LMFDB - Embedded newform 192.2.k.a.143.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(47,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("192.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.k (of order $4$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.163368480538624.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 - 2x^8 + 16x^6 - 8x^4 - 32*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			143.2
Root			$-1.35164 - 0.416001i$ of defining polynomial
Character	$\chi$	$=$	192.143
Dual form			192.2.k.a.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.966579 + 1.43726i) q^{3} +(-1.57184 + 1.57184i) q^{5} -2.24914 q^{7} +(-1.13145 - 2.77846i) q^{9} +O(q^{10})$	\(q+(-0.966579 + 1.43726i) q^{3} +(-1.57184 + 1.57184i) q^{5} -2.24914 q^{7} +(-1.13145 - 2.77846i) q^{9} +(-1.13145 - 1.13145i) q^{11} +(-3.24914 + 3.24914i) q^{13} +(-0.739839 - 3.77846i) q^{15} +1.66400i q^{17} +(3.77846 + 3.77846i) q^{19} +(2.17397 - 3.23261i) q^{21} +2.26290i q^{23} +0.0586332i q^{25} +(5.08701 + 1.05941i) q^{27} +(-3.23584 - 3.23584i) q^{29} +1.30777i q^{31} +(2.71982 - 0.532554i) q^{33} +(3.53529 - 3.53529i) q^{35} +(2.30777 + 2.30777i) q^{37} +(-1.52932 - 7.81042i) q^{39} +10.2143 q^{41} +(-3.77846 + 3.77846i) q^{43} +(6.14575 + 2.58884i) q^{45} +3.74258 q^{47} -1.94137 q^{49} +(-2.39161 - 1.60839i) q^{51} +(0.972946 - 0.972946i) q^{53} +3.55691 q^{55} +(-9.08281 + 1.77846i) q^{57} +(-3.88352 - 3.88352i) q^{59} +(4.19051 - 4.19051i) q^{61} +(2.54479 + 6.24914i) q^{63} -10.2143i q^{65} +(-8.02760 - 8.02760i) q^{67} +(-3.25238 - 2.18727i) q^{69} +11.0950i q^{71} +6.38101i q^{73} +(-0.0842713 - 0.0566736i) q^{75} +(2.54479 + 2.54479i) q^{77} +2.69223i q^{79} +(-6.43965 + 6.28736i) q^{81} +(-2.61113 + 2.61113i) q^{83} +(-2.61555 - 2.61555i) q^{85} +(7.77846 - 1.52306i) q^{87} -7.35247 q^{89} +(7.30777 - 7.30777i) q^{91} +(-1.87961 - 1.26407i) q^{93} -11.8783 q^{95} -5.67418 q^{97} +(-1.86351 + 4.42386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} + 8 q^{7}+O(q^{10}) $ 12 * q + 2 * q^3 + 8 * q^7	$ 12 q + 2 q^{3} + 8 q^{7} - 4 q^{13} + 12 q^{19} - 8 q^{21} - 10 q^{27} - 4 q^{33} - 4 q^{37} - 20 q^{39} - 12 q^{43} - 12 q^{45} - 20 q^{49} - 24 q^{51} - 24 q^{55} + 12 q^{61} - 28 q^{67} + 4 q^{69} + 34 q^{75} - 4 q^{81} + 32 q^{85} + 60 q^{87} + 56 q^{91} + 28 q^{93} - 8 q^{97} + 52 q^{99}+O(q^{100}) $ 12 * q + 2 * q^3 + 8 * q^7 - 4 * q^13 + 12 * q^19 - 8 * q^21 - 10 * q^27 - 4 * q^33 - 4 * q^37 - 20 * q^39 - 12 * q^43 - 12 * q^45 - 20 * q^49 - 24 * q^51 - 24 * q^55 + 12 * q^61 - 28 * q^67 + 4 * q^69 + 34 * q^75 - 4 * q^81 + 32 * q^85 + 60 * q^87 + 56 * q^91 + 28 * q^93 - 8 * q^97 + 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.966579	+	1.43726i	−0.558055	+	0.829804i
$3$	−0.966579	+	1.43726i	−0.558055	+	0.829804i
$4$		0			0
$5$	−1.57184	+	1.57184i	−0.702949	+	0.702949i	−0.965042	−	0.262094i	$-0.915587\pi$
$5$	−1.57184	+	1.57184i	−0.702949	+	0.702949i	0.262094	+	0.965042i	$0.415587\pi$
$6$		0			0
$7$	−2.24914			−0.850095			−0.425048	−	0.905171i	$-0.639743\pi$
$7$	−2.24914			−0.850095			−0.425048	+	0.905171i	$0.639743\pi$
$8$		0			0
$9$	−1.13145	−	2.77846i	−0.377150	−	0.926152i
$10$		0			0
$11$	−1.13145	−	1.13145i	−0.341145	−	0.341145i	0.515653	−	0.856798i	$-0.327549\pi$
$11$	−1.13145	−	1.13145i	−0.341145	−	0.341145i	−0.856798	+	0.515653i	$0.827549\pi$
$12$		0			0
$13$	−3.24914	+	3.24914i	−0.901149	+	0.901149i	−0.995536	−	0.0943862i	$-0.969911\pi$
$13$	−3.24914	+	3.24914i	−0.901149	+	0.901149i	0.0943862	+	0.995536i	$0.469911\pi$
$14$		0			0
$15$	−0.739839	−	3.77846i	−0.191026	−	0.975593i
$16$		0			0
$17$			1.66400i			0.403580i	0.979429	+	0.201790i	$0.0646758\pi$
$17$			1.66400i			0.403580i	−0.979429	+	0.201790i	$0.935324\pi$
$18$		0			0
$19$	3.77846	+	3.77846i	0.866838	+	0.866838i	0.992121	−	0.125283i	$-0.0399840\pi$
$19$	3.77846	+	3.77846i	0.866838	+	0.866838i	−0.125283	+	0.992121i	$0.539984\pi$
$20$		0			0
$21$	2.17397	−	3.23261i	0.474400	−	0.705412i
$22$		0			0
$23$			2.26290i			0.471847i	0.971772	+	0.235923i	$0.0758114\pi$
$23$			2.26290i			0.471847i	−0.971772	+	0.235923i	$0.924189\pi$
$24$		0			0
$25$			0.0586332i			0.0117266i
$26$		0			0
$27$	5.08701	+	1.05941i	0.978995	+	0.203884i
$28$		0			0
$29$	−3.23584	−	3.23584i	−0.600881	−	0.600881i	0.339665	−	0.940546i	$-0.389686\pi$
$29$	−3.23584	−	3.23584i	−0.600881	−	0.600881i	−0.940546	+	0.339665i	$0.889686\pi$
$30$		0			0
$31$			1.30777i			0.234883i	0.993080	+	0.117442i	$0.0374693\pi$
$31$			1.30777i			0.234883i	−0.993080	+	0.117442i	$0.962531\pi$
$32$		0			0
$33$	2.71982	−	0.532554i	0.473461	−	0.0927058i
$34$		0			0
$35$	3.53529	−	3.53529i	0.597573	−	0.597573i
$36$		0			0
$37$	2.30777	+	2.30777i	0.379396	+	0.379396i	0.870884	−	0.491488i	$-0.163547\pi$
$37$	2.30777	+	2.30777i	0.379396	+	0.379396i	−0.491488	+	0.870884i	$0.663547\pi$
$38$		0			0
$39$	−1.52932	−	7.81042i	−0.244887	−	1.25067i
$40$		0			0
$41$	10.2143			1.59520			0.797600	−	0.603187i	$-0.206103\pi$
$41$	10.2143			1.59520			0.797600	+	0.603187i	$0.206103\pi$
$42$		0			0
$43$	−3.77846	+	3.77846i	−0.576209	+	0.576209i	−0.933857	−	0.357647i	$-0.883579\pi$
$43$	−3.77846	+	3.77846i	−0.576209	+	0.576209i	0.357647	+	0.933857i	$0.383579\pi$
$44$		0			0
$45$	6.14575	+	2.58884i	0.916154	+	0.385921i
$46$		0			0
$47$	3.74258			0.545911			0.272955	−	0.962027i	$-0.411999\pi$
$47$	3.74258			0.545911			0.272955	+	0.962027i	$0.411999\pi$
$48$		0			0
$49$	−1.94137			−0.277338
$50$		0			0
$51$	−2.39161	−	1.60839i	−0.334892	−	0.225220i
$52$		0			0
$53$	0.972946	−	0.972946i	0.133644	−	0.133644i	−0.637120	−	0.770765i	$-0.719874\pi$
$53$	0.972946	−	0.972946i	0.133644	−	0.133644i	0.770765	+	0.637120i	$0.219874\pi$
$54$		0			0
$55$	3.55691			0.479614
$56$		0			0
$57$	−9.08281	+	1.77846i	−1.20305	+	0.235562i
$58$		0			0
$59$	−3.88352	−	3.88352i	−0.505591	−	0.505591i	0.407579	−	0.913170i	$-0.366373\pi$
$59$	−3.88352	−	3.88352i	−0.505591	−	0.505591i	−0.913170	+	0.407579i	$0.866373\pi$
$60$		0			0
$61$	4.19051	−	4.19051i	0.536539	−	0.536539i	−0.385971	−	0.922511i	$-0.626134\pi$
$61$	4.19051	−	4.19051i	0.536539	−	0.536539i	0.922511	+	0.385971i	$0.126134\pi$
$62$		0			0
$63$	2.54479	+	6.24914i	0.320613	+	0.787318i
$64$		0			0
$65$		−	10.2143i		−	1.26692i
$66$		0			0
$67$	−8.02760	−	8.02760i	−0.980727	−	0.980727i	0.0190906	−	0.999818i	$-0.493923\pi$
$67$	−8.02760	−	8.02760i	−0.980727	−	0.980727i	−0.999818	+	0.0190906i	$0.993923\pi$
$68$		0			0
$69$	−3.25238	−	2.18727i	−0.391540	−	0.263316i
$70$		0			0
