LMFDB - Embedded newform 42.9.c.a.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,9,Mod(13,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("42.13");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	42.c (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:	$17.1099016226$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 7731 x^{10} + 218714 x^{9} + 46944238 x^{8} + 954612102 x^{7} + \cdots + 37\!\cdots\!84 $ x^12 - 2x^11 + 7731x^10 + 218714x^9 + 46944238x^8 + 954612102x^7 + 95335059229x^6 + 576178351086x^5 + 122405480888457x^4 + 247993465027288x^3 + 91263792176643256x^2 - 730882789543557696*x + 37671313072244229184
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{18}\cdot 7^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.4
Root			$-26.5796 + 46.0372i$ of defining polynomial
Character	$\chi$	$=$	42.13
Dual form			42.9.c.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.3137 q^{2} +46.7654i q^{3} +128.000 q^{4} -1217.44i q^{5} -529.090i q^{6} +(1530.45 + 1850.01i) q^{7} -1448.15 q^{8} -2187.00 q^{9} +O(q^{10})$	\(q-11.3137 q^{2} +46.7654i q^{3} +128.000 q^{4} -1217.44i q^{5} -529.090i q^{6} +(1530.45 + 1850.01i) q^{7} -1448.15 q^{8} -2187.00 q^{9} +13773.8i q^{10} -6834.76 q^{11} +5985.97i q^{12} +17796.6i q^{13} +(-17315.0 - 20930.5i) q^{14} +56934.2 q^{15} +16384.0 q^{16} -74768.9i q^{17} +24743.1 q^{18} -75027.4i q^{19} -155833. i q^{20} +(-86516.4 + 71571.8i) q^{21} +77326.4 q^{22} -411787. q^{23} -67723.5i q^{24} -1.09154e6 q^{25} -201345. i q^{26} -102276. i q^{27} +(195897. + 236801. i) q^{28} +238815. q^{29} -644137. q^{30} -1.56519e6i q^{31} -185364. q^{32} -319630. i q^{33} +845913. i q^{34} +(2.25228e6 - 1.86323e6i) q^{35} -279936. q^{36} -3.44583e6 q^{37} +848838. i q^{38} -832262. q^{39} +1.76305e6i q^{40} +801213. i q^{41} +(978822. - 809743. i) q^{42} +2.39098e6 q^{43} -874849. q^{44} +2.66255e6i q^{45} +4.65884e6 q^{46} -3.96652e6i q^{47} +766204. i q^{48} +(-1.08027e6 + 5.66268e6i) q^{49} +1.23494e7 q^{50} +3.49659e6 q^{51} +2.27796e6i q^{52} -8.82223e6 q^{53} +1.15712e6i q^{54} +8.32093e6i q^{55} +(-2.21632e6 - 2.67910e6i) q^{56} +3.50868e6 q^{57} -2.70188e6 q^{58} -1.19343e7i q^{59} +7.28758e6 q^{60} +6.09385e6i q^{61} +1.77081e7i q^{62} +(-3.34708e6 - 4.04597e6i) q^{63} +2.09715e6 q^{64} +2.16663e7 q^{65} +3.61620e6i q^{66} -2.76399e7 q^{67} -9.57042e6i q^{68} -1.92574e7i q^{69} +(-2.54817e7 + 2.10801e7i) q^{70} -8.48069e6 q^{71} +3.16711e6 q^{72} +1.38747e7i q^{73} +3.89851e7 q^{74} -5.10465e7i q^{75} -9.60350e6i q^{76} +(-1.04602e7 - 1.26444e7i) q^{77} +9.41597e6 q^{78} +4.60156e7 q^{79} -1.99466e7i q^{80} +4.78297e6 q^{81} -9.06469e6i q^{82} +7.71406e7i q^{83} +(-1.10741e7 + 9.16120e6i) q^{84} -9.10269e7 q^{85} -2.70508e7 q^{86} +1.11683e7i q^{87} +9.89779e6 q^{88} -3.73113e7i q^{89} -3.01233e7i q^{90} +(-3.29238e7 + 2.72367e7i) q^{91} -5.27088e7 q^{92} +7.31966e7 q^{93} +4.48761e7i q^{94} -9.13416e7 q^{95} -8.66861e6i q^{96} -1.35344e7i q^{97} +(1.22219e7 - 6.40659e7i) q^{98} +1.49476e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 1536 q^{4} + 6420 q^{7} - 26244 q^{9}+O(q^{10}) $ 12 * q + 1536 * q^4 + 6420 * q^7 - 26244 * q^9	$ 12 q + 1536 q^{4} + 6420 q^{7} - 26244 q^{9} + 4344 q^{11} - 12288 q^{14} + 59616 q^{15} + 196608 q^{16} - 224856 q^{21} - 508416 q^{22} + 499800 q^{23} - 3001476 q^{25} + 821760 q^{28} - 1278408 q^{29} + 705024 q^{30} + 2028912 q^{35} - 3359232 q^{36} + 7068648 q^{37} - 5473008 q^{39} + 1513728 q^{42} - 11388024 q^{43} + 556032 q^{44} + 8171520 q^{46} - 12346788 q^{49} + 30019584 q^{50} + 16727472 q^{51} + 19714968 q^{53} - 1572864 q^{56} - 10386144 q^{57} - 17696256 q^{58} + 7630848 q^{60} - 14040540 q^{63} + 25165824 q^{64} - 93770592 q^{65} - 9394008 q^{67} + 11218944 q^{70} + 5393208 q^{71} + 58512384 q^{74} + 24982968 q^{77} + 32638464 q^{78} + 134560968 q^{79} + 57395628 q^{81} - 28781568 q^{84} - 102074640 q^{85} - 282934272 q^{86} - 65077248 q^{88} - 96105408 q^{91} + 63974400 q^{92} + 202339296 q^{93} - 378351840 q^{95} + 387747840 q^{98} - 9500328 q^{99}+O(q^{100}) $ 12 * q + 1536 * q^4 + 6420 * q^7 - 26244 * q^9 + 4344 * q^11 - 12288 * q^14 + 59616 * q^15 + 196608 * q^16 - 224856 * q^21 - 508416 * q^22 + 499800 * q^23 - 3001476 * q^25 + 821760 * q^28 - 1278408 * q^29 + 705024 * q^30 + 2028912 * q^35 - 3359232 * q^36 + 7068648 * q^37 - 5473008 * q^39 + 1513728 * q^42 - 11388024 * q^43 + 556032 * q^44 + 8171520 * q^46 - 12346788 * q^49 + 30019584 * q^50 + 16727472 * q^51 + 19714968 * q^53 - 1572864 * q^56 - 10386144 * q^57 - 17696256 * q^58 + 7630848 * q^60 - 14040540 * q^63 + 25165824 * q^64 - 93770592 * q^65 - 9394008 * q^67 + 11218944 * q^70 + 5393208 * q^71 + 58512384 * q^74 + 24982968 * q^77 + 32638464 * q^78 + 134560968 * q^79 + 57395628 * q^81 - 28781568 * q^84 - 102074640 * q^85 - 282934272 * q^86 - 65077248 * q^88 - 96105408 * q^91 + 63974400 * q^92 + 202339296 * q^93 - 378351840 * q^95 + 387747840 * q^98 - 9500328 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$1$	$-1$

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 $

$2$	−11.3137			−0.707107
$2$	−11.3137			−0.707107
$3$			46.7654i			0.577350i
$3$			46.7654i			0.577350i
$4$	128.000			0.500000
$5$		−	1217.44i		−	1.94791i	−0.226742	−	0.973955i	$-0.572807\pi$
$5$		−	1217.44i		−	1.94791i	0.226742	−	0.973955i	$-0.427193\pi$
$6$		−	529.090i		−	0.408248i
$7$	1530.45	+	1850.01i	0.637420	+	0.770517i
$7$	1530.45	+	1850.01i	0.637420	+	0.770517i
$8$	−1448.15			−0.353553
$9$	−2187.00			−0.333333
$10$			13773.8i			1.37738i
$11$	−6834.76			−0.466823			−0.233412	−	0.972378i	$-0.574989\pi$
$11$	−6834.76			−0.466823			−0.233412	+	0.972378i	$0.574989\pi$
$12$			5985.97i			0.288675i
$13$			17796.6i			0.623107i	0.950229	+	0.311553i	$0.100849\pi$
$13$			17796.6i			0.623107i	−0.950229	+	0.311553i	$0.899151\pi$
$14$	−17315.0	−	20930.5i	−0.450724	−	0.544837i
$15$	56934.2			1.12463
$16$	16384.0			0.250000
$17$		−	74768.9i		−	0.895211i	−0.894231	−	0.447605i	$-0.852277\pi$
$17$		−	74768.9i		−	0.895211i	0.894231	−	0.447605i	$-0.147723\pi$
$18$	24743.1			0.235702
$19$		−	75027.4i		−	0.575712i	−0.957674	−	0.287856i	$-0.907058\pi$
$19$		−	75027.4i		−	0.575712i	0.957674	−	0.287856i	$-0.0929425\pi$
$20$		−	155833.i		−	0.973955i
$21$	−86516.4	+	71571.8i	−0.444858	+	0.368015i
$22$	77326.4			0.330094
$23$	−411787.			−1.47150			−0.735752	−	0.677251i	$-0.763171\pi$
$23$	−411787.			−1.47150			−0.735752	+	0.677251i	$0.763171\pi$
$24$		−	67723.5i		−	0.204124i
$25$	−1.09154e6			−2.79435
$26$		−	201345.i		−	0.440603i
$27$		−	102276.i		−	0.192450i
$28$	195897.	+	236801.i	0.318710	+	0.385258i
$29$	238815.			0.337652			0.168826	−	0.985646i	$-0.446002\pi$
$29$	238815.			0.337652			0.168826	+	0.985646i	$0.446002\pi$
$30$	−644137.			−0.795231
$31$		−	1.56519e6i		−	1.69480i	−0.530951	−	0.847402i	$-0.678165\pi$
$31$		−	1.56519e6i		−	1.69480i	0.530951	−	0.847402i	$-0.321835\pi$
$32$	−185364.			−0.176777
$33$		−	319630.i		−	0.269520i
$34$			845913.i			0.633009i
$35$	2.25228e6	−	1.86323e6i	1.50090	−	1.24164i
$36$	−279936.			−0.166667
$37$	−3.44583e6			−1.83860			−0.919299	−	0.393559i	$-0.871244\pi$
$37$	−3.44583e6			−1.83860			−0.919299	+	0.393559i	$0.871244\pi$
$38$			848838.i			0.407090i
$39$	−832262.			−0.359751
$40$			1.76305e6i			0.688690i
$41$			801213.i			0.283539i	0.989900	+	0.141769i	$0.0452792\pi$
$41$			801213.i			0.283539i	−0.989900	+	0.141769i	$0.954721\pi$
$42$	978822.	−	809743.i	0.314562	−	0.260226i
$43$	2.39098e6			0.699362			0.349681	−	0.936869i	$-0.386290\pi$
$43$	2.39098e6			0.699362			0.349681	+	0.936869i	$0.386290\pi$
$44$	−874849.			−0.233412
$45$			2.66255e6i			0.649303i
