LMFDB - Embedded newform 16.11.f.a.3.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,11,Mod(3,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("16.3");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	16.f (of order $4$, degree $2$, 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:	$10.1657160428$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.19
Character	$\chi$	$=$	16.3
Dual form			16.11.f.a.11.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(32.0000 + 0.0155982i) q^{2} +(-39.7294 + 39.7294i) q^{3} +(1024.00 + 0.998283i) q^{4} +(-4096.79 + 4096.79i) q^{5} +(-1271.96 + 1270.72i) q^{6} -7866.10 q^{7} +(32768.0 + 47.9176i) q^{8} +55892.1i q^{9} +O(q^{10})$	\(q+(32.0000 + 0.0155982i) q^{2} +(-39.7294 + 39.7294i) q^{3} +(1024.00 + 0.998283i) q^{4} +(-4096.79 + 4096.79i) q^{5} +(-1271.96 + 1270.72i) q^{6} -7866.10 q^{7} +(32768.0 + 47.9176i) q^{8} +55892.1i q^{9} +(-131161. + 131033. i) q^{10} +(-47646.0 - 47646.0i) q^{11} +(-40722.6 + 40643.3i) q^{12} +(225159. + 225159. i) q^{13} +(-251715. - 122.697i) q^{14} -325526. i q^{15} +(1.04857e6 + 2044.48i) q^{16} -784967. q^{17} +(-871.816 + 1.78855e6i) q^{18} +(-1.71755e6 + 1.71755e6i) q^{19} +(-4.19920e6 + 4.19102e6i) q^{20} +(312516. - 312516. i) q^{21} +(-1.52393e6 - 1.52542e6i) q^{22} +1.21656e7 q^{23} +(-1.30376e6 + 1.29995e6i) q^{24} -2.38018e7i q^{25} +(7.20159e6 + 7.20861e6i) q^{26} +(-4.56655e6 - 4.56655e6i) q^{27} +(-8.05488e6 - 7852.59i) q^{28} +(3.70103e6 + 3.70103e6i) q^{29} +(5077.62 - 1.04168e7i) q^{30} -3.97315e7i q^{31} +(3.35543e7 + 81779.3i) q^{32} +3.78590e6 q^{33} +(-2.51189e7 - 12244.1i) q^{34} +(3.22258e7 - 3.22258e7i) q^{35} +(-55796.2 + 5.72335e7i) q^{36} +(6.77209e6 - 6.77209e6i) q^{37} +(-5.49884e7 + 5.49348e7i) q^{38} -1.78909e7 q^{39} +(-1.34440e8 + 1.34047e8i) q^{40} +6.98548e7i q^{41} +(1.00054e7 - 9.99562e6i) q^{42} +(1.43783e8 + 1.43783e8i) q^{43} +(-4.87420e7 - 4.88371e7i) q^{44} +(-2.28978e8 - 2.28978e8i) q^{45} +(3.89300e8 + 189761. i) q^{46} +2.76759e8i q^{47} +(-4.17405e7 + 4.15780e7i) q^{48} -2.20600e8 q^{49} +(371264. - 7.61657e8i) q^{50} +(3.11863e7 - 3.11863e7i) q^{51} +(2.30338e8 + 2.30788e8i) q^{52} +(-1.93276e8 + 1.93276e8i) q^{53} +(-1.46058e8 - 1.46201e8i) q^{54} +3.90392e8 q^{55} +(-2.57756e8 - 376924. i) q^{56} -1.36475e8i q^{57} +(1.18375e8 + 1.18491e8i) q^{58} +(4.10183e8 + 4.10183e8i) q^{59} +(324968. - 3.33339e8i) q^{60} +(2.74442e8 + 2.74442e8i) q^{61} +(619739. - 1.27141e9i) q^{62} -4.39653e8i q^{63} +(1.07374e9 + 3.14032e6i) q^{64} -1.84486e9 q^{65} +(1.21149e8 + 59053.2i) q^{66} +(-8.74431e8 + 8.74431e8i) q^{67} +(-8.03806e8 - 783620. i) q^{68} +(-4.83333e8 + 4.83333e8i) q^{69} +(1.03173e9 - 1.03072e9i) q^{70} +2.68244e9 q^{71} +(-2.67822e6 + 1.83147e9i) q^{72} -2.43302e9i q^{73} +(2.16812e8 - 2.16601e8i) q^{74} +(9.45631e8 + 9.45631e8i) q^{75} +(-1.76048e9 + 1.75706e9i) q^{76} +(3.74788e8 + 3.74788e8i) q^{77} +(-5.72509e8 - 279066. i) q^{78} -1.43988e8i q^{79} +(-4.30417e9 + 4.28741e9i) q^{80} -2.93752e9 q^{81} +(-1.08961e6 + 2.23535e9i) q^{82} +(-2.28572e8 + 2.28572e8i) q^{83} +(3.20328e8 - 3.19704e8i) q^{84} +(3.21585e9 - 3.21585e9i) q^{85} +(4.59881e9 + 4.60330e9i) q^{86} -2.94080e8 q^{87} +(-1.55898e9 - 1.56355e9i) q^{88} +1.16686e9i q^{89} +(-7.32374e9 - 7.33088e9i) q^{90} +(-1.77113e9 - 1.77113e9i) q^{91} +(1.24576e10 + 1.21447e7i) q^{92} +(1.57851e9 + 1.57851e9i) q^{93} +(-4.31693e6 + 8.85628e9i) q^{94} -1.40729e10i q^{95} +(-1.33634e9 + 1.32985e9i) q^{96} +4.04358e9 q^{97} +(-7.05919e9 - 3.44095e6i) q^{98} +(2.66304e9 - 2.66304e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 2 q^{2} - 2 q^{3} - 1256 q^{4} - 2 q^{5} - 17216 q^{6} - 4 q^{7} + 69124 q^{8}+O(q^{10}) $ 38 * q - 2 * q^2 - 2 * q^3 - 1256 * q^4 - 2 * q^5 - 17216 * q^6 - 4 * q^7 + 69124 * q^8	\( 38 q - 2 q^{2} - 2 q^{3} - 1256 q^{4} - 2 q^{5} - 17216 q^{6} - 4 q^{7} + 69124 q^{8} - 147364 q^{10} - 45906 q^{11} - 10988 q^{12} - 2 q^{13} + 757836 q^{14} - 469032 q^{16} - 4 q^{17} + 2066926 q^{18} - 5107042 q^{19} + 5301516 q^{20} - 118100 q^{21} - 20568924 q^{22} - 8279748 q^{23} + 58519728 q^{24} - 18451512 q^{26} - 25871552 q^{27} - 36459784 q^{28} - 29652306 q^{29} + 132781252 q^{30} - 52661752 q^{32} - 4 q^{33} + 68474900 q^{34} + 14674460 q^{35} - 15810676 q^{36} - 94618130 q^{37} + 156046000 q^{38} - 279841732 q^{39} - 125381720 q^{40} + 107395416 q^{42} + 172486862 q^{43} + 73663988 q^{44} + 19649346 q^{45} - 437620836 q^{46} + 625190376 q^{48} + 1049193778 q^{49} - 875760314 q^{50} - 72924900 q^{51} - 771392444 q^{52} + 607072398 q^{53} + 913650464 q^{54} - 1427102468 q^{55} - 1385623464 q^{56} + 37561720 q^{58} + 1543683854 q^{59} + 318869600 q^{60} + 1673280158 q^{61} - 983062992 q^{62} - 867678656 q^{64} + 1098715212 q^{65} + 768197860 q^{66} - 4830427746 q^{67} - 855827792 q^{68} + 1698121420 q^{69} - 5103882496 q^{70} + 7572888316 q^{71} + 6888513460 q^{72} + 2513658844 q^{74} - 11656678318 q^{75} - 2250244316 q^{76} - 1336459028 q^{77} + 14243324268 q^{78} - 13115458328 q^{80} - 8523250762 q^{81} + 2724305648 q^{82} + 16141605438 q^{83} - 1633924184 q^{84} + 4779968748 q^{85} - 4025865500 q^{86} - 31832612676 q^{87} + 1023457912 q^{88} + 18960485240 q^{90} + 19874217404 q^{91} + 28060187160 q^{92} - 15001617056 q^{93} - 14829002256 q^{94} + 23525947312 q^{96} - 4 q^{97} - 43134832310 q^{98} - 25616384098 q^{99}+O(q^{100}) \) 38 * q - 2 * q^2 - 2 * q^3 - 1256 * q^4 - 2 * q^5 - 17216 * q^6 - 4 * q^7 + 69124 * q^8 - 147364 * q^10 - 45906 * q^11 - 10988 * q^12 - 2 * q^13 + 757836 * q^14 - 469032 * q^16 - 4 * q^17 + 2066926 * q^18 - 5107042 * q^19 + 5301516 * q^20 - 118100 * q^21 - 20568924 * q^22 - 8279748 * q^23 + 58519728 * q^24 - 18451512 * q^26 - 25871552 * q^27 - 36459784 * q^28 - 29652306 * q^29 + 132781252 * q^30 - 52661752 * q^32 - 4 * q^33 + 68474900 * q^34 + 14674460 * q^35 - 15810676 * q^36 - 94618130 * q^37 + 156046000 * q^38 - 279841732 * q^39 - 125381720 * q^40 + 107395416 * q^42 + 172486862 * q^43 + 73663988 * q^44 + 19649346 * q^45 - 437620836 * q^46 + 625190376 * q^48 + 1049193778 * q^49 - 875760314 * q^50 - 72924900 * q^51 - 771392444 * q^52 + 607072398 * q^53 + 913650464 * q^54 - 1427102468 * q^55 - 1385623464 * q^56 + 37561720 * q^58 + 1543683854 * q^59 + 318869600 * q^60 + 1673280158 * q^61 - 983062992 * q^62 - 867678656 * q^64 + 1098715212 * q^65 + 768197860 * q^66 - 4830427746 * q^67 - 855827792 * q^68 + 1698121420 * q^69 - 5103882496 * q^70 + 7572888316 * q^71 + 6888513460 * q^72 + 2513658844 * q^74 - 11656678318 * q^75 - 2250244316 * q^76 - 1336459028 * q^77 + 14243324268 * q^78 - 13115458328 * q^80 - 8523250762 * q^81 + 2724305648 * q^82 + 16141605438 * q^83 - 1633924184 * q^84 + 4779968748 * q^85 - 4025865500 * q^86 - 31832612676 * q^87 + 1023457912 * q^88 + 18960485240 * q^90 + 19874217404 * q^91 + 28060187160 * q^92 - 15001617056 * q^93 - 14829002256 * q^94 + 23525947312 * q^96 - 4 * q^97 - 43134832310 * q^98 - 25616384098 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	32.0000	+	0.0155982i	1.00000	+	0.000487443i
$2$	32.0000	+	0.0155982i	1.00000	+	0.000487443i
$3$	−39.7294	+	39.7294i	−0.163496	+	0.163496i	−0.784113	−	0.620618i	$-0.786882\pi$
$3$	−39.7294	+	39.7294i	−0.163496	+	0.163496i	0.620618	+	0.784113i	$0.286882\pi$
$4$	1024.00	+	0.998283i	1.00000	+	0.000974886i
$5$	−4096.79	+	4096.79i	−1.31097	+	1.31097i	−0.390275	+	0.920698i	$0.627620\pi$
$5$	−4096.79	+	4096.79i	−1.31097	+	1.31097i	−0.920698	+	0.390275i	$0.872380\pi$
$6$	−1271.96	+	1270.72i	−0.163575	+	0.163416i
$7$	−7866.10			−0.468025			−0.234013	−	0.972234i	$-0.575186\pi$
$7$	−7866.10			−0.468025			−0.234013	+	0.972234i	$0.575186\pi$
$8$	32768.0	+	47.9176i	0.999999	+	0.00146233i
$9$			55892.1i			0.946538i
$10$	−131161.	+	131033.i	−1.31161	+	1.31033i
$11$	−47646.0	−	47646.0i	−0.295844	−	0.295844i	0.543539	−	0.839384i	$-0.317084\pi$
$11$	−47646.0	−	47646.0i	−0.295844	−	0.295844i	−0.839384	+	0.543539i	$0.817084\pi$
$12$	−40722.6	+	40643.3i	−0.163655	+	0.163336i
$13$	225159.	+	225159.i	0.606420	+	0.606420i	0.942009	−	0.335589i	$-0.108935\pi$
$13$	225159.	+	225159.i	0.606420	+	0.606420i	−0.335589	+	0.942009i	$0.608935\pi$
$14$	−251715.	−	122.697i	−0.468025	−	0.000228136i
$15$		−	325526.i		−	0.428677i
$16$	1.04857e6	+	2044.48i	0.999998	+	0.00194977i
$17$	−784967.			−0.552849			−0.276425	−	0.961036i	$-0.589150\pi$
$17$	−784967.			−0.552849			−0.276425	+	0.961036i	$0.589150\pi$
$18$	−871.816	+	1.78855e6i	−0.000461384	+	0.946538i
$19$	−1.71755e6	+	1.71755e6i	−0.693651	+	0.693651i	−0.963033	−	0.269382i	$-0.913181\pi$
$19$	−1.71755e6	+	1.71755e6i	−0.693651	+	0.693651i	0.269382	+	0.963033i	$0.413181\pi$
$20$	−4.19920e6	+	4.19102e6i	−1.31225	+	1.30969i
$21$	312516.	−	312516.i	0.0765200	−	0.0765200i
$22$	−1.52393e6	−	1.52542e6i	−0.295700	−	0.295989i
$23$	1.21656e7			1.89014			0.945072	−	0.326862i	$-0.105991\pi$
$23$	1.21656e7			1.89014			0.945072	+	0.326862i	$0.105991\pi$
$24$	−1.30376e6	+	1.29995e6i	−0.163735	+	0.163256i
$25$		−	2.38018e7i		−	2.43730i
$26$	7.20159e6	+	7.20861e6i	0.606124	+	0.606715i
$27$	−4.56655e6	−	4.56655e6i	−0.318250	−	0.318250i
$28$	−8.05488e6	−	7852.59i	−0.468025	−	0.000456271i
$29$	3.70103e6	+	3.70103e6i	0.180440	+	0.180440i	0.791548	−	0.611108i	$-0.209276\pi$
$29$	3.70103e6	+	3.70103e6i	0.180440	+	0.180440i	−0.611108	+	0.791548i	$0.709276\pi$
$30$	5077.62	−	1.04168e7i	0.000208956	−	0.428677i
$31$		−	3.97315e7i		−	1.38780i	−0.720072	−	0.693900i	$-0.755891\pi$
$31$		−	3.97315e7i		−	1.38780i	0.720072	−	0.693900i	$-0.244109\pi$
$32$	3.35543e7	+	81779.3i	0.999997	+	0.00243721i
$33$	3.78590e6			0.0967385
$34$	−2.51189e7	−	12244.1i	−0.552849	−	0.000269483i
$35$	3.22258e7	−	3.22258e7i	0.613568	−	0.613568i
$36$	−55796.2	+	5.72335e7i	−0.000922767	+	0.946538i
$37$	6.77209e6	−	6.77209e6i	0.0976594	−	0.0976594i	−0.656589	−	0.754248i	$-0.728001\pi$
$37$	6.77209e6	−	6.77209e6i	0.0976594	−	0.0976594i	0.754248	+	0.656589i	$0.228001\pi$
$38$	−5.49884e7	+	5.49348e7i	−0.693989	+	0.693313i
$39$	−1.78909e7			−0.198294
$40$	−1.34440e8	+	1.34047e8i	−1.31289	+	1.30905i
$41$			6.98548e7i			0.602944i	0.953475	+	0.301472i	$0.0974780\pi$
$41$			6.98548e7i			0.602944i	−0.953475	+	0.301472i	$0.902522\pi$
$42$	1.00054e7	−	9.99562e6i	0.0765573	−	0.0764827i