$71$			11.0950i			1.31674i	0.752695	+	0.658370i	$0.228754\pi$
$71$			11.0950i			1.31674i	−0.752695	+	0.658370i	$0.771246\pi$
$72$		0			0
$73$			6.38101i			0.746841i	0.927662	+	0.373421i	$0.121815\pi$
$73$			6.38101i			0.746841i	−0.927662	+	0.373421i	$0.878185\pi$
$74$		0			0
$75$	−0.0842713	−	0.0566736i	−0.00973081	−	0.00654410i
$76$		0			0
$77$	2.54479	+	2.54479i	0.290005	+	0.290005i
$78$		0			0
$79$			2.69223i			0.302899i	0.988465	+	0.151450i	$0.0483941\pi$
$79$			2.69223i			0.302899i	−0.988465	+	0.151450i	$0.951606\pi$
$80$		0			0
$81$	−6.43965	+	6.28736i	−0.715516	+	0.698596i
$82$		0			0
$83$	−2.61113	+	2.61113i	−0.286608	+	0.286608i	−0.835738	−	0.549129i	$-0.814960\pi$
$83$	−2.61113	+	2.61113i	−0.286608	+	0.286608i	0.549129	+	0.835738i	$0.314960\pi$
$84$		0			0
$85$	−2.61555	−	2.61555i	−0.283696	−	0.283696i
$86$		0			0
$87$	7.77846	−	1.52306i	0.833938	−	0.163289i
$88$		0			0
$89$	−7.35247			−0.779360			−0.389680	−	0.920950i	$-0.627414\pi$
$89$	−7.35247			−0.779360			−0.389680	+	0.920950i	$0.627414\pi$
$90$		0			0
$91$	7.30777	−	7.30777i	0.766063	−	0.766063i
$92$		0			0
$93$	−1.87961	−	1.26407i	−0.194907	−	0.131078i
$94$		0			0
$95$	−11.8783			−1.21868
$96$		0			0
$97$	−5.67418			−0.576126			−0.288063	−	0.957611i	$-0.593011\pi$
$97$	−5.67418			−0.576126			−0.288063	+	0.957611i	$0.593011\pi$
$98$		0			0
$99$	−1.86351	+	4.42386i	−0.187289	+	0.444614i
$100$		0			0
$101$	−10.3064	+	10.3064i	−1.02553	+	1.02553i	−0.0258621	+	0.999666i	$0.508233\pi$
$101$	−10.3064	+	10.3064i	−1.02553	+	1.02553i	−0.999666	+	0.0258621i	$0.991767\pi$
$102$		0			0
$103$	8.13187			0.801257			0.400629	−	0.916241i	$-0.368792\pi$
$103$	8.13187			0.801257			0.400629	+	0.916241i	$0.368792\pi$
$104$		0			0
$105$	1.66400	+	8.49828i	0.162390	+	0.829347i
$106$		0			0
$107$	2.40384	+	2.40384i	0.232388	+	0.232388i	0.813689	−	0.581301i	$-0.197456\pi$
$107$	2.40384	+	2.40384i	0.232388	+	0.232388i	−0.581301	+	0.813689i	$0.697456\pi$
$108$		0			0
$109$	8.92332	−	8.92332i	0.854699	−	0.854699i	−0.136009	−	0.990708i	$-0.543427\pi$
$109$	8.92332	−	8.92332i	0.854699	−	0.854699i	0.990708	+	0.136009i	$0.0434275\pi$
$110$		0			0
$111$	−5.54752	+	1.08623i	−0.526548	+	0.103100i
$112$		0			0
$113$			15.9027i			1.49600i	0.663697	+	0.748002i	$0.268986\pi$
$113$			15.9027i			1.49600i	−0.663697	+	0.748002i	$0.731014\pi$
$114$		0			0
$115$	−3.55691	−	3.55691i	−0.331684	−	0.331684i
$116$		0			0
$117$	12.7038	+	5.35136i	1.17447	+	0.494734i
$118$		0			0
$119$		−	3.74258i		−	0.343081i
$120$		0			0
$121$		−	8.43965i		−	0.767241i
$122$		0			0
$123$	−9.87290	+	14.6806i	−0.890209	+	1.32370i
$124$		0			0
$125$	−7.95137	−	7.95137i	−0.711192	−	0.711192i
$126$		0			0
$127$		−	7.42504i		−	0.658866i	−0.944179	−	0.329433i	$-0.893142\pi$
$127$		−	7.42504i		−	0.658866i	0.944179	−	0.329433i	$-0.106858\pi$
$128$		0			0
$129$	−1.77846	−	9.08281i	−0.156584	−	0.799697i
$130$		0			0
$131$	3.88352	−	3.88352i	0.339305	−	0.339305i	−0.516801	−	0.856106i	$-0.672877\pi$
$131$	3.88352	−	3.88352i	0.339305	−	0.339305i	0.856106	+	0.516801i	$0.172877\pi$
$132$		0			0
$133$	−8.49828	−	8.49828i	−0.736894	−	0.736894i
$134$		0			0
$135$	−9.66119	+	6.33074i	−0.831503	+	0.544864i
$136$		0			0
$137$	2.72911			0.233164			0.116582	−	0.993181i	$-0.462806\pi$
$137$	2.72911			0.233164			0.116582	+	0.993181i	$0.462806\pi$
$138$		0			0
$139$	0.0275977	−	0.0275977i	0.00234080	−	0.00234080i	−0.705935	−	0.708276i	$-0.749473\pi$
$139$	0.0275977	−	0.0275977i	0.00234080	−	0.00234080i	0.708276	+	0.705935i	$0.249473\pi$
$140$		0			0
$141$	−3.61750	+	5.37907i	−0.304648	+	0.452999i
$142$		0			0
$143$	7.35247			0.614845
$144$		0			0
$145$	10.1725			0.844777
$146$		0			0
$147$	1.87649	−	2.79025i	0.154770	−	0.230136i
$148$		0			0
$149$	12.5693	−	12.5693i	1.02972	−	1.02972i	0.0301744	−	0.999545i	$-0.490394\pi$
$149$	12.5693	−	12.5693i	1.02972	−	1.02972i	0.999545	−	0.0301744i	$-0.00960626\pi$
$150$		0			0
$151$	−16.8647			−1.37243			−0.686214	−	0.727399i	$-0.740729\pi$
$151$	−16.8647			−1.37243			−0.686214	+	0.727399i	$0.740729\pi$
$152$		0			0
$153$	4.62336	−	1.88273i	0.373777	−	0.152210i
$154$		0			0
$155$	−2.05561	−	2.05561i	−0.165111	−	0.165111i
$156$		0			0
$157$	−5.36641	+	5.36641i	−0.428286	+	0.428286i	−0.888044	−	0.459758i	$-0.847936\pi$
$157$	−5.36641	+	5.36641i	−0.428286	+	0.428286i	0.459758	+	0.888044i	$0.347936\pi$
$158$		0			0
$159$	0.457950	+	2.33881i	0.0363178	+	0.185480i
$160$		0			0
$161$		−	5.08957i		−	0.401115i
$162$		0			0
$163$	8.77502	+	8.77502i	0.687313	+	0.687313i	0.961637	−	0.274325i	$-0.0884543\pi$
$163$	8.77502	+	8.77502i	0.687313	+	0.687313i	−0.274325	+	0.961637i	$0.588454\pi$
$164$		0			0
$165$	−3.43804	+	5.11222i	−0.267651	+	0.397986i
$166$		0			0
$167$		−	16.9678i		−	1.31301i	−0.754321	−	0.656505i	$-0.772034\pi$
$167$		−	16.9678i		−	1.31301i	0.754321	−	0.656505i	$-0.227966\pi$
$168$		0			0
$169$		−	8.11383i		−	0.624141i
$170$		0			0
$171$	6.22315	−	14.7734i	0.475896	−	1.12975i
$172$		0			0
$173$	16.3119	+	16.3119i	1.24017	+	1.24017i	0.959930	+	0.280241i	$0.0904144\pi$
$173$	16.3119	+	16.3119i	1.24017	+	1.24017i	0.280241	+	0.959930i	$0.409586\pi$
$174$		0			0
$175$		−	0.131874i		−	0.00996875i
$176$		0			0
$177$	9.33537	−	1.82791i	0.701689	−	0.137394i
$178$		0			0
$179$	1.33873	−	1.33873i	0.100062	−	0.100062i	−0.655304	−	0.755365i	$-0.727459\pi$
$179$	1.33873	−	1.33873i	0.100062	−	0.100062i	0.755365	+	0.655304i	$0.227459\pi$
$180$		0			0
$181$	10.2457	+	10.2457i	0.761557	+	0.761557i	0.976604	−	0.215047i	$-0.0689904\pi$
$181$	10.2457	+	10.2457i	0.761557	+	0.761557i	−0.215047	+	0.976604i	$0.568990\pi$
$182$		0			0
$183$	1.97240	+	10.0733i	0.145804	+	0.744641i
$184$		0			0
$185$	−7.25491			−0.533391
$186$		0			0
$187$	1.88273	−	1.88273i	0.137679	−	0.137679i
$188$		0			0
$189$	−11.4414	−	2.38276i	−0.832239	−	0.173320i
$190$		0			0
$191$	24.5398			1.77563			0.887817	−	0.460197i	$-0.152221\pi$
$191$	24.5398			1.77563			0.887817	+	0.460197i	$0.152221\pi$
$192$		0			0
$193$	8.38101			0.603279			0.301639	−	0.953422i	$-0.402466\pi$
$193$	8.38101			0.603279			0.301639	+	0.953422i	$0.402466\pi$
$194$		0			0
$195$	14.6806	+	9.87290i	1.05130	+	0.707013i
$196$		0			0
$197$	1.28995	−	1.28995i	0.0919052	−	0.0919052i	−0.659659	−	0.751565i	$-0.729299\pi$
$197$	1.28995	−	1.28995i	0.0919052	−	0.0919052i	0.751565	+	0.659659i	$0.229299\pi$
$198$		0			0
$199$	13.0992			0.928579			0.464290	−	0.885683i	$-0.346310\pi$
$199$	13.0992			0.928579			0.464290	+	0.885683i	$0.346310\pi$
$200$		0			0
