LMFDB - Embedded newform 12.10.b.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,10,Mod(11,12)]

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, 1]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	12.b (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:	$6.18043003397$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 43 x^{14} - 1652 x^{12} - 2031680 x^{10} + 40456192 x^{8} - 33287045120 x^{6} + \cdots + 72\!\cdots\!36 $ x^16 + 43x^14 - 1652x^12 - 2031680x^10 + 40456192x^8 - 33287045120x^6 - 443455373312x^4 + 189115999977472*x^2 + 72057594037927936
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{68}\cdot 3^{24} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.3
Root			$9.08786 - 6.73875i$ of defining polynomial
Character	$\chi$	$=$	12.11
Dual form			12.10.b.a.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-18.1757 - 13.4775i) q^{2} +(-122.433 + 68.5072i) q^{3} +(148.714 + 489.927i) q^{4} +8.50078i q^{5} +(3148.61 + 404.916i) q^{6} -3636.61i q^{7} +(3899.99 - 10909.1i) q^{8} +(10296.5 - 16775.0i) q^{9} +O(q^{10})$	\(q+(-18.1757 - 13.4775i) q^{2} +(-122.433 + 68.5072i) q^{3} +(148.714 + 489.927i) q^{4} +8.50078i q^{5} +(3148.61 + 404.916i) q^{6} -3636.61i q^{7} +(3899.99 - 10909.1i) q^{8} +(10296.5 - 16775.0i) q^{9} +(114.569 - 154.508i) q^{10} +37751.8 q^{11} +(-51771.0 - 49795.0i) q^{12} +131336. q^{13} +(-49012.4 + 66098.1i) q^{14} +(-582.365 - 1040.77i) q^{15} +(-217912. + 145718. i) q^{16} +469110. i q^{17} +(-413232. + 166128. i) q^{18} -995479. i q^{19} +(-4164.76 + 1264.19i) q^{20} +(249134. + 445240. i) q^{21} +(-686166. - 508799. i) q^{22} +679160. q^{23} +(269864. + 1.60280e6i) q^{24} +1.95305e6 q^{25} +(-2.38713e6 - 1.77008e6i) q^{26} +(-111417. + 2.75920e6i) q^{27} +(1.78167e6 - 540816. i) q^{28} -4.79104e6i q^{29} +(-3442.11 + 26765.6i) q^{30} -2.38709e6i q^{31} +(5.92463e6 + 288376. i) q^{32} +(-4.62205e6 + 2.58627e6i) q^{33} +(6.32242e6 - 8.52641e6i) q^{34} +30914.1 q^{35} +(9.74978e6 + 2.54985e6i) q^{36} -1.41054e7 q^{37} +(-1.34166e7 + 1.80936e7i) q^{38} +(-1.60798e7 + 8.99747e6i) q^{39} +(92735.6 + 33153.0i) q^{40} +937320. i q^{41} +(1.47252e6 - 1.14503e7i) q^{42} +1.34564e7i q^{43} +(5.61422e6 + 1.84956e7i) q^{44} +(142601. + 87528.4i) q^{45} +(-1.23442e7 - 9.15338e6i) q^{46} +4.24198e7 q^{47} +(1.66968e7 - 3.27692e7i) q^{48} +2.71286e7 q^{49} +(-3.54982e7 - 2.63223e7i) q^{50} +(-3.21374e7 - 5.74343e7i) q^{51} +(1.95315e7 + 6.43450e7i) q^{52} -6.30732e7i q^{53} +(3.92122e7 - 4.86488e7i) q^{54} +320919. i q^{55} +(-3.96721e7 - 1.41828e7i) q^{56} +(6.81975e7 + 1.21879e8i) q^{57} +(-6.45712e7 + 8.70806e7i) q^{58} +7.41726e7 q^{59} +(423296. - 440094. i) q^{60} +2.40223e7 q^{61} +(-3.21720e7 + 4.33872e7i) q^{62} +(-6.10044e7 - 3.74444e7i) q^{63} +(-1.03798e8 - 8.50906e7i) q^{64} +1.11646e6i q^{65} +(1.18866e8 + 1.52863e7i) q^{66} +2.43733e7i q^{67} +(-2.29829e8 + 6.97633e7i) q^{68} +(-8.31514e7 + 4.65274e7i) q^{69} +(-561886. - 416644. i) q^{70} +1.11670e8 q^{71} +(-1.42844e8 - 1.77748e8i) q^{72} -1.48559e8 q^{73} +(2.56376e8 + 1.90105e8i) q^{74} +(-2.39117e8 + 1.33798e8i) q^{75} +(4.87712e8 - 1.48042e8i) q^{76} -1.37289e8i q^{77} +(4.13526e8 + 5.31801e7i) q^{78} +3.13750e7i q^{79} +(-1.23872e6 - 1.85242e6i) q^{80} +(-1.75384e8 - 3.45449e8i) q^{81} +(1.26327e7 - 1.70365e7i) q^{82} -2.06349e8 q^{83} +(-1.81085e8 + 1.88271e8i) q^{84} -3.98780e6 q^{85} +(1.81358e8 - 2.44580e8i) q^{86} +(3.28221e8 + 5.86580e8i) q^{87} +(1.47232e8 - 4.11836e8i) q^{88} -2.06918e8i q^{89} +(-1.41221e6 - 3.51280e6i) q^{90} -4.77619e8i q^{91} +(1.01001e8 + 3.32739e8i) q^{92} +(1.63533e8 + 2.92258e8i) q^{93} +(-7.71011e8 - 5.71713e8i) q^{94} +8.46235e6 q^{95} +(-7.45124e8 + 3.70573e8i) q^{96} +2.91546e8 q^{97} +(-4.93083e8 - 3.65626e8i) q^{98} +(3.88711e8 - 6.33288e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 344 q^{4} - 1608 q^{6} - 13872 q^{9}+O(q^{10}) $ 16 * q - 344 * q^4 - 1608 * q^6 - 13872 * q^9	$ 16 q - 344 q^{4} - 1608 q^{6} - 13872 q^{9} - 15952 q^{10} + 42600 q^{12} - 97312 q^{13} + 164896 q^{16} + 256944 q^{18} + 356448 q^{21} + 322128 q^{22} + 166176 q^{24} - 2743728 q^{25} - 1447056 q^{28} + 3286128 q^{30} + 4715520 q^{33} - 13198144 q^{34} - 6827448 q^{36} + 10997600 q^{37} + 23411264 q^{40} + 23964432 q^{42} - 251904 q^{45} - 41256288 q^{46} - 87722976 q^{48} - 21356624 q^{49} + 132124208 q^{52} + 179732232 q^{54} - 88439904 q^{57} - 271309360 q^{58} - 414400704 q^{60} + 50685152 q^{61} + 742710400 q^{64} + 790585104 q^{66} + 63713280 q^{69} - 1188731232 q^{70} - 1250220480 q^{72} + 23382176 q^{73} + 1645242192 q^{76} + 2079579408 q^{78} + 349756560 q^{81} - 3274996000 q^{82} - 3734920464 q^{84} - 247261184 q^{85} + 4467199680 q^{88} + 5726283888 q^{90} - 262825248 q^{93} - 6146963136 q^{94} - 6944875392 q^{96} + 30926624 q^{97}+O(q^{100}) $ 16 * q - 344 * q^4 - 1608 * q^6 - 13872 * q^9 - 15952 * q^10 + 42600 * q^12 - 97312 * q^13 + 164896 * q^16 + 256944 * q^18 + 356448 * q^21 + 322128 * q^22 + 166176 * q^24 - 2743728 * q^25 - 1447056 * q^28 + 3286128 * q^30 + 4715520 * q^33 - 13198144 * q^34 - 6827448 * q^36 + 10997600 * q^37 + 23411264 * q^40 + 23964432 * q^42 - 251904 * q^45 - 41256288 * q^46 - 87722976 * q^48 - 21356624 * q^49 + 132124208 * q^52 + 179732232 * q^54 - 88439904 * q^57 - 271309360 * q^58 - 414400704 * q^60 + 50685152 * q^61 + 742710400 * q^64 + 790585104 * q^66 + 63713280 * q^69 - 1188731232 * q^70 - 1250220480 * q^72 + 23382176 * q^73 + 1645242192 * q^76 + 2079579408 * q^78 + 349756560 * q^81 - 3274996000 * q^82 - 3734920464 * q^84 - 247261184 * q^85 + 4467199680 * q^88 + 5726283888 * q^90 - 262825248 * q^93 - 6146963136 * q^94 - 6944875392 * q^96 + 30926624 * q^97

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 $

$2$	−18.1757	−	13.4775i	−0.803261	−	0.595627i
$2$	−18.1757	−	13.4775i	−0.803261	−	0.595627i
$3$	−122.433	+	68.5072i	−0.872673	+	0.488305i
$3$	−122.433	+	68.5072i	−0.872673	+	0.488305i
$4$	148.714	+	489.927i	0.290458	+	0.956888i
$5$			8.50078i			0.00608266i	0.999995	+	0.00304133i	$0.000968087\pi$
$5$			8.50078i			0.00608266i	−0.999995	+	0.00304133i	$0.999032\pi$
$6$	3148.61	+	404.916i	0.991832	+	0.127551i
$7$		−	3636.61i		−	0.572474i	−0.958159	−	0.286237i	$-0.907595\pi$
$7$		−	3636.61i		−	0.572474i	0.958159	−	0.286237i	$-0.0924045\pi$
$8$	3899.99	−	10909.1i	0.336635	−	0.941635i
$9$	10296.5	−	16775.0i	0.523117	−	0.852261i
$10$	114.569	−	154.508i	0.00362300	−	0.00488597i
$11$	37751.8			0.777446			0.388723	−	0.921355i	$-0.372916\pi$
$11$	37751.8			0.777446			0.388723	+	0.921355i	$0.372916\pi$
$12$	−51771.0	−	49795.0i	−0.720727	−	0.693219i
$13$	131336.			1.27538			0.637689	−	0.770294i	$-0.279890\pi$
$13$	131336.			1.27538			0.637689	+	0.770294i	$0.279890\pi$
$14$	−49012.4	+	66098.1i	−0.340981	+	0.459847i
$15$	−582.365	−	1040.77i	−0.00297019	−	0.00530818i
$16$	−217912.	+	145718.i	−0.831269	+	0.555871i
$17$			469110.i			1.36224i	0.732171	+	0.681121i	$0.238507\pi$
$17$			469110.i			1.36224i	−0.732171	+	0.681121i	$0.761493\pi$
$18$	−413232.	+	166128.i	−0.927829	+	0.373006i
$19$		−	995479.i		−	1.75243i	−0.481920	−	0.876215i	$-0.660060\pi$
$19$		−	995479.i		−	1.75243i	0.481920	−	0.876215i	$-0.339940\pi$
$20$	−4164.76	+	1264.19i	−0.00582043	+	0.00176676i
$21$	249134.	+	445240.i	0.279542	+	0.499583i
$22$	−686166.	−	508799.i	−0.624492	−	0.463067i
$23$	679160.			0.506054			0.253027	−	0.967459i	$-0.418574\pi$
$23$	679160.			0.506054			0.253027	+	0.967459i	$0.418574\pi$
$24$	269864.	+	1.60280e6i	0.166033	+	0.986120i
$25$	1.95305e6			0.999963
$26$	−2.38713e6	−	1.77008e6i	−1.02446	−	0.759649i
$27$	−111417.	+	2.75920e6i	−0.0403473	+	0.999186i
$28$	1.78167e6	−	540816.i	0.547794	−	0.166279i
$29$		−	4.79104e6i		−	1.25788i	−0.777454	−	0.628939i	$-0.783489\pi$
$29$		−	4.79104e6i		−	1.25788i	0.777454	−	0.628939i	$-0.216511\pi$
$30$	−3442.11	+	26765.6i	−0.000775851	+	0.00603298i
$31$		−	2.38709e6i		−	0.464239i	−0.972687	−	0.232120i	$-0.925434\pi$
$31$		−	2.38709e6i		−	0.464239i	0.972687	−	0.232120i	$-0.0745661\pi$
$32$	5.92463e6	+	288376.i	0.998818	+	0.0486166i
$33$	−4.62205e6	+	2.58627e6i	−0.678456	+	0.379630i
$34$	6.32242e6	−	8.52641e6i	0.811388	−	1.09424i
$35$	30914.1			0.00348217
$36$	9.74978e6	+	2.54985e6i	0.967461	+	0.253019i
$37$	−1.41054e7			−1.23731			−0.618653	−	0.785664i	$-0.712321\pi$
$37$	−1.41054e7			−1.23731			−0.618653	+	0.785664i	$0.712321\pi$
$38$	−1.34166e7	+	1.80936e7i	−1.04379	+	1.40766i
$39$	−1.60798e7	+	8.99747e6i	−1.11299	+	0.622773i
$40$	92735.6	+	33153.0i	0.00572765	+	0.00204764i
$41$			937320.i			0.0518037i	0.999664	+	0.0259018i	$0.00824573\pi$
$41$			937320.i			0.0518037i	−0.999664	+	0.0259018i	$0.991754\pi$
$42$	1.47252e6	−	1.14503e7i	0.0730198	−	0.567798i
$43$			1.34564e7i			0.600234i	0.953902	+	0.300117i	$0.0970257\pi$
$43$			1.34564e7i			0.600234i	−0.953902	+	0.300117i	$0.902974\pi$
$44$	5.61422e6	+	1.84956e7i	0.225815	+	0.743928i
$45$	142601.	+	87528.4i	0.00518402	+	0.00318195i
$46$	−1.23442e7	−	9.15338e6i	−0.406494	−	0.301419i
$47$	4.24198e7			1.26803			0.634013	−	0.773322i	$-0.281406\pi$
$47$	4.24198e7			1.26803			0.634013	+	0.773322i	$0.281406\pi$
$48$	1.66968e7	−	3.27692e7i	0.453992	−	0.891006i
$49$	2.71286e7			0.672273
$50$	−3.54982e7	−	2.63223e7i	−0.803232	−	0.595605i
$51$	−3.21374e7	−	5.74343e7i	−0.665189	−	1.18879i
$52$	1.95315e7	+	6.43450e7i	0.370443	+	1.22039i
