LMFDB - Embedded newform 147.6.e.i.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$23.5764215125$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.6.e.i.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+(3.00000 - 5.19615i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(39.0000 - 67.5500i) q^{5} -54.0000 q^{6} +168.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-234.000 - 405.300i) q^{10} +(-222.000 - 384.515i) q^{11} +(-18.0000 + 31.1769i) q^{12} +442.000 q^{13} -702.000 q^{15} +(568.000 - 983.805i) q^{16} +(-63.0000 - 109.119i) q^{17} +(243.000 + 420.888i) q^{18} +(1342.00 - 2324.41i) q^{19} -312.000 q^{20} -2664.00 q^{22} +(-2100.00 + 3637.31i) q^{23} +(-756.000 - 1309.43i) q^{24} +(-1479.50 - 2562.57i) q^{25} +(1326.00 - 2296.70i) q^{26} +729.000 q^{27} -5442.00 q^{29} +(-2106.00 + 3647.70i) q^{30} +(40.0000 + 69.2820i) q^{31} +(-720.000 - 1247.08i) q^{32} +(-1998.00 + 3460.64i) q^{33} -756.000 q^{34} +324.000 q^{36} +(2717.00 - 4705.98i) q^{37} +(-8052.00 - 13946.5i) q^{38} +(-1989.00 - 3445.05i) q^{39} +(6552.00 - 11348.4i) q^{40} -7962.00 q^{41} -11524.0 q^{43} +(-888.000 + 1538.06i) q^{44} +(3159.00 + 5471.55i) q^{45} +(12600.0 + 21823.8i) q^{46} +(-6960.00 + 12055.1i) q^{47} -10224.0 q^{48} -17754.0 q^{50} +(-567.000 + 982.073i) q^{51} +(-884.000 - 1531.13i) q^{52} +(4797.00 + 8308.65i) q^{53} +(2187.00 - 3788.00i) q^{54} -34632.0 q^{55} -24156.0 q^{57} +(-16326.0 + 28277.5i) q^{58} +(13746.0 + 23808.8i) q^{59} +(1404.00 + 2431.80i) q^{60} +(24739.0 - 42849.2i) q^{61} +480.000 q^{62} +27712.0 q^{64} +(17238.0 - 29857.1i) q^{65} +(11988.0 + 20763.8i) q^{66} +(29678.0 + 51403.8i) q^{67} +(-252.000 + 436.477i) q^{68} +37800.0 q^{69} +32040.0 q^{71} +(-6804.00 + 11784.9i) q^{72} +(-30923.0 - 53560.2i) q^{73} +(-16302.0 - 28235.9i) q^{74} +(-13315.5 + 23063.1i) q^{75} -10736.0 q^{76} -23868.0 q^{78} +(32888.0 - 56963.7i) q^{79} +(-44304.0 - 76736.8i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-23886.0 + 41371.8i) q^{82} -40188.0 q^{83} -9828.00 q^{85} +(-34572.0 + 59880.5i) q^{86} +(24489.0 + 42416.2i) q^{87} +(-37296.0 - 64598.6i) q^{88} +(-3987.00 + 6905.69i) q^{89} +37908.0 q^{90} +16800.0 q^{92} +(360.000 - 623.538i) q^{93} +(41760.0 + 72330.4i) q^{94} +(-104676. - 181304. i) q^{95} +(-6480.00 + 11223.7i) q^{96} +143662. q^{97} +35964.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{2} - 9 q^{3} - 4 q^{4} + 78 q^{5} - 108 q^{6} + 336 q^{8} - 81 q^{9} - 468 q^{10} - 444 q^{11} - 36 q^{12} + 884 q^{13} - 1404 q^{15} + 1136 q^{16} - 126 q^{17} + 486 q^{18} + 2684 q^{19} - 624 q^{20}+ \cdots + 71928 q^{99}+O(q^{100}) $ 2 * q + 6 * q^2 - 9 * q^3 - 4 * q^4 + 78 * q^5 - 108 * q^6 + 336 * q^8 - 81 * q^9 - 468 * q^10 - 444 * q^11 - 36 * q^12 + 884 * q^13 - 1404 * q^15 + 1136 * q^16 - 126 * q^17 + 486 * q^18 + 2684 * q^19 - 624 * q^20 - 5328 * q^22 - 4200 * q^23 - 1512 * q^24 - 2959 * q^25 + 2652 * q^26 + 1458 * q^27 - 10884 * q^29 - 4212 * q^30 + 80 * q^31 - 1440 * q^32 - 3996 * q^33 - 1512 * q^34 + 648 * q^36 + 5434 * q^37 - 16104 * q^38 - 3978 * q^39 + 13104 * q^40 - 15924 * q^41 - 23048 * q^43 - 1776 * q^44 + 6318 * q^45 + 25200 * q^46 - 13920 * q^47 - 20448 * q^48 - 35508 * q^50 - 1134 * q^51 - 1768 * q^52 + 9594 * q^53 + 4374 * q^54 - 69264 * q^55 - 48312 * q^57 - 32652 * q^58 + 27492 * q^59 + 2808 * q^60 + 49478 * q^61 + 960 * q^62 + 55424 * q^64 + 34476 * q^65 + 23976 * q^66 + 59356 * q^67 - 504 * q^68 + 75600 * q^69 + 64080 * q^71 - 13608 * q^72 - 61846 * q^73 - 32604 * q^74 - 26631 * q^75 - 21472 * q^76 - 47736 * q^78 + 65776 * q^79 - 88608 * q^80 - 6561 * q^81 - 47772 * q^82 - 80376 * q^83 - 19656 * q^85 - 69144 * q^86 + 48978 * q^87 - 74592 * q^88 - 7974 * q^89 + 75816 * q^90 + 33600 * q^92 + 720 * q^93 + 83520 * q^94 - 209352 * q^95 - 12960 * q^96 + 287324 * q^97 + 71928 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	3.00000	−	5.19615i	0.530330	−	0.918559i	−0.469044	−	0.883175i	$-0.655401\pi$
$2$	3.00000	−	5.19615i	0.530330	−	0.918559i	0.999374	−	0.0353837i	$-0.0112653\pi$
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$4$	−2.00000	−	3.46410i	−0.0625000	−	0.108253i
$5$	39.0000	−	67.5500i	0.697653	−	1.20837i	−0.271625	−	0.962403i	$-0.587561\pi$
$5$	39.0000	−	67.5500i	0.697653	−	1.20837i	0.969278	−	0.245968i	$-0.0791057\pi$
$6$	−54.0000			−0.612372
$7$		0			0
$7$		0			0
$8$	168.000			0.928078
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	−234.000	−	405.300i	−0.739973	−	1.28167i
$11$	−222.000	−	384.515i	−0.553186	−	0.958146i	−0.998042	−	0.0625444i	$-0.980079\pi$
$11$	−222.000	−	384.515i	−0.553186	−	0.958146i	0.444856	−	0.895602i	$-0.353255\pi$
$12$	−18.0000	+	31.1769i	−0.0360844	+	0.0625000i
$13$	442.000			0.725377			0.362689	−	0.931910i	$-0.381859\pi$
$13$	442.000			0.725377			0.362689	+	0.931910i	$0.381859\pi$
$14$		0			0
$15$	−702.000			−0.805581
$16$	568.000	−	983.805i	0.554688	−	0.960747i
$17$	−63.0000	−	109.119i	−0.0528711	−	0.0915754i	0.838379	−	0.545088i	$-0.183504\pi$
$17$	−63.0000	−	109.119i	−0.0528711	−	0.0915754i	−0.891250	+	0.453513i	$0.850171\pi$
$18$	243.000	+	420.888i	0.176777	+	0.306186i
$19$	1342.00	−	2324.41i	0.852842	−	1.47717i	−0.0257909	−	0.999667i	$-0.508210\pi$
$19$	1342.00	−	2324.41i	0.852842	−	1.47717i	0.878633	−	0.477498i	$-0.158456\pi$
$20$	−312.000			−0.174413
$21$		0			0
$22$	−2664.00			−1.17348
$23$	−2100.00	+	3637.31i	−0.827751	+	1.43371i	0.0720476	+	0.997401i	$0.477047\pi$
$23$	−2100.00	+	3637.31i	−0.827751	+	1.43371i	−0.899799	+	0.436306i	$0.856287\pi$
$24$	−756.000	−	1309.43i	−0.267913	−	0.464039i
$25$	−1479.50	−	2562.57i	−0.473440	−	0.820022i
$26$	1326.00	−	2296.70i	0.384689	−	0.666301i
$27$	729.000			0.192450
$28$		0			0
$29$	−5442.00			−1.20161			−0.600805	−	0.799396i	$-0.705153\pi$
$29$	−5442.00			−1.20161			−0.600805	+	0.799396i	$0.705153\pi$
$30$	−2106.00	+	3647.70i	−0.427224	+	0.739973i
$31$	40.0000	+	69.2820i	0.00747577	+	0.0129484i	0.869739	−	0.493512i	$-0.164287\pi$
$31$	40.0000	+	69.2820i	0.00747577	+	0.0129484i	−0.862263	+	0.506460i	$0.830954\pi$
$32$	−720.000	−	1247.08i	−0.124296	−	0.215287i
$33$	−1998.00	+	3460.64i	−0.319382	+	0.553186i
$34$	−756.000			−0.112157
$35$		0			0
$36$	324.000			0.0416667
$37$	2717.00	−	4705.98i	0.326276	−	0.565127i	−0.655494	−	0.755201i	$-0.727539\pi$
$37$	2717.00	−	4705.98i	0.326276	−	0.565127i	0.981770	+	0.190074i	$0.0608727\pi$
$38$	−8052.00	−	13946.5i	−0.904575	−	1.56677i
$39$	−1989.00	−	3445.05i	−0.209398	−	0.362689i
$40$	6552.00	−	11348.4i	0.647476	−	1.12146i
$41$	−7962.00			−0.739712			−0.369856	−	0.929089i	$-0.620593\pi$
$41$	−7962.00			−0.739712			−0.369856	+	0.929089i	$0.620593\pi$
$42$		0			0
$43$	−11524.0			−0.950456			−0.475228	−	0.879863i	$-0.657634\pi$
$43$	−11524.0			−0.950456			−0.475228	+	0.879863i	$0.657634\pi$
$44$	−888.000	+	1538.06i	−0.0691483	+	0.119768i
$45$	3159.00	+	5471.55i	0.232551	+	0.402790i
$46$	12600.0	+	21823.8i	0.877962	+	1.52068i
$47$	−6960.00	+	12055.1i	−0.459584	+	0.796022i	−0.998939	−	0.0460561i	$-0.985335\pi$
$47$	−6960.00	+	12055.1i	−0.459584	+	0.796022i	0.539355	+	0.842078i	$0.318668\pi$
$48$	−10224.0			−0.640498
$49$		0			0
$50$	−17754.0			−1.00432
$51$	−567.000	+	982.073i	−0.0305251	+	0.0528711i
$52$	−884.000	−	1531.13i	−0.0453361	−	0.0785244i
$53$	4797.00	+	8308.65i	0.234574	+	0.406294i	0.959149	−	0.282902i	$-0.0912971\pi$
$53$	4797.00	+	8308.65i	0.234574	+	0.406294i	−0.724575	+	0.689196i	$0.757964\pi$
$54$	2187.00	−	3788.00i	0.102062	−	0.176777i
$55$	−34632.0			−1.54373
$56$		0			0
$57$	−24156.0			−0.984777
$58$	−16326.0	+	28277.5i	−0.637250	+	1.10375i
$59$	13746.0	+	23808.8i	0.514098	+	0.890445i	0.999866	+	0.0163567i	$0.00520675\pi$
$59$	13746.0	+	23808.8i	0.514098	+	0.890445i	−0.485768	+	0.874088i	$0.661460\pi$
$60$	1404.00	+	2431.80i	0.0503488	+	0.0872067i
$61$	24739.0	−	42849.2i	0.851251	−	1.47441i	−0.0288292	−	0.999584i	$-0.509178\pi$
$61$	24739.0	−	42849.2i	0.851251	−	1.47441i	0.880080	−	0.474825i	$-0.157489\pi$
$62$	480.000			0.0158585
$63$		0			0
$64$	27712.0			0.845703
$65$	17238.0	−	29857.1i	0.506062	−	0.876525i
$66$	11988.0	+	20763.8i	0.338756	+	0.586742i
$67$	29678.0	+	51403.8i	0.807695	+	1.39897i	0.914456	+	0.404685i	$0.132619\pi$
$67$	29678.0	+	51403.8i	0.807695	+	1.39897i	−0.106761	+	0.994285i	$0.534048\pi$
