LMFDB - Embedded newform 12.19.d.a.7.17

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			7.17
Root			$246.626 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.19.d.a.7.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(506.695 - 73.5121i) q^{2} -11364.0i q^{3} +(251336. - 74496.4i) q^{4} +2.11462e6 q^{5} +(-835390. - 5.75808e6i) q^{6} -4.00973e7i q^{7} +(1.21874e8 - 5.62232e7i) q^{8} -1.29140e8 q^{9} +O(q^{10})$	\(q+(506.695 - 73.5121i) q^{2} -11364.0i q^{3} +(251336. - 74496.4i) q^{4} +2.11462e6 q^{5} +(-835390. - 5.75808e6i) q^{6} -4.00973e7i q^{7} +(1.21874e8 - 5.62232e7i) q^{8} -1.29140e8 q^{9} +(1.07147e9 - 1.55450e8i) q^{10} +2.33195e9i q^{11} +(-8.46576e8 - 2.85618e9i) q^{12} +4.89591e9 q^{13} +(-2.94763e9 - 2.03171e10i) q^{14} -2.40305e10i q^{15} +(5.76200e10 - 3.74473e10i) q^{16} -2.82918e10 q^{17} +(-6.54347e10 + 9.49336e9i) q^{18} -4.35994e11i q^{19} +(5.31479e11 - 1.57531e11i) q^{20} -4.55665e11 q^{21} +(1.71426e11 + 1.18159e12i) q^{22} +7.05248e10i q^{23} +(-6.38920e11 - 1.38498e12i) q^{24} +6.56904e11 q^{25} +(2.48073e12 - 3.59909e11i) q^{26} +1.46755e12i q^{27} +(-2.98710e12 - 1.00779e13i) q^{28} -2.17394e12 q^{29} +(-1.76653e12 - 1.21761e13i) q^{30} -3.60455e13i q^{31} +(2.64430e13 - 2.32101e13i) q^{32} +2.65002e13 q^{33} +(-1.43353e13 + 2.07979e12i) q^{34} -8.47904e13i q^{35} +(-3.24576e13 + 9.62048e12i) q^{36} +2.32202e14 q^{37} +(-3.20508e13 - 2.20916e14i) q^{38} -5.56371e13i q^{39} +(2.57717e14 - 1.18891e14i) q^{40} -6.17691e14 q^{41} +(-2.30883e14 + 3.34969e13i) q^{42} +1.00150e15i q^{43} +(1.73722e14 + 5.86102e14i) q^{44} -2.73082e14 q^{45} +(5.18443e12 + 3.57346e13i) q^{46} +1.05758e15i q^{47} +(-4.25550e14 - 6.54793e14i) q^{48} +2.06213e13 q^{49} +(3.32850e14 - 4.82904e13i) q^{50} +3.21507e14i q^{51} +(1.23052e15 - 3.64728e14i) q^{52} +1.66975e15 q^{53} +(1.07882e14 + 7.43599e14i) q^{54} +4.93117e15i q^{55} +(-2.25440e15 - 4.88683e15i) q^{56} -4.95463e15 q^{57} +(-1.10153e15 + 1.59811e14i) q^{58} +1.58115e16i q^{59} +(-1.79018e15 - 6.03972e15i) q^{60} +7.61656e13 q^{61} +(-2.64978e15 - 1.82641e16i) q^{62} +5.17817e15i q^{63} +(1.16923e16 - 1.37043e16i) q^{64} +1.03530e16 q^{65} +(1.34275e16 - 1.94808e15i) q^{66} +1.27874e16i q^{67} +(-7.11074e15 + 2.10764e15i) q^{68} +8.01443e14 q^{69} +(-6.23312e15 - 4.29629e16i) q^{70} -8.50536e15i q^{71} +(-1.57389e16 + 7.26067e15i) q^{72} -8.52967e16 q^{73} +(1.17656e17 - 1.70697e16i) q^{74} -7.46505e15i q^{75} +(-3.24800e16 - 1.09581e17i) q^{76} +9.35047e16 q^{77} +(-4.09000e15 - 2.81910e16i) q^{78} +2.56421e16i q^{79} +(1.21844e17 - 7.91866e16i) q^{80} +1.66772e16 q^{81} +(-3.12981e17 + 4.54077e16i) q^{82} +3.31464e17i q^{83} +(-1.14525e17 + 3.39454e16i) q^{84} -5.98263e16 q^{85} +(7.36224e16 + 5.07456e17i) q^{86} +2.47047e16i q^{87} +(1.31109e17 + 2.84204e17i) q^{88} +1.22179e17 q^{89} +(-1.38369e17 + 2.00748e16i) q^{90} -1.96313e17i q^{91} +(5.25385e15 + 1.77254e16i) q^{92} -4.09620e17 q^{93} +(7.77452e16 + 5.35873e17i) q^{94} -9.21960e17i q^{95} +(-2.63759e17 - 3.00498e17i) q^{96} -7.04078e15 q^{97} +(1.04487e16 - 1.51591e15i) q^{98} -3.01148e17i 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 $

$2$	506.695	−	73.5121i	0.989639	−	0.143578i
$2$	506.695	−	73.5121i	0.989639	−	0.143578i
$3$		−	11364.0i		−	0.577350i
$3$		−	11364.0i		−	0.577350i
$4$	251336.	−	74496.4i	0.958771	−	0.284181i
$5$	2.11462e6			1.08268			0.541342	−	0.840803i	$-0.317917\pi$
$5$	2.11462e6			1.08268			0.541342	+	0.840803i	$0.317917\pi$
$6$	−835390.	−	5.75808e6i	−0.0828950	−	0.571368i
$7$		−	4.00973e7i		−	0.993648i	−0.867851	−	0.496824i	$-0.834499\pi$
$7$		−	4.00973e7i		−	0.993648i	0.867851	−	0.496824i	$-0.165501\pi$
$8$	1.21874e8	−	5.62232e7i	0.908034	−	0.418896i
$9$	−1.29140e8			−0.333333
$10$	1.07147e9	−	1.55450e8i	1.07147	−	0.155450i
$11$			2.33195e9i			0.988972i	0.869185	+	0.494486i	$0.164644\pi$
$11$			2.33195e9i			0.988972i	−0.869185	+	0.494486i	$0.835356\pi$
$12$	−8.46576e8	−	2.85618e9i	−0.164072	−	0.553546i
$13$	4.89591e9			0.461682			0.230841	−	0.972991i	$-0.425852\pi$
$13$	4.89591e9			0.461682			0.230841	+	0.972991i	$0.425852\pi$
$14$	−2.94763e9	−	2.03171e10i	−0.142666	−	0.983353i
$15$		−	2.40305e10i		−	0.625088i
$16$	5.76200e10	−	3.74473e10i	0.838482	−	0.544929i
$17$	−2.82918e10			−0.238572			−0.119286	−	0.992860i	$-0.538061\pi$
$17$	−2.82918e10			−0.238572			−0.119286	+	0.992860i	$0.538061\pi$
$18$	−6.54347e10	+	9.49336e9i	−0.329880	+	0.0478594i
$19$		−	4.35994e11i		−	1.35113i	−0.737299	−	0.675566i	$-0.763899\pi$
$19$		−	4.35994e11i		−	1.35113i	0.737299	−	0.675566i	$-0.236101\pi$
$20$	5.31479e11	−	1.57531e11i	1.03805	−	0.307678i
$21$	−4.55665e11			−0.573683
$22$	1.71426e11	+	1.18159e12i	0.141995	+	0.978726i
$23$			7.05248e10i			0.0391554i	0.999808	+	0.0195777i	$0.00623217\pi$
$23$			7.05248e10i			0.0391554i	−0.999808	+	0.0195777i	$0.993768\pi$
$24$	−6.38920e11	−	1.38498e12i	−0.241849	−	0.524254i
$25$	6.56904e11			0.172204
$26$	2.48073e12	−	3.59909e11i	0.456899	−	0.0662876i
$27$			1.46755e12i			0.192450i
$28$	−2.98710e12	−	1.00779e13i	−0.282376	−	0.952681i
$29$	−2.17394e12			−0.149853			−0.0749266	−	0.997189i	$-0.523872\pi$
$29$	−2.17394e12			−0.149853			−0.0749266	+	0.997189i	$0.523872\pi$
$30$	−1.76653e12	−	1.21761e13i	−0.0897490	−	0.618611i
$31$		−	3.60455e13i		−	1.36331i	−0.731673	−	0.681656i	$-0.761260\pi$
$31$		−	3.60455e13i		−	1.36331i	0.731673	−	0.681656i	$-0.238740\pi$
$32$	2.64430e13	−	2.32101e13i	0.751554	−	0.659671i
$33$	2.65002e13			0.570984
$34$	−1.43353e13	+	2.07979e12i	−0.236100	+	0.0342538i
$35$		−	8.47904e13i		−	1.07581i
$36$	−3.24576e13	+	9.62048e12i	−0.319590	+	0.0947271i
$37$	2.32202e14			1.78670			0.893348	−	0.449365i	$-0.148350\pi$
$37$	2.32202e14			1.78670			0.893348	+	0.449365i	$0.148350\pi$
$38$	−3.20508e13	−	2.20916e14i	−0.193993	−	1.33713i
$39$		−	5.56371e13i		−	0.266552i
$40$	2.57717e14	−	1.18891e14i	0.983114	−	0.453531i
$41$	−6.17691e14			−1.88676			−0.943380	−	0.331715i	$-0.892373\pi$
$41$	−6.17691e14			−1.88676			−0.943380	+	0.331715i	$0.892373\pi$
$42$	−2.30883e14	+	3.34969e13i	−0.567739	+	0.0823684i
$43$			1.00150e15i			1.99267i	0.0855409	+	0.996335i	$0.472738\pi$
$43$			1.00150e15i			1.99267i	−0.0855409	+	0.996335i	$0.527262\pi$
$44$	1.73722e14	+	5.86102e14i	0.281047	+	0.948198i
$45$	−2.73082e14			−0.360894
$46$	5.18443e12	+	3.57346e13i	0.00562186	+	0.0387497i
$47$			1.05758e15i			0.945005i	0.881329	+	0.472503i	$0.156649\pi$
$47$			1.05758e15i			0.945005i	−0.881329	+	0.472503i	$0.843351\pi$
$48$	−4.25550e14	−	6.54793e14i	−0.314615	−	0.484098i
$49$	2.06213e13			0.0126634
$50$	3.32850e14	−	4.82904e13i	0.170419	−	0.0247247i
$51$			3.21507e14i			0.137740i
$52$	1.23052e15	−	3.64728e14i	0.442648	−	0.131202i
$53$	1.66975e15			0.506022			0.253011	−	0.967463i	$-0.418579\pi$
$53$	1.66975e15			0.506022			0.253011	+	0.967463i	$0.418579\pi$
$54$	1.07882e14	+	7.43599e14i	0.0276317	+	0.190456i
$55$			4.93117e15i			1.07074i
$56$	−2.25440e15	−	4.88683e15i	−0.416235	−	0.902267i
$57$	−4.95463e15			−0.780077
$58$	−1.10153e15	+	1.59811e14i	−0.148301	+	0.0215157i
$59$			1.58115e16i			1.82518i	0.408877	+	0.912590i	$0.365921\pi$
$59$			1.58115e16i			1.82518i	−0.408877	+	0.912590i	$0.634079\pi$
$60$	−1.79018e15	−	6.03972e15i	−0.177638	−	0.599316i
$61$	7.61656e13			0.00651314			0.00325657	−	0.999995i	$-0.498963\pi$
$61$	7.61656e13			0.00651314			0.00325657	+	0.999995i	$0.498963\pi$
$62$	−2.64978e15	−	1.82641e16i	−0.195742	−	1.34919i
$63$			5.17817e15i			0.331216i
$64$	1.16923e16	−	1.37043e16i	0.649053	−	0.760743i
$65$	1.03530e16			0.499856
$66$	1.34275e16	−	1.94808e15i	0.565068	−	0.0819808i
$67$			1.27874e16i			0.470011i	0.971994	+	0.235006i	$0.0755109\pi$
$67$			1.27874e16i			0.470011i	−0.971994	+	0.235006i	$0.924489\pi$
$68$	−7.11074e15	+	2.10764e15i	−0.228736	+	0.0677978i
$69$	8.01443e14			0.0226064
$70$	−6.23312e15	−	4.29629e16i	−0.154462	−	1.06466i
$71$		−	8.50536e15i		−	0.185510i	−0.995689	−	0.0927551i	$-0.970433\pi$
$71$		−	8.50536e15i		−	0.185510i	0.995689	−	0.0927551i	$-0.0295674\pi$
$72$	−1.57389e16	+	7.26067e15i	−0.302678	+	0.139632i
$73$	−8.52967e16			−1.44886			−0.724430	−	0.689349i	$-0.757897\pi$
$73$	−8.52967e16			−1.44886			−0.724430	+	0.689349i	$0.757897\pi$
$74$	1.17656e17	−	1.70697e16i	1.76818	−	0.256531i
$75$		−	7.46505e15i		−	0.0994217i
$76$	−3.24800e16	−	1.09581e17i	−0.383967	−	1.29543i
$77$	9.35047e16			0.982691
