LMFDB - Embedded newform 12.21.d.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,21,Mod(7,12)]

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, 0]))

N = Newforms(chi, 21, names="a")

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

chi := DirichletCharacter("12.7");

S:= CuspForms(chi, 21);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	12.d (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:	$30.4216518123$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} - 1800529 x^{18} + 10471600 x^{17} + 1401323871170 x^{16} - 8255926364216 x^{15} + \cdots + 17\!\cdots\!88 $ x^20 - 8x^19 - 1800529x^18 + 10471600x^17 + 1401323871170x^16 - 8255926364216x^15 - 618094244121155086x^14 + 4776792556997860420x^13 + 170108290172014159730219x^12 - 1822962046954348428067604x^11 - 30268361797163656482757584955x^10 + 429273525493411897272285527056x^9 + 3482282078039849041741632502870994x^8 - 60435809630459978311045044131417084x^7 - 250759366568586243949566404606021171194x^6 + 4820660604980619237148365440042241179296x^5 + 10477847059140453507669781324292395546888841x^4 - 190400851192787000531616700775511384585564956x^3 - 219026547432574645023476742933634147067753863733x^2 + 2495516610278349515190181419629668858430612303484*x + 1754305378275820584806685198344335887914554128464688
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{174}\cdot 3^{82}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.1
Root			$470.592 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.21.d.a.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1009.00 - 174.621i) q^{2} +34092.0i q^{3} +(987591. + 352385. i) q^{4} +5.90557e6 q^{5} +(5.95317e6 - 3.43988e7i) q^{6} -2.05952e8i q^{7} +(-9.34947e8 - 5.28011e8i) q^{8} -1.16226e9 q^{9} +O(q^{10})$	\(q+(-1009.00 - 174.621i) q^{2} +34092.0i q^{3} +(987591. + 352385. i) q^{4} +5.90557e6 q^{5} +(5.95317e6 - 3.43988e7i) q^{6} -2.05952e8i q^{7} +(-9.34947e8 - 5.28011e8i) q^{8} -1.16226e9 q^{9} +(-5.95872e9 - 1.03123e9i) q^{10} -6.76899e9i q^{11} +(-1.20135e10 + 3.36689e10i) q^{12} +1.26265e10 q^{13} +(-3.59635e10 + 2.07805e11i) q^{14} +2.01332e11i q^{15} +(8.51161e11 + 6.96025e11i) q^{16} -4.23901e11 q^{17} +(1.17272e12 + 2.02955e11i) q^{18} +2.41340e12i q^{19} +(5.83228e12 + 2.08103e12i) q^{20} +7.02130e12 q^{21} +(-1.18201e12 + 6.82992e12i) q^{22} +2.16590e13i q^{23} +(1.80009e13 - 3.18742e13i) q^{24} -6.04917e13 q^{25} +(-1.27401e13 - 2.20484e12i) q^{26} -3.96238e13i q^{27} +(7.25743e13 - 2.03396e14i) q^{28} -5.86863e14 q^{29} +(3.51568e13 - 2.03145e14i) q^{30} -1.62128e15i q^{31} +(-7.37282e14 - 8.50921e14i) q^{32} +2.30768e14 q^{33} +(4.27716e14 + 7.40219e13i) q^{34} -1.21626e15i q^{35} +(-1.14784e15 - 4.09564e14i) q^{36} +2.36165e15 q^{37} +(4.21430e14 - 2.43512e15i) q^{38} +4.30461e14i q^{39} +(-5.52139e15 - 3.11821e15i) q^{40} -5.51421e15 q^{41} +(-7.08450e15 - 1.22606e15i) q^{42} -2.09388e16i q^{43} +(2.38529e15 - 6.68499e15i) q^{44} -6.86381e15 q^{45} +(3.78211e15 - 2.18540e16i) q^{46} -4.99979e16i q^{47} +(-2.37289e16 + 2.90177e16i) q^{48} +3.73762e16 q^{49} +(6.10362e16 + 1.05631e16i) q^{50} -1.44516e16i q^{51} +(1.24698e16 + 4.44938e15i) q^{52} -2.14062e17 q^{53} +(-6.91914e15 + 3.99804e16i) q^{54} -3.99747e16i q^{55} +(-1.08745e17 + 1.92554e17i) q^{56} -8.22775e16 q^{57} +(5.92145e17 + 1.02478e17i) q^{58} +5.17989e17i q^{59} +(-7.09465e16 + 1.98834e17i) q^{60} +1.08120e18 q^{61} +(-2.83110e17 + 1.63588e18i) q^{62} +2.39370e17i q^{63} +(5.95330e17 + 9.87325e17i) q^{64} +7.45664e16 q^{65} +(-2.32845e17 - 4.02969e16i) q^{66} -2.98959e18i q^{67} +(-4.18641e17 - 1.49376e17i) q^{68} -7.38397e17 q^{69} +(-2.12385e17 + 1.22721e18i) q^{70} -6.13386e18i q^{71} +(1.08665e18 + 6.13687e17i) q^{72} -4.46233e18 q^{73} +(-2.38290e18 - 4.12393e17i) q^{74} -2.06228e18i q^{75} +(-8.50446e17 + 2.38345e18i) q^{76} -1.39408e18 q^{77} +(7.51674e16 - 4.34335e17i) q^{78} -1.16938e19i q^{79} +(5.02659e18 + 4.11042e18i) q^{80} +1.35085e18 q^{81} +(5.56384e18 + 9.62895e17i) q^{82} -1.74622e19i q^{83} +(6.93417e18 + 2.47420e18i) q^{84} -2.50337e18 q^{85} +(-3.65634e18 + 2.11272e19i) q^{86} -2.00073e19i q^{87} +(-3.57410e18 + 6.32865e18i) q^{88} -3.64001e19 q^{89} +(6.92559e18 + 1.19856e18i) q^{90} -2.60044e18i q^{91} +(-7.63231e18 + 2.13902e19i) q^{92} +5.52727e19 q^{93} +(-8.73068e18 + 5.04480e19i) q^{94} +1.42525e19i q^{95} +(2.90096e19 - 2.51354e19i) q^{96} +2.48785e19 q^{97} +(-3.77126e19 - 6.52666e18i) q^{98} +7.86734e18i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 1254 q^{2} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} + 434160000 q^{8} - 23245229340 q^{9}+O(q^{10}) $ 20 * q + 1254 * q^2 - 485524 * q^4 + 1476984 * q^5 - 36019890 * q^6 + 434160000 * q^8 - 23245229340 * q^9	$ 20 q + 1254 q^{2} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} + 434160000 q^{8} - 23245229340 q^{9} + 3166779028 q^{10} + 35789598900 q^{12} - 197410187576 q^{13} + 1179712421976 q^{14} + 1592658749552 q^{16} + 4951946877000 q^{17} - 1457475879618 q^{18} - 20688414141528 q^{20} - 19078957703376 q^{21} + 54807260127768 q^{22} + 58196896476048 q^{24} + 513048947332092 q^{25} - 142319404376100 q^{26} - 10\!\cdots\!28 q^{28}+ \cdots + 30\!\cdots\!50 q^{98}+O(q^{100}) $ 20 * q + 1254 * q^2 - 485524 * q^4 + 1476984 * q^5 - 36019890 * q^6 + 434160000 * q^8 - 23245229340 * q^9 + 3166779028 * q^10 + 35789598900 * q^12 - 197410187576 * q^13 + 1179712421976 * q^14 + 1592658749552 * q^16 + 4951946877000 * q^17 - 1457475879618 * q^18 - 20688414141528 * q^20 - 19078957703376 * q^21 + 54807260127768 * q^22 + 58196896476048 * q^24 + 513048947332092 * q^25 - 142319404376100 * q^26 - 1064314324942128 * q^28 - 1120225678237608 * q^29 + 919562090032260 * q^30 + 926940361437984 * q^32 - 1250504741372400 * q^33 + 1615904447739868 * q^34 + 564305836503708 * q^36 + 13452822768639208 * q^37 + 30625874417040840 * q^38 - 42278345025251456 * q^40 + 26778887480335560 * q^41 + 34752013424992728 * q^42 - 160483087306778736 * q^44 - 1716641590575528 * q^45 + 312713467885194624 * q^46 - 170793646915261968 * q^48 - 198082137742572844 * q^49 + 575620844246091282 * q^50 - 896547684604982408 * q^52 + 241769380233802968 * q^53 + 41864530192578630 * q^54 - 2099928347597457216 * q^56 + 595468774322860464 * q^57 + 1656374273217670084 * q^58 + 94322711748139416 * q^60 + 430703667006221224 * q^61 + 1718273064332222664 * q^62 - 3197273374119743872 * q^64 - 1146808855391494992 * q^65 + 1921733716920631128 * q^66 + 4484111570418829944 * q^68 - 4519043719923504960 * q^69 - 12213680959006457904 * q^70 - 504607438512720000 * q^72 + 12562724768160620200 * q^73 - 22136012572796109780 * q^74 + 28495592855672115888 * q^76 + 19985445258493440192 * q^77 - 20625251537531633940 * q^78 + 49505459663687019552 * q^80 + 27017034353459841780 * q^81 - 50718250504081238180 * q^82 + 24536705912722373616 * q^84 - 15354475681609135696 * q^85 - 85391409389241086952 * q^86 + 66078172926918803520 * q^88 + 43679060294354361384 * q^89 - 3680625238748114076 * q^90 - 64869958570030809216 * q^92 - 50732545022865845424 * q^93 + 95503492747592513424 * q^94 - 89530085825201077920 * q^96 + 7230988441427384872 * q^97 + 304648861287114073350 * q^98

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 $

$2$	−1009.00	−	174.621i	−0.985353	−	0.170528i
$2$	−1009.00	−	174.621i	−0.985353	−	0.170528i
$3$			34092.0i			0.577350i
$3$			34092.0i			0.577350i
$4$	987591.	+	352385.i	0.941840	+	0.336061i
$5$	5.90557e6			0.604730			0.302365	−	0.953192i	$-0.402224\pi$
$5$	5.90557e6			0.604730			0.302365	+	0.953192i	$0.402224\pi$
$6$	5.95317e6	−	3.43988e7i	0.0984545	−	0.568894i
$7$		−	2.05952e8i		−	0.729096i	−0.931185	−	0.364548i	$-0.881223\pi$
$7$		−	2.05952e8i		−	0.729096i	0.931185	−	0.364548i	$-0.118777\pi$
$8$	−9.34947e8	−	5.28011e8i	−0.870737	−	0.491749i
$9$	−1.16226e9			−0.333333
$10$	−5.95872e9	−	1.03123e9i	−0.595872	−	0.103123i
$11$		−	6.76899e9i		−	0.260974i	−0.991450	−	0.130487i	$-0.958346\pi$
$11$		−	6.76899e9i		−	0.260974i	0.991450	−	0.130487i	$-0.0416541\pi$
$12$	−1.20135e10	+	3.36689e10i	−0.194025	+	0.543772i
$13$	1.26265e10			0.0915900			0.0457950	−	0.998951i	$-0.485418\pi$
$13$	1.26265e10			0.0915900			0.0457950	+	0.998951i	$0.485418\pi$
$14$	−3.59635e10	+	2.07805e11i	−0.124331	+	0.718417i
$15$			2.01332e11i			0.349141i
$16$	8.51161e11	+	6.96025e11i	0.774126	+	0.633031i
$17$	−4.23901e11			−0.210269			−0.105134	−	0.994458i	$-0.533527\pi$
$17$	−4.23901e11			−0.210269			−0.105134	+	0.994458i	$0.533527\pi$
$18$	1.17272e12	+	2.02955e11i	0.328451	+	0.0568427i
$19$			2.41340e12i			0.393634i	0.980440	+	0.196817i	$0.0630606\pi$
$19$			2.41340e12i			0.393634i	−0.980440	+	0.196817i	$0.936939\pi$
$20$	5.83228e12	+	2.08103e12i	0.569559	+	0.203226i
$21$	7.02130e12			0.420944
$22$	−1.18201e12	+	6.82992e12i	−0.0445034	+	0.257151i
$23$			2.16590e13i			0.522829i	0.965227	+	0.261415i	$0.0841890\pi$
$23$			2.16590e13i			0.522829i	−0.965227	+	0.261415i	$0.915811\pi$
$24$	1.80009e13	−	3.18742e13i	0.283911	−	0.502720i
$25$	−6.04917e13			−0.634302
$26$	−1.27401e13	−	2.20484e12i	−0.0902485	−	0.0156187i
$27$		−	3.96238e13i		−	0.192450i
$28$	7.25743e13	−	2.03396e14i	0.245021	−	0.686692i