$201$	19.2971	−	3.77846i	1.36111	−	0.266512i
$202$		0			0
$203$	7.27787	+	7.27787i	0.510806	+	0.510806i
$204$		0			0
$205$	−16.0552	+	16.0552i	−1.12134	+	1.12134i
$206$		0			0
$207$	6.28736	−	2.56035i	0.437002	−	0.177957i
$208$		0			0
$209$		−	8.55026i		−	0.591434i
$210$		0			0
$211$	8.47068	+	8.47068i	0.583146	+	0.583146i	0.935766	−	0.352621i	$-0.114709\pi$
$211$	8.47068	+	8.47068i	0.583146	+	0.583146i	−0.352621	+	0.935766i	$0.614709\pi$
$212$		0			0
$213$	−15.9465	−	10.7242i	−1.09264	−	0.734813i
$214$		0			0
$215$		−	11.8783i		−	0.810091i
$216$		0			0
$217$		−	2.94137i		−	0.199673i
$218$		0			0
$219$	−9.17120	−	6.16776i	−0.619732	−	0.416778i
$220$		0			0
$221$	−5.40658	−	5.40658i	−0.363686	−	0.363686i
$222$		0			0
$223$		−	21.5715i		−	1.44454i	−0.691613	−	0.722268i	$-0.743100\pi$
$223$		−	21.5715i		−	1.44454i	0.691613	−	0.722268i	$-0.256900\pi$
$224$		0			0
$225$	0.162910	−	0.0663404i	0.0108606	−	0.00442269i
$226$		0			0
$227$	−16.7523	+	16.7523i	−1.11189	+	1.11189i	−0.118994	+	0.992895i	$0.537967\pi$
$227$	−16.7523	+	16.7523i	−1.11189	+	1.11189i	−0.992895	+	0.118994i	$0.962033\pi$
$228$		0			0
$229$	3.36641	+	3.36641i	0.222458	+	0.222458i	0.809533	−	0.587074i	$-0.199720\pi$
$229$	3.36641	+	3.36641i	0.222458	+	0.222458i	−0.587074	+	0.809533i	$0.699720\pi$
$230$		0			0
$231$	−6.11727	+	1.19779i	−0.402487	+	0.0788087i
$232$		0			0
$233$	−0.501329			−0.0328431			−0.0164216	−	0.999865i	$-0.505227\pi$
$233$	−0.501329			−0.0328431			−0.0164216	+	0.999865i	$0.505227\pi$
$234$		0			0
$235$	−5.88273	+	5.88273i	−0.383747	+	0.383747i
$236$		0			0
$237$	−3.86944	−	2.60225i	−0.251347	−	0.169034i
$238$		0			0
$239$	−30.4585			−1.97019			−0.985097	−	0.171999i	$-0.944978\pi$
$239$	−30.4585			−1.97019			−0.985097	+	0.171999i	$0.944978\pi$
$240$		0			0
$241$	−15.4948			−0.998111			−0.499055	−	0.866570i	$-0.666320\pi$
$241$	−15.4948			−0.998111			−0.499055	+	0.866570i	$0.666320\pi$
$242$		0			0
$243$	−2.81216	−	15.3327i	−0.180400	−	0.983593i
$244$		0			0
$245$	3.05152	−	3.05152i	0.194954	−	0.194954i
$246$		0			0
$247$	−24.5535			−1.56230
$248$		0			0
$249$	−1.22901	−	6.27674i	−0.0778856	−	0.397772i
$250$		0			0
$251$	12.2265	+	12.2265i	0.771730	+	0.771730i	0.978409	−	0.206679i	$-0.0662656\pi$
$251$	12.2265	+	12.2265i	0.771730	+	0.771730i	−0.206679	+	0.978409i	$0.566266\pi$
$252$		0			0
$253$	2.56035	−	2.56035i	0.160968	−	0.160968i
$254$		0			0
$255$	6.28736	−	1.23109i	0.393730	−	0.0770941i
$256$		0			0
$257$			7.48515i			0.466911i	0.972367	+	0.233455i	$0.0750033\pi$
$257$			7.48515i			0.466911i	−0.972367	+	0.233455i	$0.924997\pi$
$258$		0			0
$259$	−5.19051	−	5.19051i	−0.322522	−	0.322522i
$260$		0			0
$261$	−5.32946	+	12.6518i	−0.329885	+	0.783129i
$262$		0			0
$263$			10.2659i			0.633023i	0.948589	+	0.316511i	$0.102512\pi$
$263$			10.2659i			0.633023i	−0.948589	+	0.316511i	$0.897488\pi$
$264$		0			0
$265$			3.05863i			0.187890i
$266$		0			0
$267$	7.10675	−	10.5674i	0.434926	−	0.646716i
$268$		0			0
$269$	−2.76963	−	2.76963i	−0.168867	−	0.168867i	0.617614	−	0.786481i	$-0.288099\pi$
$269$	−2.76963	−	2.76963i	−0.168867	−	0.168867i	−0.786481	+	0.617614i	$0.788099\pi$
$270$		0			0
$271$			28.6854i			1.74251i	0.490830	+	0.871255i	$0.336694\pi$
$271$			28.6854i			1.74251i	−0.490830	+	0.871255i	$0.663306\pi$
$272$		0			0
$273$	3.43965	+	17.5667i	0.208177	+	1.06319i
$274$		0			0
$275$	0.0663404	−	0.0663404i	0.00400048	−	0.00400048i
$276$		0			0
$277$	−0.806055	−	0.806055i	−0.0484311	−	0.0484311i	0.682476	−	0.730908i	$-0.260903\pi$
$277$	−0.806055	−	0.806055i	−0.0484311	−	0.0484311i	−0.730908	+	0.682476i	$0.760903\pi$
$278$		0			0
$279$	3.63359	−	1.47968i	0.217538	−	0.0885861i
$280$		0			0
$281$	−22.3228			−1.33167			−0.665833	−	0.746101i	$-0.731924\pi$
$281$	−22.3228			−1.33167			−0.665833	+	0.746101i	$0.731924\pi$
$282$		0			0
$283$	−8.08279	+	8.08279i	−0.480472	+	0.480472i	−0.905282	−	0.424810i	$-0.860341\pi$
$283$	−8.08279	+	8.08279i	−0.480472	+	0.480472i	0.424810	+	0.905282i	$0.360341\pi$
$284$		0			0
$285$	11.4813	−	17.0722i	0.680093	−	1.01127i
$286$		0			0
$287$	−22.9733			−1.35607
$288$		0			0
$289$	14.2311			0.837123
$290$		0			0
$291$	5.48455	−	8.15529i	0.321510	−	0.478071i
$292$		0			0
$293$	6.37953	−	6.37953i	0.372696	−	0.372696i	−0.495762	−	0.868458i	$-0.665111\pi$
$293$	6.37953	−	6.37953i	0.372696	−	0.372696i	0.868458	+	0.495762i	$0.165111\pi$
$294$		0			0
$295$	12.2086			0.710809
$296$		0			0
$297$	−4.55702	−	6.95436i	−0.264425	−	0.403533i
$298$		0			0
$299$	−7.35247	−	7.35247i	−0.425204	−	0.425204i
$300$		0			0
$301$	8.49828	−	8.49828i	0.489833	−	0.489833i
$302$		0			0
$303$	−4.85106	−	24.7750i	−0.278686	−	1.42329i
$304$		0			0
$305$			13.1736i			0.754319i
$306$		0			0
$307$	6.58795	+	6.58795i	0.375994	+	0.375994i	0.869655	−	0.493661i	$-0.164341\pi$
$307$	6.58795	+	6.58795i	0.375994	+	0.375994i	−0.493661	+	0.869655i	$0.664341\pi$
$308$		0			0
$309$	−7.86010	+	11.6876i	−0.447146	+	0.664887i
$310$		0			0
$311$			9.52861i			0.540318i	0.962816	+	0.270159i	$0.0870763\pi$
$311$			9.52861i			0.540318i	−0.962816	+	0.270159i	$0.912924\pi$
$312$		0			0
$313$			25.1690i			1.42264i	0.702870	+	0.711319i	$0.251902\pi$
$313$			25.1690i			1.42264i	−0.702870	+	0.711319i	$0.748098\pi$
$314$		0			0
$315$	−13.8227	−	5.82265i	−0.778818	−	0.328069i
$316$		0			0
$317$	15.5287	+	15.5287i	0.872178	+	0.872178i	0.992709	−	0.120532i	$-0.0384600\pi$
$317$	15.5287	+	15.5287i	0.872178	+	0.872178i	−0.120532	+	0.992709i	$0.538460\pi$
$318$		0			0
$319$			7.32238i			0.409975i
$320$		0			0
$321$	−5.77846	+	1.13145i	−0.322522	+	0.0631513i
$322$		0			0
$323$	−6.28736	+	6.28736i	−0.349838	+	0.349838i
$324$		0			0
$325$	−0.190507	−	0.190507i	−0.0105674	−	0.0105674i
$326$		0			0
$327$	4.20006	+	21.4503i	0.232264	+	1.18620i
$328$		0			0
$329$	−8.41758			−0.464076
$330$		0			0
$331$	−2.58795	+	2.58795i	−0.142247	+	0.142247i	−0.774644	−	0.632397i	$-0.782071\pi$
$331$	−2.58795	+	2.58795i	−0.142247	+	0.142247i	0.632397	+	0.774644i	$0.282071\pi$
$332$		0			0
$333$	3.80092	−	9.02318i	0.208289	−	0.494467i
$334$		0			0
$335$	25.2362			1.37880
$336$		0			0
$337$	−23.1690			−1.26210			−0.631049	−	0.775743i	$-0.717375\pi$
$337$	−23.1690			−1.26210			−0.631049	+	0.775743i	$0.717375\pi$
$338$		0			0
$339$	−22.8564	−	15.3713i	−1.24139	−	0.834852i
$340$		0			0
$341$	1.47968	−	1.47968i	0.0801291	−	0.0801291i
$342$		0			0
$343$	20.1104			1.08586
$344$		0			0
$345$	8.55026	−	1.67418i	0.460331	−	0.0901349i
$346$		0			0
$347$	6.72235	+	6.72235i	0.360875	+	0.360875i	0.864135	−	0.503260i	$-0.167866\pi$
