LMFDB - Embedded newform 12.10.b.a.11.15

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			11.15
Root			$-11.2559 - 1.14184i$ of defining polynomial
Character	$\chi$	$=$	12.11
Dual form			12.10.b.a.11.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(22.5119 - 2.28368i) q^{2} +(-69.9307 + 121.625i) q^{3} +(501.570 - 102.820i) q^{4} +852.450i q^{5} +(-1296.52 + 2897.71i) q^{6} +9640.14i q^{7} +(11056.5 - 3460.10i) q^{8} +(-9902.41 - 17010.7i) q^{9} +O(q^{10})$	\(q+(22.5119 - 2.28368i) q^{2} +(-69.9307 + 121.625i) q^{3} +(501.570 - 102.820i) q^{4} +852.450i q^{5} +(-1296.52 + 2897.71i) 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} +(-22569.6 + 68193.8i) 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} +(-261769. - 360328. 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} +(-352350. + 1.58671e6i) 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} +(-2.47016e6 - 1.10522e6i) 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} +(-6.71578e6 - 7.51387e6i) 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} +(-2.79344e7 - 1.24986e7i) 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} +(-4.30852e6 + 3.65245e7i) 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} +(6.21307e7 - 6.63971e6i) 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} +(-5.81318e7 - 1.92394e7i) 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} +(-6.42708e7 + 1.43645e8i) 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} +(-1.68344e8 - 1.53815e8i) 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} +(6.33427e7 - 1.41571e8i) 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} +(-6.57398e8 - 2.17574e8i) 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} +(3.07162e8 - 2.23145e8i) 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} +(-1.35823e7 + 8.32075e8i) 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	$0.901350\pi$
$6$	−1296.52	+	2897.71i	−0.408411	+	0.912798i
$7$			9640.14i			1.51755i	0.651354	+	0.758774i	$0.274201\pi$
$7$			9640.14i			1.51755i	−0.651354	+	0.758774i	$0.725799\pi$
$8$	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	$-0.329485\pi$
$11$	49571.9			1.02087			0.510433	+	0.859918i	$0.329485\pi$
$12$	−22569.6	+	68193.8i	−0.314201	+	0.949356i
$13$	−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	$-0.293713\pi$
$18$	−261769.	−	360328.i	−0.587749	−	0.809044i
$19$		−	186389.i		−	0.328118i	−0.986451	−	0.164059i	$-0.947541\pi$
$19$		−	186389.i		−	0.328118i	0.986451	−	0.164059i	$-0.0524587\pi$
$20$	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	$-0.558557\pi$
$23$	−490997.			−0.365850			−0.182925	+	0.983127i	$0.558557\pi$
$24$	−352350.	+	1.58671e6i	−0.216782	+	0.976220i
$25$	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	$0.987853\pi$
$30$	−2.47016e6	−	1.10522e6i	−0.556774	−	0.249116i
$31$			3.55527e6i			0.691424i	0.938341	+	0.345712i	$0.112363\pi$
$31$			3.55527e6i			0.691424i	−0.938341	+	0.345712i	$0.887637\pi$
$32$	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
$36$	−6.71578e6	−	7.51387e6i	−0.666401	−	0.745594i
$37$	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	$0.802178\pi$
$42$	−2.79344e7	−	1.24986e7i	−1.38521	−	0.619783i
$43$		−	1.45325e7i		−	0.648237i	−0.946017	−	0.324118i	$-0.894932\pi$
$43$		−	1.45325e7i		−	0.648237i	0.946017	−	0.324118i	$-0.105068\pi$
$44$	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	$-0.591197\pi$
$47$	−1.89079e7			−0.565202			−0.282601	+	0.959238i	$0.591197\pi$
$48$	−4.30852e6	+	3.65245e7i	−0.117150	+	0.993114i
$49$	−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	$-0.280900\pi$
$54$	6.21307e7	−	6.63971e6i	0.994338	−	0.106262i
$55$			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	$-0.793111\pi$
$59$	−1.48196e8			−1.59222			−0.796108	+	0.605154i	$0.793111\pi$
$60$	−5.81318e7	−	1.92394e7i	−0.579073	−	0.191651i
$61$	−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
$66$	−6.42708e7	+	1.43645e8i	−0.416933	+	0.931844i
$67$		−	1.70277e8i		−	1.03233i	−0.856488	−	0.516166i	$-0.827359\pi$
$67$		−	1.70277e8i		−	1.03233i	0.856488	−	0.516166i	$-0.172641\pi$
$68$	−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	$-0.573552\pi$
