LMFDB - Embedded newform 12.16.b.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,16,Mod(11,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	12.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:	$17.1232206120$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	12.11
Dual form			12.16.b.a.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-171.504 + 57.9158i) q^{2} +(-3751.22 + 526.541i) q^{3} +(26059.5 - 19865.6i) q^{4} -172529. i q^{5} +(612856. - 307559. i) q^{6} +3.89480e6i q^{7} +(-3.31879e6 + 4.91630e6i) q^{8} +(1.37944e7 - 3.95035e6i) q^{9} +O(q^{10})$	\(q+(-171.504 + 57.9158i) q^{2} +(-3751.22 + 526.541i) q^{3} +(26059.5 - 19865.6i) q^{4} -172529. i q^{5} +(612856. - 307559. i) q^{6} +3.89480e6i q^{7} +(-3.31879e6 + 4.91630e6i) q^{8} +(1.37944e7 - 3.95035e6i) q^{9} +(9.99218e6 + 2.95896e7i) q^{10} +4.37602e7 q^{11} +(-8.72949e7 + 8.82418e7i) q^{12} -4.08923e7 q^{13} +(-2.25570e8 - 6.67975e8i) q^{14} +(9.08439e7 + 6.47196e8i) q^{15} +(2.84455e8 - 1.03538e9i) q^{16} +1.05000e9i q^{17} +(-2.13702e9 + 1.47642e9i) q^{18} -4.29470e9i q^{19} +(-3.42741e9 - 4.49603e9i) q^{20} +(-2.05077e9 - 1.46103e10i) q^{21} +(-7.50507e9 + 2.53441e9i) q^{22} -2.27826e10 q^{23} +(9.86087e9 - 2.01896e10i) q^{24} +7.51168e8 q^{25} +(7.01322e9 - 2.36831e9i) q^{26} +(-4.96659e10 + 2.20819e10i) q^{27} +(7.73726e10 + 1.01497e11i) q^{28} -1.81630e10i q^{29} +(-5.30630e10 - 1.05736e11i) q^{30} -1.17167e11i q^{31} +(1.11794e10 + 1.94046e11i) q^{32} +(-1.64154e11 + 2.30416e10i) q^{33} +(-6.08114e10 - 1.80079e11i) q^{34} +6.71968e11 q^{35} +(2.81000e11 - 3.76979e11i) q^{36} -1.02702e12 q^{37} +(2.48731e11 + 7.36559e11i) q^{38} +(1.53396e11 - 2.15315e10i) q^{39} +(8.48207e11 + 5.72589e11i) q^{40} +1.37636e12i q^{41} +(1.19788e12 + 2.38695e12i) q^{42} -7.55931e11i q^{43} +(1.14037e12 - 8.69324e11i) q^{44} +(-6.81551e11 - 2.37994e12i) q^{45} +(3.90731e12 - 1.31947e12i) q^{46} -2.91641e12 q^{47} +(-5.21886e11 + 4.03371e12i) q^{48} -1.04219e13 q^{49} +(-1.28829e11 + 4.35045e10i) q^{50} +(-5.52866e11 - 3.93877e12i) q^{51} +(-1.06563e12 + 8.12352e11i) q^{52} -1.31652e13i q^{53} +(7.23902e12 - 6.66359e12i) q^{54} -7.54993e12i q^{55} +(-1.91480e13 - 1.29260e13i) q^{56} +(2.26133e12 + 1.61104e13i) q^{57} +(1.05193e12 + 3.11504e12i) q^{58} -1.15444e12 q^{59} +(1.52243e13 + 1.50609e13i) q^{60} -1.08094e13 q^{61} +(6.78581e12 + 2.00946e13i) q^{62} +(1.53858e13 + 5.37265e13i) q^{63} +(-1.31557e13 - 3.26323e13i) q^{64} +7.05513e12i q^{65} +(2.68187e13 - 1.34589e13i) q^{66} -5.22313e13i q^{67} +(2.08588e13 + 2.73624e13i) q^{68} +(8.54625e13 - 1.19960e13i) q^{69} +(-1.15245e14 + 3.89175e13i) q^{70} +2.62413e12 q^{71} +(-2.63597e13 + 8.09279e13i) q^{72} +3.29769e13 q^{73} +(1.76139e14 - 5.94810e13i) q^{74} +(-2.81780e12 + 3.95521e11i) q^{75} +(-8.53168e13 - 1.11918e14i) q^{76} +1.70437e14i q^{77} +(-2.50611e13 + 1.25768e13i) q^{78} +1.56201e14i q^{79} +(-1.78633e14 - 4.90769e13i) q^{80} +(1.74681e14 - 1.08985e14i) q^{81} +(-7.97132e13 - 2.36053e14i) q^{82} -3.43200e13 q^{83} +(-3.43684e14 - 3.39996e14i) q^{84} +1.81155e14 q^{85} +(4.37804e13 + 1.29645e14i) q^{86} +(9.56359e12 + 6.81336e13i) q^{87} +(-1.45231e14 + 2.15138e14i) q^{88} -5.29425e14i q^{89} +(2.54725e14 + 3.68698e14i) q^{90} -1.59268e14i q^{91} +(-5.93703e14 + 4.52590e14i) q^{92} +(6.16932e13 + 4.39519e14i) q^{93} +(5.00177e14 - 1.68906e14i) q^{94} -7.40962e14 q^{95} +(-1.44110e14 - 7.22024e14i) q^{96} -9.09865e14 q^{97} +(1.78740e15 - 6.03593e14i) q^{98} +(6.03647e14 - 1.72868e14i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 26968 q^{4} + 823656 q^{6} - 3812052 q^{9}+O(q^{10}) $ 28 * q + 26968 * q^4 + 823656 * q^6 - 3812052 * q^9	\( 28 q + 26968 q^{4} + 823656 q^{6} - 3812052 q^{9} - 43831600 q^{10} - 226414248 q^{12} + 124527272 q^{13} - 1459325408 q^{16} - 4234777584 q^{18} - 7261350648 q^{21} - 2533670160 q^{22} - 18487781856 q^{24} - 146804950740 q^{25} + 5481093840 q^{28} + 8237058960 q^{30} + 204574669728 q^{33} + 450165745472 q^{34} + 232631927160 q^{36} + 386069193224 q^{37} + 1945471012160 q^{40} + 1938106219632 q^{42} - 5007113912640 q^{45} + 2270790222432 q^{46} + 5846474725152 q^{48} - 18480860963084 q^{49} - 6113229405424 q^{52} + 1626598700568 q^{54} + 8085872464056 q^{57} - 19395437098192 q^{58} - 10924219377600 q^{60} - 16392792556696 q^{61} + 21633892829056 q^{64} + 4928819126448 q^{66} + 137029869973056 q^{69} + 91772543171040 q^{70} + 66924493142592 q^{72} + 158451626683736 q^{73} - 205265768291280 q^{76} + 58364283489648 q^{78} + 116126816635836 q^{81} - 750029796726880 q^{82} - 92605433207856 q^{84} - 30099357052160 q^{85} - 619691835246912 q^{88} - 471443548913520 q^{90} - 777661615138584 q^{93} + 13\!\cdots\!00 q^{94}+ \cdots - 824166397720648 q^{97}+O(q^{100}) \) 28 * q + 26968 * q^4 + 823656 * q^6 - 3812052 * q^9 - 43831600 * q^10 - 226414248 * q^12 + 124527272 * q^13 - 1459325408 * q^16 - 4234777584 * q^18 - 7261350648 * q^21 - 2533670160 * q^22 - 18487781856 * q^24 - 146804950740 * q^25 + 5481093840 * q^28 + 8237058960 * q^30 + 204574669728 * q^33 + 450165745472 * q^34 + 232631927160 * q^36 + 386069193224 * q^37 + 1945471012160 * q^40 + 1938106219632 * q^42 - 5007113912640 * q^45 + 2270790222432 * q^46 + 5846474725152 * q^48 - 18480860963084 * q^49 - 6113229405424 * q^52 + 1626598700568 * q^54 + 8085872464056 * q^57 - 19395437098192 * q^58 - 10924219377600 * q^60 - 16392792556696 * q^61 + 21633892829056 * q^64 + 4928819126448 * q^66 + 137029869973056 * q^69 + 91772543171040 * q^70 + 66924493142592 * q^72 + 158451626683736 * q^73 - 205265768291280 * q^76 + 58364283489648 * q^78 + 116126816635836 * q^81 - 750029796726880 * q^82 - 92605433207856 * q^84 - 30099357052160 * q^85 - 619691835246912 * q^88 - 471443548913520 * q^90 - 777661615138584 * q^93 + 1301107064491200 * q^94 + 525428335287168 * q^96 - 824166397720648 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−171.504	+	57.9158i	−0.947437	+	0.319943i
$2$	−171.504	+	57.9158i	−0.947437	+	0.319943i
$3$	−3751.22	+	526.541i	−0.990292	+	0.139003i
$3$	−3751.22	+	526.541i	−0.990292	+	0.139003i
$4$	26059.5	−	19865.6i	0.795273	−	0.606251i
$5$		−	172529.i		−	0.987616i	−0.869571	−	0.493808i	$-0.835605\pi$
$5$		−	172529.i		−	0.987616i	0.869571	−	0.493808i	$-0.164395\pi$
$6$	612856.	−	307559.i	0.893766	−	0.448533i
$7$			3.89480e6i			1.78752i	0.448550	+	0.893758i	$0.351941\pi$
$7$			3.89480e6i			1.78752i	−0.448550	+	0.893758i	$0.648059\pi$
$8$	−3.31879e6	+	4.91630e6i	−0.559506	+	0.828826i
$9$	1.37944e7	−	3.95035e6i	0.961357	−	0.275306i
$10$	9.99218e6	+	2.95896e7i	0.315981	+	0.935704i
$11$	4.37602e7			0.677071			0.338536	−	0.940954i	$-0.390068\pi$
$11$	4.37602e7			0.677071			0.338536	+	0.940954i	$0.390068\pi$
$12$	−8.72949e7	+	8.82418e7i	−0.703282	+	0.710911i
$13$	−4.08923e7			−0.180745			−0.0903726	−	0.995908i	$-0.528806\pi$
$13$	−4.08923e7			−0.180745			−0.0903726	+	0.995908i	$0.528806\pi$
$14$	−2.25570e8	−	6.67975e8i	−0.571902	−	1.69356i
$15$	9.08439e7	+	6.47196e8i	0.137281	+	0.978028i
$16$	2.84455e8	−	1.03538e9i	0.264920	−	0.964271i
$17$			1.05000e9i			0.620613i	0.950637	+	0.310307i	$0.100432\pi$
$17$			1.05000e9i			0.620613i	−0.950637	+	0.310307i	$0.899568\pi$
$18$	−2.13702e9	+	1.47642e9i	−0.822742	+	0.568414i
$19$		−	4.29470e9i		−	1.10225i	−0.834422	−	0.551125i	$-0.814199\pi$
$19$		−	4.29470e9i		−	1.10225i	0.834422	−	0.551125i	$-0.185801\pi$
$20$	−3.42741e9	−	4.49603e9i	−0.598743	−	0.785425i
$21$	−2.05077e9	−	1.46103e10i	−0.248469	−	1.77016i
$22$	−7.50507e9	+	2.53441e9i	−0.641482	+	0.216624i
$23$	−2.27826e10			−1.39522			−0.697612	−	0.716475i	$-0.745754\pi$
$23$	−2.27826e10			−1.39522			−0.697612	+	0.716475i	$0.745754\pi$
$24$	9.86087e9	−	2.01896e10i	0.438865	−	0.898553i
$25$	7.51168e8			0.0246143
$26$	7.01322e9	−	2.36831e9i	0.171245	−	0.0578281i
$27$	−4.96659e10	+	2.20819e10i	−0.913755	+	0.406265i
$28$	7.73726e10	+	1.01497e11i	1.08368	+	1.42156i
$29$		−	1.81630e10i		−	0.195526i	−0.995210	−	0.0977628i	$-0.968831\pi$
$29$		−	1.81630e10i		−	0.195526i	0.995210	−	0.0977628i	$-0.0311686\pi$
$30$	−5.30630e10	−	1.05736e11i	−0.442978	−	0.882698i
$31$		−	1.17167e11i		−	0.764878i	−0.923981	−	0.382439i	$-0.875084\pi$
$31$		−	1.17167e11i		−	0.764878i	0.923981	−	0.382439i	$-0.124916\pi$
$32$	1.11794e10	+	1.94046e11i	0.0575167	+	0.998345i
$33$	−1.64154e11	+	2.30416e10i	−0.670498	+	0.0941147i
$34$	−6.08114e10	−	1.80079e11i	−0.198561	−	0.587992i
$35$	6.71968e11			1.76538
$36$	2.81000e11	−	3.76979e11i	0.597637	−	0.801767i
$37$	−1.02702e12			−1.77856			−0.889279	−	0.457366i	$-0.848793\pi$
$37$	−1.02702e12			−1.77856			−0.889279	+	0.457366i	$0.848793\pi$
$38$	2.48731e11	+	7.36559e11i	0.352657	+	1.04431i
$39$	1.53396e11	−	2.15315e10i	0.178991	−	0.0251241i
$40$	8.48207e11	+	5.72589e11i	0.818562	+	0.552577i
$41$			1.37636e12i			1.10371i	0.833940	+	0.551854i	$0.186080\pi$
$41$			1.37636e12i			1.10371i	−0.833940	+	0.551854i	$0.813920\pi$
$42$	1.19788e12	+	2.38695e12i	0.801759	+	1.59762i
$43$		−	7.55931e11i		−	0.424100i	−0.977259	−	0.212050i	$-0.931986\pi$
$43$		−	7.55931e11i		−	0.424100i	0.977259	−	0.212050i	$-0.0680140\pi$
$44$	1.14037e12	−	8.69324e11i	0.538457	−	0.410475i
$45$	−6.81551e11	−	2.37994e12i	−0.271897	−	0.949451i
$46$	3.90731e12	−	1.31947e12i	1.32189	−	0.446392i
$47$	−2.91641e12			−0.839681			−0.419840	−	0.907598i	$-0.637914\pi$
$47$	−2.91641e12			−0.839681			−0.419840	+	0.907598i	$0.637914\pi$
$48$	−5.21886e11	+	4.03371e12i	−0.128312	+	0.991734i
