LMFDB - Embedded newform 4.17.b.b.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,17,Mod(3,4)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 17, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	4.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:	$6.49298175427$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5152x^{4} + 242526x^{3} + 17329473x^{2} + 402444531x + 64957563630 $ x^6 - x^5 + 5152x^4 + 242526x^3 + 17329473x^2 + 402444531x + 64957563630
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.1
Root			$-46.2446 + 35.5107i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.17.b.b.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-212.978 - 142.043i) q^{2} +2908.07i q^{3} +(25183.6 + 60504.2i) q^{4} +20884.7 q^{5} +(413070. - 619356. i) q^{6} -8.01505e6i q^{7} +(3.23062e6 - 1.64632e7i) q^{8} +3.45899e7 q^{9} +O(q^{10})$	\(q+(-212.978 - 142.043i) q^{2} +2908.07i q^{3} +(25183.6 + 60504.2i) q^{4} +20884.7 q^{5} +(413070. - 619356. i) q^{6} -8.01505e6i q^{7} +(3.23062e6 - 1.64632e7i) q^{8} +3.45899e7 q^{9} +(-4.44799e6 - 2.96652e6i) q^{10} -1.22693e8i q^{11} +(-1.75950e8 + 7.32357e7i) q^{12} +4.11898e8 q^{13} +(-1.13848e9 + 1.70703e9i) q^{14} +6.07341e7i q^{15} +(-3.02654e9 + 3.04743e9i) q^{16} +1.07999e10 q^{17} +(-7.36690e9 - 4.91325e9i) q^{18} -3.07436e10i q^{19} +(5.25952e8 + 1.26361e9i) q^{20} +2.33083e10 q^{21} +(-1.74276e10 + 2.61309e10i) q^{22} +6.36764e10i q^{23} +(4.78762e10 + 9.39485e9i) q^{24} -1.52152e11 q^{25} +(-8.77254e10 - 5.85072e10i) q^{26} +2.25772e11i q^{27} +(4.84944e11 - 2.01848e11i) q^{28} -3.76057e11 q^{29} +(8.62685e9 - 1.29351e10i) q^{30} -3.36655e11i q^{31} +(1.07745e12 - 2.19138e11i) q^{32} +3.56798e11 q^{33} +(-2.30015e12 - 1.53405e12i) q^{34} -1.67392e11i q^{35} +(8.71098e11 + 2.09283e12i) q^{36} +1.97558e12 q^{37} +(-4.36690e12 + 6.54771e12i) q^{38} +1.19783e12i q^{39} +(6.74705e10 - 3.43830e11i) q^{40} +4.08883e12 q^{41} +(-4.96417e12 - 3.31078e12i) q^{42} -1.53830e13i q^{43} +(7.42341e12 - 3.08984e12i) q^{44} +7.22399e11 q^{45} +(9.04478e12 - 1.35617e13i) q^{46} +2.29977e13i q^{47} +(-8.86212e12 - 8.80138e12i) q^{48} -3.10082e13 q^{49} +(3.24050e13 + 2.16121e13i) q^{50} +3.14069e13i q^{51} +(1.03731e13 + 2.49215e13i) q^{52} -5.35569e13 q^{53} +(3.20694e13 - 4.80847e13i) q^{54} -2.56240e12i q^{55} +(-1.31954e14 - 2.58936e13i) q^{56} +8.94043e13 q^{57} +(8.00921e13 + 5.34163e13i) q^{58} -6.70947e13i q^{59} +(-3.67466e12 + 1.52950e12i) q^{60} +1.86362e14 q^{61} +(-4.78195e13 + 7.17003e13i) q^{62} -2.77240e14i q^{63} +(-2.60601e14 - 1.06373e14i) q^{64} +8.60236e12 q^{65} +(-7.59903e13 - 5.06807e13i) q^{66} +1.58513e14i q^{67} +(2.71981e14 + 6.53439e14i) q^{68} -1.85175e14 q^{69} +(-2.37768e13 + 3.56509e13i) q^{70} +8.90997e14i q^{71} +(1.11747e14 - 5.69461e14i) q^{72} -2.83994e14 q^{73} +(-4.20756e14 - 2.80617e14i) q^{74} -4.42467e14i q^{75} +(1.86011e15 - 7.74234e14i) q^{76} -9.83388e14 q^{77} +(1.70143e14 - 2.55111e14i) q^{78} -1.41787e15i q^{79} +(-6.32083e13 + 6.36446e13i) q^{80} +8.32419e14 q^{81} +(-8.70833e14 - 5.80790e14i) q^{82} +2.82485e15i q^{83} +(5.86988e14 + 1.41025e15i) q^{84} +2.25553e14 q^{85} +(-2.18505e15 + 3.27625e15i) q^{86} -1.09360e15i q^{87} +(-2.01992e15 - 3.96373e14i) q^{88} +2.93963e15 q^{89} +(-1.53855e14 - 1.02612e14i) q^{90} -3.30139e15i q^{91} +(-3.85269e15 + 1.60360e15i) q^{92} +9.79016e14 q^{93} +(3.26666e15 - 4.89801e15i) q^{94} -6.42070e14i q^{95} +(6.37268e14 + 3.13330e15i) q^{96} +1.34225e15 q^{97} +(6.60407e15 + 4.40449e15i) q^{98} -4.24392e15i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 164 q^{2} - 160368 q^{4} - 506740 q^{5} - 1187136 q^{6} - 33829184 q^{8} - 137574522 q^{9}+O(q^{10}) $ 6 * q - 164 * q^2 - 160368 * q^4 - 506740 * q^5 - 1187136 * q^6 - 33829184 * q^8 - 137574522 * q^9	\( 6 q - 164 q^{2} - 160368 q^{4} - 506740 q^{5} - 1187136 q^{6} - 33829184 q^{8} - 137574522 q^{9} - 142269000 q^{10} + 254142720 q^{12} + 2544478092 q^{13} + 1073417856 q^{14} + 145019136 q^{16} + 1579205132 q^{17} - 22662764964 q^{18} + 4421361440 q^{20} - 27228321792 q^{21} - 138624795840 q^{22} + 403778497536 q^{24} + 271424476050 q^{25} - 190529582152 q^{26} + 1617685224960 q^{28} - 1158411768436 q^{29} - 4663806986880 q^{30} + 4663321578496 q^{32} - 767957621760 q^{33} - 5461346085192 q^{34} + 14104690258320 q^{36} + 8581446019212 q^{37} - 20462346561600 q^{38} + 18971054755200 q^{40} + 1840369253132 q^{41} - 20386577111040 q^{42} + 3644055863040 q^{44} - 34166370110580 q^{45} + 5034653652864 q^{46} - 56248898088960 q^{48} - 5527245758202 q^{49} + 129240587956500 q^{50} - 103374802254048 q^{52} + 130668269409932 q^{53} + 366965883430272 q^{54} - 342617610295296 q^{56} - 122486852367360 q^{57} + 69923529928632 q^{58} - 641633781542400 q^{60} - 429486008315508 q^{61} + 619512054551040 q^{62} - 516434037731328 q^{64} + 12\!\cdots\!00 q^{65}+ \cdots + 13\!\cdots\!56 q^{98}+O(q^{100}) \) 6 * q - 164 * q^2 - 160368 * q^4 - 506740 * q^5 - 1187136 * q^6 - 33829184 * q^8 - 137574522 * q^9 - 142269000 * q^10 + 254142720 * q^12 + 2544478092 * q^13 + 1073417856 * q^14 + 145019136 * q^16 + 1579205132 * q^17 - 22662764964 * q^18 + 4421361440 * q^20 - 27228321792 * q^21 - 138624795840 * q^22 + 403778497536 * q^24 + 271424476050 * q^25 - 190529582152 * q^26 + 1617685224960 * q^28 - 1158411768436 * q^29 - 4663806986880 * q^30 + 4663321578496 * q^32 - 767957621760 * q^33 - 5461346085192 * q^34 + 14104690258320 * q^36 + 8581446019212 * q^37 - 20462346561600 * q^38 + 18971054755200 * q^40 + 1840369253132 * q^41 - 20386577111040 * q^42 + 3644055863040 * q^44 - 34166370110580 * q^45 + 5034653652864 * q^46 - 56248898088960 * q^48 - 5527245758202 * q^49 + 129240587956500 * q^50 - 103374802254048 * q^52 + 130668269409932 * q^53 + 366965883430272 * q^54 - 342617610295296 * q^56 - 122486852367360 * q^57 + 69923529928632 * q^58 - 641633781542400 * q^60 - 429486008315508 * q^61 + 619512054551040 * q^62 - 516434037731328 * q^64 + 1237661666277400 * q^65 - 54995333852160 * q^66 + 1716626085477152 * q^68 - 265820219762688 * q^69 - 1698017749451520 * q^70 + 1539597157891776 * q^72 - 1145601039770868 * q^73 - 771134490565192 * q^74 + 2768729450169600 * q^76 - 665543599687680 * q^77 - 7024870687386240 * q^78 + 4403327011381760 * q^80 - 277566121727226 * q^81 - 3459247029640008 * q^82 + 3591637752471552 * q^84 - 1934080153645800 * q^85 + 2096299590206784 * q^86 + 719241463526400 * q^88 + 20426758995091724 * q^89 + 1627824908547000 * q^90 - 9798772065277440 * q^92 - 20365632048291840 * q^93 + 16900683550077696 * q^94 - 32790566117523456 * q^96 + 4182396554403852 * q^97 + 13584426279160156 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−212.978	−	142.043i	−0.831947	−	0.554855i
$2$	−212.978	−	142.043i	−0.831947	−	0.554855i
$3$			2908.07i			0.443235i	0.975134	+	0.221618i	$0.0711337\pi$
$3$			2908.07i			0.443235i	−0.975134	+	0.221618i	$0.928866\pi$
$4$	25183.6	+	60504.2i	0.384272	+	0.923220i
$5$	20884.7			0.0534648			0.0267324	−	0.999643i	$-0.491490\pi$
$5$	20884.7			0.0534648			0.0267324	+	0.999643i	$0.491490\pi$
$6$	413070.	−	619356.i	0.245931	−	0.368748i
$7$		−	8.01505e6i		−	1.39034i	−0.718844	−	0.695172i	$-0.755328\pi$
$7$		−	8.01505e6i		−	1.39034i	0.718844	−	0.695172i	$-0.244672\pi$
$8$	3.23062e6	−	1.64632e7i	0.192560	−	0.981285i
$9$	3.45899e7			0.803542
$10$	−4.44799e6	−	2.96652e6i	−0.0444799	−	0.0296652i
$11$		−	1.22693e8i		−	0.572370i	−0.958174	−	0.286185i	$-0.907613\pi$
$11$		−	1.22693e8i		−	0.572370i	0.958174	−	0.286185i	$-0.0923872\pi$
$12$	−1.75950e8	+	7.32357e7i	−0.409204	+	0.170323i
$13$	4.11898e8			0.504944			0.252472	−	0.967604i	$-0.418756\pi$
$13$	4.11898e8			0.504944			0.252472	+	0.967604i	$0.418756\pi$
$14$	−1.13848e9	+	1.70703e9i	−0.771439	+	1.15669i
$15$			6.07341e7i			0.0236975i
$16$	−3.02654e9	+	3.04743e9i	−0.704671	+	0.709534i
$17$	1.07999e10			1.54821			0.774103	−	0.633060i	$-0.218201\pi$
$17$	1.07999e10			1.54821			0.774103	+	0.633060i	$0.218201\pi$
$18$	−7.36690e9	−	4.91325e9i	−0.668505	−	0.445850i
$19$		−	3.07436e10i		−	1.81019i	−0.425205	−	0.905097i	$-0.639798\pi$
$19$		−	3.07436e10i		−	1.81019i	0.425205	−	0.905097i	$-0.360202\pi$
$20$	5.25952e8	+	1.26361e9i	0.0205450	+	0.0493598i
$21$	2.33083e10			0.616249
$22$	−1.74276e10	+	2.61309e10i	−0.317582	+	0.476181i
$23$			6.36764e10i			0.813122i	0.913624	+	0.406561i	$0.133272\pi$
$23$			6.36764e10i			0.813122i	−0.913624	+	0.406561i	$0.866728\pi$
$24$	4.78762e10	+	9.39485e9i	0.434940	+	0.0853493i
$25$	−1.52152e11			−0.997142
$26$	−8.77254e10	−	5.85072e10i	−0.420086	−	0.280171i
$27$			2.25772e11i			0.799394i
$28$	4.84944e11	−	2.01848e11i	1.28359	−	0.534270i
$29$	−3.76057e11			−0.751744			−0.375872	−	0.926672i	$-0.622657\pi$
$29$	−3.76057e11			−0.751744			−0.375872	+	0.926672i	$0.622657\pi$
$30$	8.62685e9	−	1.29351e10i	0.0131487	−	0.0197151i
$31$		−	3.36655e11i		−	0.394722i	−0.980331	−	0.197361i	$-0.936763\pi$
$31$		−	3.36655e11i		−	0.394722i	0.980331	−	0.197361i	$-0.0632372\pi$
$32$	1.07745e12	−	2.19138e11i	0.979938	−	0.199305i
$33$	3.56798e11			0.253695
$34$	−2.30015e12	−	1.53405e12i	−1.28803	−	0.859030i
$35$		−	1.67392e11i		−	0.0743345i
$36$	8.71098e11	+	2.09283e12i	0.308778	+	0.741847i
