LMFDB - Embedded newform 8.12.b.a.5.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [8,12,Mod(5,8)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8.5"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	8.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.14674544448$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 48 x^{8} + 8836 x^{7} - 92554 x^{6} - 2200342 x^{5} - 88894588 x^{4} + \cdots + 34431558027300 $ x^10 - x^9 - 48x^8 + 8836x^7 - 92554x^6 - 2200342x^5 - 88894588x^4 + 2040335460x^3 + 7439251985x^2 - 747501940689x + 34431558027300
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{2}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.10
Root			$20.8472 + 5.89062i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.12.b.a.5.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(43.6944 + 11.7812i) q^{2} -381.717i q^{3} +(1770.40 + 1029.55i) q^{4} -8937.55i q^{5} +(4497.10 - 16678.9i) q^{6} +10175.0 q^{7} +(65227.5 + 65843.1i) q^{8} +31439.0 q^{9} +(105295. - 390521. i) q^{10} -408594. i q^{11} +(392996. - 675794. i) q^{12} +1.94255e6i q^{13} +(444591. + 119874. i) q^{14} -3.41162e6 q^{15} +(2.07436e6 + 3.64544e6i) q^{16} -9.64991e6 q^{17} +(1.37371e6 + 370391. i) q^{18} +1.27489e7i q^{19} +(9.20165e6 - 1.58231e7i) q^{20} -3.88398e6i q^{21} +(4.81374e6 - 1.78533e7i) q^{22} +2.34581e7 q^{23} +(2.51334e7 - 2.48984e7i) q^{24} -3.10517e7 q^{25} +(-2.28857e7 + 8.48786e7i) q^{26} -7.96209e7i q^{27} +(1.80139e7 + 1.04757e7i) q^{28} +4.83134e7i q^{29} +(-1.49069e8 - 4.01931e7i) q^{30} +2.63557e8 q^{31} +(4.76903e7 + 1.83724e8i) q^{32} -1.55967e8 q^{33} +(-4.21647e8 - 1.13688e8i) q^{34} -9.09397e7i q^{35} +(5.56598e7 + 3.23680e7i) q^{36} +7.91290e7i q^{37} +(-1.50198e8 + 5.57057e8i) q^{38} +7.41505e8 q^{39} +(5.88476e8 - 5.82974e8i) q^{40} -6.96380e8 q^{41} +(4.57581e7 - 1.69708e8i) q^{42} -4.03606e8i q^{43} +(4.20667e8 - 7.23376e8i) q^{44} -2.80988e8i q^{45} +(1.02499e9 + 2.76365e8i) q^{46} -5.59625e8 q^{47} +(1.39153e9 - 7.91820e8i) q^{48} -1.87380e9 q^{49} +(-1.35679e9 - 3.65828e8i) q^{50} +3.68354e9i q^{51} +(-1.99995e9 + 3.43910e9i) q^{52} +2.88775e9i q^{53} +(9.38032e8 - 3.47899e9i) q^{54} -3.65183e9 q^{55} +(6.63690e8 + 6.69954e8i) q^{56} +4.86648e9 q^{57} +(-5.69191e8 + 2.11102e9i) q^{58} -9.84523e9i q^{59} +(-6.03994e9 - 3.51243e9i) q^{60} -5.65364e9i q^{61} +(1.15160e10 + 3.10503e9i) q^{62} +3.19892e8 q^{63} +(-8.06933e7 + 8.58956e9i) q^{64} +1.73617e10 q^{65} +(-6.81489e9 - 1.83749e9i) q^{66} +1.28196e10i q^{67} +(-1.70842e10 - 9.93505e9i) q^{68} -8.95435e9i q^{69} +(1.07138e9 - 3.97356e9i) q^{70} -3.63445e9 q^{71} +(2.05069e9 + 2.07004e9i) q^{72} -2.56732e9 q^{73} +(-9.32237e8 + 3.45749e9i) q^{74} +1.18530e10i q^{75} +(-1.31256e10 + 2.25707e10i) q^{76} -4.15744e9i q^{77} +(3.23996e10 + 8.73585e9i) q^{78} -2.59475e10 q^{79} +(3.25813e10 - 1.85397e10i) q^{80} -2.48233e10 q^{81} +(-3.04279e10 - 8.20422e9i) q^{82} -3.80496e10i q^{83} +(3.99874e9 - 6.87621e9i) q^{84} +8.62466e10i q^{85} +(4.75498e9 - 1.76353e10i) q^{86} +1.84420e10 q^{87} +(2.69031e10 - 2.66515e10i) q^{88} -2.00557e10 q^{89} +(3.31039e9 - 1.22776e10i) q^{90} +1.97655e10i q^{91} +(4.15303e10 + 2.41512e10i) q^{92} -1.00604e11i q^{93} +(-2.44525e10 - 6.59307e9i) q^{94} +1.13944e11 q^{95} +(7.01305e10 - 1.82042e10i) q^{96} -6.90643e10 q^{97} +(-8.18744e10 - 2.20756e10i) q^{98} -1.28458e10i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9} + 29864 q^{10} - 476216 q^{12} + 2264272 q^{14} + 3391792 q^{15} + 3757072 q^{16} + 2639732 q^{17} + 2329130 q^{18}+ \cdots - 6194726778 q^{98}+O(q^{100}) $ 10 * q + 22 * q^2 + 436 * q^4 - 24308 * q^6 - 33616 * q^7 - 208472 * q^8 - 472394 * q^9 + 29864 * q^10 - 476216 * q^12 + 2264272 * q^14 + 3391792 * q^15 + 3757072 * q^16 + 2639732 * q^17 + 2329130 * q^18 + 8296432 * q^20 - 24201892 * q^22 - 45357808 * q^23 + 10668944 * q^24 - 41502654 * q^25 - 101931080 * q^26 - 95722144 * q^28 + 261362768 * q^30 + 442035392 * q^31 + 343908512 * q^32 - 54732216 * q^33 - 187103796 * q^34 - 431195700 * q^36 + 375100844 * q^38 - 431459312 * q^39 + 1519138784 * q^40 - 654907964 * q^41 - 3697737056 * q^42 - 4127012952 * q^44 + 6028867440 * q^46 - 560226528 * q^47 + 9357606048 * q^48 + 1143661722 * q^49 - 9626584226 * q^50 - 11595427248 * q^52 + 20050494008 * q^54 + 5632783984 * q^55 + 18698733760 * q^56 - 783862360 * q^57 - 22828679464 * q^58 - 43681325472 * q^60 + 40774631744 * q^62 - 14483624624 * q^63 + 55266728512 * q^64 - 80291360 * q^65 - 83128448712 * q^66 - 83303223768 * q^68 + 100120831168 * q^70 - 11769460176 * q^71 + 112862051672 * q^72 + 32304890372 * q^73 - 102103996184 * q^74 - 97501928568 * q^76 + 144445560944 * q^78 + 57291670496 * q^79 + 128322038976 * q^80 - 23172996094 * q^81 - 123309929604 * q^82 - 199990865984 * q^84 + 130201908124 * q^86 - 73844404272 * q^87 + 169216119632 * q^88 - 108276011804 * q^89 - 228506434984 * q^90 - 141139403232 * q^92 + 145336130016 * q^94 + 70146835376 * q^95 + 109508068928 * q^96 + 60995282900 * q^97 - 6194726778 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	43.6944	+	11.7812i	0.965519	+	0.260331i
$2$	43.6944	+	11.7812i	0.965519	+	0.260331i
$3$		−	381.717i		−	0.906932i	−0.891274	−	0.453466i	$-0.850187\pi$
$3$		−	381.717i		−	0.906932i	0.891274	−	0.453466i	$-0.149813\pi$
$4$	1770.40	+	1029.55i	0.864455	+	0.502709i
$5$		−	8937.55i		−	1.27904i	−0.768775	−	0.639519i	$-0.779133\pi$
$5$		−	8937.55i		−	1.27904i	0.768775	−	0.639519i	$-0.220867\pi$
$6$	4497.10	−	16678.9i	0.236103	−	0.875661i
$7$	10175.0			0.228821			0.114410	−	0.993434i	$-0.463502\pi$
$7$	10175.0			0.228821			0.114410	+	0.993434i	$0.463502\pi$
$8$	65227.5	+	65843.1i	0.703778	+	0.710420i
$9$	31439.0			0.177474
$10$	105295.	−	390521.i	0.332973	−	1.23494i
$11$		−	408594.i		−	0.764948i	−0.923966	−	0.382474i	$-0.875072\pi$
$11$		−	408594.i		−	0.764948i	0.923966	−	0.382474i	$-0.124928\pi$
$12$	392996.	−	675794.i	0.455923	−	0.784002i
$13$			1.94255e6i			1.45106i	0.688193	+	0.725528i	$0.258404\pi$
$13$			1.94255e6i			1.45106i	−0.688193	+	0.725528i	$0.741596\pi$
$14$	444591.	+	119874.i	0.220931	+	0.0595692i
$15$	−3.41162e6			−1.16000
$16$	2.07436e6	+	3.64544e6i	0.494567	+	0.869140i
$17$	−9.64991e6			−1.64837			−0.824184	−	0.566322i	$-0.808366\pi$
$17$	−9.64991e6			−1.64837			−0.824184	+	0.566322i	$0.808366\pi$
$18$	1.37371e6	+	370391.i	0.171355	+	0.0462020i
$19$			1.27489e7i			1.18121i	0.806959	+	0.590607i	$0.201112\pi$
$19$			1.27489e7i			1.18121i	−0.806959	+	0.590607i	$0.798888\pi$
$20$	9.20165e6	−	1.58231e7i	0.642985	−	1.10567i
$21$		−	3.88398e6i		−	0.207525i
$22$	4.81374e6	−	1.78533e7i	0.199140	−	0.738572i
$23$	2.34581e7			0.759957			0.379979	−	0.924995i	$-0.375931\pi$
$23$	2.34581e7			0.759957			0.379979	+	0.924995i	$0.375931\pi$
$24$	2.51334e7	−	2.48984e7i	0.644303	−	0.638279i
$25$	−3.10517e7			−0.635939
$26$	−2.28857e7	+	8.48786e7i	−0.377755	+	1.40102i
$27$		−	7.96209e7i		−	1.06789i
$28$	1.80139e7	+	1.04757e7i	0.197805	+	0.115030i
$29$			4.83134e7i			0.437400i	0.975792	+	0.218700i	$0.0701815\pi$
$29$			4.83134e7i			0.437400i	−0.975792	+	0.218700i	$0.929818\pi$
$30$	−1.49069e8	−	4.01931e7i	−1.12000	−	0.301984i
$31$	2.63557e8			1.65343			0.826714	−	0.562622i	$-0.190207\pi$
$31$	2.63557e8			1.65343			0.826714	+	0.562622i	$0.190207\pi$
$32$	4.76903e7	+	1.83724e8i	0.251250	+	0.967922i
$33$	−1.55967e8			−0.693756
$34$	−4.21647e8	−	1.13688e8i	−1.59153	−	0.429121i
$35$		−	9.09397e7i		−	0.292671i
$36$	5.56598e7	+	3.23680e7i	0.153419	+	0.0892179i
$37$			7.91290e7i			0.187597i	0.995591	+	0.0937985i	$0.0299010\pi$
$37$			7.91290e7i			0.187597i	−0.995591	+	0.0937985i	$0.970099\pi$
$38$	−1.50198e8	+	5.57057e8i	−0.307507	+	1.14048i
$39$	7.41505e8			1.31601
$40$	5.88476e8	−	5.82974e8i	0.908655	−	0.900159i
$41$	−6.96380e8			−0.938718			−0.469359	−	0.883008i	$-0.655515\pi$
$41$	−6.96380e8			−0.938718			−0.469359	+	0.883008i	$0.655515\pi$
$42$	4.57581e7	−	1.69708e8i	0.0540252	−	0.200369i
$43$		−	4.03606e8i		−	0.418679i	−0.977843	−	0.209339i	$-0.932869\pi$
$43$		−	4.03606e8i		−	0.418679i	0.977843	−	0.209339i	$-0.0671314\pi$
$44$	4.20667e8	−	7.23376e8i	0.384546	−	0.661263i
$45$		−	2.80988e8i		−	0.226996i
$46$	1.02499e9	+	2.76365e8i	0.733753	+	0.197840i
$47$	−5.59625e8			−0.355925			−0.177963	−	0.984037i	$-0.556951\pi$
$47$	−5.59625e8			−0.355925			−0.177963	+	0.984037i	$0.556951\pi$
$48$	1.39153e9	−	7.91820e8i	0.788251	−	0.448538i
$49$	−1.87380e9			−0.947641
$50$	−1.35679e9	−	3.65828e8i	−0.614012	−	0.165555i
$51$			3.68354e9i			1.49496i
$52$	−1.99995e9	+	3.43910e9i	−0.729459	+	1.25437i
$53$			2.88775e9i			0.948510i	0.880388	+	0.474255i	$0.157283\pi$
$53$			2.88775e9i			0.948510i	−0.880388	+	0.474255i	$0.842717\pi$
$54$	9.38032e8	−	3.47899e9i	0.278005	−	1.03107i
$55$	−3.65183e9			−0.978397
