LMFDB - Embedded newform 12.21.d.a.7.13

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			7.13
Root			$-516.519 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.21.d.a.7.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(578.030 - 845.256i) q^{2} +34092.0i q^{3} +(-380338. - 977166. i) q^{4} -1.01328e7 q^{5} +(2.88164e7 + 1.97062e7i) q^{6} -2.56091e7i q^{7} +(-1.04580e9 - 2.43348e8i) q^{8} -1.16226e9 q^{9} +O(q^{10})$	\(q+(578.030 - 845.256i) q^{2} +34092.0i q^{3} +(-380338. - 977166. i) q^{4} -1.01328e7 q^{5} +(2.88164e7 + 1.97062e7i) q^{6} -2.56091e7i q^{7} +(-1.04580e9 - 2.43348e8i) q^{8} -1.16226e9 q^{9} +(-5.85703e9 + 8.56477e9i) q^{10} -2.46193e9i q^{11} +(3.33135e10 - 1.29665e10i) q^{12} +1.51813e11 q^{13} +(-2.16462e10 - 1.48028e10i) q^{14} -3.45445e11i q^{15} +(-8.10197e11 + 7.43308e11i) q^{16} +1.62872e12 q^{17} +(-6.71822e11 + 9.82408e11i) q^{18} +1.08662e13i q^{19} +(3.85387e12 + 9.90138e12i) q^{20} +8.73064e11 q^{21} +(-2.08096e12 - 1.42307e12i) q^{22} +3.59775e13i q^{23} +(8.29622e12 - 3.56535e13i) q^{24} +7.30521e12 q^{25} +(8.77525e13 - 1.28321e14i) q^{26} -3.96238e13i q^{27} +(-2.50243e13 + 9.74012e12i) q^{28} +5.31243e14 q^{29} +(-2.91990e14 - 1.99678e14i) q^{30} +2.12245e13i q^{31} +(1.59967e14 + 1.11448e15i) q^{32} +8.39319e13 q^{33} +(9.41451e14 - 1.37669e15i) q^{34} +2.59490e14i q^{35} +(4.42053e14 + 1.13572e15i) q^{36} +7.03864e15 q^{37} +(9.18468e15 + 6.28096e15i) q^{38} +5.17560e15i q^{39} +(1.05969e16 + 2.46579e15i) q^{40} -5.52721e15 q^{41} +(5.04657e14 - 7.37962e14i) q^{42} +1.84735e16i q^{43} +(-2.40571e15 + 9.36365e14i) q^{44} +1.17769e16 q^{45} +(3.04102e16 + 2.07961e16i) q^{46} -5.35067e16i q^{47} +(-2.53408e16 - 2.76212e16i) q^{48} +7.91364e16 q^{49} +(4.22263e15 - 6.17477e15i) q^{50} +5.55264e16i q^{51} +(-5.77403e16 - 1.48347e17i) q^{52} -2.55430e17 q^{53} +(-3.34922e16 - 2.29037e16i) q^{54} +2.49461e16i q^{55} +(-6.23193e15 + 2.67820e16i) q^{56} -3.70448e17 q^{57} +(3.07074e17 - 4.49036e17i) q^{58} +4.45225e17i q^{59} +(-3.37558e17 + 1.31386e17i) q^{60} -4.92690e17 q^{61} +(1.79401e16 + 1.22684e16i) q^{62} +2.97645e16i q^{63} +(1.03448e18 + 5.08989e17i) q^{64} -1.53828e18 q^{65} +(4.85151e16 - 7.09439e16i) q^{66} -3.83097e17i q^{67} +(-6.19466e17 - 1.59153e18i) q^{68} -1.22654e18 q^{69} +(2.19336e17 + 1.49993e17i) q^{70} +1.23861e18i q^{71} +(1.21550e18 + 2.82834e17i) q^{72} -3.02562e18 q^{73} +(4.06854e18 - 5.94945e18i) q^{74} +2.49049e17i q^{75} +(1.06180e19 - 4.13282e18i) q^{76} -6.30477e16 q^{77} +(4.37471e18 + 2.99165e18i) q^{78} +1.74087e19i q^{79} +(8.20952e18 - 7.53175e18i) q^{80} +1.35085e18 q^{81} +(-3.19489e18 + 4.67190e18i) q^{82} +1.37283e19i q^{83} +(-3.32060e17 - 8.53129e17i) q^{84} -1.65035e19 q^{85} +(1.56148e19 + 1.06782e19i) q^{86} +1.81111e19i q^{87} +(-5.99106e17 + 2.57469e18i) q^{88} +1.36785e18 q^{89} +(6.80741e18 - 9.95450e18i) q^{90} -3.88779e18i q^{91} +(3.51560e19 - 1.36836e19i) q^{92} -7.23584e17 q^{93} +(-4.52268e19 - 3.09285e19i) q^{94} -1.10104e20i q^{95} +(-3.79947e19 + 5.45359e18i) q^{96} -1.27359e20 q^{97} +(4.57432e19 - 6.68905e19i) q^{98} +2.86140e18i 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 $

$2$	578.030	−	845.256i	0.564482	−	0.825445i
$2$	578.030	−	845.256i	0.564482	−	0.825445i
$3$			34092.0i			0.577350i
$3$			34092.0i			0.577350i
$4$	−380338.	−	977166.i	−0.362719	−	0.931899i
$5$	−1.01328e7			−1.03759			−0.518797	−	0.854898i	$-0.673620\pi$
$5$	−1.01328e7			−1.03759			−0.518797	+	0.854898i	$0.673620\pi$
$6$	2.88164e7	+	1.97062e7i	0.476571	+	0.325904i
$7$		−	2.56091e7i		−	0.0906596i	−0.998972	−	0.0453298i	$-0.985566\pi$
$7$		−	2.56091e7i		−	0.0906596i	0.998972	−	0.0453298i	$-0.0144339\pi$
$8$	−1.04580e9	−	2.43348e8i	−0.973980	−	0.226636i
$9$	−1.16226e9			−0.333333
$10$	−5.85703e9	+	8.56477e9i	−0.585703	+	0.856477i
$11$		−	2.46193e9i		−	0.0949179i	−0.998873	−	0.0474590i	$-0.984888\pi$
$11$		−	2.46193e9i		−	0.0949179i	0.998873	−	0.0474590i	$-0.0151123\pi$
$12$	3.33135e10	−	1.29665e10i	0.538032	−	0.209416i
$13$	1.51813e11			1.10122			0.550612	−	0.834761i	$-0.314394\pi$
$13$	1.51813e11			1.10122			0.550612	+	0.834761i	$0.314394\pi$
$14$	−2.16462e10	−	1.48028e10i	−0.0748345	−	0.0511757i
$15$		−	3.45445e11i		−	0.599055i
$16$	−8.10197e11	+	7.43308e11i	−0.736870	+	0.676035i
$17$	1.62872e12			0.807901			0.403951	−	0.914781i	$-0.367637\pi$
$17$	1.62872e12			0.807901			0.403951	+	0.914781i	$0.367637\pi$
$18$	−6.71822e11	+	9.82408e11i	−0.188161	+	0.275148i
$19$			1.08662e13i			1.77231i	0.463389	+	0.886155i	$0.346633\pi$
$19$			1.08662e13i			1.77231i	−0.463389	+	0.886155i	$0.653367\pi$
$20$	3.85387e12	+	9.90138e12i	0.376355	+	0.966932i
$21$	8.73064e11			0.0523423
$22$	−2.08096e12	−	1.42307e12i	−0.0783495	−	0.0535795i
$23$			3.59775e13i			0.868466i	0.900801	+	0.434233i	$0.142981\pi$
$23$			3.59775e13i			0.868466i	−0.900801	+	0.434233i	$0.857019\pi$
$24$	8.29622e12	−	3.56535e13i	0.130848	−	0.562327i
$25$	7.30521e12			0.0766007
$26$	8.77525e13	−	1.28321e14i	0.621621	−	0.909000i
$27$		−	3.96238e13i		−	0.192450i
$28$	−2.50243e13	+	9.74012e12i	−0.0844855	+	0.0328839i
$29$	5.31243e14			1.26274			0.631369	−	0.775483i	$-0.282494\pi$
$29$	5.31243e14			1.26274			0.631369	+	0.775483i	$0.282494\pi$
$30$	−2.91990e14	−	1.99678e14i	−0.494487	−	0.338156i
$31$			2.12245e13i			0.0258953i	0.999916	+	0.0129476i	$0.00412147\pi$
$31$			2.12245e13i			0.0258953i	−0.999916	+	0.0129476i	$0.995879\pi$
$32$	1.59967e14	+	1.11448e15i	0.142079	+	0.989855i
$33$	8.39319e13			0.0548009
$34$	9.41451e14	−	1.37669e15i	0.456046	−	0.666878i
$35$			2.59490e14i			0.0940678i
$36$	4.42053e14	+	1.13572e15i	0.120906	+	0.310633i
$37$	7.03864e15			1.46376			0.731882	−	0.681431i	$-0.238642\pi$
$37$	7.03864e15			1.46376			0.731882	+	0.681431i	$0.238642\pi$
$38$	9.18468e15	+	6.28096e15i	1.46294	+	1.00044i
$39$			5.17560e15i			0.635792i
$40$	1.05969e16	+	2.46579e15i	1.01060	+	0.235156i
$41$	−5.52721e15			−0.411782			−0.205891	−	0.978575i	$-0.566009\pi$
$41$	−5.52721e15			−0.411782			−0.205891	+	0.978575i	$0.566009\pi$
$42$	5.04657e14	−	7.37962e14i	0.0295463	−	0.0432057i
$43$			1.84735e16i			0.854801i	0.904062	+	0.427401i	$0.140571\pi$
$43$			1.84735e16i			0.854801i	−0.904062	+	0.427401i	$0.859429\pi$
$44$	−2.40571e15	+	9.36365e14i	−0.0884539	+	0.0344285i
$45$	1.17769e16			0.345865
$46$	3.04102e16	+	2.07961e16i	0.716871	+	0.490234i
$47$		−	5.35067e16i		−	1.01725i	−0.860987	−	0.508627i	$-0.830153\pi$
$47$		−	5.35067e16i		−	1.01725i	0.860987	−	0.508627i	$-0.169847\pi$
$48$	−2.53408e16	−	2.76212e16i	−0.390309	−	0.425432i
$49$	7.91364e16			0.991781
$50$	4.22263e15	−	6.17477e15i	0.0432397	−	0.0632296i
$51$			5.55264e16i			0.466442i
$52$	−5.77403e16	−	1.48347e17i	−0.399435	−	1.02623i
$53$	−2.55430e17			−1.46054			−0.730271	−	0.683158i	$-0.760606\pi$
$53$	−2.55430e17			−1.46054			−0.730271	+	0.683158i	$0.760606\pi$
$54$	−3.34922e16	−	2.29037e16i	−0.158857	−	0.108635i
$55$			2.49461e16i			0.0984862i
$56$	−6.23193e15	+	2.67820e16i	−0.0205467	+	0.0883006i
$57$	−3.70448e17			−1.02324
$58$	3.07074e17	−	4.49036e17i	0.712793	−	1.04232i
$59$			4.45225e17i			0.871082i	0.900169	+	0.435541i	$0.143443\pi$
$59$			4.45225e17i			0.871082i	−0.900169	+	0.435541i	$0.856557\pi$
$60$	−3.37558e17	+	1.31386e17i	−0.558258	+	0.217289i
$61$	−4.92690e17			−0.690677			−0.345339	−	0.938478i	$-0.612236\pi$
$61$	−4.92690e17			−0.690677			−0.345339	+	0.938478i	$0.612236\pi$
$62$	1.79401e16	+	1.22684e16i	0.0213751	+	0.0146174i
$63$			2.97645e16i			0.0302199i
$64$	1.03448e18	+	5.08989e17i	0.897272	+	0.441477i
$65$	−1.53828e18			−1.14262
$66$	4.85151e16	−	7.09439e16i	0.0309341	−	0.0452351i
$67$		−	3.83097e17i		−	0.210165i	−0.994463	−	0.105083i	$-0.966489\pi$
$67$		−	3.83097e17i		−	0.210165i	0.994463	−	0.105083i	$-0.0335107\pi$
$68$	−6.19466e17	−	1.59153e18i	−0.293041	−	0.752882i
$69$	−1.22654e18			−0.501409
$70$	2.19336e17	+	1.49993e17i	0.0776478	+	0.0530996i
$71$			1.23861e18i			0.380498i	0.981736	+	0.190249i	$0.0609295\pi$
$71$			1.23861e18i			0.380498i	−0.981736	+	0.190249i	$0.939070\pi$
$72$	1.21550e18	+	2.82834e17i	0.324660	+	0.0755453i
$73$	−3.02562e18			−0.704022			−0.352011	−	0.935996i	$-0.614502\pi$
$73$	−3.02562e18			−0.704022			−0.352011	+	0.935996i	$0.614502\pi$
$74$	4.06854e18	−	5.94945e18i	0.826270	−	1.20826i
$75$			2.49049e17i			0.0442254i
$76$	1.06180e19	−	4.13282e18i	1.65161	−	0.642851i
