LMFDB - Embedded newform 63.6.e.e.46.3

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			46.3
Root			$-0.874091 - 1.51397i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.6.e.e.37.3

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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

)

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

$2$	1.37409	+	2.37999i	0.242907	+	0.420728i	0.961541	−	0.274661i	$-0.0885656\pi$
$2$	1.37409	+	2.37999i	0.242907	+	0.420728i	−0.718634	+	0.695389i	$0.755232\pi$
$3$		0			0
$3$		0			0
$4$	12.2237	−	21.1722i	0.381992	−	0.661630i
$5$	29.1836	+	50.5475i	0.522053	+	0.904222i	0.999671	+	0.0256544i	$0.00816693\pi$
$5$	29.1836	+	50.5475i	0.522053	+	0.904222i	−0.477618	+	0.878568i	$0.658500\pi$
$6$		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	−0.854967	−	0.518683i	$-0.826423\pi$
$11$	8.71205	−	15.0897i	0.0217089	−	0.0376010i	0.876676	+	0.481082i	$0.159756\pi$
$12$		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	−0.566153	−	0.824300i	$-0.691569\pi$
$17$	513.318	−	889.092i	0.430788	−	0.746147i	0.996941	+	0.0781529i	$0.0249022\pi$
$18$		0			0
$19$	869.702	+	1506.37i	0.552696	+	0.957297i	0.998079	+	0.0619572i	$0.0197342\pi$
$19$	869.702	+	1506.37i	0.552696	+	0.957297i	−0.445383	+	0.895340i	$0.646932\pi$
$20$	1426.93			0.797680
$21$		0			0
$22$	47.8846			0.0210930
$23$	1968.11	+	3408.87i	0.775764	+	1.34366i	0.934364	+	0.356320i	$0.115969\pi$
$23$	1968.11	+	3408.87i	0.775764	+	1.34366i	−0.158599	+	0.987343i	$0.550698\pi$
$24$		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	−0.684296	−	0.729205i	$-0.739890\pi$
$31$	1548.27	−	2681.68i	0.289362	−	0.501190i	0.973658	+	0.228015i	$0.0732236\pi$
$32$	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	0.674720	−	0.738073i	$-0.264264\pi$
$37$	−2513.43	−	4353.39i	−0.301830	−	0.522785i	−0.976551	+	0.215288i	$0.930931\pi$
$38$	−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	0.662760	−	0.748832i	$-0.269385\pi$
$47$	−4802.62	−	8318.38i	−0.317127	−	0.549280i	−0.979887	+	0.199551i	$0.936051\pi$
$48$		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	0.428078	+	0.903742i	$0.359191\pi$
$53$	−11628.3	+	20140.7i	−0.568624	+	0.984886i	−0.996702	+	0.0811440i	$0.974143\pi$
$54$		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	−0.897747	−	0.440511i	$-0.854797\pi$
$59$	−1801.62	+	3120.50i	−0.0673803	+	0.116706i	0.830367	+	0.557217i	$0.188131\pi$
$60$		0			0
$61$	−11438.3	−	19811.7i	−0.393584	−	0.681707i	0.599336	−	0.800498i	$-0.295431\pi$
$61$	−11438.3	−	19811.7i	−0.393584	−	0.681707i	−0.992919	+	0.118791i	$0.962098\pi$
$62$	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	0.345758	+	0.938324i	$0.387622\pi$
$67$	−23506.4	+	40714.2i	−0.639733	+	1.10805i	−0.985491	+	0.169726i	$0.945712\pi$
$68$	−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	−0.896754	−	0.442529i	$-0.854081\pi$
$73$	−2965.67	+	5136.70i	−0.0651353	+	0.112818i	0.831619	+	0.555347i	$0.187415\pi$
$74$	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	0.921284	+	0.388890i	$0.127141\pi$
$79$	44234.4	+	76616.3i	0.797431	+	1.38119i	−0.123854	+	0.992300i	$0.539525\pi$
$80$	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	0.667433	−	0.744670i	$-0.267393\pi$
$89$	−23253.9	−	40277.0i	−0.311187	−	0.538992i	−0.978620	+	0.205679i	$0.934060\pi$
$90$		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	−0.956355	−	0.292209i	$-0.905610\pi$
$101$	−23078.7	+	39973.5i	−0.225117	+	0.389914i	0.731238	+	0.682123i	$0.238943\pi$
$102$		0			0
$103$	40986.8	+	70991.2i	0.380672	+	0.659343i	0.991158	−	0.132683i	$-0.0423594\pi$
$103$	40986.8	+	70991.2i	0.380672	+	0.659343i	−0.610487	+	0.792027i	$0.709026\pi$
$104$	138054.			1.25160
$105$		0			0
$106$	−63913.2			−0.552491