$78$	−4.09000e15	−	2.81910e16i	−0.0382711	−	0.263791i
$79$			2.56421e16i			0.213949i	0.994262	+	0.106974i	$0.0341163\pi$
$79$			2.56421e16i			0.213949i	−0.994262	+	0.106974i	$0.965884\pi$
$80$	1.21844e17	−	7.91866e16i	0.907811	−	0.589986i
$81$	1.66772e16			0.111111
$82$	−3.12981e17	+	4.54077e16i	−1.86721	+	0.270898i
$83$			3.31464e17i			1.77310i	0.462630	+	0.886552i	$0.346906\pi$
$83$			3.31464e17i			1.77310i	−0.462630	+	0.886552i	$0.653094\pi$
$84$	−1.14525e17	+	3.39454e16i	−0.550030	+	0.163030i
$85$	−5.98263e16			−0.258298
$86$	7.36224e16	+	5.07456e17i	0.286104	+	1.97202i
$87$			2.47047e16i			0.0865178i
$88$	1.31109e17	+	2.84204e17i	0.414276	+	0.898021i
$89$	1.22179e17			0.348729			0.174364	−	0.984681i	$-0.444213\pi$
$89$	1.22179e17			0.348729			0.174364	+	0.984681i	$0.444213\pi$
$90$	−1.38369e17	+	2.00748e16i	−0.357155	+	0.0518166i
$91$		−	1.96313e17i		−	0.458750i
$92$	5.25385e15	+	1.77254e16i	0.0111272	+	0.0375410i
$93$	−4.09620e17			−0.787109
$94$	7.77452e16	+	5.35873e17i	0.135682	+	0.935214i
$95$		−	9.21960e17i		−	1.46285i
$96$	−2.63759e17	−	3.00498e17i	−0.380861	−	0.433910i
$97$	−7.04078e15			−0.00926137			−0.00463068	−	0.999989i	$-0.501474\pi$
$97$	−7.04078e15			−0.00926137			−0.00463068	+	0.999989i	$0.501474\pi$
$98$	1.04487e16	−	1.51591e15i	0.0125322	−	0.00181819i
$99$		−	3.01148e17i		−	0.329657i
$100$	1.65104e17	−	4.89370e16i	0.165104	−	0.0489370i
$101$	1.55415e18			1.42102			0.710512	−	0.703686i	$-0.248464\pi$
$101$	1.55415e18			1.42102			0.710512	+	0.703686i	$0.248464\pi$
$102$	2.36347e16	+	1.62906e17i	0.0197764	+	0.136313i
$103$		−	1.74561e18i		−	1.33787i	−0.743322	−	0.668933i	$-0.766751\pi$
$103$		−	1.74561e18i		−	1.33787i	0.743322	−	0.668933i	$-0.233249\pi$
$104$	5.96686e17	−	2.75264e17i	0.419224	−	0.193397i
$105$	−9.63556e17			−0.621117
$106$	8.46056e17	−	1.22747e17i	0.500779	−	0.0726538i
$107$		−	7.59072e17i		−	0.412885i	−0.978459	−	0.206442i	$-0.933811\pi$
$107$		−	7.59072e17i		−	0.412885i	0.978459	−	0.206442i	$-0.0661886\pi$
$108$	1.09327e17	+	3.68847e17i	0.0546907	+	0.184515i
$109$	−1.50618e18			−0.693485			−0.346743	−	0.937960i	$-0.612712\pi$
$109$	−1.50618e18			−0.693485			−0.346743	+	0.937960i	$0.612712\pi$
$110$	3.62501e17	+	2.49860e18i	0.153736	+	1.05965i
$111$		−	2.63874e18i		−	1.03155i
$112$	−1.50153e18	−	2.31041e18i	−0.541468	−	0.833156i
$113$	3.99379e18			1.32947			0.664736	−	0.747079i	$-0.268544\pi$
$113$	3.99379e18			1.32947			0.664736	+	0.747079i	$0.268544\pi$
$114$	−2.51049e18	+	3.64225e17i	−0.771994	+	0.112002i
$115$			1.49133e17i			0.0423929i
$116$	−5.46390e17	+	1.61951e17i	−0.143675	+	0.0425855i
$117$	−6.32259e17			−0.153894
$118$	1.16234e18	+	8.01162e18i	0.262056	+	1.80627i
$119$			1.13442e18i			0.237057i
$120$	−1.35107e18	−	2.92870e18i	−0.261846	−	0.567601i
$121$	1.21949e17			0.0219335
$122$	3.85928e16	−	5.59909e15i	0.00644566	−	0.000935146i
$123$			7.01943e18i			1.08932i
$124$	−2.68526e18	−	9.05952e18i	−0.387428	−	1.30710i
$125$	−6.67752e18			−0.896242
$126$	3.80658e17	+	2.62375e18i	0.0475554	+	0.327784i
$127$			5.86273e18i			0.682128i	0.940040	+	0.341064i	$0.110787\pi$
$127$			5.86273e18i			0.682128i	−0.940040	+	0.341064i	$0.889213\pi$
$128$	4.91700e18	−	7.80344e18i	0.533102	−	0.846051i
$129$	1.13810e19			1.15047
$130$	5.24580e18	−	7.61069e17i	0.494677	−	0.0717685i
$131$			1.34071e19i			1.18003i	0.807391	+	0.590017i	$0.200879\pi$
$131$			1.34071e19i			1.18003i	−0.807391	+	0.590017i	$0.799121\pi$
$132$	6.66045e18	−	1.97417e18i	0.547442	−	0.162263i
$133$	−1.74822e19			−1.34255
$134$	9.40027e17	+	6.47930e18i	0.0674834	+	0.465142i
$135$			3.10330e18i			0.208363i
$136$	−3.44804e18	+	1.59065e18i	−0.216632	+	0.0999369i
$137$	−9.10202e18			−0.535368			−0.267684	−	0.963507i	$-0.586258\pi$
$137$	−9.10202e18			−0.535368			−0.267684	+	0.963507i	$0.586258\pi$
$138$	4.06087e17	−	5.89158e16i	0.0223721	−	0.00324578i
$139$			1.80926e18i			0.0934047i	0.998909	+	0.0467023i	$0.0148712\pi$
$139$			1.80926e18i			0.0934047i	−0.998909	+	0.0467023i	$0.985129\pi$
$140$	−6.31658e18	−	2.13109e19i	−0.305724	−	1.03145i
$141$	1.20184e19			0.545599
$142$	−6.25247e17	−	4.30962e18i	−0.0266352	−	0.183588i
$143$			1.14170e19i			0.456591i
$144$	−7.44106e18	+	4.83595e18i	−0.279494	+	0.181643i
$145$	−4.59705e18			−0.162244
$146$	−4.32194e19	+	6.27034e18i	−1.43385	+	0.208025i
$147$		−	2.34340e17i		−	0.00731123i
$148$	5.83607e19	−	1.72982e19i	1.71303	−	0.507746i
$149$	2.18525e19			0.603705			0.301853	−	0.953355i	$-0.402395\pi$
$149$	2.18525e19			0.603705			0.301853	+	0.953355i	$0.402395\pi$
$150$	−5.48771e17	−	3.78250e18i	−0.0142748	−	0.0983916i
$151$			3.33279e19i			0.816611i	0.912845	+	0.408305i	$0.133880\pi$
$151$			3.33279e19i			0.816611i	−0.912845	+	0.408305i	$0.866120\pi$
$152$	−2.45130e19	−	5.31365e19i	−0.565983	−	1.22687i
$153$	3.65361e18			0.0795241
$154$	4.73784e19	−	6.87372e18i	0.972509	−	0.141093i
$155$		−	7.62223e19i		−	1.47604i
$156$	−4.14476e18	−	1.39836e19i	−0.0757492	−	0.255563i
$157$	9.01303e18			0.155516			0.0777578	−	0.996972i	$-0.475224\pi$
$157$	9.01303e18			0.155516			0.0777578	+	0.996972i	$0.475224\pi$
$158$	1.88500e18	+	1.29927e19i	0.0307184	+	0.211732i
$159$		−	1.89750e19i		−	0.292152i
$160$	5.59167e19	−	4.90805e19i	0.813696	−	0.714215i
$161$	2.82785e18			0.0389067
$162$	8.45025e18	−	1.22597e18i	0.109960	−	0.0159531i
$163$		−	1.02656e20i		−	1.26385i	−0.775028	−	0.631927i	$-0.782264\pi$
$163$		−	1.02656e20i		−	1.26385i	0.775028	−	0.631927i	$-0.217736\pi$
$164$	−1.55248e20	+	4.60158e19i	−1.80897	+	0.536182i
$165$	5.60377e19			0.618194
$166$	2.43666e19	+	1.67951e20i	0.254579	+	1.75473i
$167$			1.94536e19i			0.192554i	0.995355	+	0.0962770i	$0.0306935\pi$
$167$			1.94536e19i			0.192554i	−0.995355	+	0.0962770i	$0.969307\pi$
$168$	−5.55339e19	+	2.56189e19i	−0.520924	+	0.240313i
$169$	−8.84855e19			−0.786849
$170$	−3.03137e19	+	4.39795e18i	−0.255622	+	0.0370860i
$171$			5.63043e19i			0.450377i
$172$	7.46082e19	+	2.51713e20i	0.566279	+	1.91051i
$173$	−1.54568e20			−1.11354			−0.556769	−	0.830667i	$-0.687959\pi$
$173$	−1.54568e20			−1.11354			−0.556769	+	0.830667i	$0.687959\pi$
$174$	1.81609e18	+	1.25177e19i	0.0124221	+	0.0856214i
$175$		−	2.63401e19i		−	0.171110i
$176$	8.73250e19	+	1.34367e20i	0.538920	+	0.829236i
$177$	1.79682e20			1.05377
$178$	6.19077e19	−	8.98165e18i	0.345115	−	0.0500699i
$179$		−	2.13911e19i		−	0.113385i	−0.998392	−	0.0566926i	$-0.981944\pi$
$179$		−	2.13911e19i		−	0.113385i	0.998392	−	0.0566926i	$-0.0180555\pi$
$180$	−6.86353e19	+	2.03436e19i	−0.346015	+	0.102559i
$181$	−3.04453e20			−1.46020			−0.730100	−	0.683340i	$-0.760527\pi$
$181$	−3.04453e20			−1.46020			−0.730100	+	0.683340i	$0.760527\pi$
$182$	−1.44314e19	−	9.94707e19i	−0.0658665	−	0.453997i
$183$		−	8.65545e17i		−	0.00376036i
$184$	3.96513e18	+	8.59517e18i	0.0164020	+	0.0355544i
$185$	4.91018e20			1.93443
$186$	−2.07553e20	+	3.01120e19i	−0.778954	+	0.113012i
$187$		−	6.59749e19i		−	0.235941i
$188$	7.87862e19	+	2.65809e20i	0.268553	+	0.906043i
$189$	5.88446e19			0.191228
$190$	−6.77752e19	−	4.67152e20i	−0.210033	−	1.44769i
$191$		−	5.50430e19i		−	0.162705i	−0.996685	−	0.0813527i	$-0.974076\pi$
$191$		−	5.50430e19i		−	0.162705i	0.996685	−	0.0813527i	$-0.0259240\pi$
$192$	−1.55736e20	−	1.32871e20i	−0.439215	−	0.374731i
$193$	−3.71487e20			−0.999834			−0.499917	−	0.866073i	$-0.666636\pi$
$193$	−3.71487e20			−0.999834			−0.499917	+	0.866073i	$0.666636\pi$
$194$	−3.56753e18	+	5.17582e17i	−0.00916541	+	0.00132973i
$195$		−	1.17651e20i		−	0.288592i
$196$	5.18287e18	−	1.53621e18i	0.0121413	−	0.00359871i
$197$	5.79158e20			1.29599			0.647994	−	0.761645i	$-0.275608\pi$
$197$	5.79158e20			1.29599			0.647994	+	0.761645i	$0.275608\pi$
$198$	−2.21380e19	−	1.52590e20i	−0.0473317	−	0.326242i
$199$		−	5.55607e20i		−	1.13525i	−0.823288	−	0.567623i	$-0.807863\pi$
$199$		−	5.55607e20i		−	1.13525i	0.823288	−	0.567623i	$-0.192137\pi$
$200$	8.00598e19	−	3.69333e19i	0.156367	−	0.0721353i
$201$	1.45316e20			0.271361
$202$	7.87481e20	−	1.14249e20i	1.40630	−	0.204028i
$203$			8.71692e19i			0.148901i
$204$	2.39512e19	+	8.08064e19i	0.0391431	+	0.132061i
$205$	−1.30618e21			−2.04276
$206$	−1.28324e20	−	8.84494e20i	−0.192089	−	1.32401i
$207$		−	9.10759e18i		−	0.0130518i
$208$	2.82103e20	−	1.83338e20i	0.387112	−	0.251584i
$209$	1.01671e21			1.33623
$210$	−4.88229e20	+	7.08330e19i	−0.614682	+	0.0891789i
