LMFDB - Embedded newform 12.21.d.a.7.11

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			7.11
Root			$-360.777 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.21.d.a.7.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(171.720 - 1009.50i) q^{2} +34092.0i q^{3} +(-989600. - 346703. i) q^{4} +1.74429e7 q^{5} +(3.44158e7 + 5.85428e6i) q^{6} +3.10877e8i q^{7} +(-5.19931e8 + 9.39464e8i) q^{8} -1.16226e9 q^{9} +O(q^{10})$	\(q+(171.720 - 1009.50i) q^{2} +34092.0i q^{3} +(-989600. - 346703. i) q^{4} +1.74429e7 q^{5} +(3.44158e7 + 5.85428e6i) q^{6} +3.10877e8i q^{7} +(-5.19931e8 + 9.39464e8i) q^{8} -1.16226e9 q^{9} +(2.99530e9 - 1.76086e10i) q^{10} +2.01328e9i q^{11} +(1.18198e10 - 3.37374e10i) q^{12} -1.45678e11 q^{13} +(3.13830e11 + 5.33839e10i) q^{14} +5.94662e11i q^{15} +(8.59106e11 + 6.86195e11i) q^{16} -3.62965e12 q^{17} +(-1.99584e11 + 1.17330e12i) q^{18} -3.83031e11i q^{19} +(-1.72615e13 - 6.04750e12i) q^{20} -1.05984e13 q^{21} +(2.03240e12 + 3.45721e11i) q^{22} +7.19248e13i q^{23} +(-3.20282e13 - 1.77255e13i) q^{24} +2.08887e14 q^{25} +(-2.50159e13 + 1.47062e14i) q^{26} -3.96238e13i q^{27} +(1.07782e14 - 3.07644e14i) q^{28} -2.72055e14 q^{29} +(6.00310e14 + 1.02116e14i) q^{30} +3.17152e14i q^{31} +(8.40239e14 - 7.49433e14i) q^{32} -6.86367e13 q^{33} +(-6.23284e14 + 3.66413e15i) q^{34} +5.42259e15i q^{35} +(1.15017e15 + 4.02960e14i) q^{36} +1.82474e15 q^{37} +(-3.86670e14 - 6.57743e13i) q^{38} -4.96644e15i q^{39} +(-9.06909e15 + 1.63870e16i) q^{40} +7.50925e15 q^{41} +(-1.81996e15 + 1.06991e16i) q^{42} +9.17442e15i q^{43} +(6.98011e14 - 1.99234e15i) q^{44} -2.02732e16 q^{45} +(7.26080e16 + 1.23510e16i) q^{46} +7.76790e16i q^{47} +(-2.33937e16 + 2.92886e16i) q^{48} -1.68522e16 q^{49} +(3.58701e16 - 2.10871e17i) q^{50} -1.23742e17i q^{51} +(1.44163e17 + 5.05070e16i) q^{52} -5.62237e16 q^{53} +(-4.00002e16 - 6.80421e15i) q^{54} +3.51174e16i q^{55} +(-2.92058e17 - 1.61635e17i) q^{56} +1.30583e16 q^{57} +(-4.67173e16 + 2.74639e17i) q^{58} -3.58906e17i q^{59} +(2.06171e17 - 5.88477e17i) q^{60} -6.85010e17 q^{61} +(3.20165e17 + 5.44614e16i) q^{62} -3.61320e17i q^{63} +(-6.12265e17 - 9.76913e17i) q^{64} -2.54104e18 q^{65} +(-1.17863e16 + 6.92887e16i) q^{66} +1.47872e18i q^{67} +(3.59190e18 + 1.25841e18i) q^{68} -2.45206e18 q^{69} +(5.47410e18 + 9.31169e17i) q^{70} -5.13613e18i q^{71} +(6.04296e17 - 1.09190e18i) q^{72} +8.06334e17 q^{73} +(3.13345e17 - 1.84207e18i) q^{74} +7.12135e18i q^{75} +(-1.32798e17 + 3.79048e17i) q^{76} -6.25883e17 q^{77} +(-5.01362e18 - 8.52840e17i) q^{78} +1.03563e19i q^{79} +(1.49853e19 + 1.19692e19i) q^{80} +1.35085e18 q^{81} +(1.28949e18 - 7.58058e18i) q^{82} +2.51104e19i q^{83} +(1.04882e19 + 3.67450e18i) q^{84} -6.33115e19 q^{85} +(9.26157e18 + 1.57543e18i) q^{86} -9.27488e18i q^{87} +(-1.89141e18 - 1.04677e18i) q^{88} -2.22524e18 q^{89} +(-3.48132e18 + 2.04658e19i) q^{90} -4.52879e19i q^{91} +(2.49366e19 - 7.11768e19i) q^{92} -1.08123e19 q^{93} +(7.84169e19 + 1.33391e19i) q^{94} -6.68117e18i q^{95} +(2.55496e19 + 2.86454e19i) q^{96} +5.14949e19 q^{97} +(-2.89387e18 + 1.70123e19i) q^{98} -2.33996e18i 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 $

$2$	171.720	−	1009.50i	0.167696	−	0.985839i
$2$	171.720	−	1009.50i	0.167696	−	0.985839i
$3$			34092.0i			0.577350i
$3$			34092.0i			0.577350i
$4$	−989600.	−	346703.i	−0.943756	−	0.330642i
$5$	1.74429e7			1.78615			0.893075	−	0.449907i	$-0.148543\pi$
$5$	1.74429e7			1.78615			0.893075	+	0.449907i	$0.148543\pi$
$6$	3.44158e7	+	5.85428e6i	0.569174	+	0.0968191i
$7$			3.10877e8i			1.10055i	0.834985	+	0.550273i	$0.185476\pi$
$7$			3.10877e8i			1.10055i	−0.834985	+	0.550273i	$0.814524\pi$
$8$	−5.19931e8	+	9.39464e8i	−0.484223	+	0.874944i
$9$	−1.16226e9			−0.333333
$10$	2.99530e9	−	1.76086e10i	0.299530	−	1.76086i
$11$			2.01328e9i			0.0776207i	0.999247	+	0.0388103i	$0.0123568\pi$
$11$			2.01328e9i			0.0776207i	−0.999247	+	0.0388103i	$0.987643\pi$
$12$	1.18198e10	−	3.37374e10i	0.190896	−	0.544878i
$13$	−1.45678e11			−1.05672			−0.528360	−	0.849020i	$-0.677193\pi$
$13$	−1.45678e11			−1.05672			−0.528360	+	0.849020i	$0.677193\pi$
$14$	3.13830e11	+	5.33839e10i	1.08496	+	0.184557i
$15$			5.94662e11i			1.03123i
$16$	8.59106e11	+	6.86195e11i	0.781352	+	0.624091i
$17$	−3.62965e12			−1.80043			−0.900213	−	0.435450i	$-0.856589\pi$
$17$	−3.62965e12			−1.80043			−0.900213	+	0.435450i	$0.856589\pi$
$18$	−1.99584e11	+	1.17330e12i	−0.0558986	+	0.328613i
$19$		−	3.83031e11i		−	0.0624738i	−0.999512	−	0.0312369i	$-0.990055\pi$
$19$		−	3.83031e11i		−	0.0624738i	0.999512	−	0.0312369i	$-0.00994464\pi$
$20$	−1.72615e13	−	6.04750e12i	−1.68569	−	0.590576i
$21$	−1.05984e13			−0.635400
$22$	2.03240e12	+	3.45721e11i	0.0765215	+	0.0130167i
$23$			7.19248e13i			1.73620i	0.496387	+	0.868101i	$0.334660\pi$
$23$			7.19248e13i			1.73620i	−0.496387	+	0.868101i	$0.665340\pi$
$24$	−3.20282e13	−	1.77255e13i	−0.505149	−	0.279567i
$25$	2.08887e14			2.19033
$26$	−2.50159e13	+	1.47062e14i	−0.177207	+	1.04176i
$27$		−	3.96238e13i		−	0.192450i
$28$	1.07782e14	−	3.07644e14i	0.363886	−	1.03865i
$29$	−2.72055e14			−0.646660			−0.323330	−	0.946286i	$-0.604802\pi$
$29$	−2.72055e14			−0.646660			−0.323330	+	0.946286i	$0.604802\pi$
$30$	6.00310e14	+	1.02116e14i	1.01663	+	0.172934i
$31$			3.17152e14i			0.386946i	0.981106	+	0.193473i	$0.0619752\pi$
$31$			3.17152e14i			0.386946i	−0.981106	+	0.193473i	$0.938025\pi$
$32$	8.40239e14	−	7.49433e14i	0.746282	−	0.665630i
$33$	−6.86367e13			−0.0448143
$34$	−6.23284e14	+	3.66413e15i	−0.301924	+	1.77493i
$35$			5.42259e15i			1.96574i
$36$	1.15017e15	+	4.02960e14i	0.314585	+	0.110214i
$37$	1.82474e15			0.379475			0.189737	−	0.981835i	$-0.439236\pi$
$37$	1.82474e15			0.379475			0.189737	+	0.981835i	$0.439236\pi$
$38$	−3.86670e14	−	6.57743e13i	−0.0615891	−	0.0104766i
$39$		−	4.96644e15i		−	0.610098i
$40$	−9.06909e15	+	1.63870e16i	−0.864896	+	1.56278i
$41$	7.50925e15			0.559446			0.279723	−	0.960081i	$-0.409757\pi$
$41$	7.50925e15			0.559446			0.279723	+	0.960081i	$0.409757\pi$
$42$	−1.81996e15	+	1.06991e16i	−0.106554	+	0.626402i
$43$			9.17442e15i			0.424516i	0.977214	+	0.212258i	$0.0680817\pi$
$43$			9.17442e15i			0.424516i	−0.977214	+	0.212258i	$0.931918\pi$
$44$	6.98011e14	−	1.99234e15i	0.0256646	−	0.0732550i
$45$	−2.02732e16			−0.595384
$46$	7.26080e16	+	1.23510e16i	1.71162	+	0.291154i
$47$			7.76790e16i			1.47681i	0.674356	+	0.738406i	$0.264421\pi$
$47$			7.76790e16i			1.47681i	−0.674356	+	0.738406i	$0.735579\pi$
$48$	−2.33937e16	+	2.92886e16i	−0.360319	+	0.451114i
$49$	−1.68522e16			−0.211201
$50$	3.58701e16	−	2.10871e17i	0.367310	−	2.15932i
$51$		−	1.23742e17i		−	1.03948i
$52$	1.44163e17	+	5.05070e16i	0.997287	+	0.349396i
$53$	−5.62237e16			−0.321485			−0.160743	−	0.986996i	$-0.551389\pi$
$53$	−5.62237e16			−0.321485			−0.160743	+	0.986996i	$0.551389\pi$
$54$	−4.00002e16	−	6.80421e15i	−0.189725	−	0.0322730i
$55$			3.51174e16i			0.138642i
$56$	−2.92058e17	−	1.61635e17i	−0.962916	−	0.532910i
$57$	1.30583e16			0.0360693
$58$	−4.67173e16	+	2.74639e17i	−0.108442	+	0.637503i
$59$		−	3.58906e17i		−	0.702199i	−0.936338	−	0.351099i	$-0.885808\pi$
$59$		−	3.58906e17i		−	0.702199i	0.936338	−	0.351099i	$-0.114192\pi$
$60$	2.06171e17	−	5.88477e17i	0.340969	−	0.973234i
$61$	−6.85010e17			−0.960281			−0.480141	−	0.877192i	$-0.659414\pi$
$61$	−6.85010e17			−0.960281			−0.480141	+	0.877192i	$0.659414\pi$
$62$	3.20165e17	+	5.44614e16i	0.381466	+	0.0648892i
$63$		−	3.61320e17i		−	0.366849i
$64$	−6.12265e17	−	9.76913e17i	−0.531055	−	0.847337i
$65$	−2.54104e18			−1.88746
$66$	−1.17863e16	+	6.92887e16i	−0.00751517	+	0.0441797i
$67$			1.47872e18i			0.811218i	0.914047	+	0.405609i	$0.132941\pi$
$67$			1.47872e18i			0.811218i	−0.914047	+	0.405609i	$0.867059\pi$
$68$	3.59190e18	+	1.25841e18i	1.69916	+	0.595296i
$69$	−2.45206e18			−1.00240
$70$	5.47410e18	+	9.31169e17i	1.93790	+	0.329646i
$71$		−	5.13613e18i		−	1.57780i	−0.614520	−	0.788902i	$-0.710650\pi$
$71$		−	5.13613e18i		−	1.57780i	0.614520	−	0.788902i	$-0.289350\pi$
$72$	6.04296e17	−	1.09190e18i	0.161408	−	0.291648i
$73$	8.06334e17			0.187623			0.0938116	−	0.995590i	$-0.470095\pi$
$73$	8.06334e17			0.187623			0.0938116	+	0.995590i	$0.470095\pi$
$74$	3.13345e17	−	1.84207e18i	0.0636363	−	0.374101i
$75$			7.12135e18i			1.26459i
$76$	−1.32798e17	+	3.79048e17i	−0.0206565	+	0.0589601i