$107$	−1426.84	−	2471.35i	−0.0120480	−	0.0208677i	0.859939	−	0.510398i	$-0.170502\pi$
$107$	−1426.84	−	2471.35i	−0.0120480	−	0.0208677i	−0.871987	+	0.489530i	$0.837168\pi$
$108$		0			0
$109$	83139.2	−	144001.i	0.670254	−	1.16091i	−0.307578	−	0.951523i	$-0.599518\pi$
$109$	83139.2	−	144001.i	0.670254	−	1.16091i	0.977832	−	0.209391i	$-0.0671483\pi$
$110$	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	0.593376	−	0.804926i	$-0.297795\pi$
$131$	−78644.9	−	136217.i	−0.400398	−	0.693510i	−0.993774	+	0.111415i	$0.964462\pi$
$132$		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	−0.992507	−	0.122185i	$-0.961010\pi$
$137$	−85773.8	+	148564.i	−0.390439	+	0.676260i	0.602069	+	0.798444i	$0.294343\pi$
$138$		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	0.997818	−	0.0660304i	$-0.0210334\pi$
$149$	119706.	+	207338.i	0.441725	+	0.765090i	−0.556093	+	0.831120i	$0.687700\pi$
$150$		0			0
$151$	−108520.	+	187962.i	−0.387317	+	0.670852i	−0.992088	−	0.125547i	$-0.959931\pi$
$151$	−108520.	+	187962.i	−0.387317	+	0.670852i	0.604771	+	0.796400i	$0.293265\pi$
$152$	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	−0.968913	−	0.247400i	$-0.920424\pi$
$157$	−83452.2	+	144543.i	−0.270202	+	0.468004i	0.698711	+	0.715404i	$0.253757\pi$
$158$	−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	−0.949677	−	0.313230i	$-0.898589\pi$
$163$	−253086.	−	438358.i	−0.746104	−	1.29229i	0.203574	−	0.979060i	$-0.434744\pi$
$164$	−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	−0.891911	−	0.452210i	$-0.850636\pi$
$173$	−329718.	−	571088.i	−0.837581	−	1.45073i	0.0543304	−	0.998523i	$-0.482698\pi$
$174$		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	−0.753384	−	0.657581i	$-0.771580\pi$
$179$	82645.0	−	143145.i	0.192790	−	0.333922i	0.946174	+	0.323659i	$0.104913\pi$
$180$		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	0.991449	−	0.130494i	$-0.0416564\pi$
$191$	192955.	+	334208.i	0.382713	+	0.662879i	−0.608736	+	0.793373i	$0.708323\pi$
$192$		0			0
$193$	−248148.	+	429805.i	−0.479531	+	0.830573i	−0.999724	−	0.0234760i	$-0.992527\pi$
$193$	−248148.	+	429805.i	−0.479531	+	0.830573i	0.520193	+	0.854049i	$0.325860\pi$
$194$	−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	−0.830089	−	0.557631i	$-0.811710\pi$
$199$	37919.4	−	65678.3i	0.0678779	−	0.117568i	0.897967	+	0.440063i	$0.145044\pi$
$200$	−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	−0.986324	−	0.164817i	$-0.947297\pi$
$227$	−272058.	+	471218.i	−0.350426	+	0.606956i	0.635898	+	0.771773i	$0.280630\pi$
$228$		0			0
$229$	116781.	+	202271.i	0.147158	+	0.254885i	0.930176	−	0.367114i	$-0.119654\pi$
$229$	116781.	+	202271.i	0.147158	+	0.254885i	−0.783018	+	0.621999i	$0.786321\pi$
$230$	−631385.			−0.787000
$231$		0			0
$232$	−873917.			−1.06598
$233$	−309050.	−	535290.i	−0.372940	−	0.645951i	0.617077	−	0.786903i	$-0.288317\pi$
$233$	−309050.	−	535290.i	−0.372940	−	0.645951i	−0.990016	+	0.140952i	$0.954984\pi$
$234$		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	0.482964	+	0.875640i	$0.339560\pi$
$241$	−466018.	+	807167.i	−0.516845	+	0.895202i	−0.999809	+	0.0195613i	$0.993773\pi$
$242$	−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	0.884116	−	0.467267i	$-0.154761\pi$
$257$	39593.5	+	68578.0i	0.0373931	+	0.0647667i	−0.846723	+	0.532034i	$0.821428\pi$
$258$		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	−0.946219	−	0.323526i	$-0.895132\pi$
$263$	−216414.	+	374840.i	−0.192928	+	0.334162i	0.753291	+	0.657687i	$0.228465\pi$
$264$		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	−0.867012	−	0.498287i	$-0.833963\pi$
$269$	−2345.93	+	4063.27i	−0.00197667	+	0.00342369i	0.865035	+	0.501711i	$0.167296\pi$
$270$		0			0
