LMFDB - Embedded newform 28.11.h.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [28,11,Mod(5,28)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(28, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("28.5");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	28.h (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:	$17.7900030749$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 79898 x^{12} + 4721335 x^{11} + 4633670218 x^{10} + 292539163887 x^{9} + \cdots + 11\!\cdots\!96 $ x^14 - x^13 + 79898x^12 + 4721335x^11 + 4633670218x^10 + 292539163887x^9 + 133292114133081x^8 + 12163687652876400x^7 + 2822863385909300508x^6 + 181256215798122091092x^5 + 20264966189773139004588x^4 + 594831266394560780992416x^3 + 70725272841335064815779824x^2 + 2041523046616929235889899248x + 119317009140393922616982769296
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{13}\cdot 7^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.3
Root			$31.0272 + 53.7407i$ of defining polynomial
Character	$\chi$	$=$	28.17
Dual form			28.11.h.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-105.874 - 61.1265i) q^{3} +(1184.15 - 683.667i) q^{5} +(-10934.6 + 12763.6i) q^{7} +(-22051.6 - 38194.5i) q^{9} +O(q^{10})$	\(q+(-105.874 - 61.1265i) q^{3} +(1184.15 - 683.667i) q^{5} +(-10934.6 + 12763.6i) q^{7} +(-22051.6 - 38194.5i) q^{9} +(63448.8 - 109896. i) q^{11} +464820. i q^{13} -167161. q^{15} +(2.16216e6 + 1.24832e6i) q^{17} +(-915215. + 528400. i) q^{19} +(1.93789e6 - 682938. i) q^{21} +(3.95437e6 + 6.84917e6i) q^{23} +(-3.94801e6 + 6.83816e6i) q^{25} +1.26107e7i q^{27} +2.65525e7 q^{29} +(1.32767e7 + 7.66531e6i) q^{31} +(-1.34352e7 + 7.75681e6i) q^{33} +(-4.22218e6 + 2.25896e7i) q^{35} +(3.76006e7 + 6.51261e7i) q^{37} +(2.84129e7 - 4.92125e7i) q^{39} -1.41947e8i q^{41} -2.12847e8 q^{43} +(-5.22246e7 - 3.01519e7i) q^{45} +(1.79065e6 - 1.03383e6i) q^{47} +(-4.33425e7 - 2.79130e8i) q^{49} +(-1.52611e8 - 2.64331e8i) q^{51} +(-3.78792e7 + 6.56086e7i) q^{53} -1.73511e8i q^{55} +1.29197e8 q^{57} +(-2.01413e8 - 1.16286e8i) q^{59} +(-2.15307e8 + 1.24308e8i) q^{61} +(7.28624e8 + 1.36186e8i) q^{63} +(3.17782e8 + 5.50415e8i) q^{65} +(-5.17303e8 + 8.95996e8i) q^{67} -9.66869e8i q^{69} -1.53341e9 q^{71} +(2.82152e9 + 1.62900e9i) q^{73} +(8.35986e8 - 4.82657e8i) q^{75} +(7.08883e8 + 2.01151e9i) q^{77} +(1.06084e9 + 1.83742e9i) q^{79} +(-5.31277e8 + 9.20199e8i) q^{81} +3.41655e9i q^{83} +3.41375e9 q^{85} +(-2.81122e9 - 1.62306e9i) q^{87} +(3.67847e9 - 2.12377e9i) q^{89} +(-5.93277e9 - 5.08264e9i) q^{91} +(-9.37108e8 - 1.62312e9i) q^{93} +(-7.22499e8 + 1.25140e9i) q^{95} -1.03067e10i q^{97} -5.59658e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 243 q^{3} + 3333 q^{5} - 8810 q^{7} + 152334 q^{9}+O(q^{10}) $ 14 * q - 243 * q^3 + 3333 * q^5 - 8810 * q^7 + 152334 * q^9	$ 14 q - 243 q^{3} + 3333 q^{5} - 8810 q^{7} + 152334 q^{9} + 43575 q^{11} - 295974 q^{15} - 4046547 q^{17} + 10506141 q^{19} - 6849963 q^{21} + 8356047 q^{23} + 16247798 q^{25} + 9638748 q^{29} + 26706309 q^{31} - 68091003 q^{33} + 57757869 q^{35} - 56337841 q^{37} - 47717712 q^{39} + 102867212 q^{43} + 277176762 q^{45} - 494767563 q^{47} - 228310402 q^{49} + 584803989 q^{51} - 280243257 q^{53} - 2426437062 q^{57} - 540103875 q^{59} + 3020130381 q^{61} + 44180910 q^{63} - 156676464 q^{65} - 1385714225 q^{67} + 5251025724 q^{71} + 5335510437 q^{73} - 1896380046 q^{75} - 832139025 q^{77} - 5240397281 q^{79} - 4471861527 q^{81} - 8239454118 q^{85} + 21846639978 q^{87} + 9313203429 q^{89} - 17599015344 q^{91} - 1809384507 q^{93} - 19347043443 q^{95} + 29066774940 q^{99}+O(q^{100}) $ 14 * q - 243 * q^3 + 3333 * q^5 - 8810 * q^7 + 152334 * q^9 + 43575 * q^11 - 295974 * q^15 - 4046547 * q^17 + 10506141 * q^19 - 6849963 * q^21 + 8356047 * q^23 + 16247798 * q^25 + 9638748 * q^29 + 26706309 * q^31 - 68091003 * q^33 + 57757869 * q^35 - 56337841 * q^37 - 47717712 * q^39 + 102867212 * q^43 + 277176762 * q^45 - 494767563 * q^47 - 228310402 * q^49 + 584803989 * q^51 - 280243257 * q^53 - 2426437062 * q^57 - 540103875 * q^59 + 3020130381 * q^61 + 44180910 * q^63 - 156676464 * q^65 - 1385714225 * q^67 + 5251025724 * q^71 + 5335510437 * q^73 - 1896380046 * q^75 - 832139025 * q^77 - 5240397281 * q^79 - 4471861527 * q^81 - 8239454118 * q^85 + 21846639978 * q^87 + 9313203429 * q^89 - 17599015344 * q^91 - 1809384507 * q^93 - 19347043443 * q^95 + 29066774940 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−105.874	−	61.1265i	−0.435697	−	0.251550i	0.266074	−	0.963953i	$-0.414273\pi$
$3$	−105.874	−	61.1265i	−0.435697	−	0.251550i	−0.701771	+	0.712403i	$0.747607\pi$
$4$		0			0
$5$	1184.15	−	683.667i	0.378927	−	0.218773i	−0.298425	−	0.954433i	$-0.596461\pi$
$5$	1184.15	−	683.667i	0.378927	−	0.218773i	0.677351	+	0.735660i	$0.263128\pi$
$6$		0			0
$7$	−10934.6	+	12763.6i	−0.650600	+	0.759420i
$7$	−10934.6	+	12763.6i	−0.650600	+	0.759420i
$8$		0			0
$9$	−22051.6	−	38194.5i	−0.373446	−	0.646827i
$10$		0			0
$11$	63448.8	−	109896.i	0.393967	−	0.682371i	−0.599002	−	0.800748i	$-0.704436\pi$
$11$	63448.8	−	109896.i	0.393967	−	0.682371i	0.992969	+	0.118377i	$0.0377691\pi$
$12$		0			0
$13$			464820.i			1.25190i	0.779865	+	0.625948i	$0.215288\pi$
$13$			464820.i			1.25190i	−0.779865	+	0.625948i	$0.784712\pi$
$14$		0			0
$15$	−167161.			−0.220129
$16$		0			0
$17$	2.16216e6	+	1.24832e6i	1.52280	+	0.879189i	0.999637	+	0.0269574i	$0.00858185\pi$
$17$	2.16216e6	+	1.24832e6i	1.52280	+	0.879189i	0.523164	+	0.852232i	$0.324751\pi$
$18$		0			0
$19$	−915215.	+	528400.i	−0.369620	+	0.213400i	−0.673292	−	0.739376i	$-0.735120\pi$
$19$	−915215.	+	528400.i	−0.369620	+	0.213400i	0.303673	+	0.952776i	$0.401787\pi$
$20$		0			0
$21$	1.93789e6	−	682938.i	0.474496	−	0.167219i
$22$		0			0
$23$	3.95437e6	+	6.84917e6i	0.614382	+	1.06414i	0.990493	+	0.137566i	$0.0439279\pi$
$23$	3.95437e6	+	6.84917e6i	0.614382	+	1.06414i	−0.376111	+	0.926575i	$0.622739\pi$
$24$		0			0
$25$	−3.94801e6	+	6.83816e6i	−0.404276	+	0.700227i
$26$		0			0
$27$			1.26107e7i			0.878860i
$28$		0			0
$29$	2.65525e7			1.29454			0.647269	−	0.762262i	$-0.275911\pi$
$29$	2.65525e7			1.29454			0.647269	+	0.762262i	$0.275911\pi$
$30$		0			0
$31$	1.32767e7	+	7.66531e6i	0.463748	+	0.267745i	0.713619	−	0.700534i	$-0.247055\pi$
$31$	1.32767e7	+	7.66531e6i	0.463748	+	0.267745i	−0.249871	+	0.968279i	$0.580388\pi$
$32$		0			0
$33$	−1.34352e7	+	7.75681e6i	−0.343300	+	0.198204i
$34$		0			0
$35$	−4.22218e6	+	2.25896e7i	−0.0803889	+	0.430099i
$36$		0			0
$37$	3.76006e7	+	6.51261e7i	0.542233	+	0.939175i	0.998775	+	0.0494737i	$0.0157544\pi$
$37$	3.76006e7	+	6.51261e7i	0.542233	+	0.939175i	−0.456542	+	0.889702i	$0.650912\pi$
$38$		0			0
$39$	2.84129e7	−	4.92125e7i	0.314914	−	0.545447i
$40$		0			0
$41$		−	1.41947e8i		−	1.22520i	−0.790393	−	0.612600i	$-0.790124\pi$
$41$		−	1.41947e8i		−	1.22520i	0.790393	−	0.612600i	$-0.209876\pi$
$42$		0			0
$43$	−2.12847e8			−1.44785			−0.723927	−	0.689876i	$-0.757665\pi$
$43$	−2.12847e8			−1.44785			−0.723927	+	0.689876i	$0.757665\pi$
$44$		0			0
$45$	−5.22246e7	−	3.01519e7i	−0.283017	−	0.163400i
$46$		0			0
$47$	1.79065e6	−	1.03383e6i	0.00780769	−	0.00450777i	−0.496091	−	0.868270i	$-0.665232\pi$
$47$	1.79065e6	−	1.03383e6i	0.00780769	−	0.00450777i	0.503899	+	0.863763i	$0.331898\pi$
$48$		0			0
