LMFDB - Embedded newform 4.15.b.a.3.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,15,Mod(3,4)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 15, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	4.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.97315872608$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 88x^{4} - 1824x^{3} + 325632x^{2} + 21572352x + 982333440 $ x^6 - x^5 + 88x^4 - 1824x^3 + 325632x^2 + 21572352x + 982333440
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.2
Root			$-24.5778 + 14.3983i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.15.b.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-114.311 + 57.5931i) q^{2} +2948.24i q^{3} +(9750.07 - 13167.1i) q^{4} -81680.5 q^{5} +(-169798. - 337016. i) q^{6} -1.09921e6i q^{7} +(-356209. + 2.06668e6i) q^{8} -3.90914e6 q^{9} +O(q^{10})$	\(q+(-114.311 + 57.5931i) q^{2} +2948.24i q^{3} +(9750.07 - 13167.1i) q^{4} -81680.5 q^{5} +(-169798. - 337016. i) q^{6} -1.09921e6i q^{7} +(-356209. + 2.06668e6i) q^{8} -3.90914e6 q^{9} +(9.33699e6 - 4.70423e6i) q^{10} +4.90926e6i q^{11} +(3.88196e7 + 2.87455e7i) q^{12} -7.29644e7 q^{13} +(6.33071e7 + 1.25652e8i) q^{14} -2.40814e8i q^{15} +(-7.83078e7 - 2.56760e8i) q^{16} -4.69361e8 q^{17} +(4.46858e8 - 2.25139e8i) q^{18} +6.82881e8i q^{19} +(-7.96390e8 + 1.07549e9i) q^{20} +3.24074e9 q^{21} +(-2.82739e8 - 5.61183e8i) q^{22} +9.17041e8i q^{23} +(-6.09306e9 - 1.05019e9i) q^{24} +5.68188e8 q^{25} +(8.34064e9 - 4.20224e9i) q^{26} +2.57627e9i q^{27} +(-1.44734e10 - 1.07174e10i) q^{28} -1.00105e10 q^{29} +(1.38692e10 + 2.75277e10i) q^{30} -3.41422e10i q^{31} +(2.37390e10 + 2.48405e10i) q^{32} -1.44737e10 q^{33} +(5.36532e10 - 2.70320e10i) q^{34} +8.97842e10i q^{35} +(-3.81143e10 + 5.14718e10i) q^{36} -4.99005e10 q^{37} +(-3.93292e10 - 7.80609e10i) q^{38} -2.15116e11i q^{39} +(2.90953e10 - 1.68807e11i) q^{40} +1.91904e11 q^{41} +(-3.70453e11 + 1.86644e11i) q^{42} +3.10023e11i q^{43} +(6.46405e10 + 4.78656e10i) q^{44} +3.19300e11 q^{45} +(-5.28152e10 - 1.04828e11i) q^{46} +4.62878e11i q^{47} +(7.56988e11 - 2.30870e11i) q^{48} -5.30046e11 q^{49} +(-6.49503e10 + 3.27237e10i) q^{50} -1.38379e12i q^{51} +(-7.11407e11 + 9.60726e11i) q^{52} -5.28568e11 q^{53} +(-1.48375e11 - 2.94496e11i) q^{54} -4.00991e11i q^{55} +(2.27172e12 + 3.91549e11i) q^{56} -2.01329e12 q^{57} +(1.14431e12 - 5.76534e11i) q^{58} +8.92307e11i q^{59} +(-3.17081e12 - 2.34795e12i) q^{60} +3.16992e12 q^{61} +(1.96636e12 + 3.90284e12i) q^{62} +4.29697e12i q^{63} +(-4.14428e12 - 1.47234e12i) q^{64} +5.95976e12 q^{65} +(1.65450e12 - 8.33583e11i) q^{66} -5.43679e12i q^{67} +(-4.57630e12 + 6.18011e12i) q^{68} -2.70365e12 q^{69} +(-5.17095e12 - 1.02633e13i) q^{70} +2.22157e12i q^{71} +(1.39247e12 - 8.07893e12i) q^{72} -8.53427e12 q^{73} +(5.70419e12 - 2.87393e12i) q^{74} +1.67515e12i q^{75} +(8.99154e12 + 6.65813e12i) q^{76} +5.39632e12 q^{77} +(1.23892e13 + 2.45902e13i) q^{78} -1.09319e13i q^{79} +(6.39622e12 + 2.09723e13i) q^{80} -2.62927e13 q^{81} +(-2.19368e13 + 1.10524e13i) q^{82} +8.13058e12i q^{83} +(3.15974e13 - 4.26710e13i) q^{84} +3.83377e13 q^{85} +(-1.78552e13 - 3.54390e13i) q^{86} -2.95132e13i q^{87} +(-1.01459e13 - 1.74872e12i) q^{88} -6.18420e13 q^{89} +(-3.64996e13 + 1.83895e13i) q^{90} +8.02033e13i q^{91} +(1.20747e13 + 8.94121e12i) q^{92} +1.00659e14 q^{93} +(-2.66586e13 - 5.29121e13i) q^{94} -5.57781e13i q^{95} +(-7.32357e13 + 6.99883e13i) q^{96} +7.86895e13 q^{97} +(6.05901e13 - 3.05270e13i) q^{98} -1.91910e13i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 92 q^{2} - 1392 q^{4} + 8060 q^{5} + 50784 q^{6} + 446272 q^{8} - 2998698 q^{9}+O(q^{10}) $ 6 * q - 92 * q^2 - 1392 * q^4 + 8060 * q^5 + 50784 * q^6 + 446272 * q^8 - 2998698 * q^9	\( 6 q - 92 q^{2} - 1392 q^{4} + 8060 q^{5} + 50784 q^{6} + 446272 q^{8} - 2998698 q^{9} + 5796840 q^{10} + 193920 q^{12} - 80775396 q^{13} + 175232064 q^{14} - 353013504 q^{16} - 120131764 q^{17} + 1599402372 q^{18} - 5047343200 q^{20} + 1226658048 q^{21} + 9916985760 q^{22} - 24092176896 q^{24} + 3942973410 q^{25} + 39549467048 q^{26} - 65094731520 q^{28} - 8035796644 q^{29} + 99698873280 q^{30} - 85711465472 q^{32} - 37769804160 q^{33} + 98089165512 q^{34} - 27478990320 q^{36} + 31334118396 q^{37} - 165268841760 q^{38} + 435607171200 q^{40} + 83362750892 q^{41} - 830203906560 q^{42} + 915657452160 q^{44} + 271078769820 q^{45} - 1712365889856 q^{46} + 2292961843200 q^{48} - 551978693658 q^{49} - 1639579094580 q^{50} + 1057159118496 q^{52} + 76712275004 q^{53} + 445471858368 q^{54} - 560223046656 q^{56} - 2647253865600 q^{57} + 4483777382184 q^{58} - 9544013748480 q^{60} + 6210000787932 q^{61} + 10375644284160 q^{62} - 14398852657152 q^{64} - 7189912943720 q^{65} + 15071210499840 q^{66} - 18507298307296 q^{68} + 19348372347648 q^{69} + 12679529923200 q^{70} - 5286233111232 q^{72} - 29882649313236 q^{73} - 1536652566808 q^{74} + 21457134000000 q^{76} + 37339673521920 q^{77} - 29727224255040 q^{78} + 57843429624320 q^{80} - 98651978873946 q^{81} - 71900577251064 q^{82} + 102961968764928 q^{84} + 151199882653560 q^{85} - 100164269733216 q^{86} + 51557990330880 q^{88} - 180966014731924 q^{89} - 84934442792280 q^{90} + 82241452266240 q^{92} + 295002300748800 q^{93} - 40381697410176 q^{94} - 82703070928896 q^{96} - 345459072299124 q^{97} + 121406102961892 q^{98}+O(q^{100}) \) 6 * q - 92 * q^2 - 1392 * q^4 + 8060 * q^5 + 50784 * q^6 + 446272 * q^8 - 2998698 * q^9 + 5796840 * q^10 + 193920 * q^12 - 80775396 * q^13 + 175232064 * q^14 - 353013504 * q^16 - 120131764 * q^17 + 1599402372 * q^18 - 5047343200 * q^20 + 1226658048 * q^21 + 9916985760 * q^22 - 24092176896 * q^24 + 3942973410 * q^25 + 39549467048 * q^26 - 65094731520 * q^28 - 8035796644 * q^29 + 99698873280 * q^30 - 85711465472 * q^32 - 37769804160 * q^33 + 98089165512 * q^34 - 27478990320 * q^36 + 31334118396 * q^37 - 165268841760 * q^38 + 435607171200 * q^40 + 83362750892 * q^41 - 830203906560 * q^42 + 915657452160 * q^44 + 271078769820 * q^45 - 1712365889856 * q^46 + 2292961843200 * q^48 - 551978693658 * q^49 - 1639579094580 * q^50 + 1057159118496 * q^52 + 76712275004 * q^53 + 445471858368 * q^54 - 560223046656 * q^56 - 2647253865600 * q^57 + 4483777382184 * q^58 - 9544013748480 * q^60 + 6210000787932 * q^61 + 10375644284160 * q^62 - 14398852657152 * q^64 - 7189912943720 * q^65 + 15071210499840 * q^66 - 18507298307296 * q^68 + 19348372347648 * q^69 + 12679529923200 * q^70 - 5286233111232 * q^72 - 29882649313236 * q^73 - 1536652566808 * q^74 + 21457134000000 * q^76 + 37339673521920 * q^77 - 29727224255040 * q^78 + 57843429624320 * q^80 - 98651978873946 * q^81 - 71900577251064 * q^82 + 102961968764928 * q^84 + 151199882653560 * q^85 - 100164269733216 * q^86 + 51557990330880 * q^88 - 180966014731924 * q^89 - 84934442792280 * q^90 + 82241452266240 * q^92 + 295002300748800 * q^93 - 40381697410176 * q^94 - 82703070928896 * q^96 - 345459072299124 * q^97 + 121406102961892 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−114.311	+	57.5931i	−0.893056	+	0.449946i
$2$	−114.311	+	57.5931i	−0.893056	+	0.449946i
$3$			2948.24i			1.34807i	0.738698	+	0.674037i	$0.235441\pi$
$3$			2948.24i			1.34807i	−0.738698	+	0.674037i	$0.764559\pi$
$4$	9750.07	−	13167.1i	0.595097	−	0.803654i
$5$	−81680.5			−1.04551			−0.522755	−	0.852483i	$-0.675096\pi$
$5$	−81680.5			−1.04551			−0.522755	+	0.852483i	$0.675096\pi$
$6$	−169798.	−	337016.i	−0.606561	−	1.20390i
$7$		−	1.09921e6i		−	1.33474i	−0.744728	−	0.667368i	$-0.767421\pi$
$7$		−	1.09921e6i		−	1.33474i	0.744728	−	0.667368i	$-0.232579\pi$
$8$	−356209.	+	2.06668e6i	−0.169854	+	0.985469i
$9$	−3.90914e6			−0.817303
$10$	9.33699e6	−	4.70423e6i	0.933699	−	0.470423i
$11$			4.90926e6i			0.251923i	0.992035	+	0.125961i	$0.0402015\pi$
$11$			4.90926e6i			0.251923i	−0.992035	+	0.125961i	$0.959798\pi$
$12$	3.88196e7	+	2.87455e7i	1.08338	+	0.802235i
$13$	−7.29644e7			−1.16281			−0.581403	−	0.813616i	$-0.697496\pi$
$13$	−7.29644e7			−1.16281			−0.581403	+	0.813616i	$0.697496\pi$
$14$	6.33071e7	+	1.25652e8i	0.600559	+	1.19199i
$15$		−	2.40814e8i		−	1.40943i
$16$	−7.83078e7	−	2.56760e8i	−0.291719	−	0.956504i
$17$	−4.69361e8			−1.14384			−0.571919	−	0.820310i	$-0.693801\pi$
$17$	−4.69361e8			−1.14384			−0.571919	+	0.820310i	$0.693801\pi$
$18$	4.46858e8	−	2.25139e8i	0.729897	−	0.367742i
$19$			6.82881e8i			0.763958i	0.924171	+	0.381979i	$0.124757\pi$
$19$			6.82881e8i			0.763958i	−0.924171	+	0.381979i	$0.875243\pi$
$20$	−7.96390e8	+	1.07549e9i	−0.622180	+	0.840229i
$21$	3.24074e9			1.79932
$22$	−2.82739e8	−	5.61183e8i	−0.113352	−	0.224981i
$23$			9.17041e8i			0.269336i	0.990891	+	0.134668i	$0.0429967\pi$
$23$			9.17041e8i			0.269336i	−0.990891	+	0.134668i	$0.957003\pi$
$24$	−6.09306e9	−	1.05019e9i	−1.32849	−	0.228975i
$25$	5.68188e8			0.0930920
$26$	8.34064e9	−	4.20224e9i	1.03845	−	0.523200i
$27$			2.57627e9i			0.246289i
$28$	−1.44734e10	−	1.07174e10i	−1.07267	−	0.794297i
$29$	−1.00105e10			−0.580321			−0.290161	−	0.956978i	$-0.593709\pi$
$29$	−1.00105e10			−0.580321			−0.290161	+	0.956978i	$0.593709\pi$
$30$	1.38692e10	+	2.75277e10i	0.634165	+	1.25870i
$31$		−	3.41422e10i		−	1.24097i	−0.784220	−	0.620483i	$-0.786937\pi$