$211$			1.32488e21i			1.59821i	0.601191	+	0.799106i	$0.294693\pi$
$211$			1.32488e21i			1.59821i	−0.601191	+	0.799106i	$0.705307\pi$
$212$	4.19669e20	−	1.24391e20i	0.485159	−	0.143802i
$213$	−9.66548e19			−0.107104
$214$	−5.58010e19	−	3.84618e20i	−0.0592813	−	0.408607i
$215$			2.11779e21i			2.15743i
$216$	8.25102e19	+	1.78856e20i	0.0806165	+	0.174751i
$217$	−1.44533e21			−1.35465
$218$	−7.63172e20	+	1.10722e20i	−0.686300	+	0.0995694i
$219$			9.69310e20i			0.836500i
$220$	3.67354e20	+	1.23938e21i	0.304285	+	1.02660i
$221$	−1.38514e20			−0.110145
$222$	−1.93979e20	−	1.33704e21i	−0.148108	−	1.02086i
$223$		−	7.39937e20i		−	0.542564i	−0.962500	−	0.271282i	$-0.912552\pi$
$223$		−	7.39937e20i		−	0.542564i	0.962500	−	0.271282i	$-0.0874476\pi$
$224$	−9.30663e20	−	1.06029e21i	−0.655481	−	0.746781i
$225$	−8.48327e19			−0.0574012
$226$	2.02363e21	−	2.93592e20i	1.31570	−	0.190883i
$227$		−	1.20144e21i		−	0.750707i	−0.926882	−	0.375353i	$-0.877521\pi$
$227$		−	1.20144e21i		−	0.750707i	0.926882	−	0.375353i	$-0.122479\pi$
$228$	−1.24528e21	+	3.69102e20i	−0.747915	+	0.221683i
$229$	2.62760e21			1.51719			0.758595	−	0.651562i	$-0.225886\pi$
$229$	2.62760e21			1.51719			0.758595	+	0.651562i	$0.225886\pi$
$230$	1.09631e19	+	7.55649e19i	0.00608670	+	0.0419537i
$231$		−	1.06259e21i		−	0.567357i
$232$	−2.64948e20	+	1.22226e20i	−0.136072	+	0.0627729i
$233$	−7.32324e20			−0.361826			−0.180913	−	0.983499i	$-0.557905\pi$
$233$	−7.32324e20			−0.361826			−0.180913	+	0.983499i	$0.557905\pi$
$234$	−3.20362e20	+	4.64787e19i	−0.152300	+	0.0220959i
$235$			2.23638e21i			1.02314i
$236$	1.17790e21	+	3.97400e21i	0.518682	+	1.74993i
$237$	2.91396e20			0.123523
$238$	8.33938e19	+	5.74807e20i	0.0340362	+	0.234601i
$239$			3.22783e20i			0.126861i	0.997986	+	0.0634307i	$0.0202042\pi$
$239$			3.22783e20i			0.126861i	−0.997986	+	0.0634307i	$0.979796\pi$
$240$	−8.99875e20	−	1.38464e21i	−0.340629	−	0.524125i
$241$	−1.83644e21			−0.669611			−0.334806	−	0.942287i	$-0.608671\pi$
$241$	−1.83644e21			−0.669611			−0.334806	+	0.942287i	$0.608671\pi$
$242$	6.17908e19	−	8.96469e18i	0.0217063	−	0.00314918i
$243$		−	1.89519e20i		−	0.0641500i
$244$	1.91432e19	−	5.67407e18i	0.00624461	−	0.00185091i
$245$	4.36061e19			0.0137105
$246$	5.16013e20	+	3.55671e21i	0.156403	+	1.07803i
$247$		−	2.13459e21i		−	0.623794i
$248$	−2.02659e21	−	4.39302e21i	−0.571086	−	1.23793i
$249$	3.76676e21			1.02370
$250$	−3.38347e21	+	4.90878e20i	−0.886956	+	0.128681i
$251$		−	3.86039e21i		−	0.976266i	−0.872769	−	0.488133i	$-0.837678\pi$
$251$		−	3.86039e21i		−	0.976266i	0.872769	−	0.488133i	$-0.162322\pi$
$252$	3.85755e20	+	1.30146e21i	0.0941254	+	0.317560i
$253$	−1.64460e20			−0.0387236
$254$	4.30981e20	+	2.97061e21i	0.0979388	+	0.675061i
$255$			6.79865e20i			0.149129i
$256$	1.91777e21	−	4.31543e21i	0.406104	−	0.913827i
$257$	−5.30431e21			−1.08450			−0.542251	−	0.840216i	$-0.682428\pi$
$257$	−5.30431e21			−1.08450			−0.542251	+	0.840216i	$0.682428\pi$
$258$	5.76672e21	−	8.36644e20i	1.13855	−	0.165182i
$259$		−	9.31068e21i		−	1.77535i
$260$	2.60207e21	−	7.71260e20i	0.479247	−	0.142050i
$261$	2.80743e20			0.0499511
$262$	9.85587e20	+	6.79333e21i	0.169427	+	1.16781i
$263$		−	8.03733e21i		−	1.33509i	−0.744570	−	0.667544i	$-0.767346\pi$
$263$		−	8.03733e21i		−	1.33509i	0.744570	−	0.667544i	$-0.232654\pi$
$264$	3.22969e21	−	1.48993e21i	0.518473	−	0.239182i
$265$	3.53089e21			0.547862
$266$	−8.85813e21	+	1.28515e21i	−1.32864	+	0.192761i
$267$		−	1.38844e21i		−	0.201339i
$268$	9.52614e20	+	3.21393e21i	0.133568	+	0.450633i
$269$	9.04731e19			0.0122673			0.00613365	−	0.999981i	$-0.498048\pi$
$269$	9.04731e19			0.0122673			0.00613365	+	0.999981i	$0.498048\pi$
$270$	2.28130e20	+	1.57243e21i	0.0299163	+	0.206204i
$271$			2.86801e21i			0.363795i	0.983318	+	0.181897i	$0.0582239\pi$
$271$			2.86801e21i			0.363795i	−0.983318	+	0.181897i	$0.941776\pi$
$272$	−1.63017e21	+	1.05945e21i	−0.200039	+	0.130005i
$273$	−2.23090e21			−0.264859
$274$	−4.61195e21	+	6.69109e20i	−0.529822	+	0.0768673i
$275$			1.53186e21i			0.170305i
$276$	2.01431e20	−	5.97047e19i	0.0216743	−	0.00642431i
$277$	1.54553e22			1.60976			0.804879	−	0.593439i	$-0.202230\pi$
$277$	1.54553e22			1.60976			0.804879	+	0.593439i	$0.202230\pi$
$278$	1.33003e20	+	9.16745e20i	0.0134109	+	0.0924369i
$279$			4.65492e21i			0.454438i
$280$	−4.76719e21	−	1.03338e22i	−0.450651	−	0.976869i
$281$	2.73147e21			0.250058			0.125029	−	0.992153i	$-0.460098\pi$
$281$	2.73147e21			0.250058			0.125029	+	0.992153i	$0.460098\pi$
$282$	6.08965e21	−	8.83495e20i	0.539946	−	0.0783362i
$283$			6.10059e21i			0.523955i	0.965074	+	0.261977i	$0.0843746\pi$
$283$			6.10059e21i			0.523955i	−0.965074	+	0.261977i	$0.915625\pi$
$284$	−6.33619e20	−	2.13770e21i	−0.0527185	−	0.177862i
$285$	−1.04771e22			−0.844576
$286$	8.39287e20	+	5.78494e21i	0.0655566	+	0.451860i
$287$			2.47677e22i			1.87477i
$288$	−3.41485e21	+	2.99736e21i	−0.250518	+	0.219890i
$289$	−1.32627e22			−0.943083
$290$	−2.32931e21	+	3.37939e20i	−0.160563	+	0.0232947i
$291$			8.00113e19i			0.00534705i
$292$	−2.14381e22	+	6.35430e21i	−1.38912	+	0.411739i
$293$	−2.22688e22			−1.39923			−0.699614	−	0.714521i	$-0.746645\pi$
$293$	−2.22688e22			−1.39923			−0.699614	+	0.714521i	$0.746645\pi$
$294$	−1.72268e19	−	1.18739e20i	−0.00104973	−	0.00723548i
$295$			3.34353e22i			1.97609i
$296$	2.82995e22	−	1.30551e22i	1.62238	−	0.748439i
$297$	−3.42224e21			−0.190328
$298$	1.10726e22	−	1.60642e21i	0.597450	−	0.0866789i
$299$			3.45283e20i			0.0180774i
$300$	−5.56120e20	−	1.87624e21i	−0.0282538	−	0.0953226i
$301$	4.01575e22			1.98001
$302$	2.45000e21	+	1.68871e22i	0.117248	+	0.808150i
$303$		−	1.76614e22i		−	0.820428i
$304$	−1.63268e22	−	2.51220e22i	−0.736272	−	1.13290i
$305$	1.61061e20			0.00705167
$306$	1.85126e21	−	2.68584e20i	0.0787001	−	0.0114179i
$307$		−	9.47293e21i		−	0.391056i	−0.980698	−	0.195528i	$-0.937358\pi$
$307$		−	9.47293e21i		−	0.391056i	0.980698	−	0.195528i	$-0.0626420\pi$
$308$	2.35011e22	−	6.96576e21i	0.942175	−	0.279262i
$309$	−1.98371e22			−0.772418
$310$	−5.60326e21	−	3.86215e22i	−0.211927	−	1.46074i
$311$		−	2.79856e22i		−	1.02823i	−0.857721	−	0.514116i	$-0.828120\pi$
$311$		−	2.79856e22i		−	1.02823i	0.857721	−	0.514116i	$-0.171880\pi$
$312$	−3.12809e21	−	6.78073e21i	−0.111658	−	0.242039i
$313$	2.45896e22			0.852809			0.426405	−	0.904533i	$-0.359780\pi$
$313$	2.45896e22			0.852809			0.426405	+	0.904533i	$0.359780\pi$
$314$	4.56686e21	−	6.62566e20i	0.153904	−	0.0223287i
$315$			1.09498e22i			0.358602i
$316$	1.91025e21	+	6.44478e21i	0.0608003	+	0.205128i
$317$	−1.90694e22			−0.589935			−0.294968	−	0.955507i	$-0.595309\pi$
$317$	−1.90694e22			−0.589935			−0.294968	+	0.955507i	$0.595309\pi$
$318$	−1.39490e21	−	9.61456e21i	−0.0419467	−	0.289125i
$319$		−	5.06952e21i		−	0.148201i
$320$	2.47247e22	−	2.89794e22i	0.702719	−	0.823644i
$321$	−8.62608e21			−0.238379
$322$	1.43286e21	−	2.07881e20i	0.0385036	−	0.00558615i
$323$			1.23350e22i			0.322343i
$324$	4.19158e21	−	1.24239e21i	0.106530	−	0.0315757i
$325$	3.21614e21			0.0795033
$326$	−7.54647e21	−	5.20154e22i	−0.181462	−	1.25076i
$327$			1.71162e22i			0.400384i
$328$	−7.52806e22	+	3.47286e22i	−1.71324	+	0.790355i
$329$	4.24062e22			0.939003
$330$	2.83940e22	−	4.11945e21i	0.611789	−	0.0887593i
$331$		−	1.58883e22i		−	0.333138i	−0.986030	−	0.166569i	$-0.946731\pi$
$331$		−	1.58883e22i		−	0.333138i	0.986030	−	0.166569i	$-0.0532689\pi$
$332$	2.46929e22	+	8.33089e22i	0.503883	+	1.70000i
$333$	−2.99866e22			−0.595565
$334$	1.43008e21	+	9.85707e21i	0.0276466	+	0.190559i
$335$			2.70404e22i			0.508873i
$336$	−2.62554e22	+	1.70634e22i	−0.481023	+	0.312617i
$337$	−3.90371e22			−0.696320			−0.348160	−	0.937435i	$-0.613193\pi$
$337$	−3.90371e22			−0.696320			−0.348160	+	0.937435i	$0.613193\pi$
$338$	−4.48352e22	+	6.50475e21i	−0.778697	+	0.112974i
$339$		−	4.53854e22i		−	0.767571i
$340$	−1.50365e22	+	4.45684e21i	−0.247649	+	0.0734035i
$341$	8.40561e22			1.34828
$342$	4.13905e21	+	2.85291e22i	0.0646644	+	0.445711i
$343$		−	6.61218e22i		−	1.00623i
$344$	5.63076e22	+	1.22057e23i	0.834720	+	1.80941i
$345$	1.69474e21			0.0244755
$346$	−7.83190e22	+	1.13626e22i	−1.10200	+	0.159880i
$347$			1.46780e22i			0.201234i	0.994925	+	0.100617i	$0.0320817\pi$
$347$			1.46780e22i			0.201234i	−0.994925	+	0.100617i	$0.967918\pi$
$348$	1.84041e21	+	6.20917e21i	0.0245867	+	0.0829507i
$349$	−1.11202e22			−0.144772			−0.0723860	−	0.997377i	$-0.523061\pi$
