LMFDB - Embedded newform 98.13.d.b.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,13,Mod(19,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("98.19");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	98.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$89.5713940931$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 51570 x^{14} + 1743306357 x^{12} + 34303771893750 x^{10} + \cdots + 24\!\cdots\!96 $ x^16 + 51570x^14 + 1743306357x^12 + 34303771893750x^10 + 490016452747859435x^8 + 4318992197678245462380x^6 + 27578712253339290626452398x^4 + 100997229845590062592768165320*x^2 + 243579618669480443960727421550596
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{54}\cdot 3^{8}\cdot 7^{8} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.4
Root			$-68.6895 + 118.974i$ of defining polynomial
Character	$\chi$	$=$	98.19
Dual form			98.13.d.b.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-22.6274 + 39.1918i) q^{2} +(928.383 - 536.002i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(-987.816 - 570.316i) q^{5} +48513.4i q^{6} +92681.9 q^{8} +(308876. - 534989. i) q^{9} +O(q^{10})$	\(q+(-22.6274 + 39.1918i) q^{2} +(928.383 - 536.002i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(-987.816 - 570.316i) q^{5} +48513.4i q^{6} +92681.9 q^{8} +(308876. - 534989. i) q^{9} +(44703.4 - 25809.5i) q^{10} +(1.45307e6 + 2.51679e6i) q^{11} +(-1.90133e6 - 1.09773e6i) q^{12} -491015. i q^{13} -1.22276e6 q^{15} +(-2.09715e6 + 3.63237e6i) q^{16} +(2.72891e7 - 1.57554e7i) q^{17} +(1.39781e7 + 2.42108e7i) q^{18} +(1.00071e7 + 5.77763e6i) q^{19} +2.33601e6i q^{20} -1.31517e8 q^{22} +(-3.41682e6 + 5.91811e6i) q^{23} +(8.60443e7 - 4.96777e7i) q^{24} +(-1.21420e8 - 2.10305e8i) q^{25} +(1.92438e7 + 1.11104e7i) q^{26} -9.25255e7i q^{27} +5.16944e8 q^{29} +(2.76679e7 - 4.79223e7i) q^{30} +(-1.09378e9 + 6.31491e8i) q^{31} +(-9.49063e7 - 1.64382e8i) q^{32} +(2.69801e9 + 1.55769e9i) q^{33} +1.42602e9i q^{34} -1.26516e9 q^{36} +(-1.74968e9 + 3.03053e9i) q^{37} +(-4.52872e8 + 2.61466e8i) q^{38} +(-2.63185e8 - 4.55850e8i) q^{39} +(-9.15526e7 - 5.28579e7i) q^{40} +8.38090e9i q^{41} -6.25311e8 q^{43} +(2.97588e9 - 5.15438e9i) q^{44} +(-6.10225e8 + 3.52313e8i) q^{45} +(-1.54628e8 - 2.67823e8i) q^{46} +(1.37694e10 + 7.94978e9i) q^{47} +4.49631e9i q^{48} +1.09897e10 q^{50} +(1.68898e10 - 2.92541e10i) q^{51} +(-8.70875e8 + 5.02800e8i) q^{52} +(-1.26808e10 - 2.19638e10i) q^{53} +(3.62625e9 + 2.09361e9i) q^{54} -3.31483e9i q^{55} +1.23873e10 q^{57} +(-1.16971e10 + 2.02600e10i) q^{58} +(3.75917e10 - 2.17035e10i) q^{59} +(1.25211e9 + 2.16871e9i) q^{60} +(6.56463e9 + 3.79009e9i) q^{61} -5.71561e10i q^{62} +8.58993e9 q^{64} +(-2.80034e8 + 4.85033e8i) q^{65} +(-1.22098e11 + 7.04932e10i) q^{66} +(-1.25301e10 - 2.17028e10i) q^{67} +(-5.58882e10 - 3.22670e10i) q^{68} +7.32569e9i q^{69} +1.41685e11 q^{71} +(2.86272e10 - 4.95838e10i) q^{72} +(1.18652e11 - 6.85039e10i) q^{73} +(-7.91813e10 - 1.37146e11i) q^{74} +(-2.25448e11 - 1.30163e11i) q^{75} -2.36652e10i q^{76} +2.38208e10 q^{78} +(8.42279e10 - 1.45887e11i) q^{79} +(4.14320e9 - 2.39208e9i) q^{80} +(1.14555e11 + 1.98416e11i) q^{81} +(-3.28463e11 - 1.89638e11i) q^{82} -7.26397e10i q^{83} -3.59422e10 q^{85} +(1.41492e10 - 2.45071e10i) q^{86} +(4.79922e11 - 2.77083e11i) q^{87} +(1.34673e11 + 2.33261e11i) q^{88} +(5.19206e11 + 2.99763e11i) q^{89} -3.18878e10i q^{90} +1.39953e10 q^{92} +(-6.76961e11 + 1.17253e12i) q^{93} +(-6.23133e11 + 3.59766e11i) q^{94} +(-6.59014e9 - 1.14145e10i) q^{95} +(-1.76219e11 - 1.01740e11i) q^{96} -5.96235e11i q^{97} +1.79527e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16384 q^{4} + 1478904 q^{9}+O(q^{10}) $ 16 * q - 16384 * q^4 + 1478904 * q^9	$ 16 q - 16384 q^{4} + 1478904 q^{9} + 213840 q^{11} + 131764608 q^{15} - 33554432 q^{16} - 32547840 q^{18} - 442675200 q^{22} - 156731760 q^{23} - 191237000 q^{25} + 617707296 q^{29} + 2203567104 q^{30} - 6057590784 q^{36} + 3243600880 q^{37} - 13521315264 q^{39} + 42012604000 q^{43} + 437944320 q^{44} - 9664610304 q^{46} + 52518979584 q^{50} + 80965832832 q^{51} - 180445637520 q^{53} - 126291924480 q^{57} + 94193264640 q^{58} - 134926958592 q^{60} + 137438953472 q^{64} + 424890168192 q^{65} - 369211259440 q^{67} + 1148116288608 q^{71} - 66657976320 q^{72} - 450517137408 q^{74} - 502001694720 q^{78} + 607826610128 q^{79} - 919051941384 q^{81} - 494404521216 q^{85} + 413092638720 q^{86} + 453299404800 q^{88} + 641973288960 q^{92} - 2292312458880 q^{93} + 1053641981376 q^{95} - 3601908512928 q^{99}+O(q^{100}) $ 16 * q - 16384 * q^4 + 1478904 * q^9 + 213840 * q^11 + 131764608 * q^15 - 33554432 * q^16 - 32547840 * q^18 - 442675200 * q^22 - 156731760 * q^23 - 191237000 * q^25 + 617707296 * q^29 + 2203567104 * q^30 - 6057590784 * q^36 + 3243600880 * q^37 - 13521315264 * q^39 + 42012604000 * q^43 + 437944320 * q^44 - 9664610304 * q^46 + 52518979584 * q^50 + 80965832832 * q^51 - 180445637520 * q^53 - 126291924480 * q^57 + 94193264640 * q^58 - 134926958592 * q^60 + 137438953472 * q^64 + 424890168192 * q^65 - 369211259440 * q^67 + 1148116288608 * q^71 - 66657976320 * q^72 - 450517137408 * q^74 - 502001694720 * q^78 + 607826610128 * q^79 - 919051941384 * q^81 - 494404521216 * q^85 + 413092638720 * q^86 + 453299404800 * q^88 + 641973288960 * q^92 - 2292312458880 * q^93 + 1053641981376 * q^95 - 3601908512928 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−22.6274	+	39.1918i	−0.353553	+	0.612372i
$2$	−22.6274	+	39.1918i	−0.353553	+	0.612372i
$3$	928.383	−	536.002i	1.27350	−	0.735257i	0.297856	−	0.954611i	$-0.403728\pi$
$3$	928.383	−	536.002i	1.27350	−	0.735257i	0.975645	+	0.219354i	$0.0703950\pi$
$4$	−1024.00	−	1773.62i	−0.250000	−	0.433013i
$5$	−987.816	−	570.316i	−0.0632202	−	0.0365002i	0.468057	−	0.883698i	$-0.344954\pi$
$5$	−987.816	−	570.316i	−0.0632202	−	0.0365002i	−0.531277	+	0.847198i	$0.678288\pi$
$6$			48513.4i			1.03981i
$7$		0			0
$7$		0			0
$8$	92681.9			0.353553
$9$	308876.	−	534989.i	0.581204	−	1.00668i
$10$	44703.4	−	25809.5i	0.0447034	−	0.0258095i
$11$	1.45307e6	+	2.51679e6i	0.820219	+	1.42066i	0.905519	+	0.424305i	$0.139482\pi$
$11$	1.45307e6	+	2.51679e6i	0.820219	+	1.42066i	−0.0853005	+	0.996355i	$0.527185\pi$
$12$	−1.90133e6	−	1.09773e6i	−0.636751	−	0.367628i
$13$		−	491015.i		−	0.101727i	−0.998706	−	0.0508633i	$-0.983803\pi$
$13$		−	491015.i		−	0.101727i	0.998706	−	0.0508633i	$-0.0161973\pi$
$14$		0			0
$15$	−1.22276e6			−0.107348
$16$	−2.09715e6	+	3.63237e6i	−0.125000	+	0.216506i
$17$	2.72891e7	−	1.57554e7i	1.13057	−	0.652733i	0.186490	−	0.982457i	$-0.440289\pi$
$17$	2.72891e7	−	1.57554e7i	1.13057	−	0.652733i	0.944077	+	0.329724i	$0.106956\pi$
$18$	1.39781e7	+	2.42108e7i	0.410974	+	0.711827i
$19$	1.00071e7	+	5.77763e6i	0.212710	+	0.122808i	0.602570	−	0.798066i	$-0.294143\pi$
$19$	1.00071e7	+	5.77763e6i	0.212710	+	0.122808i	−0.389860	+	0.920874i	$0.627477\pi$
$20$			2.33601e6i			0.0365002i
$21$		0			0
$22$	−1.31517e8			−1.15996
$23$	−3.41682e6	+	5.91811e6i	−0.0230810	+	0.0399775i	−0.877335	−	0.479878i	$-0.840681\pi$
$23$	−3.41682e6	+	5.91811e6i	−0.0230810	+	0.0399775i	0.854254	+	0.519856i	$0.174014\pi$
$24$	8.60443e7	−	4.96777e7i	0.450251	−	0.259952i
$25$	−1.21420e8	−	2.10305e8i	−0.497335	−	0.861410i
$26$	1.92438e7	+	1.11104e7i	0.0622946	+	0.0359658i
$27$		−	9.25255e7i		−	0.238825i
$28$		0			0
$29$	5.16944e8			0.869071			0.434536	−	0.900655i	$-0.356913\pi$
$29$	5.16944e8			0.869071			0.434536	+	0.900655i	$0.356913\pi$
$30$	2.76679e7	−	4.79223e7i	0.0379533	−	0.0657370i
$31$	−1.09378e9	+	6.31491e8i	−1.23242	+	0.711537i	−0.967533	−	0.252744i	$-0.918667\pi$
$31$	−1.09378e9	+	6.31491e8i	−1.23242	+	0.711537i	−0.264884	+	0.964280i	$0.585334\pi$
$32$	−9.49063e7	−	1.64382e8i	−0.0883883	−	0.153093i
$33$	2.69801e9	+	1.55769e9i	2.08910	+	1.20614i
$34$			1.42602e9i			0.923104i
$35$		0			0
$36$	−1.26516e9			−0.581204
$37$	−1.74968e9	+	3.03053e9i	−0.681942	+	1.18116i	0.292445	+	0.956282i	$0.405531\pi$
$37$	−1.74968e9	+	3.03053e9i	−0.681942	+	1.18116i	−0.974387	+	0.224876i	$0.927802\pi$
$38$	−4.52872e8	+	2.61466e8i	−0.150409	+	0.0868386i
$39$	−2.63185e8	−	4.55850e8i	−0.0747952	−	0.129549i
$40$	−9.15526e7	−	5.28579e7i	−0.0223517	−	0.0129048i
$41$			8.38090e9i			1.76436i	0.470911	+	0.882181i	$0.343925\pi$
$41$			8.38090e9i			1.76436i	−0.470911	+	0.882181i	$0.656075\pi$
$42$		0			0
$43$	−6.25311e8			−0.0989203			−0.0494601	−	0.998776i	$-0.515750\pi$
$43$	−6.25311e8			−0.0989203			−0.0494601	+	0.998776i	$0.515750\pi$
$44$	2.97588e9	−	5.15438e9i	0.410109	−	0.710330i
$45$	−6.10225e8	+	3.52313e8i	−0.0734877	+	0.0424282i
$46$	−1.54628e8	−	2.67823e8i	−0.0163208	−	0.0282684i
$47$	1.37694e10	+	7.94978e9i	1.27740	+	0.737510i	0.976370	−	0.216103i	$-0.0693348\pi$
$47$	1.37694e10	+	7.94978e9i	1.27740	+	0.737510i	0.301034	+	0.953613i	$0.402668\pi$
$48$			4.49631e9i			0.367628i
$49$		0			0
$50$	1.09897e10			0.703339
$51$	1.68898e10	−	2.92541e10i	0.959853	−	1.66251i
$52$	−8.70875e8	+	5.02800e8i	−0.0440489	+	0.0254317i
$53$	−1.26808e10	−	2.19638e10i	−0.572126	−	0.990952i	−0.996347	−	0.0853931i	$-0.972785\pi$