$271$	−52632.1	−	91161.5i	−0.0435339	−	0.0754029i	0.843437	−	0.537227i	$-0.180528\pi$
$271$	−52632.1	−	91161.5i	−0.0435339	−	0.0754029i	−0.886971	+	0.461825i	$0.847195\pi$
$272$	−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	−0.677072	−	0.735917i	$-0.736751\pi$
$277$	381558.	−	660879.i	0.298787	−	0.517514i	0.975859	+	0.218403i	$0.0700847\pi$
$278$	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	−0.556040	−	0.831155i	$-0.687680\pi$
$283$	595214.	−	1.03094e6i	0.441781	−	0.765188i	0.997822	+	0.0659675i	$0.0210134\pi$
$284$	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	−0.539407	−	0.842045i	$-0.681352\pi$
$311$	783816.	−	1.35761e6i	0.459529	−	0.795928i	0.998936	+	0.0461175i	$0.0146849\pi$
$312$		0			0
$313$	−186476.	−	322986.i	−0.107588	−	0.186347i	0.807205	−	0.590271i	$-0.200979\pi$
$313$	−186476.	−	322986.i	−0.107588	−	0.186347i	−0.914792	+	0.403924i	$0.867646\pi$
$314$	−458684.			−0.262536
$315$		0			0
$316$	2.16284e6			1.21845
$317$	−1.51408e6	−	2.62246e6i	−0.846253	−	1.46575i	−0.884528	−	0.466487i	$-0.845520\pi$
$317$	−1.51408e6	−	2.62246e6i	−0.846253	−	1.46575i	0.0382747	−	0.999267i	$-0.487814\pi$
$318$		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	0.700625	−	0.713529i	$-0.252905\pi$
$331$	−533448.	−	923959.i	−0.267622	−	0.463535i	−0.968247	+	0.249995i	$0.919571\pi$
$332$	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	−0.999998	−	0.00206105i	$-0.999344\pi$
$347$	−1.11748e6	+	1.93553e6i	−0.498214	+	0.862932i	0.501784	+	0.864993i	$0.332677\pi$
$348$		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	0.494739	+	0.869041i	$0.335264\pi$
$353$	−1.18287e6	+	2.04879e6i	−0.505242	+	0.875105i	−0.999982	+	0.00606386i	$0.998070\pi$
$354$		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	0.871202	−	0.490924i	$-0.163341\pi$
$359$	25514.3	+	44192.1i	0.0104484	+	0.0180971i	−0.860754	+	0.509021i	$0.830007\pi$
$360$		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	0.226597	+	0.973989i	$0.427240\pi$
$367$	−1.88411e6	+	3.26338e6i	−0.730200	+	1.26474i	−0.956797	+	0.290755i	$0.906093\pi$
$368$	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	−0.869639	−	0.493689i	$-0.835648\pi$
$373$	−2.31720e6	−	4.01351e6i	−0.862366	−	1.49366i	0.00727258	−	0.999974i	$-0.497685\pi$
$374$	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	−0.958317	−	0.285706i	$-0.907772\pi$
$383$	−2.08586e6	−	3.61281e6i	−0.726588	−	1.25849i	0.231730	−	0.972780i	$-0.425562\pi$
$384$		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	−0.537658	−	0.843163i	$-0.680691\pi$
$389$	1.37697e6	−	2.38498e6i	0.461371	−	0.799119i	0.999030	+	0.0440442i	$0.0140242\pi$
$390$		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	0.994104	−	0.108430i	$-0.0345825\pi$
$397$	1.26602e6	+	2.19281e6i	0.403148	+	0.698274i	−0.590956	+	0.806704i	$0.701249\pi$
$398$	208419.			0.0659522
$399$		0			0
$400$	100299.			0.0313434
$401$	−1.07873e6	−	1.86842e6i	−0.335007	−	0.580249i	0.648479	−	0.761232i	$-0.275405\pi$
$401$	−1.07873e6	−	1.86842e6i	−0.335007	−	0.580249i	−0.983486	+	0.180983i	$0.942072\pi$
$402$		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	−0.345841	−	0.938293i	$-0.612406\pi$
$409$	2.16402e6	−	3.74819e6i	0.639665	−	1.10793i	0.985506	−	0.169640i	$-0.0542604\pi$
$410$	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	−0.110317	−	0.993896i	$-0.535187\pi$
$431$	3.10672e6	−	5.38100e6i	0.805581	−	1.39531i	0.915898	−	0.401411i	$-0.131480\pi$
$432$		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	0.687297	−	0.726377i	$-0.258797\pi$
$439$	−1.15248e6	−	1.99616e6i	−0.285413	−	0.494349i	−0.972709	+	0.232028i	$0.925464\pi$
$440$	157765.			0.0388488
$441$		0			0
$442$	2.51084e6			0.611313
$443$	766328.	+	1.32732e6i	0.185526	+	0.321341i	0.943754	−	0.330649i	$-0.107268\pi$