$71$	−9.80762e7			−0.458037			−0.229019	+	0.973422i	$0.573552\pi$
$72$	−1.68344e8	−	1.53815e8i	−0.738248	−	0.674530i
$73$	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
$78$	6.33427e7	−	1.41571e8i	0.193763	−	0.433060i
$79$			4.25799e8i			1.22994i	0.788551	+	0.614969i	$0.210831\pi$
$79$			4.25799e8i			1.22994i	−0.788551	+	0.614969i	$0.789169\pi$
$80$	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	$-0.406275\pi$
$83$	2.50953e8			0.580418			0.290209	+	0.956963i	$0.406275\pi$
$84$	−6.57398e8	−	2.17574e8i	−1.44069	−	0.476815i
$85$	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	$-0.105852\pi$
$90$	3.07162e8	−	2.23145e8i	0.493487	−	0.358505i
$91$		−	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
$96$	−1.35823e7	+	8.32075e8i	−0.0163213	+	0.999867i
$97$	−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	$-0.0271278\pi$
$102$	1.59111e9	+	7.11907e8i	1.45546	+	0.651212i
$103$			3.27147e8i			0.286402i	0.989694	+	0.143201i	$0.0457395\pi$
$103$			3.27147e8i			0.286402i	−0.989694	+	0.143201i	$0.954261\pi$
$104$	−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	$-0.487357\pi$
$107$	1.07682e8			0.0794173			0.0397087	+	0.999211i	$0.487357\pi$
$108$	1.38352e9	−	2.91359e8i	0.978537	−	0.206073i
$109$	−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	$-0.134830\pi$
$114$	5.40102e8	+	2.41657e8i	0.299505	+	0.134007i
$115$		−	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
$120$	−1.35259e9	−	3.00361e8i	−0.595459	−	0.132229i
$121$	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
$126$	3.47361e9	−	2.52349e9i	1.22776	−	0.891936i
$127$			5.65069e8i			0.192746i	0.995345	+	0.0963729i	$0.0307241\pi$
$127$			5.65069e8i			0.192746i	−0.995345	+	0.0963729i	$0.969276\pi$
$128$	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	$-0.664200\pi$
$131$	−3.32537e9			−0.986550			−0.493275	+	0.869874i	$0.664200\pi$
$132$	−1.11882e9	+	3.38050e9i	−0.320757	+	0.969165i
$133$	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	$0.763134\pi$
$138$	6.36586e8	−	1.42277e9i	0.149417	−	0.333947i
$139$		−	2.77299e9i		−	0.630060i	−0.949082	−	0.315030i	$-0.897985\pi$
$139$		−	2.77299e9i		−	0.630060i	0.949082	−	0.315030i	$-0.102015\pi$
$140$	−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
$144$	−4.14101e9	−	3.07821e9i	−0.802555	−	0.596578i
$145$	−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	$-0.254821\pi$
$150$	−1.59012e9	+	3.55391e9i	−0.256459	+	0.573186i
$151$			7.11792e9i			1.11418i	0.830451	+	0.557092i	$0.188083\pi$
$151$			7.11792e9i			1.11418i	−0.830451	+	0.557092i	$0.811917\pi$
$152$	−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
$156$	1.10266e9	−	3.33168e9i	0.149067	−	0.450404i
$157$	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
$162$	−3.53728e9	+	8.02098e9i	−0.403508	+	0.914976i
$163$		−	7.65624e9i		−	0.849515i	−0.905307	−	0.424758i	$-0.860359\pi$
$163$		−	7.65624e9i		−	0.849515i	0.905307	−	0.424758i	$-0.139641\pi$
$164$	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	$-0.528292\pi$
$167$	−1.78443e9			−0.177531			−0.0887656	+	0.996053i	$0.528292\pi$
$168$	−1.52961e10	−	3.39671e9i	−1.48146	−	0.328978i
$169$	−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	$-0.0444639\pi$
$174$	−8.42153e8	−	3.76803e8i	−0.0696497	−	0.0311632i
$175$			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	$-0.649619\pi$
$179$	−1.24421e10			−0.905846			−0.452923	+	0.891550i	$0.649619\pi$
$180$	6.40520e9	−	5.72487e9i	0.454785	−	0.406480i
$181$	−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
$186$	−1.03021e10	−	4.60946e9i	−0.631131	−	0.282385i
$187$		−	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	$-0.501388\pi$
$191$	−1.60370e8			−0.00871911			−0.00435956	+	0.999990i	$0.501388\pi$
$192$	1.59443e9	+	1.87626e10i	0.0846742	+	0.996409i
$193$	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	$0.938109\pi$
$198$	−1.29764e10	−	1.78621e10i	−0.600012	−	0.825925i
$199$			2.61720e10i			1.18304i	0.806291	+	0.591519i	$0.201471\pi$
$199$			2.61720e10i			1.18304i	−0.806291	+	0.591519i	$0.798529\pi$
$200$	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
