LMFDB - Embedded newform 1344.2.u.a.1231.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(559,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 2]))

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

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

chi := DirichletCharacter("1344.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.u (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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1231.5
Character	$\chi$	$=$	1344.1231
Dual form			1344.2.u.a.559.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(1.45584 - 1.45584i) q^{5} +(2.11390 + 1.59104i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(1.45584 - 1.45584i) q^{5} +(2.11390 + 1.59104i) q^{7} -1.00000i q^{9} +(2.03232 - 2.03232i) q^{11} +(4.25498 + 4.25498i) q^{13} +2.05887i q^{15} -2.62164i q^{17} +(-2.19851 + 2.19851i) q^{19} +(-2.61979 + 0.369721i) q^{21} -4.12640 q^{23} +0.761053i q^{25} +(0.707107 + 0.707107i) q^{27} +(5.04401 - 5.04401i) q^{29} +1.60368 q^{31} +2.87413i q^{33} +(5.39381 - 0.761208i) q^{35} +(-6.27770 - 6.27770i) q^{37} -6.01745 q^{39} +2.45431 q^{41} +(5.72710 - 5.72710i) q^{43} +(-1.45584 - 1.45584i) q^{45} -6.44501 q^{47} +(1.93718 + 6.72661i) q^{49} +(1.85378 + 1.85378i) q^{51} +(5.91522 + 5.91522i) q^{53} -5.91746i q^{55} -3.10916i q^{57} +(5.64190 + 5.64190i) q^{59} +(9.13901 + 9.13901i) q^{61} +(1.59104 - 2.11390i) q^{63} +12.3891 q^{65} +(4.56801 + 4.56801i) q^{67} +(2.91780 - 2.91780i) q^{69} +1.11894 q^{71} -4.88201 q^{73} +(-0.538145 - 0.538145i) q^{75} +(7.52962 - 1.06263i) q^{77} -12.6543i q^{79} -1.00000 q^{81} +(-7.46008 + 7.46008i) q^{83} +(-3.81668 - 3.81668i) q^{85} +7.13330i q^{87} -8.42954 q^{89} +(2.22478 + 15.7645i) q^{91} +(-1.13398 + 1.13398i) q^{93} +6.40137i q^{95} +7.55912i q^{97} +(-2.03232 - 2.03232i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 8 q^{11} + 16 q^{23} + 16 q^{29} - 24 q^{35} + 16 q^{37} + 8 q^{43} + 16 q^{53} - 56 q^{67} + 128 q^{71} - 64 q^{81} - 8 q^{91} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^11 + 16 * q^23 + 16 * q^29 - 24 * q^35 + 16 * q^37 + 8 * q^43 + 16 * q^53 - 56 * q^67 + 128 * q^71 - 64 * q^81 - 8 * q^91 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	1.45584	−	1.45584i	0.651072	−	0.651072i	−0.302179	−	0.953251i	$-0.597714\pi$
$5$	1.45584	−	1.45584i	0.651072	−	0.651072i	0.953251	+	0.302179i	$0.0977141\pi$
$6$		0			0
$7$	2.11390	+	1.59104i	0.798981	+	0.601357i
$7$	2.11390	+	1.59104i	0.798981	+	0.601357i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	2.03232	−	2.03232i	0.612767	−	0.612767i	−0.330899	−	0.943666i	$-0.607352\pi$
$11$	2.03232	−	2.03232i	0.612767	−	0.612767i	0.943666	+	0.330899i	$0.107352\pi$
$12$		0			0
$13$	4.25498	+	4.25498i	1.18012	+	1.18012i	0.979713	+	0.200405i	$0.0642258\pi$
$13$	4.25498	+	4.25498i	1.18012	+	1.18012i	0.200405	+	0.979713i	$0.435774\pi$
$14$		0			0
$15$			2.05887i			0.531598i
$16$		0			0
$17$		−	2.62164i		−	0.635840i	−0.948118	−	0.317920i	$-0.897016\pi$
$17$		−	2.62164i		−	0.635840i	0.948118	−	0.317920i	$-0.102984\pi$
$18$		0			0
$19$	−2.19851	+	2.19851i	−0.504373	+	0.504373i	−0.912794	−	0.408421i	$-0.866080\pi$
$19$	−2.19851	+	2.19851i	−0.504373	+	0.504373i	0.408421	+	0.912794i	$0.366080\pi$
$20$		0			0
$21$	−2.61979	+	0.369721i	−0.571685	+	0.0806798i
$22$		0			0
$23$	−4.12640			−0.860413			−0.430206	−	0.902731i	$-0.641559\pi$
$23$	−4.12640			−0.860413			−0.430206	+	0.902731i	$0.641559\pi$
$24$		0			0
$25$			0.761053i			0.152211i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$	5.04401	−	5.04401i	0.936649	−	0.936649i	−0.0614609	−	0.998109i	$-0.519576\pi$
$29$	5.04401	−	5.04401i	0.936649	−	0.936649i	0.998109	+	0.0614609i	$0.0195760\pi$
$30$		0			0
$31$	1.60368			0.288030			0.144015	−	0.989575i	$-0.453999\pi$
$31$	1.60368			0.288030			0.144015	+	0.989575i	$0.453999\pi$
$32$		0			0
$33$			2.87413i			0.500322i
$34$		0			0
$35$	5.39381	−	0.761208i	0.911720	−	0.128668i
$36$		0			0
$37$	−6.27770	−	6.27770i	−1.03205	−	1.03205i	−0.999469	−	0.0325776i	$-0.989628\pi$
$37$	−6.27770	−	6.27770i	−1.03205	−	1.03205i	−0.0325776	−	0.999469i	$-0.510372\pi$
$38$		0			0
$39$	−6.01745			−0.963562
$40$		0			0
$41$	2.45431			0.383299			0.191650	−	0.981463i	$-0.438616\pi$
$41$	2.45431			0.383299			0.191650	+	0.981463i	$0.438616\pi$
$42$		0			0
$43$	5.72710	−	5.72710i	0.873375	−	0.873375i	−0.119463	−	0.992839i	$-0.538117\pi$
$43$	5.72710	−	5.72710i	0.873375	−	0.873375i	0.992839	+	0.119463i	$0.0381174\pi$
$44$		0			0
$45$	−1.45584	−	1.45584i	−0.217024	−	0.217024i
$46$		0			0
$47$	−6.44501			−0.940101			−0.470051	−	0.882640i	$-0.655764\pi$
$47$	−6.44501			−0.940101			−0.470051	+	0.882640i	$0.655764\pi$
$48$		0			0
$49$	1.93718	+	6.72661i	0.276741	+	0.960945i
$50$		0			0
$51$	1.85378	+	1.85378i	0.259581	+	0.259581i
$52$		0			0
$53$	5.91522	+	5.91522i	0.812518	+	0.812518i	0.985011	−	0.172493i	$-0.0551822\pi$
$53$	5.91522	+	5.91522i	0.812518	+	0.812518i	−0.172493	+	0.985011i	$0.555182\pi$
$54$		0			0
$55$		−	5.91746i		−	0.797911i
$56$		0			0
$57$		−	3.10916i		−	0.411819i
$58$		0			0
$59$	5.64190	+	5.64190i	0.734512	+	0.734512i	0.971510	−	0.236998i	$-0.0761634\pi$
$59$	5.64190	+	5.64190i	0.734512	+	0.734512i	−0.236998	+	0.971510i	$0.576163\pi$
$60$		0			0
$61$	9.13901	+	9.13901i	1.17013	+	1.17013i	0.982178	+	0.187952i	$0.0601851\pi$
$61$	9.13901	+	9.13901i	1.17013	+	1.17013i	0.187952	+	0.982178i	$0.439815\pi$
$62$		0			0
$63$	1.59104	−	2.11390i	0.200452	−	0.266327i
$64$		0			0
$65$	12.3891			1.53668
$66$		0			0
$67$	4.56801	+	4.56801i	0.558071	+	0.558071i	0.928758	−	0.370687i	$-0.120878\pi$
$67$	4.56801	+	4.56801i	0.558071	+	0.558071i	−0.370687	+	0.928758i	$0.620878\pi$
$68$		0			0
$69$	2.91780	−	2.91780i	0.351262	−	0.351262i
$70$		0			0
$71$	1.11894			0.132793			0.0663967	−	0.997793i	$-0.478850\pi$
$71$	1.11894			0.132793			0.0663967	+	0.997793i	$0.478850\pi$
$72$		0			0
$73$	−4.88201			−0.571396			−0.285698	−	0.958320i	$-0.592225\pi$
$73$	−4.88201			−0.571396			−0.285698	+	0.958320i	$0.592225\pi$
$74$		0			0
$75$	−0.538145	−	0.538145i	−0.0621397	−	0.0621397i
$76$		0			0
$77$	7.52962	−	1.06263i	0.858080	−	0.121098i
$78$		0			0
