LMFDB - Embedded newform 12.18.b.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,18,Mod(11,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	12.b (of order $2$, degree $1$, 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:	$21.9866504813$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	12.11
Dual form			12.18.b.a.11.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-296.839 + 207.264i) q^{2} +(2157.01 + 11157.4i) q^{3} +(45154.9 - 123048. i) q^{4} -1.59510e6i q^{5} +(-2.95282e6 - 2.86488e6i) q^{6} -3.40503e6i q^{7} +(1.20998e7 + 4.58846e7i) q^{8} +(-1.19835e8 + 4.81332e7i) q^{9} +O(q^{10})$	\(q+(-296.839 + 207.264i) q^{2} +(2157.01 + 11157.4i) q^{3} +(45154.9 - 123048. i) q^{4} -1.59510e6i q^{5} +(-2.95282e6 - 2.86488e6i) q^{6} -3.40503e6i q^{7} +(1.20998e7 + 4.58846e7i) q^{8} +(-1.19835e8 + 4.81332e7i) q^{9} +(3.30608e8 + 4.73489e8i) q^{10} +4.20451e8 q^{11} +(1.47030e9 + 2.38395e8i) q^{12} -2.89905e9 q^{13} +(7.05742e8 + 1.01075e9i) q^{14} +(1.77972e10 - 3.44065e9i) q^{15} +(-1.31019e10 - 1.11125e10i) q^{16} +2.65876e10i q^{17} +(2.55953e10 - 3.91253e10i) q^{18} +1.07679e11i q^{19} +(-1.96275e11 - 7.20267e10i) q^{20} +(3.79913e10 - 7.34469e9i) q^{21} +(-1.24806e11 + 8.71446e10i) q^{22} +1.73628e10 q^{23} +(-4.85853e11 + 2.33976e11i) q^{24} -1.78141e12 q^{25} +(8.60552e11 - 6.00871e11i) q^{26} +(-7.95526e11 - 1.23322e12i) q^{27} +(-4.18984e11 - 1.53754e11i) q^{28} -2.16210e12i q^{29} +(-4.56977e12 + 4.71004e12i) q^{30} +6.70462e12i q^{31} +(6.19239e12 + 5.83051e11i) q^{32} +(9.06918e11 + 4.69114e12i) q^{33} +(-5.51066e12 - 7.89223e12i) q^{34} -5.43137e12 q^{35} +(5.11587e11 + 1.69189e13i) q^{36} -1.76840e13 q^{37} +(-2.23179e13 - 3.19632e13i) q^{38} +(-6.25329e12 - 3.23459e13i) q^{39} +(7.31906e13 - 1.93004e13i) q^{40} +1.33551e13i q^{41} +(-9.75501e12 + 1.00544e13i) q^{42} +1.66460e13i q^{43} +(1.89854e13 - 5.17359e13i) q^{44} +(7.67774e13 + 1.91149e14i) q^{45} +(-5.15397e12 + 3.59870e12i) q^{46} -2.06687e13 q^{47} +(9.57253e13 - 1.70153e14i) q^{48} +2.21036e14 q^{49} +(5.28792e14 - 3.69223e14i) q^{50} +(-2.96648e14 + 5.73497e13i) q^{51} +(-1.30906e14 + 3.56724e14i) q^{52} +4.56778e14i q^{53} +(4.91746e14 + 2.01184e14i) q^{54} -6.70663e14i q^{55} +(1.56238e14 - 4.12002e13i) q^{56} +(-1.20141e15 + 2.32264e14i) q^{57} +(4.48126e14 + 6.41795e14i) q^{58} -2.10892e15 q^{59} +(3.80264e14 - 2.34528e15i) q^{60} -6.78410e14 q^{61} +(-1.38963e15 - 1.99019e15i) q^{62} +(1.63895e14 + 4.08041e14i) q^{63} +(-1.95899e15 + 1.11039e15i) q^{64} +4.62428e15i q^{65} +(-1.24152e15 - 1.20454e15i) q^{66} +4.32415e15i q^{67} +(3.27156e15 + 1.20056e15i) q^{68} +(3.74518e13 + 1.93724e14i) q^{69} +(1.61224e15 - 1.12573e15i) q^{70} +3.83176e15 q^{71} +(-3.65855e15 - 4.91617e15i) q^{72} -3.10272e15 q^{73} +(5.24932e15 - 3.66527e15i) q^{74} +(-3.84252e15 - 1.98759e16i) q^{75} +(1.32497e16 + 4.86221e15i) q^{76} -1.43165e15i q^{77} +(8.56037e15 + 8.30544e15i) q^{78} +1.62026e16i q^{79} +(-1.77255e16 + 2.08989e16i) q^{80} +(1.20436e16 - 1.15361e16i) q^{81} +(-2.76804e15 - 3.96432e15i) q^{82} -1.61319e16 q^{83} +(8.11741e14 - 5.00641e15i) q^{84} +4.24099e16 q^{85} +(-3.45012e15 - 4.94118e15i) q^{86} +(2.41234e16 - 4.66367e15i) q^{87} +(5.08738e15 + 1.92922e16i) q^{88} -4.61754e16i q^{89} +(-6.24088e16 - 4.08272e16i) q^{90} +9.87137e15i q^{91} +(7.84017e14 - 2.13647e15i) q^{92} +(-7.48060e16 + 1.44619e16i) q^{93} +(6.13529e15 - 4.28390e15i) q^{94} +1.71758e17 q^{95} +(6.85171e15 + 7.03486e16i) q^{96} -4.10423e16 q^{97} +(-6.56122e16 + 4.58130e16i) q^{98} +(-5.03847e16 + 2.02377e16i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 54808 q^{4} - 4960776 q^{6} + 79874976 q^{9}+O(q^{10}) $ 32 * q - 54808 * q^4 - 4960776 * q^6 + 79874976 * q^9	$ 32 q - 54808 q^{4} - 4960776 q^{6} + 79874976 q^{9} + 46839088 q^{10} + 2598308520 q^{12} + 221287360 q^{13} - 41721285088 q^{16} + 27568791600 q^{18} + 128365169856 q^{21} - 493958165040 q^{22} - 253565784288 q^{24} - 3063689463648 q^{25} - 2695436033040 q^{28} - 2169979068432 q^{30} - 17644793625600 q^{33} + 6944208632512 q^{34} - 12909384040056 q^{36} - 7970760699200 q^{37} + 21066454663744 q^{40} + 55835180334480 q^{42} + 154013263804416 q^{45} + 235918828815264 q^{46} + 299462725247520 q^{48} - 248591781347488 q^{49} + 544732086739120 q^{52} + 487051858173384 q^{54} - 21\!\cdots\!20 q^{57}+ \cdots + 90\!\cdots\!60 q^{97}+O(q^{100}) $ 32 * q - 54808 * q^4 - 4960776 * q^6 + 79874976 * q^9 + 46839088 * q^10 + 2598308520 * q^12 + 221287360 * q^13 - 41721285088 * q^16 + 27568791600 * q^18 + 128365169856 * q^21 - 493958165040 * q^22 - 253565784288 * q^24 - 3063689463648 * q^25 - 2695436033040 * q^28 - 2169979068432 * q^30 - 17644793625600 * q^33 + 6944208632512 * q^34 - 12909384040056 * q^36 - 7970760699200 * q^37 + 21066454663744 * q^40 + 55835180334480 * q^42 + 154013263804416 * q^45 + 235918828815264 * q^46 + 299462725247520 * q^48 - 248591781347488 * q^49 + 544732086739120 * q^52 + 487051858173384 * q^54 - 2151740586697920 * q^57 + 230877304263760 * q^58 - 345098683994304 * q^60 - 4956543779318336 * q^61 + 1003775054518400 * q^64 - 2371521654206832 * q^66 + 891375297976320 * q^69 - 949041839387232 * q^70 + 5817303713532480 * q^72 - 4887976236943040 * q^73 - 2051936325547056 * q^76 + 22261766802491280 * q^78 + 28021308982751520 * q^81 + 7596239161270240 * q^82 - 8356700998055568 * q^84 + 59910783041540096 * q^85 - 18469777603302720 * q^88 - 68814047068261392 * q^90 + 5961488029786560 * q^93 - 61915224567506112 * q^94 - 45410293501908864 * q^96 + 9062030716970560 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−296.839	+	207.264i	−0.819910	+	0.572493i
$2$	−296.839	+	207.264i	−0.819910	+	0.572493i
$3$	2157.01	+	11157.4i	0.189811	+	0.981821i
$3$	2157.01	+	11157.4i	0.189811	+	0.981821i
$4$	45154.9	−	123048.i	0.344505	−	0.938785i
$5$		−	1.59510e6i		−	1.82618i	−0.407759	−	0.913089i	$-0.633690\pi$
$5$		−	1.59510e6i		−	1.82618i	0.407759	−	0.913089i	$-0.366310\pi$
$6$	−2.95282e6	−	2.86488e6i	−0.717713	−	0.696339i
$7$		−	3.40503e6i		−	0.223248i	−0.993751	−	0.111624i	$-0.964395\pi$
$7$		−	3.40503e6i		−	0.223248i	0.993751	−	0.111624i	$-0.0356052\pi$
$8$	1.20998e7	+	4.58846e7i	0.254984	+	0.966945i
$9$	−1.19835e8	+	4.81332e7i	−0.927944	+	0.372721i
$10$	3.30608e8	+	4.73489e8i	1.04547	+	1.49730i
$11$	4.20451e8			0.591395			0.295698	−	0.955282i	$-0.404448\pi$
$11$	4.20451e8			0.591395			0.295698	+	0.955282i	$0.404448\pi$
$12$	1.47030e9	+	2.38395e8i	0.987109	+	0.160050i
$13$	−2.89905e9			−0.985684			−0.492842	−	0.870119i	$-0.664042\pi$
$13$	−2.89905e9			−0.985684			−0.492842	+	0.870119i	$0.664042\pi$
$14$	7.05742e8	+	1.01075e9i	0.127808	+	0.183043i
$15$	1.77972e10	−	3.44065e9i	1.79298	−	0.346629i
$16$	−1.31019e10	−	1.11125e10i	−0.762633	−	0.646831i
$17$			2.65876e10i			0.924407i	0.886774	+	0.462203i	$0.152941\pi$
$17$			2.65876e10i			0.924407i	−0.886774	+	0.462203i	$0.847059\pi$
$18$	2.55953e10	−	3.91253e10i	0.547450	−	0.836838i
$19$			1.07679e11i			1.45453i	0.686355	+	0.727266i	$0.259209\pi$
$19$			1.07679e11i			1.45453i	−0.686355	+	0.727266i	$0.740791\pi$
$20$	−1.96275e11	−	7.20267e10i	−1.71439	−	0.629127i
$21$	3.79913e10	−	7.34469e9i	0.219190	−	0.0423750i
$22$	−1.24806e11	+	8.71446e10i	−0.484891	+	0.338569i
$23$	1.73628e10			0.0462311			0.0231155	−	0.999733i	$-0.492641\pi$
$23$	1.73628e10			0.0462311			0.0231155	+	0.999733i	$0.492641\pi$
$24$	−4.85853e11	+	2.33976e11i	−0.900968	+	0.433886i
$25$	−1.78141e12			−2.33493
$26$	8.60552e11	−	6.00871e11i	0.808172	−	0.564297i
$27$	−7.95526e11	−	1.23322e12i	−0.542079	−	0.840328i
$28$	−4.18984e11	−	1.53754e11i	−0.209582	−	0.0769100i
$29$		−	2.16210e12i		−	0.802587i	−0.915949	−	0.401294i	$-0.868561\pi$
$29$		−	2.16210e12i		−	0.802587i	0.915949	−	0.401294i	$-0.131439\pi$
$30$	−4.56977e12	+	4.71004e12i	−1.27164	+	1.31067i
$31$			6.70462e12i			1.41189i	0.708269	+	0.705943i	$0.249476\pi$
$31$			6.70462e12i			1.41189i	−0.708269	+	0.705943i	$0.750524\pi$
$32$	6.19239e12	+	5.83051e11i	0.995597	+	0.0937415i
$33$	9.06918e11	+	4.69114e12i	0.112253	+	0.580644i
$34$	−5.51066e12	−	7.89223e12i	−0.529216	−	0.757930i
$35$	−5.43137e12			−0.407691
$36$	5.11587e11	+	1.69189e13i	0.0302238	+	0.999543i
$37$	−1.76840e13			−0.827689			−0.413844	−	0.910348i	$-0.635814\pi$
$37$	−1.76840e13			−0.827689			−0.413844	+	0.910348i	$0.635814\pi$
$38$	−2.23179e13	−	3.19632e13i	−0.832709	−	1.19259i
$39$	−6.25329e12	−	3.23459e13i	−0.187094	−	0.967765i
$40$	7.31906e13	−	1.93004e13i	1.76581	−	0.465647i
$41$			1.33551e13i			0.261207i	0.991435	+	0.130603i	$0.0416915\pi$
$41$			1.33551e13i			0.261207i	−0.991435	+	0.130603i	$0.958309\pi$
$42$	−9.75501e12	+	1.00544e13i	−0.155456	+	0.160228i
$43$			1.66460e13i			0.217184i	0.994086	+	0.108592i	$0.0346342\pi$
$43$			1.66460e13i			0.217184i	−0.994086	+	0.108592i	$0.965366\pi$
$44$	1.89854e13	−	5.17359e13i	0.203738	−	0.555193i
$45$	7.67774e13	+	1.91149e14i	0.680655	+	1.69459i
$46$	−5.15397e12	+	3.59870e12i	−0.0379053	+	0.0264669i
$47$	−2.06687e13			−0.126614			−0.0633071	−	0.997994i	$-0.520165\pi$
$47$	−2.06687e13			−0.126614			−0.0633071	+	0.997994i	$0.520165\pi$
$48$	9.57253e13	−	1.70153e14i	0.490316	−	0.871545i
$49$	2.21036e14			0.950160
$50$	5.28792e14	−	3.69223e14i	1.91443	−	1.33673i
$51$	−2.96648e14	+	5.73497e13i	−0.907601	+	0.175463i
$52$	−1.30906e14	+	3.56724e14i	−0.339573	+	0.925345i
