LMFDB - Embedded newform 12.21.d.a.7.18

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			7.18
Root			$-558.687 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.21.d.a.7.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(981.162 + 293.082i) q^{2} -34092.0i q^{3} +(876782. + 575122. i) q^{4} +1.08427e7 q^{5} +(9.99175e6 - 3.34497e7i) q^{6} +4.06904e8i q^{7} +(6.91707e8 + 8.21257e8i) q^{8} -1.16226e9 q^{9} +O(q^{10})$	\(q+(981.162 + 293.082i) q^{2} -34092.0i q^{3} +(876782. + 575122. i) q^{4} +1.08427e7 q^{5} +(9.99175e6 - 3.34497e7i) q^{6} +4.06904e8i q^{7} +(6.91707e8 + 8.21257e8i) q^{8} -1.16226e9 q^{9} +(1.06384e10 + 3.17779e9i) q^{10} +2.22298e9i q^{11} +(1.96070e10 - 2.98912e10i) q^{12} -1.75188e11 q^{13} +(-1.19256e11 + 3.99238e11i) q^{14} -3.69647e11i q^{15} +(4.37980e11 + 1.00851e12i) q^{16} +3.29319e12 q^{17} +(-1.14037e12 - 3.40638e11i) q^{18} +1.26021e12i q^{19} +(9.50664e12 + 6.23585e12i) q^{20} +1.38721e13 q^{21} +(-6.51515e11 + 2.18110e12i) q^{22} +3.97059e13i q^{23} +(2.79983e13 - 2.35816e13i) q^{24} +2.21957e13 q^{25} +(-1.71887e14 - 5.13444e13i) q^{26} +3.96238e13i q^{27} +(-2.34019e14 + 3.56766e14i) q^{28} +2.63518e14 q^{29} +(1.08337e14 - 3.62684e14i) q^{30} -8.61414e14i q^{31} +(1.34152e14 + 1.11788e15i) q^{32} +7.57856e13 q^{33} +(3.23116e15 + 9.65177e14i) q^{34} +4.41192e15i q^{35} +(-1.01905e15 - 6.68442e14i) q^{36} -1.00930e15 q^{37} +(-3.69345e14 + 1.23647e15i) q^{38} +5.97249e15i q^{39} +(7.49994e15 + 8.90461e15i) q^{40} +2.19849e16 q^{41} +(1.36108e16 + 4.06568e15i) q^{42} +3.71555e16i q^{43} +(-1.27848e15 + 1.94906e15i) q^{44} -1.26020e16 q^{45} +(-1.16371e16 + 3.89579e16i) q^{46} -8.27174e16i q^{47} +(3.43822e16 - 1.49316e16i) q^{48} -8.57784e16 q^{49} +(2.17776e16 + 6.50516e15i) q^{50} -1.12271e17i q^{51} +(-1.53601e17 - 1.00754e17i) q^{52} +1.21767e17 q^{53} +(-1.16130e16 + 3.88773e16i) q^{54} +2.41030e16i q^{55} +(-3.34173e17 + 2.81458e17i) q^{56} +4.29630e16 q^{57} +(2.58554e17 + 7.72324e16i) q^{58} -5.44449e17i q^{59} +(2.12592e17 - 3.24100e17i) q^{60} -4.97765e17 q^{61} +(2.52465e17 - 8.45187e17i) q^{62} -4.72928e17i q^{63} +(-1.96005e17 + 1.13614e18i) q^{64} -1.89950e18 q^{65} +(7.43579e16 + 2.22114e16i) q^{66} -3.24323e18i q^{67} +(2.88741e18 + 1.89399e18i) q^{68} +1.35365e18 q^{69} +(-1.29305e18 + 4.32880e18i) q^{70} -2.30034e18i q^{71} +(-8.03944e17 - 9.54516e17i) q^{72} -2.29913e18 q^{73} +(-9.90290e17 - 2.95809e17i) q^{74} -7.56694e17i q^{75} +(-7.24774e17 + 1.10493e18i) q^{76} -9.04537e17 q^{77} +(-1.75043e18 + 5.85998e18i) q^{78} -7.16859e17i q^{79} +(4.74887e18 + 1.09350e19i) q^{80} +1.35085e18 q^{81} +(2.15708e19 + 6.44339e18i) q^{82} -5.66725e18i q^{83} +(1.21628e19 + 7.97818e18i) q^{84} +3.57070e19 q^{85} +(-1.08896e19 + 3.64556e19i) q^{86} -8.98384e18i q^{87} +(-1.82563e18 + 1.53765e18i) q^{88} -3.74863e19 q^{89} +(-1.23646e19 - 3.69342e18i) q^{90} -7.12845e19i q^{91} +(-2.28358e19 + 3.48134e19i) q^{92} -2.93673e19 q^{93} +(2.42430e19 - 8.11591e19i) q^{94} +1.36640e19i q^{95} +(3.81107e19 - 4.57352e18i) q^{96} -1.04779e20 q^{97} +(-8.41625e19 - 2.51401e19i) q^{98} -2.58368e18i 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 $

$2$	981.162	+	293.082i	0.958166	+	0.286213i
$2$	981.162	+	293.082i	0.958166	+	0.286213i
$3$		−	34092.0i		−	0.577350i
$3$		−	34092.0i		−	0.577350i
$4$	876782.	+	575122.i	0.836164	+	0.548479i
$5$	1.08427e7			1.11029			0.555144	−	0.831754i	$-0.312663\pi$
$5$	1.08427e7			1.11029			0.555144	+	0.831754i	$0.312663\pi$
$6$	9.99175e6	−	3.34497e7i	0.165245	−	0.553197i
$7$			4.06904e8i			1.44049i	0.693718	+	0.720247i	$0.255971\pi$
$7$			4.06904e8i			1.44049i	−0.693718	+	0.720247i	$0.744029\pi$
$8$	6.91707e8	+	8.21257e8i	0.644202	+	0.764855i
$9$	−1.16226e9			−0.333333
$10$	1.06384e10	+	3.17779e9i	1.06384	+	0.317779i
$11$			2.22298e9i			0.0857053i	0.999081	+	0.0428527i	$0.0136446\pi$
$11$			2.22298e9i			0.0857053i	−0.999081	+	0.0428527i	$0.986355\pi$
$12$	1.96070e10	−	2.98912e10i	0.316665	−	0.482760i
$13$	−1.75188e11			−1.27078			−0.635389	−	0.772192i	$-0.719160\pi$
$13$	−1.75188e11			−1.27078			−0.635389	+	0.772192i	$0.719160\pi$
$14$	−1.19256e11	+	3.99238e11i	−0.412288	+	1.38023i
$15$		−	3.69647e11i		−	0.641025i
$16$	4.37980e11	+	1.00851e12i	0.398341	+	0.917237i
$17$	3.29319e12			1.63353			0.816767	−	0.576968i	$-0.195764\pi$
$17$	3.29319e12			1.63353			0.816767	+	0.576968i	$0.195764\pi$
$18$	−1.14037e12	−	3.40638e11i	−0.319389	−	0.0954044i
$19$			1.26021e12i			0.205545i	0.994705	+	0.102772i	$0.0327713\pi$
$19$			1.26021e12i			0.205545i	−0.994705	+	0.102772i	$0.967229\pi$
$20$	9.50664e12	+	6.23585e12i	0.928383	+	0.608970i
$21$	1.38721e13			0.831669
$22$	−6.51515e11	+	2.18110e12i	−0.0245300	+	0.0821199i
$23$			3.97059e13i			0.958466i	0.877688	+	0.479233i	$0.159085\pi$
$23$			3.97059e13i			0.958466i	−0.877688	+	0.479233i	$0.840915\pi$
$24$	2.79983e13	−	2.35816e13i	0.441589	−	0.371930i
$25$	2.21957e13			0.232739
$26$	−1.71887e14	−	5.13444e13i	−1.21762	−	0.363713i
$27$			3.96238e13i			0.192450i
$28$	−2.34019e14	+	3.56766e14i	−0.790081	+	1.20449i
$29$	2.63518e14			0.626368			0.313184	−	0.949692i	$-0.398604\pi$
$29$	2.63518e14			0.626368			0.313184	+	0.949692i	$0.398604\pi$
$30$	1.08337e14	−	3.62684e14i	0.183470	−	0.614208i
$31$		−	8.61414e14i		−	1.05098i	−0.850799	−	0.525491i	$-0.823882\pi$
$31$		−	8.61414e14i		−	1.05098i	0.850799	−	0.525491i	$-0.176118\pi$
$32$	1.34152e14	+	1.11788e15i	0.119151	+	0.992876i
$33$	7.57856e13			0.0494820
$34$	3.23116e15	+	9.65177e14i	1.56520	+	0.467539i
$35$			4.41192e15i			1.59936i
$36$	−1.01905e15	−	6.68442e14i	−0.278721	−	0.182826i
$37$	−1.00930e15			−0.209896			−0.104948	−	0.994478i	$-0.533468\pi$
$37$	−1.00930e15			−0.209896			−0.104948	+	0.994478i	$0.533468\pi$
$38$	−3.69345e14	+	1.23647e15i	−0.0588296	+	0.196946i
$39$			5.97249e15i			0.733684i
$40$	7.49994e15	+	8.90461e15i	0.715250	+	0.849209i
$41$	2.19849e16			1.63790			0.818948	−	0.573867i	$-0.194557\pi$
$41$	2.19849e16			1.63790			0.818948	+	0.573867i	$0.194557\pi$
$42$	1.36108e16	+	4.06568e15i	0.796877	+	0.238035i
$43$			3.71555e16i			1.71925i	0.510926	+	0.859625i	$0.329303\pi$
$43$			3.71555e16i			1.71925i	−0.510926	+	0.859625i	$0.670697\pi$
$44$	−1.27848e15	+	1.94906e15i	−0.0470076	+	0.0716637i
$45$	−1.26020e16			−0.370096
$46$	−1.16371e16	+	3.89579e16i	−0.274326	+	0.918370i
$47$		−	8.27174e16i		−	1.57260i	−0.617845	−	0.786300i	$-0.711994\pi$
$47$		−	8.27174e16i		−	1.57260i	0.617845	−	0.786300i	$-0.288006\pi$
$48$	3.43822e16	−	1.49316e16i	0.529567	−	0.229982i
$49$	−8.57784e16			−1.07502
$50$	2.17776e16	+	6.50516e15i	0.223002	+	0.0666128i
$51$		−	1.12271e17i		−	0.943121i
$52$	−1.53601e17	−	1.00754e17i	−1.06258	−	0.696995i
$53$	1.21767e17			0.696257			0.348129	−	0.937447i	$-0.386817\pi$
$53$	1.21767e17			0.696257			0.348129	+	0.937447i	$0.386817\pi$
$54$	−1.16130e16	+	3.88773e16i	−0.0550817	+	0.184399i
$55$			2.41030e16i			0.0951576i
$56$	−3.34173e17	+	2.81458e17i	−1.10177	+	0.927969i
$57$	4.29630e16			0.118671
$58$	2.58554e17	+	7.72324e16i	0.600165	+	0.179275i
$59$		−	5.44449e17i		−	1.06522i	−0.846362	−	0.532608i	$-0.821212\pi$
$59$		−	5.44449e17i		−	1.06522i	0.846362	−	0.532608i	$-0.178788\pi$
$60$	2.12592e17	−	3.24100e17i	0.351589	−	0.536002i
$61$	−4.97765e17			−0.697793			−0.348896	−	0.937161i	$-0.613443\pi$
$61$	−4.97765e17			−0.697793			−0.348896	+	0.937161i	$0.613443\pi$
$62$	2.52465e17	−	8.45187e17i	0.300805	−	1.00702i
$63$		−	4.72928e17i		−	0.480164i
$64$	−1.96005e17	+	1.13614e18i	−0.170007	+	0.985443i
$65$	−1.89950e18			−1.41093
$66$	7.43579e16	+	2.22114e16i	0.0474120	+	0.0141624i
$67$		−	3.24323e18i		−	1.77922i	−0.456719	−	0.889611i	$-0.650975\pi$
$67$		−	3.24323e18i		−	1.77922i	0.456719	−	0.889611i	$-0.349025\pi$
$68$	2.88741e18	+	1.89399e18i	1.36590	+	0.895960i
$69$	1.35365e18			0.553371
$70$	−1.29305e18	+	4.32880e18i	−0.457758	+	1.53245i
$71$		−	2.30034e18i		−	0.706655i	−0.935500	−	0.353328i	$-0.885050\pi$
$71$		−	2.30034e18i		−	0.706655i	0.935500	−	0.353328i	$-0.114950\pi$
$72$	−8.03944e17	−	9.54516e17i	−0.214734	−	0.254952i
$73$	−2.29913e18			−0.534977			−0.267489	−	0.963561i	$-0.586194\pi$
$73$	−2.29913e18			−0.534977			−0.267489	+	0.963561i	$0.586194\pi$
$74$	−9.90290e17	−	2.95809e17i	−0.201115	−	0.0600751i
$75$		−	7.56694e17i		−	0.134372i
$76$	−7.24774e17	+	1.10493e18i	−0.112737	+	0.171869i
