LMFDB - Embedded newform 196.6.d.b.195.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,6,Mod(195,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("196.195");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	196.d (of order $2$, degree $1$, 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:	$31.4352286833$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			195.2
Character	$\chi$	$=$	196.195
Dual form			196.6.d.b.195.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.63257 - 0.523620i) q^{2} +19.4483 q^{3} +(31.4516 + 5.89865i) q^{4} +50.4561i q^{5} +(-109.544 - 10.1835i) q^{6} +(-174.065 - 49.6932i) q^{8} +135.237 q^{9} +O(q^{10})$	\(q+(-5.63257 - 0.523620i) q^{2} +19.4483 q^{3} +(31.4516 + 5.89865i) q^{4} +50.4561i q^{5} +(-109.544 - 10.1835i) q^{6} +(-174.065 - 49.6932i) q^{8} +135.237 q^{9} +(26.4198 - 284.197i) q^{10} -282.201i q^{11} +(611.682 + 114.719i) q^{12} +783.423i q^{13} +981.286i q^{15} +(954.412 + 371.044i) q^{16} +459.209i q^{17} +(-761.734 - 70.8129i) q^{18} -2628.74 q^{19} +(-297.622 + 1586.93i) q^{20} +(-147.766 + 1589.52i) q^{22} +3088.12i q^{23} +(-3385.27 - 966.450i) q^{24} +579.186 q^{25} +(410.216 - 4412.68i) q^{26} -2095.80 q^{27} +2371.45 q^{29} +(513.820 - 5527.16i) q^{30} -1876.42 q^{31} +(-5181.50 - 2589.68i) q^{32} -5488.34i q^{33} +(240.451 - 2586.53i) q^{34} +(4253.44 + 797.717i) q^{36} +3591.25 q^{37} +(14806.6 + 1376.46i) q^{38} +15236.3i q^{39} +(2507.32 - 8782.63i) q^{40} +12855.3i q^{41} -20317.1i q^{43} +(1664.60 - 8875.68i) q^{44} +6823.55i q^{45} +(1617.00 - 17394.0i) q^{46} -10635.7 q^{47} +(18561.7 + 7216.19i) q^{48} +(-3262.30 - 303.273i) q^{50} +8930.84i q^{51} +(-4621.14 + 24640.0i) q^{52} -36234.1 q^{53} +(11804.8 + 1097.40i) q^{54} +14238.7 q^{55} -51124.6 q^{57} +(-13357.3 - 1241.74i) q^{58} +3939.62 q^{59} +(-5788.26 + 30863.1i) q^{60} +23290.0i q^{61} +(10569.0 + 982.528i) q^{62} +(27829.2 + 17299.7i) q^{64} -39528.5 q^{65} +(-2873.80 + 30913.4i) q^{66} +1456.93i q^{67} +(-2708.71 + 14442.9i) q^{68} +60058.7i q^{69} +72920.6i q^{71} +(-23540.1 - 6720.38i) q^{72} +22100.1i q^{73} +(-20228.0 - 1880.45i) q^{74} +11264.2 q^{75} +(-82678.2 - 15506.0i) q^{76} +(7978.01 - 85819.3i) q^{78} -2413.89i q^{79} +(-18721.4 + 48155.9i) q^{80} -73622.5 q^{81} +(6731.27 - 72408.2i) q^{82} -22323.5 q^{83} -23169.9 q^{85} +(-10638.4 + 114438. i) q^{86} +46120.7 q^{87} +(-14023.5 + 49121.3i) q^{88} +63771.6i q^{89} +(3572.94 - 38434.1i) q^{90} +(-18215.7 + 97126.4i) q^{92} -36493.2 q^{93} +(59906.3 + 5569.06i) q^{94} -132636. i q^{95} +(-100772. - 50364.9i) q^{96} +70890.8i q^{97} -38164.1i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 24 q^{4} - 72 q^{8} + 2272 q^{9}+O(q^{10}) $ 36 * q + 24 * q^4 - 72 * q^8 + 2272 * q^9	$ 36 q + 24 q^{4} - 72 q^{8} + 2272 q^{9} - 1328 q^{16} + 3560 q^{18} + 13768 q^{22} - 15224 q^{25} + 176 q^{29} + 11672 q^{30} - 2320 q^{32} - 27920 q^{36} - 23444 q^{37} - 18192 q^{44} + 2080 q^{46} - 51168 q^{50} + 66972 q^{53} - 1668 q^{57} + 96872 q^{58} - 28624 q^{60} + 44544 q^{64} - 30712 q^{65} - 296128 q^{72} - 34304 q^{74} + 127704 q^{78} - 320804 q^{81} + 71212 q^{85} + 504992 q^{86} - 110536 q^{88} - 190176 q^{92} + 330324 q^{93}+O(q^{100}) $ 36 * q + 24 * q^4 - 72 * q^8 + 2272 * q^9 - 1328 * q^16 + 3560 * q^18 + 13768 * q^22 - 15224 * q^25 + 176 * q^29 + 11672 * q^30 - 2320 * q^32 - 27920 * q^36 - 23444 * q^37 - 18192 * q^44 + 2080 * q^46 - 51168 * q^50 + 66972 * q^53 - 1668 * q^57 + 96872 * q^58 - 28624 * q^60 + 44544 * q^64 - 30712 * q^65 - 296128 * q^72 - 34304 * q^74 + 127704 * q^78 - 320804 * q^81 + 71212 * q^85 + 504992 * q^86 - 110536 * q^88 - 190176 * q^92 + 330324 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−5.63257	−	0.523620i	−0.995707	−	0.0925637i
$2$	−5.63257	−	0.523620i	−0.995707	−	0.0925637i
$3$	19.4483			1.24761			0.623805	−	0.781580i	$-0.285586\pi$
$3$	19.4483			1.24761			0.623805	+	0.781580i	$0.285586\pi$
$4$	31.4516	+	5.89865i	0.982864	+	0.184333i
$5$			50.4561i			0.902585i	0.892376	+	0.451293i	$0.149037\pi$
$5$			50.4561i			0.902585i	−0.892376	+	0.451293i	$0.850963\pi$
$6$	−109.544	−	10.1835i	−1.24225	−	0.115483i
$7$		0			0
$7$		0			0
$8$	−174.065	−	49.6932i	−0.961582	−	0.274519i
$9$	135.237			0.556532
$10$	26.4198	−	284.197i	0.0835467	−	0.898710i
$11$		−	282.201i		−	0.703196i	−0.936151	−	0.351598i	$-0.885638\pi$
$11$		−	282.201i		−	0.703196i	0.936151	−	0.351598i	$-0.114362\pi$
$12$	611.682	+	114.719i	1.22623	+	0.229975i
$13$			783.423i			1.28570i	0.765994	+	0.642848i	$0.222247\pi$
$13$			783.423i			1.28570i	−0.765994	+	0.642848i	$0.777753\pi$
$14$		0			0
$15$			981.286i			1.12608i
$16$	954.412	+	371.044i	0.932043	+	0.362348i
$17$			459.209i			0.385379i	0.981260	+	0.192689i	$0.0617210\pi$
$17$			459.209i			0.385379i	−0.981260	+	0.192689i	$0.938279\pi$
$18$	−761.734	−	70.8129i	−0.554143	−	0.0515147i
$19$	−2628.74			−1.67057			−0.835283	−	0.549820i	$-0.814696\pi$
$19$	−2628.74			−1.67057			−0.835283	+	0.549820i	$0.814696\pi$
$20$	−297.622	+	1586.93i	−0.166376	+	0.887119i
$21$		0			0