$347$	6.72235	+	6.72235i	0.360875	+	0.360875i	−0.503260	+	0.864135i	$0.667866\pi$
$348$		0			0
$349$	−2.75086	+	2.75086i	−0.147250	+	0.147250i	−0.776888	−	0.629638i	$-0.783203\pi$
$349$	−2.75086	+	2.75086i	−0.147250	+	0.147250i	0.629638	+	0.776888i	$0.283203\pi$
$350$		0			0
$351$	−19.9706	+	13.0862i	−1.06595	+	0.698491i
$352$		0			0
$353$		−	23.1928i		−	1.23443i	−0.786796	−	0.617213i	$-0.788262\pi$
$353$		−	23.1928i		−	1.23443i	0.786796	−	0.617213i	$-0.211738\pi$
$354$		0			0
$355$	−17.4396	−	17.4396i	−0.925600	−	0.925600i
$356$		0			0
$357$	5.37907	+	3.61750i	0.284690	+	0.191458i
$358$		0			0
$359$		−	27.3664i		−	1.44434i	−0.691713	−	0.722172i	$-0.743144\pi$
$359$		−	27.3664i		−	1.44434i	0.691713	−	0.722172i	$-0.256856\pi$
$360$		0			0
$361$			9.55348i			0.502815i
$362$		0			0
$363$	12.1300	+	8.15759i	0.636659	+	0.428162i
$364$		0			0
$365$	−10.0299	−	10.0299i	−0.524991	−	0.524991i
$366$		0			0
$367$			26.0406i			1.35931i	0.733533	+	0.679654i	$0.237870\pi$
$367$			26.0406i			1.35931i	−0.733533	+	0.679654i	$0.762130\pi$
$368$		0			0
$369$	−11.5569	−	28.3799i	−0.601629	−	1.47740i
$370$		0			0
$371$	−2.18829	+	2.18829i	−0.113611	+	0.113611i
$372$		0			0
$373$	−13.1319	−	13.1319i	−0.679943	−	0.679943i	0.280044	−	0.959987i	$-0.409651\pi$
$373$	−13.1319	−	13.1319i	−0.679943	−	0.679943i	−0.959987	+	0.280044i	$0.909651\pi$
$374$		0			0
$375$	19.1138	−	3.74258i	0.987034	−	0.193266i
$376$		0			0
$377$	21.0274			1.08297
$378$		0			0
$379$	17.4526	−	17.4526i	0.896482	−	0.896482i	−0.0986413	−	0.995123i	$-0.531450\pi$
$379$	17.4526	−	17.4526i	0.896482	−	0.896482i	0.995123	+	0.0986413i	$0.0314496\pi$
$380$		0			0
$381$	10.6717	+	7.17689i	0.546729	+	0.367683i
$382$		0			0
$383$	26.4965			1.35391			0.676953	−	0.736027i	$-0.263300\pi$
$383$	26.4965			1.35391			0.676953	+	0.736027i	$0.263300\pi$
$384$		0			0
$385$	−8.00000			−0.407718
$386$		0			0
$387$	14.7734	+	6.22315i	0.750975	+	0.316341i
$388$		0			0
$389$	−2.35506	+	2.35506i	−0.119406	+	0.119406i	−0.764285	−	0.644879i	$-0.776908\pi$
$389$	−2.35506	+	2.35506i	−0.119406	+	0.119406i	0.644879	+	0.764285i	$0.276908\pi$
$390$		0			0
$391$	−3.76547			−0.190428
$392$		0			0
$393$	1.82791	+	9.33537i	0.0922058	+	0.470907i
$394$		0			0
$395$	−4.23175	−	4.23175i	−0.212923	−	0.212923i
$396$		0			0
$397$	4.68879	−	4.68879i	0.235324	−	0.235324i	−0.579587	−	0.814910i	$-0.696786\pi$
$397$	4.68879	−	4.68879i	0.235324	−	0.235324i	0.814910	+	0.579587i	$0.196786\pi$
$398$		0			0
$399$	20.4285	−	4.00000i	1.02271	−	0.200250i
$400$		0			0
$401$		−	5.18714i		−	0.259033i	−0.991577	−	0.129517i	$-0.958657\pi$
$401$		−	5.18714i		−	0.259033i	0.991577	−	0.129517i	$-0.0413426\pi$
$402$		0			0
$403$	−4.24914	−	4.24914i	−0.211665	−	0.211665i
$404$		0			0
$405$	0.239367	−	20.0048i	0.0118943	−	0.994048i
$406$		0			0
$407$		−	5.22225i		−	0.258858i
$408$		0			0
$409$			14.8793i			0.735734i	0.929878	+	0.367867i	$0.119912\pi$
$409$			14.8793i			0.735734i	−0.929878	+	0.367867i	$0.880088\pi$
$410$		0			0
$411$	−2.63790	+	3.92245i	−0.130118	+	0.193480i
$412$		0			0
$413$	8.73458	+	8.73458i	0.429801	+	0.429801i
$414$		0			0
$415$		−	8.20855i		−	0.402942i
$416$		0			0
$417$	0.0129898	+	0.0663404i	0.000636111	+	0.00324870i
$418$		0			0
$419$	25.3026	−	25.3026i	1.23611	−	1.23611i	0.274533	−	0.961578i	$-0.411477\pi$
$419$	25.3026	−	25.3026i	1.23611	−	1.23611i	0.961578	−	0.274533i	$-0.0885232\pi$
$420$		0			0
$421$	7.13187	+	7.13187i	0.347586	+	0.347586i	0.859210	−	0.511623i	$-0.170956\pi$
$421$	7.13187	+	7.13187i	0.347586	+	0.347586i	−0.511623	+	0.859210i	$0.670956\pi$
$422$		0			0
$423$	−4.23453	−	10.3986i	−0.205890	−	0.505597i
$424$		0			0
$425$	−0.0975657			−0.00473263
$426$		0			0
$427$	−9.42504	+	9.42504i	−0.456110	+	0.456110i
$428$		0			0
$429$	−7.10675	+	10.5674i	−0.343117	+	0.510200i
$430$		0			0
$431$	−15.4882			−0.746038			−0.373019	−	0.927824i	$-0.621677\pi$
$431$	−15.4882			−0.746038			−0.373019	+	0.927824i	$0.621677\pi$
$432$		0			0
$433$	25.5500			1.22786			0.613928	−	0.789362i	$-0.289588\pi$
$433$	25.5500			1.22786			0.613928	+	0.789362i	$0.289588\pi$
$434$		0			0
$435$	−9.83249	+	14.6205i	−0.471432	+	0.700999i
$436$		0			0
$437$	−8.55026	+	8.55026i	−0.409014	+	0.409014i
$438$		0			0
$439$	−2.63703			−0.125859			−0.0629293	−	0.998018i	$-0.520044\pi$
$439$	−2.63703			−0.125859			−0.0629293	+	0.998018i	$0.520044\pi$
$440$		0			0
$441$	2.19656	+	5.39400i	0.104598	+	0.256857i
$442$		0			0
$443$	−14.8580	−	14.8580i	−0.705927	−	0.705927i	0.259749	−	0.965676i	$-0.416360\pi$
$443$	−14.8580	−	14.8580i	−0.705927	−	0.705927i	−0.965676	+	0.259749i	$0.916360\pi$
$444$		0			0
$445$	11.5569	−	11.5569i	0.547850	−	0.547850i
$446$		0			0
$447$	5.91617	+	30.2147i	0.279825	+	1.42910i
$448$		0			0
$449$			31.7079i			1.49639i	0.663480	+	0.748194i	$0.269079\pi$
$449$			31.7079i			1.49639i	−0.663480	+	0.748194i	$0.730921\pi$
$450$		0			0
$451$	−11.5569	−	11.5569i	−0.544194	−	0.544194i
$452$		0			0
$453$	16.3011	−	24.2390i	0.765891	−	1.13885i
$454$		0			0
$455$			22.9733i			1.07701i
$456$		0			0
$457$		−	23.8759i		−	1.11687i	−0.829550	−	0.558433i	$-0.811403\pi$
$457$		−	23.8759i		−	1.11687i	0.829550	−	0.558433i	$-0.188597\pi$
$458$		0			0
$459$	−1.76286	+	8.46480i	−0.0822833	+	0.395103i
$460$		0			0
$461$	0.921303	+	0.921303i	0.0429094	+	0.0429094i	0.728236	−	0.685327i	$-0.240341\pi$
$461$	0.921303	+	0.921303i	0.0429094	+	0.0429094i	−0.685327	+	0.728236i	$0.740341\pi$
$462$		0			0
$463$		−	26.1510i		−	1.21534i	−0.794190	−	0.607670i	$-0.792105\pi$
$463$		−	26.1510i		−	1.21534i	0.794190	−	0.607670i	$-0.207895\pi$
$464$		0			0
$465$	4.94137	−	0.967542i	0.229150	−	0.0448687i
$466$		0			0
$467$	16.2510	−	16.2510i	0.752005	−	0.752005i	−0.222848	−	0.974853i	$-0.571535\pi$
$467$	16.2510	−	16.2510i	0.752005	−	0.752005i	0.974853	+	0.222848i	$0.0715355\pi$
$468$		0			0
$469$	18.0552	+	18.0552i	0.833711	+	0.833711i
$470$		0			0
$471$	−2.52588	−	12.9000i	−0.116386	−	0.594400i
$472$		0			0
$473$	8.55026			0.393141
$474$		0			0
$475$	−0.221543	+	0.221543i	−0.0101651	+	0.0101651i
$476$		0			0
$477$	−3.80413	−	1.60245i	−0.174179	−	0.0733712i
$478$		0			0
$479$	−11.7456			−0.536669			−0.268335	−	0.963326i	$-0.586473\pi$
$479$	−11.7456			−0.536669			−0.268335	+	0.963326i	$0.586473\pi$
$480$		0			0
$481$	−14.9966			−0.683784
$482$		0			0
$483$	7.31506	+	4.91948i	0.332847	+	0.223844i
$484$		0			0
$485$	8.91891	−	8.91891i	0.404987	−	0.404987i
$486$		0			0
$487$	0.783513			0.0355044			0.0177522	−	0.999842i	$-0.494349\pi$