$49$	−1.04219e13			−2.19521
$50$	−1.28829e11	+	4.35045e10i	−0.0233205	+	0.00787516i
$51$	−5.52866e11	−	3.93877e12i	−0.0862668	−	0.614588i
$52$	−1.06563e12	+	8.12352e11i	−0.143742	+	0.109577i
$53$		−	1.31652e13i		−	1.53942i	−0.638394	−	0.769710i	$-0.720401\pi$
$53$		−	1.31652e13i		−	1.53942i	0.638394	−	0.769710i	$-0.279599\pi$
$54$	7.23902e12	−	6.66359e12i	0.735744	−	0.677260i
$55$		−	7.54993e12i		−	0.668687i
$56$	−1.91480e13	−	1.29260e13i	−1.48154	−	1.00013i
$57$	2.26133e12	+	1.61104e13i	0.153216	+	1.09155i
$58$	1.05193e12	+	3.11504e12i	0.0625570	+	0.185248i
$59$	−1.15444e12			−0.0603922			−0.0301961	−	0.999544i	$-0.509613\pi$
$59$	−1.15444e12			−0.0603922			−0.0301961	+	0.999544i	$0.509613\pi$
$60$	1.52243e13	+	1.50609e13i	0.702107	+	0.694573i
$61$	−1.08094e13			−0.440380			−0.220190	−	0.975457i	$-0.570668\pi$
$61$	−1.08094e13			−0.440380			−0.220190	+	0.975457i	$0.570668\pi$
$62$	6.78581e12	+	2.00946e13i	0.244717	+	0.724673i
$63$	1.53858e13	+	5.37265e13i	0.492114	+	1.71844i
$64$	−1.31557e13	−	3.26323e13i	−0.373906	−	0.927466i
$65$			7.05513e12i			0.178507i
$66$	2.68187e13	−	1.34589e13i	0.605143	−	0.303689i
$67$		−	5.22313e13i		−	1.05286i	−0.850219	−	0.526429i	$-0.823531\pi$
$67$		−	5.22313e13i		−	1.05286i	0.850219	−	0.526429i	$-0.176469\pi$
$68$	2.08588e13	+	2.73624e13i	0.376247	+	0.493557i
$69$	8.54625e13	−	1.19960e13i	1.38168	−	0.193940i
$70$	−1.15245e14	+	3.89175e13i	−1.67259	+	0.564820i
$71$	2.62413e12			0.0342411			0.0171206	−	0.999853i	$-0.494550\pi$
$71$	2.62413e12			0.0342411			0.0171206	+	0.999853i	$0.494550\pi$
$72$	−2.63597e13	+	8.09279e13i	−0.309703	+	0.950833i
$73$	3.29769e13			0.349372			0.174686	−	0.984624i	$-0.444109\pi$
$73$	3.29769e13			0.349372			0.174686	+	0.984624i	$0.444109\pi$
$74$	1.76139e14	−	5.94810e13i	1.68507	−	0.569036i
$75$	−2.81780e12	+	3.95521e11i	−0.0243753	+	0.00342145i
$76$	−8.53168e13	−	1.11918e14i	−0.668241	−	0.876591i
$77$			1.70437e14i			1.21028i
$78$	−2.50611e13	+	1.25768e13i	−0.161544	+	0.0810702i
$79$			1.56201e14i			0.915123i	0.889178	+	0.457562i	$0.151277\pi$
$79$			1.56201e14i			0.915123i	−0.889178	+	0.457562i	$0.848723\pi$
$80$	−1.78633e14	−	4.90769e13i	−0.952329	−	0.261639i
$81$	1.74681e14	−	1.08985e14i	0.848413	−	0.529335i
$82$	−7.97132e13	−	2.36053e14i	−0.353124	−	1.04569i
$83$	−3.43200e13			−0.138823			−0.0694115	−	0.997588i	$-0.522112\pi$
$83$	−3.43200e13			−0.138823			−0.0694115	+	0.997588i	$0.522112\pi$
$84$	−3.43684e14	−	3.39996e14i	−1.27076	−	1.25713i
$85$	1.81155e14			0.612927
$86$	4.37804e13	+	1.29645e14i	0.135688	+	0.401808i
$87$	9.56359e12	+	6.81336e13i	0.0271786	+	0.193627i
$88$	−1.45231e14	+	2.15138e14i	−0.378825	+	0.561175i
$89$		−	5.29425e14i		−	1.26876i	−0.773022	−	0.634379i	$-0.781256\pi$
$89$		−	5.29425e14i		−	1.26876i	0.773022	−	0.634379i	$-0.218744\pi$
$90$	2.54725e14	+	3.68698e14i	0.561375	+	0.812554i
$91$		−	1.59268e14i		−	0.323085i
$92$	−5.93703e14	+	4.52590e14i	−1.10959	+	0.845856i
$93$	6.16932e13	+	4.39519e14i	0.106320	+	0.757452i
$94$	5.00177e14	−	1.68906e14i	0.795545	−	0.268650i
$95$	−7.40962e14			−1.08860
$96$	−1.44110e14	−	7.22024e14i	−0.195731	−	0.980658i
$97$	−9.09865e14			−1.14338			−0.571688	−	0.820471i	$-0.693711\pi$
$97$	−9.09865e14			−1.14338			−0.571688	+	0.820471i	$0.693711\pi$
$98$	1.78740e15	−	6.03593e14i	2.07982	−	0.702342i
$99$	6.03647e14	−	1.72868e14i	0.650907	−	0.186402i
$100$	1.95751e13	−	1.49224e13i	0.0195751	−	0.0149224i
$101$		−	6.24144e13i		−	0.0579261i	−0.999580	−	0.0289630i	$-0.990779\pi$
$101$		−	6.24144e13i		−	0.0579261i	0.999580	−	0.0289630i	$-0.00922051\pi$
$102$	3.22936e14	+	6.43496e14i	0.278365	+	0.554683i
$103$		−	9.11953e14i		−	0.730623i	−0.930885	−	0.365311i	$-0.880962\pi$
$103$		−	9.11953e14i		−	0.730623i	0.930885	−	0.365311i	$-0.119038\pi$
$104$	1.35713e14	−	2.01039e14i	0.101128	−	0.149806i
$105$	−2.52070e15	+	3.53819e14i	−1.74824	+	0.245392i
$106$	7.62470e14	+	2.25788e15i	0.492526	+	1.45850i
$107$	−8.41506e13			−0.0506616			−0.0253308	−	0.999679i	$-0.508064\pi$
$107$	−8.41506e13			−0.0506616			−0.0253308	+	0.999679i	$0.508064\pi$
$108$	−8.55597e14	+	1.56209e15i	−0.480387	+	0.877057i
$109$	8.51236e14			0.446017			0.223009	−	0.974816i	$-0.428412\pi$
$109$	8.51236e14			0.446017			0.223009	+	0.974816i	$0.428412\pi$
$110$	4.37260e14	+	1.29485e15i	0.213941	+	0.633538i
$111$	3.85260e15	−	5.40771e14i	1.76129	−	0.247224i
$112$	4.03259e15	+	1.10790e15i	1.72365	+	0.473548i
$113$			2.64592e14i			0.105801i	0.998600	+	0.0529003i	$0.0168465\pi$
$113$			2.64592e14i			0.105801i	−0.998600	+	0.0529003i	$0.983153\pi$
$114$	−1.32087e15	−	2.63203e15i	−0.494396	−	0.985155i
$115$			3.93067e15i			1.37795i
$116$	−3.60820e14	−	4.73320e14i	−0.118538	−	0.155496i
$117$	−5.64086e14	+	1.61539e14i	−0.173761	+	0.0497603i
$118$	1.97991e14	−	6.68603e13i	0.0572178	−	0.0193220i
$119$	−4.08953e15			−1.10936
$120$	−3.48330e15	−	1.70129e15i	−0.887425	−	0.433430i
$121$	−2.26229e15			−0.541575
$122$	1.85386e15	−	6.26035e14i	0.417232	−	0.140896i
$123$	−7.24713e14	−	5.16305e15i	−0.153418	−	1.09299i
$124$	−2.32759e15	−	3.05331e15i	−0.463708	−	0.608287i
$125$		−	5.39478e15i		−	1.01193i
$126$	−5.75035e15	−	8.32325e15i	−1.01605	−	1.47066i
$127$		−	4.68687e15i		−	0.780468i	−0.920716	−	0.390234i	$-0.872394\pi$
$127$		−	4.68687e15i		−	0.780468i	0.920716	−	0.390234i	$-0.127606\pi$
$128$	4.14618e15	+	4.83467e15i	0.650989	+	0.759087i
$129$	3.98029e14	+	2.83566e15i	0.0589511	+	0.419983i
$130$	−4.08604e14	−	1.20999e15i	−0.0571120	−	0.169124i
$131$	−9.77222e15			−1.28961			−0.644806	−	0.764347i	$-0.723062\pi$
$131$	−9.77222e15			−1.28961			−0.644806	+	0.764347i	$0.723062\pi$
$132$	−3.82005e15	+	3.86148e15i	−0.476172	+	0.481337i
$133$	1.67270e16			1.97029
$134$	3.02502e15	+	8.95789e15i	0.336854	+	0.997516i
$135$	3.80979e15	+	8.56883e15i	0.401234	+	0.902440i
$136$	−5.16210e15	−	3.48472e15i	−0.514380	−	0.347237i
$137$		−	1.18160e15i		−	0.111446i	−0.998446	−	0.0557230i	$-0.982254\pi$
$137$		−	1.18160e15i		−	0.111446i	0.998446	−	0.0557230i	$-0.0177464\pi$
$138$	−1.39624e16	+	7.00699e15i	−1.24701	+	0.625804i
$139$			1.84056e16i			1.55718i	0.627534	+	0.778589i	$0.284064\pi$
$139$			1.84056e16i			1.55718i	−0.627534	+	0.778589i	$0.715936\pi$
$140$	1.75112e16	−	1.33491e16i	1.40396	−	1.07026i
$141$	1.09401e16	−	1.53561e15i	0.831529	−	0.116718i
$142$	−4.50050e14	+	1.51979e14i	−0.0324413	+	0.0109552i
$143$	−1.78946e15			−0.122377
$144$	−1.66205e14	−	1.54061e16i	−0.0107876	−	0.999942i
$145$	−3.13366e15			−0.193104
$146$	−5.65569e15	+	1.90989e15i	−0.331008	+	0.111779i
$147$	3.90949e16	−	5.48756e15i	2.17390	−	0.305140i
$148$	−2.67638e16	+	2.04025e16i	−1.41444	+	1.07825i
$149$			3.19014e16i			1.60292i	0.598048	+	0.801461i	$0.295943\pi$
$149$			3.19014e16i			1.60292i	−0.598048	+	0.801461i	$0.704057\pi$
$150$	4.60358e14	−	2.31029e14i	0.0219994	−	0.0110403i
$151$		−	2.92312e16i		−	1.32898i	−0.747295	−	0.664492i	$-0.768648\pi$
$151$		−	2.92312e16i		−	1.32898i	0.747295	−	0.664492i	$-0.231352\pi$
$152$	2.11140e16	+	1.42532e16i	0.913575	+	0.616716i
$153$	4.14785e15	+	1.44841e16i	0.170859	+	0.596630i
$154$	−9.87101e15	−	2.92307e16i	−0.387219	−	1.14666i
$155$	−2.02147e16			−0.755406
$156$	3.56970e15	−	3.60841e15i	0.127115	−	0.128494i
$157$	−1.98904e16			−0.675142			−0.337571	−	0.941300i	$-0.609605\pi$
$157$	−1.98904e16			−0.675142			−0.337571	+	0.941300i	$0.609605\pi$
$158$	−9.04649e15	−	2.67891e16i	−0.292787	−	0.867022i
$159$	6.93200e15	+	4.93854e16i	0.213983	+	1.52447i
$160$	3.34787e16	−	1.92878e15i	0.985981	−	0.0568044i
$161$		−	8.87336e16i		−	2.49399i
$162$	−2.36465e16	+	2.88082e16i	−0.634461	+	0.772955i
$163$		−	2.36220e16i		−	0.605215i	−0.953115	−	0.302607i	$-0.902143\pi$
$163$		−	2.36220e16i		−	0.605215i	0.953115	−	0.302607i	$-0.0978571\pi$
$164$	2.73423e16	+	3.58674e16i	0.669124	+	0.877750i
$165$	3.97535e15	+	2.83214e16i	0.0929492	+	0.662195i
$166$	5.88603e15	−	1.98767e15i	0.131526	−	0.0444154i
$167$	−6.41482e16			−1.37028			−0.685142	−	0.728409i	$-0.740260\pi$
$167$	−6.41482e16			−1.37028			−0.685142	+	0.728409i	$0.740260\pi$
$168$	7.86345e16	+	3.84061e16i	1.60618	+	0.784478i
$169$	−4.95137e16			−0.967331
$170$	−3.10689e16	+	1.04918e16i	−0.580710	+	0.196102i
$171$	−1.69655e16	−	5.92428e16i	−0.303457	−	1.05966i
$172$	−1.50170e16	−	1.96992e16i	−0.257111	−	0.337276i
$173$		−	3.42992e16i		−	0.562261i	−0.959670	−	0.281130i	$-0.909291\pi$
$173$		−	3.42992e16i		−	0.562261i	0.959670	−	0.281130i	$-0.0907093\pi$
$174$	−5.58621e15	−	1.11313e16i	−0.0876996	−	0.174754i
$175$			2.92565e15i			0.0439984i
$176$	1.24478e16	−	4.53084e16i	0.179369	−	0.652880i
$177$	4.33056e15	−	6.07860e14i	0.0598059	−	0.00839468i
$178$	3.06621e16	+	9.07986e16i	0.405930	+	1.20207i
$179$	2.01998e16			0.256418			0.128209	−	0.991747i	$-0.459077\pi$
$179$	2.01998e16			0.256418			0.128209	+	0.991747i	$0.459077\pi$
$180$	−6.50400e16	−	4.84807e16i	−0.791838	−	0.590236i
$181$	−1.14051e17			−1.33202			−0.666010	−	0.745943i	$-0.731999\pi$
$181$	−1.14051e17			−1.33202			−0.666010	+	0.745943i	$0.731999\pi$
$182$	9.22411e15	+	2.73151e16i	0.103369	+	0.306103i
$183$	4.05484e16	−	5.69159e15i	0.436105	−	0.0612140i
$184$	7.56106e16	−	1.12006e17i	0.780637	−	1.15640i
$185$			1.77192e17i			1.75653i
$186$	−3.60357e16	−	7.18064e16i	−0.343073	−	0.683622i
$187$			4.59481e16i			0.420199i
$188$	−7.60002e16	+	5.79363e16i	−0.667776	+	0.509057i
$189$	−8.60048e16	−	1.93439e17i	−0.726205	−	1.63335i
$190$	1.27078e17	−	4.29134e16i	1.03138	−	0.348290i
$191$	1.46993e17			1.14695			0.573477	−	0.819221i	$-0.305594\pi$