$22$	−147.766	+	1589.52i	−0.0650905	+	0.700177i
$23$			3088.12i			1.21724i	0.793464	+	0.608618i	$0.208276\pi$
$23$			3088.12i			1.21724i	−0.793464	+	0.608618i	$0.791724\pi$
$24$	−3385.27	−	966.450i	−1.19968	−	0.342493i
$25$	579.186			0.185339
$26$	410.216	−	4412.68i	0.119009	−	1.28018i
$27$	−2095.80			−0.553275
$28$		0			0
$29$	2371.45			0.523623			0.261811	−	0.965119i	$-0.415680\pi$
$29$	2371.45			0.523623			0.261811	+	0.965119i	$0.415680\pi$
$30$	513.820	−	5527.16i	0.104234	−	1.12124i
$31$	−1876.42			−0.350691			−0.175346	−	0.984507i	$-0.556104\pi$
$31$	−1876.42			−0.350691			−0.175346	+	0.984507i	$0.556104\pi$
$32$	−5181.50	−	2589.68i	−0.894501	−	0.447066i
$33$		−	5488.34i		−	0.877315i
$34$	240.451	−	2586.53i	0.0356721	−	0.383724i
$35$		0			0
$36$	4253.44	+	797.717i	0.546996	+	0.102587i
$37$	3591.25			0.431262			0.215631	−	0.976475i	$-0.430819\pi$
$37$	3591.25			0.431262			0.215631	+	0.976475i	$0.430819\pi$
$38$	14806.6	+	1376.46i	1.66339	+	0.154634i
$39$			15236.3i			1.60405i
$40$	2507.32	−	8782.63i	0.247777	−	0.867910i
$41$			12855.3i			1.19432i	0.802121	+	0.597162i	$0.203705\pi$
$41$			12855.3i			1.19432i	−0.802121	+	0.597162i	$0.796295\pi$
$42$		0			0
$43$		−	20317.1i		−	1.67568i	−0.545915	−	0.837841i	$-0.683818\pi$
$43$		−	20317.1i		−	1.67568i	0.545915	−	0.837841i	$-0.316182\pi$
$44$	1664.60	−	8875.68i	0.129622	−	0.691146i
$45$			6823.55i			0.502318i
$46$	1617.00	−	17394.0i	0.112672	−	1.21201i
$47$	−10635.7			−0.702298			−0.351149	−	0.936320i	$-0.614209\pi$
$47$	−10635.7			−0.702298			−0.351149	+	0.936320i	$0.614209\pi$
$48$	18561.7	+	7216.19i	1.16283	+	0.452069i
$49$		0			0
$50$	−3262.30	−	303.273i	−0.184544	−	0.0171557i
$51$			8930.84i			0.480803i
$52$	−4621.14	+	24640.0i	−0.236996	+	1.26366i
$53$	−36234.1			−1.77185			−0.885926	−	0.463826i	$-0.846476\pi$
$53$	−36234.1			−1.77185			−0.885926	+	0.463826i	$0.846476\pi$
$54$	11804.8	+	1097.40i	0.550900	+	0.0512132i
$55$	14238.7			0.634695
$56$		0			0
$57$	−51124.6			−2.08422
$58$	−13357.3	−	1241.74i	−0.521375	−	0.0484685i
$59$	3939.62			0.147341			0.0736706	−	0.997283i	$-0.476529\pi$
$59$	3939.62			0.147341			0.0736706	+	0.997283i	$0.476529\pi$
$60$	−5788.26	+	30863.1i	−0.207572	+	1.10678i
$61$			23290.0i			0.801393i	0.916211	+	0.400697i	$0.131232\pi$
$61$			23290.0i			0.801393i	−0.916211	+	0.400697i	$0.868768\pi$
$62$	10569.0	+	982.528i	0.349186	+	0.0324613i
$63$		0			0
$64$	27829.2	+	17299.7i	0.849279	+	0.527945i
$65$	−39528.5			−1.16045
$66$	−2873.80	+	30913.4i	−0.0812076	+	0.873549i
$67$			1456.93i			0.0396507i	0.999803	+	0.0198253i	$0.00631101\pi$
$67$			1456.93i			0.0396507i	−0.999803	+	0.0198253i	$0.993689\pi$
$68$	−2708.71	+	14442.9i	−0.0710379	+	0.378775i
$69$			60058.7i			1.51864i
$70$		0			0
$71$			72920.6i			1.71674i	0.513033	+	0.858369i	$0.328522\pi$
$71$			72920.6i			1.71674i	−0.513033	+	0.858369i	$0.671478\pi$
$72$	−23540.1	−	6720.38i	−0.535151	−	0.152779i
$73$			22100.1i			0.485385i	0.970103	+	0.242693i	$0.0780307\pi$
$73$			22100.1i			0.485385i	−0.970103	+	0.242693i	$0.921969\pi$
$74$	−20228.0	−	1880.45i	−0.429411	−	0.0399192i
$75$	11264.2			0.231232
$76$	−82678.2	−	15506.0i	−1.64194	−	0.307940i
$77$		0			0
$78$	7978.01	−	85819.3i	0.148477	−	1.59716i
$79$		−	2413.89i		−	0.0435160i	−0.999763	−	0.0217580i	$-0.993074\pi$
$79$		−	2413.89i		−	0.0435160i	0.999763	−	0.0217580i	$-0.00692634\pi$
$80$	−18721.4	+	48155.9i	−0.327050	+	0.841248i
$81$	−73622.5			−1.24680
$82$	6731.27	−	72408.2i	0.110551	−	1.18920i
$83$	−22323.5			−0.355686			−0.177843	−	0.984059i	$-0.556912\pi$
$83$	−22323.5			−0.355686			−0.177843	+	0.984059i	$0.556912\pi$
$84$		0			0
$85$	−23169.9			−0.347837
$86$	−10638.4	+	114438.i	−0.155107	+	1.66849i
$87$	46120.7			0.653277
$88$	−14023.5	+	49121.3i	−0.193041	+	0.676181i
$89$			63771.6i			0.853399i	0.904394	+	0.426699i	$0.140324\pi$
$89$			63771.6i			0.853399i	−0.904394	+	0.426699i	$0.859676\pi$
$90$	3572.94	−	38434.1i	0.0464964	−	0.500161i
$91$		0			0
$92$	−18215.7	+	97126.4i	−0.224376	+	1.19638i
$93$	−36493.2			−0.437526
$94$	59906.3	+	5569.06i	0.699283	+	0.0650073i
$95$		−	132636.i		−	1.50783i
$96$	−100772.	−	50364.9i	−1.11599	−	0.557764i
$97$			70890.8i			0.764998i	0.923956	+	0.382499i	$0.124936\pi$
$97$			70890.8i			0.764998i	−0.923956	+	0.382499i	$0.875064\pi$
$98$		0			0
$99$		−	38164.1i		−	0.391352i
$100$	18216.3	+	3416.41i	0.182163	+	0.0341641i
$101$			4209.85i			0.0410642i	0.999789	+	0.0205321i	$0.00653603\pi$
$101$			4209.85i			0.0410642i	−0.999789	+	0.0205321i	$0.993464\pi$
$102$	4676.36	−	50303.6i	0.0445049	−	0.478739i
$103$	129646.			1.20411			0.602056	−	0.798454i	$-0.294348\pi$
$103$	129646.			1.20411			0.602056	+	0.798454i	$0.294348\pi$
$104$	38930.8	−	136366.i	0.352948	−	1.23630i
$105$		0			0
$106$	204091.	+	18972.9i	1.76425	+	0.164009i
$107$		−	107198.i		−	0.905163i	−0.891723	−	0.452582i	$-0.850503\pi$
$107$		−	107198.i		−	0.905163i	0.891723	−	0.452582i	$-0.149497\pi$
$108$	−65916.4	−	12362.4i	−0.543794	−	0.101987i
$109$	164739.			1.32810			0.664051	−	0.747687i	$-0.268836\pi$
$109$	164739.			1.32810			0.664051	+	0.747687i	$0.268836\pi$