$29$	−5.86863e14			−1.39494			−0.697472	−	0.716612i	$-0.745692\pi$
$29$	−5.86863e14			−1.39494			−0.697472	+	0.716612i	$0.745692\pi$
$30$	3.51568e13	−	2.03145e14i	0.0595384	−	0.344027i
$31$		−	1.62128e15i		−	1.97807i	−0.147678	−	0.989035i	$-0.547180\pi$
$31$		−	1.62128e15i		−	1.97807i	0.147678	−	0.989035i	$-0.452820\pi$
$32$	−7.37282e14	−	8.50921e14i	−0.654838	−	0.755769i
$33$	2.30768e14			0.150673
$34$	4.27716e14	+	7.40219e13i	0.207189	+	0.0358568i
$35$		−	1.21626e15i		−	0.440906i
$36$	−1.14784e15	−	4.09564e14i	−0.313947	−	0.112020i
$37$	2.36165e15			0.491131			0.245566	−	0.969380i	$-0.421026\pi$
$37$	2.36165e15			0.491131			0.245566	+	0.969380i	$0.421026\pi$
$38$	4.21430e14	−	2.43512e15i	0.0671258	−	0.387869i
$39$			4.30461e14i			0.0528795i
$40$	−5.52139e15	−	3.11821e15i	−0.526561	−	0.297375i
$41$	−5.51421e15			−0.410813			−0.205407	−	0.978677i	$-0.565852\pi$
$41$	−5.51421e15			−0.410813			−0.205407	+	0.978677i	$0.565852\pi$
$42$	−7.08450e15	−	1.22606e15i	−0.414778	−	0.0717828i
$43$		−	2.09388e16i		−	0.968872i	−0.874827	−	0.484436i	$-0.839025\pi$
$43$		−	2.09388e16i		−	0.968872i	0.874827	−	0.484436i	$-0.160975\pi$
$44$	2.38529e15	−	6.68499e15i	0.0877031	−	0.245796i
$45$	−6.86381e15			−0.201577
$46$	3.78211e15	−	2.18540e16i	0.0891571	−	0.515171i
$47$		−	4.99979e16i		−	0.950547i	−0.879838	−	0.475273i	$-0.842349\pi$
$47$		−	4.99979e16i		−	0.950547i	0.879838	−	0.475273i	$-0.157651\pi$
$48$	−2.37289e16	+	2.90177e16i	−0.365481	+	0.446942i
$49$	3.73762e16			0.468419
$50$	6.10362e16	+	1.05631e16i	0.625011	+	0.108166i
$51$		−	1.44516e16i		−	0.121399i
$52$	1.24698e16	+	4.44938e15i	0.0862632	+	0.0307798i
$53$	−2.14062e17			−1.22400			−0.612001	−	0.790857i	$-0.709635\pi$
$53$	−2.14062e17			−1.22400			−0.612001	+	0.790857i	$0.709635\pi$
$54$	−6.91914e15	+	3.99804e16i	−0.0328182	+	0.189631i
$55$		−	3.99747e16i		−	0.157819i
$56$	−1.08745e17	+	1.92554e17i	−0.358532	+	0.634851i
$57$	−8.22775e16			−0.227265
$58$	5.92145e17	+	1.02478e17i	1.37451	+	0.237877i
$59$			5.17989e17i			1.01344i	0.862109	+	0.506722i	$0.169143\pi$
$59$			5.17989e17i			1.01344i	−0.862109	+	0.506722i	$0.830857\pi$
$60$	−7.09465e16	+	1.98834e17i	−0.117333	+	0.328835i
$61$	1.08120e18			1.51568			0.757838	−	0.652443i	$-0.226256\pi$
$61$	1.08120e18			1.51568			0.757838	+	0.652443i	$0.226256\pi$
$62$	−2.83110e17	+	1.63588e18i	−0.337317	+	1.94910i
$63$			2.39370e17i			0.243032i
$64$	5.95330e17	+	9.87325e17i	0.516366	+	0.856368i
$65$	7.45664e16			0.0553872
$66$	−2.32845e17	−	4.02969e16i	−0.148466	−	0.0256940i
$67$		−	2.98959e18i		−	1.64007i	−0.572311	−	0.820036i	$-0.693953\pi$
$67$		−	2.98959e18i		−	1.64007i	0.572311	−	0.820036i	$-0.306047\pi$
$68$	−4.18641e17	−	1.49376e17i	−0.198040	−	0.0706631i
$69$	−7.38397e17			−0.301856
$70$	−2.12385e17	+	1.22721e18i	−0.0751870	+	0.434448i
$71$		−	6.13386e18i		−	1.88430i	−0.335191	−	0.942150i	$-0.608801\pi$
$71$		−	6.13386e18i		−	1.88430i	0.335191	−	0.942150i	$-0.391199\pi$
$72$	1.08665e18	+	6.13687e17i	0.290246	+	0.163916i
$73$	−4.46233e18			−1.03832			−0.519162	−	0.854676i	$-0.673756\pi$
$73$	−4.46233e18			−1.03832			−0.519162	+	0.854676i	$0.673756\pi$
$74$	−2.38290e18	−	4.12393e17i	−0.483938	−	0.0837517i
$75$		−	2.06228e18i		−	0.366214i
$76$	−8.50446e17	+	2.38345e18i	−0.132285	+	0.370741i
$77$	−1.39408e18			−0.190275
$78$	7.51674e16	−	4.34335e17i	0.00901745	−	0.0521050i
$79$		−	1.16938e19i		−	1.23505i	−0.786549	−	0.617527i	$-0.788134\pi$
$79$		−	1.16938e19i		−	1.23505i	0.786549	−	0.617527i	$-0.211866\pi$
$80$	5.02659e18	+	4.11042e18i	0.468137	+	0.382813i
$81$	1.35085e18			0.111111
$82$	5.56384e18	+	9.62895e17i	0.404796	+	0.0700552i
$83$		−	1.74622e19i		−	1.12543i	−0.826651	−	0.562714i	$-0.809757\pi$
$83$		−	1.74622e19i		−	1.12543i	0.826651	−	0.562714i	$-0.190243\pi$
$84$	6.93417e18	+	2.47420e18i	0.396462	+	0.141463i
$85$	−2.50337e18			−0.127156
$86$	−3.65634e18	+	2.11272e19i	−0.165220	+	0.954680i
$87$		−	2.00073e19i		−	0.805371i
$88$	−3.57410e18	+	6.32865e18i	−0.128334	+	0.227240i
$89$	−3.64001e19			−1.16735			−0.583677	−	0.811986i	$-0.698387\pi$
$89$	−3.64001e19			−1.16735			−0.583677	+	0.811986i	$0.698387\pi$
$90$	6.92559e18	+	1.19856e18i	0.198624	+	0.0343745i
$91$		−	2.60044e18i		−	0.0667779i
$92$	−7.63231e18	+	2.13902e19i	−0.175702	+	0.492422i
$93$	5.52727e19			1.14204
$94$	−8.73068e18	+	5.04480e19i	−0.162095	+	0.936624i
$95$			1.42525e19i			0.238043i
$96$	2.90096e19	−	2.51354e19i	0.436344	−	0.378071i
$97$	2.48785e19			0.337371			0.168685	−	0.985670i	$-0.446048\pi$
$97$	2.48785e19			0.337371			0.168685	+	0.985670i	$0.446048\pi$
$98$	−3.77126e19	−	6.52666e18i	−0.461558	−	0.0798786i
$99$			7.86734e18i			0.0869913i
$100$	−5.97411e19	−	2.13164e19i	−0.597411	−	0.213164i
$101$	−2.64097e19			−0.239083			−0.119542	−	0.992829i	$-0.538142\pi$
$101$	−2.64097e19			−0.239083			−0.119542	+	0.992829i	$0.538142\pi$
$102$	−2.52355e18	+	1.45817e19i	−0.0207019	+	0.119621i
$103$			3.98038e19i			0.296178i	0.988974	+	0.148089i	$0.0473122\pi$
$103$			3.98038e19i			0.296178i	−0.988974	+	0.148089i	$0.952688\pi$
$104$	−1.18051e19	−	6.66691e18i	−0.0797508	−	0.0450393i
$105$	4.14647e19			0.254557
$106$	2.15989e20	+	3.73798e19i	1.20607	+	0.208727i
$107$			3.02934e20i			1.53996i	0.638065	+	0.769982i	$0.279735\pi$
$107$			3.02934e20i			1.53996i	−0.638065	+	0.769982i	$0.720265\pi$
$108$	1.39628e19	−	3.91321e19i	0.0646749	−	0.181257i
$109$	1.35701e20			0.573218			0.286609	−	0.958048i	$-0.407472\pi$
$109$	1.35701e20			0.573218			0.286609	+	0.958048i	$0.407472\pi$
$110$	−6.98042e18	+	4.03345e19i	−0.0269125	+	0.155507i
$111$			8.05132e19i			0.283555i
$112$	1.43348e20	−	1.75298e20i	0.461541	−	0.564413i
$113$	−3.70898e20			−1.09262			−0.546311	−	0.837582i	$-0.683968\pi$
$113$	−3.70898e20			−1.09262			−0.546311	+	0.837582i	$0.683968\pi$
$114$	8.30181e19	+	1.43674e19i	0.223936	+	0.0387551i
$115$			1.27909e20i			0.316171i
$116$	−5.79580e20	−	2.06802e20i	−1.31381	−	0.468786i
$117$	−1.46752e19			−0.0305300
$118$	9.04516e19	−	5.22651e20i	0.172821	−	0.998601i
$119$			8.73031e19i			0.153306i
$120$	1.06306e20	−	1.88235e20i	0.171690	−	0.304010i
$121$	6.26931e20			0.931893
$122$	−1.09093e21	−	1.88799e20i	−1.49347	−	0.258465i
$123$		−	1.87990e20i		−	0.237183i
$124$	5.71316e20	−	1.60116e21i	0.664752	−	1.86303i
$125$	−9.20437e20			−0.988311
$126$	4.17989e19	−	2.41524e20i	0.0414438	−	0.239472i
$127$		−	2.10185e20i		−	0.192559i	−0.995354	−	0.0962795i	$-0.969306\pi$
$127$		−	2.10185e20i		−	0.192559i	0.995354	−	0.0962795i	$-0.0306942\pi$
$128$	−4.28281e20	−	1.10017e21i	−0.362768	−	0.931879i
$129$	7.13843e20			0.559378
$130$	−7.52376e19	−	1.30208e19i	−0.0545760	−	0.00944508i
$131$			1.58116e21i			1.06234i	0.847265	+	0.531171i	$0.178248\pi$
$131$			1.58116e21i			1.06234i	−0.847265	+	0.531171i	$0.821752\pi$
$132$	2.27905e20	+	8.13193e19i	0.141910	+	0.0506354i
$133$	4.97043e20			0.286997
$134$	−5.22044e20	+	3.01650e21i	−0.279679	+	1.61605i
$135$		−	2.34001e20i		−	0.116380i
$136$	3.96325e20	+	2.23824e20i	0.183089	+	0.103399i
$137$	2.24984e20			0.0965930			0.0482965	−	0.998833i	$-0.484621\pi$
$137$	2.24984e20			0.0965930			0.0482965	+	0.998833i	$0.484621\pi$
$138$	7.45044e20	+	1.28940e20i	0.297434	+	0.0514749i
$139$			1.83608e21i			0.681934i	0.940075	+	0.340967i	$0.110754\pi$
$139$			1.83608e21i			0.681934i	−0.940075	+	0.340967i	$0.889246\pi$
$140$	4.28593e20	−	1.20117e21i	0.148171	−	0.415263i
$141$	1.70453e21			0.548798
$142$	−1.07110e21	+	6.18907e21i	−0.321326	+	1.85670i
$143$		−	8.54684e19i		−	0.0239026i
$144$	−9.89271e20	−	8.08963e20i	−0.258042	−	0.211010i
$145$	−3.46576e21			−0.843564
$146$	4.50250e21	+	7.79216e20i	1.02312	+	0.177064i
$147$			1.27423e21i			0.270442i
$148$	2.33234e21	+	8.32210e20i	0.462567	+	0.165050i
$149$	4.24159e20			0.0786441			0.0393221	−	0.999227i	$-0.487480\pi$
$149$	4.24159e20			0.0786441			0.0393221	+	0.999227i	$0.487480\pi$
$150$	−3.60117e20	+	2.08084e21i	−0.0624498	+	0.360850i
$151$		−	2.20341e21i		−	0.357541i	−0.983891	−	0.178771i	$-0.942788\pi$
$151$		−	2.20341e21i		−	0.357541i	0.983891	−	0.178771i	$-0.0572120\pi$
$152$	1.27430e21	−	2.25640e21i	0.193569	−	0.342752i
$153$	4.92683e20			0.0700896
$154$	1.40663e21	+	2.43436e20i	0.187488	+	0.0324473i
$155$		−	9.57459e21i		−	1.19620i
$156$	−1.51688e20	+	4.25119e20i	−0.0177707	+	0.0498041i
$157$	−7.03267e21			−0.772901			−0.386450	−	0.922310i	$-0.626299\pi$
$157$	−7.03267e21			−0.772901			−0.386450	+	0.922310i	$0.626299\pi$
$158$	−2.04199e21	+	1.17991e22i	−0.210612	+	1.21696i
$159$		−	7.29781e21i		−	0.706677i
$160$	−4.35407e21	−	5.02517e21i	−0.396000	−	0.457036i
$161$	4.46071e21			0.381193
$162$	−1.36301e21	−	2.35887e20i	−0.109484	−	0.0189476i
$163$		−	1.38896e22i		−	1.04909i	−0.851382	−	0.524546i	$-0.824235\pi$
$163$		−	1.38896e22i		−	1.04909i	0.851382	−	0.524546i	$-0.175765\pi$
$164$	−5.44578e21	−	1.94313e21i	−0.386920	−	0.138058i
$165$	1.36282e21			0.0911167
$166$	−3.04926e21	+	1.76194e22i	−0.191917	+	1.10894i
$167$		−	1.87374e22i		−	1.11057i	−0.831661	−	0.555284i	$-0.812610\pi$
$167$		−	1.87374e22i		−	1.11057i	0.831661	−	0.555284i	$-0.187390\pi$
$168$	−6.56454e21	−	3.70732e21i	−0.366532	−	0.206999i
$169$	−1.88455e22			−0.991611
$170$	2.52591e21	+	4.37141e20i	0.125293	+	0.0216837i
$171$		−	2.80500e21i		−	0.131211i
