LMFDB - Embedded newform 98.10.c.l.67.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,10,Mod(67,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("98.67"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,48,-71] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$50.4735119441$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 4038x^{4} - 137923x^{3} + 16368349x^{2} - 286546260x + 5038160400 $ x^6 - x^5 + 4038x^4 - 137923x^3 + 16368349x^2 - 286546260x + 5038160400
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$-35.2598 - 61.0717i$ of defining polynomial
Character	$\chi$	$=$	98.67
Dual form			98.10.c.l.79.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(8.00000 + 13.8564i) q^{2} +(-86.7292 + 150.219i) q^{3} +(-128.000 + 221.703i) q^{4} +(1172.77 + 2031.30i) q^{5} -2775.34 q^{6} -4096.00 q^{8} +(-5202.42 - 9010.85i) q^{9} +(-18764.4 + 32500.9i) q^{10} +(35554.8 - 61582.8i) q^{11} +(-22202.7 - 38456.2i) q^{12} -89420.8 q^{13} -406855. q^{15} +(-32768.0 - 56755.8i) q^{16} +(16147.2 - 27967.9i) q^{17} +(83238.7 - 144174. i) q^{18} +(-389534. - 674693. i) q^{19} -600460. q^{20} +1.13775e6 q^{22} +(-886420. - 1.53532e6i) q^{23} +(355243. - 615299. i) q^{24} +(-1.77424e6 + 3.07307e6i) q^{25} +(-715366. - 1.23905e6i) q^{26} -1.60938e6 q^{27} -212075. q^{29} +(-3.25484e6 - 5.63755e6i) q^{30} +(-2.15631e6 + 3.73483e6i) q^{31} +(524288. - 908093. i) q^{32} +(6.16728e6 + 1.06821e7i) q^{33} +516712. q^{34} +2.66364e6 q^{36} +(-3.10051e6 - 5.37024e6i) q^{37} +(6.23254e6 - 1.07951e7i) q^{38} +(7.75540e6 - 1.34327e7i) q^{39} +(-4.80368e6 - 8.32022e6i) q^{40} -6.40835e6 q^{41} -6.99951e6 q^{43} +(9.10203e6 + 1.57652e7i) q^{44} +(1.22025e7 - 2.11354e7i) q^{45} +(1.41827e7 - 2.45652e7i) q^{46} +(-1.75422e7 - 3.03840e7i) q^{47} +1.13678e7 q^{48} -5.67755e7 q^{50} +(2.80088e6 + 4.85126e6i) q^{51} +(1.14459e7 - 1.98248e7i) q^{52} +(2.13451e7 - 3.69707e7i) q^{53} +(-1.28750e7 - 2.23002e7i) q^{54} +1.66791e8 q^{55} +1.35136e8 q^{57} +(-1.69660e6 - 2.93860e6i) q^{58} +(-1.45327e7 + 2.51714e7i) q^{59} +(5.20775e7 - 9.02008e7i) q^{60} +(3.09391e7 + 5.35880e7i) q^{61} -6.90018e7 q^{62} +1.67772e7 q^{64} +(-1.04870e8 - 1.81641e8i) q^{65} +(-9.86766e7 + 1.70913e8i) q^{66} +(-1.00325e8 + 1.73767e8i) q^{67} +(4.13370e6 + 7.15977e6i) q^{68} +3.07514e8 q^{69} +3.03014e7 q^{71} +(2.13091e7 + 3.69085e7i) q^{72} +(-1.45923e8 + 2.52746e8i) q^{73} +(4.96082e7 - 8.59239e7i) q^{74} +(-3.07756e8 - 5.33049e8i) q^{75} +1.99441e8 q^{76} +2.48173e8 q^{78} +(5.44357e7 + 9.42854e7i) q^{79} +(7.68589e7 - 1.33124e8i) q^{80} +(2.41979e8 - 4.19120e8i) q^{81} +(-5.12668e7 - 8.87966e7i) q^{82} -2.16661e8 q^{83} +7.57483e7 q^{85} +(-5.59961e7 - 9.69880e7i) q^{86} +(1.83931e7 - 3.18578e7i) q^{87} +(-1.45633e8 + 2.52243e8i) q^{88} +(-9.32523e7 - 1.61518e8i) q^{89} +3.90481e8 q^{90} +4.53847e8 q^{92} +(-3.74030e8 - 6.47838e8i) q^{93} +(2.80675e8 - 4.86144e8i) q^{94} +(9.13671e8 - 1.58252e9i) q^{95} +(9.09422e7 + 1.57516e8i) q^{96} +9.53814e8 q^{97} -7.39884e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 48 q^{2} - 71 q^{3} - 768 q^{4} + 1085 q^{5} - 2272 q^{6} - 24576 q^{8} - 9106 q^{9} - 17360 q^{10} + 2555 q^{11} - 18176 q^{12} - 36140 q^{13} - 706146 q^{15} - 196608 q^{16} - 20759 q^{17} + 145696 q^{18}+ \cdots - 2607425268 q^{99}+O(q^{100}) $ 6 * q + 48 * q^2 - 71 * q^3 - 768 * q^4 + 1085 * q^5 - 2272 * q^6 - 24576 * q^8 - 9106 * q^9 - 17360 * q^10 + 2555 * q^11 - 18176 * q^12 - 36140 * q^13 - 706146 * q^15 - 196608 * q^16 - 20759 * q^17 + 145696 * q^18 - 1220649 * q^19 - 555520 * q^20 + 81760 * q^22 - 1960903 * q^23 + 290816 * q^24 - 863572 * q^25 - 289120 * q^26 - 5777318 * q^27 - 5212292 * q^29 - 5649168 * q^30 + 9377989 * q^31 + 3145728 * q^32 + 10778103 * q^33 - 664288 * q^34 + 4662272 * q^36 - 25814913 * q^37 + 19530384 * q^38 + 37990822 * q^39 - 4444160 * q^40 - 418500 * q^41 + 5888616 * q^43 + 654080 * q^44 + 37350558 * q^45 + 31374448 * q^46 - 48391269 * q^47 + 9306112 * q^48 - 27634304 * q^50 - 75441987 * q^51 + 4625920 * q^52 + 102186411 * q^53 - 46218544 * q^54 + 456557402 * q^55 + 86169178 * q^57 - 41698336 * q^58 - 144220135 * q^59 + 90386688 * q^60 - 280936871 * q^61 + 300095648 * q^62 + 100663296 * q^64 - 186819738 * q^65 - 172449648 * q^66 + 170710399 * q^67 - 5314304 * q^68 + 1807308342 * q^69 + 939517376 * q^71 + 37298176 * q^72 - 613838539 * q^73 + 413038608 * q^74 - 902254676 * q^75 + 624972288 * q^76 + 1215706304 * q^78 + 197445809 * q^79 + 71106560 * q^80 + 887872901 * q^81 - 3348000 * q^82 + 2148362872 * q^83 + 822545038 * q^85 + 47108928 * q^86 - 753428670 * q^87 - 10465280 * q^88 - 805730427 * q^89 + 1195217856 * q^90 + 1003982336 * q^92 - 1721516327 * q^93 + 774260304 * q^94 + 1799421743 * q^95 + 74448896 * q^96 + 4525836188 * q^97 - 2607425268 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	8.00000	+	13.8564i	0.353553	+	0.612372i
$2$	8.00000	+	13.8564i	0.353553	+	0.612372i
$3$	−86.7292	+	150.219i	−0.618187	+	1.07073i	0.371629	+	0.928381i	$0.378799\pi$
$3$	−86.7292	+	150.219i	−0.618187	+	1.07073i	−0.989816	+	0.142350i	$0.954534\pi$
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	1172.77	+	2031.30i	0.839169	+	1.45348i	0.890591	+	0.454806i	$0.150291\pi$
$5$	1172.77	+	2031.30i	0.839169	+	1.45348i	−0.0514219	+	0.998677i	$0.516375\pi$
$6$	−2775.34			−0.874248
$7$		0			0
$7$		0			0
$8$	−4096.00			−0.353553
$9$	−5202.42	−	9010.85i	−0.264310	−	0.457799i
$10$	−18764.4	+	32500.9i	−0.593382	+	1.02777i
$11$	35554.8	−	61582.8i	0.732203	−	1.26821i	−0.223737	−	0.974650i	$-0.571826\pi$
$11$	35554.8	−	61582.8i	0.732203	−	1.26821i	0.955940	−	0.293563i	$-0.0948410\pi$
$12$	−22202.7	−	38456.2i	−0.309093	−	0.535366i
$13$	−89420.8			−0.868347			−0.434174	−	0.900829i	$-0.642960\pi$
$13$	−89420.8			−0.868347			−0.434174	+	0.900829i	$0.642960\pi$
$14$		0			0
$15$	−406855.			−2.07505
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	16147.2	−	27967.9i	0.0468898	−	0.0812155i	−0.841628	−	0.540058i	$-0.818402\pi$
$17$	16147.2	−	27967.9i	0.0468898	−	0.0812155i	0.888518	+	0.458842i	$0.151736\pi$
$18$	83238.7	−	144174.i	0.186896	−	0.323713i
$19$	−389534.	−	674693.i	−0.685732	−	1.18772i	−0.973206	−	0.229934i	$-0.926149\pi$
$19$	−389534.	−	674693.i	−0.685732	−	1.18772i	0.287475	−	0.957788i	$-0.407184\pi$
$20$	−600460.			−0.839169
$21$		0			0
$22$	1.13775e6			1.03549
$23$	−886420.	−	1.53532e6i	−0.660487	−	1.14400i	−0.980488	−	0.196580i	$-0.937016\pi$
$23$	−886420.	−	1.53532e6i	−0.660487	−	1.14400i	0.320001	−	0.947417i	$-0.396317\pi$
$24$	355243.	−	615299.i	0.218562	−	0.378561i
$25$	−1.77424e6	+	3.07307e6i	−0.908408	+	1.57341i
$26$	−715366.	−	1.23905e6i	−0.307007	−	0.531752i
$27$	−1.60938e6			−0.582801
$28$		0			0
$29$	−212075.			−0.0556799			−0.0278399	−	0.999612i	$-0.508863\pi$
$29$	−212075.			−0.0556799			−0.0278399	+	0.999612i	$0.508863\pi$
$30$	−3.25484e6	−	5.63755e6i	−0.733642	−	1.27071i
$31$	−2.15631e6	+	3.73483e6i	−0.419356	+	0.726346i	−0.995875	−	0.0907380i	$-0.971077\pi$
$31$	−2.15631e6	+	3.73483e6i	−0.419356	+	0.726346i	0.576519	+	0.817084i	$0.304411\pi$
$32$	524288.	−	908093.i	0.0883883	−	0.153093i
$33$	6.16728e6	+	1.06821e7i	0.905277	+	1.56799i
$34$	516712.			0.0663122
$35$		0			0
$36$	2.66364e6			0.264310
$37$	−3.10051e6	−	5.37024e6i	−0.271973	−	0.471071i	0.697394	−	0.716688i	$-0.254343\pi$
$37$	−3.10051e6	−	5.37024e6i	−0.271973	−	0.471071i	−0.969367	+	0.245617i	$0.921009\pi$
$38$	6.23254e6	−	1.07951e7i	0.484886	−	0.839846i
$39$	7.75540e6	−	1.34327e7i	0.536801	−	0.929766i
$40$	−4.80368e6	−	8.32022e6i	−0.296691	−	0.513884i
$41$	−6.40835e6			−0.354176			−0.177088	−	0.984195i	$-0.556668\pi$
$41$	−6.40835e6			−0.354176			−0.177088	+	0.984195i	$0.556668\pi$
$42$		0			0
$43$	−6.99951e6			−0.312219			−0.156110	−	0.987740i	$-0.549895\pi$
$43$	−6.99951e6			−0.312219			−0.156110	+	0.987740i	$0.549895\pi$
$44$	9.10203e6	+	1.57652e7i	0.366101	+	0.634106i
$45$	1.22025e7	−	2.11354e7i	0.443602	−	0.768341i
$46$	1.41827e7	−	2.45652e7i	0.467035	−	0.808928i
$47$	−1.75422e7	−	3.03840e7i	−0.524377	−	0.908248i	−0.999597	−	0.0283808i	$-0.990965\pi$
$47$	−1.75422e7	−	3.03840e7i	−0.524377	−	0.908248i	0.475220	−	0.879867i	$-0.342368\pi$
$48$	1.13678e7			0.309093
$49$		0			0
$50$	−5.67755e7			−1.28468
$51$	2.80088e6	+	4.85126e6i	0.0579733	+	0.100413i
$52$	1.14459e7	−	1.98248e7i	0.217087	−	0.376005i
$53$	2.13451e7	−	3.69707e7i	0.371583	−	0.643601i	−0.618226	−	0.786000i	$-0.712148\pi$
$53$	2.13451e7	−	3.69707e7i	0.371583	−	0.643601i	0.989809	+	0.142400i	$0.0454818\pi$
$54$	−1.28750e7	−	2.23002e7i	−0.206051	−	0.356891i
$55$	1.66791e8			2.45777
$56$		0			0
$57$	1.35136e8			1.69564
$58$	−1.69660e6	−	2.93860e6i	−0.0196858	−	0.0340968i
$59$	−1.45327e7	+	2.51714e7i	−0.156139	+	0.270441i	−0.933473	−	0.358647i	$-0.883238\pi$