$443$	766328.	+	1.32732e6i	0.185526	+	0.321341i	−0.758228	+	0.651990i	$0.773934\pi$
$444$		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	0.689814	−	0.723986i	$-0.257692\pi$
$457$	−1.25941e6	−	2.18137e6i	−0.282083	−	0.488583i	−0.971898	+	0.235403i	$0.924359\pi$
$458$	−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	0.878772	−	0.477242i	$-0.158364\pi$
$467$	122922.	+	212908.i	0.0260819	+	0.0451751i	−0.852690	+	0.522417i	$0.825030\pi$
$468$		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	−0.868027	−	0.496516i	$-0.834612\pi$
$479$	−20175.6	+	34945.1i	−0.00401779	+	0.00695901i	0.864010	+	0.503475i	$0.167946\pi$
$480$		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	−0.663508	−	0.748169i	$-0.730933\pi$
$487$	1.65484e6	−	2.86627e6i	0.316180	−	0.547639i	0.979688	+	0.200530i	$0.0642664\pi$
$488$	−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	0.972597	−	0.232495i	$-0.0746891\pi$
$499$	1.58498e6	+	2.74526e6i	0.284952	+	0.493551i	−0.687646	+	0.726046i	$0.741356\pi$
$500$	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	0.986564	−	0.163375i	$-0.0522382\pi$
$509$	2.05629e6	+	3.56159e6i	0.351795	+	0.609326i	−0.634769	+	0.772702i	$0.718905\pi$
$510$		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	−0.281301	−	0.959620i	$-0.590766\pi$
$521$	4.27758e6	−	7.40898e6i	0.690404	−	1.19582i	0.971705	−	0.236196i	$-0.0759007\pi$
$522$		0			0
$523$	896820.	+	1.55334e6i	0.143368	+	0.248320i	0.928763	−	0.370675i	$-0.120874\pi$
$523$	896820.	+	1.55334e6i	0.143368	+	0.248320i	−0.785395	+	0.618995i	$0.787540\pi$
$524$	−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	0.878858	−	0.477084i	$-0.158306\pi$
$541$	178780.	+	309657.i	0.0262619	+	0.0454870i	−0.852596	+	0.522571i	$0.824973\pi$
$542$	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	−0.983355	−	0.181692i	$-0.941843\pi$
$557$	−2.44799e6	+	4.24005e6i	−0.334328	+	0.579072i	0.649028	+	0.760765i	$0.275176\pi$
$558$		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	−0.973326	−	0.229426i	$-0.926315\pi$
$563$	−2.16583e6	+	3.75133e6i	−0.287974	+	0.498786i	0.685352	+	0.728212i	$0.259648\pi$
$564$		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	0.786102	−	0.618097i	$-0.212096\pi$
$569$	−1.09848e6	−	1.90262e6i	−0.142236	−	0.246361i	−0.928338	+	0.371736i	$0.878763\pi$
$570$		0			0
$571$	3.73846e6	−	6.47520e6i	0.479846	−	0.831118i	−0.519886	−	0.854235i	$-0.674026\pi$
$571$	3.73846e6	−	6.47520e6i	0.479846	−	0.831118i	0.999733	+	0.0231172i	$0.00735908\pi$
$572$	−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	−0.820151	−	0.572147i	$-0.806111\pi$
$577$	683110.	−	1.18318e6i	0.0854183	−	0.147949i	0.905569	+	0.424198i	$0.139444\pi$
$578$	−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	0.999023	+	0.0442028i	$0.0140748\pi$
$593$	4.60523e6	+	7.97649e6i	0.537792	+	0.931483i	−0.461231	+	0.887280i	$0.652592\pi$
$594$		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	0.152612	+	0.988286i	$0.451231\pi$
$599$	−6.84581e6	+	1.18573e7i	−0.779575	+	1.35026i	−0.932187	+	0.361977i	$0.882102\pi$
$600$		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	0.934940	+	0.354807i	$0.115453\pi$
$607$	7.03281e6	+	1.21812e7i	0.774742	+	1.34189i	−0.160198	+	0.987085i	$0.551213\pi$
$608$	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	0.225842	+	0.974164i	$0.427487\pi$
$613$	−6.79842e6	+	1.17752e7i	−0.730729	+	1.26566i	−0.956572	+	0.291497i	$0.905847\pi$
$614$	−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	−0.663602	−	0.748086i	$-0.730973\pi$
$619$	3.01299e6	−	5.21865e6i	0.316061	−	0.547434i	0.979662	+	0.200653i	$0.0643063\pi$
$620$	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	−0.131265	−	0.991347i	$-0.541904\pi$