$49$	−4.33425e7	−	2.79130e8i	−0.153438	−	0.988158i
$50$		0			0
$51$	−1.52611e8	−	2.64331e8i	−0.442319	−	0.766120i
$52$		0			0
$53$	−3.78792e7	+	6.56086e7i	−0.0905776	+	0.156885i	−0.907754	−	0.419502i	$-0.862205\pi$
$53$	−3.78792e7	+	6.56086e7i	−0.0905776	+	0.156885i	0.817177	+	0.576387i	$0.195538\pi$
$54$		0			0
$55$		−	1.73511e8i		−	0.344758i
$56$		0			0
$57$	1.29197e8			0.214723
$58$		0			0
$59$	−2.01413e8	−	1.16286e8i	−0.281726	−	0.162655i	0.352479	−	0.935820i	$-0.385339\pi$
$59$	−2.01413e8	−	1.16286e8i	−0.281726	−	0.162655i	−0.634205	+	0.773165i	$0.718672\pi$
$60$		0			0
$61$	−2.15307e8	+	1.24308e8i	−0.254923	+	0.147180i	−0.622016	−	0.783004i	$-0.713686\pi$
$61$	−2.15307e8	+	1.24308e8i	−0.254923	+	0.147180i	0.367093	+	0.930184i	$0.380353\pi$
$62$		0			0
$63$	7.28624e8	+	1.36186e8i	0.734177	+	0.137224i
$64$		0			0
$65$	3.17782e8	+	5.50415e8i	0.273882	+	0.474377i
$66$		0			0
$67$	−5.17303e8	+	8.95996e8i	−0.383152	+	0.663639i	−0.991511	−	0.130023i	$-0.958495\pi$
$67$	−5.17303e8	+	8.95996e8i	−0.383152	+	0.663639i	0.608359	+	0.793662i	$0.291828\pi$
$68$		0			0
$69$		−	9.66869e8i		−	0.618190i
$70$		0			0
$71$	−1.53341e9			−0.849896			−0.424948	−	0.905218i	$-0.639708\pi$
$71$	−1.53341e9			−0.849896			−0.424948	+	0.905218i	$0.639708\pi$
$72$		0			0
$73$	2.82152e9	+	1.62900e9i	1.36103	+	0.785793i	0.989761	−	0.142731i	$-0.0455885\pi$
$73$	2.82152e9	+	1.62900e9i	1.36103	+	0.785793i	0.371272	+	0.928524i	$0.378922\pi$
$74$		0			0
$75$	8.35986e8	−	4.82657e8i	0.352284	−	0.203391i
$76$		0			0
$77$	7.08883e8	+	2.01151e9i	0.261891	+	0.743137i
$78$		0			0
$79$	1.06084e9	+	1.83742e9i	0.344757	+	0.597136i	0.985310	−	0.170778i	$-0.0546281\pi$
$79$	1.06084e9	+	1.83742e9i	0.344757	+	0.597136i	−0.640553	+	0.767914i	$0.721295\pi$
$80$		0			0
$81$	−5.31277e8	+	9.20199e8i	−0.152369	+	0.263911i
$82$		0			0
$83$			3.41655e9i			0.867355i	0.901068	+	0.433678i	$0.142784\pi$
$83$			3.41655e9i			0.867355i	−0.901068	+	0.433678i	$0.857216\pi$
$84$		0			0
$85$	3.41375e9			0.769373
$86$		0			0
$87$	−2.81122e9	−	1.62306e9i	−0.564026	−	0.325641i
$88$		0			0
$89$	3.67847e9	−	2.12377e9i	0.658745	−	0.380326i	−0.133054	−	0.991109i	$-0.542478\pi$
$89$	3.67847e9	−	2.12377e9i	0.658745	−	0.380326i	0.791799	+	0.610782i	$0.209145\pi$
$90$		0			0
$91$	−5.93277e9	−	5.08264e9i	−0.950715	−	0.814484i
$92$		0			0
$93$	−9.37108e8	−	1.62312e9i	−0.134702	−	0.233311i
$94$		0			0
$95$	−7.22499e8	+	1.25140e9i	−0.0933725	+	0.161726i
$96$		0			0
$97$		−	1.03067e10i		−	1.20023i	−0.799915	−	0.600113i	$-0.795122\pi$
$97$		−	1.03067e10i		−	1.20023i	0.799915	−	0.600113i	$-0.204878\pi$
$98$		0			0
$99$	−5.59658e9			−0.588501
$100$		0			0
$101$	2.32718e9	+	1.34360e9i	0.221423	+	0.127839i	0.606609	−	0.795000i	$-0.292529\pi$
$101$	2.32718e9	+	1.34360e9i	0.221423	+	0.127839i	−0.385186	+	0.922839i	$0.625863\pi$
$102$		0			0
$103$	−1.34473e10	+	7.76379e9i	−1.15997	+	0.669711i	−0.951298	−	0.308274i	$-0.900249\pi$
$103$	−1.34473e10	+	7.76379e9i	−1.15997	+	0.669711i	−0.208676	+	0.977985i	$0.566915\pi$
$104$		0			0
$105$	1.82784e9	−	2.13357e9i	0.143216	−	0.167171i
$106$		0			0
$107$	−1.07622e10	−	1.86406e10i	−0.767327	−	1.32905i	−0.939007	−	0.343897i	$-0.888253\pi$
$107$	−1.07622e10	−	1.86406e10i	−0.767327	−	1.32905i	0.171680	−	0.985153i	$-0.445080\pi$
$108$		0			0
$109$	2.02466e9	−	3.50681e9i	0.131589	−	0.227919i	−0.792700	−	0.609611i	$-0.791325\pi$
$109$	2.02466e9	−	3.50681e9i	0.131589	−	0.227919i	0.924289	+	0.381693i	$0.124659\pi$
$110$		0			0
$111$		−	9.19358e9i		−	0.545594i
$112$		0			0
$113$	1.79199e10			0.972623			0.486312	−	0.873786i	$-0.338342\pi$
$113$	1.79199e10			0.972623			0.486312	+	0.873786i	$0.338342\pi$
$114$		0			0
$115$	9.36511e9	+	5.40695e9i	0.465611	+	0.268821i
$116$		0			0
$117$	1.77536e10	−	1.02500e10i	0.809760	−	0.467515i
$118$		0			0
$119$	−3.95755e10	+	1.39469e10i	−1.65841	+	0.584445i
$120$		0			0
$121$	4.91722e9	+	8.51688e9i	0.189580	+	0.328362i
$122$		0			0
$123$	−8.67672e9	+	1.50285e10i	−0.308198	+	0.533815i
$124$		0			0
$125$			2.41494e10i			0.791327i
$126$		0			0
$127$	1.24292e10			0.376206			0.188103	−	0.982149i	$-0.439766\pi$
$127$	1.24292e10			0.376206			0.188103	+	0.982149i	$0.439766\pi$
$128$		0			0
$129$	2.25350e10	+	1.30106e10i	0.630825	+	0.364207i
$130$		0			0
$131$	2.39836e10	−	1.38469e10i	0.621666	−	0.358919i	−0.155851	−	0.987781i	$-0.549812\pi$
$131$	2.39836e10	−	1.38469e10i	0.621666	−	0.358919i	0.777518	+	0.628861i	$0.216479\pi$
$132$		0			0
$133$	3.26328e9	−	1.74593e10i	0.0784145	−	0.419535i
$134$		0			0
$135$	8.62150e9	+	1.49329e10i	0.192271	+	0.333023i
$136$		0			0
$137$	−3.80119e10	+	6.58386e10i	−0.787620	+	1.36420i	0.139801	+	0.990180i	$0.455354\pi$
$137$	−3.80119e10	+	6.58386e10i	−0.787620	+	1.36420i	−0.927421	+	0.374019i	$0.877980\pi$
$138$		0			0
$139$		−	1.95300e10i		−	0.376381i	−0.982133	−	0.188191i	$-0.939738\pi$
$139$		−	1.95300e10i		−	0.376381i	0.982133	−	0.188191i	$-0.0602623\pi$
$140$		0			0
$141$	−2.52779e8			−0.00453571
$142$		0			0
$143$	5.10821e10	+	2.94923e10i	0.854257	+	0.493206i
$144$		0			0
$145$	3.14420e10	−	1.81530e10i	0.490535	−	0.283211i
$146$		0			0
$147$	−1.24734e10	+	3.22021e10i	−0.181718	+	0.469135i
$148$		0			0
$149$	−5.08805e9	−	8.81276e9i	−0.0692819	−	0.120000i	0.829303	−	0.558798i	$-0.188737\pi$
$149$	−5.08805e9	−	8.81276e9i	−0.0692819	−	0.120000i	−0.898585	+	0.438799i	$0.855404\pi$
$150$		0			0
$151$	−3.85551e10	+	6.67794e10i	−0.491131	+	0.850663i	−0.999948	−	0.0102114i	$-0.996750\pi$
$151$	−3.85551e10	+	6.67794e10i	−0.491131	+	0.850663i	0.508817	+	0.860875i	$0.330083\pi$
$152$		0			0
$153$		−	1.10110e11i		−	1.31332i
$154$		0			0
$155$	2.09621e10			0.234302
$156$		0			0
$157$	9.48175e10	+	5.47429e10i	0.994009	+	0.573891i	0.906470	−	0.422270i	$-0.138767\pi$
$157$	9.48175e10	+	5.47429e10i	0.994009	+	0.573891i	0.0875387	+	0.996161i	$0.472100\pi$
$158$		0			0
$159$	8.02086e9	−	4.63084e9i	0.0789287	−	0.0455695i
$160$		0			0
$161$	−1.30660e11	−	2.44213e10i	−1.20785	−	0.225756i
$162$		0			0
$163$	−1.10164e11	−	1.90810e11i	−0.957419	−	1.65830i	−0.728732	−	0.684798i	$-0.759890\pi$
$163$	−1.10164e11	−	1.90810e11i	−0.957419	−	1.65830i	−0.228687	−	0.973500i	$-0.573443\pi$
$164$		0			0
$165$	−1.06061e10	+	1.83704e10i	−0.0867237	+	0.150210i
$166$		0			0
$167$		−	1.45562e11i		−	1.12064i	−0.828276	−	0.560320i	$-0.810678\pi$
$167$		−	1.45562e11i		−	1.12064i	0.828276	−	0.560320i	$-0.189322\pi$
$168$		0			0
$169$	−7.81994e10			−0.567244
$170$		0			0
$171$	4.03639e10	+	2.33041e10i	0.276066	+	0.159387i
$172$		0			0
$173$	−6.60811e10	+	3.81519e10i	−0.426429	+	0.246199i	−0.697824	−	0.716269i	$-0.745848\pi$
$173$	−6.60811e10	+	3.81519e10i	−0.426429	+	0.246199i	0.271395	+	0.962468i	$0.412515\pi$
$174$		0			0
$175$	−4.41092e10	−	1.25164e11i	−0.268744	−	0.762584i
$176$		0			0
$177$	1.42163e10	+	2.46233e10i	0.0818314	+	0.141736i
$178$		0			0
$179$	−1.10622e11	+	1.91603e11i	−0.601973	+	1.04265i	0.390549	+	0.920582i	$0.372285\pi$
$179$	−1.10622e11	+	1.91603e11i	−0.601973	+	1.04265i	−0.992522	+	0.122066i	$0.961048\pi$
$180$		0			0
$181$		−	3.08359e11i		−	1.58732i	−0.608365	−	0.793658i	$-0.708174\pi$
$181$		−	3.08359e11i		−	1.58732i	0.608365	−	0.793658i	$-0.291826\pi$
$182$		0			0
$183$	3.03940e10			0.148092
$184$		0			0
$185$	8.90492e10	+	5.14126e10i	0.410933	+	0.237252i
$186$		0			0
$187$	2.74373e11	−	1.58409e11i	1.19987	−	0.692743i