$53$	−1.26808e10	−	2.19638e10i	−0.572126	−	0.990952i	0.424221	−	0.905559i	$-0.360548\pi$
$54$	3.62625e9	+	2.09361e9i	0.146250	+	0.0844372i
$55$		−	3.31483e9i		−	0.119753i
$56$		0			0
$57$	1.23873e10			0.361183
$58$	−1.16971e10	+	2.02600e10i	−0.307263	+	0.532195i
$59$	3.75917e10	−	2.17035e10i	0.891209	−	0.514539i	0.0168709	−	0.999858i	$-0.494630\pi$
$59$	3.75917e10	−	2.17035e10i	0.891209	−	0.514539i	0.874338	+	0.485318i	$0.161296\pi$
$60$	1.25211e9	+	2.16871e9i	0.0268370	+	0.0464831i
$61$	6.56463e9	+	3.79009e9i	0.127418	+	0.0735649i	0.562354	−	0.826896i	$-0.309896\pi$
$61$	6.56463e9	+	3.79009e9i	0.127418	+	0.0735649i	−0.434936	+	0.900461i	$0.643229\pi$
$62$		−	5.71561e10i		−	1.00626i
$63$		0			0
$64$	8.58993e9			0.125000
$65$	−2.80034e8	+	4.85033e8i	−0.00371304	+	0.00643118i
$66$	−1.22098e11	+	7.04932e10i	−1.47722	+	0.852872i
$67$	−1.25301e10	−	2.17028e10i	−0.138518	−	0.239920i	0.788418	−	0.615140i	$-0.210901\pi$
$67$	−1.25301e10	−	2.17028e10i	−0.138518	−	0.239920i	−0.926936	+	0.375220i	$0.877567\pi$
$68$	−5.58882e10	−	3.22670e10i	−0.565284	−	0.326367i
$69$			7.32569e9i			0.0678819i
$70$		0			0
$71$	1.41685e11			1.10604			0.553022	−	0.833167i	$-0.313474\pi$
$71$	1.41685e11			1.10604			0.553022	+	0.833167i	$0.313474\pi$
$72$	2.86272e10	−	4.95838e10i	0.205487	−	0.355914i
$73$	1.18652e11	−	6.85039e10i	0.784040	−	0.452666i	−0.0538198	−	0.998551i	$-0.517140\pi$
$73$	1.18652e11	−	6.85039e10i	0.784040	−	0.452666i	0.837860	+	0.545885i	$0.183806\pi$
$74$	−7.91813e10	−	1.37146e11i	−0.482206	−	0.835205i
$75$	−2.25448e11	−	1.30163e11i	−1.26672	−	0.731338i
$76$		−	2.36652e10i		−	0.122808i
$77$		0			0
$78$	2.38208e10			0.105776
$79$	8.42279e10	−	1.45887e11i	0.346492	−	0.600142i	−0.639131	−	0.769097i	$-0.720706\pi$
$79$	8.42279e10	−	1.45887e11i	0.346492	−	0.600142i	0.985624	+	0.168955i	$0.0540394\pi$
$80$	4.14320e9	−	2.39208e9i	0.0158050	−	0.00912505i
$81$	1.14555e11	+	1.98416e11i	0.405607	+	0.702532i
$82$	−3.28463e11	−	1.89638e11i	−1.08045	−	0.623796i
$83$		−	7.26397e10i		−	0.222180i	−0.993810	−	0.111090i	$-0.964566\pi$
$83$		−	7.26397e10i		−	0.222180i	0.993810	−	0.111090i	$-0.0354342\pi$
$84$		0			0
$85$	−3.59422e10			−0.0952996
$86$	1.41492e10	−	2.45071e10i	0.0349736	−	0.0605760i
$87$	4.79922e11	−	2.77083e11i	1.10676	−	0.638990i
$88$	1.34673e11	+	2.33261e11i	0.289991	+	0.502279i
$89$	5.19206e11	+	2.99763e11i	1.04472	+	0.603169i	0.921166	−	0.389169i	$-0.127238\pi$
$89$	5.19206e11	+	2.99763e11i	1.04472	+	0.603169i	0.123552	+	0.992338i	$0.460571\pi$
$90$		−	3.18878e10i		−	0.0600025i
$91$		0			0
$92$	1.39953e10			0.0230810
$93$	−6.76961e11	+	1.17253e12i	−1.04632	+	1.81229i
$94$	−6.23133e11	+	3.59766e11i	−0.903262	+	0.521498i
$95$	−6.59014e9	−	1.14145e10i	−0.00896506	−	0.0155279i
$96$	−1.76219e11	−	1.01740e11i	−0.225125	−	0.129976i
$97$		−	5.96235e11i		−	0.715792i	−0.933761	−	0.357896i	$-0.883494\pi$
$97$		−	5.96235e11i		−	0.715792i	0.933761	−	0.357896i	$-0.116506\pi$
$98$		0			0
$99$	1.79527e12			1.90686
$100$	−2.48668e11	+	4.30705e11i	−0.248668	+	0.430705i
$101$	−2.62599e11	+	1.51612e11i	−0.247381	+	0.142825i	−0.618564	−	0.785734i	$-0.712285\pi$
$101$	−2.62599e11	+	1.51612e11i	−0.247381	+	0.142825i	0.371184	+	0.928559i	$0.378952\pi$
$102$	7.64347e11	+	1.32389e12i	0.678718	+	1.17557i
$103$	1.89963e12	+	1.09675e12i	1.59091	+	0.918513i	0.993151	+	0.116838i	$0.0372757\pi$
$103$	1.89963e12	+	1.09675e12i	1.59091	+	0.918513i	0.597760	+	0.801675i	$0.296058\pi$
$104$		−	4.55082e10i		−	0.0359658i
$105$		0			0
$106$	1.14774e12			0.809109
$107$	1.11510e12	−	1.93141e12i	0.743038	−	1.28698i	−0.208067	−	0.978115i	$-0.566717\pi$
$107$	1.11510e12	−	1.93141e12i	0.743038	−	1.28698i	0.951106	−	0.308866i	$-0.0999494\pi$
$108$	−1.64105e11	+	9.47461e10i	−0.103414	+	0.0597061i
$109$	1.23619e12	+	2.14115e12i	0.737100	+	1.27670i	0.953796	+	0.300456i	$0.0971388\pi$
$109$	1.23619e12	+	2.14115e12i	0.737100	+	1.27670i	−0.216696	+	0.976239i	$0.569528\pi$
$110$	1.29914e11	+	7.50060e10i	0.0733332	+	0.0423389i
$111$			3.75132e12i			2.00561i
$112$		0			0
$113$	2.28940e12			1.09964			0.549820	−	0.835283i	$-0.314696\pi$
$113$	2.28940e12			1.09964			0.549820	+	0.835283i	$0.314696\pi$
$114$	−2.80292e11	+	4.85480e11i	−0.127697	+	0.221178i
$115$	6.75038e9	−	3.89733e9i	0.00291838	−	0.00168492i
$116$	−5.29350e11	−	9.16862e11i	−0.217268	−	0.376319i
$117$	−2.62688e11	−	1.51663e11i	−0.102406	−	0.0591240i
$118$			1.96438e12i			0.727669i
$119$		0			0
$120$	−1.13328e11			−0.0379533
$121$	−2.65360e12	+	4.59616e12i	−0.845518	+	1.46448i
$122$	−2.97081e11	+	1.71520e11i	−0.0900983	+	0.0520183i
$123$	4.49218e12	+	7.78068e12i	1.29726	+	2.24692i
$124$	2.24005e12	+	1.29329e12i	0.616209	+	0.355768i
$125$			5.55465e11i			0.145612i
$126$		0			0
$127$	2.34183e12			0.558127			0.279064	−	0.960273i	$-0.409976\pi$
$127$	2.34183e12			0.558127			0.279064	+	0.960273i	$0.409976\pi$
$128$	−1.94368e11	+	3.36655e11i	−0.0441942	+	0.0765466i
$129$	−5.80528e11	+	3.35168e11i	−0.125975	+	0.0727318i
$130$	−1.26729e10	−	2.19501e10i	−0.00262552	−	0.00454753i
$131$	−6.13754e12	−	3.54351e12i	−1.21441	−	0.701142i	−0.250696	−	0.968066i	$-0.580660\pi$
$131$	−6.13754e12	−	3.54351e12i	−1.21441	−	0.701142i	−0.963718	+	0.266923i	$0.913993\pi$
$132$		−	6.38032e12i		−	1.20614i
$133$		0			0
$134$	1.13410e12			0.195894
$135$	−5.27687e10	+	9.13981e10i	−0.00871714	+	0.0150985i
$136$	2.52921e12	−	1.46024e12i	0.399716	−	0.230776i
$137$	2.04298e12	+	3.53855e12i	0.308988	+	0.535182i	0.978141	−	0.207942i	$-0.0666765\pi$
$137$	2.04298e12	+	3.53855e12i	0.308988	+	0.535182i	−0.669154	+	0.743124i	$0.733343\pi$
$138$	−2.87107e11	−	1.65762e11i	−0.0415690	−	0.0239999i
$139$		−	9.72215e12i		−	1.34795i	−0.738754	−	0.673975i	$-0.764586\pi$
$139$		−	9.72215e12i		−	1.34795i	0.738754	−	0.673975i	$-0.235414\pi$
$140$		0			0
$141$	1.70444e13			2.16904
$142$	−3.20596e12	+	5.55288e12i	−0.391046	+	0.677311i
$143$	1.23578e12	−	7.13478e11i	0.144519	−	0.0834381i
$144$	1.29552e12	+	2.24391e12i	0.145301	+	0.251669i
$145$	−5.10645e11	−	2.94821e11i	−0.0549428	−	0.0317213i
$146$			6.20026e12i			0.640166i
$147$		0			0
$148$	7.16668e12			0.681942
$149$	3.27066e12	−	5.66495e12i	0.298895	−	0.517701i	−0.676989	−	0.735993i	$-0.736715\pi$
$149$	3.27066e12	−	5.66495e12i	0.298895	−	0.517701i	0.975883	+	0.218293i	$0.0700487\pi$
$150$	1.02026e13	−	5.89048e12i	0.895703	−	0.517134i
$151$	−7.23099e12	−	1.25244e13i	−0.610008	−	1.05657i	−0.991238	−	0.132085i	$-0.957833\pi$
$151$	−7.23099e12	−	1.25244e13i	−0.610008	−	1.05657i	0.381230	−	0.924480i	$-0.375501\pi$
$152$	9.27481e11	+	5.35482e11i	0.0752045	+	0.0434193i
$153$		−	1.94658e13i		−	1.51749i
$154$		0			0
$155$	1.44060e12			0.103885
$156$	−5.39003e11	+	9.33581e11i	−0.0373976	+	0.0647746i
$157$	−2.32283e13	+	1.34109e13i	−1.55103	+	0.895487i	−0.552970	+	0.833201i	$0.686506\pi$
$157$	−2.32283e13	+	1.34109e13i	−1.55103	+	0.895487i	−0.998058	+	0.0622854i	$0.980161\pi$
$158$	3.81172e12	+	6.60209e12i	0.245007	+	0.424365i
$159$	−2.35453e13	−	1.35939e13i	−1.45721	−	0.841319i
$160$			2.16506e11i			0.0129048i
$161$		0			0
$162$	−1.03684e13			−0.573615
$163$	1.33160e12	−	2.30640e12i	0.0709984	−	0.122973i	−0.828341	−	0.560225i	$-0.810715\pi$
$163$	1.33160e12	−	2.30640e12i	0.0709984	−	0.122973i	0.899339	+	0.437252i	$0.144048\pi$
$164$	1.48645e13	−	8.58204e12i	0.763991	−	0.441090i
$165$	−1.77675e12	−	3.07743e12i	−0.0880489	−	0.152505i
$166$	2.84688e12	+	1.64365e12i	0.136057	+	0.0785526i
$167$			3.67875e13i			1.69591i	0.530071	+	0.847953i	$0.322165\pi$
$167$			3.67875e13i			1.69591i	−0.530071	+	0.847953i	$0.677835\pi$
$168$		0			0
$169$	2.30570e13			0.989652
$170$	8.13279e11	−	1.40864e12i	0.0336935	−	0.0583588i
$171$	6.18193e12	−	3.56914e12i	0.247256	−	0.142754i
$172$	6.40318e11	+	1.10906e12i	0.0247301	+	0.0428337i
$173$	1.30549e13	+	7.53726e12i	0.486965	+	0.281149i	0.723314	−	0.690519i	$-0.242618\pi$
$173$	1.30549e13	+	7.53726e12i	0.486965	+	0.281149i	−0.236350	+	0.971668i	$0.575951\pi$
$174$			2.50787e13i			0.903669i
$175$		0			0
$176$	−1.21892e13			−0.410109
$177$	2.32663e13	−	4.02984e13i	0.756637	−	1.31053i
$178$	−2.34966e13	+	1.35657e13i	−0.738728	+	0.426505i
$179$	2.03350e13	+	3.52213e13i	0.618197	+	1.07075i	0.989815	+	0.142363i	$0.0454700\pi$
$179$	2.03350e13	+	3.52213e13i	0.618197	+	1.07075i	−0.371617	+	0.928386i	$0.621197\pi$
$180$	1.24974e12	+	7.21538e11i	0.0367439	+	0.0212141i
$181$		−	7.64135e11i		−	0.0217319i	−0.999941	−	0.0108660i	$-0.996541\pi$
$181$		−	7.64135e11i		−	0.0217319i	0.999941	−	0.0108660i	$-0.00345881\pi$
$182$		0			0
$183$	8.12599e12			0.216356
$184$	−3.16678e11	+	5.48502e11i	−0.00816038	+	0.0141342i
$185$	3.45672e12	−	1.99574e12i	0.0862250	−	0.0497820i
$186$	−3.06358e13	−	5.30627e13i	−0.739863	−	1.28148i
$187$	7.93059e13	+	4.57873e13i	1.85462	+	1.07077i
$188$		−	3.25623e13i		−	0.737510i
$189$		0			0
$190$	5.96472e11			0.0126785
$191$	−1.55077e12	+	2.68601e12i	−0.0319409	+	0.0553232i	−0.881554	−	0.472083i	$-0.843502\pi$
$191$	−1.55077e12	+	2.68601e12i	−0.0319409	+	0.0553232i	0.849613	+	0.527406i	$0.176835\pi$
$192$	7.97475e12	−	4.60422e12i	0.159188	−	0.0919071i