$53$			4.56778e14i			1.00777i	0.863771	+	0.503884i	$0.168096\pi$
$53$			4.56778e14i			1.00777i	−0.863771	+	0.503884i	$0.831904\pi$
$54$	4.91746e14	+	2.01184e14i	0.925537	+	0.378657i
$55$		−	6.70663e14i		−	1.07999i
$56$	1.56238e14	−	4.12002e13i	0.215869	−	0.0569248i
$57$	−1.20141e15	+	2.32264e14i	−1.42809	+	0.276086i
$58$	4.48126e14	+	6.41795e14i	0.459475	+	0.658049i
$59$	−2.10892e15			−1.86990			−0.934948	−	0.354786i	$-0.884554\pi$
$59$	−2.10892e15			−1.86990			−0.934948	+	0.354786i	$0.884554\pi$
$60$	3.80264e14	−	2.34528e15i	0.292280	−	1.80264i
$61$	−6.78410e14			−0.453095			−0.226547	−	0.974000i	$-0.572744\pi$
$61$	−6.78410e14			−0.453095			−0.226547	+	0.974000i	$0.572744\pi$
$62$	−1.38963e15	−	1.99019e15i	−0.808294	−	1.15762i
$63$	1.63895e14	+	4.08041e14i	0.0832092	+	0.207162i
$64$	−1.95899e15	+	1.11039e15i	−0.869966	+	0.493112i
$65$			4.62428e15i			1.80003i
$66$	−1.24152e15	−	1.20454e15i	−0.424452	−	0.411812i
$67$			4.32415e15i			1.30096i	0.759522	+	0.650482i	$0.225433\pi$
$67$			4.32415e15i			1.30096i	−0.759522	+	0.650482i	$0.774567\pi$
$68$	3.27156e15	+	1.20056e15i	0.867819	+	0.318462i
$69$	3.74518e13	+	1.93724e14i	0.00877517	+	0.0453906i
$70$	1.61224e15	−	1.12573e15i	0.334270	−	0.233400i
$71$	3.83176e15			0.704211			0.352105	−	0.935960i	$-0.385466\pi$
$71$	3.83176e15			0.704211			0.352105	+	0.935960i	$0.385466\pi$
$72$	−3.65855e15	−	4.91617e15i	−0.597012	−	0.802232i
$73$	−3.10272e15			−0.450297			−0.225148	−	0.974325i	$-0.572287\pi$
$73$	−3.10272e15			−0.450297			−0.225148	+	0.974325i	$0.572287\pi$
$74$	5.24932e15	−	3.66527e15i	0.678630	−	0.473846i
$75$	−3.84252e15	−	1.98759e16i	−0.443195	−	2.29248i
$76$	1.32497e16	+	4.86221e15i	1.36549	+	0.501093i
$77$		−	1.43165e15i		−	0.132028i
$78$	8.56037e15	+	8.30544e15i	0.707438	+	0.686370i
$79$			1.62026e16i			1.20159i	0.799405	+	0.600793i	$0.205148\pi$
$79$			1.62026e16i			1.20159i	−0.799405	+	0.600793i	$0.794852\pi$
$80$	−1.77255e16	+	2.08989e16i	−1.18123	+	1.39270i
$81$	1.20436e16	−	1.15361e16i	0.722158	−	0.691728i
$82$	−2.76804e15	−	3.96432e15i	−0.149539	−	0.214166i
$83$	−1.61319e16			−0.786181			−0.393091	−	0.919500i	$-0.628594\pi$
$83$	−1.61319e16			−0.786181			−0.393091	+	0.919500i	$0.628594\pi$
$84$	8.11741e14	−	5.00641e15i	0.0357309	−	0.220370i
$85$	4.24099e16			1.68813
$86$	−3.45012e15	−	4.94118e15i	−0.124336	−	0.178071i
$87$	2.41234e16	−	4.66367e15i	0.787997	−	0.152340i
$88$	5.08738e15	+	1.92922e16i	0.150797	+	0.571847i
$89$		−	4.61754e16i		−	1.24336i	−0.783273	−	0.621678i	$-0.786451\pi$
$89$		−	4.61754e16i		−	1.24336i	0.783273	−	0.621678i	$-0.213549\pi$
$90$	−6.24088e16	−	4.08272e16i	−1.52822	−	0.999742i
$91$			9.87137e15i			0.220052i
$92$	7.84017e14	−	2.13647e15i	0.0159268	−	0.0434010i
$93$	−7.48060e16	+	1.44619e16i	−1.38622	+	0.267991i
$94$	6.13529e15	−	4.28390e15i	0.103812	−	0.0724857i
$95$	1.71758e17			2.65624
$96$	6.85171e15	+	7.03486e16i	0.0969379	+	0.995290i
$97$	−4.10423e16			−0.531706			−0.265853	−	0.964014i	$-0.585654\pi$
$97$	−4.10423e16			−0.531706			−0.265853	+	0.964014i	$0.585654\pi$
$98$	−6.56122e16	+	4.58130e16i	−0.779046	+	0.543960i
$99$	−5.03847e16	+	2.02377e16i	−0.548781	+	0.220425i
$100$	−8.04394e16	+	2.19200e17i	−0.804394	+	2.19200i
$101$		−	1.13934e17i		−	1.04694i	−0.852044	−	0.523469i	$-0.824637\pi$
$101$		−	1.13934e17i		−	1.04694i	0.852044	−	0.523469i	$-0.175363\pi$
$102$	7.61702e16	−	7.85082e16i	0.643700	−	0.663459i
$103$			8.49818e16i			0.661012i	0.943804	+	0.330506i	$0.107219\pi$
$103$			8.49818e16i			0.661012i	−0.943804	+	0.330506i	$0.892781\pi$
$104$	−3.50780e16	−	1.33022e17i	−0.251334	−	0.953102i
$105$	−1.17155e16	−	6.06000e16i	−0.0773843	−	0.400279i
$106$	−9.46739e16	−	1.35590e17i	−0.576940	−	0.826279i
$107$	−2.14022e17			−1.20419			−0.602096	−	0.798424i	$-0.705667\pi$
$107$	−2.14022e17			−1.20419			−0.602096	+	0.798424i	$0.705667\pi$
$108$	−1.87668e17	+	4.22023e16i	−0.975635	+	0.219399i
$109$	1.03117e17			0.495682			0.247841	−	0.968801i	$-0.420279\pi$
$109$	1.03117e17			0.495682			0.247841	+	0.968801i	$0.420279\pi$
$110$	1.39005e17	+	1.99079e17i	0.618288	+	0.885498i
$111$	−3.81447e16	−	1.97308e17i	−0.157104	−	0.812642i
$112$	−3.78383e16	+	4.46125e16i	−0.144404	+	0.170256i
$113$			2.73618e17i			0.968230i	0.875004	+	0.484115i	$0.160858\pi$
$113$			2.73618e17i			0.968230i	−0.875004	+	0.484115i	$0.839142\pi$
$114$	3.08486e17	−	3.17955e17i	1.01285	−	1.04394i
$115$		−	2.76955e16i		−	0.0844262i
$116$	−2.66043e17	−	9.76293e16i	−0.753457	−	0.276495i
$117$	3.47407e17	−	1.39541e17i	0.914659	−	0.367385i
$118$	6.26009e17	−	4.37103e17i	1.53315	−	1.07050i
$119$	9.05316e16			0.206372
$120$	3.73215e17	+	7.74985e17i	0.792353	+	1.64533i
$121$	−3.28668e17			−0.650252
$122$	2.01379e17	−	1.40610e17i	0.371497	−	0.259393i
$123$	−1.49008e17	+	2.88071e16i	−0.256458	+	0.0495799i
$124$	8.24992e17	+	3.02746e17i	1.32546	+	0.486401i
$125$			1.62456e18i			2.43782i
$126$	−1.33223e17	−	8.71529e16i	−0.186823	−	0.122217i
$127$		−	3.14274e17i		−	0.412075i	−0.978544	−	0.206038i	$-0.933943\pi$
$127$		−	3.14274e17i		−	0.412075i	0.978544	−	0.206038i	$-0.0660569\pi$
$128$	3.51360e17	−	7.35636e17i	0.430991	−	0.902356i
$129$	−1.85726e17	+	3.59056e16i	−0.213236	+	0.0412239i
$130$	−9.58450e17	−	1.37267e18i	−1.03051	−	1.47587i
$131$	5.62144e17			0.566294			0.283147	−	0.959077i	$-0.408622\pi$
$131$	5.62144e17			0.566294			0.283147	+	0.959077i	$0.408622\pi$
$132$	6.18189e17	+	1.00233e17i	0.583772	+	0.0946528i
$133$	3.66649e17			0.324722
$134$	−8.96243e17	−	1.28358e18i	−0.744792	−	1.06667i
$135$	−1.96711e18	+	1.26895e18i	−1.53459	+	0.989933i
$136$	−1.21996e18	+	3.21705e17i	−0.893850	+	0.235709i
$137$		−	4.23757e17i		−	0.291737i	−0.989304	−	0.145869i	$-0.953402\pi$
$137$		−	4.23757e17i		−	0.291737i	0.989304	−	0.145869i	$-0.0465977\pi$
$138$	−5.12693e16	−	4.97424e16i	−0.0331806	−	0.0321925i
$139$		−	1.38341e18i		−	0.842028i	−0.907054	−	0.421014i	$-0.861674\pi$
$139$		−	1.38341e18i		−	0.842028i	0.907054	−	0.421014i	$-0.138326\pi$
$140$	−2.45253e17	+	6.68321e17i	−0.140451	+	0.382734i
$141$	−4.45827e16	−	2.30609e17i	−0.0240328	−	0.124312i
$142$	−1.13742e18	+	7.94188e17i	−0.577389	+	0.403155i
$143$	−1.21891e18			−0.582929
$144$	2.10495e18	+	7.01022e17i	0.948768	+	0.315974i
$145$	−3.44877e18			−1.46567
$146$	9.21009e17	−	6.43084e17i	0.369203	−	0.257791i
$147$	4.76777e17	+	2.46619e18i	0.180351	+	0.932887i
$148$	−7.98521e17	+	2.17599e18i	−0.285143	+	0.777021i
$149$		−	1.15957e18i		−	0.391034i	−0.980700	−	0.195517i	$-0.937362\pi$
$149$		−	1.15957e18i		−	0.391034i	0.980700	−	0.195517i	$-0.0626384\pi$
$150$	5.26018e18	+	5.10352e18i	1.67581	+	1.62590i
$151$		−	3.15362e18i		−	0.949522i	−0.880115	−	0.474761i	$-0.842535\pi$
$151$		−	3.15362e18i		−	0.949522i	0.880115	−	0.474761i	$-0.157465\pi$
$152$	−4.94078e18	+	1.30289e18i	−1.40645	+	0.370883i
$153$	−1.27975e18	−	3.18612e18i	−0.344546	−	0.857797i
$154$	2.96730e17	+	4.24970e17i	0.0755850	+	0.108251i
$155$	1.06945e19			2.57836
$156$	−4.26247e18	−	6.91118e17i	−0.972977	−	0.157759i
$157$	7.04105e18			1.52227			0.761133	−	0.648596i	$-0.224644\pi$
$157$	7.04105e18			1.52227			0.761133	+	0.648596i	$0.224644\pi$
$158$	−3.35823e18	−	4.80957e18i	−0.687899	−	0.985192i
$159$	−5.09646e18	+	9.85276e17i	−0.989448	+	0.191286i
$160$	9.30026e17	−	9.87749e18i	0.171189	−	1.81814i
$161$		−	5.91210e16i		−	0.0103210i
$162$	−1.18398e18	+	5.92056e18i	−0.196096	+	0.980585i
$163$			5.89492e18i			0.926581i	0.886206	+	0.463291i	$0.153331\pi$
$163$			5.89492e18i			0.926581i	−0.886206	+	0.463291i	$0.846669\pi$
$164$	1.64332e18	+	6.03048e17i	0.245217	+	0.0899869i
$165$	7.48285e18	−	1.44663e18i	1.06036	−	0.204995i
$166$	4.78859e18	−	3.34358e18i	0.644598	−	0.450083i
$167$	9.03607e18			1.15582			0.577909	−	0.816101i	$-0.303869\pi$
$167$	9.03607e18			1.15582			0.577909	+	0.816101i	$0.303869\pi$
$168$	7.96695e17	+	1.65434e18i	0.0968642	+	0.201139i
$169$	−2.45910e17			−0.0284276
$170$	−1.25889e19	+	8.79006e18i	−1.38412	+	0.966443i
$171$	−5.18291e18	−	1.29036e19i	−0.542135	−	1.34972i
$172$	2.04826e18	+	7.51648e17i	0.203889	+	0.0748209i
$173$			2.61815e18i			0.248086i	0.992277	+	0.124043i	$0.0395861\pi$
$173$			2.61815e18i			0.248086i	−0.992277	+	0.124043i	$0.960414\pi$
$174$	−6.19415e18	+	6.38428e18i	−0.558873	+	0.576027i
$175$			6.06576e18i			0.521269i
$176$	−5.50873e18	−	4.67225e18i	−0.451018	−	0.382533i
$177$	−4.54895e18	−	2.35300e19i	−0.354927	−	1.83590i
$178$	9.57052e18	+	1.37067e19i	0.711812	+	1.01944i
$179$	−4.98753e18			−0.353700			−0.176850	−	0.984238i	$-0.556591\pi$
$179$	−4.98753e18			−0.353700			−0.176850	+	0.984238i	$0.556591\pi$
$180$	2.69874e19	−	8.16034e17i	1.82534	−	0.0551940i
$181$	−1.03000e19			−0.664611			−0.332305	−	0.943172i	$-0.607826\pi$
$181$	−1.03000e19			−0.664611			−0.332305	+	0.943172i	$0.607826\pi$
$182$	−2.04598e18	−	2.93021e18i	−0.125978	−	0.180423i
$183$	−1.46334e18	−	7.56929e18i	−0.0860023	−	0.444858i
$184$	2.10087e17	+	7.96686e17i	0.0117882	+	0.0447029i
$185$			2.82079e19i			1.51151i
$186$	1.92079e19	−	1.97975e19i	0.983151	−	1.01333i
$187$			1.11788e19i			0.546690i
$188$	−9.33295e17	+	2.54326e18i	−0.0436192	+	0.118863i
$189$	−4.19915e18	+	2.70879e18i	−0.187602	+	0.121018i
$190$	−5.09845e19	+	3.55994e19i	−2.17787	+	1.52068i
$191$	1.93201e19			0.789271			0.394636	−	0.918838i	$-0.370871\pi$
$191$	1.93201e19			0.789271			0.394636	+	0.918838i	$0.370871\pi$
$192$	−1.66146e19	−	1.94621e19i	−0.649277	−	0.760552i
