LMFDB - Embedded newform 12.18.b.a.11.4

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			11.4
Character	$\chi$	$=$	12.11
Dual form			12.18.b.a.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-347.385 + 101.959i) q^{2} +(-7870.26 - 8197.51i) q^{3} +(110281. - 70838.2i) q^{4} +134607. i q^{5} +(3.56982e6 + 2.04525e6i) q^{6} -2.80624e6i q^{7} +(-3.10872e7 + 3.58523e7i) q^{8} +(-5.25830e6 + 1.29033e8i) q^{9} +O(q^{10})$	\(q+(-347.385 + 101.959i) q^{2} +(-7870.26 - 8197.51i) q^{3} +(110281. - 70838.2i) q^{4} +134607. i q^{5} +(3.56982e6 + 2.04525e6i) q^{6} -2.80624e6i q^{7} +(-3.10872e7 + 3.58523e7i) q^{8} +(-5.25830e6 + 1.29033e8i) q^{9} +(-1.37244e7 - 4.67604e7i) q^{10} -5.54594e8 q^{11} +(-1.44863e9 - 3.46512e8i) q^{12} -2.35334e9 q^{13} +(2.86122e8 + 9.74846e8i) q^{14} +(1.10344e9 - 1.05939e9i) q^{15} +(7.14376e9 - 1.56242e10i) q^{16} +1.08615e10i q^{17} +(-1.13295e10 - 4.53603e10i) q^{18} +7.40293e10i q^{19} +(9.53532e9 + 1.48445e10i) q^{20} +(-2.30042e10 + 2.20858e10i) q^{21} +(1.92657e11 - 5.65459e10i) q^{22} +3.02161e11 q^{23} +(5.38564e11 - 2.73286e10i) q^{24} +7.44820e11 q^{25} +(8.17514e11 - 2.39945e11i) q^{26} +(1.09913e12 - 9.72418e11i) q^{27} +(-1.98789e11 - 3.09474e11i) q^{28} +6.09136e11i q^{29} +(-2.75305e11 + 4.80523e11i) q^{30} -8.07659e12i q^{31} +(-8.88607e11 + 6.15597e12i) q^{32} +(4.36479e12 + 4.54629e12i) q^{33} +(-1.10743e12 - 3.77311e12i) q^{34} +3.77740e11 q^{35} +(8.56058e12 + 1.46023e13i) q^{36} +8.88899e12 q^{37} +(-7.54797e12 - 2.57167e13i) q^{38} +(1.85214e13 + 1.92915e13i) q^{39} +(-4.82596e12 - 4.18456e12i) q^{40} -9.16942e13i q^{41} +(5.73946e12 - 1.00178e13i) q^{42} +1.20588e14i q^{43} +(-6.11609e13 + 3.92864e13i) q^{44} +(-1.73688e13 - 7.07803e11i) q^{45} +(-1.04966e14 + 3.08081e13i) q^{46} -1.60081e14 q^{47} +(-1.84303e14 + 6.44051e13i) q^{48} +2.24756e14 q^{49} +(-2.58739e14 + 7.59413e13i) q^{50} +(8.90371e13 - 8.54826e13i) q^{51} +(-2.59528e14 + 1.66706e14i) q^{52} -6.69502e14i q^{53} +(-2.82676e14 + 4.49870e14i) q^{54} -7.46522e13i q^{55} +(1.00610e14 + 8.72382e13i) q^{56} +(6.06856e14 - 5.82629e14i) q^{57} +(-6.21071e13 - 2.11605e14i) q^{58} +1.36222e15 q^{59} +(4.66429e13 - 1.94996e14i) q^{60} +2.81814e15 q^{61} +(8.23483e14 + 2.80569e15i) q^{62} +(3.62098e14 + 1.47560e13i) q^{63} +(-3.18970e14 - 2.22909e15i) q^{64} -3.16776e14i q^{65} +(-1.97980e15 - 1.13428e15i) q^{66} +2.11322e15i q^{67} +(7.69408e14 + 1.19781e15i) q^{68} +(-2.37808e15 - 2.47697e15i) q^{69} +(-1.31221e14 + 3.85140e13i) q^{70} +2.37596e15 q^{71} +(-4.46266e15 - 4.19980e15i) q^{72} +4.74029e15 q^{73} +(-3.08790e15 + 9.06315e14i) q^{74} +(-5.86193e15 - 6.10568e15i) q^{75} +(5.24410e15 + 8.16399e15i) q^{76} +1.55632e15i q^{77} +(-8.40100e15 - 4.81316e15i) q^{78} +7.86350e15i q^{79} +(2.10312e15 + 9.61600e14i) q^{80} +(-1.66219e16 - 1.35699e15i) q^{81} +(9.34908e15 + 3.18532e16i) q^{82} -1.36807e16 q^{83} +(-9.72396e14 + 4.06522e15i) q^{84} -1.46203e15 q^{85} +(-1.22951e16 - 4.18906e16i) q^{86} +(4.99340e15 - 4.79406e15i) q^{87} +(1.72408e16 - 1.98834e16i) q^{88} +1.78957e16i q^{89} +(6.10581e15 - 1.52502e15i) q^{90} +6.60403e15i q^{91} +(3.33225e16 - 2.14045e16i) q^{92} +(-6.62079e16 + 6.35648e16i) q^{93} +(5.56096e16 - 1.63217e16i) q^{94} -9.96486e15 q^{95} +(5.74572e16 - 4.11647e16i) q^{96} -2.02574e16 q^{97} +(-7.80767e16 + 2.29159e16i) q^{98} +(2.91622e15 - 7.15609e16i) 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 $

$2$	−347.385	+	101.959i	−0.959524	+	0.281625i
$2$	−347.385	+	101.959i	−0.959524	+	0.281625i
$3$	−7870.26	−	8197.51i	−0.692561	−	0.721359i
$3$	−7870.26	−	8197.51i	−0.692561	−	0.721359i
$4$	110281.	−	70838.2i	0.841374	−	0.540453i
$5$			134607.i			0.154107i	0.997027	+	0.0770535i	$0.0245512\pi$
$5$			134607.i			0.154107i	−0.997027	+	0.0770535i	$0.975449\pi$
$6$	3.56982e6	+	2.04525e6i	0.867682	+	0.497119i
$7$		−	2.80624e6i		−	0.183989i	−0.995760	−	0.0919944i	$-0.970676\pi$
$7$		−	2.80624e6i		−	0.183989i	0.995760	−	0.0919944i	$-0.0293242\pi$
$8$	−3.10872e7	+	3.58523e7i	−0.655114	+	0.755530i
$9$	−5.25830e6	+	1.29033e8i	−0.0407177	+	0.999171i
$10$	−1.37244e7	−	4.67604e7i	−0.0434005	−	0.147869i
$11$	−5.54594e8			−0.780076			−0.390038	−	0.920799i	$-0.627538\pi$
$11$	−5.54594e8			−0.780076			−0.390038	+	0.920799i	$0.627538\pi$
$12$	−1.44863e9	−	3.46512e8i	−0.972564	−	0.232636i
$13$	−2.35334e9			−0.800140			−0.400070	−	0.916485i	$-0.631014\pi$
$13$	−2.35334e9			−0.800140			−0.400070	+	0.916485i	$0.631014\pi$
$14$	2.86122e8	+	9.74846e8i	0.0518159	+	0.176542i
$15$	1.10344e9	−	1.05939e9i	0.111167	−	0.106729i
$16$	7.14376e9	−	1.56242e10i	0.415822	−	0.909446i
$17$			1.08615e10i			0.377636i	0.982012	+	0.188818i	$0.0604656\pi$
$17$			1.08615e10i			0.377636i	−0.982012	+	0.188818i	$0.939534\pi$
$18$	−1.13295e10	−	4.53603e10i	−0.242322	−	0.970196i
$19$			7.40293e10i			0.999995i	0.866027	+	0.499997i	$0.166666\pi$
$19$			7.40293e10i			0.999995i	−0.866027	+	0.499997i	$0.833334\pi$
$20$	9.53532e9	+	1.48445e10i	0.0832876	+	0.129662i
$21$	−2.30042e10	+	2.20858e10i	−0.132722	+	0.127424i
$22$	1.92657e11	−	5.65459e10i	0.748502	−	0.219689i
$23$	3.02161e11			0.804547			0.402273	−	0.915520i	$-0.368220\pi$
$23$	3.02161e11			0.804547			0.402273	+	0.915520i	$0.368220\pi$
$24$	5.38564e11	−	2.73286e10i	0.998715	−	0.0506783i
$25$	7.44820e11			0.976251
$26$	8.17514e11	−	2.39945e11i	0.767754	−	0.225340i
$27$	1.09913e12	−	9.72418e11i	0.748960	−	0.662615i
$28$	−1.98789e11	−	3.09474e11i	−0.0994373	−	0.154804i
$29$			6.09136e11i			0.226116i	0.993588	+	0.113058i	$0.0360646\pi$
$29$			6.09136e11i			0.226116i	−0.993588	+	0.113058i	$0.963935\pi$
$30$	−2.75305e11	+	4.80523e11i	−0.0766095	+	0.133716i
$31$		−	8.07659e12i		−	1.70080i	−0.526136	−	0.850401i	$-0.676360\pi$
$31$		−	8.07659e12i		−	1.70080i	0.526136	−	0.850401i	$-0.323640\pi$
$32$	−8.88607e11	+	6.15597e12i	−0.142868	+	0.989742i
$33$	4.36479e12	+	4.54629e12i	0.540251	+	0.562715i
$34$	−1.10743e12	−	3.77311e12i	−0.106352	−	0.362351i
$35$	3.77740e11			0.0283540
$36$	8.56058e12	+	1.46023e13i	0.505746	+	0.862683i
$37$	8.88899e12			0.416043			0.208021	−	0.978124i	$-0.433298\pi$
$37$	8.88899e12			0.416043			0.208021	+	0.978124i	$0.433298\pi$
$38$	−7.54797e12	−	2.57167e13i	−0.281624	−	0.959520i
$39$	1.85214e13	+	1.92915e13i	0.554146	+	0.577188i
$40$	−4.82596e12	−	4.18456e12i	−0.116433	−	0.100958i
$41$		−	9.16942e13i		−	1.79341i	−0.442630	−	0.896704i	$-0.645955\pi$
$41$		−	9.16942e13i		−	1.79341i	0.442630	−	0.896704i	$-0.354045\pi$
$42$	5.73946e12	−	1.00178e13i	0.0914644	−	0.159644i
$43$			1.20588e14i			1.57334i	0.617371	+	0.786672i	$0.288198\pi$
$43$			1.20588e14i			1.57334i	−0.617371	+	0.786672i	$0.711802\pi$
$44$	−6.11609e13	+	3.92864e13i	−0.656336	+	0.421594i
$45$	−1.73688e13	−	7.07803e11i	−0.153979	−	0.00627489i
$46$	−1.04966e14	+	3.08081e13i	−0.771982	+	0.226581i
$47$	−1.60081e14			−0.980634			−0.490317	−	0.871544i	$-0.663119\pi$
$47$	−1.60081e14			−0.980634			−0.490317	+	0.871544i	$0.663119\pi$
$48$	−1.84303e14	+	6.44051e13i	−0.944019	+	0.329890i
$49$	2.24756e14			0.966148
$50$	−2.58739e14	+	7.59413e13i	−0.936737	+	0.274937i
$51$	8.90371e13	−	8.54826e13i	0.272411	−	0.261536i
$52$	−2.59528e14	+	1.66706e14i	−0.673217	+	0.432438i
$53$		−	6.69502e14i		−	1.47709i	−0.674204	−	0.738545i	$-0.735513\pi$
$53$		−	6.69502e14i		−	1.47709i	0.674204	−	0.738545i	$-0.264487\pi$
$54$	−2.82676e14	+	4.49870e14i	−0.532037	+	0.846721i
$55$		−	7.46522e13i		−	0.120215i
$56$	1.00610e14	+	8.72382e13i	0.139009	+	0.120534i
$57$	6.06856e14	−	5.82629e14i	0.721355	−	0.692558i
$58$	−6.21071e13	−	2.11605e14i	−0.0636800	−	0.216964i
$59$	1.36222e15			1.20783			0.603915	−	0.797049i	$-0.293607\pi$
$59$	1.36222e15			1.20783			0.603915	+	0.797049i	$0.293607\pi$
$60$	4.66429e13	−	1.94996e14i	0.0358509	−	0.149879i
$61$	2.81814e15			1.88217			0.941087	−	0.338165i	$-0.109806\pi$
$61$	2.81814e15			1.88217			0.941087	+	0.338165i	$0.109806\pi$
$62$	8.23483e14	+	2.80569e15i	0.478989	+	1.63196i
$63$	3.62098e14	+	1.47560e13i	0.183836	+	0.00749161i
$64$	−3.18970e14	−	2.22909e15i	−0.141651	−	0.989917i
$65$		−	3.16776e14i		−	0.123307i
$66$	−1.97980e15	−	1.13428e15i	−0.676858	−	0.387791i
$67$			2.11322e15i			0.635782i	0.948127	+	0.317891i	$0.102975\pi$
$67$			2.11322e15i			0.635782i	−0.948127	+	0.317891i	$0.897025\pi$
$68$	7.69408e14	+	1.19781e15i	0.204094	+	0.317733i
$69$	−2.37808e15	−	2.47697e15i	−0.557198	−	0.580367i
$70$	−1.31221e14	+	3.85140e13i	−0.0272063	+	0.00798520i
$71$	2.37596e15			0.436660			0.218330	−	0.975875i	$-0.429939\pi$
$71$	2.37596e15			0.436660			0.218330	+	0.975875i	$0.429939\pi$
$72$	−4.46266e15	−	4.19980e15i	−0.728229	−	0.685334i
$73$	4.74029e15			0.687955			0.343978	−	0.938978i	$-0.388226\pi$
$73$	4.74029e15			0.687955			0.343978	+	0.938978i	$0.388226\pi$
$74$	−3.08790e15	+	9.06315e14i	−0.399203	+	0.117168i
$75$	−5.86193e15	−	6.10568e15i	−0.676114	−	0.704227i
$76$	5.24410e15	+	8.16399e15i	0.540450	+	0.841370i
