245$		0			0
$246$		0			0
$247$	19.0130	+	5.07819i	1.20977	+	0.323118i
$248$		0			0
$249$		−	29.6317i		−	1.87783i
$250$		0			0
$251$	6.39001	−	11.0678i	0.403334	−	0.698595i	−0.590792	−	0.806824i	$-0.701185\pi$
$251$	6.39001	−	11.0678i	0.403334	−	0.698595i	0.994126	+	0.108229i	$0.0345180\pi$
$252$		0			0
$253$	2.30171	+	1.32889i	0.144707	+	0.0835468i
$254$		0			0
$255$	17.1691	+	9.91261i	1.07517	+	0.620752i
$256$		0			0
$257$	−0.335695	+	0.581441i	−0.0209401	+	0.0362693i	−0.876306	−	0.481756i	$-0.839999\pi$
$257$	−0.335695	+	0.581441i	−0.0209401	+	0.0362693i	0.855365	+	0.518025i	$0.173333\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.725602	−	1.25678i	−0.0449136	−	0.0777926i
$262$		0			0
$263$	−18.9702			−1.16976			−0.584878	−	0.811122i	$-0.698857\pi$
$263$	−18.9702			−1.16976			−0.584878	+	0.811122i	$0.698857\pi$
$264$		0			0
$265$		−	15.1596i		−	0.931244i
$266$		0			0
$267$	−4.54550	−	2.62435i	−0.278180	−	0.160607i
$268$		0			0
$269$	−4.79241	−	8.30070i	−0.292198	−	0.506102i	0.682131	−	0.731230i	$-0.261053\pi$
$269$	−4.79241	−	8.30070i	−0.292198	−	0.506102i	−0.974329	+	0.225128i	$0.927720\pi$
$270$		0			0
$271$	9.06856	+	5.23574i	0.550876	+	0.318048i	0.749475	−	0.662032i	$-0.230306\pi$
$271$	9.06856	+	5.23574i	0.550876	+	0.318048i	−0.198599	+	0.980081i	$0.563639\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−36.1766	−	20.8866i	−2.18153	−	1.25951i
$276$		0			0
$277$	−9.66856	−	16.7464i	−0.580927	−	1.00620i	−0.995370	−	0.0961199i	$-0.969357\pi$
$277$	−9.66856	−	16.7464i	−0.580927	−	1.00620i	0.414443	−	0.910075i	$-0.363977\pi$
$278$		0			0
$279$	−0.720544	−	0.416006i	−0.0431379	−	0.0249057i
$280$		0			0
$281$			18.7039i			1.11578i	0.829915	+	0.557890i	$0.188389\pi$
$281$			18.7039i			1.11578i	−0.829915	+	0.557890i	$0.811611\pi$
$282$		0			0
$283$	1.17591			0.0699007			0.0349504	−	0.999389i	$-0.488873\pi$
$283$	1.17591			0.0699007			0.0349504	+	0.999389i	$0.488873\pi$
$284$		0			0
$285$	−18.5613	−	32.1492i	−1.09948	−	1.90435i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	4.25174	−	7.36423i	0.250102	−	0.433190i
$290$		0			0
$291$	14.8573	+	8.57789i	0.870953	+	0.502845i
$292$		0			0
$293$	5.63521	+	3.25349i	0.329213	+	0.190071i	0.655491	−	0.755203i	$-0.272462\pi$
$293$	5.63521	+	3.25349i	0.329213	+	0.190071i	−0.326279	+	0.945274i	$0.605795\pi$
$294$		0			0
$295$	−14.7715	+	25.5851i	−0.860033	+	1.48962i
$296$		0			0
$297$		−	21.8589i		−	1.26838i
$298$		0			0
$299$	1.56722	+	1.56471i	0.0906349	+	0.0904898i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	11.2832			0.648204
$304$		0			0
$305$	47.5601	−	27.4589i	2.72329	−	1.57229i
$306$		0			0
$307$		−	27.0573i		−	1.54424i	−0.635475	−	0.772121i	$-0.719196\pi$
$307$		−	27.0573i		−	1.54424i	0.635475	−	0.772121i	$-0.280804\pi$
$308$		0			0
$309$	4.50505	+	7.80297i	0.256283	+	0.443895i
$310$		0			0
$311$	15.4531	−	26.7655i	0.876263	−	1.51773i	0.0208511	−	0.999783i	$-0.493362\pi$
$311$	15.4531	−	26.7655i	0.876263	−	1.51773i	0.855412	−	0.517949i	$-0.173304\pi$
$312$		0			0
$313$	15.0408	+	26.0514i	0.850157	+	1.47251i	0.881066	+	0.472993i	$0.156826\pi$
$313$	15.0408	+	26.0514i	0.850157	+	1.47251i	−0.0309097	+	0.999522i	$0.509840\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.27661	−	1.89175i	0.184033	−	0.106251i	−0.405153	−	0.914249i	$-0.632782\pi$
$317$	3.27661	−	1.89175i	0.184033	−	0.106251i	0.589186	+	0.807997i	$0.299448\pi$
$318$		0			0
$319$	−34.6908	+	20.0288i	−1.94231	+	1.12140i
$320$		0			0
$321$	−4.87338	+	8.44093i	−0.272005	+	0.471127i
$322$		0			0
$323$	13.7782	−	7.95486i	0.766641	−	0.442620i
$324$		0			0
$325$	−24.6325	−	24.5930i	−1.36636	−	1.36417i
$326$		0			0
$327$	10.4736	+	6.04696i	0.579194	+	0.334398i
$328$		0			0
$329$		0			0
$330$		0			0
$331$		−	23.2552i		−	1.27822i	−0.769115	−	0.639110i	$-0.779303\pi$
$331$		−	23.2552i		−	1.27822i	0.769115	−	0.639110i	$-0.220697\pi$
$332$		0			0
$333$	0.152688	+	0.0881547i	0.00836728	+	0.00483085i
$334$		0			0
$335$	1.03649	+	1.79525i	0.0566295	+	0.0980852i
$336$		0			0
$337$	6.51910			0.355118			0.177559	−	0.984110i	$-0.443180\pi$
$337$	6.51910			0.355118			0.177559	+	0.984110i	$0.443180\pi$
$338$		0			0
$339$	−5.83449	+	10.1056i	−0.316886	+	0.548862i
$340$		0			0
$341$	−11.4830	+	19.8892i	−0.621840	+	1.07706i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		−	4.17758i		−	0.224913i
$346$		0			0
$347$	6.55696	+	11.3570i	0.351996	+	0.609675i	0.986599	−	0.163163i	$-0.0521696\pi$
$347$	6.55696	+	11.3570i	0.351996	+	0.609675i	−0.634603	+	0.772838i	$0.718836\pi$