$37$	1.97558e12			0.562446			0.281223	−	0.959642i	$-0.409260\pi$
$37$	1.97558e12			0.562446			0.281223	+	0.959642i	$0.409260\pi$
$38$	−4.36690e12	+	6.54771e12i	−1.00440	+	1.50599i
$39$			1.19783e12i			0.223809i
$40$	6.74705e10	−	3.43830e11i	0.0102952	−	0.0524642i
$41$	4.08883e12			0.512069			0.256035	−	0.966668i	$-0.417584\pi$
$41$	4.08883e12			0.512069			0.256035	+	0.966668i	$0.417584\pi$
$42$	−4.96417e12	−	3.31078e12i	−0.512687	−	0.341929i
$43$		−	1.53830e13i		−	1.31611i	−0.752968	−	0.658057i	$-0.771379\pi$
$43$		−	1.53830e13i		−	1.31611i	0.752968	−	0.658057i	$-0.228621\pi$
$44$	7.42341e12	−	3.08984e12i	0.528423	−	0.219946i
$45$	7.22399e11			0.0429612
$46$	9.04478e12	−	1.35617e13i	0.451165	−	0.676474i
$47$			2.29977e13i			0.965830i	0.875667	+	0.482915i	$0.160422\pi$
$47$			2.29977e13i			0.965830i	−0.875667	+	0.482915i	$0.839578\pi$
$48$	−8.86212e12	−	8.80138e12i	−0.314491	−	0.312335i
$49$	−3.10082e13			−0.933056
$50$	3.24050e13	+	2.16121e13i	0.829569	+	0.553269i
$51$			3.14069e13i			0.686220i
$52$	1.03731e13	+	2.49215e13i	0.194035	+	0.466174i
$53$	−5.35569e13			−0.860218			−0.430109	−	0.902777i	$-0.641525\pi$
$53$	−5.35569e13			−0.860218			−0.430109	+	0.902777i	$0.641525\pi$
$54$	3.20694e13	−	4.80847e13i	0.443548	−	0.665053i
$55$		−	2.56240e12i		−	0.0306017i
$56$	−1.31954e14	−	2.58936e13i	−1.36432	−	0.267724i
$57$	8.94043e13			0.802342
$58$	8.00921e13	+	5.34163e13i	0.625411	+	0.417109i
$59$		−	6.70947e13i		−	0.456954i	−0.973549	−	0.228477i	$-0.926625\pi$
$59$		−	6.70947e13i		−	0.456954i	0.973549	−	0.228477i	$-0.0733745\pi$
$60$	−3.67466e12	+	1.52950e12i	−0.0218780	+	0.00910627i
$61$	1.86362e14			0.972117			0.486058	−	0.873926i	$-0.338434\pi$
$61$	1.86362e14			0.972117			0.486058	+	0.873926i	$0.338434\pi$
$62$	−4.78195e13	+	7.17003e13i	−0.219014	+	0.328388i
$63$		−	2.77240e14i		−	1.11720i
$64$	−2.60601e14	−	1.06373e14i	−0.925841	−	0.377912i
$65$	8.60236e12			0.0269967
$66$	−7.59903e13	−	5.06807e13i	−0.211060	−	0.140764i
$67$			1.58513e14i			0.390362i	0.980767	+	0.195181i	$0.0625294\pi$
$67$			1.58513e14i			0.390362i	−0.980767	+	0.195181i	$0.937471\pi$
$68$	2.71981e14	+	6.53439e14i	0.594931	+	1.42933i
$69$	−1.85175e14			−0.360404
$70$	−2.37768e13	+	3.56509e13i	−0.0412449	+	0.0618423i
$71$			8.90997e14i			1.37978i	0.723915	+	0.689890i	$0.242341\pi$
$71$			8.90997e14i			1.37978i	−0.723915	+	0.689890i	$0.757659\pi$
$72$	1.11747e14	−	5.69461e14i	0.154730	−	0.788504i
$73$	−2.83994e14			−0.352148			−0.176074	−	0.984377i	$-0.556340\pi$
$73$	−2.83994e14			−0.352148			−0.176074	+	0.984377i	$0.556340\pi$
$74$	−4.20756e14	−	2.80617e14i	−0.467926	−	0.312076i
$75$		−	4.42467e14i		−	0.441968i
$76$	1.86011e15	−	7.74234e14i	1.67121	−	0.695606i
$77$	−9.83388e14			−0.795791
$78$	1.70143e14	−	2.55111e14i	0.124182	−	0.186197i
$79$		−	1.41787e15i		−	0.934590i	−0.884102	−	0.467295i	$-0.845229\pi$
$79$		−	1.41787e15i		−	0.934590i	0.884102	−	0.467295i	$-0.154771\pi$
$80$	−6.32083e13	+	6.36446e13i	−0.0376751	+	0.0379351i
$81$	8.32419e14			0.449223
$82$	−8.70833e14	−	5.80790e14i	−0.426014	−	0.284124i
$83$			2.82485e15i			1.25421i	0.778935	+	0.627105i	$0.215760\pi$
$83$			2.82485e15i			1.25421i	−0.778935	+	0.627105i	$0.784240\pi$
$84$	5.86988e14	+	1.41025e15i	0.236807	+	0.568934i
$85$	2.25553e14			0.0827745
$86$	−2.18505e15	+	3.27625e15i	−0.730252	+	1.09494i
$87$		−	1.09360e15i		−	0.333199i
$88$	−2.01992e15	−	3.96373e14i	−0.561658	−	0.110215i
$89$	2.93963e15			0.746746			0.373373	−	0.927681i	$-0.378201\pi$
$89$	2.93963e15			0.746746			0.373373	+	0.927681i	$0.378201\pi$
$90$	−1.53855e14	−	1.02612e14i	−0.0357415	−	0.0238373i
$91$		−	3.30139e15i		−	0.702045i
$92$	−3.85269e15	+	1.60360e15i	−0.750691	+	0.312460i
$93$	9.79016e14			0.174955
$94$	3.26666e15	−	4.89801e15i	0.535896	−	0.803520i
$95$		−	6.42070e14i		−	0.0967817i
$96$	6.37268e14	+	3.13330e15i	0.0883390	+	0.434343i
$97$	1.34225e15			0.171261			0.0856307	−	0.996327i	$-0.472709\pi$
$97$	1.34225e15			0.171261			0.0856307	+	0.996327i	$0.472709\pi$
$98$	6.60407e15	+	4.40449e15i	0.776253	+	0.517711i
$99$		−	4.24392e15i		−	0.459924i
$100$	−3.83173e15	−	9.20581e15i	−0.383173	−	0.920581i
$101$	−9.59476e15			−0.886060			−0.443030	−	0.896507i	$-0.646096\pi$
$101$	−9.59476e15			−0.886060			−0.443030	+	0.896507i	$0.646096\pi$
$102$	4.46112e15	−	6.68898e15i	0.380752	−	0.570898i
$103$			1.77633e16i			1.40225i	0.713039	+	0.701124i	$0.247318\pi$
$103$			1.77633e16i			1.40225i	−0.713039	+	0.701124i	$0.752682\pi$
$104$	1.33069e15	−	6.78117e15i	0.0972319	−	0.495494i
$105$	4.86787e14			0.0329477
$106$	1.14065e16	+	7.60738e15i	0.715655	+	0.477296i
$107$			1.40865e15i			0.0819844i	0.999159	+	0.0409922i	$0.0130519\pi$
$107$			1.40865e15i			0.0819844i	−0.999159	+	0.0409922i	$0.986948\pi$
$108$	−1.36602e16	+	5.68577e15i	−0.738016	+	0.307184i
$109$	−3.24531e16			−1.62871			−0.814355	−	0.580367i	$-0.802909\pi$
$109$	−3.24531e16			−1.62871			−0.814355	+	0.580367i	$0.802909\pi$
$110$	−3.63970e14	+	5.45735e14i	−0.0169795	+	0.0254590i
$111$			5.74512e15i			0.249296i
$112$	2.44253e16	+	2.42579e16i	0.986497	+	0.979735i
$113$	3.76957e16			1.41796			0.708980	−	0.705229i	$-0.249156\pi$
$113$	3.76957e16			1.41796			0.708980	+	0.705229i	$0.249156\pi$
$114$	−1.90412e16	−	1.26992e16i	−0.667506	−	0.445184i
$115$			1.32986e15i			0.0434734i
$116$	−9.47048e15	−	2.27530e16i	−0.288874	−	0.694025i
$117$	1.42475e16			0.405744
$118$	−9.53033e15	+	1.42897e16i	−0.253543	+	0.380161i
$119$		−	8.65619e16i		−	2.15254i
$120$	9.99880e14	+	1.96209e14i	0.0232540	+	0.00456319i
$121$	3.08963e16			0.672393
$122$	−3.96911e16	−	2.64714e16i	−0.808750	−	0.539384i
$123$			1.18906e16i			0.226967i
$124$	2.03690e16	−	8.47820e15i	0.364416	−	0.151681i
$125$	−6.36439e15			−0.106777
$126$	−3.93799e16	+	5.90461e16i	−0.619884	+	0.929451i
$127$			8.61032e16i			1.27230i	0.771565	+	0.636150i	$0.219474\pi$
$127$			8.61032e16i			1.27230i	−0.771565	+	0.636150i	$0.780526\pi$
$128$	4.03929e16	+	5.96717e16i	0.560564	+	0.828111i
$129$	4.47348e16			0.583348
$130$	−1.83212e15	−	1.22190e15i	−0.0224598	−	0.0149793i
$131$		−	9.74192e15i		−	0.112324i	−0.998422	−	0.0561622i	$-0.982114\pi$
$131$		−	9.74192e15i		−	0.112324i	0.998422	−	0.0561622i	$-0.0178864\pi$
$132$	8.98547e15	+	2.15878e16i	0.0974876	+	0.234216i
$133$	−2.46411e17			−2.51679
$134$	2.25157e16	−	3.37599e16i	0.216594	−	0.324760i
$135$			4.71519e15i			0.0427394i
$136$	3.48904e16	−	1.77801e17i	0.298122	−	1.51923i
$137$	1.41062e17			1.13670			0.568348	−	0.822788i	$-0.307583\pi$
$137$	1.41062e17			1.13670			0.568348	+	0.822788i	$0.307583\pi$
$138$	3.94383e16	+	2.63028e16i	0.299837	+	0.199972i
$139$			6.63698e16i			0.476269i	0.971232	+	0.238134i	$0.0765359\pi$
$139$			6.63698e16i			0.476269i	−0.971232	+	0.238134i	$0.923464\pi$
$140$	1.01279e16	−	4.21554e15i	0.0686271	−	0.0285646i
$141$	−6.68788e16			−0.428090
$142$	1.26560e17	−	1.89763e17i	0.765578	−	1.14790i
$143$		−	5.05368e16i		−	0.289015i
$144$	−1.04688e17	+	1.05410e17i	−0.566233	+	0.570141i
$145$	−7.85384e15			−0.0401918
$146$	6.04845e16	+	4.03393e16i	0.292969	+	0.195391i
$147$		−	9.01738e16i		−	0.413563i
$148$	4.97523e16	+	1.19531e17i	0.216132	+	0.519262i
$149$	5.12770e15			0.0211073			0.0105537	−	0.999944i	$-0.496641\pi$
$149$	5.12770e15			0.0211073			0.0105537	+	0.999944i	$0.496641\pi$
$150$	−6.28494e16	+	9.42360e16i	−0.245228	+	0.367694i
$151$			2.37125e16i			0.0877329i	0.999037	+	0.0438664i	$0.0139676\pi$
$151$			2.37125e16i			0.0877329i	−0.999037	+	0.0438664i	$0.986032\pi$
$152$	−5.06138e17	−	9.93207e16i	−1.77632	−	0.348571i
$153$	3.73567e17			1.24405
$154$	2.09440e17	+	1.39683e17i	0.662056	+	0.441549i
$155$		−	7.03094e15i		−	0.0211038i
$156$	−7.24735e16	+	3.01656e16i	−0.206625	+	0.0860034i
$157$	−3.07726e17			−0.833619			−0.416809	−	0.908994i	$-0.636852\pi$
$157$	−3.07726e17			−0.833619			−0.416809	+	0.908994i	$0.636852\pi$
$158$	−2.01399e17	+	3.01977e17i	−0.518562	+	0.777529i
$159$		−	1.55747e17i		−	0.381279i
$160$	2.25023e16	−	4.57663e15i	0.0523922	−	0.0106558i
$161$	5.10370e17			1.13052
$162$	−1.77287e17	−	1.18239e17i	−0.373730	−	0.249254i
$163$			2.88371e17i			0.578696i	0.957224	+	0.289348i	$0.0934385\pi$
$163$			2.88371e17i			0.578696i	−0.957224	+	0.289348i	$0.906561\pi$
$164$	1.02972e17	+	2.47391e17i	0.196774	+	0.472752i
$165$	7.45162e15			0.0135637
$166$	4.01249e17	−	6.01631e17i	0.695904	−	1.04344i
$167$		−	1.16307e17i		−	0.192254i	−0.995369	−	0.0961271i	$-0.969354\pi$
$167$		−	1.16307e17i		−	0.192254i	0.995369	−	0.0961271i	$-0.0306455\pi$
$168$	7.53003e16	−	3.83730e17i	0.118665	−	0.604717i
$169$	−4.95757e17			−0.745032
$170$	−4.80379e16	−	3.20382e16i	−0.0688640	−	0.0459279i
$171$		−	1.06342e18i		−	1.45457i
$172$	9.30735e17	−	3.87400e17i	1.21506	−	0.505745i
$173$	−7.68393e17			−0.957667			−0.478834	−	0.877906i	$-0.658940\pi$
$173$	−7.68393e17			−0.957667			−0.478834	+	0.877906i	$0.658940\pi$
$174$	−1.55338e17	+	2.32913e17i	−0.184877	+	0.277204i
$175$			1.21950e18i			1.38637i
$176$	3.73897e17	+	3.71334e17i	0.406116	+	0.403332i
$177$	1.95116e17			0.202538
$178$	−6.26078e17	−	4.17554e17i	−0.621253	−	0.414336i
$179$			1.34720e18i			1.27823i	0.769112	+	0.639114i	$0.220699\pi$
$179$			1.34720e18i			1.27823i	−0.769112	+	0.639114i	$0.779301\pi$