$56$	6.63690e8	+	6.69954e8i	0.161039	+	0.162559i
$57$	4.86648e9			1.07128
$58$	−5.69191e8	+	2.11102e9i	−0.113869	+	0.422318i
$59$		−	9.84523e9i		−	1.79283i	−0.443213	−	0.896417i	$-0.646161\pi$
$59$		−	9.84523e9i		−	1.79283i	0.443213	−	0.896417i	$-0.353839\pi$
$60$	−6.03994e9	−	3.51243e9i	−1.00277	−	0.583143i
$61$		−	5.65364e9i		−	0.857066i	−0.903526	−	0.428533i	$-0.859031\pi$
$61$		−	5.65364e9i		−	0.857066i	0.903526	−	0.428533i	$-0.140969\pi$
$62$	1.15160e10	+	3.10503e9i	1.59642	+	0.430439i
$63$	3.19892e8			0.0406098
$64$	−8.06933e7	+	8.58956e9i	−0.00939394	+	0.999956i
$65$	1.73617e10			1.85596
$66$	−6.81489e9	−	1.83749e9i	−0.669834	−	0.180606i
$67$			1.28196e10i			1.16001i	0.814613	+	0.580005i	$0.196949\pi$
$67$			1.28196e10i			1.16001i	−0.814613	+	0.580005i	$0.803051\pi$
$68$	−1.70842e10	−	9.93505e9i	−1.42494	−	0.828650i
$69$		−	8.95435e9i		−	0.689230i
$70$	1.07138e9	−	3.97356e9i	0.0761913	−	0.282579i
$71$	−3.63445e9			−0.239066			−0.119533	−	0.992830i	$-0.538140\pi$
$71$	−3.63445e9			−0.239066			−0.119533	+	0.992830i	$0.538140\pi$
$72$	2.05069e9	+	2.07004e9i	0.124902	+	0.126081i
$73$	−2.56732e9			−0.144945			−0.0724727	−	0.997370i	$-0.523089\pi$
$73$	−2.56732e9			−0.144945			−0.0724727	+	0.997370i	$0.523089\pi$
$74$	−9.32237e8	+	3.45749e9i	−0.0488373	+	0.181129i
$75$			1.18530e10i			0.576754i
$76$	−1.31256e10	+	2.25707e10i	−0.593807	+	1.02111i
$77$		−	4.15744e9i		−	0.175036i
$78$	3.23996e10	+	8.73585e9i	1.27063	+	0.342598i
$79$	−2.59475e10			−0.948739			−0.474370	−	0.880326i	$-0.657324\pi$
$79$	−2.59475e10			−0.948739			−0.474370	+	0.880326i	$0.657324\pi$
$80$	3.25813e10	−	1.85397e10i	1.11166	−	0.632570i
$81$	−2.48233e10			−0.791029
$82$	−3.04279e10	−	8.20422e9i	−0.906350	−	0.244377i
$83$		−	3.80496e10i		−	1.06028i	−0.847910	−	0.530140i	$-0.822140\pi$
$83$		−	3.80496e10i		−	1.06028i	0.847910	−	0.530140i	$-0.177860\pi$
$84$	3.99874e9	−	6.87621e9i	0.104325	−	0.179396i
$85$			8.62466e10i			2.10833i
$86$	4.75498e9	−	1.76353e10i	0.108995	−	0.404243i
$87$	1.84420e10			0.396692
$88$	2.69031e10	−	2.66515e10i	0.543434	−	0.538353i
$89$	−2.00557e10			−0.380709			−0.190354	−	0.981715i	$-0.560964\pi$
$89$	−2.00557e10			−0.380709			−0.190354	+	0.981715i	$0.560964\pi$
$90$	3.31039e9	−	1.22776e10i	0.0590942	−	0.219169i
$91$			1.97655e10i			0.332032i
$92$	4.15303e10	+	2.41512e10i	0.656949	+	0.382038i
$93$		−	1.00604e11i		−	1.49955i
$94$	−2.44525e10	−	6.59307e9i	−0.343653	−	0.0926584i
$95$	1.13944e11			1.51082
$96$	7.01305e10	−	1.82042e10i	0.877840	−	0.227866i
$97$	−6.90643e10			−0.816600			−0.408300	−	0.912848i	$-0.633878\pi$
$97$	−6.90643e10			−0.816600			−0.408300	+	0.912848i	$0.633878\pi$
$98$	−8.18744e10	−	2.20756e10i	−0.914966	−	0.246700i
$99$		−	1.28458e10i		−	0.135758i
$100$	−5.49741e10	−	3.19693e10i	−0.549741	−	0.319693i
$101$			3.00032e10i			0.284053i	0.989863	+	0.142027i	$0.0453619\pi$
$101$			3.00032e10i			0.284053i	−0.989863	+	0.142027i	$0.954638\pi$
$102$	−4.33966e10	+	1.60950e11i	−0.389184	+	1.44341i
$103$	4.46196e10			0.379246			0.189623	−	0.981857i	$-0.439273\pi$
$103$	4.46196e10			0.379246			0.189623	+	0.981857i	$0.439273\pi$
$104$	−1.27904e11	+	1.26708e11i	−1.03086	+	1.02122i
$105$	−3.47132e10			−0.265432
$106$	−3.40212e10	+	1.26178e11i	−0.246927	+	0.915805i
$107$			1.84556e10i			0.127209i	0.997975	+	0.0636044i	$0.0202596\pi$
$107$			1.84556e10i			0.127209i	−0.997975	+	0.0636044i	$0.979740\pi$
$108$	8.19736e10	−	1.40961e11i	0.536838	−	0.923143i
$109$			9.05577e8i			0.00563741i	0.999996	+	0.00281871i	$0.000897223\pi$
$109$			9.05577e8i			0.00563741i	−0.999996	+	0.00281871i	$0.999103\pi$
$110$	−1.59564e11	−	4.30230e10i	−0.944662	−	0.254707i
$111$	3.02049e10			0.170138
$112$	2.11067e10	+	3.70924e10i	0.113167	+	0.198877i
$113$	1.77827e11			0.907957			0.453978	−	0.891013i	$-0.350004\pi$
$113$	1.77827e11			0.907957			0.453978	+	0.891013i	$0.350004\pi$
$114$	2.12638e11	+	5.73332e10i	1.03434	+	0.278888i
$115$		−	2.09658e11i		−	0.972014i
$116$	−4.97410e10	+	8.55342e10i	−0.219885	+	0.378112i
$117$			6.10719e10i			0.257525i
$118$	1.15989e11	−	4.30182e11i	0.466730	−	1.73102i
$119$	−9.81879e10			−0.377181
$120$	−2.22531e11	−	2.24631e11i	−0.816383	−	0.824088i
$121$	1.18363e11			0.414855
$122$	6.66069e10	−	2.47033e11i	0.223121	−	0.827514i
$123$			2.65820e11i			0.851353i
$124$	4.66603e11	+	2.71345e11i	1.42932	+	0.831194i
$125$		−	1.58877e11i		−	0.465648i
$126$	1.39775e10	+	3.76873e9i	0.0392095	+	0.0105720i
$127$	−5.40179e11			−1.45083			−0.725417	−	0.688310i	$-0.758353\pi$
$127$	−5.40179e11			−1.45083			−0.725417	+	0.688310i	$0.758353\pi$
$128$	−1.04721e11	+	3.74365e11i	−0.269390	+	0.963031i
$129$	−1.54063e11			−0.379713
$130$	7.58607e11	+	2.04542e11i	1.79196	+	0.483163i
$131$			2.23934e11i			0.507141i	0.967317	+	0.253570i	$0.0816049\pi$
$131$			2.23934e11i			0.507141i	−0.967317	+	0.253570i	$0.918395\pi$
$132$	−2.76125e11	−	1.60576e11i	−0.599721	−	0.348757i
$133$			1.29720e11i			0.270286i
$134$	−1.51030e11	+	5.60143e11i	−0.301986	+	1.12001i
$135$	−7.11616e11			−1.36587
$136$	−6.29439e11	−	6.35380e11i	−1.16008	−	1.17103i
$137$	3.35319e11			0.593602			0.296801	−	0.954939i	$-0.404080\pi$
$137$	3.35319e11			0.593602			0.296801	+	0.954939i	$0.404080\pi$
$138$	1.05493e11	−	3.91255e11i	0.179428	−	0.665465i
$139$		−	2.72700e10i		−	0.0445763i	−0.999752	−	0.0222881i	$-0.992905\pi$
$139$		−	2.72700e10i		−	0.0445763i	0.999752	−	0.0222881i	$-0.00709512\pi$
$140$	9.36269e10	−	1.61000e11i	0.147128	−	0.253001i
$141$			2.13618e11i			0.322800i
$142$	−1.58805e11	−	4.28184e10i	−0.230823	−	0.0622363i
$143$	7.93714e11			1.10998
$144$	6.52159e10	+	1.14609e11i	0.0877728	+	0.154250i
$145$	4.31803e11			0.559451
$146$	−1.12178e11	−	3.02462e10i	−0.139948	−	0.0377338i
$147$			7.15260e11i			0.859446i
$148$	−8.14671e10	+	1.40090e11i	−0.0943068	+	0.162169i
$149$		−	1.14880e12i		−	1.28151i	−0.767747	−	0.640753i	$-0.778622\pi$
$149$		−	1.14880e12i		−	1.28151i	0.767747	−	0.640753i	$-0.221378\pi$
$150$	−1.39643e11	+	5.17909e11i	−0.150147	+	0.556867i
$151$	4.51160e11			0.467689			0.233845	−	0.972274i	$-0.424869\pi$
$151$	4.51160e11			0.467689			0.233845	+	0.972274i	$0.424869\pi$
$152$	−8.39428e11	+	8.31579e11i	−0.839158	+	0.831312i
$153$	−3.03384e11			−0.292543
$154$	4.89798e10	−	1.81657e11i	0.0455673	−	0.169001i
$155$		−	2.35556e12i		−	2.11480i
$156$	1.31276e12	+	7.63416e11i	1.13763	+	0.661570i
$157$			8.98082e10i			0.0751395i	0.999294	+	0.0375697i	$0.0119616\pi$
$157$			8.98082e10i			0.0751395i	−0.999294	+	0.0375697i	$0.988038\pi$
$158$	−1.13376e12	−	3.05694e11i	−0.916026	−	0.246986i
$159$	1.10230e12			0.860234
$160$	1.64204e12	−	4.26235e11i	1.23801	−	0.321358i
$161$	2.38686e11			0.173894
$162$	−1.08464e12	−	2.92449e11i	−0.763754	−	0.205929i
$163$			3.45737e11i			0.235350i	0.993052	+	0.117675i	$0.0375441\pi$
$163$			3.45737e11i			0.235350i	−0.993052	+	0.117675i	$0.962456\pi$
$164$	−1.23287e12	−	7.16957e11i	−0.811480	−	0.471902i
$165$			1.39396e12i			0.887340i
$166$	4.48271e11	−	1.66255e12i	0.276024	−	1.02372i
$167$	6.61651e11			0.394174			0.197087	−	0.980386i	$-0.436852\pi$
$167$	6.61651e11			0.394174			0.197087	+	0.980386i	$0.436852\pi$
$168$	2.55733e11	−	2.53342e11i	0.147430	−	0.146051i
$169$	−1.98134e12			−1.10556
$170$	−1.01609e12	+	3.76849e12i	−0.548863	+	2.03563i
$171$			4.00813e11i			0.209635i
$172$	4.15532e11	−	7.14546e11i	0.210474	−	0.361929i
$173$			2.94318e12i			1.44399i	0.691900	+	0.721993i	$0.256774\pi$
$173$			2.94318e12i			1.44399i	−0.691900	+	0.721993i	$0.743226\pi$
$174$	8.05814e11	+	2.17270e11i	0.383014	+	0.103271i
$175$	−3.15952e11			−0.145516
$176$	1.48950e12	−	8.47571e11i	0.664846	−	0.378318i
$177$	−3.75809e12			−1.62598
$178$	−8.76322e11	−	2.36281e11i	−0.367582	−	0.0991103i
$179$			8.70295e11i			0.353977i	0.984213	+	0.176988i	$0.0566355\pi$
$179$			8.70295e11i			0.353977i	−0.984213	+	0.176988i	$0.943364\pi$
$180$	2.89291e11	−	4.97462e11i	0.114113	−	0.196228i
$181$		−	4.02698e12i		−	1.54080i	−0.637559	−	0.770401i	$-0.720056\pi$
$181$		−	4.02698e12i		−	1.54080i	0.637559	−	0.770401i	$-0.279944\pi$
$182$	−2.32862e11	+	8.63641e11i	−0.0864382	+	0.320583i
$183$	−2.15809e12			−0.777301
$184$	1.53011e12	+	1.54455e12i	0.534841	+	0.539889i
$185$	7.07219e11			0.239944
$186$	1.18524e12	−	4.39585e12i	0.390379	−	1.44784i
$187$			3.94289e12i			1.26092i
$188$	−9.90762e11	−	5.76161e11i	−0.307681	−	0.178927i
$189$		−	8.10143e11i		−	0.244355i
$190$	4.97872e12	+	1.34240e12i	1.45872	+	0.393313i
$191$	5.16393e12			1.46993			0.734965	−	0.678105i	$-0.237199\pi$
$191$	5.16393e12			1.46993			0.734965	+	0.678105i	$0.237199\pi$
$192$	3.27878e12	+	3.08020e10i	0.906892	+	0.00851966i
$193$	2.61981e12			0.704214			0.352107	−	0.935960i	$-0.385465\pi$
$193$	2.61981e12			0.704214			0.352107	+	0.935960i	$0.385465\pi$