$31$		−	3.41422e10i		−	1.24097i	0.784220	−	0.620483i	$-0.213063\pi$
$32$	2.37390e10	+	2.48405e10i	0.690897	+	0.722953i
$33$	−1.44737e10			−0.339610
$34$	5.36532e10	−	2.70320e10i	1.02151	−	0.514666i
$35$			8.97842e10i			1.39548i
$36$	−3.81143e10	+	5.14718e10i	−0.486375	+	0.656829i
$37$	−4.99005e10			−0.525646			−0.262823	−	0.964844i	$-0.584653\pi$
$37$	−4.99005e10			−0.525646			−0.262823	+	0.964844i	$0.584653\pi$
$38$	−3.93292e10	−	7.80609e10i	−0.343740	−	0.682257i
$39$		−	2.15116e11i		−	1.56755i
$40$	2.90953e10	−	1.68807e11i	0.177584	−	1.03032i
$41$	1.91904e11			0.985366			0.492683	−	0.870209i	$-0.336016\pi$
$41$	1.91904e11			0.985366			0.492683	+	0.870209i	$0.336016\pi$
$42$	−3.70453e11	+	1.86644e11i	−1.60690	+	0.809598i
$43$			3.10023e11i			1.14055i	0.821454	+	0.570275i	$0.193163\pi$
$43$			3.10023e11i			1.14055i	−0.821454	+	0.570275i	$0.806837\pi$
$44$	6.46405e10	+	4.78656e10i	0.202459	+	0.149918i
$45$	3.19300e11			0.854499
$46$	−5.28152e10	−	1.04828e11i	−0.121187	−	0.240532i
$47$			4.62878e11i			0.913654i	0.889556	+	0.456827i	$0.151014\pi$
$47$			4.62878e11i			0.913654i	−0.889556	+	0.456827i	$0.848986\pi$
$48$	7.56988e11	−	2.30870e11i	1.28944	−	0.393259i
$49$	−5.30046e11			−0.781521
$50$	−6.49503e10	+	3.27237e10i	−0.0831363	+	0.0418864i
$51$		−	1.38379e12i		−	1.54198i
$52$	−7.11407e11	+	9.60726e11i	−0.691982	+	0.934494i
$53$	−5.28568e11			−0.449956			−0.224978	−	0.974364i	$-0.572231\pi$
$53$	−5.28568e11			−0.449956			−0.224978	+	0.974364i	$0.572231\pi$
$54$	−1.48375e11	−	2.94496e11i	−0.110817	−	0.219950i
$55$		−	4.00991e11i		−	0.263388i
$56$	2.27172e12	+	3.91549e11i	1.31534	+	0.226710i
$57$	−2.01329e12			−1.02987
$58$	1.14431e12	−	5.76534e11i	0.518259	−	0.261113i
$59$			8.92307e11i			0.358550i	0.983799	+	0.179275i	$0.0573753\pi$
$59$			8.92307e11i			0.358550i	−0.983799	+	0.179275i	$0.942625\pi$
$60$	−3.17081e12	−	2.34795e12i	−1.13269	−	0.838745i
$61$	3.16992e12			1.00865			0.504324	−	0.863514i	$-0.331742\pi$
$61$	3.16992e12			1.00865			0.504324	+	0.863514i	$0.331742\pi$
$62$	1.96636e12	+	3.90284e12i	0.558368	+	1.10825i
$63$			4.29697e12i			1.09088i
$64$	−4.14428e12	−	1.47234e12i	−0.942299	−	0.334771i
$65$	5.95976e12			1.21573
$66$	1.65450e12	−	8.33583e11i	0.303291	−	0.152806i
$67$		−	5.43679e12i		−	0.897055i	−0.893769	−	0.448528i	$-0.851949\pi$
$67$		−	5.43679e12i		−	0.897055i	0.893769	−	0.448528i	$-0.148051\pi$
$68$	−4.57630e12	+	6.18011e12i	−0.680695	+	0.919250i
$69$	−2.70365e12			−0.363084
$70$	−5.17095e12	−	1.02633e13i	−0.627891	−	1.24624i
$71$			2.22157e12i			0.244260i	0.992514	+	0.122130i	$0.0389725\pi$
$71$			2.22157e12i			0.244260i	−0.992514	+	0.122130i	$0.961028\pi$
$72$	1.39247e12	−	8.07893e12i	0.138822	−	0.805427i
$73$	−8.53427e12			−0.772514			−0.386257	−	0.922391i	$-0.626232\pi$
$73$	−8.53427e12			−0.772514			−0.386257	+	0.922391i	$0.626232\pi$
$74$	5.70419e12	−	2.87393e12i	0.469431	−	0.236512i
$75$			1.67515e12i			0.125495i
$76$	8.99154e12	+	6.65813e12i	0.613958	+	0.454629i
$77$	5.39632e12			0.336250
$78$	1.23892e13	+	2.45902e13i	0.705312	+	1.39991i
$79$		−	1.09319e13i		−	0.569252i	−0.958639	−	0.284626i	$-0.908131\pi$
$79$		−	1.09319e13i		−	0.569252i	0.958639	−	0.284626i	$-0.0918694\pi$
$80$	6.39622e12	+	2.09723e13i	0.304996	+	1.00003i
$81$	−2.62927e13			−1.14932
$82$	−2.19368e13	+	1.10524e13i	−0.879987	+	0.443362i
$83$			8.13058e12i			0.299623i	0.988715	+	0.149811i	$0.0478667\pi$
$83$			8.13058e12i			0.299623i	−0.988715	+	0.149811i	$0.952133\pi$
$84$	3.15974e13	−	4.26710e13i	1.07077	−	1.44603i
$85$	3.83377e13			1.19590
$86$	−1.78552e13	−	3.54390e13i	−0.513186	−	1.01857i
$87$		−	2.95132e13i		−	0.782316i
$88$	−1.01459e13	−	1.74872e12i	−0.248262	−	0.0427900i
$89$	−6.18420e13			−1.39815			−0.699075	−	0.715049i	$-0.746405\pi$
$89$	−6.18420e13			−1.39815			−0.699075	+	0.715049i	$0.746405\pi$
$90$	−3.64996e13	+	1.83895e13i	−0.763115	+	0.384478i
$91$			8.02033e13i			1.55204i
$92$	1.20747e13	+	8.94121e12i	0.216453	+	0.160281i
$93$	1.00659e14			1.67291
$94$	−2.66586e13	−	5.29121e13i	−0.411095	−	0.815943i
$95$		−	5.57781e13i		−	0.798726i
$96$	−7.32357e13	+	6.99883e13i	−0.974594	+	0.931380i
$97$	7.86895e13			0.973900			0.486950	−	0.873430i	$-0.338109\pi$
$97$	7.86895e13			0.973900			0.486950	+	0.873430i	$0.338109\pi$
$98$	6.05901e13	−	3.05270e13i	0.697942	−	0.351642i
$99$		−	1.91910e13i		−	0.205897i
$100$	5.53988e12	−	7.48137e12i	0.0553988	−	0.0748137i
$101$	−6.76553e13			−0.631034			−0.315517	−	0.948920i	$-0.602178\pi$
$101$	−6.76553e13			−0.631034			−0.315517	+	0.948920i	$0.602178\pi$
$102$	7.96967e13	+	1.58182e14i	0.693808	+	1.37707i
$103$			2.12142e14i			1.72491i	0.506132	+	0.862456i	$0.331075\pi$
$103$			2.12142e14i			1.72491i	−0.506132	+	0.862456i	$0.668925\pi$
$104$	2.59906e13	−	1.50794e14i	0.197507	−	1.14591i
$105$	−2.64705e14			−1.88121
$106$	6.04212e13	−	3.04419e13i	0.401836	−	0.202456i
$107$		−	2.80059e14i		−	1.74406i	−0.489449	−	0.872032i	$-0.662802\pi$
$107$		−	2.80059e14i		−	1.74406i	0.489449	−	0.872032i	$-0.337198\pi$
$108$	3.39219e13	+	2.51188e13i	0.197931	+	0.146566i
$109$	1.85065e14			1.01237			0.506183	−	0.862426i	$-0.331056\pi$
$109$	1.85065e14			1.01237			0.506183	+	0.862426i	$0.331056\pi$
$110$	2.30943e13	+	4.58377e13i	0.118510	+	0.235220i
$111$		−	1.47119e14i		−	0.708609i
$112$	−2.82233e14	+	8.60769e13i	−1.27668	+	0.389368i
$113$	−3.29356e14			−1.39996			−0.699981	−	0.714162i	$-0.746808\pi$
$113$	−3.29356e14			−1.39996			−0.699981	+	0.714162i	$0.746808\pi$
$114$	2.30142e14	−	1.15952e14i	0.919733	−	0.463387i
$115$		−	7.49044e13i		−	0.281593i
$116$	−9.76027e13	+	1.31808e14i	−0.345347	+	0.466377i
$117$	2.85228e14			0.950365
$118$	−5.13907e13	−	1.02001e14i	−0.161328	−	0.320206i
$119$			5.15928e14i			1.52672i
$120$	4.97684e14	+	8.57799e13i	1.38895	+	0.239396i
$121$	3.55649e14			0.936535
$122$	−3.62358e14	+	1.82566e14i	−0.900780	+	0.453838i
$123$			5.65779e14i			1.32835i
$124$	−4.49553e14	−	3.32889e14i	−0.997307	−	0.738495i
$125$	4.52128e14			0.948182
$126$	−2.47476e14	−	4.91192e14i	−0.490839	−	0.974220i
$127$		−	5.08059e14i		−	0.953429i	−0.879058	−	0.476715i	$-0.841828\pi$
$127$		−	5.08059e14i		−	0.953429i	0.879058	−	0.476715i	$-0.158172\pi$
$128$	5.58534e14	−	7.03770e13i	0.992155	−	0.125015i
$129$	−9.14021e14			−1.53755
$130$	−6.81267e14	+	3.43241e14i	−1.08571	+	0.547011i
$131$		−	8.76324e14i		−	1.32363i	−0.749668	−	0.661814i	$-0.769787\pi$
$131$		−	8.76324e14i		−	1.32363i	0.749668	−	0.661814i	$-0.230213\pi$
$132$	−1.41119e14	+	1.90576e14i	−0.202101	+	0.272929i
$133$	7.50631e14			1.01968
$134$	3.13122e14	+	6.21486e14i	0.403627	+	0.801120i
$135$		−	2.10431e14i		−	0.257498i
$136$	1.67191e14	−	9.70019e14i	0.194285	−	1.12722i
$137$	−7.70700e14			−0.850827			−0.425414	−	0.904999i	$-0.639871\pi$
$137$	−7.70700e14			−0.850827			−0.425414	+	0.904999i	$0.639871\pi$
$138$	3.09058e14	−	1.55712e14i	0.324255	−	0.163368i
$139$			1.67539e15i			1.67113i	0.549388	+	0.835567i	$0.314861\pi$
$139$			1.67539e15i			1.67113i	−0.549388	+	0.835567i	$0.685139\pi$
$140$	1.18220e15	+	8.75402e14i	1.12148	+	0.830446i
$141$	−1.36467e15			−1.23167
$142$	−1.27947e14	−	2.53951e14i	−0.109904	−	0.218138i
$143$		−	3.58201e14i		−	0.292937i
$144$	3.06116e14	+	1.00371e15i	0.238423	+	0.781754i
$145$	8.17660e14			0.606732
$146$	9.75562e14	−	4.91515e14i	0.689898	−	0.347590i
$147$		−	1.56270e15i		−	1.05355i
$148$	−4.86534e14	+	6.57044e14i	−0.312810	+	0.422437i
$149$	6.40824e13			0.0393038			0.0196519	−	0.999807i	$-0.493744\pi$
$149$	6.40824e13			0.0393038			0.0196519	+	0.999807i	$0.493744\pi$
$150$	−9.64773e13	−	1.91489e14i	−0.0564659	−	0.112074i
$151$		−	3.11313e14i		−	0.173924i	−0.996212	−	0.0869618i	$-0.972284\pi$
$151$		−	3.11313e14i		−	0.173924i	0.996212	−	0.0869618i	$-0.0277158\pi$
$152$	−1.41130e15	−	2.43248e14i	−0.752858	−	0.129761i
$153$	1.83480e15			0.934863
$154$	−6.16859e14	+	3.10791e14i	−0.300290	+	0.151295i
$155$			2.78875e15i			1.29744i
$156$	−2.83245e15	−	2.09740e15i	−1.25977	−	0.932843i
$157$	−1.13617e15			−0.483222			−0.241611	−	0.970373i	$-0.577676\pi$
$157$	−1.13617e15			−0.483222			−0.241611	+	0.970373i	$0.577676\pi$
$158$	6.29600e14	+	1.24963e15i	0.256133	+	0.508374i
$159$		−	1.55834e15i		−	0.606574i
$160$	−1.93902e15	−	2.02898e15i	−0.722340	−	0.755855i
$161$	1.00802e15			0.359492
$162$	3.00555e15	−	1.51428e15i	1.02641	−	0.517132i
$163$			1.63279e13i			0.00534092i	0.999996	+	0.00267046i	$0.000850035\pi$
$163$			1.63279e13i			0.00534092i	−0.999996	+	0.00267046i	$0.999150\pi$
$164$	1.87108e15	−	2.52682e15i	0.586388	−	0.791893i
$165$	1.18222e15			0.355066
$166$	−4.68265e14	−	9.29416e14i	−0.134814	−	0.267580i
$167$			4.16001e15i			1.14836i	0.818728	+	0.574181i	$0.194680\pi$
$167$			4.16001e15i			1.14836i	−0.818728	+	0.574181i	$0.805320\pi$
$168$	−1.15438e15	+	6.69757e15i	−0.305622	+	1.77318i
$169$	1.38642e15			0.352118
$170$	−4.38242e15	+	2.20799e15i	−1.06800	+	0.538088i
$171$		−	2.66947e15i		−	0.624386i
$172$	4.08209e15	+	3.02274e15i	0.916608	+	0.678738i
$173$	−1.71620e15			−0.370036			−0.185018	−	0.982735i	$-0.559234\pi$
$173$	−1.71620e15			−0.370036			−0.185018	+	0.982735i	$0.559234\pi$
$174$	1.69976e15	+	3.37369e15i	0.352000	+	0.698651i
$175$		−	6.24560e14i		−	0.124253i
$176$	1.26050e15	−	3.84433e14i	0.240965	−	0.0734907i
$177$	−2.63073e15			−0.483352