$77$	−6.25883e17			−0.0854251
$78$	−5.01362e18	−	8.52840e17i	−0.601458	−	0.102311i
$79$			1.03563e19i			1.09379i	0.837201	+	0.546896i	$0.184191\pi$
$79$			1.03563e19i			1.09379i	−0.837201	+	0.546896i	$0.815809\pi$
$80$	1.49853e19	+	1.19692e19i	1.39561	+	1.11472i
$81$	1.35085e18			0.111111
$82$	1.28949e18	−	7.58058e18i	0.0938167	−	0.551523i
$83$			2.51104e19i			1.61835i	0.587566	+	0.809176i	$0.300086\pi$
$83$			2.51104e19i			1.61835i	−0.587566	+	0.809176i	$0.699914\pi$
$84$	1.04882e19	+	3.67450e18i	0.599663	+	0.210090i
$85$	−6.33115e19			−3.21583
$86$	9.26157e18	+	1.57543e18i	0.418504	+	0.0711895i
$87$		−	9.27488e18i		−	0.373350i
$88$	−1.89141e18	−	1.04677e18i	−0.0679138	−	0.0375858i
$89$	−2.22524e18			−0.0713636			−0.0356818	−	0.999363i	$-0.511360\pi$
$89$	−2.22524e18			−0.0713636			−0.0356818	+	0.999363i	$0.511360\pi$
$90$	−3.48132e18	+	2.04658e19i	−0.0998432	+	0.586952i
$91$		−	4.52879e19i		−	1.16297i
$92$	2.49366e19	−	7.11768e19i	0.574061	−	1.63855i
$93$	−1.08123e19			−0.223403
$94$	7.84169e19	+	1.33391e19i	1.45590	+	0.247655i
$95$		−	6.68117e18i		−	0.111588i
$96$	2.55496e19	+	2.86454e19i	0.384302	+	0.430866i
$97$	5.14949e19			0.698308			0.349154	−	0.937065i	$-0.386469\pi$
$97$	5.14949e19			0.698308			0.349154	+	0.937065i	$0.386469\pi$
$98$	−2.89387e18	+	1.70123e19i	−0.0354175	+	0.208210i
$99$		−	2.33996e18i		−	0.0258736i
$100$	−2.06714e20	−	7.24216e19i	−2.06714	−	0.724216i
$101$	1.15679e20			1.04723			0.523613	−	0.851956i	$-0.324584\pi$
$101$	1.15679e20			1.04723			0.523613	+	0.851956i	$0.324584\pi$
$102$	−1.24917e20	−	2.12490e19i	−1.02476	−	0.174316i
$103$		−	1.68432e20i		−	1.25329i	−0.779305	−	0.626645i	$-0.784428\pi$
$103$		−	1.68432e20i		−	1.25329i	0.779305	−	0.626645i	$-0.215572\pi$
$104$	7.57424e19	−	1.36859e20i	0.511689	−	0.924572i
$105$	−1.84867e20			−1.13492
$106$	−9.65476e18	+	5.67578e19i	−0.0539117	+	0.316932i
$107$		−	5.66639e19i		−	0.288050i	−0.989574	−	0.144025i	$-0.953995\pi$
$107$		−	5.66639e19i		−	0.288050i	0.989574	−	0.144025i	$-0.0460046\pi$
$108$	−1.37377e19	+	3.92117e19i	−0.0636320	+	0.181626i
$109$	−9.31855e19			−0.393626			−0.196813	−	0.980441i	$-0.563059\pi$
$109$	−9.31855e19			−0.393626			−0.196813	+	0.980441i	$0.563059\pi$
$110$	3.54510e19	+	6.03037e18i	0.136679	+	0.0232497i
$111$			6.22089e19i			0.219090i
$112$	−2.13322e20	+	2.67076e20i	−0.686840	+	0.859914i
$113$	4.90837e20			1.44595			0.722974	−	0.690876i	$-0.242775\pi$
$113$	4.90837e20			1.44595			0.722974	+	0.690876i	$0.242775\pi$
$114$	2.24237e18	−	1.31823e19i	0.00604866	−	0.0355585i
$115$			1.25458e21i			3.10112i
$116$	2.69225e20	+	9.43222e19i	0.610290	+	0.213813i
$117$	1.69316e20			0.352240
$118$	−3.62315e20	−	6.16314e19i	−0.692255	−	0.117756i
$119$		−	1.12837e21i		−	1.98145i
$120$	−5.58664e20	−	3.09183e20i	−0.902273	−	0.499348i
$121$	6.68697e20			0.993975
$122$	−1.17630e20	+	6.91517e20i	−0.161035	+	0.946683i
$123$			2.56005e20i			0.322996i
$124$	1.09958e20	−	3.13854e20i	0.127941	−	0.365183i
$125$	1.98010e21			2.12612
$126$	−3.64752e20	−	6.20461e19i	−0.361654	−	0.0615189i
$127$		−	7.49527e20i		−	0.686673i	−0.939212	−	0.343337i	$-0.888443\pi$
$127$		−	7.49527e20i		−	0.686673i	0.939212	−	0.343337i	$-0.111557\pi$
$128$	−1.09133e21	+	4.50325e20i	−0.924393	+	0.381440i
$129$	−3.12774e20			−0.245094
$130$	−4.36349e20	+	2.56518e21i	−0.316519	+	1.86073i
$131$			7.14284e20i			0.479908i	0.970784	+	0.239954i	$0.0771323\pi$
$131$			7.14284e20i			0.479908i	−0.970784	+	0.239954i	$0.922868\pi$
$132$	6.79229e19	+	2.37965e19i	0.0422938	+	0.0148175i
$133$	1.19076e20			0.0687553
$134$	1.49277e21	+	2.53926e20i	0.799730	+	0.136038i
$135$		−	6.91152e20i		−	0.343745i
$136$	1.88717e21	−	3.40992e21i	0.871808	−	1.57527i
$137$	−2.06878e21			−0.888196			−0.444098	−	0.895978i	$-0.646476\pi$
$137$	−2.06878e21			−0.888196			−0.444098	+	0.895978i	$0.646476\pi$
$138$	−4.21068e20	+	2.47535e21i	−0.168098	+	0.988202i
$139$		−	6.85202e19i		−	0.0254490i	−0.999919	−	0.0127245i	$-0.995950\pi$
$139$		−	6.85202e19i		−	0.0254490i	0.999919	−	0.0127245i	$-0.00405044\pi$
$140$	1.88003e21	−	5.36619e21i	0.649956	−	1.85518i
$141$	−2.64823e21			−0.852638
$142$	−5.18492e21	−	8.81979e20i	−1.55546	−	0.264591i
$143$		−	2.93291e20i		−	0.0820234i
$144$	−9.98505e20	−	7.97538e20i	−0.260451	−	0.208030i
$145$	−4.74542e21			−1.15503
$146$	1.38464e20	−	8.13994e20i	0.0314636	−	0.184966i
$147$		−	5.74525e20i		−	0.121937i
$148$	−1.80576e21	−	6.32642e20i	−0.358132	−	0.125470i
$149$	4.50924e21			0.836066			0.418033	−	0.908432i	$-0.362720\pi$
$149$	4.50924e21			0.836066			0.418033	+	0.908432i	$0.362720\pi$
$150$	7.18900e21	+	1.22288e21i	1.24668	+	0.212066i
$151$		−	3.93665e21i		−	0.638789i	−0.947622	−	0.319394i	$-0.896521\pi$
$151$		−	3.93665e21i		−	0.638789i	0.947622	−	0.319394i	$-0.103479\pi$
$152$	3.59844e20	+	1.99150e20i	0.0546611	+	0.0302513i
$153$	4.21860e21			0.600142
$154$	−1.07477e20	+	6.31828e20i	−0.0143254	+	0.0842154i
$155$			5.53204e21i			0.691144i
$156$	−1.72188e21	+	4.91479e21i	−0.201724	+	0.575784i
$157$	−4.26006e21			−0.468187			−0.234093	−	0.972214i	$-0.575212\pi$
$157$	−4.26006e21			−0.468187			−0.234093	+	0.972214i	$0.575212\pi$
$158$	1.04547e22	+	1.77839e21i	1.07830	+	0.183424i
$159$		−	1.91678e21i		−	0.185609i
$160$	1.46562e22	−	1.30723e22i	1.33297	−	1.18892i
$161$	−2.23598e22			−1.91077
$162$	2.31969e20	−	1.36368e21i	0.0186329	−	0.109538i
$163$			7.87686e21i			0.594945i	0.954730	+	0.297473i	$0.0961437\pi$
$163$			7.87686e21i			0.594945i	−0.954730	+	0.297473i	$0.903856\pi$
$164$	−7.43116e21	−	2.60348e21i	−0.527981	−	0.184976i
$165$	−1.19722e21			−0.0800451
$166$	2.53489e22	+	4.31197e21i	1.59543	+	0.271391i
$167$			8.60648e20i			0.0510106i	0.999675	+	0.0255053i	$0.00811948\pi$
$167$			8.60648e20i			0.0510106i	−0.999675	+	0.0255053i	$0.991881\pi$
$168$	5.51044e21	−	9.95682e21i	0.307676	−	0.555940i
$169$	2.21708e21			0.116658
$170$	−1.08719e22	+	6.39129e22i	−0.539281	+	3.17029i
$171$			4.45182e20i			0.0208246i
$172$	3.18080e21	−	9.07901e21i	0.140363	−	0.400640i
$173$	−3.41737e22			−1.42309			−0.711543	−	0.702642i	$-0.752003\pi$
$173$	−3.41737e22			−1.42309			−0.711543	+	0.702642i	$0.752003\pi$
$174$	−9.36298e21	−	1.59269e21i	−0.368062	−	0.0626091i
$175$			6.49380e22i			2.41056i
$176$	−1.38150e21	+	1.72962e21i	−0.0484423	+	0.0606491i
$177$	1.22358e22			0.405415
$178$	−3.82119e20	+	2.24638e21i	−0.0119674	+	0.0703530i
$179$		−	6.28141e22i		−	1.86006i	−0.367484	−	0.930030i	$-0.619781\pi$
$179$		−	6.28141e22i		−	1.86006i	0.367484	−	0.930030i	$-0.380219\pi$
$180$	2.00623e22	+	7.02878e21i	0.561897	+	0.196859i
$181$	5.40065e22			1.43107			0.715534	−	0.698578i	$-0.246183\pi$
$181$	5.40065e22			1.43107			0.715534	+	0.698578i	$0.246183\pi$
$182$	−4.57181e22	−	7.77685e21i	−1.14650	−	0.195025i
$183$		−	2.33533e22i		−	0.554419i
$184$	−6.75708e22	−	3.73959e22i	−1.51908	−	0.840710i
$185$	3.18287e22			0.677799
$186$	−1.85670e21	+	1.09150e22i	−0.0374638	+	0.220240i
$187$		−	7.30750e21i		−	0.139750i
$188$	2.69316e22	−	7.68712e22i	0.488296	−	1.39375i
$189$	1.23181e22			0.211800
$190$	−6.74463e21	−	1.14729e21i	−0.110007	−	0.0187128i
$191$			4.95680e22i			0.767128i	0.923514	+	0.383564i	$0.125303\pi$
$191$			4.95680e22i			0.767128i	−0.923514	+	0.383564i	$0.874697\pi$
$192$	3.33049e22	−	2.08733e22i	0.489210	−	0.306605i
$193$	3.17658e22			0.442982			0.221491	−	0.975162i	$-0.428908\pi$
$193$	3.17658e22			0.442982			0.221491	+	0.975162i	$0.428908\pi$
$194$	8.84273e21	−	5.19841e22i	0.117103	−	0.688419i
$195$		−	8.66291e22i		−	1.08973i
$196$	1.66769e22	+	5.84271e21i	0.199322	+	0.0698319i
$197$	−2.47988e22			−0.281688			−0.140844	−	0.990032i	$-0.544982\pi$
$197$	−2.47988e22			−0.281688			−0.140844	+	0.990032i	$0.544982\pi$
$198$	−2.36219e21	−	4.01819e20i	−0.0255072	−	0.00433888i
$199$		−	1.45412e22i		−	0.149303i	−0.997210	−	0.0746517i	$-0.976215\pi$
$199$		−	1.45412e22i		−	0.149303i	0.997210	−	0.0746517i	$-0.0237845\pi$
$200$	−1.08607e23	+	1.96241e23i	−1.06061	+	1.91642i
$201$	−5.04124e22			−0.468357
$202$	1.98644e22	−	1.16778e23i	0.175615	−	1.03240i
$203$		−	8.45755e22i		−	0.711679i
$204$	−4.29017e22	+	1.22455e23i	−0.343694	+	0.981012i
$205$	1.30983e23			0.999255
$206$	−1.70032e23	−	2.89231e22i	−1.23554	−	0.210171i
$207$		−	8.35954e22i		−	0.578734i
$208$	−1.25153e23	−	9.99634e22i	−0.825671	−	0.659489i
$209$	7.71149e20			0.00484926
$210$	−3.17454e22	+	1.86623e23i	−0.190321	+	1.11885i