$77$	−9.04537e17			−0.123458
$78$	−1.75043e18	+	5.85998e18i	−0.209990	+	0.702991i
$79$		−	7.16859e17i		−	0.0757116i	−0.999283	−	0.0378558i	$-0.987947\pi$
$79$		−	7.16859e17i		−	0.0757116i	0.999283	−	0.0378558i	$-0.0120528\pi$
$80$	4.74887e18	+	1.09350e19i	0.442273	+	1.01840i
$81$	1.35085e18			0.111111
$82$	2.15708e19	+	6.44339e18i	1.56938	+	0.468788i
$83$		−	5.66725e18i		−	0.365251i	−0.983183	−	0.182626i	$-0.941540\pi$
$83$		−	5.66725e18i		−	0.365251i	0.983183	−	0.182626i	$-0.0584596\pi$
$84$	1.21628e19	+	7.97818e18i	0.695412	+	0.456153i
$85$	3.57070e19			1.81369
$86$	−1.08896e19	+	3.64556e19i	−0.492072	+	1.64733i
$87$		−	8.98384e18i		−	0.361634i
$88$	−1.82563e18	+	1.53765e18i	−0.0655522	+	0.0552116i
$89$	−3.74863e19			−1.20219			−0.601095	−	0.799178i	$-0.705269\pi$
$89$	−3.74863e19			−1.20219			−0.601095	+	0.799178i	$0.705269\pi$
$90$	−1.23646e19	−	3.69342e18i	−0.354613	−	0.105926i
$91$		−	7.12845e19i		−	1.83055i
$92$	−2.28358e19	+	3.48134e19i	−0.525699	+	0.801435i
$93$	−2.93673e19			−0.606785
$94$	2.42430e19	−	8.11591e19i	0.450099	−	1.50681i
$95$			1.36640e19i			0.228214i
$96$	3.81107e19	−	4.57352e18i	0.573237	−	0.0687920i
$97$	−1.04779e20			−1.42087			−0.710436	−	0.703762i	$-0.751502\pi$
$97$	−1.04779e20			−1.42087			−0.710436	+	0.703762i	$0.751502\pi$
$98$	−8.41625e19	−	2.51401e19i	−1.03005	−	0.307685i
$99$		−	2.58368e18i		−	0.0285684i
$100$	1.94608e19	+	1.27652e19i	0.194608	+	0.127652i
$101$	−2.25555e19			−0.204192			−0.102096	−	0.994775i	$-0.532555\pi$
$101$	−2.25555e19			−0.204192			−0.102096	+	0.994775i	$0.532555\pi$
$102$	3.29048e19	−	1.10156e20i	0.269934	−	0.903667i
$103$		−	3.10300e19i		−	0.230892i	−0.993314	−	0.115446i	$-0.963170\pi$
$103$		−	3.10300e19i		−	0.230892i	0.993314	−	0.115446i	$-0.0368298\pi$
$104$	−1.21178e20	−	1.43874e20i	−0.818638	−	0.971961i
$105$	1.50411e20			0.923392
$106$	1.19473e20	+	3.56877e19i	0.667130	+	0.199278i
$107$			6.94168e19i			0.352880i	0.984311	+	0.176440i	$0.0564581\pi$
$107$			6.94168e19i			0.352880i	−0.984311	+	0.176440i	$0.943542\pi$
$108$	−2.27885e19	+	3.47414e19i	−0.105555	+	0.160920i
$109$	3.13857e20			1.32577			0.662883	−	0.748723i	$-0.269333\pi$
$109$	3.13857e20			1.32577			0.662883	+	0.748723i	$0.269333\pi$
$110$	−7.06415e18	+	2.36489e19i	−0.0272353	+	0.0911768i
$111$			3.44091e19i			0.121184i
$112$	−4.10368e20	+	1.78216e20i	−1.32127	+	0.573807i
$113$	−2.66271e20			−0.784402			−0.392201	−	0.919879i	$-0.628286\pi$
$113$	−2.66271e20			−0.784402			−0.392201	+	0.919879i	$0.628286\pi$
$114$	4.21536e19	+	1.25917e19i	0.113707	+	0.0339653i
$115$			4.30517e20i			1.06417i
$116$	2.31048e20	+	1.51555e20i	0.523747	+	0.343550i
$117$	2.03614e20			0.423593
$118$	1.59568e20	−	5.34193e20i	0.304879	−	1.02065i
$119$			1.34001e21i			2.35309i
$120$	3.03575e20	−	2.55687e20i	0.490291	−	0.412950i
$121$	6.67808e20			0.992655
$122$	−4.88388e20	−	1.45886e20i	−0.668601	−	0.199717i
$123$		−	7.49509e20i		−	0.945640i
$124$	4.95419e20	−	7.55272e20i	0.576442	−	0.878793i
$125$	−7.93376e20			−0.851881
$126$	1.38607e20	−	4.64019e20i	0.137429	−	0.460077i
$127$			1.78781e21i			1.63789i	0.573872	+	0.818945i	$0.305441\pi$
$127$			1.78781e21i			1.63789i	−0.573872	+	0.818945i	$0.694559\pi$
$128$	−5.25295e20	+	1.05729e21i	−0.444942	+	0.895559i
$129$	1.26670e21			0.992609
$130$	−1.86371e21	−	5.56709e20i	−1.35190	−	0.403826i
$131$			1.97946e20i			0.132994i	0.997787	+	0.0664971i	$0.0211823\pi$
$131$			1.97946e20i			0.132994i	−0.997787	+	0.0664971i	$0.978818\pi$
$132$	6.64474e19	+	4.35860e19i	0.0413751	+	0.0271399i
$133$	−5.12783e20			−0.296086
$134$	9.50534e20	−	3.18214e21i	0.509237	−	1.70479i
$135$			4.29627e20i			0.213675i
$136$	2.27792e21	+	2.70456e21i	1.05233	+	1.24942i
$137$	−1.12094e21			−0.481258			−0.240629	−	0.970617i	$-0.577354\pi$
$137$	−1.12094e21			−0.481258			−0.240629	+	0.970617i	$0.577354\pi$
$138$	1.32815e21	+	3.96731e20i	0.530221	+	0.158382i
$139$		−	4.76472e21i		−	1.76966i	−0.465917	−	0.884828i	$-0.654275\pi$
$139$		−	4.76472e21i		−	1.76966i	0.465917	−	0.884828i	$-0.345725\pi$
$140$	−2.53739e21	+	3.86829e21i	−0.877217	+	1.33733i
$141$	−2.82000e21			−0.907941
$142$	6.74187e20	−	2.25700e21i	0.202254	−	0.677093i
$143$		−	3.89438e20i		−	0.108912i
$144$	−5.09048e20	−	1.17216e21i	−0.132780	−	0.305746i
$145$	2.85723e21			0.695449
$146$	−2.25582e21	−	6.73835e20i	−0.512597	−	0.153117i
$147$			2.92435e21i			0.620664i
$148$	−8.84939e20	−	5.80473e20i	−0.175508	−	0.115124i
$149$	3.69753e21			0.685565			0.342782	−	0.939415i	$-0.388631\pi$
$149$	3.69753e21			0.685565			0.342782	+	0.939415i	$0.388631\pi$
$150$	2.21774e20	−	7.42440e20i	0.0384589	−	0.128750i
$151$		−	9.66514e21i		−	1.56834i	−0.620549	−	0.784168i	$-0.713090\pi$
$151$		−	9.66514e21i		−	1.56834i	0.620549	−	0.784168i	$-0.286910\pi$
$152$	−1.03496e21	+	8.71695e20i	−0.157212	+	0.132412i
$153$	−3.82755e21			−0.544511
$154$	−8.87497e20	−	2.65104e20i	−0.118293	−	0.0353353i
$155$		−	9.34002e21i		−	1.16689i
$156$	−3.43491e21	+	5.23657e21i	−0.402411	+	0.613480i
$157$	−2.37257e21			−0.260749			−0.130374	−	0.991465i	$-0.541618\pi$
$157$	−2.37257e21			−0.260749			−0.130374	+	0.991465i	$0.541618\pi$
$158$	2.10099e20	−	7.03354e20i	0.0216697	−	0.0725443i
$159$		−	4.15127e21i		−	0.401984i
$160$	1.45457e21	+	1.21208e22i	0.132292	+	1.10238i
$161$	−1.61565e22			−1.38066
$162$	1.32540e21	+	3.95911e20i	0.106463	+	0.0318015i
$163$			8.99875e21i			0.679683i	0.940483	+	0.339841i	$0.110373\pi$
$163$			8.99875e21i			0.679683i	−0.940483	+	0.339841i	$0.889627\pi$
$164$	1.92760e22	+	1.26440e22i	1.36955	+	0.898353i
$165$	8.21717e20			0.0549393
$166$	1.66097e21	−	5.56049e21i	0.104540	−	0.349971i
$167$		−	8.70176e20i		−	0.0515754i	−0.999667	−	0.0257877i	$-0.991791\pi$
$167$		−	8.70176e20i		−	0.0515754i	0.999667	−	0.0257877i	$-0.00820939\pi$
$168$	9.59545e21	+	1.13926e22i	0.535763	+	0.636107i
$169$	1.16857e22			0.614877
$170$	3.50343e22	+	1.04651e22i	1.73782	+	0.519103i
$171$		−	1.46469e21i		−	0.0685149i
$172$	−2.13690e22	+	3.25773e22i	−0.942973	+	1.43757i
$173$	2.95562e22			1.23080			0.615399	−	0.788216i	$-0.288995\pi$
$173$	2.95562e22			1.23080			0.615399	+	0.788216i	$0.288995\pi$
$174$	2.63300e21	−	8.81460e21i	0.103504	−	0.346505i
$175$			9.03151e21i			0.335258i
$176$	−2.24190e21	+	9.73620e20i	−0.0786122	+	0.0341399i
$177$	−1.85613e22			−0.615002
$178$	−3.67802e22	−	1.09866e22i	−1.15190	−	0.344082i
$179$			1.16112e21i			0.0343833i	0.999852	+	0.0171916i	$0.00547254\pi$
$179$			1.16112e21i			0.0343833i	−0.999852	+	0.0171916i	$0.994527\pi$
$180$	−1.10492e22	−	7.24769e21i	−0.309461	−	0.202990i
$181$	2.01826e22			0.534799			0.267399	−	0.963586i	$-0.413836\pi$
$181$	2.01826e22			0.534799			0.267399	+	0.963586i	$0.413836\pi$
$182$	2.08922e22	−	6.99416e22i	0.523927	−	1.75397i
$183$			1.69698e22i			0.402871i
$184$	−3.26088e22	+	2.74648e22i	−0.733088	+	0.617446i
$185$	−1.09435e22			−0.233045
$186$	−2.88141e22	−	8.60704e21i	−0.581400	−	0.173670i
$187$			7.32069e21i			0.140003i
$188$	4.75726e22	−	7.25251e22i	0.862538	−	1.31495i
$189$	−1.61231e22			−0.277223
$190$	−4.00468e21	+	1.34066e22i	−0.0653178	+	0.218667i
$191$		−	5.34479e22i		−	0.827174i	−0.910465	−	0.413587i	$-0.864276\pi$
$191$		−	5.34479e22i		−	0.827174i	0.910465	−	0.413587i	$-0.135724\pi$
$192$	3.87332e22	+	6.68220e21i	0.568946	+	0.0981539i
$193$	−4.84741e22			−0.675985			−0.337992	−	0.941149i	$-0.609748\pi$
$193$	−4.84741e22			−0.675985			−0.337992	+	0.941149i	$0.609748\pi$
$194$	−1.02805e23	−	3.07087e22i	−1.36143	−	0.406672i
$195$			6.47576e22i			0.814600i
$196$	−7.52089e22	−	4.93330e22i	−0.898894	−	0.589627i
$197$	4.34599e22			0.493658			0.246829	−	0.969059i	$-0.420611\pi$
$197$	4.34599e22			0.493658			0.246829	+	0.969059i	$0.420611\pi$
$198$	7.57230e20	−	2.53501e21i	0.00817666	−	0.0273733i
$199$		−	4.98177e22i		−	0.511508i	−0.966742	−	0.255754i	$-0.917676\pi$
$199$		−	4.98177e22i		−	0.511508i	0.966742	−	0.255754i	$-0.0823237\pi$
$200$	1.53529e22	+	1.82284e22i	0.149931	+	0.178011i
$201$	−1.10568e23			−1.02723
$202$	−2.21306e22	−	6.61061e21i	−0.195650	−	0.0584424i
$203$			1.07226e23i			0.902280i
$204$	6.45698e22	−	9.84375e22i	0.517282	−	0.788604i
$205$	2.38375e23			1.81854
$206$	9.09435e21	−	3.04455e22i	0.0660845	−	0.221233i
$207$		−	4.61487e22i		−	0.319489i
$208$	−7.67287e22	−	1.76679e23i	−0.506203	−	1.16561i
$209$	−2.80141e21			−0.0176163
$210$	1.47577e23	+	4.40827e22i	0.884763	+	0.264287i
