LMFDB - Embedded newform 98.6.c.a.79.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,6,Mod(67,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("98.67"); S:= CuspForms(chi, 6); N := Newforms(S);

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

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,-4,-8,-16,-10,64,0,128,179] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$15.7176143417$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	98.79
Dual form			98.6.c.a.67.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 + 3.46410i) q^{2} +(-4.00000 - 6.92820i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-5.00000 + 8.66025i) q^{5} +32.0000 q^{6} +64.0000 q^{8} +(89.5000 - 155.019i) q^{9} +(-20.0000 - 34.6410i) q^{10} +(170.000 + 294.449i) q^{11} +(-64.0000 + 110.851i) q^{12} -294.000 q^{13} +80.0000 q^{15} +(-128.000 + 221.703i) q^{16} +(-613.000 - 1061.75i) q^{17} +(358.000 + 620.074i) q^{18} +(-1216.00 + 2106.17i) q^{19} +160.000 q^{20} -1360.00 q^{22} +(-1000.00 + 1732.05i) q^{23} +(-256.000 - 443.405i) q^{24} +(1512.50 + 2619.73i) q^{25} +(588.000 - 1018.45i) q^{26} -3376.00 q^{27} -6746.00 q^{29} +(-160.000 + 277.128i) q^{30} +(-4428.00 - 7669.52i) q^{31} +(-512.000 - 886.810i) q^{32} +(1360.00 - 2355.59i) q^{33} +4904.00 q^{34} -2864.00 q^{36} +(-4591.00 + 7951.85i) q^{37} +(-4864.00 - 8424.70i) q^{38} +(1176.00 + 2036.89i) q^{39} +(-320.000 + 554.256i) q^{40} -14574.0 q^{41} +8108.00 q^{43} +(2720.00 - 4711.18i) q^{44} +(895.000 + 1550.19i) q^{45} +(-4000.00 - 6928.20i) q^{46} +(156.000 - 270.200i) q^{47} +2048.00 q^{48} -12100.0 q^{50} +(-4904.00 + 8493.98i) q^{51} +(2352.00 + 4073.78i) q^{52} +(7317.00 + 12673.4i) q^{53} +(6752.00 - 11694.8i) q^{54} -3400.00 q^{55} +19456.0 q^{57} +(13492.0 - 23368.8i) q^{58} +(13828.0 + 23950.8i) q^{59} +(-640.000 - 1108.51i) q^{60} +(-17169.0 + 29737.6i) q^{61} +35424.0 q^{62} +4096.00 q^{64} +(1470.00 - 2546.11i) q^{65} +(5440.00 + 9422.36i) q^{66} +(-6158.00 - 10666.0i) q^{67} +(-9808.00 + 16988.0i) q^{68} +16000.0 q^{69} +36920.0 q^{71} +(5728.00 - 9921.19i) q^{72} +(30859.0 + 53449.4i) q^{73} +(-18364.0 - 31807.4i) q^{74} +(12100.0 - 20957.8i) q^{75} +38912.0 q^{76} -9408.00 q^{78} +(32376.0 - 56076.9i) q^{79} +(-1280.00 - 2217.03i) q^{80} +(-8244.50 - 14279.9i) q^{81} +(29148.0 - 50485.8i) q^{82} -77056.0 q^{83} +12260.0 q^{85} +(-16216.0 + 28086.9i) q^{86} +(26984.0 + 46737.7i) q^{87} +(10880.0 + 18844.7i) q^{88} +(4083.00 - 7071.96i) q^{89} -7160.00 q^{90} +32000.0 q^{92} +(-35424.0 + 61356.2i) q^{93} +(624.000 + 1080.80i) q^{94} +(-12160.0 - 21061.7i) q^{95} +(-4096.00 + 7094.48i) q^{96} +20650.0 q^{97} +60860.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} - 8 q^{3} - 16 q^{4} - 10 q^{5} + 64 q^{6} + 128 q^{8} + 179 q^{9} - 40 q^{10} + 340 q^{11} - 128 q^{12} - 588 q^{13} + 160 q^{15} - 256 q^{16} - 1226 q^{17} + 716 q^{18} - 2432 q^{19} + 320 q^{20}+ \cdots + 121720 q^{99}+O(q^{100}) $ 2 * q - 4 * q^2 - 8 * q^3 - 16 * q^4 - 10 * q^5 + 64 * q^6 + 128 * q^8 + 179 * q^9 - 40 * q^10 + 340 * q^11 - 128 * q^12 - 588 * q^13 + 160 * q^15 - 256 * q^16 - 1226 * q^17 + 716 * q^18 - 2432 * q^19 + 320 * q^20 - 2720 * q^22 - 2000 * q^23 - 512 * q^24 + 3025 * q^25 + 1176 * q^26 - 6752 * q^27 - 13492 * q^29 - 320 * q^30 - 8856 * q^31 - 1024 * q^32 + 2720 * q^33 + 9808 * q^34 - 5728 * q^36 - 9182 * q^37 - 9728 * q^38 + 2352 * q^39 - 640 * q^40 - 29148 * q^41 + 16216 * q^43 + 5440 * q^44 + 1790 * q^45 - 8000 * q^46 + 312 * q^47 + 4096 * q^48 - 24200 * q^50 - 9808 * q^51 + 4704 * q^52 + 14634 * q^53 + 13504 * q^54 - 6800 * q^55 + 38912 * q^57 + 26984 * q^58 + 27656 * q^59 - 1280 * q^60 - 34338 * q^61 + 70848 * q^62 + 8192 * q^64 + 2940 * q^65 + 10880 * q^66 - 12316 * q^67 - 19616 * q^68 + 32000 * q^69 + 73840 * q^71 + 11456 * q^72 + 61718 * q^73 - 36728 * q^74 + 24200 * q^75 + 77824 * q^76 - 18816 * q^78 + 64752 * q^79 - 2560 * q^80 - 16489 * q^81 + 58296 * q^82 - 154112 * q^83 + 24520 * q^85 - 32432 * q^86 + 53968 * q^87 + 21760 * q^88 + 8166 * q^89 - 14320 * q^90 + 64000 * q^92 - 70848 * q^93 + 1248 * q^94 - 24320 * q^95 - 8192 * q^96 + 41300 * q^97 + 121720 * q^99

Character values

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

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

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 $

$2$	−2.00000	+	3.46410i	−0.353553	+	0.612372i
$2$	−2.00000	+	3.46410i	−0.353553	+	0.612372i
$3$	−4.00000	−	6.92820i	−0.256600	−	0.444444i	0.708729	−	0.705481i	$-0.249269\pi$
$3$	−4.00000	−	6.92820i	−0.256600	−	0.444444i	−0.965329	+	0.261037i	$0.915936\pi$
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	−5.00000	+	8.66025i	−0.0894427	+	0.154919i	−0.907276	−	0.420536i	$-0.861842\pi$
$5$	−5.00000	+	8.66025i	−0.0894427	+	0.154919i	0.817833	+	0.575456i	$0.195175\pi$
$6$	32.0000			0.362887
$7$		0			0
$7$		0			0
$8$	64.0000			0.353553
$9$	89.5000	−	155.019i	0.368313	−	0.637936i
$10$	−20.0000	−	34.6410i	−0.0632456	−	0.109545i
$11$	170.000	+	294.449i	0.423611	+	0.733716i	0.996290	−	0.0860642i	$-0.0274290\pi$
$11$	170.000	+	294.449i	0.423611	+	0.733716i	−0.572679	+	0.819780i	$0.694096\pi$
$12$	−64.0000	+	110.851i	−0.128300	+	0.222222i
$13$	−294.000			−0.482491			−0.241245	−	0.970464i	$-0.577556\pi$
$13$	−294.000			−0.482491			−0.241245	+	0.970464i	$0.577556\pi$
$14$		0			0
$15$	80.0000			0.0918040
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	−613.000	−	1061.75i	−0.514444	−	0.891043i	−0.999860	−	0.0167597i	$-0.994665\pi$
$17$	−613.000	−	1061.75i	−0.514444	−	0.891043i	0.485415	−	0.874284i	$-0.338668\pi$
$18$	358.000	+	620.074i	0.260436	+	0.451089i
$19$	−1216.00	+	2106.17i	−0.772769	+	1.33847i	0.163271	+	0.986581i	$0.447795\pi$
$19$	−1216.00	+	2106.17i	−0.772769	+	1.33847i	−0.936040	+	0.351894i	$0.885538\pi$
$20$	160.000			0.0894427
$21$		0			0
$22$	−1360.00			−0.599076
$23$	−1000.00	+	1732.05i	−0.394167	+	0.682718i	−0.992994	−	0.118161i	$-0.962300\pi$
$23$	−1000.00	+	1732.05i	−0.394167	+	0.682718i	0.598827	+	0.800878i	$0.295634\pi$
$24$	−256.000	−	443.405i	−0.0907218	−	0.157135i
$25$	1512.50	+	2619.73i	0.484000	+	0.838313i
$26$	588.000	−	1018.45i	0.170586	−	0.295464i
$27$	−3376.00			−0.891237
$28$		0			0
$29$	−6746.00			−1.48954			−0.744769	−	0.667323i	$-0.767440\pi$
$29$	−6746.00			−1.48954			−0.744769	+	0.667323i	$0.767440\pi$
$30$	−160.000	+	277.128i	−0.0324576	+	0.0562183i
$31$	−4428.00	−	7669.52i	−0.827567	−	1.43339i	−0.899941	−	0.436011i	$-0.856391\pi$
$31$	−4428.00	−	7669.52i	−0.827567	−	1.43339i	0.0723738	−	0.997378i	$-0.476943\pi$
$32$	−512.000	−	886.810i	−0.0883883	−	0.153093i
$33$	1360.00	−	2355.59i	0.217397	−	0.376543i
$34$	4904.00			0.727534
$35$		0			0
$36$	−2864.00			−0.368313
$37$	−4591.00	+	7951.85i	−0.551319	+	0.954913i	0.446861	+	0.894604i	$0.352542\pi$
$37$	−4591.00	+	7951.85i	−0.551319	+	0.954913i	−0.998180	+	0.0603090i	$0.980791\pi$
$38$	−4864.00	−	8424.70i	−0.546430	−	0.946445i
$39$	1176.00	+	2036.89i	0.123807	+	0.214440i
$40$	−320.000	+	554.256i	−0.0316228	+	0.0547723i
$41$	−14574.0			−1.35400			−0.677001	−	0.735982i	$-0.736721\pi$
$41$	−14574.0			−1.35400			−0.677001	+	0.735982i	$0.736721\pi$
$42$		0			0
$43$	8108.00			0.668717			0.334359	−	0.942446i	$-0.391480\pi$
$43$	8108.00			0.668717			0.334359	+	0.942446i	$0.391480\pi$
$44$	2720.00	−	4711.18i	0.211805	−	0.366858i
$45$	895.000	+	1550.19i	0.0658858	+	0.114118i
$46$	−4000.00	−	6928.20i	−0.278718	−	0.482754i
$47$	156.000	−	270.200i	0.0103010	−	0.0178419i	−0.860829	−	0.508894i	$-0.830054\pi$
$47$	156.000	−	270.200i	0.0103010	−	0.0178419i	0.871130	+	0.491053i	$0.163388\pi$
$48$	2048.00			0.128300
$49$		0			0
$50$	−12100.0			−0.684479
$51$	−4904.00	+	8493.98i	−0.264013	+	0.457284i
$52$	2352.00	+	4073.78i	0.120623	+	0.208925i
$53$	7317.00	+	12673.4i	0.357803	+	0.619732i	0.987593	−	0.157033i	$-0.0501928\pi$
$53$	7317.00	+	12673.4i	0.357803	+	0.619732i	−0.629791	+	0.776765i	$0.716859\pi$
$54$	6752.00	−	11694.8i	0.315100	−	0.545769i
$55$	−3400.00			−0.151556
$56$		0			0
$57$	19456.0			0.793170
$58$	13492.0	−	23368.8i	0.526631	−	0.912151i
$59$	13828.0	+	23950.8i	0.517165	+	0.895757i	0.999801	+	0.0199355i	$0.00634608\pi$
$59$	13828.0	+	23950.8i	0.517165	+	0.895757i	−0.482636	+	0.875821i	$0.660321\pi$
$60$	−640.000	−	1108.51i	−0.0229510	−	0.0397523i
$61$	−17169.0	+	29737.6i	−0.590773	+	1.02325i	0.403356	+	0.915043i	$0.367844\pi$