$77$			1.55632e15i			0.143525i
$78$	−8.40100e15	−	4.81316e15i	−0.694267	−	0.397765i
$79$			7.86350e15i			0.583157i	0.956547	+	0.291578i	$0.0941804\pi$
$79$			7.86350e15i			0.583157i	−0.956547	+	0.291578i	$0.905820\pi$
$80$	2.10312e15	+	9.61600e14i	0.140152	+	0.0640811i
$81$	−1.66219e16	−	1.35699e15i	−0.996684	−	0.0813680i
$82$	9.34908e15	+	3.18532e16i	0.505069	+	1.72082i
$83$	−1.36807e16			−0.666722			−0.333361	−	0.942799i	$-0.608183\pi$
$83$	−1.36807e16			−0.666722			−0.333361	+	0.942799i	$0.608183\pi$
$84$	−9.72396e14	+	4.06522e15i	−0.0428025	+	0.178941i
$85$	−1.46203e15			−0.0581963
$86$	−1.22951e16	−	4.18906e16i	−0.443094	−	1.50966i
$87$	4.99340e15	−	4.79406e15i	0.163111	−	0.156599i
$88$	1.72408e16	−	1.98834e16i	0.511039	−	0.589371i
$89$			1.78957e16i			0.481873i	0.970541	+	0.240937i	$0.0774546\pi$
$89$			1.78957e16i			0.481873i	−0.970541	+	0.240937i	$0.922545\pi$
$90$	6.10581e15	−	1.52502e15i	0.149514	−	0.0373435i
$91$			6.60403e15i			0.147217i
$92$	3.33225e16	−	2.14045e16i	0.676925	−	0.434819i
$93$	−6.62079e16	+	6.35648e16i	−1.22689	+	1.17791i
$94$	5.56096e16	−	1.63217e16i	0.940942	−	0.276171i
$95$	−9.96486e15			−0.154106
$96$	5.74572e16	−	4.11647e16i	0.812904	−	0.582398i
$97$	−2.02574e16			−0.262437			−0.131218	−	0.991353i	$-0.541889\pi$
$97$	−2.02574e16			−0.262437			−0.131218	+	0.991353i	$0.541889\pi$
$98$	−7.80767e16	+	2.29159e16i	−0.927043	+	0.272092i
$99$	2.91622e15	−	7.15609e16i	0.0317629	−	0.779429i
$100$	8.21393e16	−	5.27618e16i	0.821393	−	0.527618i
$101$			1.00511e17i			0.923600i	0.886984	+	0.461800i	$0.152796\pi$
$101$			1.00511e17i			0.923600i	−0.886984	+	0.461800i	$0.847204\pi$
$102$	−2.22144e16	+	3.87735e16i	−0.187730	+	0.327668i
$103$		−	9.94180e15i		−	0.0773301i	−0.999252	−	0.0386650i	$-0.987689\pi$
$103$		−	9.94180e15i		−	0.0773301i	0.999252	−	0.0386650i	$-0.0123105\pi$
$104$	7.31587e16	−	8.43725e16i	0.524183	−	0.604530i
$105$	−2.97291e15	−	3.09653e15i	−0.0196369	−	0.0204534i
$106$	6.82620e16	+	2.32575e17i	0.415986	+	1.41730i
$107$	1.31772e17			0.741416			0.370708	−	0.928750i	$-0.379115\pi$
$107$	1.31772e17			0.741416			0.370708	+	0.928750i	$0.379115\pi$
$108$	5.23288e16	−	1.85100e17i	0.272044	−	0.962285i
$109$	1.80641e17			0.868343			0.434172	−	0.900830i	$-0.357041\pi$
$109$	1.80641e17			0.868343			0.434172	+	0.900830i	$0.357041\pi$
$110$	7.61148e15	+	2.59330e16i	0.0338557	+	0.115349i
$111$	−6.99587e16	−	7.28676e16i	−0.288135	−	0.300116i
$112$	−4.38452e16	−	2.00471e16i	−0.167328	−	0.0765066i
$113$		−	2.28657e17i		−	0.809127i	−0.914510	−	0.404564i	$-0.867423\pi$
$113$		−	2.28657e17i		−	0.809127i	0.914510	−	0.404564i	$-0.132577\pi$
$114$	−1.51408e17	+	2.64271e17i	−0.497116	+	0.867678i
$115$			4.06729e16i			0.123986i
$116$	4.31501e16	+	6.71759e16i	0.122205	+	0.190248i
$117$	1.23746e16	−	3.03658e17i	0.0325799	−	0.799476i
$118$	−4.73215e17	+	1.38891e17i	−1.15894	+	0.340155i
$119$	3.04799e16			0.0694808
$120$	3.67862e15	+	7.24944e16i	0.00780988	+	0.153909i
$121$	−1.97873e17			−0.391481
$122$	−9.78981e17	+	2.87336e17i	−1.80599	+	0.530068i
$123$	−7.51665e17	+	7.21657e17i	−1.29369	+	1.24205i
$124$	−5.72131e17	−	8.90691e17i	−0.919203	−	1.43101i
$125$			2.02955e17i			0.304554i
$126$	−1.27292e17	+	3.17932e16i	−0.178505	+	0.0445846i
$127$			2.97031e17i			0.389467i	0.980856	+	0.194734i	$0.0623842\pi$
$127$			2.97031e17i			0.389467i	−0.980856	+	0.194734i	$0.937616\pi$
$128$	3.38082e17	+	7.41832e17i	0.414703	+	0.909957i
$129$	9.88525e17	−	9.49062e17i	1.13495	−	1.08964i
$130$	3.22982e16	+	1.10043e17i	0.0347264	+	0.118316i
$131$	1.38466e18			1.39488			0.697438	−	0.716645i	$-0.254323\pi$
$131$	1.38466e18			1.39488			0.697438	+	0.716645i	$0.254323\pi$
$132$	8.03403e17	+	1.92173e17i	0.758674	+	0.181474i
$133$	2.07744e17			0.183988
$134$	−2.15462e17	−	7.34099e17i	−0.179052	−	0.610048i
$135$	1.30894e17	+	1.47951e17i	0.102114	+	0.115420i
$136$	−3.89409e17	−	3.37653e17i	−0.285315	−	0.247395i
$137$		−	1.46098e18i		−	1.00582i	−0.864339	−	0.502910i	$-0.832263\pi$
$137$		−	1.46098e18i		−	1.00582i	0.864339	−	0.502910i	$-0.167737\pi$
$138$	1.07866e18	+	6.17993e17i	0.698091	+	0.399955i
$139$		−	1.27720e18i		−	0.777382i	−0.921368	−	0.388691i	$-0.872927\pi$
$139$		−	1.27720e18i		−	0.777382i	0.921368	−	0.388691i	$-0.127073\pi$
$140$	4.16574e16	−	2.67584e16i	0.0238563	−	0.0153240i
$141$	1.25988e18	+	1.31226e18i	0.679149	+	0.707389i
$142$	−8.25374e17	+	2.42251e17i	−0.418986	+	0.122975i
$143$	1.30515e18			0.624170
$144$	1.97847e18	+	1.00394e18i	0.891761	+	0.452507i
$145$	−8.19940e16			−0.0348461
$146$	−1.64670e18	+	4.83316e17i	−0.660110	+	0.193746i
$147$	−1.76888e18	−	1.84244e18i	−0.669117	−	0.696940i
$148$	9.80284e17	−	6.29680e17i	0.350048	−	0.224851i
$149$			4.37571e18i			1.47559i	0.675026	+	0.737794i	$0.264133\pi$
$149$			4.37571e18i			1.47559i	−0.675026	+	0.737794i	$0.735867\pi$
$150$	2.65888e18	+	1.52334e18i	0.847076	+	0.485313i
$151$		−	2.85645e18i		−	0.860047i	−0.902818	−	0.430023i	$-0.858505\pi$
$151$		−	2.85645e18i		−	0.860047i	0.902818	−	0.430023i	$-0.141495\pi$
$152$	−2.65412e18	−	2.30136e18i	−0.755526	−	0.655111i
$153$	−1.40149e18	−	5.71129e16i	−0.377323	−	0.0153765i
$154$	−1.58682e17	−	5.40643e17i	−0.0404204	−	0.137716i
$155$	1.08717e18			0.262105
$156$	3.40913e18	+	8.15460e17i	0.778187	+	0.186142i
$157$	−7.37462e18			−1.59438			−0.797192	−	0.603726i	$-0.793682\pi$
$157$	−7.37462e18			−1.59438			−0.797192	+	0.603726i	$0.793682\pi$
$158$	−8.01756e17	−	2.73166e18i	−0.164232	−	0.559553i
$159$	−5.48825e18	+	5.26915e18i	−1.06551	+	1.02298i
$160$	−8.28637e17	−	1.19613e17i	−0.152526	−	0.0220170i
$161$		−	8.47935e17i		−	0.148028i
$162$	5.91255e18	−	1.22336e18i	0.979258	−	0.202617i
$163$			6.37187e18i			1.00155i	0.865578	+	0.500774i	$0.166951\pi$
$163$			6.37187e18i			1.00155i	−0.865578	+	0.500774i	$0.833049\pi$
$164$	−6.49546e18	−	1.01121e19i	−0.969253	−	1.50893i
$165$	−6.11962e17	+	5.87532e17i	−0.0867184	+	0.0832564i
$166$	4.75247e18	−	1.39488e18i	0.639736	−	0.187766i
$167$	4.02143e18			0.514388			0.257194	−	0.966360i	$-0.417202\pi$
$167$	4.02143e18			0.514388			0.257194	+	0.966360i	$0.417202\pi$
$168$	−7.66907e16	−	1.51134e18i	−0.00932424	−	0.183752i
$169$	−3.11221e18			−0.359776
$170$	5.07888e17	−	1.49068e17i	0.0558408	−	0.0163896i
$171$	−9.55222e18	−	3.89268e17i	−0.999166	−	0.0407175i
$172$	8.54227e18	+	1.32986e19i	0.850318	+	1.32377i
$173$			1.38386e19i			1.31129i	0.755068	+	0.655647i	$0.227604\pi$
$173$			1.38386e19i			1.31129i	−0.755068	+	0.655647i	$0.772396\pi$
$174$	−1.24583e18	+	2.17451e18i	−0.112407	+	0.196197i
$175$		−	2.09015e18i		−	0.179619i
$176$	−3.96188e18	+	8.66506e18i	−0.324373	+	0.709437i
$177$	−1.07210e19	−	1.11668e19i	−0.836496	−	0.871279i
$178$	−1.82463e18	−	6.21668e18i	−0.135708	−	0.462369i
$179$	1.70214e19			1.20710			0.603552	−	0.797324i	$-0.293752\pi$
$179$	1.70214e19			1.20710			0.603552	+	0.797324i	$0.293752\pi$
$180$	−1.96558e18	+	1.15231e18i	−0.132945	+	0.0779390i
$181$	1.90673e19			1.23033			0.615166	−	0.788398i	$-0.289089\pi$
$181$	1.90673e19			1.23033			0.615166	+	0.788398i	$0.289089\pi$
$182$	−6.73342e17	−	2.29414e18i	−0.0414600	−	0.141258i
$183$	−2.21795e19	−	2.31018e19i	−1.30352	−	1.35772i
$184$	−9.39333e18	+	1.08331e19i	−0.527070	+	0.607859i
$185$			1.19652e18i			0.0641151i
$186$	1.65186e19	−	2.88320e19i	0.845500	−	1.47576i
$187$		−	6.02371e18i		−	0.294585i
$188$	−1.76538e19	+	1.13398e19i	−0.825080	+	0.529986i
$189$	−2.72884e18	−	3.08444e18i	−0.121914	−	0.137800i
$190$	3.46164e18	−	1.01601e18i	0.147869	−	0.0434002i
$191$	4.08577e19			1.66913			0.834565	−	0.550910i	$-0.185719\pi$
$191$	4.08577e19			1.66913			0.834565	+	0.550910i	$0.185719\pi$
$192$	−1.57627e19	+	2.01583e19i	−0.615983	+	0.787759i
$193$	3.26397e19			1.22042			0.610210	−	0.792239i	$-0.291085\pi$
$193$	3.26397e19			1.22042			0.610210	+	0.792239i	$0.291085\pi$
$194$	7.03713e18	−	2.06543e18i	0.251815	−	0.0739089i
$195$	−2.59677e18	+	2.49311e18i	−0.0889488	+	0.0853978i
$196$	2.47862e19	−	1.59213e19i	0.812892	−	0.522157i
$197$		−	1.46321e19i		−	0.459561i	−0.973242	−	0.229781i	$-0.926199\pi$
$197$		−	1.46321e19i		−	0.459561i	0.973242	−	0.229781i	$-0.0738009\pi$
$198$	6.28325e18	+	2.51565e19i	0.189030	+	0.756827i
$199$			3.66713e19i			1.05700i	0.848934	+	0.528500i	$0.177245\pi$
$199$			3.66713e19i			1.05700i	−0.848934	+	0.528500i	$0.822755\pi$
$200$	−2.31544e19	+	2.67035e19i	−0.639556	+	0.737587i
$201$	1.73231e19	−	1.66315e19i	0.458627	−	0.440318i
$202$	−1.02481e19	−	3.49162e19i	−0.260109	−	0.886216i
$203$	1.70938e18			0.0416028
$204$	3.76363e18	−	1.57343e19i	0.0878518	−	0.367275i
$205$	1.23427e19			0.276377
$206$	1.01366e18	+	3.45363e18i	0.0217781	+	0.0742001i
$207$	−1.58885e18	+	3.89887e19i	−0.0327593	+	0.803879i
$208$	−1.68117e19	+	3.67690e19i	−0.332715	+	0.727684i
$209$		−	4.10562e19i		−	0.780072i
$210$	1.34846e18	+	7.72571e17i	0.0246023	+	0.0140953i
$211$			1.77818e19i			0.311584i	0.987790	+	0.155792i	$0.0497930\pi$
