LMFDB - Embedded newform 49.6.c.f.18.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,6,Mod(18,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("49.18");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$N$	$=$	$49 = 7^{2}$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	49.c (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:	$7.85880717084$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{37})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{3} + 10x^{2} + 9x + 81$ x^4 - x^3 + 10x^2 + 9x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$2^{2}$
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.2
Root			$-1.27069 - 2.20090i$ of defining polynomial
Character	$\chi$	$=$	49.18
Dual form			49.6.c.f.30.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.54138 + 4.40180i) q^{2} +(1.04138 - 1.80373i) q^{3} +(3.08276 - 5.33950i) q^{4} +(20.9138 + 36.2238i) q^{5} +10.5862 q^{6} +193.986 q^{8} +(119.331 + 206.687i) q^{9} +(-106.300 + 184.117i) q^{10} +(-36.0482 + 62.4374i) q^{11} +(-6.42066 - 11.1209i) q^{12} +632.317 q^{13} +87.1170 q^{15} +(394.345 + 683.025i) q^{16} +(-987.962 + 1711.20i) q^{17} +(-606.531 + 1050.54i) q^{18} +(-932.463 - 1615.07i) q^{19} +257.889 q^{20} -366.449 q^{22} +(-206.855 - 358.284i) q^{23} +(202.014 - 349.898i) q^{24} +(687.725 - 1191.17i) q^{25} +(1606.96 + 2783.34i) q^{26} +1003.19 q^{27} +731.934 q^{29} +(221.398 + 383.472i) q^{30} +(3061.59 - 5302.83i) q^{31} +(1099.42 - 1904.25i) q^{32} +(75.0799 + 130.042i) q^{33} -10043.2 q^{34} +1471.48 q^{36} +(-5175.19 - 8963.69i) q^{37} +(4739.49 - 8209.03i) q^{38} +(658.483 - 1140.53i) q^{39} +(4056.99 + 7026.92i) q^{40} +3529.84 q^{41} -14515.2 q^{43} +(222.256 + 384.959i) q^{44} +(-4991.33 + 8645.24i) q^{45} +(1051.40 - 1821.07i) q^{46} +(-10711.7 - 18553.1i) q^{47} +1642.65 q^{48} +6991.08 q^{50} +(2057.69 + 3564.03i) q^{51} +(1949.28 - 3376.26i) q^{52} +(-6289.73 + 10894.1i) q^{53} +(2549.48 + 4415.83i) q^{54} -3015.62 q^{55} -3884.20 q^{57} +(1860.12 + 3221.83i) q^{58} +(-18067.0 + 31292.9i) q^{59} +(268.561 - 465.161i) q^{60} +(2012.40 + 3485.58i) q^{61} +31122.6 q^{62} +36414.2 q^{64} +(13224.2 + 22904.9i) q^{65} +(-381.613 + 660.974i) q^{66} +(-7782.97 + 13480.5i) q^{67} +(6091.31 + 10550.5i) q^{68} -861.661 q^{69} +12180.8 q^{71} +(23148.6 + 40094.5i) q^{72} +(9794.56 - 16964.7i) q^{73} +(26304.3 - 45560.3i) q^{74} +(-1432.37 - 2480.93i) q^{75} -11498.2 q^{76} +6693.83 q^{78} +(-18044.9 - 31254.7i) q^{79} +(-16494.5 + 28569.3i) q^{80} +(-27952.7 + 48415.6i) q^{81} +(8970.66 + 15537.6i) q^{82} +24572.6 q^{83} -82648.2 q^{85} +(-36888.7 - 63893.2i) q^{86} +(762.222 - 1320.21i) q^{87} +(-6992.86 + 12112.0i) q^{88} +(-35121.7 - 60832.5i) q^{89} -50739.5 q^{90} -2550.74 q^{92} +(-6376.56 - 11044.5i) q^{93} +(54444.8 - 94301.2i) q^{94} +(39002.7 - 67554.7i) q^{95} +(-2289.83 - 3966.10i) q^{96} -105758. q^{97} -17206.7 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q - 2 q^{2} - 8 q^{3} - 12 q^{4} - 38 q^{5} + 164 q^{6} + 192 q^{8} + 380 q^{9} - 778 q^{10} - 424 q^{11} - 196 q^{12} + 1848 q^{13} + 1784 q^{15} + 2064 q^{16} - 2346 q^{17} - 212 q^{18} - 360 q^{19}+ \cdots - 133888 q^{99}+O(q^{100})$ 4 * q - 2 * q^2 - 8 * q^3 - 12 * q^4 - 38 * q^5 + 164 * q^6 + 192 * q^8 + 380 * q^9 - 778 * q^10 - 424 * q^11 - 196 * q^12 + 1848 * q^13 + 1784 * q^15 + 2064 * q^16 - 2346 * q^17 - 212 * q^18 - 360 * q^19 + 3416 * q^20 + 4252 * q^22 + 12 * q^23 + 1392 * q^24 - 1872 * q^25 + 1148 * q^26 - 5744 * q^27 - 14104 * q^29 - 5258 * q^30 + 3548 * q^31 + 8096 * q^32 - 3398 * q^33 - 14844 * q^34 - 2192 * q^36 - 11090 * q^37 + 20138 * q^38 - 1624 * q^39 + 15936 * q^40 - 7000 * q^41 - 25360 * q^43 - 5948 * q^44 + 1300 * q^45 + 5118 * q^46 - 22956 * q^47 - 22432 * q^48 + 59984 * q^50 + 384 * q^51 - 1400 * q^52 - 3042 * q^53 + 32546 * q^54 + 50152 * q^55 - 38116 * q^57 + 58852 * q^58 - 65808 * q^59 - 14084 * q^60 - 42486 * q^61 + 98724 * q^62 + 70912 * q^64 + 3164 * q^65 - 25894 * q^66 - 42312 * q^67 + 5460 * q^68 - 10308 * q^69 - 4416 * q^71 + 32448 * q^72 - 50506 * q^73 + 47370 * q^74 - 35608 * q^75 - 77672 * q^76 + 55048 * q^78 - 9004 * q^79 + 68816 * q^80 - 51178 * q^81 + 67732 * q^82 + 208656 * q^83 - 106212 * q^85 - 86776 * q^86 + 80008 * q^87 + 20496 * q^88 - 26666 * q^89 - 261304 * q^90 - 20568 * q^92 - 38718 * q^93 + 98034 * q^94 + 198140 * q^95 + 54880 * q^96 - 418264 * q^97 - 133888 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$ .

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

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	2.54138	+	4.40180i	0.449257	+	0.778136i	0.998338	−	0.0576333i	$-0.0183554\pi$
$2$	2.54138	+	4.40180i	0.449257	+	0.778136i	−0.549081	+	0.835769i	$0.685022\pi$
$3$	1.04138	−	1.80373i	0.0668046	−	0.115709i	−0.830688	−	0.556738i	$-0.812053\pi$
$3$	1.04138	−	1.80373i	0.0668046	−	0.115709i	0.897493	+	0.441029i	$0.145386\pi$
$4$	3.08276	−	5.33950i	0.0963363	−	0.166859i
$5$	20.9138	+	36.2238i	0.374118	+	0.647991i	0.990195	−	0.139695i	$-0.0446123\pi$
$5$	20.9138	+	36.2238i	0.374118	+	0.647991i	−0.616077	+	0.787686i	$0.711279\pi$
$6$	10.5862			0.120050
$7$		0			0
$7$		0			0
$8$	193.986			1.07163
$9$	119.331	+	206.687i	0.491074	+	0.850566i
$10$	−106.300	+	184.117i	−0.336150	+	0.582229i
$11$	−36.0482	+	62.4374i	−0.0898260	+	0.155583i	−0.907437	−	0.420187i	$-0.861964\pi$
$11$	−36.0482	+	62.4374i	−0.0898260	+	0.155583i	0.817611	+	0.575770i	$0.195298\pi$
$12$	−6.42066	−	11.1209i	−0.0128714	−	0.0222940i
$13$	632.317			1.03771			0.518856	−	0.854862i	$-0.326358\pi$
$13$	632.317			1.03771			0.518856	+	0.854862i	$0.326358\pi$
$14$		0			0
$15$	87.1170			0.0999712
$16$	394.345	+	683.025i	0.385102	+	0.667017i
$17$	−987.962	+	1711.20i	−0.829121	+	1.43608i	0.0696071	+	0.997574i	$0.477825\pi$
$17$	−987.962	+	1711.20i	−0.829121	+	1.43608i	−0.898728	+	0.438506i	$0.855508\pi$
$18$	−606.531	+	1050.54i	−0.441237	+	0.764245i
$19$	−932.463	−	1615.07i	−0.592581	−	1.02638i	−0.993883	−	0.110434i	$-0.964776\pi$
$19$	−932.463	−	1615.07i	−0.592581	−	1.02638i	0.401303	−	0.915945i	$-0.368557\pi$
$20$	257.889			0.144164
$21$		0			0
$22$	−366.449			−0.161420
$23$	−206.855	−	358.284i	−0.0815356	−	0.141224i	0.822374	−	0.568947i	$-0.192649\pi$
$23$	−206.855	−	358.284i	−0.0815356	−	0.141224i	−0.903910	+	0.427723i	$0.859316\pi$
$24$	202.014	−	349.898i	0.0715901	−	0.123998i
$25$	687.725	−	1191.17i	0.220072	−	0.381176i
$26$	1606.96	+	2783.34i	0.466199	+	0.807481i
$27$	1003.19			0.264833
$28$		0			0
$29$	731.934			0.161613			0.0808066	−	0.996730i	$-0.474250\pi$
$29$	731.934			0.161613			0.0808066	+	0.996730i	$0.474250\pi$
$30$	221.398	+	383.472i	0.0449128	+	0.0777912i
$31$	3061.59	−	5302.83i	0.572193	−	0.991067i	−0.424148	−	0.905593i	$-0.639426\pi$
$31$	3061.59	−	5302.83i	0.572193	−	0.991067i	0.996340	−	0.0854740i	$-0.0272405\pi$
$32$	1099.42	−	1904.25i	0.189797	−	0.328738i
$33$	75.0799	+	130.042i	0.0120016	+	0.0207874i
$34$	−10043.2			−1.48995
$35$		0			0
$36$	1471.48			0.189233
$37$	−5175.19	−	8963.69i	−0.621473	−	1.07642i	−0.989212	−	0.146493i	$-0.953201\pi$
$37$	−5175.19	−	8963.69i	−0.621473	−	1.07642i	0.367739	−	0.929929i	$-0.380132\pi$
$38$	4739.49	−	8209.03i	0.532442	−	0.922216i
$39$	658.483	−	1140.53i	0.0693240	−	0.120073i
$40$	4056.99	+	7026.92i	0.400917	+	0.694408i
$41$	3529.84			0.327941			0.163970	−	0.986465i	$-0.447570\pi$
$41$	3529.84			0.327941			0.163970	+	0.986465i	$0.447570\pi$
$42$		0			0
$43$	−14515.2			−1.19716			−0.598581	−	0.801062i	$-0.704269\pi$
$43$	−14515.2			−1.19716			−0.598581	+	0.801062i	$0.704269\pi$
$44$	222.256	+	384.959i	0.0173070	+	0.0299766i
$45$	−4991.33	+	8645.24i	−0.367439	+	0.636423i
$46$	1051.40	−	1821.07i	0.0732608	−	0.126892i
$47$	−10711.7	−	18553.1i	−0.707314	−	1.22510i	−0.965850	−	0.259102i	$-0.916574\pi$
$47$	−10711.7	−	18553.1i	−0.707314	−	1.22510i	0.258536	−	0.966002i	$-0.416760\pi$
$48$	1642.65			0.102906
$49$		0			0
$50$	6991.08			0.395475