$172$	7.37851e21	−	2.06789e22i	0.325600	−	0.912522i
$173$	3.56106e22			1.48292			0.741460	−	0.670997i	$-0.234134\pi$
$173$	3.56106e22			1.48292			0.741460	+	0.670997i	$0.234134\pi$
$174$	−3.49369e21	+	2.01874e22i	−0.137338	+	0.793574i
$175$			1.24584e22i			0.462467i
$176$	4.71139e21	−	5.76150e21i	0.165205	−	0.202027i
$177$	−1.76592e22			−0.585113
$178$	3.67278e22	+	6.35622e21i	1.15026	+	0.199067i
$179$			2.77215e21i			0.0820891i	0.999157	+	0.0410446i	$0.0130686\pi$
$179$			2.77215e21i			0.0820891i	−0.999157	+	0.0410446i	$0.986931\pi$
$180$	−6.77864e21	−	2.41871e21i	−0.189853	−	0.0677420i
$181$	−9.24582e21			−0.244996			−0.122498	−	0.992469i	$-0.539091\pi$
$181$	−9.24582e21			−0.244996			−0.122498	+	0.992469i	$0.539091\pi$
$182$	−4.54091e20	+	2.62385e21i	−0.0113875	+	0.0657998i
$183$			3.68601e22i			0.875076i
$184$	1.14362e22	−	2.02500e22i	0.257101	−	0.455247i
$185$	1.39469e22			0.297002
$186$	−5.57702e22	−	9.65177e21i	−1.12531	−	0.194750i
$187$			2.86938e21i			0.0548747i
$188$	1.76185e22	−	4.93775e22i	0.319441	−	0.895263i
$189$	−8.16058e21			−0.140315
$190$	2.48878e21	−	1.43808e22i	0.0405930	−	0.234556i
$191$			4.29885e22i			0.665301i	0.943050	+	0.332651i	$0.107943\pi$
$191$			4.29885e22i			0.665301i	−0.943050	+	0.332651i	$0.892057\pi$
$192$	−3.36598e22	+	2.02960e22i	−0.494424	+	0.298124i
$193$	−9.00989e22			−1.25645			−0.628227	−	0.778030i	$-0.716219\pi$
$193$	−9.00989e22			−1.25645			−0.628227	+	0.778030i	$0.716219\pi$
$194$	−2.51025e22	−	4.34431e21i	−0.332429	−	0.0575312i
$195$			2.54211e21i			0.0319778i
$196$	3.69124e22	+	1.31708e22i	0.441175	+	0.157417i
$197$	1.15963e23			1.31721			0.658606	−	0.752488i	$-0.271146\pi$
$197$	1.15963e23			1.31721			0.658606	+	0.752488i	$0.271146\pi$
$198$	1.37380e21	−	7.93815e21i	0.0148345	−	0.0857171i
$199$			1.56229e23i			1.60410i	0.597259	+	0.802048i	$0.296256\pi$
$199$			1.56229e23i			1.60410i	−0.597259	+	0.802048i	$0.703744\pi$
$200$	5.65565e22	+	3.19403e22i	0.552310	+	0.311917i
$201$	1.01921e23			0.946897
$202$	2.66474e22	+	4.61168e21i	0.235581	+	0.0407704i
$203$			1.20865e23i			1.01705i
$204$	5.09253e21	−	1.42723e22i	0.0407974	−	0.114338i
$205$	−3.25645e22			−0.248431
$206$	6.95057e21	−	4.01621e22i	0.0505066	−	0.291840i
$207$		−	2.51734e22i		−	0.174276i
$208$	1.07471e22	+	8.78834e21i	0.0709022	+	0.0579793i
$209$	1.63363e22			0.102728
$210$	−4.18380e22	−	7.24060e21i	−0.250829	−	0.0434092i
$211$			1.17155e23i			0.669787i	0.942256	+	0.334893i	$0.108700\pi$
$211$			1.17155e23i			0.669787i	−0.942256	+	0.334893i	$0.891300\pi$
$212$	−2.11406e23	−	7.54325e22i	−1.15281	−	0.411339i
$213$	2.09115e23			1.08790
$214$	5.28987e22	−	3.05661e23i	0.262607	−	1.51741i
$215$		−	1.23655e23i		−	0.585906i
$216$	−2.09218e22	+	3.70461e22i	−0.0946371	+	0.167573i
$217$	−3.33906e23			−1.44220
$218$	−1.36923e23	−	2.36963e22i	−0.564822	−	0.0977498i
$219$		−	1.52130e23i		−	0.599477i
$220$	1.40865e22	−	3.94787e22i	0.0530367	−	0.148640i
$221$	−5.35237e21			−0.0192585
$222$	1.40593e22	−	8.12379e22i	0.0483541	−	0.279402i
$223$		−	2.42049e23i		−	0.795894i	−0.917408	−	0.397947i	$-0.869723\pi$
$223$		−	2.42049e23i		−	0.795894i	0.917408	−	0.397947i	$-0.130277\pi$
$224$	−1.75249e23	+	1.51844e23i	−0.551029	+	0.477440i
$225$	7.03072e22			0.211434
$226$	3.74236e23	+	6.47665e22i	1.07662	+	0.186323i
$227$		−	3.47473e23i		−	0.956451i	−0.878237	−	0.478226i	$-0.841280\pi$
$227$		−	3.47473e23i		−	0.956451i	0.878237	−	0.478226i	$-0.158720\pi$
$228$	−8.12565e22	−	2.89934e22i	−0.214047	−	0.0763748i
$229$	−6.89301e23			−1.73802			−0.869009	−	0.494796i	$-0.835243\pi$
$229$	−6.89301e23			−1.73802			−0.869009	+	0.494796i	$0.835243\pi$
$230$	2.23355e22	−	1.29060e23i	0.0539160	−	0.311540i
$231$		−	4.75271e22i		−	0.109855i
$232$	5.48685e23	+	3.09870e23i	1.21463	+	0.685962i
$233$	3.89392e22			0.0825710			0.0412855	−	0.999147i	$-0.486855\pi$
$233$	3.89392e22			0.0825710			0.0412855	+	0.999147i	$0.486855\pi$
$234$	1.48073e22	+	2.56260e21i	0.0300828	+	0.00520623i
$235$		−	2.95266e23i		−	0.574824i
$236$	−1.82532e23	+	5.11561e23i	−0.340579	+	0.954503i
$237$	3.98666e23			0.713059
$238$	1.52449e22	−	8.80889e22i	0.0261430	−	0.151061i
$239$		−	1.44771e23i		−	0.238069i	−0.992890	−	0.119034i	$-0.962020\pi$
$239$		−	1.44771e23i		−	0.238069i	0.992890	−	0.119034i	$-0.0379799\pi$
$240$	−1.40132e23	+	1.71366e23i	−0.221017	+	0.270279i
$241$	5.15881e22			0.0780511			0.0390255	−	0.999238i	$-0.487575\pi$
$241$	5.15881e22			0.0780511			0.0390255	+	0.999238i	$0.487575\pi$
$242$	−6.32574e23	−	1.09475e23i	−0.918243	−	0.158914i
$243$			4.60532e22i			0.0641500i
$244$	1.06778e24	+	3.80998e23i	1.42752	+	0.509359i
$245$	2.20727e23			0.283267
$246$	−3.28270e22	+	1.89682e23i	−0.0404464	+	0.233709i
$247$			3.04727e22i			0.0360530i
$248$	−8.56056e23	+	1.51581e24i	−0.972714	+	1.72238i
$249$	5.95321e23			0.649767
$250$	9.28722e23	+	1.60727e23i	0.973835	+	0.168535i
$251$			1.23652e24i			1.24584i	0.782284	+	0.622922i	$0.214055\pi$
$251$			1.23652e24i			1.24584i	−0.782284	+	0.622922i	$0.785945\pi$
$252$	−8.43504e22	+	2.36399e23i	−0.0816736	+	0.228897i
$253$	1.46610e23			0.136445
$254$	−3.67026e22	+	2.12077e23i	−0.0328367	+	0.189738i
$255$		−	8.53449e22i		−	0.0734135i
$256$	2.40024e23	+	1.18486e24i	0.198543	+	0.980092i
$257$	−8.60196e23			−0.684331			−0.342166	−	0.939640i	$-0.611160\pi$
$257$	−8.60196e23			−0.684331			−0.342166	+	0.939640i	$0.611160\pi$
$258$	−7.20268e23	−	1.24652e23i	−0.551185	−	0.0953898i
$259$		−	4.86385e23i		−	0.358082i
$260$	7.36411e22	+	2.62761e22i	0.0521659	+	0.0186135i
$261$	6.82088e23			0.464981
$262$	2.76104e23	−	1.59540e24i	0.181159	−	1.04678i
$263$		−	1.72793e24i		−	1.09136i	−0.837993	−	0.545681i	$-0.816271\pi$
$263$		−	1.72793e24i		−	1.09136i	0.837993	−	0.545681i	$-0.183729\pi$
$264$	−2.15756e23	−	1.21848e23i	−0.131197	−	0.0740934i
$265$	−1.26416e24			−0.740190
$266$	−5.01518e23	−	8.67942e22i	−0.282794	−	0.0489411i
$267$		−	1.24095e24i		−	0.673972i
$268$	1.05349e24	−	2.95249e24i	0.551164	−	1.54469i
$269$	2.20117e23			0.110951			0.0554754	−	0.998460i	$-0.482333\pi$
$269$	2.20117e23			0.110951			0.0554754	+	0.998460i	$0.482333\pi$
$270$	−4.08614e22	+	2.36107e23i	−0.0198461	+	0.114676i
$271$			6.79773e23i			0.318179i	0.987264	+	0.159089i	$0.0508558\pi$
$271$			6.79773e23i			0.318179i	−0.987264	+	0.159089i	$0.949144\pi$
$272$	−3.60808e23	−	2.95046e23i	−0.162775	−	0.133107i
$273$	8.86541e22			0.0385543
$274$	−2.27009e23	−	3.92869e22i	−0.0951782	−	0.0164718i
$275$			4.09468e23i			0.165536i
$276$	−7.29235e23	−	2.60200e23i	−0.284300	−	0.101442i
$277$	−2.13863e24			−0.804153			−0.402076	−	0.915606i	$-0.631711\pi$
$277$	−2.13863e24			−0.804153			−0.402076	+	0.915606i	$0.631711\pi$
$278$	3.20617e23	−	1.85260e24i	0.116289	−	0.671946i
$279$			1.88435e24i			0.659357i
$280$	−6.42200e23	+	1.13714e24i	−0.216815	+	0.383914i
$281$	2.80680e24			0.914425			0.457212	−	0.889358i	$-0.348848\pi$
$281$	2.80680e24			0.914425			0.457212	+	0.889358i	$0.348848\pi$
$282$	−1.71987e24	−	2.97646e23i	−0.540760	−	0.0935856i
$283$			3.40662e24i			1.03386i	0.856029	+	0.516928i	$0.172924\pi$
$283$			3.40662e24i			1.03386i	−0.856029	+	0.516928i	$0.827076\pi$
$284$	2.16148e24	−	6.05774e24i	0.633239	−	1.77471i
$285$	−4.85895e23			−0.137434
$286$	−1.49246e22	+	8.62377e22i	−0.00407607	+	0.0235525i
$287$			1.13566e24i			0.299522i
$288$	8.56914e23	+	9.88992e23i	0.218279	+	0.251923i
$289$	−3.88454e24			−0.955787
$290$	3.49695e24	+	6.05193e23i	0.831208	+	0.143851i
$291$			8.48158e23i			0.194781i
$292$	−4.40696e24	−	1.57246e24i	−0.977936	−	0.348940i
$293$	7.02659e24			1.50684			0.753422	−	0.657537i	$-0.228402\pi$
$293$	7.02659e24			1.50684			0.753422	+	0.657537i	$0.228402\pi$
$294$	2.22507e23	−	1.28570e24i	0.0461179	−	0.266480i
$295$			3.05902e24i			0.612861i
$296$	−2.20801e24	−	1.24698e24i	−0.427646	−	0.241513i
$297$	−2.68213e23			−0.0502244
$298$	−4.27977e23	−	7.40671e22i	−0.0774922	−	0.0134110i
$299$			2.73476e23i			0.0478859i
$300$	7.26718e23	−	2.03669e24i	0.123070	−	0.344915i
$301$	−4.31237e24			−0.706401
$302$	−3.84762e23	+	2.22325e24i	−0.0609709	+	0.352304i
$303$		−	9.00357e23i		−	0.138035i
$304$	−1.67979e24	+	2.05419e24i	−0.249183	+	0.304723i
$305$	6.38508e24			0.916574
$306$	−4.97118e23	−	8.60328e22i	−0.0690630	−	0.0119523i
$307$		−	1.66365e24i		−	0.223707i	−0.993725	−	0.111853i	$-0.964321\pi$
$307$		−	1.66365e24i		−	0.223707i	0.993725	−	0.111853i	$-0.0356787\pi$
$308$	−1.37679e24	−	4.91255e23i	−0.179209	−	0.0639440i
$309$	−1.35699e24			−0.170998
$310$	−1.67192e24	+	9.66078e24i	−0.203986	+	1.17868i
$311$			2.45007e24i			0.289451i	0.989472	+	0.144726i	$0.0462299\pi$
$311$			2.45007e24i			0.289451i	−0.989472	+	0.144726i	$0.953770\pi$
$312$	2.27288e23	−	4.02458e23i	0.0260034	−	0.0460442i
$313$	1.50967e25			1.67278			0.836390	−	0.548134i	$-0.184662\pi$
$313$	1.50967e25			1.67278			0.836390	+	0.548134i	$0.184662\pi$
$314$	7.09597e24	+	1.22805e24i	0.761580	+	0.131801i
$315$			1.41361e24i			0.146969i
$316$	4.12074e24	−	1.15487e25i	0.415053	−	1.16322i
$317$	−1.24603e25			−1.21600			−0.608002	−	0.793935i	$-0.708029\pi$
$317$	−1.24603e25			−1.21600			−0.608002	+	0.793935i	$0.708029\pi$
$318$	−1.27435e24	+	7.36350e24i	−0.120508	+	0.696327i
$319$			3.97247e24i			0.364044i
$320$	3.51576e24	+	5.83071e24i	0.312262	+	0.517871i
