LMFDB - Embedded newform 12.19.d.a.7.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,19,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, 19, names="a")

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

chi := DirichletCharacter("12.7");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 19 $
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:	$24.6463365252$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 332091 x^{16} - 8722796 x^{15} + 44065046710 x^{14} + 2562387593326 x^{13} + \cdots + 51\!\cdots\!09 $ x^18 - 5x^17 - 332091x^16 - 8722796x^15 + 44065046710x^14 + 2562387593326x^13 - 2939418299568910x^12 - 270086571564720600x^11 + 99892143837893471971x^10 + 13287383366374675095257x^9 - 1404426939389796697311653x^8 - 302846077765145575240351608x^7 - 3048385818268269033396834566x^6 + 2387968325606677017735731037126x^5 + 189341038803558425525784877687654x^4 + 5034939808459428548543033598246780x^3 + 5944618618967029844099743191417597x^2 - 1074790996286169638673503552568280077*x + 5142216036403070733098077860515333409
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{139}\cdot 3^{67}\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.11
Root			$-52.7154 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.19.d.a.7.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(148.471 - 490.000i) q^{2} -11364.0i q^{3} +(-218057. - 145502. i) q^{4} -3.24964e6 q^{5} +(-5.56836e6 - 1.68722e6i) q^{6} -7.85072e7i q^{7} +(-1.03671e8 + 8.52451e7i) q^{8} -1.29140e8 q^{9} +O(q^{10})$	\(q+(148.471 - 490.000i) q^{2} -11364.0i q^{3} +(-218057. - 145502. i) q^{4} -3.24964e6 q^{5} +(-5.56836e6 - 1.68722e6i) q^{6} -7.85072e7i q^{7} +(-1.03671e8 + 8.52451e7i) q^{8} -1.29140e8 q^{9} +(-4.82477e8 + 1.59232e9i) q^{10} -2.80435e8i q^{11} +(-1.65348e9 + 2.47799e9i) q^{12} +1.28099e10 q^{13} +(-3.84686e10 - 1.16560e10i) q^{14} +3.69288e10i q^{15} +(2.63780e10 + 6.34552e10i) q^{16} -8.93043e10 q^{17} +(-1.91736e10 + 6.32787e10i) q^{18} -2.10695e11i q^{19} +(7.08606e11 + 4.72828e11i) q^{20} -8.92155e11 q^{21} +(-1.37413e11 - 4.16365e10i) q^{22} +5.65577e11i q^{23} +(9.68724e11 + 1.17812e12i) q^{24} +6.74545e12 q^{25} +(1.90190e12 - 6.27687e12i) q^{26} +1.46755e12i q^{27} +(-1.14229e13 + 1.71190e13i) q^{28} +8.21275e12 q^{29} +(1.80951e13 + 5.48286e12i) q^{30} +4.08407e12i q^{31} +(3.50095e13 - 3.50397e12i) q^{32} -3.18686e12 q^{33} +(-1.32591e13 + 4.37591e13i) q^{34} +2.55120e14i q^{35} +(2.81599e13 + 1.87901e13i) q^{36} -1.03516e14 q^{37} +(-1.03240e14 - 3.12820e13i) q^{38} -1.45572e14i q^{39} +(3.36893e14 - 2.77016e14i) q^{40} +2.18283e14 q^{41} +(-1.32459e14 + 4.37156e14i) q^{42} -7.14701e14i q^{43} +(-4.08038e13 + 6.11508e13i) q^{44} +4.19659e14 q^{45} +(2.77133e14 + 8.39718e13i) q^{46} -1.15571e14i q^{47} +(7.21104e14 - 2.99759e14i) q^{48} -4.53497e15 q^{49} +(1.00150e15 - 3.30527e15i) q^{50} +1.01485e15i q^{51} +(-2.79329e15 - 1.86387e15i) q^{52} -4.38158e15 q^{53} +(7.19099e14 + 2.17888e14i) q^{54} +9.11314e14i q^{55} +(6.69235e15 + 8.13892e15i) q^{56} -2.39433e15 q^{57} +(1.21936e15 - 4.02425e15i) q^{58} -1.59649e15i q^{59} +(5.37321e15 - 8.05258e15i) q^{60} +9.13936e15 q^{61} +(2.00120e15 + 6.06366e14i) q^{62} +1.01384e16i q^{63} +(3.48094e15 - 1.76749e16i) q^{64} -4.16276e16 q^{65} +(-4.73157e14 + 1.56156e15i) q^{66} +1.99042e16i q^{67} +(1.94734e16 + 1.29939e16i) q^{68} +6.42721e15 q^{69} +(1.25009e17 + 3.78779e16i) q^{70} +4.69447e16i q^{71} +(1.33881e16 - 1.10086e16i) q^{72} -8.14567e16 q^{73} +(-1.53692e16 + 5.07230e16i) q^{74} -7.66552e16i q^{75} +(-3.06564e16 + 4.59434e16i) q^{76} -2.20162e16 q^{77} +(-7.13303e16 - 2.16132e16i) q^{78} +5.80762e16i q^{79} +(-8.57190e16 - 2.06207e17i) q^{80} +1.66772e16 q^{81} +(3.24086e16 - 1.06959e17i) q^{82} +6.82268e16i q^{83} +(1.94540e17 + 1.29810e17i) q^{84} +2.90207e17 q^{85} +(-3.50204e17 - 1.06112e17i) q^{86} -9.33296e16i q^{87} +(2.39057e16 + 2.90730e16i) q^{88} -4.94088e17 q^{89} +(6.23072e16 - 2.05633e17i) q^{90} -1.00567e18i q^{91} +(8.22925e16 - 1.23328e17i) q^{92} +4.64113e16 q^{93} +(-5.66300e16 - 1.71590e16i) q^{94} +6.84681e17i q^{95} +(-3.98191e16 - 3.97847e17i) q^{96} +1.02855e18 q^{97} +(-6.73311e17 + 2.22214e18i) q^{98} +3.62155e16i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 170 q^{2} - 436932 q^{4} - 1721764 q^{5} - 6731586 q^{6} + 108558736 q^{8} - 2324522934 q^{9}+O(q^{10}) $ 18 * q - 170 * q^2 - 436932 * q^4 - 1721764 * q^5 - 6731586 * q^6 + 108558736 * q^8 - 2324522934 * q^9	$ 18 q - 170 q^{2} - 436932 q^{4} - 1721764 q^{5} - 6731586 q^{6} + 108558736 q^{8} - 2324522934 q^{9} + 1397074644 q^{10} - 6468699852 q^{12} + 1799208612 q^{13} - 48147537912 q^{14} - 119537094672 q^{16} - 282984271180 q^{17} + 21953827710 q^{18} + 491637621128 q^{20} + 254050055640 q^{21} + 272503644408 q^{22} + 4483423343232 q^{24} + 20224739695878 q^{25} - 2765456970196 q^{26} + 27756503338032 q^{28} + 1812741883820 q^{29} - 3579410315772 q^{30} + 216191588070880 q^{32} + 17014318866216 q^{33} - 275796423660708 q^{34} + 56425469699916 q^{36} + 197439381411156 q^{37} - 676030464010008 q^{38} + 19\!\cdots\!68 q^{40}+ \cdots - 37\!\cdots\!22 q^{98}+O(q^{100}) $ 18 * q - 170 * q^2 - 436932 * q^4 - 1721764 * q^5 - 6731586 * q^6 + 108558736 * q^8 - 2324522934 * q^9 + 1397074644 * q^10 - 6468699852 * q^12 + 1799208612 * q^13 - 48147537912 * q^14 - 119537094672 * q^16 - 282984271180 * q^17 + 21953827710 * q^18 + 491637621128 * q^20 + 254050055640 * q^21 + 272503644408 * q^22 + 4483423343232 * q^24 + 20224739695878 * q^25 - 2765456970196 * q^26 + 27756503338032 * q^28 + 1812741883820 * q^29 - 3579410315772 * q^30 + 216191588070880 * q^32 + 17014318866216 * q^33 - 275796423660708 * q^34 + 56425469699916 * q^36 + 197439381411156 * q^37 - 676030464010008 * q^38 + 1941137842438368 * q^40 - 204669372669676 * q^41 - 1059935698181880 * q^42 + 3599128179401424 * q^44 + 222348883607532 * q^45 - 3847169819651040 * q^46 + 1457367907812912 * q^48 - 3424095824368878 * q^49 - 10192520264009358 * q^50 + 4228291003193208 * q^52 - 14112687314785972 * q^53 + 869318113288518 * q^54 - 6591066595001856 * q^56 - 9662233004693640 * q^57 + 17584741731886020 * q^58 + 193536143011224 * q^60 + 4171094773122132 * q^61 + 77227021488187896 * q^62 - 53424456043095936 * q^64 + 35585253307254712 * q^65 + 40644920520184824 * q^66 - 91403316760947112 * q^68 + 26342656148137824 * q^69 + 264958129332427248 * q^70 - 14019292862113968 * q^72 - 83809473755653692 * q^73 + 55949505142092092 * q^74 - 129026923617832848 * q^76 - 354619239852167328 * q^77 - 34535086926497028 * q^78 + 43257628406200352 * q^80 + 300189270593998242 * q^81 - 458290372754774916 * q^82 + 324078384809786832 * q^84 + 166017223439872920 * q^85 - 975848731010420424 * q^86 + 1151342491040801280 * q^88 - 660650117825905468 * q^89 - 180418447249326972 * q^90 + 1359275349780859584 * q^92 - 447365281400937432 * q^93 - 2087066679318498384 * q^94 + 257905715132447136 * q^96 + 2412557706093917220 * q^97 - 3767017570512990122 * 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 $

$2$	148.471	−	490.000i	0.289982	−	0.957032i
$2$	148.471	−	490.000i	0.289982	−	0.957032i
$3$		−	11364.0i		−	0.577350i
$3$		−	11364.0i		−	0.577350i
$4$	−218057.	−	145502.i	−0.831820	−	0.555045i
$5$	−3.24964e6			−1.66381			−0.831907	−	0.554914i	$-0.812751\pi$
$5$	−3.24964e6			−1.66381			−0.831907	+	0.554914i	$0.812751\pi$
$6$	−5.56836e6	−	1.68722e6i	−0.552543	−	0.167421i
$7$		−	7.85072e7i		−	1.94548i	−0.231895	−	0.972741i	$-0.574493\pi$
$7$		−	7.85072e7i		−	1.94548i	0.231895	−	0.972741i	$-0.425507\pi$
$8$	−1.03671e8	+	8.52451e7i	−0.772409	+	0.635126i
$9$	−1.29140e8			−0.333333
$10$	−4.82477e8	+	1.59232e9i	−0.482477	+	1.59232i
$11$		−	2.80435e8i		−	0.118932i	−0.998230	−	0.0594660i	$-0.981060\pi$
$11$		−	2.80435e8i		−	0.118932i	0.998230	−	0.0594660i	$-0.0189398\pi$
$12$	−1.65348e9	+	2.47799e9i	−0.320455	+	0.480252i
$13$	1.28099e10			1.20797			0.603986	−	0.796995i	$-0.293578\pi$
$13$	1.28099e10			1.20797			0.603986	+	0.796995i	$0.293578\pi$
$14$	−3.84686e10	−	1.16560e10i	−1.86189	−	0.564155i
$15$			3.69288e10i			0.960604i
$16$	2.63780e10	+	6.34552e10i	0.383851	+	0.923395i
$17$	−8.93043e10			−0.753064			−0.376532	−	0.926404i	$-0.622884\pi$
$17$	−8.93043e10			−0.753064			−0.376532	+	0.926404i	$0.622884\pi$
$18$	−1.91736e10	+	6.32787e10i	−0.0966608	+	0.319011i
$19$		−	2.10695e11i		−	0.652937i	−0.945208	−	0.326468i	$-0.894141\pi$
$19$		−	2.10695e11i		−	0.652937i	0.945208	−	0.326468i	$-0.105859\pi$
$20$	7.08606e11	+	4.72828e11i	1.38400	+	0.923492i
$21$	−8.92155e11			−1.12322
$22$	−1.37413e11	−	4.16365e10i	−0.113822	−	0.0344882i
$23$			5.65577e11i			0.314009i	0.987598	+	0.157004i	$0.0501837\pi$
$23$			5.65577e11i			0.314009i	−0.987598	+	0.157004i	$0.949816\pi$
$24$	9.68724e11	+	1.17812e12i	0.366690	+	0.445950i
$25$	6.74545e12			1.76828
$26$	1.90190e12	−	6.27687e12i	0.350290	−	1.15607i
$27$			1.46755e12i			0.192450i
$28$	−1.14229e13	+	1.71190e13i	−1.07983	+	1.61829i
$29$	8.21275e12			0.566118			0.283059	−	0.959103i	$-0.408651\pi$
$29$	8.21275e12			0.566118			0.283059	+	0.959103i	$0.408651\pi$
$30$	1.80951e13	+	5.48286e12i	0.919329	+	0.278558i