$193$	5.83222e18			0.218071			0.109035	−	0.994038i	$-0.465224\pi$
$193$	5.83222e18			0.218071			0.109035	+	0.994038i	$0.465224\pi$
$194$	1.21829e19	−	8.50660e18i	0.435951	−	0.304398i
$195$	−5.15950e19	+	9.97463e18i	−1.76731	+	0.341666i
$196$	9.98087e18	−	2.71982e19i	0.327335	−	0.891996i
$197$			1.93877e19i			0.608924i	0.952525	+	0.304462i	$0.0984766\pi$
$197$			1.93877e19i			0.608924i	−0.952525	+	0.304462i	$0.901523\pi$
$198$	1.07616e19	−	1.64503e19i	0.323760	−	0.494902i
$199$			3.48996e18i			0.100593i	0.998734	+	0.0502967i	$0.0160167\pi$
$199$			3.48996e18i			0.100593i	−0.998734	+	0.0502967i	$0.983983\pi$
$200$	−2.15547e19	−	8.17392e19i	−0.595371	−	2.25775i
$201$	−4.82463e19	+	9.32724e18i	−1.27731	+	0.246937i
$202$	2.36144e19	+	3.38200e19i	0.599365	+	0.858396i
$203$	−7.36201e18			−0.179176
$204$	−6.33833e18	+	3.90917e19i	−0.147951	+	0.912490i
$205$	2.13027e19			0.477010
$206$	−1.76137e19	−	2.52259e19i	−0.378424	−	0.541970i
$207$	−2.08067e18	+	8.35729e17i	−0.0428998	+	0.0172313i
$208$	3.79832e19	+	3.22157e19i	0.751715	+	0.637571i
$209$			4.52736e19i			0.860204i
$210$	1.60378e19	+	1.55602e19i	0.292605	+	0.283891i
$211$		−	6.30855e19i		−	1.10542i	−0.833373	−	0.552712i	$-0.813593\pi$
$211$		−	6.30855e19i		−	1.10542i	0.833373	−	0.552712i	$-0.186407\pi$
$212$	5.62059e19	+	2.06258e19i	0.946078	+	0.347181i
$213$	8.26515e18	+	4.27525e19i	0.133667	+	0.691408i
$214$	6.35300e19	−	4.43591e19i	0.987329	−	0.689391i
$215$	2.65520e19			0.396617
$216$	4.69601e19	−	5.14241e19i	0.674329	−	0.738431i
$217$	2.28294e19			0.315201
$218$	−3.06090e19	+	2.13724e19i	−0.406414	+	0.283774i
$219$	−6.69260e18	−	3.46183e19i	−0.0854713	−	0.442110i
$220$	−8.25239e19	−	3.02837e19i	−1.01388	−	0.372063i
$221$		−	7.70788e19i		−	0.911173i
$222$	5.22177e19	+	5.06627e19i	0.594043	+	0.576352i
$223$			8.54903e19i			0.936108i	0.883700	+	0.468054i	$0.155045\pi$
$223$			8.54903e19i			0.936108i	−0.883700	+	0.468054i	$0.844955\pi$
$224$	1.98531e18	−	2.10853e19i	0.0209276	−	0.222265i
$225$	2.13475e20	−	8.57450e19i	2.16668	−	0.870277i
$226$	−5.67114e19	−	8.12207e19i	−0.554305	−	0.793862i
$227$	−4.52223e18			−0.0425729			−0.0212864	−	0.999773i	$-0.506776\pi$
$227$	−4.52223e18			−0.0425729			−0.0212864	+	0.999773i	$0.506776\pi$
$228$	−2.56700e19	+	1.58320e20i	−0.232798	+	1.43578i
$229$	−6.05347e19			−0.528935			−0.264468	−	0.964395i	$-0.585196\pi$
$229$	−6.05347e19			−0.528935			−0.264468	+	0.964395i	$0.585196\pi$
$230$	5.74029e18	+	8.22110e18i	0.0483334	+	0.0692219i
$231$	1.59735e19	−	3.08808e18i	0.129628	−	0.0250604i
$232$	9.92069e19	−	2.61610e19i	0.776058	−	0.204647i
$233$		−	1.87425e19i		−	0.141352i	−0.997499	−	0.0706762i	$-0.977484\pi$
$233$		−	1.87425e19i		−	0.141352i	0.997499	−	0.0706762i	$-0.0225157\pi$
$234$	−7.42022e19	+	1.13426e20i	−0.539613	+	0.824858i
$235$			3.29688e19i			0.231220i
$236$	−9.52279e19	+	2.59499e20i	−0.644187	+	1.75543i
$237$	−1.80779e20	+	3.49492e19i	−1.17974	+	0.228074i
$238$	−2.68733e19	+	1.87640e19i	−0.169206	+	0.118146i
$239$	−1.17971e19			−0.0716794			−0.0358397	−	0.999358i	$-0.511411\pi$
$239$	−1.17971e19			−0.0716794			−0.0358397	+	0.999358i	$0.511411\pi$
$240$	−2.71412e20	−	1.52692e20i	−1.59160	−	0.895405i
$241$	−1.59912e20			−0.905183			−0.452591	−	0.891718i	$-0.649500\pi$
$241$	−1.59912e20			−0.905183			−0.452591	+	0.891718i	$0.649500\pi$
$242$	9.75614e19	−	6.81211e19i	0.533148	−	0.372264i
$243$	1.54691e20	+	1.09491e20i	0.816226	+	0.577732i
$244$	−3.06336e19	+	8.34773e19i	−0.156093	+	0.425358i
$245$		−	3.52575e20i		−	1.73516i
$246$	3.82608e19	−	3.94352e19i	0.181888	−	0.187471i
$247$		−	3.12166e20i		−	1.43371i
$248$	−3.07638e20	+	8.11246e19i	−1.36522	+	0.360009i
$249$	−3.47967e19	−	1.79990e20i	−0.149226	−	0.771889i
$250$	−3.36714e20	−	4.82234e20i	−1.39563	−	1.99879i
$251$	2.72221e20			1.09067			0.545336	−	0.838217i	$-0.316402\pi$
$251$	2.72221e20			1.09067			0.545336	+	0.838217i	$0.316402\pi$
$252$	5.76095e19	−	1.74197e18i	0.223146	−	0.00674740i
$253$	7.30023e18			0.0273408
$254$	6.51377e19	+	9.32887e19i	0.235910	+	0.337864i
$255$	9.14786e19	+	4.73184e20i	0.320426	+	1.65744i
$256$	4.81737e19	+	2.91190e20i	0.163219	+	0.986590i
$257$			4.62929e20i			1.51734i	0.651475	+	0.758670i	$0.274151\pi$
$257$			4.62929e20i			1.51734i	−0.651475	+	0.758670i	$0.725849\pi$
$258$	4.76888e19	−	4.91525e19i	0.151234	−	0.155876i
$259$			6.02147e19i			0.184780i
$260$	5.69011e20	+	2.08809e20i	1.68985	+	0.620120i
$261$	1.04069e20	+	2.59094e20i	0.299141	+	0.744756i
$262$	−1.66866e20	+	1.16512e20i	−0.464310	+	0.324199i
$263$	−7.10188e20			−1.91315			−0.956576	−	0.291482i	$-0.905852\pi$
$263$	−7.10188e20			−1.91315			−0.956576	+	0.291482i	$0.905852\pi$
$264$	−2.04278e20	+	9.83755e19i	−0.532828	+	0.256598i
$265$	7.28608e20			1.84037
$266$	−1.08836e20	+	7.59932e19i	−0.266242	+	0.185901i
$267$	5.15197e20	−	9.96008e19i	1.22075	−	0.236003i
$268$	5.32080e20	+	1.95257e20i	1.22133	+	0.448188i
$269$		−	5.56590e20i		−	1.23777i	−0.785480	−	0.618887i	$-0.787584\pi$
$269$		−	5.56590e20i		−	1.23777i	0.785480	−	0.618887i	$-0.212416\pi$
$270$	3.20908e20	−	7.84385e20i	0.691495	−	1.69020i
$271$		−	3.65309e20i		−	0.762818i	−0.924406	−	0.381409i	$-0.875439\pi$
$271$		−	3.65309e20i		−	0.762818i	0.924406	−	0.381409i	$-0.124561\pi$
$272$	2.95454e20	−	3.48349e20i	0.597935	−	0.704983i
$273$	−1.10139e20	+	2.12926e19i	−0.216052	+	0.0417683i
$274$	8.78297e19	+	1.25788e20i	0.167017	+	0.239198i
$275$	−7.48996e20			−1.38087
$276$	2.55286e19	+	4.13920e18i	0.0456351	+	0.00739928i
$277$	−7.41764e20			−1.28584			−0.642921	−	0.765932i	$-0.722278\pi$
$277$	−7.41764e20			−1.28584			−0.642921	+	0.765932i	$0.722278\pi$
$278$	2.86733e20	+	4.10652e20i	0.482055	+	0.690387i
$279$	−3.22715e20	−	8.03446e20i	−0.526239	−	1.31015i
$280$	−6.57186e19	−	2.49216e20i	−0.103955	−	0.394215i
$281$			1.61444e20i			0.247752i	0.992298	+	0.123876i	$0.0395325\pi$
$281$			1.61444e20i			0.247752i	−0.992298	+	0.123876i	$0.960467\pi$
$282$	6.10310e19	+	5.92135e19i	0.0908726	+	0.0881664i
$283$		−	1.18227e20i		−	0.170818i	−0.996346	−	0.0854089i	$-0.972780\pi$
$283$		−	1.18227e20i		−	0.170818i	0.996346	−	0.0854089i	$-0.0272196\pi$
$284$	1.73023e20	−	4.71492e20i	0.242604	−	0.661102i
$285$	3.70484e20	+	1.91637e21i	0.504183	+	2.60795i
$286$	3.61820e20	−	2.52637e20i	0.477949	−	0.333722i
$287$	4.54745e19			0.0583139
$288$	−7.70128e20	+	2.28190e20i	−0.958797	+	0.284093i
$289$	1.20341e20			0.145472
$290$	1.02373e21	−	7.14806e20i	1.20172	−	0.839084i
$291$	−8.85286e19	−	4.57925e20i	−0.100924	−	0.522040i
$292$	−1.40103e20	+	3.81785e20i	−0.155129	+	0.422732i
$293$		−	2.73963e20i		−	0.294658i	−0.989088	−	0.147329i	$-0.952932\pi$
$293$		−	2.73963e20i		−	0.294658i	0.989088	−	0.147329i	$-0.0470676\pi$
$294$	−6.52679e20	−	6.33242e20i	−0.681942	−	0.661634i
$295$			3.36394e21i			3.41476i
$296$	−2.13974e20	−	8.11425e20i	−0.211048	−	0.800330i
$297$	−3.34480e20	−	5.18509e20i	−0.320583	−	0.496966i
$298$	2.40338e20	+	3.44206e20i	0.223864	+	0.320612i
$299$	−5.03358e19			−0.0455692
$300$	−2.61921e21	−	4.24678e20i	−2.30483	−	0.373705i
$301$	5.66801e19			0.0484859
$302$	6.53633e20	+	9.36117e20i	0.543594	+	0.778522i
$303$	1.27121e21	−	2.45757e20i	1.02791	−	0.198721i
$304$	1.19657e21	−	1.41080e21i	0.940837	−	1.10927i
$305$			1.08213e21i			0.827432i
$306$	1.04025e21	+	6.80518e20i	0.773579	+	0.506067i
$307$		−	1.90011e21i		−	1.37437i	−0.726483	−	0.687185i	$-0.758846\pi$
$307$		−	1.90011e21i		−	1.37437i	0.726483	−	0.687185i	$-0.241154\pi$
$308$	−1.76162e20	−	6.46460e19i	−0.123946	−	0.0454842i
$309$	−9.48175e20	+	1.83306e20i	−0.648995	+	0.125467i
$310$	−3.17456e21	+	2.21660e21i	−2.11402	+	1.47609i
$311$	−6.24434e20			−0.404597			−0.202299	−	0.979324i	$-0.564841\pi$
$311$	−6.24434e20			−0.404597			−0.202299	+	0.979324i	$0.564841\pi$
$312$	1.40851e21	−	6.78308e20i	0.888069	−	0.427674i
$313$	−2.28514e21			−1.40212			−0.701060	−	0.713102i	$-0.747290\pi$
$313$	−2.28514e21			−1.40212			−0.701060	+	0.713102i	$0.747290\pi$
$314$	−2.09006e21	+	1.45936e21i	−1.24812	+	0.871486i
$315$	6.50867e20	−	2.61429e20i	0.378314	−	0.151955i
$316$	1.99371e21	+	7.31627e20i	1.12803	+	0.413952i
$317$		−	2.99608e21i		−	1.65025i	−0.564950	−	0.825125i	$-0.691105\pi$
$317$		−	2.99608e21i		−	1.65025i	0.564950	−	0.825125i	$-0.308895\pi$
$318$	1.30862e21	−	1.34878e21i	0.701749	−	0.723288i
$319$		−	9.09057e20i		−	0.474646i
$320$	1.77118e21	+	3.12479e21i	0.900511	+	1.58871i
$321$	−4.61647e20	−	2.38792e21i	−0.228569	−	1.18230i
$322$	1.22537e19	+	1.75494e19i	0.00590870	+	0.00846229i
$323$	−2.86291e21			−1.34458
$324$	−8.75668e20	−	2.00285e21i	−0.400596	−	0.916255i
$325$	5.16440e21			2.30150
$326$	−1.22181e21	−	1.74984e21i	−0.530461	−	0.759713i
$327$	2.22423e20	+	1.15051e21i	0.0940859	+	0.486671i
$328$	−6.12793e20	+	1.61594e20i	−0.252573	+	0.0666037i
$329$			7.03777e19i			0.0282664i
$330$	−1.92137e21	+	1.98034e21i	−0.752042	+	0.775125i
$331$			1.32030e21i			0.503655i	0.967772	+	0.251828i	$0.0810316\pi$
$331$			1.32030e21i			0.503655i	−0.967772	+	0.251828i	$0.918968\pi$
$332$	−7.28436e20	+	1.98501e21i	−0.270843	+	0.738055i
$333$	2.11916e21	−	8.51190e20i	0.768048	−	0.308497i
$334$	−2.68226e21	+	1.87286e21i	−0.947667	+	0.661698i
$335$	6.89746e21			2.37579
$336$	−5.79377e20	−	3.25948e20i	−0.194571	−	0.109462i
$337$	1.72037e21			0.563335			0.281668	−	0.959512i	$-0.409112\pi$
$337$	1.72037e21			0.563335			0.281668	+	0.959512i	$0.409112\pi$
$338$	7.29958e19	−	5.09684e19i	0.0233080	−	0.0162746i