$53$		−	6.30732e7i		−	1.09800i	−0.835822	−	0.549001i	$-0.815008\pi$
$53$		−	6.30732e7i		−	1.09800i	0.835822	−	0.549001i	$-0.184992\pi$
$54$	3.92122e7	−	4.86488e7i	0.627551	−	0.778575i
$55$			320919.i			0.00472894i
$56$	−3.96721e7	−	1.41828e7i	−0.539062	−	0.192715i
$57$	6.81975e7	+	1.21879e8i	0.855720	+	1.52930i
$58$	−6.45712e7	+	8.70806e7i	−0.749226	+	1.01041i
$59$	7.41726e7			0.796910			0.398455	−	0.917188i	$-0.369547\pi$
$59$	7.41726e7			0.796910			0.398455	+	0.917188i	$0.369547\pi$
$60$	423296.	−	440094.i	0.00421662	−	0.00438394i
$61$	2.40223e7			0.222142			0.111071	−	0.993812i	$-0.464572\pi$
$61$	2.40223e7			0.222142			0.111071	+	0.993812i	$0.464572\pi$
$62$	−3.21720e7	+	4.33872e7i	−0.276513	+	0.372905i
$63$	−6.10044e7	−	3.74444e7i	−0.487897	−	0.299471i
$64$	−1.03798e8	−	8.50906e7i	−0.773354	−	0.633974i
$65$			1.11646e6i			0.00775770i
$66$	1.18866e8	+	1.52863e7i	0.771095	+	0.0991642i
$67$			2.43733e7i			0.147767i	0.997267	+	0.0738836i	$0.0235393\pi$
$67$			2.43733e7i			0.147767i	−0.997267	+	0.0738836i	$0.976461\pi$
$68$	−2.29829e8	+	6.97633e7i	−1.30351	+	0.395673i
$69$	−8.31514e7	+	4.65274e7i	−0.441620	+	0.247109i
$70$	−561886.	−	416644.i	−0.00279709	−	0.00207407i
$71$	1.11670e8			0.521524			0.260762	−	0.965403i	$-0.416026\pi$
$71$	1.11670e8			0.521524			0.260762	+	0.965403i	$0.416026\pi$
$72$	−1.42844e8	−	1.77748e8i	−0.626420	−	0.779486i
$73$	−1.48559e8			−0.612275			−0.306138	−	0.951987i	$-0.599037\pi$
$73$	−1.48559e8			−0.612275			−0.306138	+	0.951987i	$0.599037\pi$
$74$	2.56376e8	+	1.90105e8i	0.993880	+	0.736973i
$75$	−2.39117e8	+	1.33798e8i	−0.872641	+	0.488287i
$76$	4.87712e8	−	1.48042e8i	1.67688	−	0.509007i
$77$		−	1.37289e8i		−	0.445068i
$78$	4.13526e8	+	5.31801e7i	1.26496	+	0.162676i
$79$			3.13750e7i			0.0906279i	0.998973	+	0.0453140i	$0.0144288\pi$
$79$			3.13750e7i			0.0906279i	−0.998973	+	0.0453140i	$0.985571\pi$
$80$	−1.23872e6	−	1.85242e6i	−0.00338117	−	0.00505633i
$81$	−1.75384e8	−	3.45449e8i	−0.452697	−	0.891664i
$82$	1.26327e7	−	1.70365e7i	0.0308556	−	0.0416119i
$83$	−2.06349e8			−0.477255			−0.238627	−	0.971111i	$-0.576697\pi$
$83$	−2.06349e8			−0.477255			−0.238627	+	0.971111i	$0.576697\pi$
$84$	−1.81085e8	+	1.88271e8i	−0.396850	+	0.412598i
$85$	−3.98780e6			−0.00828606
$86$	1.81358e8	−	2.44580e8i	0.357515	−	0.482145i
$87$	3.28221e8	+	5.86580e8i	0.614228	+	1.09772i
$88$	1.47232e8	−	4.11836e8i	0.261715	−	0.732070i
$89$		−	2.06918e8i		−	0.349578i	−0.984606	−	0.174789i	$-0.944076\pi$
$89$		−	2.06918e8i		−	0.349578i	0.984606	−	0.174789i	$-0.0559243\pi$
$90$	−1.41221e6	−	3.51280e6i	−0.00226887	−	0.00564367i
$91$		−	4.77619e8i		−	0.730121i
$92$	1.01001e8	+	3.32739e8i	0.146987	+	0.484237i
$93$	1.63533e8	+	2.92258e8i	0.226690	+	0.405129i
$94$	−7.71011e8	−	5.71713e8i	−1.01856	−	0.755271i
$95$	8.46235e6			0.0106594
$96$	−7.45124e8	+	3.70573e8i	−0.895381	+	0.445301i
$97$	2.91546e8			0.334375			0.167188	−	0.985925i	$-0.446531\pi$
$97$	2.91546e8			0.334375			0.167188	+	0.985925i	$0.446531\pi$
$98$	−4.93083e8	−	3.65626e8i	−0.540011	−	0.400424i
$99$	3.88711e8	−	6.33288e8i	0.406695	−	0.662586i
$100$	2.90447e8	+	9.56852e8i	0.290447	+	0.956852i
$101$			1.65655e9i			1.58402i	0.610511	+	0.792008i	$0.290964\pi$
$101$			1.65655e9i			1.58402i	−0.610511	+	0.792008i	$0.709036\pi$
$102$	−1.89950e8	+	1.47704e9i	−0.173756	+	1.35111i
$103$		−	9.33342e7i		−	0.0817096i	−0.999165	−	0.0408548i	$-0.986992\pi$
$103$		−	9.33342e7i		−	0.0817096i	0.999165	−	0.0408548i	$-0.0130081\pi$
$104$	5.12210e8	−	1.43275e9i	0.429337	−	1.20094i
$105$	−3.78489e6	+	2.11784e6i	−0.00303880	+	0.00170036i
$106$	−8.50068e8	+	1.14640e9i	−0.654000	+	0.881983i
$107$	−1.73479e9			−1.27944			−0.639722	−	0.768607i	$-0.720950\pi$
$107$	−1.73479e9			−1.27944			−0.639722	+	0.768607i	$0.720950\pi$
$108$	−1.36837e9	+	3.55746e8i	−0.967828	+	0.251613i
$109$	8.46232e8			0.574209			0.287105	−	0.957899i	$-0.407307\pi$
$109$	8.46232e8			0.574209			0.287105	+	0.957899i	$0.407307\pi$
$110$	4.32519e6	−	5.83294e6i	0.00281668	−	0.00379857i
$111$	1.72696e9	−	9.66321e8i	1.07976	−	0.604182i
$112$	5.29921e8	+	7.92462e8i	0.318222	+	0.475880i
$113$		−	1.72064e8i		−	0.0992746i	−0.998767	−	0.0496373i	$-0.984193\pi$
$113$		−	1.72064e8i		−	0.0992746i	0.998767	−	0.0496373i	$-0.0158065\pi$
$114$	4.03086e8	−	3.13437e9i	0.223525	−	1.73812i
$115$			5.77339e6i			0.00307816i
$116$	2.34726e9	−	7.12496e8i	1.20365	−	0.365360i
$117$	1.35230e9	−	2.20317e9i	0.667172	−	1.08695i
$118$	−1.34814e9	−	9.99660e8i	−0.640127	−	0.474661i
$119$	1.70597e9			0.779848
$120$	−1.36251e7	+	2.29405e6i	−0.00599824	+	0.00100992i
$121$	−9.32753e8			−0.395578
$122$	−4.36622e8	−	3.23760e8i	−0.178438	−	0.132313i
$123$	−6.42132e7	−	1.14759e8i	−0.0252960	−	0.0452077i
$124$	1.16950e9	−	3.54995e8i	0.444225	−	0.134842i
$125$			3.32056e7i			0.0121651i
$126$	6.04142e8	+	1.50277e9i	0.213536	+	0.531158i
$127$			5.42024e9i			1.84885i	0.381361	+	0.924426i	$0.375455\pi$
$127$			5.42024e9i			1.84885i	−0.381361	+	0.924426i	$0.624545\pi$
$128$	7.39793e8	+	2.94552e9i	0.243593	+	0.969877i
$129$	−9.21860e8	−	1.64750e9i	−0.293097	−	0.523808i
$130$	1.50471e7	−	2.02925e7i	0.00462069	−	0.00623146i
$131$	−5.75052e9			−1.70603			−0.853014	−	0.521888i	$-0.825228\pi$
$131$	−5.75052e9			−1.70603			−0.853014	+	0.521888i	$0.825228\pi$
$132$	−1.95445e9	−	1.87985e9i	−0.560326	−	0.538940i
$133$	−3.62017e9			−1.00322
$134$	3.28491e8	−	4.43003e8i	0.0880141	−	0.118696i
$135$	−2.34554e7	−	947132.i	−0.00607771	−	0.000245419i
$136$	5.11755e9	+	1.82952e9i	1.28273	+	0.458578i
$137$			3.31922e9i			0.804995i	0.915421	+	0.402497i	$0.131858\pi$
$137$			3.31922e9i			0.804995i	−0.915421	+	0.402497i	$0.868142\pi$
$138$	2.13841e9	+	2.75003e8i	0.501921	+	0.0645479i
$139$		−	4.83877e9i		−	1.09943i	−0.835352	−	0.549716i	$-0.814736\pi$
$139$		−	4.83877e9i		−	1.09943i	0.835352	−	0.549716i	$-0.185264\pi$
$140$	4.59736e6	+	1.51456e7i	0.00101142	+	0.00333205i
$141$	−5.19357e9	+	2.90606e9i	−1.10657	+	0.619183i
$142$	−2.02968e9	−	1.50503e9i	−0.418920	−	0.310633i
$143$	4.95817e9			0.991537
$144$	2.00694e8	+	5.15588e9i	0.0388958	+	0.999243i
$145$	4.07276e7			0.00765125
$146$	2.70017e9	+	2.00221e9i	0.491817	+	0.364687i
$147$	−3.32143e9	+	1.85851e9i	−0.586675	+	0.328274i
$148$	−2.09767e9	−	6.91060e9i	−0.359385	−	1.18396i
$149$		−	9.11644e9i		−	1.51526i	−0.652684	−	0.757630i	$-0.726357\pi$
$149$		−	9.11644e9i		−	1.51526i	0.652684	−	0.757630i	$-0.273643\pi$
$150$	6.14940e9	+	7.90823e8i	0.991795	+	0.127547i
$151$		−	3.42795e8i		−	0.0536585i	−0.999640	−	0.0268293i	$-0.991459\pi$
$151$		−	3.42795e8i		−	0.0536585i	0.999640	−	0.0268293i	$-0.00854104\pi$
$152$	−1.08597e10	−	3.88236e9i	−1.65015	−	0.589929i
$153$	7.86934e9	+	4.83019e9i	1.16099	+	0.712612i
$154$	−1.85031e9	+	2.49532e9i	−0.265094	+	0.357506i
$155$	2.02922e7			0.00282381
$156$	−6.79940e9	−	6.53988e9i	−0.919200	−	0.884116i
$157$	9.08474e9			1.19334			0.596670	−	0.802487i	$-0.296490\pi$
$157$	9.08474e9			1.19334			0.596670	+	0.802487i	$0.296490\pi$
$158$	4.22857e8	−	5.70264e8i	0.0539804	−	0.0727979i
$159$	4.32097e9	+	7.72222e9i	0.536160	+	0.958197i
$160$	−2.45142e6	+	5.03640e7i	−0.000295719	+	0.00607547i
$161$		−	2.46984e9i		−	0.289703i
$162$	−1.46805e9	+	8.64253e9i	−0.167465	+	0.985878i
$163$		−	8.31270e9i		−	0.922355i	−0.887308	−	0.461177i	$-0.847427\pi$
$163$		−	8.31270e9i		−	0.922355i	0.887308	−	0.461177i	$-0.152573\pi$
$164$	−4.59218e8	+	1.39393e8i	−0.0495703	+	0.0150468i
$165$	−2.19853e7	−	3.92910e7i	−0.00230916	−	0.00412682i
$166$	3.75054e9	+	2.78106e9i	0.383360	+	0.284266i
$167$	1.54677e10			1.53886			0.769432	−	0.638728i	$-0.220539\pi$
$167$	1.54677e10			1.53886			0.769432	+	0.638728i	$0.220539\pi$
$168$	5.82878e9	−	9.81390e8i	0.564529	−	0.0950495i
$169$	6.64466e9			0.626589
$170$	7.24811e7	+	5.37455e7i	0.00665587	+	0.00493540i
$171$	−1.66992e10	−	1.02500e10i	−1.49353	−	0.916726i
$172$	−6.59264e9	+	2.00116e9i	−0.574356	+	0.174342i
$173$			9.36379e9i			0.794775i	0.917651	+	0.397388i	$0.130083\pi$
$173$			9.36379e9i			0.794775i	−0.917651	+	0.397388i	$0.869917\pi$
$174$	1.93997e9	−	1.50851e10i	0.160444	−	1.24760i
$175$		−	7.10250e9i		−	0.572453i
$176$	−8.22657e9	+	5.50112e9i	−0.646266	+	0.432159i
$177$	−9.08115e9	+	5.08136e9i	−0.695442	+	0.389135i
$178$	−2.78874e9	+	3.76089e9i	−0.208218	+	0.280802i
$179$	−6.41259e8			−0.0466869			−0.0233434	−	0.999728i	$-0.507431\pi$
$179$	−6.41259e8			−0.0466869			−0.0233434	+	0.999728i	$0.507431\pi$
$180$	−2.16757e7	+	8.28807e7i	−0.00153903	+	0.00588474i
$181$	−1.11545e10			−0.772495			−0.386247	−	0.922395i	$-0.626229\pi$
$181$	−1.11545e10			−0.772495			−0.386247	+	0.922395i	$0.626229\pi$
$182$	−6.43710e9	+	8.68107e9i	−0.434880	+	0.586478i
$183$	−2.94111e9	+	1.64570e9i	−0.193857	+	0.108473i
$184$	2.64872e9	−	7.40901e9i	0.170355	−	0.476519i
$185$		−	1.19907e8i		−	0.00752612i
$186$	9.66573e8	−	7.51602e9i	0.0592143	−	0.460447i
$187$			1.77097e10i			1.05907i
$188$	6.30843e9	+	2.07826e10i	0.368308	+	1.21336i
$189$	1.00341e10	+	4.05181e8i	0.572008	+	0.0230978i
$190$	−1.53809e8	−	1.14051e8i	−0.00856232	−	0.00634905i
$191$	3.23519e9			0.175894			0.0879468	−	0.996125i	$-0.471969\pi$
$191$	3.23519e9			0.175894			0.0879468	+	0.996125i	$0.471969\pi$
$192$	1.85376e10	+	3.30696e9i	0.984458	+	0.175620i
$193$	−1.54402e10			−0.801022			−0.400511	−	0.916292i	$-0.631167\pi$
$193$	−1.54402e10			−0.801022			−0.400511	+	0.916292i	$0.631167\pi$
$194$	−5.29906e9	−	3.92931e9i	−0.268591	−	0.199163i