$31$			4.08407e12i			0.154468i	0.997013	+	0.0772339i	$0.0246088\pi$
$31$			4.08407e12i			0.154468i	−0.997013	+	0.0772339i	$0.975391\pi$
$32$	3.50095e13	−	3.50397e12i	0.995029	−	0.0995889i
$33$	−3.18686e12			−0.0686654
$34$	−1.32591e13	+	4.37591e13i	−0.218375	+	0.720707i
$35$			2.55120e14i			3.23692i
$36$	2.81599e13	+	1.87901e13i	0.277273	+	0.185015i
$37$	−1.03516e14			−0.796514			−0.398257	−	0.917274i	$-0.630385\pi$
$37$	−1.03516e14			−0.796514			−0.398257	+	0.917274i	$0.630385\pi$
$38$	−1.03240e14	−	3.12820e13i	−0.624881	−	0.189340i
$39$		−	1.45572e14i		−	0.697423i
$40$	3.36893e14	−	2.77016e14i	1.28515	−	1.05673i
$41$	2.18283e14			0.666752			0.333376	−	0.942794i	$-0.391812\pi$
$41$	2.18283e14			0.666752			0.333376	+	0.942794i	$0.391812\pi$
$42$	−1.32459e14	+	4.37156e14i	−0.325715	+	1.07496i
$43$		−	7.14701e14i		−	1.42203i	−0.703178	−	0.711014i	$-0.748236\pi$
$43$		−	7.14701e14i		−	1.42203i	0.703178	−	0.711014i	$-0.251764\pi$
$44$	−4.08038e13	+	6.11508e13i	−0.0660126	+	0.0989301i
$45$	4.19659e14			0.554605
$46$	2.77133e14	+	8.39718e13i	0.300516	+	0.0910570i
$47$		−	1.15571e14i		−	0.103269i	−0.998666	−	0.0516345i	$-0.983557\pi$
$47$		−	1.15571e14i		−	0.103269i	0.998666	−	0.0516345i	$-0.0164431\pi$
$48$	7.21104e14	−	2.99759e14i	0.533122	−	0.221616i
$49$	−4.53497e15			−2.78490
$50$	1.00150e15	−	3.30527e15i	0.512770	−	1.69230i
$51$			1.01485e15i			0.434782i
$52$	−2.79329e15	−	1.86387e15i	−1.00482	−	0.670478i
$53$	−4.38158e15			−1.32785			−0.663924	−	0.747800i	$-0.731110\pi$
$53$	−4.38158e15			−1.32785			−0.663924	+	0.747800i	$0.731110\pi$
$54$	7.19099e14	+	2.17888e14i	0.184181	+	0.0558071i
$55$			9.11314e14i			0.197881i
$56$	6.69235e15	+	8.13892e15i	1.23563	+	1.50271i
$57$	−2.39433e15			−0.376973
$58$	1.21936e15	−	4.02425e15i	0.164164	−	0.541793i
$59$		−	1.59649e15i		−	0.184289i	−0.995746	−	0.0921444i	$-0.970628\pi$
$59$		−	1.59649e15i		−	0.184289i	0.995746	−	0.0921444i	$-0.0293721\pi$
$60$	5.37321e15	−	8.05258e15i	0.533178	−	0.799050i
$61$	9.13936e15			0.781533			0.390767	−	0.920490i	$-0.372210\pi$
$61$	9.13936e15			0.781533			0.390767	+	0.920490i	$0.372210\pi$
$62$	2.00120e15	+	6.06366e14i	0.147831	+	0.0447929i
$63$			1.01384e16i			0.648494i
$64$	3.48094e15	−	1.76749e16i	0.193231	−	0.981153i
$65$	−4.16276e16			−2.00984
$66$	−4.73157e14	+	1.56156e15i	−0.0199118	+	0.0657150i
$67$			1.99042e16i			0.731595i	0.930694	+	0.365798i	$0.119204\pi$
$67$			1.99042e16i			0.731595i	−0.930694	+	0.365798i	$0.880796\pi$
$68$	1.94734e16	+	1.29939e16i	0.626414	+	0.417984i
$69$	6.42721e15			0.181293
$70$	1.25009e17	+	3.78779e16i	3.09784	+	0.938650i
$71$			4.69447e16i			1.02391i	0.859013	+	0.511955i	$0.171078\pi$
$71$			4.69447e16i			1.02391i	−0.859013	+	0.511955i	$0.828922\pi$
$72$	1.33881e16	−	1.10086e16i	0.257470	−	0.211709i
$73$	−8.14567e16			−1.38363			−0.691816	−	0.722073i	$-0.743189\pi$
$73$	−8.14567e16			−1.38363			−0.691816	+	0.722073i	$0.743189\pi$
$74$	−1.53692e16	+	5.07230e16i	−0.230975	+	0.762289i
$75$		−	7.66552e16i		−	1.02092i
$76$	−3.06564e16	+	4.59434e16i	−0.362409	+	0.543126i
$77$	−2.20162e16			−0.231380
$78$	−7.13303e16	−	2.16132e16i	−0.667456	−	0.202240i
$79$			5.80762e16i			0.484568i	0.970205	+	0.242284i	$0.0778965\pi$
$79$			5.80762e16i			0.484568i	−0.970205	+	0.242284i	$0.922103\pi$
$80$	−8.57190e16	−	2.06207e17i	−0.638656	−	1.53636i
$81$	1.66772e16			0.111111
$82$	3.24086e16	−	1.06959e17i	0.193346	−	0.638103i
$83$			6.82268e16i			0.364966i	0.983209	+	0.182483i	$0.0584134\pi$
$83$			6.82268e16i			0.364966i	−0.983209	+	0.182483i	$0.941587\pi$
$84$	1.94540e17	+	1.29810e17i	0.934321	+	0.623440i
$85$	2.90207e17			1.25296
$86$	−3.50204e17	−	1.06112e17i	−1.36093	−	0.412363i
$87$		−	9.33296e16i		−	0.326848i
$88$	2.39057e16	+	2.90730e16i	0.0755368	+	0.0918641i
$89$	−4.94088e17			−1.41024			−0.705122	−	0.709086i	$-0.749108\pi$
$89$	−4.94088e17			−1.41024			−0.705122	+	0.709086i	$0.749108\pi$
$90$	6.23072e16	−	2.05633e17i	0.160826	−	0.530775i
$91$		−	1.00567e18i		−	2.35009i
$92$	8.22925e16	−	1.23328e17i	0.174289	−	0.261199i
$93$	4.64113e16			0.0891820
$94$	−5.66300e16	−	1.71590e16i	−0.0988317	−	0.0299462i
$95$			6.84681e17i			1.08637i
$96$	−3.98191e16	−	3.97847e17i	−0.0574977	−	0.574480i
$97$	1.02855e18			1.35295			0.676474	−	0.736466i	$-0.263507\pi$
$97$	1.02855e18			1.35295			0.676474	+	0.736466i	$0.263507\pi$
$98$	−6.73311e17	+	2.22214e18i	−0.807571	+	2.66524i
$99$			3.62155e16i			0.0396440i
$100$	−1.47089e18	−	9.81474e17i	−1.47089	−	0.981474i
$101$	7.28406e17			0.666010			0.333005	−	0.942925i	$-0.391937\pi$
$101$	7.28406e17			0.666010			0.333005	+	0.942925i	$0.391937\pi$
$102$	4.97278e17	+	1.50676e17i	0.416100	+	0.126079i
$103$			1.07631e18i			0.824901i	0.910980	+	0.412451i	$0.135327\pi$
$103$			1.07631e18i			0.824901i	−0.910980	+	0.412451i	$0.864673\pi$
$104$	−1.32802e18	+	1.09198e18i	−0.933048	+	0.767213i
$105$	2.89918e18			1.86884
$106$	−6.50538e17	+	2.14698e18i	−0.385052	+	1.27079i
$107$		−	1.95313e18i		−	1.06237i	−0.847254	−	0.531187i	$-0.821746\pi$
$107$		−	1.95313e18i		−	1.06237i	0.847254	−	0.531187i	$-0.178254\pi$
$108$	2.13531e17	−	3.20008e17i	0.106818	−	0.160084i
$109$	−1.29855e18			−0.597889			−0.298945	−	0.954270i	$-0.596635\pi$
$109$	−1.29855e18			−0.597889			−0.298945	+	0.954270i	$0.596635\pi$
$110$	4.46544e17	+	1.35304e17i	0.189378	+	0.0573819i
$111$			1.17636e18i			0.459868i
$112$	4.98169e18	−	2.07086e18i	1.79645	−	0.746774i
$113$	1.21645e18			0.404938			0.202469	−	0.979289i	$-0.435104\pi$
$113$	1.21645e18			0.404938			0.202469	+	0.979289i	$0.435104\pi$
$114$	−3.55489e17	+	1.17322e18i	−0.109316	+	0.360775i
$115$		−	1.83792e18i		−	0.522452i
$116$	−1.79085e18	−	1.19497e18i	−0.470908	−	0.314221i
$117$	−1.65428e18			−0.402657
$118$	−7.82282e17	−	2.37033e17i	−0.176370	−	0.0534405i
$119$			7.01103e18i			1.46507i
$120$	−3.14800e18	−	3.82845e18i	−0.610104	−	0.741979i
$121$	5.48127e18			0.985855
$122$	1.35693e18	−	4.47829e18i	0.226631	−	0.747952i
$123$		−	2.48056e18i		−	0.384950i
$124$	5.94239e17	−	8.90559e17i	0.0857365	−	0.128489i
$125$	−9.52389e18			−1.27827
$126$	4.96784e18	+	1.50526e18i	0.620629	+	0.188052i
$127$		−	9.61802e18i		−	1.11906i	−0.828811	−	0.559529i	$-0.810982\pi$
$127$		−	9.61802e18i		−	1.11906i	0.828811	−	0.559529i	$-0.189018\pi$
$128$	−8.14388e18	−	4.32987e18i	−0.882961	−	0.469445i
$129$	−8.12185e18			−0.821008
$130$	−6.18050e18	+	2.03976e19i	−0.582818	+	1.92348i
$131$			9.06644e17i			0.0797986i	0.999204	+	0.0398993i	$0.0127037\pi$
$131$			9.06644e17i			0.0797986i	−0.999204	+	0.0398993i	$0.987296\pi$
$132$	6.94917e17	+	4.63694e17i	0.0571173	+	0.0381124i
$133$	−1.65410e19			−1.27028
$134$	9.75305e18	+	2.95519e18i	0.700160	+	0.212150i
$135$		−	4.76900e18i		−	0.320201i
$136$	9.25826e18	−	7.61275e18i	0.581674	−	0.478290i
$137$	−6.55464e18			−0.385535			−0.192768	−	0.981244i	$-0.561746\pi$
$137$	−6.55464e18			−0.385535			−0.192768	+	0.981244i	$0.561746\pi$
$138$	9.54255e17	−	3.14934e18i	0.0525718	−	0.173503i
$139$			1.00765e19i			0.520208i	0.965581	+	0.260104i	$0.0837569\pi$
$139$			1.00765e19i			0.520208i	−0.965581	+	0.260104i	$0.916243\pi$
$140$	3.71204e19	−	5.56306e19i	1.79664	−	2.69254i
$141$	−1.31335e18			−0.0596223
$142$	2.30029e19	+	6.96992e18i	0.979914	+	0.296916i
$143$		−	3.59236e18i		−	0.143666i
$144$	−3.40646e18	−	8.19462e18i	−0.127950	−	0.307798i
$145$	−2.66885e19			−0.941915
$146$	−1.20939e19	+	3.99138e19i	−0.401229	+	1.32418i
$147$			5.15353e19i			1.60786i
$148$	2.25724e19	+	1.50618e19i	0.662557	+	0.442101i
$149$	5.96703e19			1.64847			0.824237	−	0.566246i	$-0.191605\pi$
$149$	5.96703e19			1.64847			0.824237	+	0.566246i	$0.191605\pi$
$150$	−3.75611e19	−	1.13811e19i	−0.977050	−	0.296048i
$151$		−	7.42465e18i		−	0.181921i	−0.995854	−	0.0909606i	$-0.971006\pi$
$151$		−	7.42465e18i		−	0.181921i	0.995854	−	0.0909606i	$-0.0289937\pi$
$152$	1.79607e19	+	2.18429e19i	0.414697	+	0.504334i
$153$	1.15328e19			0.251021
$154$	−3.26877e18	+	1.07879e19i	−0.0670961	+	0.221438i
$155$		−	1.32717e19i		−	0.257006i
$156$	−2.11809e19	+	3.17429e19i	−0.387101	+	0.580130i
$157$	−4.08793e19			−0.705353			−0.352676	−	0.935745i	$-0.614728\pi$
$157$	−4.08793e19			−0.705353			−0.352676	+	0.935745i	$0.614728\pi$
$158$	2.84574e19	+	8.62263e18i	0.463747	+	0.140516i
$159$			4.97923e19i			0.766633i
$160$	−1.13768e20	+	1.13866e19i	−1.65554	+	0.165697i
$161$	4.44019e19			0.610898
$162$	2.47608e18	−	8.17183e18i	0.0322203	−	0.106337i
$163$		−	4.04650e19i		−	0.498186i	−0.968480	−	0.249093i	$-0.919868\pi$
$163$		−	4.04650e19i		−	0.498186i	0.968480	−	0.249093i	$-0.0801324\pi$
$164$	−4.75980e19	−	3.17605e19i	−0.554618	−	0.370077i
$165$	1.03562e19			0.114247
$166$	3.34312e19	+	1.01297e19i	0.349284	+	0.105834i
$167$			1.06328e19i			0.105245i	0.998614	+	0.0526225i	$0.0167580\pi$
$167$			1.06328e19i			0.105245i	−0.998614	+	0.0526225i	$0.983242\pi$
$168$	9.24905e19	−	7.60518e19i	0.867588	−	0.713388i
$169$	5.16389e19			0.459195
$170$	4.30873e19	−	1.42201e20i	0.363336	−	1.19912i
$171$			2.72091e19i			0.217646i
$172$	−1.03990e20	+	1.55845e20i	−0.789289	+	1.18287i
$173$	3.06069e19			0.220498			0.110249	−	0.993904i	$-0.464835\pi$
$173$	3.06069e19			0.220498			0.110249	+	0.993904i	$0.464835\pi$