$487$	0.783513			0.0355044			0.0177522	+	0.999842i	$0.494349\pi$
$488$		0			0
$489$	−21.0938	+	4.13026i	−0.953893	+	0.186777i
$490$		0			0
$491$	10.0382	+	10.0382i	0.453018	+	0.453018i	0.896355	−	0.443337i	$-0.146206\pi$
$491$	10.0382	+	10.0382i	0.453018	+	0.453018i	−0.443337	+	0.896355i	$0.646206\pi$
$492$		0			0
$493$	5.38445	−	5.38445i	0.242504	−	0.242504i
$494$		0			0
$495$	−4.02447	−	9.88273i	−0.180886	−	0.444196i
$496$		0			0
$497$		−	24.9543i		−	1.11935i
$498$		0			0
$499$	29.9655	+	29.9655i	1.34144	+	1.34144i	0.894627	+	0.446815i	$0.147442\pi$
$499$	29.9655	+	29.9655i	1.34144	+	1.34144i	0.446815	+	0.894627i	$0.352558\pi$
$500$		0			0
$501$	24.3872	+	16.4008i	1.08954	+	0.732732i
$502$		0			0
$503$			21.7131i			0.968138i	0.875030	+	0.484069i	$0.160842\pi$
$503$			21.7131i			0.968138i	−0.875030	+	0.484069i	$0.839158\pi$
$504$		0			0
$505$		−	32.4001i		−	1.44179i
$506$		0			0
$507$	11.6617	+	7.84266i	0.517914	+	0.348305i
$508$		0			0
$509$	−16.1276	−	16.1276i	−0.714842	−	0.714842i	0.252702	−	0.967544i	$-0.418681\pi$
$509$	−16.1276	−	16.1276i	−0.714842	−	0.714842i	−0.967544	+	0.252702i	$0.918681\pi$
$510$		0			0
$511$		−	14.3518i		−	0.634886i
$512$		0			0
$513$	15.2181	+	23.2240i	0.671896	+	1.02536i
$514$		0			0
$515$	−12.7820	+	12.7820i	−0.563243	+	0.563243i
$516$		0			0
$517$	−4.23453	−	4.23453i	−0.186235	−	0.186235i
$518$		0			0
$519$	−39.2112	+	7.67774i	−1.72118	+	0.337015i
$520$		0			0
$521$	−5.68847			−0.249216			−0.124608	−	0.992206i	$-0.539767\pi$
$521$	−5.68847			−0.249216			−0.124608	+	0.992206i	$0.539767\pi$
$522$		0			0
$523$	−13.6612	+	13.6612i	−0.597362	+	0.597362i	−0.939610	−	0.342248i	$-0.888812\pi$
$523$	−13.6612	+	13.6612i	−0.597362	+	0.597362i	0.342248	+	0.939610i	$0.388812\pi$
$524$		0			0
$525$	0.189538	+	0.127467i	0.00827211	+	0.00556311i
$526$		0			0
$527$	−2.17614			−0.0947941
$528$		0			0
$529$	17.8793			0.777361
$530$		0			0
$531$	−6.39619	+	15.1842i	−0.277571	+	0.658938i
$532$		0			0
$533$	−33.1876	+	33.1876i	−1.43751	+	1.43751i
$534$		0			0
$535$	−7.55691			−0.326714
$536$		0			0
$537$	0.630120	+	3.21811i	0.0271917	+	0.138871i
$538$		0			0
$539$	2.19656	+	2.19656i	0.0946124	+	0.0946124i
$540$		0			0
$541$	−24.5715	+	24.5715i	−1.05641	+	1.05641i	−0.0581016	+	0.998311i	$0.518505\pi$
$541$	−24.5715	+	24.5715i	−1.05641	+	1.05641i	−0.998311	+	0.0581016i	$0.981495\pi$
$542$		0			0
$543$	−24.6291	+	4.82248i	−1.05693	+	0.206953i
$544$		0			0
$545$			28.0521i			1.20162i
$546$		0			0
$547$	−3.56990	−	3.56990i	−0.152638	−	0.152638i	0.626657	−	0.779295i	$-0.284423\pi$
$547$	−3.56990	−	3.56990i	−0.152638	−	0.152638i	−0.779295	+	0.626657i	$0.784423\pi$
$548$		0			0
$549$	−16.3845	−	6.90180i	−0.699273	−	0.294562i
$550$		0			0
$551$		−	24.4530i		−	1.04173i
$552$		0			0
$553$		−	6.05520i		−	0.257493i
$554$		0			0
$555$	7.01244	−	10.4272i	0.297662	−	0.442610i
$556$		0			0
$557$	−18.1602	−	18.1602i	−0.769473	−	0.769473i	0.208540	−	0.978014i	$-0.433129\pi$
$557$	−18.1602	−	18.1602i	−0.769473	−	0.769473i	−0.978014	+	0.208540i	$0.933129\pi$
$558$		0			0
$559$		−	24.5535i		−	1.03850i
$560$		0			0
$561$	0.886172	+	4.52579i	0.0374142	+	0.191079i
$562$		0			0
$563$	−6.91748	+	6.91748i	−0.291537	+	0.291537i	−0.837687	−	0.546150i	$-0.816093\pi$
$563$	−6.91748	+	6.91748i	−0.291537	+	0.291537i	0.546150	+	0.837687i	$0.316093\pi$
$564$		0			0
$565$	−24.9966	−	24.9966i	−1.05161	−	1.05161i
$566$		0			0
$567$	14.4837	−	14.1412i	0.608257	−	0.593873i
$568$		0			0
$569$	36.2961			1.52161			0.760807	−	0.648979i	$-0.224804\pi$
$569$	36.2961			1.52161			0.760807	+	0.648979i	$0.224804\pi$
$570$		0			0
$571$	33.5224	−	33.5224i	1.40287	−	1.40287i	0.612056	−	0.790814i	$-0.290343\pi$
$571$	33.5224	−	33.5224i	1.40287	−	1.40287i	0.790814	−	0.612056i	$-0.209657\pi$
$572$		0			0
$573$	−23.7196	+	35.2701i	−0.990901	+	1.47343i
$574$		0			0
$575$	−0.132681			−0.00553317
$576$		0			0
$577$	−18.9345			−0.788253			−0.394127	−	0.919056i	$-0.628953\pi$
$577$	−18.9345			−0.788253			−0.394127	+	0.919056i	$0.628953\pi$
$578$		0			0
$579$	−8.10092	+	12.0457i	−0.336663	+	0.500603i
$580$		0			0
$581$	5.87279	−	5.87279i	0.243644	−	0.243644i
$582$		0			0
$583$	−2.20168			−0.0911842
$584$		0			0
$585$	−28.3799	+	11.5569i	−1.17336	+	0.477820i
$586$		0			0
$587$	−29.6211	−	29.6211i	−1.22259	−	1.22259i	−0.966707	−	0.255885i	$-0.917633\pi$
$587$	−29.6211	−	29.6211i	−1.22259	−	1.22259i	−0.255885	−	0.966707i	$-0.582367\pi$
$588$		0			0
$589$	−4.94137	+	4.94137i	−0.203605	+	0.203605i
$590$		0			0
$591$	0.607159	+	3.10084i	0.0249752	+	0.127551i
$592$		0			0
$593$		−	21.6263i		−	0.888086i	−0.896005	−	0.444043i	$-0.853544\pi$
$593$		−	21.6263i		−	0.888086i	0.896005	−	0.444043i	$-0.146456\pi$
$594$		0			0
$595$	5.88273	+	5.88273i	0.241169	+	0.241169i
$596$		0			0
$597$	−12.6614	+	18.8270i	−0.518198	+	0.770539i
$598$		0			0
$599$			29.8079i			1.21792i	0.793201	+	0.608959i	$0.208413\pi$
$599$			29.8079i			1.21792i	−0.793201	+	0.608959i	$0.791587\pi$
$600$		0			0
$601$		−	32.8432i		−	1.33970i	−0.742495	−	0.669851i	$-0.766358\pi$
$601$		−	32.8432i		−	1.33970i	0.742495	−	0.669851i	$-0.233642\pi$
$602$		0			0
$603$	−13.2215	+	31.3872i	−0.538422	+	1.27818i
$604$		0			0
$605$	13.2658	+	13.2658i	0.539331	+	0.539331i
$606$		0			0
$607$		−	6.95597i		−	0.282334i	−0.989986	−	0.141167i	$-0.954915\pi$
$607$		−	6.95597i		−	0.282334i	0.989986	−	0.141167i	$-0.0450855\pi$
$608$		0			0
$609$	−17.4948	+	3.42557i	−0.708927	+	0.138811i
$610$		0			0
$611$	−12.1602	+	12.1602i	−0.491947	+	0.491947i
$612$		0			0
$613$	−13.5389	−	13.5389i	−0.546830	−	0.546830i	0.378693	−	0.925522i	$-0.376374\pi$
$613$	−13.5389	−	13.5389i	−0.546830	−	0.546830i	−0.925522	+	0.378693i	$0.876374\pi$
$614$		0			0
$615$	−7.55691	−	38.5942i	−0.304724	−	1.55627i
$616$		0			0
$617$	−8.91891			−0.359062			−0.179531	−	0.983752i	$-0.557458\pi$
$617$	−8.91891			−0.359062			−0.179531	+	0.983752i	$0.557458\pi$
$618$		0			0
$619$	1.64658	−	1.64658i	0.0661818	−	0.0661818i	−0.673241	−	0.739423i	$-0.735098\pi$
$619$	1.64658	−	1.64658i	0.0661818	−	0.0661818i	0.739423	+	0.673241i	$0.235098\pi$
$620$		0			0
$621$	−2.39734	+	11.5114i	−0.0962018	+	0.461936i
$622$		0			0
$623$	16.5367			0.662531
$624$		0			0
$625$	24.7034			0.988136
$626$		0			0
$627$	12.2890	+	8.26451i	0.490774	+	0.330053i
$628$		0			0
$629$	−3.84014	+	3.84014i	−0.153116	+	0.153116i
$630$		0			0
$631$	−19.2457			−0.766159			−0.383080	−	0.923715i	$-0.625137\pi$
$631$	−19.2457			−0.766159			−0.383080	+	0.923715i	$0.625137\pi$
$632$		0			0