$77$	−6.30477e16			−0.00860522
$78$	4.37471e18	+	2.99165e18i	0.524811	+	0.358893i
$79$			1.74087e19i			1.83864i	0.393514	+	0.919319i	$0.371259\pi$
$79$			1.74087e19i			1.83864i	−0.393514	+	0.919319i	$0.628741\pi$
$80$	8.20952e18	−	7.53175e18i	0.764571	−	0.701449i
$81$	1.35085e18			0.111111
$82$	−3.19489e18	+	4.67190e18i	−0.232444	+	0.339903i
$83$			1.37283e19i			0.884784i	0.896822	+	0.442392i	$0.145870\pi$
$83$			1.37283e19i			0.884784i	−0.896822	+	0.442392i	$0.854130\pi$
$84$	−3.32060e17	−	8.53129e17i	−0.0189856	−	0.0487777i
$85$	−1.65035e19			−0.838273
$86$	1.56148e19	+	1.06782e19i	0.705591	+	0.482520i
$87$			1.81111e19i			0.729042i
$88$	−5.99106e17	+	2.57469e18i	−0.0215118	+	0.0924481i
$89$	1.36785e18			0.0438669			0.0219335	−	0.999759i	$-0.493018\pi$
$89$	1.36785e18			0.0438669			0.0219335	+	0.999759i	$0.493018\pi$
$90$	6.80741e18	−	9.95450e18i	0.195234	−	0.285492i
$91$		−	3.88779e18i		−	0.0998365i
$92$	3.51560e19	−	1.36836e19i	0.809322	−	0.315009i
$93$	−7.23584e17			−0.0149506
$94$	−4.52268e19	−	3.09285e19i	−0.839687	−	0.574222i
$95$		−	1.10104e20i		−	1.83894i
$96$	−3.79947e19	+	5.45359e18i	−0.571493	+	0.0820296i
$97$	−1.27359e20			−1.72707			−0.863537	−	0.504286i	$-0.831756\pi$
$97$	−1.27359e20			−1.72707			−0.863537	+	0.504286i	$0.831756\pi$
$98$	4.57432e19	−	6.68905e19i	0.559843	−	0.818661i
$99$			2.86140e18i			0.0316393i
$100$	−2.77845e18	−	7.13840e18i	−0.0277845	−	0.0713840i
$101$	−8.08429e19			−0.731861			−0.365930	−	0.930642i	$-0.619249\pi$
$101$	−8.08429e19			−0.731861			−0.365930	+	0.930642i	$0.619249\pi$
$102$	4.69340e19	+	3.20959e19i	0.385022	+	0.263298i
$103$			1.64525e20i			1.22422i	0.790773	+	0.612110i	$0.209679\pi$
$103$			1.64525e20i			1.22422i	−0.790773	+	0.612110i	$0.790321\pi$
$104$	−1.58766e20	−	3.69434e19i	−1.07257	−	0.249577i
$105$	−8.84654e18			−0.0543101
$106$	−1.47646e20	+	2.15904e20i	−0.824450	+	1.20560i
$107$		−	2.52857e20i		−	1.28540i	−0.766120	−	0.642698i	$-0.777815\pi$
$107$		−	2.52857e20i		−	1.28540i	0.766120	−	0.642698i	$-0.222185\pi$
$108$	−3.87190e19	+	1.50704e19i	−0.179344	+	0.0698053i
$109$	3.77940e20			1.59646			0.798229	−	0.602354i	$-0.205771\pi$
$109$	3.77940e20			1.59646			0.798229	+	0.602354i	$0.205771\pi$
$110$	2.10858e19	+	1.44196e19i	0.0812950	+	0.0555937i
$111$			2.39961e20i			0.845105i
$112$	1.90354e19	+	2.07484e19i	0.0612890	+	0.0668043i
$113$	6.13714e20			1.80793			0.903965	−	0.427607i	$-0.140643\pi$
$113$	6.13714e20			1.80793			0.903965	+	0.427607i	$0.140643\pi$
$114$	−2.14130e20	+	3.13124e20i	−0.577603	+	0.844631i
$115$		−	3.64551e20i		−	0.901115i
$116$	−2.02052e20	−	5.19112e20i	−0.458019	−	1.17674i
$117$	−1.76446e20			−0.367075
$118$	3.76329e20	+	2.57353e20i	0.719031	+	0.491711i
$119$		−	4.17101e19i		−	0.0732440i
$120$	−8.40635e19	+	3.61268e20i	−0.135767	+	0.583467i
$121$	6.66689e20			0.990991
$122$	−2.84789e20	+	4.16449e20i	−0.389875	+	0.570116i
$123$		−	1.88433e20i		−	0.237742i
$124$	2.07399e19	−	8.07249e18i	0.0241318	−	0.00939270i
$125$	8.92313e20			0.958113
$126$	2.51586e19	+	1.72047e19i	0.0249448	+	0.0170586i
$127$			3.38653e20i			0.310254i	0.987895	+	0.155127i	$0.0495787\pi$
$127$			3.38653e20i			0.310254i	−0.987895	+	0.155127i	$0.950421\pi$
$128$	1.02819e21	−	5.80193e20i	0.870910	−	0.491443i
$129$	−6.29798e20			−0.493520
$130$	−8.89174e20	+	1.30024e21i	−0.644991	+	0.943172i
$131$		−	2.54836e21i		−	1.71217i	−0.516833	−	0.856087i	$-0.672889\pi$
$131$		−	2.54836e21i		−	1.71217i	0.516833	−	0.856087i	$-0.327111\pi$
$132$	−3.19225e19	−	8.20154e19i	−0.0198773	−	0.0510689i
$133$	2.78272e20			0.160677
$134$	−3.23815e20	−	2.21442e20i	−0.173480	−	0.118635i
$135$			4.01498e20i			0.199685i
$136$	−1.70332e21	−	3.96347e20i	−0.786879	−	0.183099i
$137$	−1.22462e20			−0.0525771			−0.0262886	−	0.999654i	$-0.508369\pi$
$137$	−1.22462e20			−0.0525771			−0.0262886	+	0.999654i	$0.508369\pi$
$138$	−7.08980e20	+	1.03674e21i	−0.283037	+	0.413886i
$139$			1.74896e21i			0.649580i	0.945786	+	0.324790i	$0.105294\pi$
$139$			1.74896e21i			0.649580i	−0.945786	+	0.324790i	$0.894706\pi$
$140$	2.53565e20	−	9.86942e19i	0.0876616	−	0.0341202i
$141$	1.82415e21			0.587312
$142$	1.04695e21	+	7.15956e20i	0.314080	+	0.214785i
$143$		−	3.73752e20i		−	0.104526i
$144$	9.41661e20	−	8.63918e20i	0.245623	−	0.225345i
$145$	−5.38295e21			−1.31021
$146$	−1.74890e21	+	2.55742e21i	−0.397408	+	0.581131i
$147$			2.69792e21i			0.572605i
$148$	−2.67706e21	−	6.87792e21i	−0.530935	−	1.36408i
$149$	−8.10245e21			−1.50229			−0.751145	−	0.660137i	$-0.770498\pi$
$149$	−8.10245e21			−1.50229			−0.751145	+	0.660137i	$0.770498\pi$
$150$	2.10510e20	+	1.43958e20i	0.0365056	+	0.0249645i
$151$			4.34401e21i			0.704890i	0.935833	+	0.352445i	$0.114650\pi$
$151$			4.34401e21i			0.704890i	−0.935833	+	0.352445i	$0.885350\pi$
$152$	2.64426e21	−	1.13638e22i	0.401669	−	1.72619i
$153$	−1.89300e21			−0.269300
$154$	−3.64434e19	+	5.32914e19i	−0.00485749	+	0.00710313i
$155$		−	2.15062e20i		−	0.0268688i
$156$	5.05743e21	−	1.96848e21i	0.592493	−	0.230614i
$157$	−1.27615e21			−0.140251			−0.0701254	−	0.997538i	$-0.522340\pi$
$157$	−1.27615e21			−0.140251			−0.0701254	+	0.997538i	$0.522340\pi$
$158$	1.47148e22	+	1.00628e22i	1.51769	+	1.03788i
$159$		−	8.70812e21i		−	0.843244i
$160$	−1.62091e21	−	1.12927e22i	−0.147421	−	1.02707i
$161$	9.21352e20			0.0787348
$162$	7.80833e20	−	1.14182e21i	0.0627203	−	0.0917161i
$163$			5.33421e21i			0.402897i	0.979499	+	0.201449i	$0.0645649\pi$
$163$			5.33421e21i			0.402897i	−0.979499	+	0.201449i	$0.935435\pi$
$164$	2.10221e21	+	5.40100e21i	0.149361	+	0.383739i
$165$	−8.50461e20			−0.0568610
$166$	1.16040e22	+	7.93540e21i	0.730341	+	0.499445i
$167$			2.50480e22i			1.48460i	0.670069	+	0.742299i	$0.266265\pi$
$167$			2.50480e22i			1.48460i	−0.670069	+	0.742299i	$0.733735\pi$
$168$	−9.13052e20	−	2.12459e20i	−0.0509804	−	0.0118626i
$169$	4.04223e21			0.212694
$170$	−9.53949e21	+	1.39496e22i	−0.473191	+	0.691949i
$171$		−	1.26293e22i		−	0.590770i
$172$	1.80517e22	−	7.02619e21i	0.796588	−	0.310053i
$173$	4.34731e21			0.181034			0.0905169	−	0.995895i	$-0.471148\pi$
$173$	4.34731e21			0.181034			0.0905169	+	0.995895i	$0.471148\pi$
$174$	1.53085e22	+	1.04688e22i	0.601784	+	0.411531i
$175$		−	1.87080e20i		−	0.00694458i
$176$	1.82997e21	+	1.99464e21i	0.0641678	+	0.0699421i
$177$	−1.51786e22			−0.502920
$178$	7.90656e20	−	1.15618e21i	0.0247621	−	0.0362097i
$179$			4.03999e22i			1.19633i	0.801374	+	0.598163i	$0.204103\pi$
$179$			4.03999e22i			1.19633i	−0.801374	+	0.598163i	$0.795897\pi$
$180$	−4.47921e21	−	1.15080e22i	−0.125452	−	0.322311i
$181$	5.66413e22			1.50089			0.750443	−	0.660935i	$-0.229840\pi$
$181$	5.66413e22			1.50089			0.750443	+	0.660935i	$0.229840\pi$
$182$	−3.28618e21	−	2.24726e21i	−0.0824095	−	0.0563559i
$183$		−	1.67968e22i		−	0.398763i
$184$	8.75507e21	−	3.76254e22i	0.196826	−	0.845868i
$185$	−7.13208e22			−1.51879
$186$	−4.18254e20	+	6.11614e20i	−0.00843937	+	0.0123409i
$187$		−	4.00980e21i		−	0.0766843i
$188$	−5.22849e22	+	2.03507e22i	−0.947978	+	0.368977i
$189$	−1.01473e21			−0.0174474
$190$	−9.30660e22	−	6.36434e22i	−1.51794	−	1.03805i
$191$		−	1.19964e23i		−	1.85659i	−0.371841	−	0.928296i	$-0.621273\pi$
$191$		−	1.19964e23i		−	1.85659i	0.371841	−	0.928296i	$-0.378727\pi$
$192$	−1.73524e22	+	3.52676e22i	−0.254887	+	0.518040i
$193$	7.01262e22			0.977929			0.488965	−	0.872304i	$-0.337375\pi$
$193$	7.01262e22			0.977929			0.488965	+	0.872304i	$0.337375\pi$
$194$	−7.36171e22	+	1.07651e23i	−0.974903	+	1.42560i
$195$		−	5.24431e22i		−	0.659694i
$196$	−3.00986e22	−	7.73295e22i	−0.359738	−	0.924239i
$197$	2.34532e22			0.266403			0.133202	−	0.991089i	$-0.457474\pi$
$197$	2.34532e22			0.266403			0.133202	+	0.991089i	$0.457474\pi$
$198$	2.41862e21	+	1.65398e21i	0.0261165	+	0.0178598i
$199$			1.11263e22i			0.114240i	0.998367	+	0.0571200i	$0.0181918\pi$
$199$			1.11263e22i			0.114240i	−0.998367	+	0.0571200i	$0.981808\pi$
$200$	−7.63981e21	−	1.77771e21i	−0.0746075	−	0.0173604i
$201$	1.30605e22			0.121339
$202$	−4.67296e22	+	6.83330e22i	−0.413122	+	0.604111i
$203$		−	1.36046e22i		−	0.114479i
$204$	5.42585e22	−	2.11188e22i	0.434677	−	0.169187i
$205$	5.60058e22			0.427262
$206$	1.39066e23	+	9.51004e22i	1.01053	+	0.691051i
$207$		−	4.18153e22i		−	0.289489i
$208$	−1.22998e23	+	1.12844e23i	−0.811458	+	0.744465i
$209$	2.67517e22			0.168224
$210$	−5.11356e21	+	7.47759e21i	−0.0306571	+	0.0448300i