$51$	2057.69	+	3564.03i	0.110778	+	0.191874i
$52$	1949.28	−	3376.26i	0.0999693	−	0.173152i
$53$	−6289.73	+	10894.1i	−0.307569	+	0.532725i	−0.977830	−	0.209400i	$-0.932849\pi$
$53$	−6289.73	+	10894.1i	−0.307569	+	0.532725i	0.670261	+	0.742125i	$0.266182\pi$
$54$	2549.48	+	4415.83i	0.118978	+	0.206076i
$55$	−3015.62			−0.134422
$56$		0			0
$57$	−3884.20			−0.158349
$58$	1860.12	+	3221.83i	0.0726059	+	0.125757i
$59$	−18067.0	+	31292.9i	−0.675702	+	1.17035i	0.300561	+	0.953763i	$0.402826\pi$
$59$	−18067.0	+	31292.9i	−0.675702	+	1.17035i	−0.976263	+	0.216588i	$0.930507\pi$
$60$	268.561	−	465.161i	0.00963086	−	0.0166811i
$61$	2012.40	+	3485.58i	0.0692451	+	0.119936i	0.898569	−	0.438832i	$-0.144608\pi$
$61$	2012.40	+	3485.58i	0.0692451	+	0.119936i	−0.829324	+	0.558768i	$0.811274\pi$
$62$	31122.6			1.02825
$63$		0			0
$64$	36414.2			1.11127
$65$	13224.2	+	22904.9i	0.388226	+	0.672428i
$66$	−381.613	+	660.974i	−0.0107836	+	0.0186777i
$67$	−7782.97	+	13480.5i	−0.211816	+	0.366876i	−0.952283	−	0.305217i	$-0.901271\pi$
$67$	−7782.97	+	13480.5i	−0.211816	+	0.366876i	0.740467	+	0.672093i	$0.234604\pi$
$68$	6091.31	+	10550.5i	0.159749	+	0.276693i
$69$	−861.661			−0.0217878
$70$		0			0
$71$	12180.8			0.286766			0.143383	−	0.989667i	$-0.454202\pi$
$71$	12180.8			0.286766			0.143383	+	0.989667i	$0.454202\pi$
$72$	23148.6	+	40094.5i	0.526251	+	0.911494i
$73$	9794.56	−	16964.7i	0.215119	−	0.372596i	−0.738191	−	0.674592i	$-0.764320\pi$
$73$	9794.56	−	16964.7i	0.215119	−	0.372596i	0.953309	+	0.301996i	$0.0976529\pi$
$74$	26304.3	−	45560.3i	0.558402	−	0.967181i
$75$	−1432.37	−	2480.93i	−0.0294037	−	0.0509286i
$76$	−11498.2			−0.228348
$77$		0			0
$78$	6693.83			0.124577
$79$	−18044.9	−	31254.7i	−0.325302	−	0.563439i	0.656272	−	0.754525i	$-0.272133\pi$
$79$	−18044.9	−	31254.7i	−0.325302	−	0.563439i	−0.981573	+	0.191085i	$0.938799\pi$
$80$	−16494.5	+	28569.3i	−0.288147	+	0.499085i
$81$	−27952.7	+	48415.6i	−0.473382	+	0.819922i
$82$	8970.66	+	15537.6i	0.147330	+	0.255182i
$83$	24572.6			0.391522			0.195761	−	0.980652i	$-0.437282\pi$
$83$	24572.6			0.391522			0.195761	+	0.980652i	$0.437282\pi$
$84$		0			0
$85$	−82648.2			−1.24076
$86$	−36888.7	−	63893.2i	−0.537833	−	0.931555i
$87$	762.222	−	1320.21i	0.0107965	−	0.0187001i
$88$	−6992.86	+	12112.0i	−0.0962605	+	0.166728i
$89$	−35121.7	−	60832.5i	−0.470002	−	0.814068i	0.529409	−	0.848367i	$-0.322414\pi$
$89$	−35121.7	−	60832.5i	−0.470002	−	0.814068i	−0.999412	+	0.0342986i	$0.989080\pi$
$90$	−50739.5			−0.660298
$91$		0			0
$92$	−2550.74			−0.0314193
$93$	−6376.56	−	11044.5i	−0.0764503	−	0.132416i
$94$	54444.8	−	94301.2i	0.635531	−	1.10077i
$95$	39002.7	−	67554.7i	0.443390	−	0.767974i
$96$	−2289.83	−	3966.10i	−0.0253586	−	0.0439224i
$97$	−105758.			−1.14126			−0.570630	−	0.821207i	$-0.693301\pi$
$97$	−105758.			−1.14126			−0.570630	+	0.821207i	$0.693301\pi$
$98$		0			0
$99$	−17206.7			−0.176445
$100$	−4240.18	−	7344.22i	−0.0424018	−	0.0734422i
$101$	18230.9	−	31576.8i	0.177830	−	0.308010i	−0.763307	−	0.646036i	$-0.776426\pi$
$101$	18230.9	−	31576.8i	0.177830	−	0.308010i	0.941137	+	0.338025i	$0.109759\pi$
$102$	−10458.8	+	18115.1i	−0.0995359	+	0.172401i
$103$	32260.0	+	55876.0i	0.299621	+	0.518958i	0.976049	−	0.217550i	$-0.0698065\pi$
$103$	32260.0	+	55876.0i	0.299621	+	0.518958i	−0.676428	+	0.736508i	$0.736473\pi$
$104$	122661.			1.11205
$105$		0			0
$106$	−63938.4			−0.552710
$107$	−33022.8	−	57197.2i	−0.278840	−	0.482964i	0.692257	−	0.721651i	$-0.256616\pi$
$107$	−33022.8	−	57197.2i	−0.278840	−	0.482964i	−0.971097	+	0.238687i	$0.923283\pi$
$108$	3092.59	−	5356.52i	0.0255131	−	0.0441900i
$109$	18969.0	−	32855.3i	0.152925	−	0.264874i	−0.779377	−	0.626556i	$-0.784464\pi$
$109$	18969.0	−	32855.3i	0.152925	−	0.264874i	0.932302	+	0.361682i	$0.117797\pi$
$110$	−7663.85	−	13274.2i	−0.0603900	−	0.104599i
$111$	−21557.4			−0.166069
$112$		0			0
$113$	123802.			0.912080			0.456040	−	0.889959i	$-0.349267\pi$
$113$	123802.			0.912080			0.456040	+	0.889959i	$0.349267\pi$
$114$	−9871.22	−	17097.5i	−0.0711392	−	0.123217i
$115$	8652.27	−	14986.2i	0.0610078	−	0.105669i
$116$	2256.38	−	3908.16i	0.0155692	−	0.0269667i
$117$	75455.1	+	130692.i	0.509594	+	0.882642i
$118$	−183660.			−1.21426
$119$		0			0
$120$	16899.5			0.107132
$121$	77926.6	+	134973.i	0.483863	+	0.838075i
$122$	−10228.5	+	17716.4i	−0.0622177	+	0.107764i
$123$	3675.91	−	6366.86i	0.0219079	−	0.0379457i
$124$	−18876.3	−	32694.7i	−0.110246	−	0.190952i
$125$	188243.			1.07757
$126$		0			0
$127$	128724.			0.708189			0.354095	−	0.935210i	$-0.384789\pi$
$127$	128724.			0.708189			0.354095	+	0.935210i	$0.384789\pi$
$128$	57361.0	+	99352.2i	0.309451	+	0.535985i
$129$	−15115.9	+	26181.5i	−0.0799760	+	0.138522i
$130$	−67215.3	+	116420.i	−0.348827	+	0.604186i
$131$	−73951.1	−	128087.i	−0.376501	−	0.652120i	0.614049	−	0.789268i	$-0.289540\pi$
$131$	−73951.1	−	128087.i	−0.376501	−	0.652120i	−0.990551	+	0.137148i	$0.956206\pi$
$132$	925.814			0.00462476
$133$		0			0
$134$	−79118.0			−0.380639
$135$	20980.5	+	36339.3i	0.0990789	+	0.171610i
$136$	−191651.	+	331950.i	−0.888514	+	1.53895i
$137$	45578.7	−	78944.6i	0.207472	−	0.359353i	−0.743445	−	0.668797i	$-0.766810\pi$
$137$	45578.7	−	78944.6i	0.207472	−	0.359353i	0.950918	+	0.309444i	$0.100143\pi$
$138$	−2189.81	−	3792.86i	−0.00978833	−	0.0169539i
$139$	334657.			1.46914			0.734570	−	0.678533i	$-0.237384\pi$
$139$	334657.			1.46914			0.734570	+	0.678533i	$0.237384\pi$
$140$		0			0
$141$	−44619.7			−0.189007
$142$	30955.9	+	53617.3i	0.128832	+	0.223143i
$143$	−22793.9	+	39480.2i	−0.0932135	+	0.161451i
$144$	−94115.1	+	163012.i	−0.378228	+	0.655110i
$145$	15307.5	+	26513.4i	0.0604623	+	0.104724i
$146$	99566.9			0.386574
$147$		0			0
$148$	−63815.5			−0.239482
$149$	−69135.7	−	119746.i	−0.255115	−	0.441873i	0.709812	−	0.704392i	$-0.248780\pi$
$149$	−69135.7	−	119746.i	−0.255115	−	0.441873i	−0.964927	+	0.262519i	$0.915447\pi$
$150$	7280.38	−	12610.0i	0.0264196	−	0.0457601i
$151$	−55584.6	+	96275.4i	−0.198386	+	0.343615i	−0.948005	−	0.318254i	$-0.896903\pi$
$151$	−55584.6	+	96275.4i	−0.198386	+	0.343615i	0.749619	+	0.661870i	$0.230237\pi$
$152$	−180885.	−	313302.i	−0.635029	−	1.09990i
$153$	−471578.			−1.62864
$154$		0			0
$155$	256118.			0.856270
$156$	−4059.90	−	7031.95i	−0.0133568	−	0.0231347i
$157$	−19074.3	+	33037.6i	−0.0617587	+	0.106969i	−0.895252	−	0.445561i	$-0.853004\pi$
$157$	−19074.3	+	33037.6i	−0.0617587	+	0.106969i	0.833493	+	0.552530i	$0.186338\pi$
$158$	91717.9	−	158860.i	0.292288	−	0.506258i
$159$	13100.0	+	22689.9i	0.0410941	+	0.0711770i
$160$	91972.3			0.284025
$161$		0			0
$162$	−284154.			−0.850681
$163$	106452.	+	184381.i	0.313824	+	0.543559i	0.979187	−	0.202961i	$-0.0650565\pi$
$163$	106452.	+	184381.i	0.313824	+	0.543559i	−0.665363	+	0.746520i	$0.731723\pi$
$164$	10881.7	−	18847.6i	0.0315926	−	0.0547200i
$165$	−3140.41	+	5439.36i	−0.00898001	+	0.0155538i
$166$	62448.3	+	108164.i	0.175894	+	0.304657i
$167$	120396.			0.334057			0.167028	−	0.985952i	$-0.446583\pi$
$167$	120396.			0.334057			0.167028	+	0.985952i	$0.446583\pi$
$168$		0			0
$169$	28532.2			0.0768456
$170$	−210041.	−	363801.i	−0.557418	−	0.965477i
$171$	222543.	−	385457.i	0.582002	−	1.00806i
$172$	−44747.0	+	77504.1i	−0.115330	+	0.199758i
$173$	356457.	+	617402.i	0.905507	+	1.56838i	0.820235	+	0.572027i	$0.193843\pi$
$173$	356457.	+	617402.i	0.905507	+	1.56838i	0.0852723	+	0.996358i	$0.472824\pi$
$174$	7748.39			0.0194016
$175$		0			0
$176$	−56861.7			−0.138369
$177$	37629.2	+	65175.7i	0.0902801	+	0.156370i
$178$	178515.	−	309197.i	0.422304	−	0.731451i
$179$	374869.	−	649292.i	0.874474	−	1.51463i	0.0171519	−	0.999853i	$-0.494540\pi$
$179$	374869.	−	649292.i	0.874474	−	1.51463i	0.857322	−	0.514780i	$-0.172127\pi$
$180$	30774.2	+	53302.5i	0.0707955	+	0.122621i
$181$	−623718.			−1.41511			−0.707557	−	0.706656i	$-0.750203\pi$
$181$	−623718.			−1.41511			−0.707557	+	0.706656i	$0.750203\pi$
$182$		0			0
