LMFDB - Embedded newform 98.6.c.b.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.b.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	0.965329	−	0.261037i	$-0.0840643\pi$
$3$	4.00000	+	6.92820i	0.256600	+	0.444444i	−0.708729	+	0.705481i	$0.750731\pi$
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	5.00000	−	8.66025i	0.0894427	−	0.154919i	−0.817833	−	0.575456i	$-0.804825\pi$
$5$	5.00000	−	8.66025i	0.0894427	−	0.154919i	0.907276	+	0.420536i	$0.138158\pi$
$6$	−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	$-0.422444\pi$
$13$	294.000			0.482491			0.241245	+	0.970464i	$0.422444\pi$
$14$		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	$0.00533502\pi$
$17$	613.000	+	1061.75i	0.514444	+	0.891043i	−0.485415	+	0.874284i	$0.661332\pi$
$18$	358.000	+	620.074i	0.260436	+	0.451089i
$19$	1216.00	−	2106.17i	0.772769	−	1.33847i	−0.163271	−	0.986581i	$-0.552205\pi$
$19$	1216.00	−	2106.17i	0.772769	−	1.33847i	0.936040	−	0.351894i	$-0.114462\pi$
$20$	−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	$0.143609\pi$
$31$	4428.00	+	7669.52i	0.827567	+	1.43339i	−0.0723738	+	0.997378i	$0.523057\pi$
$32$	−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	$-0.263279\pi$
$41$	14574.0			1.35400			0.677001	+	0.735982i	$0.263279\pi$
$42$		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	−0.871130	−	0.491053i	$-0.836612\pi$
$47$	−156.000	+	270.200i	−0.0103010	+	0.0178419i	0.860829	+	0.508894i	$0.169946\pi$
$48$	−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	$-0.993654\pi$
$59$	−13828.0	−	23950.8i	−0.517165	−	0.895757i	0.482636	−	0.875821i	$-0.339679\pi$
$60$	−640.000	−	1108.51i	−0.0229510	−	0.0397523i
$61$	17169.0	−	29737.6i	0.590773	−	1.02325i	−0.403356	−	0.915043i	$-0.632156\pi$
$61$	17169.0	−	29737.6i	0.590773	−	1.02325i	0.994129	−	0.108205i	$-0.0345103\pi$
$62$	−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	$-0.929618\pi$
$73$	−30859.0	−	53449.4i	−0.677758	−	1.17391i	0.297896	−	0.954598i	$-0.403715\pi$
$74$	−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	$-0.289609\pi$
$83$	77056.0			1.22775			0.613877	+	0.789402i	$0.289609\pi$
$84$		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	−0.892051	−	0.451934i	$-0.850734\pi$
$89$	−4083.00	+	7071.96i	−0.0546392	+	0.0946379i	0.837412	+	0.546572i	$0.184068\pi$
$90$	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	$-0.535540\pi$
$97$	−20650.0			−0.222839			−0.111419	+	0.993773i	$0.535540\pi$
$98$		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	$0.196006\pi$
$101$	93125.0	+	161297.i	0.908370	+	1.57334i	0.0920418	+	0.995755i	$0.470661\pi$
$102$	−19616.0	−	33975.9i	−0.186685	−	0.323348i
$103$	−30032.0	+	52016.9i	−0.278927	+	0.483116i	−0.971118	−	0.238598i	$-0.923312\pi$
$103$	−30032.0	+	52016.9i	−0.278927	+	0.483116i	0.692191	+	0.721714i	$0.256646\pi$
$104$	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	−0.642765	−	0.766064i	$-0.722213\pi$
$131$	67184.0	−	116366.i	0.342048	−	0.592445i	0.984813	+	0.173619i	$0.0555460\pi$
$132$	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	$-0.742962\pi$
$139$	−314944.			−1.38260			−0.691300	+	0.722568i	$0.742962\pi$
$140$		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	0.999597	−	0.0283780i	$-0.00903422\pi$