$178$	7.06923e15	−	3.56167e15i	1.24863	−	0.629092i
$179$		−	9.91848e15i		−	1.68451i	−0.539078	−	0.842256i	$-0.681227\pi$
$179$		−	9.91848e15i		−	1.68451i	0.539078	−	0.842256i	$-0.318773\pi$
$180$	3.11320e15	−	4.20425e15i	0.508510	−	0.686721i
$181$	−1.24532e16			−1.95673			−0.978366	−	0.206884i	$-0.933668\pi$
$181$	−1.24532e16			−1.95673			−0.978366	+	0.206884i	$0.933668\pi$
$182$	−4.61916e15	−	9.16813e15i	−0.698334	−	1.38606i
$183$			9.34569e15i			1.35973i
$184$	−1.89523e15	−	3.26658e14i	−0.265422	−	0.0457477i
$185$	4.07590e15			0.549568
$186$	−1.15065e16	+	5.79729e15i	−1.49401	+	0.752721i
$187$		−	2.30422e15i		−	0.288159i
$188$	6.09475e15	+	4.51309e15i	0.734261	+	0.543712i
$189$	2.83187e15			0.328731
$190$	3.21243e15	+	6.37605e15i	0.359384	+	0.713307i
$191$		−	5.36016e15i		−	0.578021i	−0.957326	−	0.289011i	$-0.906674\pi$
$191$		−	5.36016e15i		−	0.578021i	0.957326	−	0.289011i	$-0.0933263\pi$
$192$	4.34081e15	−	1.22183e16i	0.451296	−	1.27029i
$193$	1.72612e16			1.73049			0.865245	−	0.501349i	$-0.167163\pi$
$193$	1.72612e16			1.73049			0.865245	+	0.501349i	$0.167163\pi$
$194$	−8.99508e15	+	4.53197e15i	−0.869747	+	0.438203i
$195$			1.75708e16i			1.63889i
$196$	−5.16798e15	+	6.97914e15i	−0.465081	+	0.628072i
$197$	−3.83258e15			−0.332834			−0.166417	−	0.986055i	$-0.553220\pi$
$197$	−3.83258e15			−0.332834			−0.166417	+	0.986055i	$0.553220\pi$
$198$	1.10527e15	+	2.19374e15i	0.0926426	+	0.183878i
$199$		−	8.15094e15i		−	0.659532i	−0.944063	−	0.329766i	$-0.893030\pi$
$199$		−	8.15094e15i		−	0.659532i	0.944063	−	0.329766i	$-0.106970\pi$
$200$	−2.02394e14	+	1.17426e15i	−0.0158120	+	0.0917393i
$201$	1.60290e16			1.20930
$202$	7.73376e15	−	3.89648e15i	0.563548	−	0.283931i
$203$			1.10036e16i			0.774576i
$204$	−1.82204e16	−	1.34920e16i	−1.23922	−	0.917627i
$205$	−1.56748e16			−1.03021
$206$	−1.22179e16	−	2.42502e16i	−0.776118	−	1.54044i
$207$		−	3.58484e15i		−	0.220129i
$208$	5.71368e15	+	1.87343e16i	0.339213	+	1.11223i
$209$	−3.35244e15			−0.192458
$210$	3.02588e16	−	1.52452e16i	1.68003	−	0.846444i
$211$			5.93713e14i			0.0318859i	0.999873	+	0.0159430i	$0.00507502\pi$
$211$			5.93713e14i			0.0318859i	−0.999873	+	0.0159430i	$0.994925\pi$
$212$	−5.15357e15	+	6.95969e15i	−0.267767	+	0.361609i
$213$	−6.54973e15			−0.329280
$214$	1.61294e16	+	3.20138e16i	0.784735	+	1.55755i
$215$		−	2.53228e16i		−	1.19246i
$216$	−5.32432e15	−	9.17691e14i	−0.242710	−	0.0418331i
$217$	−3.75296e16			−1.65636
$218$	−2.11549e16	+	1.06584e16i	−0.904100	+	0.455510i
$219$		−	2.51611e16i		−	1.04141i
$220$	−5.27987e15	−	3.90969e15i	−0.211673	−	0.156741i
$221$	3.42466e16			1.33006
$222$	8.47302e15	+	1.68173e16i	0.318836	+	0.632828i
$223$			1.54317e16i			0.562704i	0.959605	+	0.281352i	$0.0907828\pi$
$223$			1.54317e16i			0.562704i	−0.959605	+	0.281352i	$0.909217\pi$
$224$	2.73050e16	−	2.60942e16i	0.964952	−	0.922165i
$225$	−2.22113e15			−0.0760844
$226$	3.76490e16	−	1.89686e16i	1.25024	−	0.629907i
$227$			4.44026e16i			1.42964i	0.699308	+	0.714820i	$0.253492\pi$
$227$			4.44026e16i			1.42964i	−0.699308	+	0.714820i	$0.746508\pi$
$228$	−1.96298e16	+	2.65092e16i	−0.612874	+	0.827661i
$229$	−1.37801e16			−0.417257			−0.208628	−	0.977995i	$-0.566900\pi$
$229$	−1.37801e16			−0.417257			−0.208628	+	0.977995i	$0.566900\pi$
$230$	4.31397e15	+	8.56240e15i	0.126702	+	0.251478i
$231$			1.59096e16i			0.453290i
$232$	3.56582e15	−	2.06884e16i	0.0985697	−	0.571889i
$233$	5.96868e15			0.160098			0.0800492	−	0.996791i	$-0.474492\pi$
$233$	5.96868e15			0.160098			0.0800492	+	0.996791i	$0.474492\pi$
$234$	−3.26047e16	+	1.64271e16i	−0.848729	+	0.427613i
$235$		−	3.78081e16i		−	0.955234i
$236$	1.17491e16	+	8.70005e15i	0.288150	+	0.213372i
$237$	3.22297e16			0.767394
$238$	−2.97139e16	−	5.89763e16i	−0.686943	−	1.36345i
$239$			4.38433e16i			0.984278i	0.870517	+	0.492139i	$0.163785\pi$
$239$			4.38433e16i			0.984278i	−0.870517	+	0.492139i	$0.836215\pi$
$240$	−6.18312e16	+	1.88576e16i	−1.34812	+	0.411157i
$241$	9.28157e15			0.196563			0.0982816	−	0.995159i	$-0.468665\pi$
$241$	9.28157e15			0.196563			0.0982816	+	0.995159i	$0.468665\pi$
$242$	−4.06546e16	+	2.04829e16i	−0.836378	+	0.421390i
$243$		−	6.51950e16i		−	1.30308i
$244$	3.09070e16	−	4.17386e16i	0.600244	−	0.810605i
$245$	4.32944e16			0.817088
$246$	−3.25850e16	−	6.46749e16i	−0.597684	−	1.18629i
$247$		−	4.98260e16i		−	0.888335i
$248$	7.05610e16	+	1.21618e16i	1.22293	+	0.210783i
$249$	−2.39709e16			−0.403914
$250$	−5.16833e16	+	2.60395e16i	−0.846779	+	0.426631i
$251$			5.86421e16i			0.934316i	0.884174	+	0.467158i	$0.154722\pi$
$251$			5.86421e16i			0.934316i	−0.884174	+	0.467158i	$0.845278\pi$
$252$	5.65785e16	+	4.18958e16i	0.876693	+	0.649182i
$253$	−4.50199e15			−0.0678517
$254$	2.92607e16	+	5.80768e16i	0.428992	+	0.851465i
$255$			1.13029e17i			1.61216i
$256$	−5.97934e16	+	4.02126e16i	−0.829800	+	0.558061i
$257$	−1.04285e17			−1.40828			−0.704141	−	0.710060i	$-0.748668\pi$
$257$	−1.04285e17			−1.40828			−0.704141	+	0.710060i	$0.748668\pi$
$258$	1.04483e17	−	5.26413e16i	1.37311	−	0.691813i
$259$			5.48513e16i			0.701598i
$260$	5.81081e16	−	7.84726e16i	0.723475	−	0.977023i
$261$	3.91323e16			0.474298
$262$	5.04702e16	+	1.00174e17i	0.595561	+	1.18207i
$263$		−	1.40742e17i		−	1.61709i	−0.588434	−	0.808545i	$-0.700255\pi$
$263$		−	1.40742e17i		−	1.61709i	0.588434	−	0.808545i	$-0.299745\pi$
$264$	5.15565e15	−	2.99124e16i	0.0576841	−	0.334676i
$265$	4.31737e16			0.470433
$266$	−8.58055e16	+	4.32312e16i	−0.910634	+	0.458802i
$267$		−	1.82325e17i		−	1.88481i
$268$	−7.15866e16	−	5.30091e16i	−0.720922	−	0.533835i
$269$	−3.96167e16			−0.388698			−0.194349	−	0.980932i	$-0.562259\pi$
$269$	−3.96167e16			−0.388698			−0.194349	+	0.980932i	$0.562259\pi$
$270$	1.21194e16	+	2.40546e16i	0.115860	+	0.229960i
$271$			2.85994e16i			0.266423i	0.991088	+	0.133212i	$0.0425290\pi$
$271$			2.85994e16i			0.266423i	−0.991088	+	0.133212i	$0.957471\pi$
$272$	3.67546e16	+	1.20513e17i	0.333680	+	1.09409i
$273$	−2.36459e17			−2.09226
$274$	8.80996e16	−	4.43870e16i	0.759836	−	0.382826i
$275$			2.78938e15i			0.0234520i
$276$	−2.63608e16	+	3.55992e16i	−0.216070	+	0.291794i
$277$	1.26075e17			1.00756			0.503781	−	0.863832i	$-0.331942\pi$
$277$	1.26075e17			1.00756			0.503781	+	0.863832i	$0.331942\pi$
$278$	−9.64907e16	−	1.91515e17i	−0.751921	−	1.49242i
$279$			1.33467e17i			1.01425i
$280$	−1.85555e17	−	3.19820e16i	−1.37520	−	0.237028i
$281$	1.24455e17			0.899635			0.449818	−	0.893120i	$-0.351489\pi$
$281$	1.24455e17			0.899635			0.449818	+	0.893120i	$0.351489\pi$
$282$	1.55997e17	−	7.85958e16i	1.09995	−	0.554186i
$283$			1.96560e17i			1.35205i	0.736881	+	0.676023i	$0.236298\pi$
$283$			1.96560e17i			1.35205i	−0.736881	+	0.676023i	$0.763702\pi$
$284$	2.92516e16	+	2.16605e16i	0.196300	+	0.145358i
$285$	1.64447e17			1.07674
$286$	2.06299e16	+	4.09464e16i	0.131806	+	0.261609i
$287$		−	2.10944e17i		−	1.31520i
$288$	−9.27991e16	−	9.71048e16i	−0.564672	−	0.590872i
$289$	5.19222e16			0.308367
$290$	−9.34676e16	+	4.70916e16i	−0.541845	+	0.272997i
$291$			2.31995e17i			1.31289i
$292$	−8.32097e16	+	1.12371e17i	−0.459721	+	0.620834i
$293$	−8.68418e16			−0.468442			−0.234221	−	0.972183i	$-0.575254\pi$
$293$	−8.68418e16			−0.468442			−0.234221	+	0.972183i	$0.575254\pi$
$294$	9.00008e16	+	1.78634e17i	0.474040	+	0.940877i
$295$		−	7.28841e16i		−	0.374868i
$296$	1.77750e16	−	1.03128e17i	0.0892829	−	0.518008i
$297$	−1.26476e16			−0.0620458
$298$	−7.32533e15	+	3.69070e15i	−0.0351005	+	0.0176846i
$299$		−	6.69113e16i		−	0.313185i
$300$	2.20569e16	+	1.63329e16i	0.100854	+	0.0746816i
$301$	3.40781e17			1.52233
$302$	1.79295e16	+	3.55865e16i	0.0782563	+	0.155323i
$303$		−	1.99464e17i		−	0.850680i
$304$	1.75336e17	−	5.34749e16i	0.730729	−	0.222861i
$305$	−2.58921e17			−1.05455
$306$	−2.09738e17	+	1.05672e17i	−0.834885	+	0.420638i
$307$			3.44813e16i			0.134158i	0.997748	+	0.0670788i	$0.0213679\pi$
$307$			3.44813e16i			0.134158i	−0.997748	+	0.0670788i	$0.978632\pi$
$308$	5.26145e16	−	7.10537e16i	0.200102	−	0.270229i
$309$	−6.25446e17			−2.32531
$310$	−1.60613e17	−	3.18786e17i	−0.583779	−	1.15869i
$311$			2.33238e17i			0.828851i	0.910083	+	0.414426i	$0.136018\pi$
$311$			2.33238e17i			0.828851i	−0.910083	+	0.414426i	$0.863982\pi$
$312$	4.44576e17	+	7.66263e16i	1.54477	+	0.266254i
$313$	4.09151e16			0.139019			0.0695094	−	0.997581i	$-0.477857\pi$
$313$	4.09151e16			0.139019			0.0695094	+	0.997581i	$0.477857\pi$
$314$	1.29877e17	−	6.54358e16i	0.431545	−	0.217424i
$315$		−	3.50979e17i		−	1.14053i
$316$	−1.43941e17	−	1.06586e17i	−0.457482	−	0.338760i
$317$	−5.10326e17			−1.58647			−0.793237	−	0.608913i	$-0.791606\pi$
$317$	−5.10326e17			−1.58647			−0.793237	+	0.608913i	$0.791606\pi$
$318$	8.97499e16	+	1.78136e17i	0.272925	+	0.541704i
$319$		−	4.91440e16i		−	0.146196i
$320$	3.38507e17	+	1.20261e17i	0.985184	+	0.350007i
$321$	8.25679e17			2.35113
$322$	−1.15228e17	+	5.80552e16i	−0.321046	+	0.161752i
$323$		−	3.20518e17i		−	0.873845i
$324$	−2.56356e17	+	3.46198e17i	−0.683956	+	0.923655i
$325$	−4.14575e16			−0.108248
$326$	−9.40372e14	−	1.86646e15i	−0.00240313	−	0.00476974i
$327$			5.45614e17i			1.36474i
$328$	−6.83580e16	+	3.96604e17i	−0.167368	+	0.971048i
$329$	5.08801e17			1.21949
