LMFDB - Embedded newform 95.11.j.a.31.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [95,11,Mod(31,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("95.31"); S:= CuspForms(chi, 11); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 11, names="a")

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	95.j (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$60.3589390040$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.10
Character	$\chi$	$=$	95.31
Dual form			95.11.j.a.46.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-44.7004 + 25.8078i) q^{2} +(159.805 - 92.2637i) q^{3} +(820.085 - 1420.43i) q^{4} +(-698.771 - 1210.31i) q^{5} +(-4762.24 + 8248.45i) q^{6} +20604.6 q^{7} +31804.0i q^{8} +(-12499.3 + 21649.5i) q^{9} +(62470.7 + 36067.5i) q^{10} +206573. q^{11} -302656. i q^{12} +(450241. + 259947. i) q^{13} +(-921036. + 531760. i) q^{14} +(-223335. - 128942. i) q^{15} +(18976.8 + 32868.8i) q^{16} +(-753528. - 1.30515e6i) q^{17} -1.29032e6i q^{18} +(885783. + 2.31224e6i) q^{19} -2.29221e6 q^{20} +(3.29273e6 - 1.90106e6i) q^{21} +(-9.23391e6 + 5.33120e6i) q^{22} +(-4.75845e6 + 8.24188e6i) q^{23} +(2.93435e6 + 5.08244e6i) q^{24} +(-976562. + 1.69146e6i) q^{25} -2.68346e7 q^{26} +1.55091e7i q^{27} +(1.68975e7 - 2.92674e7i) q^{28} +(4.96888e6 + 2.86878e6i) q^{29} +1.33109e7 q^{30} -1.46599e7i q^{31} +(-2.99006e7 - 1.72631e7i) q^{32} +(3.30115e7 - 1.90592e7i) q^{33} +(6.73661e7 + 3.88938e7i) q^{34} +(-1.43979e7 - 2.49379e7i) q^{35} +(2.05010e7 + 3.55088e7i) q^{36} +1.65304e7i q^{37} +(-9.92687e7 - 8.04980e7i) q^{38} +9.59346e7 q^{39} +(3.84926e7 - 2.22237e7i) q^{40} +(1.06529e8 - 6.15047e7i) q^{41} +(-9.81243e7 + 1.69956e8i) q^{42} +(-2.67095e7 - 4.62623e7i) q^{43} +(1.69408e8 - 2.93423e8i) q^{44} +3.49367e7 q^{45} -4.91220e8i q^{46} +(7.47709e7 - 1.29507e8i) q^{47} +(6.06520e6 + 3.50174e6i) q^{48} +1.42076e8 q^{49} -1.00812e8i q^{50} +(-2.40836e8 - 1.39047e8i) q^{51} +(7.38472e8 - 4.26357e8i) q^{52} +(1.52988e8 + 8.83277e7i) q^{53} +(-4.00255e8 - 6.93263e8i) q^{54} +(-1.44348e8 - 2.50017e8i) q^{55} +6.55309e8i q^{56} +(3.54889e8 + 2.87783e8i) q^{57} -2.96148e8 q^{58} +(-1.11731e9 + 6.45077e8i) q^{59} +(-3.66307e8 + 2.11487e8i) q^{60} +(-4.07302e8 + 7.05467e8i) q^{61} +(3.78339e8 + 6.55303e8i) q^{62} +(-2.57544e8 + 4.46079e8i) q^{63} +1.74323e9 q^{64} -7.26573e8i q^{65} +(-9.83753e8 + 1.70391e9i) q^{66} +(6.51980e8 + 3.76421e8i) q^{67} -2.47183e9 q^{68} +1.75613e9i q^{69} +(1.28719e9 + 7.43157e8i) q^{70} +(1.59050e9 - 9.18273e8i) q^{71} +(-6.88539e8 - 3.97528e8i) q^{72} +(1.34744e9 + 2.33383e9i) q^{73} +(-4.26613e8 - 7.38916e8i) q^{74} +3.60405e8i q^{75} +(4.01079e9 + 6.38041e8i) q^{76} +4.25637e9 q^{77} +(-4.28831e9 + 2.47586e9i) q^{78} +(-2.37139e9 + 1.36912e9i) q^{79} +(2.65209e7 - 4.59356e7i) q^{80} +(6.92853e8 + 1.20006e9i) q^{81} +(-3.17460e9 + 5.49857e9i) q^{82} -3.96260e9 q^{83} -6.23612e9i q^{84} +(-1.05309e9 + 1.82400e9i) q^{85} +(2.38786e9 + 1.37863e9i) q^{86} +1.05874e9 q^{87} +6.56985e9i q^{88} +(6.37121e8 + 3.67842e8i) q^{89} +(-1.56168e9 + 9.01639e8i) q^{90} +(9.27705e9 + 5.35611e9i) q^{91} +(7.80466e9 + 1.35181e10i) q^{92} +(-1.35258e9 - 2.34273e9i) q^{93} +7.71869e9i q^{94} +(2.17956e9 - 2.68780e9i) q^{95} -6.37104e9 q^{96} +(-4.69861e9 + 2.71274e9i) q^{97} +(-6.35084e9 + 3.66666e9i) q^{98} +(-2.58203e9 + 4.47220e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 132 q^{3} + 37474 q^{4} - 1022 q^{6} - 76620 q^{7} + 1448988 q^{9} + 93750 q^{10} + 418144 q^{11} - 1256574 q^{13} + 612480 q^{14} - 20575630 q^{16} + 3635834 q^{17} + 10572814 q^{19} + 8494308 q^{21}+ \cdots - 8878413234 q^{99}+O(q^{100}) $ 136 * q - 132 * q^3 + 37474 * q^4 - 1022 * q^6 - 76620 * q^7 + 1448988 * q^9 + 93750 * q^10 + 418144 * q^11 - 1256574 * q^13 + 612480 * q^14 - 20575630 * q^16 + 3635834 * q^17 + 10572814 * q^19 + 8494308 * q^21 - 31311360 * q^22 - 11728554 * q^23 - 1627348 * q^24 - 132812500 * q^25 - 5280948 * q^26 - 81401852 * q^28 - 36928518 * q^29 + 79750000 * q^30 + 196574250 * q^32 + 359004150 * q^33 + 205341462 * q^34 + 19937500 * q^35 - 1128154804 * q^36 + 1584974 * q^38 + 224945180 * q^39 + 96000000 * q^40 + 1170402744 * q^41 + 173440898 * q^42 - 390292220 * q^43 - 49120052 * q^44 - 148625000 * q^45 - 445097680 * q^47 + 362033562 * q^48 + 3958185060 * q^49 + 995976516 * q^51 + 7766334 * q^52 + 815693040 * q^53 + 2049344062 * q^54 + 3831676392 * q^57 + 3983452220 * q^58 + 2842939668 * q^59 - 1389656250 * q^60 + 1929307508 * q^61 - 2885441744 * q^62 - 5022307122 * q^63 - 29425336368 * q^64 + 2939512012 * q^66 + 1891858296 * q^67 + 18554561860 * q^68 - 810562500 * q^70 - 8973340848 * q^71 + 7541812308 * q^72 + 4947578188 * q^73 - 23389998076 * q^74 + 15724739728 * q^76 - 5682818404 * q^77 - 10507817400 * q^78 + 16066927146 * q^79 + 3604750000 * q^80 - 43776877608 * q^81 - 13564413998 * q^82 + 2628386824 * q^83 - 2399750000 * q^85 + 38885030448 * q^86 + 12840668220 * q^87 - 35640122064 * q^89 + 3198281250 * q^90 + 4174912572 * q^91 - 23134882520 * q^92 - 36221884016 * q^93 - 1613500000 * q^95 + 13864395128 * q^96 - 23558943450 * q^97 + 31730410686 * q^98 - 8878413234 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−44.7004	+	25.8078i	−1.39689	+	0.806494i	−0.994065	−	0.108784i	$-0.965304\pi$
$2$	−44.7004	+	25.8078i	−1.39689	+	0.806494i	−0.402823	+	0.915278i	$0.631971\pi$
$3$	159.805	−	92.2637i	0.657635	−	0.379686i	−0.133740	−	0.991016i	$-0.542699\pi$
$3$	159.805	−	92.2637i	0.657635	−	0.379686i	0.791375	+	0.611331i	$0.209365\pi$
$4$	820.085	−	1420.43i	0.800864	−	1.38714i
$5$	−698.771	−	1210.31i	−0.223607	−	0.387298i
$5$	−698.771	−	1210.31i	−0.223607	−	0.387298i
$6$	−4762.24	+	8248.45i	−0.612429	+	1.06076i
$7$	20604.6			1.22596			0.612978	−	0.790100i	$-0.289972\pi$
$7$	20604.6			1.22596			0.612978	+	0.790100i	$0.289972\pi$
$8$			31804.0i			0.970580i
$9$	−12499.3	+	21649.5i	−0.211677	+	0.366636i
$10$	62470.7	+	36067.5i	0.624707	+	0.360675i
$11$	206573.			1.28266			0.641329	−	0.767266i	$-0.278383\pi$
$11$	206573.			1.28266			0.641329	+	0.767266i	$0.278383\pi$
$12$		−	302656.i		−	1.21631i
$13$	450241.	+	259947.i	1.21263	+	0.700112i	0.963331	−	0.268315i	$-0.0864666\pi$
$13$	450241.	+	259947.i	1.21263	+	0.700112i	0.249298	+	0.968427i	$0.419800\pi$
$14$	−921036.	+	531760.i	−1.71252	+	0.988725i
$15$	−223335.	−	128942.i	−0.294103	−	0.169801i
$16$	18976.8	+	32868.8i	0.0180977	+	0.0313462i
$17$	−753528.	−	1.30515e6i	−0.530707	−	0.919212i	−0.999358	−	0.0358283i	$-0.988593\pi$
$17$	−753528.	−	1.30515e6i	−0.530707	−	0.919212i	0.468651	−	0.883384i	$-0.344740\pi$
$18$		−	1.29032e6i		−	0.682865i
$19$	885783.	+	2.31224e6i	0.357733	+	0.933824i
$19$	885783.	+	2.31224e6i	0.357733	+	0.933824i
$20$	−2.29221e6			−0.716315
$21$	3.29273e6	−	1.90106e6i	0.806231	−	0.465478i
$22$	−9.23391e6	+	5.33120e6i	−1.79173	+	1.03446i
$23$	−4.75845e6	+	8.24188e6i	−0.739309	+	1.28052i	0.213497	+	0.976944i	$0.431515\pi$
$23$	−4.75845e6	+	8.24188e6i	−0.739309	+	1.28052i	−0.952807	+	0.303578i	$0.901819\pi$
$24$	2.93435e6	+	5.08244e6i	0.368515	+	0.638287i
$25$	−976562.	+	1.69146e6i	−0.100000	+	0.173205i
$26$	−2.68346e7			−2.25854
$27$			1.55091e7i			1.08086i
$28$	1.68975e7	−	2.92674e7i	0.981824	−	1.70057i
$29$	4.96888e6	+	2.86878e6i	0.242252	+	0.139865i	0.616212	−	0.787581i	$-0.288667\pi$
$29$	4.96888e6	+	2.86878e6i	0.242252	+	0.139865i	−0.373959	+	0.927445i	$0.622000\pi$
$30$	1.33109e7			0.547773
$31$		−	1.46599e7i		−	0.512062i	−0.966669	−	0.256031i	$-0.917585\pi$
$31$		−	1.46599e7i		−	0.512062i	0.966669	−	0.256031i	$-0.0824149\pi$
$32$	−2.99006e7	−	1.72631e7i	−0.891108	−	0.514481i
$33$	3.30115e7	−	1.90592e7i	0.843521	−	0.487007i
$34$	6.73661e7	+	3.88938e7i	1.48268	+	0.856024i
$35$	−1.43979e7	−	2.49379e7i	−0.274132	−	0.474810i
$36$	2.05010e7	+	3.55088e7i	0.339049	+	0.587251i
$37$			1.65304e7i			0.238383i	0.992871	+	0.119191i	$0.0380302\pi$
$37$			1.65304e7i			0.238383i	−0.992871	+	0.119191i	$0.961970\pi$
$38$	−9.92687e7	−	8.04980e7i	−1.25284	−	1.01594i
$39$	9.59346e7			1.06329
$40$	3.84926e7	−	2.22237e7i	0.375904	−	0.217028i
$41$	1.06529e8	−	6.15047e7i	0.919495	−	0.530871i	0.0360210	−	0.999351i	$-0.488532\pi$
$41$	1.06529e8	−	6.15047e7i	0.919495	−	0.530871i	0.883474	+	0.468480i	$0.155198\pi$
$42$	−9.81243e7	+	1.69956e8i	−0.750810	+	1.30044i
$43$	−2.67095e7	−	4.62623e7i	−0.181687	−	0.314691i	0.760768	−	0.649024i	$-0.224822\pi$
$43$	−2.67095e7	−	4.62623e7i	−0.181687	−	0.314691i	−0.942455	+	0.334333i	$0.891489\pi$
$44$	1.69408e8	−	2.93423e8i	1.02723	−	1.77922i
$45$	3.49367e7			0.189330
$46$		−	4.91220e8i		−	2.38499i
$47$	7.47709e7	−	1.29507e8i	0.326019	−	0.564682i	−0.655699	−	0.755023i	$-0.727626\pi$
$47$	7.47709e7	−	1.29507e8i	0.326019	−	0.564682i	0.981718	+	0.190340i	$0.0609592\pi$
$48$	6.06520e6	+	3.50174e6i	0.0238034	+	0.0137429i
$49$	1.42076e8			0.502967
$50$		−	1.00812e8i		−	0.322597i
$51$	−2.40836e8	−	1.39047e8i	−0.698024	−	0.403004i
$52$	7.38472e8	−	4.26357e8i	1.94230	−	1.12139i
$53$	1.52988e8	+	8.83277e7i	0.365829	+	0.211212i	0.671635	−	0.740882i	$-0.265592\pi$
$53$	1.52988e8	+	8.83277e7i	0.365829	+	0.211212i	−0.305806	+	0.952094i	$0.598926\pi$
$54$	−4.00255e8	−	6.93263e8i	−0.871703	−	1.50983i
$55$	−1.44348e8	−	2.50017e8i	−0.286811	−	0.496771i
$56$			6.55309e8i			1.18989i
$57$	3.54889e8	+	2.87783e8i	0.589818	+	0.478289i
$58$	−2.96148e8			−0.451199
$59$	−1.11731e9	+	6.45077e8i	−1.56283	+	0.902301i	−0.565862	+	0.824500i	$0.691457\pi$
$59$	−1.11731e9	+	6.45077e8i	−1.56283	+	0.902301i	−0.996969	+	0.0778013i	$0.975210\pi$