$46$	4.65884e6			1.04051
$47$		−	3.96652e6i		−	0.812866i	−0.913681	−	0.406433i	$-0.866773\pi$
$47$		−	3.96652e6i		−	0.812866i	0.913681	−	0.406433i	$-0.133227\pi$
$48$			766204.i			0.144338i
$49$	−1.08027e6	+	5.66268e6i	−0.187391	+	0.982285i
$50$	1.23494e7			1.97591
$51$	3.49659e6			0.516850
$52$			2.27796e6i			0.311553i
$53$	−8.82223e6			−1.11808			−0.559042	−	0.829139i	$-0.688831\pi$
$53$	−8.82223e6			−1.11808			−0.559042	+	0.829139i	$0.688831\pi$
$54$			1.15712e6i			0.136083i
$55$			8.32093e6i			0.909329i
$56$	−2.21632e6	−	2.67910e6i	−0.225362	−	0.272419i
$57$	3.50868e6			0.332388
$58$	−2.70188e6			−0.238756
$59$		−	1.19343e7i		−	0.984890i	−0.870344	−	0.492445i	$-0.836103\pi$
$59$		−	1.19343e7i		−	0.984890i	0.870344	−	0.492445i	$-0.163897\pi$
$60$	7.28758e6			0.562313
$61$			6.09385e6i			0.440121i	0.975486	+	0.220061i	$0.0706255\pi$
$61$			6.09385e6i			0.440121i	−0.975486	+	0.220061i	$0.929375\pi$
$62$			1.77081e7i			1.19841i
$63$	−3.34708e6	−	4.04597e6i	−0.212473	−	0.256839i
$64$	2.09715e6			0.125000
$65$	2.16663e7			1.21376
$66$			3.61620e6i			0.190580i
$67$	−2.76399e7			−1.37163			−0.685816	−	0.727775i	$-0.740555\pi$
$67$	−2.76399e7			−1.37163			−0.685816	+	0.727775i	$0.740555\pi$
$68$		−	9.57042e6i		−	0.447605i
$69$		−	1.92574e7i		−	0.849573i
$70$	−2.54817e7	+	2.10801e7i	−1.06129	+	0.877970i
$71$	−8.48069e6			−0.333732			−0.166866	−	0.985980i	$-0.553365\pi$
$71$	−8.48069e6			−0.333732			−0.166866	+	0.985980i	$0.553365\pi$
$72$	3.16711e6			0.117851
$73$			1.38747e7i			0.488576i	0.969703	+	0.244288i	$0.0785542\pi$
$73$			1.38747e7i			0.488576i	−0.969703	+	0.244288i	$0.921446\pi$
$74$	3.89851e7			1.30009
$75$		−	5.10465e7i		−	1.61332i
$76$		−	9.60350e6i		−	0.287856i
$77$	−1.04602e7	−	1.26444e7i	−0.297562	−	0.359695i
$78$	9.41597e6			0.254382
$79$	4.60156e7			1.18140			0.590700	−	0.806891i	$-0.298852\pi$
$79$	4.60156e7			1.18140			0.590700	+	0.806891i	$0.298852\pi$
$80$		−	1.99466e7i		−	0.486977i
$81$	4.78297e6			0.111111
$82$		−	9.06469e6i		−	0.200492i
$83$			7.71406e7i			1.62544i	0.582655	+	0.812720i	$0.302014\pi$
$83$			7.71406e7i			1.62544i	−0.582655	+	0.812720i	$0.697986\pi$
$84$	−1.10741e7	+	9.16120e6i	−0.222429	+	0.184007i
$85$	−9.10269e7			−1.74379
$86$	−2.70508e7			−0.494523
$87$			1.11683e7i			0.194943i
$88$	9.89779e6			0.165047
$89$		−	3.73113e7i		−	0.594675i	−0.954772	−	0.297338i	$-0.903901\pi$
$89$		−	3.73113e7i		−	0.594675i	0.954772	−	0.297338i	$-0.0960987\pi$
$90$		−	3.01233e7i		−	0.459127i
$91$	−3.29238e7	+	2.72367e7i	−0.480114	+	0.397181i
$92$	−5.27088e7			−0.735752
$93$	7.31966e7			0.978496
$94$			4.48761e7i			0.574783i
$95$	−9.13416e7			−1.12144
$96$		−	8.66861e6i		−	0.102062i
$97$		−	1.35344e7i		−	0.152880i	−0.997074	−	0.0764402i	$-0.975645\pi$
$97$		−	1.35344e7i		−	0.152880i	0.997074	−	0.0764402i	$-0.0243554\pi$
$98$	1.22219e7	−	6.40659e7i	0.132506	−	0.694581i
$99$	1.49476e7			0.155608
$100$	−1.39718e8			−1.39718
$101$		−	7.59658e7i		−	0.730017i	−0.931004	−	0.365008i	$-0.881066\pi$
$101$		−	7.59658e7i		−	0.730017i	0.931004	−	0.365008i	$-0.118934\pi$
$102$	−3.95595e7			−0.365468
$103$		−	1.30594e8i		−	1.16031i	−0.814507	−	0.580154i	$-0.802992\pi$
$103$		−	1.30594e8i		−	1.16031i	0.814507	−	0.580154i	$-0.197008\pi$
$104$		−	2.57722e7i		−	0.220302i
$105$	8.71347e7	+	1.05329e8i	0.716859	+	0.866543i
$106$	9.98121e7			0.790605
$107$	3.75075e7			0.286143			0.143072	−	0.989712i	$-0.454302\pi$
$107$	3.75075e7			0.286143			0.143072	+	0.989712i	$0.454302\pi$
$108$		−	1.30913e7i		−	0.0962250i
$109$	9.08581e7			0.643662			0.321831	−	0.946797i	$-0.395702\pi$
$109$	9.08581e7			0.643662			0.321831	+	0.946797i	$0.395702\pi$
$110$		−	9.41406e7i		−	0.642993i
$111$		−	1.61146e8i		−	1.06152i
$112$	2.50748e7	+	3.03106e7i	0.159355	+	0.192629i
$113$	1.20942e8			0.741762			0.370881	−	0.928680i	$-0.379056\pi$
$113$	1.20942e8			0.741762			0.370881	+	0.928680i	$0.379056\pi$
$114$	−3.96962e7			−0.235033
$115$			5.01328e8i			2.86636i
$116$	3.05683e7			0.168826
$117$		−	3.89211e7i		−	0.207702i
$118$			1.35021e8i			0.696422i
$119$	1.38323e8	−	1.14430e8i	0.689775	−	0.570625i
$120$	−8.24495e7			−0.397615
$121$	−1.67645e8			−0.782076
$122$		−	6.89440e7i		−	0.311213i
$123$	−3.74690e7			−0.163701
$124$		−	2.00344e8i		−	0.847402i
$125$			8.53329e8i			3.49524i
$126$	3.78679e7	+	4.57750e7i	0.150241	+	0.181612i
$127$	2.18852e8			0.841269			0.420634	−	0.907230i	$-0.361808\pi$
$127$	2.18852e8			0.841269			0.420634	+	0.907230i	$0.361808\pi$
$128$	−2.37266e7			−0.0883883
$129$			1.11815e8i			0.403777i
$130$	−2.45126e8			−0.858255
$131$		−	2.96185e7i		−	0.100572i	−0.998735	−	0.0502861i	$-0.983987\pi$
$131$		−	2.96185e7i		−	0.100572i	0.998735	−	0.0502861i	$-0.0160133\pi$
$132$		−	4.09126e7i		−	0.134760i
$133$	1.38801e8	−	1.14825e8i	0.443596	−	0.366970i
$134$	3.12710e8			0.969891
$135$	−1.24515e8			−0.374875
$136$			1.08277e8i			0.316505i
$137$	5.49370e8			1.55949			0.779745	−	0.626097i	$-0.215349\pi$
$137$	5.49370e8			1.55949			0.779745	+	0.626097i	$0.215349\pi$
$138$			2.17872e8i			0.600739i
$139$		−	3.91626e8i		−	1.04909i	−0.851383	−	0.524544i	$-0.824236\pi$
$139$		−	3.91626e8i		−	1.04909i	0.851383	−	0.524544i	$-0.175764\pi$
$140$	2.88292e8	−	2.38494e8i	0.750448	−	0.620818i
$141$	1.85496e8			0.469308
$142$	9.59481e7			0.235984
$143$		−	1.21635e8i		−	0.290881i
$144$	−3.58318e7			−0.0833333
$145$		−	2.90744e8i		−	0.657716i
$146$		−	1.56974e8i		−	0.345475i
$147$	−2.64817e8	−	5.05194e7i	−0.567123	−	0.108191i
$148$	−4.41066e8			−0.919299
$149$	−4.23415e8			−0.859054			−0.429527	−	0.903054i	$-0.641320\pi$
$149$	−4.23415e8			−0.859054			−0.429527	+	0.903054i	$0.641320\pi$
$150$			5.77525e8i			1.14079i
$151$	9.17270e8			1.76437			0.882184	−	0.470904i	$-0.156072\pi$
$151$	9.17270e8			1.76437			0.882184	+	0.470904i	$0.156072\pi$
$152$			1.08651e8i			0.203545i
$153$			1.63520e8i			0.298404i
$154$	1.18344e8	+	1.43055e8i	0.210408	+	0.254343i
$155$	−1.90553e9			−3.30133
$156$	−1.06530e8			−0.179875
$157$		−	2.19023e8i		−	0.360487i	−0.983622	−	0.180244i	$-0.942311\pi$
$157$		−	2.19023e8i		−	0.360487i	0.983622	−	0.180244i	$-0.0576887\pi$
$158$	−5.20607e8			−0.835376
$159$		−	4.12575e8i		−	0.645527i
$160$			2.25670e8i			0.344345i
$161$	−6.30218e8	−	7.61811e8i	−0.937966	−	1.13382i
$162$	−5.41131e7			−0.0785674
$163$	3.06386e8			0.434029			0.217015	−	0.976168i	$-0.430368\pi$
$163$	3.06386e8			0.434029			0.217015	+	0.976168i	$0.430368\pi$
$164$			1.02555e8i			0.141769i
$165$	−3.89131e8			−0.525002
$166$		−	8.72746e8i		−	1.14936i
$167$			1.70707e8i			0.219475i	0.993961	+	0.109737i	$0.0350010\pi$
$167$			1.70707e8i			0.219475i	−0.993961	+	0.109737i	$0.964999\pi$
$168$	1.25289e8	−	1.03647e8i	0.157281	−	0.130113i
$169$	4.99013e8			0.611738
$170$	1.02985e9			1.23305
$171$			1.64085e8i			0.191904i
$172$	3.06045e8			0.349681
$173$		−	1.99383e8i		−	0.222589i	−0.993787	−	0.111294i	$-0.964500\pi$
$173$		−	1.99383e8i		−	0.222589i	0.993787	−	0.111294i	$-0.0354997\pi$
$174$		−	1.26354e8i		−	0.137846i
$175$	−1.67055e9	−	2.01937e9i	−1.78118	−	2.15309i
$176$	−1.11981e8			−0.116706
$177$	5.58111e8			0.568627
$178$			4.22129e8i			0.420499i
$179$	−1.53247e9			−1.49272			−0.746361	−	0.665542i	$-0.768201\pi$
$179$	−1.53247e9			−1.49272			−0.746361	+	0.665542i	$0.768201\pi$
$180$			3.40806e8i			0.324652i
$181$		−	1.18396e9i		−	1.10312i	−0.834134	−	0.551562i	$-0.814032\pi$
$181$		−	1.18396e9i		−	1.10312i	0.834134	−	0.551562i	$-0.185968\pi$
$182$	3.72490e8	−	3.08148e8i	0.339492	−	0.280849i
$183$	−2.84981e8			−0.254104
$184$	5.96332e8			0.520255
$185$			4.19510e9i			3.58142i
$186$	−8.28125e8			−0.691901
$187$			5.11027e8i			0.417905i
$188$		−	5.07715e8i		−	0.406433i