$194$	−3.01773e12	−	8.13663e11i	−0.788443	−	0.212586i
$195$		−	6.62724e12i		−	1.68323i
$196$	−3.31738e12	−	1.92916e12i	−0.819193	−	0.476388i
$197$		−	9.51398e11i		−	0.228453i	−0.993455	−	0.114227i	$-0.963561\pi$
$197$		−	9.51398e11i		−	0.228453i	0.993455	−	0.114227i	$-0.0364390\pi$
$198$	1.51339e11	−	5.61289e11i	0.0353421	−	0.131077i
$199$	−7.34864e12			−1.66923			−0.834613	−	0.550837i	$-0.814309\pi$
$199$	−7.34864e12			−1.66923			−0.834613	+	0.550837i	$0.814309\pi$
$200$	−2.02543e12	−	2.04454e12i	−0.447560	−	0.451784i
$201$	4.89344e12			1.05205
$202$	−3.53475e11	+	1.31097e12i	−0.0739479	+	0.274259i
$203$			4.91589e11i			0.100086i
$204$	−3.79238e12	+	6.52135e12i	−0.751529	+	1.29232i
$205$			6.22393e12i			1.20066i
$206$	1.94963e12	+	5.25674e11i	0.366169	+	0.0987294i
$207$	7.37499e11			0.134873
$208$	−7.08145e12	+	4.02956e12i	−1.26117	+	0.717644i
$209$	5.20912e12			0.903567
$210$	−1.51678e12	−	4.08965e11i	−0.256280	−	0.0691003i
$211$			6.80722e11i			0.112051i	0.998429	+	0.0560256i	$0.0178428\pi$
$211$			6.80722e11i			0.112051i	−0.998429	+	0.0560256i	$0.982157\pi$
$212$	−2.97308e12	+	5.11248e12i	−0.476825	+	0.819945i
$213$			1.38733e12i			0.216817i
$214$	−2.17430e11	+	8.06406e11i	−0.0331164	+	0.122823i
$215$	−3.60725e12			−0.535506
$216$	5.24248e12	−	5.19347e12i	0.758650	−	0.751557i
$217$	2.68170e12			0.378339
$218$	−1.06688e10	+	3.95687e10i	−0.00146759	+	0.00544303i
$219$			9.79991e11i			0.131456i
$220$	−6.46521e12	−	3.75973e12i	−0.845781	−	0.491850i
$221$		−	1.87454e13i		−	2.39187i
$222$	1.31979e12	+	3.55851e11i	0.164271	+	0.0442922i
$223$	−1.19442e12			−0.145037			−0.0725187	−	0.997367i	$-0.523104\pi$
$223$	−1.19442e12			−0.145037			−0.0725187	+	0.997367i	$0.523104\pi$
$224$	4.85249e11	+	1.86939e12i	0.0574911	+	0.221481i
$225$	−9.76236e11			−0.112863
$226$	7.77003e12	+	2.09502e12i	0.876650	+	0.236369i
$227$			5.02675e12i			0.553535i	0.960937	+	0.276768i	$0.0892632\pi$
$227$			5.02675e12i			0.553535i	−0.960937	+	0.276768i	$0.910737\pi$
$228$	8.61564e12	+	5.01028e12i	0.926074	+	0.538543i
$229$			2.86620e12i			0.300754i	0.988629	+	0.150377i	$0.0480487\pi$
$229$			2.86620e12i			0.300754i	−0.988629	+	0.150377i	$0.951951\pi$
$230$	2.47003e12	−	9.16087e12i	0.253046	−	0.938499i
$231$	−1.58697e12			−0.158746
$232$	−3.18110e12	+	3.15136e12i	−0.310737	+	0.307832i
$233$	−9.05833e12			−0.864153			−0.432077	−	0.901837i	$-0.642219\pi$
$233$	−9.05833e12			−0.864153			−0.432077	+	0.901837i	$0.642219\pi$
$234$	−7.19503e11	+	2.66850e12i	−0.0670417	+	0.248645i
$235$			5.00168e12i			0.455242i
$236$	1.01361e13	−	1.74300e13i	0.901274	−	1.54982i
$237$			9.90461e12i			0.860442i
$238$	−4.29026e12	−	1.15678e12i	−0.364176	−	0.0981919i
$239$	1.48753e13			1.23389			0.616947	−	0.787005i	$-0.288369\pi$
$239$	1.48753e13			1.23389			0.616947	+	0.787005i	$0.288369\pi$
$240$	−7.07693e12	−	1.24368e13i	−0.573698	−	1.00820i
$241$	1.65832e12			0.131394			0.0656969	−	0.997840i	$-0.479073\pi$
$241$	1.65832e12			0.131394			0.0656969	+	0.997840i	$0.479073\pi$
$242$	5.17180e12	+	1.39446e12i	0.400551	+	0.108000i
$243$		−	4.62911e12i		−	0.350480i
$244$	5.82070e12	−	1.00092e13i	0.430855	−	0.740896i
$245$			1.67472e13i			1.21207i
$246$	−3.13169e12	+	1.16149e13i	−0.221634	+	0.821998i
$247$	−2.47654e13			−1.71401
$248$	1.71912e13	+	1.73534e13i	1.16365	+	1.17463i
$249$	−1.45242e13			−0.961601
$250$	1.87177e12	−	6.94206e12i	0.121223	−	0.449592i
$251$		−	1.60614e13i		−	1.01760i	−0.860883	−	0.508802i	$-0.830088\pi$
$251$		−	1.60614e13i		−	1.01760i	0.860883	−	0.508802i	$-0.169912\pi$
$252$	5.66339e11	+	3.29345e11i	0.0351054	+	0.0204149i
$253$		−	9.58481e12i		−	0.581327i
$254$	−2.36028e13	−	6.36398e12i	−1.40081	−	0.377697i
$255$	3.29218e13			1.91211
$256$	−8.98623e12	+	1.51239e13i	−0.510808	+	0.859695i
$257$	−2.90477e13			−1.61614			−0.808072	−	0.589084i	$-0.799489\pi$
$257$	−2.90477e13			−1.61614			−0.808072	+	0.589084i	$0.799489\pi$
$258$	−6.73171e12	−	1.81506e12i	−0.366621	−	0.0988512i
$259$			8.05138e11i			0.0429261i
$260$	3.07372e13	+	1.78747e13i	1.60439	+	0.933006i
$261$			1.51892e12i			0.0776271i
$262$	−2.63822e12	+	9.78468e12i	−0.132024	+	0.489654i
$263$	−7.15627e12			−0.350695			−0.175348	−	0.984507i	$-0.556105\pi$
$263$	−7.15627e12			−0.350695			−0.175348	+	0.984507i	$0.556105\pi$
$264$	−1.01733e13	−	1.02694e13i	−0.488250	−	0.492858i
$265$	2.58094e13			1.21318
$266$	−1.52827e12	+	5.66806e12i	−0.0703639	+	0.260967i
$267$			7.65561e12i			0.345277i
$268$	−1.31984e13	+	2.26958e13i	−0.583147	+	1.00278i
$269$			9.77777e12i			0.423255i	0.977350	+	0.211627i	$0.0678764\pi$
$269$			9.77777e12i			0.423255i	−0.977350	+	0.211627i	$0.932124\pi$
$270$	−3.10936e13	−	8.38371e12i	−1.31878	−	0.355579i
$271$	3.73866e13			1.55376			0.776882	−	0.629647i	$-0.216800\pi$
$271$	3.73866e13			1.55376			0.776882	+	0.629647i	$0.216800\pi$
$272$	−2.00174e13	−	3.51781e13i	−0.815228	−	1.43266i
$273$	7.54482e12			0.301130
$274$	1.46516e13	+	3.95048e12i	0.573134	+	0.154533i
$275$			1.26875e13i			0.486460i
$276$	9.21894e12	−	1.58528e13i	0.346482	−	0.595808i
$277$		−	2.28097e13i		−	0.840391i	−0.907433	−	0.420196i	$-0.861961\pi$
$277$		−	2.28097e13i		−	0.840391i	0.907433	−	0.420196i	$-0.138039\pi$
$278$	3.21274e11	−	1.19155e12i	0.0116046	−	0.0430392i
$279$	8.28598e12			0.293441
$280$	5.98775e12	−	5.93176e12i	0.207919	−	0.205975i
$281$	−8.47235e12			−0.288482			−0.144241	−	0.989543i	$-0.546074\pi$
$281$	−8.47235e12			−0.288482			−0.144241	+	0.989543i	$0.546074\pi$
$282$	−2.51669e12	+	9.33393e12i	−0.0840349	+	0.311670i
$283$		−	5.48093e13i		−	1.79485i	−0.441163	−	0.897427i	$-0.645434\pi$
$283$		−	5.48093e13i		−	1.79485i	0.441163	−	0.897427i	$-0.354566\pi$
$284$	−6.43445e12	−	3.74185e12i	−0.206662	−	0.120181i
$285$		−	4.34944e13i		−	1.37021i
$286$	3.46809e13	+	9.35093e12i	1.07171	+	0.288963i
$287$	−7.08567e12			−0.214798
$288$	1.49934e12	+	5.77610e12i	0.0445903	+	0.171781i
$289$	5.88488e13			1.71712
$290$	1.88674e13	+	5.08718e12i	0.540161	+	0.145642i
$291$			2.63630e13i			0.740601i
$292$	−4.54520e12	−	2.64318e12i	−0.125299	−	0.0728655i
$293$			5.59919e13i			1.51479i	0.652955	+	0.757396i	$0.273529\pi$
$293$			5.59919e13i			1.51479i	−0.652955	+	0.757396i	$0.726471\pi$
$294$	−8.42665e12	+	3.12529e13i	−0.223740	+	0.829812i
$295$	−8.79923e13			−2.29310
$296$	−5.21010e12	+	5.16138e12i	−0.133273	+	0.132027i
$297$	−3.25326e13			−0.816879
$298$	1.35343e13	−	5.01962e13i	0.333616	−	1.23732i
$299$			4.55685e13i			1.10274i
$300$	−1.22032e13	+	2.09846e13i	−0.289940	+	0.498578i
$301$		−	4.10670e12i		−	0.0958025i
$302$	1.97132e13	+	5.31522e12i	0.451563	+	0.121754i
$303$	1.14527e13			0.257617
$304$	−4.64754e13	+	2.64459e13i	−1.02664	+	0.584189i
$305$	−5.05297e13			−1.09622
$306$	−1.32562e13	−	3.57423e12i	−0.282456	−	0.0761580i
$307$			3.49392e13i			0.731226i	0.930767	+	0.365613i	$0.119141\pi$
$307$			3.49392e13i			0.731226i	−0.930767	+	0.365613i	$0.880859\pi$
$308$	4.28029e12	−	7.36036e12i	0.0879922	−	0.151311i
$309$		−	1.70321e13i		−	0.343950i
$310$	2.77514e13	−	1.02925e14i	0.550548	−	2.04188i
$311$	−8.77394e13			−1.71006			−0.855032	−	0.518575i	$-0.826463\pi$
$311$	−8.77394e13			−1.71006			−0.855032	+	0.518575i	$0.826463\pi$
$312$	4.83665e13	+	4.88230e13i	0.926178	+	0.934919i
$313$	9.47630e13			1.78297			0.891487	−	0.453046i	$-0.149663\pi$
$313$	9.47630e13			1.78297			0.891487	+	0.453046i	$0.149663\pi$
$314$	−1.05805e12	+	3.92412e12i	−0.0195611	+	0.0725486i
$315$		−	2.85905e12i		−	0.0519415i
$316$	−4.59376e13	−	2.67142e13i	−0.820143	−	0.476940i
$317$			7.45724e13i			1.30844i	0.756306	+	0.654218i	$0.227002\pi$
$317$			7.45724e13i			1.30844i	−0.756306	+	0.654218i	$0.772998\pi$
$318$	4.81645e13	+	1.29865e13i	0.830573	+	0.223946i
$319$	1.97405e13			0.334588
$320$	7.67696e13	+	7.21201e11i	1.27898	+	0.0120152i
$321$	7.04482e12			0.115370
$322$	1.04293e13	+	2.81202e12i	0.167898	+	0.0452700i
$323$		−	1.23026e14i		−	1.94707i
$324$	−4.39473e13	−	2.55568e13i	−0.683809	−	0.397658i
$325$		−	6.03196e13i		−	0.922783i
$326$	−4.07321e12	+	1.51068e13i	−0.0612688	+	0.227235i
$327$	3.45674e11			0.00511275
$328$	−4.54231e13	−	4.58518e13i	−0.660649	−	0.666884i
$329$	−5.69419e12			−0.0814431
$330$	−1.64226e13	+	6.09085e13i	−0.231002	+	0.856744i
$331$			9.05611e13i			1.25282i	0.779495	+	0.626409i	$0.215476\pi$
$331$			9.05611e13i			1.25282i	−0.779495	+	0.626409i	$0.784524\pi$
$332$	3.91739e13	−	6.73631e13i	0.533012	−	0.916564i
$333$			2.48774e12i			0.0332936i
$334$	2.89105e13	+	7.79507e12i	0.380583	+	0.102616i
$335$	1.14575e14			1.48370
$336$	1.41588e13	−	8.05677e12i	0.180368	−	0.102635i
$337$	3.77207e13			0.472733			0.236366	−	0.971664i	$-0.424043\pi$
$337$	3.77207e13			0.472733			0.236366	+	0.971664i	$0.424043\pi$
$338$	−8.65737e13	−	2.33427e13i	−1.06744	−	0.287812i
$339$		−	6.78794e13i		−	0.823455i
$340$	−8.87950e13	+	1.52691e14i	−1.05988	+	1.82255i