$174$	−4.57316e19	−	1.38567e19i	−0.312804	−	0.0947802i
$175$		−	5.29566e20i		−	3.44016i
$176$	1.77951e19	−	7.39733e18i	0.109821	−	0.0456521i
$177$	−1.81425e19			−0.106399
$178$	−7.33577e19	+	2.42103e20i	−0.408946	+	1.34965i
$179$			1.21245e20i			0.642669i	0.946966	+	0.321335i	$0.104131\pi$
$179$			1.21245e20i			0.642669i	−0.946966	+	0.321335i	$0.895869\pi$
$180$	−9.15094e19	−	6.10611e19i	−0.461332	−	0.307831i
$181$	3.70908e19			0.177893			0.0889465	−	0.996036i	$-0.471650\pi$
$181$	3.70908e19			0.177893			0.0889465	+	0.996036i	$0.471650\pi$
$182$	−4.92780e20	−	1.49313e20i	−2.24911	−	0.681483i
$183$		−	1.03860e20i		−	0.451218i
$184$	−4.82127e19	−	5.86340e19i	−0.199435	−	0.242543i
$185$	3.36391e20			1.32525
$186$	6.89073e18	−	2.27416e19i	0.0258612	−	0.0853500i
$187$			2.50441e19i			0.0895634i
$188$	−1.68158e19	+	2.52011e19i	−0.0573189	+	0.0859012i
$189$	1.15213e20			0.374408
$190$	3.35494e20	+	1.01655e20i	1.03969	+	0.315027i
$191$			6.19506e20i			1.83124i	0.402046	+	0.915620i	$0.368299\pi$
$191$			6.19506e20i			1.83124i	−0.402046	+	0.915620i	$0.631701\pi$
$192$	−2.00857e20	−	3.95574e19i	−0.566469	−	0.111562i
$193$	1.11735e20			0.300727			0.150364	−	0.988631i	$-0.451956\pi$
$193$	1.11735e20			0.300727			0.150364	+	0.988631i	$0.451956\pi$
$194$	1.52710e20	−	5.03992e20i	0.392331	−	1.29481i
$195$			4.73056e20i			1.16038i
$196$	9.88880e20	+	6.59845e20i	2.31654	+	1.54574i
$197$	−8.64014e20			−1.93341			−0.966707	−	0.255886i	$-0.917633\pi$
$197$	−8.64014e20			−1.93341			−0.966707	+	0.255886i	$0.917633\pi$
$198$	1.77456e19	+	5.37695e18i	0.0379406	+	0.0114961i
$199$			1.99004e20i			0.406615i	0.979115	+	0.203307i	$0.0651691\pi$
$199$			1.99004e20i			0.406615i	−0.979115	+	0.203307i	$0.934831\pi$
$200$	−6.99307e20	+	5.75017e20i	−1.36583	+	1.12308i
$201$	2.26191e20			0.422387
$202$	1.08147e20	−	3.56919e20i	0.193131	−	0.637393i
$203$		−	6.44760e20i		−	1.10137i
$204$	1.47663e20	−	2.21295e20i	0.241323	−	0.361660i
$205$	−7.09340e20			−1.10935
$206$	5.27392e20	+	1.59801e20i	0.789457	+	0.239207i
$207$		−	7.30388e19i		−	0.104670i
$208$	3.37900e20	+	8.12857e20i	0.463680	+	1.11543i
$209$	−5.90862e19			−0.0776551
$210$	4.30444e20	−	1.42060e21i	0.541930	−	1.78854i
$211$		−	1.46444e21i		−	1.76657i	−0.468838	−	0.883284i	$-0.655327\pi$
$211$		−	1.46444e21i		−	1.76657i	0.468838	−	0.883284i	$-0.344673\pi$
$212$	9.55434e20	+	6.37528e20i	1.10453	+	0.737015i
$213$	5.33479e20			0.591154
$214$	−9.57035e20	−	2.89983e20i	−1.01673	−	0.308070i
$215$			2.32252e21i			2.36599i
$216$	−1.25101e20	−	1.52142e20i	−0.122230	−	0.148650i
$217$	3.20629e20			0.300514
$218$	−1.92797e20	+	6.36291e20i	−0.173377	+	0.572199i
$219$			9.25672e20i			0.798841i
$220$	1.32598e20	−	1.98718e20i	0.109833	−	0.164601i
$221$	−1.14398e21			−0.909680
$222$	5.76416e20	+	1.74655e20i	0.440108	+	0.133353i
$223$		−	1.67187e21i		−	1.22591i	−0.790117	−	0.612956i	$-0.789980\pi$
$223$		−	1.67187e21i		−	1.22591i	0.790117	−	0.612956i	$-0.210020\pi$
$224$	−2.75087e20	−	2.74849e21i	−0.193748	−	1.93581i
$225$	−8.71109e20			−0.589427
$226$	1.80607e20	−	5.96061e20i	0.117425	−	0.387538i
$227$		−	1.86110e21i		−	1.16288i	−0.813588	−	0.581442i	$-0.802489\pi$
$227$		−	1.86110e21i		−	1.16288i	0.813588	−	0.581442i	$-0.197511\pi$
$228$	5.22100e20	+	3.48379e20i	0.313574	+	0.209237i
$229$	−1.76589e21			−1.01964			−0.509818	−	0.860282i	$-0.670287\pi$
$229$	−1.76589e21			−1.01964			−0.509818	+	0.860282i	$0.670287\pi$
$230$	−9.00583e20	−	2.72878e20i	−0.500003	−	0.151502i
$231$			2.50192e20i			0.133587i
$232$	−8.51424e20	+	7.00097e20i	−0.437274	+	0.359556i
$233$	−2.87638e21			−1.42116			−0.710581	−	0.703616i	$-0.751568\pi$
$233$	−2.87638e21			−1.42116			−0.710581	+	0.703616i	$0.751568\pi$
$234$	−2.45612e20	+	8.10596e20i	−0.116763	+	0.385356i
$235$			3.75565e20i			0.171820i
$236$	−2.32292e20	+	3.48126e20i	−0.102289	+	0.153295i
$237$	6.59977e20			0.279765
$238$	3.43541e21	+	1.04093e21i	1.40212	+	0.424845i
$239$			3.89869e21i			1.53228i	0.642675	+	0.766139i	$0.277825\pi$
$239$			3.89869e21i			1.53228i	−0.642675	+	0.766139i	$0.722175\pi$
$240$	−2.34333e21	+	9.74109e20i	−0.887017	+	0.368728i
$241$	−7.55109e20			−0.275332			−0.137666	−	0.990479i	$-0.543960\pi$
$241$	−7.55109e20			−0.275332			−0.137666	+	0.990479i	$0.543960\pi$
$242$	8.13810e20	−	2.68583e21i	0.285881	−	0.943495i
$243$		−	1.89519e20i		−	0.0641500i
$244$	−1.99290e21	−	1.32979e21i	−0.650095	−	0.433786i
$245$	1.47370e22			4.63356
$246$	−1.21548e21	−	3.68291e20i	−0.368409	−	0.111629i
$247$		−	2.69898e21i		−	0.788729i
$248$	−3.48147e20	−	4.23399e20i	−0.0981064	−	0.119312i
$249$	7.75329e20			0.210713
$250$	−1.41402e21	+	4.66671e21i	−0.370677	+	1.22335i
$251$		−	3.12914e21i		−	0.791336i	−0.918394	−	0.395668i	$-0.870513\pi$
$251$		−	3.12914e21i		−	0.791336i	0.918394	−	0.395668i	$-0.129487\pi$
$252$	1.47516e21	−	2.21075e21i	0.359943	−	0.539430i
$253$	1.58608e20			0.0373457
$254$	−4.71283e21	−	1.42800e21i	−1.07097	−	0.324507i
$255$		−	3.29790e21i		−	0.723396i
$256$	−3.33077e21	+	3.34765e21i	−0.705318	+	0.708891i
$257$	−3.48836e21			−0.713219			−0.356609	−	0.934254i	$-0.616067\pi$
$257$	−3.48836e21			−0.713219			−0.356609	+	0.934254i	$0.616067\pi$
$258$	−1.20586e21	+	3.97971e21i	−0.238078	+	0.785731i
$259$			8.12678e21i			1.54960i
$260$	9.07719e21	+	6.05689e21i	1.67183	+	1.11555i
$261$	−1.06060e21			−0.188706
$262$	4.44256e20	+	1.34610e20i	0.0763698	+	0.0231402i
$263$		−	7.96671e21i		−	1.32336i	−0.749787	−	0.661679i	$-0.769844\pi$
$263$		−	7.96671e21i		−	1.32336i	0.749787	−	0.661679i	$-0.230156\pi$
$264$	3.30385e20	−	2.71665e20i	0.0530378	−	0.0436112i
$265$	1.42386e22			2.20929
$266$	−2.45586e21	+	8.10512e21i	−0.368358	+	1.21569i
$267$			5.61481e21i			0.814205i
$268$	2.89609e21	−	4.34024e21i	0.406068	−	0.608556i
$269$	−6.70813e21			−0.909560			−0.454780	−	0.890604i	$-0.650282\pi$
$269$	−6.70813e21			−0.909560			−0.454780	+	0.890604i	$0.650282\pi$
$270$	−2.33681e21	−	7.08058e20i	−0.306443	−	0.0928527i
$271$			9.28477e21i			1.17773i	0.808230	+	0.588867i	$0.200426\pi$
$271$			9.28477e21i			1.17773i	−0.808230	+	0.588867i	$0.799574\pi$
$272$	−2.35567e21	−	5.66683e21i	−0.289064	−	0.695376i
$273$	−1.14284e22			−1.35682
$274$	−9.73174e20	+	3.21178e21i	−0.111798	+	0.368969i
$275$		−	1.89166e21i		−	0.210305i
$276$	−1.40150e21	−	9.35170e20i	−0.150803	−	0.100626i
$277$	−1.41687e21			−0.147575			−0.0737873	−	0.997274i	$-0.523509\pi$
$277$	−1.41687e21			−0.147575			−0.0737873	+	0.997274i	$0.523509\pi$
$278$	4.93750e21	+	1.49607e21i	0.497856	+	0.150851i
$279$		−	5.27417e20i		−	0.0514892i
$280$	−2.17477e22	−	2.64485e22i	−2.05585	−	2.50023i
$281$	5.96318e21			0.545910			0.272955	−	0.962027i	$-0.411999\pi$
$281$	5.96318e21			0.545910			0.272955	+	0.962027i	$0.411999\pi$
$282$	−1.94995e20	+	6.43543e20i	−0.0172894	+	0.0570605i
$283$		−	3.34780e21i		−	0.287529i	−0.989612	−	0.143765i	$-0.954079\pi$
$283$		−	3.34780e21i		−	0.287529i	0.989612	−	0.143765i	$-0.0459208\pi$
$284$	6.83053e21	−	1.02366e22i	0.568315	−	0.851709i
$285$	7.78071e21			0.627213
$286$	−1.76026e21	−	5.33361e20i	−0.137493	−	0.0416607i
$287$		−	1.71368e22i		−	1.29715i
$288$	−4.52113e21	+	4.52504e20i	−0.331676	+	0.0331963i
$289$	−6.08783e21			−0.432894
$290$	−3.96246e21	+	1.30774e22i	−0.273139	+	0.901443i
$291$		−	1.16885e22i		−	0.781125i
$292$	1.77622e22	+	1.18521e22i	1.15093	+	0.767978i
$293$	−1.32285e21			−0.0831193			−0.0415596	−	0.999136i	$-0.513233\pi$
$293$	−1.32285e21			−0.0831193			−0.0415596	+	0.999136i	$0.513233\pi$
$294$	2.52523e22	+	7.65150e21i	1.53878	+	0.466252i
$295$			5.18803e21i			0.306622i
$296$	1.07316e22	−	8.82426e21i	0.615234	−	0.505886i
$297$	4.11552e20			0.0228885
$298$	8.85931e21	−	2.92385e22i	0.478028	−	1.57764i
$299$			7.24501e21i			0.379313i
$300$	−1.11535e22	+	1.67152e22i	−0.566655	+	0.849219i
$301$	−5.61092e22			−2.76653
$302$	−3.63808e21	−	1.10234e21i	−0.174104	−	0.0527539i
$303$		−	8.27759e21i		−	0.384521i
$304$	1.33697e22	−	5.55770e21i	0.602919	−	0.250630i
$305$	−2.96996e22			−1.30033
$306$	1.71228e21	−	5.65106e21i	0.0727918	−	0.240236i
$307$			4.10106e22i			1.69298i	0.532408	+	0.846488i	$0.321287\pi$
$307$			4.10106e22i			1.69298i	−0.532408	+	0.846488i	$0.678713\pi$
$308$	4.80078e21	+	3.20339e21i	0.192467	+	0.128426i
$309$	1.22312e22			0.476257
$310$	−6.50316e21	−	1.97047e21i	−0.245963	−	0.0745271i
$311$			4.50548e22i			1.65538i	0.561186	+	0.827690i	$0.310345\pi$
$311$			4.50548e22i			1.65538i	−0.561186	+	0.827690i	$0.689655\pi$
$312$	1.24093e22	+	1.50916e22i	0.442951	+	0.538695i
$313$	3.85055e22			1.33544			0.667719	−	0.744413i	$-0.267271\pi$
$313$	3.85055e22			1.33544			0.667719	+	0.744413i	$0.267271\pi$
$314$	−6.06938e21	+	2.00309e22i	−0.204540	+	0.675045i
$315$		−	3.29462e22i		−	1.07897i
$316$	8.45018e21	−	1.26639e22i	0.268957	−	0.403073i
$317$	−1.56074e22			−0.482834			−0.241417	−	0.970421i	$-0.577612\pi$
$317$	−1.56074e22			−0.482834			−0.241417	+	0.970421i	$0.577612\pi$
$318$	2.43982e22	+	7.39270e21i	0.733693	+	0.222310i
$319$		−	2.30315e21i		−	0.0673295i
$320$	−1.13118e22	+	5.74370e22i	−0.321501	+	1.63246i
$321$	−2.21954e22			−0.613362
$322$	6.59239e21	−	2.17569e22i	0.177150	−	0.584649i
$323$			1.88159e22i			0.491703i
