LMFDB - Embedded newform 12.10.b.a.11.1

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			11.1
Root			$11.2559 - 1.14184i$ of defining polynomial
Character	$\chi$	$=$	12.11
Dual form			12.10.b.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-22.5119 - 2.28368i) q^{2} +(69.9307 - 121.625i) q^{3} +(501.570 + 102.820i) q^{4} +852.450i q^{5} +(-1852.02 + 2578.31i) q^{6} -9640.14i q^{7} +(-11056.5 - 3460.10i) q^{8} +(-9902.41 - 17010.7i) q^{9} +O(q^{10})$	\(q+(-22.5119 - 2.28368i) q^{2} +(69.9307 - 121.625i) q^{3} +(501.570 + 102.820i) q^{4} +852.450i q^{5} +(-1852.02 + 2578.31i) q^{6} -9640.14i q^{7} +(-11056.5 - 3460.10i) q^{8} +(-9902.41 - 17010.7i) q^{9} +(1946.73 - 19190.3i) q^{10} -49571.9 q^{11} +(47580.6 - 53813.3i) q^{12} -48856.1 q^{13} +(-22015.0 + 217018. i) q^{14} +(103679. + 59612.4i) q^{15} +(241000. + 103143. i) q^{16} -549092. i q^{17} +(184075. + 405556. i) q^{18} +186389. i q^{19} +(-87649.0 + 427563. i) q^{20} +(-1.17248e6 - 674141. i) q^{21} +(1.11596e6 + 113207. i) q^{22} +490997. q^{23} +(-1.19402e6 + 1.10278e6i) q^{24} +1.22645e6 q^{25} +(1.09984e6 + 111572. i) q^{26} +(-2.76141e6 + 14815.6i) q^{27} +(991200. - 4.83520e6i) q^{28} +290627. i q^{29} +(-2.19788e6 - 1.57876e6i) q^{30} -3.55527e6i q^{31} +(-5.18982e6 - 2.87231e6i) q^{32} +(-3.46660e6 + 6.02919e6i) q^{33} +(-1.25395e6 + 1.23611e7i) q^{34} +8.21774e6 q^{35} +(-3.21771e6 - 9.55020e6i) q^{36} +1.53731e7 q^{37} +(425654. - 4.19597e6i) q^{38} +(-3.41654e6 + 5.94213e6i) q^{39} +(2.94956e6 - 9.42509e6i) q^{40} +2.10696e7i q^{41} +(2.48553e7 + 1.78538e7i) q^{42} +1.45325e7i q^{43} +(-2.48638e7 - 5.09699e6i) q^{44} +(1.45007e7 - 8.44131e6i) q^{45} +(-1.10533e7 - 1.12128e6i) q^{46} +1.89079e7 q^{47} +(2.93981e7 - 2.20988e7i) q^{48} -5.25787e7 q^{49} +(-2.76098e7 - 2.80083e6i) q^{50} +(-6.67835e7 - 3.83984e7i) q^{51} +(-2.45047e7 - 5.02338e6i) q^{52} -8.87287e7i q^{53} +(6.21983e7 + 5.97266e6i) q^{54} -4.22576e7i q^{55} +(-3.33559e7 + 1.06586e8i) q^{56} +(2.26696e7 + 1.30343e7i) q^{57} +(663700. - 6.54256e6i) q^{58} +1.48196e8 q^{59} +(4.58731e7 + 4.05601e7i) q^{60} -8.37636e7 q^{61} +(-8.11911e6 + 8.00357e7i) q^{62} +(-1.63985e8 + 9.54606e7i) q^{63} +(1.10273e8 + 7.65130e7i) q^{64} -4.16474e7i q^{65} +(9.18084e7 - 1.27812e8i) q^{66} +1.70277e8i q^{67} +(5.64577e7 - 2.75408e8i) q^{68} +(3.43357e7 - 5.97176e7i) q^{69} +(-1.84997e8 - 1.87667e7i) q^{70} +9.80762e7 q^{71} +(5.06270e7 + 2.22341e8i) q^{72} +1.94920e8 q^{73} +(-3.46077e8 - 3.51073e7i) q^{74} +(8.57667e7 - 1.49168e8i) q^{75} +(-1.91646e7 + 9.34872e7i) q^{76} +4.77880e8i q^{77} +(9.04826e7 - 1.25966e8i) q^{78} -4.25799e8i q^{79} +(-8.79241e7 + 2.05441e8i) q^{80} +(-1.91305e8 + 3.36893e8i) q^{81} +(4.81164e7 - 4.74317e8i) q^{82} -2.50953e8 q^{83} +(-5.18767e8 - 4.58684e8i) q^{84} +4.68074e8 q^{85} +(3.31878e7 - 3.27155e8i) q^{86} +(3.53476e7 + 2.03237e7i) q^{87} +(5.48090e8 + 1.71524e8i) q^{88} -3.86456e8i q^{89} +(-3.45716e8 + 1.56915e8i) q^{90} +4.70979e8i q^{91} +(2.46269e8 + 5.04843e7i) q^{92} +(-4.32410e8 - 2.48622e8i) q^{93} +(-4.25653e8 - 4.31797e7i) q^{94} -1.58888e8 q^{95} +(-7.12273e8 + 4.30351e8i) q^{96} -1.59328e8 q^{97} +(1.18365e9 + 1.20073e8i) q^{98} +(4.90881e8 + 8.43251e8i) 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 $

$2$	−22.5119	−	2.28368i	−0.994894	−	0.100926i
$2$	−22.5119	−	2.28368i	−0.994894	−	0.100926i
$3$	69.9307	−	121.625i	0.498450	−	0.866918i
$3$	69.9307	−	121.625i	0.498450	−	0.866918i
$4$	501.570	+	102.820i	0.979628	+	0.200820i
$5$			852.450i			0.609964i	0.952358	+	0.304982i	$0.0986504\pi$
$5$			852.450i			0.609964i	−0.952358	+	0.304982i	$0.901350\pi$
$6$	−1852.02	+	2578.31i	−0.583400	+	0.812185i
$7$		−	9640.14i		−	1.51755i	−0.651354	−	0.758774i	$-0.725799\pi$
$7$		−	9640.14i		−	1.51755i	0.651354	−	0.758774i	$-0.274201\pi$
$8$	−11056.5	−	3460.10i	−0.954358	−	0.298665i
$9$	−9902.41	−	17010.7i	−0.503094	−	0.864231i
$10$	1946.73	−	19190.3i	0.0615609	−	0.606849i
$11$	−49571.9			−1.02087			−0.510433	−	0.859918i	$-0.670515\pi$
$11$	−49571.9			−1.02087			−0.510433	+	0.859918i	$0.670515\pi$
$12$	47580.6	−	53813.3i	0.662391	−	0.749158i
$13$	−48856.1			−0.474431			−0.237216	−	0.971457i	$-0.576235\pi$
$13$	−48856.1			−0.474431			−0.237216	+	0.971457i	$0.576235\pi$
$14$	−22015.0	+	217018.i	−0.153159	+	1.50980i
$15$	103679.	+	59612.4i	0.528789	+	0.304037i
$16$	241000.	+	103143.i	0.919342	+	0.393459i
$17$		−	549092.i		−	1.59450i	−0.603648	−	0.797251i	$-0.706287\pi$
$17$		−	549092.i		−	1.59450i	0.603648	−	0.797251i	$-0.293713\pi$
$18$	184075.	+	405556.i	0.413303	+	0.910594i
$19$			186389.i			0.328118i	0.986451	+	0.164059i	$0.0524587\pi$
$19$			186389.i			0.328118i	−0.986451	+	0.164059i	$0.947541\pi$
$20$	−87649.0	+	427563.i	−0.122493	+	0.597538i
$21$	−1.17248e6	−	674141.i	−1.31559	−	0.756422i
$22$	1.11596e6	+	113207.i	1.01565	+	0.103031i
$23$	490997.			0.365850			0.182925	−	0.983127i	$-0.441443\pi$
$23$	490997.			0.365850			0.182925	+	0.983127i	$0.441443\pi$
$24$	−1.19402e6	+	1.10278e6i	−0.734618	+	0.678481i
$25$	1.22645e6			0.627944
$26$	1.09984e6	+	111572.i	0.472009	+	0.0478822i
$27$	−2.76141e6	+	14815.6i	−0.999986	+	0.00536516i
$28$	991200.	−	4.83520e6i	0.304755	−	1.48663i
$29$			290627.i			0.0763035i	0.999272	+	0.0381518i	$0.0121470\pi$
$29$			290627.i			0.0763035i	−0.999272	+	0.0381518i	$0.987853\pi$
$30$	−2.19788e6	−	1.57876e6i	−0.495404	−	0.355853i
$31$		−	3.55527e6i		−	0.691424i	−0.938341	−	0.345712i	$-0.887637\pi$
$31$		−	3.55527e6i		−	0.691424i	0.938341	−	0.345712i	$-0.112363\pi$
$32$	−5.18982e6	−	2.87231e6i	−0.874938	−	0.484235i
$33$	−3.46660e6	+	6.02919e6i	−0.508851	+	0.885007i
$34$	−1.25395e6	+	1.23611e7i	−0.160926	+	1.58636i
$35$	8.21774e6			0.925649
$36$	−3.21771e6	−	9.55020e6i	−0.319290	−	0.947657i
$37$	1.53731e7			1.34851			0.674254	−	0.738499i	$-0.264465\pi$
$37$	1.53731e7			1.34851			0.674254	+	0.738499i	$0.264465\pi$
$38$	425654.	−	4.19597e6i	0.0331155	−	0.326442i
$39$	−3.41654e6	+	5.94213e6i	−0.236480	+	0.411293i
$40$	2.94956e6	−	9.42509e6i	0.182175	−	0.582124i
$41$			2.10696e7i			1.16447i	0.813019	+	0.582237i	$0.197822\pi$
$41$			2.10696e7i			1.16447i	−0.813019	+	0.582237i	$0.802178\pi$
$42$	2.48553e7	+	1.78538e7i	1.23253	+	0.885336i
$43$			1.45325e7i			0.648237i	0.946017	+	0.324118i	$0.105068\pi$
$43$			1.45325e7i			0.648237i	−0.946017	+	0.324118i	$0.894932\pi$
$44$	−2.48638e7	−	5.09699e6i	−1.00007	−	0.205011i
$45$	1.45007e7	−	8.44131e6i	0.527150	−	0.306869i
$46$	−1.10533e7	−	1.12128e6i	−0.363982	−	0.0369236i
$47$	1.89079e7			0.565202			0.282601	−	0.959238i	$-0.408803\pi$
$47$	1.89079e7			0.565202			0.282601	+	0.959238i	$0.408803\pi$
$48$	2.93981e7	−	2.20988e7i	0.799343	−	0.600875i
$49$	−5.25787e7			−1.30295
$50$	−2.76098e7	−	2.80083e6i	−0.624738	−	0.0633756i
$51$	−6.67835e7	−	3.83984e7i	−1.38230	−	0.794780i
$52$	−2.45047e7	−	5.02338e6i	−0.464766	−	0.0952755i
$53$		−	8.87287e7i		−	1.54462i	−0.635243	−	0.772312i	$-0.719100\pi$
$53$		−	8.87287e7i		−	1.54462i	0.635243	−	0.772312i	$-0.280900\pi$
$54$	6.21983e7	+	5.97266e6i	0.995421	+	0.0955863i
$55$		−	4.22576e7i		−	0.622691i
$56$	−3.33559e7	+	1.06586e8i	−0.453238	+	1.44828i
$57$	2.26696e7	+	1.30343e7i	0.284451	+	0.163550i
$58$	663700.	−	6.54256e6i	0.00770098	−	0.0759139i
$59$	1.48196e8			1.59222			0.796108	−	0.605154i	$-0.206889\pi$
$59$	1.48196e8			1.59222			0.796108	+	0.605154i	$0.206889\pi$
$60$	4.58731e7	+	4.05601e7i	0.456959	+	0.404034i
$61$	−8.37636e7			−0.774588			−0.387294	−	0.921956i	$-0.626590\pi$
$61$	−8.37636e7			−0.774588			−0.387294	+	0.921956i	$0.626590\pi$
$62$	−8.11911e6	+	8.00357e7i	−0.0697824	+	0.687894i
$63$	−1.63985e8	+	9.54606e7i	−1.31151	+	0.763469i
$64$	1.10273e8	+	7.65130e7i	0.821599	+	0.570066i
$65$		−	4.16474e7i		−	0.289386i
$66$	9.18084e7	−	1.27812e8i	0.595572	−	0.829132i
$67$			1.70277e8i			1.03233i	0.856488	+	0.516166i	$0.172641\pi$
$67$			1.70277e8i			1.03233i	−0.856488	+	0.516166i	$0.827359\pi$
$68$	5.64577e7	−	2.75408e8i	0.320209	−	1.56202i
$69$	3.43357e7	−	5.97176e7i	0.182358	−	0.317162i
$70$	−1.84997e8	−	1.87667e7i	−0.920922	−	0.0934216i
$71$	9.80762e7			0.458037			0.229019	−	0.973422i	$-0.426448\pi$
$71$	9.80762e7			0.458037			0.229019	+	0.973422i	$0.426448\pi$
$72$	5.06270e7	+	2.22341e8i	0.222017	+	0.975043i
$73$	1.94920e8			0.803349			0.401675	−	0.915782i	$-0.368428\pi$
$73$	1.94920e8			0.803349			0.401675	+	0.915782i	$0.368428\pi$
$74$	−3.46077e8	−	3.51073e7i	−1.34162	−	0.136099i
$75$	8.57667e7	−	1.49168e8i	0.312999	−	0.544376i
$76$	−1.91646e7	+	9.34872e7i	−0.0658927	+	0.321433i
$77$			4.77880e8i			1.54921i
$78$	9.04826e7	−	1.25966e8i	0.276783	−	0.385326i
$79$		−	4.25799e8i		−	1.22994i	−0.788551	−	0.614969i	$-0.789169\pi$
$79$		−	4.25799e8i		−	1.22994i	0.788551	−	0.614969i	$-0.210831\pi$
$80$	−8.79241e7	+	2.05441e8i	−0.239996	+	0.560765i