$59$	−1.45327e7	+	2.51714e7i	−0.156139	+	0.270441i	0.777334	+	0.629088i	$0.216572\pi$
$60$	5.20775e7	−	9.02008e7i	0.518763	−	0.898524i
$61$	3.09391e7	+	5.35880e7i	0.286103	+	0.495546i	0.972876	−	0.231327i	$-0.0743066\pi$
$61$	3.09391e7	+	5.35880e7i	0.286103	+	0.495546i	−0.686773	+	0.726872i	$0.740973\pi$
$62$	−6.90018e7			−0.593059
$63$		0			0
$64$	1.67772e7			0.125000
$65$	−1.04870e8	−	1.81641e8i	−0.728690	−	1.26213i
$66$	−9.86766e7	+	1.70913e8i	−0.640127	+	1.10873i
$67$	−1.00325e8	+	1.73767e8i	−0.608234	+	1.05349i	0.383297	+	0.923625i	$0.374789\pi$
$67$	−1.00325e8	+	1.73767e8i	−0.608234	+	1.05349i	−0.991531	+	0.129867i	$0.958545\pi$
$68$	4.13370e6	+	7.15977e6i	0.0234449	+	0.0406078i
$69$	3.07514e8			1.63322
$70$		0			0
$71$	3.03014e7			0.141514			0.0707571	−	0.997494i	$-0.477458\pi$
$71$	3.03014e7			0.141514			0.0707571	+	0.997494i	$0.477458\pi$
$72$	2.13091e7	+	3.69085e7i	0.0934478	+	0.161856i
$73$	−1.45923e8	+	2.52746e8i	−0.601411	+	1.04167i	0.391197	+	0.920307i	$0.372061\pi$
$73$	−1.45923e8	+	2.52746e8i	−0.601411	+	1.04167i	−0.992608	+	0.121367i	$0.961272\pi$
$74$	4.96082e7	−	8.59239e7i	0.192314	−	0.333097i
$75$	−3.07756e8	−	5.33049e8i	−1.12313	−	1.94532i
$76$	1.99441e8			0.685732
$77$		0			0
$78$	2.48173e8			0.759151
$79$	5.44357e7	+	9.42854e7i	0.157240	+	0.272347i	0.933872	−	0.357607i	$-0.116407\pi$
$79$	5.44357e7	+	9.42854e7i	0.157240	+	0.272347i	−0.776633	+	0.629954i	$0.783074\pi$
$80$	7.68589e7	−	1.33124e8i	0.209792	−	0.363371i
$81$	2.41979e8	−	4.19120e8i	0.624590	−	1.08182i
$82$	−5.12668e7	−	8.87966e7i	−0.125220	−	0.216887i
$83$	−2.16661e8			−0.501106			−0.250553	−	0.968103i	$-0.580612\pi$
$83$	−2.16661e8			−0.501106			−0.250553	+	0.968103i	$0.580612\pi$
$84$		0			0
$85$	7.57483e7			0.157394
$86$	−5.59961e7	−	9.69880e7i	−0.110386	−	0.191194i
$87$	1.83931e7	−	3.18578e7i	0.0344206	−	0.0596182i
$88$	−1.45633e8	+	2.52243e8i	−0.258873	+	0.448381i
$89$	−9.32523e7	−	1.61518e8i	−0.157545	−	0.272876i	0.776438	−	0.630194i	$-0.217025\pi$
$89$	−9.32523e7	−	1.61518e8i	−0.157545	−	0.272876i	−0.933983	+	0.357318i	$0.883691\pi$
$90$	3.90481e8			0.627348
$91$		0			0
$92$	4.53847e8			0.660487
$93$	−3.74030e8	−	6.47838e8i	−0.518481	−	0.898035i
$94$	2.80675e8	−	4.86144e8i	0.370791	−	0.642228i
$95$	9.13671e8	−	1.58252e9i	1.15089	−	1.99340i
$96$	9.09422e7	+	1.57516e8i	0.109281	+	0.189280i
$97$	9.53814e8			1.09393			0.546966	−	0.837155i	$-0.315783\pi$
$97$	9.53814e8			1.09393			0.546966	+	0.837155i	$0.315783\pi$
$98$		0			0
$99$	−7.39884e8			−0.774115
$100$	−4.54204e8	−	7.86705e8i	−0.454204	−	0.786705i
$101$	−9.73745e8	+	1.68657e9i	−0.931105	+	1.61272i	−0.149670	+	0.988736i	$0.547821\pi$
$101$	−9.73745e8	+	1.68657e9i	−0.931105	+	1.61272i	−0.781436	+	0.623986i	$0.785512\pi$
$102$	−4.48140e7	+	7.76202e7i	−0.0409933	+	0.0710025i
$103$	−6.91594e8	−	1.19788e9i	−0.605458	−	1.04868i	−0.991979	−	0.126403i	$-0.959657\pi$
$103$	−6.91594e8	−	1.19788e9i	−0.605458	−	1.04868i	0.386521	−	0.922281i	$-0.373677\pi$
$104$	3.66268e8			0.307007
$105$		0			0
$106$	6.83042e8			0.525498
$107$	9.59157e8	+	1.66131e9i	0.707396	+	1.22525i	0.965820	+	0.259214i	$0.0834636\pi$
$107$	9.59157e8	+	1.66131e9i	0.707396	+	1.22525i	−0.258424	+	0.966032i	$0.583203\pi$
$108$	2.06000e8	−	3.56803e8i	0.145700	−	0.252360i
$109$	−9.42525e8	+	1.63250e9i	−0.639548	+	1.10773i	0.345983	+	0.938241i	$0.387545\pi$
$109$	−9.42525e8	+	1.63250e9i	−0.639548	+	1.10773i	−0.985532	+	0.169490i	$0.945788\pi$
$110$	1.33433e9	+	2.31113e9i	0.868952	+	1.50507i
$111$	1.07562e9			0.672520
$112$		0			0
$113$	−1.65917e9			−0.957277			−0.478639	−	0.878012i	$-0.658870\pi$
$113$	−1.65917e9			−0.957277			−0.478639	+	0.878012i	$0.658870\pi$
$114$	1.08109e9	+	1.87250e9i	0.599500	+	1.03836i
$115$	2.07914e9	−	3.60118e9i	1.10852	−	1.92001i
$116$	2.71456e7	−	4.70175e7i	0.0139200	−	0.0241101i
$117$	4.65204e8	+	8.05758e8i	0.229513	+	0.397528i
$118$	−4.65046e8			−0.220814
$119$		0			0
$120$	1.66648e9			0.733642
$121$	−1.34932e9	−	2.33709e9i	−0.572242	−	0.991152i
$122$	−4.95025e8	+	8.57409e8i	−0.202306	+	0.350404i
$123$	5.55791e8	−	9.62658e8i	0.218947	−	0.379227i
$124$	−5.52014e8	−	9.56117e8i	−0.209678	−	0.363173i
$125$	−3.74196e9			−1.37089
$126$		0			0
$127$	−2.50752e9			−0.855319			−0.427659	−	0.903940i	$-0.640662\pi$
$127$	−2.50752e9			−0.855319			−0.427659	+	0.903940i	$0.640662\pi$
$128$	1.34218e8	+	2.32472e8i	0.0441942	+	0.0765466i
$129$	6.07062e8	−	1.05146e9i	0.193010	−	0.334303i
$130$	1.67793e9	−	2.90625e9i	0.515261	−	0.892459i
$131$	−1.52573e9	−	2.64265e9i	−0.452645	−	0.784004i	0.545904	−	0.837848i	$-0.316186\pi$
$131$	−1.52573e9	−	2.64265e9i	−0.452645	−	0.784004i	−0.998549	+	0.0538433i	$0.982853\pi$
$132$	−3.15765e9			−0.905277
$133$		0			0
$134$	−3.21039e9			−0.860173
$135$	−1.88743e9	−	3.26913e9i	−0.489069	−	0.847092i
$136$	−6.61391e7	+	1.14556e8i	−0.0165780	+	0.0287140i
$137$	−3.65274e9	+	6.32673e9i	−0.885882	+	1.53439i	−0.0411834	+	0.999152i	$0.513113\pi$
$137$	−3.65274e9	+	6.32673e9i	−0.885882	+	1.53439i	−0.844699	+	0.535242i	$0.820221\pi$
$138$	2.46011e9	+	4.26104e9i	0.577430	+	1.00014i
$139$	−2.79289e9			−0.634581			−0.317290	−	0.948328i	$-0.602773\pi$
$139$	−2.79289e9			−0.634581			−0.317290	+	0.948328i	$0.602773\pi$
$140$		0			0
$141$	6.08569e9			1.29665
$142$	2.42411e8	+	4.19868e8i	0.0500328	+	0.0866594i
$143$	−3.17934e9	+	5.50678e9i	−0.635806	+	1.10125i
$144$	−3.40946e8	+	5.90535e8i	−0.0660776	+	0.114450i
$145$	−2.48716e8	−	4.30789e8i	−0.0467248	−	0.0809298i
$146$	−4.66954e9			−0.850523
$147$		0			0
$148$	1.58746e9			0.271973
$149$	1.26713e9	+	2.19473e9i	0.210611	+	0.364789i	0.951906	−	0.306390i	$-0.0991212\pi$
$149$	1.26713e9	+	2.19473e9i	0.210611	+	0.364789i	−0.741295	+	0.671180i	$0.765788\pi$
$150$	4.92410e9	−	8.52879e9i	0.794175	−	1.37555i
$151$	−1.55428e9	+	2.69210e9i	−0.243295	+	0.421400i	−0.961651	−	0.274276i	$-0.911562\pi$
$151$	−1.55428e9	+	2.69210e9i	−0.243295	+	0.421400i	0.718356	+	0.695676i	$0.244895\pi$
$152$	1.59553e9	+	2.76354e9i	0.242443	+	0.419923i
$153$	−3.36019e8			−0.0495738
$154$		0			0
$155$	−1.01154e10			−1.40764
$156$	1.98538e9	+	3.43878e9i	0.268400	+	0.464883i
$157$	−5.81990e9	+	1.00804e10i	−0.764481	+	1.32412i	0.176039	+	0.984383i	$0.443671\pi$
$157$	−5.81990e9	+	1.00804e10i	−0.764481	+	1.32412i	−0.940520	+	0.339737i	$0.889662\pi$
$158$	−8.70971e8	+	1.50857e9i	−0.111185	+	0.192578i
$159$	3.70248e9	+	6.41288e9i	0.459415	+	0.795731i
$160$	2.45949e9			0.296691
$161$		0			0
$162$	7.74333e9			0.883304
$163$	6.18632e9	+	1.07150e10i	0.686417	+	1.18891i	0.972989	+	0.230851i	$0.0741510\pi$
$163$	6.18632e9	+	1.07150e10i	0.686417	+	1.18891i	−0.286572	+	0.958059i	$0.592516\pi$
$164$	8.20268e8	−	1.42075e9i	0.0885439	−	0.153363i
$165$	−1.44657e10	+	2.50553e10i	−1.51936	+	2.63161i
$166$	−1.73329e9	−	3.00215e9i	−0.177168	−	0.306864i
$167$	−6.26181e9			−0.622982			−0.311491	−	0.950249i	$-0.600828\pi$
$167$	−6.26181e9			−0.622982			−0.311491	+	0.950249i	$0.600828\pi$
$168$		0			0
$169$	−2.60842e9			−0.245973
$170$	6.05986e8	+	1.04960e9i	0.0556471	+	0.0963836i
$171$	−4.05304e9	+	7.02007e9i	−0.362492	+	0.627854i
$172$	8.95937e8	−	1.55181e9i	0.0780548	−	0.135195i
$173$	−4.39565e8	−	7.61348e8i	−0.0373091	−	0.0646213i	0.846768	−	0.531963i	$-0.178545\pi$
$173$	−4.39565e8	−	7.61348e8i	−0.0373091	−	0.0646213i	−0.884077	+	0.467341i	$0.845212\pi$
$174$	5.88579e8			0.0486780
$175$		0			0
$176$	−4.66024e9			−0.366101
$177$	−2.52082e9	−	4.36619e9i	−0.193047	−	0.334367i
$178$	1.49204e9	−	2.58428e9i	0.111401	−	0.192952i
$179$	8.36715e9	−	1.44923e10i	0.609170	−	1.05511i	−0.382207	−	0.924077i	$-0.624836\pi$
$179$	8.36715e9	−	1.44923e10i	0.609170	−	1.05511i	0.991377	−	0.131037i	$-0.0418308\pi$
$180$	3.12385e9	+	5.41066e9i	0.221801	+	0.384170i
$181$	3.33844e9			0.231201			0.115601	−	0.993296i	$-0.463121\pi$
$181$	3.33844e9			0.231201			0.115601	+	0.993296i	$0.463121\pi$
$182$		0			0
$183$	−1.07333e10			−0.707462
$184$	3.63078e9	+	6.28869e9i	0.233517	+	0.404464i
$185$	7.27240e9	−	1.25962e10i	0.456462	−	0.790616i
$186$	5.98447e9	−	1.03654e10i	0.366621	−	0.635007i
$187$	−1.14823e9	−	1.98878e9i	−0.0686657	−	0.118932i
$188$	8.98161e9			0.524377
$189$		0			0
$190$	2.92375e10			1.62760
$191$	5.89031e9	+	1.02023e10i	0.320249	+	0.554688i	0.980539	−	0.196323i	$-0.0629000\pi$
$191$	5.89031e9	+	1.02023e10i	0.320249	+	0.554688i	−0.660290	+	0.751011i	$0.729567\pi$
$192$	−1.45508e9	+	2.52026e9i	−0.0772734	+	0.133841i
$193$	1.60936e10	−	2.78750e10i	0.834923	−	1.44613i	−0.0591699	−	0.998248i	$-0.518845\pi$
$193$	1.60936e10	−	2.78750e10i	0.834923	−	1.44613i	0.894093	−	0.447881i	$-0.147821\pi$
$194$	7.63051e9	+	1.32164e10i	0.386764	+	0.669894i
$195$	3.63813e10			1.80187
$196$		0			0
$197$	−2.41075e10			−1.14039			−0.570195	−	0.821509i	$-0.693132\pi$
$197$	−2.41075e10			−1.14039			−0.570195	+	0.821509i	$0.693132\pi$