$60$	−3.66307e8	+	2.11487e8i	−0.471074	+	0.271975i
$61$	−4.07302e8	+	7.05467e8i	−0.482244	+	0.835271i	−0.999792	−	0.0203829i	$-0.993511\pi$
$61$	−4.07302e8	+	7.05467e8i	−0.482244	+	0.835271i	0.517548	+	0.855654i	$0.326845\pi$
$62$	3.78339e8	+	6.55303e8i	0.412975	+	0.715293i
$63$	−2.57544e8	+	4.46079e8i	−0.259507	+	0.449479i
$64$	1.74323e9			1.62351
$65$		−	7.26573e8i		−	0.626199i
$66$	−9.83753e8	+	1.70391e9i	−0.785536	+	1.36059i
$67$	6.51980e8	+	3.76421e8i	0.482903	+	0.278804i	0.721626	−	0.692284i	$-0.243395\pi$
$67$	6.51980e8	+	3.76421e8i	0.482903	+	0.278804i	−0.238722	+	0.971088i	$0.576729\pi$
$68$	−2.47183e9			−1.70010
$69$			1.75613e9i			1.12282i
$70$	1.28719e9	+	7.43157e8i	0.765863	+	0.442171i
$71$	1.59050e9	−	9.18273e8i	0.881537	−	0.508956i	0.0103724	−	0.999946i	$-0.496698\pi$
$71$	1.59050e9	−	9.18273e8i	0.881537	−	0.508956i	0.871165	+	0.490990i	$0.163365\pi$
$72$	−6.88539e8	−	3.97528e8i	−0.355849	−	0.205450i
$73$	1.34744e9	+	2.33383e9i	0.649973	+	1.12579i	0.983129	+	0.182914i	$0.0585531\pi$
$73$	1.34744e9	+	2.33383e9i	0.649973	+	1.12579i	−0.333156	+	0.942872i	$0.608114\pi$
$74$	−4.26613e8	−	7.38916e8i	−0.192254	−	0.332994i
$75$			3.60405e8i			0.151874i
$76$	4.01079e9	+	6.38041e8i	1.58184	+	0.251640i
$77$	4.25637e9			1.57248
$78$	−4.28831e9	+	2.47586e9i	−1.48530	+	0.857537i
$79$	−2.37139e9	+	1.36912e9i	−0.770667	+	0.444945i	−0.833113	−	0.553103i	$-0.813443\pi$
$79$	−2.37139e9	+	1.36912e9i	−0.770667	+	0.444945i	0.0624453	+	0.998048i	$0.480110\pi$
$80$	2.65209e7	−	4.59356e7i	0.00809354	−	0.0140184i
$81$	6.92853e8	+	1.20006e9i	0.198708	+	0.344173i
$82$	−3.17460e9	+	5.49857e9i	−0.856288	+	1.48313i
$83$	−3.96260e9			−1.00598			−0.502991	−	0.864292i	$-0.667767\pi$
$83$	−3.96260e9			−1.00598			−0.502991	+	0.864292i	$0.667767\pi$
$84$		−	6.23612e9i		−	1.49114i
$85$	−1.05309e9	+	1.82400e9i	−0.237339	+	0.411084i
$86$	2.38786e9	+	1.37863e9i	0.507593	+	0.293059i
$87$	1.05874e9			0.212418
$88$			6.56985e9i			1.24492i
$89$	6.37121e8	+	3.67842e8i	0.114096	+	0.0658736i	0.555962	−	0.831208i	$-0.312350\pi$
$89$	6.37121e8	+	3.67842e8i	0.114096	+	0.0658736i	−0.441866	+	0.897081i	$0.645683\pi$
$90$	−1.56168e9	+	9.01639e8i	−0.264473	+	0.152693i
$91$	9.27705e9	+	5.35611e9i	1.48663	+	0.858306i
$92$	7.80466e9	+	1.35181e10i	1.18417	+	2.05105i
$93$	−1.35258e9	−	2.34273e9i	−0.194423	−	0.336750i
$94$			7.71869e9i			1.05173i
$95$	2.17956e9	−	2.68780e9i	0.281677	−	0.347359i
$96$	−6.37104e9			−0.781365
$97$	−4.69861e9	+	2.71274e9i	−0.547156	+	0.315900i	−0.747974	−	0.663728i	$-0.768973\pi$
$97$	−4.69861e9	+	2.71274e9i	−0.547156	+	0.315900i	0.200818	+	0.979628i	$0.435640\pi$
$98$	−6.35084e9	+	3.66666e9i	−0.702588	+	0.405639i
$99$	−2.58203e9	+	4.47220e9i	−0.271510	+	0.470268i
$100$	1.60173e9	+	2.77427e9i	0.160173	+	0.277427i
$101$	1.41214e9	−	2.44589e9i	0.134360	−	0.232718i	−0.790993	−	0.611825i	$-0.790435\pi$
$101$	1.41214e9	−	2.44589e9i	0.134360	−	0.232718i	0.925353	+	0.379107i	$0.123769\pi$
$102$	1.43539e10			1.30008
$103$		−	9.78982e9i		−	0.844478i	−0.906484	−	0.422239i	$-0.861244\pi$
$103$		−	9.78982e9i		−	0.844478i	0.906484	−	0.422239i	$-0.138756\pi$
$104$	−8.26733e9	+	1.43194e10i	−0.679515	+	1.17695i
$105$	−4.60173e9	−	2.65681e9i	−0.360558	−	0.208168i
$106$	−9.11817e9			−0.681363
$107$			7.73407e9i			0.551429i	0.961240	+	0.275714i	$0.0889144\pi$
$107$			7.73407e9i			0.551429i	−0.961240	+	0.275714i	$0.911086\pi$
$108$	2.20296e10	+	1.27188e10i	1.49929	+	0.865618i
$109$	−2.56246e10	+	1.47944e10i	−1.66543	+	0.961534i	−0.695370	+	0.718652i	$0.744760\pi$
$109$	−2.56246e10	+	1.47944e10i	−1.66543	+	0.961534i	−0.970056	+	0.242882i	$0.921907\pi$
$110$	1.29048e10	+	7.45058e9i	0.801286	+	0.462623i
$111$	1.52516e9	+	2.64165e9i	0.0905105	+	0.156769i
$112$	3.91010e8	+	6.77250e8i	0.0221870	+	0.0384290i
$113$		−	1.27533e10i		−	0.692199i	−0.938198	−	0.346100i	$-0.887506\pi$
$113$		−	1.27533e10i		−	0.692199i	0.938198	−	0.346100i	$-0.112494\pi$
$114$	−2.32907e10	−	3.70511e9i	−1.20965	−	0.192432i
$115$	1.33003e10			0.661258
$116$	8.14980e9	−	4.70529e9i	0.388023	−	0.224025i
$117$	−1.12554e10	+	6.49832e9i	−0.513372	+	0.296396i
$118$	3.32960e10	−	5.76704e10i	1.45540	−	2.52083i
$119$	−1.55262e10	−	2.68921e10i	−0.650623	−	1.12691i
$120$	4.10088e9	−	7.10293e9i	0.164805	−	0.285451i
$121$	1.67351e10			0.645211
$122$		−	4.20462e10i		−	1.55571i
$123$	1.13493e10	−	1.96575e10i	0.403128	−	0.698238i
$124$	−2.08233e10	−	1.20224e10i	−0.710300	−	0.410092i
$125$	2.72958e9			0.0894427
$126$		−	2.65866e10i		−	0.837163i
$127$	4.48093e10	+	2.58707e10i	1.35628	+	0.783049i	0.989120	−	0.147109i	$-0.0469969\pi$
$127$	4.48093e10	+	2.58707e10i	1.35628	+	0.783049i	0.367160	+	0.930158i	$0.380330\pi$
$128$	−4.73048e10	+	2.73114e10i	−1.37675	+	0.794868i
$129$	−8.53666e9	−	4.92864e9i	−0.238968	−	0.137968i
$130$	1.87513e10	+	3.24781e10i	0.505026	+	0.874730i
$131$	3.82348e10	+	6.62247e10i	0.991066	+	1.71658i	0.611036	+	0.791603i	$0.290753\pi$
$131$	3.82348e10	+	6.62247e10i	0.991066	+	1.71658i	0.380030	+	0.924974i	$0.375914\pi$
$132$		−	6.25207e10i		−	1.56011i
$133$	1.82512e10	+	4.76429e10i	0.438565	+	1.14483i
$134$	−3.88583e10			−0.899415
$135$	1.87708e10	−	1.08373e10i	0.418613	−	0.241687i
$136$	4.15089e10	−	2.39652e10i	0.892168	−	0.515094i
$137$	4.33324e10	−	7.50540e10i	0.897863	−	1.55514i	0.0676425	−	0.997710i	$-0.478452\pi$
$137$	4.33324e10	−	7.50540e10i	0.897863	−	1.55514i	0.830221	−	0.557435i	$-0.188214\pi$
$138$	−4.53218e10	−	7.84996e10i	−0.905548	−	1.56846i
$139$	−4.52008e9	+	7.82900e9i	−0.0871108	+	0.150880i	−0.906289	−	0.422659i	$-0.861097\pi$
$139$	−4.52008e9	+	7.82900e9i	−0.0871108	+	0.150880i	0.819178	+	0.573539i	$0.194430\pi$
$140$	−4.72301e10			−0.878170
$141$		−	2.75946e10i		−	0.495140i
$142$	−4.73972e10	+	8.20944e10i	−0.820939	+	1.42191i
$143$	9.30078e10	+	5.36981e10i	1.55539	+	0.898004i
$144$	−9.48790e8			−0.0153235
$145$		−	8.01849e9i		−	0.125099i
$146$	−1.20462e11	−	6.95489e10i	−1.81588	−	1.04840i
$147$	2.27044e10	−	1.31084e10i	0.330769	−	0.190969i
$148$	2.34803e10	+	1.35563e10i	0.330670	+	0.190912i
$149$	−2.89426e10	−	5.01301e10i	−0.394100	−	0.682602i	0.598886	−	0.800835i	$-0.295610\pi$
$149$	−2.89426e10	−	5.01301e10i	−0.394100	−	0.682602i	−0.992986	+	0.118233i	$0.962277\pi$
$150$	−9.30126e9	−	1.61103e10i	−0.122486	−	0.212151i
$151$		−	6.47845e10i		−	0.825252i	−0.910901	−	0.412626i	$-0.864612\pi$
$151$		−	6.47845e10i		−	0.825252i	0.910901	−	0.412626i	$-0.135388\pi$
$152$	−7.35384e10	+	2.81714e10i	−0.906350	+	0.347209i
$153$	3.76744e10			0.449355
$154$	−1.90261e11	+	1.09847e11i	−2.19658	+	1.26820i
$155$	−1.77430e10	+	1.02439e10i	−0.198321	+	0.114500i
$156$	7.86745e10	−	1.36268e11i	0.851551	−	1.47493i
$157$	8.23904e10	+	1.42704e11i	0.863731	+	1.49603i	0.868302	+	0.496036i	$0.165211\pi$
$157$	8.23904e10	+	1.42704e11i	0.863731	+	1.49603i	−0.00457168	+	0.999990i	$0.501455\pi$
$158$	7.06680e10	−	1.22401e11i	0.717691	−	1.24308i
$159$	3.25978e10			0.320776
$160$			4.82519e10i			0.460166i
$161$	−9.80461e10	+	1.69821e11i	−0.906360	+	1.56986i
$162$	−6.19416e10	−	3.57620e10i	−0.555146	−	0.320514i
$163$	2.00986e11			1.74674			0.873368	−	0.487061i	$-0.161931\pi$
$163$	2.00986e11			1.74674			0.873368	+	0.487061i	$0.161931\pi$
$164$		−	2.01756e11i		−	1.70062i
$165$	−4.61350e10	−	2.66361e10i	−0.377234	−	0.217796i
$166$	1.77130e11	−	1.02266e11i	1.40524	−	0.811318i
$167$	1.49362e10	+	8.62341e9i	0.114989	+	0.0663891i	0.556392	−	0.830920i	$-0.312185\pi$
$167$	1.49362e10	+	8.62341e9i	0.114989	+	0.0663891i	−0.441402	+	0.897309i	$0.645519\pi$
$168$	6.04612e10	+	1.04722e11i	0.451783	+	0.782512i
$169$	6.62154e10	+	1.14688e11i	0.480314	+	0.831928i
$170$		−	1.08712e11i		−	0.765651i
$171$	−6.11305e10	−	9.72471e9i	−0.418097	−	0.0665114i
$172$	−8.76164e10			−0.582027
$173$	−1.53310e11	+	8.85136e10i	−0.989327	+	0.571188i	−0.905073	−	0.425256i	$-0.860184\pi$
$173$	−1.53310e11	+	8.85136e10i	−0.989327	+	0.571188i	−0.0842542	+	0.996444i	$0.526851\pi$
$174$	−4.73260e10	+	2.73237e10i	−0.296725	+	0.171314i
$175$	−2.01217e10	+	3.48518e10i	−0.122596	+	0.212342i
$176$	3.92011e9	+	6.78982e9i	0.0232132	+	0.0402064i
$177$	−1.19034e11	+	2.06174e11i	−0.685182	+	1.18677i
$178$	−3.79728e10			−0.212507
$179$			7.84261e10i			0.426772i	0.976968	+	0.213386i	$0.0684491\pi$
$179$			7.84261e10i			0.426772i	−0.976968	+	0.213386i	$0.931551\pi$
$180$	2.86510e10	−	4.96251e10i	0.151627	−	0.262627i
$181$	6.21935e10	+	3.59074e10i	0.320149	+	0.184838i	0.651459	−	0.758684i	$-0.274157\pi$
$181$	6.21935e10	+	3.59074e10i	0.320149	+	0.184838i	−0.331310	+	0.943522i	$0.607491\pi$
$182$	−5.52917e11			−2.76887
$183$			1.50317e11i			0.732405i
$184$	−2.62124e11	−	1.51337e11i	−1.24285	−	0.717559i
$185$	2.00069e10	−	1.15510e10i	0.0923252	−	0.0533040i
$186$	1.20921e11	+	6.98140e10i	0.543173	+	0.313601i
$187$	−1.55659e11	−	2.69609e11i	−0.680716	−	1.17903i
$188$	−1.22637e11	−	2.12414e11i	−0.522194	−	0.904467i
$189$			3.19559e11i			1.32508i
$190$	−2.80612e10	+	1.76395e11i	−0.113328	+	0.712392i
$191$	1.30918e11			0.515032			0.257516	−	0.966274i	$-0.417096\pi$
$191$	1.30918e11			0.515032			0.257516	+	0.966274i	$0.417096\pi$
$192$	2.78577e11	−	1.60837e11i	1.06768	−	0.616423i
$193$	−1.00640e11	+	5.81046e10i	−0.375824	+	0.216982i	−0.676000	−	0.736902i	$-0.736288\pi$
$193$	−1.00640e11	+	5.81046e10i	−0.375824	+	0.216982i	0.300176	+	0.953884i	$0.402955\pi$
$194$	1.40020e11	−	2.42522e11i	0.509543	−	0.882555i
$195$	−6.70363e10	−	1.16110e11i	−0.237759	−	0.411811i
$196$	1.16514e11	−	2.01808e11i	0.402808	−	0.697684i
$197$	3.19811e11			1.07786			0.538930	−	0.842351i	$-0.318829\pi$