$341$		−	1.07688e14i		−	1.26479i
$342$	−4.72208e12	+	1.75133e13i	−0.0545745	+	0.202407i
$343$	−3.91852e13			−0.445661
$344$	2.65747e13	−	2.63262e13i	0.297438	−	0.294657i
$345$	−8.00299e13			−0.881551
$346$	−3.46743e13	+	1.28601e14i	−0.375915	+	1.39420i
$347$			4.95297e13i			0.528510i	0.964453	+	0.264255i	$0.0851261\pi$
$347$			4.95297e13i			0.528510i	−0.964453	+	0.264255i	$0.914874\pi$
$348$	3.26499e13	+	1.89870e13i	0.342922	+	0.199421i
$349$			4.22844e13i			0.437160i	0.975819	+	0.218580i	$0.0701425\pi$
$349$			4.22844e13i			0.437160i	−0.975819	+	0.218580i	$0.929858\pi$
$350$	−1.38053e13	−	3.72230e12i	−0.140499	−	0.0378824i
$351$	1.54668e14			1.54957
$352$	7.50684e13	−	1.94860e13i	0.740410	−	0.192193i
$353$	−5.42310e13			−0.526607			−0.263304	−	0.964713i	$-0.584812\pi$
$353$	−5.42310e13			−0.526607			−0.263304	+	0.964713i	$0.584812\pi$
$354$	−1.64208e14	−	4.42750e13i	−1.56991	−	0.423293i
$355$			3.24831e13i			0.305775i
$356$	−3.55067e13	−	2.06483e13i	−0.329106	−	0.191386i
$357$			3.74800e13i			0.342078i
$358$	−1.02532e13	+	3.80270e13i	−0.0921512	+	0.341771i
$359$	1.11001e14			0.982441			0.491220	−	0.871035i	$-0.336551\pi$
$359$	1.11001e14			0.982441			0.491220	+	0.871035i	$0.336551\pi$
$360$	1.85011e13	−	1.83281e13i	0.161263	−	0.159755i
$361$	−4.60446e13			−0.395266
$362$	4.74428e13	−	1.75956e14i	0.401119	−	1.48767i
$363$		−	4.51812e13i		−	0.376245i
$364$	−2.03495e13	+	3.49929e13i	−0.166915	+	0.287027i
$365$			2.29456e13i			0.185391i
$366$	−9.42966e13	−	2.54250e13i	−0.750499	−	0.202356i
$367$	−1.37111e14			−1.07500			−0.537502	−	0.843262i	$-0.680632\pi$
$367$	−1.37111e14			−1.07500			−0.537502	+	0.843262i	$0.680632\pi$
$368$	4.86605e13	+	8.55149e13i	0.375849	+	0.660509i
$369$	−2.18935e13			−0.166598
$370$	3.09015e13	+	8.33192e12i	0.231670	+	0.0624648i
$371$			2.93829e13i			0.217039i
$372$	1.03577e14	−	1.78110e14i	0.753837	−	1.29629i
$373$			1.24348e14i			0.891744i	0.895097	+	0.445872i	$0.147106\pi$
$373$			1.24348e14i			0.891744i	−0.895097	+	0.445872i	$0.852894\pi$
$374$	−4.64521e13	+	1.72282e14i	−0.328255	+	1.21744i
$375$	−6.06463e13			−0.422311
$376$	−3.65029e13	−	3.68474e13i	−0.250492	−	0.252856i
$377$	−9.38512e13			−0.634691
$378$	9.54449e12	−	3.53987e13i	0.0636133	−	0.235930i
$379$		−	2.76010e14i		−	1.81305i	−0.422157	−	0.906523i	$-0.638727\pi$
$379$		−	2.76010e14i		−	1.81305i	0.422157	−	0.906523i	$-0.361273\pi$
$380$	2.01727e14	+	1.17311e14i	1.30603	+	0.759502i
$381$			2.06196e14i			1.31581i
$382$	2.25635e14	+	6.08374e13i	1.41925	+	0.382668i
$383$	1.30866e14			0.811396			0.405698	−	0.914007i	$-0.367028\pi$
$383$	1.30866e14			0.811396			0.405698	+	0.914007i	$0.367028\pi$
$384$	1.42902e14	+	3.99740e13i	0.873404	+	0.244318i
$385$	−3.71574e13			−0.223878
$386$	1.14471e14	+	3.08646e13i	0.679933	+	0.183329i
$387$		−	1.26890e13i		−	0.0743047i
$388$	−1.22272e14	−	7.11051e13i	−0.705914	−	0.410512i
$389$		−	2.65449e14i		−	1.51098i	−0.655161	−	0.755489i	$-0.727399\pi$
$389$		−	2.65449e14i		−	1.51098i	0.655161	−	0.755489i	$-0.272601\pi$
$390$	7.80771e13	−	2.89573e14i	0.438196	−	1.62519i
$391$	−2.26368e14			−1.25269
$392$	−1.22223e14	−	1.23377e14i	−0.666929	−	0.673223i
$393$	8.54795e13			0.459942
$394$	1.12086e13	−	4.15708e13i	0.0594735	−	0.220576i
$395$			2.31907e14i			1.21347i
$396$	1.32254e13	−	2.27422e13i	0.0682470	−	0.117357i
$397$		−	2.55728e14i		−	1.30146i	−0.759309	−	0.650730i	$-0.774463\pi$
$397$		−	2.55728e14i		−	1.30146i	0.759309	−	0.650730i	$-0.225537\pi$
$398$	−3.21095e14	−	8.65761e13i	−1.61167	−	0.434551i
$399$	4.95165e13			0.245131
$400$	−6.44125e13	−	1.13197e14i	−0.314514	−	0.552720i
$401$	4.93538e13			0.237698			0.118849	−	0.992912i	$-0.462079\pi$
$401$	4.93538e13			0.237698			0.118849	+	0.992912i	$0.462079\pi$
$402$	2.13816e14	+	5.76508e13i	1.01577	+	0.273881i
$403$			5.11973e14i			2.39922i
$404$	−3.08898e13	+	5.31178e13i	−0.142796	+	0.245551i
$405$			2.21860e14i			1.01176i
$406$	−5.79153e12	+	2.14797e13i	−0.0260555	+	0.0966351i
$407$	3.23316e13			0.143502
$408$	−2.42535e14	+	2.40268e14i	−1.06205	+	1.05212i
$409$	2.01464e14			0.870400			0.435200	−	0.900334i	$-0.356678\pi$
$409$	2.01464e14			0.870400			0.435200	+	0.900334i	$0.356678\pi$
$410$	−7.33256e13	+	2.71951e14i	−0.312568	+	1.15926i
$411$		−	1.27997e14i		−	0.538357i
$412$	7.89947e13	+	4.59380e13i	0.327841	+	0.190650i
$413$		−	1.00175e14i		−	0.410238i
$414$	3.22246e13	+	8.68865e12i	0.130222	+	0.0351116i
$415$	−3.40070e14			−1.35614
$416$	−3.56893e14	+	9.26409e13i	−1.40451	+	0.364577i
$417$	−1.04094e13			−0.0404276
$418$	2.27610e14	+	6.13699e13i	0.872411	+	0.235226i
$419$		−	3.36722e14i		−	1.27378i	−0.770954	−	0.636891i	$-0.780220\pi$
$419$		−	3.36722e14i		−	1.27378i	0.770954	−	0.636891i	$-0.219780\pi$
$420$	−6.14565e13	−	3.57390e13i	−0.229455	−	0.133435i
$421$		−	1.20703e12i		−	0.00444800i	−0.999998	−	0.00222400i	$-0.999292\pi$
$421$		−	1.20703e12i		−	0.00444800i	0.999998	−	0.00222400i	$-0.000707922\pi$
$422$	−8.01975e12	+	2.97438e13i	−0.0291704	+	0.108188i
$423$	−1.75941e13			−0.0631675
$424$	−1.90138e14	+	1.88360e14i	−0.673841	+	0.667540i
$425$	2.99646e14			1.04826
$426$	−1.63445e13	+	6.06187e13i	−0.0564441	+	0.209341i
$427$		−	5.75259e13i		−	0.196115i
$428$	−1.90009e13	+	3.26739e13i	−0.0639491	+	0.109966i
$429$		−	3.02974e14i		−	1.00668i
$430$	−1.57617e14	−	4.24979e13i	−0.517042	−	0.139409i
$431$	−1.87948e13			−0.0608714			−0.0304357	−	0.999537i	$-0.509689\pi$
$431$	−1.87948e13			−0.0608714			−0.0304357	+	0.999537i	$0.509689\pi$
$432$	2.90253e14	−	1.65163e14i	0.928145	−	0.528142i
$433$	3.13621e14			0.990197			0.495098	−	0.868837i	$-0.335132\pi$
$433$	3.13621e14			0.990197			0.495098	+	0.868837i	$0.335132\pi$
$434$	1.17175e14	+	3.15937e13i	0.365294	+	0.0984934i
$435$		−	1.64827e14i		−	0.507384i
$436$	−9.32336e11	+	1.60324e12i	−0.00283398	+	0.00487329i
$437$			2.99065e14i			0.897672i
$438$	−1.15455e13	+	4.28201e13i	−0.0342220	+	0.126923i
$439$	4.95205e14			1.44954			0.724771	−	0.688990i	$-0.241946\pi$
$439$	4.95205e14			1.44954			0.724771	+	0.688990i	$0.241946\pi$
$440$	−2.38199e14	−	2.40448e14i	−0.688574	−	0.695073i
$441$	−5.89103e13			−0.168182
$442$	2.20845e14	−	8.19071e14i	0.622679	−	2.30940i
$443$		−	2.99673e14i		−	0.834500i	−0.908792	−	0.417250i	$-0.862994\pi$
$443$		−	2.99673e14i		−	0.834500i	0.908792	−	0.417250i	$-0.137006\pi$
$444$	5.34749e13	+	3.10974e13i	0.147077	+	0.0855299i
$445$			1.79249e14i			0.486941i
$446$	−5.21894e13	−	1.40717e13i	−0.140036	−	0.0377577i
$447$	−4.38517e14			−1.16224
$448$	−8.21055e11	+	8.73988e13i	−0.00214953	+	0.228811i
$449$	2.49937e14			0.646362			0.323181	−	0.946337i	$-0.395248\pi$
$449$	2.49937e14			0.646362			0.323181	+	0.946337i	$0.395248\pi$
$450$	−4.26561e13	−	1.15013e13i	−0.108971	−	0.0293817i
$451$			2.84536e14i			0.718070i
$452$	3.14825e14	+	1.83081e14i	0.784888	+	0.456438i
$453$		−	1.72215e14i		−	0.424162i
$454$	−5.92214e13	+	2.19641e14i	−0.144102	+	0.534449i
$455$	1.76655e14			0.424681
$456$	3.17428e14	+	3.20424e14i	0.753943	+	0.761059i
$457$	−7.22584e14			−1.69570			−0.847851	−	0.530235i	$-0.822104\pi$
$457$	−7.22584e14			−1.69570			−0.847851	+	0.530235i	$0.822104\pi$
$458$	−3.37674e13	+	1.25237e14i	−0.0782955	+	0.290383i
$459$			7.68334e14i			1.76027i
$460$	2.15853e14	−	3.71179e14i	0.488641	−	0.840263i
$461$		−	2.69171e13i		−	0.0602107i	−0.999547	−	0.0301054i	$-0.990416\pi$
$461$		−	2.69171e13i		−	0.0602107i	0.999547	−	0.0301054i	$-0.00958428\pi$
$462$	−6.93416e13	−	1.86964e13i	−0.153272	−	0.0413265i
$463$	−6.06138e13			−0.132396			−0.0661982	−	0.997806i	$-0.521087\pi$
$463$	−6.06138e13			−0.132396			−0.0661982	+	0.997806i	$0.521087\pi$
$464$	−1.76123e14	+	1.00219e14i	−0.380161	+	0.216323i
$465$	−8.99156e14			−1.91798
$466$	−3.95799e14	−	1.06718e14i	−0.834357	−	0.224966i
$467$		−	2.97151e13i		−	0.0619063i	−0.999521	−	0.0309531i	$-0.990146\pi$
$467$		−	2.97151e13i		−	0.0619063i	0.999521	−	0.0309531i	$-0.00985426\pi$
$468$	−6.28765e13	+	1.08122e14i	−0.129460	+	0.222619i
$469$			1.30439e14i			0.265434i
$470$	−5.89259e13	+	2.18545e14i	−0.118514	+	0.439545i
$471$	3.42813e13			0.0681464
$472$	6.48241e14	−	6.42179e14i	1.27366	−	1.26176i
$473$	−1.64911e14			−0.320267
$474$	−1.16689e14	+	4.32776e14i	−0.224000	+	0.830774i
$475$		−	3.95876e14i		−	0.751180i
$476$	−1.73832e14	−	1.01089e14i	−0.326056	−	0.189612i
$477$			9.07879e13i			0.168336i
$478$	6.49968e14	+	1.75250e14i	1.19135	+	0.321221i
$479$	1.21025e14			0.219296			0.109648	−	0.993970i	$-0.465028\pi$
$479$	1.21025e14			0.219296			0.109648	+	0.993970i	$0.465028\pi$
$480$	−1.62701e14	−	6.26795e14i	−0.291450	−	1.12279i
$481$	−1.53712e14			−0.272214
$482$	7.24594e13	+	1.95371e13i	0.126863	+	0.0342059i
$483$		−	9.11106e13i		−	0.157710i
$484$	2.09550e14	+	1.21860e14i	0.358624	+	0.208552i
$485$			6.17266e14i			1.04446i