$198$	−5.91908e9	−	1.02521e10i	−0.273691	−	0.474047i
$199$	5.72788e9	−	9.92098e9i	0.258914	−	0.448452i	−0.707037	−	0.707176i	$-0.749969\pi$
$199$	5.72788e9	−	9.92098e9i	0.258914	−	0.448452i	0.965951	+	0.258724i	$0.0833021\pi$
$200$	7.26727e9	−	1.25873e10i	0.321171	−	0.556284i
$201$	−1.74022e10	−	3.01414e10i	−0.752005	−	1.30251i
$202$	−3.11598e10			−1.31678
$203$		0			0
$204$	−1.43405e9			−0.0579733
$205$	−7.51554e9	−	1.30173e10i	−0.297213	−	0.514788i
$206$	1.10655e10	−	1.91660e10i	0.428123	−	0.741531i
$207$	−9.22306e9	+	1.59748e10i	−0.349147	+	0.604740i
$208$	2.93014e9	+	5.07515e9i	0.108543	+	0.188003i
$209$	−5.53993e10			−2.00838
$210$		0			0
$211$	2.03945e10			0.708339			0.354169	−	0.935181i	$-0.384764\pi$
$211$	2.03945e10			0.708339			0.354169	+	0.935181i	$0.384764\pi$
$212$	5.46433e9	+	9.46450e9i	0.185791	+	0.321800i
$213$	−2.62802e9	+	4.55186e9i	−0.0874822	+	0.151524i
$214$	−1.53465e10	+	2.65809e10i	−0.500205	+	0.866380i
$215$	−8.20884e9	−	1.42181e10i	−0.262005	−	0.453805i
$216$	6.59200e9			0.206051
$217$		0			0
$218$	−3.01608e10			−0.904458
$219$	−2.53116e10	−	4.38410e10i	−0.743568	−	1.28790i
$220$	−2.13493e10	+	3.69780e10i	−0.614442	+	1.06424i
$221$	−1.44390e9	+	2.50091e9i	−0.0407166	+	0.0705233i
$222$	8.60496e9	+	1.49042e10i	0.237772	+	0.411833i
$223$	5.72310e10			1.54974			0.774871	−	0.632119i	$-0.217815\pi$
$223$	5.72310e10			1.54974			0.774871	+	0.632119i	$0.217815\pi$
$224$		0			0
$225$	3.69213e10			0.960407
$226$	−1.32734e10	−	2.29901e10i	−0.338449	−	0.586210i
$227$	7.62484e9	−	1.32066e10i	0.190596	−	0.330122i	−0.754852	−	0.655895i	$-0.772291\pi$
$227$	7.62484e9	−	1.32066e10i	0.190596	−	0.330122i	0.945448	+	0.325773i	$0.105625\pi$
$228$	−1.72974e10	+	2.99600e10i	−0.423910	+	0.734234i
$229$	−1.74014e10	−	3.01402e10i	−0.418144	−	0.724246i	0.577609	−	0.816313i	$-0.303986\pi$
$229$	−1.74014e10	−	3.01402e10i	−0.418144	−	0.724246i	−0.995753	+	0.0920674i	$0.970652\pi$
$230$	6.65325e10			1.56768
$231$		0			0
$232$	8.68659e8			0.0196858
$233$	−3.71391e10	−	6.43268e10i	−0.825524	−	1.42985i	−0.901518	−	0.432741i	$-0.857546\pi$
$233$	−3.71391e10	−	6.43268e10i	−0.825524	−	1.42985i	0.0759945	−	0.997108i	$-0.475787\pi$
$234$	−7.44327e9	+	1.28921e10i	−0.162290	+	0.281095i
$235$	4.11461e10	−	7.12671e10i	0.880082	−	1.52435i
$236$	−3.72037e9	−	6.44387e9i	−0.0780697	−	0.135221i
$237$	−1.88847e10			−0.388814
$238$		0			0
$239$	6.12890e10			1.21504			0.607522	−	0.794303i	$-0.292164\pi$
$239$	6.12890e10			1.21504			0.607522	+	0.794303i	$0.292164\pi$
$240$	1.33318e10	+	2.30914e10i	0.259382	+	0.449262i
$241$	−2.14369e10	+	3.71299e10i	−0.409342	+	0.709001i	−0.994816	−	0.101690i	$-0.967575\pi$
$241$	−2.14369e10	+	3.71299e10i	−0.409342	+	0.709001i	0.585474	+	0.810691i	$0.300908\pi$
$242$	2.15891e10	−	3.73934e10i	0.404636	−	0.700851i
$243$	2.61347e10	+	4.52666e10i	0.480827	+	0.832816i
$244$	−1.58408e10			−0.286103
$245$		0			0
$246$	1.77853e10			0.309637
$247$	3.48324e10	+	6.03315e10i	0.595453	+	1.03136i
$248$	8.83223e9	−	1.52979e10i	0.148265	−	0.256802i
$249$	1.87909e10	−	3.25467e10i	0.309777	−	0.536550i
$250$	−2.99357e10	−	5.18501e10i	−0.484684	−	0.839498i
$251$	2.70921e10			0.430835			0.215417	−	0.976522i	$-0.430889\pi$
$251$	2.70921e10			0.430835			0.215417	+	0.976522i	$0.430889\pi$
$252$		0			0
$253$	−1.26066e11			−1.93444
$254$	−2.00602e10	−	3.47452e10i	−0.302401	−	0.523774i
$255$	−6.56959e9	+	1.13789e10i	−0.0972988	+	0.168526i
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	−4.17372e10	−	7.22909e10i	−0.596793	−	1.03368i	−0.993291	−	0.115641i	$-0.963108\pi$
$257$	−4.17372e10	−	7.22909e10i	−0.596793	−	1.03368i	0.396498	−	0.918036i	$-0.370225\pi$
$258$	1.94260e10			0.272957
$259$		0			0
$260$	5.36936e10			0.728690
$261$	1.10330e9	+	1.91098e9i	0.0147168	+	0.0254902i
$262$	2.44117e10	−	4.22824e10i	0.320068	−	0.554375i
$263$	−2.51663e10	+	4.35893e10i	−0.324354	+	0.561797i	−0.981381	−	0.192070i	$-0.938480\pi$
$263$	−2.51663e10	+	4.35893e10i	−0.324354	+	0.561797i	0.657028	+	0.753866i	$0.271813\pi$
$264$	−2.52612e10	−	4.37537e10i	−0.320064	−	0.554366i
$265$	1.00132e11			1.24728
$266$		0			0
$267$	3.23508e10			0.389569
$268$	−2.56831e10	−	4.44844e10i	−0.304117	−	0.526746i
$269$	1.64843e10	−	2.85517e10i	0.191949	−	0.332466i	−0.753947	−	0.656935i	$-0.771852\pi$
$269$	1.64843e10	−	2.85517e10i	0.191949	−	0.332466i	0.945896	+	0.324470i	$0.105186\pi$
$270$	3.01989e10	−	5.23061e10i	0.345824	−	0.598984i
$271$	1.18673e10	+	2.05547e10i	0.133656	+	0.231499i	0.925083	−	0.379764i	$-0.123995\pi$
$271$	1.18673e10	+	2.05547e10i	0.133656	+	0.231499i	−0.791427	+	0.611263i	$0.790662\pi$
$272$	−2.11645e9			−0.0234449
$273$		0			0
$274$	−1.16888e11			−1.25283
$275$	1.26165e11	+	2.18525e11i	1.33028	+	2.30411i
$276$	−3.93618e10	+	6.81767e10i	−0.408305	+	0.707204i
$277$	4.15751e10	−	7.20101e10i	0.424301	−	0.734911i	−0.572054	−	0.820216i	$-0.693853\pi$
$277$	4.15751e10	−	7.20101e10i	0.424301	−	0.734911i	0.996355	+	0.0853053i	$0.0271866\pi$
$278$	−2.23431e10	−	3.86994e10i	−0.224358	−	0.388600i
$279$	4.48720e10			0.443360
$280$		0			0
$281$	1.48862e11			1.42431			0.712154	−	0.702023i	$-0.247720\pi$
$281$	1.48862e11			1.42431			0.712154	+	0.702023i	$0.247720\pi$
$282$	4.86855e10	+	8.43257e10i	0.458436	+	0.794034i
$283$	2.96776e10	−	5.14031e10i	0.275036	−	0.476377i	−0.695108	−	0.718905i	$-0.744644\pi$
$283$	2.96776e10	−	5.14031e10i	0.275036	−	0.476377i	0.970144	+	0.242529i	$0.0779769\pi$
$284$	−3.87858e9	+	6.71789e9i	−0.0353785	+	0.0612774i
$285$	1.58484e11	+	2.74502e11i	1.42293	+	2.46459i
$286$	−1.01739e11			−0.899166
$287$		0			0
$288$	−1.09103e10			−0.0934478
$289$	5.87725e10	+	1.01797e11i	0.495603	+	0.858409i
$290$	3.97946e9	−	6.89262e9i	0.0330394	−	0.0572260i
$291$	−8.27235e10	+	1.43281e11i	−0.676255	+	1.17131i
$292$	−3.73563e10	−	6.47030e10i	−0.300705	−	0.520837i
$293$	−9.10565e10			−0.721783			−0.360892	−	0.932608i	$-0.617528\pi$
$293$	−9.10565e10			−0.721783			−0.360892	+	0.932608i	$0.617528\pi$
$294$		0			0
$295$	−6.81743e10			−0.524109
$296$	1.26997e10	+	2.19965e10i	0.0961569	+	0.166549i
$297$	−5.72211e10	+	9.91098e10i	−0.426729	+	0.739116i
$298$	−2.02740e10	+	3.51156e10i	−0.148925	+	0.257945i
$299$	7.92644e10	+	1.37290e11i	0.573532	+	0.993387i
$300$	1.57571e11			1.12313
$301$		0			0
$302$	−4.97370e10			−0.344071
$303$	−1.68904e11	−	2.92551e11i	−1.15119	−	1.99393i
$304$	−2.55285e10	+	4.42167e10i	−0.171433	+	0.296931i
$305$	−7.25691e10	+	1.25693e11i	−0.480178	+	0.831693i
$306$	−2.68815e9	−	4.65602e9i	−0.0175270	−	0.0303576i
$307$	−6.61649e10			−0.425114			−0.212557	−	0.977149i	$-0.568179\pi$
$307$	−6.61649e10			−0.425114			−0.212557	+	0.977149i	$0.568179\pi$
$308$		0			0
$309$	2.39926e11			1.49714
$310$	−8.09235e10	−	1.40164e11i	−0.497676	−	0.862001i
$311$	4.42158e9	−	7.65840e9i	0.0268013	−	0.0464212i	−0.852314	−	0.523031i	$-0.824801\pi$
$311$	4.42158e9	−	7.65840e9i	0.0268013	−	0.0464212i	0.879115	+	0.476610i	$0.158135\pi$
$312$	−3.17661e10	+	5.50205e10i	−0.189788	+	0.328722i
$313$	7.90785e9	+	1.36968e10i	0.0465703	+	0.0806621i	0.888371	−	0.459126i	$-0.151838\pi$
$313$	7.90785e9	+	1.36968e10i	0.0465703	+	0.0806621i	−0.841801	+	0.539789i	$0.818504\pi$
$314$	−1.86237e11			−1.08114
$315$		0			0
$316$	−2.78711e10			−0.157240
$317$	−1.07701e11	−	1.86544e11i	−0.599039	−	1.03757i	−0.992963	−	0.118423i	$-0.962216\pi$
$317$	−1.07701e11	−	1.86544e11i	−0.599039	−	1.03757i	0.393924	−	0.919143i	$-0.371117\pi$
$318$	−5.92397e10	+	1.02606e11i	−0.324856	+	0.562667i
$319$	−7.54029e9	+	1.30602e10i	−0.0407690	+	0.0706139i
$320$	1.96759e10	+	3.40796e10i	0.104896	+	0.181685i
$321$	−3.32748e11			−1.74921
$322$		0			0
$323$	−2.51596e10			−0.128615
$324$	6.19467e10	+	1.07295e11i	0.312295	+	0.540911i
$325$	1.58653e11	−	2.74796e11i	0.788814	−	1.36627i
$326$	−9.89812e10	+	1.71440e11i	−0.485370	+	0.840686i
$327$	−1.63489e11	−	2.83171e11i	−0.790721	−	1.36957i
$328$	2.62486e10			0.125220
$329$		0			0
$330$	−4.62901e11			−2.14870
$331$	2.01566e10	+	3.49123e10i	0.0922980	+	0.159865i	0.908478	−	0.417933i	$-0.137245\pi$
$331$	2.01566e10	+	3.49123e10i	0.0922980	+	0.159865i	−0.816180	+	0.577798i	$0.803912\pi$
$332$	2.77326e10	−	4.80343e10i	0.125277	−	0.216985i
$333$	−3.22603e10	+	5.58765e10i	−0.143770	+	0.249018i
$334$	−5.00945e10	−	8.67662e10i	−0.220258	−	0.381497i
$335$	−4.70632e11			−2.04164
$336$		0			0
$337$	−1.47587e11			−0.623324			−0.311662	−	0.950193i	$-0.600886\pi$
$337$	−1.47587e11			−0.623324			−0.311662	+	0.950193i	$0.600886\pi$
$338$	−2.08674e10	−	3.61434e10i	−0.0869647	−	0.150627i
$339$	1.43898e11	−	2.49239e11i	0.591776	−	1.02499i
$340$	−9.69578e9	+	1.67936e10i	−0.0393485	+	0.0681535i
$341$	1.53334e11	+	2.65583e11i	0.614107	+	1.06367i
$342$	−1.29697e11			−0.512641
$343$		0			0
$344$	2.86700e10			0.110386
$345$	3.60645e11	+	6.24655e11i	1.37055	+	2.37385i
