LMFDB - Embedded newform 12.19.d.a.7.1

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			7.1
Root			$-280.970 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.19.d.a.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-450.888 - 242.578i) q^{2} -11364.0i q^{3} +(144456. + 218751. i) q^{4} -780888. q^{5} +(-2.75665e6 + 5.12388e6i) q^{6} +2.45477e7i q^{7} +(-1.20691e7 - 1.33674e8i) q^{8} -1.29140e8 q^{9} +O(q^{10})$	\(q+(-450.888 - 242.578i) q^{2} -11364.0i q^{3} +(144456. + 218751. i) q^{4} -780888. q^{5} +(-2.75665e6 + 5.12388e6i) q^{6} +2.45477e7i q^{7} +(-1.20691e7 - 1.33674e8i) q^{8} -1.29140e8 q^{9} +(3.52093e8 + 1.89426e8i) q^{10} -5.20124e8i q^{11} +(2.48588e9 - 1.64159e9i) q^{12} +1.83928e10 q^{13} +(5.95474e9 - 1.10683e10i) q^{14} +8.87400e9i q^{15} +(-2.69846e10 + 6.31997e10i) q^{16} +3.86243e10 q^{17} +(5.82277e10 + 3.13266e10i) q^{18} -8.98393e10i q^{19} +(-1.12804e11 - 1.70820e11i) q^{20} +2.78960e11 q^{21} +(-1.26171e11 + 2.34517e11i) q^{22} -1.99933e12i q^{23} +(-1.51907e12 + 1.37153e11i) q^{24} -3.20491e12 q^{25} +(-8.29307e12 - 4.46168e12i) q^{26} +1.46755e12i q^{27} +(-5.36984e12 + 3.54606e12i) q^{28} -1.93833e13 q^{29} +(2.15264e12 - 4.00118e12i) q^{30} -1.86409e13i q^{31} +(2.74979e13 - 2.19501e13i) q^{32} -5.91068e12 q^{33} +(-1.74152e13 - 9.36942e12i) q^{34} -1.91690e13i q^{35} +(-1.86550e13 - 2.82495e13i) q^{36} -9.76781e13 q^{37} +(-2.17931e13 + 4.05075e13i) q^{38} -2.09015e14i q^{39} +(9.42464e12 + 1.04384e14i) q^{40} -1.26042e14 q^{41} +(-1.25780e14 - 6.76695e13i) q^{42} +4.41179e14i q^{43} +(1.13778e14 - 7.51348e13i) q^{44} +1.00844e14 q^{45} +(-4.84993e14 + 9.01472e14i) q^{46} -1.38830e15i q^{47} +(7.18200e14 + 3.06652e14i) q^{48} +1.02582e15 q^{49} +(1.44506e15 + 7.77441e14i) q^{50} -4.38926e14i q^{51} +(2.65694e15 + 4.02344e15i) q^{52} +1.00823e15 q^{53} +(3.55995e14 - 6.61699e14i) q^{54} +4.06158e14i q^{55} +(3.28139e15 - 2.96270e14i) q^{56} -1.02093e15 q^{57} +(8.73971e15 + 4.70197e15i) q^{58} -1.06141e16i q^{59} +(-1.94120e15 + 1.28190e15i) q^{60} -2.00860e16 q^{61} +(-4.52187e15 + 8.40495e15i) q^{62} -3.17010e15i q^{63} +(-1.77231e16 + 3.22666e15i) q^{64} -1.43627e16 q^{65} +(2.66505e15 + 1.43380e15i) q^{66} -5.21446e16i q^{67} +(5.57951e15 + 8.44911e15i) q^{68} -2.27203e16 q^{69} +(-4.64999e15 + 8.64308e15i) q^{70} -6.60477e16i q^{71} +(1.55861e15 + 1.72627e16i) q^{72} -7.78349e14 q^{73} +(4.40419e16 + 2.36946e16i) q^{74} +3.64206e16i q^{75} +(1.96524e16 - 1.29778e16i) q^{76} +1.27678e16 q^{77} +(-5.07025e16 + 9.42424e16i) q^{78} +5.19901e15i q^{79} +(2.10719e16 - 4.93519e16i) q^{80} +1.66772e16 q^{81} +(5.68308e16 + 3.05750e16i) q^{82} -4.99644e16i q^{83} +(4.02974e16 + 6.10228e16i) q^{84} -3.01613e16 q^{85} +(1.07020e17 - 1.98922e17i) q^{86} +2.20272e17i q^{87} +(-6.95270e16 + 6.27744e15i) q^{88} +2.80778e17 q^{89} +(-4.54694e16 - 2.44626e16i) q^{90} +4.51500e17i q^{91} +(4.37355e17 - 2.88814e17i) q^{92} -2.11835e17 q^{93} +(-3.36772e17 + 6.25969e17i) q^{94} +7.01545e16i q^{95} +(-2.49441e17 - 3.12485e17i) q^{96} +3.77943e17 q^{97} +(-4.62531e17 - 2.48842e17i) q^{98} +6.71688e16i 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 $

$2$	−450.888	−	242.578i	−0.880640	−	0.473785i
$2$	−450.888	−	242.578i	−0.880640	−	0.473785i
$3$		−	11364.0i		−	0.577350i
$3$		−	11364.0i		−	0.577350i
$4$	144456.	+	218751.i	0.551055	+	0.834469i
$5$	−780888.			−0.399815			−0.199907	−	0.979815i	$-0.564064\pi$
$5$	−780888.			−0.399815			−0.199907	+	0.979815i	$0.564064\pi$
$6$	−2.75665e6	+	5.12388e6i	−0.273540	+	0.508438i
$7$			2.45477e7i			0.608315i	0.952622	+	0.304158i	$0.0983749\pi$
$7$			2.45477e7i			0.608315i	−0.952622	+	0.304158i	$0.901625\pi$
$8$	−1.20691e7	−	1.33674e8i	−0.0899220	−	0.995949i
$9$	−1.29140e8			−0.333333
$10$	3.52093e8	+	1.89426e8i	0.352093	+	0.189426i
$11$		−	5.20124e8i		−	0.220583i	−0.993899	−	0.110292i	$-0.964822\pi$
$11$		−	5.20124e8i		−	0.220583i	0.993899	−	0.110292i	$-0.0351785\pi$
$12$	2.48588e9	−	1.64159e9i	0.481781	−	0.318152i
$13$	1.83928e10			1.73443			0.867215	−	0.497934i	$-0.165908\pi$
$13$	1.83928e10			1.73443			0.867215	+	0.497934i	$0.165908\pi$
$14$	5.95474e9	−	1.10683e10i	0.288211	−	0.535707i
$15$			8.87400e9i			0.230833i
$16$	−2.69846e10	+	6.31997e10i	−0.392677	+	0.919676i
$17$	3.86243e10			0.325702			0.162851	−	0.986651i	$-0.447931\pi$
$17$	3.86243e10			0.325702			0.162851	+	0.986651i	$0.447931\pi$
$18$	5.82277e10	+	3.13266e10i	0.293547	+	0.157928i
$19$		−	8.98393e10i		−	0.278410i	−0.990264	−	0.139205i	$-0.955545\pi$
$19$		−	8.98393e10i		−	0.278410i	0.990264	−	0.139205i	$-0.0444546\pi$
$20$	−1.12804e11	−	1.70820e11i	−0.220320	−	0.333633i
$21$	2.78960e11			0.351211
$22$	−1.26171e11	+	2.34517e11i	−0.104509	+	0.194254i
$23$		−	1.99933e12i		−	1.11003i	−0.831842	−	0.555013i	$-0.812713\pi$
$23$		−	1.99933e12i		−	1.11003i	0.831842	−	0.555013i	$-0.187287\pi$
$24$	−1.51907e12	+	1.37153e11i	−0.575011	+	0.0519165i
$25$	−3.20491e12			−0.840148
$26$	−8.29307e12	−	4.46168e12i	−1.52741	−	0.821748i
$27$			1.46755e12i			0.192450i
$28$	−5.36984e12	+	3.54606e12i	−0.507620	+	0.335215i
$29$	−1.93833e13			−1.33612			−0.668062	−	0.744106i	$-0.732876\pi$
$29$	−1.93833e13			−1.33612			−0.668062	+	0.744106i	$0.732876\pi$
$30$	2.15264e12	−	4.00118e12i	0.109365	−	0.203281i
$31$		−	1.86409e13i		−	0.705036i	−0.935805	−	0.352518i	$-0.885325\pi$
$31$		−	1.86409e13i		−	0.705036i	0.935805	−	0.352518i	$-0.114675\pi$
$32$	2.74979e13	−	2.19501e13i	0.781536	−	0.623860i
$33$	−5.91068e12			−0.127354
$34$	−1.74152e13	−	9.36942e12i	−0.286827	−	0.154313i
$35$		−	1.91690e13i		−	0.243213i
$36$	−1.86550e13	−	2.82495e13i	−0.183685	−	0.278156i
$37$	−9.76781e13			−0.751592			−0.375796	−	0.926703i	$-0.622631\pi$
$37$	−9.76781e13			−0.751592			−0.375796	+	0.926703i	$0.622631\pi$
$38$	−2.17931e13	+	4.05075e13i	−0.131906	+	0.245179i
$39$		−	2.09015e14i		−	1.00137i
$40$	9.42464e12	+	1.04384e14i	0.0359522	+	0.398195i
$41$	−1.26042e14			−0.385000			−0.192500	−	0.981297i	$-0.561660\pi$
$41$	−1.26042e14			−0.385000			−0.192500	+	0.981297i	$0.561660\pi$
$42$	−1.25780e14	−	6.76695e13i	−0.309291	−	0.166399i
$43$			4.41179e14i			0.877807i	0.898534	+	0.438904i	$0.144633\pi$
$43$			4.41179e14i			0.877807i	−0.898534	+	0.438904i	$0.855367\pi$
$44$	1.13778e14	−	7.51348e13i	0.184070	−	0.121553i
$45$	1.00844e14			0.133272
$46$	−4.84993e14	+	9.01472e14i	−0.525914	+	0.977533i
$47$		−	1.38830e15i		−	1.24052i	−0.784397	−	0.620260i	$-0.787027\pi$
$47$		−	1.38830e15i		−	1.24052i	0.784397	−	0.620260i	$-0.212973\pi$
$48$	7.18200e14	+	3.06652e14i	0.530975	+	0.226712i
$49$	1.02582e15			0.629953
$50$	1.44506e15	+	7.77441e14i	0.739868	+	0.398050i
$51$		−	4.38926e14i		−	0.188044i
$52$	2.65694e15	+	4.02344e15i	0.955766	+	1.44733i
$53$	1.00823e15			0.305545			0.152773	−	0.988261i	$-0.451180\pi$
$53$	1.00823e15			0.305545			0.152773	+	0.988261i	$0.451180\pi$
$54$	3.55995e14	−	6.61699e14i	0.0911800	−	0.169479i
$55$			4.06158e14i			0.0881924i
$56$	3.28139e15	−	2.96270e14i	0.605851	−	0.0547009i
$57$	−1.02093e15			−0.160740
$58$	8.73971e15	+	4.70197e15i	1.17664	+	0.633036i
$59$		−	1.06141e16i		−	1.22523i	−0.790383	−	0.612613i	$-0.790118\pi$
$59$		−	1.06141e16i		−	1.22523i	0.790383	−	0.612613i	$-0.209882\pi$
$60$	−1.94120e15	+	1.28190e15i	−0.192623	+	0.127202i
$61$	−2.00860e16			−1.71762			−0.858808	−	0.512298i	$-0.828794\pi$
$61$	−2.00860e16			−1.71762			−0.858808	+	0.512298i	$0.828794\pi$
$62$	−4.52187e15	+	8.40495e15i	−0.334036	+	0.620884i
$63$		−	3.17010e15i		−	0.202772i
$64$	−1.77231e16	+	3.22666e15i	−0.983828	+	0.179115i
$65$	−1.43627e16			−0.693451
$66$	2.66505e15	+	1.43380e15i	0.112153	+	0.0603383i
$67$		−	5.21446e16i		−	1.91662i	−0.285729	−	0.958311i	$-0.592236\pi$
$67$		−	5.21446e16i		−	1.91662i	0.285729	−	0.958311i	$-0.407764\pi$
$68$	5.57951e15	+	8.44911e15i	0.179480	+	0.271788i
$69$	−2.27203e16			−0.640874
$70$	−4.64999e15	+	8.64308e15i	−0.115231	+	0.214184i
$71$		−	6.60477e16i		−	1.44056i	−0.693682	−	0.720281i	$-0.744013\pi$
$71$		−	6.60477e16i		−	1.44056i	0.693682	−	0.720281i	$-0.255987\pi$
$72$	1.55861e15	+	1.72627e16i	0.0299740	+	0.331983i
$73$	−7.78349e14			−0.0132211			−0.00661057	−	0.999978i	$-0.502104\pi$
$73$	−7.78349e14			−0.0132211			−0.00661057	+	0.999978i	$0.502104\pi$
$74$	4.40419e16	+	2.36946e16i	0.661882	+	0.356093i
$75$			3.64206e16i			0.485060i
$76$	1.96524e16	−	1.29778e16i	0.232324	−	0.153419i
