LMFDB - Embedded newform 112.10.i.c.65.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,10,Mod(65,112)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("112.65");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	112.i (of order $3$, degree $2$, not 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:	$57.6840136504$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 430 x^{8} + 61 x^{7} + 146753 x^{6} + 23608 x^{5} + 16136944 x^{4} + 30575648 x^{3} + \cdots + 761760000 $ x^10 - x^9 + 430x^8 + 61x^7 + 146753x^6 + 23608x^5 + 16136944x^4 + 30575648x^3 + 1399072384x^2 + 1034227200x + 761760000
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{3}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			65.5
Root			$-5.11725 + 8.86334i$ of defining polynomial
Character	$\chi$	$=$	112.65
Dual form			112.10.i.c.81.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(79.7348 + 138.105i) q^{3} +(1014.15 - 1756.56i) q^{5} +(4235.51 + 4734.35i) q^{7} +(-2873.78 + 4977.54i) q^{9} +O(q^{10})$	\(q+(79.7348 + 138.105i) q^{3} +(1014.15 - 1756.56i) q^{5} +(4235.51 + 4734.35i) q^{7} +(-2873.78 + 4977.54i) q^{9} +(4289.29 + 7429.26i) q^{11} -38438.1 q^{13} +323452. q^{15} +(150942. + 261439. i) q^{17} +(-458143. + 793527. i) q^{19} +(-316119. + 962436. i) q^{21} +(966607. - 1.67421e6i) q^{23} +(-1.08043e6 - 1.87136e6i) q^{25} +2.22228e6 q^{27} +4.52529e6 q^{29} +(147255. + 255054. i) q^{31} +(-684011. + 1.18474e6i) q^{33} +(1.26116e7 - 2.63858e6i) q^{35} +(8.05632e6 - 1.39540e7i) q^{37} +(-3.06486e6 - 5.30849e6i) q^{39} +1.28783e7 q^{41} -1.15410e7 q^{43} +(5.82889e6 + 1.00959e7i) q^{45} +(-1.39268e7 + 2.41219e7i) q^{47} +(-4.47455e6 + 4.01048e7i) q^{49} +(-2.40707e7 + 4.16916e7i) q^{51} +(2.11827e7 + 3.66896e7i) q^{53} +1.73999e7 q^{55} -1.46120e8 q^{57} +(1.17321e6 + 2.03205e6i) q^{59} +(4.34201e6 - 7.52057e6i) q^{61} +(-3.57374e7 + 7.47691e6i) q^{63} +(-3.89820e7 + 6.75188e7i) q^{65} +(1.26144e8 + 2.18488e8i) q^{67} +3.08289e8 q^{69} +2.50094e8 q^{71} +(-2.32270e7 - 4.02303e7i) q^{73} +(1.72296e8 - 2.98426e8i) q^{75} +(-1.70054e7 + 5.17737e7i) q^{77} +(5.53584e7 - 9.58836e7i) q^{79} +(2.33758e8 + 4.04880e8i) q^{81} -2.81805e8 q^{83} +6.12310e8 q^{85} +(3.60823e8 + 6.24964e8i) q^{87} +(1.45677e8 - 2.52321e8i) q^{89} +(-1.62805e8 - 1.81980e8i) q^{91} +(-2.34827e7 + 4.06733e7i) q^{93} +(9.29250e8 + 1.60951e9i) q^{95} +1.01107e8 q^{97} -4.93059e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 161 q^{3} + 1533 q^{5} + 1036 q^{7} - 35734 q^{9}+O(q^{10}) $ 10 * q - 161 * q^3 + 1533 * q^5 + 1036 * q^7 - 35734 * q^9	$ 10 q - 161 q^{3} + 1533 q^{5} + 1036 q^{7} - 35734 q^{9} - 42213 q^{11} - 319676 q^{13} - 151394 q^{15} + 324681 q^{17} + 16121 q^{19} - 1557857 q^{21} - 2638863 q^{23} - 1304092 q^{25} + 18331558 q^{27} + 15292500 q^{29} - 19179237 q^{31} + 1689359 q^{33} + 43746759 q^{35} + 39566985 q^{37} + 44299486 q^{39} - 53436852 q^{41} - 101835992 q^{43} + 85098230 q^{45} - 32509659 q^{47} - 49024598 q^{49} - 44168403 q^{51} - 25714707 q^{53} + 144695222 q^{55} - 121710346 q^{57} - 46776513 q^{59} - 113075039 q^{61} - 318071530 q^{63} - 338113566 q^{65} + 126707879 q^{67} + 1323616182 q^{69} + 1188736032 q^{71} - 859257651 q^{73} + 169061732 q^{75} + 1911891891 q^{77} + 527065417 q^{79} + 551662715 q^{81} + 144863208 q^{83} - 1197360222 q^{85} + 340781350 q^{87} + 1661554797 q^{89} - 726641384 q^{91} - 423057489 q^{93} + 1197123495 q^{95} + 869770188 q^{97} + 1900777180 q^{99}+O(q^{100}) $ 10 * q - 161 * q^3 + 1533 * q^5 + 1036 * q^7 - 35734 * q^9 - 42213 * q^11 - 319676 * q^13 - 151394 * q^15 + 324681 * q^17 + 16121 * q^19 - 1557857 * q^21 - 2638863 * q^23 - 1304092 * q^25 + 18331558 * q^27 + 15292500 * q^29 - 19179237 * q^31 + 1689359 * q^33 + 43746759 * q^35 + 39566985 * q^37 + 44299486 * q^39 - 53436852 * q^41 - 101835992 * q^43 + 85098230 * q^45 - 32509659 * q^47 - 49024598 * q^49 - 44168403 * q^51 - 25714707 * q^53 + 144695222 * q^55 - 121710346 * q^57 - 46776513 * q^59 - 113075039 * q^61 - 318071530 * q^63 - 338113566 * q^65 + 126707879 * q^67 + 1323616182 * q^69 + 1188736032 * q^71 - 859257651 * q^73 + 169061732 * q^75 + 1911891891 * q^77 + 527065417 * q^79 + 551662715 * q^81 + 144863208 * q^83 - 1197360222 * q^85 + 340781350 * q^87 + 1661554797 * q^89 - 726641384 * q^91 - 423057489 * q^93 + 1197123495 * q^95 + 869770188 * q^97 + 1900777180 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	79.7348	+	138.105i	0.568332	+	0.984381i	0.996731	+	0.0807907i	$0.0257445\pi$
$3$	79.7348	+	138.105i	0.568332	+	0.984381i	−0.428399	+	0.903590i	$0.640922\pi$
$4$		0			0
$5$	1014.15	−	1756.56i	0.725666	−	1.25689i	−0.233034	−	0.972469i	$-0.574865\pi$
$5$	1014.15	−	1756.56i	0.725666	−	1.25689i	0.958699	−	0.284421i	$-0.0918014\pi$
$6$		0			0
$7$	4235.51	+	4734.35i	0.666752	+	0.745280i
$7$	4235.51	+	4734.35i	0.666752	+	0.745280i
$8$		0			0
$9$	−2873.78	+	4977.54i	−0.146003	+	0.252885i
$10$		0			0
$11$	4289.29	+	7429.26i	0.0883320	+	0.152996i	0.906806	−	0.421548i	$-0.138513\pi$
$11$	4289.29	+	7429.26i	0.0883320	+	0.152996i	−0.818474	+	0.574543i	$0.805180\pi$
$12$		0			0
$13$	−38438.1			−0.373265			−0.186633	−	0.982430i	$-0.559757\pi$
$13$	−38438.1			−0.373265			−0.186633	+	0.982430i	$0.559757\pi$
$14$		0			0
$15$	323452.			1.64968
$16$		0			0
$17$	150942.	+	261439.i	0.438318	+	0.759190i	0.997560	−	0.0698150i	$-0.0222409\pi$
$17$	150942.	+	261439.i	0.438318	+	0.759190i	−0.559242	+	0.829005i	$0.688908\pi$
$18$		0			0
$19$	−458143.	+	793527.i	−0.806510	+	1.39692i	0.108757	+	0.994068i	$0.465313\pi$
$19$	−458143.	+	793527.i	−0.806510	+	1.39692i	−0.915267	+	0.402848i	$0.868020\pi$
$20$		0			0
$21$	−316119.	+	962436.i	−0.354702	+	1.07990i
$22$		0			0
$23$	966607.	−	1.67421e6i	0.720236	−	1.24749i	−0.240669	−	0.970607i	$-0.577367\pi$
$23$	966607.	−	1.67421e6i	0.720236	−	1.24749i	0.960905	−	0.276878i	$-0.0892999\pi$
$24$		0			0
$25$	−1.08043e6	−	1.87136e6i	−0.553182	−	0.958139i
$26$		0			0
$27$	2.22228e6			0.804751
$28$		0			0
$29$	4.52529e6			1.18811			0.594054	−	0.804425i	$-0.297527\pi$
$29$	4.52529e6			1.18811			0.594054	+	0.804425i	$0.297527\pi$
$30$		0			0
$31$	147255.	+	255054.i	0.0286380	+	0.0496025i	0.879989	−	0.474994i	$-0.157550\pi$
$31$	147255.	+	255054.i	0.0286380	+	0.0496025i	−0.851351	+	0.524596i	$0.824216\pi$
$32$		0			0
$33$	−684011.	+	1.18474e6i	−0.100404	+	0.173905i
$34$		0			0
$35$	1.26116e7	−	2.63858e6i	1.42057	−	0.297210i
$36$		0			0
$37$	8.05632e6	−	1.39540e7i	0.706690	−	1.22402i	−0.259388	−	0.965773i	$-0.583521\pi$
$37$	8.05632e6	−	1.39540e7i	0.706690	−	1.22402i	0.966078	−	0.258250i	$-0.0831458\pi$
$38$		0			0
$39$	−3.06486e6	−	5.30849e6i	−0.212139	−	0.367435i
$40$		0			0
$41$	1.28783e7			0.711757			0.355878	−	0.934532i	$-0.384182\pi$
$41$	1.28783e7			0.711757			0.355878	+	0.934532i	$0.384182\pi$
$42$		0			0
$43$	−1.15410e7			−0.514795			−0.257398	−	0.966306i	$-0.582865\pi$
$43$	−1.15410e7			−0.514795			−0.257398	+	0.966306i	$0.582865\pi$
$44$		0			0
$45$	5.82889e6	+	1.00959e7i	0.211899	+	0.367020i
$46$		0			0
$47$	−1.39268e7	+	2.41219e7i	−0.416304	+	0.721059i	−0.995564	−	0.0940834i	$-0.970008\pi$
$47$	−1.39268e7	+	2.41219e7i	−0.416304	+	0.721059i	0.579261	+	0.815142i	$0.303341\pi$
$48$		0			0
$49$	−4.47455e6	+	4.01048e7i	−0.110884	+	0.993833i
$50$		0			0
