LMFDB - Embedded newform 8.12.b.a.5.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,12,Mod(5,8)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.14674544448$
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			5.8
Root			$9.13304 + 20.2317i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.12.b.a.5.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(20.2661 + 40.4634i) q^{2} +712.065i q^{3} +(-1226.57 + 1640.07i) q^{4} -7122.63i q^{5} +(-28812.6 + 14430.8i) q^{6} +46911.8 q^{7} +(-91220.5 - 16393.5i) q^{8} -329890. q^{9} +O(q^{10})$	\(q+(20.2661 + 40.4634i) q^{2} +712.065i q^{3} +(-1226.57 + 1640.07i) q^{4} -7122.63i q^{5} +(-28812.6 + 14430.8i) q^{6} +46911.8 q^{7} +(-91220.5 - 16393.5i) q^{8} -329890. q^{9} +(288206. - 144348. i) q^{10} +677681. i q^{11} +(-1.16784e6 - 873399. i) q^{12} +438277. i q^{13} +(950718. + 1.89821e6i) q^{14} +5.07178e6 q^{15} +(-1.18535e6 - 4.02332e6i) q^{16} +5.66172e6 q^{17} +(-6.68557e6 - 1.33485e7i) q^{18} +2.20071e6i q^{19} +(1.16816e7 + 8.73642e6i) q^{20} +3.34042e7i q^{21} +(-2.74213e7 + 1.37339e7i) q^{22} -2.68123e7 q^{23} +(1.16732e7 - 6.49550e7i) q^{24} -1.90375e6 q^{25} +(-1.77342e7 + 8.88217e6i) q^{26} -1.08763e8i q^{27} +(-5.75407e7 + 7.69385e7i) q^{28} +4.65452e6i q^{29} +(1.02785e8 + 2.05221e8i) q^{30} +2.65446e8 q^{31} +(1.38775e8 - 1.29500e8i) q^{32} -4.82553e8 q^{33} +(1.14741e8 + 2.29092e8i) q^{34} -3.34135e8i q^{35} +(4.04634e8 - 5.41042e8i) q^{36} +2.71979e8i q^{37} +(-8.90482e7 + 4.45998e7i) q^{38} -3.12082e8 q^{39} +(-1.16765e8 + 6.49730e8i) q^{40} +6.32013e8 q^{41} +(-1.35165e9 + 6.76973e8i) q^{42} -1.17468e9i q^{43} +(-1.11144e9 - 8.31225e8i) q^{44} +2.34968e9i q^{45} +(-5.43379e8 - 1.08491e9i) q^{46} +3.27045e8 q^{47} +(2.86487e9 - 8.44043e8i) q^{48} +2.23388e8 q^{49} +(-3.85815e7 - 7.70320e7i) q^{50} +4.03151e9i q^{51} +(-7.18805e8 - 5.37579e8i) q^{52} -3.75087e9i q^{53} +(4.40091e9 - 2.20420e9i) q^{54} +4.82687e9 q^{55} +(-4.27932e9 - 7.69049e8i) q^{56} -1.56705e9 q^{57} +(-1.88337e8 + 9.43288e7i) q^{58} -1.31771e9i q^{59} +(-6.22090e9 + 8.31806e9i) q^{60} -4.24691e9i q^{61} +(5.37954e9 + 1.07408e10i) q^{62} -1.54757e10 q^{63} +(8.05244e9 + 2.99085e9i) q^{64} +3.12169e9 q^{65} +(-9.77946e9 - 1.95257e10i) q^{66} +7.41724e9i q^{67} +(-6.94450e9 + 9.28561e9i) q^{68} -1.90921e10i q^{69} +(1.35202e10 - 6.77161e9i) q^{70} -1.51874e10 q^{71} +(3.00927e10 + 5.40805e9i) q^{72} +9.14718e9 q^{73} +(-1.10052e10 + 5.51196e9i) q^{74} -1.35559e9i q^{75} +(-3.60932e9 - 2.69933e9i) q^{76} +3.17912e10i q^{77} +(-6.32468e9 - 1.26279e10i) q^{78} +4.97008e10 q^{79} +(-2.86567e10 + 8.44278e9i) q^{80} +1.90073e10 q^{81} +(1.28084e10 + 2.55734e10i) q^{82} +1.15914e10i q^{83} +(-5.47852e10 - 4.09727e10i) q^{84} -4.03263e10i q^{85} +(4.75314e10 - 2.38061e10i) q^{86} -3.31432e9 q^{87} +(1.11096e10 - 6.18185e10i) q^{88} -8.86540e10 q^{89} +(-9.50762e10 + 4.76189e10i) q^{90} +2.05604e10i q^{91} +(3.28872e10 - 4.39739e10i) q^{92} +1.89015e11i q^{93} +(6.62792e9 + 1.32333e10i) q^{94} +1.56748e10 q^{95} +(9.22125e10 + 9.88169e10i) q^{96} -1.71286e10 q^{97} +(4.52720e9 + 9.03904e9i) q^{98} -2.23560e11i 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}+O(q^{10}) $ 10 * q + 22 * q^2 + 436 * q^4 - 24308 * q^6 - 33616 * q^7 - 208472 * q^8 - 472394 * q^9	\( 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9} + 29864 q^{10} - 476216 q^{12} + 2264272 q^{14} + 3391792 q^{15} + 3757072 q^{16} + 2639732 q^{17} + 2329130 q^{18} + 8296432 q^{20} - 24201892 q^{22} - 45357808 q^{23} + 10668944 q^{24} - 41502654 q^{25} - 101931080 q^{26} - 95722144 q^{28} + 261362768 q^{30} + 442035392 q^{31} + 343908512 q^{32} - 54732216 q^{33} - 187103796 q^{34} - 431195700 q^{36} + 375100844 q^{38} - 431459312 q^{39} + 1519138784 q^{40} - 654907964 q^{41} - 3697737056 q^{42} - 4127012952 q^{44} + 6028867440 q^{46} - 560226528 q^{47} + 9357606048 q^{48} + 1143661722 q^{49} - 9626584226 q^{50} - 11595427248 q^{52} + 20050494008 q^{54} + 5632783984 q^{55} + 18698733760 q^{56} - 783862360 q^{57} - 22828679464 q^{58} - 43681325472 q^{60} + 40774631744 q^{62} - 14483624624 q^{63} + 55266728512 q^{64} - 80291360 q^{65} - 83128448712 q^{66} - 83303223768 q^{68} + 100120831168 q^{70} - 11769460176 q^{71} + 112862051672 q^{72} + 32304890372 q^{73} - 102103996184 q^{74} - 97501928568 q^{76} + 144445560944 q^{78} + 57291670496 q^{79} + 128322038976 q^{80} - 23172996094 q^{81} - 123309929604 q^{82} - 199990865984 q^{84} + 130201908124 q^{86} - 73844404272 q^{87} + 169216119632 q^{88} - 108276011804 q^{89} - 228506434984 q^{90} - 141139403232 q^{92} + 145336130016 q^{94} + 70146835376 q^{95} + 109508068928 q^{96} + 60995282900 q^{97} - 6194726778 q^{98}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

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 $

$2$	20.2661	+	40.4634i	0.447821	+	0.894123i
$2$	20.2661	+	40.4634i	0.447821	+	0.894123i
$3$			712.065i			1.69181i	0.533330	+	0.845907i	$0.320941\pi$
$3$			712.065i			1.69181i	−0.533330	+	0.845907i	$0.679059\pi$
$4$	−1226.57	+	1640.07i	−0.598912	+	0.800815i
$5$		−	7122.63i		−	1.01931i	−0.860379	−	0.509654i	$-0.829773\pi$
$5$		−	7122.63i		−	1.01931i	0.860379	−	0.509654i	$-0.170227\pi$
$6$	−28812.6	+	14430.8i	−1.51269	+	0.757631i
$7$	46911.8			1.05498			0.527488	−	0.849562i	$-0.323134\pi$
$7$	46911.8			1.05498			0.527488	+	0.849562i	$0.323134\pi$
$8$	−91220.5	−	16393.5i	−0.984233	−	0.176879i
$9$	−329890.			−1.86224
$10$	288206.	−	144348.i	0.911387	−	0.456468i
$11$			677681.i			1.26872i	0.773038	+	0.634360i	$0.218736\pi$
$11$			677681.i			1.26872i	−0.773038	+	0.634360i	$0.781264\pi$
$12$	−1.16784e6	−	873399.i	−1.35483	−	1.01325i
$13$			438277.i			0.327386i	0.986511	+	0.163693i	$0.0523407\pi$
$13$			438277.i			0.327386i	−0.986511	+	0.163693i	$0.947659\pi$
$14$	950718.	+	1.89821e6i	0.472441	+	0.943279i
$15$	5.07178e6			1.72448
$16$	−1.18535e6	−	4.02332e6i	−0.282608	−	0.959235i
$17$	5.66172e6			0.967117			0.483559	−	0.875312i	$-0.339344\pi$
$17$	5.66172e6			0.967117			0.483559	+	0.875312i	$0.339344\pi$
$18$	−6.68557e6	−	1.33485e7i	−0.833950	−	1.66507i
$19$			2.20071e6i			0.203900i	0.994790	+	0.101950i	$0.0325082\pi$
$19$			2.20071e6i			0.203900i	−0.994790	+	0.101950i	$0.967492\pi$
$20$	1.16816e7	+	8.73642e6i	0.816277	+	0.610476i
$21$			3.34042e7i			1.78482i
$22$	−2.74213e7	+	1.37339e7i	−1.13439	+	0.568160i
$23$	−2.68123e7			−0.868621			−0.434310	−	0.900763i	$-0.643008\pi$
$23$	−2.68123e7			−0.868621			−0.434310	+	0.900763i	$0.643008\pi$
$24$	1.16732e7	−	6.49550e7i	0.299247	−	1.66514i
$25$	−1.90375e6			−0.0389887
$26$	−1.77342e7	+	8.88217e6i	−0.292724	+	0.146611i
$27$		−	1.08763e8i		−	1.45875i
$28$	−5.75407e7	+	7.69385e7i	−0.631838	+	0.844840i
$29$			4.65452e6i			0.0421391i	0.999778	+	0.0210696i	$0.00670715\pi$
$29$			4.65452e6i			0.0421391i	−0.999778	+	0.0210696i	$0.993293\pi$
$30$	1.02785e8	+	2.05221e8i	0.772259	+	1.54190i
$31$	2.65446e8			1.66528			0.832638	−	0.553818i	$-0.186830\pi$
$31$	2.65446e8			1.66528			0.832638	+	0.553818i	$0.186830\pi$
$32$	1.38775e8	−	1.29500e8i	0.731116	−	0.682253i
$33$	−4.82553e8			−2.14644
$34$	1.14741e8	+	2.29092e8i	0.433096	+	0.864722i
$35$		−	3.34135e8i		−	1.07535i
$36$	4.04634e8	−	5.41042e8i	1.11532	−	1.49131i
$37$			2.71979e8i			0.644802i	0.946603	+	0.322401i	$0.104490\pi$
$37$			2.71979e8i			0.644802i	−0.946603	+	0.322401i	$0.895510\pi$
$38$	−8.90482e7	+	4.45998e7i	−0.182312	+	0.0913109i
$39$	−3.12082e8			−0.553877
$40$	−1.16765e8	+	6.49730e8i	−0.180294	+	1.00324i
$41$	6.32013e8			0.851952			0.425976	−	0.904735i	$-0.359931\pi$
$41$	6.32013e8			0.851952			0.425976	+	0.904735i	$0.359931\pi$
$42$	−1.35165e9	+	6.76973e8i	−1.59585	+	0.799282i
$43$		−	1.17468e9i		−	1.21855i	−0.792960	−	0.609273i	$-0.791461\pi$
$43$		−	1.17468e9i		−	1.21855i	0.792960	−	0.609273i	$-0.208539\pi$
$44$	−1.11144e9	−	8.31225e8i	−1.01601	−	0.759852i
$45$			2.34968e9i			1.89819i
$46$	−5.43379e8	−	1.08491e9i	−0.388987	−	0.776654i
$47$	3.27045e8			0.208003			0.104001	−	0.994577i	$-0.466835\pi$
$47$	3.27045e8			0.208003			0.104001	+	0.994577i	$0.466835\pi$
$48$	2.86487e9	−	8.44043e8i	1.62285	−	0.478121i
$49$	2.23388e8			0.112975
$50$	−3.85815e7	−	7.70320e7i	−0.0174600	−	0.0348607i
$51$			4.03151e9i			1.63618i
$52$	−7.18805e8	−	5.37579e8i	−0.262176	−	0.196076i
$53$		−	3.75087e9i		−	1.23201i	−0.787741	−	0.616006i	$-0.788750\pi$
$53$		−	3.75087e9i		−	1.23201i	0.787741	−	0.616006i	$-0.211250\pi$
$54$	4.40091e9	−	2.20420e9i	1.30430	−	0.653258i
$55$	4.82687e9			1.29322
$56$	−4.27932e9	−	7.69049e8i	−1.03834	−	0.186603i
$57$	−1.56705e9			−0.344962
$58$	−1.88337e8	+	9.43288e7i	−0.0376776	+	0.0188708i
$59$		−	1.31771e9i		−	0.239956i	−0.992777	−	0.119978i	$-0.961718\pi$
$59$		−	1.31771e9i		−	0.239956i	0.992777	−	0.119978i	$-0.0382825\pi$