$348$		0			0
$349$	−8.41298	+	4.85724i	−0.450336	+	0.260002i	−0.707972	−	0.706240i	$-0.750390\pi$
$349$	−8.41298	+	4.85724i	−0.450336	+	0.260002i	0.257636	+	0.966242i	$0.417057\pi$
$350$		0			0
$351$	4.70004	−	17.5972i	0.250869	−	0.939267i
$352$		0			0
$353$			30.3262i			1.61410i	0.590484	+	0.807049i	$0.298937\pi$
$353$			30.3262i			1.61410i	−0.590484	+	0.807049i	$0.701063\pi$
$354$		0			0
$355$	35.2257			1.86959
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−9.16725	+	5.29271i	−0.483829	+	0.279339i	−0.722011	−	0.691882i	$-0.756782\pi$
$359$	−9.16725	+	5.29271i	−0.483829	+	0.279339i	0.238182	+	0.971221i	$0.423449\pi$
$360$		0			0
$361$	−10.7909			−0.567943
$362$		0			0
$363$	13.7225			0.720247
$364$		0			0
$365$	28.2050			1.47631
$366$		0			0
$367$	−26.6376			−1.39047			−0.695234	−	0.718783i	$-0.744699\pi$
$367$	−26.6376			−1.39047			−0.695234	+	0.718783i	$0.744699\pi$
$368$		0			0
$369$	−1.63235	+	0.942438i	−0.0849768	+	0.0490614i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−6.14128			−0.317984			−0.158992	−	0.987280i	$-0.550824\pi$
$373$	−6.14128			−0.317984			−0.158992	+	0.987280i	$0.550824\pi$
$374$		0			0
$375$			31.6531i			1.63456i
$376$		0			0
$377$	−32.2339	+	8.66473i	−1.66013	+	0.446256i
$378$		0			0
$379$	20.4175	−	11.7880i	1.04877	−	0.605510i	0.126469	−	0.991971i	$-0.459636\pi$
$379$	20.4175	−	11.7880i	1.04877	−	0.605510i	0.922306	+	0.386460i	$0.126302\pi$
$380$		0			0
$381$	18.0205	+	31.2124i	0.923217	+	1.59906i
$382$		0			0
$383$		−	20.1768i		−	1.03099i	−0.856894	−	0.515493i	$-0.827609\pi$
$383$		−	20.1768i		−	1.03099i	0.856894	−	0.515493i	$-0.172391\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.100570	−	0.174193i	0.00511227	−	0.00885472i
$388$		0			0
$389$	16.4253	−	28.4494i	0.832795	−	1.44244i	−0.0630179	−	0.998012i	$-0.520073\pi$
$389$	16.4253	−	28.4494i	0.832795	−	1.44244i	0.895813	−	0.444431i	$-0.146594\pi$
$390$		0			0
$391$	1.79039			0.0905438
$392$		0			0
$393$	−4.37468	−	7.57716i	−0.220673	−	0.382217i
$394$		0			0
$395$	−1.09960	−	0.634855i	−0.0553269	−	0.0319430i
$396$		0			0
$397$			25.2635i			1.26794i	0.773358	+	0.633970i	$0.218576\pi$
$397$			25.2635i			1.26794i	−0.773358	+	0.633970i	$0.781424\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	25.3059	+	14.6104i	1.26372	+	0.729608i	0.973792	−	0.227441i	$-0.0730360\pi$
$401$	25.3059	+	14.6104i	1.26372	+	0.729608i	0.289926	+	0.957049i	$0.406369\pi$
$402$		0			0
$403$	−13.5208	+	13.5424i	−0.673517	+	0.674597i
$404$		0			0
$405$	−31.3142	+	18.0793i	−1.55602	+	0.898367i
$406$		0			0
$407$	2.43333	−	4.21466i	0.120616	−	0.208913i
$408$		0			0
$409$	23.6697	−	13.6657i	1.17039	−	0.675727i	0.216620	−	0.976256i	$-0.430497\pi$
$409$	23.6697	−	13.6657i	1.17039	−	0.675727i	0.953773	+	0.300529i	$0.0971633\pi$
$410$		0			0
$411$	19.8980	−	11.4881i	0.981497	−	0.566668i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	31.9214	+	55.2895i	1.56696	+	2.71406i
$416$		0			0
$417$	−14.0444	+	24.3257i	−0.687758	+	1.19123i
$418$		0			0
$419$	10.1693	+	17.6137i	0.496802	+	0.860486i	0.999993	−	0.00368888i	$-0.00117421\pi$
$419$	10.1693	+	17.6137i	0.496802	+	0.860486i	−0.503191	+	0.864175i	$0.667841\pi$
$420$		0			0
$421$			21.0712i			1.02695i	0.858106	+	0.513473i	$0.171641\pi$
$421$			21.0712i			1.02695i	−0.858106	+	0.513473i	$0.828359\pi$
$422$		0			0
$423$	−0.771210	+	0.445258i	−0.0374975	+	0.0216492i
$424$		0			0
$425$	−28.1400			−1.36499
$426$		0			0
$427$		0			0
$428$		0			0
$429$	26.7808	+	7.15289i	1.29299	+	0.345345i
$430$		0			0
$431$		−	29.6333i		−	1.42739i	−0.700458	−	0.713694i	$-0.747021\pi$
$431$		−	29.6333i		−	1.42739i	0.700458	−	0.713694i	$-0.252979\pi$
$432$		0			0
$433$	14.2983	−	24.7653i	0.687130	−	1.19014i	−0.285632	−	0.958339i	$-0.592204\pi$
$433$	14.2983	−	24.7653i	0.687130	−	1.19014i	0.972762	−	0.231805i	$-0.0744631\pi$
$434$		0			0
$435$	54.5279	+	31.4817i	2.61441	+	1.50943i
$436$		0			0
$437$	−2.90335	−	1.67625i	−0.138886	−	0.0801859i
$438$		0			0
$439$	10.9124	−	18.9009i	0.520821	−	0.902088i	−0.478886	−	0.877877i	$-0.658959\pi$
$439$	10.9124	−	18.9009i	0.520821	−	0.902088i	0.999707	−	0.0242113i	$-0.00770744\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.16478	+	5.48156i	0.150363	+	0.260437i	0.931361	−	0.364097i	$-0.118622\pi$
$443$	3.16478	+	5.48156i	0.150363	+	0.260437i	−0.780998	+	0.624534i	$0.785289\pi$
$444$		0			0
$445$	11.3086			0.536077
$446$		0			0
$447$			28.3051i			1.33879i
$448$		0			0
$449$	21.2777	+	12.2847i	1.00415	+	0.579749i	0.909475	−	0.415759i	$-0.136484\pi$