$43$	1.43783e8	+	1.43783e8i	0.978059	+	0.978059i	0.999764	−	0.0217051i	$-0.00690951\pi$
$43$	1.43783e8	+	1.43783e8i	0.978059	+	0.978059i	−0.0217051	+	0.999764i	$0.506910\pi$
$44$	−4.87420e7	−	4.88371e7i	−0.295556	−	0.296133i
$45$	−2.28978e8	−	2.28978e8i	−1.24089	−	1.24089i
$46$	3.89300e8	+	189761.i	1.89014	+	0.000921338i
$47$			2.76759e8i			1.20674i	0.797463	+	0.603368i	$0.206175\pi$
$47$			2.76759e8i			1.20674i	−0.797463	+	0.603368i	$0.793825\pi$
$48$	−4.17405e7	+	4.15780e7i	−0.163814	+	0.163177i
$49$	−2.20600e8			−0.780953
$50$	371264.	−	7.61657e8i	0.00118805	−	2.43730i
$51$	3.11863e7	−	3.11863e7i	0.0903884	−	0.0903884i
$52$	2.30338e8	+	2.30788e8i	0.605828	+	0.607011i
$53$	−1.93276e8	+	1.93276e8i	−0.462167	+	0.462167i	−0.899365	−	0.437198i	$-0.855971\pi$
$53$	−1.93276e8	+	1.93276e8i	−0.462167	+	0.462167i	0.437198	+	0.899365i	$0.355971\pi$
$54$	−1.46058e8	−	1.46201e8i	−0.318095	−	0.318406i
$55$	3.90392e8			0.775688
$56$	−2.57756e8	−	376924.i	−0.468025	−	0.000684407i
$57$		−	1.36475e8i		−	0.226818i
$58$	1.18375e8	+	1.18491e8i	0.180352	+	0.180528i
$59$	4.10183e8	+	4.10183e8i	0.573743	+	0.573743i	0.933172	−	0.359430i	$-0.117029\pi$
$59$	4.10183e8	+	4.10183e8i	0.573743	+	0.573743i	−0.359430	+	0.933172i	$0.617029\pi$
$60$	324968.	−	3.33339e8i	0.000417911	−	0.428677i
$61$	2.74442e8	+	2.74442e8i	0.324938	+	0.324938i	0.850658	−	0.525720i	$-0.176204\pi$
$61$	2.74442e8	+	2.74442e8i	0.324938	+	0.324938i	−0.525720	+	0.850658i	$0.676204\pi$
$62$	619739.	−	1.27141e9i	0.000676473	−	1.38780i
$63$		−	4.39653e8i		−	0.443004i
$64$	1.07374e9	+	3.14032e6i	0.999996	+	0.00292465i
$65$	−1.84486e9			−1.59000
$66$	1.21149e8	+	59053.2i	0.0967385	+	4.71545e-5i
$67$	−8.74431e8	+	8.74431e8i	−0.647667	+	0.647667i	−0.952429	−	0.304762i	$-0.901423\pi$
$67$	−8.74431e8	+	8.74431e8i	−0.647667	+	0.647667i	0.304762	+	0.952429i	$0.401423\pi$
$68$	−8.03806e8	−	783620.i	−0.552849	−	0.000538965i
$69$	−4.83333e8	+	4.83333e8i	−0.309030	+	0.309030i
$70$	1.03173e9	−	1.03072e9i	0.613867	−	0.613269i
$71$	2.68244e9			1.48675			0.743376	−	0.668874i	$-0.233223\pi$
$71$	2.68244e9			1.48675			0.743376	+	0.668874i	$0.233223\pi$
$72$	−2.67822e6	+	1.83147e9i	−0.00138415	+	0.946537i
$73$		−	2.43302e9i		−	1.17363i	−0.809721	−	0.586815i	$-0.800382\pi$
$73$		−	2.43302e9i		−	1.17363i	0.809721	−	0.586815i	$-0.199618\pi$
$74$	2.16812e8	−	2.16601e8i	0.0977070	−	0.0976118i
$75$	9.45631e8	+	9.45631e8i	0.398488	+	0.398488i
$76$	−1.76048e9	+	1.75706e9i	−0.694327	+	0.692975i
$77$	3.74788e8	+	3.74788e8i	0.138463	+	0.138463i
$78$	−5.72509e8	−	279066.i	−0.198294	−	9.66570e-5i
$79$		−	1.43988e8i		−	0.0467942i	−0.999726	−	0.0233971i	$-0.992552\pi$
$79$		−	1.43988e8i		−	0.0467942i	0.999726	−	0.0233971i	$-0.00744821\pi$
$80$	−4.30417e9	+	4.28741e9i	−1.31353	+	1.30841i
$81$	−2.93752e9			−0.842473
$82$	−1.08961e6	+	2.23535e9i	−0.000293901	+	0.602944i
$83$	−2.28572e8	+	2.28572e8i	−0.0580273	+	0.0580273i	−0.735525	−	0.677498i	$-0.763064\pi$
$83$	−2.28572e8	+	2.28572e8i	−0.0580273	+	0.0580273i	0.677498	+	0.735525i	$0.263064\pi$
$84$	3.20328e8	−	3.19704e8i	0.0765946	−	0.0764454i
$85$	3.21585e9	−	3.21585e9i	0.724771	−	0.724771i
$86$	4.59881e9	+	4.60330e9i	0.977582	+	0.978536i
$87$	−2.94080e8			−0.0590023
$88$	−1.55898e9	−	1.56355e9i	−0.295412	−	0.296277i
$89$			1.16686e9i			0.208963i	0.994527	+	0.104482i	$0.0333183\pi$
$89$			1.16686e9i			0.208963i	−0.994527	+	0.104482i	$0.966682\pi$
$90$	−7.32374e9	−	7.33088e9i	−1.24028	−	1.24149i
$91$	−1.77113e9	−	1.77113e9i	−0.283820	−	0.283820i
$92$	1.24576e10	+	1.21447e7i	1.89014	+	0.00184268i
$93$	1.57851e9	+	1.57851e9i	0.226899	+	0.226899i
$94$	−4.31693e6	+	8.85628e9i	−0.000588215	+	1.20674i
$95$		−	1.40729e10i		−	1.81872i
$96$	−1.33634e9	+	1.32985e9i	−0.163894	+	0.163097i
$97$	4.04358e9			0.470876			0.235438	−	0.971889i	$-0.424347\pi$
$97$	4.04358e9			0.470876			0.235438	+	0.971889i	$0.424347\pi$
$98$	−7.05919e9	−	3.44095e6i	−0.780952	−	0.000380670i
$99$	2.66304e9	−	2.66304e9i	0.280028	−	0.280028i
$100$	2.37609e7	−	2.43730e10i	0.00237609	−	2.43730i
$101$	7.06137e9	−	7.06137e9i	0.671866	−	0.671866i	−0.286280	−	0.958146i	$-0.592419\pi$
$101$	7.06137e9	−	7.06137e9i	0.671866	−	0.671866i	0.958146	+	0.286280i	$0.0924189\pi$
$102$	9.98448e8	−	9.97475e8i	0.0904325	−	0.0903444i
$103$	−9.13100e9			−0.787648			−0.393824	−	0.919186i	$-0.628848\pi$
$103$	−9.13100e9			−0.787648			−0.393824	+	0.919186i	$0.628848\pi$
$104$	7.36722e9	+	7.38880e9i	0.605532	+	0.607306i
$105$			2.56062e9i			0.200631i
$106$	−6.18786e9	+	6.18183e9i	−0.462393	+	0.461942i
$107$	5.76779e9	+	5.76779e9i	0.411236	+	0.411236i	0.882169	−	0.470933i	$-0.156083\pi$
$107$	5.76779e9	+	5.76779e9i	0.411236	+	0.411236i	−0.470933	+	0.882169i	$0.656083\pi$
$108$	−4.67158e9	−	4.68070e9i	−0.317940	−	0.318561i
$109$	1.57318e10	+	1.57318e10i	1.02246	+	1.02246i	0.999742	+	0.0227200i	$0.00723263\pi$
$109$	1.57318e10	+	1.57318e10i	1.02246	+	1.02246i	0.0227200	+	0.999742i	$0.492767\pi$
$110$	1.24925e10	+	6.08940e6i	0.775688	+	0.000378104i
$111$			5.38102e8i			0.0319338i
$112$	−8.24819e9	−	1.60821e7i	−0.468024	−	0.000912542i
$113$	−2.04107e10			−1.10781			−0.553905	−	0.832580i	$-0.686863\pi$
$113$	−2.04107e10			−1.10781			−0.553905	+	0.832580i	$0.686863\pi$
$114$	2.12875e6	−	4.36718e9i	0.000110561	−	0.226818i
$115$	−4.98400e10	+	4.98400e10i	−2.47793	+	2.47793i
$116$	3.78616e9	+	3.79355e9i	0.180264	+	0.180616i
$117$	−1.25846e10	+	1.25846e10i	−0.573999	+	0.573999i
$118$	1.31194e10	+	1.31322e10i	0.573463	+	0.574022i
$119$	6.17463e9			0.258747
$120$	1.55984e7	−	1.06668e10i	0.000626866	−	0.428676i
$121$		−	2.13971e10i		−	0.824952i
$122$	8.77786e9	+	8.78642e9i	0.324780	+	0.325097i
$123$	−2.77529e9	−	2.77529e9i	−0.0985787	−	0.0985787i
$124$	3.96633e7	−	4.06850e10i	0.00135295	−	1.38780i
$125$	5.75032e10	+	5.75032e10i	1.88426	+	1.88426i
$126$	6.85779e6	−	1.40689e10i	0.000215939	−	0.443004i
$127$		−	5.78955e10i		−	1.75237i	−0.481973	−	0.876186i	$-0.660080\pi$
$127$		−	5.78955e10i		−	1.75237i	0.481973	−	0.876186i	$-0.339920\pi$
$128$	3.43595e10	+	1.17239e8i	0.999994	+	0.00341210i
$129$	−1.14248e10			−0.319817
$130$	−5.90356e10	−	2.87765e7i	−1.59000	−	0.000775035i
$131$	−6.85669e9	+	6.85669e9i	−0.177729	+	0.177729i	−0.790365	−	0.612636i	$-0.790109\pi$
$131$	−6.85669e9	+	6.85669e9i	−0.177729	+	0.177729i	0.612636	+	0.790365i	$0.290109\pi$
$132$	3.87676e9	+	3.77940e6i	0.0967385	+	9.43091e-5i
$133$	1.35104e10	−	1.35104e10i	0.324646	−	0.324646i
$134$	−2.79954e10	+	2.79681e10i	−0.647982	+	0.647351i
$135$	3.74164e10			0.834436
$136$	−2.57218e10	−	3.76137e7i	−0.552849	−	0.000808448i
$137$			1.16650e10i			0.241702i	0.992671	+	0.120851i	$0.0385624\pi$
$137$			1.16650e10i			0.241702i	−0.992671	+	0.120851i	$0.961438\pi$
$138$	−1.54742e10	+	1.54591e10i	−0.309181	+	0.308880i
$139$	−3.73248e10	−	3.73248e10i	−0.719322	−	0.719322i	0.249144	−	0.968466i	$-0.419851\pi$
$139$	−3.73248e10	−	3.73248e10i	−0.719322	−	0.719322i	−0.968466	+	0.249144i	$0.919851\pi$
$140$	3.30313e10	−	3.29670e10i	0.614166	−	0.612970i
$141$	−1.09955e10	−	1.09955e10i	−0.197296	−	0.197296i
$142$	8.58381e10	+	4.18412e7i	1.48675	+	0.000724707i
$143$		−	2.14559e10i		−	0.358812i
$144$	−1.14271e8	+	5.86071e10i	−0.00184553	+	0.946537i
$145$	−3.03247e10			−0.473104
$146$	3.79507e7	−	7.78566e10i	0.000572078	−	1.17363i
$147$	8.76430e9	−	8.76430e9i	0.127682	−	0.127682i
$148$	6.94137e9	−	6.92785e9i	0.0977545	−	0.0975641i
$149$	7.14764e10	−	7.14764e10i	0.973266	−	0.973266i	−0.0263858	−	0.999652i	$-0.508400\pi$
$149$	7.14764e10	−	7.14764e10i	0.973266	−	0.973266i	0.999652	+	0.0263858i	$0.00839982\pi$
$150$	3.02454e10	+	3.02749e10i	0.398294	+	0.398682i
$151$	−5.64069e10			−0.718534			−0.359267	−	0.933235i	$-0.616973\pi$
$151$	−5.64069e10			−0.718534			−0.359267	+	0.933235i	$0.616973\pi$
$152$	−5.63629e10	+	5.61983e10i	−0.694665	+	0.692636i
$153$		−	4.38735e10i		−	0.523293i
$154$	1.19874e10	+	1.19991e10i	0.138395	+	0.138530i
$155$	1.62772e11	+	1.62772e11i	1.81937	+	1.81937i
$156$	−1.83203e10	−	1.78602e7i	−0.198294	−	0.000193314i
$157$	−9.60474e10	−	9.60474e10i	−1.00690	−	1.00690i	−0.999976	−	0.00692591i	$-0.997795\pi$
$157$	−9.60474e10	−	9.60474e10i	−1.00690	−	1.00690i	−0.00692591	−	0.999976i	$-0.502205\pi$
$158$	2.24596e6	−	4.60763e9i	2.28095e−5	−	0.0467942i
$159$		−	1.53575e10i		−	0.151125i
$160$	−1.37800e11	+	1.37130e11i	−1.31416	+	1.30777i
$161$	−9.56959e10			−0.884635
$162$	−9.40007e10	−	4.58200e7i	−0.842473	−	0.000410658i
$163$	9.44616e10	−	9.44616e10i	0.820951	−	0.820951i	−0.165293	−	0.986244i	$-0.552857\pi$
$163$	9.44616e10	−	9.44616e10i	0.820951	−	0.820951i	0.986244	+	0.165293i	$0.0528570\pi$
$164$	−6.97349e7	+	7.15313e10i	−0.000587802	+	0.602944i
$165$	−1.55100e10	+	1.55100e10i	−0.126822	+	0.126822i
$166$	−7.31787e9	+	7.31074e9i	−0.0580556	+	0.0579991i
$167$	1.66884e11			1.28479			0.642394	−	0.766375i	$-0.277941\pi$
$167$	1.66884e11			1.28479			0.642394	+	0.766375i	$0.277941\pi$
$168$	1.02555e10	−	1.02255e10i	0.0766319	−	0.0764081i
$169$		−	3.64650e10i		−	0.264510i
$170$	1.02957e11	−	1.02857e11i	0.725124	−	0.724417i
$171$	−9.59975e10	−	9.59975e10i	−0.656568	−	0.656568i
$172$	1.47090e11	+	1.47377e11i	0.977105	+	0.979012i
$173$	5.30756e10	+	5.30756e10i	0.342503	+	0.342503i	0.857307	−	0.514805i	$-0.172136\pi$
$173$	5.30756e10	+	5.30756e10i	0.342503	+	0.342503i	−0.514805	+	0.857307i	$0.672136\pi$
$174$	−9.41055e9	−	4.58711e6i	−0.0590023	−	2.87603e-5i
$175$			1.87227e11i			1.14072i
$176$	−4.98630e10	−	5.00578e10i	−0.295267	−	0.296421i
$177$	−3.25926e10			−0.187609
$178$	−1.82009e7	+	3.73396e10i	−0.000101858	+	0.208963i
$179$	−1.60253e11	+	1.60253e11i	−0.872048	+	0.872048i	−0.992695	−	0.120647i	$-0.961503\pi$
$179$	−1.60253e11	+	1.60253e11i	−0.872048	+	0.872048i	0.120647	+	0.992695i	$0.461503\pi$
$180$	−2.34245e11	−	2.34702e11i	−1.23968	−	1.24210i
$181$	−2.26715e11	+	2.26715e11i	−1.16704	+	1.16704i	−0.184143	+	0.982899i	$0.558951\pi$
$181$	−2.26715e11	+	2.26715e11i	−1.16704	+	1.16704i	−0.982899	+	0.184143i	$0.941049\pi$
$182$	−5.66484e10	−	5.67036e10i	−0.283681	−	0.283958i
$183$	−2.18068e10			−0.106252
$184$	3.98642e11	+	5.82947e8i	1.89014	+	0.00276401i
$185$			5.54877e10i			0.256058i
$186$	5.04877e10	+	5.05369e10i	0.226788	+	0.227010i
$187$	3.74006e10	+	3.74006e10i	0.163557	+	0.163557i