$321$	−1.03276e25			−0.889099
$322$	−4.50086e24	−	7.78932e23i	−0.375610	−	0.0650041i
$323$		−	1.02304e24i		−	0.0827691i
$324$	1.33409e24	+	4.76020e23i	0.104649	+	0.0373401i
$325$	−7.63796e23			−0.0580957
$326$	−2.42541e24	+	1.40146e25i	−0.178900	+	1.03373i
$327$			4.62633e24i			0.330947i
$328$	5.15549e24	+	2.91156e24i	0.357710	+	0.202017i
$329$	−1.02972e25			−0.693040
$330$	−1.37508e24	−	2.37976e23i	−0.0897821	−	0.0155380i
$331$		−	1.80663e25i		−	1.14443i	−0.820104	−	0.572215i	$-0.806084\pi$
$331$		−	1.80663e25i		−	1.14443i	0.820104	−	0.572215i	$-0.193916\pi$
$332$	6.15342e24	−	1.72455e25i	0.378213	−	1.05997i
$333$	−2.74485e24			−0.163710
$334$	−3.27195e24	+	1.89061e25i	−0.189383	+	1.09430i
$335$		−	1.76552e25i		−	0.991801i
$336$	5.97625e24	+	4.88700e24i	0.325864	+	0.266471i
$337$	2.99368e25			1.58455			0.792276	−	0.610163i	$-0.208896\pi$
$337$	2.99368e25			1.58455			0.792276	+	0.610163i	$0.208896\pi$
$338$	1.90152e25	+	3.29082e24i	0.977087	+	0.169098i
$339$		−	1.26446e25i		−	0.630826i
$340$	−2.47231e24	−	8.82152e23i	−0.119761	−	0.0427321i
$341$	−1.09744e25			−0.516225
$342$	−4.89812e23	+	2.83025e24i	−0.0223753	+	0.129290i
$343$		−	2.41310e25i		−	1.07062i
$344$	−1.10559e25	+	1.95766e25i	−0.476441	+	0.843632i
$345$	−4.36065e24			−0.182541
$346$	−3.59311e25	−	6.21835e24i	−1.46120	−	0.252880i
$347$		−	1.43147e25i		−	0.565573i	−0.959183	−	0.282787i	$-0.908741\pi$
$347$		−	1.43147e25i		−	0.565573i	0.959183	−	0.282787i	$-0.0912588\pi$
$348$	7.05028e24	−	1.97590e25i	0.270654	−	0.758531i
$349$	6.25217e24			0.233226			0.116613	−	0.993177i	$-0.462796\pi$
$349$	6.25217e24			0.233226			0.116613	+	0.993177i	$0.462796\pi$
$350$	2.17549e24	−	1.25705e25i	0.0788637	−	0.455693i
$351$		−	5.00308e23i		−	0.0176265i
$352$	−5.75987e24	+	4.99065e24i	−0.197236	+	0.170896i
$353$	−3.54447e25			−1.17979			−0.589894	−	0.807480i	$-0.700831\pi$
$353$	−3.54447e25			−1.17979			−0.589894	+	0.807480i	$0.700831\pi$
$354$	1.78182e25	+	3.08367e24i	0.576542	+	0.0997782i
$355$		−	3.62239e25i		−	1.13949i
$356$	−3.59484e25	−	1.28269e25i	−1.09946	−	0.392302i
$357$	−2.97633e24			−0.0885114
$358$	4.84074e23	−	2.79710e24i	0.0139985	−	0.0808868i
$359$			2.11289e25i			0.594199i	0.954847	+	0.297099i	$0.0960192\pi$
$359$			2.11289e25i			0.594199i	−0.954847	+	0.297099i	$0.903981\pi$
$360$	6.41730e24	+	3.62417e24i	0.175520	+	0.0991251i
$361$	3.17655e25			0.845052
$362$	9.32904e24	+	1.61451e24i	0.241408	+	0.0417788i
$363$			2.13733e25i			0.538028i
$364$	9.16357e23	−	2.56817e24i	0.0224415	−	0.0628942i
$365$	−2.63526e25			−0.627906
$366$	6.43654e24	−	3.71919e25i	0.149225	−	0.862258i
$367$			3.58317e25i			0.808365i	0.914678	+	0.404182i	$0.132444\pi$
$367$			3.58317e25i			0.808365i	−0.914678	+	0.404182i	$0.867556\pi$
$368$	−1.50752e25	+	1.84353e25i	−0.330967	+	0.404736i
$369$	6.40895e24			0.136938
$370$	−1.40724e25	−	2.43541e24i	−0.292652	−	0.0506472i
$371$			4.40865e25i			0.892415i
$372$	5.45868e25	+	1.94773e25i	1.07562	+	0.383795i
$373$	7.05709e25			1.35375			0.676873	−	0.736100i	$-0.263335\pi$
$373$	7.05709e25			1.35375			0.676873	+	0.736100i	$0.263335\pi$
$374$	5.01054e23	−	2.89521e24i	0.00935768	−	0.0540709i
$375$		−	3.13795e25i		−	0.570602i
$376$	−2.63995e25	+	4.67454e25i	−0.467430	+	0.827676i
$377$	−7.41000e24			−0.127763
$378$	8.23404e24	+	1.42501e24i	0.138259	+	0.0239276i
$379$			1.20689e26i			1.97368i	0.161710	+	0.986838i	$0.448299\pi$
$379$			1.20689e26i			1.97368i	−0.161710	+	0.986838i	$0.551701\pi$
$380$	−5.02237e24	+	1.40756e25i	−0.0799968	+	0.224198i
$381$	7.16560e24			0.111174
$382$	7.50668e24	−	4.33754e25i	0.113453	−	0.655556i
$383$			9.86961e25i			1.45316i	0.687084	+	0.726578i	$0.258890\pi$
$383$			9.86961e25i			1.45316i	−0.687084	+	0.726578i	$0.741110\pi$
$384$	3.75069e25	−	1.46009e25i	0.538021	−	0.209444i
$385$	−8.23286e24			−0.115065
$386$	9.09099e25	+	1.57331e25i	1.23805	+	0.214261i
$387$			2.43363e25i			0.322957i
$388$	2.45698e25	+	8.76683e24i	0.317749	+	0.113377i
$389$	4.70979e25			0.593615			0.296808	−	0.954937i	$-0.404078\pi$
$389$	4.70979e25			0.593615			0.296808	+	0.954937i	$0.404078\pi$
$390$	4.43906e23	−	2.56500e24i	0.00545312	−	0.0315094i
$391$		−	9.18126e24i		−	0.109935i
$392$	−3.49447e25	−	1.97350e25i	−0.407869	−	0.230344i
$393$	−5.39050e25			−0.613343
$394$	−1.17006e26	−	2.02495e25i	−1.29792	−	0.224622i
$395$		−	6.90587e25i		−	0.746875i
$396$	−2.77233e24	+	7.76971e24i	−0.0292344	+	0.0819319i
$397$	−5.03199e25			−0.517410			−0.258705	−	0.965956i	$-0.583296\pi$
$397$	−5.03199e25			−0.517410			−0.258705	+	0.965956i	$0.583296\pi$
$398$	2.72808e25	−	1.57635e26i	0.273544	−	1.58060i
$399$			1.69452e25i			0.165698i
$400$	−5.14882e25	−	4.21038e25i	−0.491030	−	0.401533i
$401$	−1.03621e26			−0.963842			−0.481921	−	0.876215i	$-0.660061\pi$
$401$	−1.03621e26			−0.963842			−0.481921	+	0.876215i	$0.660061\pi$
$402$	−1.02838e26	−	1.77975e25i	−0.933027	−	0.161473i
$403$		−	2.04711e25i		−	0.181172i
$404$	−2.60819e25	−	9.30637e24i	−0.225178	−	0.0803465i
$405$	7.97754e24			0.0671922
$406$	2.11056e25	−	1.21953e26i	0.173435	−	1.00215i
$407$		−	1.59860e25i		−	0.128172i
$408$	−7.63061e24	+	1.35115e25i	−0.0596977	+	0.105706i
$409$	1.69384e26			1.29312			0.646560	−	0.762863i	$-0.276207\pi$
$409$	1.69384e26			1.29312			0.646560	+	0.762863i	$0.276207\pi$
$410$	3.28576e25	+	5.68644e24i	0.244792	+	0.0423645i
$411$			7.67014e24i			0.0557680i
$412$	−1.40263e25	+	3.93099e25i	−0.0995337	+	0.278952i
$413$	1.06681e26			0.738899
$414$	−4.39580e24	+	2.54000e25i	−0.0297190	+	0.171724i
$415$		−	1.03124e26i		−	0.680581i
$416$	−9.30926e24	−	1.07441e25i	−0.0599766	−	0.0692209i
$417$	−6.25954e25			−0.393715
$418$	−1.64833e25	−	2.85265e24i	−0.101224	−	0.0175181i
$419$		−	7.62924e25i		−	0.457448i	−0.973491	−	0.228724i	$-0.926545\pi$
$419$		−	7.62924e25i		−	0.457448i	0.973491	−	0.228724i	$-0.0734553\pi$
$420$	4.09502e25	+	1.46116e25i	0.239752	+	0.0855468i
$421$	−1.31909e25			−0.0754143			−0.0377072	−	0.999289i	$-0.512005\pi$
$421$	−1.31909e25			−0.0754143			−0.0377072	+	0.999289i	$0.512005\pi$
$422$	2.04577e25	−	1.18210e26i	0.114218	−	0.659976i
$423$			5.81107e25i			0.316849i
$424$	2.00137e26	+	1.13027e26i	1.06578	+	0.601901i
$425$	2.56425e25			0.133374
$426$	−2.10997e26	−	3.65159e25i	−1.07197	−	0.185518i
$427$		−	2.22674e26i		−	1.10507i
$428$	−1.06750e26	+	2.99175e26i	−0.517522	+	1.45040i
$429$	2.91378e24			0.0138002
$430$	−2.15928e25	+	1.24768e26i	−0.0999134	+	0.577324i
$431$		−	3.31943e25i		−	0.150069i	−0.997181	−	0.0750344i	$-0.976093\pi$
$431$		−	3.31943e25i		−	0.150069i	0.997181	−	0.0750344i	$-0.0239067\pi$
$432$	2.75791e25	−	3.37262e25i	0.121827	−	0.148981i
$433$	−2.91084e26			−1.25643			−0.628217	−	0.778038i	$-0.716215\pi$
$433$	−2.91084e26			−1.25643			−0.628217	+	0.778038i	$0.716215\pi$
$434$	3.36911e26	+	5.83069e25i	1.42108	+	0.245936i
$435$		−	1.18154e26i		−	0.487032i
$436$	1.34018e26	+	4.78192e25i	0.539879	+	0.192636i
$437$	−5.22718e25			−0.205804
$438$	−2.65650e25	+	1.53499e26i	−0.102228	+	0.590696i
$439$			1.21156e26i			0.455721i	0.973694	+	0.227861i	$0.0731731\pi$
$439$			1.21156e26i			0.455721i	−0.973694	+	0.227861i	$0.926827\pi$
$440$	−2.11071e25	+	3.73742e25i	−0.0776072	+	0.137419i
$441$	−4.34409e25			−0.156140
$442$	5.40054e24	+	9.34635e23i	0.0189764	+	0.00328412i
$443$		−	1.34686e26i		−	0.462683i	−0.972873	−	0.231342i	$-0.925689\pi$
$443$		−	1.34686e26i		−	0.462683i	0.972873	−	0.231342i	$-0.0743115\pi$
$444$	−2.83717e25	+	7.95141e25i	−0.0952917	+	0.267063i
$445$	−2.14963e26			−0.705934
$446$	−4.22669e25	+	2.44228e26i	−0.135722	+	0.784237i
$447$			1.44604e25i			0.0454052i
$448$	2.03341e26	−	1.22609e26i	0.624375	−	0.376481i
$449$	5.47469e26			1.64398			0.821990	−	0.569502i	$-0.192864\pi$
$449$	5.47469e26			1.64398			0.821990	+	0.569502i	$0.192864\pi$
$450$	−7.09401e25	−	1.22771e25i	−0.208337	−	0.0360554i
$451$			3.73256e25i			0.107212i
$452$	−3.66295e26	−	1.30699e26i	−1.02908	−	0.367187i
$453$	7.51186e25			0.206427
$454$	−6.06761e25	+	3.50601e26i	−0.163102	+	0.942442i
$455$		−	1.53571e25i		−	0.0403826i
$456$	7.69251e25	+	4.34434e25i	0.197888	+	0.111757i
$457$	−4.62101e26			−1.16299			−0.581494	−	0.813551i	$-0.697532\pi$
$457$	−4.62101e26			−1.16299			−0.581494	+	0.813551i	$0.697532\pi$
$458$	6.95506e26	+	1.20366e26i	1.71256	+	0.296381i
$459$			1.67965e25i			0.0404663i
$460$	−4.50731e25	+	1.26321e26i	−0.106253	+	0.297782i
$461$	4.88785e26			1.12748			0.563739	−	0.825953i	$-0.309362\pi$
$461$	4.88785e26			1.12748			0.563739	+	0.825953i	$0.309362\pi$
$462$	−8.29922e24	+	4.79549e25i	−0.0187334	+	0.108246i
$463$			5.75750e26i			1.27182i	0.771765	+	0.635908i	$0.219374\pi$
$463$			5.75750e26i			1.27182i	−0.771765	+	0.635908i	$0.780626\pi$
$464$	−4.99515e26	−	4.08471e26i	−1.07986	−	0.883043i
$465$	3.26417e26			0.690626
$466$	−3.92897e25	−	6.79959e24i	−0.0813616	−	0.0140807i
$467$		−	9.45663e26i		−	1.91676i	−0.285496	−	0.958380i	$-0.592158\pi$
$467$		−	9.45663e26i		−	1.91676i	0.285496	−	0.958380i	$-0.407842\pi$
$468$	−1.44931e25	−	5.17134e24i	−0.0287544	−	0.0102599i
$469$	−6.15710e26			−1.19577
$470$	−5.15596e25	+	2.97924e26i	−0.0980237	+	0.566404i
$471$		−	2.39758e26i		−	0.446235i
$472$	2.73504e26	−	4.84292e26i	0.498360	−	0.882444i
$473$	−1.41734e26			−0.252850