$324$	−3.63657e21	−	2.42656e21i	−0.0924245	−	0.0616716i
$325$	8.64088e22			2.13603
$326$	−1.98279e22	−	6.00788e21i	−0.476780	−	0.144465i
$327$			1.47567e22i			0.345192i
$328$	−2.26296e22	+	1.86075e22i	−0.515005	+	0.423471i
$329$	−9.07319e21			−0.200908
$330$	1.53759e21	−	5.07452e21i	0.0331295	−	0.109338i
$331$		−	5.95974e22i		−	1.24961i	−0.780780	−	0.624806i	$-0.785178\pi$
$331$		−	5.95974e22i		−	1.24961i	0.780780	−	0.624806i	$-0.214822\pi$
$332$	9.92711e21	−	1.48773e22i	0.202572	−	0.303586i
$333$	1.33681e22			0.265505
$334$	5.21010e21	+	1.57867e21i	0.100723	+	0.0305192i
$335$		−	6.46814e22i		−	1.21724i
$336$	−2.35333e22	−	5.66119e22i	−0.431150	−	1.03718i
$337$	6.14145e22			1.09547			0.547737	−	0.836651i	$-0.315489\pi$
$337$	6.14145e22			1.09547			0.547737	+	0.836651i	$0.315489\pi$
$338$	7.66688e21	−	2.53031e22i	0.133158	−	0.439464i
$339$		−	1.38237e22i		−	0.233791i
$340$	−6.32815e22	−	4.22256e22i	−1.04224	−	0.695449i
$341$	1.14532e21			0.0183712
$342$	1.33325e22	+	4.03977e21i	0.208294	+	0.0631134i
$343$			2.28185e23i			3.47249i
$344$	6.09248e22	+	7.40937e22i	0.903167	+	1.09839i
$345$	−2.08861e22			−0.301638
$346$	4.54424e21	−	1.49974e22i	0.0639405	−	0.211024i
$347$		−	1.39191e23i		−	1.90829i	−0.299343	−	0.954146i	$-0.596767\pi$
$347$		−	1.39191e23i		−	1.90829i	0.299343	−	0.954146i	$-0.403233\pi$
$348$	−1.35796e22	+	2.03512e22i	−0.181415	+	0.271879i
$349$	−9.75742e22			−1.27030			−0.635150	−	0.772389i	$-0.719062\pi$
$349$	−9.75742e22			−1.27030			−0.635150	+	0.772389i	$0.719062\pi$
$350$	−2.59488e23	−	7.86253e22i	−3.29234	−	0.997584i
$351$			1.87992e22i			0.232474i
$352$	−9.82638e20	−	9.81789e21i	−0.0118443	−	0.118341i
$353$	−5.24693e22			−0.616499			−0.308250	−	0.951306i	$-0.599743\pi$
$353$	−5.24693e22			−0.616499			−0.308250	+	0.951306i	$0.599743\pi$
$354$	−2.69364e21	+	8.88984e21i	−0.0308539	+	0.101827i
$355$		−	1.52553e23i		−	1.70360i
$356$	1.07739e23	+	7.18906e22i	1.17307	+	0.782749i
$357$	7.96732e22			0.845860
$358$	5.94102e22	+	1.80014e22i	0.615055	+	0.186363i
$359$		−	7.85016e22i		−	0.792553i	−0.918131	−	0.396277i	$-0.870302\pi$
$359$		−	7.85016e22i		−	0.792553i	0.918131	−	0.396277i	$-0.129698\pi$
$360$	−4.35064e22	+	3.57739e22i	−0.428382	+	0.352244i
$361$	5.97351e22			0.573674
$362$	5.50691e21	−	1.81745e22i	0.0515858	−	0.170249i
$363$		−	6.22891e22i		−	0.569184i
$364$	−1.46327e23	+	2.19293e23i	−1.30440	+	1.95485i
$365$	2.64705e23			2.30211
$366$	−5.08912e22	−	1.54201e22i	−0.431830	−	0.130845i
$367$		−	1.19371e23i		−	0.988337i	−0.869366	−	0.494168i	$-0.835473\pi$
$367$		−	1.19371e23i		−	0.988337i	0.869366	−	0.494168i	$-0.164527\pi$
$368$	−3.58889e22	+	1.49188e22i	−0.289954	+	0.120532i
$369$	−2.81891e22			−0.222251
$370$	4.99442e22	−	1.64832e23i	0.384300	−	1.26831i
$371$			3.43986e23i			2.58330i
$372$	−1.01203e22	−	6.75292e21i	−0.0741834	−	0.0495000i
$373$	−1.65383e23			−1.18334			−0.591672	−	0.806179i	$-0.701532\pi$
$373$	−1.65383e23			−1.18334			−0.591672	+	0.806179i	$0.701532\pi$
$374$	1.22716e22	+	3.71832e21i	0.0857151	+	0.0259718i
$375$			1.08229e23i			0.738012i
$376$	9.85190e21	+	1.19814e22i	0.0655887	+	0.0797658i
$377$	1.05205e23			0.683854
$378$	1.71058e22	−	5.64544e22i	0.108572	−	0.358321i
$379$		−	7.01819e22i		−	0.434983i	−0.976062	−	0.217492i	$-0.930213\pi$
$379$		−	7.01819e22i		−	0.434983i	0.976062	−	0.217492i	$-0.0697874\pi$
$380$	9.96223e22	−	1.49299e23i	0.602982	−	0.903661i
$381$	−1.09299e23			−0.646088
$382$	3.03558e23	+	9.19786e22i	1.75255	+	0.531027i
$383$			1.81734e23i			1.02482i	0.858741	+	0.512410i	$0.171247\pi$
$383$			1.81734e23i			1.02482i	−0.858741	+	0.512410i	$0.828753\pi$
$384$	−4.92046e22	+	9.25470e22i	−0.271034	+	0.509778i
$385$	7.15447e22			0.384973
$386$	1.65894e22	−	5.47501e22i	0.0872056	−	0.287806i
$387$			9.22966e22i			0.474009i
$388$	−2.24283e23	−	1.49656e23i	−1.12541	−	0.750947i
$389$	−2.80846e23			−1.37696			−0.688482	−	0.725254i	$-0.741723\pi$
$389$	−2.80846e23			−1.37696			−0.688482	+	0.725254i	$0.741723\pi$
$390$	2.31798e23	+	7.02351e22i	1.11052	+	0.336490i
$391$		−	5.05085e22i		−	0.236469i
$392$	4.70144e23	−	3.86584e23i	2.15108	−	1.76876i
$393$	1.03031e22			0.0460717
$394$	−1.28281e23	+	4.23367e23i	−0.560656	+	1.85034i
$395$		−	1.88727e23i		−	0.806231i
$396$	5.26941e21	−	7.89703e21i	0.0220042	−	0.0329767i
$397$	−2.91789e23			−1.19111			−0.595557	−	0.803313i	$-0.703069\pi$
$397$	−2.91789e23			−1.19111			−0.595557	+	0.803313i	$0.703069\pi$
$398$	9.75119e22	+	2.95463e22i	0.389144	+	0.117911i
$399$			1.87972e23i			0.733394i
$400$	1.77932e23	+	4.28034e23i	0.678755	+	1.63282i
$401$	2.84042e23			1.05946			0.529728	−	0.848168i	$-0.322294\pi$
$401$	2.84042e23			1.05946			0.529728	+	0.848168i	$0.322294\pi$
$402$	3.35828e22	−	1.10834e23i	0.122485	−	0.404238i
$403$			5.23166e22i			0.186593i
$404$	−1.58834e23	−	1.05984e23i	−0.554001	−	0.369666i
$405$	−5.41948e22			−0.184868
$406$	−3.15933e23	−	9.57282e22i	−1.05405	−	0.319378i
$407$			2.90297e22i			0.0947310i
$408$	−8.65112e22	−	1.05211e23i	−0.276141	−	0.335829i
$409$	−3.64062e23			−1.13675			−0.568375	−	0.822769i	$-0.692428\pi$
$409$	−3.64062e23			−1.13675			−0.568375	+	0.822769i	$0.692428\pi$
$410$	−1.05316e23	+	3.47577e23i	−0.321693	+	1.06169i
$411$			7.44869e22i			0.222589i
$412$	1.56605e23	−	2.34696e23i	0.457857	−	0.686170i
$413$	−1.25336e23			−0.358530
$414$	−3.57890e22	−	1.08441e22i	−0.100172	−	0.0303523i
$415$		−	2.21712e23i		−	0.607236i
$416$	4.48469e23	−	4.48856e22i	1.20197	−	0.120301i
$417$	1.14509e23			0.300343
$418$	−8.77259e21	+	2.89523e22i	−0.0225186	+	0.0743184i
$419$		−	1.52468e23i		−	0.383048i	−0.981488	−	0.191524i	$-0.938657\pi$
$419$		−	1.52468e23i		−	0.383048i	0.981488	−	0.191524i	$-0.0613430\pi$
$420$	−6.32186e23	−	4.21835e23i	−1.55454	−	1.03729i
$421$	5.86962e22			0.141277			0.0706384	−	0.997502i	$-0.477496\pi$
$421$	5.86962e22			0.141277			0.0706384	+	0.997502i	$0.477496\pi$
$422$	−7.17578e23	−	2.17427e23i	−1.69066	−	0.512274i
$423$			1.49249e22i			0.0344230i
$424$	4.54243e23	−	3.73509e23i	1.02564	−	0.843350i
$425$	−6.02398e23			−1.33163
$426$	7.92061e22	−	2.61405e23i	0.171424	−	0.565753i
$427$		−	7.17506e23i		−	1.52046i
$428$	−2.84184e23	+	4.25894e23i	−0.589665	+	0.883705i
$429$	−4.08235e22			−0.0829459
$430$	1.13804e24	+	3.44827e23i	2.26433	+	0.686096i
$431$		−	5.71465e22i		−	0.111351i	−0.998449	−	0.0556755i	$-0.982269\pi$
$431$		−	5.71465e22i		−	0.111351i	0.998449	−	0.0556755i	$-0.0177312\pi$
$432$	−9.31235e22	+	3.87110e22i	−0.177707	+	0.0738721i
$433$	3.32466e22			0.0621379			0.0310689	−	0.999517i	$-0.490109\pi$
$433$	3.32466e22			0.0621379			0.0310689	+	0.999517i	$0.490109\pi$
$434$	4.76041e22	−	1.57108e23i	0.0871438	−	0.287602i
$435$			3.03288e23i			0.543815i
$436$	2.83158e23	+	1.88941e23i	0.497337	+	0.331855i
$437$	1.19164e23			0.205028
$438$	4.53580e23	+	1.37435e23i	0.764516	+	0.231650i
$439$			3.43057e23i			0.566481i	0.959049	+	0.283241i	$0.0914095\pi$
$439$			3.43057e23i			0.566481i	−0.959049	+	0.283241i	$0.908591\pi$
$440$	−7.76850e22	−	9.44768e22i	−0.125679	−	0.152845i
$441$	5.85646e23			0.928299
$442$	−1.69848e23	+	5.60551e23i	−0.263791	+	0.870593i
$443$		−	2.68036e23i		−	0.407905i	−0.978981	−	0.203952i	$-0.934621\pi$
$443$		−	2.68036e23i		−	0.407905i	0.978981	−	0.203952i	$-0.0653788\pi$
$444$	1.71162e23	−	2.56513e23i	0.255247	−	0.382527i
$445$	1.60561e24			2.34638
$446$	−8.19218e23	−	2.48225e23i	−1.17324	−	0.355493i
$447$		−	6.78093e23i		−	0.951746i
$448$	−1.38761e24	−	2.73279e23i	−1.90882	−	0.375927i
$449$	2.08604e23			0.281258			0.140629	−	0.990062i	$-0.455087\pi$
$449$	2.08604e23			0.281258			0.140629	+	0.990062i	$0.455087\pi$
$450$	−1.29334e23	+	4.26844e23i	−0.170923	+	0.564100i
$451$		−	6.12142e22i		−	0.0792982i
$452$	−2.65255e23	−	1.76995e23i	−0.336835	−	0.224759i
$453$	−8.43736e22			−0.105032
$454$	−9.11939e23	−	2.76319e23i	−1.11292	−	0.337216i
$455$			3.26807e24i			3.91011i
$456$	2.48223e23	−	2.04105e23i	0.291177	−	0.239425i
$457$	−8.03712e23			−0.924389			−0.462195	−	0.886779i	$-0.652938\pi$
$457$	−8.03712e23			−0.924389			−0.462195	+	0.886779i	$0.652938\pi$
$458$	−2.62184e23	+	8.65289e23i	−0.295677	+	0.975824i
$459$		−	1.31058e23i		−	0.144927i
$460$	−2.67421e23	+	4.00771e23i	−0.289984	+	0.434586i
$461$	1.25284e24			1.33225			0.666126	−	0.745839i	$-0.267951\pi$
$461$	1.25284e24			1.33225			0.666126	+	0.745839i	$0.267951\pi$
$462$	1.22594e23	+	3.71462e22i	0.127847	+	0.0387380i
$463$		−	3.76319e23i		−	0.384882i	−0.981309	−	0.192441i	$-0.938360\pi$
$463$		−	3.76319e23i		−	0.384882i	0.981309	−	0.192441i	$-0.0616403\pi$
$464$	2.16636e23	+	5.21142e23i	0.217305	+	0.522751i
$465$	−1.50820e23			−0.148382
$466$	−4.27059e23	+	1.40943e24i	−0.412112	+	1.36010i
$467$		−	1.82521e24i		−	1.72767i	−0.503777	−	0.863834i	$-0.668057\pi$
$467$		−	1.82521e24i		−	1.72767i	0.503777	−	0.863834i	$-0.331943\pi$
$468$	3.60726e23	+	2.40700e23i	0.334938	+	0.223493i
$469$	1.56262e24			1.42331
$470$	1.84027e23	+	5.57605e22i	0.164438	+	0.0498249i
$471$			4.64551e23i			0.407235i
$472$	1.36093e23	+	1.65510e23i	0.117047	+	0.142346i
$473$	−2.00427e23			−0.169125
$474$	9.79874e22	−	3.23389e23i	0.0811270	−	0.267744i
$475$		−	1.42123e24i		−	1.15457i
$476$	1.02012e24	−	1.52880e24i	0.813181	−	1.21868i