$449$	21.2777	+	12.2847i	1.00415	+	0.579749i	0.0946799	+	0.995508i	$0.469817\pi$
$450$		0			0
$451$	26.0141	+	45.0578i	1.22496	+	2.12169i
$452$		0			0
$453$	−9.80697	−	5.66206i	−0.460772	−	0.266027i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.90240	+	2.25305i	0.182547	+	0.105393i	0.588489	−	0.808505i	$-0.299723\pi$
$457$	3.90240	+	2.25305i	0.182547	+	0.105393i	−0.405942	+	0.913899i	$0.633056\pi$
$458$		0			0
$459$	−7.36249	−	12.7522i	−0.343652	−	0.595222i
$460$		0			0
$461$	−0.260026	−	0.150126i	−0.0121106	−	0.00699206i	0.493932	−	0.869500i	$-0.335559\pi$
$461$	−0.260026	−	0.150126i	−0.0121106	−	0.00699206i	−0.506043	+	0.862508i	$0.668892\pi$
$462$		0			0
$463$		−	19.2907i		−	0.896514i	−0.893905	−	0.448257i	$-0.852045\pi$
$463$		−	19.2907i		−	0.896514i	0.893905	−	0.448257i	$-0.147955\pi$
$464$		0			0
$465$	36.0986			1.67403
$466$		0			0
$467$	6.97544	+	12.0818i	0.322785	+	0.559080i	0.981062	−	0.193696i	$-0.0620477\pi$
$467$	6.97544	+	12.0818i	0.322785	+	0.559080i	−0.658277	+	0.752776i	$0.728714\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	6.56323	−	11.3679i	0.302418	−	0.523803i
$472$		0			0
$473$	−4.80824	−	2.77604i	−0.221083	−	0.127642i
$474$		0			0
$475$	45.6327	+	26.3460i	2.09377	+	1.20884i
$476$		0			0
$477$	0.310397	−	0.537623i	0.0142121	−	0.0246161i
$478$		0			0
$479$			27.4521i			1.25432i	0.778890	+	0.627160i	$0.215783\pi$
$479$			27.4521i			1.25432i	−0.778890	+	0.627160i	$0.784217\pi$
$480$		0			0
$481$	2.86514	−	2.86974i	0.130639	−	0.130849i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−36.9629			−1.67840
$486$		0			0
$487$	−12.1206	+	6.99785i	−0.549238	+	0.317103i	−0.748815	−	0.662780i	$-0.769377\pi$
$487$	−12.1206	+	6.99785i	−0.549238	+	0.317103i	0.199577	+	0.979882i	$0.436043\pi$
$488$		0			0
$489$		−	0.155577i		−	0.00703543i
$490$		0			0
$491$	−3.76330	−	6.51823i	−0.169836	−	0.294164i	0.768526	−	0.639818i	$-0.220990\pi$
$491$	−3.76330	−	6.51823i	−0.169836	−	0.294164i	−0.938362	+	0.345654i	$0.887657\pi$
$492$		0			0
$493$	−13.4922	+	23.3691i	−0.607656	+	1.05249i
$494$		0			0
$495$	−1.29831	−	2.24874i	−0.0583546	−	0.101073i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.01193	−	0.584239i	0.0453003	−	0.0261541i	−0.477179	−	0.878806i	$-0.658341\pi$
$499$	1.01193	−	0.584239i	0.0453003	−	0.0261541i	0.522479	+	0.852652i	$0.325007\pi$
$500$		0			0
$501$	28.4825	−	16.4444i	1.27250	−	0.734680i
$502$		0			0
$503$	−5.30877	+	9.19505i	−0.236706	+	0.409987i	−0.959767	−	0.280797i	$-0.909401\pi$
$503$	−5.30877	+	9.19505i	−0.236706	+	0.409987i	0.723061	+	0.690784i	$0.242735\pi$
$504$		0			0
$505$	−21.0533	+	12.1551i	−0.936859	+	0.540896i
$506$		0			0
$507$	20.0215	+	11.5167i	0.889185	+	0.511473i
$508$		0			0
$509$	−21.0450	−	12.1503i	−0.932803	−	0.538554i	−0.0451058	−	0.998982i	$-0.514363\pi$
$509$	−21.0450	−	12.1503i	−0.932803	−	0.538554i	−0.887697	+	0.460428i	$0.847696\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$			27.5725i			1.21736i
$514$		0			0
$515$	−16.8119	−	9.70633i	−0.740819	−	0.427712i
$516$		0			0
$517$	12.2905	+	21.2877i	0.540534	+	0.936232i
$518$		0			0
$519$	−0.730063			−0.0320462
$520$		0			0
$521$	5.66400	−	9.81034i	0.248144	−	0.429799i	−0.714867	−	0.699261i	$-0.753513\pi$
$521$	5.66400	−	9.81034i	0.248144	−	0.429799i	0.963011	+	0.269462i	$0.0868459\pi$
$522$		0			0
$523$	15.1328	−	26.2108i	0.661711	−	1.14612i	−0.318454	−	0.947938i	$-0.603164\pi$
$523$	15.1328	−	26.2108i	0.661711	−	1.14612i	0.980166	−	0.198180i	$-0.0635029\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			15.4708i			0.673919i
$528$		0			0
$529$	11.3114	+	19.5919i	0.491798	+	0.851820i
$530$		0			0
$531$	−1.04772	+	0.604904i	−0.0454674	+	0.0262506i
$532$		0			0
$533$	11.2541	+	41.8666i	0.487468	+	1.81344i
$534$		0			0
$535$		−	20.9998i		−	0.907902i
$536$		0			0
$537$	3.82840			0.165208
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−9.65868	+	5.57644i	−0.415259	+	0.239750i	−0.693047	−	0.720893i	$-0.743732\pi$
$541$	−9.65868	+	5.57644i	−0.415259	+	0.239750i	0.277788	+	0.960642i	$0.410399\pi$
$542$		0			0
$543$	11.5509			0.495698
$544$		0			0
$545$	−26.0569			−1.11616
$546$		0			0
$547$	4.87804			0.208570			0.104285	−	0.994547i	$-0.466745\pi$
$547$	4.87804			0.208570			0.104285	+	0.994547i	$0.466745\pi$
$548$		0			0
$549$	2.24892			0.0959814
$550$		0			0
$551$	43.7586	−	25.2640i	1.86418	−	1.07628i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−7.64955			−0.324705
$556$		0			0
$557$			3.02585i			0.128209i	0.997943	+	0.0641047i	$0.0204192\pi$