$68$	−252.000	+	436.477i	−0.00660889	+	0.0114469i
$69$	37800.0			0.955805
$70$		0			0
$71$	32040.0			0.754304			0.377152	−	0.926151i	$-0.376903\pi$
$71$	32040.0			0.754304			0.377152	+	0.926151i	$0.376903\pi$
$72$	−6804.00	+	11784.9i	−0.154680	+	0.267913i
$73$	−30923.0	−	53560.2i	−0.679164	−	1.17635i	−0.975233	−	0.221180i	$-0.929009\pi$
$73$	−30923.0	−	53560.2i	−0.679164	−	1.17635i	0.296069	−	0.955166i	$-0.404324\pi$
$74$	−16302.0	−	28235.9i	−0.346068	−	0.599408i
$75$	−13315.5	+	23063.1i	−0.273341	+	0.473440i
$76$	−10736.0			−0.213210
$77$		0			0
$78$	−23868.0			−0.444201
$79$	32888.0	−	56963.7i	0.592884	−	1.02691i	−0.400958	−	0.916097i	$-0.631323\pi$
$79$	32888.0	−	56963.7i	0.592884	−	1.02691i	0.993842	−	0.110809i	$-0.0353441\pi$
$80$	−44304.0	−	76736.8i	−0.773959	−	1.34054i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	−23886.0	+	41371.8i	−0.392291	+	0.679469i
$83$	−40188.0			−0.640326			−0.320163	−	0.947362i	$-0.603738\pi$
$83$	−40188.0			−0.640326			−0.320163	+	0.947362i	$0.603738\pi$
$84$		0			0
$85$	−9828.00			−0.147543
$86$	−34572.0	+	59880.5i	−0.504056	+	0.873050i
$87$	24489.0	+	42416.2i	0.346875	+	0.600805i
$88$	−37296.0	−	64598.6i	−0.513400	−	0.889234i
$89$	−3987.00	+	6905.69i	−0.0533545	+	0.0924127i	−0.891469	−	0.453081i	$-0.850325\pi$
$89$	−3987.00	+	6905.69i	−0.0533545	+	0.0924127i	0.838115	+	0.545494i	$0.183658\pi$
$90$	37908.0			0.493315
$91$		0			0
$92$	16800.0			0.206938
$93$	360.000	−	623.538i	0.00431614	−	0.00747577i
$94$	41760.0	+	72330.4i	0.487462	+	0.844309i
$95$	−104676.	−	181304.i	−1.18998	−	2.06110i
$96$	−6480.00	+	11223.7i	−0.0717624	+	0.124296i
$97$	143662.			1.55029			0.775144	−	0.631784i	$-0.217677\pi$
$97$	143662.			1.55029			0.775144	+	0.631784i	$0.217677\pi$
$98$		0			0
$99$	35964.0			0.368791
$100$	−5918.00	+	10250.3i	−0.0591800	+	0.102503i
$101$	−1353.00	−	2343.46i	−0.0131976	−	0.0228589i	0.859351	−	0.511386i	$-0.170868\pi$
$101$	−1353.00	−	2343.46i	−0.0131976	−	0.0228589i	−0.872549	+	0.488527i	$0.837534\pi$
$102$	3402.00	+	5892.44i	0.0323768	+	0.0560783i
$103$	65884.0	−	114114.i	0.611909	−	1.05986i	−0.379009	−	0.925393i	$-0.623735\pi$
$103$	65884.0	−	114114.i	0.611909	−	1.05986i	0.990918	−	0.134465i	$-0.0429315\pi$
$104$	74256.0			0.673206
$105$		0			0
$106$	57564.0			0.497607
$107$	64458.0	−	111645.i	0.544274	−	0.942710i	−0.454378	−	0.890809i	$-0.650139\pi$
$107$	64458.0	−	111645.i	0.544274	−	0.942710i	0.998652	−	0.0519010i	$-0.0165280\pi$
$108$	−1458.00	−	2525.33i	−0.0120281	−	0.0208333i
$109$	50489.0	+	87449.5i	0.407034	+	0.705003i	0.994556	−	0.104205i	$-0.0332298\pi$
$109$	50489.0	+	87449.5i	0.407034	+	0.705003i	−0.587522	+	0.809208i	$0.699896\pi$
$110$	−103896.	+	179953.i	−0.818686	+	1.41800i
$111$	−48906.0			−0.376751
$112$		0			0
$113$	220146.			1.62186			0.810932	−	0.585140i	$-0.198960\pi$
$113$	220146.			1.62186			0.810932	+	0.585140i	$0.198960\pi$
$114$	−72468.0	+	125518.i	−0.522257	+	0.904575i
$115$	163800.	+	283710.i	1.15497	+	2.00046i
$116$	10884.0	+	18851.6i	0.0751006	+	0.130078i
$117$	−17901.0	+	31005.4i	−0.120896	+	0.209398i
$118$	164952.			1.09057
$119$		0			0
$120$	−117936.			−0.747641
$121$	−18042.5	+	31250.5i	−0.112030	+	0.194041i
$122$	−148434.	−	257095.i	−0.902888	−	1.56385i
$123$	35829.0	+	62057.6i	0.213536	+	0.369856i
$124$	160.000	−	277.128i	0.000934471	−	0.00161855i
$125$	12948.0			0.0741187
$126$		0			0
$127$	−74320.0			−0.408880			−0.204440	−	0.978879i	$-0.565537\pi$
$127$	−74320.0			−0.408880			−0.204440	+	0.978879i	$0.565537\pi$
$128$	106176.	−	183902.i	0.572798	−	0.992115i
$129$	51858.0	+	89820.7i	0.274373	+	0.475228i
$130$	−103428.	−	179143.i	−0.536760	−	0.929695i
$131$	−77658.0	+	134508.i	−0.395374	+	0.684808i	−0.993149	−	0.116856i	$-0.962718\pi$
$131$	−77658.0	+	134508.i	−0.395374	+	0.684808i	0.597775	+	0.801664i	$0.296052\pi$
$132$	15984.0			0.0798455
$133$		0			0
$134$	356136.			1.71338
$135$	28431.0	−	49243.9i	0.134263	−	0.232551i
$136$	−10584.0	−	18332.0i	−0.0490685	−	0.0849891i
$137$	132123.	+	228844.i	0.601419	+	1.04169i	0.992606	+	0.121377i	$0.0387310\pi$
$137$	132123.	+	228844.i	0.601419	+	1.04169i	−0.391188	+	0.920311i	$0.627936\pi$
$138$	113400.	−	196415.i	0.506892	−	0.877962i
$139$	−224612.			−0.986043			−0.493022	−	0.870017i	$-0.664108\pi$
$139$	−224612.			−0.986043			−0.493022	+	0.870017i	$0.664108\pi$
$140$		0			0
$141$	125280.			0.530682
$142$	96120.0	−	166485.i	0.400030	−	0.692873i
$143$	−98124.0	−	169956.i	−0.401269	−	0.695018i
$144$	46008.0	+	79688.2i	0.184896	+	0.320249i
$145$	−212238.	+	367607.i	−0.838307	+	1.45199i
$146$	−371076.			−1.44072
$147$		0			0
$148$	−21736.0			−0.0815690
$149$	41037.0	−	71078.2i	0.151429	−	0.262283i	−0.780324	−	0.625376i	$-0.784946\pi$
$149$	41037.0	−	71078.2i	0.151429	−	0.262283i	0.931753	+	0.363092i	$0.118279\pi$
$150$	79893.0	+	138379.i	0.289922	+	0.502159i
$151$	143516.	+	248577.i	0.512222	+	0.887194i	0.999900	+	0.0141703i	$0.00451071\pi$
$151$	143516.	+	248577.i	0.512222	+	0.887194i	−0.487678	+	0.873024i	$0.662156\pi$
$152$	225456.	−	390501.i	0.791503	−	1.37092i
$153$	10206.0			0.0352474
$154$		0			0
$155$	6240.00			0.0208620
$156$	−7956.00	+	13780.2i	−0.0261748	+	0.0453361i
$157$	64939.0	+	112478.i	0.210260	+	0.364181i	0.951796	−	0.306732i	$-0.0992356\pi$
$157$	64939.0	+	112478.i	0.210260	+	0.364181i	−0.741536	+	0.670913i	$0.765902\pi$
$158$	−197328.	−	341782.i	−0.628848	−	1.08920i
$159$	43173.0	−	74777.8i	0.135431	−	0.234574i
$160$	−112320.			−0.346862
$161$		0			0
$162$	−39366.0			−0.117851
$163$	−277642.	+	480890.i	−0.818495	+	1.41768i	0.0882955	+	0.996094i	$0.471858\pi$
$163$	−277642.	+	480890.i	−0.818495	+	1.41768i	−0.906791	+	0.421581i	$0.861475\pi$
$164$	15924.0	+	27581.2i	0.0462320	+	0.0800761i
$165$	155844.	+	269930.i	0.445636	+	0.771864i
$166$	−120564.	+	208823.i	−0.339584	+	0.588177i
$167$	−43512.0			−0.120731			−0.0603654	−	0.998176i	$-0.519227\pi$
$167$	−43512.0			−0.120731			−0.0603654	+	0.998176i	$0.519227\pi$
$168$		0			0
$169$	−175929.			−0.473828
$170$	−29484.0	+	51067.8i	−0.0782464	+	0.135527i
$171$	108702.	+	188277.i	0.284281	+	0.492388i
$172$	23048.0	+	39920.3i	0.0594035	+	0.102890i
$173$	−9165.00	+	15874.2i	−0.0232818	+	0.0403253i	−0.877432	−	0.479702i	$-0.840745\pi$
$173$	−9165.00	+	15874.2i	−0.0232818	+	0.0403253i	0.854150	+	0.520027i	$0.174078\pi$
$174$	293868.			0.735833
$175$		0			0
$176$	−504384.			−1.22738
$177$	123714.	−	214279.i	0.296815	−	0.514098i
$178$	23922.0	+	41434.1i	0.0565910	+	0.0980185i
$179$	76662.0	+	132782.i	0.178833	+	0.309748i	0.941481	−	0.337066i	$-0.109434\pi$
$179$	76662.0	+	132782.i	0.178833	+	0.309748i	−0.762648	+	0.646814i	$0.776101\pi$
$180$	12636.0	−	21886.2i	0.0290689	−	0.0503488i
$181$	382066.			0.866846			0.433423	−	0.901191i	$-0.357306\pi$
$181$	382066.			0.866846			0.433423	+	0.901191i	$0.357306\pi$
$182$		0			0
$183$	−445302.			−0.982940
$184$	−352800.	+	611068.i	−0.768217	+	1.33059i
$185$	−211926.	−	367067.i	−0.455255	−	0.788525i
$186$	−2160.00	−	3741.23i	−0.00457795	−	0.00792925i
$187$	−27972.0	+	48448.9i	−0.0584951	+	0.101316i
$188$	55680.0			0.114896
$189$		0			0
$190$	−1.25611e6			−2.52432
$191$	136704.	−	236778.i	0.271143	−	0.469633i	−0.698012	−	0.716086i	$-0.745932\pi$
$191$	136704.	−	236778.i	0.271143	−	0.469633i	0.969155	+	0.246453i	$0.0792652\pi$
$192$	−124704.	−	215994.i	−0.244133	−	0.422852i
$193$	−76801.0	−	133023.i	−0.148414	−	0.257060i	0.782228	−	0.622993i	$-0.214083\pi$
$193$	−76801.0	−	133023.i	−0.148414	−	0.257060i	−0.930641	+	0.365933i	$0.880750\pi$
$194$	430986.	−	746490.i	0.822165	−	1.42403i
$195$	−310284.			−0.584350
$196$		0			0
$197$	154422.			0.283494			0.141747	−	0.989903i	$-0.454728\pi$
$197$	154422.			0.283494			0.141747	+	0.989903i	$0.454728\pi$
$198$	107892.	−	186874.i	0.195581	−	0.338756i
$199$	−183428.	−	317707.i	−0.328347	−	0.568714i	0.653837	−	0.756635i	$-0.273158\pi$
$199$	−183428.	−	317707.i	−0.328347	−	0.568714i	−0.982184	+	0.187922i	$0.939825\pi$
$200$	−248556.	−	430512.i	−0.439389	−	0.761044i
$201$	267102.	−	462634.i	0.466323	−	0.807695i
$202$	−16236.0			−0.0279963
$203$		0			0
$204$	4536.00			0.00763128
$205$	−310518.	+	537833.i	−0.516062	+	0.893846i
$206$	−395304.	−	684687.i	−0.649028	−	1.12415i
$207$	−170100.	−	294622.i	−0.275917	−	0.477902i
$208$	251056.	−	434842.i	0.402358	−	0.696904i
$209$	−1.19170e6			−1.88712