$195$	−7.64855e7	−	1.36691e8i	−0.00378812	−	0.00676993i
$196$	4.03442e9	+	1.32910e10i	0.195267	+	0.643290i
$197$		−	1.96466e10i		−	0.929371i	−0.885476	−	0.464685i	$-0.846167\pi$
$197$		−	1.96466e10i		−	0.929371i	0.885476	−	0.464685i	$-0.153833\pi$
$198$	−1.56002e10	+	6.27161e9i	−0.721337	+	0.289992i
$199$			3.51449e10i			1.58863i	0.607506	+	0.794315i	$0.292170\pi$
$199$			3.51449e10i			1.58863i	−0.607506	+	0.794315i	$0.707830\pi$
$200$	7.61689e9	−	2.13060e10i	0.336622	−	0.941600i
$201$	−1.66975e9	−	2.98409e9i	−0.0721554	−	0.128953i
$202$	2.23262e10	−	3.01091e10i	0.943482	−	1.27238i
$203$	−1.74232e10			−0.720103
$204$	2.33593e10	−	2.42863e10i	0.944331	−	0.981805i
$205$	−7.96795e6			−0.000315104
$206$	−1.25791e9	+	1.69642e9i	−0.0486684	+	0.0656342i
$207$	6.99298e9	−	1.13930e10i	0.264726	−	0.431290i
$208$	−2.86197e10	+	1.91380e10i	−1.06018	+	0.708945i
$209$		−	3.75811e10i		−	1.36242i
$210$	9.73363e7	+	1.25176e7i	0.00345373	+	0.000444155i
$211$		−	2.16250e10i		−	0.751079i	−0.926806	−	0.375540i	$-0.877457\pi$
$211$		−	2.16250e10i		−	0.751079i	0.926806	−	0.375540i	$-0.122543\pi$
$212$	3.09012e10	−	9.37988e9i	1.05067	−	0.318923i
$213$	−1.36721e10	+	7.65020e9i	−0.455120	+	0.254662i
$214$	3.15312e10	+	2.33807e10i	1.02773	+	0.762071i
$215$	−1.14390e8			−0.00365102
$216$	2.96658e10	+	1.19763e10i	0.927286	+	0.374353i
$217$	−8.68094e9			−0.265765
$218$	−1.53809e10	−	1.14051e10i	−0.461240	−	0.342015i
$219$	1.81885e10	−	1.01774e10i	0.534316	−	0.298977i
$220$	−1.57227e8	+	4.77253e7i	−0.00452507	+	0.00137356i
$221$			6.16110e10i			1.73737i
$222$	−4.44123e10	−	5.71150e9i	−1.22720	−	0.157820i
$223$		−	5.65338e9i		−	0.153086i	−0.997066	−	0.0765431i	$-0.975612\pi$
$223$		−	5.65338e9i		−	0.153086i	0.997066	−	0.0765431i	$-0.0243883\pi$
$224$	1.04871e9	−	2.15456e10i	0.0278318	−	0.571797i
$225$	2.01096e10	−	3.27626e10i	0.523098	−	0.852229i
$226$	−2.31900e9	+	3.12740e9i	−0.0591306	+	0.0797434i
$227$	−1.89716e10			−0.474229			−0.237114	−	0.971482i	$-0.576202\pi$
$227$	−1.89716e10			−0.474229			−0.237114	+	0.971482i	$0.576202\pi$
$228$	−4.95699e10	+	5.15369e10i	−1.21482	+	1.26302i
$229$	5.32245e10			1.27894			0.639472	−	0.768814i	$-0.279153\pi$
$229$	5.32245e10			1.27894			0.639472	+	0.768814i	$0.279153\pi$
$230$	7.78109e7	−	1.04936e8i	0.00183343	−	0.00247257i
$231$	9.40526e9	+	1.68086e10i	0.217329	+	0.388399i
$232$	−5.22658e10	−	1.86850e10i	−1.18446	−	0.423446i
$233$			6.79267e10i			1.50987i	0.655801	+	0.754934i	$0.272331\pi$
$233$			6.79267e10i			1.50987i	−0.655801	+	0.754934i	$0.727669\pi$
$234$	−5.42723e10	+	2.18185e10i	−1.18333	+	0.475723i
$235$			3.60601e8i			0.00771298i
$236$	1.10305e10	+	3.63391e10i	0.231469	+	0.762554i
$237$	−2.14942e9	−	3.84133e9i	−0.0442540	−	0.0790886i
$238$	−3.10073e10	−	2.29922e10i	−0.626422	−	0.464499i
$239$	−1.64367e10			−0.325854			−0.162927	−	0.986638i	$-0.552094\pi$
$239$	−1.64367e10			−0.325854			−0.162927	+	0.986638i	$0.552094\pi$
$240$	2.78564e8	+	1.41936e8i	0.00541969	+	0.00276148i
$241$	−1.33367e10			−0.254666			−0.127333	−	0.991860i	$-0.540642\pi$
$241$	−1.33367e10			−0.254666			−0.127333	+	0.991860i	$0.540642\pi$
$242$	1.69535e10	+	1.25712e10i	0.317753	+	0.235617i
$243$	4.51385e10	+	3.02792e10i	0.830460	+	0.557078i
$244$	3.57246e9	+	1.17692e10i	0.0645227	+	0.212565i
$245$			2.30615e8i			0.00408921i
$246$	−3.79536e8	+	2.95125e9i	−0.00660762	+	0.0513805i
$247$		−	1.30742e11i		−	2.23501i
$248$	−2.60410e10	−	9.30965e9i	−0.437144	−	0.156279i
$249$	2.52638e10	−	1.41364e10i	0.416487	−	0.233046i
$250$	4.47528e8	−	6.03535e8i	0.00724586	−	0.00977176i
$251$	3.17132e10			0.504322			0.252161	−	0.967685i	$-0.418859\pi$
$251$	3.17132e10			0.504322			0.252161	+	0.967685i	$0.418859\pi$
$252$	9.27281e9	−	3.54562e10i	0.144847	−	0.553847i
$253$	2.56395e10			0.393430
$254$	7.30513e10	−	9.85169e10i	1.10123	−	1.48511i
$255$	4.88237e8	−	2.73193e8i	0.00723102	−	0.00404612i
$256$	2.62519e10	−	6.35075e10i	0.382016	−	0.924156i
$257$			8.53045e8i			0.0121976i	0.999981	+	0.00609878i	$0.00194131\pi$
$257$			8.53045e8i			0.0121976i	−0.999981	+	0.00609878i	$0.998059\pi$
$258$	−5.44871e9	+	4.23689e10i	−0.0765606	+	0.595331i
$259$			5.12958e10i			0.708326i
$260$	−5.46983e8	+	1.66033e8i	−0.00742324	+	0.00225328i
$261$	−8.03699e10	−	4.93310e10i	−1.07204	−	0.658018i
$262$	1.04520e11	+	7.75026e10i	1.37039	+	1.01616i
$263$	−1.24073e11			−1.59911			−0.799554	−	0.600594i	$-0.794931\pi$
$263$	−1.24073e11			−1.59911			−0.799554	+	0.600594i	$0.794931\pi$
$264$	1.01878e10	+	6.05087e10i	0.129081	+	0.766655i
$265$	5.36171e8			0.00667878
$266$	6.57993e10	+	4.87909e10i	0.805849	+	0.597546i
$267$	1.41754e10	+	2.53336e10i	0.170700	+	0.305067i
$268$	−1.19411e10	+	3.62466e9i	−0.141397	+	0.0429201i
$269$		−	1.11788e11i		−	1.30170i	−0.759206	−	0.650850i	$-0.774412\pi$
$269$		−	1.11788e11i		−	1.30170i	0.759206	−	0.650850i	$-0.225588\pi$
$270$	4.13553e8	+	3.33334e8i	0.00473581	+	0.00381718i
$271$			1.39529e11i			1.57145i	0.618575	+	0.785726i	$0.287710\pi$
$271$			1.39529e11i			1.57145i	−0.618575	+	0.785726i	$0.712290\pi$
$272$	−6.83578e10	−	1.02225e11i	−0.757230	−	1.13239i
$273$	3.27203e10	+	5.84761e10i	0.356522	+	0.637157i
$274$	4.47347e10	−	6.03292e10i	0.479476	−	0.646621i
$275$	7.37312e10			0.777417
$276$	−3.51608e10	−	3.38188e10i	−0.364727	−	0.350806i
$277$	−8.66980e10			−0.884810			−0.442405	−	0.896815i	$-0.645875\pi$
$277$	−8.66980e10			−0.884810			−0.442405	+	0.896815i	$0.645875\pi$
$278$	−6.52145e10	+	8.79482e10i	−0.654851	+	0.883131i
$279$	−4.00436e10	−	2.45787e10i	−0.395653	−	0.242851i
$280$	1.20565e8	−	3.37244e8i	0.00117222	−	0.00327893i
$281$		−	6.49020e9i		−	0.0620983i	−0.999518	−	0.0310492i	$-0.990115\pi$
$281$		−	6.49020e9i		−	0.0620983i	0.999518	−	0.0310492i	$-0.00988484\pi$
$282$	1.33563e11	+	1.71765e10i	1.25767	+	0.161738i
$283$		−	2.72852e10i		−	0.252864i	−0.991975	−	0.126432i	$-0.959647\pi$
$283$		−	2.72852e10i		−	0.252864i	0.991975	−	0.126432i	$-0.0403526\pi$
$284$	1.66069e10	+	5.47101e10i	0.151480	+	0.499040i
$285$	−1.03607e9	+	5.79732e8i	−0.00930221	+	0.00520506i
$286$	−9.01183e10	−	6.68237e10i	−0.796463	−	0.590586i
$287$	3.40867e9			0.0296563
$288$	6.58405e10	−	9.64166e10i	0.563933	−	0.825821i
$289$	−1.01476e11			−0.855703
$290$	−7.40253e8	−	5.48906e8i	−0.00614595	−	0.00455729i
$291$	−3.56947e10	+	1.99730e10i	−0.291800	+	0.163277i
$292$	−2.20929e10	−	7.27831e10i	−0.177840	−	0.585879i
$293$			3.14382e10i			0.249203i	0.992207	+	0.124602i	$0.0397653\pi$
$293$			3.14382e10i			0.249203i	−0.992207	+	0.124602i	$0.960235\pi$
$294$	8.54175e10	+	1.09848e10i	0.666782	+	0.0857493i
$295$			6.30525e8i			0.00484734i
$296$	−5.50109e10	+	1.53877e11i	−0.416520	+	1.16509i
$297$	−4.20619e9	+	1.04165e11i	−0.0313678	+	0.776813i
$298$	−1.22867e11	+	1.65698e11i	−0.902529	+	1.21715i
$299$	8.91983e10			0.645411
$300$	−1.01112e11	−	9.72523e10i	−0.720701	−	0.693193i
$301$	4.89357e10			0.343618
$302$	−4.62002e9	+	6.23056e9i	−0.0319605	+	0.0431018i
$303$	−1.13486e11	−	2.02816e11i	−0.773482	−	1.38233i
$304$	1.45059e11	+	2.16927e11i	0.974125	+	1.45674i
$305$			2.04208e8i			0.00135121i
$306$	−7.79320e10	−	1.93851e11i	−0.508124	−	1.26393i
$307$			1.17741e11i			0.756494i	0.925705	+	0.378247i	$0.123473\pi$
$307$			1.17741e11i			0.756494i	−0.925705	+	0.378247i	$0.876527\pi$
$308$	6.72613e10	−	2.04168e10i	0.425880	−	0.129273i
$309$	6.39407e9	+	1.14271e10i	0.0398992	+	0.0713058i
$310$	−3.68825e8	−	2.73487e8i	−0.00226826	−	0.00168194i
$311$	−5.94195e10			−0.360169			−0.180085	−	0.983651i	$-0.557637\pi$
$311$	−5.94195e10			−0.360169			−0.180085	+	0.983651i	$0.557637\pi$
$312$	3.54428e10	+	2.10506e11i	0.211755	+	1.25768i
$313$	1.14335e11			0.673334			0.336667	−	0.941624i	$-0.390700\pi$
$313$	1.14335e11			0.673334			0.336667	+	0.941624i	$0.390700\pi$
$314$	−1.65122e11	−	1.22440e11i	−0.958564	−	0.710785i
$315$	3.18307e8	−	5.18585e8i	0.00182158	−	0.00296772i
$316$	−1.53715e10	+	4.66591e9i	−0.0867208	+	0.0263236i
$317$			1.54743e10i			0.0860687i	0.999074	+	0.0430344i	$0.0137025\pi$
$317$			1.54743e10i			0.0860687i	−0.999074	+	0.0430344i	$0.986298\pi$
$318$	2.55394e10	−	1.98593e11i	0.140052	−	1.08903i
$319$		−	1.80870e11i		−	0.977932i
$320$	7.23336e8	−	8.82363e8i	0.00385625	−	0.00470405i
$321$	2.12396e11	−	1.18846e11i	1.11654	−	0.624758i
$322$	−3.32873e10	+	4.48912e10i	−0.172555	+	0.232707i
$323$	4.66989e11			2.38723
$324$	1.43163e11	−	1.37299e11i	0.721734	−	0.692171i
$325$	2.56506e11			1.27533
$326$	−1.12034e11	+	1.51089e11i	−0.549379	+	0.740892i
$327$	−1.03606e11	+	5.79730e10i	−0.501097	+	0.280389i
$328$	1.02253e10	+	3.65554e9i	0.0487802	+	0.0174389i
$329$		−	1.54264e11i		−	0.725913i
$330$	−1.29946e8	+	1.01045e9i	−0.000603182	+	0.00469031i
$331$			5.95950e10i			0.272887i	0.990648	+	0.136444i	$0.0435673\pi$
$331$			5.95950e10i			0.272887i	−0.990648	+	0.136444i	$0.956433\pi$
$332$	−3.06870e10	−	1.01096e11i	−0.138622	−	0.456679i
$333$	−1.45236e11	+	2.36618e11i	−0.647256	+	1.05451i
$334$	−2.81136e11	−	2.08465e11i	−1.23611	−	0.916589i
$335$	−2.07192e8			−0.000898818
$336$	−1.19169e11	−	6.07199e10i	−0.510078	−	0.259899i
$337$	−1.50229e11			−0.634480			−0.317240	−	0.948345i	$-0.602756\pi$
$337$	−1.50229e11			−0.634480			−0.317240	+	0.948345i	$0.602756\pi$
$338$	−1.20772e11	−	8.95534e10i	−0.503315	−	0.373213i
$339$	1.17877e10	+	2.10663e10i	0.0484762	+	0.0866343i
$340$	−5.93042e8	−	1.95373e9i	−0.00240675	−	0.00792883i
$341$		−	9.01170e10i		−	0.360921i