$79$		−	12.6543i		−	1.42373i	−0.702319	−	0.711863i	$-0.747852\pi$
$79$		−	12.6543i		−	1.42373i	0.702319	−	0.711863i	$-0.252148\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−7.46008	+	7.46008i	−0.818850	+	0.818850i	−0.985941	−	0.167091i	$-0.946563\pi$
$83$	−7.46008	+	7.46008i	−0.818850	+	0.818850i	0.167091	+	0.985941i	$0.446563\pi$
$84$		0			0
$85$	−3.81668	−	3.81668i	−0.413978	−	0.413978i
$86$		0			0
$87$			7.13330i			0.764770i
$88$		0			0
$89$	−8.42954			−0.893529			−0.446765	−	0.894652i	$-0.647424\pi$
$89$	−8.42954			−0.893529			−0.446765	+	0.894652i	$0.647424\pi$
$90$		0			0
$91$	2.22478	+	15.7645i	0.233220	+	1.65256i
$92$		0			0
$93$	−1.13398	+	1.13398i	−0.117588	+	0.117588i
$94$		0			0
$95$			6.40137i			0.656766i
$96$		0			0
$97$			7.55912i			0.767512i	0.923435	+	0.383756i	$0.125370\pi$
$97$			7.55912i			0.767512i	−0.923435	+	0.383756i	$0.874630\pi$
$98$		0			0
$99$	−2.03232	−	2.03232i	−0.204256	−	0.204256i
$100$		0			0
$101$	10.1032	−	10.1032i	1.00531	−	1.00531i	0.00531931	−	0.999986i	$-0.498307\pi$
$101$	10.1032	−	10.1032i	1.00531	−	1.00531i	0.999986	−	0.00531931i	$-0.00169320\pi$
$102$		0			0
$103$		−	12.6345i		−	1.24492i	−0.782653	−	0.622459i	$-0.786134\pi$
$103$		−	12.6345i		−	1.24492i	0.782653	−	0.622459i	$-0.213866\pi$
$104$		0			0
$105$	−3.27574	+	4.35226i	−0.319680	+	0.424737i
$106$		0			0
$107$	8.35660	−	8.35660i	0.807863	−	0.807863i	−0.176447	−	0.984310i	$-0.556460\pi$
$107$	8.35660	−	8.35660i	0.807863	−	0.807863i	0.984310	+	0.176447i	$0.0564604\pi$
$108$		0			0
$109$	−6.13023	+	6.13023i	−0.587169	+	0.587169i	−0.936864	−	0.349695i	$-0.886285\pi$
$109$	−6.13023	+	6.13023i	−0.587169	+	0.587169i	0.349695	+	0.936864i	$0.386285\pi$
$110$		0			0
$111$	8.87800			0.842663
$112$		0			0
$113$	−3.30678			−0.311075			−0.155538	−	0.987830i	$-0.549711\pi$
$113$	−3.30678			−0.311075			−0.155538	+	0.987830i	$0.549711\pi$
$114$		0			0
$115$	−6.00738	+	6.00738i	−0.560191	+	0.560191i
$116$		0			0
$117$	4.25498	−	4.25498i	0.393373	−	0.393373i
$118$		0			0
$119$	4.17113	−	5.54189i	0.382366	−	0.508024i
$120$		0			0
$121$			2.73937i			0.249034i
$122$		0			0
$123$	−1.73546	+	1.73546i	−0.156481	+	0.156481i
$124$		0			0
$125$	8.38718	+	8.38718i	0.750172	+	0.750172i
$126$		0			0
$127$		−	1.04445i		−	0.0926800i	−0.998926	−	0.0463400i	$-0.985244\pi$
$127$		−	1.04445i		−	0.0926800i	0.998926	−	0.0463400i	$-0.0147558\pi$
$128$		0			0
$129$			8.09935i			0.713108i
$130$		0			0
$131$	9.23515	−	9.23515i	0.806879	−	0.806879i	−0.177282	−	0.984160i	$-0.556730\pi$
$131$	9.23515	−	9.23515i	0.806879	−	0.806879i	0.984160	+	0.177282i	$0.0567303\pi$
$132$		0			0
$133$	−8.14536	+	1.14952i	−0.706292	+	0.0996764i
$134$		0			0
$135$	2.05887			0.177199
$136$		0			0
$137$			9.76694i			0.834446i	0.908804	+	0.417223i	$0.136997\pi$
$137$			9.76694i			0.834446i	−0.908804	+	0.417223i	$0.863003\pi$
$138$		0			0
$139$	11.3905	+	11.3905i	0.966129	+	0.966129i	0.999445	−	0.0333160i	$-0.0106068\pi$
$139$	11.3905	+	11.3905i	0.966129	+	0.966129i	−0.0333160	+	0.999445i	$0.510607\pi$
$140$		0			0
$141$	4.55731	−	4.55731i	0.383795	−	0.383795i
$142$		0			0
$143$	17.2949			1.44627
$144$		0			0
$145$		−	14.6865i		−	1.21965i
$146$		0			0
$147$	−6.12623	−	3.38664i	−0.505283	−	0.279325i
$148$		0			0
$149$	8.40150	+	8.40150i	0.688278	+	0.688278i	0.961851	−	0.273573i	$-0.0882056\pi$
$149$	8.40150	+	8.40150i	0.688278	+	0.688278i	−0.273573	+	0.961851i	$0.588206\pi$
$150$		0			0
$151$	0.335023			0.0272638			0.0136319	−	0.999907i	$-0.495661\pi$
$151$	0.335023			0.0272638			0.0136319	+	0.999907i	$0.495661\pi$
$152$		0			0
$153$	−2.62164			−0.211947
$154$		0			0
$155$	2.33471	−	2.33471i	0.187528	−	0.187528i
$156$		0			0
$157$	−15.1793	−	15.1793i	−1.21144	−	1.21144i	−0.970552	−	0.240891i	$-0.922560\pi$
$157$	−15.1793	−	15.1793i	−1.21144	−	1.21144i	−0.240891	−	0.970552i	$-0.577440\pi$
$158$		0			0
$159$	−8.36538			−0.663418
$160$		0			0
$161$	−8.72281	−	6.56526i	−0.687453	−	0.517415i
$162$		0			0
$163$	6.07238	+	6.07238i	0.475626	+	0.475626i	0.903729	−	0.428104i	$-0.140818\pi$
$163$	6.07238	+	6.07238i	0.475626	+	0.475626i	−0.428104	+	0.903729i	$0.640818\pi$
$164$		0			0
$165$	4.18428	+	4.18428i	0.325746	+	0.325746i
$166$		0			0
$167$			2.39755i			0.185528i	0.995688	+	0.0927641i	$0.0295703\pi$
$167$			2.39755i			0.185528i	−0.995688	+	0.0927641i	$0.970430\pi$
$168$		0			0
$169$			23.2097i			1.78536i
$170$		0			0
$171$	2.19851	+	2.19851i	0.168124	+	0.168124i
$172$		0			0
$173$	−11.7817	−	11.7817i	−0.895745	−	0.895745i	0.0993113	−	0.995056i	$-0.468336\pi$
$173$	−11.7817	−	11.7817i	−0.895745	−	0.895745i	−0.995056	+	0.0993113i	$0.968336\pi$
$174$		0			0
$175$	−1.21086	+	1.60879i	−0.0915328	+	0.121613i
$176$		0			0
$177$	−7.97885			−0.599727
$178$		0			0
$179$	4.98181	+	4.98181i	0.372358	+	0.372358i	0.868335	−	0.495977i	$-0.165190\pi$
$179$	4.98181	+	4.98181i	0.372358	+	0.372358i	−0.495977	+	0.868335i	$0.665190\pi$
$180$		0			0
$181$	6.14825	−	6.14825i	0.456996	−	0.456996i	−0.440672	−	0.897668i	$-0.645260\pi$
$181$	6.14825	−	6.14825i	0.456996	−	0.456996i	0.897668	+	0.440672i	$0.145260\pi$
$182$		0			0
$183$	−12.9245			−0.955408
$184$		0			0
$185$	−18.2787			−1.34387
$186$		0			0
$187$	−5.32800	−	5.32800i	−0.389622	−	0.389622i
$188$		0			0
$189$	0.369721	+	2.61979i	0.0268933	+	0.190562i
$190$		0			0
$191$		−	1.80175i		−	0.130370i	−0.997873	−	0.0651850i	$-0.979236\pi$
$191$		−	1.80175i		−	0.130370i	0.997873	−	0.0651850i	$-0.0207637\pi$
$192$		0			0
$193$	−14.7352			−1.06066			−0.530332	−	0.847790i	$-0.677933\pi$
$193$	−14.7352			−1.06066			−0.530332	+	0.847790i	$0.677933\pi$
$194$		0			0
$195$	−8.76045	+	8.76045i	−0.627349	+	0.627349i
$196$		0			0
$197$	−16.2693	−	16.2693i	−1.15914	−	1.15914i	−0.984662	−	0.174475i	$-0.944177\pi$
$197$	−16.2693	−	16.2693i	−1.15914	−	1.15914i	−0.174475	−	0.984662i	$-0.555823\pi$
$198$		0			0
$199$		−	4.58062i		−	0.324712i	−0.986732	−	0.162356i	$-0.948091\pi$
$199$		−	4.58062i		−	0.324712i	0.986732	−	0.162356i	$-0.0519092\pi$
$200$		0			0
$201$	−6.46014			−0.455663
$202$		0			0
$203$	18.6878	−	2.63733i	1.31162	−	0.185105i
$204$		0			0
$205$	3.57309	−	3.57309i	0.249556	−	0.249556i
$206$		0			0
$207$			4.12640i			0.286804i