$61$	−17169.0	+	29737.6i	−0.590773	+	1.02325i	−0.994129	+	0.108205i	$0.965490\pi$
$62$	35424.0			1.17036
$63$		0			0
$64$	4096.00			0.125000
$65$	1470.00	−	2546.11i	0.0431553	−	0.0747471i
$66$	5440.00	+	9422.36i	0.153723	+	0.266256i
$67$	−6158.00	−	10666.0i	−0.167592	−	0.290277i	0.769981	−	0.638067i	$-0.220266\pi$
$67$	−6158.00	−	10666.0i	−0.167592	−	0.290277i	−0.937573	+	0.347790i	$0.886932\pi$
$68$	−9808.00	+	16988.0i	−0.257222	+	0.445522i
$69$	16000.0			0.404573
$70$		0			0
$71$	36920.0			0.869192			0.434596	−	0.900625i	$-0.356891\pi$
$71$	36920.0			0.869192			0.434596	+	0.900625i	$0.356891\pi$
$72$	5728.00	−	9921.19i	0.130218	−	0.225545i
$73$	30859.0	+	53449.4i	0.677758	+	1.17391i	0.975655	+	0.219313i	$0.0703817\pi$
$73$	30859.0	+	53449.4i	0.677758	+	1.17391i	−0.297896	+	0.954598i	$0.596285\pi$
$74$	−18364.0	−	31807.4i	−0.389841	−	0.675225i
$75$	12100.0	−	20957.8i	0.248389	−	0.430222i
$76$	38912.0			0.772769
$77$		0			0
$78$	−9408.00			−0.175090
$79$	32376.0	−	56076.9i	0.583654	−	1.01092i	−0.411388	−	0.911460i	$-0.634956\pi$
$79$	32376.0	−	56076.9i	0.583654	−	1.01092i	0.995042	−	0.0994580i	$-0.0317109\pi$
$80$	−1280.00	−	2217.03i	−0.0223607	−	0.0387298i
$81$	−8244.50	−	14279.9i	−0.139621	−	0.241831i
$82$	29148.0	−	50485.8i	0.478712	−	0.829153i
$83$	−77056.0			−1.22775			−0.613877	−	0.789402i	$-0.710391\pi$
$83$	−77056.0			−1.22775			−0.613877	+	0.789402i	$0.710391\pi$
$84$		0			0
$85$	12260.0			0.184053
$86$	−16216.0	+	28086.9i	−0.236427	+	0.409504i
$87$	26984.0	+	46737.7i	0.382215	+	0.662017i
$88$	10880.0	+	18844.7i	0.149769	+	0.259408i
$89$	4083.00	−	7071.96i	0.0546392	−	0.0946379i	−0.837412	−	0.546572i	$-0.815932\pi$
$89$	4083.00	−	7071.96i	0.0546392	−	0.0946379i	0.892051	+	0.451934i	$0.149266\pi$
$90$	−7160.00			−0.0931766
$91$		0			0
$92$	32000.0			0.394167
$93$	−35424.0	+	61356.2i	−0.424708	+	0.735615i
$94$	624.000	+	1080.80i	0.00728392	+	0.0126161i
$95$	−12160.0	−	21061.7i	−0.138237	−	0.239434i
$96$	−4096.00	+	7094.48i	−0.0453609	+	0.0785674i
$97$	20650.0			0.222839			0.111419	−	0.993773i	$-0.464460\pi$
$97$	20650.0			0.222839			0.111419	+	0.993773i	$0.464460\pi$
$98$		0			0
$99$	60860.0			0.624085
$100$	24200.0	−	41915.6i	0.242000	−	0.419156i
$101$	−93125.0	−	161297.i	−0.908370	−	1.57334i	−0.816328	−	0.577588i	$-0.803994\pi$
$101$	−93125.0	−	161297.i	−0.908370	−	1.57334i	−0.0920418	−	0.995755i	$-0.529339\pi$
$102$	−19616.0	−	33975.9i	−0.186685	−	0.323348i
$103$	30032.0	−	52016.9i	0.278927	−	0.483116i	−0.692191	−	0.721714i	$-0.743354\pi$
$103$	30032.0	−	52016.9i	0.278927	−	0.483116i	0.971118	+	0.238598i	$0.0766878\pi$
$104$	−18816.0			−0.170586
$105$		0			0
$106$	−58536.0			−0.506009
$107$	−23946.0	+	41475.7i	−0.202196	+	0.350215i	−0.949236	−	0.314565i	$-0.898141\pi$
$107$	−23946.0	+	41475.7i	−0.202196	+	0.350215i	0.747039	+	0.664780i	$0.231475\pi$
$108$	27008.0	+	46779.2i	0.222809	+	0.385917i
$109$	−11051.0	−	19140.9i	−0.0890913	−	0.154311i	0.818036	−	0.575167i	$-0.195063\pi$
$109$	−11051.0	−	19140.9i	−0.0890913	−	0.154311i	−0.907127	+	0.420856i	$0.861730\pi$
$110$	6800.00	−	11777.9i	0.0535830	−	0.0928085i
$111$	73456.0			0.565874
$112$		0			0
$113$	−245054.			−1.80537			−0.902684	−	0.430304i	$-0.858406\pi$
$113$	−245054.			−1.80537			−0.902684	+	0.430304i	$0.858406\pi$
$114$	−38912.0	+	67397.6i	−0.280428	+	0.485716i
$115$	−10000.0	−	17320.5i	−0.0705108	−	0.122128i
$116$	53968.0	+	93475.3i	0.372384	+	0.644989i
$117$	−26313.0	+	45575.5i	−0.177707	+	0.307798i
$118$	−110624.			−0.731382
$119$		0			0
$120$	5120.00			0.0324576
$121$	22725.5	−	39361.7i	0.141107	−	0.244405i
$122$	−68676.0	−	118950.i	−0.417739	−	0.723546i
$123$	58296.0	+	100972.i	0.347437	+	0.601778i
$124$	−70848.0	+	122712.i	−0.413784	+	0.716694i
$125$	−61500.0			−0.352047
$126$		0			0
$127$	−96696.0			−0.531985			−0.265992	−	0.963975i	$-0.585700\pi$
$127$	−96696.0			−0.531985			−0.265992	+	0.963975i	$0.585700\pi$
$128$	−8192.00	+	14189.0i	−0.0441942	+	0.0765466i
$129$	−32432.0	−	56173.9i	−0.171593	−	0.297208i
$130$	5880.00	+	10184.5i	0.0305154	+	0.0528542i
$131$	−67184.0	+	116366.i	−0.342048	+	0.592445i	−0.984813	−	0.173619i	$-0.944454\pi$
$131$	−67184.0	+	116366.i	−0.342048	+	0.592445i	0.642765	+	0.766064i	$0.277787\pi$
$132$	−43520.0			−0.217397
$133$		0			0
$134$	49264.0			0.237011
$135$	16880.0	−	29237.0i	0.0797146	−	0.138070i
$136$	−39232.0	−	67951.8i	−0.181883	−	0.315031i
$137$	147331.	+	255185.i	0.670645	+	1.16159i	0.977721	+	0.209906i	$0.0673159\pi$
$137$	147331.	+	255185.i	0.670645	+	1.16159i	−0.307076	+	0.951685i	$0.599351\pi$
$138$	−32000.0	+	55425.6i	−0.143038	+	0.247750i
$139$	314944.			1.38260			0.691300	−	0.722568i	$-0.257038\pi$
$139$	314944.			1.38260			0.691300	+	0.722568i	$0.257038\pi$
$140$		0			0
$141$	−2496.00			−0.0105730
$142$	−73840.0	+	127895.i	−0.307306	+	0.532269i
$143$	−49980.0	−	86567.9i	−0.204388	−	0.354011i
$144$	22912.0	+	39684.7i	0.0920782	+	0.159484i
$145$	33730.0	−	58422.1i	0.133228	−	0.230758i
$146$	−246872.			−0.958495
$147$		0			0
$148$	146912.			0.551319
$149$	−56811.0	+	98399.5i	−0.209636	+	0.363101i	−0.951600	−	0.307339i	$-0.900561\pi$
$149$	−56811.0	+	98399.5i	−0.209636	+	0.363101i	0.741964	+	0.670440i	$0.233895\pi$
$150$	48400.0	+	83831.3i	0.175637	+	0.304213i
$151$	−204104.	−	353518.i	−0.728466	−	1.26174i	−0.957531	−	0.288329i	$-0.906900\pi$
$151$	−204104.	−	353518.i	−0.728466	−	1.26174i	0.229066	−	0.973411i	$-0.426433\pi$
$152$	−77824.0	+	134795.i	−0.273215	+	0.473222i
$153$	−219454.			−0.757905
$154$		0			0
$155$	88560.0			0.296080
$156$	18816.0	−	32590.3i	0.0619036	−	0.107220i
$157$	−146773.	−	254218.i	−0.475223	−	0.823110i	0.524375	−	0.851488i	$-0.324299\pi$
$157$	−146773.	−	254218.i	−0.475223	−	0.823110i	−0.999597	+	0.0283780i	$0.990966\pi$
$158$	129504.	+	224308.i	0.412706	+	0.714827i
$159$	58536.0	−	101387.i	0.183624	−	0.318047i
$160$	10240.0			0.0316228
$161$		0			0
$162$	65956.0			0.197454
$163$	158558.	−	274631.i	0.467433	−	0.809617i	−0.531875	−	0.846823i	$-0.678512\pi$
$163$	158558.	−	274631.i	0.467433	−	0.809617i	0.999308	+	0.0372057i	$0.0118457\pi$
$164$	116592.	+	201943.i	0.338500	+	0.586300i
$165$	13600.0	+	23555.9i	0.0388892	+	0.0673581i
$166$	154112.	−	266930.i	0.434076	−	0.751842i
$167$	141568.			0.392802			0.196401	−	0.980524i	$-0.437075\pi$
$167$	141568.			0.392802			0.196401	+	0.980524i	$0.437075\pi$
$168$		0			0
$169$	−284857.			−0.767203
$170$	−24520.0	+	42469.9i	−0.0650726	+	0.112709i
$171$	217664.	+	377005.i	0.569241	+	0.985955i
$172$	−64864.0	−	112348.i	−0.167179	−	0.289563i
$173$	35611.0	−	61680.1i	0.0904626	−	0.156686i	−0.817243	−	0.576293i	$-0.804499\pi$
$173$	35611.0	−	61680.1i	0.0904626	−	0.156686i	0.907706	+	0.419607i	$0.137832\pi$
$174$	−215872.			−0.540534
$175$		0			0
$176$	−87040.0			−0.211805
$177$	110624.	−	191606.i	0.265409	−	0.459702i
$178$	16332.0	+	28287.9i	0.0386358	+	0.0669191i
$179$	−242814.	−	420566.i	−0.566423	−	0.981074i	−0.996916	−	0.0784798i	$-0.974993\pi$
$179$	−242814.	−	420566.i	−0.566423	−	0.981074i	0.430492	−	0.902594i	$-0.358340\pi$
$180$	14320.0	−	24803.0i	0.0329429	−	0.0570588i
$181$	657090.			1.49083			0.745416	−	0.666600i	$-0.232251\pi$
$181$	657090.			1.49083			0.745416	+	0.666600i	$0.232251\pi$
$182$		0			0
$183$	274704.			0.606369
$184$	−64000.0	+	110851.i	−0.139359	+	0.241377i
$185$	−45910.0	−	79518.5i	−0.0986229	−	0.170820i
$186$	−141696.	−	245425.i	−0.300314	−	0.520159i
$187$	208420.	−	360994.i	0.435848	−	0.754911i
$188$	−4992.00			−0.0103010
$189$		0			0
$190$	97280.0			0.195497
$191$	−34152.0	+	59153.0i	−0.0677381	+	0.117326i	−0.897905	−	0.440189i	$-0.854912\pi$
$191$	−34152.0	+	59153.0i	−0.0677381	+	0.117326i	0.830167	+	0.557514i	$0.188245\pi$
$192$	−16384.0	−	28377.9i	−0.0320750	−	0.0555556i
$193$	−176377.	−	305494.i	−0.340839	−	0.590350i	0.643750	−	0.765236i	$-0.277378\pi$
$193$	−176377.	−	305494.i	−0.340839	−	0.590350i	−0.984589	+	0.174886i	$0.944044\pi$
$194$	−41300.0	+	71533.7i	−0.0787854	+	0.136460i
$195$	−23520.0			−0.0442946
$196$		0			0
$197$	196982.			0.361627			0.180814	−	0.983517i	$-0.442127\pi$
$197$	196982.			0.361627			0.180814	+	0.983517i	$0.442127\pi$
$198$	−121720.	+	210825.i	−0.220647	+	0.382173i
$199$	551960.	+	956023.i	0.988041	+	1.71134i	0.627555	+	0.778572i	$0.284056\pi$
$199$	551960.	+	956023.i	0.988041	+	1.71134i	0.360486	+	0.932765i	$0.382611\pi$
$200$	96800.0	+	167663.i	0.171120	+	0.296388i