$342$	1.65376e11	+	4.11364e11i	0.653667	+	1.62596i
$343$		−	2.45407e11i		−	0.957333i
$344$	1.46797e11	+	5.24798e10i	0.565201	+	0.202060i
$345$	−3.95519e8	−	7.06852e8i	−0.00150308	−	0.00268623i
$346$	1.26200e11	−	1.70194e11i	0.473389	−	0.638412i
$347$	−3.54510e11			−1.31264			−0.656320	−	0.754482i	$-0.727888\pi$
$347$	−3.54510e11			−1.31264			−0.656320	+	0.754482i	$0.727888\pi$
$348$	−2.38570e11	+	2.48037e11i	−0.871985	+	0.906587i
$349$	2.47425e10			0.0892747			0.0446374	−	0.999003i	$-0.485787\pi$
$349$	2.47425e10			0.0892747			0.0446374	+	0.999003i	$0.485787\pi$
$350$	−9.57239e10	+	1.29093e11i	−0.340968	+	0.459829i
$351$	−1.46331e10	+	3.62382e11i	−0.0514581	+	1.27434i
$352$	2.23665e11	+	1.08867e10i	0.776526	+	0.0377968i
$353$			2.09277e11i			0.717356i	0.933461	+	0.358678i	$0.116772\pi$
$353$			2.09277e11i			0.717356i	−0.933461	+	0.358678i	$0.883228\pi$
$354$	2.33540e11	+	3.00337e10i	0.790401	+	0.101647i
$355$			9.49282e8i			0.00317225i
$356$	1.01375e11	−	3.07717e10i	0.334507	−	0.101538i
$357$	−2.08867e11	+	1.16871e11i	−0.680553	+	0.380804i
$358$	1.16553e10	+	8.64256e9i	0.0375017	+	0.0278079i
$359$	−9.20750e10			−0.292561			−0.146281	−	0.989243i	$-0.546730\pi$
$359$	−9.20750e10			−0.292561			−0.146281	+	0.989243i	$0.546730\pi$
$360$	1.51100e9	−	1.21428e9i	0.00474135	−	0.00381030i
$361$	−6.68291e11			−2.07101
$362$	2.02741e11	+	1.50334e11i	0.620515	+	0.460118i
$363$	1.14199e11	−	6.39003e10i	0.345211	−	0.193163i
$364$	2.33998e11	−	7.10287e10i	0.698644	−	0.212069i
$365$		−	1.26287e9i		−	0.00372426i
$366$	7.56368e10	+	9.72701e9i	0.220327	+	0.0283344i
$367$			1.25874e11i			0.362193i	0.983465	+	0.181097i	$0.0579646\pi$
$367$			1.25874e11i			0.362193i	−0.983465	+	0.181097i	$0.942035\pi$
$368$	−1.47997e11	+	9.89660e10i	−0.420667	+	0.281301i
$369$	1.57236e10	+	9.65113e9i	0.0441502	+	0.0270994i
$370$	−1.61604e9	+	2.17939e9i	−0.00448276	+	0.00604544i
$371$	−2.29373e11			−0.628578
$372$	−1.18865e11	+	1.23582e11i	−0.321819	+	0.334590i
$373$	4.72508e11			1.26392			0.631960	−	0.775001i	$-0.282251\pi$
$373$	4.72508e11			1.26392			0.631960	+	0.775001i	$0.282251\pi$
$374$	2.38683e11	−	3.21887e11i	0.630810	−	0.850709i
$375$	−2.27482e9	−	4.06544e9i	−0.00594028	−	0.0106162i
$376$	1.65437e11	−	4.62761e11i	0.426862	−	1.19402i
$377$		−	6.29236e11i		−	1.60427i
$378$	−1.76917e11	−	1.42600e11i	−0.445714	−	0.359257i
$379$			5.45235e10i			0.135740i	0.997694	+	0.0678699i	$0.0216203\pi$
$379$			5.45235e10i			0.135740i	−0.997694	+	0.0678699i	$0.978380\pi$
$380$	1.25847e9	+	4.14593e9i	0.00309612	+	0.0101999i
$381$	−3.71326e11	−	6.63615e11i	−0.902803	−	1.61344i
$382$	−5.88020e10	−	4.36023e10i	−0.141289	−	0.104767i
$383$	2.04719e11			0.486142			0.243071	−	0.970008i	$-0.421845\pi$
$383$	2.04719e11			0.486142			0.243071	+	0.970008i	$0.421845\pi$
$384$	−2.92364e11	−	3.09946e11i	−0.686173	−	0.727438i
$385$	1.16706e9			0.00270720
$386$	2.80636e11	+	2.08095e11i	0.643430	+	0.477110i
$387$	2.25732e11	+	1.38554e11i	0.511556	+	0.313993i
$388$	4.33570e10	+	1.42836e11i	0.0971218	+	0.319960i
$389$			7.88082e11i			1.74501i	0.488603	+	0.872506i	$0.337507\pi$
$389$			7.88082e11i			1.74501i	−0.488603	+	0.872506i	$0.662493\pi$
$390$	−4.52073e8	+	3.51529e9i	−0.000989504	+	0.00769433i
$391$			3.18601e11i			0.689368i
$392$	1.05802e11	−	2.95948e11i	0.226310	−	0.633036i
$393$	7.04051e11	−	3.93952e11i	1.48881	−	0.833062i
$394$	−2.64787e11	+	3.57091e11i	−0.553558	+	0.746528i
$395$	−2.66712e8			−0.000551259
$396$	3.68071e11	+	9.62612e10i	0.752149	+	0.196708i
$397$	3.22298e11			0.651179			0.325589	−	0.945511i	$-0.394437\pi$
$397$	3.22298e11			0.651179			0.325589	+	0.945511i	$0.394437\pi$
$398$	4.73665e11	−	6.38783e11i	0.946231	−	1.27609i
$399$	4.43227e11	−	2.48008e11i	0.875485	−	0.489878i
$400$	−4.25594e11	+	2.84595e11i	−0.831238	+	0.555850i
$401$			6.07663e11i			1.17358i	0.809738	+	0.586791i	$0.199609\pi$
$401$			6.07663e11i			1.17358i	−0.809738	+	0.586791i	$0.800391\pi$
$402$	−9.86916e9	+	7.67421e10i	−0.0188479	+	0.146560i
$403$		−	3.13511e11i		−	0.592080i
$404$	−8.11590e11	+	2.46353e11i	−1.51572	+	0.460089i
$405$	2.93659e9	−	1.49090e9i	0.00542369	−	0.00275360i
$406$	3.16679e11	+	2.34821e11i	0.578431	+	0.428913i
$407$	−5.32503e11			−0.961938
$408$	−7.51891e11	+	1.26596e11i	−1.34333	+	0.226177i
$409$	−4.07273e11			−0.719666			−0.359833	−	0.933017i	$-0.617166\pi$
$409$	−4.07273e11			−0.719666			−0.359833	+	0.933017i	$0.617166\pi$
$410$	1.44823e8	+	1.07388e8i	0.000253111	+	0.000187684i
$411$	−2.27390e11	−	4.06380e11i	−0.393083	−	0.702497i
$412$	4.57269e10	−	1.38801e10i	0.0781869	−	0.0237332i
$413$		−	2.69737e11i		−	0.456211i
$414$	−2.80651e11	+	1.12827e11i	−0.469532	+	0.188761i
$415$		−	1.75412e9i		−	0.00290298i
$416$	7.78117e11	+	3.78742e10i	1.27387	+	0.0620046i
$417$	3.31491e11	+	5.92424e11i	0.536858	+	0.959445i
$418$	−5.06499e11	+	6.83063e11i	−0.811494	+	1.09438i
$419$	−4.53776e11			−0.719248			−0.359624	−	0.933097i	$-0.617095\pi$
$419$	−4.53776e11			−0.719248			−0.359624	+	0.933097i	$0.617095\pi$
$420$	−1.60045e9	−	1.53937e9i	−0.00250969	−	0.00241390i
$421$	−4.45646e10			−0.0691386			−0.0345693	−	0.999402i	$-0.511006\pi$
$421$	−4.45646e10			−0.0691386			−0.0345693	+	0.999402i	$0.511006\pi$
$422$	−2.91451e11	+	3.93051e11i	−0.447363	+	0.603313i
$423$	4.36776e11	−	7.11594e11i	0.663326	−	1.08069i
$424$	−6.88070e11	−	2.45985e11i	−1.03392	−	0.369626i
$425$			9.16196e11i			1.36219i
$426$	3.51605e11	+	4.52170e10i	0.517264	+	0.0665210i
$427$		−	8.73598e10i		−	0.127170i
$428$	−2.57989e11	−	8.49922e11i	−0.371624	−	1.22428i
$429$	−6.07042e11	+	3.39670e11i	−0.865288	+	0.484172i
$430$	2.07912e9	+	1.54169e9i	0.00293272	+	0.00217465i
$431$	1.13939e12			1.59047			0.795235	−	0.606302i	$-0.207348\pi$
$431$	1.13939e12			1.59047			0.795235	+	0.606302i	$0.207348\pi$
$432$	−3.77786e11	−	6.17499e11i	−0.521878	−	0.853020i
$433$	7.27355e11			0.994377			0.497188	−	0.867643i	$-0.334366\pi$
$433$	7.27355e11			0.994377			0.497188	+	0.867643i	$0.334366\pi$
$434$	1.57782e11	+	1.16997e11i	0.213479	+	0.158297i
$435$	−4.98638e9	+	2.79013e9i	−0.00667704	+	0.00373614i
$436$	1.25847e11	+	4.14592e11i	0.166783	+	0.549454i
$437$		−	6.76090e11i		−	0.886825i
$438$	−4.67755e11	−	6.01540e10i	−0.607274	−	0.0780964i
$439$			3.67434e11i			0.472160i	0.971734	+	0.236080i	$0.0758628\pi$
$439$			3.67434e11i			0.472160i	−0.971734	+	0.236080i	$0.924137\pi$
$440$	3.50093e9	+	1.25158e9i	0.00445294	+	0.00159193i
$441$	2.79330e11	−	4.55084e11i	0.351678	−	0.572952i
$442$	8.30362e11	−	1.11983e12i	1.03483	−	1.39556i
$443$	−1.07540e12			−1.32664			−0.663320	−	0.748336i	$-0.730853\pi$
$443$	−1.07540e12			−1.32664			−0.663320	+	0.748336i	$0.730853\pi$
$444$	7.30250e11	+	7.02378e11i	0.891760	+	0.857724i
$445$	1.75897e9			0.00212636
$446$	−7.61934e10	+	1.02754e11i	−0.0911822	+	0.122968i
$447$	6.24542e11	+	1.11615e12i	0.739909	+	1.32233i
$448$	−3.09442e11	+	3.77473e11i	−0.362934	+	0.442725i
$449$		−	8.79035e11i		−	1.02070i	−0.859967	−	0.510350i	$-0.829516\pi$
$449$		−	8.79035e11i		−	1.02070i	0.859967	−	0.510350i	$-0.170484\pi$
$450$	−8.07064e11	+	3.24456e11i	−0.927795	+	0.372992i
$451$			3.53855e10i			0.0402745i
$452$	8.42989e10	−	2.55884e10i	0.0949946	−	0.0288350i
$453$	2.34840e10	+	4.19694e10i	0.0262017	+	0.0468264i
$454$	3.44823e11	+	2.55690e11i	0.380929	+	0.282463i
$455$	4.06013e9			0.00444108
$456$	1.59556e12	−	2.68644e11i	1.72811	−	0.290961i
$457$	−8.41095e11			−0.902033			−0.451016	−	0.892516i	$-0.648938\pi$
$457$	−8.41095e11			−0.902033			−0.451016	+	0.892516i	$0.648938\pi$
$458$	−9.67394e11	−	7.17333e11i	−1.02733	−	0.761774i
$459$	−1.29437e12	−	5.22668e10i	−1.36113	−	0.0549628i
$460$	−2.82854e9	+	8.58586e8i	−0.00294545	+	0.000894074i
$461$		−	7.41163e11i		−	0.764293i	−0.924102	−	0.382146i	$-0.875185\pi$
$461$		−	7.41163e11i		−	0.764293i	0.924102	−	0.382146i	$-0.124815\pi$
$462$	5.55904e10	−	4.32268e11i	0.0567689	−	0.441432i
$463$			1.05967e12i			1.07166i	0.844325	+	0.535831i	$0.180001\pi$
$463$			1.05967e12i			1.07166i	−0.844325	+	0.535831i	$0.819999\pi$
$464$	6.98141e11	+	1.04403e12i	0.699218	+	1.04564i
$465$	−2.48442e9	+	1.39016e9i	−0.00246426	+	0.00137888i
$466$	9.15482e11	−	1.23462e12i	0.899318	−	1.21282i
$467$	1.29895e12			1.26376			0.631880	−	0.775066i	$-0.282283\pi$
$467$	1.29895e12			1.26376			0.631880	+	0.775066i	$0.282283\pi$
$468$	1.28050e12	+	3.34887e11i	1.23388	+	0.322695i
$469$	8.86364e10			0.0845930
$470$	4.86000e9	−	6.55419e9i	0.00459406	−	0.00619554i
$471$	−1.11227e12	+	6.22371e11i	−1.04140	+	0.582713i
$472$	2.89273e11	−	8.09154e11i	0.268268	−	0.750399i
$473$			5.08002e11i			0.466649i
$474$	−1.27043e10	+	9.87877e10i	−0.0115597	+	0.0898877i
$475$		−	1.94422e12i		−	1.75237i
$476$	2.53702e11	+	8.35800e11i	0.226513	+	0.746228i
$477$	−1.05806e12	−	6.49434e11i	−0.935784	−	0.574384i
$478$	2.98749e11	+	2.21525e11i	0.261746	+	0.194088i
$479$	6.40124e11			0.555590			0.277795	−	0.960640i	$-0.410396\pi$
$479$	6.40124e11			0.555590			0.277795	+	0.960640i	$0.410396\pi$
$480$	−3.15016e9	−	6.33413e9i	−0.00270861	−	0.00544630i
$481$	−1.85255e12			−1.57803
$482$	2.42404e11	+	1.79745e11i	0.204563	+	0.151686i
$483$	1.69202e11	+	3.02390e11i	0.141463	+	0.252816i
$484$	−1.38714e11	−	4.56980e11i	−0.114899	−	0.378524i
$485$			2.47837e9i			0.00203389i
$486$	−4.12338e11	−	1.15870e12i	−0.335266	−	0.942123i
$487$		−	1.20673e12i		−	0.972142i	−0.873919	−	0.486071i	$-0.838430\pi$
$487$		−	1.20673e12i		−	0.972142i	0.873919	−	0.486071i	$-0.161570\pi$