$188$	−2.76284e8	+	2.83401e11i	−0.00117643	+	1.20673i
$189$	3.59209e10	+	3.59209e10i	0.148949	+	0.148949i
$190$	2.19511e8	−	4.50332e11i	0.000886521	−	1.81872i
$191$		−	2.48913e11i		−	0.979220i	−0.871941	−	0.489610i	$-0.837139\pi$
$191$		−	2.48913e11i		−	0.979220i	0.871941	−	0.489610i	$-0.162861\pi$
$192$	−4.27837e10	+	4.25342e10i	−0.163973	+	0.163017i
$193$	1.43928e10			0.0537476			0.0268738	−	0.999639i	$-0.491445\pi$
$193$	1.43928e10			0.0537476			0.0268738	+	0.999639i	$0.491445\pi$
$194$	1.29394e11	+	6.30724e7i	0.470876	+	0.000229525i
$195$	7.32953e10	−	7.32953e10i	0.259958	−	0.259958i
$196$	−2.25894e11	−	2.20221e8i	−0.780952	−	0.000761340i
$197$	1.19427e11	−	1.19427e11i	0.402504	−	0.402504i	−0.476611	−	0.879114i	$-0.658135\pi$
$197$	1.19427e11	−	1.19427e11i	0.402504	−	0.402504i	0.879114	+	0.476611i	$0.158135\pi$
$198$	8.52588e10	−	8.51757e10i	0.280165	−	0.279892i
$199$	3.46794e11			1.11124			0.555618	−	0.831438i	$-0.312482\pi$
$199$	3.46794e11			1.11124			0.555618	+	0.831438i	$0.312482\pi$
$200$	1.14052e9	−	7.79936e11i	0.00356414	−	2.43730i
$201$		−	6.94813e10i		−	0.211781i
$202$	2.26074e11	−	2.25854e11i	0.672193	−	0.671538i
$203$	−2.91127e10	−	2.91127e10i	−0.0844504	−	0.0844504i
$204$	3.19659e10	−	3.19036e10i	0.0904765	−	0.0903003i
$205$	−2.86181e11	−	2.86181e11i	−0.790444	−	0.790444i
$206$	−2.92192e11	−	1.42427e8i	−0.787648	−	0.000383934i
$207$			6.79962e11i			1.78909i
$208$	2.35636e11	+	2.36557e11i	0.605236	+	0.607601i
$209$	1.63669e11			0.410426
$210$	−3.99411e7	+	8.19399e10i	−9.77964e−5	+	0.200631i
$211$	1.03987e11	−	1.03987e11i	0.248637	−	0.248637i	−0.571774	−	0.820411i	$-0.693745\pi$
$211$	1.03987e11	−	1.03987e11i	0.248637	−	0.248637i	0.820411	+	0.571774i	$0.193745\pi$
$212$	−1.98108e11	+	1.97722e11i	−0.462618	+	0.461717i
$213$	−1.06572e11	+	1.06572e11i	−0.243077	+	0.243077i
$214$	1.84479e11	+	1.84659e11i	0.411035	+	0.411436i
$215$	−1.17810e12			−2.56442
$216$	−1.49418e11	−	1.49855e11i	−0.317785	−	0.318716i
$217$			3.12532e11i			0.649525i
$218$	5.03174e11	+	5.03664e11i	1.02196	+	1.02296i
$219$	9.66625e10	+	9.66625e10i	0.191883	+	0.191883i
$220$	3.99761e11	+	3.89722e8i	0.775688	+	0.000756208i
$221$	−1.76743e11	−	1.76743e11i	−0.335259	−	0.335259i
$222$	−8.39342e6	+	1.72193e10i	−1.55659e−5	+	0.0319338i
$223$			1.36267e11i			0.247097i	0.992339	+	0.123548i	$0.0394274\pi$
$223$			1.36267e11i			0.247097i	−0.992339	+	0.123548i	$0.960573\pi$
$224$	−2.63942e11	−	6.43284e8i	−0.468024	−	0.00114068i
$225$	1.33033e12			2.30700
$226$	−6.53141e11	−	3.18369e8i	−1.10781	−	0.000539994i
$227$	6.35682e11	−	6.35682e11i	1.05466	−	1.05466i	0.0562376	−	0.998417i	$-0.482090\pi$
$227$	6.35682e11	−	6.35682e11i	1.05466	−	1.05466i	0.998417	−	0.0562376i	$-0.0179104\pi$
$228$	1.36240e8	−	1.39750e11i	0.000221122	−	0.226818i
$229$	−2.44558e11	+	2.44558e11i	−0.388333	+	0.388333i	−0.874093	−	0.485759i	$-0.838543\pi$
$229$	−2.44558e11	+	2.44558e11i	−0.388333	+	0.388333i	0.485759	+	0.874093i	$0.338543\pi$
$230$	−1.59566e12	+	1.59410e12i	−2.47914	+	2.47672i
$231$	−2.97803e10			−0.0452761
$232$	1.21098e11	+	1.21453e11i	0.180176	+	0.180704i
$233$			7.23362e11i			1.05336i	0.850064	+	0.526679i	$0.176563\pi$
$233$			7.23362e11i			1.05336i	−0.850064	+	0.526679i	$0.823437\pi$
$234$	−4.02905e11	+	4.02512e11i	−0.574279	+	0.573720i
$235$	−1.13382e12	−	1.13382e12i	−1.58200	−	1.58200i
$236$	4.19617e11	+	4.20436e11i	0.573183	+	0.574302i
$237$	5.72058e9	+	5.72058e9i	0.00765065	+	0.00765065i
$238$	1.97588e11	+	9.63130e7i	0.258747	+	0.000126125i
$239$		−	2.26001e11i		−	0.289815i	−0.989445	−	0.144907i	$-0.953712\pi$
$239$		−	2.26001e11i		−	0.289815i	0.989445	−	0.144907i	$-0.0462885\pi$
$240$	6.65533e8	−	3.41339e11i	0.000835822	−	0.428676i
$241$	7.97971e11			0.981526			0.490763	−	0.871293i	$-0.336718\pi$
$241$	7.97971e11			0.981526			0.490763	+	0.871293i	$0.336718\pi$
$242$	3.33756e8	−	6.84708e11i	0.000402117	−	0.824952i
$243$	3.86356e11	−	3.86356e11i	0.455991	−	0.455991i
$244$	2.80754e11	+	2.81302e11i	0.324622	+	0.325255i
$245$	9.03751e11	−	9.03751e11i	1.02381	−	1.02381i
$246$	−8.87661e10	−	8.88527e10i	−0.0985307	−	0.0986268i
$247$	−7.73445e11			−0.841288
$248$	1.90384e9	−	1.30192e12i	0.00202942	−	1.38780i
$249$		−	1.81621e10i		−	0.0189744i
$250$	1.83921e12	+	1.84100e12i	1.88335	+	1.88518i
$251$	2.26272e11	+	2.26272e11i	0.227124	+	0.227124i	0.811490	−	0.584366i	$-0.198657\pi$
$251$	2.26272e11	+	2.26272e11i	0.227124	+	0.227124i	−0.584366	+	0.811490i	$0.698657\pi$
$252$	4.38898e8	−	4.50205e11i	0.000431878	−	0.443003i
$253$	−5.79643e11	−	5.79643e11i	−0.559189	−	0.559189i
$254$	9.03065e8	−	1.85266e12i	0.000854182	−	1.75237i
$255$			2.55528e11i			0.236994i
$256$	1.09950e12	+	4.28758e9i	0.999992	+	0.00389954i
$257$	−6.43396e11			−0.573869			−0.286935	−	0.957950i	$-0.592636\pi$
$257$	−6.43396e11			−0.573869			−0.286935	+	0.957950i	$0.592636\pi$
$258$	−3.65595e11	−	1.78207e8i	−0.319817	−	0.000155892i
$259$	−5.32699e10	+	5.32699e10i	−0.0457070	+	0.0457070i
$260$	−1.88914e12	−	1.84170e9i	−1.59000	−	0.00155007i
$261$	−2.06859e11	+	2.06859e11i	−0.170793	+	0.170793i
$262$	−2.19521e11	+	2.19307e11i	−0.177816	+	0.177642i
$263$	7.34864e11			0.584021			0.292010	−	0.956415i	$-0.405676\pi$
$263$	7.34864e11			0.584021			0.292010	+	0.956415i	$0.405676\pi$
$264$	1.24056e11	+	1.81411e8i	0.0967384	+	0.000141464i
$265$		−	1.58363e12i		−	1.21178i
$266$	4.32544e11	−	4.32122e11i	0.324804	−	0.324488i
$267$	−4.63588e10	−	4.63588e10i	−0.0341645	−	0.0341645i
$268$	−8.96290e11	+	8.94544e11i	−0.648298	+	0.647035i
$269$	8.94141e11	+	8.94141e11i	0.634811	+	0.634811i	0.949271	−	0.314460i	$-0.101823\pi$
$269$	8.94141e11	+	8.94141e11i	0.634811	+	0.634811i	−0.314460	+	0.949271i	$0.601823\pi$
$270$	1.19732e12	+	5.83627e8i	0.834436	+	0.000406740i
$271$			1.03065e12i			0.705123i	0.935789	+	0.352561i	$0.114689\pi$
$271$			1.03065e12i			0.705123i	−0.935789	+	0.352561i	$0.885311\pi$
$272$	−8.23096e11	−	1.60485e9i	−0.552848	−	0.00107793i
$273$	1.40732e11			0.0928065
$274$	−1.81952e8	+	3.73279e11i	−0.000117816	+	0.241702i
$275$	−1.13406e12	+	1.13406e12i	−0.721062	+	0.721062i
$276$	−4.95415e11	+	4.94450e11i	−0.309331	+	0.308729i
$277$	−1.03888e12	+	1.03888e12i	−0.637040	+	0.637040i	−0.949824	−	0.312784i	$-0.898738\pi$
$277$	−1.03888e12	+	1.03888e12i	−0.637040	+	0.637040i	0.312784	+	0.949824i	$0.398738\pi$
$278$	−1.19381e12	−	1.19498e12i	−0.718971	−	0.719673i
$279$	2.22068e12			1.31361
$280$	1.05752e12	−	1.05443e12i	0.614465	−	0.612670i
$281$			1.50146e12i			0.857002i	0.903541	+	0.428501i	$0.140958\pi$
$281$			1.50146e12i			0.857002i	−0.903541	+	0.428501i	$0.859042\pi$
$282$	−3.51683e11	−	3.52026e11i	−0.197200	−	0.197392i
$283$	−6.42928e11	−	6.42928e11i	−0.354185	−	0.354185i	0.507479	−	0.861664i	$-0.330577\pi$
$283$	−6.42928e11	−	6.42928e11i	−0.354185	−	0.354185i	−0.861664	+	0.507479i	$0.830577\pi$
$284$	2.74682e12	+	2.67784e9i	1.48675	+	0.00144941i
$285$	5.59108e11	+	5.59108e11i	0.297352	+	0.297352i
$286$	3.34673e8	−	6.86589e11i	0.000174900	−	0.358812i
$287$		−	5.49485e11i		−	0.282193i
$288$	−4.57082e9	+	1.87542e12i	−0.00230692	+	0.946536i
$289$	−1.39982e12			−0.694358
$290$	−9.70391e11	−	4.73010e8i	−0.473104	−	0.000230611i
$291$	−1.60649e11	+	1.60649e11i	−0.0769862	+	0.0769862i
$292$	2.42884e9	−	2.49141e12i	0.00114416	−	1.17363i
$293$	−1.32244e12	+	1.32244e12i	−0.612402	+	0.612402i	−0.943571	−	0.331169i	$-0.892557\pi$
$293$	−1.32244e12	+	1.32244e12i	−0.612402	+	0.612402i	0.331169	+	0.943571i	$0.392557\pi$
$294$	2.80594e11	−	2.80321e11i	0.127745	−	0.127620i
$295$	−3.36086e12			−1.50432
$296$	2.22232e11	−	2.21583e11i	0.0978021	−	0.0975165i
$297$			4.35156e11i			0.188305i
$298$	2.28836e12	−	2.28613e12i	0.973740	−	0.972792i
$299$	2.73920e12	+	2.73920e12i	1.14622	+	1.14622i
$300$	9.67382e11	+	9.69270e11i	0.398100	+	0.398876i
$301$	−1.13101e12	−	1.13101e12i	−0.457756	−	0.457756i
$302$	−1.80502e12	−	8.79844e8i	−0.718534	−	0.000350244i
$303$			5.61089e11i			0.219694i
$304$	−1.80449e12	+	1.79747e12i	−0.695003	+	0.692298i
$305$	−2.24866e12			−0.851971
$306$	6.84347e8	−	1.40395e12i	0.000255076	−	0.523293i
$307$	1.83262e11	−	1.83262e11i	0.0672016	−	0.0672016i	−0.672707	−	0.739909i	$-0.734869\pi$
$307$	1.83262e11	−	1.83262e11i	0.0672016	−	0.0672016i	0.739909	+	0.672707i	$0.234869\pi$
$308$	3.83409e11	+	3.84157e11i	0.138328	+	0.138598i
$309$	3.62770e11	−	3.62770e11i	0.128777	−	0.128777i
$310$	5.20616e12	+	5.21123e12i	1.81848	+	1.82025i
$311$	4.07591e12			1.40095			0.700475	−	0.713677i	$-0.252972\pi$
$311$	4.07591e12			1.40095			0.700475	+	0.713677i	$0.252972\pi$
$312$	−5.86249e11	−	8.57289e8i	−0.198294	−	0.000289971i
$313$		−	1.13036e12i		−	0.376268i	−0.982143	−	0.188134i	$-0.939756\pi$
$313$		−	1.13036e12i		−	0.376268i	0.982143	−	0.188134i	$-0.0602439\pi$
$314$	−3.07202e12	−	3.07501e12i	−1.00641	−	1.00739i
$315$	1.80117e12	+	1.80117e12i	0.580766	+	0.580766i
$316$	1.43741e8	−	1.47444e11i	4.56190e−5	−	0.0467942i
$317$	−2.16326e12	−	2.16326e12i	−0.675790	−	0.675790i	0.283255	−	0.959045i	$-0.408586\pi$
$317$	−2.16326e12	−	2.16326e12i	−0.675790	−	0.675790i	−0.959045	+	0.283255i	$0.908586\pi$
$318$	2.39549e8	−	4.91440e11i	7.36647e−5	−	0.151125i
$319$		−	3.52679e11i		−	0.106764i
$320$	−4.41174e12	+	4.38601e12i	−1.31480	+	1.30713i
$321$	−4.58302e11			−0.134470
$322$	−3.06227e12	−	1.49268e9i	−0.884635	−	0.000431209i
$323$	1.34822e12	−	1.34822e12i	0.383485	−	0.383485i
$324$	−3.00802e12	−	2.93248e9i	−0.842473	−	0.000821316i
$325$	5.35919e12	−	5.35919e12i	1.47803	−	1.47803i
$326$	3.02425e12	−	3.02130e12i	0.821351	−	0.820551i
$327$	−1.25003e12			−0.334336
$328$	−3.34728e9	+	2.28900e12i	−0.000881703	+	0.602944i
$329$		−	2.17701e12i		−	0.564782i
$330$	−4.96563e11	+	4.96079e11i	−0.126883	+	0.126760i
$331$	2.29311e12	+	2.29311e12i	0.577145	+	0.577145i	0.934116	−	0.356971i	$-0.116190\pi$
$331$	2.29311e12	+	2.29311e12i	0.577145	+	0.577145i	−0.356971	+	0.934116i	$0.616190\pi$
$332$	−2.34286e11	+	2.33830e11i	−0.0580839	+	0.0579707i
$333$	3.78506e11	+	3.78506e11i	0.0924383	+	0.0924383i
$334$	5.34027e12	+	2.60308e9i	1.28479	+	0.000626261i
$335$		−	7.16472e12i		−	1.69815i
$336$	3.28335e11	−	3.27057e11i	0.0766691	−	0.0763707i
$337$	−3.97826e12			−0.915258			−0.457629	−	0.889143i	$-0.651301\pi$
$337$	−3.97826e12			−0.915258			−0.457629	+	0.889143i	$0.651301\pi$