$81$	−1.91305e8	+	3.36893e8i	−0.493792	+	0.869580i
$82$	4.81164e7	−	4.74317e8i	0.117525	−	1.15853i
$83$	−2.50953e8			−0.580418			−0.290209	−	0.956963i	$-0.593725\pi$
$83$	−2.50953e8			−0.580418			−0.290209	+	0.956963i	$0.593725\pi$
$84$	−5.18767e8	−	4.58684e8i	−1.13688	−	1.00521i
$85$	4.68074e8			0.972588
$86$	3.31878e7	−	3.27155e8i	0.0654237	−	0.644927i
$87$	3.53476e7	+	2.03237e7i	0.0661489	+	0.0380335i
$88$	5.48090e8	+	1.71524e8i	0.974271	+	0.304896i
$89$		−	3.86456e8i		−	0.652897i	−0.945215	−	0.326449i	$-0.894148\pi$
$89$		−	3.86456e8i		−	0.652897i	0.945215	−	0.326449i	$-0.105852\pi$
$90$	−3.45716e8	+	1.56915e8i	−0.555429	+	0.252100i
$91$			4.70979e8i			0.719972i
$92$	2.46269e8	+	5.04843e7i	0.358397	+	0.0734702i
$93$	−4.32410e8	−	2.48622e8i	−0.599408	−	0.344641i
$94$	−4.25653e8	−	4.31797e7i	−0.562316	−	0.0570433i
$95$	−1.58888e8			−0.200140
$96$	−7.12273e8	+	4.30351e8i	−0.855905	+	0.517133i
$97$	−1.59328e8			−0.182734			−0.0913671	−	0.995817i	$-0.529124\pi$
$97$	−1.59328e8			−0.182734			−0.0913671	+	0.995817i	$0.529124\pi$
$98$	1.18365e9	+	1.20073e8i	1.29630	+	0.131501i
$99$	4.90881e8	+	8.43251e8i	0.513592	+	0.882264i
$100$	6.15152e8	+	1.26104e8i	0.615152	+	0.126104i
$101$		−	1.78039e8i		−	0.170242i	−0.996371	−	0.0851212i	$-0.972872\pi$
$101$		−	1.78039e8i		−	0.170242i	0.996371	−	0.0851212i	$-0.0271278\pi$
$102$	1.41573e9	+	1.01693e9i	1.29503	+	0.930231i
$103$		−	3.27147e8i		−	0.286402i	−0.989694	−	0.143201i	$-0.954261\pi$
$103$		−	3.27147e8i		−	0.286402i	0.989694	−	0.143201i	$-0.0457395\pi$
$104$	5.40175e8	+	1.69047e8i	0.452777	+	0.141696i
$105$	5.74672e8	−	9.99485e8i	0.461390	−	0.802462i
$106$	−2.02628e8	+	1.99745e9i	−0.155892	+	1.53674i
$107$	−1.07682e8			−0.0794173			−0.0397087	−	0.999211i	$-0.512643\pi$
$107$	−1.07682e8			−0.0794173			−0.0397087	+	0.999211i	$0.512643\pi$
$108$	−1.38656e9	−	2.76497e8i	−0.980691	−	0.195562i
$109$	−1.83135e9			−1.24266			−0.621328	−	0.783550i	$-0.713407\pi$
$109$	−1.83135e9			−1.24266			−0.621328	+	0.783550i	$0.713407\pi$
$110$	−9.65030e7	+	9.51297e8i	−0.0628454	+	0.619511i
$111$	1.07505e9	−	1.86976e9i	0.672165	−	1.16905i
$112$	9.94312e8	−	2.32327e9i	0.597092	−	1.39515i
$113$		−	1.42480e9i		−	0.822054i	−0.911623	−	0.411027i	$-0.865170\pi$
$113$		−	1.42480e9i		−	0.822054i	0.911623	−	0.411027i	$-0.134830\pi$
$114$	−4.80570e8	−	3.45197e8i	−0.266492	−	0.191424i
$115$			4.18550e8i			0.223155i
$116$	−2.98823e7	+	1.45770e8i	−0.0153233	+	0.0747491i
$117$	4.83793e8	+	8.31074e8i	0.238684	+	0.410018i
$118$	−3.33617e9	−	3.38433e8i	−1.58409	−	0.160695i
$119$	−5.29332e9			−2.41973
$120$	−9.40064e8	−	1.01784e9i	−0.413849	−	0.448090i
$121$	9.94249e7			0.0421659
$122$	1.88568e9	+	1.91290e8i	0.770633	+	0.0781758i
$123$	2.56260e9	+	1.47341e9i	1.00950	+	0.580432i
$124$	3.65553e8	−	1.78321e9i	0.138852	−	0.677338i
$125$			2.71043e9i			0.992987i
$126$	3.90962e9	−	1.77451e9i	1.38187	−	0.627206i
$127$		−	5.65069e8i		−	0.192746i	−0.995345	−	0.0963729i	$-0.969276\pi$
$127$		−	5.65069e8i		−	0.192746i	0.995345	−	0.0963729i	$-0.0307241\pi$
$128$	−2.30772e9	−	1.97428e9i	−0.759870	−	0.650075i
$129$	1.76752e9	+	1.01627e9i	0.561968	+	0.323114i
$130$	−9.51094e7	+	9.37560e8i	−0.0292064	+	0.287908i
$131$	3.32537e9			0.986550			0.493275	−	0.869874i	$-0.335800\pi$
$131$	3.32537e9			0.986550			0.493275	+	0.869874i	$0.335800\pi$
$132$	−2.35866e9	+	2.66762e9i	−0.676212	+	0.764790i
$133$	1.79682e9			0.497934
$134$	3.88859e8	−	3.83326e9i	0.104189	−	1.02706i
$135$	−1.26296e7	−	2.35396e9i	−0.00327255	−	0.609955i
$136$	−1.89991e9	+	6.07102e9i	−0.476221	+	1.52173i
$137$			5.58570e9i			1.35467i	0.735672	+	0.677337i	$0.236866\pi$
$137$			5.58570e9i			1.35467i	−0.735672	+	0.677337i	$0.763134\pi$
$138$	−9.09338e8	+	1.26594e9i	−0.213437	+	0.297138i
$139$			2.77299e9i			0.630060i	0.949082	+	0.315030i	$0.102015\pi$
$139$			2.77299e9i			0.630060i	−0.949082	+	0.315030i	$0.897985\pi$
$140$	4.12177e9	+	8.44949e8i	0.906791	+	0.185889i
$141$	1.32224e9	−	2.29968e9i	0.281725	−	0.489984i
$142$	−2.20788e9	−	2.23975e8i	−0.455699	−	0.0462277i
$143$	2.42189e9			0.484330
$144$	−6.31952e8	−	5.12093e9i	−0.122477	−	0.992471i
$145$	−2.47745e8			−0.0465424
$146$	−4.38802e9	−	4.45137e8i	−0.799247	−	0.0810785i
$147$	−3.67686e9	+	6.39490e9i	−0.649456	+	1.12955i
$148$	7.71068e9	+	1.58066e9i	1.32104	+	0.270808i
$149$		−	8.63640e9i		−	1.43547i	−0.696316	−	0.717736i	$-0.745179\pi$
$149$		−	8.63640e9i		−	1.43547i	0.696316	−	0.717736i	$-0.254821\pi$
$150$	−2.27142e9	+	3.16218e9i	−0.366342	+	0.510007i
$151$		−	7.11792e9i		−	1.11418i	−0.830451	−	0.557092i	$-0.811917\pi$
$151$		−	7.11792e9i		−	1.11418i	0.830451	−	0.557092i	$-0.188083\pi$
$152$	6.44925e8	−	2.06081e9i	0.0979971	−	0.313142i
$153$	−9.34042e9	+	5.43733e9i	−1.37802	+	0.802185i
$154$	1.09133e9	−	1.07580e10i	0.156355	−	1.54130i
$155$	3.03069e9			0.421744
$156$	−2.32460e9	+	2.62910e9i	−0.314259	+	0.355424i
$157$	6.88915e9			0.904935			0.452467	−	0.891781i	$-0.350544\pi$
$157$	6.88915e9			0.904935			0.452467	+	0.891781i	$0.350544\pi$
$158$	−9.72392e8	+	9.58555e9i	−0.124132	+	1.22366i
$159$	−1.07917e10	−	6.20486e9i	−1.33906	−	0.769919i
$160$	2.44850e9	−	4.42406e9i	0.295366	−	0.533680i
$161$		−	4.73328e9i		−	0.555195i
$162$	5.07600e9	−	7.14722e9i	0.579034	−	0.815304i
$163$			7.65624e9i			0.849515i	0.905307	+	0.424758i	$0.139641\pi$
$163$			7.65624e9i			0.849515i	−0.905307	+	0.424758i	$0.860359\pi$
$164$	−2.16638e9	+	1.05679e10i	−0.233850	+	1.14075i
$165$	−5.13959e9	−	2.95510e9i	−0.539822	−	0.310380i
$166$	5.64942e9	+	5.73097e8i	0.577454	+	0.0585790i
$167$	1.78443e9			0.177531			0.0887656	−	0.996053i	$-0.471708\pi$
$167$	1.78443e9			0.177531			0.0887656	+	0.996053i	$0.471708\pi$
$168$	1.06309e10	+	1.15105e10i	1.02963	+	1.11482i
$169$	−8.21759e9			−0.774915
$170$	−1.05372e10	−	1.06893e9i	−0.967622	−	0.0981590i
$171$	3.17061e9	−	1.84570e9i	0.283570	−	0.165074i
$172$	−1.49424e9	+	7.28908e9i	−0.130179	+	0.635031i
$173$		−	3.28081e9i		−	0.278467i	−0.990260	−	0.139234i	$-0.955536\pi$
$173$		−	3.28081e9i		−	0.278467i	0.990260	−	0.139234i	$-0.0444639\pi$
$174$	−7.49327e8	−	5.38248e8i	−0.0619726	−	0.0445154i
$175$		−	1.18232e10i		−	0.952935i
$176$	−1.19468e10	−	5.11299e9i	−0.938525	−	0.401668i
$177$	1.03634e10	−	1.80244e10i	0.793641	−	1.38032i
$178$	−8.82543e8	+	8.69985e9i	−0.0658940	+	0.649564i
$179$	1.24421e10			0.905846			0.452923	−	0.891550i	$-0.350381\pi$
$179$	1.24421e10			0.905846			0.452923	+	0.891550i	$0.350381\pi$
$180$	8.14107e9	−	2.74294e9i	0.578036	−	0.194755i
$181$	−5.97352e9			−0.413692			−0.206846	−	0.978374i	$-0.566320\pi$
$181$	−5.97352e9			−0.413692			−0.206846	+	0.978374i	$0.566320\pi$
$182$	1.07557e9	−	1.06026e10i	0.0726636	−	0.716296i
$183$	−5.85764e9	+	1.01878e10i	−0.386094	+	0.671505i
$184$	−5.42869e9	−	1.69890e9i	−0.349152	−	0.109266i
$185$			1.31048e10i			0.822541i
$186$	9.16659e9	+	6.58444e9i	0.561565	+	0.403377i
$187$			2.72195e10i			1.62777i
$188$	9.48364e9	+	1.94411e9i	0.553688	+	0.113504i
$189$	1.42824e8	+	2.66204e10i	0.00814188	+	1.51753i
$190$	3.57686e9	+	3.62849e8i	0.199118	+	0.0201992i
$191$	1.60370e8			0.00871911			0.00435956	−	0.999990i	$-0.498612\pi$
$191$	1.60370e8			0.00871911			0.00435956	+	0.999990i	$0.498612\pi$
$192$	1.70174e10	−	8.06140e9i	0.903727	−	0.428110i
$193$	1.94915e10			1.01120			0.505600	−	0.862768i	$-0.331271\pi$
$193$	1.94915e10			1.01120			0.505600	+	0.862768i	$0.331271\pi$
$194$	3.58678e9	+	3.63855e8i	0.181801	+	0.0184426i
$195$	−5.06537e9	−	2.91243e9i	−0.250874	−	0.144244i
$196$	−2.63719e10	−	5.40615e9i	−1.27641	−	0.261659i
$197$			8.16890e9i			0.386425i	0.981157	+	0.193213i	$0.0618907\pi$
$197$			8.16890e9i			0.386425i	−0.981157	+	0.193213i	$0.938109\pi$
$198$	−9.12494e9	−	2.01042e10i	−0.421926	−	0.929594i
$199$		−	2.61720e10i		−	1.18304i	−0.806291	−	0.591519i	$-0.798529\pi$
$199$		−	2.61720e10i		−	1.18304i	0.806291	−	0.591519i	$-0.201471\pi$
$200$	−1.35602e10	−	4.24365e9i	−0.599284	−	0.187545i
$201$	2.07100e10	+	1.19076e10i	0.894948	+	0.514566i
$202$	−4.06584e8	+	4.00798e9i	−0.0171818	+	0.169373i
$203$	2.80168e9			0.115794
$204$	−2.95484e10	−	2.61261e10i	−1.19453	−	1.05618i
$205$	−1.79608e10			−0.710287
$206$	−7.47101e8	+	7.36470e9i	−0.0289053	+	0.284939i
$207$	−4.86205e9	−	8.35218e9i	−0.184057	−	0.316179i
$208$	−1.17743e10	−	5.03915e9i	−0.436165	−	0.186669i
$209$		−	9.23967e9i		−	0.334964i
$210$	−1.52195e10	+	2.11879e10i	−0.540023	+	0.751798i
$211$		−	1.08650e10i		−	0.377364i	−0.982038	−	0.188682i	$-0.939579\pi$
$211$		−	1.08650e10i		−	0.377364i	0.982038	−	0.188682i	$-0.0604215\pi$
$212$	9.12310e9	−	4.45036e10i	0.310192	−	1.51316i
$213$	6.85853e9	−	1.19285e10i	0.228309	−	0.397081i
$214$	2.42412e9	+	2.45911e8i	0.0790118	+	0.00801524i
$215$	−1.23883e10			−0.395401
$216$	3.05827e10	+	9.39094e9i	0.955947	+	0.293540i
$217$	−3.42733e10			−1.04927
$218$	4.12270e10	+	4.18222e9i	1.23631	+	0.125416i