$633$	−20.3622	+	3.98701i	−0.809324	+	0.158469i
$634$		0			0
$635$	11.6710	+	11.6710i	0.463149	+	0.463149i
$636$		0			0
$637$	6.30777	−	6.30777i	0.249923	−	0.249923i
$638$		0			0
$639$	30.8271	−	12.5535i	1.21950	−	0.496608i
$640$		0			0
$641$		−	16.6343i		−	0.657016i	−0.944501	−	0.328508i	$-0.893454\pi$
$641$		−	16.6343i		−	0.657016i	0.944501	−	0.328508i	$-0.106546\pi$
$642$		0			0
$643$	4.77502	+	4.77502i	0.188308	+	0.188308i	0.794964	−	0.606656i	$-0.207489\pi$
$643$	4.77502	+	4.77502i	0.188308	+	0.188308i	−0.606656	+	0.794964i	$0.707489\pi$
$644$		0			0
$645$	17.0722	+	11.4813i	0.672217	+	0.452075i
$646$		0			0
$647$			48.2095i			1.89531i	0.319293	+	0.947656i	$0.396555\pi$
$647$			48.2095i			1.89531i	−0.319293	+	0.947656i	$0.603445\pi$
$648$		0			0
$649$			8.78801i			0.344960i
$650$		0			0
$651$	4.22752	+	2.84306i	0.165689	+	0.111428i
$652$		0			0
$653$	−24.2281	−	24.2281i	−0.948121	−	0.948121i	0.0505983	−	0.998719i	$-0.483887\pi$
$653$	−24.2281	−	24.2281i	−0.948121	−	0.948121i	−0.998719	+	0.0505983i	$0.983887\pi$
$654$		0			0
$655$			12.2086i			0.477028i
$656$		0			0
$657$	17.7294	−	7.21979i	0.691689	−	0.281671i
$658$		0			0
$659$	−9.47442	+	9.47442i	−0.369071	+	0.369071i	−0.867138	−	0.498067i	$-0.834043\pi$
$659$	−9.47442	+	9.47442i	−0.369071	+	0.369071i	0.498067	+	0.867138i	$0.334043\pi$
$660$		0			0
$661$	23.0406	+	23.0406i	0.896175	+	0.896175i	0.995095	−	0.0989204i	$-0.0315389\pi$
$661$	23.0406	+	23.0406i	0.896175	+	0.896175i	−0.0989204	+	0.995095i	$0.531539\pi$
$662$		0			0
$663$	12.9966	−	2.54479i	0.504745	−	0.0988313i
$664$		0			0
$665$	26.7159			1.03600
$666$		0			0
$667$	7.32238	−	7.32238i	0.283524	−	0.283524i
$668$		0			0
$669$	31.0039	+	20.8506i	1.19868	+	0.806130i
$670$		0			0
$671$	−9.48269			−0.366075
$672$		0			0
$673$	29.7846			1.14811			0.574055	−	0.818816i	$-0.305369\pi$
$673$	29.7846			1.14811			0.574055	+	0.818816i	$0.305369\pi$
$674$		0			0
$675$	−0.0621166	+	0.298267i	−0.00239087	+	0.0114803i
$676$		0			0
$677$	5.59631	−	5.59631i	0.215084	−	0.215084i	−0.591339	−	0.806423i	$-0.701401\pi$
$677$	5.59631	−	5.59631i	0.215084	−	0.215084i	0.806423	+	0.591339i	$0.201401\pi$
$678$		0			0
$679$	12.7620			0.489762
$680$		0			0
$681$	−7.88503	−	40.2699i	−0.302155	−	1.54314i
$682$		0			0
$683$	−19.5790	−	19.5790i	−0.749168	−	0.749168i	0.225155	−	0.974323i	$-0.427711\pi$
$683$	−19.5790	−	19.5790i	−0.749168	−	0.749168i	−0.974323	+	0.225155i	$0.927711\pi$
$684$		0			0
$685$	−4.28973	+	4.28973i	−0.163902	+	0.163902i
$686$		0			0
$687$	−8.09231	+	1.58451i	−0.308741	+	0.0604529i
$688$		0			0
$689$			6.32248i			0.240867i
$690$		0			0
$691$	−3.98701	−	3.98701i	−0.151673	−	0.151673i	0.627192	−	0.778865i	$-0.284204\pi$
$691$	−3.98701	−	3.98701i	−0.151673	−	0.151673i	−0.778865	+	0.627192i	$0.784204\pi$
$692$		0			0
$693$	4.19129	−	9.94988i	0.159214	−	0.377965i
$694$		0			0
$695$			0.0867582i			0.00329093i
$696$		0			0
$697$			16.9966i			0.643791i
$698$		0			0
$699$	0.484574	−	0.720541i	0.0183283	−	0.0272534i
$700$		0			0
$701$	15.2117	+	15.2117i	0.574537	+	0.574537i	0.933393	−	0.358856i	$-0.116833\pi$
$701$	15.2117	+	15.2117i	0.574537	+	0.574537i	−0.358856	+	0.933393i	$0.616833\pi$
$702$		0			0
$703$			17.4396i			0.657749i
$704$		0			0
$705$	−2.76891	−	14.1412i	−0.104283	−	0.532587i
$706$		0			0
$707$	23.1806	−	23.1806i	0.871796	−	0.871796i
$708$		0			0
$709$	20.3009	+	20.3009i	0.762416	+	0.762416i	0.976759	−	0.214342i	$-0.0687608\pi$
$709$	20.3009	+	20.3009i	0.762416	+	0.762416i	−0.214342	+	0.976759i	$0.568761\pi$
$710$		0			0
$711$	7.48024	−	3.04612i	0.280531	−	0.114238i
$712$		0			0
$713$	−2.95936			−0.110829
$714$		0			0
$715$	−11.5569	+	11.5569i	−0.432204	+	0.432204i
$716$		0			0
$717$	29.4405	−	43.7768i	1.09948	−	1.63488i
$718$		0			0
$719$	3.52314			0.131391			0.0656954	−	0.997840i	$-0.479073\pi$
$719$	3.52314			0.131391			0.0656954	+	0.997840i	$0.479073\pi$
$720$		0			0
$721$	−18.2897			−0.681145
$722$		0			0
$723$	14.9770	−	22.2702i	0.557000	−	0.828236i
$724$		0			0
$725$	0.189728	−	0.189728i	0.00704631	−	0.00704631i
$726$		0			0
$727$	−20.3664			−0.755348			−0.377674	−	0.925939i	$-0.623276\pi$
$727$	−20.3664			−0.755348			−0.377674	+	0.925939i	$0.623276\pi$
$728$		0			0
$729$	24.7553	+	10.7785i	0.916863	+	0.399202i
$730$		0			0
$731$	−6.28736	−	6.28736i	−0.232547	−	0.232547i
$732$		0			0
$733$	2.48024	−	2.48024i	0.0916096	−	0.0916096i	−0.659817	−	0.751426i	$-0.729366\pi$
$733$	2.48024	−	2.48024i	0.0916096	−	0.0916096i	0.751426	+	0.659817i	$0.229366\pi$
$734$		0			0
$735$	1.43630	+	7.33537i	0.0529787	+	0.270569i
$736$		0			0
$737$			18.1656i			0.669140i
$738$		0			0
$739$	−15.7931	−	15.7931i	−0.580957	−	0.580957i	0.354209	−	0.935166i	$-0.384750\pi$
$739$	−15.7931	−	15.7931i	−0.580957	−	0.580957i	−0.935166	+	0.354209i	$0.884750\pi$
$740$		0			0
$741$	23.7329	−	35.2898i	0.871849	−	1.29640i
$742$		0			0
$743$		−	38.5942i		−	1.41588i	−0.706271	−	0.707941i	$-0.749624\pi$
$743$		−	38.5942i		−	1.41588i	0.706271	−	0.707941i	$-0.250376\pi$
$744$		0			0
$745$			39.5139i			1.44768i
$746$		0			0
$747$	10.2093	+	4.30055i	0.373537	+	0.157349i
$748$		0			0
$749$	−5.40658	−	5.40658i	−0.197552	−	0.197552i
$750$		0			0
$751$			17.6527i			0.644156i	0.946713	+	0.322078i	$0.104381\pi$
$751$			17.6527i			0.644156i	−0.946713	+	0.322078i	$0.895619\pi$
$752$		0			0
$753$	−29.3906	+	5.75481i	−1.07105	+	0.209717i
$754$		0			0
$755$	26.5086	−	26.5086i	0.964747	−	0.964747i
$756$		0			0
$757$	−32.7440	−	32.7440i	−1.19010	−	1.19010i	−0.977039	−	0.213062i	$-0.931657\pi$
$757$	−32.7440	−	32.7440i	−1.19010	−	1.19010i	−0.213062	−	0.977039i	$-0.568343\pi$
$758$		0			0
$759$	1.20512	+	6.15468i	0.0437429	+	0.223401i
$760$		0			0
$761$	6.69113			0.242553			0.121277	−	0.992619i	$-0.461301\pi$
$761$	6.69113			0.242553			0.121277	+	0.992619i	$0.461301\pi$
$762$		0			0
$763$	−20.0698	+	20.0698i	−0.726576	+	0.726576i
$764$		0			0
$765$	−4.30783	+	10.2265i	−0.155750	+	0.369741i
$766$		0			0
$767$	25.2362			0.911227
$768$		0			0
$769$	−5.03265			−0.181482			−0.0907411	−	0.995875i	$-0.528924\pi$
$769$	−5.03265			−0.181482			−0.0907411	+	0.995875i	$0.528924\pi$
$770$		0			0
$771$	−10.7581	−	7.23499i	−0.387445	−	0.260562i
$772$		0			0
$773$	10.6859	−	10.6859i	0.384344	−	0.384344i	−0.488320	−	0.872665i	$-0.662390\pi$
$773$	10.6859	−	10.6859i	0.384344	−	0.384344i	0.872665	+	0.488320i	$0.162390\pi$
$774$		0			0
$775$	−0.0766789			−0.00275439
$776$		0			0
$777$	12.4772	−	2.44309i	0.447616	−	0.0876452i
$778$		0			0
$779$	38.5942	+	38.5942i	1.38278	+	1.38278i
