LMFDB - Embedded newform 63.6.e.e.37.3

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 98x^{6} + 83x^{5} + 9122x^{4} - 91x^{3} + 28567x^{2} + 2058x + 86436 $ x^8 - x^7 + 98x^6 + 83x^5 + 9122x^4 - 91x^3 + 28567x^2 + 2058x + 86436
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.3
Root			$-0.874091 + 1.51397i$ of defining polynomial
Character	$\chi$	$=$	63.37
Dual form			63.6.e.e.46.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37409 - 2.37999i) q^{2} +(12.2237 + 21.1722i) q^{4} +(29.1836 - 50.5475i) q^{5} +(-21.4366 + 127.857i) q^{7} +155.128 q^{8} +O(q^{10})$	\(q+(1.37409 - 2.37999i) q^{2} +(12.2237 + 21.1722i) q^{4} +(29.1836 - 50.5475i) q^{5} +(-21.4366 + 127.857i) q^{7} +155.128 q^{8} +(-80.2019 - 138.914i) q^{10} +(8.71205 + 15.0897i) q^{11} +889.933 q^{13} +(274.844 + 226.706i) q^{14} +(-178.000 + 308.305i) q^{16} +(513.318 + 889.092i) q^{17} +(869.702 - 1506.37i) q^{19} +1426.93 q^{20} +47.8846 q^{22} +(1968.11 - 3408.87i) q^{23} +(-140.869 - 243.993i) q^{25} +(1222.85 - 2118.04i) q^{26} +(-2969.05 + 1109.04i) q^{28} -5633.53 q^{29} +(1548.27 + 2681.68i) q^{31} +(2971.22 + 5146.31i) q^{32} +2821.38 q^{34} +(5837.27 + 4814.91i) q^{35} +(-2513.43 + 4353.39i) q^{37} +(-2390.10 - 4139.77i) q^{38} +(4527.20 - 7841.34i) q^{40} -18367.0 q^{41} -1630.91 q^{43} +(-212.988 + 368.906i) q^{44} +(-5408.72 - 9368.19i) q^{46} +(-4802.62 + 8318.38i) q^{47} +(-15887.9 - 5481.65i) q^{49} -774.269 q^{50} +(10878.3 + 18841.8i) q^{52} +(-11628.3 - 20140.7i) q^{53} +1017.00 q^{55} +(-3325.41 + 19834.2i) q^{56} +(-7740.98 + 13407.8i) q^{58} +(-1801.62 - 3120.50i) q^{59} +(-11438.3 + 19811.7i) q^{61} +8509.83 q^{62} +4938.92 q^{64} +(25971.5 - 44983.9i) q^{65} +(-23506.4 - 40714.2i) q^{67} +(-12549.3 + 21736.1i) q^{68} +(19480.4 - 7276.56i) q^{70} +1599.63 q^{71} +(-2965.67 - 5136.70i) q^{73} +(6907.36 + 11963.9i) q^{74} +42524.1 q^{76} +(-2116.09 + 790.427i) q^{77} +(44234.4 - 76616.3i) q^{79} +(10389.4 + 17994.9i) q^{80} +(-25237.9 + 43713.3i) q^{82} +95823.9 q^{83} +59921.9 q^{85} +(-2241.02 + 3881.56i) q^{86} +(1351.48 + 2340.84i) q^{88} +(-23253.9 + 40277.0i) q^{89} +(-19077.1 + 113784. i) q^{91} +96230.8 q^{92} +(13198.5 + 22860.4i) q^{94} +(-50762.1 - 87922.5i) q^{95} -75981.8 q^{97} +(-34877.8 + 30281.0i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 69 q^{4} + 258 q^{7} - 246 q^{8}+O(q^{10}) $ 8 * q + 3 * q^2 - 69 * q^4 + 258 * q^7 - 246 * q^8	$ 8 q + 3 q^{2} - 69 q^{4} + 258 q^{7} - 246 q^{8} - 283 q^{10} + 402 q^{11} + 924 q^{13} - 1926 q^{14} - 3273 q^{16} + 276 q^{17} - 510 q^{19} - 9438 q^{20} + 2750 q^{22} + 6900 q^{23} - 2814 q^{25} - 15138 q^{26} - 26221 q^{28} - 1080 q^{29} + 6410 q^{31} + 15519 q^{32} + 42288 q^{34} + 33108 q^{35} - 15250 q^{37} - 41250 q^{38} + 8547 q^{40} - 8616 q^{41} + 58396 q^{43} + 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 64252 q^{49} + 14604 q^{50} + 47476 q^{52} + 13692 q^{53} + 146248 q^{55} + 15921 q^{56} - 52309 q^{58} + 34830 q^{59} + 5364 q^{61} - 32058 q^{62} - 146974 q^{64} + 66864 q^{65} + 5994 q^{67} - 58272 q^{68} - 4307 q^{70} - 178536 q^{71} - 59638 q^{73} - 185442 q^{74} + 42616 q^{76} + 75660 q^{77} + 44062 q^{79} - 33381 q^{80} - 57596 q^{82} + 416892 q^{83} + 72648 q^{85} - 136968 q^{86} - 87597 q^{88} - 77520 q^{89} + 104722 q^{91} - 316512 q^{92} + 73722 q^{94} - 221376 q^{95} - 377260 q^{97} - 382479 q^{98}+O(q^{100}) $ 8 * q + 3 * q^2 - 69 * q^4 + 258 * q^7 - 246 * q^8 - 283 * q^10 + 402 * q^11 + 924 * q^13 - 1926 * q^14 - 3273 * q^16 + 276 * q^17 - 510 * q^19 - 9438 * q^20 + 2750 * q^22 + 6900 * q^23 - 2814 * q^25 - 15138 * q^26 - 26221 * q^28 - 1080 * q^29 + 6410 * q^31 + 15519 * q^32 + 42288 * q^34 + 33108 * q^35 - 15250 * q^37 - 41250 * q^38 + 8547 * q^40 - 8616 * q^41 + 58396 * q^43 + 70743 * q^44 - 61800 * q^46 - 15060 * q^47 - 64252 * q^49 + 14604 * q^50 + 47476 * q^52 + 13692 * q^53 + 146248 * q^55 + 15921 * q^56 - 52309 * q^58 + 34830 * q^59 + 5364 * q^61 - 32058 * q^62 - 146974 * q^64 + 66864 * q^65 + 5994 * q^67 - 58272 * q^68 - 4307 * q^70 - 178536 * q^71 - 59638 * q^73 - 185442 * q^74 + 42616 * q^76 + 75660 * q^77 + 44062 * q^79 - 33381 * q^80 - 57596 * q^82 + 416892 * q^83 + 72648 * q^85 - 136968 * q^86 - 87597 * q^88 - 77520 * q^89 + 104722 * q^91 - 316512 * q^92 + 73722 * q^94 - 221376 * q^95 - 377260 * q^97 - 382479 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.37409	−	2.37999i	0.242907	−	0.420728i	−0.718634	−	0.695389i	$-0.755232\pi$
$2$	1.37409	−	2.37999i	0.242907	−	0.420728i	0.961541	+	0.274661i	$0.0885656\pi$
$3$		0			0
$3$		0			0
$4$	12.2237	+	21.1722i	0.381992	+	0.661630i
$5$	29.1836	−	50.5475i	0.522053	−	0.904222i	−0.477618	−	0.878568i	$-0.658500\pi$
$5$	29.1836	−	50.5475i	0.522053	−	0.904222i	0.999671	−	0.0256544i	$-0.00816693\pi$
$6$		0			0
$7$	−21.4366	+	127.857i	−0.165352	+	0.986235i
$7$	−21.4366	+	127.857i	−0.165352	+	0.986235i
$8$	155.128			0.856969
$9$		0			0
$10$	−80.2019	−	138.914i	−0.253621	−	0.439284i
$11$	8.71205	+	15.0897i	0.0217089	+	0.0376010i	0.876676	−	0.481082i	$-0.159756\pi$
$11$	8.71205	+	15.0897i	0.0217089	+	0.0376010i	−0.854967	+	0.518683i	$0.826423\pi$
$12$		0			0
$13$	889.933			1.46049			0.730246	−	0.683185i	$-0.239406\pi$
$13$	889.933			1.46049			0.730246	+	0.683185i	$0.239406\pi$
$14$	274.844	+	226.706i	0.374771	+	0.309132i
$15$		0			0
$16$	−178.000	+	308.305i	−0.173828	+	0.301079i
$17$	513.318	+	889.092i	0.430788	+	0.746147i	0.996941	−	0.0781529i	$-0.0249022\pi$
$17$	513.318	+	889.092i	0.430788	+	0.746147i	−0.566153	+	0.824300i	$0.691569\pi$
$18$		0			0
$19$	869.702	−	1506.37i	0.552696	−	0.957297i	−0.445383	−	0.895340i	$-0.646932\pi$
$19$	869.702	−	1506.37i	0.552696	−	0.957297i	0.998079	−	0.0619572i	$-0.0197342\pi$
$20$	1426.93			0.797680
$21$		0			0
$22$	47.8846			0.0210930
$23$	1968.11	−	3408.87i	0.775764	−	1.34366i	−0.158599	−	0.987343i	$-0.550698\pi$
$23$	1968.11	−	3408.87i	0.775764	−	1.34366i	0.934364	−	0.356320i	$-0.115969\pi$
$24$		0			0
$25$	−140.869	−	243.993i	−0.0450782	−	0.0780777i
$26$	1222.85	−	2118.04i	0.354764	−	0.614469i
$27$		0			0
$28$	−2969.05	+	1109.04i	−0.715686	+	0.267332i
$29$	−5633.53			−1.24390			−0.621950	−	0.783057i	$-0.713659\pi$
$29$	−5633.53			−1.24390			−0.621950	+	0.783057i	$0.713659\pi$