$641$	8.24828e6	−	1.42864e7i	0.792900	−	1.37334i	0.924164	−	0.381995i	$-0.124763\pi$
$642$		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	−0.772504	−	0.635010i	$-0.780996\pi$
$647$	1.74287e6	−	3.01873e6i	0.163683	−	0.283507i	0.936187	+	0.351503i	$0.114329\pi$
$648$		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	0.965334	+	0.261019i	$0.0840586\pi$
$653$	7.72245e6	+	1.33757e7i	0.708716	+	1.22753i	−0.256618	+	0.966513i	$0.582608\pi$
$654$		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	−0.988575	−	0.150729i	$-0.951838\pi$
$661$	−4.08610e6	+	7.07733e6i	−0.363752	+	0.630037i	0.624823	+	0.780766i	$0.285171\pi$
$662$	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	0.886701	−	0.462344i	$-0.152991\pi$
$677$	512185.	+	887131.i	0.0429492	+	0.0743902i	−0.843752	+	0.536734i	$0.819658\pi$
$678$		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	−0.955177	−	0.296037i	$-0.904335\pi$
$683$	−2.69688e6	+	4.67114e6i	−0.221213	+	0.383152i	0.733964	+	0.679189i	$0.237668\pi$
$684$		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	0.883500	−	0.468430i	$-0.155180\pi$
$691$	452826.	+	784318.i	0.0360775	+	0.0624881i	−0.847423	+	0.530919i	$0.821847\pi$
$692$	−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	0.773145	−	0.634230i	$-0.218683\pi$
$709$	−2.17755e6	−	3.77162e6i	−0.162687	−	0.281781i	−0.935831	+	0.352448i	$0.885349\pi$
$710$	−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	−0.999930	−	0.0118076i	$-0.996241\pi$
$719$	−7.07221e6	−	1.22494e7i	−0.510191	−	0.883676i	0.489739	−	0.871869i	$-0.337092\pi$
$720$		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	0.967832	+	0.251598i	$0.0809562\pi$
$733$	1.02089e7	+	1.76823e7i	0.701806	+	1.21556i	−0.266025	+	0.963966i	$0.585710\pi$
$734$	−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	−1.00000		3.61537e-5i	$-0.999988\pi$
$739$	−7.42256e6	+	1.28563e7i	−0.499969	+	0.865971i	0.500031	+	0.866007i	$0.333322\pi$
$740$	−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	−0.978391	−	0.206764i	$-0.933707\pi$
$751$	−1.03287e7	−	1.78898e7i	−0.668258	−	1.15746i	0.310133	−	0.950693i	$-0.399627\pi$
$752$	−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	0.999941	+	0.0108563i	$0.00345572\pi$
$761$	8.13761e6	+	1.40948e7i	0.509372	+	0.882259i	−0.490569	+	0.871402i	$0.663211\pi$
$762$		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	−0.831743	−	0.555161i	$-0.812657\pi$
$773$	1.07839e6	−	1.86782e6i	0.0649121	−	0.112431i	0.896655	+	0.442730i	$0.145990\pi$
$774$		0			0
$775$	436206.	+	755531.i	0.0260878	+	0.0451854i
$776$	−1.17869e7			−0.702661
$777$		0			0
$778$	7.56833e6			0.448282
$779$	−1.59738e7	−	2.76674e7i	−0.943115	−	1.63352i
$780$		0			0
$781$	13936.1	−	24138.0i	0.000817548	−	0.00141603i
$782$	5.55279e6	+	9.61771e6i	0.324709	+	0.562412i
$783$		0			0
$784$	4.51808e6	+	3.92260e6i	0.262521	+	0.227921i
$785$	−9.74175e6			−0.564239
$786$		0			0
$787$	−7.00503e6	+	1.21331e7i	−0.403156	+	0.698286i	−0.994105	−	0.108423i	$-0.965420\pi$
$787$	−7.00503e6	+	1.21331e7i	−0.403156	+	0.698286i	0.590949	+	0.806709i	$0.298753\pi$
$788$	−5.39604e6	+	9.34622e6i	−0.309571	+	0.536192i
$789$		0			0
$790$	−1.41908e7			−0.808980
$791$	5.58002e6	+	3.32817e7i	0.317099	+	1.89132i
$792$		0			0
$793$	−1.01793e7	−	1.76311e7i	−0.574825	−	0.995627i
$794$	−3.47926e6	+	6.02625e6i	−0.195855	+	0.339231i
$795$		0			0
$796$	−927034.	−	1.60567e6i	−0.0518577	−	0.0898202i
$797$	−4.73289e6			−0.263925			−0.131963	−	0.991255i	$-0.542128\pi$
$797$	−4.73289e6			−0.263925			−0.131963	+	0.991255i	$0.542128\pi$
$798$		0			0
$799$	−9.86107e6			−0.546459
$800$	837108.	+	1.44991e6i	0.0462441	+	0.0800972i
$801$		0			0
$802$	2.96456e6	−	5.13477e6i	0.162751	−	0.281893i