$349$	−1.11202e22			−0.144772			−0.0723860	+	0.997377i	$0.523061\pi$
$350$	−1.93631e21	−	1.33464e22i	−0.0245676	−	0.169337i
$351$			7.18498e21i			0.0888508i
$352$	5.41247e22	+	6.16636e22i	0.652397	+	0.743267i
$353$	−2.51623e21			−0.0295650			−0.0147825	−	0.999891i	$-0.504706\pi$
$353$	−2.51623e21			−0.0295650			−0.0147825	+	0.999891i	$0.504706\pi$
$354$	9.10439e22	−	1.32088e22i	1.04285	−	0.151298i
$355$		−	1.79856e22i		−	0.200849i
$356$	3.07081e22	−	9.10192e21i	0.334351	−	0.0991022i
$357$	1.28916e22			0.136865
$358$	−1.57251e21	−	1.08388e22i	−0.0162797	−	0.112210i
$359$		−	1.30312e23i		−	1.31563i	−0.753181	−	0.657813i	$-0.771482\pi$
$359$		−	1.30312e23i		−	1.31563i	0.753181	−	0.657813i	$-0.228518\pi$
$360$	−3.32817e22	+	1.53535e22i	−0.327705	+	0.151177i
$361$	−8.59633e22			−0.825559
$362$	−1.54265e23	+	2.23809e22i	−1.44507	+	0.209653i
$363$		−	1.38582e21i		−	0.0126633i
$364$	−1.46246e22	−	4.93405e22i	−0.130368	−	0.439836i
$365$	−1.80370e23			−1.56866
$366$	−6.36280e19	−	4.38567e20i	−0.000539907	−	0.00372140i
$367$			1.34131e23i			1.11054i	0.831670	+	0.555270i	$0.187385\pi$
$367$			1.34131e23i			1.11054i	−0.831670	+	0.555270i	$0.812615\pi$
$368$	2.64096e21	+	4.06364e21i	0.0213369	+	0.0328311i
$369$	7.97687e22			0.628920
$370$	2.48797e23	−	3.60958e22i	1.91438	−	0.277742i
$371$		−	6.69525e22i		−	0.502808i
$372$	−1.02952e23	+	3.05152e22i	−0.754657	+	0.223682i
$373$	1.82941e23			1.30898			0.654488	−	0.756072i	$-0.272884\pi$
$373$	1.82941e23			1.30898			0.654488	+	0.756072i	$0.272884\pi$
$374$	−4.84995e21	−	3.34292e22i	−0.0338761	−	0.233497i
$375$			7.58832e22i			0.517445i
$376$	5.94608e22	+	1.28892e23i	0.395858	+	0.858097i
$377$	−1.06434e22			−0.0691846
$378$	2.98163e22	−	4.32579e21i	0.189246	−	0.0274561i
$379$		−	4.40960e22i		−	0.273304i	−0.990619	−	0.136652i	$-0.956366\pi$
$379$		−	4.40960e22i		−	0.273304i	0.990619	−	0.136652i	$-0.0436343\pi$
$380$	−6.86827e22	−	2.31722e23i	−0.415714	−	1.40254i
$381$	6.66239e22			0.393827
$382$	−4.04633e21	−	2.78900e22i	−0.0233610	−	0.161020i
$383$			6.22935e22i			0.351280i	0.984454	+	0.175640i	$0.0561995\pi$
$383$			6.22935e22i			0.351280i	−0.984454	+	0.175640i	$0.943801\pi$
$384$	−8.86782e22	−	5.58767e22i	−0.488468	−	0.307787i
$385$	1.97726e23			1.06394
$386$	−1.88231e23	+	2.73088e22i	−0.989474	+	0.143554i
$387$		−	1.29334e23i		−	0.664223i
$388$	−1.76960e21	+	5.24513e20i	−0.00887953	+	0.00263191i
$389$	−1.77093e23			−0.868270			−0.434135	−	0.900848i	$-0.642946\pi$
$389$	−1.77093e23			−0.868270			−0.434135	+	0.900848i	$0.642946\pi$
$390$	−8.64877e21	−	5.96132e22i	−0.0414355	−	0.285602i
$391$		−	1.99527e21i		−	0.00934139i
$392$	2.51321e21	−	1.15940e21i	0.0114988	−	0.00530465i
$393$	1.52359e23			0.681293
$394$	2.93457e23	−	4.25751e22i	1.28256	−	0.186076i
$395$			5.42232e22i			0.231639i
$396$	−2.24344e22	−	7.56893e22i	−0.0936825	−	0.316066i
$397$	−4.64850e23			−1.89757			−0.948787	−	0.315917i	$-0.897688\pi$
$397$	−4.64850e23			−1.89757			−0.948787	+	0.315917i	$0.897688\pi$
$398$	−4.08438e22	−	2.81523e23i	−0.162997	−	1.12348i
$399$			1.98667e23i			0.775122i
$400$	3.78508e22	−	2.45993e22i	0.144390	−	0.0938387i
$401$	6.07149e22			0.226462			0.113231	−	0.993569i	$-0.463880\pi$
$401$	6.07149e22			0.226462			0.113231	+	0.993569i	$0.463880\pi$
$402$	7.36307e22	−	1.06825e22i	0.268550	−	0.0389616i
$403$		−	1.76475e23i		−	0.629417i
$404$	3.90614e23	−	1.15779e23i	1.36244	−	0.403828i
$405$	3.52658e22			0.120298
$406$	6.40799e21	+	4.41682e22i	0.0213790	+	0.147359i
$407$			5.41483e23i			1.76699i
$408$	1.80762e22	+	3.91835e22i	0.0576986	+	0.125072i
$409$	−2.80194e23			−0.874882			−0.437441	−	0.899247i	$-0.644115\pi$
$409$	−2.80194e23			−0.874882			−0.437441	+	0.899247i	$0.644115\pi$
$410$	−6.61835e23	+	9.60199e22i	−2.02160	+	0.293296i
$411$			1.03435e23i			0.309095i
$412$	−1.30042e23	−	4.38735e23i	−0.380197	−	1.28271i
$413$	6.33999e23			1.81359
$414$	−6.69518e20	−	4.61477e21i	−0.00187395	−	0.0129166i
$415$			7.00920e23i			1.91971i
$416$	1.29462e23	−	1.13635e23i	0.346979	−	0.304559i
$417$	2.05604e22			0.0539272
$418$	5.15164e23	−	7.47407e22i	1.32239	−	0.191854i
$419$		−	5.49311e23i		−	1.38004i	−0.723790	−	0.690021i	$-0.757601\pi$
$419$		−	5.49311e23i		−	1.38004i	0.723790	−	0.690021i	$-0.242399\pi$
$420$	−2.42176e23	+	7.17815e22i	−0.595509	+	0.176510i
$421$	−5.73273e23			−1.37982			−0.689910	−	0.723895i	$-0.742350\pi$
$421$	−5.73273e23			−1.37982			−0.689910	+	0.723895i	$0.742350\pi$
$422$	9.73946e22	+	6.71310e23i	0.229468	+	1.58165i
$423$		−	1.36577e23i		−	0.315002i
$424$	2.03500e23	−	9.38788e22i	0.459485	−	0.211970i
$425$	−1.85850e22			−0.0410830
$426$	−4.89745e22	+	7.10529e21i	−0.105995	+	0.0153779i
$427$		−	3.05403e21i		−	0.00647177i
$428$	−5.65482e22	−	1.90782e23i	−0.117334	−	0.395862i
$429$	1.29743e23			0.263613
$430$	1.55683e23	+	1.07307e24i	0.309760	+	2.13508i
$431$			7.07647e23i			1.37886i	0.724351	+	0.689431i	$0.242140\pi$
$431$			7.07647e23i			1.37886i	−0.724351	+	0.689431i	$0.757860\pi$
$432$	5.49556e22	+	8.45601e22i	0.104872	+	0.161366i
$433$	−4.42762e23			−0.827522			−0.413761	−	0.910386i	$-0.635785\pi$
$433$	−4.42762e23			−0.827522			−0.413761	+	0.910386i	$0.635785\pi$
$434$	−7.32339e23	+	1.06249e23i	−1.34062	+	0.194499i
$435$			5.22409e22i			0.0936714i
$436$	−3.78556e23	+	1.12205e23i	−0.664893	+	0.197076i
$437$	3.07484e22			0.0529041
$438$	7.12560e22	+	4.91145e23i	0.120103	+	0.827833i
$439$		−	6.30236e23i		−	1.04069i	−0.853955	−	0.520346i	$-0.825803\pi$
$439$		−	6.30236e23i		−	1.04069i	0.853955	−	0.520346i	$-0.174197\pi$
$440$	2.77246e23	+	6.00983e23i	0.448530	+	0.972273i
$441$	−2.66304e21			−0.00422114
$442$	−7.01844e22	+	1.01825e22i	−0.109003	+	0.0158144i
$443$		−	5.50842e23i		−	0.838289i	−0.907920	−	0.419144i	$-0.862330\pi$
$443$		−	5.50842e23i		−	0.838289i	0.907920	−	0.419144i	$-0.137670\pi$
$444$	−1.96577e23	−	6.63211e23i	−0.293147	−	0.989019i
$445$	2.58362e23			0.377563
$446$	−5.43943e22	−	3.74923e23i	−0.0779004	−	0.536943i
$447$		−	2.48332e23i		−	0.348549i
$448$	−5.49506e23	−	4.68830e23i	−0.755911	−	0.644930i
$449$	9.80720e23			1.32229			0.661147	−	0.750257i	$-0.270070\pi$
$449$	9.80720e23			1.32229			0.661147	+	0.750257i	$0.270070\pi$
$450$	−4.29843e22	+	6.23623e21i	−0.0568064	+	0.00824156i
$451$		−	1.44042e24i		−	1.86595i
$452$	1.00378e24	−	2.97523e23i	1.27466	−	0.377811i
$453$	3.78738e23			0.471471
$454$	−8.83205e22	−	6.08765e23i	−0.107785	−	0.742929i
$455$		−	4.15126e23i		−	0.496681i
$456$	−6.03842e23	+	2.78565e23i	−0.708337	+	0.326771i
$457$	−1.91990e23			−0.220817			−0.110408	−	0.993886i	$-0.535216\pi$
$457$	−1.91990e23			−0.220817			−0.110408	+	0.993886i	$0.535216\pi$
$458$	1.33139e24	−	1.93160e23i	1.50147	−	0.217836i
$459$		−	4.15195e22i		−	0.0459133i
$460$	1.11099e22	+	3.74825e22i	0.0120473	+	0.0406451i
$461$	1.00430e24			1.06796			0.533982	−	0.845496i	$-0.320695\pi$
$461$	1.00430e24			1.06796			0.533982	+	0.845496i	$0.320695\pi$
$462$	−7.81129e22	−	5.38407e23i	−0.0814601	−	0.561478i
$463$			1.14804e23i			0.117416i	0.998275	+	0.0587082i	$0.0186981\pi$
$463$			1.14804e23i			0.117416i	−0.998275	+	0.0587082i	$0.981302\pi$
$464$	−1.25263e23	+	8.14082e22i	−0.125649	+	0.0816594i
$465$	−8.66189e23			−0.852190
$466$	−3.71065e23	+	5.38346e22i	−0.358077	+	0.0519504i
$467$		−	1.05269e24i		−	0.996431i	−0.867053	−	0.498215i	$-0.833989\pi$
$467$		−	1.05269e24i		−	0.996431i	0.867053	−	0.498215i	$-0.166011\pi$
$468$	−1.58909e23	+	4.71010e22i	−0.147549	+	0.0437338i
$469$	5.12739e23			0.467026
$470$	1.64401e23	+	1.13317e24i	0.146901	+	1.01254i
$471$		−	1.02424e23i		−	0.0897869i
$472$	8.88974e23	+	1.92702e24i	0.764559	+	1.65733i
$473$	−2.33545e24			−1.97070
$474$	1.47649e23	−	2.14212e22i	0.122244	−	0.0177353i
$475$		−	2.86406e23i		−	0.232670i
$476$	8.45105e22	+	2.85121e23i	0.0673671	+	0.227283i
$477$	−2.15632e23			−0.168674
$478$	2.37285e22	+	1.63553e23i	0.0182145	+	0.125547i
$479$			4.71368e23i			0.355092i	0.984113	+	0.177546i	$0.0568158\pi$
$479$			4.71368e23i			0.355092i	−0.984113	+	0.177546i	$0.943184\pi$
$480$	−5.57750e23	−	6.35437e23i	−0.412352	−	0.469787i
$481$	1.13684e24			0.824886
$482$	−9.30514e23	+	1.35000e23i	−0.662673	+	0.0961416i
$483$		−	3.21357e22i		−	0.0224628i
$484$	3.06501e22	−	9.08473e21i	0.0210292	−	0.00623310i
$485$	−1.48885e22			−0.0100271
$486$	−1.39320e22	−	9.60285e22i	−0.00921055	−	0.0634854i
