LMFDB - Embedded newform 12.21.d.a.7.3

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			7.3
Root			$604.769 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.21.d.a.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-831.424 - 597.755i) q^{2} -34092.0i q^{3} +(333954. + 993975. i) q^{4} -5.52569e6 q^{5} +(-2.03786e7 + 2.83449e7i) q^{6} -2.40780e8i q^{7} +(3.16496e8 - 1.02604e9i) q^{8} -1.16226e9 q^{9} +O(q^{10})$	\(q+(-831.424 - 597.755i) q^{2} -34092.0i q^{3} +(333954. + 993975. i) q^{4} -5.52569e6 q^{5} +(-2.03786e7 + 2.83449e7i) q^{6} -2.40780e8i q^{7} +(3.16496e8 - 1.02604e9i) q^{8} -1.16226e9 q^{9} +(4.59419e9 + 3.30301e9i) q^{10} +1.17412e10i q^{11} +(3.38866e10 - 1.13852e10i) q^{12} -1.31897e11 q^{13} +(-1.43927e11 + 2.00190e11i) q^{14} +1.88382e11i q^{15} +(-8.76461e11 + 6.63884e11i) q^{16} -1.84923e12 q^{17} +(9.66332e11 + 6.94747e11i) q^{18} -3.34940e12i q^{19} +(-1.84533e12 - 5.49240e12i) q^{20} -8.20864e12 q^{21} +(7.01834e12 - 9.76189e12i) q^{22} +5.78871e13i q^{23} +(-3.49796e13 - 1.07900e13i) q^{24} -6.48342e13 q^{25} +(1.09662e14 + 7.88422e13i) q^{26} +3.96238e13i q^{27} +(2.39329e14 - 8.04093e13i) q^{28} +6.89396e14 q^{29} +(1.12606e14 - 1.56625e14i) q^{30} -3.48950e14i q^{31} +(1.12555e15 - 2.80603e13i) q^{32} +4.00280e14 q^{33} +(1.53749e15 + 1.10538e15i) q^{34} +1.33047e15i q^{35} +(-3.88142e14 - 1.15526e15i) q^{36} +3.15210e15 q^{37} +(-2.00212e15 + 2.78477e15i) q^{38} +4.49663e15i q^{39} +(-1.74886e15 + 5.66956e15i) q^{40} +1.86052e16 q^{41} +(6.82486e15 + 4.90676e15i) q^{42} +1.40510e15i q^{43} +(-1.16704e16 + 3.92101e15i) q^{44} +6.42229e15 q^{45} +(3.46023e16 - 4.81287e16i) q^{46} -1.07376e15i q^{47} +(2.26331e16 + 2.98803e16i) q^{48} +2.18175e16 q^{49} +(5.39047e16 + 3.87550e16i) q^{50} +6.30437e16i q^{51} +(-4.40476e16 - 1.31102e17i) q^{52} -1.68440e16 q^{53} +(2.36853e16 - 3.29441e16i) q^{54} -6.48781e16i q^{55} +(-2.47049e17 - 7.62057e16i) q^{56} -1.14188e17 q^{57} +(-5.73180e17 - 4.12090e17i) q^{58} +6.06716e17i q^{59} +(-1.87247e17 + 6.29108e16i) q^{60} -7.66597e17 q^{61} +(-2.08587e17 + 2.90126e17i) q^{62} +2.79849e17i q^{63} +(-9.52582e17 - 6.49473e17i) q^{64} +7.28823e17 q^{65} +(-3.32802e17 - 2.39269e17i) q^{66} -1.19477e18i q^{67} +(-6.17557e17 - 1.83808e18i) q^{68} +1.97348e18 q^{69} +(7.95296e17 - 1.10619e18i) q^{70} +4.68826e18i q^{71} +(-3.67851e17 + 1.19252e18i) q^{72} +8.31694e18 q^{73} +(-2.62073e18 - 1.88418e18i) q^{74} +2.21032e18i q^{75} +(3.32922e18 - 1.11855e18i) q^{76} +2.82703e18 q^{77} +(2.68788e18 - 3.73861e18i) q^{78} +1.79551e19i q^{79} +(4.84305e18 - 3.66842e18i) q^{80} +1.35085e18 q^{81} +(-1.54688e19 - 1.11214e19i) q^{82} +1.72296e19i q^{83} +(-2.74131e18 - 8.15919e18i) q^{84} +1.02182e19 q^{85} +(8.39906e17 - 1.16823e18i) q^{86} -2.35028e19i q^{87} +(1.20469e19 + 3.71603e18i) q^{88} +1.92566e19 q^{89} +(-5.33965e18 - 3.83896e18i) q^{90} +3.17581e19i q^{91} +(-5.75383e19 + 1.93316e19i) q^{92} -1.18964e19 q^{93} +(-6.41847e17 + 8.92751e17i) q^{94} +1.85077e19i q^{95} +(-9.56631e17 - 3.83722e19i) q^{96} +1.24589e19 q^{97} +(-1.81396e19 - 1.30415e19i) q^{98} -1.36463e19i 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 $

$2$	−831.424	−	597.755i	−0.811937	−	0.583745i
$2$	−831.424	−	597.755i	−0.811937	−	0.583745i
$3$		−	34092.0i		−	0.577350i
$3$		−	34092.0i		−	0.577350i
$4$	333954.	+	993975.i	0.318484	+	0.947928i
$5$	−5.52569e6			−0.565830			−0.282915	−	0.959145i	$-0.591302\pi$
$5$	−5.52569e6			−0.565830			−0.282915	+	0.959145i	$0.591302\pi$
$6$	−2.03786e7	+	2.83449e7i	−0.337025	+	0.468772i
$7$		−	2.40780e8i		−	0.852392i	−0.904631	−	0.426196i	$-0.859853\pi$
$7$		−	2.40780e8i		−	0.852392i	0.904631	−	0.426196i	$-0.140147\pi$
$8$	3.16496e8	−	1.02604e9i	0.294760	−	0.955571i
$9$	−1.16226e9			−0.333333
$10$	4.59419e9	+	3.30301e9i	0.459419	+	0.330301i
$11$			1.17412e10i			0.452673i	0.974049	+	0.226337i	$0.0726749\pi$
$11$			1.17412e10i			0.452673i	−0.974049	+	0.226337i	$0.927325\pi$
$12$	3.38866e10	−	1.13852e10i	0.547287	−	0.183877i
$13$	−1.31897e11			−0.956757			−0.478379	−	0.878154i	$-0.658775\pi$
$13$	−1.31897e11			−0.956757			−0.478379	+	0.878154i	$0.658775\pi$
$14$	−1.43927e11	+	2.00190e11i	−0.497579	+	0.692088i
$15$			1.88382e11i			0.326682i
$16$	−8.76461e11	+	6.63884e11i	−0.797136	+	0.603799i
$17$	−1.84923e12			−0.917277			−0.458639	−	0.888623i	$-0.651663\pi$
$17$	−1.84923e12			−0.917277			−0.458639	+	0.888623i	$0.651663\pi$
$18$	9.66332e11	+	6.94747e11i	0.270646	+	0.194582i
$19$		−	3.34940e12i		−	0.546300i	−0.961972	−	0.273150i	$-0.911935\pi$
$19$		−	3.34940e12i		−	0.546300i	0.961972	−	0.273150i	$-0.0880655\pi$
$20$	−1.84533e12	−	5.49240e12i	−0.180208	−	0.536367i
$21$	−8.20864e12			−0.492128
$22$	7.01834e12	−	9.76189e12i	0.264246	−	0.367542i
$23$			5.78871e13i			1.39734i	0.715442	+	0.698672i	$0.246225\pi$
$23$			5.78871e13i			1.39734i	−0.715442	+	0.698672i	$0.753775\pi$
$24$	−3.49796e13	−	1.07900e13i	−0.551699	−	0.170180i
$25$	−6.48342e13			−0.679836
$26$	1.09662e14	+	7.88422e13i	0.776827	+	0.558502i
$27$			3.96238e13i			0.192450i
$28$	2.39329e14	−	8.04093e13i	0.808006	−	0.271473i
$29$	6.89396e14			1.63866			0.819329	−	0.573323i	$-0.194346\pi$
$29$	6.89396e14			1.63866			0.819329	+	0.573323i	$0.194346\pi$
$30$	1.12606e14	−	1.56625e14i	0.190699	−	0.265246i
$31$		−	3.48950e14i		−	0.425742i	−0.977080	−	0.212871i	$-0.931719\pi$
$31$		−	3.48950e14i		−	0.425742i	0.977080	−	0.212871i	$-0.0682815\pi$
$32$	1.12555e15	−	2.80603e13i	0.999689	−	0.0249226i
$33$	4.00280e14			0.261351
$34$	1.53749e15	+	1.10538e15i	0.744771	+	0.535456i
$35$			1.33047e15i			0.482309i
$36$	−3.88142e14	−	1.15526e15i	−0.106161	−	0.315976i
$37$	3.15210e15			0.655514			0.327757	−	0.944762i	$-0.393707\pi$
$37$	3.15210e15			0.655514			0.327757	+	0.944762i	$0.393707\pi$
$38$	−2.00212e15	+	2.78477e15i	−0.318900	+	0.443561i
$39$			4.49663e15i			0.552384i
$40$	−1.74886e15	+	5.66956e15i	−0.166784	+	0.540691i
$41$	1.86052e16			1.38611			0.693053	−	0.720886i	$-0.256265\pi$
$41$	1.86052e16			1.38611			0.693053	+	0.720886i	$0.256265\pi$
$42$	6.82486e15	+	4.90676e15i	0.399577	+	0.287278i
$43$			1.40510e15i			0.0650164i	0.999471	+	0.0325082i	$0.0103495\pi$
$43$			1.40510e15i			0.0650164i	−0.999471	+	0.0325082i	$0.989650\pi$
$44$	−1.16704e16	+	3.92101e15i	−0.429102	+	0.144169i
$45$	6.42229e15			0.188610
$46$	3.46023e16	−	4.81287e16i	0.815692	−	1.13456i
$47$		−	1.07376e15i		−	0.0204141i	−0.999948	−	0.0102070i	$-0.996751\pi$
$47$		−	1.07376e15i		−	0.0204141i	0.999948	−	0.0102070i	$-0.00324906\pi$
$48$	2.26331e16	+	2.98803e16i	0.348604	+	0.460227i
$49$	2.18175e16			0.273429
$50$	5.39047e16	+	3.87550e16i	0.551984	+	0.396851i
$51$			6.30437e16i			0.529590i
$52$	−4.40476e16	−	1.31102e17i	−0.304712	−	0.906938i
$53$	−1.68440e16			−0.0963133			−0.0481567	−	0.998840i	$-0.515335\pi$
$53$	−1.68440e16			−0.0963133			−0.0481567	+	0.998840i	$0.515335\pi$
$54$	2.36853e16	−	3.29441e16i	0.112342	−	0.156257i
$55$		−	6.48781e16i		−	0.256136i
$56$	−2.47049e17	−	7.62057e16i	−0.814521	−	0.251251i
$57$	−1.14188e17			−0.315406
$58$	−5.73180e17	−	4.12090e17i	−1.33049	−	0.956559i
$59$			6.06716e17i			1.18704i	0.804819	+	0.593520i	$0.202262\pi$
$59$			6.06716e17i			1.18704i	−0.804819	+	0.593520i	$0.797738\pi$
$60$	−1.87247e17	+	6.29108e16i	−0.309672	+	0.104043i
$61$	−7.66597e17			−1.07465			−0.537327	−	0.843374i	$-0.680566\pi$
$61$	−7.66597e17			−1.07465			−0.537327	+	0.843374i	$0.680566\pi$
$62$	−2.08587e17	+	2.90126e17i	−0.248525	+	0.345676i
$63$			2.79849e17i			0.284131i
$64$	−9.52582e17	−	6.49473e17i	−0.826233	−	0.563328i
$65$	7.28823e17			0.541363
$66$	−3.32802e17	−	2.39269e17i	−0.212200	−	0.152562i
$67$		−	1.19477e18i		−	0.655446i	−0.944774	−	0.327723i	$-0.893719\pi$
$67$		−	1.19477e18i		−	0.655446i	0.944774	−	0.327723i	$-0.106281\pi$
$68$	−6.17557e17	−	1.83808e18i	−0.292138	−	0.869513i
$69$	1.97348e18			0.806757
$70$	7.95296e17	−	1.10619e18i	0.281546	−	0.391605i
$71$			4.68826e18i			1.44022i	0.693861	+	0.720109i	$0.255908\pi$
$71$			4.68826e18i			1.44022i	−0.693861	+	0.720109i	$0.744092\pi$
$72$	−3.67851e17	+	1.19252e18i	−0.0982533	+	0.318524i
$73$	8.31694e18			1.93524			0.967621	−	0.252409i	$-0.0812229\pi$
$73$	8.31694e18			1.93524			0.967621	+	0.252409i	$0.0812229\pi$
$74$	−2.62073e18	−	1.88418e18i	−0.532236	−	0.382653i
$75$			2.21032e18i			0.392503i
$76$	3.32922e18	−	1.11855e18i	0.517853	−	0.173987i
