LMFDB - Embedded newform 20.11.d.d.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,11,Mod(19,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("20.19");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	20.d (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:	$12.7071450535$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	20.19
Dual form			20.11.d.d.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-23.9223 + 21.2538i) q^{2} +94.4407 q^{3} +(120.549 - 1016.88i) q^{4} +(3107.65 - 328.861i) q^{5} +(-2259.24 + 2007.23i) q^{6} -20081.9 q^{7} +(18728.8 + 26888.2i) q^{8} -50129.9 q^{9} +O(q^{10})$	\(q+(-23.9223 + 21.2538i) q^{2} +94.4407 q^{3} +(120.549 - 1016.88i) q^{4} +(3107.65 - 328.861i) q^{5} +(-2259.24 + 2007.23i) q^{6} -20081.9 q^{7} +(18728.8 + 26888.2i) q^{8} -50129.9 q^{9} +(-67352.4 + 73916.5i) q^{10} -198980. i q^{11} +(11384.7 - 96034.9i) q^{12} +352944. i q^{13} +(480404. - 426817. i) q^{14} +(293489. - 31057.9i) q^{15} +(-1.01951e6 - 245167. i) q^{16} -1.97539e6i q^{17} +(1.19922e6 - 1.06545e6i) q^{18} -3.78502e6i q^{19} +(40211.3 - 3.19975e6i) q^{20} -1.89655e6 q^{21} +(4.22910e6 + 4.76006e6i) q^{22} -4.41929e6 q^{23} +(1.76876e6 + 2.53934e6i) q^{24} +(9.54933e6 - 2.04397e6i) q^{25} +(-7.50141e6 - 8.44321e6i) q^{26} -1.03109e7 q^{27} +(-2.42085e6 + 2.04209e7i) q^{28} -1.04937e7 q^{29} +(-6.36081e6 + 6.98073e6i) q^{30} +1.45342e7i q^{31} +(2.95998e7 - 1.58036e7i) q^{32} -1.87919e7i q^{33} +(4.19846e7 + 4.72558e7i) q^{34} +(-6.24074e7 + 6.60416e6i) q^{35} +(-6.04311e6 + 5.09761e7i) q^{36} -1.27275e8i q^{37} +(8.04463e7 + 9.05463e7i) q^{38} +3.33323e7i q^{39} +(6.70450e7 + 7.73998e7i) q^{40} +9.37194e7 q^{41} +(4.53697e7 - 4.03089e7i) q^{42} -2.01807e8 q^{43} +(-2.02339e8 - 2.39869e7i) q^{44} +(-1.55786e8 + 1.64858e7i) q^{45} +(1.05719e8 - 9.39268e7i) q^{46} +6.61391e7 q^{47} +(-9.62835e7 - 2.31538e7i) q^{48} +1.20807e8 q^{49} +(-1.84999e8 + 2.51856e8i) q^{50} -1.86557e8i q^{51} +(3.58901e8 + 4.25470e7i) q^{52} +8.60363e7i q^{53} +(2.46661e8 - 2.19147e8i) q^{54} +(-6.54370e7 - 6.18361e8i) q^{55} +(-3.76109e8 - 5.39965e8i) q^{56} -3.57460e8i q^{57} +(2.51033e8 - 2.23031e8i) q^{58} +5.09233e8i q^{59} +(3.79758e6 - 3.02187e8i) q^{60} -2.18265e8 q^{61} +(-3.08907e8 - 3.47691e8i) q^{62} +1.00670e9 q^{63} +(-3.72207e8 + 1.00717e9i) q^{64} +(1.16070e8 + 1.09682e9i) q^{65} +(3.99399e8 + 4.49544e8i) q^{66} +7.20783e8 q^{67} +(-2.00873e9 - 2.38131e8i) q^{68} -4.17361e8 q^{69} +(1.35256e9 - 1.48438e9i) q^{70} +1.16390e9i q^{71} +(-9.38873e8 - 1.34790e9i) q^{72} +1.07283e9i q^{73} +(2.70509e9 + 3.04471e9i) q^{74} +(9.01845e8 - 1.93034e8i) q^{75} +(-3.84891e9 - 4.56281e8i) q^{76} +3.99590e9i q^{77} +(-7.08438e8 - 7.97383e8i) q^{78} +3.63818e9i q^{79} +(-3.24891e9 - 4.26616e8i) q^{80} +1.98635e9 q^{81} +(-2.24198e9 + 1.99190e9i) q^{82} +1.43526e9 q^{83} +(-2.28627e8 + 1.92856e9i) q^{84} +(-6.49629e8 - 6.13881e9i) q^{85} +(4.82769e9 - 4.28918e9i) q^{86} -9.91032e8 q^{87} +(5.35022e9 - 3.72666e9i) q^{88} -9.94640e8 q^{89} +(3.37637e9 - 3.70543e9i) q^{90} -7.08777e9i q^{91} +(-5.32741e8 + 4.49388e9i) q^{92} +1.37262e9i q^{93} +(-1.58220e9 + 1.40571e9i) q^{94} +(-1.24475e9 - 1.17625e10i) q^{95} +(2.79542e9 - 1.49250e9i) q^{96} -4.59239e9i q^{97} +(-2.88997e9 + 2.56761e9i) q^{98} +9.97488e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9}+O(q^{10}) $ 24 * q + 608 * q^4 + 8280 * q^5 - 19584 * q^6 + 597192 * q^9	$ 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9} + 223600 q^{10} - 1706016 q^{14} - 4733376 q^{16} + 1631520 q^{20} - 13030368 q^{21} + 10190784 q^{24} + 8826200 q^{25} - 9454368 q^{26} + 121656816 q^{29} + 103616160 q^{30} - 335231168 q^{34} - 276632160 q^{36} - 559048000 q^{40} + 892843248 q^{41} + 766329600 q^{44} - 248162040 q^{45} + 433181216 q^{46} - 738102008 q^{49} + 765396000 q^{50} + 139387968 q^{54} - 2629032384 q^{56} + 296160000 q^{60} + 228563248 q^{61} - 1875284992 q^{64} - 2069145600 q^{65} - 1440259200 q^{66} - 943422432 q^{69} + 3242642240 q^{70} + 21045467232 q^{74} + 828422400 q^{76} + 11736799680 q^{80} - 5619065544 q^{81} - 28069573632 q^{84} - 18119744000 q^{85} + 8163556416 q^{86} + 4631088816 q^{89} - 16754463600 q^{90} + 63404384 q^{94} - 5617046784 q^{96}+O(q^{100}) $ 24 * q + 608 * q^4 + 8280 * q^5 - 19584 * q^6 + 597192 * q^9 + 223600 * q^10 - 1706016 * q^14 - 4733376 * q^16 + 1631520 * q^20 - 13030368 * q^21 + 10190784 * q^24 + 8826200 * q^25 - 9454368 * q^26 + 121656816 * q^29 + 103616160 * q^30 - 335231168 * q^34 - 276632160 * q^36 - 559048000 * q^40 + 892843248 * q^41 + 766329600 * q^44 - 248162040 * q^45 + 433181216 * q^46 - 738102008 * q^49 + 765396000 * q^50 + 139387968 * q^54 - 2629032384 * q^56 + 296160000 * q^60 + 228563248 * q^61 - 1875284992 * q^64 - 2069145600 * q^65 - 1440259200 * q^66 - 943422432 * q^69 + 3242642240 * q^70 + 21045467232 * q^74 + 828422400 * q^76 + 11736799680 * q^80 - 5619065544 * q^81 - 28069573632 * q^84 - 18119744000 * q^85 + 8163556416 * q^86 + 4631088816 * q^89 - 16754463600 * q^90 + 63404384 * q^94 - 5617046784 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−23.9223	+	21.2538i	−0.747571	+	0.664182i
$2$	−23.9223	+	21.2538i	−0.747571	+	0.664182i
$3$	94.4407			0.388645			0.194323	−	0.980938i	$-0.437749\pi$
$3$	94.4407			0.388645			0.194323	+	0.980938i	$0.437749\pi$
$4$	120.549	−	1016.88i	0.117724	−	0.993046i
$5$	3107.65	−	328.861i	0.994447	−	0.105236i
$5$	3107.65	−	328.861i	0.994447	−	0.105236i
$6$	−2259.24	+	2007.23i	−0.290540	+	0.258131i
$7$	−20081.9			−1.19485			−0.597426	−	0.801924i	$-0.703810\pi$
$7$	−20081.9			−1.19485			−0.597426	+	0.801924i	$0.703810\pi$
$8$	18728.8	+	26888.2i	0.571557	+	0.820562i
$9$	−50129.9			−0.848955
$10$	−67352.4	+	73916.5i	−0.673524	+	0.739165i
$11$		−	198980.i		−	1.23551i	−0.786370	−	0.617756i	$-0.788042\pi$
$11$		−	198980.i		−	1.23551i	0.786370	−	0.617756i	$-0.211958\pi$
$12$	11384.7	−	96034.9i	0.0457527	−	0.385943i
$13$			352944.i			0.950580i	0.879829	+	0.475290i	$0.157657\pi$
$13$			352944.i			0.950580i	−0.879829	+	0.475290i	$0.842343\pi$
$14$	480404.	−	426817.i	0.893236	−	0.793600i
$15$	293489.	−	31057.9i	0.386487	−	0.0408993i
$16$	−1.01951e6	−	245167.i	−0.972282	−	0.233810i
$17$		−	1.97539e6i		−	1.39126i	−0.718401	−	0.695630i	$-0.755126\pi$
$17$		−	1.97539e6i		−	1.39126i	0.718401	−	0.695630i	$-0.244874\pi$
$18$	1.19922e6	−	1.06545e6i	0.634654	−	0.563861i
$19$		−	3.78502e6i		−	1.52862i	−0.644847	−	0.764312i	$-0.723079\pi$
$19$		−	3.78502e6i		−	1.52862i	0.644847	−	0.764312i	$-0.276921\pi$
$20$	40211.3	−	3.19975e6i	0.0125660	−	0.999921i
$21$	−1.89655e6			−0.464373
$22$	4.22910e6	+	4.76006e6i	0.820605	+	0.923633i
$23$	−4.41929e6			−0.686615			−0.343307	−	0.939223i	$-0.611547\pi$
$23$	−4.41929e6			−0.686615			−0.343307	+	0.939223i	$0.611547\pi$
$24$	1.76876e6	+	2.53934e6i	0.222133	+	0.318907i
$25$	9.54933e6	−	2.04397e6i	0.977851	−	0.209303i
$26$	−7.50141e6	−	8.44321e6i	−0.631358	−	0.710626i
$27$	−1.03109e7			−0.718587
$28$	−2.42085e6	+	2.04209e7i	−0.140662	+	1.18654i
$29$	−1.04937e7			−0.511609			−0.255804	−	0.966729i	$-0.582340\pi$
$29$	−1.04937e7			−0.511609			−0.255804	+	0.966729i	$0.582340\pi$
$30$	−6.36081e6	+	6.98073e6i	−0.261762	+	0.287273i
$31$			1.45342e7i			0.507671i	0.967247	+	0.253835i	$0.0816922\pi$
$31$			1.45342e7i			0.507671i	−0.967247	+	0.253835i	$0.918308\pi$
$32$	2.95998e7	−	1.58036e7i	0.882142	−	0.470983i
$33$		−	1.87919e7i		−	0.480176i
$34$	4.19846e7	+	4.72558e7i	0.924050	+	1.04006i
$35$	−6.24074e7	+	6.60416e6i	−1.18822	+	0.125741i
$36$	−6.04311e6	+	5.09761e7i	−0.0999420	+	0.843052i
$37$		−	1.27275e8i		−	1.83542i	−0.397250	−	0.917710i	$-0.630035\pi$
$37$		−	1.27275e8i		−	1.83542i	0.397250	−	0.917710i	$-0.369965\pi$
$38$	8.04463e7	+	9.05463e7i	1.01529	+	1.14275i
$39$			3.33323e7i			0.369438i
$40$	6.70450e7	+	7.73998e7i	0.654736	+	0.755858i
$41$	9.37194e7			0.808929			0.404464	−	0.914554i	$-0.367458\pi$
$41$	9.37194e7			0.808929			0.404464	+	0.914554i	$0.367458\pi$
$42$	4.53697e7	−	4.03089e7i	0.347152	−	0.308429i
$43$	−2.01807e8			−1.37276			−0.686380	−	0.727243i	$-0.740801\pi$
$43$	−2.01807e8			−1.37276			−0.686380	+	0.727243i	$0.740801\pi$
$44$	−2.02339e8	−	2.39869e7i	−1.22692	−	0.145449i
$45$	−1.55786e8	+	1.64858e7i	−0.844241	+	0.0893403i
$46$	1.05719e8	−	9.39268e7i	0.513293	−	0.456038i
$47$	6.61391e7			0.288383			0.144191	−	0.989550i	$-0.453942\pi$
$47$	6.61391e7			0.288383			0.144191	+	0.989550i	$0.453942\pi$
$48$	−9.62835e7	−	2.31538e7i	−0.377873	−	0.0908691i
$49$	1.20807e8			0.427672
$50$	−1.84999e8	+	2.51856e8i	−0.591998	+	0.805940i
$51$		−	1.86557e8i		−	0.540706i
$52$	3.58901e8	+	4.25470e7i	0.943970	+	0.111906i
$53$			8.60363e7i			0.205732i	0.994695	+	0.102866i	$0.0328013\pi$
$53$			8.60363e7i			0.205732i	−0.994695	+	0.102866i	$0.967199\pi$
$54$	2.46661e8	−	2.19147e8i	0.537195	−	0.477273i
$55$	−6.54370e7	−	6.18361e8i	−0.130020	−	1.22865i
$56$	−3.76109e8	−	5.39965e8i	−0.682926	−	0.980451i
$57$		−	3.57460e8i		−	0.594092i
$58$	2.51033e8	−	2.23031e8i	0.382464	−	0.339802i
$59$			5.09233e8i			0.712290i	0.934431	+	0.356145i	$0.115909\pi$