$191$	1.46993e17			1.14695			0.573477	+	0.819221i	$0.305594\pi$
$192$	6.65321e16	+	1.15484e17i	0.499197	+	0.866489i
$193$	1.78931e17			1.29124			0.645619	−	0.763659i	$-0.276599\pi$
$193$	1.78931e17			1.29124			0.645619	+	0.763659i	$0.276599\pi$
$194$	1.56046e17	−	5.26955e16i	1.08328	−	0.365815i
$195$	−3.71482e15	−	2.64654e16i	−0.0248129	−	0.176774i
$196$	−2.71590e17	+	2.07038e17i	−1.74579	+	1.33085i
$197$			6.92882e16i			0.428709i	0.976756	+	0.214355i	$0.0687648\pi$
$197$			6.92882e16i			0.428709i	−0.976756	+	0.214355i	$0.931235\pi$
$198$	−9.35163e16	+	6.46083e16i	−0.557055	+	0.384857i
$199$		−	1.94429e16i		−	0.111523i	−0.998444	−	0.0557613i	$-0.982241\pi$
$199$		−	1.94429e16i		−	0.111523i	0.998444	−	0.0557613i	$-0.0177586\pi$
$200$	−2.49297e15	+	3.69297e15i	−0.0137718	+	0.0204010i
$201$	2.75019e16	+	1.95931e17i	0.146350	+	1.04264i
$202$	3.61478e15	+	1.07043e16i	0.0185330	+	0.0548813i
$203$	7.07414e16			0.349505
$204$	−9.26536e16	−	9.16594e16i	−0.441200	−	0.436466i
$205$	2.37463e17			1.09004
$206$	5.28165e16	+	1.56404e17i	0.233757	+	0.692219i
$207$	−3.14272e17	+	8.99991e16i	−1.34131	+	0.384114i
$208$	−1.16320e16	+	4.23390e16i	−0.0478830	+	0.174287i
$209$		−	1.87937e17i		−	0.746302i
$210$	4.11819e17	−	2.06670e17i	1.57784	−	0.791831i
$211$			2.14257e17i			0.792168i	0.918214	+	0.396084i	$0.129631\pi$
$211$			2.14257e17i			0.792168i	−0.918214	+	0.396084i	$0.870369\pi$
$212$	−2.61534e17	−	3.43078e17i	−0.933274	−	1.22426i
$213$	−9.84370e15	+	1.38171e15i	−0.0339087	+	0.00475961i
$214$	1.44322e16	−	4.87365e15i	0.0479987	−	0.0162088i
$215$	−1.30420e17			−0.418848
$216$	5.62691e16	−	3.17458e17i	0.174529	−	0.984652i
$217$	4.56341e17			1.36723
$218$	−1.45991e17	+	4.93000e16i	−0.422573	+	0.142700i
$219$	−1.23704e17	+	1.73637e16i	−0.345981	+	0.0485637i
$220$	−1.49984e17	−	1.96747e17i	−0.405392	−	0.531789i
$221$		−	4.29368e16i		−	0.112173i
$222$	−6.29418e17	+	3.15871e17i	−1.58961	+	0.797741i
$223$		−	1.58454e17i		−	0.386916i	−0.981109	−	0.193458i	$-0.938030\pi$
$223$		−	1.58454e17i		−	0.386916i	0.981109	−	0.193458i	$-0.0619704\pi$
$224$	−7.55771e17	+	4.35415e16i	−1.78456	+	0.102812i
$225$	1.03619e16	−	2.96737e15i	0.0236631	−	0.00677647i
$226$	−1.53240e16	−	4.53787e16i	−0.0338501	−	0.100239i
$227$	5.75538e17			1.22993			0.614964	−	0.788555i	$-0.289170\pi$
$227$	5.75538e17			1.22993			0.614964	+	0.788555i	$0.289170\pi$
$228$	3.78972e17	+	3.74905e17i	0.783602	+	0.775194i
$229$	−3.33512e17			−0.667338			−0.333669	−	0.942690i	$-0.608287\pi$
$229$	−3.33512e17			−0.667338			−0.333669	+	0.942690i	$0.608287\pi$
$230$	−2.27648e17	−	6.74127e17i	−0.440864	−	1.30552i
$231$	−8.97423e16	−	6.39348e17i	−0.168231	−	1.19853i
$232$	8.92950e16	+	6.02793e16i	0.162057	+	0.109398i
$233$		−	8.50477e16i		−	0.149449i	−0.997204	−	0.0747246i	$-0.976192\pi$
$233$		−	8.50477e16i		−	0.149449i	0.997204	−	0.0747246i	$-0.0238078\pi$
$234$	8.73876e16	−	6.03741e16i	0.148707	−	0.102738i
$235$			5.03166e17i			0.829282i
$236$	−3.00841e16	+	2.29337e16i	−0.0480283	+	0.0366128i
$237$	−8.22461e16	−	5.85943e17i	−0.127205	−	0.906239i
$238$	7.01372e17	−	2.36848e17i	1.05104	−	0.354930i
$239$	6.87314e15			0.00998093			0.00499046	−	0.999988i	$-0.498411\pi$
$239$	6.87314e15			0.00998093			0.00499046	+	0.999988i	$0.498411\pi$
$240$	6.95933e17	+	9.00406e16i	0.979452	+	0.126723i
$241$	−5.57434e17			−0.760442			−0.380221	−	0.924896i	$-0.624152\pi$
$241$	−5.57434e17			−0.760442			−0.380221	+	0.924896i	$0.624152\pi$
$242$	3.87993e17	−	1.31022e17i	0.513108	−	0.173273i
$243$	−5.97881e17	+	5.00805e17i	−0.766597	+	0.642128i
$244$	−2.81688e17	+	2.14736e17i	−0.350223	+	0.266981i
$245$			1.79808e18i			2.16803i
$246$	4.23313e17	+	8.43513e17i	0.495050	+	0.986458i
$247$			1.75620e17i			0.199227i
$248$	5.76027e17	+	3.88852e17i	0.633951	+	0.427954i
$249$	1.28742e17	−	1.80709e16i	0.137475	−	0.0192968i
$250$	3.12443e17	+	9.25228e17i	0.323758	+	0.958736i
$251$	1.35677e18			1.36444			0.682221	−	0.731146i	$-0.261014\pi$
$251$	1.35677e18			1.36444			0.682221	+	0.731146i	$0.261014\pi$
$252$	1.46826e18	+	1.09444e18i	1.43317	+	1.06828i
$253$	−9.96971e17			−0.944667
$254$	2.71444e17	+	8.03819e17i	0.249705	+	0.739444i
$255$	−6.79554e17	+	9.53857e16i	−0.606977	+	0.0851985i
$256$	−9.91092e17	−	5.89037e17i	−0.859635	−	0.510908i
$257$		−	1.51825e18i		−	1.27892i	−0.768824	−	0.639460i	$-0.779158\pi$
$257$		−	1.51825e18i		−	1.27892i	0.768824	−	0.639460i	$-0.220842\pi$
$258$	−2.32493e17	−	4.63277e17i	−0.190223	−	0.379047i
$259$		−	4.00005e18i		−	3.17920i
$260$	1.40155e17	+	1.83853e17i	0.108220	+	0.141962i
$261$	−7.17503e16	−	2.50549e17i	−0.0538294	−	0.187970i
$262$	1.67598e18	−	5.65966e17i	1.22183	−	0.412602i
$263$	2.51464e17			0.178159			0.0890794	−	0.996025i	$-0.471608\pi$
$263$	2.51464e17			0.178159			0.0890794	+	0.996025i	$0.471608\pi$
$264$	4.31514e17	−	8.83502e17i	0.297143	−	0.608384i
$265$	−2.27138e18			−1.52036
$266$	−2.86875e18	+	9.68757e17i	−1.86673	+	0.630380i
$267$	2.78764e17	+	1.98599e18i	0.176361	+	1.25644i
$268$	−1.03761e18	−	1.36112e18i	−0.638296	−	0.837309i
$269$		−	3.42165e17i		−	0.204689i	−0.994749	−	0.102344i	$-0.967366\pi$
$269$		−	3.42165e17i		−	0.204689i	0.994749	−	0.102344i	$-0.0326344\pi$
$270$	−1.14967e18	−	1.24894e18i	−0.668872	−	0.726633i
$271$			2.43279e18i			1.37669i	0.725385	+	0.688344i	$0.241662\pi$
$271$			2.43279e18i			1.37669i	−0.725385	+	0.688344i	$0.758338\pi$
$272$	1.08714e18	+	2.98677e17i	0.598439	+	0.164413i
$273$	8.38609e16	+	5.97448e17i	0.0449097	+	0.319948i
$274$	6.84331e16	+	2.02649e17i	0.0356564	+	0.105588i
$275$	3.28713e16			0.0166656
$276$	1.98880e18	−	2.01038e18i	0.981237	−	0.991880i
$277$	3.00684e18			1.44382			0.721909	−	0.691988i	$-0.243265\pi$
$277$	3.00684e18			1.44382			0.721909	+	0.691988i	$0.243265\pi$
$278$	−1.06597e18	−	3.15664e18i	−0.498208	−	1.47533i
$279$	−4.62849e17	−	1.61625e18i	−0.210576	−	0.735320i
$280$	−2.23012e18	+	3.30360e18i	−0.987740	+	1.46319i
$281$			1.81846e18i			0.784163i	0.919930	+	0.392082i	$0.128245\pi$
$281$			1.81846e18i			0.784163i	−0.919930	+	0.392082i	$0.871755\pi$
$282$	−1.78734e18	+	8.96968e17i	−0.750478	+	0.376624i
$283$			1.20341e18i			0.492055i	0.969263	+	0.246027i	$0.0791253\pi$
$283$			1.20341e18i			0.492055i	−0.969263	+	0.246027i	$0.920875\pi$
$284$	6.83836e16	−	5.21300e16i	0.0272311	−	0.0207587i
$285$	2.77951e18	−	3.90147e17i	1.07803	−	0.151318i
$286$	3.06900e17	−	1.03638e17i	0.115945	−	0.0391538i
$287$	−5.36066e18			−1.97290
$288$	9.20763e17	+	2.63259e18i	0.330145	+	0.943930i
$289$	1.75993e18			0.614839
$290$	5.37436e17	−	1.81488e17i	0.182954	−	0.0617823i
$291$	3.41310e18	−	4.79081e17i	1.13228	−	0.158932i
$292$	8.59363e17	−	6.55107e17i	0.277847	−	0.211807i
$293$		−	4.48220e18i		−	1.41248i	−0.707970	−	0.706242i	$-0.750389\pi$
$293$		−	4.48220e18i		−	1.41248i	0.707970	−	0.706242i	$-0.249611\pi$
$294$	−6.38712e18	+	3.20535e18i	−1.96201	+	0.984624i
$295$			1.99175e17i			0.0596443i
$296$	3.40848e18	−	5.04916e18i	0.995113	−	1.47412i
$297$	−2.17339e18	+	9.66311e17i	−0.618678	+	0.275070i
$298$	−1.84759e18	−	5.47122e18i	−0.512843	−	1.51867i
$299$	9.31633e17			0.252180
$300$	−6.55732e16	+	6.62844e16i	−0.0173108	+	0.0174985i
$301$	2.94420e18			0.758086
$302$	1.69295e18	+	5.01328e18i	0.425199	+	1.25913i
$303$	3.28637e16	+	2.34130e17i	0.00805188	+	0.0573638i
$304$	−4.44663e18	−	1.22165e18i	−1.06287	−	0.292008i
$305$			1.86494e18i			0.434927i
$306$	−1.55023e18	−	2.24386e18i	−0.352765	−	0.510605i
$307$			2.40566e18i			0.534191i	0.963670	+	0.267095i	$0.0860639\pi$
$307$			2.40566e18i			0.534191i	−0.963670	+	0.267095i	$0.913936\pi$
$308$	3.38584e18	+	4.44151e18i	0.733731	+	0.962500i
$309$	4.80181e17	+	3.42094e18i	0.101558	+	0.723530i
$310$	3.46691e18	−	1.17075e18i	0.715699	−	0.241686i
$311$	−3.58128e18			−0.721664			−0.360832	−	0.932631i	$-0.617507\pi$
$311$	−3.58128e18			−0.721664			−0.360832	+	0.932631i	$0.617507\pi$
$312$	−4.03234e17	+	8.25601e17i	−0.0793228	+	0.162409i
$313$	4.06505e17			0.0780699			0.0390350	−	0.999238i	$-0.487572\pi$
$313$	4.06505e17			0.0780699			0.0390350	+	0.999238i	$0.487572\pi$
$314$	3.41128e18	−	1.15197e18i	0.639654	−	0.216007i
$315$	9.26940e18	−	2.65450e18i	1.69716	−	0.486020i
$316$	3.10302e18	+	4.07051e18i	0.554794	+	0.727773i
$317$			5.50906e18i			0.961908i	0.876746	+	0.480954i	$0.159710\pi$
$317$			5.50906e18i			0.961908i	−0.876746	+	0.480954i	$0.840290\pi$
$318$	−4.04906e18	−	8.06834e18i	−0.690480	−	1.37588i
$319$		−	7.94819e17i		−	0.132385i
$320$	−5.63004e18	+	2.26974e18i	−0.915981	+	0.369276i
$321$	3.15668e17	−	4.43088e16i	0.0501698	−	0.00704209i
$322$	5.13908e18	+	1.52182e19i	0.797933	+	2.36289i
$323$	4.50942e18			0.684071
$324$	2.38703e18	−	6.31025e18i	0.353810	−	0.935317i
$325$	−3.07170e16			−0.00444891
$326$	1.36809e18	+	4.05128e18i	0.193634	+	0.573403i
$327$	−3.19318e18	+	4.48211e17i	−0.441687	+	0.0619975i
$328$	−6.76662e18	−	4.56786e18i	−0.914783	−	0.617532i
$329$		−	1.13588e19i		−	1.50094i
$330$	−2.32205e18	−	4.62702e18i	−0.299928	−	0.597649i
$331$			9.04546e18i			1.14214i	0.820900	+	0.571072i	$0.193472\pi$
$331$			9.04546e18i			1.14214i	−0.820900	+	0.571072i	$0.806528\pi$
$332$	−8.94363e17	+	6.81788e17i	−0.110402	+	0.0841616i
$333$	−1.41672e19	+	4.05710e18i	−1.70983	+	0.489648i
$334$	1.10017e19	−	3.71519e18i	1.29826	−	0.438413i
$335$	−9.01143e18			−1.03982
$336$	−1.57105e19	−	2.03264e18i	−1.77274	−	0.229359i
$337$	7.27917e17			0.0803262			0.0401631	−	0.999193i	$-0.487212\pi$
$337$	7.27917e17			0.0803262			0.0401631	+	0.999193i	$0.487212\pi$