$51$	−2.40707e7	+	4.16916e7i	−0.498221	+	0.862944i
$52$		0			0
$53$	2.11827e7	+	3.66896e7i	0.368757	+	0.638706i	0.989372	−	0.145410i	$-0.0464500\pi$
$53$	2.11827e7	+	3.66896e7i	0.368757	+	0.638706i	−0.620614	+	0.784116i	$0.713117\pi$
$54$		0			0
$55$	1.73999e7			0.256398
$56$		0			0
$57$	−1.46120e8			−1.83346
$58$		0			0
$59$	1.17321e6	+	2.03205e6i	0.0126049	+	0.0218324i	0.872259	−	0.489044i	$-0.162654\pi$
$59$	1.17321e6	+	2.03205e6i	0.0126049	+	0.0218324i	−0.859654	+	0.510876i	$0.829321\pi$
$60$		0			0
$61$	4.34201e6	−	7.52057e6i	0.0401519	−	0.0695451i	−0.845251	−	0.534369i	$-0.820549\pi$
$61$	4.34201e6	−	7.52057e6i	0.0401519	−	0.0695451i	0.885403	+	0.464824i	$0.153882\pi$
$62$		0			0
$63$	−3.57374e7	+	7.47691e6i	−0.285818	+	0.0597984i
$64$		0			0
$65$	−3.89820e7	+	6.75188e7i	−0.270866	+	0.469153i
$66$		0			0
$67$	1.26144e8	+	2.18488e8i	0.764771	+	1.32462i	0.940368	+	0.340159i	$0.110481\pi$
$67$	1.26144e8	+	2.18488e8i	0.764771	+	1.32462i	−0.175597	+	0.984462i	$0.556186\pi$
$68$		0			0
$69$	3.08289e8			1.63733
$70$		0			0
$71$	2.50094e8			1.16799			0.583997	−	0.811756i	$-0.301488\pi$
$71$	2.50094e8			1.16799			0.583997	+	0.811756i	$0.301488\pi$
$72$		0			0
$73$	−2.32270e7	−	4.02303e7i	−0.0957282	−	0.165806i	0.814184	−	0.580607i	$-0.197185\pi$
$73$	−2.32270e7	−	4.02303e7i	−0.0957282	−	0.165806i	−0.909912	+	0.414801i	$0.863851\pi$
$74$		0			0
$75$	1.72296e8	−	2.98426e8i	0.628782	−	1.08908i
$76$		0			0
$77$	−1.70054e7	+	5.17737e7i	−0.0551289	+	0.167842i
$78$		0			0
$79$	5.53584e7	−	9.58836e7i	0.159905	−	0.276963i	−0.774929	−	0.632048i	$-0.782215\pi$
$79$	5.53584e7	−	9.58836e7i	0.159905	−	0.276963i	0.934834	+	0.355084i	$0.115548\pi$
$80$		0			0
$81$	2.33758e8	+	4.04880e8i	0.603369	+	1.04507i
$82$		0			0
$83$	−2.81805e8			−0.651774			−0.325887	−	0.945409i	$-0.605663\pi$
$83$	−2.81805e8			−0.651774			−0.325887	+	0.945409i	$0.605663\pi$
$84$		0			0
$85$	6.12310e8			1.27229
$86$		0			0
$87$	3.60823e8	+	6.24964e8i	0.675240	+	1.16955i
$88$		0			0
$89$	1.45677e8	−	2.52321e8i	0.246115	−	0.426283i	−0.716330	−	0.697762i	$-0.754179\pi$
$89$	1.45677e8	−	2.52321e8i	0.246115	−	0.426283i	0.962444	+	0.271479i	$0.0875127\pi$
$90$		0			0
$91$	−1.62805e8	−	1.81980e8i	−0.248875	−	0.278187i
$92$		0			0
$93$	−2.34827e7	+	4.06733e7i	−0.0325518	+	0.0563815i
$94$		0			0
$95$	9.29250e8	+	1.60951e9i	1.17051	+	2.02739i
$96$		0			0
$97$	1.01107e8			0.115960			0.0579798	−	0.998318i	$-0.481534\pi$
$97$	1.01107e8			0.115960			0.0579798	+	0.998318i	$0.481534\pi$
$98$		0			0
$99$	−4.93059e7			−0.0515871
$100$		0			0
$101$	5.29724e8	+	9.17509e8i	0.506528	+	0.877332i	0.999971	+	0.00755447i	$0.00240468\pi$
$101$	5.29724e8	+	9.17509e8i	0.506528	+	0.877332i	−0.493443	+	0.869778i	$0.664262\pi$
$102$		0			0
$103$	−2.52542e8	+	4.37415e8i	−0.221088	+	0.382936i	−0.955139	−	0.296159i	$-0.904294\pi$
$103$	−2.52542e8	+	4.37415e8i	−0.221088	+	0.382936i	0.734050	+	0.679095i	$0.237628\pi$
$104$		0			0
$105$	1.36998e9	+	1.53133e9i	1.09993	+	1.22947i
$106$		0			0
$107$	−943656.	+	1.63446e6i	−0.000695964	+	0.00120544i	−0.866373	−	0.499397i	$-0.833555\pi$
$107$	−943656.	+	1.63446e6i	−0.000695964	+	0.00120544i	0.865677	+	0.500603i	$0.166888\pi$
$108$		0			0
$109$	5.32240e7	+	9.21867e7i	0.0361151	+	0.0625531i	0.883518	−	0.468397i	$-0.155168\pi$
$109$	5.32240e7	+	9.21867e7i	0.0361151	+	0.0625531i	−0.847403	+	0.530950i	$0.821835\pi$
$110$		0			0
$111$	2.56948e9			1.60654
$112$		0			0
$113$	−2.40785e9			−1.38924			−0.694620	−	0.719377i	$-0.744427\pi$
$113$	−2.40785e9			−1.38924			−0.694620	+	0.719377i	$0.744427\pi$
$114$		0			0
$115$	−1.96057e9	−	3.39580e9i	−1.04530	−	1.81051i
$116$		0			0
$117$	1.10463e8	−	1.91327e8i	0.0544980	−	0.0943932i
$118$		0			0
$119$	−5.98429e8	+	1.82194e9i	−0.273559	+	0.832861i
$120$		0			0
$121$	1.14218e9	−	1.97831e9i	0.484395	−	0.838997i
$122$		0			0
$123$	1.02685e9	+	1.77856e9i	0.404515	+	0.700640i
$124$		0			0
$125$	−4.21360e8			−0.154368
$126$		0			0
$127$	−1.51077e9			−0.515326			−0.257663	−	0.966235i	$-0.582952\pi$
$127$	−1.51077e9			−0.515326			−0.257663	+	0.966235i	$0.582952\pi$
$128$		0			0
$129$	−9.20218e8	−	1.59386e9i	−0.292575	−	0.506755i
$130$		0			0
$131$	−1.02677e8	+	1.77843e8i	−0.0304617	+	0.0527612i	−0.880854	−	0.473387i	$-0.843031\pi$
$131$	−1.02677e8	+	1.77843e8i	−0.0304617	+	0.0527612i	0.850393	+	0.526149i	$0.176364\pi$
$132$		0			0
$133$	−5.69730e9	+	1.19198e9i	−1.57884	+	0.330321i
$134$		0			0
$135$	2.25372e9	−	3.90356e9i	0.583980	−	1.01148i
$136$		0			0
$137$	2.94515e9	+	5.10114e9i	0.714273	+	1.23716i	0.963239	+	0.268645i	$0.0865759\pi$
$137$	2.94515e9	+	5.10114e9i	0.714273	+	1.23716i	−0.248966	+	0.968512i	$0.580091\pi$
$138$		0			0
$139$	−1.53632e9			−0.349073			−0.174537	−	0.984651i	$-0.555843\pi$
$139$	−1.53632e9			−0.349073			−0.174537	+	0.984651i	$0.555843\pi$
$140$		0			0
$141$	−4.44179e9			−0.946395
$142$		0			0
$143$	−1.64872e8	−	2.85567e8i	−0.0329712	−	0.0571079i
$144$		0			0
$145$	4.58932e9	−	7.94893e9i	0.862169	−	1.49332i
$146$		0			0
$147$	−5.89544e9	+	2.57979e9i	−1.04133	+	0.455676i
$148$		0			0
$149$	3.06047e8	−	5.30089e8i	0.0508686	−	0.0881070i	−0.839470	−	0.543406i	$-0.817134\pi$
$149$	3.06047e8	−	5.30089e8i	0.0508686	−	0.0881070i	0.890338	+	0.455299i	$0.150468\pi$
$150$		0			0
$151$	5.27233e8	+	9.13194e8i	0.0825289	+	0.142944i	0.904336	−	0.426822i	$-0.140367\pi$
$151$	5.27233e8	+	9.13194e8i	0.0825289	+	0.142944i	−0.821807	+	0.569766i	$0.807034\pi$
$152$		0			0
$153$	−1.73510e9			−0.255984
$154$		0			0
$155$	5.97355e8			0.0831266
$156$		0			0
$157$	1.84813e9	+	3.20105e9i	0.242764	+	0.420479i	0.961500	−	0.274803i	$-0.0886128\pi$
$157$	1.84813e9	+	3.20105e9i	0.242764	+	0.420479i	−0.718737	+	0.695282i	$0.755279\pi$
$158$		0			0
$159$	−3.37800e9	+	5.85087e9i	−0.419153	+	0.725995i
$160$		0			0
$161$	1.20204e10	−	2.51488e9i	1.40994	−	0.294986i
$162$		0			0
$163$	6.57764e9	−	1.13928e10i	0.729837	−	1.26412i	−0.227114	−	0.973868i	$-0.572929\pi$
$163$	6.57764e9	−	1.13928e10i	0.729837	−	1.26412i	0.956952	−	0.290247i	$-0.0937375\pi$
$164$		0			0
$165$	1.38738e9	+	2.40301e9i	0.145719	+	0.252393i
$166$		0			0
$167$	−6.15786e9			−0.612641			−0.306320	−	0.951928i	$-0.599098\pi$
$167$	−6.15786e9			−0.612641			−0.306320	+	0.951928i	$0.599098\pi$
$168$		0			0
$169$	−9.12701e9			−0.860673
$170$		0			0
$171$	−2.63321e9	−	4.56085e9i	−0.235506	−	0.407909i
$172$		0			0
$173$	7.73798e9	−	1.34026e10i	0.656780	−	1.13758i	−0.324664	−	0.945829i	$-0.605251\pi$
$173$	7.73798e9	−	1.34026e10i	0.656780	−	1.13758i	0.981444	−	0.191747i	$-0.0614155\pi$
$174$		0			0
$175$	4.28351e9	−	1.30413e10i	0.345246	−	1.05112i
$176$		0			0
$177$	−1.87091e8	+	3.24051e8i	−0.0143276	+	0.0248161i
$178$		0			0
$179$	−1.98868e9	−	3.44450e9i	−0.144786	−	0.250777i	0.784507	−	0.620120i	$-0.212916\pi$
$179$	−1.98868e9	−	3.44450e9i	−0.144786	−	0.250777i	−0.929293	+	0.369343i	$0.879583\pi$
$180$		0			0
$181$	−2.68948e10			−1.86258			−0.931288	−	0.364283i	$-0.881314\pi$
$181$	−2.68948e10			−1.86258			−0.931288	+	0.364283i	$0.881314\pi$
$182$		0			0
$183$	1.38484e9			0.0912785
$184$		0			0
$185$	−1.63406e10	−	2.83028e10i	−1.02564	−	1.77646i
$186$		0			0
$187$	−1.29487e9	+	2.24277e9i	−0.0774351	+	0.134121i
$188$		0			0
$189$	9.41248e9	+	1.05210e10i	0.536569	+	0.599765i
$190$		0			0
$191$	8.68177e8	−	1.50373e9i	0.0472018	−	0.0817559i	−0.841459	−	0.540321i	$-0.818303\pi$