$59$			5.09233e8i			0.712290i	−0.934431	+	0.356145i	$0.884091\pi$
$60$	3.79758e6	−	3.02187e8i	0.00488372	−	0.388614i
$61$	−2.18265e8			−0.258425			−0.129212	−	0.991617i	$-0.541245\pi$
$61$	−2.18265e8			−0.258425			−0.129212	+	0.991617i	$0.541245\pi$
$62$	−3.08907e8	−	3.47691e8i	−0.337186	−	0.379520i
$63$	1.00670e9			1.01438
$64$	−3.72207e8	+	1.00717e9i	−0.346645	+	0.937997i
$65$	1.16070e8	+	1.09682e9i	0.100035	+	0.945302i
$66$	3.99399e8	+	4.49544e8i	0.318924	+	0.358965i
$67$	7.20783e8			0.533864			0.266932	−	0.963715i	$-0.413990\pi$
$67$	7.20783e8			0.533864			0.266932	+	0.963715i	$0.413990\pi$
$68$	−2.00873e9	−	2.38131e8i	−1.38158	−	0.163784i
$69$	−4.17361e8			−0.266849
$70$	1.35256e9	−	1.48438e9i	0.804762	−	0.883194i
$71$			1.16390e9i			0.645098i	0.946553	+	0.322549i	$0.104540\pi$
$71$			1.16390e9i			0.645098i	−0.946553	+	0.322549i	$0.895460\pi$
$72$	−9.38873e8	−	1.34790e9i	−0.485226	−	0.696620i
$73$			1.07283e9i			0.517506i	0.965943	+	0.258753i	$0.0833116\pi$
$73$			1.07283e9i			0.517506i	−0.965943	+	0.258753i	$0.916688\pi$
$74$	2.70509e9	+	3.04471e9i	1.21905	+	1.37211i
$75$	9.01845e8	−	1.93034e8i	0.380037	−	0.0813444i
$76$	−3.84891e9	−	4.56281e8i	−1.51799	−	0.179955i
$77$			3.99590e9i			1.47625i
$78$	−7.08438e8	−	7.97383e8i	−0.245374	−	0.276181i
$79$			3.63818e9i			1.18236i	0.806541	+	0.591179i	$0.201337\pi$
$79$			3.63818e9i			1.18236i	−0.806541	+	0.591179i	$0.798663\pi$
$80$	−3.24891e9	−	4.26616e8i	−0.991489	−	0.130193i
$81$	1.98635e9			0.569680
$82$	−2.24198e9	+	1.99190e9i	−0.604731	+	0.537276i
$83$	1.43526e9			0.364367			0.182183	−	0.983265i	$-0.441684\pi$
$83$	1.43526e9			0.364367			0.182183	+	0.983265i	$0.441684\pi$
$84$	−2.28627e8	+	1.92856e9i	−0.0546677	+	0.461144i
$85$	−6.49629e8	−	6.13881e9i	−0.146410	−	1.38353i
$86$	4.82769e9	−	4.28918e9i	1.02623	−	0.911763i
$87$	−9.91032e8			−0.198834
$88$	5.35022e9	−	3.72666e9i	1.01381	−	0.706166i
$89$	−9.94640e8			−0.178121			−0.0890606	−	0.996026i	$-0.528386\pi$
$89$	−9.94640e8			−0.178121			−0.0890606	+	0.996026i	$0.528386\pi$
$90$	3.37637e9	−	3.70543e9i	0.571792	−	0.627518i
$91$		−	7.08777e9i		−	1.13580i
$92$	−5.32741e8	+	4.49388e9i	−0.0808308	+	0.681840i
$93$			1.37262e9i			0.197304i
$94$	−1.58220e9	+	1.40571e9i	−0.215586	+	0.191539i
$95$	−1.24475e9	−	1.17625e10i	−0.160866	−	1.52014i
$96$	2.79542e9	−	1.49250e9i	0.342840	−	0.183045i
$97$		−	4.59239e9i		−	0.534786i	−0.963588	−	0.267393i	$-0.913838\pi$
$97$		−	4.59239e9i		−	0.534786i	0.963588	−	0.267393i	$-0.0861622\pi$
$98$	−2.88997e9	+	2.56761e9i	−0.319715	+	0.284052i
$99$			9.97488e9i			1.04889i
$100$	−9.27311e8	−	9.95691e9i	−0.0927311	−	0.995691i
$101$	−4.05319e9			−0.385647			−0.192824	−	0.981233i	$-0.561764\pi$
$101$	−4.05319e9			−0.385647			−0.192824	+	0.981233i	$0.561764\pi$
$102$	3.96506e9	+	4.46287e9i	0.359127	+	0.404216i
$103$	6.33329e8			0.0546315			0.0273158	−	0.999627i	$-0.491304\pi$
$103$	6.33329e8			0.0546315			0.0273158	+	0.999627i	$0.491304\pi$
$104$	−9.49001e9	+	6.61021e9i	−0.780010	+	0.543311i
$105$	−5.89380e9	+	6.23701e8i	−0.461795	+	0.0488686i
$106$	−1.82860e9	−	2.05818e9i	−0.136644	−	0.153799i
$107$	−2.41225e10			−1.71990			−0.859949	−	0.510380i	$-0.829505\pi$
$107$	−2.41225e10			−1.71990			−0.859949	+	0.510380i	$0.829505\pi$
$108$	−1.24297e9	+	1.04850e10i	−0.0845946	+	0.713590i
$109$	1.71612e10			1.11536			0.557680	−	0.830056i	$-0.311692\pi$
$109$	1.71612e10			1.11536			0.557680	+	0.830056i	$0.311692\pi$
$110$	1.47079e10	+	1.34018e10i	0.913248	+	0.832147i
$111$		−	1.20200e10i		−	0.713327i
$112$	2.04737e10	+	4.92342e9i	1.16173	+	0.279368i
$113$		−	1.15376e10i		−	0.626216i	−0.949717	−	0.313108i	$-0.898630\pi$
$113$		−	1.15376e10i		−	0.626216i	0.949717	−	0.313108i	$-0.101370\pi$
$114$	7.59741e9	+	8.55126e9i	0.394585	+	0.444126i
$115$	−1.37336e10	+	1.45333e9i	−0.682802	+	0.0722564i
$116$	−1.26500e9	+	1.06708e10i	−0.0602284	+	0.508051i
$117$		−	1.76930e10i		−	0.807000i
$118$	−1.08232e10	−	1.21820e10i	−0.473090	−	0.532487i
$119$			3.96695e10i			1.66235i
$120$	6.33178e9	+	7.30970e9i	0.254460	+	0.293760i
$121$	−1.36558e10			−0.526490
$122$	5.22139e9	−	4.63896e9i	0.193191	−	0.171641i
$123$	8.85093e9			0.314386
$124$	1.47795e10	+	1.75208e9i	0.504141	+	0.0597648i
$125$	2.90038e10	−	9.49234e9i	0.950395	−	0.311045i
$126$	−2.40826e10	+	2.13963e10i	−0.758318	+	0.673731i
$127$	3.87619e10			1.17324			0.586619	−	0.809863i	$-0.300459\pi$
$127$	3.87619e10			1.17324			0.586619	+	0.809863i	$0.300459\pi$
$128$	−1.25021e10	−	3.20045e10i	−0.363859	−	0.931454i
$129$	−1.90588e10			−0.533516
$130$	−2.60884e10	−	2.37716e10i	−0.702636	−	0.640238i
$131$			2.60443e10i			0.675081i	0.941311	+	0.337540i	$0.109595\pi$
$131$			2.60443e10i			0.675081i	−0.941311	+	0.337540i	$0.890405\pi$
$132$	−1.91091e10	−	2.26534e9i	−0.476837	−	0.0565280i
$133$			7.60104e10i			1.82648i
$134$	−1.72428e10	+	1.53194e10i	−0.399101	+	0.354583i
$135$	−3.20428e10	+	3.39087e9i	−0.714597	+	0.0756210i
$136$	5.31146e10	−	3.69966e10i	1.14161	−	0.795184i
$137$		−	2.02285e9i		−	0.0419142i	−0.999780	−	0.0209571i	$-0.993329\pi$
$137$		−	2.02285e9i		−	0.0419142i	0.999780	−	0.0209571i	$-0.00667134\pi$
$138$	9.98422e9	−	8.87052e9i	0.199489	−	0.177237i
$139$		−	9.04079e10i		−	1.74234i	−0.490983	−	0.871169i	$-0.663362\pi$
$139$		−	9.04079e10i		−	1.74234i	0.490983	−	0.871169i	$-0.336638\pi$
$140$	−8.07518e8	+	6.42570e10i	−0.0150145	+	1.19476i
$141$	6.24623e9			0.112078
$142$	−2.47374e10	−	2.78432e10i	−0.428463	−	0.482256i
$143$	7.02289e10			1.17445
$144$	5.11081e10	+	1.22902e10i	0.825424	+	0.198494i
$145$	−3.26107e10	+	3.45097e9i	−0.508768	+	0.0538395i
$146$	−2.28017e10	−	2.56645e10i	−0.343719	−	0.386873i
$147$	1.14091e10			0.166213
$148$	−1.29424e11	−	1.53429e10i	−1.82266	−	0.216072i
$149$	−2.65310e10			−0.361262			−0.180631	−	0.983551i	$-0.557814\pi$
$149$	−2.65310e10			−0.361262			−0.180631	+	0.983551i	$0.557814\pi$
$150$	−1.74715e10	+	2.37855e10i	−0.230077	+	0.313224i
$151$		−	6.12549e10i		−	0.780291i	−0.920753	−	0.390145i	$-0.872425\pi$
$151$		−	6.12549e10i		−	0.780291i	0.920753	−	0.390145i	$-0.127575\pi$
$152$	1.01772e11	−	7.08889e10i	1.25433	−	0.873696i
$153$			9.90261e10i			1.18112i
$154$	−8.49283e10	−	9.55910e10i	−0.980502	−	1.10360i
$155$	4.77973e9	+	4.51671e10i	0.0534251	+	0.504852i
$156$	3.38949e10	+	4.01817e9i	0.366869	+	0.0434916i
$157$		−	4.55319e10i		−	0.477329i	−0.971102	−	0.238664i	$-0.923290\pi$
$157$		−	4.55319e10i		−	0.477329i	0.971102	−	0.238664i	$-0.0767095\pi$
$158$	−7.73253e10	−	8.70335e10i	−0.785301	−	0.883896i
$159$			8.12533e9i			0.0799568i
$160$	8.67885e10	−	5.88462e10i	0.827680	−	0.561201i
$161$	8.87476e10			0.820403
$162$	−4.75180e10	+	4.22176e10i	−0.425876	+	0.378371i
$163$	2.22540e11			1.93406			0.967032	−	0.254656i	$-0.0819623\pi$
$163$	2.22540e11			1.93406			0.967032	+	0.254656i	$0.0819623\pi$
$164$	1.12978e10	−	9.53014e10i	0.0952300	−	0.803304i
$165$	−6.17992e9	−	5.83985e10i	−0.0505316	−	0.477509i
$166$	−3.43346e10	+	3.05047e10i	−0.272390	+	0.242006i
$167$	−1.03405e11			−0.796086			−0.398043	−	0.917367i	$-0.630310\pi$
$167$	−1.03405e11			−0.796086			−0.398043	+	0.917367i	$0.630310\pi$
$168$	−3.55200e10	−	5.09947e10i	−0.265416	−	0.381047i
$169$	1.32893e10			0.0963980
$170$	1.46014e11	+	1.33047e11i	1.02837	+	0.937046i
$171$			1.89743e11i			1.29773i
$172$	−2.43277e10	+	2.05214e11i	−0.161606	+	1.36321i
$173$			7.83241e10i			0.505435i	0.967540	+	0.252717i	$0.0813243\pi$
$173$			7.83241e10i			0.505435i	−0.967540	+	0.252717i	$0.918676\pi$
$174$	2.37077e10	−	2.10632e10i	0.148643	−	0.132062i
$175$	−1.91768e11	+	4.10468e10i	−1.16839	+	0.250086i
$176$	−4.87835e10	+	2.02863e11i	−0.288875	+	1.20127i
$177$			4.80924e10i			0.276828i
$178$	2.37940e10	−	2.11399e10i	0.133158	−	0.118305i
$179$		−	1.37989e11i		−	0.750898i	−0.926843	−	0.375449i	$-0.877489\pi$
$179$		−	1.37989e11i		−	0.750898i	0.926843	−	0.375449i	$-0.122511\pi$
$180$	−2.01579e9	+	1.60403e11i	−0.0106680	+	0.848888i
$181$	−1.50269e11			−0.773527			−0.386764	−	0.922179i	$-0.626407\pi$
$181$	−1.50269e11			−0.773527			−0.386764	+	0.922179i	$0.626407\pi$
$182$	1.50642e11	+	1.69556e11i	0.754380	+	0.849093i
$183$	−2.06131e10			−0.100436
$184$	−8.27679e10	−	1.18827e11i	−0.392440	−	0.563410i
$185$	−4.18559e10	−	3.95527e11i	−0.193152	−	1.82523i
$186$	−2.91734e10	−	3.28362e10i	−0.131046	−	0.147498i
$187$	−3.93064e11			−1.71892
$188$	7.97300e9	−	6.72555e10i	0.0339494	−	0.286377i
$189$	2.07063e11			0.858606
$190$	2.79776e11	+	2.54930e11i	1.12991	+	1.02956i
$191$			1.81401e11i			0.713629i	0.934175	+	0.356814i	$0.116137\pi$
$191$			1.81401e11i			0.713629i	−0.934175	+	0.356814i	$0.883863\pi$
$192$	−3.51515e10	+	9.51175e10i	−0.134722	+	0.364548i
$193$			6.88155e10i			0.256980i	0.991711	+	0.128490i	$0.0410130\pi$
$193$			6.88155e10i			0.256980i	−0.991711	+	0.128490i	$0.958987\pi$
$194$	9.76059e10	+	1.09860e11i	0.355195	+	0.399790i
$195$	1.09617e10	+	1.03585e11i	0.0388781	+	0.367387i
$196$	1.45631e10	−	1.22846e11i	0.0503471	−	0.424698i
$197$		−	1.58831e11i		−	0.535309i	−0.963515	−	0.267654i	$-0.913751\pi$
$197$		−	1.58831e11i		−	0.535309i	0.963515	−	0.267654i	$-0.0862485\pi$