$189$	1.89211e8	−	1.56528e8i	0.148286	−	0.122672i
$190$	1.03341e9			0.792974
$191$	4.47293e8			0.336093			0.168046	−	0.985779i	$-0.446254\pi$
$191$	4.47293e8			0.336093			0.168046	+	0.985779i	$0.446254\pi$
$192$			9.80741e7i			0.0721688i
$193$	−7.16074e7			−0.0516094			−0.0258047	−	0.999667i	$-0.508215\pi$
$193$	−7.16074e7			−0.0516094			−0.0258047	+	0.999667i	$0.508215\pi$
$194$			1.53124e8i			0.108103i
$195$			1.01323e9i			0.700762i
$196$	−1.38275e8	+	7.24823e8i	−0.0936957	+	0.491143i
$197$	1.74847e9			1.16090			0.580449	−	0.814297i	$-0.302877\pi$
$197$	1.74847e9			1.16090			0.580449	+	0.814297i	$0.302877\pi$
$198$	−1.69113e8			−0.110031
$199$		−	2.19613e8i		−	0.140038i	−0.997546	−	0.0700189i	$-0.977694\pi$
$199$		−	2.19613e8i		−	0.140038i	0.997546	−	0.0700189i	$-0.0223060\pi$
$200$	1.58072e9			0.987953
$201$		−	1.29259e9i		−	0.791913i
$202$			8.59455e8i			0.516200i
$203$	3.65493e8	+	4.41810e8i	0.215226	+	0.260166i
$204$	4.47564e8			0.258425
$205$	9.75432e8			0.552308
$206$			1.47750e9i			0.820462i
$207$	9.00579e8			0.490501
$208$			2.91579e8i			0.155777i
$209$			5.12794e8i			0.268756i
$210$	−9.85817e8	−	1.19166e9i	−0.506896	−	0.612739i
$211$	3.75750e8			0.189570			0.0947848	−	0.995498i	$-0.469784\pi$
$211$	3.75750e8			0.189570			0.0947848	+	0.995498i	$0.469784\pi$
$212$	−1.12925e9			−0.559042
$213$		−	3.96603e8i		−	0.192680i
$214$	−4.24349e8			−0.202334
$215$		−	2.91088e9i		−	1.36229i
$216$			1.48111e8i			0.0680414i
$217$	2.89561e9	−	2.39543e9i	1.30588	−	1.08030i
$218$	−1.02794e9			−0.455138
$219$	−6.48856e8			−0.282080
$220$			1.06508e9i			0.454665i
$221$	1.33063e9			0.557812
$222$			1.82315e9i			0.750605i
$223$			1.07030e9i			0.432797i	0.976305	+	0.216399i	$0.0694311\pi$
$223$			1.07030e9i			0.432797i	−0.976305	+	0.216399i	$0.930569\pi$
$224$	−2.83689e8	−	3.42925e8i	−0.112681	−	0.136209i
$225$	2.38721e9			0.931451
$226$	−1.36831e9			−0.524505
$227$			2.07113e9i			0.780016i	0.920812	+	0.390008i	$0.127528\pi$
$227$			2.07113e9i			0.780016i	−0.920812	+	0.390008i	$0.872472\pi$
$228$	4.49111e8			0.166194
$229$			4.22099e9i			1.53487i	0.641125	+	0.767436i	$0.278468\pi$
$229$			4.22099e9i			1.53487i	−0.641125	+	0.767436i	$0.721532\pi$
$230$		−	5.67188e9i		−	2.02682i
$231$	5.91319e8	−	4.89176e8i	0.207670	−	0.171798i
$232$	−3.45841e8			−0.119378
$233$	−5.32219e9			−1.80579			−0.902894	−	0.429863i	$-0.858562\pi$
$233$	−5.32219e9			−1.80579			−0.902894	+	0.429863i	$0.858562\pi$
$234$			4.40342e8i			0.146868i
$235$	−4.82902e9			−1.58339
$236$		−	1.52759e9i		−	0.492445i
$237$			2.15194e9i			0.682082i
$238$	−1.56495e9	+	1.29462e9i	−0.487744	+	0.403493i
$239$	−1.25147e9			−0.383557			−0.191779	−	0.981438i	$-0.561426\pi$
$239$	−1.25147e9			−0.383557			−0.191779	+	0.981438i	$0.561426\pi$
$240$	9.32810e8			0.281157
$241$			6.39771e9i			1.89652i	0.317500	+	0.948258i	$0.397157\pi$
$241$			6.39771e9i			1.89652i	−0.317500	+	0.948258i	$0.602843\pi$
$242$	1.89669e9			0.553011
$243$			2.23677e8i			0.0641500i
$244$			7.80012e8i			0.220061i
$245$	6.89399e9	+	1.31517e9i	1.91340	+	0.365022i
$246$	4.23914e8			0.115754
$247$	1.33523e9			0.358730
$248$			2.26663e9i			0.599204i
$249$	−3.60751e9			−0.938448
$250$		−	9.65432e9i		−	2.47151i
$251$		−	4.85954e9i		−	1.22434i	−0.790728	−	0.612168i	$-0.790298\pi$
$251$		−	4.85954e9i		−	1.22434i	0.790728	−	0.612168i	$-0.209702\pi$
$252$	−4.28427e8	−	5.17884e8i	−0.106237	−	0.128419i
$253$	2.81447e9			0.686932
$254$	−2.47602e9			−0.594867
$255$		−	4.25691e9i		−	1.00678i
$256$	2.68435e8			0.0625000
$257$		−	1.89350e9i		−	0.434044i	−0.976167	−	0.217022i	$-0.930366\pi$
$257$		−	1.89350e9i		−	0.434044i	0.976167	−	0.217022i	$-0.0696343\pi$
$258$		−	1.26504e9i		−	0.285513i
$259$	−5.27365e9	−	6.37482e9i	−1.17196	−	1.41667i
$260$	2.77329e9			0.606878
$261$	−5.22288e8			−0.112551
$262$			3.35095e8i			0.0711153i
$263$	4.03454e9			0.843279			0.421640	−	0.906763i	$-0.361455\pi$
$263$	4.03454e9			0.843279			0.421640	+	0.906763i	$0.361455\pi$
$264$			4.62874e8i			0.0952899i
$265$			1.07406e10i			2.17793i
$266$	−1.57036e9	+	1.29910e9i	−0.313670	+	0.259487i
$267$	1.74487e9			0.343336
$268$	−3.53791e9			−0.685816
$269$		−	6.61214e9i		−	1.26280i	−0.775459	−	0.631398i	$-0.782482\pi$
$269$		−	6.61214e9i		−	1.26280i	0.775459	−	0.631398i	$-0.217518\pi$
$270$	1.40873e9			0.265077
$271$		−	1.59913e8i		−	0.0296487i	−0.999890	−	0.0148243i	$-0.995281\pi$
$271$		−	1.59913e8i		−	0.0296487i	0.999890	−	0.0148243i	$-0.00471891\pi$
$272$		−	1.22501e9i		−	0.223803i
$273$	−1.27373e9	−	1.53969e9i	−0.229312	−	0.277194i
$274$	−6.21541e9			−1.10273
$275$	7.46044e9			1.30447
$276$		−	2.46495e9i		−	0.424787i
$277$	−2.73463e9			−0.464494			−0.232247	−	0.972657i	$-0.574608\pi$
$277$	−2.73463e9			−0.464494			−0.232247	+	0.972657i	$0.574608\pi$
$278$			4.43074e9i			0.741817i
$279$			3.42307e9i			0.564935i
$280$	−3.26165e9	+	2.69825e9i	−0.530647	+	0.438985i
$281$	−6.19921e9			−0.994286			−0.497143	−	0.867669i	$-0.665618\pi$
$281$	−6.19921e9			−0.994286			−0.497143	+	0.867669i	$0.665618\pi$
$282$	−2.09865e9			−0.331851
$283$			3.18227e7i			0.00496124i	0.999997	+	0.00248062i	$0.000789607\pi$
$283$			3.18227e7i			0.00496124i	−0.999997	+	0.00248062i	$0.999210\pi$
$284$	−1.08553e9			−0.166866
$285$		−	4.27162e9i		−	0.647461i
$286$			1.37614e9i			0.205684i
$287$	−1.48225e9	+	1.22621e9i	−0.218471	+	0.180733i
$288$	4.05391e8			0.0589256
$289$	1.38537e9			0.198598
$290$			3.28939e9i			0.465075i
$291$	6.32941e8			0.0882655
$292$			1.77596e9i			0.244288i
$293$			5.29339e9i			0.718230i	0.933293	+	0.359115i	$0.116921\pi$
$293$			5.29339e9i			0.718230i	−0.933293	+	0.359115i	$0.883079\pi$
$294$	2.99607e9	+	5.71562e8i	0.401016	+	0.0765022i
$295$	−1.45293e10			−1.91848
$296$	4.99009e9			0.650043
$297$			6.99031e8i			0.0898401i
$298$	4.79039e9			0.607443
$299$		−	7.32839e9i		−	0.916904i
$300$		−	6.53395e9i		−	0.806660i
$301$	3.65926e9	+	4.42334e9i	0.445787	+	0.538870i
$302$	−1.03777e10			−1.24760
$303$	3.55257e9			0.421475
$304$		−	1.22925e9i		−	0.143928i
$305$	7.41891e9			0.857316
$306$		−	1.85001e9i		−	0.211003i
$307$		−	3.02123e8i		−	0.0340118i	−0.999855	−	0.0170059i	$-0.994587\pi$
$307$		−	3.02123e8i		−	0.0340118i	0.999855	−	0.0170059i	$-0.00541341\pi$
$308$	−1.33891e9	−	1.61848e9i	−0.148781	−	0.179847i
$309$	6.10726e9			0.669904
$310$	2.15586e10			2.33439
$311$		−	8.16882e9i		−	0.873208i	−0.899654	−	0.436604i	$-0.856181\pi$
$311$		−	8.16882e9i		−	0.873208i	0.899654	−	0.436604i	$-0.143819\pi$
$312$	1.20524e9			0.127191
$313$			3.90586e9i			0.406948i	0.979080	+	0.203474i	$0.0652233\pi$
$313$			3.90586e9i			0.406948i	−0.979080	+	0.203474i	$0.934777\pi$
$314$			2.47796e9i			0.254903i
$315$	−4.92574e9	+	4.07489e9i	−0.500299	+	0.413879i
$316$	5.89000e9			0.590700
$317$	−1.03245e10			−1.02243			−0.511215	−	0.859453i	$-0.670805\pi$
$317$	−1.03245e10			−1.02243			−0.511215	+	0.859453i	$0.670805\pi$
$318$			4.66775e9i			0.456456i
$319$	−1.63224e9			−0.157624
$320$		−	2.55316e9i		−	0.243489i
$321$			1.75405e9i			0.165205i
$322$	7.13010e9	+	8.61890e9i	0.663242	+	0.801731i
$323$	−5.60971e9			−0.515384
$324$	6.12220e8			0.0555556
$325$		−	1.94257e10i		−	1.74118i
$326$	−3.46637e9			−0.306905
$327$			4.24901e9i			0.371618i
$328$		−	1.16028e9i		−	0.100246i
$329$	7.33811e9	−	6.07055e9i	0.626326	−	0.518137i
$330$	4.40252e9			0.371232
$331$	1.36600e10			1.13799			0.568996	−	0.822340i	$-0.307332\pi$
$331$	1.36600e10			1.13799			0.568996	+	0.822340i	$0.307332\pi$
$332$			9.87400e9i			0.812720i
$333$	7.53603e9			0.612866
$334$		−	1.93132e9i		−	0.155192i
$335$			3.36501e10i			2.67182i
$336$	−1.41748e9	+	1.17263e9i	−0.111214	+	0.0920037i
$337$	9.81701e9			0.761131			0.380566	−	0.924754i	$-0.375729\pi$