$201$	−49264.0	+	85327.8i	−0.0860081	+	0.148970i
$202$	745000.			1.28463
$203$		0			0
$204$	156928.			0.264013
$205$	72870.0	−	126215.i	0.121106	−	0.209761i
$206$	120128.	+	208068.i	0.197231	+	0.341615i
$207$	179000.	+	310037.i	0.290354	+	0.502907i
$208$	37632.0	−	65180.5i	0.0603113	−	0.104462i
$209$	−826880.			−1.30941
$210$		0			0
$211$	−103444.			−0.159955			−0.0799777	−	0.996797i	$-0.525485\pi$
$211$	−103444.			−0.159955			−0.0799777	+	0.996797i	$0.525485\pi$
$212$	117072.	−	202775.i	0.178901	−	0.309866i
$213$	−147680.	−	255789.i	−0.223035	−	0.386308i
$214$	−95784.0	−	165903.i	−0.142974	−	0.247639i
$215$	−40540.0	+	70217.3i	−0.0598119	+	0.103597i
$216$	−216064.			−0.315100
$217$		0			0
$218$	88408.0			0.125994
$219$	246872.	−	427595.i	0.347826	−	0.602452i
$220$	27200.0	+	47111.8i	0.0378889	+	0.0656255i
$221$	180222.	+	312154.i	0.248214	+	0.429920i
$222$	−146912.	+	254459.i	−0.200067	+	0.346526i
$223$	307328.			0.413847			0.206924	−	0.978357i	$-0.433655\pi$
$223$	307328.			0.413847			0.206924	+	0.978357i	$0.433655\pi$
$224$		0			0
$225$	541475.			0.713053
$226$	490108.	−	848892.i	0.638294	−	1.10556i
$227$	445896.	+	772315.i	0.574340	+	0.994786i	0.996113	+	0.0880844i	$0.0280745\pi$
$227$	445896.	+	772315.i	0.574340	+	0.994786i	−0.421773	+	0.906701i	$0.638592\pi$
$228$	−155648.	−	269590.i	−0.198293	−	0.343453i
$229$	−138353.	+	239634.i	−0.174341	+	0.301968i	−0.939933	−	0.341359i	$-0.889113\pi$
$229$	−138353.	+	239634.i	−0.174341	+	0.301968i	0.765592	+	0.643327i	$0.222446\pi$
$230$	80000.0			0.0997173
$231$		0			0
$232$	−431744.			−0.526631
$233$	−739717.	+	1.28123e6i	−0.892639	+	1.54610i	−0.0559390	+	0.998434i	$0.517815\pi$
$233$	−739717.	+	1.28123e6i	−0.892639	+	1.54610i	−0.836700	+	0.547662i	$0.815518\pi$
$234$	−105252.	−	182302.i	−0.125658	−	0.217646i
$235$	1560.00	+	2702.00i	0.00184270	+	0.00319165i
$236$	221248.	−	383213.i	0.258583	−	0.447878i
$237$	−518016.			−0.599063
$238$		0			0
$239$	1.00034e6			1.13280			0.566402	−	0.824129i	$-0.308335\pi$
$239$	1.00034e6			1.13280			0.566402	+	0.824129i	$0.308335\pi$
$240$	−10240.0	+	17736.2i	−0.0114755	+	0.0198762i
$241$	−679165.	−	1.17635e6i	−0.753239	−	1.30465i	−0.946245	−	0.323450i	$-0.895157\pi$
$241$	−679165.	−	1.17635e6i	−0.753239	−	1.30465i	0.193006	−	0.981198i	$-0.438176\pi$
$242$	90902.0	+	157447.i	0.0997781	+	0.172821i
$243$	−476140.	+	824699.i	−0.517272	+	0.895941i
$244$	549408.			0.590773
$245$		0			0
$246$	−466368.			−0.491350
$247$	357504.	−	619215.i	0.372854	−	0.645802i
$248$	−283392.	−	490849.i	−0.292589	−	0.506779i
$249$	308224.	+	533860.i	0.315042	+	0.545668i
$250$	123000.	−	213042.i	0.124467	−	0.215584i
$251$	−177408.			−0.177742			−0.0888708	−	0.996043i	$-0.528326\pi$
$251$	−177408.			−0.177742			−0.0888708	+	0.996043i	$0.528326\pi$
$252$		0			0
$253$	−680000.			−0.667894
$254$	193392.	−	334965.i	0.188085	−	0.325773i
$255$	−49040.0	−	84939.8i	−0.0472280	−	0.0818014i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−163329.	+	282894.i	−0.154252	+	0.267172i	−0.932786	−	0.360430i	$-0.882630\pi$
$257$	−163329.	+	282894.i	−0.154252	+	0.267172i	0.778534	+	0.627602i	$0.215963\pi$
$258$	259456.			0.242669
$259$		0			0
$260$	−47040.0			−0.0431553
$261$	−603767.	+	1.04576e6i	−0.548616	+	0.950230i
$262$	−268736.	−	465464.i	−0.241865	−	0.418922i
$263$	17460.0	+	30241.6i	0.0155652	+	0.0269597i	0.873703	−	0.486460i	$-0.161712\pi$
$263$	17460.0	+	30241.6i	0.0155652	+	0.0269597i	−0.858138	+	0.513419i	$0.828379\pi$
$264$	87040.0	−	150758.i	0.0768615	−	0.133128i
$265$	−146340.			−0.128011
$266$		0			0
$267$	−65328.0			−0.0560817
$268$	−98528.0	+	170656.i	−0.0837959	+	0.145139i
$269$	−358229.	−	620471.i	−0.301842	−	0.522806i	0.674711	−	0.738082i	$-0.264268\pi$
$269$	−358229.	−	620471.i	−0.301842	−	0.522806i	−0.976553	+	0.215276i	$0.930935\pi$
$270$	67520.0	+	116948.i	0.0563668	+	0.0976301i
$271$	476688.	−	825648.i	0.394286	−	0.682923i	−0.598724	−	0.800955i	$-0.704325\pi$
$271$	476688.	−	825648.i	0.394286	−	0.682923i	0.993010	+	0.118033i	$0.0376587\pi$
$272$	313856.			0.257222
$273$		0			0
$274$	−1.17865e6			−0.948435
$275$	−514250.	+	890707.i	−0.410055	+	0.710237i
$276$	−128000.	−	221703.i	−0.101143	−	0.175185i
$277$	923645.	+	1.59980e6i	0.723279	+	1.25276i	0.959679	+	0.281100i	$0.0906991\pi$
$277$	923645.	+	1.59980e6i	0.723279	+	1.25276i	−0.236400	+	0.971656i	$0.575968\pi$
$278$	−629888.	+	1.09100e6i	−0.488823	+	0.846666i
$279$	−1.58522e6			−1.21921
$280$		0			0
$281$	−1.99601e6			−1.50798			−0.753991	−	0.656885i	$-0.771874\pi$
$281$	−1.99601e6			−1.50798			−0.753991	+	0.656885i	$0.771874\pi$
$282$	4992.00	−	8646.40i	0.00373811	−	0.00647459i
$283$	−117044.	−	202726.i	−0.0868726	−	0.150468i	0.819315	−	0.573344i	$-0.194354\pi$
$283$	−117044.	−	202726.i	−0.0868726	−	0.150468i	−0.906188	+	0.422876i	$0.861021\pi$
$284$	−295360.	−	511579.i	−0.217298	−	0.376371i
$285$	−97280.0	+	168494.i	−0.0709433	+	0.122877i
$286$	399840.			0.289049
$287$		0			0
$288$	−183296.			−0.130218
$289$	−41609.5	+	72069.8i	−0.0293054	+	0.0507585i
$290$	134920.	+	233688.i	0.0942066	+	0.163171i
$291$	−82600.0	−	143067.i	−0.0571805	−	0.0990394i
$292$	493744.	−	855190.i	0.338879	−	0.586956i
$293$	−2.50081e6			−1.70181			−0.850905	−	0.525320i	$-0.823946\pi$
$293$	−2.50081e6			−1.70181			−0.850905	+	0.525320i	$0.823946\pi$
$294$		0			0
$295$	−276560.			−0.185027
$296$	−293824.	+	508918.i	−0.194921	+	0.337613i
$297$	−573920.	−	994059.i	−0.377538	−	0.653914i
$298$	−227244.	−	393598.i	−0.148235	−	0.256751i
$299$	294000.	−	509223.i	0.190182	−	0.329405i
$300$	−387200.			−0.248389
$301$		0			0
$302$	1.63283e6			1.03021
$303$	−745000.	+	1.29038e6i	−0.466176	+	0.807440i
$304$	−311296.	−	539180.i	−0.193192	−	0.334619i
$305$	−171690.	−	297376.i	−0.105681	−	0.183044i
$306$	438908.	−	760211.i	0.267960	−	0.464120i
$307$	2.34203e6			1.41823			0.709115	−	0.705092i	$-0.249095\pi$
$307$	2.34203e6			1.41823			0.709115	+	0.705092i	$0.249095\pi$
$308$		0			0
$309$	−480512.			−0.286291
$310$	−177120.	+	306781.i	−0.104680	+	0.181311i
$311$	81532.0	+	141218.i	0.0477999	+	0.0827919i	0.888935	−	0.458033i	$-0.151446\pi$
$311$	81532.0	+	141218.i	0.0477999	+	0.0827919i	−0.841136	+	0.540824i	$0.818112\pi$
$312$	75264.0	+	130361.i	0.0437724	+	0.0758161i
$313$	−869825.	+	1.50658e6i	−0.501847	+	0.869224i	0.498151	+	0.867090i	$0.334012\pi$
$313$	−869825.	+	1.50658e6i	−0.501847	+	0.869224i	−0.999998	+	0.00213366i	$0.999321\pi$
$314$	1.17418e6			0.672066
$315$		0			0
$316$	−1.03603e6			−0.583654
$317$	898857.	−	1.55687e6i	0.502392	−	0.870168i	−0.497604	−	0.867404i	$-0.665787\pi$
$317$	898857.	−	1.55687e6i	0.502392	−	0.870168i	0.999996	−	0.00276389i	$-0.000879776\pi$
$318$	234144.	+	405549.i	0.129842	+	0.224893i
$319$	−1.14682e6	−	1.98635e6i	−0.630984	−	1.09290i
$320$	−20480.0	+	35472.4i	−0.0111803	+	0.0193649i
$321$	383136.			0.207535
$322$		0			0
$323$	2.98163e6			1.59019
$324$	−131912.	+	228478.i	−0.0698107	+	0.120916i
$325$	−444675.	−	770200.i	−0.233526	−	0.404478i
$326$	634232.	+	1.09852e6i	0.330525	+	0.572486i
$327$	−88408.0	+	153127.i	−0.0457217	+	0.0791923i
$328$	−932736.			−0.478712
$329$		0			0
$330$	−108800.			−0.0549976
$331$	1.23771e6	−	2.14377e6i	0.620937	−	1.07549i	−0.368375	−	0.929677i	$-0.620086\pi$
$331$	1.23771e6	−	2.14377e6i	0.620937	−	1.07549i	0.989312	−	0.145817i	$-0.0465810\pi$
$332$	616448.	+	1.06772e6i	0.306938	+	0.531633i
$333$	821789.	+	1.42338e6i	0.406116	+	0.703413i
$334$	−283136.	+	490406.i	−0.138877	+	0.240541i
$335$	123160.			0.0599595
$336$		0			0
$337$	89154.0			0.0427628			0.0213814	−	0.999771i	$-0.493194\pi$
$337$	89154.0			0.0427628			0.0213814	+	0.999771i	$0.493194\pi$
$338$	569714.	−	986774.i	0.271247	−	0.469814i
$339$	980216.	+	1.69778e6i	0.463258	+	0.802386i
$340$	−98080.0	−	169880.i	−0.0460133	−	0.0796973i
$341$	1.50552e6	−	2.60764e6i	0.701133	−	1.21440i
$342$	−1.74131e6			−0.805029
$343$		0			0
$344$	518912.			0.236427
$345$	−80000.0	+	138564.i	−0.0361861	+	0.0626762i
$346$	142444.	+	246720.i	0.0639667	+	0.110794i
$347$	−469278.	−	812813.i	−0.209222	−	0.362382i	0.742248	−	0.670125i	$-0.233760\pi$
$347$	−469278.	−	812813.i	−0.209222	−	0.362382i	−0.951470	+	0.307743i	$0.900426\pi$
$348$	431744.	−	747803.i	0.191108	−	0.331008i
$349$	3.34268e6			1.46903			0.734516	−	0.678591i	$-0.237409\pi$
$349$	3.34268e6			1.46903			0.734516	+	0.678591i	$0.237409\pi$
$350$		0			0