$346$	7.03303e9	−	1.21816e10i	0.0263816	−	0.0456942i
$347$	1.95063e11	−	3.37860e11i	0.722259	−	1.25099i	−0.237833	−	0.971306i	$-0.576437\pi$
$347$	1.95063e11	−	3.37860e11i	0.722259	−	1.25099i	0.960092	−	0.279683i	$-0.0902295\pi$
$348$	4.70863e9	+	8.15559e9i	0.0172103	+	0.0298091i
$349$	2.60554e10			0.0940119			0.0470059	−	0.998895i	$-0.485032\pi$
$349$	2.60554e10			0.0940119			0.0470059	+	0.998895i	$0.485032\pi$
$350$		0			0
$351$	1.43912e11			0.506074
$352$	−3.72819e10	−	6.45742e10i	−0.129436	−	0.224190i
$353$	3.75792e10	−	6.50892e10i	0.128814	−	0.223112i	−0.794404	−	0.607390i	$-0.792216\pi$
$353$	3.75792e10	−	6.50892e10i	0.128814	−	0.223112i	0.923217	+	0.384279i	$0.125550\pi$
$354$	4.03331e10	−	6.98590e10i	0.136505	−	0.236433i
$355$	3.55367e10	+	6.15513e10i	0.118754	+	0.205688i
$356$	4.77452e10			0.157545
$357$		0			0
$358$	2.67749e11			0.861497
$359$	−1.43619e11	−	2.48755e11i	−0.456338	−	0.790400i	0.542426	−	0.840103i	$-0.317506\pi$
$359$	−1.43619e11	−	2.48755e11i	−0.456338	−	0.790400i	−0.998764	+	0.0497032i	$0.984172\pi$
$360$	−4.99815e10	+	8.65706e10i	−0.156837	+	0.271650i
$361$	−1.42130e11	+	2.46176e11i	−0.440456	+	0.762892i
$362$	2.67075e10	+	4.62588e10i	0.0817420	+	0.141581i
$363$	4.68101e11			1.41501
$364$		0			0
$365$	−6.84539e11			−2.01874
$366$	−8.58663e10	−	1.48725e11i	−0.250125	−	0.433230i
$367$	−2.54453e11	+	4.40726e11i	−0.732168	+	1.26815i	0.223787	+	0.974638i	$0.428158\pi$
$367$	−2.54453e11	+	4.40726e11i	−0.732168	+	1.26815i	−0.955955	+	0.293514i	$0.905175\pi$
$368$	−5.80924e10	+	1.00619e11i	−0.165122	+	0.285999i
$369$	3.33389e10	+	5.77447e10i	0.0936122	+	0.162141i
$370$	2.32717e11			0.645535
$371$		0			0
$372$	1.91503e11			0.518481
$373$	−5.17260e10	−	8.95921e10i	−0.138363	−	0.239651i	0.788514	−	0.615016i	$-0.210851\pi$
$373$	−5.17260e10	−	8.95921e10i	−0.138363	−	0.239651i	−0.926877	+	0.375365i	$0.877517\pi$
$374$	1.83716e10	−	3.18205e10i	0.0485540	−	0.0840980i
$375$	3.24537e11	−	5.62115e11i	0.847469	−	1.46786i
$376$	7.18528e10	+	1.24453e11i	0.185395	+	0.321114i
$377$	1.89639e10			0.0483495
$378$		0			0
$379$	1.10894e11			0.276078			0.138039	−	0.990427i	$-0.455920\pi$
$379$	1.10894e11			0.276078			0.138039	+	0.990427i	$0.455920\pi$
$380$	2.33900e11	+	4.05126e11i	0.575445	+	0.996699i
$381$	2.17475e11	−	3.76679e11i	0.528747	−	0.915817i
$382$	−9.42450e10	+	1.63237e11i	−0.226450	+	0.392224i
$383$	1.29972e11	+	2.25118e11i	0.308642	+	0.534584i	0.978066	−	0.208297i	$-0.0667922\pi$
$383$	1.29972e11	+	2.25118e11i	0.308642	+	0.534584i	−0.669424	+	0.742881i	$0.733459\pi$
$384$	−4.65624e10			−0.109281
$385$		0			0
$386$	5.14997e11			1.18076
$387$	3.64144e10	+	6.30716e10i	0.0825227	+	0.142934i
$388$	−1.22088e11	+	2.11463e11i	−0.273483	+	0.473687i
$389$	−2.91278e11	+	5.04508e11i	−0.644963	+	1.11711i	0.339347	+	0.940661i	$0.389794\pi$
$389$	−2.91278e11	+	5.04508e11i	−0.644963	+	1.11711i	−0.984310	+	0.176447i	$0.943540\pi$
$390$	2.91050e11	+	5.04114e11i	0.637056	+	1.10341i
$391$	−5.72530e10			−0.123880
$392$		0			0
$393$	5.29303e11			1.11928
$394$	−1.92860e11	−	3.34043e11i	−0.403189	−	0.698343i
$395$	−1.27682e11	+	2.21151e11i	−0.263901	+	0.457090i
$396$	9.47052e10	−	1.64034e11i	0.193529	−	0.335202i
$397$	−9.35365e10	−	1.62010e11i	−0.188983	−	0.327329i	0.755928	−	0.654655i	$-0.227186\pi$
$397$	−9.35365e10	−	1.62010e11i	−0.188983	−	0.327329i	−0.944912	+	0.327326i	$0.893853\pi$
$398$	1.83292e11			0.366159
$399$		0			0
$400$	2.32553e11			0.454204
$401$	4.41371e11	+	7.64477e11i	0.852420	+	1.47644i	0.879018	+	0.476789i	$0.158200\pi$
$401$	4.41371e11	+	7.64477e11i	0.852420	+	1.47644i	−0.0265971	+	0.999646i	$0.508467\pi$
$402$	2.78434e11	−	4.82263e11i	0.531748	−	0.921014i
$403$	1.92819e11	−	3.33972e11i	0.364147	−	0.630720i
$404$	−2.49279e11	−	4.31763e11i	−0.465553	−	0.806361i
$405$	1.13515e12			2.09655
$406$		0			0
$407$	−4.40953e11			−0.796557
$408$	−1.14724e10	−	1.98708e10i	−0.0204967	−	0.0355013i
$409$	−1.97162e11	+	3.41495e11i	−0.348393	+	0.603434i	−0.985964	−	0.166957i	$-0.946606\pi$
$409$	−1.97162e11	+	3.41495e11i	−0.348393	+	0.603434i	0.637571	+	0.770391i	$0.279939\pi$
$410$	1.20249e11	−	2.08277e11i	0.210161	−	0.364010i
$411$	−6.33598e11	−	1.09742e12i	−1.09528	−	1.89708i
$412$	3.54096e11			0.605458
$413$		0			0
$414$	−2.95138e11			−0.493769
$415$	−2.54095e11	−	4.40105e11i	−0.420513	−	0.728349i
$416$	−4.68822e10	+	8.12024e10i	−0.0767518	+	0.132938i
$417$	2.42225e11	−	4.19546e11i	0.392290	−	0.679465i
$418$	−4.43194e11	−	7.67635e11i	−0.710069	−	1.22988i
$419$	1.77960e11			0.282072			0.141036	−	0.990004i	$-0.454957\pi$
$419$	1.77960e11			0.282072			0.141036	+	0.990004i	$0.454957\pi$
$420$		0			0
$421$	3.94445e11			0.611952			0.305976	−	0.952039i	$-0.401017\pi$
$421$	3.94445e11			0.611952			0.305976	+	0.952039i	$0.401017\pi$
$422$	1.63156e11	+	2.82594e11i	0.250436	+	0.433767i
$423$	−1.82524e11	+	3.16140e11i	−0.277196	+	0.480118i
$424$	−8.74293e10	+	1.51432e11i	−0.131374	+	0.227547i
$425$	5.72980e10	+	9.92431e10i	0.0851902	+	0.147554i
$426$	−8.40965e10			−0.123719
$427$		0			0
$428$	−4.91088e11			−0.707396
$429$	−5.51483e11	−	9.55197e11i	−0.786094	−	1.36156i
$430$	1.31341e11	−	2.27490e11i	0.185265	−	0.320889i
$431$	−4.03895e11	+	6.99567e11i	−0.563795	+	0.976521i	0.433366	+	0.901218i	$0.357326\pi$
$431$	−4.03895e11	+	6.99567e11i	−0.563795	+	0.976521i	−0.997161	+	0.0753033i	$0.976008\pi$
$432$	5.27360e10	+	9.13415e10i	0.0728502	+	0.126180i
$433$	−5.77686e11			−0.789763			−0.394881	−	0.918732i	$-0.629214\pi$
$433$	−5.77686e11			−0.789763			−0.394881	+	0.918732i	$0.629214\pi$
$434$		0			0
$435$	8.62838e10			0.115539
$436$	−2.41286e11	−	4.17920e11i	−0.319774	−	0.553865i
$437$	−6.90582e11	+	1.19612e12i	−0.905834	+	1.56895i
$438$	4.04985e11	−	7.01455e11i	0.525782	−	0.910682i
$439$	−6.64142e11	−	1.15033e12i	−0.853436	−	1.47819i	−0.878089	−	0.478498i	$-0.841181\pi$
$439$	−6.64142e11	−	1.15033e12i	−0.853436	−	1.47819i	0.0246530	−	0.999696i	$-0.492152\pi$
$440$	−6.83176e11			−0.868952
$441$		0			0
$442$	−4.62048e10			−0.0575820
$443$	−2.49733e11	−	4.32551e11i	−0.308077	−	0.533606i	0.669864	−	0.742483i	$-0.266352\pi$
$443$	−2.49733e11	−	4.32551e11i	−0.308077	−	0.533606i	−0.977942	+	0.208878i	$0.933019\pi$
$444$	−1.37679e11	+	2.38468e11i	−0.168130	+	0.291210i
$445$	2.18728e11	−	3.78848e11i	0.264414	−	0.457978i
$446$	4.57848e11	+	7.93016e11i	0.547917	+	0.949020i
$447$	−4.39588e11			−0.520789
$448$		0			0
$449$	−4.51211e10			−0.0523927			−0.0261964	−	0.999657i	$-0.508340\pi$
$449$	−4.51211e10			−0.0523927			−0.0261964	+	0.999657i	$0.508340\pi$
$450$	2.95370e11	+	5.11596e11i	0.339555	+	0.588127i
$451$	−2.27848e11	+	3.94644e11i	−0.259328	+	0.449170i
$452$	2.12374e11	−	3.67842e11i	0.239319	−	0.414513i
$453$	−2.69603e11	−	4.66967e11i	−0.300804	−	0.521008i
$454$	2.43995e11			0.269544
$455$		0			0
$456$	−5.53517e11			−0.599500
$457$	−3.17610e11	−	5.50117e11i	−0.340621	−	0.589973i	0.643927	−	0.765087i	$-0.277304\pi$
$457$	−3.17610e11	−	5.50117e11i	−0.340621	−	0.589973i	−0.984548	+	0.175114i	$0.943971\pi$
$458$	2.78423e11	−	4.82243e11i	0.295672	−	0.512119i
$459$	−2.59870e10	+	4.50108e10i	−0.0273274	+	0.0473325i
$460$	5.32260e11	+	9.21901e11i	0.554260	+	0.960007i
$461$	1.21010e12			1.24786			0.623932	−	0.781479i	$-0.285534\pi$
$461$	1.21010e12			1.24786			0.623932	+	0.781479i	$0.285534\pi$
$462$		0			0
$463$	9.73087e11			0.984095			0.492047	−	0.870568i	$-0.336249\pi$
$463$	9.73087e11			0.984095			0.492047	+	0.870568i	$0.336249\pi$
$464$	6.94927e9	+	1.20365e10i	0.00695999	+	0.0120550i
$465$	8.77304e11	−	1.51954e12i	0.870186	−	1.50721i
$466$	5.94225e11	−	1.02923e12i	0.583733	−	1.01106i
$467$	8.41530e11	+	1.45757e12i	0.818735	+	1.41809i	0.906614	+	0.421960i	$0.138658\pi$
$467$	8.41530e11	+	1.45757e12i	0.818735	+	1.41809i	−0.0878789	+	0.996131i	$0.528009\pi$
$468$	−2.38185e11			−0.229513
$469$		0			0
$470$	1.31667e12			1.24462
$471$	−1.00951e12	−	1.74852e12i	−0.945185	−	1.63711i
$472$	5.95259e10	−	1.03102e11i	0.0552036	−	0.0956154i
$473$	−2.48866e11	+	4.31049e11i	−0.228608	+	0.395960i
$474$	−1.51077e11	−	2.61674e11i	−0.137466	−	0.238099i
$475$	2.76450e12			2.49170
$476$		0			0
$477$	−4.44184e11			−0.392853
$478$	4.90312e11	+	8.49245e11i	0.429583	+	0.744059i
$479$	5.82335e11	−	1.00863e12i	0.505432	−	0.875434i	−0.494548	−	0.869150i	$-0.664666\pi$
$479$	5.82335e11	−	1.00863e12i	0.505432	−	0.875434i	0.999980	−	0.00628383i	$-0.00200022\pi$
$480$	−2.13309e11	+	3.69462e11i	−0.183410	+	0.317676i
$481$	2.77250e11	+	4.80211e11i	0.236167	+	0.409053i
$482$	−6.85982e11			−0.578897
$483$		0			0
$484$	6.90850e11			0.572242
$485$	1.11861e12	+	1.93749e12i	0.917994	+	1.59001i
$486$	−4.18155e11	+	7.24265e11i	−0.339996	+	0.588890i
$487$	−1.12077e12	+	1.94123e12i	−0.902891	+	1.56385i	−0.0791677	+	0.996861i	$0.525226\pi$