$188$		0			0
$189$	−1.60957e11	−	1.37893e11i	−0.667424	−	0.571786i
$190$		0			0
$191$	1.99119e11	+	3.44885e11i	0.783334	+	1.35677i	0.929989	+	0.367586i	$0.119816\pi$
$191$	1.99119e11	+	3.44885e11i	0.783334	+	1.35677i	−0.146656	+	0.989188i	$0.546851\pi$
$192$		0			0
$193$	−2.38897e11	+	4.13782e11i	−0.892123	+	1.54520i	−0.0547971	+	0.998498i	$0.517451\pi$
$193$	−2.38897e11	+	4.13782e11i	−0.892123	+	1.54520i	−0.837326	+	0.546704i	$0.815882\pi$
$194$		0			0
$195$		−	7.76997e10i		−	0.275579i
$196$		0			0
$197$	−8.87322e10			−0.299054			−0.149527	−	0.988758i	$-0.547775\pi$
$197$	−8.87322e10			−0.299054			−0.149527	+	0.988758i	$0.547775\pi$
$198$		0			0
$199$	5.23866e11	+	3.02454e11i	1.67863	+	0.969157i	0.962537	+	0.271152i	$0.0874045\pi$
$199$	5.23866e11	+	3.02454e11i	1.67863	+	0.969157i	0.716093	+	0.698005i	$0.245929\pi$
$200$		0			0
$201$	1.09538e11	−	6.32420e10i	0.333876	−	0.192764i
$202$		0			0
$203$	−2.90342e11	+	3.38904e11i	−0.842227	+	0.983098i
$204$		0			0
$205$	−9.70444e10	−	1.68086e11i	−0.268041	−	0.464261i
$206$		0			0
$207$	1.74400e11	−	3.02070e11i	0.458876	−	0.794797i
$208$		0			0
$209$			1.34105e11i			0.336290i
$210$		0			0
$211$	5.50999e11			1.31746			0.658731	−	0.752378i	$-0.271093\pi$
$211$	5.50999e11			1.31746			0.658731	+	0.752378i	$0.271093\pi$
$212$		0			0
$213$	1.62348e11	+	9.37319e10i	0.370297	+	0.213791i
$214$		0			0
$215$	−2.52042e11	+	1.45516e11i	−0.548631	+	0.316752i
$216$		0			0
$217$	−2.43013e11	+	8.56409e10i	−0.505046	+	0.177985i
$218$		0			0
$219$	−1.99151e11	−	3.44939e11i	−0.395332	−	0.684735i
$220$		0			0
$221$	−5.80246e11	+	1.00502e12i	−1.10065	+	1.90639i
$222$		0			0
$223$		−	3.73295e11i		−	0.676905i	−0.940983	−	0.338453i	$-0.890097\pi$
$223$		−	3.73295e11i		−	0.676905i	0.940983	−	0.338453i	$-0.109903\pi$
$224$		0			0
$225$	3.48240e11			0.603901
$226$		0			0
$227$	7.42017e11	+	4.28404e11i	1.23107	+	0.710761i	0.967254	−	0.253810i	$-0.0816839\pi$
$227$	7.42017e11	+	4.28404e11i	1.23107	+	0.710761i	0.263821	+	0.964572i	$0.415017\pi$
$228$		0			0
$229$	2.97576e11	−	1.71805e11i	0.472520	−	0.272809i	−0.244774	−	0.969580i	$-0.578714\pi$
$229$	2.97576e11	−	1.71805e11i	0.472520	−	0.272809i	0.717294	+	0.696771i	$0.245380\pi$
$230$		0			0
$231$	4.79043e10	−	2.56299e11i	0.0728308	−	0.389661i
$232$		0			0
$233$	−1.41444e11	−	2.44988e11i	−0.205970	−	0.356751i	0.744471	−	0.667655i	$-0.232702\pi$
$233$	−1.41444e11	−	2.44988e11i	−0.205970	−	0.356751i	−0.950441	+	0.310904i	$0.899368\pi$
$234$		0			0
$235$	1.41360e9	−	2.44842e9i	0.00197236	−	0.00341623i
$236$		0			0
$237$		−	2.59381e11i		−	0.346894i
$238$		0			0
$239$	−1.01373e12			−1.29997			−0.649984	−	0.759948i	$-0.725224\pi$
$239$	−1.01373e12			−1.29997			−0.649984	+	0.759948i	$0.725224\pi$
$240$		0			0
$241$	−9.74813e11	−	5.62809e11i	−1.19905	−	0.692270i	−0.238704	−	0.971092i	$-0.576723\pi$
$241$	−9.74813e11	−	5.62809e11i	−1.19905	−	0.692270i	−0.960343	+	0.278822i	$0.910056\pi$
$242$		0			0
$243$	7.57381e11	−	4.37274e11i	0.893888	−	0.516086i
$244$		0			0
$245$	−2.42156e11	−	3.00899e11i	−0.274325	−	0.340871i
$246$		0			0
$247$	−2.45611e11	−	4.25411e11i	−0.267155	−	0.462726i
$248$		0			0
$249$	2.08842e11	−	3.61725e11i	0.218183	−	0.377904i
$250$		0			0
$251$			2.11216e11i			0.212011i	0.994366	+	0.106005i	$0.0338061\pi$
$251$			2.11216e11i			0.212011i	−0.994366	+	0.106005i	$0.966194\pi$
$252$		0			0
$253$	1.00360e12			0.968185
$254$		0			0
$255$	−3.61428e11	−	2.08671e11i	−0.335213	−	0.193535i
$256$		0			0
$257$	−4.51887e11	+	2.60897e11i	−0.403055	+	0.232704i	−0.687801	−	0.725899i	$-0.741424\pi$
$257$	−4.51887e11	+	2.60897e11i	−0.403055	+	0.232704i	0.284746	+	0.958603i	$0.408091\pi$
$258$		0			0
$259$	−1.24239e12	−	2.32213e11i	−1.06601	−	0.199245i
$260$		0			0
$261$	−5.85524e11	−	1.01416e12i	−0.483440	−	0.837342i
$262$		0			0
$263$	−2.81813e11	+	4.88114e11i	−0.223966	+	0.387920i	−0.956009	−	0.293339i	$-0.905234\pi$
$263$	−2.81813e11	+	4.88114e11i	−0.223966	+	0.387920i	0.732043	+	0.681259i	$0.238567\pi$
$264$		0			0
$265$			1.03587e11i			0.0792639i
$266$		0			0
$267$	−5.19274e11			−0.382684
$268$		0			0
$269$	6.90910e11	+	3.98897e11i	0.490524	+	0.283204i	0.724792	−	0.688968i	$-0.241936\pi$
$269$	6.90910e11	+	3.98897e11i	0.490524	+	0.283204i	−0.234268	+	0.972172i	$0.575269\pi$
$270$		0			0
$271$	7.44208e10	−	4.29668e10i	0.0509152	−	0.0293959i	−0.474326	−	0.880349i	$-0.657308\pi$
$271$	7.44208e10	−	4.29668e10i	0.0509152	−	0.0293959i	0.525242	+	0.850953i	$0.323975\pi$
$272$		0			0
$273$	3.17443e11	+	9.00771e11i	0.209340	+	0.594020i
$274$		0			0
$275$	5.00993e11	+	8.67745e11i	0.318543	+	0.551733i
$276$		0			0
$277$	1.20059e12	−	2.07949e12i	0.736201	−	1.27514i	−0.217994	−	0.975950i	$-0.569951\pi$
$277$	1.20059e12	−	2.07949e12i	0.736201	−	1.27514i	0.954194	−	0.299187i	$-0.0967155\pi$
$278$		0			0
$279$		−	6.76129e11i		−	0.399953i
$280$		0			0
$281$	5.65208e10			0.0322609			0.0161305	−	0.999870i	$-0.494865\pi$
$281$	5.65208e10			0.0322609			0.0161305	+	0.999870i	$0.494865\pi$
$282$		0			0
$283$	−5.09438e11	−	2.94124e11i	−0.280646	−	0.162031i	0.353070	−	0.935597i	$-0.385138\pi$
$283$	−5.09438e11	−	2.94124e11i	−0.280646	−	0.162031i	−0.633716	+	0.773566i	$0.718471\pi$
$284$		0			0
$285$	1.52988e11	−	8.83277e10i	0.0813642	−	0.0469756i
$286$		0			0
$287$	1.81175e12	+	1.55214e12i	0.930441	+	0.797115i
$288$		0			0
$289$	2.10862e12	+	3.65225e12i	1.04595	+	1.81163i
$290$		0			0
$291$	−6.30016e11	+	1.09122e12i	−0.301916	+	0.522934i
$292$		0			0
$293$			1.78020e12i			0.824388i	0.911096	+	0.412194i	$0.135237\pi$
$293$			1.78020e12i			0.824388i	−0.911096	+	0.412194i	$0.864763\pi$
$294$		0			0
$295$	−3.18003e11			−0.142338
$296$		0			0
$297$	1.38587e12	+	8.00132e11i	0.599708	+	0.346242i
$298$		0			0
$299$	−3.18364e12	+	1.83807e12i	−1.33219	+	0.769142i
$300$		0			0
$301$	2.32740e12	−	2.71669e12i	0.941975	−	1.09953i
$302$		0			0
$303$	−1.64259e11	−	2.84505e11i	−0.0643156	−	0.111398i
$304$		0			0
$305$	−1.69970e11	+	2.94397e11i	−0.0643981	+	0.111541i
$306$		0			0
$307$			7.36769e11i			0.270172i	0.990834	+	0.135086i	$0.0431310\pi$
$307$			7.36769e11i			0.270172i	−0.990834	+	0.135086i	$0.956869\pi$
$308$		0			0
$309$	1.89829e12			0.673862
$310$		0			0
$311$	−2.52685e12	−	1.45888e12i	−0.868514	−	0.501437i	−0.00166006	−	0.999999i	$-0.500528\pi$
$311$	−2.52685e12	−	1.45888e12i	−0.868514	−	0.501437i	−0.866854	+	0.498562i	$0.833862\pi$
$312$		0			0
$313$	2.93942e11	−	1.69708e11i	0.0978453	−	0.0564910i	−0.450279	−	0.892888i	$-0.648675\pi$
$313$	2.93942e11	−	1.69708e11i	0.0978453	−	0.0564910i	0.548124	+	0.836397i	$0.315342\pi$
$314$		0			0
$315$	9.55903e11	−	3.36873e11i	0.308220	−	0.108621i
$316$		0			0
$317$	−2.49142e11	−	4.31527e11i	−0.0778307	−	0.134807i	0.824483	−	0.565887i	$-0.191466\pi$
$317$	−2.49142e11	−	4.31527e11i	−0.0778307	−	0.134807i	−0.902314	+	0.431080i	$0.858133\pi$
$318$		0			0
$319$	1.68472e12	−	2.91802e12i	0.510005	−	0.883355i
$320$		0			0
$321$			2.63141e12i			0.772083i
$322$		0			0
$323$	−2.63845e12			−0.750476
$324$		0			0
$325$	−3.17851e12	−	1.83512e12i	−0.876612	−	0.506112i
$326$		0			0
$327$	−4.28718e11	+	2.47521e11i	−0.114666	+	0.0662022i
$328$		0			0
$329$	−6.38474e9	+	3.41598e10i	−0.00165639	+	0.00886208i
$330$		0			0
$331$	7.64093e10	+	1.32345e11i	0.0192312	+	0.0333094i	0.875481	−	0.483253i	$-0.160545\pi$