$30$		0			0
$31$	1548.27	+	2681.68i	0.289362	+	0.501190i	0.973658	−	0.228015i	$-0.0732236\pi$
$31$	1548.27	+	2681.68i	0.289362	+	0.501190i	−0.684296	+	0.729205i	$0.739890\pi$
$32$	2971.22	+	5146.31i	0.512933	+	0.888426i
$33$		0			0
$34$	2821.38			0.418566
$35$	5837.27	+	4814.91i	0.805452	+	0.664382i
$36$		0			0
$37$	−2513.43	+	4353.39i	−0.301830	+	0.522785i	−0.976551	−	0.215288i	$-0.930931\pi$
$37$	−2513.43	+	4353.39i	−0.301830	+	0.522785i	0.674720	+	0.738073i	$0.264264\pi$
$38$	−2390.10	−	4139.77i	−0.268508	−	0.465069i
$39$		0			0
$40$	4527.20	−	7841.34i	0.447383	−	0.774890i
$41$	−18367.0			−1.70639			−0.853195	−	0.521592i	$-0.825338\pi$
$41$	−18367.0			−1.70639			−0.853195	+	0.521592i	$0.825338\pi$
$42$		0			0
$43$	−1630.91			−0.134511			−0.0672557	−	0.997736i	$-0.521424\pi$
$43$	−1630.91			−0.134511			−0.0672557	+	0.997736i	$0.521424\pi$
$44$	−212.988	+	368.906i	−0.0165853	+	0.0287266i
$45$		0			0
$46$	−5408.72	−	9368.19i	−0.376878	−	0.652771i
$47$	−4802.62	+	8318.38i	−0.317127	+	0.549280i	−0.979887	−	0.199551i	$-0.936051\pi$
$47$	−4802.62	+	8318.38i	−0.317127	+	0.549280i	0.662760	+	0.748832i	$0.269385\pi$
$48$		0			0
$49$	−15887.9	−	5481.65i	−0.945317	−	0.326153i
$50$	−774.269			−0.0437992
$51$		0			0
$52$	10878.3	+	18841.8i	0.557896	+	0.966305i
$53$	−11628.3	−	20140.7i	−0.568624	−	0.984886i	−0.996702	−	0.0811440i	$-0.974143\pi$
$53$	−11628.3	−	20140.7i	−0.568624	−	0.984886i	0.428078	−	0.903742i	$-0.359191\pi$
$54$		0			0
$55$	1017.00			0.0453328
$56$	−3325.41	+	19834.2i	−0.141702	+	0.845172i
$57$		0			0
$58$	−7740.98	+	13407.8i	−0.302152	+	0.523343i
$59$	−1801.62	−	3120.50i	−0.0673803	−	0.116706i	0.830367	−	0.557217i	$-0.188131\pi$
$59$	−1801.62	−	3120.50i	−0.0673803	−	0.116706i	−0.897747	+	0.440511i	$0.854797\pi$
$60$		0			0
$61$	−11438.3	+	19811.7i	−0.393584	+	0.681707i	−0.992919	−	0.118791i	$-0.962098\pi$
$61$	−11438.3	+	19811.7i	−0.393584	+	0.681707i	0.599336	+	0.800498i	$0.295431\pi$
$62$	8509.83			0.281152
$63$		0			0
$64$	4938.92			0.150724
$65$	25971.5	−	44983.9i	0.762454	−	1.32061i
$66$		0			0
$67$	−23506.4	−	40714.2i	−0.639733	−	1.10805i	−0.985491	−	0.169726i	$-0.945712\pi$
$67$	−23506.4	−	40714.2i	−0.639733	−	1.10805i	0.345758	−	0.938324i	$-0.387622\pi$
$68$	−12549.3	+	21736.1i	−0.329116	+	0.570045i
$69$		0			0
$70$	19480.4	−	7276.56i	0.475174	−	0.177493i
$71$	1599.63			0.0376595			0.0188298	−	0.999823i	$-0.494006\pi$
$71$	1599.63			0.0376595			0.0188298	+	0.999823i	$0.494006\pi$
$72$		0			0
$73$	−2965.67	−	5136.70i	−0.0651353	−	0.112818i	0.831619	−	0.555347i	$-0.187415\pi$
$73$	−2965.67	−	5136.70i	−0.0651353	−	0.112818i	−0.896754	+	0.442529i	$0.854081\pi$
$74$	6907.36	+	11963.9i	0.146633	+	0.253976i
$75$		0			0
$76$	42524.1			0.844502
$77$	−2116.09	+	790.427i	−0.0406730	+	0.0151927i
$78$		0			0
$79$	44234.4	−	76616.3i	0.797431	−	1.38119i	−0.123854	−	0.992300i	$-0.539525\pi$
$79$	44234.4	−	76616.3i	0.797431	−	1.38119i	0.921284	−	0.388890i	$-0.127141\pi$
$80$	10389.4	+	17994.9i	0.181495	+	0.314359i
$81$		0			0
$82$	−25237.9	+	43713.3i	−0.414495	+	0.717926i
$83$	95823.9			1.52679			0.763394	−	0.645933i	$-0.223531\pi$
$83$	95823.9			1.52679			0.763394	+	0.645933i	$0.223531\pi$
$84$		0			0
$85$	59921.9			0.899577
$86$	−2241.02	+	3881.56i	−0.0326738	+	0.0565927i
$87$		0			0
$88$	1351.48	+	2340.84i	0.0186039	+	0.0322229i
$89$	−23253.9	+	40277.0i	−0.311187	+	0.538992i	−0.978620	−	0.205679i	$-0.934060\pi$
$89$	−23253.9	+	40277.0i	−0.311187	+	0.538992i	0.667433	+	0.744670i	$0.267393\pi$
$90$		0			0
$91$	−19077.1	+	113784.i	−0.241496	+	1.44039i
$92$	96230.8			1.18534
$93$		0			0
$94$	13198.5	+	22860.4i	0.154065	+	0.266848i
$95$	−50762.1	−	87922.5i	−0.577073	−	0.999519i
$96$		0			0
$97$	−75981.8			−0.819937			−0.409968	−	0.912100i	$-0.634460\pi$
$97$	−75981.8			−0.819937			−0.409968	+	0.912100i	$0.634460\pi$
$98$	−34877.8	+	30281.0i	−0.366846	+	0.318496i
$99$		0			0
$100$	3443.90	−	5965.01i	0.0344390	−	0.0596501i
$101$	−23078.7	−	39973.5i	−0.225117	−	0.389914i	0.731238	−	0.682123i	$-0.238943\pi$
$101$	−23078.7	−	39973.5i	−0.225117	−	0.389914i	−0.956355	+	0.292209i	$0.905610\pi$
$102$		0			0
$103$	40986.8	−	70991.2i	0.380672	−	0.659343i	−0.610487	−	0.792027i	$-0.709026\pi$
$103$	40986.8	−	70991.2i	0.380672	−	0.659343i	0.991158	+	0.132683i	$0.0423594\pi$
$104$	138054.			1.25160
$105$		0			0
$106$	−63913.2			−0.552491
$107$	−1426.84	+	2471.35i	−0.0120480	+	0.0208677i	−0.871987	−	0.489530i	$-0.837168\pi$
$107$	−1426.84	+	2471.35i	−0.0120480	+	0.0208677i	0.859939	+	0.510398i	$0.170502\pi$
$108$		0			0
$109$	83139.2	+	144001.i	0.670254	+	1.16091i	0.977832	+	0.209391i	$0.0671483\pi$
$109$	83139.2	+	144001.i	0.670254	+	1.16091i	−0.307578	+	0.951523i	$0.599518\pi$
$110$	1397.45	−	2420.45i	0.0110117	−	0.0190728i
$111$		0			0
$112$	−35603.3	−	29367.6i	−0.268192	−	0.221220i
$113$	−260304.			−1.91772			−0.958858	−	0.283886i	$-0.908376\pi$
$113$	−260304.			−1.91772			−0.958858	+	0.283886i	$0.908376\pi$
$114$		0			0
$115$	−114873.	−	198966.i	−0.809980	−	1.40293i
$116$	−68862.8	−	119274.i	−0.475160	−	0.823001i
$117$		0			0
$118$	−9902.35			−0.0654687
$119$	−124681.	+	46572.3i	−0.807108	+	0.301481i
$120$		0			0
$121$	80373.7	−	139211.i	0.499057	−	0.864393i
$122$	31434.5	+	54446.2i	0.191209	+	0.331183i
$123$		0			0
$124$	−37851.2	+	65560.3i	−0.221068	+	0.382901i
$125$	165953.			0.949973
$126$		0			0
$127$	−233743.			−1.28596			−0.642982	−	0.765882i	$-0.722303\pi$
$127$	−233743.			−1.28596			−0.642982	+	0.765882i	$0.722303\pi$
$128$	−88292.6	+	152927.i	−0.476321	+	0.825012i
$129$		0			0
$130$	−71374.4	−	123624.i	−0.370411	−	0.641571i
$131$	−78644.9	+	136217.i	−0.400398	+	0.693510i	−0.993774	−	0.111415i	$-0.964462\pi$
$131$	−78644.9	+	136217.i	−0.400398	+	0.693510i	0.593376	+	0.804926i	$0.297795\pi$
$132$		0			0
$133$	173957.	+	143489.i	0.852730	+	0.703379i
$134$	−129200.			−0.621583
$135$		0			0
$136$	79629.9	+	137923.i	0.369172	+	0.639425i
$137$	−85773.8	−	148564.i	−0.390439	−	0.676260i	0.602069	−	0.798444i	$-0.294343\pi$
$137$	−85773.8	−	148564.i	−0.390439	−	0.676260i	−0.992507	+	0.122185i	$0.961010\pi$
$138$		0			0
$139$	210625.			0.924642			0.462321	−	0.886713i	$-0.347017\pi$
$139$	210625.			0.924642			0.462321	+	0.886713i	$0.347017\pi$