$193$	−2.61226e13	−	4.52457e13i	−0.505444	−	0.875454i	−0.999980	−	0.00629733i	$-0.997995\pi$
$193$	−2.61226e13	−	4.52457e13i	−0.505444	−	0.875454i	0.494536	−	0.869157i	$-0.335338\pi$
$194$	2.33675e13	+	1.34913e13i	0.438331	+	0.253071i
$195$			6.00394e11i			0.0109202i
$196$		0			0
$197$	−1.29468e13			−0.221496			−0.110748	−	0.993849i	$-0.535325\pi$
$197$	−1.29468e13			−0.221496			−0.110748	+	0.993849i	$0.535325\pi$
$198$	−4.06223e13	+	7.03599e13i	−0.674177	+	1.16771i
$199$	4.33819e11	−	2.50466e11i	0.00698539	−	0.00403302i	−0.496503	−	0.868035i	$-0.665383\pi$
$199$	4.33819e11	−	2.50466e11i	0.00698539	−	0.00403302i	0.503489	+	0.864002i	$0.332050\pi$
$200$	−1.12534e13	−	1.94915e13i	−0.175835	−	0.304555i
$201$	−2.32655e13	−	1.34323e13i	−0.352805	−	0.203692i
$202$		−	1.37223e13i		−	0.201985i
$203$		0			0
$204$	−6.91808e13			−0.959853
$205$	4.77976e12	−	8.27878e12i	0.0643995	−	0.111543i
$206$	−8.59675e13	+	4.96333e13i	−1.12494	+	0.649487i
$207$	2.11075e12	+	3.65592e12i	0.0268296	+	0.0464702i
$208$	1.78355e12	+	1.02973e12i	0.0220245	+	0.0127158i
$209$			3.35811e13i			0.402919i
$210$		0			0
$211$	−1.26806e14			−1.43696			−0.718480	−	0.695548i	$-0.755162\pi$
$211$	−1.26806e14			−1.43696			−0.718480	+	0.695548i	$0.755162\pi$
$212$	−2.59703e13	+	4.49819e13i	−0.286063	+	0.495476i
$213$	1.31538e14	−	7.59432e13i	1.40855	−	0.813226i
$214$	5.04637e13	+	8.74057e13i	0.525407	+	0.910032i
$215$	6.17692e11	+	3.56625e11i	0.00625376	+	0.00361061i
$216$		−	8.57544e12i		−	0.0844372i
$217$		0			0
$218$	−1.11887e14			−1.04242
$219$	7.34364e13	−	1.27196e14i	0.665651	−	1.15294i
$220$	−5.87925e12	+	3.39438e12i	−0.0518544	+	0.0299381i
$221$	−7.73614e12	−	1.33994e13i	−0.0664004	−	0.115009i
$222$	−1.47021e14	−	8.48827e13i	−1.22818	−	0.709090i
$223$			4.73295e13i			0.384860i	0.981311	+	0.192430i	$0.0616369\pi$
$223$			4.73295e13i			0.384860i	−0.981311	+	0.192430i	$0.938363\pi$
$224$		0			0
$225$	−1.50015e14			−1.15621
$226$	−5.18031e13	+	8.97256e13i	−0.388781	+	0.673389i
$227$	−1.88265e12	+	1.08695e12i	−0.0137599	+	0.00794429i	−0.506864	−	0.862026i	$-0.669195\pi$
$227$	−1.88265e12	+	1.08695e12i	−0.0137599	+	0.00794429i	0.493104	+	0.869970i	$0.335862\pi$
$228$	−1.26846e13	−	2.19703e13i	−0.0902957	−	0.156397i
$229$	−1.77615e14	−	1.02546e14i	−1.23159	−	0.711058i	−0.264227	−	0.964460i	$-0.585117\pi$
$229$	−1.77615e14	−	1.02546e14i	−1.23159	−	0.711058i	−0.967361	+	0.253402i	$0.918450\pi$
$230$			3.52746e11i			0.00238284i
$231$		0			0
$232$	4.79113e13			0.307263
$233$	3.40386e13	−	5.89566e13i	0.212734	−	0.368465i	−0.739836	−	0.672788i	$-0.765097\pi$
$233$	3.40386e13	−	5.89566e13i	0.212734	−	0.368465i	0.952569	+	0.304322i	$0.0984300\pi$
$234$	1.18879e13	−	6.86347e12i	0.0724118	−	0.0418070i
$235$	−9.06777e12	−	1.57058e13i	−0.0538385	−	0.0932510i
$236$	−7.69877e13	−	4.44489e13i	−0.445604	−	0.257270i
$237$		−	1.80585e14i		−	1.01904i
$238$		0			0
$239$	1.26369e14			0.678036			0.339018	−	0.940780i	$-0.389905\pi$
$239$	1.26369e14			0.678036			0.339018	+	0.940780i	$0.389905\pi$
$240$	2.56432e12	−	4.44153e12i	0.0134185	−	0.0232415i
$241$	−2.61595e13	+	1.51032e13i	−0.133514	+	0.0770844i	−0.565269	−	0.824906i	$-0.691228\pi$
$241$	−2.61595e13	+	1.51032e13i	−0.133514	+	0.0770844i	0.431755	+	0.901991i	$0.357894\pi$
$242$	−1.20088e14	−	2.07999e14i	−0.597871	−	1.03554i
$243$	2.55287e14	+	1.47390e14i	1.23991	+	0.715863i
$244$		−	1.55242e13i		−	0.0735649i
$245$		0			0
$246$	−4.06586e14			−1.83460
$247$	2.83690e12	−	4.91366e12i	0.0124929	−	0.0216383i
$248$	−1.01373e14	+	5.85278e13i	−0.435725	+	0.251566i
$249$	−3.89350e13	−	6.74374e13i	−0.163359	−	0.282947i
$250$	−2.17697e13	−	1.25687e13i	−0.0891686	−	0.0514815i
$251$		−	2.03645e14i		−	0.814390i	−0.913341	−	0.407195i	$-0.866507\pi$
$251$		−	2.03645e14i		−	0.814390i	0.913341	−	0.407195i	$-0.133493\pi$
$252$		0			0
$253$	−1.98595e13			−0.0757260
$254$	−5.29896e13	+	9.17806e13i	−0.197328	+	0.341782i
$255$	−3.33681e13	+	1.92651e13i	−0.121364	+	0.0700696i
$256$	−8.79609e12	−	1.52353e13i	−0.0312500	−	0.0541266i
$257$	−1.98593e14	−	1.14658e14i	−0.689233	−	0.397929i	0.114092	−	0.993470i	$-0.463604\pi$
$257$	−1.98593e14	−	1.14658e14i	−0.689233	−	0.397929i	−0.803325	+	0.595541i	$0.796938\pi$
$258$		−	3.03359e13i		−	0.102858i
$259$		0			0
$260$	1.14702e12			0.00371304
$261$	1.59671e14	−	2.76559e14i	0.505108	−	0.874873i
$262$	2.77753e14	−	1.60361e14i	0.858720	−	0.495782i
$263$	−1.51432e14	−	2.62288e14i	−0.457596	−	0.792580i	0.541237	−	0.840870i	$-0.317956\pi$
$263$	−1.51432e14	−	2.62288e14i	−0.457596	−	0.792580i	−0.998833	+	0.0482899i	$0.984623\pi$
$264$	2.50056e14	+	1.44370e14i	0.738608	+	0.426436i
$265$			2.89283e13i			0.0835309i
$266$		0			0
$267$	6.42695e14			1.77393
$268$	−2.56616e13	+	4.44473e13i	−0.0692589	+	0.119960i
$269$	3.15183e13	−	1.81971e13i	0.0831858	−	0.0480274i	−0.457830	−	0.889040i	$-0.651373\pi$
$269$	3.15183e13	−	1.81971e13i	0.0831858	−	0.0480274i	0.541016	+	0.841012i	$0.318040\pi$
$270$	−2.38804e12	−	4.13621e12i	−0.00616395	−	0.0106763i
$271$	2.57375e14	+	1.48596e14i	0.649756	+	0.375137i	0.788363	−	0.615210i	$-0.210929\pi$
$271$	2.57375e14	+	1.48596e14i	0.649756	+	0.375137i	−0.138606	+	0.990348i	$0.544262\pi$
$272$			1.32166e14i			0.326367i
$273$		0			0
$274$	−1.84910e14			−0.436974
$275$	3.52862e14	−	6.11175e14i	0.815848	−	1.41309i
$276$	1.29930e13	−	7.50151e12i	0.0293937	−	0.0169705i
$277$	3.31471e14	+	5.74124e14i	0.733781	+	1.27095i	0.955256	+	0.295780i	$0.0955794\pi$
$277$	3.31471e14	+	5.74124e14i	0.733781	+	1.27095i	−0.221476	+	0.975166i	$0.571087\pi$
$278$	3.81029e14	+	2.19987e14i	0.825447	+	0.476572i
$279$			7.80210e14i			1.65419i
$280$		0			0
$281$	−4.31286e14			−0.876046			−0.438023	−	0.898964i	$-0.644321\pi$
$281$	−4.31286e14			−0.876046			−0.438023	+	0.898964i	$0.644321\pi$
$282$	−3.85671e14	+	6.68001e14i	−0.766870	+	1.32826i
$283$	−4.83658e14	+	2.79240e14i	−0.941498	+	0.543574i	−0.890430	−	0.455121i	$-0.849596\pi$
$283$	−4.83658e14	+	2.79240e14i	−0.941498	+	0.543574i	−0.0510685	+	0.998695i	$0.516263\pi$
$284$	−1.45085e14	−	2.51295e14i	−0.276511	−	0.478931i
$285$	−1.22364e13	−	7.06466e12i	−0.0228340	−	0.0131832i
$286$			6.45767e13i			0.117999i
$287$		0			0
$288$	−1.17257e14			−0.205487
$289$	2.05154e14	−	3.55337e14i	0.352121	−	0.609892i
$290$	2.31092e13	−	1.33421e13i	0.0388505	−	0.0224303i
$291$	−3.19583e14	−	5.53534e14i	−0.526291	−	0.911562i
$292$	−2.43000e14	−	1.40296e14i	−0.392020	−	0.226333i
$293$			3.66225e14i			0.578818i	0.957205	+	0.289409i	$0.0934588\pi$
$293$			3.66225e14i			0.578818i	−0.957205	+	0.289409i	$0.906541\pi$
$294$		0			0
$295$	−4.95115e13			−0.0751232
$296$	−1.62163e14	+	2.80875e14i	−0.241103	+	0.417603i
$297$	2.32867e14	−	1.34446e14i	0.339289	−	0.195888i
$298$	1.48013e14	+	2.56367e14i	0.211350	+	0.366070i
$299$	2.90588e12	+	1.67771e12i	0.00406678	+	0.00234796i
$300$			5.33146e14i			0.731338i
$301$		0			0
$302$	6.54474e14			0.862682
$303$	−1.62529e14	+	2.81508e14i	−0.210026	+	0.363776i
$304$	−4.19730e13	+	2.42331e13i	−0.0531776	+	0.0307021i
$305$	−4.32310e12	−	7.48782e12i	−0.00537027	−	0.00930158i
$306$	7.62902e14	+	4.40462e14i	0.929267	+	0.536512i
$307$		−	1.45983e14i		−	0.174370i	−0.996192	−	0.0871851i	$-0.972213\pi$
$307$		−	1.45983e14i		−	0.174370i	0.996192	−	0.0871851i	$-0.0277872\pi$
$308$		0			0
$309$	2.35145e15			2.70137
$310$	−3.25970e13	+	5.64597e13i	−0.0367289	+	0.0636163i
$311$	−1.06613e15	+	6.15528e14i	−1.17827	+	0.680277i	−0.955615	−	0.294619i	$-0.904807\pi$
$311$	−1.06613e15	+	6.15528e14i	−1.17827	+	0.680277i	−0.222660	+	0.974896i	$0.571474\pi$
$312$	−2.43925e13	−	4.22491e13i	−0.0264441	−	0.0458025i
$313$	−1.57698e15	−	9.10471e14i	−1.67711	−	0.968278i	−0.963491	−	0.267741i	$-0.913723\pi$
$313$	−1.57698e15	−	9.10471e14i	−1.67711	−	0.968278i	−0.713616	−	0.700537i	$-0.752944\pi$
$314$		−	1.21381e15i		−	1.26641i
$315$		0			0
$316$	−3.44998e14			−0.346492
$317$	−6.46806e13	+	1.12030e14i	−0.0637410	+	0.110403i	−0.896135	−	0.443782i	$-0.853636\pi$
$317$	−6.46806e13	+	1.12030e14i	−0.0637410	+	0.110403i	0.832394	+	0.554185i	$0.186970\pi$
$318$	1.06554e15	−	6.15189e14i	1.03040	−	0.594903i
$319$	7.51154e14	+	1.30104e15i	0.712828	+	1.23466i
$320$	−8.48527e12	−	4.89897e12i	−0.00790252	−	0.00456252i
$321$		−	2.39078e15i		−	2.18530i
$322$		0			0
$323$	3.64115e14			0.320644
$324$	2.34610e14	−	4.06356e14i	0.202804	−	0.351266i
$325$	−1.03263e14	+	5.96190e13i	−0.0876284	+	0.0505923i
$326$	6.02614e13	+	1.04376e14i	0.0502035	+	0.0869550i
$327$	2.29532e15	+	1.32520e15i	1.87740	+	1.08392i
$328$			7.76758e14i			0.623796i
$329$		0			0
$330$	1.60813e14			0.124520
$331$	−4.62431e14	+	8.00953e14i	−0.351624	+	0.609031i	−0.986534	−	0.163555i	$-0.947704\pi$
$331$	−4.62431e14	+	8.00953e14i	−0.351624	+	0.609031i	0.634910	+	0.772586i	$0.281037\pi$
$332$	−1.28835e14	+	7.43830e13i	−0.0962069	+	0.0555451i
$333$	1.08087e15	+	1.87211e15i	0.792696	+	1.37299i
$334$	−1.44177e15	−	8.32407e14i	−1.03853	−	0.599594i
$335$			2.85844e13i			0.0202237i
$336$		0			0
$337$	1.90391e15			1.29977			0.649884	−	0.760033i	$-0.274817\pi$