$557$			3.02585i			0.128209i	−0.997943	+	0.0641047i	$0.979581\pi$
$558$		0			0
$559$	−3.27391	−	3.26867i	−0.138472	−	0.138250i
$560$		0			0
$561$	19.4073	−	11.2048i	0.819377	−	0.473068i
$562$		0			0
$563$	13.6591	+	23.6583i	0.575664	+	0.997079i	0.995969	+	0.0896963i	$0.0285896\pi$
$563$	13.6591	+	23.6583i	0.575664	+	0.997079i	−0.420305	+	0.907383i	$0.638077\pi$
$564$		0			0
$565$		−	25.1414i		−	1.05770i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.46871	+	11.2041i	−0.271183	+	0.469702i	−0.969165	−	0.246413i	$-0.920748\pi$
$569$	−6.46871	+	11.2041i	−0.271183	+	0.469702i	0.697982	+	0.716115i	$0.254081\pi$
$570$		0			0
$571$	−5.33893	+	9.24730i	−0.223427	+	0.386988i	−0.955846	−	0.293866i	$-0.905058\pi$
$571$	−5.33893	+	9.24730i	−0.223427	+	0.386988i	0.732419	+	0.680854i	$0.238391\pi$
$572$		0			0
$573$	33.3581			1.39355
$574$		0			0
$575$	2.96483	+	5.13524i	0.123642	+	0.214154i
$576$		0			0
$577$	−4.12632	−	2.38233i	−0.171781	−	0.0991778i	0.411644	−	0.911345i	$-0.364955\pi$
$577$	−4.12632	−	2.38233i	−0.171781	−	0.0991778i	−0.583425	+	0.812167i	$0.698288\pi$
$578$		0			0
$579$			45.5149i			1.89153i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−14.8400	−	8.56788i	−0.614610	−	0.354845i
$584$		0			0
$585$	−0.561667	−	2.08947i	−0.0232221	−	0.0863890i
$586$		0			0
$587$	−27.6495	+	15.9634i	−1.14122	+	0.658881i	−0.946731	−	0.322024i	$-0.895637\pi$
$587$	−27.6495	+	15.9634i	−1.14122	+	0.658881i	−0.194485	+	0.980906i	$0.562303\pi$
$588$		0			0
$589$	14.4845	−	25.0879i	0.596825	−	1.03373i
$590$		0			0
$591$	0.907144	−	0.523740i	0.0373149	−	0.0215438i
$592$		0			0
$593$	1.10299	−	0.636812i	0.0452944	−	0.0261508i	−0.477182	−	0.878805i	$-0.658342\pi$
$593$	1.10299	−	0.636812i	0.0452944	−	0.0261508i	0.522476	+	0.852654i	$0.325008\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	14.2940	+	24.7580i	0.585015	+	1.01328i
$598$		0			0
$599$	7.57310	−	13.1170i	0.309428	−	0.535946i	−0.668809	−	0.743434i	$-0.733196\pi$
$599$	7.57310	−	13.1170i	0.309428	−	0.535946i	0.978237	+	0.207489i	$0.0665290\pi$
$600$		0			0
$601$	17.1425	+	29.6917i	0.699258	+	1.21115i	0.968724	+	0.248141i	$0.0798195\pi$
$601$	17.1425	+	29.6917i	0.699258	+	1.21115i	−0.269466	+	0.963010i	$0.586847\pi$
$602$		0			0
$603$			0.0848899i			0.00345698i
$604$		0			0
$605$	−25.6048	+	14.7829i	−1.04098	+	0.601012i
$606$		0			0
$607$	−9.47474			−0.384568			−0.192284	−	0.981339i	$-0.561589\pi$
$607$	−9.47474			−0.384568			−0.192284	+	0.981339i	$0.561589\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	5.31703	+	19.7800i	0.215104	+	0.800214i
$612$		0			0
$613$			11.6437i			0.470283i	0.971961	+	0.235141i	$0.0755553\pi$
$613$			11.6437i			0.470283i	−0.971961	+	0.235141i	$0.924445\pi$
$614$		0			0
$615$	40.8896	−	70.8229i	1.64883	−	2.85586i
$616$		0			0
$617$	−5.54295	−	3.20023i	−0.223151	−	0.128836i	0.384257	−	0.923226i	$-0.374457\pi$
$617$	−5.54295	−	3.20023i	−0.223151	−	0.128836i	−0.607408	+	0.794390i	$0.707791\pi$
$618$		0			0
$619$	−9.70507	−	5.60323i	−0.390080	−	0.225213i	0.292115	−	0.956383i	$-0.405641\pi$
$619$	−9.70507	−	5.60323i	−0.390080	−	0.225213i	−0.682195	+	0.731171i	$0.738974\pi$
$620$		0			0
$621$	−1.55143	+	2.68715i	−0.0622566	+	0.107832i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−9.96422	−	17.2585i	−0.398569	−	0.690342i
$626$		0			0
$627$	−41.9620			−1.67580
$628$		0			0
$629$		−	3.27837i		−	0.130717i
$630$		0			0
$631$	39.1148	+	22.5830i	1.55714	+	0.899013i	0.997529	+	0.0702554i	$0.0223814\pi$
$631$	39.1148	+	22.5830i	1.55714	+	0.899013i	0.559608	+	0.828758i	$0.310952\pi$
$632$		0			0
$633$	−10.1140	−	17.5179i	−0.401994	−	0.696274i
$634$		0			0
$635$	−67.2486	−	38.8260i	−2.66868	−	1.54076i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1.24926	+	0.721258i	0.0494198	+	0.0285325i
$640$		0			0
$641$	−3.57997	−	6.20069i	−0.141400	−	0.244912i	0.786624	−	0.617432i	$-0.211827\pi$
$641$	−3.57997	−	6.20069i	−0.141400	−	0.244912i	−0.928024	+	0.372520i	$0.878494\pi$
$642$		0			0
$643$	35.9015	+	20.7278i	1.41582	+	0.817423i	0.995928	−	0.0901516i	$-0.0287352\pi$
$643$	35.9015	+	20.7278i	1.41582	+	0.817423i	0.419890	+	0.907575i	$0.362068\pi$
$644$		0			0
$645$			8.72690i			0.343621i
$646$		0			0
$647$	15.5852			0.612716			0.306358	−	0.951916i	$-0.400890\pi$
$647$	15.5852			0.612716			0.306358	+	0.951916i	$0.400890\pi$
$648$		0			0
$649$	16.6972	+	28.9203i	0.655421	+	1.13522i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	11.9121	−	20.6323i	0.466156	−	0.807406i	−0.533097	−	0.846054i	$-0.678972\pi$