$140$	−30588.6	+	182444.i	−0.131898	+	0.786700i
$141$		0			0
$142$	2198.04	−	3807.12i	0.00914777	−	0.0158444i
$143$	7753.14	+	13428.8i	0.0317057	+	0.0549159i
$144$		0			0
$145$	−164407.	+	284761.i	−0.649381	+	1.12476i
$146$	−16300.4			−0.0632873
$147$		0			0
$148$	−122894.			−0.461187
$149$	119706.	−	207338.i	0.441725	−	0.765090i	−0.556093	−	0.831120i	$-0.687700\pi$
$149$	119706.	−	207338.i	0.441725	−	0.765090i	0.997818	+	0.0660304i	$0.0210334\pi$
$150$		0			0
$151$	−108520.	−	187962.i	−0.387317	−	0.670852i	0.604771	−	0.796400i	$-0.293265\pi$
$151$	−108520.	−	187962.i	−0.387317	−	0.670852i	−0.992088	+	0.125547i	$0.959931\pi$
$152$	134915.	−	233680.i	0.473643	−	0.820374i
$153$		0			0
$154$	−1026.48	+	6122.39i	−0.00348778	+	0.0208027i
$155$	180736.			0.604249
$156$		0			0
$157$	−83452.2	−	144543.i	−0.270202	−	0.468004i	0.698711	−	0.715404i	$-0.253757\pi$
$157$	−83452.2	−	144543.i	−0.270202	−	0.468004i	−0.968913	+	0.247400i	$0.920424\pi$
$158$	−121564.	−	210556.i	−0.387403	−	0.671002i
$159$		0			0
$160$	346844.			1.07111
$161$	393659.	+	324712.i	1.19689	+	0.987264i
$162$		0			0
$163$	−253086.	+	438358.i	−0.746104	+	1.29229i	0.203574	+	0.979060i	$0.434744\pi$
$163$	−253086.	+	438358.i	−0.746104	+	1.29229i	−0.949677	+	0.313230i	$0.898589\pi$
$164$	−224514.	−	388869.i	−0.651828	−	1.12900i
$165$		0			0
$166$	131671.	−	228061.i	0.370868	−	0.642362i
$167$	565560.			1.56923			0.784616	−	0.619982i	$-0.212860\pi$
$167$	565560.			1.56923			0.784616	+	0.619982i	$0.212860\pi$
$168$		0			0
$169$	420688.			1.13304
$170$	82338.1	−	142614.i	0.218514	−	0.378477i
$171$		0			0
$172$	−19935.9	−	34529.9i	−0.0513823	−	0.0889968i
$173$	−329718.	+	571088.i	−0.837581	+	1.45073i	0.0543304	+	0.998523i	$0.482698\pi$
$173$	−329718.	+	571088.i	−0.837581	+	1.45073i	−0.891911	+	0.452210i	$0.850636\pi$
$174$		0			0
$175$	34216.0	−	12780.8i	0.0844567	−	0.0315473i
$176$	−6202.98			−0.0150945
$177$		0			0
$178$	63906.0	+	110688.i	0.151179	+	0.261850i
$179$	82645.0	+	143145.i	0.192790	+	0.333922i	0.946174	−	0.323659i	$-0.104913\pi$
$179$	82645.0	+	143145.i	0.192790	+	0.333922i	−0.753384	+	0.657581i	$0.771580\pi$
$180$		0			0
$181$	148492.			0.336904			0.168452	−	0.985710i	$-0.446123\pi$
$181$	148492.			0.336904			0.168452	+	0.985710i	$0.446123\pi$
$182$	244593.	+	201754.i	0.547350	+	0.451484i
$183$		0			0
$184$	305309.	−	528811.i	0.664806	−	1.15148i
$185$	146702.	+	254095.i	0.315142	+	0.545843i
$186$		0			0
$187$	−8944.10	+	15491.6i	−0.0187039	+	0.0323961i
$188$	−234824.			−0.484560
$189$		0			0
$190$	−279007.			−0.560701
$191$	192955.	−	334208.i	0.382713	−	0.662879i	−0.608736	−	0.793373i	$-0.708323\pi$
$191$	192955.	−	334208.i	0.382713	−	0.662879i	0.991449	+	0.130494i	$0.0416564\pi$
$192$		0			0
$193$	−248148.	−	429805.i	−0.479531	−	0.830573i	0.520193	−	0.854049i	$-0.325860\pi$
$193$	−248148.	−	429805.i	−0.479531	−	0.830573i	−0.999724	+	0.0234760i	$0.992527\pi$
$194$	−104406.	+	180836.i	−0.199169	+	0.344970i
$195$		0			0
$196$	−78152.0	−	403388.i	−0.145312	−	0.750038i
$197$	−441439.			−0.810411			−0.405206	−	0.914226i	$-0.632800\pi$
$197$	−441439.			−0.810411			−0.405206	+	0.914226i	$0.632800\pi$
$198$		0			0
$199$	37919.4	+	65678.3i	0.0678779	+	0.117568i	0.897967	−	0.440063i	$-0.145044\pi$
$199$	37919.4	+	65678.3i	0.0678779	+	0.117568i	−0.830089	+	0.557631i	$0.811710\pi$
$200$	−21852.8	−	37850.1i	−0.0386306	−	0.0669102i
$201$		0			0
$202$	−126849.			−0.218730
$203$	120764.	−	720287.i	0.205682	−	1.22678i
$204$		0			0
$205$	−536016.	+	928406.i	−0.890826	+	1.54296i
$206$	−112639.	−	195097.i	−0.184936	−	0.320318i
$207$		0			0
$208$	−158408.	+	274371.i	−0.253875	+	0.439724i
$209$	30307.5			0.0479938
$210$		0			0
$211$	778704.			1.20411			0.602055	−	0.798454i	$-0.294349\pi$
$211$	778704.			1.20411			0.602055	+	0.798454i	$0.294349\pi$
$212$	284282.	−	492391.i	0.434420	−	0.752437i
$213$		0			0
$214$	3921.21	+	6791.73i	0.00585309	+	0.0101379i
$215$	−47595.9	+	82438.6i	−0.0702221	+	0.121628i
$216$		0			0
$217$	−376061.	+	140471.i	−0.542137	+	0.202506i
$218$	456963.			0.651238
$219$		0			0
$220$	12431.5	+	21532.0i	0.0173168	+	0.0299936i
$221$	456818.	+	791233.i	0.629163	+	1.08974i
$222$		0			0
$223$	738085.			0.993903			0.496951	−	0.867778i	$-0.334453\pi$
$223$	738085.			0.993903			0.496951	+	0.867778i	$0.334453\pi$
$224$	−721686.	+	269573.i	−0.961011	+	0.358969i
$225$		0			0
$226$	−357681.	+	619522.i	−0.465827	+	0.806836i
$227$	−272058.	−	471218.i	−0.350426	−	0.606956i	0.635898	−	0.771773i	$-0.280630\pi$
$227$	−272058.	−	471218.i	−0.350426	−	0.606956i	−0.986324	+	0.164817i	$0.947297\pi$
$228$		0			0
$229$	116781.	−	202271.i	0.147158	−	0.254885i	−0.783018	−	0.621999i	$-0.786321\pi$
$229$	116781.	−	202271.i	0.147158	−	0.254885i	0.930176	+	0.367114i	$0.119654\pi$
$230$	−631385.			−0.787000
$231$		0			0
$232$	−873917.			−1.06598
$233$	−309050.	+	535290.i	−0.372940	+	0.645951i	−0.990016	−	0.140952i	$-0.954984\pi$
$233$	−309050.	+	535290.i	−0.372940	+	0.645951i	0.617077	+	0.786903i	$0.288317\pi$
$234$		0			0
$235$	280316.	+	485521.i	0.331114	+	0.573506i
$236$	44045.1	−	76288.3i	0.0514775	−	0.0891617i
$237$		0			0
$238$	−60480.8	+	360734.i	−0.0692110	+	0.412805i
$239$	−937500.			−1.06164			−0.530819	−	0.847485i	$-0.678116\pi$
$239$	−937500.			−1.06164			−0.530819	+	0.847485i	$0.678116\pi$
$240$		0			0
$241$	−466018.	−	807167.i	−0.516845	−	0.895202i	−0.999809	−	0.0195613i	$-0.993773\pi$
$241$	−466018.	−	807167.i	−0.516845	−	0.895202i	0.482964	−	0.875640i	$-0.339560\pi$
$242$	−220882.	−	382578.i	−0.242449	−	0.419935i
$243$		0			0
$244$	−559276.			−0.601383
$245$	−740752.	+	643122.i	−0.788420	+	0.684508i
$246$		0			0
$247$	773976.	−	1.34057e6i	0.807208	−	1.39812i
$248$	240179.	+	416003.i	0.247974	+	0.429504i
$249$		0			0
$250$	228035.	−	394968.i	0.230755	−	0.399680i
$251$	−214975.			−0.215379			−0.107690	−	0.994185i	$-0.534345\pi$
$251$	−214975.			−0.215379			−0.107690	+	0.994185i	$0.534345\pi$
$252$		0			0
$253$	68585.1			0.0673641
$254$	−321184.	+	556306.i	−0.312370	+	0.541040i
$255$		0			0
$256$	321667.	+	557143.i	0.306765	+	0.531333i
$257$	39593.5	−	68578.0i	0.0373931	−	0.0647667i	−0.846723	−	0.532034i	$-0.821428\pi$
$257$	39593.5	−	68578.0i	0.0373931	−	0.0647667i	0.884116	+	0.467267i	$0.154761\pi$
