LMFDB - Embedded newform 1386.2.bk.d.703.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(703,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("1386.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bk (of order $6$, degree $2$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			703.16
Character	$\chi$	$=$	1386.703
Dual form			1386.2.bk.d.901.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(3.71337 - 2.14392i) q^{5} +(-0.293638 + 2.62941i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(3.71337 - 2.14392i) q^{5} +(-0.293638 + 2.62941i) q^{7} -1.00000i q^{8} +(2.14392 - 3.71337i) q^{10} +(2.21396 - 2.46949i) q^{11} -4.87511 q^{13} +(1.06040 + 2.42395i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.58834 - 2.75108i) q^{17} +(-1.05371 - 1.82508i) q^{19} -4.28783i q^{20} +(0.682601 - 3.24562i) q^{22} +(1.06040 + 1.83668i) q^{23} +(6.69276 - 11.5922i) q^{25} +(-4.22197 + 2.43755i) q^{26} +(2.13031 + 1.56900i) q^{28} -4.88335i q^{29} +(5.20074 + 3.00265i) q^{31} +(-0.866025 - 0.500000i) q^{32} -3.17668i q^{34} +(4.54684 + 10.3935i) q^{35} +(1.75907 + 3.04680i) q^{37} +(-1.82508 - 1.05371i) q^{38} +(-2.14392 - 3.71337i) q^{40} +5.28445 q^{41} +9.33232i q^{43} +(-1.03166 - 3.15209i) q^{44} +(1.83668 + 1.06040i) q^{46} +(-7.40318 + 4.27423i) q^{47} +(-6.82755 - 1.54419i) q^{49} -13.3855i q^{50} +(-2.43755 + 4.22197i) q^{52} +(-3.09716 + 5.36443i) q^{53} +(2.92688 - 13.9167i) q^{55} +(2.62941 + 0.293638i) q^{56} +(-2.44167 - 4.22910i) q^{58} +(-0.485035 - 0.280035i) q^{59} +(-1.06732 - 1.84864i) q^{61} +6.00530 q^{62} -1.00000 q^{64} +(-18.1031 + 10.4518i) q^{65} +(3.94167 - 6.82718i) q^{67} +(-1.58834 - 2.75108i) q^{68} +(9.13443 + 6.72761i) q^{70} -9.03539 q^{71} +(-0.587276 + 1.01719i) q^{73} +(3.04680 + 1.75907i) q^{74} -2.10742 q^{76} +(5.84319 + 6.54654i) q^{77} +(10.1051 - 5.83418i) q^{79} +(-3.71337 - 2.14392i) q^{80} +(4.57647 - 2.64223i) q^{82} +14.1790 q^{83} -13.6211i q^{85} +(4.66616 + 8.08202i) q^{86} +(-2.46949 - 2.21396i) q^{88} +(1.01719 - 0.587276i) q^{89} +(1.43152 - 12.8186i) q^{91} +2.12081 q^{92} +(-4.27423 + 7.40318i) q^{94} +(-7.82565 - 4.51814i) q^{95} +10.6237i q^{97} +(-6.68493 + 2.07647i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4}+O(q^{10}) $ 32 * q + 16 * q^4	$ 32 q + 16 q^{4} - 16 q^{16} + 20 q^{22} + 36 q^{25} + 12 q^{31} - 20 q^{37} - 44 q^{49} - 32 q^{64} + 48 q^{67} + 36 q^{70} + 72 q^{82} + 10 q^{88} + 144 q^{91}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 + 36 * q^25 + 12 * q^31 - 20 * q^37 - 44 * q^49 - 32 * q^64 + 48 * q^67 + 36 * q^70 + 72 * q^82 + 10 * q^88 + 144 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	3.71337	−	2.14392i	1.66067	−	0.958789i	0.688275	−	0.725450i	$-0.258368\pi$
$5$	3.71337	−	2.14392i	1.66067	−	0.958789i	0.972396	−	0.233339i	$-0.0749651\pi$
$6$		0			0
$7$	−0.293638	+	2.62941i	−0.110985	+	0.993822i
$7$	−0.293638	+	2.62941i	−0.110985	+	0.993822i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	2.14392	−	3.71337i	0.677966	−	1.17427i
$11$	2.21396	−	2.46949i	0.667534	−	0.744579i
$11$	2.21396	−	2.46949i	0.667534	−	0.744579i
$12$		0			0
$13$	−4.87511			−1.35211			−0.676056	−	0.736850i	$-0.736312\pi$
$13$	−4.87511			−1.35211			−0.676056	+	0.736850i	$0.736312\pi$
$14$	1.06040	+	2.42395i	0.283405	+	0.647828i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.58834	−	2.75108i	0.385229	−	0.667236i	−0.606572	−	0.795028i	$-0.707456\pi$
$17$	1.58834	−	2.75108i	0.385229	−	0.667236i	0.991801	+	0.127793i	$0.0407892\pi$
$18$		0			0
$19$	−1.05371	−	1.82508i	−0.241738	−	0.418703i	0.719471	−	0.694522i	$-0.244384\pi$
$19$	−1.05371	−	1.82508i	−0.241738	−	0.418703i	−0.961210	+	0.275819i	$0.911051\pi$
$20$		−	4.28783i		−	0.958789i
$21$		0			0
$22$	0.682601	−	3.24562i	0.145531	−	0.691969i
$23$	1.06040	+	1.83668i	0.221110	+	0.382973i	0.955145	−	0.296138i	$-0.0956988\pi$
$23$	1.06040	+	1.83668i	0.221110	+	0.382973i	−0.734036	+	0.679111i	$0.762365\pi$
$24$		0			0
$25$	6.69276	−	11.5922i	1.33855	−	2.31844i
$26$	−4.22197	+	2.43755i	−0.827996	+	0.478044i
$27$		0			0
$28$	2.13031	+	1.56900i	0.402591	+	0.296513i
$29$		−	4.88335i		−	0.906814i	−0.891303	−	0.453407i	$-0.850208\pi$
$29$		−	4.88335i		−	0.906814i	0.891303	−	0.453407i	$-0.149792\pi$
$30$		0			0
$31$	5.20074	+	3.00265i	0.934081	+	0.539292i	0.888100	−	0.459650i	$-0.152025\pi$
$31$	5.20074	+	3.00265i	0.934081	+	0.539292i	0.0459812	+	0.998942i	$0.485359\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$		−	3.17668i		−	0.544796i
$35$	4.54684	+	10.3935i	0.768556	+	1.75682i
$36$		0			0
$37$	1.75907	+	3.04680i	0.289190	+	0.500891i	0.973617	−	0.228190i	$-0.0732809\pi$
$37$	1.75907	+	3.04680i	0.289190	+	0.500891i	−0.684427	+	0.729081i	$0.739948\pi$
$38$	−1.82508	−	1.05371i	−0.296068	−	0.170935i
$39$		0			0
$40$	−2.14392	−	3.71337i	−0.338983	−	0.587136i
$41$	5.28445			0.825293			0.412646	−	0.910891i	$-0.364605\pi$
$41$	5.28445			0.825293			0.412646	+	0.910891i	$0.364605\pi$
$42$		0			0
$43$			9.33232i			1.42316i	0.702603	+	0.711582i	$0.252021\pi$
$43$			9.33232i			1.42316i	−0.702603	+	0.711582i	$0.747979\pi$
$44$	−1.03166	−	3.15209i	−0.155529	−	0.475196i
$45$		0			0
$46$	1.83668	+	1.06040i	0.270803	+	0.156348i
$47$	−7.40318	+	4.27423i	−1.07987	+	0.623460i	−0.930860	−	0.365376i	$-0.880940\pi$
$47$	−7.40318	+	4.27423i	−1.07987	+	0.623460i	−0.149005	+	0.988836i	$0.547607\pi$
$48$		0			0
$49$	−6.82755	−	1.54419i	−0.975365	−	0.220598i
$50$		−	13.3855i		−	1.89300i
$51$		0			0
$52$	−2.43755	+	4.22197i	−0.338028	+	0.585482i
$53$	−3.09716	+	5.36443i	−0.425427	+	0.736862i	−0.996460	−	0.0840655i	$-0.973210\pi$
$53$	−3.09716	+	5.36443i	−0.425427	+	0.736862i	0.571033	+	0.820927i	$0.306543\pi$
$54$		0			0
$55$	2.92688	−	13.9167i	0.394660	−	1.87652i
$56$	2.62941	+	0.293638i	0.351369	+	0.0392391i
$57$		0			0
$58$	−2.44167	−	4.22910i	−0.320607	−	0.555308i
$59$	−0.485035	−	0.280035i	−0.0631462	−	0.0364575i	0.468095	−	0.883678i	$-0.344941\pi$
$59$	−0.485035	−	0.280035i	−0.0631462	−	0.0364575i	−0.531241	+	0.847221i	$0.678274\pi$
$60$		0			0
$61$	−1.06732	−	1.84864i	−0.136656	−	0.236695i	0.789573	−	0.613657i	$-0.210302\pi$
$61$	−1.06732	−	1.84864i	−0.136656	−	0.236695i	−0.926229	+	0.376962i	$0.876969\pi$
$62$	6.00530			0.762674
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−18.1031	+	10.4518i	−2.24541	+	1.29639i
$66$		0			0
$67$	3.94167	−	6.82718i	0.481552	−	0.834072i	−0.518224	−	0.855245i	$-0.673407\pi$
$67$	3.94167	−	6.82718i	0.481552	−	0.834072i	0.999776	+	0.0211726i	$0.00673994\pi$
$68$	−1.58834	−	2.75108i	−0.192614	−	0.333618i
$69$		0			0
$70$	9.13443	+	6.72761i	1.09177	+	0.804104i
$71$	−9.03539			−1.07230			−0.536152	−	0.844122i	$-0.680123\pi$
$71$	−9.03539			−1.07230			−0.536152	+	0.844122i	$0.680123\pi$
$72$		0			0
$73$	−0.587276	+	1.01719i	−0.0687355	+	0.119053i	−0.898345	−	0.439291i	$-0.855230\pi$
$73$	−0.587276	+	1.01719i	−0.0687355	+	0.119053i	0.829609	+	0.558344i	$0.188563\pi$
$74$	3.04680	+	1.75907i	0.354183	+	0.204488i
$75$		0			0
$76$	−2.10742			−0.241738
$77$	5.84319	+	6.54654i	0.665893	+	0.746047i
$78$		0			0
$79$	10.1051	−	5.83418i	1.13691	−	0.656397i	0.191248	−	0.981542i	$-0.438746\pi$