$331$	7.64093e10	+	1.32345e11i	0.0192312	+	0.0333094i	−0.856250	+	0.516562i	$0.827211\pi$
$332$		0			0
$333$	1.65831e12	−	2.87227e12i	0.404989	−	0.701462i
$334$		0			0
$335$			1.41465e12i			0.335294i
$336$		0			0
$337$	−4.55667e12			−1.04833			−0.524165	−	0.851617i	$-0.675622\pi$
$337$	−4.55667e12			−1.04833			−0.524165	+	0.851617i	$0.675622\pi$
$338$		0			0
$339$	−1.89726e12	−	1.09538e12i	−0.423769	−	0.244663i
$340$		0			0
$341$	1.68478e12	−	9.72709e11i	0.365403	−	0.210965i
$342$		0			0
$343$	4.03663e12	+	2.49898e12i	0.850254	+	0.526372i
$344$		0			0
$345$	−6.61016e11	−	1.14491e12i	−0.135244	−	0.234249i
$346$		0			0
$347$	4.53298e12	−	7.85135e12i	0.901024	−	1.56062i	0.0748559	−	0.997194i	$-0.476150\pi$
$347$	4.53298e12	−	7.85135e12i	0.901024	−	1.56062i	0.826168	−	0.563424i	$-0.190516\pi$
$348$		0			0
$349$		−	3.28522e12i		−	0.634509i	−0.948340	−	0.317255i	$-0.897239\pi$
$349$		−	3.28522e12i		−	0.634509i	0.948340	−	0.317255i	$-0.102761\pi$
$350$		0			0
$351$	−5.86170e12			−1.10024
$352$		0			0
$353$	−5.16095e12	−	2.97967e12i	−0.941577	−	0.543620i	−0.0511226	−	0.998692i	$-0.516280\pi$
$353$	−5.16095e12	−	2.97967e12i	−0.941577	−	0.543620i	−0.890454	+	0.455073i	$0.849613\pi$
$354$		0			0
$355$	−1.81578e12	+	1.04834e12i	−0.322048	+	0.185935i
$356$		0			0
$357$	5.04256e12	+	9.42494e11i	0.869580	+	0.162532i
$358$		0			0
$359$	9.60930e11	+	1.66438e12i	0.161146	+	0.279113i	0.935280	−	0.353909i	$-0.115148\pi$
$359$	9.60930e11	+	1.66438e12i	0.161146	+	0.279113i	−0.774134	+	0.633022i	$0.781814\pi$
$360$		0			0
$361$	−2.50712e12	+	4.34246e12i	−0.408921	+	0.708272i
$362$		0			0
$363$		−	1.20229e12i		−	0.190755i
$364$		0			0
$365$	4.45479e12			0.687642
$366$		0			0
$367$	−6.69642e12	−	3.86618e12i	−1.00580	−	0.580700i	−0.0958419	−	0.995397i	$-0.530554\pi$
$367$	−6.69642e12	−	3.86618e12i	−1.00580	−	0.580700i	−0.909960	+	0.414697i	$0.863888\pi$
$368$		0			0
$369$	−5.42159e12	+	3.13015e12i	−0.792492	+	0.457545i
$370$		0			0
$371$	−4.23206e11	−	1.20088e12i	−0.0602118	−	0.170856i
$372$		0			0
$373$	−1.93051e12	−	3.34374e12i	−0.267379	−	0.463114i	0.700805	−	0.713353i	$-0.252824\pi$
$373$	−1.93051e12	−	3.34374e12i	−0.267379	−	0.463114i	−0.968184	+	0.250239i	$0.919491\pi$
$374$		0			0
$375$	1.47617e12	−	2.55680e12i	0.199058	−	0.344778i
$376$		0			0
$377$			1.23421e13i			1.62063i
$378$		0			0
$379$	1.15265e13			1.47401			0.737005	−	0.675887i	$-0.236239\pi$
$379$	1.15265e13			1.47401			0.737005	+	0.675887i	$0.236239\pi$
$380$		0			0
$381$	−1.31594e12	−	7.59756e11i	−0.163912	−	0.0946345i
$382$		0			0
$383$	3.52731e12	−	2.03649e12i	0.428006	−	0.247109i	−0.270491	−	0.962723i	$-0.587186\pi$
$383$	3.52731e12	−	2.03649e12i	0.428006	−	0.247109i	0.698497	+	0.715613i	$0.253853\pi$
$384$		0			0
$385$	2.21462e12	+	1.89728e12i	0.261816	+	0.224300i
$386$		0			0
$387$	4.69361e12	+	8.12957e12i	0.540695	+	0.936511i
$388$		0			0
$389$	6.91530e12	−	1.19777e13i	0.776360	−	1.34470i	−0.157667	−	0.987492i	$-0.550397\pi$
$389$	6.91530e12	−	1.19777e13i	0.776360	−	1.34470i	0.934027	−	0.357203i	$-0.116270\pi$
$390$		0			0
$391$			1.97453e13i			2.16063i
$392$		0			0
$393$	−3.38566e12			−0.361144
$394$		0			0
$395$	2.51237e12	+	1.45052e12i	0.261275	+	0.150847i
$396$		0			0
$397$	−5.47739e12	+	3.16237e12i	−0.555420	+	0.320672i	−0.751305	−	0.659955i	$-0.770575\pi$
$397$	−5.47739e12	+	3.16237e12i	−0.555420	+	0.320672i	0.195885	+	0.980627i	$0.437242\pi$
$398$		0			0
$399$	−1.41272e12	+	1.64902e12i	−0.139699	+	0.163065i
$400$		0			0
$401$	9.90532e10	+	1.71565e11i	0.00955316	+	0.0165466i	0.870762	−	0.491704i	$-0.163626\pi$
$401$	9.90532e10	+	1.71565e11i	0.00955316	+	0.0165466i	−0.861209	+	0.508250i	$0.830292\pi$
$402$		0			0
$403$	−3.56299e12	+	6.17128e12i	−0.335189	+	0.580564i
$404$		0			0
$405$			1.45287e12i			0.133337i
$406$		0			0
$407$	9.54285e12			0.854488
$408$		0			0
$409$	7.98468e12	+	4.60996e12i	0.697656	+	0.402792i	0.806474	−	0.591270i	$-0.201373\pi$
$409$	7.98468e12	+	4.60996e12i	0.697656	+	0.402792i	−0.108818	+	0.994062i	$0.534707\pi$
$410$		0			0
$411$	8.04897e12	−	4.64707e12i	0.686327	−	0.396251i
$412$		0			0
$413$	3.68660e12	−	1.29920e12i	0.306814	−	0.108125i
$414$		0			0
$415$	2.33578e12	+	4.04569e12i	0.189754	+	0.328664i
$416$		0			0
$417$	−1.19380e12	+	2.06772e12i	−0.0946786	+	0.163988i
$418$		0			0
$419$		−	1.37933e13i		−	1.06807i	−0.845463	−	0.534034i	$-0.820676\pi$
$419$		−	1.37933e13i		−	1.06807i	0.845463	−	0.534034i	$-0.179324\pi$
$420$		0			0
$421$	−1.51946e13			−1.14889			−0.574446	−	0.818543i	$-0.694782\pi$
$421$	−1.51946e13			−1.14889			−0.574446	+	0.818543i	$0.694782\pi$
$422$		0			0
$423$	−7.89736e10	−	4.55954e10i	−0.00583150	−	0.00336682i
$424$		0			0
$425$	−1.70725e13	+	9.85679e12i	−1.23126	+	0.710871i
$426$		0			0
$427$	7.67696e11	−	4.10734e12i	0.0540816	−	0.289349i
$428$		0			0
$429$	−3.60552e12	−	6.24495e12i	−0.248131	−	0.429776i
$430$		0			0
$431$	8.63764e12	−	1.49608e13i	0.580776	−	1.00593i	−0.414612	−	0.909998i	$-0.636083\pi$
$431$	8.63764e12	−	1.49608e13i	0.580776	−	1.00593i	0.995388	−	0.0959349i	$-0.0305841\pi$
$432$		0			0
$433$		−	2.99613e12i		−	0.196843i	−0.995145	−	0.0984216i	$-0.968621\pi$
$433$		−	2.99613e12i		−	0.196843i	0.995145	−	0.0984216i	$-0.0313794\pi$
$434$		0			0
$435$	−4.43853e12			−0.284966
$436$		0			0
$437$	−7.23821e12	−	4.17898e12i	−0.454175	−	0.262218i
$438$		0			0
$439$	4.22438e12	−	2.43895e12i	0.259084	−	0.149582i	−0.364833	−	0.931073i	$-0.618874\pi$
$439$	4.22438e12	−	2.43895e12i	0.259084	−	0.149582i	0.623917	+	0.781491i	$0.285540\pi$
$440$		0			0
$441$	−9.70546e12	+	7.81071e12i	−0.581866	+	0.468271i
$442$		0			0
$443$	−3.28333e12	−	5.68690e12i	−0.192441	−	0.333317i	0.753618	−	0.657313i	$-0.228307\pi$
$443$	−3.28333e12	−	5.68690e12i	−0.192441	−	0.333317i	−0.946058	+	0.323996i	$0.894974\pi$
$444$		0			0
$445$	2.90390e12	−	5.02970e12i	0.166411	−	0.288232i
$446$		0			0
$447$			1.24406e12i			0.0697114i
$448$		0			0
$449$	3.58825e12			0.196630			0.0983152	−	0.995155i	$-0.468655\pi$
$449$	3.58825e12			0.196630			0.0983152	+	0.995155i	$0.468655\pi$
$450$		0			0
$451$	−1.55995e13	−	9.00636e12i	−0.836040	−	0.482688i
$452$		0			0
$453$	8.16399e12	−	4.71348e12i	0.427968	−	0.247087i
$454$		0			0
$455$	−1.05001e13	−	1.96255e12i	−0.538439	−	0.100639i
$456$		0			0
$457$	1.44621e12	+	2.50490e12i	0.0725519	+	0.125664i	0.900019	−	0.435850i	$-0.143552\pi$
$457$	1.44621e12	+	2.50490e12i	0.0725519	+	0.125664i	−0.827467	+	0.561514i	$0.810219\pi$
$458$		0			0
$459$	−1.57422e13	+	2.72663e13i	−0.772684	+	1.33833i
$460$		0			0
$461$		−	3.87945e13i		−	1.86323i	−0.363453	−	0.931613i	$-0.618402\pi$
$461$		−	3.87945e13i		−	1.86323i	0.363453	−	0.931613i	$-0.381598\pi$
$462$		0			0
$463$	1.28928e13			0.605958			0.302979	−	0.952997i	$-0.402019\pi$
$463$	1.28928e13			0.605958			0.302979	+	0.952997i	$0.402019\pi$
$464$		0			0
$465$	−2.21935e12	−	1.28134e12i	−0.102085	−	0.0589386i
$466$		0			0
$467$	3.34349e13	−	1.93036e13i	1.50527	−	0.869070i	0.505291	−	0.862949i	$-0.331385\pi$
$467$	3.34349e13	−	1.93036e13i	1.50527	−	0.869070i	0.999981	−	0.00612071i	$-0.00194829\pi$
$468$		0			0
$469$	−5.77958e12	−	1.64000e13i	−0.254702	−	0.722737i
$470$		0			0
$471$	−6.69249e12	−	1.15917e13i	−0.288724	−	0.500085i
$472$		0			0
$473$	−1.35049e13	+	2.33911e13i	−0.570407	+	0.987973i
$474$		0			0
$475$		−	8.34451e12i		−	0.345090i
$476$		0			0
$477$	3.34118e12			0.135303