$197$	3.19811e11			1.07786			0.538930	+	0.842351i	$0.318829\pi$
$198$		−	2.66546e11i		−	0.875883i
$199$	−3.50881e10	+	6.07744e10i	−0.112433	+	0.194740i	−0.916751	−	0.399460i	$-0.869198\pi$
$199$	−3.50881e10	+	6.07744e10i	−0.112433	+	0.194740i	0.804318	+	0.594200i	$0.202531\pi$
$200$	−5.37950e10	−	3.10585e10i	−0.168109	−	0.0970580i
$201$	1.38920e11			0.423432
$202$			1.45777e11i			0.433442i
$203$	1.02382e11	+	5.91102e10i	0.296991	+	0.171468i
$204$	−3.95011e11	+	2.28060e11i	−1.11804	+	0.645503i
$205$	−1.48879e11	−	8.59554e10i	−0.411211	−	0.237413i
$206$	2.52654e11	+	4.37609e11i	0.681066	+	1.17964i
$207$	−1.18955e11	−	2.06036e11i	−0.312990	−	0.542115i
$208$			1.97319e10i			0.0506817i
$209$	1.82979e11	+	4.77647e11i	0.458850	+	1.19778i
$210$	2.74266e11			0.671545
$211$	1.03766e11	−	5.99096e10i	0.248110	−	0.143247i	−0.370788	−	0.928717i	$-0.620912\pi$
$211$	1.03766e11	−	5.99096e10i	0.248110	−	0.143247i	0.618899	+	0.785471i	$0.287579\pi$
$212$	2.50926e11	−	1.44872e11i	0.585959	−	0.338303i
$213$	1.69446e11	−	2.93490e11i	0.386487	−	0.669415i
$214$	−1.99599e11	−	3.45716e11i	−0.444724	−	0.770284i
$215$	−3.73277e10	+	6.46535e10i	−0.0812530	+	0.140734i
$216$	−4.93250e11			−1.04906
$217$		−	3.02062e11i		−	0.627765i
$218$	7.63621e11	−	1.32263e12i	1.55094	−	2.68631i
$219$	4.30656e11	+	2.48640e11i	0.854890	+	0.493571i
$220$	−4.73509e11			−0.918787
$221$		−	7.83509e11i		−	1.48622i
$222$	−1.36350e11	−	7.87218e10i	−0.252866	−	0.145992i
$223$	9.15598e11	−	5.28621e11i	1.66028	−	0.958562i	0.687696	−	0.725999i	$-0.258622\pi$
$223$	9.15598e11	−	5.28621e11i	1.66028	−	0.958562i	0.972581	−	0.232563i	$-0.0747111\pi$
$224$	−6.16091e11	−	3.55700e11i	−1.09246	−	0.630731i
$225$	−2.44128e10	−	4.22841e10i	−0.0423355	−	0.0733272i
$226$	3.29135e11	+	5.70079e11i	0.558254	+	0.966925i
$227$		−	9.69189e11i		−	1.60797i	−0.594647	−	0.803987i	$-0.702708\pi$
$227$		−	9.69189e11i		−	1.60797i	0.594647	−	0.803987i	$-0.297292\pi$
$228$	6.99814e11	−	2.68088e11i	1.13582	−	0.435114i
$229$	−8.07235e11			−1.28181			−0.640904	−	0.767621i	$-0.721440\pi$
$229$	−8.07235e11			−1.28181			−0.640904	+	0.767621i	$0.721440\pi$
$230$	−5.94528e11	+	3.43251e11i	−0.923704	+	0.533301i
$231$	6.80190e11	−	3.92708e11i	1.03412	−	0.597049i
$232$	−9.12386e10	+	1.58030e11i	−0.135750	+	0.235125i
$233$	3.73429e11	+	6.46799e11i	0.543787	+	0.941867i	0.998682	+	0.0513217i	$0.0163434\pi$
$233$	3.73429e11	+	6.46799e11i	0.543787	+	0.941867i	−0.454895	+	0.890545i	$0.650323\pi$
$234$	3.35415e11	−	5.80955e11i	0.478082	−	0.828063i
$235$	−2.08991e11			−0.291601
$236$			2.11607e12i			2.89048i
$237$	−2.52640e11	+	4.37586e11i	−0.337879	+	0.585223i
$238$	1.38805e12	+	8.01393e11i	1.81770	+	1.04945i
$239$	−7.05819e11			−0.905115			−0.452557	−	0.891735i	$-0.649488\pi$
$239$	−7.05819e11			−0.905115			−0.452557	+	0.891735i	$0.649488\pi$
$240$		−	9.78767e9i		−	0.0122920i
$241$	3.25034e11	+	1.87658e11i	0.399801	+	0.230825i	0.686398	−	0.727226i	$-0.259191\pi$
$241$	3.25034e11	+	1.87658e11i	0.399801	+	0.230825i	−0.286597	+	0.958051i	$0.592524\pi$
$242$	−7.48067e11	+	4.31897e11i	−0.901288	+	0.520359i
$243$	−5.71660e11	−	3.30048e11i	−0.674693	−	0.389534i
$244$	6.68044e11	+	1.15709e12i	0.772424	+	1.33788i
$245$	−9.92783e10	−	1.71955e11i	−0.112467	−	0.194798i
$246$			1.17160e12i			1.30048i
$247$	−2.02243e11	+	1.27132e12i	−0.219983	+	1.38284i
$248$	4.66242e11			0.496997
$249$	−6.33245e11	+	3.65604e11i	−0.661569	+	0.381957i
$250$	−1.22013e11	+	7.04443e10i	−0.124941	+	0.0721350i
$251$	7.65715e11	−	1.32626e12i	0.768597	−	1.33125i	−0.169727	−	0.985491i	$-0.554289\pi$
$251$	7.65715e11	−	1.32626e12i	0.768597	−	1.33125i	0.938324	−	0.345758i	$-0.112378\pi$
$252$	4.22416e11	+	7.31646e11i	0.415659	+	0.719943i
$253$	−9.82969e11	+	1.70255e12i	−0.948281	+	1.64247i
$254$	−2.67066e12			−2.52610
$255$			3.88647e11i			0.360458i
$256$	5.17163e11	−	8.95753e11i	0.470357	−	0.814683i
$257$	1.34755e12	+	7.78009e11i	1.20193	+	0.693935i	0.960984	−	0.276603i	$-0.0892087\pi$
$257$	1.34755e12	+	7.78009e11i	1.20193	+	0.693935i	0.240947	+	0.970538i	$0.422542\pi$
$258$	5.08789e11			0.445082
$259$			3.40603e11i			0.292247i
$260$	−1.03205e12	−	5.95852e11i	−0.868624	−	0.501501i
$261$	−1.24215e11	+	7.17157e10i	−0.102559	+	0.0592123i
$262$	−3.41823e12	−	1.97351e12i	−2.76882	−	1.59858i
$263$	5.05109e11	+	8.74874e11i	0.401426	+	0.695291i	0.993898	−	0.110300i	$-0.0351812\pi$
$263$	5.05109e11	+	8.74874e11i	0.401426	+	0.695291i	−0.592472	+	0.805591i	$0.701848\pi$
$264$	6.06158e11	+	1.04990e12i	0.472679	+	0.818704i
$265$		−	2.46883e11i		−	0.188913i
$266$	−2.04540e12	−	1.65863e12i	−1.53592	−	1.24549i
$267$	1.35754e11			0.100045
$268$	1.06936e12	−	6.17394e11i	0.773479	−	0.446569i
$269$	1.37842e12	−	7.95832e11i	0.978634	−	0.565015i	0.0767768	−	0.997048i	$-0.475537\pi$
$269$	1.37842e12	−	7.95832e11i	0.978634	−	0.565015i	0.901858	+	0.432034i	$0.142204\pi$
$270$	−5.59374e11	+	9.68864e11i	−0.389837	+	0.675218i
$271$	2.53129e11	+	4.38433e11i	0.173179	+	0.299955i	0.939530	−	0.342468i	$-0.111263\pi$
$271$	2.53129e11	+	4.38433e11i	0.173179	+	0.299955i	−0.766350	+	0.642423i	$0.777929\pi$
$272$	2.85992e10	−	4.95352e10i	0.0192092	−	0.0332713i
$273$	1.97670e12			1.30355
$274$			4.47326e12i			2.89648i
$275$	−2.01732e11	+	3.49410e11i	−0.128266	+	0.222163i
$276$	2.49445e12	+	1.44017e12i	1.55751	+	0.899227i
$277$	1.86728e12			1.14501			0.572506	−	0.819901i	$-0.305971\pi$
$277$	1.86728e12			1.14501			0.572506	+	0.819901i	$0.305971\pi$
$278$		−	4.66613e11i		−	0.281017i
$279$	3.17379e11	+	1.83239e11i	0.187740	+	0.108392i
$280$	7.93125e11	−	4.57911e11i	0.460841	−	0.266067i
$281$	−2.20323e12	−	1.27203e12i	−1.25756	−	0.726051i	−0.284958	−	0.958540i	$-0.591980\pi$
$281$	−2.20323e12	−	1.27203e12i	−1.25756	−	0.726051i	−0.972599	+	0.232489i	$0.925313\pi$
$282$	7.12155e11	+	1.23349e12i	0.399327	+	0.691655i
$283$	−7.03039e11	−	1.21770e12i	−0.387300	−	0.670822i	0.604786	−	0.796388i	$-0.293259\pi$
$283$	−7.03039e11	−	1.21770e12i	−0.387300	−	0.670822i	−0.992085	+	0.125566i	$0.959925\pi$
$284$		−	3.01225e12i		−	1.63042i
$285$	1.00320e11	−	6.30619e11i	0.0533533	−	0.335384i
$286$	−5.54332e12			−2.89694
$287$	2.19499e12	−	1.26728e12i	1.12726	−	0.650824i
$288$	7.47475e11	−	4.31555e11i	0.377254	−	0.217808i
$289$	−1.27613e11	+	2.21032e11i	−0.0633003	+	0.109639i
$290$	2.06940e11	+	3.58430e11i	0.100891	+	0.174749i
$291$	−5.00576e11	+	8.67022e11i	−0.239886	+	0.415495i
$292$	4.42006e12			2.08216
$293$		−	2.73578e12i		−	1.26690i	−0.773782	−	0.633452i	$-0.781637\pi$
$293$		−	2.73578e12i		−	1.26690i	0.773782	−	0.633452i	$-0.218363\pi$
$294$	−6.76599e11	+	1.17190e12i	−0.308031	+	0.533525i
$295$	1.56148e12	+	9.01522e11i	0.698919	+	0.403521i
$296$	−5.25732e11			−0.231369
$297$			3.20376e12i			1.38637i
$298$	2.58750e12	+	1.49389e12i	1.10103	+	0.635679i
$299$	−4.28490e12	+	2.47389e12i	−1.79302	+	1.03520i
$300$	5.11929e11	+	2.95563e11i	0.210671	+	0.121631i
$301$	−5.50340e11	−	9.53217e11i	−0.222740	−	0.385798i
$302$	1.67195e12	+	2.89590e12i	0.665561	+	1.15278i
$303$		−	5.21156e11i		−	0.204058i
$304$	−5.91913e10	+	7.29936e10i	−0.0227976	+	0.0281136i
$305$	1.13844e12			0.431332
$306$	−1.68406e12	+	9.72293e11i	−0.627698	+	0.362402i
$307$	1.51964e12	−	8.77367e11i	0.557250	−	0.321728i	−0.194791	−	0.980845i	$-0.562403\pi$
$307$	1.51964e12	−	8.77367e11i	0.557250	−	0.321728i	0.752041	+	0.659116i	$0.229070\pi$
$308$	3.49058e12	−	6.04587e12i	1.25934	−	2.18125i
$309$	−9.03245e11	−	1.56447e12i	−0.320637	−	0.555359i
$310$	5.28746e11	−	9.15814e11i	0.184688	−	0.319889i
$311$	5.28937e11			0.181803			0.0909017	−	0.995860i	$-0.471025\pi$
$311$	5.28937e11			0.181803			0.0909017	+	0.995860i	$0.471025\pi$
$312$			3.05110e12i			1.03201i
$313$	−2.61520e12	+	4.52966e12i	−0.870529	+	1.50780i	−0.00907922	+	0.999959i	$0.502890\pi$
$313$	−2.61520e12	+	4.52966e12i	−0.870529	+	1.50780i	−0.861450	+	0.507842i	$0.830443\pi$
$314$	−7.36577e12	−	4.25263e12i	−2.41307	−	1.39319i
$315$	7.19858e11			0.232110
$316$			4.49118e12i			1.42536i
$317$	−1.51928e12	−	8.77157e11i	−0.474615	−	0.274019i	0.243554	−	0.969887i	$-0.421687\pi$
$317$	−1.51928e12	−	8.77157e11i	−0.474615	−	0.274019i	−0.718170	+	0.695868i	$0.755020\pi$
$318$	−1.45713e12	+	8.41276e11i	−0.448088	+	0.258704i
$319$	1.02644e12	+	5.92614e11i	0.310727	+	0.179398i
$320$	−1.21812e12	−	2.10984e12i	−0.363027	−	0.628782i
$321$	7.13574e11	+	1.23595e12i	0.209370	+	0.362639i
$322$		−	1.01214e13i		−	2.92390i
$323$	2.35036e12	−	2.89842e12i	0.668530	−	0.824420i
$324$	2.27279e12			0.636553
$325$	−8.79377e11	+	5.07708e11i	−0.242526	+	0.140022i
$326$	−8.98415e12	+	5.18700e12i	−2.43999	+	1.40873i
$327$	−2.72997e12	+	4.72845e12i	−0.730162	+	1.26468i
$328$	1.95609e12	+	3.38805e12i	0.515252	+	0.892443i
$329$	1.54063e12	−	2.66845e12i	0.399685	−	0.692275i
$330$	2.74967e12			0.702605
$331$			4.97056e11i			0.125102i	0.998042	+	0.0625511i	$0.0199236\pi$
$331$			4.97056e11i			0.125102i	−0.998042	+	0.0625511i	$0.980076\pi$
$332$	−3.24967e12	+	5.62860e12i	−0.805655	+	1.39544i
$333$	−3.57874e11	−	2.06619e11i	−0.0873996	−	0.0504602i
$334$	−8.90205e11			−0.214169
$335$		−	1.05213e12i		−	0.249370i
$336$	1.24971e11	+	7.21521e10i	0.0291819	+	0.0168482i
$337$	6.84697e12	−	3.95310e12i	1.57525	−	0.909470i	0.579740	−	0.814802i	$-0.303154\pi$
$337$	6.84697e12	−	3.95310e12i	1.57525	−	0.909470i	0.995509	−	0.0946683i	$-0.0301790\pi$
$338$	−5.91971e12	−	3.41775e12i	−1.34189	−	0.774741i
$339$	−1.17667e12	−	2.03805e12i	−0.262818	−	0.455215i
$340$	1.72724e12	+	2.99167e12i	0.380153	+	0.658445i
$341$		−	3.02834e12i		−	0.656800i