$258$		0			0
$259$	−502733.	−	414682.i	−0.465680	−	0.384119i
$260$	1.26988e6			1.16501
$261$		0			0
$262$	216130.	+	374349.i	0.194519	+	0.336917i
$263$	−216414.	−	374840.i	−0.192928	−	0.334162i	0.753291	−	0.657687i	$-0.228465\pi$
$263$	−216414.	−	374840.i	−0.192928	−	0.334162i	−0.946219	+	0.323526i	$0.895132\pi$
$264$		0			0
$265$	−1.35742e6			−1.18741
$266$	580535.	−	216849.i	0.503065	−	0.187911i
$267$		0			0
$268$	574672.	−	995361.i	0.488746	−	0.846533i
$269$	−2345.93	−	4063.27i	−0.00197667	−	0.00342369i	0.865035	−	0.501711i	$-0.167296\pi$
$269$	−2345.93	−	4063.27i	−0.00197667	−	0.00342369i	−0.867012	+	0.498287i	$0.833963\pi$
$270$		0			0
$271$	−52632.1	+	91161.5i	−0.0435339	+	0.0754029i	−0.886971	−	0.461825i	$-0.847195\pi$
$271$	−52632.1	+	91161.5i	−0.0435339	+	0.0754029i	0.843437	+	0.537227i	$0.180528\pi$
$272$	−365482.			−0.299533
$273$		0			0
$274$	−471444.			−0.379362
$275$	2454.52	−	4251.35i	0.00195720	−	0.00338997i
$276$		0			0
$277$	381558.	+	660879.i	0.298787	+	0.517514i	0.975859	−	0.218403i	$-0.0700847\pi$
$277$	381558.	+	660879.i	0.298787	+	0.517514i	−0.677072	+	0.735917i	$0.736751\pi$
$278$	289418.	−	501287.i	0.224602	−	0.389023i
$279$		0			0
$280$	905524.	+	746927.i	0.690248	+	0.569355i
$281$	729540.			0.551167			0.275584	−	0.961277i	$-0.411129\pi$
$281$	729540.			0.551167			0.275584	+	0.961277i	$0.411129\pi$
$282$		0			0
$283$	595214.	+	1.03094e6i	0.441781	+	0.765188i	0.997822	−	0.0659675i	$-0.0210134\pi$
$283$	595214.	+	1.03094e6i	0.441781	+	0.765188i	−0.556040	+	0.831155i	$0.687680\pi$
$284$	19553.5	+	33867.7i	0.0143856	+	0.0249167i
$285$		0			0
$286$	42614.1			0.0308062
$287$	393726.	−	2.34835e6i	0.282156	−	1.68290i
$288$		0			0
$289$	182938.	−	316859.i	0.128843	−	0.223162i
$290$	451820.	+	782575.i	0.315479	+	0.546425i
$291$		0			0
$292$	72503.3	−	125579.i	0.0497623	−	0.0861909i
$293$	1.02503e6			0.697537			0.348769	−	0.937209i	$-0.386600\pi$
$293$	1.02503e6			0.697537			0.348769	+	0.937209i	$0.386600\pi$
$294$		0			0
$295$	−210311.			−0.140704
$296$	−389903.	+	675332.i	−0.258659	+	0.448011i
$297$		0			0
$298$	−328975.	−	569801.i	−0.214596	−	0.371692i
$299$	1.75149e6	−	3.03366e6i	1.13300	−	1.96241i
$300$		0			0
$301$	34961.2	−	208524.i	0.0222418	−	0.132660i
$302$	−596464.			−0.376328
$303$		0			0
$304$	309614.	+	536267.i	0.192148	+	0.332811i
$305$	667623.	+	1.15636e6i	0.410943	+	0.711774i
$306$		0			0
$307$	−709845.			−0.429850			−0.214925	−	0.976631i	$-0.568951\pi$
$307$	−709845.			−0.429850			−0.214925	+	0.976631i	$0.568951\pi$
$308$	−42601.5	−	35140.1i	−0.0255887	−	0.0211070i
$309$		0			0
$310$	248348.	−	430151.i	0.146776	−	0.254224i
$311$	783816.	+	1.35761e6i	0.459529	+	0.795928i	0.998936	−	0.0461175i	$-0.0146849\pi$
$311$	783816.	+	1.35761e6i	0.459529	+	0.795928i	−0.539407	+	0.842045i	$0.681352\pi$
$312$		0			0
$313$	−186476.	+	322986.i	−0.107588	+	0.186347i	−0.914792	−	0.403924i	$-0.867646\pi$
$313$	−186476.	+	322986.i	−0.107588	+	0.186347i	0.807205	+	0.590271i	$0.200979\pi$
$314$	−458684.			−0.262536
$315$		0			0
$316$	2.16284e6			1.21845
$317$	−1.51408e6	+	2.62246e6i	−0.846253	+	1.46575i	0.0382747	+	0.999267i	$0.487814\pi$
$317$	−1.51408e6	+	2.62246e6i	−0.846253	+	1.46575i	−0.884528	+	0.466487i	$0.845520\pi$
$318$		0			0
$319$	−49079.6	−	85008.3i	−0.0270037	−	0.0467719i
$320$	144136.	−	249650.i	0.0786858	−	0.136288i
$321$		0			0
$322$	1.31373e6	−	490723.i	0.706103	−	0.263752i
$323$	1.78573e6			0.952380
$324$		0			0
$325$	−125364.	−	217137.i	−0.0658363	−	0.114032i
$326$	695526.	+	1.20469e6i	0.362468	+	0.627813i
$327$		0			0
$328$	−2.84923e6			−1.46232
$329$	−960613.	−	792367.i	−0.489281	−	0.403586i
$330$		0			0
$331$	−533448.	+	923959.i	−0.267622	+	0.463535i	−0.968247	−	0.249995i	$-0.919571\pi$
$331$	−533448.	+	923959.i	−0.267622	+	0.463535i	0.700625	+	0.713529i	$0.252905\pi$
$332$	1.17133e6	+	2.02880e6i	0.583221	+	1.01017i
$333$		0			0
$334$	777130.	−	1.34603e6i	0.381178	−	0.660219i
$335$	−2.74401e6			−1.33590
$336$		0			0
$337$	1.55734e6			0.746981			0.373490	−	0.927634i	$-0.378161\pi$
$337$	1.55734e6			0.746981			0.373490	+	0.927634i	$0.378161\pi$
$338$	578064.	−	1.00124e6i	0.275222	−	0.476699i
$339$		0			0
$340$	732470.	+	1.26868e6i	0.343631	+	0.595187i
$341$	−26977.1	+	46725.8i	−0.0125635	+	0.0217606i
$342$		0			0
$343$	1.04145e6	−	1.91388e6i	0.477973	−	0.878374i
$344$	−253000.			−0.115272
$345$		0			0
$346$	906124.	+	1.56945e6i	0.406909	+	0.704787i
$347$	−1.11748e6	−	1.93553e6i	−0.498214	−	0.862932i	0.501784	−	0.864993i	$-0.332677\pi$
$347$	−1.11748e6	−	1.93553e6i	−0.498214	−	0.862932i	−0.999998	+	0.00206105i	$0.999344\pi$
$348$		0			0
$349$	−1.72982e6			−0.760218			−0.380109	−	0.924942i	$-0.624114\pi$
$349$	−1.72982e6			−0.760218			−0.380109	+	0.924942i	$0.624114\pi$
$350$	16597.7	−	98995.8i	0.00724231	−	0.0431963i
$351$		0			0
$352$	−51770.9	+	89669.8i	−0.0222705	+	0.0385736i
$353$	−1.18287e6	−	2.04879e6i	−0.505242	−	0.875105i	−0.999982	−	0.00606386i	$-0.998070\pi$
$353$	−1.18287e6	−	2.04879e6i	−0.505242	−	0.875105i	0.494739	−	0.869041i	$-0.335264\pi$
$354$		0			0
$355$	46683.1	−	80857.6i	0.0196603	−	0.0340526i
$356$	−1.13700e6			−0.475484
$357$		0			0
$358$	454247.			0.187320
$359$	25514.3	−	44192.1i	0.0104484	−	0.0180971i	−0.860754	−	0.509021i	$-0.830007\pi$
$359$	25514.3	−	44192.1i	0.0104484	−	0.0180971i	0.871202	+	0.490924i	$0.163341\pi$
$360$		0			0
$361$	−274712.	−	475815.i	−0.110945	−	0.192163i
$362$	204041.	−	353410.i	0.0818364	−	0.141745i
$363$		0			0
$364$	−2.64226e6	+	986968.i	−1.04525	+	0.390436i
$365$	−346197.			−0.136016
$366$		0			0
$367$	−1.88411e6	−	3.26338e6i	−0.730200	−	1.26474i	−0.956797	−	0.290755i	$-0.906093\pi$
$367$	−1.88411e6	−	3.26338e6i	−0.730200	−	1.26474i	0.226597	−	0.973989i	$-0.427240\pi$
$368$	700648.	+	1.21356e6i	0.269699	+	0.467133i
$369$		0			0
$370$	806328.			0.306201
$371$	2.82441e6	−	1.05501e6i	1.06535	−	0.397943i
$372$		0			0
$373$	−2.31720e6	+	4.01351e6i	−0.862366	+	1.49366i	0.00727258	+	0.999974i	$0.497685\pi$
$373$	−2.31720e6	+	4.01351e6i	−0.862366	+	1.49366i	−0.869639	+	0.493689i	$0.835648\pi$
$374$	24580.0	+	42573.8i	0.00908663	+	0.0157385i
$375$		0			0
$376$	−745020.	+	1.29041e6i	−0.271768	+	0.470716i
$377$	−5.01346e6			−1.81670
$378$		0			0