$338$	8.49182e18	−	2.86763e18i	0.916485	−	0.309490i
$339$	−1.39318e17	−	9.92542e17i	−0.0147066	−	0.104773i
$340$	4.72082e18	−	3.59876e18i	0.487445	−	0.371588i
$341$		−	5.12725e18i		−	0.517877i
$342$	6.34076e18	+	9.17783e18i	0.626535	+	0.906869i
$343$		−	2.21004e19i		−	2.13646i
$344$	3.71638e18	+	2.50877e18i	0.351506	+	0.237287i
$345$	−2.06966e18	−	1.47448e19i	−0.191538	−	1.36457i
$346$	1.98646e18	+	5.88246e18i	0.179891	+	0.532706i
$347$	−5.10775e18			−0.452646			−0.226323	−	0.974052i	$-0.572671\pi$
$347$	−5.10775e18			−0.452646			−0.226323	+	0.974052i	$0.572671\pi$
$348$	1.60274e18	+	1.58554e18i	0.139001	+	0.137510i
$349$	−1.78678e19			−1.51663			−0.758315	−	0.651889i	$-0.773977\pi$
$349$	−1.78678e19			−1.51663			−0.758315	+	0.651889i	$0.773977\pi$
$350$	−1.69441e17	−	5.01762e17i	−0.0140770	−	0.0416857i
$351$	2.03095e18	−	9.02983e17i	0.165157	−	0.0734304i
$352$	4.89213e17	+	8.49151e18i	0.0389429	+	0.675950i
$353$			1.55040e19i			1.20818i	0.796916	+	0.604091i	$0.206464\pi$
$353$			1.55040e19i			1.20818i	−0.796916	+	0.604091i	$0.793536\pi$
$354$	−7.07505e17	+	3.55058e17i	−0.0539765	+	0.0270879i
$355$		−	4.52740e17i		−	0.0338171i
$356$	−1.05174e19	−	1.37966e19i	−0.769186	−	1.00901i
$357$	1.53407e19	−	2.15330e18i	1.09859	−	0.154203i
$358$	−3.46435e18	+	1.16989e18i	−0.242940	+	0.0820391i
$359$	−2.44224e19			−1.67718			−0.838589	−	0.544764i	$-0.816619\pi$
$359$	−2.44224e19			−1.67718			−0.838589	+	0.544764i	$0.816619\pi$
$360$	1.39624e19	+	4.54782e18i	0.939058	+	0.305868i
$361$	−3.26329e18			−0.214957
$362$	1.95603e19	−	6.60537e18i	1.26200	−	0.426170i
$363$	8.48636e18	−	1.19119e18i	0.536317	−	0.0752803i
$364$	−3.16395e18	−	4.15043e18i	−0.195871	−	0.256941i
$365$		−	5.68949e18i		−	0.345046i
$366$	−6.62460e18	+	3.32453e18i	−0.393597	+	0.197525i
$367$			1.16167e19i			0.676221i	0.941106	+	0.338111i	$0.109788\pi$
$367$			1.16167e19i			0.676221i	−0.941106	+	0.338111i	$0.890212\pi$
$368$	−6.48063e18	+	2.35886e19i	−0.369622	+	1.34537i
$369$	5.43711e18	+	1.89861e19i	0.303858	+	1.06106i
$370$	−1.02622e19	−	3.03892e19i	−0.561990	−	1.66420i
$371$	5.12756e19			2.75174
$372$	1.03390e19	+	1.02281e19i	0.543760	+	0.537925i
$373$	−3.99820e18			−0.206086			−0.103043	−	0.994677i	$-0.532858\pi$
$373$	−3.99820e18			−0.206086			−0.103043	+	0.994677i	$0.532858\pi$
$374$	−2.66112e18	−	7.88030e18i	−0.134440	−	0.398112i
$375$	2.84057e18	+	2.02370e19i	0.140660	+	1.00210i
$376$	9.67894e18	−	1.43379e19i	0.469806	−	0.695950i
$377$			7.42729e17i			0.0353403i
$378$	2.59534e19	+	2.81945e19i	1.21061	+	1.31515i
$379$			1.27210e19i			0.581736i	0.956763	+	0.290868i	$0.0939440\pi$
$379$			1.27210e19i			0.581736i	−0.956763	+	0.290868i	$0.906056\pi$
$380$	−1.93091e19	+	1.47197e19i	−0.865735	+	0.659965i
$381$	2.46783e18	+	1.75815e19i	0.108487	+	0.772892i
$382$	−2.52099e19	+	8.51322e18i	−1.08667	+	0.366960i
$383$	−7.02109e18			−0.296766			−0.148383	−	0.988930i	$-0.547407\pi$
$383$	−7.02109e18			−0.296766			−0.148383	+	0.988930i	$0.547407\pi$
$384$	−1.80989e19	−	1.59528e19i	−0.750184	−	0.661229i
$385$	2.94055e19			1.19529
$386$	−3.06875e19	+	1.03630e19i	−1.22337	+	0.413122i
$387$	−2.98619e18	−	1.04276e19i	−0.116758	−	0.407712i
$388$	−2.37106e19	+	1.80750e19i	−0.909296	+	0.693172i
$389$		−	2.83676e19i		−	1.06709i	−0.845772	−	0.533545i	$-0.820859\pi$
$389$		−	2.83676e19i		−	1.06709i	0.845772	−	0.533545i	$-0.179141\pi$
$390$	2.16987e18	+	4.32378e18i	0.0800662	+	0.159543i
$391$		−	2.39216e19i		−	0.865895i
$392$	3.45881e19	−	5.12372e19i	1.22823	−	1.81945i
$393$	3.66578e19	−	5.14548e18i	1.27709	−	0.179259i
$394$	−4.01288e18	−	1.18832e19i	−0.137162	−	0.406175i
$395$	2.69492e19			0.903791
$396$	1.22966e19	−	1.64967e19i	0.404643	−	0.542853i
$397$	9.87931e18			0.319005			0.159503	−	0.987198i	$-0.449011\pi$
$397$	9.87931e18			0.319005			0.159503	+	0.987198i	$0.449011\pi$
$398$	1.12605e18	+	3.33454e18i	0.0356808	+	0.105661i
$399$	−6.27466e19	+	8.80744e18i	−1.95116	+	0.273876i
$400$	2.13674e17	−	7.77742e17i	0.00652080	−	0.0237348i
$401$			5.49232e19i			1.64503i	0.568746	+	0.822513i	$0.307429\pi$
$401$			5.49232e19i			1.64503i	−0.568746	+	0.822513i	$0.692571\pi$
$402$	−1.60642e19	−	3.20102e19i	−0.472241	−	0.941009i
$403$			4.79123e18i			0.138248i
$404$	−1.23990e18	−	1.62649e18i	−0.0351178	−	0.0460671i
$405$	−1.88032e19	−	3.01376e19i	−0.522780	−	0.837906i
$406$	−1.21325e19	+	4.09705e18i	−0.331134	+	0.111822i
$407$	−4.49428e19			−1.20421
$408$	2.11990e19	+	1.03539e19i	0.557654	+	0.272365i
$409$	−1.71544e19			−0.443049			−0.221524	−	0.975155i	$-0.571103\pi$
$409$	−1.71544e19			−0.443049			−0.221524	+	0.975155i	$0.571103\pi$
$410$	−4.07260e19	+	1.37529e19i	−1.03274	+	0.348750i
$411$	6.22159e17	+	4.43243e18i	0.0154913	+	0.110364i
$412$	−1.81165e19	−	2.37651e19i	−0.442941	−	0.581045i
$413$		−	4.49631e18i		−	0.107952i
$414$	4.86867e19	−	3.36366e19i	1.14791	−	0.793066i
$415$			5.92121e18i			0.137104i
$416$	−4.57152e17	−	7.93501e18i	−0.0103959	−	0.180446i
$417$	−9.69129e18	−	6.90434e19i	−0.216452	−	1.54206i
$418$	1.08845e19	+	3.22320e19i	0.238774	+	0.707074i
$419$	3.22322e19			0.694521			0.347260	−	0.937769i	$-0.387112\pi$
$419$	3.22322e19			0.694521			0.347260	+	0.937769i	$0.387112\pi$
$420$	−5.86594e19	+	5.92956e19i	−1.24156	+	1.25503i
$421$	2.74110e19			0.569914			0.284957	−	0.958540i	$-0.408021\pi$
$421$	2.74110e19			0.569914			0.284957	+	0.958540i	$0.408021\pi$
$422$	−1.24089e19	−	3.67461e19i	−0.253448	−	0.750530i
$423$	−4.02301e19	+	1.15208e19i	−0.807233	+	0.231169i
$424$	6.47239e19	+	4.36924e19i	1.27591	+	0.861314i
$425$			7.88724e17i			0.0152759i
$426$	1.60821e18	−	8.07076e17i	0.0306036	−	0.0153583i
$427$		−	4.21004e19i		−	0.787186i
$428$	−2.19292e18	+	1.67170e18i	−0.0402898	+	0.0307136i
$429$	6.71265e18	−	9.42223e17i	0.121189	−	0.0170108i
$430$	2.23677e19	−	7.55340e18i	0.396832	−	0.134007i
$431$	7.64963e19			1.33371			0.666854	−	0.745188i	$-0.267640\pi$
$431$	7.64963e19			1.33371			0.666854	+	0.745188i	$0.267640\pi$
$432$	8.73543e18	+	5.77043e19i	0.149677	+	0.988735i
$433$	8.90203e18			0.149910			0.0749548	−	0.997187i	$-0.476119\pi$
$433$	8.90203e18			0.149910			0.0749548	+	0.997187i	$0.476119\pi$
$434$	−7.82645e19	+	2.64294e19i	−1.29536	+	0.437435i
$435$	1.17550e19	−	1.65000e18i	0.191230	−	0.0268420i
$436$	2.21828e19	−	1.69103e19i	0.354706	−	0.270398i
$437$			9.78443e19i			1.53789i
$438$	2.02101e19	−	1.01424e19i	0.312257	−	0.156705i
$439$			5.66667e19i			0.860685i	0.902666	+	0.430342i	$0.141607\pi$
$439$			5.66667e19i			0.860685i	−0.902666	+	0.430342i	$0.858393\pi$
$440$	3.71177e19	+	2.50566e19i	0.554225	+	0.374134i
$441$	−1.43764e20	+	4.11701e19i	−2.11038	+	0.604356i
$442$	2.48672e18	+	7.36385e18i	0.0358889	+	0.106277i
$443$	8.98271e19			1.27462			0.637308	−	0.770609i	$-0.280048\pi$
$443$	8.98271e19			1.27462			0.637308	+	0.770609i	$0.280048\pi$
$444$	8.96541e19	−	9.06265e19i	1.25083	−	1.26440i
$445$	−9.13413e19			−1.25305
$446$	9.17700e18	+	2.71756e19i	0.123791	+	0.366579i
$447$	−1.67974e19	−	1.19669e20i	−0.222810	−	1.58736i
$448$	1.27096e20	−	5.12387e19i	1.65786	−	0.668363i
$449$		−	1.21780e20i		−	1.56217i	−0.624422	−	0.781087i	$-0.714666\pi$
$449$		−	1.21780e20i		−	1.56217i	0.624422	−	0.781087i	$-0.285334\pi$
$450$	−1.60526e18	+	1.10904e18i	−0.0202512	+	0.0139911i
$451$			6.02300e19i			0.747289i
$452$	5.25628e18	+	6.89513e18i	0.0641417	+	0.0841404i
$453$	1.53914e19	+	1.09653e20i	0.184732	+	1.31608i
$454$	−9.87073e19	+	3.33327e19i	−1.16528	+	0.393507i
$455$	−2.74783e19			−0.319084
$456$	−8.67083e19	−	4.23495e19i	−0.990431	−	0.483739i
$457$	−1.00075e20			−1.12448			−0.562242	−	0.826972i	$-0.690061\pi$
$457$	−1.00075e20			−1.12448			−0.562242	+	0.826972i	$0.690061\pi$
$458$	5.71988e19	−	1.93156e19i	0.632261	−	0.213510i
$459$	−2.31860e19	−	5.21490e19i	−0.252133	−	0.567089i
$460$	7.80852e19	+	1.02431e20i	0.835382	+	1.09584i
$461$		−	4.79947e19i		−	0.505169i	−0.967575	−	0.252584i	$-0.918719\pi$
$461$		−	4.79947e19i		−	0.505169i	0.967575	−	0.252584i	$-0.0812805\pi$
$462$	5.24195e19	+	1.04453e20i	0.542848	+	1.08170i
$463$		−	3.70157e19i		−	0.377163i	−0.982058	−	0.188582i	$-0.939611\pi$
$463$		−	3.70157e19i		−	0.377163i	0.982058	−	0.188582i	$-0.0603890\pi$
$464$	−1.88056e19	−	5.16657e18i	−0.188540	−	0.0517986i
$465$	7.58299e19	−	1.06439e19i	0.748072	−	0.105003i
$466$	4.92561e18	+	1.45861e19i	0.0478151	+	0.141594i
$467$	−8.13340e19			−0.776954			−0.388477	−	0.921458i	$-0.626999\pi$
$467$	−8.13340e19			−0.776954			−0.388477	+	0.921458i	$0.626999\pi$
$468$	−1.14907e19	+	1.54156e19i	−0.108020	+	0.144916i
$469$	2.03430e20			1.88200
$470$	−2.91413e19	−	8.62952e19i	−0.265323	−	0.785693i
$471$	7.46131e19	−	1.04731e19i	0.668588	−	0.0938465i
$472$	3.83134e18	−	5.67557e18i	0.0337898	−	0.0500547i
$473$		−	3.30797e19i		−	0.287146i
$474$	4.80409e19	+	9.57285e19i	0.410463	+	0.817906i
$475$		−	3.22604e18i		−	0.0271311i
$476$	−1.06571e20	+	8.12410e19i	−0.882241	+	0.672548i
$477$	−5.20069e19	−	1.81606e20i	−0.423812	−	1.47993i
$478$	−1.17877e18	+	3.98063e17i	−0.00945630	+	0.00319332i
$479$	−2.08531e20			−1.64685			−0.823424	−	0.567427i	$-0.807939\pi$
$479$	−2.08531e20			−1.64685			−0.823424	+	0.567427i	$0.807939\pi$
$480$	−1.24570e20	+	2.48632e19i	−0.968513	+	0.193307i
$481$	4.19974e19			0.321466
$482$	9.56024e19	−	3.22843e19i	0.720470	−	0.243298i
$483$	4.67219e19	+	3.32859e20i	0.346671	+	2.46977i
$484$	−5.89542e19	+	4.49418e19i	−0.430700	+	0.328330i
$485$			1.56978e20i			1.12922i
$486$	7.35346e19	−	1.20517e20i	0.520859	−	0.853643i