$219$	1.36309e10	−	2.37072e10i	0.400430	−	0.696438i
$220$	4.34493e9	−	2.11951e10i	0.125049	−	0.610005i
$221$			2.68265e10i			0.756481i
$222$	−2.84714e10	+	3.96367e10i	−0.786719	+	1.09524i
$223$			3.32611e10i			0.900669i	0.892860	+	0.450335i	$0.148695\pi$
$223$			3.32611e10i			0.900669i	−0.892860	+	0.450335i	$0.851305\pi$
$224$	−2.76894e10	+	5.00306e10i	−0.734849	+	1.32776i
$225$	−1.21448e10	−	2.08628e10i	−0.315915	−	0.542689i
$226$	−3.25379e9	+	3.20749e10i	−0.0829662	+	0.817856i
$227$	−1.53552e10			−0.383830			−0.191915	−	0.981412i	$-0.561470\pi$
$227$	−1.53552e10			−0.383830			−0.191915	+	0.981412i	$0.561470\pi$
$228$	1.00302e10	+	8.86851e9i	0.245812	+	0.217342i
$229$	5.67393e10			1.36340			0.681702	−	0.731630i	$-0.261240\pi$
$229$	5.67393e10			1.36340			0.681702	+	0.731630i	$0.261240\pi$
$230$	9.55837e8	−	9.42235e9i	0.0225221	−	0.222016i
$231$	5.81223e10	+	3.34185e10i	1.34304	+	0.772205i
$232$	1.00560e9	−	3.21331e9i	0.0227892	−	0.0728209i
$233$		−	4.88466e10i		−	1.08576i	−0.839811	−	0.542879i	$-0.817334\pi$
$233$		−	4.88466e10i		−	1.08576i	0.839811	−	0.542879i	$-0.182666\pi$
$234$	−8.99317e9	−	1.98139e10i	−0.196084	−	0.432014i
$235$			1.61181e10i			0.344753i
$236$	7.43306e10	+	1.52375e10i	1.55978	+	0.319750i
$237$	−5.17880e10	−	2.97764e10i	−1.06626	−	0.613063i
$238$	1.19163e11	+	1.20883e10i	2.40738	+	0.244213i
$239$	−7.01538e10			−1.39079			−0.695393	−	0.718629i	$-0.744770\pi$
$239$	−7.01538e10			−1.39079			−0.695393	+	0.718629i	$0.744770\pi$
$240$	1.88382e10	+	2.50604e10i	0.366512	+	0.487570i
$241$	−8.51441e9			−0.162584			−0.0812920	−	0.996690i	$-0.525905\pi$
$241$	−8.51441e9			−0.162584			−0.0812920	+	0.996690i	$0.525905\pi$
$242$	−2.23824e9	−	2.27055e8i	−0.0419506	−	0.00425561i
$243$	2.75966e10	+	4.68267e10i	0.507724	+	0.861520i
$244$	−4.20133e10	−	8.61258e9i	−0.758808	−	0.155553i
$245$		−	4.48207e10i		−	0.794752i
$246$	−5.43241e10	−	3.90215e10i	−0.945768	−	0.679353i
$247$		−	9.10624e9i		−	0.155669i
$248$	−1.23016e10	+	3.93087e10i	−0.206504	+	0.659866i
$249$	−1.75493e10	+	3.05222e10i	−0.289309	+	0.503175i
$250$	6.18977e9	−	6.10169e10i	0.100218	−	0.987917i
$251$	−4.35965e10			−0.693298			−0.346649	−	0.937995i	$-0.612681\pi$
$251$	−4.35965e10			−0.693298			−0.346649	+	0.937995i	$0.612681\pi$
$252$	−9.20653e10	+	3.10192e10i	−1.43811	+	0.484538i
$253$	−2.43396e10			−0.373484
$254$	−1.29044e9	+	1.27208e10i	−0.0194530	+	0.191762i
$255$	3.27327e10	−	5.69296e10i	0.484787	−	0.843154i
$256$	4.74426e10	+	4.97149e10i	0.690381	+	0.723446i
$257$			3.99285e10i			0.570931i	0.958389	+	0.285465i	$0.0921482\pi$
$257$			3.99285e10i			0.570931i	−0.958389	+	0.285465i	$0.907852\pi$
$258$	−3.74695e10	−	2.69146e10i	−0.526488	−	0.378181i
$259$		−	1.48199e11i		−	2.04643i
$260$	4.28218e9	−	2.08890e10i	0.0581146	−	0.283490i
$261$	4.94376e9	−	2.87790e9i	0.0659439	−	0.0383879i
$262$	−7.48603e10	−	7.59409e9i	−0.981512	−	0.0995681i
$263$	7.31435e10			0.942703			0.471352	−	0.881945i	$-0.343766\pi$
$263$	7.31435e10			0.942703			0.471352	+	0.881945i	$0.343766\pi$
$264$	5.91899e10	−	5.46668e10i	0.749946	−	0.692638i
$265$	7.56368e10			0.942165
$266$	−4.04498e10	−	4.10337e9i	−0.495392	−	0.0502543i
$267$	−4.70028e10	−	2.70251e10i	−0.566009	−	0.325437i
$268$	−1.75079e10	+	8.54058e10i	−0.207313	+	1.01130i
$269$			8.29389e10i			0.965769i	0.875684	+	0.482884i	$0.160411\pi$
$269$			8.29389e10i			0.965769i	−0.875684	+	0.482884i	$0.839589\pi$
$270$	−5.09139e9	+	5.30210e10i	−0.0583042	+	0.607171i
$271$			1.46478e11i			1.64972i	0.565335	+	0.824861i	$0.308747\pi$
$271$			1.46478e11i			1.64972i	−0.565335	+	0.824861i	$0.691253\pi$
$272$	5.66349e10	−	1.32331e11i	0.627370	−	1.46589i
$273$	5.72830e10	+	3.29359e10i	0.624157	+	0.358870i
$274$	1.27560e10	−	1.25745e11i	0.136721	−	1.34776i
$275$	−6.07976e10			−0.641047
$276$	2.33619e10	−	2.64221e10i	0.242336	−	0.274080i
$277$	5.27219e10			0.538061			0.269031	−	0.963132i	$-0.413297\pi$
$277$	5.27219e10			0.538061			0.269031	+	0.963132i	$0.413297\pi$
$278$	6.33263e9	−	6.24252e10i	0.0635891	−	0.626842i
$279$	−6.04775e10	+	3.52057e10i	−0.597550	+	0.347852i
$280$	−9.08592e10	−	2.84342e10i	−0.883400	−	0.276458i
$281$			9.60149e10i			0.918671i	0.888263	+	0.459336i	$0.151912\pi$
$281$			9.60149e10i			0.918671i	−0.888263	+	0.459336i	$0.848088\pi$
$282$	−3.50179e10	+	4.87506e10i	−0.329738	+	0.459049i
$283$			1.44522e9i			0.0133936i	0.999978	+	0.00669679i	$0.00213167\pi$
$283$			1.44522e9i			0.0133936i	−0.999978	+	0.00669679i	$0.997868\pi$
$284$	4.91920e10	+	1.00842e10i	0.448706	+	0.0919833i
$285$	−1.11111e10	+	1.93247e10i	−0.0997598	+	0.173505i
$286$	−5.45212e10	−	5.53083e9i	−0.481857	−	0.0488813i
$287$	2.03114e11			1.76714
$288$	2.53183e9	+	1.16725e11i	0.0216855	+	0.999765i
$289$	−1.82914e11			−1.54244
$290$	5.57720e9	+	5.65771e8i	0.0463047	+	0.00469732i
$291$	−1.11419e10	+	1.93783e10i	−0.0910840	+	0.158416i
$292$	9.77661e10	+	2.00417e10i	0.786983	+	0.161329i
$293$		−	1.32219e11i		−	1.04807i	−0.851697	−	0.524035i	$-0.824426\pi$
$293$		−	1.32219e11i		−	1.04807i	0.851697	−	0.524035i	$-0.175574\pi$
$294$	9.73771e10	−	1.35564e11i	0.760140	−	1.05824i
$295$			1.26330e11i			0.971194i
$296$	−1.69972e11	−	5.31925e10i	−1.28696	−	0.402752i
$297$	1.36888e11	−	7.34437e8i	1.02085	−	0.00547710i
$298$	−1.97228e10	+	1.94422e11i	−0.144876	+	1.42814i
$299$	−2.39882e10			−0.173571
$300$	5.83554e10	−	6.59995e10i	0.415945	−	0.470430i
$301$	1.40096e11			0.983730
$302$	−1.62551e10	+	1.60238e11i	−0.112450	+	1.10850i
$303$	−2.16540e10	−	1.24504e10i	−0.147586	−	0.0848574i
$304$	−1.92247e10	+	4.49198e10i	−0.129101	+	0.301652i
$305$		−	7.14043e10i		−	0.472471i
$306$	2.22688e11	−	1.01074e11i	1.45194	−	0.659012i
$307$		−	2.14365e11i		−	1.37731i	−0.725091	−	0.688654i	$-0.758202\pi$
$307$		−	2.14365e11i		−	1.37731i	0.725091	−	0.688654i	$-0.241798\pi$
$308$	−4.91357e10	+	2.39690e11i	−0.311113	+	1.51765i
$309$	−3.97894e10	−	2.28776e10i	−0.248287	−	0.142757i
$310$	−6.82265e10	−	6.92113e9i	−0.419590	−	0.0425647i
$311$	1.16357e10			0.0705295			0.0352647	−	0.999378i	$-0.488773\pi$
$311$	1.16357e10			0.0705295			0.0352647	+	0.999378i	$0.488773\pi$
$312$	5.83352e10	−	5.38774e10i	0.348526	−	0.321893i
$313$	−3.00924e11			−1.77218			−0.886090	−	0.463513i	$-0.846589\pi$
$313$	−3.00924e11			−1.77218			−0.886090	+	0.463513i	$0.846589\pi$
$314$	−1.55088e11	−	1.57327e10i	−0.900314	−	0.0913311i
$315$	−8.13754e10	−	1.39789e11i	−0.465689	−	0.799975i
$316$	4.37807e10	−	2.13568e11i	0.246997	−	1.20488i
$317$		−	2.06086e10i		−	0.114626i	−0.998356	−	0.0573130i	$-0.981747\pi$
$317$		−	2.06086e10i		−	0.114626i	0.998356	−	0.0573130i	$-0.0182533\pi$
$318$	2.28771e11	+	1.64328e11i	1.25452	+	0.901133i
$319$		−	1.44069e10i		−	0.0778956i
$320$	−6.52235e10	+	9.40024e10i	−0.347720	+	0.501146i
$321$	−7.53026e9	+	1.30968e10i	−0.0395856	+	0.0688483i
$322$	−1.08093e10	+	1.06555e11i	−0.0560334	+	0.552360i
$323$	1.02345e11			0.523184
$324$	−1.30592e11	+	1.49305e11i	−0.658362	+	0.752701i
$325$	−5.99197e10			−0.297916
$326$	1.74844e10	−	1.72356e11i	0.0857378	−	0.845178i
$327$	−1.28067e11	+	2.22738e11i	−0.619403	+	1.07728i
$328$	7.29030e10	−	2.32956e11i	0.347787	−	1.11132i
$329$		−	1.82275e11i		−	0.857720i
$330$	1.08953e11	+	7.82620e10i	0.505740	+	0.363277i
$331$			4.53841e10i			0.207815i	0.994587	+	0.103908i	$0.0331346\pi$
$331$			4.53841e10i			0.207815i	−0.994587	+	0.103908i	$0.966865\pi$
$332$	−1.25870e11	−	2.58030e10i	−0.568594	−	0.116560i
$333$	−1.52231e11	−	2.61507e11i	−0.678427	−	1.16542i
$334$	−4.01708e10	−	4.07507e9i	−0.176625	−	0.0179174i
$335$	−1.45153e11			−0.629685
$336$	−2.13036e11	−	2.83402e11i	−0.911856	−	1.21304i
$337$	2.00079e11			0.845019			0.422510	−	0.906358i	$-0.361149\pi$
$337$	2.00079e11			0.845019			0.422510	+	0.906358i	$0.361149\pi$
$338$	1.84993e11	+	1.87664e10i	0.770958	+	0.0782087i
$339$	−1.73291e11	−	9.96370e10i	−0.712653	−	0.409753i
$340$	2.34771e11	+	4.81274e10i	0.952775	+	0.195316i
$341$			1.76241e11i			0.705851i
$342$	−7.55913e10	+	3.43096e10i	−0.298782	+	0.135612i
$343$			1.17852e11i			0.459740i
$344$	5.02841e10	−	1.60679e11i	0.193605	−	0.618650i
$345$	5.09063e10	+	2.92695e10i	0.193457	+	0.111232i
$346$	−7.49234e9	+	7.38573e10i	−0.0281045	+	0.277045i
$347$	3.11082e11			1.15184			0.575919	−	0.817507i	$-0.304644\pi$
$347$	3.11082e11			1.15184			0.575919	+	0.817507i	$0.304644\pi$
$348$	1.56396e10	+	1.38282e10i	0.0571634	+	0.0505428i
$349$	2.73302e11			0.986116			0.493058	−	0.869996i	$-0.335879\pi$
$349$	2.73302e11			0.986116			0.493058	+	0.869996i	$0.335879\pi$
$350$	−2.70004e10	+	2.66162e11i	−0.0961755	+	0.948069i
$351$	1.34912e11	−	7.23832e8i	0.474424	−	0.00254540i
$352$	2.57269e11	+	1.42386e11i	0.893194	+	0.494339i
$353$			5.49363e10i			0.188310i	0.995558	+	0.0941550i	$0.0300149\pi$
$353$			5.49363e10i			0.188310i	−0.995558	+	0.0941550i	$0.969985\pi$