$183$	8382.69			0.0185036
$184$	−40127.1	−	69502.2i	−0.0873762	−	0.151340i
$185$	216466.	−	374930.i	0.465008	−	0.805417i
$186$	32410.5	−	56136.7i	0.0686916	−	0.118977i
$187$	−71228.6	−	123372.i	−0.148953	−	0.257995i
$188$	−132086.			−0.272560
$189$		0			0
$190$	396483.			0.796784
$191$	−208863.	−	361761.i	−0.414265	−	0.717528i	0.581086	−	0.813842i	$-0.302628\pi$
$191$	−208863.	−	361761.i	−0.414265	−	0.717528i	−0.995351	+	0.0963141i	$0.969295\pi$
$192$	37921.1	−	65681.3i	0.0742383	−	0.128585i
$193$	−385350.	+	667446.i	−0.744667	+	1.28980i	0.205683	+	0.978619i	$0.434058\pi$
$193$	−385350.	+	667446.i	−0.744667	+	1.28980i	−0.950350	+	0.311183i	$0.899275\pi$
$194$	−268772.	−	465527.i	−0.512719	−	0.888056i
$195$	55085.6			0.103741
$196$		0			0
$197$	−479193.			−0.879721			−0.439861	−	0.898066i	$-0.644972\pi$
$197$	−479193.			−0.879721			−0.439861	+	0.898066i	$0.644972\pi$
$198$	−43728.8	−	75740.4i	−0.0792692	−	0.137298i
$199$	−214343.	+	371253.i	−0.383687	+	0.664565i	−0.991586	−	0.129449i	$-0.958679\pi$
$199$	−214343.	+	371253.i	−0.383687	+	0.664565i	0.607899	+	0.794014i	$0.292012\pi$
$200$	133409.	−	231072.i	0.235836	−	0.408481i
$201$	16210.1	+	28076.7i	0.0283006	+	0.0490180i
$202$	185327.			0.319565
$203$		0			0
$204$	25373.5			0.0426879
$205$	73822.4	+	127864.i	0.122688	+	0.212502i
$206$	−163970.	+	284005.i	−0.269213	+	0.466291i
$207$	49368.5	−	85508.8i	0.0800800	−	0.138703i
$208$	249351.	+	431889.i	0.399625	+	0.692171i
$209$	134455.			0.212917
$210$		0			0
$211$	−588544.			−0.910066			−0.455033	−	0.890475i	$-0.650373\pi$
$211$	−588544.			−0.910066			−0.455033	+	0.890475i	$0.650373\pi$
$212$	38779.5	+	67168.1i	0.0592601	+	0.102642i
$213$	12684.8	−	21970.7i	0.0191573	−	0.0331815i
$214$	167847.	−	290720.i	0.250541	−	0.433950i
$215$	−303569.	−	525797.i	−0.447879	−	0.775750i
$216$	194605.			0.283804
$217$		0			0
$218$	192830.			0.274811
$219$	−20399.7	−	35333.4i	−0.0287418	−	0.0497823i
$220$	−9296.45	+	16101.9i	−0.0129497	+	0.0224296i
$221$	−624706.	+	1.08202e6i	−0.860389	+	1.49024i
$222$	−54785.5	−	94891.3i	−0.0746077	−	0.129224i
$223$	363249.			0.489151			0.244575	−	0.969630i	$-0.421351\pi$
$223$	363249.			0.489151			0.244575	+	0.969630i	$0.421351\pi$
$224$		0			0
$225$	328268.			0.432287
$226$	314629.	+	544954.i	0.409758	+	0.709722i
$227$	−421521.	+	730095.i	−0.542943	+	0.940405i	0.455790	+	0.890087i	$0.349357\pi$
$227$	−421521.	+	730095.i	−0.542943	+	0.940405i	−0.998733	+	0.0503177i	$0.983977\pi$
$228$	−11974.1	+	20739.7i	−0.0152547	+	0.0264219i
$229$	−284333.	−	492479.i	−0.358293	−	0.620582i	0.629382	−	0.777096i	$-0.283308\pi$
$229$	−284333.	−	492479.i	−0.358293	−	0.620582i	−0.987676	+	0.156513i	$0.949975\pi$
$230$	87954.8			0.109633
$231$		0			0
$232$	141985.			0.173190
$233$	528255.	+	914965.i	0.637461	+	1.10412i	0.985988	+	0.166817i	$0.0533488\pi$
$233$	528255.	+	914965.i	0.637461	+	1.10412i	−0.348526	+	0.937299i	$0.613318\pi$
$234$	−383520.	+	664277.i	−0.457877	+	0.793066i
$235$	448043.	−	776034.i	0.529237	−	0.916666i
$236$	111392.	+	192937.i	0.130189	+	0.225495i
$237$	−75166.5			−0.0869267
$238$		0			0
$239$	853715.			0.966759			0.483379	−	0.875411i	$-0.339409\pi$
$239$	853715.			0.966759			0.483379	+	0.875411i	$0.339409\pi$
$240$	34354.1	+	59503.1i	0.0384991	+	0.0666825i
$241$	−194444.	+	336787.i	−0.215651	+	0.373519i	−0.953474	−	0.301476i	$-0.902521\pi$
$241$	−194444.	+	336787.i	−0.215651	+	0.373519i	0.737823	+	0.674995i	$0.235854\pi$
$242$	−396082.	+	686034.i	−0.434757	+	0.753022i
$243$	180106.	+	311953.i	0.195665	+	0.338902i
$244$	24815.0			0.0266833
$245$		0			0
$246$	37367.5			0.0393692
$247$	−589612.	−	1.02124e6i	−0.614928	−	1.06509i
$248$	593906.	−	1.02868e6i	0.613181	−	1.06206i
$249$	25589.4	−	44322.2i	0.0261555	−	0.0453026i
$250$	478398.	+	828609.i	0.484104	+	0.838493i
$251$	839328.			0.840906			0.420453	−	0.907314i	$-0.361871\pi$
$251$	839328.			0.840906			0.420453	+	0.907314i	$0.361871\pi$
$252$		0			0
$253$	29827.1			0.0292961
$254$	327136.	+	566616.i	0.318159	+	0.551067i
$255$	−86068.3	+	149075.i	−0.0828882	+	0.143567i
$256$	291075.	−	504157.i	0.277591	−	0.480802i
$257$	145993.	+	252867.i	0.137879	+	0.238814i	0.926694	−	0.375817i	$-0.122638\pi$
$257$	145993.	+	252867.i	0.137879	+	0.238814i	−0.788814	+	0.614632i	$0.789305\pi$
$258$	−153661.			−0.143719
$259$		0			0
$260$	163068.			0.149601
$261$	87342.4	+	151282.i	0.0793641	+	0.137463i
$262$	375876.	−	651037.i	0.338292	−	0.585939i
$263$	144248.	−	249844.i	0.128594	−	0.222731i	−0.794538	−	0.607214i	$-0.792287\pi$
$263$	144248.	−	249844.i	0.128594	−	0.222731i	0.923132	+	0.384483i	$0.125620\pi$
$264$	14564.5	+	25226.4i	0.0128613	+	0.0222764i
$265$	−526169.			−0.460268
$266$		0			0
$267$	−146300.			−0.125593
$268$	47986.1	+	83114.4i	0.0408111	+	0.0706869i
$269$	−129685.	+	224621.i	−0.109272	+	0.189265i	−0.915476	−	0.402374i	$-0.868185\pi$
$269$	−129685.	+	224621.i	−0.109272	+	0.189265i	0.806204	+	0.591638i	$0.201519\pi$
$270$	−106639.	+	184704.i	−0.0890237	+	0.154194i
$271$	−1.09776e6	−	1.90137e6i	−0.907994	−	1.57269i	−0.816847	−	0.576854i	$-0.804280\pi$
$271$	−1.09776e6	−	1.90137e6i	−0.907994	−	1.57269i	−0.0911464	−	0.995838i	$-0.529053\pi$
$272$	−1.55839e6			−1.27719
$273$		0			0
$274$	463331.			0.372834
$275$	49582.5	+	85879.5i	0.0395364	+	0.0684790i
$276$	−2656.30	+	4600.84i	−0.00209896	+	0.00363550i
$277$	−63495.3	+	109977.i	−0.0497213	+	0.0861198i	−0.889815	−	0.456322i	$-0.849167\pi$
$277$	−63495.3	+	109977.i	−0.0497213	+	0.0861198i	0.840094	+	0.542441i	$0.182500\pi$
$278$	850491.	+	1.47309e6i	0.660021	+	1.14319i
$279$	1.46137e6			1.12396
$280$		0			0
$281$	−2.22759e6			−1.68294			−0.841472	−	0.540301i	$-0.818310\pi$
$281$	−2.22759e6			−1.68294			−0.841472	+	0.540301i	$0.818310\pi$
$282$	−113396.	−	196407.i	−0.0849129	−	0.147073i
$283$	594473.	−	1.02966e6i	0.441231	−	0.764235i	−0.556550	−	0.830814i	$-0.687875\pi$
$283$	594473.	−	1.02966e6i	0.441231	−	0.764235i	0.997781	+	0.0665792i	$0.0212085\pi$
$284$	37550.4	−	65039.1i	0.0276260	−	0.0478497i
$285$	−81233.4	−	140700.i	−0.0592410	−	0.102608i
$286$	−231712.			−0.167507
$287$		0			0
$288$	524780.			0.372817
$289$	−1.24221e6	−	2.15157e6i	−0.874884	−	1.51534i
$290$	−77804.5	+	134761.i	−0.0543263	+	0.0940958i
$291$	−110135.	+	190759.i	−0.0762415	+	0.132054i
$292$	−60388.6	−	104596.i	−0.0414475	−	0.0717891i
$293$	−1.83223e6			−1.24684			−0.623421	−	0.781886i	$-0.714258\pi$
$293$	−1.83223e6			−1.24684			−0.623421	+	0.781886i	$0.714258\pi$
$294$		0			0
$295$	−1.51140e6			−1.01117
$296$	−1.00392e6	−	1.73883e6i	−0.665991	−	1.15353i
$297$	−36163.1	+	62636.4i	−0.0237889	+	0.0412037i
$298$	351400.	−	608643.i	0.229225	−	0.397029i
$299$	−130798.	−	226549.i	−0.0846104	−	0.146550i
$300$	−17662.6			−0.0113306
$301$		0			0
$302$	−565047.			−0.356506
$303$	−37970.6	−	65767.1i	−0.0237597	−	0.0411530i
$304$	735423.	−	1.27379e6i	0.456408	−	0.790522i
$305$	−84173.8	+	145793.i	−0.0518117	+	0.0897404i
$306$	−1.19846e6	−	2.07579e6i	−0.731678	−	1.26730i
$307$	717638.			0.434569			0.217285	−	0.976108i	$-0.430280\pi$
$307$	717638.			0.434569			0.217285	+	0.976108i	$0.430280\pi$
$308$		0			0
$309$	134380.			0.0800642
$310$	650893.	+	1.12738e6i	0.384685	+	0.666294i
$311$	−428446.	+	742090.i	−0.251186	+	0.435067i	−0.963853	−	0.266436i	$-0.914154\pi$
$311$	−428446.	+	742090.i	−0.251186	+	0.435067i	0.712667	+	0.701503i	$0.247487\pi$
$312$	127737.	−	221247.i	0.0742898	−	0.128674i
$313$	808495.	+	1.40035e6i	0.466462	+	0.807936i	0.999266	−	0.0383025i	$-0.0121950\pi$
$313$	808495.	+	1.40035e6i	0.466462	+	0.807936i	−0.532804	+	0.846239i	$0.678862\pi$
$314$	−193900.			−0.110982
$315$		0			0
$316$	−222512.			−0.125354
$317$	1.13280e6	+	1.96206e6i	0.633145	+	1.09664i	0.986905	+	0.161303i	$0.0515698\pi$
$317$	1.13280e6	+	1.96206e6i	0.633145	+	1.09664i	−0.353760	+	0.935336i	$0.615097\pi$
$318$	−66584.3	+	115327.i	−0.0369236	+	0.0639535i
$319$	−26384.9	+	45700.0i	−0.0145171	+	0.0251443i
$320$	761561.	+	1.31906e6i	0.415747	+	0.720096i