$337$	1.90391e15			1.29977			0.649884	+	0.760033i	$0.274817\pi$
$338$	−5.21720e14	+	9.03646e14i	−0.349895	+	0.606035i
$339$	2.12544e15	−	1.22712e15i	1.40039	−	0.808517i
$340$	3.68048e13	+	6.37478e13i	0.0238249	+	0.0412659i
$341$	−3.17866e15	−	1.83520e15i	−2.02170	−	1.16723i
$342$			3.23042e14i			0.201884i
$343$		0			0
$344$	−5.79550e13			−0.0349736
$345$	4.17796e12	−	7.23643e12i	0.00247770	−	0.00429151i
$346$	−5.90798e14	+	3.41097e14i	−0.344336	+	0.198803i
$347$	8.61015e14	+	1.49132e15i	0.493212	+	0.854269i	0.999969	−	0.00782010i	$-0.00248924\pi$
$347$	8.61015e14	+	1.49132e15i	0.493212	+	0.854269i	−0.506757	+	0.862089i	$0.669156\pi$
$348$	−9.82880e14	−	5.67466e14i	−0.553382	−	0.319495i
$349$		−	1.49883e15i		−	0.829467i	−0.909943	−	0.414733i	$-0.863875\pi$
$349$		−	1.49883e15i		−	0.829467i	0.909943	−	0.414733i	$-0.136125\pi$
$350$		0			0
$351$	−4.54314e13			−0.0242948
$352$	2.75810e14	−	4.77718e14i	0.144996	−	0.251140i
$353$	1.55114e14	−	8.95549e13i	0.0801681	−	0.0462851i	−0.459380	−	0.888240i	$-0.651928\pi$
$353$	1.55114e14	−	8.95549e13i	0.0801681	−	0.0462851i	0.539548	+	0.841955i	$0.318595\pi$
$354$	1.05291e15	+	1.82370e15i	0.535023	+	0.926687i
$355$	−1.39958e14	−	8.08049e13i	−0.0699243	−	0.0403708i
$356$		−	1.22783e15i		−	0.603169i
$357$		0			0
$358$	−1.84052e15			−0.874263
$359$	2.64393e14	−	4.57942e14i	0.123505	−	0.213916i	−0.797643	−	0.603130i	$-0.793920\pi$
$359$	2.64393e14	−	4.57942e14i	0.123505	−	0.213916i	0.921147	+	0.389214i	$0.127253\pi$
$360$	−5.65568e13	+	3.26531e13i	−0.0259818	+	0.0150006i
$361$	−1.03990e15	−	1.80115e15i	−0.469836	−	0.813780i
$362$	2.99478e13	+	1.72904e13i	0.0133080	+	0.00768340i
$363$			5.68933e15i			2.48669i
$364$		0			0
$365$	−1.56275e14			−0.0660896
$366$	−1.83870e14	+	3.18472e14i	−0.0764935	+	0.132491i
$367$	−5.84737e14	+	3.37598e14i	−0.239312	+	0.138167i	−0.614860	−	0.788636i	$-0.710788\pi$
$367$	−5.84737e14	+	3.37598e14i	−0.239312	+	0.138167i	0.375549	+	0.926803i	$0.377454\pi$
$368$	−1.43312e13	−	2.48223e13i	−0.00577026	−	0.00999438i
$369$	4.48369e15	+	2.58866e15i	1.77614	+	1.02545i
$370$			1.80633e14i			0.0704024i
$371$		0			0
$372$	2.77283e15			1.04632
$373$	−9.24257e14	+	1.60086e15i	−0.343194	+	0.594430i	−0.985024	−	0.172417i	$-0.944842\pi$
$373$	−9.24257e14	+	1.60086e15i	−0.343194	+	0.594430i	0.641830	+	0.766847i	$0.278176\pi$
$374$	−3.58898e15	+	2.07210e15i	−1.31142	+	0.757147i
$375$	2.97730e14	+	5.15684e14i	0.107062	+	0.185437i
$376$	1.27618e15	+	7.36801e14i	0.451631	+	0.260749i
$377$		−	2.53827e14i		−	0.0884077i
$378$		0			0
$379$	2.24253e15			0.756663			0.378332	−	0.925670i	$-0.376498\pi$
$379$	2.24253e15			0.756663			0.378332	+	0.925670i	$0.376498\pi$
$380$	−1.34966e13	+	2.33768e13i	−0.00448253	+	0.00776397i
$381$	2.17411e15	−	1.25523e15i	0.710776	−	0.410367i
$382$	−7.01798e13	−	1.21555e14i	−0.0225856	−	0.0391194i
$383$	7.70438e14	+	4.44812e14i	0.244087	+	0.140924i	0.617054	−	0.786921i	$-0.288326\pi$
$383$	7.70438e14	+	4.44812e14i	0.244087	+	0.140924i	−0.372967	+	0.927845i	$0.621659\pi$
$384$			4.16727e14i			0.129976i
$385$		0			0
$386$	2.36435e15			0.714805
$387$	−1.93143e14	+	3.34534e14i	−0.0574929	+	0.0995806i
$388$	−1.05749e15	+	6.10544e14i	−0.309947	+	0.178948i
$389$	−3.71319e14	−	6.43144e14i	−0.107164	−	0.185614i	0.807456	−	0.589928i	$-0.200844\pi$
$389$	−3.71319e14	−	6.43144e14i	−0.107164	−	0.185614i	−0.914620	+	0.404314i	$0.867510\pi$
$390$	−2.35306e13	−	1.35854e13i	−0.00668720	−	0.00386086i
$391$			2.15333e14i			0.0602630i
$392$		0			0
$393$	−7.59732e15			−2.06208
$394$	2.92953e14	−	5.07409e14i	0.0783106	−	0.135638i
$395$	−1.66403e14	+	9.60730e13i	−0.0438106	+	0.0252941i
$396$	−1.83836e15	−	3.18413e15i	−0.476715	−	0.825694i
$397$	1.72844e15	+	9.97913e14i	0.441479	+	0.254888i	0.704225	−	0.709977i	$-0.251295\pi$
$397$	1.72844e15	+	9.97913e14i	0.441479	+	0.254888i	−0.262746	+	0.964865i	$0.584628\pi$
$398$			2.26696e13i			0.00570354i
$399$		0			0
$400$	1.01854e15			0.248668
$401$	−1.14213e15	+	1.97823e15i	−0.274695	+	0.475785i	−0.970058	−	0.242873i	$-0.921910\pi$
$401$	−1.14213e15	+	1.97823e15i	−0.274695	+	0.475785i	0.695363	+	0.718658i	$0.255243\pi$
$402$	1.05287e15	−	6.07877e14i	0.249471	−	0.144032i
$403$	3.10072e14	+	5.37060e14i	0.0723823	+	0.125370i
$404$	5.37804e14	+	3.10501e14i	0.123690	+	0.0714126i
$405$		−	2.61331e14i		−	0.0592190i
$406$		0			0
$407$	−1.01696e16			−2.23737
$408$	1.56538e15	−	2.71132e15i	0.339359	−	0.587787i
$409$	−3.06090e15	+	1.76721e15i	−0.653897	+	0.377528i	−0.789948	−	0.613174i	$-0.789892\pi$
$409$	−3.06090e15	+	1.76721e15i	−0.653897	+	0.377528i	0.136050	+	0.990702i	$0.456559\pi$
$410$	2.16307e14	+	3.74655e14i	0.0455374	+	0.0788730i
$411$	3.79334e15	+	2.19008e15i	0.786992	+	0.454370i
$412$		−	4.49230e15i		−	0.918513i
$413$		0			0
$414$	−1.91043e14			−0.0379428
$415$	−4.14275e13	+	7.17546e13i	−0.00810962	+	0.0140463i
$416$	−8.07143e13	+	4.66004e13i	−0.0155737	+	0.00899145i
$417$	−5.21109e15	−	9.02588e15i	−0.991089	−	1.71662i
$418$	−1.31611e15	−	7.59854e14i	−0.246736	−	0.142453i
$419$			2.73391e15i			0.505243i	0.967565	+	0.252621i	$0.0812927\pi$
$419$			2.73391e15i			0.505243i	−0.967565	+	0.252621i	$0.918707\pi$
$420$		0			0
$421$	3.49107e15			0.626998			0.313499	−	0.949589i	$-0.398499\pi$
$421$	3.49107e15			0.626998			0.313499	+	0.949589i	$0.398499\pi$
$422$	2.86929e15	−	4.96975e15i	0.508042	−	0.879954i
$423$	8.50608e15	−	4.91099e15i	1.48487	−	0.857288i
$424$	−1.17528e15	−	2.03565e15i	−0.202277	−	0.350354i
$425$	−6.62688e15	−	3.82603e15i	−1.12454	−	0.649255i
$426$			6.87360e15i			1.15008i
$427$		0			0
$428$	−4.56745e15			−0.743038
$429$	7.64852e14	−	1.32476e15i	0.122697	−	0.212517i
$430$	−2.79535e13	+	1.61390e13i	−0.00442208	+	0.00255309i
$431$	−4.42045e15	−	7.65645e15i	−0.689609	−	1.19444i	−0.971964	−	0.235128i	$-0.924449\pi$
$431$	−4.42045e15	−	7.65645e15i	−0.689609	−	1.19444i	0.282355	−	0.959310i	$-0.408884\pi$
$432$	3.36087e14	+	1.94040e14i	0.0517070	+	0.0298531i
$433$		−	4.47537e15i		−	0.679049i	−0.940597	−	0.339525i	$-0.889734\pi$
$433$		−	4.47537e15i		−	0.679049i	0.940597	−	0.339525i	$-0.110266\pi$
$434$		0			0
$435$	−6.32099e14			−0.0932931
$436$	2.53172e15	−	4.38507e15i	0.368550	−	0.638348i
$437$	−6.83853e13	+	3.94823e13i	−0.00981915	+	0.00566909i
$438$	3.32335e15	+	5.75622e15i	0.470687	+	0.815253i
$439$	−2.39455e15	−	1.38249e15i	−0.334531	−	0.193142i	0.323320	−	0.946290i	$-0.395201\pi$
$439$	−2.39455e15	−	1.38249e15i	−0.334531	−	0.193142i	−0.657851	+	0.753148i	$0.728534\pi$
$440$		−	3.07225e14i		−	0.0423389i
$441$		0			0
$442$	7.00195e14			0.0939043
$443$	5.34437e15	−	9.25672e15i	0.707089	−	1.22471i	−0.258843	−	0.965919i	$-0.583341\pi$
$443$	5.34437e15	−	9.25672e15i	0.707089	−	1.22471i	0.965932	−	0.258795i	$-0.0833253\pi$
$444$	6.65342e15	−	3.84135e15i	0.868455	−	0.501402i
$445$	−3.41920e14	−	5.92222e14i	−0.0440315	−	0.0762649i
$446$	−1.85493e15	−	1.07095e15i	−0.235678	−	0.136069i
$447$		−	7.01233e15i		−	0.879057i
$448$		0			0
$449$	−5.18103e15			−0.632321			−0.316161	−	0.948706i	$-0.602394\pi$
$449$	−5.18103e15			−0.632321			−0.316161	+	0.948706i	$0.602394\pi$
$450$	3.39444e15	−	5.87935e15i	0.408784	−	0.708034i
$451$	−2.10929e16	+	1.21780e16i	−2.50656	+	1.44716i
$452$	−2.34434e15	−	4.06052e15i	−0.274910	−	0.476158i
$453$	−1.34262e16	−	7.75165e15i	−1.55369	−	0.897026i
$454$		−	9.83796e13i		−	0.0112349i
$455$		0			0
$456$	1.14808e15			0.127697
$457$	−4.24136e15	+	7.34624e15i	−0.465594	+	0.806433i	−0.999228	−	0.0392828i	$-0.987493\pi$
$457$	−4.24136e15	+	7.34624e15i	−0.465594	+	0.806433i	0.533634	+	0.845716i	$0.320826\pi$
$458$	8.03792e15	−	4.64069e15i	0.870865	−	0.502794i
$459$	−1.45778e15	−	2.52494e15i	−0.155889	−	0.270007i
$460$	−1.38248e13	−	7.98174e12i	−0.00145919	−	0.000842462i
$461$		−	2.25369e15i		−	0.234795i	−0.993085	−	0.117397i	$-0.962545\pi$
$461$		−	2.25369e15i		−	0.234795i	0.993085	−	0.117397i	$-0.0374551\pi$
$462$		0			0
$463$	−8.71667e15			−0.884840			−0.442420	−	0.896808i	$-0.645880\pi$
$463$	−8.71667e15			−0.884840			−0.442420	+	0.896808i	$0.645880\pi$
$464$	−1.08411e15	+	1.87773e15i	−0.108634	+	0.188159i
$465$	1.33743e15	−	7.72163e14i	0.132298	−	0.0763821i
$466$	1.54041e15	+	2.66807e15i	0.150425	+	0.260544i
$467$	3.11493e15	+	1.79841e15i	0.300294	+	0.173375i	0.642575	−	0.766223i	$-0.277866\pi$
$467$	3.11493e15	+	1.79841e15i	0.300294	+	0.173375i	−0.342281	+	0.939598i	$0.611199\pi$
$468$			6.21211e14i			0.0591240i
$469$		0			0
$470$	8.20720e14			0.0761392
$471$	−1.43765e16	+	2.49008e16i	−1.31682	+	2.28081i
$472$	3.48407e15	−	2.01153e15i	0.315090	−	0.181917i
$473$	−9.08619e14	−	1.57377e15i	−0.0811363	−	0.140532i
$474$	7.07747e15	+	4.08618e15i	0.624034	+	0.360286i
$475$		−	2.80607e15i		−	0.244308i
$476$		0			0
$477$	−1.56672e16			−1.33009
$478$	−2.85940e15	+	4.95263e15i	−0.239722	+	0.415211i
$479$	−5.20079e15	+	3.00268e15i	−0.430582	+	0.248597i	−0.699595	−	0.714540i	$-0.746636\pi$
$479$	−5.20079e15	+	3.00268e15i	−0.430582	+	0.248597i	0.269012	+	0.963137i	$0.413303\pi$
$480$	1.16048e14	+	2.01001e14i	0.00948832	+	0.0164342i
$481$	1.48804e15	+	8.59118e14i	0.120155	+	0.0693717i
$482$		−	1.36698e15i		−	0.109014i