$180$	1.81926e16	+	4.37081e16i	0.0165088	+	0.0396627i
$181$	−5.40539e17			−0.469244			−0.234622	−	0.972087i	$-0.575385\pi$
$181$	−5.40539e17			−0.469244			−0.234622	+	0.972087i	$0.575385\pi$
$182$	−4.68938e17	+	7.03124e17i	−0.389533	+	0.584064i
$183$			5.41953e17i			0.430877i
$184$	1.04832e18	+	2.05714e17i	0.797905	+	0.156575i
$185$	4.12594e16			0.0300711
$186$	−2.08509e17	−	1.39062e17i	−0.145553	−	0.0970746i
$187$		−	1.32507e18i		−	0.886147i
$188$	−1.39145e18	+	5.79164e17i	−0.891674	+	0.371141i
$189$	1.80958e18			1.11143
$190$	−9.12014e16	+	1.36747e17i	−0.0536998	+	0.0805173i
$191$		−	2.63366e18i		−	1.48694i	−0.668769	−	0.743470i	$-0.733178\pi$
$191$		−	2.63366e18i		−	1.48694i	0.668769	−	0.743470i	$-0.266822\pi$
$192$	3.09339e17	−	7.57846e17i	0.167504	−	0.410366i
$193$	−3.18650e17			−0.165522			−0.0827608	−	0.996569i	$-0.526374\pi$
$193$	−3.18650e17			−0.165522			−0.0827608	+	0.996569i	$0.526374\pi$
$194$	−2.85870e17	−	1.90657e17i	−0.142480	−	0.0950253i
$195$			2.50163e16i			0.0119659i
$196$	−7.80898e17	−	1.87612e18i	−0.358547	−	0.861416i
$197$	2.60436e18			1.14808			0.574040	−	0.818827i	$-0.305375\pi$
$197$	2.60436e18			1.14808			0.574040	+	0.818827i	$0.305375\pi$
$198$	−6.02819e17	+	9.03863e17i	−0.255191	+	0.382632i
$199$		−	1.69903e18i		−	0.690839i	−0.938448	−	0.345420i	$-0.887737\pi$
$199$		−	1.69903e18i		−	0.690839i	0.938448	−	0.345420i	$-0.112263\pi$
$200$	−4.91544e17	+	2.50491e18i	−0.192009	+	0.978480i
$201$	−4.60967e17			−0.173022
$202$	2.04348e18	+	1.36287e18i	0.737155	+	0.491635i
$203$			3.01412e18i			1.04518i
$204$	−1.90025e18	+	7.90938e17i	−0.633532	+	0.263695i
$205$	8.53940e16			0.0273777
$206$	2.52315e18	−	3.78319e18i	0.778045	−	1.16660i
$207$			2.20256e18i			0.653378i
$208$	−1.24663e18	+	1.25523e18i	−0.355819	+	0.358275i
$209$	−3.77201e18			−1.03610
$210$	−1.03675e17	−	6.91447e16i	−0.0274107	−	0.0182812i
$211$			8.88977e17i			0.226272i	0.993580	+	0.113136i	$0.0360896\pi$
$211$			8.88977e17i			0.226272i	−0.993580	+	0.113136i	$0.963910\pi$
$212$	−1.34876e18	−	3.24041e18i	−0.330557	−	0.794170i
$213$	−2.59108e18			−0.611567
$214$	2.00088e17	−	3.00011e17i	0.0454895	−	0.0682067i
$215$		−	3.21269e17i		−	0.0703658i
$216$	3.71694e18	+	7.29384e17i	0.784433	+	0.153931i
$217$	−2.69831e18			−0.548800
$218$	6.91181e18	+	4.60973e18i	1.35500	+	0.903698i
$219$		−	8.25872e17i		−	0.156085i
$220$	1.55036e17	−	6.45304e16i	0.0282521	−	0.0117593i
$221$	4.44846e18			0.781757
$222$	8.16054e17	−	1.22359e18i	0.138323	−	0.207401i
$223$			5.81069e18i			0.950142i	0.879947	+	0.475071i	$0.157578\pi$
$223$			5.81069e18i			0.950142i	−0.879947	+	0.475071i	$0.842422\pi$
$224$	−1.75640e18	−	8.63584e18i	−0.277102	−	1.36245i
$225$	−5.26291e18			−0.801246
$226$	−8.02836e18	−	5.35440e18i	−1.17967	−	0.786762i
$227$		−	9.78862e18i		−	1.38840i	−0.719782	−	0.694200i	$-0.755758\pi$
$227$		−	9.78862e18i		−	1.38840i	0.719782	−	0.694200i	$-0.244242\pi$
$228$	2.25152e18	+	5.40933e18i	0.308317	+	0.740738i
$229$	1.27212e19			1.68206			0.841032	−	0.540985i	$-0.181948\pi$
$229$	1.27212e19			1.68206			0.841032	+	0.540985i	$0.181948\pi$
$230$	1.88897e17	−	2.83232e17i	0.0241214	−	0.0361676i
$231$		−	2.85976e18i		−	0.352723i
$232$	−1.21490e18	+	6.19112e18i	−0.144756	+	0.737675i
$233$	−4.21991e18			−0.485798			−0.242899	−	0.970052i	$-0.578098\pi$
$233$	−4.21991e18			−0.485798			−0.242899	+	0.970052i	$0.578098\pi$
$234$	−3.03441e18	−	2.02376e18i	−0.337557	−	0.225129i
$235$			4.80299e17i			0.0516379i
$236$	4.05951e18	−	1.68969e18i	0.421869	−	0.175594i
$237$	4.12327e18			0.414243
$238$	−1.22955e19	+	1.84358e19i	−1.19435	+	1.79080i
$239$			8.47899e17i			0.0796454i	0.999207	+	0.0398227i	$0.0126793\pi$
$239$			8.47899e17i			0.0796454i	−0.999207	+	0.0398227i	$0.987321\pi$
$240$	−1.85083e17	−	1.83814e17i	−0.0168142	−	0.0166989i
$241$	4.06546e18			0.357251			0.178626	−	0.983917i	$-0.442835\pi$
$241$	4.06546e18			0.357251			0.178626	+	0.983917i	$0.442835\pi$
$242$	−6.58024e18	−	4.38859e18i	−0.559395	−	0.373080i
$243$			1.21395e19i			0.998505i
$244$	4.69327e18	+	1.12757e19i	0.373557	+	0.897478i
$245$	−6.47596e17			−0.0498856
$246$	1.68898e18	−	2.53244e18i	0.125934	−	0.188825i
$247$		−	1.26632e19i		−	0.914046i
$248$	−5.54243e18	−	1.08760e18i	−0.387335	−	0.0760077i
$249$	−8.21484e18			−0.555910
$250$	1.35548e18	+	9.04017e17i	0.0888326	+	0.0592457i
$251$			8.96061e17i			0.0568785i	0.999596	+	0.0284392i	$0.00905371\pi$
$251$			8.96061e17i			0.0568785i	−0.999596	+	0.0284392i	$0.990946\pi$
$252$	1.67742e19	−	6.98190e18i	1.03142	−	0.429308i
$253$	7.81262e18			0.465407
$254$	1.22304e19	−	1.83381e19i	0.705942	−	1.05849i
$255$			6.55923e17i			0.0366886i
$256$	−1.26882e17	−	1.84463e19i	−0.00687830	−	0.999976i
$257$	−1.01410e19			−0.532862			−0.266431	−	0.963854i	$-0.585844\pi$
$257$	−1.01410e19			−0.532862			−0.266431	+	0.963854i	$0.585844\pi$
$258$	−9.52755e18	−	6.35426e18i	−0.485315	−	0.323674i
$259$		−	1.58344e19i		−	0.781994i
$260$	2.16639e17	+	5.20479e17i	0.0103741	+	0.0249239i
$261$	−1.30078e19			−0.604058
$262$	−1.38377e18	+	2.07482e18i	−0.0623238	+	0.0934479i
$263$			3.75483e19i			1.64038i	0.572092	+	0.820190i	$0.306132\pi$
$263$			3.75483e19i			1.64038i	−0.572092	+	0.820190i	$0.693868\pi$
$264$	1.15268e18	−	5.87405e18i	0.0488514	−	0.248947i
$265$	−1.11852e18			−0.0459914
$266$	5.24803e19	+	3.50010e19i	2.09384	+	1.39646i
$267$			8.54865e18i			0.330984i
$268$	−9.59071e18	+	3.99194e18i	−0.360390	+	0.150005i
$269$	−2.11943e19			−0.773039			−0.386519	−	0.922281i	$-0.626323\pi$
$269$	−2.11943e19			−0.773039			−0.386519	+	0.922281i	$0.626323\pi$
$270$	6.69759e17	−	1.00423e18i	0.0237142	−	0.0355569i
$271$		−	1.85665e19i		−	0.638227i	−0.947716	−	0.319114i	$-0.896615\pi$
$271$		−	1.85665e19i		−	0.638227i	0.947716	−	0.319114i	$-0.103385\pi$
$272$	−3.26863e19	+	3.29119e19i	−1.09098	+	1.09851i
$273$	9.60065e18			0.311171
$274$	−3.00431e19	−	2.00368e19i	−0.945672	−	0.630702i
$275$			1.86679e19i			0.570734i
$276$	−4.66338e18	−	1.12039e19i	−0.138493	−	0.332733i
$277$	3.27126e19			0.943793			0.471896	−	0.881654i	$-0.343570\pi$
$277$	3.27126e19			0.943793			0.471896	+	0.881654i	$0.343570\pi$
$278$	9.42736e18	−	1.41353e19i	0.264260	−	0.396230i
$279$		−	1.16449e19i		−	0.317176i
$280$	−2.75581e18	−	5.40780e17i	−0.0729433	−	0.0143138i
$281$	8.62462e18			0.221865			0.110933	−	0.993828i	$-0.464616\pi$
$281$	8.62462e18			0.221865			0.110933	+	0.993828i	$0.464616\pi$
$282$	1.42437e19	+	9.49965e18i	0.356148	+	0.237528i
$283$		−	3.29539e19i		−	0.800968i	−0.916304	−	0.400484i	$-0.868842\pi$
$283$		−	3.29539e19i		−	0.800968i	0.916304	−	0.400484i	$-0.131158\pi$
$284$	−5.39090e19	+	2.24385e19i	−1.27384	+	0.530210i
$285$	1.86718e18			0.0428971
$286$	−7.17840e18	+	1.07633e19i	−0.160361	+	0.240445i
$287$		−	3.27722e19i		−	0.711952i
$288$	3.72689e19	−	7.57996e18i	0.787421	−	0.160150i
$289$	6.79768e19			1.39694
$290$	1.67270e18	+	1.11558e18i	0.0334375	+	0.0223007i
$291$			3.90335e18i			0.0759091i
$292$	−7.15199e18	−	1.71828e19i	−0.135321	−	0.325110i
$293$	−3.10886e19			−0.572348			−0.286174	−	0.958178i	$-0.592384\pi$
$293$	−3.10886e19			−0.572348			−0.286174	+	0.958178i	$0.592384\pi$
$294$	−1.28086e19	+	1.92051e19i	−0.229468	+	0.344063i
$295$		−	1.40125e18i		−	0.0244309i
$296$	6.38235e18	−	3.25245e19i	0.108305	−	0.551920i
$297$	2.77006e19			0.457549
$298$	−1.09209e18	−	7.28354e17i	−0.0175602	−	0.0117115i
$299$			2.62282e19i			0.410581i
$300$	2.67711e19	−	1.11429e19i	0.408034	−	0.169836i
$301$	−1.23296e20			−1.82985
$302$	3.36820e18	−	5.05026e18i	0.0486790	−	0.0729891i
$303$		−	2.79022e19i		−	0.392733i
$304$	9.36887e19	+	9.30465e19i	1.28440	+	1.27559i
$305$	3.89211e18			0.0519741
$306$	−7.95618e19	−	5.30626e19i	−1.03498	−	0.690267i
$307$			8.30079e19i			1.05199i	0.850487	+	0.525996i	$0.176307\pi$
$307$			8.30079e19i			1.05199i	−0.850487	+	0.525996i	$0.823693\pi$
$308$	−2.47653e19	−	5.94990e19i	−0.305800	−	0.734690i
$309$	−5.16568e19			−0.621526
$310$	−9.98695e17	+	1.49744e18i	−0.0117095	+	0.0175572i
$311$			1.27201e20i			1.45347i	0.686918	+	0.726735i	$0.258963\pi$
$311$			1.27201e20i			1.45347i	−0.686918	+	0.726735i	$0.741037\pi$
$312$	1.97201e19	+	3.86972e18i	0.219620	+	0.0430966i
$313$	−8.09185e17			−0.00878402			−0.00439201	−	0.999990i	$-0.501398\pi$
$313$	−8.09185e17			−0.00878402			−0.00439201	+	0.999990i	$0.501398\pi$
$314$	6.55391e19	+	4.37103e19i	0.693526	+	0.462538i
$315$		−	5.79007e18i		−	0.0597309i
$316$	8.57873e19	−	3.57072e19i	0.862832	−	0.359136i
$317$	3.42169e19			0.335557			0.167779	−	0.985825i	$-0.446341\pi$
$317$	3.42169e19			0.335557			0.167779	+	0.985825i	$0.446341\pi$
$318$	−2.21228e19	+	3.31708e19i	−0.211555	+	0.317204i
$319$			4.61394e19i			0.430276i
$320$	−5.44258e18	−	2.22156e18i	−0.0494999	−	0.0202050i
$321$	−4.09643e18			−0.0363384
$322$	−1.08698e20	−	7.24944e19i	−0.940532	−	0.627274i
$323$		−	3.32028e20i		−	2.80255i
$324$	2.09633e19	+	5.03648e19i	0.172624	+	0.414732i
$325$	−6.26710e19			−0.503500
$326$	4.09611e19	−	6.14168e19i	0.321093	−	0.481445i
$327$		−	9.43757e19i		−	0.721902i
$328$	1.32095e19	−	6.73154e19i	0.0986039	−	0.502486i
$329$	1.84328e20			1.34284
$330$	−1.58703e18	−	1.05845e18i	−0.0112843	−	0.00752591i
$331$			1.28124e20i			0.889218i	0.895725	+	0.444609i	$0.146657\pi$