$211$			2.51058e23i			1.43532i	0.696393	+	0.717660i	$0.254787\pi$
$211$			2.51058e23i			1.43532i	−0.696393	+	0.717660i	$0.745213\pi$
$212$	9.71500e22	+	2.49598e23i	0.529766	+	1.36108i
$213$	−4.22268e22			−0.219681
$214$	−2.13729e23	−	1.46159e23i	−1.06102	−	0.725583i
$215$		−	1.87188e23i		−	0.886936i
$216$	−9.64238e21	+	4.14386e22i	−0.0436161	+	0.187442i
$217$	5.43540e20			0.00234765
$218$	2.18460e23	−	3.19456e23i	0.901172	−	1.31779i
$219$		−	1.03149e23i		−	0.406467i
$220$	2.43765e22	−	9.48795e21i	0.0917792	−	0.0357228i
$221$	2.47262e23			0.889680
$222$	2.02828e23	+	1.38705e23i	0.697588	+	0.477047i
$223$			3.06135e23i			1.00662i	0.864107	+	0.503308i	$0.167884\pi$
$223$			3.06135e23i			1.00662i	−0.864107	+	0.503308i	$0.832116\pi$
$224$	2.85408e22	−	4.09661e21i	0.0897398	−	0.0128809i
$225$	−8.49056e21			−0.0255336
$226$	3.54745e23	−	5.18745e23i	1.02054	−	1.49235i
$227$		−	2.66047e23i		−	0.732317i	−0.930552	−	0.366159i	$-0.880673\pi$
$227$		−	2.66047e23i		−	0.732317i	0.930552	−	0.366159i	$-0.119327\pi$
$228$	1.40896e23	+	3.61990e23i	0.371150	+	0.953559i
$229$	4.77186e23			1.20319			0.601593	−	0.798803i	$-0.294533\pi$
$229$	4.77186e23			1.20319			0.601593	+	0.798803i	$0.294533\pi$
$230$	−3.08139e23	−	2.10722e23i	−0.743821	−	0.508664i
$231$		−	2.14942e21i		−	0.00496822i
$232$	−5.55575e23	−	1.29277e23i	−1.22988	−	0.286181i
$233$	−4.07539e23			−0.864192			−0.432096	−	0.901828i	$-0.642226\pi$
$233$	−4.07539e23			−0.864192			−0.432096	+	0.901828i	$0.642226\pi$
$234$	−1.01991e23	+	1.49142e23i	−0.207207	+	0.303000i
$235$			5.42170e23i			1.05550i
$236$	4.35059e23	−	1.69336e23i	0.811760	−	0.315958i
$237$	−5.93497e23			−1.06154
$238$	−3.52557e22	−	2.41097e22i	−0.0604589	−	0.0413449i
$239$			1.98674e23i			0.326710i	0.986567	+	0.163355i	$0.0522315\pi$
$239$			1.98674e23i			0.326710i	−0.986567	+	0.163355i	$0.947768\pi$
$240$	2.56772e23	+	2.79879e23i	0.404982	+	0.441426i
$241$	−6.70532e23			−1.01449			−0.507247	−	0.861801i	$-0.669337\pi$
$241$	−6.70532e23			−1.01449			−0.507247	+	0.861801i	$0.669337\pi$
$242$	3.85366e23	−	5.63523e23i	0.559397	−	0.818008i
$243$			4.60532e22i			0.0641500i
$244$	1.87389e23	+	4.81440e23i	0.250522	+	0.643641i
$245$	−8.01870e23			−1.02907
$246$	−1.59274e23	−	1.08920e23i	−0.196243	−	0.134201i
$247$			1.64962e24i			1.95171i
$248$	5.16494e21	−	2.21966e22i	0.00586879	−	0.0252215i
$249$	−4.68026e23			−0.510830
$250$	5.15783e23	−	7.54232e23i	0.540838	−	0.790870i
$251$		−	1.63149e24i		−	1.64380i	−0.569634	−	0.821899i	$-0.692915\pi$
$251$		−	1.63149e24i		−	1.64380i	0.569634	−	0.821899i	$-0.307085\pi$
$252$	2.90848e22	−	1.13206e22i	0.0281618	−	0.0109613i
$253$	8.85740e22			0.0824330
$254$	2.86248e23	+	1.95751e23i	0.256098	+	0.175133i
$255$		−	5.62635e23i		−	0.483977i
$256$	1.03912e23	−	1.20445e24i	0.0859542	−	0.996299i
$257$	−9.04162e23			−0.719308			−0.359654	−	0.933086i	$-0.617105\pi$
$257$	−9.04162e23			−0.719308			−0.359654	+	0.933086i	$0.617105\pi$
$258$	−3.64042e23	+	5.32341e23i	−0.278583	+	0.407373i
$259$		−	1.80253e23i		−	0.132704i
$260$	5.85068e23	+	1.50316e24i	0.414451	+	1.06481i
$261$	−6.17443e23			−0.420912
$262$	−2.15402e24	−	1.47303e24i	−1.41330	−	0.966492i
$263$		−	2.92372e23i		−	0.184662i	−0.995728	−	0.0923311i	$-0.970568\pi$
$263$		−	2.92372e23i		−	0.184662i	0.995728	−	0.0923311i	$-0.0294318\pi$
$264$	−8.77762e22	−	2.04247e22i	−0.0533749	−	0.0124198i
$265$	2.58821e24			1.51545
$266$	1.60850e23	−	2.35211e23i	0.0906993	−	0.132630i
$267$			4.66325e22i			0.0253266i
$268$	−3.74350e23	+	1.45707e23i	−0.195853	+	0.0762310i
$269$	−4.63383e22			−0.0233570			−0.0116785	−	0.999932i	$-0.503717\pi$
$269$	−4.63383e22			−0.0233570			−0.0116785	+	0.999932i	$0.503717\pi$
$270$	3.39368e23	+	2.32078e23i	0.164829	+	0.112719i
$271$			2.94243e23i			0.137725i	0.997626	+	0.0688626i	$0.0219370\pi$
$271$			2.94243e23i			0.137725i	−0.997626	+	0.0688626i	$0.978063\pi$
$272$	−1.31959e24	+	1.21064e24i	−0.595318	+	0.546169i
$273$	1.32542e23			0.0576406
$274$	−7.07869e22	+	1.03512e23i	−0.0296789	+	0.0433995i
$275$		−	1.79849e22i		−	0.00727077i
$276$	4.66502e23	+	1.19854e24i	0.181871	+	0.467263i
$277$	2.58310e24			0.971278			0.485639	−	0.874159i	$-0.338587\pi$
$277$	2.58310e24			0.971278			0.485639	+	0.874159i	$0.338587\pi$
$278$	1.47832e24	+	1.01095e24i	0.536193	+	0.366677i
$279$		−	2.46684e22i		−	0.00863175i
$280$	6.31466e22	−	2.71376e23i	0.0213191	−	0.0916201i
$281$	3.74668e24			1.22063			0.610314	−	0.792160i	$-0.291043\pi$
$281$	3.74668e24			1.22063			0.610314	+	0.792160i	$0.291043\pi$
$282$	1.05441e24	−	1.54187e24i	0.331527	−	0.484794i
$283$			2.70526e24i			0.821002i	0.911860	+	0.410501i	$0.134646\pi$
$283$			2.70526e24i			0.821002i	−0.911860	+	0.410501i	$0.865354\pi$
$284$	1.21033e24	−	4.71093e23i	0.354586	−	0.138014i
$285$	3.75366e24			1.06171
$286$	−3.15916e23	−	2.16040e23i	−0.0862803	−	0.0590030i
$287$			1.41547e23i			0.0373320i
$288$	−1.85924e23	−	1.29531e24i	−0.0473598	−	0.329952i
$289$	−1.41149e24			−0.347296
$290$	−3.11151e24	+	4.54997e24i	−0.739589	+	1.08150i
$291$		−	4.34190e24i		−	0.997127i
$292$	1.15076e24	+	2.95654e24i	0.255362	+	0.656077i
$293$	−6.16073e23			−0.132116			−0.0660581	−	0.997816i	$-0.521042\pi$
$293$	−6.16073e23			−0.132116			−0.0660581	+	0.997816i	$0.521042\pi$
$294$	2.28043e24	+	1.55948e24i	0.472654	+	0.323225i
$295$		−	4.51135e24i		−	0.903830i
$296$	−7.36102e24	−	1.71284e24i	−1.42568	−	0.331741i
$297$	−9.75508e22			−0.0182670
$298$	−4.68346e24	+	6.84865e24i	−0.848017	+	1.24006i
$299$			5.46186e24i			0.956376i
$300$	2.43362e23	−	9.47229e22i	0.0412136	−	0.0160414i
$301$	4.73090e23			0.0774959
$302$	3.67180e24	+	2.51097e24i	0.581848	+	0.397898i
$303$		−	2.75609e24i		−	0.422540i
$304$	−8.07690e24	−	8.80372e24i	−1.19814	−	1.30596i
$305$	4.99230e24			0.716642
$306$	−1.09421e24	+	1.60007e24i	−0.152015	+	0.222293i
$307$		−	1.09809e25i		−	1.47657i	−0.674488	−	0.738286i	$-0.735635\pi$
$307$		−	1.09809e25i		−	1.47657i	0.674488	−	0.738286i	$-0.264365\pi$
$308$	2.39795e22	+	6.16081e22i	0.00312128	+	0.00801919i
$309$	−5.60898e24			−0.706804
$310$	−1.81783e23	−	1.24313e23i	−0.0221787	−	0.0151669i
$311$		−	1.81546e24i		−	0.214478i	−0.994233	−	0.107239i	$-0.965799\pi$
$311$		−	1.81546e24i		−	0.214478i	0.994233	−	0.107239i	$-0.0342010\pi$
$312$	1.25947e24	−	5.41266e24i	0.144093	−	0.619248i
$313$	−9.07798e24			−1.00588			−0.502940	−	0.864321i	$-0.667748\pi$
$313$	−9.07798e24			−1.00588			−0.502940	+	0.864321i	$0.667748\pi$
$314$	−7.37653e23	+	1.07867e24i	−0.0791691	+	0.115769i
$315$		−	3.01596e23i		−	0.0313559i
$316$	1.70112e25	−	6.62121e24i	1.71342	−	0.666909i
$317$	−1.57293e25			−1.53503			−0.767513	−	0.641034i	$-0.778506\pi$
$317$	−1.57293e25			−1.53503			−0.767513	+	0.641034i	$0.778506\pi$
$318$	−7.36059e24	−	5.03356e24i	−0.696051	−	0.475996i
$319$		−	1.30788e24i		−	0.119856i
$320$	−1.04822e25	−	5.15745e24i	−0.931004	−	0.458074i
$321$	8.62038e24			0.742123
$322$	5.32569e23	−	7.78778e23i	0.0444444	−	0.0649912i
$323$			1.76980e25i			1.43185i
$324$	−5.13781e23	−	1.32001e24i	−0.0403021	−	0.103544i
$325$	1.10903e24			0.0843545
$326$	4.50877e24	+	3.08334e24i	0.332570	+	0.227428i
$327$			1.28847e25i			0.921715i
$328$	5.78037e24	+	1.34504e24i	0.401067	+	0.0933245i
$329$	−1.37026e24			−0.0922238
$330$	−4.91592e23	+	7.18857e23i	−0.0320971	+	0.0469357i
$331$			9.85446e24i			0.624242i	0.950042	+	0.312121i	$0.101039\pi$
$331$			9.85446e24i			0.624242i	−0.950042	+	0.312121i	$0.898961\pi$
$332$	1.34149e25	−	5.22142e24i	0.824529	−	0.320928i
$333$	−8.18074e24			−0.487922
$334$	2.11720e25	+	1.44785e25i	1.22545	+	0.838029i
$335$			3.88183e24i			0.218066i
$336$	−7.07354e23	+	6.48955e23i	−0.0385695	+	0.0353852i
$337$	9.48792e23			0.0502195			0.0251097	−	0.999685i	$-0.492006\pi$
$337$	9.48792e23			0.0502195			0.0251097	+	0.999685i	$0.492006\pi$
$338$	2.33653e24	−	3.41672e24i	0.120062	−	0.175567i
$339$			2.09227e25i			1.04381i
$340$	6.27690e24	+	1.61266e25i	0.304058	+	0.781186i
$341$	5.22531e22			0.00245792
$342$	−1.06750e25	−	7.30012e24i	−0.487648	−	0.333479i
$343$		−	4.07002e24i		−	0.180574i
$344$	4.49550e24	−	1.93197e25i	0.193729	−	0.832559i
$345$	1.24283e25			0.520259
$346$	2.51288e24	−	3.67459e24i	0.102190	−	0.149434i
$347$		−	3.11615e25i		−	1.23119i	−0.788065	−	0.615593i	$-0.788917\pi$
$347$		−	3.11615e25i		−	1.23119i	0.788065	−	0.615593i	$-0.211083\pi$
$348$	1.76976e25	−	6.88835e24i	0.679393	−	0.264437i