$198$	−2.12004e11	−	2.38622e11i	−0.696657	−	0.784123i
$199$		−	4.21020e11i		−	1.34908i	−0.738239	−	0.674539i	$-0.764342\pi$
$199$		−	4.21020e11i		−	1.34908i	0.738239	−	0.674539i	$-0.235658\pi$
$200$	2.33806e11	+	2.18483e11i	0.730644	+	0.682759i
$201$	6.80713e10			0.207484
$202$	9.69614e10	−	8.61458e10i	0.288298	−	0.256140i
$203$	2.10733e11			0.611297
$204$	−1.89706e11	−	2.24893e10i	−0.536946	−	0.0636538i
$205$	2.91247e11	−	3.08207e10i	0.804437	−	0.0851281i
$206$	−1.51507e10	+	1.34607e10i	−0.0408409	+	0.0362853i
$207$	2.21539e11			0.582905
$208$	8.65303e10	−	3.59830e11i	0.222255	−	0.924232i
$209$	−7.53146e11			−1.88863
$210$	1.27737e11	−	1.40186e11i	0.312767	−	0.343249i
$211$		−	4.83255e11i		−	1.15548i	−0.816219	−	0.577742i	$-0.803934\pi$
$211$		−	4.83255e11i		−	1.15548i	0.816219	−	0.577742i	$-0.196066\pi$
$212$	8.74886e10	+	1.03716e10i	0.204302	+	0.0242195i
$213$			1.09920e11i			0.250714i
$214$	5.77064e11	−	5.12695e11i	1.28575	−	1.14233i
$215$	−6.27146e11	+	6.63666e10i	−1.36514	+	0.144463i
$216$	−1.93111e11	−	2.77242e11i	−0.410714	−	0.589645i
$217$		−	2.91874e11i		−	0.606592i
$218$	−4.10534e11	+	3.64741e11i	−0.833810	+	0.740802i
$219$			1.01319e11i			0.201126i
$220$	−6.36687e11	−	8.00125e9i	−1.23541	−	0.0155255i
$221$	6.97201e11			1.32250
$222$	2.55471e11	+	2.87545e11i	0.473779	+	0.533262i
$223$	7.41346e11			1.34430			0.672151	−	0.740414i	$-0.265371\pi$
$223$	7.41346e11			1.34430			0.672151	+	0.740414i	$0.265371\pi$
$224$	−5.94419e11	+	3.17366e11i	−1.05403	+	0.562756i
$225$	−4.78707e11	+	1.02464e11i	−0.830151	+	0.177688i
$226$	2.45219e11	+	2.76006e11i	0.415922	+	0.468141i
$227$	−4.66330e11			−0.773685			−0.386843	−	0.922146i	$-0.626434\pi$
$227$	−4.66330e11			−0.773685			−0.386843	+	0.922146i	$0.626434\pi$
$228$	−3.63494e11	−	4.30915e10i	−0.589961	−	0.0699386i
$229$	6.80666e11			1.08083			0.540414	−	0.841399i	$-0.318267\pi$
$229$	6.80666e11			1.08083			0.540414	+	0.841399i	$0.318267\pi$
$230$	2.97650e11	−	3.26659e11i	0.462452	−	0.507522i
$231$			3.77376e11i			0.573739i
$232$	−1.96534e11	−	2.82156e11i	−0.292414	−	0.419807i
$233$			1.14942e12i			1.67378i	0.547369	+	0.836892i	$0.315630\pi$
$233$			1.14942e12i			1.67378i	−0.547369	+	0.836892i	$0.684370\pi$
$234$	3.76045e11	+	4.23258e11i	0.535995	+	0.603289i
$235$	2.05537e11	−	2.17506e10i	0.286781	−	0.0303481i
$236$	5.17829e11	+	6.13875e10i	0.707337	+	0.0838533i
$237$			3.43592e11i			0.459517i
$238$	−8.43130e11	−	9.48985e11i	−1.10410	−	1.24272i
$239$			5.70858e11i			0.732047i	0.930606	+	0.366023i	$0.119281\pi$
$239$			5.70858e11i			0.732047i	−0.930606	+	0.366023i	$0.880719\pi$
$240$	−3.06829e11	−	4.02899e10i	−0.385337	−	0.0505988i
$241$	−1.57187e12			−1.93344			−0.966719	−	0.255840i	$-0.917648\pi$
$241$	−1.57187e12			−1.93344			−0.966719	+	0.255840i	$0.917648\pi$
$242$	3.26678e11	−	2.90238e11i	0.393589	−	0.349686i
$243$	7.96443e11			0.939990
$244$	−2.63116e10	+	2.21949e11i	−0.0304227	+	0.256628i
$245$	3.75425e11	−	3.97287e10i	0.425297	−	0.0450063i
$246$	−2.11734e11	+	1.88116e11i	−0.235026	+	0.208810i
$247$	1.33590e12			1.45308
$248$	−3.90798e11	+	2.72208e11i	−0.416576	+	0.290163i
$249$	1.35547e11			0.141609
$250$	−4.92087e11	+	8.43519e11i	−0.503897	+	0.863764i
$251$		−	3.37622e11i		−	0.338893i	−0.985539	−	0.169446i	$-0.945802\pi$
$251$		−	3.37622e11i		−	0.338893i	0.985539	−	0.169446i	$-0.0541979\pi$
$252$	1.21357e11	−	1.02370e12i	0.119416	−	1.00732i
$253$			8.79352e11i			0.848321i
$254$	−9.27271e11	+	8.23838e11i	−0.877078	+	0.779244i
$255$	−6.13515e10	−	5.79754e11i	−0.0569015	−	0.537704i
$256$	9.79297e11	+	4.99902e11i	0.890666	+	0.454659i
$257$		−	1.58528e12i		−	1.41397i	−0.707230	−	0.706983i	$-0.750056\pi$
$257$		−	1.58528e12i		−	1.41397i	0.707230	−	0.706983i	$-0.249944\pi$
$258$	4.55930e11	−	4.05073e11i	0.398841	−	0.354352i
$259$			2.55593e12i			2.19306i
$260$	1.12933e12	+	1.41923e10i	0.950505	+	0.0119450i
$261$	5.26048e11			0.434333
$262$	−5.53540e11	−	6.23038e11i	−0.448377	−	0.504670i
$263$	−1.08215e12			−0.860017			−0.430008	−	0.902825i	$-0.641489\pi$
$263$	−1.08215e12			−0.860017			−0.430008	+	0.902825i	$0.641489\pi$
$264$	5.05279e11	−	3.51949e11i	0.394014	−	0.274448i
$265$	2.82940e10	+	2.67371e11i	0.0216504	+	0.204590i
$266$	−1.61551e12	−	1.81834e12i	−1.21312	−	1.36542i
$267$	−9.39345e10			−0.0692260
$268$	8.68897e10	−	7.32950e11i	0.0628484	−	0.530152i
$269$	1.04444e12			0.741517			0.370758	−	0.928729i	$-0.379098\pi$
$269$	1.04444e12			0.741517			0.370758	+	0.928729i	$0.379098\pi$
$270$	6.94467e11	−	7.62149e11i	0.483986	−	0.531155i
$271$		−	1.29600e12i		−	0.886662i	−0.896358	−	0.443331i	$-0.853797\pi$
$271$		−	1.29600e12i		−	0.886662i	0.896358	−	0.443331i	$-0.146203\pi$
$272$	−4.84301e11	+	2.01393e12i	−0.325290	+	1.35270i
$273$		−	6.69375e11i		−	0.441424i
$274$	4.29933e10	+	4.83912e10i	0.0278387	+	0.0313338i
$275$	−4.06710e11	−	1.90013e12i	−0.258596	−	1.20815i
$276$	−5.03124e10	+	4.24406e11i	−0.0314145	+	0.264994i
$277$			1.69663e12i			1.04037i	0.854054	+	0.520184i	$0.174137\pi$
$277$			1.69663e12i			1.04037i	−0.854054	+	0.520184i	$0.825863\pi$
$278$	1.92152e12	+	2.16276e12i	1.15723	+	1.30252i
$279$		−	7.28598e11i		−	0.430990i
$280$	−1.34639e12	−	1.55433e12i	−0.782313	−	0.903138i
$281$	−1.13457e12			−0.647592			−0.323796	−	0.946127i	$-0.604959\pi$
$281$	−1.13457e12			−0.647592			−0.323796	+	0.946127i	$0.604959\pi$
$282$	−1.49424e11	+	1.32756e11i	−0.0837866	+	0.0744406i
$283$	−1.25948e11			−0.0693837			−0.0346919	−	0.999398i	$-0.511045\pi$
$283$	−1.25948e11			−0.0693837			−0.0346919	+	0.999398i	$0.511045\pi$
$284$	1.18355e12	+	1.40307e11i	0.640612	+	0.0759432i
$285$	−1.17555e11	−	1.11086e12i	−0.0625197	−	0.590793i
$286$	−1.68003e12	+	1.49263e12i	−0.877987	+	0.780051i
$287$	−1.88206e12			−0.966551
$288$	−1.48384e12	+	7.92233e11i	−0.748899	+	0.399844i
$289$	−1.88617e12			−0.935602
$290$	7.06775e11	−	7.75657e11i	0.344581	−	0.378164i
$291$		−	4.33709e11i		−	0.207842i
$292$	1.09094e12	+	1.29328e11i	0.513908	+	0.0609227i
$293$		−	3.67054e12i		−	1.69978i	−0.526964	−	0.849888i	$-0.676670\pi$
$293$		−	3.67054e12i		−	1.69978i	0.526964	−	0.849888i	$-0.323330\pi$
$294$	−2.72931e11	+	2.42487e11i	−0.124256	+	0.110395i
$295$	1.67467e11	+	1.58252e12i	0.0749583	+	0.708335i
$296$	3.42220e12	−	2.38371e12i	1.50608	−	1.04905i
$297$			2.05168e12i			0.887823i
$298$	6.34682e11	−	5.63886e11i	0.270069	−	0.239944i
$299$		−	1.55976e12i		−	0.652682i
$300$	−8.75759e10	−	9.40338e11i	−0.0360395	−	0.386970i
$301$	4.05267e12			1.64025
$302$	1.30190e12	+	1.46536e12i	0.518255	+	0.583322i
$303$	−3.82786e11			−0.149880
$304$	−9.27965e11	+	3.85888e12i	−0.357407	+	1.48625i
$305$	−6.78290e11	+	7.17789e10i	−0.256990	+	0.0271955i
$306$	−2.10469e12	−	2.36893e12i	−0.784477	−	0.882968i
$307$	−1.65876e12			−0.608262			−0.304131	−	0.952630i	$-0.598366\pi$
$307$	−1.65876e12			−0.608262			−0.304131	+	0.952630i	$0.598366\pi$
$308$	4.06335e12	+	4.81702e11i	1.46599	+	0.173790i
$309$	5.98121e10			0.0212323
$310$	−1.07432e12	−	9.78912e11i	−0.375253	−	0.341928i
$311$			1.47617e12i			0.507381i	0.967285	+	0.253691i	$0.0816445\pi$
$311$			1.47617e12i			0.507381i	−0.967285	+	0.253691i	$0.918355\pi$
$312$	−8.96244e11	+	6.24273e11i	−0.303147	+	0.211155i
$313$		−	4.13023e12i		−	1.37484i	−0.726259	−	0.687421i	$-0.758743\pi$
$313$		−	4.13023e12i		−	1.37484i	0.726259	−	0.687421i	$-0.241257\pi$
$314$	9.67727e11	+	1.08923e12i	0.317033	+	0.356837i
$315$	3.12848e12	−	3.31066e11i	1.00874	−	0.106748i
$316$	3.69959e12	+	4.38579e11i	1.17414	+	0.139191i
$317$		−	4.04562e12i		−	1.26383i	−0.775037	−	0.631916i	$-0.782269\pi$
$317$		−	4.04562e12i		−	1.26383i	0.775037	−	0.631916i	$-0.217731\pi$
$318$	−1.72694e11	−	1.94376e11i	−0.0531059	−	0.0597734i
$319$			2.08804e12i			0.632099i
$320$	−8.25470e11	+	3.25232e12i	−0.246009	+	0.969267i
$321$	−2.27814e12			−0.668430
$322$	−2.12304e12	+	1.88623e12i	−0.613309	+	0.544897i
$323$	−7.47690e12			−2.12671
$324$	2.39452e11	−	2.01988e12i	0.0670647	−	0.565718i
$325$	7.21406e11	+	3.37037e12i	0.198959	+	0.929525i
$326$	−5.32367e12	+	4.72984e12i	−1.44585	+	1.28457i
$327$	1.62071e12			0.433479
$328$	1.75525e12	+	2.51994e12i	0.462349	+	0.663776i
$329$	−1.32820e12			−0.344575
$330$	1.38903e12	+	1.26568e12i	0.354929	+	0.323410i
$331$			4.40361e12i			1.10833i	0.832407	+	0.554164i	$0.186962\pi$
$331$			4.40361e12i			1.10833i	−0.832407	+	0.554164i	$0.813038\pi$
$332$	1.73019e11	−	1.45948e12i	0.0428946	−	0.361833i
$333$			6.38031e12i			1.55819i
$334$	2.47369e12	−	2.19776e12i	0.595130	−	0.528746i
$335$	2.23994e12	−	2.37038e11i	0.530900	−	0.0561815i
$336$	1.93355e12	+	4.64972e11i	0.451502	+	0.108575i
$337$			5.34596e12i			1.22992i	0.788559	+	0.614959i	$0.210828\pi$
$337$			5.34596e12i			1.22992i	−0.788559	+	0.614959i	$0.789172\pi$
$338$	−3.17910e11	+	2.82448e11i	−0.0720643	+	0.0640258i
$339$		−	1.08962e12i		−	0.243376i
$340$	−6.32075e12	−	7.94329e10i	−1.39115	−	0.0174826i
$341$	2.89202e12			0.627234
$342$	−4.03277e12	−	4.53908e12i	−0.861931	−	0.970147i
$343$	3.24661e12			0.683847
$344$	−3.77961e12	−	5.42623e12i	−0.784611	−	1.12643i
$345$	−1.29701e12	+	1.37254e11i	−0.265368	+	0.0280821i
$346$	−1.66469e12	−	1.87369e12i	−0.335701	−	0.377848i