$77$	1.27678e16			0.134184
$78$	−5.07025e16	+	9.42424e16i	−0.474436	+	0.881850i
$79$			5.19901e15i			0.0433787i	0.999765	+	0.0216894i	$0.00690448\pi$
$79$			5.19901e15i			0.0433787i	−0.999765	+	0.0216894i	$0.993096\pi$
$80$	2.10719e16	−	4.93519e16i	0.156998	−	0.367700i
$81$	1.66772e16			0.111111
$82$	5.68308e16	+	3.05750e16i	0.339047	+	0.182407i
$83$		−	4.99644e16i		−	0.267275i	−0.991030	−	0.133637i	$-0.957334\pi$
$83$		−	4.99644e16i		−	0.267275i	0.991030	−	0.133637i	$-0.0426657\pi$
$84$	4.02974e16	+	6.10228e16i	0.193537	+	0.293075i
$85$	−3.01613e16			−0.130221
$86$	1.07020e17	−	1.98922e17i	0.415892	−	0.773032i
$87$			2.20272e17i			0.771411i
$88$	−6.95270e16	+	6.27744e15i	−0.219690	+	0.0198353i
$89$	2.80778e17			0.801408			0.400704	−	0.916208i	$-0.368766\pi$
$89$	2.80778e17			0.801408			0.400704	+	0.916208i	$0.368766\pi$
$90$	−4.54694e16	−	2.44626e16i	−0.117364	−	0.0631421i
$91$			4.51500e17i			1.05508i
$92$	4.37355e17	−	2.88814e17i	0.926282	−	0.611685i
$93$	−2.11835e17			−0.407053
$94$	−3.36772e17	+	6.25969e17i	−0.587740	+	1.09245i
$95$			7.01545e16i			0.111312i
$96$	−2.49441e17	−	3.12485e17i	−0.360186	−	0.451220i
$97$	3.77943e17			0.497142			0.248571	−	0.968614i	$-0.420039\pi$
$97$	3.77943e17			0.497142			0.248571	+	0.968614i	$0.420039\pi$
$98$	−4.62531e17	−	2.48842e17i	−0.554762	−	0.298462i
$99$			6.71688e16i			0.0735277i
$100$	−4.62968e17	−	7.01078e17i	−0.462968	−	0.701078i
$101$	1.72768e18			1.57969			0.789844	−	0.613308i	$-0.210162\pi$
$101$	1.72768e18			1.57969			0.789844	+	0.613308i	$0.210162\pi$
$102$	−1.06474e17	+	1.97907e17i	−0.0890926	+	0.165599i
$103$			1.98261e18i			1.51951i	0.650210	+	0.759755i	$0.274681\pi$
$103$			1.98261e18i			1.51951i	−0.650210	+	0.759755i	$0.725319\pi$
$104$	−2.21985e17	−	2.45863e18i	−0.155963	−	1.72740i
$105$	−2.17837e17			−0.140419
$106$	−4.54597e17	−	2.44574e17i	−0.269075	−	0.144763i
$107$		−	2.24161e18i		−	1.21929i	−0.792676	−	0.609643i	$-0.791313\pi$
$107$		−	2.24161e18i		−	1.21929i	0.792676	−	0.609643i	$-0.208687\pi$
$108$	−3.21027e17	+	2.11996e17i	−0.160594	+	0.106051i
$109$	−1.51967e18			−0.699700			−0.349850	−	0.936806i	$-0.613767\pi$
$109$	−1.51967e18			−0.699700			−0.349850	+	0.936806i	$0.613767\pi$
$110$	9.85251e16	−	1.83132e17i	0.0417843	−	0.0776658i
$111$			1.11001e18i			0.433932i
$112$	−1.55141e18	−	6.62409e17i	−0.559453	−	0.238871i
$113$	−3.07901e18			−1.02495			−0.512477	−	0.858701i	$-0.671272\pi$
$113$	−3.07901e18			−1.02495			−0.512477	+	0.858701i	$0.671272\pi$
$114$	4.60326e17	+	2.47656e17i	0.141554	+	0.0761562i
$115$			1.56125e18i			0.443805i
$116$	−2.80003e18	−	4.24013e18i	−0.736277	−	1.11495i
$117$	−2.37524e18			−0.578143
$118$	−2.57475e18	+	4.78578e18i	−0.580494	+	1.07898i
$119$			9.48139e17i			0.198130i
$120$	1.18622e18	−	1.07102e17i	0.229898	−	0.0207570i
$121$	5.28939e18			0.951343
$122$	9.05656e18	+	4.87244e18i	1.51260	+	0.813781i
$123$			1.43234e18i			0.222280i
$124$	4.07772e18	−	2.69278e18i	0.588331	−	0.388514i
$125$	5.48153e18			0.735719
$126$	−7.68996e17	+	1.42936e18i	−0.0960703	+	0.178569i
$127$		−	1.37536e19i		−	1.60023i	−0.599847	−	0.800115i	$-0.704772\pi$
$127$		−	1.37536e19i		−	1.60023i	0.599847	−	0.800115i	$-0.295228\pi$
$128$	8.77383e18	+	2.84437e18i	0.951261	+	0.308387i
$129$	5.01356e18			0.506802
$130$	6.47597e18	+	3.48408e18i	0.610681	+	0.328547i
$131$			9.02697e18i			0.794512i	0.917708	+	0.397256i	$0.130037\pi$
$131$			9.02697e18i			0.794512i	−0.917708	+	0.397256i	$0.869963\pi$
$132$	−8.53831e17	−	1.29297e18i	−0.0701789	−	0.106273i
$133$	2.20535e18			0.169361
$134$	−1.26491e19	+	2.35114e19i	−0.908067	+	1.68785i
$135$		−	1.14599e18i		−	0.0769444i
$136$	−4.66162e17	−	5.16307e18i	−0.0292878	−	0.324383i
$137$	−1.86710e19			−1.09821			−0.549103	−	0.835755i	$-0.685030\pi$
$137$	−1.86710e19			−1.09821			−0.549103	+	0.835755i	$0.685030\pi$
$138$	1.02443e19	+	5.51145e18i	0.564379	+	0.303636i
$139$		−	3.16534e19i		−	1.63413i	−0.576543	−	0.817067i	$-0.695599\pi$
$139$		−	3.16534e19i		−	1.63413i	0.576543	−	0.817067i	$-0.304401\pi$
$140$	4.19324e18	−	2.76908e18i	0.202954	−	0.134024i
$141$	−1.57767e19			−0.716214
$142$	−1.60217e19	+	2.97801e19i	−0.682518	+	1.26862i
$143$		−	9.56651e18i		−	0.382586i
$144$	3.48479e18	−	8.16162e18i	0.130892	−	0.306559i
$145$	1.51362e19			0.534202
$146$	3.50948e17	+	1.88811e17i	0.0116431	+	0.00626398i
$147$		−	1.16574e19i		−	0.363703i
$148$	−1.41102e19	−	2.13672e19i	−0.414168	−	0.627180i
$149$	−6.77675e19			−1.87217			−0.936084	−	0.351776i	$-0.885578\pi$
$149$	−6.77675e19			−1.87217			−0.936084	+	0.351776i	$0.885578\pi$
$150$	8.83483e18	−	1.64216e19i	0.229814	−	0.427163i
$151$			2.23990e18i			0.0548827i	0.999623	+	0.0274413i	$0.00873594\pi$
$151$			2.23990e18i			0.0548827i	−0.999623	+	0.0274413i	$0.991264\pi$
$152$	−1.20092e19	+	1.08428e18i	−0.277282	+	0.0250351i
$153$	−4.98795e18			−0.108567
$154$	−5.75687e18	−	3.09720e18i	−0.118168	−	0.0635745i
$155$			1.45565e19i			0.281884i
$156$	4.57223e19	−	3.01934e19i	0.835615	−	0.551812i
$157$	1.97247e19			0.340341			0.170170	−	0.985415i	$-0.445568\pi$
$157$	1.97247e19			0.340341			0.170170	+	0.985415i	$0.445568\pi$
$158$	1.26117e18	−	2.34417e18i	0.0205522	−	0.0382011i
$159$		−	1.14575e19i		−	0.176407i
$160$	−2.14728e19	+	1.71406e19i	−0.312470	+	0.249428i
$161$	4.90789e19			0.675245
$162$	−7.51954e18	−	4.04552e18i	−0.0978489	−	0.0526428i
$163$			2.60392e19i			0.320582i	0.987070	+	0.160291i	$0.0512433\pi$
$163$			2.60392e19i			0.320582i	−0.987070	+	0.160291i	$0.948757\pi$
$164$	−1.82075e19	−	2.75718e19i	−0.212156	−	0.321271i
$165$	4.61558e18			0.0509179
$166$	−1.21203e19	+	2.25283e19i	−0.126631	+	0.235373i
$167$			1.36553e20i			1.35162i	0.737076	+	0.675809i	$0.236206\pi$
$167$			1.36553e20i			1.35162i	−0.737076	+	0.675809i	$0.763794\pi$
$168$	−3.36680e18	−	3.72897e19i	−0.0315816	−	0.349788i
$169$	2.25838e20			2.00825
$170$	1.35994e19	+	7.31647e18i	0.114677	+	0.0616966i
$171$			1.16019e19i			0.0928032i
$172$	−9.65084e19	+	6.37309e19i	−0.732503	+	0.483720i
$173$	−8.05566e19			−0.580345			−0.290172	−	0.956974i	$-0.593713\pi$
$173$	−8.05566e19			−0.580345			−0.290172	+	0.956974i	$0.593713\pi$
$174$	5.34332e19	−	9.93180e19i	0.365483	−	0.679336i
$175$		−	7.86732e19i		−	0.511075i
$176$	3.28716e19	+	1.40353e19i	0.202865	+	0.0866179i
$177$	−1.20619e20			−0.707384
$178$	−1.26600e20	−	6.81107e19i	−0.705752	−	0.379695i
$179$			3.01516e20i			1.59821i	0.601192	+	0.799105i	$0.294693\pi$
$179$			3.01516e20i			1.59821i	−0.601192	+	0.799105i	$0.705307\pi$
$180$	1.45675e19	+	2.20597e19i	0.0734400	+	0.111211i
$181$	2.63376e20			1.26319			0.631596	−	0.775298i	$-0.282400\pi$
$181$	2.63376e20			1.26319			0.631596	+	0.775298i	$0.282400\pi$
$182$	1.09524e20	−	2.03576e20i	0.499882	−	0.929146i
$183$			2.28258e20i			0.991666i
$184$	−2.67258e20	+	2.41301e19i	−1.10553	+	0.0998158i
$185$	7.62757e19			0.300497
$186$	9.55138e19	+	5.13865e19i	0.358467	+	0.192856i
$187$		−	2.00894e19i		−	0.0718444i
$188$	3.03693e20	−	2.00548e20i	1.03517	−	0.683594i
$189$	−3.60249e19			−0.117070
$190$	1.70179e19	−	3.16318e19i	0.0527381	−	0.0980261i
$191$		−	3.92625e20i		−	1.16059i	−0.814407	−	0.580294i	$-0.802938\pi$
$191$		−	3.92625e20i		−	1.16059i	0.814407	−	0.580294i	$-0.197062\pi$
$192$	3.66677e19	+	2.01405e20i	0.103412	+	0.568013i
$193$	1.07288e20			0.288759			0.144380	−	0.989522i	$-0.453881\pi$
$193$	1.07288e20			0.288759			0.144380	+	0.989522i	$0.453881\pi$
$194$	−1.70410e20	−	9.16806e19i	−0.437803	−	0.235539i
$195$			1.63217e20i			0.400364i
$196$	1.48186e20	+	2.24400e20i	0.347138	+	0.525676i
$197$	−5.37873e20			−1.20360			−0.601802	−	0.798645i	$-0.705550\pi$
$197$	−5.37873e20			−1.20360			−0.601802	+	0.798645i	$0.705550\pi$
$198$	1.62937e19	−	3.02856e19i	0.0348364	−	0.0647515i
$199$		−	2.86120e20i		−	0.584617i	−0.956324	−	0.292308i	$-0.905577\pi$
$199$		−	2.86120e20i		−	0.584617i	0.956324	−	0.292308i	$-0.0944234\pi$
$200$	3.86805e19	+	4.28413e20i	0.0755478	+	0.836744i
$201$	−5.92571e20			−1.10656
$202$	−7.78990e20	−	4.19098e20i	−1.39114	−	0.748433i
$203$		−	4.75817e20i		−	0.812784i
$204$	9.60156e19	−	6.34054e19i	0.156917	−	0.103623i
$205$	9.84248e19			0.153929
$206$	4.80939e20	−	8.93937e20i	0.719921	−	1.33814i
$207$			2.58193e20i			0.370009i
$208$	−4.96321e20	+	1.16242e21i	−0.681071	+	1.59511i
$209$	−4.67276e19			−0.0614125
$210$	9.82198e19	+	5.28424e19i	0.123659	+	0.0665286i