$339$	−3.05287e21	+	5.90198e20i	−0.950628	+	0.183781i
$340$	1.91501e21	−	5.21847e21i	0.581569	−	1.58479i
$341$			2.81896e21i			0.834983i
$342$	4.21296e21	+	2.75607e21i	1.21721	+	0.796284i
$343$		−	1.54475e21i		−	0.435370i
$344$	−7.63794e20	+	2.01413e20i	−0.210005	+	0.0553785i
$345$	3.09009e20	−	5.97394e19i	0.0828914	−	0.0160250i
$346$	−5.42650e20	−	7.77170e20i	−0.142028	−	0.203408i
$347$	6.64264e21			1.69645			0.848223	−	0.529639i	$-0.177673\pi$
$347$	6.64264e21			1.69645			0.848223	+	0.529639i	$0.177673\pi$
$348$	5.15432e20	−	3.17893e21i	0.128454	−	0.792241i
$349$	−4.10476e21			−0.998325			−0.499162	−	0.866509i	$-0.666359\pi$
$349$	−4.10476e21			−0.998325			−0.499162	+	0.866509i	$0.666359\pi$
$350$	−1.25722e21	−	1.80055e21i	−0.298422	−	0.427393i
$351$	2.30627e21	+	3.57517e21i	0.534318	+	0.828297i
$352$	2.60360e21	+	2.45145e20i	0.588791	+	0.0554383i
$353$		−	3.90908e21i		−	0.862958i	−0.902123	−	0.431479i	$-0.857992\pi$
$353$		−	3.90908e21i		−	0.862958i	0.902123	−	0.431479i	$-0.142008\pi$
$354$	6.22724e21	+	6.04179e21i	1.34205	+	1.30208i
$355$		−	6.11205e21i		−	1.28601i
$356$	−5.68181e21	−	2.08505e21i	−1.16724	−	0.428342i
$357$	1.95277e20	+	1.01010e21i	0.0391717	+	0.202620i
$358$	1.48049e21	−	1.03374e21i	0.290002	−	0.202490i
$359$	−9.13565e21			−1.74758			−0.873789	−	0.486305i	$-0.838344\pi$
$359$	−9.13565e21			−1.74758			−0.873789	+	0.486305i	$0.838344\pi$
$360$	−7.84178e21	+	5.83576e21i	−1.46502	+	1.09025i
$361$	−6.11427e21			−1.11566
$362$	3.05743e21	−	2.13481e21i	0.544921	−	0.380485i
$363$	−7.08940e20	−	3.66708e21i	−0.123425	−	0.638430i
$364$	1.21466e21	+	4.45741e20i	0.206581	+	0.0758089i
$365$			4.94916e21i			0.822322i
$366$	2.00322e21	+	1.94356e21i	0.325192	+	0.315507i
$367$			8.96148e21i			1.42141i	0.703492	+	0.710703i	$0.251623\pi$
$367$			8.96148e21i			1.42141i	−0.703492	+	0.710703i	$0.748377\pi$
$368$	−2.27487e20	−	1.92944e20i	−0.0352574	−	0.0299037i
$369$	−6.42824e20	−	1.60041e21i	−0.0973572	−	0.242385i
$370$	−5.84648e21	−	8.37319e21i	−0.865327	−	1.23930i
$371$	1.55535e21			0.224982
$372$	−1.59834e21	+	9.85779e21i	−0.225972	+	1.39368i
$373$	3.10114e20			0.0428545			0.0214272	−	0.999770i	$-0.493179\pi$
$373$	3.10114e20			0.0428545			0.0214272	+	0.999770i	$0.493179\pi$
$374$	−2.31696e21	−	3.31830e21i	−0.312976	−	0.448236i
$375$	−1.81259e22	+	3.50420e21i	−2.39350	+	0.462725i
$376$	−2.50088e20	−	9.48377e20i	−0.0322847	−	0.122429i
$377$			6.26803e21i			0.791097i
$378$	6.85037e20	−	1.67441e21i	0.0845344	−	0.206624i
$379$		−	5.29394e21i		−	0.638772i	−0.947625	−	0.319386i	$-0.896523\pi$
$379$		−	5.29394e21i		−	0.638772i	0.947625	−	0.319386i	$-0.103477\pi$
$380$	7.75572e21	−	2.11346e22i	0.915086	−	2.49363i
$381$	3.50648e21	−	6.77891e20i	0.404584	−	0.0782164i
$382$	−5.73497e21	+	4.00437e21i	−0.647131	+	0.451852i
$383$	−2.46064e21			−0.271556			−0.135778	−	0.990739i	$-0.543353\pi$
$383$	−2.46064e21			−0.271556			−0.135778	+	0.990739i	$0.543353\pi$
$384$	8.96567e21	+	2.33349e21i	0.967759	+	0.251878i
$385$	−2.28363e21			−0.241107
$386$	−1.73123e21	+	1.20881e21i	−0.178798	+	0.124844i
$387$	−8.01225e20	−	1.99477e21i	−0.0809490	−	0.201534i
$388$	−1.85326e21	+	5.05018e21i	−0.183175	+	0.499157i
$389$			3.02738e21i			0.292749i	0.989229	+	0.146375i	$0.0467605\pi$
$389$			3.02738e21i			0.292749i	−0.989229	+	0.146375i	$0.953239\pi$
$390$	1.32480e22	−	1.36547e22i	1.25343	−	1.29191i
$391$			4.61636e20i			0.0427363i
$392$	2.67450e21	+	1.01422e22i	0.242276	+	0.918753i
$393$	1.21255e21	+	6.27206e21i	0.107489	+	0.555999i
$394$	−4.01838e21	−	5.75502e21i	−0.348604	−	0.499263i
$395$	2.58448e22			2.19431
$396$	2.15098e20	+	7.11359e21i	0.0178742	+	0.591125i
$397$	−4.45720e20			−0.0362529			−0.0181265	−	0.999836i	$-0.505770\pi$
$397$	−4.45720e20			−0.0362529			−0.0181265	+	0.999836i	$0.505770\pi$
$398$	−7.23346e20	−	1.03596e21i	−0.0575890	−	0.0824776i
$399$	7.90865e20	+	4.09084e21i	0.0616358	+	0.318818i
$400$	2.33399e22	+	1.97959e22i	1.78069	+	1.51031i
$401$			2.01357e22i			1.50397i	0.659178	+	0.751987i	$0.270904\pi$
$401$			2.01357e22i			1.50397i	−0.659178	+	0.751987i	$0.729096\pi$
$402$	1.23882e22	−	1.27684e22i	0.905912	−	0.933719i
$403$		−	1.94370e22i		−	1.39167i
$404$	−1.40194e22	−	5.14467e21i	−0.982850	−	0.360675i
$405$	−1.84012e22	−	1.92107e22i	−1.26322	−	1.31879i
$406$	2.18533e21	−	1.52588e21i	0.146908	−	0.102577i
$407$	−7.43528e21			−0.489491
$408$	−6.22085e21	−	1.29177e22i	−0.401087	−	0.832861i
$409$	2.26782e22			1.43206			0.716030	−	0.698070i	$-0.245958\pi$
$409$	2.26782e22			1.43206			0.716030	+	0.698070i	$0.245958\pi$
$410$	−6.32349e21	+	4.41530e21i	−0.391106	+	0.273085i
$411$	4.72802e21	−	9.14048e20i	0.286434	−	0.0553750i
$412$	1.04569e22	+	3.83734e21i	0.620548	+	0.227722i
$413$			7.18093e21i			0.417451i
$414$	4.44408e20	−	6.79326e20i	0.0253092	−	0.0386879i
$415$			2.57321e22i			1.43571i
$416$	−1.79521e22	−	1.69030e21i	−0.981343	−	0.0923995i
$417$	1.54353e22	−	2.98404e21i	0.826720	−	0.159826i
$418$	−9.38360e21	−	1.34390e22i	−0.492460	−	0.705290i
$419$	−2.19204e22			−1.12727			−0.563636	−	0.826023i	$-0.690598\pi$
$419$	−2.19204e22			−1.12727			−0.563636	+	0.826023i	$0.690598\pi$
$420$	−7.98574e21	−	1.29481e21i	−0.402435	−	0.0652509i
$421$	1.63880e22			0.809337			0.404668	−	0.914464i	$-0.367387\pi$
$421$	1.63880e22			0.809337			0.404668	+	0.914464i	$0.367387\pi$
$422$	1.30754e22	+	1.87262e22i	0.632847	+	0.906347i
$423$	2.47684e21	−	9.94854e20i	0.117491	−	0.0471917i
$424$	−2.09591e22	+	5.52693e21i	−0.974457	+	0.256965i
$425$		−	4.73634e22i		−	2.15842i
$426$	−1.13145e22	−	1.09775e22i	−0.505421	−	0.490369i
$427$			2.31001e21i			0.101153i
$428$	−9.66413e21	+	2.63350e22i	−0.414850	+	1.13048i
$429$	−2.62920e21	−	1.35999e22i	−0.110646	−	0.572332i
$430$	−7.88168e21	+	5.50329e21i	−0.325190	+	0.227060i
$431$	3.34997e22			1.35514			0.677569	−	0.735459i	$-0.263034\pi$
$431$	3.34997e22			1.35514			0.677569	+	0.735459i	$0.263034\pi$
$432$	−3.28119e21	+	2.49978e22i	−0.130143	+	0.991495i
$433$	−9.76947e21			−0.379948			−0.189974	−	0.981789i	$-0.560840\pi$
$433$	−9.76947e21			−0.379948			−0.189974	+	0.981789i	$0.560840\pi$
$434$	−6.77667e21	+	4.73173e21i	−0.258436	+	0.180450i
$435$	−7.43902e21	−	3.84792e22i	−0.278200	−	1.43902i
$436$	4.65622e21	−	1.26883e22i	0.170765	−	0.465338i
$437$			1.86960e21i			0.0672446i
$438$	9.16177e21	+	8.88893e21i	0.323184	+	0.313559i
$439$			3.10317e22i			1.07364i	0.843698	+	0.536819i	$0.180374\pi$
$439$			3.10317e22i			1.07364i	−0.843698	+	0.536819i	$0.819626\pi$
$440$	3.07731e22	−	8.11489e21i	1.04429	−	0.275382i
$441$	−2.64878e22	+	1.06392e22i	−0.881695	+	0.354144i
$442$	1.59757e22	+	2.28800e22i	0.521639	+	0.747079i
$443$	5.42700e21			0.173832			0.0869158	−	0.996216i	$-0.472299\pi$
$443$	5.42700e21			0.173832			0.0869158	+	0.996216i	$0.472299\pi$
$444$	−2.60008e22	−	4.21578e21i	−0.817019	−	0.132472i
$445$	−7.36545e22			−2.27059
$446$	−1.77191e22	−	2.53769e22i	−0.535915	−	0.767524i
$447$	1.29378e22	−	2.50121e21i	0.383925	−	0.0742225i
$448$	3.78091e21	+	6.67042e21i	0.110086	+	0.194218i
$449$		−	4.40350e22i		−	1.25807i	−0.777378	−	0.629034i	$-0.783451\pi$
$449$		−	4.40350e22i		−	1.25807i	0.777378	−	0.629034i	$-0.216549\pi$
$450$	−4.55958e22	+	6.96982e22i	−1.27826	+	1.95396i
$451$			5.61517e21i			0.154476i
$452$	3.36683e22	+	1.23552e22i	0.908960	+	0.333560i
$453$	3.51861e22	−	6.80238e21i	0.932260	−	0.180230i
$454$	1.34238e21	−	9.37298e20i	0.0349059	−	0.0243727i
$455$	1.57458e22			0.401854
$456$	−2.51942e22	−	5.23159e22i	−0.631101	−	1.31049i
$457$	3.63485e22			0.893714			0.446857	−	0.894605i	$-0.352543\pi$
$457$	3.63485e22			0.893714			0.446857	+	0.894605i	$0.352543\pi$
$458$	1.79691e22	−	1.25467e22i	0.433679	−	0.302811i
$459$	3.27883e22	−	2.11511e22i	0.776804	−	0.501101i
$460$	−3.40788e21	−	1.25059e21i	−0.0792580	−	0.0290852i
$461$			3.65727e21i			0.0835025i	0.999128	+	0.0417512i	$0.0132937\pi$
$461$			3.65727e21i			0.0835025i	−0.999128	+	0.0417512i	$0.986706\pi$
$462$	−4.10151e21	+	4.22740e21i	−0.0919362	+	0.0947581i
$463$			7.75615e22i			1.70690i	0.521176	+	0.853449i	$0.325493\pi$
$463$			7.75615e22i			1.70690i	−0.521176	+	0.853449i	$0.674507\pi$
$464$	−2.40263e22	+	2.83277e22i	−0.519138	+	0.612080i
$465$	2.30682e22	+	1.19323e23i	0.489400	+	2.53148i
$466$	3.88466e21	+	5.56352e21i	0.0809232	+	0.115896i
$467$	−7.43989e22			−1.52185			−0.760927	−	0.648837i	$-0.775256\pi$
$467$	−7.43989e22			−1.52185			−0.760927	+	0.648837i	$0.775256\pi$
$468$	−1.48312e21	−	4.90489e22i	−0.0297911	−	0.985233i
$469$	1.47239e22			0.290438
$470$	−6.83325e21	−	9.78642e21i	−0.132372	−	0.189580i
$471$	1.51876e22	+	7.85598e22i	0.288943	+	1.49459i
$472$	−2.55175e22	−	9.67667e22i	−0.476794	−	1.80809i
$473$			6.99883e21i			0.128442i
$474$	4.64185e22	−	4.78433e22i	0.836711	−	0.862394i
$475$		−	1.91820e23i		−	3.39623i
$476$	4.08794e21	−	1.11398e22i	0.0710961	−	0.193739i
$477$	−2.19862e22	−	5.47379e22i	−0.375616	−	0.935152i
$478$	3.50185e21	−	2.44513e21i	0.0587707	−	0.0410359i
$479$	−7.97619e22			−1.31505			−0.657527	−	0.753431i	$-0.728397\pi$
$479$	−7.97619e22			−1.31505			−0.657527	+	0.753431i	$0.728397\pi$
$480$	1.12213e23	−	1.09292e22i	1.81758	−	0.177026i
$481$	5.12670e22			0.815839
$482$	4.74682e22	−	3.31441e22i	0.742169	−	0.518211i
$483$	6.59636e20	−	1.27525e20i	0.0101334	−	0.00195904i
$484$	−1.48410e22	+	4.04420e22i	−0.224015	+	0.610446i
$485$			6.54666e22i			0.970990i
$486$	−6.86119e22	−	4.39481e20i	−0.999979	−	0.00640518i