$321$	−137557.			−0.0745111
$322$		0			0
$323$	3.68495e6			1.96528
$324$	172343.	+	298507.i	0.0912078	+	0.157977i
$325$	434860.	−	753200.i	0.228371	−	0.395551i
$326$	−541072.	+	937163.i	−0.281975	+	0.488395i
$327$	−39508.0	−	68429.8i	−0.0204322	−	0.0353896i
$328$	684740.			0.351432
$329$		0			0
$330$	−31924.0			−0.0161373
$331$	−354825.	−	614575.i	−0.178010	−	0.308322i	0.763189	−	0.646175i	$-0.223633\pi$
$331$	−354825.	−	614575.i	−0.178010	−	0.308322i	−0.941199	+	0.337853i	$0.890299\pi$
$332$	75751.5	−	131205.i	0.0377178	−	0.0653291i
$333$	1.23512e6	−	2.13929e6i	0.610379	−	1.05721i
$334$	305972.	+	529958.i	0.150077	+	0.259941i
$335$	−651086.			−0.316976
$336$		0			0
$337$	603572.			0.289504			0.144752	−	0.989468i	$-0.453762\pi$
$337$	603572.			0.289504			0.144752	+	0.989468i	$0.453762\pi$
$338$	72511.3	+	125593.i	0.0345234	+	0.0597963i
$339$	128925.	−	223305.i	0.0609312	−	0.105536i
$340$	−254785.	+	441300.i	−0.119530	+	0.207032i
$341$	220730.	+	382315.i	0.102796	+	0.178047i
$342$	2.26227e6			1.04587
$343$		0			0
$344$	−2.81576e6			−1.28292
$345$	−18020.6	−	31212.6i	−0.00815121	−	0.0141183i
$346$	−1.81179e6	+	3.13811e6i	−0.813611	+	1.40922i
$347$	−878655.	+	1.52188e6i	−0.391737	+	0.678509i	−0.992679	−	0.120784i	$-0.961459\pi$
$347$	−878655.	+	1.52188e6i	−0.391737	+	0.678509i	0.600942	+	0.799293i	$0.294792\pi$
$348$	−4699.50	−	8139.77i	−0.00208019	−	0.00360300i
$349$	−391875.			−0.172220			−0.0861102	−	0.996286i	$-0.527444\pi$
$349$	−391875.			−0.172220			−0.0861102	+	0.996286i	$0.527444\pi$
$350$		0			0
$351$	634333.			0.274821
$352$	79264.3	+	137290.i	0.0340974	+	0.0590584i
$353$	246204.	−	426437.i	0.105162	−	0.182145i	−0.808643	−	0.588300i	$-0.799797\pi$
$353$	246204.	−	426437.i	0.105162	−	0.182145i	0.913804	+	0.406155i	$0.133131\pi$
$354$	−191260.	+	331273.i	−0.0811179	+	0.140500i
$355$	254746.	+	441233.i	0.107284	+	0.185822i
$356$	−433087.			−0.181113
$357$		0			0
$358$	3.81074e6			1.57145
$359$	1.88516e6	+	3.26519e6i	0.771991	+	1.33713i	0.936470	+	0.350747i	$0.114072\pi$
$359$	1.88516e6	+	3.26519e6i	0.771991	+	1.33713i	−0.164480	+	0.986380i	$0.552594\pi$
$360$	−968251.	+	1.67706e6i	−0.393760	+	0.682012i
$361$	−500924.	+	867625.i	−0.202304	+	0.350400i
$362$	−1.58510e6	−	2.74548e6i	−0.635750	−	1.10115i
$363$	324605.			0.129297
$364$		0			0
$365$	819367.			0.321919
$366$	21303.6	+	36899.0i	0.00831286	+	0.0143983i
$367$	−1.09884e6	+	1.90325e6i	−0.425863	+	0.737617i	−0.996501	−	0.0835854i	$-0.973363\pi$
$367$	−1.09884e6	+	1.90325e6i	−0.425863	+	0.737617i	0.570637	+	0.821202i	$0.306696\pi$
$368$	163145.	−	282575.i	0.0627991	−	0.108771i
$369$	421219.	+	729573.i	0.161043	+	0.278935i
$370$	2.20049e6			0.835632
$371$		0			0
$372$	−78629.7			−0.0294598
$373$	828178.	+	1.43445e6i	0.308213	+	0.533841i	0.977972	−	0.208738i	$-0.0669356\pi$
$373$	828178.	+	1.43445e6i	0.308213	+	0.533841i	−0.669758	+	0.742579i	$0.733602\pi$
$374$	362038.	−	627068.i	0.133837	−	0.231812i
$375$	196033.	−	339539.i	0.0719864	−	0.124684i
$376$	−2.07791e6	−	3.59905e6i	−0.757981	−	1.31286i
$377$	462814.			0.167708
$378$		0			0
$379$	−2.82050e6			−1.00862			−0.504310	−	0.863523i	$-0.668253\pi$
$379$	−2.82050e6			−1.00862			−0.504310	+	0.863523i	$0.668253\pi$
$380$	−240472.	−	416510.i	−0.0854291	−	0.147968i
$381$	134050.	−	232182.i	0.0473103	−	0.0819439i
$382$	1.06160e6	−	1.83875e6i	0.372223	−	0.644709i
$383$	1.62422e6	+	2.81324e6i	0.565781	+	0.979962i	0.996977	+	0.0777034i	$0.0247587\pi$
$383$	1.62422e6	+	2.81324e6i	0.565781	+	0.979962i	−0.431195	+	0.902259i	$0.641908\pi$
$384$	238939.			0.0826911
$385$		0			0
$386$	−3.91729e6			−1.33819
$387$	−1.73212e6	−	3.00012e6i	−0.587895	−	1.01826i
$388$	−326027.	+	564696.i	−0.109945	+	0.190430i
$389$	−2.32674e6	+	4.03003e6i	−0.779604	+	1.35031i	0.152566	+	0.988293i	$0.451246\pi$
$389$	−2.32674e6	+	4.03003e6i	−0.779604	+	1.35031i	−0.932170	+	0.362021i	$0.882087\pi$
$390$	139994.	+	242476.i	0.0466065	+	0.0807248i
$391$	817461.			0.270411
$392$		0			0
$393$	−308045.			−0.100608
$394$	−1.21781e6	−	2.10931e6i	−0.395221	−	0.684543i
$395$	754775.	−	1.30731e6i	0.243402	−	0.421585i
$396$	−53044.1	+	91875.2i	−0.0169981	+	0.0294415i
$397$	−581804.	−	1.00771e6i	−0.185268	−	0.320894i	0.758399	−	0.651791i	$-0.225982\pi$
$397$	−581804.	−	1.00771e6i	−0.185268	−	0.320894i	−0.943667	+	0.330897i	$0.892649\pi$
$398$	−2.17891e6			−0.689495
$399$		0			0
$400$	1.08480e6			0.339001
$401$	−161190.	−	279189.i	−0.0500584	−	0.0867037i	0.839910	−	0.542725i	$-0.182607\pi$
$401$	−161190.	−	279189.i	−0.0500584	−	0.0867037i	−0.889969	+	0.456021i	$0.849274\pi$
$402$	−82392.0	+	142707.i	−0.0254284	+	0.0440434i
$403$	1.93589e6	−	3.35307e6i	0.593771	−	1.02844i
$404$	−112403.	−	194688.i	−0.0342630	−	0.0593452i
$405$	−2.33839e6			−0.708403
$406$		0			0
$407$	746226.			0.223298
$408$	399164.	+	691372.i	0.118714	+	0.205618i
$409$	693451.	−	1.20109e6i	0.204978	−	0.355033i	−0.745148	−	0.666900i	$-0.767621\pi$
$409$	693451.	−	1.20109e6i	0.204978	−	0.355033i	0.950126	+	0.311867i	$0.100954\pi$
$410$	−375222.	+	649903.i	−0.110237	+	0.190936i
$411$	−94929.6	−	164423.i	−0.0277202	−	0.0480129i
$412$	397800.			0.115457
$413$		0			0
$414$	501857.			0.143906
$415$	513907.	+	890112.i	0.146475	+	0.253702i
$416$	695182.	−	1.20409e6i	0.196954	−	0.341135i
$417$	348506.	−	603630.i	0.0981454	−	0.169993i
$418$	341700.	+	591842.i	0.0956543	+	0.165678i
$419$	−4.90871e6			−1.36594			−0.682971	−	0.730446i	$-0.739312\pi$
$419$	−4.90871e6			−1.36594			−0.682971	+	0.730446i	$0.739312\pi$
$420$		0			0
$421$	2.43924e6			0.670733			0.335367	−	0.942088i	$-0.391140\pi$
$421$	2.43924e6			0.670733			0.335367	+	0.942088i	$0.391140\pi$
$422$	−1.49572e6	−	2.59065e6i	−0.408854	−	0.708155i
$423$	2.55647e6	−	4.42793e6i	0.694687	−	1.20323i
$424$	−1.22012e6	+	2.11331e6i	−0.329601	+	0.570886i
$425$	1.35889e6	+	2.35367e6i	0.364933	+	0.632082i
$426$	128948.			0.0344263
$427$		0			0
$428$	−407206.			−0.107450
$429$	47474.3	+	82227.9i	0.0124542	+	0.0215713i
$430$	1.54297e6	−	2.67250e6i	0.402426	−	0.697022i
$431$	2.61376e6	−	4.52717e6i	0.677755	−	1.17391i	−0.297900	−	0.954597i	$-0.596286\pi$
$431$	2.61376e6	−	4.52717e6i	0.677755	−	1.17391i	0.975655	−	0.219309i	$-0.0703803\pi$
$432$	395602.	+	685202.i	0.101988	+	0.176648i
$433$	2.63022e6			0.674174			0.337087	−	0.941473i	$-0.390558\pi$
$433$	2.63022e6			0.674174			0.337087	+	0.941473i	$0.390558\pi$
$434$		0			0
$435$	63763.9			0.0161567
$436$	−116954.	−	202570.i	−0.0294645	−	0.0510340i
$437$	−385770.	+	668173.i	−0.0966328	+	0.167373i
$438$	103687.	−	179591.i	0.0258249	−	0.0447301i
$439$	1.27706e6	+	2.21193e6i	0.316264	+	0.547785i	0.979705	−	0.200443i	$-0.0642382\pi$
$439$	1.27706e6	+	2.21193e6i	0.316264	+	0.547785i	−0.663442	+	0.748228i	$0.730905\pi$
$440$	−584990.			−0.144051
$441$		0			0
$442$	−6.35046e6			−1.54614
$443$	−1.91950e6	−	3.32467e6i	−0.464707	−	0.804896i	0.534481	−	0.845180i	$-0.320507\pi$
$443$	−1.91950e6	−	3.32467e6i	−0.464707	−	0.804896i	−0.999188	+	0.0402844i	$0.987174\pi$
$444$	−66456.3	+	115106.i	−0.0159985	+	0.0277102i
$445$	1.46906e6	−	2.54448e6i	0.351672	−	0.609114i
$446$	923155.	+	1.59895e6i	0.219754	+	0.380626i
$447$	−287986.			−0.0681715
$448$		0			0
$449$	1.49369e6			0.349658			0.174829	−	0.984599i	$-0.444063\pi$
$449$	1.49369e6			0.349658			0.174829	+	0.984599i	$0.444063\pi$
$450$	834253.	+	1.44497e6i	0.194208	+	0.336378i
$451$	−127244.	+	220394.i	−0.0294576	+	0.0510221i
$452$	381653.	−	661043.i	0.0878664	−	0.152189i
$453$	115770.	+	200519.i	0.0265063	+	0.0459102i
$454$	−4.28498e6			−0.975684
$455$		0			0
$456$	−753481.			−0.169692
$457$	1.08111e6	+	1.87253e6i	0.242146	+	0.419410i	0.961325	−	0.275415i	$-0.0888153\pi$
$457$	1.08111e6	+	1.87253e6i	0.242146	+	0.419410i	−0.719179	+	0.694825i	$0.755482\pi$
$458$	1.44520e6	−	2.50316e6i	0.321932	−	0.557602i
$459$	−991112.	+	1.71666e6i	−0.219579	+	0.380322i
$460$	−53345.8	−	92397.6i	−0.0117545	−	0.0203594i