$60$	−6.22090e9	+	8.31806e9i	−1.03281	+	1.38099i
$61$		−	4.24691e9i		−	0.643812i	−0.946772	−	0.321906i	$-0.895676\pi$
$61$		−	4.24691e9i		−	0.643812i	0.946772	−	0.321906i	$-0.104324\pi$
$62$	5.37954e9	+	1.07408e10i	0.745746	+	1.48896i
$63$	−1.54757e10			−1.96462
$64$	8.05244e9	+	2.99085e9i	0.937427	+	0.348181i
$65$	3.12169e9			0.333708
$66$	−9.77946e9	−	1.95257e10i	−0.961221	−	1.91918i
$67$			7.41724e9i			0.671168i	0.942010	+	0.335584i	$0.108934\pi$
$67$			7.41724e9i			0.671168i	−0.942010	+	0.335584i	$0.891066\pi$
$68$	−6.94450e9	+	9.28561e9i	−0.579218	+	0.774482i
$69$		−	1.90921e10i		−	1.46955i
$70$	1.35202e10	−	6.77161e9i	0.961491	−	0.481563i
$71$	−1.51874e10			−0.998993			−0.499497	−	0.866316i	$-0.666482\pi$
$71$	−1.51874e10			−0.998993			−0.499497	+	0.866316i	$0.666482\pi$
$72$	3.00927e10	+	5.40805e9i	1.83288	+	0.329391i
$73$	9.14718e9			0.516430			0.258215	−	0.966087i	$-0.416866\pi$
$73$	9.14718e9			0.516430			0.258215	+	0.966087i	$0.416866\pi$
$74$	−1.10052e10	+	5.51196e9i	−0.576533	+	0.288756i
$75$		−	1.35559e9i		−	0.0659617i
$76$	−3.60932e9	−	2.69933e9i	−0.163286	−	0.122118i
$77$			3.17912e10i			1.33847i
$78$	−6.32468e9	−	1.26279e10i	−0.248038	−	0.495234i
$79$	4.97008e10			1.81725			0.908625	−	0.417613i	$-0.137133\pi$
$79$	4.97008e10			1.81725			0.908625	+	0.417613i	$0.137133\pi$
$80$	−2.86567e10	+	8.44278e9i	−0.977756	+	0.288065i
$81$	1.90073e10			0.605692
$82$	1.28084e10	+	2.55734e10i	0.381522	+	0.761750i
$83$			1.15914e10i			0.323002i	0.986873	+	0.161501i	$0.0516335\pi$
$83$			1.15914e10i			0.323002i	−0.986873	+	0.161501i	$0.948366\pi$
$84$	−5.47852e10	−	4.09727e10i	−1.42931	−	1.06895i
$85$		−	4.03263e10i		−	0.985790i
$86$	4.75314e10	−	2.38061e10i	1.08953	−	0.545691i
$87$	−3.31432e9			−0.0712916
$88$	1.11096e10	−	6.18185e10i	0.224410	−	1.24872i
$89$	−8.86540e10			−1.68288			−0.841440	−	0.540350i	$-0.818292\pi$
$89$	−8.86540e10			−1.68288			−0.841440	+	0.540350i	$0.818292\pi$
$90$	−9.50762e10	+	4.76189e10i	−1.69722	+	0.850052i
$91$			2.05604e10i			0.345385i
$92$	3.28872e10	−	4.39739e10i	0.520228	−	0.695604i
$93$			1.89015e11i			2.81734i
$94$	6.62792e9	+	1.32333e10i	0.0931481	+	0.185980i
$95$	1.56748e10			0.207837
$96$	9.22125e10	+	9.88169e10i	1.15425	+	1.23691i
$97$	−1.71286e10			−0.202524			−0.101262	−	0.994860i	$-0.532288\pi$
$97$	−1.71286e10			−0.202524			−0.101262	+	0.994860i	$0.532288\pi$
$98$	4.52720e9	+	9.03904e9i	0.0505925	+	0.101013i
$99$		−	2.23560e11i		−	2.36266i
$100$	2.33508e9	−	3.12227e9i	0.0233508	−	0.0312227i
$101$		−	1.70368e11i		−	1.61295i	−0.591266	−	0.806476i	$-0.701372\pi$
$101$		−	1.70368e11i		−	1.61295i	0.591266	−	0.806476i	$-0.298628\pi$
$102$	−1.63129e11	+	8.17029e10i	−1.46295	+	0.732718i
$103$	−1.33231e9			−0.0113240			−0.00566199	−	0.999984i	$-0.501802\pi$
$103$	−1.33231e9			−0.0113240			−0.00566199	+	0.999984i	$0.501802\pi$
$104$	7.18491e9	−	3.99799e10i	0.0579079	−	0.322224i
$105$	2.37926e11			1.81929
$106$	1.51773e11	−	7.60155e10i	1.10157	−	0.551721i
$107$		−	6.52156e10i		−	0.449512i	−0.974415	−	0.224756i	$-0.927842\pi$
$107$		−	6.52156e10i		−	0.449512i	0.974415	−	0.224756i	$-0.0721584\pi$
$108$	1.78379e11	+	1.33406e11i	1.16819	+	0.873661i
$109$			1.54610e11i			0.962482i	0.876588	+	0.481241i	$0.159814\pi$
$109$			1.54610e11i			0.962482i	−0.876588	+	0.481241i	$0.840186\pi$
$110$	9.78218e10	+	1.95312e11i	0.579130	+	1.15629i
$111$	−1.93667e11			−1.09089
$112$	−5.56067e10	−	1.88741e11i	−0.298145	−	1.01197i
$113$	−3.63886e11			−1.85795			−0.928975	−	0.370143i	$-0.879309\pi$
$113$	−3.63886e11			−1.85795			−0.928975	+	0.370143i	$0.879309\pi$
$114$	−3.17579e10	−	6.34081e10i	−0.154481	−	0.308438i
$115$			1.90974e11i			0.885392i
$116$	−7.63372e9	−	5.70910e9i	−0.0337456	−	0.0252376i
$117$		−	1.44583e11i		−	0.609671i
$118$	5.33188e10	−	2.67047e10i	0.214551	−	0.107458i
$119$	2.65601e11			1.02029
$120$	−4.62650e11	−	8.31442e10i	−1.69729	−	0.305025i
$121$	−1.73940e11			−0.609650
$122$	1.71844e11	−	8.60682e10i	0.575647	−	0.288313i
$123$			4.50035e11i			1.44134i
$124$	−3.25588e11	+	4.35349e11i	−0.997354	+	1.33358i
$125$		−	3.34225e11i		−	0.979566i
$126$	−3.13632e11	−	6.26200e11i	−0.879797	−	1.75661i
$127$	2.59654e11			0.697388			0.348694	−	0.937237i	$-0.386625\pi$
$127$	2.59654e11			0.697388			0.348694	+	0.937237i	$0.386625\pi$
$128$	4.21715e10	+	3.86442e11i	0.108484	+	0.994098i
$129$	8.36447e11			2.06156
$130$	6.32644e10	+	1.26314e11i	0.149441	+	0.298376i
$131$			1.76251e11i			0.399154i	0.979882	+	0.199577i	$0.0639568\pi$
$131$			1.76251e11i			0.399154i	−0.979882	+	0.199577i	$0.936043\pi$
$132$	5.91886e11	−	7.91420e11i	1.28553	−	1.71890i
$133$			1.03239e11i			0.215110i
$134$	−3.00127e11	+	1.50318e11i	−0.600107	+	0.300563i
$135$	−7.74678e11			−1.48691
$136$	−5.16465e11	−	9.28154e10i	−0.951868	−	0.171063i
$137$	4.09711e11			0.725295			0.362647	−	0.931926i	$-0.381873\pi$
$137$	4.09711e11			0.725295			0.362647	+	0.931926i	$0.381873\pi$
$138$	7.72530e11	−	3.86921e11i	1.31395	−	0.658094i
$139$		−	7.40408e10i		−	0.121029i	−0.998167	−	0.0605146i	$-0.980726\pi$
$139$		−	7.40408e10i		−	0.121029i	0.998167	−	0.0605146i	$-0.0192742\pi$
$140$	5.48005e11	+	4.09841e11i	0.861153	+	0.644038i
$141$			2.32877e11i			0.351902i
$142$	−3.07789e11	−	6.14534e11i	−0.447370	−	0.893223i
$143$	−2.97012e11			−0.415362
$144$	3.91034e11	+	1.32725e12i	0.526284	+	1.78632i
$145$	3.31524e10			0.0429527
$146$	1.85378e11	+	3.70126e11i	0.231268	+	0.461752i
$147$			1.59067e11i			0.191132i
$148$	−4.46065e11	−	3.33602e11i	−0.516367	−	0.386180i
$149$		−	4.10299e11i		−	0.457695i	−0.973462	−	0.228847i	$-0.926504\pi$
$149$		−	4.10299e11i		−	0.457695i	0.973462	−	0.228847i	$-0.0734957\pi$
$150$	5.48518e10	−	2.74725e10i	0.0589779	−	0.0295391i
$151$	−3.52303e11			−0.365210			−0.182605	−	0.983186i	$-0.558453\pi$
$151$	−3.52303e11			−0.365210			−0.182605	+	0.983186i	$0.558453\pi$
$152$	3.60774e10	−	2.00750e11i	0.0360658	−	0.200685i
$153$	−1.86774e12			−1.80100
$154$	−1.28638e12	+	6.44284e11i	−1.19676	+	0.599395i
$155$		−	1.89067e12i		−	1.69743i
$156$	3.82791e11	−	5.11836e11i	0.331724	−	0.443553i
$157$		−	1.57639e12i		−	1.31891i	−0.751744	−	0.659455i	$-0.770787\pi$
$157$		−	1.57639e12i		−	1.31891i	0.751744	−	0.659455i	$-0.229213\pi$
$158$	1.00724e12	+	2.01106e12i	0.813803	+	1.62485i
$159$	2.67087e12			2.08434
$160$	−9.22382e11	−	9.88443e11i	−0.695426	−	0.745233i
$161$	−1.25781e12			−0.916374
$162$	3.85203e11	+	7.69098e11i	0.271242	+	0.541563i
$163$			1.04456e12i			0.711052i	0.934666	+	0.355526i	$0.115698\pi$
$163$			1.04456e12i			0.711052i	−0.934666	+	0.355526i	$0.884302\pi$
$164$	−7.75210e11	+	1.03655e12i	−0.510244	+	0.682255i
$165$			3.43705e12i			2.18788i
$166$	−4.69026e11	+	2.34912e11i	−0.288804	+	0.144647i
$167$	−1.18115e12			−0.703665			−0.351833	−	0.936063i	$-0.614441\pi$
$167$	−1.18115e12			−0.703665			−0.351833	+	0.936063i	$0.614441\pi$
$168$	5.47613e11	−	3.04715e12i	0.315698	−	1.75668i
$169$	1.60007e12			0.892818
$170$	1.63174e12	−	8.17256e11i	0.881418	−	0.441458i
$171$		−	7.25992e11i		−	0.379711i
$172$	1.92655e12	+	1.44083e12i	0.975830	+	0.729803i
$173$			1.49392e11i			0.0732949i	0.999328	+	0.0366474i	$0.0116679\pi$
$173$			1.49392e11i			0.0732949i	−0.999328	+	0.0366474i	$0.988332\pi$
$174$	−6.71682e10	−	1.34109e11i	−0.0319259	−	0.0637435i
$175$	−8.93081e10			−0.0411322
$176$	2.72653e12	−	8.03287e11i	1.21700	−	0.358551i
$177$	9.38292e11			0.405962
$178$	−1.79667e12	−	3.58724e12i	−0.753630	−	1.50470i
$179$		−	3.36195e12i		−	1.36741i	−0.729758	−	0.683705i	$-0.760367\pi$
$179$		−	3.36195e12i		−	1.36741i	0.729758	−	0.683705i	$-0.239633\pi$
$180$	−3.85364e12	−	2.88206e12i	−1.52010	−	1.13685i
$181$			4.77708e12i			1.82781i	0.405931	+	0.913904i	$0.366947\pi$
$181$			4.77708e12i			1.82781i	−0.405931	+	0.913904i	$0.633053\pi$
$182$	−8.31942e11	+	4.16678e11i	−0.308817	+	0.154671i
$183$	3.02408e12			1.08921
$184$	2.44583e12	+	4.39547e11i	0.854925	+	0.153641i
$185$	1.93721e12			0.657252
$186$	−7.64817e12	+	3.83058e12i	−2.51905	+	1.26166i
$187$			3.83684e12i			1.22700i
$188$	−4.01144e11	+	5.36376e11i	−0.124575	+	0.166572i
$189$		−	5.10226e12i		−	1.53894i
$190$	3.17668e11	+	6.34257e11i	0.0930740	+	0.185832i
$191$	−3.37887e12			−0.961808			−0.480904	−	0.876773i	$-0.659691\pi$
$191$	−3.37887e12			−0.961808			−0.480904	+	0.876773i	$0.659691\pi$
$192$	−2.12968e12	+	5.73386e12i	−0.589057	+	1.58595i
$193$	−8.72768e11			−0.234603			−0.117302	−	0.993096i	$-0.537424\pi$
$193$	−8.72768e11			−0.234603			−0.117302	+	0.993096i	$0.537424\pi$
$194$	−3.47129e11	−	6.93080e11i	−0.0906945	−	0.181081i
$195$			2.22285e12i			0.564572i
$196$	−2.74001e11	+	3.66372e11i	−0.0676620	+	0.0904718i
$197$			5.42908e10i			0.0130365i	0.999979	+	0.00651827i	$0.00207484\pi$