$77$	2.82703e18			0.385855
$78$	2.68788e18	−	3.73861e18i	0.322452	−	0.448501i
$79$			1.79551e19i			1.89635i	0.317756	+	0.948173i	$0.397071\pi$
$79$			1.79551e19i			1.89635i	−0.317756	+	0.948173i	$0.602929\pi$
$80$	4.84305e18	−	3.66842e18i	0.451044	−	0.341648i
$81$	1.35085e18			0.111111
$82$	−1.54688e19	−	1.11214e19i	−1.12543	−	0.809133i
$83$			1.72296e19i			1.11044i	0.831704	+	0.555219i	$0.187366\pi$
$83$			1.72296e19i			1.11044i	−0.831704	+	0.555219i	$0.812634\pi$
$84$	−2.74131e18	−	8.15919e18i	−0.156735	−	0.466503i
$85$	1.02182e19			0.519023
$86$	8.39906e17	−	1.16823e18i	0.0379530	−	0.0527892i
$87$		−	2.35028e19i		−	0.946080i
$88$	1.20469e19	+	3.71603e18i	0.432561	+	0.133430i
$89$	1.92566e19			0.617561			0.308780	−	0.951133i	$-0.400079\pi$
$89$	1.92566e19			0.617561			0.308780	+	0.951133i	$0.400079\pi$
$90$	−5.33965e18	−	3.83896e18i	−0.153140	−	0.110100i
$91$			3.17581e19i			0.815532i
$92$	−5.75383e19	+	1.93316e19i	−1.32458	+	0.445031i
$93$	−1.18964e19			−0.245802
$94$	−6.41847e17	+	8.92751e17i	−0.0119166	+	0.0165749i
$95$			1.85077e19i			0.309113i
$96$	−9.56631e17	−	3.83722e19i	−0.0143891	−	0.577171i
$97$	1.24589e19			0.168952			0.0844759	−	0.996426i	$-0.473078\pi$
$97$	1.24589e19			0.168952			0.0844759	+	0.996426i	$0.473078\pi$
$98$	−1.81396e19	−	1.30415e19i	−0.222007	−	0.159613i
$99$		−	1.36463e19i		−	0.150891i
$100$	−2.16517e19	−	6.44436e19i	−0.216517	−	0.644436i
$101$	−6.99208e19			−0.632984			−0.316492	−	0.948595i	$-0.602505\pi$
$101$	−6.99208e19			−0.632984			−0.316492	+	0.948595i	$0.602505\pi$
$102$	3.76847e19	−	5.24160e19i	0.309146	−	0.429994i
$103$		−	2.06372e20i		−	1.53560i	−0.640689	−	0.767801i	$-0.721351\pi$
$103$		−	2.06372e20i		−	1.53560i	0.640689	−	0.767801i	$-0.278649\pi$
$104$	−4.17449e19	+	1.35331e20i	−0.282014	+	0.914250i
$105$	4.53584e19			0.278461
$106$	1.40045e19	+	1.00686e19i	0.0782004	+	0.0562224i
$107$			1.22424e20i			0.622340i	0.950354	+	0.311170i	$0.100721\pi$
$107$			1.22424e20i			0.622340i	−0.950354	+	0.311170i	$0.899279\pi$
$108$	−3.93850e19	+	1.32325e19i	−0.182429	+	0.0612922i
$109$	−2.64682e20			−1.11805			−0.559023	−	0.829152i	$-0.688824\pi$
$109$	−2.64682e20			−1.11805			−0.559023	+	0.829152i	$0.688824\pi$
$110$	−3.87812e19	+	5.39411e19i	−0.149518	+	0.207966i
$111$		−	1.07461e20i		−	0.378461i
$112$	1.59850e20	+	2.11034e20i	0.514673	+	0.679472i
$113$	−4.93131e20			−1.45271			−0.726354	−	0.687321i	$-0.758786\pi$
$113$	−4.93131e20			−1.45271			−0.726354	+	0.687321i	$0.758786\pi$
$114$	9.49382e19	+	6.82562e19i	0.256090	+	0.184117i
$115$		−	3.19866e20i		−	0.790660i
$116$	2.30227e20	+	6.85242e20i	0.521886	+	1.55333i
$117$	1.53299e20			0.318919
$118$	3.62667e20	−	5.04438e20i	0.692928	−	0.963802i
$119$			4.45256e20i			0.781879i
$120$	1.93286e20	+	5.96220e19i	0.312168	+	0.0962928i
$121$	5.34895e20			0.795087
$122$	6.37367e20	+	4.58237e20i	0.872551	+	0.627324i
$123$		−	6.34289e20i		−	0.800269i
$124$	3.46848e20	−	1.16533e20i	0.403573	−	0.135592i
$125$	8.85224e20			0.950502
$126$	1.67281e20	−	2.32673e20i	0.165860	−	0.230696i
$127$		−	1.88418e21i		−	1.72617i	−0.505056	−	0.863086i	$-0.668528\pi$
$127$		−	1.88418e21i		−	1.72617i	0.505056	−	0.863086i	$-0.331472\pi$
$128$	4.03773e20	+	1.10940e21i	0.342009	+	0.939697i
$129$	4.79027e19			0.0375372
$130$	−6.05960e20	−	4.35657e20i	−0.439552	−	0.316018i
$131$			7.50602e20i			0.504309i	0.967687	+	0.252155i	$0.0811391\pi$
$131$			7.50602e20i			0.504309i	−0.967687	+	0.252155i	$0.918861\pi$
$132$	1.33675e20	+	3.97868e20i	0.0832360	+	0.247742i
$133$	−8.06467e20			−0.465661
$134$	−7.14181e20	+	9.93361e20i	−0.382613	+	0.532181i
$135$		−	2.18949e20i		−	0.108894i
$136$	−5.85272e20	+	1.89737e21i	−0.270376	+	0.876524i
$137$	−3.21757e21			−1.38141			−0.690704	−	0.723138i	$-0.742699\pi$
$137$	−3.21757e21			−1.38141			−0.690704	+	0.723138i	$0.742699\pi$
$138$	−1.64080e21	−	1.17966e21i	−0.655036	−	0.470940i
$139$			1.86048e21i			0.690999i	0.938419	+	0.345500i	$0.112291\pi$
$139$			1.86048e21i			0.690999i	−0.938419	+	0.345500i	$0.887709\pi$
$140$	−1.32246e21	+	4.44317e20i	−0.457195	+	0.153608i
$141$	−3.66067e19			−0.0117861
$142$	2.80243e21	−	3.89793e21i	0.840720	−	1.16937i
$143$		−	1.54863e21i		−	0.433098i
$144$	1.01868e21	−	7.71607e20i	0.265712	−	0.201266i
$145$	−3.80939e21			−0.927203
$146$	−6.91490e21	−	4.97149e21i	−1.57129	−	1.12969i
$147$		−	7.43801e20i		−	0.157864i
$148$	1.05266e21	+	3.13311e21i	0.208771	+	0.621381i
$149$	3.60783e21			0.668934			0.334467	−	0.942407i	$-0.391444\pi$
$149$	3.60783e21			0.668934			0.334467	+	0.942407i	$0.391444\pi$
$150$	1.32123e21	−	1.83772e21i	0.229122	−	0.318688i
$151$			8.34968e21i			1.35488i	0.735579	+	0.677439i	$0.236910\pi$
$151$			8.34968e21i			1.35488i	−0.735579	+	0.677439i	$0.763090\pi$
$152$	−3.43661e21	−	1.06007e21i	−0.522028	−	0.161027i
$153$	2.14928e21			0.305759
$154$	−2.35046e21	−	1.68987e21i	−0.313290	−	0.225241i
$155$			1.92819e21i			0.240898i
$156$	−4.46954e21	+	1.50167e21i	−0.523621	+	0.175925i
$157$	9.82145e21			1.07939			0.539696	−	0.841860i	$-0.318539\pi$
$157$	9.82145e21			1.07939			0.539696	+	0.841860i	$0.318539\pi$
$158$	1.07328e22	−	1.49283e22i	1.10698	−	1.53971i
$159$			5.74245e20i			0.0556065i
$160$	−6.21944e21	+	1.55053e20i	−0.565655	+	0.0141019i
$161$	1.39380e22			1.19108
$162$	−1.12313e21	−	8.07478e20i	−0.0902152	−	0.0648606i
$163$			1.25888e22i			0.950841i	0.879759	+	0.475420i	$0.157704\pi$
$163$			1.25888e22i			0.950841i	−0.879759	+	0.475420i	$0.842296\pi$
$164$	6.21330e21	+	1.84931e22i	0.441452	+	1.31393i
$165$	−2.21182e21			−0.147880
$166$	1.02991e22	−	1.43251e22i	0.648213	−	0.901606i
$167$		−	1.44352e21i		−	0.0855576i	−0.999085	−	0.0427788i	$-0.986379\pi$
$167$		−	1.44352e21i		−	0.0855576i	0.999085	−	0.0427788i	$-0.0136211\pi$
$168$	−2.59800e21	+	8.42237e21i	−0.145060	+	0.470264i
$169$	−1.60811e21			−0.0846151
$170$	−8.49569e21	−	6.10800e21i	−0.421414	−	0.302977i
$171$			3.89288e21i			0.182100i
$172$	−1.39664e21	+	4.69240e20i	−0.0616309	+	0.0207067i
$173$	1.66137e22			0.691840			0.345920	−	0.938264i	$-0.387567\pi$
$173$	1.66137e22			0.691840			0.345920	+	0.938264i	$0.387567\pi$
$174$	−1.40489e22	+	1.95408e22i	−0.552270	+	0.768158i
$175$			1.56107e22i			0.579486i
$176$	−7.79478e21	−	1.02907e22i	−0.273324	−	0.360842i
$177$	2.06841e22			0.685338
$178$	−1.60104e22	−	1.15107e22i	−0.501421	−	0.360498i
$179$		−	2.56764e22i		−	0.760334i	−0.924918	−	0.380167i	$-0.875867\pi$
$179$		−	2.56764e22i		−	0.760334i	0.924918	−	0.380167i	$-0.124133\pi$
$180$	2.14475e21	+	6.38360e21i	0.0600692	+	0.178789i
$181$	−4.11002e22			−1.08908			−0.544539	−	0.838736i	$-0.683295\pi$
$181$	−4.11002e22			−1.08908			−0.544539	+	0.838736i	$0.683295\pi$
$182$	1.89836e22	−	2.64045e22i	0.476063	−	0.662161i
$183$			2.61348e22i			0.620452i
$184$	5.93943e22	+	1.83210e22i	1.33526	+	0.411881i
$185$	−1.74175e22			−0.370910
$186$	9.89095e21	+	7.11113e21i	0.199576	+	0.143486i
$187$		−	2.17121e22i		−	0.415227i
$188$	1.06729e21	−	3.58588e20i	0.0193511	−	0.00650155i
$189$	9.54059e21			0.164043
$190$	1.10631e22	−	1.53878e22i	0.180443	−	0.250980i
$191$		−	7.63954e22i		−	1.18232i	−0.806556	−	0.591158i	$-0.798671\pi$
$191$		−	7.63954e22i		−	1.18232i	0.806556	−	0.591158i	$-0.201329\pi$
$192$	−2.21418e22	+	3.24754e22i	−0.325238	+	0.477026i
$193$	−1.37759e23			−1.92109			−0.960544	−	0.278129i	$-0.910286\pi$
$193$	−1.37759e23			−1.92109			−0.960544	+	0.278129i	$0.910286\pi$
$194$	−1.03586e22	−	7.44737e21i	−0.137178	−	0.0986247i
$195$		−	2.48470e22i		−	0.312556i
$196$	7.28604e21	+	2.16860e22i	0.0870825	+	0.259191i
$197$	1.51839e22			0.172473			0.0862364	−	0.996275i	$-0.472516\pi$
$197$	1.51839e22			0.172473			0.0862364	+	0.996275i	$0.472516\pi$
$198$	−8.15715e21	+	1.13459e22i	−0.0880819	+	0.122514i
$199$		−	7.89826e21i		−	0.0810962i	−0.999178	−	0.0405481i	$-0.987090\pi$
$199$		−	7.89826e21i		−	0.0810962i	0.999178	−	0.0405481i	$-0.0129104\pi$
$200$	−2.05198e22	+	6.65223e22i	−0.200388	+	0.649632i
$201$	−4.07321e22			−0.378422
$202$	5.81338e22	+	4.17955e22i	0.513943	+	0.369501i
$203$		−	1.65992e23i		−	1.39678i
$204$	−6.26639e22	+	2.10537e22i	−0.502014	+	0.168666i
$205$	−1.02807e23			−0.784301
$206$	−1.23360e23	+	1.71583e23i	−0.896400	+	1.24681i
$207$		−	6.72799e22i		−	0.465781i
$208$	1.15603e23	−	8.75644e22i	0.762666	−	0.577689i
$209$	3.93259e22			0.247295
$210$	−3.77121e22	−	2.71132e22i	−0.226093	−	0.162550i