$803$	51674.2	+	89502.3i	0.00282804	+	0.00489830i
$804$		0			0
$805$	2.79018e7	+	1.04222e7i	1.51755	+	0.566853i
$806$	7.57318e6			0.410621
$807$		0			0
$808$	−3.58015e6	+	6.20101e6i	−0.192918	+	0.334144i
$809$	4.05446e6	−	7.02253e6i	0.217802	−	0.377244i	−0.736334	−	0.676618i	$-0.763445\pi$
$809$	4.05446e6	−	7.02253e6i	0.217802	−	0.377244i	0.954136	+	0.299375i	$0.0967780\pi$
$810$		0			0
$811$	−9.13444e6			−0.487674			−0.243837	−	0.969816i	$-0.578406\pi$
$811$	−9.13444e6			−0.487674			−0.243837	+	0.969816i	$0.578406\pi$
$812$	1.67262e7	+	6.24778e6i	0.890241	+	0.332534i
$813$		0			0
$814$	−120355.	−	208460.i	−0.00636651	−	0.0110271i
$815$	1.47719e7	−	2.55858e7i	0.779011	−	1.34929i
$816$		0			0
$817$	−1.41841e6	−	2.45675e6i	−0.0743439	−	0.128767i
$818$	1.18942e7			0.621517
$819$		0			0
$820$	−2.62085e7			−1.36115
$821$	850776.	+	1.47359e6i	0.0440511	+	0.0762988i	0.887210	−	0.461365i	$-0.152640\pi$
$821$	850776.	+	1.47359e6i	0.0440511	+	0.0762988i	−0.843159	+	0.537664i	$0.819307\pi$
$822$		0			0
$823$	1.24604e7	−	2.15820e7i	0.641256	−	1.11069i	−0.343897	−	0.939007i	$-0.611747\pi$
$823$	1.24604e7	−	2.15820e7i	0.641256	−	1.11069i	0.985153	−	0.171680i	$-0.0549196\pi$
$824$	6.35820e6	+	1.10127e7i	0.326224	+	0.565037i
$825$		0			0
$826$	212273.	+	1.26609e6i	0.0108254	+	0.0645674i
$827$	1.91232e7			0.972292			0.486146	−	0.873878i	$-0.338402\pi$
$827$	1.91232e7			0.972292			0.486146	+	0.873878i	$0.338402\pi$
$828$		0			0
$829$	1.10134e7	−	1.90757e7i	0.556588	−	0.964038i	−0.441190	−	0.897414i	$-0.645444\pi$
$829$	1.10134e7	−	1.90757e7i	0.556588	−	0.964038i	0.997778	−	0.0666248i	$-0.0212231\pi$
$830$	−7.68527e6	+	1.33113e7i	−0.387225	+	0.670694i
$831$		0			0
$832$	4.39531e6			0.220131
$833$	−3.28187e6	+	1.69397e7i	−0.163874	+	0.845849i
$834$		0			0
$835$	1.65051e7	+	2.85877e7i	0.819222	+	1.41893i
$836$	370472.	−	641676.i	0.0183332	−	0.0317541i
$837$		0			0
$838$	2.07664e6	+	3.59685e6i	0.102153	+	0.176935i
$839$	−4.28039e6			−0.209932			−0.104966	−	0.994476i	$-0.533473\pi$
$839$	−4.28039e6			−0.209932			−0.104966	+	0.994476i	$0.533473\pi$
$840$		0			0
$841$	1.12255e7			0.547286
$842$	1.53330e6	+	2.65575e6i	0.0745325	+	0.129094i
$843$		0			0
$844$	9.51869e6	−	1.64869e7i	0.459961	−	0.796676i
$845$	1.22772e7	+	2.12648e7i	0.591504	+	1.02452i
$846$		0			0
$847$	1.60762e7	−	1.32606e7i	0.769974	−	0.635117i
$848$	8.27933e6			0.395372
$849$		0			0
$850$	−397446.	+	688396.i	−0.0188682	+	0.0326807i
$851$	9.89342e6	−	1.71359e7i	0.468298	−	0.811116i
$852$		0			0
$853$	−1.72415e7			−0.811341			−0.405670	−	0.914019i	$-0.632962\pi$
$853$	−1.72415e7			−0.811341			−0.405670	+	0.914019i	$0.632962\pi$
$854$	−7.63519e6	−	2.85199e6i	−0.358241	−	0.133815i
$855$		0			0
$856$	−221342.	−	383376.i	−0.0103248	−	0.0178830i
$857$	1.04170e7	−	1.80427e7i	0.484495	−	0.839171i	−0.515346	−	0.856982i	$-0.672337\pi$
$857$	1.04170e7	−	1.80427e7i	0.484495	−	0.839171i	0.999841	+	0.0178115i	$0.00566989\pi$
$858$		0			0
$859$	7.91782e6	+	1.37141e7i	0.366119	+	0.634137i	0.988955	−	0.148215i	$-0.0473529\pi$
$859$	7.91782e6	+	1.37141e7i	0.366119	+	0.634137i	−0.622836	+	0.782353i	$0.714020\pi$
$860$	−2.32720e6			−0.107297
$861$		0			0
$862$	1.70757e7			0.782726
$863$	−7.96408e6	−	1.37942e7i	−0.364006	−	0.630477i	0.624610	−	0.780937i	$-0.285258\pi$
$863$	−7.96408e6	−	1.37942e7i	−0.364006	−	0.630477i	−0.988616	+	0.150460i	$0.951925\pi$
$864$		0			0
$865$	1.92447e7	−	3.33328e7i	0.874523	−	1.51472i
$866$	4.45368e6	+	7.71400e6i	0.201801	+	0.349530i
$867$		0			0
$868$	−7.57095e6	+	6.24494e6i	−0.341076	+	0.281338i
$869$	1.54149e6			0.0692455
$870$		0			0
$871$	−2.09191e7	+	3.62330e7i	−0.934325	+	1.61830i
$872$	1.28972e7	−	2.23386e7i	0.574387	−	0.994868i
$873$		0			0
$874$	−1.88159e7			−0.833195