$208$		0			0
$209$			8.93615i			0.618126i
$210$		0			0
$211$	−7.65114	−	7.65114i	−0.526727	−	0.526727i	0.392868	−	0.919595i	$-0.371483\pi$
$211$	−7.65114	−	7.65114i	−0.526727	−	0.526727i	−0.919595	+	0.392868i	$0.871483\pi$
$212$		0			0
$213$	−0.791207	+	0.791207i	−0.0542126	+	0.0542126i
$214$		0			0
$215$		−	16.6755i		−	1.13726i
$216$		0			0
$217$	3.39004	+	2.55153i	0.230131	+	0.173209i
$218$		0			0
$219$	3.45210	−	3.45210i	0.233272	−	0.233272i
$220$		0			0
$221$	11.1550	−	11.1550i	0.750366	−	0.750366i
$222$		0			0
$223$	−27.6669			−1.85271			−0.926357	−	0.376646i	$-0.877077\pi$
$223$	−27.6669			−1.85271			−0.926357	+	0.376646i	$0.877077\pi$
$224$		0			0
$225$	0.761053			0.0507368
$226$		0			0
$227$	−7.05607	+	7.05607i	−0.468328	+	0.468328i	−0.901372	−	0.433045i	$-0.857439\pi$
$227$	−7.05607	+	7.05607i	−0.468328	+	0.468328i	0.433045	+	0.901372i	$0.357439\pi$
$228$		0			0
$229$	−14.2353	+	14.2353i	−0.940697	+	0.940697i	−0.998337	−	0.0576403i	$-0.981642\pi$
$229$	−14.2353	+	14.2353i	−0.940697	+	0.940697i	0.0576403	+	0.998337i	$0.481642\pi$
$230$		0			0
$231$	−4.57286	+	6.07564i	−0.300872	+	0.399748i
$232$		0			0
$233$		−	10.1492i		−	0.664895i	−0.943122	−	0.332448i	$-0.892126\pi$
$233$		−	10.1492i		−	0.664895i	0.943122	−	0.332448i	$-0.107874\pi$
$234$		0			0
$235$	−9.38291	+	9.38291i	−0.612073	+	0.612073i
$236$		0			0
$237$	8.94798	+	8.94798i	0.581234	+	0.581234i
$238$		0			0
$239$			19.5587i			1.26514i	0.774501	+	0.632572i	$0.218001\pi$
$239$			19.5587i			1.26514i	−0.774501	+	0.632572i	$0.781999\pi$
$240$		0			0
$241$		−	7.34719i		−	0.473274i	−0.971598	−	0.236637i	$-0.923955\pi$
$241$		−	7.34719i		−	0.473274i	0.971598	−	0.236637i	$-0.0760452\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	12.6131	+	6.97265i	0.805822	+	0.445466i
$246$		0			0
$247$	−18.7092			−1.19044
$248$		0			0
$249$		−	10.5501i		−	0.668588i
$250$		0			0
$251$	−19.0912	−	19.0912i	−1.20502	−	1.20502i	−0.972619	−	0.232404i	$-0.925341\pi$
$251$	−19.0912	−	19.0912i	−1.20502	−	1.20502i	−0.232404	−	0.972619i	$-0.574659\pi$
$252$		0			0
$253$	−8.38615	+	8.38615i	−0.527232	+	0.527232i
$254$		0			0
$255$	5.39761			0.338011
$256$		0			0
$257$		−	17.7877i		−	1.10957i	−0.831995	−	0.554783i	$-0.812801\pi$
$257$		−	17.7877i		−	1.10957i	0.831995	−	0.554783i	$-0.187199\pi$
$258$		0			0
$259$	−3.28239	−	23.2585i	−0.203958	−	1.44521i
$260$		0			0
$261$	−5.04401	−	5.04401i	−0.312216	−	0.312216i
$262$		0			0
$263$	13.0906			0.807201			0.403601	−	0.914935i	$-0.367759\pi$
$263$	13.0906			0.807201			0.403601	+	0.914935i	$0.367759\pi$
$264$		0			0
$265$	17.2232			1.05802
$266$		0			0
$267$	5.96058	−	5.96058i	0.364782	−	0.364782i
$268$		0			0
$269$	−13.7294	−	13.7294i	−0.837096	−	0.837096i	0.151380	−	0.988476i	$-0.451628\pi$
$269$	−13.7294	−	13.7294i	−0.837096	−	0.837096i	−0.988476	+	0.151380i	$0.951628\pi$
$270$		0			0
$271$	−13.4624			−0.817780			−0.408890	−	0.912584i	$-0.634084\pi$
$271$	−13.4624			−0.817780			−0.408890	+	0.912584i	$0.634084\pi$
$272$		0			0
$273$	−12.7203	−	9.57400i	−0.769868	−	0.579445i
$274$		0			0
$275$	1.54670	+	1.54670i	0.0932695	+	0.0932695i
$276$		0			0
$277$	−21.3721	−	21.3721i	−1.28412	−	1.28412i	−0.938300	−	0.345823i	$-0.887600\pi$
$277$	−21.3721	−	21.3721i	−1.28412	−	1.28412i	−0.345823	−	0.938300i	$-0.612400\pi$
$278$		0			0
$279$		−	1.60368i		−	0.0960101i
$280$		0			0
$281$			6.68698i			0.398912i	0.979907	+	0.199456i	$0.0639174\pi$
$281$			6.68698i			0.398912i	−0.979907	+	0.199456i	$0.936083\pi$
$282$		0			0
$283$	−7.67454	−	7.67454i	−0.456204	−	0.456204i	0.441203	−	0.897407i	$-0.354552\pi$
$283$	−7.67454	−	7.67454i	−0.456204	−	0.456204i	−0.897407	+	0.441203i	$0.854552\pi$
$284$		0			0
$285$	−4.52645	−	4.52645i	−0.268124	−	0.268124i
$286$		0			0
$287$	5.18819	+	3.90491i	0.306249	+	0.230500i
$288$		0			0
$289$	10.1270			0.595708
$290$		0			0
$291$	−5.34510	−	5.34510i	−0.313335	−	0.313335i
$292$		0			0
$293$	4.59094	−	4.59094i	0.268206	−	0.268206i	−0.560171	−	0.828377i	$-0.689265\pi$
$293$	4.59094	−	4.59094i	0.268206	−	0.268206i	0.828377	+	0.560171i	$0.189265\pi$
$294$		0			0
$295$	16.4274			0.956441
$296$		0			0
$297$	2.87413			0.166774
$298$		0			0
$299$	−17.5577	−	17.5577i	−1.01539	−	1.01539i
$300$		0			0
$301$	21.2186	−	2.99450i	1.22302	−	0.172600i
$302$		0			0
$303$			14.2881i			0.820828i
$304$		0			0
$305$	26.6099			1.52368
$306$		0			0
$307$	−2.83780	+	2.83780i	−0.161962	+	0.161962i	−0.783435	−	0.621473i	$-0.786534\pi$
$307$	−2.83780	+	2.83780i	−0.161962	+	0.161962i	0.621473	+	0.783435i	$0.286534\pi$
$308$		0			0
$309$	8.93396	+	8.93396i	0.508235	+	0.508235i
$310$		0			0
$311$		−	26.0055i		−	1.47464i	−0.675544	−	0.737319i	$-0.736091\pi$
$311$		−	26.0055i		−	1.47464i	0.675544	−	0.737319i	$-0.263909\pi$
$312$		0			0
$313$	−11.5559			−0.653176			−0.326588	−	0.945167i	$-0.605899\pi$
$313$	−11.5559			−0.653176			−0.326588	+	0.945167i	$0.605899\pi$
$314$		0			0
$315$	−0.761208	−	5.39381i	−0.0428892	−	0.303907i
$316$		0			0
$317$	−14.5580	+	14.5580i	−0.817661	+	0.817661i	−0.985769	−	0.168108i	$-0.946234\pi$
$317$	−14.5580	+	14.5580i	−0.817661	+	0.817661i	0.168108	+	0.985769i	$0.446234\pi$
$318$		0			0
$319$		−	20.5020i		−	1.14789i
$320$		0			0
$321$			11.8180i			0.659618i
$322$		0			0
$323$	5.76369	+	5.76369i	0.320701	+	0.320701i
$324$		0			0
$325$	−3.23826	+	3.23826i	−0.179626	+	0.179626i
$326$		0			0
$327$		−	8.66945i		−	0.479422i
$328$		0			0
$329$	−13.6241	−	10.2543i	−0.751123	−	0.565336i
$330$		0			0
$331$	−13.7898	+	13.7898i	−0.757955	+	0.757955i	−0.975950	−	0.217995i	$-0.930048\pi$
$331$	−13.7898	+	13.7898i	−0.757955	+	0.757955i	0.217995	+	0.975950i	$0.430048\pi$
$332$		0			0
$333$	−6.27770	+	6.27770i	−0.344016	+	0.344016i
$334$		0			0
$335$	13.3006			0.726689
$336$		0			0
$337$	29.1785			1.58945			0.794726	−	0.606968i	$-0.207614\pi$
$337$	29.1785			1.58945			0.794726	+	0.606968i	$0.207614\pi$
$338$		0			0
$339$	2.33824	−	2.33824i	0.126996	−	0.126996i
$340$		0			0
$341$	3.25920	−	3.25920i	0.176495	−	0.176495i
$342$		0			0
$343$	−6.60728	+	17.3016i	−0.356760	+	0.934196i
$344$		0			0
$345$		−	8.49571i		−	0.457394i
$346$		0			0
$347$	−14.8088	+	14.8088i	−0.794978	+	0.794978i	−0.982299	−	0.187321i	$-0.940020\pi$