$342$	2.98353e12	−	1.14294e12i	0.637676	−	0.244284i
$343$	−2.89288e12			−0.609341
$344$	1.47132e12	−	8.49469e11i	0.305433	−	0.176342i
$345$	2.12545e12	−	1.22713e12i	0.434867	−	0.251071i
$346$	4.56868e12	−	7.91319e12i	0.921320	−	1.59577i
$347$	6.22705e11	+	1.07856e12i	0.123776	+	0.214385i	0.921254	−	0.388962i	$-0.127166\pi$
$347$	6.22705e11	+	1.07856e12i	0.123776	+	0.214385i	−0.797478	+	0.603348i	$0.793833\pi$
$348$	8.68254e11	−	1.50386e12i	0.170118	−	0.294653i
$349$	1.98875e12			0.384108			0.192054	−	0.981384i	$-0.438485\pi$
$349$	1.98875e12			0.384108			0.192054	+	0.981384i	$0.438485\pi$
$350$		−	2.07719e12i		−	0.395490i
$351$	−4.03154e12	+	6.98283e12i	−0.756720	+	1.31068i
$352$	−6.17667e12	−	3.56610e12i	−1.14299	−	0.659903i
$353$	−9.01324e11			−0.164440			−0.0822200	−	0.996614i	$-0.526201\pi$
$353$	−9.01324e11			−0.164440			−0.0822200	+	0.996614i	$0.526201\pi$
$354$		−	1.22881e13i		−	2.21038i
$355$	−2.22279e12	−	1.28333e12i	−0.394236	−	0.227612i
$356$	1.04499e12	−	6.03323e11i	0.182751	−	0.105512i
$357$	−4.96233e12	−	2.86500e12i	−0.855746	−	0.494065i
$358$	−2.02401e12	−	3.50568e12i	−0.344189	−	0.596152i
$359$	−2.98979e12	−	5.17847e12i	−0.501382	−	0.868419i	−0.999999	−	0.00159640i	$-0.999492\pi$
$359$	−2.98979e12	−	5.17847e12i	−0.501382	−	0.868419i	0.498617	−	0.866823i	$-0.333841\pi$
$360$			1.11112e12i			0.183760i
$361$	−4.56184e12	+	4.09629e12i	−0.744054	+	0.668120i
$362$	−3.70677e12			−0.596283
$363$	2.67436e12	−	1.54404e12i	0.424314	−	0.244978i
$364$	1.52159e13	−	8.78492e12i	2.38118	−	1.37477i
$365$	1.88310e12	−	3.26163e12i	0.290677	−	0.503467i
$366$	−3.87934e12	−	6.71921e12i	−0.590680	−	1.02309i
$367$	4.06509e12	−	7.04094e12i	0.610576	−	1.05755i	−0.380568	−	0.924753i	$-0.624272\pi$
$367$	4.06509e12	−	7.04094e12i	0.610576	−	1.05755i	0.991144	−	0.132795i	$-0.0423952\pi$
$368$	−3.61201e11			−0.0535192
$369$			3.07507e12i			0.449493i
$370$	−5.96210e11	+	1.03267e12i	−0.0859787	+	0.148919i
$371$	3.15226e12	+	1.81996e12i	0.448490	+	0.258936i
$372$	−4.43691e12			−0.622824
$373$		−	9.19101e12i		−	1.27297i	−0.771288	−	0.636487i	$-0.780387\pi$
$373$		−	9.19101e12i		−	1.27297i	0.771288	−	0.636487i	$-0.219613\pi$
$374$	1.39160e13	+	8.03442e12i	1.90177	+	1.09799i
$375$	4.36201e11	−	2.51841e11i	0.0588207	−	0.0339601i
$376$	4.11884e12	+	2.37801e12i	0.548069	+	0.316428i
$377$	1.49146e12	+	2.58329e12i	0.195842	+	0.339208i
$378$	−8.24712e12	−	1.42844e13i	−1.06867	−	1.85099i
$379$		−	7.74342e12i		−	0.990231i	−0.868827	−	0.495116i	$-0.835126\pi$
$379$		−	7.74342e12i		−	0.990231i	0.868827	−	0.495116i	$-0.164874\pi$
$380$	−2.03040e12	−	5.30013e12i	−0.256250	−	0.668912i
$381$	9.54769e12			1.18925
$382$	−5.85211e12	+	3.37872e12i	−0.719442	+	0.415370i
$383$	2.64419e12	−	1.52662e12i	0.320847	−	0.185241i	−0.330923	−	0.943658i	$-0.607360\pi$
$383$	2.64419e12	−	1.52662e12i	0.320847	−	0.185241i	0.651770	+	0.758416i	$0.274027\pi$
$384$	−5.03971e12	+	8.72903e12i	−0.603600	+	1.04547i
$385$	−2.97423e12	−	5.15151e12i	−0.351618	−	0.609019i
$386$	2.99910e12	−	5.19460e12i	0.349989	−	0.606199i
$387$	1.33541e12			0.153836
$388$			8.89872e12i			1.01197i
$389$	−4.10194e12	+	7.10478e12i	−0.460513	+	0.797632i	−0.998987	−	0.0450107i	$-0.985668\pi$
$389$	−4.10194e12	+	7.10478e12i	−0.460513	+	0.797632i	0.538474	+	0.842642i	$0.319001\pi$
$390$	5.99310e12	+	3.46012e12i	0.664246	+	0.383502i
$391$	1.43425e13			1.56943
$392$			4.51857e12i			0.488169i
$393$	1.22203e13	+	7.05537e12i	1.30352	+	0.752588i
$394$	−1.42957e13	+	8.25361e12i	−1.50565	+	0.869287i
$395$	3.31411e12	+	1.91340e12i	0.344653	+	0.198985i
$396$	4.23496e12	+	7.33517e12i	0.434884	+	0.753242i
$397$	1.98353e12	+	3.43558e12i	0.201134	+	0.348375i	0.948894	−	0.315594i	$-0.102204\pi$
$397$	1.98353e12	+	3.43558e12i	0.201134	+	0.348375i	−0.747760	+	0.663969i	$0.768871\pi$
$398$		−	3.62219e12i		−	0.362707i
$399$	7.31235e12	+	5.92966e12i	0.723090	+	0.586361i
$400$	−7.41282e10			−0.00723908
$401$	−9.29650e12	+	5.36734e12i	−0.896598	+	0.517651i	−0.876095	−	0.482139i	$-0.839860\pi$
$401$	−9.29650e12	+	5.36734e12i	−0.896598	+	0.517651i	−0.0205028	+	0.999790i	$0.506527\pi$
$402$	−6.20977e12	+	3.58521e12i	−0.591487	+	0.341495i
$403$	3.81079e12	−	6.60048e12i	0.358501	−	0.620941i
$404$	−2.31614e12	−	4.01168e12i	−0.215208	−	0.372752i
$405$	9.68291e11	−	1.67713e12i	0.0888650	−	0.153919i
$406$	−6.10202e12			−0.553150
$407$			3.41474e12i			0.305763i
$408$	4.42223e12	−	7.65953e12i	0.391148	−	0.677487i
$409$	4.87377e12	+	2.81387e12i	0.425842	+	0.245860i	0.697574	−	0.716513i	$-0.254263\pi$
$409$	4.87377e12	+	2.81387e12i	0.425842	+	0.245860i	−0.271731	+	0.962373i	$0.587596\pi$
$410$	8.87327e12			0.765887
$411$		−	1.59920e13i		−	1.36362i
$412$	−1.39057e13	−	8.02848e12i	−1.17141	−	0.676312i
$413$	−2.30217e13	+	1.32916e13i	−1.91596	+	1.10618i
$414$	1.06347e13	+	6.13993e12i	0.874424	+	0.504849i
$415$	2.76895e12	+	4.79597e12i	0.224944	+	0.389615i
$416$	−8.97499e12	−	1.55451e13i	−0.720389	−	1.24775i
$417$			1.66816e12i			0.132299i
$418$	−2.05063e13	−	1.66287e13i	−1.60696	−	1.30310i
$419$	1.02283e13			0.792015			0.396007	−	0.918247i	$-0.370395\pi$
$419$	1.02283e13			0.792015			0.396007	+	0.918247i	$0.370395\pi$
$420$	−7.54762e12	+	4.35762e12i	−0.577515	+	0.333429i
$421$	−1.96235e13	+	1.13296e13i	−1.48377	+	0.856653i	−0.999830	−	0.0184495i	$-0.994127\pi$
$421$	−1.96235e13	+	1.13296e13i	−1.48377	+	0.856653i	−0.483937	+	0.875103i	$0.660794\pi$
$422$	−3.09227e12	+	5.35597e12i	−0.231055	+	0.400199i
$423$	1.86917e12	+	3.23750e12i	0.138022	+	0.239061i
$424$	−2.80917e12	+	4.86563e12i	−0.204998	+	0.355066i
$425$	2.94347e12			0.212283
$426$			1.74922e13i			1.24680i
$427$	−8.39230e12	+	1.45359e13i	−0.591210	+	1.02401i
$428$	1.09857e13	+	6.34260e12i	0.764907	+	0.441620i
$429$	1.98175e13			1.36384
$430$		−	3.85338e12i		−	0.262120i
$431$	−1.88338e13	−	1.08737e13i	−1.26634	−	0.731124i	−0.292049	−	0.956403i	$-0.594337\pi$
$431$	−1.88338e13	−	1.08737e13i	−1.26634	−	0.731124i	−0.974294	+	0.225280i	$0.927670\pi$
$432$	−5.09766e11	+	2.94313e11i	−0.0338807	+	0.0195610i
$433$	1.17183e13	+	6.76555e12i	0.769882	+	0.444492i	0.832833	−	0.553525i	$-0.186718\pi$
$433$	1.17183e13	+	6.76555e12i	0.769882	+	0.444492i	−0.0629505	+	0.998017i	$0.520051\pi$
$434$	7.79555e12	+	1.35023e13i	0.506288	+	0.876917i
$435$	−7.39815e11	−	1.28140e12i	−0.0474982	−	0.0822693i
$436$			4.85306e13i			3.08023i
$437$	−2.32721e13	−	3.70216e12i	−1.46026	−	0.232299i
$438$	−2.56674e13			−1.59225
$439$	−4.42260e12	+	2.55339e12i	−0.271241	+	0.156601i	−0.629451	−	0.777040i	$-0.716720\pi$
$439$	−4.42260e12	+	2.55339e12i	−0.271241	+	0.156601i	0.358211	+	0.933641i	$0.383387\pi$
$440$	7.95154e12	−	4.59082e12i	0.482156	−	0.278373i
$441$	−1.77585e12	+	3.07586e12i	−0.106467	+	0.184406i
$442$	2.02206e13	+	3.50232e13i	1.19863	+	2.07608i
$443$	−1.36265e13	+	2.36017e13i	−0.798665	+	1.38333i	0.121821	+	0.992552i	$0.461126\pi$
$443$	−1.36265e13	+	2.36017e13i	−0.798665	+	1.38333i	−0.920486	+	0.390776i	$0.872207\pi$
$444$	5.00303e12			0.289947
$445$		−	1.02815e12i		−	0.0589191i
$446$	−2.72851e13	+	4.72591e13i	−1.54615	+	2.67801i
$447$	−9.25038e12	−	5.34071e12i	−0.518348	−	0.299269i
$448$	3.59186e13			1.99035
$449$		−	5.86161e12i		−	0.321207i	−0.987019	−	0.160604i	$-0.948656\pi$
$449$		−	5.86161e12i		−	0.321207i	0.987019	−	0.160604i	$-0.0513441\pi$
$450$	2.18252e12	+	1.26008e12i	0.118276	+	0.0682865i
$451$	2.20061e13	−	1.27052e13i	1.17940	−	0.680925i
$452$	−1.81152e13	−	1.04588e13i	−0.960175	−	0.554357i
$453$	−5.97726e12	−	1.03529e13i	−0.313337	−	0.542715i
$454$	2.50126e13	+	4.33231e13i	1.29682	+	2.24616i
$455$		−	1.49708e13i		−	0.767692i
$456$	−9.15263e12	+	1.12869e13i	−0.464218	+	0.572465i
$457$	1.48393e13			0.744445			0.372223	−	0.928144i	$-0.378596\pi$
$457$	1.48393e13			0.744445			0.372223	+	0.928144i	$0.378596\pi$
$458$	3.60838e13	−	2.08330e13i	1.79054	−	1.03377i
$459$	2.02417e13	−	1.16865e13i	0.993535	−	0.573618i
$460$	1.09073e13	−	1.88921e13i	0.529578	−	0.917256i
$461$	−1.52177e11	−	2.63578e11i	−0.00730877	−	0.0126592i	0.862348	−	0.506316i	$-0.168993\pi$
$461$	−1.52177e11	−	2.63578e11i	−0.00730877	−	0.0126592i	−0.869657	+	0.493657i	$0.835660\pi$
$462$	−2.02699e13	+	3.51084e13i	−0.963032	+	1.66802i
$463$	3.73133e13			1.75371			0.876856	−	0.480752i	$-0.159636\pi$
$463$	3.73133e13			1.75371			0.876856	+	0.480752i	$0.159636\pi$
$464$			2.17762e11i			0.0101249i
$465$	−1.89028e12	+	3.27406e12i	−0.0869484	+	0.150599i
$466$	−3.33849e13	−	1.92748e13i	−1.51922	−	0.877121i
$467$	−2.17168e13			−0.977712			−0.488856	−	0.872365i	$-0.662586\pi$
$467$	−2.17168e13			−0.977712			−0.488856	+	0.872365i	$0.662586\pi$
$468$			2.13167e13i			0.949490i
$469$	1.34338e13	+	7.75601e12i	0.592018	+	0.341802i
$470$	9.34199e12	−	5.39360e12i	0.407333	−	0.235174i
$471$	2.63329e13	+	1.52033e13i	1.13604	+	0.655893i
$472$	−2.05160e13	−	3.55347e13i	−0.875755	−	1.51685i
$473$	−5.51748e12	−	9.55655e12i	−0.233042	−	0.403641i
$474$		−	2.60803e13i		−	1.08999i
$475$	−4.77607e12	−	7.59783e11i	−0.197516	−	0.0314211i
$476$	−5.09311e13			−2.08424
$477$	−3.82450e12	+	2.20807e12i	−0.154875	+	0.0894174i
$478$	3.15504e13	−	1.82156e13i	1.26434	−	0.729969i
$479$	1.75393e12	−	3.03789e12i	0.0695560	−	0.120474i	−0.829150	−	0.559026i	$-0.811175\pi$
$479$	1.75393e12	−	3.03789e12i	0.0695560	−	0.120474i	0.898706	+	0.438552i	$0.144508\pi$
$480$	4.45190e12	+	7.71091e12i	0.174719	+	0.302621i
$481$	−4.29702e12	+	7.44266e12i	−0.166895	+	0.289070i
$482$	−1.93722e13			−0.744636
$483$			3.61844e13i			1.37653i
$484$	1.37242e13	−	2.37710e13i	0.516727	−	0.894997i