$204$	3.74447e10	+	1.23928e10i	1.51375	+	0.500994i
$205$	−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
$210$	1.06544e10	−	2.38127e10i	0.378045	−	0.844930i
$211$			1.08650e10i			0.377364i	0.982038	+	0.188682i	$0.0604215\pi$
$211$			1.08650e10i			0.377364i	−0.982038	+	0.188682i	$0.939579\pi$
$212$	−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
$216$	3.04802e10	−	9.71856e9i	0.952742	−	0.303781i
$217$	−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
$222$	−1.99315e10	+	4.45468e10i	−0.550746	+	1.23092i
$223$		−	3.32611e10i		−	0.900669i	−0.892860	−	0.450335i	$-0.851305\pi$
$223$		−	3.32611e10i		−	0.900669i	0.892860	−	0.450335i	$-0.148695\pi$
$224$	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	$-0.438530\pi$
$227$	1.53552e10			0.383830			0.191915	+	0.981412i	$0.438530\pi$
$228$	1.27106e10	+	4.20672e9i	0.311501	+	0.103095i
$229$	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	$-0.182666\pi$
$234$	1.27890e10	+	1.76042e10i	0.278846	+	0.383836i
$235$		−	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	$-0.255230\pi$
$239$	7.01538e10			1.39079			0.695393	+	0.718629i	$0.255230\pi$
$240$	−3.11354e10	−	3.67280e9i	−0.605764	−	0.0714573i
$241$	−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
$246$	−6.10538e10	−	2.73171e10i	−1.06293	−	0.475584i
$247$			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	$-0.387319\pi$
$251$	4.35965e10			0.693298			0.346649	+	0.937995i	$0.387319\pi$
$252$	7.24347e10	−	6.47411e10i	1.13147	−	1.01129i
$253$	−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	$0.907852\pi$
$258$	4.21112e10	+	1.88417e10i	0.591709	+	0.264747i
$259$			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	$-0.656234\pi$
$263$	−7.31435e10			−0.942703			−0.471352	+	0.881945i	$0.656234\pi$
$264$	−1.74667e10	+	7.86563e10i	−0.221306	+	0.996589i
$265$	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	$0.839589\pi$
$270$	5.66002e9	+	5.29633e10i	0.0648159	+	0.606510i
$271$		−	1.46478e11i		−	1.64972i	−0.565335	−	0.824861i	$-0.691253\pi$
$271$		−	1.46478e11i		−	1.64972i	0.565335	−	0.824861i	$-0.308747\pi$
$272$	−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
$276$	1.10816e10	−	3.34829e10i	0.114951	−	0.347322i
$277$	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	$0.848088\pi$
$282$	2.45144e10	−	5.47897e10i	0.230835	−	0.515915i
$283$		−	1.44522e9i		−	0.0133936i	−0.999978	−	0.00669679i	$-0.997868\pi$
$283$		−	1.44522e9i		−	0.0133936i	0.999978	−	0.00669679i	$-0.00213167\pi$
$284$	−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
$288$	−1.00252e11	−	5.98395e10i	−0.858667	−	0.512533i
$289$	−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	$-0.175574\pi$
$294$	6.81692e10	−	1.52358e11i	0.532139	−	1.18933i
$295$		−	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
$300$	−2.76805e10	+	8.36365e10i	−0.197301	+	0.596143i
$301$	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
$306$	−1.97853e11	+	1.43735e11i	−1.29002	+	0.937166i
$307$			2.14365e11i			1.37731i	0.725091	+	0.688654i	$0.241798\pi$
$307$			2.14365e11i			1.37731i	−0.725091	+	0.688654i	$0.758202\pi$
$308$	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	$-0.511227\pi$
$311$	−1.16357e10			−0.0705295			−0.0352647	+	0.999378i	$0.511227\pi$
$312$	1.72144e10	−	7.75205e10i	0.102848	−	0.463149i
$313$	−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	$-0.0182533\pi$
$318$	2.57110e11	+	1.15038e11i	1.40993	+	0.630842i
$319$			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
$324$	−6.13135e10	+	1.88645e11i	−0.309103	+	0.951029i
$325$	−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
$330$	−1.22450e11	−	5.47877e10i	−0.568391	−	0.254314i
$331$		−	4.53841e10i		−	0.207815i	−0.994587	−	0.103908i	$-0.966865\pi$
$331$		−	4.53841e10i		−	0.207815i	0.994587	−	0.103908i	$-0.0331346\pi$
$332$	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
$336$	−3.52102e11	−	4.15347e10i	−1.50710	−	0.177781i
$337$	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
$342$	−6.71613e10	+	4.87909e10i	−0.265461	+	0.192851i
$343$		−	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	$-0.695356\pi$