$477$	5.65838e23			0.442616
$478$	1.91036e24	+	5.78842e23i	1.46644	+	0.444334i
$479$			7.03422e23i			0.529903i	0.964262	+	0.264951i	$0.0853559\pi$
$479$			7.03422e23i			0.529903i	−0.964262	+	0.264951i	$0.914644\pi$
$480$	1.29398e23	+	1.29286e24i	0.0956655	+	0.955828i
$481$	−1.32604e24			−0.962166
$482$	−1.12112e23	+	3.70004e23i	−0.0798413	+	0.263501i
$483$		−	5.04583e23i		−	0.352702i
$484$	−1.19523e24	−	7.97534e23i	−0.820054	−	0.547194i
$485$	−3.34243e24			−2.25106
$486$	−9.28645e22	−	2.81381e22i	−0.0613936	−	0.0186024i
$487$			1.01232e24i			0.656985i	0.944507	+	0.328493i	$0.106541\pi$
$487$			1.01232e24i			0.656985i	−0.944507	+	0.328493i	$0.893459\pi$
$488$	−9.47487e23	+	7.79086e23i	−0.603663	+	0.496372i
$489$	−4.59844e23			−0.287628
$490$	2.18802e24	−	7.22114e24i	1.34365	−	4.43446i
$491$		−	3.18068e24i		−	1.91772i	−0.283871	−	0.958862i	$-0.591619\pi$
$491$		−	3.18068e24i		−	1.91772i	0.283871	−	0.958862i	$-0.408381\pi$
$492$	−3.60926e23	+	5.40903e23i	−0.213664	+	0.320209i
$493$	−7.33434e23			−0.426323
$494$	−1.32250e24	−	4.00721e23i	−0.754838	−	0.228717i
$495$		−	1.17687e23i		−	0.0659603i
$496$	−2.59156e23	+	1.07730e23i	−0.142635	+	0.0592925i
$497$	3.68550e24			1.99200
$498$	1.15114e23	−	3.79911e23i	0.0611031	−	0.201659i
$499$			1.93414e24i			1.00828i	0.863621	+	0.504142i	$0.168191\pi$
$499$			1.93414e24i			1.00828i	−0.863621	+	0.504142i	$0.831809\pi$
$500$	2.07675e24	+	1.38574e24i	1.06330	+	0.709500i
$501$	1.20832e23			0.0607632
$502$	−1.53328e24	−	4.64586e23i	−0.757334	−	0.229474i
$503$			5.89179e23i			0.285848i	0.989734	+	0.142924i	$0.0456505\pi$
$503$			5.89179e23i			0.285848i	−0.989734	+	0.142924i	$0.954350\pi$
$504$	−8.64252e23	−	1.05106e24i	−0.411875	−	0.500902i
$505$	−2.36706e24			−1.10812
$506$	2.35487e22	−	7.77180e22i	0.0108296	−	0.0357410i
$507$		−	5.86824e23i		−	0.265116i
$508$	−1.39944e24	+	2.09727e24i	−0.621127	+	0.930855i
$509$	−1.94801e24			−0.849438			−0.424719	−	0.905325i	$-0.639627\pi$
$509$	−1.94801e24			−0.849438			−0.424719	+	0.905325i	$0.639627\pi$
$510$	−1.61597e24	−	4.89643e23i	−0.692314	−	0.209772i
$511$			6.39493e24i			2.69183i
$512$	1.14583e24	+	2.12911e24i	0.473902	+	0.880577i
$513$	3.09204e23			0.125658
$514$	−5.17920e23	+	1.70930e24i	−0.206821	+	0.682573i
$515$		−	3.49762e24i		−	1.37248i
$516$	1.77102e24	+	1.18174e24i	0.682932	+	0.455696i
$517$	−3.24103e22			−0.0122820
$518$	3.98212e24	+	1.20659e24i	1.48302	+	0.449358i
$519$		−	3.47816e23i		−	0.127305i
$520$	4.31558e24	−	3.54855e24i	1.55242	−	1.27650i
$521$	−3.69716e24			−1.30716			−0.653581	−	0.756857i	$-0.726734\pi$
$521$	−3.69716e24			−1.30716			−0.653581	+	0.756857i	$0.726734\pi$
$522$	−1.57468e23	+	5.19693e23i	−0.0547214	+	0.180598i
$523$		−	1.97245e24i		−	0.673739i	−0.941551	−	0.336869i	$-0.890632\pi$
$523$		−	1.97245e24i		−	0.673739i	0.941551	−	0.336869i	$-0.109368\pi$
$524$	1.31918e23	−	1.97700e23i	0.0442918	−	0.0663781i
$525$	−6.01799e24			−1.98617
$526$	−3.90369e24	−	1.18283e24i	−1.26650	−	0.383750i
$527$		−	3.64725e23i		−	0.116324i
$528$	−8.40631e22	−	2.02223e23i	−0.0263573	−	0.0634053i
$529$	2.92427e24			0.901399
$530$	2.11401e24	−	6.97690e24i	0.640656	−	2.11436i
$531$			2.06171e23i			0.0614296i
$532$	3.60689e24	+	2.40675e24i	1.05664	+	0.705060i
$533$	2.79619e24			0.805418
$534$	2.75126e24	+	8.33636e23i	0.779220	+	0.236105i
$535$			6.34697e24i			1.76759i
$536$	−1.69673e24	−	2.06349e24i	−0.464655	−	0.565091i
$537$	1.37783e24			0.371045
$538$	−9.95963e23	+	3.28699e24i	−0.263756	+	0.870478i
$539$			1.27177e24i			0.331214i
$540$	−6.93897e23	+	1.03991e24i	−0.177726	+	0.266350i
$541$	2.71128e24			0.682967			0.341483	−	0.939888i	$-0.389071\pi$
$541$	2.71128e24			0.682967			0.341483	+	0.939888i	$0.389071\pi$
$542$	4.54954e24	+	1.37852e24i	1.12713	+	0.341522i
$543$		−	4.21499e23i		−	0.102707i
$544$	−3.12649e24	+	3.12920e23i	−0.749321	+	0.0749968i
$545$	4.21982e24			0.994777
$546$	−1.69679e24	+	5.59994e24i	−0.393455	+	1.29852i
$547$		−	1.29654e23i		−	0.0295734i	−0.999891	−	0.0147867i	$-0.995293\pi$
$547$		−	1.29654e23i		−	0.0295734i	0.999891	−	0.0147867i	$-0.00470692\pi$
$548$	1.42928e24	+	9.53712e23i	0.320696	+	0.213989i
$549$	−1.18026e24			−0.260511
$550$	−9.26916e23	−	2.80857e23i	−0.201269	−	0.0609848i
$551$		−	1.73038e24i		−	0.369639i
$552$	−6.66315e23	+	5.47889e23i	−0.140032	+	0.115144i
$553$	4.55940e24			0.942717
$554$	−2.10364e23	+	6.94267e23i	−0.0427941	+	0.141234i
$555$		−	3.82274e24i		−	0.765134i
$556$	1.46615e24	−	2.19725e24i	0.288739	−	0.432720i
$557$	2.33090e24			0.451677			0.225838	−	0.974165i	$-0.427488\pi$
$557$	2.33090e24			0.451677			0.225838	+	0.974165i	$0.427488\pi$
$558$	−2.58435e23	−	7.83062e22i	−0.0492769	−	0.0149310i
$559$		−	9.15527e24i		−	1.71777i
$560$	−1.61887e25	+	6.72956e24i	−2.98896	+	1.24249i
$561$	2.84601e23			0.0517095
$562$	8.85359e23	−	2.92196e24i	0.158304	−	0.522453i
$563$			2.16524e24i			0.381005i	0.981687	+	0.190502i	$0.0610117\pi$
$563$			2.16524e24i			0.381005i	−0.981687	+	0.190502i	$0.938988\pi$
$564$	2.86385e23	+	1.91095e23i	0.0495951	+	0.0330931i
$565$	−3.95302e24			−0.673741
$566$	−1.64042e24	−	4.97051e23i	−0.275174	−	0.0833784i
$567$		−	1.30928e24i		−	0.216165i
$568$	−4.00181e24	−	4.86680e24i	−0.650311	−	0.790877i
$569$	−1.99896e24			−0.319737			−0.159868	−	0.987138i	$-0.551107\pi$
$569$	−1.99896e24			−0.319737			−0.159868	+	0.987138i	$0.551107\pi$
$570$	1.15521e24	−	3.81255e24i	0.181881	−	0.600263i
$571$			5.72889e24i			0.887862i	0.896061	+	0.443931i	$0.146416\pi$
$571$			5.72889e24i			0.887862i	−0.896061	+	0.443931i	$0.853584\pi$
$572$	−5.22694e23	+	7.83338e23i	−0.0797413	+	0.119505i
$573$	7.04006e24			1.05727
$574$	−8.39702e24	−	2.54431e24i	−1.24142	−	0.376152i
$575$			3.81508e24i			0.555255i
$576$	−4.49529e23	+	2.28254e24i	−0.0644103	+	0.327051i
$577$	−9.69138e24			−1.36711			−0.683555	−	0.729899i	$-0.739567\pi$
$577$	−9.69138e24			−1.36711			−0.683555	+	0.729899i	$0.739567\pi$
$578$	−9.03866e23	+	2.98304e24i	−0.125532	+	0.414294i
$579$		−	1.26975e24i		−	0.173625i
$580$	5.81960e24	+	3.88322e24i	0.783504	+	0.522805i
$581$	5.35630e24			0.710034
$582$	−5.72735e24	−	1.73540e24i	−0.747562	−	0.226513i
$583$			1.22875e24i			0.157924i
$584$	8.44469e24	−	6.94378e24i	1.06873	−	0.878781i
$585$	5.37580e24			0.669947
$586$	−1.96405e23	+	6.48197e23i	−0.0241031	+	0.0795478i
$587$			7.16078e23i			0.0865401i	0.999063	+	0.0432701i	$0.0137776\pi$
$587$			7.16078e23i			0.0865401i	−0.999063	+	0.0432701i	$0.986222\pi$
$588$	7.49847e24	−	1.12376e25i	0.892435	−	1.33745i
$589$	8.60491e23			0.100858
$590$	2.54213e24	+	7.70271e23i	0.293447	+	0.0889151i
$591$			9.81864e24i			1.11626i
$592$	−2.73055e24	−	6.56865e24i	−0.305742	−	0.735497i
$593$	−2.81707e24			−0.310674			−0.155337	−	0.987862i	$-0.549646\pi$
$593$	−2.81707e24			−0.310674			−0.155337	+	0.987862i	$0.549646\pi$
$594$	6.11035e22	−	2.01661e23i	0.00663725	−	0.0219050i
$595$		−	2.27833e25i		−	2.43761i
$596$	−1.30115e25	−	8.68213e24i	−1.37123	−	0.914976i
$597$	2.26147e24			0.234759
$598$	3.55006e24	+	1.07567e24i	0.363015	+	0.109994i
$599$		−	1.82246e25i		−	1.83576i	−0.396859	−	0.917879i	$-0.629900\pi$
$599$		−	1.82246e25i		−	1.83576i	0.396859	−	0.917879i	$-0.370100\pi$
$600$	6.53448e24	+	7.94692e24i	0.648410	+	0.788565i
$601$	1.22217e25			1.19471			0.597354	−	0.801978i	$-0.296219\pi$
$601$	1.22217e25			1.19471			0.597354	+	0.801978i	$0.296219\pi$
$602$	−8.33058e24	+	2.74935e25i	−0.802245	+	2.64766i
$603$		−	2.57043e24i		−	0.243865i
$604$	−1.08030e24	+	1.61899e24i	−0.100974	+	0.151326i
$605$	−1.78122e25			−1.64028
$606$	−4.05602e24	−	1.22898e24i	−0.367999	−	0.111504i
$607$			1.64447e25i			1.47004i	0.678048	+	0.735018i	$0.262826\pi$
$607$			1.64447e25i			1.47004i	−0.678048	+	0.735018i	$0.737174\pi$
$608$	−7.38268e23	−	7.37630e24i	−0.0650252	−	0.649691i
$609$	−7.32705e24			−0.635877
$610$	−4.40953e24	+	1.45528e25i	−0.377072	+	1.24445i
$611$		−	1.48046e24i		−	0.124746i
$612$	−2.51480e24	−	1.67804e24i	−0.208805	−	0.139328i
$613$	1.77838e25			1.45505			0.727527	−	0.686079i	$-0.240669\pi$
$613$	1.77838e25			1.45505			0.727527	+	0.686079i	$0.240669\pi$
$614$	2.00952e25	+	6.08888e24i	1.62023	+	0.490933i
$615$			8.06093e24i			0.640485i
$616$	2.28244e24	−	1.87677e24i	0.178720	−	0.146955i
$617$	−6.94926e24			−0.536256			−0.268128	−	0.963383i	$-0.586405\pi$
$617$	−6.94926e24			−0.536256			−0.268128	+	0.963383i	$0.586405\pi$
$618$	1.81597e24	−	5.99327e24i	0.138106	−	0.455793i
$619$		−	1.55138e25i		−	1.16279i	−0.813620	−	0.581396i	$-0.802507\pi$
$619$		−	1.55138e25i		−	1.16279i	0.813620	−	0.581396i	$-0.197493\pi$
$620$	−1.93106e24	+	2.89399e24i	−0.142650	+	0.213783i
$621$	−8.30011e23			−0.0604310
$622$	2.20769e25	+	6.68933e24i	1.58425	+	0.480031i
$623$			3.87895e25i			2.74360i
$624$	9.23730e24	−	3.83990e24i	0.643997	−	0.267706i
$625$	5.21734e24			0.358533
$626$	5.71695e24	−	1.88677e25i	0.387254	−	1.27806i
$627$			6.71455e23i			0.0448342i
$628$	8.91400e24	+	5.94800e24i	0.586727	+	0.391502i
$629$	9.24445e24			0.599826
$630$	−1.61437e25	−	4.89156e24i	−1.03261	−	0.312883i
$631$			1.00616e25i			0.634459i	0.948349	+	0.317230i	$0.102753\pi$
$631$			1.00616e25i			0.634459i	−0.948349	+	0.317230i	$0.897247\pi$
$632$	−4.95071e24	−	6.02082e24i	−0.307761	−	0.374284i