$354$	−2.74462e11	+	3.82096e11i	−0.928898	+	1.29317i
$355$			8.36050e10i			0.279386i
$356$	3.97354e10	−	1.93834e11i	0.131115	−	0.639596i
$357$	−3.70166e11	+	6.43802e11i	−1.20612	+	2.09771i
$358$	−2.80095e11	−	2.84138e10i	−0.901220	−	0.0914230i
$359$	5.25472e11			1.66965			0.834823	−	0.550518i	$-0.185570\pi$
$359$	5.25472e11			1.66965			0.834823	+	0.550518i	$0.185570\pi$
$360$	−1.89535e11	+	4.31570e10i	−0.594741	+	0.135422i
$361$	2.87947e11			0.892339
$362$	1.34475e11	+	1.36416e10i	0.411580	+	0.0417521i
$363$	6.95285e9	−	1.20926e10i	0.0210176	−	0.0365544i
$364$	−4.84261e10	+	2.36229e11i	−0.144585	+	0.705305i
$365$			1.66160e11i			0.490014i
$366$	1.55132e11	−	2.15969e11i	0.451894	−	0.629109i
$367$		−	3.26879e11i		−	0.940567i	−0.882515	−	0.470284i	$-0.844152\pi$
$367$		−	3.26879e11i		−	0.940567i	0.882515	−	0.470284i	$-0.155848\pi$
$368$	1.18330e11	+	5.06428e10i	0.336342	+	0.143947i
$369$	3.58409e11	−	2.08640e11i	1.00637	−	0.585840i
$370$	2.99272e10	−	2.95014e11i	0.0830154	−	0.818341i
$371$	−8.55358e11			−2.34404
$372$	−1.91320e11	−	1.69162e11i	−0.517986	−	0.457993i
$373$	−4.36004e10			−0.116627			−0.0583137	−	0.998298i	$-0.518572\pi$
$373$	−4.36004e10			−0.116627			−0.0583137	+	0.998298i	$0.518572\pi$
$374$	6.21608e10	−	6.12763e11i	0.164284	−	1.61946i
$375$	3.29657e11	+	1.89542e11i	0.860838	+	0.494955i
$376$	−2.09055e11	−	6.54233e10i	−0.539405	−	0.168806i
$377$		−	1.41989e10i		−	0.0362008i
$378$	5.75773e10	−	5.99601e11i	0.145057	−	1.51060i
$379$			1.76715e11i			0.439944i	0.975506	+	0.219972i	$0.0705967\pi$
$379$			1.76715e11i			0.439944i	−0.975506	+	0.219972i	$0.929403\pi$
$380$	−7.96931e10	−	1.63368e10i	−0.196063	−	0.0401922i
$381$	−6.87267e10	−	3.95157e10i	−0.167095	−	0.0960742i
$382$	−3.61022e9	−	3.66234e8i	−0.00867459	−	0.000879981i
$383$	−6.77940e11			−1.60989			−0.804946	−	0.593348i	$-0.797806\pi$
$383$	−6.77940e11			−1.60989			−0.804946	+	0.593348i	$0.797806\pi$
$384$	−4.01503e11	+	1.42615e11i	−0.942320	+	0.334714i
$385$	−4.07369e11			−0.944963
$386$	−4.38790e11	−	4.45124e10i	−1.00604	−	0.102056i
$387$	2.47208e11	−	1.43907e11i	0.560227	−	0.326124i
$388$	−7.99142e10	−	1.63821e10i	−0.179012	−	0.0366968i
$389$			1.56109e11i			0.345665i	0.984951	+	0.172833i	$0.0552920\pi$
$389$			1.56109e11i			0.345665i	−0.984951	+	0.172833i	$0.944708\pi$
$390$	1.07380e11	+	7.71319e10i	0.235035	+	0.168828i
$391$		−	2.69602e11i		−	0.583349i
$392$	5.81335e11	+	1.81928e11i	1.24348	+	0.389145i
$393$	2.32545e11	−	4.04449e11i	0.491746	−	0.855258i
$394$	1.86552e10	−	1.83897e11i	0.0390002	−	0.384452i
$395$	3.62973e11			0.750217
$396$	1.59508e11	+	4.73421e11i	0.325952	+	0.967430i
$397$	3.73860e11			0.755357			0.377678	−	0.925937i	$-0.376723\pi$
$397$	3.73860e11			0.755357			0.377678	+	0.925937i	$0.376723\pi$
$398$	−5.97687e10	+	5.89182e11i	−0.119399	+	1.17700i
$399$	1.25653e11	−	2.18539e11i	0.248195	−	0.431668i
$400$	2.95575e11	+	1.26500e11i	0.577296	+	0.247070i
$401$			6.53181e11i			1.26149i	0.775990	+	0.630745i	$0.217251\pi$
$401$			6.53181e11i			1.26149i	−0.775990	+	0.630745i	$0.782749\pi$
$402$	−4.39028e11	−	3.15357e11i	−0.838445	−	0.602262i
$403$			1.73696e11i			0.328033i
$404$	1.83059e10	−	8.92987e10i	0.0341882	−	0.166774i
$405$	−2.87185e11	−	1.63078e11i	−0.530412	−	0.301195i
$406$	−6.30712e10	−	6.39816e9i	−0.115203	−	0.0116866i
$407$	−7.62074e11			−1.37665
$408$	6.05527e11	+	6.55628e11i	1.08184	+	1.17135i
$409$	−1.11068e12			−1.96261			−0.981306	−	0.192455i	$-0.938355\pi$
$409$	−1.11068e12			−1.96261			−0.981306	+	0.192455i	$0.938355\pi$
$410$	4.04332e11	+	4.10168e10i	0.706660	+	0.0716861i
$411$	6.79362e11	+	3.90612e11i	1.17439	+	0.675238i
$412$	3.36373e10	−	1.64087e11i	0.0575153	−	0.280567i
$413$		−	1.42863e12i		−	2.41626i
$414$	9.03801e10	+	1.99127e11i	0.151207	+	0.333141i
$415$		−	2.13925e11i		−	0.354034i
$416$	2.53554e11	+	1.40330e11i	0.415098	+	0.229736i
$417$	3.37266e11	+	1.93917e11i	0.546210	+	0.314053i
$418$	−2.11005e10	+	2.08002e11i	−0.0338064	+	0.333254i
$419$	1.29569e11			0.205371			0.102685	−	0.994714i	$-0.467257\pi$
$419$	1.29569e11			0.205371			0.102685	+	0.994714i	$0.467257\pi$
$420$	3.91005e11	−	4.42223e11i	0.613141	−	0.693458i
$421$	4.83302e11			0.749806			0.374903	−	0.927064i	$-0.377676\pi$
$421$	4.83302e11			0.749806			0.374903	+	0.927064i	$0.377676\pi$
$422$	−2.48123e10	+	2.44592e11i	−0.0380856	+	0.375437i
$423$	−1.87234e11	−	3.21636e11i	−0.284350	−	0.488465i
$424$	−3.07010e11	+	9.81026e11i	−0.461325	+	1.47412i
$425$		−	6.73436e11i		−	1.00126i
$426$	−1.81639e11	+	2.52871e11i	−0.267219	+	0.372011i
$427$			8.07493e11i			1.17547i
$428$	−5.40099e10	−	1.10719e10i	−0.0777995	−	0.0159486i
$429$	1.69364e11	−	2.94563e11i	0.241415	−	0.419875i
$430$	2.78883e11	+	2.82909e10i	0.393382	+	0.0399061i
$431$	6.80345e11			0.949689			0.474844	−	0.880070i	$-0.342504\pi$
$431$	6.80345e11			0.949689			0.474844	+	0.880070i	$0.342504\pi$
$432$	−6.67028e11	−	2.81249e11i	−0.921440	−	0.388521i
$433$	−1.06106e12			−1.45059			−0.725293	−	0.688440i	$-0.758296\pi$
$433$	−1.06106e12			−1.45059			−0.725293	+	0.688440i	$0.758296\pi$
$434$	7.71556e11	+	7.82693e10i	1.04391	+	0.105898i
$435$	−1.73250e10	+	3.01320e10i	−0.0231991	+	0.0403484i
$436$	−9.18547e11	−	1.88299e11i	−1.21734	−	0.249551i
$437$			9.15165e10i			0.120042i
$438$	−3.60997e11	+	5.02566e11i	−0.468674	+	0.652468i
$439$			8.34728e11i			1.07264i	0.844014	+	0.536321i	$0.180186\pi$
$439$			8.34728e11i			1.07264i	−0.844014	+	0.536321i	$0.819814\pi$
$440$	−1.46215e11	+	4.67219e11i	−0.185976	+	0.594270i
$441$	5.20656e11	+	8.94399e11i	0.655507	+	1.12605i
$442$	6.12632e10	−	6.03914e11i	0.0763483	−	0.752619i
$443$	−3.08701e11			−0.380821			−0.190411	−	0.981705i	$-0.560982\pi$
$443$	−3.08701e11			−0.380821			−0.190411	+	0.981705i	$0.560982\pi$
$444$	7.31461e11	−	8.27276e11i	0.893240	−	1.01025i
$445$	3.29434e11			0.398244
$446$	7.59580e10	−	7.48771e11i	0.0909005	−	0.896070i
$447$	−1.05040e12	−	6.03949e11i	−1.24444	−	0.715511i
$448$	7.37596e11	−	1.06305e12i	0.865102	−	1.24682i
$449$			1.07807e12i			1.25181i	0.779899	+	0.625905i	$0.215270\pi$
$449$			1.07807e12i			1.25181i	−0.779899	+	0.625905i	$0.784730\pi$
$450$	2.25759e11	+	4.97396e11i	0.259531	+	0.571802i
$451$		−	1.04446e12i		−	1.18877i
$452$	1.46498e11	−	7.14635e11i	0.165085	−	0.805307i
$453$	−8.65719e11	−	4.97761e11i	−0.965907	−	0.555366i
$454$	3.45674e11	+	3.50664e10i	0.381870	+	0.0387383i
$455$	−4.01486e11			−0.439157
$456$	−2.05546e11	−	2.22553e11i	−0.222622	−	0.241041i
$457$	1.03847e12			1.11370			0.556852	−	0.830611i	$-0.312009\pi$
$457$	1.03847e12			1.11370			0.556852	+	0.830611i	$0.312009\pi$
$458$	−1.27731e12	−	1.29575e11i	−1.35644	−	0.137602i
$459$	8.13513e9	+	1.51627e12i	0.00855475	+	1.59448i
$460$	−4.30354e10	+	2.09932e11i	−0.0448142	+	0.218609i
$461$			1.69987e12i			1.75292i	0.481479	+	0.876458i	$0.340100\pi$
$461$			1.69987e12i			1.75292i	−0.481479	+	0.876458i	$0.659900\pi$
$462$	−1.23212e12	−	8.85045e11i	−1.25825	−	0.903809i
$463$		−	1.97554e12i		−	1.99789i	−0.0459672	−	0.998943i	$-0.514637\pi$
$463$		−	1.97554e12i		−	1.99789i	0.0459672	−	0.998943i	$-0.485363\pi$
$464$	−2.99761e10	+	7.00411e10i	−0.0300223	+	0.0701491i
$465$	2.11938e11	−	3.68608e11i	0.210218	−	0.365617i
$466$	−1.11550e11	+	1.09963e12i	−0.109581	+	1.08021i
$467$	1.64533e12			1.60077			0.800383	−	0.599489i	$-0.204630\pi$
$467$	1.64533e12			1.60077			0.800383	+	0.599489i	$0.204630\pi$
$468$	1.57205e11	+	4.66585e11i	0.151481	+	0.449598i
$469$	1.64149e12			1.56661
$470$	3.68086e10	−	3.62848e11i	0.0347943	−	0.342992i
$471$	4.81763e11	−	8.37895e11i	0.451065	−	0.784505i
$472$	−1.63852e12	−	5.12773e11i	−1.51954	−	0.475539i
$473$		−	7.20406e11i		−	0.661763i
$474$	1.09784e12	+	7.88591e11i	0.998938	+	0.717545i
$475$			2.28598e11i			0.206040i
$476$	−2.65497e12	−	5.44260e11i	−2.37044	−	0.485932i
$477$	−1.50934e12	+	8.78628e11i	−1.33491	+	0.777092i
$478$	1.57929e12	+	1.60209e11i	1.38369	+	0.140366i
$479$	−5.97084e11			−0.518233			−0.259117	−	0.965846i	$-0.583431\pi$
$479$	−5.97084e11			−0.518233			−0.259117	+	0.965846i	$0.583431\pi$
$480$	−3.66853e11	−	6.07177e11i	−0.315432	−	0.522071i
$481$	−7.51069e11			−0.639775
$482$	1.91675e11	+	1.94442e10i	0.161754	+	0.0164089i
$483$	−5.75686e11	−	3.31001e11i	−0.481309	−	0.276737i
$484$	4.98685e10	+	1.02229e10i	0.0413069	+	0.00846777i
$485$		−	1.35819e11i		−	0.111461i
$486$	−5.14314e11	−	1.11718e12i	−0.418182	−	0.908363i
$487$			1.40528e12i			1.13210i	0.824372	+	0.566048i	$0.191528\pi$
$487$			1.40528e12i			1.13210i	−0.824372	+	0.566048i	$0.808472\pi$
$488$	9.26129e11	+	2.89830e11i	0.739235	+	0.231342i
$489$	9.31192e11	+	5.35406e11i	0.736460	+	0.423441i
$490$	−1.02356e11	+	1.00900e12i	−0.0802108	+	0.790694i
$491$	1.50098e11			0.116549			0.0582746	−	0.998301i	$-0.481440\pi$
$491$	1.50098e11			0.116549			0.0582746	+	0.998301i	$0.481440\pi$