$110$	−80200.7	−	7455.69i	−0.631970	−	0.0587497i
$111$	69843.8			0.538047
$112$		0			0
$113$	−150634.			−1.10975			−0.554877	−	0.831932i	$-0.687235\pi$
$113$	−150634.			−1.10975			−0.554877	+	0.831932i	$0.687235\pi$
$114$	287963.	+	26769.8i	2.07527	+	0.192923i
$115$	−155814.			−1.09866
$116$	74585.9	+	13988.3i	0.514650	+	0.0965208i
$117$			105948.i			0.715531i
$118$	−22190.2	−	2062.86i	−0.146709	−	0.0136385i
$119$		0			0
$120$	48763.3	−	170807.i	0.309129	−	1.08281i
$121$	81413.6			0.505515
$122$	12195.1	−	131183.i	0.0741799	−	0.797953i
$123$			250014.i			1.49005i
$124$	−59016.4	−	11068.3i	−0.344682	−	0.0646439i
$125$			186899.i			1.06987i
$126$		0			0
$127$			326.767i			0.00179775i	1.00000		0.000898875i	$0.000286121\pi$
$127$			326.767i			0.00179775i	−1.00000		0.000898875i	$0.999714\pi$
$128$	−147691.	−	112014.i	−0.796764	−	0.604290i
$129$		−	395134.i		−	2.09060i
$130$	222647.	+	20697.9i	1.15547	+	0.107416i
$131$	94890.0			0.483106			0.241553	−	0.970388i	$-0.422343\pi$
$131$	94890.0			0.483106			0.241553	+	0.970388i	$0.422343\pi$
$132$	32373.7	−	172617.i	0.161718	−	0.862282i
$133$		0			0
$134$	762.875	−	8206.23i	0.00367021	−	0.0394804i
$135$		−	105746.i		−	0.499378i
$136$	22819.6	−	79932.1i	0.105794	−	0.370573i
$137$	−167868.			−0.764128			−0.382064	−	0.924136i	$-0.624787\pi$
$137$	−167868.			−0.764128			−0.382064	+	0.924136i	$0.624787\pi$
$138$	31447.9	−	338285.i	0.140571	−	1.51212i
$139$	65338.5			0.286835			0.143418	−	0.989662i	$-0.454191\pi$
$139$	65338.5			0.286835			0.143418	+	0.989662i	$0.454191\pi$
$140$		0			0
$141$	−206846.			−0.876194
$142$	38182.6	−	410730.i	0.158908	−	1.70937i
$143$	221083.			0.904096
$144$	129072.	+	50179.0i	0.518712	+	0.201658i
$145$			119654.i			0.472614i
$146$	11572.0	−	124480.i	0.0449291	−	0.483301i
$147$		0			0
$148$	112951.	+	21183.5i	0.423872	+	0.0794957i
$149$	57741.3			0.213069			0.106535	−	0.994309i	$-0.466024\pi$
$149$	57741.3			0.213069			0.106535	+	0.994309i	$0.466024\pi$
$150$	−63446.3	−	5898.15i	−0.230239	−	0.0214036i
$151$		−	356148.i		−	1.27112i	−0.772050	−	0.635562i	$-0.780769\pi$
$151$		−	356148.i		−	1.27112i	0.772050	−	0.635562i	$-0.219231\pi$
$152$	457571.	+	130631.i	1.60639	+	0.458602i
$153$			62102.2i			0.214476i
$154$		0			0
$155$		−	94676.6i		−	0.316529i
$156$	−89873.4	+	479206.i	−0.295678	+	1.57656i
$157$		−	404432.i		−	1.30947i	−0.755857	−	0.654736i	$-0.772780\pi$
$157$		−	404432.i		−	1.30947i	0.755857	−	0.654736i	$-0.227220\pi$
$158$	−1263.96	+	13596.4i	−0.00402801	+	0.0433292i
$159$	−704692.			−2.21058
$160$	130665.	−	261438.i	0.403515	−	0.807364i
$161$		0			0
$162$	414684.	+	38550.2i	1.24145	+	0.115409i
$163$			595436.i			1.75536i	0.479247	+	0.877680i	$0.340910\pi$
$163$			595436.i			1.75536i	−0.479247	+	0.877680i	$0.659090\pi$
$164$	−75828.7	+	404320.i	−0.220153	+	1.17386i
$165$	276920.			0.791852
$166$	125739.	+	11689.0i	0.354159	+	0.0329236i
$167$	−103432.			−0.286989			−0.143494	−	0.989651i	$-0.545834\pi$
$167$	−103432.			−0.286989			−0.143494	+	0.989651i	$0.545834\pi$
$168$		0			0
$169$	−242459.			−0.653013
$170$	130506.	+	12132.2i	0.346344	+	0.0321971i
$171$	−355504.			−0.929724
$172$	119844.	−	639007.i	0.308883	−	1.64697i
$173$			446448.i			1.13411i	0.823680	+	0.567055i	$0.191917\pi$
$173$			446448.i			1.13411i	−0.823680	+	0.567055i	$0.808083\pi$
$174$	−259778.	−	24149.7i	−0.650473	−	0.0604698i
$175$		0			0
$176$	104709.	−	269336.i	0.254802	−	0.655409i
$177$	76619.0			0.183825
$178$	33392.0	−	359198.i	0.0789938	−	0.849735i
$179$			418841.i			0.977048i	0.872550	+	0.488524i	$0.162465\pi$
$179$			418841.i			0.977048i	−0.872550	+	0.488524i	$0.837535\pi$
$180$	−40249.7	+	214612.i	−0.0925936	+	0.493710i
$181$		−	517374.i		−	1.17384i	−0.809645	−	0.586919i	$-0.800341\pi$
$181$		−	517374.i		−	1.17384i	0.809645	−	0.586919i	$-0.199659\pi$
$182$		0			0
$183$			452952.i			0.999827i
$184$	153459.	−	537533.i	0.334154	−	1.17047i
$185$			181200.i			0.389251i
$186$	205550.	+	19108.5i	0.435648	+	0.0404991i
$187$	129589.			0.270997
$188$	−334510.	−	62736.2i	−0.690263	−	0.129456i
$189$		0			0
$190$	−69450.7	+	747081.i	−0.139570	+	1.50136i
$191$		−	45067.0i		−	0.0893872i	−0.999001	−	0.0446936i	$-0.985769\pi$
$191$		−	45067.0i		−	0.0893872i	0.999001	−	0.0446936i	$-0.0142312\pi$
$192$	541231.	+	336450.i	1.05957	+	0.658669i
$193$	45264.7			0.0874714			0.0437357	−	0.999043i	$-0.486074\pi$
$193$	45264.7			0.0874714			0.0437357	+	0.999043i	$0.486074\pi$
$194$	37119.8	−	399297.i	0.0708111	−	0.761714i
$195$	−768762.			−1.44779
$196$		0			0
$197$	328341.			0.602780			0.301390	−	0.953501i	$-0.402549\pi$
$197$	328341.			0.602780			0.301390	+	0.953501i	$0.402549\pi$
$198$	−19983.5	+	214962.i	−0.0362250	+	0.389671i
$199$	−111669.			−0.199894			−0.0999471	−	0.994993i	$-0.531867\pi$
$199$	−111669.			−0.199894			−0.0999471	+	0.994993i	$0.531867\pi$
$200$	−100816.	−	28781.6i	−0.178219	−	0.0508792i
$201$			28334.8i			0.0494686i
$202$	2204.36	−	23712.3i	0.00380105	−	0.0408879i
$203$		0			0
$204$	−52679.9	+	280890.i	−0.0886277	+	0.472564i
$205$	−648627.			−1.07798