$633$	−1.66419e25			−1.01993
$634$	−2.31725e24	+	7.64765e24i	−0.140013	+	0.462088i
$635$			3.12551e25i			1.86190i
$636$	7.24486e24	−	1.08575e25i	0.425516	−	0.637701i
$637$	−5.80926e25			−3.36408
$638$	−1.12854e24	−	3.41951e23i	−0.0644365	−	0.0195244i
$639$		−	6.06245e24i		−	0.341303i
$640$	2.64647e25	+	1.40705e25i	1.46908	+	0.781070i
$641$	−1.06184e25			−0.581215			−0.290607	−	0.956842i	$-0.593857\pi$
$641$	−1.06184e25			−0.581215			−0.290607	+	0.956842i	$0.593857\pi$
$642$	−3.29537e24	+	1.08757e25i	−0.177864	+	0.587007i
$643$		−	2.24126e25i		−	1.19287i	−0.802662	−	0.596434i	$-0.796584\pi$
$643$		−	2.24126e25i		−	1.19287i	0.802662	−	0.596434i	$-0.203416\pi$
$644$	−9.68213e24	−	6.46055e24i	−0.508157	−	0.339076i
$645$	2.63931e25			1.36601
$646$	9.21981e24	+	2.79362e24i	0.470576	+	0.142585i
$647$		−	1.98644e24i		−	0.0999856i	−0.998750	−	0.0499928i	$-0.984080\pi$
$647$		−	1.98644e24i		−	0.0999856i	0.998750	−	0.0499928i	$-0.0159198\pi$
$648$	−1.72894e24	+	1.42165e24i	−0.0858232	+	0.0705695i
$649$	−4.47713e23			−0.0219178
$650$	1.28292e25	−	4.23403e25i	0.619411	−	2.04425i
$651$		−	3.64362e24i		−	0.173502i
$652$	−5.88773e24	+	8.82367e24i	−0.276515	+	0.414401i
$653$	−8.84446e24			−0.409687			−0.204844	−	0.978795i	$-0.565669\pi$
$653$	−8.84446e24			−0.409687			−0.204844	+	0.978795i	$0.565669\pi$
$654$	7.23080e24	+	2.19095e24i	0.330359	+	0.100099i
$655$		−	2.94626e24i		−	0.132770i
$656$	5.75786e24	+	1.38512e25i	0.255933	+	0.615676i
$657$	1.05193e25			0.461211
$658$	−1.34710e24	+	4.44586e24i	−0.0582597	+	0.192275i
$659$		−	4.11362e25i		−	1.75491i	−0.479658	−	0.877455i	$-0.659239\pi$
$659$		−	4.11362e25i		−	1.75491i	0.479658	−	0.877455i	$-0.340761\pi$
$660$	−2.25823e24	−	1.50684e24i	−0.0950326	−	0.0634120i
$661$	−2.31734e25			−0.962003			−0.481002	−	0.876720i	$-0.659727\pi$
$661$	−2.31734e25			−0.962003			−0.481002	+	0.876720i	$0.659727\pi$
$662$	−2.92027e25	−	8.84848e24i	−1.19592	−	0.362366i
$663$			1.30002e25i			0.525204i
$664$	−5.81600e24	−	7.07314e24i	−0.231799	−	0.281903i
$665$	5.37524e25			2.11350
$666$	1.98478e24	−	6.55038e24i	0.0769917	−	0.254096i
$667$			4.64495e24i			0.177766i
$668$	1.54710e24	−	2.31856e24i	0.0584157	−	0.0875449i
$669$	−1.89991e25			−0.707781
$670$	−3.16939e25	−	9.60331e24i	−1.16494	−	0.352978i
$671$		−	2.56300e24i		−	0.0929493i
$672$	−3.12339e25	+	3.12609e24i	−1.11764	+	0.111861i
$673$	1.93843e25			0.684406			0.342203	−	0.939626i	$-0.388827\pi$
$673$	1.93843e25			0.684406			0.342203	+	0.939626i	$0.388827\pi$
$674$	9.11827e24	−	3.00931e25i	0.317668	−	1.04840i
$675$			9.89927e24i			0.340306i
$676$	−1.12602e25	−	7.51355e24i	−0.381967	−	0.254874i
$677$	2.60844e25			0.873136			0.436568	−	0.899671i	$-0.356194\pi$
$677$	2.60844e25			0.873136			0.436568	+	0.899671i	$0.356194\pi$
$678$	−6.77363e24	−	2.05242e24i	−0.223745	−	0.0677952i
$679$		−	8.07488e25i		−	2.63214i
$680$	−3.00860e25	+	2.47387e25i	−0.967797	+	0.795787i
$681$	−2.11495e25			−0.671391
$682$	1.70046e23	−	5.61206e23i	0.00532731	−	0.0175818i
$683$			1.30632e25i			0.403890i	0.979397	+	0.201945i	$0.0647262\pi$
$683$			1.30632e25i			0.403890i	−0.979397	+	0.201945i	$0.935274\pi$
$684$	3.95897e24	−	5.93314e24i	0.120803	−	0.181042i
$685$	2.13002e25			0.641459
$686$	1.11811e26	+	3.38789e25i	3.32328	+	1.00696i
$687$			2.00676e25i			0.588687i
$688$	4.53515e25	−	1.88524e25i	1.31309	−	0.545846i
$689$	−5.61278e25			−1.60400
$690$	−3.10098e24	+	1.02342e25i	−0.0874697	+	0.288677i
$691$			4.83608e25i			1.34645i	0.739436	+	0.673226i	$0.235092\pi$
$691$			4.83608e25i			1.34645i	−0.739436	+	0.673226i	$0.764908\pi$
$692$	−6.67404e24	−	4.45336e24i	−0.183415	−	0.122386i
$693$	2.84318e24			0.0771267
$694$	−6.82034e25	−	2.06658e25i	−1.82630	−	0.553371i
$695$		−	3.27450e25i		−	0.865531i
$696$	7.95589e24	+	9.67557e24i	0.207590	+	0.252461i
$697$	−1.94936e25			−0.502107
$698$	−1.44869e25	+	4.78114e25i	−0.368365	+	1.21572i
$699$			3.26872e25i			0.820508i
$700$	−7.70528e25	+	1.15476e26i	−1.90944	+	2.86159i
$701$	6.77047e25			1.65637			0.828184	−	0.560457i	$-0.189374\pi$
$701$	6.77047e25			1.65637			0.828184	+	0.560457i	$0.189374\pi$
$702$	9.21160e24	+	2.79113e24i	0.222485	+	0.0674134i
$703$			2.18103e25i			0.520073i
$704$	−4.95666e24	−	9.76179e23i	−0.116691	−	0.0229814i
$705$	4.26792e24			0.0992005
$706$	−7.79016e24	+	2.57100e25i	−0.178774	+	0.590009i
$707$		−	5.71851e25i		−	1.29571i
$708$	3.95610e24	+	2.63977e24i	0.0885050	+	0.0590563i
$709$	1.59031e25			0.351289			0.175645	−	0.984454i	$-0.443799\pi$
$709$	1.59031e25			0.351289			0.175645	+	0.984454i	$0.443799\pi$
$710$	−7.47512e25	−	2.26497e25i	−1.63039	−	0.494013i
$711$		−	7.49997e24i		−	0.161523i
$712$	5.12226e25	−	4.21186e25i	1.08928	−	0.895682i
$713$	−2.30986e24			−0.0485042
$714$	1.18292e25	−	3.90399e25i	0.245285	−	0.809515i
$715$			1.16739e25i			0.239034i
$716$	1.76414e25	−	2.64383e25i	0.356710	−	0.534585i
$717$	4.43047e25			0.884661
$718$	−3.84658e25	−	1.16552e25i	−0.758499	−	0.229826i
$719$			4.44288e25i			0.865176i	0.901592	+	0.432588i	$0.142399\pi$
$719$			4.44288e25i			0.865176i	−0.901592	+	0.432588i	$0.857601\pi$
$720$	1.10698e25	+	2.66295e25i	0.212885	+	0.512120i
$721$	8.44980e25			1.60483
$722$	8.86893e24	−	2.92702e25i	0.166355	−	0.549024i
$723$			8.58104e24i			0.158963i
$724$	−8.08790e24	−	5.39677e24i	−0.147975	−	0.0987386i
$725$	5.53987e25			1.00105
$726$	−3.05217e25	−	9.24812e24i	−0.544727	−	0.165053i
$727$			4.59312e25i			0.809652i	0.914394	+	0.404826i	$0.132668\pi$
$727$			4.59312e25i			0.809652i	−0.914394	+	0.404826i	$0.867332\pi$
$728$	8.57286e25	+	1.04259e26i	1.49260	+	1.81523i
$729$	−2.15369e24			−0.0370370
$730$	3.93010e25	−	1.29705e26i	0.667571	−	2.20319i
$731$			6.38259e25i			1.07088i
$732$	−1.51117e25	+	2.26473e25i	−0.250446	+	0.375333i
$733$	4.92550e25			0.806334			0.403167	−	0.915126i	$-0.367909\pi$
$733$	4.92550e25			0.806334			0.403167	+	0.915126i	$0.367909\pi$
$734$	−5.84919e25	−	1.77232e25i	−0.945870	−	0.286600i
$735$		−	1.67471e26i		−	2.67518i
$736$	1.98177e24	+	1.98006e25i	0.0312718	+	0.312448i
$737$	5.58184e24			0.0870101
$738$	−4.18526e24	+	1.38126e25i	−0.0644488	+	0.212701i
$739$			8.90792e25i			1.35512i	0.735469	+	0.677558i	$0.236962\pi$
$739$			8.90792e25i			1.35512i	−0.735469	+	0.677558i	$0.763038\pi$
$740$	−7.33523e25	−	4.89454e25i	−1.10237	−	0.735574i
$741$	−3.06712e25			−0.455373
$742$	1.68553e26	+	5.10719e25i	2.47230	+	0.749112i
$743$		−	3.50573e25i		−	0.508017i	−0.967202	−	0.254009i	$-0.918251\pi$
$743$		−	3.50573e25i		−	0.508017i	0.967202	−	0.254009i	$-0.0817492\pi$
$744$	−4.81150e24	+	3.95634e24i	−0.0688850	+	0.0566418i
$745$	−1.93907e26			−2.74275
$746$	−2.45545e25	+	8.10376e25i	−0.343149	+	1.13250i
$747$		−	8.81082e24i		−	0.121655i
$748$	3.64396e24	−	5.46103e24i	0.0497117	−	0.0745007i
$749$	−1.53335e26			−2.06683
$750$	5.30324e25	+	1.60689e25i	0.706301	+	0.214011i
$751$		−	1.43880e26i		−	1.89339i	−0.322130	−	0.946695i	$-0.604399\pi$
$751$		−	1.43880e26i		−	1.89339i	0.322130	−	0.946695i	$-0.395601\pi$
$752$	7.33361e24	−	3.04854e24i	0.0953580	−	0.0396398i
$753$	−3.55595e25			−0.456878
$754$	1.56199e25	−	5.15504e25i	0.198306	−	0.654470i
$755$			2.41274e25i			0.302683i
$756$	−2.51230e25	−	1.67637e25i	−0.311440	−	0.207813i
$757$	−3.45886e24			−0.0423711			−0.0211855	−	0.999776i	$-0.506744\pi$
$757$	−3.45886e24			−0.0423711			−0.0211855	+	0.999776i	$0.506744\pi$
$758$	−3.43892e25	−	1.04200e25i	−0.416293	−	0.126137i
$759$		−	1.80242e24i		−	0.0215615i
$760$	−5.83657e25	−	7.09816e25i	−0.689978	−	0.839118i
$761$	−1.21894e26			−1.42403			−0.712014	−	0.702165i	$-0.752217\pi$
$761$	−1.21894e26			−1.42403			−0.712014	+	0.702165i	$0.752217\pi$
$762$	−1.62277e25	+	5.35566e25i	−0.187354	+	0.618327i
$763$			1.01946e26i			1.16318i
$764$	9.01391e25	−	1.35087e26i	1.01642	−	1.52326i
$765$	−3.74773e25			−0.417653
$766$	8.90498e25	+	2.69823e25i	0.980786	+	0.297180i
$767$		−	2.04510e25i		−	0.222616i
$768$	3.80426e25	+	3.78508e25i	0.409279	+	0.407215i
$769$	1.34307e26			1.42811			0.714054	−	0.700090i	$-0.246857\pi$
$769$	1.34307e26			1.42811			0.714054	+	0.700090i	$0.246857\pi$
$770$	1.06223e25	−	3.50569e25i	0.111636	−	0.368432i
$771$			3.96416e25i			0.411777i
$772$	−2.43645e25	−	1.62576e25i	−0.250151	−	0.166917i
$773$	−1.46504e26			−1.48674			−0.743369	−	0.668882i	$-0.766773\pi$
$773$	−1.46504e26			−1.48674			−0.743369	+	0.668882i	$0.766773\pi$
$774$	4.52254e25	+	1.37034e25i	0.453642	+	0.137454i
$775$			2.75489e25i			0.273142i
$776$	−1.06631e26	+	8.76792e25i	−1.04503	+	0.859292i
$777$	9.23526e25			0.894664
$778$	−4.16975e25	+	1.37615e26i	−0.399295	+	1.31780i
$779$		−	4.59910e25i		−	0.435347i
$780$	6.88304e25	−	1.03153e26i	0.644064	−	0.965229i
$781$	1.31650e25			0.121776
$782$	−2.47492e25	−	7.49905e24i	−0.226308	−	0.0685717i
$783$			1.20526e25i			0.108949i
$784$	−1.19623e26	−	2.87767e26i	−1.06898	−	2.57156i
$785$	1.32843e26			1.17358
$786$	1.52971e24	−	5.04852e24i	0.0133600	−	0.0440921i
$787$			1.37453e26i			1.18681i	0.804904	+	0.593405i	$0.202217\pi$
$787$			1.37453e26i			1.18681i	−0.804904	+	0.593405i	$0.797783\pi$
$788$	1.88404e26	+	1.25716e26i	1.60825	+	1.07313i
$789$	−9.05336e25			−0.764041
$790$	−9.24761e25	−	2.80204e25i	−0.771589	−	0.233793i