$485$	6.56651e12	+	3.79118e12i	0.244695	+	0.141275i
$486$	3.40712e13			1.25663
$487$		−	8.95322e12i		−	0.326840i	−0.986557	−	0.163420i	$-0.947748\pi$
$487$		−	8.95322e12i		−	0.326840i	0.986557	−	0.163420i	$-0.0522525\pi$
$488$	−2.24366e13	−	1.29538e13i	−0.810697	−	0.468056i
$489$	3.21186e13	−	1.85437e13i	1.14872	−	0.663211i
$490$	8.87557e12	+	5.12431e12i	0.314207	+	0.181407i
$491$	5.60844e12	+	9.71410e12i	0.196533	+	0.340404i	0.947402	−	0.320046i	$-0.103699\pi$
$491$	5.60844e12	+	9.71410e12i	0.196533	+	0.340404i	−0.750869	+	0.660451i	$0.770365\pi$
$492$	−1.86148e13	−	3.22417e13i	−0.645702	−	1.11839i
$493$		−	8.64683e12i		−	0.296908i
$494$	−2.37697e13	−	6.20481e13i	−0.807957	−	2.10908i
$495$	7.21699e12			0.242845
$496$	4.81853e11	−	2.78198e11i	0.0160512	−	0.00926714i
$497$	3.27716e13	−	1.89207e13i	1.08073	−	0.623957i
$498$	1.88709e13	−	3.26853e13i	0.616092	−	1.06710i
$499$	1.57492e13	+	2.72784e13i	0.509044	+	0.881690i	0.999945	+	0.0104747i	$0.00333427\pi$
$499$	1.57492e13	+	2.72784e13i	0.509044	+	0.881690i	−0.490901	+	0.871215i	$0.663332\pi$
$500$	2.23848e12	−	3.87717e12i	0.0716315	−	0.124069i
$501$	3.18251e12			0.100828
$502$			7.90457e13i			2.47947i
$503$	−6.56230e12	+	1.13662e13i	−0.203805	+	0.353001i	−0.949751	−	0.313005i	$-0.898664\pi$
$503$	−6.56230e12	+	1.13662e13i	−0.203805	+	0.353001i	0.745946	+	0.666006i	$0.231998\pi$
$504$	−1.41871e13	−	8.19092e12i	−0.436255	−	0.251872i
$505$	−3.94704e12			−0.120175
$506$		−	1.01473e14i		−	3.05913i
$507$	2.11631e13	+	1.22185e13i	0.631743	+	0.364737i
$508$	7.34948e13	−	4.24323e13i	2.17239	−	1.25423i
$509$	−3.56332e13	−	2.05728e13i	−1.04295	−	0.602150i	−0.122286	−	0.992495i	$-0.539022\pi$
$509$	−3.56332e13	−	2.05728e13i	−1.04295	−	0.602150i	−0.920669	+	0.390345i	$0.872356\pi$
$510$	−1.00301e13	−	1.73727e13i	−0.290707	−	0.503519i
$511$	2.77635e13	+	4.80878e13i	0.796838	+	1.38016i
$512$		−	2.54644e12i		−	0.0723743i
$513$	−3.58607e13	+	1.37377e13i	−1.00933	+	0.386658i
$514$	−8.03148e13			−2.23862
$515$	−1.18487e13	+	6.84084e12i	−0.327065	+	0.188831i
$516$	−1.40016e13	+	8.08381e12i	−0.382761	+	0.220987i
$517$	1.54457e13	−	2.67527e13i	0.418171	−	0.724294i
$518$	−8.79021e12	−	1.52251e13i	−0.235695	−	0.408236i
$519$	−1.63332e13	+	2.82899e13i	−0.433744	+	0.751267i
$520$	2.31079e13			0.607776
$521$			7.11900e12i			0.185452i	0.995692	+	0.0927258i	$0.0295580\pi$
$521$			7.11900e12i			0.185452i	−0.995692	+	0.0927258i	$0.970442\pi$
$522$	3.70165e12	−	6.41144e12i	0.0955087	−	0.165426i
$523$	−4.86491e13	−	2.80876e13i	−1.24327	−	0.717804i	−0.273514	−	0.961868i	$-0.588186\pi$
$523$	−4.86491e13	−	2.80876e13i	−1.24327	−	0.717804i	−0.969759	+	0.244064i	$0.921519\pi$
$524$	1.25423e14			3.17484
$525$			7.42601e12i			0.186191i
$526$	−4.51571e13	−	2.60715e13i	−1.12150	−	0.647496i
$527$	−1.91333e13	+	1.10466e13i	−0.470693	+	0.271755i
$528$	1.25291e12	+	7.23367e11i	0.0305316	+	0.0176274i
$529$	−2.45724e13	−	4.25607e13i	−0.593157	−	1.02738i
$530$	6.37152e12	+	1.10358e13i	0.152357	+	0.263891i
$531$		−	3.22521e13i		−	0.763986i
$532$	8.26408e13	+	1.31466e13i	1.93926	+	0.308500i
$533$	6.39517e13			1.48668
$534$	−6.06825e12	+	3.50351e12i	−0.139752	+	0.0806857i
$535$	9.36061e12	−	5.40435e12i	0.213567	−	0.123303i
$536$	−1.19717e13	+	2.07355e13i	−0.270602	+	0.468696i
$537$	7.23588e12	+	1.25329e13i	0.162039	+	0.280660i
$538$	−4.10773e13	+	7.11480e13i	−0.911362	+	1.57852i
$539$	2.93490e13			0.645134
$540$		−	3.55500e13i		−	0.774232i
$541$	−7.15433e12	+	1.23917e13i	−0.154377	+	0.267389i	−0.932832	−	0.360312i	$-0.882670\pi$
$541$	−7.15433e12	+	1.23917e13i	−0.154377	+	0.267389i	0.778455	+	0.627700i	$0.216004\pi$
$542$	−2.26300e13	−	1.30654e13i	−0.483824	−	0.279336i
$543$	1.32518e13			0.280722
$544$			5.20330e13i			1.09216i
$545$	3.58115e13	+	2.06758e13i	0.744801	+	0.430011i
$546$	−8.83591e13	+	5.10142e13i	−1.82091	+	1.05130i
$547$	−5.34585e13	−	3.08643e13i	−1.09164	−	0.630260i	−0.157629	−	0.987498i	$-0.550385\pi$
$547$	−5.34585e13	−	3.08643e13i	−1.09164	−	0.630260i	−0.934013	+	0.357238i	$0.883718\pi$
$548$	−7.10725e13	−	1.23101e14i	−1.43813	−	2.49092i
$549$	−1.01820e13	−	1.76357e13i	−0.204160	−	0.353616i
$550$		−	2.08250e13i		−	0.413782i
$551$	−2.23196e12	+	1.40304e13i	−0.0439470	+	0.276255i
$552$	−5.58518e13			−1.08979
$553$	−4.88616e13	+	2.82102e13i	−0.944804	+	0.545483i
$554$	−8.34681e13	+	4.81903e13i	−1.59945	+	0.923445i
$555$	2.13147e12	−	3.69181e12i	0.0404775	−	0.0701092i
$556$	7.41369e12	+	1.28409e13i	0.139528	+	0.241669i
$557$	−3.77384e12	+	6.53648e12i	−0.0703894	+	0.121918i	−0.899072	−	0.437801i	$-0.855758\pi$
$557$	−3.77384e12	+	6.53648e12i	−0.0703894	+	0.121918i	0.828683	+	0.559719i	$0.189091\pi$
$558$	−1.89160e13			−0.349669
$559$		−	2.77722e13i		−	0.508805i
$560$	5.46454e11	−	9.46486e11i	0.00992232	−	0.0171860i
$561$	−4.97502e13	−	2.87233e13i	−0.895325	−	0.516916i
$562$	1.31314e14			2.34222
$563$		−	6.61453e12i		−	0.116938i	−0.998289	−	0.0584692i	$-0.981378\pi$
$563$		−	6.61453e12i		−	0.116938i	0.998289	−	0.0584692i	$-0.0186219\pi$
$564$	−3.91961e13	−	2.26299e13i	−0.686827	−	0.396540i
$565$	−1.54354e13	+	8.91165e12i	−0.268088	+	0.154780i
$566$	6.28522e13	+	3.62878e13i	1.08203	+	0.624709i
$567$	1.42760e13	+	2.47267e13i	0.243607	+	0.421940i
$568$	2.92047e13	+	5.05841e13i	0.493982	+	0.855602i
$569$			4.38926e13i			0.735918i	0.929842	+	0.367959i	$0.119943\pi$
$569$			4.38926e13i			0.735918i	−0.929842	+	0.367959i	$0.880057\pi$
$570$	1.17906e13	+	3.07779e13i	0.195957	+	0.511523i
$571$	7.81462e13			1.28744			0.643720	−	0.765261i	$-0.277390\pi$
$571$	7.81462e13			1.28744			0.643720	+	0.765261i	$0.277390\pi$
$572$	1.52549e14	−	8.80739e13i	2.49131	−	1.43836i
$573$	2.09215e13	−	1.20790e13i	0.338703	−	0.195550i
$574$	−6.54114e13	+	1.13296e14i	−1.04977	+	1.81826i
$575$	−9.29385e12	−	1.60974e13i	−0.147862	−	0.256104i
$576$	−2.17892e13	+	3.77400e13i	−0.343660	+	0.595236i
$577$	−5.86831e13			−0.917559			−0.458780	−	0.888550i	$-0.651713\pi$
$577$	−5.86831e13			−0.917559			−0.458780	+	0.888550i	$0.651713\pi$
$578$		−	1.31736e13i		−	0.204205i
$579$	−1.07219e13	+	1.85708e13i	−0.164770	+	0.285390i
$580$	−1.13897e13	−	6.57584e12i	−0.173529	−	0.100187i
$581$	−8.16480e13			−1.23329
$582$		−	5.16750e13i		−	0.773866i
$583$	3.16033e13	+	1.82462e13i	0.469234	+	0.270912i
$584$	−7.42252e13	+	4.28539e13i	−1.09266	+	0.630850i
$585$	1.57299e13	+	9.08168e12i	0.229587	+	0.132552i
$586$	7.06045e13	+	1.22291e14i	1.02175	+	1.76972i
$587$	4.95019e13	+	8.57398e13i	0.710283	+	1.23025i	0.964751	+	0.263165i	$0.0847664\pi$
$587$	4.95019e13	+	8.57398e13i	0.710283	+	1.23025i	−0.254468	+	0.967081i	$0.581900\pi$
$588$		−	4.30000e13i		−	0.611762i
$589$	3.38972e13	−	1.29855e13i	0.478175	−	0.183182i
$590$	−9.30652e13			−1.30175
$591$	5.11075e13	−	2.95069e13i	0.708838	−	0.409248i
$592$	−5.43335e11	+	3.13695e11i	−0.00747238	+	0.00431418i
$593$	2.97019e13	−	5.14452e13i	0.405052	−	0.701571i	−0.589275	−	0.807932i	$-0.700587\pi$
$593$	2.97019e13	−	5.14452e13i	0.405052	−	0.701571i	0.994328	+	0.106361i	$0.0339200\pi$
$594$	−8.26821e13	−	1.43210e14i	−1.11810	−	1.93660i
$595$	−2.16985e13	+	3.75829e13i	−0.290968	+	0.503971i
$596$	−9.49416e13			−1.26248
$597$			1.29494e13i			0.170757i
$598$	1.27691e14	−	2.21168e14i	1.66976	−	2.89211i
$599$	−1.06838e14	−	6.16831e13i	−1.38546	−	0.799893i	−0.392656	−	0.919685i	$-0.628444\pi$
$599$	−1.06838e14	−	6.16831e13i	−1.38546	−	0.799893i	−0.992799	+	0.119792i	$0.961777\pi$
$600$	−1.14623e13			−0.147406
$601$			8.81464e12i			0.112417i	0.998419	+	0.0562086i	$0.0179012\pi$
$601$			8.81464e12i			0.112417i	−0.998419	+	0.0562086i	$0.982099\pi$
$602$	4.92009e13	+	2.84061e13i	0.622287	+	0.359277i
$603$	−1.62986e13	+	9.41001e12i	−0.204439	+	0.118033i
$604$	−9.20218e13	−	5.31288e13i	−1.14474	−	0.660915i
$605$	−1.16940e13	−	2.02546e13i	−0.144274	−	0.249889i
$606$	1.34499e13	+	2.32959e13i	0.164572	+	0.285047i
$607$			4.64598e13i			0.563812i	0.959442	+	0.281906i	$0.0909666\pi$
$607$			4.64598e13i			0.563812i	−0.959442	+	0.281906i	$0.909033\pi$
$608$	1.34310e13	−	8.44288e13i	0.161656	−	1.01618i
$609$	2.18149e13			0.260415
$610$	−5.08888e13	+	2.93807e13i	−0.602523	+	0.347867i
$611$	6.73299e13	−	3.88729e13i	0.790682	−	0.456500i
$612$	3.08962e13	−	5.35138e13i	0.359872	−	0.623316i
$613$	4.32923e13	+	7.49844e13i	0.500159	+	0.866300i	1.00000		0.000183276i	$5.83385e-5\pi$
$613$	4.32923e13	+	7.49844e13i	0.500159	+	0.866300i	−0.499841	+	0.866117i	$0.666608\pi$
$614$	−4.52858e13	+	7.84373e13i	−0.518944	+	0.898837i
$615$	−3.17222e13			−0.360569
$616$			1.35369e14i			1.52622i
$617$	−8.01812e13	+	1.38878e14i	−0.896699	+	1.55313i	−0.0650110	+	0.997885i	$0.520708\pi$
$617$	−8.01812e13	+	1.38878e14i	−0.896699	+	1.55313i	−0.831688	+	0.555243i	$0.812625\pi$
$618$	8.07508e13	+	4.66215e13i	0.895787	+	0.517183i
$619$	1.86527e13			0.205252			0.102626	−	0.994720i	$-0.467276\pi$
$619$	1.86527e13			0.205252			0.102626	+	0.994720i	$0.467276\pi$
$620$			3.36035e13i			0.366797i
$621$	−1.27824e14	−	7.37992e13i	−1.38406	−	0.799086i
$622$	−2.36437e13	+	1.36507e13i	−0.253959	+	0.146623i
$623$	1.31276e13	+	7.57925e12i	0.139877	+	0.0807581i
$624$	1.82053e12	+	3.15326e12i	0.0192431	+	0.0333301i
$625$	−1.90735e12	−	3.30362e12i	−0.0200000	−	0.0346410i
$626$		−	2.69970e14i		−	2.80831i
$627$	7.33105e13	+	5.94482e13i	0.756534	+	0.613481i
$628$	2.70268e14			2.76692
$629$	2.15746e13	−	1.24561e13i	0.219124	−	0.126511i
$630$	−3.21779e13	+	1.85779e13i	−0.324232	+	0.187195i
$631$	7.99644e13	−	1.38502e14i	0.799374	−	1.38456i	−0.120651	−	0.992695i	$-0.538498\pi$