$483$		0			0
$484$	1.08691e16			0.845518
$485$	−3.40042e14	+	5.88970e14i	−0.0261265	+	0.0452525i
$486$	−1.15530e16	+	6.67010e15i	−0.876749	+	0.506192i
$487$	−5.72599e15	−	9.91771e15i	−0.429217	−	0.743426i	0.567587	−	0.823314i	$-0.307877\pi$
$487$	−5.72599e15	−	9.91771e15i	−0.429217	−	0.743426i	−0.996804	+	0.0798877i	$0.974544\pi$
$488$	6.08423e14	+	3.51273e14i	0.0450491	+	0.0260091i
$489$		−	2.85497e15i		−	0.208808i
$490$		0			0
$491$	−1.14179e16			−0.814883			−0.407442	−	0.913231i	$-0.633579\pi$
$491$	−1.14179e16			−0.814883			−0.407442	+	0.913231i	$0.633579\pi$
$492$	9.19998e15	−	1.59348e16i	0.648629	−	1.12346i
$493$	1.41070e16	−	8.14465e15i	0.982543	−	0.567272i
$494$	1.28384e14	+	2.22367e14i	0.00883381	+	0.0153006i
$495$	−1.77340e15	−	1.02387e15i	−0.120552	−	0.0696007i
$496$		−	5.29733e15i		−	0.355768i
$497$		0			0
$498$	3.52400e15			0.231025
$499$	5.66028e15	−	9.80390e15i	0.366636	−	0.635032i	−0.622401	−	0.782698i	$-0.713843\pi$
$499$	5.66028e15	−	9.80390e15i	0.366636	−	0.635032i	0.989037	+	0.147666i	$0.0471762\pi$
$500$	9.85183e14	−	5.68796e14i	0.0630517	−	0.0364029i
$501$	1.97182e16	+	3.41529e16i	1.24693	+	2.15974i
$502$	7.98124e15	+	4.60797e15i	0.498710	+	0.287930i
$503$			9.12462e15i			0.563387i	0.959504	+	0.281694i	$0.0908962\pi$
$503$			9.12462e15i			0.563387i	−0.959504	+	0.281694i	$0.909104\pi$
$504$		0			0
$505$	3.45866e14			0.0208526
$506$	4.49369e14	−	7.78330e14i	0.0267732	−	0.0463725i
$507$	2.14057e16	−	1.23586e16i	1.26032	−	0.727648i
$508$	−2.39803e15	−	4.15352e15i	−0.139532	−	0.241676i
$509$	8.09835e15	+	4.67558e15i	0.465682	+	0.268862i	0.714430	−	0.699706i	$-0.246686\pi$
$509$	8.09835e15	+	4.67558e15i	0.465682	+	0.268862i	−0.248748	+	0.968568i	$0.580019\pi$
$510$		−	1.74368e15i		−	0.0990934i
$511$		0			0
$512$	7.96131e14			0.0441942
$513$	5.34578e14	−	9.25916e14i	0.0293297	−	0.0508005i
$514$	8.98731e15	−	5.18883e15i	0.487361	−	0.281378i
$515$	−1.25099e15	−	2.16678e15i	−0.0670518	−	0.116137i
$516$	1.18892e15	+	6.86424e14i	0.0629876	+	0.0363659i
$517$			4.62063e16i			2.41968i
$518$		0			0
$519$	1.61599e16			0.826867
$520$	−2.59541e13	+	4.49537e13i	−0.00131276	+	0.00227377i
$521$	−3.05917e16	+	1.76621e16i	−1.52960	+	0.883113i	−0.530219	+	0.847861i	$0.677890\pi$
$521$	−3.05917e16	+	1.76621e16i	−1.52960	+	0.883113i	−0.999378	+	0.0352523i	$0.988777\pi$
$522$	7.22591e15	+	1.25156e16i	0.357165	+	0.618628i
$523$	−2.03670e15	−	1.17589e15i	−0.0995213	−	0.0574587i	0.449413	−	0.893324i	$-0.351633\pi$
$523$	−2.03670e15	−	1.17589e15i	−0.0995213	−	0.0574587i	−0.548935	+	0.835865i	$0.684966\pi$
$524$			1.45142e16i			0.701142i
$525$		0			0
$526$	1.37060e16			0.647139
$527$	−1.98988e16	+	3.44657e16i	−0.928887	+	1.60888i
$528$	−1.13163e16	+	6.53344e15i	−0.522275	+	0.301536i
$529$	1.09340e16	+	1.89382e16i	0.498935	+	0.864180i
$530$	−1.13375e15	−	6.54572e14i	−0.0511520	−	0.0295326i
$531$		−	2.68148e16i		−	1.19621i
$532$		0			0
$533$	4.11515e15			0.179483
$534$	−1.45425e16	+	2.51884e16i	−0.627181	+	1.08631i
$535$	−2.20303e15	+	1.27192e15i	−0.0939501	+	0.0542421i
$536$	−1.16131e15	−	2.01145e15i	−0.0489735	−	0.0848245i
$537$	3.77574e16	+	2.17993e16i	1.57455	+	0.909067i
$538$			1.64701e15i			0.0679209i
$539$		0			0
$540$	2.16141e14			0.00871714
$541$	9.32351e15	−	1.61488e16i	0.371874	−	0.644105i	−0.617980	−	0.786194i	$-0.712049\pi$
$541$	9.32351e15	−	1.61488e16i	0.371874	−	0.644105i	0.989854	+	0.142089i	$0.0453820\pi$
$542$	−1.16475e16	+	6.72467e15i	−0.459447	+	0.265262i
$543$	−4.09578e14	−	7.09410e14i	−0.0159786	−	0.0276757i
$544$	−5.17982e15	−	2.99057e15i	−0.199858	−	0.115388i
$545$		−	2.82008e15i		−	0.107617i
$546$		0			0
$547$	2.59639e16			0.969273			0.484636	−	0.874716i	$-0.338952\pi$
$547$	2.59639e16			0.969273			0.484636	+	0.874716i	$0.338952\pi$
$548$	4.18403e15	−	7.24695e15i	0.154494	−	0.267591i
$549$	4.05531e15	−	2.34134e15i	0.148112	−	0.0855125i
$550$	1.59687e16	+	2.76586e16i	0.576891	+	0.999205i
$551$	5.17313e15	+	2.98671e15i	0.184860	+	0.106729i
$552$			6.78959e14i			0.0239999i
$553$		0			0
$554$	−3.00013e16			−1.03772
$555$	2.13944e15	−	3.70561e15i	0.0732052	−	0.126795i
$556$	−1.72434e16	+	9.95549e15i	−0.583679	+	0.336987i
$557$	−1.00110e16	−	1.73396e16i	−0.335234	−	0.580642i	0.648296	−	0.761389i	$-0.275482\pi$
$557$	−1.00110e16	−	1.73396e16i	−0.335234	−	0.580642i	−0.983530	+	0.180746i	$0.942149\pi$
$558$	−3.05779e16	−	1.76541e16i	−1.01298	−	0.584846i
$559$			3.07037e14i			0.0100628i
$560$		0			0
$561$	9.81683e16			3.14916
$562$	9.75888e15	−	1.69029e16i	0.309729	−	0.536467i
$563$	1.47553e16	−	8.51900e15i	0.463339	−	0.267509i	−0.250108	−	0.968218i	$-0.580466\pi$
$563$	1.47553e16	−	8.51900e15i	0.463339	−	0.267509i	0.713447	+	0.700709i	$0.247133\pi$
$564$	−1.74535e16	−	3.02303e16i	−0.542259	−	0.939220i
$565$	−2.26150e15	−	1.30568e15i	−0.0695194	−	0.0401371i
$566$		−	2.52739e16i		−	0.768730i
$567$		0			0
$568$	1.31316e16			0.391046
$569$	−1.01528e16	+	1.75852e16i	−0.299167	+	0.518172i	−0.975946	−	0.218014i	$-0.930042\pi$
$569$	−1.01528e16	+	1.75852e16i	−0.299167	+	0.518172i	0.676779	+	0.736186i	$0.263375\pi$
$570$	5.53754e14	−	3.19710e14i	0.0161461	−	0.00932196i
$571$	4.52784e15	+	7.84244e15i	0.130639	+	0.226274i	0.923923	−	0.382578i	$-0.124964\pi$
$571$	4.52784e15	+	7.84244e15i	0.130639	+	0.226274i	−0.793284	+	0.608852i	$0.791630\pi$
$572$	−2.53088e15	−	1.46120e15i	−0.0722595	−	0.0417191i
$573$			3.32486e15i			0.0939389i
$574$		0			0
$575$	1.65948e15			0.0459161
$576$	2.65322e15	−	4.59552e15i	0.0726506	−	0.125834i
$577$	5.01347e16	−	2.89453e16i	1.35858	−	0.784374i	0.369143	−	0.929372i	$-0.379651\pi$
$577$	5.01347e16	−	2.89453e16i	1.35858	−	0.784374i	0.989432	+	0.144999i	$0.0463178\pi$
$578$	9.28420e15	+	1.60807e16i	0.248987	+	0.431259i
$579$	−4.85036e16	−	2.80036e16i	−1.28737	−	0.743262i
$580$			1.20759e15i			0.0317213i
$581$		0			0
$582$	2.89254e16			0.744288
$583$	3.68522e16	−	6.38298e16i	0.938537	−	1.62559i
$584$	1.09969e16	−	6.34907e15i	0.277200	−	0.160042i
$585$	1.72991e14	+	2.99630e14i	0.00431608	+	0.00747566i
$586$	−1.43530e16	−	8.28673e15i	−0.354452	−	0.204643i
$587$		−	5.59880e16i		−	1.36857i	−0.729215	−	0.684284i	$-0.760115\pi$
$587$		−	5.59880e16i		−	1.36857i	0.729215	−	0.684284i	$-0.239885\pi$
$588$		0			0
$589$	−1.45941e16			−0.349531
$590$	1.12032e15	−	1.94045e15i	0.0265601	−	0.0460034i
$591$	−1.20196e16	+	6.93952e15i	−0.282075	+	0.162856i
$592$	−7.33868e15	−	1.27110e16i	−0.170486	−	0.295290i
$593$	2.70024e16	+	1.55899e16i	0.620976	+	0.358520i	0.777249	−	0.629193i	$-0.216615\pi$
$593$	2.70024e16	+	1.55899e16i	0.620976	+	0.358520i	−0.156273	+	0.987714i	$0.549948\pi$
$594$			1.21686e16i			0.277028i
$595$		0			0
$596$	−1.33966e16			−0.298895
$597$	2.68500e14	−	4.65056e14i	0.00593060	−	0.0102721i
$598$	−1.31505e14	+	7.59246e13i	−0.00287565	+	0.00166026i
$599$	1.74707e16	+	3.02602e16i	0.378224	+	0.655104i	0.990804	−	0.135305i	$-0.0432014\pi$
$599$	1.74707e16	+	3.02602e16i	0.378224	+	0.655104i	−0.612580	+	0.790409i	$0.709868\pi$
$600$	−2.08950e16	−	1.20637e16i	−0.447851	−	0.258567i
$601$		−	2.44503e16i		−	0.518844i	−0.965764	−	0.259422i	$-0.916468\pi$
$601$		−	2.44503e16i		−	0.518844i	0.965764	−	0.259422i	$-0.0835320\pi$
$602$		0			0
$603$	−1.54810e16			−0.322029
$604$	−1.48091e16	+	2.56500e16i	−0.305004	+	0.528283i
$605$	5.24253e15	−	3.02677e15i	0.106908	−	0.0617231i
$606$	−7.35520e15	−	1.27396e16i	−0.148511	−	0.257229i
$607$	−6.00308e16	−	3.46588e16i	−1.20017	−	0.692917i	−0.239575	−	0.970878i	$-0.577008\pi$
$607$	−6.00308e16	−	3.46588e16i	−1.20017	−	0.692917i	−0.960592	+	0.277961i	$0.910342\pi$
$608$		−	2.19333e15i		−	0.0434193i
$609$		0			0
$610$	3.91282e14			0.00759471
$611$	3.90346e15	−	6.76100e15i	0.0750244	−	0.129946i
$612$	−3.45250e16	+	1.99330e16i	−0.657091	+	0.379371i
$613$	−2.51944e15	−	4.36380e15i	−0.0474834	−	0.0822436i	0.841307	−	0.540558i	$-0.181787\pi$
$613$	−2.51944e15	−	4.36380e15i	−0.0474834	−	0.0822436i	−0.888790	+	0.458314i	$0.848453\pi$
$614$	5.72135e15	+	3.30322e15i	0.106780	+	0.0616492i
$615$		−	1.02478e16i		−	0.189401i
$616$		0			0
$617$	1.01129e16			0.183301			0.0916505	−	0.995791i	$-0.470786\pi$
$617$	1.01129e16			0.183301			0.0916505	+	0.995791i	$0.470786\pi$
$618$	−5.32071e16	+	9.21575e16i	−0.955079	+	1.65424i
$619$	3.61789e16	−	2.08879e16i	0.643148	−	0.371322i	−0.142678	−	0.989769i	$-0.545571\pi$
$619$	3.61789e16	−	2.08879e16i	0.643148	−	0.371322i	0.785826	+	0.618448i	$0.212238\pi$
$620$	−1.47517e15	−	2.55507e15i	−0.0259712	−	0.0449835i
$621$	5.47576e14	+	3.16143e14i	0.00954761	+	0.00551232i
$622$		−	5.57113e16i		−	0.962057i
$623$		0			0
$624$	2.20776e15			0.0373976
$625$	−2.93267e16	+	5.07954e16i	−0.492021	+	0.852205i
$626$	7.13661e16	−	4.12032e16i	1.18589	−	0.684676i
$627$	1.79996e16	+	3.11762e16i	0.296249	+	0.513118i
$628$	4.75716e16	+	2.74655e16i	0.775514	+	0.447743i
$629$			1.10267e17i			1.78051i
$630$		0			0
$631$	1.76249e16			0.279222			0.139611	−	0.990206i	$-0.455415\pi$
$631$	1.76249e16			0.279222			0.139611	+	0.990206i	$0.455415\pi$
$632$	7.80640e15	−	1.35211e16i	0.122504	−	0.212182i
$633$	−1.17724e17	+	6.79682e16i	−1.82997	+	1.05653i