$347$	−14.8088	+	14.8088i	−0.794978	+	0.794978i	0.187321	+	0.982299i	$0.440020\pi$
$348$		0			0
$349$	0.726030	+	0.726030i	0.0388635	+	0.0388635i	0.726271	−	0.687408i	$-0.241252\pi$
$349$	0.726030	+	0.726030i	0.0388635	+	0.0388635i	−0.687408	+	0.726271i	$0.741252\pi$
$350$		0			0
$351$			6.01745i			0.321187i
$352$		0			0
$353$			24.9308i			1.32693i	0.748206	+	0.663466i	$0.230915\pi$
$353$			24.9308i			1.32693i	−0.748206	+	0.663466i	$0.769085\pi$
$354$		0			0
$355$	1.62899	−	1.62899i	0.0864580	−	0.0864580i
$356$		0			0
$357$	0.969274	+	6.86814i	0.0512994	+	0.363500i
$358$		0			0
$359$	−15.6388			−0.825385			−0.412692	−	0.910870i	$-0.635412\pi$
$359$	−15.6388			−0.825385			−0.412692	+	0.910870i	$0.635412\pi$
$360$		0			0
$361$			9.33310i			0.491216i
$362$		0			0
$363$	−1.93703	−	1.93703i	−0.101668	−	0.101668i
$364$		0			0
$365$	−7.10744	+	7.10744i	−0.372020	+	0.372020i
$366$		0			0
$367$	10.4876			0.547446			0.273723	−	0.961809i	$-0.411745\pi$
$367$	10.4876			0.547446			0.273723	+	0.961809i	$0.411745\pi$
$368$		0			0
$369$		−	2.45431i		−	0.127766i
$370$		0			0
$371$	3.09286	+	21.9156i	0.160573	+	1.13780i
$372$		0			0
$373$	−6.72499	−	6.72499i	−0.348207	−	0.348207i	0.511235	−	0.859441i	$-0.329188\pi$
$373$	−6.72499	−	6.72499i	−0.348207	−	0.348207i	−0.859441	+	0.511235i	$0.829188\pi$
$374$		0			0
$375$	−11.8613			−0.612513
$376$		0			0
$377$	42.9243			2.21071
$378$		0			0
$379$	−18.8704	+	18.8704i	−0.969305	+	0.969305i	−0.999543	−	0.0302379i	$-0.990374\pi$
$379$	−18.8704	+	18.8704i	−0.969305	+	0.969305i	0.0302379	+	0.999543i	$0.490374\pi$
$380$		0			0
$381$	0.738538	+	0.738538i	0.0378365	+	0.0378365i
$382$		0			0
$383$	−28.2583			−1.44393			−0.721965	−	0.691930i	$-0.756761\pi$
$383$	−28.2583			−1.44393			−0.721965	+	0.691930i	$0.756761\pi$
$384$		0			0
$385$	9.41492	−	12.5090i	0.479829	−	0.637515i
$386$		0			0
$387$	−5.72710	−	5.72710i	−0.291125	−	0.291125i
$388$		0			0
$389$	13.1440	+	13.1440i	0.666428	+	0.666428i	0.956887	−	0.290459i	$-0.0938081\pi$
$389$	13.1440	+	13.1440i	0.666428	+	0.666428i	−0.290459	+	0.956887i	$0.593808\pi$
$390$		0			0
$391$			10.8179i			0.547085i
$392$		0			0
$393$			13.0605i			0.658814i
$394$		0			0
$395$	−18.4227	−	18.4227i	−0.926948	−	0.926948i
$396$		0			0
$397$	−1.70051	−	1.70051i	−0.0853461	−	0.0853461i	0.663145	−	0.748491i	$-0.269221\pi$
$397$	−1.70051	−	1.70051i	−0.0853461	−	0.0853461i	−0.748491	+	0.663145i	$0.769221\pi$
$398$		0			0
$399$	4.94680	−	6.57248i	0.247650	−	0.329035i
$400$		0			0
$401$	−27.0027			−1.34845			−0.674225	−	0.738526i	$-0.735522\pi$
$401$	−27.0027			−1.34845			−0.674225	+	0.738526i	$0.735522\pi$
$402$		0			0
$403$	6.82364	+	6.82364i	0.339910	+	0.339910i
$404$		0			0
$405$	−1.45584	+	1.45584i	−0.0723413	+	0.0723413i
$406$		0			0
$407$	−25.5165			−1.26481
$408$		0			0
$409$	7.63749			0.377650			0.188825	−	0.982011i	$-0.439532\pi$
$409$	7.63749			0.377650			0.188825	+	0.982011i	$0.439532\pi$
$410$		0			0
$411$	−6.90627	−	6.90627i	−0.340661	−	0.340661i
$412$		0			0
$413$	2.94995	+	20.9029i	0.145157	+	1.02857i
$414$		0			0
$415$			21.7214i			1.06626i
$416$		0			0
$417$	−16.1086			−0.788841
$418$		0			0
$419$	21.4308	−	21.4308i	1.04696	−	1.04696i	0.0481219	−	0.998841i	$-0.484676\pi$
$419$	21.4308	−	21.4308i	1.04696	−	1.04696i	0.998841	−	0.0481219i	$-0.0153236\pi$
$420$		0			0
$421$	2.91129	+	2.91129i	0.141888	+	0.141888i	0.774483	−	0.632595i	$-0.218010\pi$
$421$	2.91129	+	2.91129i	0.141888	+	0.141888i	−0.632595	+	0.774483i	$0.718010\pi$
$422$		0			0
$423$			6.44501i			0.313367i
$424$		0			0
$425$	1.99520			0.0967815
$426$		0			0
$427$	4.77847	+	33.8595i	0.231246	+	1.63858i
$428$		0			0
$429$	−12.2294	+	12.2294i	−0.590439	+	0.590439i
$430$		0			0
$431$		−	23.3497i		−	1.12471i	−0.826894	−	0.562357i	$-0.809895\pi$
$431$		−	23.3497i		−	1.12471i	0.826894	−	0.562357i	$-0.190105\pi$
$432$		0			0
$433$			9.99037i			0.480107i	0.970760	+	0.240053i	$0.0771650\pi$
$433$			9.99037i			0.480107i	−0.970760	+	0.240053i	$0.922835\pi$
$434$		0			0
$435$	10.3850	+	10.3850i	0.497921	+	0.497921i
$436$		0			0
$437$	9.07193	−	9.07193i	0.433969	−	0.433969i
$438$		0			0
$439$			5.51270i			0.263107i	0.991309	+	0.131553i	$0.0419965\pi$
$439$			5.51270i			0.263107i	−0.991309	+	0.131553i	$0.958003\pi$
$440$		0			0
$441$	6.72661	−	1.93718i	0.320315	−	0.0922469i
$442$		0			0
$443$	1.00204	−	1.00204i	0.0476083	−	0.0476083i	−0.682902	−	0.730510i	$-0.739282\pi$
$443$	1.00204	−	1.00204i	0.0476083	−	0.0476083i	0.730510	+	0.682902i	$0.239282\pi$
$444$		0			0
$445$	−12.2721	+	12.2721i	−0.581752	+	0.581752i
$446$		0			0
$447$	−11.8815			−0.561977
$448$		0			0
$449$	−23.4082			−1.10470			−0.552352	−	0.833611i	$-0.686269\pi$
$449$	−23.4082			−1.10470			−0.552352	+	0.833611i	$0.686269\pi$
$450$		0			0
$451$	4.98794	−	4.98794i	0.234873	−	0.234873i
$452$		0			0
$453$	−0.236897	+	0.236897i	−0.0111304	+	0.0111304i
$454$		0			0
$455$	26.1895	+	19.7116i	1.22778	+	0.924095i
$456$		0			0
$457$		−	2.22721i		−	0.104184i	−0.998642	−	0.0520922i	$-0.983411\pi$
$457$		−	2.22721i		−	0.104184i	0.998642	−	0.0520922i	$-0.0165890\pi$
$458$		0			0
$459$	1.85378	−	1.85378i	0.0865269	−	0.0865269i
$460$		0			0
$461$	−12.3595	−	12.3595i	−0.575637	−	0.575637i	0.358061	−	0.933698i	$-0.383438\pi$
$461$	−12.3595	−	12.3595i	−0.575637	−	0.575637i	−0.933698	+	0.358061i	$0.883438\pi$
$462$		0			0
$463$		−	5.20724i		−	0.242001i	−0.992652	−	0.121001i	$-0.961390\pi$
$463$		−	5.20724i		−	0.242001i	0.992652	−	0.121001i	$-0.0386103\pi$
$464$		0			0
$465$			3.30178i			0.153116i
$466$		0			0
$467$	9.60600	−	9.60600i	0.444513	−	0.444513i	−0.449013	−	0.893525i	$-0.648224\pi$
$467$	9.60600	−	9.60600i	0.444513	−	0.444513i	0.893525	+	0.449013i	$0.148224\pi$
$468$		0			0
$469$	2.38845	+	16.9242i	0.110288	+	0.781488i
$470$		0			0
$471$	21.4668			0.989139
$472$		0			0
$473$		−	23.2786i		−	1.07035i
$474$		0			0
$475$	−1.67318	−	1.67318i	−0.0767709	−	0.0767709i
$476$		0			0
$477$	5.91522	−	5.91522i	0.270839	−	0.270839i
$478$		0			0
$479$	9.29342			0.424627			0.212314	−	0.977202i	$-0.431900\pi$
$479$	9.29342			0.424627			0.212314	+	0.977202i	$0.431900\pi$
$480$		0			0
$481$		−	53.4229i		−	2.43587i