$351$	992544.			0.430013
$352$	174080.	−	301515.i	0.0748845	−	0.129704i
$353$	1.88303e6	+	3.26151e6i	0.804305	+	1.39310i	0.916759	+	0.399440i	$0.130795\pi$
$353$	1.88303e6	+	3.26151e6i	0.804305	+	1.39310i	−0.112454	+	0.993657i	$0.535871\pi$
$354$	442496.	+	766426.i	0.187673	+	0.325059i
$355$	−184600.	+	319737.i	−0.0777429	+	0.134655i
$356$	−130656.			−0.0546392
$357$		0			0
$358$	1.94251e6			0.801044
$359$	769672.	−	1.33311e6i	0.315188	−	0.545921i	−0.664290	−	0.747475i	$-0.731266\pi$
$359$	769672.	−	1.33311e6i	0.315188	−	0.545921i	0.979477	+	0.201554i	$0.0645991\pi$
$360$	57280.0	+	99211.9i	0.0232941	+	0.0403466i
$361$	−1.71926e6	−	2.97785e6i	−0.694343	−	1.20264i
$362$	−1.31418e6	+	2.27623e6i	−0.527088	+	0.912944i
$363$	−363608.			−0.144833
$364$		0			0
$365$	−617180.			−0.242482
$366$	−549408.	+	951603.i	−0.214384	+	0.371324i
$367$	429656.	+	744186.i	0.166516	+	0.288414i	0.937193	−	0.348812i	$-0.113415\pi$
$367$	429656.	+	744186.i	0.166516	+	0.288414i	−0.770677	+	0.637226i	$0.780082\pi$
$368$	−256000.	−	443405.i	−0.0985418	−	0.170679i
$369$	−1.30437e6	+	2.25924e6i	−0.498696	+	0.863767i
$370$	367280.			0.139474
$371$		0			0
$372$	1.13357e6			0.424708
$373$	488293.	−	845748.i	0.181722	−	0.314752i	−0.760745	−	0.649051i	$-0.775166\pi$
$373$	488293.	−	845748.i	0.181722	−	0.314752i	0.942467	+	0.334299i	$0.108499\pi$
$374$	833680.	+	1.44398e6i	0.308191	+	0.533803i
$375$	246000.	+	426084.i	0.0903352	+	0.156465i
$376$	9984.00	−	17292.8i	0.00364196	−	0.00630806i
$377$	1.98332e6			0.718688
$378$		0			0
$379$	106444.			0.0380648			0.0190324	−	0.999819i	$-0.493941\pi$
$379$	106444.			0.0380648			0.0190324	+	0.999819i	$0.493941\pi$
$380$	−194560.	+	336988.i	−0.0691185	+	0.119717i
$381$	386784.	+	669930.i	0.136507	+	0.236438i
$382$	−136608.	−	236612.i	−0.0478980	−	0.0829618i
$383$	1.00317e6	−	1.73754e6i	0.349445	−	0.605256i	−0.636706	−	0.771106i	$-0.719704\pi$
$383$	1.00317e6	−	1.73754e6i	0.349445	−	0.605256i	0.986151	+	0.165851i	$0.0530369\pi$
$384$	131072.			0.0453609
$385$		0			0
$386$	1.41102e6			0.482018
$387$	725666.	−	1.25689e6i	0.246297	−	0.426599i
$388$	−165200.	−	286135.i	−0.0557097	−	0.0964920i
$389$	342001.	+	592363.i	0.114592	+	0.198479i	0.917616	−	0.397467i	$-0.130111\pi$
$389$	342001.	+	592363.i	0.114592	+	0.198479i	−0.803025	+	0.595946i	$0.796777\pi$
$390$	47040.0	−	81475.7i	0.0156605	−	0.0271248i
$391$	2.45200e6			0.811108
$392$		0			0
$393$	1.07494e6			0.351079
$394$	−393964.	+	682366.i	−0.127854	+	0.221450i
$395$	323760.	+	560769.i	0.104407	+	0.180839i
$396$	−486880.	−	843301.i	−0.156021	−	0.270237i
$397$	111435.	−	193011.i	0.0354850	−	0.0614619i	−0.847737	−	0.530416i	$-0.822036\pi$
$397$	111435.	−	193011.i	0.0354850	−	0.0614619i	0.883223	+	0.468954i	$0.155369\pi$
$398$	−4.41568e6			−1.39730
$399$		0			0
$400$	−774400.			−0.242000
$401$	−950361.	+	1.64607e6i	−0.295140	+	0.511197i	−0.975017	−	0.222129i	$-0.928700\pi$
$401$	−950361.	+	1.64607e6i	−0.295140	+	0.511197i	0.679878	+	0.733326i	$0.262033\pi$
$402$	−197056.	−	341311.i	−0.0608169	−	0.105338i
$403$	1.30183e6	+	2.25484e6i	0.399294	+	0.691597i
$404$	−1.49000e6	+	2.58076e6i	−0.454185	+	0.786672i
$405$	164890.			0.0499524
$406$		0			0
$407$	−3.12188e6			−0.934179
$408$	−313856.	+	543615.i	−0.0933426	+	0.161674i
$409$	−888577.	−	1.53906e6i	−0.262656	−	0.454933i	0.704291	−	0.709911i	$-0.251265\pi$
$409$	−888577.	−	1.53906e6i	−0.262656	−	0.454933i	−0.966947	+	0.254978i	$0.917932\pi$
$410$	291480.	+	504858.i	0.0856346	+	0.148323i
$411$	1.17865e6	−	2.04148e6i	0.344175	−	0.596129i
$412$	−961024.			−0.278927
$413$		0			0
$414$	−1.43200e6			−0.410622
$415$	385280.	−	667325.i	0.109814	−	0.190203i
$416$	150528.	+	260722.i	0.0426466	+	0.0738660i
$417$	−1.25978e6	−	2.18200e6i	−0.354775	−	0.614489i
$418$	1.65376e6	−	2.86440e6i	0.462948	−	0.801849i
$419$	28056.0			0.00780712			0.00390356	−	0.999992i	$-0.498757\pi$
$419$	28056.0			0.00780712			0.00390356	+	0.999992i	$0.498757\pi$
$420$		0			0
$421$	−2.70897e6			−0.744902			−0.372451	−	0.928052i	$-0.621482\pi$
$421$	−2.70897e6			−0.744902			−0.372451	+	0.928052i	$0.621482\pi$
$422$	206888.	−	358341.i	0.0565528	−	0.0979523i
$423$	−27924.0	−	48365.8i	−0.00758799	−	0.0131428i
$424$	468288.	+	811099.i	0.126502	+	0.219108i
$425$	1.85432e6	−	3.21179e6i	0.497982	−	0.862530i
$426$	1.18144e6			0.315419
$427$		0			0
$428$	766272.			0.202196
$429$	−399840.	+	692543.i	−0.104892	+	0.181679i
$430$	−162160.	−	280869.i	−0.0422934	−	0.0732543i
$431$	−2.76949e6	−	4.79690e6i	−0.718136	−	1.24385i	−0.961737	−	0.273973i	$-0.911662\pi$
$431$	−2.76949e6	−	4.79690e6i	−0.718136	−	1.24385i	0.243601	−	0.969876i	$-0.421671\pi$
$432$	432128.	−	748468.i	0.111405	−	0.192958i
$433$	−868294.			−0.222560			−0.111280	−	0.993789i	$-0.535495\pi$
$433$	−868294.			−0.222560			−0.111280	+	0.993789i	$0.535495\pi$
$434$		0			0
$435$	−539680.			−0.136746
$436$	−176816.	+	306254.i	−0.0445457	+	0.0771553i
$437$	−2.43200e6	−	4.21235e6i	−0.609200	−	1.05517i
$438$	987488.	+	1.71038e6i	0.245950	+	0.425998i
$439$	568836.	−	985253.i	0.140872	−	0.243998i	−0.786953	−	0.617013i	$-0.788343\pi$
$439$	568836.	−	985253.i	0.140872	−	0.243998i	0.927825	+	0.373015i	$0.121676\pi$
$440$	−217600.			−0.0535830
$441$		0			0
$442$	−1.44178e6			−0.351028
$443$	−876994.	+	1.51900e6i	−0.212318	+	0.367746i	−0.952440	−	0.304727i	$-0.901435\pi$
$443$	−876994.	+	1.51900e6i	−0.212318	+	0.367746i	0.740121	+	0.672473i	$0.234768\pi$
$444$	−587648.	−	1.01784e6i	−0.141469	−	0.245031i
$445$	40830.0	+	70719.6i	0.00977416	+	0.0169293i
$446$	−614656.	+	1.06462e6i	−0.146317	+	0.253429i
$447$	908976.			0.215171
$448$		0			0
$449$	2.41674e6			0.565736			0.282868	−	0.959159i	$-0.408714\pi$
$449$	2.41674e6			0.565736			0.282868	+	0.959159i	$0.408714\pi$
$450$	−1.08295e6	+	1.87572e6i	−0.252102	+	0.436654i
$451$	−2.47758e6	−	4.29129e6i	−0.573570	−	0.993452i
$452$	1.96043e6	+	3.39557e6i	0.451342	+	0.781747i
$453$	−1.63283e6	+	2.82815e6i	−0.373849	+	0.647525i
$454$	−3.56717e6			−0.812239
$455$		0			0
$456$	1.24518e6			0.280428
$457$	63715.0	−	110358.i	0.0142709	−	0.0247179i	−0.858802	−	0.512308i	$-0.828791\pi$
$457$	63715.0	−	110358.i	0.0142709	−	0.0247179i	0.873073	+	0.487590i	$0.162124\pi$
$458$	−553412.	−	958538.i	−0.123278	−	0.213523i
$459$	2.06949e6	+	3.58446e6i	0.458491	+	0.794130i
$460$	−160000.	+	277128.i	−0.0352554	+	0.0610641i
$461$	−128198.			−0.0280950			−0.0140475	−	0.999901i	$-0.504472\pi$
$461$	−128198.			−0.0280950			−0.0140475	+	0.999901i	$0.504472\pi$
$462$		0			0
$463$	−4.01653e6			−0.870760			−0.435380	−	0.900247i	$-0.643386\pi$
$463$	−4.01653e6			−0.870760			−0.435380	+	0.900247i	$0.643386\pi$
$464$	863488.	−	1.49561e6i	0.186192	−	0.322494i
$465$	−354240.	−	613562.i	−0.0759740	−	0.131591i
$466$	−2.95887e6	−	5.12491e6i	−0.631191	−	1.09325i
$467$	−4.33623e6	+	7.51057e6i	−0.920069	+	1.59361i	−0.120763	+	0.992681i	$0.538534\pi$
$467$	−4.33623e6	+	7.51057e6i	−0.920069	+	1.59361i	−0.799306	+	0.600925i	$0.794799\pi$
$468$	842016.			0.177707
$469$		0			0
$470$	−12480.0			−0.00260597
$471$	−1.17418e6	+	2.03375e6i	−0.243884	+	0.422420i
$472$	884992.	+	1.53285e6i	0.182846	+	0.316698i
$473$	1.37836e6	+	2.38739e6i	0.283276	+	0.490648i
$474$	1.03603e6	−	1.79446e6i	0.211801	−	0.366850i
$475$	−7.35680e6			−1.49608
$476$		0			0
$477$	2.61949e6			0.527133
$478$	−2.00069e6	+	3.46529e6i	−0.400507	+	0.693698i
$479$	−4.14473e6	−	7.17889e6i	−0.825387	−	1.42961i	−0.901623	−	0.432523i	$-0.857624\pi$
$479$	−4.14473e6	−	7.17889e6i	−0.825387	−	1.42961i	0.0762360	−	0.997090i	$-0.475710\pi$
$480$	−40960.0	−	70944.8i	−0.00811441	−	0.0140546i
$481$	1.34975e6	−	2.33784e6i	0.266006	−	0.460736i
$482$	5.43332e6			1.06524
$483$		0			0
$484$	−727216.			−0.141107
$485$	−103250.	+	178834.i	−0.0199313	+	0.0345220i
$486$	−1.90456e6	−	3.29879e6i	−0.365767	−	0.633526i
$487$	4.45885e6	+	7.72295e6i	0.851923	+	1.47557i	0.879471	+	0.475953i	$0.157897\pi$
$487$	4.45885e6	+	7.72295e6i	0.851923	+	1.47557i	−0.0275478	+	0.999620i	$0.508770\pi$
$488$	−1.09882e6	+	1.90321e6i	−0.208870	+	0.361773i
$489$	−2.53693e6			−0.479773
$490$		0			0
$491$	−5.71537e6			−1.06989			−0.534947	−	0.844886i	$-0.679668\pi$
$491$	−5.71537e6			−1.06989			−0.534947	+	0.844886i	$0.679668\pi$
$492$	932736.	−	1.61555e6i	0.173718	−	0.300889i
$493$	4.13530e6	+	7.16255e6i	0.766284	+	1.32724i
$494$	1.43002e6	+	2.47686e6i	0.263647	+	0.456651i
$495$	−304300.	+	527063.i	−0.0558199	+	0.0966829i