$157$	146773.	+	254218.i	0.475223	+	0.823110i	−0.524375	+	0.851488i	$0.675701\pi$
$158$	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	$-0.562925\pi$
$167$	−141568.			−0.392802			−0.196401	+	0.980524i	$0.562925\pi$
$168$		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	−0.907706	−	0.419607i	$-0.862168\pi$
$173$	−35611.0	+	61680.1i	−0.0904626	+	0.156686i	0.817243	+	0.576293i	$0.195501\pi$
$174$	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	$-0.767749\pi$
$181$	−657090.			−1.49083			−0.745416	+	0.666600i	$0.767749\pi$
$182$		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	$-0.715944\pi$
$199$	−551960.	−	956023.i	−0.988041	−	1.71134i	−0.360486	−	0.932765i	$-0.617389\pi$
$200$	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	$-0.566345\pi$
$223$	−307328.			−0.413847			−0.206924	+	0.978357i	$0.566345\pi$
$224$		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	$-0.971925\pi$
$227$	−445896.	−	772315.i	−0.574340	−	0.994786i	0.421773	−	0.906701i	$-0.361408\pi$
$228$	−155648.	−	269590.i	−0.198293	−	0.343453i
$229$	138353.	−	239634.i	0.174341	−	0.301968i	−0.765592	−	0.643327i	$-0.777554\pi$
$229$	138353.	−	239634.i	0.174341	−	0.301968i	0.939933	+	0.341359i	$0.110887\pi$
$230$	−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	$0.104843\pi$
$241$	679165.	+	1.17635e6i	0.753239	+	1.30465i	−0.193006	+	0.981198i	$0.561824\pi$
$242$	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	$-0.471674\pi$
$251$	177408.			0.177742			0.0888708	+	0.996043i	$0.471674\pi$
$252$		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	−0.778534	−	0.627602i	$-0.784037\pi$
$257$	163329.	−	282894.i	0.154252	−	0.267172i	0.932786	+	0.360430i	$0.117370\pi$
$258$	−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	0.976553	−	0.215276i	$-0.0690651\pi$
$269$	358229.	+	620471.i	0.301842	+	0.522806i	−0.674711	+	0.738082i	$0.735732\pi$
$270$	67520.0	+	116948.i	0.0563668	+	0.0976301i
$271$	−476688.	+	825648.i	−0.394286	+	0.682923i	−0.993010	−	0.118033i	$-0.962341\pi$
$271$	−476688.	+	825648.i	−0.394286	+	0.682923i	0.598724	+	0.800955i	$0.295675\pi$
$272$	−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	0.906188	−	0.422876i	$-0.138979\pi$
$283$	117044.	+	202726.i	0.0868726	+	0.150468i	−0.819315	+	0.573344i	$0.805646\pi$
$284$	−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	$-0.176054\pi$
$293$	2.50081e6			1.70181			0.850905	+	0.525320i	$0.176054\pi$
$294$		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	$-0.750905\pi$
$307$	−2.34203e6			−1.41823			−0.709115	+	0.705092i	$0.750905\pi$
$308$		0			0
$309$	−480512.			−0.286291
$310$	−177120.	+	306781.i	−0.104680	+	0.181311i
$311$	−81532.0	−	141218.i	−0.0477999	−	0.0827919i	0.841136	−	0.540824i	$-0.181888\pi$
$311$	−81532.0	−	141218.i	−0.0477999	−	0.0827919i	−0.888935	+	0.458033i	$0.848554\pi$
$312$	75264.0	+	130361.i	0.0437724	+	0.0758161i
$313$	869825.	−	1.50658e6i	0.501847	−	0.869224i	−0.498151	−	0.867090i	$-0.665988\pi$
$313$	869825.	−	1.50658e6i	0.501847	−	0.869224i	0.999998	−	0.00213366i	$-0.000679165\pi$
$314$	−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	$-0.762591\pi$
$349$	−3.34268e6			−1.46903			−0.734516	+	0.678591i	$0.762591\pi$