$211$			1.43049e23i			0.817825i	0.912574	+	0.408913i	$0.134092\pi$
$211$			1.43049e23i			0.817825i	−0.912574	+	0.408913i	$0.865908\pi$
$212$	5.56390e22	+	1.94929e22i	0.303404	+	0.106296i
$213$	1.75101e23			0.910945
$214$	−5.72021e22	−	9.73034e21i	−0.283971	−	0.0483048i
$215$			1.60028e23i			0.758249i
$216$	3.72251e22	+	2.06016e22i	0.168383	+	0.0931888i
$217$	−9.85952e22			−0.425852
$218$	−1.60019e22	+	9.40707e22i	−0.0660093	+	0.388052i
$219$			2.74895e22i			0.108324i
$220$	1.21753e22	−	3.47522e22i	0.0458409	−	0.130844i
$221$	5.28759e23			1.90255
$222$	6.27998e22	+	1.06825e22i	0.215987	+	0.0367404i
$223$			3.50170e23i			1.15141i	0.817657	+	0.575706i	$0.195273\pi$
$223$			3.50170e23i			1.15141i	−0.817657	+	0.575706i	$0.804727\pi$
$224$	2.32981e23	+	2.61211e23i	0.732556	+	0.821318i
$225$	−2.42781e23			−0.730111
$226$	8.42867e22	−	4.95499e23i	0.242479	−	1.42547i
$227$		−	4.89500e23i		−	1.34739i	−0.739008	−	0.673697i	$-0.764706\pi$
$227$		−	4.89500e23i		−	1.34739i	0.739008	−	0.673697i	$-0.235294\pi$
$228$	−1.29225e22	−	4.52735e21i	−0.0340406	−	0.0119260i
$229$	−5.15014e23			−1.29857			−0.649283	−	0.760547i	$-0.724931\pi$
$229$	−5.15014e23			−1.29857			−0.649283	+	0.760547i	$0.724931\pi$
$230$	1.26649e24	+	2.15436e23i	3.05720	+	0.520044i
$231$		−	2.13376e22i		−	0.0493202i
$232$	1.41450e23	−	2.55586e23i	0.313128	−	0.565792i
$233$	−5.33275e23			−1.13082			−0.565408	−	0.824811i	$-0.691281\pi$
$233$	−5.33275e23			−1.13082			−0.565408	+	0.824811i	$0.691281\pi$
$234$	2.90750e22	−	1.70924e23i	0.0590692	−	0.347252i
$235$			1.35495e24i			2.63781i
$236$	−1.24434e23	+	3.55173e23i	−0.232176	+	0.662705i
$237$	−3.53067e23			−0.631501
$238$	−1.13909e24	−	1.93765e23i	−1.95339	−	0.332281i
$239$		−	1.18302e24i		−	1.94541i	−0.232041	−	0.972706i	$-0.574540\pi$
$239$		−	1.18302e24i		−	1.94541i	0.232041	−	0.972706i	$-0.425460\pi$
$240$	−4.08054e23	+	5.10877e23i	−0.643584	+	0.805757i
$241$	3.21503e23			0.486423			0.243212	−	0.969973i	$-0.421799\pi$
$241$	3.21503e23			0.486423			0.243212	+	0.969973i	$0.421799\pi$
$242$	1.14829e23	−	6.75049e23i	0.166685	−	0.979899i
$243$			4.60532e22i			0.0641500i
$244$	6.77886e23	+	2.37495e23i	0.906272	+	0.317509i
$245$	−2.93951e23			−0.377237
$246$	2.58437e23	+	4.39613e22i	0.318422	+	0.0541651i
$247$			5.57992e22i			0.0660174i
$248$	−2.97953e23	−	1.64897e23i	−0.338556	−	0.187368i
$249$	−8.56063e23			−0.934356
$250$	3.40023e23	−	1.99891e24i	0.356540	−	2.09601i
$251$		−	2.57752e23i		−	0.259696i	−0.991534	−	0.129848i	$-0.958551\pi$
$251$		−	2.57752e23i		−	0.259696i	0.991534	−	0.129848i	$-0.0414489\pi$
$252$	−1.25271e23	+	3.57563e23i	−0.121295	+	0.346216i
$253$	−1.44805e23			−0.134765
$254$	−7.56647e23	−	1.28709e23i	−0.676949	−	0.115152i
$255$		−	2.15841e24i		−	1.85666i
$256$	2.67199e23	+	1.17903e24i	0.221022	+	0.975269i
$257$	−2.53621e23			−0.201769			−0.100884	−	0.994898i	$-0.532167\pi$
$257$	−2.53621e23			−0.201769			−0.100884	+	0.994898i	$0.532167\pi$
$258$	−5.37097e22	+	3.15745e23i	−0.0411013	+	0.241624i
$259$			5.67269e23i			0.417630i
$260$	2.51462e24	+	8.80987e23i	1.78130	+	0.624074i
$261$	3.16199e23			0.215553
$262$	7.21069e23	+	1.22657e23i	0.473112	+	0.0804785i
$263$			8.51858e23i			0.538034i	0.963135	+	0.269017i	$0.0866988\pi$
$263$			8.51858e23i			0.538034i	−0.963135	+	0.269017i	$0.913301\pi$
$264$	3.56863e22	−	6.44817e22i	0.0217001	−	0.0392100i
$265$	−9.80703e23			−0.574221
$266$	2.04477e22	−	1.20207e23i	0.0115300	−	0.0677817i
$267$		−	7.58628e22i		−	0.0412018i
$268$	5.12677e23	−	1.46334e24i	0.268223	−	0.765592i
$269$	6.89764e23			0.347679			0.173839	−	0.984774i	$-0.444383\pi$
$269$	6.89764e23			0.347679			0.173839	+	0.984774i	$0.444383\pi$
$270$	−6.97718e23	−	1.18685e23i	−0.338877	−	0.0576445i
$271$			1.73834e24i			0.813658i	0.913504	+	0.406829i	$0.133366\pi$
$271$			1.73834e24i			0.813658i	−0.913504	+	0.406829i	$0.866634\pi$
$272$	−3.11825e24	−	2.49065e24i	−1.40677	−	1.12363i
$273$	1.54395e24			0.671441
$274$	−3.55252e23	+	2.08843e24i	−0.148947	+	0.875618i
$275$			4.20547e23i			0.170015i
$276$	2.42656e24	+	8.50136e23i	0.946019	+	0.331434i
$277$	9.20295e23			0.346043			0.173021	−	0.984918i	$-0.444647\pi$
$277$	9.20295e23			0.346043			0.173021	+	0.984918i	$0.444647\pi$
$278$	−6.91710e22	−	1.17663e22i	−0.0250886	−	0.00426768i
$279$		−	3.68613e23i		−	0.128982i
$280$	−5.09433e24	−	2.81937e24i	−1.71991	−	0.951858i
$281$	4.38288e24			1.42789			0.713947	−	0.700200i	$-0.246906\pi$
$281$	4.38288e24			1.42789			0.713947	+	0.700200i	$0.246906\pi$
$282$	−4.54755e23	+	2.67339e24i	−0.142984	+	0.840563i
$283$			2.59800e24i			0.788450i	0.919014	+	0.394225i	$0.128987\pi$
$283$			2.59800e24i			0.788450i	−0.919014	+	0.394225i	$0.871013\pi$
$284$	−1.78071e24	+	5.08272e24i	−0.521688	+	1.48906i
$285$	2.27774e23			0.0644252
$286$	−2.96076e23	−	5.03640e22i	−0.0808618	−	0.0137550i
$287$			2.33445e24i			0.615696i
$288$	−9.76577e23	+	8.71037e23i	−0.248761	+	0.221877i
$289$	9.11011e24			2.24153
$290$	−8.14885e23	+	4.79049e24i	−0.193694	+	1.13868i
$291$			1.75556e24i			0.403168i
$292$	−7.97949e23	−	2.79559e23i	−0.177071	−	0.0620361i
$293$	−5.30536e24			−1.13773			−0.568865	−	0.822431i	$-0.692617\pi$
$293$	−5.30536e24			−1.13773			−0.568865	+	0.822431i	$0.692617\pi$
$294$	−5.79982e23	−	9.86576e22i	−0.120210	−	0.0204483i
$295$		−	6.26035e24i		−	1.25423i
$296$	−9.48737e23	+	1.71428e24i	−0.183751	+	0.332019i
$297$	7.97738e22			0.0149381
$298$	7.74328e23	−	4.55207e24i	0.140205	−	0.824226i
$299$		−	1.04779e25i		−	1.83468i
$300$	2.46899e24	−	7.04729e24i	0.418126	−	1.19346i
$301$	−2.85212e24			−0.467199
$302$	−3.97404e24	−	6.76003e23i	−0.629743	−	0.107122i
$303$			3.94372e24i			0.604616i
$304$	2.62834e23	−	3.29064e23i	0.0389893	−	0.0488141i
$305$	−1.19485e25			−1.71521
$306$	7.24419e23	−	4.25867e24i	0.100641	−	0.591643i
$307$		−	4.37133e24i		−	0.587800i	−0.955836	−	0.293900i	$-0.905047\pi$
$307$		−	4.37133e24i		−	0.587800i	0.955836	−	0.293900i	$-0.0949533\pi$
$308$	6.19374e23	+	2.16995e23i	0.0806205	+	0.0282451i
$309$	5.74216e24			0.723587
$310$	5.58459e24	+	9.49964e23i	0.681356	+	0.115902i
$311$			6.69500e24i			0.790945i	0.918478	+	0.395473i	$0.129419\pi$
$311$			6.69500e24i			0.790945i	−0.918478	+	0.395473i	$0.870581\pi$
$312$	4.66580e24	+	2.58221e24i	0.533802	+	0.295424i
$313$	6.38230e24			0.707187			0.353593	−	0.935399i	$-0.384960\pi$
$313$	6.38230e24			0.707187			0.353593	+	0.935399i	$0.384960\pi$
$314$	−7.31539e23	+	4.30053e24i	−0.0785129	+	0.461557i
$315$		−	6.30247e24i		−	0.655247i
$316$	3.59057e24	−	1.02486e25i	0.361653	−	1.03227i
$317$	1.76008e25			1.71767			0.858837	−	0.512248i	$-0.171187\pi$
$317$	1.76008e25			1.71767			0.858837	+	0.512248i	$0.171187\pi$
$318$	−1.93498e24	−	3.29150e23i	−0.182981	−	0.0311259i
$319$		−	5.47722e23i		−	0.0501942i
$320$	−1.06797e25	−	1.70402e25i	−0.948545	−	1.51347i
$321$	1.93178e24			0.166306
$322$	−3.83963e24	+	2.25722e25i	−0.320428	+	1.88371i
$323$			1.39027e24i			0.112479i
$324$	−1.33680e24	−	4.68344e23i	−0.104862	−	0.0367380i
$325$	−3.04301e25			−2.31457
$326$	7.95168e24	+	1.35262e24i	0.586520	+	0.0997697i
$327$		−	3.17688e24i		−	0.227260i
$328$	−3.90429e24	+	7.05467e24i	−0.270897	+	0.489484i
$329$	−2.41486e25			−1.62530
$330$	−2.05587e23	+	1.20859e24i	−0.0134232	+	0.0789116i
$331$		−	5.52807e24i		−	0.350182i	−0.984552	−	0.175091i	$-0.943978\pi$
$331$		−	5.52807e24i		−	0.350182i	0.984552	−	0.175091i	$-0.0560220\pi$
$332$	8.70586e24	−	2.48493e25i	0.535095	−	1.52733i
$333$	−2.12082e24			−0.126492
$334$	8.68823e23	+	1.47791e23i	0.0502883	+	0.00855427i
$335$			2.57931e25i			1.44896i
$336$	−9.10515e24	−	7.27257e24i	−0.496471	−	0.396547i
$337$	1.25347e25			0.663460			0.331730	−	0.943374i	$-0.392368\pi$
$337$	1.25347e25			0.663460			0.331730	+	0.943374i	$0.392368\pi$
$338$	3.80718e23	−	2.23814e24i	0.0195631	−	0.115006i
$339$			1.67336e25i			0.834818i
$340$	6.26531e25	+	2.19503e25i	3.03496	+	1.06329i
$341$	−6.38516e23			−0.0300350
$342$	4.49411e23	+	7.64469e22i	0.0205297	+	0.00349220i
$343$			1.95666e25i			0.868109i
$344$	−8.61904e24	−	4.77006e24i	−0.371428	−	0.205561i
$345$	−4.27709e25			−1.79043
$346$	−5.86832e24	+	3.44983e25i	−0.238645	+	1.40293i
$347$			2.15912e25i			0.853066i	0.904472	+	0.426533i	$0.140265\pi$
$347$			2.15912e25i			0.853066i	−0.904472	+	0.426533i	$0.859735\pi$
$348$	−3.21563e24	+	9.17842e24i	−0.123445	+	0.352351i