$496$	2.26714e6			0.413784
$497$		0			0
$498$	−2.46579e6			−0.445536
$499$	−62558.0	+	108354.i	−0.0112469	+	0.0194801i	−0.871594	−	0.490228i	$-0.836913\pi$
$499$	−62558.0	+	108354.i	−0.0112469	+	0.0194801i	0.860347	+	0.509708i	$0.170247\pi$
$500$	492000.	+	852169.i	0.0880116	+	0.152441i
$501$	−566272.	−	980812.i	−0.100793	−	0.174579i
$502$	354816.	−	614559.i	0.0628411	−	0.108844i
$503$	−2.77116e6			−0.488362			−0.244181	−	0.969730i	$-0.578519\pi$
$503$	−2.77116e6			−0.488362			−0.244181	+	0.969730i	$0.578519\pi$
$504$		0			0
$505$	1.86250e6			0.324988
$506$	1.36000e6	−	2.35559e6i	0.236136	−	0.409000i
$507$	1.13943e6	+	1.97355e6i	0.196864	+	0.340979i
$508$	773568.	+	1.33986e6i	0.132996	+	0.230356i
$509$	69267.0	−	119974.i	0.0118504	−	0.0205254i	−0.860039	−	0.510228i	$-0.829561\pi$
$509$	69267.0	−	119974.i	0.0118504	−	0.0205254i	0.871890	+	0.489702i	$0.162894\pi$
$510$	392320.			0.0667905
$511$		0			0
$512$	262144.			0.0441942
$513$	4.10522e6	−	7.11044e6i	0.688720	−	1.19290i
$514$	−653316.	−	1.13158e6i	−0.109073	−	0.188919i
$515$	300320.	+	520169.i	0.0498961	+	0.0864225i
$516$	−518912.	+	898782.i	−0.0857965	+	0.148604i
$517$	106080.			0.0174545
$518$		0			0
$519$	−569776.			−0.0928508
$520$	94080.0	−	162951.i	0.0152577	−	0.0264271i
$521$	901407.	+	1.56128e6i	0.145488	+	0.251992i	0.929555	−	0.368684i	$-0.120192\pi$
$521$	901407.	+	1.56128e6i	0.145488	+	0.251992i	−0.784067	+	0.620676i	$0.786858\pi$
$522$	−2.41507e6	−	4.18302e6i	−0.387930	−	0.671914i
$523$	−4.88624e6	+	8.46321e6i	−0.781124	+	1.35295i	0.150163	+	0.988661i	$0.452020\pi$
$523$	−4.88624e6	+	8.46321e6i	−0.781124	+	1.35295i	−0.931287	+	0.364286i	$0.881313\pi$
$524$	2.14989e6			0.342048
$525$		0			0
$526$	−139680.			−0.0220125
$527$	−5.42873e6	+	9.40283e6i	−0.851474	+	1.47480i
$528$	348160.	+	603031.i	0.0543493	+	0.0941358i
$529$	1.21817e6	+	2.10993e6i	0.189265	+	0.327816i
$530$	292680.	−	506937.i	0.0452588	−	0.0783906i
$531$	4.95042e6			0.761914
$532$		0			0
$533$	4.28476e6			0.653293
$534$	130656.	−	226303.i	0.0198279	−	0.0343429i
$535$	−239460.	−	414757.i	−0.0361700	−	0.0626483i
$536$	−394112.	−	682622.i	−0.0592526	−	0.102629i
$537$	−1.94251e6	+	3.36453e6i	−0.290689	+	0.503487i
$538$	2.86583e6			0.426869
$539$		0			0
$540$	−540160.			−0.0797146
$541$	−1.22752e6	+	2.12613e6i	−0.180316	+	0.312317i	−0.941988	−	0.335646i	$-0.891045\pi$
$541$	−1.22752e6	+	2.12613e6i	−0.180316	+	0.312317i	0.761672	+	0.647963i	$0.224379\pi$
$542$	1.90675e6	+	3.30259e6i	0.278802	+	0.482899i
$543$	−2.62836e6	−	4.55245e6i	−0.382547	−	0.662592i
$544$	−627712.	+	1.08723e6i	−0.0909417	+	0.157516i
$545$	221020.			0.0318743
$546$		0			0
$547$	1.32081e7			1.88744			0.943721	−	0.330743i	$-0.107299\pi$
$547$	1.32081e7			1.88744			0.943721	+	0.330743i	$0.107299\pi$
$548$	2.35730e6	−	4.08296e6i	0.335323	−	0.580796i
$549$	3.07325e6	+	5.32303e6i	0.435178	+	0.753751i
$550$	−2.05700e6	−	3.56283e6i	−0.289953	−	0.502213i
$551$	8.20314e6	−	1.42082e7i	1.15107	−	1.99371i
$552$	1.02400e6			0.143038
$553$		0			0
$554$	−7.38916e6			−1.02287
$555$	−367280.	+	636148.i	−0.0506133	+	0.0876648i
$556$	−2.51955e6	−	4.36399e6i	−0.345650	−	0.598683i
$557$	−3.91646e6	−	6.78351e6i	−0.534880	−	0.926439i	−0.999169	−	0.0407552i	$-0.987024\pi$
$557$	−3.91646e6	−	6.78351e6i	−0.534880	−	0.926439i	0.464290	−	0.885683i	$-0.346310\pi$
$558$	3.17045e6	−	5.49138e6i	0.431057	−	0.746613i
$559$	−2.38375e6			−0.322650
$560$		0			0
$561$	−3.33472e6			−0.447355
$562$	3.99201e6	−	6.91437e6i	0.533152	−	0.923446i
$563$	−1.78954e6	−	3.09957e6i	−0.237942	−	0.412127i	0.722182	−	0.691703i	$-0.243139\pi$
$563$	−1.78954e6	−	3.09957e6i	−0.237942	−	0.412127i	−0.960123	+	0.279576i	$0.909806\pi$
$564$	19968.0	+	34585.6i	0.00264324	+	0.00457823i
$565$	1.22527e6	−	2.12223e6i	0.161477	−	0.279686i
$566$	936352.			0.122856
$567$		0			0
$568$	2.36288e6			0.307306
$569$	1.69791e6	−	2.94086e6i	0.219853	−	0.380797i	−0.734910	−	0.678165i	$-0.762775\pi$
$569$	1.69791e6	−	2.94086e6i	0.219853	−	0.380797i	0.954763	+	0.297368i	$0.0961088\pi$
$570$	−389120.	−	673976.i	−0.0501645	−	0.0868874i
$571$	738474.	+	1.27907e6i	0.0947862	+	0.164174i	0.909519	−	0.415662i	$-0.136450\pi$
$571$	738474.	+	1.27907e6i	0.0947862	+	0.164174i	−0.814733	+	0.579836i	$0.803117\pi$
$572$	−799680.	+	1.38509e6i	−0.102194	+	0.177006i
$573$	546432.			0.0695264
$574$		0			0
$575$	−6.05000e6			−0.763108
$576$	366592.	−	634956.i	0.0460391	−	0.0797421i
$577$	7.49804e6	+	1.29870e7i	0.937580	+	1.62394i	0.769968	+	0.638082i	$0.220272\pi$
$577$	7.49804e6	+	1.29870e7i	0.937580	+	1.62394i	0.167612	+	0.985853i	$0.446395\pi$
$578$	−166438.	−	288279.i	−0.0207221	−	0.0358917i
$579$	−1.41102e6	+	2.44395e6i	−0.174918	+	0.302968i
$580$	−1.07936e6			−0.133228
$581$		0			0
$582$	660800.			0.0808654
$583$	−2.48778e6	+	4.30896e6i	−0.303138	+	0.525051i
$584$	1.97498e6	+	3.42076e6i	0.239624	+	0.415040i
$585$	−263130.	−	455755.i	−0.0317893	−	0.0550606i
$586$	5.00161e6	−	8.66305e6i	0.601681	−	1.04214i
$587$	−3.29291e6			−0.394444			−0.197222	−	0.980359i	$-0.563192\pi$
$587$	−3.29291e6			−0.394444			−0.197222	+	0.980359i	$0.563192\pi$
$588$		0			0
$589$	2.15378e7			2.55807
$590$	553120.	−	958032.i	0.0654168	−	0.113305i
$591$	−787928.	−	1.36473e6i	−0.0927936	−	0.160723i
$592$	−1.17530e6	−	2.03567e6i	−0.137830	−	0.238728i
$593$	5.89542e6	−	1.02112e7i	0.688459	−	1.19245i	−0.283877	−	0.958861i	$-0.591621\pi$
$593$	5.89542e6	−	1.02112e7i	0.688459	−	1.19245i	0.972336	−	0.233586i	$-0.0750459\pi$
$594$	4.59136e6			0.533919
$595$		0			0
$596$	1.81795e6			0.209636
$597$	4.41568e6	−	7.64818e6i	0.507063	−	0.878259i
$598$	1.17600e6	+	2.03689e6i	0.134479	+	0.232924i
$599$	763212.	+	1.32192e6i	0.0869117	+	0.150535i	0.906204	−	0.422840i	$-0.138967\pi$
$599$	763212.	+	1.32192e6i	0.0869117	+	0.150535i	−0.819293	+	0.573376i	$0.805634\pi$
$600$	774400.	−	1.34130e6i	0.0878187	−	0.152107i
$601$	−1.00142e7			−1.13092			−0.565458	−	0.824777i	$-0.691301\pi$
$601$	−1.00142e7			−1.13092			−0.565458	+	0.824777i	$0.691301\pi$
$602$		0			0
$603$	−2.20456e6			−0.246905
$604$	−3.26566e6	+	5.65630e6i	−0.364233	+	0.630870i
$605$	227255.	+	393617.i	0.0252421	+	0.0437206i
$606$	−2.98000e6	−	5.16151e6i	−0.329636	−	0.570946i
$607$	−6.03298e6	+	1.04494e7i	−0.664599	+	1.15112i	0.314795	+	0.949160i	$0.398064\pi$
$607$	−6.03298e6	+	1.04494e7i	−0.664599	+	1.15112i	−0.979394	+	0.201960i	$0.935269\pi$
$608$	2.49037e6			0.273215
$609$		0			0
$610$	1.37352e6			0.149455
$611$	−45864.0	+	79438.8i	−0.00497014	+	0.00860854i
$612$	1.75563e6	+	3.04084e6i	0.189476	+	0.328183i
$613$	−2.90975e6	−	5.03984e6i	−0.312755	−	0.541708i	0.666203	−	0.745771i	$-0.267919\pi$
$613$	−2.90975e6	−	5.03984e6i	−0.312755	−	0.541708i	−0.978958	+	0.204063i	$0.934585\pi$
$614$	−4.68406e6	+	8.11304e6i	−0.501420	+	0.868485i
$615$	−1.16592e6			−0.124303
$616$		0			0
$617$	−4.16589e6			−0.440550			−0.220275	−	0.975438i	$-0.570695\pi$
$617$	−4.16589e6			−0.440550			−0.220275	+	0.975438i	$0.570695\pi$
$618$	961024.	−	1.66454e6i	0.101219	−	0.175317i
$619$	4.04045e6	+	6.99827e6i	0.423841	+	0.734115i	0.996311	−	0.0858108i	$-0.0273481\pi$
$619$	4.04045e6	+	6.99827e6i	0.423841	+	0.734115i	−0.572470	+	0.819926i	$0.694015\pi$
$620$	−708480.	−	1.22712e6i	−0.0740199	−	0.128206i
$621$	3.37600e6	−	5.84740e6i	0.351296	−	0.608463i
$622$	−652256.			−0.0675993
$623$		0			0
$624$	−602112.			−0.0619036
$625$	−4.41906e6	+	7.65404e6i	−0.452512	+	0.783774i
$626$	−3.47930e6	−	6.02632e6i	−0.354859	−	0.614634i
$627$	3.30752e6	+	5.72879e6i	0.335996	+	0.581961i
$628$	−2.34837e6	+	4.06749e6i	−0.237611	+	0.411555i
$629$	1.12571e7			1.13449
$630$		0			0
$631$	−8.40878e6			−0.840735			−0.420368	−	0.907354i	$-0.638099\pi$
$631$	−8.40878e6			−0.840735			−0.420368	+	0.907354i	$0.638099\pi$
$632$	2.07206e6	−	3.58892e6i	0.206353	−	0.357414i
$633$	413776.	+	716681.i	0.0410446	+	0.0710913i
$634$	3.59543e6	+	6.22746e6i	0.355245	+	0.615302i
$635$	483480.	−	837412.i	0.0475822	−	0.0824147i
$636$	−1.87315e6			−0.183624
$637$		0			0
$638$	9.17456e6			0.892347
$639$	3.30434e6	−	5.72328e6i	0.320135	−	0.554489i
$640$	−81920.0	−	141890.i	−0.00790569	−	0.0136931i
$641$	−3.14880e6	−	5.45388e6i	−0.302691	−	0.524277i	0.674053	−	0.738683i	$-0.264552\pi$
$641$	−3.14880e6	−	5.45388e6i	−0.302691	−	0.524277i	−0.976745	+	0.214406i	$0.931218\pi$
$642$	−766272.	+	1.32722e6i	−0.0733745	+	0.127088i