$337$	9.81701e9			0.761131			0.380566	+	0.924754i	$0.375729\pi$
$338$	−5.64569e9			−0.432564
$339$			5.65592e9i			0.428257i
$340$	−1.16514e10			−0.871895
$341$			1.06977e10i			0.791174i
$342$		−	1.85641e9i		−	0.135697i
$343$	−1.21293e10	+	6.66790e9i	−0.876314	+	0.481740i
$344$	−3.46251e9			−0.247262
$345$	−2.34448e10			−1.65489
$346$			2.25576e9i			0.157394i
$347$	1.52070e10			1.04888			0.524441	−	0.851447i	$-0.324274\pi$
$347$	1.52070e10			1.04888			0.524441	+	0.851447i	$0.324274\pi$
$348$			1.42954e9i			0.0974717i
$349$		−	2.71134e10i		−	1.82760i	−0.406162	−	0.913801i	$-0.633133\pi$
$349$		−	2.71134e10i		−	1.82760i	0.406162	−	0.913801i	$-0.366867\pi$
$350$	1.89001e10	+	2.28465e10i	1.25948	+	1.52247i
$351$	1.82016e9			0.119917
$352$	1.26692e9			0.0825234
$353$		−	2.59922e10i		−	1.67395i	−0.547238	−	0.836977i	$-0.684321\pi$
$353$		−	2.59922e10i		−	1.67395i	0.547238	−	0.836977i	$-0.315679\pi$
$354$	−6.31430e9			−0.402080
$355$			1.03248e10i			0.650080i
$356$		−	4.77584e9i		−	0.297338i
$357$	5.35135e9	+	6.46874e9i	0.329451	+	0.398242i
$358$	1.73379e10			1.05551
$359$	−1.08402e10			−0.652620			−0.326310	−	0.945263i	$-0.605805\pi$
$359$	−1.08402e10			−0.652620			−0.326310	+	0.945263i	$0.605805\pi$
$360$		−	3.85578e9i		−	0.229563i
$361$	1.13545e10			0.668556
$362$			1.33950e10i			0.780026i
$363$		−	7.83998e9i		−	0.451532i
$364$	−4.21425e9	+	3.48629e9i	−0.240057	+	0.198590i
$365$	1.68917e10			0.951702
$366$	3.22419e9			0.179679
$367$		−	1.65482e10i		−	0.912195i	−0.889930	−	0.456097i	$-0.849247\pi$
$367$		−	1.65482e10i		−	0.912195i	0.889930	−	0.456097i	$-0.150753\pi$
$368$	−6.74672e9			−0.367876
$369$		−	1.75225e9i		−	0.0945130i
$370$		−	4.74622e10i		−	2.53245i
$371$	−1.35019e10	−	1.63212e10i	−0.712690	−	0.861503i
$372$	9.36916e9			0.489248
$373$	−1.98907e10			−1.02758			−0.513789	−	0.857916i	$-0.671759\pi$
$373$	−1.98907e10			−1.02758			−0.513789	+	0.857916i	$0.671759\pi$
$374$		−	5.78161e9i		−	0.295503i
$375$	−3.99063e10			−2.01798
$376$			5.74414e9i			0.287391i
$377$			4.25008e9i			0.210393i
$378$	−2.14068e9	+	1.77091e9i	−0.104854	+	0.0867419i
$379$	5.53707e9			0.268363			0.134182	−	0.990957i	$-0.457159\pi$
$379$	5.53707e9			0.268363			0.134182	+	0.990957i	$0.457159\pi$
$380$	−1.16917e10			−0.560718
$381$			1.02347e10i			0.485707i
$382$	−5.06055e9			−0.237653
$383$			1.21057e10i			0.562593i	0.959621	+	0.281296i	$0.0907644\pi$
$383$			1.21057e10i			0.562593i	−0.959621	+	0.281296i	$0.909236\pi$
$384$		−	1.10958e9i		−	0.0510310i
$385$	−1.53938e10	+	1.27347e10i	−0.700653	+	0.579625i
$386$	8.10145e8			0.0364933
$387$	−5.22907e9			−0.233121
$388$		−	1.73240e9i		−	0.0764402i
$389$	−3.12057e10			−1.36281			−0.681406	−	0.731906i	$-0.738631\pi$
$389$	−3.12057e10			−1.36281			−0.681406	+	0.731906i	$0.738631\pi$
$390$		−	1.14634e10i		−	0.495514i
$391$			3.07889e10i			1.31731i
$392$	1.56440e9	−	8.20044e9i	0.0662529	−	0.347290i
$393$	1.38512e9			0.0580654
$394$	−1.97817e10			−0.820878
$395$		−	5.60214e10i		−	2.30126i
$396$	1.91329e9			0.0778038
$397$		−	1.13444e10i		−	0.456686i	−0.973581	−	0.228343i	$-0.926669\pi$
$397$		−	1.13444e10i		−	0.456686i	0.973581	−	0.228343i	$-0.0733308\pi$
$398$			2.48463e9i			0.0990216i
$399$	5.36985e9	+	6.49110e9i	0.211870	+	0.256110i
$400$	−1.78839e10			−0.698588
$401$	−2.73259e10			−1.05681			−0.528404	−	0.848993i	$-0.677209\pi$
$401$	−2.73259e10			−1.05681			−0.528404	+	0.848993i	$0.677209\pi$
$402$			1.46240e10i			0.559967i
$403$	2.78549e10			1.05604
$404$		−	9.72362e9i		−	0.365008i
$405$		−	5.82300e9i		−	0.216434i
$406$	−4.13508e9	−	4.99851e9i	−0.152188	−	0.183965i
$407$	2.35514e10			0.858300
$408$	−5.06361e9			−0.182734
$409$		−	2.95072e10i		−	1.05447i	−0.849719	−	0.527236i	$-0.823228\pi$
$409$		−	2.95072e10i		−	1.05447i	0.849719	−	0.527236i	$-0.176772\pi$
$410$	−1.10358e10			−0.390541
$411$			2.56915e10i			0.900372i
$412$		−	1.67160e10i		−	0.580154i
$413$	2.20785e10	−	1.82647e10i	0.758874	−	0.627789i
$414$	−1.01889e10			−0.346837
$415$	9.39144e10			3.16621
$416$		−	3.29884e9i		−	0.110151i
$417$	1.83145e10			0.605691
$418$		−	5.80160e9i		−	0.190039i
$419$		−	3.64761e10i		−	1.18346i	−0.806138	−	0.591728i	$-0.798446\pi$
$419$		−	3.64761e10i		−	1.18346i	0.806138	−	0.591728i	$-0.201554\pi$
$420$	1.11532e10	+	1.34821e10i	0.358430	+	0.433272i
$421$	−4.19322e10			−1.33481			−0.667405	−	0.744695i	$-0.732595\pi$
$421$	−4.19322e10			−1.33481			−0.667405	+	0.744695i	$0.732595\pi$
$422$	−4.25112e9			−0.134046
$423$			8.67479e9i			0.270955i
$424$	1.27760e10			0.395303
$425$			8.16135e10i			2.50153i
$426$			4.48705e9i			0.136246i
$427$	−1.12737e10	+	9.32630e9i	−0.339121	+	0.280542i
$428$	4.80096e9			0.143072
$429$	5.68831e9			0.167940
$430$			3.29329e10i			0.963287i
$431$	3.82882e10			1.10957			0.554787	−	0.831993i	$-0.312800\pi$
$431$	3.82882e10			1.10957			0.554787	+	0.831993i	$0.312800\pi$
$432$		−	1.67569e9i		−	0.0481125i
$433$			1.79221e10i			0.509845i	0.966962	+	0.254922i	$0.0820499\pi$
$433$			1.79221e10i			0.509845i	−0.966962	+	0.254922i	$0.917950\pi$
$434$	−3.27601e10	+	2.71012e10i	−0.923393	+	0.763889i
$435$	1.35967e10			0.379732
$436$	1.16298e10			0.321831
$437$			3.08953e10i			0.847163i
$438$	7.34096e9			0.199460
$439$			3.42534e10i			0.922242i	0.887337	+	0.461121i	$0.152553\pi$
$439$			3.42534e10i			0.922242i	−0.887337	+	0.461121i	$0.847447\pi$
$440$		−	1.20500e10i		−	0.321496i
$441$	2.36256e9	−	1.23843e10i	0.0624638	−	0.327428i
$442$	−1.50543e10			−0.394433
$443$	4.82910e10			1.25387			0.626934	−	0.779073i	$-0.284310\pi$
$443$	4.82910e10			1.25387			0.626934	+	0.779073i	$0.284310\pi$
$444$		−	2.06266e10i		−	0.530758i
$445$	−4.54243e10			−1.15837
$446$		−	1.21090e10i		−	0.306034i
$447$		−	1.98011e10i		−	0.495975i
$448$	3.20958e9	+	3.87975e9i	0.0796775	+	0.0963146i
$449$	−4.76923e10			−1.17344			−0.586722	−	0.809788i	$-0.699582\pi$
$449$	−4.76923e10			−1.17344			−0.586722	+	0.809788i	$0.699582\pi$
$450$	−2.70082e10			−0.658635
$451$		−	5.47610e9i		−	0.132363i
$452$	1.54806e10			0.370881
$453$			4.28965e10i			1.01866i
$454$		−	2.34321e10i		−	0.551554i
$455$	3.31591e10	+	4.00829e10i	0.773672	+	0.935219i
$456$	−5.08112e9			−0.117517
$457$	7.82767e10			1.79460			0.897300	−	0.441421i	$-0.145525\pi$
$457$	7.82767e10			1.79460			0.897300	+	0.441421i	$0.145525\pi$
$458$		−	4.77550e10i		−	1.08532i
$459$	−7.64705e9			−0.172283
$460$			6.41700e10i			1.43318i
$461$			6.31966e10i			1.39923i	0.714519	+	0.699616i	$0.246646\pi$
$461$			6.31966e10i			1.39923i	−0.714519	+	0.699616i	$0.753354\pi$
$462$	−6.69001e9	+	5.53440e9i	−0.146845	+	0.121479i
$463$	−2.70505e10			−0.588642			−0.294321	−	0.955707i	$-0.595094\pi$
$463$	−2.70505e10			−0.588642			−0.294321	+	0.955707i	$0.595094\pi$
$464$	3.91274e9			0.0844130
$465$		−	8.91127e10i		−	1.90602i
$466$	6.02137e10			1.27688
$467$			2.75204e10i			0.578612i	0.957237	+	0.289306i	$0.0934245\pi$
$467$			2.75204e10i			0.578612i	−0.957237	+	0.289306i	$0.906576\pi$
$468$		−	4.98190e9i		−	0.103851i
$469$	−4.23014e10	−	5.11342e10i	−0.874306	−	1.05687i
$470$	5.46341e10			1.11962
$471$	1.02427e10			0.208128
$472$			1.72827e10i			0.348211i
$473$	−1.63418e10			−0.326478
$474$		−	2.43464e10i		−	0.482305i
$475$			8.18957e10i			1.60874i
$476$	1.77054e10	−	1.46470e10i	0.344887	−	0.285313i
$477$	1.92942e10			0.372695
$478$	1.41588e10			0.271216
$479$			7.48433e9i			0.142171i	0.997470	+	0.0710855i	$0.0226463\pi$
$479$			7.48433e9i			0.142171i	−0.997470	+	0.0710855i	$0.977354\pi$
$480$	−1.05535e10			−0.198808
$481$		−	6.13239e10i		−	1.14564i
$482$		−	7.23819e10i		−	1.34104i
$483$	3.56264e10	−	2.94724e10i	0.654610	−	0.541535i
$484$	−2.14586e10			−0.391038