$482$		0			0
$483$	10.8103	−	1.52562i	0.491885	−	0.0694179i
$484$		0			0
$485$	11.0049	+	11.0049i	0.499706	+	0.499706i
$486$		0			0
$487$	23.9682			1.08610			0.543051	−	0.839700i	$-0.317269\pi$
$487$	23.9682			1.08610			0.543051	+	0.839700i	$0.317269\pi$
$488$		0			0
$489$	−8.58764			−0.388347
$490$		0			0
$491$	−0.332724	+	0.332724i	−0.0150156	+	0.0150156i	−0.714575	−	0.699559i	$-0.753380\pi$
$491$	−0.332724	+	0.332724i	−0.0150156	+	0.0150156i	0.699559	+	0.714575i	$0.253380\pi$
$492$		0			0
$493$	−13.2235	−	13.2235i	−0.595559	−	0.595559i
$494$		0			0
$495$	−5.91746			−0.265970
$496$		0			0
$497$	2.36532	+	1.78027i	0.106099	+	0.0798561i
$498$		0			0
$499$	13.0243	+	13.0243i	0.583046	+	0.583046i	0.935739	−	0.352693i	$-0.114734\pi$
$499$	13.0243	+	13.0243i	0.583046	+	0.583046i	−0.352693	+	0.935739i	$0.614734\pi$
$500$		0			0
$501$	−1.69533	−	1.69533i	−0.0757416	−	0.0757416i
$502$		0			0
$503$			40.8349i			1.82074i	0.413799	+	0.910368i	$0.364201\pi$
$503$			40.8349i			1.82074i	−0.413799	+	0.910368i	$0.635799\pi$
$504$		0			0
$505$		−	29.4173i		−	1.30905i
$506$		0			0
$507$	−16.4117	−	16.4117i	−0.728869	−	0.728869i
$508$		0			0
$509$	−3.90616	−	3.90616i	−0.173138	−	0.173138i	0.615219	−	0.788356i	$-0.289068\pi$
$509$	−3.90616	−	3.90616i	−0.173138	−	0.173138i	−0.788356	+	0.615219i	$0.789068\pi$
$510$		0			0
$511$	−10.3201	−	7.76748i	−0.456535	−	0.343613i
$512$		0			0
$513$	−3.10916			−0.137273
$514$		0			0
$515$	−18.3939	−	18.3939i	−0.810531	−	0.810531i
$516$		0			0
$517$	−13.0983	+	13.0983i	−0.576063	+	0.576063i
$518$		0			0
$519$	16.6618			0.731373
$520$		0			0
$521$	1.69009			0.0740443			0.0370222	−	0.999314i	$-0.488213\pi$
$521$	1.69009			0.0740443			0.0370222	+	0.999314i	$0.488213\pi$
$522$		0			0
$523$	27.1102	+	27.1102i	1.18545	+	1.18545i	0.978312	+	0.207136i	$0.0664143\pi$
$523$	27.1102	+	27.1102i	1.18545	+	1.18545i	0.207136	+	0.978312i	$0.433586\pi$
$524$		0			0
$525$	−0.281377	−	1.99380i	−0.0122803	−	0.0870165i
$526$		0			0
$527$		−	4.20428i		−	0.183141i
$528$		0			0
$529$	−5.97286			−0.259690
$530$		0			0
$531$	5.64190	−	5.64190i	0.244837	−	0.244837i
$532$		0			0
$533$	10.4430	+	10.4430i	0.452339	+	0.452339i
$534$		0			0
$535$		−	24.3318i		−	1.05195i
$536$		0			0
$537$	−7.04534			−0.304029
$538$		0			0
$539$	17.6076	+	9.73364i	0.758412	+	0.419257i
$540$		0			0
$541$	27.7496	−	27.7496i	1.19305	−	1.19305i	0.216842	−	0.976207i	$-0.430424\pi$
$541$	27.7496	−	27.7496i	1.19305	−	1.19305i	0.976207	−	0.216842i	$-0.0695755\pi$
$542$		0			0
$543$			8.69494i			0.373136i
$544$		0			0
$545$			17.8493i			0.764579i
$546$		0			0
$547$	−3.86424	−	3.86424i	−0.165223	−	0.165223i	0.619653	−	0.784876i	$-0.287273\pi$
$547$	−3.86424	−	3.86424i	−0.165223	−	0.165223i	−0.784876	+	0.619653i	$0.787273\pi$
$548$		0			0
$549$	9.13901	−	9.13901i	0.390043	−	0.390043i
$550$		0			0
$551$			22.1786i			0.944841i
$552$		0			0
$553$	20.1336	−	26.7501i	0.856167	−	1.13753i
$554$		0			0
$555$	12.9250	−	12.9250i	0.548634	−	0.548634i
$556$		0			0
$557$	6.29412	−	6.29412i	0.266691	−	0.266691i	−0.561075	−	0.827765i	$-0.689612\pi$
$557$	6.29412	−	6.29412i	0.266691	−	0.266691i	0.827765	+	0.561075i	$0.189612\pi$
$558$		0			0
$559$	48.7374			2.06137
$560$		0			0
$561$	7.53492			0.318125
$562$		0			0
$563$	−25.3954	+	25.3954i	−1.07029	+	1.07029i	−0.0729527	+	0.997335i	$0.523242\pi$
$563$	−25.3954	+	25.3954i	−1.07029	+	1.07029i	−0.997335	+	0.0729527i	$0.976758\pi$
$564$		0			0
$565$	−4.81414	+	4.81414i	−0.202532	+	0.202532i
$566$		0			0
$567$	−2.11390	−	1.59104i	−0.0887756	−	0.0668174i
$568$		0			0
$569$			13.6726i			0.573184i	0.958053	+	0.286592i	$0.0925225\pi$
$569$			13.6726i			0.573184i	−0.958053	+	0.286592i	$0.907478\pi$
$570$		0			0
$571$	19.3274	−	19.3274i	0.808825	−	0.808825i	−0.175631	−	0.984456i	$-0.556197\pi$
$571$	19.3274	−	19.3274i	0.808825	−	0.808825i	0.984456	+	0.175631i	$0.0561966\pi$
$572$		0			0
$573$	1.27403	+	1.27403i	0.0532233	+	0.0532233i
$574$		0			0
$575$		−	3.14040i		−	0.130964i
$576$		0			0
$577$			20.1432i			0.838572i	0.907854	+	0.419286i	$0.137720\pi$
$577$			20.1432i			0.838572i	−0.907854	+	0.419286i	$0.862280\pi$
$578$		0			0
$579$	10.4194	−	10.4194i	0.433015	−	0.433015i
$580$		0			0
$581$	−27.6392	+	3.90061i	−1.14667	+	0.161825i
$582$		0			0
$583$	24.0432			0.995768
$584$		0			0
$585$		−	12.3891i		−	0.512228i
$586$		0			0
$587$	16.0788	+	16.0788i	0.663643	+	0.663643i	0.956237	−	0.292593i	$-0.0945183\pi$
$587$	16.0788	+	16.0788i	0.663643	+	0.663643i	−0.292593	+	0.956237i	$0.594518\pi$
$588$		0			0
$589$	−3.52572	+	3.52572i	−0.145275	+	0.145275i
$590$		0			0
$591$	23.0082			0.946431
$592$		0			0
$593$		−	26.3515i		−	1.08212i	−0.840982	−	0.541062i	$-0.818022\pi$
$593$		−	26.3515i		−	1.08212i	0.840982	−	0.541062i	$-0.181978\pi$
$594$		0			0
$595$	−1.99561	−	14.1406i	−0.0818120	−	0.579708i
$596$		0			0
$597$	3.23899	+	3.23899i	0.132563	+	0.132563i
$598$		0			0
$599$	3.16415			0.129284			0.0646419	−	0.997909i	$-0.479409\pi$
$599$	3.16415			0.129284			0.0646419	+	0.997909i	$0.479409\pi$
$600$		0			0
$601$	−14.2899			−0.582897			−0.291448	−	0.956587i	$-0.594137\pi$
$601$	−14.2899			−0.582897			−0.291448	+	0.956587i	$0.594137\pi$
$602$		0			0
$603$	4.56801	−	4.56801i	0.186024	−	0.186024i
$604$		0			0
$605$	3.98809	+	3.98809i	0.162139	+	0.162139i
$606$		0			0
$607$	−40.0580			−1.62590			−0.812952	−	0.582331i	$-0.802141\pi$
$607$	−40.0580			−1.62590			−0.812952	+	0.582331i	$0.802141\pi$
$608$		0			0
$609$	−11.3494	+	15.0791i	−0.459900	+	0.611037i
$610$		0			0
$611$	−27.4234	−	27.4234i	−1.10943	−	1.10943i
$612$		0			0
$613$	17.9779	+	17.9779i	0.726119	+	0.726119i	0.969844	−	0.243725i	$-0.0783694\pi$
$613$	17.9779	+	17.9779i	0.726119	+	0.726119i	−0.243725	+	0.969844i	$0.578369\pi$
$614$		0			0
$615$			5.05311i			0.203761i
$616$		0			0
$617$		−	15.5177i		−	0.624720i	−0.949964	−	0.312360i	$-0.898880\pi$
$617$		−	15.5177i		−	0.624720i	0.949964	−	0.312360i	$-0.101120\pi$
$618$		0			0
$619$	−19.6755	−	19.6755i	−0.790824	−	0.790824i	0.190804	−	0.981628i	$-0.438891\pi$
$619$	−19.6755	−	19.6755i	−0.790824	−	0.790824i	−0.981628	+	0.190804i	$0.938891\pi$
$620$		0			0
$621$	−2.91780	−	2.91780i	−0.117087	−	0.117087i