$211$			2.42719e23i			1.38765i	0.720143	+	0.693825i	$0.244076\pi$
$211$			2.42719e23i			1.38765i	−0.720143	+	0.693825i	$0.755924\pi$
$212$	1.06763e23	+	7.00307e22i	0.582186	+	0.381883i
$213$	−7.84229e22			−0.407988
$214$	−2.03448e22	+	6.81091e22i	−0.100999	+	0.338117i
$215$			4.02865e23i			1.90886i
$216$	−3.25413e22	+	2.74080e22i	−0.147196	+	0.123977i
$217$	3.50513e23			1.51393
$218$	3.07945e23	+	9.19860e22i	1.27030	+	0.379452i
$219$			7.83819e22i			0.308869i
$220$	−1.38621e22	+	2.11330e22i	−0.0521920	+	0.0795674i
$221$	−5.76927e23			−2.07586
$222$	−1.00847e22	+	3.37609e22i	−0.0346843	+	0.116114i
$223$		−	4.14135e23i		−	1.36174i	−0.732406	−	0.680868i	$-0.761603\pi$
$223$		−	4.14135e23i		−	1.36174i	0.732406	−	0.680868i	$-0.238397\pi$
$224$	−4.54869e23	+	5.45871e22i	−1.43023	+	0.171637i
$225$	−2.57972e22			−0.0775795
$226$	−2.61255e23	−	7.80392e22i	−0.751588	−	0.224506i
$227$		−	5.11331e23i		−	1.40748i	−0.710455	−	0.703742i	$-0.751511\pi$
$227$		−	5.11331e23i		−	1.40748i	0.710455	−	0.703742i	$-0.248489\pi$
$228$	3.76691e22	+	2.47090e22i	0.0992287	+	0.0650888i
$229$	7.06383e23			1.78109			0.890544	−	0.454898i	$-0.150324\pi$
$229$	7.06383e23			1.78109			0.890544	+	0.454898i	$0.150324\pi$
$230$	−1.26177e23	+	4.22407e23i	−0.304580	+	1.01965i
$231$			3.08374e22i			0.0712785i
$232$	1.82277e23	+	2.16416e23i	0.403508	+	0.479081i
$233$	−3.30392e23			−0.700600			−0.350300	−	0.936638i	$-0.613920\pi$
$233$	−3.30392e23			−0.700600			−0.350300	+	0.936638i	$0.613920\pi$
$234$	1.99778e23	+	5.96756e22i	0.405872	+	0.121238i
$235$		−	8.96876e23i		−	1.74604i
$236$	3.13125e23	−	4.77363e23i	0.584249	−	0.890695i
$237$	−2.44391e22			−0.0437121
$238$	−3.92734e23	+	1.31477e24i	−0.673487	+	2.25466i
$239$			6.27168e23i			1.03135i	0.856785	+	0.515674i	$0.172458\pi$
$239$			6.27168e23i			1.03135i	−0.856785	+	0.515674i	$0.827542\pi$
$240$	3.72794e23	−	1.61898e23i	0.587972	−	0.255346i
$241$	2.47493e23			0.374449			0.187225	−	0.982317i	$-0.440051\pi$
$241$	2.47493e23			0.374449			0.187225	+	0.982317i	$0.440051\pi$
$242$	6.55228e23	+	1.95723e23i	0.951128	+	0.284111i
$243$		−	4.60532e22i		−	0.0641500i
$244$	−4.36432e23	−	2.86276e23i	−0.583469	−	0.382725i
$245$	−9.30065e23			−1.19358
$246$	2.19668e23	−	7.35390e23i	0.270655	−	0.906080i
$247$		−	2.20773e23i		−	0.261202i
$248$	7.07443e23	−	5.95846e23i	0.803849	−	0.677045i
$249$	−1.93208e23			−0.210878
$250$	−7.78430e23	−	2.32524e23i	−0.816243	−	0.243819i
$251$		−	7.91153e23i		−	0.797119i	−0.917142	−	0.398559i	$-0.869510\pi$
$251$		−	7.91153e23i		−	0.797119i	0.917142	−	0.398559i	$-0.130490\pi$
$252$	2.71992e23	−	4.14655e23i	0.263360	−	0.401496i
$253$	−8.82653e22			−0.0821457
$254$	−5.23976e23	+	1.75413e24i	−0.468785	+	1.56937i
$255$		−	1.21732e24i		−	1.04714i
$256$	−8.25272e23	+	8.83418e23i	−0.682649	+	0.730746i
$257$	−1.38732e24			−1.10368			−0.551842	−	0.833949i	$-0.686075\pi$
$257$	−1.38732e24			−1.10368			−0.551842	+	0.833949i	$0.686075\pi$
$258$	1.24284e24	+	3.71249e23i	0.951084	+	0.284098i
$259$		−	4.10689e23i		−	0.302354i
$260$	−1.66544e24	−	1.09244e24i	−1.17977	−	0.773865i
$261$	−3.06277e23			−0.208789
$262$	−5.80143e22	+	1.94217e23i	−0.0380647	+	0.127431i
$263$		−	3.27873e23i		−	0.207085i	−0.994625	−	0.103542i	$-0.966982\pi$
$263$		−	3.27873e23i		−	0.207085i	0.994625	−	0.103542i	$-0.0330177\pi$
$264$	5.24214e22	+	6.22395e22i	0.0318764	+	0.0378466i
$265$	1.32027e24			0.773046
$266$	−5.03124e23	−	1.50288e23i	−0.283699	−	0.0847436i
$267$			1.27798e24i			0.694085i
$268$	1.86526e24	−	2.84361e24i	0.975867	−	1.48772i
$269$	2.84111e24			1.43207			0.716036	−	0.698063i	$-0.245955\pi$
$269$	2.84111e24			1.43207			0.716036	+	0.698063i	$0.245955\pi$
$270$	−1.25916e23	+	4.21533e23i	−0.0611566	+	0.204736i
$271$			1.11038e24i			0.519732i	0.965645	+	0.259866i	$0.0836785\pi$
$271$			1.11038e24i			0.519732i	−0.965645	+	0.259866i	$0.916322\pi$
$272$	1.44235e24	+	3.32123e24i	0.650703	+	1.49834i
$273$	−2.43023e24			−1.05687
$274$	−1.09983e24	−	3.28529e23i	−0.461125	−	0.137742i
$275$			4.93405e22i			0.0199469i
$276$	1.18686e24	+	7.78516e23i	0.462709	+	0.303512i
$277$	1.87397e24			0.704637			0.352318	−	0.935880i	$-0.385393\pi$
$277$	1.87397e24			0.704637			0.352318	+	0.935880i	$0.385393\pi$
$278$	1.39645e24	−	4.67496e24i	0.506499	−	1.69563i
$279$			1.00119e24i			0.350327i
$280$	−3.62332e24	+	3.05175e24i	−1.22328	+	1.03031i
$281$	−6.88002e23			−0.224144			−0.112072	−	0.993700i	$-0.535749\pi$
$281$	−6.88002e23			−0.224144			−0.112072	+	0.993700i	$0.535749\pi$
$282$	−2.76687e24	−	8.26491e23i	−0.869958	−	0.259865i
$283$			4.89739e24i			1.48628i	0.669136	+	0.743140i	$0.266664\pi$
$283$			4.89739e24i			1.48628i	−0.669136	+	0.743140i	$0.733336\pi$
$284$	1.32297e24	−	2.01689e24i	0.387586	−	0.590880i
$285$	4.65833e23			0.131759
$286$	1.14137e23	−	3.82101e23i	0.0311722	−	0.104356i
$287$			8.94575e24i			2.35938i
$288$	−1.55920e23	−	1.29927e24i	−0.0397171	−	0.330959i
$289$	6.78090e24			1.66843
$290$	2.80341e24	+	8.37404e23i	0.666356	+	0.199047i
$291$			3.57211e24i			0.820341i
$292$	−2.01584e24	−	1.32228e24i	−0.447329	−	0.293424i
$293$	4.74940e24			1.01850			0.509251	−	0.860618i	$-0.329922\pi$
$293$	4.74940e24			1.01850			0.509251	+	0.860618i	$0.329922\pi$
$294$	−8.57076e23	+	2.86926e24i	−0.177642	+	0.594699i
$295$		−	5.90328e24i		−	1.18270i
$296$	−6.98142e23	−	8.28898e23i	−0.135216	−	0.160540i
$297$	−8.80827e22			−0.0164940
$298$	3.62787e24	+	1.08368e24i	0.656885	+	0.196218i
$299$		−	6.95598e24i		−	1.21800i
$300$	4.35192e23	−	6.63456e23i	0.0737001	−	0.112357i
$301$	−1.51187e25			−2.47657
$302$	2.83268e24	−	9.48307e24i	0.448878	−	1.50273i
$303$			7.68960e23i			0.117890i
$304$	−1.27094e24	+	5.51947e23i	−0.188533	+	0.0818769i
$305$	−5.39710e24			−0.774750
$306$	−3.75545e24	−	1.12179e24i	−0.521732	−	0.155846i
$307$			3.63868e23i			0.0489282i	0.999701	+	0.0244641i	$0.00778795\pi$
$307$			3.63868e23i			0.0489282i	−0.999701	+	0.0244641i	$0.992212\pi$
$308$	−7.93082e23	−	5.20219e23i	−0.103231	−	0.0677141i
$309$	−1.05787e24			−0.133306
$310$	2.73739e24	−	9.16407e24i	0.333980	−	1.11808i
$311$		−	6.32495e24i		−	0.747228i	−0.927584	−	0.373614i	$-0.878119\pi$
$311$		−	6.32495e24i		−	0.747228i	0.927584	−	0.373614i	$-0.121881\pi$
$312$	−4.90495e24	+	4.13121e24i	−0.561162	+	0.472641i
$313$	2.83902e24			0.314575			0.157288	−	0.987553i	$-0.449725\pi$
$313$	2.83902e24			0.314575			0.157288	+	0.987553i	$0.449725\pi$
$314$	−2.32787e24	−	6.95357e23i	−0.249840	−	0.0746296i
$315$		−	5.12780e24i		−	0.533121i
$316$	4.12281e23	−	6.28528e23i	0.0415263	−	0.0633073i
$317$	−3.59726e24			−0.351058			−0.175529	−	0.984474i	$-0.556164\pi$
$317$	−3.59726e24			−0.351058			−0.175529	+	0.984474i	$0.556164\pi$
$318$	1.21666e24	−	4.07306e24i	0.115053	−	0.385168i
$319$			5.85794e23i			0.0536831i
$320$	−2.12522e24	+	1.23188e25i	−0.188757	+	1.09412i
$321$	2.36655e24			0.203735
$322$	−1.58521e25	−	4.73518e24i	−1.32291	−	0.395164i
$323$			4.15011e24i			0.335764i
$324$	1.18440e24	+	7.76905e23i	0.0929071	+	0.0609421i
$325$	−3.88841e24			−0.295759
$326$	−2.63737e24	+	8.82923e24i	−0.194534	+	0.651249i
$327$		−	1.07000e25i		−	0.765432i
$328$	1.52071e25	+	1.80553e25i	1.05514	+	1.25275i
$329$	3.36580e25			2.26532
$330$	8.06237e23	+	2.40831e23i	0.0526409	+	0.0157243i
$331$			1.56939e25i			0.994145i	0.867709	+	0.497072i	$0.165592\pi$
$331$			1.56939e25i			0.994145i	−0.867709	+	0.497072i	$0.834408\pi$
$332$	3.25936e24	−	4.96894e24i	0.200333	−	0.305410i
$333$	1.17307e24			0.0699654
$334$	2.55033e23	−	8.53784e23i	0.0147616	−	0.0494178i
$335$		−	3.51653e25i		−	1.97545i
$336$	6.07573e24	+	1.39902e25i	0.331288	+	0.762838i
$337$	−2.46452e25			−1.30447			−0.652234	−	0.758018i	$-0.726168\pi$
$337$	−2.46452e25			−1.30447			−0.652234	+	0.758018i	$0.726168\pi$
$338$	1.14656e25	+	3.42487e24i	0.589154	+	0.175986i
$339$			9.07769e24i			0.452875i
$340$	3.13072e25	+	2.05359e25i	1.51654	+	0.994773i
$341$	1.91490e24			0.0900748
$342$	4.29275e23	−	1.43710e24i	0.0196099	−	0.0656487i
$343$		−	2.43576e24i		−	0.108067i
$344$	−3.05143e25	+	2.57007e25i	−1.31498	+	1.10754i
$345$	1.46772e25			0.614401
$346$	2.89994e25	+	8.66238e24i	1.17931	+	0.352271i
$347$		−	1.48755e24i		−	0.0587729i	−0.999568	−	0.0293865i	$-0.990645\pi$
$347$		−	1.48755e24i		−	0.0587729i	0.999568	−	0.0293865i	$-0.00935535\pi$
$348$	5.16680e24	−	7.87686e24i	0.198349	−	0.302385i
$349$	−5.08767e25			−1.89786			−0.948931	−	0.315483i	$-0.897833\pi$