$79$	10.1051	−	5.83418i	1.13691	−	0.656397i	0.945664	+	0.325145i	$0.105413\pi$
$80$	−3.71337	−	2.14392i	−0.415168	−	0.239697i
$81$		0			0
$82$	4.57647	−	2.64223i	0.505387	−	0.291785i
$83$	14.1790			1.55635			0.778174	−	0.628049i	$-0.216146\pi$
$83$	14.1790			1.55635			0.778174	+	0.628049i	$0.216146\pi$
$84$		0			0
$85$		−	13.6211i		−	1.47741i
$86$	4.66616	+	8.08202i	0.503165	+	0.871507i
$87$		0			0
$88$	−2.46949	−	2.21396i	−0.263248	−	0.236009i
$89$	1.01719	−	0.587276i	0.107822	−	0.0622512i	−0.445119	−	0.895471i	$-0.646839\pi$
$89$	1.01719	−	0.587276i	0.107822	−	0.0622512i	0.552941	+	0.833220i	$0.313505\pi$
$90$		0			0
$91$	1.43152	−	12.8186i	0.150064	−	1.34376i
$92$	2.12081			0.221110
$93$		0			0
$94$	−4.27423	+	7.40318i	−0.440853	+	0.763580i
$95$	−7.82565	−	4.51814i	−0.802895	−	0.463552i
$96$		0			0
$97$			10.6237i			1.07867i	0.842091	+	0.539335i	$0.181325\pi$
$97$			10.6237i			1.07867i	−0.842091	+	0.539335i	$0.818675\pi$
$98$	−6.68493	+	2.07647i	−0.675280	+	0.209755i
$99$		0			0
$100$	−6.69276	−	11.5922i	−0.669276	−	1.15922i
$101$	−6.13518	+	10.6264i	−0.610473	+	1.05737i	0.380688	+	0.924704i	$0.375687\pi$
$101$	−6.13518	+	10.6264i	−0.610473	+	1.05737i	−0.991161	+	0.132667i	$0.957646\pi$
$102$		0			0
$103$	−7.24855	+	4.18495i	−0.714221	+	0.412355i	−0.812622	−	0.582791i	$-0.801960\pi$
$103$	−7.24855	+	4.18495i	−0.714221	+	0.412355i	0.0984012	+	0.995147i	$0.468627\pi$
$104$			4.87511i			0.478044i
$105$		0			0
$106$			6.19431i			0.601645i
$107$	2.26797	−	1.30941i	0.219252	−	0.126585i	−0.386352	−	0.922352i	$-0.626265\pi$
$107$	2.26797	−	1.30941i	0.219252	−	0.126585i	0.605604	+	0.795766i	$0.292932\pi$
$108$		0			0
$109$	−13.9308	−	8.04296i	−1.33433	−	0.770376i	−0.348370	−	0.937357i	$-0.613265\pi$
$109$	−13.9308	−	8.04296i	−1.33433	−	0.770376i	−0.985960	+	0.166981i	$0.946598\pi$
$110$	−4.42359	−	13.5156i	−0.421773	−	1.28867i
$111$		0			0
$112$	2.42395	−	1.06040i	0.229042	−	0.100199i
$113$	16.8879			1.58868			0.794339	−	0.607475i	$-0.207818\pi$
$113$	16.8879			1.58868			0.794339	+	0.607475i	$0.207818\pi$
$114$		0			0
$115$	7.87536	+	4.54684i	0.734381	+	0.423995i
$116$	−4.22910	−	2.44167i	−0.392662	−	0.226704i
$117$		0			0
$118$	−0.560070			−0.0515587
$119$	6.76732	+	4.98421i	0.620359	+	0.456902i
$120$		0			0
$121$	−1.19676	−	10.9347i	−0.108796	−	0.994064i
$122$	−1.84864	−	1.06732i	−0.167368	−	0.0966302i
$123$		0			0
$124$	5.20074	−	3.00265i	0.467041	−	0.269646i
$125$		−	35.9557i		−	3.21597i
$126$		0			0
$127$			6.44412i			0.571823i	0.958256	+	0.285912i	$0.0922964\pi$
$127$			6.44412i			0.571823i	−0.958256	+	0.285912i	$0.907704\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−10.4518	+	18.1031i	−0.916686	+	1.58775i
$131$	6.09103	+	10.5500i	0.532176	+	0.921755i	0.999294	+	0.0375605i	$0.0119587\pi$
$131$	6.09103	+	10.5500i	0.532176	+	0.921755i	−0.467119	+	0.884195i	$0.654708\pi$
$132$		0			0
$133$	5.10830	−	2.23472i	0.442945	−	0.193775i
$134$		−	7.88335i		−	0.681017i
$135$		0			0
$136$	−2.75108	−	1.58834i	−0.235903	−	0.136199i
$137$	−7.72367	+	13.3778i	−0.659878	+	1.14294i	0.320769	+	0.947157i	$0.396059\pi$
$137$	−7.72367	+	13.3778i	−0.659878	+	1.14294i	−0.980647	+	0.195784i	$0.937275\pi$
$138$		0			0
$139$	−19.2043			−1.62889			−0.814446	−	0.580240i	$-0.802959\pi$
$139$	−19.2043			−1.62889			−0.814446	+	0.580240i	$0.802959\pi$
$140$	11.2745	+	1.25907i	0.952865	+	0.106411i
$141$		0			0
$142$	−7.82488	+	4.51769i	−0.656649	+	0.379117i
$143$	−10.7933	+	12.0390i	−0.902581	+	1.00675i
$144$		0			0
$145$	−10.4695	−	18.1337i	−0.869443	−	1.50592i
$146$			1.17455i			0.0972067i
$147$		0			0
$148$	3.51814			0.289190
$149$	−16.6735	+	9.62644i	−1.36594	+	0.788629i	−0.990407	−	0.138179i	$-0.955875\pi$
$149$	−16.6735	+	9.62644i	−1.36594	+	0.788629i	−0.375538	+	0.926807i	$0.622542\pi$
$150$		0			0
$151$	13.0091	+	7.51080i	1.05866	+	0.611220i	0.925063	−	0.379815i	$-0.124012\pi$
$151$	13.0091	+	7.51080i	1.05866	+	0.611220i	0.133602	+	0.991035i	$0.457346\pi$
$152$	−1.82508	+	1.05371i	−0.148034	+	0.0854674i
$153$		0			0
$154$	8.33362	+	2.74787i	0.671542	+	0.221430i
$155$	25.7497			2.06827
$156$		0			0
$157$	−8.27721	−	4.77885i	−0.660594	−	0.381394i	0.131909	−	0.991262i	$-0.457889\pi$
$157$	−8.27721	−	4.77885i	−0.660594	−	0.381394i	−0.792503	+	0.609868i	$0.791223\pi$
$158$	5.83418	−	10.1051i	0.464143	−	0.803919i
$159$		0			0
$160$	−4.28783			−0.338983
$161$	−5.14074	+	2.24892i	−0.405147	+	0.177240i
$162$		0			0
$163$	9.02830	+	15.6375i	0.707151	+	1.22482i	0.965910	+	0.258879i	$0.0833532\pi$
$163$	9.02830	+	15.6375i	0.707151	+	1.22482i	−0.258759	+	0.965942i	$0.583314\pi$
$164$	2.64223	−	4.57647i	0.206323	−	0.357362i
$165$		0			0
$166$	12.2794	−	7.08950i	0.953065	−	0.550252i
$167$	−8.36990			−0.647682			−0.323841	−	0.946111i	$-0.604974\pi$
$167$	−8.36990			−0.647682			−0.323841	+	0.946111i	$0.604974\pi$
$168$		0			0
$169$	10.7667			0.828207
$170$	−6.81053	−	11.7962i	−0.522344	−	0.904726i
$171$		0			0
$172$	8.08202	+	4.66616i	0.616249	+	0.355791i
$173$	−10.9140	−	18.9037i	−0.829778	−	1.43722i	−0.898212	−	0.439563i	$-0.855133\pi$
$173$	−10.9140	−	18.9037i	−0.829778	−	1.43722i	0.0684337	−	0.997656i	$-0.478200\pi$
$174$		0			0
$175$	28.5153	+	21.0019i	2.15556	+	1.58759i
$176$	−3.24562	−	0.682601i	−0.244648	−	0.0514530i
$177$		0			0
$178$	0.587276	−	1.01719i	0.0440182	−	0.0762418i
$179$	0.639776	−	1.10812i	0.0478191	−	0.0828251i	−0.841125	−	0.540841i	$-0.818106\pi$
$179$	0.639776	−	1.10812i	0.0478191	−	0.0828251i	0.888944	+	0.458015i	$0.151440\pi$
$180$		0			0
$181$			6.92820i			0.514969i	0.966282	+	0.257485i	$0.0828937\pi$
$181$			6.92820i			0.514969i	−0.966282	+	0.257485i	$0.917106\pi$
$182$	−5.16959	−	11.8170i	−0.383195	−	0.875936i
$183$		0			0
$184$	1.83668	−	1.06040i	0.135401	−	0.0781741i
$185$	13.0642	+	7.54260i	0.960497	+	0.554543i
$186$		0			0
$187$	−3.27725	−	10.0132i	−0.239656	−	0.732236i
$188$			8.54846i			0.623460i
$189$		0			0
$190$	−9.03629			−0.655561
$191$	3.25190	+	5.63245i	0.235299	+	0.407550i	0.959360	−	0.282187i	$-0.0910597\pi$
$191$	3.25190	+	5.63245i	0.235299	+	0.407550i	−0.724060	+	0.689736i	$0.757726\pi$
$192$		0			0
$193$	16.5736	+	9.56875i	1.19299	+	0.688774i	0.958984	−	0.283461i	$-0.0914828\pi$
$193$	16.5736	+	9.56875i	1.19299	+	0.688774i	0.234007	+	0.972235i	$0.424816\pi$
$194$	5.31184	+	9.20037i	0.381368	+	0.660548i
$195$		0			0
$196$	−4.75108	+	5.14074i	−0.339363	+	0.367196i
$197$		−	8.24855i		−	0.587685i	−0.955854	−	0.293842i	$-0.905066\pi$
$197$		−	8.24855i		−	0.587685i	0.955854	−	0.293842i	$-0.0949341\pi$
$198$		0			0
$199$	−11.6551	−	6.72908i	−0.826209	−	0.477012i	0.0263442	−	0.999653i	$-0.491613\pi$
$199$	−11.6551	−	6.72908i	−0.826209	−	0.477012i	−0.852553	+	0.522641i	$0.824947\pi$
$200$	−11.5922	−	6.69276i	−0.819692	−	0.473249i
$201$		0			0
$202$			12.2704i			0.863339i
$203$	12.8403	+	1.43394i	0.901212	+	0.100643i
$204$		0			0
$205$	19.6231	−	11.3294i	1.37054	−	0.791281i
$206$	−4.18495	+	7.24855i	−0.291579	+	0.505030i
$207$		0			0
$208$	2.43755	+	4.22197i	0.169014	+	0.292741i
$209$	−6.83990	−	1.43853i	−0.473126	−	0.0995052i
$210$		0			0
$211$			0.0942445i			0.00648806i	0.999995	+	0.00324403i	$0.00103261\pi$
$211$			0.0942445i			0.00648806i	−0.999995	+	0.00324403i	$0.998967\pi$