$486$	5.45366e13	−	2.02266e14i	0.0912408	−	0.338395i
$487$	6.01563e14			0.995111			0.497556	−	0.867432i	$-0.334231\pi$
$487$	6.01563e14			0.995111			0.497556	+	0.867432i	$0.334231\pi$
$488$	3.72253e14	−	3.68773e14i	0.608877	−	0.603184i
$489$	1.31974e14			0.213446
$490$	−1.97302e14	+	7.31757e14i	−0.315539	+	1.17028i
$491$			8.74926e13i			0.138364i	0.997604	+	0.0691820i	$0.0220389\pi$
$491$			8.74926e13i			0.138364i	−0.997604	+	0.0691820i	$0.977961\pi$
$492$	−2.73675e14	+	4.70609e14i	−0.427983	+	0.735957i
$493$		−	4.66220e14i		−	0.720995i
$494$	−1.08211e15	−	2.91767e14i	−1.65491	−	0.446209i
$495$	−1.14810e14			−0.173640
$496$	5.46713e14	+	9.60781e14i	0.817730	+	1.43706i
$497$	−3.69806e13			−0.0547033
$498$	−6.34625e14	−	1.71113e14i	−0.928445	−	0.250335i
$499$		−	8.99853e14i		−	1.30202i	−0.759068	−	0.651011i	$-0.774345\pi$
$499$		−	8.99853e14i		−	1.30202i	0.759068	−	0.651011i	$-0.225655\pi$
$500$	1.63572e14	−	2.81277e14i	0.234085	−	0.402532i
$501$		−	2.52564e14i		−	0.357489i
$502$	1.89224e14	−	7.01796e14i	0.264914	−	0.982517i
$503$	6.87292e14			0.951738			0.475869	−	0.879516i	$-0.342134\pi$
$503$	6.87292e14			0.951738			0.475869	+	0.879516i	$0.342134\pi$
$504$	2.08658e13	+	2.10627e13i	0.0285803	+	0.0288500i
$505$	2.68155e14			0.363315
$506$	1.12921e14	−	4.18803e14i	0.151338	−	0.561283i
$507$			7.56313e14i			1.00267i
$508$	−9.56336e14	−	5.56141e14i	−1.25418	−	0.729347i
$509$		−	1.78689e14i		−	0.231819i	−0.993260	−	0.115910i	$-0.963022\pi$
$509$		−	1.78689e14i		−	0.231819i	0.993260	−	0.115910i	$-0.0369783\pi$
$510$	1.43850e15	+	3.87860e14i	1.84618	+	0.497781i
$511$	−2.61225e13			−0.0331666
$512$	−5.70826e14	+	5.54962e14i	−0.717000	+	0.697073i
$513$	1.01508e15			1.26141
$514$	−1.26922e15	−	3.42218e14i	−1.56042	−	0.420732i
$515$		−	3.98790e14i		−	0.485070i
$516$	−2.72754e14	−	1.58616e14i	−0.328245	−	0.190885i
$517$			2.28659e14i			0.272264i
$518$	−9.48553e12	+	3.51800e13i	−0.0111750	+	0.0414460i
$519$	1.12346e15			1.30960
$520$	1.13246e15	+	1.14315e15i	1.30618	+	1.31851i
$521$	3.87660e14			0.442429			0.221215	−	0.975225i	$-0.428998\pi$
$521$	3.87660e14			0.442429			0.221215	+	0.975225i	$0.428998\pi$
$522$	−1.78948e13	+	6.63685e13i	−0.0202088	+	0.0749505i
$523$		−	3.70738e14i		−	0.414293i	−0.978310	−	0.207146i	$-0.933582\pi$
$523$		−	3.70738e14i		−	0.414293i	0.978310	−	0.207146i	$-0.0664177\pi$
$524$	−2.30551e14	+	3.96454e14i	−0.254944	+	0.438400i
$525$			1.20604e14i			0.131973i
$526$	−3.12689e14	−	8.43097e13i	−0.338603	−	0.0912969i
$527$	−2.54330e15			−2.72546
$528$	−3.23532e14	−	5.68568e14i	−0.343108	−	0.602971i
$529$	−4.02529e14			−0.422465
$530$	1.12773e15	+	3.04067e14i	1.17135	+	0.315829i
$531$		−	3.09524e14i		−	0.318182i
$532$	−1.33553e14	+	2.29658e14i	−0.135875	+	0.233651i
$533$		−	1.35275e15i		−	1.36213i
$534$	−9.01925e13	+	3.34507e14i	−0.0898863	+	0.333372i
$535$	1.64948e14			0.162705
$536$	−8.44079e14	+	8.36187e14i	−0.824094	+	0.816388i
$537$	3.32207e14			0.321033
$538$	−1.15194e14	+	4.27234e14i	−0.110186	+	0.408661i
$539$			7.65621e14i			0.724896i
$540$	−1.25985e15	−	7.32643e14i	−1.18073	−	0.686636i
$541$			1.32152e15i			1.22599i	0.790086	+	0.612995i	$0.210036\pi$
$541$			1.32152e15i			1.22599i	−0.790086	+	0.612995i	$0.789964\pi$
$542$	1.63359e15	+	4.40460e14i	1.50019	+	0.404493i
$543$	−1.53717e15			−1.39740
$544$	−4.60207e14	−	1.77292e15i	−0.414152	−	1.59549i
$545$	8.09364e12			0.00721046
$546$	3.29667e14	+	8.88874e13i	0.290747	+	0.0783936i
$547$			1.58642e15i			1.38513i	0.721357	+	0.692563i	$0.243519\pi$
$547$			1.58642e15i			1.38513i	−0.721357	+	0.692563i	$0.756481\pi$
$548$	5.93651e14	+	3.45228e14i	0.513143	+	0.298409i
$549$		−	1.77745e14i		−	0.152107i
$550$	−1.49475e14	+	5.54375e14i	−0.126641	+	0.469687i
$551$	−6.15943e14			−0.516662
$552$	5.89582e14	−	5.84069e14i	0.489643	−	0.485064i
$553$	−2.64016e14			−0.217091
$554$	2.68727e14	−	9.96658e14i	0.218780	−	0.811414i
$555$		−	2.69958e14i		−	0.217613i
$556$	2.80758e13	−	4.82789e13i	0.0224089	−	0.0385342i
$557$			1.21582e15i			0.960869i	0.877031	+	0.480435i	$0.159521\pi$
$557$			1.21582e15i			0.960869i	−0.877031	+	0.480435i	$0.840479\pi$
$558$	3.62051e14	+	9.76191e13i	0.283323	+	0.0763918i
$559$	7.84025e14			0.607526
$560$	3.31515e14	−	1.88642e14i	0.254372	−	0.144745i
$561$	1.50507e15			1.14356
$562$	−3.70194e14	−	9.98148e13i	−0.278535	−	0.0751009i
$563$			2.27297e15i			1.69355i	0.531951	+	0.846775i	$0.321459\pi$
$563$			2.27297e15i			1.69355i	−0.531951	+	0.846775i	$0.678541\pi$
$564$	−2.19931e14	+	3.78191e14i	−0.162275	+	0.279046i
$565$		−	1.58933e15i		−	1.16131i
$566$	6.45722e14	−	2.39486e15i	0.467256	−	1.73297i
$567$	−2.52578e14			−0.181004
$568$	−2.37066e14	−	2.39304e14i	−0.168249	−	0.169837i
$569$	−3.01866e14			−0.212176			−0.106088	−	0.994357i	$-0.533833\pi$
$569$	−3.01866e14			−0.212176			−0.106088	+	0.994357i	$0.533833\pi$
$570$	5.12418e14	−	1.90046e15i	0.356708	−	1.32296i
$571$		−	2.23731e15i		−	1.54251i	−0.636529	−	0.771253i	$-0.719630\pi$
$571$		−	2.23731e15i		−	1.54251i	0.636529	−	0.771253i	$-0.280370\pi$
$572$	1.40519e15	+	8.17167e14i	0.959530	+	0.557998i
$573$		−	1.97116e15i		−	1.33313i
$574$	−3.09604e14	−	8.34780e13i	−0.207392	−	0.0559186i
$575$	−7.28414e14			−0.483287
$576$	−2.53692e12	+	2.70047e14i	−0.00166718	+	0.177466i
$577$	−1.67626e15			−1.09113			−0.545564	−	0.838069i	$-0.683684\pi$
$577$	−1.67626e15			−1.09113			−0.545564	+	0.838069i	$0.683684\pi$
$578$	2.57137e15	+	6.93312e14i	1.65791	+	0.447019i
$579$		−	1.00003e15i		−	0.638675i
$580$	7.64467e14	+	4.44563e14i	0.483620	+	0.281241i
$581$		−	3.87155e14i		−	0.242614i
$582$	−3.10589e14	+	1.15192e15i	−0.192801	+	0.715064i
$583$	1.17991e15			0.725561
$584$	−1.67460e14	−	1.69040e14i	−0.102009	−	0.102972i
$585$	5.45833e14			0.329384
$586$	−6.59654e14	+	2.44653e15i	−0.394348	+	1.46256i
$587$		−	1.50304e15i		−	0.890144i	−0.895495	−	0.445072i	$-0.853178\pi$
$587$		−	1.50304e15i		−	0.890144i	0.895495	−	0.445072i	$-0.146822\pi$
$588$	−7.36395e14	+	1.26630e15i	−0.432052	+	0.742953i
$589$			3.36007e15i			1.95305i
$590$	−3.84477e15	−	1.03666e15i	−2.21403	−	0.596966i
$591$	−3.63165e14			−0.207192
$592$	−2.88460e14	+	1.64142e14i	−0.163048	+	0.0927792i
$593$	−1.38749e14			−0.0777015			−0.0388507	−	0.999245i	$-0.512370\pi$
$593$	−1.38749e14			−0.0777015			−0.0388507	+	0.999245i	$0.512370\pi$
$594$	−1.42149e15	−	3.83274e14i	−0.788713	−	0.212659i
$595$			8.77560e14i			0.482429i
$596$	1.18275e15	−	2.03384e15i	0.644225	−	1.10780i
$597$			2.80510e15i			1.51387i
$598$	−5.36853e14	+	1.99109e15i	−0.287077	+	1.06472i
$599$	1.44893e15			0.767717			0.383859	−	0.923392i	$-0.374595\pi$
$599$	1.44893e15			0.767717			0.383859	+	0.923392i	$0.374595\pi$
$600$	−7.80437e14	+	7.73140e14i	−0.409738	+	0.405906i
$601$	−7.86748e13			−0.0409285			−0.0204643	−	0.999791i	$-0.506514\pi$
$601$	−7.86748e13			−0.0409285			−0.0204643	+	0.999791i	$0.506514\pi$
$602$	4.83820e13	−	1.79440e14i	0.0249404	−	0.0924992i
$603$			4.03034e14i			0.205872i
$604$	7.98735e14	+	4.64491e14i	0.404296	+	0.235112i
$605$		−	1.05788e15i		−	0.530616i
$606$	5.00421e14	+	1.34927e14i	0.248734	+	0.0670657i
$607$	1.57249e15			0.774550			0.387275	−	0.921964i	$-0.373416\pi$
$607$	1.57249e15			0.774550			0.387275	+	0.921964i	$0.373416\pi$
$608$	−2.34228e15	+	6.08000e14i	−1.14332	+	0.296779i
$609$	1.87648e14			0.0907713
$610$	−2.20787e15	−	5.95303e14i	−1.05842	−	0.285380i
$611$		−	1.08710e15i		−	0.516467i
$612$	−5.37112e14	−	3.12348e14i	−0.252890	−	0.147064i
$613$		−	8.60982e14i		−	0.401755i	−0.979616	−	0.200878i	$-0.935621\pi$
$613$		−	8.60982e14i		−	0.401755i	0.979616	−	0.200878i	$-0.0643794\pi$
$614$	−4.11627e14	+	1.52665e15i	−0.190361	+	0.706013i
$615$	2.37578e15			1.08891
$616$	2.73739e14	−	2.71179e14i	0.124349	−	0.123186i
$617$	−9.54957e14			−0.429947			−0.214974	−	0.976620i	$-0.568967\pi$
$617$	−9.54957e14			−0.429947			−0.214974	+	0.976620i	$0.568967\pi$
$618$	2.00659e14	−	7.44206e14i	0.0895409	−	0.332090i
$619$		−	1.65458e13i		−	0.00731793i	−0.999993	−	0.00365896i	$-0.998835\pi$
$619$		−	1.65458e13i		−	0.00731793i	0.999993	−	0.00365896i	$-0.00116469\pi$
$620$	2.42516e15	−	4.17029e15i	1.06313	−	1.82815i
$621$		−	1.86775e15i		−	0.811550i
$622$	−3.83372e15	−	1.03368e15i	−1.65110	−	0.445183i
$623$	−2.04067e14			−0.0871141
$624$	1.53815e15	+	2.70311e15i	0.650854	+	1.14380i
$625$	−2.93617e15			−1.23152
$626$	4.14062e15	+	1.11643e15i	1.72150	+	0.464164i
$627$		−	1.98841e15i		−	0.819474i
$628$	−9.24620e13	+	1.58997e14i	−0.0377733	+	0.0649547i
$629$		−	7.63587e14i		−	0.309229i
$630$	3.36832e13	−	1.24925e14i	0.0135220	−	0.0501505i
$631$	2.66470e15			1.06044			0.530221	−	0.847859i	$-0.322109\pi$
$631$	2.66470e15			1.06044			0.530221	+	0.847859i	$0.322109\pi$
$632$	−1.69249e15	−	1.70847e15i	−0.667702	−	0.674004i
$633$	2.59843e14			0.101623