$210$		0			0
$211$	520244.			0.804453			0.402227	−	0.915540i	$-0.368236\pi$
$211$	520244.			0.804453			0.402227	+	0.915540i	$0.368236\pi$
$212$	19188.0	−	33234.6i	0.0293218	−	0.0507868i
$213$	−144180.	−	249727.i	−0.217749	−	0.377152i
$214$	−386748.	−	669867.i	−0.577289	−	0.999895i
$215$	−449436.	+	778446.i	−0.663089	+	1.14850i
$216$	122472.			0.178609
$217$		0			0
$218$	605868.			0.863449
$219$	−278307.	+	482042.i	−0.392115	+	0.679164i
$220$	69264.0	+	119969.i	0.0964830	+	0.167113i
$221$	−27846.0	−	48230.7i	−0.0383515	−	0.0664267i
$222$	−146718.	+	254123.i	−0.199803	+	0.346068i
$223$	−304736.			−0.410357			−0.205178	−	0.978725i	$-0.565777\pi$
$223$	−304736.			−0.410357			−0.205178	+	0.978725i	$0.565777\pi$
$224$		0			0
$225$	239679.			0.315627
$226$	660438.	−	1.14391e6i	0.860124	−	1.48978i
$227$	144294.	+	249925.i	0.185859	+	0.321917i	0.943866	−	0.330330i	$-0.107160\pi$
$227$	144294.	+	249925.i	0.185859	+	0.321917i	−0.758007	+	0.652247i	$0.773827\pi$
$228$	48312.0	+	83678.8i	0.0615486	+	0.106605i
$229$	386095.	−	668736.i	0.486525	−	0.842687i	−0.513355	−	0.858177i	$-0.671597\pi$
$229$	386095.	−	668736.i	0.486525	−	0.842687i	0.999880	+	0.0154899i	$0.00493079\pi$
$230$	1.96560e6			2.45005
$231$		0			0
$232$	−914256.			−1.11519
$233$	−126117.	+	218441.i	−0.152189	+	0.263599i	−0.932032	−	0.362376i	$-0.881966\pi$
$233$	−126117.	+	218441.i	−0.152189	+	0.263599i	0.779843	+	0.625975i	$0.215299\pi$
$234$	107406.	+	186033.i	0.128230	+	0.222100i
$235$	542880.	+	940296.i	0.641260	+	1.11069i
$236$	54984.0	−	95235.1i	0.0642623	−	0.111306i
$237$	−591984.			−0.684603
$238$		0			0
$239$	−1.45114e6			−1.64329			−0.821643	−	0.570002i	$-0.806942\pi$
$239$	−1.45114e6			−1.64329			−0.821643	+	0.570002i	$0.806942\pi$
$240$	−398736.	+	690631.i	−0.446845	+	0.773959i
$241$	−73199.0	−	126784.i	−0.0811825	−	0.140612i	0.822576	−	0.568656i	$-0.192536\pi$
$241$	−73199.0	−	126784.i	−0.0811825	−	0.140612i	−0.903758	+	0.428043i	$0.859203\pi$
$242$	108255.	+	187503.i	0.118825	+	0.205812i
$243$	−29524.5	+	51137.9i	−0.0320750	+	0.0555556i
$244$	−197912.			−0.212813
$245$		0			0
$246$	429948.			0.452979
$247$	593164.	−	1.02739e6i	0.618632	−	1.07150i
$248$	6720.00	+	11639.4i	0.00693809	+	0.0120171i
$249$	180846.	+	313234.i	0.184846	+	0.320163i
$250$	38844.0	−	67279.8i	0.0393074	−	0.0680824i
$251$	−607860.			−0.609003			−0.304501	−	0.952512i	$-0.598490\pi$
$251$	−607860.			−0.609003			−0.304501	+	0.952512i	$0.598490\pi$
$252$		0			0
$253$	1.86480e6			1.83160
$254$	−222960.	+	386178.i	−0.216842	+	0.375581i
$255$	44226.0	+	76601.7i	0.0425919	+	0.0737714i
$256$	−193664.	−	335436.i	−0.184692	−	0.319897i
$257$	47793.0	−	82779.9i	0.0451369	−	0.0781794i	−0.842574	−	0.538580i	$-0.818961\pi$
$257$	47793.0	−	82779.9i	0.0451369	−	0.0781794i	0.887711	+	0.460401i	$0.152294\pi$
$258$	622296.			0.582033
$259$		0			0
$260$	−137904.			−0.126515
$261$	220401.	−	381746.i	0.200268	−	0.346875i
$262$	465948.	+	807046.i	0.419357	+	0.726348i
$263$	1.10017e6	+	1.90555e6i	0.980779	+	1.69876i	0.659370	+	0.751819i	$0.270823\pi$
$263$	1.10017e6	+	1.90555e6i	0.980779	+	1.69876i	0.321410	+	0.946940i	$0.395843\pi$
$264$	−335664.	+	581387.i	−0.296411	+	0.513400i
$265$	748332.			0.654605
$266$		0			0
$267$	71766.0			0.0616085
$268$	118712.	−	205615.i	0.100962	−	0.174871i
$269$	885123.	+	1.53308e6i	0.745801	+	1.29177i	0.949820	+	0.312798i	$0.101266\pi$
$269$	885123.	+	1.53308e6i	0.745801	+	1.29177i	−0.204019	+	0.978967i	$0.565400\pi$
$270$	−170586.	−	295464.i	−0.142408	−	0.246658i
$271$	−111752.	+	193560.i	−0.0924341	+	0.160101i	−0.908535	−	0.417809i	$-0.862798\pi$
$271$	−111752.	+	193560.i	−0.0924341	+	0.160101i	0.816101	+	0.577910i	$0.196131\pi$
$272$	−143136.			−0.117308
$273$		0			0
$274$	1.58548e6			1.27580
$275$	−656898.	+	1.13778e6i	−0.523801	+	0.907250i
$276$	−75600.0	−	130943.i	−0.0597378	−	0.103469i
$277$	171389.	+	296854.i	0.134210	+	0.232458i	0.925295	−	0.379248i	$-0.123817\pi$
$277$	171389.	+	296854.i	0.134210	+	0.232458i	−0.791086	+	0.611705i	$0.790484\pi$
$278$	−673836.	+	1.16712e6i	−0.522928	+	0.905739i
$279$	−6480.00			−0.00498384
$280$		0			0
$281$	480378.			0.362925			0.181463	−	0.983398i	$-0.441917\pi$
$281$	480378.			0.362925			0.181463	+	0.983398i	$0.441917\pi$
$282$	375840.	−	650974.i	0.281436	−	0.487462i
$283$	−14990.0	−	25963.4i	−0.0111259	−	0.0192706i	0.860409	−	0.509604i	$-0.170208\pi$
$283$	−14990.0	−	25963.4i	−0.0111259	−	0.0192706i	−0.871535	+	0.490334i	$0.836875\pi$
$284$	−64080.0	−	110990.i	−0.0471440	−	0.0816558i
$285$	−942084.	+	1.63174e6i	−0.687033	+	1.18998i
$286$	−1.17749e6			−0.851219
$287$		0			0
$288$	116640.			0.0828641
$289$	701990.	−	1.21588e6i	0.494409	−	0.856342i
$290$	1.27343e6	+	2.20564e6i	0.889159	+	1.54007i
$291$	−646479.	−	1.11973e6i	−0.447530	−	0.775144i
$292$	−123692.	+	214241.i	−0.0848955	+	0.147043i
$293$	198066.			0.134785			0.0673924	−	0.997727i	$-0.478532\pi$
$293$	198066.			0.134785			0.0673924	+	0.997727i	$0.478532\pi$
$294$		0			0
$295$	2.14438e6			1.43465
$296$	456456.	−	790605.i	0.302810	−	0.524482i
$297$	−161838.	−	280312.i	−0.106461	−	0.184395i
$298$	−246222.	−	426469.i	−0.160615	−	0.278193i
$299$	−928200.	+	1.60769e6i	−0.600432	+	1.03998i
$300$	106524.			0.0683352
$301$		0			0
$302$	1.72219e6			1.08659
$303$	−12177.0	+	21091.2i	−0.00761963	+	0.0131976i
$304$	−1.52451e6	−	2.64053e6i	−0.946121	−	1.63873i
$305$	−1.92964e6	−	3.34224e6i	−1.18776	−	2.05725i
$306$	30618.0	−	53031.9i	0.0186928	−	0.0323768i
$307$	1.04564e6			0.633191			0.316595	−	0.948561i	$-0.397460\pi$
$307$	1.04564e6			0.633191			0.316595	+	0.948561i	$0.397460\pi$
$308$		0			0
$309$	−1.18591e6			−0.706572
$310$	18720.0	−	32424.0i	0.0110637	−	0.0191629i
$311$	918588.	+	1.59104e6i	0.538542	+	0.932783i	0.998983	+	0.0450920i	$0.0143581\pi$
$311$	918588.	+	1.59104e6i	0.538542	+	0.932783i	−0.460441	+	0.887691i	$0.652309\pi$
$312$	−334152.	−	578768.i	−0.194338	−	0.336603i
$313$	−182747.	+	316527.i	−0.105436	+	0.182621i	−0.913916	−	0.405903i	$-0.866957\pi$
$313$	−182747.	+	316527.i	−0.105436	+	0.182621i	0.808480	+	0.588523i	$0.200291\pi$
$314$	779268.			0.446029
$315$		0			0
$316$	−263104.			−0.148221
$317$	14169.0	−	24541.4i	0.00791938	−	0.0137168i	−0.862039	−	0.506843i	$-0.830812\pi$
$317$	14169.0	−	24541.4i	0.00791938	−	0.0137168i	0.869958	+	0.493126i	$0.164146\pi$
$318$	−259038.	−	448667.i	−0.143647	−	0.248803i
$319$	1.20812e6	+	2.09253e6i	0.664714	+	1.15132i
$320$	1.08077e6	−	1.87195e6i	0.590007	−	1.02192i
$321$	−1.16024e6			−0.628473
$322$		0			0
$323$	−338184.			−0.180363
$324$	−13122.0	+	22728.0i	−0.00694444	+	0.0120281i
$325$	−653939.	−	1.13266e6i	−0.343423	−	0.594825i
$326$	1.66585e6	+	2.88534e6i	0.868145	+	1.50367i
$327$	454401.	−	787046.i	0.235001	−	0.407034i
$328$	−1.33762e6			−0.686510
$329$		0			0
$330$	1.87013e6			0.945337
$331$	−966958.	+	1.67482e6i	−0.485107	+	0.840230i	−0.999854	−	0.0171123i	$-0.994553\pi$
$331$	−966958.	+	1.67482e6i	−0.485107	+	0.840230i	0.514746	+	0.857342i	$0.327886\pi$
$332$	80376.0	+	139215.i	0.0400204	+	0.0693173i
$333$	220077.	+	381185.i	0.108759	+	0.188376i
$334$	−130536.	+	226095.i	−0.0640271	+	0.110898i
$335$	4.62977e6			2.25397
$336$		0			0
$337$	−1.88817e6			−0.905664			−0.452832	−	0.891596i	$-0.649586\pi$
$337$	−1.88817e6			−0.905664			−0.452832	+	0.891596i	$0.649586\pi$
$338$	−527787.	+	914154.i	−0.251285	+	0.435239i
$339$	−990657.	−	1.71587e6i	−0.468192	−	0.810932i
$340$	19656.0	+	34045.2i	0.00922142	+	0.0159720i
$341$	17760.0	−	30761.2i	0.00827098	−	0.0143258i
$342$	1.30442e6			0.603050
$343$		0			0
$344$	−1.93603e6			−0.882097
$345$	1.47420e6	−	2.55339e6i	0.666820	−	1.15497i
$346$	54990.0	+	95245.5i	0.0246941	+	0.0427715i
$347$	−1.45969e6	−	2.52825e6i	−0.650782	−	1.12719i	−0.982933	−	0.183962i	$-0.941108\pi$
$347$	−1.45969e6	−	2.52825e6i	−0.650782	−	1.12719i	0.332151	−	0.943226i	$-0.392226\pi$
$348$	97956.0	−	169665.i	0.0433594	−	0.0751006i
$349$	780682.			0.343092			0.171546	−	0.985176i	$-0.445124\pi$
$349$	780682.			0.343092			0.171546	+	0.985176i	$0.445124\pi$
$350$		0			0
$351$	322218.			0.139599
$352$	−319680.	+	553702.i	−0.137518	+	0.238188i
$353$	667185.	+	1.15560e6i	0.284977	+	0.493594i	0.972604	−	0.232470i	$-0.0746808\pi$
$353$	667185.	+	1.15560e6i	0.284977	+	0.493594i	−0.687627	+	0.726064i	$0.741347\pi$