$211$		−	1.56167e21i		−	1.88385i	−0.335817	−	0.941927i	$-0.609012\pi$
$211$		−	1.56167e21i		−	1.88385i	0.335817	−	0.941927i	$-0.390988\pi$
$212$	1.45644e20	+	2.20551e20i	0.168372	+	0.254968i
$213$	−7.50565e20			−0.831709
$214$	−5.43765e20	+	1.01071e21i	−0.577680	+	1.07375i
$215$		−	3.44512e20i		−	0.350960i
$216$	1.96173e20	−	1.77120e19i	0.191670	−	0.0173055i
$217$	4.57591e20			0.428884
$218$	6.85202e20	+	3.68639e20i	0.616184	+	0.331507i
$219$			8.84515e18i			0.00763323i
$220$	−8.88476e19	+	5.86719e19i	−0.0735938	+	0.0485989i
$221$	7.10408e20			0.564908
$222$	2.69265e20	−	5.00491e20i	0.205590	−	0.382138i
$223$			1.40171e21i			1.02781i	0.857847	+	0.513906i	$0.171802\pi$
$223$			1.40171e21i			1.02781i	−0.857847	+	0.513906i	$0.828198\pi$
$224$	5.38825e20	+	6.75010e20i	0.379503	+	0.475420i
$225$	4.13883e20			0.280049
$226$	1.38829e21	+	7.46900e20i	0.902616	+	0.485608i
$227$		−	3.93400e20i		−	0.245811i	−0.992418	−	0.122906i	$-0.960779\pi$
$227$		−	3.93400e20i		−	0.245811i	0.992418	−	0.122906i	$-0.0392212\pi$
$228$	−1.47480e20	−	2.23330e20i	−0.0885765	−	0.134132i
$229$	6.46504e20			0.373295			0.186647	−	0.982427i	$-0.440238\pi$
$229$	6.46504e20			0.373295			0.186647	+	0.982427i	$0.440238\pi$
$230$	3.78725e20	−	7.03949e20i	0.210268	−	0.390832i
$231$		−	1.45094e20i		−	0.0774712i
$232$	2.33940e20	+	2.59105e21i	0.120147	+	1.33071i
$233$	−1.45918e21			−0.720949			−0.360474	−	0.932769i	$-0.617385\pi$
$233$	−1.45918e21			−0.720949			−0.360474	+	0.932769i	$0.617385\pi$
$234$	1.07097e21	+	5.76182e20i	0.509136	+	0.273916i
$235$			1.08411e21i			0.495978i
$236$	2.32185e21	−	1.53327e21i	1.02241	−	0.675167i
$237$	5.90815e19			0.0250447
$238$	2.29998e20	−	4.27504e20i	0.0938709	−	0.174481i
$239$			2.30943e20i			0.0907660i	0.998970	+	0.0453830i	$0.0144508\pi$
$239$			2.30943e20i			0.0907660i	−0.998970	+	0.0453830i	$0.985549\pi$
$240$	−5.60834e20	−	2.39461e20i	−0.212292	−	0.0906429i
$241$	2.51358e21			0.916514			0.458257	−	0.888820i	$-0.348474\pi$
$241$	2.51358e21			0.916514			0.458257	+	0.888820i	$0.348474\pi$
$242$	−2.38492e21	−	1.28309e21i	−0.837791	−	0.450732i
$243$		−	1.89519e20i		−	0.0641500i
$244$	−2.90155e21	−	4.39384e21i	−0.946501	−	1.43330i
$245$	−8.01054e20			−0.251864
$246$	3.47454e20	−	6.45825e20i	0.105313	−	0.195749i
$247$		−	1.65239e21i		−	0.482882i
$248$	−2.49180e21	+	2.24979e20i	−0.702180	+	0.0633983i
$249$	−5.67795e20			−0.154311
$250$	−2.47156e21	−	1.32970e21i	−0.647903	−	0.348573i
$251$			6.70039e21i			1.69448i	0.531211	+	0.847240i	$0.321737\pi$
$251$			6.70039e21i			1.69448i	−0.531211	+	0.847240i	$0.678263\pi$
$252$	6.93462e20	−	4.57939e20i	0.169207	−	0.111738i
$253$	−1.03990e21			−0.244853
$254$	−3.33632e21	+	6.20132e21i	−0.758165	+	1.40923i
$255$			3.42752e20i			0.0751829i
$256$	−3.26603e21	−	3.41083e21i	−0.691610	−	0.722272i
$257$	−3.04661e21			−0.622900			−0.311450	−	0.950263i	$-0.600815\pi$
$257$	−3.04661e21			−0.622900			−0.311450	+	0.950263i	$0.600815\pi$
$258$	−2.26055e21	−	1.21618e21i	−0.446310	−	0.240115i
$259$		−	2.39778e21i		−	0.457205i
$260$	−2.07477e21	−	3.14185e21i	−0.382130	−	0.578663i
$261$	2.50317e21			0.445375
$262$	2.18974e21	−	4.07015e21i	0.376428	−	0.699679i
$263$			3.80295e21i			0.631712i	0.948807	+	0.315856i	$0.102292\pi$
$263$			3.80295e21i			0.631712i	−0.948807	+	0.315856i	$0.897708\pi$
$264$	7.13367e19	+	7.90104e20i	0.0114519	+	0.126838i
$265$	−7.87313e20			−0.122161
$266$	−9.94366e20	−	5.34970e20i	−0.149146	−	0.0802406i
$267$		−	3.19076e21i		−	0.462693i
$268$	1.14067e22	−	7.53259e21i	1.59936	−	1.05616i
$269$	1.06178e22			1.43967			0.719837	−	0.694143i	$-0.244217\pi$
$269$	1.06178e22			1.43967			0.719837	+	0.694143i	$0.244217\pi$
$270$	−2.77992e20	+	5.16713e20i	−0.0364551	+	0.0677603i
$271$			8.38266e20i			0.106331i	0.998586	+	0.0531653i	$0.0169310\pi$
$271$			8.38266e20i			0.106331i	−0.998586	+	0.0531653i	$0.983069\pi$
$272$	−1.04226e21	+	2.44105e21i	−0.127896	+	0.299541i
$273$	5.13084e21			0.609151
$274$	8.41855e21	+	4.52919e21i	0.967124	+	0.520314i
$275$			1.66695e21i			0.185323i
$276$	−3.28208e21	−	4.97009e21i	−0.353157	−	0.534789i
$277$	−4.05605e21			−0.422459			−0.211230	−	0.977436i	$-0.567747\pi$
$277$	−4.05605e21			−0.422459			−0.211230	+	0.977436i	$0.567747\pi$
$278$	−7.67843e21	+	1.42721e22i	−0.774229	+	1.43908i
$279$			2.40729e21i			0.235012i
$280$	−2.56240e21	+	2.31353e20i	−0.242228	+	0.0218702i
$281$	−5.52170e21			−0.505494			−0.252747	−	0.967532i	$-0.581334\pi$
$281$	−5.52170e21			−0.505494			−0.252747	+	0.967532i	$0.581334\pi$
$282$	7.11350e21	+	3.82707e21i	0.630727	+	0.339332i
$283$			7.69526e21i			0.660915i	0.943821	+	0.330457i	$0.107203\pi$
$283$			7.69526e21i			0.660915i	−0.943821	+	0.330457i	$0.892797\pi$
$284$	1.44480e22	−	9.54096e21i	1.20211	−	0.793829i
$285$	7.97235e20			0.0642662
$286$	−2.32063e21	+	4.31342e21i	−0.181264	+	0.336921i
$287$		−	3.09404e21i		−	0.234201i
$288$	−3.55108e21	+	2.83464e21i	−0.260512	+	0.207953i
$289$	−1.25712e22			−0.893918
$290$	−6.82474e21	−	3.67172e21i	−0.470440	−	0.253097i
$291$		−	4.29494e21i		−	0.287025i
$292$	−1.12437e20	−	1.70265e20i	−0.00728557	−	0.0110326i
$293$	2.82135e21			0.177275			0.0886376	−	0.996064i	$-0.471749\pi$
$293$	2.82135e21			0.177275			0.0886376	+	0.996064i	$0.471749\pi$
$294$	−2.82784e21	+	5.25620e21i	−0.172317	+	0.320292i
$295$			8.28845e21i			0.489863i
$296$	1.17889e21	+	1.30570e22i	0.0675846	+	0.748547i
$297$	7.63306e20			0.0424513
$298$	3.05555e22	+	1.64389e22i	1.64871	+	0.887006i
$299$		−	3.67731e22i		−	1.92526i
$300$	−7.96703e21	+	5.26116e21i	−0.404767	+	0.267295i
$301$	−1.08299e22			−0.533983
$302$	5.43350e20	−	1.00994e21i	0.0260026	−	0.0483319i
$303$		−	1.96333e22i		−	0.912033i
$304$	5.67782e21	+	2.42427e21i	0.256047	+	0.109325i
$305$	1.56850e22			0.686728
$306$	2.24901e21	+	1.20997e21i	0.0956088	+	0.0514376i
$307$			5.40722e21i			0.223218i	0.993752	+	0.111609i	$0.0356004\pi$
$307$			5.40722e21i			0.223218i	−0.993752	+	0.111609i	$0.964400\pi$
$308$	1.84439e21	+	2.79298e21i	0.0739428	+	0.111972i
$309$	2.25304e22			0.877289
$310$	3.53108e21	−	6.56333e21i	0.133553	−	0.248238i
$311$		−	2.79590e22i		−	1.02725i	−0.858013	−	0.513627i	$-0.828301\pi$
$311$		−	2.79590e22i		−	1.02725i	0.858013	−	0.513627i	$-0.171699\pi$
$312$	−2.79399e22	+	2.52263e21i	−0.997317	+	0.0900456i
$313$	−3.63872e22			−1.26197			−0.630986	−	0.775794i	$-0.717350\pi$
$313$	−3.63872e22			−1.26197			−0.630986	+	0.775794i	$0.717350\pi$
$314$	−8.89363e21	−	4.78478e21i	−0.299718	−	0.161248i
$315$			2.47549e21i			0.0810712i
$316$	−1.13729e21	+	7.51027e20i	−0.0361982	+	0.0239041i
$317$	−6.24798e20			−0.0193289			−0.00966443	−	0.999953i	$-0.503076\pi$
$317$	−6.24798e20			−0.0193289			−0.00966443	+	0.999953i	$0.503076\pi$
$318$	−2.77933e21	+	5.16604e21i	−0.0835789	+	0.155351i
$319$			1.00817e22i			0.294726i
$320$	1.38397e22	−	2.51966e21i	0.393349	−	0.0716130i
$321$	−2.54736e22			−0.703955
$322$	−2.21291e22	−	1.19055e22i	−0.594648	−	0.319921i
$323$		−	3.46998e21i		−	0.0906786i
$324$	2.40911e21	+	3.64815e21i	0.0612283	+	0.0927188i
$325$	−5.89472e22			−1.45718
$326$	6.31654e21	−	1.17408e22i	0.151887	−	0.282318i
$327$			1.72695e22i			0.403972i
$328$	1.52122e21	+	1.68485e22i	0.0346200	+	0.383440i
$329$	3.40797e22			0.754627
$330$	−2.08111e21	−	1.11964e21i	−0.0448404	−	0.0241242i
$331$		−	1.50844e22i		−	0.316282i	−0.987417	−	0.158141i	$-0.949450\pi$
$331$		−	1.50844e22i		−	0.316282i	0.987417	−	0.158141i	$-0.0505501\pi$
$332$	1.09298e22	−	7.21765e21i	0.223032	−	0.147283i
$333$	1.26142e22			0.250531
$334$	3.31249e22	−	6.15703e22i	0.640377	−	1.19029i
$335$			4.07191e22i			0.766294i
$336$	−7.52761e21	+	1.76302e22i	−0.137912	+	0.323000i
$337$	3.51223e22			0.626489			0.313245	−	0.949672i	$-0.398584\pi$
$337$	3.51223e22			0.626489			0.313245	+	0.949672i	$0.398584\pi$
$338$	−1.01828e23	−	5.47834e22i	−1.76854	−	0.951478i
$339$			3.49898e22i			0.591758i
$340$	−4.35697e21	−	6.59781e21i	−0.0717587	−	0.108665i
$341$	−9.69557e21			−0.155519
$342$	2.81436e21	−	5.23114e21i	0.0439688	−	0.0817262i
$343$			6.51554e22i			0.991525i
$344$	5.89742e22	−	5.32465e21i	0.874251	−	0.0789342i
$345$	1.77420e22			0.256231
$346$	3.63220e22	+	1.95413e22i	0.511075	+	0.274959i
$347$		−	5.71687e22i		−	0.783778i	−0.920013	−	0.391889i	$-0.871822\pi$
$347$		−	5.71687e22i		−	0.783778i	0.920013	−	0.391889i	$-0.128178\pi$
$348$	−4.81847e22	+	3.18196e22i	−0.643719	+	0.425090i