$331$			1.28124e20i			0.889218i	−0.895725	+	0.444609i	$0.853343\pi$
$332$	−1.70915e20	+	7.11398e19i	−1.15791	+	0.481957i
$333$	6.83351e19			0.451950
$334$	−1.65207e19	+	2.47710e19i	−0.106673	+	0.159945i
$335$			3.31050e18i			0.0208706i
$336$	−7.05435e19	+	7.10304e19i	−0.434253	+	0.437250i
$337$	9.12598e19			0.548580			0.274290	−	0.961647i	$-0.411557\pi$
$337$	9.12598e19			0.548580			0.274290	+	0.961647i	$0.411557\pi$
$338$	1.05585e20	+	7.04187e19i	0.619827	+	0.413385i
$339$			1.09622e20i			0.628490i
$340$	5.68024e18	+	1.36469e19i	0.0318079	+	0.0764191i
$341$	−4.13051e19			−0.225927
$342$	−1.51051e20	+	2.26485e20i	−0.807075	+	1.21012i
$343$		−	1.78316e19i		−	0.0930757i
$344$	−2.53254e20	−	4.96966e19i	−1.29148	−	0.253431i
$345$	−3.86733e18			−0.0192690
$346$	1.63651e20	+	1.09145e20i	0.796728	+	0.531366i
$347$		−	4.44288e18i		−	0.0211363i	−0.999944	−	0.0105681i	$-0.996636\pi$
$347$		−	4.44288e18i		−	0.0211363i	0.999944	−	0.0105681i	$-0.00336401\pi$
$348$	6.61673e19	−	2.75408e19i	0.307616	−	0.128039i
$349$	−2.74791e20			−1.24853			−0.624265	−	0.781212i	$-0.714602\pi$
$349$	−2.74791e20			−1.24853			−0.624265	+	0.781212i	$0.714602\pi$
$350$	1.73222e20	−	2.59728e20i	0.769234	−	1.15339i
$351$			9.29952e19i			0.403649i
$352$	−2.68866e19	−	1.32195e20i	−0.114076	−	0.560887i
$353$	1.04150e20			0.431979			0.215990	−	0.976396i	$-0.430702\pi$
$353$	1.04150e20			0.431979			0.215990	+	0.976396i	$0.430702\pi$
$354$	−4.15555e19	−	2.77148e19i	−0.168501	−	0.112379i
$355$			1.86082e19i			0.0737696i
$356$	7.40306e19	+	1.77860e20i	0.286953	+	0.689411i
$357$	2.51728e20			0.954081
$358$	1.91360e20	−	2.86925e20i	0.709231	−	1.06342i
$359$		−	3.31485e20i		−	1.20146i	−0.799453	−	0.600728i	$-0.794877\pi$
$359$		−	3.31485e20i		−	1.20146i	0.799453	−	0.600728i	$-0.205123\pi$
$360$	2.33379e18	−	1.18930e19i	0.00827261	−	0.0421572i
$361$	−6.56724e20			−2.27680
$362$	1.15123e20	+	7.67798e19i	0.390386	+	0.260362i
$363$			8.98484e19i			0.298028i
$364$	1.99748e20	−	8.31408e19i	0.648142	−	0.269776i
$365$	−5.93112e18			−0.0188275
$366$	7.69806e19	−	1.15424e20i	0.239074	−	0.358466i
$367$			1.64874e20i			0.500985i	0.968119	+	0.250493i	$0.0805925\pi$
$367$			1.64874e20i			0.500985i	−0.968119	+	0.250493i	$0.919407\pi$
$368$	−1.94049e20	−	1.92719e20i	−0.576938	−	0.572983i
$369$	1.41432e20			0.411469
$370$	−8.78737e18	−	5.86061e18i	−0.0250176	−	0.0166851i
$371$			4.29261e20i			1.19600i
$372$	2.46552e19	+	5.92345e19i	0.0672302	+	0.161522i
$373$	3.33516e20			0.890114			0.445057	−	0.895502i	$-0.353183\pi$
$373$	3.33516e20			0.890114			0.445057	+	0.895502i	$0.353183\pi$
$374$	−1.88217e20	+	2.82211e20i	−0.491683	+	0.737227i
$375$		−	1.85081e19i		−	0.0473273i
$376$	3.78616e20	+	7.42967e19i	0.947755	+	0.185980i
$377$	−1.54897e20			−0.379588
$378$	−3.85401e20	−	2.57038e20i	−0.924653	−	0.616684i
$379$		−	3.65318e20i		−	0.858138i	−0.903272	−	0.429069i	$-0.858842\pi$
$379$		−	3.65318e20i		−	0.858138i	0.903272	−	0.429069i	$-0.141158\pi$
$380$	3.88479e19	−	1.61696e19i	0.0893508	−	0.0371905i
$381$	−2.50394e20			−0.563929
$382$	−3.74093e20	+	5.60914e20i	−0.825037	+	1.23706i
$383$		−	4.15911e19i		−	0.0898277i	−0.998991	−	0.0449138i	$-0.985699\pi$
$383$		−	4.15911e19i		−	0.0898277i	0.998991	−	0.0449138i	$-0.0143013\pi$
$384$	−1.73529e20	+	1.17465e20i	−0.367048	+	0.248462i
$385$	−2.05378e19			−0.0425468
$386$	6.78655e19	+	4.52619e19i	0.137705	+	0.0918406i
$387$		−	5.32096e20i		−	1.05755i
$388$	3.38027e19	+	8.12117e19i	0.0658109	+	0.158112i
$389$	6.84573e20			1.30564			0.652820	−	0.757513i	$-0.273586\pi$
$389$	6.84573e20			1.30564			0.652820	+	0.757513i	$0.273586\pi$
$390$	3.55338e18	−	5.32792e18i	0.00663934	−	0.00995499i
$391$			6.87699e20i			1.25888i
$392$	−1.00176e20	+	5.10495e20i	−0.179669	+	0.915594i
$393$	2.83301e19			0.0497861
$394$	−5.54674e20	−	3.69932e20i	−0.955141	−	0.637018i
$395$		−	2.96119e19i		−	0.0499677i
$396$	2.56775e20	−	1.06877e20i	0.424611	−	0.176736i
$397$	8.61557e20			1.39624			0.698120	−	0.715981i	$-0.254020\pi$
$397$	8.61557e20			1.39624			0.698120	+	0.715981i	$0.254020\pi$
$398$	−2.41335e20	+	3.61857e20i	−0.383316	+	0.574742i
$399$		−	7.16580e20i		−	1.11553i
$400$	4.60493e20	−	4.63671e20i	0.702656	−	0.707506i
$401$	−6.05379e20			−0.905467			−0.452733	−	0.891646i	$-0.649551\pi$
$401$	−6.05379e20			−0.905467			−0.452733	+	0.891646i	$0.649551\pi$
$402$	9.81761e19	+	6.54771e19i	0.143945	+	0.0960022i
$403$		−	1.38668e20i		−	0.199313i
$404$	−2.41631e20	−	5.80523e20i	−0.340488	−	0.818028i
$405$	1.73848e19			0.0240176
$406$	4.28134e20	−	6.41942e20i	0.579925	−	0.869536i
$407$		−	2.42389e20i		−	0.321927i
$408$	5.17058e20	+	1.01464e20i	0.673377	+	0.132138i
$409$	−3.22735e20			−0.412154			−0.206077	−	0.978536i	$-0.566070\pi$
$409$	−3.22735e20			−0.412154			−0.206077	+	0.978536i	$0.566070\pi$
$410$	−1.81871e19	−	1.21296e19i	−0.0227768	−	0.0151906i
$411$			4.10217e20i			0.503824i
$412$	−1.07475e21	+	4.47343e20i	−1.29458	+	0.538844i
$413$	−5.37768e20			−0.635323
$414$	3.12858e20	−	4.69097e20i	0.362530	−	0.543576i
$415$			5.89960e19i			0.0670561i
$416$	4.43801e20	−	9.02625e19i	0.494813	−	0.100638i
$417$	−1.93008e20			−0.211099
$418$	8.03356e20	+	5.35787e20i	0.861981	+	0.574886i
$419$			1.72049e21i			1.81109i	0.424245	+	0.905547i	$0.360540\pi$
$419$			1.72049e21i			1.81109i	−0.424245	+	0.905547i	$0.639460\pi$
$420$	1.22591e19	+	2.94526e19i	0.0126609	+	0.0304179i
$421$	−1.25573e20			−0.127245			−0.0636223	−	0.997974i	$-0.520265\pi$
$421$	−1.25573e20			−0.127245			−0.0636223	+	0.997974i	$0.520265\pi$
$422$	1.26273e20	−	1.89333e20i	0.125548	−	0.188246i
$423$			7.95486e20i			0.776086i
$424$	−1.73022e20	+	8.81720e20i	−0.165643	+	0.844119i
$425$	−1.64322e21			−1.54378
$426$	5.51844e20	+	3.68045e20i	0.508791	+	0.339331i
$427$		−	1.49370e21i		−	1.35158i
$428$	−8.52289e19	+	3.54748e19i	−0.0756897	+	0.0315043i
$429$	1.46965e20			0.128101
$430$	−4.56340e19	+	6.84234e19i	−0.0390428	+	0.0585406i
$431$			1.00565e21i			0.844557i	0.906466	+	0.422279i	$0.138770\pi$
$431$			1.00565e21i			0.844557i	−0.906466	+	0.422279i	$0.861230\pi$
$432$	−6.88025e20	−	6.83309e20i	−0.567197	−	0.563309i
$433$	1.06994e21			0.865875			0.432937	−	0.901424i	$-0.357477\pi$
$433$	1.06994e21			0.865875			0.432937	+	0.901424i	$0.357477\pi$
$434$	5.74682e20	+	3.83276e20i	0.456572	+	0.304504i
$435$		−	2.28395e19i		−	0.0178144i
$436$	−8.17286e20	−	1.96355e21i	−0.625867	−	1.50366i
$437$	1.95764e21			1.47191
$438$	−1.17309e20	+	1.75893e20i	−0.0866043	+	0.129854i
$439$		−	1.68877e21i		−	1.22421i	−0.790777	−	0.612104i	$-0.790323\pi$
$439$		−	1.68877e21i		−	1.22421i	0.790777	−	0.612104i	$-0.209677\pi$
$440$	−4.21853e19	−	8.27813e18i	−0.0300290	−	0.00589265i
$441$	−1.07257e21			−0.749750
$442$	−9.47426e20	−	6.31872e20i	−0.650380	−	0.433762i
$443$		−	1.63136e21i		−	1.09982i	−0.835225	−	0.549909i	$-0.814662\pi$
$443$		−	1.63136e21i		−	1.09982i	0.835225	−	0.549909i	$-0.185338\pi$
$444$	−3.47604e20	+	1.44683e20i	−0.230155	+	0.0957974i
$445$	6.13933e19			0.0399246
$446$	8.25367e20	−	1.23755e21i	0.527191	−	0.790468i
$447$			1.49117e19i			0.00935551i
$448$	−8.52584e20	+	2.08873e21i	−0.525428	+	1.28724i
$449$	2.20546e21			1.33515			0.667574	−	0.744544i	$-0.267333\pi$
$449$	2.20546e21			1.33515			0.667574	+	0.744544i	$0.267333\pi$
$450$	1.12089e21	+	7.47559e20i	0.666594	+	0.444575i
$451$		−	5.01670e20i		−	0.293093i
$452$	9.49313e20	+	2.28074e21i	0.544882	+	1.30909i
$453$	−6.89576e19			−0.0388863
$454$	−1.39040e21	+	2.08476e21i	−0.770361	+	1.15508i
$455$		−	6.89484e19i		−	0.0375347i
$456$	2.88831e20	−	1.47188e21i	0.154499	−	0.787326i
$457$	1.78288e21			0.937113			0.468557	−	0.883433i	$-0.344774\pi$
$457$	1.78288e21			0.937113			0.468557	+	0.883433i	$0.344774\pi$
$458$	−2.70933e21	−	1.80695e21i	−1.39939	−	0.933302i
$459$			2.43832e21i			1.23763i
$460$	−8.04622e19	+	3.34907e19i	−0.0401355	+	0.0167056i
$461$	−3.96968e21			−1.94602			−0.973012	−	0.230755i	$-0.925881\pi$
$461$	−3.96968e21			−1.94602			−0.973012	+	0.230755i	$0.925881\pi$
$462$	−4.06208e20	+	6.09067e20i	−0.195710	+	0.293447i
$463$			1.07770e21i			0.510328i	0.966898	+	0.255164i	$0.0821295\pi$
$463$			1.07770e21i			0.510328i	−0.966898	+	0.255164i	$0.917870\pi$
$464$	1.13815e21	−	1.14601e21i	0.529732	−	0.533388i
$465$	2.04464e19			0.00935393
$466$	8.98749e20	+	5.99408e20i	0.404158	+	0.269547i
$467$		−	1.75887e21i		−	0.777499i	−0.921344	−	0.388749i	$-0.872907\pi$
$467$		−	1.75887e21i		−	0.777499i	0.921344	−	0.388749i	$-0.127093\pi$
$468$	3.58804e20	+	8.62033e20i	0.155916	+	0.374591i
$469$	1.27049e21			0.542737
$470$	6.82231e19	−	1.02293e20i	0.0286516	−	0.0429600i
$471$		−	8.94889e20i		−	0.369489i
$472$	−1.10460e21	−	2.16757e20i	−0.448402	−	0.0879910i
$473$	−1.88738e21			−0.753304
$474$	−8.78168e20	−	5.85682e20i	−0.344628	−	0.229845i
$475$			4.67768e21i			1.80502i
$476$	5.23735e21	−	2.17994e21i	1.98727	−	0.827159i
$477$	−1.85253e21			−0.691221
$478$	1.20438e20	−	1.80584e20i	0.0441917	−	0.0662608i
$479$		−	1.24125e21i		−	0.447895i	−0.974601	−	0.223947i	$-0.928106\pi$
$479$		−	1.24125e21i		−	0.447895i	0.974601	−	0.223947i	$-0.0718944\pi$
$480$	1.33091e19	+	6.54381e19i	0.00472303	+	0.0232221i
$481$	8.13738e20			0.284004
$482$	−8.65856e20	−	5.77470e20i	−0.297214	−	0.198223i
$483$			1.48419e21i			0.501086i