$461$	6.11949e6			1.34111			0.670553	−	0.741862i	$-0.266057\pi$
$461$	6.11949e6			1.34111			0.670553	+	0.741862i	$0.266057\pi$
$462$		0			0
$463$	3.93615e6			0.853335			0.426667	−	0.904409i	$-0.359687\pi$
$463$	3.93615e6			0.853335			0.426667	+	0.904409i	$0.359687\pi$
$464$	288634.	+	499929.i	0.0622376	+	0.107799i
$465$	266716.	−	461966.i	0.0572028	−	0.0990782i
$466$	−2.68500e6	+	4.65055e6i	−0.572768	+	0.992063i
$467$	−2.73522e6	−	4.73754e6i	−0.580363	−	1.00522i	−0.995436	−	0.0954306i	$-0.969577\pi$
$467$	−2.73522e6	−	4.73754e6i	−0.580363	−	1.00522i	0.415073	−	0.909788i	$-0.363756\pi$
$468$	930441.			0.196369
$469$		0			0
$470$	4.55459e6			0.951054
$471$	39727.1	+	68809.4i	0.00825154	+	0.0142921i
$472$	−3.50475e6	+	6.07040e6i	−0.724105	+	1.25419i
$473$	523248.	−	906293.i	0.107536	−	0.186258i
$474$	−191027.	−	330868.i	−0.0390524	−	0.0676408i
$475$	−2.56511e6			−0.521641
$476$		0			0
$477$	−3.00224e6			−0.604157
$478$	2.16962e6	+	3.75788e6i	0.434323	+	0.752270i
$479$	−3.33145e6	+	5.77023e6i	−0.663428	+	1.14909i	0.316280	+	0.948666i	$0.397566\pi$
$479$	−3.33145e6	+	5.77023e6i	−0.663428	+	1.14909i	−0.979709	+	0.200426i	$0.935767\pi$
$480$	95778.2	−	165893.i	0.0189742	−	0.0328643i
$481$	−3.27236e6	−	5.66790e6i	−0.644910	−	1.11702i
$482$	−1.97663e6			−0.387531
$483$		0			0
$484$	960916.			0.186454
$485$	−2.21181e6	−	3.83096e6i	−0.426966	−	0.739526i
$486$	−915437.	+	1.58558e6i	−0.175808	+	0.304508i
$487$	−4.76846e6	+	8.25922e6i	−0.911079	+	1.57804i	−0.0985363	+	0.995133i	$0.531416\pi$
$487$	−4.76846e6	+	8.25922e6i	−0.911079	+	1.57804i	−0.812543	+	0.582902i	$0.801917\pi$
$488$	390378.	+	676154.i	0.0742054	+	0.128527i
$489$	443430.			0.0838595
$490$		0			0
$491$	−8.19294e6			−1.53369			−0.766843	−	0.641835i	$-0.778173\pi$
$491$	−8.19294e6			−1.53369			−0.766843	+	0.641835i	$0.778173\pi$
$492$	−22663.9	−	39255.0i	−0.00422106	−	0.00731110i
$493$	−723123.	+	1.25249e6i	−0.133997	+	0.232090i
$494$	2.99686e6	−	5.19071e6i	0.552521	−	0.956995i
$495$	−359858.	−	623292.i	−0.0660112	−	0.114335i
$496$	4.82928e6			0.881411
$497$		0			0
$498$	260130.			0.0470021
$499$	2.15718e6	+	3.73635e6i	0.387825	+	0.671733i	0.992157	−	0.125000i	$-0.0398931\pi$
$499$	2.15718e6	+	3.73635e6i	0.387825	+	0.671733i	−0.604332	+	0.796733i	$0.706560\pi$
$500$	580309.	−	1.00512e6i	0.103809	−	0.179802i
$501$	125378.	−	217161.i	0.0223165	−	0.0386534i
$502$	2.13305e6	+	3.69455e6i	0.377783	+	0.654339i
$503$	1.04015e7			1.83306			0.916529	−	0.399968i	$-0.130979\pi$
$503$	1.04015e7			1.83306			0.916529	+	0.399968i	$0.130979\pi$
$504$		0			0
$505$	1.52511e6			0.266117
$506$	75802.0	+	131293.i	0.0131615	+	0.0227963i
$507$	29712.9	−	51464.3i	0.00513364	−	0.00889173i
$508$	396825.	−	687320.i	0.0682243	−	0.118168i
$509$	−1.54698e6	−	2.67945e6i	−0.264661	−	0.458406i	0.702814	−	0.711374i	$-0.251927\pi$
$509$	−1.54698e6	−	2.67945e6i	−0.264661	−	0.458406i	−0.967475	+	0.252968i	$0.918593\pi$
$510$	−874930.			−0.148952
$511$		0			0
$512$	6.63004e6			1.11774
$513$	−935435.	−	1.62022e6i	−0.156935	−	0.271820i
$514$	−742048.	+	1.28527e6i	−0.123887	+	0.214578i
$515$	−1.34936e6	+	2.33716e6i	−0.224187	+	0.388303i
$516$	93197.4	+	161423.i	0.0154092	+	0.0266895i
$517$	1.54455e6			0.254141
$518$		0			0
$519$	1.48483e6			0.241968
$520$	2.56531e6	+	4.44324e6i	0.416036	+	0.720596i
$521$	−3.80087e6	+	6.58331e6i	−0.613464	+	1.06255i	0.377188	+	0.926137i	$0.376891\pi$
$521$	−3.80087e6	+	6.58331e6i	−0.613464	+	1.06255i	−0.990652	+	0.136414i	$0.956442\pi$
$522$	−443941.	+	768928.i	−0.0713097	+	0.123512i
$523$	2.37835e6	+	4.11942e6i	0.380208	+	0.658539i	0.991092	−	0.133181i	$-0.0425192\pi$
$523$	2.37835e6	+	4.11942e6i	0.380208	+	0.658539i	−0.610884	+	0.791720i	$0.709186\pi$
$524$	−911895.			−0.145083
$525$		0			0
$526$	1.46635e6			0.231086
$527$	6.04947e6	+	1.04780e7i	0.948835	+	1.64343i
$528$	−59214.7	+	102563.i	−0.00924368	+	0.0160105i
$529$	3.13259e6	−	5.42581e6i	0.486704	−	0.842996i
$530$	−1.33720e6	−	2.31609e6i	−0.206779	−	0.358151i
$531$	−8.62380e6			−1.32728
$532$		0			0
$533$	2.23198e6			0.340308
$534$	−371805.	−	643984.i	−0.0564237	−	0.0977287i
$535$	1.38127e6	−	2.39242e6i	0.208638	−	0.361371i
$536$	−1.50979e6	+	2.61503e6i	−0.226989	+	0.393156i
$537$	−780763.	−	1.35232e6i	−0.116838	−	0.202369i
$538$	−1.31832e6			−0.196365
$539$		0			0
$540$	258711.			0.0381796
$541$	−5.50261e6	−	9.53079e6i	−0.808305	−	1.40003i	−0.914037	−	0.405631i	$-0.867052\pi$
$541$	−5.50261e6	−	9.53079e6i	−0.808305	−	1.40003i	0.105732	−	0.994395i	$-0.466281\pi$
$542$	5.57964e6	−	9.66421e6i	0.815845	−	1.41309i
$543$	−649528.	+	1.12502e6i	−0.0945362	+	0.163742i
$544$	2.17237e6	+	3.76266e6i	0.314729	+	0.545127i
$545$	1.58686e6			0.228848
$546$		0			0
$547$	−4.46311e6			−0.637778			−0.318889	−	0.947792i	$-0.603310\pi$
$547$	−4.46311e6			−0.637778			−0.318889	+	0.947792i	$0.603310\pi$
$548$	−281017.	−	486735.i	−0.0399743	−	0.0692375i
$549$	−480283.	+	831875.i	−0.0680090	+	0.117795i
$550$	−252016.	+	436505.i	−0.0355240	+	0.0615294i
$551$	−682501.	−	1.18213e6i	−0.0957688	−	0.165876i
$552$	−167150.			−0.0233485
$553$		0			0
$554$	−645463.			−0.0893505
$555$	−450847.	−	780890.i	−0.0621294	−	0.107611i
$556$	1.03167e6	−	1.78690e6i	0.141532	−	0.245140i
$557$	3.22611e6	−	5.58779e6i	0.440597	−	0.763136i	−0.557137	−	0.830421i	$-0.688100\pi$
$557$	3.22611e6	−	5.58779e6i	0.440597	−	0.763136i	0.997734	+	0.0672845i	$0.0214335\pi$
$558$	3.71390e6	+	6.43266e6i	0.504945	+	0.874591i
$559$	−9.17823e6			−1.24231
$560$		0			0
$561$	−296704.			−0.0398031
$562$	−5.66116e6	−	9.80541e6i	−0.756074	−	1.30956i
$563$	873740.	−	1.51336e6i	0.116175	−	0.201220i	−0.802074	−	0.597225i	$-0.796270\pi$
$563$	873740.	−	1.51336e6i	0.116175	−	0.201220i	0.918249	+	0.396004i	$0.129603\pi$
$564$	−137552.	+	238247.i	−0.0182083	+	0.0315377i
$565$	2.58918e6	+	4.48459e6i	0.341225	+	0.591019i
$566$	6.04313e6			0.792905
$567$		0			0
$568$	2.36290e6			0.307308
$569$	−256394.	−	444088.i	−0.0331992	−	0.0575027i	0.848948	−	0.528476i	$-0.177236\pi$
$569$	−256394.	−	444088.i	−0.0331992	−	0.0575027i	−0.882148	+	0.470973i	$0.843903\pi$
$570$	412890.	−	715146.i	0.0532288	−	0.0921951i
$571$	−2.61182e6	+	4.52380e6i	−0.335238	+	0.580649i	−0.983530	−	0.180742i	$-0.942150\pi$
$571$	−2.61182e6	+	4.52380e6i	−0.335238	+	0.580649i	0.648293	+	0.761391i	$0.275483\pi$
$572$	140536.	+	243416.i	0.0179597	+	0.0311071i
$573$	−870024.			−0.110699
$574$		0			0
$575$	−569038.			−0.0717748
$576$	4.34535e6	+	7.52637e6i	0.545718	+	0.945212i
$577$	3.31987e6	−	5.75018e6i	0.415127	−	0.719021i	−0.580315	−	0.814392i	$-0.697070\pi$
$577$	3.31987e6	−	5.75018e6i	0.415127	−	0.719021i	0.995442	+	0.0953713i	$0.0304038\pi$
$578$	6.31386e6	−	1.09359e7i	0.786096	−	1.36156i
$579$	802593.	+	1.39013e6i	0.0994945	+	0.172329i
$580$	188758.			0.0232989
$581$		0			0
$582$	−1.11958e6			−0.137008
$583$	−453467.	−	785429.i	−0.0552554	−	0.0957051i
$584$	1.90001e6	−	3.29092e6i	0.230528	−	0.399286i
$585$	−3.15611e6	+	5.46654e6i	−0.381296	+	0.660424i
$586$	−4.65640e6	−	8.06512e6i	−0.560152	−	0.970212i
$587$	−774096.			−0.0927256			−0.0463628	−	0.998925i	$-0.514763\pi$
$587$	−774096.			−0.0927256			−0.0463628	+	0.998925i	$0.514763\pi$
$588$		0			0
$589$	−1.14193e7			−1.35628
$590$	−3.84104e6	−	6.65287e6i	−0.454275	−	0.786827i
$591$	−499023.	+	864333.i	−0.0587695	+	0.101792i
$592$	4.08162e6	−	7.06957e6i	0.478661	−	0.829065i
$593$	−7.18778e6	−	1.24496e7i	−0.839379	−	1.45385i	−0.890415	−	0.455150i	$-0.849585\pi$
$593$	−7.18778e6	−	1.24496e7i	−0.839379	−	1.45385i	0.0510354	−	0.998697i	$-0.483748\pi$
$594$	−367617.			−0.0427494
$595$		0			0
$596$	−852515.			−0.0983075
$597$	446426.	+	773232.i	0.0512641	+	0.0887920i
$598$	664816.	−	1.15150e6i	0.0760236	−	0.131677i
$599$	−6.04174e6	+	1.04646e7i	−0.688010	+	1.19167i	0.284471	+	0.958685i	$0.408182\pi$
$599$	−6.04174e6	+	1.04646e7i	−0.688010	+	1.19167i	−0.972481	+	0.232984i	$0.925151\pi$
$600$	−277860.	−	481267.i	−0.0315099	−	0.0545768i
$601$	−5.75607e6			−0.650040			−0.325020	−	0.945707i	$-0.605371\pi$