$211$			1.77818e19i			0.311584i	−0.987790	+	0.155792i	$0.950207\pi$
$212$	−4.74264e19	−	7.38331e19i	−0.798298	−	1.24279i
$213$	−1.86994e19	−	1.94770e19i	−0.302414	−	0.314989i
$214$	−4.57757e19	+	1.34354e19i	−0.711406	+	0.208801i
$215$	−1.62320e19			−0.242463
$216$	6.94366e17	+	6.96362e19i	0.00997083	+	0.999950i
$217$	−2.26649e19			−0.312929
$218$	−6.27520e19	+	1.84180e19i	−0.833197	+	0.244547i
$219$	−3.73073e19	−	3.88586e19i	−0.476451	−	0.496263i
$220$	−5.28823e18	−	8.23269e18i	−0.0649707	−	0.101146i
$221$		−	2.55607e19i		−	0.302161i
$222$	3.17321e19	+	1.81802e19i	0.360993	+	0.206823i
$223$		−	6.34142e19i		−	0.694377i	−0.937795	−	0.347189i	$-0.887136\pi$
$223$		−	6.34142e19i		−	0.694377i	0.937795	−	0.347189i	$-0.112864\pi$
$224$	1.72751e19	+	2.49365e18i	0.182101	+	0.0262861i
$225$	−3.91649e18	+	9.61065e19i	−0.0397507	+	0.975441i
$226$	2.33137e19	+	7.94319e19i	0.227871	+	0.776378i
$227$	−5.73032e19			−0.539460			−0.269730	−	0.962936i	$-0.586934\pi$
$227$	−5.73032e19			−0.539460			−0.269730	+	0.962936i	$0.586934\pi$
$228$	2.56520e19	−	1.07241e20i	0.232635	−	0.972559i
$229$	−5.79001e19			−0.505915			−0.252958	−	0.967477i	$-0.581403\pi$
$229$	−5.79001e19			−0.505915			−0.252958	+	0.967477i	$0.581403\pi$
$230$	−4.14698e18	−	1.41292e19i	−0.0349177	−	0.118968i
$231$	1.27580e19	−	1.22487e19i	0.103533	−	0.0994001i
$232$	−2.18389e19	−	1.89363e19i	−0.170837	−	0.148132i
$233$			1.81167e20i			1.36633i	0.730266	+	0.683163i	$0.239396\pi$
$233$			1.81167e20i			1.36633i	−0.730266	+	0.683163i	$0.760604\pi$
$234$	2.66621e19	+	1.06748e20i	0.193892	+	0.776292i
$235$		−	2.15480e19i		−	0.151123i
$236$	1.50227e20	−	9.64974e19i	1.01624	−	0.652775i
$237$	6.44611e19	−	6.18877e19i	0.420666	−	0.403872i
$238$	−1.05883e19	+	3.10771e18i	−0.0666685	+	0.0195675i
$239$	6.74958e19			0.410104			0.205052	−	0.978751i	$-0.434264\pi$
$239$	6.74958e19			0.410104			0.205052	+	0.978751i	$0.434264\pi$
$240$	−8.66938e18	−	2.48084e19i	−0.0508385	−	0.145480i
$241$	−1.98868e20			−1.12569			−0.562846	−	0.826562i	$-0.690294\pi$
$241$	−1.98868e20			−1.12569			−0.562846	+	0.826562i	$0.690294\pi$
$242$	6.87381e19	−	2.01750e19i	0.375636	−	0.110251i
$243$	1.19695e20	+	1.46938e20i	0.631569	+	0.775319i
$244$	3.10787e20	−	1.99632e20i	1.58361	−	1.01723i
$245$			3.02537e19i			0.148890i
$246$	1.87537e20	−	3.27332e20i	0.891537	−	1.55611i
$247$		−	1.74216e20i		−	0.800136i
$248$	2.89564e20	+	2.51079e20i	1.28501	+	1.11422i
$249$	1.07671e20	+	1.12148e20i	0.461746	+	0.480946i
$250$	−2.06931e19	−	7.05035e19i	−0.0857702	−	0.292227i
$251$	−6.11901e18			−0.0245163			−0.0122581	−	0.999925i	$-0.503902\pi$
$251$	−6.11901e18			−0.0245163			−0.0122581	+	0.999925i	$0.503902\pi$
$252$	4.09777e19	−	2.40231e19i	0.158724	−	0.0930516i
$253$	−1.67576e20			−0.627608
$254$	−3.02851e19	−	1.03184e20i	−0.109684	−	0.373703i
$255$	1.15066e19	+	1.19850e19i	0.0403045	+	0.0419805i
$256$	−1.93081e20	−	2.23231e20i	−0.654185	−	0.756335i
$257$			2.88111e20i			0.944339i	0.881508	+	0.472170i	$0.156529\pi$
$257$			2.88111e20i			0.944339i	−0.881508	+	0.472170i	$0.843471\pi$
$258$	−2.46633e20	+	4.30479e20i	−0.782139	+	1.36516i
$259$		−	2.49447e19i		−	0.0765472i
$260$	−2.24398e19	−	3.49342e19i	−0.0666417	−	0.103748i
$261$	−7.85987e19	−	3.20302e18i	−0.225928	−	0.00920693i
$262$	−4.81009e20	+	1.41178e20i	−1.33842	+	0.392833i
$263$	−5.20471e20			−1.40208			−0.701039	−	0.713123i	$-0.747280\pi$
$263$	−5.20471e20			−1.40208			−0.701039	+	0.713123i	$0.747280\pi$
$264$	−2.98684e20	+	1.51563e19i	−0.779074	+	0.0395329i
$265$	9.01197e19			0.227630
$266$	−7.21671e19	+	2.11814e19i	−0.176541	+	0.0518157i
$267$	1.46700e20	−	1.40843e20i	0.347604	−	0.333727i
$268$	1.49696e20	+	2.33047e20i	0.343610	+	0.534930i
$269$		−	6.23017e20i		−	1.38550i	−0.721179	−	0.692749i	$-0.756399\pi$
$269$		−	6.23017e20i		−	1.38550i	0.721179	−	0.692749i	$-0.243601\pi$
$270$	−6.05557e19	−	3.80501e19i	−0.130486	−	0.0819906i
$271$			1.09756e20i			0.229187i	0.993412	+	0.114594i	$0.0365566\pi$
$271$			1.09756e20i			0.229187i	−0.993412	+	0.114594i	$0.963443\pi$
$272$	1.69702e20	+	7.75918e19i	0.343439	+	0.157029i
$273$	5.41367e19	−	5.19754e19i	0.106196	−	0.101957i
$274$	1.48961e20	+	5.07523e20i	0.283264	+	0.965108i
$275$	−4.13073e20			−0.761550
$276$	−4.37720e20	−	1.04702e20i	−0.782473	−	0.187167i
$277$	5.03063e20			0.872056			0.436028	−	0.899933i	$-0.356385\pi$
$277$	5.03063e20			0.872056			0.436028	+	0.899933i	$0.356385\pi$
$278$	1.30223e20	+	4.43682e20i	0.218931	+	0.745917i
$279$	1.04215e21	+	4.24691e19i	1.69939	+	0.0692528i
$280$	−1.17429e19	+	1.35428e19i	−0.0185751	+	0.0214223i
$281$		−	1.15552e21i		−	1.77326i	−0.462477	−	0.886631i	$-0.653039\pi$
$281$		−	1.15552e21i		−	1.77326i	0.462477	−	0.886631i	$-0.346961\pi$
$282$	−5.71459e20	−	3.27404e20i	−0.850879	−	0.487492i
$283$			7.93266e20i			1.14613i	0.819510	+	0.573066i	$0.194246\pi$
$283$			7.93266e20i			1.14613i	−0.819510	+	0.573066i	$0.805754\pi$
$284$	2.62023e20	−	1.68309e20i	0.367395	−	0.235994i
$285$	7.84260e19	+	8.16870e19i	0.106728	+	0.111166i
$286$	−4.53388e20	+	1.33072e20i	−0.598906	+	0.175782i
$287$	−2.57316e20			−0.329967
$288$	−7.89652e20	−	1.47030e20i	−0.983104	−	0.183050i
$289$	7.09269e20			0.857391
$290$	2.84835e19	−	8.36004e18i	0.0334357	−	0.00981354i
$291$	1.59431e20	+	1.66061e20i	0.181754	+	0.189311i
$292$	5.22762e20	−	3.35793e20i	0.578828	−	0.371807i
$293$			4.77610e19i			0.0513687i	0.999670	+	0.0256843i	$0.00817648\pi$
$293$			4.77610e19i			0.0513687i	−0.999670	+	0.0256843i	$0.991824\pi$
$294$	8.02337e20	+	4.59681e20i	0.838310	+	0.480290i
$295$			1.83365e20i			0.186135i
$296$	−2.76334e20	+	3.18691e20i	−0.272555	+	0.314333i
$297$	−6.09573e20	+	5.39297e20i	−0.584246	+	0.516890i
$298$	−4.46144e20	−	1.52006e21i	−0.415563	−	1.41586i
$299$	−7.11086e20			−0.643750
$300$	−1.07897e21	−	2.58089e20i	−0.949466	−	0.227111i
$301$	3.38400e20			0.289478
$302$	2.91241e20	+	9.92286e20i	0.242211	+	0.825236i
$303$	8.23944e20	−	7.91051e20i	0.666247	−	0.639649i
$304$	1.15665e21	+	5.28847e20i	0.909442	+	0.415820i
$305$			3.79342e20i			0.290056i
$306$	4.92680e20	−	1.23055e20i	0.366381	−	0.0915095i
$307$		−	1.20604e21i		−	0.872338i	−0.899865	−	0.436169i	$-0.856335\pi$
$307$		−	1.20604e21i		−	0.872338i	0.899865	−	0.436169i	$-0.143665\pi$
$308$	1.10247e20	+	1.71632e20i	0.0775687	+	0.120759i
$309$	−8.14980e19	+	7.82445e19i	−0.0557828	+	0.0535558i
$310$	−3.77665e20	+	1.10847e20i	−0.251497	+	0.0738155i
$311$	1.04568e21			0.677543			0.338771	−	0.940869i	$-0.389989\pi$
$311$	1.04568e21			0.677543			0.338771	+	0.940869i	$0.389989\pi$
$312$	−1.26742e21	+	6.43135e19i	−0.799112	+	0.0405497i
$313$	8.50788e20			0.522029			0.261015	−	0.965335i	$-0.415943\pi$
$313$	8.50788e20			0.522029			0.261015	+	0.965335i	$0.415943\pi$
$314$	2.56183e21	−	7.51911e20i	1.52985	−	0.449019i
$315$	−1.98627e18	+	4.87409e19i	−0.00115451	+	0.0283305i
$316$	5.57036e20	+	8.67191e20i	0.315169	+	0.490653i
$317$			1.21407e21i			0.668712i	0.942447	+	0.334356i	$0.108519\pi$
$317$			1.21407e21i			0.668712i	−0.942447	+	0.334356i	$0.891481\pi$
$318$	1.36930e21	−	2.39000e21i	0.734290	−	1.28165i
$319$		−	3.37823e20i		−	0.176388i
$320$	3.00052e20	−	4.29355e19i	0.152553	−	0.0218294i
$321$	−1.03708e21	−	1.08020e21i	−0.513476	−	0.534827i
$322$	8.64549e19	+	2.94560e20i	0.0416883	+	0.142036i
$323$	−8.04067e20			−0.377634
$324$	−1.92920e21	+	1.02782e21i	−0.882560	+	0.470200i
$325$	−1.75281e21			−0.781137
$326$	−6.49671e20	−	2.21349e21i	−0.282061	−	0.961010i
$327$	−1.42169e21	−	1.48081e21i	−0.601381	−	0.626387i
$328$	3.28745e21	+	2.85052e21i	1.35497	+	1.17489i
$329$			4.49225e20i			0.180426i
$330$	1.52682e20	−	2.66495e20i	0.0597613	−	0.104309i
$331$			2.67431e21i			1.02017i	0.860123	+	0.510087i	$0.170387\pi$
$331$			2.67431e21i			1.02017i	−0.860123	+	0.510087i	$0.829613\pi$
$332$	−1.50872e21	+	9.69117e20i	−0.560963	+	0.360332i
$333$	−4.67410e19	+	1.14697e21i	−0.0169403	+	0.415698i
$334$	−1.39698e21	+	4.10022e20i	−0.493568	+	0.144865i
$335$	−2.84454e20			−0.0979784
$336$	1.80736e20	+	5.17197e20i	0.0606962	+	0.173689i
$337$	−3.67525e21			−1.20346			−0.601732	−	0.798698i	$-0.705522\pi$
$337$	−3.67525e21			−1.20346			−0.601732	+	0.798698i	$0.705522\pi$
$338$	1.08114e21	−	3.17319e20i	0.345214	−	0.101322i
$339$	−1.87442e21	+	1.79959e21i	−0.583671	+	0.560370i
$340$	−1.61234e20	+	1.03568e20i	−0.0489649	+	0.0314524i
$341$			4.47922e21i			1.32675i
$342$	3.35799e21	−	8.38712e20i	0.970191	−	0.242321i
$343$		−	1.28354e21i		−	0.361749i
$344$	−4.32337e21	−	3.74876e21i	−1.18871	−	1.03072i
$345$	3.33417e20	−	3.20106e20i	0.0894386	−	0.0858681i
$346$	−1.41097e21	−	4.80732e21i	−0.369293	−	1.25822i
$347$	−6.10690e20			−0.155963			−0.0779813	−	0.996955i	$-0.524847\pi$
$347$	−6.10690e20			−0.155963			−0.0779813	+	0.996955i	$0.524847\pi$
$348$	2.11073e20	−	8.82415e20i	0.0526028	−	0.219912i
$349$	−1.67389e21			−0.407108			−0.203554	−	0.979064i	$-0.565249\pi$