$206$	−730241.	−	67885.3i	−1.19894	−	0.111457i
$207$			417629.i			0.677431i
$208$	−290685.	+	747709.i	−0.465869	+	1.19832i
$209$			741833.i			1.17474i
$210$		0			0
$211$		−	868214.i		−	1.34252i	−0.741222	−	0.671260i	$-0.765753\pi$
$211$		−	868214.i		−	1.34252i	0.741222	−	0.671260i	$-0.234247\pi$
$212$	−1.13962e6	−	213732.i	−1.74149	−	0.326610i
$213$			1.41818e6i			2.14182i
$214$	−56130.9	+	603799.i	−0.0837853	+	0.901277i
$215$	1.02512e6			1.51245
$216$	364806.	+	104147.i	0.532019	+	0.151884i
$217$		0			0
$218$	−927906.	−	86260.8i	−1.32240	−	0.122934i
$219$			429809.i			0.605572i
$220$	447832.	+	83989.3i	0.623819	+	0.116995i
$221$	−359755.			−0.495480
$222$	−393400.	−	36571.6i	−0.535737	−	0.0498037i
$223$	779832.			1.05012			0.525060	−	0.851065i	$-0.324043\pi$
$223$	779832.			1.05012			0.525060	+	0.851065i	$0.324043\pi$
$224$		0			0
$225$	78327.6			0.103147
$226$	848456.	+	78874.9i	1.10499	+	0.102723i
$227$	830660.			1.06994			0.534969	−	0.844872i	$-0.320323\pi$
$227$	830660.			1.06994			0.534969	+	0.844872i	$0.320323\pi$
$228$	−1.60795e6	−	301566.i	−2.04850	−	0.384189i
$229$		−	585784.i		−	0.738157i	−0.929398	−	0.369078i	$-0.879673\pi$
$229$		−	585784.i		−	0.738157i	0.929398	−	0.369078i	$-0.120327\pi$
$230$	877635.	+	81587.4i	1.09394	+	0.101696i
$231$		0			0
$232$	−412786.	−	117845.i	−0.503506	−	0.143744i
$233$	46758.4			0.0564247			0.0282124	−	0.999602i	$-0.491019\pi$
$233$	46758.4			0.0564247			0.0282124	+	0.999602i	$0.491019\pi$
$234$	55476.5	−	596760.i	0.0662322	−	0.712459i
$235$		−	536635.i		−	0.633884i
$236$	123908.	+	23238.4i	0.144816	+	0.0271598i
$237$		−	46946.1i		−	0.0542911i
$238$		0			0
$239$			74738.8i			0.0846353i	0.999104	+	0.0423177i	$0.0134742\pi$
$239$			74738.8i			0.0846353i	−0.999104	+	0.0423177i	$0.986526\pi$
$240$	−364100.	+	936551.i	−0.408031	+	1.04955i
$241$		−	520886.i		−	0.577697i	−0.957375	−	0.288849i	$-0.906728\pi$
$241$		−	520886.i		−	0.577697i	0.957375	−	0.288849i	$-0.0932724\pi$
$242$	−458568.	−	42629.8i	−0.503344	−	0.0467923i
$243$	−922555.			−1.00225
$244$	−137380.	+	732510.i	−0.147723	+	0.787661i
$245$		0			0
$246$	130912.	−	1.40822e6i	0.137925	−	1.48365i
$247$		−	2.05942e6i		−	2.14784i
$248$	326618.	+	93245.2i	0.337218	+	0.0962714i
$249$	−434155.			−0.443758
$250$	97863.8	−	1.05272e6i	0.0990312	−	1.06528i
$251$	1.22290e6			1.22520			0.612598	−	0.790394i	$-0.290124\pi$
$251$	1.22290e6			1.22520			0.612598	+	0.790394i	$0.290124\pi$
$252$		0			0
$253$	871470.			0.855955
$254$	171.102	−	1840.54i	0.000166407	−	0.00179003i
$255$	−450615.			−0.433966
$256$	773228.	+	708258.i	0.737408	+	0.675447i
$257$		−	1.12277e6i		−	1.06038i	−0.847880	−	0.530188i	$-0.822121\pi$
$257$		−	1.12277e6i		−	1.06038i	0.847880	−	0.530188i	$-0.177879\pi$
$258$	−206900.	+	2.22562e6i	−0.193513	+	2.08162i
$259$		0			0
$260$	−1.24323e6	−	233164.i	−1.14056	−	0.213909i
$261$	320708.			0.291413
$262$	−534474.	−	49686.3i	−0.481032	−	0.0447181i
$263$		−	1.51750e6i		−	1.35282i	−0.736525	−	0.676411i	$-0.763535\pi$
$263$		−	1.51750e6i		−	1.35282i	0.736525	−	0.676411i	$-0.236465\pi$
$264$	−272733.	+	955326.i	−0.240840	+	0.843610i
$265$		−	1.82823e6i		−	1.59925i
$266$		0			0
$267$			1.24025e6i			1.06471i
$268$	−8593.89	+	45822.7i	−0.00730891	+	0.0389712i
$269$			679637.i			0.572660i	0.958131	+	0.286330i	$0.0924353\pi$
$269$			679637.i			0.572660i	−0.958131	+	0.286330i	$0.907565\pi$
$270$	−55370.6	+	595621.i	−0.0462243	+	0.497234i
$271$	1.41400e6			1.16957			0.584785	−	0.811188i	$-0.301179\pi$
$271$	1.41400e6			1.16957			0.584785	+	0.811188i	$0.301179\pi$
$272$	−170387.	+	438274.i	−0.139641	+	0.359190i
$273$		0			0
$274$	945527.	+	87898.9i	0.760847	+	0.0707305i
$275$		−	163447.i		−	0.130330i
$276$	−354265.	+	1.88895e6i	−0.279934	+	1.49261i
$277$	343742.			0.269174			0.134587	−	0.990902i	$-0.457029\pi$
$277$	343742.			0.269174			0.134587	+	0.990902i	$0.457029\pi$
$278$	−368024.	−	34212.5i	−0.285604	−	0.0265505i
$279$	−253762.			−0.195171
$280$		0			0
$281$	475918.			0.359556			0.179778	−	0.983707i	$-0.442462\pi$
$281$	475918.			0.359556			0.179778	+	0.983707i	$0.442462\pi$
$282$	1.16508e6	+	108309.i	0.872432	+	0.0811038i
$283$	837949.			0.621944			0.310972	−	0.950419i	$-0.399345\pi$
$283$	837949.			0.621944			0.310972	+	0.950419i	$0.399345\pi$
$284$	−430132.	+	2.29347e6i	−0.316451	+	1.68732i
$285$		−	2.57955e6i		−	1.88118i
$286$	−1.24526e6	−	115763.i	−0.900215	−	0.0836865i
$287$		0			0
$288$	−700733.	−	350222.i	−0.497819	−	0.248806i
$289$	1.20898e6			0.851483
$290$	62653.1	−	673959.i	0.0437469	−	0.470585i
$291$			1.37871e6i			0.954420i
$292$	−130361.	+	695084.i	−0.0894724	+	0.477068i
$293$			1.34073e6i			0.912374i	0.889884	+	0.456187i	$0.150785\pi$
$293$			1.34073e6i			0.912374i	−0.889884	+	0.456187i	$0.849215\pi$
$294$		0			0
$295$			198778.i			0.132988i
$296$	−625111.	−	178461.i	−0.414694	−	0.118390i
$297$			591437.i			0.389061i
$298$	−325232.	−	30234.5i	−0.212155	−	0.0197225i
$299$	−2.41930e6			−1.56499
$300$	354277.	+	66443.5i	0.227269	+	0.0426235i
$301$		0			0
$302$	−186486.	+	2.00603e6i	−0.117660	+	1.26567i
$303$			81874.5i			0.0512321i