$487$		−	5.24157e22i		−	0.750698i	−0.926883	−	0.375349i	$-0.877523\pi$
$487$		−	5.24157e22i		−	0.750698i	0.926883	−	0.375349i	$-0.122477\pi$
$488$	−8.20864e21	−	3.11286e22i	−0.115532	−	0.438118i
$489$	−6.57720e22	+	1.27154e22i	−0.909737	+	0.175875i
$490$	7.30763e22	+	1.04658e23i	0.993368	+	1.42268i
$491$	−1.60391e22			−0.214283			−0.107142	−	0.994244i	$-0.534170\pi$
$491$	−1.60391e22			−0.214283			−0.107142	+	0.994244i	$0.534170\pi$
$492$	−3.18378e21	+	1.96360e22i	−0.0418061	+	0.257840i
$493$	5.74849e22			0.741917
$494$	6.47008e22	+	9.26630e22i	0.820788	+	1.17551i
$495$	3.22812e22	+	8.03687e22i	0.402536	+	1.00217i
$496$	7.45049e22	−	8.78435e22i	0.913252	−	1.07675i
$497$		−	1.30473e22i		−	0.157214i
$498$	4.76346e22	+	4.62160e22i	0.564252	+	0.547449i
$499$			9.75244e21i			0.113569i	0.998386	+	0.0567843i	$0.0180847\pi$
$499$			9.75244e21i			0.113569i	−0.998386	+	0.0567843i	$0.981915\pi$
$500$	1.99900e23	+	7.33570e22i	2.28859	+	0.839840i
$501$	1.94909e22	+	1.00819e23i	0.219387	+	1.13481i
$502$	−8.08057e22	+	5.64217e22i	−0.894253	+	0.624402i
$503$	−9.41516e22			−1.02447			−0.512236	−	0.858845i	$-0.671183\pi$
$503$	−9.41516e22			−1.02447			−0.512236	+	0.858845i	$0.671183\pi$
$504$	−1.67397e22	+	1.24575e22i	−0.179097	+	0.133282i
$505$	−1.81736e23			−1.91190
$506$	−2.16699e21	+	1.51308e21i	−0.0224170	+	0.0156524i
$507$	−5.30431e20	−	2.74372e21i	−0.00539586	−	0.0279108i
$508$	−3.86709e22	−	1.41910e22i	−0.386850	−	0.141962i
$509$		−	2.52160e21i		−	0.0248071i	−0.999923	−	0.0124035i	$-0.996052\pi$
$509$		−	2.52160e21i		−	0.0248071i	0.999923	−	0.0124035i	$-0.00394827\pi$
$510$	−1.25229e23	−	1.21499e23i	−1.21159	−	1.17551i
$511$			1.05649e22i			0.100528i
$512$	−7.46532e22	−	7.64519e22i	−0.698640	−	0.715473i
$513$	1.32791e23	−	8.56611e22i	1.22228	−	0.788471i
$514$	−9.59487e22	−	1.37415e23i	−0.868666	−	1.24408i
$515$	1.35555e23			1.20713
$516$	−3.96831e21	+	2.44746e22i	−0.0347603	+	0.214384i
$517$	−8.69020e21			−0.0748790
$518$	−1.24804e22	−	1.78741e22i	−0.105785	−	0.151503i
$519$	−2.92118e22	+	5.64738e21i	−0.243576	+	0.0470895i
$520$	−2.12183e23	+	5.59530e22i	−1.74053	+	0.458981i
$521$		−	1.01876e22i		−	0.0822152i	−0.999155	−	0.0411076i	$-0.986911\pi$
$521$		−	1.01876e22i		−	0.0822152i	0.999155	−	0.0411076i	$-0.0130886\pi$
$522$	−8.45927e22	−	5.53396e22i	−0.671636	−	0.439377i
$523$			1.83078e22i			0.143012i	0.997440	+	0.0715060i	$0.0227805\pi$
$523$			1.83078e22i			0.143012i	−0.997440	+	0.0715060i	$0.977219\pi$
$524$	2.53836e22	−	6.91709e22i	0.195091	−	0.531628i
$525$	−6.76780e22	+	1.30839e22i	−0.511792	+	0.0989425i
$526$	2.10812e23	−	1.47197e23i	1.56861	−	1.09527i
$527$	−1.78260e23			−1.30516
$528$	4.02478e22	−	7.15411e22i	0.289971	−	0.515427i
$529$	−1.40749e23			−0.997863
$530$	−2.16279e23	+	1.51015e23i	−1.50893	+	1.05360i
$531$	2.52722e23	−	1.01509e23i	1.73516	−	0.696949i
$532$	1.65560e22	−	4.51155e22i	0.111868	−	0.304844i
$533$		−	3.87171e22i		−	0.257467i
$534$	−1.32287e23	+	1.36348e23i	−0.865798	+	0.892373i
$535$			3.41386e23i			2.19907i
$536$	−1.98412e23	+	5.23215e22i	−1.25796	+	0.331726i
$537$	−1.07581e22	−	5.56478e22i	−0.0671361	−	0.347270i
$538$	1.15361e23	+	1.65218e23i	0.708616	+	1.01486i
$539$	9.29350e22			0.561920
$540$	6.73169e22	+	2.99349e23i	0.400661	+	1.78168i
$541$	1.28083e23			0.750438			0.375219	−	0.926936i	$-0.377568\pi$
$541$	1.28083e23			0.750438			0.375219	+	0.926936i	$0.377568\pi$
$542$	7.57155e22	+	1.08438e23i	0.436708	+	0.625442i
$543$	−2.22171e22	−	1.14921e23i	−0.126150	−	0.652528i
$544$	−1.55019e22	+	1.64641e23i	−0.0866553	+	0.920336i
$545$		−	1.64481e23i		−	0.905204i
$546$	2.82803e22	−	2.91483e22i	0.153231	−	0.157934i
$547$		−	2.32825e23i		−	1.24205i	−0.783792	−	0.621024i	$-0.786717\pi$
$547$		−	2.32825e23i		−	1.24205i	0.783792	−	0.621024i	$-0.213283\pi$
$548$	−5.21426e22	−	1.91347e22i	−0.273879	−	0.100505i
$549$	8.12971e22	−	3.26541e22i	0.420446	−	0.168878i
$550$	2.22331e23	−	1.55240e23i	1.13219	−	0.790536i
$551$	2.32811e23			1.16739
$552$	−8.43578e21	+	4.06248e21i	−0.0416527	+	0.0200590i
$553$	5.51704e22			0.268252
$554$	2.20185e23	−	1.53741e23i	1.05427	−	0.736135i
$555$	−3.14726e23	+	6.08446e22i	−1.48403	+	0.286901i
$556$	−1.70227e23	−	6.24679e22i	−0.790483	−	0.290082i
$557$		−	2.92608e23i		−	1.33819i	−0.743179	−	0.669093i	$-0.766683\pi$
$557$		−	2.92608e23i		−	1.33819i	0.743179	−	0.669093i	$-0.233317\pi$
$558$	2.62320e23	+	1.71607e23i	1.18152	+	0.772937i
$559$		−	4.82576e22i		−	0.214075i
$560$	7.11615e22	+	6.03560e22i	0.310919	+	0.263707i
$561$	−1.24726e23	+	2.41127e22i	−0.536751	+	0.103768i
$562$	−3.34615e22	−	4.79228e22i	−0.141836	−	0.203134i
$563$	3.14580e23			1.31344			0.656719	−	0.754135i	$-0.271944\pi$
$563$	3.14580e23			1.31344			0.656719	+	0.754135i	$0.271944\pi$
$564$	−3.03892e22	−	4.92732e21i	−0.124982	−	0.0202646i
$565$	4.36449e23			1.76816
$566$	2.45043e22	+	3.50945e22i	0.0977919	+	0.140055i
$567$	−3.92807e22	−	4.10087e22i	−0.154427	−	0.161221i
$568$	4.63636e22	+	1.75819e23i	0.179563	+	0.680933i
$569$			1.92492e23i			0.734442i	0.930134	+	0.367221i	$0.119691\pi$
$569$			1.92492e23i			0.734442i	−0.930134	+	0.367221i	$0.880309\pi$
$570$	−5.07170e23	−	4.92066e23i	−1.90642	−	1.84964i
$571$			2.60890e22i			0.0966162i	0.998832	+	0.0483081i	$0.0153829\pi$
$571$			2.60890e22i			0.0966162i	−0.998832	+	0.0483081i	$0.984617\pi$
$572$	−5.50398e22	+	1.49985e23i	−0.200822	+	0.547245i
$573$	4.16737e22	+	2.15562e23i	0.149812	+	0.774923i
$574$	−1.34986e22	+	9.42526e21i	−0.0478122	+	0.0333843i
$575$	−3.09303e22			−0.107946
$576$	1.81308e23	−	2.27356e23i	0.623486	−	0.781834i
$577$	3.51595e23			1.19137			0.595687	−	0.803217i	$-0.296880\pi$
$577$	3.51595e23			1.19137			0.595687	+	0.803217i	$0.296880\pi$
$578$	−3.57218e22	+	2.49423e22i	−0.119274	+	0.0832819i
$579$	1.25802e22	+	6.50724e22i	0.0413922	+	0.214106i
$580$	−1.55729e23	+	4.24365e23i	−0.504929	+	1.37595i
$581$			5.49297e22i			0.175513i
$582$	1.21190e23	+	1.17581e23i	0.381612	+	0.370248i
$583$			1.92053e23i			0.595990i
$584$	−3.75424e22	−	1.42367e23i	−0.114819	−	0.435412i
$585$	−2.22582e23	−	5.54150e23i	−0.670910	−	1.67033i
$586$	5.67829e22	+	8.13230e22i	0.168689	+	0.241593i
$587$	−5.16608e23			−1.51265			−0.756324	−	0.654198i	$-0.773006\pi$
$587$	−5.16608e23			−1.51265			−0.756324	+	0.654198i	$0.773006\pi$
$588$	3.24989e23	+	5.26938e22i	0.937912	+	0.152073i
$589$	−7.21943e23			−2.05363
$590$	−6.97224e23	−	9.98548e23i	−1.95493	−	2.79980i
$591$	−2.16316e23	+	4.18194e22i	−0.597854	+	0.115580i
$592$	2.31695e23	+	1.96514e23i	0.631223	+	0.535375i
$593$			7.44212e23i			1.99863i	0.0370530	+	0.999313i	$0.488203\pi$
$593$			7.44212e23i			1.99863i	−0.0370530	+	0.999313i	$0.511797\pi$
$594$	2.06755e23	+	8.45879e22i	0.547358	+	0.223936i
$595$		−	1.44407e23i		−	0.376872i
$596$	−1.42683e23	−	5.23603e22i	−0.367096	−	0.134713i
$597$	−3.89389e22	+	7.52789e21i	−0.0987648	+	0.0190938i
$598$	1.49416e22	−	1.04328e22i	0.0373627	−	0.0260880i
$599$	5.70944e23			1.40756			0.703778	−	0.710420i	$-0.251495\pi$
$599$	5.70944e23			1.40756			0.703778	+	0.710420i	$0.251495\pi$
$600$	8.65503e23	−	4.16807e23i	2.10370	−	1.01309i
$601$	−5.31374e23			−1.27341			−0.636704	−	0.771108i	$-0.719703\pi$
$601$	−5.31374e23			−1.27341			−0.636704	+	0.771108i	$0.719703\pi$
$602$	−1.68249e22	+	1.17478e22i	−0.0397541	+	0.0277578i
$603$	−2.08135e23	−	5.18184e23i	−0.484896	−	1.20722i
$604$	−3.88047e23	−	1.42401e23i	−0.891396	−	0.327115i
$605$			5.24258e23i			1.18748i
$606$	−3.26407e23	+	3.36426e23i	−0.729024	+	0.751402i
$607$			2.59676e23i			0.571910i	0.958243	+	0.285955i	$0.0923109\pi$
$607$			2.59676e23i			0.571910i	−0.958243	+	0.285955i	$0.907689\pi$
$608$	−6.27821e22	+	6.66787e23i	−0.136350	+	1.44813i
$609$	−1.58799e22	−	8.21409e22i	−0.0340096	−	0.175919i
$610$	−2.24288e23	−	3.21219e23i	−0.473698	−	0.678419i
$611$	5.99198e22			0.124802
$612$	−4.49833e23	+	1.36019e22i	−0.923984	+	0.0279391i
$613$	−1.99953e23			−0.405055			−0.202527	−	0.979277i	$-0.564915\pi$
$613$	−1.99953e23			−0.405055			−0.202527	+	0.979277i	$0.564915\pi$
$614$	3.93826e23	+	5.64028e23i	0.786816	+	1.12686i
$615$	4.59502e22	+	2.37683e23i	0.0905418	+	0.468339i
$616$	6.56907e22	−	1.73227e22i	0.127664	−	0.0336651i
$617$			2.78943e23i			0.534676i	0.963603	+	0.267338i	$0.0861441\pi$
$617$			2.78943e23i			0.534676i	−0.963603	+	0.267338i	$0.913856\pi$
$618$	2.43463e23	−	2.50936e23i	0.460288	−	0.474417i
$619$			4.83126e23i			0.900929i	0.892794	+	0.450464i	$0.148742\pi$
$619$			4.83126e23i			0.900929i	−0.892794	+	0.450464i	$0.851258\pi$
$620$	4.82911e23	−	1.31595e24i	0.888255	−	2.42052i
$621$	−1.38126e22	−	2.14122e22i	−0.0250609	−	0.0388493i
$622$	1.85356e23	−	1.29423e23i	0.331734	−	0.231629i
$623$	−1.57229e23			−0.277577
$624$	−2.77513e23	+	4.93283e23i	−0.483297	+	0.859067i
$625$	1.23224e24			2.11697
$626$	6.78318e23	−	4.73628e23i	1.14961	−	0.802703i
$627$	−5.05135e23	+	9.76555e22i	−0.844566	+	0.163276i
$628$	3.17938e23	−	8.66390e23i	0.524427	−	1.42908i
$629$		−	4.70176e23i		−	0.765121i
$630$	−1.39018e23	+	2.12504e23i	−0.223191	+	0.341171i
$631$		−	9.44875e23i		−	1.49667i	−0.663324	−	0.748333i	$-0.730855\pi$
$631$		−	9.44875e23i		−	1.49667i	0.663324	−	0.748333i	$-0.269145\pi$
$632$	−7.43450e23	+	1.96049e23i	−1.16187	+	0.306386i
$633$	7.03870e23	−	1.36076e23i	1.08533	−	0.209822i
$634$	6.20981e23	+	8.89354e23i	0.944756	+	1.35306i
$635$	−5.01298e23			−0.752523