$474$	−4.02254e26	−	6.96154e25i	−0.702615	−	0.121597i
$475$		−	1.45991e26i		−	0.249683i
$476$	−3.07643e25	+	8.62197e25i	−0.0515202	+	0.144390i
$477$	2.48797e26			0.408000
$478$	−2.52800e25	+	1.46074e26i	−0.0405974	+	0.234582i
$479$			1.12306e27i			1.76624i	0.469150	+	0.883118i	$0.344560\pi$
$479$			1.12306e27i			1.76624i	−0.469150	+	0.883118i	$0.655440\pi$
$480$	1.71318e26	−	1.48439e26i	0.263870	−	0.228631i
$481$	2.98192e25			0.0449827
$482$	−5.20524e25	−	9.00835e24i	−0.0769078	−	0.0133099i
$483$			1.52074e26i			0.220082i
$484$	6.19151e26	+	2.20921e26i	0.877694	+	0.313173i
$485$	1.46922e26			0.204018
$486$	8.04184e24	−	4.64677e25i	0.0109394	−	0.0632104i
$487$		−	1.00388e26i		−	0.133780i	−0.997760	−	0.0668901i	$-0.978692\pi$
$487$		−	1.00388e26i		−	0.133780i	0.997760	−	0.0668901i	$-0.0213077\pi$
$488$	−1.01086e27	−	5.70884e26i	−1.31975	−	0.745331i
$489$	4.73524e26			0.605694
$490$	−2.22714e26	−	3.85436e25i	−0.279118	−	0.0483050i
$491$			8.18959e26i			1.00565i	0.864388	+	0.502825i	$0.167706\pi$
$491$			8.18959e26i			1.00565i	−0.864388	+	0.502825i	$0.832294\pi$
$492$	6.62449e25	−	1.85657e26i	0.0797080	−	0.223389i
$493$	2.48772e26			0.293313
$494$	5.32117e24	−	3.07470e25i	0.00614805	−	0.0355249i
$495$			4.64611e25i			0.0526062i
$496$	1.12845e27	−	1.37997e27i	1.25218	−	1.53128i
$497$	−1.26328e27			−1.37384
$498$	−6.00679e26	−	1.03955e26i	−0.640249	−	0.110804i
$499$		−	4.06033e26i		−	0.424185i	−0.977250	−	0.212093i	$-0.931972\pi$
$499$		−	4.06033e26i		−	0.424185i	0.977250	−	0.212093i	$-0.0680279\pi$
$500$	−9.09015e26	−	3.24348e26i	−0.930831	−	0.332133i
$501$	6.38796e26			0.641187
$502$	2.15922e26	−	1.24765e27i	0.212451	−	1.22760i
$503$		−	9.34933e25i		−	0.0901780i	−0.998983	−	0.0450890i	$-0.985643\pi$
$503$		−	9.34933e25i		−	0.0901780i	0.998983	−	0.0450890i	$-0.0143571\pi$
$504$	1.26390e26	−	2.23798e26i	0.119511	−	0.211617i
$505$	−1.55964e26			−0.144581
$506$	−1.47929e26	−	2.56011e25i	−0.134446	−	0.0232677i
$507$		−	6.42481e26i		−	0.572507i
$508$	7.40660e25	−	2.07576e26i	0.0647115	−	0.181360i
$509$	−1.37706e27			−1.17971			−0.589853	−	0.807511i	$-0.700814\pi$
$509$	−1.37706e27			−1.17971			−0.589853	+	0.807511i	$0.700814\pi$
$510$	−1.49030e25	+	8.61131e25i	−0.0125191	+	0.0723382i
$511$			9.19024e26i			0.757038i
$512$	−3.52831e25	−	1.23744e27i	−0.0285015	−	0.999594i
$513$	9.56279e25			0.0757550
$514$	8.67939e26	+	1.50208e26i	0.674308	+	0.116698i
$515$			2.35064e26i			0.179108i
$516$	7.04985e26	+	2.51548e26i	0.526845	+	0.187985i
$517$	−3.38435e26			−0.248068
$518$	−8.49330e25	+	4.90763e26i	−0.0610631	+	0.352837i
$519$			1.21403e27i			0.856165i
$520$	−6.97156e25	−	3.93719e25i	−0.0482277	−	0.0272366i
$521$	1.85746e27			1.26050			0.630248	−	0.776394i	$-0.282953\pi$
$521$	1.85746e27			1.26050			0.630248	+	0.776394i	$0.282953\pi$
$522$	−6.88228e26	−	1.19107e26i	−0.458170	−	0.0792924i
$523$			1.77848e26i			0.116154i	0.998312	+	0.0580768i	$0.0184968\pi$
$523$			1.77848e26i			0.116154i	−0.998312	+	0.0580768i	$0.981503\pi$
$524$	−5.57179e26	+	1.56154e27i	−0.357011	+	1.00056i
$525$	−4.24730e26			−0.267005
$526$	−3.01733e26	+	1.74348e27i	−0.186108	+	1.07538i
$527$			6.87263e26i			0.415927i
$528$	1.96421e26	+	1.60620e26i	0.116640	+	0.0953809i
$529$	1.24704e27			0.726650
$530$	1.27554e27	+	2.20749e26i	0.729348	+	0.126223i
$531$		−	6.02038e26i		−	0.337815i
$532$	4.90876e26	+	1.75151e26i	0.270306	+	0.0964486i
$533$	−6.96249e25			−0.0376264
$534$	−2.16696e26	+	1.25212e27i	−0.114931	+	0.664100i
$535$			1.78900e27i			0.931263i
$536$	−1.57854e27	+	2.79511e27i	−0.806504	+	1.42807i
$537$	−9.45079e25			−0.0473942
$538$	−2.22098e26	−	3.84370e25i	−0.109326	−	0.0189202i
$539$		−	2.52999e26i		−	0.122245i
$540$	8.24584e25	−	2.31097e26i	0.0391109	−	0.109612i
$541$	1.96989e27			0.917212			0.458606	−	0.888640i	$-0.348349\pi$
$541$	1.96989e27			0.917212			0.458606	+	0.888640i	$0.348349\pi$
$542$	1.18703e26	−	6.85892e26i	0.0542584	−	0.313518i
$543$		−	3.15208e26i		−	0.141449i
$544$	3.12534e26	+	3.60706e26i	0.137692	+	0.158915i
$545$	8.01394e26			0.346642
$546$	−8.94521e25	−	1.54809e25i	−0.0379896	−	0.00657459i
$547$		−	3.47749e27i		−	1.45008i	−0.688706	−	0.725040i	$-0.741821\pi$
$547$		−	3.47749e27i		−	1.45008i	0.688706	−	0.725040i	$-0.258179\pi$
$548$	2.22192e26	+	7.92810e25i	0.0909752	+	0.0324611i
$549$	−1.25663e27			−0.505225
$550$	7.15016e25	−	4.13154e26i	0.0282286	−	0.163112i
$551$		−	1.41633e27i		−	0.549098i
$552$	6.90362e26	+	3.89882e26i	0.262837	+	0.148437i
$553$	−2.40837e27			−0.900474
$554$	2.15788e27	+	3.73450e26i	0.792374	+	0.137131i
$555$			4.75476e26i			0.171474i
$556$	−6.47006e26	+	1.81329e27i	−0.229171	+	0.642273i
$557$	1.20852e26			0.0420438			0.0210219	−	0.999779i	$-0.493308\pi$
$557$	1.20852e26			0.0420438			0.0210219	+	0.999779i	$0.493308\pi$
$558$	3.29048e26	−	1.90132e27i	0.112439	−	0.649699i
$559$		−	2.64382e26i		−	0.0887390i
$560$	8.46548e26	−	1.03523e27i	0.279108	−	0.341317i
$561$	−9.78228e25			−0.0316819
$562$	−2.83206e27	−	4.90126e26i	−0.901031	−	0.155935i
$563$		−	3.65310e27i		−	1.14177i	−0.821031	−	0.570884i	$-0.806601\pi$
$563$		−	3.65310e27i		−	1.14177i	0.821031	−	0.570884i	$-0.193399\pi$
$564$	1.68338e27	+	6.00650e26i	0.516880	+	0.184430i
$565$	−2.19036e27			−0.660741
$566$	5.94868e26	−	3.43729e27i	0.176301	−	1.01871i
$567$		−	2.78210e26i		−	0.0810107i
$568$	−3.23874e27	+	5.73483e27i	−0.926602	+	1.64073i
$569$	−1.09913e27			−0.308976			−0.154488	−	0.987995i	$-0.549373\pi$
$569$	−1.09913e27			−0.308976			−0.154488	+	0.987995i	$0.549373\pi$
$570$	4.90269e26	+	8.48474e25i	0.135421	+	0.0234364i
$571$		−	5.14817e27i		−	1.39731i	−0.715461	−	0.698653i	$-0.753783\pi$
$571$		−	5.14817e27i		−	1.39731i	0.715461	−	0.698653i	$-0.246217\pi$
$572$	3.01178e25	−	8.44078e25i	0.00803273	−	0.0225124i
$573$	−1.46556e27			−0.384112
$574$	1.98310e26	−	1.14588e27i	0.0510770	−	0.295135i
$575$		−	1.31019e27i		−	0.331632i
$576$	−6.91929e26	−	1.14753e27i	−0.172122	−	0.285456i
$577$	3.58695e26			0.0876934			0.0438467	−	0.999038i	$-0.486039\pi$
$577$	3.58695e26			0.0876934			0.0438467	+	0.999038i	$0.486039\pi$
$578$	3.91951e27	+	6.78322e26i	0.941787	+	0.162989i
$579$		−	3.07165e27i		−	0.725414i
$580$	−3.42275e27	−	1.22128e27i	−0.794503	−	0.283489i
$581$	−3.59637e27			−0.820546
$582$	1.48106e26	−	8.55792e26i	0.0332157	−	0.191928i
$583$			1.44899e27i			0.319432i
$584$	4.17204e27	+	2.35616e27i	0.904107	+	0.510595i
$585$	−8.66657e25			−0.0184624
$586$	−7.08984e27	−	1.22699e27i	−1.48477	−	0.256959i
$587$		−	4.41382e27i		−	0.908728i	−0.890816	−	0.454364i	$-0.849867\pi$
$587$		−	4.41382e27i		−	0.908728i	0.890816	−	0.454364i	$-0.150133\pi$
$588$	−4.49019e26	+	1.25842e27i	−0.0908848	+	0.254713i
$589$	3.91280e27			0.778637
$590$	5.34168e26	−	3.08655e27i	0.104510	−	0.603884i
$591$			3.95339e27i			0.760493i
$592$	2.01014e27	+	1.64377e27i	0.380198	+	0.310902i
$593$	5.21372e27			0.969618			0.484809	−	0.874620i	$-0.338889\pi$
$593$	5.21372e27			0.969618			0.484809	+	0.874620i	$0.338889\pi$
$594$	2.70627e26	+	4.68356e25i	0.0494888	+	0.00856468i
$595$			5.15574e26i			0.0927089i
$596$	4.18896e26	+	1.49467e26i	0.0740702	+	0.0264292i
$597$	−5.32615e27			−0.926125
$598$	4.77547e25	−	2.75938e26i	0.00816590	−	0.0471845i
$599$			1.17097e28i			1.96914i	0.174994	+	0.984569i	$0.444009\pi$
$599$			1.17097e28i			1.96914i	−0.174994	+	0.984569i	$0.555991\pi$
$600$	−1.08891e27	+	1.92812e27i	−0.180085	+	0.318876i
$601$	6.38551e27			1.03861			0.519303	−	0.854590i	$-0.326192\pi$
$601$	6.38551e27			1.03861			0.519303	+	0.854590i	$0.326192\pi$
$602$	4.35119e27	+	7.53030e26i	0.696054	+	0.120461i
$603$			3.47468e27i			0.546691i
$604$	7.76450e26	−	2.17607e27i	0.120156	−	0.336747i
$605$	3.70238e27			0.563543
$606$	−1.57221e26	+	9.08461e26i	−0.0235388	+	0.136013i
$607$			1.18450e28i			1.74441i	0.489136	+	0.872207i	$0.337312\pi$
$607$			1.18450e28i			1.74441i	−0.489136	+	0.872207i	$0.662688\pi$
$608$	2.05361e27	−	1.77936e27i	0.297497	−	0.257767i
$609$	−4.12054e27			−0.587193
$610$	−6.44255e27	−	1.11497e27i	−0.903149	−	0.156302i
$611$		−	6.31297e26i		−	0.0870606i
$612$	4.86570e26	+	1.73614e26i	0.0660132	+	0.0235544i
$613$	1.20216e28			1.60456			0.802281	−	0.596947i	$-0.203620\pi$
$613$	1.20216e28			1.60456			0.802281	+	0.596947i	$0.203620\pi$
$614$	−2.90509e26	+	1.67863e27i	−0.0381483	+	0.220430i
$615$		−	1.11019e27i		−	0.143432i
$616$	1.30340e27	+	7.36092e26i	0.165680	+	0.0935675i
$617$	−7.64204e27			−0.955779			−0.477889	−	0.878420i	$-0.658598\pi$
$617$	−7.64204e27			−0.955779			−0.477889	+	0.878420i	$0.658598\pi$
$618$	1.36920e27	+	2.36959e26i	0.168494	+	0.0291600i
$619$			2.55907e26i			0.0309867i	0.999880	+	0.0154934i	$0.00493188\pi$
$619$			2.55907e26i			0.0309867i	−0.999880	+	0.0154934i	$0.995068\pi$
$620$	3.37395e27	−	9.45578e27i	0.401996	−	1.12663i
$621$	8.58211e26			0.100619
$622$	4.27834e26	−	2.47213e27i	0.0493596	−	0.285211i
$623$			7.49666e27i			0.851114i
$624$	−2.99612e26	+	3.66391e26i	−0.0334744	+	0.0409354i
$625$	3.33242e26			0.0366403
$626$	−1.52326e28	−	2.63620e27i	−1.64828	−	0.285256i
$627$			5.56935e26i			0.0593102i
$628$	−6.94540e27	−	2.47821e27i	−0.727949	−	0.259742i
$629$	−1.00110e27			−0.103270
$630$	2.46846e26	−	1.42634e27i	0.0250623	−	0.144816i
$631$		−	1.32161e27i		−	0.132072i	−0.997817	−	0.0660358i	$-0.978965\pi$