$487$	−1.12077e12	+	1.94123e12i	−0.902891	+	1.56385i	−0.823723	+	0.566992i	$0.808107\pi$
$488$	−1.26726e11	−	2.19497e11i	−0.101153	−	0.175202i
$489$	−2.14614e12			−1.69734
$490$		0			0
$491$	1.65508e11			0.128515			0.0642573	−	0.997933i	$-0.479532\pi$
$491$	1.65508e11			0.128515			0.0642573	+	0.997933i	$0.479532\pi$
$492$	1.42282e11	+	2.46440e11i	0.109473	+	0.189613i
$493$	−3.42443e9	+	5.93128e9i	−0.00261082	+	0.00452207i
$494$	−5.57319e11	+	9.65305e11i	−0.421049	+	0.729278i
$495$	−8.67717e11	−	1.50293e12i	−0.649613	−	1.12516i
$496$	2.82631e11			0.209678
$497$		0			0
$498$	6.01307e11			0.438091
$499$	6.06773e11	+	1.05096e12i	0.438100	+	0.758812i	0.997543	−	0.0700572i	$-0.0223182\pi$
$499$	6.06773e11	+	1.05096e12i	0.438100	+	0.758812i	−0.559443	+	0.828869i	$0.688985\pi$
$500$	4.78971e11	−	8.29602e11i	0.342724	−	0.593615i
$501$	5.43082e11	−	9.40646e11i	0.385120	−	0.667047i
$502$	2.16737e11	+	3.75399e11i	0.152323	+	0.263831i
$503$	−8.95258e10			−0.0623580			−0.0311790	−	0.999514i	$-0.509926\pi$
$503$	−8.95258e10			−0.0623580			−0.0311790	+	0.999514i	$0.509926\pi$
$504$		0			0
$505$	−4.56793e12			−3.12542
$506$	−1.00853e12	−	1.74682e12i	−0.683929	−	1.18460i
$507$	2.26227e11	−	3.91836e11i	0.152058	−	0.263371i
$508$	3.20963e11	−	5.55924e11i	0.213830	−	0.370364i
$509$	6.66954e11	+	1.15520e12i	0.440419	+	0.762828i	0.997720	−	0.0674822i	$-0.0214966\pi$
$509$	6.66954e11	+	1.15520e12i	0.440419	+	0.762828i	−0.557302	+	0.830310i	$0.688163\pi$
$510$	−2.10227e11			−0.137601
$511$		0			0
$512$	−6.87195e10			−0.0441942
$513$	6.26907e11	+	1.08583e12i	0.399645	+	0.692206i
$514$	6.67795e11	−	1.15665e12i	0.421997	−	0.730919i
$515$	1.62217e12	−	2.80968e12i	1.01616	−	1.76005i
$516$	1.55408e11	+	2.69174e11i	0.0965049	+	0.167151i
$517$	−2.49484e12			−1.53580
$518$		0			0
$519$	1.52492e11			0.0922561
$520$	4.29549e11	+	7.44001e11i	0.257631	+	0.446230i
$521$	−2.86045e11	+	4.95444e11i	−0.170084	+	0.294595i	−0.938449	−	0.345417i	$-0.887737\pi$
$521$	−2.86045e11	+	4.95444e11i	−0.170084	+	0.294595i	0.768365	+	0.640012i	$0.221071\pi$
$522$	−1.76528e10	+	3.05756e10i	−0.0104063	+	0.0180243i
$523$	−1.25008e12	−	2.16521e12i	−0.730602	−	1.26544i	−0.956626	−	0.291318i	$-0.905906\pi$
$523$	−1.25008e12	−	2.16521e12i	−0.730602	−	1.26544i	0.226024	−	0.974122i	$-0.427427\pi$
$524$	7.81175e11			0.452645
$525$		0			0
$526$	−8.05322e11			−0.458705
$527$	6.96368e10	+	1.20615e11i	0.0393270	+	0.0681164i
$528$	4.04179e11	−	7.00059e11i	0.226319	−	0.391996i
$529$	−6.70905e11	+	1.16204e12i	−0.372486	+	0.645165i
$530$	8.01053e11	+	1.38747e12i	0.440981	+	0.763802i
$531$	3.02421e11			0.165077
$532$		0			0
$533$	5.73039e11			0.307547
$534$	2.58806e11	+	4.48266e11i	0.137733	+	0.238561i
$535$	−2.24975e12	+	3.89668e12i	−1.18725	+	2.05638i
$536$	4.10930e11	−	7.11751e11i	0.215043	−	0.372466i
$537$	1.45135e12	+	2.51382e12i	0.753162	+	1.30452i
$538$	5.27499e11			0.271457
$539$		0			0
$540$	9.66366e11			0.489069
$541$	−5.24154e11	−	9.07861e11i	−0.263070	−	0.455650i	0.703986	−	0.710213i	$-0.251402\pi$
$541$	−5.24154e11	−	9.07861e11i	−0.263070	−	0.455650i	−0.967056	+	0.254563i	$0.918068\pi$
$542$	−1.89876e11	+	3.28875e11i	−0.0945091	+	0.163694i
$543$	−2.89541e11	+	5.01499e11i	−0.142926	+	0.247554i
$544$	−1.69316e10	−	2.93264e10i	−0.00828902	−	0.0143570i
$545$	−4.42147e12			−2.14676
$546$		0			0
$547$	−3.50622e12			−1.67454			−0.837272	−	0.546786i	$-0.815851\pi$
$547$	−3.50622e12			−1.67454			−0.837272	+	0.546786i	$0.815851\pi$
$548$	−9.35101e11	−	1.61964e12i	−0.442941	−	0.767197i
$549$	3.21916e11	−	5.57575e11i	0.151240	−	0.261956i
$550$	−2.01864e12	+	3.49639e12i	−0.940649	+	1.62925i
$551$	8.26104e10	+	1.43085e11i	0.0381815	+	0.0661322i
$552$	−1.25958e12			−0.577430
$553$		0			0
$554$	1.33040e12			0.600052
$555$	1.26146e12	+	2.18491e12i	0.564358	+	0.977497i
$556$	3.57490e11	−	6.19190e11i	0.158645	−	0.274782i
$557$	−1.12138e12	+	1.94228e12i	−0.493631	+	0.854994i	−0.999973	−	0.00733847i	$-0.997664\pi$
$557$	−1.12138e12	+	1.94228e12i	−0.493631	+	0.854994i	0.506342	+	0.862333i	$0.330997\pi$
$558$	3.58976e11	+	6.21765e11i	0.156752	+	0.271502i
$559$	6.25901e11			0.271115
$560$		0			0
$561$	3.98339e11			0.169793
$562$	1.19089e12	+	2.06269e12i	0.503569	+	0.872207i
$563$	1.01923e12	−	1.76536e12i	0.427547	−	0.740533i	−0.569107	−	0.822263i	$-0.692711\pi$
$563$	1.01923e12	−	1.76536e12i	0.427547	−	0.740533i	0.996655	+	0.0817298i	$0.0260445\pi$
$564$	−7.78968e11	+	1.34921e12i	−0.324163	+	0.561467i
$565$	−1.94583e12	−	3.37028e12i	−0.803317	−	1.39139i
$566$	9.49683e11			0.388960
$567$		0			0
$568$	−1.24114e11			−0.0500328
$569$	−6.24361e11	−	1.08142e12i	−0.249707	−	0.432505i	0.713738	−	0.700413i	$-0.247001\pi$
$569$	−6.24361e11	−	1.08142e12i	−0.249707	−	0.432505i	−0.963444	+	0.267908i	$0.913668\pi$
$570$	−2.53574e12	+	4.39204e12i	−1.00616	+	1.74273i
$571$	−1.14336e12	+	1.98036e12i	−0.450113	+	0.779619i	−0.998393	−	0.0566765i	$-0.981950\pi$
$571$	−1.14336e12	+	1.98036e12i	−0.450113	+	0.779619i	0.548280	+	0.836295i	$0.315283\pi$
$572$	−8.13911e11	−	1.40974e12i	−0.317903	−	0.550624i
$573$	−2.04345e12			−0.791896
$574$		0			0
$575$	6.29087e12			2.39997
$576$	−8.72821e10	−	1.51177e11i	−0.0330388	−	0.0572249i
$577$	−1.30799e12	+	2.26550e12i	−0.491260	+	0.850888i	−0.999949	−	0.0100624i	$-0.996797\pi$
$577$	−1.30799e12	+	2.26550e12i	−0.491260	+	0.850888i	0.508689	+	0.860950i	$0.330130\pi$
$578$	−9.40360e11	+	1.62875e12i	−0.350444	+	0.606987i
$579$	2.79158e12	+	4.83516e12i	1.03228	+	1.78796i
$580$	1.27343e11			0.0467248
$581$		0			0
$582$	−2.64715e12			−0.956369
$583$	−1.51784e12	−	2.62897e12i	−0.544148	−	0.942492i
$584$	5.97701e11	−	1.03525e12i	0.212631	−	0.368287i
$585$	−1.09116e12	+	1.88994e12i	−0.385200	+	0.667187i
$586$	−7.28452e11	−	1.26172e12i	−0.255189	−	0.442000i
$587$	3.09779e12			1.07691			0.538457	−	0.842653i	$-0.319007\pi$
$587$	3.09779e12			1.07691			0.538457	+	0.842653i	$0.319007\pi$
$588$		0			0
$589$	3.35982e12			1.15026
$590$	−5.45394e11	−	9.44651e11i	−0.185301	−	0.320950i
$591$	2.09082e12	−	3.62141e12i	0.704974	−	1.22105i
$592$	−2.03195e11	+	3.51944e11i	−0.0679932	+	0.117768i
$593$	−1.31976e12	−	2.28590e12i	−0.438278	−	0.759120i	0.559279	−	0.828980i	$-0.311078\pi$
$593$	−1.31976e12	−	2.28590e12i	−0.438278	−	0.759120i	−0.997557	+	0.0698599i	$0.977745\pi$
$594$	−1.83107e12			−0.603486
$595$		0			0
$596$	−6.48769e11			−0.210611
$597$	9.93550e11	+	1.72088e12i	0.320114	+	0.554454i
$598$	−1.26823e12	+	2.19664e12i	−0.405548	+	0.702430i
$599$	1.89224e12	−	3.27745e12i	0.600558	−	1.04020i	−0.392178	−	0.919889i	$-0.628278\pi$
$599$	1.89224e12	−	3.27745e12i	0.600558	−	1.04020i	0.992737	−	0.120308i	$-0.0383882\pi$
$600$	1.26057e12	+	2.18337e12i	0.397087	+	0.687775i
$601$	5.10190e11			0.159513			0.0797567	−	0.996814i	$-0.474586\pi$
$601$	5.10190e11			0.159513			0.0797567	+	0.996814i	$0.474586\pi$
$602$		0			0
$603$	2.08772e12			0.643050
$604$	−3.97896e11	−	6.89177e11i	−0.121648	−	0.210700i
$605$	3.16489e12	−	5.48175e12i	0.960415	−	1.66349i
$606$	2.70247e12	−	4.68081e12i	0.814017	−	1.40992i
$607$	2.44927e12	+	4.24227e12i	0.732299	+	1.26838i	0.955898	+	0.293697i	$0.0948858\pi$
$607$	2.44927e12	+	4.24227e12i	0.732299	+	1.26838i	−0.223600	+	0.974681i	$0.571781\pi$
$608$	−8.16912e11			−0.242443
$609$		0			0
$610$	−2.32221e12			−0.679074
$611$	1.56864e12	+	2.71696e12i	0.455341	+	0.788674i
$612$	4.30104e10	−	7.44963e10i	0.0123935	−	0.0214661i
$613$	−2.18246e12	+	3.78013e12i	−0.624272	+	1.08127i	0.364409	+	0.931239i	$0.381271\pi$
$613$	−2.18246e12	+	3.78013e12i	−0.624272	+	1.08127i	−0.988681	+	0.150032i	$0.952062\pi$
$614$	−5.29319e11	−	9.16808e11i	−0.150300	−	0.260328i
$615$	2.60727e12			0.734933
$616$		0			0
$617$	−3.81081e12			−1.05861			−0.529303	−	0.848433i	$-0.677547\pi$
$617$	−3.81081e12			−1.05861			−0.529303	+	0.848433i	$0.677547\pi$
$618$	1.91941e12	+	3.32451e12i	0.529321	+	0.916810i
$619$	−7.62819e11	+	1.32124e12i	−0.208840	+	0.361721i	−0.951349	−	0.308114i	$-0.900302\pi$
$619$	−7.62819e11	+	1.32124e12i	−0.208840	+	0.361721i	0.742509	+	0.669836i	$0.233635\pi$
$620$	1.29478e12	−	2.24262e12i	0.351910	−	0.609527i
$621$	1.42658e12	+	2.47091e12i	0.384933	+	0.666723i
$622$	1.41491e11			0.0379028
$623$		0			0
$624$	−1.01652e12			−0.268400
$625$	−9.23168e11	−	1.59897e12i	−0.242003	−	0.419162i
$626$	−1.26526e11	+	2.19149e11i	−0.0329302	+	0.0570367i
$627$	4.80473e12	−	8.32204e12i	1.24155	−	2.15043i
$628$	−1.48989e12	−	2.58057e12i	−0.382241	−	0.662060i
$629$	−2.00259e11			−0.0510110
$630$		0			0
$631$	−6.08153e12			−1.52715			−0.763573	−	0.645721i	$-0.776557\pi$
$631$	−6.08153e12			−1.52715			−0.763573	+	0.645721i	$0.776557\pi$
$632$	−2.22969e11	−	3.86193e11i	−0.0555926	−	0.0962892i
$633$	−1.76880e12	+	3.06364e12i	−0.437886	+	0.758441i
$634$	1.72322e12	−	2.98471e12i	0.423584	−	0.733670i