$349$	−2.47464e25			−0.923118			−0.461559	−	0.887109i	$-0.652710\pi$
$349$	−2.47464e25			−0.923118			−0.461559	+	0.887109i	$0.652710\pi$
$350$	6.55548e25	+	1.11512e25i	2.37643	+	0.404241i
$351$			5.77231e24i			0.203366i
$352$	1.50882e24	+	1.69164e24i	0.0516666	+	0.0579269i
$353$	3.48790e25			1.16096			0.580480	−	0.814274i	$-0.302865\pi$
$353$	3.48790e25			1.16096			0.580480	+	0.814274i	$0.302865\pi$
$354$	2.10113e24	−	1.23520e25i	0.0679863	−	0.399674i
$355$		−	8.95889e25i		−	2.81819i
$356$	2.20210e24	+	7.71498e23i	0.0673499	+	0.0235958i
$357$	3.84685e25			1.14399
$358$	−6.34108e25	−	1.07865e25i	−1.83372	−	0.311924i
$359$		−	2.09341e25i		−	0.588722i	−0.955694	−	0.294361i	$-0.904893\pi$
$359$		−	2.09341e25i		−	0.588722i	0.955694	−	0.294361i	$-0.0951069\pi$
$360$	1.05407e25	−	1.90459e25i	0.288299	−	0.520927i
$361$	3.74433e25			0.996097
$362$	9.27402e24	−	5.45195e25i	0.239984	−	1.41080i
$363$			2.27972e25i			0.573872i
$364$	−1.57015e25	+	4.48169e25i	−0.384526	+	1.09756i
$365$	1.40648e25			0.335123
$366$	−2.35752e25	−	4.01024e24i	−0.546567	−	0.0929736i
$367$		−	2.73855e25i		−	0.617817i	−0.951092	−	0.308908i	$-0.900036\pi$
$367$		−	2.73855e25i		−	0.617817i	0.951092	−	0.308908i	$-0.0999637\pi$
$368$	−4.93544e25	+	6.17910e25i	−1.08355	+	1.35659i
$369$	−8.72771e24			−0.186482
$370$	5.46563e24	−	3.21310e25i	0.113664	−	0.668201i
$371$		−	1.74787e25i		−	0.353809i
$372$	1.06999e25	+	3.74867e24i	0.210838	+	0.0738665i
$373$	−8.31955e25			−1.59592			−0.797961	−	0.602709i	$-0.794088\pi$
$373$	−8.31955e25			−1.59592			−0.797961	+	0.602709i	$0.794088\pi$
$374$	−7.37691e24	−	1.25485e24i	−0.137771	−	0.0234355i
$375$			6.75055e25i			1.22751i
$376$	−7.29767e25	−	4.03877e25i	−1.29213	−	0.715107i
$377$	3.96323e25			0.683339
$378$	2.11527e24	−	1.24351e25i	0.0355180	−	0.208801i
$379$			1.02773e26i			1.68069i	0.542054	+	0.840344i	$0.317647\pi$
$379$			1.02773e26i			1.68069i	−0.542054	+	0.840344i	$0.682353\pi$
$380$	−2.31638e24	+	6.61168e24i	−0.0368956	+	0.105312i
$381$	2.55529e25			0.396451
$382$	5.00389e25	+	8.51184e24i	0.756265	+	0.128644i
$383$		−	8.26584e25i		−	1.21702i	−0.793545	−	0.608512i	$-0.791767\pi$
$383$		−	8.26584e25i		−	1.21702i	0.793545	−	0.608512i	$-0.208233\pi$
$384$	−1.53525e25	−	3.72056e25i	−0.220225	−	0.533699i
$385$	−1.09172e25			−0.152582
$386$	5.45483e24	−	3.20675e25i	0.0742863	−	0.436709i
$387$		−	1.06631e25i		−	0.141505i
$388$	−5.09594e25	−	1.78534e25i	−0.659032	−	0.230890i
$389$	3.32287e25			0.418811			0.209405	−	0.977829i	$-0.432847\pi$
$389$	3.32287e25			0.418811			0.209405	+	0.977829i	$0.432847\pi$
$390$	−8.74520e25	−	1.48760e25i	−1.07429	−	0.182742i
$391$		−	2.61062e26i		−	3.12590i
$392$	8.76198e24	−	1.58320e25i	0.102268	−	0.184789i
$393$	−2.43513e25			−0.277075
$394$	−4.25845e24	+	2.50343e25i	−0.0472378	+	0.277699i
$395$			1.80644e26i			1.95368i
$396$	−8.11271e23	+	2.31562e24i	−0.00855488	+	0.0244183i
$397$	9.57914e25			0.984966			0.492483	−	0.870322i	$-0.336089\pi$
$397$	9.57914e25			0.984966			0.492483	+	0.870322i	$0.336089\pi$
$398$	−1.46793e25	−	2.49702e24i	−0.147189	−	0.0250375i
$399$			4.05952e24i			0.0396959i
$400$	1.79456e26	+	1.43337e26i	1.71142	+	1.36697i
$401$	7.24475e25			0.673876			0.336938	−	0.941527i	$-0.390609\pi$
$401$	7.24475e25			0.673876			0.336938	+	0.941527i	$0.390609\pi$
$402$	−8.65684e24	+	5.08913e25i	−0.0785415	+	0.461725i
$403$		−	4.62020e25i		−	0.408894i
$404$	−1.14476e26	−	4.01062e25i	−0.988326	−	0.346257i
$405$	2.35627e25			0.198461
$406$	−8.53789e25	−	1.45233e25i	−0.701601	−	0.119346i
$407$			3.67371e24i			0.0294551i
$408$	1.16251e26	+	6.43372e25i	0.909484	+	0.503339i
$409$	1.98324e26			1.51406			0.757029	−	0.653381i	$-0.226650\pi$
$409$	1.98324e26			1.51406			0.757029	+	0.653381i	$0.226650\pi$
$410$	2.24924e25	−	1.32227e26i	0.167571	−	0.985104i
$411$		−	7.05288e25i		−	0.512800i
$412$	−5.83958e25	+	1.66680e26i	−0.414390	+	1.18280i
$413$	1.11575e26			0.772802
$414$	−8.43895e25	−	1.43550e25i	−0.570539	−	0.0970512i
$415$			4.37998e26i			2.89062i
$416$	−1.22404e26	+	1.09176e26i	−0.788612	+	0.703385i
$417$	2.33599e24			0.0146930
$418$	1.32422e23	−	7.78474e23i	0.000813200	−	0.00478059i
$419$		−	5.23334e25i		−	0.313790i	−0.987615	−	0.156895i	$-0.949852\pi$
$419$		−	5.23334e25i		−	0.313790i	0.987615	−	0.156895i	$-0.0501484\pi$
$420$	1.82944e26	+	6.40938e25i	1.07109	+	0.375252i
$421$	−1.49357e26			−0.853894			−0.426947	−	0.904277i	$-0.640411\pi$
$421$	−1.49357e26			−0.853894			−0.426947	+	0.904277i	$0.640411\pi$
$422$	1.44408e26	+	2.45644e25i	0.806244	+	0.137146i
$423$		−	9.02833e25i		−	0.492271i
$424$	2.92324e25	−	5.28202e25i	0.155671	−	0.281282i
$425$	−7.58184e26			−3.94353
$426$	3.00684e25	−	1.76764e26i	0.152762	−	0.898045i
$427$		−	2.12954e26i		−	1.05683i
$428$	−1.96455e25	+	5.60746e25i	−0.0952415	+	0.271849i
$429$	9.99885e24			0.0473562
$430$	1.61548e26	+	2.74801e25i	0.747512	+	0.127155i
$431$			3.56809e26i			1.61311i	0.591160	+	0.806554i	$0.298670\pi$
$431$			3.56809e26i			1.61311i	−0.591160	+	0.806554i	$0.701330\pi$
$432$	2.71896e25	−	3.40410e25i	0.120106	−	0.150371i
$433$	−7.71851e25			−0.333161			−0.166581	−	0.986028i	$-0.553273\pi$
$433$	−7.71851e25			−0.333161			−0.166581	+	0.986028i	$0.553273\pi$
$434$	−1.69308e25	+	9.95318e25i	−0.0714135	+	0.419821i
$435$		−	1.61781e26i		−	0.666858i
$436$	9.22164e25	+	3.23077e25i	0.371487	+	0.130149i
$437$	2.75494e25			0.108467
$438$	2.77506e25	+	4.72051e24i	0.106790	+	0.0181655i
$439$			1.97754e26i			0.743841i	0.928264	+	0.371921i	$0.121301\pi$
$439$			1.97754e26i			0.743841i	−0.928264	+	0.371921i	$0.878699\pi$
$440$	−3.29916e25	−	1.82586e25i	−0.121304	−	0.0671338i
$441$	1.95867e25			0.0704003
$442$	9.07988e25	−	5.33782e26i	0.319049	−	1.87560i
$443$		−	2.12289e26i		−	0.729273i	−0.931150	−	0.364636i	$-0.881193\pi$
$443$		−	2.12289e26i		−	0.729273i	0.931150	−	0.364636i	$-0.118807\pi$
$444$	2.15680e25	−	6.15619e25i	0.0724403	−	0.206768i
$445$	−3.88146e25			−0.127466
$446$	3.53497e26	+	6.01314e25i	1.13511	+	0.193087i
$447$			1.53729e26i			0.482703i
$448$	3.03700e26	−	1.90339e26i	0.932533	−	0.584451i
$449$	4.10517e24			0.0123273			0.00616364	−	0.999981i	$-0.498038\pi$
$449$	4.10517e24			0.0123273			0.00616364	+	0.999981i	$0.498038\pi$
$450$	−4.16904e25	+	2.45087e26i	−0.122437	+	0.719772i
$451$			1.51182e25i			0.0434246i
$452$	−4.85732e26	−	1.70175e26i	−1.36462	−	0.478091i
$453$	1.34208e26			0.368805
$454$	−4.94150e26	−	8.40572e25i	−1.32831	−	0.225952i
$455$		−	7.89951e26i		−	2.07724i
$456$	−6.78941e24	+	1.22678e25i	−0.0174656	+	0.0315586i
$457$	1.93320e26			0.486537			0.243268	−	0.969959i	$-0.421780\pi$
$457$	1.93320e26			0.486537			0.243268	+	0.969959i	$0.421780\pi$
$458$	−8.84384e25	+	5.19906e26i	−0.217764	+	1.28018i
$459$			1.43820e26i			0.346492i
$460$	4.34965e26	−	1.24153e27i	1.02536	−	2.92670i
$461$	−1.78975e26			−0.412840			−0.206420	−	0.978463i	$-0.566181\pi$
$461$	−1.78975e26			−0.412840			−0.206420	+	0.978463i	$0.566181\pi$
$462$	−2.15402e25	−	3.66409e24i	−0.0486218	−	0.00827079i
$463$			4.78519e26i			1.05704i	0.848922	+	0.528518i	$0.177252\pi$
$463$			4.78519e26i			1.05704i	−0.848922	+	0.528518i	$0.822748\pi$
$464$	−2.33724e26	−	1.86683e26i	−0.505269	−	0.403575i
$465$	−1.88598e26			−0.399032
$466$	−9.15742e25	+	5.38341e26i	−0.189633	+	1.11480i
$467$		−	6.84335e26i		−	1.38707i	−0.720421	−	0.693537i	$-0.756051\pi$
$467$		−	6.84335e26i		−	1.38707i	0.720421	−	0.693537i	$-0.243949\pi$
$468$	−1.67555e26	−	5.87023e25i	−0.332429	−	0.116465i
$469$	−4.59700e26			−0.892783
$470$	1.36782e27	+	2.32672e26i	2.60045	+	0.442349i
$471$		−	1.45234e26i		−	0.270308i
$472$	3.37179e26	+	1.86606e26i	0.614385	+	0.340021i
$473$	−1.84707e25			−0.0329512
$474$	−6.06288e25	+	3.56421e26i	−0.105900	+	0.622558i
$475$		−	8.00101e25i		−	0.136839i
$476$	−3.91211e26	+	1.11664e27i	−0.655151	+	1.87001i
$477$	6.53467e25			0.107162
$478$	−1.19425e27	−	2.03148e26i	−1.91786	−	0.326237i
$479$			1.10396e27i			1.73620i	0.496391	+	0.868099i	$0.334658\pi$
$479$			1.10396e27i			1.73620i	−0.496391	+	0.868099i	$0.665342\pi$
$480$	4.45659e26	+	4.99658e26i	0.686420	+	0.769592i
$481$	−2.65824e26			−0.400999
$482$	5.52086e25	−	3.24557e26i	0.0815710	−	0.479535i
$483$		−	7.62288e26i		−	1.10318i
$484$	−6.61742e26	−	2.31839e26i	−0.938070	−	0.328650i
$485$	8.98219e26			1.24728
$486$	4.64906e25	+	7.90827e24i	0.0632416	+	0.0107577i
$487$			1.06556e27i			1.42001i	0.704199	+	0.710003i	$0.251306\pi$