$484$	7.78080e20	+	1.86935e21i	0.258381	+	0.620766i
$485$	2.80325e19			0.00915646
$486$	1.72433e21	−	2.58545e21i	0.554026	−	0.830703i
$487$		−	2.00656e21i		−	0.634191i	−0.948394	−	0.317095i	$-0.897292\pi$
$487$		−	2.00656e21i		−	0.634191i	0.948394	−	0.317095i	$-0.102708\pi$
$488$	6.02064e20	−	3.06812e21i	0.187191	−	0.953924i
$489$	−8.38602e20			−0.256499
$490$	1.37924e20	+	9.19864e19i	0.0415022	+	0.0276793i
$491$		−	2.15312e21i		−	0.637406i	−0.947855	−	0.318703i	$-0.896753\pi$
$491$		−	2.15312e21i		−	0.637406i	0.947855	−	0.318703i	$-0.103247\pi$
$492$	−7.19431e20	+	2.99448e20i	−0.209541	+	0.0872170i
$493$	−4.06138e21			−1.16385
$494$	−1.79872e21	+	2.69699e21i	−0.507163	+	0.760438i
$495$		−	8.86330e19i		−	0.0245897i
$496$	1.02593e21	+	1.01890e21i	0.280069	+	0.278149i
$497$	7.14139e21			1.91837
$498$	1.74958e21	+	1.16686e21i	0.462488	+	0.308449i
$499$		−	3.88611e21i		−	1.01090i	−0.862855	−	0.505452i	$-0.831326\pi$
$499$		−	3.88611e21i		−	1.01090i	0.862855	−	0.505452i	$-0.168674\pi$
$500$	−1.60278e20	−	3.85072e20i	−0.0410313	−	0.0985785i
$501$	3.38230e20			0.0852139
$502$	1.27279e20	−	1.90842e20i	0.0315593	−	0.0473199i
$503$			6.23175e21i			1.52078i	0.649468	+	0.760389i	$0.274992\pi$
$503$			6.23175e21i			1.52078i	−0.649468	+	0.760389i	$0.725008\pi$
$504$	−4.56426e21	−	8.95656e20i	−1.09629	−	0.215128i
$505$	−2.00384e20			−0.0473730
$506$	−1.66392e21	−	1.10973e21i	−0.387194	−	0.258233i
$507$		−	1.44169e21i		−	0.330224i
$508$	−5.20960e21	+	2.16839e21i	−1.17461	+	0.488909i
$509$	−3.00972e21			−0.668012			−0.334006	−	0.942571i	$-0.608401\pi$
$509$	−3.00972e21			−0.668012			−0.334006	+	0.942571i	$0.608401\pi$
$510$	9.31692e19	−	1.39697e20i	0.0203569	−	0.0305230i
$511$			2.27622e21i			0.489607i
$512$	−2.59314e21	+	3.94669e21i	−0.549120	+	0.835744i
$513$	6.94105e21			1.44706
$514$	2.15981e21	+	1.44045e21i	0.443313	+	0.295661i
$515$			3.70980e20i			0.0749710i
$516$	1.12658e21	+	2.70664e21i	0.224164	+	0.538559i
$517$	2.82164e21			0.552812
$518$	−2.24916e21	+	3.37238e21i	−0.433893	+	0.650577i
$519$		−	2.23454e21i		−	0.424472i
$520$	2.77910e19	−	1.41623e20i	0.00519848	−	0.0264915i
$521$	−1.87599e21			−0.345563			−0.172782	−	0.984960i	$-0.555276\pi$
$521$	−1.87599e21			−0.345563			−0.172782	+	0.984960i	$0.555276\pi$
$522$	2.77037e21	+	1.84766e21i	0.502544	+	0.335165i
$523$		−	2.42581e21i		−	0.433354i	−0.976243	−	0.216677i	$-0.930478\pi$
$523$		−	2.42581e21i		−	0.433354i	0.976243	−	0.216677i	$-0.0695218\pi$
$524$	5.89426e20	−	2.45337e20i	0.103700	−	0.0431631i
$525$	−3.54640e21			−0.614488
$526$	5.33347e21	−	7.99698e21i	0.910173	−	1.36471i
$527$		−	3.63585e21i		−	0.611112i
$528$	−1.07986e21	+	1.08732e21i	−0.178771	+	0.180005i
$529$	2.07793e21			0.338833
$530$	2.38220e20	+	1.58878e20i	0.0382624	+	0.0255186i
$531$		−	2.32080e21i		−	0.367182i
$532$	−6.20553e21	−	1.49089e22i	−0.967132	−	2.32355i
$533$	1.68418e21			0.258566
$534$	1.21427e21	−	1.82068e21i	0.183648	−	0.275361i
$535$			2.94191e19i			0.00438328i
$536$	2.60964e21	+	5.12096e20i	0.383056	+	0.0751680i
$537$	−3.91775e21			−0.566556
$538$	4.51393e21	+	3.01050e21i	0.643127	+	0.428925i
$539$			3.80447e21i			0.534053i
$540$	−2.85288e20	+	1.18745e20i	−0.0394579	+	0.0164236i
$541$	−8.19551e21			−1.11686			−0.558429	−	0.829552i	$-0.688596\pi$
$541$	−8.19551e21			−1.11686			−0.558429	+	0.829552i	$0.688596\pi$
$542$	−2.63724e21	+	3.95426e21i	−0.354124	+	0.530971i
$543$		−	1.57192e21i		−	0.207985i
$544$	1.16364e22	−	2.36667e21i	1.51715	−	0.308565i
$545$	−6.77773e20			−0.0870787
$546$	−2.04473e21	−	1.36370e21i	−0.258878	−	0.172655i
$547$			1.21191e22i			1.51207i	0.654534	+	0.756033i	$0.272865\pi$
$547$			1.21191e22i			1.51207i	−0.654534	+	0.756033i	$0.727135\pi$
$548$	3.55245e21	+	8.53482e21i	0.436800	+	1.04942i
$549$	6.44623e21			0.781137
$550$	2.65164e21	−	3.97586e21i	0.316675	−	0.474820i
$551$			1.15613e22i			1.36080i
$552$	−5.98230e20	+	3.04858e21i	−0.0693994	+	0.353660i
$553$	−1.13643e22			−1.29940
$554$	−6.96707e21	−	4.64659e21i	−0.785186	−	0.523668i
$555$			1.19985e20i			0.0133286i
$556$	−4.01565e21	+	1.67143e21i	−0.439701	+	0.183017i
$557$	−4.91878e20			−0.0530904			−0.0265452	−	0.999648i	$-0.508451\pi$
$557$	−4.91878e20			−0.0530904			−0.0265452	+	0.999648i	$0.508451\pi$
$558$	−1.65407e21	+	2.48010e21i	−0.175987	+	0.263874i
$559$		−	6.33623e21i		−	0.664563i
$560$	5.10115e20	+	5.06618e20i	0.0527429	+	0.0523813i
$561$	3.85339e21			0.392771
$562$	−1.83686e21	−	1.22507e21i	−0.184580	−	0.123103i
$563$		−	5.70450e21i		−	0.565133i	−0.959248	−	0.282567i	$-0.908814\pi$
$563$		−	5.70450e21i		−	0.565133i	0.959248	−	0.282567i	$-0.0911858\pi$
$564$	−1.68425e21	−	4.04644e21i	−0.164503	−	0.395221i
$565$	7.87262e20			0.0758110
$566$	−4.68087e21	+	7.01847e21i	−0.444421	+	0.666363i
$567$		−	6.67188e21i		−	0.624574i
$568$	1.46687e22	+	2.87847e21i	1.35396	+	0.265690i
$569$	−1.36181e21			−0.123942			−0.0619709	−	0.998078i	$-0.519739\pi$
$569$	−1.36181e21			−0.123942			−0.0619709	+	0.998078i	$0.519739\pi$
$570$	−3.97669e20	−	2.65220e20i	−0.0356881	−	0.0238017i
$571$		−	2.50144e21i		−	0.221361i	−0.993856	−	0.110680i	$-0.964697\pi$
$571$		−	2.50144e21i		−	0.221361i	0.993856	−	0.110680i	$-0.0353030\pi$
$572$	3.05769e21	−	1.27270e21i	0.266824	−	0.111060i
$573$	7.65887e21			0.659065
$574$	−4.65506e21	+	6.97978e21i	−0.395030	+	0.592306i
$575$		−	9.68847e21i		−	0.810798i
$576$	−9.01416e21	−	3.67942e21i	−0.743953	−	0.303669i
$577$	7.04236e21			0.573207			0.286603	−	0.958049i	$-0.407474\pi$
$577$	7.04236e21			0.573207			0.286603	+	0.958049i	$0.407474\pi$
$578$	−1.44776e22	−	9.65563e21i	−1.16218	−	0.775100i
$579$		−	9.26654e20i		−	0.0733651i
$580$	−1.97788e20	−	4.75190e20i	−0.0154446	−	0.0371059i
$581$	2.26413e22			1.74378
$582$	5.54444e20	−	8.31330e20i	0.0421186	−	0.0631524i
$583$			6.57103e21i			0.492363i
$584$	−9.17475e20	+	4.67545e21i	−0.0678096	+	0.345558i
$585$	2.97555e20			0.0216930
$586$	6.62121e21	+	4.41592e21i	0.476164	+	0.317570i
$587$		−	6.86684e21i		−	0.487138i	−0.969884	−	0.243569i	$-0.921682\pi$
$587$		−	6.86684e21i		−	0.487138i	0.969884	−	0.243569i	$-0.0783182\pi$
$588$	5.45589e21	−	2.27090e21i	0.381810	−	0.158921i
$589$	−1.03500e22			−0.714524
$590$	−1.99038e20	+	2.98437e20i	−0.0135556	+	0.0203253i
$591$			7.57367e21i			0.508869i
$592$	−5.97917e21	+	6.02044e21i	−0.396340	+	0.399075i
$593$	−4.47095e21			−0.292390			−0.146195	−	0.989256i	$-0.546703\pi$
$593$	−4.47095e21			−0.292390			−0.146195	+	0.989256i	$0.546703\pi$
$594$	−5.89963e21	−	3.93467e21i	−0.380656	−	0.253873i
$595$		−	1.80782e21i		−	0.115085i
$596$	1.29134e20	+	3.10247e20i	0.00811094	+	0.0194867i
$597$	4.94090e21			0.306204
$598$	3.72553e21	−	5.58604e21i	0.227813	−	0.341581i
$599$		−	1.16626e22i		−	0.703686i	−0.936059	−	0.351843i	$-0.885555\pi$
$599$		−	1.16626e22i		−	0.703686i	0.936059	−	0.351843i	$-0.114445\pi$
$600$	−7.28444e21	−	1.42944e21i	−0.433697	−	0.0851054i
$601$	−2.93277e22			−1.72299			−0.861495	−	0.507767i	$-0.830471\pi$
$601$	−2.93277e22			−1.72299			−0.861495	+	0.507767i	$0.830471\pi$
$602$	2.62593e22	+	1.75133e22i	1.52234	+	1.01530i
$603$			5.48295e21i			0.313672i
$604$	−1.43471e21	+	5.97168e20i	−0.0809968	+	0.0337133i
$605$	6.45259e20			0.0359493
$606$	−3.96331e21	+	5.94257e21i	−0.217910	+	0.326733i
$607$			3.02402e22i			1.64087i	0.571738	+	0.820436i	$0.306269\pi$
$607$			3.02402e22i			1.64087i	−0.571738	+	0.820436i	$0.693731\pi$
$608$	−6.73708e21	−	3.31247e22i	−0.360781	−	1.77388i
$609$	−8.76526e21			−0.463262
$610$	−8.28936e20	−	5.52847e20i	−0.0432397	−	0.0288381i
$611$			9.47269e21i			0.487690i
$612$	9.40778e21	+	2.26024e22i	0.478053	+	1.14853i
$613$	2.49845e22			1.25310			0.626551	−	0.779381i	$-0.284466\pi$
$613$	2.49845e22			1.25310			0.626551	+	0.779381i	$0.284466\pi$
$614$	1.17907e22	−	1.76789e22i	0.583703	−	0.875202i
$615$			2.48332e20i			0.0121348i
$616$	−3.17695e21	+	1.61897e22i	−0.153237	+	0.780898i
$617$	−3.75621e22			−1.78842			−0.894209	−	0.447650i	$-0.852261\pi$
$617$	−3.75621e22			−1.78842			−0.894209	+	0.447650i	$0.852261\pi$
$618$	1.10018e22	+	7.33748e21i	0.517077	+	0.344857i
$619$			1.74823e22i			0.811098i	0.914073	+	0.405549i	$0.132920\pi$
$619$			1.74823e22i			0.811098i	−0.914073	+	0.405549i	$0.867080\pi$
$620$	4.25401e20	−	1.77065e20i	0.0194834	−	0.00810958i
$621$	−1.43764e22			−0.650005
$622$	1.80679e22	−	2.70910e22i	0.806465	−	1.20921i
$623$		−	2.35613e22i		−	1.03823i
$624$	−3.65029e21	−	3.62527e21i	−0.158800	−	0.157712i
$625$	2.30836e22			0.991433
$626$	1.72339e20	+	1.14939e20i	0.00730784	+	0.00487386i
$627$		−	1.09692e22i		−	0.459237i
$628$	−7.74966e21	−	1.86187e22i	−0.320336	−	0.769613i
$629$	2.13361e22			0.870783
$630$	−8.22438e20	+	1.23316e21i	−0.0331420	+	0.0496929i
$631$		−	2.85630e22i		−	1.13650i	−0.822857	−	0.568249i	$-0.807621\pi$
$631$		−	2.85630e22i		−	1.13650i	0.822857	−	0.568249i	$-0.192379\pi$
$632$	−2.33428e22	−	4.58061e21i	−0.917099	−	0.179964i
$633$	−2.58521e21			−0.100292
$634$	−7.28746e21	−	4.86027e21i	−0.279166	−	0.186186i
$635$			1.79824e21i			0.0680233i
$636$	9.42334e21	−	3.92227e21i	0.352004	−	0.146515i
$637$	−1.27722e22			−0.471141
$638$	6.55378e21	−	9.82670e21i	0.238741	−	0.357966i
$639$			3.08195e22i			1.10871i
$640$	8.43594e20	+	1.24622e21i	0.0299705	+	0.0442748i
