LMFDB - Embedded newform 63.6.e.d.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.e (of order $3$, degree $2$, 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:	$10.1041806482$
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:	$\Z[a_1, \ldots, a_{5}]$
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			46.1
Root			$-1.27069 - 2.20090i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.6.e.d.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.54138 - 4.40180i) q^{2} +(3.08276 - 5.33950i) q^{4} +(20.9138 + 36.2238i) q^{5} +(-127.159 + 25.2522i) q^{7} -193.986 q^{8} +O(q^{10})$	\(q+(-2.54138 - 4.40180i) q^{2} +(3.08276 - 5.33950i) q^{4} +(20.9138 + 36.2238i) q^{5} +(-127.159 + 25.2522i) q^{7} -193.986 q^{8} +(106.300 - 184.117i) q^{10} +(36.0482 - 62.4374i) q^{11} -632.317 q^{13} +(434.314 + 495.552i) q^{14} +(394.345 + 683.025i) q^{16} +(-987.962 + 1711.20i) q^{17} +(932.463 + 1615.07i) q^{19} +257.889 q^{20} -366.449 q^{22} +(206.855 + 358.284i) q^{23} +(687.725 - 1191.17i) q^{25} +(1606.96 + 2783.34i) q^{26} +(-257.166 + 756.810i) q^{28} -731.934 q^{29} +(-3061.59 + 5302.83i) q^{31} +(-1099.42 + 1904.25i) q^{32} +10043.2 q^{34} +(-3574.10 - 4078.05i) q^{35} +(-5175.19 - 8963.69i) q^{37} +(4739.49 - 8209.03i) q^{38} +(-4056.99 - 7026.92i) q^{40} +3529.84 q^{41} -14515.2 q^{43} +(-222.256 - 384.959i) q^{44} +(1051.40 - 1821.07i) q^{46} +(-10711.7 - 18553.1i) q^{47} +(15531.7 - 6422.06i) q^{49} -6991.08 q^{50} +(-1949.28 + 3376.26i) q^{52} +(6289.73 - 10894.1i) q^{53} +3015.62 q^{55} +(24667.0 - 4898.57i) q^{56} +(1860.12 + 3221.83i) q^{58} +(-18067.0 + 31292.9i) q^{59} +(-2012.40 - 3485.58i) q^{61} +31122.6 q^{62} +36414.2 q^{64} +(-13224.2 - 22904.9i) q^{65} +(-7782.97 + 13480.5i) q^{67} +(6091.31 + 10550.5i) q^{68} +(-8867.61 + 26096.4i) q^{70} -12180.8 q^{71} +(-9794.56 + 16964.7i) q^{73} +(-26304.3 + 45560.3i) q^{74} +11498.2 q^{76} +(-3007.17 + 8849.75i) q^{77} +(-18044.9 - 31254.7i) q^{79} +(-16494.5 + 28569.3i) q^{80} +(-8970.66 - 15537.6i) q^{82} +24572.6 q^{83} -82648.2 q^{85} +(36888.7 + 63893.2i) q^{86} +(-6992.86 + 12112.0i) q^{88} +(-35121.7 - 60832.5i) q^{89} +(80404.6 - 15967.4i) q^{91} +2550.74 q^{92} +(-54444.8 + 94301.2i) q^{94} +(-39002.7 + 67554.7i) q^{95} +105758. q^{97} +(-67740.5 - 52046.4i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 12 q^{4} - 38 q^{5} - 168 q^{7} - 192 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 12 * q^4 - 38 * q^5 - 168 * q^7 - 192 * q^8	$ 4 q + 2 q^{2} - 12 q^{4} - 38 q^{5} - 168 q^{7} - 192 q^{8} + 778 q^{10} + 424 q^{11} - 1848 q^{13} + 2674 q^{14} + 2064 q^{16} - 2346 q^{17} + 360 q^{19} + 3416 q^{20} + 4252 q^{22} - 12 q^{23} - 1872 q^{25} + 1148 q^{26} + 2548 q^{28} + 14104 q^{29} - 3548 q^{31} - 8096 q^{32} + 14844 q^{34} - 27496 q^{35} - 11090 q^{37} + 20138 q^{38} - 15936 q^{40} - 7000 q^{41} - 25360 q^{43} + 5948 q^{44} + 5118 q^{46} - 22956 q^{47} + 4900 q^{49} - 59984 q^{50} + 1400 q^{52} + 3042 q^{53} - 50152 q^{55} + 57792 q^{56} + 58852 q^{58} - 65808 q^{59} + 42486 q^{61} + 98724 q^{62} + 70912 q^{64} - 3164 q^{65} - 42312 q^{67} + 5460 q^{68} - 113050 q^{70} + 4416 q^{71} + 50506 q^{73} - 47370 q^{74} + 77672 q^{76} - 65338 q^{77} - 9004 q^{79} + 68816 q^{80} - 67732 q^{82} + 208656 q^{83} - 106212 q^{85} + 86776 q^{86} + 20496 q^{88} - 26666 q^{89} + 135632 q^{91} + 20568 q^{92} - 98034 q^{94} - 198140 q^{95} + 418264 q^{97} - 98686 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 12 * q^4 - 38 * q^5 - 168 * q^7 - 192 * q^8 + 778 * q^10 + 424 * q^11 - 1848 * q^13 + 2674 * q^14 + 2064 * q^16 - 2346 * q^17 + 360 * q^19 + 3416 * q^20 + 4252 * q^22 - 12 * q^23 - 1872 * q^25 + 1148 * q^26 + 2548 * q^28 + 14104 * q^29 - 3548 * q^31 - 8096 * q^32 + 14844 * q^34 - 27496 * q^35 - 11090 * q^37 + 20138 * q^38 - 15936 * q^40 - 7000 * q^41 - 25360 * q^43 + 5948 * q^44 + 5118 * q^46 - 22956 * q^47 + 4900 * q^49 - 59984 * q^50 + 1400 * q^52 + 3042 * q^53 - 50152 * q^55 + 57792 * q^56 + 58852 * q^58 - 65808 * q^59 + 42486 * q^61 + 98724 * q^62 + 70912 * q^64 - 3164 * q^65 - 42312 * q^67 + 5460 * q^68 - 113050 * q^70 + 4416 * q^71 + 50506 * q^73 - 47370 * q^74 + 77672 * q^76 - 65338 * q^77 - 9004 * q^79 + 68816 * q^80 - 67732 * q^82 + 208656 * q^83 - 106212 * q^85 + 86776 * q^86 + 20496 * q^88 - 26666 * q^89 + 135632 * q^91 + 20568 * q^92 - 98034 * q^94 - 198140 * q^95 + 418264 * q^97 - 98686 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	0.549081	−	0.835769i	$-0.314978\pi$
$2$	−2.54138	−	4.40180i	−0.449257	−	0.778136i	−0.998338	+	0.0576333i	$0.981645\pi$
$3$		0			0
$3$		0			0
$4$	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	$0.711279\pi$
$6$		0			0
$7$	−127.159	+	25.2522i	−0.980846	+	0.194784i
$7$	−127.159	+	25.2522i	−0.980846	+	0.194784i
$8$	−193.986			−1.07163