$212$	3.09716	+	5.36443i	0.212714	+	0.368431i
$213$		0			0
$214$	1.30941	−	2.26797i	0.0895094	−	0.155035i
$215$	20.0077	+	34.6544i	1.36451	+	2.36341i
$216$		0			0
$217$	−9.42233	+	12.7932i	−0.639629	+	0.868457i
$218$	−16.0859			−1.08948
$219$		0			0
$220$	−10.5888	−	9.49309i	−0.713894	−	0.640024i
$221$	−7.74332	+	13.4118i	−0.520872	+	0.902177i
$222$		0			0
$223$		−	12.5353i		−	0.839423i	−0.907658	−	0.419711i	$-0.862131\pi$
$223$		−	12.5353i		−	0.839423i	0.907658	−	0.419711i	$-0.137869\pi$
$224$	1.56900	−	2.13031i	0.104833	−	0.142338i
$225$		0			0
$226$	14.6253	−	8.44394i	0.972862	−	0.561682i
$227$	1.54419	−	2.67461i	0.102491	−	0.177520i	−0.810219	−	0.586127i	$-0.800652\pi$
$227$	1.54419	−	2.67461i	0.102491	−	0.177520i	0.912711	+	0.408607i	$0.133985\pi$
$228$		0			0
$229$	−12.5978	+	7.27333i	−0.832484	+	0.480635i	−0.854702	−	0.519118i	$-0.826260\pi$
$229$	−12.5978	+	7.27333i	−0.832484	+	0.480635i	0.0222183	+	0.999753i	$0.492927\pi$
$230$	9.09368			0.599619
$231$		0			0
$232$	−4.88335			−0.320607
$233$	24.3981	−	14.0863i	1.59837	−	0.922821i	0.606572	−	0.795028i	$-0.292544\pi$
$233$	24.3981	−	14.0863i	1.59837	−	0.922821i	0.991801	−	0.127793i	$-0.0407893\pi$
$234$		0			0
$235$	−18.3272	+	31.7436i	−1.19553	+	2.07072i
$236$	−0.485035	+	0.280035i	−0.0315731	+	0.0182287i
$237$		0			0
$238$	8.35277	+	0.932794i	0.541430	+	0.0604640i
$239$			5.26960i			0.340862i	0.985370	+	0.170431i	$0.0545160\pi$
$239$			5.26960i			0.340862i	−0.985370	+	0.170431i	$0.945484\pi$
$240$		0			0
$241$	3.56857	−	6.18094i	0.229872	−	0.398149i	−0.727898	−	0.685685i	$-0.759503\pi$
$241$	3.56857	−	6.18094i	0.229872	−	0.398149i	0.957770	+	0.287536i	$0.0928360\pi$
$242$	−6.50378	−	8.87135i	−0.418079	−	0.570272i
$243$		0			0
$244$	−2.13463			−0.136656
$245$	−28.6639	+	8.90356i	−1.83127	+	0.568827i
$246$		0			0
$247$	5.13696	+	8.89748i	0.326857	+	0.566133i
$248$	3.00265	−	5.20074i	0.190669	−	0.330248i
$249$		0			0
$250$	−17.9778	−	31.1385i	−1.13702	−	1.96937i
$251$			1.34282i			0.0847578i	0.999102	+	0.0423789i	$0.0134937\pi$
$251$			1.34282i			0.0847578i	−0.999102	+	0.0423789i	$0.986506\pi$
$252$		0			0
$253$	6.88335	+	1.44767i	0.432752	+	0.0910140i
$254$	3.22206	+	5.58077i	0.202170	+	0.350169i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−24.3146	+	14.0381i	−1.51670	+	0.875670i	−0.516897	+	0.856048i	$0.672913\pi$
$257$	−24.3146	+	14.0381i	−1.51670	+	0.875670i	−0.999807	+	0.0196218i	$0.993754\pi$
$258$		0			0
$259$	−8.52781	+	3.73066i	−0.529892	+	0.231812i
$260$			20.9037i			1.29639i
$261$		0			0
$262$	10.5500	+	6.09103i	0.651779	+	0.376305i
$263$	17.1185	+	9.88335i	1.05557	+	0.609433i	0.924203	−	0.381901i	$-0.124730\pi$
$263$	17.1185	+	9.88335i	1.05557	+	0.609433i	0.131366	+	0.991334i	$0.458064\pi$
$264$		0			0
$265$			26.5602i			1.63158i
$266$	3.30655	−	4.48948i	0.202738	−	0.275267i
$267$		0			0
$268$	−3.94167	−	6.82718i	−0.240776	−	0.417036i
$269$	−11.5384	−	6.66169i	−0.703508	−	0.406170i	0.105145	−	0.994457i	$-0.466469\pi$
$269$	−11.5384	−	6.66169i	−0.703508	−	0.406170i	−0.808653	+	0.588287i	$0.799803\pi$
$270$		0			0
$271$	−3.15682	−	5.46777i	−0.191763	−	0.332144i	0.754071	−	0.656792i	$-0.228087\pi$
$271$	−3.15682	−	5.46777i	−0.191763	−	0.332144i	−0.945835	+	0.324649i	$0.894754\pi$
$272$	−3.17668			−0.192614
$273$		0			0
$274$			15.4473i			0.933208i
$275$	−13.8093	−	42.1923i	−0.832732	−	2.54429i
$276$		0			0
$277$	−12.6662	−	7.31285i	−0.761040	−	0.439386i	0.0686292	−	0.997642i	$-0.478137\pi$
$277$	−12.6662	−	7.31285i	−0.761040	−	0.439386i	−0.829669	+	0.558256i	$0.811471\pi$
$278$	−16.6315	+	9.60217i	−0.997488	+	0.575900i
$279$		0			0
$280$	10.3935	−	4.54684i	0.621130	−	0.271726i
$281$			8.53845i			0.509361i	0.967025	+	0.254681i	$0.0819704\pi$
$281$			8.53845i			0.509361i	−0.967025	+	0.254681i	$0.918030\pi$
$282$		0			0
$283$	−14.4109	+	24.9603i	−0.856636	+	1.48374i	0.0184823	+	0.999829i	$0.494117\pi$
$283$	−14.4109	+	24.9603i	−0.856636	+	1.48374i	−0.875119	+	0.483908i	$0.839217\pi$
$284$	−4.51769	+	7.82488i	−0.268076	+	0.464321i
$285$		0			0
$286$	−3.32775	+	15.8228i	−0.196774	+	0.935619i
$287$	−1.55172	+	13.8950i	−0.0915950	+	0.820194i
$288$		0			0
$289$	3.45436	+	5.98313i	0.203198	+	0.351949i
$290$	−18.1337	−	10.4695i	−1.06485	−	0.614789i
$291$		0			0
$292$	0.587276	+	1.01719i	0.0343678	+	0.0595267i
$293$	−19.7174			−1.15190			−0.575950	−	0.817485i	$-0.695368\pi$
$293$	−19.7174			−1.15190			−0.575950	+	0.817485i	$0.695368\pi$
$294$		0			0
$295$	−2.40149			−0.139820
$296$	3.04680	−	1.75907i	0.177092	−	0.102244i
$297$		0			0
$298$	−9.62644	+	16.6735i	−0.557645	+	0.965869i
$299$	−5.16959	−	8.95399i	−0.298965	−	0.517823i
$300$		0			0
$301$	−24.5385	−	2.74032i	−1.41437	−	0.157950i
$302$	15.0216			0.864396
$303$		0			0
$304$	−1.05371	+	1.82508i	−0.0604346	+	0.104676i
$305$	−7.92668	−	4.57647i	−0.453880	−	0.262048i
$306$		0			0
$307$	−11.7075			−0.668183			−0.334092	−	0.942541i	$-0.608430\pi$
$307$	−11.7075			−0.668183			−0.334092	+	0.942541i	$0.608430\pi$
$308$	8.59106	−	1.78708i	0.489521	−	0.101828i
$309$		0			0
$310$	22.2999	−	12.8749i	1.26655	−	0.731243i
$311$	11.0534	+	6.38165i	0.626778	+	0.361870i	0.779503	−	0.626398i	$-0.215472\pi$
$311$	11.0534	+	6.38165i	0.626778	+	0.361870i	−0.152725	+	0.988269i	$0.548805\pi$
$312$		0			0
$313$	−25.5779	+	14.7674i	−1.44575	+	0.834703i	−0.998224	−	0.0595689i	$-0.981027\pi$
$313$	−25.5779	+	14.7674i	−1.44575	+	0.834703i	−0.447524	+	0.894272i	$0.647694\pi$
$314$	−9.55770			−0.539372
$315$		0			0
$316$		−	11.6684i		−	0.656397i
$317$	5.55217	+	9.61664i	0.311841	+	0.540124i	0.978761	−	0.205005i	$-0.0657210\pi$
$317$	5.55217	+	9.61664i	0.311841	+	0.540124i	−0.666920	+	0.745129i	$0.732388\pi$
$318$		0			0
$319$	−12.0594	−	10.8115i	−0.675195	−	0.605330i
$320$	−3.71337	+	2.14392i	−0.207584	+	0.119849i
$321$		0			0
$322$	−3.32755	+	4.51799i	−0.185437	+	0.251778i
$323$	−6.69461			−0.372498
$324$		0			0
$325$	−32.6279	+	56.5132i	−1.80987	+	3.13479i
$326$	15.6375	+	9.02830i	0.866079	+	0.500031i
$327$		0			0
$328$		−	5.28445i		−	0.291785i
$329$	−9.06483	−	20.7211i	−0.499760	−	1.14239i
$330$		0			0
$331$	2.64279	+	4.57744i	0.145261	+	0.251599i	0.929470	−	0.368897i	$-0.120265\pi$
$331$	2.64279	+	4.57744i	0.145261	+	0.251599i	−0.784209	+	0.620496i	$0.786931\pi$
$332$	7.08950	−	12.2794i	0.389087	−	0.673919i
$333$		0			0
$334$	−7.24855	+	4.18495i	−0.396623	+	0.228990i
$335$		−	33.8025i		−	1.84683i
$336$		0			0
$337$			15.6626i			0.853195i	0.904442	+	0.426598i	$0.140288\pi$
$337$			15.6626i			0.853195i	−0.904442	+	0.426598i	$0.859712\pi$
$338$	9.32423	−	5.38335i	0.507171	−	0.292815i
$339$		0			0
$340$	−11.7962	−	6.81053i	−0.639738	−	0.369353i
$341$	18.9293	−	6.19543i	1.02508	−	0.335502i
$342$		0			0
$343$	6.06513	−	17.4990i	0.327486	−	0.944856i
$344$	9.33232			0.503165
$345$		0			0
$346$	−18.9037	−	10.9140i	−1.01627	−	0.586742i
$347$	15.9179	+	9.19022i	0.854519	+	0.493357i	0.862173	−	0.506614i	$-0.169103\pi$
$347$	15.9179	+	9.19022i	0.854519	+	0.493357i	−0.00765395	+	0.999971i	$0.502436\pi$
$348$		0			0
$349$	19.8918			1.06478			0.532392	−	0.846498i	$-0.321293\pi$
$349$	19.8918			1.06478			0.532392	+	0.846498i	$0.321293\pi$