$191$	8.68177e8	−	1.50373e9i	0.0472018	−	0.0817559i	0.888661	+	0.458565i	$0.151636\pi$
$192$		0			0
$193$	−7.30896e9	−	1.26595e10i	−0.379182	−	0.656763i	0.611761	−	0.791042i	$-0.290461\pi$
$193$	−7.30896e9	−	1.26595e10i	−0.379182	−	0.656763i	−0.990943	+	0.134280i	$0.957128\pi$
$194$		0			0
$195$	−1.24329e10			−0.615767
$196$		0			0
$197$	−4.40160e9			−0.208215			−0.104108	−	0.994566i	$-0.533199\pi$
$197$	−4.40160e9			−0.208215			−0.104108	+	0.994566i	$0.533199\pi$
$198$		0			0
$199$	−1.76429e10	−	3.05585e10i	−0.797502	−	1.38131i	−0.921238	−	0.388999i	$-0.872821\pi$
$199$	−1.76429e10	−	3.05585e10i	−0.797502	−	1.38131i	0.123736	−	0.992315i	$-0.460512\pi$
$200$		0			0
$201$	−2.01162e10	+	3.48423e10i	−0.869288	+	1.50565i
$202$		0			0
$203$	1.91669e10	+	2.14243e10i	0.792173	+	0.885472i
$204$		0			0
$205$	1.30605e10	−	2.26215e10i	0.516498	−	0.894600i
$206$		0			0
$207$	5.55564e9	+	9.62266e9i	0.210314	+	0.364274i
$208$		0			0
$209$	−7.86042e9			−0.284962
$210$		0			0
$211$	−1.08123e10			−0.375533			−0.187766	−	0.982214i	$-0.560125\pi$
$211$	−1.08123e10			−0.375533			−0.187766	+	0.982214i	$0.560125\pi$
$212$		0			0
$213$	1.99412e10	+	3.45391e10i	0.663808	+	1.14975i
$214$		0			0
$215$	−1.17043e10	+	2.02724e10i	−0.373569	+	0.647041i
$216$		0			0
$217$	−5.83812e8	+	1.77744e9i	−0.0178733	+	0.0544159i
$218$		0			0
$219$	3.70400e9	−	6.41551e9i	0.108811	−	0.188466i
$220$		0			0
$221$	−5.80193e9	−	1.00492e10i	−0.163609	−	0.283379i
$222$		0			0
$223$	−3.21844e10			−0.871512			−0.435756	−	0.900065i	$-0.643519\pi$
$223$	−3.21844e10			−0.871512			−0.435756	+	0.900065i	$0.643519\pi$
$224$		0			0
$225$	1.24197e10			0.323065
$226$		0			0
$227$	−4.50385e9	−	7.80090e9i	−0.112582	−	0.194997i	0.804229	−	0.594320i	$-0.202579\pi$
$227$	−4.50385e9	−	7.80090e9i	−0.112582	−	0.194997i	−0.916810	+	0.399323i	$0.869245\pi$
$228$		0			0
$229$	−2.31909e10	+	4.01679e10i	−0.557261	+	0.965204i	0.440463	+	0.897771i	$0.354814\pi$
$229$	−2.31909e10	+	4.01679e10i	−0.557261	+	0.965204i	−0.997724	+	0.0674334i	$0.978519\pi$
$230$		0			0
$231$	−8.50612e9	+	1.77964e9i	−0.196552	+	0.0411223i
$232$		0			0
$233$	2.17672e10	−	3.77018e10i	0.483838	−	0.838032i	−0.515990	−	0.856595i	$-0.672576\pi$
$233$	2.17672e10	−	3.77018e10i	0.483838	−	0.838032i	0.999828	+	0.0185626i	$0.00590900\pi$
$234$		0			0
$235$	2.82476e10	+	4.89263e10i	0.604194	+	1.04650i
$236$		0			0
$237$	1.76560e10			0.363517
$238$		0			0
$239$	2.74289e10			0.543773			0.271887	−	0.962329i	$-0.412352\pi$
$239$	2.74289e10			0.543773			0.271887	+	0.962329i	$0.412352\pi$
$240$		0			0
$241$	5.75409e9	+	9.96638e9i	0.109875	+	0.190310i	0.915720	−	0.401818i	$-0.131622\pi$
$241$	5.75409e9	+	9.96638e9i	0.109875	+	0.190310i	−0.805844	+	0.592128i	$0.798288\pi$
$242$		0			0
$243$	−1.54067e10	+	2.66852e10i	−0.283453	+	0.490955i
$244$		0			0
$245$	6.59084e10	+	4.85320e10i	1.16867	+	0.860559i
$246$		0			0
$247$	1.76102e10	−	3.05017e10i	0.301042	−	0.521420i
$248$		0			0
$249$	−2.24697e10	−	3.89186e10i	−0.370424	−	0.641594i
$250$		0			0
$251$	2.69146e10			0.428012			0.214006	−	0.976832i	$-0.431349\pi$
$251$	2.69146e10			0.428012			0.214006	+	0.976832i	$0.431349\pi$
$252$		0			0
$253$	1.65842e10			0.254480
$254$		0			0
$255$	4.88224e10	+	8.45630e10i	0.723084	+	1.25242i
$256$		0			0
$257$	1.78979e10	−	3.10001e10i	0.255919	−	0.443265i	−0.709225	−	0.704982i	$-0.750955\pi$
$257$	1.78979e10	−	3.10001e10i	0.255919	−	0.443265i	0.965145	+	0.261716i	$0.0842885\pi$
$258$		0			0
$259$	1.00186e11	−	2.09606e10i	1.38343	−	0.289438i
$260$		0			0
$261$	−1.30047e10	+	2.25248e10i	−0.173468	+	0.300455i
$262$		0			0
$263$	−6.63817e10	−	1.14976e11i	−0.855554	−	1.48186i	−0.876130	−	0.482075i	$-0.839883\pi$
$263$	−6.63817e10	−	1.14976e11i	−0.855554	−	1.48186i	0.0205759	−	0.999788i	$-0.493450\pi$
$264$		0			0
$265$	8.59298e10			1.07038
$266$		0			0
$267$	4.64623e10			0.559499
$268$		0			0
$269$	−3.64397e10	−	6.31154e10i	−0.424316	−	0.734937i	0.572040	−	0.820226i	$-0.306152\pi$
$269$	−3.64397e10	−	6.31154e10i	−0.424316	−	0.734937i	−0.996356	+	0.0852884i	$0.972819\pi$
$270$		0			0
$271$	2.06838e10	−	3.58253e10i	0.232953	−	0.403486i	−0.725723	−	0.687987i	$-0.758495\pi$
$271$	2.06838e10	−	3.58253e10i	0.232953	−	0.403486i	0.958676	+	0.284501i	$0.0918279\pi$
$272$		0			0
$273$	1.21510e10	−	3.69943e10i	0.132398	−	0.403091i
$274$		0			0
$275$	9.26857e9	−	1.60536e10i	0.0977273	−	0.169269i
$276$		0			0
$277$	8.09314e10	+	1.40177e11i	0.825958	+	1.43060i	0.901185	+	0.433435i	$0.142699\pi$
$277$	8.09314e10	+	1.40177e11i	0.825958	+	1.43060i	−0.0752266	+	0.997166i	$0.523968\pi$
$278$		0			0
$279$	−1.69272e9			−0.0167250
$280$		0			0
$281$	1.39939e11			1.33894			0.669471	−	0.742838i	$-0.266521\pi$
$281$	1.39939e11			1.33894			0.669471	+	0.742838i	$0.266521\pi$
$282$		0			0
$283$	8.86550e10	+	1.53555e11i	0.821607	+	1.42306i	0.904485	+	0.426505i	$0.140255\pi$
$283$	8.86550e10	+	1.53555e11i	0.821607	+	1.42306i	−0.0828783	+	0.996560i	$0.526411\pi$
$284$		0			0
$285$	−1.48187e11	+	2.56668e11i	−1.33048	+	2.30446i
$286$		0			0
$287$	5.45462e10	+	6.09705e10i	0.474565	+	0.530458i
$288$		0			0
$289$	1.37270e10	−	2.37759e10i	0.115754	−	0.200492i
$290$		0			0
$291$	8.06172e9	+	1.39633e10i	0.0659036	+	0.114148i
$292$		0			0
$293$	−1.65710e11			−1.31355			−0.656773	−	0.754088i	$-0.728079\pi$
$293$	−1.65710e11			−1.31355			−0.656773	+	0.754088i	$0.728079\pi$
$294$		0			0
$295$	4.75922e9			0.0365879
$296$		0			0
$297$	9.53199e9	+	1.65099e10i	0.0710853	+	0.123123i
$298$		0			0
$299$	−3.71546e10	+	6.43536e10i	−0.268839	+	0.465643i
$300$		0			0
$301$	−4.88819e10	−	5.46391e10i	−0.343241	−	0.383667i
$302$		0			0
$303$	−8.44749e10	+	1.46315e11i	−0.575753	+	0.997233i
$304$		0			0
$305$	−8.80688e9	−	1.52540e10i	−0.0582737	−	0.100933i
$306$		0			0
$307$	−2.12825e11			−1.36741			−0.683706	−	0.729757i	$-0.739633\pi$
$307$	−2.12825e11			−1.36741			−0.683706	+	0.729757i	$0.739633\pi$
$308$		0			0
$309$	−8.05455e10			−0.502606
$310$		0			0
$311$	−7.94338e10	−	1.37583e11i	−0.481486	−	0.833959i	0.518288	−	0.855206i	$-0.326570\pi$
$311$	−7.94338e10	−	1.37583e11i	−0.481486	−	0.833959i	−0.999774	+	0.0212476i	$0.993236\pi$
$312$		0			0
$313$	1.48658e11	−	2.57484e11i	0.875468	−	1.51635i	0.0192038	−	0.999816i	$-0.493887\pi$
$313$	1.48658e11	−	2.57484e11i	0.875468	−	1.51635i	0.856264	−	0.516539i	$-0.172780\pi$
$314$		0			0
$315$	−2.31094e10	+	7.03574e10i	−0.132249	+	0.402636i
$316$		0			0
$317$	−7.66580e10	+	1.32776e11i	−0.426374	+	0.738502i	−0.996548	−	0.0830226i	$-0.973543\pi$
$317$	−7.66580e10	+	1.32776e11i	−0.426374	+	0.738502i	0.570174	+	0.821524i	$0.306876\pi$
$318$		0			0
$319$	1.94103e10	+	3.36196e10i	0.104948	+	0.181775i
$320$		0			0
$321$	−3.00969e8			−0.00158216
$322$		0			0
$323$	−2.76612e11			−1.41403
$324$		0			0
$325$	4.15298e10	+	7.19318e10i	0.206483	+	0.357640i
$326$		0			0
$327$	−8.48762e9	+	1.47010e10i	−0.0410507	+	0.0711019i
$328$		0			0
$329$	−1.73188e11	+	3.62342e10i	−0.814962	+	0.170505i
$330$		0			0
$331$	1.22438e11	−	2.12070e11i	0.560650	−	0.971074i	−0.436790	−	0.899563i	$-0.643885\pi$
$331$	1.22438e11	−	2.12070e11i	0.560650	−	0.971074i	0.997440	−	0.0715104i	$-0.0227819\pi$
$332$		0			0
$333$	4.63043e10	+	8.02013e10i	0.206358	+	0.357423i
$334$		0			0
$335$	5.11716e11			2.21987
$336$		0			0