$349$	−5.08767e25			−1.89786			−0.948931	+	0.315483i	$0.897833\pi$
$350$	−2.64697e24	+	8.86137e24i	−0.0959554	+	0.321233i
$351$		−	6.94159e24i		−	0.244561i
$352$	−2.48502e24	+	2.98218e23i	−0.0850948	+	0.0102119i
$353$	−1.95323e25			−0.650139			−0.325070	−	0.945690i	$-0.605388\pi$
$353$	−1.95323e25			−0.650139			−0.325070	+	0.945690i	$0.605388\pi$
$354$	−1.82117e25	−	5.44000e24i	−0.589274	−	0.176022i
$355$		−	2.49417e25i		−	0.784591i
$356$	−3.28673e25	−	2.15592e25i	−1.00523	−	0.659376i
$357$	4.56837e25			1.35856
$358$	−3.40304e23	+	1.13925e24i	−0.00984094	+	0.0329449i
$359$			5.73145e25i			1.61183i	0.592030	+	0.805916i	$0.298327\pi$
$359$			5.73145e25i			1.61183i	−0.592030	+	0.805916i	$0.701673\pi$
$360$	−8.71689e24	−	1.03495e25i	−0.238417	−	0.283070i
$361$	3.60018e25			0.957751
$362$	1.98024e25	+	5.91515e24i	0.512426	+	0.153066i
$363$		−	2.27669e25i		−	0.573109i
$364$	4.09973e25	−	6.25009e25i	1.00402	−	1.53064i
$365$	−2.49287e25			−0.593979
$366$	−4.97355e24	+	1.66501e25i	−0.115307	+	0.386017i
$367$		−	5.03084e24i		−	0.113496i	−0.998389	−	0.0567480i	$-0.981927\pi$
$367$		−	5.03084e24i		−	0.113496i	0.998389	−	0.0567480i	$-0.0180731\pi$
$368$	−4.00439e25	+	1.73904e25i	−0.879141	+	0.381796i
$369$	−2.55522e25			−0.545966
$370$	−1.07374e25	−	3.20735e24i	−0.223296	−	0.0667006i
$371$			4.95473e25i			1.00295i
$372$	−2.57487e25	−	1.68898e25i	−0.507372	−	0.332809i
$373$	1.98335e25			0.380461			0.190231	−	0.981739i	$-0.439076\pi$
$373$	1.98335e25			0.380461			0.190231	+	0.981739i	$0.439076\pi$
$374$	−2.14556e24	+	7.18278e24i	−0.0400706	+	0.134146i
$375$			2.70477e25i			0.491834i
$376$	6.79322e25	−	5.72162e25i	1.20281	−	1.01307i
$377$	−4.61650e25			−0.795975
$378$	−1.58193e25	−	4.72538e24i	−0.265626	−	0.0793449i
$379$		−	2.57553e25i		−	0.421187i	−0.977574	−	0.210594i	$-0.932460\pi$
$379$		−	2.57553e25i		−	0.421187i	0.977574	−	0.210594i	$-0.0675397\pi$
$380$	−7.85847e24	+	1.19803e25i	−0.125171	+	0.190824i
$381$	6.09500e25			0.945636
$382$	1.56646e25	−	5.24410e25i	0.236748	−	0.792570i
$383$		−	4.53587e25i		−	0.667841i	−0.942601	−	0.333920i	$-0.891628\pi$
$383$		−	4.53587e25i		−	0.667841i	0.942601	−	0.333920i	$-0.108372\pi$
$384$	3.60451e25	+	1.79083e25i	0.517051	+	0.256887i
$385$	−9.80758e24			−0.137074
$386$	−4.75610e25	−	1.42069e25i	−0.647706	−	0.193476i
$387$		−	4.31844e25i		−	0.573083i
$388$	−9.18679e25	−	6.02605e25i	−1.18808	−	0.779319i
$389$	8.63918e25			1.08887			0.544436	−	0.838803i	$-0.316744\pi$
$389$	8.63918e25			1.08887			0.544436	+	0.838803i	$0.316744\pi$
$390$	−1.89793e25	+	6.35377e25i	−0.233149	+	0.780522i
$391$			1.30759e26i			1.56569i
$392$	−5.93335e25	−	7.04461e25i	−0.692531	−	0.822236i
$393$	6.74835e24			0.0767842
$394$	4.26412e25	+	1.27373e25i	0.473006	+	0.141291i
$395$		−	7.77265e24i		−	0.0840617i
$396$	1.48593e24	−	2.26532e24i	0.0156692	−	0.0238879i
$397$	−8.17463e25			−0.840549			−0.420275	−	0.907397i	$-0.638066\pi$
$397$	−8.17463e25			−0.840549			−0.420275	+	0.907397i	$0.638066\pi$
$398$	1.46007e25	−	4.88792e25i	0.146400	−	0.490110i
$399$			1.74818e25i			0.170945i
$400$	9.72128e24	+	2.23846e25i	0.0927093	+	0.213477i
$401$	3.34733e24			0.0311354			0.0155677	−	0.999879i	$-0.495044\pi$
$401$	3.34733e24			0.0311354			0.0155677	+	0.999879i	$0.495044\pi$
$402$	−1.08485e26	−	3.24056e25i	−0.984261	−	0.294008i
$403$			1.50909e26i			1.33556i
$404$	−1.97762e25	−	1.29722e25i	−0.170738	−	0.111995i
$405$	1.46468e25			0.123365
$406$	−3.14261e25	+	1.05206e26i	−0.258244	+	0.864534i
$407$		−	2.24366e24i		−	0.0179892i
$408$	9.22037e25	−	7.76589e25i	0.721351	−	0.607561i
$409$	−9.22978e25			−0.704626			−0.352313	−	0.935882i	$-0.614605\pi$
$409$	−9.22978e25			−0.704626			−0.352313	+	0.935882i	$0.614605\pi$
$410$	2.33884e26	+	6.98635e25i	1.74246	+	0.520489i
$411$			3.82152e25i			0.277854i
$412$	1.78461e25	−	2.72065e25i	0.126640	−	0.193064i
$413$	2.21538e26			1.53444
$414$	1.35254e25	−	4.52793e25i	0.0914419	−	0.306123i
$415$		−	6.14481e25i		−	0.405534i
$416$	−2.35018e25	−	1.95838e26i	−0.151415	−	1.26173i
$417$	−1.62439e26			−1.02171
$418$	−2.74864e24	−	8.21044e23i	−0.0168793	−	0.00504201i
$419$			1.47185e26i			0.882518i	0.897380	+	0.441259i	$0.145468\pi$
$419$			1.47185e26i			0.882518i	−0.897380	+	0.441259i	$0.854532\pi$
$420$	1.31877e26	+	8.65046e25i	0.772107	+	0.506461i
$421$	−9.92668e25			−0.567523			−0.283761	−	0.958895i	$-0.591582\pi$
$421$	−9.92668e25			−0.567523			−0.283761	+	0.958895i	$0.591582\pi$
$422$	−7.11368e25	+	2.38147e26i	−0.397164	+	1.32960i
$423$			9.61392e25i			0.524200i
$424$	8.42268e25	+	1.00002e26i	0.448530	+	0.532536i
$425$	7.30947e25			0.380186
$426$	−7.69456e25	−	2.29844e25i	−0.390920	−	0.116771i
$427$		−	2.02543e26i		−	1.00517i
$428$	−3.99231e25	+	6.08633e25i	−0.193547	+	0.295065i
$429$	−1.32767e25			−0.0628806
$430$	−1.18072e26	+	3.95275e26i	−0.546341	+	1.82901i
$431$		−	4.04297e26i		−	1.82780i	−0.405942	−	0.913899i	$-0.633057\pi$
$431$		−	4.04297e26i		−	1.82780i	0.405942	−	0.913899i	$-0.366943\pi$
$432$	−3.99611e25	+	1.73544e25i	−0.176522	+	0.0766607i
$433$	4.45830e26			1.92438			0.962188	−	0.272386i	$-0.0878129\pi$
$433$	4.45830e26			1.92438			0.962188	+	0.272386i	$0.0878129\pi$
$434$	3.43910e26	+	1.02729e26i	1.45060	+	0.433307i
$435$		−	9.74086e25i		−	0.401518i
$436$	2.75184e26	+	1.80506e26i	1.10856	+	0.727156i
$437$	−5.00377e25			−0.197008
$438$	−2.29723e25	+	7.69053e25i	−0.0884024	+	0.295948i
$439$		−	9.40767e25i		−	0.353864i	−0.984223	−	0.176932i	$-0.943383\pi$
$439$		−	9.40767e25i		−	0.353864i	0.984223	−	0.176932i	$-0.0566173\pi$
$440$	−1.97947e25	+	1.66722e25i	−0.0727818	+	0.0613007i
$441$	9.96969e25			0.358340
$442$	−5.66058e26	−	1.69087e26i	−1.98902	−	0.594138i
$443$			3.81433e25i			0.131033i	0.997851	+	0.0655166i	$0.0208695\pi$
$443$			3.81433e25i			0.131033i	−0.997851	+	0.0655166i	$0.979130\pi$
$444$	−1.97895e25	+	3.01693e25i	−0.0664667	+	0.101329i
$445$	−4.06451e26			−1.33478
$446$	1.21376e26	−	4.06333e26i	0.389747	−	1.30477i
$447$		−	1.26056e26i		−	0.395811i
$448$	−4.62299e26	−	7.97553e25i	−1.41952	−	0.244895i
$449$	−5.44962e26			−1.63645			−0.818226	−	0.574897i	$-0.805042\pi$
$449$	−5.44962e26			−1.63645			−0.818226	+	0.574897i	$0.805042\pi$
$450$	−2.53112e25	−	7.56070e24i	−0.0743341	−	0.0222043i
$451$			4.88720e25i			0.140377i
$452$	−2.33461e26	−	1.53138e26i	−0.655889	−	0.430228i
$453$	−3.29504e26			−0.905479
$454$	1.49862e26	−	5.01699e26i	0.402841	−	1.34860i
$455$		−	7.72913e26i		−	2.03243i
$456$	2.97178e25	+	3.52836e25i	0.0764483	+	0.0907664i
$457$	1.19829e26			0.301577			0.150789	−	0.988566i	$-0.451819\pi$
$457$	1.19829e26			0.301577			0.150789	+	0.988566i	$0.451819\pi$
$458$	6.93076e26	+	2.07028e26i	1.70658	+	0.509771i
$459$			1.30489e26i			0.314374i
$460$	−2.47600e26	+	3.77470e26i	−0.583677	+	0.889824i
$461$	9.74164e24			0.0224710			0.0112355	−	0.999937i	$-0.496424\pi$
$461$	9.74164e24			0.0224710			0.0112355	+	0.999937i	$0.496424\pi$
$462$	−9.03791e24	+	3.02565e25i	−0.0204008	+	0.0682966i
$463$		−	5.30350e26i		−	1.17153i	−0.810481	−	0.585764i	$-0.800794\pi$
$463$		−	5.30350e26i		−	1.17153i	0.810481	−	0.585764i	$-0.199206\pi$
$464$	1.15416e26	+	2.65761e26i	0.249508	+	0.574529i
$465$	−3.18419e26			−0.673706
$466$	−3.24168e26	−	9.68320e25i	−0.671291	−	0.200521i
$467$			5.90423e26i			1.19673i	0.801225	+	0.598363i	$0.204182\pi$
$467$			5.90423e26i			1.19673i	−0.801225	+	0.598363i	$0.795818\pi$
$468$	1.78525e26	+	1.17103e26i	0.354193	+	0.232332i
$469$	1.31968e27			2.56296
$470$	2.62858e26	−	8.79980e26i	0.499739	−	1.67299i
$471$			8.08854e25i			0.150543i
$472$	4.47133e26	−	3.76599e26i	0.814736	−	0.686214i
$473$	−8.25959e25			−0.147349
$474$	−2.39787e25	−	7.16267e24i	−0.0418835	−	0.0125110i
$475$			2.79712e25i			0.0478382i
$476$	−7.70671e26	+	1.17490e27i	−1.29062	+	1.96757i
$477$	−1.41525e26			−0.232086
$478$	−1.83812e26	+	6.15354e26i	−0.295185	+	0.988202i
$479$			8.87503e26i			1.39577i	0.716209	+	0.697886i	$0.245876\pi$
$479$			8.87503e26i			1.39577i	−0.716209	+	0.697886i	$0.754124\pi$
$480$	4.13221e26	−	4.95891e25i	0.636458	−	0.0763789i
$481$	1.76817e26			0.266732
$482$	2.42831e26	+	7.25359e25i	0.358785	+	0.107172i
$483$			5.50806e26i			0.797127i
$484$	5.85522e26	+	3.84071e26i	0.830022	+	0.544451i
$485$	−1.13608e27			−1.57758
$486$	1.34974e25	−	4.51856e25i	0.0183606	−	0.0614664i
$487$		−	2.47255e26i		−	0.329500i	−0.986335	−	0.164750i	$-0.947318\pi$