$631$	7.99644e13	−	1.38502e14i	0.799374	−	1.38456i	0.920025	−	0.391861i	$-0.128169\pi$
$632$	−4.35435e13	−	7.54195e13i	−0.431855	−	0.747994i
$633$	1.10550e13	−	1.91477e13i	0.108777	−	0.188408i
$634$	9.05500e13			0.883979
$635$		−	7.23107e13i		−	0.700380i
$636$	2.67329e13	−	4.63028e13i	0.256898	−	0.444961i
$637$	6.39683e13	+	3.69321e13i	0.609912	+	0.352133i
$638$	−6.11762e13			−0.578735
$639$			4.59112e13i			0.430938i
$640$	6.61105e13	+	3.81689e13i	0.615702	+	0.355476i
$641$	5.32037e12	−	3.07172e12i	0.0491645	−	0.0283851i	−0.475216	−	0.879869i	$-0.657630\pi$
$641$	5.32037e12	−	3.07172e12i	0.0491645	−	0.0283851i	0.524381	+	0.851484i	$0.324297\pi$
$642$	−6.37941e13	−	3.68316e13i	−0.584932	−	0.337711i
$643$	−8.42484e13	−	1.45923e14i	−0.766491	−	1.32760i	−0.939455	−	0.342673i	$-0.888668\pi$
$643$	−8.42484e13	−	1.45923e14i	−0.766491	−	1.32760i	0.172964	−	0.984928i	$-0.444666\pi$
$644$	1.60812e14	+	2.78535e14i	1.45174	+	2.51449i
$645$			1.37760e13i			0.123402i
$646$	−3.02601e13	+	1.90218e14i	−0.268972	+	1.69079i
$647$	5.93465e13			0.523448			0.261724	−	0.965143i	$-0.415709\pi$
$647$	5.93465e13			0.523448			0.261724	+	0.965143i	$0.415709\pi$
$648$	−3.81665e13	+	2.20355e13i	−0.334047	+	0.192862i
$649$	−2.30806e14	+	1.33256e14i	−2.00458	+	1.15734i
$650$	2.62057e13	−	4.53896e13i	0.225854	−	0.391191i
$651$	−2.78693e13	−	4.82711e13i	−0.238353	−	0.412840i
$652$	1.64825e14	−	2.85486e14i	1.39890	−	2.42296i
$653$	8.91043e13			0.750469			0.375235	−	0.926930i	$-0.377562\pi$
$653$	8.91043e13			0.750469			0.375235	+	0.926930i	$0.377562\pi$
$654$		−	2.81818e14i		−	2.35548i
$655$	5.34348e13	−	9.25518e13i	0.443218	−	0.767676i
$656$	4.04317e12	+	2.33433e12i	0.0332815	+	0.0192151i
$657$	−6.73684e13			−0.550338
$658$			1.59041e14i			1.28937i
$659$	−1.98928e14	−	1.14851e14i	−1.60055	−	0.924076i	−0.991378	−	0.131035i	$-0.958170\pi$
$659$	−1.98928e14	−	1.14851e14i	−1.60055	−	0.924076i	−0.609169	−	0.793041i	$-0.708497\pi$
$660$	−7.56692e13	+	4.36877e13i	−0.604226	+	0.348850i
$661$	2.72921e13	+	1.57571e13i	0.216286	+	0.124873i	0.604230	−	0.796810i	$-0.293481\pi$
$661$	2.72921e13	+	1.57571e13i	0.216286	+	0.124873i	−0.387943	+	0.921683i	$0.626814\pi$
$662$	−1.28279e13	−	2.22186e13i	−0.100894	−	0.174754i
$663$	−7.22894e13	−	1.25209e14i	−0.564296	−	0.977390i
$664$		−	1.26026e14i		−	0.976386i
$665$	4.49091e13	−	5.53811e13i	0.345323	−	0.425847i
$666$	2.13295e13			0.162783
$667$	−4.72883e13	+	2.73019e13i	−0.358199	+	0.206806i
$668$	2.44979e13	−	1.41438e13i	0.184181	−	0.106337i
$669$	9.75450e13	−	1.68953e14i	0.727905	−	1.26077i
$670$	2.71531e13	+	4.70305e13i	0.201115	+	0.348342i
$671$	−8.41376e13	+	1.45731e14i	−0.618554	+	1.07137i
$672$	−1.31273e14			−0.957919
$673$			5.31615e13i			0.385054i	0.981292	+	0.192527i	$0.0616684\pi$
$673$			5.31615e13i			0.385054i	−0.981292	+	0.192527i	$0.938332\pi$
$674$	−2.04042e14	+	3.53411e14i	−1.46696	+	2.54086i
$675$	−2.62329e13	−	1.51456e13i	−0.187210	−	0.108086i
$676$	2.17209e14			1.53867
$677$			1.05253e14i			0.740104i	0.929011	+	0.370052i	$0.120660\pi$
$677$			1.05253e14i			0.740104i	−0.929011	+	0.370052i	$0.879340\pi$
$678$	1.05195e14	+	6.07344e13i	0.734255	+	0.423923i
$679$	−9.68132e13	+	5.58951e13i	−0.670788	+	0.387280i
$680$	−5.80105e13	−	3.34924e13i	−0.398990	−	0.230357i
$681$	−8.94209e13	−	1.54882e14i	−0.610525	−	1.05746i
$682$	7.81549e13	+	1.35368e14i	0.529705	+	0.917476i
$683$			4.88869e12i			0.0328919i	0.999865	+	0.0164460i	$0.00523515\pi$
$683$			4.88869e12i			0.0328919i	−0.999865	+	0.0164460i	$0.994765\pi$
$684$	−6.39454e13	+	7.88564e13i	−0.427099	+	0.526692i
$685$	−1.21118e14			−0.803073
$686$	1.29313e14	−	7.46589e13i	0.851181	−	0.491430i
$687$	−1.29001e14	+	7.44785e13i	−0.842962	+	0.486684i
$688$	1.01372e12	−	1.75582e12i	0.00657624	−	0.0113904i
$689$	4.59210e13	+	7.95375e13i	0.295744	+	0.512243i
$690$	−6.33391e13	+	1.09707e14i	−0.404974	+	0.701435i
$691$	7.79377e13			0.494717			0.247359	−	0.968924i	$-0.420437\pi$
$691$	7.79377e13			0.494717			0.247359	+	0.968924i	$0.420437\pi$
$692$			2.90355e14i			1.82978i
$693$	−5.32017e13	+	9.21481e13i	−0.332859	+	0.576528i
$694$	−5.56703e13	−	3.21413e13i	−0.345801	−	0.199648i
$695$	1.26340e13			0.0779142
$696$			3.36720e13i			0.206169i
$697$	−1.60546e14	−	9.26910e13i	−0.975965	−	0.563474i
$698$	−8.88981e13	+	5.13253e13i	−0.536556	+	0.309781i
$699$	1.19352e14	+	6.89079e13i	0.715227	+	0.412936i
$700$	3.30030e13	+	5.71629e13i	0.196365	+	0.340114i
$701$	−7.13948e13	−	1.23659e14i	−0.421771	−	0.730528i	0.574342	−	0.818615i	$-0.305258\pi$
$701$	−7.13948e13	−	1.23659e14i	−0.421771	−	0.730528i	−0.996113	+	0.0880873i	$0.971925\pi$
$702$		−	4.16180e14i		−	2.44116i
$703$	−3.82223e13	+	1.46424e13i	−0.222607	+	0.0852775i
$704$	3.60104e14			2.08241
$705$	−3.33979e13	+	1.92823e13i	−0.191767	+	0.110717i
$706$	4.02895e13	−	2.32612e13i	0.229704	−	0.132620i
$707$	2.90966e13	−	5.03967e13i	0.164719	−	0.285302i
$708$	1.95236e14	+	3.38159e14i	1.09748	+	1.90088i
$709$	9.03108e13	−	1.56423e14i	0.504090	−	0.873110i	−0.495898	−	0.868381i	$-0.665161\pi$
$709$	9.03108e13	−	1.56423e14i	0.504090	−	0.873110i	0.999989	−	0.00472967i	$-0.00150550\pi$
$710$	1.32479e14			0.734270
$711$		−	6.84524e13i		−	0.376739i
$712$	−1.16988e13	+	2.02630e13i	−0.0639356	+	0.110740i
$713$	1.20825e14	+	6.97583e13i	0.655706	+	0.378572i
$714$	2.95758e14			1.59384
$715$		−	1.50091e14i		−	0.803200i
$716$	1.11399e14	+	6.43161e13i	0.591991	+	0.341786i
$717$	−1.12794e14	+	6.51214e13i	−0.595235	+	0.343659i
$718$	2.67290e14	+	1.54320e14i	1.40075	+	0.808723i
$719$	−1.56301e14	−	2.70721e14i	−0.813423	−	1.40889i	−0.910455	−	0.413608i	$-0.864268\pi$
$719$	−1.56301e14	−	2.70721e14i	−0.813423	−	1.40889i	0.0970320	−	0.995281i	$-0.469065\pi$
$720$	6.62987e11	+	1.14833e12i	0.00342644	+	0.00593476i
$721$		−	2.01716e14i		−	1.03529i
$722$	9.82001e13	−	3.00837e14i	0.500525	−	1.53336i
$723$	6.92562e13			0.350564
$724$	1.02008e14	−	5.88942e13i	0.512791	−	0.296060i
$725$	−9.70484e12	+	5.60309e12i	−0.0484505	+	0.0279729i
$726$	−7.96967e13	+	1.38039e14i	−0.395146	+	0.684413i
$727$	−7.14535e13	−	1.23761e14i	−0.351845	−	0.609414i	0.634728	−	0.772736i	$-0.281112\pi$
$727$	−7.14535e13	−	1.23761e14i	−0.351845	−	0.609414i	−0.986573	+	0.163322i	$0.947779\pi$
$728$	−1.70345e14	+	2.95047e14i	−0.833055	+	1.44289i
$729$	−2.03630e14			−0.989019
$730$			1.94395e14i			0.937716i
$731$	−4.02528e13	+	6.97199e13i	−0.192845	+	0.334018i
$732$	2.13514e14	+	1.23272e14i	1.01595	+	0.586557i
$733$	2.71885e13			0.128489			0.0642444	−	0.997934i	$-0.479536\pi$
$733$	2.71885e13			0.128489			0.0642444	+	0.997934i	$0.479536\pi$
$734$			4.19644e14i			1.96970i
$735$	−3.17304e13	−	1.83196e13i	−0.147924	−	0.0854041i
$736$	2.84561e14	−	1.64291e14i	1.31761	−	0.760722i
$737$	1.34682e14	+	7.77585e13i	0.619399	+	0.357610i
$738$	−7.93607e13	−	1.37457e14i	−0.362513	−	0.627891i
$739$	5.71563e13	+	9.89976e13i	0.259323	+	0.449161i	0.966061	−	0.258315i	$-0.0831671\pi$
$739$	5.71563e13	+	9.89976e13i	0.259323	+	0.449161i	−0.706737	+	0.707476i	$0.749834\pi$
$740$		−	3.78911e13i		−	0.170757i
$741$	8.49772e13	+	2.21824e14i	0.380375	+	0.992926i
$742$	−1.87877e14			−0.835321
$743$	5.67872e13	−	3.27861e13i	0.250788	−	0.144792i	−0.369337	−	0.929295i	$-0.620415\pi$
$743$	5.67872e13	−	3.27861e13i	0.250788	−	0.144792i	0.620125	+	0.784503i	$0.287082\pi$
$744$	7.45081e13	−	4.30172e13i	0.326843	−	0.188703i
$745$	−4.04486e13	+	7.00590e13i	−0.176247	+	0.305269i
$746$	2.37200e14	+	4.10842e14i	1.02664	+	1.77820i
$747$	4.95299e13	−	8.57883e13i	0.212944	−	0.368829i
$748$	−5.10614e14			−2.18064
$749$			1.59358e14i			0.676027i
$750$	−1.29989e13	+	2.25148e13i	−0.0547773	+	0.0948770i
$751$	−3.10188e13	−	1.79087e13i	−0.129845	−	0.0749661i	0.433670	−	0.901072i	$-0.357218\pi$
$751$	−3.10188e13	−	1.79087e13i	−0.129845	−	0.0749661i	−0.563516	+	0.826105i	$0.690552\pi$
$752$	5.67566e12			0.0236008
$753$		−	2.82591e14i		−	1.16730i
$754$	−1.33338e14	−	7.69827e13i	−0.547138	−	0.315890i
$755$	−7.84092e13	+	4.52696e13i	−0.319619	+	0.184532i
$756$	4.53911e14	+	2.62066e14i	1.83807	+	1.06121i
$757$	−1.84024e14	−	3.18739e14i	−0.740278	−	1.28220i	−0.952369	−	0.304949i	$-0.901360\pi$
$757$	−1.84024e14	−	3.18739e14i	−0.740278	−	1.28220i	0.212090	−	0.977250i	$-0.431973\pi$
$758$	1.99841e14	+	3.46134e14i	0.798615	+	1.38324i
$759$			3.62769e14i			1.44020i
$760$	8.54826e13	+	6.93187e13i	0.337139	+	0.273390i
$761$	−3.80709e14			−1.49166			−0.745830	−	0.666137i	$-0.767947\pi$
$761$	−3.80709e14			−1.49166			−0.745830	+	0.666137i	$0.767947\pi$
$762$	−4.26785e14	+	2.46405e14i	−1.66125	+	0.959123i
$763$	−5.27986e14	+	3.04833e14i	−2.04174	+	1.17880i
$764$	1.07364e14	−	1.85960e14i	0.412471	−	0.714420i
$765$	−2.63258e13	−	4.55976e13i	−0.100479	−	0.174034i
$766$	−7.87976e13	+	1.36481e14i	−0.298792	+	0.517523i
$767$	−6.70743e14			−2.52685
$768$		−	1.90862e14i		−	0.714352i
$769$	2.39826e14	−	4.15391e14i	0.891794	−	1.54463i	0.0540719	−	0.998537i	$-0.482780\pi$
$769$	2.39826e14	−	4.15391e14i	0.891794	−	1.54463i	0.837722	−	0.546096i	$-0.183887\pi$
$770$	2.65898e14	+	1.53517e14i	0.982341	+	0.567155i
$771$	2.87128e14			1.05391
$772$			1.90603e14i			0.695092i
$773$	2.44108e14	+	1.40936e14i	0.884474	+	0.510651i	0.872131	−	0.489273i	$-0.162738\pi$
$773$	2.44108e14	+	1.40936e14i	0.884474	+	0.510651i	0.0123430	+	0.999924i	$0.496071\pi$
$774$	−5.96932e13	+	3.44639e13i	−0.214892	+	0.124068i
$775$	2.47966e13	+	1.43163e13i	0.0886917	+	0.0512062i
$776$	−8.62760e13	−	1.49434e14i	−0.306607	−	0.531058i
$777$	3.14253e13	+	5.44302e13i	0.110962	+	0.192192i
$778$		−	4.23449e14i		−	1.48560i