$211$			2.12146e23i			1.21286i	0.795136	+	0.606431i	$0.207399\pi$
$211$			2.12146e23i			1.21286i	−0.795136	+	0.606431i	$0.792601\pi$
$212$	−5.62512e21	−	1.67425e22i	−0.0306742	−	0.0912982i
$213$	1.59832e23			0.831510
$214$	7.31794e22	−	1.01786e23i	0.363288	−	0.505301i
$215$		−	7.76415e21i		−	0.0367883i
$216$	4.06554e22	+	1.25408e22i	0.183900	+	0.0567266i
$217$	−8.40201e22			−0.362899
$218$	2.20063e23	+	1.58215e23i	0.907782	+	0.652653i
$219$		−	2.83541e23i		−	1.11731i
$220$	6.44872e22	−	2.16663e22i	0.242799	−	0.0815752i
$221$	2.43908e23			0.877612
$222$	−6.42354e22	+	8.93457e22i	−0.220925	+	0.307287i
$223$			3.40514e23i			1.11966i	0.828607	+	0.559831i	$0.189134\pi$
$223$			3.40514e23i			1.11966i	−0.828607	+	0.559831i	$0.810866\pi$
$224$	−6.75635e21	−	2.71009e23i	−0.0212438	−	0.852127i
$225$	7.53543e22			0.226612
$226$	4.10001e23	+	2.94772e23i	1.17951	+	0.848011i
$227$			4.14078e23i			1.13979i	0.821718	+	0.569894i	$0.193016\pi$
$227$			4.14078e23i			1.13979i	−0.821718	+	0.569894i	$0.806984\pi$
$228$	−3.81334e22	−	1.13500e23i	−0.100452	−	0.298983i
$229$	2.44774e23			0.617178			0.308589	−	0.951196i	$-0.400143\pi$
$229$	2.44774e23			0.617178			0.308589	+	0.951196i	$0.400143\pi$
$230$	−1.91201e23	+	2.65944e23i	−0.461544	+	0.641966i
$231$		−	9.63791e22i		−	0.222773i
$232$	2.18191e23	−	7.07345e23i	0.483011	−	1.56586i
$233$	1.58866e22			0.0336877			0.0168438	−	0.999858i	$-0.494638\pi$
$233$	1.58866e22			0.0336877			0.0168438	+	0.999858i	$0.494638\pi$
$234$	−1.27456e23	−	9.16352e22i	−0.258942	−	0.186167i
$235$			5.93328e21i			0.0115509i
$236$	−6.03060e23	+	2.02615e23i	−1.12523	+	0.378053i
$237$	6.12125e23			1.09486
$238$	2.66154e23	−	3.70196e23i	0.456418	−	0.634837i
$239$			8.91319e22i			0.146573i	0.997311	+	0.0732866i	$0.0233488\pi$
$239$			8.91319e22i			0.146573i	−0.997311	+	0.0732866i	$0.976651\pi$
$240$	−1.25064e23	−	1.65109e23i	−0.197251	−	0.260410i
$241$	−1.20240e24			−1.81919			−0.909593	−	0.415500i	$-0.863606\pi$
$241$	−1.20240e24			−1.81919			−0.909593	+	0.415500i	$0.863606\pi$
$242$	−4.44724e23	−	3.19736e23i	−0.645561	−	0.464128i
$243$		−	4.60532e22i		−	0.0641500i
$244$	−2.56008e23	−	7.61978e23i	−0.342260	−	1.01869i
$245$	−1.20557e23			−0.154714
$246$	−3.79149e23	+	5.27363e23i	−0.467153	+	0.649768i
$247$			4.41776e23i			0.522676i
$248$	−3.58036e23	−	1.10441e23i	−0.406827	−	0.125492i
$249$	5.87391e23			0.641112
$250$	−7.35996e23	−	5.29147e23i	−0.771748	−	0.554851i
$251$			1.77981e24i			1.79324i	0.442806	+	0.896618i	$0.353983\pi$
$251$			1.77981e24i			1.79324i	−0.442806	+	0.896618i	$0.646017\pi$
$252$	−2.78163e23	+	9.34567e22i	−0.269335	+	0.0904909i
$253$	−6.79662e23			−0.632540
$254$	−1.12628e24	+	1.56655e24i	−1.00764	+	1.40154i
$255$		−	3.48360e23i		−	0.299658i
$256$	3.27441e23	−	1.16374e24i	0.270853	−	0.962621i
$257$	1.34374e24			1.06902			0.534508	−	0.845163i	$-0.320497\pi$
$257$	1.34374e24			1.06902			0.534508	+	0.845163i	$0.320497\pi$
$258$	−3.98274e22	−	2.86340e22i	−0.0304779	−	0.0219122i
$259$		−	7.58960e23i		−	0.558755i
$260$	2.43393e23	+	7.24431e23i	0.172415	+	0.513173i
$261$	−8.01258e23			−0.546220
$262$	4.48676e23	−	6.24068e23i	0.294388	−	0.409467i
$263$		−	2.40335e24i		−	1.51796i	−0.651114	−	0.758980i	$-0.725698\pi$
$263$		−	2.40335e24i		−	1.51796i	0.651114	−	0.758980i	$-0.274302\pi$
$264$	1.26687e23	−	4.10702e23i	0.0770357	−	0.249739i
$265$	9.30747e22			0.0544970
$266$	6.70515e23	+	4.82069e23i	0.378088	+	0.271827i
$267$		−	6.56496e23i		−	0.356549i
$268$	1.18757e24	−	3.98999e23i	0.621316	−	0.208749i
$269$	1.35700e24			0.684003			0.342002	−	0.939699i	$-0.388895\pi$
$269$	1.35700e24			0.684003			0.342002	+	0.939699i	$0.388895\pi$
$270$	−1.30878e23	+	1.82039e23i	−0.0635664	+	0.0884152i
$271$			2.25529e24i			1.05563i	0.849361	+	0.527813i	$0.176988\pi$
$271$			2.25529e24i			1.05563i	−0.849361	+	0.527813i	$0.823012\pi$
$272$	1.62077e24	−	1.22767e24i	0.731195	−	0.553851i
$273$	1.08270e24			0.470848
$274$	2.67516e24	+	1.92332e24i	1.12162	+	0.806390i
$275$		−	7.61230e23i		−	0.307743i
$276$	6.59053e23	+	1.96159e24i	0.256939	+	0.764748i
$277$	−2.31992e24			−0.872320			−0.436160	−	0.899869i	$-0.643662\pi$
$277$	−2.31992e24			−0.872320			−0.436160	+	0.899869i	$0.643662\pi$
$278$	1.11211e24	−	1.54685e24i	0.403367	−	0.561048i
$279$			4.05572e23i			0.141914i
$280$	1.36511e24	+	4.21089e23i	0.460881	+	0.142165i
$281$	−2.00661e24			−0.653731			−0.326865	−	0.945071i	$-0.605992\pi$
$281$	−2.00661e24			−0.653731			−0.326865	+	0.945071i	$0.605992\pi$
$282$	3.04356e22	+	2.18818e22i	0.00956955	+	0.00688006i
$283$			2.91470e24i			0.884565i	0.896876	+	0.442283i	$0.145831\pi$
$283$			2.91470e24i			0.884565i	−0.896876	+	0.442283i	$0.854169\pi$
$284$	−4.66001e24	+	1.56566e24i	−1.36522	+	0.458686i
$285$	6.30965e23			0.178466
$286$	−9.25699e23	+	1.28757e24i	−0.252819	+	0.351649i
$287$		−	4.47976e24i		−	1.18151i
$288$	−1.30818e24	+	3.26134e22i	−0.333230	+	0.00830752i
$289$	−6.44597e23			−0.158603
$290$	3.16721e24	+	2.27708e24i	0.752831	+	0.541250i
$291$		−	4.24749e23i		−	0.0975443i
$292$	2.77748e24	+	8.26683e24i	0.616342	+	1.83447i
$293$	−2.04625e24			−0.438816			−0.219408	−	0.975633i	$-0.570413\pi$
$293$	−2.04625e24			−0.438816			−0.219408	+	0.975633i	$0.570413\pi$
$294$	−4.44611e23	+	6.18414e23i	−0.0921524	+	0.128176i
$295$		−	3.35252e24i		−	0.671663i
$296$	9.97626e23	−	3.23417e24i	0.193219	−	0.626391i
$297$	−4.65229e23			−0.0871170
$298$	−2.99963e24	−	2.15660e24i	−0.543132	−	0.390487i
$299$		−	7.63514e24i		−	1.33692i
$300$	−2.19701e24	+	7.38147e23i	−0.372065	+	0.125006i
$301$	3.38320e23			0.0554194
$302$	4.99106e24	−	6.94212e24i	0.790903	−	1.10008i
$303$			2.38374e24i			0.365454i
$304$	2.22361e24	+	2.93562e24i	0.329855	+	0.435475i
$305$	4.23597e24			0.608072
$306$	−1.78696e24	−	1.28474e24i	−0.248257	−	0.178485i
$307$		−	4.96011e24i		−	0.666972i	−0.942755	−	0.333486i	$-0.891775\pi$
$307$		−	4.96011e24i		−	0.666972i	0.942755	−	0.333486i	$-0.108225\pi$
$308$	9.44100e23	+	2.81000e24i	0.122888	+	0.365763i
$309$	−7.03562e24			−0.886580
$310$	1.15259e24	−	1.60314e24i	0.140623	−	0.195594i
$311$			4.37702e24i			0.517101i	0.965998	+	0.258550i	$0.0832448\pi$
$311$			4.37702e24i			0.517101i	−0.965998	+	0.258550i	$0.916755\pi$
$312$	4.61371e24	+	1.42317e24i	0.527843	+	0.162821i
$313$	−2.84158e24			−0.314860			−0.157430	−	0.987530i	$-0.550321\pi$
$313$	−2.84158e24			−0.314860			−0.157430	+	0.987530i	$0.550321\pi$
$314$	−8.16579e24	−	5.87082e24i	−0.876399	−	0.630090i
$315$		−	1.54636e24i		−	0.160770i
$316$	−1.78469e25	+	5.99619e24i	−1.79760	+	0.603955i
$317$	−5.07053e24			−0.494835			−0.247418	−	0.968909i	$-0.579582\pi$
$317$	−5.07053e24			−0.494835			−0.247418	+	0.968909i	$0.579582\pi$
$318$	3.43258e23	−	4.77441e23i	0.0324600	−	0.0451490i
$319$			8.09431e24i			0.741777i
$320$	5.26367e24	+	3.58879e24i	0.467508	+	0.318748i
$321$	4.17366e24			0.359308
$322$	−1.15884e25	−	8.33152e24i	−0.967085	−	0.695289i
$323$			6.19379e24i			0.501108i
$324$	4.51123e23	+	1.34271e24i	0.0353871	+	0.105325i
$325$	8.55145e24			0.650438
$326$	7.52501e24	−	1.04666e25i	0.555049	−	0.772023i
$327$			9.02353e24i			0.645504i
$328$	5.88848e24	−	1.90897e25i	0.408569	−	1.32452i
$329$	−2.58540e23			−0.0174008
$330$	1.83896e24	+	1.32213e24i	0.120070	+	0.0863244i
$331$			3.26438e24i			0.206786i	0.994641	+	0.103393i	$0.0329699\pi$
$331$			3.26438e24i			0.206786i	−0.994641	+	0.103393i	$0.967030\pi$
$332$	−1.71258e25	+	5.75390e24i	−1.05262	+	0.353656i
$333$	−3.66356e24			−0.218505
$334$	−8.62872e23	+	1.20018e24i	−0.0499438	+	0.0694674i
$335$			6.60194e24i			0.370871i
$336$	7.19455e24	−	5.44959e24i	0.392294	−	0.297147i
$337$	1.81586e25			0.961132			0.480566	−	0.876959i	$-0.340431\pi$
$337$	1.81586e25			0.961132			0.480566	+	0.876959i	$0.340431\pi$
$338$	1.33702e24	+	9.61254e23i	0.0687021	+	0.0493936i
$339$			1.68118e25i			0.838721i
$340$	3.41243e24	+	1.01567e25i	0.165300	+	0.491997i
$341$	4.09709e24			0.192722
$342$	2.32699e24	−	3.23663e24i	0.106300	−	0.147854i
$343$		−	2.44655e25i		−	1.08546i
$344$	1.44169e24	+	4.44709e23i	0.0621278	+	0.0191642i
$345$	−1.09049e25			−0.456488
$346$	−1.38130e25	−	9.93093e24i	−0.561730	−	0.403858i
$347$			4.22049e25i			1.66751i	0.552136	+	0.833754i	$0.313813\pi$
$347$			4.22049e25i			1.66751i	−0.552136	+	0.833754i	$0.686187\pi$
$348$	2.33612e25	−	7.84888e24i	0.896816	−	0.301311i