$330$	−1.35140e17	+	6.80875e16i	−0.317094	+	0.159761i
$331$			4.46968e17i			1.02679i	0.858153	+	0.513394i	$0.171612\pi$
$331$			4.46968e17i			1.02679i	−0.858153	+	0.513394i	$0.828388\pi$
$332$	1.07056e17	+	7.92737e16i	0.240793	+	0.178305i
$333$	1.95068e17			0.429612
$334$	−2.39588e17	−	4.75535e17i	−0.516701	−	1.02555i
$335$			4.44080e17i			0.937881i
$336$	−2.53775e17	−	8.32091e17i	−0.524897	−	1.72106i
$337$	−6.42271e17			−1.30109			−0.650547	−	0.759466i	$-0.725460\pi$
$337$	−6.42271e17			−1.30109			−0.650547	+	0.759466i	$0.725460\pi$
$338$	−1.58483e17	+	7.98483e16i	−0.314461	+	0.158434i
$339$		−	9.71019e17i		−	1.88725i
$340$	3.73795e17	−	5.04795e17i	0.711674	−	0.961086i
$341$	1.67613e17			0.312627
$342$	1.53743e17	+	3.05151e17i	0.280940	+	0.557611i
$343$		−	1.62879e17i		−	0.291612i
$344$	−6.40717e17	−	1.10433e17i	−1.12398	−	0.193727i
$345$	2.20836e17			0.379608
$346$	1.96180e17	−	9.88410e16i	0.330463	−	0.166496i
$347$			6.78908e17i			1.12074i	0.828243	+	0.560370i	$0.189341\pi$
$347$			6.78908e17i			1.12074i	−0.828243	+	0.560370i	$0.810659\pi$
$348$	−3.88603e17	−	2.87756e17i	−0.628711	−	0.465554i
$349$	1.59374e17			0.252720			0.126360	−	0.991984i	$-0.459671\pi$
$349$	1.59374e17			0.252720			0.126360	+	0.991984i	$0.459671\pi$
$350$	3.59703e16	+	7.13942e16i	0.0559073	+	0.110965i
$351$		−	1.87976e17i		−	0.286386i
$352$	−1.21948e17	+	1.16541e17i	−0.182128	+	0.174053i
$353$	4.20198e17			0.615220			0.307610	−	0.951512i	$-0.400471\pi$
$353$	4.20198e17			0.615220			0.307610	+	0.951512i	$0.400471\pi$
$354$	3.00722e17	−	1.51512e17i	0.431661	−	0.217483i
$355$		−	1.81459e17i		−	0.255376i
$356$	−6.02964e17	+	8.14278e17i	−0.832035	+	1.12363i
$357$	−1.52108e18			−2.05814
$358$	5.71236e17	+	1.13379e18i	0.757940	+	1.50436i
$359$		−	6.81761e17i		−	0.887097i	−0.896250	−	0.443549i	$-0.853719\pi$
$359$		−	6.81761e17i		−	0.887097i	0.896250	−	0.443549i	$-0.146281\pi$
$360$	−1.13738e17	+	6.59891e17i	−0.145140	+	0.842082i
$361$	3.32680e17			0.416367
$362$	1.42354e18	−	7.17219e17i	1.74747	−	0.880424i
$363$			1.04854e18i			1.26252i
$364$	1.05604e18	+	7.81988e17i	1.24730	+	0.923614i
$365$	6.97084e17			0.807672
$366$	−5.38247e17	−	1.06832e18i	−0.611807	−	1.21432i
$367$		−	1.31363e18i		−	1.46491i	−0.680814	−	0.732457i	$-0.738374\pi$
$367$		−	1.31363e18i		−	1.46491i	0.680814	−	0.732457i	$-0.261626\pi$
$368$	2.35459e17	−	7.18115e16i	0.257621	−	0.0785704i
$369$	−7.50179e17			−0.805342
$370$	−4.65921e17	+	2.34744e17i	−0.490795	+	0.247276i
$371$			5.81009e17i			0.600572i
$372$	9.81436e17	−	1.32539e18i	0.995546	−	1.34444i
$373$	−1.80553e18			−1.79739			−0.898695	−	0.438575i	$-0.855483\pi$
$373$	−1.80553e18			−1.79739			−0.898695	+	0.438575i	$0.855483\pi$
$374$	1.32707e17	+	2.63398e17i	0.129656	+	0.257342i
$375$			1.33298e18i			1.27822i
$376$	−9.56620e17	−	1.64881e17i	−0.900378	−	0.155187i
$377$	7.30407e17			0.674801
$378$	−3.23714e17	+	1.63096e17i	−0.293575	+	0.147911i
$379$		−	5.56600e17i		−	0.495528i	−0.968820	−	0.247764i	$-0.920304\pi$
$379$		−	5.56600e17i		−	0.495528i	0.968820	−	0.247764i	$-0.0796958\pi$
$380$	−7.34433e17	−	5.43840e17i	−0.641900	−	0.475320i
$381$	1.49788e18			1.28529
$382$	3.08708e17	+	6.12725e17i	0.260078	+	0.516205i
$383$		−	6.77328e17i		−	0.560283i	−0.959959	−	0.280141i	$-0.909619\pi$
$383$		−	6.77328e17i		−	0.560283i	0.959959	−	0.280141i	$-0.0903814\pi$
$384$	2.07488e17	+	1.64669e18i	0.168529	+	1.33750i
$385$	−4.40774e17			−0.351553
$386$	−1.97314e18	+	9.94124e17i	−1.54542	+	0.778627i
$387$		−	1.21192e18i		−	0.932175i
$388$	7.67228e17	−	1.03611e18i	0.579565	−	0.782679i
$389$	−3.94973e17			−0.293035			−0.146518	−	0.989208i	$-0.546807\pi$
$389$	−3.94973e17			−0.293035			−0.146518	+	0.989208i	$0.546807\pi$
$390$	−1.01196e18	−	2.00854e18i	−0.737411	−	1.46362i
$391$		−	4.30423e17i		−	0.308077i
$392$	1.88807e17	−	1.09543e18i	0.132744	−	0.770165i
$393$	2.58361e18			1.78435
$394$	4.38107e17	−	2.20730e17i	0.297240	−	0.149757i
$395$			8.92920e17i			0.595159i
$396$	−2.52689e17	−	1.87113e17i	−0.165470	−	0.122529i
$397$	4.50573e17			0.289889			0.144945	−	0.989440i	$-0.453700\pi$
$397$	4.50573e17			0.289889			0.144945	+	0.989440i	$0.453700\pi$
$398$	4.69438e17	+	9.31743e17i	0.296754	+	0.588999i
$399$			2.21304e18i			1.37461i
$400$	−4.44936e16	−	1.45888e17i	−0.0271567	−	0.0890429i
$401$	−1.76006e18			−1.05564			−0.527820	−	0.849356i	$-0.676991\pi$
$401$	−1.76006e18			−1.05564			−0.527820	+	0.849356i	$0.676991\pi$
$402$	−1.83229e18	+	9.23157e17i	−1.07997	+	0.544118i
$403$			2.49116e18i			1.44300i
$404$	−6.59644e17	+	8.90822e17i	−0.375526	+	0.507133i
$405$	2.14760e18			1.20162
$406$	−6.33733e17	−	1.25784e18i	−0.348517	−	0.691739i
$407$		−	2.44975e17i		−	0.132422i
$408$	2.85985e18	+	4.92918e17i	1.51957	+	0.261911i
$409$	−1.15236e18			−0.601901			−0.300950	−	0.953640i	$-0.597304\pi$
$409$	−1.15236e18			−0.601901			−0.300950	+	0.953640i	$0.597304\pi$
$410$	1.79181e18	−	9.02762e17i	0.920035	−	0.463539i
$411$		−	2.27221e18i		−	1.14698i
$412$	2.79329e18	+	2.06840e18i	1.38623	+	1.02649i
$413$	9.80835e17			0.478570
$414$	2.06462e17	+	4.09787e17i	0.0990461	+	0.196587i
$415$		−	6.64110e17i		−	0.313259i
$416$	−1.73210e18	−	1.81247e18i	−0.803379	−	0.840654i
$417$	−4.93944e18			−2.25281
$418$	3.83221e17	−	1.93077e17i	0.171876	−	0.0865959i
$419$		−	1.51013e18i		−	0.666066i	−0.942915	−	0.333033i	$-0.891928\pi$
$419$		−	1.51013e18i		−	0.666066i	0.942915	−	0.333033i	$-0.108072\pi$
$420$	−2.58089e18	+	3.48539e18i	−1.11950	+	1.51184i
$421$	−4.01385e16			−0.0171233			−0.00856163	−	0.999963i	$-0.502725\pi$
$421$	−4.01385e16			−0.0171233			−0.00856163	+	0.999963i	$0.502725\pi$
$422$	−3.41938e16	−	6.78680e16i	−0.0143470	−	0.0284759i
$423$		−	1.80945e18i		−	0.746732i
$424$	1.88281e17	−	1.09238e18i	0.0764266	−	0.443418i
$425$	−2.66686e17			−0.106482
$426$	7.48707e17	−	3.77219e17i	0.294066	−	0.148158i
$427$		−	3.48442e18i		−	1.34628i
$428$	−3.68755e18	−	2.73059e18i	−1.40162	−	1.03789i
$429$	1.05606e18			0.394901
$430$	1.45842e18	+	2.89468e18i	0.536541	+	1.06493i
$431$			1.79163e18i			0.648496i	0.945972	+	0.324248i	$0.105111\pi$
$431$			1.79163e18i			0.648496i	−0.945972	+	0.324248i	$0.894889\pi$
$432$	6.61482e17	−	2.01742e17i	0.235576	−	0.0718473i
$433$	−2.26536e18			−0.793820			−0.396910	−	0.917858i	$-0.629917\pi$
$433$	−2.26536e18			−0.793820			−0.396910	+	0.917858i	$0.629917\pi$
$434$	4.29005e18	−	2.16144e18i	1.47922	−	0.745274i
$435$			2.41066e18i			0.817919i
$436$	1.80439e18	−	2.43676e18i	0.602456	−	0.813592i
$437$	−6.26230e17			−0.205761
$438$	1.44910e18	+	2.87619e18i	0.468577	+	0.930034i
$439$			5.73841e18i			1.82616i	0.407776	+	0.913082i	$0.366304\pi$
$439$			5.73841e18i			1.82616i	−0.407776	+	0.913082i	$0.633696\pi$
$440$	8.28719e17	+	1.42837e17i	0.259561	+	0.0447374i
$441$	2.07202e18			0.638739
$442$	−3.91477e18	+	1.97237e18i	−1.18782	+	0.598457i
$443$			1.37351e16i			0.00410209i	0.999998	+	0.00205104i	$0.000652868\pi$
$443$			1.37351e16i			0.00410209i	−0.999998	+	0.00205104i	$0.999347\pi$
$444$	−1.93712e18	−	1.43442e18i	−0.569477	−	0.421691i
$445$	5.05129e18			1.46178
$446$	−8.88759e17	−	1.76401e18i	−0.253186	−	0.502526i
$447$			1.88930e17i			0.0529845i
$448$	−1.61841e18	+	4.55544e18i	−0.446831	+	1.25772i
$449$	−1.04253e17			−0.0283378			−0.0141689	−	0.999900i	$-0.504510\pi$
$449$	−1.04253e17			−0.0283378			−0.0141689	+	0.999900i	$0.504510\pi$
$450$	2.53899e17	−	1.27922e17i	0.0679476	−	0.0342339i
$451$			9.42108e17i			0.248236i
$452$	−3.21124e18	+	4.33665e18i	−0.833113	+	1.12508i
$453$	9.17825e17			0.234462
$454$	−2.55728e18	−	5.07571e18i	−0.643261	−	1.27675i
$455$		−	6.55105e18i		−	1.62267i
$456$	7.17154e17	−	4.16083e18i	0.174928	−	1.01491i
$457$	6.06077e18			1.45584			0.727921	−	0.685661i	$-0.240487\pi$
$457$	6.06077e18			1.45584			0.727921	+	0.685661i	$0.240487\pi$
$458$	1.57522e18	−	7.93637e17i	0.372633	−	0.187743i
$459$		−	1.20920e18i		−	0.281715i
$460$	−9.86271e17	−	7.30323e17i	−0.226304	−	0.167575i
$461$	9.53265e17			0.215430			0.107715	−	0.994182i	$-0.465647\pi$
$461$	9.53265e17			0.215430			0.107715	+	0.994182i	$0.465647\pi$
$462$	−9.16285e17	−	1.81865e18i	−0.203956	−	0.404813i
$463$			1.80388e18i			0.395495i	0.980253	+	0.197748i	$0.0633627\pi$
$463$			1.80388e18i			0.395495i	−0.980253	+	0.197748i	$0.936637\pi$
$464$	7.83898e17	+	2.57028e18i	0.169291	+	0.555079i
$465$	−8.22191e18			−1.74905
$466$	−6.82286e17	+	3.43755e17i	−0.142977	+	0.0720356i
$467$			4.98642e18i			1.02937i	0.857380	+	0.514684i	$0.172091\pi$
$467$			4.98642e18i			1.02937i	−0.857380	+	0.514684i	$0.827909\pi$
$468$	2.78099e18	−	3.75561e18i	0.565559	−	0.763764i
$469$	−5.97619e18			−1.19733
$470$	2.17749e18	+	4.32189e18i	0.429804	+	0.853077i
$471$		−	3.34971e18i		−	0.651420i
$472$	−1.84411e18	−	3.17848e17i	−0.353340	−	0.0609011i
$473$	−1.52198e18			−0.287330
$474$	−3.68422e18	+	1.85621e18i	−0.685325	+	0.345286i
$475$			3.88005e17i			0.0711184i
$476$	6.79326e18	+	5.03033e18i	1.22696	+	0.908548i
$477$	2.06624e18			0.367750
$478$	−2.52507e18	−	5.01178e18i	−0.442872	−	0.879015i
$479$		−	7.81614e17i		−	0.135096i	−0.997716	−	0.0675482i	$-0.978482\pi$
$479$		−	7.81614e17i		−	0.135096i	0.997716	−	0.0675482i	$-0.0215176\pi$
$480$	5.98192e18	−	5.71668e18i	1.01895	−	0.973767i
$481$	3.64096e18			0.611224
$482$	−1.06099e18	+	5.34555e17i	−0.175542	+	0.0884429i