$349$	−1.67389e21			−0.407108			−0.203554	+	0.979064i	$0.565249\pi$
$350$	2.13110e20	+	7.26085e20i	0.0505854	+	0.172349i
$351$	−2.58664e21	+	2.28843e21i	−0.599273	+	0.530185i
$352$	4.92816e20	−	3.41406e21i	0.111448	−	0.772074i
$353$		−	5.30500e21i		−	1.17112i	−0.810630	−	0.585558i	$-0.800875\pi$
$353$		−	5.30500e21i		−	1.17112i	0.810630	−	0.585558i	$-0.199125\pi$
$354$	4.86289e21	+	2.78608e21i	1.04801	+	0.600435i
$355$			3.19821e20i			0.0672924i
$356$	1.26770e21	+	1.97354e21i	0.260430	+	0.405436i
$357$	−2.39885e20	−	2.49860e20i	−0.0481197	−	0.0501206i
$358$	−5.91298e21	+	1.73549e21i	−1.15825	+	0.339951i
$359$	8.02815e21			1.53572			0.767861	−	0.640616i	$-0.221321\pi$
$359$	8.02815e21			1.53572			0.767861	+	0.640616i	$0.221321\pi$
$360$	5.65323e20	−	6.00705e20i	0.105615	−	0.112225i
$361$	5.53526e16			1.01001e−5
$362$	−6.62371e21	+	1.94409e21i	−1.18053	+	0.346492i
$363$	1.55731e21	+	1.62207e21i	0.271125	+	0.282398i
$364$	4.67818e20	+	7.28297e20i	0.0795638	+	0.123864i
$365$			6.38076e20i			0.106019i
$366$	1.00603e22	+	5.76380e21i	1.63313	+	0.935664i
$367$		−	1.10674e22i		−	1.75543i	−0.479187	−	0.877713i	$-0.659068\pi$
$367$		−	1.10674e22i		−	1.75543i	0.479187	−	0.877713i	$-0.340932\pi$
$368$	2.15856e21	−	4.72101e21i	0.334548	−	0.731692i
$369$	1.18316e22	+	4.82155e20i	1.79192	+	0.0730236i
$370$	−1.21996e20	−	4.15653e20i	−0.0180564	−	0.0615200i
$371$	−1.87878e21			−0.271768
$372$	−2.79863e21	+	1.17000e22i	−0.395668	+	1.65414i
$373$	8.31780e21			1.14943			0.574716	−	0.818353i	$-0.305112\pi$
$373$	8.31780e21			1.14943			0.574716	+	0.818353i	$0.305112\pi$
$374$	6.14173e20	+	2.09255e21i	0.0829625	+	0.282661i
$375$	1.66373e21	−	1.59731e21i	0.219693	−	0.210922i
$376$	4.97646e21	−	5.73925e21i	0.642427	−	0.740898i
$377$		−	1.43350e21i		−	0.180924i
$378$	1.26244e21	+	7.93256e20i	0.155787	+	0.0978888i
$379$			4.24000e21i			0.511603i	0.966729	+	0.255801i	$0.0823393\pi$
$379$			4.24000e21i			0.511603i	−0.966729	+	0.255801i	$0.917661\pi$
$380$	−1.09893e21	+	7.05893e20i	−0.129661	+	0.0832872i
$381$	2.43492e21	−	2.33771e21i	0.280946	−	0.269730i
$382$	−1.41933e22	+	4.16582e21i	−1.60157	+	0.470069i
$383$	1.63146e22			1.80047			0.900237	−	0.435399i	$-0.143393\pi$
$383$	1.63146e22			1.80047			0.900237	+	0.435399i	$0.143393\pi$
$384$	3.42038e21	−	8.60984e21i	0.369198	−	0.929351i
$385$	−2.09492e20			−0.0221183
$386$	−1.13386e22	+	3.32792e21i	−1.17102	+	0.343701i
$387$	−1.55599e22	−	6.34090e20i	−1.57204	−	0.0640630i
$388$	−2.23400e21	+	1.43500e21i	−0.220808	+	0.141835i
$389$		−	1.02588e22i		−	0.992032i	−0.868313	−	0.496016i	$-0.834796\pi$
$389$		−	1.02588e22i		−	0.992032i	0.868313	−	0.496016i	$-0.165204\pi$
$390$	6.47885e20	−	1.13083e21i	0.0612983	−	0.106991i
$391$			3.28191e21i			0.303826i
$392$	−6.98702e21	+	8.05799e21i	−0.632937	+	0.729954i
$393$	−1.08976e22	−	1.13507e22i	−0.966037	−	1.00621i
$394$	1.49188e21	+	5.08297e21i	0.129424	+	0.440960i
$395$	−1.05848e21			−0.0898686
$396$	−4.74765e21	−	8.09836e21i	−0.394520	−	0.672958i
$397$	−1.91940e21			−0.156115			−0.0780577	−	0.996949i	$-0.524872\pi$
$397$	−1.91940e21			−0.156115			−0.0780577	+	0.996949i	$0.524872\pi$
$398$	−3.73897e21	−	1.27390e22i	−0.297678	−	1.01422i
$399$	−1.63500e21	−	1.70298e21i	−0.127423	−	0.132721i
$400$	5.32082e21	−	1.16372e22i	0.405946	−	0.887848i
$401$			1.74973e22i			1.30691i	0.756967	+	0.653453i	$0.226680\pi$
$401$			1.74973e22i			1.30691i	−0.756967	+	0.653453i	$0.773320\pi$
$402$	−4.32205e21	+	7.54380e21i	−0.316059	+	0.551657i
$403$			1.90069e22i			1.36088i
$404$	7.12005e21	+	1.10845e22i	0.499162	+	0.777093i
$405$	1.82660e20	−	2.23742e21i	0.0125394	−	0.153596i
$406$	−5.93814e20	+	1.74287e20i	−0.0399189	+	0.0117164i
$407$	−4.92978e21			−0.324545
$408$	2.96829e20	+	5.84960e21i	0.0191379	+	0.377151i
$409$	5.06763e21			0.320005			0.160003	−	0.987117i	$-0.448850\pi$
$409$	5.06763e21			0.320005			0.160003	+	0.987117i	$0.448850\pi$
$410$	−4.28766e21	+	1.25845e21i	−0.265190	+	0.0778347i
$411$	−1.19764e22	+	1.14983e22i	−0.725557	+	0.696592i
$412$	−7.04259e20	−	1.09639e21i	−0.0417933	−	0.0650636i
$413$		−	3.82272e21i		−	0.222227i
$414$	−3.42332e21	−	1.37061e22i	−0.194959	−	0.780568i
$415$		−	1.84152e21i		−	0.102747i
$416$	2.09119e21	−	1.44871e22i	0.114314	−	0.791932i
$417$	−1.04699e22	+	1.00519e22i	−0.560772	+	0.538385i
$418$	4.18605e21	+	1.42623e22i	0.219688	+	0.748498i
$419$	8.08768e21			0.415915			0.207958	−	0.978138i	$-0.433318\pi$
$419$	8.08768e21			0.415915			0.207958	+	0.978138i	$0.433318\pi$
$420$	−5.47206e20	−	1.30891e20i	−0.0275761	−	0.00659617i
$421$	−8.54440e21			−0.421972			−0.210986	−	0.977489i	$-0.567667\pi$
$421$	−8.54440e21			−0.421972			−0.210986	+	0.977489i	$0.567667\pi$
$422$	−1.81302e21	−	6.17714e21i	−0.0877500	−	0.298973i
$423$	8.41751e20	−	2.06557e22i	0.0399292	−	0.979821i
$424$	2.40032e22	+	2.08130e22i	1.11599	+	0.967663i
$425$			8.08985e21i			0.368667i
$426$	8.48176e21	+	4.85943e21i	0.378883	+	0.217072i
$427$		−	7.90839e21i		−	0.346299i
$428$	1.45319e22	−	9.33451e21i	0.623808	−	0.400700i
$429$	−1.02718e22	−	1.06990e22i	−0.432276	−	0.450251i
$430$	5.63877e21	−	1.65501e21i	0.232650	−	0.0682839i
$431$	2.00133e22			0.809585			0.404792	−	0.914409i	$-0.367344\pi$
$431$	2.00133e22			0.809585			0.404792	+	0.914409i	$0.367344\pi$
$432$	−7.34127e21	−	2.41198e22i	−0.291179	−	0.956669i
$433$	6.35239e21			0.247053			0.123527	−	0.992341i	$-0.460580\pi$
$433$	6.35239e21			0.247053			0.123527	+	0.992341i	$0.460580\pi$
$434$	7.87343e21	−	2.31089e21i	0.300263	−	0.0881286i
$435$	6.45313e20	+	6.72147e20i	0.0241330	+	0.0251365i
$436$	1.99212e22	−	1.27963e22i	0.730602	−	0.469299i
$437$			2.23687e22i			0.804542i
$438$	1.69220e22	+	9.69506e21i	0.596927	+	0.341996i
$439$		−	4.89796e22i		−	1.69460i	−0.531117	−	0.847298i	$-0.678228\pi$
$439$		−	4.89796e22i		−	1.69460i	0.531117	−	0.847298i	$-0.321772\pi$
$440$	2.67645e21	+	2.32073e21i	0.0908262	+	0.0787547i
$441$	−1.18183e21	+	2.90009e22i	−0.0393394	+	0.965347i
$442$	2.60615e21	+	8.87942e21i	0.0850963	+	0.289931i
$443$	−5.07865e22			−1.62673			−0.813367	−	0.581751i	$-0.802368\pi$
$443$	−5.07865e22			−1.62673			−0.813367	+	0.581751i	$0.802368\pi$
$444$	−1.28769e22	−	3.08014e21i	−0.404628	−	0.0967867i
$445$	−2.40888e21			−0.0742601
$446$	6.46567e21	+	2.20291e22i	0.195554	+	0.666272i
$447$	3.58699e22	−	3.44380e22i	1.06443	−	1.02194i
$448$	−6.25538e21	+	8.95106e20i	−0.182134	+	0.0260622i
$449$			3.31286e22i			0.946476i	0.880935	+	0.473238i	$0.156915\pi$
$449$			3.31286e22i			0.946476i	−0.880935	+	0.473238i	$0.843085\pi$
$450$	−8.43841e21	−	3.37853e22i	−0.236567	−	0.947155i
$451$			5.08530e22i			1.39900i
$452$	−1.61976e22	−	2.52164e22i	−0.437295	−	0.680779i
$453$	−2.34158e22	+	2.24810e22i	−0.620402	+	0.595635i
$454$	1.99063e22	−	5.84259e21i	0.517625	−	0.151926i
$455$	−8.88949e20			−0.0226872
$456$	2.02312e21	+	3.98695e22i	0.0506780	+	0.998710i
$457$	6.78390e21			0.166798			0.0833992	−	0.996516i	$-0.473422\pi$
$457$	6.78390e21			0.166798			0.0833992	+	0.996516i	$0.473422\pi$
$458$	2.01136e22	−	5.90345e21i	0.485438	−	0.142479i
$459$	1.05619e22	+	1.19382e22i	0.250227	+	0.282834i
$460$	2.88120e21	+	4.48543e21i	0.0670087	+	0.104319i
$461$		−	7.66403e22i		−	1.74984i	−0.484264	−	0.874922i	$-0.660913\pi$
$461$		−	7.66403e22i		−	1.74984i	0.484264	−	0.874922i	$-0.339087\pi$
$462$	−3.18307e21	+	5.55580e21i	−0.0713492	+	0.124534i
$463$			1.17895e22i			0.259451i	0.991550	+	0.129726i	$0.0414097\pi$
$463$			1.17895e22i			0.259451i	−0.991550	+	0.129726i	$0.958590\pi$
$464$	9.51724e21	+	4.35152e21i	0.205640	+	0.0940239i
$465$	−8.55627e21	−	8.91205e21i	−0.181524	−	0.189072i
$466$	−1.84717e22	−	6.29348e22i	−0.384792	−	1.31102i
$467$	−5.39002e22			−1.10255			−0.551273	−	0.834325i	$-0.685858\pi$
$467$	−5.39002e22			−1.10255			−0.551273	+	0.834325i	$0.685858\pi$
$468$	−2.01460e22	−	3.43642e22i	−0.404667	−	0.690267i
$469$	5.93019e21			0.116977
$470$	2.19701e21	+	7.48544e21i	0.0425600	+	0.145006i
$471$	5.80402e22	+	6.04536e22i	1.10421	+	1.15012i
$472$	−4.23477e22	+	4.88387e22i	−0.791266	+	0.912552i
$473$		−	6.68776e22i		−	1.22733i
$474$	−1.60828e22	+	2.80713e22i	−0.289898	+	0.505995i
$475$			5.51385e22i			0.976246i
$476$	3.36135e21	−	2.15914e21i	0.0584594	−	0.0375511i
$477$	8.63879e22	+	3.52044e21i	1.47587	+	0.0601438i
$478$	−2.34470e22	+	6.88182e21i	−0.393505	+	0.115496i
$479$	2.06480e22			0.340429			0.170215	−	0.985407i	$-0.445554\pi$
$479$	2.06480e22			0.340429			0.170215	+	0.985407i	$0.445554\pi$
$480$	5.54106e21	+	7.73415e21i	0.0897516	+	0.125274i
$481$	−2.09188e22			−0.332892
$482$	6.90837e22	−	2.02764e22i	1.08013	−	0.317023i
$483$	−6.95096e21	+	6.67347e21i	−0.106781	+	0.102518i
$484$	−2.18216e22	+	1.40170e22i	−0.329382	+	0.211577i
$485$		−	2.72679e21i		−	0.0404434i
$486$	−5.65618e22	−	3.88401e22i	−0.824356	−	0.566072i
$487$		−	1.16419e23i		−	1.66736i	−0.552249	−	0.833679i	$-0.686230\pi$
$487$		−	1.16419e23i		−	1.66736i	0.552249	−	0.833679i	$-0.313770\pi$