$791$		−	9.55001e25i		−	0.787799i
$792$	−3.08719e24	−	3.75449e24i	−0.0251789	−	0.0306214i
$793$	1.17075e26			0.944070
$794$	−4.33221e25	+	1.42976e26i	−0.345402	+	1.13993i
$795$		−	1.61807e26i		−	1.27554i
$796$	2.89554e25	−	4.33941e25i	0.225690	−	0.338231i
$797$	−2.14046e25			−0.164961			−0.0824807	−	0.996593i	$-0.526284\pi$
$797$	−2.14046e25			−0.164961			−0.0824807	+	0.996593i	$0.526284\pi$
$798$	9.21064e25	+	2.79084e25i	0.701882	+	0.212671i
$799$			1.03210e25i			0.0777681i
$800$	2.36155e26	−	2.36359e25i	1.75949	−	0.176101i
$801$	6.38066e25			0.470081
$802$	4.21720e25	−	1.39181e26i	0.307223	−	1.01393i
$803$			2.28433e25i			0.164558i
$804$	−4.93224e25	−	3.29111e25i	−0.351350	−	0.234444i
$805$	−1.44290e26			−1.01642
$806$	2.56352e25	+	7.76750e24i	0.178575	+	0.0541086i
$807$			7.62311e25i			0.525134i
$808$	−7.55145e25	+	6.20930e25i	−0.514432	+	0.423000i
$809$	−5.27592e25			−0.355436			−0.177718	−	0.984081i	$-0.556871\pi$
$809$	−5.27592e25			−0.355436			−0.177718	+	0.984081i	$0.556871\pi$
$810$	−8.04636e24	+	2.65555e25i	−0.0536086	+	0.176925i
$811$		−	5.57329e25i		−	0.367218i	−0.982999	−	0.183609i	$-0.941222\pi$
$811$		−	5.57329e25i		−	0.367218i	0.982999	−	0.183609i	$-0.0587780\pi$
$812$	−9.38137e25	+	1.40594e26i	−0.611311	+	0.916144i
$813$	1.05512e26			0.679965
$814$	1.42245e25	+	4.31006e24i	0.0906606	+	0.0274703i
$815$			1.31497e26i			0.828889i
$816$	−6.43977e25	+	2.67698e25i	−0.401476	+	0.166891i
$817$	−1.50584e26			−0.928494
$818$	−5.40526e25	+	1.78390e26i	−0.329638	+	1.08791i
$819$			1.29873e26i			0.783362i
$820$	1.54676e26	+	1.03210e26i	0.922782	+	0.615740i
$821$	1.12835e26			0.665817			0.332909	−	0.942959i	$-0.391970\pi$
$821$	1.12835e26			0.665817			0.332909	+	0.942959i	$0.391970\pi$
$822$	3.64986e25	+	1.10591e25i	0.213025	+	0.0645468i
$823$			2.14556e26i			1.23863i	0.785142	+	0.619316i	$0.212590\pi$
$823$			2.14556e26i			1.23863i	−0.785142	+	0.619316i	$0.787410\pi$
$824$	−9.17501e25	−	1.11582e26i	−0.523916	−	0.637161i
$825$	−2.14968e25			−0.121420
$826$	−1.86088e25	+	6.14148e25i	−0.103968	+	0.343125i
$827$			1.25341e26i			0.692699i	0.938105	+	0.346350i	$0.112579\pi$
$827$			1.25341e26i			0.692699i	−0.938105	+	0.346350i	$0.887421\pi$
$828$	−1.06273e25	+	1.59266e25i	−0.0580963	+	0.0870663i
$829$	2.68872e26			1.45397			0.726984	−	0.686654i	$-0.240921\pi$
$829$	2.68872e26			1.45397			0.726984	+	0.686654i	$0.240921\pi$
$830$	−1.08639e26	−	3.29179e25i	−0.581144	−	0.176088i
$831$			1.61013e25i			0.0852023i
$832$	4.45906e25	−	2.26414e26i	0.233418	−	1.18520i
$833$	4.04992e26			2.09721
$834$	1.70013e25	−	5.61097e25i	0.0870940	−	0.287437i
$835$		−	3.45529e25i		−	0.175108i
$836$	1.28842e25	+	8.59714e24i	0.0645951	+	0.0431020i
$837$	−5.99356e24			−0.0297273
$838$	−7.47095e25	−	2.26371e25i	−0.366589	−	0.111077i
$839$		−	3.84977e26i		−	1.86886i	−0.356148	−	0.934430i	$-0.615910\pi$
$839$		−	3.84977e26i		−	1.86886i	0.356148	−	0.934430i	$-0.384090\pi$
$840$	−3.00561e26	+	2.47141e26i	−1.44351	+	1.18695i
$841$	−1.43008e26			−0.679511
$842$	8.71468e24	−	2.87611e25i	0.0409678	−	0.135206i
$843$		−	6.77655e25i		−	0.315181i
$844$	−2.13079e26	+	3.19332e26i	−0.980524	+	1.46947i
$845$	−1.67808e26			−0.764015
$846$	7.31321e24	+	2.21592e24i	0.0329439	+	0.00998206i
$847$		−	4.30319e26i		−	1.91796i
$848$	−1.15577e26	−	2.78034e26i	−0.509695	−	1.22613i
$849$	−3.80444e25			−0.166005
$850$	−8.94386e25	+	2.95175e26i	−0.386149	+	1.27441i
$851$		−	5.85465e25i		−	0.250112i
$852$	−1.16329e26	−	7.76221e25i	−0.491734	−	0.328117i
$853$	1.18346e26			0.495007			0.247503	−	0.968887i	$-0.420390\pi$
$853$	1.18346e26			0.495007			0.247503	+	0.968887i	$0.420390\pi$
$854$	−3.51578e26	−	1.06529e26i	−1.45513	−	0.440906i
$855$		−	8.84198e25i		−	0.362122i
$856$	1.66495e26	+	2.02483e26i	0.674741	+	0.820588i
$857$	4.61066e26			1.84899			0.924497	−	0.381189i	$-0.124485\pi$
$857$	4.61066e26			1.84899			0.924497	+	0.381189i	$0.124485\pi$
$858$	−6.06111e24	+	2.00035e25i	−0.0240528	+	0.0793818i
$859$		−	2.39881e26i		−	0.942013i	−0.882130	−	0.471007i	$-0.843891\pi$
$859$		−	2.39881e26i		−	0.942013i	0.882130	−	0.471007i	$-0.156109\pi$
$860$	3.37930e26	−	5.06441e26i	1.31323	−	1.96808i
$861$	−1.94742e26			−0.748912
$862$	−2.80018e25	−	8.48459e24i	−0.106566	−	0.0322898i
$863$		−	2.65534e26i		−	1.00005i	−0.866010	−	0.500027i	$-0.833323\pi$
$863$		−	2.65534e26i		−	1.00005i	0.866010	−	0.500027i	$-0.166677\pi$
$864$	5.14224e24	+	5.13780e25i	0.0191659	+	0.191493i
$865$	−9.94614e25			−0.366868
$866$	4.93616e24	−	1.62909e25i	0.0180189	−	0.0594679i
$867$			6.91820e25i			0.249932i
$868$	−6.99153e25	−	4.66520e25i	−0.249974	−	0.166799i
$869$	1.62866e25			0.0576306
$870$	1.48611e26	+	4.50294e25i	0.520448	+	0.157697i
$871$			2.54971e26i			0.883746i
$872$	1.34622e26	−	1.10695e26i	0.461815	−	0.379735i
$873$	−1.32828e26			−0.450983
$874$	1.76924e25	−	5.83905e25i	0.0594544	−	0.196218i
$875$			7.47694e26i			2.48686i
$876$	1.34687e26	−	2.01849e26i	0.443392	−	0.664492i
$877$	3.32311e26			1.08280			0.541400	−	0.840765i	$-0.317894\pi$
$877$	3.32311e26			1.08280			0.541400	+	0.840765i	$0.317894\pi$
$878$	1.68098e26	+	5.09340e25i	0.542140	+	0.164270i
$879$			1.50328e25i			0.0479889i
$880$	−5.78276e25	+	2.40386e25i	−0.182722	+	0.0759567i
$881$	−4.38592e26			−1.37176			−0.685879	−	0.727715i	$-0.740582\pi$
$881$	−4.38592e26			−1.37176			−0.685879	+	0.727715i	$0.740582\pi$
$882$	8.69515e25	−	2.86967e26i	0.269190	−	0.888412i
$883$			1.43824e26i			0.440742i	0.975416	+	0.220371i	$0.0707268\pi$
$883$			1.43824e26i			0.440742i	−0.975416	+	0.220371i	$0.929273\pi$
$884$	2.49453e26	+	1.66451e26i	0.756690	+	0.504913i
$885$	5.89566e25			0.177029
$886$	−1.31338e26	−	3.97955e25i	−0.390378	−	0.118285i
$887$		−	7.85884e25i		−	0.231231i	−0.993294	−	0.115615i	$-0.963116\pi$
$887$		−	7.85884e25i		−	0.231231i	0.993294	−	0.115615i	$-0.0368840\pi$
$888$	−1.00279e26	−	1.21954e26i	−0.292074	−	0.355206i
$889$	−7.55084e26			−2.17710
$890$	2.38386e26	−	7.86748e26i	0.680410	−	2.24557i
$891$		−	4.67687e24i		−	0.0132147i
$892$	−2.43260e26	+	3.64563e26i	−0.680436	+	1.01974i
$893$	−2.43503e25			−0.0674281
$894$	−3.32266e26	−	1.00677e26i	−0.910852	−	0.275990i
$895$		−	3.94003e26i		−	1.06928i
$896$	−3.39926e26	+	6.39353e26i	−0.913297	+	1.71779i
$897$	8.23322e25			0.218997
$898$	3.09716e25	−	1.02216e26i	0.0815599	−	0.269173i
$899$			3.35415e25i			0.0874469i
$900$	1.89951e26	+	1.26748e26i	0.490297	+	0.327158i
$901$	3.91294e26			0.999955
$902$	−2.99950e25	−	9.08853e24i	−0.0758909	−	0.0229951i
$903$			6.37624e26i			1.59726i
$904$	−1.26111e26	+	1.03696e26i	−0.312777	+	0.257186i
$905$	−1.20532e26			−0.295981
$906$	−1.25270e25	+	4.13431e25i	−0.0304575	+	0.100519i
$907$		−	3.87633e25i		−	0.0933158i	−0.998911	−	0.0466579i	$-0.985143\pi$
$907$		−	3.87633e25i		−	0.0933158i	0.998911	−	0.0466579i	$-0.0148571\pi$
$908$	−2.70793e26	+	4.05825e26i	−0.645453	+	0.967311i
$909$	−9.40664e25			−0.222003
$910$	1.60136e27	+	4.85213e26i	3.74210	+	1.13386i
$911$		−	1.42226e26i		−	0.329089i	−0.986370	−	0.164544i	$-0.947385\pi$
$911$		−	1.42226e26i		−	0.329089i	0.986370	−	0.164544i	$-0.0526154\pi$
$912$	−6.31577e25	−	1.51933e26i	−0.144701	−	0.348095i
$913$	1.91332e25			0.0434061
$914$	−1.19328e26	+	3.93819e26i	−0.268057	+	0.884670i
$915$			3.37506e26i			0.750744i
$916$	3.85065e26	+	2.56940e26i	0.848154	+	0.565944i
$917$	7.11781e25			0.155247
$918$	−6.42186e25	−	1.94583e25i	−0.138700	−	0.0420264i
$919$		−	7.92494e26i		−	1.69495i	−0.530836	−	0.847475i	$-0.678122\pi$
$919$		−	7.92494e26i		−	1.69495i	0.530836	−	0.847475i	$-0.321878\pi$
$920$	1.56674e26	+	1.90539e26i	0.331823	+	0.403547i
$921$	4.66044e26			0.977440
$922$	1.86010e26	−	6.13891e26i	0.386330	−	1.27501i
$923$			6.01358e26i			1.23685i
$924$	3.64033e25	−	5.45560e25i	0.0741469	−	0.111121i
$925$	−6.98264e26			−1.40846
$926$	−1.84396e26	−	5.58724e25i	−0.368344	−	0.111609i
$927$		−	1.38995e26i		−	0.274967i
$928$	2.87524e26	−	2.87773e25i	0.563304	−	0.0563790i
$929$	−4.72731e26			−0.917218			−0.458609	−	0.888638i	$-0.651652\pi$
$929$	−4.72731e26			−0.917218			−0.458609	+	0.888638i	$0.651652\pi$
$930$	−2.23924e25	+	7.39018e25i	−0.0430283	+	0.142007i
$931$			9.55493e26i			1.81836i
$932$	6.27215e26	+	4.18519e26i	1.18215	+	0.788808i
$933$	5.12002e26			0.955734
$934$	−8.94352e26	−	2.70990e26i	−1.65343	−	0.500993i
$935$		−	8.13842e25i		−	0.149017i
$936$	1.71500e26	−	1.41019e26i	0.311016	−	0.255738i
$937$	−1.94810e26			−0.349909			−0.174955	−	0.984577i	$-0.555978\pi$
$937$	−1.94810e26			−0.349909			−0.174955	+	0.984577i	$0.555978\pi$
$938$	2.32004e26	−	7.65685e26i	0.412733	−	1.36215i
$939$		−	4.37576e26i		−	0.771016i
$940$	5.46454e25	−	8.18945e25i	0.0953680	−	0.142924i
$941$	−7.08325e25			−0.122441			−0.0612203	−	0.998124i	$-0.519499\pi$
$941$	−7.08325e25			−0.122441			−0.0612203	+	0.998124i	$0.519499\pi$
$942$	2.27630e26	+	6.89724e25i	0.389737	+	0.118091i
$943$			1.23456e26i			0.209366i
$944$	1.01306e26	−	4.21123e25i	0.170171	−	0.0707394i
$945$	−3.74401e26			−0.622946
$946$	−2.97577e25	+	9.82095e25i	−0.0490432	+	0.161858i
$947$		−	4.77213e25i		−	0.0779045i	−0.999241	−	0.0389522i	$-0.987598\pi$
$947$		−	4.77213e25i		−	0.0779045i	0.999241	−	0.0389522i	$-0.0124020\pi$