$197$			5.42908e10i			0.0130365i	−0.999979	+	0.00651827i	$0.997925\pi$
$198$	9.04600e12	−	4.53069e12i	2.11251	−	1.05805i
$199$	−4.82354e12			−1.09566			−0.547828	−	0.836591i	$-0.684545\pi$
$199$	−4.82354e12			−1.09566			−0.547828	+	0.836591i	$0.684545\pi$
$200$	1.73661e11	+	3.12091e10i	0.0383740	+	0.00689630i
$201$	−5.28156e12			−1.13549
$202$	6.89368e12	−	3.45270e12i	1.44218	−	0.722315i
$203$			2.18352e11i			0.0444558i
$204$	−6.61196e12	−	4.94494e12i	−1.31028	−	0.979930i
$205$		−	4.50160e12i		−	0.868401i
$206$	−2.70006e10	−	5.39096e10i	−0.00507112	−	0.0101250i
$207$	8.84509e12			1.61758
$208$	1.76333e12	−	5.19510e11i	0.314041	−	0.0925222i
$209$	−1.49138e12			−0.258692
$210$	4.82183e12	+	9.62730e12i	0.814715	+	1.62667i
$211$		−	1.17667e12i		−	0.193688i	−0.995300	−	0.0968438i	$-0.969125\pi$
$211$		−	1.17667e12i		−	0.193688i	0.995300	−	0.0968438i	$-0.0308747\pi$
$212$	6.15169e12	+	4.60072e12i	0.986614	+	0.737867i
$213$		−	1.08144e13i		−	1.69011i
$214$	2.63885e12	−	1.32167e12i	0.401919	−	0.201301i
$215$	−8.36680e12			−1.24207
$216$	−1.78301e12	+	9.92141e12i	−0.258022	+	1.43575i
$217$	1.24525e13			1.75683
$218$	−6.25606e12	+	3.13334e12i	−0.860577	+	0.431020i
$219$			6.51339e12i			0.873705i
$220$	−5.92051e12	+	7.91640e12i	−0.774523	+	1.03563i
$221$			2.48140e12i			0.316621i
$222$	−3.92487e12	−	7.83643e12i	−0.488522	−	0.975387i
$223$	6.58715e12			0.799873			0.399936	−	0.916543i	$-0.369032\pi$
$223$	6.58715e12			0.799873			0.399936	+	0.916543i	$0.369032\pi$
$224$	6.51018e12	−	6.07508e12i	0.771310	−	0.719760i
$225$	6.28027e11			0.0726063
$226$	−7.37454e12	−	1.47241e13i	−0.832029	−	1.66124i
$227$		−	4.82280e11i		−	0.0531077i	−0.999647	−	0.0265538i	$-0.991547\pi$
$227$		−	4.82280e11i		−	0.0531077i	0.999647	−	0.0265538i	$-0.00845334\pi$
$228$	1.92210e12	−	2.57007e12i	0.206602	−	0.276250i
$229$		−	4.01542e12i		−	0.421343i	−0.977557	−	0.210672i	$-0.932435\pi$
$229$		−	4.01542e12i		−	0.421343i	0.977557	−	0.210672i	$-0.0675651\pi$
$230$	−7.72745e12	+	3.87029e12i	−0.791649	+	0.396497i
$231$	−2.26374e13			−2.26444
$232$	7.63038e10	−	4.24587e11i	0.00745354	−	0.0414747i
$233$	−9.52761e12			−0.908921			−0.454461	−	0.890767i	$-0.650168\pi$
$233$	−9.52761e12			−0.908921			−0.454461	+	0.890767i	$0.650168\pi$
$234$	5.85033e12	−	2.93014e12i	0.545121	−	0.273024i
$235$		−	2.32942e12i		−	0.212019i
$236$	2.16113e12	+	1.61626e12i	0.192161	+	0.143713i
$237$			3.53902e13i			3.07445i
$238$	5.38270e12	+	1.07471e13i	0.456906	+	0.912261i
$239$	1.79805e13			1.49146			0.745732	−	0.666246i	$-0.232100\pi$
$239$	1.79805e13			1.49146			0.745732	+	0.666246i	$0.232100\pi$
$240$	−6.01181e12	−	2.04054e13i	−0.487353	−	1.65418i
$241$	1.36089e13			1.07828			0.539139	−	0.842217i	$-0.318750\pi$
$241$	1.36089e13			1.07828			0.539139	+	0.842217i	$0.318750\pi$
$242$	−3.52509e12	−	7.03821e12i	−0.273014	−	0.545102i
$243$		−	5.73261e12i		−	0.434028i
$244$	6.96523e12	+	5.20914e12i	0.515574	+	0.385587i
$245$		−	1.59111e12i		−	0.115156i
$246$	−1.82099e13	+	9.12044e12i	−1.28874	+	0.645465i
$247$	−9.64522e11			−0.0667542
$248$	−2.42141e13	−	4.35158e12i	−1.63902	−	0.294553i
$249$	−8.25381e12			−0.546460
$250$	1.35239e13	−	6.77343e12i	0.875853	−	0.438671i
$251$			1.39140e12i			0.0881550i	0.999028	+	0.0440775i	$0.0140349\pi$
$251$			1.39140e12i			0.0881550i	−0.999028	+	0.0440775i	$0.985965\pi$
$252$	1.89821e13	−	2.53812e13i	1.17663	−	1.57329i
$253$		−	1.81702e13i		−	1.10204i
$254$	5.26217e12	+	1.05065e13i	0.312305	+	0.623551i
$255$	2.87150e13			1.66777
$256$	−1.47821e13	+	9.53806e12i	−0.840265	+	0.542176i
$257$	−6.23108e12			−0.346682			−0.173341	−	0.984862i	$-0.555456\pi$
$257$	−6.23108e12			−0.346682			−0.173341	+	0.984862i	$0.555456\pi$
$258$	1.69515e13	+	3.38455e13i	0.923209	+	1.84328i
$259$			1.27590e13i			0.680251i
$260$	−3.82898e12	+	5.11978e12i	−0.199862	+	0.267238i
$261$		−	1.53548e12i		−	0.0784731i
$262$	−7.13173e12	+	3.57192e12i	−0.356893	+	0.178750i
$263$	2.96783e13			1.45439			0.727196	−	0.686429i	$-0.240823\pi$
$263$	2.96783e13			1.45439			0.727196	+	0.686429i	$0.240823\pi$
$264$	4.40188e13	+	7.91074e12i	2.11260	+	0.379661i
$265$	−2.67161e13			−1.25580
$266$	−4.17741e12	+	2.09225e12i	−0.192335	+	0.0963309i
$267$		−	6.31274e13i		−	2.84712i
$268$	−1.21648e13	−	9.09778e12i	−0.537481	−	0.401971i
$269$			4.00365e13i			1.73308i	0.499108	+	0.866540i	$0.333661\pi$
$269$			4.00365e13i			1.73308i	−0.499108	+	0.866540i	$0.666339\pi$
$270$	−1.56997e13	−	3.13461e13i	−0.665871	−	1.32948i
$271$	−3.33746e13			−1.38703			−0.693513	−	0.720445i	$-0.743938\pi$
$271$	−3.33746e13			−1.38703			−0.693513	+	0.720445i	$0.743938\pi$
$272$	−6.71109e12	−	2.27789e13i	−0.273316	−	0.927693i
$273$	−1.46403e13			−0.584327
$274$	8.30324e12	+	1.65783e13i	0.324802	+	0.648503i
$275$		−	1.29013e12i		−	0.0494658i
$276$	3.13123e13	+	2.34178e13i	1.17683	+	0.880129i
$277$		−	3.64877e13i		−	1.34434i	−0.740399	−	0.672168i	$-0.765363\pi$
$277$		−	3.64877e13i		−	1.34434i	0.740399	−	0.672168i	$-0.234637\pi$
$278$	2.99594e12	−	1.50052e12i	0.108215	−	0.0541994i
$279$	−8.75678e13			−3.10114
$280$	−5.47765e12	+	3.04800e13i	−0.190206	+	1.05839i
$281$	4.24615e13			1.44581			0.722904	−	0.690949i	$-0.242807\pi$
$281$	4.24615e13			1.44581			0.722904	+	0.690949i	$0.242807\pi$
$282$	−9.42300e12	+	4.71951e12i	−0.314644	+	0.157589i
$283$			4.88215e13i			1.59877i	0.600819	+	0.799385i	$0.294841\pi$
$283$			4.88215e13i			1.59877i	−0.600819	+	0.799385i	$0.705159\pi$
$284$	1.86284e13	−	2.49084e13i	0.598309	−	0.800008i
$285$			1.11615e13i			0.351622i
$286$	−6.01928e12	−	1.20181e13i	−0.186008	−	0.371384i
$287$	2.96489e13			0.898789
$288$	−4.57805e13	+	4.27208e13i	−1.36151	+	1.27052i
$289$	−2.21685e12			−0.0646842
$290$	6.71869e11	+	1.34146e12i	0.0192352	+	0.0384050i
$291$		−	1.21966e13i		−	0.342633i
$292$	−1.12197e13	+	1.50020e13i	−0.309296	+	0.413565i
$293$		−	7.51961e11i		−	0.0203434i	−0.999948	−	0.0101717i	$-0.996762\pi$
$293$		−	7.51961e11i		−	0.0203434i	0.999948	−	0.0101717i	$-0.00323781\pi$
$294$	−6.43638e12	+	3.22366e12i	−0.170896	+	0.0855932i
$295$	−9.38553e12			−0.244589
$296$	4.45870e12	−	2.48101e13i	0.114052	−	0.634635i
$297$	7.37066e13			1.85074
$298$	1.66021e13	−	8.31515e12i	0.409235	−	0.204965i
$299$		−	1.17512e13i		−	0.284375i
$300$	2.22326e12	+	1.66273e12i	0.0528231	+	0.0395053i
$301$		−	5.51062e13i		−	1.28554i
$302$	−7.13979e12	−	1.42554e13i	−0.163549	−	0.326543i
$303$	1.21313e14			2.72882
$304$	8.85417e12	−	2.60860e12i	0.195588	−	0.0576240i
$305$	−3.02492e13			−0.656243
$306$	−3.78518e13	−	7.55752e13i	−0.806527	−	1.61032i
$307$			7.81614e13i			1.63580i	0.575357	+	0.817902i	$0.304863\pi$
$307$			7.81614e13i			1.63580i	−0.575357	+	0.817902i	$0.695137\pi$
$308$	−5.21398e13	−	3.89942e13i	−1.07187	−	0.801625i
$309$		−	9.48689e11i		−	0.0191581i
$310$	7.65030e13	−	3.83165e13i	1.51771	−	0.760145i
$311$	−4.05759e13			−0.790836			−0.395418	−	0.918501i	$-0.629400\pi$
$311$	−4.05759e13			−0.790836			−0.395418	+	0.918501i	$0.629400\pi$
$312$	2.84683e13	+	5.11612e12i	0.545144	+	0.0979694i
$313$	−8.06348e13			−1.51715			−0.758576	−	0.651585i	$-0.774104\pi$
$313$	−8.06348e13			−1.51715			−0.758576	+	0.651585i	$0.774104\pi$
$314$	6.37860e13	−	3.19472e13i	1.17927	−	0.590636i
$315$			1.10228e14i			2.00255i
$316$	−6.09617e13	+	8.15128e13i	−1.08837	+	1.45528i
$317$			1.37340e13i			0.240974i	0.992715	+	0.120487i	$0.0384456\pi$
$317$			1.37340e13i			0.240974i	−0.992715	+	0.120487i	$0.961554\pi$
$318$	5.41280e13	+	1.08072e14i	0.933411	+	1.86365i
$319$	−3.15428e12			−0.0534627
$320$	2.13027e13	−	5.73546e13i	0.354903	−	0.955527i
$321$	4.64378e13			0.760491
$322$	−2.54909e13	−	5.08953e13i	−0.410372	−	0.819351i
$323$			1.24598e13i			0.197196i
$324$	−2.33138e13	+	3.11732e13i	−0.362756	+	0.485047i
$325$		−	8.34369e11i		−	0.0127644i
$326$	−4.22664e13	+	2.11691e13i	−0.635768	+	0.318424i
$327$	−1.10093e14			−1.62834
$328$	−5.76526e13	−	1.03609e13i	−0.838519	−	0.150693i
$329$	1.53423e13			0.219438
$330$	−1.39075e14	+	6.96555e13i	−1.95624	+	0.979780i
$331$		−	1.05061e14i		−	1.45341i	−0.686950	−	0.726705i	$-0.741051\pi$
$331$		−	1.05061e14i		−	1.45341i	0.686950	−	0.726705i	$-0.258949\pi$
$332$	−1.90106e13	−	1.42177e13i	−0.258665	−	0.193450i
$333$		−	8.97233e13i		−	1.20078i
$334$	−2.39374e13	−	4.77935e13i	−0.315116	−	0.629163i
$335$	5.28303e13			0.684127
$336$	1.34396e14	−	3.95956e13i	1.71207	−	0.504406i
$337$	1.04456e14			1.30909			0.654547	−	0.756021i	$-0.272859\pi$
$337$	1.04456e14			1.30909			0.654547	+	0.756021i	$0.272859\pi$
$338$	3.24272e13	+	6.47444e13i	0.399823	+	0.798289i
$339$		−	2.59111e14i		−	3.14331i
$340$	6.61379e13	+	4.94631e13i	0.789435	+	0.590402i
$341$			1.79887e14i			2.11277i
$342$	2.93761e13	−	1.47130e13i	0.339508	−	0.170043i
$343$	−8.22804e13			−0.935791
$344$	−1.92571e13	+	1.07155e14i	−0.215536	+	1.19933i