$488$	−8.76083e22	+	1.01037e23i	−1.23304	+	1.42204i
$489$	5.22335e22	−	5.01482e22i	0.722476	−	0.693634i
$490$	−3.08464e21	−	1.05097e22i	−0.0419313	−	0.142864i
$491$	−9.35209e22			−1.24944			−0.624721	−	0.780848i	$-0.714787\pi$
$491$	−9.35209e22			−1.24944			−0.624721	+	0.780848i	$0.714787\pi$
$492$	−3.17731e22	+	1.32831e23i	−0.417212	+	1.74420i
$493$	−6.61612e21			−0.0853895
$494$	1.77629e22	+	6.05200e22i	0.225338	+	0.767750i
$495$	9.63260e21	+	3.92543e20i	0.120116	+	0.00489489i
$496$	−1.26190e23	−	5.76972e22i	−1.54679	−	0.707230i
$497$		−	6.66753e21i		−	0.0803407i
$498$	−4.88377e22	−	2.79804e22i	−0.578503	−	0.331440i
$499$		−	5.78705e21i		−	0.0673911i	−0.999432	−	0.0336955i	$-0.989272\pi$
$499$		−	5.78705e21i		−	0.0673911i	0.999432	−	0.0336955i	$-0.0107277\pi$
$500$	1.43770e22	+	2.23820e22i	0.164597	+	0.256244i
$501$	−3.16497e22	−	3.29657e22i	−0.356245	−	0.371058i
$502$	2.12565e21	−	6.23890e20i	0.0235240	−	0.00690440i
$503$	3.01191e22			0.327729			0.163864	−	0.986483i	$-0.447604\pi$
$503$	3.01191e22			0.327729			0.163864	+	0.986483i	$0.447604\pi$
$504$	−1.17857e22	+	1.25233e22i	−0.126094	+	0.133986i
$505$	−1.35295e22			−0.142333
$506$	5.82135e22	−	1.70860e22i	0.602205	−	0.176750i
$507$	2.44939e22	+	2.55124e22i	0.249167	+	0.259528i
$508$	2.10412e22	+	3.27568e22i	0.210489	+	0.327688i
$509$			4.82657e22i			0.474829i	0.971408	+	0.237414i	$0.0762999\pi$
$509$			4.82657e22i			0.474829i	−0.971408	+	0.237414i	$0.923700\pi$
$510$	−5.21919e21	−	2.99021e21i	−0.0504959	−	0.0289305i
$511$		−	1.33024e22i		−	0.126576i
$512$	8.98339e22	+	5.78605e22i	0.840709	+	0.541487i
$513$	7.19874e22	+	8.13681e22i	0.662611	+	0.748957i
$514$	−2.93756e22	−	1.00085e23i	−0.265950	−	0.906117i
$515$	1.33824e21			0.0119171
$516$	4.17853e22	−	1.74689e23i	0.366017	−	1.53018i
$517$	8.87797e22			0.764969
$518$	2.54334e21	+	8.66540e21i	0.0215576	+	0.0734489i
$519$	1.13442e23	−	1.08913e23i	0.945913	−	0.908151i
$520$	1.13571e22	+	9.84768e21i	0.0931623	+	0.0807803i
$521$		−	8.36427e22i		−	0.675006i	−0.941325	−	0.337503i	$-0.890418\pi$
$521$		−	8.36427e22i		−	0.675006i	0.941325	−	0.337503i	$-0.109582\pi$
$522$	2.76306e22	−	6.90118e21i	0.219377	−	0.0547929i
$523$			4.90854e22i			0.383432i	0.981450	+	0.191716i	$0.0614052\pi$
$523$			4.90854e22i			0.383432i	−0.981450	+	0.191716i	$0.938595\pi$
$524$	1.52701e23	−	9.80865e22i	1.17361	−	0.753865i
$525$	−1.71340e22	+	1.64500e22i	−0.129570	+	0.124397i
$526$	1.80804e23	−	5.30668e22i	1.34533	−	0.394861i
$527$	8.77237e22			0.642283
$528$	1.02213e23	−	3.57187e22i	0.736407	−	0.257340i
$529$	−4.97490e22			−0.352705
$530$	−3.13062e22	+	9.18854e21i	−0.218417	+	0.0641064i
$531$	−7.16297e21	+	1.75772e23i	−0.0491801	+	1.20683i
$532$	2.29101e22	−	1.47162e22i	0.154803	−	0.0994368i
$533$			2.15788e23i			1.43498i
$534$	−3.66011e22	+	6.38843e22i	−0.239548	+	0.418113i
$535$			1.77375e22i			0.114257i
$536$	−7.57636e22	−	6.56940e22i	−0.480352	−	0.416510i
$537$	−1.33963e23	−	1.39533e23i	−0.835993	−	0.870755i
$538$	6.35224e22	+	2.16427e23i	0.390191	+	1.32942i
$539$	−1.24648e23			−0.753669
$540$	2.49157e22	+	7.04383e21i	0.148295	+	0.0419239i
$541$	−2.08840e23			−1.22359			−0.611795	−	0.791016i	$-0.709552\pi$
$541$	−2.08840e23			−1.22359			−0.611795	+	0.791016i	$0.709552\pi$
$542$	−1.11907e22	−	3.81277e22i	−0.0645449	−	0.219911i
$543$	−1.50065e23	−	1.56305e23i	−0.852080	−	0.887511i
$544$	−6.68630e22	−	9.65159e21i	−0.373762	−	0.0539521i
$545$			2.43156e22i			0.133818i
$546$	−1.35069e22	+	2.35752e22i	−0.0731843	+	0.127737i
$547$		−	8.74688e21i		−	0.0466618i	−0.999728	−	0.0233309i	$-0.992573\pi$
$547$		−	8.74688e21i		−	0.0466618i	0.999728	−	0.0233309i	$-0.00742712\pi$
$548$	−1.03493e23	−	1.61118e23i	−0.543598	−	0.846271i
$549$	−1.48186e22	+	3.63634e23i	−0.0766379	+	1.88061i
$550$	1.43495e23	−	4.21166e22i	0.730726	−	0.214472i
$551$	−4.50939e22			−0.226115
$552$	1.62733e23	−	8.25763e21i	0.803513	−	0.0407730i
$553$	2.20669e22			0.107294
$554$	−1.74756e23	+	5.12919e22i	−0.836759	+	0.245593i
$555$	9.80849e21	−	9.41692e21i	0.0462500	−	0.0444037i
$556$	−9.04749e22	−	1.40851e23i	−0.420138	−	0.654070i
$557$		−	9.99552e22i		−	0.457126i	−0.973529	−	0.228563i	$-0.926597\pi$
$557$		−	9.99552e22i		−	0.457126i	0.973529	−	0.228563i	$-0.0734027\pi$
$558$	−3.66356e23	+	9.15034e22i	−1.65011	+	0.412142i
$559$		−	2.83785e23i		−	1.25890i
$560$	2.69848e21	−	5.90187e21i	0.0117902	−	0.0257864i
$561$	−4.93794e22	+	4.74081e22i	−0.212501	+	0.204018i
$562$	1.17816e23	+	4.01410e23i	0.499396	+	1.70149i
$563$	−1.90425e23			−0.795065			−0.397533	−	0.917588i	$-0.630133\pi$
$563$	−1.90425e23			−0.795065			−0.397533	+	0.917588i	$0.630133\pi$
$564$	2.31898e23	+	5.54698e22i	0.953729	+	0.228131i
$565$	3.07788e22			0.124692
$566$	−8.08808e22	−	2.75569e23i	−0.322780	−	1.09974i
$567$	−3.80804e21	+	4.66450e22i	−0.0149708	+	0.183379i
$568$	−7.38621e22	+	8.51837e22i	−0.286062	+	0.329910i
$569$		−	2.96221e22i		−	0.113021i	−0.998402	−	0.0565107i	$-0.982002\pi$
$569$		−	2.96221e22i		−	0.113021i	0.998402	−	0.0565107i	$-0.0179975\pi$
$570$	−3.55728e22	−	2.03806e22i	−0.133715	−	0.0766091i
$571$			3.30583e23i			1.22426i	0.790758	+	0.612129i	$0.209687\pi$
$571$			3.30583e23i			1.22426i	−0.790758	+	0.612129i	$0.790313\pi$
$572$	1.43932e23	−	9.24543e22i	0.525161	−	0.337334i
$573$	−3.21560e23	−	3.34931e23i	−1.15597	−	1.20404i
$574$	8.93877e22	−	2.62358e22i	0.316612	−	0.0929271i
$575$	2.25055e23			0.785439
$576$	2.89304e23	−	2.94364e22i	0.994863	−	0.101226i
$577$	5.05854e22			0.171408			0.0857039	−	0.996321i	$-0.472686\pi$
$577$	5.05854e22			0.171408			0.0857039	+	0.996321i	$0.472686\pi$
$578$	−2.46389e23	+	7.23165e22i	−0.822688	+	0.241463i
$579$	−2.56883e23	−	2.67565e23i	−0.845216	−	0.880362i
$580$	−9.04235e21	+	5.80831e21i	−0.0293186	+	0.0188327i
$581$			3.83914e22i			0.122669i
$582$	−7.23154e22	−	4.14315e22i	−0.227712	−	0.130462i
$583$			3.71302e23i			1.15224i
$584$	−1.47362e23	+	1.69950e23i	−0.450689	+	0.519771i
$585$	4.08746e22	+	1.66570e21i	0.123205	+	0.00502079i
$586$	−4.86967e21	−	1.65914e22i	−0.0144667	−	0.0492895i
$587$	4.74610e23			1.38968			0.694838	−	0.719166i	$-0.255476\pi$
$587$	4.74610e23			1.38968			0.694838	+	0.719166i	$0.255476\pi$
$588$	−3.25589e23	−	7.78805e22i	−0.939641	−	0.224761i
$589$	5.97904e23			1.70079
$590$	−1.86957e22	−	6.36981e22i	−0.0524204	−	0.178601i
$591$	−1.19947e23	+	1.15158e23i	−0.331509	+	0.318274i
$592$	6.35009e22	−	1.38883e23i	0.173000	−	0.378368i
$593$			2.00045e23i			0.537233i	0.963247	+	0.268617i	$0.0865664\pi$
$593$			2.00045e23i			0.537233i	−0.963247	+	0.268617i	$0.913434\pi$
$594$	1.56770e23	−	2.49495e23i	0.415029	−	0.660507i
$595$			4.10281e21i			0.0107075i
$596$	3.09968e23	+	4.82556e23i	0.797486	+	1.24152i
$597$	3.00613e23	−	2.88612e23i	0.762476	−	0.732037i
$598$	2.47021e23	−	7.25018e22i	0.617694	−	0.181296i
$599$	4.55631e23			1.12327			0.561636	−	0.827384i	$-0.310172\pi$
$599$	4.55631e23			1.12327			0.561636	+	0.827384i	$0.310172\pi$
$600$	4.01133e23	−	2.03549e22i	0.974997	−	0.0494747i
$601$	6.38962e22			0.153124			0.0765618	−	0.997065i	$-0.475606\pi$
$601$	6.38962e22			0.153124			0.0765618	+	0.997065i	$0.475606\pi$
$602$	−1.17555e23	+	3.45030e22i	−0.277761	+	0.0815243i
$603$	−2.72675e23	−	1.11119e22i	−0.635254	−	0.0258876i
$604$	−2.02346e23	−	3.15011e23i	−0.464815	−	0.723621i
$605$		−	2.66351e22i		−	0.0603300i
$606$	−2.05571e23	+	3.58808e23i	−0.459139	+	0.801391i
$607$		−	1.33444e22i		−	0.0293898i	−0.999892	−	0.0146949i	$-0.995322\pi$
$607$		−	1.33444e22i		−	0.0293898i	0.999892	−	0.0146949i	$-0.00467769\pi$
$608$	−4.55722e23	−	6.57829e22i	−0.989737	−	0.142867i
$609$	−1.34533e22	−	1.40127e22i	−0.0288125	−	0.0300106i
$610$	−3.86774e22	−	1.31778e23i	−0.0816872	−	0.278316i
$611$	3.76724e23			0.784644
$612$	−1.58603e23	+	9.29806e22i	−0.325780	+	0.190988i
$613$	−2.90744e23			−0.588975			−0.294487	−	0.955655i	$-0.595149\pi$
$613$	−2.90744e23			−0.588975			−0.294487	+	0.955655i	$0.595149\pi$
$614$	1.22967e23	+	4.18960e23i	0.245673	+	0.837030i
$615$	−9.71401e22	−	1.01179e23i	−0.191408	−	0.199367i
$616$	−5.57977e22	−	4.83818e22i	−0.108438	−	0.0940255i
$617$		−	3.81342e23i		−	0.730955i	−0.930820	−	0.365478i	$-0.880906\pi$
$617$		−	3.81342e23i		−	0.730955i	0.930820	−	0.365478i	$-0.119094\pi$
$618$	2.03334e22	−	3.54904e22i	0.0384422	−	0.0670980i
$619$		−	8.09213e23i		−	1.50901i	−0.656294	−	0.754505i	$-0.727877\pi$
$619$		−	8.09213e23i		−	1.50901i	0.656294	−	0.754505i	$-0.272123\pi$
$620$	1.19893e23	−	7.70128e22i	0.220529	−	0.141656i
$621$	3.32115e23	−	2.93826e23i	0.602573	−	0.533104i
$622$	−3.63255e23	+	1.06617e23i	−0.650119	+	0.190813i
$623$	5.02195e22			0.0886593
$624$	4.33726e23	−	1.51567e23i	0.755347	−	0.263959i
$625$	5.40934e23			0.929317
$626$	−2.95551e23	+	8.67457e22i	−0.500900	+	0.147017i
$627$	−3.36558e23	+	3.23122e23i	−0.562712	+	0.540248i
$628$	−8.13278e23	+	5.22405e23i	−1.34147	+	0.861689i
$629$			9.65476e22i			0.157113i