$350$	35.1959	+	3.93050i	1.88130	+	0.210094i
$351$		0			0
$352$	−3.15209	+	1.03166i	−0.168007	+	0.0549877i
$353$	21.5403	+	12.4363i	1.14647	+	0.661917i	0.948025	−	0.318195i	$-0.103077\pi$
$353$	21.5403	+	12.4363i	1.14647	+	0.661917i	0.198448	+	0.980111i	$0.436410\pi$
$354$		0			0
$355$	−33.5518	+	19.3711i	−1.78074	+	1.02811i
$356$		−	1.17455i		−	0.0622512i
$357$		0			0
$358$		−	1.27955i		−	0.0676264i
$359$	21.6821	−	12.5181i	1.14434	−	0.660682i	0.196835	−	0.980437i	$-0.436934\pi$
$359$	21.6821	−	12.5181i	1.14434	−	0.660682i	0.947500	+	0.319754i	$0.103600\pi$
$360$		0			0
$361$	7.27938	−	12.6083i	0.383125	−	0.663592i
$362$	3.46410	+	6.00000i	0.182069	+	0.315353i
$363$		0			0
$364$	−10.3855	−	7.64905i	−0.544349	−	0.400919i
$365$			5.03629i			0.263611i
$366$		0			0
$367$	32.3007	+	18.6488i	1.68608	+	0.973460i	0.957470	+	0.288533i	$0.0931675\pi$
$367$	32.3007	+	18.6488i	1.68608	+	0.973460i	0.728612	+	0.684927i	$0.240166\pi$
$368$	1.06040	−	1.83668i	0.0552774	−	0.0957433i
$369$		0			0
$370$	15.0852			0.784243
$371$	−13.1958	−	9.71889i	−0.685093	−	0.504579i
$372$		0			0
$373$	4.25221	−	2.45501i	0.220171	−	0.127116i	−0.385858	−	0.922558i	$-0.626095\pi$
$373$	4.25221	−	2.45501i	0.220171	−	0.127116i	0.606029	+	0.795442i	$0.292761\pi$
$374$	−7.84477	−	7.03304i	−0.405643	−	0.363670i
$375$		0			0
$376$	4.27423	+	7.40318i	0.220427	+	0.381790i
$377$			23.8068i			1.22611i
$378$		0			0
$379$	−5.28557			−0.271502			−0.135751	−	0.990743i	$-0.543345\pi$
$379$	−5.28557			−0.271502			−0.135751	+	0.990743i	$0.543345\pi$
$380$	−7.82565	+	4.51814i	−0.401448	+	0.231776i
$381$		0			0
$382$	5.63245	+	3.25190i	0.288181	+	0.166382i
$383$	3.46120	−	1.99832i	0.176859	−	0.102110i	−0.408957	−	0.912554i	$-0.634107\pi$
$383$	3.46120	−	1.99832i	0.176859	−	0.102110i	0.585816	+	0.810444i	$0.300774\pi$
$384$		0			0
$385$	35.7332	+	11.7824i	1.82113	+	0.600488i
$386$	19.1375			0.974073
$387$		0			0
$388$	9.20037	+	5.31184i	0.467078	+	0.269668i
$389$	8.80253	−	15.2464i	0.446306	−	0.773024i	−0.551836	−	0.833952i	$-0.686073\pi$
$389$	8.80253	−	15.2464i	0.446306	−	0.773024i	0.998142	+	0.0609281i	$0.0194060\pi$
$390$		0			0
$391$	6.73713			0.340711
$392$	−1.54419	+	6.82755i	−0.0779933	+	0.344844i
$393$		0			0
$394$	−4.12427	−	7.14345i	−0.207778	−	0.359882i
$395$	25.0160	−	43.3290i	1.25869	−	2.18012i
$396$		0			0
$397$	−3.87066	+	2.23472i	−0.194263	+	0.112158i	−0.593977	−	0.804482i	$-0.702443\pi$
$397$	−3.87066	+	2.23472i	−0.194263	+	0.112158i	0.399714	+	0.916640i	$0.369109\pi$
$398$	−13.4582			−0.674596
$399$		0			0
$400$	−13.3855			−0.669276
$401$	−11.4531	−	19.8374i	−0.571942	−	0.990632i	−0.996367	−	0.0851691i	$-0.972857\pi$
$401$	−11.4531	−	19.8374i	−0.571942	−	0.990632i	0.424425	−	0.905463i	$-0.360476\pi$
$402$		0			0
$403$	−25.3542	−	14.6383i	−1.26298	−	0.729183i
$404$	6.13518	+	10.6264i	0.305236	+	0.528685i
$405$		0			0
$406$	11.8370	−	5.17832i	0.587460	−	0.256996i
$407$	11.4186	+	2.40149i	0.565997	+	0.119037i
$408$		0			0
$409$	0.204972	−	0.355022i	0.0101352	−	0.0175547i	−0.860913	−	0.508752i	$-0.830107\pi$
$409$	0.204972	−	0.355022i	0.0101352	−	0.0175547i	0.871049	+	0.491197i	$0.163440\pi$
$410$	11.3294	−	19.6231i	0.559520	−	0.969118i
$411$		0			0
$412$			8.36990i			0.412355i
$413$	0.878751	−	1.19313i	0.0432405	−	0.0587099i
$414$		0			0
$415$	52.6519	−	30.3986i	2.58458	−	1.49221i
$416$	4.22197	+	2.43755i	0.206999	+	0.119511i
$417$		0			0
$418$	−6.64279	+	2.17415i	−0.324910	+	0.106341i
$419$			16.0552i			0.784349i	0.919891	+	0.392174i	$0.128277\pi$
$419$			16.0552i			0.784349i	−0.919891	+	0.392174i	$0.871723\pi$
$420$		0			0
$421$	32.2892			1.57368			0.786839	−	0.617159i	$-0.211716\pi$
$421$	32.2892			1.57368			0.786839	+	0.617159i	$0.211716\pi$
$422$	0.0471222	+	0.0816181i	0.00229387	+	0.00397311i
$423$		0			0
$424$	5.36443	+	3.09716i	0.260520	+	0.150411i
$425$	−21.2607	−	36.8246i	−1.03130	−	1.78626i
$426$		0			0
$427$	5.17424	−	2.26357i	0.250399	−	0.109542i
$428$		−	2.61882i		−	0.126585i
$429$		0			0
$430$	34.6544	+	20.0077i	1.67118	+	0.964857i
$431$	17.0908	+	9.86737i	0.823234	+	0.475294i	0.851530	−	0.524305i	$-0.175675\pi$
$431$	17.0908	+	9.86737i	0.823234	+	0.475294i	−0.0282964	+	0.999600i	$0.509008\pi$
$432$		0			0
$433$		−	24.4830i		−	1.17658i	−0.808651	−	0.588289i	$-0.799802\pi$
$433$		−	24.4830i		−	1.17658i	0.808651	−	0.588289i	$-0.200198\pi$
$434$	−1.76339	+	15.7904i	−0.0846452	+	0.757962i
$435$		0			0
$436$	−13.9308	+	8.04296i	−0.667165	+	0.385188i
$437$	2.23472	−	3.87066i	0.106901	−	0.185159i
$438$		0			0
$439$	3.83068	+	6.63494i	0.182828	+	0.316668i	0.942843	−	0.333238i	$-0.108141\pi$
$439$	3.83068	+	6.63494i	0.182828	+	0.316668i	−0.760014	+	0.649907i	$0.774808\pi$
$440$	−13.9167	−	2.92688i	−0.663452	−	0.139533i
$441$		0			0
$442$			15.4866i			0.736625i
$443$	−4.90259	−	8.49153i	−0.232929	−	0.403445i	0.725740	−	0.687969i	$-0.241498\pi$
$443$	−4.90259	−	8.49153i	−0.232929	−	0.403445i	−0.958669	+	0.284524i	$0.908164\pi$
$444$		0			0
$445$	2.51814	−	4.36155i	0.119371	−	0.206757i
$446$	−6.26763	−	10.8559i	−0.296781	−	0.514039i
$447$		0			0
$448$	0.293638	−	2.62941i	0.0138731	−	0.124228i
$449$	5.58791			0.263710			0.131855	−	0.991269i	$-0.457907\pi$
$449$	5.58791			0.263710			0.131855	+	0.991269i	$0.457907\pi$
$450$		0			0
$451$	11.6996	−	13.0499i	0.550911	−	0.614496i
$452$	8.44394	−	14.6253i	0.397169	−	0.687918i
$453$		0			0
$454$		−	3.08838i		−	0.144945i
$455$	−22.1663	−	50.6694i	−1.03917	−	2.37542i
$456$		0			0
$457$	15.6988	−	9.06372i	0.734360	−	0.423983i	−0.0856551	−	0.996325i	$-0.527298\pi$
$457$	15.6988	−	9.06372i	0.734360	−	0.423983i	0.820015	+	0.572342i	$0.193965\pi$
$458$	−7.27333	+	12.5978i	−0.339860	+	0.588655i
$459$		0			0
$460$	7.87536	−	4.54684i	0.367190	−	0.211997i
$461$	−0.253895			−0.0118251			−0.00591254	−	0.999983i	$-0.501882\pi$
$461$	−0.253895			−0.0118251			−0.00591254	+	0.999983i	$0.501882\pi$
$462$		0			0
$463$	−38.0406			−1.76790			−0.883949	−	0.467584i	$-0.845125\pi$
$463$	−38.0406			−1.76790			−0.883949	+	0.467584i	$0.845125\pi$
$464$	−4.22910	+	2.44167i	−0.196331	+	0.113352i
$465$		0			0
$466$	14.0863	−	24.3981i	0.652533	−	1.13022i
$467$	13.6270	−	7.86755i	0.630582	−	0.364067i	−0.150395	−	0.988626i	$-0.548055\pi$
$467$	13.6270	−	7.86755i	0.630582	−	0.364067i	0.780977	+	0.624559i	$0.214721\pi$
$468$		0			0
$469$	16.7940	+	12.3690i	0.775475	+	0.571146i
$470$			36.6544i			1.69074i
$471$		0			0
$472$	−0.280035	+	0.485035i	−0.0128897	+	0.0223256i
$473$	23.0461	+	20.6614i	1.05966	+	0.950011i
$474$		0			0
$475$	−28.2090			−1.29432
$476$	7.70011	−	3.36856i	0.352934	−	0.154398i
$477$		0			0
$478$	2.63480	+	4.56360i	0.120513	+	0.208734i
$479$	−1.29863	+	2.24929i	−0.0593358	+	0.102773i	−0.894167	−	0.447733i	$-0.852232\pi$
$479$	−1.29863	+	2.24929i	−0.0593358	+	0.102773i	0.834832	+	0.550505i	$0.185565\pi$
$480$		0			0
$481$	−8.57567	−	14.8535i	−0.391017	−	0.677261i
$482$		−	7.13714i		−	0.325088i
$483$		0			0
$484$	−10.0681	−	4.43093i	−0.457641	−	0.201406i
$485$	22.7763	+	39.4497i	1.03422	+	1.79132i
$486$		0			0
$487$	−6.44929	+	11.1705i	−0.292245	+	0.506184i	−0.974340	−	0.225080i	$-0.927736\pi$
$487$	−6.44929	+	11.1705i	−0.292245	+	0.506184i	0.682095	+	0.731264i	$0.261069\pi$