$347$	−3.11082e11			−1.15184			−0.575919	+	0.817507i	$0.695356\pi$
$348$	−1.98189e10	−	6.55932e9i	−0.0724393	−	0.0239747i
$349$	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	$0.969985\pi$
$354$	1.92138e11	−	4.29429e11i	0.650279	−	1.45337i
$355$		−	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	$-0.814430\pi$
$359$	−5.25472e11			−1.66965			−0.834823	+	0.550518i	$0.814430\pi$
$360$	1.31119e11	−	1.43505e11i	0.411439	−	0.450304i
$361$	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
$366$	1.08601e11	−	2.42723e11i	0.316350	−	0.707043i
$367$			3.26879e11i			0.940567i	0.882515	+	0.470284i	$0.155848\pi$
$367$			3.26879e11i			0.940567i	−0.882515	+	0.470284i	$0.844152\pi$
$368$	−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
$372$	−2.42447e11	−	8.02408e10i	−0.656408	−	0.217246i
$373$	−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
$378$	6.40078e10	+	5.98948e11i	0.161257	+	1.50896i
$379$		−	1.76715e11i		−	0.439944i	−0.975506	−	0.219972i	$-0.929403\pi$
$379$		−	1.76715e11i		−	0.439944i	0.975506	−	0.219972i	$-0.0705967\pi$
$380$	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	$-0.202194\pi$
$383$	6.77940e11			1.60989			0.804946	+	0.593348i	$0.202194\pi$
$384$	7.87416e10	+	4.18740e11i	0.184805	+	0.982775i
$385$	−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	$0.944708\pi$
$390$	1.20682e11	+	5.39965e10i	0.264151	+	0.118188i
$391$			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
$396$	−3.32914e11	−	3.72477e11i	−0.680305	−	0.761151i
$397$	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	$0.782749\pi$
$402$	4.93414e11	+	2.20767e11i	0.942311	+	0.421616i
$403$		−	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
$408$	8.71251e11	+	1.93473e11i	1.55658	+	0.345660i
$409$	−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
$414$	1.28528e11	+	1.76920e11i	0.215028	+	0.295989i
$415$			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	$-0.532743\pi$
$419$	−1.29569e11			−0.205371			−0.102685	+	0.994714i	$0.532743\pi$
$420$	1.85471e11	−	5.60399e11i	0.290840	−	0.878771i
$421$	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
$426$	1.27157e11	−	2.84197e11i	0.187068	−	0.418096i
$427$		−	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	$-0.657496\pi$
$431$	−6.80345e11			−0.949689			−0.474844	+	0.880070i	$0.657496\pi$
$432$	6.63972e11	−	2.88390e11i	0.917218	−	0.398385i
$433$	−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
$438$	−2.52718e11	+	5.64823e11i	−0.328097	+	0.733296i
$439$		−	8.34728e11i		−	1.07264i	−0.844014	−	0.536321i	$-0.819814\pi$
$439$		−	8.34728e11i		−	1.07264i	0.844014	−	0.536321i	$-0.180186\pi$
$440$	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	$-0.439018\pi$
$443$	3.08701e11			0.380821			0.190411	+	0.981705i	$0.439018\pi$
$444$	−3.46964e11	+	1.04835e12i	−0.423703	+	1.28022i
$445$	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	$0.784730\pi$
$450$	−3.21047e11	−	4.41926e11i	−0.369073	−	0.508034i
$451$			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
$456$	2.95746e11	+	6.56743e10i	0.320315	+	0.0711302i
$457$	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	$0.659900\pi$
$462$	−1.38476e12	−	6.19580e11i	−1.41412	−	0.632715i
$463$			1.97554e12i			1.99789i	0.0459672	+	0.998943i	$0.485363\pi$
$463$			1.97554e12i			1.99789i	−0.0459672	+	0.998943i	$0.514637\pi$
$464$	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	$-0.795370\pi$
$467$	−1.64533e12			−1.60077			−0.800383	+	0.599489i	$0.795370\pi$
$468$	3.28107e11	+	3.67098e11i	0.316161	+	0.353733i
$469$	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
$474$	−1.23384e12	−	5.52056e11i	−1.12268	−	0.502320i
$475$		−	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	$-0.416569\pi$
$479$	5.97084e11			0.518233			0.259117	+	0.965846i	$0.416569\pi$
$480$	−7.09303e11	−	1.15783e10i	−0.609882	−	0.00995537i
$481$	−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
$486$	−7.28189e11	−	9.91135e11i	−0.592081	−	0.805879i
$487$		−	1.40528e12i		−	1.13210i	−0.824372	−	0.566048i	$-0.808472\pi$
$487$		−	1.40528e12i		−	1.13210i	0.824372	−	0.566048i	$-0.191528\pi$
$488$	−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	$-0.518560\pi$