$487$			1.92997e24i			1.25253i	0.779608	+	0.626267i	$0.215418\pi$
$487$			1.92997e24i			1.25253i	−0.779608	+	0.626267i	$0.784582\pi$
$488$	9.28263e21	−	4.28228e21i	0.00591416	−	0.00272833i
$489$	−1.16658e24			−0.729686
$490$	2.20950e22	−	3.20558e21i	0.0135684	−	0.00196853i
$491$			9.63500e23i			0.580922i	0.956887	+	0.290461i	$0.0938087\pi$
$491$			9.63500e23i			0.580922i	−0.956887	+	0.290461i	$0.906191\pi$
$492$	5.22922e23	+	1.76423e24i	0.309565	+	1.04441i
$493$	6.15047e22			0.0357508
$494$	−1.56918e23	−	1.08158e24i	−0.0895633	−	0.617331i
$495$		−	6.36812e23i		−	0.356915i
$496$	−1.34980e24	−	2.07694e24i	−0.742909	−	1.14311i
$497$	−3.41042e23			−0.184332
$498$	1.90860e24	−	2.76902e23i	1.01310	−	0.146981i
$499$			1.91388e24i			0.997723i	0.866682	+	0.498862i	$0.166248\pi$
$499$			1.91388e24i			0.997723i	−0.866682	+	0.498862i	$0.833752\pi$
$500$	−1.67830e24	+	4.97451e23i	−0.859290	+	0.254695i
$501$	2.21071e23			0.111171
$502$	−2.83786e23	−	1.95604e24i	−0.140171	−	0.966151i
$503$			3.34258e24i			1.62170i	0.585257	+	0.810848i	$0.300994\pi$
$503$			3.34258e24i			1.62170i	−0.585257	+	0.810848i	$0.699006\pi$
$504$	2.91133e23	+	6.31086e23i	0.138745	+	0.300756i
$505$	3.28643e24			1.53852
$506$	−8.33311e22	+	1.20898e22i	−0.0383224	+	0.00555987i
$507$			1.00555e24i			0.454288i
$508$	4.36752e23	+	1.47351e24i	0.193848	+	0.654005i
$509$	−1.48939e24			−0.649452			−0.324726	−	0.945808i	$-0.605272\pi$
$509$	−1.48939e24			−0.649452			−0.324726	+	0.945808i	$0.605272\pi$
$510$	4.99783e22	+	3.44484e23i	0.0214116	+	0.147583i
$511$			3.42016e24i			1.43966i
$512$	6.54490e23	−	2.32758e24i	0.270691	−	0.962666i
$513$	6.39841e23			0.260026
$514$	−2.68767e24	+	3.89931e23i	−1.07327	+	0.155711i
$515$		−	3.69130e24i		−	1.44849i
$516$	2.86046e24	−	8.47847e23i	1.10304	−	0.326942i
$517$	−2.46623e24			−0.934584
$518$	−6.84447e23	−	4.71767e24i	−0.254901	−	1.75695i
$519$			1.75651e24i			0.642902i
$520$	1.26176e24	−	5.82077e23i	0.453886	−	0.209387i
$521$	1.05042e23			0.0371385			0.0185693	−	0.999828i	$-0.494089\pi$
$521$	1.05042e23			0.0371385			0.0185693	+	0.999828i	$0.494089\pi$
$522$	1.42251e23	−	2.06380e22i	0.0494335	−	0.00717189i
$523$		−	4.71334e24i		−	1.60995i	−0.593305	−	0.804977i	$-0.702177\pi$
$523$		−	4.71334e24i		−	1.60995i	0.593305	−	0.804977i	$-0.297823\pi$
$524$	9.98784e23	+	3.36970e24i	0.335344	+	1.13138i
$525$	−2.99328e23			−0.0987902
$526$	−5.90841e23	−	4.07248e24i	−0.191690	−	1.32126i
$527$			1.01979e24i			0.325249i
$528$	1.52694e24	−	9.92360e23i	0.478759	−	0.311146i
$529$	3.23918e24			0.998467
$530$	1.78908e24	−	2.59563e23i	0.542185	−	0.0786610i
$531$		−	2.04190e24i		−	0.608393i
$532$	−4.39390e24	+	1.30236e24i	−1.28720	+	0.381528i
$533$	−3.02416e24			−0.871084
$534$	−1.02067e23	−	7.03518e23i	−0.0289078	−	0.199252i
$535$		−	1.60515e24i		−	0.447024i
$536$	7.18947e23	+	1.55845e24i	0.196886	+	0.426786i
$537$	−2.43089e23			−0.0654630
$538$	4.58423e22	−	6.65087e21i	0.0121402	−	0.00176132i
$539$			4.80877e22i			0.0125238i
$540$	2.31185e23	+	7.79970e23i	0.0592127	+	0.199772i
$541$	3.17833e24			0.800615			0.400308	−	0.916381i	$-0.368903\pi$
$541$	3.17833e24			0.800615			0.400308	+	0.916381i	$0.368903\pi$
$542$	2.10833e23	+	1.45320e24i	0.0522330	+	0.360025i
$543$			3.45979e24i			0.843047i
$544$	−7.48119e23	+	6.56655e23i	−0.179300	+	0.157379i
$545$	−3.18498e24			−0.750825
$546$	−1.13038e24	+	1.63998e23i	−0.262115	+	0.0380281i
$547$			1.21766e22i			0.00277740i	0.999999	+	0.00138870i	$0.000442038\pi$
$547$			1.21766e22i			0.00277740i	−0.999999	+	0.00138870i	$0.999558\pi$
$548$	−2.28767e24	+	6.78068e23i	−0.513296	+	0.152142i
$549$	−9.83604e21			−0.00217105
$550$	1.12611e23	+	7.76188e23i	0.0244520	+	0.168540i
$551$			9.47826e23i			0.202472i
$552$	9.76753e22	−	4.50597e22i	0.0205274	−	0.00946971i
$553$	1.02818e24			0.212590
$554$	7.83115e24	−	1.13615e24i	1.59308	−	0.231126i
$555$		−	5.57993e24i		−	1.11684i
$556$	1.34784e23	+	4.54733e23i	0.0265439	+	0.0895537i
$557$	−3.62232e24			−0.701923			−0.350962	−	0.936390i	$-0.614145\pi$
$557$	−3.62232e24			−0.701923			−0.350962	+	0.936390i	$0.614145\pi$
$558$	3.42193e23	+	2.35862e24i	0.0652474	+	0.449729i
$559$			4.90326e24i			0.919980i
$560$	−3.17517e24	−	4.88562e24i	−0.586239	−	0.902044i
$561$	−7.49738e23			−0.136221
$562$	1.38402e24	−	2.00796e23i	0.247467	−	0.0359028i
$563$		−	9.74148e24i		−	1.71415i	−0.515190	−	0.857076i	$-0.672279\pi$
$563$		−	9.74148e24i		−	1.71415i	0.515190	−	0.857076i	$-0.327721\pi$
$564$	3.02065e24	−	8.95326e23i	0.523104	−	0.155049i
$565$	8.44533e24			1.43940
$566$	4.48467e23	+	3.09114e24i	0.0752285	+	0.518526i
$567$		−	6.68710e23i		−	0.110405i
$568$	−4.78199e23	−	1.03658e24i	−0.0777094	−	0.168450i
$569$	−1.59016e24			−0.254348			−0.127174	−	0.991880i	$-0.540591\pi$
$569$	−1.59016e24			−0.254348			−0.127174	+	0.991880i	$0.540591\pi$
$570$	−5.30871e24	+	7.70196e23i	−0.835825	+	0.121263i
$571$		−	7.74737e24i		−	1.20069i	−0.799743	−	0.600343i	$-0.795031\pi$
$571$		−	7.74737e24i		−	1.20069i	0.799743	−	0.600343i	$-0.204969\pi$
$572$	8.50526e23	+	2.86950e24i	0.129755	+	0.437766i
$573$	−6.25508e23			−0.0939380
$574$	1.82073e24	+	1.25497e25i	0.269177	+	1.85535i
$575$			4.63281e22i			0.00674269i
$576$	−1.50995e24	+	1.76978e24i	−0.216351	+	0.253581i
$577$	−4.96607e23			−0.0700537			−0.0350268	−	0.999386i	$-0.511152\pi$
$577$	−4.96607e23			−0.0700537			−0.0350268	+	0.999386i	$0.511152\pi$
$578$	−6.72013e24	+	9.74966e23i	−0.933312	+	0.135406i
$579$			4.22157e24i			0.577254i
$580$	−1.15541e24	+	3.42464e23i	−0.155554	+	0.0461066i
$581$	1.32908e25			1.76184
$582$	5.88180e21	+	4.05413e22i	0.000767721	+	0.00529165i
$583$			3.89377e24i			0.500442i
$584$	−1.03955e25	+	4.79565e24i	−1.31561	+	0.606921i
$585$	−1.33698e24			−0.166619
$586$	−1.12835e25	+	1.63703e24i	−1.38473	+	0.200899i
$587$		−	2.35008e24i		−	0.284014i	−0.989866	−	0.142007i	$-0.954644\pi$
$587$		−	2.35008e24i		−	0.284014i	0.989866	−	0.142007i	$-0.0453555\pi$
$588$	−1.74575e22	−	5.88981e22i	−0.00207772	−	0.00700979i
$589$	−1.57156e25			−1.84202
$590$	2.45790e24	+	1.69415e25i	0.283724	+	1.95562i
$591$		−	6.58154e24i		−	0.748239i
$592$	1.33795e25	−	8.69533e24i	1.49811	−	0.973623i
$593$	7.54021e24			0.831556			0.415778	−	0.909466i	$-0.363509\pi$
$593$	7.54021e24			0.831556			0.415778	+	0.909466i	$0.363509\pi$
$594$	−1.73403e24	+	2.51576e23i	−0.188356	+	0.0273269i
$595$			2.39887e24i			0.256658i
$596$	5.49232e24	−	1.62793e24i	0.578815	−	0.171562i
$597$	−6.31391e24			−0.655435
$598$	2.53825e22	+	1.74953e23i	0.00259552	+	0.0178901i
$599$			1.46586e25i			1.47656i	0.674495	+	0.738279i	$0.264361\pi$
$599$			1.46586e25i			1.47656i	−0.674495	+	0.738279i	$0.735639\pi$
$600$	−4.19709e23	−	9.09798e23i	−0.0416473	−	0.0902784i
$601$	−6.58842e24			−0.644037			−0.322018	−	0.946733i	$-0.604361\pi$
$601$	−6.58842e24			−0.644037			−0.322018	+	0.946733i	$0.604361\pi$
$602$	2.03476e25	−	2.95206e24i	1.95950	−	0.284287i
$603$		−	1.65136e24i		−	0.156670i
$604$	2.48281e24	+	8.37649e24i	0.232066	+	0.782942i
$605$	2.57874e23			0.0237471
$606$	−1.29832e24	−	8.94893e24i	−0.117796	−	0.811928i
$607$		−	3.27052e24i		−	0.292360i	−0.989258	−	0.146180i	$-0.953302\pi$
$607$		−	3.27052e24i		−	0.292360i	0.989258	−	0.146180i	$-0.0466979\pi$
$608$	−1.01195e25	−	1.15290e25i	−0.891303	−	1.01545i
$609$	9.90590e23			0.0859683
$610$	8.16089e22	−	1.18399e22i	0.00697861	−	0.00101247i
$611$			5.17784e24i			0.436292i
$612$	9.18282e23	−	2.72181e23i	0.0762454	−	0.0225993i
$613$	−2.59264e24			−0.212128			−0.106064	−	0.994359i	$-0.533825\pi$
$613$	−2.59264e24			−0.212128			−0.106064	+	0.994359i	$0.533825\pi$
$614$	−6.96375e23	−	4.79989e24i	−0.0561471	−	0.387004i
$615$			1.48434e25i			1.17939i
$616$	1.13958e25	−	5.25713e24i	0.892317	−	0.411645i
$617$	1.76336e25			1.36073			0.680367	−	0.732871i	$-0.261820\pi$
$617$	1.76336e25			1.36073			0.680367	+	0.732871i	$0.261820\pi$
$618$	−1.00514e25	+	1.45827e24i	−0.764415	+	0.110902i
$619$		−	1.75512e25i		−	1.31550i	−0.753236	−	0.657750i	$-0.771508\pi$
$619$		−	1.75512e25i		−	1.31550i	0.753236	−	0.657750i	$-0.228492\pi$
$620$	−5.67829e24	−	1.91574e25i	−0.419462	−	1.41518i
$621$	−1.03498e23			−0.00753546
$622$	−2.05728e24	−	1.41802e25i	−0.147632	−	1.01758i
$623$		−	4.89906e24i		−	0.346514i
$624$	−2.08346e24	−	3.20581e24i	−0.145252	−	0.223499i
$625$	−1.66263e25			−1.14255
$626$	1.24594e25	−	1.80763e24i	0.843973	−	0.122445i
$627$		−	1.15539e25i		−	0.771474i