$488$	−1.84864	+	1.06732i	−0.0836842	+	0.0483151i
$489$		0			0
$490$	−20.3718	+	22.0426i	−0.920306	+	0.995785i
$491$			18.6508i			0.841698i	0.907131	+	0.420849i	$0.138268\pi$
$491$			18.6508i			0.841698i	−0.907131	+	0.420849i	$0.861732\pi$
$492$		0			0
$493$	−13.4345	−	7.75640i	−0.605059	−	0.349331i
$494$	8.89748	+	5.13696i	0.400317	+	0.231123i
$495$		0			0
$496$		−	6.00530i		−	0.269646i
$497$	2.65314	−	23.7577i	0.119009	−	1.06568i
$498$		0			0
$499$	−13.1159	−	22.7174i	−0.587149	−	1.01697i	−0.994604	−	0.103746i	$-0.966917\pi$
$499$	−13.1159	−	22.7174i	−0.587149	−	1.01697i	0.407455	−	0.913225i	$-0.366416\pi$
$500$	−31.1385	−	17.9778i	−1.39256	−	0.803993i
$501$		0			0
$502$	0.671408	+	1.16291i	0.0299664	+	0.0519033i
$503$	−19.9823			−0.890965			−0.445482	−	0.895291i	$-0.646968\pi$
$503$	−19.9823			−0.890965			−0.445482	+	0.895291i	$0.646968\pi$
$504$		0			0
$505$			52.6132i			2.34126i
$506$	6.68499	−	2.18796i	0.297184	−	0.0972665i
$507$		0			0
$508$	5.58077	+	3.22206i	0.247607	+	0.142956i
$509$	10.2144	−	5.89730i	0.452746	−	0.261393i	−0.256243	−	0.966612i	$-0.582485\pi$
$509$	10.2144	−	5.89730i	0.452746	−	0.261393i	0.708989	+	0.705219i	$0.249151\pi$
$510$		0			0
$511$	−2.50217	−	1.84287i	−0.110689	−	0.0815240i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−14.0381	+	24.3146i	−0.619192	+	1.07247i
$515$	−17.9444	+	31.0806i	−0.790723	+	1.36957i
$516$		0			0
$517$	−5.83519	+	27.7451i	−0.256631	+	1.22023i
$518$	−5.51997	+	7.49475i	−0.242534	+	0.329300i
$519$		0			0
$520$	10.4518	+	18.1031i	0.458343	+	0.793873i
$521$	−1.94014	−	1.12014i	−0.0849991	−	0.0490743i	0.456898	−	0.889519i	$-0.348960\pi$
$521$	−1.94014	−	1.12014i	−0.0849991	−	0.0490743i	−0.541897	+	0.840445i	$0.682294\pi$
$522$		0			0
$523$	−17.7386	−	30.7242i	−0.775655	−	1.34347i	−0.934426	−	0.356159i	$-0.884086\pi$
$523$	−17.7386	−	30.7242i	−0.775655	−	1.34347i	0.158770	−	0.987316i	$-0.449247\pi$
$524$	12.1821			0.532176
$525$		0			0
$526$	19.7667			0.861869
$527$	16.5211	−	9.53845i	0.719670	−	0.415501i
$528$		0			0
$529$	9.25108	−	16.0233i	0.402221	−	0.696667i
$530$	13.2801	+	23.0018i	0.576850	+	0.999134i
$531$		0			0
$532$	0.618820	−	5.54128i	0.0268293	−	0.240245i
$533$	−25.7623			−1.11589
$534$		0			0
$535$	5.61453	−	9.72466i	0.242737	−	0.420434i
$536$	−6.82718	−	3.94167i	−0.294889	−	0.170254i
$537$		0			0
$538$	−13.3234			−0.574412
$539$	−18.9293	+	13.4418i	−0.815342	+	0.578979i
$540$		0			0
$541$	−4.07668	+	2.35367i	−0.175270	+	0.101192i	−0.585069	−	0.810984i	$-0.698932\pi$
$541$	−4.07668	+	2.35367i	−0.175270	+	0.101192i	0.409798	+	0.912176i	$0.365599\pi$
$542$	−5.46777	−	3.15682i	−0.234861	−	0.135597i
$543$		0			0
$544$	−2.75108	+	1.58834i	−0.117952	+	0.0680994i
$545$	−68.9737			−2.95451
$546$		0			0
$547$		−	41.7618i		−	1.78560i	−0.450449	−	0.892802i	$-0.648736\pi$
$547$		−	41.7618i		−	1.78560i	0.450449	−	0.892802i	$-0.351264\pi$
$548$	7.72367	+	13.3778i	0.329939	+	0.571471i
$549$		0			0
$550$	−33.0554	−	29.6350i	−1.40949	−	1.26364i
$551$	−8.91251	+	5.14564i	−0.379686	+	0.219212i
$552$		0			0
$553$	12.3732	+	28.2835i	0.526162	+	1.20274i
$554$	−14.6257			−0.621386
$555$		0			0
$556$	−9.60217	+	16.6315i	−0.407223	+	0.705331i
$557$	−13.9612	−	8.06049i	−0.591554	−	0.341534i	0.174158	−	0.984718i	$-0.444280\pi$
$557$	−13.9612	−	8.06049i	−0.591554	−	0.341534i	−0.765712	+	0.643184i	$0.777613\pi$
$558$		0			0
$559$		−	45.4961i		−	1.92428i
$560$	6.72761	−	9.13443i	0.284294	−	0.386000i
$561$		0			0
$562$	4.26923	+	7.39452i	0.180086	+	0.311919i
$563$	−4.62388	+	8.00879i	−0.194873	+	0.337530i	−0.946859	−	0.321649i	$-0.895763\pi$
$563$	−4.62388	+	8.00879i	−0.194873	+	0.337530i	0.751986	+	0.659179i	$0.229096\pi$
$564$		0			0
$565$	62.7110	−	36.2062i	2.63827	−	1.52321i
$566$			28.8217i			1.21147i
$567$		0			0
$568$			9.03539i			0.379117i
$569$	−5.85068	+	3.37789i	−0.245273	+	0.141609i	−0.617598	−	0.786494i	$-0.711894\pi$
$569$	−5.85068	+	3.37789i	−0.245273	+	0.141609i	0.372325	+	0.928103i	$0.378561\pi$
$570$		0			0
$571$	−25.0733	−	14.4761i	−1.04928	−	0.605805i	−0.126836	−	0.991924i	$-0.540482\pi$
$571$	−25.0733	−	14.4761i	−1.04928	−	0.605805i	−0.922449	+	0.386119i	$0.873815\pi$
$572$	5.02946	+	15.3668i	0.210292	+	0.642518i
$573$		0			0
$574$	5.60366	+	12.8093i	0.233892	+	0.534648i
$575$	28.3881			1.18387
$576$		0			0
$577$	29.1717	+	16.8423i	1.21443	+	0.701154i	0.963722	−	0.266908i	$-0.0860020\pi$
$577$	29.1717	+	16.8423i	1.21443	+	0.701154i	0.250712	+	0.968062i	$0.419335\pi$
$578$	5.98313	+	3.45436i	0.248865	+	0.143683i
$579$		0			0
$580$	−20.9390			−0.869443
$581$	−4.16350	+	37.2824i	−0.172731	+	1.54673i
$582$		0			0
$583$	6.39043	+	19.5250i	0.264665	+	0.808645i
$584$	1.01719	+	0.587276i	0.0420917	+	0.0243017i
$585$		0			0
$586$	−17.0757	+	9.85868i	−0.705392	+	0.407258i
$587$		−	41.0762i		−	1.69540i	−0.530479	−	0.847698i	$-0.677988\pi$
$587$		−	41.0762i		−	1.69540i	0.530479	−	0.847698i	$-0.322012\pi$
$588$		0			0
$589$		−	12.6557i		−	0.521470i
$590$	−2.07975	+	1.20074i	−0.0856219	+	0.0494338i
$591$		0			0
$592$	1.75907	−	3.04680i	0.0722974	−	0.125223i
$593$	−3.93910	−	6.82272i	−0.161759	−	0.280176i	0.773740	−	0.633503i	$-0.218384\pi$
$593$	−3.93910	−	6.82272i	−0.161759	−	0.280176i	−0.935500	+	0.353327i	$0.885050\pi$
$594$		0			0
$595$	35.8153	+	3.99966i	1.46828	+	0.163970i
$596$			19.2529i			0.788629i
$597$		0			0
$598$	−8.95399	−	5.16959i	−0.366156	−	0.211400i
$599$	−17.5709	+	30.4336i	−0.717926	+	1.24348i	0.243894	+	0.969802i	$0.421575\pi$
$599$	−17.5709	+	30.4336i	−0.717926	+	1.24348i	−0.961820	+	0.273682i	$0.911758\pi$
$600$		0			0
$601$	−27.5573			−1.12409			−0.562044	−	0.827108i	$-0.689985\pi$
$601$	−27.5573			−1.12409			−0.562044	+	0.827108i	$0.689985\pi$
$602$	−22.6211	+	9.89603i	−0.921967	+	0.403332i
$603$		0			0
$604$	13.0091	−	7.51080i	0.529332	−	0.305610i
$605$	−27.8871	−	38.0389i	−1.13377	−	1.54650i
$606$		0			0
$607$	−20.6453	−	35.7588i	−0.837968	−	1.45140i	−0.891591	−	0.452842i	$-0.850410\pi$
$607$	−20.6453	−	35.7588i	−0.837968	−	1.45140i	0.0536227	−	0.998561i	$-0.482923\pi$
$608$			2.10742i			0.0854674i
$609$		0			0
$610$	−9.15294			−0.370592
$611$	36.0913	−	20.8373i	1.46010	−	0.842988i
$612$		0			0
$613$	29.3234	+	16.9299i	1.18436	+	0.683792i	0.957020	−	0.290023i	$-0.0936631\pi$
$613$	29.3234	+	16.9299i	1.18436	+	0.683792i	0.227342	+	0.973815i	$0.426996\pi$
$614$	−10.1390	+	5.85376i	−0.409177	+	0.236238i
$615$		0			0
$616$	6.54654	−	5.84319i	0.263768	−	0.235429i
$617$	−2.73195			−0.109984			−0.0549922	−	0.998487i	$-0.517513\pi$
$617$	−2.73195			−0.109984			−0.0549922	+	0.998487i	$0.517513\pi$
$618$		0			0
$619$	1.07356	+	0.619823i	0.0431502	+	0.0249128i	0.521420	−	0.853300i	$-0.325403\pi$
$619$	1.07356	+	0.619823i	0.0431502	+	0.0249128i	−0.478270	+	0.878213i	$0.658736\pi$
$620$	12.8749	−	22.2999i	0.517067	−	0.895586i
$621$		0			0
$622$	12.7633			0.511762
$623$	1.24550	+	2.84706i	0.0499000	+	0.114065i
$624$		0			0
$625$	−43.6222	−	75.5558i	−1.74489	−	3.02223i
$626$	−14.7674	+	25.5779i	−0.590224	+	1.02230i
$627$		0			0
$628$	−8.27721	+	4.77885i	−0.330297	+	0.190697i
$629$	11.1760			0.445616
$630$		0			0
$631$	−11.4378			−0.455331			−0.227665	−	0.973739i	$-0.573109\pi$