$354$	−742284.	−	1.28567e6i	−0.314820	−	0.545284i
$355$	1.24956e6	−	2.16430e6i	0.526243	−	0.911479i
$356$	31896.0			0.0133386
$357$		0			0
$358$	919944.			0.379362
$359$	−508716.	+	881122.i	−0.208324	+	0.360828i	−0.951187	−	0.308616i	$-0.900134\pi$
$359$	−508716.	+	881122.i	−0.208324	+	0.360828i	0.742863	+	0.669444i	$0.233468\pi$
$360$	530712.	+	919220.i	0.215825	+	0.373821i
$361$	−2.36388e6	−	4.09436e6i	−0.954679	−	1.65355i
$362$	1.14620e6	−	1.98527e6i	0.459715	−	0.796249i
$363$	324765.			0.129361
$364$		0			0
$365$	−4.82399e6			−1.89528
$366$	−1.33591e6	+	2.31386e6i	−0.521283	+	0.902888i
$367$	418840.	+	725452.i	0.162324	+	0.281154i	0.935702	−	0.352792i	$-0.114768\pi$
$367$	418840.	+	725452.i	0.162324	+	0.281154i	−0.773378	+	0.633946i	$0.781434\pi$
$368$	2.38560e6	+	4.13198e6i	0.918286	+	1.59052i
$369$	322461.	−	558519.i	0.123285	−	0.213536i
$370$	−2.54311e6			−0.965742
$371$		0			0
$372$	−2880.00			−0.00107903
$373$	759965.	−	1.31630e6i	0.282827	−	0.489871i	−0.689253	−	0.724521i	$-0.742061\pi$
$373$	759965.	−	1.31630e6i	0.282827	−	0.489871i	0.972080	+	0.234650i	$0.0753943\pi$
$374$	167832.	+	290694.i	0.0620434	+	0.107462i
$375$	−58266.0	−	100920.i	−0.0213962	−	0.0370593i
$376$	−1.16928e6	+	2.02525e6i	−0.426529	+	0.738770i
$377$	−2.40536e6			−0.871620
$378$		0			0
$379$	2.64465e6			0.945737			0.472869	−	0.881133i	$-0.343219\pi$
$379$	2.64465e6			0.945737			0.472869	+	0.881133i	$0.343219\pi$
$380$	−418704.	+	725217.i	−0.148747	+	0.257637i
$381$	334440.	+	579267.i	0.118034	+	0.204440i
$382$	−820224.	−	1.42067e6i	−0.287590	−	0.498121i
$383$	1.00668e6	−	1.74362e6i	0.350667	−	0.607373i	−0.635700	−	0.771936i	$-0.719288\pi$
$383$	1.00668e6	−	1.74362e6i	0.350667	−	0.607373i	0.986366	+	0.164564i	$0.0526217\pi$
$384$	−1.91117e6			−0.661410
$385$		0			0
$386$	−921612.			−0.314833
$387$	466722.	−	808386.i	0.158409	−	0.274373i
$388$	−287324.	−	497660.i	−0.0968930	−	0.167824i
$389$	363117.	+	628937.i	0.121667	+	0.210733i	0.920425	−	0.390919i	$-0.127843\pi$
$389$	363117.	+	628937.i	0.121667	+	0.210733i	−0.798758	+	0.601652i	$0.794509\pi$
$390$	−930852.	+	1.61228e6i	−0.309898	+	0.536760i
$391$	529200.			0.175056
$392$		0			0
$393$	1.39784e6			0.456538
$394$	463266.	−	802400.i	0.150345	−	0.260406i
$395$	−2.56526e6	−	4.44317e6i	−0.827255	−	1.43285i
$396$	−71928.0	−	124583.i	−0.0230494	−	0.0399228i
$397$	2.28789e6	−	3.96274e6i	0.728549	−	1.26188i	−0.228947	−	0.973439i	$-0.573528\pi$
$397$	2.28789e6	−	3.96274e6i	0.728549	−	1.26188i	0.957496	−	0.288446i	$-0.0931385\pi$
$398$	−2.20114e6			−0.696529
$399$		0			0
$400$	−3.36142e6			−1.05045
$401$	16935.0	−	29332.3i	0.00525926	−	0.00910930i	−0.863384	−	0.504548i	$-0.831659\pi$
$401$	16935.0	−	29332.3i	0.00525926	−	0.00910930i	0.868643	+	0.495438i	$0.164993\pi$
$402$	−1.60261e6	−	2.77581e6i	−0.494610	−	0.856690i
$403$	17680.0	+	30622.7i	0.00542275	+	0.00939248i
$404$	−5412.00	+	9373.86i	−0.00164970	+	0.00285736i
$405$	−511758.			−0.155034
$406$		0			0
$407$	−2.41270e6			−0.721966
$408$	−95256.0	+	164988.i	−0.0283297	+	0.0490685i
$409$	−2.93089e6	−	5.07645e6i	−0.866346	−	1.50056i	−0.865704	−	0.500556i	$-0.833129\pi$
$409$	−2.93089e6	−	5.07645e6i	−0.866346	−	1.50056i	−0.000641640	−	1.00000i	$-0.500204\pi$
$410$	1.86311e6	+	3.22700e6i	0.547367	+	0.948067i
$411$	1.18911e6	−	2.05959e6i	0.347229	−	0.601419i
$412$	−527072.			−0.152977
$413$		0			0
$414$	−2.04120e6			−0.585308
$415$	−1.56733e6	+	2.71470e6i	−0.446726	+	0.773751i
$416$	−318240.	−	551208.i	−0.0901616	−	0.156164i
$417$	1.01075e6	+	1.75068e6i	0.284646	+	0.493022i
$418$	−3.57509e6	+	6.19223e6i	−1.00080	+	1.73343i
$419$	−302748.			−0.0842454			−0.0421227	−	0.999112i	$-0.513412\pi$
$419$	−302748.			−0.0842454			−0.0421227	+	0.999112i	$0.513412\pi$
$420$		0			0
$421$	−5.36708e6			−1.47582			−0.737909	−	0.674900i	$-0.764187\pi$
$421$	−5.36708e6			−1.47582			−0.737909	+	0.674900i	$0.764187\pi$
$422$	1.56073e6	−	2.70327e6i	0.426626	−	0.738938i
$423$	−563760.	−	976461.i	−0.153195	−	0.265341i
$424$	805896.	+	1.39585e6i	0.217703	+	0.377073i
$425$	−186417.	+	322884.i	−0.0500626	+	0.0867109i
$426$	−1.73016e6			−0.461915
$427$		0			0
$428$	−515664.			−0.136068
$429$	−883116.	+	1.52960e6i	−0.231673	+	0.401269i
$430$	2.69662e6	+	4.67068e6i	0.703312	+	1.21817i
$431$	−588528.	−	1.01936e6i	−0.152607	−	0.264323i	0.779578	−	0.626305i	$-0.215433\pi$
$431$	−588528.	−	1.01936e6i	−0.152607	−	0.264323i	−0.932185	+	0.361982i	$0.882100\pi$
$432$	414072.	−	717194.i	0.106750	−	0.184896i
$433$	3.66249e6			0.938766			0.469383	−	0.882995i	$-0.344476\pi$
$433$	3.66249e6			0.938766			0.469383	+	0.882995i	$0.344476\pi$
$434$		0			0
$435$	3.82028e6			0.967994
$436$	201956.	−	349798.i	0.0508792	−	0.0881254i
$437$	5.63640e6	+	9.76253e6i	1.41188	+	2.44545i
$438$	1.66984e6	+	2.89225e6i	0.415901	+	0.720362i
$439$	−1.26837e6	+	2.19688e6i	−0.314113	+	0.544059i	−0.979248	−	0.202663i	$-0.935040\pi$
$439$	−1.26837e6	+	2.19688e6i	−0.314113	+	0.544059i	0.665136	+	0.746722i	$0.268374\pi$
$440$	−5.81818e6			−1.43270
$441$		0			0
$442$	−334152.			−0.0813558
$443$	−3.00752e6	+	5.20917e6i	−0.728113	+	1.26113i	0.229566	+	0.973293i	$0.426269\pi$
$443$	−3.00752e6	+	5.20917e6i	−0.728113	+	1.26113i	−0.957680	+	0.287836i	$0.907064\pi$
$444$	97812.0	+	169415.i	0.0235470	+	0.0407845i
$445$	310986.	+	538644.i	0.0744459	+	0.128944i
$446$	−914208.	+	1.58345e6i	−0.217625	+	0.376937i
$447$	−738666.			−0.174856
$448$		0			0
$449$	5.65965e6			1.32487			0.662436	−	0.749119i	$-0.269523\pi$
$449$	5.65965e6			1.32487			0.662436	+	0.749119i	$0.269523\pi$
$450$	719037.	−	1.24541e6i	0.167386	−	0.289922i
$451$	1.76756e6	+	3.06151e6i	0.409198	+	0.708752i
$452$	−440292.	−	762608.i	−0.101367	−	0.175572i
$453$	1.29164e6	−	2.23719e6i	0.295731	−	0.512222i
$454$	1.73153e6			0.394267
$455$		0			0
$456$	−4.05821e6			−0.913949
$457$	3.23080e6	−	5.59590e6i	0.723634	−	1.25337i	−0.235900	−	0.971777i	$-0.575804\pi$
$457$	3.23080e6	−	5.59590e6i	0.723634	−	1.25337i	0.959534	−	0.281593i	$-0.0908629\pi$
$458$	−2.31657e6	−	4.01242e6i	−0.516038	−	0.893804i
$459$	−45927.0	−	79547.9i	−0.0101750	−	0.0176237i
$460$	655200.	−	1.13484e6i	0.144371	−	0.250058i
$461$	3.37353e6			0.739320			0.369660	−	0.929167i	$-0.379474\pi$
$461$	3.37353e6			0.739320			0.369660	+	0.929167i	$0.379474\pi$
$462$		0			0
$463$	−4.54974e6			−0.986358			−0.493179	−	0.869928i	$-0.664165\pi$
$463$	−4.54974e6			−0.986358			−0.493179	+	0.869928i	$0.664165\pi$
$464$	−3.09106e6	+	5.35387e6i	−0.666518	+	1.15444i
$465$	−28080.0	−	48636.0i	−0.00602233	−	0.0104310i
$466$	756702.	+	1.31065e6i	0.161421	+	0.279589i
$467$	1.00568e6	−	1.74189e6i	0.213386	−	0.369596i	−0.739386	−	0.673282i	$-0.764884\pi$
$467$	1.00568e6	−	1.74189e6i	0.213386	−	0.369596i	0.952772	+	0.303686i	$0.0982173\pi$
$468$	143208.			0.0302240
$469$		0			0
$470$	6.51456e6			1.36032
$471$	584451.	−	1.01230e6i	0.121394	−	0.210260i
$472$	2.30933e6	+	3.99987e6i	0.477123	+	0.826402i
$473$	2.55833e6	+	4.43115e6i	0.525779	+	0.910676i
$474$	−1.77595e6	+	3.07604e6i	−0.363066	+	0.628848i
$475$	−7.94196e6			−1.61508
$476$		0			0
$477$	−777114.			−0.156383
$478$	−4.35341e6	+	7.54032e6i	−0.871484	+	1.50946i
$479$	−3.80201e6	−	6.58527e6i	−0.757137	−	1.31140i	−0.944305	−	0.329071i	$-0.893264\pi$
$479$	−3.80201e6	−	6.58527e6i	−0.757137	−	1.31140i	0.187168	−	0.982328i	$-0.440069\pi$
$480$	505440.	+	875448.i	0.100131	+	0.173431i
$481$	1.20091e6	−	2.08004e6i	0.236673	−	0.409930i
$482$	−878388.			−0.172214
$483$		0			0
$484$	144340.			0.0280074
$485$	5.60282e6	−	9.70437e6i	1.08156	−	1.87332i
$486$	177147.	+	306828.i	0.0340207	+	0.0589256i
$487$	−336556.	−	582932.i	−0.0643035	−	0.111377i	0.832081	−	0.554654i	$-0.187149\pi$
$487$	−336556.	−	582932.i	−0.0643035	−	0.111377i	−0.896385	+	0.443277i	$0.853816\pi$
$488$	4.15615e6	−	7.19867e6i	0.790027	−	1.36837i
$489$	4.99756e6			0.945117
$490$		0			0
$491$	−2.47170e6			−0.462692			−0.231346	−	0.972872i	$-0.574313\pi$
$491$	−2.47170e6			−0.462692			−0.231346	+	0.972872i	$0.574313\pi$
$492$	143316.	−	248231.i	0.0266920	−	0.0462320i
$493$	342846.	+	593827.i	0.0635304	+	0.110038i
$494$	−3.55898e6	−	6.16434e6i	−0.656158	−	1.13650i
$495$	1.40260e6	−	2.42937e6i	0.257288	−	0.445636i
$496$	90880.0			0.0165869
$497$		0			0
$498$	2.17015e6			0.392118
$499$	−3.04076e6	+	5.26675e6i	−0.546677	+	0.946873i	0.451822	+	0.892108i	$0.350774\pi$