$9$		0			0
$10$	106.300	−	184.117i	0.336150	−	0.582229i
$11$	36.0482	−	62.4374i	0.0898260	−	0.155583i	−0.817611	−	0.575770i	$-0.804702\pi$
$11$	36.0482	−	62.4374i	0.0898260	−	0.155583i	0.907437	+	0.420187i	$0.138036\pi$
$12$		0			0
$13$	−632.317			−1.03771			−0.518856	−	0.854862i	$-0.673642\pi$
$13$	−632.317			−1.03771			−0.518856	+	0.854862i	$0.673642\pi$
$14$	434.314	+	495.552i	0.592220	+	0.675724i
$15$		0			0
$16$	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	$0.855508\pi$
$18$		0			0
$19$	932.463	+	1615.07i	0.592581	+	1.02638i	0.993883	+	0.110434i	$0.0352242\pi$
$19$	932.463	+	1615.07i	0.592581	+	1.02638i	−0.401303	+	0.915945i	$0.631443\pi$
$20$	257.889			0.144164
$21$		0			0
$22$	−366.449			−0.161420
$23$	206.855	+	358.284i	0.0815356	+	0.141224i	0.903910	−	0.427723i	$-0.140684\pi$
$23$	206.855	+	358.284i	0.0815356	+	0.141224i	−0.822374	+	0.568947i	$0.807351\pi$
$24$		0			0
$25$	687.725	−	1191.17i	0.220072	−	0.381176i
$26$	1606.96	+	2783.34i	0.466199	+	0.807481i
$27$		0			0
$28$	−257.166	+	756.810i	−0.0619896	+	0.182428i
$29$	−731.934			−0.161613			−0.0808066	−	0.996730i	$-0.525750\pi$
$29$	−731.934			−0.161613			−0.0808066	+	0.996730i	$0.525750\pi$
$30$		0			0
$31$	−3061.59	+	5302.83i	−0.572193	+	0.991067i	0.424148	+	0.905593i	$0.360574\pi$
$31$	−3061.59	+	5302.83i	−0.572193	+	0.991067i	−0.996340	+	0.0854740i	$0.972760\pi$
$32$	−1099.42	+	1904.25i	−0.189797	+	0.328738i
$33$		0			0
$34$	10043.2			1.48995
$35$	−3574.10	−	4078.05i	−0.493170	−	0.562707i
$36$		0			0
$37$	−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
$39$		0			0
$40$	−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
$45$		0			0
$46$	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	$-0.416760\pi$
$48$		0			0
$49$	15531.7	−	6422.06i	0.924118	−	0.382106i
$50$	−6991.08			−0.395475
$51$		0			0
$52$	−1949.28	+	3376.26i	−0.0999693	+	0.173152i
$53$	6289.73	−	10894.1i	0.307569	−	0.532725i	−0.670261	−	0.742125i	$-0.733818\pi$
$53$	6289.73	−	10894.1i	0.307569	−	0.532725i	0.977830	+	0.209400i	$0.0671512\pi$
$54$		0			0
$55$	3015.62			0.134422
$56$	24667.0	−	4898.57i	1.05111	−	0.208737i
$57$		0			0
$58$	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	$0.930507\pi$
$60$		0			0
$61$	−2012.40	−	3485.58i	−0.0692451	−	0.119936i	0.829324	−	0.558768i	$-0.188726\pi$
$61$	−2012.40	−	3485.58i	−0.0692451	−	0.119936i	−0.898569	+	0.438832i	$0.855392\pi$
$62$	31122.6			1.02825
$63$		0			0
$64$	36414.2			1.11127
$65$	−13224.2	−	22904.9i	−0.388226	−	0.672428i
$66$		0			0
$67$	−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
$69$		0			0
$70$	−8867.61	+	26096.4i	−0.216303	+	0.636553i
$71$	−12180.8			−0.286766			−0.143383	−	0.989667i	$-0.545798\pi$
$71$	−12180.8			−0.286766			−0.143383	+	0.989667i	$0.545798\pi$
$72$		0			0
$73$	−9794.56	+	16964.7i	−0.215119	+	0.372596i	−0.953309	−	0.301996i	$-0.902347\pi$
$73$	−9794.56	+	16964.7i	−0.215119	+	0.372596i	0.738191	+	0.674592i	$0.235680\pi$
$74$	−26304.3	+	45560.3i	−0.558402	+	0.967181i
$75$		0			0
$76$	11498.2			0.228348
$77$	−3007.17	+	8849.75i	−0.0578004	+	0.170100i
$78$		0			0
$79$	−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
$81$		0			0
$82$	−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
$87$		0			0
$88$	−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	$0.989080\pi$
$90$		0			0
$91$	80404.6	−	15967.4i	1.01784	−	0.202130i
$92$	2550.74			0.0314193
$93$		0			0
$94$	−54444.8	+	94301.2i	−0.635531	+	1.10077i
$95$	−39002.7	+	67554.7i	−0.443390	+	0.767974i
$96$		0			0
$97$	105758.			1.14126			0.570630	−	0.821207i	$-0.306699\pi$
$97$	105758.			1.14126			0.570630	+	0.821207i	$0.306699\pi$
$98$	−67740.5	−	52046.4i	−0.712497	−	0.547426i
$99$		0			0
$100$	−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	$0.109759\pi$
$102$		0			0
$103$	−32260.0	−	55876.0i	−0.299621	−	0.518958i	0.676428	−	0.736508i	$-0.263527\pi$
$103$	−32260.0	−	55876.0i	−0.299621	−	0.518958i	−0.976049	+	0.217550i	$0.930193\pi$
$104$	122661.			1.11205
$105$		0			0
$106$	−63938.4			−0.552710
$107$	33022.8	+	57197.2i	0.278840	+	0.482964i	0.971097	−	0.238687i	$-0.0767169\pi$
$107$	33022.8	+	57197.2i	0.278840	+	0.482964i	−0.692257	+	0.721651i	$0.743384\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	−67392.2	−	76894.5i	−0.507650	−	0.579229i
$113$	−123802.			−0.912080			−0.456040	−	0.889959i	$-0.650733\pi$
$113$	−123802.			−0.912080			−0.456040	+	0.889959i	$0.650733\pi$
$114$		0			0
$115$	−8652.27	+	14986.2i	−0.0610078	+	0.105669i
$116$	−2256.38	+	3908.16i	−0.0155692	+	0.0269667i
$117$		0			0
$118$	183660.			1.21426
$119$	82416.5	−	242542.i	0.533515	−	1.57007i
$120$		0			0
$121$	77926.6	+	134973.i	0.483863	+	0.838075i
$122$	−10228.5	+	17716.4i	−0.0622177	+	0.107764i
$123$		0			0
$124$	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
$129$		0			0