$634$	−2.92711e15	−	5.06991e15i	−0.0450717	−	0.0780664i
$635$	−2.31330e15	−	1.33558e15i	−0.0352849	−	0.0203717i
$636$			5.56805e16i			0.841319i
$637$		0			0
$638$	−6.79867e16			−1.00809
$639$	4.37630e16	−	7.57997e16i	0.642838	−	1.11343i
$640$	3.84000e14	−	2.21702e14i	0.00558793	−	0.00322619i
$641$	−4.59888e16	−	7.96549e16i	−0.662985	−	1.14832i	−0.979827	−	0.199845i	$-0.935956\pi$
$641$	−4.59888e16	−	7.96549e16i	−0.662985	−	1.14832i	0.316843	−	0.948478i	$-0.397377\pi$
$642$	9.36992e16	+	5.40973e16i	1.33821	+	0.772619i
$643$			8.41252e16i			1.19031i	0.803611	+	0.595155i	$0.202909\pi$
$643$			8.41252e16i			1.19031i	−0.803611	+	0.595155i	$0.797091\pi$
$644$		0			0
$645$	7.64606e14			0.0106189
$646$	−8.23899e15	+	1.42703e16i	−0.113365	+	0.196354i
$647$	2.41251e16	−	1.39286e16i	0.328885	−	0.189882i	−0.326461	−	0.945211i	$-0.605856\pi$
$647$	2.41251e16	−	1.39286e16i	0.328885	−	0.189882i	0.655346	+	0.755329i	$0.272523\pi$
$648$	1.06172e16	+	1.83896e16i	0.143404	+	0.248383i
$649$	1.09246e17	+	6.30734e16i	1.46197	+	0.844070i
$650$		−	5.39609e15i		−	0.0715483i
$651$		0			0
$652$	−5.45424e15			−0.0709984
$653$	6.09122e16	−	1.05503e17i	0.785643	−	1.36077i	−0.142971	−	0.989727i	$-0.545665\pi$
$653$	6.09122e16	−	1.05503e17i	0.785643	−	1.36077i	0.928614	−	0.371047i	$-0.121001\pi$
$654$	−1.03874e17	+	5.99718e16i	−1.32752	+	0.766444i
$655$	4.04184e15	+	7.00067e15i	0.0511837	+	0.0886527i
$656$	−3.04426e16	−	1.75760e16i	−0.381995	−	0.220545i
$657$		−	8.46368e16i		−	1.05237i
$658$		0			0
$659$	−3.66111e16			−0.446993			−0.223496	−	0.974705i	$-0.571747\pi$
$659$	−3.66111e16			−0.446993			−0.223496	+	0.974705i	$0.571747\pi$
$660$	−3.63879e15	+	6.30258e15i	−0.0440244	+	0.0762526i
$661$	−6.69327e16	+	3.86436e16i	−0.802471	+	0.463307i	−0.844335	−	0.535816i	$-0.820004\pi$
$661$	−6.69327e16	+	3.86436e16i	−0.802471	+	0.463307i	0.0418632	+	0.999123i	$0.486671\pi$
$662$	−2.09272e16	−	3.62470e16i	−0.248636	−	0.430650i
$663$	−1.43642e16	−	8.29317e15i	−0.169122	−	0.0976426i
$664$		−	6.73238e15i		−	0.0785526i
$665$		0			0
$666$	−9.78288e16			−1.12104
$667$	−1.76630e15	+	3.05933e15i	−0.0200591	+	0.0347433i
$668$	6.52471e16	−	3.76704e16i	0.734349	−	0.423977i
$669$	2.53687e16	+	4.39399e16i	0.282971	+	0.490120i
$670$	−1.12028e15	−	6.46792e14i	−0.0123844	−	0.00715016i
$671$			2.20290e16i			0.241357i
$672$		0			0
$673$	1.52714e17			1.64357			0.821787	−	0.569795i	$-0.192977\pi$
$673$	1.52714e17			1.64357			0.821787	+	0.569795i	$0.192977\pi$
$674$	−4.30805e16	+	7.46175e16i	−0.459537	+	0.795942i
$675$	−1.94586e16	+	1.12344e16i	−0.205726	+	0.118776i
$676$	−2.36104e16	−	4.08943e16i	−0.247413	−	0.428532i
$677$	9.30327e15	+	5.37125e15i	0.0966282	+	0.0557883i	0.547535	−	0.836783i	$-0.315566\pi$
$677$	9.30327e15	+	5.37125e15i	0.0966282	+	0.0557883i	−0.450907	+	0.892571i	$0.648899\pi$
$678$			1.11066e17i			1.14342i
$679$		0			0
$680$	−3.33119e15			−0.0336935
$681$	−1.16522e15	+	2.01821e15i	−0.0116822	+	0.0202341i
$682$	1.43850e17	−	8.30516e16i	1.42956	−	0.825357i
$683$	−5.15173e16	−	8.92305e16i	−0.507491	−	0.879001i	−0.999962	−	0.00867194i	$-0.997240\pi$
$683$	−5.15173e16	−	8.92305e16i	−0.507491	−	0.879001i	0.492471	−	0.870329i	$-0.336094\pi$
$684$	−1.26606e16	−	7.30960e15i	−0.123628	−	0.0713768i
$685$		−	4.66058e15i		−	0.0451124i
$686$		0			0
$687$	−2.19859e17			−2.09124
$688$	1.31137e15	−	2.27136e15i	0.0123650	−	0.0214169i
$689$	−1.07846e16	+	6.22647e15i	−0.100806	+	0.0582005i
$690$	1.89073e14	+	3.27484e14i	0.00175200	+	0.00303456i
$691$	−4.94278e16	−	2.85371e16i	−0.454049	−	0.262145i	0.255490	−	0.966812i	$-0.417763\pi$
$691$	−4.94278e16	−	2.85371e16i	−0.454049	−	0.262145i	−0.709539	+	0.704666i	$0.751097\pi$
$692$		−	3.08726e16i		−	0.281149i
$693$		0			0
$694$	−7.79302e16			−0.697508
$695$	−5.54470e15	+	9.60369e15i	−0.0492004	+	0.0852176i
$696$	4.44801e16	−	2.56806e16i	0.391300	−	0.225917i
$697$	1.32044e17	+	2.28708e17i	1.15166	+	1.99473i
$698$	5.87418e16	+	3.39146e16i	0.507942	+	0.293261i
$699$		−	7.29790e16i		−	0.625655i
$700$		0			0
$701$	−1.95015e17			−1.64347			−0.821733	−	0.569873i	$-0.806992\pi$
$701$	−1.95015e17			−1.64347			−0.821733	+	0.569873i	$0.806992\pi$
$702$	1.02800e15	−	1.78054e15i	0.00858952	−	0.0148775i
$703$	−3.50185e16	+	2.02180e16i	−0.290112	+	0.167496i
$704$	1.24818e16	+	2.16190e16i	0.102527	+	0.177583i
$705$	−1.68367e16	−	9.72068e15i	−0.137127	−	0.0791702i
$706$			8.10559e15i			0.0654570i
$707$		0			0
$708$	−9.52987e16			−0.756637
$709$	5.41504e15	−	9.37912e15i	0.0426309	−	0.0738388i	−0.843923	−	0.536465i	$-0.819759\pi$
$709$	5.41504e15	−	9.37912e15i	0.0426309	−	0.0738388i	0.886554	+	0.462626i	$0.153093\pi$
$710$	6.33379e15	−	3.65681e15i	0.0494440	−	0.0285465i
$711$	−5.20319e16	−	9.01220e16i	−0.402766	−	0.697611i
$712$	4.81210e16	+	2.77827e16i	0.369364	+	0.213252i
$713$		−	8.63077e15i		−	0.0656920i
$714$		0			0
$715$	−1.62763e15			−0.0121820
$716$	4.16462e16	−	7.21333e16i	0.309099	−	0.535374i
$717$	1.17319e17	−	6.77340e16i	0.863480	−	0.498531i
$718$	1.19651e16	+	2.07241e16i	0.0873310	+	0.151262i
$719$	−8.70703e16	−	5.02700e16i	−0.630226	−	0.363861i	0.150613	−	0.988593i	$-0.451875\pi$
$719$	−8.70703e16	−	5.02700e16i	−0.630226	−	0.363861i	−0.780840	+	0.624731i	$0.785208\pi$
$720$		−	2.95542e15i		−	0.0212141i
$721$		0			0
$722$	9.41206e16			0.664449
$723$	−1.61907e16	+	2.80431e16i	−0.113354	+	0.196334i
$724$	−1.35528e15	+	7.82474e14i	−0.00941021	+	0.00543299i
$725$	−6.27672e16	−	1.08716e17i	−0.432220	−	0.748627i
$726$	−2.22975e17	−	1.28735e17i	−1.52278	−	0.879178i
$727$		−	1.63046e17i		−	1.10434i	−0.833731	−	0.552171i	$-0.813799\pi$
$727$		−	1.63046e17i		−	1.10434i	0.833731	−	0.552171i	$-0.186201\pi$
$728$		0			0
$729$	1.94246e17			1.29416
$730$	3.53611e15	−	6.12471e15i	0.0233662	−	0.0404714i
$731$	−1.70642e16	+	9.85202e15i	−0.111836	+	0.0645685i
$732$	−8.32101e15	−	1.44124e16i	−0.0540891	−	0.0936851i
$733$	−1.43263e16	−	8.27130e15i	−0.0923657	−	0.0533274i	0.453106	−	0.891457i	$-0.350316\pi$
$733$	−1.43263e16	−	8.27130e15i	−0.0923657	−	0.0533274i	−0.545471	+	0.838129i	$0.683649\pi$
$734$		−	3.05559e16i		−	0.195397i
$735$		0			0
$736$	1.29711e15			0.00816038
$737$	3.64142e16	−	6.30712e16i	0.227230	−	0.393574i
$738$	−2.02909e17	+	1.17149e17i	−1.25592	+	0.725106i
$739$	−1.27128e17	−	2.20192e17i	−0.780503	−	1.35187i	−0.931649	−	0.363359i	$-0.881630\pi$
$739$	−1.27128e17	−	2.20192e17i	−0.780503	−	1.35187i	0.151146	−	0.988511i	$-0.451704\pi$
$740$	−7.07935e15	−	4.08727e15i	−0.0431125	−	0.0248910i
$741$		−	6.08235e15i		−	0.0367419i
$742$		0			0
$743$	−1.70698e17			−1.01460			−0.507300	−	0.861770i	$-0.669356\pi$
$743$	−1.70698e17			−1.01460			−0.507300	+	0.861770i	$0.669356\pi$
$744$	−6.27421e16	+	1.08672e17i	−0.369931	+	0.640740i
$745$	−6.46162e15	+	3.73062e15i	−0.0377924	+	0.0218194i
$746$	−4.18271e16	−	7.24467e16i	−0.242675	−	0.420325i
$747$	−3.88614e16	−	2.24366e16i	−0.223663	−	0.129132i
$748$		−	1.87545e17i		−	1.07077i
$749$		0			0
$750$	−2.69475e16			−0.151409
$751$	9.46716e16	−	1.63976e17i	0.527692	−	0.913989i	−0.471787	−	0.881712i	$-0.656391\pi$
$751$	9.46716e16	−	1.63976e17i	0.527692	−	0.913989i	0.999479	−	0.0322765i	$-0.0102757\pi$
$752$	−5.77531e16	+	3.33438e16i	−0.319351	+	0.184377i
$753$	−1.09154e17	−	1.89061e17i	−0.598785	−	1.03713i
$754$	9.94796e15	+	5.74346e15i	0.0541385	+	0.0312568i
$755$			1.64958e16i			0.0890617i
$756$		0			0
$757$	8.85304e16			0.470454			0.235227	−	0.971940i	$-0.424417\pi$
$757$	8.85304e16			0.470454			0.235227	+	0.971940i	$0.424417\pi$
$758$	−5.07426e16	+	8.78888e16i	−0.267521	+	0.463360i
$759$	−1.84372e16	+	1.06447e16i	−0.0964372	+	0.0556780i
$760$	−6.10787e14	−	1.05791e15i	−0.00316963	−	0.00548996i
$761$	−3.70981e16	−	2.14186e16i	−0.191005	−	0.110277i	0.401448	−	0.915882i	$-0.368507\pi$
$761$	−3.70981e16	−	2.14186e16i	−0.191005	−	0.110277i	−0.592453	+	0.805605i	$0.701840\pi$
$762$			1.13610e17i			0.580346i
$763$		0			0
$764$	6.35195e15			0.0319409
$765$	−1.11017e16	+	1.92287e16i	−0.0553885	+	0.0959358i
$766$	−3.48660e16	+	2.01299e16i	−0.172596	+	0.0996481i
$767$	−1.06568e16	−	1.84581e16i	−0.0523424	−	0.0906597i
$768$	−1.63323e16	−	9.42945e15i	−0.0795939	−	0.0459535i
$769$			2.46242e17i			1.19071i	0.803464	+	0.595353i	$0.202988\pi$
$769$			2.46242e17i			1.19071i	−0.803464	+	0.595353i	$0.797012\pi$
$770$		0			0
$771$	−2.45828e17			−1.17032
$772$	−5.34991e16	+	9.26632e16i	−0.252722	+	0.437727i
$773$	1.68583e17	−	9.73317e16i	0.790202	−	0.456223i	−0.0498319	−	0.998758i	$-0.515869\pi$
$773$	1.68583e17	−	9.73317e16i	0.790202	−	0.456223i	0.840034	+	0.542535i	$0.182535\pi$
$774$	−8.74068e15	−	1.51393e16i	−0.0406536	−	0.0704141i
$775$	2.65612e17	+	1.53351e17i	1.22585	+	0.707745i
$776$		−	5.52602e16i		−	0.253071i
$777$		0			0
$778$	3.36080e16			0.151553
$779$	−4.84217e16	+	8.38689e16i	−0.216678	+	0.375298i
$780$	1.06487e15	−	6.14804e14i	0.00472857	−	0.00273004i
$781$	2.05877e17	+	3.56590e17i	0.907198	+	1.57131i
$782$	−8.43931e15	−	4.87244e15i	−0.0369034	−	0.0213062i
$783$		−	4.78305e16i		−	0.207556i
$784$		0			0
$785$	3.05937e16			0.130742