$488$	9.36867e10	−	2.62061e11i	0.0747806	−	0.209176i
$489$	5.69480e11	+	1.01775e12i	0.450390	+	0.804914i
$490$	3.10811e9	−	4.19159e9i	0.00243564	−	0.00328471i
$491$	−1.57811e12			−1.22538			−0.612691	−	0.790323i	$-0.709913\pi$
$491$	−1.57811e12			−1.22538			−0.612691	+	0.790323i	$0.709913\pi$
$492$	4.66738e10	−	4.85260e10i	0.0359113	−	0.0373363i
$493$	2.24752e12			1.71353
$494$	−1.76208e12	+	2.37634e12i	−1.33123	+	1.79530i
$495$	5.38344e9	+	3.30435e9i	0.00403029	+	0.00247379i
$496$	3.47843e11	+	5.20177e11i	0.258057	+	0.385908i
$497$		−	4.06101e11i		−	0.298559i
$498$	−6.49711e11	−	8.35539e10i	−0.473356	−	0.0608744i
$499$			1.99736e12i			1.44213i	0.692869	+	0.721063i	$0.256346\pi$
$499$			1.99736e12i			1.44213i	−0.692869	+	0.721063i	$0.743654\pi$
$500$	−1.62683e10	+	4.93814e9i	−0.0116406	+	0.00353345i
$501$	−1.89375e12	+	1.05965e12i	−1.34293	+	0.751435i
$502$	−5.76410e11	−	4.27414e11i	−0.405102	−	0.300388i
$503$	2.26115e12			1.57497			0.787487	−	0.616331i	$-0.211382\pi$
$503$	2.26115e12			1.57497			0.787487	+	0.616331i	$0.211382\pi$
$504$	−6.46401e11	+	5.19468e11i	−0.446236	+	0.358609i
$505$	−1.40820e10			−0.00963503
$506$	−4.66017e11	−	3.45556e11i	−0.316027	−	0.234337i
$507$	−8.13524e11	+	4.55208e11i	−0.546808	+	0.305966i
$508$	−2.65552e12	+	8.06068e11i	−1.76914	+	0.537013i
$509$			1.54479e12i			1.02009i	0.860147	+	0.510046i	$0.170372\pi$
$509$			1.54479e12i			1.02009i	−0.860147	+	0.510046i	$0.829628\pi$
$510$	−1.25560e10	−	1.61472e9i	−0.00821838	−	0.00105690i
$511$			5.40252e11i			0.350512i
$512$	−1.33307e12	+	8.00485e11i	−0.857310	+	0.514800i
$513$	2.74673e12	+	1.10913e11i	1.75100	+	0.0707059i
$514$	1.14969e10	−	1.55047e10i	0.00726519	−	0.00979782i
$515$	7.93413e8			0.000497012
$516$	6.70061e11	−	6.96651e11i	0.416093	−	0.432605i
$517$	1.60142e12			0.985822
$518$	6.91339e11	−	9.32339e11i	0.421898	−	0.568971i
$519$	−6.41488e11	−	1.14643e12i	−0.388092	−	0.693579i
$520$	1.21795e10	+	4.35418e9i	0.00730492	+	0.00261151i
$521$		−	2.51532e12i		−	1.49563i	−0.663910	−	0.747813i	$-0.731104\pi$
$521$		−	2.51532e12i		−	1.49563i	0.663910	−	0.747813i	$-0.268896\pi$
$522$	7.95924e11	+	1.97981e12i	0.469196	+	1.16710i
$523$		−	2.74314e12i		−	1.60321i	−0.597854	−	0.801605i	$-0.703980\pi$
$523$		−	2.74314e12i		−	1.60321i	0.597854	−	0.801605i	$-0.296020\pi$
$524$	−8.55184e11	−	2.81733e12i	−0.495529	−	1.63248i
$525$	4.86573e11	+	8.69578e11i	0.279532	+	0.499565i
$526$	2.25513e12	+	1.67220e12i	1.28450	+	0.952472i
$527$	1.11981e12			0.632406
$528$	6.30334e11	−	1.23710e12i	0.352954	−	0.692709i
$529$	−1.33989e12			−0.743909
$530$	−9.74530e9	−	7.22625e9i	−0.00536480	−	0.00397806i
$531$	7.63719e11	−	1.24425e12i	0.416877	−	0.679175i
$532$	−5.38371e11	−	1.77362e12i	−0.291393	−	0.959971i
$533$			1.23104e11i			0.0660692i
$534$	8.37846e10	−	6.51505e11i	0.0445891	−	0.346722i
$535$		−	1.47471e10i		−	0.00778242i
$536$	2.65890e11	+	9.50558e10i	0.139143	+	0.0497436i
$537$	7.85110e10	−	4.39309e10i	0.0407424	−	0.0227974i
$538$	−1.50663e12	+	2.03183e12i	−0.775328	+	1.04561i
$539$	1.02415e12			0.522656
$540$	−3.02412e9	−	1.16323e10i	−0.00153048	−	0.00588697i
$541$	4.25694e11			0.213653			0.106827	−	0.994278i	$-0.465931\pi$
$541$	4.25694e11			0.213653			0.106827	+	0.994278i	$0.465931\pi$
$542$	1.88049e12	−	2.53603e12i	0.935999	−	1.26229i
$543$	1.36567e12	−	7.64162e11i	0.674135	−	0.377213i
$544$	−1.35280e11	+	2.77930e12i	−0.0662276	+	1.36063i
$545$			7.19363e9i			0.00349272i
$546$	1.93396e11	−	1.50383e12i	0.0931279	−	0.724158i
$547$			1.65077e12i			0.788397i	0.919025	+	0.394198i	$0.128978\pi$
$547$			1.65077e12i			0.788397i	−0.919025	+	0.394198i	$0.871022\pi$
$548$	−1.62617e12	+	4.93615e11i	−0.770290	+	0.233817i
$549$	2.47346e11	−	4.02975e11i	0.116206	−	0.189323i
$550$	−1.34012e12	−	9.93711e11i	−0.624469	−	0.463050i
$551$	−4.76938e12			−2.20434
$552$	1.83281e11	+	1.08856e12i	0.0840216	+	0.499030i
$553$	1.14099e11			0.0518822
$554$	1.57580e12	+	1.16847e12i	0.710734	+	0.527017i
$555$	8.21448e9	+	1.46805e10i	0.00367504	+	0.00656784i
$556$	2.37064e12	−	7.19594e11i	1.05203	−	0.319338i
$557$			8.04249e10i			0.0354032i	0.999843	+	0.0177016i	$0.00563489\pi$
$557$			8.04249e10i			0.0354032i	−0.999843	+	0.0177016i	$0.994365\pi$
$558$	3.96562e11	+	9.86424e11i	0.173164	+	0.430735i
$559$			1.76731e12i			0.765525i
$560$	−6.73655e9	+	4.50474e9i	−0.00289462	+	0.00193564i
$561$	−1.21324e12	−	2.16825e12i	−0.517148	−	0.924221i
$562$	−8.74717e10	+	1.17964e11i	−0.0369874	+	0.0498812i
$563$	1.14042e12			0.478383			0.239191	−	0.970972i	$-0.423118\pi$
$563$	1.14042e12			0.478383			0.239191	+	0.970972i	$0.423118\pi$
$564$	−2.19612e12	−	2.11229e12i	−0.913901	−	0.879020i
$565$	1.46268e9			0.000603854
$566$	−3.67736e11	+	4.95928e11i	−0.150613	+	0.203116i
$567$	−1.25626e12	+	6.37804e11i	−0.510455	+	0.259157i
$568$	4.35512e11	−	1.21822e12i	0.175563	−	0.491085i
$569$			2.12867e12i			0.851342i	0.904878	+	0.425671i	$0.139962\pi$
$569$			2.12867e12i			0.851342i	−0.904878	+	0.425671i	$0.860038\pi$
$570$	2.66446e10	+	3.42654e9i	0.0105724	+	0.00135963i
$571$			3.67544e12i			1.44693i	0.690362	+	0.723464i	$0.257451\pi$
$571$			3.67544e12i			1.44693i	−0.690362	+	0.723464i	$0.742549\pi$
$572$	7.37350e11	+	2.42914e12i	0.287999	+	0.948790i
$573$	−3.96093e11	+	2.21634e11i	−0.153498	+	0.0858897i
$574$	−6.19551e10	−	4.59403e10i	−0.0238217	−	0.0176641i
$575$	1.32644e12			0.506036
$576$	−2.49615e12	+	8.65077e11i	−0.944866	+	0.327457i
$577$	−2.91553e12			−1.09503			−0.547516	−	0.836795i	$-0.684426\pi$
$577$	−2.91553e12			−1.09503			−0.547516	+	0.836795i	$0.684426\pi$
$578$	1.84440e12	+	1.36764e12i	0.687353	+	0.509679i
$579$	1.89038e12	−	1.05776e12i	0.699030	−	0.391143i
$580$	6.05677e9	+	1.99535e10i	0.00222236	+	0.00732139i
$581$			7.50410e11i			0.273216i
$582$	9.17964e11	+	1.18052e11i	0.331644	+	0.0426500i
$583$		−	2.38112e12i		−	0.853637i
$584$	−5.79380e11	+	1.62064e12i	−0.206113	+	0.576540i
$585$	1.87287e10	+	1.14956e10i	0.00661158	+	0.00405818i
$586$	4.23709e11	−	5.71413e11i	0.148432	−	0.200175i
$587$	−3.59172e12			−1.24862			−0.624311	−	0.781176i	$-0.714620\pi$
$587$	−3.59172e12			−1.24862			−0.624311	+	0.781176i	$0.714620\pi$
$588$	−1.40448e12	−	1.35087e12i	−0.484526	−	0.466032i
$589$	−2.37630e12			−0.813547
$590$	8.49789e9	−	1.14602e10i	0.00288720	−	0.00389368i
$591$	1.34593e12	+	2.40538e12i	0.453816	+	0.811037i
$592$	3.07373e12	−	2.05541e12i	1.02853	−	0.687782i
$593$			1.17516e12i			0.390256i	0.980778	+	0.195128i	$0.0625123\pi$
$593$			1.17516e12i			0.390256i	−0.980778	+	0.195128i	$0.937488\pi$
$594$	1.48033e12	−	1.83658e12i	0.487887	−	0.605300i
$595$			1.45021e10i			0.00474356i
$596$	4.46639e12	−	1.35574e12i	1.44993	−	0.440119i
$597$	−2.40768e12	−	4.30288e12i	−0.775736	−	1.38636i
$598$	−1.62124e12	−	1.20217e12i	−0.518433	−	0.384424i
$599$	−5.75593e12			−1.82682			−0.913408	−	0.407045i	$-0.866559\pi$
$599$	−5.75593e12			−1.82682			−0.913408	+	0.407045i	$0.866559\pi$
$600$	5.27058e11	+	3.13036e12i	0.166027	+	0.986084i
$601$	4.18734e11			0.130919			0.0654596	−	0.997855i	$-0.479149\pi$
$601$	4.18734e11			0.130919			0.0654596	+	0.997855i	$0.479149\pi$
$602$	−8.89442e11	−	6.59530e11i	−0.276015	−	0.204668i
$603$	4.08864e11	+	2.50960e11i	0.125936	+	0.0772996i
$604$	1.67945e11	−	5.09786e10i	0.0513452	−	0.0155855i
$605$		−	7.92913e9i		−	0.00240617i
$606$	−6.70766e11	+	5.21584e12i	−0.202043	+	1.57108i
$607$		−	4.09403e12i		−	1.22406i	−0.790836	−	0.612029i	$-0.790354\pi$
$607$		−	4.09403e12i		−	1.22406i	0.790836	−	0.612029i	$-0.209646\pi$
$608$	2.87073e11	−	5.89784e12i	0.0851973	−	1.75036i
$609$	2.13316e12	−	1.19361e12i	0.628415	−	0.351630i
$610$	2.75221e9	−	3.71163e9i	0.000804818	−	0.00108538i
$611$	5.57125e12			1.61721
$612$	−1.19616e12	+	4.57372e12i	−0.344673	+	1.31792i
$613$	1.78118e12			0.509489			0.254745	−	0.967008i	$-0.418009\pi$
$613$	1.78118e12			0.509489			0.254745	+	0.967008i	$0.418009\pi$
$614$	1.58686e12	−	2.14003e12i	0.450588	−	0.607662i
$615$	9.75537e8	−	5.45862e8i	0.000274983	−	0.000153867i
$616$	−1.49769e12	−	5.35424e11i	−0.419091	−	0.149825i
$617$			2.52268e12i			0.700774i	0.936605	+	0.350387i	$0.113950\pi$
$617$			2.52268e12i			0.700774i	−0.936605	+	0.350387i	$0.886050\pi$
$618$	3.77925e10	−	2.93873e11i	0.0104222	−	0.0810422i
$619$		−	5.53696e11i		−	0.151587i	−0.997124	−	0.0757937i	$-0.975851\pi$
$619$		−	5.53696e11i		−	0.151587i	0.997124	−	0.0757937i	$-0.0241490\pi$
$620$	3.01773e9	+	9.94167e9i	0.000820197	+	0.00270207i
$621$	−7.56701e10	+	1.87394e12i	−0.0204179	+	0.505642i
$622$	1.07999e12	+	8.00825e11i	0.289310	+	0.214527i
$623$	−7.52482e11			−0.200124
$624$	2.19289e12	−	4.30378e12i	0.579011	−	1.13637i
$625$	3.81427e12			0.999889
$626$	−2.07813e12	−	1.54095e12i	−0.540863	−	0.401056i
$627$	2.57458e12	+	4.60115e12i	0.665276	+	1.18895i
$628$	1.35103e12	+	4.45086e12i	0.346615	+	1.14189i
$629$		−	6.61697e12i		−	1.68551i
$630$	−1.27747e10	+	5.13568e9i	−0.00323086	+	0.00129887i
$631$		−	7.99164e11i		−	0.200680i	−0.994953	−	0.100340i	$-0.968007\pi$
$631$		−	7.99164e11i		−	0.200680i	0.994953	−	0.100340i	$-0.0319930\pi$
$632$	3.42272e11	+	1.22362e11i	0.0853385	+	0.0305085i
$633$	1.48147e12	+	2.64761e12i	0.366756	+	0.655447i
$634$	2.08555e11	−	2.81257e11i	0.0512648	−	0.0691357i
$635$	−4.60763e10			−0.0112459
$636$	−3.14073e12	+	3.26536e12i	−0.761156	+	0.791360i
$637$	3.56297e12			0.857402
$638$	−2.43768e12	+	3.28745e12i	−0.582483	+	0.785535i