$634$	−8.78556e14	+	3.25840e15i	−0.340626	+	1.26332i
$635$			4.82788e15i			1.85567i
$636$	1.95152e15	+	1.13487e15i	0.743634	+	0.432448i
$637$		−	3.63994e15i		−	1.37508i
$638$	8.62551e14	+	2.32568e14i	0.323051	+	0.0871036i
$639$	−1.14264e14			−0.0424281
$640$	3.34591e15	+	9.35954e14i	1.23175	+	0.344560i
$641$	2.68473e15			0.979901			0.489951	−	0.871750i	$-0.337015\pi$
$641$	2.68473e15			0.979901			0.489951	+	0.871750i	$0.337015\pi$
$642$	3.07819e14	+	8.29967e13i	0.111392	+	0.0300343i
$643$			4.42246e14i			0.158673i	0.996848	+	0.0793367i	$0.0252802\pi$
$643$			4.42246e14i			0.158673i	−0.996848	+	0.0793367i	$0.974720\pi$
$644$	4.22571e14	+	2.45739e14i	0.150324	+	0.0874182i
$645$			1.37695e15i			0.485668i
$646$	1.44940e15	−	5.37554e15i	0.506884	−	1.87994i
$647$	−3.79844e15			−1.31714			−0.658570	−	0.752520i	$-0.728838\pi$
$647$	−3.79844e15			−1.31714			−0.658570	+	0.752520i	$0.728838\pi$
$648$	−1.61916e15	−	1.63444e15i	−0.556708	−	0.561963i
$649$	−4.02270e15			−1.37142
$650$	7.10639e14	−	2.63563e15i	0.240229	−	0.890965i
$651$		−	1.02365e15i		−	0.343128i
$652$	−3.55953e14	+	6.12094e14i	−0.118313	+	0.203449i
$653$			5.25844e15i			1.73314i	0.499052	+	0.866572i	$0.333682\pi$
$653$			5.25844e15i			1.73314i	−0.499052	+	0.866572i	$0.666318\pi$
$654$	1.51040e13	+	4.07247e12i	0.00493646	+	0.00133101i
$655$	2.00142e15			0.648652
$656$	−1.44454e15	−	2.53861e15i	−0.464258	−	0.815877i
$657$	−8.07141e13			−0.0257241
$658$	−2.48804e14	−	6.70846e13i	−0.0786349	−	0.0212022i
$659$		−	3.68455e15i		−	1.15482i	−0.816454	−	0.577410i	$-0.804063\pi$
$659$		−	3.68455e15i		−	1.15482i	0.816454	−	0.577410i	$-0.195937\pi$
$660$	−1.43515e15	+	2.46788e15i	−0.446074	+	0.767066i
$661$			1.45382e15i			0.448130i	0.974574	+	0.224065i	$0.0719327\pi$
$661$			1.45382e15i			0.448130i	−0.974574	+	0.224065i	$0.928067\pi$
$662$	−1.06692e15	+	3.95702e15i	−0.326147	+	1.20962i
$663$	−7.15546e15			−2.16927
$664$	2.50530e15	−	2.48188e15i	0.753244	−	0.746201i
$665$	1.15938e15			0.345707
$666$	−2.93086e13	+	1.08700e14i	−0.00866737	+	0.0321457i
$667$			1.13334e15i			0.332405i
$668$	1.17139e15	+	6.81202e14i	0.340746	+	0.198155i
$669$			4.55930e14i			0.131539i
$670$	5.00631e15	+	1.34984e15i	1.43254	+	0.386252i
$671$	−2.31004e15			−0.655611
$672$	7.13579e14	−	1.85228e14i	0.200868	−	0.0521406i
$673$	4.59102e15			1.28182			0.640909	−	0.767617i	$-0.278557\pi$
$673$	4.59102e15			1.28182			0.640909	+	0.767617i	$0.278557\pi$
$674$	1.64818e15	+	4.44397e14i	0.456432	+	0.123067i
$675$			2.47237e15i			0.679113i
$676$	−3.50778e15	−	2.03989e15i	−0.955709	−	0.555776i
$677$			2.08953e15i			0.564691i	0.959313	+	0.282345i	$0.0911124\pi$
$677$			2.08953e15i			0.564691i	−0.959313	+	0.282345i	$0.908888\pi$
$678$	7.99704e14	−	2.96595e15i	0.214371	−	0.795062i
$679$	−7.02730e14			−0.186855
$680$	−5.67874e15	+	5.62564e15i	−1.49780	+	1.48379i
$681$	1.91880e15			0.502019
$682$	1.26869e15	−	4.70535e15i	0.329263	−	1.22118i
$683$		−	3.35863e14i		−	0.0864667i	−0.999065	−	0.0432333i	$-0.986234\pi$
$683$		−	3.35863e14i		−	0.0864667i	0.999065	−	0.0432333i	$-0.0137659\pi$
$684$	−4.12657e14	+	7.09602e14i	−0.105385	+	0.181220i
$685$		−	2.99693e15i		−	0.759240i
$686$	−1.71218e15	−	4.61650e14i	−0.430294	−	0.116019i
$687$	1.09408e15			0.272763
$688$	1.47132e15	−	8.37225e14i	0.363891	−	0.207065i
$689$	−5.60960e15			−1.37634
$690$	−3.49686e15	−	9.42852e14i	−0.851155	−	0.229495i
$691$			6.13314e14i			0.148099i	0.997255	+	0.0740497i	$0.0235923\pi$
$691$			6.13314e14i			0.148099i	−0.997255	+	0.0740497i	$0.976408\pi$
$692$	−3.03015e15	+	5.21062e15i	−0.725906	+	1.24826i
$693$		−	1.30706e14i		−	0.0310644i
$694$	−5.83521e14	+	2.16417e15i	−0.137588	+	0.510287i
$695$	−2.43727e14			−0.0570148
$696$	1.20293e15	+	1.21428e15i	0.279183	+	0.281818i
$697$	6.72000e15			1.54735
$698$	−4.98163e14	+	1.84759e15i	−0.113806	+	0.422087i
$699$			3.45772e15i			0.783728i
$700$	−5.59362e14	−	3.25288e14i	−0.125792	−	0.0731524i
$701$		−	7.14041e15i		−	1.59321i	−0.604498	−	0.796606i	$-0.706626\pi$
$701$		−	7.14041e15i		−	1.59321i	0.604498	−	0.796606i	$-0.293374\pi$
$702$	6.75811e15	+	1.82218e15i	1.49614	+	0.403400i
$703$	−1.00881e15			−0.221592
$704$	3.50964e15	+	3.29708e13i	0.764914	+	0.00718587i
$705$	1.90923e15			0.412874
$706$	−2.36959e15	−	6.38909e14i	−0.508450	−	0.137092i
$707$			3.05283e14i			0.0649973i
$708$	−6.65335e15	−	3.86914e15i	−1.40559	−	0.817394i
$709$		−	1.70696e15i		−	0.357823i	−0.983865	−	0.178911i	$-0.942742\pi$
$709$		−	1.70696e15i		−	0.357823i	0.983865	−	0.178911i	$-0.0572576\pi$
$710$	−3.82691e14	+	1.41933e15i	−0.0796027	+	0.295231i
$711$	−8.15765e14			−0.168377
$712$	−1.30818e15	−	1.32053e15i	−0.267934	−	0.270463i
$713$	6.18254e15			1.25653
$714$	−4.41561e14	+	1.63767e15i	−0.0890534	+	0.330282i
$715$		−	7.09386e15i		−	1.41971i
$716$	−8.96011e14	+	1.54077e15i	−0.177947	+	0.305997i
$717$		−	5.67816e15i		−	1.11906i
$718$	4.85011e15	+	1.30773e15i	0.948566	+	0.255760i
$719$	7.81443e15			1.51666			0.758330	−	0.651870i	$-0.226015\pi$
$719$	7.81443e15			1.51666			0.758330	+	0.651870i	$0.226015\pi$
$720$	1.02432e15	−	5.82871e14i	0.197292	−	0.112265i
$721$	4.54005e14			0.0867793
$722$	−2.01189e15	−	5.42463e14i	−0.381637	−	0.102900i
$723$		−	6.33009e14i		−	0.119165i
$724$	4.14597e15	−	7.12938e15i	0.774576	−	1.33196i
$725$		−	1.50021e15i		−	0.278160i
$726$	5.32290e14	−	1.97417e15i	0.0979484	−	0.363272i
$727$	9.77013e12			0.00178427			0.000892136	−	1.00000i	$-0.499716\pi$
$727$	9.77013e12			0.00178427			0.000892136		1.00000i	$0.499716\pi$
$728$	−1.30142e15	+	1.28925e15i	−0.235882	+	0.233677i
$729$	−6.16439e15			−1.10889
$730$	−2.70327e14	+	1.00259e15i	−0.0482630	+	0.178998i
$731$			3.89476e15i			0.690137i
$732$	−3.82070e15	−	2.22186e15i	−0.671942	−	0.390756i
$733$			1.07577e16i			1.87780i	0.344191	+	0.938900i	$0.388153\pi$
$733$			1.07577e16i			1.87780i	−0.344191	+	0.938900i	$0.611847\pi$
$734$	−5.99100e15	−	1.61534e15i	−1.03794	−	0.279857i
$735$	6.39267e15			1.09926
$736$	1.11872e15	+	4.30981e15i	0.190939	+	0.735580i
$737$	5.23799e15			0.887346
$738$	−9.56624e14	−	2.57933e14i	−0.160854	−	0.0433707i
$739$			1.55149e14i			0.0258944i	0.999916	+	0.0129472i	$0.00412133\pi$
$739$			1.55149e14i			0.0258944i	−0.999916	+	0.0129472i	$0.995879\pi$
$740$	1.25206e15	+	7.28117e14i	0.207421	+	0.120622i
$741$			9.45339e15i			1.55449i
$742$	−3.46167e14	+	1.28387e15i	−0.0565020	+	0.209555i
$743$	−6.27422e15			−1.01653			−0.508266	−	0.861200i	$-0.669713\pi$
$743$	−6.27422e15			−1.01653			−0.508266	+	0.861200i	$0.669713\pi$
$744$	6.62410e15	−	6.56216e15i	1.06531	−	1.05535i
$745$	−1.02675e16			−1.63910
$746$	−1.46497e15	+	5.43332e15i	−0.232149	+	0.860996i
$747$		−	1.19624e15i		−	0.188172i
$748$	−4.05940e15	+	6.98051e15i	−0.633874	+	1.09000i
$749$			1.87786e14i			0.0291080i
$750$	−2.64990e15	−	7.14488e14i	−0.407749	−	0.109941i
$751$	−6.57869e15			−1.00489			−0.502447	−	0.864608i	$-0.667567\pi$
$751$	−6.57869e15			−1.00489			−0.502447	+	0.864608i	$0.667567\pi$
$752$	−1.16086e15	−	2.04008e15i	−0.176029	−	0.309349i
$753$	−6.13093e15			−0.922898
$754$	−4.10077e15	−	1.10568e15i	−0.612806	−	0.165230i
$755$		−	4.03226e15i		−	0.598192i
$756$	8.34082e14	−	1.43428e15i	0.122840	−	0.211234i
$757$		−	2.54343e15i		−	0.371871i	−0.982562	−	0.185935i	$-0.940468\pi$
$757$		−	2.54343e15i		−	0.371871i	0.982562	−	0.185935i	$-0.0595315\pi$
$758$	3.25174e15	−	1.20601e16i	0.471992	−	1.75053i
$759$	−3.65869e15			−0.527225
$760$	7.43228e15	+	7.50243e15i	1.06328	+	1.07332i
$761$	−5.98810e15			−0.850498			−0.425249	−	0.905076i	$-0.639813\pi$
$761$	−5.98810e15			−0.850498			−0.425249	+	0.905076i	$0.639813\pi$
$762$	−2.42924e15	+	9.00960e15i	−0.342545	+	1.27044i
$763$			9.21426e12i			0.00128996i
$764$	9.14224e15	+	5.31651e15i	1.27069	+	0.738947i
$765$			2.71151e15i			0.374173i
$766$	5.71810e15	+	1.54176e15i	0.783418	+	0.211232i
$767$	1.91249e16			2.60150
$768$	5.77306e15	+	3.43020e15i	0.779685	+	0.463268i
$769$	−7.50045e15			−1.00576			−0.502878	−	0.864358i	$-0.667725\pi$
$769$	−7.50045e15			−1.00576			−0.502878	+	0.864358i	$0.667725\pi$
$770$	−1.62357e15	−	4.37760e14i	−0.216158	−	0.0582823i
$771$			1.10880e16i			1.46573i
$772$	4.63813e15	+	2.69722e15i	0.608762	+	0.354015i
$773$		−	6.98863e15i		−	0.910762i	−0.890297	−	0.455381i	$-0.849503\pi$
$773$		−	6.98863e15i		−	0.910762i	0.890297	−	0.455381i	$-0.150497\pi$
$774$	1.49492e14	−	5.54437e14i	0.0193438	−	0.0717426i
$775$	−8.18390e15			−1.05148
$776$	−4.50489e15	−	4.54741e15i	−0.574705	−	0.580129i
$777$	3.07335e14			0.0389311
$778$	3.12732e15	−	1.15986e16i	0.393355	−	1.45888i
$779$		−	8.87809e15i		−	1.10883i
$780$	6.82307e15	−	1.17329e16i	0.846173	−	1.45507i
$781$			1.48501e15i			0.182873i
$782$	−9.89103e15	−	2.66690e15i	−1.20950	−	0.326114i
$783$	3.84675e15			0.467094
$784$	−3.88693e15	−	6.83080e15i	−0.468672	−	0.823632i