$349$	3.86296e22			0.502911			0.251456	−	0.967869i	$-0.419091\pi$
$349$	3.86296e22			0.502911			0.251456	+	0.967869i	$0.419091\pi$
$350$	−1.90844e22	+	3.54728e22i	−0.242140	+	0.450073i
$351$			2.69922e22i			0.333791i
$352$	−1.14168e22	−	1.43023e22i	−0.137613	−	0.172394i
$353$	1.25652e23			1.47638			0.738189	−	0.674594i	$-0.235681\pi$
$353$	1.25652e23			1.47638			0.738189	+	0.674594i	$0.235681\pi$
$354$	5.43855e22	+	2.92595e22i	0.622951	+	0.335148i
$355$			5.15758e22i			0.575958i
$356$	4.05600e22	+	6.14205e22i	0.441620	+	0.668750i
$357$	1.07746e22			0.114390
$358$	7.31413e22	−	1.35950e23i	0.757208	−	1.40745i
$359$			1.87777e23i			1.89580i	0.318569	+	0.947900i	$0.396798\pi$
$359$			1.87777e23i			1.89580i	−0.318569	+	0.947900i	$0.603202\pi$
$360$	−1.21710e21	−	1.34802e22i	−0.0119841	−	0.132732i
$361$	9.60562e22			0.922488
$362$	−1.18753e23	−	6.38893e22i	−1.11242	−	0.598482i
$363$		−	6.01085e22i		−	0.549258i
$364$	−9.87662e22	+	6.52218e22i	−0.880432	+	0.581407i
$365$	6.07804e20			0.00528601
$366$	5.53703e22	−	1.02919e23i	0.469837	−	0.873301i
$367$		−	3.61216e22i		−	0.299070i	−0.988756	−	0.149535i	$-0.952222\pi$
$367$		−	3.61216e22i		−	0.299070i	0.988756	−	0.149535i	$-0.0477776\pi$
$368$	1.26357e23	+	5.39509e22i	1.02086	+	0.435881i
$369$	1.62771e22			0.128333
$370$	−3.43918e22	−	1.85028e22i	−0.264630	−	0.142371i
$371$			2.47497e22i			0.185868i
$372$	−3.06008e22	−	4.63391e22i	−0.224309	−	0.339673i
$373$	1.28154e22			0.0916965			0.0458483	−	0.998948i	$-0.485401\pi$
$373$	1.28154e22			0.0916965			0.0458483	+	0.998948i	$0.485401\pi$
$374$	−4.87325e21	+	9.05808e21i	−0.0340388	+	0.0632691i
$375$		−	6.22920e22i		−	0.424767i
$376$	−1.85580e23	+	1.67556e22i	−1.23549	+	0.111550i
$377$	−3.56513e23			−2.31741
$378$	1.62432e22	+	8.73886e21i	0.103097	+	0.0554662i
$379$		−	1.60595e23i		−	0.995356i	−0.867362	−	0.497678i	$-0.834186\pi$
$379$		−	1.60595e23i		−	0.995356i	0.867362	−	0.497678i	$-0.165814\pi$
$380$	−1.53464e22	+	1.01342e22i	−0.0928866	+	0.0613392i
$381$	−1.56295e23			−0.923893
$382$	−9.52422e22	+	1.77030e23i	−0.549869	+	1.02206i
$383$		−	6.79246e22i		−	0.383035i	−0.981489	−	0.191517i	$-0.938659\pi$
$383$		−	6.79246e22i		−	0.383035i	0.981489	−	0.191517i	$-0.0613409\pi$
$384$	3.23234e22	−	9.97057e22i	0.178047	−	0.549211i
$385$	−9.97026e21			−0.0536488
$386$	−4.83749e22	−	2.60258e22i	−0.254293	−	0.136810i
$387$		−	5.69740e22i		−	0.292602i
$388$	5.45960e22	+	8.26754e22i	0.273952	+	0.414850i
$389$	−1.52788e23			−0.749103			−0.374552	−	0.927206i	$-0.622203\pi$
$389$	−1.52788e23			−0.749103			−0.374552	+	0.927206i	$0.622203\pi$
$390$	3.95930e22	−	7.35928e22i	0.189687	−	0.352577i
$391$		−	7.72226e22i		−	0.361538i
$392$	−1.23808e22	−	1.37126e23i	−0.0566466	−	0.627401i
$393$	1.02582e23			0.458711
$394$	2.42520e23	+	1.30476e23i	1.05994	+	0.570250i
$395$		−	4.05985e21i		−	0.0173435i
$396$	−1.46933e22	+	9.70293e21i	−0.0613566	+	0.0405178i
$397$	−6.57435e22			−0.268373			−0.134186	−	0.990956i	$-0.542842\pi$
$397$	−6.57435e22			−0.268373			−0.134186	+	0.990956i	$0.542842\pi$
$398$	−6.94066e22	+	1.29008e23i	−0.276983	+	0.514837i
$399$		−	2.50616e22i		−	0.0977805i
$400$	8.64831e22	−	2.02549e23i	0.329907	−	0.772664i
$401$	−1.38141e23			−0.515257			−0.257628	−	0.966244i	$-0.582941\pi$
$401$	−1.38141e23			−0.515257			−0.257628	+	0.966244i	$0.582941\pi$
$402$	2.67183e23	+	1.43745e23i	0.974483	+	0.524273i
$403$		−	3.42858e23i		−	1.22284i
$404$	2.49573e23	+	3.77932e23i	0.870495	+	1.31820i
$405$	−1.30230e22			−0.0444239
$406$	−1.15423e23	+	2.14540e23i	−0.385085	+	0.715771i
$407$			5.08047e22i			0.165788i
$408$	−5.86730e22	+	5.29746e21i	−0.187282	+	0.0169093i
$409$	4.91312e23			1.53408			0.767040	−	0.641600i	$-0.221729\pi$
$409$	4.91312e23			1.53408			0.767040	+	0.641600i	$0.221729\pi$
$410$	−4.43785e22	−	2.38757e22i	−0.135556	−	0.0729292i
$411$			2.12178e23i			0.634049i
$412$	−4.33699e23	+	2.86400e23i	−1.26798	+	0.837333i
$413$	2.60553e23			0.745323
$414$	6.26320e22	−	1.16416e23i	0.175305	−	0.325844i
$415$			3.90166e22i			0.106860i
$416$	5.05762e23	−	4.03723e23i	1.35552	−	1.08204i
$417$	−3.59709e23			−0.943467
$418$	2.10689e22	+	1.13351e22i	0.0540823	+	0.0290963i
$419$		−	2.93489e23i		−	0.737337i	−0.929561	−	0.368669i	$-0.879814\pi$
$419$		−	2.93489e23i		−	0.737337i	0.929561	−	0.368669i	$-0.120186\pi$
$420$	−3.14677e22	−	4.76520e22i	−0.0773788	−	0.117176i
$421$	5.52721e23			1.33035			0.665176	−	0.746686i	$-0.268356\pi$
$421$	5.52721e23			1.33035			0.665176	+	0.746686i	$0.268356\pi$
$422$	−3.78827e23	+	7.04138e23i	−0.892543	+	1.65900i
$423$			1.79286e23i			0.413506i
$424$	−1.21684e22	−	1.34774e23i	−0.0274752	−	0.304307i
$425$	−1.23788e23			−0.273638
$426$	3.38420e23	+	1.82071e23i	0.732437	+	0.394052i
$427$		−	4.93067e23i		−	1.04485i
$428$	4.90354e23	−	3.23813e23i	1.01746	−	0.671893i
$429$	−1.08714e23			−0.220886
$430$	−8.35710e22	+	1.55336e23i	−0.166280	+	0.309070i
$431$			7.61935e23i			1.48465i	0.670043	+	0.742323i	$0.266276\pi$
$431$			7.61935e23i			1.48465i	−0.670043	+	0.742323i	$0.733724\pi$
$432$	−9.27485e22	−	3.96011e22i	−0.176992	−	0.0755707i
$433$	−2.05645e23			−0.384351			−0.192175	−	0.981361i	$-0.561554\pi$
$433$	−2.05645e23			−0.384351			−0.192175	+	0.981361i	$0.561554\pi$
$434$	−2.06322e23	−	1.11002e23i	−0.377693	−	0.203199i
$435$		−	1.72008e23i		−	0.308422i
$436$	−2.19525e23	−	3.32430e23i	−0.385573	−	0.583878i
$437$	−1.79618e23			−0.309042
$438$	2.14564e21	−	3.98817e21i	0.00361651	−	0.00672213i
$439$			6.49612e23i			1.07269i	0.844000	+	0.536344i	$0.180195\pi$
$439$			6.49612e23i			1.07269i	−0.844000	+	0.536344i	$0.819805\pi$
$440$	5.42928e22	−	4.90198e21i	0.0878351	−	0.00793044i
$441$	−1.32475e23			−0.209984
$442$	−3.20314e23	−	1.72329e23i	−0.497481	−	0.267645i
$443$		−	1.52884e23i		−	0.232663i	−0.993210	−	0.116332i	$-0.962886\pi$
$443$		−	1.52884e23i		−	0.232663i	0.993210	−	0.116332i	$-0.0371136\pi$
$444$	−2.42816e23	+	1.60348e23i	−0.362102	+	0.239120i
$445$	−2.19257e23			−0.320415
$446$	3.40023e23	−	6.32013e23i	0.486962	−	0.905133i
$447$			7.70109e23i			1.08090i
$448$	−7.92071e22	−	4.35061e23i	−0.108959	−	0.598478i
$449$	7.69333e23			1.03728			0.518642	−	0.854992i	$-0.326438\pi$
$449$	7.69333e23			1.03728			0.518642	+	0.854992i	$0.326438\pi$
$450$	−1.86615e23	−	1.00399e23i	−0.246623	−	0.132683i
$451$			6.55575e22i			0.0849245i
$452$	−4.44780e23	−	6.73536e23i	−0.564806	−	0.855293i
$453$	2.54541e22			0.0316865
$454$	−9.54302e22	+	1.77379e23i	−0.116462	+	0.216471i
$455$		−	3.52571e23i		−	0.421837i
$456$	1.23218e22	+	1.36472e23i	0.0144541	+	0.160089i
$457$	−1.44927e23			−0.166687			−0.0833437	−	0.996521i	$-0.526560\pi$
$457$	−1.44927e23			−0.166687			−0.0833437	+	0.996521i	$0.526560\pi$
$458$	−2.91501e23	−	1.56828e23i	−0.328738	−	0.176862i
$459$			5.66830e22i			0.0626814i
$460$	−3.41525e23	+	2.25532e23i	−0.370341	+	0.244561i
$461$	−2.25982e23			−0.240306			−0.120153	−	0.992755i	$-0.538339\pi$
$461$	−2.25982e23			−0.240306			−0.120153	+	0.992755i	$0.538339\pi$
$462$	−3.51965e22	+	6.54209e22i	−0.0367047	+	0.0682243i
$463$			5.64150e23i			0.576986i	0.957482	+	0.288493i	$0.0931542\pi$
$463$			5.64150e23i			0.576986i	−0.957482	+	0.288493i	$0.906846\pi$
$464$	5.23051e23	−	1.22502e24i	0.524665	−	1.22880i
$465$	1.65419e23			0.162746
$466$	6.57925e23	+	3.53964e23i	0.634897	+	0.341575i
$467$		−	3.07517e23i		−	0.291083i	−0.989352	−	0.145542i	$-0.953507\pi$
$467$		−	3.07517e23i		−	0.291083i	0.989352	−	0.145542i	$-0.0464925\pi$
$468$	−3.43118e23	−	5.19587e23i	−0.318589	−	0.482443i
$469$	1.28003e24			1.16591
$470$	2.62981e23	−	4.88812e23i	0.234987	−	0.436778i
$471$		−	2.24151e23i		−	0.196496i
$472$	−1.41883e24	+	1.28103e23i	−1.22026	+	0.110175i
$473$	2.29468e23			0.193629
$474$	−2.66391e22	−	1.43319e22i	−0.0220554	−	0.0118658i
$475$			2.87927e23i			0.233905i
$476$	−2.07406e23	+	1.36964e23i	−0.165333	+	0.109180i
$477$	−1.30203e23			−0.101848
$478$	5.60217e22	−	1.04129e23i	0.0430036	−	0.0799322i
$479$		−	1.57139e23i		−	0.118376i	−0.998247	−	0.0591880i	$-0.981149\pi$
$479$		−	1.57139e23i		−	0.118376i	0.998247	−	0.0591880i	$-0.0188511\pi$
$480$	1.94785e23	+	2.44016e23i	0.144008	+	0.180405i
$481$	−1.79657e24			−1.30358
$482$	−1.13334e24	−	6.09739e23i	−0.807119	−	0.434231i
$483$		−	5.57732e23i		−	0.389853i
$484$	7.64083e23	+	1.15706e24i	0.524242	+	0.793866i
$485$	−2.95131e23			−0.198765
$486$	−4.59732e22	+	8.54519e22i	−0.0303933	+	0.0564931i