$639$	1.14981e12	−	1.87327e12i	0.272818	−	0.444474i
$640$	−2.50392e10	+	6.28882e9i	−0.00589944	+	0.00148170i
$641$			6.72935e11i			0.157439i	0.996897	+	0.0787194i	$0.0250831\pi$
$641$			6.72935e11i			0.157439i	−0.996897	+	0.0787194i	$0.974917\pi$
$642$	−5.46219e12	−	7.02447e11i	−1.26899	−	0.163195i
$643$		−	5.84866e11i		−	0.134930i	−0.997722	−	0.0674648i	$-0.978509\pi$
$643$		−	5.84866e11i		−	0.134930i	0.997722	−	0.0674648i	$-0.0214910\pi$
$644$	1.21004e12	−	3.67301e11i	0.277213	−	0.0841464i
$645$	1.40050e10	−	7.83653e9i	0.00318615	−	0.00178281i
$646$	−8.48786e12	−	6.29384e12i	−1.91757	−	1.42190i
$647$	−2.97803e12			−0.668127			−0.334064	−	0.942551i	$-0.608420\pi$
$647$	−2.97803e12			−0.668127			−0.334064	+	0.942551i	$0.608420\pi$
$648$	−4.45252e12	+	5.66028e11i	−0.992016	+	0.126110i
$649$	2.80014e12			0.619554
$650$	−4.66219e12	−	3.45706e12i	−1.02442	−	0.759621i
$651$	1.06283e12	−	5.94707e11i	0.231926	−	0.129774i
$652$	4.07261e12	−	1.23622e12i	0.882590	−	0.267905i
$653$			4.44723e12i			0.957150i	0.878047	+	0.478575i	$0.158846\pi$
$653$			4.44723e12i			0.957150i	−0.878047	+	0.478575i	$0.841154\pi$
$654$	2.66445e12	+	3.42653e11i	0.569519	+	0.0732411i
$655$		−	4.88839e10i		−	0.0103772i
$656$	−1.36584e11	−	2.04253e11i	−0.0287961	−	0.0430628i
$657$	−1.52964e12	+	2.49209e12i	−0.320292	+	0.521818i
$658$	−2.07910e12	+	2.80387e12i	−0.432373	+	0.583098i
$659$	5.90518e12			1.21969			0.609844	−	0.792522i	$-0.291232\pi$
$659$	5.90518e12			1.21969			0.609844	+	0.792522i	$0.291232\pi$
$660$	1.59802e10	−	1.66143e10i	0.00327819	−	0.00340828i
$661$	−3.41126e12			−0.695038			−0.347519	−	0.937673i	$-0.612976\pi$
$661$	−3.41126e12			−0.695038			−0.347519	+	0.937673i	$0.612976\pi$
$662$	8.03191e11	−	1.08318e12i	0.162539	−	0.219200i
$663$	−4.22080e12	−	7.54320e12i	−0.848367	−	1.51616i
$664$	−8.04758e11	+	2.25107e12i	−0.160660	+	0.449400i
$665$		−	3.07743e10i		−	0.00610226i
$666$	5.82880e12	−	2.34329e12i	1.14801	−	0.461522i
$667$		−	3.25388e12i		−	0.636555i
$668$	2.30026e12	+	7.57802e12i	0.446975	+	1.47252i
$669$	3.87297e11	+	6.92158e11i	0.0747527	+	0.133594i
$670$	3.76587e9	+	2.79243e9i	0.000721986	+	0.000535360i
$671$	9.06883e11			0.172703
$672$	1.34763e12	+	2.70973e12i	0.254923	+	0.512583i
$673$	−6.84494e12			−1.28618			−0.643090	−	0.765791i	$-0.722348\pi$
$673$	−6.84494e12			−1.28618			−0.643090	+	0.765791i	$0.722348\pi$
$674$	2.73051e12	+	2.02471e12i	0.509653	+	0.377913i
$675$	−2.17603e11	+	5.38886e12i	−0.0403458	+	0.999149i
$676$	9.88156e11	+	3.25540e12i	0.181998	+	0.599576i
$677$			6.99806e12i			1.28035i	0.768229	+	0.640175i	$0.221138\pi$
$677$			6.99806e12i			1.28035i	−0.768229	+	0.640175i	$0.778862\pi$
$678$	6.96717e10	−	5.41763e11i	0.0126626	−	0.0984637i
$679$		−	1.06024e12i		−	0.191421i
$680$	−1.55524e10	+	4.35032e10i	−0.00278937	+	0.00780244i
$681$	2.32274e12	−	1.29969e12i	0.413847	−	0.231568i
$682$	−1.21455e12	+	1.63794e12i	−0.214974	+	0.289914i
$683$	−1.58289e12			−0.278329			−0.139164	−	0.990269i	$-0.544442\pi$
$683$	−1.58289e12			−0.278329			−0.139164	+	0.990269i	$0.544442\pi$
$684$	2.53832e12	−	9.70570e12i	0.443398	−	1.69541i
$685$	−2.82159e10			−0.00489651
$686$	−3.30747e12	+	4.46045e12i	−0.570213	+	0.768989i
$687$	−6.51641e12	+	3.64626e12i	−1.11610	+	0.624515i
$688$	−1.96084e12	−	2.93231e12i	−0.333652	−	0.498956i
$689$		−	8.28378e12i		−	1.40037i
$690$	−2.33774e9	+	1.81782e10i	−0.000392623	+	0.00305302i
$691$			7.09186e12i			1.18334i	0.806181	+	0.591669i	$0.201531\pi$
$691$			7.09186e12i			1.18334i	−0.806181	+	0.591669i	$0.798469\pi$
$692$	−4.58757e12	+	1.39253e12i	−0.760511	+	0.230848i
$693$	−2.30302e12	−	1.41359e12i	−0.379314	−	0.232823i
$694$	6.44348e12	+	4.77791e12i	1.05439	+	0.781844i
$695$	4.11333e10			0.00668748
$696$	7.67910e12	−	1.29293e12i	1.24042	−	0.208849i
$697$	−4.39706e11			−0.0705691
$698$	−4.49712e11	−	3.33466e11i	−0.0717109	−	0.0531744i
$699$	−4.65347e12	−	8.31645e12i	−0.737276	−	1.31762i
$700$	3.47970e12	−	1.05624e12i	0.547774	−	0.166273i
$701$		−	7.26220e12i		−	1.13589i	−0.823066	−	0.567946i	$-0.807738\pi$
$701$		−	7.26220e12i		−	1.13589i	0.823066	−	0.567946i	$-0.192262\pi$
$702$	5.14997e12	−	6.38935e12i	0.800365	−	0.992978i
$703$			1.40416e13i			2.16829i
$704$	−3.91855e12	−	3.21232e12i	−0.601241	−	0.492881i
$705$	−2.47038e10	−	4.41494e10i	−0.00376628	−	0.00673091i
$706$	2.82053e12	−	3.80376e12i	0.427276	−	0.576224i
$707$	6.02425e12			0.906808
$708$	−3.83999e12	−	3.69342e12i	−0.574355	−	0.552433i
$709$	−1.28950e12			−0.191652			−0.0958259	−	0.995398i	$-0.530549\pi$
$709$	−1.28950e12			−0.191652			−0.0958259	+	0.995398i	$0.530549\pi$
$710$	1.27939e10	−	1.72539e10i	0.00188948	−	0.00254815i
$711$	5.26317e11	+	3.23053e11i	0.0772386	+	0.0474090i
$712$	−2.25729e12	−	8.06980e11i	−0.329175	−	0.117680i
$713$		−	1.62122e12i		−	0.234930i
$714$	5.37143e12	+	6.90775e11i	0.773479	+	0.0994706i
$715$			4.21483e10i			0.00603119i
$716$	−9.53643e10	−	3.14170e11i	−0.0135605	−	0.0446741i
$717$	2.01239e12	−	1.12603e12i	0.284364	−	0.159116i
$718$	1.67353e12	+	1.24094e12i	0.235003	+	0.174257i
$719$	1.01630e13			1.41821			0.709106	−	0.705101i	$-0.249099\pi$
$719$	1.01630e13			1.41821			0.709106	+	0.705101i	$0.249099\pi$
$720$	−4.38290e10	+	1.70605e9i	−0.00607806	+	0.000236590i
$721$	−3.39420e11			−0.0467767
$722$	1.21467e13	+	9.00688e12i	1.66356	+	1.23355i
$723$	1.63285e12	−	9.13660e11i	0.222240	−	0.124355i
$724$	−1.65883e12	−	5.46487e12i	−0.224377	−	0.739191i
$725$		−	9.35715e12i		−	1.25783i
$726$	−2.93687e12	−	3.77687e11i	−0.392347	−	0.0504565i
$727$		−	5.26898e12i		−	0.699554i	−0.936833	−	0.349777i	$-0.886257\pi$
$727$		−	5.26898e12i		−	0.699554i	0.936833	−	0.349777i	$-0.113743\pi$
$728$	−5.21037e12	−	1.86271e12i	−0.687508	−	0.245784i
$729$	−7.60077e12	−	6.14844e11i	−0.996744	−	0.0806289i
$730$	−1.70203e10	+	2.29536e10i	−0.00221827	+	0.00299156i
$731$	−6.31252e12			−0.817663
$732$	−1.24366e12	−	1.19619e12i	−0.160104	−	0.153993i
$733$	5.48316e11			0.0701557			0.0350778	−	0.999385i	$-0.488832\pi$
$733$	5.48316e11			0.0701557			0.0350778	+	0.999385i	$0.488832\pi$
$734$	1.69647e12	−	2.28786e12i	0.215732	−	0.290936i
$735$	−1.57988e10	−	2.82348e10i	−0.00199678	−	0.00356854i
$736$	4.02377e12	+	1.95854e11i	0.505456	+	0.0246027i
$737$			9.20136e11i			0.114881i
$738$	−1.55715e11	−	3.87331e11i	−0.0193231	−	0.0480649i
$739$			4.81338e12i			0.593677i	0.954928	+	0.296838i	$0.0959323\pi$
$739$			4.81338e12i			0.593677i	−0.954928	+	0.296838i	$0.904068\pi$
$740$	5.87455e10	−	1.78318e10i	0.00720165	−	0.00218602i
$741$	8.95679e12	+	1.60071e13i	1.09137	+	1.95043i
$742$	4.16902e12	+	3.09137e12i	0.504913	+	0.374398i
$743$	−8.92459e12			−1.07433			−0.537166	−	0.843477i	$-0.680505\pi$
$743$	−8.92459e12			−1.07433			−0.537166	+	0.843477i	$0.680505\pi$
$744$	3.82604e12	−	6.44190e11i	0.457796	−	0.0770789i
$745$	7.74969e10			0.00921682
$746$	−8.58818e12	−	6.36823e12i	−1.01526	−	0.752825i
$747$	−2.12467e12	+	3.46151e12i	−0.249660	+	0.406745i
$748$	−8.67646e12	+	2.63369e12i	−1.01341	+	0.307615i
$749$			6.30878e12i			0.732449i
$750$	−1.34455e10	+	1.04551e11i	−0.00155167	+	0.0120657i
$751$		−	1.36175e13i		−	1.56213i	−0.624449	−	0.781066i	$-0.714676\pi$
$751$		−	1.36175e13i		−	1.56213i	0.624449	−	0.781066i	$-0.285324\pi$
$752$	−9.24379e12	+	6.18134e12i	−1.05407	+	0.704859i
$753$	−3.88273e12	+	2.17258e12i	−0.440108	+	0.246263i
$754$	−8.48053e12	+	1.14368e13i	−0.955546	+	1.28865i
$755$	2.91403e9			0.000326387
$756$	1.29371e12	+	4.97625e12i	0.144042	+	0.554057i
$757$	−6.38847e12			−0.707075			−0.353538	−	0.935420i	$-0.615021\pi$
$757$	−6.38847e12			−0.707075			−0.353538	+	0.935420i	$0.615021\pi$
$758$	7.34840e11	−	9.91003e11i	0.0808502	−	0.109034i
$759$	−3.13911e12	+	1.75649e12i	−0.343336	+	0.192114i
$760$	3.30031e10	−	9.23163e10i	0.00358834	−	0.0100373i
$761$			2.02350e12i			0.218712i	0.994003	+	0.109356i	$0.0348788\pi$
$761$			2.02350e12i			0.218712i	−0.994003	+	0.109356i	$0.965121\pi$
$762$	−2.19475e12	+	1.70662e13i	−0.235823	+	1.83375i
$763$		−	3.07742e12i		−	0.328720i
$764$	4.81119e11	+	1.58501e12i	0.0510896	+	0.168310i
$765$	−4.10604e10	+	6.68955e10i	−0.00433458	+	0.00706188i
$766$	−3.72091e12	−	2.75910e12i	−0.390499	−	0.289559i
$767$	9.74153e12			1.01636
$768$	1.13663e12	+	9.57384e12i	0.117895	+	0.993026i
$769$	1.43406e13			1.47877			0.739383	−	0.673285i	$-0.235117\pi$
$769$	1.43406e13			1.47877			0.739383	+	0.673285i	$0.235117\pi$
$770$	−2.12122e10	−	1.57290e10i	−0.00217459	−	0.00161248i
$771$	−5.84398e10	−	1.04441e11i	−0.00595612	−	0.0106445i
$772$	−2.29617e12	−	7.56455e12i	−0.232663	−	0.766488i
$773$			1.20725e13i			1.21616i	0.793877	+	0.608079i	$0.208059\pi$
$773$			1.20725e13i			1.21616i	−0.793877	+	0.608079i	$0.791941\pi$
$774$	−2.23548e12	−	5.56061e12i	−0.223891	−	0.556914i
$775$		−	4.66212e12i		−	0.464222i
$776$	1.13703e12	−	3.18049e12i	0.112562	−	0.314860i
$777$	−3.51414e12	−	6.28029e12i	−0.345879	−	0.618137i
$778$	1.06214e13	−	1.43240e13i	1.03938	−	1.40170i
$779$	9.33082e11			0.0907823
$780$	5.55941e10	−	5.78002e10i	0.00537778	−	0.00559118i
$781$	4.21574e12			0.405456
$782$	4.29394e12	−	5.79080e12i	0.410606	−	0.553743i
$783$	1.32194e13	+	5.33803e11i	1.25685	+	0.0507520i
$784$	−5.91166e12	+	3.95314e12i	−0.558840	+	0.373697i
$785$			7.72274e10i			0.00725868i
$786$	−1.81061e13	−	2.32848e12i	−1.69209	−	0.217606i
$787$		−	1.76431e13i		−	1.63942i	−0.572782	−	0.819708i	$-0.694136\pi$
$787$		−	1.76431e13i		−	1.63942i	0.572782	−	0.819708i	$-0.305864\pi$