$379$	−4.17169e6			−1.49181			−0.745905	−	0.666052i	$-0.767983\pi$
$379$	−4.17169e6			−1.49181			−0.745905	+	0.666052i	$0.767983\pi$
$380$	1.24101e6	−	2.14949e6i	0.440875	−	0.763617i
$381$		0			0
$382$	−530276.	−	918465.i	−0.185928	−	0.322036i
$383$	−2.08586e6	+	3.61281e6i	−0.726588	+	1.25849i	0.231730	+	0.972780i	$0.425562\pi$
$383$	−2.08586e6	+	3.61281e6i	−0.726588	+	1.25849i	−0.958317	+	0.285706i	$0.907772\pi$
$384$		0			0
$385$	−21800.9	+	130030.i	−0.00749590	+	0.0447088i
$386$	−1.36391e6			−0.465927
$387$		0			0
$388$	−928783.	−	1.60870e6i	−0.313209	−	0.542495i
$389$	1.37697e6	+	2.38498e6i	0.461371	+	0.799119i	0.999030	−	0.0440442i	$-0.0140242\pi$
$389$	1.37697e6	+	2.38498e6i	0.461371	+	0.799119i	−0.537658	+	0.843163i	$0.680691\pi$
$390$		0			0
$391$	4.04106e6			1.33676
$392$	−2.46466e6	−	850357.i	−0.810108	−	0.279503i
$393$		0			0
$394$	−606578.	+	1.05062e6i	−0.196855	+	0.340962i
$395$	−2.58184e6	−	4.47189e6i	−0.832602	−	1.44211i
$396$		0			0
$397$	1.26602e6	−	2.19281e6i	0.403148	−	0.698274i	−0.590956	−	0.806704i	$-0.701249\pi$
$397$	1.26602e6	−	2.19281e6i	0.403148	−	0.698274i	0.994104	+	0.108430i	$0.0345825\pi$
$398$	208419.			0.0659522
$399$		0			0
$400$	100299.			0.0313434
$401$	−1.07873e6	+	1.86842e6i	−0.335007	+	0.580249i	−0.983486	−	0.180983i	$-0.942072\pi$
$401$	−1.07873e6	+	1.86842e6i	−0.335007	+	0.580249i	0.648479	+	0.761232i	$0.275405\pi$
$402$		0			0
$403$	1.37785e6	+	2.38651e6i	0.422611	+	0.731983i
$404$	564217.	−	977252.i	0.171986	−	0.297888i
$405$		0			0
$406$	−1.54834e6	−	1.27716e6i	−0.466177	−	0.384529i
$407$	−87588.5			−0.0262096
$408$		0			0
$409$	2.16402e6	+	3.74819e6i	0.639665	+	1.10793i	0.985506	+	0.169640i	$0.0542604\pi$
$409$	2.16402e6	+	3.74819e6i	0.639665	+	1.10793i	−0.345841	+	0.938293i	$0.612406\pi$
$410$	1.47307e6	+	2.55143e6i	0.432776	+	0.749590i
$411$		0			0
$412$	2.00405e6			0.581655
$413$	437599.	−	163457.i	0.126241	−	0.0471552i
$414$		0			0
$415$	2.79649e6	−	4.84366e6i	0.797064	−	1.38056i
$416$	2.64419e6	+	4.57987e6i	0.749134	+	1.29754i
$417$		0			0
$418$	41645.3	−	72131.8i	0.0116580	−	0.0201923i
$419$	1.51129e6			0.420544			0.210272	−	0.977643i	$-0.432565\pi$
$419$	1.51129e6			0.420544			0.210272	+	0.977643i	$0.432565\pi$
$420$		0			0
$421$	1.11586e6			0.306835			0.153418	−	0.988161i	$-0.450972\pi$
$421$	1.11586e6			0.306835			0.153418	+	0.988161i	$0.450972\pi$
$422$	1.07001e6	−	1.85331e6i	0.292487	−	0.506603i
$423$		0			0
$424$	−1.80387e6	−	3.12439e6i	−0.487293	−	0.844016i
$425$	144621.	−	250492.i	0.0388383	−	0.0672699i
$426$		0			0
$427$	−2.28787e6	−	1.88717e6i	−0.607243	−	0.500888i
$428$	−69765.2			−0.0184090
$429$		0			0
$430$	130802.	+	226556.i	0.0341149	+	0.0590887i
$431$	3.10672e6	+	5.38100e6i	0.805581	+	1.39531i	0.915898	+	0.401411i	$0.131480\pi$
$431$	3.10672e6	+	5.38100e6i	0.805581	+	1.39531i	−0.110317	+	0.993896i	$0.535187\pi$
$432$		0			0
$433$	3.24118e6			0.830775			0.415388	−	0.909644i	$-0.363646\pi$
$433$	3.24118e6			0.830775			0.415388	+	0.909644i	$0.363646\pi$
$434$	−182422.	+	1.08804e6i	−0.0464892	+	0.277282i
$435$		0			0
$436$	−2.03255e6	+	3.52047e6i	−0.512064	+	0.886920i
$437$	−3.42334e6	−	5.92939e6i	−0.857524	−	1.48527i
$438$		0			0
$439$	−1.15248e6	+	1.99616e6i	−0.285413	+	0.494349i	−0.972709	−	0.232028i	$-0.925464\pi$
$439$	−1.15248e6	+	1.99616e6i	−0.285413	+	0.494349i	0.687297	+	0.726377i	$0.258797\pi$
$440$	157765.			0.0388488
$441$		0			0
$442$	2.51084e6			0.611313
$443$	766328.	−	1.32732e6i	0.185526	−	0.321341i	−0.758228	−	0.651990i	$-0.773934\pi$
$443$	766328.	−	1.32732e6i	0.185526	−	0.321341i	0.943754	+	0.330649i	$0.107268\pi$
$444$		0			0
$445$	1.35727e6	+	2.35086e6i	0.324912	+	0.562764i
$446$	1.01420e6	−	1.75664e6i	0.241426	−	0.418162i
$447$		0			0
$448$	−105874.	+	631476.i	−0.0249226	+	0.148649i
$449$	3.55718e6			0.832702			0.416351	−	0.909204i	$-0.363309\pi$
$449$	3.55718e6			0.832702			0.416351	+	0.909204i	$0.363309\pi$
$450$		0			0
$451$	−160014.	−	277153.i	−0.0370439	−	0.0641620i
$452$	−3.18189e6	−	5.51119e6i	−0.732553	−	1.26882i
$453$		0			0
$454$	−1.49533e6			−0.340484
$455$	5.19478e6	+	4.28494e6i	1.17636	+	0.970324i
$456$		0			0
$457$	−1.25941e6	+	2.18137e6i	−0.282083	+	0.488583i	−0.971898	−	0.235403i	$-0.924359\pi$
$457$	−1.25941e6	+	2.18137e6i	−0.282083	+	0.488583i	0.689814	+	0.723986i	$0.257692\pi$
$458$	−320936.	−	555877.i	−0.0714915	−	0.123827i
$459$		0			0
$460$	2.80836e6	−	4.86423e6i	0.618812	−	1.07181i
$461$	6.63271e6			1.45358			0.726789	−	0.686861i	$-0.241012\pi$
$461$	6.63271e6			1.45358			0.726789	+	0.686861i	$0.241012\pi$
$462$		0			0
$463$	−4.40432e6			−0.954830			−0.477415	−	0.878678i	$-0.658426\pi$
$463$	−4.40432e6			−0.954830			−0.477415	+	0.878678i	$0.658426\pi$
$464$	1.00277e6	−	1.73685e6i	0.216225	−	0.374512i
$465$		0			0
$466$	849325.	+	1.47107e6i	0.181180	+	0.313812i
$467$	122922.	−	212908.i	0.0260819	−	0.0451751i	−0.852690	−	0.522417i	$-0.825030\pi$
$467$	122922.	−	212908.i	0.0260819	−	0.0451751i	0.878772	+	0.477242i	$0.158364\pi$
$468$		0			0
$469$	5.70951e6	−	2.13269e6i	1.19858	−	0.447708i
$470$	1.54072e6			0.321720
$471$		0			0
$472$	−279482.	−	484076.i	−0.0577428	−	0.100014i
$473$	−14208.6	−	24610.0i	−0.00292010	−	0.00505776i
$474$		0			0
$475$	−490057.			−0.0996581
$476$	−2.51010e6	−	2.07047e6i	−0.507778	−	0.418843i
$477$		0			0
$478$	−1.28821e6	+	2.23125e6i	−0.257880	+	0.446661i
$479$	−20175.6	−	34945.1i	−0.00401779	−	0.00695901i	0.864010	−	0.503475i	$-0.167946\pi$
$479$	−20175.6	−	34945.1i	−0.00401779	−	0.00695901i	−0.868027	+	0.496516i	$0.834612\pi$
$480$		0			0
$481$	−2.23678e6	+	3.87422e6i	−0.440820	+	0.763523i
$482$	−2.56140e6			−0.502181
$483$		0			0
$484$	3.92987e6			0.762544
$485$	−2.21743e6	+	3.84069e6i	−0.428050	+	0.741405i
$486$		0			0
$487$	1.65484e6	+	2.86627e6i	0.316180	+	0.547639i	0.979688	−	0.200530i	$-0.0642664\pi$
$487$	1.65484e6	+	2.86627e6i	0.316180	+	0.547639i	−0.663508	+	0.748169i	$0.730933\pi$
$488$	−1.77440e6	+	3.07335e6i	−0.337289	+	0.584202i
$489$		0			0
$490$	512768.	+	2.64669e6i	0.0964785	+	0.497982i
$491$	1.97959e6			0.370570			0.185285	−	0.982685i	$-0.440679\pi$
$491$	1.97959e6			0.370570			0.185285	+	0.982685i	$0.440679\pi$
$492$		0			0
$493$	−2.89179e6	−	5.00872e6i	−0.535857	−	0.928132i