$631$	−11.4378			−0.455331			−0.227665	+	0.973739i	$0.573109\pi$
$632$	−5.83418	−	10.1051i	−0.232071	−	0.401959i
$633$		0			0
$634$	9.61664	+	5.55217i	0.381926	+	0.220505i
$635$	13.8157	+	23.9294i	0.548258	+	0.949610i
$636$		0			0
$637$	33.2851	+	7.52809i	1.31880	+	0.298274i
$638$	−15.8495	−	3.33338i	−0.627487	−	0.131970i
$639$		0			0
$640$	−2.14392	+	3.71337i	−0.0847457	+	0.146784i
$641$	12.3886	−	21.4577i	0.489321	−	0.847530i	−0.510603	−	0.859817i	$-0.670578\pi$
$641$	12.3886	−	21.4577i	0.489321	−	0.847530i	0.999925	+	0.0122870i	$0.00391116\pi$
$642$		0			0
$643$		−	35.2862i		−	1.39155i	−0.718259	−	0.695776i	$-0.755061\pi$
$643$		−	35.2862i		−	1.39155i	0.718259	−	0.695776i	$-0.244939\pi$
$644$	−0.622751	+	5.57647i	−0.0245398	+	0.219744i
$645$		0			0
$646$	−5.79770	+	3.34730i	−0.228107	+	0.131698i
$647$	30.1967	+	17.4341i	1.18716	+	0.685405i	0.957659	−	0.287904i	$-0.0929585\pi$
$647$	30.1967	+	17.4341i	1.18716	+	0.685405i	0.229497	+	0.973309i	$0.426292\pi$
$648$		0			0
$649$	−1.76539	+	0.577803i	−0.0692977	+	0.0226807i
$650$			65.2558i			2.55954i
$651$		0			0
$652$	18.0566			0.707151
$653$	0.602841	+	1.04415i	0.0235910	+	0.0408608i	0.877580	−	0.479430i	$-0.159157\pi$
$653$	0.602841	+	1.04415i	0.0235910	+	0.0408608i	−0.853989	+	0.520291i	$0.825823\pi$
$654$		0			0
$655$	45.2365	+	26.1173i	1.76754	+	1.02049i
$656$	−2.64223	−	4.57647i	−0.103162	−	0.178681i
$657$		0			0
$658$	−18.2109	−	13.4125i	−0.709935	−	0.522875i
$659$			20.7870i			0.809747i	0.914373	+	0.404873i	$0.132684\pi$
$659$			20.7870i			0.809747i	−0.914373	+	0.404873i	$0.867316\pi$
$660$		0			0
$661$	−22.6264	−	13.0634i	−0.880066	−	0.508107i	−0.00938615	−	0.999956i	$-0.502988\pi$
$661$	−22.6264	−	13.0634i	−0.880066	−	0.508107i	−0.870680	+	0.491849i	$0.836321\pi$
$662$	4.57744	+	2.64279i	0.177907	+	0.102715i
$663$		0			0
$664$		−	14.1790i		−	0.550252i
$665$	14.1779	−	19.2501i	0.549797	−	0.746488i
$666$		0			0
$667$	8.96912	−	5.17832i	0.347286	−	0.200505i
$668$	−4.18495	+	7.24855i	−0.161921	+	0.280455i
$669$		0			0
$670$	−16.9012	−	29.2738i	−0.652952	−	1.13095i
$671$	−6.92820	−	1.45710i	−0.267460	−	0.0562508i
$672$		0			0
$673$		−	38.9993i		−	1.50331i	−0.659555	−	0.751656i	$-0.729255\pi$
$673$		−	38.9993i		−	1.50331i	0.659555	−	0.751656i	$-0.270745\pi$
$674$	7.83129	+	13.5642i	0.301650	+	0.522473i
$675$		0			0
$676$	5.38335	−	9.32423i	0.207052	−	0.358624i
$677$	−23.1373	−	40.0750i	−0.889239	−	1.54021i	−0.840777	−	0.541382i	$-0.817901\pi$
$677$	−23.1373	−	40.0750i	−0.889239	−	1.54021i	−0.0484622	−	0.998825i	$-0.515432\pi$
$678$		0			0
$679$	−27.9340	−	3.11952i	−1.07201	−	0.119716i
$680$	−13.6211			−0.522344
$681$		0			0
$682$	13.2955	−	14.8300i	0.509111	−	0.567871i
$683$	−15.2443	+	26.4039i	−0.583306	+	1.01032i	0.411778	+	0.911284i	$0.364908\pi$
$683$	−15.2443	+	26.4039i	−0.583306	+	1.01032i	−0.995084	+	0.0990317i	$0.968425\pi$
$684$		0			0
$685$			66.2356i			2.53073i
$686$	−3.49693	−	18.1871i	−0.133514	−	0.694388i
$687$		0			0
$688$	8.08202	−	4.66616i	0.308124	−	0.177896i
$689$	15.0990	−	26.1522i	0.575225	−	0.996319i
$690$		0			0
$691$	18.4279	−	10.6393i	0.701029	−	0.404739i	−0.106702	−	0.994291i	$-0.534029\pi$
$691$	18.4279	−	10.6393i	0.701029	−	0.404739i	0.807731	+	0.589552i	$0.200696\pi$
$692$	−21.8281			−0.829778
$693$		0			0
$694$	18.3804			0.697712
$695$	−71.3129	+	41.1725i	−2.70505	+	1.56176i
$696$		0			0
$697$	8.39350	−	14.5380i	0.317926	−	0.550665i
$698$	17.2268	−	9.94590i	0.652044	−	0.376458i
$699$		0			0
$700$	32.4458	−	14.1941i	1.22634	−	0.536485i
$701$		−	16.1936i		−	0.611622i	−0.952092	−	0.305811i	$-0.901072\pi$
$701$		−	16.1936i		−	0.611622i	0.952092	−	0.305811i	$-0.0989276\pi$
$702$		0			0
$703$	3.70711	−	6.42090i	0.139816	−	0.242169i
$704$	−2.21396	+	2.46949i	−0.0834418	+	0.0930724i
$705$		0			0
$706$	24.8726			0.936091
$707$	−26.1397	−	19.2522i	−0.983085	−	0.724054i
$708$		0			0
$709$	−23.4938	−	40.6925i	−0.882328	−	1.52824i	−0.848745	−	0.528802i	$-0.822642\pi$
$709$	−23.4938	−	40.6925i	−0.882328	−	1.52824i	−0.0335831	−	0.999436i	$-0.510692\pi$
$710$	−19.3711	+	33.5518i	−0.726985	+	1.25918i
$711$		0			0
$712$	−0.587276	−	1.01719i	−0.0220091	−	0.0381209i
$713$			12.7361i			0.476971i
$714$		0			0
$715$	−14.2689	+	67.8453i	−0.533625	+	2.53727i
$716$	−0.639776	−	1.10812i	−0.0239096	−	0.0414126i
$717$		0			0
$718$	12.5181	−	21.6821i	0.467173	−	0.809167i
$719$	1.09971	−	0.634916i	0.0410122	−	0.0236784i	−0.479354	−	0.877622i	$-0.659129\pi$
$719$	1.09971	−	0.634916i	0.0410122	−	0.0236784i	0.520366	+	0.853943i	$0.325796\pi$
$720$		0			0
$721$	−8.87548	−	20.2882i	−0.330540	−	0.755573i
$722$		−	14.5588i		−	0.541821i
$723$		0			0
$724$	6.00000	+	3.46410i	0.222988	+	0.128742i
$725$	−56.6087	−	32.6830i	−2.10239	−	1.21382i
$726$		0			0
$727$			9.29280i			0.344651i	0.985040	+	0.172325i	$0.0551281\pi$
$727$			9.29280i			0.344651i	−0.985040	+	0.172325i	$0.944872\pi$
$728$	−12.8186	−	1.43152i	−0.475090	−	0.0530556i
$729$		0			0
$730$	2.51814	+	4.36155i	0.0932007	+	0.161428i
$731$	25.6740	+	14.8229i	0.949586	+	0.548244i
$732$		0			0
$733$	−1.68863	−	2.92479i	−0.0623709	−	0.108030i	0.833154	−	0.553041i	$-0.186533\pi$
$733$	−1.68863	−	2.92479i	−0.0623709	−	0.108030i	−0.895525	+	0.445012i	$0.853200\pi$
$734$	37.2976			1.37668
$735$		0			0
$736$		−	2.12081i		−	0.0781741i
$737$	−8.13294	−	24.8490i	−0.299581	−	0.915325i
$738$		0			0
$739$	−13.8105	−	7.97348i	−0.508026	−	0.293309i	0.223996	−	0.974590i	$-0.428090\pi$
$739$	−13.8105	−	7.97348i	−0.508026	−	0.293309i	−0.732022	+	0.681281i	$0.761423\pi$
$740$	13.0642	−	7.54260i	0.480249	−	0.277272i
$741$		0			0
$742$	−16.2874	−	1.81889i	−0.597928	−	0.0667735i
$743$		−	29.0682i		−	1.06641i	−0.845986	−	0.533205i	$-0.820987\pi$
$743$		−	29.0682i		−	1.06641i	0.845986	−	0.533205i	$-0.179013\pi$
$744$		0			0
$745$	−41.2766	+	71.4931i	−1.51226	+	2.61930i
$746$	2.45501	−	4.25221i	0.0898844	−	0.155684i
$747$		0			0
$748$	−10.3103	−	2.16840i	−0.376981	−	0.0792847i
$749$	2.77701	+	6.34789i	0.101470	+	0.231947i
$750$		0			0
$751$	−5.30142	−	9.18233i	−0.193452	−	0.335068i	0.752940	−	0.658089i	$-0.228635\pi$
$751$	−5.30142	−	9.18233i	−0.193452	−	0.335068i	−0.946392	+	0.323021i	$0.895302\pi$
$752$	7.40318	+	4.27423i	0.269966	+	0.155865i
$753$		0			0
$754$	11.9034	+	20.6173i	0.433497	+	0.750839i
$755$	64.4101			2.34412
$756$		0			0
$757$	34.0152			1.23630			0.618152	−	0.786058i	$-0.287881\pi$
$757$	34.0152			1.23630			0.618152	+	0.786058i	$0.287881\pi$
$758$	−4.57744	+	2.64279i	−0.166260	+	0.0959903i
$759$		0			0
$760$	−4.51814	+	7.82565i	−0.163890	+	0.283866i
$761$	23.8366	+	41.2862i	0.864077	+	1.49663i	0.867961	+	0.496633i	$0.165430\pi$
$761$	23.8366	+	41.2862i	0.864077	+	1.49663i	−0.00388374	+	0.999992i	$0.501236\pi$
$762$		0			0
$763$	25.2388	−	34.2680i	0.913707	−	1.24059i
$764$	6.50380			0.235299
$765$		0			0
$766$	1.99832	−	3.46120i	0.0722024	−	0.125058i
$767$	2.36460	+	1.36520i	0.0853807	+	0.0492946i
$768$		0			0
$769$	32.5377			1.17334			0.586669	−	0.809827i	$-0.300439\pi$
$769$	32.5377			1.17334			0.586669	+	0.809827i	$0.300439\pi$
$770$	36.8370	−	7.66270i	1.32751	−	0.276145i
$771$		0			0
$772$	16.5736	−	9.56875i	0.596495	−	0.344387i