$349$	4.62043e25			1.72357			0.861784	−	0.507275i	$-0.169347\pi$
$349$	4.62043e25			1.72357			0.861784	+	0.507275i	$0.169347\pi$
$350$	9.33140e24	−	1.29791e25i	0.338272	−	0.470506i
$351$		−	5.22626e24i		−	0.184128i
$352$	3.29461e23	+	1.32153e25i	0.0112818	+	0.452532i
$353$	1.81280e25			0.603397			0.301698	−	0.953403i	$-0.402446\pi$
$353$	1.81280e25			0.603397			0.301698	+	0.953403i	$0.402446\pi$
$354$	−1.71973e25	−	1.23640e25i	−0.556451	−	0.400062i
$355$		−	2.59059e25i		−	0.814919i
$356$	6.43083e24	+	1.91406e25i	0.196683	+	0.585404i
$357$	1.51796e25			0.451418
$358$	−1.53482e25	+	2.13480e25i	−0.443841	+	0.617343i
$359$			1.96376e25i			0.552261i	0.961120	+	0.276131i	$0.0890522\pi$
$359$			1.96376e25i			0.552261i	−0.961120	+	0.276131i	$0.910948\pi$
$360$	2.03263e24	−	6.58951e24i	0.0555947	−	0.180230i
$361$	2.63715e25			0.701557
$362$	3.41717e25	+	2.45679e25i	0.884262	+	0.635743i
$363$		−	1.82356e25i		−	0.459044i
$364$	−3.15668e25	+	1.06058e25i	−0.773066	+	0.259734i
$365$	−4.59568e25			−1.09502
$366$	1.56222e25	−	2.17291e25i	0.362186	−	0.503768i
$367$		−	1.78925e25i		−	0.403656i	−0.979421	−	0.201828i	$-0.935312\pi$
$367$		−	1.78925e25i		−	0.403656i	0.979421	−	0.201828i	$-0.0646882\pi$
$368$	−3.84303e25	−	5.07358e25i	−0.843715	−	1.11387i
$369$	−2.16242e25			−0.462036
$370$	1.44813e25	+	1.04114e25i	0.301156	+	0.216517i
$371$			4.05569e24i			0.0820967i
$372$	−3.97285e24	−	1.18247e25i	−0.0782840	−	0.233003i
$373$	−4.68130e25			−0.898003			−0.449001	−	0.893531i	$-0.648220\pi$
$373$	−4.68130e25			−0.898003			−0.449001	+	0.893531i	$0.648220\pi$
$374$	−1.29785e25	+	1.80519e25i	−0.242386	+	0.337138i
$375$		−	3.01790e25i		−	0.548773i
$376$	−1.10172e24	−	3.39841e23i	−0.0195071	−	0.00601725i
$377$	−9.09293e25			−1.56780
$378$	−7.93227e24	−	5.70293e24i	−0.133192	−	0.0957592i
$379$		−	1.66214e24i		−	0.0271817i	−0.999908	−	0.0135908i	$-0.995674\pi$
$379$		−	1.66214e24i		−	0.0271817i	0.999908	−	0.0135908i	$-0.00432623\pi$
$380$	−1.83962e25	+	6.18074e24i	−0.293017	+	0.0984474i
$381$	−6.42353e25			−0.996606
$382$	−4.56657e25	+	6.35169e25i	−0.690171	+	0.959966i
$383$		−	7.95012e24i		−	0.117054i	−0.998286	−	0.0585269i	$-0.981360\pi$
$383$		−	7.95012e24i		−	0.117054i	0.998286	−	0.0585269i	$-0.0186404\pi$
$384$	3.78215e25	−	1.37654e25i	0.542534	−	0.197459i
$385$	−1.56213e25			−0.218328
$386$	1.14536e26	+	8.23462e25i	1.55980	+	1.12143i
$387$		−	1.63310e24i		−	0.0216721i
$388$	4.16070e24	+	1.23838e25i	0.0538083	+	0.160154i
$389$	−1.09764e26			−1.38345			−0.691726	−	0.722160i	$-0.743149\pi$
$389$	−1.09764e26			−1.38345			−0.691726	+	0.722160i	$0.743149\pi$
$390$	−1.48524e25	+	2.06584e25i	−0.182453	+	0.253776i
$391$		−	1.07046e26i		−	1.28175i
$392$	6.90515e24	−	2.23856e25i	0.0805958	−	0.261281i
$393$	2.55895e25			0.291163
$394$	−1.26242e25	−	9.07624e24i	−0.140037	−	0.100680i
$395$		−	9.92144e25i		−	1.07301i
$396$	1.35641e25	−	4.55724e24i	0.143034	−	0.0480563i
$397$	1.85326e26			1.90560			0.952800	−	0.303600i	$-0.0981885\pi$
$397$	1.85326e26			1.90560			0.952800	+	0.303600i	$0.0981885\pi$
$398$	−4.72122e24	+	6.56680e24i	−0.0473395	+	0.0658450i
$399$			2.74940e25i			0.268850i
$400$	5.68246e25	−	4.30424e25i	0.541922	−	0.410484i
$401$	1.16750e26			1.08596			0.542980	−	0.839746i	$-0.317296\pi$
$401$	1.16750e26			1.08596			0.542980	+	0.839746i	$0.317296\pi$
$402$	3.38656e25	+	2.43478e25i	0.307255	+	0.220902i
$403$			4.60256e25i			0.407332i
$404$	−2.33504e25	−	6.94995e25i	−0.201595	−	0.600024i
$405$	−7.46439e24			−0.0628701
$406$	−9.92227e25	+	1.38010e26i	−0.815363	+	1.13410i
$407$			3.70093e25i			0.296734i
$408$	6.46852e25	+	1.99531e25i	0.506061	+	0.156102i
$409$	−1.51509e26			−1.15666			−0.578328	−	0.815804i	$-0.696295\pi$
$409$	−1.51509e26			−1.15666			−0.578328	+	0.815804i	$0.696295\pi$
$410$	8.54760e25	+	6.14532e25i	0.636803	+	0.457832i
$411$			1.09693e26i			0.797556i
$412$	2.05129e26	−	6.89188e25i	1.45564	−	0.489064i
$413$	1.46085e26			1.01182
$414$	−4.02169e25	+	5.59381e25i	−0.271897	+	0.378185i
$415$		−	9.52055e25i		−	0.628320i
$416$	−1.48457e26	+	3.70108e24i	−0.956460	+	0.0238449i
$417$	6.34275e25			0.398949
$418$	−3.26965e25	−	2.35072e25i	−0.200788	−	0.144357i
$419$			9.59340e24i			0.0575218i	0.999586	+	0.0287609i	$0.00915614\pi$
$419$			9.59340e24i			0.0575218i	−0.999586	+	0.0287609i	$0.990844\pi$
$420$	1.51476e25	+	4.50851e25i	0.0886853	+	0.263961i
$421$	3.05679e25			0.174761			0.0873806	−	0.996175i	$-0.472150\pi$
$421$	3.05679e25			0.174761			0.0873806	+	0.996175i	$0.472150\pi$
$422$	1.26812e26	−	1.76383e26i	0.708002	−	0.984767i
$423$			1.24799e24i			0.00680469i
$424$	−5.33106e24	+	1.72826e25i	−0.0283893	+	0.0920343i
$425$	1.19893e26			0.623598
$426$	−1.32888e26	−	9.55403e25i	−0.675134	−	0.485390i
$427$			1.84581e26i			0.916026i
$428$	−1.21686e26	+	4.08839e25i	−0.589934	+	0.198205i
$429$	−5.27957e25			−0.250049
$430$	−4.64106e24	+	6.45530e24i	−0.0214750	+	0.0298698i
$431$		−	1.37906e26i		−	0.623463i	−0.950170	−	0.311732i	$-0.899091\pi$
$431$		−	1.37906e26i		−	0.623463i	0.950170	−	0.311732i	$-0.100909\pi$
$432$	−2.63056e25	−	3.47287e25i	−0.116201	−	0.153409i
$433$	−1.82619e26			−0.788256			−0.394128	−	0.919055i	$-0.628953\pi$
$433$	−1.82619e26			−0.788256			−0.394128	+	0.919055i	$0.628953\pi$
$434$	6.98563e25	+	5.02234e25i	0.294651	+	0.211841i
$435$			1.29869e26i			0.535321i
$436$	−8.83917e25	−	2.63087e26i	−0.356079	−	1.05983i
$437$	1.93887e26			0.763368
$438$	−1.69488e26	+	2.35743e26i	−0.652225	+	0.907187i
$439$			2.66738e26i			1.00332i	0.865065	+	0.501660i	$0.167277\pi$
$439$			2.66738e26i			1.00332i	−0.865065	+	0.501660i	$0.832723\pi$
$440$	−6.65673e25	−	2.05336e25i	−0.244756	−	0.0754987i
$441$	−2.53576e25			−0.0911429
$442$	−2.02790e26	−	1.45797e26i	−0.712566	−	0.512302i
$443$			2.17825e26i			0.748290i	0.927370	+	0.374145i	$0.122064\pi$
$443$			2.17825e26i			0.748290i	−0.927370	+	0.374145i	$0.877936\pi$
$444$	1.06814e26	−	3.58871e25i	0.358754	−	0.120534i
$445$	−1.06406e26			−0.349435
$446$	2.03544e26	−	2.83112e26i	0.653597	−	0.909095i
$447$		−	1.22998e26i		−	0.386209i
$448$	−1.56380e26	+	2.29362e26i	−0.480176	+	0.704274i
$449$	−4.18686e26			−1.25726			−0.628630	−	0.777705i	$-0.716384\pi$
$449$	−4.18686e26			−1.25726			−0.628630	+	0.777705i	$0.716384\pi$
$450$	−6.26513e25	−	4.50434e25i	−0.183995	−	0.132284i
$451$			2.18447e26i			0.627453i
$452$	−1.64683e26	−	4.90160e26i	−0.462663	−	1.37706i
$453$	2.84657e26			0.782239
$454$	2.47517e26	−	3.44274e26i	0.665345	−	0.925436i
$455$		−	1.75486e26i		−	0.461453i
$456$	−3.61399e25	+	1.17161e26i	−0.0929691	+	0.301393i
$457$	1.69605e26			0.426851			0.213425	−	0.976959i	$-0.431538\pi$
$457$	1.69605e26			0.426851			0.213425	+	0.976959i	$0.431538\pi$
$458$	−2.03511e26	−	1.46315e26i	−0.501109	−	0.360274i
$459$		−	7.32733e25i		−	0.176530i
$460$	3.17939e26	−	1.06821e26i	0.749489	−	0.251812i
$461$	3.83519e26			0.884663			0.442332	−	0.896852i	$-0.354151\pi$
$461$	3.83519e26			0.884663			0.442332	+	0.896852i	$0.354151\pi$
$462$	−5.76111e25	+	8.01319e25i	−0.130043	+	0.180878i
$463$			5.21913e26i			1.15289i	0.817136	+	0.576445i	$0.195561\pi$
$463$			5.21913e26i			1.15289i	−0.817136	+	0.576445i	$0.804439\pi$
$464$	−6.04228e26	+	4.57679e26i	−1.30623	+	0.989421i
$465$	6.57358e25			0.139082
$466$	−1.32085e25	−	9.49628e24i	−0.0273523	−	0.0196650i
$467$		−	8.07616e26i		−	1.63695i	−0.574540	−	0.818476i	$-0.694819\pi$
$467$		−	8.07616e26i		−	1.63695i	0.574540	−	0.818476i	$-0.305181\pi$
$468$	5.11948e25	+	1.52375e26i	0.101571	+	0.302313i
$469$	−2.87677e26			−0.558697
$470$	3.54665e24	−	4.93307e24i	0.00674278	−	0.00937861i
$471$		−	3.34833e26i		−	0.623187i
$472$	6.22513e26	+	1.92023e26i	1.13430	+	0.349892i
$473$	−1.64975e25			−0.0294312
$474$	−5.08935e26	−	3.65901e26i	−0.888954	−	0.639116i
$475$			2.17156e26i			0.371394i
$476$	−4.42573e26	+	1.48695e26i	−0.741166	+	0.249016i
$477$	1.95771e25			0.0321044
$478$	5.32790e25	−	7.41064e25i	0.0855613	−	0.119008i
$479$			1.20617e26i			0.189694i	0.995492	+	0.0948471i	$0.0302362\pi$
$479$			1.20617e26i			0.189694i	−0.995492	+	0.0948471i	$0.969764\pi$
$480$	5.28605e24	+	2.12033e26i	0.00814176	+	0.326581i
$481$	−4.15753e26			−0.627168
$482$	9.99700e26	+	7.18738e26i	1.47706	+	1.06194i
$483$		−	4.75174e26i		−	0.687673i
$484$	1.78630e26	+	5.31672e26i	0.253222	+	0.753686i
$485$	−6.88440e25			−0.0955980
$486$	−2.75285e25	+	3.82897e25i	−0.0374473	+	0.0520858i