$653$	11.9121	−	20.6323i	0.466156	−	0.807406i	0.999253	+	0.0386482i	$0.0123052\pi$
$654$		0			0
$655$	16.3254	+	9.42545i	0.637884	+	0.368283i
$656$		0			0
$657$	1.00027	+	0.577505i	0.0390242	+	0.0225306i
$658$		0			0
$659$	−2.01861	+	3.49634i	−0.0786340	+	0.136198i	−0.902661	−	0.430353i	$-0.858389\pi$
$659$	−2.01861	+	3.49634i	−0.0786340	+	0.136198i	0.824027	+	0.566551i	$0.191723\pi$
$660$		0			0
$661$		−	37.1979i		−	1.44683i	−0.690412	−	0.723416i	$-0.742571\pi$
$661$		−	37.1979i		−	1.44683i	0.690412	−	0.723416i	$-0.257429\pi$
$662$		0			0
$663$	18.0328	−	4.84737i	0.700336	−	0.188256i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	5.68614			0.220168
$668$		0			0
$669$	−3.60998	+	2.08422i	−0.139570	+	0.0805808i
$670$		0			0
$671$		−	62.0768i		−	2.39645i
$672$		0			0
$673$	−5.02863	−	8.70984i	−0.193839	−	0.335740i	0.752680	−	0.658387i	$-0.228761\pi$
$673$	−5.02863	−	8.70984i	−0.193839	−	0.335740i	−0.946519	+	0.322647i	$0.895427\pi$
$674$		0			0
$675$	24.3841	−	42.2346i	0.938546	−	1.62561i
$676$		0			0
$677$	−9.94034	−	17.2172i	−0.382038	−	0.661710i	0.609315	−	0.792928i	$-0.291444\pi$
$677$	−9.94034	−	17.2172i	−0.382038	−	0.661710i	−0.991353	+	0.131219i	$0.958111\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	12.6963	−	7.33019i	0.486522	−	0.280893i
$682$		0			0
$683$	17.2194	−	9.94161i	0.658881	−	0.380405i	−0.132970	−	0.991120i	$-0.542451\pi$
$683$	17.2194	−	9.94161i	0.658881	−	0.380405i	0.791850	+	0.610715i	$0.209118\pi$
$684$		0			0
$685$	−24.7517	+	42.8712i	−0.945715	+	1.63803i
$686$		0			0
$687$	−26.5808	+	15.3464i	−1.01412	+	0.585503i
$688$		0			0
$689$	−10.1045	−	10.0883i	−0.384950	−	0.384334i
$690$		0			0
$691$	−16.5968	−	9.58219i	−0.631373	−	0.364524i	0.149910	−	0.988700i	$-0.452101\pi$
$691$	−16.5968	−	9.58219i	−0.631373	−	0.364524i	−0.781284	+	0.624176i	$0.785435\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	60.5187i		−	2.29561i
$696$		0			0
$697$	30.3527	+	17.5241i	1.14969	+	0.663773i
$698$		0			0
$699$	−3.67585	−	6.36676i	−0.139033	−	0.240813i
$700$		0			0
$701$	18.5012			0.698780			0.349390	−	0.936977i	$-0.386389\pi$
$701$	18.5012			0.698780			0.349390	+	0.936977i	$0.386389\pi$
$702$		0			0
$703$	−3.06938	+	5.31631i	−0.115764	+	0.200509i
$704$		0			0
$705$	19.3184	−	33.4605i	0.727575	−	1.26020i
$706$		0			0
$707$		0			0
$708$		0			0
$709$			24.0214i			0.902144i	0.892488	+	0.451072i	$0.148958\pi$
$709$			24.0214i			0.902144i	−0.892488	+	0.451072i	$0.851042\pi$
$710$		0			0
$711$	−0.0259977	−	0.0450294i	−0.000974990	−	0.00168873i
$712$		0			0
$713$	2.82325	−	1.63001i	0.105732	−	0.0610442i
$714$		0			0
$715$	−57.6756	+	15.5037i	−2.15695	+	0.579805i
$716$		0			0
$717$		−	10.3739i		−	0.387422i
$718$		0			0
$719$	24.4297			0.911076			0.455538	−	0.890216i	$-0.349447\pi$
$719$	24.4297			0.911076			0.455538	+	0.890216i	$0.349447\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−43.7707	+	25.2710i	−1.62785	+	0.939840i
$724$		0			0
$725$	−89.3705			−3.31914
$726$		0			0
$727$	−20.9000			−0.775138			−0.387569	−	0.921841i	$-0.626685\pi$
$727$	−20.9000			−0.775138			−0.387569	+	0.921841i	$0.626685\pi$
$728$		0			0
$729$	25.4456			0.942428
$730$		0			0
$731$	−3.74010			−0.138332
$732$		0			0
$733$	−6.13248	+	3.54059i	−0.226508	+	0.130775i	−0.608960	−	0.793201i	$-0.708413\pi$
$733$	−6.13248	+	3.54059i	−0.226508	+	0.130775i	0.382452	+	0.923975i	$0.375080\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.34321			0.0863134
$738$		0			0
$739$		−	23.7150i		−	0.872371i	−0.899857	−	0.436186i	$-0.856329\pi$
$739$		−	23.7150i		−	0.872371i	0.899857	−	0.436186i	$-0.143671\pi$
$740$		0			0
$741$	−33.7809	−	9.02256i	−1.24097	−	0.331452i
$742$		0			0
$743$	−36.5813	+	21.1202i	−1.34204	+	0.774825i	−0.987106	−	0.160067i	$-0.948829\pi$
$743$	−36.5813	+	21.1202i	−1.34204	+	0.774825i	−0.354931	+	0.934893i	$0.615496\pi$
$744$		0			0
$745$	−30.4923	−	52.8143i	−1.11715	−	1.93497i
$746$		0			0
$747$			2.61441i			0.0956561i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	12.0710	−	20.9076i	0.440478	−	0.762930i	−0.557247	−	0.830347i	$-0.688142\pi$
$751$	12.0710	−	20.9076i	0.440478	−	0.762930i	0.997725	+	0.0674164i	$0.0214756\pi$
$752$		0			0
$753$	−11.3533	+	19.6645i	−0.413737	+	0.716614i
$754$		0			0
$755$	24.3983			0.887947
$756$		0			0
$757$	15.9716	+	27.6636i	0.580497	+	1.00545i	0.995420	+	0.0955942i	$0.0304751\pi$
$757$	15.9716	+	27.6636i	0.580497	+	1.00545i	−0.414923	+	0.909856i	$0.636192\pi$
$758$		0			0