$304$	−2.50890e6	−	975379.i	−1.55704	−	0.605326i
$305$	−1.17512e6			−0.723326
$306$	32517.9	−	349795.i	0.0198527	−	0.213555i
$307$	−2.39821e6			−1.45225			−0.726126	−	0.687562i	$-0.758681\pi$
$307$	−2.39821e6			−1.45225			−0.726126	+	0.687562i	$0.758681\pi$
$308$		0			0
$309$	2.52140e6			1.50226
$310$	−49574.5	+	533272.i	−0.0292991	+	0.315170i
$311$	−25655.4			−0.0150410			−0.00752051	−	0.999972i	$-0.502394\pi$
$311$	−25655.4			−0.0150410			−0.00752051	+	0.999972i	$0.502394\pi$
$312$	757139.	−	2.65210e6i	0.440341	−	1.54242i
$313$		−	19004.7i		−	0.0109648i	−0.999985	−	0.00548238i	$-0.998255\pi$
$313$		−	19004.7i		−	0.0109648i	0.999985	−	0.00548238i	$-0.00174510\pi$
$314$	−211769.	+	2.27799e6i	−0.121210	+	1.30385i
$315$		0			0
$316$	14238.7	−	75920.7i	0.00802142	−	0.0427703i
$317$	1.12473e6			0.628637			0.314319	−	0.949318i	$-0.398224\pi$
$317$	1.12473e6			0.628637			0.314319	+	0.949318i	$0.398224\pi$
$318$	3.96923e6	+	368991.i	2.20109	+	0.204620i
$319$		−	669225.i		−	0.368210i
$320$	−872874.	+	1.40415e6i	−0.476515	+	0.766547i
$321$		−	2.08482e6i		−	1.12929i
$322$		0			0
$323$		−	1.20714e6i		−	0.643801i
$324$	−2.31555e6	−	434273.i	−1.22544	−	0.229827i
$325$			453748.i			0.238290i
$326$	311782.	−	3.35383e6i	0.162483	−	1.74782i
$327$	3.20391e6			1.65695
$328$	638820.	−	2.23765e6i	0.327864	−	1.14844i
$329$		0			0
$330$	−1.55977e6	−	145001.i	−0.788453	−	0.0732968i
$331$			3.20656e6i			1.60868i	0.594172	+	0.804338i	$0.297480\pi$
$331$			3.20656e6i			1.60868i	−0.594172	+	0.804338i	$0.702520\pi$
$332$	−702111.	−	131678.i	−0.349591	−	0.0655646i
$333$	485671.			0.240011
$334$	582590.	+	54159.2i	0.285757	+	0.0265648i
$335$	−73510.7			−0.0357881
$336$		0			0
$337$	−91356.8			−0.0438194			−0.0219097	−	0.999760i	$-0.506975\pi$
$337$	−91356.8			−0.0438194			−0.0219097	+	0.999760i	$0.506975\pi$
$338$	1.36567e6	+	126956.i	0.650209	+	0.0604453i
$339$	−2.92958e6			−1.38454
$340$	−728731.	−	136671.i	−0.341877	−	0.0641178i
$341$			529527.i			0.246605i
$342$	2.00240e6	+	186149.i	0.925733	+	0.0860587i
$343$		0			0
$344$	−1.00962e6	+	3.53650e6i	−0.460006	+	1.61130i
$345$	−3.03033e6			−1.37070
$346$	233769.	−	2.51465e6i	0.104978	−	1.12924i
$347$			843119.i			0.375894i	0.982179	+	0.187947i	$0.0601833\pi$
$347$			843119.i			0.375894i	−0.982179	+	0.187947i	$0.939817\pi$
$348$	1.45057e6	+	272050.i	0.642083	+	0.120420i
$349$		−	3.57936e6i		−	1.57305i	−0.617561	−	0.786523i	$-0.711879\pi$
$349$		−	3.57936e6i		−	1.57305i	0.617561	−	0.786523i	$-0.288121\pi$
$350$		0			0
$351$		−	1.64190e6i		−	0.711343i
$352$	−730810.	+	1.46223e6i	−0.314375	+	0.629010i
$353$		−	570389.i		−	0.243632i	−0.992553	−	0.121816i	$-0.961128\pi$
$353$		−	570389.i		−	0.243632i	0.992553	−	0.121816i	$-0.0388718\pi$
$354$	−431562.	−	40119.2i	−0.183035	−	0.0170155i
$355$	−3.67928e6			−1.54950
$356$	−376166.	+	2.00572e6i	−0.157309	+	0.838775i
$357$		0			0
$358$	219313.	−	2.35915e6i	0.0904392	−	0.972854i
$359$			1.07500e6i			0.440223i	0.975475	+	0.220112i	$0.0706422\pi$
$359$			1.07500e6i			0.440223i	−0.975475	+	0.220112i	$0.929358\pi$
$360$	339084.	−	1.18774e6i	0.137896	−	0.483020i
$361$	4.43418e6			1.79079
$362$	−270907.	+	2.91415e6i	−0.108655	+	1.16880i
$363$	1.58336e6			0.630686
$364$		0			0
$365$	−1.11508e6			−0.438102
$366$	237175.	−	2.55128e6i	0.0925477	−	0.995534i
$367$	2.49054e6			0.965224			0.482612	−	0.875834i	$-0.339688\pi$
$367$	2.49054e6			0.965224			0.482612	+	0.875834i	$0.339688\pi$
$368$	−1.14583e6	+	2.94734e6i	−0.441062	+	1.13452i
$369$			1.73851e6i			0.664680i
$370$	94880.0	−	1.02062e6i	0.0360305	−	0.387580i
$371$		0			0
$372$	−1.14777e6	−	215260.i	−0.430029	−	0.0806504i
$373$	−587841.			−0.218770			−0.109385	−	0.993999i	$-0.534888\pi$
$373$	−587841.			−0.218770			−0.109385	+	0.993999i	$0.534888\pi$
$374$	−729920.	−	67855.4i	−0.269834	−	0.0250845i
$375$			3.63487e6i			1.33478i
$376$	1.85130e6	+	528522.i	0.675317	+	0.192794i
$377$			1.85785e6i			0.673219i
$378$		0			0
$379$			507765.i			0.181579i	0.995870	+	0.0907894i	$0.0289390\pi$
$379$			507765.i			0.181579i	−0.995870	+	0.0907894i	$0.971061\pi$
$380$	782372.	−	4.17162e6i	0.277942	−	1.48199i
$381$			6355.08i			0.00224289i
$382$	−23598.0	+	253843.i	−0.00827402	+	0.0890035i
$383$	460563.			0.160433			0.0802163	−	0.996777i	$-0.474439\pi$
$383$	460563.			0.160433			0.0802163	+	0.996777i	$0.474439\pi$
$384$	−2.87235e6	−	2.17848e6i	−0.994051	−	0.753919i
$385$		0			0
$386$	−254956.	−	23701.5i	−0.0870958	−	0.00809668i
$387$		−	2.74764e6i		−	0.932571i
$388$	−418159.	+	2.22963e6i	−0.141014	+	0.751889i
$389$	1.62440e6			0.544277			0.272138	−	0.962258i	$-0.412269\pi$
$389$	1.62440e6			0.544277			0.272138	+	0.962258i	$0.412269\pi$
$390$	4.33011e6	+	402539.i	1.44157	+	0.134013i
$391$	−1.41809e6			−0.469097
$392$		0			0
$393$	1.84545e6			0.602728
$394$	−1.84940e6	−	171925.i	−0.600192	−	0.0557956i
$395$	121795.			0.0392769
$396$	225117.	−	1.20032e6i	0.0721389	−	0.384645i
$397$			3.81010e6i			1.21328i	0.794977	+	0.606639i	$0.207483\pi$
$397$			3.81010e6i			1.21328i	−0.794977	+	0.606639i	$0.792517\pi$
$398$	628984.	+	58472.1i	0.199036	+	0.0185030i