$641$	3.82378e22			1.34162			0.670809	−	0.741630i	$-0.265947\pi$
$641$	3.82378e22			1.34162			0.670809	+	0.741630i	$0.265947\pi$
$642$	8.72452e20	+	5.81869e20i	0.0302316	+	0.0201625i
$643$		−	4.63594e22i		−	1.58654i	−0.608872	−	0.793269i	$-0.708378\pi$
$643$		−	4.63594e22i		−	1.58654i	0.608872	−	0.793269i	$-0.291622\pi$
$644$	1.28530e22	+	3.08795e22i	0.434426	+	1.04372i
$645$	9.34273e20			0.0311886
$646$	−4.71622e22	+	7.07147e22i	−1.55501	+	2.33158i
$647$			1.48835e22i			0.484699i	0.970189	+	0.242349i	$0.0779180\pi$
$647$			1.48835e22i			0.484699i	−0.970189	+	0.242349i	$0.922082\pi$
$648$	2.68923e21	−	1.37043e22i	0.0865023	−	0.440816i
$649$	−8.23203e21			−0.261547
$650$	1.33476e22	+	8.90197e21i	0.418886	+	0.279370i
$651$		−	7.84687e21i		−	0.243247i
$652$	−1.74476e22	+	7.26223e21i	−0.534264	+	0.222377i
$653$	−2.67284e21			−0.0808477			−0.0404238	−	0.999183i	$-0.512871\pi$
$653$	−2.67284e21			−0.0808477			−0.0404238	+	0.999183i	$0.512871\pi$
$654$	−1.34054e22	+	2.01000e22i	−0.400551	+	0.600584i
$655$		−	2.03457e20i		−	0.00600540i
$656$	−1.23750e22	+	1.24604e22i	−0.360840	+	0.363331i
$657$	−9.82330e21			−0.282966
$658$	−3.92578e22	−	2.61824e22i	−1.11717	−	0.745080i
$659$			5.31164e22i			1.49329i	0.665221	+	0.746647i	$0.268337\pi$
$659$			5.31164e22i			1.49329i	−0.665221	+	0.746647i	$0.731663\pi$
$660$	1.87659e20	+	4.50854e20i	0.00521216	+	0.0125223i
$661$	5.33611e22			1.46424			0.732122	−	0.681173i	$-0.238530\pi$
$661$	5.33611e22			1.46424			0.732122	+	0.681173i	$0.238530\pi$
$662$	1.81992e22	−	2.72877e22i	0.493387	−	0.739782i
$663$			1.29364e22i			0.346502i
$664$	4.65061e22	+	9.12600e21i	1.23074	+	0.241510i
$665$	−5.14622e21			−0.134560
$666$	−1.45539e22	−	9.70652e21i	−0.375998	−	0.250767i
$667$		−	2.39460e22i		−	0.611259i
$668$	7.03708e21	−	2.92904e21i	0.177493	−	0.0738778i
$669$	−1.68979e22			−0.421137
$670$	4.70233e20	−	7.05065e20i	0.0115802	−	0.0173632i
$671$		−	2.28652e22i		−	0.556411i
$672$	2.51136e22	−	5.10774e21i	0.603886	−	0.122822i
$673$	8.77020e21			0.208396			0.104198	−	0.994557i	$-0.466772\pi$
$673$	8.77020e21			0.208396			0.104198	+	0.994557i	$0.466772\pi$
$674$	−1.94364e22	−	1.29628e22i	−0.456390	−	0.304383i
$675$		−	3.43517e22i		−	0.797109i
$676$	−1.24849e22	−	2.99953e22i	−0.286295	−	0.687828i
$677$	−8.48321e22			−1.92243			−0.961216	−	0.275797i	$-0.911058\pi$
$677$	−8.48321e22			−1.92243			−0.961216	+	0.275797i	$0.911058\pi$
$678$	1.55710e22	−	2.33470e22i	0.348721	−	0.522870i
$679$		−	1.07582e22i		−	0.238112i
$680$	7.28675e20	−	3.71333e21i	0.0159391	−	0.0812254i
$681$	2.84660e22			0.615388
$682$	8.79710e21	+	5.86710e21i	0.187960	+	0.125357i
$683$			6.16719e21i			0.130233i	0.997878	+	0.0651166i	$0.0207419\pi$
$683$			6.16719e21i			0.130233i	−0.997878	+	0.0651166i	$0.979258\pi$
$684$	6.43410e22	−	2.67806e22i	1.34289	−	0.558949i
$685$	2.94603e21			0.0607733
$686$	−2.53285e21	+	3.79774e21i	−0.0516436	+	0.0774341i
$687$			3.69940e22i			0.745551i
$688$	4.68786e22	+	4.65572e22i	0.933828	+	0.927427i
$689$	−2.20600e22			−0.434361
$690$	8.23657e20	+	5.49326e20i	0.0160307	+	0.0106915i
$691$			7.44424e22i			1.43218i	0.698010	+	0.716088i	$0.254069\pi$
$691$			7.44424e22i			1.43218i	−0.698010	+	0.716088i	$0.745931\pi$
$692$	−1.93509e22	−	4.64910e22i	−0.368004	−	0.884137i
$693$	−3.40153e22			−0.639452
$694$	−6.31080e20	+	9.46238e20i	−0.0117276	+	0.0175843i
$695$			1.38611e21i			0.0254636i
$696$	−1.80042e22	−	3.53300e21i	−0.326964	−	0.0641608i
$697$	4.41590e22			0.792788
$698$	5.85246e22	+	3.90321e22i	1.03871	+	0.692754i
$699$		−	1.22718e22i		−	0.215323i
$700$	−7.37851e22	+	3.07115e22i	−1.27992	+	0.532742i
$701$	−3.70247e22			−0.634961			−0.317481	−	0.948265i	$-0.602837\pi$
$701$	−3.70247e22			−0.634961			−0.317481	+	0.948265i	$0.602837\pi$
$702$	1.32093e22	−	1.98060e22i	0.223967	−	0.335814i
$703$		−	6.07364e22i		−	1.01814i
$704$	−1.30512e22	+	3.19738e22i	−0.216306	+	0.529924i
$705$	−1.39674e21			−0.0228878
$706$	−2.21818e22	−	1.47938e22i	−0.359384	−	0.239686i
$707$			7.69025e22i			1.23193i
$708$	4.91373e21	+	1.18053e22i	0.0778296	+	0.186987i
$709$	−1.37266e22			−0.214978			−0.107489	−	0.994206i	$-0.534281\pi$
$709$	−1.37266e22			−0.214978			−0.107489	+	0.994206i	$0.534281\pi$
$710$	2.64316e21	−	3.96315e21i	0.0409315	−	0.0613724i
$711$		−	4.90441e22i		−	0.750982i
$712$	9.49683e21	−	4.83959e22i	0.143793	−	0.732771i
$713$	2.14370e22			0.320957
$714$	−5.36126e22	−	3.57561e22i	−0.793745	−	0.529377i
$715$		−	1.05545e21i		−	0.0154521i
$716$	−8.15112e22	+	3.39274e22i	−1.18009	+	0.491186i
$717$	−2.46575e21			−0.0353017
$718$	−4.70851e22	+	7.05991e22i	−0.666634	+	0.999548i
$719$			1.84266e22i			0.257997i	0.991645	+	0.128999i	$0.0411763\pi$
$719$			1.84266e22i			0.257997i	−0.991645	+	0.128999i	$0.958824\pi$
$720$	−2.18637e21	+	2.20146e21i	−0.0302735	+	0.0304825i
$721$	1.42374e23			1.94961
$722$	1.39868e23	+	9.32831e22i	1.89418	+	1.26330i
$723$			1.18226e22i			0.158346i
$724$	−1.36127e22	−	3.27049e22i	−0.180317	−	0.433215i
$725$	5.72177e22			0.749595
$726$	1.27623e22	−	1.91358e22i	0.165362	−	0.247944i
$727$		−	1.11665e22i		−	0.143101i	−0.997437	−	0.0715507i	$-0.977205\pi$
$727$		−	1.11665e22i		−	0.143101i	0.997437	−	0.0715507i	$-0.0227948\pi$
$728$	−5.43515e22	−	1.06655e22i	−0.688907	−	0.135186i
$729$	5.30450e20			0.00665004
$730$	1.26320e21	+	8.42473e20i	0.0156635	+	0.0104466i
$731$		−	1.66135e23i		−	2.03762i
$732$	−3.27904e22	+	1.36483e22i	−0.397794	+	0.165574i
$733$	−1.07239e23			−1.28683			−0.643414	−	0.765518i	$-0.722483\pi$
$733$	−1.07239e23			−1.28683			−0.643414	+	0.765518i	$0.722483\pi$
$734$	2.34192e22	−	3.51147e22i	0.277974	−	0.416793i
$735$		−	1.88325e21i		−	0.0221111i
$736$	1.39539e22	+	6.86083e22i	0.162059	+	0.796809i
$737$	1.94484e22			0.223431
$738$	−3.01220e22	−	2.00894e22i	−0.342321	−	0.228306i
$739$		−	1.55835e23i		−	1.75190i	−0.482402	−	0.875950i	$-0.660236\pi$
$739$		−	1.55835e23i		−	1.75190i	0.482402	−	0.875950i	$-0.339764\pi$
$740$	1.03906e21	+	2.49637e21i	0.0115555	+	0.0277622i
$741$	3.68255e22			0.405138
$742$	6.09735e22	−	9.14234e22i	0.663606	−	0.995007i
$743$			1.74048e23i			1.87395i	0.349396	+	0.936975i	$0.386387\pi$
$743$			1.74048e23i			1.87395i	−0.349396	+	0.936975i	$0.613613\pi$
$744$	3.16283e21	−	1.61178e22i	0.0336893	−	0.171681i
$745$	1.07091e20			0.00112850
$746$	−7.10317e22	−	4.73736e22i	−0.740528	−	0.493885i
$747$			9.77110e22i			1.00781i
$748$	8.01722e22	−	3.33700e22i	0.818108	−	0.340521i
$749$	1.12904e22			0.113987
$750$	−2.62894e21	+	3.94182e21i	−0.0262598	+	0.0393738i
$751$		−	1.69399e22i		−	0.167414i	−0.996490	−	0.0837069i	$-0.973324\pi$
$751$		−	1.69399e22i		−	0.167414i	0.996490	−	0.0837069i	$-0.0266760\pi$
$752$	−7.00837e22	−	6.96033e22i	−0.685290	−	0.680592i
$753$	−2.60581e21			−0.0252105
$754$	3.29898e22	+	2.20021e22i	0.315797	+	0.210617i
$755$			4.95229e20i			0.00469062i
$756$	4.55717e22	+	1.09487e23i	0.427092	+	1.02610i
$757$	−1.65475e23			−1.53449			−0.767246	−	0.641352i	$-0.778374\pi$
$757$	−1.65475e23			−1.53449			−0.767246	+	0.641352i	$0.778374\pi$
$758$	−5.18908e22	+	7.78049e22i	−0.476143	+	0.713926i
$759$			2.27196e22i			0.206285i
$760$	−1.05705e22	−	2.07428e21i	−0.0949705	−	0.0186363i
$761$	−6.44028e22			−0.572568			−0.286284	−	0.958145i	$-0.592420\pi$
$761$	−6.44028e22			−0.572568			−0.286284	+	0.958145i	$0.592420\pi$
$762$	5.33285e22	+	3.55667e22i	0.469159	+	0.312899i
$763$			2.60113e23i			2.26447i
$764$	1.59348e23	−	6.63252e22i	1.37277	−	0.571389i
$765$	7.80184e21			0.0665129
$766$	−5.90772e21	+	8.85801e21i	−0.0498414	+	0.0747319i
$767$		−	2.76362e22i		−	0.230736i
$768$	5.36431e22	−	3.68982e20i	0.443225	−	0.00304871i
$769$	−1.30870e23			−1.07011			−0.535056	−	0.844817i	$-0.679709\pi$
$769$	−1.30870e23			−1.07011			−0.535056	+	0.844817i	$0.679709\pi$
$770$	4.37410e21	+	2.91724e21i	0.0353967	+	0.0236073i
$771$		−	2.94907e22i		−	0.236183i
$772$	−8.02475e21	−	1.92796e22i	−0.0636053	−	0.152813i
$773$	5.04534e22			0.395781			0.197890	−	0.980224i	$-0.436591\pi$
$773$	5.04534e22			0.395781			0.197890	+	0.980224i	$0.436591\pi$
$774$	−7.55805e22	+	1.13325e23i	−0.586789	+	0.879828i
$775$			5.12227e22i			0.393594i
$776$	4.33630e21	−	2.20978e22i	0.0329781	−	0.168056i
$777$	4.60475e22			0.346607
$778$	−1.45799e23	−	9.72388e22i	−1.08622	−	0.724441i
$779$		−	1.25705e23i		−	0.926945i
$780$	−1.51359e21	+	6.30000e20i	−0.0110472	+	0.00459816i
$781$	1.09319e23			0.789744
$782$	9.76828e22	−	1.46465e23i	0.698496	−	1.04732i
$783$		−	8.49033e22i		−	0.600939i
$784$	9.38474e22	−	9.44951e22i	0.657497	−	0.662035i
$785$	−6.42677e21			−0.0445693
$786$	−6.03371e21	−	4.02410e21i	−0.0414194	−	0.0276241i
$787$		−	4.64368e22i		−	0.315547i	−0.987475	−	0.157774i	$-0.949568\pi$
$787$		−	4.64368e22i		−	0.315547i	0.987475	−	0.157774i	$-0.0504316\pi$
$788$	6.55873e22	+	1.57575e23i	0.441174	+	1.05993i
$789$	−1.09193e23			−0.727074
$790$	−4.20616e21	+	6.30669e21i	−0.0277248	+	0.0415704i
$791$		−	3.02133e23i		−	1.97145i
$792$	−6.98687e22	−	1.37105e22i	−0.451316	−	0.0885628i
$793$	7.67621e22			0.490864
$794$	−1.83493e23	−	1.22378e23i	−1.16160	−	0.774711i
$795$		−	3.25273e21i		−	0.0203850i
$796$	1.02798e23	−	4.27878e22i	0.637797	−	0.265470i
$797$	2.20040e23			1.35156			0.675779	−	0.737104i	$-0.263807\pi$