$759$	−4.08951	−	2.36108i	−0.148440	−	0.0857018i
$760$		0			0
$761$		−	42.2716i		−	1.53234i	−0.642635	−	0.766172i	$-0.722159\pi$
$761$		−	42.2716i		−	1.53234i	0.642635	−	0.766172i	$-0.277841\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.51484	−	0.874590i	−0.0547690	−	0.0316209i
$766$		0			0
$767$	7.22343	+	26.8721i	0.260823	+	0.970294i
$768$		0			0
$769$	2.36768	−	1.36698i	0.0853808	−	0.0492946i	−0.456702	−	0.889620i	$-0.650969\pi$
$769$	2.36768	−	1.36698i	0.0853808	−	0.0492946i	0.542083	+	0.840325i	$0.317636\pi$
$770$		0			0
$771$	0.596439	−	1.03306i	0.0214802	−	0.0372048i
$772$		0			0
$773$	−16.9343	+	9.77703i	−0.609085	+	0.351655i	−0.772607	−	0.634884i	$-0.781048\pi$
$773$	−16.9343	+	9.77703i	−0.609085	+	0.351655i	0.163523	+	0.986540i	$0.447714\pi$
$774$		0			0
$775$	−44.3738	+	25.6192i	−1.59395	+	0.920270i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−32.8139	−	56.8353i	−1.17568	−	2.03634i
$780$		0			0
$781$	19.9089	−	34.4832i	0.712396	−	1.23391i
$782$		0			0
$783$	−23.3827	−	40.5001i	−0.835630	−	1.44735i
$784$		0			0
$785$			28.2816i			1.00941i
$786$		0			0
$787$	28.0930	−	16.2195i	1.00141	−	0.578163i	0.0927426	−	0.995690i	$-0.470437\pi$
$787$	28.0930	−	16.2195i	1.00141	−	0.578163i	0.908664	+	0.417528i	$0.137103\pi$
$788$		0			0
$789$	33.7050			1.19993
$790$		0			0
$791$		0			0
$792$		0			0
$793$	13.3476	−	49.9740i	0.473987	−	1.77463i
$794$		0			0
$795$			26.9344i			0.955265i
$796$		0			0
$797$	−12.9397	+	22.4123i	−0.458349	+	0.793883i	−0.998874	−	0.0474447i	$-0.984892\pi$
$797$	−12.9397	+	22.4123i	−0.458349	+	0.793883i	0.540525	+	0.841328i	$0.318226\pi$
$798$		0			0
$799$	14.3402	+	8.27933i	0.507320	+	0.292902i
$800$		0			0
$801$	0.401050	+	0.231546i	0.0141704	+	0.00818129i
$802$		0			0
$803$	15.9409	−	27.6104i	0.562541	−	0.974350i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	8.51481	+	14.7481i	0.299735	+	0.519157i
$808$		0			0
$809$	22.4133			0.788008			0.394004	−	0.919109i	$-0.371090\pi$
$809$	22.4133			0.788008			0.394004	+	0.919109i	$0.371090\pi$
$810$		0			0
$811$		−	5.44486i		−	0.191195i	−0.995420	−	0.0955974i	$-0.969524\pi$
$811$		−	5.44486i		−	0.191195i	0.995420	−	0.0955974i	$-0.0304761\pi$
$812$		0			0
$813$	−16.1124	−	9.30247i	−0.565085	−	0.326252i
$814$		0			0
$815$	0.167599	+	0.290290i	0.00587074	+	0.0101684i
$816$		0			0
$817$	6.06505	+	3.50166i	0.212189	+	0.122508i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−26.6843	−	15.4062i	−0.931288	−	0.537679i	−0.0440690	−	0.999028i	$-0.514032\pi$
$821$	−26.6843	−	15.4062i	−0.931288	−	0.537679i	−0.887219	+	0.461349i	$0.847365\pi$
$822$		0			0
$823$	0.102850	+	0.178141i	0.00358513	+	0.00620962i	0.867812	−	0.496892i	$-0.165525\pi$
$823$	0.102850	+	0.178141i	0.00358513	+	0.00620962i	−0.864227	+	0.503102i	$0.832192\pi$
$824$		0			0
$825$	64.2759	+	37.1097i	2.23780	+	1.29199i
$826$		0			0
$827$		−	9.66411i		−	0.336054i	−0.985782	−	0.168027i	$-0.946260\pi$
$827$		−	9.66411i		−	0.336054i	0.985782	−	0.168027i	$-0.0537396\pi$
$828$		0			0
$829$	30.5334			1.06047			0.530234	−	0.847851i	$-0.322104\pi$
$829$	30.5334			1.06047			0.530234	+	0.847851i	$0.322104\pi$
$830$		0			0
$831$	17.1784	+	29.7538i	0.595912	+	1.03215i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−35.4301	+	61.3668i	−1.22611	+	2.12369i
$836$		0			0
$837$	−23.2197	−	13.4059i	−0.802592	−	0.463377i
$838$		0			0
$839$	33.0722	+	19.0942i	1.14178	+	0.659206i	0.946871	−	0.321615i	$-0.104226\pi$
$839$	33.0722	+	19.0942i	1.14178	+	0.659206i	0.194909	+	0.980821i	$0.437559\pi$
$840$		0			0
$841$	−28.3501	+	49.1037i	−0.977588	+	1.69323i
$842$		0			0
$843$		−	33.2317i		−	1.14456i
$844$		0			0
$845$	−49.7645	+	0.0797454i	−1.71195	+	0.00274333i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−2.08928			−0.0717038
$850$		0			0
$851$	−0.598268	+	0.345410i	−0.0205084	+	0.0118405i
$852$		0			0
$853$			28.3480i			0.970618i	0.874343	+	0.485309i	$0.161293\pi$
$853$			28.3480i			0.970618i	−0.874343	+	0.485309i	$0.838707\pi$
$854$		0			0
$855$	1.63767	+	2.83653i	0.0560071	+	0.0970071i
$856$		0			0
$857$	12.9244	−	22.3857i	0.441489	−	0.764681i	−0.556311	−	0.830974i	$-0.687784\pi$
$857$	12.9244	−	22.3857i	0.441489	−	0.764681i	0.997800	+	0.0662926i	$0.0211171\pi$
$858$		0			0
$859$	9.80418	+	16.9813i	0.334514	+	0.579396i	0.983391	−	0.181497i	$-0.0580944\pi$
$859$	9.80418	+	16.9813i	0.334514	+	0.579396i	−0.648877	+	0.760893i	$0.724761\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	11.6366	−	6.71841i	0.396115	−	0.228697i	−0.288691	−	0.957422i	$-0.593220\pi$