$491$	−1.50098e11			−0.116549			−0.0582746	+	0.998301i	$0.518560\pi$
$492$	−1.43682e12	−	4.75533e11i	−1.10550	−	0.365879i
$493$	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
$498$	−3.25365e11	+	7.27189e11i	−0.237049	+	0.529804i
$499$		−	2.05737e12i		−	1.48546i	−0.669592	−	0.742729i	$-0.733531\pi$
$499$		−	2.05737e12i		−	1.48546i	0.669592	−	0.742729i	$-0.266469\pi$
$500$	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	$-0.781114\pi$
$503$	−2.21881e12			−1.54548			−0.772740	+	0.634722i	$0.781114\pi$
$504$	1.48279e12	−	1.62286e12i	1.02363	−	1.12033i
$505$	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	$-0.0722604\pi$
$510$	−6.06865e11	+	1.35634e12i	−0.397216	+	0.887777i
$511$			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
$516$	9.91030e11	+	3.27993e11i	0.615408	+	0.203677i
$517$	−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	$0.983216\pi$
$522$	1.04721e11	−	7.60770e10i	0.0617329	−	0.0448473i
$523$		−	1.28372e11i		−	0.0750259i	−0.999296	−	0.0375129i	$-0.988056\pi$
$523$		−	1.28372e11i		−	0.0750259i	0.999296	−	0.0375129i	$-0.0119435\pi$
$524$	−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
$528$	−2.13581e11	+	1.81059e12i	−0.119594	+	1.01384i
$529$	−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
$534$	1.11984e12	+	5.01047e11i	0.595963	+	0.266650i
$535$			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
$540$	2.48369e11	+	1.17938e12i	0.125697	+	0.596872i
$541$	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
$546$	1.36476e12	+	6.10633e11i	0.657189	+	0.294044i
$547$			2.14818e12i			1.02595i	0.858403	+	0.512976i	$0.171457\pi$
$547$			2.14818e12i			1.02595i	−0.858403	+	0.512976i	$0.828543\pi$
$548$	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
$552$	1.73003e11	−	7.79071e11i	0.0793099	−	0.357150i
$553$	−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	$0.815194\pi$
$558$	1.28106e12	−	9.30658e11i	0.559392	−	0.406384i
$559$			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	$-0.0757600\pi$
$563$	4.63339e12			1.94362			0.971810	+	0.235766i	$0.0757600\pi$
$564$	4.26744e11	−	1.28940e12i	0.177587	−	0.536578i
$565$	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	$0.906797\pi$
$570$	−2.06000e11	+	4.60410e11i	−0.0817393	+	0.182687i
$571$		−	4.20925e12i		−	1.65708i	−0.559933	−	0.828538i	$-0.689173\pi$
$571$		−	4.20925e12i		−	1.65708i	0.559933	−	0.828538i	$-0.310827\pi$
$572$	−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
$576$	−2.39351e12	−	1.11816e12i	−0.906011	−	0.423255i
$577$	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
$582$	2.06572e11	−	4.61687e11i	0.0746307	−	0.166799i
$583$		−	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	$-0.353601\pi$
$587$	2.55370e12			0.887765			0.443883	+	0.896085i	$0.353601\pi$
$588$	1.18668e12	−	3.58554e12i	0.409388	−	1.23696i
$589$	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	$-0.0880137\pi$
$594$	3.07993e12	−	3.29143e11i	1.01509	−	0.108479i
$595$			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	$-0.530999\pi$
$599$	−6.12725e11			−0.194467			−0.0972333	+	0.995262i	$0.530999\pi$
$600$	−4.32141e11	+	1.94603e12i	−0.136127	+	0.613012i
$601$	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
$606$	5.15905e11	+	2.30830e11i	0.155397	+	0.0695289i
$607$			3.84906e12i			1.15081i	0.817867	+	0.575407i	$0.195156\pi$
$607$			3.84906e12i			1.15081i	−0.817867	+	0.575407i	$0.804844\pi$
$608$	−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
$612$	−4.12580e12	+	3.68758e12i	−1.18885	+	1.06258i
$613$	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	$0.636761\pi$
$618$	−9.47979e11	−	4.24152e11i	−0.261427	−	0.116970i
$619$			3.04023e12i			0.832335i	0.909288	+	0.416167i	$0.136627\pi$
$619$			3.04023e12i			0.832335i	−0.909288	+	0.416167i	$0.863373\pi$
$620$	−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
$624$	2.10497e11	−	1.78444e12i	0.0555796	−	0.471164i
$625$	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
$630$	2.15115e12	+	2.96108e12i	0.544049	+	0.748890i
$631$		−	6.69357e12i		−	1.68084i	−0.541938	−	0.840419i	$-0.682309\pi$