$130$	−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	$0.956206\pi$
$132$		0			0
$133$	−159355.	−	181824.i	−0.781153	−	0.891295i
$134$	79118.0			0.380639
$135$		0			0
$136$	191651.	−	331950.i	0.888514	−	1.53895i
$137$	−45578.7	+	78944.6i	−0.207472	+	0.359353i	−0.950918	−	0.309444i	$-0.899857\pi$
$137$	−45578.7	+	78944.6i	−0.207472	+	0.359353i	0.743445	+	0.668797i	$0.233190\pi$
$138$		0			0
$139$	−334657.			−1.46914			−0.734570	−	0.678533i	$-0.762616\pi$
$139$	−334657.			−1.46914			−0.734570	+	0.678533i	$0.762616\pi$
$140$	−32792.9	+	6512.26i	−0.141403	+	0.0280809i
$141$		0			0
$142$	30955.9	+	53617.3i	0.128832	+	0.223143i
$143$	−22793.9	+	39480.2i	−0.0932135	+	0.161451i
$144$		0			0
$145$	−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	0.964927	−	0.262519i	$-0.0845532\pi$
$149$	69135.7	+	119746.i	0.255115	+	0.441873i	−0.709812	+	0.704392i	$0.751220\pi$
$150$		0			0
$151$	−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
$153$		0			0
$154$	46597.2	−	9253.63i	0.158328	−	0.0314420i
$155$	−256118.			−0.856270
$156$		0			0
$157$	19074.3	−	33037.6i	0.0617587	−	0.106969i	−0.833493	−	0.552530i	$-0.813662\pi$
$157$	19074.3	−	33037.6i	0.0617587	−	0.106969i	0.895252	+	0.445561i	$0.146996\pi$
$158$	−91717.9	+	158860.i	−0.292288	+	0.506258i
$159$		0			0
$160$	−91972.3			−0.284025
$161$	−35350.9	−	40335.4i	−0.107482	−	0.122637i
$162$		0			0
$163$	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
$165$		0			0
$166$	−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
$171$		0			0
$172$	−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	$0.472824\pi$
$174$		0			0
$175$	−57370.5	+	168835.i	−0.141610	+	0.416741i
$176$	56861.7			0.138369
$177$		0			0
$178$	−178515.	+	309197.i	−0.422304	+	0.731451i
$179$	−374869.	+	649292.i	−0.874474	+	1.51463i	−0.0171519	+	0.999853i	$0.505460\pi$
$179$	−374869.	+	649292.i	−0.874474	+	1.51463i	−0.857322	+	0.514780i	$0.827873\pi$
$180$		0			0
$181$	623718.			1.41511			0.707557	−	0.706656i	$-0.249797\pi$
$181$	623718.			1.41511			0.707557	+	0.706656i	$0.249797\pi$
$182$	−274624.	−	313346.i	−0.614554	−	0.701206i
$183$		0			0
$184$	−40127.1	−	69502.2i	−0.0873762	−	0.151340i
$185$	216466.	−	374930.i	0.465008	−	0.805417i
$186$		0			0
$187$	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	0.995351	−	0.0963141i	$-0.0307053\pi$
$191$	208863.	+	361761.i	0.414265	+	0.717528i	−0.581086	+	0.813842i	$0.697372\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	13589.8	−	102729.i	0.0252681	−	0.191009i
$197$	479193.			0.879721			0.439861	−	0.898066i	$-0.355028\pi$
$197$	479193.			0.879721			0.439861	+	0.898066i	$0.355028\pi$
$198$		0			0
$199$	214343.	−	371253.i	0.383687	−	0.664565i	−0.607899	−	0.794014i	$-0.707988\pi$
$199$	214343.	−	371253.i	0.383687	−	0.664565i	0.991586	+	0.129449i	$0.0413210\pi$
$200$	−133409.	+	231072.i	−0.235836	+	0.408481i
$201$		0			0
$202$	−185327.			−0.319565
$203$	93071.7	−	18482.9i	0.158518	−	0.0314797i
$204$		0			0
$205$	73822.4	+	127864.i	0.122688	+	0.212502i
$206$	−163970.	+	284005.i	−0.269213	+	0.466291i
$207$		0			0
$208$	−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
$213$		0			0
$214$	167847.	−	290720.i	0.250541	−	0.433950i
$215$	−303569.	−	525797.i	−0.447879	−	0.775750i
$216$		0			0
$217$	255400.	−	751612.i	0.368189	−	1.08354i
$218$	−192830.			−0.274811
$219$		0			0
$220$	9296.45	−	16101.9i	0.0129497	−	0.0224296i
$221$	624706.	−	1.08202e6i	0.860389	−	1.49024i
$222$		0			0
$223$	−363249.			−0.489151			−0.244575	−	0.969630i	$-0.578649\pi$
$223$	−363249.			−0.489151			−0.244575	+	0.969630i	$0.578649\pi$
$224$	91714.4	−	269905.i	0.122129	−	0.359410i
$225$		0			0
$226$	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	$0.983977\pi$
$228$		0			0
$229$	284333.	+	492479.i	0.358293	+	0.620582i	0.987676	−	0.156513i	$-0.0500254\pi$
$229$	284333.	+	492479.i	0.358293	+	0.620582i	−0.629382	+	0.777096i	$0.716692\pi$
$230$	87954.8			0.109633
$231$		0			0
$232$	141985.			0.173190
$233$	−528255.	−	914965.i	−0.637461	−	1.10412i	−0.985988	−	0.166817i	$-0.946651\pi$
$233$	−528255.	−	914965.i	−0.637461	−	1.10412i	0.348526	−	0.937299i	$-0.386682\pi$
$234$		0			0
$235$	448043.	−	776034.i	0.529237	−	0.916666i
$236$	111392.	+	192937.i	0.130189	+	0.225495i
$237$		0			0
$238$	−1.27707e6	+	253611.i	−1.46142	+	0.290219i
$239$	−853715.			−0.966759			−0.483379	−	0.875411i	$-0.660591\pi$
$239$	−853715.			−0.966759			−0.483379	+	0.875411i	$0.660591\pi$
$240$		0			0
$241$	194444.	−	336787.i	0.215651	−	0.373519i	−0.737823	−	0.674995i	$-0.764146\pi$
$241$	194444.	−	336787.i	0.215651	−	0.373519i	0.953474	+	0.301476i	$0.0974792\pi$
$242$	396082.	−	686034.i	0.434757	−	0.753022i
$243$		0			0
$244$	−24815.0			−0.0266833
$245$	557458.	+	428306.i	0.593330	+	0.455867i
$246$		0			0
$247$	−589612.	−	1.02124e6i	−0.614928	−	1.06509i