$338$	5.68788e8	−	1.16688e12i	0.000128934	−	0.264510i
$339$	8.10904e11	−	8.10904e11i	0.181122	−	0.181122i
$340$	3.29624e12	−	3.28982e12i	0.725477	−	0.724064i
$341$	−1.89305e12	+	1.89305e12i	−0.410573	+	0.410573i
$342$	−3.07042e12	−	3.07342e12i	−0.656248	−	0.656888i
$343$	3.95724e12			0.833530
$344$	4.70459e12	+	4.71837e12i	0.976628	+	0.979488i
$345$		−	3.96023e12i		−	0.810261i
$346$	1.69759e12	+	1.69925e12i	0.342336	+	0.342670i
$347$	−6.05938e12	−	6.05938e12i	−1.20443	−	1.20443i	−0.972806	−	0.231621i	$-0.925597\pi$
$347$	−6.05938e12	−	6.05938e12i	−1.20443	−	1.20443i	−0.231621	−	0.972806i	$-0.574403\pi$
$348$	−3.01138e11	−	2.93575e8i	−0.0590023	−	5.75205e-5i
$349$	5.16486e12	+	5.16486e12i	0.997542	+	0.997542i	0.999997	−	0.00245532i	$-0.000781552\pi$
$349$	5.16486e12	+	5.16486e12i	0.997542	+	0.997542i	−0.00245532	+	0.999997i	$0.500782\pi$
$350$	−2.92040e9	+	5.99127e12i	−0.000556035	+	1.14072i
$351$		−	2.05640e12i		−	0.385987i
$352$	−1.59483e12	−	1.60263e12i	−0.295123	−	0.296565i
$353$	9.12677e11			0.166511			0.0832556	−	0.996528i	$-0.473468\pi$
$353$	9.12677e11			0.166511			0.0832556	+	0.996528i	$0.473468\pi$
$354$	−1.04296e12	−	5.08386e8i	−0.187609	−	9.14486e-5i
$355$	−1.09894e13	+	1.09894e13i	−1.94909	+	1.94909i
$356$	−1.16486e9	+	1.19487e12i	−0.000203715	+	0.208963i
$357$	−2.45314e11	+	2.45314e11i	−0.0423041	+	0.0423041i
$358$	−5.13059e12	+	5.12559e12i	−0.872473	+	0.871623i
$359$	4.35693e12			0.730648			0.365324	−	0.930880i	$-0.380958\pi$
$359$	4.35693e12			0.730648			0.365324	+	0.930880i	$0.380958\pi$
$360$	−7.49219e12	−	7.51413e12i	−1.23907	−	1.24270i
$361$			2.31114e11i			0.0376956i
$362$	−7.25840e12	+	7.25133e12i	−1.16761	+	1.16647i
$363$	8.50096e11	+	8.50096e11i	0.134876	+	0.134876i
$364$	−1.81186e12	−	1.81540e12i	−0.283543	−	0.284096i
$365$	9.96757e12	+	9.96757e12i	1.53860	+	1.53860i
$366$	−6.97819e11	−	3.40147e8i	−0.106252	−	5.17918e-5i
$367$		−	8.14745e12i		−	1.22375i	−0.790956	−	0.611873i	$-0.790416\pi$
$367$		−	8.14745e12i		−	1.22375i	0.790956	−	0.611873i	$-0.209584\pi$
$368$	1.27565e13	+	2.48724e10i	1.89014	+	0.00368535i
$369$	−3.90434e12			−0.570710
$370$	−8.65507e8	+	1.77561e12i	−0.000124814	+	0.256058i
$371$	1.52033e12	−	1.52033e12i	0.216306	−	0.216306i
$372$	1.61482e12	+	1.61797e12i	0.226678	+	0.227120i
$373$	−5.91476e11	+	5.91476e11i	−0.0819206	+	0.0819206i	−0.746880	−	0.664959i	$-0.768449\pi$
$373$	−5.91476e11	+	5.91476e11i	−0.0819206	+	0.0819206i	0.664959	+	0.746880i	$0.268449\pi$
$374$	1.19623e12	+	1.19740e12i	0.163478	+	0.163637i
$375$	−4.56914e12			−0.616138
$376$	−1.32616e10	+	9.06882e12i	−0.00176464	+	1.20673i
$377$			1.66664e12i			0.218845i
$378$	1.14891e12	+	1.15003e12i	0.148877	+	0.149022i
$379$	−2.35265e11	−	2.35265e11i	−0.0300858	−	0.0300858i	0.691904	−	0.721990i	$-0.256772\pi$
$379$	−2.35265e11	−	2.35265e11i	−0.0300858	−	0.0300858i	−0.721990	+	0.691904i	$0.756772\pi$
$380$	1.40487e10	−	1.44106e13i	0.00177304	−	1.81872i
$381$	2.30016e12	+	2.30016e12i	0.286505	+	0.286505i
$382$	3.88259e9	−	7.96521e12i	0.000477314	−	0.979220i
$383$			1.10631e13i			1.34241i	0.741273	+	0.671204i	$0.234223\pi$
$383$			1.10631e13i			1.34241i	−0.741273	+	0.671204i	$0.765777\pi$
$384$	−1.36974e12	+	1.36043e12i	−0.164053	+	0.162937i
$385$	−3.07086e12			−0.363042
$386$	4.60570e11	+	2.24502e8i	0.0537476	+	2.61989e-5i
$387$	−8.03634e12	+	8.03634e12i	−0.925771	+	0.925771i
$388$	4.14062e12	+	4.03663e9i	0.470876	+	0.000459051i
$389$	−1.86896e12	+	1.86896e12i	−0.209822	+	0.209822i	−0.804192	−	0.594370i	$-0.797402\pi$
$389$	−1.86896e12	+	1.86896e12i	−0.209822	+	0.209822i	0.594370	+	0.804192i	$0.297402\pi$
$390$	2.34659e12	−	2.34431e12i	0.260085	−	0.259831i
$391$	−9.54961e12			−1.04497
$392$	−7.22861e12	−	1.05706e10i	−0.780952	−	0.00114201i
$393$		−	5.44825e11i		−	0.0581158i
$394$	3.82351e12	−	3.81979e12i	0.402700	−	0.402307i
$395$	5.89891e11	+	5.89891e11i	0.0613460	+	0.0613460i
$396$	2.72961e12	−	2.72429e12i	0.280301	−	0.279755i
$397$	−7.89729e12	−	7.89729e12i	−0.800803	−	0.800803i	0.182418	−	0.983221i	$-0.441608\pi$
$397$	−7.89729e12	−	7.89729e12i	−0.800803	−	0.800803i	−0.983221	+	0.182418i	$0.941608\pi$
$398$	1.10974e13	+	5.40935e9i	1.11124	+	0.000541664i
$399$			1.07352e12i			0.106156i
$400$	4.86623e10	−	2.49579e13i	0.00475218	−	2.43730i
$401$	1.39612e13			1.34648			0.673241	−	0.739423i	$-0.264902\pi$
$401$	1.39612e13			1.34648			0.673241	+	0.739423i	$0.264902\pi$
$402$	1.08378e9	−	2.22340e12i	0.000103231	−	0.211781i
$403$	8.94592e12	−	8.94592e12i	0.841589	−	0.841589i
$404$	7.23789e12	−	7.22380e12i	0.672520	−	0.671210i
$405$	1.20344e13	−	1.20344e13i	1.10446	−	1.10446i
$406$	−9.31151e11	−	9.32060e11i	−0.0844093	−	0.0844916i
$407$	−6.45326e11			−0.0577840
$408$	1.02341e12	−	1.02042e12i	0.0905205	−	0.0902562i
$409$			1.05407e13i			0.920989i	0.887663	+	0.460494i	$0.152328\pi$
$409$			1.05407e13i			0.920989i	−0.887663	+	0.460494i	$0.847672\pi$
$410$	−9.15332e12	−	9.16225e12i	−0.790059	−	0.790829i
$411$	−4.63443e11	−	4.63443e11i	−0.0395173	−	0.0395173i
$412$	−9.35014e12	−	9.11533e9i	−0.787648	−	0.000767867i
$413$	−3.22654e12	−	3.22654e12i	−0.268526	−	0.268526i
$414$	−1.06062e10	+	2.17588e13i	−0.000872082	+	1.78909i
$415$		−	1.87282e12i		−	0.152145i
$416$	7.53666e12	+	7.57349e12i	0.604940	+	0.607896i
$417$	2.96579e12			0.235212
$418$	5.23740e12	+	2.55294e9i	0.410426	+	0.000200059i
$419$	7.75045e12	−	7.75045e12i	0.600145	−	0.600145i	−0.340206	−	0.940351i	$-0.610497\pi$
$419$	7.75045e12	−	7.75045e12i	0.600145	−	0.600145i	0.940351	+	0.340206i	$0.110497\pi$
$420$	−2.55623e9	+	2.62208e12i	−0.000195593	+	0.200631i
$421$	1.67319e11	−	1.67319e11i	0.0126513	−	0.0126513i	−0.700753	−	0.713404i	$-0.747152\pi$
$421$	1.67319e11	−	1.67319e11i	0.0126513	−	0.0126513i	0.713404	+	0.700753i	$0.247152\pi$
$422$	3.32920e12	−	3.32596e12i	0.248759	−	0.248516i
$423$	−1.54686e13			−1.14222
$424$	−6.34253e12	+	6.32401e12i	−0.462843	+	0.461491i
$425$			1.86836e13i			1.34746i
$426$	−3.41196e12	+	3.40864e12i	−0.243196	+	0.242959i
$427$	−2.15879e12	−	2.15879e12i	−0.152079	−	0.152079i
$428$	5.90046e12	+	5.91197e12i	0.410834	+	0.411636i
$429$	8.52431e11	+	8.52431e11i	0.0586641	+	0.0586641i
$430$	−3.76991e13	−	1.83762e10i	−2.56442	−	0.00125001i
$431$			1.83709e12i			0.123522i	0.998091	+	0.0617610i	$0.0196717\pi$
$431$			1.83709e12i			0.123522i	−0.998091	+	0.0617610i	$0.980328\pi$
$432$	−4.77903e12	−	4.79770e12i	−0.317629	−	0.318870i
$433$	−1.98831e12			−0.130631			−0.0653153	−	0.997865i	$-0.520805\pi$
$433$	−1.98831e12			−0.130631			−0.0653153	+	0.997865i	$0.520805\pi$
$434$	−4.87493e9	+	1.00010e13i	−0.000316606	+	0.649525i
$435$	1.20478e12	−	1.20478e12i	0.0773504	−	0.0773504i
$436$	1.60937e13	+	1.61251e13i	1.02146	+	1.02346i
$437$	−2.08950e13	+	2.08950e13i	−1.31110	+	1.31110i
$438$	3.09169e12	+	3.09471e12i	0.191790	+	0.191977i
$439$	1.31573e13			0.806947			0.403473	−	0.914991i	$-0.367803\pi$
$439$	1.31573e13			0.806947			0.403473	+	0.914991i	$0.367803\pi$
$440$	1.27923e13	+	1.87066e10i	0.775688	+	0.00113431i
$441$		−	1.23298e13i		−	0.739202i
$442$	−5.65301e12	−	5.65852e12i	−0.335095	−	0.335422i
$443$	−1.11241e13	−	1.11241e13i	−0.652001	−	0.652001i	0.301474	−	0.953474i	$-0.402521\pi$
$443$	−1.11241e13	−	1.11241e13i	−0.652001	−	0.652001i	−0.953474	+	0.301474i	$0.902521\pi$
$444$	−5.37179e8	+	5.51017e11i	−3.11318e−5	+	0.0319337i
$445$	−4.78039e12	−	4.78039e12i	−0.273945	−	0.273945i
$446$	−2.12552e9	+	4.36055e12i	−0.000120446	+	0.247097i
$447$			5.67944e12i			0.318249i
$448$	−8.44612e12	−	2.47021e10i	−0.468023	−	0.00136881i
$449$	2.17778e13			1.19339			0.596694	−	0.802469i	$-0.296481\pi$
$449$	2.17778e13			1.19339			0.596694	+	0.802469i	$0.296481\pi$
$450$	4.25706e13	+	2.07508e10i	2.30700	+	0.00112453i
$451$	3.32831e12	−	3.32831e12i	0.178378	−	0.178378i
$452$	−2.09005e13	−	2.03756e10i	−1.10781	−	0.00107999i
$453$	2.24101e12	−	2.24101e12i	0.117477	−	0.117477i
$454$	2.03517e13	−	2.03319e13i	1.05517	−	1.05414i
$455$	1.45119e13			0.744160
$456$	6.53953e9	−	4.47199e12i	0.000331682	−	0.226818i
$457$		−	3.01965e13i		−	1.51487i	−0.652910	−	0.757435i	$-0.726452\pi$
$457$		−	3.01965e13i		−	1.51487i	0.652910	−	0.757435i	$-0.273548\pi$
$458$	−7.82967e12	+	7.82204e12i	−0.388523	+	0.388144i
$459$	3.58459e12	+	3.58459e12i	0.175945	+	0.175945i
$460$	−5.10859e13	+	5.09864e13i	−2.48034	+	2.47551i
$461$	−1.91937e13	−	1.91937e13i	−0.921839	−	0.921839i	0.0753205	−	0.997159i	$-0.476002\pi$
$461$	−1.91937e13	−	1.91937e13i	−0.921839	−	0.921839i	−0.997159	+	0.0753205i	$0.976002\pi$
$462$	−9.52968e11	−	4.64518e8i	−0.0452761	−	2.20695e-5i
$463$			1.75628e13i			0.825445i	0.910857	+	0.412722i	$0.135422\pi$
$463$			1.75628e13i			0.825445i	−0.910857	+	0.412722i	$0.864578\pi$
$464$	3.87324e12	+	3.88837e12i	0.180088	+	0.180791i
$465$	−1.29337e13			−0.594917
$466$	−1.12831e10	+	2.31476e13i	−0.000513452	+	1.05336i
$467$	1.39895e13	−	1.39895e13i	0.629821	−	0.629821i	−0.318202	−	0.948023i	$-0.603079\pi$
$467$	1.39895e13	−	1.39895e13i	0.629821	−	0.629821i	0.948023	+	0.318202i	$0.103079\pi$
$468$	−1.28992e13	+	1.28741e13i	−0.574559	+	0.573440i
$469$	6.87836e12	−	6.87836e12i	0.303124	−	0.303124i
$470$	−3.62646e13	−	3.63000e13i	−1.58123	−	1.58277i
$471$	7.63181e12			0.329248
$472$	1.34212e13	+	1.34605e13i	0.572903	+	0.574581i
$473$		−	1.37014e13i		−	0.578707i
$474$	1.82969e11	+	1.83148e11i	0.00764692	+	0.00765438i
$475$	4.08807e13	+	4.08807e13i	1.69064	+	1.69064i
$476$	6.32282e12	+	6.16403e9i	0.258747	+	0.000252249i
$477$	−1.08026e13	−	1.08026e13i	−0.437459	−	0.437459i
$478$	3.52520e9	−	7.23203e12i	0.000141268	−	0.289815i
$479$		−	3.29762e12i		−	0.130775i	−0.997860	−	0.0653873i	$-0.979172\pi$
$479$		−	3.29762e12i		−	0.130775i	0.997860	−	0.0653873i	$-0.0208283\pi$
$480$	2.66213e10	−	1.09228e13i	0.00104478	−	0.428675i
$481$	3.04960e12			0.118445
$482$	2.55351e13	+	1.24469e10i	0.981526	+	0.000478438i
$483$	3.80194e12	−	3.80194e12i	0.144634	−	0.144634i
$484$	2.13604e10	−	2.19107e13i	0.000804234	−	0.824952i
$485$	−1.65657e13	+	1.65657e13i	−0.617306	+	0.617306i
$486$	1.23694e13	−	1.23574e13i	0.456213	−	0.455769i
$487$	1.00658e13			0.367453			0.183726	−	0.982977i	$-0.441184\pi$
$487$	1.00658e13			0.367453			0.183726	+	0.982977i	$0.441184\pi$
$488$	8.97975e12	+	9.00605e12i	0.324463	+	0.325413i
$489$			7.50581e12i			0.268444i