$780$		0			0
$781$	12.5535	−	12.5535i	0.449199	−	0.449199i
$782$		0			0
$783$	−13.0327	−	19.8888i	−0.465750	−	0.710769i
$784$		0			0
$785$		−	16.8703i		−	0.602126i
$786$		0			0
$787$	−16.0974	−	16.0974i	−0.573810	−	0.573810i	0.359381	−	0.933191i	$-0.382988\pi$
$787$	−16.0974	−	16.0974i	−0.573810	−	0.573810i	−0.933191	+	0.359381i	$0.882988\pi$
$788$		0			0
$789$	−14.7548	−	9.92281i	−0.525285	−	0.353262i
$790$		0			0
$791$		−	35.7675i		−	1.27175i
$792$		0			0
$793$			27.2311i			0.967005i
$794$		0			0
$795$	−4.39606	−	2.95641i	−0.155912	−	0.104853i
$796$		0			0
$797$	2.63695	+	2.63695i	0.0934055	+	0.0934055i	0.752266	−	0.658860i	$-0.228961\pi$
$797$	2.63695	+	2.63695i	0.0934055	+	0.0934055i	−0.658860	+	0.752266i	$0.728961\pi$
$798$		0			0
$799$			6.22766i			0.220319i
$800$		0			0
$801$	8.31894	+	20.4285i	0.293935	+	0.721806i
$802$		0			0
$803$	7.21979	−	7.21979i	0.254781	−	0.254781i
$804$		0			0
$805$	8.00000	+	8.00000i	0.281963	+	0.281963i
$806$		0			0
$807$	6.65775	−	1.30362i	0.234364	−	0.0458896i
$808$		0			0
$809$	−6.62090			−0.232778			−0.116389	−	0.993204i	$-0.537132\pi$
$809$	−6.62090			−0.232778			−0.116389	+	0.993204i	$0.537132\pi$
$810$		0			0
$811$	−4.01299	+	4.01299i	−0.140915	+	0.140915i	−0.774045	−	0.633130i	$-0.781770\pi$
$811$	−4.01299	+	4.01299i	−0.140915	+	0.140915i	0.633130	+	0.774045i	$0.281770\pi$
$812$		0			0
$813$	−41.2284	−	27.7267i	−1.44594	−	0.972417i
$814$		0			0
$815$	−27.5859			−0.966291
$816$		0			0
$817$	−28.5535			−0.998960
$818$		0			0
$819$	−28.5727	−	12.0360i	−0.998411	−	0.420571i
$820$		0			0
$821$	−7.91085	+	7.91085i	−0.276090	+	0.276090i	−0.831546	−	0.555456i	$-0.812544\pi$
$821$	−7.91085	+	7.91085i	−0.276090	+	0.276090i	0.555456	+	0.831546i	$0.312544\pi$
$822$		0			0
$823$	44.9751			1.56773			0.783866	−	0.620930i	$-0.213245\pi$
$823$	44.9751			1.56773			0.783866	+	0.620930i	$0.213245\pi$
$824$		0			0
$825$	0.0312253	+	0.159472i	0.00108713	+	0.00555210i
$826$		0			0
$827$	−9.75631	−	9.75631i	−0.339260	−	0.339260i	0.516829	−	0.856089i	$-0.327112\pi$
$827$	−9.75631	−	9.75631i	−0.339260	−	0.339260i	−0.856089	+	0.516829i	$0.827112\pi$
$828$		0			0
$829$	18.6336	−	18.6336i	0.647171	−	0.647171i	−0.305137	−	0.952308i	$-0.598702\pi$
$829$	18.6336	−	18.6336i	0.647171	−	0.647171i	0.952308	+	0.305137i	$0.0987023\pi$
$830$		0			0
$831$	1.93763	−	0.379397i	0.0672156	−	0.0131611i
$832$		0			0
$833$		−	3.23044i		−	0.111928i
$834$		0			0
$835$	26.6707	+	26.6707i	0.922979	+	0.922979i
$836$		0			0
$837$	−1.38547	+	6.65266i	−0.0478888	+	0.229949i
$838$		0			0
$839$			37.8109i			1.30538i	0.757626	+	0.652689i	$0.226359\pi$
$839$			37.8109i			1.30538i	−0.757626	+	0.652689i	$0.773641\pi$
$840$		0			0
$841$		−	8.05863i		−	0.277884i
$842$		0			0
$843$	21.5767	−	32.0837i	0.743142	−	1.10502i
$844$		0			0
$845$	12.7536	+	12.7536i	0.438739	+	0.438739i
$846$		0			0
$847$			18.9820i			0.652228i
$848$		0			0
$849$	−3.80444	−	19.4298i	−0.130568	−	0.666828i
$850$		0			0
$851$	−5.22225	+	5.22225i	−0.179017	+	0.179017i
$852$		0			0
$853$	24.0992	+	24.0992i	0.825142	+	0.825142i	0.986840	−	0.161699i	$-0.0516972\pi$
$853$	24.0992	+	24.0992i	0.825142	+	0.825142i	−0.161699	+	0.986840i	$0.551697\pi$
$854$		0			0
$855$	13.4396	+	33.0033i	0.459626	+	1.12869i
$856$		0			0
$857$	−0.794026			−0.0271234			−0.0135617	−	0.999908i	$-0.504317\pi$
$857$	−0.794026			−0.0271234			−0.0135617	+	0.999908i	$0.504317\pi$
$858$		0			0
$859$	−2.65775	+	2.65775i	−0.0906814	+	0.0906814i	−0.750992	−	0.660311i	$-0.770424\pi$
$859$	−2.65775	+	2.65775i	−0.0906814	+	0.0906814i	0.660311	+	0.750992i	$0.270424\pi$
$860$		0			0
$861$	22.2055	−	33.0187i	0.756762	−	1.12527i
$862$		0			0
$863$	−21.4069			−0.728699			−0.364349	−	0.931262i	$-0.618709\pi$
$863$	−21.4069			−0.728699			−0.364349	+	0.931262i	$0.618709\pi$
$864$		0			0
$865$	−51.2794			−1.74355
$866$		0			0
$867$	−13.7555	+	20.4538i	−0.467161	+	0.694648i
$868$		0			0
$869$	3.04612	−	3.04612i	0.103332	−	0.103332i
$870$		0			0
$871$	52.1656			1.76756
$872$		0			0
$873$	6.42004	+	15.7655i	0.217286	+	0.533580i
$874$		0			0
$875$	17.8837	+	17.8837i	0.604581	+	0.604581i
$876$		0			0
$877$	−20.0923	+	20.0923i	−0.678470	+	0.678470i	−0.959654	−	0.281184i	$-0.909273\pi$
$877$	−20.0923	+	20.0923i	−0.678470	+	0.678470i	0.281184	+	0.959654i	$0.409273\pi$
$878$		0			0
$879$	3.00274	+	15.3354i	0.101280	+	0.517249i
$880$		0			0
$881$		−	10.8132i		−	0.364305i	−0.983270	−	0.182152i	$-0.941694\pi$
$881$		−	10.8132i		−	0.364305i	0.983270	−	0.182152i	$-0.0583064\pi$
$882$		0			0
$883$	−12.5665	−	12.5665i	−0.422895	−	0.422895i	0.463304	−	0.886199i	$-0.346664\pi$
$883$	−12.5665	−	12.5665i	−0.422895	−	0.422895i	−0.886199	+	0.463304i	$0.846664\pi$
$884$		0			0
$885$	−11.8005	+	17.5469i	−0.396671	+	0.589833i
$886$		0			0
$887$		−	12.0977i		−	0.406201i	−0.979158	−	0.203101i	$-0.934898\pi$
$887$		−	12.0977i		−	0.406201i	0.979158	−	0.203101i	$-0.0651018\pi$
$888$		0			0
$889$			16.7000i			0.560099i
$890$		0			0
$891$	14.4000	+	0.172302i	0.482417	+	0.00577235i
$892$		0			0
$893$	14.1412	+	14.1412i	0.473216	+	0.473216i
$894$		0			0
$895$			4.20855i			0.140676i
$896$		0			0
$897$	17.6742	−	3.46069i	0.590124	−	0.115549i
$898$		0			0
$899$	4.23175	−	4.23175i	0.141137	−	0.141137i
$900$		0			0
$901$	1.61899	+	1.61899i	0.0539362	+	0.0539362i
$902$		0			0
$903$	4.00000	+	20.4285i	0.133112	+	0.679819i
$904$		0			0
$905$	−32.2092			−1.07067
$906$		0			0
$907$	14.3388	−	14.3388i	0.476112	−	0.476112i	−0.427774	−	0.903886i	$-0.640702\pi$
$907$	14.3388	−	14.3388i	0.476112	−	0.476112i	0.903886	+	0.427774i	$0.140702\pi$
$908$		0			0
$909$	40.2972	+	16.9748i	1.33657	+	0.563018i
$910$		0			0
$911$	28.0629			0.929765			0.464882	−	0.885372i	$-0.346097\pi$
$911$	28.0629			0.929765			0.464882	+	0.885372i	$0.346097\pi$
$912$		0			0
$913$	5.90871			0.195550
$914$		0			0
$915$	−18.9340	−	12.7334i	−0.625937	−	0.420952i
$916$		0			0
$917$	−8.73458	+	8.73458i	−0.288441	+	0.288441i
$918$		0			0
$919$	−25.4734			−0.840289			−0.420144	−	0.907457i	$-0.638021\pi$
$919$	−25.4734			−0.840289			−0.420144	+	0.907457i	$0.638021\pi$
$920$		0			0
$921$	−15.8364	+	3.10084i	−0.521827	+	0.102176i
$922$		0			0
$923$	−36.0494	−	36.0494i	−1.18658	−	1.18658i
$924$		0			0
$925$	−0.135312	+	0.135312i	−0.00444903	+	0.00444903i
$926$		0			0
$927$	−9.20080	−	22.5941i	−0.302194	−	0.742086i
$928$		0			0
$929$			43.3502i			1.42227i	0.703054	+	0.711137i	$0.251819\pi$
$929$			43.3502i			1.42227i	−0.703054	+	0.711137i	$0.748181\pi$
$930$		0			0