$948$	−1.43912e26	−	9.60278e25i	−0.232714	−	0.155282i
$949$	−1.04345e27			−1.67139
$950$	−6.96403e26	−	2.11011e26i	−1.10496	−	0.334806i
$951$			1.77363e26i			0.278765i
$952$	−5.97656e26	−	7.26840e26i	−0.930505	−	1.13164i
$953$	6.14436e26			0.947634			0.473817	−	0.880623i	$-0.342876\pi$
$953$	6.14436e26			0.947634			0.473817	+	0.880623i	$0.342876\pi$
$954$	8.40106e25	−	2.77261e26i	0.128351	−	0.423598i
$955$		−	2.01317e27i		−	3.04684i
$956$	5.67266e26	−	8.50136e26i	0.850483	−	1.27458i
$957$	−2.61729e25			−0.0388727
$958$	3.44677e26	+	1.04438e26i	0.507134	+	0.153662i
$959$			5.14587e26i			0.750051i
$960$	6.52713e26	+	1.28547e26i	0.942500	+	0.185618i
$961$	6.82374e26			0.976140
$962$	−1.96878e26	+	6.49759e26i	−0.279011	+	0.920824i
$963$			2.52228e26i			0.354125i
$964$	1.64657e26	+	1.09870e26i	0.229026	+	0.152821i
$965$	−3.63098e26			−0.500355
$966$	−2.47246e26	−	7.49159e25i	−0.337547	−	0.102277i
$967$			3.27729e26i			0.443279i	0.975129	+	0.221639i	$0.0711407\pi$
$967$			3.27729e26i			0.443279i	−0.975129	+	0.221639i	$0.928859\pi$
$968$	−5.68249e26	+	4.67252e26i	−0.761483	+	0.626142i
$969$	2.13824e26			0.283885
$970$	−4.96253e26	+	1.63779e27i	−0.652766	+	2.15433i
$971$		−	1.67349e25i		−	0.0218097i	−0.999941	−	0.0109048i	$-0.996529\pi$
$971$		−	1.67349e25i		−	0.0218097i	0.999941	−	0.0109048i	$-0.00347119\pi$
$972$	−2.75754e25	+	4.13259e25i	−0.0356061	+	0.0533613i
$973$	7.91079e26			1.01206
$974$	4.96036e26	+	1.50300e26i	0.628756	+	0.190514i
$975$		−	9.81948e26i		−	1.23324i
$976$	2.41078e26	+	5.79940e26i	0.299992	+	0.721664i
$977$	−7.79300e26			−0.960846			−0.480423	−	0.877037i	$-0.659517\pi$
$977$	−7.79300e26			−0.960846			−0.480423	+	0.877037i	$0.659517\pi$
$978$	−6.82735e25	+	2.25324e26i	−0.0834069	+	0.275269i
$979$			1.38560e26i			0.167723i
$980$	−3.21350e27	−	2.14426e27i	−3.85429	−	2.57183i
$981$	1.67695e26			0.199296
$982$	−1.55853e27	−	4.72238e26i	−1.83532	−	0.556106i
$983$			6.19838e26i			0.723264i	0.932321	+	0.361632i	$0.117780\pi$
$983$			6.19838e26i			0.723264i	−0.932321	+	0.361632i	$0.882220\pi$
$984$	2.11456e26	+	2.57162e26i	0.244491	+	0.297339i
$985$	2.80773e27			3.21684
$986$	−1.08894e26	+	3.59383e26i	−0.123626	+	0.408005i
$987$			1.03108e26i			0.115994i
$988$	−3.92707e26	+	5.88531e26i	−0.437780	+	0.656081i
$989$	4.04219e26			0.446529
$990$	−5.76668e25	−	1.74731e25i	−0.0631261	−	0.0191273i
$991$		−	1.37132e26i		−	0.148757i	−0.997230	−	0.0743783i	$-0.976303\pi$
$991$		−	1.37132e26i		−	0.148757i	0.997230	−	0.0743783i	$-0.0236972\pi$
$992$	1.43105e25	+	1.42981e26i	0.0153833	+	0.153700i
$993$	−6.77264e26			−0.721464
$994$	5.47189e26	−	1.80589e27i	0.577644	−	1.90640i
$995$		−	6.46690e26i		−	0.676532i
$996$	−1.69066e26	−	1.12812e26i	−0.175276	−	0.116955i
$997$	−4.28424e26			−0.440166			−0.220083	−	0.975481i	$-0.570633\pi$
$997$	−4.28424e26			−0.440166			−0.220083	+	0.975481i	$0.570633\pi$
$998$	9.47729e26	+	2.87164e26i	0.964960	+	0.292385i
$999$		−	1.51915e26i		−	0.153289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.19.d.a.7.11	✓	18
3.2	odd	2		36.19.d.e.19.8		18
4.3	odd	2	inner	12.19.d.a.7.12	yes	18
12.11	even	2		36.19.d.e.19.7		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.19.d.a.7.11	✓	18	1.1	even	1	trivial
12.19.d.a.7.12	yes	18	4.3	odd	2	inner
36.19.d.e.19.7		18	12.11	even	2
36.19.d.e.19.8		18	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:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(148.471 - 490.000i) q^{2} -11364.0i q^{3} +(-218057. - 145502. i) q^{4} -3.24964e6 q^{5} +(-5.56836e6 - 1.68722e6i) q^{6} -7.85072e7i q^{7} +(-1.03671e8 + 8.52451e7i) q^{8} -1.29140e8 q^{9} +O(q^{10})\)	\(q+(148.471 - 490.000i) q^{2} -11364.0i q^{3} +(-218057. - 145502. i) q^{4} -3.24964e6 q^{5} +(-5.56836e6 - 1.68722e6i) q^{6} -7.85072e7i q^{7} +(-1.03671e8 + 8.52451e7i) q^{8} -1.29140e8 q^{9} +(-4.82477e8 + 1.59232e9i) q^{10} -2.80435e8i q^{11} +(-1.65348e9 + 2.47799e9i) q^{12} +1.28099e10 q^{13} +(-3.84686e10 - 1.16560e10i) q^{14} +3.69288e10i q^{15} +(2.63780e10 + 6.34552e10i) q^{16} -8.93043e10 q^{17} +(-1.91736e10 + 6.32787e10i) q^{18} -2.10695e11i q^{19} +(7.08606e11 + 4.72828e11i) q^{20} -8.92155e11 q^{21} +(-1.37413e11 - 4.16365e10i) q^{22} +5.65577e11i q^{23} +(9.68724e11 + 1.17812e12i) q^{24} +6.74545e12 q^{25} +(1.90190e12 - 6.27687e12i) q^{26} +1.46755e12i q^{27} +(-1.14229e13 + 1.71190e13i) q^{28} +8.21275e12 q^{29} +(1.80951e13 + 5.48286e12i) q^{30} +4.08407e12i q^{31} +(3.50095e13 - 3.50397e12i) q^{32} -3.18686e12 q^{33} +(-1.32591e13 + 4.37591e13i) q^{34} +2.55120e14i q^{35} +(2.81599e13 + 1.87901e13i) q^{36} -1.03516e14 q^{37} +(-1.03240e14 - 3.12820e13i) q^{38} -1.45572e14i q^{39} +(3.36893e14 - 2.77016e14i) q^{40} +2.18283e14 q^{41} +(-1.32459e14 + 4.37156e14i) q^{42} -7.14701e14i q^{43} +(-4.08038e13 + 6.11508e13i) q^{44} +4.19659e14 q^{45} +(2.77133e14 + 8.39718e13i) q^{46} -1.15571e14i q^{47} +(7.21104e14 - 2.99759e14i) q^{48} -4.53497e15 q^{49} +(1.00150e15 - 3.30527e15i) q^{50} +1.01485e15i q^{51} +(-2.79329e15 - 1.86387e15i) q^{52} -4.38158e15 q^{53} +(7.19099e14 + 2.17888e14i) q^{54} +9.11314e14i q^{55} +(6.69235e15 + 8.13892e15i) q^{56} -2.39433e15 q^{57} +(1.21936e15 - 4.02425e15i) q^{58} -1.59649e15i q^{59} +(5.37321e15 - 8.05258e15i) q^{60} +9.13936e15 q^{61} +(2.00120e15 + 6.06366e14i) q^{62} +1.01384e16i q^{63} +(3.48094e15 - 1.76749e16i) q^{64} -4.16276e16 q^{65} +(-4.73157e14 + 1.56156e15i) q^{66} +1.99042e16i q^{67} +(1.94734e16 + 1.29939e16i) q^{68} +6.42721e15 q^{69} +(1.25009e17 + 3.78779e16i) q^{70} +4.69447e16i q^{71} +(1.33881e16 - 1.10086e16i) q^{72} -8.14567e16 q^{73} +(-1.53692e16 + 5.07230e16i) q^{74} -7.66552e16i q^{75} +(-3.06564e16 + 4.59434e16i) q^{76} -2.20162e16 q^{77} +(-7.13303e16 - 2.16132e16i) q^{78} +5.80762e16i q^{79} +(-8.57190e16 - 2.06207e17i) q^{80} +1.66772e16 q^{81} +(3.24086e16 - 1.06959e17i) q^{82} +6.82268e16i q^{83} +(1.94540e17 + 1.29810e17i) q^{84} +2.90207e17 q^{85} +(-3.50204e17 - 1.06112e17i) q^{86} -9.33296e16i q^{87} +(2.39057e16 + 2.90730e16i) q^{88} -4.94088e17 q^{89} +(6.23072e16 - 2.05633e17i) q^{90} -1.00567e18i q^{91} +(8.22925e16 - 1.23328e17i) q^{92} +4.64113e16 q^{93} +(-5.66300e16 - 1.71590e16i) q^{94} +6.84681e17i q^{95} +(-3.98191e16 - 3.97847e17i) q^{96} +1.02855e18 q^{97} +(-6.73311e17 + 2.22214e18i) q^{98} +3.62155e16i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 170 q^{2} - 436932 q^{4} - 1721764 q^{5} - 6731586 q^{6} + 108558736 q^{8} - 2324522934 q^{9}+O(q^{10}) \) 18 * q - 170 * q^2 - 436932 * q^4 - 1721764 * q^5 - 6731586 * q^6 + 108558736 * q^8 - 2324522934 * q^9	\( 18 q - 170 q^{2} - 436932 q^{4} - 1721764 q^{5} - 6731586 q^{6} + 108558736 q^{8} - 2324522934 q^{9} + 1397074644 q^{10} - 6468699852 q^{12} + 1799208612 q^{13} - 48147537912 q^{14} - 119537094672 q^{16} - 282984271180 q^{17} + 21953827710 q^{18} + 491637621128 q^{20} + 254050055640 q^{21} + 272503644408 q^{22} + 4483423343232 q^{24} + 20224739695878 q^{25} - 2765456970196 q^{26} + 27756503338032 q^{28} + 1812741883820 q^{29} - 3579410315772 q^{30} + 216191588070880 q^{32} + 17014318866216 q^{33} - 275796423660708 q^{34} + 56425469699916 q^{36} + 197439381411156 q^{37} - 676030464010008 q^{38} + 19\!\cdots\!68 q^{40}+ \cdots - 37\!\cdots\!22 q^{98}+O(q^{100}) \) 18 * q - 170 * q^2 - 436932 * q^4 - 1721764 * q^5 - 6731586 * q^6 + 108558736 * q^8 - 2324522934 * q^9 + 1397074644 * q^10 - 6468699852 * q^12 + 1799208612 * q^13 - 48147537912 * q^14 - 119537094672 * q^16 - 282984271180 * q^17 + 21953827710 * q^18 + 491637621128 * q^20 + 254050055640 * q^21 + 272503644408 * q^22 + 4483423343232 * q^24 + 20224739695878 * q^25 - 2765456970196 * q^26 + 27756503338032 * q^28 + 1812741883820 * q^29 - 3579410315772 * q^30 + 216191588070880 * q^32 + 17014318866216 * q^33 - 275796423660708 * q^34 + 56425469699916 * q^36 + 197439381411156 * q^37 - 676030464010008 * q^38 + 1941137842438368 * q^40 - 204669372669676 * q^41 - 1059935698181880 * q^42 + 3599128179401424 * q^44 + 222348883607532 * q^45 - 3847169819651040 * q^46 + 1457367907812912 * q^48 - 3424095824368878 * q^49 - 10192520264009358 * q^50 + 4228291003193208 * q^52 - 14112687314785972 * q^53 + 869318113288518 * q^54 - 6591066595001856 * q^56 - 9662233004693640 * q^57 + 17584741731886020 * q^58 + 193536143011224 * q^60 + 4171094773122132 * q^61 + 77227021488187896 * q^62 - 53424456043095936 * q^64 + 35585253307254712 * q^65 + 40644920520184824 * q^66 - 91403316760947112 * q^68 + 26342656148137824 * q^69 + 264958129332427248 * q^70 - 14019292862113968 * q^72 - 83809473755653692 * q^73 + 55949505142092092 * q^74 - 129026923617832848 * q^76 - 354619239852167328 * q^77 - 34535086926497028 * q^78 + 43257628406200352 * q^80 + 300189270593998242 * q^81 - 458290372754774916 * q^82 + 324078384809786832 * q^84 + 166017223439872920 * q^85 - 975848731010420424 * q^86 + 1151342491040801280 * q^88 - 660650117825905468 * q^89 - 180418447249326972 * q^90 + 1359275349780859584 * q^92 - 447365281400937432 * q^93 - 2087066679318498384 * q^94 + 257905715132447136 * q^96 + 2412557706093917220 * q^97 - 3767017570512990122 * q^98

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