$487$			2.20436e24i			1.43061i	0.698812	+	0.715305i	$0.253712\pi$
$487$			2.20436e24i			1.43061i	−0.698812	+	0.715305i	$0.746288\pi$
$488$	2.42421e23	+	2.68498e24i	0.154451	+	1.71066i
$489$	2.95909e23			0.185088
$490$	3.61185e23	+	1.94318e23i	0.221802	+	0.119330i
$491$		−	2.16823e24i		−	1.30729i	−0.756802	−	0.653644i	$-0.773239\pi$
$491$		−	2.16823e24i		−	1.30729i	0.756802	−	0.653644i	$-0.226761\pi$
$492$	−3.13326e23	+	2.06910e23i	−0.185486	+	0.122488i
$493$	−7.48669e23			−0.435178
$494$	−4.00834e23	+	7.45044e23i	−0.228782	+	0.425245i
$495$		−	5.24514e22i		−	0.0293975i
$496$	1.17810e24	+	5.03016e23i	0.648405	+	0.276852i
$497$	1.62132e24			0.876316
$498$	2.56012e23	+	1.37735e23i	0.135893	+	0.0731104i
$499$		−	1.77378e24i		−	0.924688i	−0.886701	−	0.462344i	$-0.847008\pi$
$499$		−	1.77378e24i		−	0.924688i	0.886701	−	0.462344i	$-0.152992\pi$
$500$	7.91838e23	+	1.19909e24i	0.405421	+	0.613934i
$501$	1.55179e24			0.780358
$502$	1.62537e24	−	3.02112e24i	0.802819	−	1.49223i
$503$			3.77156e24i			1.82982i	0.403656	+	0.914911i	$0.367739\pi$
$503$			3.77156e24i			1.82982i	−0.403656	+	0.914911i	$0.632261\pi$
$504$	−4.23759e23	+	3.82603e22i	−0.201950	+	0.0182336i
$505$	−1.34913e24			−0.631582
$506$	4.68877e23	+	2.52256e23i	0.215627	+	0.116008i
$507$		−	2.56642e24i		−	1.15946i
$508$	3.00861e24	−	1.98678e24i	1.33534	−	0.881814i
$509$	1.49513e24			0.651956			0.325978	−	0.945377i	$-0.394306\pi$
$509$	1.49513e24			0.651956			0.325978	+	0.945377i	$0.394306\pi$
$510$	8.31442e22	−	1.54543e23i	0.0356205	−	0.0662091i
$511$		−	1.91067e22i		−	0.00804262i
$512$	6.45222e23	+	2.33017e24i	0.266858	+	0.963736i
$513$	1.31843e23			0.0535799
$514$	1.37368e24	+	7.39040e23i	0.548551	+	0.295121i
$515$		−	1.54820e24i		−	0.607522i
$516$	7.24237e23	+	1.09672e24i	0.279276	+	0.422911i
$517$	−7.22089e23			−0.273638
$518$	−5.81648e23	+	1.08113e24i	−0.216617	+	0.402633i
$519$			9.15444e23i			0.335062i
$520$	1.73345e23	+	1.91992e24i	0.0623565	+	0.690642i
$521$	−3.98236e24			−1.40799			−0.703997	−	0.710203i	$-0.748603\pi$
$521$	−3.98236e24			−1.40799			−0.703997	+	0.710203i	$0.748603\pi$
$522$	−1.12865e24	−	6.07214e23i	−0.392215	−	0.211012i
$523$		−	5.10304e24i		−	1.74307i	−0.490336	−	0.871533i	$-0.663126\pi$
$523$		−	5.10304e24i		−	1.74307i	0.490336	−	0.871533i	$-0.336874\pi$
$524$	−1.97466e24	+	1.30400e24i	−0.662995	+	0.437819i
$525$	−8.94041e23			−0.295069
$526$	9.22513e23	−	1.71470e24i	0.299296	−	0.556311i
$527$		−	7.19992e23i		−	0.229632i
$528$	1.59497e23	−	3.73553e23i	0.0500089	−	0.117124i
$529$	−7.53151e23			−0.232157
$530$	3.54990e23	+	1.90985e23i	0.107580	+	0.0578783i
$531$			1.37071e24i			0.408409i
$532$	3.18575e23	+	4.82423e23i	0.0933271	+	0.141326i
$533$	−2.31826e24			−0.667756
$534$	−7.74009e23	+	1.43868e24i	−0.219217	+	0.407466i
$535$			1.75044e24i			0.487488i
$536$	−6.97038e24	+	6.29340e23i	−1.90886	+	0.172346i
$537$	3.42643e24			0.922727
$538$	−4.78744e24	−	2.57565e24i	−1.26784	−	0.682096i
$539$		−	5.33555e23i		−	0.138957i
$540$	2.50687e23	−	1.65545e23i	0.0642077	−	0.0424006i
$541$	−5.27585e24			−1.32898			−0.664488	−	0.747299i	$-0.731350\pi$
$541$	−5.27585e24			−1.32898			−0.664488	+	0.747299i	$0.731350\pi$
$542$	2.03345e23	−	3.77964e23i	0.0503778	−	0.0936390i
$543$		−	2.99300e24i		−	0.729304i
$544$	1.06209e24	−	8.47808e23i	0.254548	−	0.203192i
$545$	1.18670e24			0.279750
$546$	−2.31343e24	−	1.24463e24i	−0.536443	−	0.288607i
$547$		−	2.36598e24i		−	0.539666i	−0.962907	−	0.269833i	$-0.913032\pi$
$547$		−	2.36598e24i		−	0.539666i	0.962907	−	0.269833i	$-0.0869684\pi$
$548$	−2.69714e24	−	4.08431e24i	−0.605172	−	0.916418i
$549$	2.59392e24			0.572539
$550$	4.04365e23	−	7.51607e23i	0.0878031	−	0.163203i
$551$			1.74139e24i			0.371990i
$552$	2.74214e23	+	3.03711e24i	0.0576287	+	0.638277i
$553$	−1.27624e23			−0.0263879
$554$	1.82882e24	+	9.83908e23i	0.372035	+	0.200155i
$555$		−	8.66796e23i		−	0.173492i
$556$	6.92422e24	−	4.57252e24i	1.36363	−	0.900497i
$557$	4.62411e24			0.896049			0.448024	−	0.894021i	$-0.352128\pi$
$557$	4.62411e24			0.896049			0.448024	+	0.894021i	$0.352128\pi$
$558$	5.83955e23	−	1.08542e24i	0.111345	−	0.206961i
$559$			8.11451e24i			1.52250i
$560$	1.21148e24	+	5.17268e23i	0.223678	+	0.0955043i
$561$	−2.28296e23			−0.0414794
$562$	2.48967e24	+	1.33944e24i	0.445158	+	0.239495i
$563$			2.45059e24i			0.431216i	0.976480	+	0.215608i	$0.0691734\pi$
$563$			2.45059e24i			0.431216i	−0.976480	+	0.215608i	$0.930827\pi$
$564$	−2.27903e24	−	3.45116e24i	−0.394673	−	0.597658i
$565$	2.40436e24			0.409792
$566$	1.86670e24	−	3.46970e24i	0.313132	−	0.582028i
$567$			4.09387e23i			0.0675906i
$568$	−8.82885e24	+	7.97138e23i	−1.43473	+	0.129538i
$569$	3.31024e24			0.529479			0.264739	−	0.964320i	$-0.414714\pi$
$569$	3.31024e24			0.529479			0.264739	+	0.964320i	$0.414714\pi$
$570$	−3.59463e23	−	1.93392e23i	−0.0565954	−	0.0304484i
$571$			1.14964e25i			1.78171i	0.454288	+	0.890855i	$0.349894\pi$
$571$			1.14964e25i			1.78171i	−0.454288	+	0.890855i	$0.650106\pi$
$572$	2.09268e24	−	1.38194e24i	0.319256	−	0.210826i
$573$	−4.46179e24			−0.670065
$574$	−7.50547e23	+	1.39507e24i	−0.110961	+	0.206247i
$575$			6.40766e24i			0.932586i
$576$	2.28876e24	−	4.16691e23i	0.327943	−	0.0597052i
$577$	9.31559e24			1.31410			0.657050	−	0.753847i	$-0.271804\pi$
$577$	9.31559e24			1.31410			0.657050	+	0.753847i	$0.271804\pi$
$578$	5.66822e24	+	3.04951e24i	0.787220	+	0.423525i
$579$		−	1.21922e24i		−	0.166715i
$580$	2.18651e24	+	3.31106e24i	0.294375	+	0.445775i
$581$	1.22651e24			0.162587
$582$	−1.04186e24	+	1.93653e24i	−0.135988	+	0.252766i
$583$		−	5.24403e23i		−	0.0673981i
$584$	9.39400e21	+	1.04045e23i	0.00118887	+	0.0131676i
$585$	1.85480e24			0.231150
$586$	−1.27211e24	−	6.84397e23i	−0.156116	−	0.0839904i
$587$		−	1.05678e25i		−	1.27715i	−0.769558	−	0.638577i	$-0.779524\pi$
$587$		−	1.05678e25i		−	1.27715i	0.769558	−	0.638577i	$-0.220476\pi$
$588$	2.55008e24	−	1.68398e24i	0.303499	−	0.200420i
$589$	−1.67469e24			−0.196289
$590$	2.01060e24	−	3.73716e24i	0.232090	−	0.431394i
$591$			6.11238e24i			0.694901i
$592$	2.63580e24	−	6.17323e24i	0.295133	−	0.691221i
$593$	6.22195e24			0.686174			0.343087	−	0.939304i	$-0.388527\pi$
$593$	6.22195e24			0.686174			0.343087	+	0.939304i	$0.388527\pi$
$594$	−3.44165e23	−	1.85161e23i	−0.0373843	−	0.0201128i
$595$		−	7.40391e23i		−	0.0792152i
$596$	−9.78940e24	−	1.48242e25i	−1.03167	−	1.56227i
$597$	−3.25147e24			−0.337529
$598$	−8.92035e24	+	1.65806e25i	−0.912161	+	1.69546i
$599$			4.37749e24i			0.440945i	0.975393	+	0.220472i	$0.0707599\pi$
$599$			4.37749e24i			0.440945i	−0.975393	+	0.220472i	$0.929240\pi$
$600$	4.86848e24	−	4.39564e23i	0.483095	−	0.0436176i
$601$	−4.00184e24			−0.391192			−0.195596	−	0.980685i	$-0.562664\pi$
$601$	−4.00184e24			−0.391192			−0.195596	+	0.980685i	$0.562664\pi$
$602$	4.88309e24	+	2.62711e24i	0.470247	+	0.252993i
$603$			6.73396e24i			0.638874i
$604$	−4.89979e23	+	3.23566e23i	−0.0457979	+	0.0302434i
$605$	−4.13042e24			−0.380361
$606$	−4.76262e24	+	8.85243e24i	−0.432108	+	0.803173i
$607$			3.02929e24i			0.270797i	0.990791	+	0.135398i	$0.0432314\pi$
$607$			3.02929e24i			0.270797i	−0.990791	+	0.135398i	$0.956769\pi$
$608$	−1.97198e24	−	2.47039e24i	−0.173688	−	0.217587i
$609$	−5.40717e24			−0.469261
$610$	−7.07216e24	−	3.80483e24i	−0.604761	−	0.325362i
$611$		−	2.55347e25i		−	2.15159i
$612$	−7.20538e23	−	1.09112e24i	−0.0598266	−	0.0905961i
$613$	−4.48281e24			−0.366780			−0.183390	−	0.983040i	$-0.558707\pi$
$613$	−4.48281e24			−0.366780			−0.183390	+	0.983040i	$0.558707\pi$
$614$	1.31167e24	−	2.43805e24i	0.105757	−	0.196575i
$615$		−	1.11850e24i		−	0.0888708i
$616$	−1.54097e23	−	1.70673e24i	−0.0120661	−	0.133640i
$617$	−8.37028e24			−0.645913			−0.322956	−	0.946414i	$-0.604677\pi$
$617$	−8.37028e24			−0.645913			−0.322956	+	0.946414i	$0.604677\pi$
$618$	−1.01587e25	−	5.46538e24i	−0.772576	−	0.415647i
$619$		−	2.43340e25i		−	1.82389i	−0.410313	−	0.911945i	$-0.634581\pi$
$619$		−	2.43340e25i		−	1.82389i	0.410313	−	0.911945i	$-0.365419\pi$
$620$	−3.18424e24	+	2.10276e24i	−0.235223	+	0.155334i
$621$	2.93410e24			0.213625
$622$	−6.78224e24	+	1.26064e25i	−0.486698	+	0.904642i
$623$			6.89247e24i			0.487508i
$624$	1.32097e25	+	5.64018e24i	0.920940	+	0.393216i
$625$	7.94530e24			0.545997
$626$	1.64066e25	+	8.82674e24i	1.11134	+	0.597904i
$627$			5.31011e23i			0.0354565i