$631$		−	1.32161e27i		−	0.132072i	0.997817	−	0.0660358i	$-0.0210352\pi$
$632$	−6.17448e27	+	1.09331e28i	−0.607337	+	1.07541i
$633$	−3.99405e27			−0.386702
$634$	1.25724e28	+	2.17583e27i	1.19819	+	0.207363i
$635$		−	1.24126e27i		−	0.116446i
$636$	2.57164e27	−	7.20725e27i	0.237487	−	0.665577i
$637$	4.71929e26			0.0429025
$638$	6.93676e26	−	4.00823e27i	0.0620797	−	0.358712i
$639$			7.12914e27i			0.628100i
$640$	−2.52924e27	−	6.49712e27i	−0.219377	−	0.563535i
$641$	−1.25919e28			−1.07526			−0.537629	−	0.843182i	$-0.680680\pi$
$641$	−1.25919e28			−1.07526			−0.537629	+	0.843182i	$0.680680\pi$
$642$	1.04206e28	+	1.80342e27i	0.876076	+	0.151616i
$643$		−	1.36334e28i		−	1.12848i	−0.825611	−	0.564240i	$-0.809169\pi$
$643$		−	1.36334e28i		−	1.12848i	0.825611	−	0.564240i	$-0.190831\pi$
$644$	4.40535e27	+	1.57189e27i	0.359023	+	0.128104i
$645$	4.21565e27			0.338273
$646$	−1.78644e26	+	1.03225e27i	−0.0141145	+	0.0815567i
$647$			1.73575e28i			1.35034i	0.737660	+	0.675172i	$0.235931\pi$
$647$			1.73575e28i			1.35034i	−0.737660	+	0.675172i	$0.764069\pi$
$648$	−1.26297e27	−	7.13265e26i	−0.0967486	−	0.0546388i
$649$	3.50626e27			0.264483
$650$	7.70672e26	+	1.33375e26i	0.0572448	+	0.00990695i
$651$		−	1.13835e28i		−	0.832657i
$652$	4.89449e27	−	1.37173e28i	0.352559	−	0.988078i
$653$	−2.24570e27			−0.159301			−0.0796507	−	0.996823i	$-0.525381\pi$
$653$	−2.24570e27			−0.159301			−0.0796507	+	0.996823i	$0.525381\pi$
$654$	8.07853e26	−	4.66797e27i	0.0564358	−	0.326100i
$655$			9.33767e27i			0.642430i
$656$	−4.69348e27	−	3.83803e27i	−0.318021	−	0.260058i
$657$	5.18639e27			0.346108
$658$	1.03898e28	+	1.79810e27i	0.682889	+	0.118183i
$659$		−	1.47202e28i		−	0.952925i	−0.879195	−	0.476463i	$-0.841919\pi$
$659$		−	1.47202e28i		−	0.952925i	0.879195	−	0.476463i	$-0.158081\pi$
$660$	1.34591e27	+	4.80236e26i	0.0858174	+	0.0306207i
$661$	4.08923e27			0.256819			0.128409	−	0.991721i	$-0.459013\pi$
$661$	4.08923e27			0.256819			0.128409	+	0.991721i	$0.459013\pi$
$662$	−3.15475e27	+	1.82289e28i	−0.195158	+	1.12767i
$663$		−	1.82473e26i		−	0.0111189i
$664$	−9.22024e27	+	1.63262e28i	−0.553428	+	0.979953i
$665$	2.93532e27			0.173556
$666$	2.76956e27	+	4.79308e26i	0.161313	+	0.0279172i
$667$		−	1.27109e28i		−	0.729317i
$668$	6.60279e27	−	1.85049e28i	0.373218	−	1.04598i
$669$	8.25194e27			0.459510
$670$	−3.08297e27	+	1.78141e28i	−0.169130	+	0.977274i
$671$		−	7.31861e27i		−	0.395552i
$672$	−5.17667e27	−	5.97457e27i	−0.275650	−	0.318137i
$673$	−2.80038e28			−1.46915			−0.734576	−	0.678527i	$-0.762619\pi$
$673$	−2.80038e28			−1.46915			−0.734576	+	0.678527i	$0.762619\pi$
$674$	−3.02063e28	−	5.22759e27i	−1.56134	−	0.270211i
$675$			2.39691e27i			0.122071i
$676$	−1.86117e28	−	6.64089e27i	−0.933939	−	0.333242i
$677$	−4.33444e27			−0.214312			−0.107156	−	0.994242i	$-0.534174\pi$
$677$	−4.33444e27			−0.214312			−0.107156	+	0.994242i	$0.534174\pi$
$678$	−2.20802e27	+	1.27585e28i	−0.107574	+	0.621586i
$679$		−	5.12377e27i		−	0.245976i
$680$	2.34052e27	+	1.32181e27i	0.110719	+	0.0625287i
$681$	1.18460e28			0.552207
$682$	1.10732e28	+	1.91637e27i	0.508664	+	0.0880309i
$683$		−	3.99129e28i		−	1.80678i	−0.428815	−	0.903392i	$-0.641069\pi$
$683$		−	3.99129e28i		−	1.80678i	0.428815	−	0.903392i	$-0.358931\pi$
$684$	9.88441e26	−	2.77019e27i	0.0440950	−	0.123580i
$685$	1.32866e27			0.0584127
$686$	−4.21378e27	+	2.43482e28i	−0.182571	+	1.05494i
$687$		−	2.34996e28i		−	1.00345i
$688$	1.45739e28	−	1.78222e28i	0.613326	−	0.750029i
$689$	−2.70285e27			−0.112106
$690$	4.39991e27	+	7.61461e26i	0.179867	+	0.0311284i
$691$			5.95285e26i			0.0239852i	0.999928	+	0.0119926i	$0.00381746\pi$
$691$			5.95285e26i			0.0239852i	−0.999928	+	0.0119926i	$0.996183\pi$
$692$	3.51687e28	+	1.25486e28i	1.39667	+	0.498352i
$693$	1.62029e27			0.0634250
$694$	−2.49965e27	+	1.44436e28i	−0.0964461	+	0.557289i
$695$			1.08431e28i			0.412386i
$696$	−1.05641e28	+	1.87058e28i	−0.396040	+	0.701266i
$697$	2.33748e27			0.0863812
$698$	−6.30845e27	−	1.09176e27i	−0.229810	−	0.0397716i
$699$			1.32751e27i			0.0476724i
$700$	−4.39015e27	+	1.23038e28i	−0.155417	+	0.435570i
$701$	−3.68199e27			−0.128500			−0.0642498	−	0.997934i	$-0.520465\pi$
$701$	−3.68199e27			−0.128500			−0.0642498	+	0.997934i	$0.520465\pi$
$702$	−8.73642e25	+	5.04811e26i	−0.00300582	+	0.0173683i
$703$			5.69960e27i			0.193326i
$704$	6.68319e27	−	4.02978e27i	0.223490	−	0.134758i
$705$	1.00662e28			0.331875
$706$	3.57637e28	+	6.18938e27i	1.16251	+	0.201187i
$707$			5.43911e27i			0.174315i
$708$	−1.74401e28	−	6.22286e27i	−0.551083	−	0.196633i
$709$	−4.99831e28			−1.55726			−0.778629	−	0.627485i	$-0.784084\pi$
$709$	−4.99831e28			−1.55726			−0.778629	+	0.627485i	$0.784084\pi$
$710$	−6.32545e27	+	3.65500e28i	−0.194316	+	1.12280i
$711$			1.35913e28i			0.411685i
$712$	3.40322e28	+	1.92197e28i	1.01646	+	0.574045i
$713$	3.51154e28			1.03419
$714$	3.00312e27	+	5.19730e26i	0.0872150	+	0.0150937i
$715$		−	5.04739e26i		−	0.0144546i
$716$	−9.76863e26	+	2.73775e27i	−0.0275869	+	0.0773149i
$717$	4.93552e27			0.137449
$718$	3.68954e27	−	2.13190e28i	0.101328	−	0.585495i
$719$			3.72480e28i			1.00882i	0.863464	+	0.504410i	$0.168290\pi$
$719$			3.72480e28i			1.00882i	−0.863464	+	0.504410i	$0.831710\pi$
$720$	−5.84221e27	−	4.77739e27i	−0.156046	−	0.127604i
$721$	8.19766e27			0.215942
$722$	−3.20514e28	−	5.54692e27i	−0.832674	−	0.144105i
$723$			1.75874e27i			0.0450628i
$724$	−9.13109e27	−	3.25809e27i	−0.230747	−	0.0823337i
$725$	3.55003e28			0.884815
$726$	3.73222e27	−	2.15657e28i	0.0917490	−	0.530148i
$727$			3.79351e28i			0.919809i	0.887968	+	0.459904i	$0.152116\pi$
$727$			3.79351e28i			0.919809i	−0.887968	+	0.459904i	$0.847884\pi$
$728$	−1.37306e27	+	2.43127e27i	−0.0328380	+	0.0581460i
$729$	−1.57004e27			−0.0370370
$730$	2.65898e28	+	4.60171e27i	0.618709	+	0.107076i
$731$			8.87595e27i			0.203724i
$732$	−1.29890e28	+	3.64027e28i	−0.294079	+	0.824181i
$733$	−4.54335e28			−1.01470			−0.507349	−	0.861741i	$-0.669374\pi$
$733$	−4.54335e28			−1.01470			−0.507349	+	0.861741i	$0.669374\pi$
$734$	6.25697e27	−	3.61543e28i	0.137849	−	0.796524i
$735$			7.52503e27i			0.163544i
$736$	1.84301e28	−	1.59688e28i	0.395138	−	0.342368i
$737$	−2.02365e28			−0.428016
$738$	−6.46664e27	−	1.11914e27i	−0.134932	−	0.0233517i
$739$		−	1.16698e28i		−	0.240226i	−0.992760	−	0.120113i	$-0.961674\pi$
$739$		−	1.16698e28i		−	0.240226i	0.992760	−	0.120113i	$-0.0383257\pi$
$740$	1.37738e28	+	4.91467e27i	0.279728	+	0.0998107i
$741$	−1.03887e27			−0.0208152
$742$	7.69843e27	−	4.44834e28i	0.152182	−	0.879343i
$743$		−	3.71645e28i		−	0.724837i	−0.932015	−	0.362419i	$-0.881951\pi$
$743$		−	3.71645e28i		−	0.724837i	0.932015	−	0.362419i	$-0.118049\pi$
$744$	−5.16770e28	−	2.91846e28i	−0.994416	−	0.561597i
$745$	2.50490e27			0.0475585
$746$	−7.12061e28	−	1.23231e28i	−1.33392	−	0.230852i
$747$			2.02956e28i			0.375143i
$748$	−1.01113e27	+	2.83377e27i	−0.0184412	+	0.0516832i
$749$	6.23898e28			1.12278
$750$	−5.47951e27	+	3.16619e28i	−0.0973037	+	0.562244i
$751$		−	1.05584e28i		−	0.185011i	−0.995712	−	0.0925056i	$-0.970512\pi$
$751$		−	1.05584e28i		−	0.185011i	0.995712	−	0.0925056i	$-0.0294876\pi$
$752$	3.47998e28	−	4.25563e28i	0.601726	−	0.735843i
$753$	−4.21554e28			−0.719288
$754$	7.47670e27	+	1.29394e27i	0.125892	+	0.0217872i
$755$		−	1.30124e28i		−	0.216216i
$756$	−8.05932e27	−	2.87567e27i	−0.132154	−	0.0471543i
$757$	−3.28744e28			−0.531984			−0.265992	−	0.963975i	$-0.585700\pi$
$757$	−3.28744e28			−0.531984			−0.265992	+	0.963975i	$0.585700\pi$
$758$	2.10748e28	−	1.21775e29i	0.336567	−	1.94477i
$759$			4.99821e27i			0.0787764i
$760$	7.52547e27	−	1.33253e28i	0.117057	−	0.207272i
$761$	1.00236e29			1.53879			0.769394	−	0.638775i	$-0.220558\pi$
$761$	1.00236e29			1.53879			0.769394	+	0.638775i	$0.220558\pi$
$762$	−7.23010e27	−	1.25126e27i	−0.109546	−	0.0189583i
$763$		−	2.79479e28i		−	0.417931i
$764$	−1.51485e28	+	4.24550e28i	−0.223582	+	0.626607i
$765$	2.90957e27			0.0423853
$766$	1.72344e28	−	9.95845e28i	0.247804	−	1.43187i
$767$			6.54036e27i			0.0928214i
$768$	−4.03942e28	+	8.18287e27i	−0.565856	+	0.114629i
$769$	−2.66201e28			−0.368084			−0.184042	−	0.982918i	$-0.558918\pi$
$769$	−2.66201e28			−0.368084			−0.184042	+	0.982918i	$0.558918\pi$
$770$	8.30697e27	+	1.43763e27i	0.113380	+	0.0196218i
$771$		−	2.93258e28i		−	0.395099i
$772$	−8.89809e28	−	3.17495e28i	−1.18338	−	0.422245i
$773$	−2.90154e28			−0.380919			−0.190460	−	0.981695i	$-0.560998\pi$
$773$	−2.90154e28			−0.380919			−0.190460	+	0.981695i	$0.560998\pi$
$774$	4.24963e27	−	2.45554e28i	0.0550733	−	0.318227i
$775$			9.80742e28i			1.25469i
$776$	−2.32601e28	−	1.31361e28i	−0.293761	−	0.165902i
$777$	1.65818e28			0.206739
$778$	−4.75218e28	−	8.22427e27i	−0.584920	−	0.101228i
$779$		−	1.33080e28i		−	0.161710i
$780$	−8.95804e26	+	2.51057e27i	−0.0107465	+	0.0301180i
$781$	−4.15200e28			−0.491753
$782$	−1.60324e27	+	9.26391e27i	−0.0187470	+	0.108324i
$783$			2.32537e28i			0.268457i
$784$	3.18131e28	+	2.60148e28i	0.362615	+	0.296524i
$785$	−4.15319e28			−0.467396
$786$	5.43902e28	+	9.41294e27i	0.604359	+	0.104592i
$787$			1.18527e29i			1.30038i	0.759771	+	0.650191i	$0.225311\pi$
$787$			1.18527e29i			1.30038i	−0.759771	+	0.650191i	$0.774689\pi$