$630$	−4.27959e21	−	1.71344e22i	−0.00687080	−	0.0275089i
$631$		−	1.87901e23i		−	0.297632i	−0.988865	−	0.148816i	$-0.952454\pi$
$631$		−	1.87901e23i		−	0.297632i	0.988865	−	0.148816i	$-0.0475462\pi$
$632$	−2.81924e23	−	2.44454e23i	−0.440593	−	0.382034i
$633$	1.45767e23	−	1.39948e23i	0.224764	−	0.215791i
$634$	−1.23785e23	−	4.21749e23i	−0.188326	−	0.641645i
$635$	−3.99825e22			−0.0600196
$636$	−2.31991e23	+	9.69864e23i	−0.343625	+	1.43656i
$637$	−5.28926e23			−0.773054
$638$	3.44442e22	+	1.17355e23i	0.0496752	+	0.169248i
$639$	−1.24935e22	+	3.06578e23i	−0.0177798	+	0.436298i
$640$	−9.98558e22	+	4.55082e22i	−0.140231	+	0.0639087i
$641$			8.33460e23i			1.15503i	0.816382	+	0.577513i	$0.195977\pi$
$641$			8.33460e23i			1.15503i	−0.816382	+	0.577513i	$0.804023\pi$
$642$	4.70403e23	+	2.69507e23i	0.643313	+	0.368572i
$643$			5.47775e23i			0.739280i	0.929175	+	0.369640i	$0.120519\pi$
$643$			5.47775e23i			0.739280i	−0.929175	+	0.369640i	$0.879481\pi$
$644$	−6.00662e22	−	9.35108e22i	−0.0800019	−	0.124547i
$645$	1.27750e23	+	1.33062e23i	0.167921	+	0.174903i
$646$	2.79321e23	−	8.19821e22i	0.362349	−	0.106351i
$647$	−7.67898e23			−0.983144			−0.491572	−	0.870837i	$-0.663578\pi$
$647$	−7.67898e23			−0.983144			−0.491572	+	0.870837i	$0.663578\pi$
$648$	5.65379e23	−	5.53747e23i	0.714418	−	0.699719i
$649$	−7.55480e23			−0.942199
$650$	6.08901e23	−	1.78716e23i	0.749520	−	0.219988i
$651$	1.78378e23	+	1.85795e23i	0.216722	+	0.225734i
$652$	4.51372e23	+	7.02693e23i	0.541290	+	0.842677i
$653$		−	1.44848e24i		−	1.71455i	−0.514856	−	0.857276i	$-0.672155\pi$
$653$		−	1.44848e24i		−	1.71455i	0.514856	−	0.857276i	$-0.327845\pi$
$654$	6.44857e23	+	3.69456e23i	0.753446	+	0.431670i
$655$			1.86384e23i			0.214960i
$656$	−1.43265e24	−	6.55042e23i	−1.63101	−	0.745738i
$657$	−2.49258e22	+	6.11654e23i	−0.0280120	+	0.687385i
$658$	−4.58026e22	−	1.56054e23i	−0.0508125	−	0.173123i
$659$	7.69858e23			0.843111			0.421555	−	0.906803i	$-0.361484\pi$
$659$	7.69858e23			0.843111			0.421555	+	0.906803i	$0.361484\pi$
$660$	−2.58679e22	+	1.08144e23i	−0.0279664	+	0.116917i
$661$	−5.39065e23			−0.575346			−0.287673	−	0.957729i	$-0.592882\pi$
$661$	−5.39065e23			−0.575346			−0.287673	+	0.957729i	$0.592882\pi$
$662$	−2.72671e23	−	9.29017e23i	−0.287307	−	0.978882i
$663$	−2.09534e23	+	2.01170e23i	−0.217967	+	0.209265i
$664$	4.25295e23	−	4.90485e23i	0.436779	−	0.503729i
$665$			2.79638e22i			0.0283538i
$666$	−1.00708e23	−	4.03207e23i	−0.100816	−	0.403643i
$667$			1.84057e23i			0.181921i
$668$	4.43486e23	−	2.84871e23i	0.432793	−	0.278002i
$669$	−5.19839e23	+	4.99086e23i	−0.500895	+	0.480899i
$670$	9.88149e22	−	2.90027e22i	0.0940127	−	0.0275932i
$671$	−1.56293e24			−1.46824
$672$	−1.15518e23	−	1.61239e23i	−0.107155	−	0.149565i
$673$	−1.23256e24			−1.12896			−0.564480	−	0.825447i	$-0.690923\pi$
$673$	−1.23256e24			−1.12896			−0.564480	+	0.825447i	$0.690923\pi$
$674$	1.27673e24	−	3.74726e23i	1.15475	−	0.338926i
$675$	8.18658e23	−	7.24277e23i	0.731173	−	0.646878i
$676$	−3.43217e23	+	2.20464e23i	−0.302706	+	0.194442i
$677$			1.54878e24i			1.34892i	0.738312	+	0.674459i	$0.235623\pi$
$677$			1.54878e24i			1.34892i	−0.738312	+	0.674459i	$0.764377\pi$
$678$	4.67659e23	−	8.16263e23i	0.402233	−	0.702066i
$679$			5.68473e22i			0.0482855i
$680$	4.54505e22	−	5.24171e22i	0.0381252	−	0.0439691i
$681$	4.50991e23	+	4.69744e23i	0.373609	+	0.389144i
$682$	−4.56698e23	−	1.55602e24i	−0.373648	−	1.27305i
$683$	−5.73867e23			−0.463698			−0.231849	−	0.972752i	$-0.574478\pi$
$683$	−5.73867e23			−0.463698			−0.231849	+	0.972752i	$0.574478\pi$
$684$	−1.08100e24	+	6.33734e23i	−0.862678	+	0.505743i
$685$	1.96658e23			0.155004
$686$	1.30868e23	+	4.45881e23i	0.101878	+	0.347107i
$687$	4.55689e23	+	4.74637e23i	0.350377	+	0.364947i
$688$	1.88409e24	+	8.61455e23i	1.43087	+	0.654231i
$689$			1.57557e24i			1.18188i
$690$	−8.31862e22	+	1.45195e23i	−0.0616359	+	0.107581i
$691$		−	2.64087e24i		−	1.93278i	−0.257075	−	0.966391i	$-0.582759\pi$
$691$		−	2.64087e24i		−	1.93278i	0.257075	−	0.966391i	$-0.417241\pi$
$692$	9.80301e23	+	1.52613e24i	0.708692	+	1.10329i
$693$	−2.00817e23	−	8.18361e21i	−0.143406	−	0.00584403i
$694$	2.12144e23	−	6.22655e22i	0.149650	−	0.0439230i
$695$	1.71921e23			0.119800
$696$	1.66468e22	+	3.28059e23i	0.0114592	+	0.225825i
$697$	9.95935e23			0.677255
$698$	5.81483e23	−	1.70668e23i	0.390631	−	0.114652i
$699$	1.48512e24	−	1.42583e24i	0.985612	−	0.946264i
$700$	−1.48062e23	−	2.30503e23i	−0.0970758	−	0.151127i
$701$		−	1.01647e24i		−	0.658401i	−0.944260	−	0.329200i	$-0.893221\pi$
$701$		−	1.01647e24i		−	0.658401i	0.944260	−	0.329200i	$-0.106779\pi$
$702$	6.65232e23	−	1.05870e24i	0.425704	−	0.677495i
$703$			6.58046e23i			0.416041i
$704$	1.76899e23	+	1.23624e24i	0.110499	+	0.772210i
$705$	−1.76640e23	+	1.69588e23i	−0.109014	+	0.104662i
$706$	5.40894e23	+	1.84288e24i	0.329816	+	1.12372i
$707$	2.82059e23			0.169932
$708$	−1.97336e24	−	4.72026e23i	−1.17469	−	0.280985i
$709$	1.55107e24			0.912303			0.456151	−	0.889902i	$-0.349228\pi$
$709$	1.55107e24			0.912303			0.456151	+	0.889902i	$0.349228\pi$
$710$	−3.26087e22	−	1.11101e23i	−0.0189513	−	0.0645687i
$711$	−1.01465e24	−	4.13486e22i	−0.582673	−	0.0237448i
$712$	−6.41600e23	−	5.56326e23i	−0.364070	−	0.315682i
$713$		−	2.44043e24i		−	1.36837i
$714$	1.08808e23	+	6.23390e22i	0.0602873	+	0.0345402i
$715$			1.75682e23i			0.0961890i
$716$	1.87713e24	−	1.20577e24i	1.01563	−	0.652382i
$717$	−5.31209e23	−	5.53298e23i	−0.284022	−	0.295833i
$718$	−2.78886e24	+	8.18544e23i	−1.47356	+	0.432498i
$719$	2.20285e23			0.115024			0.0575121	−	0.998345i	$-0.481683\pi$
$719$	2.20285e23			0.115024			0.0575121	+	0.998345i	$0.481683\pi$
$720$	−1.35137e23	+	2.66316e23i	−0.0697346	+	0.137427i
$721$	−2.78991e22			−0.0142279
$722$	−1.92287e19	+	5.64371e18i	−9.69131e−6	+	2.84445e-6i
$723$	1.56514e24	+	1.63022e24i	0.779611	+	0.812028i
$724$	2.10276e24	−	1.35070e24i	1.03517	−	0.664936i
$725$			4.53697e23i			0.220746i
$726$	−7.06371e23	−	4.04699e23i	−0.339681	−	0.194613i
$727$			2.69189e24i			1.27943i	0.768614	+	0.639713i	$0.220947\pi$
$727$			2.69189e24i			1.27943i	−0.768614	+	0.639713i	$0.779053\pi$
$728$	−2.36770e23	−	2.05301e23i	−0.111227	−	0.0964438i
$729$	2.62499e23	−	2.13764e24i	0.121883	−	0.992544i
$730$	−6.50577e22	−	2.21658e23i	−0.0298576	−	0.101728i
$731$	−1.30977e24			−0.594151
$732$	−4.08246e24	−	9.76521e23i	−1.83053	−	0.437862i
$733$	2.64729e24			1.17332			0.586662	−	0.809832i	$-0.300442\pi$
$733$	2.64729e24			1.17332			0.586662	+	0.809832i	$0.300442\pi$
$734$	1.12842e24	+	3.84463e24i	0.494372	+	1.68437i
$735$	2.48005e23	−	2.38104e23i	0.107403	−	0.103116i
$736$	−2.68502e23	+	1.86009e24i	−0.114944	+	0.796293i
$737$		−	1.17198e24i		−	0.495958i
$738$	−4.15928e24	+	1.03885e24i	−1.73996	+	0.434582i
$739$		−	1.19295e23i		−	0.0493336i	−0.999696	−	0.0246668i	$-0.992148\pi$
$739$		−	1.19295e23i		−	0.0493336i	0.999696	−	0.0246668i	$-0.00785248\pi$
$740$	8.47594e22	+	1.31953e23i	0.0346512	+	0.0539448i
$741$	−1.42814e24	+	1.37112e24i	−0.577185	+	0.554143i
$742$	6.52662e23	−	1.91559e23i	0.260768	−	0.0765368i
$743$	−3.21740e24			−1.27087			−0.635433	−	0.772156i	$-0.719178\pi$
$743$	−3.21740e24			−1.27087			−0.635433	+	0.772156i	$0.719178\pi$
$744$	−2.20722e23	−	4.34976e24i	−0.0861937	−	1.69862i
$745$	−5.89001e23			−0.227399
$746$	−2.88948e24	+	8.48077e23i	−1.10291	+	0.323709i
$747$	7.19372e22	−	1.76526e24i	0.0271474	−	0.666169i
$748$	−4.26709e23	−	6.64298e23i	−0.159209	−	0.247856i
$749$		−	3.69785e23i		−	0.136412i
$750$	−4.15093e23	+	7.24513e23i	−0.151400	+	0.264256i
$751$			4.99842e24i			1.80257i	0.433222	+	0.901287i	$0.357376\pi$
$751$			4.99842e24i			1.80257i	−0.433222	+	0.901287i	$0.642624\pi$
$752$	−1.14358e24	+	2.50113e24i	−0.407769	+	0.891834i
$753$	4.81582e22	+	5.01607e22i	0.0169790	+	0.0176850i
$754$	1.46159e23	+	4.97977e23i	0.0509529	+	0.173601i
$755$	3.84498e23			0.132539
$756$	−5.19434e23	−	1.46847e23i	−0.177050	−	0.0500531i
$757$	−1.67910e24			−0.565930			−0.282965	−	0.959130i	$-0.591318\pi$
$757$	−1.67910e24			−0.565930			−0.282965	+	0.959130i	$0.591318\pi$
$758$	−4.32307e23	−	1.47291e24i	−0.144080	−	0.490895i
$759$	1.31887e24	+	1.37371e24i	0.434657	+	0.452730i
$760$	3.09780e23	−	3.57263e23i	0.100957	−	0.116432i
$761$		−	3.16859e24i		−	1.02117i	−0.859828	−	0.510584i	$-0.829429\pi$
$761$		−	3.16859e24i		−	1.02117i	0.859828	−	0.510584i	$-0.170571\pi$
$762$	−6.07503e23	+	1.06035e24i	−0.193611	+	0.337934i
$763$		−	5.06923e23i		−	0.159766i
$764$	4.50581e24	−	2.89429e24i	1.40436	−	0.902086i
$765$	7.68779e21	−	1.88650e23i	0.00236962	−	0.0581481i
$766$	−5.66745e24	+	1.66343e24i	−1.72760	+	0.507059i
$767$	−3.20577e24			−0.966433
$768$	−3.10337e23	+	3.33967e24i	−0.0925260	+	0.995710i
$769$	6.27580e24			1.85053			0.925263	−	0.379327i	$-0.123844\pi$
$769$	6.27580e24			1.85053			0.925263	+	0.379327i	$0.123844\pi$
$770$	7.27744e22	−	2.13596e22i	0.0212230	−	0.00622907i