$349$	−2.05021e24			−0.0764795			−0.0382397	−	0.999269i	$-0.512175\pi$
$349$	−2.05021e24			−0.0764795			−0.0382397	+	0.999269i	$0.512175\pi$
$350$	−1.58130e23	−	1.08138e23i	−0.00573237	−	0.00392010i
$351$		−	6.01540e24i		−	0.211931i
$352$	2.74376e24	−	3.93827e23i	0.0939550	−	0.0134859i
$353$	1.06138e25			0.353284			0.176642	−	0.984275i	$-0.443477\pi$
$353$	1.06138e25			0.353284			0.176642	+	0.984275i	$0.443477\pi$
$354$	−8.77368e24	+	1.28298e25i	−0.283889	+	0.415133i
$355$		−	1.25506e25i		−	0.394802i
$356$	−5.20244e23	−	1.33661e24i	−0.0159114	−	0.0408795i
$357$	1.42198e24			0.0422874
$358$	3.41482e25	+	2.33523e25i	0.987502	+	0.675305i
$359$			1.57428e25i			0.442727i	0.975191	+	0.221364i	$0.0710507\pi$
$359$			1.57428e25i			0.442727i	−0.975191	+	0.221364i	$0.928949\pi$
$360$	−1.23163e25	−	2.86589e24i	−0.336865	−	0.0783853i
$361$	−8.04833e25			−2.14108
$362$	3.27404e25	−	4.78764e25i	0.847224	−	1.23890i
$363$			2.27287e25i			0.572149i
$364$	−3.79902e24	+	1.47868e24i	−0.0930374	+	0.0362126i
$365$	3.06579e25			0.730489
$366$	−1.41976e25	−	9.70903e24i	−0.329157	−	0.225095i
$367$		−	2.91434e25i		−	0.657475i	−0.944421	−	0.328738i	$-0.893377\pi$
$367$		−	2.91434e25i		−	0.657475i	0.944421	−	0.328738i	$-0.106623\pi$
$368$	−2.67424e25	−	2.91489e25i	−0.587113	−	0.639947i
$369$	6.42406e24			0.137261
$370$	−4.12255e25	+	6.02843e25i	−0.857332	+	1.25368i
$371$			6.54134e24i			0.132412i
$372$	2.75207e23	+	7.07062e23i	0.00542288	+	0.0139325i
$373$	−1.86058e25			−0.356911			−0.178455	−	0.983948i	$-0.557110\pi$
$373$	−1.86058e25			−0.356911			−0.178455	+	0.983948i	$0.557110\pi$
$374$	−3.38930e24	−	2.31778e24i	−0.0632987	−	0.0432869i
$375$			3.04207e25i			0.553167i
$376$	−1.30208e25	+	5.59574e25i	−0.230546	+	0.990785i
$377$	8.06495e25			1.39056
$378$	−5.86543e23	+	8.57705e23i	−0.00984878	+	0.0144019i
$379$		−	1.00245e26i		−	1.63934i	−0.572834	−	0.819672i	$-0.694156\pi$
$379$		−	1.00245e26i		−	1.63934i	0.572834	−	0.819672i	$-0.305844\pi$
$380$	−1.07590e26	+	4.18768e25i	−1.71370	+	0.667018i
$381$	−1.15453e25			−0.179125
$382$	−1.01400e26	−	6.93427e25i	−1.53252	−	1.04801i
$383$			4.60469e25i			0.677973i	0.940791	+	0.338987i	$0.110084\pi$
$383$			4.60469e25i			0.677973i	−0.940791	+	0.338987i	$0.889916\pi$
$384$	1.97799e25	+	3.50530e25i	0.283735	+	0.502820i
$385$	6.38846e23			0.00892872
$386$	4.05351e25	−	5.92746e25i	0.552024	−	0.807227i
$387$		−	2.14711e25i		−	0.284934i
$388$	4.84394e25	+	1.24451e26i	0.626443	+	1.60946i
$389$	3.95295e25			0.498225			0.249112	−	0.968475i	$-0.419861\pi$
$389$	3.95295e25			0.498225			0.249112	+	0.968475i	$0.419861\pi$
$390$	−4.43278e25	−	3.03137e25i	−0.544541	−	0.372385i
$391$			5.85975e25i			0.701635i
$392$	−8.27611e25	−	1.92577e25i	−0.965974	−	0.224773i
$393$	8.68785e25			0.988524
$394$	1.35566e25	−	1.98239e25i	0.150380	−	0.219901i
$395$		−	1.76398e26i		−	1.90776i
$396$	2.79607e24	−	1.08830e24i	0.0294846	−	0.0114762i
$397$	5.81871e25			0.598304			0.299152	−	0.954205i	$-0.403296\pi$
$397$	5.81871e25			0.598304			0.299152	+	0.954205i	$0.403296\pi$
$398$	9.40453e24	+	6.43131e24i	0.0942988	+	0.0644865i
$399$			9.48684e24i			0.0927668i
$400$	−5.91866e24	+	5.43002e24i	−0.0564447	+	0.0517847i
$401$	−1.11039e26			−1.03283			−0.516417	−	0.856337i	$-0.672734\pi$
$401$	−1.11039e26			−1.03283			−0.516417	+	0.856337i	$0.672734\pi$
$402$	7.54938e24	−	1.10395e25i	0.0684938	−	0.100159i
$403$			3.22215e24i			0.0285165i
$404$	3.07477e25	+	7.89970e25i	0.265460	+	0.682020i
$405$	−1.36878e25			−0.115288
$406$	−1.14994e25	−	7.86389e24i	−0.0944963	−	0.0646215i
$407$		−	1.73286e25i		−	0.138937i
$408$	1.35123e25	−	5.80696e25i	0.105712	−	0.454305i
$409$	2.22027e25			0.169501			0.0847507	−	0.996402i	$-0.472991\pi$
$409$	2.22027e25			0.169501			0.0847507	+	0.996402i	$0.472991\pi$
$410$	3.23731e25	−	4.73392e25i	0.241182	−	0.352682i
$411$		−	4.17498e24i		−	0.0303554i
$412$	1.60768e26	−	6.25752e25i	1.14085	−	0.444048i
$413$	1.14018e25			0.0789720
$414$	−3.53446e25	−	2.41705e25i	−0.238957	−	0.163411i
$415$		−	1.39106e26i		−	0.918046i
$416$	2.42851e25	+	1.69192e26i	0.156461	+	1.09005i
$417$	−5.96256e25			−0.375035
$418$	1.54633e25	−	2.26120e25i	0.0949595	−	0.138860i
$419$			3.29517e26i			1.97577i	0.155173	+	0.987887i	$0.450406\pi$
$419$			3.29517e26i			1.97577i	−0.155173	+	0.987887i	$0.549594\pi$
$420$	3.36468e24	+	8.64454e24i	0.0196993	+	0.0506115i
$421$	2.74871e26			1.57148			0.785738	−	0.618559i	$-0.212283\pi$
$421$	2.74871e26			1.57148			0.785738	+	0.618559i	$0.212283\pi$
$422$	2.12208e26	+	1.45119e26i	1.18478	+	0.810213i
$423$			6.21888e25i			0.339085i
$424$	2.67130e26	+	6.21585e25i	1.42254	+	0.331011i
$425$	1.18982e25			0.0618858
$426$	−2.44083e25	+	3.56924e25i	−0.124006	+	0.181334i
$427$			1.26173e25i			0.0626165i
$428$	−2.47083e26	+	9.61711e25i	−1.19786	+	0.466237i
$429$	1.27420e25			0.0603480
$430$	−1.58221e26	−	1.08200e26i	−0.732117	−	0.500660i
$431$			1.50714e26i			0.681365i	0.940178	+	0.340683i	$0.110658\pi$
$431$			1.50714e26i			0.681365i	−0.940178	+	0.340683i	$0.889342\pi$
$432$	2.94527e25	+	3.21031e25i	0.130103	+	0.141811i
$433$	−2.12497e26			−0.917219			−0.458610	−	0.888638i	$-0.651652\pi$
$433$	−2.12497e26			−0.917219			−0.458610	+	0.888638i	$0.651652\pi$
$434$	3.14182e23	−	4.59430e23i	0.00132521	−	0.00193786i
$435$		−	1.83515e26i		−	0.756449i
$436$	−1.43745e26	−	3.69310e26i	−0.579065	−	1.48774i
$437$	−3.90937e26			−1.53919
$438$	−8.71876e25	−	5.96234e25i	−0.335516	−	0.229444i
$439$			3.80266e26i			1.43035i	0.698945	+	0.715175i	$0.253653\pi$
$439$			3.80266e26i			1.43035i	−0.698945	+	0.715175i	$0.746347\pi$
$440$	6.07059e24	−	2.60887e25i	0.0223205	−	0.0959236i
$441$	−9.19772e25			−0.330594
$442$	1.42925e26	−	2.08999e26i	0.502209	−	0.734382i
$443$		−	2.13036e25i		−	0.0731840i	−0.999330	−	0.0365920i	$-0.988350\pi$
$443$		−	2.13036e25i		−	0.0731840i	0.999330	−	0.0365920i	$-0.0116502\pi$
$444$	2.34482e26	−	9.12664e25i	0.787552	−	0.306536i
$445$	−1.38600e25			−0.0455160
$446$	2.58762e26	+	1.76955e26i	0.830906	+	0.568217i
$447$		−	2.76228e26i		−	0.867348i
$448$	1.30347e25	−	2.64922e25i	0.0400241	−	0.0813463i
$449$	−7.48905e24			−0.0224886			−0.0112443	−	0.999937i	$-0.503579\pi$
$449$	−7.48905e24			−0.0224886			−0.0112443	+	0.999937i	$0.503579\pi$
$450$	−4.90780e24	+	7.17670e24i	−0.0144132	+	0.0210765i
$451$			1.36076e25i			0.0390855i
$452$	−2.33419e26	−	5.99700e26i	−0.655770	−	1.68481i
$453$	−1.48096e26			−0.406968
$454$	−2.24878e26	−	1.53783e26i	−0.604488	−	0.413380i
$455$			3.93940e25i			0.103590i
$456$	3.87416e26	+	9.01480e25i	0.996619	+	0.231904i
$457$	−4.11472e26			−1.03557			−0.517783	−	0.855512i	$-0.673243\pi$
$457$	−4.11472e26			−1.03557			−0.517783	+	0.855512i	$0.673243\pi$
$458$	2.75828e26	−	4.03344e26i	0.679178	−	0.993164i
$459$		−	6.45362e25i		−	0.155481i
$460$	−3.56227e26	+	1.38653e26i	−0.839748	+	0.326852i
$461$	−3.61232e26			−0.833252			−0.416626	−	0.909078i	$-0.636788\pi$
$461$	−3.61232e26			−0.833252			−0.416626	+	0.909078i	$0.636788\pi$
$462$	−1.81681e24	−	1.24243e24i	−0.00410100	−	0.00280448i
$463$			2.53075e26i			0.559035i	0.960141	+	0.279518i	$0.0901745\pi$
$463$			2.53075e26i			0.559035i	−0.960141	+	0.279518i	$0.909825\pi$
$464$	−4.30411e26	+	3.94877e26i	−0.930473	+	0.853654i
$465$	7.33190e24			0.0155127
$466$	−2.35570e26	+	3.44475e26i	−0.487821	+	0.713343i
$467$		−	2.90318e26i		−	0.588445i	−0.955737	−	0.294222i	$-0.904939\pi$
$467$		−	2.90318e26i		−	0.588445i	0.955737	−	0.294222i	$-0.0950606\pi$
$468$	6.71094e25	+	1.72418e26i	0.133145	+	0.342076i
$469$	−9.81077e24			−0.0190535
$470$	4.58272e26	+	3.13391e26i	0.871254	+	0.595809i
$471$		−	4.35064e25i		−	0.0809738i
$472$	1.08345e26	−	4.65617e26i	0.197418	−	0.848417i
$473$	4.54804e25			0.0811359
$474$	−3.43059e26	+	5.01657e26i	−0.599219	+	0.876241i
$475$			7.93795e25i			0.135760i
$476$	−4.07577e25	+	1.58640e25i	−0.0682560	+	0.0265670i
$477$	2.96877e26			0.486847
$478$	1.67930e26	+	1.14840e26i	0.269681	+	0.184422i
$479$		−	2.15557e26i		−	0.339006i	−0.985530	−	0.169503i	$-0.945784\pi$
$479$		−	2.15557e26i		−	0.339006i	0.985530	−	0.169503i	$-0.0542162\pi$
$480$	3.84991e26	−	5.52599e25i	0.592978	−	0.0851134i
$481$	1.06856e27			1.61193
$482$	−3.87588e26	+	5.66771e26i	−0.572664	+	0.837408i
$483$			3.14107e25i			0.0454575i
$484$	−2.53567e26	−	6.51466e26i	−0.359451	−	0.923503i
$485$	1.29049e27			1.79200
$486$	3.89267e25	+	2.66201e25i	0.0529523	+	0.0362116i