$622$		0			0
$623$	−17.8192	−	13.4117i	−0.713913	−	0.537330i
$624$		0			0
$625$	20.6155			0.824621
$626$		0			0
$627$	−6.31881	−	6.31881i	−0.252349	−	0.252349i
$628$		0			0
$629$	−16.4578	+	16.4578i	−0.656217	+	0.656217i
$630$		0			0
$631$	19.7977			0.788133			0.394067	−	0.919082i	$-0.371068\pi$
$631$	19.7977			0.788133			0.394067	+	0.919082i	$0.371068\pi$
$632$		0			0
$633$	10.8204			0.430070
$634$		0			0
$635$	−1.52055	−	1.52055i	−0.0603414	−	0.0603414i
$636$		0			0
$637$	−20.3789	+	36.8643i	−0.807442	+	1.46061i
$638$		0			0
$639$		−	1.11894i		−	0.0442644i
$640$		0			0
$641$	0.116929			0.00461840			0.00230920	−	0.999997i	$-0.499265\pi$
$641$	0.116929			0.00461840			0.00230920	+	0.999997i	$0.499265\pi$
$642$		0			0
$643$	−10.1626	+	10.1626i	−0.400775	+	0.400775i	−0.878506	−	0.477731i	$-0.841459\pi$
$643$	−10.1626	+	10.1626i	−0.400775	+	0.400775i	0.477731	+	0.878506i	$0.341459\pi$
$644$		0			0
$645$	11.7914	+	11.7914i	0.464285	+	0.464285i
$646$		0			0
$647$			38.7050i			1.52165i	0.648956	+	0.760826i	$0.275206\pi$
$647$			38.7050i			1.52165i	−0.648956	+	0.760826i	$0.724794\pi$
$648$		0			0
$649$	22.9323			0.900170
$650$		0			0
$651$	−4.20132	+	0.592916i	−0.164663	+	0.0232382i
$652$		0			0
$653$	0.370118	−	0.370118i	0.0144838	−	0.0144838i	−0.699828	−	0.714312i	$-0.746740\pi$
$653$	0.370118	−	0.370118i	0.0144838	−	0.0144838i	0.714312	+	0.699828i	$0.246740\pi$
$654$		0			0
$655$		−	26.8898i		−	1.05067i
$656$		0			0
$657$			4.88201i			0.190465i
$658$		0			0
$659$	−27.7484	−	27.7484i	−1.08093	−	1.08093i	−0.996423	−	0.0845024i	$-0.973070\pi$
$659$	−27.7484	−	27.7484i	−1.08093	−	1.08093i	−0.0845024	−	0.996423i	$-0.526930\pi$
$660$		0			0
$661$	−5.43808	+	5.43808i	−0.211517	+	0.211517i	−0.804912	−	0.593395i	$-0.797787\pi$
$661$	−5.43808	+	5.43808i	−0.211517	+	0.211517i	0.593395	+	0.804912i	$0.297787\pi$
$662$		0			0
$663$			15.7755i			0.612672i
$664$		0			0
$665$	−10.1848	+	13.5319i	−0.394951	+	0.524744i
$666$		0			0
$667$	−20.8136	+	20.8136i	−0.805905	+	0.805905i
$668$		0			0
$669$	19.5635	−	19.5635i	0.756367	−	0.756367i
$670$		0			0
$671$	37.1467			1.43403
$672$		0			0
$673$	6.84406			0.263819			0.131910	−	0.991262i	$-0.457889\pi$
$673$	6.84406			0.263819			0.131910	+	0.991262i	$0.457889\pi$
$674$		0			0
$675$	−0.538145	+	0.538145i	−0.0207132	+	0.0207132i
$676$		0			0
$677$	−14.6398	+	14.6398i	−0.562652	+	0.562652i	−0.930060	−	0.367408i	$-0.880245\pi$
$677$	−14.6398	+	14.6398i	−0.562652	+	0.562652i	0.367408	+	0.930060i	$0.380245\pi$
$678$		0			0
$679$	−12.0269	+	15.9793i	−0.461548	+	0.613227i
$680$		0			0
$681$		−	9.97878i		−	0.382388i
$682$		0			0
$683$	18.6836	−	18.6836i	0.714909	−	0.714909i	−0.252649	−	0.967558i	$-0.581302\pi$
$683$	18.6836	−	18.6836i	0.714909	−	0.714909i	0.967558	+	0.252649i	$0.0813019\pi$
$684$		0			0
$685$	14.2191	+	14.2191i	0.543284	+	0.543284i
$686$		0			0
$687$		−	20.1318i		−	0.768076i
$688$		0			0
$689$			50.3382i			1.91773i
$690$		0			0
$691$	18.7939	−	18.7939i	0.714955	−	0.714955i	−0.252613	−	0.967567i	$-0.581290\pi$
$691$	18.7939	−	18.7939i	0.714955	−	0.714955i	0.967567	+	0.252613i	$0.0812899\pi$
$692$		0			0
$693$	−1.06263	−	7.52962i	−0.0403659	−	0.286027i
$694$		0			0
$695$	33.1655			1.25804
$696$		0			0
$697$		−	6.43432i		−	0.243717i
$698$		0			0
$699$	7.17656	+	7.17656i	0.271442	+	0.271442i
$700$		0			0
$701$	−22.1829	+	22.1829i	−0.837837	+	0.837837i	−0.988574	−	0.150737i	$-0.951835\pi$
$701$	−22.1829	+	22.1829i	−0.837837	+	0.837837i	0.150737	+	0.988574i	$0.451835\pi$
$702$		0			0
$703$	27.6032			1.04107
$704$		0			0
$705$		−	13.2694i		−	0.499756i
$706$		0			0
$707$	37.4318	−	5.28260i	1.40777	−	0.198673i
$708$		0			0
$709$	8.01481	+	8.01481i	0.301003	+	0.301003i	0.841406	−	0.540403i	$-0.181728\pi$
$709$	8.01481	+	8.01481i	0.301003	+	0.301003i	−0.540403	+	0.841406i	$0.681728\pi$
$710$		0			0
$711$	−12.6543			−0.474575
$712$		0			0
$713$	−6.61744			−0.247825
$714$		0			0
$715$	25.1787	−	25.1787i	0.941629	−	0.941629i
$716$		0			0
$717$	−13.8301	−	13.8301i	−0.516493	−	0.516493i
$718$		0			0
$719$	−0.825104			−0.0307712			−0.0153856	−	0.999882i	$-0.504898\pi$
$719$	−0.825104			−0.0307712			−0.0153856	+	0.999882i	$0.504898\pi$
$720$		0			0
$721$	20.1020	−	26.7082i	0.748639	−	0.994665i
$722$		0			0
$723$	5.19525	+	5.19525i	0.193213	+	0.193213i
$724$		0			0
$725$	3.83875	+	3.83875i	0.142568	+	0.142568i
$726$		0			0
$727$		−	19.0810i		−	0.707675i	−0.935307	−	0.353837i	$-0.884877\pi$
$727$		−	19.0810i		−	0.707675i	0.935307	−	0.353837i	$-0.115123\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−15.0144	−	15.0144i	−0.555327	−	0.555327i
$732$		0			0
$733$	−32.9626	−	32.9626i	−1.21750	−	1.21750i	−0.968504	−	0.248999i	$-0.919899\pi$
$733$	−32.9626	−	32.9626i	−1.21750	−	1.21750i	−0.248999	−	0.968504i	$-0.580101\pi$
$734$		0			0
$735$	−13.8492	+	3.98841i	−0.510836	+	0.147115i
$736$		0			0
$737$	18.5673			0.683935
$738$		0			0
$739$	−15.0066	−	15.0066i	−0.552025	−	0.552025i	0.375000	−	0.927025i	$-0.377643\pi$
$739$	−15.0066	−	15.0066i	−0.552025	−	0.552025i	−0.927025	+	0.375000i	$0.877643\pi$
$740$		0			0
$741$	13.2294	−	13.2294i	0.485995	−	0.485995i
$742$		0			0
$743$	−29.6092			−1.08626			−0.543128	−	0.839650i	$-0.682760\pi$
$743$	−29.6092			−1.08626			−0.543128	+	0.839650i	$0.682760\pi$
$744$		0			0
$745$	24.4625			0.896237
$746$		0			0
$747$	7.46008	+	7.46008i	0.272950	+	0.272950i
$748$		0			0
$749$	30.9608	−	4.36937i	1.13128	−	0.159653i
$750$		0			0
$751$		−	28.5009i		−	1.04001i	−0.854162	−	0.520007i	$-0.825929\pi$
$751$		−	28.5009i		−	1.04001i	0.854162	−	0.520007i	$-0.174071\pi$
$752$		0			0
$753$	26.9990			0.983897
$754$		0			0
$755$	0.487741	−	0.487741i	0.0177507	−	0.0177507i
$756$		0			0
$757$	−9.55095	−	9.55095i	−0.347135	−	0.347135i	0.511906	−	0.859041i	$-0.328940\pi$
$757$	−9.55095	−	9.55095i	−0.347135	−	0.347135i	−0.859041	+	0.511906i	$0.828940\pi$
$758$		0			0
$759$		−	11.8598i		−	0.430484i
$760$		0			0
$761$	14.3571			0.520446			0.260223	−	0.965549i	$-0.416204\pi$
$761$	14.3571			0.520446			0.260223	+	0.965549i	$0.416204\pi$
$762$		0			0
$763$	−22.7121	+	3.20528i	−0.822235	+	0.116039i
$764$		0			0
$765$	−3.81668	+	3.81668i	−0.137993	+	0.137993i