$248$	593906.	−	1.02868e6i	0.613181	−	1.06206i
$249$		0			0
$250$	−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
$255$		0			0
$256$	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	$0.789305\pi$
$258$		0			0
$259$	884423.	+	1.00913e6i	0.819239	+	0.934752i
$260$	−163068.			−0.149601
$261$		0			0
$262$	−375876.	+	651037.i	−0.338292	+	0.585939i
$263$	−144248.	+	249844.i	−0.128594	+	0.222731i	−0.923132	−	0.384483i	$-0.874380\pi$
$263$	−144248.	+	249844.i	−0.128594	+	0.222731i	0.794538	+	0.607214i	$0.207713\pi$
$264$		0			0
$265$	526169.			0.460268
$266$	−395371.	+	1.16353e6i	−0.342611	+	1.00826i
$267$		0			0
$268$	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	$0.201519\pi$
$270$		0			0
$271$	1.09776e6	+	1.90137e6i	0.907994	+	1.57269i	0.816847	+	0.576854i	$0.195720\pi$
$271$	1.09776e6	+	1.90137e6i	0.907994	+	1.57269i	0.0911464	+	0.995838i	$0.470947\pi$
$272$	−1.55839e6			−1.27719
$273$		0			0
$274$	463331.			0.372834
$275$	−49582.5	−	85879.5i	−0.0395364	−	0.0684790i
$276$		0			0
$277$	−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
$279$		0			0
$280$	693327.	+	791086.i	0.528497	+	0.603016i
$281$	2.22759e6			1.68294			0.841472	−	0.540301i	$-0.181690\pi$
$281$	2.22759e6			1.68294			0.841472	+	0.540301i	$0.181690\pi$
$282$		0			0
$283$	−594473.	+	1.02966e6i	−0.441231	+	0.764235i	−0.997781	−	0.0665792i	$-0.978792\pi$
$283$	−594473.	+	1.02966e6i	−0.441231	+	0.764235i	0.556550	+	0.830814i	$0.312125\pi$
$284$	−37550.4	+	65039.1i	−0.0276260	+	0.0478497i
$285$		0			0
$286$	231712.			0.167507
$287$	−448850.	+	89136.0i	−0.321659	+	0.0638776i
$288$		0			0
$289$	−1.24221e6	−	2.15157e6i	−0.874884	−	1.51534i
$290$	−77804.5	+	134761.i	−0.0543263	+	0.0940958i
$291$		0			0
$292$	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
$297$		0			0
$298$	351400.	−	608643.i	0.229225	−	0.397029i
$299$	−130798.	−	226549.i	−0.0846104	−	0.146550i
$300$		0			0
$301$	1.84574e6	−	366541.i	1.17423	−	0.233188i
$302$	565047.			0.356506
$303$		0			0
$304$	−735423.	+	1.27379e6i	−0.456408	+	0.790522i
$305$	84173.8	−	145793.i	0.0518117	−	0.0897404i
$306$		0			0
$307$	−717638.			−0.434569			−0.217285	−	0.976108i	$-0.569720\pi$
$307$	−717638.			−0.434569			−0.217285	+	0.976108i	$0.569720\pi$
$308$	37982.9	+	43338.4i	0.0228145	+	0.0260313i
$309$		0			0
$310$	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	$0.247487\pi$
$312$		0			0
$313$	−808495.	−	1.40035e6i	−0.466462	−	0.807936i	0.532804	−	0.846239i	$-0.321138\pi$
$313$	−808495.	−	1.40035e6i	−0.466462	−	0.807936i	−0.999266	+	0.0383025i	$0.987805\pi$
$314$	−193900.			−0.110982
$315$		0			0
$316$	−222512.			−0.125354
$317$	−1.13280e6	−	1.96206e6i	−0.633145	−	1.09664i	−0.986905	−	0.161303i	$-0.948430\pi$
$317$	−1.13280e6	−	1.96206e6i	−0.633145	−	1.09664i	0.353760	−	0.935336i	$-0.384903\pi$
$318$		0			0
$319$	−26384.9	+	45700.0i	−0.0145171	+	0.0251443i
$320$	761561.	+	1.31906e6i	0.415747	+	0.720096i
$321$		0			0
$322$	−87708.2	+	258115.i	−0.0471412	+	0.138731i
$323$	−3.68495e6			−1.96528
$324$		0			0
$325$	−434860.	+	753200.i	−0.228371	+	0.395551i
$326$	541072.	−	937163.i	0.281975	−	0.488395i
$327$		0			0
$328$	−684740.			−0.351432
$329$	1.83059e6	+	2.08870e6i	0.932396	+	1.06386i
$330$		0			0
$331$	−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
$333$		0			0
$334$	−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
$339$		0			0
$340$	−254785.	+	441300.i	−0.119530	+	0.207032i
$341$	220730.	+	382315.i	0.102796	+	0.178047i
$342$		0			0
$343$	−1.81281e6	+	1.20883e6i	−0.831990	+	0.554791i
$344$	2.81576e6			1.28292
$345$		0			0
$346$	1.81179e6	−	3.13811e6i	0.813611	−	1.40922i
$347$	878655.	−	1.52188e6i	0.391737	−	0.678509i	−0.600942	−	0.799293i	$-0.705208\pi$
$347$	878655.	−	1.52188e6i	0.391737	−	0.678509i	0.992679	+	0.120784i	$0.0385409\pi$
$348$		0			0
$349$	391875.			0.172220			0.0861102	−	0.996286i	$-0.472556\pi$
$349$	391875.			0.172220			0.0861102	+	0.996286i	$0.472556\pi$
$350$	888977.	−	176540.i	0.387901	−	0.0770323i
$351$		0			0
$352$	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	$0.133131\pi$
$354$		0			0
$355$	−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	$-0.885928\pi$
$359$	−1.88516e6	−	3.26519e6i	−0.771991	−	1.33713i	0.164480	−	0.986380i	$-0.447406\pi$
$360$		0			0
$361$	−500924.	+	867625.i	−0.202304	+	0.350400i
$362$	−1.58510e6	−	2.74548e6i	−0.635750	−	1.10115i
$363$		0			0
$364$	162611.	−	478544.i	0.0643273	−	0.189308i
$365$	−819367.			−0.321919
$366$		0			0
$367$	1.09884e6	−	1.90325e6i	0.425863	−	0.737617i	−0.570637	−	0.821202i	$-0.693304\pi$
$367$	1.09884e6	−	1.90325e6i	0.425863	−	0.737617i	0.996501	+	0.0835854i	$0.0266371\pi$
$368$	−163145.	+	282575.i	−0.0627991	+	0.108771i
$369$		0			0
$370$	−2.20049e6			−0.835632
$371$	−524694.	+	1.54411e6i	−0.197911	+	0.582431i