$345$	−1.35986e14			−1.49792
$346$	−6.04490e12	+	3.02759e12i	−0.0655346	+	0.0328230i
$347$			9.42783e13i			1.00600i	0.864285	+	0.503002i	$0.167771\pi$
$347$			9.42783e13i			1.00600i	−0.864285	+	0.503002i	$0.832229\pi$
$348$	4.06525e12	−	5.43571e12i	0.0426974	−	0.0570914i
$349$		−	1.27537e14i		−	1.31855i	−0.751902	−	0.659275i	$-0.770863\pi$
$349$		−	1.27537e14i		−	1.31855i	0.751902	−	0.659275i	$-0.229137\pi$
$350$	−1.80993e12	−	3.61371e12i	−0.0184199	−	0.0367772i
$351$	4.76683e13			0.477574
$352$	8.77598e13	+	9.40453e13i	0.865588	+	0.927582i
$353$	−7.74607e13			−0.752178			−0.376089	−	0.926584i	$-0.622731\pi$
$353$	−7.74607e13			−0.752178			−0.376089	+	0.926584i	$0.622731\pi$
$354$	1.90155e13	+	3.79665e13i	0.181798	+	0.362980i
$355$			1.08174e14i			1.01828i
$356$	1.08741e14	−	1.45399e14i	1.00790	−	1.34768i
$357$			1.89125e14i			1.72613i
$358$	1.36036e14	−	6.81335e13i	1.22263	−	0.612356i
$359$	6.39874e13			0.566337			0.283169	−	0.959070i	$-0.408614\pi$
$359$	6.39874e13			0.566337			0.283169	+	0.959070i	$0.408614\pi$
$360$	3.85196e13	−	2.14339e14i	0.335751	−	1.86826i
$361$	1.11647e14			0.958425
$362$	−1.93297e14	+	9.68127e13i	−1.63429	+	0.818531i
$363$		−	1.23857e14i		−	1.03141i
$364$	−3.37204e13	−	2.52188e13i	−0.276589	−	0.206855i
$365$		−	6.51520e13i		−	0.526402i
$366$	6.12862e13	+	1.22364e14i	0.487772	+	0.973889i
$367$	5.20969e13			0.408459			0.204230	−	0.978923i	$-0.434531\pi$
$367$	5.20969e13			0.408459			0.204230	+	0.978923i	$0.434531\pi$
$368$	3.17818e13	+	1.07874e14i	0.245480	+	0.833212i
$369$	−2.08495e14			−1.58654
$370$	3.92596e13	+	7.83861e13i	0.294332	+	0.587664i
$371$		−	1.75960e14i		−	1.29974i
$372$	−3.09997e14	−	2.31840e14i	−2.25617	−	1.68734i
$373$		−	1.73946e12i		−	0.0124743i	−0.999981	−	0.00623714i	$-0.998015\pi$
$373$		−	1.73946e12i		−	0.0124743i	0.999981	−	0.00623714i	$-0.00198536\pi$
$374$	−1.55252e14	+	7.77577e13i	−1.09709	+	0.549477i
$375$	2.37990e14			1.65725
$376$	−2.98332e13	−	5.36141e12i	−0.204723	−	0.0367914i
$377$	−2.03997e12			−0.0137958
$378$	2.06455e14	−	1.03403e14i	1.37600	−	0.689172i
$379$			1.41851e14i			0.931788i	0.884841	+	0.465894i	$0.154267\pi$
$379$			1.41851e14i			0.931788i	−0.884841	+	0.465894i	$0.845733\pi$
$380$	−1.92263e13	+	2.57078e13i	−0.124476	+	0.166439i
$381$			1.84891e14i			1.17985i
$382$	−6.84765e13	−	1.36721e14i	−0.430718	−	0.859975i
$383$	−7.39881e13			−0.458742			−0.229371	−	0.973339i	$-0.573667\pi$
$383$	−7.39881e13			−0.458742			−0.229371	+	0.973339i	$0.573667\pi$
$384$	−2.75172e14	+	3.00288e13i	−1.68183	+	0.183534i
$385$	2.26437e14			1.36431
$386$	−1.76876e13	−	3.53152e13i	−0.105060	−	0.209764i
$387$			3.87514e14i			2.26922i
$388$	2.10094e13	−	2.80920e13i	0.121294	−	0.162184i
$389$		−	8.95274e13i		−	0.509605i	−0.966993	−	0.254802i	$-0.917990\pi$
$389$		−	8.95274e13i		−	0.509605i	0.966993	−	0.254802i	$-0.0820104\pi$
$390$	−8.99439e13	+	4.50484e13i	−0.504796	+	0.252827i
$391$	−1.51803e14			−0.840058
$392$	−2.03776e13	−	3.66211e12i	−0.111193	−	0.0199829i
$393$	−1.25502e14			−0.675294
$394$	−2.19679e12	+	1.10026e12i	−0.0116563	+	0.00583804i
$395$		−	3.54001e14i		−	1.85234i
$396$	3.66654e14	+	2.74213e14i	1.89205	+	1.41502i
$397$			7.42172e13i			0.377709i	0.982005	+	0.188854i	$0.0604774\pi$
$397$			7.42172e13i			0.377709i	−0.982005	+	0.188854i	$0.939523\pi$
$398$	−9.77543e13	−	1.95177e14i	−0.490658	−	0.979652i
$399$	−7.35131e13			−0.363926
$400$	2.25660e12	+	7.65939e12i	0.0110185	+	0.0373994i
$401$	2.65661e13			0.127948			0.0639740	−	0.997952i	$-0.479623\pi$
$401$	2.65661e13			0.127948			0.0639740	+	0.997952i	$0.479623\pi$
$402$	−1.07037e14	−	2.13710e14i	−0.508497	−	1.01527i
$403$			1.16339e14i			0.545189i
$404$	2.79416e14	+	2.08969e14i	1.29168	+	0.966017i
$405$		−	1.35382e14i		−	0.617387i
$406$	−8.83525e12	+	4.42513e12i	−0.0397489	+	0.0199082i
$407$	−1.84315e14			−0.818073
$408$	6.60906e13	−	3.67757e14i	0.289407	−	1.61039i
$409$	3.52450e14			1.52272			0.761358	−	0.648332i	$-0.224533\pi$
$409$	3.52450e14			1.52272			0.761358	+	0.648332i	$0.224533\pi$
$410$	1.82150e14	−	9.12297e13i	0.776458	−	0.388889i
$411$			2.91741e14i			1.22706i
$412$	1.63417e12	−	2.18507e12i	0.00678207	−	0.00906841i
$413$		−	6.18159e13i		−	0.253148i
$414$	1.79255e14	+	3.57902e14i	0.724386	+	1.44631i
$415$	8.25611e13			0.329239
$416$	5.67570e13	+	6.08220e13i	0.223360	+	0.239358i
$417$	5.27219e13			0.204759
$418$	−3.02244e13	−	6.03463e13i	−0.115848	−	0.231303i
$419$		−	1.77434e14i		−	0.671211i	−0.942003	−	0.335605i	$-0.891059\pi$
$419$		−	1.77434e14i		−	0.671211i	0.942003	−	0.335605i	$-0.108941\pi$
$420$	−2.91834e14	+	3.90215e14i	−1.08959	+	1.45691i
$421$		−	4.89008e14i		−	1.80204i	−0.433778	−	0.901020i	$-0.642820\pi$
$421$		−	4.89008e14i		−	1.80204i	0.433778	−	0.901020i	$-0.357180\pi$
$422$	4.76121e13	−	2.38465e13i	0.173181	−	0.0867375i
$423$	−1.07889e14			−0.387351
$424$	−6.14900e13	+	3.42157e14i	−0.217918	+	1.21259i
$425$	−1.07785e13			−0.0377067
$426$	4.37588e14	−	2.19166e14i	1.51117	−	0.756868i
$427$		−	1.99230e14i		−	0.679206i
$428$	1.06958e14	+	7.99917e13i	0.359976	+	0.269218i
$429$		−	2.11492e14i		−	0.702715i
$430$	−1.69562e14	−	3.38549e14i	−0.556227	−	1.11057i
$431$	−1.36467e14			−0.441981			−0.220991	−	0.975276i	$-0.570929\pi$
$431$	−1.36467e14			−0.441981			−0.220991	+	0.975276i	$0.570929\pi$
$432$	−4.37588e14	+	1.28922e14i	−1.39928	+	0.412254i
$433$	−3.18191e14			−1.00463			−0.502313	−	0.864686i	$-0.667517\pi$
$433$	−3.18191e14			−1.00463			−0.502313	+	0.864686i	$0.667517\pi$
$434$	2.52364e14	+	5.03871e14i	0.786744	+	1.57082i
$435$			2.36067e13i			0.0726681i
$436$	−2.53571e14	−	1.89641e14i	−0.770770	−	0.576442i
$437$		−	5.90060e13i		−	0.177112i
$438$	−2.63554e14	+	1.32001e14i	−0.781199	+	0.391263i
$439$	7.43290e13			0.217572			0.108786	−	0.994065i	$-0.465304\pi$
$439$	7.43290e13			0.217572			0.108786	+	0.994065i	$0.465304\pi$
$440$	−4.40310e14	−	7.91294e13i	−1.27283	−	0.228743i
$441$	−7.36934e13			−0.210386
$442$	−1.00406e14	+	5.02883e13i	−0.283098	+	0.141790i
$443$			4.90710e14i			1.36648i	0.730193	+	0.683241i	$0.239430\pi$
$443$			4.90710e14i			1.36648i	−0.730193	+	0.683241i	$0.760570\pi$
$444$	2.37547e14	−	3.17627e14i	0.653345	−	0.873598i
$445$			6.31450e14i			1.71537i
$446$	1.33496e14	+	2.66539e14i	0.358200	+	0.715185i
$447$	2.92160e14			0.774335
$448$	3.77754e14	+	1.40306e14i	0.988964	+	0.367322i
$449$	−5.17795e14			−1.33907			−0.669535	−	0.742781i	$-0.733507\pi$
$449$	−5.17795e14			−1.33907			−0.669535	+	0.742781i	$0.733507\pi$
$450$	1.27276e13	+	2.54121e13i	0.0325146	+	0.0649190i
$451$			4.28304e14i			1.08089i
$452$	4.46332e14	−	5.96798e14i	1.11275	−	1.48787i
$453$		−	2.50862e14i		−	0.617868i
$454$	1.95147e13	−	9.77393e12i	0.0474848	−	0.0237827i
$455$	1.46444e14			0.352054
$456$	1.42947e14	+	2.56894e13i	0.339523	+	0.0610166i
$457$	−4.15226e14			−0.974417			−0.487209	−	0.873286i	$-0.661985\pi$
$457$	−4.15226e14			−0.974417			−0.487209	+	0.873286i	$0.661985\pi$
$458$	1.62478e14	−	8.13769e13i	0.376733	−	0.188687i
$459$		−	6.15785e14i		−	1.41078i
$460$	−3.13210e14	−	2.34243e14i	−0.709035	−	0.530272i
$461$			6.88053e13i			0.153910i	0.997035	+	0.0769550i	$0.0245198\pi$
$461$			6.88053e13i			0.153910i	−0.997035	+	0.0769550i	$0.975480\pi$
$462$	−4.58772e14	−	9.15987e14i	−1.01407	−	2.02469i
$463$	−5.04889e14			−1.10281			−0.551405	−	0.834238i	$-0.685908\pi$
$463$	−5.04889e14			−1.10281			−0.551405	+	0.834238i	$0.685908\pi$
$464$	1.87266e13	−	5.51721e12i	0.0404213	−	0.0119089i
$465$	1.34628e15			2.87174
$466$	−1.93087e14	−	3.85519e14i	−0.407034	−	0.812688i
$467$		−	3.62647e14i		−	0.755512i	−0.925905	−	0.377756i	$-0.876696\pi$
$467$		−	3.62647e14i		−	0.755512i	0.925905	−	0.377756i	$-0.123304\pi$
$468$	2.37126e14	+	1.77342e14i	0.488234	+	0.365140i
$469$			3.47956e14i			0.708066i
$470$	9.42562e13	−	4.72082e13i	0.189571	−	0.0949466i
$471$	1.12249e15			2.23135
$472$	−2.16018e13	+	1.20202e14i	−0.0424433	+	0.236173i
$473$	7.96057e14			1.54599
$474$	−1.43201e15	+	7.17221e14i	−2.74894	+	1.37680i
$475$		−	4.18959e12i		−	0.00794982i
$476$	−3.25779e14	+	4.35604e14i	−0.611062	+	0.817060i
$477$			1.23738e15i			2.29430i
$478$	3.64394e14	+	7.27551e14i	0.667909	+	1.33355i
$479$	−6.63079e14			−1.20149			−0.600745	−	0.799441i	$-0.705129\pi$
$479$	−6.63079e14			−1.20149			−0.600745	+	0.799441i	$0.705129\pi$
$480$	7.03836e14	−	6.56796e14i	1.26080	−	1.17653i
$481$	−1.19202e14			−0.211100
$482$	2.75800e14	+	5.50664e14i	0.482876	+	0.964113i
$483$		−	8.95643e14i		−	1.55034i
$484$	2.13350e14	−	2.85274e14i	0.365127	−	0.488217i
$485$			1.22000e14i			0.206434i
$486$	2.31961e14	−	1.16178e14i	0.388075	−	0.194367i
$487$	8.43883e14			1.39596			0.697980	−	0.716117i	$-0.254082\pi$
$487$	8.43883e14			1.39596			0.697980	+	0.716117i	$0.254082\pi$