$766$		0			0
$767$			48.0123i			1.73362i
$768$		0			0
$769$			9.21833i			0.332421i	0.986090	+	0.166211i	$0.0531532\pi$
$769$			9.21833i			0.332421i	−0.986090	+	0.166211i	$0.946847\pi$
$770$		0			0
$771$	12.5778	+	12.5778i	0.452978	+	0.452978i
$772$		0			0
$773$	−5.17651	+	5.17651i	−0.186186	+	0.186186i	−0.794045	−	0.607859i	$-0.792029\pi$
$773$	−5.17651	+	5.17651i	−0.186186	+	0.186186i	0.607859	+	0.794045i	$0.292029\pi$
$774$		0			0
$775$			1.22049i			0.0438412i
$776$		0			0
$777$	18.7672	+	14.1253i	0.673271	+	0.506741i
$778$		0			0
$779$	−5.39584	+	5.39584i	−0.193326	+	0.193326i
$780$		0			0
$781$	2.27403	−	2.27403i	0.0813713	−	0.0813713i
$782$		0			0
$783$	7.13330			0.254923
$784$		0			0
$785$	−44.1974			−1.57747
$786$		0			0
$787$	−18.8037	+	18.8037i	−0.670278	+	0.670278i	−0.957780	−	0.287502i	$-0.907175\pi$
$787$	−18.8037	+	18.8037i	−0.670278	+	0.670278i	0.287502	+	0.957780i	$0.407175\pi$
$788$		0			0
$789$	−9.25646	+	9.25646i	−0.329539	+	0.329539i
$790$		0			0
$791$	−6.99021	−	5.26121i	−0.248543	−	0.187067i
$792$		0			0
$793$			77.7726i			2.76178i
$794$		0			0
$795$	−12.1787	+	12.1787i	−0.431933	+	0.431933i
$796$		0			0
$797$	−1.09486	−	1.09486i	−0.0387818	−	0.0387818i	0.687450	−	0.726232i	$-0.258730\pi$
$797$	−1.09486	−	1.09486i	−0.0387818	−	0.0387818i	−0.726232	+	0.687450i	$0.758730\pi$
$798$		0			0
$799$			16.8965i			0.597754i
$800$		0			0
$801$			8.42954i			0.297843i
$802$		0			0
$803$	−9.92180	+	9.92180i	−0.350133	+	0.350133i
$804$		0			0
$805$	−22.2570	+	3.14105i	−0.784456	+	0.110707i
$806$		0			0
$807$	19.4163			0.683486
$808$		0			0
$809$		−	25.0442i		−	0.880508i	−0.897873	−	0.440254i	$-0.854888\pi$
$809$		−	25.0442i		−	0.880508i	0.897873	−	0.440254i	$-0.145112\pi$
$810$		0			0
$811$	9.52822	+	9.52822i	0.334581	+	0.334581i	0.854323	−	0.519742i	$-0.173972\pi$
$811$	9.52822	+	9.52822i	0.334581	+	0.334581i	−0.519742	+	0.854323i	$0.673972\pi$
$812$		0			0
$813$	9.51932	−	9.51932i	0.333857	−	0.333857i
$814$		0			0
$815$	17.6808			0.619333
$816$		0			0
$817$			25.1822i			0.881014i
$818$		0			0
$819$	15.7645	−	2.22478i	0.550855	−	0.0777400i
$820$		0			0
$821$	−19.5964	−	19.5964i	−0.683921	−	0.683921i	0.276961	−	0.960881i	$-0.410673\pi$
$821$	−19.5964	−	19.5964i	−0.683921	−	0.683921i	−0.960881	+	0.276961i	$0.910673\pi$
$822$		0			0
$823$	23.5112			0.819548			0.409774	−	0.912187i	$-0.365608\pi$
$823$	23.5112			0.819548			0.409774	+	0.912187i	$0.365608\pi$
$824$		0			0
$825$	−2.18736			−0.0761543
$826$		0			0
$827$	−12.7077	+	12.7077i	−0.441890	+	0.441890i	−0.892647	−	0.450757i	$-0.851154\pi$
$827$	−12.7077	+	12.7077i	−0.441890	+	0.441890i	0.450757	+	0.892647i	$0.351154\pi$
$828$		0			0
$829$	−0.293728	−	0.293728i	−0.0102016	−	0.0102016i	0.701988	−	0.712189i	$-0.252296\pi$
$829$	−0.293728	−	0.293728i	−0.0102016	−	0.0102016i	−0.712189	+	0.701988i	$0.752296\pi$
$830$		0			0
$831$	30.2247			1.04848
$832$		0			0
$833$	17.6347	−	5.07859i	0.611007	−	0.175963i
$834$		0			0
$835$	3.49046	+	3.49046i	0.120792	+	0.120792i
$836$		0			0
$837$	1.13398	+	1.13398i	0.0391959	+	0.0391959i
$838$		0			0
$839$			19.0230i			0.656746i	0.944548	+	0.328373i	$0.106500\pi$
$839$			19.0230i			0.656746i	−0.944548	+	0.328373i	$0.893500\pi$
$840$		0			0
$841$		−	21.8840i		−	0.754621i
$842$		0			0
$843$	−4.72841	−	4.72841i	−0.162855	−	0.162855i
$844$		0			0
$845$	33.7896	+	33.7896i	1.16240	+	1.16240i
$846$		0			0
$847$	−4.35845	+	5.79077i	−0.149758	+	0.198973i
$848$		0			0
$849$	10.8534			0.372489
$850$		0			0
$851$	25.9043	+	25.9043i	0.887986	+	0.887986i
$852$		0			0
$853$	7.00403	−	7.00403i	0.239813	−	0.239813i	−0.576959	−	0.816773i	$-0.695761\pi$
$853$	7.00403	−	7.00403i	0.239813	−	0.239813i	0.816773	+	0.576959i	$0.195761\pi$
$854$		0			0
$855$	6.40137			0.218922
$856$		0			0
$857$	42.0725			1.43717			0.718585	−	0.695439i	$-0.244790\pi$
$857$	42.0725			1.43717			0.718585	+	0.695439i	$0.244790\pi$
$858$		0			0
$859$	−31.3118	−	31.3118i	−1.06834	−	1.06834i	−0.997486	−	0.0708573i	$-0.977426\pi$
$859$	−31.3118	−	31.3118i	−1.06834	−	1.06834i	−0.0708573	−	0.997486i	$-0.522574\pi$
$860$		0			0
$861$	−6.42979	+	0.907412i	−0.219127	+	0.0309245i
$862$		0			0
$863$			22.4531i			0.764314i	0.924097	+	0.382157i	$0.124819\pi$
$863$			22.4531i			0.764314i	−0.924097	+	0.382157i	$0.875181\pi$
$864$		0			0
$865$	−34.3045			−1.16639
$866$		0			0
$867$	−7.16089	+	7.16089i	−0.243197	+	0.243197i
$868$		0			0
$869$	−25.7177	−	25.7177i	−0.872412	−	0.872412i
$870$		0			0
$871$			38.8736i			1.31718i
$872$		0			0
$873$	7.55912			0.255837
$874$		0			0
$875$	4.38536	+	31.0740i	0.148252	+	1.05049i
$876$		0			0
$877$	23.2048	−	23.2048i	0.783572	−	0.783572i	−0.196860	−	0.980432i	$-0.563074\pi$
$877$	23.2048	−	23.2048i	0.783572	−	0.783572i	0.980432	+	0.196860i	$0.0630745\pi$
$878$		0			0
$879$			6.49257i			0.218989i
$880$		0			0
$881$		−	7.70987i		−	0.259752i	−0.991530	−	0.129876i	$-0.958542\pi$
$881$		−	7.70987i		−	0.259752i	0.991530	−	0.129876i	$-0.0414580\pi$
$882$		0			0
$883$	34.6172	+	34.6172i	1.16496	+	1.16496i	0.983375	+	0.181586i	$0.0581230\pi$
$883$	34.6172	+	34.6172i	1.16496	+	1.16496i	0.181586	+	0.983375i	$0.441877\pi$
$884$		0			0
$885$	−11.6159	+	11.6159i	−0.390465	+	0.390465i
$886$		0			0
$887$		−	11.7991i		−	0.396174i	−0.980184	−	0.198087i	$-0.936527\pi$
$887$		−	11.7991i		−	0.396174i	0.980184	−	0.198087i	$-0.0634729\pi$
$888$		0			0
$889$	1.66176	−	2.20787i	0.0557337	−	0.0740496i
$890$		0			0
$891$	−2.03232	+	2.03232i	−0.0680852	+	0.0680852i
$892$		0			0
$893$	14.1694	−	14.1694i	0.474162	−	0.474162i
$894$		0			0
$895$	14.5054			0.484864
$896$		0			0
$897$	24.8304			0.829062
$898$		0			0
$899$	8.08899	−	8.08899i	0.269783	−	0.269783i
$900$		0			0
$901$	15.5075	−	15.5075i	0.516631	−	0.516631i
$902$		0			0
$903$	−12.8864	+	17.1212i	−0.428832	+	0.569759i
$904$		0			0
$905$		−	17.9018i		−	0.595074i
$906$		0			0
$907$	8.57668	−	8.57668i	0.284784	−	0.284784i	−0.550229	−	0.835014i	$-0.685460\pi$
$907$	8.57668	−	8.57668i	0.284784	−	0.284784i	0.835014	+	0.550229i	$0.185460\pi$
$908$		0			0
$909$	−10.1032	−	10.1032i	−0.335102	−	0.335102i
$910$		0			0
$911$		−	41.5002i		−	1.37496i	−0.726202	−	0.687482i	$-0.758716\pi$