$483$			2.97189e18i			0.484622i
$484$	3.46760e18	−	4.68285e18i	0.557329	−	0.752650i
$485$	−6.42739e18			−1.01822
$486$	3.75478e18	+	7.45251e18i	0.586315	+	1.16372i
$487$		−	1.09338e19i		−	1.68294i	−0.540307	−	0.841468i	$-0.681692\pi$
$487$		−	1.09338e19i		−	1.68294i	0.540307	−	0.841468i	$-0.318308\pi$
$488$	−1.12916e18	+	6.55121e18i	−0.171323	+	0.993992i
$489$	−4.81384e16			−0.00719995
$490$	−4.94903e18	+	2.49346e18i	−0.729705	+	0.367646i
$491$			2.12840e18i			0.309373i	0.987964	+	0.154686i	$0.0494367\pi$
$491$			2.12840e18i			0.309373i	−0.987964	+	0.154686i	$0.950563\pi$
$492$	7.44965e18	+	5.51639e18i	1.06753	+	0.790495i
$493$	4.69852e18			0.663794
$494$	2.86963e18	+	5.69566e18i	0.399703	+	0.793333i
$495$			1.56753e18i			0.215268i
$496$	−8.76634e18	+	2.67360e18i	−1.18699	+	0.362014i
$497$	2.44198e18			0.326023
$498$	2.74014e18	−	1.38056e18i	0.360717	−	0.181739i
$499$		−	2.24625e18i		−	0.291577i	−0.989316	−	0.145789i	$-0.953428\pi$
$499$		−	2.24625e18i		−	0.291577i	0.989316	−	0.145789i	$-0.0465719\pi$
$500$	4.40828e18	−	5.95320e18i	0.564260	−	0.762010i
$501$	−1.22647e19			−1.54808
$502$	−3.37738e18	−	6.70345e18i	−0.420392	−	0.834396i
$503$			8.51955e18i			1.04578i	0.852400	+	0.522891i	$0.175146\pi$
$503$			8.51955e18i			1.04578i	−0.852400	+	0.522891i	$0.824854\pi$
$504$	−8.88046e18	−	1.53062e18i	−1.07503	−	0.185291i
$505$	5.52612e18			0.659752
$506$	5.14628e17	−	2.59284e17i	0.0605954	−	0.0305296i
$507$			4.08750e18i			0.474681i
$508$	−6.68965e18	−	4.95361e18i	−0.766227	−	0.567383i
$509$	1.21923e19			1.37740			0.688699	−	0.725047i	$-0.258182\pi$
$509$	1.21923e19			1.37740			0.688699	+	0.725047i	$0.258182\pi$
$510$	−6.50966e18	−	1.29204e19i	−0.725383	−	1.43974i
$511$			9.38098e18i			1.03110i
$512$	4.51908e18	−	8.04043e18i	0.489960	−	0.871745i
$513$	−1.75929e18			−0.188155
$514$	1.19209e19	−	6.00609e18i	1.25767	−	0.633651i
$515$		−	1.73279e19i		−	1.80341i
$516$	−8.91176e18	+	1.20350e19i	−0.914989	+	1.23565i
$517$	−2.27239e18			−0.230170
$518$	−3.15906e18	−	6.27012e18i	−0.315682	−	0.626567i
$519$		−	5.05975e18i		−	0.498836i
$520$	−2.12292e18	+	1.23169e19i	−0.206496	+	1.19806i
$521$	2.24317e18			0.215277			0.107639	−	0.994190i	$-0.465671\pi$
$521$	2.24317e18			0.215277			0.107639	+	0.994190i	$0.465671\pi$
$522$	−4.47325e18	+	2.25375e18i	−0.423575	+	0.213409i
$523$		−	4.84461e18i		−	0.452633i	−0.974054	−	0.226317i	$-0.927332\pi$
$523$		−	4.84461e18i		−	0.452633i	0.974054	−	0.226317i	$-0.0726684\pi$
$524$	−1.15386e19	−	8.54422e18i	−1.06374	−	0.787687i
$525$	1.84135e18			0.167503
$526$	8.10578e18	+	1.60884e19i	0.727603	+	1.44415i
$527$			1.60250e19i			1.41946i
$528$	1.13340e18	+	3.71625e18i	0.0990709	+	0.324839i
$529$	1.07519e19			0.927458
$530$	−4.93523e18	+	2.48651e18i	−0.420123	+	0.211670i
$531$		−	3.48815e18i		−	0.293044i
$532$	7.31871e18	−	9.88361e18i	0.606810	−	0.819472i
$533$	−1.40022e19			−1.14579
$534$	1.05007e19	+	2.08418e19i	0.848063	+	1.68324i
$535$			2.28753e19i			1.82344i
$536$	1.12361e19	+	1.93663e18i	0.884020	+	0.152368i
$537$	2.92420e19			2.27085
$538$	4.52863e18	−	2.28165e18i	0.347129	−	0.174893i
$539$		−	2.60213e18i		−	0.196883i
$540$	−2.77076e18	−	2.05172e18i	−0.206939	−	0.153236i
$541$	−2.44277e19			−1.80095			−0.900475	−	0.434908i	$-0.856781\pi$
$541$	−2.44277e19			−1.80095			−0.900475	+	0.434908i	$0.856781\pi$
$542$	−1.64713e18	−	3.26923e18i	−0.119876	−	0.237931i
$543$		−	3.67150e19i		−	2.63782i
$544$	−1.11422e19	−	1.16592e19i	−0.790275	−	0.826942i
$545$	−1.51162e19			−1.05844
$546$	2.70298e19	−	1.36184e19i	1.86851	−	0.941406i
$547$			1.61060e19i			1.09920i	0.835429	+	0.549599i	$0.185219\pi$
$547$			1.61060e19i			1.09920i	−0.835429	+	0.549599i	$0.814781\pi$
$548$	−7.51438e18	+	1.01479e19i	−0.506325	+	0.683771i
$549$	−1.23917e19			−0.824372
$550$	−1.60649e17	−	3.18858e17i	−0.0105521	−	0.0209439i
$551$		−	6.83596e18i		−	0.443341i
$552$	9.63066e17	−	5.58759e18i	0.0616712	−	0.357808i
$553$	−1.20164e19			−0.759801
$554$	−1.44118e19	+	7.26107e18i	−0.899809	+	0.453348i
$555$			1.20167e19i			0.740858i
$556$	2.20599e19	+	1.63351e19i	1.34301	+	0.994487i
$557$	−1.12923e19			−0.678884			−0.339442	−	0.940627i	$-0.610238\pi$
$557$	−1.12923e19			−0.678884			−0.339442	+	0.940627i	$0.610238\pi$
$558$	−7.68675e18	−	1.52567e19i	−0.456356	−	0.905778i
$559$		−	2.26206e19i		−	1.32624i
$560$	2.30530e19	−	7.03081e18i	1.33478	−	0.407089i
$561$	6.79338e18			0.388459
$562$	−1.42265e19	+	7.16772e18i	−0.803424	+	0.404787i
$563$		−	2.32051e19i		−	1.29427i	−0.762376	−	0.647135i	$-0.775967\pi$
$563$		−	2.32051e19i		−	1.29427i	0.762376	−	0.647135i	$-0.224033\pi$
$564$	−1.33057e19	+	1.79688e19i	−0.732964	+	0.989838i
$565$	2.69019e19			1.46367
$566$	−1.13205e19	−	2.24691e19i	−0.608347	−	1.20745i
$567$			2.89013e19i			1.53404i
$568$	−4.59128e18	−	7.91344e17i	−0.240711	−	0.0414885i
$569$	2.03393e19			1.05330			0.526648	−	0.850083i	$-0.323448\pi$
$569$	2.03393e19			1.05330			0.526648	+	0.850083i	$0.323448\pi$
$570$	−1.87981e19	+	9.47101e18i	−0.961591	+	0.484476i
$571$		−	8.30855e18i		−	0.419829i	−0.977720	−	0.209914i	$-0.932681\pi$
$571$		−	8.30855e18i		−	0.419829i	0.977720	−	0.209914i	$-0.0673185\pi$
$572$	−4.71646e18	−	3.49248e18i	−0.235420	−	0.174326i
$573$	1.58030e19			0.779215
$574$	1.21489e19	+	2.41132e19i	0.591771	+	1.17455i
$575$			5.21052e17i			0.0250730i
$576$	1.62005e19	+	5.75557e18i	0.770144	+	0.273610i
$577$	−2.07299e19			−0.973567			−0.486784	−	0.873523i	$-0.661830\pi$
$577$	−2.07299e19			−0.973567			−0.486784	+	0.873523i	$0.661830\pi$
$578$	−5.93528e18	+	2.99036e18i	−0.275389	+	0.138749i
$579$			5.08900e19i			2.33283i
$580$	7.97224e18	−	1.07662e19i	0.361064	−	0.487602i
$581$	8.93724e18			0.399917
$582$	−1.33613e19	−	2.65196e19i	−0.590729	−	1.17248i
$583$		−	2.59488e18i		−	0.113354i
$584$	3.03998e18	−	1.76376e19i	0.131214	−	0.761289i
$585$	−2.32975e19			−0.993616
$586$	9.92699e18	−	5.00149e18i	0.418345	−	0.210774i
$587$			1.91370e19i			0.796908i	0.917188	+	0.398454i	$0.130453\pi$
$587$			1.91370e19i			0.796908i	−0.917188	+	0.398454i	$0.869547\pi$
$588$	−2.05762e19	−	1.52364e19i	−0.846688	−	0.626963i
$589$	2.33151e19			0.948046
$590$	4.19762e18	+	8.33146e18i	0.168671	+	0.334778i
$591$		−	1.12994e19i		−	0.448685i
$592$	3.90760e18	+	1.28124e19i	0.153341	+	0.502782i
$593$	3.66977e19			1.42317			0.711584	−	0.702601i	$-0.247978\pi$
$593$	3.66977e19			1.42317			0.711584	+	0.702601i	$0.247978\pi$
$594$	1.44576e18	−	7.28413e17i	0.0554103	−	0.0279173i
$595$		−	4.21412e19i		−	1.59620i
$596$	6.24808e17	−	8.43777e17i	0.0233896	−	0.0315867i
$597$	2.40309e19			0.889098
$598$	3.85363e18	+	7.64871e18i	0.140916	+	0.279692i
$599$			1.40056e19i			0.506191i	0.967441	+	0.253095i	$0.0814486\pi$
$599$			1.40056e19i			0.506191i	−0.967441	+	0.253095i	$0.918551\pi$
$600$	−3.46201e18	−	5.96705e17i	−0.123671	−	0.0213158i
$601$	−4.92264e19			−1.73811			−0.869054	−	0.494717i	$-0.835272\pi$
$601$	−4.92264e19			−1.73811			−0.869054	+	0.494717i	$0.835272\pi$
$602$	−3.89551e19	+	1.96266e19i	−1.35953	+	0.684968i
$603$			2.12532e19i			0.733166i
$604$	−4.09908e18	−	3.03532e18i	−0.139774	−	0.103501i
$605$	−2.90496e19			−0.979157
$606$	1.14878e19	+	2.28010e19i	0.382760	+	0.759705i
$607$		−	3.01738e19i		−	0.993823i	−0.867801	−	0.496912i	$-0.834467\pi$
$607$		−	3.01738e19i		−	0.993823i	0.867801	−	0.496912i	$-0.165533\pi$
$608$	−1.69631e19	+	1.62109e19i	−0.552306	+	0.527816i
$609$	−3.24413e19			−1.04418
$610$	2.95975e19	−	1.49121e19i	0.941774	−	0.474492i
$611$		−	3.37736e19i		−	1.06240i
$612$	1.78894e19	−	2.41589e19i	0.556334	−	0.751306i
$613$	−2.74397e19			−0.843637			−0.421818	−	0.906680i	$-0.638608\pi$
$613$	−2.74397e19			−0.843637			−0.421818	+	0.906680i	$0.638608\pi$
$614$	−1.98589e18	−	3.94160e18i	−0.0603637	−	0.119810i
$615$		−	4.62131e19i		−	1.38880i
$616$	−1.92222e18	+	1.11525e19i	−0.0571134	+	0.331364i
$617$	4.38772e19			1.28897			0.644485	−	0.764617i	$-0.277072\pi$
$617$	4.38772e19			1.28897			0.644485	+	0.764617i	$0.277072\pi$
$618$	7.14955e19	−	3.60214e19i	2.07663	−	1.04626i
$619$			4.15587e18i			0.119351i	0.998218	+	0.0596757i	$0.0190067\pi$
$619$			4.15587e18i			0.119351i	−0.998218	+	0.0596757i	$0.980993\pi$
$620$	3.67197e19	+	2.71905e19i	1.04270	+	0.772104i
$621$	−2.36254e18			−0.0663344
$622$	−1.34329e19	−	2.66617e19i	−0.372938	−	0.740210i
$623$			6.79775e19i			1.86616i
$624$	−5.52332e19	+	1.68453e19i	−1.49937	+	0.457284i
$625$	−4.03980e19			−1.08443
$626$	−4.67706e18	+	2.35643e18i	−0.124152	+	0.0625510i
$627$		−	9.88379e18i		−	0.259448i
$628$	−1.10778e19	+	1.49601e19i	−0.287564	+	0.388344i
$629$	2.34214e19			0.601254
$630$	2.02140e19	+	4.01208e19i	0.513177	+	1.01856i
$631$			4.77489e19i			1.19883i	0.800438	+	0.599416i	$0.204600\pi$
$631$			4.77489e19i			1.19883i	−0.800438	+	0.599416i	$0.795400\pi$
$632$	2.25927e19	+	3.89403e18i	0.560980	+	0.0966896i
$633$	−1.75041e18			−0.0429846
$634$	5.83359e19	−	2.93913e19i	1.41681	−	0.713828i
$635$			4.14985e19i			0.996820i
$636$	−2.05188e19	−	1.51940e19i	−0.487475	−	0.360970i
$637$	3.86744e19			0.908757
$638$	2.83035e18	+	5.61770e18i	0.0657803	+	0.130561i
$639$		−	8.68443e18i		−	0.199634i
$640$	−4.56213e19	+	5.74843e18i	−1.03731	+	0.130704i
$641$	−2.76966e19			−0.622903			−0.311452	−	0.950262i	$-0.600815\pi$