$635$	−2.94076e12	−	5.09354e12i	−0.717757	−	1.24319i
$636$	−1.89567e12			−0.459415
$637$		0			0
$638$	−2.41289e11			−0.0576560
$639$	−1.57640e11	−	2.73041e11i	−0.0374036	−	0.0647850i
$640$	−3.14814e11	+	5.45274e11i	−0.0741727	+	0.128471i
$641$	6.84081e11	−	1.18486e12i	0.160047	−	0.277209i	−0.774839	−	0.632159i	$-0.782169\pi$
$641$	6.84081e11	−	1.18486e12i	0.160047	−	0.277209i	0.934885	+	0.354950i	$0.115502\pi$
$642$	−2.66198e12	−	4.61069e12i	−0.618440	−	1.07117i
$643$	2.94301e12			0.678958			0.339479	−	0.940614i	$-0.389749\pi$
$643$	2.94301e12			0.678958			0.339479	+	0.940614i	$0.389749\pi$
$644$		0			0
$645$	2.84779e12			0.647871
$646$	−2.01277e11	−	3.48622e11i	−0.0454724	−	0.0787605i
$647$	−2.20167e12	+	3.81341e12i	−0.493951	+	0.855547i	−0.999976	−	0.00697131i	$-0.997781\pi$
$647$	−2.20167e12	+	3.81341e12i	−0.493951	+	0.855547i	0.506025	+	0.862519i	$0.331114\pi$
$648$	−9.91147e11	+	1.71672e12i	−0.220826	+	0.382482i
$649$	1.03342e12	+	1.78993e12i	0.228651	+	0.396036i
$650$	5.07691e12			1.11555
$651$		0			0
$652$	−3.16740e12			−0.686417
$653$	−3.43720e11	−	5.95340e11i	−0.0739767	−	0.128131i	0.826664	−	0.562696i	$-0.190236\pi$
$653$	−3.43720e11	−	5.95340e11i	−0.0739767	−	0.128131i	−0.900641	+	0.434564i	$0.856902\pi$
$654$	2.61582e12	−	4.53074e12i	0.559124	−	0.968432i
$655$	3.57868e12	−	6.19846e12i	0.759691	−	1.31582i
$656$	2.09989e11	+	3.63711e11i	0.0442719	+	0.0766813i
$657$	3.03661e12			0.635836
$658$		0			0
$659$	7.48190e12			1.54535			0.772676	−	0.634800i	$-0.218918\pi$
$659$	7.48190e12			1.54535			0.772676	+	0.634800i	$0.218918\pi$
$660$	−3.70321e12	−	6.41415e12i	−0.759680	−	1.31580i
$661$	4.14386e12	−	7.17738e12i	0.844303	−	1.46238i	−0.0419217	−	0.999121i	$-0.513348\pi$
$661$	4.14386e12	−	7.17738e12i	0.844303	−	1.46238i	0.886225	−	0.463255i	$-0.153319\pi$
$662$	−3.22506e11	+	5.58597e11i	−0.0652645	+	0.113041i
$663$	−2.50457e11	−	4.33804e11i	−0.0503410	−	0.0871931i
$664$	8.87444e11			0.177168
$665$		0			0
$666$	−1.03233e12			−0.203322
$667$	1.87987e11	+	3.25604e11i	0.0367758	+	0.0636976i
$668$	8.01512e11	−	1.38826e12i	0.155746	−	0.269759i
$669$	−4.96360e12	+	8.59721e12i	−0.958031	+	1.65936i
$670$	−3.76506e12	−	6.52127e12i	−0.721830	−	1.25025i
$671$	4.40013e12			0.837943
$672$		0			0
$673$	−2.54077e11			−0.0477416			−0.0238708	−	0.999715i	$-0.507599\pi$
$673$	−2.54077e11			−0.0477416			−0.0238708	+	0.999715i	$0.507599\pi$
$674$	−1.18070e12	−	2.04503e12i	−0.220378	−	0.381707i
$675$	2.85541e12	−	4.94572e12i	0.529422	−	0.916985i
$676$	3.33878e11	−	5.78294e11i	0.0614933	−	0.106510i
$677$	4.85902e12	+	8.41607e12i	0.888995	+	1.53979i	0.841065	+	0.540934i	$0.181929\pi$
$677$	4.85902e12	+	8.41607e12i	0.888995	+	1.53979i	0.0479305	+	0.998851i	$0.484737\pi$
$678$	4.60475e12			0.836898
$679$		0			0
$680$	−3.10265e11			−0.0556471
$681$	1.32259e12	+	2.29080e12i	0.235648	+	0.408155i
$682$	−2.45335e12	+	4.24932e12i	−0.434239	+	0.752125i
$683$	3.77058e12	−	6.53084e12i	0.663003	−	1.14835i	−0.316820	−	0.948486i	$-0.602615\pi$
$683$	3.77058e12	−	6.53084e12i	0.663003	−	1.14835i	0.979823	−	0.199869i	$-0.0640515\pi$
$684$	−1.03758e12	−	1.79714e12i	−0.181246	−	0.313927i
$685$	−1.71353e13			−2.97362
$686$		0			0
$687$	6.03685e12			1.03396
$688$	2.29360e11	+	3.97263e11i	0.0390274	+	0.0675974i
$689$	−1.90869e12	+	3.30595e12i	−0.322663	+	0.558869i
$690$	−5.77031e12	+	9.99448e12i	−0.969122	+	1.67857i
$691$	−5.14662e12	−	8.91420e12i	−0.858758	−	1.48741i	−0.873115	−	0.487515i	$-0.837903\pi$
$691$	−5.14662e12	−	8.91420e12i	−0.858758	−	1.48741i	0.0143570	−	0.999897i	$-0.495430\pi$
$692$	2.25057e11			0.0373091
$693$		0			0
$694$	6.24203e12			1.02143
$695$	−3.27543e12	−	5.67320e12i	−0.532520	−	0.922352i
$696$	−7.53381e10	+	1.30489e11i	−0.0121695	+	0.0210782i
$697$	−1.03477e11	+	1.79228e11i	−0.0166072	+	0.0287646i
$698$	2.08443e11	+	3.61034e11i	0.0332382	+	0.0575703i
$699$	1.28842e13			2.04131
$700$		0			0
$701$	9.10623e12			1.42432			0.712160	−	0.702017i	$-0.247717\pi$
$701$	9.10623e12			1.42432			0.712160	+	0.702017i	$0.247717\pi$
$702$	1.15129e12	+	1.99410e12i	0.178924	+	0.309906i
$703$	−2.41551e12	+	4.18378e12i	−0.373001	+	0.646056i
$704$	5.96511e11	−	1.03319e12i	0.0915254	−	0.158527i
$705$	7.13713e12	+	1.23619e13i	1.08811	+	1.88466i
$706$	1.20254e12			0.182170
$707$		0			0
$708$	1.29066e12			0.193047
$709$	−3.26486e12	−	5.65491e12i	−0.485240	−	0.840461i	0.514616	−	0.857421i	$-0.327935\pi$
$709$	−3.26486e12	−	5.65491e12i	−0.485240	−	0.840461i	−0.999856	+	0.0169599i	$0.994601\pi$
$710$	−5.68587e11	+	9.84821e11i	−0.0839719	+	0.145444i
$711$	5.66395e11	−	9.81025e11i	0.0831201	−	0.143968i
$712$	3.81961e11	+	6.61577e11i	0.0557005	+	0.0964762i
$713$	7.64557e12			1.10792
$714$		0			0
$715$	−1.49146e13			−2.13419
$716$	2.14199e12	+	3.71004e12i	0.304585	+	0.527557i
$717$	−5.31555e12	+	9.20680e12i	−0.751124	+	1.30098i
$718$	2.29790e12	−	3.98008e12i	0.322680	−	0.558897i
$719$	−5.24753e12	−	9.08899e12i	−0.732276	−	1.26834i	−0.955908	−	0.293666i	$-0.905125\pi$
$719$	−5.24753e12	−	9.08899e12i	−0.732276	−	1.26834i	0.223632	−	0.974674i	$-0.428209\pi$
$720$	−1.59941e12			−0.221801
$721$		0			0
$722$	−4.54815e12			−0.622899
$723$	−3.71842e12	−	6.44049e12i	−0.506099	−	0.876590i
$724$	−4.27321e11	+	7.40141e11i	−0.0578003	+	0.100113i
$725$	3.76271e11	−	6.51720e11i	0.0505801	−	0.0876073i
$726$	3.74481e12	+	6.48620e12i	0.500282	+	0.866513i
$727$	−3.77271e12			−0.500898			−0.250449	−	0.968130i	$-0.580578\pi$
$727$	−3.77271e12			−0.500898			−0.250449	+	0.968130i	$0.580578\pi$
$728$		0			0
$729$	4.59195e11			0.0602176
$730$	−5.47631e12	−	9.48525e12i	−0.713732	−	1.23622i
$731$	−1.13023e11	+	1.95761e11i	−0.0146399	+	0.0253570i
$732$	1.37386e12	−	2.37960e12i	0.176865	−	0.306340i
$733$	−6.93047e12	−	1.20039e13i	−0.886737	−	1.53587i	−0.843710	−	0.536799i	$-0.819633\pi$
$733$	−6.93047e12	−	1.20039e13i	−0.886737	−	1.53587i	−0.0430263	−	0.999074i	$-0.513700\pi$
$734$	−8.14250e12			−1.03544
$735$		0			0
$736$	−1.85896e12			−0.233517
$737$	7.13405e12	+	1.23565e13i	0.890702	+	1.54274i
$738$	−5.33422e11	+	9.23915e11i	−0.0661939	+	0.114651i
$739$	7.34297e11	−	1.27184e12i	0.0905673	−	0.156867i	−0.817183	−	0.576379i	$-0.804465\pi$
$739$	7.34297e11	−	1.27184e12i	0.0905673	−	0.156867i	0.907750	+	0.419512i	$0.137799\pi$
$740$	1.86173e12	+	3.22462e12i	0.228231	+	0.395308i
$741$	−1.20840e13			−1.47241
$742$		0			0
$743$	−4.86883e12			−0.586104			−0.293052	−	0.956096i	$-0.594671\pi$
$743$	−4.86883e12			−0.586104			−0.293052	+	0.956096i	$0.594671\pi$
$744$	1.53203e12	+	2.65355e12i	0.183311	+	0.317503i
$745$	−2.97211e12	+	5.14784e12i	−0.353477	+	0.612240i
$746$	8.27616e11	−	1.43347e12i	0.0978372	−	0.169459i
$747$	1.12716e12	+	1.95230e12i	0.132447	+	0.229406i
$748$	5.87891e11			0.0686657
$749$		0			0
$750$	1.03852e13			1.19850
$751$	5.71359e12	+	9.89624e12i	0.655435	+	1.13525i	0.981785	+	0.189998i	$0.0608481\pi$
$751$	5.71359e12	+	9.89624e12i	0.655435	+	1.13525i	−0.326349	+	0.945249i	$0.605819\pi$
$752$	−1.14965e12	+	1.99124e12i	−0.131094	+	0.227062i
$753$	−2.34968e12	+	4.06976e12i	−0.266336	+	0.461308i
$754$	1.51711e11	+	2.62772e11i	0.0170941	+	0.0296079i
$755$	−7.29129e12			−0.816663
$756$		0			0
$757$	4.87971e12			0.540085			0.270043	−	0.962848i	$-0.412962\pi$
$757$	4.87971e12			0.540085			0.270043	+	0.962848i	$0.412962\pi$
$758$	8.87152e11	+	1.53659e12i	0.0976083	+	0.169063i
$759$	1.09336e13	−	1.89376e13i	1.19585	−	2.07127i
$760$	−3.74240e12	+	6.48202e12i	−0.406901	+	0.704773i
$761$	5.62833e12	+	9.74856e12i	0.608343	+	1.05368i	0.991514	+	0.130004i	$0.0414989\pi$
$761$	5.62833e12	+	9.74856e12i	0.608343	+	1.05368i	−0.383170	+	0.923678i	$0.625168\pi$
$762$	6.95922e12			0.747761
$763$		0			0
$764$	−3.01584e12			−0.320249
$765$	−3.94074e11	−	6.82557e11i	−0.0416008	−	0.0720547i
$766$	−2.07955e12	+	3.60189e12i	−0.218243	+	0.378008i
$767$	1.29953e12	−	2.25084e12i	0.135583	−	0.234837i
$768$	−3.72499e11	−	6.45188e11i	−0.0386367	−	0.0669207i
$769$	1.61412e13			1.66444			0.832220	−	0.554446i	$-0.187070\pi$
$769$	1.61412e13			1.66444			0.832220	+	0.554446i	$0.187070\pi$
$770$		0			0
$771$	1.44793e13			1.47572
$772$	4.11997e12	+	7.13600e12i	0.417462	+	0.723065i
$773$	7.01910e12	−	1.21574e13i	0.707089	−	1.22471i	−0.258844	−	0.965919i	$-0.583342\pi$
$773$	7.01910e12	−	1.21574e13i	0.707089	−	1.22471i	0.965932	−	0.258794i	$-0.0833252\pi$
$774$	−5.82630e11	+	1.00914e12i	−0.0583524	+	0.101069i
$775$	−7.65159e12	−	1.32529e13i	−0.761893	−	1.31964i
$776$	−3.90682e12			−0.386764
$777$		0			0
$778$	−9.32090e12			−0.912115
$779$	2.49627e12	+	4.32366e12i	0.242869	+	0.420662i
$780$	−4.65681e12	+	8.06583e12i	−0.450467	+	0.780231i
$781$	1.07736e12	−	1.86604e12i	0.103617	−	0.179470i
$782$	−4.58024e11	−	7.93321e11i	−0.0437983	−	0.0758610i
$783$	3.41308e11			0.0324503
$784$		0			0
$785$	−2.73017e13			−2.56612