$601$	−5.75607e6			−0.650040			−0.325020	+	0.945707i	$0.605371\pi$
$602$		0			0
$603$	−3.71500e6			−0.416069
$604$	342708.	+	593588.i	0.0382237	+	0.0662053i
$605$	−3.25948e6	+	5.64559e6i	−0.362043	+	0.627077i
$606$	192996.	−	334278.i	0.0213484	−	0.0369766i
$607$	2.10060e6	+	3.63835e6i	0.231405	+	0.400805i	0.958222	−	0.286026i	$-0.0923344\pi$
$607$	2.10060e6	+	3.63835e6i	0.231405	+	0.400805i	−0.726817	+	0.686831i	$0.759001\pi$
$608$	−4.10067e6			−0.449879
$609$		0			0
$610$	−855671.			−0.0931070
$611$	−6.77317e6	−	1.17315e7i	−0.733988	−	1.27130i
$612$	−1.45376e6	+	2.51799e6i	−0.156897	+	0.271754i
$613$	1.32271e6	−	2.29101e6i	0.142172	−	0.246249i	−0.786142	−	0.618046i	$-0.787925\pi$
$613$	1.32271e6	−	2.29101e6i	0.142172	−	0.246249i	0.928314	+	0.371796i	$0.121258\pi$
$614$	1.82379e6	+	3.15890e6i	0.195233	+	0.338154i
$615$	307509.			0.0327846
$616$		0			0
$617$	6.43533e6			0.680546			0.340273	−	0.940327i	$-0.389480\pi$
$617$	6.43533e6			0.680546			0.340273	+	0.940327i	$0.389480\pi$
$618$	341511.	+	591514.i	0.0359694	+	0.0623009i
$619$	7.05885e6	−	1.22263e7i	0.740469	−	1.28253i	−0.211812	−	0.977310i	$-0.567937\pi$
$619$	7.05885e6	−	1.22263e7i	0.740469	−	1.28253i	0.952282	−	0.305220i	$-0.0987301\pi$
$620$	789551.	−	1.36754e6i	0.0824899	−	0.142877i
$621$	−207515.	−	359426.i	−0.0215933	−	0.0374008i
$622$	−4.35538e6			−0.451388
$623$		0			0
$624$	1.03868e6			0.106787
$625$	1.78774e6	+	3.09646e6i	0.183065	+	0.317077i
$626$	−4.10939e6	+	7.11767e6i	−0.419123	+	0.725942i
$627$	140018.	−	242519.i	0.0142238	−	0.0246364i
$628$	117603.	+	203694.i	0.0118992	+	0.0206101i
$629$	2.04516e7			2.06111
$630$		0			0
$631$	−4.70856e6			−0.470777			−0.235388	−	0.971901i	$-0.575636\pi$
$631$	−4.70856e6			−0.470777			−0.235388	+	0.971901i	$0.575636\pi$
$632$	−3.50046e6	−	6.06298e6i	−0.348604	−	0.603800i
$633$	−612899.	+	1.06157e6i	−0.0607966	+	0.105303i
$634$	−5.75773e6	+	9.97268e6i	−0.568890	+	0.985346i
$635$	2.69210e6	+	4.66286e6i	0.264946	+	0.458900i
$636$	161537.			0.0158354
$637$		0			0
$638$	−268217.			−0.0260876
$639$	1.45354e6	+	2.51761e6i	0.140824	+	0.243914i
$640$	−2.39928e6	+	4.15567e6i	−0.231542	+	0.401043i
$641$	5.20870e6	−	9.02173e6i	0.500707	−	0.867251i	−0.499292	−	0.866434i	$-0.666407\pi$
$641$	5.20870e6	−	9.02173e6i	0.500707	−	0.867251i	1.00000		0.000816994i	$-0.000260057\pi$
$642$	−349586.	−	605500.i	−0.0334746	−	0.0579798i
$643$	−1.27284e7			−1.21407			−0.607037	−	0.794674i	$-0.707642\pi$
$643$	−1.27284e7			−1.21407			−0.607037	+	0.794674i	$0.707642\pi$
$644$		0			0
$645$	−1.26452e6			−0.119682
$646$	9.36487e6	+	1.62204e7i	0.882918	+	1.52926i
$647$	−8.06740e6	+	1.39731e7i	−0.757657	+	1.31230i	0.186385	+	0.982477i	$0.440323\pi$
$647$	−8.06740e6	+	1.39731e7i	−0.757657	+	1.31230i	−0.944042	+	0.329824i	$0.893011\pi$
$648$	−5.42245e6	+	9.39196e6i	−0.507292	+	0.878655i
$649$	−1.30256e6	−	2.25611e6i	−0.121391	−	0.210256i
$650$	4.42058e6			0.410390
$651$		0			0
$652$	1.31267e6			0.120931
$653$	7.51475e6	+	1.30159e7i	0.689654	+	1.19452i	0.971950	+	0.235189i	$0.0755708\pi$
$653$	7.51475e6	+	1.30159e7i	0.689654	+	1.19452i	−0.282296	+	0.959327i	$0.591096\pi$
$654$	200810.	−	347812.i	0.0183586	−	0.0317981i
$655$	3.09320e6	−	5.35758e6i	0.281712	−	0.487939i
$656$	1.39197e6	+	2.41097e6i	0.126291	+	0.218742i
$657$	4.67518e6			0.422557
$658$		0			0
$659$	1.67927e7			1.50628			0.753140	−	0.657860i	$-0.228538\pi$
$659$	1.67927e7			1.50628			0.753140	+	0.657860i	$0.228538\pi$
$660$	19362.3	+	33536.5i	0.00173020	+	0.00299680i
$661$	5.42702e6	−	9.39987e6i	0.483123	−	0.836794i	−0.516689	−	0.856173i	$-0.672836\pi$
$661$	5.42702e6	−	9.39987e6i	0.483123	−	0.836794i	0.999812	+	0.0193794i	$0.00616905\pi$
$662$	1.80349e6	−	3.12374e6i	0.159944	−	0.277032i
$663$	1.30111e6	+	2.25359e6i	0.114956	+	0.199110i
$664$	4.76675e6			0.419567
$665$		0			0
$666$	1.25557e7			1.09687
$667$	−151404.	−	262240.i	−0.0131772	−	0.0228236i
$668$	371152.	−	642853.i	0.0321818	−	0.0557405i
$669$	378281.	−	655202.i	0.0326775	−	0.0565992i
$670$	−1.65466e6	−	2.86595e6i	−0.142404	−	0.246651i
$671$	−290174.			−0.0248801
$672$		0			0
$673$	1.23697e7			1.05274			0.526371	−	0.850255i	$-0.323552\pi$
$673$	1.23697e7			1.05274			0.526371	+	0.850255i	$0.323552\pi$
$674$	1.53391e6	+	2.65680e6i	0.130062	+	0.225273i
$675$	689917.	−	1.19497e6i	0.0582824	−	0.100948i
$676$	87958.1	−	152348.i	0.00740302	−	0.0128224i
$677$	−502503.	−	870361.i	−0.0421373	−	0.0729840i	0.844188	−	0.536048i	$-0.180083\pi$
$677$	−502503.	−	870361.i	−0.0421373	−	0.0729840i	−0.886325	+	0.463064i	$0.846750\pi$
$678$	1.31060e6			0.109495
$679$		0			0
$680$	−1.60326e7			−1.32963
$681$	877928.	+	1.52062e6i	0.0725422	+	0.125647i
$682$	−1.12192e6	+	1.94322e6i	−0.0923633	+	0.159978i
$683$	−935093.	+	1.61963e6i	−0.0767014	+	0.132851i	−0.901825	−	0.432102i	$-0.857772\pi$
$683$	−935093.	+	1.61963e6i	−0.0767014	+	0.132851i	0.825123	+	0.564952i	$0.191105\pi$
$684$	−1.37210e6	−	2.37654e6i	−0.112136	−	0.194225i
$685$	3.81290e6			0.310476
$686$		0			0
$687$	−1.18440e6			−0.0957426
$688$	−5.72401e6	−	9.91427e6i	−0.461030	−	0.798527i
$689$	−3.97711e6	+	6.88855e6i	−0.319168	+	0.552815i
$690$	91594.5	−	158646.i	0.00732397	−	0.0126855i
$691$	9.69333e6	+	1.67893e7i	0.772286	+	1.33764i	0.936307	+	0.351181i	$0.114220\pi$
$691$	9.69333e6	+	1.67893e7i	0.772286	+	1.33764i	−0.164022	+	0.986457i	$0.552447\pi$
$692$	4.39549e6			0.348933
$693$		0			0
$694$	−8.93199e6			−0.703963
$695$	6.99896e6	+	1.21226e7i	0.549631	+	0.951989i
$696$	147861.	−	256102.i	0.0115699	−	0.0200397i
$697$	−3.48735e6	+	6.04026e6i	−0.271902	+	0.470949i
$698$	−995905.	−	1.72496e6i	−0.0773712	−	0.134011i
$699$	2.20046e6			0.170342
$700$		0			0
$701$	1.17488e7			0.903024			0.451512	−	0.892265i	$-0.350885\pi$
$701$	1.17488e7			0.903024			0.451512	+	0.892265i	$0.350885\pi$
$702$	1.61208e6	+	2.79221e6i	0.123465	+	0.213848i
$703$	−9.65134e6	+	1.67166e7i	−0.736545	+	1.27573i
$704$	−1.31267e6	+	2.27361e6i	−0.0998214	+	0.172896i
$705$	−933168.	−	1.61629e6i	−0.0707110	−	0.122475i
$706$	2.50279e6			0.188978
$707$		0			0
$708$	464008.			0.0347890
$709$	−8.39738e6	−	1.45447e7i	−0.627377	−	1.08665i	−0.988076	−	0.153966i	$-0.950795\pi$
$709$	−8.39738e6	−	1.45447e7i	−0.627377	−	1.08665i	0.360699	−	0.932682i	$-0.382538\pi$
$710$	−1.29481e6	+	2.24268e6i	−0.0963965	+	0.166964i
$711$	4.30663e6	−	7.45931e6i	0.319495	−	0.553381i
$712$	−6.81312e6	−	1.18007e7i	−0.503670	−	0.872382i
$713$	−2.53322e6			−0.186616
$714$		0			0
$715$	−1.90683e6			−0.139491
$716$	−2.31126e6	−	4.00323e6i	−0.168487	−	0.291828i
$717$	889043.	−	1.53987e6i	0.0645840	−	0.111863i
$718$	−9.58182e6	+	1.65962e7i	−0.693644	+	1.20143i
$719$	−8.25652e6	−	1.43007e7i	−0.595628	−	1.03166i	−0.993458	−	0.114199i	$-0.963570\pi$
$719$	−8.25652e6	−	1.43007e7i	−0.595628	−	1.03166i	0.397830	−	0.917459i	$-0.369763\pi$
$720$	−7.87323e6			−0.566007
$721$		0			0
$722$	−5.09215e6			−0.363545
$723$	404981.	+	701447.i	0.0288130	+	0.0499056i
$724$	−1.92277e6	+	3.33034e6i	−0.136327	+	0.236125i
$725$	503369.	−	871861.i	0.0355665	−	0.0616030i
$726$	824945.	+	1.42885e6i	0.0580876	+	0.100611i
$727$	1.25756e6			0.0882453			0.0441227	−	0.999026i	$-0.485951\pi$
$727$	1.25756e6			0.0882453			0.0441227	+	0.999026i	$0.485951\pi$
$728$		0			0
$729$	−1.28348e7			−0.894479
$730$	2.08232e6	+	3.60669e6i	0.144624	+	0.250496i
$731$	1.43405e7	−	2.48385e7i	0.992592	−	1.71922i
$732$	25841.9	−	44759.4i	0.00178257	−	0.00308750i
$733$	−991661.	−	1.71761e6i	−0.0681716	−	0.118077i	0.829925	−	0.557875i	$-0.188383\pi$
$733$	−991661.	−	1.71761e6i	−0.0681716	−	0.118077i	−0.898096	+	0.439798i	$0.855050\pi$
$734$	−1.11703e7			−0.765288
$735$		0			0
$736$	−909684.			−0.0619007
$737$	−561125.	−	971896.i	−0.0380532	−	0.0659100i
$738$	−2.14096e6	+	3.70825e6i	−0.144700	+	0.250627i
$739$	1.19404e7	−	2.06813e7i	0.804278	−	1.39305i	−0.112499	−	0.993652i	$-0.535885\pi$
$739$	1.19404e7	−	2.06813e7i	0.804278	−	1.39305i	0.916777	−	0.399399i	$-0.130781\pi$