$487$		−	2.47255e26i		−	0.329500i	0.986335	−	0.164750i	$-0.0526817\pi$
$488$	−3.44308e26	−	4.08793e26i	−0.449519	−	0.533710i
$489$	3.06785e26			0.392415
$490$	−9.12544e26	−	2.72585e26i	−1.14365	−	0.341619i
$491$			5.10527e26i			0.626907i	0.949603	+	0.313454i	$0.101486\pi$
$491$			5.10527e26i			0.626907i	−0.949603	+	0.313454i	$0.898514\pi$
$492$	4.31060e26	−	6.57156e26i	0.518664	−	0.790710i
$493$	8.67815e26			1.02319
$494$	6.47046e25	−	2.16614e26i	0.0747594	−	0.250275i
$495$		−	2.80139e25i		−	0.0317192i
$496$	8.68748e26	−	3.77283e26i	0.964000	−	0.418649i
$497$	9.36015e26			1.01793
$498$	−1.89568e26	−	5.66258e25i	−0.202056	−	0.0603560i
$499$			1.56000e27i			1.62975i	0.579640	+	0.814873i	$0.303193\pi$
$499$			1.56000e27i			1.62975i	−0.579640	+	0.814873i	$0.696807\pi$
$500$	−6.95617e26	−	4.56288e26i	−0.712312	−	0.467239i
$501$	−2.96660e25			−0.0297771
$502$	2.31873e26	−	7.76249e26i	0.228146	−	0.763772i
$503$			1.58987e27i			1.53349i	0.641951	+	0.766746i	$0.278125\pi$
$503$			1.58987e27i			1.53349i	−0.641951	+	0.766746i	$0.721875\pi$
$504$	3.88396e26	−	3.27128e26i	0.367256	−	0.309323i
$505$	−2.44561e26			−0.226712
$506$	−8.66025e25	−	2.58690e25i	−0.0787092	−	0.0235112i
$507$		−	3.98389e26i		−	0.354999i
$508$	−1.02821e27	+	1.56752e27i	−0.898348	+	1.36954i
$509$	1.26816e27			1.08641			0.543207	−	0.839599i	$-0.317210\pi$
$509$	1.26816e27			1.08641			0.543207	+	0.839599i	$0.317210\pi$
$510$	3.56775e26	−	1.19439e27i	0.299704	−	1.00333i
$511$		−	9.35525e26i		−	0.770631i
$512$	−1.06864e27	+	6.24904e26i	−0.863240	+	0.504793i
$513$	−4.99342e25			−0.0395571
$514$	−1.36118e27	−	4.06598e26i	−1.05751	−	0.315889i
$515$		−	3.36448e26i		−	0.256357i
$516$	1.11062e27	+	7.28510e26i	0.829984	+	0.544426i
$517$	1.83879e26			0.134780
$518$	1.20366e26	−	4.02953e26i	0.0865377	−	0.289705i
$519$		−	1.00763e27i		−	0.710602i
$520$	−1.31390e27	−	1.55998e27i	−0.908923	−	1.07916i
$521$	−2.20934e27			−1.49929			−0.749643	−	0.661842i	$-0.769775\pi$
$521$	−2.20934e27			−1.49929			−0.749643	+	0.661842i	$0.769775\pi$
$522$	−3.00507e26	−	8.97642e25i	−0.200055	−	0.0597583i
$523$			4.80077e26i			0.313541i	0.987635	+	0.156770i	$0.0501082\pi$
$523$			4.80077e26i			0.313541i	−0.987635	+	0.156770i	$0.949892\pi$
$524$	−1.13843e26	+	1.73555e26i	−0.0729446	+	0.111205i
$525$	3.07902e26			0.193562
$526$	9.60938e25	−	3.21697e26i	0.0592704	−	0.198422i
$527$		−	2.83681e27i		−	1.71681i
$528$	3.31926e25	+	7.64308e25i	0.0197107	+	0.0453867i
$529$	1.39596e26			0.0813423
$530$	1.29540e27	+	3.86949e26i	0.740706	+	0.221256i
$531$			6.32793e26i			0.355072i
$532$	−4.49599e26	−	2.94913e26i	−0.247576	−	0.162397i
$533$	−3.85149e27			−2.08140
$534$	−3.74554e26	+	1.25391e27i	−0.198656	+	0.665048i
$535$			7.52662e26i			0.391798i
$536$	2.66353e27	−	2.24337e27i	1.36085	−	1.14618i
$537$	3.95849e25			0.0198512
$538$	2.78759e27	+	8.32678e26i	1.37216	+	0.409878i
$539$		−	1.90683e26i		−	0.0921350i
$540$	−2.47088e26	+	3.76689e26i	−0.117196	+	0.178667i
$541$	−7.55750e26			−0.351889			−0.175945	−	0.984400i	$-0.556298\pi$
$541$	−7.55750e26			−0.351889			−0.175945	+	0.984400i	$0.556298\pi$
$542$	−3.25433e26	+	1.08947e27i	−0.148754	+	0.497990i
$543$		−	6.88063e26i		−	0.308766i
$544$	4.41790e26	+	3.68139e27i	0.194638	+	1.62190i
$545$	3.40304e27			1.47198
$546$	−2.38445e27	−	7.12256e26i	−1.01265	−	0.302489i
$547$		−	2.59713e26i		−	0.108298i	−0.998533	−	0.0541491i	$-0.982755\pi$
$547$		−	2.59713e26i		−	0.108298i	0.998533	−	0.0541491i	$-0.0172446\pi$
$548$	−9.82823e26	−	6.44679e26i	−0.402411	−	0.263960i
$549$	5.78533e26			0.232598
$550$	−1.44608e25	+	4.84110e25i	−0.00570908	+	0.0191125i
$551$			3.32087e26i			0.128747i
$552$	9.36330e26	+	1.11170e27i	0.356483	+	0.423249i
$553$	2.91692e26			0.109062
$554$	1.83867e27	+	5.49228e26i	0.675159	+	0.201676i
$555$			3.73086e26i			0.134549i
$556$	2.74029e27	−	4.17762e27i	0.970620	−	1.47972i
$557$	4.06596e26			0.141453			0.0707264	−	0.997496i	$-0.477468\pi$
$557$	4.06596e26			0.141453			0.0707264	+	0.997496i	$0.477468\pi$
$558$	−2.93431e26	+	9.82328e26i	−0.100268	+	0.335672i
$559$		−	6.50919e27i		−	2.18478i
$560$	−4.44948e27	+	1.93233e27i	−1.46699	+	0.637091i
$561$	2.49577e26			0.0808305
$562$	−6.75041e26	−	2.01641e26i	−0.214767	−	0.0641529i
$563$		−	2.35274e26i		−	0.0735344i	−0.999324	−	0.0367672i	$-0.988294\pi$
$563$		−	2.35274e26i		−	0.0735344i	0.999324	−	0.0367672i	$-0.0117060\pi$
$564$	−2.47252e27	−	1.62184e27i	−0.759187	−	0.497987i
$565$	−2.88708e27			−0.870912
$566$	−1.43534e27	+	4.80513e27i	−0.425393	+	1.42410i
$567$			5.49667e26i			0.160055i
$568$	1.88917e27	−	1.59116e27i	0.540489	−	0.455229i
$569$	2.80911e27			0.789672			0.394836	−	0.918752i	$-0.370801\pi$
$569$	2.80911e27			0.789672			0.394836	+	0.918752i	$0.370801\pi$
$570$	4.57057e26	+	1.36527e26i	0.126247	+	0.0377112i
$571$			3.45827e26i			0.0938638i	0.998898	+	0.0469319i	$0.0149444\pi$
$571$			3.45827e26i			0.0938638i	−0.998898	+	0.0469319i	$0.985056\pi$
$572$	2.23974e26	−	3.41452e26i	0.0597362	−	0.0910687i
$573$	−1.82214e27			−0.477569
$574$	−2.62184e27	+	8.77723e27i	−0.675285	+	2.26068i
$575$			8.81300e26i			0.223072i
$576$	2.27809e26	−	1.32049e27i	0.0566692	−	0.328481i
$577$	−5.10473e27			−1.24800			−0.624000	−	0.781424i	$-0.714493\pi$
$577$	−5.10473e27			−1.24800			−0.624000	+	0.781424i	$0.714493\pi$
$578$	6.65316e27	+	1.98736e27i	1.59864	+	0.477527i
$579$			1.65258e27i			0.390280i
$580$	2.50517e27	+	1.64326e27i	0.581510	+	0.381440i
$581$	2.30603e27			0.526142
$582$	−1.04692e27	+	3.50481e27i	−0.234792	+	0.786023i
$583$			2.70684e26i			0.0596730i
$584$	−1.59032e27	−	1.88818e27i	−0.344633	−	0.409180i
$585$	2.20771e27			0.470310
$586$	4.65993e27	+	1.39196e27i	0.975895	+	0.291509i
$587$		−	4.59839e27i		−	0.946727i	−0.880867	−	0.473363i	$-0.843040\pi$
$587$		−	4.59839e27i		−	0.946727i	0.880867	−	0.473363i	$-0.156960\pi$
$588$	−1.68186e27	+	2.56402e27i	−0.340421	+	0.518977i
$589$	1.08556e27			0.216024
$590$	1.73015e27	−	5.79207e27i	0.338503	−	1.13322i
$591$		−	1.48163e27i		−	0.285014i
$592$	−4.42055e26	−	1.01790e27i	−0.0836102	−	0.192525i
$593$	7.79284e27			1.44927			0.724634	−	0.689133i	$-0.242009\pi$
$593$	7.79284e27			1.44927			0.724634	+	0.689133i	$0.242009\pi$
$594$	−8.64234e25	−	2.58155e25i	−0.0158040	−	0.00472080i
$595$			1.45293e28i			2.61261i
$596$	3.24192e27	+	2.12653e27i	0.573245	+	0.376018i
$597$	−1.69838e27			−0.295319
$598$	2.03867e27	−	6.82494e27i	0.348607	−	1.16704i
$599$		−	8.52442e27i		−	1.43350i	−0.697332	−	0.716748i	$-0.745630\pi$
$599$		−	8.52442e27i		−	1.43350i	0.697332	−	0.716748i	$-0.254370\pi$
$600$	6.21441e26	−	5.23411e26i	0.102775	−	0.0865625i
$601$	−7.25496e27			−1.18002			−0.590011	−	0.807395i	$-0.700877\pi$
$601$	−7.25496e27			−1.18002			−0.590011	+	0.807395i	$0.700877\pi$
$602$	−1.48339e28	−	4.43103e27i	−2.37296	−	0.708826i
$603$			3.76949e27i			0.593074i
$604$	5.55864e27	−	8.47422e27i	0.860199	−	1.31139i
$605$	7.24081e27			1.10213
$606$	−2.25369e26	+	7.54475e26i	−0.0337417	+	0.112958i
$607$			4.33708e26i			0.0638721i	0.999490	+	0.0319360i	$0.0101673\pi$
$607$			4.33708e26i			0.0638721i	−0.999490	+	0.0319360i	$0.989833\pi$
$608$	−1.40876e27	+	1.69060e26i	−0.204080	+	0.0244909i
$609$	3.65556e27			0.520931
$610$	−5.29543e27	−	1.58179e27i	−0.742339	−	0.221744i
$611$			1.44911e28i			1.99842i
$612$	−3.35593e27	−	2.20131e27i	−0.455301	−	0.298653i
$613$	−5.67757e27			−0.757806			−0.378903	−	0.925436i	$-0.623699\pi$
$613$	−5.67757e27			−0.757806			−0.378903	+	0.925436i	$0.623699\pi$
$614$	−1.06643e26	+	3.57013e26i	−0.0140039	+	0.0468814i
$615$		−	8.12667e27i		−	1.04993i
$616$	−6.25674e26	−	7.42858e26i	−0.0795319	−	0.0944275i
$617$	−7.32653e27			−0.916319			−0.458160	−	0.888870i	$-0.651491\pi$
$617$	−7.32653e27			−0.916319			−0.458160	+	0.888870i	$0.651491\pi$
$618$	−1.03795e27	−	3.10044e26i	−0.127729	−	0.0381539i
$619$			7.02785e27i			0.850974i	0.904965	+	0.425487i	$0.139897\pi$
$619$			7.02785e27i			0.850974i	−0.904965	+	0.425487i	$0.860103\pi$
$620$	5.37165e27	−	8.18916e27i	0.640016	−	0.975713i
$621$	−1.57330e27			−0.184457
$622$	1.85373e27	−	6.20580e27i	0.213866	−	0.715968i
$623$		−	1.52533e28i		−	1.73175i
$624$	−6.02333e27	+	2.61583e27i	−0.672962	+	0.292256i
$625$	−1.07190e28			−1.17857
$626$	2.78554e27	+	8.32066e26i	0.301415	+	0.0900356i
$627$			9.55056e25i			0.0101708i
$628$	−2.08022e27	−	1.36452e27i	−0.218029	−	0.143015i