$643$	4.39762e6			0.419460			0.209730	−	0.977759i	$-0.432741\pi$
$643$	4.39762e6			0.419460			0.209730	+	0.977759i	$0.432741\pi$
$644$		0			0
$645$	648640.			0.0613910
$646$	−5.96326e6	+	1.03287e7i	−0.562215	+	0.973786i
$647$	−3.27698e6	−	5.67590e6i	−0.307761	−	0.533058i	0.670111	−	0.742261i	$-0.266246\pi$
$647$	−3.27698e6	−	5.67590e6i	−0.307761	−	0.533058i	−0.977872	+	0.209203i	$0.932913\pi$
$648$	−527648.	−	913913.i	−0.0493636	−	0.0855003i
$649$	−4.70152e6	+	8.14327e6i	−0.438154	+	0.758905i
$650$	3.55740e6			0.330255
$651$		0			0
$652$	−5.07386e6			−0.467433
$653$	−1.89826e6	+	3.28788e6i	−0.174210	+	0.301740i	−0.939888	−	0.341484i	$-0.889070\pi$
$653$	−1.89826e6	+	3.28788e6i	−0.174210	+	0.301740i	0.765678	+	0.643224i	$0.222404\pi$
$654$	−353632.	−	612509.i	−0.0323301	−	0.0559974i
$655$	−671840.	−	1.16366e6i	−0.0611875	−	0.105980i
$656$	1.86547e6	−	3.23109e6i	0.169250	−	0.293150i
$657$	1.10475e7			0.998508
$658$		0			0
$659$	−8.82684e6			−0.791757			−0.395879	−	0.918303i	$-0.629560\pi$
$659$	−8.82684e6			−0.791757			−0.395879	+	0.918303i	$0.629560\pi$
$660$	217600.	−	376894.i	0.0194446	−	0.0336790i
$661$	170635.	+	295548.i	0.0151902	+	0.0263103i	0.873521	−	0.486787i	$-0.161831\pi$
$661$	170635.	+	295548.i	0.0151902	+	0.0263103i	−0.858330	+	0.513097i	$0.828498\pi$
$662$	4.95082e6	+	8.57508e6i	0.439069	+	0.760489i
$663$	1.44178e6	−	2.49723e6i	0.127384	−	0.220635i
$664$	−4.93158e6			−0.434076
$665$		0			0
$666$	−6.57431e6			−0.574334
$667$	6.74600e6	−	1.16844e7i	0.587127	−	1.01693i
$668$	−1.13254e6	−	1.96162e6i	−0.0982006	−	0.170088i
$669$	−1.22931e6	−	2.12923e6i	−0.106193	−	0.183932i
$670$	−246320.	+	426639.i	−0.0211989	+	0.0367175i
$671$	−1.16749e7			−1.00103
$672$		0			0
$673$	4.41807e6			0.376006			0.188003	−	0.982168i	$-0.439799\pi$
$673$	4.41807e6			0.376006			0.188003	+	0.982168i	$0.439799\pi$
$674$	−178308.	+	308839.i	−0.0151189	+	0.0261868i
$675$	−5.10620e6	−	8.84420e6i	−0.431359	−	0.747135i
$676$	2.27886e6	+	3.94709e6i	0.191801	+	0.332209i
$677$	−8.19289e6	+	1.41905e7i	−0.687014	+	1.18994i	0.285786	+	0.958294i	$0.407745\pi$
$677$	−8.19289e6	+	1.41905e7i	−0.687014	+	1.18994i	−0.972799	+	0.231649i	$0.925588\pi$
$678$	−7.84173e6			−0.655145
$679$		0			0
$680$	784640.			0.0650726
$681$	3.56717e6	−	6.17852e6i	0.294751	−	0.510524i
$682$	6.02208e6	+	1.04305e7i	0.495776	+	0.858709i
$683$	8.76997e6	+	1.51900e7i	0.719360	+	1.24597i	0.961254	+	0.275665i	$0.0888980\pi$
$683$	8.76997e6	+	1.51900e7i	0.719360	+	1.24597i	−0.241894	+	0.970303i	$0.577769\pi$
$684$	3.48262e6	−	6.03208e6i	0.284621	−	0.492977i
$685$	−2.94662e6			−0.239937
$686$		0			0
$687$	2.21365e6			0.178944
$688$	−1.03782e6	+	1.79756e6i	−0.0835897	+	0.144782i
$689$	−2.15120e6	−	3.72598e6i	−0.172636	−	0.299015i
$690$	−320000.	−	554256.i	−0.0255875	−	0.0443188i
$691$	−1.57319e6	+	2.72485e6i	−0.125339	+	0.217094i	−0.921865	−	0.387510i	$-0.873335\pi$
$691$	−1.57319e6	+	2.72485e6i	−0.125339	+	0.217094i	0.796526	+	0.604604i	$0.206669\pi$
$692$	−1.13955e6			−0.0904626
$693$		0			0
$694$	3.75422e6			0.295884
$695$	−1.57472e6	+	2.72750e6i	−0.123663	+	0.214191i
$696$	1.72698e6	+	2.99121e6i	0.135134	+	0.234058i
$697$	8.93386e6	+	1.54739e7i	0.696558	+	1.20647i
$698$	−6.68536e6	+	1.15794e7i	−0.519382	+	0.899595i
$699$	1.18355e7			0.916205
$700$		0			0
$701$	−1.90919e7			−1.46742			−0.733709	−	0.679464i	$-0.762212\pi$
$701$	−1.90919e7			−1.46742			−0.733709	+	0.679464i	$0.762212\pi$
$702$	−1.98509e6	+	3.43827e6i	−0.152033	+	0.263328i
$703$	−1.11653e7	−	1.93389e7i	−0.852084	−	1.47585i
$704$	696320.	+	1.20606e6i	0.0529514	+	0.0917145i
$705$	12480.0	−	21616.0i	0.000945675	−	0.00163796i
$706$	−1.50642e7			−1.13746
$707$		0			0
$708$	−3.53997e6			−0.265409
$709$	−495487.	+	858209.i	−0.0370183	+	0.0641176i	−0.883941	−	0.467598i	$-0.845119\pi$
$709$	−495487.	+	858209.i	−0.0370183	+	0.0641176i	0.846923	+	0.531716i	$0.178453\pi$
$710$	−738400.	−	1.27895e6i	−0.0549725	−	0.0952152i
$711$	−5.79530e6	−	1.00378e7i	−0.429934	−	0.744668i
$712$	261312.	−	452606.i	0.0193179	−	0.0334595i
$713$	1.77120e7			1.30480
$714$		0			0
$715$	999600.			0.0731242
$716$	−3.88502e6	+	6.72906e6i	−0.283212	+	0.490537i
$717$	−4.00138e6	−	6.93059e6i	−0.290678	−	0.503468i
$718$	3.07869e6	+	5.33244e6i	0.222872	+	0.386025i
$719$	8.45072e6	−	1.46371e7i	0.609638	−	1.05592i	−0.381663	−	0.924302i	$-0.624648\pi$
$719$	8.45072e6	−	1.46371e7i	0.609638	−	1.05592i	0.991300	−	0.131621i	$-0.0420183\pi$
$720$	−458240.			−0.0329429
$721$		0			0
$722$	1.37541e7			0.981950
$723$	−5.43332e6	+	9.41079e6i	−0.386562	+	0.669546i
$724$	−5.25672e6	−	9.10491e6i	−0.372708	−	0.645549i
$725$	−1.02033e7	−	1.76727e7i	−0.720936	−	1.24870i
$726$	727216.	−	1.25958e6i	0.0512061	−	0.0886916i
$727$	−2.34302e7			−1.64414			−0.822071	−	0.569384i	$-0.807182\pi$
$727$	−2.34302e7			−1.64414			−0.822071	+	0.569384i	$0.807182\pi$
$728$		0			0
$729$	3.61141e6			0.251686
$730$	1.23436e6	−	2.13797e6i	0.0857304	−	0.148489i
$731$	−4.97020e6	−	8.60865e6i	−0.344018	−	0.595856i
$732$	−2.19763e6	−	3.80641e6i	−0.151592	−	0.262566i
$733$	−487905.	+	845076.i	−0.0335409	+	0.0580946i	−0.882309	−	0.470671i	$-0.844012\pi$
$733$	−487905.	+	845076.i	−0.0335409	+	0.0580946i	0.848768	+	0.528766i	$0.177345\pi$
$734$	−3.43725e6			−0.235489
$735$		0			0
$736$	2.04800e6			0.139359
$737$	2.09372e6	−	3.62643e6i	0.141987	−	0.245929i
$738$	−5.21749e6	−	9.03696e6i	−0.352631	−	0.610775i
$739$	3.15104e6	+	5.45776e6i	0.212247	+	0.367623i	0.952418	−	0.304796i	$-0.0985884\pi$
$739$	3.15104e6	+	5.45776e6i	0.212247	+	0.367623i	−0.740170	+	0.672420i	$0.765255\pi$
$740$	−734560.	+	1.27230e6i	−0.0493115	+	0.0854100i
$741$	−5.72006e6			−0.382697
$742$		0			0
$743$	−6.95698e6			−0.462326			−0.231163	−	0.972915i	$-0.574253\pi$
$743$	−6.95698e6			−0.462326			−0.231163	+	0.972915i	$0.574253\pi$
$744$	−2.26714e6	+	3.92679e6i	−0.150157	+	0.260079i
$745$	−568110.	−	983995.i	−0.0375009	−	0.0649535i
$746$	1.95317e6	+	3.38299e6i	0.128497	+	0.222564i
$747$	−6.89651e6	+	1.19451e7i	−0.452197	+	0.783229i
$748$	−6.66944e6			−0.435848
$749$		0			0
$750$	−1.96800e6			−0.127753
$751$	−1.37267e7	+	2.37754e7i	−0.888112	+	1.53825i	−0.0460065	+	0.998941i	$0.514649\pi$
$751$	−1.37267e7	+	2.37754e7i	−0.888112	+	1.53825i	−0.842105	+	0.539313i	$0.818684\pi$
$752$	39936.0	+	69171.2i	0.00257525	+	0.00446047i
$753$	709632.	+	1.22912e6i	0.0456085	+	0.0789962i
$754$	−3.96665e6	+	6.87044e6i	−0.254095	+	0.440105i
$755$	4.08208e6			0.260624
$756$		0			0
$757$	−1.96889e7			−1.24877			−0.624384	−	0.781118i	$-0.714650\pi$
$757$	−1.96889e7			−1.24877			−0.624384	+	0.781118i	$0.714650\pi$
$758$	−212888.	+	368733.i	−0.0134579	+	0.0233098i
$759$	2.72000e6	+	4.71118e6i	0.171382	+	0.296842i
$760$	−778240.	−	1.34795e6i	−0.0488742	−	0.0846526i
$761$	1.41040e7	−	2.44288e7i	0.882835	−	1.52911i	0.0346592	−	0.999399i	$-0.488965\pi$
$761$	1.41040e7	−	2.44288e7i	0.882835	−	1.52911i	0.848175	−	0.529715i	$-0.177701\pi$
$762$	−3.09427e6			−0.193051
$763$		0			0
$764$	1.09286e6			0.0677381
$765$	1.09727e6	−	1.90053e6i	0.0677891	−	0.117414i
$766$	4.01269e6	+	6.95018e6i	0.247095	+	0.427981i
$767$	−4.06543e6	−	7.04153e6i	−0.249527	−	0.432194i
$768$	−262144.	+	454047.i	−0.0160375	+	0.0277778i
$769$	−1.38081e6			−0.0842009			−0.0421005	−	0.999113i	$-0.513405\pi$
$769$	−1.38081e6			−0.0842009			−0.0421005	+	0.999113i	$0.513405\pi$
$770$		0			0
$771$	2.61326e6			0.158324
$772$	−2.82203e6	+	4.88790e6i	−0.170419	+	0.295175i
$773$	7.71736e6	+	1.33669e7i	0.464537	+	0.804601i	0.999181	−	0.0404762i	$-0.0128875\pi$
$773$	7.71736e6	+	1.33669e7i	0.464537	+	0.804601i	−0.534644	+	0.845078i	$0.679554\pi$
$774$	2.90266e6	+	5.02756e6i	0.174158	+	0.301651i
$775$	1.33947e7	−	2.32003e7i	0.801085	−	1.38752i
$776$	1.32160e6			0.0787854
$777$		0			0
$778$	−2.73601e6			−0.162057
$779$	1.77220e7	−	3.06954e7i	1.04633	−	1.81230i
$780$	188160.	+	325903.i	0.0110737	+	0.0191801i
$781$	6.27640e6	+	1.08710e7i	0.368199	+	0.637740i
$782$	−4.90400e6	+	8.49398e6i	−0.286770	+	0.496700i
$783$	2.27745e7			1.32753
$784$		0			0
$785$	2.93546e6			0.170021
$786$	−2.14989e6	+	3.72372e6i	−0.124125	+	0.214991i
$787$	3.55054e6	+	6.14971e6i	0.204342	+	0.353930i	0.949923	−	0.312485i	$-0.101161\pi$
$787$	3.55054e6	+	6.14971e6i	0.204342	+	0.353930i	−0.745581	+	0.666415i	$0.767828\pi$
$788$	−1.57586e6	−	2.72946e6i	−0.0904068	−	0.156589i
$789$	139680.	−	241933.i	0.00798807	−	0.0138357i
$790$	−2.59008e6			−0.147654