$488$	−6.96218e13	+	3.87406e14i	−0.113877	+	0.633661i
$489$	−7.43794e14			−1.20297
$490$	6.43817e13	−	3.22456e13i	0.102964	−	0.0515693i
$491$			2.11986e14i			0.335242i	0.985852	+	0.167621i	$0.0536085\pi$
$491$			2.11986e14i			0.335242i	−0.985852	+	0.167621i	$0.946392\pi$
$492$	−7.38088e14	−	5.52000e14i	−1.15425	−	0.863239i
$493$			2.63526e13i			0.0407535i
$494$	−1.95471e13	−	3.90278e13i	−0.0298940	−	0.0596865i
$495$	−1.59234e15			−2.40828
$496$	−3.14645e14	−	1.06797e15i	−0.470621	−	1.59739i
$497$	−7.12468e14			−1.05391
$498$	−1.67272e14	−	3.33977e14i	−0.244716	−	0.488602i
$499$		−	2.74797e14i		−	0.397612i	−0.980039	−	0.198806i	$-0.936294\pi$
$499$		−	2.74797e14i		−	0.397612i	0.980039	−	0.198806i	$-0.0637063\pi$
$500$	5.48152e14	+	4.09951e14i	0.784451	+	0.586674i
$501$		−	8.41059e14i		−	1.19047i
$502$	−5.63008e13	+	2.81983e13i	−0.0788214	+	0.0394777i
$503$	4.70000e14			0.650840			0.325420	−	0.945570i	$-0.394494\pi$
$503$	4.70000e14			0.650840			0.325420	+	0.945570i	$0.394494\pi$
$504$	1.41170e15	+	2.53701e14i	1.93364	+	0.347500i
$505$	−1.21347e15			−1.64410
$506$	7.35226e14	−	3.68238e14i	0.985356	−	0.493515i
$507$			1.13936e15i			1.51048i
$508$	−3.18484e14	+	4.25850e14i	−0.417674	+	0.558479i
$509$		−	1.16919e15i		−	1.51683i	−0.651772	−	0.758415i	$-0.725974\pi$
$509$		−	1.16919e15i		−	1.51683i	0.651772	−	0.758415i	$-0.274026\pi$
$510$	5.81940e14	+	1.16191e15i	0.746865	+	1.49120i
$511$	4.29111e14			0.544822
$512$	−6.85517e14	−	4.04835e14i	−0.861061	−	0.508502i
$513$	2.39356e14			0.297439
$514$	−1.26280e14	−	2.52131e14i	−0.155252	−	0.309976i
$515$			9.48952e12i			0.0115426i
$516$	−1.02596e15	+	1.37183e15i	−1.23469	+	1.65092i
$517$			2.21632e14i			0.263897i
$518$	−5.16274e14	+	2.58576e14i	−0.608228	+	0.304631i
$519$	−1.06377e14			−0.124001
$520$	−2.84762e14	−	5.11754e13i	−0.328446	−	0.0590260i
$521$	4.05582e13			0.0462883			0.0231442	−	0.999732i	$-0.492632\pi$
$521$	4.05582e13			0.0462883			0.0231442	+	0.999732i	$0.492632\pi$
$522$	6.21306e13	−	3.11181e13i	0.0701646	−	0.0351419i
$523$		−	1.09058e15i		−	1.21871i	−0.792899	−	0.609353i	$-0.791429\pi$
$523$		−	1.09058e15i		−	1.21871i	0.792899	−	0.609353i	$-0.208571\pi$
$524$	−2.89064e14	−	2.16185e14i	−0.319648	−	0.239058i
$525$		−	6.35932e13i		−	0.0695880i
$526$	6.01462e14	+	1.20088e15i	0.651308	+	1.30041i
$527$	1.50288e15			1.61052
$528$	5.71992e14	+	1.94147e15i	0.606602	+	2.05894i
$529$	−2.33913e14			−0.245498
$530$	−5.41430e14	−	1.08102e15i	−0.562374	−	1.12284i
$531$			4.34698e14i			0.446856i
$532$	−1.69319e14	−	1.26630e14i	−0.172263	−	0.128832i
$533$			2.76997e14i			0.278917i
$534$	2.55435e15	−	1.27935e15i	2.54568	−	1.27500i
$535$	−4.64507e14			−0.458191
$536$	1.21595e14	−	6.76605e14i	0.118716	−	0.660585i
$537$	2.39392e15			2.31341
$538$	−1.62001e15	+	8.11383e14i	−1.54959	+	0.776110i
$539$			1.51386e14i			0.143333i
$540$	9.50198e14	−	1.27052e15i	0.890530	−	1.19074i
$541$		−	1.83489e15i		−	1.70226i	−0.524956	−	0.851129i	$-0.675918\pi$
$541$		−	1.83489e15i		−	1.70226i	0.524956	−	0.851129i	$-0.324082\pi$
$542$	−6.76371e14	−	1.35045e15i	−0.621139	−	1.24017i
$543$	−3.40159e15			−3.09231
$544$	7.85705e14	−	7.33193e14i	0.707075	−	0.659818i
$545$	1.10123e15			0.981066
$546$	−2.96702e14	−	5.92397e14i	−0.261674	−	0.522461i
$547$			1.04288e15i			0.910554i	0.890350	+	0.455277i	$0.150460\pi$
$547$			1.04288e15i			0.910554i	−0.890350	+	0.455277i	$0.849540\pi$
$548$	−5.02540e14	+	6.71954e14i	−0.434388	+	0.580827i
$549$			1.40101e15i			1.19893i
$550$	5.22032e13	−	2.61459e13i	0.0442285	−	0.0221518i
$551$	−1.02432e13			−0.00859218
$552$	−3.12986e14	+	1.74159e15i	−0.259932	+	1.44637i
$553$	2.33155e15			1.91716
$554$	1.47642e15	−	7.39462e14i	1.20200	−	0.602022i
$555$			1.37942e15i			1.11195i
$556$	1.21432e14	+	9.08164e13i	0.0969219	+	0.0724858i
$557$		−	6.38384e14i		−	0.504520i	−0.967659	−	0.252260i	$-0.918826\pi$
$557$		−	6.38384e14i		−	0.504520i	0.967659	−	0.252260i	$-0.0811739\pi$
$558$	−1.77466e15	−	3.54329e15i	−1.38876	−	2.77280i
$559$	5.14835e14			0.398936
$560$	−1.34433e15	+	3.96066e14i	−1.03151	+	0.303902i
$561$	−2.73208e15			−2.07586
$562$	8.60528e14	+	1.71814e15i	0.647463	+	1.29273i
$563$			2.04703e15i			1.52520i	0.646869	+	0.762601i	$0.276078\pi$
$563$			2.04703e15i			1.52520i	−0.646869	+	0.762601i	$0.723922\pi$
$564$	−3.81935e14	−	2.85641e14i	−0.281808	−	0.210758i
$565$			2.59183e15i			1.89382i
$566$	−1.97549e15	+	9.89421e14i	−1.42950	+	0.715964i
$567$	8.91664e14			0.638991
$568$	1.38540e15	+	2.48975e14i	0.983241	+	0.176701i
$569$	−1.99463e15			−1.40199			−0.700995	−	0.713166i	$-0.747261\pi$
$569$	−1.99463e15			−1.40199			−0.700995	+	0.713166i	$0.747261\pi$
$570$	−4.51633e14	+	2.26200e14i	−0.314394	+	0.157464i
$571$		−	2.69123e15i		−	1.85546i	−0.373246	−	0.927732i	$-0.621755\pi$
$571$		−	2.69123e15i		−	1.85546i	0.373246	−	0.927732i	$-0.378245\pi$
$572$	3.64307e14	−	4.87121e14i	0.248765	−	0.332628i
$573$		−	2.40598e15i		−	1.62720i
$574$	6.00866e14	+	1.19969e15i	0.402497	+	0.803628i
$575$	5.10437e13			0.0338664
$576$	−2.65642e15	−	9.86651e14i	−1.74571	−	0.648395i
$577$	7.31830e14			0.476369			0.238184	−	0.971220i	$-0.423448\pi$
$577$	7.31830e14			0.476369			0.238184	+	0.971220i	$0.423448\pi$
$578$	−4.49269e13	−	8.97013e13i	−0.0289670	−	0.0578356i
$579$		−	6.21468e14i		−	0.396905i
$580$	−4.06638e13	+	5.43722e13i	−0.0257249	+	0.0343972i
$581$			5.43772e14i			0.340759i
$582$	4.93518e14	−	2.47178e14i	0.306356	−	0.153438i
$583$	2.54190e15			1.56308
$584$	−8.34411e14	−	1.49954e14i	−0.508288	−	0.0913458i
$585$	−1.02981e15			−0.621443
$586$	3.04269e13	−	1.52393e13i	0.0181895	−	0.00911021i
$587$			2.12940e15i			1.26109i	0.776151	+	0.630547i	$0.217169\pi$
$587$			2.12940e15i			1.26109i	−0.776151	+	0.630547i	$0.782831\pi$
$588$	−2.60880e14	−	1.95107e14i	−0.153062	−	0.114472i
$589$			5.84169e14i			0.339550i
$590$	−1.90208e14	−	3.79770e14i	−0.109532	−	0.218693i
$591$	−3.86586e13			−0.0220554
$592$	1.09426e15	−	3.22390e14i	0.618517	−	0.182227i
$593$	2.35649e15			1.31967			0.659833	−	0.751412i	$-0.270627\pi$
$593$	2.35649e15			1.31967			0.659833	+	0.751412i	$0.270627\pi$
$594$	1.49374e15	+	2.98242e15i	0.828801	+	1.65479i
$595$		−	1.89178e15i		−	1.03999i
$596$	6.72918e14	+	5.03261e14i	0.366529	+	0.274119i
$597$		−	3.43468e15i		−	1.85365i
$598$	4.75494e14	−	2.38151e14i	0.254266	−	0.127349i
$599$	−4.81602e14			−0.255177			−0.127588	−	0.991827i	$-0.540724\pi$
$599$	−4.81602e14			−0.255177			−0.127588	+	0.991827i	$0.540724\pi$
$600$	−2.22229e13	+	1.23658e14i	−0.0116673	+	0.0649217i
$601$	−3.11568e15			−1.62085			−0.810425	−	0.585842i	$-0.800764\pi$
$601$	−3.11568e15			−1.62085			−0.810425	+	0.585842i	$0.800764\pi$
$602$	2.22978e15	−	1.11679e15i	1.14943	−	0.575691i
$603$		−	2.44687e15i		−	1.24987i
$604$	4.32125e14	−	5.77800e14i	0.218729	−	0.292466i
$605$			1.23891e15i			0.621421i
$606$	2.45855e15	+	4.90875e15i	1.22202	+	2.43990i
$607$	−1.92688e15			−0.949113			−0.474556	−	0.880225i	$-0.657392\pi$
$607$	−1.92688e15			−0.949113			−0.474556	+	0.880225i	$0.657392\pi$
$608$	2.84992e14	+	3.05404e14i	0.139112	+	0.149075i
$609$	−1.55481e14			−0.0752109
$610$	−6.13032e14	−	1.22398e15i	−0.293879	−	0.586762i
$611$			1.43336e14i			0.0680973i
$612$	2.29092e15	−	3.06323e15i	1.07864	−	1.44227i
$613$			2.68890e15i			1.25470i	0.778735	+	0.627352i	$0.215861\pi$
$613$			2.68890e15i			1.25470i	−0.778735	+	0.627352i	$0.784139\pi$
$614$	−3.16268e15	+	1.58403e15i	−1.46261	+	0.732548i
$615$	3.20543e15			1.46917
$616$	5.21170e14	−	2.90001e15i	0.236747	−	1.31736i
$617$	6.93877e14			0.312402			0.156201	−	0.987725i	$-0.450075\pi$
$617$	6.93877e14			0.312402			0.156201	+	0.987725i	$0.450075\pi$
$618$	3.83872e13	−	1.92262e13i	0.0171297	−	0.00857940i
$619$		−	2.44341e15i		−	1.08068i	−0.841446	−	0.540341i	$-0.818295\pi$
$619$		−	2.44341e15i		−	1.08068i	0.841446	−	0.540341i	$-0.181705\pi$
$620$	3.10083e15	+	2.31904e15i	1.35933	+	1.01661i
$621$			2.91618e15i			1.26710i
$622$	−8.22315e14	−	1.64184e15i	−0.354153	−	0.707105i
$623$	−4.15892e15			−1.77540
$624$	3.69925e14	+	1.25561e15i	0.156530	+	0.531299i
$625$	−2.47352e15			−1.03747
$626$	−1.63415e15	−	3.26276e15i	−0.679413	−	1.35652i
$627$		−	1.06196e15i		−	0.437660i
$628$	2.58539e15	+	1.93355e15i	1.05620	+	0.789912i
$629$			1.53987e15i			0.623599i
$630$	−4.46019e15	+	2.23389e15i	−1.79053	+	0.896784i
$631$	−1.74730e15			−0.695352			−0.347676	−	0.937615i	$-0.613029\pi$
$631$	−1.74730e15			−0.695352			−0.347676	+	0.937615i	$0.613029\pi$
$632$	−4.53374e15	−	8.14771e14i	−1.78860	−	0.321434i
$633$	8.37867e14			0.327684
$634$	−5.55723e14	+	2.78334e14i	−0.215460	+	0.107913i
$635$		−	1.84942e15i		−	0.710853i
$636$	−3.27601e15	+	4.38040e15i	−1.24833	+	1.66917i
$637$			9.79059e13i			0.0369864i
$638$	−6.39248e13	−	1.27633e14i	−0.0239418	−	0.0478023i