$629$	−3.32383e27			−0.342873
$630$	1.50287e27	−	5.03120e27i	0.152586	−	0.510818i
$631$		−	6.89099e27i		−	0.688633i	−0.938854	−	0.344317i	$-0.888111\pi$
$631$		−	6.89099e27i		−	0.688633i	0.938854	−	0.344317i	$-0.111889\pi$
$632$	5.88725e26	−	4.95856e26i	0.0579084	−	0.0487736i
$633$	8.27478e27			0.801160
$634$	−3.52949e27	−	1.05429e27i	−0.336372	−	0.100477i
$635$			1.93846e28i			1.81853i
$636$	2.38749e27	−	3.63975e27i	0.220480	−	0.336125i
$637$	1.50273e28			1.36611
$638$	−1.71686e26	+	5.74758e26i	−0.0153648	+	0.0514373i
$639$			2.67359e27i			0.235552i
$640$	−5.69559e27	+	1.14638e28i	−0.494014	+	0.994329i
$641$	−8.22572e27			−0.702415			−0.351207	−	0.936298i	$-0.614229\pi$
$641$	−8.22572e27			−0.702415			−0.351207	+	0.936298i	$0.614229\pi$
$642$	2.32197e27	+	6.93595e26i	0.195212	+	0.0583117i
$643$		−	3.32443e27i		−	0.275174i	−0.990490	−	0.137587i	$-0.956065\pi$
$643$		−	3.32443e27i		−	0.275174i	0.990490	−	0.137587i	$-0.0439346\pi$
$644$	−1.41657e28	−	9.29195e27i	−1.15446	−	0.757266i
$645$	1.37344e28			1.10208
$646$	−1.21632e27	+	4.07193e27i	−0.0961001	+	0.321718i
$647$			3.88181e27i			0.301989i	0.988535	+	0.150994i	$0.0482476\pi$
$647$			3.88181e27i			0.301989i	−0.988535	+	0.150994i	$0.951752\pi$
$648$	9.34393e26	+	1.10940e27i	0.0715780	+	0.0849839i
$649$	1.21030e27			0.0912947
$650$	−3.81516e27	−	1.13962e27i	−0.283386	−	0.0846501i
$651$		−	1.19497e28i		−	0.874069i
$652$	−5.17538e27	+	7.88994e27i	−0.372792	+	0.568326i
$653$	8.34292e27			0.591815			0.295908	−	0.955217i	$-0.404378\pi$
$653$	8.34292e27			0.591815			0.295908	+	0.955217i	$0.404378\pi$
$654$	3.13598e27	−	1.04984e28i	0.219077	−	0.733411i
$655$			2.14625e27i			0.147662i
$656$	9.62897e27	+	2.21721e28i	0.652441	+	1.50234i
$657$	2.67219e27			0.178326
$658$	3.30240e28	+	9.86456e27i	2.17055	+	0.648364i
$659$			1.23750e28i			0.801107i	0.916273	+	0.400553i	$0.131182\pi$
$659$			1.23750e28i			0.801107i	−0.916273	+	0.400553i	$0.868818\pi$
$660$	7.20466e26	+	4.72588e26i	0.0459382	+	0.0301330i
$661$	1.73300e28			1.08839			0.544195	−	0.838959i	$-0.316835\pi$
$661$	1.73300e28			1.08839			0.544195	+	0.838959i	$0.316835\pi$
$662$	−4.59959e27	+	1.53982e28i	−0.284537	+	0.952556i
$663$			1.96686e28i			1.19850i
$664$	4.65427e27	−	3.92008e27i	0.279364	−	0.235296i
$665$	−5.55993e27			−0.328740
$666$	1.15098e27	+	3.43807e26i	0.0670385	+	0.0200250i
$667$			1.04632e28i			0.600353i
$668$	5.00458e26	−	7.62954e26i	0.0282880	−	0.0431255i
$669$	−1.41187e28			−0.786199
$670$	1.03063e28	−	3.45028e28i	0.565399	−	1.89281i
$671$		−	1.10652e27i		−	0.0598045i
$672$	1.86098e27	+	1.55074e28i	0.0990944	+	0.825744i
$673$	−7.49156e27			−0.393027			−0.196513	−	0.980501i	$-0.562962\pi$
$673$	−7.49156e27			−0.393027			−0.196513	+	0.980501i	$0.562962\pi$
$674$	−2.41809e28	−	7.22307e27i	−1.24990	−	0.373356i
$675$			8.79477e26i			0.0447906i
$676$	1.02458e28	+	6.72071e27i	0.514138	+	0.337247i
$677$	−1.00673e28			−0.497765			−0.248883	−	0.968534i	$-0.580063\pi$
$677$	−1.00673e28			−0.497765			−0.248883	+	0.968534i	$0.580063\pi$
$678$	−2.66051e27	+	8.90668e27i	−0.129619	+	0.433929i
$679$		−	4.26348e28i		−	2.04676i
$680$	2.46987e28	+	2.93246e28i	1.16838	+	1.38721i
$681$	−1.74323e28			−0.812612
$682$	1.87883e27	+	5.61224e26i	0.0863066	+	0.0257806i
$683$		−	3.17275e27i		−	0.143625i	−0.997418	−	0.0718124i	$-0.977122\pi$
$683$		−	3.17275e27i		−	0.143625i	0.997418	−	0.0718124i	$-0.0228783\pi$
$684$	8.42377e26	−	1.28421e27i	0.0375790	−	0.0572897i
$685$	−1.21540e28			−0.534335
$686$	7.13879e26	−	2.38988e27i	0.0309302	−	0.103546i
$687$		−	2.40820e28i		−	1.02831i
$688$	−3.74719e28	+	1.62734e28i	−1.57696	+	0.684847i
$689$	−2.13320e28			−0.884789
$690$	1.44007e28	+	4.30162e27i	0.588698	+	0.175850i
$691$		−	1.45368e28i		−	0.585716i	−0.956156	−	0.292858i	$-0.905394\pi$
$691$		−	1.45368e28i		−	0.585716i	0.956156	−	0.292858i	$-0.0946063\pi$
$692$	2.59143e28	+	1.69984e28i	1.02915	+	0.675067i
$693$	1.05131e27			0.0411527
$694$	4.35975e26	−	1.45953e27i	0.0168216	−	0.0563142i
$695$		−	5.16622e28i		−	1.96483i
$696$	7.37804e27	−	6.21418e27i	0.276598	−	0.232965i
$697$	7.24007e28			2.67556
$698$	−4.99183e28	−	1.49111e28i	−1.81847	−	0.543193i
$699$			1.12637e28i			0.404492i
$700$	−5.19422e27	+	7.91866e27i	−0.183882	+	0.280331i
$701$	−2.65106e28			−0.925207			−0.462604	−	0.886565i	$-0.653085\pi$
$701$	−2.65106e28			−0.925207			−0.462604	+	0.886565i	$0.653085\pi$
$702$	2.03446e27	−	6.81082e27i	0.0699967	−	0.234330i
$703$		−	1.27193e27i		−	0.0431431i
$704$	−2.52561e27	−	4.35715e26i	−0.0844577	−	0.0145705i
$705$	−3.05762e28			−1.00808
$706$	−1.91644e28	−	5.72457e27i	−0.622941	−	0.186078i
$707$		−	9.17791e27i		−	0.294137i
$708$	−1.62742e28	−	1.06750e28i	−0.514243	−	0.337316i
$709$	−4.17843e28			−1.30182			−0.650910	−	0.759155i	$-0.725613\pi$
$709$	−4.17843e28			−1.30182			−0.650910	+	0.759155i	$0.725613\pi$
$710$	7.30998e27	−	2.44719e28i	0.224560	−	0.751768i
$711$			8.33177e26i			0.0252372i
$712$	−2.59296e28	−	3.07859e28i	−0.774453	−	0.919501i
$713$	3.42033e28			1.00733
$714$	4.48231e28	+	1.33891e28i	1.30173	+	0.388838i
$715$		−	4.22254e27i		−	0.120924i
$716$	−6.67787e26	+	1.01805e27i	−0.0188585	+	0.0287501i
$717$	2.13814e28			0.595449
$718$	−1.67979e28	+	5.62348e28i	−0.461327	+	1.54440i
$719$		−	1.42659e28i		−	0.386376i	−0.981162	−	0.193188i	$-0.938117\pi$
$719$		−	1.42659e28i		−	0.386376i	0.981162	−	0.193188i	$-0.0618828\pi$
$720$	−5.51943e27	−	1.27093e28i	−0.147424	−	0.339466i
$721$	1.26262e28			0.332599
$722$	3.53236e28	+	1.05515e28i	0.917685	+	0.274121i
$723$		−	8.43753e27i		−	0.216188i
$724$	1.76957e28	+	1.16074e28i	0.447179	+	0.293326i
$725$	5.84896e27			0.145780
$726$	6.67257e27	−	2.23380e28i	0.164031	−	0.549134i
$727$			3.65582e28i			0.886423i	0.896417	+	0.443212i	$0.146161\pi$
$727$			3.65582e28i			0.886423i	−0.896417	+	0.443212i	$0.853839\pi$
$728$	5.85429e28	−	4.93079e28i	1.40010	−	1.17924i
$729$	−1.57004e27			−0.0370370
$730$	−2.44591e28	−	7.30615e27i	−0.569130	−	0.170004i
$731$			1.22360e29i			2.80845i
$732$	−9.75971e27	+	1.48788e28i	−0.220966	+	0.336866i
$733$	5.49596e27			0.122745			0.0613725	−	0.998115i	$-0.480452\pi$
$733$	5.49596e27			0.122745			0.0613725	+	0.998115i	$0.480452\pi$
$734$	1.47445e27	−	4.93607e27i	0.0324840	−	0.108748i
$735$			3.17077e28i			0.689115i
$736$	−4.43864e28	+	5.32664e27i	−0.951638	+	0.114202i
$737$	7.20963e27			0.152489
$738$	−2.50709e28	−	7.48891e27i	−0.523126	−	0.156263i
$739$		−	4.62461e28i		−	0.951987i	−0.879449	−	0.475993i	$-0.842089\pi$
$739$		−	4.62461e28i		−	0.951987i	0.879449	−	0.475993i	$-0.157911\pi$
$740$	−9.59509e27	−	6.29387e27i	−0.194864	−	0.127820i
$741$	−7.52658e27			−0.150805
$742$	−1.45214e28	+	4.86140e28i	−0.287059	+	0.960997i
$743$		−	4.73860e27i		−	0.0924192i	−0.998932	−	0.0462096i	$-0.985286\pi$
$743$		−	4.73860e27i		−	0.0924192i	0.998932	−	0.0462096i	$-0.0147142\pi$
$744$	−2.03136e28	−	2.41181e28i	−0.390892	−	0.464103i
$745$	4.00910e28			0.761174
$746$	1.94599e28	+	5.81284e27i	0.364545	+	0.108893i
$747$			6.58683e27i			0.121750i
$748$	−4.21029e27	+	6.41865e27i	−0.0767885	+	0.117065i
$749$	−2.82459e28			−0.508321
$750$	−7.92721e27	+	2.65382e28i	−0.140769	+	0.471258i
$751$			3.47303e28i			0.608568i	0.952581	+	0.304284i	$0.0984172\pi$
$751$			3.47303e28i			0.608568i	−0.952581	+	0.304284i	$0.901583\pi$
$752$	8.34216e28	−	3.62286e28i	1.44245	−	0.626431i
$753$	−2.69719e28			−0.460217
$754$	−4.52954e28	−	1.35301e28i	−0.762676	−	0.227819i
$755$		−	1.04796e29i		−	1.74130i
$756$	−1.41364e28	−	9.27273e27i	−0.231804	−	0.152051i
$757$	6.10046e28			0.987197			0.493599	−	0.869690i	$-0.335681\pi$
$757$	6.10046e28			0.987197			0.493599	+	0.869690i	$0.335681\pi$
$758$	7.54843e27	−	2.52702e28i	0.120549	−	0.403567i
$759$			3.00914e27i			0.0474268i
$760$	−1.12217e28	+	9.45148e27i	−0.174551	+	0.147016i
$761$	−5.63347e27			−0.0864827			−0.0432413	−	0.999065i	$-0.513768\pi$
$761$	−5.63347e27			−0.0864827			−0.0432413	+	0.999065i	$0.513768\pi$
$762$	5.98018e28	+	1.78634e28i	0.906076	+	0.270653i
$763$			1.27710e29i			1.90976i
$764$	3.07391e28	−	4.68621e28i	0.453688	−	0.691653i
$765$	−4.15008e28			−0.604564
$766$	1.32938e28	−	4.45042e28i	0.191145	−	0.639902i
$767$			9.53808e28i			1.35365i
$768$	3.01174e28	+	2.81351e28i	0.421897	+	0.394128i
$769$	−3.75164e28			−0.518750			−0.259375	−	0.965777i	$-0.583517\pi$
$769$	−3.75164e28			−0.518750			−0.259375	+	0.965777i	$0.583517\pi$