$350$		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	$-0.869205\pi$
$353$	−1.88303e6	−	3.26151e6i	−0.804305	−	1.39310i	0.112454	−	0.993657i	$-0.464129\pi$
$354$	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	0.770677	−	0.637226i	$-0.219918\pi$
$367$	−429656.	−	744186.i	−0.166516	−	0.288414i	−0.937193	+	0.348812i	$0.886585\pi$
$368$	−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	−0.986151	−	0.165851i	$-0.946963\pi$
$383$	−1.00317e6	+	1.73754e6i	−0.349445	+	0.605256i	0.636706	+	0.771106i	$0.280296\pi$
$384$	−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	−0.883223	−	0.468954i	$-0.844631\pi$
$397$	−111435.	+	193011.i	−0.0354850	+	0.0614619i	0.847737	+	0.530416i	$0.177964\pi$
$398$	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	0.966947	−	0.254978i	$-0.0820683\pi$
$409$	888577.	+	1.53906e6i	0.262656	+	0.454933i	−0.704291	+	0.709911i	$0.748735\pi$
$410$	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	$-0.501243\pi$
$419$	−28056.0			−0.00780712			−0.00390356	+	0.999992i	$0.501243\pi$
$420$		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	$-0.464505\pi$
$433$	868294.			0.222560			0.111280	+	0.993789i	$0.464505\pi$
$434$		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	−0.927825	−	0.373015i	$-0.878324\pi$
$439$	−568836.	+	985253.i	−0.140872	+	0.243998i	0.786953	+	0.617013i	$0.211657\pi$
$440$	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	$-0.495528\pi$
$461$	128198.			0.0280950			0.0140475	+	0.999901i	$0.495528\pi$
$462$		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	$-0.461466\pi$
$467$	4.33623e6	−	7.51057e6i	0.920069	−	1.59361i	0.799306	−	0.600925i	$-0.205201\pi$
$468$	−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	$0.142376\pi$
$479$	4.14473e6	+	7.17889e6i	0.825387	+	1.42961i	−0.0762360	+	0.997090i	$0.524290\pi$
$480$	−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	$-0.421481\pi$
$503$	2.77116e6			0.488362			0.244181	+	0.969730i	$0.421481\pi$
$504$		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	−0.871890	−	0.489702i	$-0.837106\pi$
$509$	−69267.0	+	119974.i	−0.0118504	+	0.0205254i	0.860039	+	0.510228i	$0.170439\pi$
$510$	−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	0.784067	−	0.620676i	$-0.213142\pi$
$521$	−901407.	−	1.56128e6i	−0.145488	−	0.251992i	−0.929555	+	0.368684i	$0.879808\pi$
$522$	−2.41507e6	−	4.18302e6i	−0.387930	−	0.671914i
$523$	4.88624e6	−	8.46321e6i	0.781124	−	1.35295i	−0.150163	−	0.988661i	$-0.547980\pi$
$523$	4.88624e6	−	8.46321e6i	0.781124	−	1.35295i	0.931287	−	0.364286i	$-0.118687\pi$
$524$	−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	0.960123	−	0.279576i	$-0.0901940\pi$
$563$	1.78954e6	+	3.09957e6i	0.237942	+	0.412127i	−0.722182	+	0.691703i	$0.756861\pi$
$564$	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	$-0.779728\pi$
$577$	−7.49804e6	−	1.29870e7i	−0.937580	−	1.62394i	−0.167612	−	0.985853i	$-0.553605\pi$
$578$	−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	$-0.436808\pi$
$587$	3.29291e6			0.394444			0.197222	+	0.980359i	$0.436808\pi$
$588$		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	$0.408379\pi$
$593$	−5.89542e6	+	1.02112e7i	−0.688459	+	1.19245i	−0.972336	+	0.233586i	$0.924954\pi$