$785$	8.02666e14			0.0961063
$786$	3.73498e15	+	1.00705e15i	0.444083	+	0.119737i
$787$			2.82969e15i			0.334102i	0.985948	+	0.167051i	$0.0534244\pi$
$787$			2.82969e15i			0.334102i	−0.985948	+	0.167051i	$0.946576\pi$
$788$	9.79510e14	−	1.68436e15i	0.114846	−	0.197488i
$789$			2.73167e15i			0.318057i
$790$	−2.73216e15	+	1.01331e16i	−0.315905	+	1.17163i
$791$	1.80939e15			0.207759
$792$	8.45806e14	−	8.37897e14i	0.0964456	−	0.0955438i
$793$	1.09825e16			1.24365
$794$	3.01280e15	−	1.11739e16i	0.338811	−	1.25659i
$795$		−	9.85189e15i		−	1.10027i
$796$	−1.30101e16	−	7.56578e15i	−1.44297	−	0.839136i
$797$			7.15437e15i			0.788044i	0.919101	+	0.394022i	$0.128917\pi$
$797$			7.15437e15i			0.788044i	−0.919101	+	0.394022i	$0.871083\pi$
$798$	2.16359e15	+	5.83366e14i	0.236679	+	0.0638153i
$799$	5.40033e15			0.586696
$800$	−1.48087e15	−	5.70494e15i	−0.159779	−	0.615540i
$801$	−6.30532e14			−0.0675660
$802$	2.15648e15	+	5.81449e14i	0.229502	+	0.0618803i
$803$			1.04899e15i			0.110876i
$804$	8.66337e15	+	5.03804e15i	0.909450	+	0.528875i
$805$		−	2.13327e15i		−	0.222417i
$806$	−6.03168e15	+	2.23704e16i	−0.624591	+	2.31649i
$807$	3.73234e15			0.383864
$808$	−1.97550e15	+	1.95703e15i	−0.201797	+	0.199910i
$809$	−6.06373e15			−0.615209			−0.307605	−	0.951514i	$-0.599527\pi$
$809$	−6.06373e15			−0.615209			−0.307605	+	0.951514i	$0.599527\pi$
$810$	−2.61378e15	+	9.69403e15i	−0.263392	+	0.976870i
$811$			1.25004e16i			1.25115i	0.780164	+	0.625576i	$0.215136\pi$
$811$			1.25004e16i			1.25115i	−0.780164	+	0.625576i	$0.784864\pi$
$812$	−5.06115e14	+	8.70312e14i	−0.0503142	+	0.0865200i
$813$		−	1.42711e16i		−	1.40916i
$814$	1.41271e15	+	3.80906e14i	0.138554	+	0.0373580i
$815$	3.09004e15			0.301021
$816$	−1.34281e16	+	7.64099e15i	−1.29933	+	0.739356i
$817$	5.14554e15			0.494549
$818$	8.80284e15	+	2.37349e15i	0.840388	+	0.226592i
$819$			6.21407e14i			0.0589271i
$820$	−6.40784e15	+	1.10189e16i	−0.603581	+	1.03791i
$821$		−	9.11023e15i		−	0.852397i	−0.904630	−	0.426198i	$-0.859853\pi$
$821$		−	9.11023e15i		−	0.852397i	0.904630	−	0.426198i	$-0.140147\pi$
$822$	1.50796e15	−	5.59276e15i	0.140151	−	0.519794i
$823$	−1.90354e16			−1.75737			−0.878683	−	0.477407i	$-0.841577\pi$
$823$	−1.90354e16			−1.75737			−0.878683	+	0.477407i	$0.841577\pi$
$824$	2.91042e15	+	2.93789e15i	0.266905	+	0.269424i
$825$	4.84305e15			0.441187
$826$	1.18019e15	−	4.37710e15i	0.106798	−	0.396092i
$827$		−	6.03027e15i		−	0.542071i	−0.962569	−	0.271036i	$-0.912634\pi$
$827$		−	6.03027e15i		−	0.542071i	0.962569	−	0.271036i	$-0.0873661\pi$
$828$	1.30567e15	+	7.59291e14i	0.116592	+	0.0678018i
$829$			1.35457e16i			1.20158i	0.799408	+	0.600788i	$0.205146\pi$
$829$			1.35457e16i			1.20158i	−0.799408	+	0.600788i	$0.794854\pi$
$830$	−1.48592e16	−	4.00645e15i	−1.30938	−	0.353045i
$831$	−8.70687e15			−0.762178
$832$	−1.66857e16	−	1.56751e14i	−1.45099	−	0.0136311i
$833$	1.80820e16			1.56206
$834$	−4.54834e14	−	1.22636e14i	−0.0390337	−	0.0105246i
$835$		−	5.91354e15i		−	0.504164i
$836$	9.22226e15	+	5.36305e15i	0.781093	+	0.454231i
$837$		−	2.09846e16i		−	1.76568i
$838$	3.96701e15	−	1.47129e16i	0.331605	−	1.22986i
$839$	5.63944e15			0.468322			0.234161	−	0.972198i	$-0.424766\pi$
$839$	5.63944e15			0.468322			0.234161	+	0.972198i	$0.424766\pi$
$840$	−2.26426e15	−	2.28563e15i	−0.186805	−	0.188569i
$841$	9.86633e15			0.808682
$842$	1.42203e13	−	5.27403e13i	0.00115795	−	0.00429463i
$843$			3.23404e15i			0.261634i
$844$	−7.00837e14	+	1.20515e15i	−0.0563292	+	0.0968633i
$845$			1.77084e16i			1.41406i
$846$	−7.68762e14	−	2.07280e14i	−0.0609895	−	0.0164445i
$847$	1.20434e15			0.0949275
$848$	−1.05271e16	+	5.99023e15i	−0.824388	+	0.469101i
$849$	−2.09217e16			−1.62781
$850$	1.30929e16	+	3.53020e15i	1.01212	+	0.272895i
$851$			1.85621e15i			0.142566i
$852$	−1.42833e15	+	2.45614e15i	−0.108996	+	0.187428i
$853$			2.66012e15i			0.201689i	0.994902	+	0.100844i	$0.0321544\pi$
$853$			2.66012e15i			0.201689i	−0.994902	+	0.100844i	$0.967846\pi$
$854$	6.77726e14	−	2.51356e15i	0.0510547	−	0.189353i
$855$	3.58229e15			0.268131
$856$	−1.21517e15	+	1.20381e15i	−0.0903717	+	0.0895267i
$857$	6.62417e15			0.489482			0.244741	−	0.969588i	$-0.421297\pi$
$857$	6.62417e15			0.489482			0.244741	+	0.969588i	$0.421297\pi$
$858$	3.56941e15	−	1.32383e16i	0.262070	−	0.971967i
$859$			2.28112e16i			1.66412i	0.554683	+	0.832062i	$0.312839\pi$
$859$			2.28112e16i			1.66412i	−0.554683	+	0.832062i	$0.687161\pi$
$860$	−6.38629e15	−	3.71384e15i	−0.462922	−	0.269204i
$861$			2.70472e15i			0.194807i
$862$	−8.21229e14	−	2.21426e14i	−0.0587725	−	0.0158467i
$863$	−2.00538e16			−1.42606			−0.713031	−	0.701133i	$-0.752678\pi$
$863$	−2.00538e16			−1.42606			−0.713031	+	0.701133i	$0.752678\pi$
$864$	1.46282e16	−	3.79714e15i	1.03363	−	0.268307i
$865$	2.63048e16			1.84691
$866$	1.37035e16	+	3.69484e15i	0.956054	+	0.257779i
$867$		−	2.24636e16i		−	1.55731i
$868$	4.74769e15	+	2.76094e15i	0.327057	+	0.190195i
$869$			1.06020e16i			0.725736i
$870$	1.94186e15	−	7.20201e15i	0.132088	−	0.489889i
$871$	−2.49026e16			−1.68324
$872$	−5.96260e13	+	5.90685e13i	−0.00400493	+	0.00396748i
$873$	−2.17131e15			−0.144925
$874$	−3.52336e15	+	1.30675e16i	−0.233692	+	0.866720i
$875$		−	1.61658e15i		−	0.106550i
$876$	−1.00895e15	+	1.73498e15i	−0.0660840	+	0.113638i
$877$		−	2.76399e16i		−	1.79903i	−0.436887	−	0.899516i	$-0.643919\pi$
$877$		−	2.76399e16i		−	1.79903i	0.436887	−	0.899516i	$-0.356081\pi$
$878$	2.16377e16	+	5.83413e15i	1.39956	+	0.377361i
$879$	2.13731e16			1.37381
$880$	−7.57521e15	−	1.33125e16i	−0.483883	−	0.850364i
$881$	−2.51486e16			−1.59642			−0.798208	−	0.602382i	$-0.794218\pi$
$881$	−2.51486e16			−1.59642			−0.798208	+	0.602382i	$0.794218\pi$
$882$	−2.57405e15	−	6.94036e14i	−0.162383	−	0.0437829i
$883$		−	1.31245e16i		−	0.822810i	−0.911453	−	0.411405i	$-0.865038\pi$
$883$		−	1.31245e16i		−	0.822810i	0.911453	−	0.411405i	$-0.134962\pi$
$884$	1.92993e16	−	3.31870e16i	1.20242	−	2.06767i
$885$			3.35882e16i			2.07969i
$886$	3.53051e15	−	1.30940e16i	0.217246	−	0.805726i
$887$	−5.71207e15			−0.349312			−0.174656	−	0.984630i	$-0.555881\pi$
$887$	−5.71207e15			−0.349312			−0.174656	+	0.984630i	$0.555881\pi$
$888$	1.97019e15	+	1.98878e15i	0.119739	+	0.120869i
$889$	−5.49633e15			−0.331981
$890$	−2.11177e15	+	7.83218e15i	−0.126766	+	0.470151i
$891$			1.01426e16i			0.605096i
$892$	−2.11460e15	−	1.22971e15i	−0.125378	−	0.0729116i
$893$		−	7.13461e15i		−	0.420424i
$894$	−1.91608e16	−	5.16628e15i	−1.12216	−	0.302567i
$895$	7.77831e15			0.452750
$896$	−1.06554e15	+	3.80917e15i	−0.0616420	+	0.220362i
$897$	1.73943e16			1.00011
$898$	1.09208e16	+	2.94457e15i	0.624075	+	0.168268i
$899$			1.27333e16i			0.723209i
$900$	−1.72833e15	−	1.00508e15i	−0.0975649	−	0.0567372i
$901$		−	2.78665e16i		−	1.56349i
$902$	−3.35219e15	+	1.24327e16i	−0.186936	+	0.693310i
$903$	−1.56760e15			−0.0868864
$904$	1.15992e16	+	1.17086e16i	0.639000	+	0.645031i
$905$	−3.59913e16			−1.97075
$906$	2.02891e15	−	7.52485e15i	0.110423	−	0.409537i
$907$			1.52922e16i			0.827235i	0.910451	+	0.413618i	$0.135735\pi$
$907$			1.52922e16i			0.827235i	−0.910451	+	0.413618i	$0.864265\pi$
$908$	−5.17529e15	+	8.89938e15i	−0.278267	+	0.478506i
$909$			9.43271e14i			0.0504121i
$910$	7.71884e15	+	2.08121e15i	0.410038	+	0.110558i
$911$	−5.29684e14			−0.0279683			−0.0139842	−	0.999902i	$-0.504451\pi$
$911$	−5.29684e14			−0.0279683			−0.0139842	+	0.999902i	$0.504451\pi$
$912$	1.00948e16	+	1.77404e16i	0.529820	+	0.931093i
$913$	−1.55468e16			−0.811058
$914$	−3.15729e16	−	8.51294e15i	−1.63723	−	0.441444i
$915$			1.92881e16i			0.994198i
$916$	−2.95089e15	+	5.07433e15i	−0.151192	+	0.259988i
$917$			2.27853e15i			0.116044i
$918$	−9.05193e15	+	3.35719e16i	−0.458254	+	1.69958i
$919$	2.61618e16			1.31654			0.658268	−	0.752783i	$-0.271289\pi$
$919$	2.61618e16			1.31654			0.658268	+	0.752783i	$0.271289\pi$
$920$	1.38045e16	−	1.36754e16i	0.690539	−	0.684082i
$921$	1.33369e16			0.663173
$922$	3.17117e14	−	1.17613e15i	0.0156747	−	0.0581346i
$923$		−	7.06011e15i		−	0.346898i
$924$	−2.80957e15	−	1.63386e15i	−0.137229	−	0.0798030i
$925$		−	2.45709e15i		−	0.119300i
$926$	−2.64848e15	−	7.14105e14i	−0.127831	−	0.0344669i
$927$	1.40280e15			0.0673063
$928$	−8.87631e15	+	2.30408e15i	−0.423369	+	0.109896i
$929$	−2.14173e16			−1.01550			−0.507749	−	0.861505i	$-0.669522\pi$
$929$	−2.14173e16			−1.01550			−0.507749	+	0.861505i	$0.669522\pi$
$930$	−3.92881e16	−	1.05932e16i	−1.85185	−	0.499309i
$931$		−	2.38889e16i		−	1.11937i
$932$	−1.60369e16	−	9.32600e15i	−0.747022	−	0.434418i
$933$			3.34916e16i			1.55091i
$934$	3.50081e14	−	1.29838e15i	0.0161161	−	0.0597717i
$935$	3.52398e16			1.61276
$936$	−4.02116e15	+	3.98356e15i	−0.182951	+	0.181240i
$937$	1.84540e16			0.834685			0.417343	−	0.908749i	$-0.362961\pi$