$788$	1.14524e29	+	4.08635e28i	1.24060	+	0.442664i
$789$	5.89085e28			0.630098
$790$	−1.20591e28	+	6.96804e28i	−0.127363	+	0.735935i
$791$			7.63870e28i			0.796627i
$792$	4.15404e27	−	7.35554e27i	0.0427779	−	0.0757465i
$793$	1.36517e28			0.138821
$794$	5.07728e28	+	8.78690e27i	0.509831	+	0.0882329i
$795$		−	4.30977e28i		−	0.427349i
$796$	−5.50527e28	+	1.54290e29i	−0.539074	+	1.51080i
$797$	1.66328e28			0.160835			0.0804177	−	0.996761i	$-0.474375\pi$
$797$	1.66328e28			0.160835			0.0804177	+	0.996761i	$0.474375\pi$
$798$	2.95898e27	−	1.70977e28i	0.0282562	−	0.163271i
$799$			2.11942e28i			0.199870i
$800$	4.45994e28	+	5.14737e28i	0.415365	+	0.479386i
$801$	4.23064e28			0.389118
$802$	1.04554e29	+	1.80945e28i	0.949725	+	0.164362i
$803$			3.02055e28i			0.270976i
$804$	1.00656e29	+	3.59154e28i	0.891825	+	0.318215i
$805$	2.63430e28			0.230519
$806$	−3.57467e27	+	2.06553e28i	−0.0308949	+	0.178518i
$807$			7.50421e27i			0.0640575i
$808$	2.46916e28	+	1.39446e28i	0.208179	+	0.117569i
$809$	−1.08111e29			−0.900295			−0.450147	−	0.892954i	$-0.648629\pi$
$809$	−1.08111e29			−0.900295			−0.450147	+	0.892954i	$0.648629\pi$
$810$	−8.04935e27	−	1.39305e27i	−0.0662080	−	0.0114582i
$811$		−	1.49142e29i		−	1.21169i	−0.795581	−	0.605847i	$-0.792834\pi$
$811$		−	1.49142e29i		−	1.21169i	0.795581	−	0.605847i	$-0.207166\pi$
$812$	−4.25912e28	+	1.19366e29i	−0.341790	+	0.957897i
$813$	−2.31748e28			−0.183701
$814$	−2.79148e27	+	1.61299e28i	−0.0218570	+	0.126295i
$815$		−	8.20260e28i		−	0.634418i
$816$	1.00587e28	−	1.23006e28i	0.0768492	−	0.0939780i
$817$	5.05336e28			0.381381
$818$	−1.70908e29	−	2.95779e28i	−1.27418	−	0.220513i
$819$			3.02239e27i			0.0222593i
$820$	−3.21604e28	−	1.14753e28i	−0.233982	−	0.0834880i
$821$	−1.28207e29			−0.921465			−0.460733	−	0.887539i	$-0.652413\pi$
$821$	−1.28207e29			−0.921465			−0.460733	+	0.887539i	$0.652413\pi$
$822$	1.33937e27	−	7.73918e27i	0.00951002	−	0.0549512i
$823$		−	1.98827e29i		−	1.39469i	−0.716737	−	0.697343i	$-0.754365\pi$
$823$		−	1.98827e29i		−	1.39469i	0.716737	−	0.697343i	$-0.245635\pi$
$824$	2.10169e28	−	3.72144e28i	0.145645	−	0.257893i
$825$	−1.39596e28			−0.0955724
$826$	−1.07641e29	−	1.86287e28i	−0.728076	−	0.126003i
$827$		−	3.50038e28i		−	0.233916i	−0.993137	−	0.116958i	$-0.962686\pi$
$827$		−	3.50038e28i		−	0.233916i	0.993137	−	0.116958i	$-0.0373143\pi$
$828$	8.87074e27	−	2.48610e28i	0.0585675	−	0.164141i
$829$	2.08460e29			1.35981			0.679904	−	0.733301i	$-0.262021\pi$
$829$	2.08460e29			1.35981			0.679904	+	0.733301i	$0.262021\pi$
$830$	−1.80076e28	+	1.04052e29i	−0.116058	+	0.670612i
$831$		−	7.29102e28i		−	0.464278i
$832$	7.51691e27	+	1.24664e28i	0.0472940	+	0.0784347i
$833$	−1.58438e28			−0.0984938
$834$	6.31588e28	+	1.09305e28i	0.387948	+	0.0671395i
$835$		−	1.10655e29i		−	0.671594i
$836$	1.61336e28	+	5.75666e27i	0.0967537	+	0.0345230i
$837$	−6.42413e28			−0.380680
$838$	−1.33223e28	+	7.69792e28i	−0.0780077	+	0.450747i
$839$		−	2.15016e28i		−	0.124409i	−0.998063	−	0.0622043i	$-0.980187\pi$
$839$		−	2.15016e28i		−	0.124409i	0.998063	−	0.0622043i	$-0.0198130\pi$
$840$	−3.87673e28	−	2.18938e28i	−0.221653	−	0.125178i
$841$	1.67413e29			0.945867
$842$	1.33096e28	+	2.30341e27i	0.0743097	+	0.0128603i
$843$			9.56892e28i			0.527943i
$844$	−4.12837e28	+	1.15701e29i	−0.225089	+	0.630832i
$845$	−1.11294e29			−0.599657
$846$	1.01473e28	−	5.86337e28i	0.0540317	−	0.312208i
$847$		−	1.29117e29i		−	0.679439i
$848$	−1.82202e29	−	1.48993e29i	−0.947531	−	0.774831i
$849$	−1.16138e29			−0.596897
$850$	−2.58733e28	−	4.47771e27i	−0.131420	−	0.0227440i
$851$			5.11509e28i			0.256778i
$852$	2.06520e29	+	7.36891e28i	1.02463	+	0.365601i
$853$	−9.99709e28			−0.490211			−0.245106	−	0.969496i	$-0.578823\pi$
$853$	−9.99709e28			−0.490211			−0.245106	+	0.969496i	$0.578823\pi$
$854$	−3.88836e28	+	2.24679e29i	−0.188446	+	1.08889i
$855$		−	1.65651e28i		−	0.0793475i
$856$	1.59953e29	−	2.83228e29i	0.757276	−	1.34090i
$857$	−6.23666e28			−0.291839			−0.145920	−	0.989296i	$-0.546614\pi$
$857$	−6.23666e28			−0.291839			−0.145920	+	0.989296i	$0.546614\pi$
$858$	−2.94001e27	−	5.08808e26i	−0.0135980	−	0.00235332i
$859$			1.81838e29i			0.831291i	0.909527	+	0.415646i	$0.136444\pi$
$859$			1.81838e29i			0.831291i	−0.909527	+	0.415646i	$0.863556\pi$
$860$	4.35743e28	−	1.22121e29i	0.196900	−	0.551830i
$861$	−3.87169e28			−0.172929
$862$	−5.79641e27	+	3.34931e28i	−0.0255910	+	0.147871i
$863$		−	2.84892e29i		−	1.24329i	−0.783299	−	0.621645i	$-0.786465\pi$
$863$		−	2.84892e29i		−	1.24329i	0.783299	−	0.621645i	$-0.213535\pi$
$864$	−3.37167e28	+	2.92139e28i	−0.145448	+	0.126024i
$865$	2.10301e29			0.896767
$866$	2.93704e29	+	5.08294e28i	1.23803	+	0.214257i
$867$		−	1.32432e29i		−	0.551824i
$868$	−3.29763e29	−	1.17664e29i	−1.35833	−	0.484668i
$869$	−7.91555e28			−0.322317
$870$	−2.06322e28	+	1.19218e29i	−0.0830527	+	0.479898i
$871$		−	3.77479e28i		−	0.150214i
$872$	−1.26874e29	−	7.16519e28i	−0.499122	−	0.281879i
$873$	−2.89154e28			−0.112457
$874$	5.27423e28	+	9.12774e27i	0.202789	+	0.0350953i
$875$			1.89565e29i			0.720574i
$876$	5.36082e28	−	1.50242e29i	0.201461	−	0.564611i
$877$	4.00375e29			1.48755			0.743773	−	0.668432i	$-0.233034\pi$
$877$	4.00375e29			1.48755			0.743773	+	0.668432i	$0.233034\pi$
$878$	2.11563e28	−	1.22246e29i	0.0777133	−	0.449046i
$879$			2.39550e29i			0.869977i
$880$	2.78234e28	−	3.40249e28i	0.0999042	−	0.122172i
$881$	−2.97318e29			−1.05551			−0.527754	−	0.849397i	$-0.676966\pi$
$881$	−2.97318e29			−1.05551			−0.527754	+	0.849397i	$0.676966\pi$
$882$	4.38319e28	+	7.58569e27i	0.153853	+	0.0266262i
$883$		−	2.28684e28i		−	0.0793649i	−0.999212	−	0.0396825i	$-0.987365\pi$
$883$		−	2.28684e28i		−	0.0793649i	0.999212	−	0.0396825i	$-0.0126346\pi$
$884$	−5.28595e27	−	1.88610e27i	−0.0181385	−	0.00647204i
$885$	−1.04288e29			−0.353835
$886$	−2.35189e28	+	1.35898e29i	−0.0789005	+	0.455906i
$887$			2.10400e28i			0.0697926i	0.999391	+	0.0348963i	$0.0111101\pi$
$887$			2.10400e28i			0.0697926i	−0.999391	+	0.0348963i	$0.988890\pi$
$888$	4.25119e28	−	7.52755e28i	0.139438	−	0.246902i
$889$	−4.32879e28			−0.140394
$890$	2.16898e29	+	3.75371e28i	0.695594	+	0.120382i
$891$		−	9.14390e27i		−	0.0289971i
$892$	8.52946e28	−	2.39046e29i	0.267469	−	0.749605i
$893$	1.20665e29			0.374168
$894$	2.52509e27	−	1.45906e28i	0.00774287	−	0.0447401i
$895$			1.63711e28i			0.0496418i
$896$	−2.26582e29	+	8.82052e28i	−0.679430	+	0.264493i
$897$	−9.32335e27			−0.0276470
$898$	−5.52397e29	−	9.55996e28i	−1.61990	−	0.280345i
$899$			9.51470e29i			2.75930i
$900$	6.94348e28	+	2.47752e28i	0.199137	+	0.0710547i
$901$	9.07412e28			0.257369
$902$	6.51783e27	−	3.76616e28i	0.0182826	−	0.105641i
$903$		−	1.47017e29i		−	0.407841i
$904$	3.46770e29	+	1.95838e29i	0.951386	+	0.537295i
$905$	−5.46018e28			−0.148157
$906$	−7.57948e28	−	1.31173e28i	−0.203403	−	0.0352015i
$907$			6.83150e29i			1.81319i	0.422004	+	0.906594i	$0.361327\pi$
$907$			6.83150e29i			1.81319i	−0.422004	+	0.906594i	$0.638673\pi$
$908$	1.22445e29	−	3.43162e29i	0.321426	−	0.900824i
$909$	3.06949e28			0.0796944
$910$	−2.68167e27	+	1.54953e28i	−0.00688637	+	0.0397911i
$911$		−	2.83829e29i		−	0.720897i	−0.932779	−	0.360449i	$-0.882624\pi$
$911$		−	2.83829e29i		−	0.720897i	0.932779	−	0.360449i	$-0.117376\pi$
$912$	−7.00314e28	−	5.72672e28i	−0.175932	−	0.143866i
$913$	−1.18201e29			−0.293708
$914$	4.66261e29	+	8.06925e28i	1.14595	+	0.198322i
$915$			2.17680e29i			0.529184i
$916$	−6.80748e29	−	2.42900e29i	−1.63694	−	0.584080i
$917$	3.25644e29			0.774549
$918$	2.93303e27	−	1.69477e28i	0.00690064	−	0.0398735i
$919$			1.08421e28i			0.0252324i	0.999920	+	0.0126162i	$0.00401596\pi$
$919$			1.08421e28i			0.0252324i	−0.999920	+	0.0126162i	$0.995984\pi$
$920$	6.75372e28	−	1.19588e29i	0.155476	−	0.275301i
$921$	5.67172e28			0.129157
$922$	−4.93184e29	−	8.53520e28i	−1.11096	−	0.192267i
$923$		−	7.74489e28i		−	0.172583i
$924$	1.67478e28	−	4.69373e28i	0.0369181	−	0.103466i
$925$	−1.42860e29			−0.311526
$926$	1.00538e29	−	5.80933e29i	0.216880	−	1.25319i
$927$		−	4.62624e28i		−	0.0987259i
$928$	4.32683e29	+	4.99374e29i	0.913462	+	1.05426i
$929$	6.85256e29			1.43118			0.715592	−	0.698518i	$-0.246157\pi$
$929$	6.85256e29			1.43118			0.715592	+	0.698518i	$0.246157\pi$
$930$	−3.29355e29	−	5.69991e28i	−0.680510	−	0.117771i
$931$			9.02036e28i			0.184386i
$932$	3.84560e28	+	1.37216e28i	0.0777687	+	0.0277489i
$933$	−8.35278e28			−0.167115
$934$	−1.65133e29	+	9.54175e29i	−0.326862	+	1.88868i
$935$			1.69453e28i			0.0331844i
$936$	1.37206e28	+	7.74870e27i	0.0265836	+	0.0150131i
$937$	−1.50628e29			−0.288741			−0.144371	−	0.989524i	$-0.546116\pi$
$937$	−1.50628e29			−0.288741			−0.144371	+	0.989524i	$0.546116\pi$
$938$	6.21253e29	+	1.07516e29i	1.17826	+	0.203913i
$939$			5.14676e29i			0.965780i
$940$	1.04047e29	−	2.91602e29i	0.193176	−	0.541392i
$941$	3.69077e29			0.677986			0.338993	−	0.940789i	$-0.389914\pi$
$941$	3.69077e29			0.677986			0.338993	+	0.940789i	$0.389914\pi$
$942$	−4.18667e28	+	2.41916e29i	−0.0760956	+	0.439698i
$943$		−	1.19432e29i		−	0.214785i
$944$	−3.60533e29	+	4.40892e29i	−0.641542	+	0.784534i
$945$	−4.81928e28			−0.0848525
$946$	1.43010e29	+	2.47497e28i	0.249147	+	0.0431181i