$485$	−1.64774e10			−0.297797
$486$		−	2.53062e9i		−	0.0453609i
$487$	2.30436e10			0.409670			0.204835	−	0.978797i	$-0.434334\pi$
$487$	2.30436e10			0.409670			0.204835	+	0.978797i	$0.434334\pi$
$488$		−	8.82483e9i		−	0.155606i
$489$			1.43283e10i			0.250587i
$490$	−7.79966e10	−	1.48795e10i	−1.35298	−	0.258109i
$491$	3.80570e10			0.654800			0.327400	−	0.944886i	$-0.393828\pi$
$491$	3.80570e10			0.654800			0.327400	+	0.944886i	$0.393828\pi$
$492$	−4.79604e9			−0.0818507
$493$		−	1.78559e10i		−	0.302270i
$494$	−1.51064e10			−0.253660
$495$		−	1.81979e10i		−	0.303110i
$496$		−	2.56440e10i		−	0.423701i
$497$	−1.29792e10	−	1.56894e10i	−0.212727	−	0.257146i
$498$	4.08143e10			0.663583
$499$	−8.45945e10			−1.36439			−0.682197	−	0.731168i	$-0.738976\pi$
$499$	−8.45945e10			−1.36439			−0.682197	+	0.731168i	$0.738976\pi$
$500$			1.09226e11i			1.74762i
$501$	−7.98315e9			−0.126714
$502$			5.49795e10i			0.865736i
$503$		−	7.57063e10i		−	1.18266i	−0.806430	−	0.591330i	$-0.798603\pi$
$503$		−	7.57063e10i		−	1.18266i	0.806430	−	0.591330i	$-0.201397\pi$
$504$	4.84710e9	+	5.85919e9i	0.0751207	+	0.0908062i
$505$	−9.24841e10			−1.42201
$506$	−3.18420e10			−0.485734
$507$			2.33365e10i			0.353187i
$508$	2.80130e10			0.420634
$509$		−	9.98826e10i		−	1.48805i	−0.668150	−	0.744027i	$-0.732913\pi$
$509$		−	9.98826e10i		−	1.48805i	0.668150	−	0.744027i	$-0.267087\pi$
$510$			4.81614e10i			0.711899i
$511$	−2.56683e10	+	2.12345e10i	−0.376456	+	0.311428i
$512$	−3.03700e9			−0.0441942
$513$	−7.67349e9			−0.110796
$514$			2.14225e10i			0.306915i
$515$	−1.58990e11			−2.26018
$516$			1.43123e10i			0.201888i
$517$			2.71102e10i			0.379464i
$518$	5.96646e10	+	7.21229e10i	0.828701	+	1.00174i
$519$	9.32422e9			0.128512
$520$	−3.13762e10			−0.429127
$521$			1.68206e10i			0.228292i	0.993464	+	0.114146i	$0.0364132\pi$
$521$			1.68206e10i			0.228292i	−0.993464	+	0.114146i	$0.963587\pi$
$522$	5.90901e9			0.0795853
$523$			3.08071e10i			0.411760i	0.978577	+	0.205880i	$0.0660057\pi$
$523$			3.08071e10i			0.411760i	−0.978577	+	0.205880i	$0.933994\pi$
$524$		−	3.79117e9i		−	0.0502861i
$525$	9.44365e10	−	7.81238e10i	1.24309	−	1.02836i
$526$	−4.56457e10			−0.596289
$527$	−1.17027e11			−1.51721
$528$		−	5.23682e9i		−	0.0673801i
$529$	9.12578e10			1.16533
$530$		−	1.21516e11i		−	1.54003i
$531$			2.61002e10i			0.328297i
$532$	1.77666e10	−	1.46976e10i	0.221798	−	0.183485i
$533$	−1.42588e10			−0.176675
$534$	−1.97410e10			−0.242775
$535$		−	4.56633e10i		−	0.557381i
$536$	4.00269e10			0.484945
$537$		−	7.16663e10i		−	0.861823i
$538$			7.48078e10i			0.892931i
$539$	7.38341e9	−	3.87030e10i	0.0874787	−	0.458553i
$540$	−1.59379e10			−0.187438
$541$	5.42687e10			0.633520			0.316760	−	0.948506i	$-0.397405\pi$
$541$	5.42687e10			0.633520			0.316760	+	0.948506i	$0.397405\pi$
$542$			1.80920e9i			0.0209648i
$543$	5.53685e10			0.636888
$544$			1.38594e10i			0.158252i
$545$		−	1.10615e11i		−	1.25380i
$546$	1.44106e10	+	1.74196e10i	0.162148	+	0.196006i
$547$	−3.51808e10			−0.392967			−0.196484	−	0.980507i	$-0.562952\pi$
$547$	−3.51808e10			−0.392967			−0.196484	+	0.980507i	$0.562952\pi$
$548$	7.03194e10			0.779745
$549$		−	1.33272e10i		−	0.146707i
$550$	−8.44052e10			−0.922398
$551$		−	1.79176e10i		−	0.194390i
$552$			2.78877e10i			0.300370i
$553$	7.04244e10	+	8.51294e10i	0.753048	+	0.910288i
$554$	3.09388e10			0.328447
$555$	−1.96186e11			−2.06774
$556$		−	5.01281e10i		−	0.524544i
$557$	5.74714e10			0.597077			0.298539	−	0.954398i	$-0.403501\pi$
$557$	5.74714e10			0.597077			0.298539	+	0.954398i	$0.403501\pi$
$558$		−	3.87276e10i		−	0.399469i
$559$			4.25512e10i			0.435777i
$560$	3.69014e10	−	3.05272e10i	0.375224	−	0.310409i
$561$	−2.38984e10			−0.241278
$562$	7.01361e10			0.703066
$563$			1.39516e11i			1.38864i	0.719667	+	0.694319i	$0.244294\pi$
$563$			1.39516e11i			1.38864i	−0.719667	+	0.694319i	$0.755706\pi$
$564$	2.37435e10			0.234654
$565$		−	1.47241e11i		−	1.44489i
$566$		−	3.60032e8i		−	0.00350813i
$567$	7.32007e9	+	8.84854e9i	0.0708244	+	0.0856129i
$568$	1.22814e10			0.117992
$569$	−2.02150e11			−1.92852			−0.964260	−	0.264959i	$-0.914641\pi$
$569$	−2.02150e11			−1.92852			−0.964260	+	0.264959i	$0.914641\pi$
$570$			4.83279e10i			0.457824i
$571$	−5.03533e10			−0.473679			−0.236839	−	0.971549i	$-0.576111\pi$
$571$	−5.03533e10			−0.473679			−0.236839	+	0.971549i	$0.576111\pi$
$572$		−	1.55693e10i		−	0.145440i
$573$			2.09178e10i			0.194043i
$574$	1.67698e10	−	1.38730e10i	0.154483	−	0.127798i
$575$	4.49484e11			4.11190
$576$	−4.58647e9			−0.0416667
$577$			1.47634e11i			1.33193i	0.745982	+	0.665966i	$0.231981\pi$
$577$			1.47634e11i			1.33193i	−0.745982	+	0.665966i	$0.768019\pi$
$578$	−1.56737e10			−0.140430
$579$		−	3.34875e9i		−	0.0297967i
$580$		−	3.72152e10i		−	0.328858i
$581$	−1.42711e11	+	1.18060e11i	−1.25243	+	1.03609i
$582$	−7.16091e9			−0.0624132
$583$	6.02978e10			0.521948
$584$		−	2.00927e10i		−	0.172738i
$585$	−4.73842e10			−0.404585
$586$		−	5.98879e10i		−	0.507865i
$587$			6.36281e10i			0.535916i	0.963431	+	0.267958i	$0.0863488\pi$
$587$			6.36281e10i			0.535916i	−0.963431	+	0.267958i	$0.913651\pi$
$588$	−3.38966e10	−	6.46649e9i	−0.283561	−	0.0540953i
$589$	−1.17432e11			−0.975720
$590$	1.64380e11			1.35657
$591$			8.17679e10i			0.670244i
$592$	−5.64565e10			−0.459650
$593$			1.61114e10i			0.130291i	0.997876	+	0.0651456i	$0.0207512\pi$
$593$			1.61114e10i			0.130291i	−0.997876	+	0.0651456i	$0.979249\pi$
$594$		−	7.90863e9i		−	0.0635266i
$595$	−1.39312e11	−	1.68401e11i	−1.11153	−	1.34362i
$596$	−5.41971e10			−0.429527
$597$	1.02703e10			0.0808508
$598$			8.29113e10i			0.648349i
$599$	2.92376e10			0.227109			0.113554	−	0.993532i	$-0.463776\pi$
$599$	2.92376e10			0.227109			0.113554	+	0.993532i	$0.463776\pi$
$600$			7.39232e10i			0.570395i
$601$		−	2.30971e10i		−	0.177035i	−0.996075	−	0.0885176i	$-0.971787\pi$
$601$		−	2.30971e10i		−	0.177035i	0.996075	−	0.0885176i	$-0.0282129\pi$
$602$	−4.13998e10	−	5.00443e10i	−0.315219	−	0.381038i
$603$	6.04486e10			0.457211
$604$	1.17411e11			0.882184
$605$			2.04098e11i			1.52341i
$606$	−4.01927e10			−0.298028
$607$		−	1.43053e11i		−	1.05376i	−0.849939	−	0.526881i	$-0.823361\pi$
$607$		−	1.43053e11i		−	1.05376i	0.849939	−	0.526881i	$-0.176639\pi$
$608$			1.39074e10i			0.101772i
$609$	−2.06614e10	+	1.70924e10i	−0.150207	+	0.124261i
$610$	−8.39354e10			−0.606214
$611$	7.05905e10			0.506502
$612$			2.09305e10i			0.149202i
$613$	1.73771e11			1.23065			0.615326	−	0.788272i	$-0.289024\pi$
$613$	1.73771e11			1.23065			0.615326	+	0.788272i	$0.289024\pi$
$614$			3.41813e9i			0.0240500i
$615$			4.56164e10i			0.318875i
$616$	1.51480e10	+	1.83110e10i	0.105204	+	0.127171i
$617$	−7.74418e10			−0.534361			−0.267181	−	0.963647i	$-0.586092\pi$
$617$	−7.74418e10			−0.534361			−0.267181	+	0.963647i	$0.586092\pi$
$618$	−6.90958e10			−0.473694
$619$		−	1.30673e11i		−	0.890070i	−0.895513	−	0.445035i	$-0.853191\pi$
$619$		−	1.30673e11i		−	0.890070i	0.895513	−	0.445035i	$-0.146809\pi$
$620$	−2.43908e11			−1.65066
$621$			4.21159e10i			0.283191i
$622$			9.24196e10i			0.617451i
$623$	6.90262e10	−	5.71028e10i	0.458207	−	0.379058i
$624$	−1.36358e10			−0.0899377
$625$	6.12496e11			4.01405
$626$		−	4.41897e10i		−	0.287756i
$627$	−2.39810e10			−0.155166
$628$		−	2.80349e10i		−	0.180244i
$629$			2.57641e11i			1.64593i
$630$	5.57284e10	−	4.61021e10i	0.353765	−	0.292657i
$631$	7.73549e9			0.0487944			0.0243972	−	0.999702i	$-0.492233\pi$
$631$	7.73549e9			0.0487944			0.0243972	+	0.999702i	$0.492233\pi$
$632$	−6.66377e10			−0.417688
$633$			1.75721e10i			0.109448i
$634$	1.16809e11			0.722968
$635$		−	2.66439e11i		−	1.63872i
$636$		−	5.28096e10i		−	0.322763i