$487$			2.39743e19i			0.167216i	0.996499	+	0.0836082i	$0.0266444\pi$
$487$			2.39743e19i			0.167216i	−0.996499	+	0.0836082i	$0.973356\pi$
$488$	3.58741e19	−	5.31423e19i	0.246395	−	0.364999i
$489$	1.24380e19	+	8.86113e19i	0.0841265	+	0.599340i
$490$	−1.04138e20	−	3.08379e20i	−0.693644	−	2.05407i
$491$	2.45200e19			0.160845			0.0804227	−	0.996761i	$-0.474373\pi$
$491$	2.45200e19			0.160845			0.0804227	+	0.996761i	$0.474373\pi$
$492$	−1.21453e20	−	1.20150e20i	−0.784638	−	0.776219i
$493$	1.90711e19			0.121346
$494$	−1.01712e19	−	3.01196e19i	−0.0637411	−	0.188755i
$495$	−2.98248e19	−	1.04147e20i	−0.184094	−	0.642846i
$496$	−1.21312e20	−	3.33287e19i	−0.737549	−	0.202631i
$497$			1.02205e19i			0.0612065i
$498$	−2.10332e19	+	1.05554e19i	−0.124075	+	0.0622667i
$499$		−	2.58155e20i		−	1.50012i	−0.661369	−	0.750061i	$-0.730024\pi$
$499$		−	2.58155e20i		−	1.50012i	0.661369	−	0.750061i	$-0.269976\pi$
$500$	−1.07171e20	−	1.40585e20i	−0.613481	−	0.804758i
$501$	2.40634e20	−	3.37767e19i	1.35698	−	0.190473i
$502$	−2.32693e20	+	7.85787e19i	−1.29272	+	0.436543i
$503$	1.05944e20			0.579852			0.289926	−	0.957049i	$-0.406369\pi$
$503$	1.05944e20			0.579852			0.289926	+	0.957049i	$0.406369\pi$
$504$	−3.15198e20	−	1.02666e20i	−1.69963	−	0.553600i
$505$	−1.07683e19			−0.0572088
$506$	1.70985e20	−	5.77404e19i	0.895012	−	0.302239i
$507$	1.85737e20	−	2.60710e19i	0.957940	−	0.134462i
$508$	−9.31077e19	−	1.22138e20i	−0.473160	−	0.620686i
$509$		−	1.94283e20i		−	0.972862i	−0.873719	−	0.486431i	$-0.838299\pi$
$509$		−	1.94283e20i		−	0.972862i	0.873719	−	0.486431i	$-0.161701\pi$
$510$	1.11022e20	−	5.57160e19i	0.547814	−	0.274918i
$511$			1.28439e20i			0.624509i
$512$	2.04091e20	+	4.36226e19i	0.977911	+	0.209019i
$513$	9.48353e19	+	2.13300e20i	0.447806	+	1.00719i
$514$	8.79304e19	+	2.60386e20i	0.409181	+	1.21170i
$515$	−1.57339e20			−0.721575
$516$	6.67047e19	+	6.59890e19i	0.301497	+	0.298262i
$517$	−1.27623e20			−0.568524
$518$	2.31666e20	+	6.86027e20i	1.01716	+	3.01209i
$519$	1.80599e19	+	1.28664e20i	0.0781557	+	0.556802i
$520$	−3.46852e19	−	2.34145e19i	−0.147951	−	0.0998757i
$521$			1.32245e20i			0.556030i	0.960577	+	0.278015i	$0.0896764\pi$
$521$			1.32245e20i			0.556030i	−0.960577	+	0.278015i	$0.910324\pi$
$522$	2.68162e19	+	3.88147e19i	0.111140	+	0.160867i
$523$			1.82317e20i			0.744842i	0.928064	+	0.372421i	$0.121472\pi$
$523$			1.82317e20i			0.744842i	−0.928064	+	0.372421i	$0.878528\pi$
$524$	−2.54659e20	+	1.94131e20i	−1.02559	+	0.781828i
$525$	−1.54047e18	−	1.09748e19i	−0.00611589	−	0.0435713i
$526$	−4.31271e19	+	1.45637e19i	−0.168794	+	0.0570006i
$527$	1.23025e20			0.474693
$528$	−2.28378e19	+	1.76516e20i	−0.0868761	+	0.671474i
$529$	2.52411e20			0.946653
$530$	3.89551e20	−	1.31549e20i	1.44044	−	0.486426i
$531$	−1.59248e19	+	4.56043e18i	−0.0580584	+	0.0166264i
$532$	4.35897e20	−	3.32292e20i	1.56692	−	1.19449i
$533$		−	5.62828e19i		−	0.199490i
$534$	−1.62829e20	−	3.24461e20i	−0.569080	−	1.13397i
$535$			1.45185e19i			0.0500342i
$536$	2.56785e20	+	1.73345e20i	0.872636	+	0.589080i
$537$	−7.57738e19	+	1.06360e19i	−0.253929	+	0.0356428i
$538$	1.98168e19	+	5.86829e19i	0.0654887	+	0.193930i
$539$	−4.56065e20			−1.48631
$540$	2.69506e20	+	1.47616e20i	0.866195	+	0.474438i
$541$	−3.68575e20			−1.16828			−0.584140	−	0.811653i	$-0.698568\pi$
$541$	−3.68575e20			−1.16828			−0.584140	+	0.811653i	$0.698568\pi$
$542$	−1.40897e20	−	4.17235e20i	−0.440461	−	1.30432i
$543$	4.27831e20	−	6.00527e19i	1.31909	−	0.185154i
$544$	−2.03748e20	+	1.17383e19i	−0.619586	+	0.0356956i
$545$		−	1.46863e20i		−	0.440494i
$546$	−4.89842e19	−	9.76080e19i	−0.144914	−	0.288762i
$547$		−	3.66624e20i		−	1.06983i	−0.844905	−	0.534916i	$-0.820343\pi$
$547$		−	3.66624e20i		−	1.06983i	0.844905	−	0.534916i	$-0.179657\pi$
$548$	−2.34732e19	−	3.07918e19i	−0.0675643	−	0.0886301i
$549$	−1.49109e20	+	4.27009e19i	−0.423362	+	0.121239i
$550$	−5.63757e18	+	1.90377e18i	−0.0157896	+	0.00533204i
$551$	−7.80047e19			−0.215518
$552$	−2.24656e20	+	4.59972e20i	−0.612316	+	1.25368i
$553$	−6.08370e20			−1.63580
$554$	−5.15687e20	+	1.74144e20i	−1.36793	+	0.461939i
$555$	−9.32989e19	−	6.64686e20i	−0.244163	−	1.73948i
$556$	3.65638e20	+	4.79640e20i	0.944040	+	1.23838i
$557$			3.18417e20i			0.811114i	0.914070	+	0.405557i	$0.132922\pi$
$557$			3.18417e20i			0.811114i	−0.914070	+	0.405557i	$0.867078\pi$
$558$	1.72987e20	+	2.50387e20i	0.434767	+	0.629297i
$559$			3.09118e19i			0.0766541i
$560$	1.91145e20	−	6.95740e20i	0.467684	−	1.70230i
$561$	−2.41936e19	−	1.72361e20i	−0.0584088	−	0.416120i
$562$	−1.05318e20	−	3.11874e20i	−0.250887	−	0.742945i
$563$	−1.18420e19			−0.0278363			−0.0139182	−	0.999903i	$-0.504430\pi$
$563$	−1.18420e19			−0.0278363			−0.0139182	+	0.999903i	$0.504430\pi$
$564$	2.54588e20	−	2.57349e20i	0.590533	−	0.596938i
$565$	4.56499e19			0.104490
$566$	−6.96962e19	−	2.06389e20i	−0.157429	−	0.466191i
$567$	4.24476e20	+	6.80346e20i	0.946195	+	1.51655i
$568$	−8.70894e18	+	1.29010e19i	−0.0191581	+	0.0283800i
$569$		−	7.78881e20i		−	1.69094i	−0.534020	−	0.845472i	$-0.679319\pi$
$569$		−	7.78881e20i		−	1.69094i	0.534020	−	0.845472i	$-0.320681\pi$
$570$	−4.54103e20	+	2.27889e20i	−0.972955	+	0.488273i
$571$			2.47283e20i			0.522905i	0.965216	+	0.261452i	$0.0842015\pi$
$571$			2.47283e20i			0.522905i	−0.965216	+	0.261452i	$0.915799\pi$
$572$	−4.66324e19	+	3.55487e19i	−0.0973235	+	0.0741914i
$573$	−5.51403e20	+	7.73979e19i	−1.13582	+	0.159430i
$574$	9.19377e20	−	3.10467e20i	1.86919	−	0.631214i
$575$	−1.71135e19			−0.0343424
$576$	−3.10384e20	−	3.98174e20i	−0.614795	−	0.788687i
$577$	8.63573e20			1.68842			0.844210	−	0.536012i	$-0.180070\pi$
$577$	8.63573e20			1.68842			0.844210	+	0.536012i	$0.180070\pi$
$578$	−3.01836e20	+	1.01928e20i	−0.582522	+	0.196713i
$579$	−6.71211e20	+	9.42147e19i	−1.27870	+	0.179486i
$580$	−8.16617e19	+	6.22521e19i	−0.153571	+	0.117070i
$581$		−	1.33669e20i		−	0.248148i
$582$	−5.57616e20	+	2.79837e20i	−1.02191	+	0.512841i
$583$		−	5.76110e20i		−	1.04230i
$584$	−1.09443e20	+	1.62124e20i	−0.195476	+	0.289569i
$585$	2.78702e19	+	9.73215e19i	0.0491441	+	0.171609i
$586$	2.59590e20	+	7.68716e20i	0.451914	+	1.33824i
$587$	−2.17267e20			−0.373428			−0.186714	−	0.982414i	$-0.559784\pi$
$587$	−2.17267e20			−0.373428			−0.186714	+	0.982414i	$0.559784\pi$
$588$	9.09779e20	−	9.19647e20i	1.54385	−	1.56060i
$589$	−5.03196e20			−0.843087
$590$	−1.15354e19	−	3.41593e19i	−0.0190828	−	0.0565092i
$591$	−3.64831e19	−	2.59915e20i	−0.0595917	−	0.424547i
$592$	−2.92143e20	+	1.06336e21i	−0.471175	+	1.71501i
$593$			5.31272e20i			0.846072i	0.906113	+	0.423036i	$0.139036\pi$
$593$			5.31272e20i			0.846072i	−0.906113	+	0.423036i	$0.860964\pi$
$594$	3.16781e20	−	2.91600e20i	0.498151	−	0.458553i
$595$			7.05564e20i			1.09562i
$596$	6.33741e20	+	8.31334e20i	0.971772	+	1.27476i
$597$	1.02375e19	+	7.29346e19i	0.0155019	+	0.110440i
$598$	−1.59779e20	+	5.39563e19i	−0.238925	+	0.0806832i
$599$	8.54948e20			1.26252			0.631261	−	0.775571i	$-0.282538\pi$
$599$	8.54948e20			1.26252			0.631261	+	0.775571i	$0.282538\pi$
$600$	7.40717e18	−	1.51658e19i	0.0108023	−	0.0221172i
$601$	1.07580e21			1.54943			0.774717	−	0.632308i	$-0.217892\pi$
$601$	1.07580e21			1.54943			0.774717	+	0.632308i	$0.217892\pi$
$602$	−5.04943e20	+	1.70516e20i	−0.718239	+	0.242544i
$603$	−2.06332e20	−	7.20500e20i	−0.289858	−	1.01217i
$604$	−5.80697e20	−	7.61752e20i	−0.805698	−	1.05691i
$605$			3.90312e20i			0.534868i
$606$	−1.91961e19	−	3.82510e19i	−0.0259818	−	0.0517724i
$607$			2.34478e20i			0.313464i	0.987641	+	0.156732i	$0.0500959\pi$
$607$			2.34478e20i			0.313464i	−0.987641	+	0.156732i	$0.949904\pi$
$608$	8.33370e20	−	4.80121e19i	1.10043	−	0.0633978i
$609$	−2.65367e20	+	3.72483e19i	−0.346112	+	0.0485821i
$610$	−1.08009e20	−	3.19845e20i	−0.139152	−	0.412066i
$611$	1.19259e20			0.151768
$612$	3.95826e20	+	2.95049e20i	0.497587	+	0.370901i
$613$	8.66071e20			1.07547			0.537737	−	0.843113i	$-0.319279\pi$
$613$	8.66071e20			1.07547			0.537737	+	0.843113i	$0.319279\pi$
$614$	−1.39326e20	−	4.12581e20i	−0.170910	−	0.506112i
$615$	−8.90778e20	+	1.25034e20i	−1.07946	+	0.151518i
$616$	−8.37921e20	−	5.65645e20i	−1.00311	−	0.677156i
$617$			1.00657e21i			1.19043i	0.803565	+	0.595217i	$0.202934\pi$
$617$			1.00657e21i			1.19043i	−0.803565	+	0.595217i	$0.797066\pi$
$618$	−2.80479e20	−	5.58896e20i	−0.327708	−	0.653006i
$619$			1.12221e21i			1.29537i	0.761908	+	0.647685i	$0.224263\pi$
$619$			1.12221e21i			1.29537i	−0.761908	+	0.647685i	$0.775737\pi$
$620$	−5.26786e20	+	4.01578e20i	−0.600754	+	0.457965i
$621$	1.13152e21	−	5.03084e20i	1.27489	−	0.566831i
$622$	6.14205e20	−	2.07412e20i	0.683731	−	0.230891i
$623$	2.06200e21			2.26793
$624$	2.13411e19	−	1.64948e20i	0.0231917	−	0.179251i
$625$	−9.07834e20			−0.974780
$626$	−6.97175e19	+	2.35431e19i	−0.0739663	+	0.0249779i
$627$	9.89565e19	+	7.04993e20i	0.103738	+	0.739057i
$628$	−5.18333e20	+	3.95134e20i	−0.536922	+	0.409305i
$629$		−	1.07837e21i		−	1.10380i
$630$	−1.43601e21	+	9.92104e20i	−1.45245	+	1.00347i
$631$		−	7.23813e20i		−	0.723447i	−0.932286	−	0.361723i	$-0.882189\pi$
$631$		−	7.23813e20i		−	0.723447i	0.932286	−	0.361723i	$-0.117811\pi$
$632$	−7.67929e20	−	5.18397e20i	−0.758478	−	0.512017i
$633$	−1.12815e20	−	8.03727e20i	−0.110113	−	0.784478i
$634$	−3.19062e20	−	9.44829e20i	−0.307755	−	0.911347i
$635$	−8.08624e20			−0.770803
$636$	1.16172e21	+	1.14925e21i	1.09439	+	1.08265i
$637$	4.26176e20			0.396774
$638$	4.60326e19	+	1.36315e20i	0.0423555	+	0.125426i