$487$			5.71583e26i			0.761710i	0.924635	+	0.380855i	$0.124370\pi$
$487$			5.71583e26i			0.761710i	−0.924635	+	0.380855i	$0.875630\pi$
$488$	5.15256e26	+	1.19895e26i	0.672705	+	0.156532i
$489$	−1.81854e26			−0.232613
$490$	−4.63505e26	+	6.77785e26i	−0.580889	+	0.849437i
$491$		−	1.46370e27i		−	1.79737i	−0.438592	−	0.898686i	$-0.644523\pi$
$491$		−	1.46370e27i		−	1.79737i	0.438592	−	0.898686i	$-0.355477\pi$
$492$	−1.84131e26	+	7.16685e25i	−0.221552	+	0.0862337i
$493$	8.65248e26			1.02017
$494$	1.39435e27	+	9.53532e26i	1.61103	+	1.10171i
$495$		−	2.89939e25i		−	0.0328287i
$496$	−1.57763e25	−	1.71960e25i	−0.0175061	−	0.0190814i
$497$	3.17198e25			0.0344958
$498$	−2.70533e26	+	3.95602e26i	−0.288355	+	0.421662i
$499$			1.20854e27i			1.26257i	0.775553	+	0.631283i	$0.217471\pi$
$499$			1.20854e27i			1.26257i	−0.775553	+	0.631283i	$0.782529\pi$
$500$	−3.39381e26	−	8.71938e26i	−0.347526	−	0.892864i
$501$	−8.53936e26			−0.857133
$502$	−1.37903e27	−	9.43053e26i	−1.35686	−	0.927895i
$503$			2.76949e25i			0.0267129i	0.999911	+	0.0133564i	$0.00425161\pi$
$503$			2.76949e25i			0.0267129i	−0.999911	+	0.0133564i	$0.995748\pi$
$504$	7.24313e24	−	3.11277e25i	0.00684890	−	0.0294335i
$505$	8.19161e26			0.759374
$506$	5.11984e25	−	7.48677e25i	0.0465320	−	0.0680439i
$507$			1.37808e26i			0.122799i
$508$	3.30920e26	−	1.28803e26i	0.289125	−	0.112535i
$509$	−7.69101e26			−0.658879			−0.329440	−	0.944177i	$-0.606860\pi$
$509$	−7.69101e26			−0.658879			−0.329440	+	0.944177i	$0.606860\pi$
$510$	−4.75571e26	−	3.25220e26i	−0.399497	−	0.273197i
$511$			7.74834e25i			0.0638263i
$512$	−9.58005e26	−	7.84042e26i	−0.773870	−	0.633344i
$513$	4.30558e26			0.341081
$514$	−5.22633e26	+	7.64248e26i	−0.406037	+	0.593749i
$515$		−	1.66709e27i		−	1.27024i
$516$	2.39537e26	+	6.15418e26i	0.179009	+	0.459910i
$517$	−1.31730e26			−0.0965556
$518$	−1.52360e26	−	1.04192e26i	−0.109540	−	0.0749092i
$519$			1.48208e26i			0.104520i
$520$	1.60874e27	+	3.74339e26i	1.11289	+	0.258959i
$521$	8.80621e26			0.597602			0.298801	−	0.954315i	$-0.403413\pi$
$521$	8.80621e26			0.597602			0.298801	+	0.954315i	$0.403413\pi$
$522$	−3.56901e26	+	5.21897e26i	−0.237598	+	0.347440i
$523$		−	2.11853e27i		−	1.38362i	−0.722078	−	0.691812i	$-0.756813\pi$
$523$		−	2.11853e27i		−	1.38362i	0.722078	−	0.691812i	$-0.243187\pi$
$524$	−2.49017e27	+	9.69239e26i	−1.59557	+	0.621038i
$525$	6.37791e24			0.00400946
$526$	−2.47129e26	−	1.69000e26i	−0.152429	−	0.104239i
$527$			3.45688e25i			0.0209208i
$528$	−6.80013e25	+	6.23872e25i	−0.0403811	+	0.0370473i
$529$	4.21773e26			0.245766
$530$	1.49606e27	−	2.18770e27i	0.855444	−	1.25092i
$531$		−	5.17468e26i		−	0.290361i
$532$	−1.05838e26	−	2.71918e26i	−0.0582806	−	0.149735i
$533$	−8.39102e26			−0.453464
$534$	3.94164e25	+	2.69550e25i	0.0209057	+	0.0142964i
$535$			2.56213e27i			1.33372i
$536$	−9.32261e25	+	4.00644e26i	−0.0476310	+	0.204697i
$537$	−1.37731e27			−0.690699
$538$	−2.67849e25	+	3.91677e25i	−0.0131846	+	0.0192799i
$539$		−	1.94828e26i		−	0.0941378i
$540$	3.92330e26	−	1.52705e26i	0.186086	−	0.0724295i
$541$	−3.29798e27			−1.53559			−0.767795	−	0.640696i	$-0.778646\pi$
$541$	−3.29798e27			−1.53559			−0.767795	+	0.640696i	$0.778646\pi$
$542$	2.48711e26	+	1.70081e26i	0.113685	+	0.0777434i
$543$			1.93101e27i			0.866537i
$544$	2.60542e26	+	1.81518e27i	0.114786	+	0.799705i
$545$	−3.82957e27			−1.65647
$546$	7.66135e25	−	1.12032e26i	0.0325371	−	0.0475792i
$547$		−	3.05027e27i		−	1.27194i	−0.771715	−	0.635968i	$-0.780601\pi$
$547$		−	3.05027e27i		−	1.27194i	0.771715	−	0.635968i	$-0.219399\pi$
$548$	4.65771e25	+	1.19666e26i	0.0190707	+	0.0489966i
$549$	5.72634e26			0.230226
$550$	−1.52018e25	−	1.03958e25i	−0.00600162	−	0.00410422i
$551$			5.77256e27i			2.23796i
$552$	1.28272e27	+	2.98478e26i	0.488362	+	0.113637i
$553$	4.45821e26			0.166690
$554$	1.49311e27	−	2.18338e27i	0.548269	−	0.801737i
$555$		−	2.43146e27i		−	0.876876i
$556$	1.70903e27	−	6.65198e26i	0.605343	−	0.235615i
$557$	3.64606e27			1.26845			0.634224	−	0.773150i	$-0.281320\pi$
$557$	3.64606e27			1.26845			0.634224	+	0.773150i	$0.281320\pi$
$558$	−2.08511e25	−	1.42591e25i	−0.00712504	−	0.00487247i
$559$			2.80452e27i			0.941327i
$560$	−1.92881e26	−	2.10238e26i	−0.0635931	−	0.0693157i
$561$	1.36702e26			0.0442737
$562$	2.16569e27	−	3.16690e27i	0.689023	−	1.00756i
$563$			2.16235e27i			0.675837i	0.941175	+	0.337919i	$0.109723\pi$
$563$			2.16235e27i			0.675837i	−0.941175	+	0.337919i	$0.890277\pi$
$564$	−6.93794e26	−	1.78250e27i	−0.213029	−	0.547315i
$565$	−6.21861e27			−1.87590
$566$	2.28664e27	+	1.56372e27i	0.677692	+	0.463441i
$567$		−	3.45941e25i		−	0.0100733i
$568$	3.01415e26	−	1.29535e27i	0.0862345	−	0.370597i
$569$	1.82053e27			0.511771			0.255886	−	0.966707i	$-0.417633\pi$
$569$	1.82053e27			0.511771			0.255886	+	0.966707i	$0.417633\pi$
$570$	2.16973e27	−	3.17280e27i	0.599317	−	0.876384i
$571$		−	5.66873e27i		−	1.53860i	−0.638889	−	0.769299i	$-0.720606\pi$
$571$		−	5.66873e27i		−	1.53860i	0.638889	−	0.769299i	$-0.279394\pi$
$572$	−3.65218e26	+	1.42152e26i	−0.0974075	+	0.0379135i
$573$	4.08980e27			1.07190
$574$	1.19643e26	+	8.18183e25i	0.0308155	+	0.0210732i
$575$			2.62823e26i			0.0665251i
$576$	−1.20234e27	−	5.91578e26i	−0.299091	−	0.147159i
$577$	2.07948e27			0.508389			0.254195	−	0.967153i	$-0.418190\pi$
$577$	2.07948e27			0.508389			0.254195	+	0.967153i	$0.418190\pi$
$578$	−8.15883e26	+	1.19307e27i	−0.196042	+	0.286673i
$579$			2.39074e27i			0.564608i
$580$	2.04734e27	+	5.26004e27i	0.475237	+	1.22098i
$581$	3.51570e26			0.0802141
$582$	−3.67002e27	−	2.50975e27i	−0.823073	−	0.562860i
$583$			6.28851e26i			0.138632i
$584$	3.16420e27	+	7.36280e26i	0.685703	+	0.159557i
$585$	1.78789e27			0.380874
$586$	−3.56109e26	+	5.20739e26i	−0.0745773	+	0.109055i
$587$			1.17098e27i			0.241084i	0.992708	+	0.120542i	$0.0384632\pi$
$587$			1.17098e27i			0.241084i	−0.992708	+	0.120542i	$0.961537\pi$
$588$	2.63631e27	−	1.02612e27i	0.533610	−	0.207695i
$589$	−2.30629e26			−0.0458944
$590$	−3.81325e27	−	2.60770e27i	−0.746062	−	0.510196i
$591$			7.99564e26i			0.153808i
$592$	−5.70268e27	+	5.23188e27i	−1.07860	+	0.989556i
$593$	−1.61780e27			−0.300870			−0.150435	−	0.988620i	$-0.548067\pi$
$593$	−1.61780e27			−0.300870			−0.150435	+	0.988620i	$0.548067\pi$
$594$	−5.63873e25	+	8.24554e25i	−0.0103114	+	0.0150784i
$595$			4.22638e26i			0.0759975i
$596$	3.08167e27	+	7.91745e27i	0.544909	+	1.39998i
$597$	−3.79316e26			−0.0659565
$598$	4.61667e27	+	3.15712e27i	0.789436	+	0.539857i
$599$			6.46607e27i			1.08736i	0.839294	+	0.543678i	$0.182969\pi$
$599$			6.46607e27i			1.08736i	−0.839294	+	0.543678i	$0.817031\pi$
$600$	6.06056e25	−	2.60456e26i	0.0100231	−	0.0430746i
$601$	9.99431e25			0.0162558			0.00812790	−	0.999967i	$-0.497413\pi$
$601$	9.99431e25			0.0162558			0.00812790	+	0.999967i	$0.497413\pi$
$602$	2.73460e26	−	3.99882e26i	0.0437451	−	0.0639686i
$603$			4.45259e26i			0.0700551i
$604$	4.24482e27	−	1.65219e27i	0.656886	−	0.255677i
$605$	−6.75539e27			−1.02825
$606$	−2.32960e27	−	1.59311e27i	−0.348783	−	0.238516i
$607$		−	1.00281e28i		−	1.47683i	−0.674346	−	0.738416i	$-0.735574\pi$
$607$		−	1.00281e28i		−	1.47683i	0.674346	−	0.738416i	$-0.264426\pi$
$608$	−1.21101e28	+	1.73823e27i	−1.75433	+	0.251809i
$609$	4.63809e26			0.0660946
$610$	2.88570e27	−	4.21977e27i	0.404532	−	0.591549i
$611$		−	8.12301e27i		−	1.12022i
$612$	7.19982e26	+	1.84978e27i	0.0976804	+	0.250961i
$613$	5.08714e27			0.678998			0.339499	−	0.940606i	$-0.389742\pi$
$613$	5.08714e27			0.678998			0.339499	+	0.940606i	$0.389742\pi$
$614$	−9.28168e27	−	6.34730e27i	−1.21883	−	0.833499i
$615$			1.90935e27i			0.246680i
$616$	6.59354e25	+	1.53425e25i	0.00838130	+	0.00195025i
$617$	2.69578e27			0.337157			0.168578	−	0.985688i	$-0.446082\pi$
$617$	2.69578e27			0.337157			0.168578	+	0.985688i	$0.446082\pi$
$618$	−3.24216e27	+	4.74102e27i	−0.398978	+	0.583428i
$619$		−	1.37071e28i		−	1.65974i	−0.557958	−	0.829869i	$-0.688415\pi$
$619$		−	1.37071e28i		−	1.65974i	0.557958	−	0.829869i	$-0.311585\pi$
$620$	−2.10152e26	+	8.17965e25i	−0.0250390	+	0.00974581i
$621$	1.42557e27			0.167136
$622$	−1.53453e27	−	1.04939e27i	−0.177040	−	0.121069i
$623$		−	3.50293e25i		−	0.00397695i
$624$	−3.84707e27	−	4.19326e27i	−0.429817	−	0.468496i
$625$	−9.73826e27			−1.07073
$626$	−5.24735e27	+	7.67322e27i	−0.567801	+	0.830298i
$627$			9.12016e26i			0.0971242i