$636$	−1.08893e23	+	6.71601e23i	−0.161293	+	0.994777i
$637$	−6.40796e23			−0.936558
$638$	1.88415e23	+	2.69844e23i	0.271732	+	0.389167i
$639$	−4.59178e23	+	1.84435e23i	−0.653468	+	0.262474i
$640$	−1.17341e24	−	5.60455e23i	−1.64786	−	0.787066i
$641$			5.85869e23i			0.811909i	0.913893	+	0.405955i	$0.133061\pi$
$641$			5.85869e23i			0.811909i	−0.913893	+	0.405955i	$0.866939\pi$
$642$	6.31967e23	+	6.13146e23i	0.864264	+	0.838526i
$643$		−	7.98823e22i		−	0.107810i	−0.998546	−	0.0539048i	$-0.982833\pi$
$643$		−	7.98823e22i		−	0.107810i	0.998546	−	0.0539048i	$-0.0171667\pi$
$644$	−7.27474e21	−	2.66960e21i	−0.00968920	−	0.00355563i
$645$	5.72730e22	+	2.96252e23i	0.0752822	+	0.389406i
$646$	8.49824e23	−	5.93380e23i	1.10243	−	0.769762i
$647$	9.79931e23			1.25461			0.627306	−	0.778773i	$-0.284158\pi$
$647$	9.79931e23			1.25461			0.627306	+	0.778773i	$0.284158\pi$
$648$	6.75053e23	+	4.13030e23i	0.853002	+	0.521908i
$649$	−8.86697e23			−1.10585
$650$	−1.53300e24	+	1.07040e24i	−1.88702	+	1.31759i
$651$	4.92433e22	+	2.54717e23i	0.0598286	+	0.309471i
$652$	7.25361e23	+	2.66185e23i	0.869860	+	0.319212i
$653$		−	1.38724e24i		−	1.64206i	−0.570887	−	0.821029i	$-0.693401\pi$
$653$		−	1.38724e24i		−	1.64206i	0.570887	−	0.821029i	$-0.306599\pi$
$654$	−3.04484e23	−	2.95416e23i	−0.355757	−	0.345163i
$655$		−	8.96677e23i		−	1.03415i
$656$	1.48408e23	−	1.74978e23i	0.168957	−	0.199205i
$657$	3.71814e23	−	1.49344e23i	0.417850	−	0.167835i
$658$	−1.45868e22	−	2.08909e22i	−0.0161823	−	0.0231759i
$659$	5.76377e23			0.631219			0.315610	−	0.948889i	$-0.397791\pi$
$659$	5.76377e23			0.631219			0.315610	+	0.948889i	$0.397791\pi$
$660$	1.59882e23	−	9.86075e23i	0.172853	−	1.06607i
$661$	1.52302e24			1.62552			0.812761	−	0.582597i	$-0.197964\pi$
$661$	1.52302e24			1.62552			0.812761	+	0.582597i	$0.197964\pi$
$662$	−2.73650e23	−	3.91915e23i	−0.288339	−	0.412952i
$663$	8.59999e23	−	1.66260e23i	0.894608	−	0.172951i
$664$	−1.95193e23	−	7.40207e23i	−0.200464	−	0.760194i
$665$		−	5.84842e23i		−	0.593000i
$666$	−4.52629e23	+	6.91894e23i	−0.453118	+	0.692642i
$667$		−	3.75401e22i		−	0.0371045i
$668$	4.08023e23	−	1.11187e24i	0.398185	−	1.08506i
$669$	−9.53850e23	+	1.84404e23i	−0.919090	+	0.177684i
$670$	−2.04744e24	+	1.42960e24i	−1.94794	+	1.36012i
$671$	−2.85239e23			−0.267958
$672$	2.39539e23	−	2.33303e22i	0.222197	−	0.0216412i
$673$	3.76570e23			0.344919			0.172460	−	0.985017i	$-0.444829\pi$
$673$	3.76570e23			0.344919			0.172460	+	0.985017i	$0.444829\pi$
$674$	−5.10672e23	+	3.56571e23i	−0.461884	+	0.322505i
$675$	1.41716e24	+	2.19687e24i	1.26572	+	1.96211i
$676$	−1.11041e22	+	3.02589e22i	−0.00979342	+	0.0266874i
$677$			4.44733e23i			0.387343i	0.981066	+	0.193672i	$0.0620396\pi$
$677$			4.44733e23i			0.387343i	−0.981066	+	0.193672i	$0.937960\pi$
$678$	7.83884e23	−	8.07945e23i	0.674216	−	0.694911i
$679$			1.39750e23i			0.118702i
$680$	5.13152e23	+	1.94596e24i	0.430447	+	1.63233i
$681$	−9.75450e21	−	5.04563e22i	−0.00808080	−	0.0417989i
$682$	−5.84271e23	−	8.36779e23i	−0.478021	−	0.684610i
$683$	9.17663e23			0.741493			0.370746	−	0.928734i	$-0.379102\pi$
$683$	9.17663e23			0.741493			0.370746	+	0.928734i	$0.379102\pi$
$684$	−1.82180e24	+	5.50870e22i	−1.45387	+	0.0439615i
$685$	−6.75935e23			−0.532765
$686$	3.20172e23	+	4.58542e23i	0.249246	+	0.356964i
$687$	−1.30574e23	−	6.75409e23i	−0.100398	−	0.519320i
$688$	1.84978e23	−	2.18095e23i	0.140481	−	0.165632i
$689$		−	1.32422e24i		−	0.993341i
$690$	−7.93442e22	+	8.17797e22i	−0.0587893	+	0.0605938i
$691$			1.35725e24i			0.993338i	0.867940	+	0.496669i	$0.165444\pi$
$691$			1.35725e24i			0.993338i	−0.867940	+	0.496669i	$0.834556\pi$
$692$	3.22159e23	+	1.18222e23i	0.232900	+	0.0854669i
$693$	6.89099e22	+	1.71561e23i	0.0492095	+	0.122514i
$694$	−1.97180e24	+	1.37678e24i	−1.39093	+	0.971203i
$695$	−2.20669e24			−1.53769
$696$	5.05879e23	+	1.05046e24i	0.348231	+	0.723105i
$697$	−3.55080e23			−0.241461
$698$	1.21845e24	−	8.50771e23i	0.818536	−	0.571533i
$699$	2.09118e23	−	4.04278e22i	0.138783	−	0.0268302i
$700$	7.46382e23	+	2.73899e23i	0.489359	+	0.179579i
$701$		−	1.88752e24i		−	1.22261i	−0.791396	−	0.611304i	$-0.790645\pi$
$701$		−	1.88752e24i		−	1.22261i	0.791396	−	0.611304i	$-0.209355\pi$
$702$	−1.42560e24	−	5.83242e23i	−0.912287	−	0.373236i
$703$		−	1.90419e24i		−	1.20390i
$704$	−8.23659e23	+	4.66865e23i	−0.514494	+	0.291624i
$705$	−3.67845e23	+	7.11139e22i	−0.227017	+	0.0438881i
$706$	8.10214e23	+	1.16037e24i	0.494037	+	0.707548i
$707$	−3.87949e23			−0.233727
$708$	−3.10074e24	−	5.02754e23i	−1.84579	−	0.299277i
$709$	−1.63581e24			−0.962144			−0.481072	−	0.876681i	$-0.659753\pi$
$709$	−1.63581e24			−0.962144			−0.481072	+	0.876681i	$0.659753\pi$
$710$	1.26681e24	+	1.81430e24i	0.736234	+	1.05442i
$711$	−7.79884e23	−	1.94164e24i	−0.447856	−	1.11500i
$712$	2.11874e24	−	5.58714e23i	1.20226	−	0.317037i
$713$			1.16411e23i			0.0652730i
$714$	−2.67323e23	−	2.59362e23i	−0.148116	−	0.143705i
$715$			1.94429e24i			1.06453i
$716$	−2.25211e23	+	6.13707e23i	−0.121851	+	0.332048i
$717$	−2.54465e22	−	1.31625e23i	−0.0136055	−	0.0703763i
$718$	2.71182e24	−	1.89349e24i	1.43286	−	1.00048i
$719$	−1.78215e24			−0.930568			−0.465284	−	0.885161i	$-0.654048\pi$
$719$	−1.78215e24			−0.930568			−0.465284	+	0.885161i	$0.654048\pi$
$720$	1.11820e24	−	3.35760e24i	0.577024	−	1.73262i
$721$	2.89366e23			0.147570
$722$	1.81496e24	−	1.26727e24i	0.914745	−	0.638710i
$723$	−3.44932e23	−	1.78420e24i	−0.171814	−	0.888727i
$724$	−4.65093e23	+	1.26739e24i	−0.228961	+	0.623926i
$725$			3.85158e24i			1.87398i
$726$	9.70495e23	+	9.41593e23i	0.466694	+	0.452796i
$727$			7.43311e23i			0.353287i	0.984275	+	0.176644i	$0.0565240\pi$
$727$			7.43311e23i			0.353287i	−0.984275	+	0.176644i	$0.943476\pi$
$728$	−4.52943e23	+	1.19442e23i	−0.212778	+	0.0561099i
$729$	−8.87970e23	+	1.96212e24i	−0.412301	+	0.911048i
$730$	−1.02578e24	−	1.46910e24i	−0.470773	−	0.674230i
$731$	−4.42577e23			−0.200766
$732$	−9.97466e23	−	1.61729e23i	−0.447254	−	0.0725178i
$733$	4.02405e24			1.78353			0.891763	−	0.452502i	$-0.149468\pi$
$733$	4.02405e24			1.78353			0.891763	+	0.452502i	$0.149468\pi$
$734$	−1.85740e24	−	2.66012e24i	−0.813744	−	1.16543i
$735$	3.93382e24	−	7.60508e23i	1.70362	−	0.329353i
$736$	1.07517e23	+	1.01234e22i	0.0460275	+	0.00433377i
$737$			1.81810e24i			0.769384i
$738$	5.22523e23	+	3.41828e23i	0.218588	+	0.142998i
$739$			2.51369e24i			1.03952i	0.854311	+	0.519762i	$0.173979\pi$
$739$			2.51369e24i			1.03952i	−0.854311	+	0.519762i	$0.826021\pi$
$740$	3.47093e24	+	1.27372e24i	1.41898	+	0.520721i
$741$	3.48296e24	−	6.73344e23i	1.40765	−	0.272134i
$742$	−4.61687e23	+	3.22368e23i	−0.184465	+	0.128801i
$743$	−1.17939e24			−0.465855			−0.232928	−	0.972494i	$-0.574830\pi$
$743$	−1.17939e24			−0.465855			−0.232928	+	0.972494i	$0.574830\pi$
$744$	−1.56872e24	−	3.25746e24i	−0.612597	−	1.27206i
$745$	−1.84963e24			−0.714097
$746$	−9.20540e22	+	6.42756e22i	−0.0351368	+	0.0245339i
$747$	1.93317e24	−	7.76482e23i	0.729532	−	0.293026i
$748$	1.37553e24	+	5.04777e23i	0.513224	+	0.188337i
$749$			7.28751e23i			0.268834i
$750$	4.65418e24	−	4.79704e24i	1.69755	−	1.74966i
$751$			1.40610e24i			0.507080i	0.967325	+	0.253540i	$0.0815949\pi$
$751$			1.40610e24i			0.507080i	−0.967325	+	0.253540i	$0.918405\pi$
$752$	2.70801e23	+	2.29681e23i	0.0965602	+	0.0818980i
$753$	5.87183e23	+	3.03727e24i	0.207022	+	1.07084i
$754$	−1.29914e24	−	1.86060e24i	−0.452897	−	0.648628i
$755$	−5.03034e24			−1.73400
$756$	1.43700e23	+	6.39014e23i	0.0489803	+	0.217809i
$757$	9.91450e23			0.334161			0.167081	−	0.985943i	$-0.446566\pi$
$757$	9.91450e23			0.334161			0.167081	+	0.985943i	$0.446566\pi$
$758$	1.09725e24	+	1.57145e24i	0.365692	+	0.523735i
$759$	1.57467e22	+	8.14515e22i	0.00518959	+	0.0268438i
$760$	2.07824e24	+	7.88105e24i	0.677299	+	2.56844i
$761$		−	4.07833e24i		−	1.31436i	−0.753736	−	0.657178i	$-0.771750\pi$
$761$		−	4.07833e24i		−	1.31436i	0.753736	−	0.657178i	$-0.228250\pi$
$762$	−9.00356e23	+	9.27992e23i	−0.286944	+	0.295752i
$763$		−	3.51115e23i		−	0.110660i
$764$	8.72398e23	−	2.37731e24i	0.271908	−	0.740956i
$765$	−5.08218e24	+	2.04133e24i	−1.56649	+	0.629202i
$766$	7.30414e23	−	5.10003e23i	0.222651	−	0.155464i
$767$	6.11386e24			1.84313
$768$	−3.14501e24	+	1.16559e24i	−0.937674	+	0.347517i
$769$	−3.15157e24			−0.929295			−0.464648	−	0.885496i	$-0.653819\pi$
$769$	−3.15157e24			−0.929295			−0.464648	+	0.885496i	$0.653819\pi$
$770$	6.77870e23	−	4.73315e23i	0.197686	−	0.138032i
$771$	−5.16508e24	+	9.98543e23i	−1.48976	+	0.288008i
$772$	2.63353e23	−	7.17646e23i	0.0751263	−	0.204721i
$773$			2.76268e24i			0.779479i	0.920925	+	0.389739i	$0.127435\pi$
$773$			2.76268e24i			0.779479i	−0.920925	+	0.389739i	$0.872565\pi$
$774$	6.51279e23	+	4.26060e23i	0.181748	+	0.118897i
$775$		−	1.19437e25i		−	3.29665i
$776$	−4.96604e23	−	1.88321e24i	−0.135577	−	0.514130i
$777$	−6.71840e23	+	1.29884e23i	−0.181421	+	0.0350733i
$778$	−6.27469e23	−	8.98646e23i	−0.167597	−	0.240028i
$779$	−1.43806e24			−0.379934
$780$	−1.10240e24	+	6.79908e24i	−0.288096	+	1.77683i
$781$	1.61107e24			0.416467
$782$	−9.56807e22	−	1.37032e23i	−0.0244662	−	0.0350399i
$783$	−2.66634e24	+	1.72001e24i	−0.674436	+	0.435066i
$784$	−2.89600e24	−	2.45626e24i	−0.724624	−	0.614593i
$785$		−	1.12312e25i		−	2.77993i
$786$	−1.65991e24	−	1.61048e24i	−0.406436	−	0.394332i
$787$			6.26674e24i			1.51795i	0.651122	+	0.758973i	$0.274298\pi$