$639$	3.61984e19	−	1.03662e19i	0.0329179	−	0.00942680i
$640$	8.34122e20	−	7.15338e20i	0.749687	−	0.642927i
$641$			1.62586e21i			1.44427i	0.691752	+	0.722135i	$0.256839\pi$
$641$			1.62586e21i			1.44427i	−0.691752	+	0.722135i	$0.743161\pi$
$642$	−5.15722e19	+	2.58813e19i	−0.0452796	+	0.0227234i
$643$		−	1.72137e21i		−	1.49379i	−0.664940	−	0.746897i	$-0.731543\pi$
$643$		−	1.72137e21i		−	1.49379i	0.664940	−	0.746897i	$-0.268457\pi$
$644$	−1.76275e21	−	2.31236e21i	−1.51198	−	1.98340i
$645$	4.89236e20	−	6.86717e19i	0.414782	−	0.0582210i
$646$	−7.73385e20	+	2.61166e20i	−0.648114	+	0.218864i
$647$	8.68296e20			0.719260			0.359630	−	0.933095i	$-0.382903\pi$
$647$	8.68296e20			0.719260			0.359630	+	0.933095i	$0.382903\pi$
$648$	−4.39231e19	+	1.22048e21i	−0.0359650	+	0.999353i
$649$	−5.05185e19			−0.0408898
$650$	5.26810e18	−	1.77900e18i	0.00421506	−	0.00142340i
$651$	−1.71184e21	+	2.40283e20i	−1.35396	+	0.190049i
$652$	−4.69266e20	−	6.15578e20i	−0.366912	−	0.481311i
$653$			5.16021e20i			0.398858i	0.979912	+	0.199429i	$0.0639088\pi$
$653$			5.16021e20i			0.398858i	−0.979912	+	0.199429i	$0.936091\pi$
$654$	5.21685e20	−	2.61806e20i	0.398635	−	0.200053i
$655$			1.68600e21i			1.27364i
$656$	1.42506e21	+	3.91514e20i	1.06427	+	0.292394i
$657$	4.54897e20	−	1.30270e20i	0.335872	−	0.0961845i
$658$	6.57855e20	+	1.94809e21i	0.480215	+	1.42205i
$659$	−1.89705e21			−1.36911			−0.684553	−	0.728963i	$-0.740003\pi$
$659$	−1.89705e21			−1.36911			−0.684553	+	0.728963i	$0.740003\pi$
$660$	6.66219e20	+	6.59070e20i	0.475376	+	0.470275i
$661$	−1.17502e21			−0.828959			−0.414479	−	0.910059i	$-0.636036\pi$
$661$	−1.17502e21			−0.828959			−0.414479	+	0.910059i	$0.636036\pi$
$662$	−5.23875e20	−	1.55134e21i	−0.365421	−	1.08211i
$663$	2.26080e19	+	1.61066e20i	0.0155923	+	0.111084i
$664$	1.13901e20	−	1.68727e20i	0.0776723	−	0.115060i
$665$		−	2.88590e21i		−	1.94589i
$666$	2.19477e21	−	1.51632e21i	1.46329	−	1.01096i
$667$			4.13801e20i			0.272802i
$668$	−1.67167e21	+	1.27434e21i	−1.08975	+	0.830736i
$669$	8.34327e19	+	5.94397e20i	0.0537824	+	0.383160i
$670$	1.54550e21	−	5.21904e20i	0.985163	−	0.332682i
$671$	−4.73022e20			−0.298169
$672$	2.81214e21	−	5.61279e20i	1.75294	−	0.349872i
$673$	−2.04488e21			−1.26053			−0.630267	−	0.776378i	$-0.717055\pi$
$673$	−2.04488e21			−1.26053			−0.630267	+	0.776378i	$0.717055\pi$
$674$	−1.24841e20	+	4.21579e19i	−0.0761040	+	0.0256998i
$675$	−3.73074e19	+	1.65873e19i	−0.0224914	+	0.00999991i
$676$	−1.29030e21	+	9.83621e20i	−0.769293	+	0.586445i
$677$		−	1.28106e21i		−	0.755360i	−0.925936	−	0.377680i	$-0.876722\pi$
$677$		−	1.28106e21i		−	0.755360i	0.925936	−	0.377680i	$-0.123278\pi$
$678$	8.13776e19	+	1.62157e20i	0.0474550	+	0.0945610i
$679$		−	3.54374e21i		−	2.04380i
$680$	−6.01216e20	+	8.90614e20i	−0.342937	+	0.508010i
$681$	−2.15897e21	+	3.03044e20i	−1.21799	+	0.170963i
$682$	2.96949e20	+	8.79345e20i	0.165691	+	0.490655i
$683$	1.05077e21			0.579901			0.289950	−	0.957042i	$-0.406361\pi$
$683$	1.05077e21			0.579901			0.289950	+	0.957042i	$0.406361\pi$
$684$	−1.61901e21	−	1.20681e21i	−0.883748	−	0.658745i
$685$	−2.03860e20			−0.110066
$686$	1.27996e21	+	3.79032e21i	0.683544	+	2.02416i
$687$	1.25108e21	−	1.75608e20i	0.660859	−	0.0927617i
$688$	−7.82674e20	−	2.15029e20i	−0.408948	−	0.112353i
$689$			5.38354e20i			0.278243i
$690$	1.20891e21	+	2.40893e21i	0.618054	+	1.23156i
$691$		−	2.97575e21i		−	1.50491i	−0.658644	−	0.752455i	$-0.728870\pi$
$691$		−	2.97575e21i		−	1.50491i	0.658644	−	0.752455i	$-0.271130\pi$
$692$	−6.81374e20	−	8.93819e20i	−0.340871	−	0.447151i
$693$	6.73286e20	+	2.35108e21i	0.333196	+	1.16351i
$694$	8.76002e20	−	2.95820e20i	0.428854	−	0.144821i
$695$	3.17550e21			1.53789
$696$	−3.66705e20	−	1.79103e20i	−0.175690	−	0.0858094i
$697$	−1.44518e21			−0.684976
$698$	3.06440e21	−	1.03483e21i	1.43691	−	0.485234i
$699$	4.47811e19	+	3.19033e20i	0.0207738	+	0.147998i
$700$	5.81199e19	+	7.62410e19i	0.0266741	+	0.0349908i
$701$			1.49886e21i			0.680575i	0.940321	+	0.340287i	$0.110524\pi$
$701$			1.49886e21i			0.680575i	−0.940321	+	0.340287i	$0.889476\pi$
$702$	−2.96021e20	+	2.72490e20i	−0.132982	+	0.122411i
$703$			4.41076e21i			1.96042i
$704$	−5.75695e20	−	1.42800e21i	−0.253161	−	0.627961i
$705$	−2.64938e20	−	1.88749e21i	−0.115272	−	0.821232i
$706$	−8.97924e20	−	2.65900e21i	−0.386549	−	1.14468i
$707$	2.43091e20			0.103544
$708$	1.00777e20	−	1.01870e20i	0.0424728	−	0.0429335i
$709$	−8.12349e20			−0.338763			−0.169382	−	0.985551i	$-0.554177\pi$
$709$	−8.12349e20			−0.338763			−0.169382	+	0.985551i	$0.554177\pi$
$710$	2.62208e19	+	7.76469e19i	0.0108195	+	0.0320396i
$711$	6.17046e20	+	2.15470e21i	0.251939	+	0.879760i
$712$	2.60281e21	+	1.75705e21i	1.05158	+	0.709878i
$713$			2.66936e21i			1.06718i
$714$	−2.50629e21	+	1.25777e21i	−0.991505	+	0.497582i
$715$			3.08734e20i			0.120862i
$716$	5.26396e20	−	4.01281e20i	0.203923	−	0.155454i
$717$	−2.57827e19	+	3.61899e18i	−0.00988403	+	0.00138737i
$718$	4.18854e21	−	1.41444e21i	1.58902	−	0.536601i
$719$	−4.05458e21			−1.52223			−0.761114	−	0.648618i	$-0.775347\pi$
$719$	−4.05458e21			−1.52223			−0.761114	+	0.648618i	$0.775347\pi$
$720$	−2.65801e21	+	2.86753e19i	−0.987559	+	0.0106540i
$721$	3.55187e21			1.30600
$722$	5.59668e20	−	1.88996e20i	0.203658	−	0.0687739i
$723$	2.09106e21	−	2.93512e20i	0.753059	−	0.105703i
$724$	−2.97212e21	+	2.26570e21i	−1.05932	+	0.807538i
$725$		−	1.36435e19i		−	0.00481272i
$726$	−1.38646e21	+	6.95788e20i	−0.484041	+	0.242914i
$727$			2.72750e21i			0.942448i	0.882014	+	0.471224i	$0.156188\pi$
$727$			2.72750e21i			0.942448i	−0.882014	+	0.471224i	$0.843812\pi$
$728$	7.83007e20	+	5.28575e20i	0.267781	+	0.180768i
$729$	1.97909e21	−	2.19344e21i	0.669898	−	0.742453i
$730$	3.29511e20	+	9.75773e20i	0.110395	+	0.326909i
$731$	7.93725e20			0.263202
$732$	9.43606e20	−	9.53841e20i	0.309712	−	0.313071i
$733$	7.35135e20			0.238829			0.119415	−	0.992844i	$-0.461898\pi$
$733$	7.35135e20			0.238829			0.119415	+	0.992844i	$0.461898\pi$
$734$	−6.72793e20	−	1.99232e21i	−0.216352	−	0.640677i
$735$	−9.46766e20	−	6.74501e21i	−0.301361	−	2.14698i
$736$	−2.54696e20	−	4.42088e21i	−0.0802487	−	1.39292i
$737$		−	2.28565e21i		−	0.712859i
$738$	−2.03209e21	−	2.94131e21i	−0.627364	−	0.908068i
$739$		−	9.25192e20i		−	0.282747i	−0.989956	−	0.141374i	$-0.954848\pi$
$739$		−	9.25192e20i		−	0.282747i	0.989956	−	0.141374i	$-0.0451519\pi$
$740$	3.52003e21	+	4.61754e21i	1.06490	+	1.39692i
$741$	−9.24713e19	−	6.58790e20i	−0.0276930	−	0.197293i
$742$	−8.79400e21	+	2.96967e21i	−2.60710	+	0.880398i
$743$	−5.40289e21			−1.58566			−0.792830	−	0.609443i	$-0.791393\pi$
$743$	−5.40289e21			−1.58566			−0.792830	+	0.609443i	$0.791393\pi$
$744$	−2.36555e21	−	1.15537e21i	−0.687283	−	0.335678i
$745$	5.50392e21			1.58307
$746$	6.85709e20	−	2.31559e20i	0.195253	−	0.0659357i
$747$	−4.73424e20	+	1.35576e20i	−0.133458	+	0.0382189i
$748$	9.12787e20	+	1.19738e21i	0.254746	+	0.334173i
$749$		−	3.27750e20i		−	0.0905584i
$750$	−1.65921e21	−	3.30622e21i	−0.453882	−	0.904425i
$751$			7.63656e20i			0.206823i	0.994639	+	0.103411i	$0.0329758\pi$
$751$			7.63656e20i			0.206823i	−0.994639	+	0.103411i	$0.967024\pi$
$752$	−8.29587e20	+	3.01958e21i	−0.222448	+	0.809679i
$753$	−5.08956e21	+	7.14398e20i	−1.35120	+	0.189661i
$754$	−4.30158e19	−	1.27381e20i	−0.0113069	−	0.0334827i
$755$	−5.04325e21			−1.31253
$756$	−6.08402e21	−	3.33238e21i	−1.56775	−	0.858699i
$757$	1.15431e21			0.294513			0.147256	−	0.989098i	$-0.452956\pi$
$757$	1.15431e21			0.294513			0.147256	+	0.989098i	$0.452956\pi$
$758$	−7.36745e20	−	2.18170e21i	−0.186122	−	0.551158i
$759$	3.73986e21	−	5.24946e20i	0.935496	−	0.131311i
$760$	2.45909e21	−	3.64279e21i	0.609079	−	0.902261i
$761$		−	3.07416e21i		−	0.753949i	−0.926224	−	0.376975i	$-0.876964\pi$
$761$		−	3.07416e21i		−	0.753949i	0.926224	−	0.376975i	$-0.123036\pi$
$762$	−1.44149e21	−	2.87238e21i	−0.350066	−	0.697556i
$763$			3.31540e21i			0.797262i
$764$	3.83057e21	−	2.92011e21i	0.912143	−	0.695342i
$765$	2.49893e21	−	7.15626e20i	0.589242	−	0.168743i
$766$	1.20415e21	−	4.06632e20i	0.281167	−	0.0949481i
$767$	4.72077e19			0.0109156
$768$	4.02796e21	+	1.68776e21i	0.922307	+	0.386457i
$769$	2.51814e21			0.570995			0.285498	−	0.958379i	$-0.407841\pi$
$769$	2.51814e21			0.570995			0.285498	+	0.958379i	$0.407841\pi$
$770$	−5.04316e21	+	1.70304e21i	−1.13246	+	0.382423i
$771$	7.99419e20	+	5.69528e21i	0.177773	+	1.26650i
$772$	4.66286e21	−	3.55458e21i	1.02689	−	0.782815i
$773$		−	2.45966e21i		−	0.536450i	−0.963356	−	0.268225i	$-0.913563\pi$
$773$		−	2.45966e21i		−	0.536450i	0.963356	−	0.268225i	$-0.0864370\pi$
$774$	1.11607e21	+	1.61544e21i	0.241065	+	0.348925i
$775$		−	8.80120e19i		−	0.0188269i
$776$	3.01965e21	−	4.47317e21i	0.639725	−	0.947660i
$777$	2.10619e21	+	1.50051e22i	0.441917	+	3.14834i
$778$	1.64293e21	+	4.86517e21i	0.341408	+	1.01100i
$779$	5.91107e21			1.21656
$780$	−6.22558e20	−	6.15878e20i	−0.126902	−	0.125541i
$781$	1.14833e20			0.0231837
$782$	1.38544e21	+	4.10267e21i	0.277037	+	0.820381i
$783$	4.01075e20	+	9.02083e20i	0.0794351	+	0.178663i
$784$	−2.96456e21	+	1.07906e22i	−0.581555	+	2.11678i
$785$			3.43167e21i			0.666781i
$786$	−5.98897e21	+	3.00554e21i	−1.15261	+	0.578433i
$787$		−	2.62038e21i		−	0.499521i	−0.968308	−	0.249761i	$-0.919648\pi$
$787$		−	2.62038e21i		−	0.499521i	0.968308	−	0.249761i	$-0.0803520\pi$
$788$	1.37645e21	+	1.80562e21i	0.259905	+	0.340941i
$789$	−9.43296e20	+	1.32406e20i	−0.176429	+	0.0247645i
$790$	−4.62191e21	+	1.56079e21i	−0.856285	+	0.289161i