$399$		0			0
$400$	552782.	+	214904.i	0.172744	+	0.0671574i
$401$	1.40684e6			0.436901			0.218451	−	0.975848i	$-0.429900\pi$
$401$	1.40684e6			0.436901			0.218451	+	0.975848i	$0.429900\pi$
$402$	14836.6	−	159598.i	0.00457900	−	0.0492562i
$403$		−	1.47003e6i		−	0.450882i
$404$	−24832.4	+	132407.i	−0.00756947	+	0.0403605i
$405$		−	3.71470e6i		−	1.12535i
$406$		0			0
$407$		−	1.01345e6i		−	0.303262i
$408$	443802.	−	1.55455e6i	0.131989	−	0.462331i
$409$			1.06147e6i			0.313760i	0.987618	+	0.156880i	$0.0501436\pi$
$409$			1.06147e6i			0.313760i	−0.987618	+	0.156880i	$0.949856\pi$
$410$	3.65343e6	+	339634.i	1.07335	+	0.0997817i
$411$	−3.26475e6			−0.953334
$412$	4.07759e6	+	764737.i	1.18348	+	0.221957i
$413$		0			0
$414$	218679.	−	2.35232e6i	0.0627055	−	0.674522i
$415$		−	1.12636e6i		−	0.321037i
$416$	2.02882e6	−	4.05931e6i	0.574790	−	1.15006i
$417$	1.27072e6			0.357858
$418$	388438.	−	4.17842e6i	0.108738	−	1.16969i
$419$	1.17360e6			0.326576			0.163288	−	0.986578i	$-0.447790\pi$
$419$	1.17360e6			0.326576			0.163288	+	0.986578i	$0.447790\pi$
$420$		0			0
$421$	2.44757e6			0.673023			0.336511	−	0.941679i	$-0.390753\pi$
$421$	2.44757e6			0.673023			0.336511	+	0.941679i	$0.390753\pi$
$422$	−454614.	+	4.89028e6i	−0.124269	+	1.33676i
$423$	−1.43834e6			−0.390851
$424$	6.30708e6	+	1.80059e6i	1.70378	+	0.486407i
$425$			265967.i			0.0714259i
$426$	742588.	−	7.98801e6i	0.198255	−	2.13263i
$427$		0			0
$428$	632322.	−	3.37155e6i	0.166851	−	0.889652i
$429$	4.29969e6			1.12796
$430$	−5.77407e6	−	536774.i	−1.50595	−	0.139998i
$431$		−	5.24660e6i		−	1.36046i	−0.733001	−	0.680228i	$-0.761881\pi$
$431$		−	5.24660e6i		−	1.36046i	0.733001	−	0.680228i	$-0.238119\pi$
$432$	−2.00026e6	−	777635.i	−0.515676	−	0.200478i
$433$			3.54842e6i			0.909527i	0.890612	+	0.454763i	$0.150276\pi$
$433$			3.54842e6i			0.909527i	−0.890612	+	0.454763i	$0.849724\pi$
$434$		0			0
$435$			2.32707e6i			0.589639i
$436$	5.18133e6	+	971739.i	1.30534	+	0.244812i
$437$		−	8.11786e6i		−	2.03347i
$438$	225057.	−	2.42093e6i	0.0560540	−	0.602972i
$439$	1.45556e6			0.360471			0.180235	−	0.983624i	$-0.442314\pi$
$439$	1.45556e6			0.360471			0.180235	+	0.983624i	$0.442314\pi$
$440$	−2.47847e6	−	707569.i	−0.610311	−	0.174236i
$441$		0			0
$442$	2.02634e6	+	188375.i	0.493353	+	0.0458635i
$443$			6.00442e6i			1.45366i	0.686819	+	0.726828i	$0.259006\pi$
$443$			6.00442e6i			1.45366i	−0.686819	+	0.726828i	$0.740994\pi$
$444$	2.19670e6	+	411984.i	0.528827	+	0.0991797i
$445$	−3.21766e6			−0.770265
$446$	−4.39246e6	−	408335.i	−1.04561	−	0.0972031i
$447$	1.12297e6			0.265828
$448$		0			0
$449$	−7.63387e6			−1.78702			−0.893509	−	0.449044i	$-0.851764\pi$
$449$	−7.63387e6			−1.78702			−0.893509	+	0.449044i	$0.851764\pi$
$450$	−441185.	−	41013.8i	−0.102705	−	0.00954771i
$451$	3.62777e6			0.839844
$452$	−4.73769e6	−	888537.i	−1.09074	−	0.204564i
$453$		−	6.92648e6i		−	1.58587i
$454$	−4.67875e6	−	434950.i	−1.06534	−	0.0990375i
$455$		0			0
$456$	8.89900e6	+	2.54055e6i	2.00414	+	0.572157i
$457$	−2.29533e6			−0.514109			−0.257054	−	0.966397i	$-0.582752\pi$
$457$	−2.29533e6			−0.514109			−0.257054	+	0.966397i	$0.582752\pi$
$458$	−306728.	+	3.29947e6i	−0.0683265	+	0.734988i
$459$		−	962411.i		−	0.213221i
$460$	−4.90062e6	−	919093.i	−1.07983	−	0.202519i
$461$			914749.i			0.200470i	0.994964	+	0.100235i	$0.0319595\pi$
$461$			914749.i			0.200470i	−0.994964	+	0.100235i	$0.968041\pi$
$462$		0			0
$463$			1.83714e6i			0.398282i	0.979971	+	0.199141i	$0.0638151\pi$
$463$			1.83714e6i			0.398282i	−0.979971	+	0.199141i	$0.936185\pi$
$464$	2.26334e6	+	879912.i	0.488039	+	0.189734i
$465$		−	1.84130e6i		−	0.394905i
$466$	−263370.	−	24483.6i	−0.0561825	−	0.00522289i
$467$	7.52627e6			1.59694			0.798468	−	0.602037i	$-0.205644\pi$
$467$	7.52627e6			1.59694			0.798468	+	0.602037i	$0.205644\pi$
$468$	−624950.	+	3.33224e6i	−0.131896	+	0.703270i
$469$		0			0
$470$	−280993.	+	3.02263e6i	−0.0586746	+	0.631162i
$471$		−	7.86553e6i		−	1.63371i
$472$	−685750.	−	195772.i	−0.141681	−	0.0404479i
$473$	−5.73351e6			−1.17833
$474$	−24581.9	+	264427.i	−0.00502538	+	0.0540580i
$475$	−1.52253e6			−0.309622
$476$		0			0
$477$	−4.90020e6			−0.986093
$478$	39134.7	−	420972.i	0.00783416	−	0.0842720i
$479$	−4.98020e6			−0.991763			−0.495881	−	0.868390i	$-0.665155\pi$
$479$	−4.98020e6			−0.991763			−0.495881	+	0.868390i	$0.665155\pi$
$480$	2.54122e6	−	5.08454e6i	0.503429	−	1.00728i
$481$			2.81347e6i			0.554472i
$482$	−272746.	+	2.93393e6i	−0.0534738	+	0.575217i
$483$		0			0
$484$	2.56059e6	+	480230.i	0.496852	+	0.0931829i
$485$	−3.57687e6			−0.690476
$486$	5.19635e6	+	483068.i	0.997948	+	0.0927721i
$487$			1.92982e6i			0.368719i	0.982859	+	0.184359i	$0.0590210\pi$
$487$			1.92982e6i			0.368719i	−0.982859	+	0.184359i	$0.940979\pi$
$488$	1.15736e6	−	4.05398e6i	0.219998	−	0.770605i
$489$			1.15802e7i			2.19001i
$490$		0			0
$491$		−	1.65322e6i		−	0.309475i	−0.987956	−	0.154738i	$-0.950547\pi$
$491$		−	1.65322e6i		−	0.309475i	0.987956	−	0.154738i	$-0.0494532\pi$
$492$	−1.47474e6	+	7.86334e6i	−0.274665	+	1.46452i