$791$		0			0
$792$	3.89504e6			0.220647
$793$	5.04769e6	−	8.74285e6i	0.285042	−	0.493708i
$794$	445740.	+	772044.i	0.0250917	+	0.0434601i
$795$	585360.	+	1.01387e6i	0.0328477	+	0.0568939i
$796$	8.83136e6	−	1.52964e7i	0.494020	−	0.855669i
$797$	6.48182e6			0.361452			0.180726	−	0.983533i	$-0.442155\pi$
$797$	6.48182e6			0.361452			0.180726	+	0.983533i	$0.442155\pi$
$798$		0			0
$799$	−382512.			−0.0211972
$800$	1.54880e6	−	2.68260e6i	0.0855599	−	0.148194i
$801$	−730857.	−	1.26588e6i	−0.0402486	−	0.0697127i
$802$	−3.80144e6	−	6.58429e6i	−0.208695	−	0.361471i
$803$	−1.04921e7	+	1.81728e7i	−0.574212	+	0.994564i
$804$	1.57645e6			0.0860081
$805$		0			0
$806$	−1.04147e7			−0.564686
$807$	−2.86583e6	+	4.96377e6i	−0.154906	+	0.268304i
$808$	−5.96000e6	−	1.03230e7i	−0.321157	−	0.556261i
$809$	−8.02889e6	−	1.39065e7i	−0.431305	−	0.747042i	0.565681	−	0.824624i	$-0.308613\pi$
$809$	−8.02889e6	−	1.39065e7i	−0.431305	−	0.747042i	−0.996986	+	0.0775821i	$0.975280\pi$
$810$	−329780.	+	571196.i	−0.0176609	+	0.0305895i
$811$	4.84775e6			0.258814			0.129407	−	0.991592i	$-0.458693\pi$
$811$	4.84775e6			0.258814			0.129407	+	0.991592i	$0.458693\pi$
$812$		0			0
$813$	−7.62701e6			−0.404695
$814$	6.24376e6	−	1.08145e7i	0.330282	−	0.572066i
$815$	1.58558e6	+	2.74631e6i	0.0836169	+	0.144829i
$816$	−1.25542e6	−	2.17446e6i	−0.0660032	−	0.114321i
$817$	−9.85933e6	+	1.70769e7i	−0.516764	+	0.895061i
$818$	7.10862e6			0.371451
$819$		0			0
$820$	−2.33184e6			−0.121106
$821$	−1.08988e7	+	1.88773e7i	−0.564314	+	0.977421i	0.432799	+	0.901490i	$0.357526\pi$
$821$	−1.08988e7	+	1.88773e7i	−0.564314	+	0.977421i	−0.997113	+	0.0759303i	$0.975807\pi$
$822$	4.71459e6	+	8.16591e6i	0.243369	+	0.421527i
$823$	−1.60103e7	−	2.77307e7i	−0.823948	−	1.42712i	−0.902721	−	0.430227i	$-0.858433\pi$
$823$	−1.60103e7	−	2.77307e7i	−0.823948	−	1.42712i	0.0787724	−	0.996893i	$-0.474900\pi$
$824$	1.92205e6	−	3.32908e6i	0.0986157	−	0.170807i
$825$	8.22800e6			0.420881
$826$		0			0
$827$	2.19008e7			1.11352			0.556758	−	0.830675i	$-0.312045\pi$
$827$	2.19008e7			1.11352			0.556758	+	0.830675i	$0.312045\pi$
$828$	2.86400e6	−	4.96059e6i	0.145177	−	0.251454i
$829$	7.29997e6	+	1.26439e7i	0.368922	+	0.638992i	0.989397	−	0.145234i	$-0.0463936\pi$
$829$	7.29997e6	+	1.26439e7i	0.368922	+	0.638992i	−0.620475	+	0.784226i	$0.713060\pi$
$830$	1.54112e6	+	2.66930e6i	0.0776500	+	0.134494i
$831$	7.38916e6	−	1.27984e7i	0.371187	−	0.642914i
$832$	−1.20422e6			−0.0603113
$833$		0			0
$834$	1.00782e7			0.501728
$835$	−707840.	+	1.22601e6i	−0.0351333	+	0.0608527i
$836$	6.61504e6	+	1.14576e7i	0.327353	+	0.566993i
$837$	1.49489e7	+	2.58923e7i	0.737558	+	1.27749i
$838$	−56112.0	+	97188.8i	−0.00276023	+	0.00478086i
$839$	4.60947e6			0.226072			0.113036	−	0.993591i	$-0.463942\pi$
$839$	4.60947e6			0.226072			0.113036	+	0.993591i	$0.463942\pi$
$840$		0			0
$841$	2.49974e7			1.21872
$842$	5.41794e6	−	9.38415e6i	0.263363	−	0.456157i
$843$	7.98402e6	+	1.38287e7i	0.386948	+	0.670214i
$844$	827552.	+	1.43336e6i	0.0399889	+	0.0692628i
$845$	1.42428e6	−	2.46693e6i	0.0686207	−	0.118855i
$846$	223392.			0.0107310
$847$		0			0
$848$	−3.74630e6			−0.178901
$849$	−936352.	+	1.62181e6i	−0.0445831	+	0.0772201i
$850$	7.41730e6	+	1.28471e7i	0.352126	+	0.609901i
$851$	−9.18200e6	−	1.59037e7i	−0.434624	−	0.752790i
$852$	−2.36288e6	+	4.09263e6i	−0.111517	+	0.193154i
$853$	−1.98437e7			−0.933793			−0.466897	−	0.884312i	$-0.654628\pi$
$853$	−1.98437e7			−0.933793			−0.466897	+	0.884312i	$0.654628\pi$
$854$		0			0
$855$	−4.35328e6			−0.203658
$856$	−1.53254e6	+	2.65444e6i	−0.0714872	+	0.123820i
$857$	614799.	+	1.06486e6i	0.0285944	+	0.0495270i	0.879968	−	0.475032i	$-0.157564\pi$
$857$	614799.	+	1.06486e6i	0.0285944	+	0.0495270i	−0.851374	+	0.524559i	$0.824230\pi$
$858$	−1.59936e6	−	2.77017e6i	−0.0741700	−	0.128466i
$859$	−1.66520e7	+	2.88422e7i	−0.769989	+	1.33366i	0.167580	+	0.985859i	$0.446405\pi$
$859$	−1.66520e7	+	2.88422e7i	−0.769989	+	1.33366i	−0.937568	+	0.347801i	$0.886928\pi$
$860$	1.29728e6			0.0598119
$861$		0			0
$862$	2.21559e7			1.01560
$863$	1.18308e7	−	2.04915e7i	0.540738	−	0.936586i	−0.458124	−	0.888888i	$-0.651478\pi$
$863$	1.18308e7	−	2.04915e7i	0.540738	−	0.936586i	0.998862	−	0.0476972i	$-0.0151883\pi$
$864$	1.72851e6	+	2.99387e6i	0.0787749	+	0.136442i
$865$	356110.	+	616801.i	0.0161824	+	0.0280288i
$866$	1.73659e6	−	3.00786e6i	0.0786868	−	0.136290i
$867$	665752.			0.0300791
$868$		0			0
$869$	2.20157e7			0.988969
$870$	1.07936e6	−	1.86951e6i	0.0483469	−	0.0837392i
$871$	1.81045e6	+	3.13579e6i	0.0808615	+	0.140056i
$872$	−707264.	−	1.22502e6i	−0.0314985	−	0.0545571i
$873$	1.84818e6	−	3.20113e6i	0.0820744	−	0.142157i
$874$	1.94560e7			0.861539
$875$		0			0
$876$	−7.89990e6			−0.347826
$877$	1.18906e7	−	2.05952e7i	0.522042	−	0.904203i	−0.477629	−	0.878562i	$-0.658504\pi$
$877$	1.18906e7	−	2.05952e7i	0.522042	−	0.904203i	0.999671	−	0.0256419i	$-0.00816296\pi$
$878$	2.27534e6	+	3.94101e6i	0.0996118	+	0.172533i
$879$	1.00032e7	+	1.73261e7i	0.436685	+	0.756360i
$880$	435200.	−	753789.i	0.0189445	−	0.0328128i
$881$	−1.41871e7			−0.615818			−0.307909	−	0.951416i	$-0.599629\pi$
$881$	−1.41871e7			−0.615818			−0.307909	+	0.951416i	$0.599629\pi$
$882$		0			0
$883$	2.09281e7			0.903293			0.451647	−	0.892197i	$-0.350837\pi$
$883$	2.09281e7			0.903293			0.451647	+	0.892197i	$0.350837\pi$
$884$	2.88355e6	−	4.99446e6i	0.124107	−	0.214960i
$885$	1.10624e6	+	1.91606e6i	0.0474779	+	0.0822341i
$886$	−3.50798e6	−	6.07599e6i	−0.150132	−	0.260036i
$887$	3.99293e6	−	6.91595e6i	0.170405	−	0.295150i	−0.768156	−	0.640262i	$-0.778826\pi$
$887$	3.99293e6	−	6.91595e6i	0.170405	−	0.295150i	0.938562	+	0.345112i	$0.112159\pi$
$888$	4.70118e6			0.200067
$889$		0			0
$890$	−326640.			−0.0138227
$891$	2.80313e6	−	4.85516e6i	0.118290	−	0.204885i
$892$	−2.45862e6	−	4.25846e6i	−0.103462	−	0.179201i
$893$	379392.	+	657126.i	0.0159206	+	0.0275753i
$894$	−1.81795e6	+	3.14879e6i	−0.0760744	+	0.131765i
$895$	4.85628e6			0.202650
$896$		0			0
$897$	−4.70400e6			−0.195203
$898$	−4.83348e6	+	8.37183e6i	−0.200018	+	0.346441i
$899$	2.98713e7	+	5.17386e7i	1.23269	+	2.13509i
$900$	−4.33180e6	−	7.50290e6i	−0.178263	−	0.308761i
$901$	8.97064e6	−	1.55376e7i	0.368139	−	0.637635i
$902$	1.98206e7			0.811150
$903$		0			0
$904$	−1.56835e7			−0.638294
$905$	−3.28545e6	+	5.69057e6i	−0.133344	+	0.230959i
$906$	−6.53133e6	−	1.13126e7i	−0.264351	−	0.457869i
$907$	1.15930e7	+	2.00797e7i	0.467928	+	0.810475i	0.999328	−	0.0366458i	$-0.0116673\pi$
$907$	1.15930e7	+	2.00797e7i	0.467928	+	0.810475i	−0.531400	+	0.847121i	$0.678334\pi$
$908$	7.13434e6	−	1.23570e7i	0.287170	−	0.497393i
$909$	−3.33388e7			−1.33826
$910$		0			0
$911$	1.65299e7			0.659895			0.329948	−	0.943999i	$-0.392969\pi$
$911$	1.65299e7			0.659895			0.329948	+	0.943999i	$0.392969\pi$
$912$	−2.49037e6	+	4.31344e6i	−0.0991463	+	0.171726i
$913$	−1.30995e7	−	2.26890e7i	−0.520090	−	0.900822i
$914$	254860.	+	441430.i	0.0100910	+	0.0174782i
$915$	−1.37352e6	+	2.37901e6i	−0.0542353	+	0.0939383i
$916$	4.42730e6			0.174341
$917$		0			0
$918$	−1.65559e7			−0.648405
$919$	−6.40435e6	+	1.10927e7i	−0.250142	+	0.433258i	−0.963565	−	0.267476i	$-0.913811\pi$
$919$	−6.40435e6	+	1.10927e7i	−0.250142	+	0.433258i	0.713423	+	0.700734i	$0.247144\pi$
$920$	−640000.	−	1.10851e6i	−0.0249293	−	0.0431788i
$921$	−9.36813e6	−	1.62261e7i	−0.363918	−	0.630325i
$922$	256396.	−	444091.i	0.00993308	−	0.0172046i
$923$	−1.08545e7			−0.419377
$924$		0			0
$925$	−2.77756e7			−1.06735
$926$	8.03306e6	−	1.39137e7i	0.307860	−	0.533229i
$927$	−5.37573e6	−	9.31103e6i	−0.205465	−	0.355876i
$928$	3.45395e6	+	5.98242e6i	0.131658	+	0.228038i
$929$	−1.48659e7	+	2.57486e7i	−0.565136	+	0.978844i	0.431901	+	0.901921i	$0.357843\pi$
$929$	−1.48659e7	+	2.57486e7i	−0.565136	+	0.978844i	−0.997037	+	0.0769231i	$0.975490\pi$
$930$	2.83392e6			0.107444
$931$		0			0
$932$	2.36709e7			0.892639
$933$	652256.	−	1.12974e6i	0.0245309	−	0.0424888i
$934$	−1.73449e7	−	3.00423e7i	−0.650587	−	1.12685i
$935$	2.08420e6	+	3.60994e6i	0.0779669	+	0.135043i
$936$	−1.68403e6	+	2.91683e6i	−0.0628291	+	0.108823i
$937$	1.10970e7			0.412911			0.206456	−	0.978456i	$-0.433807\pi$
$937$	1.10970e7			0.412911			0.206456	+	0.978456i	$0.433807\pi$
$938$		0			0
$939$	1.39172e7			0.515096
$940$	24960.0	−	43232.0i	0.000921351	−	0.00159583i