$791$	−1.03053e21			−0.189120
$792$	−1.15350e21	+	3.54142e21i	−0.209691	+	0.643782i
$793$	4.42022e20			0.0795966
$794$	−1.69435e21	+	5.72168e20i	−0.302237	+	0.102063i
$795$	8.52044e21	−	1.19597e21i	1.50560	−	0.211333i
$796$	−3.86245e20	−	5.06672e20i	−0.0676106	−	0.0886909i
$797$		−	5.96139e21i		−	1.03374i	−0.856065	−	0.516868i	$-0.827098\pi$
$797$		−	5.96139e21i		−	1.03374i	0.856065	−	0.516868i	$-0.172902\pi$
$798$	1.02512e22	−	5.14454e21i	1.76098	−	0.883740i
$799$		−	3.06222e21i		−	0.521117i
$800$	8.39761e18	+	1.45761e20i	0.00141573	+	0.0245735i
$801$	−2.09141e21	−	7.30310e21i	−0.349297	−	1.21973i
$802$	−3.18092e21	−	9.41956e21i	−0.526314	−	1.55856i
$803$	1.44308e21			0.236550
$804$	4.60898e21	+	4.55953e21i	0.748487	+	0.740456i
$805$	−1.53092e22			−2.46310
$806$	−2.77488e20	−	8.21716e20i	−0.0442314	−	0.130981i
$807$	1.80164e20	+	1.28354e21i	0.0284523	+	0.202702i
$808$	3.06848e20	+	2.07140e20i	0.0480107	+	0.0324100i
$809$			6.62559e21i			1.02710i	0.858061	+	0.513548i	$0.171669\pi$
$809$			6.62559e21i			1.02710i	−0.858061	+	0.513548i	$0.828331\pi$
$810$	4.97027e21	+	4.07972e21i	0.763383	+	0.626604i
$811$		−	1.95861e21i		−	0.298051i	−0.988833	−	0.149025i	$-0.952386\pi$
$811$		−	1.95861e21i		−	0.298051i	0.988833	−	0.149025i	$-0.0476136\pi$
$812$	1.84349e21	−	1.40532e21i	0.277952	−	0.211888i
$813$	−1.28097e21	−	9.12594e21i	−0.191363	−	1.36332i
$814$	7.70789e21	−	2.60290e21i	1.14091	−	0.385278i
$815$	−4.07549e21			−0.597720
$816$	−4.23538e21	−	5.47978e20i	−0.615483	−	0.0796319i
$817$	−3.24649e21			−0.467465
$818$	2.94206e21	−	9.93513e20i	0.419761	−	0.141750i
$819$	−6.29162e20	−	2.19700e21i	−0.0889473	−	0.310600i
$820$	6.18818e21	−	4.71736e21i	0.866880	−	0.660838i
$821$			8.01561e21i			1.11266i	0.830961	+	0.556330i	$0.187791\pi$
$821$			8.01561e21i			1.11266i	−0.830961	+	0.556330i	$0.812209\pi$
$822$	−3.63411e20	−	7.24148e20i	−0.0499872	−	0.0996067i
$823$		−	8.41854e21i		−	1.14746i	−0.819044	−	0.573731i	$-0.805496\pi$
$823$		−	8.41854e21i		−	1.14746i	0.819044	−	0.573731i	$-0.194504\pi$
$824$	4.48344e21	+	3.02658e21i	0.605560	+	0.408788i
$825$	−1.23307e20	+	1.73081e19i	−0.0165038	+	0.00231656i
$826$	2.60407e20	+	7.71137e20i	0.0345385	+	0.102278i
$827$	−6.66388e21			−0.875862			−0.437931	−	0.899008i	$-0.644289\pi$
$827$	−6.66388e21			−0.875862			−0.437931	+	0.899008i	$0.644289\pi$
$828$	−6.40190e21	+	8.58855e21i	−0.833837	+	1.11865i
$829$	−4.09211e21			−0.528188			−0.264094	−	0.964497i	$-0.585073\pi$
$829$	−4.09211e21			−0.528188			−0.264094	+	0.964497i	$0.585073\pi$
$830$	−3.42932e20	−	1.01551e21i	−0.0438654	−	0.129897i
$831$	−1.12793e22	+	1.58323e21i	−1.42980	+	0.200695i
$832$	5.37966e20	+	1.33441e21i	0.0675818	+	0.167635i
$833$		−	1.09430e22i		−	1.36238i
$834$	5.66080e21	+	1.12800e22i	0.698445	+	1.39175i
$835$			1.10675e22i			1.35332i
$836$	−3.73348e21	−	4.89754e21i	−0.452446	−	0.593514i
$837$	2.58727e21	+	5.81919e21i	0.310743	+	0.698911i
$838$	−5.52797e21	+	1.86676e21i	−0.658014	+	0.222207i
$839$	−2.50195e21			−0.295164			−0.147582	−	0.989050i	$-0.547149\pi$
$839$	−2.50195e21			−0.295164			−0.147582	+	0.989050i	$0.547149\pi$
$840$	6.62619e21	−	1.35668e22i	0.774763	−	1.58629i
$841$	8.29929e21			0.961770
$842$	−4.70111e21	+	1.58753e21i	−0.539957	+	0.182340i
$843$	−9.57495e20	−	6.82145e21i	−0.109001	−	0.776551i
$844$	4.25636e21	+	5.58345e21i	0.480253	+	0.629990i
$845$			8.54257e21i			0.955352i
$846$	6.23241e21	−	4.30583e21i	0.690841	−	0.477287i
$847$		−	8.81117e21i		−	0.968073i
$848$	−1.36309e22	−	3.74490e21i	−1.48442	−	0.407822i
$849$	−6.33642e20	−	4.51424e21i	−0.0683969	−	0.487278i
$850$	−4.56796e19	−	1.35270e20i	−0.00488742	−	0.0144730i
$851$	2.33983e22			2.48149
$852$	−2.29073e20	+	2.31558e20i	−0.0240812	+	0.0243424i
$853$	−1.30947e22			−1.36451			−0.682255	−	0.731114i	$-0.739001\pi$
$853$	−1.30947e22			−1.36451			−0.682255	+	0.731114i	$0.739001\pi$
$854$	2.43828e21	+	7.22041e21i	0.251855	+	0.745809i
$855$	−1.02211e22	+	2.92705e21i	−1.04653	+	0.299699i
$856$	2.79278e20	−	4.13710e20i	0.0283455	−	0.0419897i
$857$		−	1.78356e22i		−	1.79446i	−0.441568	−	0.897228i	$-0.645578\pi$
$857$		−	1.78356e22i		−	1.79446i	0.441568	−	0.897228i	$-0.354422\pi$
$858$	−1.09668e21	+	5.50364e20i	−0.109377	+	0.0548903i
$859$			1.00607e22i			0.994671i	0.867558	+	0.497336i	$0.165688\pi$
$859$			1.00607e22i			0.994671i	−0.867558	+	0.497336i	$0.834312\pi$
$860$	−3.39869e21	+	2.59088e21i	−0.333099	+	0.253927i
$861$	2.01090e22	−	2.82261e21i	1.95374	−	0.274238i
$862$	−1.31194e22	+	4.43034e21i	−1.26360	+	0.426710i
$863$	−4.09577e21			−0.391070			−0.195535	−	0.980697i	$-0.562644\pi$
$863$	−4.09577e21			−0.391070			−0.195535	+	0.980697i	$0.562644\pi$
$864$	−4.84015e21	−	9.39062e21i	−0.458148	−	0.888876i
$865$	−5.91761e21			−0.555298
$866$	−1.52674e21	+	5.15568e20i	−0.142030	+	0.0479625i
$867$	−6.60189e21	+	9.26676e20i	−0.608871	+	0.0854643i
$868$	1.18920e22	−	9.06551e21i	1.08732	−	0.828885i
$869$			6.83537e21i			0.619604i
$870$	−1.92048e21	+	9.63786e20i	−0.172590	+	0.0866136i
$871$			2.13586e21i			0.190299i
$872$	−2.82507e21	+	4.18493e21i	−0.249549	+	0.369671i
$873$	−1.25511e22	+	3.59428e21i	−1.09919	+	0.314778i
$874$	−5.66673e21	−	1.67807e22i	−0.492036	−	1.45705i
$875$	2.10116e22			1.80883
$876$	−2.87872e21	+	2.90994e21i	−0.245708	+	0.248373i
$877$	1.69987e22			1.43853			0.719266	−	0.694734i	$-0.244478\pi$
$877$	1.69987e22			1.43853			0.719266	+	0.694734i	$0.244478\pi$
$878$	−3.28190e21	−	9.71859e21i	−0.275370	−	0.815444i
$879$	2.36006e21	+	1.68137e22i	0.196339	+	1.39877i
$880$	−7.81702e21	−	2.14762e21i	−0.644795	−	0.177148i
$881$			1.17037e22i			0.957202i	0.878032	+	0.478601i	$0.158856\pi$
$881$			1.17037e22i			0.957202i	−0.878032	+	0.478601i	$0.841144\pi$
$882$	2.22718e22	−	1.53871e22i	1.80609	−	1.24779i
$883$		−	8.92795e21i		−	0.717871i	−0.933362	−	0.358936i	$-0.883140\pi$
$883$		−	8.92795e21i		−	0.717871i	0.933362	−	0.358936i	$-0.116860\pi$
$884$	−8.52967e20	−	1.11891e21i	−0.0680049	−	0.0892081i
$885$	−1.04874e20	−	7.47149e20i	−0.00829072	−	0.0590653i
$886$	−1.54057e22	+	5.20241e21i	−1.20762	+	0.407804i
$887$	−2.45524e21			−0.190839			−0.0954196	−	0.995437i	$-0.530419\pi$
$887$	−2.45524e21			−0.190839			−0.0954196	+	0.995437i	$0.530419\pi$
$888$	−1.01274e22	+	2.07352e22i	−0.780547	+	1.59813i
$889$	1.82544e22			1.39510
$890$	1.56654e22	−	5.29011e21i	1.18718	−	0.400903i
$891$	7.64406e21	−	4.76923e21i	0.574436	−	0.358398i
$892$	−3.14779e21	−	4.12924e21i	−0.234568	−	0.307704i
$893$			1.25251e22i			0.925539i
$894$	9.81155e21	+	1.95509e22i	0.718963	+	1.43264i
$895$		−	3.48506e21i		−	0.253243i
$896$	−1.88301e22	+	1.61485e22i	−1.35688	+	1.16365i
$897$	−3.49476e21	+	4.90543e20i	−0.249732	+	0.0350537i
$898$	7.05300e21	+	2.08859e22i	0.499806	+	1.48006i
$899$	−2.12811e21			−0.149553
$900$	2.11078e20	−	2.83174e20i	0.0147104	−	0.0197349i
$901$	1.38234e22			0.955384
$902$	−3.48827e21	−	1.03297e22i	−0.239090	−	0.708010i
$903$	−1.10443e22	+	1.55024e21i	−0.750727	+	0.105376i
$904$	−1.30081e21	−	8.78124e20i	−0.0876903	−	0.0591960i
$905$			1.96772e22i			1.31552i
$906$	−8.99033e21	−	1.79145e22i	−0.596093	−	1.18780i
$907$		−	1.52946e22i		−	1.00574i	−0.864363	−	0.502869i	$-0.832278\pi$
$907$		−	1.52946e22i		−	1.00574i	0.864363	−	0.502869i	$-0.167722\pi$
$908$	1.49982e22	−	1.14334e22i	0.978130	−	0.745646i
$909$	−2.46558e20	−	8.60970e20i	−0.0159474	−	0.0556876i
$910$	4.71266e21	−	1.59143e21i	0.302312	−	0.102089i
$911$	−5.01687e21			−0.319187			−0.159593	−	0.987183i	$-0.551018\pi$
$911$	−5.01687e21			−0.319187			−0.159593	+	0.987183i	$0.551018\pi$
$912$	1.73235e22	+	2.24134e21i	1.09314	+	0.141432i
$913$	−1.50185e21			−0.0939931
$914$	1.71633e22	−	5.79592e21i	1.06538	−	0.359771i
$915$	−9.81968e20	−	6.99580e21i	−0.0604559	−	0.430704i
$916$	−8.69117e21	+	6.62543e21i	−0.530716	+	0.404574i
$917$		−	3.80609e22i		−	2.30520i
$918$	6.99675e21	+	7.60095e21i	0.420316	+	0.456612i
$919$			3.31683e22i			1.97632i	0.153424	+	0.988160i	$0.450970\pi$
$919$			3.31683e22i			1.97632i	−0.153424	+	0.988160i	$0.549030\pi$
$920$	−1.93243e22	−	1.30451e22i	−1.14208	−	0.770969i
$921$	−1.26668e21	−	9.02416e21i	−0.0742539	−	0.529005i
$922$	2.77965e21	+	8.23130e21i	0.161625	+	0.478615i
$923$	−1.07307e20			−0.00618892
$924$	−1.50397e22	−	1.48783e22i	−0.860397	−	0.851165i
$925$	−7.71468e20			−0.0437779
$926$	2.14380e21	+	6.34836e21i	0.120671	+	0.357338i
$927$	−3.60253e21	−	1.25799e22i	−0.201145	−	0.702389i
$928$	3.52447e21	−	2.03052e20i	0.195202	−	0.0112460i
$929$			6.80029e20i			0.0373603i	0.999826	+	0.0186801i	$0.00594642\pi$
$929$			6.80029e20i			0.0373603i	−0.999826	+	0.0186801i	$0.994054\pi$
$930$	−1.23887e22	+	6.21722e21i	−0.675156	+	0.338824i
$931$			4.47589e22i			2.41967i
$932$	−1.68953e21	−	2.21630e21i	−0.0906037	−	0.118853i
$933$	1.34342e22	−	1.88569e21i	0.714658	−	0.100313i
$934$	1.39491e22	−	4.71052e21i	0.736115	−	0.248581i
$935$	7.92740e21			0.414996
$936$	1.07791e21	−	3.30933e21i	0.0559774	−	0.171859i
$937$	−2.56967e21			−0.132382			−0.0661912	−	0.997807i	$-0.521085\pi$
$937$	−2.56967e21			−0.132382			−0.0661912	+	0.997807i	$0.521085\pi$
$938$	−3.48892e22	+	1.17818e22i	−1.78308	+	0.602132i
$939$	−1.52489e21	+	2.14042e20i	−0.0773120	+	0.0108519i
$940$	9.99571e21	+	1.31123e22i	0.502753	+	0.659506i
$941$			2.47202e22i			1.23347i	0.787169	+	0.616737i	$0.211546\pi$
$941$			2.47202e22i			1.23347i	−0.787169	+	0.616737i	$0.788454\pi$
$942$	−1.21899e22	+	6.11746e21i	−0.603419	+	0.302823i
$943$		−	3.13571e22i		−	1.53992i