$637$	−1.00776e11	−	1.92252e10i	−0.612069	−	0.116765i
$638$	1.84667e10			0.111457
$639$	1.85473e10			0.111244
$640$			2.88858e10i			0.172173i
$641$	1.27667e11			0.756219			0.378109	−	0.925761i	$-0.376574\pi$
$641$	1.27667e11			0.756219			0.378109	+	0.925761i	$0.376574\pi$
$642$		−	1.98448e10i		−	0.116817i
$643$			8.47609e10i			0.495852i	0.968779	+	0.247926i	$0.0797489\pi$
$643$			8.47609e10i			0.495852i	−0.968779	+	0.247926i	$0.920251\pi$
$644$	−8.06679e10	−	9.75118e10i	−0.468983	−	0.566909i
$645$	1.36128e11			0.786521
$646$	6.34667e10			0.364431
$647$		−	2.32355e10i		−	0.132597i	−0.997800	−	0.0662987i	$-0.978881\pi$
$647$		−	2.32355e10i		−	0.132597i	0.997800	−	0.0662987i	$-0.0211190\pi$
$648$	−6.92648e9			−0.0392837
$649$			8.15678e10i			0.459769i
$650$			2.19777e11i			1.23120i
$651$	1.12023e11	+	1.35414e11i	0.623713	+	0.753947i
$652$	3.92175e10			0.217015
$653$	1.06816e10			0.0587469			0.0293734	−	0.999569i	$-0.490649\pi$
$653$	1.06816e10			0.0587469			0.0293734	+	0.999569i	$0.490649\pi$
$654$		−	4.80721e10i		−	0.262774i
$655$	−3.60589e10			−0.195906
$656$			1.31271e10i			0.0708847i
$657$		−	3.03440e10i		−	0.162859i
$658$	−8.30212e10	+	6.86804e10i	−0.442880	+	0.366378i
$659$	−2.14152e11			−1.13548			−0.567742	−	0.823206i	$-0.692183\pi$
$659$	−2.14152e11			−1.13548			−0.567742	+	0.823206i	$0.692183\pi$
$660$	−4.98088e10			−0.262501
$661$			3.51318e11i			1.84033i	0.391535	+	0.920163i	$0.371944\pi$
$661$			3.51318e11i			1.84033i	−0.391535	+	0.920163i	$0.628056\pi$
$662$	−1.54545e11			−0.804682
$663$			6.22273e10i			0.322053i
$664$		−	1.11712e11i		−	0.574680i
$665$	−1.39793e11	−	1.68983e11i	−0.714825	−	0.864084i
$666$	−8.52604e10			−0.433362
$667$	−9.83409e10			−0.496856
$668$			2.18504e10i			0.109737i
$669$	−5.00528e10			−0.249876
$670$		−	3.80707e11i		−	1.88926i
$671$		−	4.16500e10i		−	0.205459i
$672$	1.60370e10	−	1.32668e10i	0.0786405	−	0.0650564i
$673$	−2.04066e11			−0.994744			−0.497372	−	0.867537i	$-0.665702\pi$
$673$	−2.04066e11			−0.994744			−0.497372	+	0.867537i	$0.665702\pi$
$674$	−1.11067e11			−0.538201
$675$			1.11639e11i			0.537773i
$676$	6.38737e10			0.305869
$677$			2.13641e11i			1.01702i	0.861056	+	0.508510i	$0.169803\pi$
$677$			2.13641e11i			1.01702i	−0.861056	+	0.508510i	$0.830197\pi$
$678$		−	6.39894e10i		−	0.302823i
$679$	2.50388e10	−	2.07136e10i	0.117797	−	0.0974490i
$680$	1.31821e11			0.616523
$681$	−9.68570e10			−0.450342
$682$		−	1.21030e11i		−	0.559445i
$683$	3.25370e9			0.0149518			0.00747592	−	0.999972i	$-0.497620\pi$
$683$	3.25370e9			0.0149518			0.00747592	+	0.999972i	$0.497620\pi$
$684$			2.10029e10i			0.0959520i
$685$		−	6.68827e11i		−	3.03775i
$686$	1.37228e11	−	7.54387e10i	0.619648	−	0.340642i
$687$	−1.97396e11			−0.886159
$688$	3.91738e10			0.174840
$689$		−	1.57005e11i		−	0.696686i
$690$	2.65247e11			1.17019
$691$		−	1.04701e11i		−	0.459239i	−0.973280	−	0.229620i	$-0.926252\pi$
$691$		−	1.04701e11i		−	0.459239i	0.973280	−	0.229620i	$-0.0737482\pi$
$692$		−	2.55210e10i		−	0.111294i
$693$	2.28765e10	+	2.76532e10i	0.0991875	+	0.119898i
$694$	−1.72048e11			−0.741672
$695$	−4.76782e11			−2.04353
$696$		−	1.61734e10i		−	0.0689229i
$697$	5.99058e10			0.253827
$698$			3.06753e11i			1.29231i
$699$		−	2.48894e11i		−	1.04257i
$700$	−2.13830e11	−	2.58479e11i	−0.890588	−	1.07655i
$701$	4.03552e11			1.67119			0.835597	−	0.549343i	$-0.185122\pi$
$701$	4.03552e11			1.67119			0.835597	+	0.549343i	$0.185122\pi$
$702$	−2.05927e10			−0.0847941
$703$			2.58532e11i			1.05850i
$704$	−1.43335e10			−0.0583529
$705$		−	2.25831e11i		−	0.914170i
$706$			2.94068e11i			1.18366i
$707$	1.40538e11	−	1.16262e11i	0.562490	−	0.465327i
$708$	7.14381e10			0.284313
$709$	2.92625e10			0.115805			0.0579025	−	0.998322i	$-0.481559\pi$
$709$	2.92625e10			0.115805			0.0579025	+	0.998322i	$0.481559\pi$
$710$		−	1.16811e11i		−	0.459676i
$711$	−1.00636e11			−0.393800
$712$			5.40325e10i			0.210249i
$713$			6.44524e11i			2.49391i
$714$	−6.05436e10	−	7.31854e10i	−0.232957	−	0.281599i
$715$	−1.48084e11			−0.566609
$716$	−1.96156e11			−0.746361
$717$		−	5.85256e10i		−	0.221447i
$718$	1.22643e11			0.461472
$719$		−	2.23248e11i		−	0.835356i	−0.908595	−	0.417678i	$-0.862844\pi$
$719$		−	2.23248e11i		−	0.835356i	0.908595	−	0.417678i	$-0.137156\pi$
$720$			4.36232e10i			0.162326i
$721$	2.41600e11	−	1.99867e11i	0.894036	−	0.739604i
$722$	−1.28461e11			−0.472740
$723$	−2.99191e11			−1.09495
$724$		−	1.51547e11i		−	0.551562i
$725$	−2.60677e11			−0.943519
$726$			8.86992e10i			0.319281i
$727$		−	2.84018e10i		−	0.101674i	−0.998707	−	0.0508369i	$-0.983811\pi$
$727$		−	2.84018e10i		−	0.101674i	0.998707	−	0.0508369i	$-0.0161889\pi$
$728$	4.76788e10	−	3.94429e10i	0.169746	−	0.140425i
$729$	−1.04604e10			−0.0370370
$730$	−1.91107e11			−0.672955
$731$		−	1.78771e11i		−	0.626076i
$732$	−3.64776e10			−0.127052
$733$			1.70768e10i			0.0591550i	0.999562	+	0.0295775i	$0.00941618\pi$
$733$			1.70768e10i			0.0591550i	−0.999562	+	0.0295775i	$0.990584\pi$
$734$			1.87222e11i			0.645019i
$735$	−6.15046e10	+	3.22400e11i	−0.210745	+	1.10470i
$736$	7.63305e10			0.260128
$737$	1.88912e11			0.640310
$738$			1.98245e10i			0.0668308i
$739$	−5.65625e11			−1.89649			−0.948246	−	0.317536i	$-0.897145\pi$
$739$	−5.65625e11			−1.89649			−0.948246	+	0.317536i	$0.897145\pi$
$740$			5.36973e11i			1.79071i
$741$			6.24425e10i			0.207113i
$742$	1.52757e11	+	1.84653e11i	0.503948	+	0.609175i
$743$	3.68308e11			1.20853			0.604263	−	0.796785i	$-0.293468\pi$
$743$	3.68308e11			1.20853			0.604263	+	0.796785i	$0.293468\pi$
$744$	−1.06000e11			−0.345951
$745$			5.15483e11i			1.67336i
$746$	2.25038e11			0.726608
$747$		−	1.68707e11i		−	0.541813i
$748$			6.54115e10i			0.208952i
$749$	5.74032e10	+	6.93893e10i	0.182393	+	0.220478i
$750$	4.51488e11			1.42692
$751$	3.22982e11			1.01536			0.507678	−	0.861547i	$-0.330504\pi$
$751$	3.22982e11			1.01536			0.507678	+	0.861547i	$0.330504\pi$
$752$		−	6.49875e10i		−	0.203216i
$753$	2.27258e11			0.706871
$754$		−	4.80842e10i		−	0.148770i
$755$		−	1.11672e12i		−	3.43683i
$756$	2.42191e10	−	2.00355e10i	0.0741430	−	0.0613358i
$757$	−1.67881e11			−0.511233			−0.255616	−	0.966778i	$-0.582278\pi$
$757$	−1.67881e11			−0.511233			−0.255616	+	0.966778i	$0.582278\pi$
$758$	−6.26448e10			−0.189762
$759$			1.31620e11i			0.396601i
$760$	1.32277e11			0.396487
$761$			3.46644e10i			0.103358i	0.998664	+	0.0516791i	$0.0164573\pi$
$761$			3.46644e10i			0.103358i	−0.998664	+	0.0516791i	$0.983543\pi$
$762$		−	1.15792e11i		−	0.343446i
$763$	1.39053e11	+	1.68088e11i	0.410283	+	0.495952i
$764$	5.72536e10			0.168046
$765$	1.99076e11			0.581263
$766$		−	1.36960e11i		−	0.397813i
$767$	2.12389e11			0.613692
$768$			1.25535e10i			0.0360844i
$769$		−	4.28896e11i		−	1.22644i	−0.789912	−	0.613220i	$-0.789874\pi$
$769$		−	4.28896e11i		−	1.22644i	0.789912	−	0.613220i	$-0.210126\pi$
$770$	1.74161e11	−	1.44077e11i	0.495437	−	0.409857i
$771$	8.85503e10			0.250595
$772$	−9.16574e9			−0.0258047
$773$		−	1.17477e11i		−	0.329029i	−0.986375	−	0.164515i	$-0.947394\pi$
$773$		−	1.17477e11i		−	0.329029i	0.986375	−	0.164515i	$-0.0526057\pi$
$774$	5.91602e10			0.164841
$775$			1.70847e12i			4.73588i
$776$			1.95999e10i			0.0540514i
$777$	2.98121e11	−	2.46624e11i	0.817915	−	0.676631i
$778$	3.53052e11			0.963653
$779$	6.01129e10			0.163237
$780$			1.29694e11i			0.350381i
$781$	5.79635e10			0.155794
$782$		−	3.48336e11i		−	0.931476i
$783$		−	2.44250e10i		−	0.0649811i
$784$	−1.76992e10	+	9.27773e10i	−0.0468479	+	0.245571i
$785$	−2.66648e11			−0.702197
$786$	−1.56709e10			−0.0410585
$787$		−	5.33414e11i		−	1.39048i	−0.718777	−	0.695241i	$-0.755298\pi$
$787$		−	5.33414e11i		−	1.39048i	0.718777	−	0.695241i	$-0.244702\pi$