$770$	−9.62283e27	−	2.87443e27i	−0.131340	−	0.0392323i
$771$			4.72963e28i			0.637212i
$772$	−4.25012e28	−	2.78785e28i	−0.565234	−	0.370764i
$773$	1.04395e29			1.37052			0.685260	−	0.728299i	$-0.259689\pi$
$773$	1.04395e29			1.37052			0.685260	+	0.728299i	$0.259689\pi$
$774$	1.26566e28	−	4.23709e28i	0.164024	−	0.549109i
$775$		−	1.91197e28i		−	0.244604i
$776$	−7.24760e28	−	8.60501e28i	−0.915329	−	1.08676i
$777$	−1.40012e28			−0.174564
$778$	8.47644e28	+	2.53199e28i	1.04332	+	0.311649i
$779$			2.77056e28i			0.336661i
$780$	−3.72435e28	+	5.67783e28i	−0.446791	+	0.681140i
$781$	5.11359e27			0.0605641
$782$	−3.83232e28	+	1.28296e29i	−0.448120	+	1.50019i
$783$			1.04416e28i			0.120545i
$784$	−3.75692e28	−	8.65086e28i	−0.428225	−	0.986049i
$785$	−2.57249e28			−0.289506
$786$	6.62122e27	+	1.97782e27i	0.0735720	+	0.0219767i
$787$			1.41674e29i			1.55433i	0.629296	+	0.777166i	$0.283343\pi$
$787$			1.41674e29i			1.55433i	−0.629296	+	0.777166i	$0.716657\pi$
$788$	3.81048e28	+	2.49947e28i	0.412779	+	0.270761i
$789$	−1.11778e28			−0.119560
$790$	2.27803e27	−	7.62623e27i	0.0240596	−	0.0805450i
$791$		−	1.08347e29i		−	1.12993i
$792$	2.12187e27	−	1.78715e27i	0.0218507	−	0.0184039i
$793$	8.72023e28			0.886739
$794$	−8.02064e28	−	2.39584e28i	−0.805386	−	0.240576i
$795$		−	4.50107e28i		−	0.446318i
$796$	2.86512e28	−	4.36792e28i	0.280552	−	0.427705i
$797$	3.56072e28			0.344314			0.172157	−	0.985070i	$-0.444926\pi$
$797$	3.56072e28			0.344314			0.172157	+	0.985070i	$0.444926\pi$
$798$	−5.12360e27	+	1.71525e28i	−0.0489268	+	0.163794i
$799$		−	2.72404e29i		−	2.56889i
$800$	2.97760e27	+	2.48121e28i	0.0277311	+	0.231081i
$801$	4.35689e28			0.400730
$802$	3.28427e27	+	9.81042e26i	0.0298329	+	0.00891136i
$803$		−	5.11091e27i		−	0.0458504i
$804$	−9.69442e28	−	6.35902e28i	−0.858937	−	0.563417i
$805$	−1.75179e29			−1.53293
$806$	−4.42288e28	+	1.48066e29i	−0.382256	+	1.27969i
$807$		−	9.68589e28i		−	0.826807i
$808$	−1.56018e28	−	1.85238e28i	−0.131541	−	0.156177i
$809$	−1.02572e28			−0.0854167			−0.0427083	−	0.999088i	$-0.513599\pi$
$809$	−1.02572e28			−0.0854167			−0.0427083	+	0.999088i	$0.513599\pi$
$810$	1.43709e28	+	4.29272e27i	0.118204	+	0.0353088i
$811$		−	1.96037e29i		−	1.59268i	−0.604847	−	0.796342i	$-0.706766\pi$
$811$		−	1.96037e29i		−	1.59268i	0.604847	−	0.796342i	$-0.293234\pi$
$812$	−6.16683e28	+	9.40141e28i	−0.494882	+	0.754454i
$813$	3.78551e28			0.300068
$814$	6.57576e26	−	2.20139e27i	0.00514875	−	0.0172367i
$815$			9.75703e28i			0.754643i
$816$	1.13227e29	−	4.91727e28i	0.865066	−	0.375684i
$817$	−4.68237e28			−0.353383
$818$	−9.05591e28	−	2.70509e28i	−0.675148	−	0.201673i
$819$			8.28512e28i			0.610182i
$820$	2.09003e29	+	1.37095e29i	1.52060	+	0.997430i
$821$	−1.31374e29			−0.944233			−0.472116	−	0.881536i	$-0.656510\pi$
$821$	−1.31374e29			−0.944233			−0.472116	+	0.881536i	$0.656510\pi$
$822$	−1.12002e28	+	3.74953e28i	−0.0795256	+	0.266231i
$823$		−	6.32692e28i		−	0.443807i	−0.975069	−	0.221903i	$-0.928773\pi$
$823$		−	6.32692e28i		−	0.443807i	0.975069	−	0.221903i	$-0.0712270\pi$
$824$	2.54836e28	−	2.14637e28i	0.176599	−	0.148741i
$825$	1.68211e27			0.0115164
$826$	2.17365e29	+	6.49290e28i	1.47024	+	0.439176i
$827$		−	1.29431e29i		−	0.864935i	−0.901649	−	0.432468i	$-0.857643\pi$
$827$		−	1.29431e29i		−	0.864935i	0.901649	−	0.432468i	$-0.142357\pi$
$828$	2.65411e28	−	4.04623e28i	0.175233	−	0.267145i
$829$	6.94223e28			0.452849			0.226425	−	0.974029i	$-0.427296\pi$
$829$	6.94223e28			0.452849			0.226425	+	0.974029i	$0.427296\pi$
$830$	1.80093e28	−	6.02905e28i	0.116069	−	0.388569i
$831$		−	6.38874e28i		−	0.406822i
$832$	3.43377e28	−	1.99037e29i	0.216042	−	1.25228i
$833$	−2.82485e29			−1.75608
$834$	−1.59378e29	−	4.76078e28i	−0.978970	−	0.292427i
$835$		−	9.43502e27i		−	0.0572635i
$836$	−2.45623e27	−	1.61115e27i	−0.0147301	−	0.00966217i
$837$	3.41325e28			0.202262
$838$	−4.31373e28	+	1.44412e29i	−0.252588	+	0.845598i
$839$		−	2.56630e28i		−	0.148487i	−0.997240	−	0.0742433i	$-0.976346\pi$
$839$		−	2.56630e28i		−	0.148487i	0.997240	−	0.0742433i	$-0.0236541\pi$
$840$	1.04040e29	+	1.23526e29i	0.594851	+	0.706261i
$841$	−1.07553e29			−0.607663
$842$	−9.73968e28	−	2.90933e28i	−0.543781	−	0.162432i
$843$			2.34553e28i			0.129409i
$844$	−1.39593e29	+	2.12812e29i	−0.761098	+	1.16030i
$845$	1.26704e29			0.682690
$846$	−2.81767e28	+	9.43281e28i	−0.150033	+	0.502270i
$847$			2.71734e29i			1.42991i
$848$	5.33314e28	+	1.22803e29i	0.277348	+	0.638633i
$849$	1.66962e29			0.858104
$850$	7.17177e28	+	2.14228e28i	0.364282	+	0.108814i
$851$		−	4.00753e28i		−	0.201178i
$852$	−6.87598e28	−	4.51028e28i	−0.341145	−	0.223773i
$853$	−3.12347e29			−1.53160			−0.765802	−	0.643076i	$-0.777658\pi$
$853$	−3.12347e29			−1.53160			−0.765802	+	0.643076i	$0.777658\pi$
$854$	5.93616e28	−	1.98727e29i	0.287692	−	0.963115i
$855$		−	1.58811e28i		−	0.0760713i
$856$	−5.70090e28	+	4.80160e28i	−0.269902	+	0.227326i
$857$	2.50658e29			1.17293			0.586466	−	0.809974i	$-0.300519\pi$
$857$	2.50658e29			1.17293			0.586466	+	0.809974i	$0.300519\pi$
$858$	−1.30266e28	−	3.89116e27i	−0.0602501	−	0.0179973i
$859$		−	4.58419e28i		−	0.209571i	−0.994495	−	0.104785i	$-0.966584\pi$
$859$		−	4.58419e28i		−	0.209571i	0.994495	−	0.104785i	$-0.0334156\pi$
$860$	−2.31696e29	+	3.53224e29i	−1.04697	+	1.59612i
$861$	3.04978e29			1.36219
$862$	1.18492e29	−	3.96681e29i	0.523140	−	1.75133i
$863$			3.44474e29i			1.50331i	0.659557	+	0.751655i	$0.270744\pi$
$863$			3.44474e29i			1.50331i	−0.659557	+	0.751655i	$0.729256\pi$
$864$	−4.42946e28	+	5.31562e27i	−0.191079	+	0.0229307i
$865$	3.20467e29			1.36654
$866$	4.37431e29	+	1.30665e29i	1.84387	+	0.550782i
$867$		−	2.31174e29i		−	0.963270i
$868$	3.07323e29	+	2.01588e29i	1.26590	+	0.830361i
$869$	1.59356e27			0.00648889
$870$	2.85487e28	−	9.55736e28i	0.114920	−	0.384721i
$871$			5.68174e29i			2.26100i
$872$	2.17097e29	+	2.57757e29i	0.854062	+	1.01402i
$873$	1.21780e29			0.473624
$874$	−4.90951e28	−	1.46652e28i	−0.188766	−	0.0563862i
$875$		−	3.22828e29i		−	1.22713i
$876$	−4.50792e28	+	6.87238e28i	−0.169408	+	0.258265i
$877$	−1.35496e29			−0.503422			−0.251711	−	0.967802i	$-0.580993\pi$
$877$	−1.35496e29			−0.503422			−0.251711	+	0.967802i	$0.580993\pi$
$878$	2.75722e28	−	9.23045e28i	0.101281	−	0.339061i
$879$		−	1.61916e29i		−	0.588033i
$880$	−2.43082e28	+	1.05566e28i	−0.0872821	+	0.0379052i
$881$	1.20935e29			0.429333			0.214666	−	0.976687i	$-0.431134\pi$
$881$	1.20935e29			0.429333			0.214666	+	0.976687i	$0.431134\pi$
$882$	9.78188e28	+	2.92194e28i	0.343349	+	0.102562i
$883$		−	7.80550e28i		−	0.270890i	−0.990785	−	0.135445i	$-0.956754\pi$
$883$		−	7.80550e28i		−	0.270890i	0.990785	−	0.135445i	$-0.0432465\pi$
$884$	−5.05839e29	−	3.31803e29i	−1.73576	−	1.13857i
$885$	−2.01254e29			−0.682830
$886$	−1.11791e28	+	3.74248e28i	−0.0375034	+	0.125552i
$887$			1.56790e29i			0.520095i	0.965596	+	0.260047i	$0.0837382\pi$
$887$			1.56790e29i			0.520095i	−0.965596	+	0.260047i	$0.916262\pi$
$888$	−2.82588e28	+	2.38010e28i	−0.0926880	+	0.0780668i
$889$	−7.27467e29			−2.35937
$890$	−3.98795e29	−	1.19124e29i	−1.27894	−	0.382031i
$891$			3.00291e27i			0.00952282i
$892$	2.38178e29	−	3.63106e29i	0.746885	−	1.13864i
$893$	1.04241e29			0.323240
$894$	3.69447e28	−	1.23681e29i	0.113286	−	0.379253i
$895$			1.25896e28i			0.0381753i
$896$	−4.30215e29	−	2.13744e29i	−1.29005	−	0.640936i
$897$	−2.37143e29			−0.703211
$898$	−5.34696e29	−	1.59719e29i	−1.56799	−	0.468374i
$899$		−	2.26998e29i		−	0.658302i
$900$	−2.26185e28	−	1.48365e28i	−0.0648692	−	0.0425508i
$901$	4.01001e29			1.13736
$902$	−1.43235e28	+	4.79513e28i	−0.0401776	+	0.134504i
$903$			5.15427e29i			1.42985i
$904$	−1.84181e29	−	2.18677e29i	−0.505314	−	0.599954i
$905$	2.18832e29			0.593780
$906$	−3.23296e29	−	9.65717e28i	−0.867599	−	0.259160i
$907$		−	6.18692e28i		−	0.164211i	−0.996624	−	0.0821054i	$-0.973836\pi$
$907$		−	6.18692e28i		−	0.164211i	0.996624	−	0.0821054i	$-0.0261644\pi$
$908$	2.94078e29	−	4.48326e29i	0.771976	−	1.17689i
$909$	2.62154e28			0.0680639
$910$	2.26527e29	−	7.58352e29i	0.581709	−	1.94741i
$911$			2.31458e29i			0.587881i	0.955824	+	0.293940i	$0.0949667\pi$
$911$			2.31458e29i			0.587881i	−0.955824	+	0.293940i	$0.905033\pi$
$912$	1.88169e28	+	4.33287e28i	0.0472716	+	0.108850i
$913$	1.25982e28			0.0313040
$914$	1.17571e29	+	3.51196e28i	0.288961	+	0.0863154i