$628$	4.85369e26	+	1.24701e27i	0.0508716	+	0.130699i
$629$	1.14640e28			1.18258
$630$	−2.54926e26	−	1.74331e26i	−0.0258826	−	0.0176999i
$631$		−	1.37160e27i		−	0.137067i	−0.997649	−	0.0685335i	$-0.978168\pi$
$631$		−	1.37160e27i		−	0.137067i	0.997649	−	0.0685335i	$-0.0218320\pi$
$632$	4.23638e27	−	1.82061e28i	0.416701	−	1.79079i
$633$	−8.55905e27			−0.828683
$634$	−9.09198e27	+	1.32952e28i	−0.866495	+	1.26708i
$635$		−	3.43148e27i		−	0.321918i
$636$	−8.50928e27	+	3.31203e27i	−0.785818	+	0.305861i
$637$	1.20139e28			1.09217
$638$	−1.10549e27	−	7.55994e26i	−0.0989348	−	0.0676568i
$639$		−	1.43959e27i		−	0.126833i
$640$	−1.04184e28	+	5.87895e27i	−0.903651	+	0.509918i
$641$	1.06161e28			0.906531			0.453266	−	0.891375i	$-0.350259\pi$
$641$	1.06161e28			0.906531			0.453266	+	0.891375i	$0.350259\pi$
$642$	4.98284e27	−	7.28642e27i	0.418916	−	0.612582i
$643$		−	4.30746e27i		−	0.356543i	−0.983981	−	0.178272i	$-0.942949\pi$
$643$		−	4.30746e27i		−	0.356543i	0.983981	−	0.178272i	$-0.0570505\pi$
$644$	−3.50425e26	−	9.00314e26i	−0.0285586	−	0.0733728i
$645$	6.38159e27			0.512073
$646$	1.49593e28	+	1.02300e28i	1.18191	+	0.808255i
$647$			1.74446e28i			1.35712i	0.734545	+	0.678561i	$0.237396\pi$
$647$			1.74446e28i			1.35712i	−0.734545	+	0.678561i	$0.762604\pi$
$648$	−1.41272e27	−	3.28727e26i	−0.108220	−	0.0251818i
$649$	1.09611e27			0.0826813
$650$	6.41050e26	−	9.37410e26i	0.0476166	−	0.0696300i
$651$			1.85303e25i			0.00135542i
$652$	5.21242e27	−	2.02881e27i	0.375459	−	0.146139i
$653$	5.28720e27			0.375054			0.187527	−	0.982259i	$-0.439953\pi$
$653$	5.28720e27			0.375054			0.187527	+	0.982259i	$0.439953\pi$
$654$	1.08909e28	+	7.44774e27i	0.760825	+	0.520292i
$655$			2.58219e28i			1.77654i
$656$	4.47813e27	−	4.10842e27i	0.303430	−	0.278379i
$657$	3.51656e27			0.234674
$658$	−7.92050e26	+	1.15822e27i	−0.0520587	+	0.0761257i
$659$		−	1.98545e28i		−	1.28530i	−0.766160	−	0.642650i	$-0.777835\pi$
$659$		−	1.98545e28i		−	1.28530i	0.766160	−	0.642650i	$-0.222165\pi$
$660$	3.23463e26	+	8.31042e26i	0.0206246	+	0.0529887i
$661$	−2.01770e28			−1.26719			−0.633594	−	0.773666i	$-0.718421\pi$
$661$	−2.01770e28			−1.26719			−0.633594	+	0.773666i	$0.718421\pi$
$662$	8.32954e27	+	5.69617e27i	0.515277	+	0.352374i
$663$			8.42963e27i			0.513657i
$664$	3.34077e27	−	1.43571e28i	0.200524	−	0.861762i
$665$	−2.81966e27			−0.166717
$666$	−4.72871e27	+	6.91481e27i	−0.275423	+	0.402752i
$667$			1.91128e28i			1.09664i
$668$	2.44761e28	−	9.52673e27i	1.38349	−	0.538492i
$669$	−1.04367e28			−0.581170
$670$	3.28114e27	+	2.24381e27i	0.180002	+	0.123095i
$671$			1.21297e27i			0.0655576i
$672$	1.39662e26	+	9.73010e26i	0.00743676	+	0.0518113i
$673$	3.36898e27			0.176745			0.0883725	−	0.996087i	$-0.471833\pi$
$673$	3.36898e27			0.176745			0.0883725	+	0.996087i	$0.471833\pi$
$674$	5.48430e26	−	8.01972e26i	0.0283480	−	0.0414534i
$675$		−	2.89460e26i		−	0.0147418i
$676$	−1.53742e27	−	3.94993e27i	−0.0771480	−	0.198209i
$677$	−2.98165e27			−0.147425			−0.0737123	−	0.997280i	$-0.523485\pi$
$677$	−2.98165e27			−0.147425			−0.0737123	+	0.997280i	$0.523485\pi$
$678$	1.76850e28	+	1.20939e28i	0.861606	+	0.589212i
$679$			3.26154e27i			0.156576i
$680$	1.72594e28	+	4.01609e27i	0.816461	+	0.189983i
$681$	9.07005e27			0.422804
$682$	3.02039e25	−	4.41673e25i	0.00138746	−	0.00202888i
$683$		−	2.73242e28i		−	1.23692i	−0.785817	−	0.618459i	$-0.787757\pi$
$683$		−	2.73242e28i		−	1.23692i	0.785817	−	0.618459i	$-0.212243\pi$
$684$	−1.23409e28	+	4.80341e27i	−0.550538	+	0.214284i
$685$	1.24088e27			0.0545537
$686$	−3.44021e27	−	2.35259e27i	−0.149054	−	0.101931i
$687$			1.62682e28i			0.694660i
$688$	−1.37315e28	−	1.49672e28i	−0.577875	−	0.629877i
$689$	−3.87777e28			−1.60838
$690$	7.18391e27	−	1.05051e28i	0.293677	−	0.429445i
$691$		−	2.89320e28i		−	1.16573i	−0.812570	−	0.582864i	$-0.801932\pi$
$691$		−	2.89320e28i		−	1.16573i	0.812570	−	0.582864i	$-0.198068\pi$
$692$	−1.65345e27	−	4.24805e27i	−0.0656644	−	0.168705i
$693$	7.32779e25			0.00286841
$694$	−2.63394e28	−	1.80123e28i	−1.01628	−	0.694982i
$695$		−	1.77218e28i		−	0.674000i
$696$	4.40731e27	−	1.89406e28i	0.165227	−	0.710072i
$697$	−9.00230e27			−0.332679
$698$	−1.18509e27	+	1.73296e27i	−0.0431713	+	0.0631296i
$699$		−	1.38938e28i		−	0.498942i
$700$	−1.82808e26	+	7.11536e25i	−0.00647165	+	0.00251893i
$701$	−1.36275e28			−0.475592			−0.237796	−	0.971315i	$-0.576425\pi$
$701$	−1.36275e28			−0.475592			−0.237796	+	0.971315i	$0.576425\pi$
$702$	−5.08455e27	−	3.47708e27i	−0.174937	−	0.119631i
$703$			7.64829e28i			2.59425i
$704$	1.25309e27	−	2.54682e27i	0.0419041	−	0.0851672i
$705$	−1.84836e28			−0.609391
$706$	6.13509e27	−	8.97137e27i	0.199422	−	0.291616i
$707$			2.07031e27i			0.0663502i
$708$	5.77300e27	+	1.48320e28i	0.182419	+	0.468670i
$709$	−1.45751e28			−0.454098			−0.227049	−	0.973883i	$-0.572908\pi$
$709$	−1.45751e28			−0.454098			−0.227049	+	0.973883i	$0.572908\pi$
$710$	−1.06084e28	−	7.25460e27i	−0.325888	−	0.222859i
$711$		−	2.02335e28i		−	0.612879i
$712$	−1.43050e27	−	3.32863e26i	−0.0427255	−	0.00994181i
$713$	−7.63605e26			−0.0224892
$714$	8.21947e26	−	1.20194e27i	0.0238705	−	0.0349059i
$715$			3.78714e27i			0.108455i
$716$	3.94774e28	−	1.53656e28i	1.11485	−	0.433930i
$717$	−6.77319e27			−0.188626
$718$	1.33066e28	+	9.09978e27i	0.365447	+	0.249912i
$719$			4.90272e28i			1.32785i	0.747801	+	0.663923i	$0.231110\pi$
$719$			4.90272e28i			1.32785i	−0.747801	+	0.663923i	$0.768890\pi$
$720$	−9.54161e27	+	8.75387e27i	−0.254857	+	0.233816i
$721$	4.21333e27			0.110987
$722$	−4.65217e28	+	6.80289e28i	−1.20860	+	1.76735i
$723$		−	2.28598e28i		−	0.585718i
$724$	−2.15429e28	−	5.53480e28i	−0.544400	−	1.39867i
$725$	3.88084e27			0.0967265
$726$	1.92116e28	+	1.31379e28i	0.472277	+	0.322968i
$727$			1.17888e28i			0.285842i	0.989734	+	0.142921i	$0.0456495\pi$
$727$			1.17888e28i			0.285842i	−0.989734	+	0.142921i	$0.954350\pi$
$728$	−9.46088e26	+	4.06586e27i	−0.0226265	+	0.0972387i
$729$	−1.57004e27			−0.0370370
$730$	1.77212e28	−	2.59137e28i	0.412348	−	0.602978i
$731$			3.00883e28i			0.690595i
$732$	−1.64132e28	+	6.38845e27i	−0.371606	+	0.144639i
$733$	8.47436e28			1.89264			0.946318	−	0.323237i	$-0.104771\pi$
$733$	8.47436e28			1.89264			0.946318	+	0.323237i	$0.104771\pi$
$734$	−2.46336e28	−	1.68458e28i	−0.542710	−	0.371133i
$735$		−	2.73373e28i		−	0.594131i
$736$	−4.00962e28	+	5.75522e27i	−0.859656	+	0.123391i
$737$	−9.43157e26			−0.0199485
$738$	3.71330e27	−	5.42997e27i	0.0774812	−	0.113301i
$739$		−	4.70822e28i		−	0.969198i	−0.874736	−	0.484599i	$-0.838966\pi$
$739$		−	4.70822e28i		−	0.969198i	0.874736	−	0.484599i	$-0.161034\pi$
$740$	2.71260e28	+	6.96922e28i	0.550895	+	1.41536i
$741$	−5.62389e28			−1.12682
$742$	5.52910e27	+	3.78109e27i	0.109299	+	0.0747443i
$743$		−	2.94650e28i		−	0.574669i	−0.957830	−	0.287335i	$-0.907231\pi$
$743$		−	2.94650e28i		−	0.574669i	0.957830	−	0.287335i	$-0.0927692\pi$
$744$	7.56726e26	+	1.76083e26i	0.0145616	+	0.00338835i
$745$	8.21001e28			1.55877
$746$	−1.07547e28	+	1.57266e28i	−0.201470	+	0.294610i
$747$		−	1.59559e28i		−	0.294928i
$748$	−3.91824e27	+	1.52508e27i	−0.0714620	+	0.0278149i
$749$	−6.47543e27			−0.116533
$750$	2.57133e28	+	1.75841e28i	0.456609	+	0.312253i
$751$		−	2.74539e28i		−	0.481065i	−0.970641	−	0.240533i	$-0.922678\pi$
$751$		−	2.74539e28i		−	0.481065i	0.970641	−	0.240533i	$-0.0773221\pi$
$752$	3.97720e28	+	4.33510e28i	0.687699	+	0.749584i
$753$	5.56208e28			0.949047
$754$	4.66179e28	−	6.81695e28i	0.784944	−	1.14783i
$755$		−	4.40167e28i		−	0.731389i
$756$	3.85940e26	+	9.91558e26i	0.00632852	+	0.0162592i
$757$	5.32057e28			0.860992			0.430496	−	0.902592i	$-0.358339\pi$
$757$	5.32057e28			0.860992			0.430496	+	0.902592i	$0.358339\pi$
$758$	−8.47325e28	−	5.79445e28i	−1.35319	−	0.925381i
$759$			3.01966e27i			0.0475927i
$760$	−2.67936e28	+	1.15147e29i	−0.416769	+	1.79109i
$761$	1.05577e29			1.62078			0.810389	−	0.585892i	$-0.199256\pi$
$761$	1.05577e29			1.62078			0.810389	+	0.585892i	$0.199256\pi$
$762$	−6.67355e27	+	9.75876e27i	−0.101113	+	0.147858i
$763$		−	9.67868e27i		−	0.144734i
$764$	−1.17225e29	+	4.56269e28i	−1.73016	+	0.673422i
$765$	1.91813e28			0.279424
$766$	3.89214e28	+	2.66165e28i	0.559630	+	0.382704i
$767$			6.75909e28i			0.959257i
$768$	4.10621e28	+	3.54257e27i	0.575214	+	0.0496257i
$769$	−4.19651e28			−0.580263			−0.290132	−	0.956987i	$-0.593699\pi$