$788$	2.23804e11			0.580449
$789$			1.88677e11i			0.486868i
$790$			6.33810e11i			1.62724i
$791$	1.85096e11	+	2.23745e11i	0.472814	+	0.571540i
$792$	−2.16465e10			−0.0550156
$793$	−1.08449e11			−0.274242
$794$			1.28347e11i			0.322926i
$795$	−5.02287e11			−1.25743
$796$		−	2.81104e10i		−	0.0700189i
$797$		−	9.16220e10i		−	0.227073i	−0.993534	−	0.113537i	$-0.963782\pi$
$797$		−	9.16220e10i		−	0.227073i	0.993534	−	0.113537i	$-0.0362180\pi$
$798$	−6.07529e10	−	7.34384e10i	−0.149815	−	0.181097i
$799$	−2.96573e11			−0.727686
$800$	2.02333e11			0.493976
$801$			8.15997e10i			0.198225i
$802$	3.09157e11			0.747276
$803$		−	9.48302e10i		−	0.228079i
$804$		−	1.65452e11i		−	0.395956i
$805$	−9.27462e11	+	7.67255e11i	−2.20858	+	1.82707i
$806$	−3.15143e11			−0.746736
$807$	3.09219e11			0.729075
$808$			1.10010e11i			0.258100i
$809$	2.85814e11			0.667252			0.333626	−	0.942706i	$-0.391728\pi$
$809$	2.85814e11			0.667252			0.333626	+	0.942706i	$0.391728\pi$
$810$			6.58797e10i			0.153042i
$811$			8.74608e10i			0.202176i	0.994877	+	0.101088i	$0.0322324\pi$
$811$			8.74608e10i			0.202176i	−0.994877	+	0.101088i	$0.967768\pi$
$812$	4.67831e10	+	5.65517e10i	0.107613	+	0.130083i
$813$	7.47837e9			0.0171177
$814$	−2.66454e11			−0.606910
$815$		−	3.73008e11i		−	0.845450i
$816$	5.72882e10			0.129213
$817$		−	1.79389e11i		−	0.402631i
$818$			3.33836e11i			0.745625i
$819$	7.20044e10	−	5.95666e10i	0.160038	−	0.132394i
$820$	1.24855e11			0.276154
$821$	1.68926e11			0.371813			0.185907	−	0.982567i	$-0.440478\pi$
$821$	1.68926e11			0.371813			0.185907	+	0.982567i	$0.440478\pi$
$822$		−	2.90666e11i		−	0.636659i
$823$	7.50969e10			0.163690			0.0818451	−	0.996645i	$-0.473919\pi$
$823$	7.50969e10			0.163690			0.0818451	+	0.996645i	$0.473919\pi$
$824$			1.89120e11i			0.410231i
$825$			3.48890e11i			0.753135i
$826$	−2.49790e11	+	2.06642e11i	−0.536605	+	0.443914i
$827$	−4.58050e11			−0.979244			−0.489622	−	0.871935i	$-0.662865\pi$
$827$	−4.58050e11			−0.979244			−0.489622	+	0.871935i	$0.662865\pi$
$828$	1.15274e11			0.245251
$829$		−	1.60511e11i		−	0.339850i	−0.985457	−	0.169925i	$-0.945647\pi$
$829$		−	1.60511e11i		−	0.339850i	0.985457	−	0.169925i	$-0.0543526\pi$
$830$	−1.06252e12			−2.23885
$831$		−	1.27886e11i		−	0.268176i
$832$			3.73221e10i			0.0778883i
$833$	4.23392e11	+	8.07709e10i	0.879352	+	0.167755i
$834$	−2.07205e11			−0.428288
$835$	2.07826e11			0.427517
$836$			6.56376e10i			0.134378i
$837$	−1.60081e11			−0.326165
$838$			4.12680e11i			0.836830i
$839$		−	6.38868e11i		−	1.28933i	−0.764466	−	0.644664i	$-0.776997\pi$
$839$		−	6.38868e11i		−	1.28933i	0.764466	−	0.644664i	$-0.223003\pi$
$840$	−1.26185e11	−	1.52532e11i	−0.253448	−	0.306369i
$841$	−4.43214e11			−0.885991
$842$	4.74409e11			0.943853
$843$		−	2.89908e11i		−	0.574051i
$844$	4.80959e10			0.0947848
$845$		−	6.07521e11i		−	1.19161i
$846$		−	9.81440e10i		−	0.191594i
$847$	−2.56571e11	−	3.10145e11i	−0.498511	−	0.602603i
$848$	−1.44543e11			−0.279521
$849$	−1.48820e9			−0.00286438
$850$		−	9.23352e11i		−	1.76885i
$851$	1.41895e12			2.70551
$852$		−	5.07651e10i		−	0.0963401i
$853$		−	7.08148e11i		−	1.33761i	−0.743440	−	0.668803i	$-0.766807\pi$
$853$		−	7.08148e11i		−	1.33761i	0.743440	−	0.668803i	$-0.233193\pi$
$854$	1.27547e11	−	1.05515e11i	0.239794	−	0.198373i
$855$	1.99764e11			0.373812
$856$	−5.43167e10			−0.101167
$857$			9.39679e11i			1.74203i	0.491255	+	0.871016i	$0.336538\pi$
$857$			9.39679e11i			1.74203i	−0.491255	+	0.871016i	$0.663462\pi$
$858$	−6.43559e10			−0.118752
$859$		−	1.01620e12i		−	1.86641i	−0.359346	−	0.933204i	$-0.617000\pi$
$859$		−	1.01620e12i		−	1.86641i	0.359346	−	0.933204i	$-0.383000\pi$
$860$		−	3.72593e11i		−	0.681147i
$861$	−5.73443e10	−	6.93181e10i	−0.104346	−	0.126135i
$862$	−4.33182e11			−0.784587
$863$	1.27360e11			0.229609			0.114805	−	0.993388i	$-0.463376\pi$
$863$	1.27360e11			0.229609			0.114805	+	0.993388i	$0.463376\pi$
$864$			1.89582e10i			0.0340207i
$865$	−2.42738e11			−0.433583
$866$		−	2.02766e11i		−	0.360515i
$867$			6.47874e10i			0.114661i
$868$	3.70639e11	−	3.06616e11i	0.652938	−	0.540151i
$869$	−3.14506e11			−0.551505
$870$	−1.53829e11			−0.268511
$871$		−	4.91896e11i		−	0.854674i
$872$	−1.31577e11			−0.227569
$873$			2.95997e10i			0.0509601i
$874$		−	3.49541e11i		−	0.599035i
$875$	−1.57867e12	+	1.30597e12i	−2.69314	+	2.22793i
$876$	−8.30535e10			−0.141040
$877$	−1.68608e11			−0.285023			−0.142511	−	0.989793i	$-0.545518\pi$
$877$	−1.68608e11			−0.285023			−0.142511	+	0.989793i	$0.545518\pi$
$878$		−	3.87533e11i		−	0.652124i
$879$	−2.47547e11			−0.414670
$880$			1.36330e11i			0.227332i
$881$		−	3.36497e11i		−	0.558569i	−0.960208	−	0.279285i	$-0.909903\pi$
$881$		−	3.36497e11i		−	0.558569i	0.960208	−	0.279285i	$-0.0900973\pi$
$882$	−2.67293e10	+	1.40112e11i	−0.0441686	+	0.231527i
$883$	7.04453e10			0.115880			0.0579401	−	0.998320i	$-0.481547\pi$
$883$	7.04453e10			0.115880			0.0579401	+	0.998320i	$0.481547\pi$
$884$	1.70320e11			0.278906
$885$		−	6.79468e11i		−	1.10763i
$886$	−5.46351e11			−0.886618
$887$			1.02490e12i			1.65572i	0.560935	+	0.827860i	$0.310442\pi$
$887$			1.02490e12i			1.65572i	−0.560935	+	0.827860i	$0.689558\pi$
$888$			2.33364e11i			0.375302i
$889$	3.34940e11	+	4.04878e11i	0.536241	+	0.648211i
$890$	5.13918e11			0.819094
$891$	−3.26904e10			−0.0518692
$892$			1.36998e11i			0.216399i
$893$	−2.97598e11			−0.467976
$894$			2.24024e11i			0.350707i
$895$			1.86569e12i			2.90769i
$896$	−3.63122e10	−	4.38944e10i	−0.0563405	−	0.0681047i
$897$	3.42715e11			0.529375
$898$	5.39577e11			0.829751
$899$		−	3.73790e11i		−	0.572254i
$900$	3.05562e11			0.465725
$901$			6.59628e11i			1.00092i
$902$			6.19550e10i			0.0935945i
$903$	−2.06859e11	+	1.71127e11i	−0.311117	+	0.257375i
$904$	−1.75143e11			−0.262253
$905$	−1.44141e12			−2.14878
$906$		−	4.85318e11i		−	0.720300i
$907$	9.15749e10			0.135315			0.0676577	−	0.997709i	$-0.478447\pi$
$907$	9.15749e10			0.135315			0.0676577	+	0.997709i	$0.478447\pi$
$908$			2.65104e11i			0.390008i
$909$			1.66137e11i			0.243339i
$910$	−3.75152e11	−	4.53486e11i	−0.547069	−	0.661300i
$911$	1.29410e11			0.187887			0.0939433	−	0.995578i	$-0.470053\pi$
$911$	1.29410e11			0.187887			0.0939433	+	0.995578i	$0.470053\pi$
$912$	5.74863e10			0.0830969
$913$		−	5.27237e11i		−	0.758793i
$914$	−8.85600e11			−1.26897
$915$			3.46948e11i			0.494972i
$916$			5.40287e11i			0.767436i
$917$	5.47946e10	−	4.53295e10i	0.0774926	−	0.0641068i
$918$	8.65165e10			0.121823
$919$	6.77797e11			0.950250			0.475125	−	0.879918i	$-0.342403\pi$
$919$	6.77797e11			0.950250			0.475125	+	0.879918i	$0.342403\pi$
$920$		−	7.26000e11i		−	1.01341i
$921$	1.41289e10			0.0196367
$922$		−	7.14988e11i		−	0.989407i
$923$		−	1.50927e11i		−	0.207951i
$924$	7.56888e10	−	6.26146e10i	0.103835	−	0.0858989i
$925$	3.76127e12			5.13769
$926$	3.06042e11			0.416233
$927$			2.85608e11i			0.386769i
$928$	−4.42676e10			−0.0596890
$929$			5.32522e11i			0.714949i	0.933923	+	0.357474i	$0.116362\pi$
$929$			5.32522e11i			0.714949i	−0.933923	+	0.357474i	$0.883638\pi$
$930$			1.00820e12i			1.34776i
$931$	4.24856e11	+	8.10502e10i	0.565513	+	0.107884i
$932$	−6.81240e11			−0.902894
$933$	3.82018e11			0.504147
$934$		−	3.11358e11i		−	0.409140i
$935$	6.22147e11			0.814041
$936$			5.63637e10i			0.0734338i
$937$		−	7.67301e11i		−	0.995423i	−0.867343	−	0.497711i	$-0.834174\pi$
$937$		−	7.67301e11i		−	0.995423i	0.867343	−	0.497711i	$-0.165826\pi$
$938$	4.78586e11	+	5.78517e11i	0.618228	+	0.747317i
$939$	−1.82659e11			−0.234952
$940$	−6.18115e11			−0.791694
$941$		−	3.05205e11i		−	0.389255i	−0.980877	−	0.194627i	$-0.937650\pi$