$347$	7.04996e12			1.40133			0.700664	−	0.713492i	$-0.252887\pi$
$347$	7.04996e12			1.40133			0.700664	+	0.713492i	$0.252887\pi$
$348$	−1.19468e11	+	1.00776e12i	−0.0234075	+	0.197452i
$349$	5.35614e12			1.03449			0.517243	−	0.855838i	$-0.326958\pi$
$349$	5.35614e12			1.03449			0.517243	+	0.855838i	$0.326958\pi$
$350$	3.71513e12	−	5.05775e12i	0.707350	−	0.962979i
$351$		−	3.63918e12i		−	0.683074i
$352$	−3.14460e12	−	5.88978e12i	−0.581906	−	1.08990i
$353$		−	5.32913e12i		−	0.972261i	−0.873886	−	0.486130i	$-0.838408\pi$
$353$		−	5.32913e12i		−	0.972261i	0.873886	−	0.486130i	$-0.161592\pi$
$354$	−1.02215e12	−	1.15048e12i	−0.183864	−	0.206948i
$355$	3.82763e11	+	3.61700e12i	0.0678873	+	0.641516i
$356$	−1.19903e11	+	1.01143e12i	−0.0209691	+	0.176883i
$357$			3.74642e12i			0.646064i
$358$	2.93281e12	+	3.30102e12i	0.498733	+	0.561349i
$359$		−	5.94891e12i		−	0.997621i	−0.866711	−	0.498810i	$-0.833770\pi$
$359$		−	5.94891e12i		−	0.997621i	0.866711	−	0.498810i	$-0.166230\pi$
$360$	−3.36096e12	−	3.88005e12i	−0.555841	−	0.641689i
$361$	−8.19534e12			−1.33669
$362$	3.59477e12	−	3.19379e12i	0.578266	−	0.513763i
$363$	−1.28966e12			−0.204618
$364$	−7.20741e12	−	8.54423e11i	−1.12790	−	0.133711i
$365$	3.52812e11	+	3.33397e12i	0.0544601	+	0.514633i
$366$	4.93112e11	−	4.38107e11i	0.0750827	−	0.0667075i
$367$	4.30747e12			0.646982			0.323491	−	0.946231i	$-0.395143\pi$
$367$	4.30747e12			0.646982			0.323491	+	0.946231i	$0.395143\pi$
$368$	4.50552e12	+	1.08347e12i	0.667584	+	0.160537i
$369$	−4.69815e12			−0.686744
$370$	9.40775e12	+	8.57230e12i	1.35668	+	1.23620i
$371$		−	1.72777e12i		−	0.245820i
$372$	1.39579e12	+	1.65468e11i	0.195932	+	0.0232273i
$373$		−	6.18537e12i		−	0.856686i	−0.903616	−	0.428343i	$-0.859097\pi$
$373$		−	6.18537e12i		−	0.856686i	0.903616	−	0.428343i	$-0.140903\pi$
$374$	9.40298e12	−	8.35412e12i	1.28501	−	1.14167i
$375$	2.73914e12	−	8.96464e11i	0.369366	−	0.120886i
$376$	1.23871e12	+	1.77836e12i	0.164827	+	0.236636i
$377$		−	3.70368e12i		−	0.486325i
$378$	−4.95342e12	+	4.40089e12i	−0.641868	+	0.570271i
$379$		−	1.18170e13i		−	1.51116i	−0.655055	−	0.755581i	$-0.727355\pi$
$379$		−	1.18170e13i		−	1.51116i	0.655055	−	0.755581i	$-0.272645\pi$
$380$	−1.21111e13	−	1.52201e11i	−1.52850	−	0.0192087i
$381$	3.66070e12			0.455973
$382$	−3.85546e12	−	4.33952e12i	−0.473980	−	0.533488i
$383$	−1.08823e13			−1.32046			−0.660231	−	0.751063i	$-0.729542\pi$
$383$	−1.08823e13			−1.32046			−0.660231	+	0.751063i	$0.729542\pi$
$384$	−1.18071e12	−	3.02253e12i	−0.141412	−	0.362005i
$385$	1.31410e12	+	1.24179e13i	0.155355	+	1.46806i
$386$	−1.46259e12	−	1.64622e12i	−0.170682	−	0.192111i
$387$	1.01166e13			1.16541
$388$	−4.66991e12	−	5.53608e11i	−0.531067	−	0.0629569i
$389$	2.39414e12			0.268783			0.134391	−	0.990928i	$-0.457092\pi$
$389$	2.39414e12			0.268783			0.134391	+	0.990928i	$0.457092\pi$
$390$	−2.46381e12	−	2.24501e12i	−0.273076	−	0.248825i
$391$			8.72982e12i			0.955259i
$392$	2.26256e12	+	3.24827e12i	0.244439	+	0.350932i
$393$			2.45964e12i			0.262367i
$394$	3.37577e12	+	3.79960e12i	0.355543	+	0.400181i
$395$	1.19646e12	+	1.13062e13i	0.124426	+	1.17579i
$396$	1.01433e13	+	1.20246e12i	1.04160	+	0.123480i
$397$		−	2.29424e12i		−	0.232641i	−0.993212	−	0.116321i	$-0.962890\pi$
$397$		−	2.29424e12i		−	0.232641i	0.993212	−	0.116321i	$-0.0371101\pi$
$398$	8.94828e12	+	1.00717e13i	0.896034	+	1.00853i
$399$			7.17848e12i			0.709852i
$400$	−1.02368e13	−	2.57332e11i	−0.999684	−	0.0251300i
$401$	3.17790e12			0.306492			0.153246	−	0.988188i	$-0.451027\pi$
$401$	3.17790e12			0.306492			0.153246	+	0.988188i	$0.451027\pi$
$402$	−1.62842e12	+	1.44678e12i	−0.155109	+	0.137807i
$403$	−5.12975e12			−0.482582
$404$	−4.88608e11	+	4.12161e12i	−0.0453997	+	0.382965i
$405$	6.17288e12	−	6.53234e11i	0.566516	−	0.0599506i
$406$	−5.04121e12	+	4.47888e12i	−0.456988	+	0.406013i
$407$	−2.53253e13			−2.26768
$408$	5.01618e12	−	3.49399e12i	0.443683	−	0.309044i
$409$	−1.17989e13			−1.03092			−0.515458	−	0.856915i	$-0.672378\pi$
$409$	−1.17989e13			−1.03092			−0.515458	+	0.856915i	$0.672378\pi$
$410$	−6.31223e12	+	6.92742e12i	−0.544833	+	0.597932i
$411$		−	1.91040e11i		−	0.0162897i
$412$	7.63471e10	−	6.44019e11i	0.00643142	−	0.0542516i
$413$		−	1.02264e13i		−	0.851081i
$414$	−5.29971e12	+	4.70855e12i	−0.435763	+	0.387155i
$415$	4.46027e12	−	4.72000e11i	0.362344	−	0.0383444i
$416$	5.57777e12	+	1.04471e13i	0.447707	+	0.838547i
$417$		−	8.53819e12i		−	0.677151i
$418$	1.80170e13	−	1.60072e13i	1.41189	−	1.25440i
$419$			1.20017e12i			0.0929338i	0.998920	+	0.0464669i	$0.0147962\pi$
$419$			1.20017e12i			0.0929338i	−0.998920	+	0.0464669i	$0.985204\pi$
$420$	−7.62626e10	+	6.06847e12i	−0.00583532	+	0.464337i
$421$	6.28498e12			0.475219			0.237609	−	0.971361i	$-0.423636\pi$
$421$	6.28498e12			0.475219			0.237609	+	0.971361i	$0.423636\pi$
$422$	1.02710e13	+	1.15606e13i	0.767452	+	0.863806i
$423$	−3.31555e12			−0.244824
$424$	−2.31336e12	+	1.61136e12i	−0.168816	+	0.117588i
$425$	−4.03764e12	−	1.88636e13i	−0.291194	−	1.36044i
$426$	−2.33622e12	−	2.62953e12i	−0.166520	−	0.187426i
$427$	4.38317e12			0.308780
$428$	−2.90794e12	+	2.45296e13i	−0.202473	+	1.70794i
$429$	6.63247e12			0.456445
$430$	1.35922e13	−	1.49169e13i	0.924587	−	1.01470i
$431$		−	5.24267e12i		−	0.352506i	−0.984345	−	0.176253i	$-0.943602\pi$
$431$		−	5.24267e12i		−	0.352506i	0.984345	−	0.176253i	$-0.0563977\pi$
$432$	1.05121e13	+	2.52791e12i	0.698670	+	0.168013i
$433$		−	1.01639e13i		−	0.667759i	−0.942616	−	0.333880i	$-0.891642\pi$
$433$		−	1.01639e13i		−	0.667759i	0.942616	−	0.333880i	$-0.108358\pi$
$434$	6.20344e12	+	6.98228e12i	0.402887	+	0.453470i
$435$	−3.07978e12	+	3.25912e11i	−0.197730	+	0.0209245i
$436$	2.06876e12	−	1.74509e13i	0.131304	−	1.10760i
$437$			1.67271e13i			1.04958i
$438$	−2.15341e12	−	2.42377e12i	−0.133585	−	0.150356i
$439$		−	2.59322e11i		−	0.0159044i	−0.999968	−	0.00795219i	$-0.997469\pi$
$439$		−	2.59322e11i		−	0.0159044i	0.999968	−	0.00795219i	$-0.00253129\pi$
$440$	1.54011e13	−	1.33406e13i	0.933871	−	0.808934i
$441$	−6.05604e12			−0.363074
$442$	−1.66786e13	+	1.48182e13i	−0.988664	+	0.878383i
$443$	−1.16943e13			−0.685417			−0.342709	−	0.939442i	$-0.611344\pi$
$443$	−1.16943e13			−0.685417			−0.342709	+	0.939442i	$0.611344\pi$
$444$	−1.22229e13	−	1.44900e12i	−0.708367	−	0.0839754i
$445$	−3.09099e12	+	3.27099e11i	−0.177132	+	0.0187447i
$446$	−1.77347e13	+	1.57565e13i	−1.00496	+	0.892862i
$447$	−2.50561e12			−0.140403
$448$	7.47461e12	−	2.02258e13i	0.414189	−	1.12077i
$449$	1.97779e13			1.08380			0.541899	−	0.840444i	$-0.317706\pi$
$449$	1.97779e13			1.08380			0.541899	+	0.840444i	$0.317706\pi$
$450$	9.27400e12	−	1.26255e13i	0.502579	−	0.684207i
$451$		−	1.86483e13i		−	0.999442i
$452$	−1.17324e13	−	1.39085e12i	−0.621862	−	0.0737204i
$453$		−	5.78496e12i		−	0.303256i
$454$	1.11557e13	−	9.91131e12i	0.578384	−	0.513868i
$455$	−2.33089e12	−	2.20263e13i	−0.119527	−	1.12950i
$456$	9.61146e12	−	6.69480e12i	0.487489	−	0.339558i
$457$			1.37176e13i			0.688171i	0.938938	+	0.344086i	$0.111811\pi$
$457$			1.37176e13i			0.688171i	−0.938938	+	0.344086i	$0.888189\pi$
$458$	−1.62831e13	+	1.44668e13i	−0.807996	+	0.717867i
$459$			2.03681e13i			0.999741i
$460$	−1.77705e11	+	1.41406e13i	−0.00862801	+	0.686561i
$461$	−3.74685e13			−1.79954			−0.899770	−	0.436365i	$-0.856266\pi$
$461$	−3.74685e13			−1.79954			−0.899770	+	0.436365i	$0.856266\pi$
$462$	−8.02069e12	−	9.02769e12i	−0.381067	−	0.428910i
$463$	4.08483e13			1.91986			0.959929	−	0.280244i	$-0.0904153\pi$
$463$	4.08483e13			1.91986			0.959929	+	0.280244i	$0.0904153\pi$
$464$	1.06984e13	+	2.57271e12i	0.497428	+	0.119619i
$465$	4.51401e11	+	4.26562e12i	0.0207634	+	0.196208i
$466$	−2.44296e13	−	2.74967e13i	−1.11170	−	1.25127i
$467$	8.08702e11			0.0364086			0.0182043	−	0.999834i	$-0.494205\pi$
$467$	8.08702e11			0.0364086			0.0182043	+	0.999834i	$0.494205\pi$
$468$	−1.79917e13	−	2.13288e12i	−0.801388	−	0.0950029i
$469$	−1.44747e13			−0.637889
$470$	−4.45463e12	+	4.88878e12i	−0.194233	+	0.213163i
$471$		−	4.30007e12i		−	0.185511i
$472$	−1.36924e13	+	9.53732e12i	−0.584478	+	0.407114i
$473$			4.01557e13i			1.69606i
$474$	−7.30266e12	−	8.21951e12i	−0.305203	−	0.343522i
$475$	−7.73648e12	−	3.61444e13i	−0.319945	−	1.49477i
$476$	4.03391e13	+	4.78212e12i	1.65079	+	0.195698i
$477$		−	4.31300e12i		−	0.174657i
$478$	−1.21329e13	−	1.36562e13i	−0.486212	−	0.547256i
$479$			1.53920e13i			0.610403i	0.952288	+	0.305202i	$0.0987239\pi$
$479$			1.53920e13i			0.610403i	−0.952288	+	0.305202i	$0.901276\pi$
$480$	8.19637e12	−	5.55748e12i	0.321674	−	0.218108i
$481$	4.49210e13			1.74471
$482$	3.76026e13	−	3.34082e13i	1.44538	−	1.28416i
$483$	8.38139e12			0.318846
$484$	−1.64619e12	+	1.38863e13i	−0.0619803	+	0.522829i
$485$	−1.51026e12	−	1.42715e13i	−0.0562785	−	0.531816i
$486$	−1.90527e13	+	1.69275e13i	−0.702709	+	0.624325i
$487$	1.35284e12			0.0493858			0.0246929	−	0.999695i	$-0.492139\pi$
$487$	1.35284e12			0.0493858			0.0246929	+	0.999695i	$0.492139\pi$
$488$	−4.08783e12	−	5.86874e12i	−0.147705	−	0.212054i
$489$	2.10169e13			0.751664