$771$	2.36179e24	−	2.26751e24i	0.681208	−	0.654013i
$772$	3.59953e24	−	2.31214e24i	1.02683	−	0.659580i
$773$			6.99366e23i			0.197323i	0.995121	+	0.0986617i	$0.0314562\pi$
$773$			6.99366e23i			0.197323i	−0.995121	+	0.0986617i	$0.968544\pi$
$774$	5.46992e24	−	1.36620e24i	1.52645	−	0.381256i
$775$		−	6.01561e24i		−	1.66041i
$776$	6.29748e23	−	7.26275e23i	0.171926	−	0.198279i
$777$	−2.04484e23	+	1.96321e23i	−0.0552180	+	0.0530137i
$778$	1.04598e24	+	3.56376e24i	0.279381	+	0.951879i
$779$	6.78806e24			1.79340
$780$	−1.09767e23	+	4.58892e23i	−0.0286857	+	0.119924i
$781$	−1.31769e24			−0.340628
$782$	−3.34621e23	−	1.14009e24i	−0.0855650	−	0.291528i
$783$	5.92335e23	+	6.69522e23i	0.149828	+	0.169352i
$784$	1.60560e24	−	3.51162e24i	0.401745	−	0.878660i
$785$		−	9.92676e23i		−	0.245706i
$786$	4.94297e24	+	2.83196e24i	1.21031	+	0.693419i
$787$		−	1.72668e24i		−	0.418241i	−0.977890	−	0.209121i	$-0.932940\pi$
$787$		−	1.72668e24i		−	0.418241i	0.977890	−	0.209121i	$-0.0670601\pi$
$788$	−1.03651e24	−	1.61364e24i	−0.248371	−	0.386663i
$789$	4.09624e24	+	4.26656e24i	0.971025	+	1.01140i
$790$	3.67701e23	−	1.07922e23i	0.0862311	−	0.0253093i
$791$	−6.41665e23			−0.148870
$792$	2.47496e24	+	2.32918e24i	0.568074	+	0.534613i
$793$	−6.63205e24			−1.50600
$794$	6.66770e23	−	1.95700e23i	0.149797	−	0.0439661i
$795$	−7.09265e23	−	7.38757e23i	−0.157648	−	0.164203i
$796$	2.59773e24	+	4.04413e24i	0.571258	+	0.889332i
$797$			6.37362e24i			1.38673i	0.720589	+	0.693363i	$0.243872\pi$
$797$			6.37362e24i			1.38673i	−0.720589	+	0.693363i	$0.756128\pi$
$798$	7.41609e23	+	4.24888e23i	0.159643	+	0.0914639i
$799$		−	1.73871e24i		−	0.370322i
$800$	−6.61853e23	+	4.58509e24i	−0.139475	+	0.966236i
$801$	−2.30913e24	−	9.41007e22i	−0.481474	−	0.0196208i
$802$	−1.78401e24	−	6.07830e24i	−0.368058	−	1.25401i
$803$	−2.62893e24			−0.536658
$804$	7.32254e23	−	3.06128e24i	0.147906	−	0.618338i
$805$	1.14138e23			0.0228121
$806$	−1.93793e24	−	6.60273e24i	−0.383258	−	1.30580i
$807$	−5.10719e24	+	4.90331e24i	−0.999441	+	0.959542i
$808$	−3.60356e24	−	3.12462e24i	−0.697807	−	0.605063i
$809$			6.66084e24i			1.27634i	0.769896	+	0.638170i	$0.220308\pi$
$809$			6.66084e24i			1.27634i	−0.769896	+	0.638170i	$0.779692\pi$
$810$	1.64672e23	+	7.95870e23i	0.0312247	+	0.150911i
$811$		−	5.55829e24i		−	1.04295i	−0.853266	−	0.521476i	$-0.825382\pi$
$811$		−	5.55829e24i		−	1.04295i	0.853266	−	0.521476i	$-0.174618\pi$
$812$	1.88512e23	−	1.21090e23i	0.0350036	−	0.0224844i
$813$	8.99728e23	−	8.63810e23i	0.165326	−	0.158726i
$814$	1.71253e24	−	5.02637e23i	0.311409	−	0.0914001i
$815$	−8.57698e23			−0.154346
$816$	−6.99535e23	−	2.00180e24i	−0.124578	−	0.356495i
$817$	−8.92707e24			−1.57334
$818$	−1.76042e24	+	5.16692e23i	−0.307053	+	0.0901215i
$819$	−8.52139e23	−	3.47260e22i	−0.147095	−	0.00599434i
$820$	1.36116e24	−	8.74334e23i	0.232536	−	0.149369i
$821$		−	4.02255e24i		−	0.680118i	−0.940404	−	0.340059i	$-0.889553\pi$
$821$		−	4.02255e24i		−	0.680118i	0.940404	−	0.340059i	$-0.110447\pi$
$822$	2.98807e24	−	5.21544e24i	0.500012	−	0.872732i
$823$			1.01194e25i			1.67593i	0.545727	+	0.837963i	$0.316253\pi$
$823$			1.01194e25i			1.67593i	−0.545727	+	0.837963i	$0.683747\pi$
$824$	3.56436e23	+	3.09063e23i	0.0584252	+	0.0506600i
$825$	3.25099e24	+	3.38617e24i	0.527420	+	0.549351i
$826$	3.89762e23	+	1.32796e24i	0.0625848	+	0.213232i
$827$	6.76495e24			1.07515			0.537574	−	0.843217i	$-0.319341\pi$
$827$	6.76495e24			1.07515			0.537574	+	0.843217i	$0.319341\pi$
$828$	2.58667e24	+	4.41225e24i	0.406896	+	0.694068i
$829$	−7.43359e24			−1.15740			−0.578702	−	0.815539i	$-0.696441\pi$
$829$	−7.43359e24			−1.15740			−0.578702	+	0.815539i	$0.696441\pi$
$830$	1.87760e23	+	6.39716e23i	0.0289360	+	0.0985879i
$831$	−3.95923e24	−	4.12386e24i	−0.603952	−	0.629065i
$832$	7.50644e23	+	5.24581e24i	0.113341	+	0.792072i
$833$			2.44118e24i			0.364852i
$834$	2.61220e24	−	4.55939e24i	0.386451	−	0.674521i
$835$			5.41313e23i			0.0792708i
$836$	−2.90835e24	−	4.52770e24i	−0.421592	−	0.656333i
$837$	−7.85382e24	−	8.87726e24i	−1.12698	−	1.27383i
$838$	−2.80954e24	+	8.24614e23i	−0.399081	+	0.117132i
$839$	2.99360e24			0.420938			0.210469	−	0.977601i	$-0.432501\pi$
$839$	2.99360e24			0.420938			0.210469	+	0.977601i	$0.432501\pi$
$840$	2.03437e23	−	1.03231e22i	0.0283176	−	0.00143693i
$841$	6.88610e24			0.948872
$842$	2.96820e24	−	8.71181e23i	0.404893	−	0.118838i
$843$	−9.47237e24	+	9.09422e24i	−1.27916	+	1.22809i
$844$	1.25963e24	+	1.96099e24i	0.168397	+	0.262159i
$845$		−	4.18926e23i		−	0.0554441i
$846$	1.81363e24	+	7.26130e24i	0.237629	+	0.951407i
$847$			5.55279e23i			0.0720282i
$848$	−1.04604e25	−	4.78276e24i	−1.34333	−	0.614206i
$849$	6.50281e24	−	6.24321e24i	0.826772	−	0.793766i
$850$	−8.24835e23	−	2.81029e24i	−0.103826	−	0.353745i
$851$	2.68590e24			0.334726
$852$	−3.44190e24	−	8.23300e23i	−0.424680	−	0.101583i
$853$	6.18515e24			0.755585			0.377793	−	0.925890i	$-0.376683\pi$
$853$	6.18515e24			0.755585			0.377793	+	0.925890i	$0.376683\pi$
$854$	8.06334e23	+	2.74726e24i	0.0975266	+	0.332282i
$855$	5.23982e22	−	1.28580e24i	0.00627486	−	0.153978i
$856$	−4.09643e24	+	4.72433e24i	−0.485712	+	0.560162i
$857$			3.54511e24i			0.416192i	0.978108	+	0.208096i	$0.0667266\pi$
$857$			3.54511e24i			0.416192i	−0.978108	+	0.208096i	$0.933273\pi$
$858$	4.65914e24	+	2.66935e24i	0.541581	+	0.310287i
$859$		−	2.87837e24i		−	0.331287i	−0.986186	−	0.165643i	$-0.947030\pi$
$859$		−	2.87837e24i		−	0.331287i	0.986186	−	0.165643i	$-0.0529701\pi$
$860$	−1.79008e24	+	1.14985e24i	−0.204003	+	0.131040i
$861$	2.02514e24	+	2.10935e24i	0.228523	+	0.238025i
$862$	−6.95232e24	+	2.04054e24i	−0.776816	+	0.228000i
$863$	7.41767e24			0.820684			0.410342	−	0.911932i	$-0.365409\pi$
$863$	7.41767e24			0.820684			0.410342	+	0.911932i	$0.365409\pi$
$864$	5.00948e24	+	7.63034e24i	0.548815	+	0.835944i
$865$	−1.86277e24			−0.202080
$866$	−2.20673e24	+	6.47685e23i	−0.237053	+	0.0695764i
$867$	−5.58213e24	−	5.81424e24i	−0.593796	−	0.618487i
$868$	−2.49949e24	+	1.60554e24i	−0.263290	+	0.169123i
$869$		−	4.36104e24i		−	0.454907i
$870$	−2.92704e23	−	1.67698e23i	−0.0302353	−	0.0173226i
$871$		−	4.97311e24i		−	0.508714i
$872$	−5.61563e24	+	6.47640e24i	−0.568864	+	0.656059i
$873$	1.06520e23	−	2.61388e24i	0.0106858	−	0.262219i
$874$	−2.28070e24	−	7.77056e24i	−0.226580	−	0.771978i
$875$	5.69541e23			0.0560346
$876$	−6.86694e24	−	1.64257e24i	−0.669080	−	0.160043i
$877$	1.12607e25			1.08660			0.543301	−	0.839538i	$-0.317174\pi$
$877$	1.12607e25			1.08660			0.543301	+	0.839538i	$0.317174\pi$
$878$	4.99392e24	+	1.70148e25i	0.477241	+	1.62601i
$879$	3.91521e23	−	3.75891e23i	0.0370553	−	0.0355760i
$880$	−1.16638e24	−	5.33297e23i	−0.109329	−	0.0499881i
$881$		−	1.33930e24i		−	0.124332i	−0.998066	−	0.0621658i	$-0.980199\pi$
$881$		−	1.33930e24i		−	0.124332i	0.998066	−	0.0621658i	$-0.0198007\pi$
$882$	−2.54636e24	−	1.01950e25i	−0.234119	−	0.937353i
$883$		−	3.51348e24i		−	0.319942i	−0.987122	−	0.159971i	$-0.948860\pi$
$883$		−	3.51348e24i		−	0.319942i	0.987122	−	0.159971i	$-0.0511401\pi$
$884$	−1.81068e24	−	2.81885e24i	−0.163304	−	0.254231i
$885$	1.50313e24	−	1.44313e24i	0.134270	−	0.128910i
$886$	1.76425e25	−	5.17815e24i	1.56089	−	0.458129i
$887$	6.84057e24			0.599434			0.299717	−	0.954028i	$-0.403108\pi$
$887$	6.84057e24			0.599434			0.299717	+	0.954028i	$0.403108\pi$
$888$	4.78729e24	−	2.42924e23i	0.415508	−	0.0210843i
$889$	8.33542e23			0.0716576
$890$	8.36809e23	−	2.45608e23i	0.0712543	−	0.0209135i
$891$	9.21839e24	+	7.52577e23i	0.777490	+	0.0634732i
$892$	−4.49215e24	−	6.99336e24i	−0.375278	−	0.584231i
$893$		−	1.18507e25i		−	0.980629i
$894$	−8.94941e24	+	1.56205e25i	−0.733543	+	1.28034i
$895$			2.29120e24i			0.186023i
$896$	2.08176e24	−	9.48740e23i	0.167422	−	0.0763008i
$897$	5.59643e24	+	5.82914e24i	0.445836	+	0.464375i
$898$	−3.37777e24	−	1.15084e25i	−0.266552	−	0.908167i
$899$	4.91974e24			0.384578
$900$	6.37610e24	+	1.08761e25i	0.493735	+	0.842195i
$901$	7.27178e24			0.557802
$902$	−5.18494e24	−	1.76656e25i	−0.393992	−	1.34237i
$903$	−2.66330e24	−	2.77404e24i	−0.200481	−	0.208817i
$904$	8.19786e24	+	7.10830e24i	0.611320	+	0.530071i
$905$			2.56660e24i			0.189603i
$906$	5.84214e24	−	1.01970e25i	0.427545	−	0.746247i
$907$			1.89054e25i			1.37064i	0.728241	+	0.685321i	$0.240338\pi$
$907$			1.89054e25i			1.37064i	−0.728241	+	0.685321i	$0.759662\pi$
$908$	−6.31943e24	+	4.05926e24i	−0.453888	+	0.291553i
$909$	−1.29693e25	−	5.28519e23i	−0.922834	−	0.0376069i
$910$	3.08808e23	−	9.06366e22i	0.0217689	−	0.00638928i
$911$	−6.55601e24			−0.457861			−0.228930	−	0.973443i	$-0.573523\pi$
$911$	−6.55601e24			−0.457861			−0.228930	+	0.973443i	$0.573523\pi$
$912$	−4.76786e24	−	1.36438e25i	−0.329889	−	0.944014i
$913$	7.58724e24			0.520094
$914$	−2.35662e24	+	6.91681e23i	−0.160047	+	0.0469746i
$915$	3.10966e24	−	2.98552e24i	0.209235	−	0.200882i
$916$	−6.38526e24	+	4.10154e24i	−0.425664	+	0.273423i