$490$	2.89341e13	−	2.89059e13i	1.02431	−	1.02331i
$491$	−3.95448e13	−	3.95448e13i	−1.38574	−	1.38574i	−0.834049	−	0.551690i	$-0.813983\pi$
$491$	−3.95448e13	−	3.95448e13i	−1.38574	−	1.38574i	−0.551690	−	0.834049i	$-0.686017\pi$
$492$	−2.83913e12	−	2.84467e12i	−0.0984826	−	0.0986748i
$493$	−2.90519e12	−	2.90519e12i	−0.0997561	−	0.0997561i
$494$	−2.47502e13	−	1.20643e10i	−0.841287	−	0.000410080i
$495$			2.18198e13i			0.734219i
$496$	8.12304e10	−	4.16614e13i	0.00270589	−	1.38780i
$497$	−2.11003e13			−0.695837
$498$	2.83295e8	−	5.81186e11i	9.24896e−6	−	0.0189744i
$499$	−3.53075e12	+	3.53075e12i	−0.114121	+	0.114121i	−0.761861	−	0.647740i	$-0.775714\pi$
$499$	−3.53075e12	+	3.53075e12i	−0.114121	+	0.114121i	0.647740	+	0.761861i	$0.275714\pi$
$500$	5.88258e13	+	5.89407e13i	1.88243	+	1.88610i
$501$	−6.63019e12	+	6.63019e12i	−0.210057	+	0.210057i
$502$	7.23719e12	+	7.24425e12i	0.227013	+	0.227235i
$503$	−2.16357e13			−0.671940			−0.335970	−	0.941873i	$-0.609064\pi$
$503$	−2.16357e13			−0.671940			−0.335970	+	0.941873i	$0.609064\pi$
$504$	2.10671e10	−	1.44065e13i	0.000647817	−	0.443003i
$505$			5.78580e13i			1.76160i
$506$	−1.85395e13	−	1.85576e13i	−0.558916	−	0.559461i
$507$	1.44873e12	+	1.44873e12i	0.0432463	+	0.0432463i
$508$	5.77961e10	−	5.92850e13i	0.00170836	−	1.75237i
$509$	−1.43988e13	−	1.43988e13i	−0.421441	−	0.421441i	0.464258	−	0.885700i	$-0.346321\pi$
$509$	−1.43988e13	−	1.43988e13i	−0.421441	−	0.421441i	−0.885700	+	0.464258i	$0.846321\pi$
$510$	−3.98576e9	+	8.17688e12i	−0.000115521	+	0.236994i
$511$			1.91384e13i			0.549288i
$512$	3.51840e13	+	1.54353e11i	0.999990	+	0.00438697i
$513$	1.56865e13			0.441510
$514$	−2.05887e13	−	1.00358e10i	−0.573869	−	0.000279729i
$515$	3.74078e13	−	3.74078e13i	1.03259	−	1.03259i
$516$	−1.16990e13	−	1.14052e10i	−0.319817	−	0.000311785i
$517$	1.31865e13	−	1.31865e13i	0.357006	−	0.357006i
$518$	−1.70547e12	+	1.70381e12i	−0.0457293	+	0.0456848i
$519$	−4.21732e12			−0.111995
$520$	−6.04524e13	−	8.84014e10i	−1.59000	−	0.00232510i
$521$			2.72285e13i			0.709308i	0.934998	+	0.354654i	$0.115401\pi$
$521$			2.72285e13i			0.709308i	−0.934998	+	0.354654i	$0.884599\pi$
$522$	−6.62270e12	+	6.61625e12i	−0.170877	+	0.170710i
$523$	−9.50492e11	−	9.50492e11i	−0.0242907	−	0.0242907i	0.694857	−	0.719148i	$-0.255468\pi$
$523$	−9.50492e11	−	9.50492e11i	−0.0242907	−	0.0242907i	−0.719148	+	0.694857i	$0.755468\pi$
$524$	−7.02809e12	+	7.01440e12i	−0.177902	+	0.177556i
$525$	−7.43843e12	−	7.43843e12i	−0.186502	−	0.186502i
$526$	2.35156e13	+	1.14625e10i	0.584021	+	0.000284677i
$527$			3.11879e13i			0.767244i
$528$	3.96980e12	+	7.74021e9i	0.0967383	+	0.000188618i
$529$	1.06576e14			2.57264
$530$	2.47017e10	−	5.06760e13i	0.000590673	−	1.21178i
$531$	−2.29260e13	+	2.29260e13i	−0.543069	+	0.543069i
$532$	1.38481e13	−	1.38212e13i	0.324963	−	0.324330i
$533$	−1.57285e13	+	1.57285e13i	−0.365637	+	0.365637i
$534$	−1.48276e12	−	1.48420e12i	−0.0341479	−	0.0341812i
$535$	−4.72589e13			−1.07824
$536$	−2.86952e13	+	2.86114e13i	−0.648613	+	0.646719i
$537$		−	1.27335e13i		−	0.285152i
$538$	2.85986e13	+	2.86264e13i	0.634502	+	0.635120i
$539$	1.05107e13	+	1.05107e13i	0.231040	+	0.231040i
$540$	3.83144e13	+	3.73522e10i	0.834435	+	0.000813480i
$541$	1.53422e13	+	1.53422e13i	0.331056	+	0.331056i	0.852987	−	0.521932i	$-0.174788\pi$
$541$	1.53422e13	+	1.53422e13i	0.331056	+	0.331056i	−0.521932	+	0.852987i	$0.674788\pi$
$542$	−1.60763e10	+	3.29808e13i	−0.000343707	+	0.705123i
$543$		−	1.80145e13i		−	0.381613i
$544$	−2.63390e13	−	6.41941e10i	−0.552848	−	0.00134741i
$545$	−1.28900e14			−2.68084
$546$	4.50341e12	+	2.19516e9i	0.0928065	+	4.52379e-5i
$547$	−6.08111e12	+	6.08111e12i	−0.124178	+	0.124178i	−0.766465	−	0.642286i	$-0.777986\pi$
$547$	−6.08111e12	+	6.08111e12i	−0.124178	+	0.124178i	0.642286	+	0.766465i	$0.277986\pi$
$548$	−1.16450e10	+	1.19449e13i	−0.000235632	+	0.241702i
$549$	−1.53391e13	+	1.53391e13i	−0.307567	+	0.307567i
$550$	−3.63076e13	+	3.62722e13i	−0.721414	+	0.720711i
$551$	−1.27134e13			−0.250325
$552$	−1.58610e13	+	1.58147e13i	−0.309482	+	0.308578i
$553$			1.13263e12i			0.0219009i
$554$	−3.32604e13	+	3.32279e13i	−0.637350	+	0.636729i
$555$	−2.20449e12	−	2.20449e12i	−0.0418643	−	0.0418643i
$556$	−3.81833e13	−	3.82578e13i	−0.718621	−	0.720023i
$557$	3.84227e13	+	3.84227e13i	0.716658	+	0.716658i	0.967919	−	0.251261i	$-0.0808454\pi$
$557$	3.84227e13	+	3.84227e13i	0.716658	+	0.716658i	−0.251261	+	0.967919i	$0.580845\pi$
$558$	7.10617e13	+	3.46386e10i	1.31361	+	0.000640308i
$559$			6.47482e13i			1.18623i
$560$	3.38570e13	−	3.37252e13i	0.614764	−	0.612371i
$561$	−2.97181e12			−0.0534818
$562$	−2.34200e10	+	4.80467e13i	−0.000417740	+	0.857001i
$563$	−3.72730e13	+	3.72730e13i	−0.658949	+	0.658949i	−0.955131	−	0.296182i	$-0.904286\pi$
$563$	−3.72730e13	+	3.72730e13i	−0.658949	+	0.658949i	0.296182	+	0.955131i	$0.404286\pi$
$564$	−1.12484e13	−	1.12703e13i	−0.197103	−	0.197488i
$565$	8.36183e13	−	8.36183e13i	1.45231	−	1.45231i
$566$	−2.05637e13	−	2.05837e13i	−0.354012	−	0.354358i
$567$	2.31068e13			0.394299
$568$	8.78982e13	+	1.28536e11i	1.48675	+	0.00217412i
$569$		−	1.09428e13i		−	0.183471i	−0.995783	−	0.0917356i	$-0.970759\pi$
$569$		−	1.09428e13i		−	0.183471i	0.995783	−	0.0917356i	$-0.0292415\pi$
$570$	1.78827e13	+	1.79002e13i	0.297207	+	0.297497i
$571$	−7.00951e12	−	7.00951e12i	−0.115480	−	0.115480i	0.647005	−	0.762485i	$-0.276021\pi$
$571$	−7.00951e12	−	7.00951e12i	−0.115480	−	0.115480i	−0.762485	+	0.647005i	$0.776021\pi$
$572$	2.14191e10	−	2.19708e13i	0.000349801	−	0.358812i
$573$	9.88917e12	+	9.88917e12i	0.160098	+	0.160098i
$574$	8.57097e9	−	1.75835e13i	0.000137553	−	0.282193i
$575$		−	2.89563e14i		−	4.60685i
$576$	−1.75519e11	+	6.00135e13i	−0.00276830	+	0.946534i
$577$	8.23045e13			1.28690			0.643450	−	0.765488i	$-0.277503\pi$
$577$	8.23045e13			1.28690			0.643450	+	0.765488i	$0.277503\pi$
$578$	−4.47943e13	−	2.18347e10i	−0.694357	−	0.000338460i
$579$	−5.71818e11	+	5.71818e11i	−0.00878750	+	0.00878750i
$580$	−3.10525e13	−	3.02727e10i	−0.473104	−	0.000461223i
$581$	1.79797e12	−	1.79797e12i	0.0271583	−	0.0271583i
$582$	−5.14327e12	+	5.13826e12i	−0.0770237	+	0.0769487i
$583$	1.84177e13			0.273459
$584$	1.16584e11	−	7.97251e13i	0.00171623	−	1.17363i
$585$		−	1.03113e14i		−	1.50500i
$586$	−4.23386e13	+	4.22973e13i	−0.612701	+	0.612104i
$587$	−3.97235e13	−	3.97235e13i	−0.569977	−	0.569977i	0.362145	−	0.932122i	$-0.382044\pi$
$587$	−3.97235e13	−	3.97235e13i	−0.569977	−	0.569977i	−0.932122	+	0.362145i	$0.882044\pi$
$588$	8.98339e12	−	8.96589e12i	0.127807	−	0.127558i
$589$	6.82408e13	+	6.82408e13i	0.962649	+	0.962649i
$590$	−1.07548e14	−	5.24234e10i	−1.50432	−	0.000733272i
$591$			9.48950e12i			0.131615i
$592$	7.11488e12	−	7.08719e12i	0.0978496	−	0.0974688i
$593$	−7.99475e12			−0.109026			−0.0545132	−	0.998513i	$-0.517361\pi$
$593$	−7.99475e12			−0.109026			−0.0545132	+	0.998513i	$0.517361\pi$
$594$	−6.78764e9	+	1.39250e13i	−9.17881e−5	+	0.188305i
$595$	−2.52962e13	+	2.52962e13i	−0.339211	+	0.339211i
$596$	7.32632e13	−	7.31205e13i	0.974214	−	0.972317i
$597$	−1.37779e13	+	1.37779e13i	−0.181682	+	0.181682i
$598$	8.76117e13	+	8.76972e13i	1.14566	+	1.14678i
$599$	6.68028e13			0.866285			0.433142	−	0.901326i	$-0.357405\pi$
$599$	6.68028e13			0.866285			0.433142	+	0.901326i	$0.357405\pi$
$600$	3.09411e13	+	3.10317e13i	0.397905	+	0.399070i
$601$		−	1.10442e14i		−	1.40852i	−0.709944	−	0.704258i	$-0.751280\pi$
$601$		−	1.10442e14i		−	1.40852i	0.709944	−	0.704258i	$-0.248720\pi$
$602$	−3.61747e13	−	3.62100e13i	−0.457533	−	0.457979i
$603$	−4.88738e13	−	4.88738e13i	−0.613041	−	0.613041i
$604$	−5.77606e13	−	5.63100e10i	−0.718533	−	0.000700489i
$605$	8.76596e13	+	8.76596e13i	1.08149	+	1.08149i
$606$	−8.75196e9	+	1.79548e13i	−0.000107088	+	0.219694i
$607$		−	1.21398e13i		−	0.147322i	−0.997283	−	0.0736610i	$-0.976532\pi$
$607$		−	1.21398e13i		−	0.147322i	0.997283	−	0.0736610i	$-0.0234683\pi$
$608$	−5.77717e13	+	5.74908e13i	−0.695340	+	0.691959i
$609$	2.31326e12			0.0276145
$610$	−7.19572e13	−	3.50750e10i	−0.851971	−	0.000415288i
$611$	−6.23148e13	+	6.23148e13i	−0.731788	+	0.731788i
$612$	4.37982e10	−	4.49264e13i	0.000510151	−	0.523293i
$613$	−2.24012e11	+	2.24012e11i	−0.00258803	+	0.00258803i	−0.708400	−	0.705812i	$-0.750583\pi$
$613$	−2.24012e11	+	2.24012e11i	−0.00258803	+	0.00258803i	0.705812	+	0.708400i	$0.250583\pi$
$614$	5.86723e12	−	5.86151e12i	0.0672343	−	0.0671688i
$615$	2.27396e13			0.258468
$616$	1.22631e13	+	1.22990e13i	0.138260	+	0.138665i
$617$			1.58964e14i			1.77776i	0.458144	+	0.888878i	$0.348514\pi$
$617$			1.58964e14i			1.77776i	−0.458144	+	0.888878i	$0.651486\pi$
$618$	1.16143e13	−	1.16030e13i	0.128840	−	0.128714i
$619$	2.98724e12	+	2.98724e12i	0.0328713	+	0.0328713i	0.723351	−	0.690480i	$-0.242601\pi$
$619$	2.98724e12	+	2.98724e12i	0.0328713	+	0.0328713i	−0.690480	+	0.723351i	$0.742601\pi$
$620$	1.66516e14	+	1.66841e14i	1.81759	+	1.82114i
$621$	−5.55548e13	−	5.55548e13i	−0.601539	−	0.601539i
$622$	1.30429e14	+	6.35768e10i	1.40095	+	0.000682883i
$623$		−	9.17865e12i		−	0.0977999i
$624$	−1.87599e13	−	3.65777e10i	−0.198294	−	0.000386628i
$625$	−2.38718e14			−2.50314
$626$	1.76316e10	−	3.61717e13i	0.000183409	−	0.376268i
$627$	−6.50247e12	+	6.50247e12i	−0.0671028	+	0.0671028i
$628$	−9.82566e13	−	9.84483e13i	−1.00592	−	1.00788i
$629$	−5.31587e12	+	5.31587e12i	−0.0539909	+	0.0539909i
$630$	5.76092e13	+	5.76654e13i	0.580483	+	0.581049i
$631$	−4.28580e13			−0.428435			−0.214217	−	0.976786i	$-0.568720\pi$
$631$	−4.28580e13			−0.428435			−0.214217	+	0.976786i	$0.568720\pi$
$632$	6.89958e9	−	4.71821e12i	6.84285e−5	−	0.0467942i
$633$			8.26268e12i			0.0813023i
$634$	−6.91905e13	−	6.92579e13i	−0.675460	−	0.676119i
$635$	2.37186e14	+	2.37186e14i	2.29731	+	2.29731i
$636$	1.53312e10	−	1.57261e13i	0.000147329	−	0.151125i
$637$	−4.96701e13	−	4.96701e13i	−0.473585	−	0.473585i
$638$	5.50115e9	−	1.12857e13i	5.20415e−5	−	0.106764i
$639$			1.49927e14i			1.40727i
$640$	−1.41244e14	+	1.40284e14i	−1.31544	+	1.30649i
$641$	−1.78419e13			−0.164874			−0.0824368	−	0.996596i	$-0.526270\pi$
$641$	−1.78419e13			−0.164874			−0.0824368	+	0.996596i	$0.526270\pi$
$642$	−1.46657e13	−	7.14868e9i	−0.134470	−	6.55467e-5i
$643$	−5.28451e13	+	5.28451e13i	−0.480784	+	0.480784i	−0.905382	−	0.424598i	$-0.860415\pi$