$490$	−8.13662e12	+	8.92962e12i	−0.288047	+	0.316120i
$491$			3.98512e13i			1.39648i	0.715865	+	0.698239i	$0.246033\pi$
$491$			3.98512e13i			1.39648i	−0.715865	+	0.698239i	$0.753967\pi$
$492$	1.06697e12	−	9.00033e12i	0.0370107	−	0.312200i
$493$			2.07291e13i			0.711781i
$494$	−3.19577e13	+	2.83930e13i	−1.08628	+	0.965109i
$495$	3.28035e12	+	3.09984e13i	0.110381	+	1.04307i
$496$	3.56331e12	−	1.48178e13i	0.118698	−	0.493599i
$497$		−	2.33734e13i		−	0.770796i
$498$	−3.24258e12	+	2.88089e12i	−0.105863	+	0.0940545i
$499$			2.28789e13i			0.739492i	0.929133	+	0.369746i	$0.120555\pi$
$499$			2.28789e13i			0.739492i	−0.929133	+	0.369746i	$0.879445\pi$
$500$	−6.15620e12	−	3.06376e13i	−0.196998	−	0.980404i
$501$	−9.76566e12			−0.309395
$502$	7.17576e12	+	8.07668e12i	0.225087	+	0.253346i
$503$	4.14427e13			1.28709			0.643544	−	0.765409i	$-0.277464\pi$
$503$	4.14427e13			1.28709			0.643544	+	0.765409i	$0.277464\pi$
$504$	1.88543e13	+	2.70684e13i	0.579774	+	0.832359i
$505$	−1.25959e13	+	1.33294e12i	−0.383506	+	0.0405838i
$506$	−1.86896e13	−	2.10361e13i	−0.563440	−	0.634180i
$507$	1.25505e12			0.0374646
$508$	4.67270e12	−	3.94161e13i	0.138118	−	1.16508i
$509$	−3.35157e13			−0.980978			−0.490489	−	0.871447i	$-0.663182\pi$
$509$	−3.35157e13			−0.980978			−0.490489	+	0.871447i	$0.663182\pi$
$510$	1.37897e13	+	1.25651e13i	0.399671	+	0.364178i
$511$		−	2.15444e13i		−	0.618344i
$512$	−3.40518e13	+	8.85503e12i	−0.967812	+	0.251675i
$513$			3.90272e13i			1.09845i
$514$	3.36932e13	+	3.79234e13i	0.939132	+	1.05704i
$515$	1.96816e12	−	2.08277e11i	0.0543282	−	0.00574918i
$516$	−2.29752e12	+	1.93805e13i	−0.0628074	+	0.529806i
$517$		−	1.31604e13i		−	0.356300i
$518$	−5.43233e13	−	6.11436e13i	−1.45659	−	1.63946i
$519$			7.39699e12i			0.196435i
$520$	−2.73178e13	+	2.36631e13i	−0.718503	+	0.622379i
$521$	4.91504e13			1.28038			0.640189	−	0.768218i	$-0.278856\pi$
$521$	4.91504e13			1.28038			0.640189	+	0.768218i	$0.278856\pi$
$522$	−1.25843e13	+	1.11805e13i	−0.324695	+	0.288476i
$523$	−2.33806e12			−0.0597512			−0.0298756	−	0.999554i	$-0.509511\pi$
$523$	−2.33806e12			−0.0597512			−0.0298756	+	0.999554i	$0.509511\pi$
$524$	2.64839e13	+	3.13961e12i	0.670386	+	0.0794729i
$525$	−1.81108e13	+	3.87649e12i	−0.454088	+	0.0971946i
$526$	2.58874e13	−	2.29997e13i	0.642923	−	0.571208i
$527$	2.87107e13			0.706302
$528$	−4.60715e12	+	1.91585e13i	−0.112270	+	0.466866i
$529$	−2.18964e13			−0.528560
$530$	−6.35951e12	−	5.79475e12i	−0.152070	−	0.138566i
$531$		−	2.55278e13i		−	0.604702i
$532$	7.72934e13	+	9.16297e12i	1.81378	+	0.215020i
$533$			3.30777e13i			0.768951i
$534$	2.24713e12	−	1.99647e12i	0.0517513	−	0.0459787i
$535$	−7.49641e13	+	7.93294e12i	−1.71035	+	0.180995i
$536$	1.34994e13	+	1.93806e13i	0.305134	+	0.438069i
$537$		−	1.30318e13i		−	0.291833i
$538$	−2.49853e13	+	2.21983e13i	−0.554336	+	0.492502i
$539$		−	2.40382e13i		−	0.528394i
$540$	−4.14616e11	+	3.29924e13i	−0.00902978	+	0.718530i
$541$	−2.96527e13			−0.639850			−0.319925	−	0.947443i	$-0.603658\pi$
$541$	−2.96527e13			−0.639850			−0.319925	+	0.947443i	$0.603658\pi$
$542$	2.75450e13	+	3.10032e13i	0.588906	+	0.662843i
$543$	−1.41915e13			−0.300627
$544$	−3.12182e13	−	5.84711e13i	−0.655260	−	1.22729i
$545$	5.33309e13	−	5.64365e12i	1.10917	−	0.117376i
$546$	1.42268e13	+	1.60130e13i	0.293186	+	0.329996i
$547$	−5.51686e13			−1.12656			−0.563281	−	0.826266i	$-0.690461\pi$
$547$	−5.51686e13			−1.12656			−0.563281	+	0.826266i	$0.690461\pi$
$548$	−2.05700e12	−	2.43852e11i	−0.0416227	−	0.00493429i
$549$	1.09416e13			0.219391
$550$	5.01145e13	+	3.68112e13i	0.995748	+	0.731420i
$551$			3.97189e13i			0.782058i
$552$	−7.81666e12	−	1.12221e13i	−0.152520	−	0.218967i
$553$		−	7.30615e13i		−	1.41274i
$554$	−3.60598e13	−	4.05871e13i	−0.690995	−	0.777749i
$555$	−3.95291e12	−	3.73539e13i	−0.0750674	−	0.709366i
$556$	−9.19340e13	−	1.08986e13i	−1.73022	−	0.205114i
$557$		−	5.24747e13i		−	0.978756i	−0.872072	−	0.489378i	$-0.837224\pi$
$557$		−	5.24747e13i		−	0.978756i	0.872072	−	0.489378i	$-0.162776\pi$
$558$	1.54855e13	+	1.74297e13i	0.286256	+	0.322195i
$559$		−	7.12266e13i		−	1.30492i
$560$	6.52442e13	+	8.56725e12i	1.18468	+	0.155561i
$561$	−3.71212e13			−0.668049
$562$	2.71416e13	−	2.41140e13i	0.484120	−	0.430119i
$563$	6.04415e13			1.06855			0.534273	−	0.845312i	$-0.320586\pi$
$563$	6.04415e13			1.06855			0.534273	+	0.845312i	$0.320586\pi$
$564$	7.52976e11	−	6.35166e12i	0.0131943	−	0.111299i
$565$	−3.79428e12	−	3.58549e13i	−0.0659003	−	0.622739i
$566$	3.01295e12	−	2.67687e12i	0.0518692	−	0.0460834i
$567$	−3.98897e13			−0.680683
$568$	−3.12953e13	+	2.17985e13i	−0.529343	+	0.368710i
$569$	3.91402e13			0.656238			0.328119	−	0.944636i	$-0.393585\pi$
$569$	3.91402e13			0.656238			0.328119	+	0.944636i	$0.393585\pi$
$570$	2.64222e13	+	2.40758e13i	0.439132	+	0.400135i
$571$		−	1.76561e13i		−	0.290881i	−0.989367	−	0.145441i	$-0.953540\pi$
$571$		−	1.76561e13i		−	0.290881i	0.989367	−	0.145441i	$-0.0464599\pi$
$572$	8.46602e12	−	7.14143e13i	0.138261	−	1.16629i
$573$			1.71316e13i			0.277348i
$574$	4.50232e13	−	4.00010e13i	0.722565	−	0.641966i
$575$	−4.22012e13	+	9.03290e12i	−0.671407	+	0.143710i
$576$	1.86587e13	−	5.04892e13i	0.294286	−	0.796317i
$577$			1.79666e13i			0.280922i	0.990086	+	0.140461i	$0.0448585\pi$
$577$			1.79666e13i			0.280922i	−0.990086	+	0.140461i	$0.955142\pi$
$578$	4.51214e13	−	4.00883e13i	0.699429	−	0.621410i
$579$			6.49898e12i			0.0998740i
$580$	−4.21964e11	+	3.35771e13i	−0.00642889	+	0.511569i
$581$	−2.88226e13			−0.435365
$582$	9.21797e12	+	1.03753e13i	0.138045	+	0.155376i
$583$	1.71195e13			0.254185
$584$	−2.88464e13	+	2.00928e13i	−0.424646	+	0.295785i
$585$	−5.81856e12	−	5.49838e13i	−0.0849251	−	0.802519i
$586$	7.80130e13	+	8.78075e13i	1.12896	+	1.27070i
$587$	8.72417e11			0.0125180			0.00625898	−	0.999980i	$-0.498008\pi$
$587$	8.72417e11			0.0125180			0.00625898	+	0.999980i	$0.498008\pi$
$588$	1.37535e12	−	1.16017e13i	0.0195671	−	0.165057i
$589$	5.50122e13			0.776038
$590$	−3.76408e13	−	3.42981e13i	−0.526500	−	0.479744i
$591$		−	1.50001e13i		−	0.208045i
$592$	−3.12038e13	+	1.29759e14i	−0.429140	+	1.78455i
$593$			5.87343e13i			0.800974i	0.916302	+	0.400487i	$0.131159\pi$
$593$			5.87343e13i			0.800974i	−0.916302	+	0.400487i	$0.868841\pi$
$594$	−4.36060e13	−	4.90807e13i	−0.589677	−	0.663711i
$595$	1.30458e13	+	1.23279e14i	0.174938	+	1.65312i
$596$	−3.19829e12	+	2.69789e13i	−0.0425291	+	0.358750i
$597$		−	3.97614e13i		−	0.524312i
$598$	3.31509e13	+	3.73130e13i	0.433500	+	0.487926i
$599$		−	2.16425e13i		−	0.280655i	−0.990105	−	0.140328i	$-0.955184\pi$
$599$		−	2.16425e13i		−	0.280655i	0.990105	−	0.140328i	$-0.0448156\pi$
$600$	2.20808e13	+	2.06337e13i	0.283961	+	0.265351i
$601$	−1.16404e13			−0.148456			−0.0742278	−	0.997241i	$-0.523649\pi$
$601$	−1.16404e13			−0.148456			−0.0742278	+	0.997241i	$0.523649\pi$
$602$	−9.69490e13	+	8.61348e13i	−1.22620	+	1.08942i
$603$	−3.61328e13			−0.453227
$604$	−6.22889e13	−	7.38422e12i	−0.774865	−	0.0918586i
$605$	−4.24374e13	+	4.49087e12i	−0.523567	+	0.0554056i
$606$	9.15711e12	−	8.13568e12i	0.112046	−	0.0995475i
$607$	−1.55538e13			−0.188752			−0.0943760	−	0.995537i	$-0.530086\pi$
$607$	−1.55538e13			−0.188752			−0.0943760	+	0.995537i	$0.530086\pi$
$608$	−5.98169e13	−	1.12036e14i	−0.719956	−	1.34846i
$609$	1.99018e13			0.237578
$610$	1.47007e13	−	1.61334e13i	0.174055	−	0.191019i
$611$			2.33434e13i			0.274131i
$612$	1.00698e14	+	1.19375e13i	1.17290	+	0.139045i
$613$			6.09416e13i			0.704062i	0.935988	+	0.352031i	$0.114509\pi$
$613$			6.09416e13i			0.704062i	−0.935988	+	0.352031i	$0.885491\pi$
$614$	3.96812e13	−	3.52549e13i	0.454719	−	0.403997i
$615$	2.75056e13	−	2.91073e12i	0.312640	−	0.0330846i
$616$	−1.07443e14	+	7.48384e13i	−1.21136	+	0.843764i
$617$			1.35014e14i			1.50991i	0.655775	+	0.754957i	$0.272342\pi$
$617$			1.35014e14i			1.50991i	−0.655775	+	0.754957i	$0.727658\pi$
$618$	−1.43084e12	+	1.27124e12i	−0.0158726	+	0.0141021i
$619$			3.76014e13i			0.413762i	0.978366	+	0.206881i	$0.0663314\pi$
$619$			3.76014e13i			0.413762i	−0.978366	+	0.206881i	$0.933669\pi$
$620$	4.65057e13	+	5.84438e11i	0.507631	+	0.00637940i
$621$	4.55670e13			0.493393
$622$	−3.13743e13	−	3.53133e13i	−0.336994	−	0.379303i
$623$	1.99742e13			0.212829
$624$	8.17199e12	−	3.39826e13i	0.0863783	−	0.359198i
$625$	8.70118e13	−	3.90371e13i	0.912385	−	0.409333i
$626$	8.77833e13	+	9.88045e13i	0.913146	+	1.02779i
$627$	−7.11277e13			−0.734008
$628$	−4.63004e13	−	5.48882e12i	−0.474009	−	0.0561928i
$629$	−2.51418e14			−2.55355
$630$	−6.78039e13	+	7.44121e13i	−0.683206	+	0.749792i
$631$			7.54478e13i			0.754223i	0.926168	+	0.377111i	$0.123083\pi$
$631$			7.54478e13i			0.754223i	−0.926168	+	0.377111i	$0.876917\pi$
$632$	−9.78241e13	+	6.81387e13i	−0.970198	+	0.675785i
$633$		−	4.56390e13i		−	0.449073i
$634$	8.59850e13	+	9.67804e13i	0.839414	+	0.944803i
$635$	1.20458e14	−	1.27473e13i	1.16672	−	0.123466i
$636$	8.26248e12	+	9.79500e11i	0.0794008	+	0.00941280i
$637$			4.26380e13i			0.406536i
$638$	−4.43788e13	−	4.99506e13i	−0.419829	−	0.472539i
$639$		−	5.83465e13i		−	0.547659i