$944$	−3.28386e20	+	1.19528e21i	−0.0159991	+	0.0582344i
$945$	−3.33739e22	+	1.48384e22i	−1.61312	+	0.717211i
$946$	1.91584e21	+	5.67332e21i	0.0918703	+	0.272053i
$947$	−2.05961e21			−0.0979852			−0.0489926	−	0.998799i	$-0.515601\pi$
$947$	−2.05961e21			−0.0979852			−0.0489926	+	0.998799i	$0.515601\pi$
$948$	−1.37834e22	−	1.36355e22i	−0.650571	−	0.643590i
$949$	−1.34850e21			−0.0631474
$950$	1.86839e20	+	5.53280e20i	0.00868040	+	0.0257050i
$951$	−2.90075e21	−	2.06657e22i	−0.133708	−	0.952569i
$952$	1.35723e22	−	2.01053e22i	0.620691	−	0.919463i
$953$		−	3.83537e22i		−	1.74025i	−0.492833	−	0.870124i	$-0.664039\pi$
$953$		−	3.83537e22i		−	1.74025i	0.492833	−	0.870124i	$-0.335961\pi$
$954$	1.94372e22	+	2.81341e22i	0.875028	+	1.26655i
$955$		−	2.53606e22i		−	1.13275i
$956$	1.79111e20	−	1.36539e20i	0.00793757	−	0.00605095i
$957$	4.18505e20	+	2.98154e21i	0.0184018	+	0.131100i
$958$	3.57639e22	−	1.20772e22i	1.56028	−	0.526897i
$959$	4.60208e21			0.199212
$960$	1.99244e22	−	1.14787e22i	0.855758	−	0.493015i
$961$	9.73720e21			0.414962
$962$	−7.20275e21	+	2.43232e21i	−0.304569	+	0.102851i
$963$	−1.16081e21	+	3.32424e20i	−0.0487039	+	0.0139475i
$964$	−1.45265e22	+	1.10738e22i	−0.604759	+	0.461018i
$965$		−	3.08709e22i		−	1.27525i
$966$	−2.72908e22	−	5.43809e22i	−1.11863	−	2.22904i
$967$			1.40018e22i			0.569490i	0.958603	+	0.284745i	$0.0919089\pi$
$967$			1.40018e22i			0.569490i	−0.958603	+	0.284745i	$0.908091\pi$
$968$	7.50807e21	−	1.11221e22i	0.303014	−	0.448871i
$969$	−1.69158e22	+	2.37439e21i	−0.677430	+	0.0950877i
$970$	−9.09153e21	−	2.69225e22i	−0.361284	−	1.06986i
$971$	−6.81068e21			−0.268563			−0.134282	−	0.990943i	$-0.542873\pi$
$971$	−6.81068e21			−0.268563			−0.134282	+	0.990943i	$0.542873\pi$
$972$	−5.63167e21	+	2.49280e22i	−0.220364	+	0.975418i
$973$	−7.16860e22			−2.78348
$974$	−1.38849e21	−	4.11170e21i	−0.0534997	−	0.158427i
$975$	1.15226e20	−	1.61738e19i	0.00440572	−	0.000618411i
$976$	−3.07479e21	+	1.11918e22i	−0.116665	+	0.424646i
$977$			4.99334e22i			1.88010i	0.341033	+	0.940051i	$0.389223\pi$
$977$			4.99334e22i			1.88010i	−0.341033	+	0.940051i	$0.610777\pi$
$978$	−7.26516e21	−	1.44769e22i	−0.271459	−	0.540921i
$979$		−	2.31677e22i		−	0.859040i
$980$	3.57201e22	+	4.68572e22i	1.31437	+	1.72417i
$981$	1.17423e22	−	3.36268e21i	0.428781	−	0.122791i
$982$	−4.20528e21	+	1.42009e21i	−0.152391	+	0.0514613i
$983$	−5.31239e21			−0.191046			−0.0955231	−	0.995427i	$-0.530452\pi$
$983$	−5.31239e21			−0.191046			−0.0955231	+	0.995427i	$0.530452\pi$
$984$	2.77883e22	+	1.35722e22i	0.991741	+	0.484379i
$985$	1.19543e22			0.423400
$986$	−3.27078e21	+	1.10452e21i	−0.114967	+	0.0388237i
$987$	5.98089e21	+	4.26095e22i	0.208635	+	1.48637i
$988$	3.48881e21	+	4.57658e21i	0.120781	+	0.158440i
$989$			1.72221e22i			0.591716i
$990$	1.11468e22	+	1.61343e22i	0.380091	+	0.550157i
$991$			6.64267e21i			0.224797i	0.993663	+	0.112399i	$0.0358533\pi$
$991$			6.64267e21i			0.224797i	−0.993663	+	0.112399i	$0.964147\pi$
$992$	2.27358e22	−	1.30985e21i	0.763611	−	0.0439932i
$993$	−4.76281e21	−	3.39315e22i	−0.158761	−	1.13106i
$994$	−5.91927e20	−	1.75286e21i	−0.0195826	−	0.0579893i
$995$	−3.35447e21			−0.110141
$996$	2.99596e21	−	3.02846e21i	0.0976318	−	0.0986908i
$997$	−2.20385e22			−0.712801			−0.356400	−	0.934333i	$-0.615996\pi$
$997$	−2.20385e22			−0.712801			−0.356400	+	0.934333i	$0.615996\pi$
$998$	1.49513e22	+	4.42747e22i	0.479953	+	1.42127i
$999$	5.10081e22	−	2.26787e22i	1.62517	−	0.722565i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.16.b.a.11.4	yes	28
3.2	odd	2	inner	12.16.b.a.11.25	yes	28
4.3	odd	2	inner	12.16.b.a.11.26	yes	28
12.11	even	2	inner	12.16.b.a.11.3	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.16.b.a.11.3	✓	28	12.11	even	2	inner
12.16.b.a.11.4	yes	28	1.1	even	1	trivial
12.16.b.a.11.25	yes	28	3.2	odd	2	inner
12.16.b.a.11.26	yes	28	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-171.504 + 57.9158i) q^{2} +(-3751.22 + 526.541i) q^{3} +(26059.5 - 19865.6i) q^{4} -172529. i q^{5} +(612856. - 307559. i) q^{6} +3.89480e6i q^{7} +(-3.31879e6 + 4.91630e6i) q^{8} +(1.37944e7 - 3.95035e6i) q^{9} +O(q^{10})\)	\(q+(-171.504 + 57.9158i) q^{2} +(-3751.22 + 526.541i) q^{3} +(26059.5 - 19865.6i) q^{4} -172529. i q^{5} +(612856. - 307559. i) q^{6} +3.89480e6i q^{7} +(-3.31879e6 + 4.91630e6i) q^{8} +(1.37944e7 - 3.95035e6i) q^{9} +(9.99218e6 + 2.95896e7i) q^{10} +4.37602e7 q^{11} +(-8.72949e7 + 8.82418e7i) q^{12} -4.08923e7 q^{13} +(-2.25570e8 - 6.67975e8i) q^{14} +(9.08439e7 + 6.47196e8i) q^{15} +(2.84455e8 - 1.03538e9i) q^{16} +1.05000e9i q^{17} +(-2.13702e9 + 1.47642e9i) q^{18} -4.29470e9i q^{19} +(-3.42741e9 - 4.49603e9i) q^{20} +(-2.05077e9 - 1.46103e10i) q^{21} +(-7.50507e9 + 2.53441e9i) q^{22} -2.27826e10 q^{23} +(9.86087e9 - 2.01896e10i) q^{24} +7.51168e8 q^{25} +(7.01322e9 - 2.36831e9i) q^{26} +(-4.96659e10 + 2.20819e10i) q^{27} +(7.73726e10 + 1.01497e11i) q^{28} -1.81630e10i q^{29} +(-5.30630e10 - 1.05736e11i) q^{30} -1.17167e11i q^{31} +(1.11794e10 + 1.94046e11i) q^{32} +(-1.64154e11 + 2.30416e10i) q^{33} +(-6.08114e10 - 1.80079e11i) q^{34} +6.71968e11 q^{35} +(2.81000e11 - 3.76979e11i) q^{36} -1.02702e12 q^{37} +(2.48731e11 + 7.36559e11i) q^{38} +(1.53396e11 - 2.15315e10i) q^{39} +(8.48207e11 + 5.72589e11i) q^{40} +1.37636e12i q^{41} +(1.19788e12 + 2.38695e12i) q^{42} -7.55931e11i q^{43} +(1.14037e12 - 8.69324e11i) q^{44} +(-6.81551e11 - 2.37994e12i) q^{45} +(3.90731e12 - 1.31947e12i) q^{46} -2.91641e12 q^{47} +(-5.21886e11 + 4.03371e12i) q^{48} -1.04219e13 q^{49} +(-1.28829e11 + 4.35045e10i) q^{50} +(-5.52866e11 - 3.93877e12i) q^{51} +(-1.06563e12 + 8.12352e11i) q^{52} -1.31652e13i q^{53} +(7.23902e12 - 6.66359e12i) q^{54} -7.54993e12i q^{55} +(-1.91480e13 - 1.29260e13i) q^{56} +(2.26133e12 + 1.61104e13i) q^{57} +(1.05193e12 + 3.11504e12i) q^{58} -1.15444e12 q^{59} +(1.52243e13 + 1.50609e13i) q^{60} -1.08094e13 q^{61} +(6.78581e12 + 2.00946e13i) q^{62} +(1.53858e13 + 5.37265e13i) q^{63} +(-1.31557e13 - 3.26323e13i) q^{64} +7.05513e12i q^{65} +(2.68187e13 - 1.34589e13i) q^{66} -5.22313e13i q^{67} +(2.08588e13 + 2.73624e13i) q^{68} +(8.54625e13 - 1.19960e13i) q^{69} +(-1.15245e14 + 3.89175e13i) q^{70} +2.62413e12 q^{71} +(-2.63597e13 + 8.09279e13i) q^{72} +3.29769e13 q^{73} +(1.76139e14 - 5.94810e13i) q^{74} +(-2.81780e12 + 3.95521e11i) q^{75} +(-8.53168e13 - 1.11918e14i) q^{76} +1.70437e14i q^{77} +(-2.50611e13 + 1.25768e13i) q^{78} +1.56201e14i q^{79} +(-1.78633e14 - 4.90769e13i) q^{80} +(1.74681e14 - 1.08985e14i) q^{81} +(-7.97132e13 - 2.36053e14i) q^{82} -3.43200e13 q^{83} +(-3.43684e14 - 3.39996e14i) q^{84} +1.81155e14 q^{85} +(4.37804e13 + 1.29645e14i) q^{86} +(9.56359e12 + 6.81336e13i) q^{87} +(-1.45231e14 + 2.15138e14i) q^{88} -5.29425e14i q^{89} +(2.54725e14 + 3.68698e14i) q^{90} -1.59268e14i q^{91} +(-5.93703e14 + 4.52590e14i) q^{92} +(6.16932e13 + 4.39519e14i) q^{93} +(5.00177e14 - 1.68906e14i) q^{94} -7.40962e14 q^{95} +(-1.44110e14 - 7.22024e14i) q^{96} -9.09865e14 q^{97} +(1.78740e15 - 6.03593e14i) q^{98} +(6.03647e14 - 1.72868e14i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 26968 q^{4} + 823656 q^{6} - 3812052 q^{9}+O(q^{10}) \) 28 * q + 26968 * q^4 + 823656 * q^6 - 3812052 * q^9	\( 28 q + 26968 q^{4} + 823656 q^{6} - 3812052 q^{9} - 43831600 q^{10} - 226414248 q^{12} + 124527272 q^{13} - 1459325408 q^{16} - 4234777584 q^{18} - 7261350648 q^{21} - 2533670160 q^{22} - 18487781856 q^{24} - 146804950740 q^{25} + 5481093840 q^{28} + 8237058960 q^{30} + 204574669728 q^{33} + 450165745472 q^{34} + 232631927160 q^{36} + 386069193224 q^{37} + 1945471012160 q^{40} + 1938106219632 q^{42} - 5007113912640 q^{45} + 2270790222432 q^{46} + 5846474725152 q^{48} - 18480860963084 q^{49} - 6113229405424 q^{52} + 1626598700568 q^{54} + 8085872464056 q^{57} - 19395437098192 q^{58} - 10924219377600 q^{60} - 16392792556696 q^{61} + 21633892829056 q^{64} + 4928819126448 q^{66} + 137029869973056 q^{69} + 91772543171040 q^{70} + 66924493142592 q^{72} + 158451626683736 q^{73} - 205265768291280 q^{76} + 58364283489648 q^{78} + 116126816635836 q^{81} - 750029796726880 q^{82} - 92605433207856 q^{84} - 30099357052160 q^{85} - 619691835246912 q^{88} - 471443548913520 q^{90} - 777661615138584 q^{93} + 13\!\cdots\!00 q^{94}+ \cdots - 824166397720648 q^{97}+O(q^{100}) \) 28 * q + 26968 * q^4 + 823656 * q^6 - 3812052 * q^9 - 43831600 * q^10 - 226414248 * q^12 + 124527272 * q^13 - 1459325408 * q^16 - 4234777584 * q^18 - 7261350648 * q^21 - 2533670160 * q^22 - 18487781856 * q^24 - 146804950740 * q^25 + 5481093840 * q^28 + 8237058960 * q^30 + 204574669728 * q^33 + 450165745472 * q^34 + 232631927160 * q^36 + 386069193224 * q^37 + 1945471012160 * q^40 + 1938106219632 * q^42 - 5007113912640 * q^45 + 2270790222432 * q^46 + 5846474725152 * q^48 - 18480860963084 * q^49 - 6113229405424 * q^52 + 1626598700568 * q^54 + 8085872464056 * q^57 - 19395437098192 * q^58 - 10924219377600 * q^60 - 16392792556696 * q^61 + 21633892829056 * q^64 + 4928819126448 * q^66 + 137029869973056 * q^69 + 91772543171040 * q^70 + 66924493142592 * q^72 + 158451626683736 * q^73 - 205265768291280 * q^76 + 58364283489648 * q^78 + 116126816635836 * q^81 - 750029796726880 * q^82 - 92605433207856 * q^84 - 30099357052160 * q^85 - 619691835246912 * q^88 - 471443548913520 * q^90 - 777661615138584 * q^93 + 1301107064491200 * q^94 + 525428335287168 * q^96 - 824166397720648 * q^97

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