$643$	−5.28451e13	+	5.28451e13i	−0.480784	+	0.480784i	0.424598	+	0.905382i	$0.360415\pi$
$644$	−9.79926e13	−	9.55317e10i	−0.884634	−	0.000862418i
$645$	4.68052e13	−	4.68052e13i	0.419271	−	0.419271i
$646$	4.31641e13	−	4.31220e13i	0.383672	−	0.383298i
$647$	−5.00297e13			−0.441272			−0.220636	−	0.975356i	$-0.570813\pi$
$647$	−5.00297e13			−0.441272			−0.220636	+	0.975356i	$0.570813\pi$
$648$	−9.62566e13	−	1.40759e11i	−0.842472	−	0.00123197i
$649$		−	3.90871e13i		−	0.339477i
$650$	1.71578e14	−	1.71411e14i	1.47875	−	1.47731i
$651$	−1.24167e13	−	1.24167e13i	−0.106194	−	0.106194i
$652$	9.68230e13	−	9.66344e13i	0.821751	−	0.820151i
$653$	−1.65504e13	−	1.65504e13i	−0.139393	−	0.139393i	0.633967	−	0.773360i	$-0.281426\pi$
$653$	−1.65504e13	−	1.65504e13i	−0.139393	−	0.139393i	−0.773360	+	0.633967i	$0.781426\pi$
$654$	−4.00011e13	−	1.94983e10i	−0.334336	−	0.000162970i
$655$		−	5.61809e13i		−	0.465996i
$656$	−1.42817e11	+	7.32480e13i	−0.00117560	+	0.602943i
$657$	1.35987e14			1.11089
$658$	3.39574e10	−	6.96643e13i	0.000275299	−	0.564782i
$659$	1.32379e14	−	1.32379e14i	1.06510	−	1.06510i	0.0673729	−	0.997728i	$-0.478538\pi$
$659$	1.32379e14	−	1.32379e14i	1.06510	−	1.06510i	0.997728	−	0.0673729i	$-0.0214617\pi$
$660$	−1.58978e13	+	1.58668e13i	−0.126945	+	0.126698i
$661$	−5.52182e13	+	5.52182e13i	−0.437598	+	0.437598i	−0.891203	−	0.453605i	$-0.850138\pi$
$661$	−5.52182e13	+	5.52182e13i	−0.437598	+	0.437598i	0.453605	+	0.891203i	$0.350138\pi$
$662$	7.33438e13	+	7.34153e13i	0.576864	+	0.577426i
$663$	1.40438e13			0.109627
$664$	−7.50079e12	+	7.47889e12i	−0.0581121	+	0.0579424i
$665$			1.10699e14i			0.851205i
$666$	1.21063e13	+	1.21181e13i	0.0923933	+	0.0924834i
$667$	4.50253e13	+	4.50253e13i	0.341058	+	0.341058i
$668$	1.70889e14	+	1.66597e11i	1.28479	+	0.00125252i
$669$	−5.41382e12	−	5.41382e12i	−0.0403993	−	0.0403993i
$670$	1.11757e11	−	2.29271e14i	0.000827750	−	1.69815i
$671$		−	2.61521e13i		−	0.192262i
$672$	1.05118e13	−	1.04607e13i	0.0767063	−	0.0763333i
$673$	−1.97279e14			−1.42891			−0.714457	−	0.699679i	$-0.753326\pi$
$673$	−1.97279e14			−1.42891			−0.714457	+	0.699679i	$0.753326\pi$
$674$	−1.27304e14	−	6.20536e10i	−0.915257	−	0.000446136i
$675$	−1.08692e14	+	1.08692e14i	−0.775673	+	0.775673i
$676$	3.64024e10	−	3.73402e13i	0.000257868	−	0.264510i
$677$	−8.23064e12	+	8.23064e12i	−0.0578749	+	0.0578749i	−0.735452	−	0.677577i	$-0.763030\pi$
$677$	−8.23064e12	+	8.23064e12i	−0.0578749	+	0.0578749i	0.677577	+	0.735452i	$0.263030\pi$
$678$	2.59616e13	−	2.59363e13i	0.181210	−	0.181034i
$679$	−3.18072e13			−0.220382
$680$	1.05531e14	−	1.05223e14i	0.725830	−	0.723710i
$681$			5.05105e13i			0.344863i
$682$	−6.06071e13	+	6.05480e13i	−0.410773	+	0.410372i
$683$	−1.12014e14	−	1.12014e14i	−0.753651	−	0.753651i	0.221507	−	0.975159i	$-0.428902\pi$
$683$	−1.12014e14	−	1.12014e14i	−0.753651	−	0.753651i	−0.975159	+	0.221507i	$0.928902\pi$
$684$	−9.82056e13	−	9.83972e13i	−0.655927	−	0.657207i
$685$	−4.77890e13	−	4.77890e13i	−0.316865	−	0.316865i
$686$	1.26632e14	+	6.17257e10i	0.833530	+	0.000406299i
$687$		−	1.94323e13i		−	0.126982i
$688$	1.50473e14	+	1.51061e14i	0.976150	+	0.979964i
$689$	−8.70359e13			−0.560535
$690$	6.17724e10	−	1.26727e14i	0.000394956	−	0.810261i
$691$	1.47030e14	−	1.47030e14i	0.933287	−	0.933287i	−0.0646224	−	0.997910i	$-0.520584\pi$
$691$	1.47030e14	−	1.47030e14i	0.933287	−	0.933287i	0.997910	+	0.0646224i	$0.0205843\pi$
$692$	5.42964e13	+	5.44023e13i	0.342169	+	0.342836i
$693$	−2.09477e13	+	2.09477e13i	−0.131060	+	0.131060i
$694$	−1.93806e14	−	1.93995e14i	−1.20384	−	1.20501i
$695$	3.05824e14			1.88602
$696$	−9.63639e12	−	1.40916e10i	−0.0590022	−	8.62808e-5i
$697$		−	5.48337e13i		−	0.333337i
$698$	1.65195e14	+	1.65356e14i	0.997055	+	0.998028i
$699$	−2.87388e13	−	2.87388e13i	−0.172219	−	0.172219i
$700$	−1.86906e11	+	1.91720e14i	−0.00111207	+	1.14072i
$701$	1.25735e14	+	1.25735e14i	0.742791	+	0.742791i	0.973114	−	0.230323i	$-0.0739784\pi$
$701$	1.25735e14	+	1.25735e14i	0.742791	+	0.742791i	−0.230323	+	0.973114i	$0.573978\pi$
$702$	3.20761e10	−	6.58048e13i	0.000188147	−	0.385987i
$703$			2.32628e13i			0.135483i
$704$	−5.10097e13	−	5.13090e13i	−0.294978	−	0.296708i
$705$	9.00923e13			0.517299
$706$	2.92057e13	+	1.42361e10i	0.166511	+	8.11648e-5i
$707$	−5.55455e13	+	5.55455e13i	−0.314450	+	0.314450i
$708$	−3.33748e13	−	3.25367e10i	−0.187609	−	0.000182897i
$709$	−5.44475e13	+	5.44475e13i	−0.303911	+	0.303911i	−0.842542	−	0.538631i	$-0.818942\pi$
$709$	−5.44475e13	+	5.44475e13i	−0.303911	+	0.303911i	0.538631	+	0.842542i	$0.318942\pi$
$710$	−3.51832e14	+	3.51490e14i	−1.95004	+	1.94814i
$711$	8.04782e12			0.0442925
$712$	−5.59132e10	+	3.82357e13i	−0.000305573	+	0.208963i
$713$		−	4.83358e14i		−	2.62314i
$714$	−7.85389e12	+	7.84623e12i	−0.0423247	+	0.0422834i
$715$	8.79004e13	+	8.79004e13i	0.470393	+	0.470393i
$716$	−1.64259e14	+	1.63939e14i	−0.872898	+	0.871198i
$717$	8.97889e12	+	8.97889e12i	0.0473835	+	0.0473835i
$718$	1.39422e14	+	6.79602e10i	0.730648	+	0.000356149i
$719$			8.43393e13i			0.438920i	0.975621	+	0.219460i	$0.0704295\pi$
$719$			8.43393e13i			0.438920i	−0.975621	+	0.219460i	$0.929570\pi$
$720$	−2.39633e14	−	2.40569e14i	−1.23846	−	1.24330i
$721$	7.18254e13			0.368639
$722$	−3.60496e9	+	7.39565e12i	−1.83744e−5	+	0.0376956i
$723$	−3.17029e13	+	3.17029e13i	−0.160475	+	0.160475i
$724$	−2.32382e14	+	2.31929e14i	−1.16818	+	1.16590i
$725$	8.80911e13	−	8.80911e13i	0.439787	−	0.439787i
$726$	2.71898e13	+	2.72163e13i	0.134810	+	0.134942i
$727$	1.70995e14			0.841998			0.420999	−	0.907061i	$-0.361680\pi$
$727$	1.70995e14			0.841998			0.420999	+	0.907061i	$0.361680\pi$
$728$	−5.79513e13	−	5.81210e13i	−0.283404	−	0.284234i
$729$		−	1.42758e14i		−	0.693368i
$730$	3.18807e14	+	3.19118e14i	1.53785	+	1.53935i
$731$	−1.12865e14	−	1.12865e14i	−0.540719	−	0.540719i
$732$	−2.23302e13	−	2.17694e10i	−0.106252	−	0.000103584i
$733$	−2.79818e14	−	2.79818e14i	−1.32238	−	1.32238i	−0.911847	−	0.410530i	$-0.865344\pi$
$733$	−2.79818e14	−	2.79818e14i	−1.32238	−	1.32238i	−0.410530	−	0.911847i	$-0.634656\pi$
$734$	1.27085e11	−	2.60718e14i	0.000596507	−	1.22375i
$735$			7.18110e13i			0.334776i
$736$	4.08209e14	+	9.94896e11i	1.89014	+	0.00460668i
$737$	8.33263e13			0.383217
$738$	−1.24939e14	−	6.09006e10i	−0.570710	−	0.000278189i
$739$	−2.95937e13	+	2.95937e13i	−0.134269	+	0.134269i	−0.771047	−	0.636778i	$-0.780267\pi$
$739$	−2.95937e13	+	2.95937e13i	−0.134269	+	0.134269i	0.636778	+	0.771047i	$0.280267\pi$
$740$	−5.53924e10	+	5.68193e13i	−0.000249627	+	0.256058i
$741$	3.07285e13	−	3.07285e13i	0.137547	−	0.137547i
$742$	4.86743e13	−	4.86268e13i	0.216411	−	0.216200i
$743$	−2.93080e14			−1.29432			−0.647161	−	0.762354i	$-0.724044\pi$
$743$	−2.93080e14			−1.29432			−0.647161	+	0.762354i	$0.724044\pi$
$744$	5.16489e13	+	5.18002e13i	0.226567	+	0.227231i
$745$			5.85648e14i			2.55185i
$746$	−1.89365e13	+	1.89180e13i	−0.0819605	+	0.0818806i
$747$	−1.27754e13	−	1.27754e13i	−0.0549251	−	0.0549251i
$748$	3.82608e13	+	3.83355e13i	0.163398	+	0.163717i
$749$	−4.53700e13	−	4.53700e13i	−0.192469	−	0.192469i
$750$	−1.46212e14	−	7.12703e10i	−0.616138	−	0.000300332i
$751$		−	2.77649e13i		−	0.116224i	−0.998310	−	0.0581120i	$-0.981492\pi$
$751$		−	2.77649e13i		−	0.116224i	0.998310	−	0.0581120i	$-0.0185080\pi$
$752$	−5.65829e11	+	2.90202e14i	−0.00235286	+	1.20673i
$753$	−1.79794e13			−0.0742676
$754$	−2.59966e10	+	5.33326e13i	−0.000106674	+	0.218845i
$755$	2.31087e14	−	2.31087e14i	0.941979	−	0.941979i
$756$	3.67471e13	+	3.68188e13i	0.148804	+	0.149094i
$757$	3.68531e13	−	3.68531e13i	0.148250	−	0.148250i	−0.629086	−	0.777336i	$-0.716571\pi$
$757$	3.68531e13	−	3.68531e13i	0.148250	−	0.148250i	0.777336	+	0.629086i	$0.216571\pi$
$758$	−7.52481e12	−	7.53215e12i	−0.0300711	−	0.0301005i
$759$	4.60578e13			0.182850
$760$	6.74339e11	−	4.61140e14i	0.00265956	−	1.81871i
$761$			2.12673e14i			0.833276i	0.909072	+	0.416638i	$0.136792\pi$
$761$			2.12673e14i			0.833276i	−0.909072	+	0.416638i	$0.863208\pi$
$762$	7.35691e13	+	7.36409e13i	0.286366	+	0.286645i
$763$	−1.23748e14	−	1.23748e14i	−0.478538	−	0.478538i
$764$	2.48486e11	−	2.54887e14i	0.000954629	−	0.979220i
$765$	1.79741e14	+	1.79741e14i	0.686023	+	0.686023i
$766$	−1.72565e11	+	3.54020e14i	−0.000654348	+	1.34241i
$767$			1.84713e14i			0.695858i
$768$	−4.38530e13	+	4.35123e13i	−0.164132	+	0.162857i
$769$	4.29140e14			1.59576			0.797879	−	0.602818i	$-0.205955\pi$
$769$	4.29140e14			1.59576			0.797879	+	0.602818i	$0.205955\pi$
$770$	−9.82675e13	−	4.78998e10i	−0.363042	−	0.000176962i
$771$	2.55618e13	−	2.55618e13i	0.0938251	−	0.0938251i
$772$	1.47382e13	+	1.43681e10i	0.0537476	+	5.23978e-5i
$773$	−2.32137e14	+	2.32137e14i	−0.841100	+	0.841100i	−0.989002	−	0.147902i	$-0.952748\pi$
$773$	−2.32137e14	+	2.32137e14i	−0.841100	+	0.841100i	0.147902	+	0.989002i	$0.452748\pi$
$774$	−2.57288e14	+	2.57037e14i	−0.926222	+	0.925319i
$775$	−9.45681e14			−3.38249
$776$	1.32500e14	+	1.93758e11i	0.470876	+	0.000688576i
$777$		−	4.23277e12i		−	0.0149458i
$778$	−5.98358e13	+	5.97775e13i	−0.209925	+	0.209720i
$779$	−1.19979e14	−	1.19979e14i	−0.418233	−	0.418233i
$780$	7.51275e13	−	7.49812e13i	0.260211	−	0.259704i
$781$	−1.27808e14	−	1.27808e14i	−0.439847	−	0.439847i
$782$	−3.05587e14	−	1.48957e11i	−1.04496	−	0.000509361i
$783$		−	3.38019e13i		−	0.114850i
$784$	−2.31315e14	−	4.51013e11i	−0.780951	−	0.00152268i
$785$	7.86972e14			2.64004
$786$	8.49828e9	−	1.74344e13i	2.83281e−5	−	0.0581158i
$787$	3.84900e14	−	3.84900e14i	1.27489	−	1.27489i	0.331404	−	0.943489i	$-0.392478\pi$
$787$	3.84900e14	−	3.84900e14i	1.27489	−	1.27489i	0.943489	−	0.331404i	$-0.107522\pi$
$788$	1.22412e14	−	1.22174e14i	0.402896	−	0.402111i
$789$	−2.91957e13	+	2.91957e13i	−0.0954848	+	0.0954848i
$790$	1.88673e13	+	1.88857e13i	0.0613161	+	0.0613759i
$791$	1.60552e14			0.518482
$792$	8.73900e13	−	8.71348e13i	0.280437	−	0.279618i
$793$			1.23586e14i			0.394098i
$794$	−2.52590e14	−	2.52837e14i	−0.800413	−	0.801193i
$795$	6.29165e13	+	6.29165e13i	0.198120	+	0.198120i
$796$	3.55117e14	+	3.46199e11i	1.11123	+	0.00108333i
$797$	−1.04839e14	−	1.04839e14i	−0.326010	−	0.326010i	0.525057	−	0.851067i	$-0.324044\pi$
$797$	−1.04839e14	−	1.04839e14i	−0.326010	−	0.326010i	−0.851067	+	0.525057i	$0.824044\pi$