$372$		0			0
$373$	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
$375$		0			0
$376$	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
$381$		0			0
$382$	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	$0.641908\pi$
$384$		0			0
$385$	−383463.	+	76151.0i	−0.131847	+	0.0261833i
$386$	3.91729e6			1.33819
$387$		0			0
$388$	326027.	−	564696.i	0.109945	−	0.190430i
$389$	2.32674e6	−	4.03003e6i	0.779604	−	1.35031i	−0.152566	−	0.988293i	$-0.548754\pi$
$389$	2.32674e6	−	4.03003e6i	0.779604	−	1.35031i	0.932170	−	0.362021i	$-0.117913\pi$
$390$		0			0
$391$	−817461.			−0.270411
$392$	−3.01293e6	+	1.24579e6i	−0.990316	+	0.409478i
$393$		0			0
$394$	−1.21781e6	−	2.10931e6i	−0.395221	−	0.684543i
$395$	754775.	−	1.30731e6i	0.243402	−	0.421585i
$396$		0			0
$397$	581804.	+	1.00771e6i	0.185268	+	0.320894i	0.943667	−	0.330897i	$-0.107351\pi$
$397$	581804.	+	1.00771e6i	0.185268	+	0.320894i	−0.758399	+	0.651791i	$0.774018\pi$
$398$	−2.17891e6			−0.689495
$399$		0			0
$400$	1.08480e6			0.339001
$401$	161190.	+	279189.i	0.0500584	+	0.0867037i	0.889969	−	0.456021i	$-0.150726\pi$
$401$	161190.	+	279189.i	0.0500584	+	0.0867037i	−0.839910	+	0.542725i	$0.817393\pi$
$402$		0			0
$403$	1.93589e6	−	3.35307e6i	0.593771	−	1.02844i
$404$	−112403.	−	194688.i	−0.0342630	−	0.0593452i
$405$		0			0
$406$	−317889.	−	362711.i	−0.0957106	−	0.109206i
$407$	−746226.			−0.223298
$408$		0			0
$409$	−693451.	+	1.20109e6i	−0.204978	+	0.355033i	−0.950126	−	0.311867i	$-0.899046\pi$
$409$	−693451.	+	1.20109e6i	−0.204978	+	0.355033i	0.745148	+	0.666900i	$0.232379\pi$
$410$	375222.	−	649903.i	0.110237	−	0.190936i
$411$		0			0
$412$	−397800.			−0.115457
$413$	1.50716e6	−	4.43540e6i	0.434794	−	1.27955i
$414$		0			0
$415$	513907.	+	890112.i	0.146475	+	0.253702i
$416$	695182.	−	1.20409e6i	0.196954	−	0.341135i
$417$		0			0
$418$	−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
$423$		0			0
$424$	−1.22012e6	+	2.11331e6i	−0.329601	+	0.570886i
$425$	1.35889e6	+	2.35367e6i	0.364933	+	0.632082i
$426$		0			0
$427$	343912.	+	392404.i	0.0912805	+	0.104151i
$428$	407206.			0.107450
$429$		0			0
$430$	−1.54297e6	+	2.67250e6i	−0.402426	+	0.697022i
$431$	−2.61376e6	+	4.52717e6i	−0.677755	+	1.17391i	0.297900	+	0.954597i	$0.403714\pi$
$431$	−2.61376e6	+	4.52717e6i	−0.677755	+	1.17391i	−0.975655	+	0.219309i	$0.929620\pi$
$432$		0			0
$433$	−2.63022e6			−0.674174			−0.337087	−	0.941473i	$-0.609442\pi$
$433$	−2.63022e6			−0.674174			−0.337087	+	0.941473i	$0.609442\pi$
$434$	−3.95751e6	+	785914.i	−1.00855	+	0.200286i
$435$		0			0
$436$	−116954.	−	202570.i	−0.0294645	−	0.0510340i
$437$	−385770.	+	668173.i	−0.0966328	+	0.167373i
$438$		0			0
$439$	−1.27706e6	−	2.21193e6i	−0.316264	−	0.547785i	0.663442	−	0.748228i	$-0.269095\pi$
$439$	−1.27706e6	−	2.21193e6i	−0.316264	−	0.547785i	−0.979705	+	0.200443i	$0.935762\pi$
$440$	−584990.			−0.144051
$441$		0			0
$442$	−6.35046e6			−1.54614
$443$	1.91950e6	+	3.32467e6i	0.464707	+	0.804896i	0.999188	−	0.0402844i	$-0.0128264\pi$
$443$	1.91950e6	+	3.32467e6i	0.464707	+	0.804896i	−0.534481	+	0.845180i	$0.679493\pi$
$444$		0			0
$445$	1.46906e6	−	2.54448e6i	0.351672	−	0.609114i
$446$	923155.	+	1.59895e6i	0.219754	+	0.380626i
$447$		0			0
$448$	−4.63039e6	+	919538.i	−1.08999	+	0.216459i
$449$	−1.49369e6			−0.349658			−0.174829	−	0.984599i	$-0.555937\pi$
$449$	−1.49369e6			−0.349658			−0.174829	+	0.984599i	$0.555937\pi$
$450$		0			0
$451$	127244.	−	220394.i	0.0294576	−	0.0510221i
$452$	−381653.	+	661043.i	−0.0878664	+	0.152189i
$453$		0			0
$454$	4.28498e6			0.975684
$455$	2.25997e6	+	2.57862e6i	0.511768	+	0.583928i
$456$		0			0
$457$	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
$459$		0			0
$460$	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
$465$		0			0
$466$	−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	$-0.363756\pi$
$468$		0			0
$469$	649261.	−	1.91070e6i	0.136297	−	0.401107i
$470$	−4.55459e6			−0.951054
$471$		0			0
$472$	3.50475e6	−	6.07040e6i	0.724105	−	1.25419i
$473$	−523248.	+	906293.i	−0.107536	+	0.186258i
$474$		0			0
$475$	2.56511e6			0.521641
$476$	−1.04098e6	−	1.18776e6i	−0.210585	−	0.240277i
$477$		0			0
$478$	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	$0.935767\pi$
$480$		0			0
$481$	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
$486$		0			0
$487$	−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
$489$		0			0
$490$	468604.	−	3.54231e6i	0.0881690	−	0.666493i
$491$	8.19294e6			1.53369			0.766843	−	0.641835i	$-0.221827\pi$
$491$	8.19294e6			1.53369			0.766843	+	0.641835i	$0.221827\pi$
$492$		0			0
$493$	723123.	−	1.25249e6i	0.133997	−	0.232090i
$494$	−2.99686e6	+	5.19071e6i	−0.552521	+	0.956995i
$495$		0			0
$496$	−4.82928e6			−0.881411
$497$	1.54889e6	−	307590.i	0.281274	−	0.0558575i
$498$		0			0