$478$		0			0
$479$	2.45528e13	+	1.41755e13i	0.973695	+	0.562163i	0.900361	−	0.435145i	$-0.143303\pi$
$479$	2.45528e13	+	1.41755e13i	0.973695	+	0.562163i	0.0733341	+	0.997307i	$0.476636\pi$
$480$		0			0
$481$	−3.02720e13	+	1.74775e13i	−1.17575	+	0.678820i
$482$		0			0
$483$	1.23407e13	+	1.05724e13i	0.469466	+	0.402195i
$484$		0			0
$485$	−7.04638e12	−	1.22047e13i	−0.262577	−	0.454798i
$486$		0			0
$487$	−4.80764e12	+	8.32707e12i	−0.175504	+	0.303982i	−0.940336	−	0.340249i	$-0.889489\pi$
$487$	−4.80764e12	+	8.32707e12i	−0.175504	+	0.303982i	0.764832	+	0.644230i	$0.222822\pi$
$488$		0			0
$489$			2.69358e13i			0.963354i
$490$		0			0
$491$	−4.49447e13			−1.57496			−0.787482	−	0.616338i	$-0.788616\pi$
$491$	−4.49447e13			−1.57496			−0.787482	+	0.616338i	$0.788616\pi$
$492$		0			0
$493$	5.74107e13	+	3.31461e13i	1.97132	+	1.13814i
$494$		0			0
$495$	−6.62717e12	+	3.82620e12i	−0.222999	+	0.128748i
$496$		0			0
$497$	1.67673e13	−	1.95718e13i	0.552943	−	0.645428i
$498$		0			0
$499$	1.59532e13	+	2.76317e13i	0.515638	+	0.893111i	0.999835	+	0.0181523i	$0.00577836\pi$
$499$	1.59532e13	+	2.76317e13i	0.515638	+	0.893111i	−0.484197	+	0.874959i	$0.660888\pi$
$500$		0			0
$501$	−8.89772e12	+	1.54113e13i	−0.281897	+	0.488260i
$502$		0			0
$503$		−	4.48957e13i		−	1.39433i	−0.716912	−	0.697163i	$-0.754445\pi$
$503$		−	4.48957e13i		−	1.39433i	0.716912	−	0.697163i	$-0.245555\pi$
$504$		0			0
$505$	3.67430e12			0.111871
$506$		0			0
$507$	8.27931e12	+	4.78006e12i	0.247146	+	0.142690i
$508$		0			0
$509$	4.62709e13	−	2.67145e13i	1.35431	−	0.781914i	0.365464	−	0.930826i	$-0.380910\pi$
$509$	4.62709e13	−	2.67145e13i	1.35431	−	0.781914i	0.988850	+	0.148912i	$0.0475771\pi$
$510$		0			0
$511$	−5.16442e13	+	1.82001e13i	−1.48224	+	0.522359i
$512$		0			0
$513$	−6.66348e12	−	1.15415e13i	−0.187549	−	0.324844i
$514$		0			0
$515$	−1.06157e13	+	1.83869e13i	−0.293030	+	0.507543i
$516$		0			0
$517$		−	2.62382e11i		−	0.00710365i
$518$		0			0
$519$	9.32839e12			0.247725
$520$		0			0
$521$	5.62594e13	+	3.24814e13i	1.46557	+	0.846148i	0.999260	−	0.0384730i	$-0.0122494\pi$
$521$	5.62594e13	+	3.24814e13i	1.46557	+	0.846148i	0.466311	+	0.884621i	$0.345583\pi$
$522$		0			0
$523$	−1.49560e13	+	8.63486e12i	−0.382215	+	0.220672i	−0.678781	−	0.734340i	$-0.737492\pi$
$523$	−1.49560e13	+	8.63486e12i	−0.382215	+	0.220672i	0.296567	+	0.955012i	$0.404158\pi$
$524$		0			0
$525$	−2.98078e12	+	1.59478e13i	−0.0747366	+	0.399858i
$526$		0			0
$527$	1.91376e13	+	3.31473e13i	0.470797	+	0.815445i
$528$		0			0
$529$	−1.05609e13	+	1.82920e13i	−0.254930	+	0.441552i
$530$		0			0
$531$			1.02571e13i			0.242971i
$532$		0			0
$533$	6.59798e13			1.53382
$534$		0			0
$535$	−2.54879e13	−	1.47155e13i	−0.581521	−	0.335742i
$536$		0			0
$537$	2.34241e13	−	1.35239e13i	0.524555	−	0.302852i
$538$		0			0
$539$	−3.34255e13	−	1.29473e13i	−0.734740	−	0.284600i
$540$		0			0
$541$	−2.21519e13	−	3.83682e13i	−0.477996	−	0.827914i	0.521686	−	0.853138i	$-0.325303\pi$
$541$	−2.21519e13	−	3.83682e13i	−0.477996	−	0.827914i	−0.999682	+	0.0252242i	$0.991970\pi$
$542$		0			0
$543$	−1.88489e13	+	3.26472e13i	−0.399288	+	0.691588i
$544$		0			0
$545$		−	5.53677e12i		−	0.115153i
$546$		0			0
$547$	4.51404e13			0.921784			0.460892	−	0.887456i	$-0.347530\pi$
$547$	4.51404e13			0.921784			0.460892	+	0.887456i	$0.347530\pi$
$548$		0			0
$549$	9.49572e12	+	5.48236e12i	0.190400	+	0.109927i
$550$		0			0
$551$	−2.43012e13	+	1.40303e13i	−0.478487	+	0.276255i
$552$		0			0
$553$	−3.50519e13	−	6.55149e12i	−0.677776	−	0.126682i
$554$		0			0
$555$	−6.28535e12	−	1.08865e13i	−0.119361	−	0.206740i
$556$		0			0
$557$	−9.18810e11	+	1.59143e12i	−0.0171376	+	0.0296832i	−0.874467	−	0.485085i	$-0.838789\pi$
$557$	−9.18810e11	+	1.59143e12i	−0.0171376	+	0.0296832i	0.857329	+	0.514768i	$0.172122\pi$
$558$		0			0
$559$		−	9.89355e13i		−	1.81256i
$560$		0			0
$561$	−3.87320e13			−0.697037
$562$		0			0
$563$	−6.68038e13	−	3.85692e13i	−1.18103	−	0.681866i	−0.224774	−	0.974411i	$-0.572164\pi$
$563$	−6.68038e13	−	3.85692e13i	−1.18103	−	0.681866i	−0.956252	+	0.292545i	$0.905498\pi$
$564$		0			0
$565$	2.12198e13	−	1.22513e13i	0.368553	−	0.212784i
$566$		0			0
$567$	−5.93571e12	−	1.68430e13i	−0.101288	−	0.287412i
$568$		0			0
$569$	−1.60937e13	−	2.78752e13i	−0.269833	−	0.467365i	0.698985	−	0.715136i	$-0.253635\pi$
$569$	−1.60937e13	−	2.78752e13i	−0.269833	−	0.467365i	−0.968819	+	0.247771i	$0.920302\pi$
$570$		0			0
$571$	−2.54437e12	+	4.40698e12i	−0.0419180	+	0.0726040i	−0.886223	−	0.463259i	$-0.846680\pi$
$571$	−2.54437e12	+	4.40698e12i	−0.0419180	+	0.0726040i	0.844305	+	0.535863i	$0.180013\pi$
$572$		0			0
$573$		−	4.86859e13i		−	0.788189i
$574$		0			0
$575$	−6.24476e13			−0.993520
$576$		0			0
$577$	6.83777e13	+	3.94779e13i	1.06914	+	0.617269i	0.927947	−	0.372712i	$-0.121572\pi$
$577$	6.83777e13	+	3.94779e13i	1.06914	+	0.617269i	0.141195	+	0.989982i	$0.454906\pi$
$578$		0			0
$579$	5.05862e13	−	2.92059e13i	0.777390	−	0.448826i
$580$		0			0
$581$	−4.36074e13	−	3.73587e13i	−0.658687	−	0.564302i
$582$		0			0
$583$	4.80677e12	+	8.32557e12i	0.0713692	+	0.123615i
$584$		0			0
$585$	1.40152e13	−	2.42751e13i	0.204560	−	0.354308i
$586$		0			0
$587$			4.18955e13i			0.601142i	0.953759	+	0.300571i	$0.0971773\pi$
$587$			4.18955e13i			0.601142i	−0.953759	+	0.300571i	$0.902823\pi$
$588$		0			0
$589$	−1.62014e13			−0.228547
$590$		0			0
$591$	9.39446e12	+	5.42389e12i	0.130297	+	0.0752270i
$592$		0			0
$593$	−1.06047e14	+	6.12265e13i	−1.44619	+	0.834960i	−0.998252	−	0.0591021i	$-0.981176\pi$
$593$	−1.06047e14	+	6.12265e13i	−1.44619	+	0.834960i	−0.447942	+	0.894063i	$0.647843\pi$
$594$		0			0
$595$	−3.73281e13	+	4.35716e13i	−0.500554	+	0.584277i
$596$		0			0
$597$	−3.69760e13	−	6.40442e13i	−0.487582	−	0.844517i
$598$		0			0
$599$	3.22111e12	−	5.57912e12i	0.0417706	−	0.0723489i	−0.844384	−	0.535738i	$-0.820033\pi$
$599$	3.22111e12	−	5.57912e12i	0.0417706	−	0.0723489i	0.886155	+	0.463389i	$0.153367\pi$
$600$		0			0
$601$			4.84779e13i			0.618261i	0.951020	+	0.309130i	$0.100038\pi$
$601$			4.84779e13i			0.618261i	−0.951020	+	0.309130i	$0.899962\pi$
$602$		0			0
$603$	4.56295e13			0.572346
$604$		0			0
$605$	1.16454e13	+	6.72348e12i	0.143674	+	0.0829502i
$606$		0			0
$607$	1.29684e14	−	7.48729e13i	1.57377	−	0.908618i	0.578072	−	0.815986i	$-0.303805\pi$
$607$	1.29684e14	−	7.48729e13i	1.57377	−	0.908618i	0.995700	−	0.0926322i	$-0.0295281\pi$
$608$		0			0
$609$	5.14558e13	−	1.81337e13i	0.614253	−	0.216471i
$610$		0			0
$611$	4.80548e11	+	8.32333e11i	0.00564326	+	0.00977442i
$612$		0			0
$613$	8.55117e12	−	1.48111e13i	0.0987923	−	0.171113i	−0.812393	−	0.583111i	$-0.801835\pi$
$613$	8.55117e12	−	1.48111e13i	0.0987923	−	0.171113i	0.911185	+	0.411997i	$0.135169\pi$
$614$		0			0
$615$			2.37280e13i			0.269702i
$616$		0			0
$617$	1.48483e14			1.66054			0.830272	−	0.557358i	$-0.188185\pi$
$617$	1.48483e14			1.66054			0.830272	+	0.557358i	$0.188185\pi$
$618$		0			0
$619$	2.88329e13	+	1.66467e13i	0.317275	+	0.183179i	0.650177	−	0.759783i	$-0.274695\pi$
$619$	2.88329e13	+	1.66467e13i	0.317275	+	0.183179i	−0.332902	+	0.942961i	$0.608028\pi$
$620$		0			0
$621$	−8.63727e13	+	4.98673e13i	−0.935230	+	0.539955i
$622$		0			0
$623$	−1.31159e13	+	7.01730e13i	−0.139752	+	0.747705i
$624$		0			0
$625$	−2.20447e13	−	3.81825e13i	−0.231155	−	0.400372i
$626$		0			0