$798$	−1.67450e10	+	3.43527e13i	−5.17452e−5	+	0.106156i
$799$		−	2.17246e14i		−	0.667143i
$800$	1.94649e12	−	7.98653e14i	0.00594023	−	2.43730i
$801$	−6.52184e13			−0.197792
$802$	4.46758e14	+	2.17769e11i	1.34648	+	0.000656334i
$803$	−1.15924e14	+	1.15924e14i	−0.347212	+	0.347212i
$804$	6.93620e10	−	7.11488e13i	0.000206463	−	0.211781i
$805$	3.92046e14	−	3.92046e14i	1.15973	−	1.15973i
$806$	2.86409e14	−	2.86130e14i	0.841999	−	0.841178i
$807$	−7.10474e13			−0.207578
$808$	2.31725e14	−	2.31049e14i	0.672847	−	0.670882i
$809$			3.40417e14i			0.982354i	0.871060	+	0.491177i	$0.163433\pi$
$809$			3.40417e14i			0.982354i	−0.871060	+	0.491177i	$0.836567\pi$
$810$	3.85289e14	−	3.84914e14i	1.10500	−	1.10392i
$811$	1.22703e13	+	1.22703e13i	0.0349746	+	0.0349746i	0.724378	−	0.689403i	$-0.242127\pi$
$811$	1.22703e13	+	1.22703e13i	0.0349746	+	0.0349746i	−0.689403	+	0.724378i	$0.742127\pi$
$812$	−2.97823e13	−	2.98404e13i	−0.0843681	−	0.0845327i
$813$	−4.09471e13	−	4.09471e13i	−0.115284	−	0.115284i
$814$	−2.06504e13	−	1.00659e10i	−0.0577840	−	2.81664e-5i
$815$			7.73979e14i			2.15249i
$816$	3.27649e13	−	3.26374e13i	0.0905645	−	0.0902120i
$817$	−4.93909e14			−1.35686
$818$	−1.64416e11	+	3.37303e14i	−0.000448930	+	0.920988i
$819$	9.89920e13	−	9.89920e13i	0.268646	−	0.268646i
$820$	−2.92763e14	−	2.93335e14i	−0.789673	−	0.791214i
$821$	−4.39755e14	+	4.39755e14i	−1.17895	+	1.17895i	−0.198937	+	0.980012i	$0.563749\pi$
$821$	−4.39755e14	+	4.39755e14i	−1.17895	+	1.17895i	−0.980012	+	0.198937i	$0.936251\pi$
$822$	−1.48229e13	−	1.48374e13i	−0.0394980	−	0.0395365i
$823$	−2.42451e14			−0.642133			−0.321067	−	0.947057i	$-0.604041\pi$
$823$	−2.42451e14			−0.642133			−0.321067	+	0.947057i	$0.604041\pi$
$824$	−2.99204e14	−	4.37536e11i	−0.787647	−	0.00115180i
$825$		−	9.01112e13i		−	0.235781i
$826$	−1.03199e14	−	1.03299e14i	−0.268395	−	0.268657i
$827$	−1.87183e14	−	1.87183e14i	−0.483882	−	0.483882i	0.422487	−	0.906369i	$-0.361157\pi$
$827$	−1.87183e14	−	1.87183e14i	−0.483882	−	0.483882i	−0.906369	+	0.422487i	$0.861157\pi$
$828$	−6.78795e11	+	6.96281e14i	−0.00174416	+	1.78909i
$829$	1.01215e13	+	1.01215e13i	0.0258508	+	0.0258508i	0.719914	−	0.694063i	$-0.244181\pi$
$829$	1.01215e13	+	1.01215e13i	0.0258508	+	0.0258508i	−0.694063	+	0.719914i	$0.744181\pi$
$830$	2.92127e10	−	5.99304e13i	7.41618e−5	−	0.152145i
$831$		−	8.25482e13i		−	0.208306i
$832$	2.41055e14	+	2.42469e14i	0.604643	+	0.608191i
$833$	1.73164e14			0.431749
$834$	9.49051e13	+	4.62609e10i	0.235212	+	0.000114652i
$835$	−6.83687e14	+	6.83687e14i	−1.68432	+	1.68432i
$836$	1.67597e14	+	1.63388e11i	0.410426	+	0.000400118i
$837$	−1.81436e14	+	1.81436e14i	−0.441668	+	0.441668i
$838$	2.48135e14	−	2.47893e14i	0.600438	−	0.599853i
$839$	3.99672e14			0.961378			0.480689	−	0.876891i	$-0.340387\pi$
$839$	3.99672e14			0.961378			0.480689	+	0.876891i	$0.340387\pi$
$840$	−1.22699e11	+	8.39064e13i	−0.000293389	+	0.200631i
$841$		−	3.93312e14i		−	0.934883i
$842$	5.35683e12	−	5.35161e12i	0.0126575	−	0.0126452i
$843$	−5.96521e13	−	5.96521e13i	−0.140116	−	0.140116i
$844$	1.06586e14	−	1.06379e14i	0.248880	−	0.248395i
$845$	1.49390e14	+	1.49390e14i	0.346766	+	0.346766i
$846$	−4.94996e14	−	2.41283e11i	−1.14222	−	0.000556768i
$847$			1.68312e14i			0.386098i
$848$	−2.03060e14	+	2.02269e14i	−0.463068	+	0.461265i
$849$	5.10863e13			0.115815
$850$	−2.91430e11	+	5.97876e14i	−0.000656811	+	1.34746i
$851$	8.23866e13	−	8.23866e13i	0.184590	−	0.184590i
$852$	−1.09236e14	+	1.09023e14i	−0.243314	+	0.242840i
$853$	2.40985e14	−	2.40985e14i	0.533636	−	0.533636i	−0.388017	−	0.921652i	$-0.626840\pi$
$853$	2.40985e14	−	2.40985e14i	0.533636	−	0.533636i	0.921652	+	0.388017i	$0.126840\pi$
$854$	−6.90475e13	−	6.91148e13i	−0.152005	−	0.152153i
$855$	7.86564e14			1.72149
$856$	1.88722e14	+	1.89275e14i	0.410634	+	0.411836i
$857$		−	2.69589e14i		−	0.583173i	−0.956544	−	0.291587i	$-0.905817\pi$
$857$		−	2.69589e14i		−	0.583173i	0.956544	−	0.291587i	$-0.0941832\pi$
$858$	2.72645e13	+	2.72911e13i	0.0586355	+	0.0586927i
$859$	5.37374e14	+	5.37374e14i	1.14898	+	1.14898i	0.986754	+	0.162221i	$0.0518657\pi$
$859$	5.37374e14	+	5.37374e14i	1.14898	+	1.14898i	0.162221	+	0.986754i	$0.448134\pi$
$860$	−1.20637e15	−	1.17608e12i	−2.56442	−	0.00250002i
$861$	2.18307e13	+	2.18307e13i	0.0461373	+	0.0461373i
$862$	−2.86553e10	+	5.87869e13i	−6.02100e−5	+	0.123522i
$863$		−	2.07415e14i		−	0.433297i	−0.976250	−	0.216649i	$-0.930487\pi$
$863$		−	2.07415e14i		−	0.433297i	0.976250	−	0.216649i	$-0.0695126\pi$
$864$	−1.52854e14	−	1.53601e14i	−0.317474	−	0.319025i
$865$	−4.34879e14			−0.898024
$866$	−6.36259e13	−	3.10140e10i	−0.130631	−	6.36750e-5i
$867$	5.56141e13	−	5.56141e13i	0.113524	−	0.113524i
$868$	−3.11995e11	+	3.20033e14i	−0.000633213	+	0.649524i
$869$	−6.86048e12	+	6.86048e12i	−0.0138438	+	0.0138438i
$870$	3.85719e13	−	3.85343e13i	0.0773881	−	0.0773127i
$871$	−3.93773e14			−0.785515
$872$	5.14747e14	+	5.16254e14i	1.02097	+	1.02396i
$873$			2.26004e14i			0.445703i
$874$	−6.68967e14	+	6.68316e14i	−1.31174	+	1.31046i
$875$	−4.52326e14	−	4.52326e14i	−0.881883	−	0.881883i
$876$	9.88858e13	+	9.90788e13i	0.191696	+	0.192070i
$877$	2.85943e14	+	2.85943e14i	0.551164	+	0.551164i	0.926777	−	0.375612i	$-0.122568\pi$
$877$	2.85943e14	+	2.85943e14i	0.551164	+	0.551164i	−0.375612	+	0.926777i	$0.622568\pi$
$878$	4.21034e14	+	2.05230e11i	0.806947	+	0.000393341i
$879$		−	1.05079e14i		−	0.200250i
$880$	4.09355e14	+	7.98150e11i	0.775687	+	0.00151242i
$881$	−5.26058e14			−0.991183			−0.495592	−	0.868556i	$-0.665049\pi$
$881$	−5.26058e14			−0.991183			−0.495592	+	0.868556i	$0.665049\pi$
$882$	1.92322e11	−	3.94553e14i	0.000360319	−	0.739201i
$883$	1.41633e14	−	1.41633e14i	0.263852	−	0.263852i	−0.562765	−	0.826617i	$-0.690262\pi$
$883$	1.41633e14	−	1.41633e14i	0.263852	−	0.263852i	0.826617	+	0.562765i	$0.190262\pi$
$884$	−1.80808e14	−	1.81161e14i	−0.334932	−	0.335585i
$885$	1.33525e14	−	1.33525e14i	0.245950	−	0.245950i
$886$	−3.55799e14	−	3.56146e14i	−0.651683	−	0.652318i
$887$	5.37627e14			0.979181			0.489591	−	0.871952i	$-0.337146\pi$
$887$	5.37627e14			0.979181			0.489591	+	0.871952i	$0.337146\pi$
$888$	−2.57846e10	+	1.76325e13i	−4.66977e−5	+	0.0319337i
$889$			4.55412e14i			0.820154i
$890$	−1.52898e14	−	1.53047e14i	−0.273811	−	0.274078i
$891$	1.39961e14	+	1.39961e14i	0.249241	+	0.249241i
$892$	−1.36033e11	+	1.39538e14i	−0.000240891	+	0.247097i
$893$	−4.75347e14	−	4.75347e14i	−0.837054	−	0.837054i
$894$	−8.85889e10	+	1.81742e14i	−0.000155129	+	0.318249i
$895$		−	1.31305e15i		−	2.28646i
$896$	−2.70275e14	−	9.22211e11i	−0.468022	−	0.00159695i
$897$	−2.17654e14			−0.374804
$898$	6.96889e14	+	3.39694e11i	1.19339	+	0.000581709i
$899$	1.47048e14	−	1.47048e14i	0.250414	−	0.250414i
$900$	1.36226e15	+	1.32805e12i	2.30700	+	0.00224906i
$901$	1.51716e14	−	1.51716e14i	0.255509	−	0.255509i
$902$	1.06558e14	−	1.06454e14i	0.178465	−	0.178291i
$903$	8.98688e13			0.149682
$904$	−6.68816e14	−	9.78030e11i	−1.10781	−	0.00161998i
$905$		−	1.85760e15i		−	3.05992i
$906$	7.17474e13	−	7.16774e13i	0.117534	−	0.117420i
$907$	6.69962e13	+	6.69962e13i	0.109147	+	0.109147i	0.759571	−	0.650424i	$-0.225409\pi$
$907$	6.69962e13	+	6.69962e13i	0.109147	+	0.109147i	−0.650424	+	0.759571i	$0.725409\pi$
$908$	6.51572e14	−	6.50303e14i	1.05568	−	1.05363i
$909$	3.94675e14	+	3.94675e14i	0.635947	+	0.635947i
$910$	4.64380e14	+	2.26359e11i	0.744160	+	0.000362736i
$911$			4.62755e14i			0.737496i	0.929529	+	0.368748i	$0.120213\pi$
$911$			4.62755e14i			0.737496i	−0.929529	+	0.368748i	$0.879787\pi$
$912$	2.79020e11	−	1.43104e14i	0.000442243	−	0.226817i
$913$	2.17811e13			0.0343341
$914$	4.71010e11	−	9.66288e14i	0.000738413	−	1.51487i
$915$	8.93381e13	−	8.93381e13i	0.139294	−	0.139294i
$916$	−2.50672e14	+	2.50183e14i	−0.388712	+	0.387955i
$917$	5.39354e13	−	5.39354e13i	0.0831816	−	0.0831816i
$918$	1.14651e14	+	1.14763e14i	0.175859	+	0.176030i
$919$	2.66800e14			0.407014			0.203507	−	0.979074i	$-0.434766\pi$
$919$	2.66800e14			0.407014			0.203507	+	0.979074i	$0.434766\pi$
$920$	−1.63554e15	+	1.63077e15i	−2.48155	+	2.47430i
$921$			1.45618e13i			0.0219743i
$922$	−6.13900e14	−	6.14499e14i	−0.921389	−	0.922288i
$923$	6.03977e14	+	6.03977e14i	0.901596	+	0.901596i
$924$	−3.04950e13	−	2.97291e10i	−0.0452760	−	4.41390e-5i
$925$	−1.61188e14	−	1.61188e14i	−0.238025	−	0.238025i
$926$	−2.73947e11	+	5.62009e14i	−0.000402357	+	0.825445i
$927$		−	5.10351e14i		−	0.745539i
$928$	1.23883e14	+	1.24488e14i	0.180000	+	0.180879i
$929$	−1.81231e14			−0.261911			−0.130955	−	0.991388i	$-0.541804\pi$
$929$	−1.81231e14			−0.261911			−0.130955	+	0.991388i	$0.541804\pi$
$930$	−4.13877e14	−	2.01742e11i	−0.594917	−	0.000289988i
$931$	3.78891e14	−	3.78891e14i	0.541709	−	0.541709i
$932$	−7.22120e11	+	7.40722e14i	−0.00102690	+	1.05336i
$933$	−1.61934e14	+	1.61934e14i	−0.229049	+	0.229049i
$934$	4.47882e14	−	4.47445e14i	0.630128	−	0.629514i
$935$	−3.06445e14			−0.428839
$936$	−4.12976e14	+	4.11770e14i	−0.574838	+	0.573159i
$937$			1.08735e15i			1.50547i	0.658325	+	0.752733i	$0.271265\pi$
$937$			1.08735e15i			1.50547i	−0.658325	+	0.752733i	$0.728735\pi$
$938$	2.20215e14	−	2.20000e14i	0.303272	−	0.302976i
$939$	4.49087e13	+	4.49087e13i	0.0615181	+	0.0615181i
$940$	−1.15990e15	−	1.16217e15i	−1.58045	−	1.58354i
$941$	−5.35603e14	−	5.35603e14i	−0.725930	−	0.725930i	0.243876	−	0.969806i	$-0.421581\pi$
$941$	−5.35603e14	−	5.35603e14i	−0.725930	−	0.725930i	−0.969806	+	0.243876i	$0.921581\pi$
$942$	2.44218e14	+	1.19042e11i	0.329248	+	0.000160490i
$943$			8.49827e14i			1.13965i
$944$	4.29268e14	+	4.30945e14i	0.572623	+	0.574860i
$945$	−2.94321e14			−0.390537
$946$	2.13717e11	−	4.38444e14i	0.000282087	−	0.578707i
$947$	−9.44254e14	+	9.44254e14i	−1.23976	+	1.23976i	−0.279666	+	0.960097i	$0.590224\pi$
$947$	−9.44254e14	+	9.44254e14i	−1.23976	+	1.23976i	−0.960097	+	0.279666i	$0.909776\pi$
$948$	5.85216e12	+	5.86358e12i	0.00764319	+	0.00765810i
$949$	5.47817e14	−	5.47817e14i	0.711712	−	0.711712i
$950$	1.30755e15	+	1.30882e15i	1.68981	+	1.69146i
$951$	1.71890e14			0.220977
$952$	2.02330e14	+	2.95873e11i	0.258747	+	0.000378374i
$953$		−	3.22831e14i		−	0.410687i	−0.978690	−	0.205344i	$-0.934169\pi$
$953$		−	3.22831e14i		−	0.410687i	0.978690	−	0.205344i	$-0.0658312\pi$