$337$	−4.96265e10			−0.209594			−0.104797	−	0.994494i	$-0.533419\pi$
$337$	−4.96265e10			−0.209594			−0.104797	+	0.994494i	$0.533419\pi$
$338$		0			0
$339$	−1.91990e11	−	3.32536e11i	−0.789550	−	1.36754i
$340$		0			0
$341$	−1.26324e9	+	2.18800e9i	−0.00505931	+	0.00876298i
$342$		0			0
$343$	−2.08822e11	+	1.48680e11i	−0.814616	+	0.580001i
$344$		0			0
$345$	3.12651e11	−	5.41527e11i	1.18816	−	2.05795i
$346$		0			0
$347$	−1.52077e11	−	2.63405e11i	−0.563094	−	0.975308i	−0.997224	−	0.0744576i	$-0.976277\pi$
$347$	−1.52077e11	−	2.63405e11i	−0.563094	−	0.975308i	0.434130	−	0.900850i	$-0.357056\pi$
$348$		0			0
$349$	4.96999e11			1.79325			0.896626	−	0.442788i	$-0.146011\pi$
$349$	4.96999e11			1.79325			0.896626	+	0.442788i	$0.146011\pi$
$350$		0			0
$351$	−8.54203e10			−0.300385
$352$		0			0
$353$	−8.82246e10	−	1.52809e11i	−0.302415	−	0.523798i	0.674267	−	0.738487i	$-0.264460\pi$
$353$	−8.82246e10	−	1.52809e11i	−0.302415	−	0.523798i	−0.976682	+	0.214689i	$0.931126\pi$
$354$		0			0
$355$	2.53632e11	−	4.39304e11i	0.847573	−	1.46804i
$356$		0			0
$357$	−2.99334e11	+	6.26262e10i	−0.975325	+	0.204056i
$358$		0			0
$359$	−8.72570e10	+	1.51134e11i	−0.277253	+	0.480215i	−0.970701	−	0.240291i	$-0.922757\pi$
$359$	−8.72570e10	+	1.51134e11i	−0.277253	+	0.480215i	0.693448	+	0.720506i	$0.256091\pi$
$360$		0			0
$361$	−2.58446e11	−	4.47641e11i	−0.800916	−	1.38723i
$362$		0			0
$363$	3.64285e11			1.10119
$364$		0			0
$365$	−9.42224e10			−0.277867
$366$		0			0
$367$	1.94008e11	+	3.36032e11i	0.558243	+	0.966905i	0.997643	+	0.0686134i	$0.0218575\pi$
$367$	1.94008e11	+	3.36032e11i	0.558243	+	0.966905i	−0.439401	+	0.898291i	$0.644809\pi$
$368$		0			0
$369$	−3.70095e10	+	6.41023e10i	−0.103919	+	0.179993i
$370$		0			0
$371$	−8.39817e10	+	2.55685e11i	−0.230145	+	0.700686i
$372$		0			0
$373$	−3.02948e11	+	5.24721e11i	−0.810360	+	1.40359i	0.102251	+	0.994759i	$0.467395\pi$
$373$	−3.02948e11	+	5.24721e11i	−0.810360	+	1.40359i	−0.912612	+	0.408827i	$0.865938\pi$
$374$		0			0
$375$	−3.35970e10	−	5.81918e10i	−0.0877324	−	0.151957i
$376$		0			0
$377$	−1.73944e11			−0.443479
$378$		0			0
$379$	−5.34706e11			−1.33119			−0.665593	−	0.746315i	$-0.731821\pi$
$379$	−5.34706e11			−1.33119			−0.665593	+	0.746315i	$0.731821\pi$
$380$		0			0
$381$	−1.20461e11	−	2.08645e11i	−0.292876	−	0.507277i
$382$		0			0
$383$	1.26206e11	−	2.18595e11i	0.299699	−	0.519094i	−0.676368	−	0.736564i	$-0.736447\pi$
$383$	1.26206e11	−	2.18595e11i	0.299699	−	0.519094i	0.976067	+	0.217470i	$0.0697804\pi$
$384$		0			0
$385$	7.36974e10	+	8.23772e10i	0.170954	+	0.191088i
$386$		0			0
$387$	3.31663e10	−	5.74457e10i	0.0751619	−	0.130184i
$388$		0			0
$389$	−4.16836e10	−	7.21981e10i	−0.0922979	−	0.159865i	0.816180	−	0.577798i	$-0.196088\pi$
$389$	−4.16836e10	−	7.21981e10i	−0.0922979	−	0.159865i	−0.908478	+	0.417933i	$0.862755\pi$
$390$		0			0
$391$	5.83606e11			1.26277
$392$		0			0
$393$	−3.27479e10			−0.0692495
$394$		0			0
$395$	−1.12283e11	−	1.94480e11i	−0.232075	−	0.401966i
$396$		0			0
$397$	−5.67001e10	+	9.82075e10i	−0.114558	+	0.198421i	−0.917603	−	0.397498i	$-0.869879\pi$
$397$	−5.67001e10	+	9.82075e10i	−0.114558	+	0.198421i	0.803045	+	0.595919i	$0.203212\pi$
$398$		0			0
$399$	−6.18891e11	−	6.91782e11i	−1.22246	−	1.36644i
$400$		0			0
$401$	−2.56734e11	+	4.44676e11i	−0.495831	+	0.858805i	−0.999988	−	0.00480724i	$-0.998470\pi$
$401$	−2.56734e11	+	4.44676e11i	−0.495831	+	0.858805i	0.504157	+	0.863612i	$0.331803\pi$
$402$		0			0
$403$	−5.66022e9	−	9.80379e9i	−0.0106896	−	0.0185149i
$404$		0			0
$405$	9.48260e11			1.75138
$406$		0			0
$407$	1.38223e11			0.249693
$408$		0			0
$409$	−3.87550e11	−	6.71256e11i	−0.684814	−	1.18613i	−0.973495	−	0.228708i	$-0.926550\pi$
$409$	−3.87550e11	−	6.71256e11i	−0.684814	−	1.18613i	0.288681	−	0.957425i	$-0.406783\pi$
$410$		0			0
$411$	−4.69662e11	+	8.13478e11i	−0.811889	+	1.40623i
$412$		0			0
$413$	−4.65133e9	+	1.41611e10i	−0.00786686	+	0.0239510i
$414$		0			0
$415$	−2.85792e11	+	4.95007e11i	−0.472970	+	0.819209i
$416$		0			0
$417$	−1.22499e11	−	2.12174e11i	−0.198390	−	0.343621i
$418$		0			0
$419$	−9.73463e11			−1.54297			−0.771483	−	0.636250i	$-0.780485\pi$
$419$	−9.73463e11			−1.54297			−0.771483	+	0.636250i	$0.780485\pi$
$420$		0			0
$421$	−8.24555e11			−1.27924			−0.639618	−	0.768693i	$-0.720907\pi$
$421$	−8.24555e11			−1.27924			−0.639618	+	0.768693i	$0.720907\pi$
$422$		0			0
$423$	−8.00451e10	−	1.38642e11i	−0.121563	−	0.210554i
$424$		0			0
$425$	3.26165e11	−	5.64935e11i	0.484939	−	0.839940i
$426$		0			0
$427$	5.39956e10	−	1.12969e10i	0.0786019	−	0.0164450i
$428$		0			0
$429$	2.62921e10	−	4.55393e10i	0.0374773	−	0.0649125i
$430$		0			0
$431$	−2.22097e11	−	3.84683e11i	−0.310024	−	0.536977i	0.668343	−	0.743853i	$-0.267004\pi$
$431$	−2.22097e11	−	3.84683e11i	−0.310024	−	0.536977i	−0.978367	+	0.206876i	$0.933670\pi$
$432$		0			0
$433$	7.57077e11			1.03501			0.517505	−	0.855680i	$-0.326861\pi$
$433$	7.57077e11			1.03501			0.517505	+	0.855680i	$0.326861\pi$
$434$		0			0
$435$	1.46371e12			1.95999
$436$		0			0
$437$	8.85688e11	+	1.53406e12i	1.16175	+	2.01222i
$438$		0			0
$439$	5.04945e10	−	8.74591e10i	0.0648865	−	0.112387i	−0.831757	−	0.555140i	$-0.812665\pi$
$439$	5.04945e10	−	8.74591e10i	0.0648865	−	0.112387i	0.896644	+	0.442753i	$0.145998\pi$
$440$		0			0
$441$	−1.86764e11	−	1.37525e11i	−0.235136	−	0.173144i
$442$		0			0
$443$	3.63399e11	−	6.29425e11i	0.448298	−	0.776475i	−0.549977	−	0.835180i	$-0.685364\pi$
$443$	3.63399e11	−	6.29425e11i	0.448298	−	0.776475i	0.998275	+	0.0587046i	$0.0186970\pi$
$444$		0			0
$445$	−2.95477e11	−	5.11781e11i	−0.357194	−	0.618678i
$446$		0			0
$447$	9.76103e10			0.115641
$448$		0			0
$449$	−1.85410e11			−0.215291			−0.107645	−	0.994189i	$-0.534331\pi$
$449$	−1.85410e11			−0.215291			−0.107645	+	0.994189i	$0.534331\pi$
$450$		0			0
$451$	5.52388e10	+	9.56764e10i	0.0628709	+	0.108896i
$452$		0			0
$453$	−8.40776e10	+	1.45627e11i	−0.0938077	+	0.162480i
$454$		0			0
$455$	−4.84766e11	+	1.01422e11i	−0.530250	+	0.110938i
$456$		0			0
$457$	4.49165e11	−	7.77977e11i	0.481707	−	0.834341i	−0.518072	−	0.855337i	$-0.673350\pi$
$457$	4.49165e11	−	7.77977e11i	0.481707	−	0.834341i	0.999780	+	0.0209954i	$0.00668354\pi$
$458$		0			0
$459$	3.35435e11	+	5.80990e11i	0.352737	+	0.610959i
$460$		0			0
$461$	−6.56915e11			−0.677416			−0.338708	−	0.940892i	$-0.609990\pi$
$461$	−6.56915e11			−0.677416			−0.338708	+	0.940892i	$0.609990\pi$
$462$		0			0
$463$	−7.36860e11			−0.745196			−0.372598	−	0.927993i	$-0.621533\pi$
$463$	−7.36860e11			−0.745196			−0.372598	+	0.927993i	$0.621533\pi$
$464$		0			0
$465$	4.76300e10	+	8.24976e10i	0.0472435	+	0.0818282i
$466$		0			0
$467$	−3.97280e11	+	6.88109e11i	−0.386519	+	0.669470i	−0.991979	−	0.126406i	$-0.959656\pi$
$467$	−3.97280e11	+	6.88109e11i	−0.386519	+	0.669470i	0.605460	+	0.795876i	$0.292989\pi$
$468$		0			0
$469$	−5.00115e11	+	1.52262e12i	−0.477301	+	1.45316i
$470$		0			0
$471$	−2.94720e11	+	5.10470e11i	−0.275941	+	0.477943i
$472$		0			0
$473$	−4.95026e10	−	8.57410e10i	−0.0454729	−	0.0787614i
$474$		0			0
$475$	1.97997e12			1.78459
$476$		0			0
$477$	−2.43498e11			−0.215359
$478$		0			0
$479$	5.76669e11	+	9.98820e11i	0.500515	+	0.866917i	1.00000		0.000594242i	$0.000189153\pi$
$479$	5.76669e11	+	9.98820e11i	0.500515	+	0.866917i	−0.499485	+	0.866322i	$0.666478\pi$