$773$	−0.925697	−	0.534451i	−0.0332950	−	0.0192229i	0.483260	−	0.875477i	$-0.339453\pi$
$773$	−0.925697	−	0.534451i	−0.0332950	−	0.0192229i	−0.516555	+	0.856254i	$0.672786\pi$
$774$		0			0
$775$	69.6146	−	40.1920i	2.50063	−	1.44374i
$776$	10.6237			0.381368
$777$		0			0
$778$		−	17.6051i		−	0.631172i
$779$	−5.56829	−	9.64457i	−0.199505	−	0.345553i
$780$		0			0
$781$	−20.0040	+	22.3128i	−0.715799	+	0.798415i
$782$	5.83452	−	3.36856i	0.208642	−	0.120460i
$783$		0			0
$784$	2.07647	+	6.68493i	0.0741597	+	0.238747i
$785$	−40.9818			−1.46270
$786$		0			0
$787$	−14.6047	+	25.2960i	−0.520600	+	0.901706i	0.479113	+	0.877753i	$0.340959\pi$
$787$	−14.6047	+	25.2960i	−0.520600	+	0.901706i	−0.999713	+	0.0239530i	$0.992375\pi$
$788$	−7.14345	−	4.12427i	−0.254475	−	0.146921i
$789$		0			0
$790$		−	50.0320i		−	1.78006i
$791$	−4.95892	+	44.4051i	−0.176319	+	1.57886i
$792$		0			0
$793$	5.20328	+	9.01234i	0.184774	+	0.320038i
$794$	−2.23472	+	3.87066i	−0.0793074	+	0.137364i
$795$		0			0
$796$	−11.6551	+	6.72908i	−0.413104	+	0.238506i
$797$		−	43.3568i		−	1.53578i	−0.640584	−	0.767888i	$-0.721308\pi$
$797$		−	43.3568i		−	1.53578i	0.640584	−	0.767888i	$-0.278692\pi$
$798$		0			0
$799$			27.1557i			0.960699i
$800$	−11.5922	+	6.69276i	−0.409846	+	0.236625i
$801$		0			0
$802$	−19.8374	−	11.4531i	−0.700483	−	0.404424i
$803$	1.21174	+	3.70230i	0.0427614	+	0.130651i
$804$		0			0
$805$	−14.2680	+	19.3724i	−0.502881	+	0.682787i
$806$	−29.2765			−1.03122
$807$		0			0
$808$	10.6264	+	6.13518i	0.373837	+	0.215835i
$809$	−37.6075	−	21.7127i	−1.32221	−	0.763378i	−0.338128	−	0.941100i	$-0.609794\pi$
$809$	−37.6075	−	21.7127i	−1.32221	−	0.763378i	−0.984081	+	0.177722i	$0.943127\pi$
$810$		0			0
$811$	12.6273			0.443404			0.221702	−	0.975114i	$-0.428839\pi$
$811$	12.6273			0.443404			0.221702	+	0.975114i	$0.428839\pi$
$812$	7.66197	−	10.4031i	0.268883	−	0.365076i
$813$		0			0
$814$	11.0895	−	3.62953i	0.388687	−	0.127215i
$815$	67.0509	+	38.7118i	2.34869	+	1.35602i
$816$		0			0
$817$	17.0323	−	9.83358i	0.595883	−	0.344033i
$818$		−	0.409944i		−	0.0143333i
$819$		0			0
$820$		−	22.6589i		−	0.791281i
$821$	−5.80875	+	3.35368i	−0.202727	+	0.117044i	−0.597927	−	0.801551i	$-0.704009\pi$
$821$	−5.80875	+	3.35368i	−0.202727	+	0.117044i	0.395200	+	0.918595i	$0.370675\pi$
$822$		0			0
$823$	−11.2696	+	19.5195i	−0.392833	+	0.680407i	−0.992822	−	0.119601i	$-0.961838\pi$
$823$	−11.2696	+	19.5195i	−0.392833	+	0.680407i	0.599989	+	0.800009i	$0.295172\pi$
$824$	4.18495	+	7.24855i	0.145790	+	0.252515i
$825$		0			0
$826$	0.164458	−	1.47265i	0.00572223	−	0.0512401i
$827$		−	43.5225i		−	1.51342i	−0.653748	−	0.756712i	$-0.726804\pi$
$827$		−	43.5225i		−	1.51342i	0.653748	−	0.756712i	$-0.273196\pi$
$828$		0			0
$829$	−35.1852	−	20.3142i	−1.22203	−	0.705541i	−0.256682	−	0.966496i	$-0.582629\pi$
$829$	−35.1852	−	20.3142i	−1.22203	−	0.705541i	−0.965351	+	0.260955i	$0.915962\pi$
$830$	30.3986	−	52.6519i	1.05515	−	1.82758i
$831$		0			0
$832$	4.87511			0.169014
$833$	−15.0927	+	16.3305i	−0.522929	+	0.565817i
$834$		0			0
$835$	−31.0806	+	17.9444i	−1.07559	+	0.620990i
$836$	−4.66576	+	5.20426i	−0.161369	+	0.179993i
$837$		0			0
$838$	8.02761	+	13.9042i	0.277309	+	0.480314i
$839$			4.66063i			0.160903i	0.996759	+	0.0804515i	$0.0256362\pi$
$839$			4.66063i			0.160903i	−0.996759	+	0.0804515i	$0.974364\pi$
$840$		0			0
$841$	5.15294			0.177688
$842$	27.9632	−	16.1446i	0.963677	−	0.556379i
$843$		0			0
$844$	0.0816181	+	0.0471222i	0.00280941	+	0.00162201i
$845$	39.9807	−	23.0829i	1.37538	−	0.794075i
$846$		0			0
$847$	29.1032	+	0.0640812i	0.999998	+	0.00220186i
$848$	6.19431			0.212714
$849$		0			0
$850$	−36.8246	−	21.2607i	−1.26307	−	0.729237i
$851$	−3.73066	+	6.46169i	−0.127885	+	0.221504i
$852$		0			0
$853$	−39.8521			−1.36451			−0.682255	−	0.731114i	$-0.739001\pi$
$853$	−39.8521			−1.36451			−0.682255	+	0.731114i	$0.739001\pi$
$854$	3.34924	−	4.54743i	0.114609	−	0.155610i
$855$		0			0
$856$	−1.30941	−	2.26797i	−0.0447547	−	0.0775174i
$857$	−24.4864	+	42.4117i	−0.836440	+	1.44876i	0.0564129	+	0.998408i	$0.482034\pi$
$857$	−24.4864	+	42.4117i	−0.836440	+	1.44876i	−0.892853	+	0.450349i	$0.851300\pi$
$858$		0			0
$859$	7.92836	−	4.57744i	0.270512	−	0.156180i	−0.358608	−	0.933488i	$-0.616749\pi$
$859$	7.92836	−	4.57744i	0.270512	−	0.156180i	0.629120	+	0.777308i	$0.283415\pi$
$860$	40.0154			1.36451
$861$		0			0
$862$	19.7347			0.672168
$863$	−14.5688	−	25.2338i	−0.495927	−	0.858970i	0.504062	−	0.863667i	$-0.331838\pi$
$863$	−14.5688	−	25.2338i	−0.495927	−	0.858970i	−0.999989	+	0.00469710i	$0.998505\pi$
$864$		0			0
$865$	−81.0557	−	46.7975i	−2.75598	−	1.59116i
$866$	−12.2415	−	21.2029i	−0.415983	−	0.720504i
$867$		0			0
$868$	6.36805	+	14.5566i	0.216146	+	0.494082i
$869$	7.96484	−	37.8711i	0.270189	−	1.28469i
$870$		0			0
$871$	−19.2161	+	33.2832i	−0.651112	+	1.12776i
$872$	−8.04296	+	13.9308i	−0.272369	+	0.471757i
$873$		0			0
$874$		−	4.46945i		−	0.151181i
$875$	94.5421	+	10.5580i	3.19610	+	0.356924i
$876$		0			0
$877$	35.8688	−	20.7089i	1.21120	−	0.699289i	0.248182	−	0.968713i	$-0.420167\pi$
$877$	35.8688	−	20.7089i	1.21120	−	0.699289i	0.963021	+	0.269425i	$0.0868335\pi$
$878$	6.63494	+	3.83068i	0.223918	+	0.129279i
$879$		0			0
$880$	−13.5156	+	4.42359i	−0.455612	+	0.149119i
$881$		−	0.854428i		−	0.0287864i	−0.999896	−	0.0143932i	$-0.995418\pi$
$881$		−	0.854428i		−	0.0287864i	0.999896	−	0.0143932i	$-0.00458166\pi$
$882$		0			0
$883$	−42.9283			−1.44465			−0.722326	−	0.691553i	$-0.756927\pi$
$883$	−42.9283			−1.44465			−0.722326	+	0.691553i	$0.756927\pi$
$884$	7.74332	+	13.4118i	0.260436	+	0.451089i
$885$		0			0
$886$	−8.49153	−	4.90259i	−0.285279	−	0.164706i
$887$	−24.0496	−	41.6551i	−0.807506	−	1.39864i	−0.914586	−	0.404391i	$-0.867483\pi$
$887$	−24.0496	−	41.6551i	−0.807506	−	1.39864i	0.107080	−	0.994250i	$-0.465850\pi$
$888$		0			0
$889$	−16.9442	−	1.89224i	−0.568291	−	0.0634637i
$890$		−	5.03629i		−	0.168817i
$891$		0			0
$892$	−10.8559	−	6.26763i	−0.363481	−	0.209856i
$893$	15.6017	+	9.00762i	0.522089	+	0.301428i
$894$		0			0
$895$		−	5.48651i		−	0.183394i
$896$	−1.06040	−	2.42395i	−0.0354256	−	0.0809785i
$897$		0			0
$898$	4.83927	−	2.79395i	0.161488	−	0.0932354i
$899$	14.6630	−	25.3970i	0.489038	−	0.847038i
$900$		0			0
$901$	9.83867	+	17.0411i	0.327774	+	0.567720i
$902$	3.60717	−	17.1513i	0.120106	−	0.571077i
$903$		0			0
$904$		−	16.8879i		−	0.561682i
$905$	14.8535	+	25.7270i	0.493747	+	0.855194i
$906$		0			0
$907$	−18.8613	+	32.6687i	−0.626279	+	1.08475i	0.362013	+	0.932173i	$0.382090\pi$
$907$	−18.8613	+	32.6687i	−0.626279	+	1.08475i	−0.988292	+	0.152574i	$0.951244\pi$
$908$	−1.54419	−	2.67461i	−0.0512457	−	0.0887601i
$909$		0			0
$910$	−44.5313	−	32.7979i	−1.47620	−	1.08724i
$911$	32.9762			1.09255			0.546275	−	0.837606i	$-0.316045\pi$
$911$	32.9762			1.09255			0.546275	+	0.837606i	$0.316045\pi$
$912$		0			0
$913$	31.3918	−	35.0149i	1.03892	−	1.15882i
$914$	9.06372	−	15.6988i	0.299801	−	0.519271i
$915$		0			0
$916$			14.5467i			0.480635i
$917$	−29.5287	+	12.9179i	−0.975124	+	0.426587i
$918$		0			0
$919$	7.30589	−	4.21806i	0.240999	−	0.139141i	−0.374637	−	0.927172i	$-0.622233\pi$