$499$	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
$501$		0			0
$502$	−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
$507$		0			0
$508$	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	$0.918593\pi$
$510$		0			0
$511$	817069.	−	2.40454e6i	0.138422	−	0.407361i
$512$	−6.63004e6			−1.11774
$513$		0			0
$514$	742048.	−	1.28527e6i	0.123887	−	0.214578i
$515$	1.34936e6	−	2.33716e6i	0.224187	−	0.388303i
$516$		0			0
$517$	−1.54455e6			−0.254141
$518$	2.19432e6	−	6.45763e6i	0.359315	−	1.05742i
$519$		0			0
$520$	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	$0.956442\pi$
$522$		0			0
$523$	−2.37835e6	−	4.11942e6i	−0.380208	−	0.658539i	0.610884	−	0.791720i	$-0.290814\pi$
$523$	−2.37835e6	−	4.11942e6i	−0.380208	−	0.658539i	−0.991092	+	0.133181i	$0.957481\pi$
$524$	−911895.			−0.145083
$525$		0			0
$526$	1.46635e6			0.231086
$527$	−6.04947e6	−	1.04780e7i	−0.948835	−	1.64343i
$528$		0			0
$529$	3.13259e6	−	5.42581e6i	0.486704	−	0.842996i
$530$	−1.33720e6	−	2.31609e6i	−0.206779	−	0.358151i
$531$		0			0
$532$	−1.46210e6	+	290355.i	−0.223974	+	0.0444786i
$533$	−2.23198e6			−0.340308
$534$		0			0
$535$	−1.38127e6	+	2.39242e6i	−0.208638	+	0.361371i
$536$	1.50979e6	−	2.61503e6i	0.226989	−	0.393156i
$537$		0			0
$538$	1.31832e6			0.196365
$539$	158912.	−	1.20126e6i	0.0235605	−	0.178100i
$540$		0			0
$541$	−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
$543$		0			0
$544$	−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
$549$		0			0
$550$	−252016.	+	436505.i	−0.0355240	+	0.0615294i
$551$	−682501.	−	1.18213e6i	−0.0957688	−	0.165876i
$552$		0			0
$553$	3.08381e6	+	3.51863e6i	0.428820	+	0.489284i
$554$	645463.			0.0893505
$555$		0			0
$556$	−1.03167e6	+	1.78690e6i	−0.141532	+	0.245140i
$557$	−3.22611e6	+	5.58779e6i	−0.440597	+	0.763136i	−0.997734	−	0.0672845i	$-0.978566\pi$
$557$	−3.22611e6	+	5.58779e6i	−0.440597	+	0.763136i	0.557137	+	0.830421i	$0.311900\pi$
$558$		0			0
$559$	9.17823e6			1.24231
$560$	1.37598e6	−	4.04936e6i	0.185414	−	0.545653i
$561$		0			0
$562$	−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	$0.129603\pi$
$564$		0			0
$565$	−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	0.882148	−	0.470973i	$-0.156097\pi$
$569$	256394.	+	444088.i	0.0331992	+	0.0575027i	−0.848948	+	0.528476i	$0.822764\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	1.53306e6	+	1.74922e6i	0.194213	+	0.221597i
$575$	569038.			0.0717748
$576$		0			0
$577$	−3.31987e6	+	5.75018e6i	−0.415127	+	0.719021i	−0.995442	−	0.0953713i	$-0.969596\pi$
$577$	−3.31987e6	+	5.75018e6i	−0.415127	+	0.719021i	0.580315	+	0.814392i	$0.302930\pi$
$578$	−6.31386e6	+	1.09359e7i	−0.786096	+	1.36156i
$579$		0			0
$580$	−188758.			−0.0232989
$581$	−3.12462e6	+	620511.i	−0.384022	+	0.0762621i
$582$		0			0
$583$	−453467.	−	785429.i	−0.0552554	−	0.0957051i
$584$	1.90001e6	−	3.29092e6i	0.230528	−	0.399286i
$585$		0			0
$586$	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
$591$		0			0
$592$	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	$-0.483748\pi$
$594$		0			0
$595$	1.05094e7	−	2.08705e6i	1.21699	−	0.241679i
$596$	852515.			0.0983075
$597$		0			0
$598$	−664816.	+	1.15150e6i	−0.0760236	+	0.131677i
$599$	6.04174e6	−	1.04646e7i	0.688010	−	1.19167i	−0.284471	−	0.958685i	$-0.591818\pi$
$599$	6.04174e6	−	1.04646e7i	0.688010	−	1.19167i	0.972481	−	0.232984i	$-0.0748489\pi$
$600$		0			0
$601$	5.75607e6			0.650040			0.325020	−	0.945707i	$-0.394629\pi$
$601$	5.75607e6			0.650040			0.325020	+	0.945707i	$0.394629\pi$
$602$	−6.30416e6	−	7.19305e6i	−0.708984	−	0.808950i
$603$		0			0
$604$	342708.	+	593588.i	0.0382237	+	0.0662053i
$605$	−3.25948e6	+	5.64559e6i	−0.362043	+	0.627077i
$606$		0			0
$607$	−2.10060e6	−	3.63835e6i	−0.231405	−	0.400805i	0.726817	−	0.686831i	$-0.240999\pi$
$607$	−2.10060e6	−	3.63835e6i	−0.231405	−	0.400805i	−0.958222	+	0.286026i	$0.907666\pi$
$608$	−4.10067e6			−0.449879
$609$		0			0
$610$	−855671.			−0.0931070
$611$	6.77317e6	+	1.17315e7i	0.733988	+	1.27130i
$612$		0			0
$613$	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
$615$		0			0
$616$	583349.	−	1.71673e6i	0.0619408	−	0.182285i
$617$	−6.43533e6			−0.680546			−0.340273	−	0.940327i	$-0.610520\pi$
$617$	−6.43533e6			−0.680546			−0.340273	+	0.940327i	$0.610520\pi$
$618$		0			0
$619$	−7.05885e6	+	1.22263e7i	−0.740469	+	1.28253i	0.211812	+	0.977310i	$0.432063\pi$
$619$	−7.05885e6	+	1.22263e7i	−0.740469	+	1.28253i	−0.952282	+	0.305220i	$0.901270\pi$
$620$	−789551.	+	1.36754e6i	−0.0824899	+	0.142877i
$621$		0			0
$622$	4.35538e6			0.451388
$623$	6.00218e6	+	6.84848e6i	0.619567	+	0.706927i
$624$		0			0
$625$	1.78774e6	+	3.09646e6i	0.183065	+	0.317077i
$626$	−4.10939e6	+	7.11767e6i	−0.419123	+	0.725942i
$627$		0			0
$628$	−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
$633$		0			0
$634$	−5.75773e6	+	9.97268e6i	−0.568890	+	0.985346i