$779$	2.36575e14	+	1.91841e14i	0.824674	+	0.668736i
$780$	−2.19902e14			−0.761651
$781$	3.28554e14	−	1.89691e14i	1.13071	−	0.652816i
$782$	−6.41116e14	+	3.70148e14i	−2.19231	+	1.26573i
$783$	−4.44922e13	+	7.70628e13i	−0.151173	+	0.261840i
$784$	2.69614e12	+	4.66986e12i	0.00910254	+	0.0157661i
$785$	1.15144e14	−	1.99435e14i	0.386272	−	0.669043i
$786$	−7.28334e14			−2.42783
$787$			1.63763e14i			0.542429i	0.962519	+	0.271214i	$0.0874252\pi$
$787$			1.63763e14i			0.542429i	−0.962519	+	0.271214i	$0.912575\pi$
$788$	2.62272e14	−	4.54268e14i	0.863219	−	1.49514i
$789$	1.61438e14	+	9.32063e13i	0.527984	+	0.304832i
$790$	−1.97523e14			−0.641922
$791$		−	2.62778e14i		−	0.848605i
$792$	−1.42234e14	−	8.21187e13i	−0.456433	−	0.263522i
$793$	−3.66768e14	+	2.11753e14i	−1.16957	+	0.675250i
$794$	−1.77329e14	−	1.02381e14i	−0.561924	−	0.324427i
$795$	−2.27784e13	−	3.94533e13i	−0.0717277	−	0.124236i
$796$	5.75504e13	+	9.96803e13i	0.180087	+	0.311920i
$797$			1.70767e14i			0.531020i	0.964108	+	0.265510i	$0.0855404\pi$
$797$			1.70767e14i			0.531020i	−0.964108	+	0.265510i	$0.914460\pi$
$798$	−4.79896e14	−	7.63425e13i	−1.48297	−	0.235913i
$799$	−2.25368e14			−0.692083
$800$	5.83996e13	−	3.37170e13i	0.178222	−	0.102896i
$801$	−1.59272e13	+	9.19556e12i	−0.0483032	+	0.0278879i
$802$	2.77038e14	−	4.79844e14i	0.834964	−	1.44620i
$803$	2.78345e14	+	4.82108e14i	0.833693	+	1.44400i
$804$	1.13926e14	−	1.97326e14i	0.339112	−	0.587358i
$805$	2.74047e14			0.810673
$806$			3.93392e14i			1.15651i
$807$	1.46853e14	−	2.54356e14i	0.429056	−	0.743147i
$808$	7.77891e13	+	4.49115e13i	0.225872	+	0.130407i
$809$	5.27174e14			1.52129			0.760643	−	0.649170i	$-0.224884\pi$
$809$	5.27174e14			1.52129			0.760643	+	0.649170i	$0.224884\pi$
$810$			9.99578e13i			0.286676i
$811$	−5.22253e14	−	3.01523e14i	−1.48860	−	0.859442i	−0.488682	−	0.872462i	$-0.662522\pi$
$811$	−5.22253e14	−	3.01523e14i	−1.48860	−	0.859442i	−0.999915	+	0.0130204i	$0.995855\pi$
$812$	1.67924e14	−	9.69507e13i	0.475698	−	0.274645i
$813$	8.09028e13	+	4.67093e13i	0.227777	+	0.131507i
$814$	−8.81269e13	−	1.52640e14i	−0.246596	−	0.427117i
$815$	−1.40443e14	−	2.43255e14i	−0.390582	−	0.676508i
$816$		−	1.05547e13i		−	0.0291738i
$817$	8.33106e13	−	1.02737e14i	0.228871	−	0.282239i
$818$	−2.90480e14			−0.793139
$819$	−2.31914e14	+	1.33896e14i	−0.629372	+	0.363368i
$820$	−2.44187e14	+	1.40981e14i	−0.658648	+	0.380270i
$821$	2.34940e14	−	4.06929e14i	0.629857	−	1.09094i	−0.357723	−	0.933828i	$-0.616447\pi$
$821$	2.34940e14	−	4.06929e14i	0.629857	−	1.09094i	0.987580	−	0.157117i	$-0.0502199\pi$
$822$	4.12719e14	+	7.14851e14i	1.09975	+	1.90483i
$823$	−1.87664e14	+	3.25043e14i	−0.497028	+	0.860878i	−0.999994	−	0.00342788i	$-0.998909\pi$
$823$	−1.87664e14	+	3.25043e14i	−0.497028	+	0.860878i	0.502966	+	0.864306i	$0.332242\pi$
$824$	3.11355e14			0.819633
$825$			7.44501e13i			0.194803i
$826$	6.86052e14	−	1.18828e15i	1.78426	−	3.09042i
$827$	5.38147e14	+	3.10699e14i	1.39115	+	0.803180i	0.993442	−	0.114333i	$-0.0364731\pi$
$827$	5.38147e14	+	3.10699e14i	1.39115	+	0.803180i	0.397706	+	0.917513i	$0.369806\pi$
$828$	−3.90212e14			−1.00265
$829$		−	4.77637e13i		−	0.121990i	−0.998138	−	0.0609952i	$-0.980573\pi$
$829$		−	4.77637e13i		−	0.121990i	0.998138	−	0.0609952i	$-0.0194274\pi$
$830$	−2.47547e14	−	1.42921e14i	−0.628444	−	0.362833i
$831$	2.98401e14	−	1.72282e14i	0.753000	−	0.434745i
$832$	7.84873e14	+	4.53147e14i	1.96871	+	1.13664i
$833$	−1.07058e14	−	1.85430e14i	−0.266928	−	0.462333i
$834$	−4.30514e13	−	7.45672e13i	−0.106698	−	0.184807i
$835$		−	2.41032e13i		−	0.0593802i
$836$	8.28522e14	+	1.31802e14i	2.02896	+	0.322769i
$837$	2.27362e14			0.553465
$838$	−4.57209e14	+	2.63970e14i	−1.10636	+	0.638755i
$839$	−6.02081e14	+	3.47612e14i	−1.44826	+	0.836151i	−0.998378	−	0.0569392i	$-0.981866\pi$
$839$	−6.02081e14	+	3.47612e14i	−1.44826	+	0.836151i	−0.449878	+	0.893090i	$0.648533\pi$
$840$	8.44971e13	−	1.46353e14i	0.202044	−	0.349950i
$841$	−1.93894e14	−	3.35834e14i	−0.460876	−	0.798260i
$842$	5.84785e14	−	1.01288e15i	1.38177	−	2.39330i
$843$	−4.69450e14			−1.10269
$844$		−	1.96524e14i		−	0.458884i
$845$	9.25388e13	−	1.60282e14i	0.214803	−	0.372050i
$846$	−1.67106e14	−	9.64785e13i	−0.385602	−	0.222627i
$847$	3.44821e14			0.791000
$848$			6.70472e12i			0.0152898i
$849$	−2.24699e14	−	1.29730e14i	−0.509404	−	0.294104i
$850$	−1.31574e14	+	7.59645e13i	−0.296535	+	0.171205i
$851$	−1.36242e14	−	7.86591e13i	−0.305254	−	0.176239i
$852$	−2.77921e14	−	4.81373e14i	−0.619047	−	1.07222i
$853$	−2.79458e14	−	4.84035e14i	−0.618830	−	1.07184i	−0.989700	−	0.143160i	$-0.954274\pi$
$853$	−2.79458e14	−	4.84035e14i	−0.618830	−	1.07184i	0.370870	−	0.928685i	$-0.379060\pi$
$854$		−	8.66347e14i		−	1.90723i
$855$	3.09463e13	+	8.07820e13i	0.0677296	+	0.176801i
$856$	−2.45974e14			−0.535206
$857$	6.67600e12	−	3.85439e12i	0.0144415	−	0.00833781i	−0.492762	−	0.870164i	$-0.664013\pi$
$857$	6.67600e12	−	3.85439e12i	0.0144415	−	0.00833781i	0.507203	+	0.861826i	$0.330679\pi$
$858$	−8.85852e14	+	5.11447e14i	−1.90513	+	1.09993i
$859$	−2.29339e14	+	3.97227e14i	−0.490356	+	0.849322i	−0.999938	−	0.0110998i	$-0.996467\pi$
$859$	−2.29339e14	+	3.97227e14i	−0.490356	+	0.849322i	0.509582	+	0.860422i	$0.329800\pi$
$860$	6.12238e13	+	1.06043e14i	0.130145	+	0.225418i
$861$	2.33848e14	−	4.05037e14i	0.494217	−	0.856009i
$862$	1.12250e15			2.35859
$863$		−	3.69065e14i		−	0.770990i	−0.922710	−	0.385495i	$-0.874031\pi$
$863$		−	3.69065e14i		−	0.770990i	0.922710	−	0.385495i	$-0.125969\pi$
$864$	2.67735e14	−	4.63731e14i	0.556080	−	0.963158i
$865$	2.14257e14	+	1.23701e14i	0.442441	+	0.255443i
$866$	−6.98416e14			−1.43392
$867$			4.70962e13i			0.0961369i
$868$	−4.29057e14	−	2.47716e14i	−0.870796	−	0.502754i
$869$	−4.89865e14	+	2.82824e14i	−0.988503	+	0.570712i
$870$	6.61401e13	+	3.81860e13i	0.132699	+	0.0766140i
$871$	1.95699e14	+	3.38960e14i	0.390388	+	0.676173i
$872$	−4.70520e14	−	8.14965e14i	−0.933245	−	1.61643i
$873$		−	1.35630e14i		−	0.267476i
$874$	1.13582e15	−	4.35115e14i	2.22716	−	0.853192i
$875$	5.62419e13			0.109653
$876$	7.06349e14	−	4.07811e14i	1.36930	−	0.790567i
$877$	3.89490e14	−	2.24872e14i	0.750754	−	0.433448i	−0.0752121	−	0.997168i	$-0.523963\pi$
$877$	3.89490e14	−	2.24872e14i	0.750754	−	0.433448i	0.825966	+	0.563719i	$0.190630\pi$
$878$	1.31795e14	−	2.28275e14i	0.252595	−	0.437508i
$879$	−2.52413e14	−	4.37193e14i	−0.481026	−	0.833161i
$880$	5.47851e12	−	9.48907e12i	0.0103812	−	0.0179808i
$881$	3.44384e14			0.648878			0.324439	−	0.945907i	$-0.394825\pi$
$881$	3.44384e14			0.648878			0.324439	+	0.945907i	$0.394825\pi$
$882$		−	1.83323e14i		−	0.343458i
$883$	−3.82943e14	+	6.63276e14i	−0.713395	+	1.23564i	0.250180	+	0.968199i	$0.419510\pi$
$883$	−3.82943e14	+	6.63276e14i	−0.713395	+	1.23564i	−0.963575	+	0.267438i	$0.913823\pi$
$884$	−1.11292e15	−	6.42544e14i	−2.06159	−	1.19026i
$885$	3.32711e14			0.612845
$886$		−	1.40668e15i		−	2.57647i
$887$	−2.53580e14	−	1.46405e14i	−0.461846	−	0.266647i	0.250974	−	0.967994i	$-0.419249\pi$
$887$	−2.53580e14	−	1.46405e14i	−0.461846	−	0.266647i	−0.712820	+	0.701347i	$0.752582\pi$
$888$	−8.40148e13	+	4.85060e13i	−0.152157	+	0.0878477i
$889$	9.23279e14	+	5.33055e14i	1.66274	+	0.959983i
$890$	2.65343e13	+	4.59587e13i	0.0475179	+	0.0823034i
$891$	1.43125e14	+	2.47900e14i	0.254875	+	0.441456i
$892$		−	1.73406e15i		−	3.07071i
$893$	3.65682e14	+	5.81731e13i	0.643942	+	0.102439i
$894$	5.51328e14			0.965433
$895$	9.49197e13	−	5.48019e13i	0.165288	−	0.0954290i
$896$	−9.74698e14	+	5.62742e14i	−1.68784	+	0.974472i
$897$	−4.56500e14	+	7.90681e14i	−0.786101	+	1.36157i
$898$	1.51275e14	+	2.62016e14i	0.259052	+	0.448690i
$899$	4.20560e13	−	7.28432e13i	0.0716193	−	0.124048i
$900$	−8.00821e13			−0.135620
$901$		−	2.66230e14i		−	0.448366i
$902$	−6.55788e14	+	1.13586e15i	−1.09832	+	1.90235i
$903$	−1.75895e14	−	1.01553e14i	−0.292964	−	0.169143i
$904$	4.05606e14			0.671834
$905$		−	1.00364e14i		−	0.165324i
$906$	5.34372e14	+	3.08520e14i	0.875392	+	0.505408i
$907$	−2.85961e14	+	1.65099e14i	−0.465876	+	0.268973i	−0.714512	−	0.699624i	$-0.753351\pi$
$907$	−2.85961e14	+	1.65099e14i	−0.465876	+	0.268973i	0.248636	+	0.968597i	$0.420018\pi$
$908$	−1.37666e15	−	7.94817e14i	−2.23048	−	1.28777i
$909$	3.53015e13	+	6.11441e13i	0.0568819	+	0.0985224i
$910$	3.86363e14	+	6.69200e14i	0.619139	+	1.07238i
$911$		−	2.08759e13i		−	0.0332701i	−0.999862	−	0.0166351i	$-0.994705\pi$
$911$		−	2.08759e13i		−	0.0332701i	0.999862	−	0.0166351i	$-0.00529535\pi$
$912$	−2.72442e12	+	1.71260e13i	−0.00431817	+	0.0271445i
$913$	−8.18568e14			−1.29033
$914$	−6.63323e14	+	3.82970e14i	−1.03991	+	0.600390i
$915$	1.81929e14	−	1.05037e14i	0.283659	−	0.163771i
$916$	−6.62001e14	+	1.14662e15i	−1.02655	+	1.77804i
$917$	7.87814e14	+	1.36453e15i	1.21500	+	2.10445i
$918$	−6.03208e14	+	1.04479e15i	−0.925238	+	1.60256i
$919$	9.63760e14			1.47025			0.735126	−	0.677931i	$-0.237123\pi$
$919$	9.63760e14			1.47025			0.735126	+	0.677931i	$0.237123\pi$
$920$			4.23001e14i			0.641804i
$921$	1.61898e14	−	2.80416e14i	0.244311	−	0.423160i
$922$	1.36048e13	+	7.85471e12i	0.0204191	+	0.0117890i
$923$	9.54808e14			1.42530
$924$		−	1.28822e15i		−	1.91262i
$925$	−2.79604e13	−	1.61430e13i	−0.0412891	−	0.0238383i
$926$	−1.66792e15	+	9.62974e14i	−2.44974	+	1.41436i
$927$	2.11944e14	+	1.22366e14i	0.309616	+	0.178757i
$928$	−9.90483e13	−	1.71557e14i	−0.143915	−	0.249269i
$929$	4.38865e14	+	7.60136e14i	0.634237	+	1.09853i	0.986676	+	0.162697i	$0.0520192\pi$
$929$	4.38865e14	+	7.60136e14i	0.634237	+	1.09853i	−0.352439	+	0.935835i	$0.614647\pi$