$788$	9.62539e12	−	2.92173e12i	0.889304	−	0.269943i
$789$	1.51906e13	−	8.49993e12i	1.39550	−	0.780852i
$790$	4.84769e9	+	3.59461e9i	0.000442805	+	0.000328345i
$791$	−6.25732e11			−0.0568321
$792$	−5.39261e12	−	6.71030e12i	−0.487007	−	0.606008i
$793$	3.15499e12			0.283315
$794$	−5.85800e12	−	4.34377e12i	−0.523067	−	0.387860i
$795$	−6.56449e10	+	3.67316e10i	−0.00582839	+	0.00326128i
$796$	−1.72184e13	+	5.22654e12i	−1.52014	+	0.461430i
$797$		−	9.87352e11i		−	0.0866781i	−0.999060	−	0.0433391i	$-0.986200\pi$
$797$		−	9.87352e11i		−	0.0866781i	0.999060	−	0.0433391i	$-0.0137996\pi$
$798$	−1.13985e13	−	1.46587e12i	−0.995027	−	0.127962i
$799$			1.98995e13i			1.72736i
$800$	1.15711e13	+	5.63214e11i	0.998781	+	0.0486148i
$801$	−3.47106e12	−	2.13054e12i	−0.297931	−	0.182870i
$802$	8.18978e12	−	1.10447e13i	0.699017	−	0.942693i
$803$	−5.60837e12			−0.476011
$804$	1.21367e12	−	1.26183e12i	0.102435	−	0.106500i
$805$	2.09956e10			0.00176217
$806$	−4.22535e12	+	5.69830e12i	−0.352659	+	0.475595i
$807$	7.65831e12	+	1.36865e13i	0.635627	+	1.13596i
$808$	1.80715e13	+	6.46055e12i	1.49156	+	0.533235i
$809$		−	1.91946e12i		−	0.157547i	−0.996893	−	0.0787736i	$-0.974900\pi$
$809$		−	1.91946e12i		−	0.157547i	0.996893	−	0.0787736i	$-0.0251004\pi$
$810$	−7.34682e10	−	1.24796e10i	−0.00599676	−	0.00101863i
$811$		−	3.33281e12i		−	0.270531i	−0.990809	−	0.135265i	$-0.956811\pi$
$811$		−	3.33281e12i		−	0.270531i	0.990809	−	0.135265i	$-0.0431887\pi$
$812$	−2.59107e12	−	8.53607e12i	−0.209159	−	0.689058i
$813$	−9.55871e12	−	1.70828e13i	−0.767347	−	1.37136i
$814$	9.67863e12	+	7.17681e12i	0.772688	+	0.572956i
$815$	7.06644e10			0.00561037
$816$	1.53724e13	+	7.83264e12i	1.21377	+	0.618447i
$817$	1.33955e13			1.05187
$818$	7.40249e12	+	5.48902e12i	0.578080	+	0.428652i
$819$	−8.01208e12	−	4.91781e12i	−0.622254	−	0.381939i
$820$	−1.18495e9	−	3.90371e9i	−9.15244e−5	−	0.000301519i
$821$		−	1.22670e12i		−	0.0942313i	−0.998889	−	0.0471157i	$-0.984997\pi$
$821$		−	1.22670e12i		−	0.0942313i	0.998889	−	0.0471157i	$-0.0150029\pi$
$822$	−1.34401e12	+	1.04509e13i	−0.102678	+	0.798419i
$823$			4.88019e12i			0.370798i	0.982663	+	0.185399i	$0.0593578\pi$
$823$			4.88019e12i			0.370798i	−0.982663	+	0.185399i	$0.940642\pi$
$824$	−1.01819e12	−	3.64003e11i	−0.0769406	−	0.0275063i
$825$	−9.02710e12	+	5.05112e12i	−0.678431	+	0.379616i
$826$	−3.63538e12	+	4.90267e12i	−0.271731	+	0.366456i
$827$	−2.37734e13			−1.76733			−0.883663	−	0.468123i	$-0.844930\pi$
$827$	−2.37734e13			−1.76733			−0.883663	+	0.468123i	$0.844930\pi$
$828$	6.62167e12	+	1.73176e12i	0.489588	+	0.128041i
$829$	−2.22756e13			−1.63808			−0.819039	−	0.573739i	$-0.805493\pi$
$829$	−2.22756e13			−1.63808			−0.819039	+	0.573739i	$0.805493\pi$
$830$	−2.36412e10	+	3.18825e10i	−0.00172909	+	0.00233185i
$831$	1.06147e13	−	5.93944e12i	0.772150	−	0.432057i
$832$	−1.36324e13	−	1.11755e13i	−0.986319	−	0.808557i
$833$			1.27263e13i			0.915798i
$834$	1.95930e12	−	1.52354e13i	0.140234	−	1.09045i
$835$			1.31487e11i			0.00936040i
$836$	1.84120e13	−	5.58884e12i	1.30368	−	0.395725i
$837$	6.58647e12	+	2.65963e11i	0.463861	+	0.0187308i
$838$	8.24771e12	+	6.11577e12i	0.577744	+	0.428403i
$839$	5.32522e12			0.371029			0.185515	−	0.982641i	$-0.440605\pi$
$839$	5.32522e12			0.371029			0.185515	+	0.982641i	$0.440605\pi$
$840$	8.34258e9	+	4.95492e10i	0.000578154	+	0.00343384i
$841$	−8.44690e12			−0.582258
$842$	8.09994e11	+	6.00619e11i	0.0555364	+	0.0411808i
$843$	4.44626e11	+	7.94613e11i	0.0303229	+	0.0541915i
$844$	1.05947e13	−	3.21595e12i	0.718699	−	0.218157i
$845$			5.64848e10i			0.00381133i
$846$	−1.75292e13	+	7.04710e12i	−1.17651	+	0.472981i
$847$			3.39206e12i			0.226458i
$848$	9.19091e12	+	1.37444e13i	0.610347	+	0.912735i
$849$	1.86923e12	+	3.34059e12i	0.123475	+	0.220668i
$850$	1.23480e13	−	1.66525e13i	0.811358	−	1.09420i
$851$	−9.57982e12			−0.626144
$852$	−5.78127e12	−	5.56061e12i	−0.375876	−	0.361530i
$853$	−2.63384e13			−1.70341			−0.851705	−	0.524021i	$-0.824431\pi$
$853$	−2.63384e13			−1.70341			−0.851705	+	0.524021i	$0.824431\pi$
$854$	−1.17739e12	+	1.58783e12i	−0.0757461	+	0.102151i
$855$	8.71327e10	−	1.41956e11i	0.00557614	−	0.00908463i
$856$	−6.76569e12	+	1.89250e13i	−0.430705	+	1.20477i
$857$		−	1.08730e13i		−	0.688551i	−0.938869	−	0.344275i	$-0.888125\pi$
$857$		−	1.08730e13i		−	0.688551i	0.938869	−	0.344275i	$-0.111875\pi$
$858$	1.56113e13	+	2.00764e12i	0.983438	+	0.126472i
$859$			9.87851e12i			0.619045i	0.950892	+	0.309523i	$0.100169\pi$
$859$			9.87851e12i			0.619045i	−0.950892	+	0.309523i	$0.899831\pi$
$860$	−1.70114e10	−	5.60426e10i	−0.00106047	−	0.00349362i
$861$	−4.17333e11	+	2.33519e11i	−0.0258802	+	0.0144813i
$862$	−2.07093e13	−	1.53561e13i	−1.27756	−	0.947326i
$863$	−1.19881e13			−0.735700			−0.367850	−	0.929885i	$-0.619906\pi$
$863$	−1.19881e13			−0.735700			−0.367850	+	0.929885i	$0.619906\pi$
$864$	−1.45579e12	+	1.63151e13i	−0.0888767	+	0.996043i
$865$	−7.95995e10			−0.00483435
$866$	−1.32202e13	−	9.80292e12i	−0.798744	−	0.592277i
$867$	1.24240e13	−	6.95184e12i	0.746749	−	0.417844i
$868$	−1.29098e12	−	4.25302e12i	−0.0771934	−	0.254307i
$869$			1.18446e12i			0.0704583i
$870$	1.28235e11	+	1.64913e10i	0.00758876	+	0.000975927i
$871$			3.20110e12i			0.188459i
$872$	3.30030e12	−	9.23161e12i	0.193299	−	0.540696i
$873$	3.00191e12	−	4.89070e12i	0.174917	−	0.284975i
$874$	−9.11200e12	+	1.22884e13i	−0.528217	+	0.712352i
$875$	1.20756e11			0.00696421
$876$	7.69106e12	+	7.39750e12i	0.441283	+	0.424440i
$877$	9.80529e12			0.559709			0.279855	−	0.960042i	$-0.409714\pi$
$877$	9.80529e12			0.559709			0.279855	+	0.960042i	$0.409714\pi$
$878$	4.95209e12	−	6.67839e12i	0.281231	−	0.379268i
$879$	−2.15375e12	−	3.84907e12i	−0.121687	−	0.217473i
$880$	−4.67638e10	−	6.99322e10i	−0.00262868	−	0.00393102i
$881$			2.74953e13i			1.53769i	0.639438	+	0.768843i	$0.279167\pi$
$881$			2.74953e13i			1.53769i	−0.639438	+	0.768843i	$0.720833\pi$
$882$	−1.12104e13	+	4.50682e12i	−0.623755	+	0.250762i
$883$			2.35944e13i			1.30613i	0.757302	+	0.653064i	$0.226517\pi$
$883$			2.35944e13i			1.30613i	−0.757302	+	0.653064i	$0.773483\pi$
$884$	−3.01849e13	+	9.16244e12i	−1.66247	+	0.504633i
$885$	−4.31955e10	−	7.71968e10i	−0.00236698	−	0.00423014i
$886$	1.95462e13	+	1.44937e13i	1.06564	+	0.790182i
$887$	2.82592e13			1.53286			0.766431	−	0.642327i	$-0.222031\pi$
$887$	2.82592e13			1.53286			0.766431	+	0.642327i	$0.222031\pi$
$888$	−3.80653e12	−	2.26082e13i	−0.205433	−	1.22013i
$889$	1.97113e13			1.05842
$890$	−3.19705e10	−	2.37065e10i	−0.00170803	−	0.00126652i
$891$	−6.62106e12	−	1.30413e13i	−0.351947	−	0.693221i
$892$	2.76974e12	−	8.40738e11i	0.146486	−	0.0444650i
$893$		−	4.22280e13i		−	2.22213i
$894$	3.69140e12	−	2.87041e13i	0.193273	−	1.50288i
$895$		−	5.45120e9i		−	0.000283980i
$896$	1.07117e13	−	2.69034e12i	0.555230	−	0.139451i
$897$	−1.09208e13	+	6.11073e12i	−0.563232	+	0.315157i
$898$	−1.18472e13	+	1.59771e13i	−0.607956	+	0.819888i
$899$	−1.14367e13			−0.583956
$900$	1.90418e13	+	4.97999e12i	0.967426	+	0.253009i
$901$	2.95882e13			1.49574
$902$	4.76907e11	−	6.43157e11i	0.0239886	−	0.0323510i
$903$	−5.99133e12	+	3.35245e12i	−0.299867	+	0.167790i
$904$	−1.87706e12	−	6.71050e11i	−0.0934804	−	0.0334193i
$905$		−	9.48217e10i		−	0.00469882i
$906$	1.38803e11	−	1.07933e12i	0.00684421	−	0.0532202i
$907$		−	2.49875e13i		−	1.22600i	−0.790084	−	0.612998i	$-0.789963\pi$
$907$		−	2.49875e13i		−	1.22600i	0.790084	−	0.612998i	$-0.210037\pi$
$908$	−2.82135e12	−	9.29469e12i	−0.137743	−	0.453784i
$909$	2.77888e13	+	1.70567e13i	1.34999	+	0.828625i
$910$	−7.37958e10	−	5.47204e10i	−0.00356735	−	0.00264523i
$911$	1.26811e13			0.609992			0.304996	−	0.952354i	$-0.401345\pi$
$911$	1.26811e13			0.609992			0.304996	+	0.952354i	$0.401345\pi$
$912$	−3.26211e13	−	1.66213e13i	−1.56143	−	0.795589i
$913$	−7.79002e12			−0.371040
$914$	1.52875e13	+	1.13359e13i	0.724568	+	0.537275i
$915$	−1.39897e10	−	2.50017e10i	−0.000659803	−	0.00117917i
$916$	7.91524e12	+	2.60761e13i	0.371479	+	1.22381i
$917$			2.09124e13i			0.976657i
$918$	2.28216e13	+	1.83948e13i	1.06061	+	0.854876i
$919$		−	1.23984e13i		−	0.573384i	−0.958023	−	0.286692i	$-0.907444\pi$
$919$		−	1.23984e13i		−	0.573384i	0.958023	−	0.286692i	$-0.0925557\pi$
$920$	6.29823e10	+	2.25162e10i	0.00289850	+	0.00103621i
$921$	−8.06612e12	−	1.44154e13i	−0.369400	−	0.660172i
$922$	−9.98902e12	+	1.34712e13i	−0.455233	+	0.613927i
$923$	1.46663e13			0.665140
$924$	−6.83629e12	+	7.10757e12i	−0.308529	+	0.320772i
$925$	−2.75486e13			−1.23726
$926$	1.42817e13	−	1.92603e13i	0.638310	−	0.860824i
$927$	−1.56569e12	−	9.61016e11i	−0.0696379	−	0.0427437i
$928$	1.38162e12	−	2.83851e13i	0.0611538	−	1.25639i
$929$		−	1.11987e13i		−	0.493283i	−0.969107	−	0.246641i	$-0.920673\pi$
$929$		−	1.11987e13i		−	0.493283i	0.969107	−	0.246641i	$-0.0793270\pi$
$930$	6.38921e10	+	8.21663e9i	0.00280075	+	0.000360181i
$931$		−	2.70060e13i		−	1.17811i
$932$	−3.32791e13	+	1.01017e13i	−1.44477	+	0.438553i
$933$	7.27488e12	−	4.07066e12i	0.314310	−	0.175872i
$934$	−2.36093e13	−	1.75065e13i	−1.01513	−	0.752730i
$935$	−1.50546e11			−0.00644196
$936$	−1.87605e13	−	2.33447e13i	−0.798922	−	0.994139i
$937$	3.15079e13			1.33534			0.667670	−	0.744457i	$-0.267292\pi$
$937$	3.15079e13			1.33534			0.667670	+	0.744457i	$0.267292\pi$
$938$	−1.61103e12	−	1.19460e12i	−0.0679503	−	0.0503858i
$939$	−1.39984e13	+	7.83280e12i	−0.587601	+	0.328792i