$494$	−2.12703e6	−	3.68412e6i	−0.392153	−	0.679229i
$495$		0			0
$496$	−1.10237e6			−0.201197
$497$	−34290.7	+	204525.i	−0.00622709	+	0.0371411i
$498$		0			0
$499$	1.58498e6	−	2.74526e6i	0.284952	−	0.493551i	−0.687646	−	0.726046i	$-0.741356\pi$
$499$	1.58498e6	−	2.74526e6i	0.284952	−	0.493551i	0.972597	+	0.232495i	$0.0746891\pi$
$500$	2.02857e6	+	3.51359e6i	0.362882	+	0.628530i
$501$		0			0
$502$	−295396.	+	511640.i	−0.0523172	+	0.0906161i
$503$	4.01273e6			0.707164			0.353582	−	0.935403i	$-0.384963\pi$
$503$	4.01273e6			0.707164			0.353582	+	0.935403i	$0.384963\pi$
$504$		0			0
$505$	−2.69408e6			−0.470092
$506$	94242.1	−	163232.i	0.0163632	−	0.0283419i
$507$		0			0
$508$	−2.85721e6	−	4.94884e6i	−0.491228	−	0.850832i
$509$	2.05629e6	−	3.56159e6i	0.351795	−	0.609326i	−0.634769	−	0.772702i	$-0.718905\pi$
$509$	2.05629e6	−	3.56159e6i	0.351795	−	0.609326i	0.986564	+	0.163375i	$0.0522382\pi$
$510$		0			0
$511$	720338.	−	269070.i	0.122035	−	0.0455840i
$512$	−3.88273e6			−0.654580
$513$		0			0
$514$	−108810.	−	188465.i	−0.0181661	−	0.0314646i
$515$	−2.39229e6	−	4.14356e6i	−0.397462	−	0.688424i
$516$		0			0
$517$	−167363.			−0.0275380
$518$	−1.67774e6	+	626691.i	−0.274727	+	0.102619i
$519$		0			0
$520$	4.02890e6	−	6.97827e6i	0.653399	−	1.13172i
$521$	4.27758e6	+	7.40898e6i	0.690404	+	1.19582i	0.971705	+	0.236196i	$0.0759007\pi$
$521$	4.27758e6	+	7.40898e6i	0.690404	+	1.19582i	−0.281301	+	0.959620i	$0.590766\pi$
$522$		0			0
$523$	896820.	−	1.55334e6i	0.143368	−	0.248320i	−0.785395	−	0.618995i	$-0.787540\pi$
$523$	896820.	−	1.55334e6i	0.143368	−	0.248320i	0.928763	+	0.370675i	$0.120874\pi$
$524$	−3.84534e6			−0.611796
$525$		0			0
$526$	−1.18949e6			−0.187455
$527$	−1.58950e6	+	2.75310e6i	−0.249307	+	0.431813i
$528$		0			0
$529$	−4.52875e6	−	7.84402e6i	−0.703621	−	1.21871i
$530$	−1.86522e6	+	3.23065e6i	−0.288430	+	0.499575i
$531$		0			0
$532$	−911571.	+	5.43701e6i	−0.139640	+	0.832877i
$533$	−1.63454e7			−2.49217
$534$		0			0
$535$	83280.6	+	144246.i	0.0125794	+	0.0217881i
$536$	−3.64650e6	−	6.31592e6i	−0.548231	−	0.949565i
$537$		0			0
$538$	−12894.1			−0.00192059
$539$	−55700.1	−	287501.i	−0.00825818	−	0.0426253i
$540$		0			0
$541$	178780.	−	309657.i	0.0262619	−	0.0454870i	−0.852596	−	0.522571i	$-0.824973\pi$
$541$	178780.	−	309657.i	0.0262619	−	0.0454870i	0.878858	+	0.477084i	$0.158306\pi$
$542$	144643.	+	250528.i	0.0211494	+	0.0366318i
$543$		0			0
$544$	−3.05036e6	+	5.28338e6i	−0.441931	+	0.765447i
$545$	9.70522e6			1.39963
$546$		0			0
$547$	−3.79404e6			−0.542167			−0.271084	−	0.962556i	$-0.587382\pi$
$547$	−3.79404e6			−0.542167			−0.271084	+	0.962556i	$0.587382\pi$
$548$	2.09695e6	−	3.63203e6i	0.298289	−	0.516652i
$549$		0			0
$550$	−6745.47	−	11683.5i	−0.000950835	−	0.00164689i
$551$	−4.89949e6	+	8.48616e6i	−0.687498	+	1.19078i
$552$		0			0
$553$	8.84771e6	+	7.29809e6i	1.23032	+	1.01484i
$554$	2.09718e6			0.290310
$555$		0			0
$556$	2.57463e6	+	4.45939e6i	0.353206	+	0.611771i
$557$	−2.44799e6	−	4.24005e6i	−0.334328	−	0.579072i	0.649028	−	0.760765i	$-0.275176\pi$
$557$	−2.44799e6	−	4.24005e6i	−0.334328	−	0.579072i	−0.983355	+	0.181692i	$0.941843\pi$
$558$		0			0
$559$	−1.45140e6			−0.196453
$560$	−2.52350e6	+	942607.i	−0.340042	+	0.127017i
$561$		0			0
$562$	1.00245e6	−	1.73630e6i	0.133882	−	0.231891i
$563$	−2.16583e6	−	3.75133e6i	−0.287974	−	0.498786i	0.685352	−	0.728212i	$-0.259648\pi$
$563$	−2.16583e6	−	3.75133e6i	−0.287974	−	0.498786i	−0.973326	+	0.229426i	$0.926315\pi$
$564$		0			0
$565$	−7.59661e6	+	1.31577e7i	−1.00115	+	1.73404i
$566$	3.27151e6			0.429248
$567$		0			0
$568$	248148.			0.0322730
$569$	−1.09848e6	+	1.90262e6i	−0.142236	+	0.246361i	−0.928338	−	0.371736i	$-0.878763\pi$
$569$	−1.09848e6	+	1.90262e6i	−0.142236	+	0.246361i	0.786102	+	0.618097i	$0.212096\pi$
$570$		0			0
$571$	3.73846e6	+	6.47520e6i	0.479846	+	0.831118i	0.999733	−	0.0231172i	$-0.00735908\pi$
$571$	3.73846e6	+	6.47520e6i	0.479846	+	0.831118i	−0.519886	+	0.854235i	$0.674026\pi$
$572$	−189545.	+	328301.i	−0.0242227	+	0.0419549i
$573$		0			0
$574$	−5.04805e6	−	4.16391e6i	−0.639505	−	0.527500i
$575$	−1.10899e6			−0.139880
$576$		0			0
$577$	683110.	+	1.18318e6i	0.0854183	+	0.147949i	0.905569	−	0.424198i	$-0.139444\pi$
$577$	683110.	+	1.18318e6i	0.0854183	+	0.147949i	−0.820151	+	0.572147i	$0.806111\pi$
$578$	−502748.	−	870785.i	−0.0625937	−	0.108415i
$579$		0			0
$580$	−8.03867e6			−0.992234
$581$	−2.05414e6	+	1.22518e7i	−0.252458	+	1.50577i
$582$		0			0
$583$	202612.	−	350934.i	0.0246884	−	0.0427616i
$584$	−460059.	−	796845.i	−0.0558189	−	0.0966812i
$585$		0			0
$586$	1.40848e6	−	2.43956e6i	0.169437	−	0.293473i
$587$	9.27217e6			1.11067			0.555336	−	0.831626i	$-0.312590\pi$
$587$	9.27217e6			1.11067			0.555336	+	0.831626i	$0.312590\pi$
$588$		0			0
$589$	5.38612e6			0.639717
$590$	−288987.	+	500540.i	−0.0341781	+	0.0591982i
$591$		0			0
$592$	−894782.	−	1.54981e6i	−0.104933	−	0.181750i
$593$	4.60523e6	−	7.97649e6i	0.537792	−	0.931483i	−0.461231	−	0.887280i	$-0.652592\pi$
$593$	4.60523e6	−	7.97649e6i	0.537792	−	0.931483i	0.999023	−	0.0442028i	$-0.0140748\pi$
$594$		0			0
$595$	−1.28452e6	+	7.66145e6i	−0.148747	+	0.887194i
$596$	5.85305e6			0.674942
$597$		0			0
$598$	−4.81340e6	−	8.33706e6i	−0.550426	−	0.953367i
$599$	−6.84581e6	−	1.18573e7i	−0.779575	−	1.35026i	−0.932187	−	0.361977i	$-0.882102\pi$
$599$	−6.84581e6	−	1.18573e7i	−0.779575	−	1.35026i	0.152612	−	0.988286i	$-0.451231\pi$
$600$		0			0
$601$	1.61113e6			0.181946			0.0909732	−	0.995853i	$-0.471002\pi$
$601$	1.61113e6			0.181946			0.0909732	+	0.995853i	$0.471002\pi$
$602$	−448246.	−	369738.i	−0.0504110	−	0.0415818i
$603$		0			0
$604$	2.65304e6	−	4.59519e6i	0.295904	−	0.512521i
$605$	−4.69119e6	−	8.12539e6i	−0.521069	−	0.902517i
$606$		0			0
$607$	7.03281e6	−	1.21812e7i	0.774742	−	1.34189i	−0.160198	−	0.987085i	$-0.551213\pi$
$607$	7.03281e6	−	1.21812e7i	0.774742	−	1.34189i	0.934940	−	0.354807i	$-0.115453\pi$
$608$	1.03363e7			1.13398
$609$		0			0
$610$	3.66950e6			0.399284
$611$	−4.27401e6	+	7.40280e6i	−0.463161	+	0.802219i
$612$		0			0
$613$	−6.79842e6	−	1.17752e7i	−0.730729	−	1.26566i	−0.956572	−	0.291497i	$-0.905847\pi$
$613$	−6.79842e6	−	1.17752e7i	−0.730729	−	1.26566i	0.225842	−	0.974164i	$-0.427487\pi$