$915$			1.83998e29i			0.447302i
$916$	6.19343e29	+	4.06256e29i	1.48928	+	0.976890i
$917$	−8.05448e28			−0.191577
$918$	−3.82439e28	+	1.28031e29i	−0.0899779	+	0.301222i
$919$		−	4.10751e29i		−	0.955925i	−0.878380	−	0.477962i	$-0.841376\pi$
$919$		−	4.10751e29i		−	0.955925i	0.878380	−	0.477962i	$-0.158624\pi$
$920$	−3.53566e29	+	2.97792e29i	−0.813939	+	0.685543i
$921$	1.24050e28			0.0282487
$922$	9.55813e27	+	2.85510e27i	0.0215310	+	0.00643150i
$923$			4.02990e29i			0.898002i
$924$	−1.77353e28	+	2.70377e28i	−0.0390948	+	0.0596005i
$925$	−2.24022e28			−0.0488510
$926$	1.55436e29	−	5.20360e29i	0.335307	−	1.12252i
$927$			3.60650e28i			0.0769642i
$928$	3.53515e28	+	2.94581e29i	0.0746326	+	0.621906i
$929$	4.29641e28			0.0897322			0.0448661	−	0.998993i	$-0.485714\pi$
$929$	4.29641e28			0.0897322			0.0448661	+	0.998993i	$0.485714\pi$
$930$	−3.12421e29	−	9.33231e28i	−0.645522	−	0.192823i
$931$		−	1.08099e29i		−	0.220965i
$932$	−2.89682e29	−	1.90016e29i	−0.585817	−	0.384265i
$933$	−2.15630e29			−0.431412
$934$	−1.73043e29	+	5.79301e29i	−0.342519	+	1.14666i
$935$			7.93757e28i			0.155443i
$936$	1.40841e29	+	1.67219e29i	0.272879	+	0.323987i
$937$	−5.84433e29			−1.12031			−0.560155	−	0.828388i	$-0.689259\pi$
$937$	−5.84433e29			−1.12031			−0.560155	+	0.828388i	$0.689259\pi$
$938$	1.29482e30	+	3.86776e29i	2.45574	+	0.733552i
$939$		−	9.67877e28i		−	0.181620i
$940$	5.15813e29	−	7.86364e29i	0.957666	−	1.45997i
$941$	5.91376e29			1.08634			0.543172	−	0.839622i	$-0.317223\pi$
$941$	5.91376e29			1.08634			0.543172	+	0.839622i	$0.317223\pi$
$942$	−2.37061e28	+	7.93617e28i	−0.0430874	+	0.144245i
$943$			8.72932e29i			1.56987i
$944$	5.49084e29	−	2.38458e29i	0.977055	−	0.424319i
$945$	−1.74817e29			−0.307797
$946$	−8.10399e28	−	2.42074e28i	−0.141185	−	0.0421732i
$947$		−	1.02843e30i		−	1.77287i	−0.462856	−	0.886433i	$-0.653175\pi$
$947$		−	1.02843e30i		−	1.77287i	0.462856	−	0.886433i	$-0.346825\pi$
$948$	−2.14278e28	−	1.40555e28i	−0.0365505	−	0.0239752i
$949$	4.02779e29			0.679837
$950$	−8.19786e27	+	2.74443e28i	−0.0136919	+	0.0458369i
$951$			1.22638e29i			0.202683i
$952$	−1.10050e30	+	9.26896e29i	−1.79978	+	1.51587i
$953$	3.82678e29			0.619304			0.309652	−	0.950850i	$-0.399787\pi$
$953$	3.82678e29			0.619304			0.309652	+	0.950850i	$0.399787\pi$
$954$	−1.38859e29	−	4.14784e28i	−0.222377	−	0.0664260i
$955$		−	5.79517e29i		−	0.918401i
$956$	−3.60699e29	+	5.49890e29i	−0.565673	+	0.862376i
$957$	1.99709e28			0.0309940
$958$	−2.60111e29	+	8.70784e29i	−0.399488	+	1.33738i
$959$		−	4.56116e29i		−	0.693249i
$960$	4.19970e29	+	7.24528e28i	0.631693	+	0.108979i
$961$	−7.02444e28			−0.104563
$962$	1.73487e29	+	5.18220e28i	0.255573	+	0.0763421i
$963$		−	8.06804e28i		−	0.117627i
$964$	2.16998e29	+	1.42339e29i	0.313101	+	0.205378i
$965$	−5.25588e29			−0.750537
$966$	−1.61431e29	+	5.40430e29i	−0.228148	+	0.763780i
$967$			5.92069e29i			0.828148i	0.910243	+	0.414074i	$0.135894\pi$
$967$			5.92069e29i			0.828148i	−0.910243	+	0.414074i	$0.864106\pi$
$968$	4.61928e29	+	5.48442e29i	0.639470	+	0.759237i
$969$	1.41485e29			0.193854
$970$	−1.11468e30	−	3.32964e29i	−1.51158	−	0.451523i
$971$			7.68885e29i			1.03197i	0.856596	+	0.515987i	$0.172575\pi$
$971$			7.68885e29i			1.03197i	−0.856596	+	0.515987i	$0.827425\pi$
$972$	2.64862e28	−	4.03786e28i	0.0351850	−	0.0536400i
$973$	1.93878e30			2.54918
$974$	7.24659e28	−	2.42597e29i	0.0943071	−	0.315715i
$975$			1.32563e29i			0.170757i
$976$	−2.18011e29	−	5.02003e29i	−0.277959	−	0.640041i
$977$	−1.05616e30			−1.33286			−0.666432	−	0.745566i	$-0.732179\pi$
$977$	−1.05616e30			−1.33286			−0.666432	+	0.745566i	$0.732179\pi$
$978$	3.01006e29	+	8.99132e28i	0.375999	+	0.112314i
$979$		−	8.33312e28i		−	0.103034i
$980$	−8.15464e29	−	5.34901e29i	−0.998031	−	0.654655i
$981$	−3.64784e29			−0.441922
$982$	−1.49626e29	+	5.00909e29i	−0.179429	+	0.600681i
$983$		−	7.85681e28i		−	0.0932633i	−0.998912	−	0.0466317i	$-0.985151\pi$
$983$		−	7.85681e28i		−	0.0932633i	0.998912	−	0.0466317i	$-0.0148487\pi$
$984$	6.15540e29	−	5.18441e29i	0.723278	−	0.609183i
$985$	4.71220e29			0.548103
$986$	8.51467e29	+	2.54341e29i	0.980390	+	0.292852i
$987$		−	1.14747e30i		−	1.30788i
$988$	1.26971e29	−	1.93570e29i	0.143264	−	0.218408i
$989$	−1.47529e30			−1.64784
$990$	8.21039e27	−	2.74862e28i	0.00907845	−	0.0303923i
$991$		−	1.09571e30i		−	1.19939i	−0.800230	−	0.599694i	$-0.795289\pi$
$991$		−	1.09571e30i		−	1.19939i	0.800230	−	0.599694i	$-0.204711\pi$
$992$	9.62957e29	−	1.15561e29i	1.04349	−	0.125226i
$993$	5.35034e29			0.573970
$994$	9.18382e29	+	2.74329e29i	0.975348	+	0.291346i
$995$		−	5.40156e29i		−	0.567921i
$996$	−1.69401e29	−	1.11118e29i	−0.176329	−	0.115662i
$997$	−1.16824e30			−1.20387			−0.601936	−	0.798545i	$-0.705604\pi$
$997$	−1.16824e30			−1.20387			−0.601936	+	0.798545i	$0.705604\pi$
$998$	−4.57209e29	+	1.53062e30i	−0.466455	+	1.56157i
$999$		−	3.99924e28i		−	0.0403945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.21.d.a.7.18	yes	20
3.2	odd	2		36.21.d.c.19.3		20
4.3	odd	2	inner	12.21.d.a.7.17	✓	20
12.11	even	2		36.21.d.c.19.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.21.d.a.7.17	✓	20	4.3	odd	2	inner
12.21.d.a.7.18	yes	20	1.1	even	1	trivial
36.21.d.c.19.3		20	3.2	odd	2
36.21.d.c.19.4		20	12.11	even	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)

\(f(q)\)	\(=\)	\(q+(981.162 + 293.082i) q^{2} -34092.0i q^{3} +(876782. + 575122. i) q^{4} +1.08427e7 q^{5} +(9.99175e6 - 3.34497e7i) q^{6} +4.06904e8i q^{7} +(6.91707e8 + 8.21257e8i) q^{8} -1.16226e9 q^{9} +O(q^{10})\)	\(q+(981.162 + 293.082i) q^{2} -34092.0i q^{3} +(876782. + 575122. i) q^{4} +1.08427e7 q^{5} +(9.99175e6 - 3.34497e7i) q^{6} +4.06904e8i q^{7} +(6.91707e8 + 8.21257e8i) q^{8} -1.16226e9 q^{9} +(1.06384e10 + 3.17779e9i) q^{10} +2.22298e9i q^{11} +(1.96070e10 - 2.98912e10i) q^{12} -1.75188e11 q^{13} +(-1.19256e11 + 3.99238e11i) q^{14} -3.69647e11i q^{15} +(4.37980e11 + 1.00851e12i) q^{16} +3.29319e12 q^{17} +(-1.14037e12 - 3.40638e11i) q^{18} +1.26021e12i q^{19} +(9.50664e12 + 6.23585e12i) q^{20} +1.38721e13 q^{21} +(-6.51515e11 + 2.18110e12i) q^{22} +3.97059e13i q^{23} +(2.79983e13 - 2.35816e13i) q^{24} +2.21957e13 q^{25} +(-1.71887e14 - 5.13444e13i) q^{26} +3.96238e13i q^{27} +(-2.34019e14 + 3.56766e14i) q^{28} +2.63518e14 q^{29} +(1.08337e14 - 3.62684e14i) q^{30} -8.61414e14i q^{31} +(1.34152e14 + 1.11788e15i) q^{32} +7.57856e13 q^{33} +(3.23116e15 + 9.65177e14i) q^{34} +4.41192e15i q^{35} +(-1.01905e15 - 6.68442e14i) q^{36} -1.00930e15 q^{37} +(-3.69345e14 + 1.23647e15i) q^{38} +5.97249e15i q^{39} +(7.49994e15 + 8.90461e15i) q^{40} +2.19849e16 q^{41} +(1.36108e16 + 4.06568e15i) q^{42} +3.71555e16i q^{43} +(-1.27848e15 + 1.94906e15i) q^{44} -1.26020e16 q^{45} +(-1.16371e16 + 3.89579e16i) q^{46} -8.27174e16i q^{47} +(3.43822e16 - 1.49316e16i) q^{48} -8.57784e16 q^{49} +(2.17776e16 + 6.50516e15i) q^{50} -1.12271e17i q^{51} +(-1.53601e17 - 1.00754e17i) q^{52} +1.21767e17 q^{53} +(-1.16130e16 + 3.88773e16i) q^{54} +2.41030e16i q^{55} +(-3.34173e17 + 2.81458e17i) q^{56} +4.29630e16 q^{57} +(2.58554e17 + 7.72324e16i) q^{58} -5.44449e17i q^{59} +(2.12592e17 - 3.24100e17i) q^{60} -4.97765e17 q^{61} +(2.52465e17 - 8.45187e17i) q^{62} -4.72928e17i q^{63} +(-1.96005e17 + 1.13614e18i) q^{64} -1.89950e18 q^{65} +(7.43579e16 + 2.22114e16i) q^{66} -3.24323e18i q^{67} +(2.88741e18 + 1.89399e18i) q^{68} +1.35365e18 q^{69} +(-1.29305e18 + 4.32880e18i) q^{70} -2.30034e18i q^{71} +(-8.03944e17 - 9.54516e17i) q^{72} -2.29913e18 q^{73} +(-9.90290e17 - 2.95809e17i) q^{74} -7.56694e17i q^{75} +(-7.24774e17 + 1.10493e18i) q^{76} -9.04537e17 q^{77} +(-1.75043e18 + 5.85998e18i) q^{78} -7.16859e17i q^{79} +(4.74887e18 + 1.09350e19i) q^{80} +1.35085e18 q^{81} +(2.15708e19 + 6.44339e18i) q^{82} -5.66725e18i q^{83} +(1.21628e19 + 7.97818e18i) q^{84} +3.57070e19 q^{85} +(-1.08896e19 + 3.64556e19i) q^{86} -8.98384e18i q^{87} +(-1.82563e18 + 1.53765e18i) q^{88} -3.74863e19 q^{89} +(-1.23646e19 - 3.69342e18i) q^{90} -7.12845e19i q^{91} +(-2.28358e19 + 3.48134e19i) q^{92} -2.93673e19 q^{93} +(2.42430e19 - 8.11591e19i) q^{94} +1.36640e19i q^{95} +(3.81107e19 - 4.57352e18i) q^{96} -1.04779e20 q^{97} +(-8.41625e19 - 2.51401e19i) q^{98} -2.58368e18i 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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