$769$	−4.19651e28			−0.580263			−0.290132	+	0.956987i	$0.593699\pi$
$770$	3.69272e26	−	5.39988e26i	0.00504010	−	0.00737017i
$771$		−	3.08247e28i		−	0.415293i
$772$	−2.66717e28	−	6.85250e28i	−0.354713	−	0.911331i
$773$	−1.22192e29			−1.60416			−0.802078	−	0.597220i	$-0.796272\pi$
$773$	−1.22192e29			−1.60416			−0.802078	+	0.597220i	$0.796272\pi$
$774$	−1.81485e28	−	1.24109e28i	−0.235197	−	0.160840i
$775$			1.55049e26i			0.00198359i
$776$	1.33192e29	+	3.09925e28i	1.68213	+	0.391417i
$777$	6.14518e27			0.0766169
$778$	2.28492e28	−	3.34125e28i	0.281239	−	0.411257i
$779$		−	6.00595e28i		−	0.729805i
$780$	−5.12456e28	+	1.99461e28i	−0.614767	+	0.239283i
$781$	3.04938e27			0.0361161
$782$	4.95298e28	+	3.38711e28i	0.579161	+	0.396061i
$783$		−	2.10498e28i		−	0.243014i
$784$	−6.41161e28	+	5.88227e28i	−0.730813	+	0.670478i
$785$	1.29309e28			0.145523
$786$	5.02184e28	−	7.34346e28i	0.558004	−	0.815972i
$787$			1.63330e29i			1.79192i	0.444130	+	0.895962i	$0.353513\pi$
$787$			1.63330e29i			1.79192i	−0.444130	+	0.895962i	$0.646487\pi$
$788$	−8.92014e27	−	2.29176e28i	−0.0966294	−	0.248261i
$789$	9.96753e27			0.106615
$790$	−1.49102e29	−	1.01963e29i	−1.57475	−	1.07690i
$791$		−	1.57166e28i		−	0.163906i
$792$	6.96317e26	−	2.99246e27i	0.00717060	−	0.0308160i
$793$	−7.47967e28			−0.760590
$794$	3.36339e28	−	4.91830e28i	0.337732	−	0.493867i
$795$			8.82372e28i			0.874945i
$796$	1.08722e28	−	4.23174e27i	0.106460	−	0.0414370i
$797$	9.43254e28			0.912106			0.456053	−	0.889953i	$-0.349263\pi$
$797$	9.43254e28			0.912106			0.456053	+	0.889953i	$0.349263\pi$
$798$	8.01881e27	+	5.48368e27i	0.0765739	+	0.0523653i
$799$		−	8.71476e28i		−	0.821841i
$800$	1.16859e27	+	8.14149e27i	0.0108834	+	0.0758236i
$801$	−1.58979e27			−0.0146223
$802$	−6.41836e28	+	9.38560e28i	−0.583016	+	0.852547i
$803$			7.44886e27i			0.0668243i
$804$	−4.96742e27	−	1.27623e28i	−0.0440120	−	0.113076i
$805$	−9.33583e27			−0.0816947
$806$	2.72354e27	+	1.86250e27i	0.0235388	+	0.0160971i
$807$		−	1.57976e27i		−	0.0134852i
$808$	8.45458e28	+	1.96730e28i	0.712817	+	0.165866i
$809$	−1.08288e29			−0.901768			−0.450884	−	0.892583i	$-0.648891\pi$
$809$	−1.08288e29			−0.901768			−0.450884	+	0.892583i	$0.648891\pi$
$810$	−7.91199e27	+	1.15697e28i	−0.0650782	+	0.0951641i
$811$			4.47513e28i			0.363578i	0.983338	+	0.181789i	$0.0581887\pi$
$811$			4.47513e28i			0.363578i	−0.983338	+	0.181789i	$0.941811\pi$
$812$	−1.32940e28	+	5.17437e27i	−0.106683	+	0.0415238i
$813$	−1.00313e28			−0.0795156
$814$	−1.46471e28	−	1.00165e28i	−0.114685	−	0.0784278i
$815$		−	5.40503e28i		−	0.418044i
$816$	−4.12732e28	−	4.49873e28i	−0.315331	−	0.343707i
$817$	−2.00736e29			−1.51497
$818$	1.28338e28	−	1.87670e28i	0.0956806	−	0.139914i
$819$			4.51863e27i			0.0332788i
$820$	−2.13012e28	−	5.47270e28i	−0.154976	−	0.398165i
$821$	−6.95849e28			−0.500131			−0.250065	−	0.968229i	$-0.580452\pi$
$821$	−6.95849e28			−0.500131			−0.250065	+	0.968229i	$0.580452\pi$
$822$	−3.52893e27	−	2.41326e27i	−0.0250567	−	0.0171351i
$823$			6.25383e26i			0.00438680i	0.999998	+	0.00219340i	$0.000698181\pi$
$823$			6.25383e26i			0.00438680i	−0.999998	+	0.00219340i	$0.999302\pi$
$824$	4.00369e28	−	1.72061e29i	0.277452	−	1.19237i
$825$	6.13140e26			0.00419778
$826$	6.59058e27	−	9.63744e27i	0.0445783	−	0.0651870i
$827$			1.08820e29i			0.727201i	0.931555	+	0.363601i	$0.118453\pi$
$827$			1.08820e29i			0.727201i	−0.931555	+	0.363601i	$0.881547\pi$
$828$	−4.08605e28	+	1.59040e28i	−0.269774	+	0.105003i
$829$	−2.65271e29			−1.73039			−0.865196	−	0.501434i	$-0.832806\pi$
$829$	−2.65271e29			−1.73039			−0.865196	+	0.501434i	$0.832806\pi$
$830$	−1.17580e29	−	8.04074e28i	−0.757797	−	0.518221i
$831$			8.80629e28i			0.560768i
$832$	1.57048e29	+	7.72711e28i	0.988098	+	0.486165i
$833$	1.28891e29			0.801261
$834$	−3.44654e28	+	5.03989e28i	−0.211701	+	0.309571i
$835$		−	2.53805e29i		−	1.54041i
$836$	−1.01747e28	−	2.61408e28i	−0.0610180	−	0.156768i
$837$	8.40994e26			0.00498355
$838$	2.78526e29	+	1.90471e29i	1.63089	+	1.11529i
$839$		−	1.43896e29i		−	0.832586i	−0.909231	−	0.416293i	$-0.863329\pi$
$839$		−	1.43896e29i		−	0.832586i	0.909231	−	0.416293i	$-0.136671\pi$
$840$	9.25173e27	+	2.15279e27i	0.0528969	+	0.0123086i
$841$	1.05224e29			0.594505
$842$	1.58884e29	−	2.32336e29i	0.887071	−	1.29717i
$843$			1.27732e29i			0.704730i
$844$	2.45325e29	−	9.54869e28i	1.33757	−	0.520618i
$845$	−4.09589e28			−0.220689
$846$	5.25654e28	+	3.59470e28i	0.279896	+	0.191407i
$847$		−	1.70733e28i		−	0.0898428i
$848$	2.06949e29	−	1.89863e29i	1.07623	−	0.987377i
$849$	−9.22276e28			−0.474006
$850$	6.87750e27	−	1.00570e28i	0.0349334	−	0.0510833i
$851$			2.53233e29i			1.27123i
$852$	1.60605e28	+	4.12626e28i	0.0796824	+	0.204720i
$853$	2.13067e29			1.04478			0.522390	−	0.852706i	$-0.325040\pi$
$853$	2.13067e29			1.04478			0.522390	+	0.852706i	$0.325040\pi$
$854$	1.06649e28	+	7.29320e27i	0.0516865	+	0.0353459i
$855$			1.27970e29i			0.612979i
$856$	−6.15322e28	+	2.64438e29i	−0.291317	+	1.25195i
$857$	1.04066e29			0.486967			0.243484	−	0.969905i	$-0.421710\pi$
$857$	1.04066e29			0.486967			0.243484	+	0.969905i	$0.421710\pi$
$858$	7.36523e27	−	1.07702e28i	0.0340654	−	0.0498140i
$859$			2.11893e29i			0.968691i	0.874877	+	0.484345i	$0.160942\pi$
$859$			2.11893e29i			0.968691i	−0.874877	+	0.484345i	$0.839058\pi$
$860$	−1.82913e29	+	7.11946e28i	−0.826535	+	0.321709i
$861$	−4.82561e27			−0.0215536
$862$	1.27392e29	+	8.71170e28i	0.562429	+	0.384619i
$863$			3.19710e28i			0.139524i	0.997564	+	0.0697619i	$0.0222240\pi$
$863$			3.19710e28i			0.139524i	−0.997564	+	0.0697619i	$0.977776\pi$
$864$	4.41598e28	−	6.33850e27i	0.190498	−	0.0273432i
$865$	−4.40502e28			−0.187840
$866$	−1.22829e29	+	1.79614e29i	−0.517754	+	0.757114i
$867$		−	4.81204e28i		−	0.200511i
$868$	−2.06729e26	−	5.31129e26i	−0.000851539	−	0.00218777i
$869$	4.28590e28			0.174520
$870$	−1.55117e29	−	1.06077e29i	−0.624407	−	0.427002i
$871$		−	5.81592e28i		−	0.231439i
$872$	−3.95250e29	−	9.19709e28i	−1.55492	−	0.361814i
$873$	1.48024e29			0.575691
$874$	−2.25973e29	+	3.30442e29i	−0.868847	+	1.27052i
$875$		−	2.28513e28i		−	0.0868621i
$876$	−1.00794e29	+	3.92317e28i	−0.378786	+	0.147433i
$877$	8.13275e28			0.302163			0.151082	−	0.988521i	$-0.451724\pi$
$877$	8.13275e28			0.302163			0.151082	+	0.988521i	$0.451724\pi$
$878$	3.21422e29	+	2.19805e29i	1.18068	+	0.807408i
$879$		−	2.10031e28i		−	0.0762773i
$880$	−1.85426e28	−	2.02112e28i	−0.0665801	−	0.0725715i
$881$	8.93073e28			0.317050			0.158525	−	0.987355i	$-0.449326\pi$
$881$	8.93073e28			0.317050			0.158525	+	0.987355i	$0.449326\pi$
$882$	−5.31656e28	+	7.77443e28i	−0.186614	+	0.272887i
$883$		−	1.48375e29i		−	0.514938i	−0.966287	−	0.257469i	$-0.917111\pi$
$883$		−	1.48375e29i		−	0.514938i	0.966287	−	0.257469i	$-0.0828885\pi$
$884$	−9.40431e28	−	2.41616e29i	−0.322704	−	0.829092i
$885$	1.53801e29			0.521826
$886$	−1.80070e28	−	1.23141e28i	−0.0604094	−	0.0413111i
$887$		−	5.77993e28i		−	0.191728i	−0.995394	−	0.0958641i	$-0.969439\pi$
$887$		−	5.77993e28i		−	0.191728i	0.995394	−	0.0958641i	$-0.0305614\pi$
$888$	5.83941e28	−	2.50952e29i	0.191531	−	0.823115i
$889$	8.67258e27			0.0281275
$890$	−8.01152e27	+	1.17153e28i	−0.0256930	+	0.0375710i
$891$		−	3.32570e27i		−	0.0105464i
$892$	2.99145e29	−	1.16435e29i	0.938064	−	0.365119i
$893$	5.81412e29			1.80289
$894$	−2.33484e29	−	1.59668e29i	−0.715948	−	0.489603i
$895$		−	4.09362e29i		−	1.24130i
$896$	−1.48582e28	−	2.63310e28i	−0.0445540	−	0.0789563i
$897$	−1.86205e29			−0.552164
$898$	−4.32890e27	+	6.33016e27i	−0.0126944	+	0.0185631i
$899$			1.12754e28i			0.0326989i
$900$	3.22929e27	+	8.29669e27i	0.00926151	+	0.0237947i
$901$	−4.16026e29			−1.17997
$902$	1.15019e28	+	7.86559e27i	0.0322629	+	0.0220631i
$903$			1.61286e28i			0.0447423i
$904$	−6.41823e29	−	1.49346e29i	−1.76089	−	0.409741i
$905$	−5.73932e29			−1.55731
$906$	−8.56038e28	+	1.25179e29i	−0.229726	+	0.335930i
$907$		−	6.61702e29i		−	1.75626i	−0.478420	−	0.878131i	$-0.658790\pi$
$907$		−	6.61702e29i		−	1.75626i	0.478420	−	0.878131i	$-0.341210\pi$
$908$	−2.59972e29	+	1.01188e29i	−0.682446	+	0.265625i
$909$	9.39606e28			0.243954
$910$	3.32980e28	+	2.27709e28i	0.0855076	+	0.0584746i
$911$		−	1.73051e29i		−	0.439531i	−0.975553	−	0.219765i	$-0.929471\pi$
$911$		−	1.73051e29i		−	0.439531i	0.975553	−	0.219765i	$-0.0705292\pi$
$912$	3.00136e29	−	2.75357e29i	0.753997	−	0.691748i
$913$	3.37982e28			0.0839818