$740$	−1.33463e6	−	2.31164e6i	−0.0895943	−	0.155182i
$741$	−2.45604e6			−0.164320
$742$		0			0
$743$	−1.90819e7			−1.26809			−0.634043	−	0.773298i	$-0.718606\pi$
$743$	−1.90819e7			−1.26809			−0.634043	+	0.773298i	$0.718606\pi$
$744$	−1.23697e6	−	2.14249e6i	−0.0819266	−	0.141901i
$745$	2.89178e6	−	5.00871e6i	0.190886	−	0.330625i
$746$	−4.20943e6	+	7.29095e6i	−0.276934	+	0.479664i
$747$	2.93227e6	+	5.07885e6i	0.192266	+	0.333015i
$748$	−878323.			−0.0573985
$749$		0			0
$750$	1.99278e6			0.129362
$751$	1.87903e6	+	3.25457e6i	0.121572	+	0.210569i	0.920388	−	0.391007i	$-0.127873\pi$
$751$	1.87903e6	+	3.25457e6i	0.121572	+	0.210569i	−0.798816	+	0.601576i	$0.794540\pi$
$752$	8.44817e6	−	1.46327e7i	0.544776	−	0.943580i
$753$	874060.	−	1.51392e6i	0.0561764	−	0.0973004i
$754$	1.17619e6	+	2.03722e6i	0.0753439	+	0.130500i
$755$	−4.64994e6			−0.296880
$756$		0			0
$757$	1.69904e7			1.07761			0.538807	−	0.842429i	$-0.318875\pi$
$757$	1.69904e7			1.07761			0.538807	+	0.842429i	$0.318875\pi$
$758$	−7.16795e6	−	1.24153e7i	−0.453129	−	0.784843i
$759$	31061.4	−	53799.8i	0.00195711	−	0.00338982i
$760$	7.56599e6	−	1.31047e7i	0.475151	−	0.822986i
$761$	1.11999e7	+	1.93988e7i	0.701056	+	1.21426i	0.968096	+	0.250579i	$0.0806211\pi$
$761$	1.11999e7	+	1.93988e7i	0.701056	+	1.21426i	−0.267040	+	0.963685i	$0.586046\pi$
$762$	1.36269e6			0.0850180
$763$		0			0
$764$	−2.57550e6			−0.159635
$765$	−9.86250e6	−	1.70824e7i	−0.609303	−	1.05534i
$766$	−8.25554e6	+	1.42990e7i	−0.508362	+	0.880510i
$767$	−1.14241e7	+	1.97871e7i	−0.701184	+	1.21449i
$768$	−606241.	−	1.05004e6i	−0.0370888	−	0.0642396i
$769$	1.87866e7			1.14560			0.572799	−	0.819696i	$-0.305858\pi$
$769$	1.87866e7			1.14560			0.572799	+	0.819696i	$0.305858\pi$
$770$		0			0
$771$	608138.			0.0368439
$772$	2.37589e6	+	4.11516e6i	0.143477	+	0.248509i
$773$	4.65419e6	−	8.06129e6i	0.280153	−	0.485239i	−0.691269	−	0.722597i	$-0.742948\pi$
$773$	4.65419e6	−	8.06129e6i	0.280153	−	0.485239i	0.971422	+	0.237358i	$0.0762815\pi$
$774$	8.80394e6	−	1.52489e7i	0.528232	−	0.914925i
$775$	−4.21106e6	−	7.29377e6i	−0.251847	−	0.436212i
$776$	−2.05156e7			−1.22301
$777$		0			0
$778$	−2.36525e7			−1.40097
$779$	−3.29144e6	−	5.70094e6i	−0.194331	−	0.336592i
$780$	169816.	−	294130.i	0.00999405	−	0.0173102i
$781$	−439095.	+	760534.i	−0.0257591	+	0.0446161i
$782$	2.07748e6	+	3.59830e6i	0.121484	+	0.210417i
$783$	734267.			0.0428006
$784$		0			0
$785$	−1.59566e6			−0.0924201
$786$	−782861.	−	1.35595e6i	−0.0451989	−	0.0782868i
$787$	8.67133e6	−	1.50192e7i	0.499056	−	0.864390i	−0.500944	−	0.865480i	$-0.667014\pi$
$787$	8.67133e6	−	1.50192e7i	0.499056	−	0.864390i	0.999999	+	0.00109025i	$0.000347038\pi$
$788$	−1.47724e6	+	2.55865e6i	−0.0847491	+	0.146790i
$789$	−300434.	−	520366.i	−0.0171813	−	0.0297589i
$790$	7.67268e6			0.437401
$791$		0			0
$792$	−3.33786e6			−0.189084
$793$	1.27247e6	+	2.20399e6i	0.0718565	+	0.124459i
$794$	2.95717e6	−	5.12197e6i	0.166466	−	0.288327i
$795$	−547943.	+	949064.i	−0.0307480	+	0.0532571i
$796$	1.32154e6	+	2.28897e6i	0.0739259	+	0.128043i
$797$	−3.10445e7			−1.73117			−0.865584	−	0.500764i	$-0.833052\pi$
$797$	−3.10445e7			−1.73117			−0.865584	+	0.500764i	$0.833052\pi$
$798$		0			0
$799$	4.23309e7			2.34580
$800$	−1.51220e6	−	2.61920e6i	−0.0835379	−	0.144692i
$801$	8.38221e6	−	1.45184e7i	0.461612	−	0.799536i
$802$	819290.	−	1.41905e6i	0.0449782	−	0.0779045i
$803$	706153.	+	1.22309e6i	0.0386465	+	0.0669377i
$804$	199887.			0.0109055
$805$		0			0
$806$	1.96794e7			1.06702
$807$	270103.	+	467832.i	0.0145997	+	0.0252875i
$808$	3.53655e6	−	6.12548e6i	0.190568	−	0.330074i
$809$	1.23519e7	−	2.13941e7i	0.663533	−	1.14927i	−0.316147	−	0.948710i	$-0.602389\pi$
$809$	1.23519e7	−	2.13941e7i	0.663533	−	1.14927i	0.979681	−	0.200563i	$-0.0642772\pi$
$810$	−5.94275e6	−	1.02931e7i	−0.318255	−	0.551233i
$811$	−8.42005e6			−0.449534			−0.224767	−	0.974413i	$-0.572162\pi$
$811$	−8.42005e6			−0.449534			−0.224767	+	0.974413i	$0.572162\pi$
$812$		0			0
$813$	−4.57273e6			−0.242633
$814$	1.89644e6	+	3.28474e6i	0.100318	+	0.173756i
$815$	−4.45265e6	+	7.71221e6i	−0.234814	+	0.406710i
$816$	−1.62288e6	+	2.81091e6i	−0.0853220	+	0.147782i
$817$	1.35349e7	+	2.34432e7i	0.709415	+	1.22874i
$818$	7.04930e6			0.368352
$819$		0			0
$820$	910307.			0.0472774
$821$	1.29413e7	+	2.24150e7i	0.670071	+	1.16060i	0.977883	+	0.209150i	$0.0670698\pi$
$821$	1.29413e7	+	2.24150e7i	0.670071	+	1.16060i	−0.307812	+	0.951447i	$0.599597\pi$
$822$	482505.	−	835723.i	0.0249070	−	0.0431402i
$823$	−8.60020e6	+	1.48960e7i	−0.442597	+	0.766601i	−0.997881	−	0.0650597i	$-0.979276\pi$
$823$	−8.60020e6	+	1.48960e7i	−0.442597	+	0.766601i	0.555284	+	0.831661i	$0.312610\pi$
$824$	6.25801e6	+	1.08392e7i	0.321084	+	0.556133i
$825$	206537.			0.0105649
$826$		0			0
$827$	−2.40337e7			−1.22196			−0.610979	−	0.791647i	$-0.709224\pi$
$827$	−2.40337e7			−1.22196			−0.610979	+	0.791647i	$0.709224\pi$
$828$	−304383.	−	527207.i	−0.0154292	−	0.0267242i
$829$	−1.62368e7	+	2.81230e7i	−0.820567	+	1.42126i	0.0846934	+	0.996407i	$0.473009\pi$
$829$	−1.62368e7	+	2.81230e7i	−0.820567	+	1.42126i	−0.905261	+	0.424857i	$0.860324\pi$
$830$	−2.61206e6	+	4.52423e6i	−0.131610	+	0.227955i
$831$	132246.	+	229056.i	0.00664323	+	0.0115064i
$832$	2.30254e7			1.15318
$833$		0			0
$834$	3.54274e6			0.176370
$835$	2.51793e6	+	4.36119e6i	0.124976	+	0.216466i
$836$	414491.	−	717920.i	0.0205116	−	0.0355272i
$837$	3.07135e6	−	5.31973e6i	0.151536	−	0.262468i
$838$	−1.24749e7	−	2.16072e7i	−0.613659	−	1.06289i
$839$	1.24404e7			0.610139			0.305069	−	0.952330i	$-0.401320\pi$
$839$	1.24404e7			0.610139			0.305069	+	0.952330i	$0.401320\pi$
$840$		0			0
$841$	−1.99754e7			−0.973881
$842$	6.19905e6	+	1.07371e7i	0.301332	+	0.521922i
$843$	−2.31977e6	+	4.01796e6i	−0.112428	+	0.194732i
$844$	−1.81434e6	+	3.14253e6i	−0.0876724	+	0.151853i
$845$	596718.	+	1.03355e6i	0.0287493	+	0.0497952i
$846$	2.59878e7			1.24837
$847$		0			0
$848$	−9.92129e6			−0.473782
$849$	−1.23815e6	−	2.14453e6i	−0.0589526	−	0.102109i
$850$	−6.90693e6	+	1.19632e7i	−0.327897	+	0.567934i
$851$	−2.14103e6	+	3.70838e6i	−0.101344	+	0.175533i
$852$	−78208.5	−	135461.i	−0.00369109	−	0.00639316i
$853$	999355.			0.0470270			0.0235135	−	0.999724i	$-0.492515\pi$
$853$	999355.			0.0470270			0.0235135	+	0.999724i	$0.492515\pi$
$854$		0			0
$855$	1.86169e7			0.870949
$856$	−6.40597e6	−	1.10955e7i	−0.298814	−	0.517561i
$857$	−1.32233e7	+	2.29034e7i	−0.615016	+	1.06524i	0.375365	+	0.926877i	$0.377517\pi$
$857$	−1.32233e7	+	2.29034e7i	−0.615016	+	1.06524i	−0.990382	+	0.138363i	$0.955816\pi$
$858$	−241301.	+	417945.i	−0.0111903	+	0.0193821i
$859$	−1.43358e7	−	2.48304e7i	−0.662887	−	1.14815i	−0.979854	−	0.199717i	$-0.935998\pi$
$859$	−1.43358e7	−	2.48304e7i	−0.662887	−	1.14815i	0.316967	−	0.948437i	$-0.397336\pi$
$860$	−3.74332e6			−0.172588
$861$		0			0
$862$	2.65703e7			1.21794
$863$	−2.04087e6	−	3.53488e6i	−0.0932798	−	0.161565i	0.815610	−	0.578603i	$-0.196402\pi$
$863$	−2.04087e6	−	3.53488e6i	−0.0932798	−	0.161565i	−0.908889	+	0.417037i	$0.863068\pi$
$864$	1.10292e6	−	1.91032e6i	0.0502645	−	0.0870607i
$865$	−1.49098e7	+	2.58244e7i	−0.677532	+	1.17352i
$866$	6.68439e6	+	1.15777e7i	0.302878	+	0.524599i
$867$	−5.17446e6			−0.233785
$868$		0			0
$869$	2.60195e6			0.116882
$870$	162048.	+	280676.i	0.00725849	+	0.0125721i
$871$	−4.92131e6	+	8.52395e6i	−0.219804	+	0.380711i
$872$	3.67973e6	−	6.37348e6i	0.163880	−	0.283848i
$873$	−1.26202e7	−	2.18589e7i	−0.560444	−	0.970717i
$874$	−3.92155e6			−0.173652
$875$		0			0
$876$	−251550.			−0.0110755
$877$	1.41202e7	+	2.44570e7i	0.619931	+	1.07375i	0.989498	+	0.144547i	$0.0461726\pi$
$877$	1.41202e7	+	2.44570e7i	0.619931	+	1.07375i	−0.369567	+	0.929204i	$0.620494\pi$
$878$	−6.49098e6	+	1.12427e7i	−0.284167	+	0.492192i
$879$	−1.90805e6	+	3.30484e6i	−0.0832948	+	0.144271i
$880$	−1.18920e6	−	2.05975e6i	−0.0517662	−	0.0896617i