$930$		−	1.95136e14i		−	0.280493i
$931$	1.25848e14	+	3.28513e14i	0.179928	+	0.469682i
$932$	1.22497e15			1.74200
$933$	8.45270e13	−	4.88017e13i	0.119560	−	0.0690282i
$934$	9.70748e14	−	5.60462e14i	1.36575	−	0.788518i
$935$	−2.17540e14	+	3.76790e14i	−0.304425	+	0.527280i
$936$	−2.06672e14	−	3.57967e14i	−0.287676	−	0.498269i
$937$	1.36321e14	−	2.36115e14i	0.188740	−	0.326907i	−0.756090	−	0.654467i	$-0.772893\pi$
$937$	1.36321e14	−	2.36115e14i	0.188740	−	0.326907i	0.944830	+	0.327560i	$0.106226\pi$
$938$	−8.00662e14			−1.10264
$939$			9.65152e14i			1.32211i
$940$	−1.71390e14	+	2.96857e14i	−0.233532	+	0.404490i
$941$	1.89406e14	+	1.09354e14i	0.256711	+	0.148212i	0.622834	−	0.782354i	$-0.285981\pi$
$941$	1.89406e14	+	1.09354e14i	0.256711	+	0.148212i	−0.366122	+	0.930567i	$0.619315\pi$
$942$	−1.56945e15			−2.11589
$943$			1.17067e15i			1.56991i
$944$	−4.24058e13	−	2.44830e13i	−0.0565673	−	0.0326592i
$945$	3.86765e14	−	2.23299e14i	0.513201	−	0.296297i
$946$	4.93267e14	+	2.84788e14i	0.651068	+	0.375894i
$947$	−3.22049e13	−	5.57805e13i	−0.0422836	−	0.0732374i	0.844109	−	0.536172i	$-0.180130\pi$
$947$	−3.22049e13	−	5.57805e13i	−0.0422836	−	0.0732374i	−0.886393	+	0.462934i	$0.846797\pi$
$948$	4.14373e14	+	7.17715e14i	0.541190	+	0.937368i
$949$			1.40105e15i			1.82022i
$950$	2.33101e14	−	8.92973e13i	0.301249	−	0.115404i
$951$	−3.23719e14			−0.416165
$952$	8.55276e14	−	4.93794e14i	1.09376	−	0.631482i
$953$	1.78921e14	−	1.03300e14i	0.227613	−	0.131413i	−0.381857	−	0.924221i	$-0.624715\pi$
$953$	1.78921e14	−	1.03300e14i	0.227613	−	0.131413i	0.609471	+	0.792809i	$0.291382\pi$
$954$	1.13971e14	−	1.97404e14i	0.144229	−	0.249812i
$955$	−9.14821e13	−	1.58452e14i	−0.115165	−	0.199471i
$956$	−5.78831e14	+	1.00257e15i	−0.724874	+	1.25552i
$957$	2.18707e14			0.272460
$958$			1.81060e14i			0.224386i
$959$	8.92849e14	−	1.54646e15i	1.10074	−	1.90654i
$960$	−3.89324e14	−	2.24776e14i	−0.477479	−	0.275673i
$961$	6.04716e14			0.737793
$962$		−	4.43587e14i		−	0.538398i
$963$	−1.67439e14	−	9.66708e13i	−0.202174	−	0.116725i
$964$	5.33111e14	−	3.07792e14i	0.640372	−	0.369719i
$965$	1.40649e14	+	8.12036e13i	0.168074	+	0.0970373i
$966$	−9.33839e14	−	1.61746e15i	−1.11016	−	1.92286i
$967$	1.58842e14	+	2.75122e14i	0.187859	+	0.325381i	0.944536	−	0.328407i	$-0.106512\pi$
$967$	1.58842e14	+	2.75122e14i	0.187859	+	0.325381i	−0.756677	+	0.653789i	$0.773179\pi$
$968$			5.32243e14i			0.626229i
$969$	1.08181e14	−	6.80035e14i	0.126628	−	0.795999i
$970$	−3.91368e14			−0.455749
$971$	−1.43399e15	+	8.27913e14i	−1.66130	+	0.959154i	−0.689210	+	0.724562i	$0.742042\pi$
$971$	−1.43399e15	+	8.27913e14i	−1.66130	+	0.959154i	−0.972094	+	0.234593i	$0.924624\pi$
$972$	−9.37619e14	+	5.41334e14i	−1.08067	+	0.623928i
$973$	−9.31345e13	+	1.61314e14i	−0.106794	+	0.184972i
$974$	2.31063e14	+	4.00213e14i	0.263594	+	0.456558i
$975$	−9.36861e13	+	1.62269e14i	−0.106329	+	0.184167i
$976$	−3.09172e13			−0.0349101
$977$		−	1.58546e15i		−	1.78107i	−0.454913	−	0.890536i	$-0.650330\pi$
$977$		−	1.58546e15i		−	1.78107i	0.454913	−	0.890536i	$-0.349670\pi$
$978$	−9.57143e14	+	1.65782e15i	−1.06975	+	1.85286i
$979$	1.31612e14	+	7.59864e13i	0.146347	+	0.0844933i
$980$	−3.25667e14			−0.360282
$981$		−	7.39680e14i		−	0.814140i
$982$	−5.01399e14	−	2.89483e14i	−0.549068	−	0.317005i
$983$	8.29997e14	−	4.79199e14i	0.904293	−	0.522094i	0.0257024	−	0.999670i	$-0.491818\pi$
$983$	8.29997e14	−	4.79199e14i	0.904293	−	0.522094i	0.878590	+	0.477576i	$0.158484\pi$
$984$	6.25188e14	+	3.60952e14i	0.677696	+	0.391268i
$985$	−2.23475e14	−	3.87069e14i	−0.241017	−	0.417453i
$986$	2.23156e14	+	3.86517e14i	0.239455	+	0.414748i
$987$		−	5.68576e14i		−	0.607019i
$988$	1.63996e15	+	1.32986e15i	1.74201	+	1.41261i
$989$	5.08384e14			0.537292
$990$	−3.22602e14	+	1.86255e14i	−0.339228	+	0.195853i
$991$	2.18043e14	−	1.25887e14i	0.228125	−	0.131708i	−0.381582	−	0.924335i	$-0.624620\pi$
$991$	2.18043e14	−	1.25887e14i	0.228125	−	0.131708i	0.609707	+	0.792627i	$0.291287\pi$
$992$	−2.53076e14	+	4.38340e14i	−0.263446	+	0.456302i
$993$	4.58602e13	+	7.94322e13i	0.0474995	+	0.0822716i
$994$	−9.76602e14	+	1.69152e15i	−1.00643	+	1.74320i
$995$	9.80742e13			0.100563
$996$			1.19931e15i			1.22358i
$997$	−7.24928e14	+	1.25561e15i	−0.735901	+	1.27462i	0.218426	+	0.975853i	$0.429908\pi$
$997$	−7.24928e14	+	1.25561e15i	−0.735901	+	1.27462i	−0.954327	+	0.298764i	$0.903426\pi$
$998$	−1.40799e15	−	8.12903e14i	−1.42215	−	0.821081i
$999$	−2.56371e14			−0.257657

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.11.j.a.31.10	✓	136
19.8	odd	6	inner	95.11.j.a.46.10	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.11.j.a.31.10	✓	136	1.1	even	1	trivial
95.11.j.a.46.10	yes	136	19.8	odd	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	95.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-44.7004 + 25.8078i) q^{2} +(159.805 - 92.2637i) q^{3} +(820.085 - 1420.43i) q^{4} +(-698.771 - 1210.31i) q^{5} +(-4762.24 + 8248.45i) q^{6} +20604.6 q^{7} +31804.0i q^{8} +(-12499.3 + 21649.5i) q^{9} +(62470.7 + 36067.5i) q^{10} +206573. q^{11} -302656. i q^{12} +(450241. + 259947. i) q^{13} +(-921036. + 531760. i) q^{14} +(-223335. - 128942. i) q^{15} +(18976.8 + 32868.8i) q^{16} +(-753528. - 1.30515e6i) q^{17} -1.29032e6i q^{18} +(885783. + 2.31224e6i) q^{19} -2.29221e6 q^{20} +(3.29273e6 - 1.90106e6i) q^{21} +(-9.23391e6 + 5.33120e6i) q^{22} +(-4.75845e6 + 8.24188e6i) q^{23} +(2.93435e6 + 5.08244e6i) q^{24} +(-976562. + 1.69146e6i) q^{25} -2.68346e7 q^{26} +1.55091e7i q^{27} +(1.68975e7 - 2.92674e7i) q^{28} +(4.96888e6 + 2.86878e6i) q^{29} +1.33109e7 q^{30} -1.46599e7i q^{31} +(-2.99006e7 - 1.72631e7i) q^{32} +(3.30115e7 - 1.90592e7i) q^{33} +(6.73661e7 + 3.88938e7i) q^{34} +(-1.43979e7 - 2.49379e7i) q^{35} +(2.05010e7 + 3.55088e7i) q^{36} +1.65304e7i q^{37} +(-9.92687e7 - 8.04980e7i) q^{38} +9.59346e7 q^{39} +(3.84926e7 - 2.22237e7i) q^{40} +(1.06529e8 - 6.15047e7i) q^{41} +(-9.81243e7 + 1.69956e8i) q^{42} +(-2.67095e7 - 4.62623e7i) q^{43} +(1.69408e8 - 2.93423e8i) q^{44} +3.49367e7 q^{45} -4.91220e8i q^{46} +(7.47709e7 - 1.29507e8i) q^{47} +(6.06520e6 + 3.50174e6i) q^{48} +1.42076e8 q^{49} -1.00812e8i q^{50} +(-2.40836e8 - 1.39047e8i) q^{51} +(7.38472e8 - 4.26357e8i) q^{52} +(1.52988e8 + 8.83277e7i) q^{53} +(-4.00255e8 - 6.93263e8i) q^{54} +(-1.44348e8 - 2.50017e8i) q^{55} +6.55309e8i q^{56} +(3.54889e8 + 2.87783e8i) q^{57} -2.96148e8 q^{58} +(-1.11731e9 + 6.45077e8i) q^{59} +(-3.66307e8 + 2.11487e8i) q^{60} +(-4.07302e8 + 7.05467e8i) q^{61} +(3.78339e8 + 6.55303e8i) q^{62} +(-2.57544e8 + 4.46079e8i) q^{63} +1.74323e9 q^{64} -7.26573e8i q^{65} +(-9.83753e8 + 1.70391e9i) q^{66} +(6.51980e8 + 3.76421e8i) q^{67} -2.47183e9 q^{68} +1.75613e9i q^{69} +(1.28719e9 + 7.43157e8i) q^{70} +(1.59050e9 - 9.18273e8i) q^{71} +(-6.88539e8 - 3.97528e8i) q^{72} +(1.34744e9 + 2.33383e9i) q^{73} +(-4.26613e8 - 7.38916e8i) q^{74} +3.60405e8i q^{75} +(4.01079e9 + 6.38041e8i) q^{76} +4.25637e9 q^{77} +(-4.28831e9 + 2.47586e9i) q^{78} +(-2.37139e9 + 1.36912e9i) q^{79} +(2.65209e7 - 4.59356e7i) q^{80} +(6.92853e8 + 1.20006e9i) q^{81} +(-3.17460e9 + 5.49857e9i) q^{82} -3.96260e9 q^{83} -6.23612e9i q^{84} +(-1.05309e9 + 1.82400e9i) q^{85} +(2.38786e9 + 1.37863e9i) q^{86} +1.05874e9 q^{87} +6.56985e9i q^{88} +(6.37121e8 + 3.67842e8i) q^{89} +(-1.56168e9 + 9.01639e8i) q^{90} +(9.27705e9 + 5.35611e9i) q^{91} +(7.80466e9 + 1.35181e10i) q^{92} +(-1.35258e9 - 2.34273e9i) q^{93} +7.71869e9i q^{94} +(2.17956e9 - 2.68780e9i) q^{95} -6.37104e9 q^{96} +(-4.69861e9 + 2.71274e9i) q^{97} +(-6.35084e9 + 3.66666e9i) q^{98} +(-2.58203e9 + 4.47220e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 132 q^{3} + 37474 q^{4} - 1022 q^{6} - 76620 q^{7} + 1448988 q^{9} + 93750 q^{10} + 418144 q^{11} - 1256574 q^{13} + 612480 q^{14} - 20575630 q^{16} + 3635834 q^{17} + 10572814 q^{19} + 8494308 q^{21}+ \cdots - 8878413234 q^{99}+O(q^{100}) \) 136 * q - 132 * q^3 + 37474 * q^4 - 1022 * q^6 - 76620 * q^7 + 1448988 * q^9 + 93750 * q^10 + 418144 * q^11 - 1256574 * q^13 + 612480 * q^14 - 20575630 * q^16 + 3635834 * q^17 + 10572814 * q^19 + 8494308 * q^21 - 31311360 * q^22 - 11728554 * q^23 - 1627348 * q^24 - 132812500 * q^25 - 5280948 * q^26 - 81401852 * q^28 - 36928518 * q^29 + 79750000 * q^30 + 196574250 * q^32 + 359004150 * q^33 + 205341462 * q^34 + 19937500 * q^35 - 1128154804 * q^36 + 1584974 * q^38 + 224945180 * q^39 + 96000000 * q^40 + 1170402744 * q^41 + 173440898 * q^42 - 390292220 * q^43 - 49120052 * q^44 - 148625000 * q^45 - 445097680 * q^47 + 362033562 * q^48 + 3958185060 * q^49 + 995976516 * q^51 + 7766334 * q^52 + 815693040 * q^53 + 2049344062 * q^54 + 3831676392 * q^57 + 3983452220 * q^58 + 2842939668 * q^59 - 1389656250 * q^60 + 1929307508 * q^61 - 2885441744 * q^62 - 5022307122 * q^63 - 29425336368 * q^64 + 2939512012 * q^66 + 1891858296 * q^67 + 18554561860 * q^68 - 810562500 * q^70 - 8973340848 * q^71 + 7541812308 * q^72 + 4947578188 * q^73 - 23389998076 * q^74 + 15724739728 * q^76 - 5682818404 * q^77 - 10507817400 * q^78 + 16066927146 * q^79 + 3604750000 * q^80 - 43776877608 * q^81 - 13564413998 * q^82 + 2628386824 * q^83 - 2399750000 * q^85 + 38885030448 * q^86 + 12840668220 * q^87 - 35640122064 * q^89 + 3198281250 * q^90 + 4174912572 * q^91 - 23134882520 * q^92 - 36221884016 * q^93 - 1613500000 * q^95 + 13864395128 * q^96 - 23558943450 * q^97 + 31730410686 * q^98 - 8878413234 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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