$937$	1.84540e16			0.834685			0.417343	+	0.908749i	$0.362961\pi$
$938$	−1.53673e15	+	5.69946e15i	−0.0691008	+	0.256282i
$939$		−	3.61727e16i		−	1.61704i
$940$	−5.14947e15	+	8.85499e15i	−0.228854	+	0.393536i
$941$			1.10663e16i			0.488946i	0.969656	+	0.244473i	$0.0786149\pi$
$941$			1.10663e16i			0.488946i	−0.969656	+	0.244473i	$0.921385\pi$
$942$	1.49790e15	+	4.03877e14i	0.0657967	+	0.0177406i
$943$	−1.63357e16			−0.713385
$944$	3.58902e16	−	2.04226e16i	1.55822	−	0.886675i
$945$	−7.24070e15			−0.312540
$946$	−7.20568e15	−	1.94285e15i	−0.309224	−	0.0833756i
$947$			1.56625e16i			0.668244i	0.942530	+	0.334122i	$0.108440\pi$
$947$			1.56625e16i			0.668244i	−0.942530	+	0.334122i	$0.891560\pi$
$948$	−1.01973e16	+	1.75352e16i	−0.432552	+	0.743814i
$949$		−	4.98715e15i		−	0.210324i
$950$	4.66391e15	−	1.72976e16i	0.195556	−	0.725279i
$951$	2.84656e16			1.18666
$952$	−6.40455e15	−	6.46500e15i	−0.265452	−	0.267957i
$953$	2.46314e16			1.01503			0.507515	−	0.861643i	$-0.330564\pi$
$953$	2.46314e16			1.01503			0.507515	+	0.861643i	$0.330564\pi$
$954$	−1.06959e15	+	3.96693e15i	−0.0438231	+	0.162532i
$955$		−	4.61529e16i		−	1.88010i
$956$	2.63353e16	+	1.53149e16i	1.06665	+	0.620290i
$957$		−	7.53530e15i		−	0.303448i
$958$	5.28812e15	+	1.42583e15i	0.211734	+	0.0570895i
$959$	3.41188e15			0.135829
$960$	2.75295e14	−	2.93043e16i	0.0108970	−	1.15995i
$961$	4.40539e16			1.73383
$962$	−6.71636e15	−	1.81092e15i	−0.262828	−	0.0708657i
$963$			5.80226e14i			0.0225763i
$964$	2.93590e15	+	1.70732e15i	0.113584	+	0.0660529i
$965$		−	2.34147e16i		−	0.900717i
$966$	1.07340e15	−	3.98102e15i	0.0410568	−	0.152272i
$967$	1.75674e16			0.668130			0.334065	−	0.942550i	$-0.391579\pi$
$967$	1.75674e16			0.668130			0.334065	+	0.942550i	$0.391579\pi$
$968$	7.72052e15	+	7.79339e15i	0.291966	+	0.294721i
$969$	−4.69611e16			−1.76586
$970$	−7.27216e15	+	2.69711e16i	−0.271906	+	1.00845i
$971$			1.47579e15i			0.0548679i	0.999624	+	0.0274339i	$0.00873359\pi$
$971$			1.47579e15i			0.0548679i	−0.999624	+	0.0274339i	$0.991266\pi$
$972$	4.76589e15	−	8.19540e15i	0.176189	−	0.302974i
$973$		−	2.77472e14i		−	0.0102000i
$974$	2.62849e16	+	7.08715e15i	0.960799	+	0.259058i
$975$	−2.30250e16			−0.836902
$976$	2.06100e16	−	1.17277e16i	0.744910	−	0.423876i
$977$	−3.43891e16			−1.23595			−0.617975	−	0.786198i	$-0.712047\pi$
$977$	−3.43891e16			−1.23595			−0.617975	+	0.786198i	$0.712047\pi$
$978$	5.76651e15	+	1.55481e15i	0.206086	+	0.0555667i
$979$			8.19463e15i			0.291222i
$980$	−1.72420e16	+	2.96492e16i	−0.609319	+	1.04778i
$981$			2.84705e13i			0.00100049i
$982$	−1.03077e15	+	3.82294e15i	−0.0360204	+	0.133593i
$983$	−3.64560e16			−1.26685			−0.633424	−	0.773805i	$-0.718351\pi$
$983$	−3.64560e16			−1.26685			−0.633424	+	0.773805i	$0.718351\pi$
$984$	−1.75024e16	+	1.73388e16i	−0.604819	+	0.599163i
$985$	−8.50317e15			−0.292201
$986$	5.49264e15	−	2.03712e16i	0.187697	−	0.696135i
$987$			2.17357e15i			0.0738634i
$988$	−4.38448e16	−	2.54972e16i	−1.48168	−	0.861647i
$989$		−	9.46782e15i		−	0.318178i
$990$	−5.01655e15	−	1.35260e15i	−0.167653	−	0.0452040i
$991$	−1.42245e16			−0.472750			−0.236375	−	0.971662i	$-0.575959\pi$
$991$	−1.42245e16			−0.472750			−0.236375	+	0.971662i	$0.575959\pi$
$992$	1.25691e16	+	4.84217e16i	0.415423	+	1.60039i
$993$	3.45687e16			1.13622
$994$	−1.61585e15	−	4.35677e14i	−0.0528171	−	0.0142410i
$995$			6.56789e16i			2.13500i
$996$	−2.57137e16	−	1.49533e16i	−0.831261	−	0.483406i
$997$			6.02174e16i			1.93597i	0.251009	+	0.967985i	$0.419238\pi$
$997$			6.02174e16i			1.93597i	−0.251009	+	0.967985i	$0.580762\pi$
$998$	1.06014e16	−	3.93185e16i	0.338957	−	1.25713i
$999$	6.30032e15			0.200333

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.12.b.a.5.10	yes	10
3.2	odd	2		72.12.d.b.37.1		10
4.3	odd	2		32.12.b.a.17.8		10
8.3	odd	2		32.12.b.a.17.3		10
8.5	even	2	inner	8.12.b.a.5.9	✓	10
16.3	odd	4		256.12.a.o.1.3		10
16.5	even	4		256.12.a.p.1.3		10
16.11	odd	4		256.12.a.o.1.8		10
16.13	even	4		256.12.a.p.1.8		10
24.5	odd	2		72.12.d.b.37.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.12.b.a.5.9	✓	10	8.5	even	2	inner
8.12.b.a.5.10	yes	10	1.1	even	1	trivial
32.12.b.a.17.3		10	8.3	odd	2
32.12.b.a.17.8		10	4.3	odd	2
72.12.d.b.37.1		10	3.2	odd	2
72.12.d.b.37.2		10	24.5	odd	2
256.12.a.o.1.3		10	16.3	odd	4
256.12.a.o.1.8		10	16.11	odd	4
256.12.a.p.1.3		10	16.5	even	4
256.12.a.p.1.8		10	16.13	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(43.6944 + 11.7812i) q^{2} -381.717i q^{3} +(1770.40 + 1029.55i) q^{4} -8937.55i q^{5} +(4497.10 - 16678.9i) q^{6} +10175.0 q^{7} +(65227.5 + 65843.1i) q^{8} +31439.0 q^{9} +(105295. - 390521. i) q^{10} -408594. i q^{11} +(392996. - 675794. i) q^{12} +1.94255e6i q^{13} +(444591. + 119874. i) q^{14} -3.41162e6 q^{15} +(2.07436e6 + 3.64544e6i) q^{16} -9.64991e6 q^{17} +(1.37371e6 + 370391. i) q^{18} +1.27489e7i q^{19} +(9.20165e6 - 1.58231e7i) q^{20} -3.88398e6i q^{21} +(4.81374e6 - 1.78533e7i) q^{22} +2.34581e7 q^{23} +(2.51334e7 - 2.48984e7i) q^{24} -3.10517e7 q^{25} +(-2.28857e7 + 8.48786e7i) q^{26} -7.96209e7i q^{27} +(1.80139e7 + 1.04757e7i) q^{28} +4.83134e7i q^{29} +(-1.49069e8 - 4.01931e7i) q^{30} +2.63557e8 q^{31} +(4.76903e7 + 1.83724e8i) q^{32} -1.55967e8 q^{33} +(-4.21647e8 - 1.13688e8i) q^{34} -9.09397e7i q^{35} +(5.56598e7 + 3.23680e7i) q^{36} +7.91290e7i q^{37} +(-1.50198e8 + 5.57057e8i) q^{38} +7.41505e8 q^{39} +(5.88476e8 - 5.82974e8i) q^{40} -6.96380e8 q^{41} +(4.57581e7 - 1.69708e8i) q^{42} -4.03606e8i q^{43} +(4.20667e8 - 7.23376e8i) q^{44} -2.80988e8i q^{45} +(1.02499e9 + 2.76365e8i) q^{46} -5.59625e8 q^{47} +(1.39153e9 - 7.91820e8i) q^{48} -1.87380e9 q^{49} +(-1.35679e9 - 3.65828e8i) q^{50} +3.68354e9i q^{51} +(-1.99995e9 + 3.43910e9i) q^{52} +2.88775e9i q^{53} +(9.38032e8 - 3.47899e9i) q^{54} -3.65183e9 q^{55} +(6.63690e8 + 6.69954e8i) q^{56} +4.86648e9 q^{57} +(-5.69191e8 + 2.11102e9i) q^{58} -9.84523e9i q^{59} +(-6.03994e9 - 3.51243e9i) q^{60} -5.65364e9i q^{61} +(1.15160e10 + 3.10503e9i) q^{62} +3.19892e8 q^{63} +(-8.06933e7 + 8.58956e9i) q^{64} +1.73617e10 q^{65} +(-6.81489e9 - 1.83749e9i) q^{66} +1.28196e10i q^{67} +(-1.70842e10 - 9.93505e9i) q^{68} -8.95435e9i q^{69} +(1.07138e9 - 3.97356e9i) q^{70} -3.63445e9 q^{71} +(2.05069e9 + 2.07004e9i) q^{72} -2.56732e9 q^{73} +(-9.32237e8 + 3.45749e9i) q^{74} +1.18530e10i q^{75} +(-1.31256e10 + 2.25707e10i) q^{76} -4.15744e9i q^{77} +(3.23996e10 + 8.73585e9i) q^{78} -2.59475e10 q^{79} +(3.25813e10 - 1.85397e10i) q^{80} -2.48233e10 q^{81} +(-3.04279e10 - 8.20422e9i) q^{82} -3.80496e10i q^{83} +(3.99874e9 - 6.87621e9i) q^{84} +8.62466e10i q^{85} +(4.75498e9 - 1.76353e10i) q^{86} +1.84420e10 q^{87} +(2.69031e10 - 2.66515e10i) q^{88} -2.00557e10 q^{89} +(3.31039e9 - 1.22776e10i) q^{90} +1.97655e10i q^{91} +(4.15303e10 + 2.41512e10i) q^{92} -1.00604e11i q^{93} +(-2.44525e10 - 6.59307e9i) q^{94} +1.13944e11 q^{95} +(7.01305e10 - 1.82042e10i) q^{96} -6.90643e10 q^{97} +(-8.18744e10 - 2.20756e10i) q^{98} -1.28458e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9} + 29864 q^{10} - 476216 q^{12} + 2264272 q^{14} + 3391792 q^{15} + 3757072 q^{16} + 2639732 q^{17} + 2329130 q^{18}+ \cdots - 6194726778 q^{98}+O(q^{100}) \) 10 * q + 22 * q^2 + 436 * q^4 - 24308 * q^6 - 33616 * q^7 - 208472 * q^8 - 472394 * q^9 + 29864 * q^10 - 476216 * q^12 + 2264272 * q^14 + 3391792 * q^15 + 3757072 * q^16 + 2639732 * q^17 + 2329130 * q^18 + 8296432 * q^20 - 24201892 * q^22 - 45357808 * q^23 + 10668944 * q^24 - 41502654 * q^25 - 101931080 * q^26 - 95722144 * q^28 + 261362768 * q^30 + 442035392 * q^31 + 343908512 * q^32 - 54732216 * q^33 - 187103796 * q^34 - 431195700 * q^36 + 375100844 * q^38 - 431459312 * q^39 + 1519138784 * q^40 - 654907964 * q^41 - 3697737056 * q^42 - 4127012952 * q^44 + 6028867440 * q^46 - 560226528 * q^47 + 9357606048 * q^48 + 1143661722 * q^49 - 9626584226 * q^50 - 11595427248 * q^52 + 20050494008 * q^54 + 5632783984 * q^55 + 18698733760 * q^56 - 783862360 * q^57 - 22828679464 * q^58 - 43681325472 * q^60 + 40774631744 * q^62 - 14483624624 * q^63 + 55266728512 * q^64 - 80291360 * q^65 - 83128448712 * q^66 - 83303223768 * q^68 + 100120831168 * q^70 - 11769460176 * q^71 + 112862051672 * q^72 + 32304890372 * q^73 - 102103996184 * q^74 - 97501928568 * q^76 + 144445560944 * q^78 + 57291670496 * q^79 + 128322038976 * q^80 - 23172996094 * q^81 - 123309929604 * q^82 - 199990865984 * q^84 + 130201908124 * q^86 - 73844404272 * q^87 + 169216119632 * q^88 - 108276011804 * q^89 - 228506434984 * q^90 - 141139403232 * q^92 + 145336130016 * q^94 + 70146835376 * q^95 + 109508068928 * q^96 + 60995282900 * q^97 - 6194726778 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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