$614$	−975391.	+	1.68943e6i	−0.104414	+	0.180850i
$615$		0			0
$616$	−328264.	+	122617.i	−0.0348555	+	0.0130197i
$617$	5.74287e6			0.607318			0.303659	−	0.952781i	$-0.401792\pi$
$617$	5.74287e6			0.607318			0.303659	+	0.952781i	$0.401792\pi$
$618$		0			0
$619$	3.01299e6	+	5.21865e6i	0.316061	+	0.547434i	0.979662	−	0.200653i	$-0.0643063\pi$
$619$	3.01299e6	+	5.21865e6i	0.316061	+	0.547434i	−0.663602	+	0.748086i	$0.730973\pi$
$620$	2.20927e6	+	3.82657e6i	0.230818	+	0.399789i
$621$		0			0
$622$	4.30814e6			0.446492
$623$	−4.65122e6	−	3.83658e6i	−0.480117	−	0.396027i
$624$		0			0
$625$	5.28334e6	−	9.15101e6i	0.541014	−	0.937064i
$626$	512470.	+	887625.i	0.0522676	+	0.0905302i
$627$		0			0
$628$	2.04020e6	−	3.53373e6i	0.206430	−	0.357547i
$629$	−5.16075e6			−0.520099
$630$		0			0
$631$	−6.90670e6			−0.690554			−0.345277	−	0.938501i	$-0.612215\pi$
$631$	−6.90670e6			−0.690554			−0.345277	+	0.938501i	$0.612215\pi$
$632$	6.86200e6	−	1.18853e7i	0.683373	−	1.18364i
$633$		0			0
$634$	4.16096e6	+	7.20700e6i	0.411122	+	0.712084i
$635$	−6.82146e6	+	1.18151e7i	−0.671341	+	1.16280i
$636$		0			0
$637$	−1.41392e7	−	4.87830e6i	−1.38063	−	0.476343i
$638$	−269759.			−0.0262376
$639$		0			0
$640$	5.15340e6	+	8.92595e6i	0.497329	+	0.861400i
$641$	8.24828e6	+	1.42864e7i	0.792900	+	1.37334i	0.924164	+	0.381995i	$0.124763\pi$
$641$	8.24828e6	+	1.42864e7i	0.792900	+	1.37334i	−0.131265	+	0.991347i	$0.541904\pi$
$642$		0			0
$643$	1.70171e7			1.62315			0.811576	−	0.584247i	$-0.198610\pi$
$643$	1.70171e7			1.62315			0.811576	+	0.584247i	$0.198610\pi$
$644$	−2.06286e6	+	1.23038e7i	−0.195999	+	1.16903i
$645$		0			0
$646$	2.45376e6	−	4.25003e6i	0.231340	−	0.400692i
$647$	1.74287e6	+	3.01873e6i	0.163683	+	0.283507i	0.936187	−	0.351503i	$-0.114329\pi$
$647$	1.74287e6	+	3.01873e6i	0.163683	+	0.283507i	−0.772504	+	0.635010i	$0.780996\pi$
$648$		0			0
$649$	31391.6	−	54371.8i	0.00292551	−	0.00506713i
$650$	−689047.			−0.0639684
$651$		0			0
$652$	−1.23746e7			−1.14002
$653$	7.72245e6	−	1.33757e7i	0.708716	−	1.22753i	−0.256618	−	0.966513i	$-0.582608\pi$
$653$	7.72245e6	−	1.33757e7i	0.708716	−	1.22753i	0.965334	−	0.261019i	$-0.0840586\pi$
$654$		0			0
$655$	4.59029e6	+	7.95061e6i	0.418058	+	0.724098i
$656$	3.26933e6	−	5.66264e6i	0.296619	−	0.513759i
$657$		0			0
$658$	−3.20580e6	+	1.19747e6i	−0.288650	+	0.107820i
$659$	3.11193e6			0.279136			0.139568	−	0.990212i	$-0.455429\pi$
$659$	3.11193e6			0.279136			0.139568	+	0.990212i	$0.455429\pi$
$660$		0			0
$661$	−4.08610e6	−	7.07733e6i	−0.363752	−	0.630037i	0.624823	−	0.780766i	$-0.285171\pi$
$661$	−4.08610e6	−	7.07733e6i	−0.363752	−	0.630037i	−0.988575	+	0.150729i	$0.951838\pi$
$662$	1.46601e6	+	2.53921e6i	0.130015	+	0.225192i
$663$		0			0
$664$	1.48650e7			1.30841
$665$	1.23297e7	−	4.60554e6i	1.08118	−	0.403856i
$666$		0			0
$667$	−1.10874e7	+	1.92039e7i	−0.964973	+	1.67138i
$668$	6.91326e6	+	1.19741e7i	0.599434	+	1.03825i
$669$		0			0
$670$	−3.77051e6	+	6.53072e6i	−0.324499	+	0.562049i
$671$	−398604.			−0.0341771
$672$		0			0
$673$	1.60182e7			1.36325			0.681627	−	0.731700i	$-0.261273\pi$
$673$	1.60182e7			1.36325			0.681627	+	0.731700i	$0.261273\pi$
$674$	2.13993e6	−	3.70647e6i	0.181447	−	0.314276i
$675$		0			0
$676$	5.14239e6	+	8.90687e6i	0.432811	+	0.749650i
$677$	512185.	−	887131.i	0.0429492	−	0.0743902i	−0.843752	−	0.536734i	$-0.819658\pi$
$677$	512185.	−	887131.i	0.0429492	−	0.0743902i	0.886701	+	0.462344i	$0.152991\pi$
$678$		0			0
$679$	1.62879e6	−	9.71483e6i	0.135579	−	0.808650i
$680$	9.29556e6			0.770910
$681$		0			0
$682$	74138.1	+	128411.i	0.00610352	+	0.0105716i
$683$	−2.69688e6	−	4.67114e6i	−0.221213	−	0.383152i	0.733964	−	0.679189i	$-0.237668\pi$
$683$	−2.69688e6	−	4.67114e6i	−0.221213	−	0.383152i	−0.955177	+	0.296037i	$0.904335\pi$
$684$		0			0
$685$	−1.00128e7			−0.815319
$686$	−3.12398e6	−	5.10850e6i	−0.253453	−	0.414460i
$687$		0			0
$688$	290302.	−	502819.i	0.0233819	−	0.0404986i
$689$	−1.03484e7	−	1.79239e7i	−0.830470	−	1.43842i
$690$		0			0
$691$	452826.	−	784318.i	0.0360775	−	0.0624881i	−0.847423	−	0.530919i	$-0.821847\pi$
$691$	452826.	−	784318.i	0.0360775	−	0.0624881i	0.883500	+	0.468430i	$0.155180\pi$
$692$	−1.61215e7			−1.27980
$693$		0			0
$694$	−6.14207e6			−0.484079
$695$	6.14682e6	−	1.06466e7i	0.482712	−	0.836082i
$696$		0			0
$697$	−9.42810e6	−	1.63300e7i	−0.735093	−	1.27322i
$698$	−2.37693e6	+	4.11697e6i	−0.184662	+	0.319845i
$699$		0			0
$700$	688845.	+	568197.i	0.0531344	+	0.0438282i
$701$	−1.12573e7			−0.865246			−0.432623	−	0.901575i	$-0.642412\pi$
$701$	−1.12573e7			−0.865246			−0.432623	+	0.901575i	$0.642412\pi$
$702$		0			0
$703$	4.37187e6	+	7.57230e6i	0.333640	+	0.577882i
$704$	43028.1	+	74526.9i	0.00327205	+	0.00566736i
$705$		0			0
$706$	−6.50147e6			−0.490908
$707$	5.60563e6	−	2.09388e6i	0.421770	−	0.157545i
$708$		0			0
$709$	−2.17755e6	+	3.77162e6i	−0.162687	+	0.281781i	−0.935831	−	0.352448i	$-0.885349\pi$
$709$	−2.17755e6	+	3.77162e6i	−0.162687	+	0.281781i	0.773145	+	0.634230i	$0.218683\pi$
$710$	−128294.	−	222211.i	−0.00955123	−	0.0165432i
$711$		0			0
$712$	−3.60733e6	+	6.24809e6i	−0.266678	+	0.461899i
$713$	1.21886e7			0.897907
$714$		0			0
$715$	905060.			0.0662082
$716$	−2.02046e6	+	3.49955e6i	−0.147288	+	0.255111i
$717$		0			0
$718$	−70118.0	−	121448.i	−0.00507597	−	0.00879183i
$719$	−7.07221e6	+	1.22494e7i	−0.510191	+	0.883676i	0.489739	+	0.871869i	$0.337092\pi$
$719$	−7.07221e6	+	1.22494e7i	−0.510191	+	0.883676i	−0.999930	+	0.0118076i	$0.996241\pi$
$720$		0			0
$721$	8.19812e6	+	6.76227e6i	0.587322	+	0.484456i
$722$	−1.50992e6			−0.107798
$723$		0			0
$724$	1.81513e6	+	3.14389e6i	0.128695	+	0.222906i
$725$	793591.	+	1.37454e6i	0.0560727	+	0.0971208i
$726$		0			0
$727$	−6.26406e6			−0.439561			−0.219781	−	0.975549i	$-0.570534\pi$
$727$	−6.26406e6			−0.439561			−0.219781	+	0.975549i	$0.570534\pi$
$728$	−2.95940e6	+	1.76511e7i	−0.206954	+	1.23437i
$729$		0			0
$730$	−475705.	+	823946.i	−0.0330393	+	0.0572258i
$731$	−837176.	−	1.45003e6i	−0.0579460	−	0.100365i
$732$		0			0
$733$	1.02089e7	−	1.76823e7i	0.701806	−	1.21556i	−0.266025	−	0.963966i	$-0.585710\pi$
$733$	1.02089e7	−	1.76823e7i	0.701806	−	1.21556i	0.967832	−	0.251598i	$-0.0809562\pi$
$734$	−1.03558e7			−0.709484
$735$		0			0
$736$	2.33908e7			1.59166