$487$		−	5.97783e26i		−	0.796626i	−0.917250	−	0.398313i	$-0.869596\pi$
$487$		−	5.97783e26i		−	0.796626i	0.917250	−	0.398313i	$-0.130404\pi$
$488$	−2.42625e26	+	7.86557e26i	−0.316765	+	1.02691i
$489$	4.29176e26			0.548968
$490$	1.00234e26	+	7.20633e25i	0.125618	+	0.0903137i
$491$			1.53267e27i			1.88206i	0.338328	+	0.941028i	$0.390139\pi$
$491$			1.53267e27i			1.88206i	−0.338328	+	0.941028i	$0.609861\pi$
$492$	6.30467e26	−	2.11823e26i	0.758598	−	0.254873i
$493$	−1.27485e27			−1.50310
$494$	2.64074e26	−	3.67303e26i	0.305110	−	0.424380i
$495$			7.54053e25i			0.0853787i
$496$	2.31663e26	+	3.05841e26i	0.257063	+	0.339375i
$497$	1.12884e27			1.22763
$498$	−4.88371e26	−	3.51116e26i	−0.520543	−	0.374246i
$499$		−	1.72410e25i		−	0.0180118i	−0.999959	−	0.00900591i	$-0.997133\pi$
$499$		−	1.72410e25i		−	0.0180118i	0.999959	−	0.00900591i	$-0.00286671\pi$
$500$	2.95624e26	+	8.79891e26i	0.302719	+	0.901008i
$501$	−4.92125e25			−0.0493967
$502$	1.06389e27	−	1.47978e27i	1.04679	−	1.45599i
$503$		−	1.81538e27i		−	1.75101i	−0.483211	−	0.875504i	$-0.660530\pi$
$503$		−	1.81538e27i		−	1.75101i	0.483211	−	0.875504i	$-0.339470\pi$
$504$	2.87135e26	+	8.85710e25i	0.271507	+	0.0837503i
$505$	3.86361e26			0.358162
$506$	5.65087e26	+	4.06271e26i	0.513583	+	0.369242i
$507$			5.48235e25i			0.0488525i
$508$	1.87282e27	−	6.29229e26i	1.63629	−	0.549758i
$509$	−7.36206e26			−0.630699			−0.315349	−	0.948976i	$-0.602122\pi$
$509$	−7.36206e26			−0.630699			−0.315349	+	0.948976i	$0.602122\pi$
$510$	−2.08234e26	+	2.89635e26i	−0.174924	+	0.243304i
$511$		−	2.00255e27i		−	1.64958i
$512$	−9.67872e26	+	7.71829e26i	−0.781841	+	0.623478i
$513$	1.32716e26			0.105135
$514$	−1.11722e27	−	8.03228e26i	−0.867974	−	0.624033i
$515$			1.14035e27i			0.868890i
$516$	1.59973e25	+	4.76140e25i	0.0119550	+	0.0355826i
$517$	1.26072e25			0.00924090
$518$	−4.53672e26	+	6.31017e26i	−0.326170	+	0.453674i
$519$		−	5.66394e26i		−	0.399434i
$520$	2.30669e26	−	7.47799e26i	0.159572	−	0.517311i
$521$	−5.40681e26			−0.366914			−0.183457	−	0.983028i	$-0.558729\pi$
$521$	−5.40681e26			−0.366914			−0.183457	+	0.983028i	$0.558729\pi$
$522$	6.66185e26	+	4.78956e26i	0.443496	+	0.318853i
$523$			1.01180e27i			0.660813i	0.943839	+	0.330407i	$0.107186\pi$
$523$			1.01180e27i			0.660813i	−0.943839	+	0.330407i	$0.892814\pi$
$524$	−7.46080e26	+	2.50667e26i	−0.478049	+	0.160614i
$525$	5.32201e26			0.334567
$526$	−1.43662e27	+	1.99821e27i	−0.886101	+	1.23249i
$527$			6.45288e26i			0.390524i
$528$	−3.50829e26	+	2.65739e26i	−0.208332	+	0.157803i
$529$	−1.63476e27			−0.952570
$530$	−7.73845e25	−	5.56358e25i	−0.0442482	−	0.0318124i
$531$		−	7.05162e26i		−	0.395680i
$532$	−2.69323e26	−	8.01608e26i	−0.148305	−	0.441413i
$533$	−2.45398e27			−1.32617
$534$	−3.92423e26	+	5.45826e26i	−0.208134	+	0.289495i
$535$		−	6.76475e26i		−	0.352139i
$536$	−1.22588e27	−	3.78140e26i	−0.626325	−	0.193199i
$537$	−8.75360e26			−0.438979
$538$	−1.12824e27	−	8.11155e26i	−0.555368	−	0.399283i
$539$			2.56163e26i			0.123774i
$540$	2.17629e26	−	7.31188e25i	0.103224	−	0.0346810i
$541$	6.14212e26			0.285987			0.142993	−	0.989724i	$-0.454327\pi$
$541$	6.14212e26			0.285987			0.142993	+	0.989724i	$0.454327\pi$
$542$	1.34811e27	−	1.87510e27i	0.616216	−	0.857101i
$543$			1.40119e27i			0.628779i
$544$	−2.08140e27	+	5.18899e25i	−0.916992	+	0.0228609i
$545$	1.46255e27			0.632624
$546$	−9.00180e26	−	6.47187e26i	−0.382299	−	0.274855i
$547$			2.36240e27i			0.985102i	0.870284	+	0.492551i	$0.163935\pi$
$547$			2.36240e27i			0.985102i	−0.870284	+	0.492551i	$0.836065\pi$
$548$	−1.07452e27	−	3.19818e27i	−0.439956	−	1.30948i
$549$	8.90986e26			0.358218
$550$	−4.55029e26	+	6.32904e26i	−0.179644	+	0.249868i
$551$		−	2.30906e27i		−	0.895199i
$552$	6.24600e26	−	2.02487e27i	0.237799	−	0.770914i
$553$	4.32323e27			1.61643
$554$	1.92884e27	+	1.38675e27i	0.708269	+	0.509213i
$555$			5.93797e26i			0.214145i
$556$	−1.84927e27	+	6.21316e26i	−0.655018	+	0.220072i
$557$	2.38279e27			0.828960			0.414480	−	0.910058i	$-0.363963\pi$
$557$	2.38279e27			0.828960			0.414480	+	0.910058i	$0.363963\pi$
$558$	2.42432e26	−	3.37202e26i	0.0828416	−	0.115225i
$559$		−	1.85329e26i		−	0.0622049i
$560$	−8.83280e26	−	1.16611e27i	−0.291218	−	0.384466i
$561$	−7.40207e26			−0.239731
$562$	1.66834e27	+	1.19946e27i	0.530788	+	0.381612i
$563$			5.99999e27i			1.87528i	0.347606	+	0.937641i	$0.386995\pi$
$563$			5.99999e27i			1.87528i	−0.347606	+	0.937641i	$0.613005\pi$
$564$	−1.22250e25	−	3.63861e25i	−0.00375367	−	0.0111724i
$565$	2.72489e27			0.821986
$566$	1.74228e27	−	2.42335e27i	0.516360	−	0.718211i
$567$		−	3.25257e26i		−	0.0947102i
$568$	4.81033e27	+	1.48381e27i	1.37623	+	0.424518i
$569$	3.54052e26			0.0995277			0.0497639	−	0.998761i	$-0.484153\pi$
$569$	3.54052e26			0.0995277			0.0497639	+	0.998761i	$0.484153\pi$
$570$	−5.24599e26	−	3.77162e26i	−0.144904	−	0.104179i
$571$			3.24615e27i			0.881063i	0.897737	+	0.440532i	$0.145210\pi$
$571$			3.24615e27i			0.881063i	−0.897737	+	0.440532i	$0.854790\pi$
$572$	1.53930e27	−	5.17171e26i	0.410546	−	0.137935i
$573$	−2.60447e27			−0.682610
$574$	−2.67780e27	+	3.72458e27i	−0.689698	+	0.959308i
$575$		−	3.75306e27i		−	0.949964i
$576$	1.10715e27	+	7.54858e26i	0.275411	+	0.187776i
$577$	8.74605e26			0.213823			0.106911	−	0.994269i	$-0.465904\pi$
$577$	8.74605e26			0.213823			0.106911	+	0.994269i	$0.465904\pi$
$578$	5.35933e26	+	3.85311e26i	0.128775	+	0.0925834i
$579$			4.69648e27i			1.10914i
$580$	−1.27216e27	−	3.78643e27i	−0.295299	−	0.878922i
$581$	4.14854e27			0.946528
$582$	−2.53896e26	+	3.53146e26i	−0.0569410	+	0.0791999i
$583$		−	1.97768e26i		−	0.0435985i
$584$	2.63228e27	−	8.53349e27i	0.570431	−	1.84926i
$585$	−8.47082e26			−0.180454
$586$	1.70130e27	+	1.22316e27i	0.356291	+	0.256157i
$587$		−	4.82514e26i		−	0.0993410i	−0.998766	−	0.0496705i	$-0.984183\pi$
$587$		−	4.82514e26i		−	0.0993410i	0.998766	−	0.0496705i	$-0.0158171\pi$
$588$	7.39320e26	−	2.48395e26i	0.149644	−	0.0502771i
$589$	−1.16877e27			−0.232583
$590$	−2.00399e27	+	2.78737e27i	−0.392080	+	0.545348i
$591$		−	5.17648e26i		−	0.0995772i
$592$	−2.76269e27	+	2.09263e27i	−0.522534	+	0.395799i
$593$	−5.40054e27			−1.00436			−0.502181	−	0.864763i	$-0.667469\pi$
$593$	−5.40054e27			−1.00436			−0.502181	+	0.864763i	$0.667469\pi$
$594$	3.86803e26	+	2.78093e26i	0.0707335	+	0.0508541i
$595$		−	2.46034e27i		−	0.442411i
$596$	1.20485e27	+	3.58609e27i	0.213045	+	0.634102i
$597$	−2.69267e26			−0.0468209
$598$	−4.56394e27	+	6.34804e27i	−0.780420	+	1.08549i
$599$		−	6.46102e27i		−	1.08651i	−0.839569	−	0.543254i	$-0.817192\pi$
$599$		−	6.46102e27i		−	1.08651i	0.839569	−	0.543254i	$-0.182808\pi$
$600$	2.26787e27	+	6.99559e26i	0.375065	+	0.115694i
$601$	5.70646e27			0.928158			0.464079	−	0.885794i	$-0.346385\pi$
$601$	5.70646e27			0.928158			0.464079	+	0.885794i	$0.346385\pi$
$602$	−2.81287e26	−	2.02232e26i	−0.0449971	−	0.0323508i
$603$			1.38864e27i			0.218482i
$604$	−8.29937e27	+	2.78841e27i	−1.28433	+	0.431506i
$605$	−2.95566e27			−0.449885
$606$	1.42489e27	−	1.98190e27i	0.213332	−	0.296725i
$607$		−	7.69256e27i		−	1.13288i	−0.824103	−	0.566440i	$-0.808320\pi$
$607$		−	7.69256e27i		−	1.13288i	0.824103	−	0.566440i	$-0.191680\pi$
$608$	−9.39852e25	−	3.76992e27i	−0.0136152	−	0.546130i
$609$	−5.65900e27			−0.806431
$610$	−3.52189e27	−	2.53207e27i	−0.493716	−	0.354959i
$611$			1.41626e26i			0.0195313i
$612$	7.17762e26	+	2.13633e27i	0.0973792	+	0.289838i
$613$	−2.28003e27			−0.304323			−0.152162	−	0.988356i	$-0.548623\pi$
$613$	−2.28003e27			−0.304323			−0.152162	+	0.988356i	$0.548623\pi$
$614$	−2.96493e27	+	4.12395e27i	−0.389342	+	0.541540i
$615$			3.50488e27i			0.452817i
$616$	8.94745e26	−	2.90064e27i	0.113734	−	0.368712i
$617$	−9.41076e27			−1.17699			−0.588495	−	0.808501i	$-0.700279\pi$
$617$	−9.41076e27			−1.17699			−0.588495	+	0.808501i	$0.700279\pi$
$618$	5.84958e27	+	4.20558e27i	0.719847	+	0.517536i
$619$		−	1.98132e27i		−	0.239910i	−0.992779	−	0.119955i	$-0.961725\pi$
$619$		−	1.98132e27i		−	0.239910i	0.992779	−	0.119955i	$-0.0382750\pi$
$620$	−1.91657e27	+	6.43928e26i	−0.228354	+	0.0767220i
$621$	−2.29370e27			−0.268919
$622$	2.61639e27	−	3.63916e27i	0.301855	−	0.419853i
$623$		−	4.63660e27i		−	0.526404i
$624$	−2.98524e27	−	3.94112e27i	−0.333529	−	0.440326i
$625$	1.29160e27			0.142013
$626$	2.36256e27	+	1.69857e27i	0.255646	+	0.183798i
$627$		−	1.34070e27i		−	0.142776i