$493$			1.08899e6i			0.201793i
$494$	−1.07835e6	+	1.15998e7i	−0.198812	+	2.13862i
$495$	1.92561e6			0.353228
$496$	−1.79087e6	−	696234.i	−0.326859	−	0.127072i
$497$		0			0
$498$	2.44541e6	+	227332.i	0.441853	+	0.0410759i
$499$		−	3.34549e6i		−	0.601462i	−0.953709	−	0.300731i	$-0.902769\pi$
$499$		−	3.34549e6i		−	0.601462i	0.953709	−	0.300731i	$-0.0972306\pi$
$500$	−1.10245e6	+	5.87827e6i	−0.197212	+	1.05154i
$501$	−2.01159e6			−0.358051
$502$	−6.88805e6	−	640333.i	−1.21994	−	0.113409i
$503$	−2.30519e6			−0.406243			−0.203122	−	0.979153i	$-0.565109\pi$
$503$	−2.30519e6			−0.406243			−0.203122	+	0.979153i	$0.565109\pi$
$504$		0			0
$505$	−212412.			−0.0370639
$506$	−4.90861e6	−	456319.i	−0.852281	−	0.0792304i
$507$	−4.71542e6			−0.814705
$508$	−1927.49	+	10277.4i	−0.000331384	+	0.00176694i
$509$			5.54196e6i			0.948132i	0.880489	+	0.474066i	$0.157214\pi$
$509$			5.54196e6i			0.948132i	−0.880489	+	0.474066i	$0.842786\pi$
$510$	2.53812e6	+	235951.i	0.432103	+	0.0401695i
$511$		0			0
$512$	−3.98440e6	−	4.39419e6i	−0.671720	−	0.740805i
$513$	5.50932e6			0.924282
$514$	−587907.	+	6.32410e6i	−0.0981523	+	1.05582i
$515$			6.54144e6i			1.08681i
$516$	2.33076e6	−	1.24276e7i	0.385365	−	2.05477i
$517$			3.00140e6i			0.493853i
$518$		0			0
$519$			8.68266e6i			1.41493i
$520$	6.88052e6	+	1.96430e6i	1.11587	+	0.318565i
$521$			216313.i			0.0349131i	0.999848	+	0.0174565i	$0.00555687\pi$
$521$			216313.i			0.0349131i	−0.999848	+	0.0174565i	$0.994443\pi$
$522$	−1.80641e6	−	167929.i	−0.290162	−	0.0269743i
$523$	2.17372e6			0.347496			0.173748	−	0.984790i	$-0.444412\pi$
$523$	2.17372e6			0.347496			0.173748	+	0.984790i	$0.444412\pi$
$524$	2.98445e6	+	559723.i	0.474827	+	0.0890522i
$525$		0			0
$526$	−794595.	+	8.54744e6i	−0.125222	+	1.34701i
$527$		−	861667.i		−	0.135149i
$528$	2.03641e6	−	5.23813e6i	0.317893	−	0.817696i
$529$	−3.10014e6			−0.481661
$530$	−957296.	+	1.02976e7i	−0.148032	+	1.59238i
$531$	532784.			0.0820002
$532$		0			0
$533$	−1.00711e7			−1.53554
$534$	649419.	−	6.98579e6i	0.0985535	−	1.06014i
$535$	5.40878e6			0.816987
$536$	72399.3	−	253600.i	0.0108849	−	0.0381273i
$537$			8.14575e6i			1.21898i
$538$	355871.	−	3.82810e6i	0.0530075	−	0.570201i
$539$		0			0
$540$	623758.	−	3.32588e6i	0.0920517	−	0.490821i
$541$	−3.99376e6			−0.586663			−0.293332	−	0.956011i	$-0.594764\pi$
$541$	−3.99376e6			−0.586663			−0.293332	+	0.956011i	$0.594764\pi$
$542$	−7.96445e6	−	740398.i	−1.16455	−	0.108260i
$543$		−	1.00621e7i		−	1.46449i
$544$	1.18920e6	−	2.37939e6i	0.172290	−	0.344722i
$545$			8.31210e6i			1.19873i
$546$		0			0
$547$		−	9.63219e6i		−	1.37644i	−0.725503	−	0.688219i	$-0.758393\pi$
$547$		−	9.63219e6i		−	1.37644i	0.725503	−	0.688219i	$-0.241607\pi$
$548$	−5.27972e6	−	990193.i	−0.751034	−	0.140854i
$549$			3.14968e6i			0.446001i
$550$	−85583.9	+	920625.i	−0.0120638	+	0.129771i
$551$	−6.23392e6			−0.874747
$552$	2.98451e6	−	1.04541e7i	0.416894	−	1.46029i
$553$		0			0
$554$	−1.93615e6	−	179990.i	−0.268018	−	0.0249157i
$555$			3.52404e6i			0.485634i
$556$	2.05500e6	+	385409.i	0.281920	+	0.0528731i
$557$	2.89267e6			0.395059			0.197529	−	0.980297i	$-0.436708\pi$
$557$	2.89267e6			0.395059			0.197529	+	0.980297i	$0.436708\pi$
$558$	1.42933e6	+	132875.i	0.194333	+	0.0180658i
$559$	1.59169e7			2.15442
$560$		0			0
$561$	2.52029e6			0.338099
$562$	−2.68064e6	−	249200.i	−0.358012	−	0.0332819i
$563$	9.86440e6			1.31160			0.655798	−	0.754937i	$-0.272332\pi$
$563$	9.86440e6			1.31160			0.655798	+	0.754937i	$0.272332\pi$
$564$	−6.50566e6	−	1.22011e6i	−0.861180	−	0.161511i
$565$		−	7.60040e6i		−	1.00165i
$566$	−4.71980e6	−	438766.i	−0.619274	−	0.0575695i
$567$		0			0
$568$	3.62366e6	−	1.26929e7i	0.471277	−	1.65078i
$569$	−1.09229e7			−1.41436			−0.707178	−	0.707035i	$-0.750032\pi$
$569$	−1.09229e7			−1.41436			−0.707178	+	0.707035i	$0.750032\pi$
$570$	−1.35070e6	+	1.45295e7i	−0.174129	+	1.87311i
$571$		−	1.33576e6i		−	0.171450i	−0.996319	−	0.0857251i	$-0.972679\pi$
$571$		−	1.33576e6i		−	0.171450i	0.996319	−	0.0857251i	$-0.0273207\pi$
$572$	6.95342e6	+	1.30409e6i	0.888604	+	0.166655i
$573$		−	876478.i		−	0.111520i
$574$		0			0
$575$			1.78859e6i			0.225602i
$576$	3.76354e6	+	2.33956e6i	0.472651	+	0.293818i
$577$			1.54084e7i			1.92671i	0.268222	+	0.963357i	$0.413564\pi$
$577$			1.54084e7i			1.92671i	−0.268222	+	0.963357i	$0.586436\pi$
$578$	−6.80969e6	−	633048.i	−0.847827	−	0.0788164i
$579$	880322.			0.109130
$580$	−705796.	+	3.76331e6i	−0.0871183	+	0.464516i
$581$		0			0
$582$	721918.	−	7.76566e6i	0.0883446	−	0.950322i
$583$			1.02253e7i			1.24596i
$584$	1.09822e6	−	3.84685e6i	0.133247	−	0.466738i
$585$	−5.34572e6			−0.645828
$586$	702033.	−	7.55176e6i	0.0844527	−	0.908457i
$587$	−1.18438e6			−0.141872			−0.0709359	−	0.997481i	$-0.522599\pi$
$587$	−1.18438e6			−0.141872			−0.0709359	+	0.997481i	$0.522599\pi$
$588$		0			0
$589$	4.93261e6			0.585853
$590$	104084.	−	1.11963e6i	0.0123099	−	0.132417i
$591$	6.38567e6			0.752035
$592$	3.42753e6	+	1.33251e6i	0.401955	+	0.156267i
$593$			1.13966e7i			1.33088i	0.746452	+	0.665439i	$0.231756\pi$