$628$	2.84935e24	+	4.31480e24i	0.187546	+	0.284004i
$629$	−3.77275e24			−0.244795
$630$	6.00500e23	−	1.11617e24i	0.0384103	−	0.0713945i
$631$		−	1.21891e25i		−	0.768613i	−0.923206	−	0.384307i	$-0.874441\pi$
$631$		−	1.21891e25i		−	0.768613i	0.923206	−	0.384307i	$-0.125559\pi$
$632$	6.94972e23	−	6.27475e22i	0.0432030	−	0.00390070i
$633$	−1.77468e25			−1.08764
$634$	2.81714e23	+	1.51562e23i	0.0170218	+	0.00915773i
$635$			1.07400e25i			0.639795i
$636$	2.50633e24	−	1.65510e24i	0.147206	−	0.0972097i
$637$	1.88677e25			1.09261
$638$	2.44561e24	−	4.54573e24i	0.139637	−	0.259548i
$639$			8.52940e24i			0.480188i
$640$	−6.85138e24	−	2.22113e24i	−0.380328	−	0.123298i
$641$	−1.10097e25			−0.602633			−0.301316	−	0.953524i	$-0.597426\pi$
$641$	−1.10097e25			−0.602633			−0.301316	+	0.953524i	$0.597426\pi$
$642$	1.14857e25	+	6.17933e24i	0.619931	+	0.333523i
$643$		−	2.74564e25i		−	1.46132i	−0.682741	−	0.730660i	$-0.739212\pi$
$643$		−	2.74564e25i		−	1.46132i	0.682741	−	0.730660i	$-0.260788\pi$
$644$	7.08972e24	+	1.07361e25i	0.372097	+	0.563471i
$645$	−3.91503e24			−0.202627
$646$	−8.41742e23	+	1.56457e24i	−0.0429622	+	0.0798552i
$647$		−	1.12269e25i		−	0.565096i	−0.959253	−	0.282548i	$-0.908820\pi$
$647$		−	1.12269e25i		−	0.565096i	0.959253	−	0.282548i	$-0.0911796\pi$
$648$	−2.01279e23	−	2.22931e24i	−0.00999134	−	0.110661i
$649$	−5.52066e24			−0.270264
$650$	2.65786e25	+	1.42993e25i	1.28325	+	0.690390i
$651$		−	5.20006e24i		−	0.247617i
$652$	−5.69611e24	+	3.76151e24i	−0.267516	+	0.176658i
$653$	−2.75606e25			−1.27665			−0.638323	−	0.769768i	$-0.720372\pi$
$653$	−2.75606e25			−1.27665			−0.638323	+	0.769768i	$0.720372\pi$
$654$	4.18921e24	−	7.78663e24i	0.191396	−	0.355754i
$655$		−	7.04905e24i		−	0.317657i
$656$	3.40119e24	−	7.96582e24i	0.151181	−	0.354076i
$657$	1.00516e23			0.00440705
$658$	−1.53661e25	−	8.26698e24i	−0.664555	−	0.357531i
$659$			3.37242e25i			1.43871i	0.694643	+	0.719355i	$0.255562\pi$
$659$			3.37242e25i			1.43871i	−0.694643	+	0.719355i	$0.744438\pi$
$660$	6.66747e23	+	1.00966e24i	0.0280586	+	0.0424894i
$661$	1.78663e25			0.741689			0.370844	−	0.928695i	$-0.379068\pi$
$661$	1.78663e25			0.741689			0.370844	+	0.928695i	$0.379068\pi$
$662$	−3.65913e24	+	6.80135e24i	−0.149850	+	0.278531i
$663$		−	8.07307e24i		−	0.326150i
$664$	−6.67894e24	+	6.03027e23i	−0.266192	+	0.0240339i
$665$	−1.72213e24			−0.0677129
$666$	−5.68758e24	−	3.05992e24i	−0.220627	−	0.118698i
$667$			3.87536e25i			1.48313i
$668$	−2.98712e25	+	1.97259e25i	−1.12788	+	0.744816i
$669$	1.59290e25			0.593407
$670$	9.87757e24	−	1.83598e25i	0.363059	−	0.674829i
$671$			1.04472e25i			0.378877i
$672$	7.67080e24	−	6.12320e24i	0.274484	−	0.219106i
$673$	2.52549e25			0.891684			0.445842	−	0.895112i	$-0.352904\pi$
$673$	2.52549e25			0.891684			0.445842	+	0.895112i	$0.352904\pi$
$674$	−1.58362e25	−	8.51990e24i	−0.551712	−	0.296821i
$675$		−	4.70336e24i		−	0.161687i
$676$	3.26236e25	+	4.94024e25i	1.10665	+	1.67582i
$677$	2.97567e25			0.996062			0.498031	−	0.867159i	$-0.334057\pi$
$677$	2.97567e25			0.996062			0.498031	+	0.867159i	$0.334057\pi$
$678$	8.48776e24	−	1.57765e25i	0.280366	−	0.521126i
$679$			9.27763e24i			0.302419i
$680$	3.64021e23	+	4.03178e24i	0.0117097	+	0.129693i
$681$	−4.47059e24			−0.141919
$682$	4.37161e24	+	2.35193e24i	0.136956	+	0.0736827i
$683$		−	1.39025e25i		−	0.429841i	−0.976632	−	0.214920i	$-0.931051\pi$
$683$		−	1.39025e25i		−	0.429841i	0.976632	−	0.214920i	$-0.0689492\pi$
$684$	−2.53792e24	+	1.67596e24i	−0.0774414	+	0.0511396i
$685$	1.45800e25			0.439079
$686$	1.58053e25	−	2.93778e25i	0.469770	−	0.873177i
$687$		−	7.34686e24i		−	0.215522i
$688$	−2.78824e25	−	1.19050e25i	−0.807298	−	0.344695i
$689$	1.85441e25			0.529947
$690$	−7.99966e24	−	4.30383e24i	−0.225647	−	0.121398i
$691$		−	4.29975e24i		−	0.119713i	−0.998207	−	0.0598564i	$-0.980936\pi$
$691$		−	4.29975e24i		−	0.119713i	0.998207	−	0.0598564i	$-0.0190643\pi$
$692$	−1.16369e25	−	1.76218e25i	−0.319802	−	0.484280i
$693$	−1.64884e24			−0.0447280
$694$	−1.38679e25	+	2.57767e25i	−0.371342	+	0.690226i
$695$			2.47178e25i			0.653351i
$696$	2.94446e25	−	2.65849e24i	0.768286	−	0.0693669i
$697$	−4.86829e24			−0.125395
$698$	−1.74176e25	−	9.37070e24i	−0.442884	−	0.238272i
$699$			1.65821e25i			0.416240i
$700$	1.72099e25	−	1.13648e25i	0.426476	−	0.281630i
$701$	−3.24246e25			−0.793254			−0.396627	−	0.917980i	$-0.629819\pi$
$701$	−3.24246e25			−0.793254			−0.396627	+	0.917980i	$0.629819\pi$
$702$	6.54773e24	−	1.21705e25i	0.158145	−	0.293950i
$703$			8.77534e24i			0.209250i
$704$	1.67826e24	+	9.21819e24i	0.0395099	+	0.217016i
$705$	1.23198e25			0.286353
$706$	−5.66551e25	−	3.04805e25i	−1.30016	−	0.699487i
$707$			4.24106e25i			0.960948i
$708$	−1.74241e25	−	2.63855e25i	−0.389808	−	0.590290i
$709$	9.61657e24			0.212424			0.106212	−	0.994343i	$-0.466128\pi$
$709$	9.61657e24			0.212424			0.106212	+	0.994343i	$0.466128\pi$
$710$	1.25112e25	−	2.32549e25i	0.272881	−	0.507212i
$711$		−	6.71401e23i		−	0.0144596i
$712$	−3.38875e24	−	3.75328e25i	−0.0720642	−	0.798161i
$713$	−3.72692e25			−0.782608
$714$	−4.85815e24	−	2.61369e24i	−0.100737	−	0.0541964i
$715$			7.47038e24i			0.152964i
$716$	−6.59570e25	+	4.35558e25i	−1.33366	+	0.880701i
$717$	2.62443e24			0.0524038
$718$	4.55506e25	−	8.46664e25i	0.898202	−	1.66952i
$719$		−	2.85213e25i		−	0.555404i	−0.960667	−	0.277702i	$-0.910427\pi$
$719$		−	2.85213e25i		−	0.555404i	0.960667	−	0.277702i	$-0.0895727\pi$
$720$	−2.72123e24	+	6.37331e24i	−0.0523327	+	0.122567i
$721$	−4.86687e25			−0.924341
$722$	−4.33106e25	−	2.33011e25i	−0.812380	−	0.437061i
$723$		−	2.85643e25i		−	0.529150i
$724$	3.80462e25	+	5.76138e25i	0.696088	+	1.05409i
$725$	6.21219e25			1.12254
$726$	−1.45810e25	+	2.71022e25i	−0.260230	+	0.483699i
$727$		−	2.62858e25i		−	0.463352i	−0.972793	−	0.231676i	$-0.925579\pi$
$727$		−	2.62858e25i		−	0.463352i	0.972793	−	0.231676i	$-0.0744210\pi$
$728$	6.03538e25	−	5.44922e24i	1.05081	−	0.0948750i
$729$	−2.15369e24			−0.0370370
$730$	−2.74051e23	−	1.47440e23i	−0.00465507	−	0.00250443i
$731$			1.70403e25i			0.285904i
$732$	−4.99316e25	+	3.29731e25i	−0.827514	+	0.546462i
$733$	−9.87148e25			−1.61602			−0.808010	−	0.589169i	$-0.799455\pi$
$733$	−9.87148e25			−1.61602			−0.808010	+	0.589169i	$0.799455\pi$
$734$	−8.76231e24	+	1.62868e25i	−0.141695	+	0.263373i
$735$			9.10316e24i			0.145414i
$736$	−4.38854e25	−	5.49772e25i	−0.692500	−	0.867525i
$737$	−2.71216e25			−0.422774
$738$	−7.33914e24	−	3.94847e24i	−0.113016	−	0.0608025i
$739$			8.52929e25i			1.29752i	0.760995	+	0.648758i	$0.224711\pi$
$739$			8.52929e25i			1.29752i	−0.760995	+	0.648758i	$0.775289\pi$
$740$	1.10185e25	+	1.66854e25i	0.165591	+	0.250756i
$741$	−1.87778e25			−0.278792
$742$	6.00373e24	−	1.11593e25i	0.0880614	−	0.163683i
$743$		−	5.59770e25i		−	0.811166i	−0.914058	−	0.405583i	$-0.867068\pi$
$743$		−	5.59770e25i		−	0.811166i	0.914058	−	0.405583i	$-0.132932\pi$
$744$	2.55666e24	+	2.83168e25i	0.0366030	+	0.405404i
$745$	5.29188e25			0.748521
$746$	−5.77831e24	−	3.10874e24i	−0.0807517	−	0.0434445i
$747$			6.45241e24i			0.0890916i
$748$	4.39458e24	−	2.90203e24i	0.0599519	−	0.0395902i
$749$	5.50263e25			0.741710
$750$	−1.51107e25	+	2.80867e25i	−0.201249	+	0.374067i
$751$		−	6.69906e25i		−	0.881565i	−0.897614	−	0.440782i	$-0.854701\pi$
$751$		−	6.69906e25i		−	0.881565i	0.897614	−	0.440782i	$-0.145299\pi$
$752$	8.77403e25	+	3.74627e25i	1.14088	+	0.487123i
$753$	7.61431e25			0.978308
$754$	1.60747e26	+	8.64823e25i	2.04081	+	1.09796i
$755$		−	1.74911e24i		−	0.0219429i
$756$	−5.20401e24	−	7.88049e24i	−0.0645122	−	0.0976916i
$757$	−6.75637e25			−0.827657			−0.413829	−	0.910355i	$-0.635809\pi$
$757$	−6.75637e25			−0.827657			−0.413829	+	0.910355i	$0.635809\pi$
$758$	−3.89568e25	+	7.24103e25i	−0.471585	+	0.876551i
$759$			1.18174e25i			0.141366i
$760$	9.37783e24	−	8.46704e23i	0.110861	−	0.0100094i
$761$	6.83608e25			0.798629			0.399315	−	0.916814i	$-0.369248\pi$
$761$	6.83608e25			0.798629			0.399315	+	0.916814i	$0.369248\pi$
$762$	7.04717e25	+	3.79139e25i	0.813617	+	0.437727i
$763$		−	3.73045e25i		−	0.425638i
$764$	8.58871e25	−	5.67169e25i	0.968474	−	0.639547i
$765$	3.89503e24			0.0434069
$766$	−1.64770e25	+	3.06264e25i	−0.181476	+	0.337316i
$767$		−	1.95223e26i		−	2.12507i
$768$	−3.87606e25	+	3.71152e25i	−0.417004	+	0.399301i
$769$	4.86260e25			0.517049			0.258524	−	0.966005i	$-0.416764\pi$