$628$	2.26530e24	−	6.71438e23i	0.149104	−	0.0441946i
$629$	−6.56941e24			−0.426256
$630$	8.04946e23	+	5.54823e24i	0.0514875	+	0.354887i
$631$			3.42904e24i			0.216226i	0.994139	+	0.108113i	$0.0344809\pi$
$631$			3.42904e24i			0.216226i	−0.994139	+	0.108113i	$0.965519\pi$
$632$	1.44168e24	+	3.12511e24i	0.0896222	+	0.194273i
$633$	1.50559e25			0.922728
$634$	−9.66239e24	+	1.40183e24i	−0.583823	+	0.0847019i
$635$			1.23974e25i			0.738529i
$636$	−1.41357e24	−	4.76911e24i	−0.0830241	−	0.280107i
$637$	1.00960e23			0.00584648
$638$	−3.72671e23	−	2.56870e24i	−0.0212784	−	0.146665i
$639$			1.09838e24i			0.0618367i
$640$	1.03976e25	−	1.65013e25i	0.577181	−	0.916005i
$641$	1.54444e25			0.845372			0.422686	−	0.906276i	$-0.361087\pi$
$641$	1.54444e25			0.845372			0.422686	+	0.906276i	$0.361087\pi$
$642$	−4.37080e24	+	6.34121e23i	−0.235909	+	0.0342261i
$643$			1.44099e25i			0.766940i	0.923553	+	0.383470i	$0.125271\pi$
$643$			1.44099e25i			0.766940i	−0.923553	+	0.383470i	$0.874729\pi$
$644$	7.10741e23	−	2.10665e23i	0.0373026	−	0.0110566i
$645$	2.40665e25			1.24559
$646$	9.06775e23	+	6.25011e24i	0.0462814	+	0.319003i
$647$		−	2.66566e25i		−	1.34173i	−0.741578	−	0.670867i	$-0.765922\pi$
$647$		−	2.66566e25i		−	1.34173i	0.741578	−	0.670867i	$-0.234078\pi$
$648$	2.03252e24	−	9.37645e23i	0.100893	−	0.0465439i
$649$	−3.68716e25			−1.80505
$650$	1.62961e24	−	2.36426e23i	0.0786796	−	0.0114150i
$651$			1.64247e25i			0.782109i
$652$	−7.64752e24	−	2.58012e25i	−0.359164	−	1.21175i
$653$	−1.56846e25			−0.726532			−0.363266	−	0.931686i	$-0.618338\pi$
$653$	−1.56846e25			−0.726532			−0.363266	+	0.931686i	$0.618338\pi$
$654$	1.25824e24	+	8.67268e24i	0.0574864	+	0.396235i
$655$			2.83509e25i			1.27760i
$656$	−3.55914e25	+	2.31308e25i	−1.58201	+	1.02815i
$657$	1.10152e25			0.482953
$658$	2.14870e25	−	3.11737e24i	0.929273	−	0.134820i
$659$			4.61589e25i			1.96919i	0.174857	+	0.984594i	$0.444054\pi$
$659$			4.61589e25i			1.96919i	−0.174857	+	0.984594i	$0.555946\pi$
$660$	1.40843e25	−	4.17461e24i	0.592707	−	0.175679i
$661$	1.83934e25			0.763569			0.381784	−	0.924251i	$-0.375310\pi$
$661$	1.83934e25			0.763569			0.381784	+	0.924251i	$0.375310\pi$
$662$	−1.16798e24	−	8.05051e24i	−0.0478314	−	0.329687i
$663$			1.57407e24i			0.0635920i
$664$	1.86360e25	+	4.03970e25i	0.742745	+	1.61004i
$665$	−3.69681e25			−1.45356
$666$	−1.51941e25	+	2.20438e24i	−0.589395	+	0.0855103i
$667$		−	1.53317e23i		−	0.00586756i
$668$	1.44923e24	+	4.88940e24i	0.0547203	+	0.184615i
$669$	−8.40864e24			−0.313250
$670$	1.98780e24	+	1.37012e25i	0.0730632	+	0.503601i
$671$			1.77614e23i			0.00644132i
$672$	−1.20491e25	+	1.05760e25i	−0.431154	+	0.378442i
$673$	1.62946e25			0.575318			0.287659	−	0.957733i	$-0.407123\pi$
$673$	1.62946e25			0.575318			0.287659	+	0.957733i	$0.407123\pi$
$674$	−1.97799e25	+	2.86970e24i	−0.689105	+	0.0999764i
$675$			9.64038e23i			0.0331406i
$676$	−2.22396e25	+	6.59185e24i	−0.754408	+	0.223608i
$677$	1.39505e25			0.466972			0.233486	−	0.972360i	$-0.424987\pi$
$677$	1.39505e25			0.466972			0.233486	+	0.972360i	$0.424987\pi$
$678$	−3.33637e24	−	2.29965e25i	−0.110206	−	0.759618i
$679$			2.82316e23i			0.00920254i
$680$	−7.29128e24	+	3.36362e24i	−0.234544	+	0.108200i
$681$	−1.36532e25			−0.433421
$682$	4.25908e25	−	6.17914e24i	1.33431	−	0.193584i
$683$		−	5.16072e25i		−	1.59560i	−0.602922	−	0.797800i	$-0.705997\pi$
$683$		−	5.16072e25i		−	1.59560i	0.602922	−	0.797800i	$-0.294003\pi$
$684$	4.19447e24	+	1.41513e25i	0.127989	+	0.431809i
$685$	−1.92473e25			−0.579635
$686$	−4.86075e24	−	3.35036e25i	−0.144473	−	0.995806i
$687$		−	2.98600e25i		−	0.875951i
$688$	3.75035e25	+	5.77065e25i	1.08586	+	1.67082i
$689$	8.17496e24			0.233621
$690$	8.58719e23	−	1.24584e23i	0.0242220	−	0.00351416i
$691$		−	2.78968e25i		−	0.776697i	−0.921512	−	0.388349i	$-0.873046\pi$
$691$		−	2.78968e25i		−	0.776697i	0.921512	−	0.388349i	$-0.126954\pi$
$692$	−3.88486e25	+	1.15148e25i	−1.06763	+	0.316447i
$693$	−1.20752e25			−0.327564
$694$	1.07901e24	+	7.43726e24i	0.0288928	+	0.199149i
$695$			3.82590e24i			0.101128i
$696$	1.38897e24	+	3.01086e24i	0.0362419	+	0.0785611i
$697$	1.74756e25			0.450128
$698$	−5.63456e24	+	8.17470e23i	−0.143272	+	0.0207861i
$699$			8.32212e24i			0.208900i
$700$	−1.96224e24	−	6.62021e24i	−0.0486262	−	0.164055i
$701$	−1.95417e24			−0.0478079			−0.0239040	−	0.999714i	$-0.507610\pi$
$701$	−1.95417e24			−0.0478079			−0.0239040	+	0.999714i	$0.507610\pi$
$702$	5.28183e23	+	3.64059e24i	0.0127570	+	0.0879302i
$703$		−	1.01239e26i		−	2.41406i
$704$	3.19577e25	+	2.72658e25i	0.752354	+	0.641896i
$705$	2.54142e25			0.590711
$706$	−1.27496e24	+	1.84973e23i	−0.0292587	+	0.00424489i
$707$		−	6.23173e25i		−	1.41200i
$708$	4.51605e25	−	1.33857e25i	1.01032	−	0.299461i
$709$	6.78287e25			1.49829			0.749147	−	0.662403i	$-0.230463\pi$
$709$	6.78287e25			1.49829			0.749147	+	0.662403i	$0.230463\pi$
$710$	−1.32216e24	−	9.11320e24i	−0.0288375	−	0.198768i
$711$		−	3.31143e24i		−	0.0713163i
$712$	1.48905e25	−	6.86931e24i	0.316658	−	0.146081i
$713$	2.54210e24			0.0533810
$714$	6.53210e24	−	9.47686e23i	0.135447	−	0.0196508i
$715$			2.41426e25i			0.494344i
$716$	−1.59356e24	−	5.37636e24i	−0.0322220	−	0.108710i
$717$	3.66810e24			0.0732435
$718$	−9.57947e24	−	6.60282e25i	−0.188895	−	1.30200i
$719$			3.31940e25i			0.646398i	0.946331	+	0.323199i	$0.104758\pi$
$719$			3.31940e25i			0.646398i	−0.946331	+	0.323199i	$0.895242\pi$
$720$	−1.57350e25	+	1.02262e25i	−0.302604	+	0.196662i
$721$	−6.99943e25			−1.32937
$722$	−4.35572e25	+	6.31934e24i	−0.817005	+	0.118532i
$723$			2.08692e25i			0.386600i
$724$	−7.65199e25	+	2.26806e25i	−1.40000	+	0.414962i
$725$	−1.42807e24			−0.0258053
$726$	−1.01875e23	−	7.02189e23i	−0.00181818	−	0.0125321i
$727$			5.31916e25i			0.937634i	0.883295	+	0.468817i	$0.155320\pi$
$727$			5.31916e25i			0.937634i	−0.883295	+	0.468817i	$0.844680\pi$
$728$	−1.10373e25	−	2.39255e25i	−0.192168	−	0.416561i
$729$	−2.15369e24			−0.0370370
$730$	−9.13925e25	+	1.32594e25i	−1.55240	+	0.225225i
$731$		−	2.83342e25i		−	0.475396i
$732$	−6.44800e22	−	2.17543e23i	−0.00106863	−	0.00360533i
$733$	6.09197e25			0.997291			0.498646	−	0.866806i	$-0.333831\pi$
$733$	6.09197e25			0.997291			0.498646	+	0.866806i	$0.333831\pi$
$734$	9.86025e24	+	6.79635e25i	0.159450	+	1.09903i
$735$		−	4.95539e23i		−	0.00791575i
$736$	1.63689e24	+	1.86489e24i	0.0258297	+	0.0294274i
$737$	−2.98195e25			−0.464828
$738$	4.04184e25	−	5.86396e24i	0.622403	−	0.0902992i
$739$			7.05456e25i			1.07317i	0.843845	+	0.536587i	$0.180287\pi$
$739$			7.05456e25i			1.07317i	−0.843845	+	0.536587i	$0.819713\pi$
$740$	1.23411e26	−	3.65791e25i	1.85467	−	0.549728i
$741$	−2.42574e25			−0.360148
$742$	−4.92182e24	−	3.39245e25i	−0.0721923	−	0.497598i
$743$		−	3.88713e23i		−	0.00563287i	−0.999996	−	0.00281644i	$-0.999103\pi$
$743$		−	3.88713e23i		−	0.00563287i	0.999996	−	0.00281644i	$-0.000896501\pi$
$744$	−4.99222e25	+	2.30302e25i	−0.714722	+	0.329716i
$745$	4.62097e25			0.653621
$746$	9.26954e25	−	1.34484e25i	1.29541	−	0.187941i
$747$		−	4.28054e25i		−	0.591034i
$748$	−4.91489e24	−	1.65819e25i	−0.0670501	−	0.226214i
$749$	−3.04367e25			−0.410262
$750$	5.57833e24	+	3.84497e25i	0.0742939	+	0.512084i
$751$		−	5.41739e25i		−	0.712904i	−0.934314	−	0.356452i	$-0.883986\pi$
$751$		−	5.41739e25i		−	0.712904i	0.934314	−	0.356452i	$-0.116014\pi$
$752$	3.96036e25	+	6.09380e25i	0.514961	+	0.792370i
$753$	−4.38695e25			−0.563648
$754$	−5.39297e24	+	7.82421e23i	−0.0684678	+	0.00993341i
$755$			7.04757e25i			0.884131i
$756$	1.47898e25	−	4.38372e24i	0.183343	−	0.0543433i
$757$	−1.02972e26			−1.26141			−0.630705	−	0.776022i	$-0.717234\pi$
$757$	−1.02972e26			−1.26141			−0.630705	+	0.776022i	$0.717234\pi$
$758$	−3.24159e24	−	2.23432e25i	−0.0392406	−	0.270473i
$759$			1.86892e24i			0.0223571i
$760$	−5.18355e25	−	1.12363e26i	−0.612781	−	1.32832i
$761$	2.35135e25			0.274697			0.137349	−	0.990523i	$-0.456142\pi$
$761$	2.35135e25			0.274697			0.137349	+	0.990523i	$0.456142\pi$
$762$	3.37580e25	−	4.89766e24i	0.389747	−	0.0565450i
$763$			6.03936e25i			0.689080i
$764$	−4.10051e24	−	1.38343e25i	−0.0462378	−	0.155997i
$765$	7.72597e24			0.0860994
$766$	4.57932e24	+	3.15638e25i	0.0504362	+	0.347641i
$767$			7.74118e25i			0.842653i
$768$	−4.90404e25	−	2.17935e25i	−0.527598	−	0.234464i
$769$	1.07612e26			1.14425			0.572127	−	0.820165i	$-0.306119\pi$
$769$	1.07612e26			1.14425			0.572127	+	0.820165i	$0.306119\pi$