$787$			6.26674e24i			1.51795i	−0.651122	+	0.758973i	$0.725702\pi$
$788$	2.38562e24	+	8.75449e23i	0.571648	+	0.209777i
$789$	−1.53188e24	−	7.92385e24i	−0.363137	−	1.87837i
$790$	−7.67175e24	+	5.35671e24i	−1.79914	+	1.25623i
$791$	9.31679e23			0.216156
$792$	−1.53824e24	−	2.06701e24i	−0.353070	−	0.474437i
$793$	1.96675e24			0.446608
$794$	1.32307e23	−	9.23819e22i	0.0297241	−	0.0207545i
$795$	1.57161e24	+	8.12937e24i	0.349322	+	1.80691i
$796$	4.29435e23	+	1.57589e23i	0.0944356	+	0.0346549i
$797$			2.22436e24i			0.483959i	0.970281	+	0.241980i	$0.0777967\pi$
$797$			2.22436e24i			0.483959i	−0.970281	+	0.241980i	$0.922203\pi$
$798$	−1.08265e24	−	1.05040e24i	−0.233057	−	0.226116i
$799$		−	5.49532e23i		−	0.117043i
$800$	−1.10312e25	−	1.03865e24i	−2.32465	−	0.218880i
$801$	2.22257e24	+	5.53342e24i	0.463425	+	1.15376i
$802$	−4.17342e24	−	5.97708e24i	−0.861014	−	1.23312i
$803$	−1.30454e24			−0.266303
$804$	−1.03085e24	+	6.35780e24i	−0.208219	+	1.28419i
$805$	−9.43040e22			−0.0188480
$806$	4.02861e24	+	5.76967e24i	0.796722	+	1.14105i
$807$	6.21010e24	−	1.20057e24i	1.21527	−	0.234943i
$808$	5.22781e24	−	1.37858e24i	1.01233	−	0.266953i
$809$			3.30856e24i			0.633981i	0.948429	+	0.316990i	$0.102672\pi$
$809$			3.30856e24i			0.633981i	−0.948429	+	0.316990i	$0.897328\pi$
$810$	9.44389e24	+	1.88858e24i	1.79072	+	0.358106i
$811$			3.48520e23i			0.0653959i	0.999465	+	0.0326980i	$0.0104099\pi$
$811$			3.48520e23i			0.0653959i	−0.999465	+	0.0326980i	$0.989590\pi$
$812$	−3.32431e23	+	9.05883e23i	−0.0617270	+	0.168208i
$813$	4.07589e24	−	7.87974e23i	0.748950	−	0.144791i
$814$	2.20708e24	−	1.54107e24i	0.401339	−	0.280230i
$815$	9.40300e24			1.69210
$816$	4.52396e24	+	2.54510e24i	0.805662	+	0.453251i
$817$	−1.79242e24			−0.315901
$818$	−6.73178e24	+	4.70039e24i	−1.17416	+	0.819843i
$819$	−4.75141e23	−	1.18293e24i	−0.0820180	−	0.204196i
$820$	9.61923e23	−	2.62127e24i	0.164332	−	0.447810i
$821$		−	2.25687e24i		−	0.381584i	−0.981630	−	0.190792i	$-0.938894\pi$
$821$		−	2.25687e24i		−	0.381584i	0.981630	−	0.190792i	$-0.0611057\pi$
$822$	−1.21401e24	+	1.25128e24i	−0.203148	+	0.209384i
$823$			7.30638e24i			1.21005i	0.796206	+	0.605026i	$0.206837\pi$
$823$			7.30638e24i			1.21005i	−0.796206	+	0.605026i	$0.793163\pi$
$824$	−3.89935e24	+	1.02826e24i	−0.639162	+	0.168548i
$825$	−1.61559e24	−	8.35685e24i	−0.262104	−	1.35576i
$826$	−1.48835e24	−	2.13158e24i	−0.238987	−	0.342272i
$827$	9.22192e24			1.46563			0.732815	−	0.680428i	$-0.238206\pi$
$827$	9.22192e24			1.46563			0.732815	+	0.680428i	$0.238206\pi$
$828$	8.88261e21	+	2.93761e23i	0.00139728	+	0.0462100i
$829$	−8.25868e24			−1.28587			−0.642935	−	0.765921i	$-0.722283\pi$
$829$	−8.25868e24			−1.28587			−0.642935	+	0.765921i	$0.722283\pi$
$830$	−5.33334e24	−	7.63828e24i	−0.821932	−	1.17715i
$831$	−1.59999e24	−	8.27615e24i	−0.244067	−	1.26247i
$832$	5.67921e24	−	3.21908e24i	0.857511	−	0.486053i
$833$			5.87682e24i			0.878334i
$834$	−3.96332e24	+	4.08497e24i	−0.586337	+	0.604334i
$835$		−	1.44135e25i		−	2.11073i
$836$	5.57084e24	+	2.04432e24i	0.807546	+	0.296344i
$837$	8.26827e24	−	5.33370e24i	1.18645	−	0.765353i
$838$	6.50682e24	−	4.54331e24i	0.924261	−	0.645354i
$839$	−5.44200e24			−0.765212			−0.382606	−	0.923912i	$-0.624973\pi$
$839$	−5.44200e24			−0.765212			−0.382606	+	0.923912i	$0.624973\pi$
$840$	2.63885e24	−	1.27081e24i	0.367316	−	0.176891i
$841$	2.58248e24			0.355854
$842$	−4.86461e24	+	3.39666e24i	−0.663583	+	0.463339i
$843$	−1.80129e24	+	3.48236e23i	−0.243248	+	0.0470261i
$844$	−7.76257e24	−	2.84862e24i	−1.03775	−	0.380823i
$845$			3.92252e23i			0.0519138i
$846$	−5.29024e23	+	8.08671e23i	−0.0693150	+	0.105956i
$847$			1.11912e24i			0.145167i
$848$	5.07594e24	−	5.98468e24i	0.651856	−	0.768558i
$849$	1.31911e24	−	2.55017e23i	0.167712	−	0.0324231i
$850$	9.81674e24	+	1.40593e25i	1.23568	+	1.76971i
$851$	−3.07045e23			−0.0382649
$852$	5.63384e24	+	9.13471e23i	0.695132	+	0.112709i
$853$	6.94695e24			0.848648			0.424324	−	0.905511i	$-0.360512\pi$
$853$	6.94695e24			0.848648			0.424324	+	0.905511i	$0.360512\pi$
$854$	−4.78783e23	−	6.85701e23i	−0.0579091	−	0.0829359i
$855$	−2.05826e25	+	8.26727e24i	−2.46484	+	0.990035i
$856$	−2.58962e24	−	9.82029e24i	−0.307050	−	1.16439i
$857$			9.95474e24i			1.16867i	0.811512	+	0.584336i	$0.198645\pi$
$857$			9.95474e24i			1.16867i	−0.811512	+	0.584336i	$0.801355\pi$
$858$	3.59922e24	+	3.49203e24i	0.418376	+	0.405916i
$859$			1.27691e25i			1.46967i	0.678245	+	0.734835i	$0.262741\pi$
$859$			1.27691e25i			1.46967i	−0.678245	+	0.734835i	$0.737259\pi$
$860$	1.19895e24	−	3.26719e24i	0.136636	−	0.372338i
$861$	9.80891e22	+	5.07378e23i	0.0110686	+	0.0572538i
$862$	−9.94401e24	+	6.94329e24i	−1.11109	+	0.775806i
$863$	−1.83011e24			−0.202482			−0.101241	−	0.994862i	$-0.532281\pi$
$863$	−1.83011e24			−0.202482			−0.101241	+	0.994862i	$0.532281\pi$
$864$	−4.20718e24	−	8.10041e24i	−0.460918	−	0.887443i
$865$	4.17622e24			0.453050
$866$	2.89996e24	−	2.02486e24i	0.311523	−	0.217517i
$867$	2.59576e23	+	1.34269e24i	0.0276123	+	0.142828i
$868$	1.03086e24	−	2.80912e24i	0.108588	−	0.295906i
$869$			6.81241e24i			0.710612i
$870$	1.01836e25	+	9.88030e24i	1.05193	+	1.02060i
$871$		−	1.25359e25i		−	1.28234i
$872$	1.24769e24	+	4.73146e24i	0.126391	+	0.479297i
$873$	4.91829e24	−	1.97550e24i	0.493393	−	0.198178i
$874$	−3.87502e23	−	5.54972e23i	−0.0384970	−	0.0551345i
$875$	5.53169e24			0.544239
$876$	−4.56193e24	−	7.39672e23i	−0.444492	−	0.0720700i
$877$	−3.12268e24			−0.301322			−0.150661	−	0.988586i	$-0.548140\pi$
$877$	−3.12268e24			−0.301322			−0.150661	+	0.988586i	$0.548140\pi$
$878$	−6.43178e24	−	9.21143e24i	−0.614650	−	0.880286i
$879$	3.05672e24	−	5.90942e23i	0.289301	−	0.0559293i
$880$	−7.45272e24	+	8.78698e24i	−0.698574	+	0.823639i
$881$		−	2.07098e24i		−	0.192257i	−0.995369	−	0.0961284i	$-0.969354\pi$
$881$		−	2.07098e24i		−	0.192257i	0.995369	−	0.0961284i	$-0.0306459\pi$
$882$	5.65750e24	−	8.64811e24i	0.520165	−	0.795130i
$883$		−	4.19315e24i		−	0.381834i	−0.981606	−	0.190917i	$-0.938854\pi$
$883$		−	4.19315e24i		−	0.381834i	0.981606	−	0.190917i	$-0.0611462\pi$
$884$	−9.48442e24	−	3.48049e24i	−0.855395	−	0.313903i
$885$	−3.75328e25	+	7.25604e24i	−3.35269	+	0.648160i
$886$	−1.61095e24	+	1.12482e24i	−0.142526	+	0.0995172i
$887$	−1.38302e25			−1.21193			−0.605967	−	0.795490i	$-0.707214\pi$
$887$	−1.38302e25			−1.21193			−0.605967	+	0.795490i	$0.707214\pi$
$888$	8.59185e24	−	4.13764e24i	0.745721	−	0.359122i
$889$	−1.07011e24			−0.0919950
$890$	2.18635e25	−	1.52660e25i	1.86168	−	1.29990i
$891$	5.06373e24	−	4.85036e24i	0.427081	−	0.409085i
$892$	1.05194e25	+	3.86031e24i	0.878803	+	0.322493i
$893$		−	2.22558e24i		−	0.184164i
$894$	−3.32203e24	+	3.42400e24i	−0.272292	+	0.280650i
$895$			7.95562e24i			0.645919i
$896$	−2.50486e24	−	1.19639e24i	−0.201449	−	0.0962179i
$897$	−1.08575e23	−	5.61616e23i	−0.00864954	−	0.0447408i
$898$	9.12689e24	+	1.30713e25i	0.720235	+	1.03150i
$899$	1.44960e25			1.13316
$900$	−9.11347e23	−	3.01395e25i	−0.0705704	−	2.33386i
$901$	−1.21446e25			−0.931588
$902$	−1.16383e24	−	1.66680e24i	−0.0884366	−	0.126657i
$903$	1.22260e23	+	6.32402e23i	0.00920316	+	0.0476045i
$904$	−1.25549e25	+	3.31073e24i	−0.936225	+	0.246884i
$905$			1.64295e25i			1.21370i
$906$	−9.03473e24	+	9.31205e24i	−0.661189	+	0.681484i
$907$		−	3.96575e24i		−	0.287517i	−0.989613	−	0.143759i	$-0.954081\pi$
$907$		−	3.96575e24i		−	0.287517i	0.989613	−	0.143759i	$-0.0459189\pi$
$908$	−2.04201e23	+	5.56453e23i	−0.0146666	+	0.0399668i
$909$	5.48401e24	+	1.36532e25i	0.390216	+	0.971500i
$910$	−4.67398e24	+	3.26355e24i	−0.329484	+	0.230059i
$911$	6.27827e23			0.0438464			0.0219232	−	0.999760i	$-0.493021\pi$
$911$	6.27827e23			0.0438464			0.0219232	+	0.999760i	$0.493021\pi$
$912$	1.83218e25	+	1.03076e25i	1.26769	+	0.713181i
$913$	−6.78269e24			−0.464944
$914$	−1.07896e25	+	7.53374e24i	−0.732765	+	0.511644i
$915$	−1.20738e25	+	2.33417e24i	−0.812390	+	0.157056i
$916$	−2.73344e24	+	7.44869e24i	−0.182221	+	0.496556i
$917$		−	1.91412e24i		−	0.126424i
$918$	−5.34899e24	+	1.30743e25i	−0.350033	+	0.855573i
$919$			1.54073e25i			0.998955i	0.866327	+	0.499477i	$0.166475\pi$
$919$			1.54073e25i			0.998955i	−0.866327	+	0.499477i	$0.833525\pi$
$920$	1.27080e24	−	3.35110e23i	0.0816355	−	0.0215274i
$921$	2.12003e25	−	4.09856e24i	1.34938	−	0.260870i
$922$	−7.58022e23	−	1.08562e24i	−0.0478046	−	0.0684645i
$923$	−1.11085e25			−0.694129
$924$	3.41298e23	−	2.10495e24i	0.0211311	−	0.130326i
$925$	3.15025e25			1.93259
$926$	−1.60757e25	−	2.30233e25i	−0.977186	−	1.39950i
$927$	−4.09045e24	−	1.01838e25i	−0.246373	−	0.613382i
$928$	1.26061e24	−	1.33885e25i	0.0752357	−	0.799053i
$929$		−	1.78683e25i		−	1.05670i	−0.849028	−	0.528348i	$-0.822812\pi$
$929$		−	1.78683e25i		−	1.05670i	0.849028	−	0.528348i	$-0.177188\pi$
$930$	−3.15790e25	−	3.06386e25i	−1.85052	−	1.79541i
$931$			2.38009e25i			1.38204i
$932$	−2.30624e24	−	8.46317e23i	−0.132699	−	0.0486965i
$933$	−1.34691e24	−	6.96706e24i	−0.0767971	−	0.397242i
$934$	2.20845e25	−	1.54202e25i	1.24778	−	0.871250i
$935$	1.78313e25			0.998353
$936$	1.06063e25	+	1.42522e25i	0.588465	+	0.790748i
$937$	−2.08377e24			−0.114568			−0.0572839	−	0.998358i	$-0.518244\pi$
$937$	−2.08377e24			−0.114568			−0.0572839	+	0.998358i	$0.518244\pi$
$938$	−4.37062e24	+	3.05174e24i	−0.238133	+	0.166273i
$939$	−4.92906e24	−	2.54962e25i	−0.266138	−	1.37663i
$940$	4.05675e24	+	1.48870e24i	0.217066	+	0.0796564i