$628$	3.27992e27	+	9.76228e27i	0.343769	+	1.02319i
$629$	−5.82894e27			−0.601288
$630$	−9.24342e26	+	1.28568e27i	−0.0938485	+	0.130535i
$631$		−	1.62150e28i		−	1.62041i	−0.586150	−	0.810203i	$-0.699357\pi$
$631$		−	1.62150e28i		−	1.62041i	0.586150	−	0.810203i	$-0.300643\pi$
$632$	1.84226e28	+	5.68272e27i	1.81209	+	0.558966i
$633$	7.23248e27			0.700246
$634$	4.21576e27	+	3.03093e27i	0.401775	+	0.288858i
$635$			1.04114e28i			0.976721i
$636$	−5.70785e26	+	1.91771e26i	−0.0527110	+	0.0177098i
$637$	−2.87766e27			−0.261605
$638$	4.83842e27	−	6.72980e27i	0.433008	−	0.602276i
$639$		−	5.44898e27i		−	0.480073i
$640$	−2.23113e27	−	6.13019e27i	−0.193519	−	0.531709i
$641$	7.91188e26			0.0675615			0.0337808	−	0.999429i	$-0.489245\pi$
$641$	7.91188e26			0.0675615			0.0337808	+	0.999429i	$0.489245\pi$
$642$	−3.47008e27	−	2.49483e27i	−0.291736	−	0.209744i
$643$		−	8.92653e27i		−	0.738879i	−0.929255	−	0.369439i	$-0.879550\pi$
$643$		−	8.92653e27i		−	0.738879i	0.929255	−	0.369439i	$-0.120450\pi$
$644$	4.65466e27	+	1.38540e28i	0.379341	+	1.12906i
$645$	−2.64695e26			−0.0212397
$646$	3.70237e27	−	5.14967e27i	0.292519	−	0.406868i
$647$			1.25756e28i			0.978331i	0.872191	+	0.489165i	$0.162699\pi$
$647$			1.25756e28i			0.978331i	−0.872191	+	0.489165i	$0.837301\pi$
$648$	4.27539e26	−	1.38602e27i	0.0327511	−	0.106175i
$649$	−7.12356e27			−0.537341
$650$	−7.10987e27	−	5.11167e27i	−0.528115	−	0.379690i
$651$			2.86441e27i			0.209520i
$652$	−1.25129e28	+	4.20408e27i	−0.901329	+	0.302827i
$653$	1.12280e28			0.796475			0.398238	−	0.917282i	$-0.369622\pi$
$653$	1.12280e28			0.796475			0.398238	+	0.917282i	$0.369622\pi$
$654$	5.39386e27	−	7.50237e27i	0.376810	−	0.524108i
$655$		−	4.14759e27i		−	0.285354i
$656$	−1.63068e28	+	1.23517e28i	−1.10492	+	0.836930i
$657$	−9.66646e27			−0.645080
$658$	2.14956e26	+	1.54544e26i	0.0141283	+	0.0101576i
$659$			1.92167e28i			1.24402i	0.783011	+	0.622008i	$0.213683\pi$
$659$			1.92167e28i			1.24402i	−0.783011	+	0.622008i	$0.786317\pi$
$660$	−7.38647e26	−	2.19849e27i	−0.0470974	−	0.140180i
$661$	1.26027e28			0.791496			0.395748	−	0.918359i	$-0.370485\pi$
$661$	1.26027e28			0.791496			0.395748	+	0.918359i	$0.370485\pi$
$662$	1.95130e27	−	2.71408e27i	0.120710	−	0.167897i
$663$		−	8.31528e27i		−	0.506689i
$664$	1.76782e28	+	5.45310e27i	1.06110	+	0.327313i
$665$	4.45628e27			0.263485
$666$	3.04597e27	+	2.18991e27i	0.177412	+	0.127551i
$667$			3.99071e28i			2.28977i
$668$	1.43482e27	−	4.82070e26i	0.0811025	−	0.0272487i
$669$	1.16088e28			0.646437
$670$	3.94634e27	−	5.48901e27i	0.216494	−	0.301124i
$671$		−	9.00074e27i		−	0.486467i
$672$	−9.23924e27	+	2.30337e26i	−0.491976	+	0.0122651i
$673$	1.86482e28			0.978334			0.489167	−	0.872190i	$-0.337301\pi$
$673$	1.86482e28			0.978334			0.489167	+	0.872190i	$0.337301\pi$
$674$	−1.50975e28	−	1.08544e28i	−0.780378	−	0.561056i
$675$		−	2.56898e27i		−	0.130834i
$676$	−5.37034e26	−	1.59842e27i	−0.0269485	−	0.0802090i
$677$	−8.32020e27			−0.411384			−0.205692	−	0.978617i	$-0.565944\pi$
$677$	−8.32020e27			−0.411384			−0.205692	+	0.978617i	$0.565944\pi$
$678$	1.00493e28	−	1.39777e28i	0.489599	−	0.680989i
$679$		−	2.99985e27i		−	0.144013i
$680$	3.23403e27	−	1.04843e28i	0.152987	−	0.495964i
$681$	1.41167e28			0.658057
$682$	−3.40641e27	−	2.44905e27i	−0.156478	−	0.112501i
$683$		−	1.00616e28i		−	0.455470i	−0.973723	−	0.227735i	$-0.926868\pi$
$683$		−	1.00616e28i		−	0.455470i	0.973723	−	0.227735i	$-0.0731320\pi$
$684$	−3.86942e27	+	1.30004e27i	−0.172618	+	0.0579958i
$685$	1.77793e28			0.781643
$686$	−1.46244e28	+	2.03412e28i	−0.633632	+	0.881325i
$687$		−	8.34482e27i		−	0.356328i
$688$	−9.32825e26	−	1.23152e27i	−0.0392569	−	0.0518270i
$689$	2.22168e27			0.0921485
$690$	9.06655e27	+	6.51843e27i	0.370639	+	0.266472i
$691$			4.34243e28i			1.74965i	0.484437	+	0.874826i	$0.339025\pi$
$691$			4.34243e28i			1.74965i	−0.484437	+	0.874826i	$0.660975\pi$
$692$	5.54822e27	+	1.65136e28i	0.220340	+	0.655815i
$693$	−3.28575e27			−0.128618
$694$	2.52282e28	−	3.50901e28i	0.973399	−	1.35391i
$695$		−	1.02804e28i		−	0.390988i
$696$	−2.41148e28	−	7.43856e27i	−0.904047	−	0.278866i
$697$	−3.44053e28			−1.27144
$698$	−3.84154e28	−	2.76189e28i	−1.39943	−	1.00612i
$699$		−	5.41604e26i		−	0.0194496i
$700$	−1.55167e28	+	5.21327e27i	−0.549312	+	0.184557i
$701$	3.07405e28			1.07283			0.536414	−	0.843955i	$-0.319778\pi$
$701$	3.07405e28			1.07283			0.536414	+	0.843955i	$0.319778\pi$
$702$	−3.12402e27	+	4.34524e27i	−0.107484	+	0.149500i
$703$		−	1.05576e28i		−	0.358107i
$704$	7.62558e27	−	1.11844e28i	0.255003	−	0.374014i
$705$	2.02277e26			0.00666892
$706$	−1.50721e28	−	1.08361e28i	−0.489920	−	0.352230i
$707$			1.68355e28i			0.539550i
$708$	6.90755e27	+	2.05595e28i	0.218269	+	0.649651i
$709$	−4.36841e28			−1.36101			−0.680505	−	0.732743i	$-0.738240\pi$
$709$	−4.36841e28			−1.36101			−0.680505	+	0.732743i	$0.738240\pi$
$710$	−1.54854e28	+	2.15387e28i	−0.475705	+	0.661663i
$711$		−	2.08685e28i		−	0.632115i
$712$	6.09464e27	−	1.97580e28i	0.182032	−	0.590124i
$713$	2.01997e28			0.594908
$714$	−1.26207e28	−	9.07370e27i	−0.366523	−	0.263513i
$715$			8.55723e27i			0.245060i
$716$	2.55217e28	−	8.57475e27i	0.720742	−	0.242154i
$717$	3.03868e27			0.0846240
$718$	1.17385e28	−	1.63272e28i	0.322380	−	0.448401i
$719$			2.08635e27i			0.0565066i	0.999601	+	0.0282533i	$0.00899450\pi$
$719$			2.08635e27i			0.0565066i	−0.999601	+	0.0282533i	$0.991005\pi$
$720$	−5.62889e27	+	4.26366e27i	−0.150348	+	0.113883i
$721$	−4.96901e28			−1.30893
$722$	−2.19259e28	−	1.57637e28i	−0.569620	−	0.409530i
$723$			4.09920e28i			1.05031i
$724$	−1.37256e28	−	4.08526e28i	−0.346853	−	1.03237i
$725$	−4.46964e28			−1.11402
$726$	−1.09004e28	+	1.51615e28i	−0.267964	+	0.372715i
$727$			7.51015e26i			0.0182098i	0.999959	+	0.00910489i	$0.00289822\pi$
$727$			7.51015e26i			0.0182098i	−0.999959	+	0.00910489i	$0.997102\pi$
$728$	3.25850e28	+	1.00513e28i	0.779299	+	0.240386i
$729$	−1.57004e27			−0.0370370
$730$	3.82096e28	+	2.74709e28i	0.889086	+	0.639212i
$731$		−	2.59835e27i		−	0.0596381i
$732$	−2.59773e28	+	8.72782e27i	−0.588144	+	0.197604i
$733$	6.27056e27			0.140045			0.0700223	−	0.997545i	$-0.477693\pi$
$733$	6.27056e27			0.140045			0.0700223	+	0.997545i	$0.477693\pi$
$734$	−1.06954e28	+	1.48763e28i	−0.235632	+	0.327743i
$735$			4.11001e27i			0.0893243i
$736$	1.62433e27	+	6.51548e28i	0.0348254	+	1.39691i
$737$	1.40280e28			0.296703
$738$	1.79788e28	+	1.29259e28i	0.375144	+	0.269711i
$739$		−	3.31684e28i		−	0.682780i	−0.939922	−	0.341390i	$-0.889102\pi$
$739$		−	3.31684e28i		−	0.682780i	0.939922	−	0.341390i	$-0.110898\pi$
$740$	−5.81665e27	−	1.73126e28i	−0.118129	−	0.351596i
$741$	1.50610e28			0.301767
$742$	2.42431e27	−	3.37200e27i	0.0479235	−	0.0666573i
$743$		−	6.96550e28i		−	1.35851i	−0.733901	−	0.679257i	$-0.762302\pi$
$743$		−	6.96550e28i		−	1.35851i	0.733901	−	0.679257i	$-0.237698\pi$
$744$	−3.76516e27	+	1.22061e28i	−0.0724527	+	0.234882i
$745$	−1.99357e28			−0.378503
$746$	3.89214e28	+	2.79827e28i	0.729122	+	0.524205i
$747$		−	2.00253e28i		−	0.370146i
$748$	2.15813e28	−	7.25084e27i	0.393605	−	0.132243i
$749$	2.94771e28			0.530477
$750$	−1.80397e28	+	2.50916e28i	−0.320343	+	0.445569i
$751$		−	1.70350e28i		−	0.298499i	−0.988800	−	0.149250i	$-0.952314\pi$
$751$		−	1.70350e28i		−	0.298499i	0.988800	−	0.149250i	$-0.0476858\pi$
$752$	7.12854e26	+	9.41111e26i	0.0123260	+	0.0162728i
$753$	6.06773e28			1.03532
$754$	7.56008e28	+	5.43534e28i	1.27295	+	0.915195i
$755$		−	4.61377e28i		−	0.766631i
$756$	3.18612e27	+	9.48311e27i	0.0522449	+	0.155501i
$757$	2.28597e27			0.0369924			0.0184962	−	0.999829i	$-0.494112\pi$
$757$	2.28597e27			0.0369924			0.0184962	+	0.999829i	$0.494112\pi$
$758$	−9.93555e26	+	1.38195e27i	−0.0158672	+	0.0220698i
$759$			2.31710e28i			0.365197i
$760$	1.89896e28	+	5.85762e27i	0.295380	+	0.0911141i
$761$	7.75549e28			1.19059			0.595296	−	0.803507i	$-0.297035\pi$
$761$	7.75549e28			1.19059			0.595296	+	0.803507i	$0.297035\pi$
$762$	5.34067e28	+	3.83969e28i	0.809182	+	0.581764i
$763$			6.37300e28i			0.953012i
$764$	7.59351e28	−	2.55126e28i	1.12075	−	0.376548i
$765$	−1.18763e28			−0.173008
$766$	−4.75222e27	+	6.60992e27i	−0.0683296	+	0.0950404i
$767$		−	8.00241e28i		−	1.13571i
$768$	−3.96741e28	−	1.11631e28i	−0.555769	−	0.156377i
$769$	−1.87568e28			−0.259356			−0.129678	−	0.991556i	$-0.541394\pi$