$931$	−7.33537	−	7.33537i	−0.240407	−	0.240407i
$932$		0			0
$933$	−13.6951	−	9.21016i	−0.448358	−	0.301527i
$934$		0			0
$935$			5.91872i			0.193563i
$936$		0			0
$937$		−	15.5500i		−	0.507998i	−0.967205	−	0.253999i	$-0.918254\pi$
$937$		−	15.5500i		−	0.507998i	0.967205	−	0.253999i	$-0.0817459\pi$
$938$		0			0
$939$	−36.1745	−	24.3279i	−1.18051	−	0.793910i
$940$		0			0
$941$	1.85373	+	1.85373i	0.0604299	+	0.0604299i	0.736676	−	0.676246i	$-0.236394\pi$
$941$	1.85373	+	1.85373i	0.0604299	+	0.0604299i	−0.676246	+	0.736676i	$0.736394\pi$
$942$		0			0
$943$			23.1138i			0.752690i
$944$		0			0
$945$	21.7294	−	14.2387i	0.706857	−	0.463186i
$946$		0			0
$947$	−31.2499	+	31.2499i	−1.01549	+	1.01549i	−0.0156087	+	0.999878i	$0.504969\pi$
$947$	−31.2499	+	31.2499i	−1.01549	+	1.01549i	−0.999878	+	0.0156087i	$0.995031\pi$
$948$		0			0
$949$	−20.7328	−	20.7328i	−0.673016	−	0.673016i
$950$		0			0
$951$	−37.3285	+	7.30909i	−1.21046	+	0.237014i
$952$		0			0
$953$	−48.9411			−1.58536			−0.792679	−	0.609639i	$-0.791314\pi$
$953$	−48.9411			−1.58536			−0.792679	+	0.609639i	$0.791314\pi$
$954$		0			0
$955$	−38.5726	+	38.5726i	−1.24818	+	1.24818i
$956$		0			0
$957$	−10.5242	−	7.07766i	−0.340199	−	0.228788i
$958$		0			0
$959$	−6.13815			−0.198211
$960$		0			0
$961$	29.2897			0.944830
$962$		0			0
$963$	3.95915	−	9.39880i	0.127582	−	0.302872i
$964$		0			0
$965$	−13.1736	+	13.1736i	−0.424074	+	0.424074i
$966$		0			0
$967$	−18.5129			−0.595334			−0.297667	−	0.954670i	$-0.596209\pi$
$967$	−18.5129			−0.595334			−0.297667	+	0.954670i	$0.596209\pi$
$968$		0			0
$969$	−2.95936	−	15.1138i	−0.0950683	−	0.485526i
$970$		0			0
$971$	0.0663404	+	0.0663404i	0.00212897	+	0.00212897i	0.708170	−	0.706041i	$-0.249521\pi$
$971$	0.0663404	+	0.0663404i	0.00212897	+	0.00212897i	−0.706041	+	0.708170i	$0.749521\pi$
$972$		0			0
$973$	−0.0620710	+	0.0620710i	−0.00198991	+	0.00198991i
$974$		0			0
$975$	0.457950	−	0.0896687i	0.0146661	−	0.00287170i
$976$		0			0
$977$			3.42557i			0.109594i	0.998498	+	0.0547969i	$0.0174511\pi$
$977$			3.42557i			0.109594i	−0.998498	+	0.0547969i	$0.982549\pi$
$978$		0			0
$979$	8.31894	+	8.31894i	0.265875	+	0.265875i
$980$		0			0
$981$	−34.8893	−	14.6968i	−1.11393	−	0.469232i
$982$		0			0
$983$		−	30.5911i		−	0.975706i	−0.872926	−	0.487853i	$-0.837780\pi$
$983$		−	30.5911i		−	0.975706i	0.872926	−	0.487853i	$-0.162220\pi$
$984$		0			0
$985$			4.05520i			0.129209i
$986$		0			0
$987$	8.13626	−	12.0983i	0.258980	−	0.385092i
$988$		0			0
$989$	−8.55026	−	8.55026i	−0.271882	−	0.271882i
$990$		0			0
$991$		−	24.2975i		−	0.771834i	−0.922533	−	0.385917i	$-0.873885\pi$
$991$		−	24.2975i		−	0.771834i	0.922533	−	0.385917i	$-0.126115\pi$
$992$		0			0
$993$	−1.21811	−	6.22102i	−0.0386554	−	0.197418i
$994$		0			0
$995$	−20.5899	+	20.5899i	−0.652743	+	0.652743i
$996$		0			0
$997$	10.3078	+	10.3078i	0.326450	+	0.326450i	0.851235	−	0.524785i	$-0.175854\pi$
$997$	10.3078	+	10.3078i	0.326450	+	0.326450i	−0.524785	+	0.851235i	$0.675854\pi$
$998$		0			0
$999$	9.29478	+	14.1845i	0.294074	+	0.448779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.k.a.143.2		12
3.2	odd	2	inner	192.2.k.a.143.5		12
4.3	odd	2		48.2.k.a.11.3	✓	12
8.3	odd	2		384.2.k.b.287.2		12
8.5	even	2		384.2.k.a.287.5		12
12.11	even	2		48.2.k.a.11.4	yes	12
16.3	odd	4	inner	192.2.k.a.47.5		12
16.5	even	4		384.2.k.b.95.5		12
16.11	odd	4		384.2.k.a.95.2		12
16.13	even	4		48.2.k.a.35.4	yes	12
24.5	odd	2		384.2.k.a.287.2		12
24.11	even	2		384.2.k.b.287.5		12
48.5	odd	4		384.2.k.b.95.2		12
48.11	even	4		384.2.k.a.95.5		12
48.29	odd	4		48.2.k.a.35.3	yes	12
48.35	even	4	inner	192.2.k.a.47.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.2.k.a.11.3	✓	12	4.3	odd	2
48.2.k.a.11.4	yes	12	12.11	even	2
48.2.k.a.35.3	yes	12	48.29	odd	4
48.2.k.a.35.4	yes	12	16.13	even	4
192.2.k.a.47.2		12	48.35	even	4	inner
192.2.k.a.47.5		12	16.3	odd	4	inner
192.2.k.a.143.2		12	1.1	even	1	trivial
192.2.k.a.143.5		12	3.2	odd	2	inner
384.2.k.a.95.2		12	16.11	odd	4
384.2.k.a.95.5		12	48.11	even	4
384.2.k.a.287.2		12	24.5	odd	2
384.2.k.a.287.5		12	8.5	even	2
384.2.k.b.95.2		12	48.5	odd	4
384.2.k.b.95.5		12	16.5	even	4
384.2.k.b.287.2		12	8.3	odd	2
384.2.k.b.287.5		12	24.11	even	2

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.k (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.966579 + 1.43726i) q^{3} +(-1.57184 + 1.57184i) q^{5} -2.24914 q^{7} +(-1.13145 - 2.77846i) q^{9} +O(q^{10})\)	\(q+(-0.966579 + 1.43726i) q^{3} +(-1.57184 + 1.57184i) q^{5} -2.24914 q^{7} +(-1.13145 - 2.77846i) q^{9} +(-1.13145 - 1.13145i) q^{11} +(-3.24914 + 3.24914i) q^{13} +(-0.739839 - 3.77846i) q^{15} +1.66400i q^{17} +(3.77846 + 3.77846i) q^{19} +(2.17397 - 3.23261i) q^{21} +2.26290i q^{23} +0.0586332i q^{25} +(5.08701 + 1.05941i) q^{27} +(-3.23584 - 3.23584i) q^{29} +1.30777i q^{31} +(2.71982 - 0.532554i) q^{33} +(3.53529 - 3.53529i) q^{35} +(2.30777 + 2.30777i) q^{37} +(-1.52932 - 7.81042i) q^{39} +10.2143 q^{41} +(-3.77846 + 3.77846i) q^{43} +(6.14575 + 2.58884i) q^{45} +3.74258 q^{47} -1.94137 q^{49} +(-2.39161 - 1.60839i) q^{51} +(0.972946 - 0.972946i) q^{53} +3.55691 q^{55} +(-9.08281 + 1.77846i) q^{57} +(-3.88352 - 3.88352i) q^{59} +(4.19051 - 4.19051i) q^{61} +(2.54479 + 6.24914i) q^{63} -10.2143i q^{65} +(-8.02760 - 8.02760i) q^{67} +(-3.25238 - 2.18727i) q^{69} +11.0950i q^{71} +6.38101i q^{73} +(-0.0842713 - 0.0566736i) q^{75} +(2.54479 + 2.54479i) q^{77} +2.69223i q^{79} +(-6.43965 + 6.28736i) q^{81} +(-2.61113 + 2.61113i) q^{83} +(-2.61555 - 2.61555i) q^{85} +(7.77846 - 1.52306i) q^{87} -7.35247 q^{89} +(7.30777 - 7.30777i) q^{91} +(-1.87961 - 1.26407i) q^{93} -11.8783 q^{95} -5.67418 q^{97} +(-1.86351 + 4.42386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} + 8 q^{7}+O(q^{10}) \) 12 * q + 2 * q^3 + 8 * q^7	\( 12 q + 2 q^{3} + 8 q^{7} - 4 q^{13} + 12 q^{19} - 8 q^{21} - 10 q^{27} - 4 q^{33} - 4 q^{37} - 20 q^{39} - 12 q^{43} - 12 q^{45} - 20 q^{49} - 24 q^{51} - 24 q^{55} + 12 q^{61} - 28 q^{67} + 4 q^{69} + 34 q^{75} - 4 q^{81} + 32 q^{85} + 60 q^{87} + 56 q^{91} + 28 q^{93} - 8 q^{97} + 52 q^{99}+O(q^{100}) \) 12 * q + 2 * q^3 + 8 * q^7 - 4 * q^13 + 12 * q^19 - 8 * q^21 - 10 * q^27 - 4 * q^33 - 4 * q^37 - 20 * q^39 - 12 * q^43 - 12 * q^45 - 20 * q^49 - 24 * q^51 - 24 * q^55 + 12 * q^61 - 28 * q^67 + 4 * q^69 + 34 * q^75 - 4 * q^81 + 32 * q^85 + 60 * q^87 + 56 * q^91 + 28 * q^93 - 8 * q^97 + 52 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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