$940$	−1.76668e11	+	5.36266e10i	−0.00738046	+	0.00224029i
$941$			2.60028e13i			1.08110i	0.841311	+	0.540551i	$0.181784\pi$
$941$			2.60028e13i			1.08110i	−0.841311	+	0.540551i	$0.818216\pi$
$942$	2.86043e13	+	3.67856e12i	1.18359	+	0.152212i
$943$			6.36591e11i			0.0262155i
$944$	−1.61631e13	+	1.08083e13i	−0.662446	+	0.442979i
$945$	−3.44435e9	+	8.52981e10i	−0.000140496	+	0.00347933i
$946$	6.84660e12	−	9.23331e12i	0.277949	−	0.374841i
$947$	1.38936e13			0.561360			0.280680	−	0.959801i	$-0.409440\pi$
$947$	1.38936e13			0.561360			0.280680	+	0.959801i	$0.409440\pi$
$948$	1.56232e12	−	1.62432e12i	0.0628250	−	0.0653180i
$949$	−1.95112e13			−0.780882
$950$	−2.62033e13	+	3.53377e13i	−1.04376	+	1.40761i
$951$	−1.06010e12	−	1.89456e12i	−0.0420278	−	0.0751099i
$952$	6.65327e12	−	1.86106e13i	0.262524	−	0.734333i
$953$		−	1.31088e13i		−	0.514809i	−0.966304	−	0.257404i	$-0.917133\pi$
$953$		−	1.31088e13i		−	0.514809i	0.966304	−	0.257404i	$-0.0828672\pi$
$954$	1.04782e13	+	2.60639e13i	0.409561	+	1.01876i
$955$			2.75017e10i			0.00106990i
$956$	−2.44437e12	−	8.05276e12i	−0.0946468	−	0.311806i
$957$	1.23909e13	+	2.21444e13i	0.477529	+	0.853415i
$958$	−1.16347e13	−	8.62727e12i	−0.446284	−	0.330924i
$959$	1.20707e13			0.460839
$960$	−2.81118e10	+	1.57584e11i	−0.00106824	+	0.00598813i
$961$	2.07414e13			0.784482
$962$	3.36714e13	+	2.49677e13i	1.26757	+	0.939919i
$963$	−1.78623e13	+	2.91013e13i	−0.669299	+	1.09042i
$964$	−1.98336e12	−	6.53400e12i	−0.0739697	−	0.243687i
$965$		−	1.31254e11i		−	0.00487235i
$966$	1.00008e12	−	7.77657e12i	0.0369520	−	0.287337i
$967$			3.36278e13i			1.23674i	0.785886	+	0.618371i	$0.212207\pi$
$967$			3.36278e13i			1.23674i	−0.785886	+	0.618371i	$0.787793\pi$
$968$	−3.63773e12	+	1.01755e13i	−0.133165	+	0.372490i
$969$	−5.71747e13	+	3.19921e13i	−2.08328	+	1.16570i
$970$	3.34022e10	−	4.50461e10i	0.00121144	−	0.00163375i
$971$	1.06691e13			0.385162			0.192581	−	0.981281i	$-0.438314\pi$
$971$	1.06691e13			0.385162			0.192581	+	0.981281i	$0.438314\pi$
$972$	−8.12183e12	+	2.66175e13i	−0.291847	+	0.956465i
$973$	−1.75967e13			−0.629397
$974$	−1.62637e13	+	2.19332e13i	−0.579034	+	0.780884i
$975$	−3.14047e13	+	1.75725e13i	−1.11295	+	0.622750i
$976$	−5.23475e12	+	3.50048e12i	−0.184659	+	0.123482i
$977$		−	4.16107e13i		−	1.46110i	−0.682859	−	0.730550i	$-0.739264\pi$
$977$		−	4.16107e13i		−	1.46110i	0.682859	−	0.730550i	$-0.260736\pi$
$978$	3.36595e12	−	2.61734e13i	0.117647	−	0.914821i
$979$		−	7.81153e12i		−	0.271778i
$980$	−1.12984e11	+	3.42957e10i	−0.00391292	+	0.00118774i
$981$	8.71324e12	−	1.41956e13i	0.300379	−	0.489376i
$982$	2.86833e13	+	2.12690e13i	0.984301	+	0.729870i
$983$	−1.25163e13			−0.427548			−0.213774	−	0.976883i	$-0.568576\pi$
$983$	−1.25163e13			−0.427548			−0.213774	+	0.976883i	$0.568576\pi$
$984$	−1.50234e12	+	2.52949e11i	−0.0510846	+	0.00860111i
$985$	1.67011e11			0.00565305
$986$	−4.08504e13	−	3.02910e13i	−1.37642	−	1.02063i
$987$	1.05682e13	+	1.88870e13i	0.354467	+	0.633485i
$988$	6.40541e13	−	1.94432e13i	2.13866	−	0.649176i
$989$			9.13905e12i			0.303751i
$990$	−5.33135e10	−	1.32614e11i	−0.00176392	−	0.00438765i
$991$		−	3.44468e13i		−	1.13453i	−0.823534	−	0.567267i	$-0.808001\pi$
$991$		−	3.44468e13i		−	1.13453i	0.823534	−	0.567267i	$-0.191999\pi$
$992$	6.88381e11	−	1.41426e13i	0.0225697	−	0.463690i
$993$	−4.08269e12	−	7.29637e12i	−0.133252	−	0.238142i
$994$	−5.47322e12	+	7.38118e12i	−0.177830	+	0.239821i
$995$	−2.98759e11			−0.00966310
$996$	1.06829e13	+	1.02751e13i	0.343970	+	0.330842i
$997$	−1.55107e13			−0.497166			−0.248583	−	0.968611i	$-0.579965\pi$
$997$	−1.55107e13			−0.497166			−0.248583	+	0.968611i	$0.579965\pi$
$998$	2.69194e13	−	3.63034e13i	0.858969	−	1.15840i
$999$	1.57158e12	−	3.89196e13i	0.0499220	−	1.23630i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.10.b.a.11.3	✓	16
3.2	odd	2	inner	12.10.b.a.11.14	yes	16
4.3	odd	2	inner	12.10.b.a.11.13	yes	16
8.3	odd	2		192.10.c.d.191.4		16
8.5	even	2		192.10.c.d.191.13		16
12.11	even	2	inner	12.10.b.a.11.4	yes	16
24.5	odd	2		192.10.c.d.191.3		16
24.11	even	2		192.10.c.d.191.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.10.b.a.11.3	✓	16	1.1	even	1	trivial
12.10.b.a.11.4	yes	16	12.11	even	2	inner
12.10.b.a.11.13	yes	16	4.3	odd	2	inner
12.10.b.a.11.14	yes	16	3.2	odd	2	inner
192.10.c.d.191.3		16	24.5	odd	2
192.10.c.d.191.4		16	8.3	odd	2
192.10.c.d.191.13		16	8.5	even	2
192.10.c.d.191.14		16	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-18.1757 - 13.4775i) q^{2} +(-122.433 + 68.5072i) q^{3} +(148.714 + 489.927i) q^{4} +8.50078i q^{5} +(3148.61 + 404.916i) q^{6} -3636.61i q^{7} +(3899.99 - 10909.1i) q^{8} +(10296.5 - 16775.0i) q^{9} +O(q^{10})\)	\(q+(-18.1757 - 13.4775i) q^{2} +(-122.433 + 68.5072i) q^{3} +(148.714 + 489.927i) q^{4} +8.50078i q^{5} +(3148.61 + 404.916i) q^{6} -3636.61i q^{7} +(3899.99 - 10909.1i) q^{8} +(10296.5 - 16775.0i) q^{9} +(114.569 - 154.508i) q^{10} +37751.8 q^{11} +(-51771.0 - 49795.0i) q^{12} +131336. q^{13} +(-49012.4 + 66098.1i) q^{14} +(-582.365 - 1040.77i) q^{15} +(-217912. + 145718. i) q^{16} +469110. i q^{17} +(-413232. + 166128. i) q^{18} -995479. i q^{19} +(-4164.76 + 1264.19i) q^{20} +(249134. + 445240. i) q^{21} +(-686166. - 508799. i) q^{22} +679160. q^{23} +(269864. + 1.60280e6i) q^{24} +1.95305e6 q^{25} +(-2.38713e6 - 1.77008e6i) q^{26} +(-111417. + 2.75920e6i) q^{27} +(1.78167e6 - 540816. i) q^{28} -4.79104e6i q^{29} +(-3442.11 + 26765.6i) q^{30} -2.38709e6i q^{31} +(5.92463e6 + 288376. i) q^{32} +(-4.62205e6 + 2.58627e6i) q^{33} +(6.32242e6 - 8.52641e6i) q^{34} +30914.1 q^{35} +(9.74978e6 + 2.54985e6i) q^{36} -1.41054e7 q^{37} +(-1.34166e7 + 1.80936e7i) q^{38} +(-1.60798e7 + 8.99747e6i) q^{39} +(92735.6 + 33153.0i) q^{40} +937320. i q^{41} +(1.47252e6 - 1.14503e7i) q^{42} +1.34564e7i q^{43} +(5.61422e6 + 1.84956e7i) q^{44} +(142601. + 87528.4i) q^{45} +(-1.23442e7 - 9.15338e6i) q^{46} +4.24198e7 q^{47} +(1.66968e7 - 3.27692e7i) q^{48} +2.71286e7 q^{49} +(-3.54982e7 - 2.63223e7i) q^{50} +(-3.21374e7 - 5.74343e7i) q^{51} +(1.95315e7 + 6.43450e7i) q^{52} -6.30732e7i q^{53} +(3.92122e7 - 4.86488e7i) q^{54} +320919. i q^{55} +(-3.96721e7 - 1.41828e7i) q^{56} +(6.81975e7 + 1.21879e8i) q^{57} +(-6.45712e7 + 8.70806e7i) q^{58} +7.41726e7 q^{59} +(423296. - 440094. i) q^{60} +2.40223e7 q^{61} +(-3.21720e7 + 4.33872e7i) q^{62} +(-6.10044e7 - 3.74444e7i) q^{63} +(-1.03798e8 - 8.50906e7i) q^{64} +1.11646e6i q^{65} +(1.18866e8 + 1.52863e7i) q^{66} +2.43733e7i q^{67} +(-2.29829e8 + 6.97633e7i) q^{68} +(-8.31514e7 + 4.65274e7i) q^{69} +(-561886. - 416644. i) q^{70} +1.11670e8 q^{71} +(-1.42844e8 - 1.77748e8i) q^{72} -1.48559e8 q^{73} +(2.56376e8 + 1.90105e8i) q^{74} +(-2.39117e8 + 1.33798e8i) q^{75} +(4.87712e8 - 1.48042e8i) q^{76} -1.37289e8i q^{77} +(4.13526e8 + 5.31801e7i) q^{78} +3.13750e7i q^{79} +(-1.23872e6 - 1.85242e6i) q^{80} +(-1.75384e8 - 3.45449e8i) q^{81} +(1.26327e7 - 1.70365e7i) q^{82} -2.06349e8 q^{83} +(-1.81085e8 + 1.88271e8i) q^{84} -3.98780e6 q^{85} +(1.81358e8 - 2.44580e8i) q^{86} +(3.28221e8 + 5.86580e8i) q^{87} +(1.47232e8 - 4.11836e8i) q^{88} -2.06918e8i q^{89} +(-1.41221e6 - 3.51280e6i) q^{90} -4.77619e8i q^{91} +(1.01001e8 + 3.32739e8i) q^{92} +(1.63533e8 + 2.92258e8i) q^{93} +(-7.71011e8 - 5.71713e8i) q^{94} +8.46235e6 q^{95} +(-7.45124e8 + 3.70573e8i) q^{96} +2.91546e8 q^{97} +(-4.93083e8 - 3.65626e8i) q^{98} +(3.88711e8 - 6.33288e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 344 q^{4} - 1608 q^{6} - 13872 q^{9}+O(q^{10}) \) 16 * q - 344 * q^4 - 1608 * q^6 - 13872 * q^9	\( 16 q - 344 q^{4} - 1608 q^{6} - 13872 q^{9} - 15952 q^{10} + 42600 q^{12} - 97312 q^{13} + 164896 q^{16} + 256944 q^{18} + 356448 q^{21} + 322128 q^{22} + 166176 q^{24} - 2743728 q^{25} - 1447056 q^{28} + 3286128 q^{30} + 4715520 q^{33} - 13198144 q^{34} - 6827448 q^{36} + 10997600 q^{37} + 23411264 q^{40} + 23964432 q^{42} - 251904 q^{45} - 41256288 q^{46} - 87722976 q^{48} - 21356624 q^{49} + 132124208 q^{52} + 179732232 q^{54} - 88439904 q^{57} - 271309360 q^{58} - 414400704 q^{60} + 50685152 q^{61} + 742710400 q^{64} + 790585104 q^{66} + 63713280 q^{69} - 1188731232 q^{70} - 1250220480 q^{72} + 23382176 q^{73} + 1645242192 q^{76} + 2079579408 q^{78} + 349756560 q^{81} - 3274996000 q^{82} - 3734920464 q^{84} - 247261184 q^{85} + 4467199680 q^{88} + 5726283888 q^{90} - 262825248 q^{93} - 6146963136 q^{94} - 6944875392 q^{96} + 30926624 q^{97}+O(q^{100}) \) 16 * q - 344 * q^4 - 1608 * q^6 - 13872 * q^9 - 15952 * q^10 + 42600 * q^12 - 97312 * q^13 + 164896 * q^16 + 256944 * q^18 + 356448 * q^21 + 322128 * q^22 + 166176 * q^24 - 2743728 * q^25 - 1447056 * q^28 + 3286128 * q^30 + 4715520 * q^33 - 13198144 * q^34 - 6827448 * q^36 + 10997600 * q^37 + 23411264 * q^40 + 23964432 * q^42 - 251904 * q^45 - 41256288 * q^46 - 87722976 * q^48 - 21356624 * q^49 + 132124208 * q^52 + 179732232 * q^54 - 88439904 * q^57 - 271309360 * q^58 - 414400704 * q^60 + 50685152 * q^61 + 742710400 * q^64 + 790585104 * q^66 + 63713280 * q^69 - 1188731232 * q^70 - 1250220480 * q^72 + 23382176 * q^73 + 1645242192 * q^76 + 2079579408 * q^78 + 349756560 * q^81 - 3274996000 * q^82 - 3734920464 * q^84 - 247261184 * q^85 + 4467199680 * q^88 + 5726283888 * q^90 - 262825248 * q^93 - 6146963136 * q^94 - 6944875392 * q^96 + 30926624 * q^97

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