$641$	−2.76966e19			−0.622903			−0.311452	+	0.950262i	$0.600815\pi$
$642$	−9.43843e19	+	4.75534e19i	−2.09969	+	1.05788i
$643$		−	7.06912e18i		−	0.155557i	−0.996971	−	0.0777783i	$-0.975217\pi$
$643$		−	7.06912e18i		−	0.155557i	0.996971	−	0.0777783i	$-0.0247826\pi$
$644$	9.82829e18	−	1.32727e19i	0.213933	−	0.288907i
$645$	7.46577e19			1.60752
$646$	1.84596e19	+	3.66388e19i	0.393183	+	0.780392i
$647$		−	7.95252e19i		−	1.67562i	−0.545964	−	0.837808i	$-0.683837\pi$
$647$		−	7.95252e19i		−	1.67562i	0.545964	−	0.837808i	$-0.316163\pi$
$648$	9.36571e18	−	5.43386e19i	0.195216	−	1.13262i
$649$	−4.38057e18			−0.0903270
$650$	4.73905e18	−	2.38767e18i	0.0966714	−	0.0487057i
$651$		−	1.10646e20i		−	2.23290i
$652$	2.14990e17	+	1.59198e17i	0.00429225	+	0.00317836i
$653$	−1.09740e19			−0.216757			−0.108379	−	0.994110i	$-0.534566\pi$
$653$	−1.09740e19			−0.216757			−0.108379	+	0.994110i	$0.534566\pi$
$654$	−3.14236e19	−	6.23698e19i	−0.614062	−	1.21879i
$655$			7.15786e19i			1.38387i
$656$	−1.50276e19	−	4.92732e19i	−0.287450	−	0.942506i
$657$	3.33616e19			0.631378
$658$	−5.81617e19	+	2.93035e19i	−1.08907	+	0.548703i
$659$			3.69518e19i			0.684601i	0.939590	+	0.342301i	$0.111206\pi$
$659$			3.69518e19i			0.684601i	−0.939590	+	0.342301i	$0.888794\pi$
$660$	1.15267e19	−	1.55663e19i	0.211299	−	0.285350i
$661$	1.34638e19			0.244206			0.122103	−	0.992517i	$-0.461036\pi$
$661$	1.34638e19			0.244206			0.122103	+	0.992517i	$0.461036\pi$
$662$	−2.57423e19	−	5.10934e19i	−0.461999	−	0.916979i
$663$			1.00967e20i			1.79302i
$664$	−1.68033e19	−	2.89619e18i	−0.295269	−	0.0508920i
$665$	−6.13119e19			−1.06609
$666$	−2.22984e19	+	1.12346e19i	−0.383667	+	0.193302i
$667$		−	9.18001e18i		−	0.156301i
$668$	5.47751e19	+	4.05604e19i	0.922886	+	0.683387i
$669$	−4.54963e19			−0.758566
$670$	−2.55759e19	−	5.07633e19i	−0.421996	−	0.837580i
$671$			1.55620e19i			0.254101i
$672$	7.69320e19	+	8.05016e19i	1.24315	+	1.30083i
$673$	8.10738e19			1.29651			0.648253	−	0.761425i	$-0.275500\pi$
$673$	8.10738e19			1.29651			0.648253	+	0.761425i	$0.275500\pi$
$674$	7.34187e19	−	3.69904e19i	1.16195	−	0.585423i
$675$			1.46381e18i			0.0229275i
$676$	1.35177e19	−	1.82551e19i	0.209544	−	0.282981i
$677$	1.44487e19			0.221671			0.110836	−	0.993839i	$-0.464647\pi$
$677$	1.44487e19			0.221671			0.110836	+	0.993839i	$0.464647\pi$
$678$	5.59240e19	+	1.10998e20i	0.849161	+	1.68542i
$679$		−	8.64965e19i		−	1.29990i
$680$	−1.36562e19	+	7.92316e19i	−0.203127	+	1.17852i
$681$	−1.30909e20			−1.92726
$682$	−1.91600e19	+	9.65335e18i	−0.279194	+	0.140666i
$683$		−	3.56963e17i		−	0.00514848i	−0.999997	−	0.00257424i	$-0.999181\pi$
$683$		−	3.56963e17i		−	0.00514848i	0.999997	−	0.00257424i	$-0.000819407\pi$
$684$	−3.51491e19	−	2.60275e19i	−0.501790	−	0.371570i
$685$	6.29511e19			0.889549
$686$	9.38069e18	+	1.86188e19i	0.131210	+	0.260426i
$687$		−	4.06269e19i		−	0.562493i
$688$	7.96013e19	−	2.42772e19i	1.09094	−	0.332720i
$689$	3.85666e19			0.523211
$690$	−2.52440e19	+	1.27186e19i	−0.339012	+	0.170803i
$691$			8.28163e19i			1.10096i	0.834850	+	0.550478i	$0.185554\pi$
$691$			8.28163e19i			1.10096i	−0.834850	+	0.550478i	$0.814446\pi$
$692$	−1.67330e19	+	2.25973e19i	−0.220207	+	0.297381i
$693$	−2.10949e19			−0.274818
$694$	−3.91004e19	−	7.76067e19i	−0.504272	−	1.00088i
$695$		−	1.36846e20i		−	1.74719i
$696$	6.09944e19	+	1.05129e19i	0.770948	+	0.132879i
$697$	−9.00724e19			−1.12710
$698$	−1.82182e19	+	9.17883e18i	−0.225693	+	0.113710i
$699$			1.75971e19i			0.215824i
$700$	−8.22362e18	−	6.08950e18i	−0.0998566	−	0.0739427i
$701$	−1.09189e20			−1.31266			−0.656331	−	0.754473i	$-0.727892\pi$
$701$	−1.09189e20			−1.31266			−0.656331	+	0.754473i	$0.727892\pi$
$702$	1.08261e19	+	2.14877e19i	0.128858	+	0.255759i
$703$		−	3.40761e19i		−	0.401572i
$704$	7.22810e18	−	2.03453e19i	0.0843364	−	0.237387i
$705$	1.11467e20			1.28773
$706$	−4.80333e19	+	2.42005e19i	−0.549426	+	0.276816i
$707$			7.43676e19i			0.842263i
$708$	−2.56498e19	+	3.46390e19i	−0.287642	+	0.388448i
$709$	−3.15046e19			−0.349825			−0.174913	−	0.984584i	$-0.555964\pi$
$709$	−3.15046e19			−0.349825			−0.174913	+	0.984584i	$0.555964\pi$
$710$	1.04508e19	+	2.07428e19i	0.114906	+	0.228065i
$711$			4.27341e19i			0.465251i
$712$	2.20287e19	−	1.27808e20i	0.237481	−	1.37783i
$713$	3.13098e19			0.334236
$714$	1.73876e20	−	8.76036e19i	1.83803	−	0.926050i
$715$			2.92580e19i			0.306269i
$716$	−1.30597e20	−	9.67059e19i	−1.35376	−	1.00245i
$717$	−1.29260e20			−1.32688
$718$	3.92647e19	+	7.79329e19i	0.399146	+	0.792227i
$719$		−	3.86358e19i		−	0.388945i	−0.980908	−	0.194472i	$-0.937701\pi$
$719$		−	3.86358e19i		−	0.388945i	0.980908	−	0.194472i	$-0.0622995\pi$
$720$	−2.50037e19	−	8.19834e19i	−0.249274	−	0.817332i
$721$	2.33190e20			2.30230
$722$	−3.80291e19	+	1.91601e19i	−0.371839	+	0.187343i
$723$			2.73643e19i			0.264982i
$724$	−1.21420e20	+	1.63972e20i	−1.16444	+	1.57253i
$725$	−5.68783e18			−0.0540232
$726$	−6.03885e19	−	1.19860e20i	−0.568065	−	1.12750i
$727$			4.69779e19i			0.437676i	0.975761	+	0.218838i	$0.0702266\pi$
$727$			4.69779e19i			0.437676i	−0.975761	+	0.218838i	$0.929773\pi$
$728$	−1.65755e20	−	2.85692e19i	−1.52949	−	0.263620i
$729$	6.64530e19			0.607326
$730$	−7.96844e19	+	4.01472e19i	−0.721296	+	0.363409i
$731$		−	1.45513e20i		−	1.30461i
$732$	1.23055e20	+	9.11211e19i	1.09275	+	0.809173i
$733$	9.92861e19			0.873294			0.436647	−	0.899633i	$-0.356166\pi$
$733$	9.92861e19			0.873294			0.436647	+	0.899633i	$0.356166\pi$
$734$	7.56563e19	+	1.50163e20i	0.659132	+	1.30825i
$735$			1.27642e20i			1.10150i
$736$	−2.27797e19	+	2.17697e19i	−0.194717	+	0.186083i
$737$	2.66906e19			0.225989
$738$	8.57539e19	−	4.32052e19i	0.719216	−	0.362361i
$739$			3.72308e19i			0.309308i	0.987969	+	0.154654i	$0.0494262\pi$
$739$			3.72308e19i			0.309308i	−0.987969	+	0.154654i	$0.950574\pi$
$740$	3.97403e19	−	5.36677e19i	0.327046	−	0.441663i
$741$	1.46899e20			1.19754
$742$	−3.34621e19	−	6.64158e19i	−0.270225	−	0.536344i
$743$		−	6.07429e18i		−	0.0485930i	−0.999705	−	0.0242965i	$-0.992265\pi$
$743$		−	6.07429e18i		−	0.0485930i	0.999705	−	0.0242965i	$-0.00773457\pi$
$744$	−3.58558e19	+	2.08031e20i	−0.284151	+	1.64861i
$745$	−5.23428e18			−0.0410926
$746$	2.06392e20	−	1.03986e20i	1.60517	−	0.808729i
$747$		−	3.17835e19i		−	0.244883i
$748$	−3.03398e19	−	2.24663e19i	−0.231580	−	0.171482i
$749$	−3.07844e20			−2.32787
$750$	−7.67706e19	−	1.52375e20i	−0.575130	−	1.14152i
$751$			1.15626e20i			0.858172i	0.903264	+	0.429086i	$0.141164\pi$
$751$			1.15626e20i			0.858172i	−0.903264	+	0.429086i	$0.858836\pi$
$752$	1.18848e20	−	3.62470e19i	0.873913	−	0.266530i
$753$	−1.72891e20			−1.25953
$754$	−8.34937e19	+	4.20664e19i	−0.602635	+	0.303624i
$755$			2.54282e19i			0.181839i
$756$	2.76109e19	−	3.72874e19i	0.195627	−	0.264186i
$757$	−9.31288e19			−0.653752			−0.326876	−	0.945067i	$-0.605996\pi$
$757$	−9.31288e19			−0.653752			−0.326876	+	0.945067i	$0.605996\pi$
$758$	3.20563e19	+	6.36255e19i	0.222961	+	0.442534i
$759$		−	1.32729e19i		−	0.0914692i
$760$	1.15275e20	+	1.98686e19i	0.787120	+	0.135667i
$761$	1.85510e20			1.25509			0.627546	−	0.778579i	$-0.284059\pi$
$761$	1.85510e20			1.25509			0.627546	+	0.778579i	$0.284059\pi$
$762$	−1.71224e20	+	8.62675e19i	−1.14784	+	0.578312i
$763$		−	2.03425e20i		−	1.35124i
$764$	−7.05775e19	−	5.22619e19i	−0.464529	−	0.343979i
$765$	−1.49867e20			−0.977409
$766$	3.90094e19	+	7.74261e19i	0.252097	+	0.500364i
$767$		−	6.51066e19i		−	0.416925i
$768$	−1.18556e20	−	1.76285e20i	−0.752308	−	1.11863i
$769$	2.13193e19			0.134057			0.0670283	−	0.997751i	$-0.478648\pi$
$769$	2.13193e19			0.134057			0.0670283	+	0.997751i	$0.478648\pi$
$770$	5.03854e19	−	2.53856e19i	0.313957	−	0.158180i
$771$		−	3.07457e20i		−	1.89847i
$772$	1.68298e20	−	2.27279e20i	1.02981	−	1.39072i
$773$	4.44231e17			0.00269372			0.00134686	−	0.999999i	$-0.499571\pi$
$773$	4.44231e17			0.00269372			0.00134686	+	0.999999i	$0.499571\pi$
$774$	6.97983e19	+	1.38536e20i	0.419429	+	0.832484i
$775$		−	1.93992e19i		−	0.115524i
$776$	−2.80299e19	+	1.62626e20i	−0.165421	+	0.959749i
$777$	−1.61715e20			−0.945807
$778$	4.51498e19	−	2.27477e19i	0.261697	−	0.131850i
$779$			1.31048e20i			0.752779i
$780$	2.31356e20	+	1.71317e20i	1.31710	+	0.975297i
$781$	−1.09063e19			−0.0615346
$782$	2.47894e19	+	4.92022e19i	0.138618	+	0.275130i
$783$		−	2.57897e19i		−	0.142927i
$784$	4.15067e19	+	1.36094e20i	0.227985	+	0.747528i
$785$	9.28032e19			0.505214
$786$	−2.95336e20	+	1.48798e20i	−1.59352	+	0.802860i
$787$			2.32384e20i			1.24275i	0.783513	+	0.621375i	$0.213426\pi$
$787$			2.32384e20i			1.24275i	−0.783513	+	0.621375i	$0.786574\pi$
$788$	−3.73679e19	+	5.04639e19i	−0.198069	+	0.267484i
$789$	4.14942e20			2.17996
$790$	−5.14261e19	−	1.02071e20i	−0.267790	−	0.531510i
$791$			3.62032e20i			1.86858i
$792$	3.96615e19	+	6.83599e18i	0.202905	+	0.0349724i
$793$	−2.31291e20			−1.17286
$794$	−5.15056e19	+	2.59499e19i	−0.258887	+	0.130435i
$795$			1.27286e20i			0.634179i
$796$	−1.07324e20	−	7.94722e19i	−0.530036	−	0.392486i
$797$	6.26695e19			0.306795			0.153397	−	0.988165i	$-0.450979\pi$
$797$	6.26695e19			0.306795			0.153397	+	0.988165i	$0.450979\pi$
$798$	−1.27456e20	−	2.52975e20i	−0.618500	−	1.22760i
$799$		−	2.17257e20i		−	1.04507i