$786$	1.71908e17	−	2.97753e17i	0.729055	−	1.26276i
$787$	1.28268e17	−	7.40554e16i	0.539845	−	0.311679i	−0.205171	−	0.978726i	$-0.565775\pi$
$787$	1.28268e17	−	7.40554e16i	0.539845	−	0.311679i	0.745016	+	0.667047i	$0.232442\pi$
$788$	1.32575e16	+	2.29627e16i	0.0553740	+	0.0959105i
$789$	−2.81173e17	−	1.62336e17i	−1.16550	−	0.672902i
$790$		−	8.69553e15i		−	0.0357712i
$791$		0			0
$792$	1.66389e17			0.674177
$793$	1.86099e15	−	3.22333e15i	0.00748352	−	0.0129618i
$794$	−7.82201e16	+	4.51604e16i	−0.312173	+	0.180233i
$795$	1.55056e16	+	2.68565e16i	0.0614166	+	0.106377i
$796$	−8.88462e14	−	5.12954e14i	−0.00349269	−	0.00201651i
$797$			1.70921e17i			0.666877i	0.942772	+	0.333438i	$0.108209\pi$
$797$			1.70921e17i			0.666877i	−0.942772	+	0.333438i	$0.891791\pi$
$798$		0			0
$799$	5.01008e17			1.92559
$800$	−2.30470e16	+	3.99186e16i	−0.0879173	+	0.152277i
$801$	3.20740e17	−	1.85179e17i	1.21439	−	0.701129i
$802$	−5.16870e16	−	8.95246e16i	−0.194239	−	0.336431i
$803$	3.44819e17	+	1.99081e17i	1.28617	+	0.742570i
$804$			5.50188e16i			0.203692i
$805$		0			0
$806$	−2.80645e16			−0.102364
$807$	1.95074e16	−	3.37878e16i	0.0706249	−	0.122326i
$808$	−2.43382e16	+	1.40517e16i	−0.0874622	+	0.0504963i
$809$	2.48078e17	+	4.29684e17i	0.884907	+	1.53270i	0.845821	+	0.533467i	$0.179111\pi$
$809$	2.48078e17	+	4.29684e17i	0.884907	+	1.53270i	0.0390858	+	0.999236i	$0.487555\pi$
$810$	1.02420e16	+	5.91325e15i	0.0362641	+	0.0209371i
$811$			3.70989e17i			1.30388i	0.758272	+	0.651938i	$0.226044\pi$
$811$			3.70989e17i			1.30388i	−0.758272	+	0.651938i	$0.773956\pi$
$812$		0			0
$813$	3.18590e17			1.10329
$814$	2.30112e17	−	3.98565e17i	0.791029	−	1.37010i
$815$	−2.63075e15	+	1.51887e15i	−0.00897707	+	0.00518291i
$816$	7.08411e16	+	1.22700e17i	0.239963	+	0.415628i
$817$	−6.25758e15	−	3.61281e15i	−0.0210414	−	0.0121482i
$818$		−	1.59950e17i		−	0.533905i
$819$		0			0
$820$	−1.95779e16			−0.0643995
$821$	−1.32051e17	+	2.28720e17i	−0.431205	+	0.746869i	−0.996977	−	0.0776924i	$-0.975245\pi$
$821$	−1.32051e17	+	2.28720e17i	−0.431205	+	0.746869i	0.565772	+	0.824562i	$0.308578\pi$
$822$	−1.71667e17	+	9.91119e16i	−0.556488	+	0.321288i
$823$	−1.88842e17	−	3.27084e17i	−0.607714	−	1.05259i	−0.991616	−	0.129218i	$-0.958753\pi$
$823$	−1.88842e17	−	3.27084e17i	−0.607714	−	1.05259i	0.383902	−	0.923374i	$-0.374580\pi$
$824$	1.76061e17	+	1.01649e17i	0.562472	+	0.324743i
$825$		−	7.56540e17i		−	2.39943i
$826$		0			0
$827$	−9.11557e16			−0.284938			−0.142469	−	0.989799i	$-0.545504\pi$
$827$	−9.11557e16			−0.284938			−0.142469	+	0.989799i	$0.545504\pi$
$828$	4.32281e15	−	7.48733e15i	0.0134148	−	0.0232351i
$829$	−4.06963e17	+	2.34960e17i	−1.25380	+	0.723882i	−0.971862	−	0.235551i	$-0.924311\pi$
$829$	−4.06963e17	+	2.34960e17i	−1.25380	+	0.723882i	−0.281938	+	0.959433i	$0.590977\pi$
$830$	−1.87480e15	−	3.24724e15i	−0.00573437	−	0.00993222i
$831$	6.15463e17	+	3.55338e17i	1.86894	+	1.07903i
$832$		−	4.21779e15i		−	0.0127158i
$833$		0			0
$834$	4.71654e17			1.40161
$835$	2.09805e16	−	3.63393e16i	0.0619009	−	0.107216i
$836$	5.95602e16	−	3.43871e16i	0.174469	−	0.100730i
$837$	5.84291e16	+	1.01202e17i	0.169932	+	0.294332i
$838$	−1.07147e17	−	6.18613e16i	−0.309397	−	0.178630i
$839$			5.97909e17i			1.71421i	0.515145	+	0.857103i	$0.327738\pi$
$839$			5.97909e17i			1.71421i	−0.515145	+	0.857103i	$0.672262\pi$
$840$		0			0
$841$	−8.65839e16			−0.244715
$842$	−7.89939e16	+	1.36821e17i	−0.221677	+	0.383956i
$843$	−4.00398e17	+	2.31170e17i	−1.11565	+	0.644119i
$844$	1.29849e17	+	2.24905e17i	0.359240	+	0.622222i
$845$	−2.27761e16	−	1.31498e16i	−0.0625660	−	0.0361225i
$846$			4.44492e17i			1.21239i
$847$		0			0
$848$	1.06374e17			0.286063
$849$	−2.99346e17	+	5.18483e17i	−0.799333	+	1.38449i
$850$	2.99899e17	−	1.73146e17i	0.795171	−	0.459092i
$851$	−1.19567e16	−	2.07096e16i	−0.0314799	−	0.0545247i
$852$	−2.69389e17	−	1.55532e17i	−0.704275	−	0.406613i
$853$		−	2.66720e16i		−	0.0692406i	−0.999401	−	0.0346203i	$-0.988978\pi$
$853$		−	2.66720e16i		−	0.0692406i	0.999401	−	0.0346203i	$-0.0110222\pi$
$854$		0			0
$855$	−8.14215e15			−0.0208421
$856$	1.03350e17	−	1.79007e17i	0.262704	−	0.455016i
$857$	1.50511e17	−	8.68975e16i	0.379912	−	0.219342i	−0.297868	−	0.954607i	$-0.596276\pi$
$857$	1.50511e17	−	8.68975e16i	0.379912	−	0.219342i	0.677780	+	0.735265i	$0.262942\pi$
$858$	3.46132e16	+	5.99519e16i	0.0867598	+	0.150272i
$859$	−5.44743e16	−	3.14508e16i	−0.135592	−	0.0782839i	0.430670	−	0.902510i	$-0.358277\pi$
$859$	−5.44743e16	−	3.14508e16i	−0.135592	−	0.0782839i	−0.566261	+	0.824226i	$0.691611\pi$
$860$		−	1.46073e15i		−	0.00361061i
$861$		0			0
$862$	4.00094e17			0.975255
$863$	−3.17904e17	+	5.50626e17i	−0.769540	+	1.33288i	0.168273	+	0.985741i	$0.446181\pi$
$863$	−3.17904e17	+	5.50626e17i	−0.769540	+	1.33288i	−0.937813	+	0.347142i	$0.887152\pi$
$864$	−1.52096e16	+	8.78125e15i	−0.0365624	+	0.0211093i
$865$	−8.59723e15	−	1.48908e16i	−0.0205240	−	0.0355486i
$866$	1.75398e17	+	1.01266e17i	0.415831	+	0.240080i
$867$		−	4.39851e17i		−	1.03560i
$868$		0			0
$869$	4.89555e17			1.13680
$870$	1.43028e16	−	2.47731e16i	0.0329841	−	0.0571301i
$871$	−1.06564e16	+	6.15247e15i	−0.0244063	+	0.0140910i
$872$	1.14573e17	+	1.98445e17i	0.260604	+	0.451380i
$873$	−3.18979e17	−	1.84163e17i	−0.720570	−	0.416022i
$874$		−	3.57353e15i		−	0.00801730i
$875$		0			0
$876$	−3.00796e17			−0.665651
$877$	4.42873e16	−	7.67078e16i	0.0973378	−	0.168594i	−0.813244	−	0.581923i	$-0.802301\pi$
$877$	4.42873e16	−	7.67078e16i	0.0973378	−	0.168594i	0.910582	+	0.413329i	$0.135634\pi$
$878$	1.08365e17	−	6.25645e16i	0.236549	−	0.136572i
$879$	1.96297e17	+	3.39997e17i	0.425580	+	0.737126i
$880$	1.20407e16	+	6.95170e15i	0.0259272	+	0.0149691i
$881$		−	1.56026e17i		−	0.333689i	−0.985983	−	0.166844i	$-0.946642\pi$
$881$		−	1.56026e17i		−	0.333689i	0.985983	−	0.166844i	$-0.0533577\pi$
$882$		0			0
$883$	−6.56199e17			−1.38443			−0.692215	−	0.721691i	$-0.743365\pi$
$883$	−6.56199e17			−1.38443			−0.692215	+	0.721691i	$0.743365\pi$
$884$	−1.58436e16	+	2.74419e16i	−0.0332002	+	0.0575044i
$885$	−4.59656e16	+	2.65383e16i	−0.0956695	+	0.0552348i
$886$	2.41859e17	+	4.18911e17i	0.499987	+	0.866004i
$887$	−6.14145e17	−	3.54577e17i	−1.26104	−	0.728062i	−0.287765	−	0.957701i	$-0.592912\pi$
$887$	−6.14145e17	−	3.54577e17i	−1.26104	−	0.728062i	−0.973276	+	0.229639i	$0.926245\pi$
$888$			3.47680e17i			0.709090i
$889$		0			0
$890$	3.09470e16			0.0622700
$891$	−3.32914e17	+	5.76623e17i	−0.665373	+	1.15246i
$892$	8.39446e16	−	4.84655e16i	0.166649	−	0.0962151i
$893$	9.18617e16	+	1.59109e17i	0.181145	+	0.313752i
$894$	2.74826e17	+	1.58671e17i	0.538310	+	0.310794i
$895$		−	4.63896e16i		−	0.0902573i
$896$		0			0
$897$	3.59703e15			0.00690540
$898$	1.17233e17	−	2.03054e17i	0.223559	−	0.387216i
$899$	−5.65420e17	+	3.26446e17i	−1.07106	+	0.618376i
$900$	1.53615e17	+	2.66069e17i	0.289054	+	0.500656i
$901$	−6.92097e17	−	3.99582e17i	−1.29365	−	0.746892i
$902$		−	1.10223e18i		−	2.04660i
$903$		0			0
$904$	2.12186e17			0.388781
$905$	−4.35798e14	+	7.54824e14i	−0.000793220	+	0.00137390i
$906$	6.07603e17	−	3.50800e17i	1.09863	−	0.634293i
$907$	2.36680e17	+	4.09943e17i	0.425127	+	0.736342i	0.996432	−	0.0843961i	$-0.0268961\pi$
$907$	2.36680e17	+	4.09943e17i	0.425127	+	0.736342i	−0.571305	+	0.820738i	$0.693563\pi$
$908$	3.85568e15	+	2.22608e15i	0.00687995	+	0.00397214i
$909$			1.87317e17i			0.332043i
$910$		0			0
$911$	−5.76025e16			−0.100770			−0.0503850	−	0.998730i	$-0.516045\pi$
$911$	−5.76025e16			−0.100770			−0.0503850	+	0.998730i	$0.516045\pi$
$912$	−2.59780e16	+	4.49952e16i	−0.0451478	+	0.0781983i
$913$	1.82819e17	−	1.05550e17i	0.315643	−	0.182236i
$914$	−1.91942e17	−	3.32453e17i	−0.329225	−	0.570234i
$915$	−8.02698e15	−	4.63438e15i	−0.0136781	−	0.00789705i
$916$			4.20028e17i			0.711058i
$917$		0			0
$918$	1.31943e17			0.220460
$919$	5.65521e17	−	9.79511e17i	0.938762	−	1.62598i	0.170979	−	0.985275i	$-0.445307\pi$
$919$	5.65521e17	−	9.79511e17i	0.938762	−	1.62598i	0.767784	−	0.640709i	$-0.221360\pi$
$920$	6.25638e14	−	3.61212e14i	0.00103180	−	0.000595711i
$921$	−7.82472e16	−	1.35528e17i	−0.128207	−	0.222061i
$922$	8.83262e16	+	5.09952e16i	0.143782	+	0.0830125i
$923$		−	6.95693e16i		−	0.112514i
$924$		0			0
$925$	8.49782e17			1.35662
$926$	1.97236e17	−	3.41622e17i	0.312838	−	0.541851i
$927$	1.17350e18	−	6.77521e17i	1.84929	−	1.06769i
$928$	−4.90612e16	−	8.49765e16i	−0.0768158	−	0.133049i
$929$	−6.89141e17	−	3.97876e17i	−1.07205	−	0.618947i	−0.143307	−	0.989678i	$-0.545774\pi$
$929$	−6.89141e17	−	3.97876e17i	−1.07205	−	0.618947i	−0.928740	+	0.370732i	$0.879107\pi$
$930$			6.98882e16i			0.108021i
$931$		0			0
$932$	−1.39422e17			−0.212734
$933$	−6.59849e17	+	1.14289e18i	−1.00036	+	1.73267i
$934$	−1.40966e17	+	8.13866e16i	−0.212340	+	0.122595i
$935$	−5.22264e16	−	9.04588e16i	−0.0781665	−	0.135388i
$936$	−2.43464e16	−	1.40564e16i	−0.0362059	−	0.0209035i
$937$		−	1.07138e18i		−	1.58309i	−0.611108	−	0.791547i	$-0.709276\pi$
$937$		−	1.07138e18i		−	1.58309i	0.611108	−	0.791547i	$-0.290724\pi$
$938$		0			0
$939$	−1.95206e18			−2.84773