$911$		−	41.5002i		−	1.37496i	0.726202	−	0.687482i	$-0.241284\pi$
$912$		0			0
$913$			30.3225i			1.00353i
$914$		0			0
$915$	−18.8160	+	18.8160i	−0.622039	+	0.622039i
$916$		0			0
$917$	34.2157	−	4.82873i	1.12990	−	0.159459i
$918$		0			0
$919$	−36.2885			−1.19705			−0.598523	−	0.801106i	$-0.704245\pi$
$919$	−36.2885			−1.19705			−0.598523	+	0.801106i	$0.704245\pi$
$920$		0			0
$921$		−	4.01326i		−	0.132241i
$922$		0			0
$923$	4.76105	+	4.76105i	0.156712	+	0.156712i
$924$		0			0
$925$	4.77766	−	4.77766i	0.157088	−	0.157088i
$926$		0			0
$927$	−12.6345			−0.414972
$928$		0			0
$929$		−	27.3809i		−	0.898338i	−0.893447	−	0.449169i	$-0.851720\pi$
$929$		−	27.3809i		−	0.898338i	0.893447	−	0.449169i	$-0.148280\pi$
$930$		0			0
$931$	−19.0475	−	10.5296i	−0.624255	−	0.345094i
$932$		0			0
$933$	18.3887	+	18.3887i	0.602019	+	0.602019i
$934$		0			0
$935$	−15.5134			−0.507343
$936$		0			0
$937$	1.69274			0.0552994			0.0276497	−	0.999618i	$-0.491198\pi$
$937$	1.69274			0.0552994			0.0276497	+	0.999618i	$0.491198\pi$
$938$		0			0
$939$	8.17123	−	8.17123i	0.266658	−	0.266658i
$940$		0			0
$941$	−16.5840	−	16.5840i	−0.540622	−	0.540622i	0.383090	−	0.923711i	$-0.374860\pi$
$941$	−16.5840	−	16.5840i	−0.540622	−	0.540622i	−0.923711	+	0.383090i	$0.874860\pi$
$942$		0			0
$943$	−10.1275			−0.329796
$944$		0			0
$945$	4.35226	+	3.27574i	0.141579	+	0.106560i
$946$		0			0
$947$	−40.2514	−	40.2514i	−1.30799	−	1.30799i	−0.922861	−	0.385134i	$-0.874155\pi$
$947$	−40.2514	−	40.2514i	−1.30799	−	1.30799i	−0.385134	−	0.922861i	$-0.625845\pi$
$948$		0			0
$949$	−20.7729	−	20.7729i	−0.674315	−	0.674315i
$950$		0			0
$951$		−	20.5882i		−	0.667617i
$952$		0			0
$953$		−	31.0983i		−	1.00737i	−0.863886	−	0.503687i	$-0.831977\pi$
$953$		−	31.0983i		−	1.00737i	0.863886	−	0.503687i	$-0.168023\pi$
$954$		0			0
$955$	−2.62306	−	2.62306i	−0.0848802	−	0.0848802i
$956$		0			0
$957$	14.4971	+	14.4971i	0.468626	+	0.468626i
$958$		0			0
$959$	−15.5396	+	20.6464i	−0.501800	+	0.666706i
$960$		0			0
$961$	−28.4282			−0.917039
$962$		0			0
$963$	−8.35660	−	8.35660i	−0.269288	−	0.269288i
$964$		0			0
$965$	−21.4521	+	21.4521i	−0.690569	+	0.690569i
$966$		0			0
$967$	44.7265			1.43831			0.719154	−	0.694851i	$-0.244530\pi$
$967$	44.7265			1.43831			0.719154	+	0.694851i	$0.244530\pi$
$968$		0			0
$969$	−8.15109			−0.261851
$970$		0			0
$971$	16.4707	+	16.4707i	0.528571	+	0.528571i	0.920146	−	0.391575i	$-0.128070\pi$
$971$	16.4707	+	16.4707i	0.528571	+	0.528571i	−0.391575	+	0.920146i	$0.628070\pi$
$972$		0			0
$973$	5.95569	+	42.2011i	0.190931	+	1.35291i
$974$		0			0
$975$		−	4.57959i		−	0.146664i
$976$		0			0
$977$	−9.44815			−0.302273			−0.151137	−	0.988513i	$-0.548293\pi$
$977$	−9.44815			−0.302273			−0.151137	+	0.988513i	$0.548293\pi$
$978$		0			0
$979$	−17.1315	+	17.1315i	−0.547525	+	0.547525i
$980$		0			0
$981$	6.13023	+	6.13023i	0.195723	+	0.195723i
$982$		0			0
$983$		−	40.2802i		−	1.28474i	−0.766395	−	0.642369i	$-0.777952\pi$
$983$		−	40.2802i		−	1.28474i	0.766395	−	0.642369i	$-0.222048\pi$
$984$		0			0
$985$	−47.3709			−1.50936
$986$		0			0
$987$	16.8846	−	2.38286i	0.537442	−	0.0758471i
$988$		0			0
$989$	−23.6323	+	23.6323i	−0.751463	+	0.751463i
$990$		0			0
$991$			26.6672i			0.847113i	0.905870	+	0.423556i	$0.139218\pi$
$991$			26.6672i			0.847113i	−0.905870	+	0.423556i	$0.860782\pi$
$992$		0			0
$993$		−	19.5017i		−	0.618868i
$994$		0			0
$995$	−6.66866	−	6.66866i	−0.211411	−	0.211411i
$996$		0			0
$997$	43.2248	−	43.2248i	1.36894	−	1.36894i	0.506994	−	0.861950i	$-0.330757\pi$
$997$	43.2248	−	43.2248i	1.36894	−	1.36894i	0.861950	−	0.506994i	$-0.169243\pi$
$998$		0			0
$999$		−	8.87800i		−	0.280888i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.u.a.1231.5		64
4.3	odd	2		336.2.u.a.139.22	yes	64
7.6	odd	2	inner	1344.2.u.a.1231.28		64
16.3	odd	4	inner	1344.2.u.a.559.28		64
16.13	even	4		336.2.u.a.307.21	yes	64
28.27	even	2		336.2.u.a.139.21	✓	64
112.13	odd	4		336.2.u.a.307.22	yes	64
112.83	even	4	inner	1344.2.u.a.559.5		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.21	✓	64	28.27	even	2
336.2.u.a.139.22	yes	64	4.3	odd	2
336.2.u.a.307.21	yes	64	16.13	even	4
336.2.u.a.307.22	yes	64	112.13	odd	4
1344.2.u.a.559.5		64	112.83	even	4	inner
1344.2.u.a.559.28		64	16.3	odd	4	inner
1344.2.u.a.1231.5		64	1.1	even	1	trivial
1344.2.u.a.1231.28		64	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.u (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(1.45584 - 1.45584i) q^{5} +(2.11390 + 1.59104i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(1.45584 - 1.45584i) q^{5} +(2.11390 + 1.59104i) q^{7} -1.00000i q^{9} +(2.03232 - 2.03232i) q^{11} +(4.25498 + 4.25498i) q^{13} +2.05887i q^{15} -2.62164i q^{17} +(-2.19851 + 2.19851i) q^{19} +(-2.61979 + 0.369721i) q^{21} -4.12640 q^{23} +0.761053i q^{25} +(0.707107 + 0.707107i) q^{27} +(5.04401 - 5.04401i) q^{29} +1.60368 q^{31} +2.87413i q^{33} +(5.39381 - 0.761208i) q^{35} +(-6.27770 - 6.27770i) q^{37} -6.01745 q^{39} +2.45431 q^{41} +(5.72710 - 5.72710i) q^{43} +(-1.45584 - 1.45584i) q^{45} -6.44501 q^{47} +(1.93718 + 6.72661i) q^{49} +(1.85378 + 1.85378i) q^{51} +(5.91522 + 5.91522i) q^{53} -5.91746i q^{55} -3.10916i q^{57} +(5.64190 + 5.64190i) q^{59} +(9.13901 + 9.13901i) q^{61} +(1.59104 - 2.11390i) q^{63} +12.3891 q^{65} +(4.56801 + 4.56801i) q^{67} +(2.91780 - 2.91780i) q^{69} +1.11894 q^{71} -4.88201 q^{73} +(-0.538145 - 0.538145i) q^{75} +(7.52962 - 1.06263i) q^{77} -12.6543i q^{79} -1.00000 q^{81} +(-7.46008 + 7.46008i) q^{83} +(-3.81668 - 3.81668i) q^{85} +7.13330i q^{87} -8.42954 q^{89} +(2.22478 + 15.7645i) q^{91} +(-1.13398 + 1.13398i) q^{93} +6.40137i q^{95} +7.55912i q^{97} +(-2.03232 - 2.03232i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 8 q^{11} + 16 q^{23} + 16 q^{29} - 24 q^{35} + 16 q^{37} + 8 q^{43} + 16 q^{53} - 56 q^{67} + 128 q^{71} - 64 q^{81} - 8 q^{91} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^11 + 16 * q^23 + 16 * q^29 - 24 * q^35 + 16 * q^37 + 8 * q^43 + 16 * q^53 - 56 * q^67 + 128 * q^71 - 64 * q^81 - 8 * q^91 + 8 * q^99

Introduction

L-functions

Modular forms

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