$800$	1.34882e19	+	1.41141e19i	0.0643170	+	0.0673012i
$801$	2.41749e20			1.14271
$802$	2.01194e20	−	1.01367e20i	0.942746	−	0.474981i
$803$		−	4.18970e19i		−	0.194614i
$804$	1.56283e20	−	2.11054e20i	0.719649	−	0.971856i
$805$	−8.23358e19			−0.375853
$806$	−1.43474e20	−	2.84768e20i	−0.649274	−	1.28868i
$807$		−	1.16799e20i		−	0.523994i
$808$	2.40994e19	−	1.39822e20i	0.107183	−	0.621864i
$809$	1.83746e20			0.810172			0.405086	−	0.914279i	$-0.367242\pi$
$809$	1.83746e20			0.810172			0.405086	+	0.914279i	$0.367242\pi$
$810$	−2.45495e20	+	1.23687e20i	−1.07312	+	0.540666i
$811$			2.96921e20i			1.28675i	0.765551	+	0.643375i	$0.222467\pi$
$811$			2.96921e20i			1.28675i	−0.765551	+	0.643375i	$0.777533\pi$
$812$	1.44886e20	+	1.07286e20i	0.622491	+	0.460948i
$813$	−8.43178e19			−0.359158
$814$	1.41089e19	+	2.80033e19i	0.0595828	+	0.118260i
$815$		−	1.33367e18i		−	0.00558399i
$816$	−3.55301e20	+	1.08361e20i	−1.47491	+	0.449825i
$817$	−2.11709e20			−0.871333
$818$	1.31727e20	−	6.63680e19i	0.537531	−	0.270823i
$819$		−	3.13526e20i		−	1.26849i
$820$	−1.52831e20	+	2.06392e20i	−0.613075	+	0.827932i
$821$	1.21912e20			0.484891			0.242445	−	0.970165i	$-0.422050\pi$
$821$	1.21912e20			0.484891			0.242445	+	0.970165i	$0.422050\pi$
$822$	1.30863e20	+	2.59738e20i	0.516078	+	1.02431i
$823$		−	4.76822e20i		−	1.86448i	−0.361844	−	0.932239i	$-0.617853\pi$
$823$		−	4.76822e20i		−	1.86448i	0.361844	−	0.932239i	$-0.382147\pi$
$824$	−4.38430e20	−	7.55671e19i	−1.69985	−	0.292983i
$825$	−8.22377e18			−0.0316150
$826$	−1.12120e20	+	5.64894e19i	−0.427390	+	0.215331i
$827$			1.90780e20i			0.721098i	0.932740	+	0.360549i	$0.117411\pi$
$827$			1.90780e20i			0.721098i	−0.932740	+	0.360549i	$0.882589\pi$
$828$	−4.72018e19	−	3.49524e19i	−0.176907	−	0.130998i
$829$	−2.09950e20			−0.780249			−0.390125	−	0.920762i	$-0.627568\pi$
$829$	−2.09950e20			−0.780249			−0.390125	+	0.920762i	$0.627568\pi$
$830$	3.82481e19	+	7.59151e19i	0.140950	+	0.279758i
$831$			3.71700e20i			1.35827i
$832$	3.02384e20	+	1.07428e20i	1.09571	+	0.389274i
$833$	2.48783e20			0.893934
$834$	5.64633e20	−	2.84478e20i	2.01189	−	1.01364i
$835$		−	3.39792e20i		−	1.20062i
$836$	−3.26865e19	+	4.41418e19i	−0.114531	+	0.154670i
$837$	8.79596e19			0.305636
$838$	8.69732e19	+	1.72625e20i	0.299694	+	0.594834i
$839$			2.14640e20i			0.733462i	0.930327	+	0.366731i	$0.119523\pi$
$839$			2.14640e20i			0.733462i	−0.930327	+	0.366731i	$0.880477\pi$
$840$	9.42904e19	−	5.47061e20i	0.319531	−	1.85388i
$841$	−1.97349e20			−0.663228
$842$	4.58828e18	−	2.31170e18i	0.0152920	−	0.00770454i
$843$			3.66921e20i			1.21277i
$844$	7.81746e18	+	5.78874e18i	0.0256253	+	0.0189752i
$845$	−1.13244e20			−0.368143
$846$	1.04212e20	+	2.06841e20i	0.335989	+	0.666873i
$847$		−	3.90934e20i		−	1.25003i
$848$	4.13910e19	+	1.35715e20i	0.131261	+	0.430384i
$849$	−5.79507e20			−1.82266
$850$	3.04851e19	−	1.53593e19i	0.0950946	−	0.0479113i
$851$		−	4.57608e19i		−	0.141575i
$852$	−6.38603e19	+	8.62407e19i	−0.195954	+	0.264628i
$853$	1.18167e20			0.359629			0.179814	−	0.983701i	$-0.442450\pi$
$853$	1.18167e20			0.359629			0.179814	+	0.983701i	$0.442450\pi$
$854$	2.00679e20	+	3.98308e20i	0.605754	+	1.20230i
$855$			2.18044e20i			0.652802i
$856$	5.78791e20	+	9.97594e19i	1.71872	+	0.296236i
$857$	−4.17254e20			−1.22895			−0.614475	−	0.788936i	$-0.710632\pi$
$857$	−4.17254e20			−1.22895			−0.614475	+	0.788936i	$0.710632\pi$
$858$	−1.20720e20	+	6.08219e19i	−0.352668	+	0.177684i
$859$			1.19956e20i			0.347591i	0.984782	+	0.173796i	$0.0556032\pi$
$859$			1.19956e20i			0.347591i	−0.984782	+	0.173796i	$0.944397\pi$
$860$	−3.33427e20	−	2.46899e20i	−0.958323	−	0.709627i
$861$	6.21912e20			1.77299
$862$	−1.03186e20	−	2.04803e20i	−0.291788	−	0.579143i
$863$		−	5.57748e20i		−	1.56445i	−0.622994	−	0.782226i	$-0.714084\pi$
$863$		−	5.57748e20i		−	1.56445i	0.622994	−	0.782226i	$-0.285916\pi$
$864$	−6.39958e19	+	6.11582e19i	−0.178055	+	0.170160i
$865$	1.40180e20			0.386876
$866$	2.58956e20	−	1.30469e20i	0.708925	−	0.357176i
$867$			1.53079e20i			0.415701i
$868$	−3.65916e20	+	4.94154e20i	−0.985696	+	1.33114i
$869$	5.36674e19			0.143407
$870$	−1.38837e20	−	2.75565e20i	−0.368020	−	0.730447i
$871$			3.96692e20i			1.04310i
$872$	−6.59217e19	+	3.82469e20i	−0.171954	+	0.997656i
$873$	−3.07608e20			−0.795972
$874$	7.15850e19	−	3.60665e19i	0.183756	−	0.0925815i
$875$		−	4.96985e20i		−	1.26557i
$876$	−3.31297e20	−	2.45322e20i	−0.836930	−	0.619738i
$877$	5.81992e20			1.45855			0.729273	−	0.684223i	$-0.239859\pi$
$877$	5.81992e20			1.45855			0.729273	+	0.684223i	$0.239859\pi$
$878$	−3.30493e20	−	6.55964e20i	−0.821675	−	1.63087i
$879$		−	2.56030e20i		−	0.631494i
$880$	−1.02958e20	+	3.14007e19i	−0.251931	+	0.0768353i
$881$	9.64672e19			0.234179			0.117090	−	0.993121i	$-0.462644\pi$
$881$	9.64672e19			0.234179			0.117090	+	0.993121i	$0.462644\pi$
$882$	−2.36855e20	+	1.19334e20i	−0.570430	+	0.287398i
$883$			3.24016e20i			0.774178i	0.922042	+	0.387089i	$0.126519\pi$
$883$			3.24016e20i			0.774178i	−0.922042	+	0.387089i	$0.873481\pi$
$884$	3.33907e20	−	4.50928e20i	0.791516	−	1.06891i
$885$	2.14880e20			0.505350
$886$	−7.91046e17	−	1.57007e18i	−0.00184572	−	0.00366339i
$887$		−	3.43357e20i		−	0.794842i	−0.917636	−	0.397421i	$-0.869905\pi$
$887$		−	3.43357e20i		−	0.794842i	0.917636	−	0.397421i	$-0.130095\pi$
$888$	3.04047e20	+	5.24050e19i	0.698313	+	0.120360i
$889$	−5.58465e20			−1.27258
$890$	−5.77418e20	+	2.90919e20i	−1.30545	+	0.657722i
$891$		−	1.29078e20i		−	0.289539i
$892$	2.03190e20	+	1.50460e20i	0.452219	+	0.334863i
$893$	−3.16091e20			−0.697993
$894$	−1.08811e19	−	2.15968e19i	−0.0238402	−	0.0473181i
$895$			8.10147e20i			1.76117i
$896$	−7.73593e19	−	6.13947e20i	−0.166862	−	1.32427i
$897$	1.97270e20			0.422197
$898$	1.19173e19	−	6.00428e18i	0.0253072	−	0.0127505i
$899$			3.41780e20i			0.720159i
$900$	−2.16561e19	+	2.92457e19i	−0.0452776	+	0.0611455i
$901$	2.48089e20			0.514677
$902$	−5.42589e19	−	1.07693e20i	−0.111693	−	0.221689i
$903$			1.00470e21i			2.05222i
$904$	1.17319e20	−	6.80672e20i	0.237789	−	1.37962i
$905$	1.01718e21			2.04578
$906$	−1.04918e20	+	5.28604e19i	−0.209388	+	0.105495i
$907$		−	5.62078e20i		−	1.11313i	−0.830804	−	0.556565i	$-0.812119\pi$
$907$		−	5.62078e20i		−	1.11313i	0.830804	−	0.556565i	$-0.187881\pi$
$908$	5.84651e20	+	4.32928e20i	1.14894	+	0.850775i
$909$	2.64474e20			0.515746
$910$	3.77295e20	+	7.48858e20i	0.730116	+	1.44914i
$911$			1.30865e20i			0.251301i	0.992075	+	0.125650i	$0.0401017\pi$
$911$			1.30865e20i			0.251301i	−0.992075	+	0.125650i	$0.959898\pi$
$912$	1.57657e20	+	5.16933e20i	0.300434	+	0.985077i
$913$	−3.99151e19			−0.0754818
$914$	−6.92813e20	+	3.49058e20i	−1.30015	+	0.655051i
$915$		−	7.63361e20i		−	1.42162i
$916$	−1.34357e20	+	1.81443e20i	−0.248308	+	0.335330i
$917$	−9.63267e20			−1.76669
$918$	6.96417e19	+	1.38225e20i	0.126757	+	0.251587i
$919$		−	3.30567e19i		−	0.0597105i	−0.999554	−	0.0298553i	$-0.990495\pi$
$919$		−	3.30567e19i		−	0.0597105i	0.999554	−	0.0298553i	$-0.00950464\pi$
$920$	1.54803e20	+	2.66816e19i	0.277501	+	0.0478297i
$921$	−1.01659e20			−0.180854
$922$	−1.08969e20	+	5.49015e19i	−0.192391	+	0.0969321i
$923$		−	1.62096e20i		−	0.284027i
$924$	2.09483e20	+	1.55120e20i	0.364288	+	0.269752i
$925$	−2.83529e19			−0.0489334
$926$	−1.03891e20	−	2.06204e20i	−0.177952	−	0.353199i
$927$		−	8.29294e20i		−	1.40978i
$928$	−2.37639e20	−	2.48665e20i	−0.400942	−	0.419545i
$929$	−4.74648e20			−0.794807			−0.397403	−	0.917644i	$-0.630089\pi$
$929$	−4.74648e20			−0.794807			−0.397403	+	0.917644i	$0.630089\pi$
$930$	9.39856e20	−	4.73525e20i	1.56200	−	0.786978i
$931$		−	3.61958e20i		−	0.597050i
$932$	5.81950e19	−	7.85900e19i	0.0952740	−	0.128664i
$933$	−6.87641e20			−1.11735
$934$	−2.87183e20	−	5.70003e20i	−0.463160	−	0.919283i
$935$			1.88210e20i			0.301273i
$936$	−1.01601e20	+	5.89474e20i	−0.161423	+	0.936555i
$937$	−2.04422e20			−0.322367			−0.161183	−	0.986924i	$-0.551531\pi$
$937$	−2.04422e20			−0.322367			−0.161183	+	0.986924i	$0.551531\pi$
$938$	6.83145e20	−	3.44187e20i	1.06928	−	0.538735i
$939$			1.20628e20i			0.187408i
$940$	−4.97822e20	−	3.68632e20i	−0.767678	−	0.568457i
$941$	−4.27194e20			−0.653880			−0.326940	−	0.945045i	$-0.606018\pi$
$941$	−4.27194e20			−0.653880			−0.326940	+	0.945045i	$0.606018\pi$
$942$	1.92920e20	+	3.82909e20i	0.293104	+	0.581754i
$943$			1.75984e20i			0.265394i
$944$	2.29108e20	−	6.98746e19i	0.342955	−	0.104596i
$945$	−2.31308e20			−0.343692
$946$	1.73979e20	−	8.76557e19i	0.256602	−	0.129283i
$947$			9.72640e20i			1.42397i	0.702192	+	0.711987i	$0.252205\pi$
$947$			9.72640e20i			1.42397i	−0.702192	+	0.711987i	$0.747795\pi$
$948$	3.14242e20	−	4.24371e20i	0.456674	−	0.616719i
$949$	6.22698e20			0.898284
$950$	−2.23464e19	−	4.43533e19i	−0.0319995	−	0.0635127i
$951$		−	1.50456e21i		−	2.13868i
$952$	−1.06626e21	−	1.83778e20i	−1.50454	−	0.259320i
$953$	1.18544e21			1.66046			0.830231	−	0.557419i	$-0.188208\pi$
$953$	1.18544e21			1.66046			0.830231	+	0.557419i	$0.188208\pi$
$954$	−2.36195e20	+	1.19001e20i	−0.328421	+	0.165468i
$955$			4.37820e20i			0.604327i
$956$	5.77287e20	+	4.27475e20i	0.791019	+	0.585741i
$957$	1.44888e20			0.197083
$958$	4.50156e19	+	8.93472e19i	0.0607861	+	0.120649i
$959$			8.47163e20i			1.13563i