$480$		0			0
$481$	−3.09670e11	+	5.36364e11i	−0.263783	+	0.456885i
$482$		0			0
$483$	1.30576e12	+	1.45955e12i	1.09170	+	1.22027i
$484$		0			0
$485$	1.02537e11	−	1.77599e11i	0.0841479	−	0.145748i
$486$		0			0
$487$	−9.72094e11	−	1.68372e12i	−0.783120	−	1.35640i	−0.930116	−	0.367266i	$-0.880294\pi$
$487$	−9.72094e11	−	1.68372e12i	−0.783120	−	1.35640i	0.146996	−	0.989137i	$-0.453039\pi$
$488$		0			0
$489$	2.09787e12			1.65916
$490$		0			0
$491$	7.04431e9			0.00546980			0.00273490	−	0.999996i	$-0.499129\pi$
$491$	7.04431e9			0.00546980			0.00273490	+	0.999996i	$0.499129\pi$
$492$		0			0
$493$	6.83056e11	+	1.18309e12i	0.520769	+	0.901999i
$494$		0			0
$495$	−5.00036e10	+	8.66087e10i	−0.0374350	+	0.0648393i
$496$		0			0
$497$	1.05927e12	+	1.18403e12i	0.778762	+	0.870481i
$498$		0			0
$499$	3.49974e10	−	6.06172e10i	0.0252687	−	0.0437667i	−0.853115	−	0.521724i	$-0.825289\pi$
$499$	3.49974e10	−	6.06172e10i	0.0252687	−	0.0437667i	0.878383	+	0.477957i	$0.158623\pi$
$500$		0			0
$501$	−4.90996e11	−	8.50430e11i	−0.348184	−	0.603072i
$502$		0			0
$503$	2.76650e12			1.92697			0.963484	−	0.267766i	$-0.0862855\pi$
$503$	2.76650e12			1.92697			0.963484	+	0.267766i	$0.0862855\pi$
$504$		0			0
$505$	2.14888e12			1.47028
$506$		0			0
$507$	−7.27740e11	−	1.26048e12i	−0.489148	−	0.847230i
$508$		0			0
$509$	−4.88478e11	+	8.46068e11i	−0.322563	+	0.558696i	−0.981016	−	0.193926i	$-0.937878\pi$
$509$	−4.88478e11	+	8.46068e11i	−0.322563	+	0.558696i	0.658453	+	0.752622i	$0.271211\pi$
$510$		0			0
$511$	9.20863e10	−	2.80360e11i	0.0597449	−	0.181896i
$512$		0			0
$513$	−1.01812e12	+	1.76344e12i	−0.649040	+	1.12417i
$514$		0			0
$515$	5.12230e11	+	8.87208e11i	0.320872	+	0.555767i
$516$		0			0
$517$	−2.38944e11			−0.147092
$518$		0			0
$519$	2.46795e12			1.49308
$520$		0			0
$521$	−5.65660e11	−	9.79751e11i	−0.336345	−	0.582567i	0.647397	−	0.762153i	$-0.275858\pi$
$521$	−5.65660e11	−	9.79751e11i	−0.336345	−	0.582567i	−0.983742	+	0.179586i	$0.942524\pi$
$522$		0			0
$523$	−1.54001e12	+	2.66738e12i	−0.900050	+	1.55893i	−0.0726222	+	0.997360i	$0.523137\pi$
$523$	−1.54001e12	+	2.66738e12i	−0.900050	+	1.55893i	−0.827428	+	0.561572i	$0.810197\pi$
$524$		0			0
$525$	2.14261e12	−	4.48274e11i	1.23091	−	0.257529i
$526$		0			0
$527$	−4.44540e10	+	7.69966e10i	−0.0251052	+	0.0434834i
$528$		0			0
$529$	−9.68084e11	−	1.67677e12i	−0.537480	−	0.930943i
$530$		0			0
$531$	−1.34862e10			−0.00736145
$532$		0			0
$533$	−4.95019e11			−0.265674
$534$		0			0
$535$	1.91401e9	+	3.31517e9i	0.00101007	+	0.00174950i
$536$		0			0
$537$	3.17135e11	−	5.49294e11i	0.164573	−	0.285049i
$538$		0			0
$539$	−3.17141e11	+	1.38778e11i	−0.161847	+	0.0708226i
$540$		0			0
$541$	1.39651e12	−	2.41883e12i	0.700901	−	1.21400i	−0.267250	−	0.963627i	$-0.586115\pi$
$541$	1.39651e12	−	2.41883e12i	0.700901	−	1.21400i	0.968151	−	0.250369i	$-0.0805518\pi$
$542$		0			0
$543$	−2.14445e12	−	3.71429e12i	−1.05856	−	1.83348i
$544$		0			0
$545$	2.15908e11			0.104830
$546$		0			0
$547$	−1.47553e12			−0.704700			−0.352350	−	0.935868i	$-0.614617\pi$
$547$	−1.47553e12			−0.704700			−0.352350	+	0.935868i	$0.614617\pi$
$548$		0			0
$549$	2.49560e10	+	4.32250e10i	0.0117246	+	0.0203076i
$550$		0			0
$551$	−2.07323e12	+	3.59094e12i	−0.958220	+	1.65969i
$552$		0			0
$553$	6.88418e11	−	1.44030e11i	0.313032	−	0.0654920i
$554$		0			0
$555$	2.60583e12	−	4.51343e12i	1.16581	−	2.01924i
$556$		0			0
$557$	−1.10846e12	−	1.91990e12i	−0.487944	−	0.845144i	0.511960	−	0.859010i	$-0.328920\pi$
$557$	−1.10846e12	−	1.91990e12i	−0.487944	−	0.845144i	−0.999904	+	0.0138652i	$0.995586\pi$
$558$		0			0
$559$	4.43614e11			0.192155
$560$		0			0
$561$	−4.12984e11			−0.176035
$562$		0			0
$563$	3.26827e11	+	5.66082e11i	0.137098	+	0.237460i	0.926397	−	0.376549i	$-0.122889\pi$
$563$	3.26827e11	+	5.66082e11i	0.137098	+	0.237460i	−0.789299	+	0.614009i	$0.789556\pi$
$564$		0			0
$565$	−2.44192e12	+	4.22953e12i	−1.00812	+	1.74612i
$566$		0			0
$567$	−9.26762e11	+	2.82156e12i	−0.376569	+	1.14648i
$568$		0			0
$569$	−1.29888e12	+	2.24973e12i	−0.519474	+	0.899756i	0.480269	+	0.877121i	$0.340539\pi$
$569$	−1.29888e12	+	2.24973e12i	−0.519474	+	0.899756i	−0.999744	+	0.0226349i	$0.992794\pi$
$570$		0			0
$571$	−5.19555e11	−	8.99896e11i	−0.204536	−	0.354266i	0.745449	−	0.666563i	$-0.232235\pi$
$571$	−5.19555e11	−	8.99896e11i	−0.204536	−	0.354266i	−0.949985	+	0.312296i	$0.898902\pi$
$572$		0			0
$573$	2.76896e11			0.107305
$574$		0			0
$575$	−4.17742e12			−1.59369
$576$		0			0
$577$	−2.33010e11	−	4.03585e11i	−0.0875152	−	0.151581i	0.818945	−	0.573872i	$-0.194559\pi$
$577$	−2.33010e11	−	4.03585e11i	−0.0875152	−	0.151581i	−0.906460	+	0.422291i	$0.861226\pi$
$578$		0			0
$579$	1.16556e12	−	2.01881e12i	0.431003	−	0.746519i
$580$		0			0
$581$	−1.19359e12	−	1.33416e12i	−0.434572	−	0.485754i
$582$		0			0
$583$	−1.81718e11	+	3.14744e11i	−0.0651461	+	0.112836i
$584$		0			0
$585$	−2.24052e11	−	3.88069e11i	−0.0790946	−	0.136996i
$586$		0			0
$587$	−5.17776e12			−1.79999			−0.899996	−	0.435897i	$-0.856431\pi$
$587$	−5.17776e12			−1.79999			−0.899996	+	0.435897i	$0.856431\pi$
$588$		0			0
$589$	−2.69856e11			−0.0923874
$590$		0			0
$591$	−3.50961e11	−	6.07882e11i	−0.118335	−	0.204963i
$592$		0			0
$593$	−1.94396e12	+	3.36705e12i	−0.645568	+	1.11816i	0.338601	+	0.940930i	$0.390046\pi$
$593$	−1.94396e12	+	3.36705e12i	−0.645568	+	1.11816i	−0.984170	+	0.177227i	$0.943287\pi$
$594$		0			0
$595$	2.59344e12	+	2.89889e12i	0.848302	+	0.948212i
$596$		0			0
$597$	2.81351e12	−	4.87315e12i	0.906493	−	1.57009i
$598$		0			0
$599$	3.53757e11	+	6.12726e11i	0.112275	+	0.194467i	0.916687	−	0.399605i	$-0.130853\pi$
$599$	3.53757e11	+	6.12726e11i	0.112275	+	0.194467i	−0.804412	+	0.594072i	$0.797519\pi$
$600$		0			0
$601$	−3.16274e12			−0.988845			−0.494422	−	0.869222i	$-0.664620\pi$
$601$	−3.16274e12			−0.988845			−0.494422	+	0.869222i	$0.664620\pi$
$602$		0			0
$603$	−1.45005e12			−0.446636
$604$		0			0
$605$	−2.31668e12	−	4.01260e12i	−0.703018	−	1.21766i
$606$		0			0
$607$	1.94652e12	−	3.37148e12i	0.581983	−	1.00802i	−0.413261	−	0.910613i	$-0.635610\pi$
$607$	1.94652e12	−	3.37148e12i	0.581983	−	1.00802i	0.995244	−	0.0974119i	$-0.0310564\pi$
$608$		0			0
$609$	−1.43053e12	+	4.35531e12i	−0.421424	+	1.28304i
$610$		0			0
$611$	5.35319e11	−	9.27200e11i	0.155392	−	0.269146i
$612$		0			0
$613$	3.04157e12	+	5.26815e12i	0.870012	+	1.50691i	0.861983	+	0.506937i	$0.169223\pi$
$613$	3.04157e12	+	5.26815e12i	0.870012	+	1.50691i	0.00802931	+	0.999968i	$0.497444\pi$
$614$		0			0
$615$	4.16552e12			1.17417
$616$		0			0
$617$	−5.40996e12			−1.50283			−0.751416	−	0.659829i	$-0.770629\pi$
$617$	−5.40996e12			−1.50283			−0.751416	+	0.659829i	$0.770629\pi$
$618$		0			0
$619$	−6.49701e11	−	1.12531e12i	−0.177871	−	0.308082i	0.763280	−	0.646068i	$-0.223588\pi$
$619$	−6.49701e11	−	1.12531e12i	−0.177871	−	0.308082i	−0.941151	+	0.337986i	$0.890254\pi$
$620$		0			0
$621$	2.14807e12	−	3.72057e12i	0.579611	−	1.00392i
$622$		0			0
$623$	1.81159e12	−	3.79018e11i	0.481797	−	0.100801i
$624$		0			0
$625$	1.68290e12	−	2.91487e12i	0.441162	−	0.764115i
$626$		0			0
$627$	−6.26750e11	−	1.08556e12i	−0.161953	−	0.280512i
$628$		0			0
$629$	4.86415e12			1.23902
$630$		0			0
$631$	3.33319e12			0.837004			0.418502	−	0.908216i	$-0.362555\pi$