$786$	4.23442e12	+	7.33423e12i	0.395724	+	0.685414i
$787$	6.72141e11	−	1.16418e12i	0.0624560	−	0.108177i	−0.833107	−	0.553112i	$-0.813440\pi$
$787$	6.72141e11	−	1.16418e12i	0.0624560	−	0.108177i	0.895563	+	0.444935i	$0.146773\pi$
$788$	3.08575e12	−	5.34468e12i	0.285097	−	0.493803i
$789$	−4.36531e12	−	7.56094e12i	−0.401022	−	0.694591i
$790$	−4.08581e12			−0.373213
$791$		0			0
$792$	3.03057e12			0.273691
$793$	−2.76660e12	−	4.79188e12i	−0.248437	−	0.430306i
$794$	1.49658e12	−	2.59216e12i	0.133631	−	0.231456i
$795$	−8.68434e12	+	1.50417e13i	−0.771054	+	1.33551i
$796$	1.46634e12	+	2.53977e12i	0.129457	+	0.224226i
$797$	9.34992e12			0.820815			0.410408	−	0.911902i	$-0.365386\pi$
$797$	9.34992e12			0.820815			0.410408	+	0.911902i	$0.365386\pi$
$798$		0			0
$799$	−1.13303e12			−0.0983517
$800$	1.86042e12	+	3.22234e12i	0.160585	+	0.278142i
$801$	−9.70275e11	+	1.68057e12i	−0.0832815	+	0.144248i
$802$	−7.06193e12	+	1.22316e13i	−0.602752	+	1.04400i
$803$	1.03765e13	+	1.79727e13i	0.880709	+	1.52543i
$804$	8.90990e12			0.752005
$805$		0			0
$806$	6.17019e12			0.514981
$807$	2.85935e12	+	4.95253e12i	0.237321	+	0.411052i
$808$	3.98846e12	−	6.90821e12i	0.329195	−	0.570183i
$809$	2.73458e12	−	4.73643e12i	0.224451	−	0.388761i	−0.731703	−	0.681623i	$-0.761274\pi$
$809$	2.73458e12	−	4.73643e12i	0.224451	−	0.388761i	0.956155	+	0.292862i	$0.0946077\pi$
$810$	9.08118e12	+	1.57291e13i	0.741241	+	1.28387i
$811$	−6.82318e12			−0.553851			−0.276925	−	0.960891i	$-0.589315\pi$
$811$	−6.82318e12			−0.553851			−0.276925	+	0.960891i	$0.589315\pi$
$812$		0			0
$813$	−4.11695e12			−0.330498
$814$	−3.52762e12	−	6.11002e12i	−0.281626	−	0.487790i
$815$	−1.45103e13	+	2.51326e13i	−1.15204	+	1.99539i
$816$	1.83558e11	−	3.17932e11i	0.0144933	−	0.0251032i
$817$	2.72655e12	+	4.72252e12i	0.214099	+	0.370830i
$818$	−6.30919e12			−0.492702
$819$		0			0
$820$	3.84796e12			0.297213
$821$	−1.13840e12	−	1.97176e12i	−0.0874479	−	0.151464i	0.818984	−	0.573817i	$-0.194538\pi$
$821$	−1.13840e12	−	1.97176e12i	−0.0874479	−	0.151464i	−0.906432	+	0.422352i	$0.861204\pi$
$822$	1.01376e13	−	1.75588e13i	0.774481	−	1.34144i
$823$	−1.08962e13	+	1.88728e13i	−0.827897	+	1.43396i	0.0717871	+	0.997420i	$0.477130\pi$
$823$	−1.08962e13	+	1.88728e13i	−0.827897	+	1.43396i	−0.899685	+	0.436541i	$0.856204\pi$
$824$	2.83277e12	+	4.90650e12i	0.214062	+	0.370766i
$825$	−4.37689e13			−3.28944
$826$		0			0
$827$	1.32468e13			0.984772			0.492386	−	0.870377i	$-0.336125\pi$
$827$	1.32468e13			0.984772			0.492386	+	0.870377i	$0.336125\pi$
$828$	−2.36110e12	−	4.08955e12i	−0.174574	−	0.302370i
$829$	3.21919e12	−	5.57580e12i	0.236729	−	0.410026i	−0.723045	−	0.690801i	$-0.757258\pi$
$829$	3.21919e12	−	5.57580e12i	0.236729	−	0.410026i	0.959774	+	0.280775i	$0.0905914\pi$
$830$	4.06551e12	−	7.04168e12i	0.297347	−	0.515021i
$831$	7.21155e12	+	1.24908e13i	0.524595	+	0.908624i
$832$	−1.50023e12			−0.108543
$833$		0			0
$834$	7.75120e12			0.554781
$835$	−7.34369e12	−	1.27196e13i	−0.522787	−	0.905494i
$836$	7.09110e12	−	1.22822e13i	0.502095	−	0.869654i
$837$	3.47031e12	−	6.01075e12i	0.244401	−	0.423315i
$838$	1.42368e12	+	2.46589e12i	0.0997274	+	0.172733i
$839$	−2.25634e12			−0.157208			−0.0786041	−	0.996906i	$-0.525046\pi$
$839$	−2.25634e12			−0.157208			−0.0786041	+	0.996906i	$0.525046\pi$
$840$		0			0
$841$	−1.44622e13			−0.996900
$842$	3.15556e12	+	5.46559e12i	0.216358	+	0.374742i
$843$	−1.29106e13	+	2.23619e13i	−0.880489	+	1.52505i
$844$	−2.61049e12	+	4.52150e12i	−0.177085	+	0.306720i
$845$	−3.05909e12	−	5.29850e12i	−0.206413	−	0.357518i
$846$	−5.84076e12			−0.392015
$847$		0			0
$848$	−2.79774e12			−0.185791
$849$	5.14783e12	+	8.91630e12i	0.340047	+	0.588980i
$850$	−9.16768e11	+	1.58789e12i	−0.0602385	+	0.104336i
$851$	−5.49671e12	+	9.52058e12i	−0.359269	+	0.622272i
$852$	−6.72772e11	−	1.16528e12i	−0.0437411	−	0.0757618i
$853$	2.07580e13			1.34250			0.671252	−	0.741229i	$-0.265757\pi$
$853$	2.07580e13			1.34250			0.671252	+	0.741229i	$0.265757\pi$
$854$		0			0
$855$	−1.90132e13			−1.21677
$856$	−3.92871e12	−	6.80472e12i	−0.250102	−	0.433190i
$857$	1.58626e12	−	2.74749e12i	0.100453	−	0.173989i	−0.811419	−	0.584466i	$-0.801304\pi$
$857$	1.58626e12	−	2.74749e12i	0.100453	−	0.173989i	0.911871	+	0.410476i	$0.134638\pi$
$858$	8.82373e12	−	1.52832e13i	0.555853	−	0.962765i
$859$	−1.46559e11	−	2.53848e11i	−0.00918426	−	0.0159076i	0.861397	−	0.507933i	$-0.169590\pi$
$859$	−1.46559e11	−	2.53848e11i	−0.00918426	−	0.0159076i	−0.870581	+	0.492025i	$0.836257\pi$
$860$	4.20293e12			0.262005
$861$		0			0
$862$	−1.29247e13			−0.797326
$863$	−6.09714e12	−	1.05606e13i	−0.374178	−	0.648095i	0.616026	−	0.787726i	$-0.288742\pi$
$863$	−6.09714e12	−	1.05606e13i	−0.374178	−	0.648095i	−0.990204	+	0.139631i	$0.955408\pi$
$864$	−8.43776e11	+	1.46146e12i	−0.0515128	+	0.0892229i
$865$	1.03102e12	−	1.78578e12i	0.0626173	−	0.108456i
$866$	−4.62149e12	−	8.00466e12i	−0.279223	−	0.483629i
$867$	−2.03892e13			−1.22550
$868$		0			0
$869$	7.74181e12			0.460525
$870$	6.90270e11	+	1.19558e12i	0.0408491	+	0.0707527i
$871$	8.97110e12	−	1.55384e13i	0.528158	−	0.914797i
$872$	3.86058e12	−	6.68672e12i	0.226115	−	0.391642i
$873$	−4.96214e12	−	8.59468e12i	−0.289138	−	0.500801i
$874$	−2.20986e13			−1.28104
$875$		0			0
$876$	1.29595e13			0.743568
$877$	9.23674e12	+	1.59985e13i	0.527255	+	0.913233i	0.999495	+	0.0317628i	$0.0101121\pi$
$877$	9.23674e12	+	1.59985e13i	0.527255	+	0.913233i	−0.472240	+	0.881470i	$0.656555\pi$
$878$	1.06263e13	−	1.84053e13i	0.603470	−	1.04524i
$879$	7.89726e12	−	1.36785e13i	0.446197	−	0.772836i
$880$	−5.46541e12	−	9.46637e12i	−0.307221	−	0.532122i
$881$	−2.16016e13			−1.20808			−0.604039	−	0.796955i	$-0.706443\pi$
$881$	−2.16016e13			−1.20808			−0.604039	+	0.796955i	$0.706443\pi$
$882$		0			0
$883$	−1.00085e13			−0.554043			−0.277022	−	0.960864i	$-0.589347\pi$
$883$	−1.00085e13			−0.554043			−0.277022	+	0.960864i	$0.589347\pi$
$884$	−3.69638e11	−	6.40232e11i	−0.0203583	−	0.0352616i
$885$	5.91270e12	−	1.02411e13i	0.323997	−	0.561180i
$886$	3.99573e12	−	6.92081e12i	0.217844	−	0.377316i
$887$	−7.52738e12	−	1.30378e13i	−0.408307	−	0.707209i	0.586393	−	0.810027i	$-0.300548\pi$
$887$	−7.52738e12	−	1.30378e13i	−0.408307	−	0.707209i	−0.994700	+	0.102818i	$0.967214\pi$
$888$	−4.40574e12			−0.237772
$889$		0			0
$890$	6.99929e12			0.373937
$891$	−1.72071e13	−	2.98035e13i	−0.914654	−	1.58423i
$892$	−7.32557e12	+	1.26883e13i	−0.387436	+	0.671058i
$893$	−1.36666e13	+	2.36712e13i	−0.719164	+	1.24563i
$894$	−3.51670e12	−	6.09110e12i	−0.184127	−	0.318917i
$895$	3.92511e13			2.04479
$896$		0			0
$897$	−2.74982e13			−1.41820
$898$	−3.60969e11	−	6.25216e11i	−0.0185236	−	0.0320839i
$899$	4.57298e11	−	7.92064e11i	0.0233497	−	0.0404429i
$900$	−4.72592e12	+	8.18554e12i	−0.240102	+	0.415868i
$901$	−6.89328e11	−	1.19395e12i	−0.0348469	−	0.0603566i
$902$	−7.29112e12			−0.366746
$903$		0			0
$904$	6.79596e12			0.338449
$905$	3.91524e12	+	6.78139e12i	0.194017	+	0.336047i
$906$	4.31366e12	−	7.47147e12i	0.212701	−	0.368408i
$907$	−1.14679e13	+	1.98630e13i	−0.562668	+	0.974569i	0.434595	+	0.900626i	$0.356892\pi$
$907$	−1.14679e13	+	1.98630e13i	−0.562668	+	0.974569i	−0.997262	+	0.0739431i	$0.976442\pi$
$908$	1.95196e12	+	3.38089e12i	0.0952981	+	0.165061i
$909$	2.02633e13			0.984403
$910$		0			0
$911$	4.04241e13			1.94450			0.972248	−	0.233952i	$-0.0751657\pi$
$911$	4.04241e13			1.94450			0.972248	+	0.233952i	$0.0751657\pi$
$912$	−4.42813e12	−	7.66975e12i	−0.211955	−	0.367117i
$913$	−7.70335e12	+	1.33426e13i	−0.366911	+	0.635509i
$914$	5.08176e12	−	8.80187e12i	0.240856	−	0.417174i
$915$	−1.25877e13	−	2.18026e13i	−0.593680	−	1.02828i
$916$	8.90954e12			0.418144
$917$		0			0
$918$	−8.31584e11			−0.0386468
$919$	−2.09498e12	−	3.62862e12i	−0.0968859	−	0.167811i	0.813508	−	0.581553i	$-0.197555\pi$
$919$	−2.09498e12	−	3.62862e12i	−0.0968859	−	0.167811i	−0.910394	+	0.413742i	$0.864222\pi$
$920$	−8.51616e12	+	1.47504e13i	−0.391921	+	0.678827i
$921$	5.73843e12	−	9.93925e12i	0.262800	−	0.455182i
$922$	9.68080e12	+	1.67676e13i	0.441186	+	0.764157i
$923$	−2.70957e12			−0.122883
$924$		0			0
$925$	2.20041e13			0.988250
$926$	7.78469e12	+	1.34835e13i	0.347930	+	0.602633i
$927$	−7.19593e12	+	1.24637e13i	−0.320057	+	0.554356i
$928$	−1.11188e11	+	1.92584e11i	−0.00492145	+	0.00852421i
$929$	2.41805e12	+	4.18818e12i	0.106511	+	0.184482i	0.914355	−	0.404915i	$-0.132699\pi$
$929$	2.41805e12	+	4.18818e12i	0.106511	+	0.184482i	−0.807844	+	0.589397i	$0.799365\pi$
$930$	2.80737e13			1.23063
$931$		0			0
$932$	1.90152e13			0.825524
$933$	7.66961e11	+	1.32841e12i	0.0331364	+	0.0573940i
$934$	−1.34645e13	+	2.33212e13i	−0.578933	+	1.00274i
$935$	2.69322e12	−	4.66479e12i	0.115244	−	0.199609i
$936$	−1.90548e12	−	3.30038e12i	−0.0811451	−	0.140547i