$492$	1.13383e12	+	1.00251e12i	0.872375	+	0.771337i
$493$	1.59581e11			0.121666
$494$	−2.07958e10	+	2.04999e11i	−0.0157110	+	0.154874i
$495$	−7.18829e11	+	4.18452e11i	−0.538149	+	0.313272i
$496$	3.66700e11	−	8.56819e11i	0.272047	−	0.635655i
$497$		−	9.45468e11i		−	0.695093i
$498$	4.64771e11	−	6.47035e11i	0.338615	−	0.471407i
$499$			2.05737e12i			1.48546i	0.669592	+	0.742729i	$0.266469\pi$
$499$			2.05737e12i			1.48546i	−0.669592	+	0.742729i	$0.733531\pi$
$500$	−2.78687e11	+	1.35947e12i	−0.199412	+	0.972758i
$501$	1.24786e11	−	2.17032e11i	0.0884905	−	0.153905i
$502$	9.81440e11	+	9.95607e10i	0.689758	+	0.0699715i
$503$	2.21881e12			1.54548			0.772740	−	0.634722i	$-0.218886\pi$
$503$	2.21881e12			1.54548			0.772740	+	0.634722i	$0.218886\pi$
$504$	2.14340e12	−	4.88052e11i	1.47967	−	0.336921i
$505$	1.51769e11			0.103842
$506$	5.47931e11	+	5.55841e10i	0.371577	+	0.0376941i
$507$	−5.74661e11	+	9.99466e11i	−0.386257	+	0.671788i
$508$	5.81005e10	−	2.83422e11i	0.0387073	−	0.188819i
$509$		−	6.81670e11i		−	0.450136i	−0.974343	−	0.225068i	$-0.927740\pi$
$509$		−	6.81670e11i		−	0.450136i	0.974343	−	0.225068i	$-0.0722604\pi$
$510$	−8.66884e11	+	1.20684e12i	−0.567407	+	0.789922i
$511$		−	1.87906e12i		−	1.21912i
$512$	−9.54489e11	−	1.22752e12i	−0.613841	−	0.789430i
$513$	−2.76147e9	−	5.14697e11i	−0.00176040	−	0.328113i
$514$	9.11840e10	−	8.98865e11i	0.0576215	−	0.568016i
$515$	2.78877e11			0.174695
$516$	7.82044e11	+	6.91467e11i	0.485632	+	0.429386i
$517$	−9.37302e11			−0.576995
$518$	−3.38439e11	+	3.33623e12i	−0.206537	+	2.03598i
$519$	−3.99030e11	−	2.29429e11i	−0.241408	−	0.138802i
$520$	−1.44104e11	+	4.60473e11i	−0.0864293	+	0.276178i
$521$			1.77270e11i			0.105406i	0.998610	+	0.0527029i	$0.0167836\pi$
$521$			1.77270e11i			0.105406i	−0.998610	+	0.0527029i	$0.983216\pi$
$522$	−1.17865e11	+	5.34971e10i	−0.0694815	+	0.0315364i
$523$			1.28372e11i			0.0750259i	0.999296	+	0.0375129i	$0.0119435\pi$
$523$			1.28372e11i			0.0750259i	−0.999296	+	0.0375129i	$0.988056\pi$
$524$	1.66790e12	+	3.41915e11i	0.966452	+	0.198119i
$525$	−1.43800e12	−	8.26803e11i	−0.826117	−	0.474991i
$526$	−1.64660e12	−	1.67037e11i	−0.937890	−	0.0951429i
$527$	−1.95217e12			−1.10248
$528$	−1.45732e12	+	1.09548e12i	−0.816022	+	0.613412i
$529$	−1.56007e12			−0.866154
$530$	−1.70273e12	−	1.72731e11i	−0.937354	−	0.0950885i
$531$	−1.46750e12	−	2.52091e12i	−0.801035	−	1.37604i
$532$	9.01229e11	+	1.84749e11i	0.487790	+	0.0999953i
$533$		−	1.02938e12i		−	0.552463i
$534$	9.96404e11	+	7.15726e11i	0.530274	+	0.380900i
$535$		−	9.17934e10i		−	0.0484417i
$536$	5.89176e11	−	1.88266e12i	0.308321	−	0.985215i
$537$	8.70083e11	−	1.51327e12i	0.451519	−	0.785294i
$538$	1.89406e11	−	1.86711e12i	0.0974707	−	0.960838i
$539$	2.60643e12			1.33014
$540$	2.35700e11	−	1.18197e12i	0.119286	−	0.598186i
$541$	1.01829e12			0.511075			0.255538	−	0.966799i	$-0.417748\pi$
$541$	1.01829e12			0.511075			0.255538	+	0.966799i	$0.417748\pi$
$542$	3.34510e11	−	3.29750e12i	0.166499	−	1.64130i
$543$	−4.17732e11	+	7.26531e11i	−0.206205	+	0.358637i
$544$	−1.57716e12	+	2.84969e12i	−0.772113	+	1.39509i
$545$		−	1.56113e12i		−	0.757975i
$546$	−1.21433e12	−	8.72265e11i	−0.584751	−	0.420031i
$547$		−	2.14818e12i		−	1.02595i	−0.858403	−	0.512976i	$-0.828543\pi$
$547$		−	2.14818e12i		−	1.02595i	0.858403	−	0.512976i	$-0.171457\pi$
$548$	−5.74322e11	+	2.80162e12i	−0.272046	+	1.32708i
$549$	8.29461e11	+	1.42487e12i	0.389691	+	0.669424i
$550$	1.36867e12	+	1.38843e11i	0.637773	+	0.0646980i
$551$	−5.41697e10			−0.0250365
$552$	−5.86261e11	+	5.41461e11i	−0.268760	+	0.248222i
$553$	−4.10477e12			−1.86649
$554$	−1.18687e12	−	1.20400e11i	−0.535314	−	0.0543042i
$555$	1.59387e12	+	9.16427e11i	0.713076	+	0.409996i
$556$	−2.85119e11	+	1.39085e12i	−0.126529	+	0.617224i
$557$			2.49210e12i			1.09703i	0.836142	+	0.548514i	$0.184806\pi$
$557$			2.49210e12i			1.09703i	−0.836142	+	0.548514i	$0.815194\pi$
$558$	1.44186e12	−	6.54435e11i	0.629607	−	0.285767i
$559$		−	7.10003e11i		−	0.307544i
$560$	1.98048e12	+	8.47601e11i	0.850988	+	0.364205i
$561$	3.31058e12	+	1.90348e12i	1.41114	+	0.811363i
$562$	2.19268e11	−	2.16148e12i	0.0927174	−	0.913980i
$563$	−4.63339e12			−1.94362			−0.971810	−	0.235766i	$-0.924240\pi$
$563$	−4.63339e12			−1.94362			−0.971810	+	0.235766i	$0.924240\pi$
$564$	8.99651e11	−	1.01750e12i	0.374385	−	0.423426i
$565$	1.21457e12			0.501423
$566$	3.30044e9	−	3.25347e10i	0.00135175	−	0.0133252i
$567$	3.24770e12	+	1.84421e12i	1.31963	+	0.749353i
$568$	−1.08438e12	−	3.39353e11i	−0.437132	−	0.136800i
$569$			1.44342e12i			0.577282i	0.957437	+	0.288641i	$0.0932034\pi$
$569$			1.44342e12i			0.577282i	−0.957437	+	0.288641i	$0.906797\pi$
$570$	2.94264e11	−	4.09662e11i	0.116761	−	0.162551i
$571$			4.20925e12i			1.65708i	0.559933	+	0.828538i	$0.310827\pi$
$571$			4.20925e12i			1.65708i	−0.559933	+	0.828538i	$0.689173\pi$
$572$	1.21474e12	+	2.49019e11i	0.474464	+	0.0972634i
$573$	1.12148e10	−	1.95050e10i	0.00434604	−	0.00755876i
$574$	−4.57248e12	−	4.63849e11i	−1.75812	−	0.178350i
$575$	6.02185e11			0.229734
$576$	2.09567e11	−	2.63348e12i	0.0793271	−	0.996849i
$577$	3.82087e12			1.43506			0.717531	−	0.696526i	$-0.245272\pi$
$577$	3.82087e12			1.43506			0.717531	+	0.696526i	$0.245272\pi$
$578$	4.11774e12	+	4.17718e11i	1.53456	+	0.155671i
$579$	1.36305e12	−	2.37066e12i	0.504033	−	0.876628i
$580$	−1.24261e11	−	2.54731e10i	−0.0455942	−	0.00934666i
$581$			2.41922e12i			0.880811i
$582$	2.95080e11	−	4.10798e11i	0.106607	−	0.148414i
$583$			4.39845e12i			1.57685i
$584$	−2.15513e12	−	6.74444e11i	−0.766683	−	0.239932i
$585$	−7.08449e11	+	4.12409e11i	−0.250096	+	0.145588i
$586$	−3.01947e11	+	2.97650e12i	−0.105777	+	1.04272i
$587$	−2.55370e12			−0.887765			−0.443883	−	0.896085i	$-0.646399\pi$
$587$	−2.55370e12			−0.887765			−0.443883	+	0.896085i	$0.646399\pi$
$588$	−2.50173e12	+	2.82943e12i	−0.863062	+	0.976116i
$589$	6.62663e11			0.226868
$590$	2.88497e11	−	2.84392e12i	0.0980183	−	0.966235i
$591$	9.93544e11	+	5.71256e11i	0.334999	+	0.192614i
$592$	3.70492e12	+	1.58563e12i	1.23974	+	0.530582i
$593$		−	1.64410e12i		−	0.545987i	−0.962016	−	0.272993i	$-0.911986\pi$
$593$		−	1.64410e12i		−	0.545987i	0.962016	−	0.272993i	$-0.0880137\pi$
$594$	−3.08329e12	−	2.96076e11i	−1.01619	−	0.0975808i
$595$		−	4.51230e12i		−	1.47595i
$596$	8.87995e11	−	4.33175e12i	0.288272	−	1.40623i
$597$	−3.18318e12	−	1.83023e12i	−1.02560	−	0.589686i
$598$	5.40019e11	+	5.47814e10i	0.172685	+	0.0175177i
$599$	6.12725e11			0.194467			0.0972333	−	0.995262i	$-0.469001\pi$
$599$	6.12725e11			0.194467			0.0972333	+	0.995262i	$0.469001\pi$
$600$	−1.46441e12	+	1.35251e12i	−0.461299	+	0.426048i
$601$	5.47081e10			0.0171047			0.00855236	−	0.999963i	$-0.497278\pi$
$601$	5.47081e10			0.0171047			0.00855236	+	0.999963i	$0.497278\pi$
$602$	−3.15382e12	−	3.19935e11i	−0.978707	−	0.0992835i
$603$	2.89653e12	−	1.68615e12i	0.892174	−	0.519361i
$604$	7.31865e11	−	3.57013e12i	0.223751	−	1.09149i
$605$			8.47548e10i			0.0257197i
$606$	4.59039e11	+	3.29732e11i	0.138268	+	0.0993194i
$607$		−	3.84906e12i		−	1.15081i	−0.817867	−	0.575407i	$-0.804844\pi$
$607$		−	3.84906e12i		−	1.15081i	0.817867	−	0.575407i	$-0.195156\pi$
$608$	5.35367e11	−	9.67326e11i	0.158886	−	0.287083i
$609$	1.95924e11	−	3.40755e11i	0.0577177	−	0.100384i
$610$	−1.63065e11	+	1.60744e12i	−0.0476844	+	0.470058i
$611$	−9.23767e11			−0.268149
$612$	−5.24394e12	+	1.76682e12i	−1.51104	+	0.509108i
$613$	3.81771e11			0.109202			0.0546010	−	0.998508i	$-0.482611\pi$
$613$	3.81771e11			0.109202			0.0546010	+	0.998508i	$0.482611\pi$
$614$	−4.89542e11	+	4.82575e12i	−0.139005	+	1.37027i
$615$	−1.25601e12	+	2.18449e12i	−0.354043	+	0.615760i
$616$	1.65351e12	−	5.28366e12i	0.462694	−	1.47850i
$617$			6.54532e12i			1.81823i	0.416551	+	0.909113i	$0.363239\pi$
$617$			6.54532e12i			1.81823i	−0.416551	+	0.909113i	$0.636761\pi$
$618$	8.43488e11	+	6.05885e11i	0.232611	+	0.167087i
$619$		−	3.04023e12i		−	0.832335i	−0.909288	−	0.416167i	$-0.863373\pi$
$619$		−	3.04023e12i		−	0.832335i	0.909288	−	0.416167i	$-0.136627\pi$
$620$	1.52010e12	+	3.11616e11i	0.413152	+	0.0846947i
$621$	−1.35584e12	+	7.27441e9i	−0.365845	+	0.00196284i
$622$	−2.61941e11	−	2.65723e10i	−0.0701693	−	0.00711822i
$623$	−3.72549e12			−0.990802
$624$	−1.43627e12	+	1.07966e12i	−0.379233	+	0.285074i
$625$	8.49087e10			0.0222583
$626$	6.77437e12	+	6.87216e11i	1.76313	+	0.178858i
$627$	−1.12378e12	−	6.46136e11i	−0.290386	−	0.166963i
$628$	3.45539e12	+	7.08343e11i	0.886500	+	0.181729i
$629$		−	8.44124e12i		−	2.15020i
$630$	1.51268e12	+	3.33275e12i	0.382573	+	0.842890i
$631$			6.69357e12i			1.68084i	0.541938	+	0.840419i	$0.317691\pi$
$631$			6.69357e12i			1.68084i	−0.541938	+	0.840419i	$0.682309\pi$
$632$	−1.47331e12	+	4.70784e12i	−0.367339	+	1.17380i
$633$	−1.32146e12	−	7.59799e11i	−0.327143	−	0.188097i