$640$	−4.93772e13	−	9.53473e13i	−0.459861	−	0.887991i
$641$	1.39673e14			1.29069			0.645346	−	0.763890i	$-0.276713\pi$
$641$	1.39673e14			1.29069			0.645346	+	0.763890i	$0.276713\pi$
$642$	5.44983e13	−	4.84193e13i	0.499698	−	0.443959i
$643$	7.36940e13			0.670467			0.335233	−	0.942135i	$-0.391185\pi$
$643$	7.36940e13			0.670467			0.335233	+	0.942135i	$0.391185\pi$
$644$	1.06984e13	−	9.02457e13i	0.0965808	−	0.814699i
$645$	−5.92281e13	+	6.26771e12i	−0.530554	+	0.0561449i
$646$	1.78864e14	−	1.58913e14i	1.58987	−	1.41252i
$647$	1.49570e14			1.31924			0.659618	−	0.751601i	$-0.270718\pi$
$647$	1.49570e14			1.31924			0.659618	+	0.751601i	$0.270718\pi$
$648$	3.72019e13	+	5.34093e13i	0.325605	+	0.467458i
$649$	1.01327e14			0.880043
$650$	−8.88910e13	−	6.52943e13i	−0.766110	−	0.562741i
$651$		−	2.75648e13i		−	0.235749i
$652$	2.68270e13	−	2.26297e14i	0.227685	−	1.92061i
$653$		−	4.17133e13i		−	0.351325i	−0.984450	−	0.175662i	$-0.943793\pi$
$653$		−	4.17133e13i		−	0.351325i	0.984450	−	0.175662i	$-0.0562067\pi$
$654$	−3.87712e13	+	3.44464e13i	−0.324056	+	0.287909i
$655$	8.56495e12	+	8.09364e13i	0.0710425	+	0.671332i
$656$	−9.55481e13	−	2.29770e13i	−0.786507	−	0.189136i
$657$		−	5.37808e13i		−	0.439340i
$658$	3.17735e13	−	2.82293e13i	0.257594	−	0.228860i
$659$		−	2.32341e14i		−	1.86938i	−0.355458	−	0.934692i	$-0.615675\pi$
$659$		−	2.32341e14i		−	1.86938i	0.355458	−	0.934692i	$-0.384325\pi$
$660$	−6.01292e13	−	7.55644e11i	−0.480138	−	0.00603390i
$661$	−1.40637e14			−1.11453			−0.557266	−	0.830334i	$-0.688150\pi$
$661$	−1.40637e14			−1.11453			−0.557266	+	0.830334i	$0.688150\pi$
$662$	−9.35935e13	−	1.05344e14i	−0.736132	−	0.828554i
$663$	6.58442e13			0.513984
$664$	2.68806e13	+	3.85914e13i	0.208257	+	0.298986i
$665$	2.49969e13	+	2.36214e14i	0.192211	+	1.81634i
$666$	−1.35606e14	−	1.52631e14i	−1.03492	−	1.16486i
$667$	4.63746e13			0.351278
$668$	−1.24654e13	+	1.05151e14i	−0.0937181	+	0.790550i
$669$	7.00133e13			0.522456
$670$	−4.85465e13	+	5.32778e13i	−0.359570	+	0.394614i
$671$			4.34304e13i			0.319287i
$672$	−5.61374e13	+	2.99722e13i	−0.409643	+	0.218712i
$673$			2.06777e13i			0.149771i	0.997192	+	0.0748853i	$0.0238591\pi$
$673$			2.06777e13i			0.149771i	−0.997192	+	0.0748853i	$0.976141\pi$
$674$	−1.13622e14	−	1.27888e14i	−0.816890	−	0.919451i
$675$	−9.84625e13	+	2.10753e13i	−0.702671	+	0.150402i
$676$	1.60201e12	−	1.35136e13i	0.0113483	−	0.0957276i
$677$			1.35666e14i			0.953957i	0.878915	+	0.476979i	$0.158268\pi$
$677$			1.35666e14i			0.953957i	−0.878915	+	0.476979i	$0.841732\pi$
$678$	2.31587e13	+	2.60662e13i	0.161646	+	0.181941i
$679$			9.22238e13i			0.638990i
$680$	1.52895e14	−	1.32440e14i	1.05159	−	0.910907i
$681$	−4.40406e13			−0.300689
$682$	−6.91836e13	+	6.14665e13i	−0.468901	+	0.416597i
$683$	−9.63487e13			−0.648250			−0.324125	−	0.946014i	$-0.605070\pi$
$683$	−9.63487e13			−0.648250			−0.324125	+	0.946014i	$0.605070\pi$
$684$	1.92946e14	+	2.28733e13i	1.28871	+	0.152774i
$685$	−6.65237e11	−	6.28631e12i	−0.00441087	−	0.0416814i
$686$	−7.76662e13	+	6.90029e13i	−0.511224	+	0.454199i
$687$	6.42826e13			0.420059
$688$	2.05745e14	+	4.94766e13i	1.33471	+	0.320965i
$689$	−3.03660e13			−0.195565
$690$	2.81103e13	−	3.08499e13i	0.179729	−	0.197246i
$691$		−	7.79765e13i		−	0.494964i	−0.968892	−	0.247482i	$-0.920397\pi$
$691$		−	7.79765e13i		−	0.494964i	0.968892	−	0.247482i	$-0.0796031\pi$
$692$	7.96462e13	+	9.44189e12i	0.501920	+	0.0595016i
$693$		−	2.00314e14i		−	1.25327i
$694$	−1.68651e14	+	1.49839e14i	−1.04759	+	0.930737i
$695$	−2.97317e13	−	2.80956e14i	−0.183356	−	1.73266i
$696$	−1.85608e13	−	2.66470e13i	−0.113645	−	0.163156i
$697$		−	1.85132e14i		−	1.12543i
$698$	−1.28131e14	+	1.13839e14i	−0.773352	+	0.687088i
$699$			1.08552e14i			0.650507i
$700$	1.86221e13	+	1.99954e14i	0.110800	+	1.18970i
$701$	6.84476e13			0.404360			0.202180	−	0.979348i	$-0.435197\pi$
$701$	6.84476e13			0.404360			0.202180	+	0.979348i	$0.435197\pi$
$702$	7.73466e13	+	8.70574e13i	0.453686	+	0.510646i
$703$	−4.81740e14			−2.80567
$704$	2.00406e14	+	7.40619e13i	1.15891	+	0.428284i
$705$	1.94111e13	−	2.05414e12i	0.111456	−	0.0117947i
$706$	1.13264e14	+	1.27485e14i	0.645759	+	0.726834i
$707$	8.13957e13			0.460791
$708$	4.89041e13	+	5.79748e12i	0.274903	+	0.0325892i
$709$	−2.02898e13			−0.113252			−0.0566261	−	0.998395i	$-0.518034\pi$
$709$	−2.02898e13			−0.113252			−0.0566261	+	0.998395i	$0.518034\pi$
$710$	−8.60318e13	−	7.83917e13i	−0.476834	−	0.434489i
$711$		−	1.82382e14i		−	1.00377i
$712$	−1.86284e13	−	2.67441e13i	−0.101807	−	0.146160i
$713$		−	6.42308e13i		−	0.348574i
$714$	−7.96258e13	−	8.96228e13i	−0.429104	−	0.482978i
$715$	2.18247e14	−	2.30956e13i	1.16793	−	0.123594i
$716$	−1.40319e14	−	1.66345e13i	−0.745676	−	0.0883984i
$717$			5.39123e13i			0.284506i
$718$	1.26437e14	+	1.42311e14i	0.662602	+	0.745792i
$719$			3.35545e14i			1.74625i	0.487498	+	0.873124i	$0.337910\pi$
$719$			3.35545e14i			1.74625i	−0.487498	+	0.873124i	$0.662090\pi$
$720$	1.62868e14	+	2.13862e13i	0.841729	+	0.110528i
$721$	−1.27184e13			−0.0652766
$722$	1.96051e14	−	1.74182e14i	0.999271	−	0.887807i
$723$	−1.48448e14			−0.751421
$724$	−1.81147e13	+	1.52805e14i	−0.0910624	+	0.768148i
$725$	−1.00208e14	+	2.14488e13i	−0.500277	+	0.107081i
$726$	3.08517e13	−	2.74103e13i	0.152966	−	0.135904i
$727$	−6.92547e13			−0.341018			−0.170509	−	0.985356i	$-0.554541\pi$
$727$	−6.92547e13			−0.341018			−0.170509	+	0.985356i	$0.554541\pi$
$728$	1.90577e14	−	1.32745e14i	0.931997	−	0.649176i
$729$	−4.20753e13			−0.204357
$730$	−7.92997e13	−	7.22575e13i	−0.382523	−	0.348553i
$731$			3.98648e14i			1.90986i
$732$	−2.48489e12	+	2.09610e13i	−0.0118236	+	0.0997372i
$733$		−	1.71681e14i		−	0.811337i	−0.914020	−	0.405669i	$-0.867039\pi$
$733$		−	1.71681e14i		−	0.811337i	0.914020	−	0.405669i	$-0.132961\pi$
$734$	−1.03044e14	+	9.15503e13i	−0.483665	+	0.429714i
$735$	3.54554e13	−	3.75201e12i	0.165290	−	0.0174915i
$736$	−1.30810e14	+	6.98406e13i	−0.605692	+	0.323384i
$737$		−	1.43422e14i		−	0.659596i
$738$	1.12390e14	−	9.98537e13i	0.513390	−	0.456123i
$739$			2.12086e14i			0.962254i	0.876651	+	0.481127i	$0.159772\pi$
$739$			2.12086e14i			0.962254i	−0.876651	+	0.481127i	$0.840228\pi$
$740$	−4.07249e14	−	5.11790e12i	−1.83528	−	0.0230639i
$741$	1.26163e14			0.564732
$742$	3.67218e13	+	4.13322e13i	0.163269	+	0.183768i
$743$	1.30199e14			0.574996			0.287498	−	0.957781i	$-0.407177\pi$
$743$	1.30199e14			0.574996			0.287498	+	0.957781i	$0.407177\pi$
$744$	−3.69072e13	+	2.57075e13i	−0.161900	+	0.112770i
$745$	−8.24491e13	+	8.72503e12i	−0.359256	+	0.0380177i
$746$	1.31463e14	+	1.47968e14i	0.568996	+	0.640433i
$747$	−7.19493e13			−0.309331
$748$	−4.73834e13	+	3.99699e14i	−0.202357	+	1.70697i
$749$	4.84424e14			2.05502
$750$	−4.64730e13	+	7.96626e13i	−0.195837	+	0.335698i
$751$		−	3.16975e14i		−	1.32686i	−0.748238	−	0.663431i	$-0.769100\pi$
$751$		−	3.16975e14i		−	1.32686i	0.748238	−	0.663431i	$-0.230900\pi$
$752$	−6.74296e13	−	1.62152e13i	−0.280389	−	0.0674267i
$753$		−	3.18853e13i		−	0.131709i
$754$	7.87174e13	+	8.86004e13i	0.323009	+	0.363562i
$755$	−2.01444e13	−	1.90359e14i	−0.0821144	−	0.775958i
$756$	2.49612e13	−	2.10558e14i	0.101078	−	0.852635i
$757$		−	2.04193e14i		−	0.821413i	−0.911768	−	0.410706i	$-0.865282\pi$
$757$		−	2.04193e14i		−	0.821413i	0.911768	−	0.410706i	$-0.134718\pi$
$758$	2.51157e14	+	2.82689e14i	1.00369	+	1.12970i
$759$			8.30467e13i			0.329696i
$760$	2.92960e14	−	2.53767e14i	1.15542	−	1.00084i
$761$	−2.25073e14			−0.881862			−0.440931	−	0.897541i	$-0.645352\pi$
$761$	−2.25073e14			−0.881862			−0.440931	+	0.897541i	$0.645352\pi$
$762$	−8.75722e13	+	7.78039e13i	−0.340872	+	0.302849i
$763$	−3.44629e14			−1.33269
$764$	1.84463e14	+	2.18677e13i	0.708666	+	0.0840109i
$765$	3.25659e13	+	3.07738e14i	0.124296	+	1.17456i
$766$	2.60329e14	−	2.31290e14i	0.987138	−	0.877027i
$767$	−1.79731e14			−0.677088
$768$	9.24856e13	+	4.72111e13i	0.346153	+	0.176701i
$769$	−3.21415e14			−1.19518			−0.597592	−	0.801800i	$-0.703876\pi$
$769$	−3.21415e14			−1.19518			−0.597592	+	0.801800i	$0.703876\pi$
$770$	−2.95363e14	−	2.69134e14i	−1.09120	−	0.994293i
$771$		−	1.49715e14i		−	0.549531i
$772$	6.99770e13	+	8.29563e12i	0.255193	+	0.0302526i
$773$		−	5.70492e13i		−	0.206706i	−0.994645	−	0.103353i	$-0.967043\pi$
$773$		−	5.70492e13i		−	0.206706i	0.994645	−	0.103353i	$-0.0329571\pi$
$774$	−2.42012e14	+	2.15016e14i	−0.871227	+	0.774046i
$775$	2.97074e13	+	1.38792e14i	0.106257	+	0.496426i
$776$	1.23481e14	−	8.60099e13i	0.438825	−	0.305661i
$777$			2.41384e14i			0.852321i
$778$	−5.72733e13	+	5.08847e13i	−0.200934	+	0.178521i
$779$		−	3.54730e14i		−	1.23655i
$780$	1.06655e14	+	1.34033e12i	0.369409	+	0.00464237i
$781$	2.31594e14			0.797026
$782$	−1.85542e14	−	2.08837e14i	−0.634466	−	0.714124i
$783$	1.08200e14			0.367636
$784$	−1.23164e14	−	2.96179e13i	−0.415818	−	0.0999940i
$785$	−1.49737e13	−	1.41497e14i	−0.0502320	−	0.474678i
$786$	−5.22768e13	−	5.88401e13i	−0.174259	−	0.196138i
$787$	3.38595e14			1.12152			0.560759	−	0.827979i	$-0.310509\pi$
$787$	3.38595e14			1.12152			0.560759	+	0.827979i	$0.310509\pi$