$797$	2.20040e23			1.35156			0.675779	+	0.737104i	$0.263807\pi$
$798$	−1.01785e23	+	1.52616e23i	−0.618958	+	0.928063i
$799$			2.48373e23i			1.49530i
$800$	−1.63936e23	+	3.33422e22i	−0.977136	+	0.198735i
$801$	1.01681e23			0.600042
$802$	1.28933e23	+	8.59898e22i	0.753300	+	0.502403i
$803$			3.48439e22i			0.201559i
$804$	−1.16088e22	−	2.78904e22i	−0.0664875	−	0.159737i
$805$	1.06589e22			0.0604430
$806$	−1.96968e22	+	2.95332e22i	−0.110590	+	0.165818i
$807$		−	6.16345e22i		−	0.342638i
$808$	−3.09970e22	+	1.57961e23i	−0.170620	+	0.869477i
$809$	9.10543e22			0.496263			0.248132	−	0.968726i	$-0.420183\pi$
$809$	9.10543e22			0.496263			0.248132	+	0.968726i	$0.420183\pi$
$810$	−3.70259e21	−	2.46939e21i	−0.0199814	−	0.0133263i
$811$			1.32185e23i			0.706344i	0.935558	+	0.353172i	$0.114897\pi$
$811$			1.32185e23i			0.706344i	−0.935558	+	0.353172i	$0.885103\pi$
$812$	−1.82367e23	+	7.59064e22i	−0.964933	+	0.401634i
$813$	5.39926e22			0.282885
$814$	−3.44297e22	+	5.16237e22i	−0.178623	+	0.267827i
$815$			6.02254e21i			0.0309399i
$816$	−9.57101e22	−	9.50540e22i	−0.486896	−	0.483559i
$817$	−4.72928e23			−2.38242
$818$	6.87356e22	+	4.58422e22i	0.342890	+	0.228686i
$819$		−	1.14194e23i		−	0.564123i
$820$	2.15053e21	+	5.16669e21i	0.0105205	+	0.0252756i
$821$	1.56343e23			0.757416			0.378708	−	0.925516i	$-0.376369\pi$
$821$	1.56343e23			0.757416			0.378708	+	0.925516i	$0.376369\pi$
$822$	5.82684e22	−	8.73674e22i	0.279549	−	0.419155i
$823$		−	3.70305e22i		−	0.175939i	−0.996123	−	0.0879693i	$-0.971962\pi$
$823$		−	3.70305e22i		−	0.175939i	0.996123	−	0.0879693i	$-0.0280377\pi$
$824$	2.92441e23	+	5.73863e22i	1.37601	+	0.270017i
$825$	−5.42875e22			−0.252969
$826$	1.14533e23	+	7.63861e22i	0.528555	+	0.352512i
$827$		−	5.39578e22i		−	0.246610i	−0.992369	−	0.123305i	$-0.960651\pi$
$827$		−	5.39578e22i		−	0.246610i	0.992369	−	0.123305i	$-0.0393493\pi$
$828$	−1.33264e23	+	5.54684e22i	−0.603212	+	0.251075i
$829$	1.78650e23			0.800880			0.400440	−	0.916323i	$-0.368857\pi$
$829$	1.78650e23			0.800880			0.400440	+	0.916323i	$0.368857\pi$
$830$	8.37997e21	−	1.25649e22i	0.0372064	−	0.0557871i
$831$			9.51304e22i			0.418322i
$832$	−1.07341e23	−	4.38148e22i	−0.467498	−	0.190824i
$833$	−3.34885e23			−1.44456
$834$	4.11065e22	+	2.74154e22i	0.175623	+	0.117129i
$835$		−	2.42905e21i		−	0.0102788i
$836$	−9.49928e22	−	2.28222e23i	−0.398144	−	0.956549i
$837$	7.60075e22			0.315539
$838$	2.44384e23	−	3.66428e23i	1.00490	−	1.50673i
$839$			3.18011e23i			1.29523i	0.761969	+	0.647613i	$0.224233\pi$
$839$			3.18011e23i			1.29523i	−0.761969	+	0.647613i	$0.775767\pi$
$840$	1.57262e21	−	8.01409e21i	0.00634440	−	0.0323311i
$841$	−1.08827e23			−0.434881
$842$	2.67443e22	+	1.78367e22i	0.105861	+	0.0706023i
$843$			2.50810e22i			0.0983385i
$844$	−5.37868e22	+	2.23877e22i	−0.208899	+	0.0869499i
$845$	−1.03537e22			−0.0398330
$846$	1.12993e23	−	1.69421e23i	0.430615	−	0.645662i
$847$		−	2.47635e23i		−	0.934857i
$848$	1.62092e23	−	1.63211e23i	0.606170	−	0.610354i
$849$	9.58322e22			0.355018
$850$	3.49971e23	+	2.33408e23i	1.28434	+	0.856574i
$851$			1.25798e23i			0.457338i
$852$	−6.52528e22	−	1.56771e23i	−0.235008	−	0.564611i
$853$	−2.55227e23			−0.910615			−0.455307	−	0.890334i	$-0.650471\pi$
$853$	−2.55227e23			−0.910615			−0.455307	+	0.890334i	$0.650471\pi$
$854$	−2.12170e23	+	3.18126e23i	−0.749929	+	1.12444i
$855$		−	2.22091e22i		−	0.0777682i
$856$	2.31909e22	+	4.55079e21i	0.0804501	+	0.0157869i
$857$	1.01988e23			0.350510			0.175255	−	0.984523i	$-0.443925\pi$
$857$	1.01988e23			0.350510			0.175255	+	0.984523i	$0.443925\pi$
$858$	−3.13003e22	−	2.08753e22i	−0.106574	−	0.0710778i
$859$		−	1.72983e21i		−	0.00583523i	−0.999996	−	0.00291761i	$-0.999071\pi$
$859$		−	1.72983e21i		−	0.00583523i	0.999996	−	0.00291761i	$-0.000928706\pi$
$860$	1.94381e22	−	8.09072e21i	0.0649631	−	0.0270396i
$861$	9.53038e22			0.315562
$862$	1.42846e23	−	2.14182e23i	0.468607	−	0.702627i
$863$		−	2.82882e23i		−	0.919432i	−0.888066	−	0.459716i	$-0.847951\pi$
$863$		−	2.82882e23i		−	0.919432i	0.888066	−	0.459716i	$-0.152049\pi$
$864$	4.94753e22	+	2.43259e23i	0.159323	+	0.783356i
$865$	−1.60477e22			−0.0512015
$866$	−2.27874e23	−	1.51977e23i	−0.720362	−	0.480435i
$867$			1.97681e23i			0.619174i
$868$	−6.79532e22	−	1.63259e23i	−0.210888	−	0.506663i
$869$	−1.73963e23			−0.534931
$870$	−3.24419e21	+	4.86432e21i	−0.00988444	+	0.0148207i
$871$			6.52913e22i			0.197111i
$872$	−1.04844e23	+	5.34283e23i	−0.313624	+	1.59823i
$873$	4.64283e22			0.137616
$874$	−4.16935e23	−	2.78069e23i	−1.22455	−	0.816696i
$875$			5.10110e22i			0.148456i
$876$	4.99687e22	−	2.07985e22i	0.144100	−	0.0599789i
$877$	5.04775e23			1.44245			0.721225	−	0.692700i	$-0.243579\pi$
$877$	5.04775e23			1.44245			0.721225	+	0.692700i	$0.243579\pi$
$878$	−2.39878e23	+	3.59672e23i	−0.679258	+	1.01848i
$879$		−	9.04078e22i		−	0.253685i
$880$	7.80872e21	+	7.75519e21i	0.0217129	+	0.0215641i
$881$	−5.50563e23			−1.51705			−0.758525	−	0.651644i	$-0.774080\pi$
$881$	−5.50563e23			−1.51705			−0.758525	+	0.651644i	$0.774080\pi$
$882$	2.28434e23	+	1.52351e23i	0.623752	+	0.416002i
$883$		−	3.13488e23i		−	0.848273i	−0.905598	−	0.424136i	$-0.860578\pi$
$883$		−	3.13488e23i		−	0.848273i	0.905598	−	0.424136i	$-0.139422\pi$
$884$	1.12028e23	+	2.69150e23i	0.300407	+	0.721734i
$885$	4.07494e21			0.0108287
$886$	−2.31724e23	+	3.47445e23i	−0.610239	+	0.914990i
$887$			3.94823e23i			1.03042i	0.857065	+	0.515209i	$0.172286\pi$
$887$			3.94823e23i			1.03042i	−0.857065	+	0.515209i	$0.827714\pi$
$888$	9.45833e22	+	1.85603e22i	0.244631	+	0.0480044i
$889$	6.90122e23			1.76893
$890$	−1.30755e22	−	8.72049e21i	−0.0332152	−	0.0221524i
$891$		−	1.02132e23i		−	0.257122i
$892$	−3.51571e23	+	1.46334e23i	−0.877191	+	0.365113i
$893$	7.07030e23			1.74834
$894$	2.11810e21	−	3.17587e21i	0.00519095	−	0.00778328i
$895$			2.81359e22i			0.0683402i
$896$	4.78272e23	−	3.23751e23i	1.15136	−	0.779377i
$897$	−7.62733e22			−0.181984
$898$	−4.69716e23	−	3.13270e23i	−1.11077	−	0.740813i
$899$			1.26602e23i			0.296730i
$900$	−1.32539e23	−	3.18428e23i	−0.307896	−	0.739726i
$901$	−5.78409e23			−1.33179
$902$	−7.12586e22	+	1.06845e23i	−0.162624	+	0.243838i
$903$		−	3.58552e23i		−	0.811054i
$904$	1.21780e23	−	6.20593e23i	0.273042	−	1.39142i
$905$	−1.12890e22			−0.0250880
$906$	1.46865e22	+	9.79495e21i	0.0323514	+	0.0215763i
$907$		−	8.29563e23i		−	1.81130i	−0.424022	−	0.905652i	$-0.639382\pi$
$907$		−	8.29563e23i		−	1.81130i	0.424022	−	0.905652i	$-0.360618\pi$
$908$	5.92252e23	−	2.46513e23i	1.28180	−	0.533523i
$909$	−3.31881e23			−0.711987
$910$	−9.79364e21	+	1.46845e22i	−0.0208263	+	0.0312269i
$911$			1.61506e23i			0.340441i	0.985406	+	0.170220i	$0.0544479\pi$
$911$			1.61506e23i			0.340441i	−0.985406	+	0.170220i	$0.945552\pi$
$912$	−2.70586e23	+	2.72453e23i	−0.565387	+	0.569289i
$913$	3.46588e23			0.717872
$914$	−3.79715e23	−	2.53245e23i	−0.779629	−	0.519962i
$915$			1.13185e22i			0.0230367i
$916$	3.20365e23	+	7.69683e23i	0.646370	+	1.55292i
$917$	−7.80820e22			−0.156169
$918$	3.46346e23	−	5.19310e23i	0.686703	−	1.02964i
$919$			1.03389e22i			0.0203212i	0.999948	+	0.0101606i	$0.00323428\pi$
$919$			1.03389e22i			0.0203212i	−0.999948	+	0.0101606i	$0.996766\pi$
$920$	2.18938e22	+	4.29628e21i	0.0426598	+	0.00837123i
$921$	−2.41393e23			−0.466280
$922$	8.45456e23	+	5.63865e23i	1.61899	+	1.07976i
$923$			3.67000e23i			0.696711i
$924$	1.73027e23	−	7.20191e22i	0.325641	−	0.135541i
$925$	−3.00588e23			−0.560839
$926$	1.53080e23	−	2.29527e23i	0.283158	−	0.424566i
$927$			6.14429e23i			1.12677i
$928$	−4.05184e23	+	8.24084e22i	−0.736662	+	0.149826i
$929$	−5.06026e23			−0.912110			−0.456055	−	0.889951i	$-0.650738\pi$
$929$	−5.06026e23			−0.912110			−0.456055	+	0.889951i	$0.650738\pi$
$930$	−4.35465e21	−	2.90427e21i	−0.00778198	−	0.00519008i
$931$			9.53301e23i			1.68901i
$932$	−1.06273e23	−	2.55322e23i	−0.186678	−	0.448498i
$933$	−3.69908e23			−0.644229
$934$	−2.49836e23	+	3.74602e23i	−0.431399	+	0.646838i
$935$		−	2.76737e22i		−	0.0473777i
$936$	4.60282e22	−	2.34560e23i	0.0781299	−	0.398150i
$937$	7.05535e23			1.18741			0.593707	−	0.804681i	$-0.297664\pi$
$937$	7.05535e23			1.18741			0.593707	+	0.804681i	$0.297664\pi$
$938$	−2.70588e23	−	1.80464e23i	−0.451528	−	0.301140i
$939$		−	2.35317e21i		−	0.00389339i
$940$	−2.90601e22	+	1.20957e22i	−0.0476732	+	0.0198430i
$941$	−5.35920e23			−0.871733			−0.435866	−	0.900011i	$-0.643558\pi$
$941$	−5.35920e23			−0.871733			−0.435866	+	0.900011i	$0.643558\pi$
$942$	−1.27113e23	+	1.90592e23i	−0.205013	+	0.307395i
$943$			2.60362e23i			0.416375i
$944$	2.04466e23	+	2.03065e23i	0.324224	+	0.322002i
$945$	3.77925e22			0.0594225
$946$	4.01971e23	+	2.68089e23i	0.626709	+	0.417975i
$947$		−	7.06321e23i		−	1.09195i	−0.837802	−	0.545974i	$-0.816160\pi$
$947$		−	7.06321e23i		−	1.09195i	0.837802	−	0.545974i	$-0.183840\pi$
$948$	1.03839e23	+	2.49475e23i	0.159182	+	0.382438i
$949$	−1.16976e23			−0.177815
$950$	6.64432e23	−	9.96246e23i	1.00152	−	1.50168i
$951$			9.95050e22i			0.148731i
$952$	−1.42509e24	−	2.79648e23i	−2.11225	−	0.414492i
$953$	4.68997e23			0.689330			0.344665	−	0.938726i	$-0.387993\pi$
$953$	4.68997e23			0.689330			0.344665	+	0.938726i	$0.387993\pi$