$631$		−	6.69357e12i		−	1.68084i	0.541938	−	0.840419i	$-0.317691\pi$
$632$	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
$636$	6.05075e12	+	2.00257e12i	1.46640	+	0.485323i
$637$	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	$-0.112718\pi$
$642$	−1.39611e11	+	3.12031e11i	−0.0324349	+	0.0724920i
$643$			3.00266e12i			0.692718i	0.938102	+	0.346359i	$0.112582\pi$
$643$			3.00266e12i			0.692718i	−0.938102	+	0.346359i	$0.887418\pi$
$644$	−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	$-0.771851\pi$
$647$	−6.72107e12			−1.50789			−0.753944	+	0.656938i	$0.771851\pi$
$648$	−9.49475e11	+	4.38678e12i	−0.211542	+	0.977369i
$649$	−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	$-0.220871\pi$
$654$	2.37437e12	−	5.30671e12i	0.507515	−	1.13429i
$655$		−	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	$-0.293721\pi$
$659$	5.84499e12			1.20726			0.603628	+	0.797266i	$0.293721\pi$
$660$	−2.88170e12	−	9.53735e11i	−0.591155	−	0.195650i
$661$	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
$666$	−4.02420e12	−	5.53936e12i	−0.792584	−	1.09100i
$667$		−	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
$672$	−8.02132e12	−	1.30936e11i	−1.51735	−	0.0247683i
$673$	−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	$0.836568\pi$
$678$	4.12865e12	+	1.84727e12i	0.750369	+	0.335736i
$679$		−	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	$-0.722956\pi$
$683$	−7.33129e12			−1.28910			−0.644551	+	0.764561i	$0.722956\pi$
$684$	−1.40050e12	+	1.25175e12i	−0.244642	+	0.218658i
$685$	−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
$690$	1.21284e12	+	5.42657e11i	0.203696	+	0.0911391i
$691$			5.56872e12i			0.929190i	0.885523	+	0.464595i	$0.153800\pi$
$691$			5.56872e12i			0.929190i	−0.885523	+	0.464595i	$0.846200\pi$
$692$	−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
$696$	−4.61141e11	−	1.02402e11i	−0.0744890	−	0.0165413i
$697$	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	$0.804954\pi$
$702$	−3.03546e12	+	3.24390e11i	−0.471745	+	0.0504139i
$703$		−	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
$708$	3.34472e12	−	1.01060e13i	0.500276	−	1.51158i
$709$	−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
$714$	−6.86288e12	+	1.53385e13i	−0.988245	+	2.20873i
$715$		−	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	$-0.490959\pi$
$719$	4.07037e11			0.0568007			0.0284003	+	0.999597i	$0.490959\pi$
$720$	2.62402e12	−	3.53000e12i	0.363891	−	0.489530i
$721$	−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
$726$	−1.28906e11	+	2.88105e11i	−0.0172210	+	0.0384889i
$727$		−	3.08205e12i		−	0.409199i	−0.978846	−	0.204599i	$-0.934411\pi$
$727$		−	3.08205e12i		−	0.409199i	0.978846	−	0.204599i	$-0.0655892\pi$
$728$	−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
$732$	1.89051e12	−	5.71216e12i	0.243376	−	0.735360i
$733$	−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
$738$	7.59198e12	−	5.51537e12i	0.942110	−	0.684418i
$739$			8.43327e12i			1.04015i	0.854121	+	0.520075i	$0.174096\pi$
$739$			8.43327e12i			1.04015i	−0.854121	+	0.520075i	$0.825904\pi$
$740$	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	$-0.664326\pi$
$743$	−8.20109e12			−0.987239			−0.493619	+	0.869678i	$0.664326\pi$
$744$	−5.64119e12	−	1.25270e12i	−0.674982	−	0.149889i
$745$	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
$750$	−7.85406e12	−	3.51412e12i	−0.906397	−	0.405547i
$751$			7.34852e12i			0.842985i	0.906832	+	0.421493i	$0.138494\pi$
$751$			7.34852e12i			0.842985i	−0.906832	+	0.421493i	$0.861506\pi$
$752$	−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
$756$	2.80874e12	+	1.33373e13i	0.312726	+	1.48498i
$757$	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	$-0.387820\pi$
$762$	−1.63741e12	−	7.32622e11i	−0.175938	−	0.0787195i
$763$		−	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
$768$	2.72889e12	+	9.24681e12i	0.283048	+	0.959106i
$769$	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	$0.764586\pi$
$774$	−5.23649e12	+	3.80417e12i	−0.524452	+	0.381000i
$775$			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
$780$	2.84009e12	+	9.39963e11i	0.274730	+	0.0909254i