$737$	409577.	−	709409.i	0.0277758	−	0.0481092i
$738$		0			0
$739$	−7.42256e6	−	1.28563e7i	−0.499969	−	0.865971i	0.500031	−	0.866007i	$-0.333322\pi$
$739$	−7.42256e6	−	1.28563e7i	−0.499969	−	0.865971i	−1.00000		3.61537e-5i	$0.999988\pi$
$740$	−3.58650e6	+	6.21200e6i	−0.240764	+	0.417015i
$741$		0			0
$742$	1.37008e6	−	8.17176e6i	0.0913558	−	0.544886i
$743$	−2.36601e7			−1.57234			−0.786168	−	0.618013i	$-0.787938\pi$
$743$	−2.36601e7			−1.57234			−0.786168	+	0.618013i	$0.787938\pi$
$744$		0			0
$745$	−6.98694e6	−	1.21017e7i	−0.461207	−	0.798834i
$746$	6.36809e6	+	1.10299e7i	0.418950	+	0.725643i
$747$		0			0
$748$	−437322.			−0.0285790
$749$	−285394.	−	235409.i	−0.0185883	−	0.0153327i
$750$		0			0
$751$	−1.03287e7	+	1.78898e7i	−0.668258	+	1.15746i	0.310133	+	0.950693i	$0.399627\pi$
$751$	−1.03287e7	+	1.78898e7i	−0.668258	+	1.15746i	−0.978391	+	0.206764i	$0.933707\pi$
$752$	−1.70973e6	−	2.96134e6i	−0.110251	−	0.190961i
$753$		0			0
$754$	−6.88895e6	+	1.19320e7i	−0.441291	+	0.764338i
$755$	−1.26680e7			−0.808799
$756$		0			0
$757$	−1.26697e7			−0.803573			−0.401787	−	0.915733i	$-0.631611\pi$
$757$	−1.26697e7			−0.803573			−0.401787	+	0.915733i	$0.631611\pi$
$758$	−5.73228e6	+	9.92860e6i	−0.362372	+	0.627646i
$759$		0			0
$760$	−7.87462e6	−	1.36392e7i	−0.494534	−	0.856557i
$761$	8.13761e6	−	1.40948e7i	0.509372	−	0.882259i	−0.490569	−	0.871402i	$-0.663211\pi$
$761$	8.13761e6	−	1.40948e7i	0.509372	−	0.882259i	0.999941	−	0.0108563i	$-0.00345572\pi$
$762$		0			0
$763$	−2.01938e7	+	7.54305e6i	−1.25576	+	0.469068i
$764$	9.43455e6			0.584774
$765$		0			0
$766$	5.73232e6	+	9.92867e6i	0.352987	+	0.611391i
$767$	−1.60332e6	−	2.77703e6i	−0.0984084	−	0.170448i
$768$		0			0
$769$	1.60471e7			0.978547			0.489273	−	0.872130i	$-0.337262\pi$
$769$	1.60471e7			0.978547			0.489273	+	0.872130i	$0.337262\pi$
$770$	279515.	+	230560.i	0.0169894	+	0.0140138i
$771$		0			0
$772$	6.06659e6	−	1.05076e7i	0.366355	−	0.634545i
$773$	1.07839e6	+	1.86782e6i	0.0649121	+	0.112431i	0.896655	−	0.442730i	$-0.145990\pi$
$773$	1.07839e6	+	1.86782e6i	0.0649121	+	0.112431i	−0.831743	+	0.555161i	$0.812657\pi$
$774$		0			0
$775$	436206.	−	755531.i	0.0260878	−	0.0451854i

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)

\(f(q)\)	\(=\)	\(q+(1.37409 - 2.37999i) q^{2} +(12.2237 + 21.1722i) q^{4} +(29.1836 - 50.5475i) q^{5} +(-21.4366 + 127.857i) q^{7} +155.128 q^{8} +O(q^{10})\)	\(q+(1.37409 - 2.37999i) q^{2} +(12.2237 + 21.1722i) q^{4} +(29.1836 - 50.5475i) q^{5} +(-21.4366 + 127.857i) q^{7} +155.128 q^{8} +(-80.2019 - 138.914i) q^{10} +(8.71205 + 15.0897i) q^{11} +889.933 q^{13} +(274.844 + 226.706i) q^{14} +(-178.000 + 308.305i) q^{16} +(513.318 + 889.092i) q^{17} +(869.702 - 1506.37i) q^{19} +1426.93 q^{20} +47.8846 q^{22} +(1968.11 - 3408.87i) q^{23} +(-140.869 - 243.993i) q^{25} +(1222.85 - 2118.04i) q^{26} +(-2969.05 + 1109.04i) q^{28} -5633.53 q^{29} +(1548.27 + 2681.68i) q^{31} +(2971.22 + 5146.31i) q^{32} +2821.38 q^{34} +(5837.27 + 4814.91i) q^{35} +(-2513.43 + 4353.39i) q^{37} +(-2390.10 - 4139.77i) q^{38} +(4527.20 - 7841.34i) q^{40} -18367.0 q^{41} -1630.91 q^{43} +(-212.988 + 368.906i) q^{44} +(-5408.72 - 9368.19i) q^{46} +(-4802.62 + 8318.38i) q^{47} +(-15887.9 - 5481.65i) q^{49} -774.269 q^{50} +(10878.3 + 18841.8i) q^{52} +(-11628.3 - 20140.7i) q^{53} +1017.00 q^{55} +(-3325.41 + 19834.2i) q^{56} +(-7740.98 + 13407.8i) q^{58} +(-1801.62 - 3120.50i) q^{59} +(-11438.3 + 19811.7i) q^{61} +8509.83 q^{62} +4938.92 q^{64} +(25971.5 - 44983.9i) q^{65} +(-23506.4 - 40714.2i) q^{67} +(-12549.3 + 21736.1i) q^{68} +(19480.4 - 7276.56i) q^{70} +1599.63 q^{71} +(-2965.67 - 5136.70i) q^{73} +(6907.36 + 11963.9i) q^{74} +42524.1 q^{76} +(-2116.09 + 790.427i) q^{77} +(44234.4 - 76616.3i) q^{79} +(10389.4 + 17994.9i) q^{80} +(-25237.9 + 43713.3i) q^{82} +95823.9 q^{83} +59921.9 q^{85} +(-2241.02 + 3881.56i) q^{86} +(1351.48 + 2340.84i) q^{88} +(-23253.9 + 40277.0i) q^{89} +(-19077.1 + 113784. i) q^{91} +96230.8 q^{92} +(13198.5 + 22860.4i) q^{94} +(-50762.1 - 87922.5i) q^{95} -75981.8 q^{97} +(-34877.8 + 30281.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 69 q^{4} + 258 q^{7} - 246 q^{8}+O(q^{10}) \) 8 * q + 3 * q^2 - 69 * q^4 + 258 * q^7 - 246 * q^8	\( 8 q + 3 q^{2} - 69 q^{4} + 258 q^{7} - 246 q^{8} - 283 q^{10} + 402 q^{11} + 924 q^{13} - 1926 q^{14} - 3273 q^{16} + 276 q^{17} - 510 q^{19} - 9438 q^{20} + 2750 q^{22} + 6900 q^{23} - 2814 q^{25} - 15138 q^{26} - 26221 q^{28} - 1080 q^{29} + 6410 q^{31} + 15519 q^{32} + 42288 q^{34} + 33108 q^{35} - 15250 q^{37} - 41250 q^{38} + 8547 q^{40} - 8616 q^{41} + 58396 q^{43} + 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 64252 q^{49} + 14604 q^{50} + 47476 q^{52} + 13692 q^{53} + 146248 q^{55} + 15921 q^{56} - 52309 q^{58} + 34830 q^{59} + 5364 q^{61} - 32058 q^{62} - 146974 q^{64} + 66864 q^{65} + 5994 q^{67} - 58272 q^{68} - 4307 q^{70} - 178536 q^{71} - 59638 q^{73} - 185442 q^{74} + 42616 q^{76} + 75660 q^{77} + 44062 q^{79} - 33381 q^{80} - 57596 q^{82} + 416892 q^{83} + 72648 q^{85} - 136968 q^{86} - 87597 q^{88} - 77520 q^{89} + 104722 q^{91} - 316512 q^{92} + 73722 q^{94} - 221376 q^{95} - 377260 q^{97} - 382479 q^{98}+O(q^{100}) \) 8 * q + 3 * q^2 - 69 * q^4 + 258 * q^7 - 246 * q^8 - 283 * q^10 + 402 * q^11 + 924 * q^13 - 1926 * q^14 - 3273 * q^16 + 276 * q^17 - 510 * q^19 - 9438 * q^20 + 2750 * q^22 + 6900 * q^23 - 2814 * q^25 - 15138 * q^26 - 26221 * q^28 - 1080 * q^29 + 6410 * q^31 + 15519 * q^32 + 42288 * q^34 + 33108 * q^35 - 15250 * q^37 - 41250 * q^38 + 8547 * q^40 - 8616 * q^41 + 58396 * q^43 + 70743 * q^44 - 61800 * q^46 - 15060 * q^47 - 64252 * q^49 + 14604 * q^50 + 47476 * q^52 + 13692 * q^53 + 146248 * q^55 + 15921 * q^56 - 52309 * q^58 + 34830 * q^59 + 5364 * q^61 - 32058 * q^62 - 146974 * q^64 + 66864 * q^65 + 5994 * q^67 - 58272 * q^68 - 4307 * q^70 - 178536 * q^71 - 59638 * q^73 - 185442 * q^74 + 42616 * q^76 + 75660 * q^77 + 44062 * q^79 - 33381 * q^80 - 57596 * q^82 + 416892 * q^83 + 72648 * q^85 - 136968 * q^86 - 87597 * q^88 - 77520 * q^89 + 104722 * q^91 - 316512 * q^92 + 73722 * q^94 - 221376 * q^95 - 377260 * q^97 - 382479 * q^98

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