$627$	8.19739e12	−	1.41983e13i	0.0845937	−	0.146521i
$628$		0			0
$629$			1.87751e14i			1.90690i
$630$		0			0
$631$	−1.31260e14			−1.31216			−0.656078	−	0.754693i	$-0.727786\pi$
$631$	−1.31260e14			−1.31216			−0.656078	+	0.754693i	$0.727786\pi$
$632$		0			0
$633$	−5.83366e13	−	3.36806e13i	−0.574014	−	0.331407i
$634$		0			0
$635$	1.47180e13	−	8.49746e12i	0.142554	−	0.0823039i
$636$		0			0
$637$	1.29745e14	−	2.01465e13i	1.23707	−	0.192089i
$638$		0			0
$639$	3.38141e13	+	5.85677e13i	0.317390	+	0.549736i
$640$		0			0
$641$	−6.94680e13	+	1.20322e14i	−0.641940	+	1.11187i	0.343059	+	0.939314i	$0.388537\pi$
$641$	−6.94680e13	+	1.20322e14i	−0.641940	+	1.11187i	−0.984999	+	0.172559i	$0.944796\pi$
$642$		0			0
$643$		−	5.84743e13i		−	0.531999i	−0.963973	−	0.265999i	$-0.914298\pi$
$643$		−	5.84743e13i		−	0.531999i	0.963973	−	0.265999i	$-0.0857019\pi$
$644$		0			0
$645$	3.55796e13			0.318715
$646$		0			0
$647$	7.89897e13	+	4.56047e13i	0.696705	+	0.402243i	0.806119	−	0.591753i	$-0.201564\pi$
$647$	7.89897e13	+	4.56047e13i	0.696705	+	0.402243i	−0.109414	+	0.993996i	$0.534897\pi$
$648$		0			0
$649$	−2.55588e13	+	1.47564e13i	−0.221981	+	0.128161i
$650$		0			0
$651$	3.09637e13	+	5.78737e12i	0.264819	+	0.0494967i
$652$		0			0
$653$	7.59569e13	+	1.31561e14i	0.639736	+	1.10806i	0.985490	+	0.169731i	$0.0542898\pi$
$653$	7.59569e13	+	1.31561e14i	0.639736	+	1.10806i	−0.345754	+	0.938325i	$0.612377\pi$
$654$		0			0
$655$	1.89334e13	−	3.27936e13i	0.157044	−	0.272008i
$656$		0			0
$657$		−	1.43689e14i		−	1.17380i
$658$		0			0
$659$	−2.05009e13			−0.164948			−0.0824738	−	0.996593i	$-0.526282\pi$
$659$	−2.05009e13			−0.164948			−0.0824738	+	0.996593i	$0.526282\pi$
$660$		0			0
$661$	−1.66595e14	−	9.61836e13i	−1.32024	−	0.762244i	−0.336477	−	0.941692i	$-0.609236\pi$
$661$	−1.66595e14	−	9.61836e13i	−1.32024	−	0.762244i	−0.983767	+	0.179448i	$0.942569\pi$
$662$		0			0
$663$	1.22866e14	−	7.09369e13i	0.959102	−	0.553738i
$664$		0			0
$665$	−8.07213e12	−	2.29053e13i	−0.0620698	−	0.176128i
$666$		0			0
$667$	1.04998e14	+	1.81862e14i	0.795341	+	1.37757i
$668$		0			0
$669$	−2.28182e13	+	3.95223e13i	−0.170275	+	0.294925i
$670$		0			0
$671$			3.15486e13i			0.231936i
$672$		0			0
$673$	−1.75602e13			−0.127190			−0.0635951	−	0.997976i	$-0.520257\pi$
$673$	−1.75602e13			−0.127190			−0.0635951	+	0.997976i	$0.520257\pi$
$674$		0			0
$675$	−8.62338e13	−	4.97871e13i	−0.615401	−	0.355302i
$676$		0			0
$677$	−1.46773e14	+	8.47395e13i	−1.03206	+	0.595858i	−0.917573	−	0.397568i	$-0.869854\pi$
$677$	−1.46773e14	+	8.47395e13i	−1.03206	+	0.595858i	−0.114483	+	0.993425i	$0.536521\pi$
$678$		0			0
$679$	1.31551e14	+	1.12701e14i	0.911476	+	0.780867i
$680$		0			0
$681$	−5.23737e13	−	9.07139e13i	−0.357583	−	0.619353i
$682$		0			0
$683$	1.32875e14	−	2.30147e14i	0.894006	−	1.54846i	0.0589754	−	0.998259i	$-0.481217\pi$
$683$	1.32875e14	−	2.30147e14i	0.894006	−	1.54846i	0.835030	−	0.550204i	$-0.185450\pi$
$684$		0			0
$685$			1.03950e14i			0.689242i
$686$		0			0
$687$	−4.20075e13			−0.274500
$688$		0			0
$689$	−3.04962e13	−	1.76070e13i	−0.196404	−	0.113394i
$690$		0			0
$691$	−1.02171e14	+	5.89887e13i	−0.648544	+	0.374437i	−0.787898	−	0.615806i	$-0.788831\pi$
$691$	−1.02171e14	+	5.89887e13i	−0.648544	+	0.374437i	0.139354	+	0.990243i	$0.455497\pi$
$692$		0			0
$693$	6.11966e13	−	7.14324e13i	0.382879	−	0.446919i
$694$		0			0
$695$	−1.33520e13	−	2.31264e13i	−0.0823423	−	0.142621i
$696$		0			0
$697$	1.77196e14	−	3.06912e14i	1.07718	−	1.86573i
$698$		0			0
$699$			3.45839e13i			0.207247i
$700$		0			0
$701$	−2.94420e14			−1.73931			−0.869654	−	0.493662i	$-0.835658\pi$
$701$	−2.94420e14			−1.73931			−0.869654	+	0.493662i	$0.835658\pi$
$702$		0			0
$703$	−6.88253e13	−	3.97363e13i	−0.400840	−	0.231425i
$704$		0			0
$705$	−2.99327e11	+	1.72817e11i	−0.00171870	+	0.000992293i
$706$		0			0
$707$	−4.25960e13	+	1.50114e13i	−0.241142	+	0.0849814i
$708$		0			0
$709$	−1.48301e14	−	2.56865e14i	−0.827775	−	1.43375i	−0.899780	−	0.436344i	$-0.856273\pi$
$709$	−1.48301e14	−	2.56865e14i	−0.827775	−	1.43375i	0.0720049	−	0.997404i	$-0.477060\pi$
$710$		0			0
$711$	4.67862e13	−	8.10361e13i	0.257496	−	0.445996i
$712$		0			0
$713$			1.21246e14i			0.657991i
$714$		0			0
$715$	8.06516e13			0.431601
$716$		0			0
$717$	1.07328e14	+	6.19658e13i	0.566392	+	0.327006i
$718$		0			0
$719$	2.79277e13	−	1.61241e13i	0.145342	−	0.0839133i	−0.425565	−	0.904928i	$-0.639925\pi$
$719$	2.79277e13	−	1.61241e13i	0.145342	−	0.0839133i	0.570908	+	0.821014i	$0.306591\pi$
$720$		0			0
$721$	4.79474e13	−	2.56530e14i	0.246087	−	1.31662i
$722$		0			0
$723$	6.88051e13	+	1.19174e14i	0.348281	+	0.603240i
$724$		0			0
$725$	−1.04829e14	+	1.81570e14i	−0.523351	+	0.906471i
$726$		0			0
$727$		−	1.08786e14i		−	0.535673i	−0.963464	−	0.267836i	$-0.913691\pi$
$727$		−	1.08786e14i		−	0.535673i	0.963464	−	0.267836i	$-0.0863087\pi$
$728$		0			0
$729$	−4.41734e13			−0.214548
$730$		0			0
$731$	−4.60209e14	−	2.65702e14i	−2.20479	−	1.27294i
$732$		0			0
$733$	−2.85644e14	+	1.64917e14i	−1.34991	+	0.779372i	−0.988237	−	0.152933i	$-0.951128\pi$
$733$	−2.85644e14	+	1.64917e14i	−1.34991	+	0.779372i	−0.361675	+	0.932304i	$0.617795\pi$
$734$		0			0
$735$	7.24516e12	+	4.66596e13i	0.0337763	+	0.217523i
$736$		0			0
$737$	6.56445e13	+	1.13700e14i	0.301899	+	0.522904i
$738$		0			0
$739$	1.14528e14	−	1.98368e14i	0.519623	−	0.900014i	−0.480117	−	0.877205i	$-0.659406\pi$
$739$	1.14528e14	−	1.98368e14i	0.519623	−	0.900014i	0.999740	−	0.0228091i	$-0.00726100\pi$
$740$		0			0
$741$			6.00534e13i			0.268811i
$742$		0			0
$743$	−2.40811e13			−0.106349			−0.0531743	−	0.998585i	$-0.516934\pi$
$743$	−2.40811e13			−0.106349			−0.0531743	+	0.998585i	$0.516934\pi$
$744$		0			0
$745$	−1.20500e13	−	6.95706e12i	−0.0525055	−	0.0303141i
$746$		0			0
$747$	1.30493e14	−	7.53403e13i	0.561029	−	0.323910i
$748$		0			0
$749$	3.55601e14	+	6.64647e13i	1.50853	+	0.281956i
$750$		0			0
$751$	1.48588e14	+	2.57362e14i	0.621990	+	1.07732i	0.989115	+	0.147146i	$0.0470088\pi$
$751$	1.48588e14	+	2.57362e14i	0.621990	+	1.07732i	−0.367125	+	0.930172i	$0.619658\pi$
$752$		0			0
$753$	1.29109e13	−	2.23624e13i	0.0533313	−	0.0923725i
$754$		0			0
$755$			1.05435e14i			0.429785i
$756$		0			0
$757$	2.33467e14			0.939175			0.469587	−	0.882886i	$-0.344403\pi$
$757$	2.33467e14			0.939175			0.469587	+	0.882886i	$0.344403\pi$
$758$		0			0
$759$	−1.06255e14	−	6.13466e13i	−0.421835	−	0.243546i
$760$		0			0
$761$	−7.24688e13	+	4.18399e13i	−0.283941	+	0.163933i	−0.635206	−	0.772343i	$-0.719085\pi$
$761$	−7.24688e13	+	4.18399e13i	−0.283941	+	0.163933i	0.351265	+	0.936276i	$0.385751\pi$
$762$		0			0
$763$	2.26205e13	+	6.41876e13i	0.0874742	+	0.248215i
$764$		0			0
$765$	−7.52786e13	−	1.30386e14i	−0.287319	−	0.497651i
$766$		0			0
$767$	5.40520e13	−	9.36207e13i	0.203627	−	0.352692i
$768$		0			0
$769$			9.16613e13i			0.340843i	0.985371	+	0.170422i	$0.0545129\pi$
$769$			9.16613e13i			0.340843i	−0.985371	+	0.170422i	$0.945487\pi$
$770$		0			0
$771$	6.37910e13			0.234146
$772$		0			0
$773$	2.41982e14	+	1.39708e14i	0.876768	+	0.506202i	0.869591	−	0.493772i	$-0.164382\pi$
$773$	2.41982e14	+	1.39708e14i	0.876768	+	0.506202i	0.00717672	+	0.999974i	$0.497716\pi$
$774$		0			0
$775$	−1.04833e14	+	6.05255e13i	−0.374965	+	0.216486i
$776$		0			0
$777$	1.17343e14	+	1.00528e14i	0.414335	+	0.354964i
$778$		0			0