$781$	−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
$786$	4.31140e12	−	9.63596e12i	0.402918	−	0.900521i
$787$		−	2.61116e12i		−	0.242631i	−0.992614	−	0.121316i	$-0.961289\pi$
$787$		−	2.61116e12i		−	0.242631i	0.992614	−	0.121316i	$-0.0387113\pi$
$788$	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
$792$	−8.34514e12	−	7.62488e12i	−0.753651	−	0.688604i
$793$	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	$-0.286171\pi$
$798$	−2.32961e12	+	5.20666e12i	−0.203362	+	0.454513i
$799$			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
$804$	1.16118e13	+	3.84308e12i	0.980051	+	0.324360i
$805$	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	$0.889230\pi$
$810$	−6.83748e12	−	3.01536e12i	−0.558102	−	0.246125i
$811$		−	1.29011e13i		−	1.04721i	−0.851962	−	0.523604i	$-0.824587\pi$
$811$		−	1.29011e13i		−	1.04721i	0.851962	−	0.523604i	$-0.175413\pi$
$812$	−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
$816$	2.00553e13	+	2.36577e12i	1.58352	+	0.186796i
$817$	−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	$-0.0452598\pi$
$822$	−1.61858e13	−	7.24195e12i	−1.23654	−	0.553264i
$823$			1.96141e13i			1.49028i	0.666906	+	0.745142i	$0.267618\pi$
$823$			1.96141e13i			1.49028i	−0.666906	+	0.745142i	$0.732382\pi$
$824$	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	$-0.317252\pi$
$827$	1.46111e13			1.08619			0.543097	+	0.839670i	$0.317252\pi$
$828$	3.29743e12	+	3.68928e12i	0.243803	+	0.272776i
$829$	−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
$834$	8.03533e12	+	3.59523e12i	0.575117	+	0.257323i
$835$		−	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	$-0.750629\pi$
$839$	−2.03377e13			−1.41701			−0.708504	+	0.705707i	$0.750629\pi$
$840$	2.89552e12	−	1.30392e13i	0.200664	−	0.903637i
$841$	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
$846$	4.94951e12	+	6.81306e12i	0.332197	+	0.457273i
$847$			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
$852$	2.21354e12	−	6.68819e12i	0.143916	−	0.434841i
$853$	−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	$-0.0476078\pi$
$858$	3.14002e12	−	7.01793e12i	0.197806	−	0.442096i
$859$		−	2.48462e13i		−	1.55701i	−0.627639	−	0.778504i	$-0.715979\pi$
$859$		−	2.48462e13i		−	1.55701i	0.627639	−	0.778504i	$-0.284021\pi$
$860$	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	$-0.237029\pi$
$863$	2.39639e13			1.47065			0.735325	+	0.677714i	$0.237029\pi$
$864$	1.42887e13	−	8.00850e12i	0.872327	−	0.488922i
$865$	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
$870$	3.21205e11	−	7.17893e11i	0.0190084	−	0.0424838i
$871$			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
$876$	−4.39927e12	+	1.32924e13i	−0.252413	+	0.762665i
$877$	−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	$-0.134322\pi$
$882$	1.37635e13	+	1.89456e13i	0.765807	+	1.05414i
$883$		−	3.39926e12i		−	0.188175i	−0.995564	−	0.0940874i	$-0.970007\pi$
$883$		−	3.39926e12i		−	0.188175i	0.995564	−	0.0940874i	$-0.0299933\pi$
$884$	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	$-0.355496\pi$
$887$	1.61695e13			0.877080			0.438540	+	0.898712i	$0.355496\pi$
$888$	−5.41672e12	+	2.43927e13i	−0.292333	+	1.31644i
$889$	−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
$894$	2.50258e13	+	1.11972e13i	1.31030	+	0.586262i
$895$		−	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
$900$	−8.23660e12	−	9.21541e12i	−0.418463	−	0.468191i
$901$	−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
$906$	−2.06257e13	−	9.22851e12i	−1.01703	−	0.455045i
$907$			2.80892e13i			1.37818i	0.724676	+	0.689090i	$0.241989\pi$
$907$			2.80892e13i			1.37818i	−0.724676	+	0.689090i	$0.758011\pi$
$908$	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	$-0.579892\pi$
$911$	−1.03264e13			−0.496724			−0.248362	+	0.968667i	$0.579892\pi$
$912$	6.80778e12	+	8.03061e11i	0.325858	+	0.0384390i
$913$	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
$918$	−3.64581e12	−	3.41155e13i	−0.169435	−	1.58547i
$919$		−	2.82634e12i		−	0.130709i	−0.997862	−	0.0653544i	$-0.979182\pi$
$919$		−	2.82634e12i		−	0.130709i	0.997862	−	0.0653544i	$-0.0208178\pi$