$635$	2.69210e6	+	4.66286e6i	0.264946	+	0.458900i
$636$		0			0
$637$	−9.82094e6	+	4.06078e6i	−0.958968	+	0.396516i
$638$	268217.			0.0260876
$639$		0			0
$640$	2.39928e6	−	4.15567e6i	0.231542	−	0.401043i
$641$	−5.20870e6	+	9.02173e6i	−0.500707	+	0.867251i	0.499292	+	0.866434i	$0.333593\pi$
$641$	−5.20870e6	+	9.02173e6i	−0.500707	+	0.867251i	−1.00000		0.000816994i	$0.999740\pi$
$642$		0			0
$643$	1.27284e7			1.21407			0.607037	−	0.794674i	$-0.292358\pi$
$643$	1.27284e7			1.21407			0.607037	+	0.794674i	$0.292358\pi$
$644$	−324349.	+	64411.8i	−0.0308175	+	0.00611999i
$645$		0			0
$646$	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	$0.893011\pi$
$648$		0			0
$649$	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	$-0.924429\pi$
$653$	−7.51475e6	−	1.30159e7i	−0.689654	−	1.19452i	0.282296	−	0.959327i	$-0.408904\pi$
$654$		0			0
$655$	3.09320e6	−	5.35758e6i	0.281712	−	0.487939i
$656$	1.39197e6	+	2.41097e6i	0.126291	+	0.218742i
$657$		0			0
$658$	4.54182e6	−	1.33661e7i	0.408945	−	1.20348i
$659$	−1.67927e7			−1.50628			−0.753140	−	0.657860i	$-0.771462\pi$
$659$	−1.67927e7			−1.50628			−0.753140	+	0.657860i	$0.771462\pi$
$660$		0			0
$661$	−5.42702e6	+	9.39987e6i	−0.483123	+	0.836794i	−0.999812	−	0.0193794i	$-0.993831\pi$
$661$	−5.42702e6	+	9.39987e6i	−0.483123	+	0.836794i	0.516689	+	0.856173i	$0.327164\pi$
$662$	−1.80349e6	+	3.12374e6i	−0.159944	+	0.277032i
$663$		0			0
$664$	−4.76675e6			−0.419567
$665$	3.25363e6	−	9.57506e6i	0.285308	−	0.839629i
$666$		0			0
$667$	−151404.	−	262240.i	−0.0131772	−	0.0228236i
$668$	371152.	−	642853.i	0.0321818	−	0.0557405i
$669$		0			0
$670$	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
$675$		0			0
$676$	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	$0.846750\pi$
$678$		0			0
$679$	−1.34481e7	+	2.67062e6i	−1.11940	+	0.222299i
$680$	1.60326e7			1.32963
$681$		0			0
$682$	1.12192e6	−	1.94322e6i	0.0923633	−	0.159978i
$683$	935093.	−	1.61963e6i	0.0767014	−	0.132851i	−0.825123	−	0.564952i	$-0.808895\pi$
$683$	935093.	−	1.61963e6i	0.0767014	−	0.132851i	0.901825	+	0.432102i	$0.142228\pi$
$684$		0			0
$685$	−3.81290e6			−0.310476
$686$	9.92808e6	+	4.90755e6i	0.805480	+	0.398157i
$687$		0			0
$688$	−5.72401e6	−	9.91427e6i	−0.461030	−	0.798527i
$689$	−3.97711e6	+	6.88855e6i	−0.319168	+	0.552815i
$690$		0			0
$691$	−9.69333e6	−	1.67893e7i	−0.772286	−	1.33764i	−0.936307	−	0.351181i	$-0.885780\pi$
$691$	−9.69333e6	−	1.67893e7i	−0.772286	−	1.33764i	0.164022	−	0.986457i	$-0.447553\pi$
$692$	4.39549e6			0.348933
$693$		0			0
$694$	−8.93199e6			−0.703963
$695$	−6.99896e6	−	1.21226e7i	−0.549631	−	0.951989i
$696$		0			0
$697$	−3.48735e6	+	6.04026e6i	−0.271902	+	0.470949i
$698$	−995905.	−	1.72496e6i	−0.0773712	−	0.134011i
$699$		0			0
$700$	724634.	+	826807.i	0.0558951	+	0.0637763i
$701$	−1.17488e7			−0.903024			−0.451512	−	0.892265i	$-0.649115\pi$
$701$	−1.17488e7			−0.903024			−0.451512	+	0.892265i	$0.649115\pi$
$702$		0			0
$703$	9.65134e6	−	1.67166e7i	0.736545	−	1.27573i
$704$	1.31267e6	−	2.27361e6i	0.0998214	−	0.172896i
$705$		0			0
$706$	−2.50279e6			−0.188978
$707$	−1.52083e6	+	4.47564e6i	−0.114428	+	0.336749i
$708$		0			0
$709$	−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
$711$		0			0
$712$	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
$717$		0			0
$718$	−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	$-0.369763\pi$
$720$		0			0
$721$	5.51314e6	+	6.29049e6i	0.394967	+	0.450657i
$722$	5.09215e6			0.363545
$723$		0			0
$724$	1.92277e6	−	3.33034e6i	0.136327	−	0.236125i
$725$	−503369.	+	871861.i	−0.0355665	+	0.0616030i
$726$		0			0
$727$	−1.25756e6			−0.0882453			−0.0441227	−	0.999026i	$-0.514049\pi$
$727$	−1.25756e6			−0.0882453			−0.0441227	+	0.999026i	$0.514049\pi$
$728$	−1.55974e7	+	3.09745e6i	−1.09075	+	0.216609i
$729$		0			0
$730$	2.08232e6	+	3.60669e6i	0.144624	+	0.250496i
$731$	1.43405e7	−	2.48385e7i	0.992592	−	1.71922i
$732$		0			0
$733$	991661.	+	1.71761e6i	0.0681716	+	0.118077i	0.898096	−	0.439798i	$-0.144950\pi$
$733$	991661.	+	1.71761e6i	0.0681716	+	0.118077i	−0.829925	+	0.557875i	$0.811617\pi$
$734$	−1.11703e7			−0.765288
$735$		0			0
$736$	−909684.			−0.0619007
$737$	561125.	+	971896.i	0.0380532	+	0.0659100i
$738$		0			0
$739$	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
$741$		0			0
$742$	8.13032e6	−	1.61458e6i	0.542123	−	0.107659i
$743$	1.90819e7			1.26809			0.634043	−	0.773298i	$-0.281394\pi$
$743$	1.90819e7			1.26809			0.634043	+	0.773298i	$0.281394\pi$
$744$		0			0
$745$	−2.89178e6	+	5.00871e6i	−0.190886	+	0.330625i
$746$	4.20943e6	−	7.29095e6i	0.276934	−	0.479664i
$747$		0			0
$748$	878323.			0.0573985
$749$	−5.64349e6	−	6.43922e6i	−0.367573	−	0.419400i
$750$		0			0
$751$	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
$753$		0			0