$941$		−	3.05205e11i		−	0.389255i	0.980877	−	0.194627i	$-0.0623497\pi$
$942$	−1.15883e11			−0.147168
$943$		−	3.29929e11i		−	0.417229i
$944$		−	1.95531e11i		−	0.246223i
$945$	−1.90564e11	−	2.30354e11i	−0.238953	−	0.288848i
$946$	1.84886e11			0.230855
$947$	−2.96388e11			−0.368520			−0.184260	−	0.982878i	$-0.558989\pi$
$947$	−2.96388e11			−0.368520			−0.184260	+	0.982878i	$0.558989\pi$
$948$			2.75448e11i			0.341041i
$949$	−2.46922e11			−0.304435
$950$		−	9.26544e11i		−	1.13755i
$951$		−	4.82831e11i		−	0.590301i
$952$	−2.00313e11	+	1.65712e11i	−0.243872	+	0.201746i
$953$	−3.79425e11			−0.459997			−0.229998	−	0.973191i	$-0.573872\pi$
$953$	−3.79425e11			−0.459997			−0.229998	+	0.973191i	$0.573872\pi$
$954$	−2.18289e11			−0.263535
$955$		−	5.44555e11i		−	0.654678i
$956$	−1.60189e11			−0.191779
$957$		−	7.63324e10i		−	0.0910041i
$958$		−	8.46756e10i		−	0.100530i
$959$	8.40781e11	+	1.01634e12i	0.994051	+	1.20161i
$960$	1.19400e11			0.140578
$961$	−1.59692e12			−1.87236
$962$			6.93801e11i			0.810092i
$963$	−8.20289e10			−0.0953810
$964$			8.18907e11i			0.948258i
$965$			8.71779e10i			0.100530i
$966$	−4.03066e11	+	3.33442e11i	−0.462879	+	0.382923i
$967$	−3.86344e10			−0.0441844			−0.0220922	−	0.999756i	$-0.507033\pi$
$967$	−3.86344e10			−0.0441844			−0.0220922	+	0.999756i	$0.507033\pi$
$968$	2.42776e11			0.276506
$969$		−	2.62340e11i		−	0.297557i
$970$	1.86420e11			0.210574
$971$			2.86060e11i			0.321796i	0.986971	+	0.160898i	$0.0514390\pi$
$971$			2.86060e11i			0.321796i	−0.986971	+	0.160898i	$0.948561\pi$
$972$			2.86307e10i			0.0320750i
$973$	7.24512e11	−	5.99362e11i	0.808340	−	0.668710i
$974$	−2.60708e11			−0.289680
$975$	9.08451e11			1.00527
$976$			9.98416e10i			0.110030i
$977$	3.96119e11			0.434758			0.217379	−	0.976087i	$-0.430249\pi$
$977$	3.96119e11			0.434758			0.217379	+	0.976087i	$0.430249\pi$
$978$		−	1.62106e11i		−	0.177192i
$979$			2.55013e11i			0.277608i
$980$	8.82431e11	+	1.68342e11i	0.956702	+	0.182511i
$981$	−1.98707e11			−0.214554
$982$	−4.30566e11			−0.463013
$983$			1.23722e12i			1.32505i	0.749041	+	0.662524i	$0.230515\pi$
$983$			1.23722e12i			1.32505i	−0.749041	+	0.662524i	$0.769485\pi$
$984$	5.42610e10			0.0578772
$985$		−	2.12867e12i		−	2.26132i
$986$			2.02017e11i			0.213737i
$987$	2.83891e11	+	3.43169e11i	0.299146	+	0.361610i
$988$	1.70909e11			0.179365
$989$	−9.84575e11			−1.02911
$990$			2.05885e11i			0.214331i
$991$	1.51224e12			1.56793			0.783964	−	0.620807i	$-0.213195\pi$
$991$	1.51224e12			1.56793			0.783964	+	0.620807i	$0.213195\pi$
$992$			2.90129e11i			0.299602i
$993$			6.38816e11i			0.657020i
$994$	1.46843e11	+	1.77505e11i	0.150421	+	0.181830i
$995$	−2.67366e11			−0.272781
$996$	−4.61761e11			−0.469224
$997$			7.15695e11i			0.724348i	0.932111	+	0.362174i	$0.117965\pi$
$997$			7.15695e11i			0.724348i	−0.932111	+	0.362174i	$0.882035\pi$
$998$	9.57078e11			0.964773
$999$			3.52425e11i			0.353838i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.9.c.a.13.4	yes	12
3.2	odd	2		126.9.c.c.55.12		12
4.3	odd	2		336.9.f.c.97.1		12
7.6	odd	2	inner	42.9.c.a.13.3	✓	12
21.20	even	2		126.9.c.c.55.7		12
28.27	even	2		336.9.f.c.97.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.9.c.a.13.3	✓	12	7.6	odd	2	inner
42.9.c.a.13.4	yes	12	1.1	even	1	trivial
126.9.c.c.55.7		12	21.20	even	2
126.9.c.c.55.12		12	3.2	odd	2
336.9.f.c.97.1		12	4.3	odd	2
336.9.f.c.97.12		12	28.27	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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	42.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-11.3137 q^{2} +46.7654i q^{3} +128.000 q^{4} -1217.44i q^{5} -529.090i q^{6} +(1530.45 + 1850.01i) q^{7} -1448.15 q^{8} -2187.00 q^{9} +O(q^{10})\)	\(q-11.3137 q^{2} +46.7654i q^{3} +128.000 q^{4} -1217.44i q^{5} -529.090i q^{6} +(1530.45 + 1850.01i) q^{7} -1448.15 q^{8} -2187.00 q^{9} +13773.8i q^{10} -6834.76 q^{11} +5985.97i q^{12} +17796.6i q^{13} +(-17315.0 - 20930.5i) q^{14} +56934.2 q^{15} +16384.0 q^{16} -74768.9i q^{17} +24743.1 q^{18} -75027.4i q^{19} -155833. i q^{20} +(-86516.4 + 71571.8i) q^{21} +77326.4 q^{22} -411787. q^{23} -67723.5i q^{24} -1.09154e6 q^{25} -201345. i q^{26} -102276. i q^{27} +(195897. + 236801. i) q^{28} +238815. q^{29} -644137. q^{30} -1.56519e6i q^{31} -185364. q^{32} -319630. i q^{33} +845913. i q^{34} +(2.25228e6 - 1.86323e6i) q^{35} -279936. q^{36} -3.44583e6 q^{37} +848838. i q^{38} -832262. q^{39} +1.76305e6i q^{40} +801213. i q^{41} +(978822. - 809743. i) q^{42} +2.39098e6 q^{43} -874849. q^{44} +2.66255e6i q^{45} +4.65884e6 q^{46} -3.96652e6i q^{47} +766204. i q^{48} +(-1.08027e6 + 5.66268e6i) q^{49} +1.23494e7 q^{50} +3.49659e6 q^{51} +2.27796e6i q^{52} -8.82223e6 q^{53} +1.15712e6i q^{54} +8.32093e6i q^{55} +(-2.21632e6 - 2.67910e6i) q^{56} +3.50868e6 q^{57} -2.70188e6 q^{58} -1.19343e7i q^{59} +7.28758e6 q^{60} +6.09385e6i q^{61} +1.77081e7i q^{62} +(-3.34708e6 - 4.04597e6i) q^{63} +2.09715e6 q^{64} +2.16663e7 q^{65} +3.61620e6i q^{66} -2.76399e7 q^{67} -9.57042e6i q^{68} -1.92574e7i q^{69} +(-2.54817e7 + 2.10801e7i) q^{70} -8.48069e6 q^{71} +3.16711e6 q^{72} +1.38747e7i q^{73} +3.89851e7 q^{74} -5.10465e7i q^{75} -9.60350e6i q^{76} +(-1.04602e7 - 1.26444e7i) q^{77} +9.41597e6 q^{78} +4.60156e7 q^{79} -1.99466e7i q^{80} +4.78297e6 q^{81} -9.06469e6i q^{82} +7.71406e7i q^{83} +(-1.10741e7 + 9.16120e6i) q^{84} -9.10269e7 q^{85} -2.70508e7 q^{86} +1.11683e7i q^{87} +9.89779e6 q^{88} -3.73113e7i q^{89} -3.01233e7i q^{90} +(-3.29238e7 + 2.72367e7i) q^{91} -5.27088e7 q^{92} +7.31966e7 q^{93} +4.48761e7i q^{94} -9.13416e7 q^{95} -8.66861e6i q^{96} -1.35344e7i q^{97} +(1.22219e7 - 6.40659e7i) q^{98} +1.49476e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 1536 q^{4} + 6420 q^{7} - 26244 q^{9}+O(q^{10}) \) 12 * q + 1536 * q^4 + 6420 * q^7 - 26244 * q^9	\( 12 q + 1536 q^{4} + 6420 q^{7} - 26244 q^{9} + 4344 q^{11} - 12288 q^{14} + 59616 q^{15} + 196608 q^{16} - 224856 q^{21} - 508416 q^{22} + 499800 q^{23} - 3001476 q^{25} + 821760 q^{28} - 1278408 q^{29} + 705024 q^{30} + 2028912 q^{35} - 3359232 q^{36} + 7068648 q^{37} - 5473008 q^{39} + 1513728 q^{42} - 11388024 q^{43} + 556032 q^{44} + 8171520 q^{46} - 12346788 q^{49} + 30019584 q^{50} + 16727472 q^{51} + 19714968 q^{53} - 1572864 q^{56} - 10386144 q^{57} - 17696256 q^{58} + 7630848 q^{60} - 14040540 q^{63} + 25165824 q^{64} - 93770592 q^{65} - 9394008 q^{67} + 11218944 q^{70} + 5393208 q^{71} + 58512384 q^{74} + 24982968 q^{77} + 32638464 q^{78} + 134560968 q^{79} + 57395628 q^{81} - 28781568 q^{84} - 102074640 q^{85} - 282934272 q^{86} - 65077248 q^{88} - 96105408 q^{91} + 63974400 q^{92} + 202339296 q^{93} - 378351840 q^{95} + 387747840 q^{98} - 9500328 q^{99}+O(q^{100}) \) 12 * q + 1536 * q^4 + 6420 * q^7 - 26244 * q^9 + 4344 * q^11 - 12288 * q^14 + 59616 * q^15 + 196608 * q^16 - 224856 * q^21 - 508416 * q^22 + 499800 * q^23 - 3001476 * q^25 + 821760 * q^28 - 1278408 * q^29 + 705024 * q^30 + 2028912 * q^35 - 3359232 * q^36 + 7068648 * q^37 - 5473008 * q^39 + 1513728 * q^42 - 11388024 * q^43 + 556032 * q^44 + 8171520 * q^46 - 12346788 * q^49 + 30019584 * q^50 + 16727472 * q^51 + 19714968 * q^53 - 1572864 * q^56 - 10386144 * q^57 - 17696256 * q^58 + 7630848 * q^60 - 14040540 * q^63 + 25165824 * q^64 - 93770592 * q^65 - 9394008 * q^67 + 11218944 * q^70 + 5393208 * q^71 + 58512384 * q^74 + 24982968 * q^77 + 32638464 * q^78 + 134560968 * q^79 + 57395628 * q^81 - 28781568 * q^84 - 102074640 * q^85 - 282934272 * q^86 - 65077248 * q^88 - 96105408 * q^91 + 63974400 * q^92 + 202339296 * q^93 - 378351840 * q^95 + 387747840 * q^98 - 9500328 * q^99

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