$917$		−	3.88568e24i		−	0.256642i
$918$	−4.88626e24	−	3.07028e24i	−0.319752	−	0.200916i
$919$			3.91192e24i			0.253635i	0.991926	+	0.126817i	$0.0404762\pi$
$919$			3.91192e24i			0.253635i	−0.991926	+	0.126817i	$0.959524\pi$
$920$	−1.45822e24	−	1.26441e24i	−0.0936754	−	0.0812252i
$921$	−9.88652e24	+	9.49183e24i	−0.629269	+	0.604148i
$922$	7.81419e24	+	2.66237e25i	0.492800	+	1.67902i
$923$	−5.59145e24			−0.349389
$924$	5.39285e23	−	2.25454e24i	0.0333892	−	0.139588i
$925$	6.62070e24			0.406162
$926$	−1.20205e24	−	4.09548e24i	−0.0730680	−	0.248950i
$927$	1.28282e24	+	5.22769e22i	0.0772660	+	0.00314871i
$928$	−3.74982e24	−	5.41283e23i	−0.223796	−	0.0323047i
$929$		−	6.68774e24i		−	0.395500i	−0.980253	−	0.197750i	$-0.936637\pi$
$929$		−	6.68774e24i		−	0.395500i	0.980253	−	0.197750i	$-0.0633633\pi$
$930$	3.88098e24	+	2.22352e24i	0.227424	+	0.130298i
$931$			1.66385e25i			0.966143i
$932$	1.28336e25	+	1.99792e25i	0.738435	+	1.14959i
$933$	−8.22980e24	−	8.57200e24i	−0.469240	−	0.488752i
$934$	1.87241e25	−	5.49562e24i	1.05792	−	0.310505i
$935$	8.10833e23			0.0453976
$936$	1.05022e25	+	9.88355e24i	0.582685	+	0.548363i
$937$	−3.05913e24			−0.168194			−0.0840970	−	0.996458i	$-0.526801\pi$
$937$	−3.05913e24			−0.168194			−0.0840970	+	0.996458i	$0.526801\pi$
$938$	−2.06006e24	+	6.04638e23i	−0.112242	+	0.0329436i
$939$	−6.69592e24	−	6.97435e24i	−0.361537	−	0.376570i
$940$	−1.52642e24	−	2.37632e24i	−0.0816746	−	0.127151i
$941$			1.67669e25i			0.889078i	0.895759	+	0.444539i	$0.146633\pi$
$941$			1.67669e25i			0.889078i	−0.895759	+	0.444539i	$0.853367\pi$
$942$	−2.63261e25	−	1.50829e25i	−1.38342	−	0.792598i
$943$		−	2.77064e25i		−	1.44288i
$944$	9.73139e24	−	2.12836e25i	0.502242	−	1.09846i
$945$	4.15187e23	−	3.67321e23i	0.0212360	−	0.0187878i
$946$	6.81879e24	+	2.32323e25i	0.345647	+	1.17765i
$947$	−2.40360e25			−1.20750			−0.603749	−	0.797174i	$-0.706327\pi$
$947$	−2.40360e25			−1.20750			−0.603749	+	0.797174i	$0.706327\pi$
$948$	2.72480e24	−	1.13913e25i	0.135664	−	0.567157i
$949$	−1.11555e25			−0.550460
$950$	−5.62188e24	−	1.91543e25i	−0.274936	−	0.936732i
$951$	9.95233e24	−	9.55502e24i	0.482381	−	0.463124i
$952$	−9.47536e23	+	1.09277e24i	−0.0455178	+	0.0524948i
$953$			1.35787e25i			0.646498i	0.946314	+	0.323249i	$0.104775\pi$
$953$			1.35787e25i			0.646498i	−0.946314	+	0.323249i	$0.895225\pi$
$954$	−3.03688e25	+	7.58510e24i	−1.43307	+	0.357932i
$955$			5.49973e24i			0.257225i
$956$	7.44348e24	−	4.78128e24i	0.345051	−	0.221642i
$957$	−2.76931e24	+	2.65875e24i	−0.127239	+	0.122159i
$958$	−7.17282e24	+	2.10526e24i	−0.326650	+	0.0958735i
$959$	−4.09987e24			−0.185060
$960$	−2.71345e24	−	2.12176e24i	−0.121399	−	0.0949274i
$961$	−4.26812e25			−1.89272
$962$	7.26688e24	−	2.13287e24i	0.319418	−	0.0937509i
$963$	−6.92897e23	+	1.70030e25i	−0.0301888	+	0.740801i
$964$	−2.19313e25	+	1.40874e25i	−0.947129	+	0.608383i
$965$			4.39354e24i			0.188075i
$966$	1.73424e24	−	3.02698e24i	0.0735873	−	0.128441i
$967$		−	2.41959e25i		−	1.01769i	−0.860858	−	0.508846i	$-0.830072\pi$
$967$		−	2.41959e25i		−	1.01769i	0.860858	−	0.508846i	$-0.169928\pi$
$968$	6.15132e24	−	7.09419e24i	0.256465	−	0.295776i
$969$	6.32822e24	+	6.59135e24i	0.261535	+	0.272410i
$970$	2.78022e23	+	9.47247e23i	0.0113899	+	0.0388064i
$971$	−3.33242e25			−1.35331			−0.676653	−	0.736302i	$-0.736570\pi$
$971$	−3.33242e25			−1.35331			−0.676653	+	0.736302i	$0.736570\pi$
$972$	2.36088e25	+	7.72546e24i	0.950410	+	0.311001i
$973$	−3.58414e24			−0.143030
$974$	1.18700e25	+	4.04423e25i	0.469570	+	1.59987i
$975$	1.37951e25	+	1.43687e25i	0.540985	+	0.563480i
$976$	2.01322e25	−	4.40312e25i	0.782649	−	1.71174i
$977$		−	9.12201e24i		−	0.351550i	−0.984430	−	0.175775i	$-0.943757\pi$
$977$		−	9.12201e24i		−	0.351550i	0.984430	−	0.175775i	$-0.0562431\pi$
$978$	−1.30320e25	+	2.27464e25i	−0.497889	+	0.869026i
$979$		−	9.92482e24i		−	0.375898i
$980$	2.14312e24	+	3.33639e24i	0.0804681	+	0.125272i
$981$	−9.49865e23	+	2.33087e25i	−0.0353570	+	0.867623i
$982$	3.24878e25	−	9.53532e24i	1.19887	−	0.351875i
$983$	2.30673e25			0.843903			0.421951	−	0.906618i	$-0.361345\pi$
$983$	2.30673e25			0.843903			0.421951	+	0.906618i	$0.361345\pi$
$984$	−2.50588e24	−	4.93832e25i	−0.0908869	−	1.79110i
$985$	1.96958e24			0.0708216
$986$	2.29834e24	−	6.74574e23i	0.0819333	−	0.0240478i
$987$	3.68253e24	−	3.53551e24i	0.130152	−	0.124956i
$988$	−1.23411e25	−	1.92126e25i	−0.432436	−	0.673214i
$989$			3.64371e25i			1.26583i
$990$	−3.38624e24	+	8.45769e23i	−0.116632	+	0.0291308i
$991$			1.23964e25i			0.423322i	0.977343	+	0.211661i	$0.0678873\pi$
$991$			1.23964e25i			0.423322i	−0.977343	+	0.211661i	$0.932113\pi$
$992$	4.97193e25	+	7.17691e24i	1.68335	+	0.242990i
$993$	2.19227e25	−	2.10475e25i	0.735912	−	0.706533i
$994$	6.79816e23	+	2.31620e24i	0.0226260	+	0.0770888i
$995$	−4.93621e24			−0.162891
$996$	1.98183e25	+	4.74053e24i	0.648430	+	0.155104i
$997$	1.62415e25			0.526887			0.263443	−	0.964675i	$-0.415142\pi$
$997$	1.62415e25			0.526887			0.263443	+	0.964675i	$0.415142\pi$
$998$	5.90043e23	+	2.01033e24i	0.0189790	+	0.0646634i
$999$	9.77020e24	−	8.64382e24i	0.311599	−	0.275676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.18.b.a.11.4	yes	32
3.2	odd	2	inner	12.18.b.a.11.29	yes	32
4.3	odd	2	inner	12.18.b.a.11.30	yes	32
12.11	even	2	inner	12.18.b.a.11.3	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.18.b.a.11.3	✓	32	12.11	even	2	inner
12.18.b.a.11.4	yes	32	1.1	even	1	trivial
12.18.b.a.11.29	yes	32	3.2	odd	2	inner
12.18.b.a.11.30	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)

\(f(q)\)	\(=\)	\(q+(-347.385 + 101.959i) q^{2} +(-7870.26 - 8197.51i) q^{3} +(110281. - 70838.2i) q^{4} +134607. i q^{5} +(3.56982e6 + 2.04525e6i) q^{6} -2.80624e6i q^{7} +(-3.10872e7 + 3.58523e7i) q^{8} +(-5.25830e6 + 1.29033e8i) q^{9} +O(q^{10})\)	\(q+(-347.385 + 101.959i) q^{2} +(-7870.26 - 8197.51i) q^{3} +(110281. - 70838.2i) q^{4} +134607. i q^{5} +(3.56982e6 + 2.04525e6i) q^{6} -2.80624e6i q^{7} +(-3.10872e7 + 3.58523e7i) q^{8} +(-5.25830e6 + 1.29033e8i) q^{9} +(-1.37244e7 - 4.67604e7i) q^{10} -5.54594e8 q^{11} +(-1.44863e9 - 3.46512e8i) q^{12} -2.35334e9 q^{13} +(2.86122e8 + 9.74846e8i) q^{14} +(1.10344e9 - 1.05939e9i) q^{15} +(7.14376e9 - 1.56242e10i) q^{16} +1.08615e10i q^{17} +(-1.13295e10 - 4.53603e10i) q^{18} +7.40293e10i q^{19} +(9.53532e9 + 1.48445e10i) q^{20} +(-2.30042e10 + 2.20858e10i) q^{21} +(1.92657e11 - 5.65459e10i) q^{22} +3.02161e11 q^{23} +(5.38564e11 - 2.73286e10i) q^{24} +7.44820e11 q^{25} +(8.17514e11 - 2.39945e11i) q^{26} +(1.09913e12 - 9.72418e11i) q^{27} +(-1.98789e11 - 3.09474e11i) q^{28} +6.09136e11i q^{29} +(-2.75305e11 + 4.80523e11i) q^{30} -8.07659e12i q^{31} +(-8.88607e11 + 6.15597e12i) q^{32} +(4.36479e12 + 4.54629e12i) q^{33} +(-1.10743e12 - 3.77311e12i) q^{34} +3.77740e11 q^{35} +(8.56058e12 + 1.46023e13i) q^{36} +8.88899e12 q^{37} +(-7.54797e12 - 2.57167e13i) q^{38} +(1.85214e13 + 1.92915e13i) q^{39} +(-4.82596e12 - 4.18456e12i) q^{40} -9.16942e13i q^{41} +(5.73946e12 - 1.00178e13i) q^{42} +1.20588e14i q^{43} +(-6.11609e13 + 3.92864e13i) q^{44} +(-1.73688e13 - 7.07803e11i) q^{45} +(-1.04966e14 + 3.08081e13i) q^{46} -1.60081e14 q^{47} +(-1.84303e14 + 6.44051e13i) q^{48} +2.24756e14 q^{49} +(-2.58739e14 + 7.59413e13i) q^{50} +(8.90371e13 - 8.54826e13i) q^{51} +(-2.59528e14 + 1.66706e14i) q^{52} -6.69502e14i q^{53} +(-2.82676e14 + 4.49870e14i) q^{54} -7.46522e13i q^{55} +(1.00610e14 + 8.72382e13i) q^{56} +(6.06856e14 - 5.82629e14i) q^{57} +(-6.21071e13 - 2.11605e14i) q^{58} +1.36222e15 q^{59} +(4.66429e13 - 1.94996e14i) q^{60} +2.81814e15 q^{61} +(8.23483e14 + 2.80569e15i) q^{62} +(3.62098e14 + 1.47560e13i) q^{63} +(-3.18970e14 - 2.22909e15i) q^{64} -3.16776e14i q^{65} +(-1.97980e15 - 1.13428e15i) q^{66} +2.11322e15i q^{67} +(7.69408e14 + 1.19781e15i) q^{68} +(-2.37808e15 - 2.47697e15i) q^{69} +(-1.31221e14 + 3.85140e13i) q^{70} +2.37596e15 q^{71} +(-4.46266e15 - 4.19980e15i) q^{72} +4.74029e15 q^{73} +(-3.08790e15 + 9.06315e14i) q^{74} +(-5.86193e15 - 6.10568e15i) q^{75} +(5.24410e15 + 8.16399e15i) q^{76} +1.55632e15i q^{77} +(-8.40100e15 - 4.81316e15i) q^{78} +7.86350e15i q^{79} +(2.10312e15 + 9.61600e14i) q^{80} +(-1.66219e16 - 1.35699e15i) q^{81} +(9.34908e15 + 3.18532e16i) q^{82} -1.36807e16 q^{83} +(-9.72396e14 + 4.06522e15i) q^{84} -1.46203e15 q^{85} +(-1.22951e16 - 4.18906e16i) q^{86} +(4.99340e15 - 4.79406e15i) q^{87} +(1.72408e16 - 1.98834e16i) q^{88} +1.78957e16i q^{89} +(6.10581e15 - 1.52502e15i) q^{90} +6.60403e15i q^{91} +(3.33225e16 - 2.14045e16i) q^{92} +(-6.62079e16 + 6.35648e16i) q^{93} +(5.56096e16 - 1.63217e16i) q^{94} -9.96486e15 q^{95} +(5.74572e16 - 4.11647e16i) q^{96} -2.02574e16 q^{97} +(-7.80767e16 + 2.29159e16i) q^{98} +(2.91622e15 - 7.15609e16i) 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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