$634$	−4.70637e10	+	4.63939e11i	−0.0115687	+	0.114041i
$635$	4.81693e11			0.117568
$636$	−4.77478e12	−	4.22177e12i	−1.15717	−	1.02315i
$637$	2.56879e12			0.618160
$638$	−3.29009e10	+	3.24327e11i	−0.00786166	+	0.0774979i
$639$	−9.71190e11	−	1.66834e12i	−0.230436	−	0.395850i
$640$	1.68297e12	−	1.96722e12i	0.396522	−	0.463493i
$641$		−	2.96427e12i		−	0.693516i	−0.937955	−	0.346758i	$-0.887282\pi$
$641$		−	2.96427e12i		−	0.693516i	0.937955	−	0.346758i	$-0.112718\pi$
$642$	1.99429e11	−	2.77637e11i	0.0463320	−	0.0645016i
$643$		−	3.00266e12i		−	0.692718i	−0.938102	−	0.346359i	$-0.887418\pi$
$643$		−	3.00266e12i		−	0.692718i	0.938102	−	0.346359i	$-0.112582\pi$
$644$	4.86676e11	−	2.37407e12i	0.111495	−	0.543885i
$645$	−8.66320e11	+	1.50673e12i	−0.197088	+	0.342780i
$646$	−2.30397e12	−	2.33723e11i	−0.520513	−	0.0528026i
$647$	6.72107e12			1.50789			0.753944	−	0.656938i	$-0.228149\pi$
$647$	6.72107e12			1.50789			0.753944	+	0.656938i	$0.228149\pi$
$648$	3.28084e12	−	3.06291e12i	0.730967	−	0.682413i
$649$	−7.34635e12			−1.62544
$650$	1.34890e12	+	1.36838e11i	0.296395	+	0.0300674i
$651$	−2.39675e12	+	4.16850e12i	−0.523008	+	0.909630i
$652$	−7.87215e11	+	3.84014e12i	−0.170600	+	0.832209i
$653$		−	5.94292e12i		−	1.27906i	−0.768767	−	0.639529i	$-0.779129\pi$
$653$		−	5.94292e12i		−	1.27906i	0.768767	−	0.639529i	$-0.220871\pi$
$654$	3.39170e12	−	4.72178e12i	0.724965	−	1.00927i
$655$			2.83471e12i			0.601759i
$656$	−2.17318e12	+	5.07778e12i	−0.458172	+	1.07055i
$657$	−1.93018e12	−	3.31573e12i	−0.404160	−	0.694280i
$658$	−4.16259e11	+	4.10335e12i	−0.0865659	+	0.853341i
$659$	−5.84499e12			−1.20726			−0.603628	−	0.797266i	$-0.706279\pi$
$659$	−5.84499e12			−1.20726			−0.603628	+	0.797266i	$0.706279\pi$
$660$	−2.27402e12	−	2.01064e12i	−0.466494	−	0.412465i
$661$	3.66821e12			0.747390			0.373695	−	0.927552i	$-0.378091\pi$
$661$	3.66821e12			0.747390			0.373695	+	0.927552i	$0.378091\pi$
$662$	1.03643e11	−	1.02168e12i	0.0209739	−	0.206754i
$663$	3.26278e12	+	1.87599e12i	0.655807	+	0.377068i
$664$	2.77465e12	+	8.68322e11i	0.553926	+	0.173350i
$665$			1.53170e12i			0.303722i
$666$	2.82980e12	+	6.23465e12i	0.557342	+	1.22794i
$667$			1.42697e11i			0.0279157i
$668$	8.95015e11	+	1.83475e11i	0.173915	+	0.0356519i
$669$	4.04540e12	+	2.32597e12i	0.780806	+	0.448939i
$670$	3.26766e12	+	3.31483e11i	0.626470	+	0.0635513i
$671$	4.15232e12			0.790750
$672$	4.14864e12	+	6.86641e12i	0.784773	+	1.29888i
$673$	−9.02868e11			−0.169651			−0.0848255	−	0.996396i	$-0.527033\pi$
$673$	−9.02868e11			−0.169651			−0.0848255	+	0.996396i	$0.527033\pi$
$674$	−4.50415e12	−	4.56917e11i	−0.840705	−	0.0852840i
$675$	−3.38674e12	+	1.81706e10i	−0.627935	+	0.00336902i
$676$	−4.12169e12	−	8.44933e11i	−0.759128	−	0.155619i
$677$			5.36926e12i			0.982347i	0.871062	+	0.491174i	$0.163432\pi$
$677$			5.36926e12i			0.982347i	−0.871062	+	0.491174i	$0.836568\pi$
$678$	3.67358e12	+	2.63876e12i	0.667660	+	0.479586i
$679$			1.53595e12i			0.277308i
$680$	−5.17524e12	−	1.61958e12i	−0.928197	−	0.290478i
$681$	−1.07380e12	+	1.86758e12i	−0.191320	+	0.332749i
$682$	4.02480e11	−	3.96752e12i	0.0712384	−	0.702247i
$683$	7.33129e12			1.28910			0.644551	−	0.764561i	$-0.277044\pi$
$683$	7.33129e12			1.28910			0.644551	+	0.764561i	$0.277044\pi$
$684$	1.78005e12	−	5.99746e11i	0.310943	−	0.104765i
$685$	−4.76153e12			−0.826302
$686$	2.69136e11	−	2.65307e12i	0.0463996	−	0.457393i
$687$	3.96782e12	−	6.90094e12i	0.679589	−	1.18196i
$688$	−1.49893e12	+	3.50235e12i	−0.255054	+	0.595952i
$689$			4.33494e12i			0.732818i
$690$	−1.07915e12	−	7.75165e11i	−0.181244	−	0.130189i
$691$		−	5.56872e12i		−	0.929190i	−0.885523	−	0.464595i	$-0.846200\pi$
$691$		−	5.56872e12i		−	0.929190i	0.885523	−	0.464595i	$-0.153800\pi$
$692$	3.37333e11	−	1.64556e12i	0.0559219	−	0.272794i
$693$	8.12906e12	−	4.73216e12i	1.33888	−	0.779399i
$694$	−7.00303e12	−	7.10412e11i	−1.14596	−	0.116250i
$695$	−2.36384e12			−0.384313
$696$	−3.20497e11	−	3.47015e11i	−0.0517705	−	0.0560539i
$697$	1.15692e13			1.85675
$698$	−6.15254e12	−	6.24135e11i	−0.981081	−	0.0995243i
$699$	−5.94098e12	−	3.41588e12i	−0.941263	−	0.541196i
$700$	1.21566e12	−	5.93015e12i	0.191369	−	0.933522i
$701$			7.35398e12i			1.15025i	0.818066	+	0.575124i	$0.195046\pi$
$701$			7.35398e12i			1.15025i	−0.818066	+	0.575124i	$0.804954\pi$
$702$	−3.03877e12	−	2.91801e11i	−0.472259	−	0.0453491i
$703$			2.86538e12i			0.442469i
$704$	−5.46645e12	−	3.79289e12i	−0.838742	−	0.581960i
$705$	1.96036e12	+	1.12715e12i	0.298872	+	0.171842i
$706$	1.25457e11	−	1.23672e12i	0.0190053	−	0.187348i
$707$	−1.71632e12			−0.258351
$708$	7.05125e12	−	7.97490e12i	1.05467	−	1.19282i
$709$	−9.53627e12			−1.41733			−0.708664	−	0.705546i	$-0.750702\pi$
$709$	−9.53627e12			−1.41733			−0.708664	+	0.705546i	$0.750702\pi$
$710$	1.90928e11	−	1.88211e12i	0.0281972	−	0.277960i
$711$	−7.24313e12	+	4.21644e12i	−1.06295	+	0.618775i
$712$	−1.33718e12	+	4.27284e12i	−0.194997	+	0.623098i
$713$		−	1.74562e12i		−	0.252958i
$714$	9.80336e12	−	1.36479e13i	1.41167	−	1.96527i
$715$			2.06454e12i			0.295424i
$716$	6.24057e12	+	1.27930e12i	0.887392	+	0.181912i
$717$	−4.90590e12	+	8.53247e12i	−0.693238	+	1.20570i
$718$	−1.18294e13	−	1.20001e12i	−1.66112	−	0.168510i
$719$	−4.07037e11			−0.0568007			−0.0284003	−	0.999597i	$-0.509041\pi$
$719$	−4.07037e11			−0.0568007			−0.0284003	+	0.999597i	$0.509041\pi$
$720$	4.36534e12	−	5.38708e11i	0.605372	−	0.0747063i
$721$	−3.15374e12			−0.434628
$722$	−6.48222e12	−	6.57580e11i	−0.887783	−	0.0900598i
$723$	−5.95418e11	+	1.03557e12i	−0.0810401	+	0.140947i
$724$	−2.99614e12	−	6.14198e11i	−0.405264	−	0.0830778i
$725$			3.56440e11i			0.0479144i
$726$	−1.84137e11	+	2.56349e11i	−0.0245996	+	0.0342465i
$727$			3.08205e12i			0.409199i	0.978846	+	0.204599i	$0.0655892\pi$
$727$			3.08205e12i			0.409199i	−0.978846	+	0.204599i	$0.934411\pi$
$728$	1.62964e12	−	5.20737e12i	0.215030	−	0.687111i
$729$	7.62516e12	−	8.18238e10i	0.999942	−	0.0107302i
$730$	3.79457e11	−	3.74057e12i	0.0494549	−	0.487512i
$731$	7.97971e12			1.03361
$732$	−3.98552e12	+	4.50759e12i	−0.513080	+	0.580289i
$733$	−9.40198e11			−0.120296			−0.0601480	−	0.998189i	$-0.519157\pi$
$733$	−9.40198e11			−0.120296			−0.0601480	+	0.998189i	$0.519157\pi$
$734$	−7.46489e11	+	7.35866e12i	−0.0949273	+	0.935765i
$735$	−5.45133e12	−	3.13434e12i	−0.688985	−	0.396144i
$736$	−2.54818e12	−	1.41029e12i	−0.320096	−	0.177157i
$737$		−	8.44096e12i		−	1.05387i
$738$	−8.54492e12	+	3.87839e12i	−1.06036	+	0.481280i
$739$		−	8.43327e12i		−	1.04015i	−0.854121	−	0.520075i	$-0.825904\pi$
$739$		−	8.43327e12i		−	1.04015i	0.854121	−	0.520075i	$-0.174096\pi$
$740$	−1.34744e12	+	6.57297e12i	−0.165183	+	0.805784i
$741$	−1.10755e12	−	6.36805e11i	−0.134953	−	0.0775934i
$742$	1.92557e13	+	1.95337e12i	2.33207	+	0.236574i
$743$	8.20109e12			0.987239			0.493619	−	0.869678i	$-0.335674\pi$
$743$	8.20109e12			0.987239			0.493619	+	0.869678i	$0.335674\pi$
$744$	3.92067e12	+	4.24506e12i	0.469118	+	0.507933i
$745$	7.36210e12			0.875585
$746$	9.81527e11	+	9.95695e10i	0.116032	+	0.0117707i
$747$	2.48504e12	+	4.26888e12i	0.292005	+	0.501615i
$748$	−2.79871e12	+	1.36525e13i	−0.326890	+	1.59461i
$749$			1.03807e12i			0.120520i
$750$	−6.98835e12	−	5.01979e12i	−0.806489	−	0.579308i
$751$		−	7.34852e12i		−	0.842985i	−0.906832	−	0.421493i	$-0.861506\pi$
$751$		−	7.34852e12i		−	0.842985i	0.906832	−	0.421493i	$-0.138494\pi$
$752$	4.55681e12	+	1.95022e12i	0.519614	+	0.222384i
$753$	−3.04873e12	+	5.30244e12i	−0.345575	+	0.601033i
$754$	−3.24258e10	+	3.19643e11i	−0.00365358	+	0.0360159i
$755$	6.06768e12			0.679612
$756$	−2.66547e12	+	1.33667e13i	−0.296774	+	1.48825i
$757$	8.75610e11			0.0969123			0.0484562	−	0.998825i	$-0.484570\pi$
$757$	8.75610e11			0.0969123			0.0484562	+	0.998825i	$0.484570\pi$
$758$	4.03562e11	−	3.97819e12i	0.0444016	−	0.437698i
$759$	−1.70209e12	+	2.96031e12i	−0.186163	+	0.323780i
$760$	1.75673e12	+	5.49767e11i	0.191005	+	0.0597747i
$761$		−	1.73665e13i		−	1.87708i	−0.345174	−	0.938539i	$-0.612180\pi$
$761$		−	1.73665e13i		−	1.87708i	0.345174	−	0.938539i	$-0.387820\pi$
$762$	1.45693e12	+	1.04652e12i	0.156545	+	0.112448i
$763$			1.76544e13i			1.88579i
$764$	8.04366e10	+	1.64892e10i	0.00854149	+	0.00175098i
$765$	−4.63505e12	−	7.96224e12i	−0.489304	−	0.840541i
$766$	1.52617e13	+	1.54820e12i	1.60167	+	0.162479i
$767$	−7.24027e12			−0.755397
$768$	9.36427e12	−	2.29362e12i	0.971289	−	0.237901i
$769$	1.14249e12			0.117811			0.0589053	−	0.998264i	$-0.481239\pi$
$769$	1.14249e12			0.117811			0.0589053	+	0.998264i	$0.481239\pi$
$770$	9.17064e12	+	9.30302e11i	0.940138	+	0.0953709i
$771$	4.85631e12	+	2.79222e12i	0.494950	+	0.284581i
$772$	9.77634e12	+	2.00412e12i	0.990600	+	0.203070i
$773$			1.33808e13i			1.34795i	0.738754	+	0.673975i	$0.235414\pi$
$773$			1.33808e13i			1.34795i	−0.738754	+	0.673975i	$0.764586\pi$