$769$	4.86260e25			0.517049			0.258524	+	0.966005i	$0.416764\pi$
$770$	4.49547e24	+	2.41857e24i	0.0472453	+	0.0254180i
$771$			3.46216e25i			0.359632i
$772$	1.54984e25	+	2.34694e25i	0.159122	+	0.240961i
$773$	6.84463e25			0.694600			0.347300	−	0.937754i	$-0.387099\pi$
$773$	6.84463e25			0.694600			0.347300	+	0.937754i	$0.387099\pi$
$774$	−1.38206e25	+	2.56889e25i	−0.138631	+	0.257677i
$775$			5.97424e25i			0.592335i
$776$	−4.56144e24	−	5.05211e25i	−0.0447040	−	0.495128i
$777$	−2.72483e25			−0.263967
$778$	6.88901e25	+	3.70629e25i	0.659691	+	0.354914i
$779$			1.13235e25i			0.107188i
$780$	−3.57040e25	+	2.35777e25i	−0.334091	+	0.220623i
$781$	−3.43529e25			−0.317764
$782$	−1.87325e25	+	3.48187e25i	−0.171291	+	0.318385i
$783$		−	2.84460e25i		−	0.257137i
$784$	−2.76814e25	+	6.48317e25i	−0.247368	+	0.579353i
$785$	−1.54028e25			−0.136073
$786$	−4.62531e25	−	2.48842e25i	−0.403960	−	0.217331i
$787$			1.12319e26i			0.969795i	0.874571	+	0.484897i	$0.161143\pi$
$787$			1.12319e26i			0.969795i	−0.874571	+	0.484897i	$0.838857\pi$
$788$	−7.76988e25	−	1.17660e26i	−0.663252	−	1.00437i
$789$	4.32167e25			0.364719
$790$	−9.84830e23	+	1.83054e24i	−0.00821708	+	0.0152734i
$791$		−	7.55826e25i		−	0.623495i
$792$	8.97873e24	−	8.10670e23i	0.0732299	−	0.00661176i
$793$	−3.69438e26			−2.97908
$794$	2.96430e25	+	1.59479e25i	0.236340	+	0.127151i
$795$			8.94701e24i			0.0705300i
$796$	6.25892e25	−	4.13317e25i	0.487845	−	0.322156i
$797$	−1.88207e26			−1.45048			−0.725240	−	0.688497i	$-0.758271\pi$
$797$	−1.88207e26			−1.45048			−0.725240	+	0.688497i	$0.758271\pi$
$798$	−6.07939e24	+	1.13000e25i	−0.0463270	+	0.0861094i
$799$		−	5.36223e25i		−	0.404040i
$800$	−8.81282e25	+	7.03481e25i	−0.656606	+	0.524134i
$801$	−3.62598e25			−0.267136
$802$	6.22861e25	+	3.35100e25i	0.453756	+	0.244121i
$803$			4.04838e23i			0.00291636i
$804$	−8.56002e25	−	1.29625e26i	−0.609776	−	0.923391i
$805$	−3.83251e25			−0.269973
$806$	−8.31697e25	+	1.54590e26i	−0.579362	+	1.07688i
$807$		−	1.20661e26i		−	0.831196i
$808$	−2.08516e25	−	2.30946e26i	−0.142049	−	1.57329i
$809$	2.61732e26			1.76327			0.881637	−	0.471927i	$-0.156442\pi$
$809$	2.61732e26			1.76327			0.881637	+	0.471927i	$0.156442\pi$
$810$	5.87192e24	+	3.15910e24i	0.0391215	+	0.0210474i
$811$			1.22176e26i			0.805007i	0.915418	+	0.402504i	$0.131860\pi$
$811$			1.22176e26i			0.805007i	−0.915418	+	0.402504i	$0.868140\pi$
$812$	1.04085e26	−	6.87345e25i	0.678243	−	0.447889i
$813$	9.52604e24			0.0613900
$814$	1.23241e25	−	2.29072e25i	0.0785481	−	0.146000i
$815$		−	2.03337e25i		−	0.128174i
$816$	2.77400e25	+	1.18442e25i	0.172940	+	0.0738406i
$817$	3.96353e25			0.244390
$818$	−2.21527e26	−	1.19182e26i	−1.35097	−	0.726824i
$819$		−	5.83068e25i		−	0.351693i
$820$	1.42180e25	+	2.15305e25i	0.0848232	+	0.128449i
$821$	−6.23123e25			−0.367693			−0.183847	−	0.982955i	$-0.558855\pi$
$821$	−6.23123e25			−0.367693			−0.183847	+	0.982955i	$0.558855\pi$
$822$	5.14696e25	−	9.56683e25i	0.300403	−	0.558369i
$823$			2.84559e25i			0.164276i	0.996621	+	0.0821381i	$0.0261748\pi$
$823$			2.84559e25i			0.164276i	−0.996621	+	0.0821381i	$0.973825\pi$
$824$	2.65024e26	−	2.39284e25i	1.51335	−	0.136637i
$825$	1.89432e25			0.106996
$826$	−1.17480e26	−	6.32043e25i	−0.656362	−	0.353123i
$827$			1.40802e26i			0.778141i	0.921208	+	0.389071i	$0.127204\pi$
$827$			1.40802e26i			0.778141i	−0.921208	+	0.389071i	$0.872796\pi$
$828$	−5.64800e25	+	3.72975e25i	−0.308761	+	0.203895i
$829$	2.89570e26			1.56590			0.782949	−	0.622086i	$-0.213715\pi$
$829$	2.89570e26			1.56590			0.782949	+	0.622086i	$0.213715\pi$
$830$	9.46458e24	−	1.75921e25i	0.0506289	−	0.0941056i
$831$			4.60928e25i			0.243907i
$832$	−3.25976e26	+	5.93472e25i	−1.70638	+	0.310663i
$833$	3.96217e25			0.205177
$834$	1.62188e26	+	8.72575e25i	0.830856	+	0.447001i
$835$		−	1.06633e26i		−	0.540397i
$836$	−6.75006e24	−	1.02217e25i	−0.0338416	−	0.0512468i
$837$	2.73564e25			0.135684
$838$	−7.11941e25	+	1.32331e26i	−0.349340	+	0.649329i
$839$			1.92196e26i			0.933013i	0.884518	+	0.466506i	$0.154488\pi$
$839$			1.92196e26i			0.933013i	−0.884518	+	0.466506i	$0.845512\pi$
$840$	2.62910e24	+	2.91191e25i	0.0126268	+	0.139850i
$841$	1.65257e26			0.785226
$842$	−2.49215e26	−	1.34078e26i	−1.17156	−	0.630302i
$843$			6.27485e25i			0.291847i
$844$	3.41617e26	−	2.25592e26i	1.57202	−	1.03811i
$845$	−1.76355e26			−0.802927
$846$	4.34908e25	−	8.08377e25i	0.195913	−	0.364150i
$847$			1.29842e26i			0.578716i
$848$	−2.72066e25	+	6.37196e25i	−0.119981	+	0.281003i
$849$	8.74489e25			0.381579
$850$	5.58143e25	+	3.00281e25i	0.240977	+	0.129646i
$851$			1.95290e26i			0.834286i
$852$	−1.08423e26	−	1.64187e26i	−0.458318	−	0.694036i
$853$	2.05278e26			0.858621			0.429310	−	0.903157i	$-0.358757\pi$
$853$	2.05278e26			0.858621			0.429310	+	0.903157i	$0.358757\pi$
$854$	−1.19607e26	+	2.22318e26i	−0.495035	+	0.920139i
$855$		−	9.05976e24i		−	0.0371041i
$856$	−2.99645e26	+	2.70542e25i	−1.21435	+	0.109641i
$857$	−2.27209e25			−0.0911166			−0.0455583	−	0.998962i	$-0.514507\pi$
$857$	−2.27209e25			−0.0911166			−0.0455583	+	0.998962i	$0.514507\pi$
$858$	4.90177e25	+	2.63716e25i	0.194521	+	0.104653i
$859$			3.22811e26i			1.26768i	0.773464	+	0.633840i	$0.218522\pi$
$859$			3.22811e26i			1.26768i	−0.773464	+	0.633840i	$0.781478\pi$
$860$	7.53623e25	−	4.97667e25i	0.292865	−	0.193398i
$861$	−3.51607e25			−0.135216
$862$	1.84829e26	−	3.43547e26i	0.703403	−	1.30744i
$863$			1.81882e26i			0.685003i	0.939517	+	0.342501i	$0.111274\pi$
$863$			1.81882e26i			0.685003i	−0.939517	+	0.342501i	$0.888726\pi$
$864$	3.22128e25	+	4.03544e25i	0.120062	+	0.150407i
$865$	6.29057e25			0.232031
$866$	9.27230e25	+	4.98851e25i	0.338475	+	0.182100i
$867$			1.42859e26i			0.516104i
$868$	6.61017e25	+	1.00099e26i	0.236339	+	0.357891i
$869$	2.70413e24			0.00956862
$870$	−4.17253e25	+	7.75562e25i	−0.146126	+	0.271609i
$871$		−	9.59084e26i		−	3.32425i
$872$	1.83411e25	+	2.03141e26i	0.0629184	+	0.696865i
$873$	−4.88076e25			−0.165714
$874$	8.09876e25	+	4.35714e25i	0.272155	+	0.146419i
$875$			1.34559e26i			0.447549i
$876$	−1.93489e24	+	1.27773e24i	−0.00636969	+	0.00420633i
$877$	−1.35504e26			−0.441524			−0.220762	−	0.975328i	$-0.570854\pi$
$877$	−1.35504e26			−0.441524			−0.220762	+	0.975328i	$0.570854\pi$
$878$	1.57582e26	−	2.92902e26i	0.508223	−	0.944652i
$879$		−	3.20618e25i		−	0.102350i
$880$	−2.56691e25	−	1.09600e25i	−0.0811085	−	0.0346311i
$881$	−1.78232e26			−0.557447			−0.278723	−	0.960371i	$-0.589911\pi$
$881$	−1.78232e26			−0.557447			−0.278723	+	0.960371i	$0.589911\pi$
$882$	5.97314e25	+	3.21355e25i	0.184921	+	0.0994874i
$883$			4.16578e25i			0.127659i	0.997961	+	0.0638293i	$0.0203313\pi$
$883$			4.16578e25i			0.127659i	−0.997961	+	0.0638293i	$0.979669\pi$
$884$	1.02623e26	+	1.55403e26i	0.311295	+	0.471398i
$885$	9.41898e25			0.282823
$886$	−3.70863e25	+	6.89335e25i	−0.110233	+	0.204893i
$887$		−	1.73090e25i		−	0.0509283i	−0.999676	−	0.0254642i	$-0.991894\pi$
$887$		−	1.73090e25i		−	0.0509283i	0.999676	−	0.0254642i	$-0.00810637\pi$
$888$	1.48380e26	−	1.33969e25i	0.432174	−	0.0390200i
$889$	3.37619e26			0.973444
$890$	9.88601e25	+	5.31868e25i	0.282170	+	0.151808i
$891$		−	8.67420e24i		−	0.0245092i
$892$	−3.06625e26	+	2.02485e26i	−0.857677	+	0.566381i
$893$	−1.24724e26			−0.345372
$894$	1.86811e26	−	3.47233e26i	0.512113	−	0.951881i
$895$		−	2.35451e26i		−	0.638988i
$896$	−6.98227e25	+	2.15378e26i	−0.187596	+	0.578667i
$897$	−4.17889e26			−1.11155
$898$	−3.46883e26	−	1.86623e26i	−0.913473	−	0.491450i
$899$			3.61323e26i			0.942016i
$900$	5.97877e25	+	9.05373e25i	0.154323	+	0.233693i
$901$	3.89421e25			0.0995167
$902$	1.59028e25	−	2.95591e25i	0.0402360	−	0.0747880i
$903$			1.23071e26i			0.308295i
$904$	3.71609e25	+	4.11583e26i	0.0921660	+	1.02080i
$905$	−2.05667e26			−0.505043
$906$	−1.14770e25	−	6.17462e24i	−0.0279044	−	0.0150126i
$907$		−	3.07527e26i		−	0.740317i	−0.928969	−	0.370158i	$-0.879303\pi$
$907$		−	3.07527e26i		−	0.740317i	0.928969	−	0.370158i	$-0.120697\pi$
$908$	8.60566e25	−	5.68289e25i	0.205122	−	0.135455i
$909$	−2.23113e26			−0.526562
$910$	−8.55261e25	+	1.58970e26i	−0.199860	+	0.371486i
$911$		−	5.54614e26i		−	1.28329i	−0.767001	−	0.641646i	$-0.778252\pi$
$911$		−	5.54614e26i		−	1.28329i	0.767001	−	0.641646i	$-0.221748\pi$
$912$	2.75494e25	−	6.45226e25i	0.0631188	−	0.147829i
$913$	−2.59877e25			−0.0589563