$941$		−	3.72429e25i		−	1.97484i	−0.158119	−	0.987420i	$-0.550543\pi$
$941$		−	3.72429e25i		−	1.97484i	0.158119	−	0.987420i	$-0.449457\pi$
$942$	−2.07909e25	−	2.01718e25i	−1.09255	−	1.06001i
$943$			2.31882e23i			0.0120759i
$944$	2.76309e25	+	2.34353e25i	1.42604	+	1.20951i
$945$	4.32080e24	+	6.69808e24i	0.221001	+	0.342594i
$946$	−1.45061e24	−	2.07753e24i	−0.0735318	−	0.105311i
$947$	−1.08697e25			−0.546063			−0.273032	−	0.962005i	$-0.588026\pi$
$947$	−1.08697e25			−0.546063			−0.273032	+	0.962005i	$0.588026\pi$
$948$	−3.86261e24	+	2.38227e25i	−0.192314	+	1.18610i
$949$	8.99496e24			0.443850
$950$	3.97574e25	+	5.69395e25i	1.94432	+	2.78460i
$951$	3.34284e25	−	6.46257e24i	1.62025	−	0.313236i
$952$	1.09541e24	+	4.15400e24i	0.0526217	+	0.199550i
$953$			2.48995e25i			1.18550i	0.805387	+	0.592749i	$0.201957\pi$
$953$			2.48995e25i			1.18550i	−0.805387	+	0.592749i	$0.798043\pi$
$954$	1.78716e25	+	1.16914e25i	0.843339	+	0.551703i
$955$		−	3.08176e25i		−	1.44135i
$956$	−5.32698e23	+	1.45162e24i	−0.0246939	+	0.0672915i
$957$	1.01427e25	−	1.96084e24i	0.466018	−	0.0900931i
$958$	2.36764e25	−	1.65318e25i	1.07823	−	0.752858i
$959$	−1.44291e24			−0.0651298
$960$	−3.10440e25	+	2.65020e25i	−1.38890	+	1.18570i
$961$	−2.24018e25			−0.993421
$962$	−1.52180e25	+	1.06258e25i	−0.668915	+	0.467062i
$963$	2.56472e25	−	1.03016e25i	1.11742	−	0.448827i
$964$	−7.22081e24	+	1.96769e25i	−0.311840	+	0.849772i
$965$		−	9.30299e24i		−	0.398236i
$966$	−1.69375e23	+	1.74573e23i	−0.00718692	+	0.00740752i
$967$			1.87690e25i			0.789436i	0.918802	+	0.394718i	$0.129158\pi$
$967$			1.87690e25i			0.789436i	−0.918802	+	0.394718i	$0.870842\pi$
$968$	−3.97682e24	−	1.50808e25i	−0.165804	−	0.628758i
$969$	−6.17533e24	−	3.19426e25i	−0.255216	−	1.32014i
$970$	−1.35689e25	−	1.94330e25i	−0.555885	−	0.796125i
$971$	−1.35284e25			−0.549392			−0.274696	−	0.961531i	$-0.588577\pi$
$971$	−1.35284e25			−0.549392			−0.274696	+	0.961531i	$0.588577\pi$
$972$	2.04578e25	−	1.40903e25i	0.823560	−	0.567229i
$973$	−4.71057e24			−0.187981
$974$	1.08639e25	+	1.55590e25i	0.429769	+	0.615505i
$975$	1.11397e25	+	5.76213e25i	0.436850	+	2.25966i
$976$	8.88849e24	+	7.53882e24i	0.345545	+	0.293076i
$977$		−	1.85343e25i		−	0.714288i	−0.934049	−	0.357144i	$-0.883750\pi$
$977$		−	1.85343e25i		−	0.714288i	0.934049	−	0.357144i	$-0.116250\pi$
$978$	1.68882e25	−	1.74066e25i	0.645215	−	0.665020i
$979$		−	1.94145e25i		−	0.735315i
$980$	−4.33838e25	−	1.59205e25i	−1.62894	−	0.597771i
$981$	−1.23569e25	+	4.96333e24i	−0.459965	+	0.184751i
$982$	4.76104e24	−	3.32434e24i	0.175693	−	0.122676i
$983$	7.57231e23			0.0277028			0.0138514	−	0.999904i	$-0.495591\pi$
$983$	7.57231e23			0.0277028			0.0138514	+	0.999904i	$0.495591\pi$
$984$	−3.12477e24	−	6.48862e24i	−0.113334	−	0.235339i
$985$	3.09253e25			1.11200
$986$	−1.70638e25	+	1.19146e25i	−0.608305	+	0.424742i
$987$	−7.85232e23	+	1.51805e23i	−0.0277525	+	0.00536527i
$988$	−3.84115e25	−	1.40958e25i	−1.34594	−	0.493919i
$989$			2.89022e23i			0.0100406i
$990$	−2.62399e25	−	1.71658e25i	−0.903780	−	0.591243i
$991$			2.53701e25i			0.866355i	0.901309	+	0.433177i	$0.142608\pi$
$991$			2.53701e25i			0.866355i	−0.901309	+	0.433177i	$0.857392\pi$
$992$	−3.90913e24	+	4.15176e25i	−0.132352	+	1.40567i
$993$	−1.47311e25	+	2.84789e24i	−0.494499	+	0.0955993i
$994$	2.70424e24	+	3.87294e24i	0.0900037	+	0.128901i
$995$	5.56685e24			0.183702
$996$	−2.37188e25	−	3.84576e24i	−0.776046	−	0.125828i
$997$	−1.38575e25			−0.449548			−0.224774	−	0.974411i	$-0.572164\pi$
$997$	−1.38575e25			−0.449548			−0.224774	+	0.974411i	$0.572164\pi$
$998$	−2.02133e24	−	2.89490e24i	−0.0650172	−	0.0931161i
$999$	1.40681e25	+	2.18083e25i	0.448673	+	0.695530i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.18.b.a.11.6	yes	32
3.2	odd	2	inner	12.18.b.a.11.27	yes	32
4.3	odd	2	inner	12.18.b.a.11.28	yes	32
12.11	even	2	inner	12.18.b.a.11.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.18.b.a.11.5	✓	32	12.11	even	2	inner
12.18.b.a.11.6	yes	32	1.1	even	1	trivial
12.18.b.a.11.27	yes	32	3.2	odd	2	inner
12.18.b.a.11.28	yes	32	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-296.839 + 207.264i) q^{2} +(2157.01 + 11157.4i) q^{3} +(45154.9 - 123048. i) q^{4} -1.59510e6i q^{5} +(-2.95282e6 - 2.86488e6i) q^{6} -3.40503e6i q^{7} +(1.20998e7 + 4.58846e7i) q^{8} +(-1.19835e8 + 4.81332e7i) q^{9} +O(q^{10})\)	\(q+(-296.839 + 207.264i) q^{2} +(2157.01 + 11157.4i) q^{3} +(45154.9 - 123048. i) q^{4} -1.59510e6i q^{5} +(-2.95282e6 - 2.86488e6i) q^{6} -3.40503e6i q^{7} +(1.20998e7 + 4.58846e7i) q^{8} +(-1.19835e8 + 4.81332e7i) q^{9} +(3.30608e8 + 4.73489e8i) q^{10} +4.20451e8 q^{11} +(1.47030e9 + 2.38395e8i) q^{12} -2.89905e9 q^{13} +(7.05742e8 + 1.01075e9i) q^{14} +(1.77972e10 - 3.44065e9i) q^{15} +(-1.31019e10 - 1.11125e10i) q^{16} +2.65876e10i q^{17} +(2.55953e10 - 3.91253e10i) q^{18} +1.07679e11i q^{19} +(-1.96275e11 - 7.20267e10i) q^{20} +(3.79913e10 - 7.34469e9i) q^{21} +(-1.24806e11 + 8.71446e10i) q^{22} +1.73628e10 q^{23} +(-4.85853e11 + 2.33976e11i) q^{24} -1.78141e12 q^{25} +(8.60552e11 - 6.00871e11i) q^{26} +(-7.95526e11 - 1.23322e12i) q^{27} +(-4.18984e11 - 1.53754e11i) q^{28} -2.16210e12i q^{29} +(-4.56977e12 + 4.71004e12i) q^{30} +6.70462e12i q^{31} +(6.19239e12 + 5.83051e11i) q^{32} +(9.06918e11 + 4.69114e12i) q^{33} +(-5.51066e12 - 7.89223e12i) q^{34} -5.43137e12 q^{35} +(5.11587e11 + 1.69189e13i) q^{36} -1.76840e13 q^{37} +(-2.23179e13 - 3.19632e13i) q^{38} +(-6.25329e12 - 3.23459e13i) q^{39} +(7.31906e13 - 1.93004e13i) q^{40} +1.33551e13i q^{41} +(-9.75501e12 + 1.00544e13i) q^{42} +1.66460e13i q^{43} +(1.89854e13 - 5.17359e13i) q^{44} +(7.67774e13 + 1.91149e14i) q^{45} +(-5.15397e12 + 3.59870e12i) q^{46} -2.06687e13 q^{47} +(9.57253e13 - 1.70153e14i) q^{48} +2.21036e14 q^{49} +(5.28792e14 - 3.69223e14i) q^{50} +(-2.96648e14 + 5.73497e13i) q^{51} +(-1.30906e14 + 3.56724e14i) q^{52} +4.56778e14i q^{53} +(4.91746e14 + 2.01184e14i) q^{54} -6.70663e14i q^{55} +(1.56238e14 - 4.12002e13i) q^{56} +(-1.20141e15 + 2.32264e14i) q^{57} +(4.48126e14 + 6.41795e14i) q^{58} -2.10892e15 q^{59} +(3.80264e14 - 2.34528e15i) q^{60} -6.78410e14 q^{61} +(-1.38963e15 - 1.99019e15i) q^{62} +(1.63895e14 + 4.08041e14i) q^{63} +(-1.95899e15 + 1.11039e15i) q^{64} +4.62428e15i q^{65} +(-1.24152e15 - 1.20454e15i) q^{66} +4.32415e15i q^{67} +(3.27156e15 + 1.20056e15i) q^{68} +(3.74518e13 + 1.93724e14i) q^{69} +(1.61224e15 - 1.12573e15i) q^{70} +3.83176e15 q^{71} +(-3.65855e15 - 4.91617e15i) q^{72} -3.10272e15 q^{73} +(5.24932e15 - 3.66527e15i) q^{74} +(-3.84252e15 - 1.98759e16i) q^{75} +(1.32497e16 + 4.86221e15i) q^{76} -1.43165e15i q^{77} +(8.56037e15 + 8.30544e15i) q^{78} +1.62026e16i q^{79} +(-1.77255e16 + 2.08989e16i) q^{80} +(1.20436e16 - 1.15361e16i) q^{81} +(-2.76804e15 - 3.96432e15i) q^{82} -1.61319e16 q^{83} +(8.11741e14 - 5.00641e15i) q^{84} +4.24099e16 q^{85} +(-3.45012e15 - 4.94118e15i) q^{86} +(2.41234e16 - 4.66367e15i) q^{87} +(5.08738e15 + 1.92922e16i) q^{88} -4.61754e16i q^{89} +(-6.24088e16 - 4.08272e16i) q^{90} +9.87137e15i q^{91} +(7.84017e14 - 2.13647e15i) q^{92} +(-7.48060e16 + 1.44619e16i) q^{93} +(6.13529e15 - 4.28390e15i) q^{94} +1.71758e17 q^{95} +(6.85171e15 + 7.03486e16i) q^{96} -4.10423e16 q^{97} +(-6.56122e16 + 4.58130e16i) q^{98} +(-5.03847e16 + 2.02377e16i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 54808 q^{4} - 4960776 q^{6} + 79874976 q^{9}+O(q^{10}) \) 32 * q - 54808 * q^4 - 4960776 * q^6 + 79874976 * q^9	\( 32 q - 54808 q^{4} - 4960776 q^{6} + 79874976 q^{9} + 46839088 q^{10} + 2598308520 q^{12} + 221287360 q^{13} - 41721285088 q^{16} + 27568791600 q^{18} + 128365169856 q^{21} - 493958165040 q^{22} - 253565784288 q^{24} - 3063689463648 q^{25} - 2695436033040 q^{28} - 2169979068432 q^{30} - 17644793625600 q^{33} + 6944208632512 q^{34} - 12909384040056 q^{36} - 7970760699200 q^{37} + 21066454663744 q^{40} + 55835180334480 q^{42} + 154013263804416 q^{45} + 235918828815264 q^{46} + 299462725247520 q^{48} - 248591781347488 q^{49} + 544732086739120 q^{52} + 487051858173384 q^{54} - 21\!\cdots\!20 q^{57}+ \cdots + 90\!\cdots\!60 q^{97}+O(q^{100}) \) 32 * q - 54808 * q^4 - 4960776 * q^6 + 79874976 * q^9 + 46839088 * q^10 + 2598308520 * q^12 + 221287360 * q^13 - 41721285088 * q^16 + 27568791600 * q^18 + 128365169856 * q^21 - 493958165040 * q^22 - 253565784288 * q^24 - 3063689463648 * q^25 - 2695436033040 * q^28 - 2169979068432 * q^30 - 17644793625600 * q^33 + 6944208632512 * q^34 - 12909384040056 * q^36 - 7970760699200 * q^37 + 21066454663744 * q^40 + 55835180334480 * q^42 + 154013263804416 * q^45 + 235918828815264 * q^46 + 299462725247520 * q^48 - 248591781347488 * q^49 + 544732086739120 * q^52 + 487051858173384 * q^54 - 2151740586697920 * q^57 + 230877304263760 * q^58 - 345098683994304 * q^60 - 4956543779318336 * q^61 + 1003775054518400 * q^64 - 2371521654206832 * q^66 + 891375297976320 * q^69 - 949041839387232 * q^70 + 5817303713532480 * q^72 - 4887976236943040 * q^73 - 2051936325547056 * q^76 + 22261766802491280 * q^78 + 28021308982751520 * q^81 + 7596239161270240 * q^82 - 8356700998055568 * q^84 + 59910783041540096 * q^85 - 18469777603302720 * q^88 - 68814047068261392 * q^90 + 5961488029786560 * q^93 - 61915224567506112 * q^94 - 45410293501908864 * q^96 + 9062030716970560 * q^97

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