$875$	−3.55747e6	−	2.12183e7i	−0.157080	−	0.936896i
$876$		0			0
$877$	−2.60367e6	−	4.50969e6i	−0.114311	−	0.197992i	0.803193	−	0.595718i	$-0.203133\pi$
$877$	−2.60367e6	−	4.50969e6i	−0.114311	−	0.197992i	−0.917504	+	0.397727i	$0.869799\pi$
$878$	3.16723e6	−	5.48581e6i	0.138658	−	0.240162i
$879$		0			0
$880$	−181026.	−	313546.i	−0.00788013	−	0.0136488i
$881$	932829.			0.0404913			0.0202457	−	0.999795i	$-0.493555\pi$
$881$	932829.			0.0404913			0.0202457	+	0.999795i	$0.493555\pi$
$882$		0			0
$883$	1.33789e7			0.577457			0.288728	−	0.957411i	$-0.406768\pi$
$883$	1.33789e7			0.577457			0.288728	+	0.957411i	$0.406768\pi$
$884$	−1.11681e7	−	1.93437e7i	−0.480670	−	0.832546i
$885$		0			0
$886$	−2.10601e6	+	3.64771e6i	−0.0901313	+	0.156112i
$887$	−3.48450e6	−	6.03533e6i	−0.148707	−	0.257568i	0.782043	−	0.623225i	$-0.214178\pi$
$887$	−3.48450e6	−	6.03533e6i	−0.148707	−	0.257568i	−0.930750	+	0.365657i	$0.880844\pi$
$888$		0			0
$889$	5.01064e6	+	2.98857e7i	0.212637	+	1.26826i
$890$	7.46004e6			0.315694
$891$		0			0
$892$	9.02216e6	−	1.56268e7i	0.379663	−	0.657596i
$893$	8.35369e6	−	1.44690e7i	0.350550	−	0.607170i
$894$		0			0
$895$	9.64753e6			0.402586
$896$	−1.76602e7	+	1.45671e7i	−0.734894	+	0.606182i
$897$		0			0
$898$	4.88788e6	+	8.46606e6i	0.202269	+	0.350341i
$899$	−8.72220e6	+	1.51073e7i	−0.359937	+	0.623429i
$900$		0			0
$901$	1.19380e7	+	2.06772e7i	0.489913	+	0.848554i
$902$	−879496.			−0.0359929
$903$		0			0
$904$	−4.03804e7			−1.64342
$905$	4.33353e6	+	7.50590e6i	0.175882	+	0.304636i
$906$		0			0
$907$	1.88282e7	−	3.26113e7i	0.759959	−	1.31629i	−0.182913	−	0.983129i	$-0.558553\pi$
$907$	1.88282e7	−	3.26113e7i	0.759959	−	1.31629i	0.942871	−	0.333158i	$-0.108114\pi$
$908$	6.65113e6	+	1.15201e7i	0.267720	+	0.463705i
$909$		0			0
$910$	1.73362e7	+	6.47565e6i	0.693987	+	0.259227i
$911$	3.09942e7			1.23733			0.618663	−	0.785657i	$-0.287675\pi$
$911$	3.09942e7			1.23733			0.618663	+	0.785657i	$0.287675\pi$
$912$		0			0
$913$	834823.	−	1.44596e6i	0.0331450	−	0.0574087i
$914$	3.46110e6	−	5.99479e6i	0.137040	−	0.237361i
$915$		0			0
$916$	5.71002e6			0.224853
$917$	−1.57304e7	+	1.29753e7i	−0.617757	+	0.509560i
$918$		0			0
$919$	−358007.	−	620086.i	−0.0139831	−	0.0242194i	0.858949	−	0.512061i	$-0.171118\pi$
$919$	−358007.	−	620086.i	−0.0139831	−	0.0242194i	−0.872932	+	0.487841i	$0.837784\pi$
$920$	−1.78201e7	+	3.08652e7i	−0.694128	+	1.20226i
$921$		0			0
$922$	9.11394e6	+	1.57858e7i	0.353085	+	0.611561i
$923$	1.42357e6			0.0550014
$924$		0			0
$925$	1.41626e6			0.0544238
$926$	−6.05193e6	−	1.04823e7i	−0.231935	−	0.401723i
$927$		0			0
$928$	−1.67385e7	+	2.89919e7i	−0.638037	+	1.10511i
$929$	2.08815e7	+	3.61678e7i	0.793820	+	1.37494i	0.923586	+	0.383392i	$0.125244\pi$
$929$	2.08815e7	+	3.61678e7i	0.793820	+	1.37494i	−0.129766	+	0.991545i	$0.541423\pi$
$930$		0			0
$931$	−2.20751e7	−	1.91657e7i	−0.834698	−	0.724686i
$932$	−1.51110e7			−0.569840
$933$		0			0
$934$	−337813.	+	585109.i	−0.0126709	+	0.0219467i
$935$	522043.	−	904204.i	0.0195289	−	0.0338250i
$936$		0			0
$937$	−2.17917e7			−0.810854			−0.405427	−	0.914127i	$-0.632877\pi$
$937$	−2.17917e7			−0.810854			−0.405427	+	0.914127i	$0.632877\pi$
$938$	2.76960e6	+	1.65191e7i	0.102780	+	0.613027i
$939$		0			0
$940$	−6.85302e6	−	1.18698e7i	−0.252966	−	0.438150i
$941$	−1.07609e6	+	1.86385e6i	−0.0396164	+	0.0686177i	−0.885154	−	0.465299i	$-0.845947\pi$
$941$	−1.07609e6	+	1.86385e6i	−0.0396164	+	0.0686177i	0.845537	+	0.533916i	$0.179280\pi$
$942$		0			0
$943$	−3.61483e7	−	6.26106e7i	−1.32376	−	2.29281i
$944$	1.28275e6			0.0468504
$945$		0			0
$946$	−78095.5			−0.00283725
$947$	−1.32125e7	−	2.28847e7i	−0.478750	−	0.829220i	0.520953	−	0.853585i	$-0.325577\pi$