$954$	3.94548e23	+	2.63138e23i	0.575060	+	0.383528i
$955$		−	5.50033e22i		−	0.0794990i
$956$	−5.13014e22	+	2.13532e22i	−0.0735303	+	0.0306055i
$957$	−1.34177e23			−0.190713
$958$	−1.76311e23	+	2.64360e23i	−0.248517	+	0.372625i
$959$		−	1.13062e24i		−	1.58040i
$960$	6.46046e21	−	1.58274e22i	0.00895557	−	0.0219401i
$961$	6.14086e23			0.844194
$962$	−1.73309e23	−	1.15586e23i	−0.236276	−	0.157581i
$963$			4.87248e22i			0.0658780i
$964$	1.02383e23	+	2.45977e23i	0.137281	+	0.329821i
$965$	−6.65490e21			−0.00884959
$966$	2.10819e23	−	3.16100e23i	0.278030	−	0.416877i
$967$		−	8.25976e23i		−	1.08033i	−0.841560	−	0.540164i	$-0.818362\pi$
$967$		−	8.25976e23i		−	1.08033i	0.841560	−	0.540164i	$-0.181638\pi$
$968$	9.98140e22	−	5.08652e23i	0.129476	−	0.659809i
$969$	9.65558e23			1.24219
$970$	−5.97031e21	−	3.98182e21i	−0.00761769	−	0.00508051i
$971$			7.53118e23i			0.953036i	0.879165	+	0.476518i	$0.158101\pi$
$971$			7.53118e23i			0.953036i	−0.879165	+	0.476518i	$0.841899\pi$
$972$	−7.34490e23	+	3.05716e23i	−0.921840	+	0.383697i
$973$	5.31958e23			0.662177
$974$	−2.85017e23	+	4.27354e23i	−0.351884	+	0.527613i
$975$		−	1.82251e23i		−	0.223169i
$976$	−5.64031e23	+	5.67924e23i	−0.685022	+	0.689750i
$977$	1.47220e23			0.177341			0.0886705	−	0.996061i	$-0.471738\pi$
$977$	1.47220e23			0.177341			0.0886705	+	0.996061i	$0.471738\pi$
$978$	1.78604e23	+	1.19118e23i	0.213393	+	0.142320i
$979$		−	3.60671e23i		−	0.427415i
$980$	−1.63088e22	−	3.91823e22i	−0.0191696	−	0.0460554i
$981$	−1.12255e24			−1.30874
$982$	−3.05835e23	+	4.58568e23i	−0.353668	+	0.530288i
$983$		−	8.61926e23i		−	0.988649i	−0.869278	−	0.494324i	$-0.835416\pi$
$983$		−	8.61926e23i		−	0.988649i	0.869278	−	0.494324i	$-0.164584\pi$
$984$	1.95758e23	+	3.84140e22i	0.222719	+	0.0437048i
$985$	5.43914e22			0.0613819
$986$	8.64987e23	+	5.76891e23i	0.968265	+	0.645770i
$987$			5.36037e23i			0.595192i
$988$	7.66177e23	−	3.18905e23i	0.843866	−	0.351242i
$989$	9.79534e23			1.07016
$990$	−1.25897e22	+	1.88769e22i	−0.0136437	+	0.0204574i
$991$			1.15127e24i			1.23762i	0.785540	+	0.618811i	$0.212385\pi$
$991$			1.15127e24i			1.23762i	−0.785540	+	0.618811i	$0.787615\pi$
$992$	−7.37740e22	−	3.62730e23i	−0.0786701	−	0.386803i
$993$	−3.72594e23			−0.394133
$994$	−1.52096e24	−	1.01438e24i	−1.59598	−	1.06442i
$995$		−	3.54838e22i		−	0.0369356i
$996$	−2.06879e23	−	4.97032e23i	−0.213620	−	0.513227i
$997$	−3.91782e23			−0.401313			−0.200657	−	0.979662i	$-0.564308\pi$
$997$	−3.91782e23			−0.401313			−0.200657	+	0.979662i	$0.564308\pi$
$998$	−5.51994e23	+	8.27657e23i	−0.560906	+	0.841019i
$999$			4.46032e23i			0.449616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.17.b.b.3.1	✓	6
3.2	odd	2		36.17.d.b.19.6		6
4.3	odd	2	inner	4.17.b.b.3.2	yes	6
8.3	odd	2		64.17.c.d.63.4		6
8.5	even	2		64.17.c.d.63.3		6
12.11	even	2		36.17.d.b.19.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.17.b.b.3.1	✓	6	1.1	even	1	trivial
4.17.b.b.3.2	yes	6	4.3	odd	2	inner
36.17.d.b.19.5		6	12.11	even	2
36.17.d.b.19.6		6	3.2	odd	2
64.17.c.d.63.3		6	8.5	even	2
64.17.c.d.63.4		6	8.3	odd	2

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:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-212.978 - 142.043i) q^{2} +2908.07i q^{3} +(25183.6 + 60504.2i) q^{4} +20884.7 q^{5} +(413070. - 619356. i) q^{6} -8.01505e6i q^{7} +(3.23062e6 - 1.64632e7i) q^{8} +3.45899e7 q^{9} +O(q^{10})\)	\(q+(-212.978 - 142.043i) q^{2} +2908.07i q^{3} +(25183.6 + 60504.2i) q^{4} +20884.7 q^{5} +(413070. - 619356. i) q^{6} -8.01505e6i q^{7} +(3.23062e6 - 1.64632e7i) q^{8} +3.45899e7 q^{9} +(-4.44799e6 - 2.96652e6i) q^{10} -1.22693e8i q^{11} +(-1.75950e8 + 7.32357e7i) q^{12} +4.11898e8 q^{13} +(-1.13848e9 + 1.70703e9i) q^{14} +6.07341e7i q^{15} +(-3.02654e9 + 3.04743e9i) q^{16} +1.07999e10 q^{17} +(-7.36690e9 - 4.91325e9i) q^{18} -3.07436e10i q^{19} +(5.25952e8 + 1.26361e9i) q^{20} +2.33083e10 q^{21} +(-1.74276e10 + 2.61309e10i) q^{22} +6.36764e10i q^{23} +(4.78762e10 + 9.39485e9i) q^{24} -1.52152e11 q^{25} +(-8.77254e10 - 5.85072e10i) q^{26} +2.25772e11i q^{27} +(4.84944e11 - 2.01848e11i) q^{28} -3.76057e11 q^{29} +(8.62685e9 - 1.29351e10i) q^{30} -3.36655e11i q^{31} +(1.07745e12 - 2.19138e11i) q^{32} +3.56798e11 q^{33} +(-2.30015e12 - 1.53405e12i) q^{34} -1.67392e11i q^{35} +(8.71098e11 + 2.09283e12i) q^{36} +1.97558e12 q^{37} +(-4.36690e12 + 6.54771e12i) q^{38} +1.19783e12i q^{39} +(6.74705e10 - 3.43830e11i) q^{40} +4.08883e12 q^{41} +(-4.96417e12 - 3.31078e12i) q^{42} -1.53830e13i q^{43} +(7.42341e12 - 3.08984e12i) q^{44} +7.22399e11 q^{45} +(9.04478e12 - 1.35617e13i) q^{46} +2.29977e13i q^{47} +(-8.86212e12 - 8.80138e12i) q^{48} -3.10082e13 q^{49} +(3.24050e13 + 2.16121e13i) q^{50} +3.14069e13i q^{51} +(1.03731e13 + 2.49215e13i) q^{52} -5.35569e13 q^{53} +(3.20694e13 - 4.80847e13i) q^{54} -2.56240e12i q^{55} +(-1.31954e14 - 2.58936e13i) q^{56} +8.94043e13 q^{57} +(8.00921e13 + 5.34163e13i) q^{58} -6.70947e13i q^{59} +(-3.67466e12 + 1.52950e12i) q^{60} +1.86362e14 q^{61} +(-4.78195e13 + 7.17003e13i) q^{62} -2.77240e14i q^{63} +(-2.60601e14 - 1.06373e14i) q^{64} +8.60236e12 q^{65} +(-7.59903e13 - 5.06807e13i) q^{66} +1.58513e14i q^{67} +(2.71981e14 + 6.53439e14i) q^{68} -1.85175e14 q^{69} +(-2.37768e13 + 3.56509e13i) q^{70} +8.90997e14i q^{71} +(1.11747e14 - 5.69461e14i) q^{72} -2.83994e14 q^{73} +(-4.20756e14 - 2.80617e14i) q^{74} -4.42467e14i q^{75} +(1.86011e15 - 7.74234e14i) q^{76} -9.83388e14 q^{77} +(1.70143e14 - 2.55111e14i) q^{78} -1.41787e15i q^{79} +(-6.32083e13 + 6.36446e13i) q^{80} +8.32419e14 q^{81} +(-8.70833e14 - 5.80790e14i) q^{82} +2.82485e15i q^{83} +(5.86988e14 + 1.41025e15i) q^{84} +2.25553e14 q^{85} +(-2.18505e15 + 3.27625e15i) q^{86} -1.09360e15i q^{87} +(-2.01992e15 - 3.96373e14i) q^{88} +2.93963e15 q^{89} +(-1.53855e14 - 1.02612e14i) q^{90} -3.30139e15i q^{91} +(-3.85269e15 + 1.60360e15i) q^{92} +9.79016e14 q^{93} +(3.26666e15 - 4.89801e15i) q^{94} -6.42070e14i q^{95} +(6.37268e14 + 3.13330e15i) q^{96} +1.34225e15 q^{97} +(6.60407e15 + 4.40449e15i) q^{98} -4.24392e15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 164 q^{2} - 160368 q^{4} - 506740 q^{5} - 1187136 q^{6} - 33829184 q^{8} - 137574522 q^{9}+O(q^{10}) \) 6 * q - 164 * q^2 - 160368 * q^4 - 506740 * q^5 - 1187136 * q^6 - 33829184 * q^8 - 137574522 * q^9	\( 6 q - 164 q^{2} - 160368 q^{4} - 506740 q^{5} - 1187136 q^{6} - 33829184 q^{8} - 137574522 q^{9} - 142269000 q^{10} + 254142720 q^{12} + 2544478092 q^{13} + 1073417856 q^{14} + 145019136 q^{16} + 1579205132 q^{17} - 22662764964 q^{18} + 4421361440 q^{20} - 27228321792 q^{21} - 138624795840 q^{22} + 403778497536 q^{24} + 271424476050 q^{25} - 190529582152 q^{26} + 1617685224960 q^{28} - 1158411768436 q^{29} - 4663806986880 q^{30} + 4663321578496 q^{32} - 767957621760 q^{33} - 5461346085192 q^{34} + 14104690258320 q^{36} + 8581446019212 q^{37} - 20462346561600 q^{38} + 18971054755200 q^{40} + 1840369253132 q^{41} - 20386577111040 q^{42} + 3644055863040 q^{44} - 34166370110580 q^{45} + 5034653652864 q^{46} - 56248898088960 q^{48} - 5527245758202 q^{49} + 129240587956500 q^{50} - 103374802254048 q^{52} + 130668269409932 q^{53} + 366965883430272 q^{54} - 342617610295296 q^{56} - 122486852367360 q^{57} + 69923529928632 q^{58} - 641633781542400 q^{60} - 429486008315508 q^{61} + 619512054551040 q^{62} - 516434037731328 q^{64} + 12\!\cdots\!00 q^{65}+ \cdots + 13\!\cdots\!56 q^{98}+O(q^{100}) \) 6 * q - 164 * q^2 - 160368 * q^4 - 506740 * q^5 - 1187136 * q^6 - 33829184 * q^8 - 137574522 * q^9 - 142269000 * q^10 + 254142720 * q^12 + 2544478092 * q^13 + 1073417856 * q^14 + 145019136 * q^16 + 1579205132 * q^17 - 22662764964 * q^18 + 4421361440 * q^20 - 27228321792 * q^21 - 138624795840 * q^22 + 403778497536 * q^24 + 271424476050 * q^25 - 190529582152 * q^26 + 1617685224960 * q^28 - 1158411768436 * q^29 - 4663806986880 * q^30 + 4663321578496 * q^32 - 767957621760 * q^33 - 5461346085192 * q^34 + 14104690258320 * q^36 + 8581446019212 * q^37 - 20462346561600 * q^38 + 18971054755200 * q^40 + 1840369253132 * q^41 - 20386577111040 * q^42 + 3644055863040 * q^44 - 34166370110580 * q^45 + 5034653652864 * q^46 - 56248898088960 * q^48 - 5527245758202 * q^49 + 129240587956500 * q^50 - 103374802254048 * q^52 + 130668269409932 * q^53 + 366965883430272 * q^54 - 342617610295296 * q^56 - 122486852367360 * q^57 + 69923529928632 * q^58 - 641633781542400 * q^60 - 429486008315508 * q^61 + 619512054551040 * q^62 - 516434037731328 * q^64 + 1237661666277400 * q^65 - 54995333852160 * q^66 + 1716626085477152 * q^68 - 265820219762688 * q^69 - 1698017749451520 * q^70 + 1539597157891776 * q^72 - 1145601039770868 * q^73 - 771134490565192 * q^74 + 2768729450169600 * q^76 - 665543599687680 * q^77 - 7024870687386240 * q^78 + 4403327011381760 * q^80 - 277566121727226 * q^81 - 3459247029640008 * q^82 + 3591637752471552 * q^84 - 1934080153645800 * q^85 + 2096299590206784 * q^86 + 719241463526400 * q^88 + 20426758995091724 * q^89 + 1627824908547000 * q^90 - 9798772065277440 * q^92 - 20365632048291840 * q^93 + 16900683550077696 * q^94 - 32790566117523456 * q^96 + 4182396554403852 * q^97 + 13584426279160156 * q^98

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