$631$	3.33319e12			0.837004			0.418502	+	0.908216i	$0.362555\pi$
$632$		0			0
$633$	−8.62118e11	−	1.49323e12i	−0.213427	−	0.369667i
$634$		0			0
$635$	−1.53215e12	+	2.65376e12i	−0.373954	+	0.647708i
$636$		0			0
$637$	1.71993e11	−	1.54155e12i	0.0413890	−	0.370963i
$638$		0			0
$639$	−7.18715e11	+	1.24485e12i	−0.170531	+	0.295368i
$640$		0			0
$641$	−9.73337e11	−	1.68587e12i	−0.227721	−	0.394424i	0.729412	−	0.684075i	$-0.239794\pi$
$641$	−9.73337e11	−	1.68587e12i	−0.227721	−	0.394424i	−0.957132	+	0.289651i	$0.906461\pi$
$642$		0			0
$643$	1.31531e12			0.303443			0.151722	−	0.988423i	$-0.451518\pi$
$643$	1.31531e12			0.303443			0.151722	+	0.988423i	$0.451518\pi$
$644$		0			0
$645$	−3.73295e12			−0.849246
$646$		0			0
$647$	−3.35402e12	−	5.80933e12i	−0.752483	−	1.30334i	−0.946616	−	0.322363i	$-0.895523\pi$
$647$	−3.35402e12	−	5.80933e12i	−0.752483	−	1.30334i	0.194134	−	0.980975i	$-0.437810\pi$
$648$		0			0
$649$	−1.00644e10	+	1.74321e10i	−0.00222684	+	0.00385699i
$650$		0			0
$651$	−2.92023e11	+	6.10966e10i	−0.0637240	+	0.0133322i
$652$		0			0
$653$	3.93686e12	−	6.81883e12i	0.847306	−	1.46758i	−0.0362978	−	0.999341i	$-0.511556\pi$
$653$	3.93686e12	−	6.81883e12i	0.847306	−	1.46758i	0.883604	−	0.468236i	$-0.155110\pi$
$654$		0			0
$655$	2.08261e11	+	3.60718e11i	0.0442101	+	0.0765741i
$656$		0			0
$657$	2.66997e11			0.0559065
$658$		0			0
$659$	−8.22995e12			−1.69986			−0.849929	−	0.526897i	$-0.823356\pi$
$659$	−8.22995e12			−1.69986			−0.849929	+	0.526897i	$0.823356\pi$
$660$		0			0
$661$	−2.84912e12	−	4.93481e12i	−0.580502	−	1.00546i	−0.995420	−	0.0955999i	$-0.969523\pi$
$661$	−2.84912e12	−	4.93481e12i	−0.580502	−	1.00546i	0.414918	−	0.909859i	$-0.363810\pi$
$662$		0			0
$663$	9.25231e11	−	1.60255e12i	0.185969	−	0.322107i
$664$		0			0
$665$	−3.68413e12	+	1.12165e13i	−0.730529	+	2.22412i
$666$		0			0
$667$	4.37418e12	−	7.57630e12i	0.855718	−	1.48215i
$668$		0			0
$669$	−2.56622e12	−	4.44482e12i	−0.495308	−	0.857899i
$670$		0			0
$671$	7.44964e10			0.0141868
$672$		0			0
$673$	9.28143e12			1.74400			0.872002	−	0.489503i	$-0.162822\pi$
$673$	9.28143e12			1.74400			0.872002	+	0.489503i	$0.162822\pi$
$674$		0			0
$675$	−2.40102e12	−	4.15869e12i	−0.445173	−	0.771063i
$676$		0			0
$677$	−6.45102e11	+	1.11735e12i	−0.118026	+	0.204428i	−0.918986	−	0.394291i	$-0.870990\pi$
$677$	−6.45102e11	+	1.11735e12i	−0.118026	+	0.204428i	0.800959	+	0.598719i	$0.204323\pi$
$678$		0			0
$679$	4.28238e11	+	4.78674e11i	0.0773163	+	0.0864223i
$680$		0			0
$681$	7.18228e11	−	1.24401e12i	0.127968	−	0.221646i
$682$		0			0
$683$	1.27194e11	+	2.20307e11i	0.0223653	+	0.0387379i	0.876991	−	0.480506i	$-0.159547\pi$
$683$	1.27194e11	+	2.20307e11i	0.0223653	+	0.0387379i	−0.854626	+	0.519244i	$0.826214\pi$
$684$		0			0
$685$	1.19473e13			2.07329
$686$		0			0
$687$	−7.39650e12			−1.26684
$688$		0			0
$689$	−8.14225e11	−	1.41028e12i	−0.137644	−	0.238407i
$690$		0			0
$691$	−7.84952e11	+	1.35958e12i	−0.130976	+	0.226857i	−0.924053	−	0.382264i	$-0.875144\pi$
$691$	−7.84952e11	+	1.35958e12i	−0.130976	+	0.226857i	0.793077	+	0.609121i	$0.208478\pi$
$692$		0			0
$693$	−2.08836e11	−	2.33432e11i	−0.0343958	−	0.0384468i
$694$		0			0
$695$	−1.55806e12	+	2.69864e12i	−0.253310	+	0.438746i
$696$		0			0
$697$	1.94388e12	+	3.36689e12i	0.311976	+	0.540359i
$698$		0			0
$699$	6.94240e12			1.09992
$700$		0			0
$701$	−8.33084e12			−1.30304			−0.651520	−	0.758632i	$-0.725868\pi$
$701$	−8.33084e12			−1.30304			−0.651520	+	0.758632i	$0.725868\pi$
$702$		0			0
$703$	7.38189e12	+	1.27858e13i	1.13990	+	1.97437i
$704$		0			0
$705$	−4.50464e12	+	7.80227e12i	−0.686767	+	1.18951i
$706$		0			0
$707$	−2.10016e12	+	6.39402e12i	−0.316129	+	0.962468i
$708$		0			0
$709$	−1.16510e12	+	2.01801e12i	−0.173163	+	0.299926i	−0.939524	−	0.342483i	$-0.888732\pi$
$709$	−1.16510e12	+	2.01801e12i	−0.173163	+	0.299926i	0.766361	+	0.642410i	$0.222065\pi$
$710$		0			0
$711$	3.18176e11	+	5.51098e11i	0.0466933	+	0.0808752i
$712$		0			0
$713$	5.69352e11			0.0825046
$714$		0			0
$715$	−6.68820e11			−0.0957044
$716$		0			0
$717$	2.18704e12	+	3.78806e12i	0.309044	+	0.535280i
$718$		0			0
$719$	−7.83347e11	+	1.35680e12i	−0.109314	+	0.189337i	−0.915492	−	0.402335i	$-0.868199\pi$
$719$	−7.83347e11	+	1.35680e12i	−0.109314	+	0.189337i	0.806179	+	0.591672i	$0.201532\pi$
$720$		0			0
$721$	−3.14052e12	+	6.57054e11i	−0.432806	+	0.0905508i
$722$		0			0
$723$	−9.17603e11	+	1.58934e12i	−0.124891	+	0.216318i
$724$		0			0
$725$	−4.88927e12	−	8.46847e12i	−0.657239	−	1.13837i
$726$		0			0
$727$	−2.09663e11			−0.0278367			−0.0139183	−	0.999903i	$-0.504430\pi$
$727$	−2.09663e11			−0.0278367			−0.0139183	+	0.999903i	$0.504430\pi$
$728$		0			0
$729$	4.28830e12			0.562356
$730$		0			0
$731$	−1.74202e12	−	3.01726e12i	−0.225644	−	0.390827i
$732$		0			0
$733$	−4.07588e12	+	7.05962e12i	−0.521498	+	0.903262i	0.478189	+	0.878257i	$0.341293\pi$
$733$	−4.07588e12	+	7.05962e12i	−0.521498	+	0.903262i	−0.999687	+	0.0250047i	$0.992040\pi$
$734$		0			0
$735$	−1.44730e12	+	1.29720e13i	−0.182922	+	1.63950i
$736$		0			0
$737$	−1.08214e12	+	1.87432e12i	−0.135107	+	0.234013i
$738$		0			0
$739$	−3.82789e12	−	6.63011e12i	−0.472128	−	0.817750i	0.527363	−	0.849640i	$-0.323181\pi$
$739$	−3.82789e12	−	6.63011e12i	−0.472128	−	0.817750i	−0.999491	+	0.0318898i	$0.989847\pi$
$740$		0			0
$741$	5.61657e12			0.684367
$742$		0			0
$743$	7.82269e12			0.941686			0.470843	−	0.882217i	$-0.343950\pi$
$743$	7.82269e12			0.941686			0.470843	+	0.882217i	$0.343950\pi$
$744$		0			0
$745$	−6.20754e11	−	1.07518e12i	−0.0738272	−	0.127872i
$746$		0			0
$747$	8.09847e11	−	1.40270e12i	0.0951613	−	0.164824i
$748$		0			0
$749$	−1.17350e10	+	2.45517e9i	−0.00136243	+	0.000285045i
$750$		0			0
$751$	5.68288e12	−	9.84304e12i	0.651912	−	1.12914i	−0.330747	−	0.943720i	$-0.607301\pi$
$751$	5.68288e12	−	9.84304e12i	0.651912	−	1.12914i	0.982658	−	0.185425i	$-0.0593660\pi$
$752$		0			0
$753$	2.14603e12	+	3.71703e12i	0.243253	+	0.421326i
$754$		0			0
$755$	2.13877e12			0.239554
$756$		0			0
$757$	−1.15682e13			−1.28037			−0.640184	−	0.768222i	$-0.721142\pi$
$757$	−1.15682e13			−1.28037			−0.640184	+	0.768222i	$0.721142\pi$
$758$		0			0
$759$	1.32234e12	+	2.29036e12i	0.144629	+	0.250505i
$760$		0			0
$761$	−1.05812e12	+	1.83272e12i	−0.114368	+	0.198091i	−0.917527	−	0.397674i	$-0.869818\pi$
$761$	−1.05812e12	+	1.83272e12i	−0.114368	+	0.198091i	0.803159	+	0.595765i	$0.203151\pi$
$762$		0			0
$763$	−2.11013e11	+	6.42439e11i	−0.0225398	+	0.0686233i
$764$		0			0
$765$	−1.75965e12	+	3.04780e12i	−0.185759	+	0.321744i
$766$		0			0
$767$	−4.50959e10	−	7.81083e10i	−0.00470498	−	0.00814926i
$768$		0			0
$769$	2.61186e12			0.269328			0.134664	−	0.990891i	$-0.457005\pi$
$769$	2.61186e12			0.269328			0.134664	+	0.990891i	$0.457005\pi$
$770$		0			0
$771$	5.70835e12			0.581789
$772$		0			0
$773$	4.15174e12	+	7.19102e12i	0.418237	+	0.724407i	0.995762	−	0.0919653i	$-0.0293149\pi$
$773$	4.15174e12	+	7.19102e12i	0.418237	+	0.724407i	−0.577525	+	0.816373i	$0.695982\pi$
$774$		0			0
$775$	3.18199e11	−	5.51137e11i	0.0316841	−	0.0548784i
$776$		0			0
$777$	1.08830e13	+	1.21648e13i	1.07116	+	1.19732i
$778$		0			0
$779$	−5.90011e12	+	1.02193e13i	−0.574039	+	0.994265i
$780$		0			0
$781$	1.07272e12	+	1.85801e12i	0.103171	+	0.178698i
$782$		0			0
$783$	1.00565e13			0.956130
$784$		0			0