$487$			1.06556e27i			1.42001i	−0.704199	+	0.710003i	$0.748694\pi$
$488$	3.56158e26	−	6.43542e26i	0.464991	−	0.840193i
$489$	−2.68538e26			−0.343492
$490$	−5.04774e25	+	2.96743e26i	−0.0632610	+	0.371895i
$491$			2.90214e26i			0.356372i	0.983997	+	0.178186i	$0.0570229\pi$
$491$			2.90214e26i			0.356372i	−0.983997	+	0.178186i	$0.942977\pi$
$492$	8.87578e25	−	2.53343e26i	0.106796	−	0.304830i
$493$	9.87462e26			1.16426
$494$	5.63292e25	+	9.58186e24i	0.0650825	+	0.0110708i
$495$		−	4.08156e25i		−	0.0462141i
$496$	−2.17628e26	+	2.72467e26i	−0.241489	+	0.302341i
$497$	1.59671e27			1.73644
$498$	−1.47004e26	+	8.64195e26i	−0.156687	+	0.921124i
$499$		−	1.96001e26i		−	0.204763i	−0.994745	−	0.102382i	$-0.967354\pi$
$499$		−	1.96001e26i		−	0.204763i	0.994745	−	0.102382i	$-0.0326463\pi$
$500$	−1.95951e27	−	6.86507e26i	−2.00653	−	0.702983i
$501$	−2.93412e25			−0.0294510
$502$	−2.60200e26	−	4.42613e25i	−0.256018	−	0.0435498i
$503$			7.65090e26i			0.737960i	0.929437	+	0.368980i	$0.120293\pi$
$503$			7.65090e26i			0.737960i	−0.929437	+	0.368980i	$0.879707\pi$
$504$	3.39448e26	+	1.87862e26i	0.320972	+	0.177637i
$505$	2.01777e27			1.87050
$506$	−2.48659e25	+	1.46180e26i	−0.0225996	+	0.132857i
$507$			7.55847e25i			0.0673526i
$508$	−2.59863e26	+	7.41732e26i	−0.227043	+	0.648052i
$509$	−1.02771e27			−0.880422			−0.440211	−	0.897894i	$-0.645096\pi$
$509$	−1.02771e27			−0.880422			−0.440211	+	0.897894i	$0.645096\pi$
$510$	−2.17892e27	−	3.70643e26i	−1.83037	−	0.311354i
$511$			2.50671e26i			0.206488i
$512$	1.23611e27	−	6.72740e25i	0.998522	−	0.0543435i
$513$	−1.51771e25			−0.0120231
$514$	−4.35519e25	+	2.56030e26i	−0.0338357	+	0.198911i
$515$		−	2.93793e27i		−	2.23856i
$516$	3.09521e26	+	1.08440e26i	0.231309	+	0.0810385i
$517$	−1.56390e26			−0.114631
$518$	5.72657e26	+	9.74116e25i	0.411715	+	0.0700347i
$519$		−	1.16505e27i		−	0.821619i
$520$	1.32117e27	−	2.38722e27i	0.913953	−	1.65142i
$521$	1.91488e27			1.29946			0.649732	−	0.760164i	$-0.274881\pi$
$521$	1.91488e27			1.29946			0.649732	+	0.760164i	$0.274881\pi$
$522$	5.42978e25	−	3.19202e26i	0.0361474	−	0.212501i
$523$			2.13379e27i			1.39359i	0.717272	+	0.696793i	$0.245390\pi$
$523$			2.13379e27i			1.39359i	−0.717272	+	0.696793i	$0.754610\pi$
$524$	2.47644e26	−	7.06855e26i	0.158678	−	0.452916i
$525$	−2.21386e27			−1.39174
$526$	8.59950e26	+	1.46281e26i	0.530415	+	0.0902260i
$527$		−	1.15115e27i		−	0.696668i
$528$	−5.89662e25	−	4.70981e25i	−0.0350158	−	0.0279682i
$529$	−3.45702e27			−2.01440
$530$	−1.68407e26	+	9.90019e26i	−0.0962943	+	0.566089i
$531$			4.17142e26i			0.234066i
$532$	−1.17837e26	−	4.12839e25i	−0.0648883	−	0.0227334i
$533$	−1.09393e27			−0.591178
$534$	−7.65834e25	−	1.30272e25i	−0.0406183	−	0.00690936i
$535$		−	9.88381e26i		−	0.514501i
$536$	−1.38920e27	−	7.68832e26i	−0.709771	−	0.392811i
$537$	2.14146e27			1.07391
$538$	1.18447e26	−	6.96316e26i	0.0583042	−	0.342755i
$539$		−	3.39282e25i		−	0.0163936i
$540$	−2.39625e26	+	6.83965e26i	−0.113656	+	0.324411i
$541$	−6.92691e26			−0.322527			−0.161264	−	0.986911i	$-0.551557\pi$
$541$	−6.92691e26			−0.322527			−0.161264	+	0.986911i	$0.551557\pi$
$542$	1.75485e27	+	2.98508e26i	0.802136	+	0.136447i
$543$			1.84119e27i			0.826228i
$544$	−3.04977e27	+	2.72018e27i	−1.34363	+	1.19842i
$545$	−1.62542e27			−0.703075
$546$	2.65128e26	−	1.55862e27i	0.112598	−	0.661932i
$547$		−	1.76725e27i		−	0.736928i	−0.929642	−	0.368464i	$-0.879884\pi$
$547$		−	1.76725e27i		−	0.736928i	0.929642	−	0.368464i	$-0.120116\pi$
$548$	2.04727e27	+	7.17253e26i	0.838241	+	0.293675i
$549$	7.96161e26			0.320094
$550$	4.24542e26	+	7.22165e25i	0.167608	+	0.0285108i
$551$			1.04205e26i			0.0403993i
$552$	1.27490e27	−	2.30362e27i	0.485384	−	0.877042i
$553$	−3.21954e27			−1.20377
$554$	1.58033e26	−	9.29037e26i	0.0580298	−	0.341142i
$555$			1.08510e27i			0.391328i
$556$	−2.37562e25	+	6.78076e25i	−0.00841450	+	0.0240176i
$557$	−1.95598e27			−0.680476			−0.340238	−	0.940339i	$-0.610508\pi$
$557$	−1.95598e27			−0.680476			−0.340238	+	0.940339i	$0.610508\pi$
$558$	−3.72115e26	−	6.32984e25i	−0.127155	−	0.0216297i
$559$		−	1.33651e27i		−	0.448595i
$560$	−3.72095e27	+	4.65858e27i	−1.22680	+	1.53594i
$561$	2.49127e26			0.0806849
$562$	7.52629e26	−	4.42451e27i	0.239452	−	1.40767i
$563$		−	6.62949e26i		−	0.207203i	−0.994619	−	0.103602i	$-0.966963\pi$
$563$		−	6.62949e26i		−	0.207203i	0.994619	−	0.103602i	$-0.0330367\pi$
$564$	2.62069e27	+	9.18150e26i	0.804682	+	0.281918i
$565$	8.56160e27			2.58268
$566$	2.62267e27	+	4.46129e26i	0.777285	+	0.132220i
$567$			4.19949e26i			0.122283i
$568$	4.82521e27	+	2.67043e27i	1.38049	+	0.764009i
$569$	−5.40332e26			−0.151893			−0.0759465	−	0.997112i	$-0.524198\pi$
$569$	−5.40332e26			−0.151893			−0.0759465	+	0.997112i	$0.524198\pi$
$570$	3.91134e25	−	2.29938e26i	0.0108038	−	0.0635128i
$571$		−	1.44523e27i		−	0.392262i	−0.980578	−	0.196131i	$-0.937162\pi$
$571$		−	1.44523e27i		−	0.392262i	0.980578	−	0.196131i	$-0.0628378\pi$
$572$	−1.01685e26	+	2.90240e26i	−0.0271204	+	0.0774101i
$573$	−1.68987e27			−0.442902
$574$	2.35663e27	+	4.00873e26i	0.606977	+	0.103250i
$575$			1.50241e28i			3.80286i
$576$	7.11612e26	+	1.13543e27i	0.177018	+	0.282446i
$577$	−4.23773e27			−1.03604			−0.518019	−	0.855369i	$-0.673330\pi$
$577$	−4.23773e27			−1.03604			−0.518019	+	0.855369i	$0.673330\pi$
$578$	1.56439e27	−	9.19664e27i	0.375895	−	2.20979i
$579$			1.08296e27i			0.255756i
$580$	4.69606e27	+	1.64525e27i	1.09007	+	0.381902i
$581$	−7.80625e27			−1.78107
$582$	1.77224e27	+	3.01466e26i	0.397459	+	0.0676096i
$583$		−	1.13194e26i		−	0.0249539i
$584$	−4.19238e26	+	7.57522e26i	−0.0908515	+	0.164160i
$585$	2.95335e27			0.629154
$586$	−9.11039e26	+	5.35576e27i	−0.190792	+	1.12162i
$587$			2.36970e27i			0.487880i	0.969790	+	0.243940i	$0.0784400\pi$
$587$			2.36970e27i			0.487880i	−0.969790	+	0.243940i	$0.921560\pi$
$588$	−1.99189e26	+	5.68550e26i	−0.0403175	+	0.115079i
$589$	1.21479e26			0.0241740
$590$	−6.31981e27	−	1.07503e27i	−1.23647	−	0.210329i
$591$		−	8.45438e26i		−	0.162632i
$592$	1.56764e27	+	1.25213e27i	0.296503	+	0.236827i
$593$	1.80136e27			0.335007			0.167503	−	0.985872i	$-0.446430\pi$
$593$	1.80136e27			0.335007			0.167503	+	0.985872i	$0.446430\pi$
$594$	1.36988e25	−	8.05315e25i	0.00250506	−	0.0147266i
$595$		−	1.96821e28i		−	3.53917i
$596$	−4.46234e27	−	1.56337e27i	−0.789043	−	0.276438i
$597$	4.95738e26			0.0862004
$598$	−1.05774e28	−	1.79926e27i	−1.80870	−	0.307668i
$599$			3.89311e25i			0.00654679i	0.999995	+	0.00327340i	$0.00104196\pi$
$599$			3.89311e25i			0.00654679i	−0.999995	+	0.00327340i	$0.998958\pi$
$600$	−6.69025e27	−	3.70261e27i	−1.10645	−	0.612344i
$601$	−3.37606e27			−0.549118			−0.274559	−	0.961570i	$-0.588532\pi$
$601$	−3.37606e27			−0.549118			−0.274559	+	0.961570i	$0.588532\pi$
$602$	−4.89766e26	+	2.87921e27i	−0.0783473	+	0.460583i
$603$		−	1.71866e27i		−	0.270406i
$604$	−1.36485e27	+	3.89571e27i	−0.211210	+	0.602861i
$605$	1.16640e28			1.77539
$606$	3.98118e27	+	6.77217e26i	0.596054	+	0.101391i
$607$			1.21727e28i			1.79267i	0.443376	+	0.896336i	$0.353781\pi$
$607$			1.21727e28i			1.79267i	−0.443376	+	0.896336i	$0.646219\pi$
$608$	−2.87056e26	−	3.21838e26i	−0.0415844	−	0.0466231i
$609$	2.88335e27			0.410888
$610$	−2.05181e27	+	1.20620e28i	−0.287633	+	1.69092i
$611$		−	1.13161e28i		−	1.56058i
$612$	−4.17473e27	−	1.46260e27i	−0.566388	−	0.198432i
$613$	−1.15978e27			−0.154800			−0.0774002	−	0.997000i	$-0.524662\pi$
$613$	−1.15978e27			−0.154800			−0.0774002	+	0.997000i	$0.524662\pi$
$614$	−4.41285e27	−	7.50646e26i	−0.579476	−	0.0985715i
$615$			4.46547e27i			0.576920i
$616$	3.25416e26	−	5.87994e26i	0.0413648	−	0.0747422i
$617$	5.05878e27			0.632694			0.316347	−	0.948644i	$-0.397544\pi$
$617$	5.05878e27			0.632694			0.316347	+	0.948644i	$0.397544\pi$
$618$	9.86046e26	−	5.79671e27i	0.121342	−	0.713340i
$619$		−	7.07796e27i		−	0.857040i	−0.903532	−	0.428520i	$-0.859035\pi$
$619$		−	7.07796e27i		−	0.857040i	0.903532	−	0.428520i	$-0.140965\pi$
$620$	1.91798e27	−	5.47451e27i	0.228521	−	0.652271i
$621$	2.84993e27			0.334132
$622$	6.75859e27	+	1.14967e27i	0.779745	+	0.132638i
$623$		−	6.91776e26i		−	0.0785389i
$624$	3.40795e27	−	4.26670e27i	0.380756	−	0.476701i
$625$	1.46177e28			1.60723
$626$	1.09597e27	−	6.44293e27i	0.118592	−	0.697172i
$627$			2.62900e25i			0.00279972i