$774$	−5.89376e12	+	2.67508e12i	−0.590280	+	0.267918i
$775$		−	4.36037e12i		−	0.434176i
$776$	1.76161e12	+	5.51292e11i	0.174394	+	0.0545762i
$777$	−1.80247e13	−	1.03636e13i	−1.77408	−	1.02004i
$778$	3.56505e11	−	3.51432e12i	0.0348865	−	0.343900i
$779$	−3.92715e12			−0.382084
$780$	−2.24118e12	−	1.98161e12i	−0.216796	−	0.191687i
$781$	−4.86182e12			−0.467594
$782$	−6.15687e11	+	6.06926e12i	−0.0588748	+	0.580370i
$783$	−4.30581e9	−	8.02539e11i	−0.000409380	−	0.0763024i
$784$	−1.26715e13	−	5.42312e12i	−1.19786	−	0.512657i
$785$			5.87266e12i			0.551977i
$786$	−6.15866e12	+	8.57384e12i	−0.575553	+	0.801261i
$787$			2.61116e12i			0.242631i	0.992614	+	0.121316i	$0.0387113\pi$
$787$			2.61116e12i			0.242631i	−0.992614	+	0.121316i	$0.961289\pi$
$788$	−8.39926e11	+	4.09727e12i	−0.0776021	+	0.378553i
$789$	5.11498e12	−	8.89610e12i	0.469891	−	0.817247i
$790$	−8.17120e12	−	8.28915e11i	−0.746387	−	0.0757161i
$791$	−1.37353e13			−1.24751
$792$	−2.50968e12	−	1.10219e13i	−0.226649	−	0.995387i
$793$	4.09236e12			0.367489
$794$	−8.41630e12	−	8.53779e11i	−0.751500	−	0.0762348i
$795$	5.28933e12	−	9.19935e12i	0.469622	−	0.816780i
$796$	2.69101e12	−	1.31271e13i	0.237578	−	1.15894i
$797$		−	1.78321e13i		−	1.56545i	−0.622368	−	0.782725i	$-0.713829\pi$
$797$		−	1.78321e13i		−	1.56545i	0.622368	−	0.782725i	$-0.286171\pi$
$798$	−3.32775e12	+	4.63276e12i	−0.290494	+	0.404415i
$799$		−	1.03822e13i		−	0.901215i
$800$	−6.36507e12	−	3.52275e12i	−0.549412	−	0.304072i
$801$	−6.57387e12	+	3.82684e12i	−0.564254	+	0.328469i
$802$	1.49166e12	−	1.47043e13i	0.127317	−	1.25505i
$803$	−9.66257e12			−0.820111
$804$	9.16316e12	+	8.10188e12i	0.773380	+	0.683807i
$805$	4.03488e12			0.338649
$806$	3.96668e11	−	3.91023e12i	0.0331069	−	0.326358i
$807$	1.00875e13	+	5.79997e12i	0.837243	+	0.481388i
$808$	−6.16031e11	+	1.96848e12i	−0.0508454	+	0.162472i
$809$			8.30937e12i			0.682024i	0.940059	+	0.341012i	$0.110770\pi$
$809$			8.30937e12i			0.682024i	−0.940059	+	0.341012i	$0.889230\pi$
$810$	6.09265e12	+	4.32703e12i	0.497306	+	0.353189i
$811$			1.29011e13i			1.04721i	0.851962	+	0.523604i	$0.175413\pi$
$811$			1.29011e13i			1.04721i	−0.851962	+	0.523604i	$0.824587\pi$
$812$	1.40524e12	+	2.88069e11i	0.113435	+	0.0232538i
$813$	1.78154e13	+	1.02433e13i	1.43017	+	0.822305i
$814$	1.71557e13	+	1.74034e12i	1.36962	+	0.138939i
$815$	−6.52656e12			−0.518174
$816$	−1.21343e13	−	1.61422e13i	−0.958096	−	1.27455i
$817$	−2.70871e12			−0.212698
$818$	2.50035e13	+	2.53644e12i	1.95259	+	0.198078i
$819$	8.01167e12	−	4.66383e12i	0.622222	−	0.362214i
$820$	−9.00860e12	−	1.84673e12i	−0.695817	−	0.142640i
$821$		−	3.68954e12i		−	0.283418i	−0.989908	−	0.141709i	$-0.954740\pi$
$821$		−	3.68954e12i		−	0.283418i	0.989908	−	0.141709i	$-0.0452598\pi$
$822$	−1.44017e13	−	1.03449e13i	−1.10025	−	0.790317i
$823$		−	1.96141e13i		−	1.49028i	−0.666906	−	0.745142i	$-0.732382\pi$
$823$		−	1.96141e13i		−	1.49028i	0.666906	−	0.745142i	$-0.267618\pi$
$824$	−1.13196e12	+	3.61709e12i	−0.0855381	+	0.273330i
$825$	−4.25162e12	+	7.39453e12i	−0.319530	+	0.555735i
$826$	−3.26254e12	+	3.21611e13i	−0.243863	+	2.40393i
$827$	−1.46111e13			−1.08619			−0.543097	−	0.839670i	$-0.682748\pi$
$827$	−1.46111e13			−1.08619			−0.543097	+	0.839670i	$0.682748\pi$
$828$	−1.57988e12	−	4.68912e12i	−0.116812	−	0.346701i
$829$	−1.49695e12			−0.110081			−0.0550403	−	0.998484i	$-0.517529\pi$
$829$	−1.49695e12			−0.110081			−0.0550403	+	0.998484i	$0.517529\pi$
$830$	−4.88537e11	+	4.81585e12i	−0.0357311	+	0.352226i
$831$	3.68688e12	−	6.41231e12i	0.268197	−	0.466455i
$832$	−5.38751e12	−	3.73812e12i	−0.389792	−	0.270457i
$833$			2.88706e13i			2.07756i
$834$	−7.14964e12	−	5.13564e12i	−0.511725	−	0.367576i
$835$			1.52114e12i			0.108288i
$836$	9.50023e11	−	4.63434e12i	0.0672676	−	0.328140i
$837$	5.26734e10	+	9.81754e12i	0.00370960	+	0.691414i
$838$	−2.91685e12	−	2.95895e11i	−0.204322	−	0.0207272i
$839$	2.03377e13			1.41701			0.708504	−	0.705707i	$-0.249371\pi$
$839$	2.03377e13			1.41701			0.708504	+	0.705707i	$0.249371\pi$
$840$	−9.81216e12	+	9.06235e12i	−0.679998	+	0.628035i
$841$	1.44227e13			0.994178
$842$	−1.08800e13	−	1.10371e12i	−0.745978	−	0.0756746i
$843$	1.16778e13	+	6.71438e12i	0.796413	+	0.457912i
$844$	1.11714e12	−	5.44957e12i	0.0757823	−	0.369676i
$845$		−	7.00508e12i		−	0.472670i
$846$	3.48047e12	+	7.66822e12i	0.233599	+	0.514669i
$847$		−	9.58470e11i		−	0.0639887i
$848$	9.15173e12	−	2.13836e13i	0.607746	−	1.42004i
$849$	1.75776e11	+	1.01066e11i	0.0116111	+	0.00667603i
$850$	−1.53792e12	+	1.51603e13i	−0.101053	+	0.996146i
$851$	7.54814e12			0.493352
$852$	4.66652e12	−	5.27780e12i	0.303400	−	0.343143i
$853$	−1.03409e13			−0.668789			−0.334395	−	0.942433i	$-0.608532\pi$
$853$	−1.03409e13			−0.668789			−0.334395	+	0.942433i	$0.608532\pi$
$854$	1.84406e12	−	1.81782e13i	0.118635	−	1.16947i
$855$	1.57337e12	+	2.70278e12i	0.100689	+	0.172967i
$856$	1.19058e12	+	3.72590e11i	0.0757926	+	0.0237191i
$857$		−	4.70599e12i		−	0.298015i	−0.988836	−	0.149007i	$-0.952392\pi$
$857$		−	4.70599e12i		−	0.298015i	0.988836	−	0.149007i	$-0.0476078\pi$
$858$	−4.48539e12	+	6.24438e12i	−0.282558	+	0.393366i
$859$			2.48462e13i			1.55701i	0.627639	+	0.778504i	$0.284021\pi$
$859$			2.48462e13i			1.55701i	−0.627639	+	0.778504i	$0.715979\pi$
$860$	−6.21358e12	−	1.27376e12i	−0.387346	−	0.0794046i
$861$	1.42039e13	−	2.47038e13i	0.880834	−	1.53197i
$862$	−1.53158e13	−	1.55369e12i	−0.944840	−	0.0958479i
$863$	−2.39639e13			−1.47065			−0.735325	−	0.677714i	$-0.762971\pi$
$863$	−2.39639e13			−1.47065			−0.735325	+	0.677714i	$0.762971\pi$
$864$	1.43738e13	+	7.85472e12i	0.877523	+	0.479534i
$865$	2.79673e12			0.169855
$866$	2.38864e13	+	2.42312e12i	1.44318	+	0.146401i
$867$	−1.27913e13	+	2.22470e13i	−0.768827	+	1.33717i
$868$	−1.71904e13	−	3.52398e12i	−1.02789	−	0.210715i
$869$			2.11077e13i			1.25560i
$870$	4.58830e11	−	6.38764e11i	0.0271528	−	0.0378010i
$871$		−	8.31906e12i		−	0.489771i
$872$	2.02482e13	+	6.33664e12i	1.18594	+	0.371138i
$873$	1.57773e12	+	2.71028e12i	0.0919326	+	0.157925i
$874$	2.08995e11	−	2.06021e12i	0.0121153	−	0.119429i
$875$	2.61290e13			1.50690
$876$	9.27443e12	−	1.04893e13i	0.532131	−	0.601836i
$877$	−2.99892e12			−0.171186			−0.0855928	−	0.996330i	$-0.527278\pi$
$877$	−2.99892e12			−0.171186			−0.0855928	+	0.996330i	$0.527278\pi$
$878$	1.90625e12	−	1.87913e13i	0.108257	−	1.06716i
$879$	−1.60812e13	−	9.24617e12i	−0.908591	−	0.522411i
$880$	4.35857e12	−	1.01841e13i	0.245003	−	0.572466i
$881$		−	1.46471e13i		−	0.819143i	−0.912278	−	0.409572i	$-0.865678\pi$
$881$		−	1.46471e13i		−	0.819143i	0.912278	−	0.409572i	$-0.134322\pi$
$882$	−9.67842e12	−	2.13236e13i	−0.538512	−	1.18646i
$883$			3.39926e12i			0.188175i	0.995564	+	0.0940874i	$0.0299933\pi$
$883$			3.39926e12i			0.188175i	−0.995564	+	0.0940874i	$0.970007\pi$
$884$	−2.75830e12	+	1.34553e13i	−0.151917	+	0.741070i
$885$	1.53649e13	+	8.83431e12i	0.841946	+	0.484092i
$886$	6.94944e12	+	7.04976e11i	0.378877	+	0.0384346i
$887$	−1.61695e13			−0.877080			−0.438540	−	0.898712i	$-0.644504\pi$
$887$	−1.61695e13			−0.877080			−0.438540	+	0.898712i	$0.644504\pi$
$888$	−1.83558e13	+	1.69531e13i	−0.990638	+	0.914937i
$889$	−5.44735e12			−0.292501
$890$	−7.41619e12	−	7.52324e11i	−0.396210	−	0.0401930i
$891$	9.48336e12	−	1.67004e13i	0.504095	−	0.887724i
$892$	−3.41991e12	+	1.66828e13i	−0.180873	+	0.882321i
$893$			3.52423e12i			0.185453i
$894$	2.22673e13	+	1.59948e13i	1.16587	+	0.837453i
$895$			1.06063e13i			0.552533i
$896$	−1.90323e13	+	2.22468e13i	−0.986520	+	1.15314i
$897$	−1.67751e12	+	2.91757e12i	−0.0865164	+	0.150472i
$898$	2.46197e12	−	2.42694e13i	0.126340	−	1.24542i
$899$	1.03326e12			0.0527581
$900$	−3.94637e12	−	1.17129e13i	−0.200496	−	0.595076i
$901$	−4.87202e13			−2.46291
$902$	−2.38522e12	+	2.35128e13i	−0.119977	+	1.18270i
$903$	9.79699e12	−	1.70392e13i	0.490341	−	0.852814i
$904$	−4.92994e12	+	1.57532e13i	−0.245518	+	0.784534i
$905$		−	5.09213e12i		−	0.252337i
$906$	1.83522e13	+	1.31826e13i	0.904924	+	0.650015i
$907$		−	2.80892e13i		−	1.37818i	−0.724676	−	0.689090i	$-0.758011\pi$
$907$		−	2.80892e13i		−	1.37818i	0.724676	−	0.689090i	$-0.241989\pi$
$908$	−7.70170e12	−	1.57882e12i	−0.376011	−	0.0770809i
$909$	−3.02856e12	+	1.76301e12i	−0.147129	+	0.0856480i
$910$	9.03821e12	+	9.16868e11i	0.436914	+	0.0443221i
$911$	1.03264e13			0.496724			0.248362	−	0.968667i	$-0.420108\pi$
$911$	1.03264e13			0.496724			0.248362	+	0.968667i	$0.420108\pi$
$912$	4.11899e12	+	5.47948e12i	0.197158	+	0.262279i
$913$	1.24402e13			0.592528
$914$	−2.33779e13	−	2.37153e12i	−1.10802	−	0.112401i
$915$	−8.68456e12	−	4.99335e12i	−0.409593	−	0.235503i
$916$	2.84587e13	+	5.83394e12i	1.33563	+	0.273799i
$917$		−	3.20570e13i		−	1.49714i
$918$	3.27954e12	−	3.41526e13i	0.152413	−	1.58720i