$499$	−3.04076e6	+	5.26675e6i	−0.546677	+	0.946873i	−0.998499	+	0.0547648i	$0.982559\pi$
$500$	−25896.0	−	44853.2i	−0.00463242	−	0.00802358i
$501$	195804.	+	339142.i	0.0348520	+	0.0603654i
$502$	−1.82358e6	+	3.15853e6i	−0.322972	+	0.559405i
$503$	846216.			0.149129			0.0745644	−	0.997216i	$-0.476243\pi$
$503$	846216.			0.149129			0.0745644	+	0.997216i	$0.476243\pi$
$504$		0			0
$505$	−211068.			−0.0368293
$506$	5.59440e6	−	9.68979e6i	0.971353	−	1.68243i
$507$	791680.	+	1.37123e6i	0.136782	+	0.236914i
$508$	148640.	+	257452.i	0.0255550	+	0.0442626i
$509$	−3.83392e6	+	6.64055e6i	−0.655917	+	1.13608i	0.325746	+	0.945457i	$0.394385\pi$
$509$	−3.83392e6	+	6.64055e6i	−0.655917	+	1.13608i	−0.981663	+	0.190625i	$0.938949\pi$
$510$	530712.			0.0903511
$511$		0			0
$512$	4.47130e6			0.753804
$513$	978318.	−	1.69450e6i	0.164129	−	0.284281i
$514$	−286758.	−	496679.i	−0.0478749	−	0.0829217i
$515$	−5.13895e6	−	8.90093e6i	−0.853801	−	1.47883i
$516$	207432.	−	359283.i	0.0342966	−	0.0594035i
$517$	6.18048e6			1.01694
$518$		0			0
$519$	164970.			0.0268835
$520$	2.89598e6	−	5.01599e6i	0.469665	−	0.813483i
$521$	−4.84469e6	−	8.39125e6i	−0.781937	−	1.35435i	−0.930812	−	0.365499i	$-0.880898\pi$
$521$	−4.84469e6	−	8.39125e6i	−0.781937	−	1.35435i	0.148875	−	0.988856i	$-0.452435\pi$
$522$	−1.32241e6	−	2.29047e6i	−0.212417	−	0.367916i
$523$	−3.75839e6	+	6.50972e6i	−0.600824	+	1.04066i	0.391872	+	0.920020i	$0.371828\pi$
$523$	−3.75839e6	+	6.50972e6i	−0.600824	+	1.04066i	−0.992696	+	0.120639i	$0.961506\pi$
$524$	621264.			0.0988435
$525$		0			0
$526$	1.32021e7			2.08055
$527$	5040.00	−	8729.54i	0.000790504	−	0.00136919i
$528$	2.26973e6	+	3.93128e6i	0.354315	+	0.613691i
$529$	−5.60183e6	−	9.70265e6i	−0.870343	−	1.50748i
$530$	2.24500e6	−	3.88845e6i	0.347157	−	0.601294i
$531$	−2.22685e6			−0.342732
$532$		0			0
$533$	−3.51920e6			−0.536570
$534$	215298.	−	372907.i	0.0326728	−	0.0565910i
$535$	−5.02772e6	−	8.70827e6i	−0.759429	−	1.31537i
$536$	4.98590e6	+	8.63584e6i	0.749604	+	1.29835i
$537$	689958.	−	1.19504e6i	0.103249	−	0.178833i
$538$	1.06215e7			1.58208
$539$		0			0
$540$	−227448.			−0.0335659
$541$	−3.67162e6	+	6.35944e6i	−0.539343	+	0.934169i	0.459597	+	0.888128i	$0.347994\pi$
$541$	−3.67162e6	+	6.35944e6i	−0.539343	+	0.934169i	−0.998940	+	0.0460415i	$0.985339\pi$
$542$	670512.	+	1.16136e6i	0.0980411	+	0.169812i
$543$	−1.71930e6	−	2.97791e6i	−0.250237	−	0.433423i
$544$	−90720.0	+	157132.i	−0.0131433	+	0.0227649i
$545$	7.87628e6			1.13587
$546$		0			0
$547$	2.18296e6			0.311945			0.155973	−	0.987761i	$-0.450149\pi$
$547$	2.18296e6			0.311945			0.155973	+	0.987761i	$0.450149\pi$
$548$	528492.	−	915375.i	0.0751774	−	0.130211i
$549$	2.00386e6	+	3.47079e6i	0.283750	+	0.491470i
$550$	3.94139e6	+	6.82668e6i	0.555575	+	0.962284i
$551$	−7.30316e6	+	1.26495e7i	−1.02478	+	1.77498i
$552$	6.35040e6			0.887061
$553$		0			0
$554$	2.05667e6			0.284702
$555$	−1.90733e6	+	3.30360e6i	−0.262842	+	0.455255i
$556$	449224.	+	778079.i	0.0616277	+	0.106742i
$557$	−6.27328e6	−	1.08656e7i	−0.856755	−	1.48394i	−0.875007	−	0.484110i	$-0.839144\pi$
$557$	−6.27328e6	−	1.08656e7i	−0.856755	−	1.48394i	0.0182524	−	0.999833i	$-0.494190\pi$
$558$	−19440.0	+	33671.1i	−0.00264308	+	0.00457795i
$559$	−5.09361e6			−0.689439
$560$		0			0
$561$	503496.			0.0675443
$562$	1.44113e6	−	2.49612e6i	0.192470	−	0.333368i
$563$	2.57986e6	+	4.46845e6i	0.343025	+	0.594136i	0.984993	−	0.172595i	$-0.0552152\pi$
$563$	2.57986e6	+	4.46845e6i	0.343025	+	0.594136i	−0.641968	+	0.766731i	$0.721882\pi$
$564$	−250560.	−	433983.i	−0.0331676	−	0.0574480i
$565$	8.58569e6	−	1.48709e7i	1.13150	−	1.95981i
$566$	−179880.			−0.0236016
$567$		0			0
$568$	5.38272e6			0.700053
$569$	−5.87260e6	+	1.01717e7i	−0.760414	+	1.31708i	0.182223	+	0.983257i	$0.441671\pi$
$569$	−5.87260e6	+	1.01717e7i	−0.760414	+	1.31708i	−0.942637	+	0.333819i	$0.891663\pi$
$570$	5.65250e6	+	9.79042e6i	0.728708	+	1.26216i
$571$	3.77364e6	+	6.53614e6i	0.484362	+	0.838940i	0.999839	−	0.0179636i	$-0.00571829\pi$
$571$	3.77364e6	+	6.53614e6i	0.484362	+	0.838940i	−0.515476	+	0.856904i	$0.672385\pi$
$572$	−392496.	+	679823.i	−0.0501586	+	0.0868772i
$573$	−2.46067e6			−0.313089
$574$		0			0
$575$	1.24278e7			1.56756
$576$	−1.12234e6	+	1.94394e6i	−0.140951	+	0.244133i
$577$	4.64242e6	+	8.04090e6i	0.580503	+	1.00546i	0.995420	+	0.0956015i	$0.0304775\pi$
$577$	4.64242e6	+	8.04090e6i	0.580503	+	1.00546i	−0.414916	+	0.909859i	$0.636189\pi$
$578$	−4.21194e6	−	7.29530e6i	−0.524400	−	0.908288i
$579$	−691209.	+	1.19721e6i	−0.0856866	+	0.148414i
$580$	1.69790e6			0.209577
$581$		0			0
$582$	−7.75775e6			−0.949354
$583$	2.12987e6	−	3.68904e6i	0.259526	−	0.449513i
$584$	−5.19506e6	−	8.99811e6i	−0.630317	−	1.09174i
$585$	1.39628e6	+	2.41842e6i	0.168687	+	0.292175i
$586$	594198.	−	1.02918e6i	0.0714804	−	0.123808i
$587$	−1.47623e6			−0.176831			−0.0884155	−	0.996084i	$-0.528180\pi$
$587$	−1.47623e6			−0.176831			−0.0884155	+	0.996084i	$0.528180\pi$
$588$		0			0
$589$	214720.			0.0255026
$590$	6.43313e6	−	1.11425e7i	0.760838	−	1.31781i
$591$	−694899.	−	1.20360e6i	−0.0818376	−	0.141747i
$592$	−3.08651e6	−	5.34600e6i	−0.361963	−	0.626938i
$593$	−6.20034e6	+	1.07393e7i	−0.724067	+	1.25412i	0.235289	+	0.971925i	$0.424396\pi$
$593$	−6.20034e6	+	1.07393e7i	−0.724067	+	1.25412i	−0.959357	+	0.282196i	$0.908937\pi$
$594$	−1.94206e6			−0.225837
$595$		0			0
$596$	−328296.			−0.0378573
$597$	−1.65085e6	+	2.85936e6i	−0.189571	+	0.328347i
$598$	5.56920e6	+	9.64614e6i	0.636854	+	1.10306i
$599$	1.84564e6	+	3.19674e6i	0.210174	+	0.364032i	0.951769	−	0.306816i	$-0.0992636\pi$
$599$	1.84564e6	+	3.19674e6i	0.210174	+	0.364032i	−0.741595	+	0.670848i	$0.765930\pi$
$600$	−2.23700e6	+	3.87460e6i	−0.253681	+	0.439389i
$601$	−9.12223e6			−1.03018			−0.515092	−	0.857135i	$-0.672242\pi$
$601$	−9.12223e6			−1.03018			−0.515092	+	0.857135i	$0.672242\pi$
$602$		0			0
$603$	−4.80784e6			−0.538464
$604$	574064.	−	994308.i	0.0640277	−	0.110899i
$605$	1.40732e6	+	2.43754e6i	0.156316	+	0.270747i
$606$	73062.0	+	126547.i	0.00808184	+	0.0139981i
$607$	−2.83957e6	+	4.91828e6i	−0.312810	+	0.541803i	−0.978970	−	0.204007i	$-0.934604\pi$
$607$	−2.83957e6	+	4.91828e6i	−0.312810	+	0.541803i	0.666160	+	0.745809i	$0.267937\pi$
$608$	−3.86496e6			−0.424020
$609$		0			0
$610$	−2.31557e7			−2.51961
$611$	−3.07632e6	+	5.32834e6i	−0.333372	+	0.577416i
$612$	−20412.0	−	35354.6i	−0.00220296	−	0.00381564i
$613$	7.00529e6	+	1.21335e7i	0.752966	+	1.30417i	0.946379	+	0.323057i	$0.104711\pi$
$613$	7.00529e6	+	1.21335e7i	0.752966	+	1.30417i	−0.193414	+	0.981117i	$0.561956\pi$
$614$	3.13691e6	−	5.43328e6i	0.335800	−	0.581623i
$615$	5.58932e6			0.595897
$616$		0			0
$617$	−253686.			−0.0268277			−0.0134139	−	0.999910i	$-0.504270\pi$
$617$	−253686.			−0.0268277			−0.0134139	+	0.999910i	$0.504270\pi$
$618$	−3.55774e6	+	6.16218e6i	−0.374716	+	0.649028i
$619$	2.15017e6	+	3.72420e6i	0.225552	+	0.390667i	0.956485	−	0.291782i	$-0.0942482\pi$
$619$	2.15017e6	+	3.72420e6i	0.225552	+	0.390667i	−0.730933	+	0.682449i	$0.760915\pi$
$620$	−12480.0	−	21616.0i	−0.00130387	−	0.00225837i
$621$	−1.53090e6	+	2.65160e6i	−0.159301	+	0.275917i
$622$	1.10231e7			1.14242
$623$		0			0
$624$	−4.51901e6			−0.464603
$625$	5.12841e6	−	8.88267e6i	0.525149	−	0.909585i
$626$	1.09648e6	+	1.89916e6i	0.111832	+	0.193699i
$627$	5.36263e6	+	9.28835e6i	0.544765	+	0.943561i
$628$	259756.	−	449911.i	0.0262825	−	0.0455226i
$629$	−684684.			−0.0690023
$630$		0			0
$631$	1.04150e7			1.04132			0.520662	−	0.853763i	$-0.325685\pi$
$631$	1.04150e7			1.04132			0.520662	+	0.853763i	$0.325685\pi$
$632$	5.52518e6	−	9.56990e6i	0.550242	−	0.953048i
$633$	−2.34110e6	−	4.05490e6i	−0.232226	−	0.402227i
$634$	−85014.0	−	147249.i	−0.00839977	−	0.0145488i
$635$	−2.89848e6	+	5.02031e6i	−0.285257	+	0.494079i
$636$	−345384.			−0.0338579
$637$		0			0
$638$	1.44975e7			1.41007
$639$	−1.29762e6	+	2.24754e6i	−0.125717	+	0.217749i
$640$	−8.28173e6	−	1.43444e7i	−0.799229	−	1.38430i
$641$	−2.26357e6	−	3.92062e6i	−0.217595	−	0.376885i	0.736477	−	0.676462i	$-0.236488\pi$
$641$	−2.26357e6	−	3.92062e6i	−0.217595	−	0.376885i	−0.954072	+	0.299577i	$0.903154\pi$
$642$	−3.48073e6	+	6.02880e6i	−0.333298	+	0.577289i
$643$	−1.49687e7			−1.42776			−0.713882	−	0.700266i	$-0.753065\pi$