$639$	5.01017e15			1.86036
$640$	2.75248e15	−	3.00372e14i	1.01329	−	0.110578i
$641$	3.92937e15			1.43418			0.717091	−	0.696980i	$-0.245473\pi$
$641$	3.92937e15			1.43418			0.717091	+	0.696980i	$0.245473\pi$
$642$	9.41112e14	+	1.87903e15i	0.340564	+	0.679972i
$643$		−	4.89004e14i		−	0.175450i	−0.996145	−	0.0877248i	$-0.972040\pi$
$643$		−	4.89004e14i		−	0.175450i	0.996145	−	0.0877248i	$-0.0279596\pi$
$644$	1.54280e15	−	2.06290e15i	0.548828	−	0.733846i
$645$		−	5.95770e15i		−	2.10136i
$646$	−5.04166e14	+	2.52511e14i	−0.176317	+	0.0883084i
$647$	−1.25528e15			−0.435277			−0.217639	−	0.976029i	$-0.569835\pi$
$647$	−1.25528e15			−0.435277			−0.217639	+	0.976029i	$0.569835\pi$
$648$	−1.73385e15	−	3.11596e14i	−0.596142	−	0.107134i
$649$	8.92984e14			0.304437
$650$	3.37614e13	−	1.69094e13i	0.0114129	−	0.00571616i
$651$			8.86701e15i			2.97223i
$652$	−1.71315e15	−	1.28123e15i	−0.569421	−	0.425858i
$653$			1.04966e15i			0.345961i	0.984925	+	0.172980i	$0.0553397\pi$
$653$			1.04966e15i			0.345961i	−0.984925	+	0.172980i	$0.944660\pi$
$654$	−2.23115e15	−	4.45472e15i	−0.729206	−	1.45594i
$655$	1.25537e15			0.406861
$656$	−7.49154e14	−	2.54279e15i	−0.240769	−	0.817222i
$657$	−3.01756e15			−0.961716
$658$	3.10927e14	+	6.20800e14i	0.0982690	+	0.196205i
$659$		−	4.18523e14i		−	0.131175i	−0.997847	−	0.0655873i	$-0.979108\pi$
$659$		−	4.18523e14i		−	0.131175i	0.997847	−	0.0655873i	$-0.0208921\pi$
$660$	−5.63700e15	−	4.21579e15i	−1.75209	−	1.31035i
$661$			1.59871e15i			0.492789i	0.969170	+	0.246394i	$0.0792459\pi$
$661$			1.59871e15i			0.492789i	−0.969170	+	0.246394i	$0.920754\pi$
$662$	4.25113e15	−	2.12918e15i	1.29953	−	0.650868i
$663$	−1.76692e15			−0.535664
$664$	1.90023e14	−	1.05737e15i	0.0571324	−	0.317909i
$665$	7.35335e14			0.219263
$666$	3.63051e15	−	1.81834e15i	1.07364	−	0.537733i
$667$		−	1.24798e14i		−	0.0366029i
$668$	1.44877e15	−	1.93717e15i	0.421434	−	0.563505i
$669$			4.69048e15i			1.35324i
$670$	1.07066e15	+	2.13769e15i	0.306367	+	0.611693i
$671$	2.87805e15			0.816817
$672$	4.32585e15	+	4.63568e15i	1.21770	+	1.30491i
$673$	−9.64803e14			−0.269374			−0.134687	−	0.990888i	$-0.543003\pi$
$673$	−9.64803e14			−0.269374			−0.134687	+	0.990888i	$0.543003\pi$
$674$	2.11692e15	+	4.22666e15i	0.586240	+	1.17049i
$675$			2.07057e14i			0.0568747i
$676$	−1.96261e15	+	2.62423e15i	−0.534720	+	0.714982i
$677$		−	2.38357e15i		−	0.644154i	−0.946714	−	0.322077i	$-0.895619\pi$
$677$		−	2.38357e15i		−	0.644154i	0.946714	−	0.322077i	$-0.104381\pi$
$678$	1.04845e16	−	5.25115e15i	2.81050	−	1.40764i
$679$	−8.03531e14			−0.213658
$680$	−6.61090e14	+	3.67859e15i	−0.174366	+	0.970247i
$681$	3.43415e14			0.0898484
$682$	−7.27886e15	+	3.64561e15i	−1.88908	+	0.946143i
$683$			6.16450e15i			1.58703i	0.608554	+	0.793513i	$0.291750\pi$
$683$			6.16450e15i			1.58703i	−0.608554	+	0.793513i	$0.708250\pi$
$684$	1.19068e15	+	8.90482e14i	0.304078	+	0.227414i
$685$		−	2.91822e15i		−	0.739299i
$686$	−1.66750e15	−	3.32934e15i	−0.419067	−	0.836712i
$687$	2.85924e15			0.712835
$688$	−4.72611e15	+	1.39240e15i	−1.16887	+	0.344372i
$689$	1.64392e15			0.403344
$690$	−2.75590e15	−	5.50245e15i	−0.670800	−	1.33932i
$691$			3.91873e15i			0.946273i	0.880989	+	0.473136i	$0.156878\pi$
$691$			3.91873e15i			0.946273i	−0.880989	+	0.473136i	$0.843122\pi$
$692$	−2.45013e14	−	1.83240e14i	−0.0586956	−	0.0438972i
$693$		−	1.04876e16i		−	2.49255i
$694$	−3.81482e15	+	1.91065e15i	−0.899491	+	0.450510i
$695$	−5.27366e14			−0.123366
$696$	3.02334e14	+	5.43333e13i	0.0701675	+	0.0126100i
$697$	3.57828e15			0.823937
$698$	5.16058e15	−	2.58467e15i	1.17895	−	0.590474i
$699$		−	6.78428e15i		−	1.53773i
$700$	1.09543e14	−	1.46471e14i	0.0246346	−	0.0329393i
$701$		−	6.65082e15i		−	1.48397i	−0.670415	−	0.741986i	$-0.733884\pi$
$701$		−	6.65082e15i		−	1.48397i	0.670415	−	0.741986i	$-0.266116\pi$
$702$	9.66050e14	+	1.92882e15i	0.213868	+	0.427010i
$703$	−5.98548e14			−0.131475
$704$	−2.02684e15	+	5.45699e15i	−0.441744	+	1.18933i
$705$	1.65870e15			0.358697
$706$	−1.56982e15	−	3.13432e15i	−0.336841	−	0.672540i
$707$		−	7.99229e15i		−	1.70163i
$708$	−1.15088e15	+	1.53886e15i	−0.243135	+	0.325100i
$709$			2.68111e15i			0.562032i	0.959703	+	0.281016i	$0.0906713\pi$
$709$			2.68111e15i			0.562032i	−0.959703	+	0.281016i	$0.909329\pi$
$710$	−4.37710e15	+	2.19227e15i	−0.910469	+	0.456008i
$711$	−1.63958e16			−3.38415
$712$	8.08707e15	+	1.45335e15i	1.65635	+	0.297667i
$713$	−7.11719e15			−1.44649
$714$	−7.65265e15	+	3.83283e15i	−1.54338	+	0.773000i
$715$			2.11551e15i			0.423381i
$716$	5.51382e15	+	4.12367e15i	1.09504	+	0.818959i
$717$			1.28033e16i			2.52328i
$718$	1.29677e15	+	2.58915e15i	0.253618	+	0.506375i
$719$	6.52644e14			0.126668			0.0633341	−	0.997992i	$-0.479827\pi$
$719$	6.52644e14			0.126668			0.0633341	+	0.997992i	$0.479827\pi$
$720$	9.45354e15	−	2.78519e15i	1.82081	−	0.536446i
$721$	−6.25008e13			−0.0119465
$722$	2.26265e15	+	4.51762e15i	0.429203	+	0.856950i
$723$			9.69045e15i			1.82425i
$724$	−7.83474e15	−	5.85944e15i	−1.46374	−	1.09470i
$725$		−	8.86102e12i		−	0.00164295i
$726$	5.01167e15	−	2.51009e15i	0.922212	−	0.461890i
$727$	−3.10318e15			−0.566718			−0.283359	−	0.959014i	$-0.591449\pi$
$727$	−3.10318e15			−0.566718			−0.283359	+	0.959014i	$0.591449\pi$
$728$	3.37057e14	−	1.87553e15i	0.0610914	−	0.339939i
$729$	7.44907e15			1.33999
$730$	2.63627e15	−	1.32038e15i	0.470668	−	0.235734i
$731$		−	6.65069e15i		−	1.17848i
$732$	−3.70925e15	+	4.95969e15i	−0.652342	+	0.872256i
$733$		−	3.09196e14i		−	0.0539712i	−0.999636	−	0.0269856i	$-0.991409\pi$
$733$		−	3.09196e14i		−	0.0539712i	0.999636	−	0.0269856i	$-0.00859082\pi$
$734$	1.05580e15	+	2.10802e15i	0.182917	+	0.365213i
$735$	1.13297e15			0.194823
$736$	−3.72087e15	+	3.47219e15i	−0.635063	+	0.592619i
$737$	−5.02653e15			−0.851524
$738$	−4.22537e15	−	8.43641e15i	−0.710485	−	1.41856i
$739$		−	4.52681e15i		−	0.755523i	−0.925903	−	0.377761i	$-0.876694\pi$
$739$		−	4.52681e15i		−	0.755523i	0.925903	−	0.377761i	$-0.123306\pi$
$740$	−2.37613e15	+	3.17716e15i	−0.393636	+	0.526337i
$741$		−	6.86802e14i		−	0.112936i
$742$	7.11994e15	−	3.56602e15i	1.16213	−	0.582053i
$743$	8.68364e15			1.40690			0.703451	−	0.710744i	$-0.251642\pi$
$743$	8.68364e15			1.40690			0.703451	+	0.710744i	$0.251642\pi$
$744$	3.09861e15	−	1.72420e16i	0.498329	−	2.77292i
$745$	−2.92241e15			−0.466532
$746$	7.03844e13	−	3.52520e13i	0.0111535	−	0.00558625i
$747$		−	3.82388e15i		−	0.601507i
$748$	−6.29268e15	−	4.70616e15i	−0.982600	−	0.734866i
$749$		−	3.05938e15i		−	0.474224i
$750$	4.82312e15	+	9.62988e15i	0.742150	+	1.48178i
$751$	1.05365e16			1.60945			0.804723	−	0.593650i	$-0.202314\pi$
$751$	1.05365e16			1.60945			0.804723	+	0.593650i	$0.202314\pi$
$752$	−3.87661e14	−	1.31581e15i	−0.0587833	−	0.199524i
$753$	−9.90769e14			−0.149142
$754$	−4.13422e13	−	8.25441e13i	−0.00617804	−	0.0123351i
$755$			2.50932e15i			0.372261i
$756$	8.36806e15	+	6.25829e15i	1.23241	+	0.921692i
$757$		−	9.90336e14i		−	0.144796i	−0.997376	−	0.0723978i	$-0.976935\pi$
$757$		−	9.90336e14i		−	0.144796i	0.997376	−	0.0723978i	$-0.0230651\pi$
$758$	−5.73978e15	+	2.87476e15i	−0.833133	+	0.417274i
$759$	1.29383e16			1.86444
$760$	−1.42987e15	−	2.56966e14i	−0.204560	−	0.0367621i
$761$	3.52431e15			0.500562			0.250281	−	0.968173i	$-0.419477\pi$
$761$	3.52431e15			0.500562			0.250281	+	0.968173i	$0.419477\pi$
$762$	−7.48130e15	+	3.74701e15i	−1.05493	+	0.528363i
$763$			7.25304e15i			1.01540i
$764$	4.14443e15	−	5.54158e15i	0.576039	−	0.770230i
$765$			1.33032e16i			1.83578i
$766$	−1.49945e15	−	2.99381e15i	−0.205435	−	0.410172i
$767$	5.77521e14			0.0785585
$768$	−6.79172e15	−	1.05258e16i	−0.917262	−	1.42157i
$769$	1.17162e15			0.157105			0.0785526	−	0.996910i	$-0.474970\pi$
$769$	1.17162e15			0.157105			0.0785526	+	0.996910i	$0.474970\pi$
$770$	4.58899e15	+	9.16242e15i	0.610968	+	1.21986i
$771$		−	4.43694e15i		−	0.586522i
$772$	1.07051e15	−	1.43140e15i	0.140507	−	0.187874i
$773$			5.80554e15i			0.756582i	0.925687	+	0.378291i	$0.123488\pi$
$773$			5.80554e15i			0.756582i	−0.925687	+	0.378291i	$0.876512\pi$
$774$	−1.56801e16	+	7.85339e15i	−2.02897	+	1.01621i
$775$	−5.05341e14			−0.0649270
$776$	1.56248e15	+	2.80797e14i	0.199331	+	0.0358223i
$777$	−9.08527e15			−1.15086
$778$	3.62258e15	−	1.81437e15i	0.455649	−	0.228212i
$779$			1.39088e15i			0.173713i
$780$	−3.64562e15	−	2.72648e15i	−0.452117	−	0.338129i
$781$		−	1.02922e16i		−	1.26744i
$782$	−3.07646e15	−	6.14248e15i	−0.376196	−	0.751115i
$783$	5.06238e14			0.0614703
$784$	−2.64792e14	−	8.98762e14i	−0.0319276	−	0.108369i
$785$	−1.12280e16			−1.34438
$786$	−2.54344e15	−	5.07825e15i	−0.302411	−	0.603796i
$787$			3.45721e15i			0.408192i	0.978951	+	0.204096i	$0.0654255\pi$
$787$			3.45721e15i			0.408192i	−0.978951	+	0.204096i	$0.934575\pi$