$863$	11.6366	−	6.71841i	0.396115	−	0.228697i	0.684807	+	0.728725i	$0.259887\pi$
$864$		0			0
$865$	1.36222	−	0.786477i	0.0463168	−	0.0267410i
$866$		0			0
$867$	−7.55418	+	13.0842i	−0.256554	+	0.444364i
$868$		0			0
$869$	−1.24294	+	0.717614i	−0.0421640	+	0.0243434i
$870$		0			0
$871$	1.88637	+	0.503832i	0.0639172	+	0.0170717i
$872$		0			0
$873$	−1.31086	−	0.756828i	−0.0443660	−	0.0256147i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		−	30.1421i		−	1.01783i	−0.860818	−	0.508914i	$-0.830047\pi$
$877$		−	30.1421i		−	1.01783i	0.860818	−	0.508914i	$-0.169953\pi$
$878$		0			0
$879$	−10.0122	−	5.78057i	−0.337704	−	0.194974i
$880$		0			0
$881$	−4.52477	−	7.83714i	−0.152443	−	0.264040i	0.779682	−	0.626176i	$-0.215381\pi$
$881$	−4.52477	−	7.83714i	−0.152443	−	0.264040i	−0.932125	+	0.362136i	$0.882048\pi$
$882$		0			0
$883$	47.3475			1.59337			0.796685	−	0.604395i	$-0.206585\pi$
$883$	47.3475			1.59337			0.796685	+	0.604395i	$0.206585\pi$
$884$		0			0
$885$	26.2450	−	45.4577i	0.882216	−	1.52804i
$886$		0			0
$887$	18.9895	−	32.8908i	0.637605	−	1.10436i	−0.348352	−	0.937364i	$-0.613258\pi$
$887$	18.9895	−	32.8908i	0.637605	−	1.10436i	0.985957	−	0.167001i	$-0.0534082\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$			40.8722i			1.36927i
$892$		0			0
$893$	−15.5030	−	26.8520i	−0.518789	−	0.898569i
$894$		0			0
$895$	−7.14339	+	4.12424i	−0.238777	+	0.137858i
$896$		0			0
$897$	−2.78453	−	2.78007i	−0.0929728	−	0.0928239i
$898$		0			0
$899$			49.1341i			1.63872i
$900$		0			0
$901$	−11.5433			−0.384563
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−21.5528	+	12.4435i	−0.716439	+	0.413636i
$906$		0			0
$907$	−27.8867			−0.925962			−0.462981	−	0.886368i	$-0.653220\pi$
$907$	−27.8867			−0.925962			−0.462981	+	0.886368i	$0.653220\pi$
$908$		0			0
$909$	−0.995519			−0.0330193
$910$		0			0
$911$	−26.1435			−0.866172			−0.433086	−	0.901353i	$-0.642575\pi$
$911$	−26.1435			−0.866172			−0.433086	+	0.901353i	$0.642575\pi$
$912$		0			0
$913$	72.1654			2.38833
$914$		0			0
$915$	−84.5014	+	48.7869i	−2.79353	+	1.61285i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−3.08812			−0.101868			−0.0509338	−	0.998702i	$-0.516220\pi$
$919$	−3.08812			−0.101868			−0.0509338	+	0.998702i	$0.516220\pi$
$920$		0			0
$921$			48.0735i			1.58408i
$922$		0			0
$923$	23.4418	−	23.4794i	0.771598	−	0.772835i
$924$		0			0
$925$	9.40312	−	5.42889i	0.309173	−	0.178501i
$926$		0			0
$927$	−0.397481	−	0.688457i	−0.0130550	−	0.0226119i
$928$		0			0
$929$			38.5771i			1.26567i	0.774286	+	0.632836i	$0.218109\pi$
$929$			38.5771i			1.26567i	−0.774286	+	0.632836i	$0.781891\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−27.4559	+	47.5550i	−0.898865	+	1.55688i
$934$		0			0
$935$	−24.1413	+	41.8140i	−0.789505	+	1.36746i
$936$		0			0
$937$	−8.28836			−0.270769			−0.135384	−	0.990793i	$-0.543227\pi$
$937$	−8.28836			−0.270769			−0.135384	+	0.990793i	$0.543227\pi$
$938$		0			0
$939$	−26.7234	−	46.2863i	−0.872086	−	1.51050i
$940$		0			0
$941$	−6.68923	−	3.86203i	−0.218063	−	0.125899i	0.386990	−	0.922084i	$-0.373515\pi$
$941$	−6.68923	−	3.86203i	−0.218063	−	0.125899i	−0.605053	+	0.796185i	$0.706848\pi$
$942$		0			0
$943$		−	7.38537i		−	0.240501i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−44.8430	−	25.8901i	−1.45720	−	0.841316i	−0.458330	−	0.888782i	$-0.651552\pi$
$947$	−44.8430	−	25.8901i	−1.45720	−	0.841316i	−0.998873	+	0.0474661i	$0.984885\pi$
$948$		0			0
$949$	18.7697	−	18.7998i	0.609290	−	0.610267i
$950$		0			0
$951$	−5.82165	+	3.36113i	−0.188780	+	0.108992i
$952$		0			0
$953$	24.3912	−	42.2468i	0.790109	−	1.36851i	−0.135791	−	0.990738i	$-0.543357\pi$
$953$	24.3912	−	42.2468i	0.790109	−	1.36851i	0.925899	−	0.377771i	$-0.123309\pi$
$954$		0			0
$955$	−62.2426	+	35.9358i	−2.01412	+	1.16285i
$956$		0			0
$957$	61.6362	−	35.5857i	1.99241	−	1.15032i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−1.41505	−	2.45095i	−0.0456469	−	0.0790627i
$962$		0			0
$963$	0.429978	−	0.744744i	0.0138559	−	0.0239990i
$964$		0			0
$965$	−49.0320	−	84.9259i	−1.57840	−	2.73386i
$966$		0			0
$967$			3.09186i			0.0994274i	0.998764	+	0.0497137i	$0.0158309\pi$
$967$			3.09186i			0.0994274i	−0.998764	+	0.0497137i	$0.984169\pi$
$968$		0			0
$969$	−24.4801	+	14.1336i	−0.786415	+	0.454037i
$970$		0			0
$971$	−54.4761			−1.74822			−0.874111	−	0.485727i	$-0.838555\pi$
$971$	−54.4761			−1.74822			−0.874111	+	0.485727i	$0.838555\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	43.7652	+	43.6951i	1.40161	+	1.39936i