$643$	−1.49687e7			−1.42776			−0.713882	+	0.700266i	$0.753065\pi$
$644$		0			0
$645$	8.08985e6			0.765669
$646$	−1.01455e6	+	1.75726e6i	−0.0956518	+	0.165674i
$647$	−8.65098e6	−	1.49839e7i	−0.812465	−	1.40723i	−0.911134	−	0.412110i	$-0.864792\pi$
$647$	−8.65098e6	−	1.49839e7i	−0.812465	−	1.40723i	0.0986691	−	0.995120i	$-0.468541\pi$
$648$	−551124.	−	954575.i	−0.0515599	−	0.0893043i
$649$	6.10322e6	−	1.05711e7i	0.568784	−	0.985163i
$650$	−7.84727e6			−0.728509
$651$		0			0
$652$	2.22114e6			0.204624
$653$	−2.03735e6	+	3.52880e6i	−0.186975	+	0.323850i	−0.944240	−	0.329258i	$-0.893202\pi$
$653$	−2.03735e6	+	3.52880e6i	−0.186975	+	0.323850i	0.757265	+	0.653107i	$0.226535\pi$
$654$	−2.72641e6	−	4.72227e6i	−0.249256	−	0.431725i
$655$	6.05732e6	+	1.04916e7i	0.551668	+	0.955516i
$656$	−4.52242e6	+	7.83305e6i	−0.410309	+	0.710676i
$657$	5.00953e6			0.452776
$658$		0			0
$659$	−3.79475e6			−0.340384			−0.170192	−	0.985411i	$-0.554439\pi$
$659$	−3.79475e6			−0.340384			−0.170192	+	0.985411i	$0.554439\pi$
$660$	623376.	−	1.07972e6i	0.0557045	−	0.0964830i
$661$	8.21307e6	+	1.42255e7i	0.731142	+	1.26638i	0.956395	+	0.292075i	$0.0943458\pi$
$661$	8.21307e6	+	1.42255e7i	0.731142	+	1.26638i	−0.225253	+	0.974300i	$0.572321\pi$
$662$	5.80175e6	+	1.00489e7i	0.514534	+	0.891199i
$663$	−250614.	+	434076.i	−0.0221422	+	0.0383515i
$664$	−6.75158e6			−0.594272
$665$		0			0
$666$	2.64092e6			0.230712
$667$	1.14282e7	−	1.97942e7i	0.994634	−	1.72276i
$668$	87024.0	+	150730.i	0.00754567	+	0.0130695i
$669$	1.37131e6	+	2.37518e6i	0.118460	+	0.205178i
$670$	1.38893e7	−	2.40570e7i	1.19535	−	2.07040i
$671$	−2.19682e7			−1.88360
$672$		0			0
$673$	5.50675e6			0.468660			0.234330	−	0.972157i	$-0.424710\pi$
$673$	5.50675e6			0.468660			0.234330	+	0.972157i	$0.424710\pi$
$674$	−5.66452e6	+	9.81124e6i	−0.480301	+	0.831906i
$675$	−1.07856e6	−	1.86811e6i	−0.0911136	−	0.157813i
$676$	351858.	+	609436.i	0.0296142	+	0.0512934i
$677$	9.19787e6	−	1.59312e7i	0.771286	−	1.33591i	−0.165572	−	0.986198i	$-0.552947\pi$
$677$	9.19787e6	−	1.59312e7i	0.771286	−	1.33591i	0.936858	−	0.349709i	$-0.113720\pi$
$678$	−1.18879e7			−0.993185
$679$		0			0
$680$	−1.65110e6			−0.136931
$681$	1.29865e6	−	2.24932e6i	0.107306	−	0.185859i
$682$	−106560.	−	184567.i	−0.00877270	−	0.0151948i
$683$	−879174.	−	1.52277e6i	−0.0721146	−	0.124906i	0.827713	−	0.561151i	$-0.189641\pi$
$683$	−879174.	−	1.52277e6i	−0.0721146	−	0.124906i	−0.899828	+	0.436245i	$0.856308\pi$
$684$	434808.	−	753110.i	0.0355351	−	0.0615486i
$685$	2.06112e7			1.67833
$686$		0			0
$687$	−6.94971e6			−0.561791
$688$	−6.54563e6	+	1.13374e7i	−0.527206	+	0.913148i
$689$	2.12027e6	+	3.67242e6i	0.170155	+	0.294717i
$690$	−8.84520e6	−	1.53203e7i	−0.707270	−	1.22503i
$691$	−2.68157e6	+	4.64462e6i	−0.213646	+	0.370045i	−0.952853	−	0.303433i	$-0.901867\pi$
$691$	−2.68157e6	+	4.64462e6i	−0.213646	+	0.370045i	0.739207	+	0.673478i	$0.235200\pi$
$692$	73320.0			0.00582046
$693$		0			0
$694$	−1.75162e7			−1.38052
$695$	−8.75987e6	+	1.51725e7i	−0.687916	+	1.19151i
$696$	4.11415e6	+	7.12592e6i	0.321927	+	0.557594i
$697$	501606.	+	868807.i	0.0391094	+	0.0677394i
$698$	2.34205e6	−	4.05654e6i	0.181952	−	0.315150i
$699$	2.27011e6			0.175733
$700$		0			0
$701$	−2.12606e7			−1.63411			−0.817054	−	0.576561i	$-0.804394\pi$
$701$	−2.12606e7			−1.63411			−0.817054	+	0.576561i	$0.804394\pi$
$702$	966654.	−	1.67429e6i	0.0740335	−	0.128230i
$703$	−7.29243e6	−	1.26309e7i	−0.556524	−	0.963928i
$704$	−6.15206e6	−	1.06557e7i	−0.467831	−	0.810307i
$705$	4.88592e6	−	8.46266e6i	0.370232	−	0.641260i
$706$	8.00622e6			0.604527
$707$		0			0
$708$	−989712.			−0.0742037
$709$	−1.03864e6	+	1.79898e6i	−0.0775980	+	0.134404i	−0.902213	−	0.431290i	$-0.858058\pi$
$709$	−1.03864e6	+	1.79898e6i	−0.0775980	+	0.134404i	0.824615	+	0.565694i	$0.191392\pi$
$710$	−7.49736e6	−	1.29858e7i	−0.558165	−	0.966770i
$711$	2.66393e6	+	4.61406e6i	0.197628	+	0.342302i
$712$	−669816.	+	1.16016e6i	−0.0495171	+	0.0857662i
$713$	−336000.			−0.0247523
$714$		0			0
$715$	−1.53073e7			−1.11979
$716$	306648.	−	531130.i	0.0223541	−	0.0387185i
$717$	6.53011e6	+	1.13105e7i	0.474376	+	0.821643i
$718$	3.05230e6	+	5.28673e6i	0.220961	+	0.382716i
$719$	2.11810e6	−	3.66865e6i	0.152800	−	0.264657i	−0.779456	−	0.626457i	$-0.784504\pi$
$719$	2.11810e6	−	3.66865e6i	0.152800	−	0.264657i	0.932256	+	0.361800i	$0.117838\pi$
$720$	7.17725e6			0.515973
$721$		0			0
$722$	−2.83665e7			−2.02518
$723$	−658791.	+	1.14106e6i	−0.0468708	+	0.0811825i
$724$	−764132.	−	1.32352e6i	−0.0541779	−	0.0938388i
$725$	8.05144e6	+	1.39455e7i	0.568890	+	0.985347i
$726$	974295.	−	1.68753e6i	0.0686039	−	0.118825i
$727$	−2.14524e7			−1.50536			−0.752678	−	0.658389i	$-0.771238\pi$
$727$	−2.14524e7			−1.50536			−0.752678	+	0.658389i	$0.771238\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−1.44720e7	+	2.50662e7i	−1.00513	+	1.74093i
$731$	726012.	+	1.25749e6i	0.0502517	+	0.0870384i
$732$	890604.	+	1.54257e6i	0.0614337	+	0.106406i
$733$	−7.44459e6	+	1.28944e7i	−0.511777	+	0.886424i	0.488130	+	0.872771i	$0.337679\pi$
$733$	−7.44459e6	+	1.28944e7i	−0.511777	+	0.886424i	−0.999907	+	0.0136528i	$0.995654\pi$
$734$	5.02608e6			0.344341
$735$		0			0
$736$	6.04800e6			0.411545
$737$	1.31770e7	−	2.28233e7i	0.893612	−	1.54778i
$738$	−1.93477e6	−	3.35111e6i	−0.130764	−	0.226490i
$739$	−3.49662e6	−	6.05632e6i	−0.235525	−	0.407941i	0.723900	−	0.689905i	$-0.242348\pi$
$739$	−3.49662e6	−	6.05632e6i	−0.235525	−	0.407941i	−0.959425	+	0.281963i	$0.909014\pi$
$740$	−847704.	+	1.46827e6i	−0.0569069	+	0.0985656i
$741$	−1.06770e7			−0.714335
$742$		0			0
$743$	1.90428e6			0.126549			0.0632745	−	0.997996i	$-0.479846\pi$
$743$	1.90428e6			0.126549			0.0632745	+	0.997996i	$0.479846\pi$
$744$	60480.0	−	104754.i	0.00400571	−	0.00693809i
$745$	−3.20089e6	−	5.54410e6i	−0.211290	−	0.365966i
$746$	−4.55979e6	−	7.89779e6i	−0.299984	−	0.519587i
$747$	1.62761e6	−	2.81911e6i	0.106721	−	0.184846i
$748$	223776.			0.0146238
$749$		0			0
$750$	−699192.			−0.0453882
$751$	−9.76806e6	+	1.69188e7i	−0.631988	+	1.09463i	0.355157	+	0.934807i	$0.384427\pi$
$751$	−9.76806e6	+	1.69188e7i	−0.631988	+	1.09463i	−0.987145	+	0.159828i	$0.948906\pi$
$752$	7.90656e6	+	1.36946e7i	0.509851	+	0.883087i
$753$	2.73537e6	+	4.73780e6i	0.175804	+	0.304501i
$754$	−7.21609e6	+	1.24986e7i	−0.462247	+	0.800635i
$755$	2.23885e7			1.42941
$756$		0			0
$757$	1.25183e6			0.0793973			0.0396986	−	0.999212i	$-0.487360\pi$
$757$	1.25183e6			0.0793973			0.0396986	+	0.999212i	$0.487360\pi$
$758$	7.93396e6	−	1.37420e7i	0.501553	−	0.868715i
$759$	−8.39160e6	−	1.45347e7i	−0.528738	−	0.915801i
$760$	−1.75856e7	−	3.04591e7i	−1.10439	−	1.91286i
$761$	1.02236e7	−	1.77078e7i	0.639944	−	1.10841i	−0.345501	−	0.938418i	$-0.612291\pi$
$761$	1.02236e7	−	1.77078e7i	0.639944	−	1.10841i	0.985445	−	0.169997i	$-0.0543757\pi$
$762$	4.01328e6			0.250387
$763$		0			0
$764$	−1.09363e6			−0.0677857
$765$	398034.	−	689415.i	0.0245905	−	0.0425919i
$766$	−6.04008e6	−	1.04617e7i	−0.371938	−	0.644216i
$767$	6.07573e6	+	1.05235e7i	0.372915	+	0.645908i
$768$	−1.74298e6	+	3.01892e6i	−0.106632	+	0.184692i
$769$	−2.21064e6			−0.134804			−0.0674020	−	0.997726i	$-0.521471\pi$
$769$	−2.21064e6			−0.134804			−0.0674020	+	0.997726i	$0.521471\pi$
$770$		0			0
$771$	−860274.			−0.0521196
$772$	−307204.	+	532093.i	−0.0185517	+	0.0321325i
$773$	6.45753e6	+	1.11848e7i	0.388703	+	0.673253i	0.992275	−	0.124055i	$-0.0395900\pi$
$773$	6.45753e6	+	1.11848e7i	0.388703	+	0.673253i	−0.603573	+	0.797308i	$0.706257\pi$
$774$	−2.80033e6	−	4.85032e6i	−0.168019	−	0.291017i
$775$	118360.	−	205006.i	0.00707865	−	0.0122606i
$776$	2.41352e7			1.43879
$777$		0			0
$778$	4.35740e6			0.258095
$779$	−1.06850e7	+	1.85070e7i	−0.630857	+	1.09268i
$780$	620568.	+	1.07486e6i	0.0365219	+	0.0632577i
$781$	−7.11288e6	−	1.23199e7i	−0.417271	−	0.722734i
$782$	1.58760e6	−	2.74980e6i	0.0928377	−	0.160800i
$783$	−3.96722e6			−0.231250
$784$		0			0
$785$	1.01305e7			0.586754
$786$	4.19353e6	−	7.26341e6i	0.242116	−	0.419357i
$787$	−6.77496e6	−	1.17346e7i	−0.389915	−	0.675353i	0.602523	−	0.798102i	$-0.294162\pi$
$787$	−6.77496e6	−	1.17346e7i	−0.389915	−	0.675353i	−0.992438	+	0.122749i	$0.960829\pi$
$788$	−308844.	−	534933.i	−0.0177184	−	0.0306891i