$785$	7.49710e12			0.704661
$786$		0			0
$787$	4.23933e12	+	7.34274e12i	0.393923	+	0.682295i	0.992963	−	0.118424i	$-0.0377843\pi$
$787$	4.23933e12	+	7.34274e12i	0.393923	+	0.682295i	−0.599040	+	0.800719i	$0.704451\pi$
$788$		0			0
$789$	1.05859e13	−	1.83353e13i	0.972478	−	1.68438i
$790$		0			0
$791$	−1.01985e13	−	1.13996e13i	−0.926278	−	1.03537i
$792$		0			0
$793$	−1.66899e11	+	2.89077e11i	−0.0149873	+	0.0259588i
$794$		0			0
$795$	6.85159e12	+	1.18673e13i	0.608331	+	1.05366i
$796$		0			0
$797$	−8.15126e12			−0.715587			−0.357794	−	0.933801i	$-0.616471\pi$
$797$	−8.15126e12			−0.715587			−0.357794	+	0.933801i	$0.616471\pi$
$798$		0			0
$799$	−8.40853e12			−0.729894
$800$		0			0
$801$	8.37291e11	+	1.45023e12i	0.0718671	+	0.124477i
$802$		0			0
$803$	1.99254e11	−	3.45119e11i	0.0169117	−	0.0292920i
$804$		0			0
$805$	7.77292e12	−	2.36650e13i	0.652383	−	1.98621i
$806$		0			0
$807$	5.81103e12	−	1.00650e13i	0.482305	−	0.835377i
$808$		0			0
$809$	1.95100e12	+	3.37922e12i	0.160136	+	0.277363i	0.934917	−	0.354866i	$-0.115474\pi$
$809$	1.95100e12	+	3.37922e12i	0.160136	+	0.277363i	−0.774782	+	0.632229i	$0.782140\pi$
$810$		0			0
$811$	1.54921e13			1.25752			0.628761	−	0.777598i	$-0.283562\pi$
$811$	1.54921e13			1.25752			0.628761	+	0.777598i	$0.283562\pi$
$812$		0			0
$813$	6.59687e12			0.529579
$814$		0			0
$815$	−1.33414e13	−	2.31080e13i	−1.05924	−	1.83465i
$816$		0			0
$817$	5.28742e12	−	9.15808e12i	0.415188	−	0.719126i
$818$		0			0
$819$	1.37368e12	−	2.87398e11i	0.106686	−	0.0223207i
$820$		0			0
$821$	3.37626e12	−	5.84785e12i	0.259353	−	0.449213i	−0.706716	−	0.707498i	$-0.749824\pi$
$821$	3.37626e12	−	5.84785e12i	0.259353	−	0.449213i	0.966069	+	0.258285i	$0.0831573\pi$
$822$		0			0
$823$	9.11164e11	+	1.57818e12i	0.0692305	+	0.119911i	0.898563	−	0.438845i	$-0.144612\pi$
$823$	9.11164e11	+	1.57818e12i	0.0692305	+	0.119911i	−0.829332	+	0.558756i	$0.811279\pi$
$824$		0			0
$825$	2.95611e12			0.222166
$826$		0			0
$827$	2.37120e13			1.76276			0.881382	−	0.472404i	$-0.156614\pi$
$827$	2.37120e13			1.76276			0.881382	+	0.472404i	$0.156614\pi$
$828$		0			0
$829$	9.38126e12	+	1.62488e13i	0.689868	+	1.19489i	0.971880	+	0.235475i	$0.0756646\pi$
$829$	9.38126e12	+	1.62488e13i	0.689868	+	1.19489i	−0.282013	+	0.959411i	$0.591002\pi$
$830$		0			0
$831$	−1.29061e13	+	2.23540e13i	−0.938838	+	1.62611i
$832$		0			0
$833$	−1.11603e13	+	4.88367e12i	−0.803110	+	0.351434i
$834$		0			0
$835$	−6.24499e12	+	1.08166e13i	−0.444573	+	0.770022i
$836$		0			0
$837$	3.27242e11	+	5.66800e11i	0.0230465	+	0.0399177i
$838$		0			0
$839$	5.63044e12			0.392296			0.196148	−	0.980574i	$-0.437157\pi$
$839$	5.63044e12			0.392296			0.196148	+	0.980574i	$0.437157\pi$
$840$		0			0
$841$	5.97112e12			0.411599
$842$		0			0
$843$	1.11580e13	+	1.93263e13i	0.760964	+	1.31803i
$844$		0			0
$845$	−9.25614e12	+	1.60321e13i	−0.624561	+	1.08177i
$846$		0			0
$847$	1.42037e13	−	2.97168e12i	0.948258	−	0.198393i
$848$		0			0
$849$	−1.41378e13	+	2.44873e13i	−0.933892	+	1.61755i
$850$		0			0
$851$	−1.55746e13	−	2.69760e13i	−1.01797	−	1.76317i
$852$		0			0
$853$	2.09580e13			1.35544			0.677719	−	0.735321i	$-0.262968\pi$
$853$	2.09580e13			1.35544			0.677719	+	0.735321i	$0.262968\pi$
$854$		0			0
$855$	−1.06819e13			−0.683595
$856$		0			0
$857$	−5.40299e12	−	9.35825e12i	−0.342153	−	0.592626i	0.642679	−	0.766135i	$-0.277823\pi$
$857$	−5.40299e12	−	9.35825e12i	−0.342153	−	0.592626i	−0.984832	+	0.173509i	$0.944489\pi$
$858$		0			0
$859$	−4.86016e12	+	8.41804e12i	−0.304566	+	0.527524i	−0.977165	−	0.212484i	$-0.931845\pi$
$859$	−4.86016e12	+	8.41804e12i	−0.304566	+	0.527524i	0.672599	+	0.740007i	$0.265178\pi$
$860$		0			0
$861$	−4.07108e12	+	1.23946e13i	−0.252462	+	0.768629i
$862$		0			0
$863$	−8.16020e12	+	1.41339e13i	−0.500786	+	0.867387i	0.499214	+	0.866479i	$0.333622\pi$
$863$	−8.16020e12	+	1.41339e13i	−0.500786	+	0.867387i	−1.00000		0.000907842i	$0.999711\pi$
$864$		0			0
$865$	−1.56949e13	−	2.71844e13i	−0.953206	−	1.65100i
$866$		0			0
$867$	4.37809e12			0.263147
$868$		0			0
$869$	9.49793e11			0.0564989
$870$		0			0
$871$	−4.84875e12	−	8.39829e12i	−0.285462	−	0.494435i
$872$		0			0
$873$	−2.90559e11	+	5.03262e11i	−0.0169305	+	0.0293245i
$874$		0			0
$875$	−1.78467e12	−	1.99486e12i	−0.102925	−	0.115047i
$876$		0			0
$877$	1.01234e13	−	1.75342e13i	0.577867	−	1.00089i	−0.417857	−	0.908513i	$-0.637219\pi$
$877$	1.01234e13	−	1.75342e13i	0.577867	−	1.00089i	0.995724	−	0.0923817i	$-0.0294480\pi$
$878$		0			0
$879$	−1.32129e13	−	2.28854e13i	−0.746531	−	1.29303i
$880$		0			0
$881$	−1.15345e13			−0.645072			−0.322536	−	0.946557i	$-0.604535\pi$
$881$	−1.15345e13			−0.645072			−0.322536	+	0.946557i	$0.604535\pi$
$882$		0			0
$883$	−1.65115e13			−0.914035			−0.457017	−	0.889458i	$-0.651082\pi$
$883$	−1.65115e13			−0.914035			−0.457017	+	0.889458i	$0.651082\pi$
$884$		0			0
$885$	3.79476e11	+	6.57271e11i	0.0207941	+	0.0360164i
$886$		0			0
$887$	−9.41136e12	+	1.63010e13i	−0.510500	+	0.884213i	0.489425	+	0.872045i	$0.337207\pi$
$887$	−9.41136e12	+	1.63010e13i	−0.510500	+	0.884213i	−0.999926	+	0.0121677i	$0.996127\pi$
$888$		0			0
$889$	−6.39888e12	−	7.15252e12i	−0.343595	−	0.384062i
$890$		0			0
$891$	−2.00531e12	+	3.47329e12i	−0.106594	+	0.184626i
$892$		0			0
$893$	−1.27609e13	−	2.21025e13i	−0.671506	−	1.16308i
$894$		0			0
$895$	−8.06729e12			−0.420266
$896$		0			0
$897$	−1.18501e13			−0.611160
$898$		0			0
$899$	6.66373e11	+	1.15419e12i	0.0340251	+	0.0589331i
$900$		0			0
$901$	−6.39472e12	+	1.10760e13i	−0.323266	+	0.559913i
$902$		0			0
$903$	3.64832e12	−	1.11075e13i	0.182599	−	0.555930i
$904$		0			0
$905$	−2.72753e13	+	4.72422e13i	−1.35161	+	2.34105i
$906$		0			0
$907$	−1.05352e13	−	1.82476e13i	−0.516906	−	0.895308i	−0.999807	−	0.0196327i	$-0.993750\pi$
$907$	−1.05352e13	−	1.82476e13i	−0.516906	−	0.895308i	0.482901	−	0.875675i	$-0.339583\pi$
$908$		0			0
$909$	−6.08925e12			−0.295819
$910$		0			0
$911$	1.97328e13			0.949198			0.474599	−	0.880202i	$-0.342593\pi$
$911$	1.97328e13			0.949198			0.474599	+	0.880202i	$0.342593\pi$
$912$		0			0
$913$	−1.20874e12	−	2.09360e12i	−0.0575725	−	0.0997186i
$914$		0			0
$915$	1.40443e12	−	2.43254e12i	0.0662377	−	0.114727i
$916$		0			0
$917$	−1.27686e12	+	2.67143e11i	−0.0596323	+	0.0124762i
$918$		0			0
$919$	1.24173e13	−	2.15074e13i	0.574259	−	0.994645i	−0.421863	−	0.906660i	$-0.638624\pi$
$919$	1.24173e13	−	2.15074e13i	0.574259	−	0.994645i	0.996122	−	0.0879858i	$-0.0280430\pi$
$920$		0			0
$921$	−1.69695e13	−	2.93921e13i	−0.777145	−	1.34605i
$922$		0			0
$923$	−9.61314e12			−0.435971
$924$		0			0
$925$	−3.48172e13			−1.56371
$926$		0			0
$927$	−1.45150e12	−	2.51407e12i	−0.0645593	−	0.111820i
$928$		0			0
$929$	1.81790e13	−	3.14869e13i	0.800754	−	1.38695i	−0.118367	−	0.992970i	$-0.537766\pi$
$929$	1.81790e13	−	3.14869e13i	0.800754	−	1.38695i	0.919121	−	0.393976i	$-0.128901\pi$
$930$		0			0
$931$	−2.97742e13	−	2.19244e13i	−1.29887	−	0.956431i
$932$		0			0
$933$	1.26673e13	−	2.19404e13i	0.547288	−	0.947931i
$934$		0			0
$935$	2.62637e12	+	4.54901e12i	0.112384	+	0.194655i
$936$		0			0
$937$	9.42112e12			0.399277			0.199639	−	0.979870i	$-0.436023\pi$
$937$	9.42112e12			0.399277			0.199639	+	0.979870i	$0.436023\pi$
$938$		0			0
$939$	4.74130e13			1.99023
$940$		0			0
$941$	1.16425e13	+	2.01654e13i	0.484054	+	0.838406i	0.999832	−	0.0183158i	$-0.00583043\pi$