$954$	−3.45516e14	−	3.45853e14i	−0.437246	−	0.437672i
$955$	1.01974e15	+	1.01974e15i	1.28373	+	1.28373i
$956$	2.25613e11	−	2.31425e14i	0.000282537	−	0.289815i
$957$	1.40117e13	+	1.40117e13i	0.0174555	+	0.0174555i
$958$	5.14369e10	−	1.05524e14i	6.37452e−5	−	0.130775i
$959$		−	9.17578e13i		−	0.113123i
$960$	1.02226e12	−	3.49530e14i	0.00125373	−	0.428675i
$961$	−7.58965e14			−0.925987
$962$	9.75871e13	+	4.75682e10i	0.118445	+	5.77353e-5i
$963$	−3.22374e14	+	3.22374e14i	−0.389250	+	0.389250i
$964$	8.17122e14	+	7.96601e11i	0.981526	+	0.000956876i
$965$	−5.89644e13	+	5.89644e13i	−0.0704617	+	0.0704617i
$966$	1.21722e14	−	1.21603e14i	0.144704	−	0.144563i
$967$	1.73464e14			0.205152			0.102576	−	0.994725i	$-0.467291\pi$
$967$	1.73464e14			0.205152			0.102576	+	0.994725i	$0.467291\pi$
$968$	1.02530e12	−	7.01141e14i	0.00120635	−	0.824951i
$969$			1.07128e14i			0.125396i
$970$	−5.30360e14	+	5.29844e14i	−0.617607	+	0.617005i
$971$	−9.78869e14	−	9.78869e14i	−1.13404	−	1.13404i	−0.989499	−	0.144542i	$-0.953829\pi$
$971$	−9.78869e14	−	9.78869e14i	−1.13404	−	1.13404i	−0.144542	−	0.989499i	$-0.546171\pi$
$972$	3.96014e14	−	3.95243e14i	0.456435	−	0.455546i
$973$	2.93600e14	+	2.93600e14i	0.336661	+	0.336661i
$974$	3.22104e14	+	1.57008e11i	0.367453	+	0.000179112i
$975$			4.25835e14i			0.483302i
$976$	2.87211e14	+	2.88334e14i	0.324304	+	0.325571i
$977$	1.62724e14			0.182801			0.0914004	−	0.995814i	$-0.470866\pi$
$977$	1.62724e14			0.182801			0.0914004	+	0.995814i	$0.470866\pi$
$978$	−1.17077e11	+	2.40186e14i	−0.000130851	+	0.268444i
$979$	5.55964e13	−	5.55964e13i	0.0618206	−	0.0618206i
$980$	9.26343e14	−	9.24539e14i	1.02481	−	1.02281i
$981$	−8.79286e14	+	8.79286e14i	−0.967799	+	0.967799i
$982$	−1.26482e15	−	1.26605e15i	−1.38506	−	1.38641i
$983$	−7.43439e14			−0.809986			−0.404993	−	0.914320i	$-0.632726\pi$
$983$	−7.43439e14			−0.809986			−0.404993	+	0.914320i	$0.632726\pi$
$984$	−9.08077e13	−	9.10737e13i	−0.0984345	−	0.0987228i
$985$			9.78531e14i			1.05534i
$986$	−9.29207e13	−	9.30113e13i	−0.0997075	−	0.0998047i
$987$	8.64914e13	+	8.64914e13i	0.0923394	+	0.0923394i
$988$	−7.92007e14	−	7.72117e11i	−0.841287	−	0.000820160i
$989$	1.74921e15	+	1.74921e15i	1.84867	+	1.84867i
$990$	−3.40350e11	+	6.98235e14i	−0.000357890	+	0.734219i
$991$		−	1.87870e15i		−	1.96558i	−0.184739	−	0.982788i	$-0.559144\pi$
$991$		−	1.87870e15i		−	1.96558i	0.184739	−	0.982788i	$-0.440856\pi$
$992$	3.24922e12	−	1.33316e15i	0.00338236	−	1.38780i
$993$	−1.82208e14			−0.188721
$994$	−6.75211e14	−	3.29127e11i	−0.695837	−	0.000339181i
$995$	−1.42074e15	+	1.42074e15i	−1.45680	+	1.45680i
$996$	1.81309e10	−	1.85980e13i	1.84979e−5	−	0.0189744i
$997$	1.72514e14	−	1.72514e14i	0.175125	−	0.175125i	−0.614102	−	0.789227i	$-0.710482\pi$
$997$	1.72514e14	−	1.72514e14i	0.175125	−	0.175125i	0.789227	+	0.614102i	$0.210482\pi$
$998$	−1.13039e14	+	1.12929e14i	−0.114176	+	0.114065i
$999$	−6.18501e13			−0.0621603

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.11.f.a.3.19	✓	38
4.3	odd	2		64.11.f.a.47.10		38
8.3	odd	2		128.11.f.a.95.10		38
8.5	even	2		128.11.f.b.95.10		38
16.3	odd	4		128.11.f.b.31.10		38
16.5	even	4		64.11.f.a.15.10		38
16.11	odd	4	inner	16.11.f.a.11.19	yes	38
16.13	even	4		128.11.f.a.31.10		38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.11.f.a.3.19	✓	38	1.1	even	1	trivial
16.11.f.a.11.19	yes	38	16.11	odd	4	inner
64.11.f.a.15.10		38	16.5	even	4
64.11.f.a.47.10		38	4.3	odd	2
128.11.f.a.31.10		38	16.13	even	4
128.11.f.a.95.10		38	8.3	odd	2
128.11.f.b.31.10		38	16.3	odd	4
128.11.f.b.95.10		38	8.5	even	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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(32.0000 + 0.0155982i) q^{2} +(-39.7294 + 39.7294i) q^{3} +(1024.00 + 0.998283i) q^{4} +(-4096.79 + 4096.79i) q^{5} +(-1271.96 + 1270.72i) q^{6} -7866.10 q^{7} +(32768.0 + 47.9176i) q^{8} +55892.1i q^{9} +O(q^{10})\)	\(q+(32.0000 + 0.0155982i) q^{2} +(-39.7294 + 39.7294i) q^{3} +(1024.00 + 0.998283i) q^{4} +(-4096.79 + 4096.79i) q^{5} +(-1271.96 + 1270.72i) q^{6} -7866.10 q^{7} +(32768.0 + 47.9176i) q^{8} +55892.1i q^{9} +(-131161. + 131033. i) q^{10} +(-47646.0 - 47646.0i) q^{11} +(-40722.6 + 40643.3i) q^{12} +(225159. + 225159. i) q^{13} +(-251715. - 122.697i) q^{14} -325526. i q^{15} +(1.04857e6 + 2044.48i) q^{16} -784967. q^{17} +(-871.816 + 1.78855e6i) q^{18} +(-1.71755e6 + 1.71755e6i) q^{19} +(-4.19920e6 + 4.19102e6i) q^{20} +(312516. - 312516. i) q^{21} +(-1.52393e6 - 1.52542e6i) q^{22} +1.21656e7 q^{23} +(-1.30376e6 + 1.29995e6i) q^{24} -2.38018e7i q^{25} +(7.20159e6 + 7.20861e6i) q^{26} +(-4.56655e6 - 4.56655e6i) q^{27} +(-8.05488e6 - 7852.59i) q^{28} +(3.70103e6 + 3.70103e6i) q^{29} +(5077.62 - 1.04168e7i) q^{30} -3.97315e7i q^{31} +(3.35543e7 + 81779.3i) q^{32} +3.78590e6 q^{33} +(-2.51189e7 - 12244.1i) q^{34} +(3.22258e7 - 3.22258e7i) q^{35} +(-55796.2 + 5.72335e7i) q^{36} +(6.77209e6 - 6.77209e6i) q^{37} +(-5.49884e7 + 5.49348e7i) q^{38} -1.78909e7 q^{39} +(-1.34440e8 + 1.34047e8i) q^{40} +6.98548e7i q^{41} +(1.00054e7 - 9.99562e6i) q^{42} +(1.43783e8 + 1.43783e8i) q^{43} +(-4.87420e7 - 4.88371e7i) q^{44} +(-2.28978e8 - 2.28978e8i) q^{45} +(3.89300e8 + 189761. i) q^{46} +2.76759e8i q^{47} +(-4.17405e7 + 4.15780e7i) q^{48} -2.20600e8 q^{49} +(371264. - 7.61657e8i) q^{50} +(3.11863e7 - 3.11863e7i) q^{51} +(2.30338e8 + 2.30788e8i) q^{52} +(-1.93276e8 + 1.93276e8i) q^{53} +(-1.46058e8 - 1.46201e8i) q^{54} +3.90392e8 q^{55} +(-2.57756e8 - 376924. i) q^{56} -1.36475e8i q^{57} +(1.18375e8 + 1.18491e8i) q^{58} +(4.10183e8 + 4.10183e8i) q^{59} +(324968. - 3.33339e8i) q^{60} +(2.74442e8 + 2.74442e8i) q^{61} +(619739. - 1.27141e9i) q^{62} -4.39653e8i q^{63} +(1.07374e9 + 3.14032e6i) q^{64} -1.84486e9 q^{65} +(1.21149e8 + 59053.2i) q^{66} +(-8.74431e8 + 8.74431e8i) q^{67} +(-8.03806e8 - 783620. i) q^{68} +(-4.83333e8 + 4.83333e8i) q^{69} +(1.03173e9 - 1.03072e9i) q^{70} +2.68244e9 q^{71} +(-2.67822e6 + 1.83147e9i) q^{72} -2.43302e9i q^{73} +(2.16812e8 - 2.16601e8i) q^{74} +(9.45631e8 + 9.45631e8i) q^{75} +(-1.76048e9 + 1.75706e9i) q^{76} +(3.74788e8 + 3.74788e8i) q^{77} +(-5.72509e8 - 279066. i) q^{78} -1.43988e8i q^{79} +(-4.30417e9 + 4.28741e9i) q^{80} -2.93752e9 q^{81} +(-1.08961e6 + 2.23535e9i) q^{82} +(-2.28572e8 + 2.28572e8i) q^{83} +(3.20328e8 - 3.19704e8i) q^{84} +(3.21585e9 - 3.21585e9i) q^{85} +(4.59881e9 + 4.60330e9i) q^{86} -2.94080e8 q^{87} +(-1.55898e9 - 1.56355e9i) q^{88} +1.16686e9i q^{89} +(-7.32374e9 - 7.33088e9i) q^{90} +(-1.77113e9 - 1.77113e9i) q^{91} +(1.24576e10 + 1.21447e7i) q^{92} +(1.57851e9 + 1.57851e9i) q^{93} +(-4.31693e6 + 8.85628e9i) q^{94} -1.40729e10i q^{95} +(-1.33634e9 + 1.32985e9i) q^{96} +4.04358e9 q^{97} +(-7.05919e9 - 3.44095e6i) q^{98} +(2.66304e9 - 2.66304e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 2 q^{2} - 2 q^{3} - 1256 q^{4} - 2 q^{5} - 17216 q^{6} - 4 q^{7} + 69124 q^{8}+O(q^{10}) \) 38 * q - 2 * q^2 - 2 * q^3 - 1256 * q^4 - 2 * q^5 - 17216 * q^6 - 4 * q^7 + 69124 * q^8	\( 38 q - 2 q^{2} - 2 q^{3} - 1256 q^{4} - 2 q^{5} - 17216 q^{6} - 4 q^{7} + 69124 q^{8} - 147364 q^{10} - 45906 q^{11} - 10988 q^{12} - 2 q^{13} + 757836 q^{14} - 469032 q^{16} - 4 q^{17} + 2066926 q^{18} - 5107042 q^{19} + 5301516 q^{20} - 118100 q^{21} - 20568924 q^{22} - 8279748 q^{23} + 58519728 q^{24} - 18451512 q^{26} - 25871552 q^{27} - 36459784 q^{28} - 29652306 q^{29} + 132781252 q^{30} - 52661752 q^{32} - 4 q^{33} + 68474900 q^{34} + 14674460 q^{35} - 15810676 q^{36} - 94618130 q^{37} + 156046000 q^{38} - 279841732 q^{39} - 125381720 q^{40} + 107395416 q^{42} + 172486862 q^{43} + 73663988 q^{44} + 19649346 q^{45} - 437620836 q^{46} + 625190376 q^{48} + 1049193778 q^{49} - 875760314 q^{50} - 72924900 q^{51} - 771392444 q^{52} + 607072398 q^{53} + 913650464 q^{54} - 1427102468 q^{55} - 1385623464 q^{56} + 37561720 q^{58} + 1543683854 q^{59} + 318869600 q^{60} + 1673280158 q^{61} - 983062992 q^{62} - 867678656 q^{64} + 1098715212 q^{65} + 768197860 q^{66} - 4830427746 q^{67} - 855827792 q^{68} + 1698121420 q^{69} - 5103882496 q^{70} + 7572888316 q^{71} + 6888513460 q^{72} + 2513658844 q^{74} - 11656678318 q^{75} - 2250244316 q^{76} - 1336459028 q^{77} + 14243324268 q^{78} - 13115458328 q^{80} - 8523250762 q^{81} + 2724305648 q^{82} + 16141605438 q^{83} - 1633924184 q^{84} + 4779968748 q^{85} - 4025865500 q^{86} - 31832612676 q^{87} + 1023457912 q^{88} + 18960485240 q^{90} + 19874217404 q^{91} + 28060187160 q^{92} - 15001617056 q^{93} - 14829002256 q^{94} + 23525947312 q^{96} - 4 q^{97} - 43134832310 q^{98} - 25616384098 q^{99}+O(q^{100}) \) 38 * q - 2 * q^2 - 2 * q^3 - 1256 * q^4 - 2 * q^5 - 17216 * q^6 - 4 * q^7 + 69124 * q^8 - 147364 * q^10 - 45906 * q^11 - 10988 * q^12 - 2 * q^13 + 757836 * q^14 - 469032 * q^16 - 4 * q^17 + 2066926 * q^18 - 5107042 * q^19 + 5301516 * q^20 - 118100 * q^21 - 20568924 * q^22 - 8279748 * q^23 + 58519728 * q^24 - 18451512 * q^26 - 25871552 * q^27 - 36459784 * q^28 - 29652306 * q^29 + 132781252 * q^30 - 52661752 * q^32 - 4 * q^33 + 68474900 * q^34 + 14674460 * q^35 - 15810676 * q^36 - 94618130 * q^37 + 156046000 * q^38 - 279841732 * q^39 - 125381720 * q^40 + 107395416 * q^42 + 172486862 * q^43 + 73663988 * q^44 + 19649346 * q^45 - 437620836 * q^46 + 625190376 * q^48 + 1049193778 * q^49 - 875760314 * q^50 - 72924900 * q^51 - 771392444 * q^52 + 607072398 * q^53 + 913650464 * q^54 - 1427102468 * q^55 - 1385623464 * q^56 + 37561720 * q^58 + 1543683854 * q^59 + 318869600 * q^60 + 1673280158 * q^61 - 983062992 * q^62 - 867678656 * q^64 + 1098715212 * q^65 + 768197860 * q^66 - 4830427746 * q^67 - 855827792 * q^68 + 1698121420 * q^69 - 5103882496 * q^70 + 7572888316 * q^71 + 6888513460 * q^72 + 2513658844 * q^74 - 11656678318 * q^75 - 2250244316 * q^76 - 1336459028 * q^77 + 14243324268 * q^78 - 13115458328 * q^80 - 8523250762 * q^81 + 2724305648 * q^82 + 16141605438 * q^83 - 1633924184 * q^84 + 4779968748 * q^85 - 4025865500 * q^86 - 31832612676 * q^87 + 1023457912 * q^88 + 18960485240 * q^90 + 19874217404 * q^91 + 28060187160 * q^92 - 15001617056 * q^93 - 14829002256 * q^94 + 23525947312 * q^96 - 4 * q^97 - 43134832310 * q^98 - 25616384098 * q^99

Introduction

L-functions

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