$947$	−1.32125e7	−	2.28847e7i	−0.478750	−	0.829220i	−0.999703	+	0.0243656i	$0.992243\pi$
$948$		0			0
$949$	−2.63925e6	+	4.57132e6i	−0.0951295	+	0.164769i
$950$	−673383.	−	1.16633e6i	−0.0242077	−	0.0419289i
$951$		0			0
$952$	−1.93415e7	−	7.22466e6i	−0.691667	−	0.258360i
$953$	−9.07051e6			−0.323519			−0.161759	−	0.986830i	$-0.551717\pi$
$953$	−9.07051e6			−0.323519			−0.161759	+	0.986830i	$0.551717\pi$
$954$		0			0
$955$	−1.12623e7	+	1.95068e7i	−0.399593	+	0.692115i
$956$	−1.14598e7	+	1.98489e7i	−0.405538	+	0.702412i
$957$		0			0
$958$	−110892.			−0.00390380
$959$	2.08337e7	+	7.78208e6i	0.731511	+	0.273243i
$960$		0			0
$961$	9.52032e6	+	1.64897e7i	0.332539	+	0.575975i
$962$	6.14709e6	−	1.06471e7i	0.214157	−	0.370930i
$963$		0			0
$964$	1.13930e7	+	1.97332e7i	0.394861	+	0.683920i
$965$	−2.89674e7			−1.00136
$966$		0			0
$967$	1.80108e7			0.619395			0.309698	−	0.950835i	$-0.399772\pi$
$967$	1.80108e7			0.619395			0.309698	+	0.950835i	$0.399772\pi$
$968$	1.24682e7	+	2.15956e7i	0.427677	+	0.740758i
$969$		0			0
$970$	6.09389e6	−	1.05549e7i	0.207953	−	0.360185i
$971$	−2.33815e7	−	4.04980e7i	−0.795838	−	1.37843i	−0.922305	−	0.386462i	$-0.873697\pi$
$971$	−2.33815e7	−	4.04980e7i	−0.795838	−	1.37843i	0.126467	−	0.991971i	$-0.459636\pi$
$972$		0			0
$973$	−4.51509e6	−	2.69300e7i	−0.152892	−	0.911914i
$974$	9.09561e6			0.307209
$975$		0			0
$976$	−4.07204e6	+	7.05298e6i	−0.136832	+	0.237000i
$977$	2.16217e6	−	3.74498e6i	0.0724690	−	0.125520i	−0.827514	−	0.561445i	$-0.810245\pi$
$977$	2.16217e6	−	3.74498e6i	0.0724690	−	0.125520i	0.899983	+	0.435925i	$0.143579\pi$
$978$		0			0
$979$	−810357.			−0.0270221
$980$	−2.26710e7	+	7.82195e6i	−0.754061	+	0.260165i
$981$		0			0
$982$	2.72013e6	+	4.71140e6i	0.0900142	+	0.155909i
$983$	1.04367e7	−	1.80768e7i	0.344491	−	0.596676i	−0.640770	−	0.767733i	$-0.721385\pi$
$983$	1.04367e7	−	1.80768e7i	0.344491	−	0.596676i	0.985261	+	0.171057i	$0.0547181\pi$
$984$		0			0
$985$	−1.28828e7	−	2.23137e7i	−0.423077	−	0.732792i
$986$	−1.58943e7			−0.520655
$987$		0			0
$988$	3.78436e7			1.23339
$989$	−3.20981e6	−	5.55956e6i	−0.104349	−	0.180738i
$990$		0			0
$991$	−2.06104e7	+	3.56983e7i	−0.666658	+	1.15469i	0.312175	+	0.950025i	$0.398942\pi$
$991$	−2.06104e7	+	3.56983e7i	−0.666658	+	1.15469i	−0.978833	+	0.204661i	$0.934391\pi$
$992$	−9.20049e6	−	1.59357e7i	−0.296846	−	0.514153i
$993$		0			0
$994$	439649.	−	362647.i	0.0141137	−	0.0116418i
$995$	4.42650e6			0.141743
$996$		0			0
$997$	2.67307e7	−	4.62990e7i	0.851674	−	1.47514i	−0.0280235	−	0.999607i	$-0.508921\pi$
$997$	2.67307e7	−	4.62990e7i	0.851674	−	1.47514i	0.879697	−	0.475535i	$-0.157745\pi$
$998$	−4.35580e6	+	7.54447e6i	−0.138434	+	0.239774i
$999$		0			0

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.e.e.46.3		8
3.2	odd	2		21.6.e.c.4.2	✓	8
7.2	even	3	inner	63.6.e.e.37.3		8
7.3	odd	6		441.6.a.v.1.2		4
7.4	even	3		441.6.a.w.1.2		4
12.11	even	2		336.6.q.j.193.1		8
21.2	odd	6		21.6.e.c.16.2	yes	8
21.5	even	6		147.6.e.o.79.2		8
21.11	odd	6		147.6.a.m.1.3		4
21.17	even	6		147.6.a.l.1.3		4
21.20	even	2		147.6.e.o.67.2		8
84.23	even	6		336.6.q.j.289.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.c.4.2	✓	8	3.2	odd	2
21.6.e.c.16.2	yes	8	21.2	odd	6
63.6.e.e.37.3		8	7.2	even	3	inner
63.6.e.e.46.3		8	1.1	even	1	trivial
147.6.a.l.1.3		4	21.17	even	6
147.6.a.m.1.3		4	21.11	odd	6
147.6.e.o.67.2		8	21.20	even	2
147.6.e.o.79.2		8	21.5	even	6
336.6.q.j.193.1		8	12.11	even	2
336.6.q.j.289.1		8	84.23	even	6
441.6.a.v.1.2		4	7.3	odd	6
441.6.a.w.1.2		4	7.4	even	3

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

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

Label	63.6.e.e.46.3

Level	$63$
Weight	$6$
Character	63.46
Analytic conductor	$10.104$
Analytic rank	$0$
Dimension	$8$
Inner twists	$2$