$779$	7.50047e13	+	1.29912e14i	0.261458	+	0.452858i
$780$		0			0
$781$	−9.72928e13	+	1.68516e14i	−0.334831	+	0.579944i
$782$		0			0
$783$			3.34844e14i			1.13772i
$784$		0			0
$785$	1.49704e14			0.502209
$786$		0			0
$787$	9.64491e13	+	5.56849e13i	0.319466	+	0.184444i	0.651155	−	0.758945i	$-0.274285\pi$
$787$	9.64491e13	+	5.56849e13i	0.319466	+	0.184444i	−0.331689	+	0.943389i	$0.607618\pi$
$788$		0			0
$789$	5.96734e13	−	3.44525e13i	0.195162	−	0.112677i
$790$		0			0
$791$	−1.95948e14	+	2.28723e14i	−0.632789	+	0.738630i
$792$		0			0
$793$	−5.77807e13	−	1.00079e14i	−0.184254	−	0.319137i
$794$		0			0
$795$	6.33191e12	−	1.09672e13i	0.0199388	−	0.0345350i
$796$		0			0
$797$			4.07783e14i			1.26805i	0.773311	+	0.634027i	$0.218599\pi$
$797$			4.07783e14i			1.26805i	−0.773311	+	0.634027i	$0.781401\pi$
$798$		0			0
$799$	5.16224e12			0.0158527
$800$		0			0
$801$	−1.62232e14	−	9.36648e13i	−0.492011	−	0.284062i
$802$		0			0
$803$	3.58044e14	−	2.06717e14i	1.07240	−	0.619153i
$804$		0			0
$805$	−1.71416e14	+	6.04092e13i	−0.507075	+	0.178700i
$806$		0			0
$807$	−4.87664e13	−	8.44659e13i	−0.142480	−	0.246782i
$808$		0			0
$809$	2.65040e14	−	4.59063e14i	0.764838	−	1.32474i	−0.175495	−	0.984480i	$-0.556152\pi$
$809$	2.65040e14	−	4.59063e14i	0.764838	−	1.32474i	0.940332	−	0.340257i	$-0.110514\pi$
$810$		0			0
$811$			1.37443e13i			0.0391758i	0.999808	+	0.0195879i	$0.00623543\pi$
$811$			1.37443e13i			0.0391758i	−0.999808	+	0.0195879i	$0.993765\pi$
$812$		0			0
$813$	−1.05057e13			−0.0295781
$814$		0			0
$815$	−2.60901e14	−	1.50631e14i	−0.725583	−	0.418916i
$816$		0			0
$817$	1.94801e14	−	1.12468e14i	0.535156	−	0.308972i
$818$		0			0
$819$	−6.33019e13	+	3.38679e14i	−0.171790	+	0.919114i
$820$		0			0
$821$	−3.18816e12	−	5.52205e12i	−0.00854720	−	0.0148042i	0.861720	−	0.507384i	$-0.169387\pi$
$821$	−3.18816e12	−	5.52205e12i	−0.00854720	−	0.0148042i	−0.870267	+	0.492580i	$0.836054\pi$
$822$		0			0
$823$	−1.66883e13	+	2.89049e13i	−0.0441990	+	0.0765548i	−0.887279	−	0.461234i	$-0.847407\pi$
$823$	−1.66883e13	+	2.89049e13i	−0.0441990	+	0.0765548i	0.843080	+	0.537789i	$0.180740\pi$
$824$		0			0
$825$		−	1.22496e14i		−	0.320517i
$826$		0			0
$827$	−5.97821e14			−1.54541			−0.772705	−	0.634766i	$-0.781097\pi$
$827$	−5.97821e14			−1.54541			−0.772705	+	0.634766i	$0.781097\pi$
$828$		0			0
$829$	1.46987e14	+	8.48632e13i	0.375411	+	0.216744i	0.675820	−	0.737067i	$-0.263790\pi$
$829$	1.46987e14	+	8.48632e13i	0.375411	+	0.216744i	−0.300409	+	0.953811i	$0.597123\pi$
$830$		0			0
$831$	−2.54223e14	+	1.46776e14i	−0.641521	+	0.370382i
$832$		0			0
$833$	2.54731e14	−	6.57629e14i	0.635123	−	1.63967i
$834$		0			0
$835$	−9.95161e13	−	1.72367e14i	−0.245166	−	0.424641i
$836$		0			0
$837$	−9.66648e13	+	1.67428e14i	−0.235310	+	0.407569i
$838$		0			0
$839$		−	5.74077e14i		−	1.38089i	−0.723383	−	0.690447i	$-0.757414\pi$
$839$		−	5.74077e14i		−	1.38089i	0.723383	−	0.690447i	$-0.242586\pi$
$840$		0			0
$841$	2.84326e14			0.675829
$842$		0			0
$843$	−5.98410e12	−	3.45492e12i	−0.0140560	−	0.00811522i
$844$		0			0
$845$	−9.25996e13	+	5.34624e13i	−0.214944	+	0.124098i
$846$		0			0
$847$	−1.62474e14	−	3.03677e13i	−0.372706	−	0.0696617i
$848$		0			0
$849$	3.59576e13	+	6.22804e13i	0.0815177	+	0.141193i
$850$		0			0
$851$	−2.97374e14	+	5.15066e14i	−0.666277	+	1.15402i
$852$		0			0
$853$			1.18410e14i			0.262205i	0.991369	+	0.131103i	$0.0418518\pi$
$853$			1.18410e14i			0.262205i	−0.991369	+	0.131103i	$0.958148\pi$
$854$		0			0
$855$	6.37290e13			0.139478
$856$		0			0
$857$	5.10689e14	+	2.94846e14i	1.10472	+	0.637810i	0.937457	−	0.348102i	$-0.113174\pi$
$857$	5.10689e14	+	2.94846e14i	1.10472	+	0.637810i	0.167263	+	0.985912i	$0.446507\pi$
$858$		0			0
$859$	8.15155e13	−	4.70630e13i	0.174291	−	0.100627i	−0.410317	−	0.911943i	$-0.634582\pi$
$859$	8.15155e13	−	4.70630e13i	0.174291	−	0.100627i	0.584607	+	0.811316i	$0.301249\pi$
$860$		0			0
$861$	−9.69409e13	−	2.75078e14i	−0.204876	−	0.581352i
$862$		0			0
$863$	−1.30394e14	−	2.25850e14i	−0.272399	−	0.471808i	0.697077	−	0.716996i	$-0.254484\pi$
$863$	−1.30394e14	−	2.25850e14i	−0.272399	−	0.471808i	−0.969476	+	0.245188i	$0.921150\pi$
$864$		0			0
$865$	−5.21664e13	+	9.03549e13i	−0.107724	+	0.186583i
$866$		0			0
$867$		−	5.15572e14i		−	1.05243i
$868$		0			0
$869$	2.69235e14			0.543291
$870$		0			0
$871$	−4.16477e14	−	2.40453e14i	−0.830807	−	0.479667i
$872$		0			0
$873$	−3.93661e14	+	2.27280e14i	−0.776338	+	0.448219i
$874$		0			0
$875$	−3.08232e14	−	2.64065e14i	−0.600949	−	0.514837i
$876$		0			0
$877$	−2.40755e14	−	4.16999e14i	−0.464063	−	0.803781i	0.535096	−	0.844791i	$-0.320276\pi$
$877$	−2.40755e14	−	4.16999e14i	−0.464063	−	0.803781i	−0.999159	+	0.0410108i	$0.986942\pi$
$878$		0			0
$879$	1.08818e14	−	1.88478e14i	0.207375	−	0.359183i
$880$		0			0
$881$		−	5.29064e14i		−	0.996848i	−0.866934	−	0.498424i	$-0.833912\pi$
$881$		−	5.29064e14i		−	0.996848i	0.866934	−	0.498424i	$-0.166088\pi$
$882$		0			0
$883$	−2.50999e14			−0.467594			−0.233797	−	0.972285i	$-0.575115\pi$
$883$	−2.50999e14			−0.467594			−0.233797	+	0.972285i	$0.575115\pi$
$884$		0			0
$885$	3.36683e13	+	1.94384e13i	0.0620162	+	0.0358051i
$886$		0			0
$887$	5.19971e14	−	3.00206e14i	0.947025	−	0.546765i	0.0548692	−	0.998494i	$-0.482526\pi$
$887$	5.19971e14	−	3.00206e14i	0.947025	−	0.546765i	0.892155	+	0.451729i	$0.149192\pi$
$888$		0			0
$889$	−1.35909e14	+	1.58641e14i	−0.244760	+	0.285698i
$890$		0			0
$891$	6.74178e13	+	1.16771e14i	0.120057	+	0.207944i
$892$		0			0
$893$	−1.09256e12	+	1.89236e12i	−0.00192392	+	0.00333232i
$894$		0			0
$895$			3.02515e14i			0.526783i
$896$		0			0
$897$	4.49420e14			0.773910
$898$		0			0
$899$	3.52529e14	+	2.03533e14i	0.600339	+	0.346606i
$900$		0			0
$901$	−1.63802e14	+	9.45709e13i	−0.275863	+	0.159270i
$902$		0			0
$903$	−4.12474e14	+	1.45361e14i	−0.687001	+	0.242108i
$904$		0			0
$905$	−2.10815e14	−	3.65142e14i	−0.347262	−	0.601476i
$906$		0			0
$907$	−5.34318e14	+	9.25466e14i	−0.870489	+	1.50773i	−0.00899709	+	0.999960i	$0.502864\pi$
$907$	−5.34318e14	+	9.25466e14i	−0.870489	+	1.50773i	−0.861492	+	0.507771i	$0.830469\pi$
$908$		0			0
$909$		−	1.18514e14i		−	0.190963i
$910$		0			0
$911$	7.85543e13			0.125192			0.0625962	−	0.998039i	$-0.480062\pi$
$911$	7.85543e13			0.125192			0.0625962	+	0.998039i	$0.480062\pi$
$912$		0			0
$913$	3.75467e14	+	2.16776e14i	0.591858	+	0.341709i
$914$		0			0
$915$	3.59909e13	−	2.07793e13i	0.0561160	−	0.0323986i
$916$		0			0
$917$	−8.55155e13	+	4.57527e14i	−0.131886	+	0.705619i
$918$		0			0
$919$	6.40461e14	+	1.10931e15i	0.977046	+	1.69229i	0.673012	+	0.739632i	$0.265000\pi$
$919$	6.40461e14	+	1.10931e15i	0.977046	+	1.69229i	0.304034	+	0.952661i	$0.401666\pi$
$920$		0			0
$921$	4.50362e13	−	7.80049e13i	0.0679616	−	0.117713i
$922$		0			0
$923$		−	7.12759e14i		−	1.06398i
$924$		0			0
$925$	−5.93790e14			−0.876848
$926$		0			0
$927$	5.93068e14	+	3.42408e14i	0.866374	+	0.500201i
$928$		0			0
$929$	−8.98110e13	+	5.18524e13i	−0.129793	+	0.0749359i	−0.563491	−	0.826122i	$-0.690542\pi$
$929$	−8.98110e13	+	5.18524e13i	−0.129793	+	0.0749359i	0.433698	+	0.901058i	$0.357209\pi$
$930$		0			0
$931$	1.87160e14	+	2.32562e14i	0.267587	+	0.332499i
$932$		0			0
$933$	1.78352e14	+	3.08915e14i	0.252273	+	0.436949i
$934$		0			0
$935$	2.16598e14	−	3.75159e14i	0.303108	−	0.524998i
$936$		0			0