$788$	−8.90407e13	−	6.65916e13i	−0.0104399	−	0.00780774i
$789$			2.11329e16i			2.46056i
$790$	1.43241e16	−	7.17421e15i	1.65622	−	0.829516i
$791$	−1.70705e16			−1.96009
$792$	−3.66494e15	+	2.03933e16i	−0.417905	+	2.32540i
$793$	1.86133e15			0.210775
$794$	−3.00308e15	+	1.50409e15i	−0.337718	+	0.169146i
$795$		−	1.90236e16i		−	2.12458i
$796$	5.91642e15	−	7.91094e15i	0.656202	−	0.877418i
$797$		−	9.03953e15i		−	0.995692i	−0.867266	−	0.497846i	$-0.834125\pi$
$797$		−	9.03953e15i		−	0.995692i	0.867266	−	0.497846i	$-0.165875\pi$
$798$	−1.48982e15	−	2.97459e15i	−0.162974	−	0.325395i
$799$	1.85164e15			0.201163
$800$	−2.64193e14	+	2.46535e14i	−0.0285053	+	0.0266002i
$801$	2.92461e16			3.13392
$802$	5.38390e14	+	1.07495e15i	0.0572978	+	0.114401i
$803$			6.19888e15i			0.655205i
$804$	6.47822e15	−	8.66212e15i	0.680060	−	0.909319i
$805$			8.95892e15i			0.934068i
$806$	−4.70746e15	+	2.35773e15i	−0.487466	+	0.244147i
$807$	−2.85086e16			−2.93205
$808$	−2.79294e15	+	1.55411e16i	−0.285298	+	1.58752i
$809$	−1.19625e16			−1.21369			−0.606843	−	0.794822i	$-0.707564\pi$
$809$	−1.19625e16			−1.21369			−0.606843	+	0.794822i	$0.707564\pi$
$810$	5.47800e15	−	2.74366e15i	0.552020	−	0.276479i
$811$			5.75039e14i			0.0575549i	0.999586	+	0.0287775i	$0.00916142\pi$
$811$			5.75039e14i			0.0575549i	−0.999586	+	0.0287775i	$0.990839\pi$
$812$	−3.58112e14	−	2.67824e14i	−0.0356008	−	0.0266251i
$813$		−	2.37649e16i		−	2.34659i
$814$	−3.73535e15	−	7.45802e15i	−0.366351	−	0.731458i
$815$	7.44001e15			0.724781
$816$	1.62201e16	−	4.77874e15i	1.56949	−	0.462399i
$817$	2.58513e15			0.248462
$818$	7.14277e15	+	1.42613e16i	0.681904	+	1.36150i
$819$		−	6.78266e15i		−	0.643189i
$820$	7.38293e15	+	5.52153e15i	0.695428	+	0.520096i
$821$			1.01251e16i			0.947358i	0.880698	+	0.473679i	$0.157074\pi$
$821$			1.01251e16i			0.947358i	−0.880698	+	0.473679i	$0.842926\pi$
$822$	−1.18048e16	+	5.91245e15i	−1.09715	+	0.549506i
$823$	3.43088e15			0.316743			0.158372	−	0.987380i	$-0.449376\pi$
$823$	3.43088e15			0.316743			0.158372	+	0.987380i	$0.449376\pi$
$824$	1.21534e14	+	2.18412e13i	0.0111454	+	0.00200298i
$825$	9.18659e14			0.0836869
$826$	2.50128e15	−	1.25277e15i	0.226346	−	0.113365i
$827$		−	6.95249e15i		−	0.624972i	−0.949922	−	0.312486i	$-0.898838\pi$
$827$		−	6.95249e15i		−	0.624972i	0.949922	−	0.312486i	$-0.101162\pi$
$828$	−1.08491e16	+	1.45066e16i	−0.968787	+	1.29538i
$829$		−	5.81905e15i		−	0.516181i	−0.966121	−	0.258091i	$-0.916907\pi$
$829$		−	5.81905e15i		−	0.516181i	0.966121	−	0.258091i	$-0.0830933\pi$
$830$	1.67319e15	+	3.34070e15i	0.147440	+	0.294380i
$831$	2.59816e16			2.27437
$832$	−1.31082e15	+	3.52920e15i	−0.113990	+	0.306901i
$833$	1.26476e15			0.109260
$834$	1.06847e15	+	2.13331e15i	0.0916954	+	0.183080i
$835$			8.41292e15i			0.717251i
$836$	1.82929e15	−	2.44597e15i	0.154934	−	0.207165i
$837$		−	2.88706e16i		−	2.42922i
$838$	7.17957e15	−	3.59588e15i	0.600145	−	0.300582i
$839$	−1.72527e15			−0.143274			−0.0716369	−	0.997431i	$-0.522822\pi$
$839$	−1.72527e15			−0.143274			−0.0716369	+	0.997431i	$0.522822\pi$
$840$	−2.17037e16	−	3.90044e15i	−1.79060	−	0.321794i
$841$	1.21788e16			0.998224
$842$	1.97869e16	−	9.91027e15i	1.61125	−	0.806992i
$843$			3.02353e16i			2.44604i
$844$	1.92982e15	+	1.44327e15i	0.155108	+	0.116002i
$845$		−	1.13967e16i		−	0.910057i
$846$	−2.18648e15	−	4.36555e15i	−0.173464	−	0.346339i
$847$	−8.15985e15			−0.643166
$848$	−1.50910e16	+	4.44608e15i	−1.18179	+	0.348177i
$849$	−3.47641e16			−2.70482
$850$	−2.18437e14	−	4.36134e14i	−0.0168859	−	0.0337144i
$851$		−	7.29238e15i		−	0.560089i
$852$	1.77364e16	+	1.32647e16i	1.35347	+	1.01223i
$853$		−	9.41428e15i		−	0.713785i	−0.934146	−	0.356892i	$-0.883836\pi$
$853$		−	9.41428e15i		−	0.713785i	0.934146	−	0.356892i	$-0.116164\pi$
$854$	8.06153e15	−	4.03761e15i	0.607294	−	0.304163i
$855$	−5.17097e15			−0.387042
$856$	−1.06911e15	+	5.94901e15i	−0.0795093	+	0.442424i
$857$	3.43482e15			0.253810			0.126905	−	0.991915i	$-0.459496\pi$
$857$	3.43482e15			0.253810			0.126905	+	0.991915i	$0.459496\pi$
$858$	8.55769e15	−	4.28612e15i	0.628314	−	0.314691i
$859$			2.51096e16i			1.83180i	0.401406	+	0.915900i	$0.368522\pi$
$859$			2.51096e16i			1.83180i	−0.401406	+	0.915900i	$0.631478\pi$
$860$	1.02625e16	−	1.37221e16i	0.743894	−	0.994672i
$861$			2.11119e16i			1.52058i
$862$	−2.76566e15	−	5.52193e15i	−0.197929	−	0.395186i
$863$	−1.71504e15			−0.121960			−0.0609798	−	0.998139i	$-0.519423\pi$
$863$	−1.71504e15			−0.121960			−0.0609798	+	0.998139i	$0.519423\pi$
$864$	−1.40848e16	−	1.50936e16i	−0.995234	−	1.06651i
$865$	1.06406e15			0.0747100
$866$	−6.44848e15	−	1.28751e16i	−0.449893	−	0.898259i
$867$		−	1.57854e15i		−	0.109434i
$868$	−1.52739e16	+	2.04230e16i	−1.05218	+	1.40689i
$869$			3.36813e16i			2.30558i
$870$	−9.55206e14	+	4.78415e14i	−0.0649742	+	0.0325423i
$871$	−3.25081e15			−0.219731
$872$	2.53461e15	−	1.41036e16i	0.170243	−	0.947306i
$873$	5.65054e15			0.377148
$874$	2.38758e15	−	1.19582e15i	0.158360	−	0.0793146i
$875$		−	1.56791e16i		−	1.03342i
$876$	−1.06824e16	−	7.98914e15i	−0.699675	−	0.523272i
$877$		−	1.38620e16i		−	0.902252i	−0.892460	−	0.451126i	$-0.851023\pi$
$877$		−	1.38620e16i		−	0.902252i	0.892460	−	0.451126i	$-0.148977\pi$
$878$	1.50636e15	+	3.00760e15i	0.0974335	+	0.194536i
$879$	5.35445e14			0.0344173
$880$	−5.72151e15	−	1.94201e16i	−0.365474	−	1.24050i
$881$	1.00462e16			0.637724			0.318862	−	0.947801i	$-0.396699\pi$
$881$	1.00462e16			0.637724			0.318862	+	0.947801i	$0.396699\pi$
$882$	−1.49348e15	−	2.98189e15i	−0.0942153	−	0.188111i
$883$		−	3.57099e15i		−	0.223875i	−0.993715	−	0.111937i	$-0.964294\pi$
$883$		−	3.57099e15i		−	0.223875i	0.993715	−	0.111937i	$-0.0357056\pi$
$884$	−4.06967e15	−	3.04362e15i	−0.253555	−	0.189628i
$885$		−	6.68311e15i		−	0.413800i
$886$	−1.98558e16	+	9.94476e15i	−1.22180	+	0.611940i
$887$	2.42981e15			0.148591			0.0742956	−	0.997236i	$-0.476329\pi$
$887$	2.42981e15			0.148591			0.0742956	+	0.997236i	$0.476329\pi$
$888$	1.76664e16	+	3.17488e15i	1.07369	+	0.192955i
$889$	1.21808e16			0.735728
$890$	−2.55506e16	+	1.27970e16i	−1.53376	+	0.768181i
$891$			1.28809e16i			0.768453i
$892$	−8.07962e15	+	1.08034e16i	−0.479054	+	0.640550i
$893$			7.19731e14i			0.0424118i
$894$	5.92093e15	+	1.18218e16i	0.346764	+	0.692351i
$895$	−2.39459e16			−1.39381
$896$	1.97834e15	+	1.81287e16i	0.114448	+	1.04875i
$897$	8.36762e15			0.481109
$898$	−1.04937e16	−	2.09518e16i	−0.599664	−	1.19729i
$899$			1.23552e15i			0.0701733i
$900$	−7.70320e14	+	1.03001e15i	−0.0434848	+	0.0581442i
$901$		−	2.12364e16i		−	1.19150i
$902$	−1.73306e16	+	8.68003e15i	−0.966447	+	0.484045i
$903$	3.92392e16			2.17489
$904$	3.31939e16	+	5.96537e15i	1.82865	+	0.328633i
$905$	3.40254e16			1.86310
$906$	1.01507e16	−	5.08400e15i	0.552450	−	0.276694i
$907$		−	1.11435e16i		−	0.602812i	−0.953496	−	0.301406i	$-0.902544\pi$
$907$		−	1.11435e16i		−	0.602812i	0.953496	−	0.301406i	$-0.0974560\pi$
$908$	7.90973e14	+	5.91552e14i	0.0425294	+	0.0318068i
$909$			5.62028e16i			3.00370i
$910$	2.96784e15	+	5.92562e15i	0.157657	+	0.314779i
$911$	−6.09398e15			−0.321773			−0.160887	−	0.986973i	$-0.551435\pi$
$911$	−6.09398e15			−0.321773			−0.160887	+	0.986973i	$0.551435\pi$
$912$	1.85750e15	+	6.30475e15i	0.0974891	+	0.330899i
$913$	−7.85525e15			−0.409799
$914$	−8.41499e15	−	1.68014e16i	−0.436365	−	0.871249i
$915$		−	2.15394e16i		−	1.11024i
$916$	6.58557e15	+	4.92521e15i	0.337418	+	0.252348i
$917$			8.26826e15i			0.421098i
$918$	2.49167e16	−	1.24795e16i	1.26141	−	0.631777i
$919$	−5.27884e15			−0.265646			−0.132823	−	0.991140i	$-0.542404\pi$
$919$	−5.27884e15			−0.265646			−0.132823	+	0.991140i	$0.542404\pi$
$920$	3.13073e15	−	1.74207e16i	0.156608	−	0.871432i
$921$	−5.56560e16			−2.76748
$922$	−2.78409e15	+	1.39441e15i	−0.137614	+	0.0689241i
$923$		−	6.65629e15i		−	0.327057i
$924$	2.77664e16	−	3.71269e16i	1.35620	−	1.81340i
$925$		−	5.17780e14i		−	0.0251400i
$926$	−1.02321e16	−	2.04295e16i	−0.493862	−	0.986047i
$927$	4.39514e14			0.0210880
$928$	6.02760e14	+	6.45931e14i	0.0287495	+	0.0308086i
$929$	7.30758e15			0.346487			0.173244	−	0.984879i	$-0.444575\pi$
$929$	7.30758e15			0.346487			0.173244	+	0.984879i	$0.444575\pi$
$930$	2.72838e16	+	5.44751e16i	1.28602	+	2.56769i
$931$			4.91612e14i			0.0230356i
$932$	1.16863e16	−	1.56259e16i	0.544364	−	0.727878i
$933$		−	2.88927e16i		−	1.33795i
$934$	1.46739e16	−	7.34944e15i	0.675521	−	0.338335i
$935$	2.73284e16			1.25069
$936$	−2.37023e15	+	1.31890e16i	−0.107838	+	0.600058i
$937$	−3.26497e16			−1.47677			−0.738384	−	0.674381i	$-0.764411\pi$
$937$	−3.26497e16			−1.47677			−0.738384	+	0.674381i	$0.764411\pi$
$938$	−1.40795e16	+	7.05170e15i	−0.633098	+	0.317087i
$939$		−	5.74173e16i		−	2.56674i