$594$	−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	$-0.308699\pi$
$601$	1.00142e7			1.13092			0.565458	+	0.824777i	$0.308699\pi$
$602$		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	$-0.601936\pi$
$607$	6.03298e6	−	1.04494e7i	0.664599	−	1.15112i	0.979394	−	0.201960i	$-0.0647311\pi$
$608$	−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	0.572470	−	0.819926i	$-0.305985\pi$
$619$	−4.04045e6	−	6.99827e6i	−0.423841	−	0.734115i	−0.996311	+	0.0858108i	$0.972652\pi$
$620$	−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	$-0.567259\pi$
$643$	−4.39762e6			−0.419460			−0.209730	+	0.977759i	$0.567259\pi$
$644$		0			0
$645$	648640.			0.0613910
$646$	−5.96326e6	+	1.03287e7i	−0.562215	+	0.973786i
$647$	3.27698e6	+	5.67590e6i	0.307761	+	0.533058i	0.977872	−	0.209203i	$-0.0670869\pi$
$647$	3.27698e6	+	5.67590e6i	0.307761	+	0.533058i	−0.670111	+	0.742261i	$0.733754\pi$
$648$	−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	0.858330	−	0.513097i	$-0.171502\pi$
$661$	−170635.	−	295548.i	−0.0151902	−	0.0263103i	−0.873521	+	0.486787i	$0.838169\pi$
$662$	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	$-0.592255\pi$
$677$	8.19289e6	−	1.41905e7i	0.687014	−	1.18994i	0.972799	−	0.231649i	$-0.0744121\pi$
$678$	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	−0.796526	−	0.604604i	$-0.793331\pi$
$691$	1.57319e6	−	2.72485e6i	0.125339	−	0.217094i	0.921865	+	0.387510i	$0.126665\pi$
$692$	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	$0.375352\pi$
$719$	−8.45072e6	+	1.46371e7i	−0.609638	+	1.05592i	−0.991300	+	0.131621i	$0.957982\pi$
$720$	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	$-0.192818\pi$
$727$	2.34302e7			1.64414			0.822071	+	0.569384i	$0.192818\pi$
$728$		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	−0.848768	−	0.528766i	$-0.822655\pi$
$733$	487905.	−	845076.i	0.0335409	−	0.0580946i	0.882309	+	0.470671i	$0.155988\pi$
$734$	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	$0.511035\pi$
$761$	−1.41040e7	+	2.44288e7i	−0.882835	+	1.52911i	−0.848175	+	0.529715i	$0.822299\pi$
$762$	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	$-0.486595\pi$
$769$	1.38081e6			0.0842009			0.0421005	+	0.999113i	$0.486595\pi$
$770$		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	0.534644	−	0.845078i	$-0.320446\pi$
$773$	−7.71736e6	−	1.33669e7i	−0.464537	−	0.804601i	−0.999181	+	0.0404762i	$0.987113\pi$
$774$	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	0.745581	−	0.666415i	$-0.232172\pi$
$787$	−3.55054e6	−	6.14971e6i	−0.204342	−	0.353930i	−0.949923	+	0.312485i	$0.898839\pi$
$788$	−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	$-0.557845\pi$
$797$	−6.48182e6			−0.361452			−0.180726	+	0.983533i	$0.557845\pi$
$798$		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	$-0.541307\pi$
$811$	−4.84775e6			−0.258814			−0.129407	+	0.991592i	$0.541307\pi$
$812$		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	0.620475	−	0.784226i	$-0.286940\pi$
$829$	−7.29997e6	−	1.26439e7i	−0.368922	−	0.638992i	−0.989397	+	0.145234i	$0.953606\pi$
$830$	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	$-0.536058\pi$
$839$	−4.60947e6			−0.226072			−0.113036	+	0.993591i	$0.536058\pi$
$840$		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	$-0.345372\pi$