$941$	−1.87157e7	−	3.24165e7i	−0.689019	−	1.19342i	−0.972155	−	0.234337i	$-0.924708\pi$
$941$	−1.87157e7	−	3.24165e7i	−0.689019	−	1.19342i	0.283136	−	0.959080i	$-0.408625\pi$
$942$	−4.69674e6	−	8.13499e6i	−0.172452	−	0.298696i
$943$	1.45740e7	−	2.52429e7i	0.533703	−	0.924400i
$944$	−7.07994e6			−0.258583
$945$		0			0
$946$	−1.10269e7			−0.400613
$947$	−7.54536e6	+	1.30690e7i	−0.273404	+	0.473550i	−0.969731	−	0.244175i	$-0.921483\pi$
$947$	−7.54536e6	+	1.30690e7i	−0.273404	+	0.473550i	0.696327	+	0.717725i	$0.254816\pi$
$948$	4.14413e6	+	7.17784e6i	0.149766	+	0.259402i
$949$	−9.07255e6	−	1.57141e7i	−0.327012	−	0.566401i
$950$	1.47136e7	−	2.54847e7i	0.528944	−	0.916158i
$951$	−1.43817e7			−0.515655
$952$		0			0
$953$	−2.15741e7			−0.769484			−0.384742	−	0.923024i	$-0.625710\pi$
$953$	−2.15741e7			−0.769484			−0.384742	+	0.923024i	$0.625710\pi$
$954$	−5.23897e6	+	9.07417e6i	−0.186370	+	0.322802i
$955$	−341520.	−	591530.i	−0.0121174	−	0.0209879i
$956$	−8.00275e6	−	1.38612e7i	−0.283201	−	0.490518i
$957$	−9.17456e6	+	1.58908e7i	−0.323821	+	0.560875i
$958$	3.31579e7			1.16727
$959$		0			0
$960$	327680.			0.0114755
$961$	−2.48998e7	+	4.31277e7i	−0.869736	+	1.50643i
$962$	5.39902e6	+	9.35137e6i	0.188095	+	0.325790i
$963$	4.28633e6	+	7.42415e6i	0.148943	+	0.257977i
$964$	−1.08666e7	+	1.88216e7i	−0.376619	+	0.652324i
$965$	3.52754e6			0.121942
$966$		0			0
$967$	−3.29467e7			−1.13304			−0.566520	−	0.824048i	$-0.691711\pi$
$967$	−3.29467e7			−1.13304			−0.566520	+	0.824048i	$0.691711\pi$
$968$	1.45443e6	−	2.51915e6i	0.0498890	−	0.0864103i
$969$	−1.19265e7	−	2.06574e7i	−0.408042	−	0.706749i
$970$	−413000.	−	715337.i	−0.0140936	−	0.0244108i
$971$	−1.12300e7	+	1.94509e7i	−0.382235	+	0.662051i	−0.991381	−	0.131007i	$-0.958179\pi$
$971$	−1.12300e7	+	1.94509e7i	−0.382235	+	0.662051i	0.609146	+	0.793058i	$0.291512\pi$
$972$	1.52365e7			0.517272
$973$		0			0
$974$	−3.56708e7			−1.20480
$975$	−3.55740e6	+	6.16160e6i	−0.119845	+	0.207578i
$976$	−4.39526e6	−	7.61282e6i	−0.147693	−	0.255812i
$977$	2.58118e7	+	4.47074e7i	0.865132	+	1.49845i	0.866916	+	0.498454i	$0.166099\pi$
$977$	2.58118e7	+	4.47074e7i	0.865132	+	1.49845i	−0.00178448	+	0.999998i	$0.500568\pi$
$978$	5.07386e6	−	8.78818e6i	0.169625	−	0.293800i
$979$	2.77644e6			0.0925831
$980$		0			0
$981$	−3.95626e6			−0.131254
$982$	1.14307e7	−	1.97986e7i	0.378265	−	0.655174i
$983$	5.51009e6	+	9.54375e6i	0.181876	+	0.315018i	0.942519	−	0.334152i	$-0.108450\pi$
$983$	5.51009e6	+	9.54375e6i	0.181876	+	0.315018i	−0.760644	+	0.649170i	$0.775116\pi$
$984$	3.73094e6	+	6.46218e6i	0.122838	+	0.212761i
$985$	−984910.	+	1.70591e6i	−0.0323449	+	0.0560230i
$986$	−3.30824e7			−1.08369
$987$		0			0
$988$	−1.14401e7			−0.372854
$989$	−8.10800e6	+	1.40435e7i	−0.263586	+	0.456545i
$990$	−1.21720e6	−	2.10825e6i	−0.0394706	−	0.0683651i
$991$	−1.60514e7	−	2.78019e7i	−0.519194	−	0.899270i	−0.999751	−	0.0223070i	$-0.992899\pi$
$991$	−1.60514e7	−	2.78019e7i	−0.519194	−	0.899270i	0.480557	−	0.876963i	$-0.340434\pi$
$992$	−4.53427e6	+	7.85359e6i	−0.146295	+	0.253390i
$993$	−1.98033e7			−0.637330
$994$		0			0
$995$	−1.10392e7			−0.353492
$996$	4.93158e6	−	8.54175e6i	0.157521	−	0.272834i
$997$	−1.40886e7	−	2.44022e7i	−0.448879	−	0.777482i	0.549434	−	0.835537i	$-0.314843\pi$
$997$	−1.40886e7	−	2.44022e7i	−0.448879	−	0.777482i	−0.998313	+	0.0580553i	$0.981510\pi$
$998$	−250232.	−	433415.i	−0.00795273	−	0.0137745i
$999$	1.54992e7	−	2.68454e7i	0.491356	−	0.851053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.6.c.a.79.1		2
7.2	even	3		14.6.a.b.1.1	✓	1
7.3	odd	6		98.6.c.b.67.1		2
7.4	even	3	inner	98.6.c.a.67.1		2
7.5	odd	6		98.6.a.b.1.1		1
7.6	odd	2		98.6.c.b.79.1		2
21.2	odd	6		126.6.a.c.1.1		1
21.5	even	6		882.6.a.g.1.1		1
28.19	even	6		784.6.a.h.1.1		1
28.23	odd	6		112.6.a.d.1.1		1
35.2	odd	12		350.6.c.f.99.2		2
35.9	even	6		350.6.a.b.1.1		1
35.23	odd	12		350.6.c.f.99.1		2
56.37	even	6		448.6.a.f.1.1		1
56.51	odd	6		448.6.a.k.1.1		1
84.23	even	6		1008.6.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.6.a.b.1.1	✓	1	7.2	even	3
98.6.a.b.1.1		1	7.5	odd	6
98.6.c.a.67.1		2	7.4	even	3	inner
98.6.c.a.79.1		2	1.1	even	1	trivial
98.6.c.b.67.1		2	7.3	odd	6
98.6.c.b.79.1		2	7.6	odd	2
112.6.a.d.1.1		1	28.23	odd	6
126.6.a.c.1.1		1	21.2	odd	6
350.6.a.b.1.1		1	35.9	even	6
350.6.c.f.99.1		2	35.23	odd	12
350.6.c.f.99.2		2	35.2	odd	12
448.6.a.f.1.1		1	56.37	even	6
448.6.a.k.1.1		1	56.51	odd	6
784.6.a.h.1.1		1	28.19	even	6
882.6.a.g.1.1		1	21.5	even	6
1008.6.a.n.1.1		1	84.23	even	6

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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 3.46410i) q^{2} +(-4.00000 - 6.92820i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-5.00000 + 8.66025i) q^{5} +32.0000 q^{6} +64.0000 q^{8} +(89.5000 - 155.019i) q^{9} +(-20.0000 - 34.6410i) q^{10} +(170.000 + 294.449i) q^{11} +(-64.0000 + 110.851i) q^{12} -294.000 q^{13} +80.0000 q^{15} +(-128.000 + 221.703i) q^{16} +(-613.000 - 1061.75i) q^{17} +(358.000 + 620.074i) q^{18} +(-1216.00 + 2106.17i) q^{19} +160.000 q^{20} -1360.00 q^{22} +(-1000.00 + 1732.05i) q^{23} +(-256.000 - 443.405i) q^{24} +(1512.50 + 2619.73i) q^{25} +(588.000 - 1018.45i) q^{26} -3376.00 q^{27} -6746.00 q^{29} +(-160.000 + 277.128i) q^{30} +(-4428.00 - 7669.52i) q^{31} +(-512.000 - 886.810i) q^{32} +(1360.00 - 2355.59i) q^{33} +4904.00 q^{34} -2864.00 q^{36} +(-4591.00 + 7951.85i) q^{37} +(-4864.00 - 8424.70i) q^{38} +(1176.00 + 2036.89i) q^{39} +(-320.000 + 554.256i) q^{40} -14574.0 q^{41} +8108.00 q^{43} +(2720.00 - 4711.18i) q^{44} +(895.000 + 1550.19i) q^{45} +(-4000.00 - 6928.20i) q^{46} +(156.000 - 270.200i) q^{47} +2048.00 q^{48} -12100.0 q^{50} +(-4904.00 + 8493.98i) q^{51} +(2352.00 + 4073.78i) q^{52} +(7317.00 + 12673.4i) q^{53} +(6752.00 - 11694.8i) q^{54} -3400.00 q^{55} +19456.0 q^{57} +(13492.0 - 23368.8i) q^{58} +(13828.0 + 23950.8i) q^{59} +(-640.000 - 1108.51i) q^{60} +(-17169.0 + 29737.6i) q^{61} +35424.0 q^{62} +4096.00 q^{64} +(1470.00 - 2546.11i) q^{65} +(5440.00 + 9422.36i) q^{66} +(-6158.00 - 10666.0i) q^{67} +(-9808.00 + 16988.0i) q^{68} +16000.0 q^{69} +36920.0 q^{71} +(5728.00 - 9921.19i) q^{72} +(30859.0 + 53449.4i) q^{73} +(-18364.0 - 31807.4i) q^{74} +(12100.0 - 20957.8i) q^{75} +38912.0 q^{76} -9408.00 q^{78} +(32376.0 - 56076.9i) q^{79} +(-1280.00 - 2217.03i) q^{80} +(-8244.50 - 14279.9i) q^{81} +(29148.0 - 50485.8i) q^{82} -77056.0 q^{83} +12260.0 q^{85} +(-16216.0 + 28086.9i) q^{86} +(26984.0 + 46737.7i) q^{87} +(10880.0 + 18844.7i) q^{88} +(4083.00 - 7071.96i) q^{89} -7160.00 q^{90} +32000.0 q^{92} +(-35424.0 + 61356.2i) q^{93} +(624.000 + 1080.80i) q^{94} +(-12160.0 - 21061.7i) q^{95} +(-4096.00 + 7094.48i) q^{96} +20650.0 q^{97} +60860.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 8 q^{3} - 16 q^{4} - 10 q^{5} + 64 q^{6} + 128 q^{8} + 179 q^{9} - 40 q^{10} + 340 q^{11} - 128 q^{12} - 588 q^{13} + 160 q^{15} - 256 q^{16} - 1226 q^{17} + 716 q^{18} - 2432 q^{19} + 320 q^{20}+ \cdots + 121720 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 8 * q^3 - 16 * q^4 - 10 * q^5 + 64 * q^6 + 128 * q^8 + 179 * q^9 - 40 * q^10 + 340 * q^11 - 128 * q^12 - 588 * q^13 + 160 * q^15 - 256 * q^16 - 1226 * q^17 + 716 * q^18 - 2432 * q^19 + 320 * q^20 - 2720 * q^22 - 2000 * q^23 - 512 * q^24 + 3025 * q^25 + 1176 * q^26 - 6752 * q^27 - 13492 * q^29 - 320 * q^30 - 8856 * q^31 - 1024 * q^32 + 2720 * q^33 + 9808 * q^34 - 5728 * q^36 - 9182 * q^37 - 9728 * q^38 + 2352 * q^39 - 640 * q^40 - 29148 * q^41 + 16216 * q^43 + 5440 * q^44 + 1790 * q^45 - 8000 * q^46 + 312 * q^47 + 4096 * q^48 - 24200 * q^50 - 9808 * q^51 + 4704 * q^52 + 14634 * q^53 + 13504 * q^54 - 6800 * q^55 + 38912 * q^57 + 26984 * q^58 + 27656 * q^59 - 1280 * q^60 - 34338 * q^61 + 70848 * q^62 + 8192 * q^64 + 2940 * q^65 + 10880 * q^66 - 12316 * q^67 - 19616 * q^68 + 32000 * q^69 + 73840 * q^71 + 11456 * q^72 + 61718 * q^73 - 36728 * q^74 + 24200 * q^75 + 77824 * q^76 - 18816 * q^78 + 64752 * q^79 - 2560 * q^80 - 16489 * q^81 + 58296 * q^82 - 154112 * q^83 + 24520 * q^85 - 32432 * q^86 + 53968 * q^87 + 21760 * q^88 + 8166 * q^89 - 14320 * q^90 + 64000 * q^92 - 70848 * q^93 + 1248 * q^94 - 24320 * q^95 - 8192 * q^96 + 41300 * q^97 + 121720 * q^99

Introduction

L-functions

Modular forms

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Database

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