$919$	7.30589	−	4.21806i	0.240999	−	0.139141i	0.615636	+	0.788031i	$0.288899\pi$
$920$	4.54684	−	7.87536i	0.149905	−	0.259643i
$921$		0			0
$922$	−0.219880	+	0.126948i	−0.00724136	+	0.00418080i
$923$	44.0485			1.44987
$924$		0			0
$925$	47.0921			1.54838
$926$	−32.9441	+	19.0203i	−1.08261	+	0.625046i
$927$		0			0
$928$	−2.44167	+	4.22910i	−0.0801518	+	0.138827i
$929$	26.8062	−	15.4766i	0.879484	−	0.507770i	0.00899559	−	0.999960i	$-0.497137\pi$
$929$	26.8062	−	15.4766i	0.879484	−	0.507770i	0.870488	+	0.492189i	$0.163803\pi$
$930$		0			0
$931$	4.37601	+	14.0880i	0.143418	+	0.461715i
$932$		−	28.1725i		−	0.922821i
$933$		0			0
$934$	7.86755	−	13.6270i	0.257434	−	0.445889i
$935$	−33.6371	−	30.1565i	−1.10005	−	0.986222i
$936$		0			0
$937$	29.7323			0.971311			0.485656	−	0.874150i	$-0.338581\pi$
$937$	29.7323			0.971311			0.485656	+	0.874150i	$0.338581\pi$
$938$	20.7285	+	2.31485i	0.676810	+	0.0755826i
$939$		0			0
$940$	18.3272	+	31.7436i	0.597767	+	1.03536i
$941$	−22.1596	+	38.3816i	−0.722383	+	1.25120i	0.237659	+	0.971349i	$0.423620\pi$
$941$	−22.1596	+	38.3816i	−0.722383	+	1.25120i	−0.960042	+	0.279856i	$0.909713\pi$
$942$		0			0
$943$	5.60366	+	9.70582i	0.182480	+	0.316065i
$944$			0.560070i			0.0182287i
$945$		0			0
$946$	30.2892	+	6.37025i	0.984786	+	0.207115i
$947$	23.2020	+	40.1870i	0.753963	+	1.30590i	0.945888	+	0.324493i	$0.105194\pi$
$947$	23.2020	+	40.1870i	0.753963	+	1.30590i	−0.191925	+	0.981410i	$0.561473\pi$
$948$		0			0
$949$	2.86304	−	4.95892i	0.0929381	−	0.160974i
$950$	−24.4297	+	14.1045i	−0.792603	+	0.457610i
$951$		0			0
$952$	4.98421	−	6.76732i	0.161539	−	0.219330i
$953$			31.5775i			1.02289i	0.859315	+	0.511447i	$0.170890\pi$
$953$			31.5775i			1.02289i	−0.859315	+	0.511447i	$0.829110\pi$
$954$		0			0
$955$	24.1510	+	13.9436i	0.781509	+	0.451204i
$956$	4.56360	+	2.63480i	0.147597	+	0.0852155i
$957$		0			0
$958$			2.59725i			0.0839134i
$959$	−32.9077	−	24.2369i	−1.06264	−	0.782650i
$960$		0			0
$961$	2.53183	+	4.38525i	0.0816718	+	0.141460i
$962$	−14.8535	−	8.57567i	−0.478896	−	0.276491i
$963$		0			0
$964$	−3.56857	−	6.18094i	−0.114936	−	0.199075i
$965$	82.0584			2.64155
$966$		0			0
$967$			6.41429i			0.206270i	0.994667	+	0.103135i	$0.0328873\pi$
$967$			6.41429i			0.206270i	−0.994667	+	0.103135i	$0.967113\pi$
$968$	−10.9347	+	1.19676i	−0.351455	+	0.0384653i
$969$		0			0
$970$	39.4497	+	22.7763i	1.26665	+	0.731302i
$971$	−9.81615	+	5.66736i	−0.315015	+	0.181874i	−0.649169	−	0.760645i	$-0.724883\pi$
$971$	−9.81615	+	5.66736i	−0.315015	+	0.181874i	0.334153	+	0.942519i	$0.391550\pi$
$972$		0			0
$973$	5.63913	−	50.4960i	0.180782	−	1.61883i
$974$			12.8986i			0.413297i
$975$		0			0
$976$	−1.06732	+	1.84864i	−0.0341639	+	0.0591737i
$977$	−6.90916	+	11.9670i	−0.221044	+	0.382859i	−0.955125	−	0.296203i	$-0.904280\pi$
$977$	−6.90916	+	11.9670i	−0.221044	+	0.382859i	0.734081	+	0.679061i	$0.237613\pi$
$978$		0			0
$979$	0.801751	−	3.81215i	0.0256241	−	0.121837i
$980$	−6.62122	+	29.2754i	−0.211507	+	0.935169i
$981$		0			0
$982$	9.32539	+	16.1520i	0.297585	+	0.515432i
$983$	−28.5452	−	16.4806i	−0.910450	−	0.525649i	−0.0298742	−	0.999554i	$-0.509511\pi$
$983$	−28.5452	−	16.4806i	−0.910450	−	0.525649i	−0.880576	+	0.473905i	$0.842844\pi$
$984$		0			0
$985$	−17.6842	−	30.6299i	−0.563465	−	0.975951i
$986$	−15.5128			−0.494028
$987$		0			0
$988$	10.2739			0.326857
$989$	−17.1404	+	9.89603i	−0.545034	+	0.314676i
$990$		0			0
$991$	0.0688518	−	0.119255i	0.00218715	−	0.00378825i	−0.864930	−	0.501893i	$-0.832637\pi$
$991$	0.0688518	−	0.119255i	0.00218715	−	0.00378825i	0.867117	+	0.498105i	$0.165970\pi$
$992$	−3.00265	−	5.20074i	−0.0953343	−	0.165124i
$993$		0			0
$994$	−9.58117	−	21.9013i	−0.303896	−	0.694669i
$995$	−57.7063			−1.82941
$996$		0			0
$997$	21.2777	−	36.8541i	0.673873	−	1.16718i	−0.302925	−	0.953015i	$-0.597963\pi$
$997$	21.2777	−	36.8541i	0.673873	−	1.16718i	0.976797	−	0.214167i	$-0.0687037\pi$
$998$	−22.7174	−	13.1159i	−0.719108	−	0.415177i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bk.d.703.16	yes	32
3.2	odd	2	inner	1386.2.bk.d.703.5	✓	32
7.5	odd	6	inner	1386.2.bk.d.901.6	yes	32
11.10	odd	2	inner	1386.2.bk.d.703.6	yes	32
21.5	even	6	inner	1386.2.bk.d.901.15	yes	32
33.32	even	2	inner	1386.2.bk.d.703.15	yes	32
77.54	even	6	inner	1386.2.bk.d.901.16	yes	32
231.131	odd	6	inner	1386.2.bk.d.901.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bk.d.703.5	✓	32	3.2	odd	2	inner
1386.2.bk.d.703.6	yes	32	11.10	odd	2	inner
1386.2.bk.d.703.15	yes	32	33.32	even	2	inner
1386.2.bk.d.703.16	yes	32	1.1	even	1	trivial
1386.2.bk.d.901.5	yes	32	231.131	odd	6	inner
1386.2.bk.d.901.6	yes	32	7.5	odd	6	inner
1386.2.bk.d.901.15	yes	32	21.5	even	6	inner
1386.2.bk.d.901.16	yes	32	77.54	even	6	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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(3.71337 - 2.14392i) q^{5} +(-0.293638 + 2.62941i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(3.71337 - 2.14392i) q^{5} +(-0.293638 + 2.62941i) q^{7} -1.00000i q^{8} +(2.14392 - 3.71337i) q^{10} +(2.21396 - 2.46949i) q^{11} -4.87511 q^{13} +(1.06040 + 2.42395i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.58834 - 2.75108i) q^{17} +(-1.05371 - 1.82508i) q^{19} -4.28783i q^{20} +(0.682601 - 3.24562i) q^{22} +(1.06040 + 1.83668i) q^{23} +(6.69276 - 11.5922i) q^{25} +(-4.22197 + 2.43755i) q^{26} +(2.13031 + 1.56900i) q^{28} -4.88335i q^{29} +(5.20074 + 3.00265i) q^{31} +(-0.866025 - 0.500000i) q^{32} -3.17668i q^{34} +(4.54684 + 10.3935i) q^{35} +(1.75907 + 3.04680i) q^{37} +(-1.82508 - 1.05371i) q^{38} +(-2.14392 - 3.71337i) q^{40} +5.28445 q^{41} +9.33232i q^{43} +(-1.03166 - 3.15209i) q^{44} +(1.83668 + 1.06040i) q^{46} +(-7.40318 + 4.27423i) q^{47} +(-6.82755 - 1.54419i) q^{49} -13.3855i q^{50} +(-2.43755 + 4.22197i) q^{52} +(-3.09716 + 5.36443i) q^{53} +(2.92688 - 13.9167i) q^{55} +(2.62941 + 0.293638i) q^{56} +(-2.44167 - 4.22910i) q^{58} +(-0.485035 - 0.280035i) q^{59} +(-1.06732 - 1.84864i) q^{61} +6.00530 q^{62} -1.00000 q^{64} +(-18.1031 + 10.4518i) q^{65} +(3.94167 - 6.82718i) q^{67} +(-1.58834 - 2.75108i) q^{68} +(9.13443 + 6.72761i) q^{70} -9.03539 q^{71} +(-0.587276 + 1.01719i) q^{73} +(3.04680 + 1.75907i) q^{74} -2.10742 q^{76} +(5.84319 + 6.54654i) q^{77} +(10.1051 - 5.83418i) q^{79} +(-3.71337 - 2.14392i) q^{80} +(4.57647 - 2.64223i) q^{82} +14.1790 q^{83} -13.6211i q^{85} +(4.66616 + 8.08202i) q^{86} +(-2.46949 - 2.21396i) q^{88} +(1.01719 - 0.587276i) q^{89} +(1.43152 - 12.8186i) q^{91} +2.12081 q^{92} +(-4.27423 + 7.40318i) q^{94} +(-7.82565 - 4.51814i) q^{95} +10.6237i q^{97} +(-6.68493 + 2.07647i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4}+O(q^{10}) \) 32 * q + 16 * q^4	\( 32 q + 16 q^{4} - 16 q^{16} + 20 q^{22} + 36 q^{25} + 12 q^{31} - 20 q^{37} - 44 q^{49} - 32 q^{64} + 48 q^{67} + 36 q^{70} + 72 q^{82} + 10 q^{88} + 144 q^{91}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 + 36 * q^25 + 12 * q^31 - 20 * q^37 - 44 * q^49 - 32 * q^64 + 48 * q^67 + 36 * q^70 + 72 * q^82 + 10 * q^88 + 144 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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