$941$	1.16425e13	+	2.01654e13i	0.484054	+	0.838406i	−0.515778	+	0.856722i	$0.672497\pi$
$942$		0			0
$943$	1.24483e13	−	2.15610e13i	0.512633	−	0.887906i
$944$		0			0
$945$	2.80265e13	−	5.86365e12i	1.14321	−	0.239180i
$946$		0			0
$947$	−1.01843e13	+	1.76397e13i	−0.411488	+	0.712717i	−0.995053	−	0.0993491i	$-0.968324\pi$
$947$	−1.01843e13	+	1.76397e13i	−0.411488	+	0.712717i	0.583565	+	0.812066i	$0.301657\pi$
$948$		0			0
$949$	8.92802e11	+	1.54638e12i	0.0357320	+	0.0618896i
$950$		0			0
$951$	−2.44493e13			−0.969289
$952$		0			0
$953$	2.26713e13			0.890344			0.445172	−	0.895445i	$-0.353143\pi$
$953$	2.26713e13			0.890344			0.445172	+	0.895445i	$0.353143\pi$
$954$		0			0
$955$	−1.76092e12	−	3.05001e12i	−0.0685054	−	0.118655i
$956$		0			0
$957$	−3.09535e12	+	5.36130e12i	−0.119291	+	0.206617i
$958$		0			0
$959$	−1.16764e13	+	3.55493e13i	−0.445785	+	1.35721i
$960$		0			0
$961$	1.31764e13	−	2.28223e13i	0.498360	−	0.863184i
$962$		0			0
$963$	−5.42373e9	−	9.39417e9i	−0.000203226	−	0.000351998i
$964$		0			0
$965$	−2.96495e13			−1.10064
$966$		0			0
$967$	−4.32858e12			−0.159194			−0.0795969	−	0.996827i	$-0.525363\pi$
$967$	−4.32858e12			−0.159194			−0.0795969	+	0.996827i	$0.525363\pi$
$968$		0			0
$969$	−2.20556e13	−	3.82014e13i	−0.803640	−	1.39195i
$970$		0			0
$971$	1.63561e13	−	2.83297e13i	0.590465	−	1.02272i	−0.403705	−	0.914889i	$-0.632278\pi$
$971$	1.63561e13	−	2.83297e13i	0.590465	−	1.02272i	0.994170	−	0.107826i	$-0.0343890\pi$
$972$		0			0
$973$	−6.50712e12	−	7.27350e12i	−0.232745	−	0.260157i
$974$		0			0
$975$	−6.62275e12	+	1.14709e13i	−0.234702	+	0.406516i
$976$		0			0
$977$	3.14481e12	+	5.44698e12i	0.110426	+	0.191263i	0.915942	−	0.401311i	$-0.131445\pi$
$977$	3.14481e12	+	5.44698e12i	0.110426	+	0.191263i	−0.805516	+	0.592573i	$0.798112\pi$
$978$		0			0
$979$	2.49941e12			0.0869591
$980$		0			0
$981$	−6.11817e11			−0.0210917
$982$		0			0
$983$	5.33975e12	+	9.24871e12i	0.182402	+	0.315930i	0.942698	−	0.333647i	$-0.108279\pi$
$983$	5.33975e12	+	9.24871e12i	0.182402	+	0.315930i	−0.760296	+	0.649577i	$0.774946\pi$
$984$		0			0
$985$	−4.46388e12	+	7.73166e12i	−0.151095	+	0.261704i
$986$		0			0
$987$	−1.88133e13	−	2.10290e13i	−0.631011	−	0.705329i
$988$		0			0
$989$	−1.11556e13	+	1.93221e13i	−0.370774	+	0.642200i
$990$		0			0
$991$	2.84247e13	+	4.92330e13i	0.936191	+	1.62153i	0.772496	+	0.635019i	$0.219008\pi$
$991$	2.84247e13	+	4.92330e13i	0.936191	+	1.62153i	0.163695	+	0.986511i	$0.447659\pi$
$992$		0			0
$993$	3.90504e13			1.27454
$994$		0			0
$995$	−7.15702e13			−2.31488
$996$		0			0
$997$	8.88145e12	+	1.53831e13i	0.284679	+	0.493079i	0.972531	−	0.232772i	$-0.0747796\pi$
$997$	8.88145e12	+	1.53831e13i	0.284679	+	0.493079i	−0.687852	+	0.725851i	$0.741446\pi$
$998$		0			0
$999$	1.79034e13	−	3.10096e13i	0.568709	−	0.985034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.10.i.c.65.5		10
4.3	odd	2		7.10.c.a.2.2	✓	10
7.4	even	3	inner	112.10.i.c.81.5		10
12.11	even	2		63.10.e.b.37.4		10
28.3	even	6		49.10.c.g.18.2		10
28.11	odd	6		7.10.c.a.4.2	yes	10
28.19	even	6		49.10.a.f.1.4		5
28.23	odd	6		49.10.a.e.1.4		5
28.27	even	2		49.10.c.g.30.2		10
84.11	even	6		63.10.e.b.46.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.c.a.2.2	✓	10	4.3	odd	2
7.10.c.a.4.2	yes	10	28.11	odd	6
49.10.a.e.1.4		5	28.23	odd	6
49.10.a.f.1.4		5	28.19	even	6
49.10.c.g.18.2		10	28.3	even	6
49.10.c.g.30.2		10	28.27	even	2
63.10.e.b.37.4		10	12.11	even	2
63.10.e.b.46.4		10	84.11	even	6
112.10.i.c.65.5		10	1.1	even	1	trivial
112.10.i.c.81.5		10	7.4	even	3	inner

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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	112.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(79.7348 + 138.105i) q^{3} +(1014.15 - 1756.56i) q^{5} +(4235.51 + 4734.35i) q^{7} +(-2873.78 + 4977.54i) q^{9} +O(q^{10})\)	\(q+(79.7348 + 138.105i) q^{3} +(1014.15 - 1756.56i) q^{5} +(4235.51 + 4734.35i) q^{7} +(-2873.78 + 4977.54i) q^{9} +(4289.29 + 7429.26i) q^{11} -38438.1 q^{13} +323452. q^{15} +(150942. + 261439. i) q^{17} +(-458143. + 793527. i) q^{19} +(-316119. + 962436. i) q^{21} +(966607. - 1.67421e6i) q^{23} +(-1.08043e6 - 1.87136e6i) q^{25} +2.22228e6 q^{27} +4.52529e6 q^{29} +(147255. + 255054. i) q^{31} +(-684011. + 1.18474e6i) q^{33} +(1.26116e7 - 2.63858e6i) q^{35} +(8.05632e6 - 1.39540e7i) q^{37} +(-3.06486e6 - 5.30849e6i) q^{39} +1.28783e7 q^{41} -1.15410e7 q^{43} +(5.82889e6 + 1.00959e7i) q^{45} +(-1.39268e7 + 2.41219e7i) q^{47} +(-4.47455e6 + 4.01048e7i) q^{49} +(-2.40707e7 + 4.16916e7i) q^{51} +(2.11827e7 + 3.66896e7i) q^{53} +1.73999e7 q^{55} -1.46120e8 q^{57} +(1.17321e6 + 2.03205e6i) q^{59} +(4.34201e6 - 7.52057e6i) q^{61} +(-3.57374e7 + 7.47691e6i) q^{63} +(-3.89820e7 + 6.75188e7i) q^{65} +(1.26144e8 + 2.18488e8i) q^{67} +3.08289e8 q^{69} +2.50094e8 q^{71} +(-2.32270e7 - 4.02303e7i) q^{73} +(1.72296e8 - 2.98426e8i) q^{75} +(-1.70054e7 + 5.17737e7i) q^{77} +(5.53584e7 - 9.58836e7i) q^{79} +(2.33758e8 + 4.04880e8i) q^{81} -2.81805e8 q^{83} +6.12310e8 q^{85} +(3.60823e8 + 6.24964e8i) q^{87} +(1.45677e8 - 2.52321e8i) q^{89} +(-1.62805e8 - 1.81980e8i) q^{91} +(-2.34827e7 + 4.06733e7i) q^{93} +(9.29250e8 + 1.60951e9i) q^{95} +1.01107e8 q^{97} -4.93059e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 161 q^{3} + 1533 q^{5} + 1036 q^{7} - 35734 q^{9}+O(q^{10}) \) 10 * q - 161 * q^3 + 1533 * q^5 + 1036 * q^7 - 35734 * q^9	\( 10 q - 161 q^{3} + 1533 q^{5} + 1036 q^{7} - 35734 q^{9} - 42213 q^{11} - 319676 q^{13} - 151394 q^{15} + 324681 q^{17} + 16121 q^{19} - 1557857 q^{21} - 2638863 q^{23} - 1304092 q^{25} + 18331558 q^{27} + 15292500 q^{29} - 19179237 q^{31} + 1689359 q^{33} + 43746759 q^{35} + 39566985 q^{37} + 44299486 q^{39} - 53436852 q^{41} - 101835992 q^{43} + 85098230 q^{45} - 32509659 q^{47} - 49024598 q^{49} - 44168403 q^{51} - 25714707 q^{53} + 144695222 q^{55} - 121710346 q^{57} - 46776513 q^{59} - 113075039 q^{61} - 318071530 q^{63} - 338113566 q^{65} + 126707879 q^{67} + 1323616182 q^{69} + 1188736032 q^{71} - 859257651 q^{73} + 169061732 q^{75} + 1911891891 q^{77} + 527065417 q^{79} + 551662715 q^{81} + 144863208 q^{83} - 1197360222 q^{85} + 340781350 q^{87} + 1661554797 q^{89} - 726641384 q^{91} - 423057489 q^{93} + 1197123495 q^{95} + 869770188 q^{97} + 1900777180 q^{99}+O(q^{100}) \) 10 * q - 161 * q^3 + 1533 * q^5 + 1036 * q^7 - 35734 * q^9 - 42213 * q^11 - 319676 * q^13 - 151394 * q^15 + 324681 * q^17 + 16121 * q^19 - 1557857 * q^21 - 2638863 * q^23 - 1304092 * q^25 + 18331558 * q^27 + 15292500 * q^29 - 19179237 * q^31 + 1689359 * q^33 + 43746759 * q^35 + 39566985 * q^37 + 44299486 * q^39 - 53436852 * q^41 - 101835992 * q^43 + 85098230 * q^45 - 32509659 * q^47 - 49024598 * q^49 - 44168403 * q^51 - 25714707 * q^53 + 144695222 * q^55 - 121710346 * q^57 - 46776513 * q^59 - 113075039 * q^61 - 318071530 * q^63 - 338113566 * q^65 + 126707879 * q^67 + 1323616182 * q^69 + 1188736032 * q^71 - 859257651 * q^73 + 169061732 * q^75 + 1911891891 * q^77 + 527065417 * q^79 + 551662715 * q^81 + 144863208 * q^83 - 1197360222 * q^85 + 340781350 * q^87 + 1661554797 * q^89 - 726641384 * q^91 - 423057489 * q^93 + 1197123495 * q^95 + 869770188 * q^97 + 1900777180 * q^99

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