$919$			2.82634e12i			0.130709i	0.997862	+	0.0653544i	$0.0208178\pi$
$919$			2.82634e12i			0.130709i	−0.997862	+	0.0653544i	$0.979182\pi$
$920$	1.44823e12	−	4.62769e12i	0.0666486	−	0.212970i
$921$	−2.60722e13	−	1.49907e13i	−1.19401	−	0.686519i
$922$	3.88196e12	−	3.82672e13i	0.176914	−	1.74396i
$923$	−4.79161e12			−0.217307
$924$	2.57163e13	+	2.27378e13i	1.16060	+	1.02618i
$925$	1.88544e13			0.846788
$926$	−4.51150e12	+	4.44731e13i	−0.201638	+	1.98768i
$927$	−5.56499e12	+	3.23954e12i	−0.247517	+	0.144087i
$928$	8.34769e11	−	1.50830e12i	0.0369488	−	0.0667609i
$929$		−	3.54590e13i		−	1.56191i	−0.624588	−	0.780955i	$-0.714733\pi$
$929$		−	3.54590e13i		−	1.56191i	0.624588	−	0.780955i	$-0.285267\pi$
$930$	−5.61291e12	+	7.81406e12i	−0.246045	+	0.342534i
$931$		−	9.80011e12i		−	0.427521i
$932$	5.02241e12	−	2.45000e13i	0.218042	−	1.06364i
$933$	8.13692e11	−	1.41519e12i	0.0351554	−	0.0611433i
$934$	−3.70395e13	−	3.75742e12i	−1.59259	−	0.161558i
$935$	−2.32033e13			−0.992881
$936$	−2.47344e12	−	1.08627e13i	−0.105332	−	0.462591i
$937$	1.95468e13			0.828412			0.414206	−	0.910183i	$-0.364059\pi$
$937$	1.95468e13			0.828412			0.414206	+	0.910183i	$0.364059\pi$
$938$	−3.69531e13	−	3.74866e12i	−1.55861	−	0.158111i
$939$	−2.10438e13	+	3.66000e13i	−0.883344	+	1.53634i
$940$	−1.65726e12	+	8.08433e12i	−0.0692334	+	0.337729i
$941$			3.40569e12i			0.141596i	0.997491	+	0.0707982i	$0.0225546\pi$
$941$			3.40569e12i			0.141596i	−0.997491	+	0.0707982i	$0.977445\pi$
$942$	−1.27589e13	+	1.77624e13i	−0.527939	+	0.734975i
$943$			1.03451e13i			0.426023i
$944$	3.57152e13	+	1.52853e13i	1.46379	+	0.626471i
$945$	−2.26925e13	+	1.21751e11i	−0.925635	+	0.00496625i
$946$	−1.64518e12	+	1.62177e13i	−0.0667887	+	0.658384i
$947$	3.98781e13			1.61124			0.805619	−	0.592434i	$-0.201833\pi$
$947$	3.98781e13			1.61124			0.805619	+	0.592434i	$0.201833\pi$
$948$	−2.29137e13	−	2.02598e13i	−0.921418	−	0.814700i
$949$	−9.52304e12			−0.381134
$950$	5.22045e11	−	5.14617e12i	0.0207947	−	0.204988i
$951$	−2.50653e12	−	1.44118e12i	−0.0993713	−	0.0571353i
$952$	5.85255e13	+	1.83154e13i	2.30929	+	0.722688i
$953$			4.74501e13i			1.86346i	0.363157	+	0.931728i	$0.381699\pi$
$953$			4.74501e13i			1.86346i	−0.363157	+	0.931728i	$0.618301\pi$
$954$	3.59845e13	−	1.63327e13i	1.40653	−	0.638397i
$955$			1.36707e11i			0.00531834i
$956$	−3.51870e13	−	7.21322e12i	−1.36245	−	0.279298i
$957$	−1.75225e12	−	1.00749e12i	−0.0675291	−	0.0388271i
$958$	1.34415e13	+	1.36355e12i	0.515587	+	0.0523030i
$959$	5.38469e13			2.05578
$960$	6.87194e12	+	1.45065e13i	0.261131	+	0.551241i
$961$	1.37997e13			0.521933
$962$	1.69080e13	+	1.71520e12i	0.636508	+	0.0645696i
$963$	1.06631e12	+	1.83174e12i	0.0399544	+	0.0686350i
$964$	−4.27057e12	−	8.75452e11i	−0.159272	−	0.0326502i
$965$			1.66155e13i			0.616796i
$966$	1.22039e13	+	8.76615e12i	0.450921	+	0.323900i
$967$			2.64896e13i			0.974220i	0.873341	+	0.487110i	$0.161949\pi$
$967$			2.64896e13i			0.974220i	−0.873341	+	0.487110i	$0.838051\pi$
$968$	−1.09929e12	−	3.44020e11i	−0.0402414	−	0.0125935i
$969$	7.15704e12	−	1.24477e13i	0.260781	−	0.453558i
$970$	−3.10169e11	+	3.05755e12i	−0.0112493	+	0.110892i
$971$	−4.16057e13			−1.50199			−0.750994	−	0.660309i	$-0.770425\pi$
$971$	−4.16057e13			−1.50199			−0.750994	+	0.660309i	$0.770425\pi$
$972$	9.02690e12	+	2.63243e13i	0.324370	+	0.945930i
$973$	2.67320e13			0.956145
$974$	3.20922e12	−	3.16355e13i	0.114257	−	1.12632i
$975$	−4.19022e12	+	7.28775e12i	−0.148497	+	0.258269i
$976$	−2.01870e13	−	8.63961e12i	−0.712112	−	0.304768i
$977$			1.34966e13i			0.473914i	0.971520	+	0.236957i	$0.0761500\pi$
$977$			1.34966e13i			0.473914i	−0.971520	+	0.236957i	$0.923850\pi$
$978$	−1.97402e13	−	1.41795e13i	−0.689964	−	0.495607i
$979$			1.91573e13i			0.666520i
$980$	4.60847e12	−	2.24807e13i	0.159602	−	0.778561i
$981$	1.81347e13	+	3.11524e13i	0.625174	+	1.07394i
$982$	−3.37899e12	−	3.42777e11i	−0.115954	−	0.0117628i
$983$	2.34570e13			0.801274			0.400637	−	0.916237i	$-0.368789\pi$
$983$	2.34570e13			0.801274			0.400637	+	0.916237i	$0.368789\pi$
$984$	−2.32351e13	−	2.51576e13i	−0.790073	−	0.855443i
$985$	−6.96358e12			−0.235705
$986$	−3.59246e12	−	3.64432e11i	−0.121045	−	0.0122792i
$987$	−2.21693e13	−	1.27466e13i	−0.743573	−	0.427531i
$988$	9.36304e11	−	4.56741e12i	0.0312616	−	0.152498i
$989$			7.13543e12i			0.237158i
$990$	1.71378e13	−	7.77855e12i	0.567018	−	0.257360i
$991$		−	1.82621e13i		−	0.601476i	−0.953707	−	0.300738i	$-0.902767\pi$
$991$		−	1.82621e13i		−	0.601476i	0.953707	−	0.300738i	$-0.0972330\pi$
$992$	−1.02118e13	+	1.84512e13i	−0.334812	+	0.604953i
$993$	5.51985e12	+	3.17374e12i	0.180159	+	0.103586i
$994$	−2.15915e12	+	2.12843e13i	−0.0701527	+	0.691544i
$995$	2.23104e13			0.721610
$996$	−1.19405e13	+	1.35046e13i	−0.384463	+	0.434825i
$997$	2.35431e12			0.0754633			0.0377316	−	0.999288i	$-0.487987\pi$
$997$	2.35431e12			0.0754633			0.0377316	+	0.999288i	$0.487987\pi$
$998$	4.69839e12	−	4.63153e13i	0.149921	−	1.47787i
$999$	−4.24514e13	+	2.27762e11i	−1.34849	+	0.00723496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.10.b.a.11.1	✓	16
3.2	odd	2	inner	12.10.b.a.11.16	yes	16
4.3	odd	2	inner	12.10.b.a.11.15	yes	16
8.3	odd	2		192.10.c.d.191.11		16
8.5	even	2		192.10.c.d.191.6		16
12.11	even	2	inner	12.10.b.a.11.2	yes	16
24.5	odd	2		192.10.c.d.191.12		16
24.11	even	2		192.10.c.d.191.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.10.b.a.11.1	✓	16	1.1	even	1	trivial
12.10.b.a.11.2	yes	16	12.11	even	2	inner
12.10.b.a.11.15	yes	16	4.3	odd	2	inner
12.10.b.a.11.16	yes	16	3.2	odd	2	inner
192.10.c.d.191.5		16	24.11	even	2
192.10.c.d.191.6		16	8.5	even	2
192.10.c.d.191.11		16	8.3	odd	2
192.10.c.d.191.12		16	24.5	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-22.5119 - 2.28368i) q^{2} +(69.9307 - 121.625i) q^{3} +(501.570 + 102.820i) q^{4} +852.450i q^{5} +(-1852.02 + 2578.31i) q^{6} -9640.14i q^{7} +(-11056.5 - 3460.10i) q^{8} +(-9902.41 - 17010.7i) q^{9} +O(q^{10})\)	\(q+(-22.5119 - 2.28368i) q^{2} +(69.9307 - 121.625i) q^{3} +(501.570 + 102.820i) q^{4} +852.450i q^{5} +(-1852.02 + 2578.31i) q^{6} -9640.14i q^{7} +(-11056.5 - 3460.10i) q^{8} +(-9902.41 - 17010.7i) q^{9} +(1946.73 - 19190.3i) q^{10} -49571.9 q^{11} +(47580.6 - 53813.3i) q^{12} -48856.1 q^{13} +(-22015.0 + 217018. i) q^{14} +(103679. + 59612.4i) q^{15} +(241000. + 103143. i) q^{16} -549092. i q^{17} +(184075. + 405556. i) q^{18} +186389. i q^{19} +(-87649.0 + 427563. i) q^{20} +(-1.17248e6 - 674141. i) q^{21} +(1.11596e6 + 113207. i) q^{22} +490997. q^{23} +(-1.19402e6 + 1.10278e6i) q^{24} +1.22645e6 q^{25} +(1.09984e6 + 111572. i) q^{26} +(-2.76141e6 + 14815.6i) q^{27} +(991200. - 4.83520e6i) q^{28} +290627. i q^{29} +(-2.19788e6 - 1.57876e6i) q^{30} -3.55527e6i q^{31} +(-5.18982e6 - 2.87231e6i) q^{32} +(-3.46660e6 + 6.02919e6i) q^{33} +(-1.25395e6 + 1.23611e7i) q^{34} +8.21774e6 q^{35} +(-3.21771e6 - 9.55020e6i) q^{36} +1.53731e7 q^{37} +(425654. - 4.19597e6i) q^{38} +(-3.41654e6 + 5.94213e6i) q^{39} +(2.94956e6 - 9.42509e6i) q^{40} +2.10696e7i q^{41} +(2.48553e7 + 1.78538e7i) q^{42} +1.45325e7i q^{43} +(-2.48638e7 - 5.09699e6i) q^{44} +(1.45007e7 - 8.44131e6i) q^{45} +(-1.10533e7 - 1.12128e6i) q^{46} +1.89079e7 q^{47} +(2.93981e7 - 2.20988e7i) q^{48} -5.25787e7 q^{49} +(-2.76098e7 - 2.80083e6i) q^{50} +(-6.67835e7 - 3.83984e7i) q^{51} +(-2.45047e7 - 5.02338e6i) q^{52} -8.87287e7i q^{53} +(6.21983e7 + 5.97266e6i) q^{54} -4.22576e7i q^{55} +(-3.33559e7 + 1.06586e8i) q^{56} +(2.26696e7 + 1.30343e7i) q^{57} +(663700. - 6.54256e6i) q^{58} +1.48196e8 q^{59} +(4.58731e7 + 4.05601e7i) q^{60} -8.37636e7 q^{61} +(-8.11911e6 + 8.00357e7i) q^{62} +(-1.63985e8 + 9.54606e7i) q^{63} +(1.10273e8 + 7.65130e7i) q^{64} -4.16474e7i q^{65} +(9.18084e7 - 1.27812e8i) q^{66} +1.70277e8i q^{67} +(5.64577e7 - 2.75408e8i) q^{68} +(3.43357e7 - 5.97176e7i) q^{69} +(-1.84997e8 - 1.87667e7i) q^{70} +9.80762e7 q^{71} +(5.06270e7 + 2.22341e8i) q^{72} +1.94920e8 q^{73} +(-3.46077e8 - 3.51073e7i) q^{74} +(8.57667e7 - 1.49168e8i) q^{75} +(-1.91646e7 + 9.34872e7i) q^{76} +4.77880e8i q^{77} +(9.04826e7 - 1.25966e8i) q^{78} -4.25799e8i q^{79} +(-8.79241e7 + 2.05441e8i) q^{80} +(-1.91305e8 + 3.36893e8i) q^{81} +(4.81164e7 - 4.74317e8i) q^{82} -2.50953e8 q^{83} +(-5.18767e8 - 4.58684e8i) q^{84} +4.68074e8 q^{85} +(3.31878e7 - 3.27155e8i) q^{86} +(3.53476e7 + 2.03237e7i) q^{87} +(5.48090e8 + 1.71524e8i) q^{88} -3.86456e8i q^{89} +(-3.45716e8 + 1.56915e8i) q^{90} +4.70979e8i q^{91} +(2.46269e8 + 5.04843e7i) q^{92} +(-4.32410e8 - 2.48622e8i) q^{93} +(-4.25653e8 - 4.31797e7i) q^{94} -1.58888e8 q^{95} +(-7.12273e8 + 4.30351e8i) q^{96} -1.59328e8 q^{97} +(1.18365e9 + 1.20073e8i) q^{98} +(4.90881e8 + 8.43251e8i) 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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