$789$	9.90155e6	−	1.71500e7i	0.566253	−	0.980779i
$790$	−3.07832e7			−1.75487
$791$		0			0
$792$	6.04195e6			0.342266
$793$	1.09346e7	−	1.89393e7i	0.617478	−	1.06950i
$794$	−1.37273e7	−	2.37765e7i	−0.772743	−	1.33843i
$795$	−3.36749e6	−	5.83267e6i	−0.188968	−	0.327303i
$796$	−733712.	+	1.27083e6i	−0.0410434	+	0.0710892i
$797$	2.45956e7			1.37155			0.685776	−	0.727813i	$-0.259463\pi$
$797$	2.45956e7			1.37155			0.685776	+	0.727813i	$0.259463\pi$
$798$		0			0
$799$	1.75392e6			0.0971948
$800$	−2.13048e6	+	3.69010e6i	−0.117694	+	0.203851i
$801$	−322947.	−	559361.i	−0.0177848	−	0.0308042i
$802$	−101610.	−	175994.i	−0.00557828	−	0.00966187i
$803$	−1.37298e7	+	2.37807e7i	−0.751408	+	1.30148i
$804$	−2.13682e6			−0.116581
$805$		0			0
$806$	212160.			0.0115034
$807$	7.96611e6	−	1.37977e7i	0.430588	−	0.745801i
$808$	−227304.	−	393702.i	−0.0122484	−	0.0212148i
$809$	−7.76186e6	−	1.34439e7i	−0.416960	−	0.722196i	0.578672	−	0.815560i	$-0.303571\pi$
$809$	−7.76186e6	−	1.34439e7i	−0.416960	−	0.722196i	−0.995632	+	0.0933643i	$0.970238\pi$
$810$	−1.53527e6	+	2.65917e6i	−0.0822192	+	0.142408i
$811$	2.66262e7			1.42153			0.710766	−	0.703429i	$-0.248349\pi$
$811$	2.66262e7			1.42153			0.710766	+	0.703429i	$0.248349\pi$
$812$		0			0
$813$	2.01154e6			0.106734
$814$	−7.23809e6	+	1.25367e7i	−0.382880	+	0.663168i
$815$	2.16561e7	+	3.75094e7i	1.14205	+	1.97809i
$816$	644112.	+	1.11563e6i	0.0338638	+	0.0586539i
$817$	−1.54652e7	+	2.67865e7i	−0.810589	+	1.40398i
$818$	−3.51707e7			−1.83780
$819$		0			0
$820$	2.48414e6			0.129016
$821$	6.19454e6	−	1.07293e7i	0.320739	−	0.555536i	−0.659902	−	0.751352i	$-0.729402\pi$
$821$	6.19454e6	−	1.07293e7i	0.320739	−	0.555536i	0.980641	+	0.195816i	$0.0627356\pi$
$822$	−7.13464e6	−	1.23576e7i	−0.368292	−	0.637901i
$823$	1.82815e6	+	3.16645e6i	0.0940831	+	0.162957i	0.909226	−	0.416304i	$-0.136675\pi$
$823$	1.82815e6	+	3.16645e6i	0.0940831	+	0.162957i	−0.815142	+	0.579261i	$0.803341\pi$
$824$	1.10685e7	−	1.91712e7i	0.567899	−	0.983630i
$825$	1.18242e7			0.604833
$826$		0			0
$827$	2.80463e7			1.42597			0.712987	−	0.701178i	$-0.247342\pi$
$827$	2.80463e7			1.42597			0.712987	+	0.701178i	$0.247342\pi$
$828$	−680400.	+	1.17849e6i	−0.0344896	+	0.0597378i
$829$	1.05577e7	+	1.82864e7i	0.533558	+	0.924150i	0.999232	+	0.0391930i	$0.0124787\pi$
$829$	1.05577e7	+	1.82864e7i	0.533558	+	0.924150i	−0.465674	+	0.884957i	$0.654188\pi$
$830$	9.40399e6	+	1.62882e7i	0.473824	+	0.820687i
$831$	1.54250e6	−	2.67169e6i	0.0774859	−	0.134210i
$832$	1.22487e7			0.613454
$833$		0			0
$834$	1.21290e7			0.603826
$835$	−1.69697e6	+	2.93923e6i	−0.0842282	+	0.145888i
$836$	2.38339e6	+	4.12816e6i	0.117945	+	0.204287i
$837$	29160.0	+	50506.6i	0.00143871	+	0.00249192i
$838$	−908244.	+	1.57312e6i	−0.0446779	+	0.0773843i
$839$	−1.33947e7			−0.656944			−0.328472	−	0.944514i	$-0.606534\pi$
$839$	−1.33947e7			−0.656944			−0.328472	+	0.944514i	$0.606534\pi$
$840$		0			0
$841$	9.10422e6			0.443867
$842$	−1.61012e7	+	2.78882e7i	−0.782671	+	1.35563i
$843$	−2.16170e6	−	3.74418e6i	−0.104768	−	0.181463i
$844$	−1.04049e6	−	1.80218e6i	−0.0502783	−	0.0870846i
$845$	−6.86123e6	+	1.18840e7i	−0.330568	+	0.572560i
$846$	−6.76512e6			−0.324975
$847$		0			0
$848$	1.08988e7			0.520461
$849$	−134910.	+	233671.i	−0.00642355	+	0.0111259i
$850$	1.11850e6	+	1.93730e6i	0.0530994	+	0.0919708i
$851$	1.14114e7	+	1.97651e7i	0.540151	+	0.935569i
$852$	−576720.	+	998908.i	−0.0272186	+	0.0471440i
$853$	−3.01513e7			−1.41884			−0.709420	−	0.704786i	$-0.751043\pi$
$853$	−3.01513e7			−1.41884			−0.709420	+	0.704786i	$0.751043\pi$
$854$		0			0
$855$	1.69575e7			0.793317
$856$	1.08289e7	−	1.87563e7i	0.505128	−	0.874908i
$857$	1.19947e7	+	2.07754e7i	0.557875	+	0.966268i	0.997674	+	0.0681717i	$0.0217166\pi$
$857$	1.19947e7	+	2.07754e7i	0.557875	+	0.966268i	−0.439798	+	0.898097i	$0.644950\pi$
$858$	5.29870e6	+	9.17761e6i	0.245726	+	0.425610i
$859$	−4.43788e6	+	7.68663e6i	−0.205207	+	0.355429i	−0.950199	−	0.311645i	$-0.899120\pi$
$859$	−4.43788e6	+	7.68663e6i	−0.205207	+	0.355429i	0.744992	+	0.667074i	$0.232453\pi$
$860$	3.59549e6			0.165772
$861$		0			0
$862$	−7.06234e6			−0.323728
$863$	4.35643e6	−	7.54556e6i	0.199115	−	0.344877i	−0.749127	−	0.662427i	$-0.769527\pi$
$863$	4.35643e6	−	7.54556e6i	0.199115	−	0.344877i	0.948242	+	0.317549i	$0.102860\pi$
$864$	−524880.	−	909119.i	−0.0239208	−	0.0414320i
$865$	714870.	+	1.23819e6i	0.0324853	+	0.0562662i
$866$	1.09875e7	−	1.90309e7i	0.497856	−	0.862311i
$867$	−1.26358e7			−0.570895
$868$		0			0
$869$	−2.92045e7			−1.31190
$870$	1.14609e7	−	1.98508e7i	0.513356	−	0.889159i
$871$	1.31177e7	+	2.27205e7i	0.585884	+	1.01478i
$872$	8.48215e6	+	1.46915e7i	0.377759	+	0.654298i
$873$	−5.81831e6	+	1.00776e7i	−0.258381	+	0.447530i
$874$	6.76368e7			2.99505
$875$		0			0
$876$	2.22646e6			0.0980288
$877$	1.47894e7	−	2.56160e7i	0.649310	−	1.12464i	−0.333978	−	0.942581i	$-0.608391\pi$
$877$	1.47894e7	−	2.56160e7i	0.649310	−	1.12464i	0.983288	−	0.182057i	$-0.0582755\pi$
$878$	7.61023e6	+	1.31813e7i	0.333167	+	0.577062i
$879$	−891297.	−	1.54377e6i	−0.0389090	−	0.0673924i
$880$	−1.96710e7	+	3.40711e7i	−0.856287	+	1.48313i
$881$	−2.45670e7			−1.06638			−0.533190	−	0.845995i	$-0.679007\pi$
$881$	−2.45670e7			−1.06638			−0.533190	+	0.845995i	$0.679007\pi$
$882$		0			0
$883$	1.45682e7			0.628788			0.314394	−	0.949293i	$-0.398199\pi$
$883$	1.45682e7			0.628788			0.314394	+	0.949293i	$0.398199\pi$
$884$	−111384.	+	192923.i	−0.00479394	+	0.00830334i
$885$	−9.64969e6	−	1.67138e7i	−0.414148	−	0.717325i
$886$	1.80451e7	+	3.12550e7i	0.772281	+	1.33763i
$887$	8.08568e6	−	1.40048e7i	0.345070	−	0.597679i	−0.640296	−	0.768128i	$-0.721188\pi$
$887$	8.08568e6	−	1.40048e7i	0.345070	−	0.597679i	0.985367	+	0.170449i	$0.0545217\pi$
$888$	−8.21621e6			−0.349654
$889$		0			0
$890$	3.73183e6			0.157924
$891$	−1.45654e6	+	2.52280e6i	−0.0614651	+	0.106461i
$892$	609472.	+	1.05564e6i	0.0256473	+	0.0444224i
$893$	1.86806e7	+	3.23558e7i	0.783904	+	1.35776i
$894$	−2.21600e6	+	3.83822e6i	−0.0927311	+	0.160615i
$895$	1.19593e7			0.499054
$896$		0			0
$897$	1.67076e7			0.693319
$898$	1.69790e7	−	2.94084e7i	0.702619	−	1.21697i
$899$	−217680.	−	377033.i	−0.00898296	−	0.0155589i
$900$	−479358.	−	830272.i	−0.0197267	−	0.0341676i
$901$	604422.	−	1.04689e6i	0.0248044	−	0.0429624i
$902$	2.12108e7			0.868041
$903$		0			0
$904$	3.69845e7			1.50522
$905$	1.49006e7	−	2.58086e7i	0.604758	−	1.04747i
$906$	−7.74986e6	−	1.34232e7i	−0.313670	−	0.543293i
$907$	−1.57223e7	−	2.72318e7i	−0.634596	−	1.09915i	−0.986601	−	0.163154i	$-0.947833\pi$
$907$	−1.57223e7	−	2.72318e7i	−0.634596	−	1.09915i	0.352005	−	0.935998i	$-0.385500\pi$
$908$	577176.	−	999698.i	0.0232324	−	0.0402397i
$909$	219186.			0.00879839
$910$		0			0
$911$	1.51427e7			0.604514			0.302257	−	0.953227i	$-0.402260\pi$
$911$	1.51427e7			0.604514			0.302257	+	0.953227i	$0.402260\pi$
$912$	−1.37206e7	+	2.37648e7i	−0.546243	+	0.946121i
$913$	8.92174e6	+	1.54529e7i	0.354219	+	0.613526i
$914$	−1.93848e7	−	3.35754e7i	−0.767530	−	1.32940i
$915$	−1.73668e7	+	3.00801e7i	−0.685751	+	1.18776i
$916$	−3.08876e6			−0.121631
$917$		0			0
$918$	−551124.			−0.0215845
$919$	−2.07438e7	+	3.59293e7i	−0.810214	+	1.40333i	0.102500	+	0.994733i	$0.467316\pi$
$919$	−2.07438e7	+	3.59293e7i	−0.810214	+	1.40333i	−0.912714	+	0.408598i	$0.866018\pi$
$920$	2.75184e7	+	4.76633e7i	1.07190	+	1.85658i
$921$	−4.70536e6	−	8.14993e6i	−0.182786	−	0.316595i
$922$	1.01206e7	−	1.75294e7i	0.392083	−	0.679108i
$923$	1.41617e7			0.547155
$924$		0			0
$925$	−1.60792e7			−0.617889
$926$	−1.36492e7	+	2.36412e7i	−0.523095	+	0.906027i
$927$	5.33660e6	+	9.24327e6i	0.203970	+	0.353286i
$928$	3.91824e6	+	6.78659e6i	0.149355	+	0.258691i
$929$	−8.92473e6	+	1.54581e7i	−0.339278	+	0.587647i	−0.984297	−	0.176520i	$-0.943516\pi$
$929$	−8.92473e6	+	1.54581e7i	−0.339278	+	0.587647i	0.645019	+	0.764166i	$0.276849\pi$
$930$	−336960.			−0.0127753
$931$		0			0
$932$	1.00894e6			0.0380473
$933$	8.26729e6	−	1.43194e7i	0.310928	−	0.538542i
$934$	−6.03407e6	−	1.04513e7i	−0.226330	−	0.392016i
$935$	2.18182e6	+	3.77902e6i	0.0816186	+	0.141368i
$936$	−3.00737e6	+	5.20891e6i	−0.112201	+	0.194338i
$937$	−2.96399e7			−1.10288			−0.551439	−	0.834215i	$-0.685921\pi$
$937$	−2.96399e7			−1.10288			−0.551439	+	0.834215i	$0.685921\pi$
$938$		0			0