$853$	1.98437e7			0.933793			0.466897	+	0.884312i	$0.345372\pi$
$854$		0			0
$855$	−4.35328e6			−0.203658
$856$	−1.53254e6	+	2.65444e6i	−0.0714872	+	0.123820i
$857$	−614799.	−	1.06486e6i	−0.0285944	−	0.0495270i	0.851374	−	0.524559i	$-0.175770\pi$
$857$	−614799.	−	1.06486e6i	−0.0285944	−	0.0495270i	−0.879968	+	0.475032i	$0.842436\pi$
$858$	−1.59936e6	−	2.77017e6i	−0.0741700	−	0.128466i
$859$	1.66520e7	−	2.88422e7i	0.769989	−	1.33366i	−0.167580	−	0.985859i	$-0.553595\pi$
$859$	1.66520e7	−	2.88422e7i	0.769989	−	1.33366i	0.937568	−	0.347801i	$-0.113072\pi$
$860$	−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	$-0.400371\pi$
$881$	1.41871e7			0.615818			0.307909	+	0.951416i	$0.400371\pi$
$882$		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	−0.938562	−	0.345112i	$-0.887841\pi$
$887$	−3.99293e6	+	6.91595e6i	−0.170405	+	0.295150i	0.768156	+	0.640262i	$0.221174\pi$
$888$	−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	$-0.642157\pi$
$929$	1.48659e7	−	2.57486e7i	0.565136	−	0.978844i	0.997037	−	0.0769231i	$-0.0245096\pi$
$930$	−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	$-0.566193\pi$
$937$	−1.10970e7			−0.412911			−0.206456	+	0.978456i	$0.566193\pi$
$938$		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	$0.0752918\pi$
$941$	1.87157e7	+	3.24165e7i	0.689019	+	1.19342i	−0.283136	+	0.959080i	$0.591375\pi$
$942$	−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	−0.609146	−	0.793058i	$-0.708488\pi$
$971$	1.12300e7	−	1.94509e7i	0.382235	−	0.662051i	0.991381	+	0.131007i	$0.0418211\pi$
$972$	−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	0.760644	−	0.649170i	$-0.224884\pi$
$983$	−5.51009e6	−	9.54375e6i	−0.181876	−	0.315018i	−0.942519	+	0.334152i	$0.891550\pi$
$984$	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	0.998313	−	0.0580553i	$-0.0184900\pi$
$997$	1.40886e7	+	2.44022e7i	0.448879	+	0.777482i	−0.549434	+	0.835537i	$0.685157\pi$
$998$	−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.b.79.1		2
7.2	even	3		98.6.a.b.1.1		1
7.3	odd	6		98.6.c.a.67.1		2
7.4	even	3	inner	98.6.c.b.67.1		2
7.5	odd	6		14.6.a.b.1.1	✓	1
7.6	odd	2		98.6.c.a.79.1		2
21.2	odd	6		882.6.a.g.1.1		1
21.5	even	6		126.6.a.c.1.1		1
28.19	even	6		112.6.a.d.1.1		1
28.23	odd	6		784.6.a.h.1.1		1
35.12	even	12		350.6.c.f.99.2		2
35.19	odd	6		350.6.a.b.1.1		1
35.33	even	12		350.6.c.f.99.1		2
56.5	odd	6		448.6.a.f.1.1		1
56.19	even	6		448.6.a.k.1.1		1
84.47	odd	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	7.5	odd	6
98.6.a.b.1.1		1	7.2	even	3
98.6.c.a.67.1		2	7.3	odd	6
98.6.c.a.79.1		2	7.6	odd	2
98.6.c.b.67.1		2	7.4	even	3	inner
98.6.c.b.79.1		2	1.1	even	1	trivial
112.6.a.d.1.1		1	28.19	even	6
126.6.a.c.1.1		1	21.5	even	6
350.6.a.b.1.1		1	35.19	odd	6
350.6.c.f.99.1		2	35.33	even	12
350.6.c.f.99.2		2	35.12	even	12
448.6.a.f.1.1		1	56.5	odd	6
448.6.a.k.1.1		1	56.19	even	6
784.6.a.h.1.1		1	28.23	odd	6
882.6.a.g.1.1		1	21.2	odd	6
1008.6.a.n.1.1		1	84.47	odd	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

Varieties

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Representations

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Database

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