$769$	−1.87568e28			−0.259356			−0.129678	+	0.991556i	$0.541394\pi$
$770$	1.29879e28	+	9.33771e27i	0.177269	+	0.127448i
$771$		−	4.58108e28i		−	0.617197i
$772$	−4.60052e28	−	1.36929e29i	−0.611835	−	1.82105i
$773$	−4.11292e28			−0.539952			−0.269976	−	0.962867i	$-0.587016\pi$
$773$	−4.11292e28			−0.539952			−0.269976	+	0.962867i	$0.587016\pi$
$774$	−9.76191e26	+	1.35779e27i	−0.0126510	+	0.0175964i
$775$			2.26239e28i			0.289435i
$776$	3.94319e27	−	1.27833e28i	0.0498002	−	0.161445i
$777$	−2.58744e28			−0.322597
$778$	9.12604e28	+	6.56120e28i	1.12328	+	0.807583i
$779$		−	6.23164e28i		−	0.757230i
$780$	2.46973e28	−	8.29776e27i	0.296281	−	0.0995439i
$781$	−5.50457e28			−0.651948
$782$	−6.39874e28	+	8.90008e28i	−0.748216	+	1.04070i
$783$			2.73165e28i			0.315360i
$784$	−1.91222e28	+	1.44843e28i	−0.217960	+	0.165096i
$785$	−5.42703e28			−0.610753
$786$	−2.12757e28	−	1.52962e28i	−0.236406	−	0.169965i
$787$			7.31038e28i			0.802034i	0.916071	+	0.401017i	$0.131343\pi$
$787$			7.31038e28i			0.802034i	−0.916071	+	0.401017i	$0.868657\pi$
$788$	5.07072e27	+	1.50924e28i	0.0549297	+	0.163492i
$789$	−8.19350e28			−0.876395
$790$	−5.93059e28	+	8.24892e28i	−0.626364	+	0.871217i
$791$			1.18736e29i			1.23828i
$792$	−1.40016e28	−	4.31900e27i	−0.144187	−	0.0444766i
$793$	1.01112e29			1.02818
$794$	−1.54085e29	−	1.10780e29i	−1.54723	−	1.11238i
$795$		−	3.17310e27i		−	0.0314639i
$796$	7.85067e27	−	2.63766e27i	0.0768734	−	0.0258278i
$797$	−6.63563e28			−0.641651			−0.320826	−	0.947138i	$-0.603960\pi$
$797$	−6.63563e28			−0.641651			−0.320826	+	0.947138i	$0.603960\pi$
$798$	1.64347e28	−	2.28592e28i	0.156940	−	0.218289i
$799$			1.98563e27i			0.0187254i
$800$	−7.29741e28	+	1.81927e27i	−0.679625	+	0.0169433i
$801$	−2.23812e28			−0.205854
$802$	−9.70688e28	−	6.97880e28i	−0.881731	−	0.633923i
$803$			9.76507e28i			0.876031i
$804$	−1.36027e28	−	4.04867e28i	−0.120521	−	0.358717i
$805$	−7.70172e28			−0.673952
$806$	2.75120e28	−	3.82667e28i	0.237778	−	0.330728i
$807$		−	4.62629e28i		−	0.394909i
$808$	−2.21297e28	+	7.17413e28i	−0.186578	+	0.604861i
$809$	−2.29927e28			−0.191472			−0.0957361	−	0.995407i	$-0.530520\pi$
$809$	−2.29927e28			−0.191472			−0.0957361	+	0.995407i	$0.530520\pi$
$810$	6.20607e27	+	4.46187e27i	0.0510465	+	0.0367001i
$811$		−	1.83767e29i		−	1.49300i	−0.665388	−	0.746498i	$-0.731734\pi$
$811$		−	1.83767e29i		−	1.49300i	0.665388	−	0.746498i	$-0.268266\pi$
$812$	1.64992e29	−	5.54338e28i	1.32405	−	0.444851i
$813$	7.68873e28			0.609466
$814$	2.21225e28	−	3.07704e28i	0.173217	−	0.240929i
$815$		−	6.95617e28i		−	0.538015i
$816$	−4.18537e28	−	5.52553e28i	−0.319766	−	0.422156i
$817$	4.70625e27			0.0355184
$818$	1.25968e29	+	9.05650e28i	0.939132	+	0.675192i
$819$		−	3.69113e28i		−	0.271844i
$820$	−3.43327e28	−	1.02187e29i	−0.249787	−	0.743462i
$821$	1.60599e29			1.15428			0.577142	−	0.816644i	$-0.304168\pi$
$821$	1.60599e29			1.15428			0.577142	+	0.816644i	$0.304168\pi$
$822$	6.55696e28	−	9.12015e28i	0.465569	−	0.647565i
$823$			1.06529e29i			0.747259i	0.927578	+	0.373630i	$0.121887\pi$
$823$			1.06529e29i			0.747259i	−0.927578	+	0.373630i	$0.878113\pi$
$824$	−2.11745e29	−	6.53159e28i	−1.46738	−	0.452634i
$825$	−2.59518e28			−0.177676
$826$	−1.21458e29	−	8.73229e28i	−0.821536	−	0.590646i
$827$			1.75689e29i			1.17406i	0.809565	+	0.587030i	$0.199703\pi$
$827$			1.75689e29i			1.17406i	−0.809565	+	0.587030i	$0.800297\pi$
$828$	6.68746e28	−	2.24684e28i	0.441527	−	0.148344i
$829$	1.46537e29			0.955875			0.477937	−	0.878394i	$-0.341385\pi$
$829$	1.46537e29			0.955875			0.477937	+	0.878394i	$0.341385\pi$
$830$	−5.69095e28	+	7.91561e28i	−0.366779	+	0.510156i
$831$			7.90907e28i			0.503634i
$832$	1.25643e29	+	8.56636e28i	0.790505	+	0.538968i
$833$	−4.03455e28			−0.250810
$834$	−5.27351e28	−	3.79141e28i	−0.323921	−	0.232884i
$835$			7.97645e27i			0.0484111i
$836$	1.31330e28	+	3.90889e28i	0.0787594	+	0.234418i
$837$	1.38267e28			0.0819341
$838$	5.73450e27	−	7.97618e27i	0.0335781	−	0.0467041i
$839$			1.94589e29i			1.12589i	0.826493	+	0.562947i	$0.190333\pi$
$839$			1.94589e29i			1.12589i	−0.826493	+	0.562947i	$0.809667\pi$
$840$	1.43558e28	−	4.65394e28i	0.0820792	−	0.266090i
$841$	2.98272e29			1.68520
$842$	−2.54149e28	−	1.82721e28i	−0.141895	−	0.102016i
$843$			6.84091e28i			0.377432i
$844$	−2.10868e29	+	7.08472e28i	−1.14971	+	0.386276i
$845$	8.88590e27			0.0478778
$846$	7.45994e26	−	1.03761e27i	0.00397220	−	0.00552498i
$847$		−	1.28792e29i		−	0.677726i
$848$	1.47631e28	−	1.11825e28i	0.0767749	−	0.0581539i
$849$	9.93679e28			0.510704
$850$	−9.96819e28	−	7.16666e28i	−0.506322	−	0.364022i
$851$			1.82466e29i			0.915979i
$852$	5.33765e28	+	1.58869e29i	0.264822	+	0.788212i
$853$	2.22289e29			1.09000			0.545001	−	0.838435i	$-0.316529\pi$
$853$	2.22289e29			1.09000			0.545001	+	0.838435i	$0.316529\pi$
$854$	1.10334e29	−	1.53465e29i	0.534725	−	0.743755i
$855$		−	2.15108e28i		−	0.103038i
$856$	1.25611e29	+	3.87466e28i	0.594690	+	0.183441i
$857$	−1.58075e29			−0.739699			−0.369850	−	0.929092i	$-0.620591\pi$
$857$	−1.58075e29			−0.739699			−0.369850	+	0.929092i	$0.620591\pi$
$858$	4.38956e28	+	3.15589e28i	0.203024	+	0.145965i
$859$		−	3.66367e29i		−	1.67488i	−0.546527	−	0.837441i	$-0.684050\pi$
$859$		−	3.66367e29i		−	1.67488i	0.546527	−	0.837441i	$-0.315950\pi$
$860$	7.71737e27	−	2.59287e27i	0.0348726	−	0.0117165i
$861$	−1.52724e29			−0.682143
$862$	−8.24341e28	+	1.14658e29i	−0.363944	+	0.506213i
$863$			2.51262e29i			1.09652i	0.836306	+	0.548262i	$0.184710\pi$
$863$			2.51262e29i			1.09652i	−0.836306	+	0.548262i	$0.815290\pi$
$864$	1.11186e27	+	4.45985e28i	0.00479635	+	0.192390i
$865$	−9.18022e28			−0.391464
$866$	1.51834e29	+	1.09162e29i	0.640014	+	0.460141i
$867$			2.19756e28i			0.0915692i
$868$	−2.80589e28	−	8.35139e28i	−0.115577	−	0.344002i
$869$	−2.10814e29			−0.858424
$870$	7.76301e28	−	1.07976e29i	0.312491	−	0.434647i
$871$			1.57587e29i			0.627103i
$872$	−8.37708e28	+	2.71573e29i	−0.329555	+	1.06837i
$873$	−1.44805e28			−0.0563172
$874$	−1.61202e29	−	1.15897e29i	−0.619807	−	0.445612i
$875$		−	2.13144e29i		−	0.810200i
$876$	2.81832e29	−	9.46897e28i	1.05913	−	0.355846i
$877$	2.78901e29			1.03622			0.518112	−	0.855313i	$-0.326635\pi$
$877$	2.78901e29			1.03622			0.518112	+	0.855313i	$0.326635\pi$
$878$	1.59444e29	−	2.21772e29i	0.585684	−	0.814633i
$879$			6.97607e28i			0.253351i
$880$	4.30715e28	+	5.68631e28i	0.154655	+	0.204176i
$881$	−7.83918e28			−0.278299			−0.139149	−	0.990271i	$-0.544437\pi$
$881$	−7.83918e28			−0.278299			−0.139149	+	0.990271i	$0.544437\pi$
$882$	2.10829e28	+	1.51576e28i	0.0740023	+	0.0532042i
$883$		−	4.47971e29i		−	1.55469i	−0.629077	−	0.777343i	$-0.716567\pi$
$883$		−	4.47971e29i		−	1.55469i	0.629077	−	0.777343i	$-0.283433\pi$
$884$	8.14540e28	+	2.42438e29i	0.279505	+	0.831913i
$885$	−1.14294e29			−0.387785
$886$	1.30206e29	−	1.81105e29i	0.436811	−	0.607564i
$887$		−	1.24347e29i		−	0.412478i	−0.978502	−	0.206239i	$-0.933878\pi$
$887$		−	1.24347e29i		−	0.412478i	0.978502	−	0.206239i	$-0.0661224\pi$
$888$	−1.10259e29	−	3.40110e28i	−0.361647	−	0.111555i
$889$	−4.53671e29			−1.47138
$890$	8.84685e28	+	6.36047e28i	0.283719	+	0.203981i
$891$			1.58606e28i			0.0502970i
$892$	−3.38463e29	+	1.13716e29i	−1.06136	+	0.356594i
$893$	−3.59646e27			−0.0111522
$894$	−7.35226e28	+	1.02263e29i	−0.225448	+	0.313578i
$895$			1.41880e29i			0.430220i
$896$	2.67120e29	−	9.72204e28i	0.800989	−	0.291526i
$897$	−2.60297e29			−0.771871
$898$	3.48105e29	+	2.50272e29i	1.02082	+	0.733919i
$899$		−	2.40565e29i		−	0.697646i
$900$	2.51649e28	+	7.49003e28i	0.0721722	+	0.214812i
$901$	3.11483e28			0.0883460
$902$	1.30578e29	−	1.81622e29i	0.366273	−	0.509452i
$903$		−	1.15340e28i		−	0.0319964i
$904$	−1.56074e29	+	5.05971e29i	−0.428200	+	1.38817i
$905$	2.27107e29			0.616233
$906$	−2.36670e29	−	1.70155e29i	−0.635129	−	0.456628i
$907$			3.22400e29i			0.855700i	0.903850	+	0.427850i	$0.140729\pi$
$907$			3.22400e29i			0.855700i	−0.903850	+	0.427850i	$0.859271\pi$
$908$	−4.11583e29	+	1.38283e29i	−1.08044	+	0.363004i
$909$	8.12663e28			0.210995
$910$	−1.04897e29	+	1.45903e29i	−0.269371	+	0.374671i
$911$		−	3.16499e29i		−	0.803875i	−0.915667	−	0.401938i	$-0.868337\pi$
$911$		−	3.16499e29i		−	0.803875i	0.915667	−	0.401938i	$-0.131663\pi$
$912$	1.00081e29	−	7.58073e28i	0.251422	−	0.190442i
$913$	−2.02296e29			−0.502666
$914$	−1.41013e29	−	1.01382e29i	−0.346576	−	0.249172i