$754$	−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
$759$		0			0
$760$	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	$0.586046\pi$
$762$		0			0
$763$	−1.58241e6	+	4.65685e6i	−0.0984027	+	0.289588i
$764$	2.57550e6			0.159635
$765$		0			0
$766$	8.25554e6	−	1.42990e7i	0.508362	−	0.880510i
$767$	1.14241e7	−	1.97871e7i	0.701184	−	1.21449i
$768$		0			0
$769$	−1.87866e7			−1.14560			−0.572799	−	0.819696i	$-0.694142\pi$
$769$	−1.87866e7			−1.14560			−0.572799	+	0.819696i	$0.694142\pi$
$770$	1.30973e6	+	1.49440e6i	0.0796075	+	0.0908321i
$771$		0			0
$772$	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	$0.0762815\pi$
$774$		0			0
$775$	4.21106e6	+	7.29377e6i	0.251847	+	0.436212i
$776$	−2.05156e7			−1.22301

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.54138 - 4.40180i) q^{2} +(3.08276 - 5.33950i) q^{4} +(20.9138 + 36.2238i) q^{5} +(-127.159 + 25.2522i) q^{7} -193.986 q^{8} +O(q^{10})\)	\(q+(-2.54138 - 4.40180i) q^{2} +(3.08276 - 5.33950i) q^{4} +(20.9138 + 36.2238i) q^{5} +(-127.159 + 25.2522i) q^{7} -193.986 q^{8} +(106.300 - 184.117i) q^{10} +(36.0482 - 62.4374i) q^{11} -632.317 q^{13} +(434.314 + 495.552i) q^{14} +(394.345 + 683.025i) q^{16} +(-987.962 + 1711.20i) q^{17} +(932.463 + 1615.07i) q^{19} +257.889 q^{20} -366.449 q^{22} +(206.855 + 358.284i) q^{23} +(687.725 - 1191.17i) q^{25} +(1606.96 + 2783.34i) q^{26} +(-257.166 + 756.810i) q^{28} -731.934 q^{29} +(-3061.59 + 5302.83i) q^{31} +(-1099.42 + 1904.25i) q^{32} +10043.2 q^{34} +(-3574.10 - 4078.05i) q^{35} +(-5175.19 - 8963.69i) q^{37} +(4739.49 - 8209.03i) q^{38} +(-4056.99 - 7026.92i) q^{40} +3529.84 q^{41} -14515.2 q^{43} +(-222.256 - 384.959i) q^{44} +(1051.40 - 1821.07i) q^{46} +(-10711.7 - 18553.1i) q^{47} +(15531.7 - 6422.06i) q^{49} -6991.08 q^{50} +(-1949.28 + 3376.26i) q^{52} +(6289.73 - 10894.1i) q^{53} +3015.62 q^{55} +(24667.0 - 4898.57i) q^{56} +(1860.12 + 3221.83i) q^{58} +(-18067.0 + 31292.9i) q^{59} +(-2012.40 - 3485.58i) q^{61} +31122.6 q^{62} +36414.2 q^{64} +(-13224.2 - 22904.9i) q^{65} +(-7782.97 + 13480.5i) q^{67} +(6091.31 + 10550.5i) q^{68} +(-8867.61 + 26096.4i) q^{70} -12180.8 q^{71} +(-9794.56 + 16964.7i) q^{73} +(-26304.3 + 45560.3i) q^{74} +11498.2 q^{76} +(-3007.17 + 8849.75i) q^{77} +(-18044.9 - 31254.7i) q^{79} +(-16494.5 + 28569.3i) q^{80} +(-8970.66 - 15537.6i) q^{82} +24572.6 q^{83} -82648.2 q^{85} +(36888.7 + 63893.2i) q^{86} +(-6992.86 + 12112.0i) q^{88} +(-35121.7 - 60832.5i) q^{89} +(80404.6 - 15967.4i) q^{91} +2550.74 q^{92} +(-54444.8 + 94301.2i) q^{94} +(-39002.7 + 67554.7i) q^{95} +105758. q^{97} +(-67740.5 - 52046.4i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 12 q^{4} - 38 q^{5} - 168 q^{7} - 192 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 12 * q^4 - 38 * q^5 - 168 * q^7 - 192 * q^8	\( 4 q + 2 q^{2} - 12 q^{4} - 38 q^{5} - 168 q^{7} - 192 q^{8} + 778 q^{10} + 424 q^{11} - 1848 q^{13} + 2674 q^{14} + 2064 q^{16} - 2346 q^{17} + 360 q^{19} + 3416 q^{20} + 4252 q^{22} - 12 q^{23} - 1872 q^{25} + 1148 q^{26} + 2548 q^{28} + 14104 q^{29} - 3548 q^{31} - 8096 q^{32} + 14844 q^{34} - 27496 q^{35} - 11090 q^{37} + 20138 q^{38} - 15936 q^{40} - 7000 q^{41} - 25360 q^{43} + 5948 q^{44} + 5118 q^{46} - 22956 q^{47} + 4900 q^{49} - 59984 q^{50} + 1400 q^{52} + 3042 q^{53} - 50152 q^{55} + 57792 q^{56} + 58852 q^{58} - 65808 q^{59} + 42486 q^{61} + 98724 q^{62} + 70912 q^{64} - 3164 q^{65} - 42312 q^{67} + 5460 q^{68} - 113050 q^{70} + 4416 q^{71} + 50506 q^{73} - 47370 q^{74} + 77672 q^{76} - 65338 q^{77} - 9004 q^{79} + 68816 q^{80} - 67732 q^{82} + 208656 q^{83} - 106212 q^{85} + 86776 q^{86} + 20496 q^{88} - 26666 q^{89} + 135632 q^{91} + 20568 q^{92} - 98034 q^{94} - 198140 q^{95} + 418264 q^{97} - 98686 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 12 * q^4 - 38 * q^5 - 168 * q^7 - 192 * q^8 + 778 * q^10 + 424 * q^11 - 1848 * q^13 + 2674 * q^14 + 2064 * q^16 - 2346 * q^17 + 360 * q^19 + 3416 * q^20 + 4252 * q^22 - 12 * q^23 - 1872 * q^25 + 1148 * q^26 + 2548 * q^28 + 14104 * q^29 - 3548 * q^31 - 8096 * q^32 + 14844 * q^34 - 27496 * q^35 - 11090 * q^37 + 20138 * q^38 - 15936 * q^40 - 7000 * q^41 - 25360 * q^43 + 5948 * q^44 + 5118 * q^46 - 22956 * q^47 + 4900 * q^49 - 59984 * q^50 + 1400 * q^52 + 3042 * q^53 - 50152 * q^55 + 57792 * q^56 + 58852 * q^58 - 65808 * q^59 + 42486 * q^61 + 98724 * q^62 + 70912 * q^64 - 3164 * q^65 - 42312 * q^67 + 5460 * q^68 - 113050 * q^70 + 4416 * q^71 + 50506 * q^73 - 47370 * q^74 + 77672 * q^76 - 65338 * q^77 - 9004 * q^79 + 68816 * q^80 - 67732 * q^82 + 208656 * q^83 - 106212 * q^85 + 86776 * q^86 + 20496 * q^88 - 26666 * q^89 + 135632 * q^91 + 20568 * q^92 - 98034 * q^94 - 198140 * q^95 + 418264 * q^97 - 98686 * q^98

Introduction

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