$914$	6.53457e25	+	3.51560e25i	0.146792	+	0.0789740i
$915$		−	1.78244e26i		−	0.396483i
$916$	9.33912e25	+	1.41423e26i	0.205706	+	0.311503i
$917$	−2.21591e26			−0.483313
$918$	1.37501e25	−	2.55577e25i	0.0296975	−	0.0551998i
$919$			2.73036e26i			0.583957i	0.956425	+	0.291978i	$0.0943135\pi$
$919$			2.73036e26i			0.583957i	−0.956425	+	0.291978i	$0.905686\pi$
$920$	2.08699e26	−	1.88429e25i	0.442007	−	0.0399078i
$921$	6.14476e25			0.128875
$922$	1.01892e26	+	5.48182e25i	0.211623	+	0.113854i
$923$		−	1.21480e27i		−	2.49856i
$924$	3.17394e25	−	2.09596e25i	0.0646473	−	0.0426909i
$925$	3.13050e26			0.631448
$926$	1.36850e26	−	2.54368e26i	0.273368	−	0.508117i
$927$		−	2.56035e26i		−	0.506503i
$928$	−5.33001e26	+	4.25466e26i	−1.04423	+	0.833554i
$929$	−1.77547e25			−0.0344487			−0.0172243	−	0.999852i	$-0.505483\pi$
$929$	−1.77547e25			−0.0344487			−0.0172243	+	0.999852i	$0.505483\pi$
$930$	−7.45856e25	−	4.01271e25i	−0.143321	−	0.0771066i
$931$		−	9.21593e25i		−	0.175385i
$932$	−2.10786e26	−	3.19196e26i	−0.397282	−	0.601609i
$933$	−3.17726e26			−0.593086
$934$	−7.45970e25	+	1.38656e26i	−0.137911	+	0.256340i
$935$			1.56876e25i			0.0287245i
$936$	2.86671e25	+	3.17508e26i	0.0519878	+	0.575801i
$937$	−6.33657e26			−1.13815			−0.569073	−	0.822287i	$-0.692698\pi$
$937$	−6.33657e26			−1.13815			−0.569073	+	0.822287i	$0.692698\pi$
$938$	−5.77151e26	−	3.10508e26i	−1.02675	−	0.552391i
$939$			4.13504e26i			0.728600i
$940$	−2.37150e26	+	1.56606e26i	−0.413878	+	0.273311i
$941$	6.91787e26			1.19582			0.597910	−	0.801563i	$-0.295998\pi$
$941$	6.91787e26			1.19582			0.597910	+	0.801563i	$0.295998\pi$
$942$	−5.43742e25	+	1.01067e26i	−0.0930968	+	0.173042i
$943$			2.51999e26i			0.427360i
$944$	6.70809e26	+	2.86417e26i	1.12681	+	0.481118i
$945$	2.81314e25			0.0468065
$946$	−1.03464e26	−	5.56639e25i	−0.170518	−	0.0917388i
$947$			3.94587e25i			0.0644158i	0.999481	+	0.0322079i	$0.0102539\pi$
$947$			3.94587e25i			0.0644158i	−0.999481	+	0.0322079i	$0.989746\pi$
$948$	8.53466e24	+	1.29241e25i	0.0138010	+	0.0208990i
$949$	−1.43160e25			−0.0229311
$950$	6.98448e25	−	1.29823e26i	0.110821	−	0.205986i
$951$			7.10019e24i			0.0111595i
$952$	1.26742e26	−	1.14432e25i	0.197327	−	0.0178162i
$953$	−6.05896e26			−0.934462			−0.467231	−	0.884135i	$-0.654748\pi$
$953$	−6.05896e26			−0.934462			−0.467231	+	0.884135i	$0.654748\pi$
$954$	5.87068e25	+	3.15843e25i	0.0896918	+	0.0482543i
$955$			3.06596e26i			0.464020i
$956$	−5.05190e25	+	3.33610e25i	−0.0757415	+	0.0500171i
$957$	1.14569e26			0.170160
$958$	−3.81184e25	+	7.08520e25i	−0.0560848	+	0.104247i
$959$		−	4.58332e26i		−	0.668055i
$960$	−2.86334e25	−	1.57275e26i	−0.0413458	−	0.227100i
$961$	3.51571e26			0.502924
$962$	8.10052e26	+	4.35809e26i	1.14799	+	0.617619i
$963$			2.89481e26i			0.406429i
$964$	3.63101e26	+	5.49848e26i	0.505050	+	0.764803i
$965$	−8.37801e25			−0.115450
$966$	−1.35293e26	+	2.51474e26i	−0.184707	+	0.343320i
$967$			5.07658e26i			0.686646i	0.939217	+	0.343323i	$0.111553\pi$
$967$			5.07658e26i			0.686646i	−0.939217	+	0.343323i	$0.888447\pi$
$968$	−6.38383e25	−	7.07054e26i	−0.0855467	−	0.947489i
$969$	−3.94328e25			−0.0523533
$970$	1.33071e26	+	7.15923e25i	0.175040	+	0.0941718i
$971$			9.44295e26i			1.23065i	0.788274	+	0.615325i	$0.210975\pi$
$971$			9.44295e26i			1.23065i	−0.788274	+	0.615325i	$0.789025\pi$
$972$	4.14575e25	−	2.73771e25i	0.0535312	−	0.0353502i
$973$	7.77019e26			0.994068
$974$	5.34729e26	−	9.93918e26i	0.677802	−	1.25985i
$975$			6.69875e26i			0.841302i
$976$	5.42013e26	−	1.26943e27i	0.674468	−	1.57965i
$977$	1.03262e27			1.27318			0.636592	−	0.771200i	$-0.280343\pi$
$977$	1.03262e27			1.27318			0.636592	+	0.771200i	$0.280343\pi$
$978$	−1.33422e26	−	7.17811e25i	−0.162996	−	0.0876921i
$979$		−	1.46039e26i		−	0.176777i
$980$	−1.15717e26	−	1.75231e26i	−0.138791	−	0.210173i
$981$	1.96251e26			0.233233
$982$	−5.25964e26	+	9.77627e26i	−0.619374	+	1.15125i
$983$			1.10199e27i			1.28587i	0.765921	+	0.642934i	$0.222283\pi$
$983$			1.10199e27i			1.28587i	−0.765921	+	0.642934i	$0.777717\pi$
$984$	1.91467e26	−	1.72871e25i	0.221379	−	0.0199879i
$985$	4.20019e26			0.481219
$986$	3.37566e26	+	1.81611e26i	0.383236	+	0.206181i
$987$		−	3.87281e26i		−	0.435684i
$988$	3.61463e26	−	2.38698e26i	0.402950	−	0.266094i
$989$	8.82061e26			0.974388
$990$	−1.27236e25	+	2.36497e25i	−0.0139281	+	0.0258886i
$991$			1.43005e26i			0.155127i	0.996987	+	0.0775635i	$0.0247140\pi$
$991$			1.43005e26i			0.155127i	−0.996987	+	0.0775635i	$0.975286\pi$
$992$	−4.09170e26	−	5.12585e26i	−0.439844	−	0.551012i
$993$	−1.71418e26			−0.182606
$994$	−7.31033e26	−	3.93296e26i	−0.771720	−	0.415186i
$995$			2.23428e26i			0.233738i
$996$	−8.20212e25	−	1.24206e26i	−0.0850339	−	0.128768i
$997$	−3.32252e26			−0.341359			−0.170679	−	0.985327i	$-0.554596\pi$
$997$	−3.32252e26			−0.341359			−0.170679	+	0.985327i	$0.554596\pi$
$998$	−4.30281e26	+	7.99777e26i	−0.438104	+	0.814318i
$999$		−	1.43347e26i		−	0.144644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.19.d.a.7.1	✓	18
3.2	odd	2		36.19.d.e.19.18		18
4.3	odd	2	inner	12.19.d.a.7.2	yes	18
12.11	even	2		36.19.d.e.19.17		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.19.d.a.7.1	✓	18	1.1	even	1	trivial
12.19.d.a.7.2	yes	18	4.3	odd	2	inner
36.19.d.e.19.17		18	12.11	even	2
36.19.d.e.19.18		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)

\(f(q)\)	\(=\)	\(q+(-450.888 - 242.578i) q^{2} -11364.0i q^{3} +(144456. + 218751. i) q^{4} -780888. q^{5} +(-2.75665e6 + 5.12388e6i) q^{6} +2.45477e7i q^{7} +(-1.20691e7 - 1.33674e8i) q^{8} -1.29140e8 q^{9} +O(q^{10})\)	\(q+(-450.888 - 242.578i) q^{2} -11364.0i q^{3} +(144456. + 218751. i) q^{4} -780888. q^{5} +(-2.75665e6 + 5.12388e6i) q^{6} +2.45477e7i q^{7} +(-1.20691e7 - 1.33674e8i) q^{8} -1.29140e8 q^{9} +(3.52093e8 + 1.89426e8i) q^{10} -5.20124e8i q^{11} +(2.48588e9 - 1.64159e9i) q^{12} +1.83928e10 q^{13} +(5.95474e9 - 1.10683e10i) q^{14} +8.87400e9i q^{15} +(-2.69846e10 + 6.31997e10i) q^{16} +3.86243e10 q^{17} +(5.82277e10 + 3.13266e10i) q^{18} -8.98393e10i q^{19} +(-1.12804e11 - 1.70820e11i) q^{20} +2.78960e11 q^{21} +(-1.26171e11 + 2.34517e11i) q^{22} -1.99933e12i q^{23} +(-1.51907e12 + 1.37153e11i) q^{24} -3.20491e12 q^{25} +(-8.29307e12 - 4.46168e12i) q^{26} +1.46755e12i q^{27} +(-5.36984e12 + 3.54606e12i) q^{28} -1.93833e13 q^{29} +(2.15264e12 - 4.00118e12i) q^{30} -1.86409e13i q^{31} +(2.74979e13 - 2.19501e13i) q^{32} -5.91068e12 q^{33} +(-1.74152e13 - 9.36942e12i) q^{34} -1.91690e13i q^{35} +(-1.86550e13 - 2.82495e13i) q^{36} -9.76781e13 q^{37} +(-2.17931e13 + 4.05075e13i) q^{38} -2.09015e14i q^{39} +(9.42464e12 + 1.04384e14i) q^{40} -1.26042e14 q^{41} +(-1.25780e14 - 6.76695e13i) q^{42} +4.41179e14i q^{43} +(1.13778e14 - 7.51348e13i) q^{44} +1.00844e14 q^{45} +(-4.84993e14 + 9.01472e14i) q^{46} -1.38830e15i q^{47} +(7.18200e14 + 3.06652e14i) q^{48} +1.02582e15 q^{49} +(1.44506e15 + 7.77441e14i) q^{50} -4.38926e14i q^{51} +(2.65694e15 + 4.02344e15i) q^{52} +1.00823e15 q^{53} +(3.55995e14 - 6.61699e14i) q^{54} +4.06158e14i q^{55} +(3.28139e15 - 2.96270e14i) q^{56} -1.02093e15 q^{57} +(8.73971e15 + 4.70197e15i) q^{58} -1.06141e16i q^{59} +(-1.94120e15 + 1.28190e15i) q^{60} -2.00860e16 q^{61} +(-4.52187e15 + 8.40495e15i) q^{62} -3.17010e15i q^{63} +(-1.77231e16 + 3.22666e15i) q^{64} -1.43627e16 q^{65} +(2.66505e15 + 1.43380e15i) q^{66} -5.21446e16i q^{67} +(5.57951e15 + 8.44911e15i) q^{68} -2.27203e16 q^{69} +(-4.64999e15 + 8.64308e15i) q^{70} -6.60477e16i q^{71} +(1.55861e15 + 1.72627e16i) q^{72} -7.78349e14 q^{73} +(4.40419e16 + 2.36946e16i) q^{74} +3.64206e16i q^{75} +(1.96524e16 - 1.29778e16i) q^{76} +1.27678e16 q^{77} +(-5.07025e16 + 9.42424e16i) q^{78} +5.19901e15i q^{79} +(2.10719e16 - 4.93519e16i) q^{80} +1.66772e16 q^{81} +(5.68308e16 + 3.05750e16i) q^{82} -4.99644e16i q^{83} +(4.02974e16 + 6.10228e16i) q^{84} -3.01613e16 q^{85} +(1.07020e17 - 1.98922e17i) q^{86} +2.20272e17i q^{87} +(-6.95270e16 + 6.27744e15i) q^{88} +2.80778e17 q^{89} +(-4.54694e16 - 2.44626e16i) q^{90} +4.51500e17i q^{91} +(4.37355e17 - 2.88814e17i) q^{92} -2.11835e17 q^{93} +(-3.36772e17 + 6.25969e17i) q^{94} +7.01545e16i q^{95} +(-2.49441e17 - 3.12485e17i) q^{96} +3.77943e17 q^{97} +(-4.62531e17 - 2.48842e17i) q^{98} +6.71688e16i 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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