$915$		−	1.44413e29i		−	0.351070i
$916$	8.17433e28	+	2.43299e29i	0.196561	+	0.585040i
$917$	1.80730e29			0.429869
$918$	−4.37995e28	+	6.09211e28i	−0.103049	+	0.143331i
$919$		−	5.72031e29i		−	1.33126i	−0.746280	−	0.665632i	$-0.768162\pi$
$919$		−	5.72031e29i		−	1.33126i	0.746280	−	0.665632i	$-0.231838\pi$
$920$	−3.28194e29	−	1.01236e29i	−0.755532	−	0.233055i
$921$	−1.69100e29			−0.385077
$922$	−3.18867e29	−	2.29251e29i	−0.718291	−	0.516418i
$923$		−	6.18368e29i		−	1.37794i
$924$	9.57984e28	−	3.21862e28i	0.211173	−	0.0709496i
$925$	−2.04364e29			−0.445642
$926$	3.11976e29	−	4.33931e29i	0.672994	−	0.936075i
$927$			2.39858e29i			0.511867i
$928$	7.75949e29	−	1.93447e28i	1.63815	−	0.0408396i
$929$	−7.85355e29			−1.64025			−0.820123	−	0.572188i	$-0.806095\pi$
$929$	−7.85355e29			−1.64025			−0.820123	+	0.572188i	$0.806095\pi$
$930$	−5.46543e28	−	3.92939e28i	−0.112926	−	0.0811887i
$931$		−	7.30755e28i		−	0.149374i
$932$	5.30539e27	+	1.57909e28i	0.0107290	+	0.0319335i
$933$	1.49221e29			0.298548
$934$	−4.82756e29	+	6.71471e29i	−0.955563	+	1.32910i
$935$			1.19974e29i			0.234948i
$936$	4.85185e28	−	1.57290e29i	0.0940046	−	0.304750i
$937$	8.90912e29			1.70781			0.853904	−	0.520430i	$-0.174229\pi$
$937$	8.90912e29			1.70781			0.853904	+	0.520430i	$0.174229\pi$
$938$	2.39181e29	+	1.71960e29i	0.453627	+	0.326136i
$939$			9.68752e28i			0.181784i
$940$	−5.89753e27	+	1.98144e27i	−0.0109494	+	0.00367877i
$941$	−2.79401e29			−0.513253			−0.256626	−	0.966511i	$-0.582611\pi$
$941$	−2.79401e29			−0.513253			−0.256626	+	0.966511i	$0.582611\pi$
$942$	−2.00148e29	+	2.78388e29i	−0.363783	+	0.505989i
$943$			1.07700e30i			1.93687i
$944$	−4.02789e29	−	5.31763e29i	−0.716734	−	0.946233i
$945$	−5.27183e28			−0.0928204
$946$	1.37164e28	+	9.86148e27i	0.0238963	+	0.0171803i
$947$		−	4.27749e29i		−	0.737376i	−0.929553	−	0.368688i	$-0.879807\pi$
$947$		−	4.27749e29i		−	0.737376i	0.929553	−	0.368688i	$-0.120193\pi$
$948$	2.04422e29	+	6.08437e29i	0.348693	+	1.03784i
$949$	−1.09698e30			−1.85156
$950$	1.29806e29	−	1.80548e29i	0.216799	−	0.301549i
$951$			1.72864e29i			0.285693i
$952$	4.56849e29	+	1.40922e29i	0.747142	+	0.230467i
$953$	8.90073e29			1.44044			0.720222	−	0.693743i	$-0.244040\pi$
$953$	8.90073e29			1.44044			0.720222	+	0.693743i	$0.244040\pi$
$954$	−1.62769e28	−	1.17023e28i	−0.0260668	−	0.0187408i
$955$			4.22137e29i			0.668990i
$956$	−8.85949e28	+	2.97660e28i	−0.138941	+	0.0466811i
$957$	2.75951e29			0.428265
$958$	7.20995e28	−	1.00284e29i	0.110733	−	0.154020i
$959$			7.74724e29i			1.17750i
$960$	1.22349e29	−	1.79449e29i	0.184029	−	0.269916i
$961$	5.50024e29			0.818744
$962$	3.45666e29	+	2.48518e29i	0.509221	+	0.366106i
$963$		−	1.42288e29i		−	0.207447i
$964$	−4.01545e29	−	1.19515e30i	−0.579381	−	1.72446i
$965$	7.61214e29			1.08701
$966$	−2.84038e29	+	3.95071e29i	−0.401425	+	0.558347i
$967$			9.00984e28i			0.126024i	0.998013	+	0.0630119i	$0.0200706\pi$
$967$			9.00984e28i			0.126024i	−0.998013	+	0.0630119i	$0.979929\pi$
$968$	1.69292e29	−	5.48822e29i	0.234360	−	0.759762i
$969$	2.11159e29			0.289315
$970$	5.72386e28	+	4.11519e28i	0.0776196	+	0.0558049i
$971$		−	3.68913e29i		−	0.495144i	−0.968870	−	0.247572i	$-0.920367\pi$
$971$		−	3.68913e29i		−	0.495144i	0.968870	−	0.247572i	$-0.0796326\pi$
$972$	4.57757e28	−	1.53797e28i	0.0608096	−	0.0204307i
$973$	4.47966e29			0.589002
$974$	−3.57328e29	+	4.97011e29i	−0.465026	+	0.646810i
$975$		−	2.91536e29i		−	0.375531i
$976$	6.71892e29	−	5.08931e29i	0.856646	−	0.648875i
$977$	6.86595e29			0.866473			0.433237	−	0.901280i	$-0.357371\pi$
$977$	6.86595e29			0.866473			0.433237	+	0.901280i	$0.357371\pi$
$978$	−3.56827e29	−	2.56542e29i	−0.445728	−	0.320457i
$979$			2.26095e29i			0.279553i
$980$	−4.02604e28	−	1.19830e29i	−0.0492740	−	0.146658i
$981$	3.07630e29			0.372682
$982$	9.16159e29	−	1.27429e30i	1.09864	−	1.52811i
$983$			1.33443e30i			1.58402i	0.610510	+	0.792009i	$0.290965\pi$
$983$			1.33443e30i			1.58402i	−0.610510	+	0.792009i	$0.709035\pi$
$984$	−6.50804e29	−	2.00750e29i	−0.764714	−	0.235887i
$985$	−8.39014e28			−0.0975903
$986$	1.05994e30	+	7.62047e29i	1.22043	+	0.877430i
$987$			8.81413e27i			0.0100463i
$988$	−4.39114e29	+	1.47533e29i	−0.495460	+	0.166464i
$989$	−8.13372e28			−0.0908503
$990$	4.50739e28	−	6.26937e28i	0.0498394	−	0.0693222i
$991$			7.62336e29i			0.834469i	0.908799	+	0.417234i	$0.137001\pi$
$991$			7.62336e29i			0.834469i	−0.908799	+	0.417234i	$0.862999\pi$
$992$	−9.79166e27	−	3.92761e29i	−0.0106106	−	0.425610i
$993$	1.11289e29			0.119388
$994$	−9.38541e29	−	6.74768e29i	−0.996758	−	0.716622i
$995$			4.36433e28i			0.0458867i
$996$	1.96162e29	+	5.83852e29i	0.204184	+	0.607728i
$997$	−6.47171e29			−0.666910			−0.333455	−	0.942766i	$-0.608215\pi$
$997$	−6.47171e29			−0.666910			−0.333455	+	0.942766i	$0.608215\pi$
$998$	−1.03059e28	+	1.43346e28i	−0.0105143	+	0.0146245i
$999$			1.24898e29i			0.126154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.21.d.a.7.3	✓	20
3.2	odd	2		36.21.d.c.19.18		20
4.3	odd	2	inner	12.21.d.a.7.4	yes	20
12.11	even	2		36.21.d.c.19.17		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.21.d.a.7.3	✓	20	1.1	even	1	trivial
12.21.d.a.7.4	yes	20	4.3	odd	2	inner
36.21.d.c.19.17		20	12.11	even	2
36.21.d.c.19.18		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)

\(f(q)\)	\(=\)	\(q+(-831.424 - 597.755i) q^{2} -34092.0i q^{3} +(333954. + 993975. i) q^{4} -5.52569e6 q^{5} +(-2.03786e7 + 2.83449e7i) q^{6} -2.40780e8i q^{7} +(3.16496e8 - 1.02604e9i) q^{8} -1.16226e9 q^{9} +O(q^{10})\)	\(q+(-831.424 - 597.755i) q^{2} -34092.0i q^{3} +(333954. + 993975. i) q^{4} -5.52569e6 q^{5} +(-2.03786e7 + 2.83449e7i) q^{6} -2.40780e8i q^{7} +(3.16496e8 - 1.02604e9i) q^{8} -1.16226e9 q^{9} +(4.59419e9 + 3.30301e9i) q^{10} +1.17412e10i q^{11} +(3.38866e10 - 1.13852e10i) q^{12} -1.31897e11 q^{13} +(-1.43927e11 + 2.00190e11i) q^{14} +1.88382e11i q^{15} +(-8.76461e11 + 6.63884e11i) q^{16} -1.84923e12 q^{17} +(9.66332e11 + 6.94747e11i) q^{18} -3.34940e12i q^{19} +(-1.84533e12 - 5.49240e12i) q^{20} -8.20864e12 q^{21} +(7.01834e12 - 9.76189e12i) q^{22} +5.78871e13i q^{23} +(-3.49796e13 - 1.07900e13i) q^{24} -6.48342e13 q^{25} +(1.09662e14 + 7.88422e13i) q^{26} +3.96238e13i q^{27} +(2.39329e14 - 8.04093e13i) q^{28} +6.89396e14 q^{29} +(1.12606e14 - 1.56625e14i) q^{30} -3.48950e14i q^{31} +(1.12555e15 - 2.80603e13i) q^{32} +4.00280e14 q^{33} +(1.53749e15 + 1.10538e15i) q^{34} +1.33047e15i q^{35} +(-3.88142e14 - 1.15526e15i) q^{36} +3.15210e15 q^{37} +(-2.00212e15 + 2.78477e15i) q^{38} +4.49663e15i q^{39} +(-1.74886e15 + 5.66956e15i) q^{40} +1.86052e16 q^{41} +(6.82486e15 + 4.90676e15i) q^{42} +1.40510e15i q^{43} +(-1.16704e16 + 3.92101e15i) q^{44} +6.42229e15 q^{45} +(3.46023e16 - 4.81287e16i) q^{46} -1.07376e15i q^{47} +(2.26331e16 + 2.98803e16i) q^{48} +2.18175e16 q^{49} +(5.39047e16 + 3.87550e16i) q^{50} +6.30437e16i q^{51} +(-4.40476e16 - 1.31102e17i) q^{52} -1.68440e16 q^{53} +(2.36853e16 - 3.29441e16i) q^{54} -6.48781e16i q^{55} +(-2.47049e17 - 7.62057e16i) q^{56} -1.14188e17 q^{57} +(-5.73180e17 - 4.12090e17i) q^{58} +6.06716e17i q^{59} +(-1.87247e17 + 6.29108e16i) q^{60} -7.66597e17 q^{61} +(-2.08587e17 + 2.90126e17i) q^{62} +2.79849e17i q^{63} +(-9.52582e17 - 6.49473e17i) q^{64} +7.28823e17 q^{65} +(-3.32802e17 - 2.39269e17i) q^{66} -1.19477e18i q^{67} +(-6.17557e17 - 1.83808e18i) q^{68} +1.97348e18 q^{69} +(7.95296e17 - 1.10619e18i) q^{70} +4.68826e18i q^{71} +(-3.67851e17 + 1.19252e18i) q^{72} +8.31694e18 q^{73} +(-2.62073e18 - 1.88418e18i) q^{74} +2.21032e18i q^{75} +(3.32922e18 - 1.11855e18i) q^{76} +2.82703e18 q^{77} +(2.68788e18 - 3.73861e18i) q^{78} +1.79551e19i q^{79} +(4.84305e18 - 3.66842e18i) q^{80} +1.35085e18 q^{81} +(-1.54688e19 - 1.11214e19i) q^{82} +1.72296e19i q^{83} +(-2.74131e18 - 8.15919e18i) q^{84} +1.02182e19 q^{85} +(8.39906e17 - 1.16823e18i) q^{86} -2.35028e19i q^{87} +(1.20469e19 + 3.71603e18i) q^{88} +1.92566e19 q^{89} +(-5.33965e18 - 3.83896e18i) q^{90} +3.17581e19i q^{91} +(-5.75383e19 + 1.93316e19i) q^{92} -1.18964e19 q^{93} +(-6.41847e17 + 8.92751e17i) q^{94} +1.85077e19i q^{95} +(-9.56631e17 - 3.83722e19i) q^{96} +1.24589e19 q^{97} +(-1.81396e19 - 1.30415e19i) q^{98} -1.36463e19i 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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