$940$	3.82041e15	+	2.85720e15i	0.169788	+	0.126981i
$941$			5.79621e15i			0.256095i	0.991768	+	0.128047i	$0.0408710\pi$
$941$			5.79621e15i			0.256095i	−0.991768	+	0.128047i	$0.959129\pi$
$942$	2.27485e16	+	4.54198e16i	0.999247	+	1.99510i
$943$	−1.69457e16			−0.740023
$944$	−5.30156e15	+	1.56194e15i	−0.230175	+	0.0678137i
$945$	−3.63415e16			−1.56866
$946$	1.61330e16	+	3.22112e16i	0.692329	+	1.38231i
$947$			1.76522e16i			0.753135i	0.926389	+	0.376567i	$0.122896\pi$
$947$			1.76522e16i			0.753135i	−0.926389	+	0.376567i	$0.877104\pi$
$948$	−5.80424e16	−	4.34087e16i	−2.46207	−	1.84133i
$949$			4.00900e15i			0.169072i
$950$	1.69525e14	−	8.49066e13i	0.00710811	−	0.00356010i
$951$	−9.77949e15			−0.407684
$952$	−2.42283e16	−	4.35414e15i	−1.00420	−	0.180467i
$953$	1.08183e16			0.445806			0.222903	−	0.974841i	$-0.428447\pi$
$953$	1.08183e16			0.445806			0.222903	+	0.974841i	$0.428447\pi$
$954$	−5.00684e16	+	2.50767e16i	−2.05139	+	1.02744i
$955$			2.40665e16i			0.980379i
$956$	−2.20543e16	+	2.94892e16i	−0.893256	+	1.19439i
$957$		−	2.24605e15i		−	0.0904491i
$958$	−1.34380e16	−	2.68304e16i	−0.538053	−	1.07428i
$959$	1.92203e16			0.765169
$960$	4.08402e16	+	1.51689e16i	1.61658	+	0.600431i
$961$	4.50529e16			1.77314
$962$	−2.41577e15	−	4.82334e15i	−0.0945349	−	0.188749i
$963$			2.15140e16i			0.837098i
$964$	−1.66923e16	+	2.23196e16i	−0.645793	+	0.863500i
$965$			6.21641e15i			0.239133i
$966$	3.62408e16	−	1.81512e16i	1.38619	−	0.694273i
$967$	−7.36605e15			−0.280149			−0.140074	−	0.990141i	$-0.544734\pi$
$967$	−7.36605e15			−0.280149			−0.140074	+	0.990141i	$0.544734\pi$
$968$	1.58669e16	+	2.85149e15i	0.600037	+	0.107834i
$969$	−8.87219e15			−0.333618
$970$	−4.93655e15	+	2.47247e15i	−0.184578	+	0.0924456i
$971$			1.36048e15i			0.0505809i	0.999680	+	0.0252905i	$0.00805106\pi$
$971$			1.36048e15i			0.0505809i	−0.999680	+	0.0252905i	$0.991949\pi$
$972$	9.40187e15	+	7.03146e15i	0.347576	+	0.259945i
$973$		−	3.47339e15i		−	0.127683i
$974$	1.71022e16	+	3.41464e16i	0.625141	+	1.24816i
$975$	5.94125e14			0.0215950
$976$	−1.70867e16	+	5.03406e15i	−0.617567	+	0.181947i
$977$	−3.47035e16			−1.24725			−0.623625	−	0.781724i	$-0.714341\pi$
$977$	−3.47035e16			−1.24725			−0.623625	+	0.781724i	$0.714341\pi$
$978$	−1.50738e16	−	3.00964e16i	−0.538715	−	1.07560i
$979$		−	6.00792e16i		−	2.13510i
$980$	2.60953e15	+	1.95161e15i	0.0922187	+	0.0689684i
$981$		−	5.10044e16i		−	1.79237i
$982$	−8.57766e15	+	4.29612e15i	−0.299748	+	0.150129i
$983$	−4.18926e15			−0.145577			−0.0727885	−	0.997347i	$-0.523190\pi$
$983$	−4.18926e15			−0.145577			−0.0727885	+	0.997347i	$0.523190\pi$
$984$	7.37765e15	−	4.10524e16i	0.254944	−	1.41862i
$985$	3.86694e14			0.0132882
$986$	−1.06631e15	+	5.34063e14i	−0.0364386	+	0.0182503i
$987$			1.09247e16i			0.371248i
$988$	1.18306e15	−	1.58188e15i	0.0399799	−	0.0534578i
$989$			3.14958e16i			1.05846i
$990$	−3.22704e16	−	6.44313e16i	−1.07848	−	2.15330i
$991$	−1.28737e16			−0.427855			−0.213928	−	0.976850i	$-0.568626\pi$
$991$	−1.28737e16			−0.427855			−0.213928	+	0.976850i	$0.568626\pi$
$992$	3.68372e16	−	3.43752e16i	1.21751	−	1.13614i
$993$	7.48103e16			2.45890
$994$	−1.44389e16	−	2.88289e16i	−0.471965	−	0.942329i
$995$			3.43563e16i			1.11681i
$996$	1.01239e16	−	1.35368e16i	0.327281	−	0.437613i
$997$			4.16368e16i			1.33861i	0.742988	+	0.669304i	$0.233408\pi$
$997$			4.16368e16i			1.33861i	−0.742988	+	0.669304i	$0.766592\pi$
$998$	1.11192e16	−	5.56906e15i	0.355514	−	0.178059i
$999$	2.95813e16			0.940603

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.12.b.a.5.8	yes	10
3.2	odd	2		72.12.d.b.37.3		10
4.3	odd	2		32.12.b.a.17.1		10
8.3	odd	2		32.12.b.a.17.10		10
8.5	even	2	inner	8.12.b.a.5.7	✓	10
16.3	odd	4		256.12.a.o.1.10		10
16.5	even	4		256.12.a.p.1.10		10
16.11	odd	4		256.12.a.o.1.1		10
16.13	even	4		256.12.a.p.1.1		10
24.5	odd	2		72.12.d.b.37.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.12.b.a.5.7	✓	10	8.5	even	2	inner
8.12.b.a.5.8	yes	10	1.1	even	1	trivial
32.12.b.a.17.1		10	4.3	odd	2
32.12.b.a.17.10		10	8.3	odd	2
72.12.d.b.37.3		10	3.2	odd	2
72.12.d.b.37.4		10	24.5	odd	2
256.12.a.o.1.1		10	16.11	odd	4
256.12.a.o.1.10		10	16.3	odd	4
256.12.a.p.1.1		10	16.13	even	4
256.12.a.p.1.10		10	16.5	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(20.2661 + 40.4634i) q^{2} +712.065i q^{3} +(-1226.57 + 1640.07i) q^{4} -7122.63i q^{5} +(-28812.6 + 14430.8i) q^{6} +46911.8 q^{7} +(-91220.5 - 16393.5i) q^{8} -329890. q^{9} +O(q^{10})\)	\(q+(20.2661 + 40.4634i) q^{2} +712.065i q^{3} +(-1226.57 + 1640.07i) q^{4} -7122.63i q^{5} +(-28812.6 + 14430.8i) q^{6} +46911.8 q^{7} +(-91220.5 - 16393.5i) q^{8} -329890. q^{9} +(288206. - 144348. i) q^{10} +677681. i q^{11} +(-1.16784e6 - 873399. i) q^{12} +438277. i q^{13} +(950718. + 1.89821e6i) q^{14} +5.07178e6 q^{15} +(-1.18535e6 - 4.02332e6i) q^{16} +5.66172e6 q^{17} +(-6.68557e6 - 1.33485e7i) q^{18} +2.20071e6i q^{19} +(1.16816e7 + 8.73642e6i) q^{20} +3.34042e7i q^{21} +(-2.74213e7 + 1.37339e7i) q^{22} -2.68123e7 q^{23} +(1.16732e7 - 6.49550e7i) q^{24} -1.90375e6 q^{25} +(-1.77342e7 + 8.88217e6i) q^{26} -1.08763e8i q^{27} +(-5.75407e7 + 7.69385e7i) q^{28} +4.65452e6i q^{29} +(1.02785e8 + 2.05221e8i) q^{30} +2.65446e8 q^{31} +(1.38775e8 - 1.29500e8i) q^{32} -4.82553e8 q^{33} +(1.14741e8 + 2.29092e8i) q^{34} -3.34135e8i q^{35} +(4.04634e8 - 5.41042e8i) q^{36} +2.71979e8i q^{37} +(-8.90482e7 + 4.45998e7i) q^{38} -3.12082e8 q^{39} +(-1.16765e8 + 6.49730e8i) q^{40} +6.32013e8 q^{41} +(-1.35165e9 + 6.76973e8i) q^{42} -1.17468e9i q^{43} +(-1.11144e9 - 8.31225e8i) q^{44} +2.34968e9i q^{45} +(-5.43379e8 - 1.08491e9i) q^{46} +3.27045e8 q^{47} +(2.86487e9 - 8.44043e8i) q^{48} +2.23388e8 q^{49} +(-3.85815e7 - 7.70320e7i) q^{50} +4.03151e9i q^{51} +(-7.18805e8 - 5.37579e8i) q^{52} -3.75087e9i q^{53} +(4.40091e9 - 2.20420e9i) q^{54} +4.82687e9 q^{55} +(-4.27932e9 - 7.69049e8i) q^{56} -1.56705e9 q^{57} +(-1.88337e8 + 9.43288e7i) q^{58} -1.31771e9i q^{59} +(-6.22090e9 + 8.31806e9i) q^{60} -4.24691e9i q^{61} +(5.37954e9 + 1.07408e10i) q^{62} -1.54757e10 q^{63} +(8.05244e9 + 2.99085e9i) q^{64} +3.12169e9 q^{65} +(-9.77946e9 - 1.95257e10i) q^{66} +7.41724e9i q^{67} +(-6.94450e9 + 9.28561e9i) q^{68} -1.90921e10i q^{69} +(1.35202e10 - 6.77161e9i) q^{70} -1.51874e10 q^{71} +(3.00927e10 + 5.40805e9i) q^{72} +9.14718e9 q^{73} +(-1.10052e10 + 5.51196e9i) q^{74} -1.35559e9i q^{75} +(-3.60932e9 - 2.69933e9i) q^{76} +3.17912e10i q^{77} +(-6.32468e9 - 1.26279e10i) q^{78} +4.97008e10 q^{79} +(-2.86567e10 + 8.44278e9i) q^{80} +1.90073e10 q^{81} +(1.28084e10 + 2.55734e10i) q^{82} +1.15914e10i q^{83} +(-5.47852e10 - 4.09727e10i) q^{84} -4.03263e10i q^{85} +(4.75314e10 - 2.38061e10i) q^{86} -3.31432e9 q^{87} +(1.11096e10 - 6.18185e10i) q^{88} -8.86540e10 q^{89} +(-9.50762e10 + 4.76189e10i) q^{90} +2.05604e10i q^{91} +(3.28872e10 - 4.39739e10i) q^{92} +1.89015e11i q^{93} +(6.62792e9 + 1.32333e10i) q^{94} +1.56748e10 q^{95} +(9.22125e10 + 9.88169e10i) q^{96} -1.71286e10 q^{97} +(4.52720e9 + 9.03904e9i) q^{98} -2.23560e11i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9}+O(q^{10}) \) 10 * q + 22 * q^2 + 436 * q^4 - 24308 * q^6 - 33616 * q^7 - 208472 * q^8 - 472394 * q^9	\( 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9} + 29864 q^{10} - 476216 q^{12} + 2264272 q^{14} + 3391792 q^{15} + 3757072 q^{16} + 2639732 q^{17} + 2329130 q^{18} + 8296432 q^{20} - 24201892 q^{22} - 45357808 q^{23} + 10668944 q^{24} - 41502654 q^{25} - 101931080 q^{26} - 95722144 q^{28} + 261362768 q^{30} + 442035392 q^{31} + 343908512 q^{32} - 54732216 q^{33} - 187103796 q^{34} - 431195700 q^{36} + 375100844 q^{38} - 431459312 q^{39} + 1519138784 q^{40} - 654907964 q^{41} - 3697737056 q^{42} - 4127012952 q^{44} + 6028867440 q^{46} - 560226528 q^{47} + 9357606048 q^{48} + 1143661722 q^{49} - 9626584226 q^{50} - 11595427248 q^{52} + 20050494008 q^{54} + 5632783984 q^{55} + 18698733760 q^{56} - 783862360 q^{57} - 22828679464 q^{58} - 43681325472 q^{60} + 40774631744 q^{62} - 14483624624 q^{63} + 55266728512 q^{64} - 80291360 q^{65} - 83128448712 q^{66} - 83303223768 q^{68} + 100120831168 q^{70} - 11769460176 q^{71} + 112862051672 q^{72} + 32304890372 q^{73} - 102103996184 q^{74} - 97501928568 q^{76} + 144445560944 q^{78} + 57291670496 q^{79} + 128322038976 q^{80} - 23172996094 q^{81} - 123309929604 q^{82} - 199990865984 q^{84} + 130201908124 q^{86} - 73844404272 q^{87} + 169216119632 q^{88} - 108276011804 q^{89} - 228506434984 q^{90} - 141139403232 q^{92} + 145336130016 q^{94} + 70146835376 q^{95} + 109508068928 q^{96} + 60995282900 q^{97} - 6194726778 q^{98}+O(q^{100}) \) 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

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