$788$	−1.61512e14	−	1.91469e13i	−0.531586	−	0.0630185i
$789$	−1.02199e14			−0.334241
$790$	−2.68922e14	−	2.45040e14i	−0.873958	−	0.796346i
$791$			2.31697e14i			0.748236i
$792$	−2.68206e14	+	1.86817e14i	−0.860683	+	0.599503i
$793$		−	7.70352e13i		−	0.245654i
$794$	4.87615e13	+	5.48835e13i	0.154516	+	0.173916i
$795$	2.67211e12	+	2.52507e13i	0.00841431	+	0.0795129i
$796$	−4.28126e14	−	5.07535e13i	−1.33970	−	0.158818i
$797$			4.36562e14i			1.35754i	0.734349	+	0.678772i	$0.237487\pi$
$797$			4.36562e14i			1.35754i	−0.734349	+	0.678772i	$0.762513\pi$
$798$	−1.52570e14	−	1.71725e14i	−0.471471	−	0.530665i
$799$		−	1.30651e14i		−	0.401215i
$800$	2.50356e14	−	2.11415e14i	0.764025	−	0.645186i
$801$	4.98612e13			0.151217
$802$	−7.60226e13	+	6.75426e13i	−0.229124	+	0.203566i
$803$	2.13472e14			0.639386
$804$	8.20592e12	−	6.92203e13i	0.0244257	−	0.206041i
$805$	2.75796e14	−	2.91857e13i	0.815848	−	0.0863357i
$806$	1.22715e14	−	1.09027e14i	0.360764	−	0.320522i
$807$	9.86374e13			0.288187
$808$	−7.59113e13	−	1.08983e14i	−0.220419	−	0.316447i
$809$	−4.65090e14			−1.34213			−0.671065	−	0.741399i	$-0.734163\pi$
$809$	−4.65090e14			−1.34213			−0.671065	+	0.741399i	$0.734163\pi$
$810$	−1.33785e14	+	1.46824e14i	−0.383693	+	0.421088i
$811$		−	5.09101e14i		−	1.45111i	−0.688166	−	0.725554i	$-0.741584\pi$
$811$		−	5.09101e14i		−	1.45111i	0.688166	−	0.725554i	$-0.258416\pi$
$812$	2.54036e13	−	2.14290e14i	0.0719641	−	0.607046i
$813$		−	1.22395e14i		−	0.344597i
$814$	6.05839e14	−	5.38260e14i	1.69525	−	1.50616i
$815$	6.91577e14	−	7.31849e13i	1.92332	−	0.203532i
$816$	−4.57378e13	+	1.90197e14i	−0.126422	+	0.525719i
$817$			7.63845e14i			2.09843i
$818$	2.82255e14	−	2.50771e14i	0.770683	−	0.684717i
$819$			3.55310e14i			0.964245i
$820$	3.76858e12	−	2.99878e14i	0.0101650	−	0.808865i
$821$	−2.27891e14			−0.610957			−0.305479	−	0.952199i	$-0.598816\pi$
$821$	−2.27891e14			−0.610957			−0.305479	+	0.952199i	$0.598816\pi$
$822$	4.06032e12	+	4.57010e12i	0.0108194	+	0.0121777i
$823$	1.27232e14			0.336975			0.168487	−	0.985704i	$-0.446112\pi$
$823$	1.27232e14			0.336975			0.168487	+	0.985704i	$0.446112\pi$
$824$	1.18615e13	+	1.70291e13i	0.0312250	+	0.0448286i
$825$	−3.84100e13	−	1.79450e14i	−0.100502	−	0.469540i
$826$	2.17349e14	+	2.44638e14i	0.565273	+	0.636243i
$827$	−1.07724e13			−0.0278473			−0.0139237	−	0.999903i	$-0.504432\pi$
$827$	−1.07724e13			−0.0278473			−0.0139237	+	0.999903i	$0.504432\pi$
$828$	2.67063e13	−	2.25278e14i	0.0686217	−	0.578852i
$829$	4.90888e14			1.25375			0.626873	−	0.779121i	$-0.284334\pi$
$829$	4.90888e14			1.25375			0.626873	+	0.779121i	$0.284334\pi$
$830$	−9.66679e13	+	1.06089e14i	−0.245410	+	0.269327i
$831$			1.60231e14i			0.404334i
$832$	−3.55473e14	−	1.31368e14i	−0.891641	−	0.329513i
$833$		−	2.38640e14i		−	0.595003i
$834$	1.81469e14	+	2.04253e14i	0.449752	+	0.506218i
$835$	−3.21347e14	+	3.40060e13i	−0.791665	+	0.0837766i
$836$	−9.07909e13	+	7.65859e14i	−0.222337	+	1.87550i
$837$		−	1.49861e14i		−	0.364806i
$838$	−2.55083e13	−	2.87108e13i	−0.0617250	−	0.0694746i
$839$		−	3.31532e14i		−	0.797473i	−0.917065	−	0.398737i	$-0.869449\pi$
$839$		−	3.31532e14i		−	0.797473i	0.917065	−	0.398737i	$-0.130551\pi$
$840$	−1.27154e14	−	1.46792e14i	−0.304042	−	0.351000i
$841$	−3.10590e14			−0.738256
$842$	−1.50351e14	+	1.33580e14i	−0.355260	+	0.315632i
$843$	−1.07150e14			−0.251683
$844$	−4.91412e14	−	5.82559e13i	−1.14745	−	0.136028i
$845$	4.12984e13	−	4.37033e12i	0.0958627	−	0.0101445i
$846$	7.93155e13	−	7.04682e13i	0.183023	−	0.162608i
$847$	2.74234e14			0.629078
$848$	2.10933e13	−	8.77150e13i	0.0481022	−	0.200030i
$849$	−1.18946e13			−0.0269656
$850$	4.97514e14	+	3.65445e14i	1.12127	+	0.823622i
$851$			5.62466e14i			1.26023i
$852$	1.11775e14	+	1.32507e13i	0.248971	+	0.0295149i
$853$			8.22258e14i			1.82080i	0.413727	+	0.910401i	$0.364227\pi$
$853$			8.22258e14i			1.82080i	−0.413727	+	0.910401i	$0.635773\pi$
$854$	−1.04855e14	+	9.31591e13i	−0.230835	+	0.205086i
$855$	6.23992e13	+	5.89655e14i	0.136568	+	1.29053i
$856$	−4.51784e14	−	6.48609e14i	−0.983020	−	1.41128i
$857$		−	6.80976e14i		−	1.47308i	−0.676392	−	0.736542i	$-0.736457\pi$
$857$		−	6.80976e14i		−	1.47308i	0.676392	−	0.736542i	$-0.263543\pi$
$858$	−1.58664e14	+	1.40965e14i	−0.341225	+	0.303163i
$859$			1.37051e14i			0.293033i	0.989208	+	0.146517i	$0.0468062\pi$
$859$			1.37051e14i			0.293033i	−0.989208	+	0.146517i	$0.953194\pi$
$860$	−8.11492e12	+	6.45732e14i	−0.0172501	+	1.37265i
$861$	−1.77743e14			−0.375645
$862$	1.11427e14	+	1.25417e14i	0.234128	+	0.263523i
$863$	−3.18751e14			−0.665882			−0.332941	−	0.942948i	$-0.608041\pi$
$863$	−3.18751e14			−0.665882			−0.332941	+	0.942948i	$0.608041\pi$
$864$	−3.05202e14	+	1.62950e14i	−0.633896	+	0.338443i
$865$	2.57578e13	+	2.43404e14i	0.0531897	+	0.502628i
$866$	2.16021e14	+	2.43143e14i	0.443514	+	0.499197i
$867$	−1.78131e14			−0.363617
$868$	−2.96800e14	−	3.51851e13i	−0.602374	−	0.0714101i
$869$	7.23927e14			1.46082
$870$	6.67483e13	−	7.32536e13i	0.133920	−	0.146971i
$871$			2.54396e14i			0.507480i
$872$	3.21408e14	+	4.61433e14i	0.637492	+	0.915222i
$873$			2.30216e14i			0.454009i
$874$	−3.55515e14	−	4.00150e14i	−0.697110	−	0.784632i
$875$	−5.82450e14	+	1.90624e14i	−1.13558	+	0.371653i
$876$	1.03029e14	+	1.22139e13i	0.199728	+	0.0236773i
$877$		−	3.95684e14i		−	0.762694i	−0.924432	−	0.381347i	$-0.875460\pi$
$877$		−	3.95684e14i		−	0.762694i	0.924432	−	0.381347i	$-0.124540\pi$
$878$	5.51159e12	+	6.20357e12i	0.0105634	+	0.0118896i
$879$		−	3.46648e14i		−	0.660609i
$880$	−8.48883e13	+	6.46470e14i	−0.160855	+	1.22500i
$881$	4.64098e14			0.874440			0.437220	−	0.899355i	$-0.355963\pi$
$881$	4.64098e14			0.874440			0.437220	+	0.899355i	$0.355963\pi$
$882$	1.44874e14	−	1.28714e14i	0.271424	−	0.241148i
$883$	7.09767e14			1.32225			0.661123	−	0.750278i	$-0.270080\pi$
$883$	7.09767e14			1.32225			0.661123	+	0.750278i	$0.270080\pi$
$884$	8.40468e13	−	7.08969e14i	0.155690	−	1.31331i
$885$	1.58157e13	+	1.49454e14i	0.0291322	+	0.275291i
$886$	2.79754e14	−	2.48548e14i	0.512398	−	0.455242i
$887$	−1.00628e15			−1.83274			−0.916368	−	0.400337i	$-0.868893\pi$
$887$	−1.00628e15			−1.83274			−0.916368	+	0.400337i	$0.868893\pi$
$888$	3.23195e14	−	2.25120e14i	0.585329	−	0.407707i
$889$	−7.78411e14			−1.40185
$890$	6.69914e13	−	7.35203e13i	0.119969	−	0.131661i
$891$		−	3.95245e14i		−	0.703846i
$892$	8.93685e13	−	7.53860e14i	0.158256	−	1.33495i
$893$		−	2.50338e14i		−	0.440829i
$894$	5.99399e13	−	5.32538e13i	0.104961	−	0.0932531i
$895$	−4.53794e13	−	4.28823e14i	−0.0790212	−	0.746728i
$896$	2.51066e14	+	6.42711e14i	0.434758	+	1.11295i
$897$		−	1.47305e14i		−	0.253662i
$898$	−4.73132e14	+	4.20356e14i	−0.810215	+	0.719839i
$899$		−	1.52517e14i		−	0.259729i
$900$	4.64860e13	+	4.99139e14i	0.0787245	+	0.845297i
$901$	1.69955e14			0.286227
$902$	3.96349e14	+	4.46110e14i	0.663811	+	0.747153i
$903$	3.82737e14			0.637473
$904$	3.10226e14	−	2.16086e14i	0.513849	−	0.357918i
$905$	−4.66982e14	+	4.94176e13i	−0.769232	+	0.0814026i
$906$	1.22953e14	+	1.38389e14i	0.201417	+	0.226705i
$907$	4.79149e14			0.780610			0.390305	−	0.920686i	$-0.372370\pi$
$907$	4.79149e14			0.780610			0.390305	+	0.920686i	$0.372370\pi$
$908$	−5.62156e13	+	4.74202e14i	−0.0910810	+	0.768305i
$909$	2.03186e14			0.327397
$910$	5.23904e14	+	4.77378e14i	0.839546	+	0.764990i
$911$			3.79171e14i			0.604287i	0.953262	+	0.302144i	$0.0977022\pi$
$911$			3.79171e14i			0.604287i	−0.953262	+	0.302144i	$0.902298\pi$
$912$	−8.76377e13	+	3.64435e14i	−0.138905	+	0.577625i
$913$		−	2.85588e14i		−	0.450180i
$914$	−2.91551e14	−	3.28155e14i	−0.457071	−	0.514456i
$915$	−6.40582e13	+	6.77885e12i	−0.0998779	+	0.0105694i
$916$	8.20536e13	−	6.92156e14i	0.127239	−	1.07331i
$917$		−	5.23018e14i		−	0.806622i
$918$	−4.32901e14	−	4.87251e14i	−0.664010	−	0.747377i
$919$		−	8.93753e14i		−	1.36345i	−0.731608	−	0.681726i	$-0.761230\pi$
$919$		−	8.93753e14i		−	1.36345i	0.731608	−	0.681726i	$-0.238770\pi$
$920$	−2.96291e14	−	3.42052e14i	−0.449551	−	0.518983i
$921$	−1.56654e14			−0.236398
$922$	8.96331e14	−	7.96349e14i	1.34528	−	1.19522i
$923$	−4.10793e14			−0.613217
$924$	3.83746e14	+	4.54923e13i	0.569749	+	0.0675426i
$925$	−2.60147e14	−	1.21539e15i	−0.384158	−	1.79477i
$926$	−9.77184e14	+	8.68183e14i	−1.43523	+	1.27514i
$927$	−3.17487e13			−0.0463797
$928$	−3.10611e14	+	1.65838e14i	−0.451312	+	0.240959i
$929$	−2.76125e14			−0.399049			−0.199525	−	0.979893i	$-0.563940\pi$
$929$	−2.76125e14			−0.399049			−0.199525	+	0.979893i	$0.563940\pi$
$930$	−1.01459e14	−	9.24492e13i	−0.145840	−	0.132889i
$931$		−	4.57256e14i		−	0.653750i
$932$	1.16882e15	+	1.38561e14i	1.66214	+	0.197044i
$933$			1.39411e14i			0.197191i
$934$	−1.93460e13	+	1.71880e13i	−0.0272180	+	0.0241819i
$935$	−1.22150e15	+	1.29264e14i	−1.70937	+	0.180891i
$936$	4.75734e14	−	3.31369e14i	0.662193	−	0.461246i
$937$		−	2.96955e14i		−	0.411143i	−0.978642	−	0.205572i	$-0.934095\pi$
$937$		−	2.96955e14i		−	0.411143i	0.978642	−	0.205572i	$-0.0659054\pi$
$938$	3.46267e14	−	3.07643e14i	0.476867	−	0.423674i
$939$		−	3.90062e14i		−	0.534326i
$940$	2.65954e12	−	2.11628e14i	0.00362382	−	0.288360i