$937$	1.70190e12			0.0721282			0.0360641	−	0.999349i	$-0.488518\pi$
$937$	1.70190e12			0.0721282			0.0360641	+	0.999349i	$0.488518\pi$
$938$		0			0
$939$	−2.74337e12			−0.115157
$940$	1.05334e13	+	1.82444e13i	0.440041	+	0.762173i
$941$	1.41493e12	−	2.45074e12i	0.0588278	−	0.101893i	−0.835112	−	0.550080i	$-0.814597\pi$
$941$	1.41493e12	−	2.45074e12i	0.0588278	−	0.101893i	0.893939	+	0.448188i	$0.147930\pi$
$942$	1.61522e13	−	2.79764e13i	0.668347	−	1.15761i
$943$	5.68049e12	+	9.83889e12i	0.233928	+	0.405176i
$944$	1.90483e12			0.0780697
$945$		0			0
$946$	−7.96372e12			−0.323300
$947$	−1.85318e13	−	3.20981e13i	−0.748761	−	1.29689i	−0.948417	−	0.317026i	$-0.897316\pi$
$947$	−1.85318e13	−	3.20981e13i	−0.748761	−	1.29689i	0.199656	−	0.979866i	$-0.436018\pi$
$948$	2.41724e12	−	4.18678e12i	0.0972035	−	0.168361i
$949$	1.30486e13	−	2.26008e13i	0.522233	−	0.904534i
$950$	2.21160e13	+	3.83060e13i	0.880948	+	1.52585i
$951$	3.73635e13			1.48127
$952$		0			0
$953$	−1.53995e12			−0.0604768			−0.0302384	−	0.999543i	$-0.509627\pi$
$953$	−1.53995e12			−0.0604768			−0.0302384	+	0.999543i	$0.509627\pi$
$954$	−3.55347e12	−	6.15479e12i	−0.138894	−	0.240572i
$955$	−1.38160e13	+	2.39300e13i	−0.537486	+	0.930953i
$956$	−7.84499e12	+	1.35879e13i	−0.303761	+	0.526129i
$957$	−1.30793e12	−	2.26540e12i	−0.0504057	−	0.0873052i
$958$	1.86347e13			0.714789
$959$		0			0
$960$	−6.82590e12			−0.259382
$961$	3.92050e12	+	6.79050e12i	0.148281	+	0.256830i
$962$	−4.43600e12	+	7.68338e12i	−0.166995	+	0.289244i
$963$	9.97987e12	−	1.72856e13i	0.373944	−	0.647690i
$964$	−5.48786e12	−	9.50524e12i	−0.204671	−	0.354500i
$965$	7.54968e13			2.80257
$966$		0			0
$967$	−1.09919e13			−0.404254			−0.202127	−	0.979359i	$-0.564785\pi$
$967$	−1.09919e13			−0.404254			−0.202127	+	0.979359i	$0.564785\pi$
$968$	5.52680e12	+	9.57270e12i	0.202318	+	0.350425i
$969$	2.18207e12	−	3.77946e12i	0.0795083	−	0.137712i
$970$	−1.78977e13	+	3.09998e13i	−0.649120	+	1.12431i
$971$	−6.62794e11	−	1.14799e12i	−0.0239272	−	0.0414432i	0.853814	−	0.520578i	$-0.174284\pi$
$971$	−6.62794e11	−	1.14799e12i	−0.0239272	−	0.0414432i	−0.877741	+	0.479135i	$0.840950\pi$
$972$	−1.33809e13			−0.480827
$973$		0			0
$974$	−3.58646e13			−1.27688
$975$	2.75198e13	+	4.76657e13i	0.975269	+	1.68922i
$976$	2.02762e12	−	3.51195e12i	0.0715258	−	0.123886i
$977$	1.36658e12	−	2.36699e12i	0.0479856	−	0.0831135i	−0.841035	−	0.540981i	$-0.818053\pi$
$977$	1.36658e12	−	2.36699e12i	0.0479856	−	0.0831135i	0.889021	+	0.457867i	$0.151387\pi$
$978$	−1.71691e13	−	2.97378e13i	−0.600099	−	1.03940i
$979$	−1.32623e13			−0.461419
$980$		0			0
$981$	1.96136e13			0.676157
$982$	1.32407e12	+	2.29335e12i	0.0454368	+	0.0786988i
$983$	3.24327e11	−	5.61751e11i	0.0110788	−	0.0191890i	−0.860433	−	0.509564i	$-0.829807\pi$
$983$	3.24327e11	−	5.61751e11i	0.0110788	−	0.0191890i	0.871512	+	0.490375i	$0.163140\pi$
$984$	−2.27652e12	+	3.94305e12i	−0.0774094	+	0.134077i
$985$	−2.82726e13	−	4.89696e13i	−0.956980	−	1.65754i
$986$	−1.09582e11			−0.00369226
$987$		0			0
$988$	−1.78342e13			−0.595453
$989$	6.20451e12	+	1.07465e13i	0.206217	+	0.357178i
$990$	1.38835e13	−	2.40469e13i	0.459346	−	0.795610i
$991$	1.97923e13	−	3.42812e13i	0.651874	−	1.12908i	−0.330793	−	0.943703i	$-0.607316\pi$
$991$	1.97923e13	−	3.42812e13i	0.651874	−	1.12908i	0.982668	−	0.185376i	$-0.0593504\pi$
$992$	2.26105e12	+	3.91626e12i	0.0741324	+	0.128401i
$993$	−6.99268e12			−0.228230
$994$		0			0
$995$	2.68700e13			0.869090
$996$	4.81046e12	+	8.33196e12i	0.154889	+	0.268275i
$997$	1.05624e13	−	1.82947e13i	0.338560	−	0.586404i	−0.645602	−	0.763674i	$-0.723393\pi$
$997$	1.05624e13	−	1.82947e13i	0.338560	−	0.586404i	0.984162	+	0.177270i	$0.0567267\pi$
$998$	−9.70836e12	+	1.68154e13i	−0.309784	+	0.536561i
$999$	4.98989e12	+	8.64274e12i	0.158506	+	0.274541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.c.l.67.1		6
7.2	even	3	inner	98.10.c.l.79.1		6
7.3	odd	6		98.10.a.g.1.1		3
7.4	even	3		98.10.a.h.1.3		3
7.5	odd	6		14.10.c.b.9.3	✓	6
7.6	odd	2		14.10.c.b.11.3	yes	6
21.5	even	6		126.10.g.e.37.3		6
21.20	even	2		126.10.g.e.109.3		6
28.19	even	6		112.10.i.a.65.1		6
28.27	even	2		112.10.i.a.81.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.c.b.9.3	✓	6	7.5	odd	6
14.10.c.b.11.3	yes	6	7.6	odd	2
98.10.a.g.1.1		3	7.3	odd	6
98.10.a.h.1.3		3	7.4	even	3
98.10.c.l.67.1		6	1.1	even	1	trivial
98.10.c.l.79.1		6	7.2	even	3	inner
112.10.i.a.65.1		6	28.19	even	6
112.10.i.a.81.1		6	28.27	even	2
126.10.g.e.37.3		6	21.5	even	6
126.10.g.e.109.3		6	21.20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(8.00000 + 13.8564i) q^{2} +(-86.7292 + 150.219i) q^{3} +(-128.000 + 221.703i) q^{4} +(1172.77 + 2031.30i) q^{5} -2775.34 q^{6} -4096.00 q^{8} +(-5202.42 - 9010.85i) q^{9} +(-18764.4 + 32500.9i) q^{10} +(35554.8 - 61582.8i) q^{11} +(-22202.7 - 38456.2i) q^{12} -89420.8 q^{13} -406855. q^{15} +(-32768.0 - 56755.8i) q^{16} +(16147.2 - 27967.9i) q^{17} +(83238.7 - 144174. i) q^{18} +(-389534. - 674693. i) q^{19} -600460. q^{20} +1.13775e6 q^{22} +(-886420. - 1.53532e6i) q^{23} +(355243. - 615299. i) q^{24} +(-1.77424e6 + 3.07307e6i) q^{25} +(-715366. - 1.23905e6i) q^{26} -1.60938e6 q^{27} -212075. q^{29} +(-3.25484e6 - 5.63755e6i) q^{30} +(-2.15631e6 + 3.73483e6i) q^{31} +(524288. - 908093. i) q^{32} +(6.16728e6 + 1.06821e7i) q^{33} +516712. q^{34} +2.66364e6 q^{36} +(-3.10051e6 - 5.37024e6i) q^{37} +(6.23254e6 - 1.07951e7i) q^{38} +(7.75540e6 - 1.34327e7i) q^{39} +(-4.80368e6 - 8.32022e6i) q^{40} -6.40835e6 q^{41} -6.99951e6 q^{43} +(9.10203e6 + 1.57652e7i) q^{44} +(1.22025e7 - 2.11354e7i) q^{45} +(1.41827e7 - 2.45652e7i) q^{46} +(-1.75422e7 - 3.03840e7i) q^{47} +1.13678e7 q^{48} -5.67755e7 q^{50} +(2.80088e6 + 4.85126e6i) q^{51} +(1.14459e7 - 1.98248e7i) q^{52} +(2.13451e7 - 3.69707e7i) q^{53} +(-1.28750e7 - 2.23002e7i) q^{54} +1.66791e8 q^{55} +1.35136e8 q^{57} +(-1.69660e6 - 2.93860e6i) q^{58} +(-1.45327e7 + 2.51714e7i) q^{59} +(5.20775e7 - 9.02008e7i) q^{60} +(3.09391e7 + 5.35880e7i) q^{61} -6.90018e7 q^{62} +1.67772e7 q^{64} +(-1.04870e8 - 1.81641e8i) q^{65} +(-9.86766e7 + 1.70913e8i) q^{66} +(-1.00325e8 + 1.73767e8i) q^{67} +(4.13370e6 + 7.15977e6i) q^{68} +3.07514e8 q^{69} +3.03014e7 q^{71} +(2.13091e7 + 3.69085e7i) q^{72} +(-1.45923e8 + 2.52746e8i) q^{73} +(4.96082e7 - 8.59239e7i) q^{74} +(-3.07756e8 - 5.33049e8i) q^{75} +1.99441e8 q^{76} +2.48173e8 q^{78} +(5.44357e7 + 9.42854e7i) q^{79} +(7.68589e7 - 1.33124e8i) q^{80} +(2.41979e8 - 4.19120e8i) q^{81} +(-5.12668e7 - 8.87966e7i) q^{82} -2.16661e8 q^{83} +7.57483e7 q^{85} +(-5.59961e7 - 9.69880e7i) q^{86} +(1.83931e7 - 3.18578e7i) q^{87} +(-1.45633e8 + 2.52243e8i) q^{88} +(-9.32523e7 - 1.61518e8i) q^{89} +3.90481e8 q^{90} +4.53847e8 q^{92} +(-3.74030e8 - 6.47838e8i) q^{93} +(2.80675e8 - 4.86144e8i) q^{94} +(9.13671e8 - 1.58252e9i) q^{95} +(9.09422e7 + 1.57516e8i) q^{96} +9.53814e8 q^{97} -7.39884e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 48 q^{2} - 71 q^{3} - 768 q^{4} + 1085 q^{5} - 2272 q^{6} - 24576 q^{8} - 9106 q^{9} - 17360 q^{10} + 2555 q^{11} - 18176 q^{12} - 36140 q^{13} - 706146 q^{15} - 196608 q^{16} - 20759 q^{17} + 145696 q^{18}+ \cdots - 2607425268 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 - 71 * q^3 - 768 * q^4 + 1085 * q^5 - 2272 * q^6 - 24576 * q^8 - 9106 * q^9 - 17360 * q^10 + 2555 * q^11 - 18176 * q^12 - 36140 * q^13 - 706146 * q^15 - 196608 * q^16 - 20759 * q^17 + 145696 * q^18 - 1220649 * q^19 - 555520 * q^20 + 81760 * q^22 - 1960903 * q^23 + 290816 * q^24 - 863572 * q^25 - 289120 * q^26 - 5777318 * q^27 - 5212292 * q^29 - 5649168 * q^30 + 9377989 * q^31 + 3145728 * q^32 + 10778103 * q^33 - 664288 * q^34 + 4662272 * q^36 - 25814913 * q^37 + 19530384 * q^38 + 37990822 * q^39 - 4444160 * q^40 - 418500 * q^41 + 5888616 * q^43 + 654080 * q^44 + 37350558 * q^45 + 31374448 * q^46 - 48391269 * q^47 + 9306112 * q^48 - 27634304 * q^50 - 75441987 * q^51 + 4625920 * q^52 + 102186411 * q^53 - 46218544 * q^54 + 456557402 * q^55 + 86169178 * q^57 - 41698336 * q^58 - 144220135 * q^59 + 90386688 * q^60 - 280936871 * q^61 + 300095648 * q^62 + 100663296 * q^64 - 186819738 * q^65 - 172449648 * q^66 + 170710399 * q^67 - 5314304 * q^68 + 1807308342 * q^69 + 939517376 * q^71 + 37298176 * q^72 - 613838539 * q^73 + 413038608 * q^74 - 902254676 * q^75 + 624972288 * q^76 + 1215706304 * q^78 + 197445809 * q^79 + 71106560 * q^80 + 887872901 * q^81 - 3348000 * q^82 + 2148362872 * q^83 + 822545038 * q^85 + 47108928 * q^86 - 753428670 * q^87 - 10465280 * q^88 - 805730427 * q^89 + 1195217856 * q^90 + 1003982336 * q^92 - 1721516327 * q^93 + 774260304 * q^94 + 1799421743 * q^95 + 74448896 * q^96 + 4525836188 * q^97 - 2607425268 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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