$939$	3.28945e6			0.121747
$940$	2.17152e6	−	3.76118e6i	0.0801575	−	0.138837i
$941$	−1.61141e7	−	2.79104e7i	−0.593242	−	1.02753i	−0.993792	−	0.111251i	$-0.964514\pi$
$941$	−1.61141e7	−	2.79104e7i	−0.593242	−	1.02753i	0.400550	−	0.916275i	$-0.368819\pi$
$942$	−3.50671e6	−	6.07379e6i	−0.128757	−	0.223014i
$943$	1.67202e7	−	2.89602e7i	0.612297	−	1.06053i
$944$	3.12309e7			1.14066
$945$		0			0
$946$	3.06999e7			1.11535
$947$	−2.42442e7	+	4.19923e7i	−0.878484	+	1.52158i	−0.0254787	+	0.999675i	$0.508111\pi$
$947$	−2.42442e7	+	4.19923e7i	−0.878484	+	1.52158i	−0.853005	+	0.521903i	$0.825222\pi$
$948$	1.18397e6	+	2.05069e6i	0.0427877	+	0.0741105i
$949$	−1.36680e7	−	2.36736e7i	−0.492650	−	0.853295i
$950$	−2.38259e7	+	4.12676e7i	−0.856524	+	1.48354i
$951$	−255042.			−0.00914451
$952$		0			0
$953$	−2.03264e7			−0.724983			−0.362491	−	0.931987i	$-0.618074\pi$
$953$	−2.03264e7			−0.724983			−0.362491	+	0.931987i	$0.618074\pi$
$954$	−2.33134e6	+	4.03800e6i	−0.0829345	+	0.143647i
$955$	−1.06629e7	−	1.84687e7i	−0.378327	−	0.655282i
$956$	2.90227e6	+	5.02688e6i	0.102705	+	0.177891i
$957$	1.08731e7	−	1.88328e7i	0.383773	−	0.664714i
$958$	−4.56241e7			−1.60613
$959$		0			0
$960$	−1.94538e7			−0.681282
$961$	1.43114e7	−	2.47880e7i	0.499888	−	0.865832i
$962$	−7.20548e6	−	1.24803e7i	−0.251030	−	0.434797i
$963$	5.22110e6	+	9.04321e6i	0.181425	+	0.314237i
$964$	−292796.	+	507138.i	−0.0101478	+	0.0175765i
$965$	−1.19810e7			−0.414165
$966$		0			0
$967$	−3.66292e6			−0.125968			−0.0629841	−	0.998015i	$-0.520062\pi$
$967$	−3.66292e6			−0.125968			−0.0629841	+	0.998015i	$0.520062\pi$
$968$	−3.03114e6	+	5.25009e6i	−0.103972	+	0.180085i
$969$	1.52183e6	+	2.63588e6i	0.0520662	+	0.0901814i
$970$	−3.36169e7	−	5.82262e7i	−1.14717	−	1.98696i
$971$	743706.	−	1.28814e6i	0.0253136	−	0.0438444i	−0.853091	−	0.521762i	$-0.825275\pi$
$971$	743706.	−	1.28814e6i	0.0253136	−	0.0438444i	0.878405	+	0.477918i	$0.158608\pi$
$972$	236196.			0.00801875
$973$		0			0
$974$	−4.03867e6			−0.136408
$975$	−5.88545e6	+	1.01939e7i	−0.198275	+	0.343423i
$976$	−2.81035e7	−	4.86767e7i	−0.944356	−	1.63567i
$977$	−2.03965e7	−	3.53278e7i	−0.683627	−	1.18408i	−0.973866	−	0.227123i	$-0.927068\pi$
$977$	−2.03965e7	−	3.53278e7i	−0.683627	−	1.18408i	0.290239	−	0.956954i	$-0.406265\pi$
$978$	1.49927e7	−	2.59681e7i	0.501224	−	0.868145i
$979$	3.54046e6			0.118060
$980$		0			0
$981$	−8.17922e6			−0.271356
$982$	−7.41510e6	+	1.28433e7i	−0.245380	+	0.425010i
$983$	−4.63163e6	−	8.02222e6i	−0.152880	−	0.264795i	0.779405	−	0.626520i	$-0.215521\pi$
$983$	−4.63163e6	−	8.02222e6i	−0.152880	−	0.264795i	−0.932285	+	0.361725i	$0.882188\pi$
$984$	6.01927e6	+	1.04257e7i	0.198178	+	0.343255i
$985$	6.02246e6	−	1.04312e7i	0.197780	−	0.342566i
$986$	4.11415e6			0.134768
$987$		0			0
$988$	−4.74531e6			−0.154658
$989$	2.42004e7	−	4.19163e7i	0.786741	−	1.36268i
$990$	−8.41558e6	−	1.45762e7i	−0.272895	−	0.472668i
$991$	2.61025e7	+	4.52109e7i	0.844303	+	1.46238i	0.886225	+	0.463255i	$0.153319\pi$
$991$	2.61025e7	+	4.52109e7i	0.844303	+	1.46238i	−0.0419218	+	0.999121i	$0.513348\pi$
$992$	57600.0	−	99766.1i	0.00185842	−	0.00321887i
$993$	1.74052e7			0.560153
$994$		0			0
$995$	−2.86148e7			−0.916289
$996$	723384.	−	1.25294e6i	0.0231058	−	0.0400204i
$997$	−9.33047e6	−	1.61609e7i	−0.297280	−	0.514904i	0.678233	−	0.734847i	$-0.262746\pi$
$997$	−9.33047e6	−	1.61609e7i	−0.297280	−	0.514904i	−0.975513	+	0.219943i	$0.929413\pi$
$998$	1.82446e7	+	3.16005e7i	0.579839	+	1.00431i
$999$	1.98069e6	−	3.43066e6i	0.0627919	−	0.108759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.e.i.79.1		2
7.2	even	3		147.6.a.b.1.1		1
7.3	odd	6		147.6.e.j.67.1		2
7.4	even	3	inner	147.6.e.i.67.1		2
7.5	odd	6		21.6.a.a.1.1	✓	1
7.6	odd	2		147.6.e.j.79.1		2
21.2	odd	6		441.6.a.j.1.1		1
21.5	even	6		63.6.a.d.1.1		1
28.19	even	6		336.6.a.r.1.1		1
35.12	even	12		525.6.d.b.274.1		2
35.19	odd	6		525.6.a.d.1.1		1
35.33	even	12		525.6.d.b.274.2		2
84.47	odd	6		1008.6.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.a.a.1.1	✓	1	7.5	odd	6
63.6.a.d.1.1		1	21.5	even	6
147.6.a.b.1.1		1	7.2	even	3
147.6.e.i.67.1		2	7.4	even	3	inner
147.6.e.i.79.1		2	1.1	even	1	trivial
147.6.e.j.67.1		2	7.3	odd	6
147.6.e.j.79.1		2	7.6	odd	2
336.6.a.r.1.1		1	28.19	even	6
441.6.a.j.1.1		1	21.2	odd	6
525.6.a.d.1.1		1	35.19	odd	6
525.6.d.b.274.1		2	35.12	even	12
525.6.d.b.274.2		2	35.33	even	12
1008.6.a.c.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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.00000 - 5.19615i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(39.0000 - 67.5500i) q^{5} -54.0000 q^{6} +168.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-234.000 - 405.300i) q^{10} +(-222.000 - 384.515i) q^{11} +(-18.0000 + 31.1769i) q^{12} +442.000 q^{13} -702.000 q^{15} +(568.000 - 983.805i) q^{16} +(-63.0000 - 109.119i) q^{17} +(243.000 + 420.888i) q^{18} +(1342.00 - 2324.41i) q^{19} -312.000 q^{20} -2664.00 q^{22} +(-2100.00 + 3637.31i) q^{23} +(-756.000 - 1309.43i) q^{24} +(-1479.50 - 2562.57i) q^{25} +(1326.00 - 2296.70i) q^{26} +729.000 q^{27} -5442.00 q^{29} +(-2106.00 + 3647.70i) q^{30} +(40.0000 + 69.2820i) q^{31} +(-720.000 - 1247.08i) q^{32} +(-1998.00 + 3460.64i) q^{33} -756.000 q^{34} +324.000 q^{36} +(2717.00 - 4705.98i) q^{37} +(-8052.00 - 13946.5i) q^{38} +(-1989.00 - 3445.05i) q^{39} +(6552.00 - 11348.4i) q^{40} -7962.00 q^{41} -11524.0 q^{43} +(-888.000 + 1538.06i) q^{44} +(3159.00 + 5471.55i) q^{45} +(12600.0 + 21823.8i) q^{46} +(-6960.00 + 12055.1i) q^{47} -10224.0 q^{48} -17754.0 q^{50} +(-567.000 + 982.073i) q^{51} +(-884.000 - 1531.13i) q^{52} +(4797.00 + 8308.65i) q^{53} +(2187.00 - 3788.00i) q^{54} -34632.0 q^{55} -24156.0 q^{57} +(-16326.0 + 28277.5i) q^{58} +(13746.0 + 23808.8i) q^{59} +(1404.00 + 2431.80i) q^{60} +(24739.0 - 42849.2i) q^{61} +480.000 q^{62} +27712.0 q^{64} +(17238.0 - 29857.1i) q^{65} +(11988.0 + 20763.8i) q^{66} +(29678.0 + 51403.8i) q^{67} +(-252.000 + 436.477i) q^{68} +37800.0 q^{69} +32040.0 q^{71} +(-6804.00 + 11784.9i) q^{72} +(-30923.0 - 53560.2i) q^{73} +(-16302.0 - 28235.9i) q^{74} +(-13315.5 + 23063.1i) q^{75} -10736.0 q^{76} -23868.0 q^{78} +(32888.0 - 56963.7i) q^{79} +(-44304.0 - 76736.8i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-23886.0 + 41371.8i) q^{82} -40188.0 q^{83} -9828.00 q^{85} +(-34572.0 + 59880.5i) q^{86} +(24489.0 + 42416.2i) q^{87} +(-37296.0 - 64598.6i) q^{88} +(-3987.00 + 6905.69i) q^{89} +37908.0 q^{90} +16800.0 q^{92} +(360.000 - 623.538i) q^{93} +(41760.0 + 72330.4i) q^{94} +(-104676. - 181304. i) q^{95} +(-6480.00 + 11223.7i) q^{96} +143662. q^{97} +35964.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{2} - 9 q^{3} - 4 q^{4} + 78 q^{5} - 108 q^{6} + 336 q^{8} - 81 q^{9} - 468 q^{10} - 444 q^{11} - 36 q^{12} + 884 q^{13} - 1404 q^{15} + 1136 q^{16} - 126 q^{17} + 486 q^{18} + 2684 q^{19} - 624 q^{20}+ \cdots + 71928 q^{99}+O(q^{100}) \) 2 * q + 6 * q^2 - 9 * q^3 - 4 * q^4 + 78 * q^5 - 108 * q^6 + 336 * q^8 - 81 * q^9 - 468 * q^10 - 444 * q^11 - 36 * q^12 + 884 * q^13 - 1404 * q^15 + 1136 * q^16 - 126 * q^17 + 486 * q^18 + 2684 * q^19 - 624 * q^20 - 5328 * q^22 - 4200 * q^23 - 1512 * q^24 - 2959 * q^25 + 2652 * q^26 + 1458 * q^27 - 10884 * q^29 - 4212 * q^30 + 80 * q^31 - 1440 * q^32 - 3996 * q^33 - 1512 * q^34 + 648 * q^36 + 5434 * q^37 - 16104 * q^38 - 3978 * q^39 + 13104 * q^40 - 15924 * q^41 - 23048 * q^43 - 1776 * q^44 + 6318 * q^45 + 25200 * q^46 - 13920 * q^47 - 20448 * q^48 - 35508 * q^50 - 1134 * q^51 - 1768 * q^52 + 9594 * q^53 + 4374 * q^54 - 69264 * q^55 - 48312 * q^57 - 32652 * q^58 + 27492 * q^59 + 2808 * q^60 + 49478 * q^61 + 960 * q^62 + 55424 * q^64 + 34476 * q^65 + 23976 * q^66 + 59356 * q^67 - 504 * q^68 + 75600 * q^69 + 64080 * q^71 - 13608 * q^72 - 61846 * q^73 - 32604 * q^74 - 26631 * q^75 - 21472 * q^76 - 47736 * q^78 + 65776 * q^79 - 88608 * q^80 - 6561 * q^81 - 47772 * q^82 - 80376 * q^83 - 19656 * q^85 - 69144 * q^86 + 48978 * q^87 - 74592 * q^88 - 7974 * q^89 + 75816 * q^90 + 33600 * q^92 + 720 * q^93 + 83520 * q^94 - 209352 * q^95 - 12960 * q^96 + 287324 * q^97 + 71928 * q^99

Introduction

L-functions

Modular forms

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Database

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