$947$		−	8.71665e29i		−	1.50262i	−0.659948	−	0.751311i	$-0.729422\pi$
$947$		−	8.71665e29i		−	1.50262i	0.659948	−	0.751311i	$-0.270578\pi$
$948$	3.93719e29	+	1.40484e29i	0.671588	+	0.239631i
$949$	−5.63434e28			−0.0951001
$950$	−2.54930e28	+	1.47305e29i	−0.0425780	+	0.246026i
$951$		−	4.24795e29i		−	0.702061i
$952$	4.60970e28	−	8.16237e28i	0.0753882	−	0.133489i
$953$	2.74118e29			0.443618			0.221809	−	0.975090i	$-0.428804\pi$
$953$	2.74118e29			0.443618			0.221809	+	0.975090i	$0.428804\pi$
$954$	−2.51036e29	−	4.34451e28i	−0.402024	−	0.0695756i
$955$			2.53871e29i			0.402328i
$956$	5.10151e28	−	1.42974e29i	0.0800056	−	0.224223i
$957$	−1.35429e29			−0.210181
$958$	1.96110e29	−	1.13317e30i	0.301193	−	1.74037i
$959$		−	4.63358e28i		−	0.0704256i
$960$	−1.98780e29	+	1.19859e29i	−0.298993	+	0.180285i
$961$	−1.95677e30			−2.91276
$962$	−3.00877e28	−	5.20706e27i	−0.0443239	−	0.00767082i
$963$		−	3.52089e29i		−	0.513322i
$964$	5.09479e28	+	1.81789e28i	0.0735116	+	0.0262299i
$965$	−5.32085e29			−0.759815
$966$	2.65553e28	−	1.53443e29i	0.0375302	−	0.216858i
$967$		−	1.35076e30i		−	1.88936i	−0.327998	−	0.944678i	$-0.606374\pi$
$967$		−	1.35076e30i		−	1.88936i	0.327998	−	0.944678i	$-0.393626\pi$
$968$	−5.86147e29	−	3.31026e29i	−0.811434	−	0.458257i
$969$	3.48775e28			0.0477867
$970$	−1.48244e29	−	2.56556e28i	−0.201030	−	0.0347908i
$971$		−	7.41402e29i		−	0.995087i	−0.867439	−	0.497544i	$-0.834235\pi$
$971$		−	7.41402e29i		−	0.995087i	0.867439	−	0.497544i	$-0.165765\pi$
$972$	−1.62285e28	+	4.54817e28i	−0.0215583	+	0.0604191i
$973$	3.78143e29			0.497196
$974$	−1.75298e28	+	1.01292e29i	−0.0228133	+	0.131821i
$975$		−	2.60393e28i		−	0.0335416i
$976$	9.20272e29	+	7.52540e29i	1.17332	+	0.959470i
$977$	−4.07488e29			−0.514244			−0.257122	−	0.966379i	$-0.582774\pi$
$977$	−4.07488e29			−0.514244			−0.257122	+	0.966379i	$0.582774\pi$
$978$	−4.77786e29	−	8.26871e28i	−0.596822	−	0.103288i
$979$			2.46392e29i			0.304649i
$980$	2.17988e29	+	7.77811e28i	0.266792	+	0.0951948i
$981$	−1.57721e29			−0.191073
$982$	1.43007e29	−	8.26331e29i	0.171492	−	0.990921i
$983$		−	4.08949e29i		−	0.485438i	−0.970097	−	0.242719i	$-0.921961\pi$
$983$		−	4.08949e29i		−	0.485438i	0.970097	−	0.242719i	$-0.0780393\pi$
$984$	−9.92609e28	+	1.75761e29i	−0.116635	+	0.206524i
$985$	6.84825e29			0.796558
$986$	−2.51011e29	−	4.34407e28i	−0.289017	−	0.0500181i
$987$		−	3.51050e29i		−	0.400127i
$988$	−1.07381e28	+	3.00946e28i	−0.0121160	+	0.0339562i
$989$	4.53512e29			0.506554
$990$	8.11307e27	−	4.68793e28i	0.00897085	−	0.0518357i
$991$		−	6.06373e29i		−	0.663749i	−0.943324	−	0.331874i	$-0.892319\pi$
$991$		−	6.06373e29i		−	0.663749i	0.943324	−	0.331874i	$-0.107681\pi$
$992$	−1.37958e30	+	1.19534e30i	−1.49497	+	1.29532i
$993$	6.15915e29			0.660737
$994$	1.27465e30	+	2.20595e29i	1.35371	+	0.234278i
$995$			9.22620e29i			0.970045i
$996$	5.87933e29	+	2.09782e29i	0.611976	+	0.218361i
$997$	−9.60862e29			−0.990169			−0.495085	−	0.868845i	$-0.664863\pi$
$997$	−9.60862e29			−0.990169			−0.495085	+	0.868845i	$0.664863\pi$
$998$	−7.09018e28	+	4.09688e29i	−0.0723356	+	0.417972i
$999$		−	9.35774e28i		−	0.0945183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.21.d.a.7.1	✓	20
3.2	odd	2		36.21.d.c.19.20		20
4.3	odd	2	inner	12.21.d.a.7.2	yes	20
12.11	even	2		36.21.d.c.19.19		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.21.d.a.7.1	✓	20	1.1	even	1	trivial
12.21.d.a.7.2	yes	20	4.3	odd	2	inner
36.21.d.c.19.19		20	12.11	even	2
36.21.d.c.19.20		20	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1009.00 - 174.621i) q^{2} +34092.0i q^{3} +(987591. + 352385. i) q^{4} +5.90557e6 q^{5} +(5.95317e6 - 3.43988e7i) q^{6} -2.05952e8i q^{7} +(-9.34947e8 - 5.28011e8i) q^{8} -1.16226e9 q^{9} +O(q^{10})\)	\(q+(-1009.00 - 174.621i) q^{2} +34092.0i q^{3} +(987591. + 352385. i) q^{4} +5.90557e6 q^{5} +(5.95317e6 - 3.43988e7i) q^{6} -2.05952e8i q^{7} +(-9.34947e8 - 5.28011e8i) q^{8} -1.16226e9 q^{9} +(-5.95872e9 - 1.03123e9i) q^{10} -6.76899e9i q^{11} +(-1.20135e10 + 3.36689e10i) q^{12} +1.26265e10 q^{13} +(-3.59635e10 + 2.07805e11i) q^{14} +2.01332e11i q^{15} +(8.51161e11 + 6.96025e11i) q^{16} -4.23901e11 q^{17} +(1.17272e12 + 2.02955e11i) q^{18} +2.41340e12i q^{19} +(5.83228e12 + 2.08103e12i) q^{20} +7.02130e12 q^{21} +(-1.18201e12 + 6.82992e12i) q^{22} +2.16590e13i q^{23} +(1.80009e13 - 3.18742e13i) q^{24} -6.04917e13 q^{25} +(-1.27401e13 - 2.20484e12i) q^{26} -3.96238e13i q^{27} +(7.25743e13 - 2.03396e14i) q^{28} -5.86863e14 q^{29} +(3.51568e13 - 2.03145e14i) q^{30} -1.62128e15i q^{31} +(-7.37282e14 - 8.50921e14i) q^{32} +2.30768e14 q^{33} +(4.27716e14 + 7.40219e13i) q^{34} -1.21626e15i q^{35} +(-1.14784e15 - 4.09564e14i) q^{36} +2.36165e15 q^{37} +(4.21430e14 - 2.43512e15i) q^{38} +4.30461e14i q^{39} +(-5.52139e15 - 3.11821e15i) q^{40} -5.51421e15 q^{41} +(-7.08450e15 - 1.22606e15i) q^{42} -2.09388e16i q^{43} +(2.38529e15 - 6.68499e15i) q^{44} -6.86381e15 q^{45} +(3.78211e15 - 2.18540e16i) q^{46} -4.99979e16i q^{47} +(-2.37289e16 + 2.90177e16i) q^{48} +3.73762e16 q^{49} +(6.10362e16 + 1.05631e16i) q^{50} -1.44516e16i q^{51} +(1.24698e16 + 4.44938e15i) q^{52} -2.14062e17 q^{53} +(-6.91914e15 + 3.99804e16i) q^{54} -3.99747e16i q^{55} +(-1.08745e17 + 1.92554e17i) q^{56} -8.22775e16 q^{57} +(5.92145e17 + 1.02478e17i) q^{58} +5.17989e17i q^{59} +(-7.09465e16 + 1.98834e17i) q^{60} +1.08120e18 q^{61} +(-2.83110e17 + 1.63588e18i) q^{62} +2.39370e17i q^{63} +(5.95330e17 + 9.87325e17i) q^{64} +7.45664e16 q^{65} +(-2.32845e17 - 4.02969e16i) q^{66} -2.98959e18i q^{67} +(-4.18641e17 - 1.49376e17i) q^{68} -7.38397e17 q^{69} +(-2.12385e17 + 1.22721e18i) q^{70} -6.13386e18i q^{71} +(1.08665e18 + 6.13687e17i) q^{72} -4.46233e18 q^{73} +(-2.38290e18 - 4.12393e17i) q^{74} -2.06228e18i q^{75} +(-8.50446e17 + 2.38345e18i) q^{76} -1.39408e18 q^{77} +(7.51674e16 - 4.34335e17i) q^{78} -1.16938e19i q^{79} +(5.02659e18 + 4.11042e18i) q^{80} +1.35085e18 q^{81} +(5.56384e18 + 9.62895e17i) q^{82} -1.74622e19i q^{83} +(6.93417e18 + 2.47420e18i) q^{84} -2.50337e18 q^{85} +(-3.65634e18 + 2.11272e19i) q^{86} -2.00073e19i q^{87} +(-3.57410e18 + 6.32865e18i) q^{88} -3.64001e19 q^{89} +(6.92559e18 + 1.19856e18i) q^{90} -2.60044e18i q^{91} +(-7.63231e18 + 2.13902e19i) q^{92} +5.52727e19 q^{93} +(-8.73068e18 + 5.04480e19i) q^{94} +1.42525e19i q^{95} +(2.90096e19 - 2.51354e19i) q^{96} +2.48785e19 q^{97} +(-3.77126e19 - 6.52666e18i) q^{98} +7.86734e18i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 1254 q^{2} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} + 434160000 q^{8} - 23245229340 q^{9}+O(q^{10}) \) 20 * q + 1254 * q^2 - 485524 * q^4 + 1476984 * q^5 - 36019890 * q^6 + 434160000 * q^8 - 23245229340 * q^9	\( 20 q + 1254 q^{2} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} + 434160000 q^{8} - 23245229340 q^{9} + 3166779028 q^{10} + 35789598900 q^{12} - 197410187576 q^{13} + 1179712421976 q^{14} + 1592658749552 q^{16} + 4951946877000 q^{17} - 1457475879618 q^{18} - 20688414141528 q^{20} - 19078957703376 q^{21} + 54807260127768 q^{22} + 58196896476048 q^{24} + 513048947332092 q^{25} - 142319404376100 q^{26} - 10\!\cdots\!28 q^{28}+ \cdots + 30\!\cdots\!50 q^{98}+O(q^{100}) \) 20 * q + 1254 * q^2 - 485524 * q^4 + 1476984 * q^5 - 36019890 * q^6 + 434160000 * q^8 - 23245229340 * q^9 + 3166779028 * q^10 + 35789598900 * q^12 - 197410187576 * q^13 + 1179712421976 * q^14 + 1592658749552 * q^16 + 4951946877000 * q^17 - 1457475879618 * q^18 - 20688414141528 * q^20 - 19078957703376 * q^21 + 54807260127768 * q^22 + 58196896476048 * q^24 + 513048947332092 * q^25 - 142319404376100 * q^26 - 1064314324942128 * q^28 - 1120225678237608 * q^29 + 919562090032260 * q^30 + 926940361437984 * q^32 - 1250504741372400 * q^33 + 1615904447739868 * q^34 + 564305836503708 * q^36 + 13452822768639208 * q^37 + 30625874417040840 * q^38 - 42278345025251456 * q^40 + 26778887480335560 * q^41 + 34752013424992728 * q^42 - 160483087306778736 * q^44 - 1716641590575528 * q^45 + 312713467885194624 * q^46 - 170793646915261968 * q^48 - 198082137742572844 * q^49 + 575620844246091282 * q^50 - 896547684604982408 * q^52 + 241769380233802968 * q^53 + 41864530192578630 * q^54 - 2099928347597457216 * q^56 + 595468774322860464 * q^57 + 1656374273217670084 * q^58 + 94322711748139416 * q^60 + 430703667006221224 * q^61 + 1718273064332222664 * q^62 - 3197273374119743872 * q^64 - 1146808855391494992 * q^65 + 1921733716920631128 * q^66 + 4484111570418829944 * q^68 - 4519043719923504960 * q^69 - 12213680959006457904 * q^70 - 504607438512720000 * q^72 + 12562724768160620200 * q^73 - 22136012572796109780 * q^74 + 28495592855672115888 * q^76 + 19985445258493440192 * q^77 - 20625251537531633940 * q^78 + 49505459663687019552 * q^80 + 27017034353459841780 * q^81 - 50718250504081238180 * q^82 + 24536705912722373616 * q^84 - 15354475681609135696 * q^85 - 85391409389241086952 * q^86 + 66078172926918803520 * q^88 + 43679060294354361384 * q^89 - 3680625238748114076 * q^90 - 64869958570030809216 * q^92 - 50732545022865845424 * q^93 + 95503492747592513424 * q^94 - 89530085825201077920 * q^96 + 7230988441427384872 * q^97 + 304648861287114073350 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more