$960$	−3.54559e20	+	9.97998e20i	−0.471835	+	1.32810i
$961$	−4.08747e20			−0.539997
$962$	−4.16202e20	+	2.09694e20i	−0.545857	+	0.275018i
$963$			1.09479e21i			1.42543i
$964$	9.04960e19	−	1.22211e20i	0.116974	−	0.157969i
$965$	−1.40990e21			−1.80925
$966$	−1.71160e20	−	3.39720e20i	−0.218054	−	0.432794i
$967$		−	3.18444e20i		−	0.402761i	−0.979513	−	0.201381i	$-0.935457\pi$
$967$		−	3.18444e20i		−	0.402761i	0.979513	−	0.201381i	$-0.0645428\pi$
$968$	−1.26685e20	+	7.35012e20i	−0.159074	+	0.922926i
$969$	9.44963e20			1.17801
$970$	7.34723e20	−	3.70174e20i	0.909330	−	0.458145i
$971$		−	6.49048e20i		−	0.797521i	−0.917055	−	0.398760i	$-0.869441\pi$
$971$		−	6.49048e20i		−	0.797521i	0.917055	−	0.398760i	$-0.130559\pi$
$972$	−8.58427e20	−	6.35656e20i	−1.04722	−	0.775457i
$973$	1.84161e21			2.23052
$974$	6.29710e20	+	1.24985e21i	0.757230	+	1.50295i
$975$		−	1.22227e20i		−	0.145926i
$976$	−2.48230e20	−	8.13908e20i	−0.294242	−	0.964777i
$977$	1.58212e21			1.86199			0.930997	−	0.365026i	$-0.118940\pi$
$977$	1.58212e21			1.86199			0.930997	+	0.365026i	$0.118940\pi$
$978$	5.50275e18	−	2.77244e18i	0.00642996	−	0.00323959i
$979$		−	3.03599e20i		−	0.352226i
$980$	4.22123e20	−	5.70060e20i	0.486247	−	0.656656i
$981$	−7.23442e20			−0.827410
$982$	−1.22581e20	−	2.43299e20i	−0.139201	−	0.276287i
$983$		−	1.41267e21i		−	1.59282i	−0.604757	−	0.796410i	$-0.706730\pi$
$983$		−	1.41267e21i		−	1.59282i	0.604757	−	0.796410i	$-0.293270\pi$
$984$	−1.16928e21	−	2.01536e20i	−1.30904	−	0.225624i
$985$	3.13047e20			0.347982
$986$	−5.37094e20	+	2.70603e20i	−0.592805	+	0.298671i
$987$			1.50007e21i			1.64396i
$988$	−6.56062e20	−	4.85807e20i	−0.713914	−	0.528646i
$989$	−2.84304e20			−0.307191
$990$	−9.02788e19	−	1.79186e20i	−0.0968588	−	0.192246i
$991$			1.47183e21i			1.56798i	0.620771	+	0.783992i	$0.286820\pi$
$991$			1.47183e21i			1.56798i	−0.620771	+	0.783992i	$0.713180\pi$
$992$	8.48109e20	−	8.10503e20i	0.897161	−	0.857380i
$993$	−1.31777e21			−1.38419
$994$	−2.79146e20	+	1.40641e20i	−0.291156	+	0.146693i
$995$			6.65773e20i			0.689548i
$996$	−2.33718e20	+	3.15626e20i	−0.240368	+	0.324607i
$997$	−1.75970e20			−0.179710			−0.0898549	−	0.995955i	$-0.528640\pi$
$997$	−1.75970e20			−0.179710			−0.0898549	+	0.995955i	$0.528640\pi$
$998$	1.29368e20	+	2.56771e20i	0.131194	+	0.260395i
$999$		−	1.28557e20i		−	0.129461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.15.b.a.3.2	yes	6
3.2	odd	2		36.15.d.c.19.5		6
4.3	odd	2	inner	4.15.b.a.3.1	✓	6
8.3	odd	2		64.15.c.d.63.6		6
8.5	even	2		64.15.c.d.63.1		6
12.11	even	2		36.15.d.c.19.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.15.b.a.3.1	✓	6	4.3	odd	2	inner
4.15.b.a.3.2	yes	6	1.1	even	1	trivial
36.15.d.c.19.5		6	3.2	odd	2
36.15.d.c.19.6		6	12.11	even	2
64.15.c.d.63.1		6	8.5	even	2
64.15.c.d.63.6		6	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-114.311 + 57.5931i) q^{2} +2948.24i q^{3} +(9750.07 - 13167.1i) q^{4} -81680.5 q^{5} +(-169798. - 337016. i) q^{6} -1.09921e6i q^{7} +(-356209. + 2.06668e6i) q^{8} -3.90914e6 q^{9} +O(q^{10})\)	\(q+(-114.311 + 57.5931i) q^{2} +2948.24i q^{3} +(9750.07 - 13167.1i) q^{4} -81680.5 q^{5} +(-169798. - 337016. i) q^{6} -1.09921e6i q^{7} +(-356209. + 2.06668e6i) q^{8} -3.90914e6 q^{9} +(9.33699e6 - 4.70423e6i) q^{10} +4.90926e6i q^{11} +(3.88196e7 + 2.87455e7i) q^{12} -7.29644e7 q^{13} +(6.33071e7 + 1.25652e8i) q^{14} -2.40814e8i q^{15} +(-7.83078e7 - 2.56760e8i) q^{16} -4.69361e8 q^{17} +(4.46858e8 - 2.25139e8i) q^{18} +6.82881e8i q^{19} +(-7.96390e8 + 1.07549e9i) q^{20} +3.24074e9 q^{21} +(-2.82739e8 - 5.61183e8i) q^{22} +9.17041e8i q^{23} +(-6.09306e9 - 1.05019e9i) q^{24} +5.68188e8 q^{25} +(8.34064e9 - 4.20224e9i) q^{26} +2.57627e9i q^{27} +(-1.44734e10 - 1.07174e10i) q^{28} -1.00105e10 q^{29} +(1.38692e10 + 2.75277e10i) q^{30} -3.41422e10i q^{31} +(2.37390e10 + 2.48405e10i) q^{32} -1.44737e10 q^{33} +(5.36532e10 - 2.70320e10i) q^{34} +8.97842e10i q^{35} +(-3.81143e10 + 5.14718e10i) q^{36} -4.99005e10 q^{37} +(-3.93292e10 - 7.80609e10i) q^{38} -2.15116e11i q^{39} +(2.90953e10 - 1.68807e11i) q^{40} +1.91904e11 q^{41} +(-3.70453e11 + 1.86644e11i) q^{42} +3.10023e11i q^{43} +(6.46405e10 + 4.78656e10i) q^{44} +3.19300e11 q^{45} +(-5.28152e10 - 1.04828e11i) q^{46} +4.62878e11i q^{47} +(7.56988e11 - 2.30870e11i) q^{48} -5.30046e11 q^{49} +(-6.49503e10 + 3.27237e10i) q^{50} -1.38379e12i q^{51} +(-7.11407e11 + 9.60726e11i) q^{52} -5.28568e11 q^{53} +(-1.48375e11 - 2.94496e11i) q^{54} -4.00991e11i q^{55} +(2.27172e12 + 3.91549e11i) q^{56} -2.01329e12 q^{57} +(1.14431e12 - 5.76534e11i) q^{58} +8.92307e11i q^{59} +(-3.17081e12 - 2.34795e12i) q^{60} +3.16992e12 q^{61} +(1.96636e12 + 3.90284e12i) q^{62} +4.29697e12i q^{63} +(-4.14428e12 - 1.47234e12i) q^{64} +5.95976e12 q^{65} +(1.65450e12 - 8.33583e11i) q^{66} -5.43679e12i q^{67} +(-4.57630e12 + 6.18011e12i) q^{68} -2.70365e12 q^{69} +(-5.17095e12 - 1.02633e13i) q^{70} +2.22157e12i q^{71} +(1.39247e12 - 8.07893e12i) q^{72} -8.53427e12 q^{73} +(5.70419e12 - 2.87393e12i) q^{74} +1.67515e12i q^{75} +(8.99154e12 + 6.65813e12i) q^{76} +5.39632e12 q^{77} +(1.23892e13 + 2.45902e13i) q^{78} -1.09319e13i q^{79} +(6.39622e12 + 2.09723e13i) q^{80} -2.62927e13 q^{81} +(-2.19368e13 + 1.10524e13i) q^{82} +8.13058e12i q^{83} +(3.15974e13 - 4.26710e13i) q^{84} +3.83377e13 q^{85} +(-1.78552e13 - 3.54390e13i) q^{86} -2.95132e13i q^{87} +(-1.01459e13 - 1.74872e12i) q^{88} -6.18420e13 q^{89} +(-3.64996e13 + 1.83895e13i) q^{90} +8.02033e13i q^{91} +(1.20747e13 + 8.94121e12i) q^{92} +1.00659e14 q^{93} +(-2.66586e13 - 5.29121e13i) q^{94} -5.57781e13i q^{95} +(-7.32357e13 + 6.99883e13i) q^{96} +7.86895e13 q^{97} +(6.05901e13 - 3.05270e13i) q^{98} -1.91910e13i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 92 q^{2} - 1392 q^{4} + 8060 q^{5} + 50784 q^{6} + 446272 q^{8} - 2998698 q^{9}+O(q^{10}) \) 6 * q - 92 * q^2 - 1392 * q^4 + 8060 * q^5 + 50784 * q^6 + 446272 * q^8 - 2998698 * q^9	\( 6 q - 92 q^{2} - 1392 q^{4} + 8060 q^{5} + 50784 q^{6} + 446272 q^{8} - 2998698 q^{9} + 5796840 q^{10} + 193920 q^{12} - 80775396 q^{13} + 175232064 q^{14} - 353013504 q^{16} - 120131764 q^{17} + 1599402372 q^{18} - 5047343200 q^{20} + 1226658048 q^{21} + 9916985760 q^{22} - 24092176896 q^{24} + 3942973410 q^{25} + 39549467048 q^{26} - 65094731520 q^{28} - 8035796644 q^{29} + 99698873280 q^{30} - 85711465472 q^{32} - 37769804160 q^{33} + 98089165512 q^{34} - 27478990320 q^{36} + 31334118396 q^{37} - 165268841760 q^{38} + 435607171200 q^{40} + 83362750892 q^{41} - 830203906560 q^{42} + 915657452160 q^{44} + 271078769820 q^{45} - 1712365889856 q^{46} + 2292961843200 q^{48} - 551978693658 q^{49} - 1639579094580 q^{50} + 1057159118496 q^{52} + 76712275004 q^{53} + 445471858368 q^{54} - 560223046656 q^{56} - 2647253865600 q^{57} + 4483777382184 q^{58} - 9544013748480 q^{60} + 6210000787932 q^{61} + 10375644284160 q^{62} - 14398852657152 q^{64} - 7189912943720 q^{65} + 15071210499840 q^{66} - 18507298307296 q^{68} + 19348372347648 q^{69} + 12679529923200 q^{70} - 5286233111232 q^{72} - 29882649313236 q^{73} - 1536652566808 q^{74} + 21457134000000 q^{76} + 37339673521920 q^{77} - 29727224255040 q^{78} + 57843429624320 q^{80} - 98651978873946 q^{81} - 71900577251064 q^{82} + 102961968764928 q^{84} + 151199882653560 q^{85} - 100164269733216 q^{86} + 51557990330880 q^{88} - 180966014731924 q^{89} - 84934442792280 q^{90} + 82241452266240 q^{92} + 295002300748800 q^{93} - 40381697410176 q^{94} - 82703070928896 q^{96} - 345459072299124 q^{97} + 121406102961892 q^{98}+O(q^{100}) \) 6 * q - 92 * q^2 - 1392 * q^4 + 8060 * q^5 + 50784 * q^6 + 446272 * q^8 - 2998698 * q^9 + 5796840 * q^10 + 193920 * q^12 - 80775396 * q^13 + 175232064 * q^14 - 353013504 * q^16 - 120131764 * q^17 + 1599402372 * q^18 - 5047343200 * q^20 + 1226658048 * q^21 + 9916985760 * q^22 - 24092176896 * q^24 + 3942973410 * q^25 + 39549467048 * q^26 - 65094731520 * q^28 - 8035796644 * q^29 + 99698873280 * q^30 - 85711465472 * q^32 - 37769804160 * q^33 + 98089165512 * q^34 - 27478990320 * q^36 + 31334118396 * q^37 - 165268841760 * q^38 + 435607171200 * q^40 + 83362750892 * q^41 - 830203906560 * q^42 + 915657452160 * q^44 + 271078769820 * q^45 - 1712365889856 * q^46 + 2292961843200 * q^48 - 551978693658 * q^49 - 1639579094580 * q^50 + 1057159118496 * q^52 + 76712275004 * q^53 + 445471858368 * q^54 - 560223046656 * q^56 - 2647253865600 * q^57 + 4483777382184 * q^58 - 9544013748480 * q^60 + 6210000787932 * q^61 + 10375644284160 * q^62 - 14398852657152 * q^64 - 7189912943720 * q^65 + 15071210499840 * q^66 - 18507298307296 * q^68 + 19348372347648 * q^69 + 12679529923200 * q^70 - 5286233111232 * q^72 - 29882649313236 * q^73 - 1536652566808 * q^74 + 21457134000000 * q^76 + 37339673521920 * q^77 - 29727224255040 * q^78 + 57843429624320 * q^80 - 98651978873946 * q^81 - 71900577251064 * q^82 + 102961968764928 * q^84 + 151199882653560 * q^85 - 100164269733216 * q^86 + 51557990330880 * q^88 - 180966014731924 * q^89 - 84934442792280 * q^90 + 82241452266240 * q^92 + 295002300748800 * q^93 - 40381697410176 * q^94 - 82703070928896 * q^96 - 345459072299124 * q^97 + 121406102961892 * q^98

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