$940$	−1.85708e16	+	3.21655e16i	−0.0269193	+	0.0466255i
$941$	−7.21278e17	+	4.16430e17i	−1.03888	+	0.599797i	−0.919515	−	0.393054i	$-0.871419\pi$
$941$	−7.21278e17	+	4.16430e17i	−1.03888	+	0.599797i	−0.119363	+	0.992851i	$0.538085\pi$
$942$	−6.50607e17	−	1.12688e18i	−0.931136	−	1.61277i
$943$	−4.95991e16	−	2.86360e16i	−0.0705348	−	0.0407233i
$944$			1.82063e17i			0.257270i
$945$		0			0
$946$	8.22388e16			0.114744
$947$	6.63412e16	−	1.14906e17i	0.0919779	−	0.159310i	−0.816365	−	0.577536i	$-0.804014\pi$
$947$	6.63412e16	−	1.14906e17i	0.0919779	−	0.159310i	0.908343	+	0.418225i	$0.137348\pi$
$948$	−3.20290e17	+	1.84919e17i	−0.441258	+	0.254761i
$949$	−3.36364e16	−	5.82600e16i	−0.0460482	−	0.0797578i
$950$	1.09975e17	+	6.34942e16i	0.149607	+	0.0863759i
$951$			1.38676e17i			0.187464i
$952$		0			0
$953$	−2.25730e17			−0.301323			−0.150662	−	0.988585i	$-0.548140\pi$
$953$	−2.25730e17			−0.301323			−0.150662	+	0.988585i	$0.548140\pi$
$954$	3.54508e17	−	6.14026e17i	0.470258	−	0.814510i
$955$	3.06375e15	−	1.76885e15i	0.00403862	−	0.00233170i
$956$	−1.29402e17	−	2.24130e17i	−0.169509	−	0.293598i
$957$	1.39472e18	+	8.05240e17i	1.81558	+	1.04822i
$958$		−	2.71771e17i		−	0.351569i
$959$		0			0
$960$	−1.05034e16			−0.0134185
$961$	4.03731e17	−	6.99283e17i	0.512569	−	0.887795i
$962$	−6.73408e16	+	3.88792e16i	−0.0849626	+	0.0490532i
$963$	−6.88855e17	−	1.19313e18i	−0.863715	−	1.49600i
$964$	5.35746e16	+	3.09313e16i	0.0667570	+	0.0385422i
$965$			5.95925e16i			0.0737952i
$966$		0			0
$967$	−8.43823e17			−1.03203			−0.516015	−	0.856580i	$-0.672585\pi$
$967$	−8.43823e17			−1.03203			−0.516015	+	0.856580i	$0.672585\pi$
$968$	−2.45940e17	+	4.25981e17i	−0.298936	+	0.517772i
$969$	3.38038e17	−	1.95167e17i	0.408341	−	0.235756i
$970$	−1.53885e16	−	2.66537e16i	−0.0184743	−	0.0319984i
$971$	7.87938e17	+	4.54916e17i	0.940106	+	0.542770i	0.889994	−	0.455973i	$-0.150709\pi$
$971$	7.87938e17	+	4.54916e17i	0.940106	+	0.542770i	0.0501124	+	0.998744i	$0.484042\pi$
$972$		−	6.03709e17i		−	0.715863i
$973$		0			0
$974$	5.18258e17			0.607005
$975$	−6.39118e16	+	1.10698e17i	−0.0743966	+	0.128859i
$976$	−2.75341e16	+	1.58968e16i	−0.0318545	+	0.0183912i
$977$	−7.11082e16	−	1.23163e17i	−0.0817621	−	0.141616i	0.822245	−	0.569134i	$-0.192721\pi$
$977$	−7.11082e16	−	1.23163e17i	−0.0817621	−	0.141616i	−0.904007	+	0.427518i	$0.859388\pi$
$978$	1.11891e17	+	6.46005e16i	0.127868	+	0.0738249i
$979$			1.74231e18i			1.97892i
$980$		0			0
$981$	1.52732e18			1.71362
$982$	2.58357e17	−	4.47487e17i	0.288105	−	0.499012i
$983$	−1.44515e18	+	8.34356e17i	−1.60174	+	0.924763i	−0.610596	+	0.791942i	$0.709070\pi$
$983$	−1.44515e18	+	8.34356e17i	−1.60174	+	0.924763i	−0.991140	+	0.132821i	$0.957596\pi$
$984$	4.16344e17	+	7.21129e17i	0.458650	+	0.794405i
$985$	1.27891e16	+	7.38377e15i	0.0140030	+	0.00808464i
$986$			7.37170e17i			0.802243i
$987$		0			0
$988$	−1.16200e16			−0.0124929
$989$	2.13658e15	−	3.70066e15i	0.00228318	−	0.00395459i
$990$	8.02547e16	−	4.63351e16i	0.0852431	−	0.0492152i
$991$	−7.63884e17	−	1.32309e18i	−0.806465	−	1.39684i	−0.915298	−	0.402778i	$-0.868045\pi$
$991$	−7.63884e17	−	1.32309e18i	−0.806465	−	1.39684i	0.108833	−	0.994060i	$-0.465289\pi$
$992$	2.07612e17	+	1.19865e17i	0.217863	+	0.125783i
$993$			9.91455e17i			1.03414i
$994$		0			0
$995$	−5.71378e14			−0.000588823
$996$	−7.97389e16	+	1.38112e17i	−0.0816797	+	0.141473i
$997$	−1.06006e18	+	6.12028e17i	−1.07935	+	0.623162i	−0.930720	−	0.365732i	$-0.880819\pi$
$997$	−1.06006e18	+	6.12028e17i	−1.07935	+	0.623162i	−0.148627	+	0.988893i	$0.547485\pi$
$998$	2.56155e17	+	4.43674e17i	0.259251	+	0.449035i
$999$	2.80401e17	+	1.61890e17i	0.282090	+	0.162865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.13.d.b.19.4		16
7.2	even	3		14.13.b.a.13.8	yes	8
7.3	odd	6	inner	98.13.d.b.31.4		16
7.4	even	3	inner	98.13.d.b.31.1		16
7.5	odd	6		14.13.b.a.13.5	✓	8
7.6	odd	2	inner	98.13.d.b.19.1		16
21.2	odd	6		126.13.c.a.55.2		8
21.5	even	6		126.13.c.a.55.3		8
28.19	even	6		112.13.c.c.97.7		8
28.23	odd	6		112.13.c.c.97.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.13.b.a.13.5	✓	8	7.5	odd	6
14.13.b.a.13.8	yes	8	7.2	even	3
98.13.d.b.19.1		16	7.6	odd	2	inner
98.13.d.b.19.4		16	1.1	even	1	trivial
98.13.d.b.31.1		16	7.4	even	3	inner
98.13.d.b.31.4		16	7.3	odd	6	inner
112.13.c.c.97.2		8	28.23	odd	6
112.13.c.c.97.7		8	28.19	even	6
126.13.c.a.55.2		8	21.2	odd	6
126.13.c.a.55.3		8	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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	98.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-22.6274 + 39.1918i) q^{2} +(928.383 - 536.002i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(-987.816 - 570.316i) q^{5} +48513.4i q^{6} +92681.9 q^{8} +(308876. - 534989. i) q^{9} +O(q^{10})\)	\(q+(-22.6274 + 39.1918i) q^{2} +(928.383 - 536.002i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(-987.816 - 570.316i) q^{5} +48513.4i q^{6} +92681.9 q^{8} +(308876. - 534989. i) q^{9} +(44703.4 - 25809.5i) q^{10} +(1.45307e6 + 2.51679e6i) q^{11} +(-1.90133e6 - 1.09773e6i) q^{12} -491015. i q^{13} -1.22276e6 q^{15} +(-2.09715e6 + 3.63237e6i) q^{16} +(2.72891e7 - 1.57554e7i) q^{17} +(1.39781e7 + 2.42108e7i) q^{18} +(1.00071e7 + 5.77763e6i) q^{19} +2.33601e6i q^{20} -1.31517e8 q^{22} +(-3.41682e6 + 5.91811e6i) q^{23} +(8.60443e7 - 4.96777e7i) q^{24} +(-1.21420e8 - 2.10305e8i) q^{25} +(1.92438e7 + 1.11104e7i) q^{26} -9.25255e7i q^{27} +5.16944e8 q^{29} +(2.76679e7 - 4.79223e7i) q^{30} +(-1.09378e9 + 6.31491e8i) q^{31} +(-9.49063e7 - 1.64382e8i) q^{32} +(2.69801e9 + 1.55769e9i) q^{33} +1.42602e9i q^{34} -1.26516e9 q^{36} +(-1.74968e9 + 3.03053e9i) q^{37} +(-4.52872e8 + 2.61466e8i) q^{38} +(-2.63185e8 - 4.55850e8i) q^{39} +(-9.15526e7 - 5.28579e7i) q^{40} +8.38090e9i q^{41} -6.25311e8 q^{43} +(2.97588e9 - 5.15438e9i) q^{44} +(-6.10225e8 + 3.52313e8i) q^{45} +(-1.54628e8 - 2.67823e8i) q^{46} +(1.37694e10 + 7.94978e9i) q^{47} +4.49631e9i q^{48} +1.09897e10 q^{50} +(1.68898e10 - 2.92541e10i) q^{51} +(-8.70875e8 + 5.02800e8i) q^{52} +(-1.26808e10 - 2.19638e10i) q^{53} +(3.62625e9 + 2.09361e9i) q^{54} -3.31483e9i q^{55} +1.23873e10 q^{57} +(-1.16971e10 + 2.02600e10i) q^{58} +(3.75917e10 - 2.17035e10i) q^{59} +(1.25211e9 + 2.16871e9i) q^{60} +(6.56463e9 + 3.79009e9i) q^{61} -5.71561e10i q^{62} +8.58993e9 q^{64} +(-2.80034e8 + 4.85033e8i) q^{65} +(-1.22098e11 + 7.04932e10i) q^{66} +(-1.25301e10 - 2.17028e10i) q^{67} +(-5.58882e10 - 3.22670e10i) q^{68} +7.32569e9i q^{69} +1.41685e11 q^{71} +(2.86272e10 - 4.95838e10i) q^{72} +(1.18652e11 - 6.85039e10i) q^{73} +(-7.91813e10 - 1.37146e11i) q^{74} +(-2.25448e11 - 1.30163e11i) q^{75} -2.36652e10i q^{76} +2.38208e10 q^{78} +(8.42279e10 - 1.45887e11i) q^{79} +(4.14320e9 - 2.39208e9i) q^{80} +(1.14555e11 + 1.98416e11i) q^{81} +(-3.28463e11 - 1.89638e11i) q^{82} -7.26397e10i q^{83} -3.59422e10 q^{85} +(1.41492e10 - 2.45071e10i) q^{86} +(4.79922e11 - 2.77083e11i) q^{87} +(1.34673e11 + 2.33261e11i) q^{88} +(5.19206e11 + 2.99763e11i) q^{89} -3.18878e10i q^{90} +1.39953e10 q^{92} +(-6.76961e11 + 1.17253e12i) q^{93} +(-6.23133e11 + 3.59766e11i) q^{94} +(-6.59014e9 - 1.14145e10i) q^{95} +(-1.76219e11 - 1.01740e11i) q^{96} -5.96235e11i q^{97} +1.79527e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16384 q^{4} + 1478904 q^{9}+O(q^{10}) \) 16 * q - 16384 * q^4 + 1478904 * q^9	\( 16 q - 16384 q^{4} + 1478904 q^{9} + 213840 q^{11} + 131764608 q^{15} - 33554432 q^{16} - 32547840 q^{18} - 442675200 q^{22} - 156731760 q^{23} - 191237000 q^{25} + 617707296 q^{29} + 2203567104 q^{30} - 6057590784 q^{36} + 3243600880 q^{37} - 13521315264 q^{39} + 42012604000 q^{43} + 437944320 q^{44} - 9664610304 q^{46} + 52518979584 q^{50} + 80965832832 q^{51} - 180445637520 q^{53} - 126291924480 q^{57} + 94193264640 q^{58} - 134926958592 q^{60} + 137438953472 q^{64} + 424890168192 q^{65} - 369211259440 q^{67} + 1148116288608 q^{71} - 66657976320 q^{72} - 450517137408 q^{74} - 502001694720 q^{78} + 607826610128 q^{79} - 919051941384 q^{81} - 494404521216 q^{85} + 413092638720 q^{86} + 453299404800 q^{88} + 641973288960 q^{92} - 2292312458880 q^{93} + 1053641981376 q^{95} - 3601908512928 q^{99}+O(q^{100}) \) 16 * q - 16384 * q^4 + 1478904 * q^9 + 213840 * q^11 + 131764608 * q^15 - 33554432 * q^16 - 32547840 * q^18 - 442675200 * q^22 - 156731760 * q^23 - 191237000 * q^25 + 617707296 * q^29 + 2203567104 * q^30 - 6057590784 * q^36 + 3243600880 * q^37 - 13521315264 * q^39 + 42012604000 * q^43 + 437944320 * q^44 - 9664610304 * q^46 + 52518979584 * q^50 + 80965832832 * q^51 - 180445637520 * q^53 - 126291924480 * q^57 + 94193264640 * q^58 - 134926958592 * q^60 + 137438953472 * q^64 + 424890168192 * q^65 - 369211259440 * q^67 + 1148116288608 * q^71 - 66657976320 * q^72 - 450517137408 * q^74 - 502001694720 * q^78 + 607826610128 * q^79 - 919051941384 * q^81 - 494404521216 * q^85 + 413092638720 * q^86 + 453299404800 * q^88 + 641973288960 * q^92 - 2292312458880 * q^93 + 1053641981376 * q^95 - 3601908512928 * q^99

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