$937$		−	6.30940e14i		−	0.873555i	−0.899570	−	0.436778i	$-0.856120\pi$
$937$		−	6.30940e14i		−	0.873555i	0.899570	−	0.436778i	$-0.143880\pi$
$938$		0			0
$939$	−4.14945e13			−0.0568412
$940$		0			0
$941$	1.24603e15	+	7.19397e14i	1.68881	+	0.975036i	0.955430	+	0.295218i	$0.0953923\pi$
$941$	1.24603e15	+	7.19397e14i	1.68881	+	0.975036i	0.733381	+	0.679817i	$0.237941\pi$
$942$		0			0
$943$	9.72219e14	−	5.61311e14i	1.30378	−	0.752740i
$944$		0			0
$945$	−2.84870e14	−	5.32445e13i	−0.377996	−	0.0706506i
$946$		0			0
$947$	2.71178e14	+	4.69695e14i	0.356045	+	0.616689i	0.987296	−	0.158890i	$-0.0507915\pi$
$947$	2.71178e14	+	4.69695e14i	0.356045	+	0.616689i	−0.631251	+	0.775579i	$0.717458\pi$
$948$		0			0
$949$	−7.57195e14	+	1.31150e15i	−0.983731	+	1.70387i
$950$		0			0
$951$			6.09168e13i			0.0783131i
$952$		0			0
$953$	−3.68037e14			−0.468196			−0.234098	−	0.972213i	$-0.575214\pi$
$953$	−3.68037e14			−0.468196			−0.234098	+	0.972213i	$0.575214\pi$
$954$		0			0
$955$	4.71573e14	+	2.72263e14i	0.593652	+	0.342745i
$956$		0			0
$957$	−3.56737e14	+	2.05962e14i	−0.444415	+	0.256583i
$958$		0			0
$959$	−4.24689e14	−	1.20509e15i	−0.523574	−	1.48568i
$960$		0			0
$961$	−2.92300e14	−	5.06279e14i	−0.356625	−	0.617693i
$962$		0			0
$963$	−4.74645e14	+	8.22110e14i	−0.573110	+	0.992655i
$964$		0			0
$965$			6.53305e14i			0.780691i
$966$		0			0
$967$	7.43446e14			0.879259			0.439630	−	0.898179i	$-0.355110\pi$
$967$	7.43446e14			0.879259			0.439630	+	0.898179i	$0.355110\pi$
$968$		0			0
$969$	2.79345e14	+	1.61280e14i	0.326980	+	0.188782i
$970$		0			0
$971$	9.61005e14	−	5.54836e14i	1.11334	−	0.642790i	0.173651	−	0.984807i	$-0.444444\pi$
$971$	9.61005e14	−	5.54836e14i	1.11334	−	0.642790i	0.939693	+	0.342018i	$0.111110\pi$
$972$		0			0
$973$	2.49273e14	+	2.13554e14i	0.285832	+	0.244874i
$974$		0			0
$975$	2.24349e14	+	3.88583e14i	0.254625	+	0.441023i
$976$		0			0
$977$	−1.69660e14	+	2.93860e14i	−0.190593	+	0.330117i	−0.945447	−	0.325776i	$-0.894374\pi$
$977$	−1.69660e14	+	2.93860e14i	−0.190593	+	0.330117i	0.754854	+	0.655893i	$0.227708\pi$
$978$		0			0
$979$		−	5.39001e14i		−	0.599344i
$980$		0			0
$981$	−1.78588e14			−0.196565
$982$		0			0
$983$	−7.80885e14	−	4.50844e14i	−0.850784	−	0.491200i	0.0101314	−	0.999949i	$-0.496775\pi$
$983$	−7.80885e14	−	4.50844e14i	−0.850784	−	0.491200i	−0.860915	+	0.508748i	$0.830108\pi$
$984$		0			0
$985$	−1.05072e14	+	6.06632e13i	−0.113320	+	0.0654251i
$986$		0			0
$987$	2.76405e12	−	3.22636e12i	0.00295094	−	0.00344451i
$988$		0			0
$989$	−8.41676e14	−	1.45782e15i	−0.889536	−	1.54072i
$990$		0			0
$991$	−1.74124e14	+	3.01591e14i	−0.182175	+	0.315537i	−0.942621	−	0.333865i	$-0.891647\pi$
$991$	−1.74124e14	+	3.01591e14i	−0.182175	+	0.315537i	0.760446	+	0.649401i	$0.224980\pi$
$992$		0			0
$993$		−	1.86825e13i		−	0.0193504i
$994$		0			0
$995$	8.27112e14			0.848103
$996$		0			0
$997$	−1.36322e15	−	7.87055e14i	−1.38385	−	0.798968i	−0.391240	−	0.920289i	$-0.627954\pi$
$997$	−1.36322e15	−	7.87055e14i	−1.38385	−	0.798968i	−0.992613	+	0.121321i	$0.961287\pi$
$998$		0			0
$999$	−8.21284e14	+	4.74169e14i	−0.825403	+	0.476547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.11.h.a.17.3	yes	14
3.2	odd	2		252.11.z.c.73.3		14
4.3	odd	2		112.11.s.c.17.5		14
7.2	even	3		196.11.h.b.117.5		14
7.3	odd	6		196.11.b.a.97.6		14
7.4	even	3		196.11.b.a.97.9		14
7.5	odd	6	inner	28.11.h.a.5.3	✓	14
7.6	odd	2		196.11.h.b.129.5		14
21.5	even	6		252.11.z.c.145.3		14
28.19	even	6		112.11.s.c.33.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.11.h.a.5.3	✓	14	7.5	odd	6	inner
28.11.h.a.17.3	yes	14	1.1	even	1	trivial
112.11.s.c.17.5		14	4.3	odd	2
112.11.s.c.33.5		14	28.19	even	6
196.11.b.a.97.6		14	7.3	odd	6
196.11.b.a.97.9		14	7.4	even	3
196.11.h.b.117.5		14	7.2	even	3
196.11.h.b.129.5		14	7.6	odd	2
252.11.z.c.73.3		14	3.2	odd	2
252.11.z.c.145.3		14	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	28.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-105.874 - 61.1265i) q^{3} +(1184.15 - 683.667i) q^{5} +(-10934.6 + 12763.6i) q^{7} +(-22051.6 - 38194.5i) q^{9} +O(q^{10})\)	\(q+(-105.874 - 61.1265i) q^{3} +(1184.15 - 683.667i) q^{5} +(-10934.6 + 12763.6i) q^{7} +(-22051.6 - 38194.5i) q^{9} +(63448.8 - 109896. i) q^{11} +464820. i q^{13} -167161. q^{15} +(2.16216e6 + 1.24832e6i) q^{17} +(-915215. + 528400. i) q^{19} +(1.93789e6 - 682938. i) q^{21} +(3.95437e6 + 6.84917e6i) q^{23} +(-3.94801e6 + 6.83816e6i) q^{25} +1.26107e7i q^{27} +2.65525e7 q^{29} +(1.32767e7 + 7.66531e6i) q^{31} +(-1.34352e7 + 7.75681e6i) q^{33} +(-4.22218e6 + 2.25896e7i) q^{35} +(3.76006e7 + 6.51261e7i) q^{37} +(2.84129e7 - 4.92125e7i) q^{39} -1.41947e8i q^{41} -2.12847e8 q^{43} +(-5.22246e7 - 3.01519e7i) q^{45} +(1.79065e6 - 1.03383e6i) q^{47} +(-4.33425e7 - 2.79130e8i) q^{49} +(-1.52611e8 - 2.64331e8i) q^{51} +(-3.78792e7 + 6.56086e7i) q^{53} -1.73511e8i q^{55} +1.29197e8 q^{57} +(-2.01413e8 - 1.16286e8i) q^{59} +(-2.15307e8 + 1.24308e8i) q^{61} +(7.28624e8 + 1.36186e8i) q^{63} +(3.17782e8 + 5.50415e8i) q^{65} +(-5.17303e8 + 8.95996e8i) q^{67} -9.66869e8i q^{69} -1.53341e9 q^{71} +(2.82152e9 + 1.62900e9i) q^{73} +(8.35986e8 - 4.82657e8i) q^{75} +(7.08883e8 + 2.01151e9i) q^{77} +(1.06084e9 + 1.83742e9i) q^{79} +(-5.31277e8 + 9.20199e8i) q^{81} +3.41655e9i q^{83} +3.41375e9 q^{85} +(-2.81122e9 - 1.62306e9i) q^{87} +(3.67847e9 - 2.12377e9i) q^{89} +(-5.93277e9 - 5.08264e9i) q^{91} +(-9.37108e8 - 1.62312e9i) q^{93} +(-7.22499e8 + 1.25140e9i) q^{95} -1.03067e10i q^{97} -5.59658e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 243 q^{3} + 3333 q^{5} - 8810 q^{7} + 152334 q^{9}+O(q^{10}) \) 14 * q - 243 * q^3 + 3333 * q^5 - 8810 * q^7 + 152334 * q^9	\( 14 q - 243 q^{3} + 3333 q^{5} - 8810 q^{7} + 152334 q^{9} + 43575 q^{11} - 295974 q^{15} - 4046547 q^{17} + 10506141 q^{19} - 6849963 q^{21} + 8356047 q^{23} + 16247798 q^{25} + 9638748 q^{29} + 26706309 q^{31} - 68091003 q^{33} + 57757869 q^{35} - 56337841 q^{37} - 47717712 q^{39} + 102867212 q^{43} + 277176762 q^{45} - 494767563 q^{47} - 228310402 q^{49} + 584803989 q^{51} - 280243257 q^{53} - 2426437062 q^{57} - 540103875 q^{59} + 3020130381 q^{61} + 44180910 q^{63} - 156676464 q^{65} - 1385714225 q^{67} + 5251025724 q^{71} + 5335510437 q^{73} - 1896380046 q^{75} - 832139025 q^{77} - 5240397281 q^{79} - 4471861527 q^{81} - 8239454118 q^{85} + 21846639978 q^{87} + 9313203429 q^{89} - 17599015344 q^{91} - 1809384507 q^{93} - 19347043443 q^{95} + 29066774940 q^{99}+O(q^{100}) \) 14 * q - 243 * q^3 + 3333 * q^5 - 8810 * q^7 + 152334 * q^9 + 43575 * q^11 - 295974 * q^15 - 4046547 * q^17 + 10506141 * q^19 - 6849963 * q^21 + 8356047 * q^23 + 16247798 * q^25 + 9638748 * q^29 + 26706309 * q^31 - 68091003 * q^33 + 57757869 * q^35 - 56337841 * q^37 - 47717712 * q^39 + 102867212 * q^43 + 277176762 * q^45 - 494767563 * q^47 - 228310402 * q^49 + 584803989 * q^51 - 280243257 * q^53 - 2426437062 * q^57 - 540103875 * q^59 + 3020130381 * q^61 + 44180910 * q^63 - 156676464 * q^65 - 1385714225 * q^67 + 5251025724 * q^71 + 5335510437 * q^73 - 1896380046 * q^75 - 832139025 * q^77 - 5240397281 * q^79 - 4471861527 * q^81 - 8239454118 * q^85 + 21846639978 * q^87 + 9313203429 * q^89 - 17599015344 * q^91 - 1809384507 * q^93 - 19347043443 * q^95 + 29066774940 * q^99

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