$881$	−1.61480e7			−0.700936			−0.350468	−	0.936575i	$-0.613978\pi$
$881$	−1.61480e7			−0.700936			−0.350468	+	0.936575i	$0.613978\pi$
$882$		0			0
$883$	−3.86021e7			−1.66613			−0.833065	−	0.553174i	$-0.813416\pi$
$883$	−3.86021e7			−1.66613			−0.833065	+	0.553174i	$0.813416\pi$
$884$	3.85164e6	+	6.67123e6i	0.165773	+	0.287128i
$885$	−1.57394e6	+	2.72615e6i	−0.0675508	+	0.117001i
$886$	9.75637e6	−	1.68985e7i	0.417546	−	0.723210i
$887$	3.64544e6	+	6.31408e6i	0.155575	+	0.269464i	0.933268	−	0.359180i	$-0.116944\pi$
$887$	3.64544e6	+	6.31408e6i	0.155575	+	0.269464i	−0.777693	+	0.628644i	$0.783610\pi$
$888$	−4.18184e6			−0.177965
$889$		0			0
$890$	1.49337e7			0.631965
$891$	−2.01529e6	−	3.49059e6i	−0.0850441	−	0.147301i
$892$	1.11981e6	−	1.93957e6i	0.0471230	−	0.0816194i
$893$	−1.99764e7	+	3.46002e7i	−0.838281	+	1.45194i
$894$	−731883.	−	1.26766e6i	−0.0306265	−	0.0530467i
$895$	3.13598e7			1.30862
$896$		0			0
$897$	−544843.			−0.0226095
$898$	3.79603e6	+	6.57491e6i	0.157086	+	0.272082i
$899$	2.24088e6	−	3.88132e6i	0.0924739	−	0.160170i
$900$	1.01197e6	−	1.75279e6i	0.0416449	−	0.0721311i
$901$	−1.24280e7	−	2.15260e7i	−0.510024	−	0.883387i
$902$	−1.29351e6			−0.0529361
$903$		0			0
$904$	2.40160e7			0.977415
$905$	−1.30443e7	−	2.25934e7i	−0.529419	−	0.916981i
$906$	−588429.	+	1.01919e6i	−0.0238163	+	0.0412510i
$907$	1.86667e7	−	3.23317e7i	0.753443	−	1.30500i	−0.192702	−	0.981257i	$-0.561725\pi$
$907$	1.86667e7	−	3.23317e7i	0.753443	−	1.30500i	0.946145	−	0.323744i	$-0.104942\pi$
$908$	2.59890e6	+	4.50142e6i	0.104610	+	0.181190i
$909$	8.70205e6			0.349311
$910$		0			0
$911$	−2475.17			−9.88120e−5			−4.94060e−5	−	1.00000i	$-0.500016\pi$
$911$	−2475.17			−9.88120e−5			−4.94060e−5		1.00000i	$0.500016\pi$
$912$	−1.53171e6	−	2.65300e6i	−0.0609804	−	0.105621i
$913$	−885798.	+	1.53425e6i	−0.0351688	+	0.0609142i
$914$	−5.49501e6	+	9.51763e6i	−0.217572	+	0.376846i
$915$	175314.	+	303653.i	0.00692252	+	0.0119902i
$916$	−3.50613e6			−0.138067
$917$		0			0
$918$	−1.00752e7			−0.394590
$919$	2.24119e6	+	3.88185e6i	0.0875366	+	0.151618i	0.906469	−	0.422272i	$-0.138767\pi$
$919$	2.24119e6	+	3.88185e6i	0.0875366	+	0.151618i	−0.818933	+	0.573890i	$0.805434\pi$
$920$	1.67842e6	−	2.90711e6i	0.0653780	−	0.113238i
$921$	747334.	−	1.29442e6i	0.0290313	−	0.0502836i
$922$	1.55520e7	+	2.69368e7i	0.602501	+	1.04356i
$923$	7.70210e6			0.297581
$924$		0			0
$925$	−1.42364e7			−0.547075
$926$	1.00033e7	+	1.73262e7i	0.383367	+	0.664011i
$927$	−7.69925e6	+	1.33355e7i	−0.294272	+	0.509694i
$928$	804703.	−	1.39379e6i	0.0306737	−	0.0531283i
$929$	1.06429e7	+	1.84341e7i	0.404596	+	0.700781i	0.994274	−	0.106857i	$-0.0340787\pi$
$929$	1.06429e7	+	1.84341e7i	0.404596	+	0.700781i	−0.589678	+	0.807638i	$0.700745\pi$
$930$	2.71131e6			0.102795
$931$		0			0
$932$	6.51394e6			0.245643
$933$	892351.	+	1.54560e6i	0.0335608	+	0.0581289i
$934$	1.39025e7	−	2.40798e7i	0.521465	−	0.903203i
$935$	2.97932e6	−	5.16034e6i	0.111452	−	0.193041i
$936$	1.46373e7	+	2.53525e7i	0.546097	+	0.945868i
$937$	−6.79757e6			−0.252932			−0.126466	−	0.991971i	$-0.540364\pi$
$937$	−6.79757e6			−0.252932			−0.126466	+	0.991971i	$0.540364\pi$
$938$		0			0
$939$	3.36781e6			0.124647
$940$	−2.76242e6	−	4.78465e6i	−0.101970	−	0.176616i
$941$	2.45441e7	−	4.25117e7i	0.903595	−	1.56507i	0.0808027	−	0.996730i	$-0.474252\pi$
$941$	2.45441e7	−	4.25117e7i	0.903595	−	1.56507i	0.822792	−	0.568342i	$-0.192415\pi$
$942$	−201924.	+	349742.i	−0.00741413	+	0.0128416i
$943$	−730166.	−	1.26468e6i	−0.0267388	−	0.0463130i
$944$	−2.84985e7			−1.04086
$945$		0			0
$946$	5.31910e6			0.193246
$947$	−1.22742e7	−	2.12596e7i	−0.444753	−	0.770334i	0.553282	−	0.832994i	$-0.313375\pi$
$947$	−1.22742e7	−	2.12596e7i	−0.444753	−	0.770334i	−0.998035	+	0.0626595i	$0.980042\pi$
$948$	−231720.	+	401351.i	−0.00837420	+	0.0145045i
$949$	6.19327e6	−	1.07271e7i	0.223231	−	0.386648i
$950$	−6.51892e6	−	1.12911e7i	−0.234351	−	0.405908i
$951$	4.71869e6			0.169188
$952$		0			0
$953$	−513120.			−0.0183015			−0.00915075	−	0.999958i	$-0.502913\pi$
$953$	−513120.			−0.0183015			−0.00915075	+	0.999958i	$0.502913\pi$
$954$	−7.62984e6	−	1.32153e7i	−0.271422	−	0.470116i
$955$	8.73625e6	−	1.51316e7i	0.309968	−	0.536880i
$956$	2.63180e6	−	4.55841e6i	0.0931340	−	0.161313i
$957$	54953.5	+	95182.3i	0.00193962	+	0.00335951i
$958$	−3.38659e7			−1.19220
$959$		0			0
$960$	3.17230e6			0.111095
$961$	−4.43206e6	−	7.67656e6i	−0.154809	−	0.268138i
$962$	1.66326e7	−	2.88086e7i	0.579460	−	1.00365i
$963$	7.88129e6	−	1.36508e7i	0.273862	−	0.474343i
$964$	1.19885e6	+	2.07647e6i	0.0415501	+	0.0719669i
$965$	−3.22366e7			−1.11437
$966$		0			0
$967$	3.34818e7			1.15144			0.575722	−	0.817645i	$-0.304721\pi$
$967$	3.34818e7			1.15144			0.575722	+	0.817645i	$0.304721\pi$
$968$	1.51167e7	+	2.61829e7i	0.518523	+	0.898108i
$969$	3.83744e6	−	6.64664e6i	0.131290	−	0.227401i
$970$	1.12421e7	−	1.94719e7i	0.383635	−	0.664475i
$971$	2.38018e6	+	4.12259e6i	0.0810143	+	0.140321i	0.903686	−	0.428196i	$-0.140851\pi$
$971$	2.38018e6	+	4.12259e6i	0.0810143	+	0.140321i	−0.822672	+	0.568517i	$0.807517\pi$
$972$	2.22090e6			0.0753986
$973$		0			0
$974$	−4.84739e7			−1.63723
$975$	−905711.	−	1.56874e6i	−0.0305125	−	0.0528492i
$976$	−1.58716e6	+	2.74904e6i	−0.0533329	+	0.0923753i
$977$	−1.43669e7	+	2.48842e7i	−0.481534	+	0.834041i	−0.999775	−	0.0211935i	$-0.993253\pi$
$977$	−1.43669e7	+	2.48842e7i	−0.481534	+	0.834041i	0.518242	+	0.855234i	$0.326587\pi$
$978$	1.12692e6	+	1.95189e6i	0.0376745	+	0.0652541i
$979$	5.06430e6			0.168874
$980$		0			0
$981$	9.05437e6			0.300390
$982$	−2.08214e7	−	3.60637e7i	−0.689019	−	1.19342i
$983$	−2.48536e7	+	4.30477e7i	−0.820362	+	1.42091i	0.0850509	+	0.996377i	$0.472895\pi$
$983$	−2.48536e7	+	4.30477e7i	−0.820362	+	1.42091i	−0.905413	+	0.424532i	$0.860439\pi$
$984$	713076.	−	1.23508e6i	0.0234773	−	0.0406638i
$985$	−1.00218e7	−	1.73582e7i	−0.329119	−	0.570051i
$986$	−7.35092e6			−0.240796
$987$		0			0
$988$	−7.27054e6			−0.236960
$989$	3.00255e6	+	5.20057e6i	0.0976113	+	0.169068i
$990$	1.82907e6	−	3.16804e6i	0.0593120	−	0.102731i
$991$	1.45533e6	−	2.52070e6i	0.0470736	−	0.0815338i	−0.841529	−	0.540213i	$-0.818344\pi$
$991$	1.45533e6	−	2.52070e6i	0.0470736	−	0.0815338i	0.888602	+	0.458679i	$0.151677\pi$
$992$	−6.73194e6	−	1.16601e7i	−0.217201	−	0.376203i
$993$	−1.47803e6			−0.0475676
$994$		0			0
$995$	−1.79309e7			−0.574176
$996$	−157772.	−	273270.i	−0.00503944	−	0.00872857i
$997$	7.16765e6	−	1.24147e7i	0.228370	−	0.395548i	−0.728955	−	0.684561i	$-0.759994\pi$
$997$	7.16765e6	−	1.24147e7i	0.228370	−	0.395548i	0.957325	+	0.289013i	$0.0933271\pi$
$998$	−1.09645e7	+	1.89910e7i	−0.348466	+	0.603561i
$999$	−5.19169e6	−	8.99227e6i	−0.164587	−	0.285073i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.6.c.f.18.2		4
7.2	even	3	inner	49.6.c.f.30.2		4
7.3	odd	6		49.6.a.d.1.1		2
7.4	even	3		49.6.a.e.1.1		2
7.5	odd	6		7.6.c.a.2.2	✓	4
7.6	odd	2		7.6.c.a.4.2	yes	4
21.5	even	6		63.6.e.d.37.1		4
21.11	odd	6		441.6.a.m.1.2		2
21.17	even	6		441.6.a.n.1.2		2
21.20	even	2		63.6.e.d.46.1		4
28.3	even	6		784.6.a.ba.1.1		2
28.11	odd	6		784.6.a.t.1.2		2
28.19	even	6		112.6.i.c.65.2		4
28.27	even	2		112.6.i.c.81.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.6.c.a.2.2	✓	4	7.5	odd	6
7.6.c.a.4.2	yes	4	7.6	odd	2
49.6.a.d.1.1		2	7.3	odd	6
49.6.a.e.1.1		2	7.4	even	3
49.6.c.f.18.2		4	1.1	even	1	trivial
49.6.c.f.30.2		4	7.2	even	3	inner
63.6.e.d.37.1		4	21.5	even	6
63.6.e.d.46.1		4	21.20	even	2
112.6.i.c.65.2		4	28.19	even	6
112.6.i.c.81.2		4	28.27	even	2
441.6.a.m.1.2		2	21.11	odd	6
441.6.a.n.1.2		2	21.17	even	6
784.6.a.t.1.2		2	28.11	odd	6
784.6.a.ba.1.1		2	28.3	even	6

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

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Modular forms

Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	49.6.c.f.18.2

Level	$49$
Weight	$6$
Character	49.18
Analytic conductor	$7.859$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$