$770$	1.00187e26	−	1.45353e25i	1.05292	−	0.152759i
$771$			6.02781e25i			0.626138i
$772$	−9.33680e25	+	2.76745e25i	−0.958611	+	0.284134i
$773$	2.29655e25			0.233056			0.116528	−	0.993187i	$-0.462823\pi$
$773$	2.29655e25			0.233056			0.116528	+	0.993187i	$0.462823\pi$
$774$	−9.50761e24	−	6.55329e25i	−0.0953680	−	0.657341i
$775$		−	2.36784e25i		−	0.234767i
$776$	−8.58090e23	+	3.95855e23i	−0.00840964	+	0.00387955i
$777$	−1.05806e26			−1.02500
$778$	−8.97322e25	+	1.30185e25i	−0.859274	+	0.124665i
$779$			2.69309e26i			2.54926i
$780$	−8.76458e24	−	2.95699e25i	−0.0820125	−	0.276693i
$781$	1.98340e25			0.183464
$782$	−1.46677e23	−	1.01100e24i	−0.00134122	−	0.00924460i
$783$		−	3.19036e24i		−	0.0288393i
$784$	1.18820e24	−	7.72211e23i	0.0106181	−	0.00690067i
$785$	1.90591e25			0.168374
$786$	7.71993e25	−	1.12002e25i	0.674234	−	0.0978188i
$787$			1.34374e26i			1.16023i	0.814536	+	0.580114i	$0.196992\pi$
$787$			1.34374e26i			1.16023i	−0.814536	+	0.580114i	$0.803008\pi$
$788$	1.45563e26	−	4.31452e25i	1.24256	−	0.368296i
$789$	−9.13361e25			−0.770814
$790$	3.98606e24	+	2.74746e25i	0.0332583	+	0.229239i
$791$		−	1.60140e26i		−	1.32103i
$792$	−1.69315e25	−	3.67022e25i	−0.138092	−	0.299340i
$793$	3.72900e23			0.00300700
$794$	−2.35537e26	+	3.41721e25i	−1.87791	+	0.272450i
$795$		−	4.01249e25i		−	0.316308i
$796$	−4.13907e25	−	1.39644e26i	−0.322616	−	1.08844i
$797$	3.88078e25			0.299085			0.149542	−	0.988755i	$-0.452220\pi$
$797$	3.88078e25			0.299085			0.149542	+	0.988755i	$0.452220\pi$
$798$	1.46044e25	+	1.00664e26i	0.111291	+	0.767091i
$799$		−	2.99209e25i		−	0.225452i
$800$	1.73705e25	−	1.52468e25i	0.129420	−	0.113598i
$801$	−1.57783e25			−0.116243
$802$	3.07640e25	−	4.46328e24i	0.224116	−	0.0325151i
$803$		−	1.98907e26i		−	1.43288i
$804$	3.65230e25	−	1.08255e25i	0.260173	−	0.0771158i
$805$	5.97983e24			0.0421236
$806$	−1.29731e25	−	8.94192e25i	−0.0903707	−	0.622896i
$807$		−	1.02813e24i		−	0.00708253i
$808$	1.89411e26	−	8.73794e25i	1.29034	−	0.595260i
$809$	−8.62221e24			−0.0580874			−0.0290437	−	0.999578i	$-0.509246\pi$
$809$	−8.62221e24			−0.0580874			−0.0290437	+	0.999578i	$0.509246\pi$
$810$	1.78690e25	−	2.59247e24i	0.119052	−	0.0172722i
$811$		−	3.33092e24i		−	0.0219471i	−0.999940	−	0.0109735i	$-0.996507\pi$
$811$		−	3.33092e24i		−	0.0219471i	0.999940	−	0.0109735i	$-0.00349305\pi$
$812$	6.49379e24	+	2.19088e25i	0.0423150	+	0.142762i
$813$	3.25920e25			0.210037
$814$	3.98055e25	+	2.74367e26i	0.253702	+	1.74869i
$815$		−	2.17079e26i		−	1.36835i
$816$	1.20396e25	+	1.85253e25i	0.0750584	+	0.115492i
$817$	4.36648e26			2.69236
$818$	−1.41973e26	+	2.05977e25i	−0.865818	+	0.125614i
$819$			2.53519e25i			0.152917i
$820$	−3.28290e26	+	9.73057e25i	−1.95854	+	0.580515i
$821$	−1.08283e26			−0.638959			−0.319480	−	0.947593i	$-0.603508\pi$
$821$	−1.08283e26			−0.638959			−0.319480	+	0.947593i	$0.603508\pi$
$822$	7.60374e24	+	5.24101e25i	0.0443794	+	0.305893i
$823$		−	2.74055e26i		−	1.58212i	−0.611738	−	0.791061i	$-0.709529\pi$
$823$		−	2.74055e26i		−	1.58212i	0.611738	−	0.791061i	$-0.290471\pi$
$824$	−9.81440e25	−	2.12745e26i	−0.560426	−	1.21483i
$825$	1.74081e25			0.0983254
$826$	3.21244e26	−	4.66066e25i	1.79480	−	0.260392i
$827$			2.39405e26i			1.32307i	0.749914	+	0.661536i	$0.230095\pi$
$827$			2.39405e26i			1.32307i	−0.749914	+	0.661536i	$0.769905\pi$
$828$	−6.78483e23	−	2.28906e24i	−0.00370908	−	0.0125137i
$829$	−1.76780e26			−0.955965			−0.477983	−	0.878369i	$-0.658632\pi$
$829$	−1.76780e26			−0.955965			−0.477983	+	0.878369i	$0.658632\pi$
$830$	5.15261e25	+	3.55153e26i	0.275629	+	1.89982i
$831$		−	1.75634e26i		−	0.929394i
$832$	5.72445e25	−	6.70952e25i	0.299656	−	0.351222i
$833$	−5.83413e23			−0.00302114
$834$	1.04179e25	−	1.51144e24i	0.0533685	−	0.00774278i
$835$			4.11370e25i			0.208475i
$836$	2.55537e26	−	7.57415e25i	1.28114	−	0.379732i
$837$	5.28984e25			0.262370
$838$	−4.03810e25	−	2.78333e26i	−0.198144	−	1.36574i
$839$		−	3.06842e26i		−	1.48956i	−0.667313	−	0.744778i	$-0.732556\pi$
$839$		−	3.06842e26i		−	1.48956i	0.667313	−	0.744778i	$-0.267444\pi$
$840$	−1.17433e26	+	5.41742e25i	−0.563996	+	0.260183i
$841$	−2.05731e26			−0.977544
$842$	−2.90475e26	+	4.21425e25i	−1.36552	+	0.198112i
$843$		−	3.10404e25i		−	0.144371i
$844$	9.86988e25	+	3.32990e26i	0.454182	+	1.53232i
$845$	−1.87113e26			−0.851909
$846$	−1.00400e25	−	6.92027e25i	−0.0452274	−	0.311738i
$847$		−	4.88981e24i		−	0.0217942i
$848$	9.62112e25	−	6.25277e25i	0.424290	−	0.275746i
$849$	6.93270e25			0.302505
$850$	−9.41692e24	+	1.36622e24i	−0.0406573	+	0.00589862i
$851$			1.63760e25i			0.0699588i
$852$	−2.42928e25	+	7.20044e24i	−0.102688	+	0.0304370i
$853$	1.98943e26			0.832124			0.416062	−	0.909336i	$-0.363410\pi$
$853$	1.98943e26			0.832124			0.416062	+	0.909336i	$0.363410\pi$
$854$	−2.24508e23	−	1.54746e24i	−0.000929206	−	0.00640472i
$855$			1.19062e26i			0.487616i
$856$	−4.26775e25	−	9.25114e25i	−0.172956	−	0.374914i
$857$	−1.01776e26			−0.408149			−0.204074	−	0.978955i	$-0.565418\pi$
$857$	−1.01776e26			−0.408149			−0.204074	+	0.978955i	$0.565418\pi$
$858$	6.57399e25	−	9.53765e24i	0.260882	−	0.0378491i
$859$			1.41647e26i			0.556249i	0.960545	+	0.278125i	$0.0897128\pi$
$859$			1.41647e26i			0.556249i	−0.960545	+	0.278125i	$0.910287\pi$
$860$	1.57768e26	+	5.32277e26i	0.613101	+	2.06848i
$861$	2.81460e26			1.08240
$862$	5.20206e25	+	3.58561e26i	0.197975	+	1.36458i
$863$			1.13535e26i			0.427594i	0.976878	+	0.213797i	$0.0685830\pi$
$863$			1.13535e26i			0.427594i	−0.976878	+	0.213797i	$0.931417\pi$
$864$	3.40619e25	+	3.88063e25i	0.126954	+	0.144637i
$865$	−3.26852e26			−1.20561
$866$	−2.24346e26	+	3.25484e25i	−0.818948	+	0.118814i
$867$			1.50717e26i			0.544489i
$868$	−3.63262e26	+	1.07672e26i	−1.29880	+	0.384967i
$869$	−5.97960e25			−0.211589
$870$	3.84033e24	+	2.64702e25i	0.0134492	+	0.0927009i
$871$			6.26059e25i			0.216996i
$872$	−1.83564e26	+	8.46820e25i	−0.629708	+	0.290498i
$873$	9.09247e23			0.00308712
$874$	1.55801e25	−	2.26038e24i	0.0523560	−	0.00759588i
$875$			2.67750e26i			0.890549i
$876$	7.22101e25	+	2.43622e26i	0.237718	+	0.802011i
$877$	−4.14630e26			−1.35103			−0.675514	−	0.737347i	$-0.736078\pi$
$877$	−4.14630e26			−1.35103			−0.675514	+	0.737347i	$0.736078\pi$
$878$	−4.63300e25	−	3.19338e26i	−0.149421	−	1.02991i
$879$			2.53062e26i			0.807844i
$880$	1.84659e26	+	2.84134e26i	0.583480	+	0.897800i
$881$	2.99445e26			0.936557			0.468279	−	0.883581i	$-0.344874\pi$
$881$	2.99445e26			0.936557			0.468279	+	0.883581i	$0.344874\pi$
$882$	−1.34935e24	+	1.95765e23i	−0.00417741	+	0.000606064i
$883$		−	4.61589e26i		−	1.41452i	−0.706953	−	0.707260i	$-0.749931\pi$
$883$		−	4.61589e26i		−	1.41452i	0.706953	−	0.707260i	$-0.250069\pi$
$884$	−3.48136e25	+	1.03188e25i	−0.105603	+	0.0313010i
$885$	3.79958e26			1.14090
$886$	−4.04936e25	−	2.79109e26i	−0.120360	−	0.829603i
$887$		−	2.71746e26i		−	0.799558i	−0.916612	−	0.399779i	$-0.869087\pi$
$887$		−	2.71746e26i		−	0.799558i	0.916612	−	0.399779i	$-0.130913\pi$
$888$	−1.48359e26	−	3.21595e26i	−0.432112	−	0.936683i
$889$	2.35079e26			0.677796
$890$	1.30911e26	−	1.89928e25i	0.373651	−	0.0542098i
$891$			3.88903e25i			0.109886i
$892$	−5.51227e25	−	1.85973e26i	−0.154187	−	0.520195i
$893$	4.61100e26			1.27683
$894$	−1.82554e25	−	1.25828e26i	−0.0500441	−	0.344938i
$895$		−	4.52340e25i		−	0.122760i
$896$	−3.12897e26	−	1.97158e26i	−0.840677	−	0.529716i
$897$	3.92379e24			0.0104370
$898$	4.96926e26	−	7.20948e25i	1.30859	−	0.189853i
$899$			7.83608e25i			0.204297i
$900$	−2.13215e25	+	6.31973e24i	−0.0550345	+	0.0163123i
$901$	−4.72403e25			−0.120723
$902$	−1.05888e26	−	7.29854e26i	−0.267910	−	1.84662i
$903$		−	4.56349e26i		−	1.14316i
$904$	4.86740e26	−	2.24544e26i	1.20721	−	0.556910i
$905$	−6.43800e26			−1.58093
$906$	1.91904e26	−	2.78418e25i	0.466586	−	0.0676929i
$907$			2.58816e26i			0.623055i	0.950237	+	0.311527i	$0.100841\pi$
$907$			2.58816e26i			0.623055i	−0.950237	+	0.311527i	$0.899159\pi$
$908$	−8.95032e25	−	3.01966e26i	−0.213337	−	0.719755i
$909$	−2.00703e26			−0.473674
$910$	−3.05168e25	−	2.10342e26i	−0.0713126	−	0.491535i
$911$			4.24096e26i			0.981293i	0.871359	+	0.490647i	$0.163239\pi$
$911$			4.24096e26i			0.981293i	−0.871359	+	0.490647i	$0.836761\pi$
$912$	−2.85486e26	+	1.85537e26i	−0.654080	+	0.425087i
$913$	−7.72957e26			−1.75355
$914$	−9.72802e25	+	1.41136e25i	−0.218529	+	0.0317045i