$628$	4.21576e27	+	1.47698e27i	0.441854	+	0.154802i
$629$	−6.62315e27			−0.683216
$630$	−6.36233e27	−	1.08226e27i	−0.645968	−	0.109882i
$631$		−	3.17893e27i		−	0.317679i	−0.987304	−	0.158839i	$-0.949225\pi$
$631$		−	3.17893e27i		−	0.317679i	0.987304	−	0.158839i	$-0.0507752\pi$
$632$	−9.72939e27	−	5.38457e27i	−0.957006	−	0.529639i
$633$	−4.87682e27			−0.472171
$634$	3.02242e27	−	1.77680e28i	0.288047	−	1.69335i
$635$		−	1.30739e28i		−	1.22650i
$636$	−6.64552e26	+	1.89684e27i	−0.0613703	+	0.175170i
$637$	2.45499e27			0.223180
$638$	−5.52925e26	−	9.40551e25i	−0.0494834	−	0.00841735i
$639$			5.96953e27i			0.525934i
$640$	−1.90360e28	+	7.85497e27i	−1.65111	+	0.681310i
$641$	−9.04682e27			−0.772531			−0.386265	−	0.922388i	$-0.626235\pi$
$641$	−9.04682e27			−0.772531			−0.386265	+	0.922388i	$0.626235\pi$
$642$	3.31726e26	−	1.95013e27i	0.0278888	−	0.163951i
$643$			7.79258e27i			0.645018i	0.946566	+	0.322509i	$0.104526\pi$
$643$			7.79258e27i			0.645018i	−0.946566	+	0.322509i	$0.895474\pi$
$644$	2.21272e28	+	7.75220e27i	1.80330	+	0.631781i
$645$	−5.45568e27			−0.437776
$646$	1.40347e27	+	2.38737e26i	0.110887	+	0.0188623i
$647$			1.68720e28i			1.31258i	0.754510	+	0.656289i	$0.227875\pi$
$647$			1.68720e28i			1.31258i	−0.754510	+	0.656289i	$0.772125\pi$
$648$	−7.02350e26	+	1.26908e27i	−0.0538026	+	0.0972160i
$649$	7.22578e26			0.0545052
$650$	−5.22548e27	+	3.07192e28i	−0.388143	+	2.28179i
$651$		−	3.36130e27i		−	0.245866i
$652$	2.73093e27	−	7.79494e27i	0.196714	−	0.561483i
$653$	2.48954e28			1.76599			0.882993	−	0.469386i	$-0.155525\pi$
$653$	2.48954e28			1.76599			0.882993	+	0.469386i	$0.155525\pi$
$654$	−3.20705e27	−	5.45534e26i	−0.224042	−	0.0381105i
$655$			1.24592e28i			0.857188i
$656$	6.45124e27	+	5.15281e27i	0.437124	+	0.349145i
$657$	−9.37171e26			−0.0625411
$658$	−4.14681e27	+	2.43780e28i	−0.272556	+	1.60228i
$659$			4.97261e27i			0.321907i	0.986962	+	0.160954i	$0.0514569\pi$
$659$			4.97261e27i			0.321907i	−0.986962	+	0.160954i	$0.948543\pi$
$660$	1.18477e27	+	4.15080e26i	0.0755431	+	0.0264663i
$661$	1.32729e27			0.0833585			0.0416793	−	0.999131i	$-0.486729\pi$
$661$	1.32729e27			0.0833585			0.0416793	+	0.999131i	$0.486729\pi$
$662$	−5.58058e27	−	9.49283e26i	−0.345223	−	0.0587240i
$663$			1.80264e28i			1.09844i
$664$	−2.35903e28	−	1.30557e28i	−1.41597	−	0.783644i
$665$	2.07702e27			0.122807
$666$	−3.64188e26	+	2.14097e27i	−0.0212121	+	0.124700i
$667$		−	1.95675e28i		−	1.12273i
$668$	2.98389e26	−	8.51697e26i	0.0168663	−	0.0481416i
$669$	−1.19380e28			−0.664768
$670$	2.60381e28	+	4.42920e27i	1.42844	+	0.242984i
$671$		−	1.37912e27i		−	0.0745377i
$672$	−8.90519e27	+	7.94279e27i	−0.474188	+	0.422941i
$673$	−2.94507e28			−1.54506			−0.772530	−	0.634978i	$-0.781009\pi$
$673$	−2.94507e28			−1.54506			−0.772530	+	0.634978i	$0.781009\pi$
$674$	2.15246e27	−	1.26538e28i	0.111259	−	0.654065i
$675$		−	8.27687e27i		−	0.421530i
$676$	−2.19403e27	−	7.68670e26i	−0.110097	−	0.0385721i
$677$	−1.68695e27			−0.0834097			−0.0417049	−	0.999130i	$-0.513279\pi$
$677$	−1.68695e27			−0.0834097			−0.0417049	+	0.999130i	$0.513279\pi$
$678$	1.68925e28	+	2.87350e27i	0.822996	+	0.139995i
$679$			1.60086e28i			0.768520i
$680$	3.29176e28	−	5.94789e28i	1.55718	−	2.81367i
$681$	1.66880e28			0.777918
$682$	−1.09646e26	+	6.44581e26i	−0.00503674	+	0.0296097i
$683$		−	8.94129e27i		−	0.404756i	−0.979307	−	0.202378i	$-0.935133\pi$
$683$		−	8.94129e27i		−	0.404756i	0.979307	−	0.202378i	$-0.0648670\pi$
$684$	1.54346e26	−	4.40553e26i	0.00688549	−	0.0196534i
$685$	−3.60855e28			−1.58645
$686$	1.97525e28	+	3.35999e27i	0.855816	+	0.145578i
$687$		−	1.75578e28i		−	0.749728i
$688$	−6.29544e27	+	7.88179e27i	−0.264936	+	0.331696i
$689$	8.19055e27			0.339720
$690$	−7.34464e27	+	4.31772e28i	−0.300248	+	1.76508i
$691$			3.40135e27i			0.137047i	0.997649	+	0.0685236i	$0.0218289\pi$
$691$			3.40135e27i			0.137047i	−0.997649	+	0.0685236i	$0.978171\pi$
$692$	3.38183e28	+	1.18481e28i	1.34305	+	0.470532i
$693$	7.27439e26			0.0284750
$694$	2.17963e28	+	3.70766e27i	0.840986	+	0.143056i
$695$		−	1.19519e27i		−	0.0454557i
$696$	8.71342e27	+	4.82229e27i	0.326660	+	0.180785i
$697$	−2.72559e28			−1.00724
$698$	−4.24946e27	+	2.49814e28i	−0.154803	+	0.910046i
$699$		−	1.81804e28i		−	0.652877i
$700$	2.25142e28	−	6.42627e28i	0.797033	−	2.27498i
$701$	−1.30136e28			−0.454168			−0.227084	−	0.973875i	$-0.572919\pi$
$701$	−1.30136e28			−0.454168			−0.227084	+	0.973875i	$0.572919\pi$
$702$	5.82714e27	+	9.91223e26i	0.200486	+	0.0341036i
$703$		−	6.98931e26i		−	0.0237073i
$704$	1.96680e27	−	1.23266e27i	0.0657709	−	0.0412209i
$705$	−4.61928e28			−1.52294
$706$	5.98944e27	−	3.52104e28i	0.194688	−	1.14452i
$707$			3.59619e28i			1.15252i
$708$	−1.21085e28	−	4.24219e27i	−0.382613	−	0.134047i
$709$	3.96371e28			1.23492			0.617461	−	0.786602i	$-0.288161\pi$
$709$	3.96371e28			1.23492			0.617461	+	0.786602i	$0.288161\pi$
$710$	−9.04399e28	−	1.53842e28i	−2.77828	−	0.472599i
$711$		−	1.20367e28i		−	0.364597i
$712$	1.15697e27	−	2.09053e27i	0.0345559	−	0.0624392i
$713$	−2.28111e28			−0.671817
$714$	6.60582e27	−	3.88339e28i	0.191842	−	1.12779i
$715$		−	5.11583e27i		−	0.146506i
$716$	−2.17778e28	+	6.21609e28i	−0.615014	+	1.75544i
$717$	4.03313e28			1.12318
$718$	−2.11330e28	−	3.59482e27i	−0.580385	−	0.0987262i
$719$		−	6.47049e28i		−	1.75246i	−0.481894	−	0.876230i	$-0.660051\pi$
$719$		−	6.47049e28i		−	1.75246i	0.481894	−	0.876230i	$-0.339949\pi$
$720$	−1.74168e28	−	1.39114e28i	−0.465204	−	0.371573i
$721$	5.23615e28			1.37930
$722$	6.42977e27	−	3.77989e28i	0.167041	−	0.981991i
$723$			1.09607e28i			0.280836i
$724$	−5.34449e28	−	1.87242e28i	−1.35058	−	0.473171i
$725$	−5.68286e28			−1.41640
$726$	2.30137e28	+	3.91474e27i	0.565745	+	0.0962358i
$727$			7.84435e28i			1.90201i	0.309174	+	0.951005i	$0.399947\pi$
$727$			7.84435e28i			1.90201i	−0.309174	+	0.951005i	$0.600053\pi$
$728$	4.25464e28	+	2.35466e28i	1.01753	+	0.563137i
$729$	−1.57004e27			−0.0370370
$730$	2.41521e27	−	1.41984e28i	0.0561987	−	0.330378i
$731$		−	3.32999e28i		−	0.764309i
$732$	−8.09667e27	+	2.31105e28i	−0.183314	+	0.523236i
$733$	4.38389e28			0.979084			0.489542	−	0.871980i	$-0.337164\pi$
$733$	4.38389e28			0.979084			0.489542	+	0.871980i	$0.337164\pi$
$734$	−2.76456e28	−	4.70265e27i	−0.609068	−	0.103605i
$735$		−	1.00214e28i		−	0.217798i
$736$	5.39028e28	+	6.04340e28i	1.15567	+	1.29570i
$737$	−2.97708e27			−0.0629673
$738$	−1.49873e27	+	8.81062e27i	−0.0312722	+	0.183841i
$739$			6.54797e28i			1.34791i	0.738771	+	0.673957i	$0.235407\pi$
$739$			6.54797e28i			1.34791i	−0.738771	+	0.673957i	$0.764593\pi$
$740$	−3.14977e28	−	1.10351e28i	−0.639677	−	0.224109i
$741$	−1.90230e27			−0.0381152
$742$	−1.76447e28	−	3.00144e27i	−0.348799	−	0.0593322i
$743$			4.88077e27i			0.0951919i	0.998867	+	0.0475959i	$0.0151560\pi$
$743$			4.88077e27i			0.0951919i	−0.998867	+	0.0475959i	$0.984844\pi$
$744$	5.62166e27	−	1.01578e28i	0.108177	−	0.195466i
$745$	7.86541e28			1.49334
$746$	−1.42864e28	+	8.39858e28i	−0.267629	+	1.57332i
$747$		−	2.91849e28i		−	0.539451i
$748$	−2.53353e27	+	7.23150e27i	−0.0462073	+	0.131890i
$749$	1.76155e28			0.317013
$750$	6.81467e28	+	1.15921e28i	1.21013	+	0.205849i
$751$			1.84696e28i			0.323637i	0.986821	+	0.161819i	$0.0517359\pi$
$751$			1.84696e28i			0.323637i	−0.986821	+	0.161819i	$0.948264\pi$
$752$	−5.33030e28	+	6.67345e28i	−0.921665	+	1.15391i
$753$	8.78727e27			0.149935
$754$	6.80568e27	−	4.00088e28i	0.114593	−	0.673662i
$755$		−	6.86665e28i		−	1.14097i
$756$	−1.21900e28	−	4.27073e27i	−0.199888	−	0.0700300i
$757$	−1.22856e29			−1.98810			−0.994050	−	0.108929i	$-0.965258\pi$
$757$	−1.22856e29			−1.98810			−0.994050	+	0.108929i	$0.965258\pi$
$758$	1.03749e29	+	1.76482e28i	1.65689	+	0.281844i
$759$		−	4.93668e27i		−	0.0778068i
$760$	6.27672e27	+	3.47374e27i	0.0976330	+	0.0540334i
$761$	2.96001e28			0.454409			0.227204	−	0.973847i	$-0.427041\pi$
$761$	2.96001e28			0.454409			0.227204	+	0.973847i	$0.427041\pi$
$762$	4.38795e27	−	2.57956e28i	0.0664831	−	0.390837i
$763$		−	2.89692e28i		−	0.433203i
$764$	1.71854e28	−	4.90525e28i	0.253645	−	0.723982i
$765$	7.35845e28			1.07194
$766$	−8.34435e28	−	1.41941e28i	−1.19979	−	0.204090i
$767$			5.22846e28i			0.742028i
$768$	−4.01954e28	+	9.10934e27i	−0.563072	+	0.127607i
$769$	1.05268e29			1.45557			0.727783	−	0.685807i	$-0.240551\pi$
$769$	1.05268e29			1.45557			0.727783	+	0.685807i	$0.240551\pi$