$976$		0			0
$977$			19.3385i			0.618693i	0.950949	+	0.309347i	$0.100110\pi$
$977$			19.3385i			0.618693i	−0.950949	+	0.309347i	$0.899890\pi$
$978$		0			0
$979$	6.39137	−	11.0702i	0.204269	−	0.353804i
$980$		0			0
$981$	−0.924090	−	0.533524i	−0.0295039	−	0.0170341i
$982$		0			0
$983$	−4.27617	−	2.46885i	−0.136389	−	0.0787440i	0.430253	−	0.902708i	$-0.358424\pi$
$983$	−4.27617	−	2.46885i	−0.136389	−	0.0787440i	−0.566642	+	0.823964i	$0.691758\pi$
$984$		0			0
$985$	−1.12842	+	1.95449i	−0.0359545	+	0.0622751i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.394057	+	0.682527i	0.0125303	+	0.0217031i
$990$		0			0
$991$	48.3434			1.53568			0.767839	−	0.640643i	$-0.221332\pi$
$991$	48.3434			1.53568			0.767839	+	0.640643i	$0.221332\pi$
$992$		0			0
$993$			41.3181i			1.31119i
$994$		0			0
$995$	−53.3422	−	30.7971i	−1.69106	−	0.976334i
$996$		0			0
$997$	−21.6634	−	37.5222i	−0.686088	−	1.18834i	−0.973094	−	0.230411i	$-0.925993\pi$
$997$	−21.6634	−	37.5222i	−0.686088	−	1.18834i	0.287005	−	0.957929i	$-0.407340\pi$
$998$		0			0
$999$	4.92043	+	2.84081i	0.155675	+	0.0898793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.bq.c.361.2		16
7.2	even	3		2548.2.bb.c.569.7		16
7.3	odd	6		364.2.u.a.309.2	yes	16
7.4	even	3		2548.2.u.c.1765.7		16
7.5	odd	6		2548.2.bb.d.569.2		16
7.6	odd	2		2548.2.bq.e.361.7		16
13.4	even	6		2548.2.bb.c.1733.7		16
21.17	even	6		3276.2.cf.c.1765.7		16
28.3	even	6		1456.2.cc.f.673.7		16
91.3	odd	6		4732.2.g.k.337.13		16
91.4	even	6		2548.2.u.c.589.7		16
91.10	odd	6		4732.2.g.k.337.14		16
91.17	odd	6		364.2.u.a.225.2	✓	16
91.24	even	12		4732.2.a.t.1.7		8
91.30	even	6	inner	2548.2.bq.c.1941.2		16
91.69	odd	6		2548.2.bb.d.1733.2		16
91.80	even	12		4732.2.a.s.1.7		8
91.82	odd	6		2548.2.bq.e.1941.7		16
273.17	even	6		3276.2.cf.c.2773.2		16
364.199	even	6		1456.2.cc.f.225.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.u.a.225.2	✓	16	91.17	odd	6
364.2.u.a.309.2	yes	16	7.3	odd	6
1456.2.cc.f.225.7		16	364.199	even	6
1456.2.cc.f.673.7		16	28.3	even	6
2548.2.u.c.589.7		16	91.4	even	6
2548.2.u.c.1765.7		16	7.4	even	3
2548.2.bb.c.569.7		16	7.2	even	3
2548.2.bb.c.1733.7		16	13.4	even	6
2548.2.bb.d.569.2		16	7.5	odd	6
2548.2.bb.d.1733.2		16	91.69	odd	6
2548.2.bq.c.361.2		16	1.1	even	1	trivial
2548.2.bq.c.1941.2		16	91.30	even	6	inner
2548.2.bq.e.361.7		16	7.6	odd	2
2548.2.bq.e.1941.7		16	91.82	odd	6
3276.2.cf.c.1765.7		16	21.17	even	6
3276.2.cf.c.2773.2		16	273.17	even	6
4732.2.a.s.1.7		8	91.80	even	12
4732.2.a.t.1.7		8	91.24	even	12
4732.2.g.k.337.13		16	91.3	odd	6
4732.2.g.k.337.14		16	91.10	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.bq (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.77673 q^{3} +(3.31518 - 1.91402i) q^{5} +0.156761 q^{9} -4.32707i q^{11} +(0.930395 - 3.48344i) q^{13} +(-5.89018 + 3.40069i) q^{15} +(-1.45744 - 2.52436i) q^{17} +5.45810i q^{19} +(-0.307112 + 0.531934i) q^{23} +(4.82696 - 8.36053i) q^{25} +5.05166 q^{27} +(-4.62872 - 8.01717i) q^{29} +(-4.59646 - 2.65377i) q^{31} +7.68802i q^{33} +(0.974022 + 0.562352i) q^{37} +(-1.65306 + 6.18913i) q^{39} +(-10.4130 + 6.01195i) q^{41} +(0.641552 - 1.11120i) q^{43} +(0.519691 - 0.300044i) q^{45} +(-4.91966 + 2.84037i) q^{47} +(2.58947 + 4.48510i) q^{51} +(1.98007 - 3.42958i) q^{53} +(-8.28210 - 14.3450i) q^{55} -9.69757i q^{57} +(-6.68359 + 3.85877i) q^{59} +14.3462 q^{61} +(-3.58295 - 13.3290i) q^{65} +0.541525i q^{67} +(0.545654 - 0.945101i) q^{69} +(7.96918 + 4.60101i) q^{71} +(6.38086 + 3.68399i) q^{73} +(-8.57618 + 14.8544i) q^{75} +(-0.165843 - 0.287249i) q^{79} -9.44571 q^{81} +16.6777i q^{83} +(-9.66335 - 5.57914i) q^{85} +(8.22397 + 14.2443i) q^{87} +(2.55836 + 1.47707i) q^{89} +(8.16665 + 4.71502i) q^{93} +(10.4469 + 18.0946i) q^{95} +(-8.36220 - 4.82792i) q^{97} -0.678314i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 28 q^{9} - 10 q^{13} + 6 q^{15} - 2 q^{17} + 22 q^{25} + 12 q^{27} - 22 q^{29} + 30 q^{31} - 12 q^{37} - 6 q^{39} - 36 q^{41} + 6 q^{43} - 30 q^{45} - 18 q^{47} + 2 q^{51} - 4 q^{53} - 2 q^{55} - 18 q^{59}+ \cdots + 42 q^{97}+O(q^{100}) \) 16 * q + 28 * q^9 - 10 * q^13 + 6 * q^15 - 2 * q^17 + 22 * q^25 + 12 * q^27 - 22 * q^29 + 30 * q^31 - 12 * q^37 - 6 * q^39 - 36 * q^41 + 6 * q^43 - 30 * q^45 - 18 * q^47 + 2 * q^51 - 4 * q^53 - 2 * q^55 - 18 * q^59 + 8 * q^61 + 52 * q^69 + 36 * q^71 - 12 * q^73 + 10 * q^75 - 4 * q^79 + 42 * q^85 - 26 * q^87 - 36 * q^89 + 42 * q^93 - 30 * q^95 + 42 * q^97

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