$920$	−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
$924$	−3.25885e13	−	1.07855e13i	−1.47075	−	0.486764i
$925$	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	$-0.285267\pi$
$930$	3.92934e12	−	8.78206e12i	0.172245	−	0.384967i
$931$			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
$936$	8.22463e12	+	7.51477e12i	0.350248	+	0.320018i
$937$	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	$0.977445\pi$
$942$	−8.93190e12	+	1.99628e13i	−0.369585	+	0.826023i
$943$		−	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	$-0.798167\pi$
$947$	−3.98781e13			−1.61124			−0.805619	+	0.592434i	$0.798167\pi$
$948$	−2.90369e13	−	9.61011e12i	−1.16765	−	0.386448i
$949$	−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	$0.618301\pi$
$954$	−3.19715e13	+	2.32264e13i	−1.24967	+	0.907851i
$955$		−	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
$960$	−1.59942e13	+	1.35918e12i	−0.607773	+	0.0516482i
$961$	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
$966$	1.37157e13	+	6.13677e12i	0.506781	+	0.226748i
$967$		−	2.64896e13i		−	0.974220i	−0.873341	−	0.487110i	$-0.838051\pi$
$967$		−	2.64896e13i		−	0.974220i	0.873341	−	0.487110i	$-0.161949\pi$
$968$	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	$-0.229575\pi$
$971$	4.16057e13			1.50199			0.750994	+	0.660309i	$0.229575\pi$
$972$	−1.86563e13	−	2.06494e13i	−0.670391	−	0.742008i
$973$	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	$0.923850\pi$
$978$	2.21856e13	+	9.92644e12i	0.775436	+	0.346952i
$979$		−	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	$-0.631211\pi$
$983$	−2.34570e13			−0.801274			−0.400637	+	0.916237i	$0.631211\pi$
$984$	−3.34315e13	−	7.42389e12i	−1.13678	−	0.252437i
$985$	−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
$990$	1.52266e13	−	1.10617e13i	0.503784	−	0.365986i
$991$			1.82621e13i			0.601476i	0.953707	+	0.300738i	$0.0972330\pi$
$991$			1.82621e13i			0.601476i	−0.953707	+	0.300738i	$0.902767\pi$
$992$	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
$996$	−5.66390e12	+	1.71134e13i	−0.182368	+	0.551023i
$997$	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.11.15	yes	16
3.2	odd	2	inner	12.10.b.a.11.2	yes	16
4.3	odd	2	inner	12.10.b.a.11.1	✓	16
8.3	odd	2		192.10.c.d.191.6		16
8.5	even	2		192.10.c.d.191.11		16
12.11	even	2	inner	12.10.b.a.11.16	yes	16
24.5	odd	2		192.10.c.d.191.5		16
24.11	even	2		192.10.c.d.191.12		16

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

\(f(q)\)	\(=\)	\(q+(22.5119 - 2.28368i) q^{2} +(-69.9307 + 121.625i) q^{3} +(501.570 - 102.820i) q^{4} +852.450i q^{5} +(-1296.52 + 2897.71i) q^{6} +9640.14i q^{7} +(11056.5 - 3460.10i) q^{8} +(-9902.41 - 17010.7i) q^{9} +O(q^{10})\)	\(q+(22.5119 - 2.28368i) q^{2} +(-69.9307 + 121.625i) q^{3} +(501.570 - 102.820i) q^{4} +852.450i q^{5} +(-1296.52 + 2897.71i) 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} +(-22569.6 + 68193.8i) 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} +(-261769. - 360328. 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} +(-352350. + 1.58671e6i) 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} +(-2.47016e6 - 1.10522e6i) 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} +(-6.71578e6 - 7.51387e6i) 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} +(-2.79344e7 - 1.24986e7i) 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} +(-4.30852e6 + 3.65245e7i) 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} +(6.21307e7 - 6.63971e6i) 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} +(-5.81318e7 - 1.92394e7i) 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} +(-6.42708e7 + 1.43645e8i) 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} +(-1.68344e8 - 1.53815e8i) 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} +(6.33427e7 - 1.41571e8i) 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} +(-6.57398e8 - 2.17574e8i) 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} +(3.07162e8 - 2.23145e8i) 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} +(-1.35823e7 + 8.32075e8i) 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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