$770$	−1.87470e27	+	1.10209e28i	−0.0255874	+	0.150421i
$771$		−	8.64643e27i		−	0.116491i
$772$	−3.14354e28	−	1.10133e28i	−0.418068	−	0.146469i
$773$	1.10369e29			1.44894			0.724470	−	0.689306i	$-0.242085\pi$
$773$	1.10369e29			1.44894			0.724470	+	0.689306i	$0.242085\pi$
$774$	−1.07644e28	−	1.83107e27i	−0.139501	−	0.0237298i
$775$			6.62488e28i			0.847541i
$776$	−2.67738e28	+	4.83776e28i	−0.338137	+	0.610981i
$777$	−1.93393e28			−0.241119
$778$	5.70605e27	−	3.35444e28i	0.0702328	−	0.412880i
$779$		−	2.87628e27i		−	0.0349507i
$780$	−3.00346e28	+	8.57282e28i	−0.360309	+	1.02844i
$781$	1.03405e28			0.122470
$782$	−2.63542e29	−	4.48296e28i	−3.08164	−	0.524201i
$783$			1.07798e28i			0.124450i
$784$	−1.44778e28	−	1.15639e28i	−0.165022	−	0.131809i
$785$	−7.43077e28			−0.836252
$786$	−4.18162e27	+	2.45826e28i	−0.0464643	+	0.273151i
$787$		−	4.31936e28i		−	0.473884i	−0.971524	−	0.236942i	$-0.923855\pi$
$787$		−	4.31936e28i		−	0.473884i	0.971524	−	0.236942i	$-0.0761452\pi$
$788$	2.45409e28	+	8.59781e27i	0.265844	+	0.0931377i
$789$	−2.90415e28			−0.310634
$790$	1.82360e29	+	3.10202e28i	1.92601	+	0.327623i
$791$			1.52590e29i			1.59133i
$792$	2.19831e27	+	1.21662e27i	0.0226379	+	0.0125286i
$793$	9.97908e28			1.01475
$794$	1.64493e28	−	9.67013e28i	0.165175	−	0.971018i
$795$		−	3.34341e28i		−	0.331526i
$796$	−5.04148e27	+	1.43900e28i	−0.0493660	+	0.140906i
$797$	−3.13409e28			−0.303059			−0.151530	−	0.988453i	$-0.548420\pi$
$797$	−3.13409e28			−0.303059			−0.151530	+	0.988453i	$0.548420\pi$
$798$	4.09808e27	+	6.97102e26i	0.0391338	+	0.00665683i
$799$		−	2.81947e29i		−	2.65889i
$800$	1.75515e29	−	1.56546e29i	1.63461	−	1.45795i
$801$	2.58631e27			0.0237879
$802$	1.24407e28	−	7.31357e28i	0.113006	−	0.664333i
$803$			1.62338e27i			0.0145634i
$804$	4.98882e28	+	1.74781e28i	0.442015	+	0.154858i
$805$	−3.90019e29			−3.41292
$806$	−4.66409e28	−	7.93383e27i	−0.403103	−	0.0685697i
$807$			2.35154e28i			0.200732i
$808$	−6.01450e28	+	1.08676e29i	−0.507091	+	0.916264i
$809$	−1.24667e29			−1.03816			−0.519081	−	0.854725i	$-0.673726\pi$
$809$	−1.24667e29			−1.03816			−0.519081	+	0.854725i	$0.673726\pi$
$810$	4.04620e27	−	2.37866e28i	0.0332811	−	0.195651i
$811$		−	3.51160e28i		−	0.285297i	−0.989773	−	0.142648i	$-0.954438\pi$
$811$		−	3.51160e28i		−	0.285297i	0.989773	−	0.142648i	$-0.0455618\pi$
$812$	−2.93226e28	+	8.36960e28i	−0.235311	+	0.671652i
$813$	−5.92634e28			−0.469766
$814$	3.70860e27	+	6.30851e26i	0.0290380	+	0.00493949i
$815$			1.37395e29i			1.06266i
$816$	8.49110e28	−	1.06307e29i	0.648727	−	0.812197i
$817$	3.51409e27			0.0265211
$818$	3.40563e28	−	2.00208e29i	0.253901	−	1.49262i
$819$			5.26364e28i			0.387656i
$820$	−1.29621e29	−	4.54122e28i	−0.943053	−	0.330395i
$821$	9.64648e28			0.693326			0.346663	−	0.937990i	$-0.387315\pi$
$821$	9.64648e28			0.693326			0.346663	+	0.937990i	$0.387315\pi$
$822$	−7.11988e28	−	1.21112e28i	−0.505538	−	0.0859944i
$823$			6.37537e28i			0.447206i	0.974680	+	0.223603i	$0.0717819\pi$
$823$			6.37537e28i			0.447206i	−0.974680	+	0.223603i	$0.928218\pi$
$824$	1.58236e29	+	8.75728e28i	1.09656	+	0.606872i
$825$	−1.43373e28			−0.0981583
$826$	1.91598e28	−	1.12635e29i	0.129596	−	0.761858i
$827$		−	2.17826e29i		−	1.45564i	−0.685766	−	0.727822i	$-0.740533\pi$
$827$		−	2.17826e29i		−	1.45564i	0.685766	−	0.727822i	$-0.259467\pi$
$828$	−2.89828e28	+	8.27261e28i	−0.191354	+	0.546184i
$829$	3.03130e28			0.197735			0.0988674	−	0.995101i	$-0.468478\pi$
$829$	3.03130e28			0.197735			0.0988674	+	0.995101i	$0.468478\pi$
$830$	4.42158e29	+	7.52132e28i	2.84969	+	0.484745i
$831$			3.13747e28i			0.199788i
$832$	8.91935e28	+	1.42315e29i	0.561177	+	0.895398i
$833$	6.11676e28			0.380252
$834$	4.01136e26	−	2.35818e27i	0.00246395	−	0.0144849i
$835$			1.50122e28i			0.0911127i
$836$	−7.63130e26	−	2.67360e26i	−0.00457652	−	0.00160337i
$837$	1.25668e28			0.0744678
$838$	−5.28305e28	−	8.98671e27i	−0.309346	−	0.0526212i
$839$		−	2.32013e29i		−	1.34243i	−0.741261	−	0.671217i	$-0.765772\pi$
$839$		−	2.32013e29i		−	1.34243i	0.741261	−	0.671217i	$-0.234228\pi$
$840$	9.61179e28	−	1.73676e29i	0.549555	−	0.992993i
$841$	−1.02981e29			−0.581830
$842$	−2.56476e28	+	1.50775e29i	−0.143194	+	0.841801i
$843$			1.49421e29i			0.824395i
$844$	4.95955e28	−	1.41561e29i	0.270407	−	0.771828i
$845$	3.86723e28			0.208369
$846$	−9.11409e28	−	1.55035e28i	−0.485300	−	0.0825517i
$847$			2.07882e29i			1.09392i
$848$	−4.83021e28	−	3.85804e28i	−0.251193	−	0.200636i
$849$	−8.85708e28			−0.455212
$850$	−1.30196e29	+	7.65386e29i	−0.661314	+	3.88769i
$851$			1.31244e29i			0.658845i
$852$	−1.73280e29	−	6.07080e28i	−0.859710	−	0.301197i
$853$	2.69319e29			1.32062			0.660309	−	0.750994i	$-0.270425\pi$
$853$	2.69319e29			1.32062			0.660309	+	0.750994i	$0.270425\pi$
$854$	−2.14977e29	−	3.65685e28i	−1.04187	−	0.177226i
$855$			7.76526e27i			0.0371959i
$856$	5.32337e28	+	2.94613e28i	0.252028	+	0.139481i
$857$	1.48524e29			0.695008			0.347504	−	0.937678i	$-0.387029\pi$
$857$	1.48524e29			0.695008			0.347504	+	0.937678i	$0.387029\pi$
$858$	1.71701e27	−	1.00938e28i	0.00794143	−	0.0466856i
$859$		−	1.59416e29i		−	0.728787i	−0.931245	−	0.364394i	$-0.881276\pi$
$859$		−	1.59416e29i		−	0.728787i	0.931245	−	0.364394i	$-0.118724\pi$
$860$	5.54823e28	−	1.58364e29i	0.250709	−	0.715603i
$861$	−7.95861e28			−0.355472
$862$	3.60199e29	+	6.12715e28i	1.59027	+	0.270511i
$863$		−	6.48325e28i		−	0.282934i	−0.989943	−	0.141467i	$-0.954818\pi$
$863$		−	6.48325e28i		−	0.282934i	0.989943	−	0.141467i	$-0.0451819\pi$
$864$	−2.96953e28	−	3.32934e28i	−0.128101	−	0.143622i
$865$	−5.96088e29			−2.54185
$866$	−1.32542e28	+	7.79182e28i	−0.0558697	+	0.328443i
$867$			3.10581e29i			1.29415i
$868$	9.75698e28	+	3.41833e28i	0.401900	+	0.140804i
$869$	−2.08502e28			−0.0849008
$870$	−1.63317e29	−	2.77810e28i	−0.657415	−	0.111829i
$871$		−	2.15417e29i		−	0.857231i
$872$	4.84500e28	−	8.75445e28i	0.190603	−	0.344401i
$873$	−5.98505e28			−0.232769
$874$	4.73080e27	−	2.78111e28i	0.0181895	−	0.106931i
$875$			6.15567e29i			2.33989i
$876$	9.53070e27	−	2.72036e28i	0.0358165	−	0.102232i
$877$	3.22506e29			1.19823			0.599117	−	0.800662i	$-0.295518\pi$
$877$	3.22506e29			1.19823			0.599117	+	0.800662i	$0.295518\pi$
$878$	1.99633e29	+	3.39584e28i	0.733308	+	0.124739i
$879$		−	1.80870e29i		−	0.656868i
$880$	−2.40974e28	+	3.01696e28i	−0.0865253	+	0.108328i
$881$	−2.46940e29			−0.876661			−0.438331	−	0.898814i	$-0.644430\pi$
$881$	−2.46940e29			−0.876661			−0.438331	+	0.898814i	$0.644430\pi$
$882$	3.36343e27	−	1.97727e28i	0.0118058	−	0.0694034i
$883$			5.66214e29i			1.96505i	0.186128	+	0.982526i	$0.440406\pi$
$883$			5.66214e29i			1.96505i	−0.186128	+	0.982526i	$0.559594\pi$
$884$	−5.23260e29	−	1.83322e29i	−1.79554	−	0.629062i
$885$	2.13427e29			0.724132
$886$	−2.14305e29	−	3.64543e28i	−0.718945	−	0.122296i
$887$		−	2.57504e29i		−	0.854178i	−0.904210	−	0.427089i	$-0.859539\pi$
$887$		−	2.57504e29i		−	0.854178i	0.904210	−	0.427089i	$-0.140461\pi$
$888$	−5.84430e28	−	3.23443e28i	−0.191692	−	0.106088i
$889$	2.33011e29			0.755716
$890$	−6.66526e27	+	3.91833e28i	−0.0213755	+	0.125661i
$891$			2.71964e27i			0.00862452i
$892$	1.21405e29	−	3.46529e29i	0.380705	−	1.08665i
$893$	2.97535e28			0.0922621
$894$	1.55189e29	+	2.63984e28i	0.475867	+	0.0809472i
$895$		−	1.09566e30i		−	3.32235i
$896$	−1.39996e29	−	3.39270e29i	−0.419792	−	1.01734i
$897$	3.57211e29			1.05925
$898$	7.04941e26	−	4.14416e27i	0.00206723	−	0.0121527i
$899$		−	8.62827e28i		−	0.250223i
$900$	2.40256e29	+	8.41728e28i	0.689047	+	0.241405i
$901$	2.04072e29			0.578810
$902$	1.52618e28	+	2.59611e27i	0.0428096	+	0.00728211i
$903$		−	9.72342e28i		−	0.269738i
$904$	−2.55201e29	+	4.61124e29i	−0.700162	+	1.26512i
$905$	9.42029e29			2.55610
$906$	2.30463e28	−	1.35483e29i	0.0618470	−	0.363582i
$907$		−	2.07670e29i		−	0.551190i	−0.961274	−	0.275595i	$-0.911125\pi$
$907$		−	2.07670e29i		−	0.551190i	0.961274	−	0.275595i	$-0.0888749\pi$
$908$	−1.69711e29	+	4.84410e29i	−0.445504	+	1.27161i
$909$	−1.34449e29			−0.349075
$910$	−7.97455e29	−	1.35651e29i	−2.04782	−	0.348344i
$911$			1.67659e29i			0.425836i	0.977070	+	0.212918i	$0.0682966\pi$
$911$			1.67659e29i			0.425836i	−0.977070	+	0.212918i	$0.931703\pi$
$912$	1.12184e28	+	8.96053e27i	0.0281828	+	0.0225105i
$913$	−5.05543e28			−0.125618
$914$	3.31971e28	−	1.95157e29i	0.0815901	−	0.479647i