$914$	−2.37843e29	+	3.47799e29i	−0.584559	+	0.854804i
$915$			1.70197e29i			0.413754i
$916$	−1.81492e29	−	4.66290e29i	−0.436419	−	1.12125i
$917$	−6.52611e28			−0.155225
$918$	−5.45496e28	−	3.73039e28i	−0.128341	−	0.0877661i
$919$		−	1.52088e29i		−	0.353948i	−0.984216	−	0.176974i	$-0.943369\pi$
$919$		−	1.52088e29i		−	0.353948i	0.984216	−	0.176974i	$-0.0566308\pi$
$920$	−8.87130e28	+	3.81249e29i	−0.204225	+	0.877668i
$921$	3.74361e29			0.852500
$922$	−2.08803e29	+	3.05333e29i	−0.470356	+	0.687804i
$923$			1.88038e29i			0.419013i
$924$	−2.10034e27	+	8.17506e26i	−0.00462988	+	0.00180207i
$925$	5.14187e28			0.112125
$926$	2.13913e29	+	1.46285e29i	0.461453	+	0.315565i
$927$		−	1.91221e29i		−	0.408073i
$928$	8.49814e28	+	5.92058e29i	0.179409	+	1.24993i
$929$	−5.33239e29			−1.11369			−0.556846	−	0.830616i	$-0.687989\pi$
$929$	−5.33239e29			−1.11369			−0.556846	+	0.830616i	$0.687989\pi$
$930$	4.23806e27	−	6.19733e27i	0.00875664	−	0.0128049i
$931$			8.59909e29i			1.75774i
$932$	1.55003e29	+	3.98234e29i	0.313459	+	0.805339i
$933$	6.18926e28			0.123829
$934$	−2.45393e29	−	1.67813e29i	−0.485729	−	0.332167i
$935$			4.06303e28i			0.0795671i
$936$	1.84528e29	+	4.29379e28i	0.357523	+	0.0831922i
$937$	3.55593e29			0.681644			0.340822	−	0.940128i	$-0.389295\pi$
$937$	3.55593e29			0.681644			0.340822	+	0.940128i	$0.389295\pi$
$938$	−5.67092e27	+	8.29261e27i	−0.0107554	+	0.0157276i
$939$		−	3.09486e29i		−	0.580745i
$940$	5.29790e29	−	2.06208e29i	0.983616	−	0.382849i
$941$	6.83628e29			1.25581			0.627904	−	0.778291i	$-0.283913\pi$
$941$	6.83628e29			1.25581			0.627904	+	0.778291i	$0.283913\pi$
$942$	−3.67741e28	−	2.51480e28i	−0.0668394	−	0.0457083i
$943$		−	1.98855e29i		−	0.357619i
$944$	−3.30939e29	−	3.60720e29i	−0.588882	−	0.641874i
$945$	1.02820e28			0.0181034
$946$	2.62891e28	−	3.84426e28i	0.0457998	−	0.0669732i
$947$			3.25369e29i			0.560888i	0.959870	+	0.280444i	$0.0904817\pi$
$947$			3.25369e29i			0.560888i	−0.959870	+	0.280444i	$0.909518\pi$
$948$	2.25730e29	+	5.79946e29i	0.385040	+	0.989245i
$949$	−4.59329e29			−0.775285
$950$	6.70960e28	+	4.58837e28i	0.112063	+	0.0766342i
$951$		−	5.36241e29i		−	0.886247i
$952$	−1.01501e28	+	4.36206e28i	−0.0165997	+	0.0713381i
$953$	5.74896e29			0.930380			0.465190	−	0.885211i	$-0.345986\pi$
$953$	5.74896e29			0.930380			0.465190	+	0.885211i	$0.345986\pi$
$954$	1.71604e29	−	2.50937e29i	0.274817	−	0.401866i
$955$			1.21556e30i			1.92639i
$956$	1.94138e29	−	7.55634e28i	0.304460	−	0.118504i
$957$	4.45882e28			0.0691991
$958$	−1.82201e29	−	1.24599e29i	−0.279831	−	0.191363i
$959$			3.13615e27i			0.00476662i
$960$	1.75828e29	−	3.57358e29i	0.264469	−	0.537516i
$961$	6.71340e29			0.999329
$962$	6.17658e29	−	9.03204e29i	0.909908	−	1.33056i
$963$			2.93886e29i			0.428465i
$964$	2.55029e29	+	6.55222e29i	0.367976	+	0.945405i
$965$	−7.10572e29			−1.01469
$966$	2.65501e28	+	1.81563e28i	0.0375227	+	0.0256600i
$967$		−	9.63443e29i		−	1.34760i	−0.738913	−	0.673801i	$-0.764661\pi$
$967$		−	9.63443e29i		−	1.34760i	0.738913	−	0.673801i	$-0.235339\pi$
$968$	−6.97225e29	−	1.62238e29i	−0.965205	−	0.224594i
$969$	−6.03358e29			−0.826680
$970$	7.45944e29	−	1.09080e30i	1.01155	−	1.47920i
$971$			7.80679e29i			1.04780i	0.851778	+	0.523902i	$0.175524\pi$
$971$			7.80679e29i			1.04780i	−0.851778	+	0.523902i	$0.824476\pi$
$972$	4.50016e28	−	1.75158e28i	0.0597813	−	0.0232684i
$973$	4.47893e28			0.0588906
$974$	4.83134e29	+	3.30392e29i	0.628750	+	0.429972i
$975$			3.78089e28i			0.0487021i
$976$	3.99176e29	−	3.66220e29i	0.508939	−	0.466922i
$977$	−5.30704e29			−0.669741			−0.334871	−	0.942264i	$-0.608693\pi$
$977$	−5.30704e29			−0.669741			−0.334871	+	0.942264i	$0.608693\pi$
$978$	−1.05117e29	+	1.53713e29i	−0.131306	+	0.192009i
$979$		−	3.36753e27i		−	0.00416375i
$980$	3.04982e29	+	7.83560e29i	0.373262	+	0.958985i
$981$	−4.39265e29			−0.532152
$982$	−1.23720e30	−	8.46065e29i	−1.48363	−	1.01459i
$983$			6.30801e29i			0.748785i	0.927270	+	0.374392i	$0.122149\pi$
$983$			6.30801e29i			0.748785i	−0.927270	+	0.374392i	$0.877851\pi$
$984$	−4.58549e28	+	1.97064e29i	−0.0538809	+	0.231556i
$985$	−2.37645e29			−0.276418
$986$	5.00139e29	−	7.31355e29i	0.575866	−	0.842092i
$987$		−	4.67148e28i		−	0.0532455i
$988$	1.61196e30	−	6.27415e29i	1.81880	−	0.707922i
$989$	−6.64632e29			−0.742366
$990$	−2.45072e28	−	1.67593e28i	−0.0270983	−	0.0185312i
$991$			1.05424e30i			1.15400i	0.816745	+	0.576998i	$0.195776\pi$
$991$			1.05424e30i			1.15400i	−0.816745	+	0.576998i	$0.804224\pi$
$992$	−2.36542e28	+	3.39522e27i	−0.0256326	+	0.00367918i
$993$	−3.35958e29			−0.360406
$994$	1.83350e28	−	2.68113e28i	0.0194723	−	0.0284744i
$995$		−	1.12740e29i		−	0.118535i
$996$	1.78008e29	+	4.57339e29i	0.185288	+	0.476042i
$997$	7.86758e29			0.810755			0.405378	−	0.914149i	$-0.367140\pi$
$997$	7.86758e29			0.810755			0.405378	+	0.914149i	$0.367140\pi$
$998$	1.02152e30	+	6.98570e29i	1.04218	+	0.712696i
$999$		−	2.78897e29i		−	0.281702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.21.d.a.7.13	✓	20
3.2	odd	2		36.21.d.c.19.8		20
4.3	odd	2	inner	12.21.d.a.7.14	yes	20
12.11	even	2		36.21.d.c.19.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.21.d.a.7.13	✓	20	1.1	even	1	trivial
12.21.d.a.7.14	yes	20	4.3	odd	2	inner
36.21.d.c.19.7		20	12.11	even	2
36.21.d.c.19.8		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)

\(f(q)\)	\(=\)	\(q+(578.030 - 845.256i) q^{2} +34092.0i q^{3} +(-380338. - 977166. i) q^{4} -1.01328e7 q^{5} +(2.88164e7 + 1.97062e7i) q^{6} -2.56091e7i q^{7} +(-1.04580e9 - 2.43348e8i) q^{8} -1.16226e9 q^{9} +O(q^{10})\)	\(q+(578.030 - 845.256i) q^{2} +34092.0i q^{3} +(-380338. - 977166. i) q^{4} -1.01328e7 q^{5} +(2.88164e7 + 1.97062e7i) q^{6} -2.56091e7i q^{7} +(-1.04580e9 - 2.43348e8i) q^{8} -1.16226e9 q^{9} +(-5.85703e9 + 8.56477e9i) q^{10} -2.46193e9i q^{11} +(3.33135e10 - 1.29665e10i) q^{12} +1.51813e11 q^{13} +(-2.16462e10 - 1.48028e10i) q^{14} -3.45445e11i q^{15} +(-8.10197e11 + 7.43308e11i) q^{16} +1.62872e12 q^{17} +(-6.71822e11 + 9.82408e11i) q^{18} +1.08662e13i q^{19} +(3.85387e12 + 9.90138e12i) q^{20} +8.73064e11 q^{21} +(-2.08096e12 - 1.42307e12i) q^{22} +3.59775e13i q^{23} +(8.29622e12 - 3.56535e13i) q^{24} +7.30521e12 q^{25} +(8.77525e13 - 1.28321e14i) q^{26} -3.96238e13i q^{27} +(-2.50243e13 + 9.74012e12i) q^{28} +5.31243e14 q^{29} +(-2.91990e14 - 1.99678e14i) q^{30} +2.12245e13i q^{31} +(1.59967e14 + 1.11448e15i) q^{32} +8.39319e13 q^{33} +(9.41451e14 - 1.37669e15i) q^{34} +2.59490e14i q^{35} +(4.42053e14 + 1.13572e15i) q^{36} +7.03864e15 q^{37} +(9.18468e15 + 6.28096e15i) q^{38} +5.17560e15i q^{39} +(1.05969e16 + 2.46579e15i) q^{40} -5.52721e15 q^{41} +(5.04657e14 - 7.37962e14i) q^{42} +1.84735e16i q^{43} +(-2.40571e15 + 9.36365e14i) q^{44} +1.17769e16 q^{45} +(3.04102e16 + 2.07961e16i) q^{46} -5.35067e16i q^{47} +(-2.53408e16 - 2.76212e16i) q^{48} +7.91364e16 q^{49} +(4.22263e15 - 6.17477e15i) q^{50} +5.55264e16i q^{51} +(-5.77403e16 - 1.48347e17i) q^{52} -2.55430e17 q^{53} +(-3.34922e16 - 2.29037e16i) q^{54} +2.49461e16i q^{55} +(-6.23193e15 + 2.67820e16i) q^{56} -3.70448e17 q^{57} +(3.07074e17 - 4.49036e17i) q^{58} +4.45225e17i q^{59} +(-3.37558e17 + 1.31386e17i) q^{60} -4.92690e17 q^{61} +(1.79401e16 + 1.22684e16i) q^{62} +2.97645e16i q^{63} +(1.03448e18 + 5.08989e17i) q^{64} -1.53828e18 q^{65} +(4.85151e16 - 7.09439e16i) q^{66} -3.83097e17i q^{67} +(-6.19466e17 - 1.59153e18i) q^{68} -1.22654e18 q^{69} +(2.19336e17 + 1.49993e17i) q^{70} +1.23861e18i q^{71} +(1.21550e18 + 2.82834e17i) q^{72} -3.02562e18 q^{73} +(4.06854e18 - 5.94945e18i) q^{74} +2.49049e17i q^{75} +(1.06180e19 - 4.13282e18i) q^{76} -6.30477e16 q^{77} +(4.37471e18 + 2.99165e18i) q^{78} +1.74087e19i q^{79} +(8.20952e18 - 7.53175e18i) q^{80} +1.35085e18 q^{81} +(-3.19489e18 + 4.67190e18i) q^{82} +1.37283e19i q^{83} +(-3.32060e17 - 8.53129e17i) q^{84} -1.65035e19 q^{85} +(1.56148e19 + 1.06782e19i) q^{86} +1.81111e19i q^{87} +(-5.99106e17 + 2.57469e18i) q^{88} +1.36785e18 q^{89} +(6.80741e18 - 9.95450e18i) q^{90} -3.88779e18i q^{91} +(3.51560e19 - 1.36836e19i) q^{92} -7.23584e17 q^{93} +(-4.52268e19 - 3.09285e19i) q^{94} -1.10104e20i q^{95} +(-3.79947e19 + 5.45359e18i) q^{96} -1.27359e20 q^{97} +(4.57432e19 - 6.68905e19i) q^{98} +2.86140e18i 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

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