$941$	7.21500e14			0.977886			0.488943	−	0.872316i	$-0.337383\pi$
$941$	7.21500e14			0.977886			0.488943	+	0.872316i	$0.337383\pi$
$942$	9.13929e13	+	1.02867e14i	0.123213	+	0.138683i
$943$	−4.14173e14			−0.555423
$944$	1.24847e14	−	5.19169e14i	0.166540	−	0.692547i
$945$	6.43479e14	−	6.80951e13i	0.853838	−	0.0903559i
$946$	−8.53463e14	−	9.60615e14i	−1.12649	−	1.26793i
$947$	−1.64992e14			−0.216627			−0.108314	−	0.994117i	$-0.534545\pi$
$947$	−1.64992e14			−0.216627			−0.108314	+	0.994117i	$0.534545\pi$
$948$	3.49392e14	+	4.14197e13i	0.456322	+	0.0540960i
$949$	−3.78648e14			−0.491931
$950$	9.53282e14	+	7.00226e14i	1.23198	+	0.904941i
$951$		−	3.82072e14i		−	0.491182i
$952$	−1.06664e15	+	7.42962e14i	−1.36406	+	0.950128i
$953$			8.63297e14i			1.09824i	0.835745	+	0.549118i	$0.185036\pi$
$953$			8.63297e14i			1.09824i	−0.835745	+	0.549118i	$0.814964\pi$
$954$	9.16677e13	+	1.03177e14i	0.116004	+	0.130569i
$955$	5.96557e13	+	5.63730e14i	0.0750992	+	0.709666i
$956$	5.80494e14	+	6.88163e13i	0.726956	+	0.0861791i
$957$			1.97196e14i			0.245662i
$958$	−3.27139e14	−	3.68211e14i	−0.405419	−	0.456320i
$959$			4.06226e13i			0.0500813i
$960$	−7.79580e13	+	3.07152e14i	−0.0956102	+	0.376701i
$961$	6.08386e14			0.742270
$962$	−1.07461e15	+	9.54744e14i	−1.30430	+	1.15881i
$963$	1.20926e15			1.46012
$964$	−1.89487e14	+	1.59840e15i	−0.227611	+	1.91999i
$965$	2.26307e13	+	2.13854e14i	0.0270435	+	0.255553i
$966$	−2.00502e14	+	1.78137e14i	−0.238360	+	0.211772i
$967$	1.77491e13			0.0209915			0.0104958	−	0.999945i	$-0.496659\pi$
$967$	1.77491e13			0.0209915			0.0104958	+	0.999945i	$0.496659\pi$
$968$	−2.55757e14	−	3.67180e14i	−0.300919	−	0.432018i
$969$	−7.06124e14			−0.826536
$970$	3.39453e14	+	3.09308e14i	0.395295	+	0.360191i
$971$			8.66070e14i			1.00336i	0.865053	+	0.501680i	$0.167284\pi$
$971$			8.66070e14i			1.00336i	−0.865053	+	0.501680i	$0.832716\pi$
$972$	9.60104e13	−	8.09887e14i	0.110659	−	0.933454i
$973$			1.81556e15i			2.08184i
$974$	−3.23630e13	+	2.87531e13i	−0.0369194	+	0.0328012i
$975$	6.81302e13	+	3.18301e14i	0.0773244	+	0.361255i
$976$	2.22524e14	+	5.35114e13i	0.251262	+	0.0604223i
$977$		−	4.90063e14i		−	0.550528i	−0.961369	−	0.275264i	$-0.911235\pi$
$977$		−	4.90063e14i		−	0.550528i	0.961369	−	0.275264i	$-0.0887652\pi$
$978$	−5.02771e14	+	4.46689e14i	−0.561922	+	0.499242i
$979$			1.97914e14i			0.220071i
$980$	4.85779e12	−	3.86551e14i	0.00537413	−	0.427638i
$981$	−8.60289e14			−0.946890
$982$	−8.46991e14	−	9.53330e14i	−0.927515	−	1.04397i
$983$	7.44254e14			0.810874			0.405437	−	0.914123i	$-0.367119\pi$
$983$	7.44254e14			0.810874			0.405437	+	0.914123i	$0.367119\pi$
$984$	1.65767e14	+	2.37985e14i	0.179690	+	0.257973i
$985$	−5.22334e13	−	4.93591e14i	−0.0563336	−	0.532336i
$986$	−4.40573e14	−	4.95887e14i	−0.472752	−	0.532106i
$987$	−1.25436e14			−0.133917
$988$	1.61041e14	−	1.35845e15i	0.171062	−	1.44297i
$989$	8.91845e14			0.942557
$990$	−7.37309e14	−	6.71832e14i	−0.775306	−	0.706455i
$991$			9.81943e14i			1.02735i	0.857985	+	0.513674i	$0.171716\pi$
$991$			9.81943e14i			1.02735i	−0.857985	+	0.513674i	$0.828284\pi$
$992$	2.29692e14	+	4.30209e14i	0.239105	+	0.447838i
$993$			4.15880e14i			0.430746i
$994$	4.96774e14	+	5.59144e14i	0.511949	+	0.576225i
$995$	−1.38457e14	−	1.30838e15i	−0.141971	−	1.34159i
$996$	1.63400e13	−	1.37835e14i	0.0166708	−	0.140625i
$997$			9.31888e14i			0.945993i	0.881064	+	0.472997i	$0.156828\pi$
$997$			9.31888e14i			0.945993i	−0.881064	+	0.472997i	$0.843172\pi$
$998$	−4.86265e14	−	5.47316e14i	−0.491157	−	0.552822i
$999$			1.31233e15i			1.31891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.11.d.d.19.6	yes	24
4.3	odd	2	inner	20.11.d.d.19.20	yes	24
5.2	odd	4		100.11.b.h.51.7		24
5.3	odd	4		100.11.b.h.51.18		24
5.4	even	2	inner	20.11.d.d.19.19	yes	24
20.3	even	4		100.11.b.h.51.17		24
20.7	even	4		100.11.b.h.51.8		24
20.19	odd	2	inner	20.11.d.d.19.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.d.d.19.5	✓	24	20.19	odd	2	inner
20.11.d.d.19.6	yes	24	1.1	even	1	trivial
20.11.d.d.19.19	yes	24	5.4	even	2	inner
20.11.d.d.19.20	yes	24	4.3	odd	2	inner
100.11.b.h.51.7		24	5.2	odd	4
100.11.b.h.51.8		24	20.7	even	4
100.11.b.h.51.17		24	20.3	even	4
100.11.b.h.51.18		24	5.3	odd	4

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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	20.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-23.9223 + 21.2538i) q^{2} +94.4407 q^{3} +(120.549 - 1016.88i) q^{4} +(3107.65 - 328.861i) q^{5} +(-2259.24 + 2007.23i) q^{6} -20081.9 q^{7} +(18728.8 + 26888.2i) q^{8} -50129.9 q^{9} +O(q^{10})\)	\(q+(-23.9223 + 21.2538i) q^{2} +94.4407 q^{3} +(120.549 - 1016.88i) q^{4} +(3107.65 - 328.861i) q^{5} +(-2259.24 + 2007.23i) q^{6} -20081.9 q^{7} +(18728.8 + 26888.2i) q^{8} -50129.9 q^{9} +(-67352.4 + 73916.5i) q^{10} -198980. i q^{11} +(11384.7 - 96034.9i) q^{12} +352944. i q^{13} +(480404. - 426817. i) q^{14} +(293489. - 31057.9i) q^{15} +(-1.01951e6 - 245167. i) q^{16} -1.97539e6i q^{17} +(1.19922e6 - 1.06545e6i) q^{18} -3.78502e6i q^{19} +(40211.3 - 3.19975e6i) q^{20} -1.89655e6 q^{21} +(4.22910e6 + 4.76006e6i) q^{22} -4.41929e6 q^{23} +(1.76876e6 + 2.53934e6i) q^{24} +(9.54933e6 - 2.04397e6i) q^{25} +(-7.50141e6 - 8.44321e6i) q^{26} -1.03109e7 q^{27} +(-2.42085e6 + 2.04209e7i) q^{28} -1.04937e7 q^{29} +(-6.36081e6 + 6.98073e6i) q^{30} +1.45342e7i q^{31} +(2.95998e7 - 1.58036e7i) q^{32} -1.87919e7i q^{33} +(4.19846e7 + 4.72558e7i) q^{34} +(-6.24074e7 + 6.60416e6i) q^{35} +(-6.04311e6 + 5.09761e7i) q^{36} -1.27275e8i q^{37} +(8.04463e7 + 9.05463e7i) q^{38} +3.33323e7i q^{39} +(6.70450e7 + 7.73998e7i) q^{40} +9.37194e7 q^{41} +(4.53697e7 - 4.03089e7i) q^{42} -2.01807e8 q^{43} +(-2.02339e8 - 2.39869e7i) q^{44} +(-1.55786e8 + 1.64858e7i) q^{45} +(1.05719e8 - 9.39268e7i) q^{46} +6.61391e7 q^{47} +(-9.62835e7 - 2.31538e7i) q^{48} +1.20807e8 q^{49} +(-1.84999e8 + 2.51856e8i) q^{50} -1.86557e8i q^{51} +(3.58901e8 + 4.25470e7i) q^{52} +8.60363e7i q^{53} +(2.46661e8 - 2.19147e8i) q^{54} +(-6.54370e7 - 6.18361e8i) q^{55} +(-3.76109e8 - 5.39965e8i) q^{56} -3.57460e8i q^{57} +(2.51033e8 - 2.23031e8i) q^{58} +5.09233e8i q^{59} +(3.79758e6 - 3.02187e8i) q^{60} -2.18265e8 q^{61} +(-3.08907e8 - 3.47691e8i) q^{62} +1.00670e9 q^{63} +(-3.72207e8 + 1.00717e9i) q^{64} +(1.16070e8 + 1.09682e9i) q^{65} +(3.99399e8 + 4.49544e8i) q^{66} +7.20783e8 q^{67} +(-2.00873e9 - 2.38131e8i) q^{68} -4.17361e8 q^{69} +(1.35256e9 - 1.48438e9i) q^{70} +1.16390e9i q^{71} +(-9.38873e8 - 1.34790e9i) q^{72} +1.07283e9i q^{73} +(2.70509e9 + 3.04471e9i) q^{74} +(9.01845e8 - 1.93034e8i) q^{75} +(-3.84891e9 - 4.56281e8i) q^{76} +3.99590e9i q^{77} +(-7.08438e8 - 7.97383e8i) q^{78} +3.63818e9i q^{79} +(-3.24891e9 - 4.26616e8i) q^{80} +1.98635e9 q^{81} +(-2.24198e9 + 1.99190e9i) q^{82} +1.43526e9 q^{83} +(-2.28627e8 + 1.92856e9i) q^{84} +(-6.49629e8 - 6.13881e9i) q^{85} +(4.82769e9 - 4.28918e9i) q^{86} -9.91032e8 q^{87} +(5.35022e9 - 3.72666e9i) q^{88} -9.94640e8 q^{89} +(3.37637e9 - 3.70543e9i) q^{90} -7.08777e9i q^{91} +(-5.32741e8 + 4.49388e9i) q^{92} +1.37262e9i q^{93} +(-1.58220e9 + 1.40571e9i) q^{94} +(-1.24475e9 - 1.17625e10i) q^{95} +(2.79542e9 - 1.49250e9i) q^{96} -4.59239e9i q^{97} +(-2.88997e9 + 2.56761e9i) q^{98} +9.97488e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9}+O(q^{10}) \) 24 * q + 608 * q^4 + 8280 * q^5 - 19584 * q^6 + 597192 * q^9	\( 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9} + 223600 q^{10} - 1706016 q^{14} - 4733376 q^{16} + 1631520 q^{20} - 13030368 q^{21} + 10190784 q^{24} + 8826200 q^{25} - 9454368 q^{26} + 121656816 q^{29} + 103616160 q^{30} - 335231168 q^{34} - 276632160 q^{36} - 559048000 q^{40} + 892843248 q^{41} + 766329600 q^{44} - 248162040 q^{45} + 433181216 q^{46} - 738102008 q^{49} + 765396000 q^{50} + 139387968 q^{54} - 2629032384 q^{56} + 296160000 q^{60} + 228563248 q^{61} - 1875284992 q^{64} - 2069145600 q^{65} - 1440259200 q^{66} - 943422432 q^{69} + 3242642240 q^{70} + 21045467232 q^{74} + 828422400 q^{76} + 11736799680 q^{80} - 5619065544 q^{81} - 28069573632 q^{84} - 18119744000 q^{85} + 8163556416 q^{86} + 4631088816 q^{89} - 16754463600 q^{90} + 63404384 q^{94} - 5617046784 q^{96}+O(q^{100}) \) 24 * q + 608 * q^4 + 8280 * q^5 - 19584 * q^6 + 597192 * q^9 + 223600 * q^10 - 1706016 * q^14 - 4733376 * q^16 + 1631520 * q^20 - 13030368 * q^21 + 10190784 * q^24 + 8826200 * q^25 - 9454368 * q^26 + 121656816 * q^29 + 103616160 * q^30 - 335231168 * q^34 - 276632160 * q^36 - 559048000 * q^40 + 892843248 * q^41 + 766329600 * q^44 - 248162040 * q^45 + 433181216 * q^46 - 738102008 * q^49 + 765396000 * q^50 + 139387968 * q^54 - 2629032384 * q^56 + 296160000 * q^60 + 228563248 * q^61 - 1875284992 * q^64 - 2069145600 * q^65 - 1440259200 * q^66 - 943422432 * q^69 + 3242642240 * q^70 + 21045467232 * q^74 + 828422400 * q^76 + 11736799680 * q^80 - 5619065544 * q^81 - 28069573632 * q^84 - 18119744000 * q^85 + 8163556416 * q^86 + 4631088816 * q^89 - 16754463600 * q^90 + 63404384 * q^94 - 5617046784 * q^96

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