$915$		−	1.83030e24i		−	0.00407128i
$916$	6.60411e26	−	1.95747e26i	1.45464	−	0.431157i
$917$	5.37590e26			1.17254
$918$	−3.05219e24	−	2.10377e25i	−0.00659215	−	0.0454375i
$919$			6.21858e26i			1.33000i	0.746843	+	0.665000i	$0.231568\pi$
$919$			6.21858e26i			1.33000i	−0.746843	+	0.665000i	$0.768432\pi$
$920$	8.38473e24	+	1.81755e25i	0.0177582	+	0.0384942i
$921$	−1.07650e26			−0.225776
$922$	5.08876e26	−	7.38285e25i	1.05690	−	0.153337i
$923$		−	4.16415e25i		−	0.0856468i
$924$	−7.91588e25	−	2.67066e26i	−0.161232	−	0.543965i
$925$	1.52535e26			0.307675
$926$	8.43949e24	+	5.81707e25i	0.0168584	+	0.116200i
$927$			2.25429e26i			0.445956i
$928$	−5.74855e25	+	5.04575e25i	−0.112623	+	0.0988539i
$929$	4.56904e26			0.886509			0.443255	−	0.896396i	$-0.353824\pi$
$929$	4.56904e26			0.886509			0.443255	+	0.896396i	$0.353824\pi$
$930$	−4.38894e26	+	6.36754e25i	−0.843360	+	0.122356i
$931$		−	8.99076e24i		−	0.0171100i
$932$	−1.84059e26	+	5.45555e25i	−0.346908	+	0.102824i
$933$	−3.18028e26			−0.593650
$934$	−7.73852e25	−	5.33391e26i	−0.143066	−	0.986107i
$935$		−	1.39512e26i		−	0.255450i
$936$	−7.70561e25	+	3.55476e25i	−0.139741	+	0.0644656i
$937$	−9.07602e24			−0.0163019			−0.00815096	−	0.999967i	$-0.502595\pi$
$937$	−9.07602e24			−0.0163019			−0.00815096	+	0.999967i	$0.502595\pi$
$938$	2.59802e26	−	3.76925e25i	0.462187	−	0.0670548i
$939$		−	2.79435e26i		−	0.492370i
$940$	1.66603e26	+	5.62084e26i	0.290758	+	0.980958i
$941$	−7.22779e25			−0.124939			−0.0624696	−	0.998047i	$-0.519898\pi$
$941$	−7.22779e25			−0.124939			−0.0624696	+	0.998047i	$0.519898\pi$
$942$	−7.52939e24	−	5.18977e25i	−0.0128915	−	0.0888567i
$943$		−	4.35625e25i		−	0.0738768i
$944$	5.92098e26	+	9.11060e26i	0.994594	+	1.53038i
$945$	1.24434e26			0.207039
$946$	−1.18336e27	+	1.71683e26i	−1.95028	+	0.282949i
$947$			7.85447e25i			0.128223i	0.997943	+	0.0641116i	$0.0204214\pi$
$947$			7.85447e25i			0.128223i	−0.997943	+	0.0641116i	$0.979579\pi$
$948$	7.32384e25	−	2.17080e25i	0.118431	−	0.0351030i
$949$	−4.17605e26			−0.668913
$950$	−2.10543e25	−	1.45121e26i	−0.0334063	−	0.230259i
$951$			2.16705e26i			0.340599i
$952$	6.37809e25	+	1.38257e26i	0.0993021	+	0.215256i
$953$	1.22997e27			1.89696			0.948479	−	0.316840i	$-0.102622\pi$
$953$	1.22997e27			1.89696			0.948479	+	0.316840i	$0.102622\pi$
$954$	−1.09260e26	+	1.58516e25i	−0.166926	+	0.0242179i
$955$		−	1.16395e26i		−	0.176158i
$956$	2.40462e25	+	8.11270e25i	0.0360516	+	0.121631i
$957$	−5.76099e25			−0.0855637
$958$	3.46513e25	+	2.38840e26i	0.0509835	+	0.351413i
$959$			3.64966e26i			0.531968i
$960$	−3.29321e26	−	2.80971e26i	−0.475531	−	0.405715i
$961$	−6.00222e26			−0.858621
$962$	5.76032e26	−	8.35716e25i	0.816340	−	0.118436i
$963$			9.80267e25i			0.137628i
$964$	−4.61563e26	+	1.36808e26i	−0.642003	+	0.190291i
$965$	−7.85552e26			−1.08250
$966$	−2.36236e24	−	1.62830e25i	−0.00322517	−	0.0222300i
$967$		−	3.77473e26i		−	0.510561i	−0.966867	−	0.255281i	$-0.917832\pi$
$967$		−	3.77473e26i		−	0.510561i	0.966867	−	0.255281i	$-0.0821679\pi$
$968$	1.48624e25	−	6.85634e24i	0.0199164	−	0.00918786i
$969$	1.40175e26			0.186105
$970$	−7.54395e24	+	1.09449e24i	−0.00992324	+	0.00143968i
$971$			3.54680e26i			0.462236i	0.972926	+	0.231118i	$0.0742383\pi$
$971$			3.54680e26i			0.462236i	−0.972926	+	0.231118i	$0.925762\pi$
$972$	−1.41185e25	−	4.76330e25i	−0.0182302	−	0.0615052i
$973$	7.25466e25			0.0928114
$974$	1.41876e26	+	9.77906e26i	0.179837	+	1.23956i
$975$		−	3.65482e25i		−	0.0459013i
$976$	4.38867e24	−	2.85219e24i	0.00546115	−	0.00354920i
$977$	−5.37931e26			−0.663247			−0.331623	−	0.943412i	$-0.607596\pi$
$977$	−5.37931e26			−0.663247			−0.331623	+	0.943412i	$0.607596\pi$
$978$	−5.91102e26	+	8.57580e25i	−0.722126	+	0.104767i
$979$			2.84915e26i			0.344883i
$980$	1.09598e25	−	3.24850e24i	0.0131452	−	0.00389626i
$981$	1.94508e26			0.231162
$982$	7.08289e25	+	4.88201e26i	0.0834078	+	0.574903i
$983$			4.65177e25i			0.0542796i	0.999632	+	0.0271398i	$0.00863992\pi$
$983$			4.65177e25i			0.0542796i	−0.999632	+	0.0271398i	$0.991360\pi$
$984$	3.94655e26	+	8.55488e26i	0.456312	+	0.989141i
$985$	1.22470e27			1.40314
$986$	3.11641e25	−	4.52134e24i	0.0353804	−	0.00513304i
$987$		−	4.81904e26i		−	0.542133i
$988$	−1.59019e26	−	5.36498e26i	−0.177271	−	0.598075i
$989$	−7.06307e25			−0.0780237
$990$	−4.68134e25	−	3.22670e26i	−0.0512452	−	0.353217i
$991$		−	1.30421e27i		−	1.41476i	−0.706833	−	0.707381i	$-0.749877\pi$
$991$		−	1.30421e27i		−	1.41476i	0.706833	−	0.707381i	$-0.250123\pi$
$992$	−8.36619e26	−	9.53149e26i	−0.899338	−	1.02460i
$993$	−1.80554e26			−0.192337
$994$	−1.72804e26	+	2.50707e25i	−0.182422	+	0.0264660i
$995$		−	1.17490e27i		−	1.22911i
$996$	9.46721e26	−	2.80610e26i	0.981495	−	0.290917i
$997$	1.47770e27			1.51820			0.759099	−	0.650975i	$-0.225640\pi$
$997$	1.47770e27			1.51820			0.759099	+	0.650975i	$0.225640\pi$
$998$	1.40693e26	+	9.69755e26i	0.143251	+	0.987386i
$999$			3.40768e26i			0.343850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.19.d.a.7.17	✓	18
3.2	odd	2		36.19.d.e.19.2		18
4.3	odd	2	inner	12.19.d.a.7.18	yes	18
12.11	even	2		36.19.d.e.19.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.19.d.a.7.17	✓	18	1.1	even	1	trivial
12.19.d.a.7.18	yes	18	4.3	odd	2	inner
36.19.d.e.19.1		18	12.11	even	2
36.19.d.e.19.2		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)

\(f(q)\)	\(=\)	\(q+(506.695 - 73.5121i) q^{2} -11364.0i q^{3} +(251336. - 74496.4i) q^{4} +2.11462e6 q^{5} +(-835390. - 5.75808e6i) q^{6} -4.00973e7i q^{7} +(1.21874e8 - 5.62232e7i) q^{8} -1.29140e8 q^{9} +O(q^{10})\)	\(q+(506.695 - 73.5121i) q^{2} -11364.0i q^{3} +(251336. - 74496.4i) q^{4} +2.11462e6 q^{5} +(-835390. - 5.75808e6i) q^{6} -4.00973e7i q^{7} +(1.21874e8 - 5.62232e7i) q^{8} -1.29140e8 q^{9} +(1.07147e9 - 1.55450e8i) q^{10} +2.33195e9i q^{11} +(-8.46576e8 - 2.85618e9i) q^{12} +4.89591e9 q^{13} +(-2.94763e9 - 2.03171e10i) q^{14} -2.40305e10i q^{15} +(5.76200e10 - 3.74473e10i) q^{16} -2.82918e10 q^{17} +(-6.54347e10 + 9.49336e9i) q^{18} -4.35994e11i q^{19} +(5.31479e11 - 1.57531e11i) q^{20} -4.55665e11 q^{21} +(1.71426e11 + 1.18159e12i) q^{22} +7.05248e10i q^{23} +(-6.38920e11 - 1.38498e12i) q^{24} +6.56904e11 q^{25} +(2.48073e12 - 3.59909e11i) q^{26} +1.46755e12i q^{27} +(-2.98710e12 - 1.00779e13i) q^{28} -2.17394e12 q^{29} +(-1.76653e12 - 1.21761e13i) q^{30} -3.60455e13i q^{31} +(2.64430e13 - 2.32101e13i) q^{32} +2.65002e13 q^{33} +(-1.43353e13 + 2.07979e12i) q^{34} -8.47904e13i q^{35} +(-3.24576e13 + 9.62048e12i) q^{36} +2.32202e14 q^{37} +(-3.20508e13 - 2.20916e14i) q^{38} -5.56371e13i q^{39} +(2.57717e14 - 1.18891e14i) q^{40} -6.17691e14 q^{41} +(-2.30883e14 + 3.34969e13i) q^{42} +1.00150e15i q^{43} +(1.73722e14 + 5.86102e14i) q^{44} -2.73082e14 q^{45} +(5.18443e12 + 3.57346e13i) q^{46} +1.05758e15i q^{47} +(-4.25550e14 - 6.54793e14i) q^{48} +2.06213e13 q^{49} +(3.32850e14 - 4.82904e13i) q^{50} +3.21507e14i q^{51} +(1.23052e15 - 3.64728e14i) q^{52} +1.66975e15 q^{53} +(1.07882e14 + 7.43599e14i) q^{54} +4.93117e15i q^{55} +(-2.25440e15 - 4.88683e15i) q^{56} -4.95463e15 q^{57} +(-1.10153e15 + 1.59811e14i) q^{58} +1.58115e16i q^{59} +(-1.79018e15 - 6.03972e15i) q^{60} +7.61656e13 q^{61} +(-2.64978e15 - 1.82641e16i) q^{62} +5.17817e15i q^{63} +(1.16923e16 - 1.37043e16i) q^{64} +1.03530e16 q^{65} +(1.34275e16 - 1.94808e15i) q^{66} +1.27874e16i q^{67} +(-7.11074e15 + 2.10764e15i) q^{68} +8.01443e14 q^{69} +(-6.23312e15 - 4.29629e16i) q^{70} -8.50536e15i q^{71} +(-1.57389e16 + 7.26067e15i) q^{72} -8.52967e16 q^{73} +(1.17656e17 - 1.70697e16i) q^{74} -7.46505e15i q^{75} +(-3.24800e16 - 1.09581e17i) q^{76} +9.35047e16 q^{77} +(-4.09000e15 - 2.81910e16i) q^{78} +2.56421e16i q^{79} +(1.21844e17 - 7.91866e16i) q^{80} +1.66772e16 q^{81} +(-3.12981e17 + 4.54077e16i) q^{82} +3.31464e17i q^{83} +(-1.14525e17 + 3.39454e16i) q^{84} -5.98263e16 q^{85} +(7.36224e16 + 5.07456e17i) q^{86} +2.47047e16i q^{87} +(1.31109e17 + 2.84204e17i) q^{88} +1.22179e17 q^{89} +(-1.38369e17 + 2.00748e16i) q^{90} -1.96313e17i q^{91} +(5.25385e15 + 1.77254e16i) q^{92} -4.09620e17 q^{93} +(7.77452e16 + 5.35873e17i) q^{94} -9.21960e17i q^{95} +(-2.63759e17 - 3.00498e17i) q^{96} -7.04078e15 q^{97} +(1.04487e16 - 1.51591e15i) q^{98} -3.01148e17i 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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