$915$		−	4.07349e29i		−	0.990275i
$916$	5.09658e29	+	1.78557e29i	1.22553	+	0.429360i
$917$	−2.22054e29			−0.528160
$918$	1.45186e29	+	2.46969e28i	0.341585	+	0.0581052i
$919$		−	6.19168e29i		−	1.44096i	−0.693473	−	0.720482i	$-0.743921\pi$
$919$		−	6.19168e29i		−	1.44096i	0.693473	−	0.720482i	$-0.256079\pi$
$920$	−1.17863e30	−	6.52293e29i	−2.71331	−	1.50163i
$921$	1.49027e29			0.339366
$922$	−3.07336e28	+	1.80675e29i	−0.0692316	+	0.406994i
$923$			7.48221e29i			1.66730i
$924$	−7.39780e27	+	2.11157e28i	−0.0163073	+	0.0465463i
$925$	3.81163e29			0.831177
$926$	4.83065e29	+	8.21715e28i	1.04207	+	0.177260i
$927$			1.95762e29i			0.417763i
$928$	−2.28591e29	+	2.03887e29i	−0.482591	+	0.430436i
$929$	−7.37653e29			−1.54062			−0.770309	−	0.637671i	$-0.779898\pi$
$929$	−7.37653e29			−1.54062			−0.770309	+	0.637671i	$0.779898\pi$
$930$	−3.23861e28	+	1.90390e29i	−0.0669160	+	0.393381i
$931$			6.45492e27i			0.0131945i
$932$	5.27729e29	+	1.84888e29i	1.06721	+	0.373895i
$933$	−2.28246e29			−0.456653
$934$	−6.90835e29	−	1.17514e29i	−1.36743	−	0.232606i
$935$		−	1.27464e29i		−	0.249615i
$936$	−8.80325e28	+	1.59066e29i	−0.170563	+	0.308191i
$937$	−4.58118e29			−0.878176			−0.439088	−	0.898444i	$-0.644698\pi$
$937$	−4.58118e29			−0.878176			−0.439088	+	0.898444i	$0.644698\pi$
$938$	−7.89398e28	+	4.64066e29i	−0.149716	+	0.880140i
$939$			2.17585e29i			0.408294i
$940$	4.69764e29	−	1.34085e30i	0.872170	−	2.48945i
$941$	−6.24488e29			−1.14717			−0.573585	−	0.819146i	$-0.694448\pi$
$941$	−6.24488e29			−1.14717			−0.573585	+	0.819146i	$0.694448\pi$
$942$	−1.46613e29	−	2.49396e28i	−0.266480	−	0.0453294i
$943$			5.40102e29i			0.971311i
$944$	2.46279e29	−	3.08338e29i	0.438236	−	0.548664i
$945$	2.14863e29			0.378307
$946$	−3.17179e27	+	1.86461e28i	−0.00552578	+	0.0324846i
$947$		−	5.45794e29i		−	0.940869i	−0.882435	−	0.470434i	$-0.844097\pi$
$947$		−	5.45794e29i		−	0.940869i	0.882435	−	0.470434i	$-0.155903\pi$
$948$	3.49395e29	+	1.22409e29i	0.595983	+	0.208801i
$949$	−1.17465e29			−0.198265
$950$	−8.07701e28	−	1.37394e28i	−0.134901	−	0.0229472i
$951$			6.00047e29i			0.991700i
$952$	1.06007e30	+	5.86676e29i	1.73366	+	0.959465i
$953$	−9.49557e28			−0.153671			−0.0768355	−	0.997044i	$-0.524482\pi$
$953$	−9.49557e28			−0.153671			−0.0768355	+	0.997044i	$0.524482\pi$
$954$	1.12214e28	−	6.59674e28i	0.0179706	−	0.105644i
$955$			8.64609e29i			1.37021i
$956$	−4.10155e29	+	1.17071e30i	−0.643235	+	1.83600i
$957$	1.86729e28			0.0289796
$958$	1.11445e30	+	1.89573e29i	1.71161	+	0.291153i
$959$		−	6.43136e29i		−	0.977501i
$960$	5.80933e29	−	3.64091e29i	0.873803	−	0.547643i
$961$	5.71205e29			0.850273
$962$	−4.56474e28	+	2.68349e29i	−0.0672458	+	0.395320i
$963$			6.58582e28i			0.0960168i
$964$	−3.18159e29	−	1.11466e29i	−0.459065	−	0.160832i
$965$	5.54087e29			0.791233
$966$	−7.69529e29	−	1.30900e29i	−1.08756	−	0.184999i
$967$			9.39368e29i			1.31393i	0.753923	+	0.656963i	$0.228159\pi$
$967$			9.39368e29i			1.31393i	−0.753923	+	0.656963i	$0.771841\pi$
$968$	−3.47676e29	+	6.28217e29i	−0.481306	+	0.869673i
$969$	−4.73970e28			−0.0649401
$970$	1.54243e29	−	9.06751e29i	0.209164	−	1.22962i
$971$			9.10663e29i			1.22226i	0.791528	+	0.611132i	$0.209286\pi$
$971$			9.10663e29i			1.22226i	−0.791528	+	0.611132i	$0.790714\pi$
$972$	1.59668e28	−	4.55742e28i	0.0212107	−	0.0605420i
$973$	2.13013e28			0.0280078
$974$	1.07569e30	+	1.82979e29i	1.39990	+	0.238129i
$975$		−	1.03742e30i		−	1.33632i
$976$	−5.88496e29	−	4.70050e29i	−0.750318	−	0.599303i
$977$	−2.60787e29			−0.329109			−0.164555	−	0.986368i	$-0.552619\pi$
$977$	−2.60787e29			−0.329109			−0.164555	+	0.986368i	$0.552619\pi$
$978$	−4.61134e28	+	2.71088e29i	−0.0576021	+	0.338628i
$979$		−	4.48003e27i		−	0.00553929i
$980$	2.90894e29	+	1.01914e29i	0.356020	+	0.124730i
$981$	1.08306e29			0.131209
$982$	2.92971e29	+	4.98357e28i	0.351326	+	0.0597621i
$983$		−	1.14626e30i		−	1.36065i	−0.732911	−	0.680325i	$-0.761839\pi$
$983$		−	1.14626e30i		−	1.36065i	0.732911	−	0.680325i	$-0.238161\pi$
$984$	−2.40508e29	−	1.33105e29i	−0.282604	−	0.156402i
$985$	−4.32562e29			−0.503137
$986$	1.69567e29	−	9.96842e29i	0.195242	−	1.14778i
$987$		−	8.23274e29i		−	0.938367i
$988$	1.93457e28	−	5.52189e28i	0.0218281	−	0.0623043i
$989$	−6.59868e29			−0.737046
$990$	−4.12033e28	−	7.00887e27i	−0.0455596	−	0.00774990i
$991$			1.26752e30i			1.38745i	0.720239	+	0.693726i	$0.244032\pi$
$991$			1.26752e30i			1.38745i	−0.720239	+	0.693726i	$0.755968\pi$
$992$	2.37684e29	+	2.66483e29i	0.257563	+	0.288771i
$993$	1.88463e29			0.202178
$994$	2.74187e29	−	1.61187e30i	0.291194	−	1.71185i
$995$		−	2.53641e29i		−	0.266678i
$996$	8.47160e29	+	2.96800e29i	0.881804	+	0.308937i
$997$	−4.03000e29			−0.415291			−0.207646	−	0.978204i	$-0.566580\pi$
$997$	−4.03000e29			−0.415291			−0.207646	+	0.978204i	$0.566580\pi$
$998$	−1.97863e29	−	3.36573e28i	−0.201864	−	0.0343379i
$999$		−	7.23030e28i		−	0.0730300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.21.d.a.7.11	✓	20
3.2	odd	2		36.21.d.c.19.10		20
4.3	odd	2	inner	12.21.d.a.7.12	yes	20
12.11	even	2		36.21.d.c.19.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.21.d.a.7.11	✓	20	1.1	even	1	trivial
12.21.d.a.7.12	yes	20	4.3	odd	2	inner
36.21.d.c.19.9		20	12.11	even	2
36.21.d.c.19.10		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)

\(f(q)\)	\(=\)	\(q+(171.720 - 1009.50i) q^{2} +34092.0i q^{3} +(-989600. - 346703. i) q^{4} +1.74429e7 q^{5} +(3.44158e7 + 5.85428e6i) q^{6} +3.10877e8i q^{7} +(-5.19931e8 + 9.39464e8i) q^{8} -1.16226e9 q^{9} +O(q^{10})\)	\(q+(171.720 - 1009.50i) q^{2} +34092.0i q^{3} +(-989600. - 346703. i) q^{4} +1.74429e7 q^{5} +(3.44158e7 + 5.85428e6i) q^{6} +3.10877e8i q^{7} +(-5.19931e8 + 9.39464e8i) q^{8} -1.16226e9 q^{9} +(2.99530e9 - 1.76086e10i) q^{10} +2.01328e9i q^{11} +(1.18198e10 - 3.37374e10i) q^{12} -1.45678e11 q^{13} +(3.13830e11 + 5.33839e10i) q^{14} +5.94662e11i q^{15} +(8.59106e11 + 6.86195e11i) q^{16} -3.62965e12 q^{17} +(-1.99584e11 + 1.17330e12i) q^{18} -3.83031e11i q^{19} +(-1.72615e13 - 6.04750e12i) q^{20} -1.05984e13 q^{21} +(2.03240e12 + 3.45721e11i) q^{22} +7.19248e13i q^{23} +(-3.20282e13 - 1.77255e13i) q^{24} +2.08887e14 q^{25} +(-2.50159e13 + 1.47062e14i) q^{26} -3.96238e13i q^{27} +(1.07782e14 - 3.07644e14i) q^{28} -2.72055e14 q^{29} +(6.00310e14 + 1.02116e14i) q^{30} +3.17152e14i q^{31} +(8.40239e14 - 7.49433e14i) q^{32} -6.86367e13 q^{33} +(-6.23284e14 + 3.66413e15i) q^{34} +5.42259e15i q^{35} +(1.15017e15 + 4.02960e14i) q^{36} +1.82474e15 q^{37} +(-3.86670e14 - 6.57743e13i) q^{38} -4.96644e15i q^{39} +(-9.06909e15 + 1.63870e16i) q^{40} +7.50925e15 q^{41} +(-1.81996e15 + 1.06991e16i) q^{42} +9.17442e15i q^{43} +(6.98011e14 - 1.99234e15i) q^{44} -2.02732e16 q^{45} +(7.26080e16 + 1.23510e16i) q^{46} +7.76790e16i q^{47} +(-2.33937e16 + 2.92886e16i) q^{48} -1.68522e16 q^{49} +(3.58701e16 - 2.10871e17i) q^{50} -1.23742e17i q^{51} +(1.44163e17 + 5.05070e16i) q^{52} -5.62237e16 q^{53} +(-4.00002e16 - 6.80421e15i) q^{54} +3.51174e16i q^{55} +(-2.92058e17 - 1.61635e17i) q^{56} +1.30583e16 q^{57} +(-4.67173e16 + 2.74639e17i) q^{58} -3.58906e17i q^{59} +(2.06171e17 - 5.88477e17i) q^{60} -6.85010e17 q^{61} +(3.20165e17 + 5.44614e16i) q^{62} -3.61320e17i q^{63} +(-6.12265e17 - 9.76913e17i) q^{64} -2.54104e18 q^{65} +(-1.17863e16 + 6.92887e16i) q^{66} +1.47872e18i q^{67} +(3.59190e18 + 1.25841e18i) q^{68} -2.45206e18 q^{69} +(5.47410e18 + 9.31169e17i) q^{70} -5.13613e18i q^{71} +(6.04296e17 - 1.09190e18i) q^{72} +8.06334e17 q^{73} +(3.13345e17 - 1.84207e18i) q^{74} +7.12135e18i q^{75} +(-1.32798e17 + 3.79048e17i) q^{76} -6.25883e17 q^{77} +(-5.01362e18 - 8.52840e17i) q^{78} +1.03563e19i q^{79} +(1.49853e19 + 1.19692e19i) q^{80} +1.35085e18 q^{81} +(1.28949e18 - 7.58058e18i) q^{82} +2.51104e19i q^{83} +(1.04882e19 + 3.67450e18i) q^{84} -6.33115e19 q^{85} +(9.26157e18 + 1.57543e18i) q^{86} -9.27488e18i q^{87} +(-1.89141e18 - 1.04677e18i) q^{88} -2.22524e18 q^{89} +(-3.48132e18 + 2.04658e19i) q^{90} -4.52879e19i q^{91} +(2.49366e19 - 7.11768e19i) q^{92} -1.08123e19 q^{93} +(7.84169e19 + 1.33391e19i) q^{94} -6.68117e18i q^{95} +(2.55496e19 + 2.86454e19i) q^{96} +5.14949e19 q^{97} +(-2.89387e18 + 1.70123e19i) q^{98} -2.33996e18i 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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