$593$			1.13966e7i			1.33088i	−0.746452	+	0.665439i	$0.768244\pi$
$594$	309688.	−	3.33131e6i	0.0360129	−	0.387391i
$595$		0			0
$596$	1.81606e6	+	340596.i	0.209418	+	0.0392757i
$597$	−2.17178e6			−0.249390
$598$	1.36269e7	+	1.26679e6i	1.55827	+	0.144862i
$599$			7.55836e6i			0.860717i	0.902658	+	0.430358i	$0.141613\pi$
$599$			7.55836e6i			0.860717i	−0.902658	+	0.430358i	$0.858387\pi$
$600$	−1.96070e6	−	559754.i	−0.222348	−	0.0634774i
$601$		−	5.16035e6i		−	0.582764i	−0.956607	−	0.291382i	$-0.905885\pi$
$601$		−	5.16035e6i		−	0.582764i	0.956607	−	0.291382i	$-0.0941150\pi$
$602$		0			0
$603$			197031.i			0.0220669i
$604$	2.10079e6	−	1.12014e7i	0.234310	−	1.24934i
$605$			4.10781e6i			0.456270i
$606$	42871.1	−	461164.i	0.00474223	−	0.0510121i
$607$	−1.20029e7			−1.32225			−0.661127	−	0.750274i	$-0.729922\pi$
$607$	−1.20029e7			−1.32225			−0.661127	+	0.750274i	$0.729922\pi$
$608$	1.36208e7	+	6.80760e6i	1.49432	+	0.746853i
$609$		0			0
$610$	6.61896e6	+	615318.i	0.720220	+	0.0669537i
$611$		−	8.33225e6i		−	0.902941i
$612$	−366319.	+	1.95322e6i	−0.0395349	+	0.210801i
$613$	−1.11102e7			−1.19418			−0.597089	−	0.802175i	$-0.703676\pi$
$613$	−1.11102e7			−1.19418			−0.597089	+	0.802175i	$0.703676\pi$
$614$	1.35081e7	+	1.25575e6i	1.44602	+	0.134426i
$615$	−1.26147e7			−1.34490
$616$		0			0
$617$	−1.74919e7			−1.84980			−0.924898	−	0.380215i	$-0.875850\pi$
$617$	−1.74919e7			−1.84980			−0.924898	+	0.380215i	$0.875850\pi$
$618$	−1.42020e7	−	1.32026e6i	−1.49581	−	0.139055i
$619$	−1.79682e7			−1.88485			−0.942427	−	0.334411i	$-0.891463\pi$
$619$	−1.79682e7			−1.88485			−0.942427	+	0.334411i	$0.891463\pi$
$620$	558464.	−	2.97773e6i	0.0583466	−	0.311105i
$621$		−	6.47209e6i		−	0.673466i
$622$	144506.	+	13433.7i	0.0149765	+	0.00139225i
$623$		0			0
$624$	−5.65333e6	+	1.45417e7i	−0.581223	+	1.49504i
$625$	−7.62021e6			−0.780310
$626$	−9951.21	+	107045.i	−0.00101494	+	0.0109177i
$627$			1.44274e7i			1.46561i
$628$	2.38560e6	−	1.27201e7i	0.241379	−	1.28703i
$629$			1.64913e6i			0.166199i
$630$		0			0
$631$		−	5.86369e6i		−	0.586269i	−0.956071	−	0.293135i	$-0.905302\pi$
$631$		−	5.86369e6i		−	0.586269i	0.956071	−	0.293135i	$-0.0946984\pi$
$632$	−119954.	+	420173.i	−0.0119460	+	0.0418442i
$633$		−	1.68853e7i		−	1.67494i
$634$	−6.33512e6	−	588931.i	−0.625938	−	0.0581890i
$635$	−16487.4			−0.00162262
$636$	−2.21637e7	−	4.15673e6i	−2.17270	−	0.407482i
$637$		0			0
$638$	−350419.	+	3.76945e6i	−0.0340829	+	0.366629i
$639$			9.86158e6i			0.955420i
$640$	5.65176e6	−	7.45192e6i	0.545424	−	0.719148i
$641$	1.03420e7			0.994165			0.497082	−	0.867703i	$-0.334405\pi$
$641$	1.03420e7			0.994165			0.497082	+	0.867703i	$0.334405\pi$
$642$	−1.09165e6	+	1.17429e7i	−0.104531	+	1.12444i
$643$	−1.19308e7			−1.13800			−0.569000	−	0.822338i	$-0.692670\pi$
$643$	−1.19308e7			−1.13800			−0.569000	+	0.822338i	$0.692670\pi$
$644$		0			0
$645$	1.99369e7			1.88694
$646$	−632083.	+	6.79930e6i	−0.0595926	+	0.641037i
$647$	−1.96855e6			−0.184878			−0.0924390	−	0.995718i	$-0.529466\pi$
$647$	−1.96855e6			−0.184878			−0.0924390	+	0.995718i	$0.529466\pi$
$648$	1.28151e7	+	3.65854e6i	1.19890	+	0.342271i
$649$		−	1.11176e6i		−	0.103610i
$650$	237591.	−	2.55576e6i	0.0220570	−	0.237267i
$651$		0			0
$652$	−3.51227e6	+	1.87274e7i	−0.323570	+	1.72528i
$653$	1.64859e7			1.51297			0.756485	−	0.654011i	$-0.226915\pi$
$653$	1.64859e7			1.51297			0.756485	+	0.654011i	$0.226915\pi$
$654$	−1.80462e7	−	1.67763e6i	−1.64984	−	0.153374i
$655$			4.78778e6i			0.436044i
$656$	−4.76988e6	+	1.22692e7i	−0.432760	+	1.11316i
$657$			2.98876e6i			0.270133i
$658$		0			0
$659$			6.17828e6i			0.554184i	0.960843	+	0.277092i	$0.0893707\pi$
$659$			6.17828e6i			0.554184i	−0.960843	+	0.277092i	$0.910629\pi$
$660$	8.70958e6	+	1.63345e6i	0.778283	+	0.145964i
$661$			6.63170e6i			0.590365i	0.955441	+	0.295183i	$0.0953805\pi$
$661$			6.63170e6i			0.590365i	−0.955441	+	0.295183i	$0.904619\pi$
$662$	1.67901e6	−	1.80611e7i	0.148905	−	1.60177i
$663$	−6.99663e6			−0.618166
$664$	3.88574e6	+	1.10933e6i	0.342021	+	0.0976425i
$665$		0			0
$666$	−2.73558e6	−	254307.i	−0.238981	−	0.0222163i
$667$			7.32331e6i			0.637372i
$668$	−3.25312e6	−	610111.i	−0.282071	−	0.0529014i
$669$	1.51664e7			1.31014
$670$	414054.	+	38491.7i	0.0356345	+	0.00331268i
$671$	6.57247e6			0.563537
$672$		0			0
$673$	−1.30304e7			−1.10897			−0.554486	−	0.832193i	$-0.687085\pi$
$673$	−1.30304e7			−1.10897			−0.554486	+	0.832193i	$0.687085\pi$
$674$	514573.	+	47836.2i	0.0436312	+	0.00405608i
$675$	−1.21386e6			−0.102544
$676$	−7.62573e6	−	1.43018e6i	−0.641822	−	0.120372i
$677$			1.80254e6i			0.151152i	0.997140	+	0.0755759i	$0.0240795\pi$
$677$			1.80254e6i			0.151152i	−0.997140	+	0.0755759i	$0.975920\pi$
$678$	1.65011e7	+	1.53398e6i	1.37860	+	0.128158i
$679$		0			0
$680$	4.03306e6	+	1.15139e6i	0.334474	+	0.0954879i
$681$	1.61549e7			1.33487
$682$	277270.	−	2.98259e6i	0.0228267	−	0.245546i
$683$		−	1.85800e7i		−	1.52403i	−0.647559	−	0.762015i	$-0.724210\pi$
$683$		−	1.85800e7i		−	1.52403i	0.647559	−	0.762015i	$-0.275790\pi$
$684$	−1.11812e7	−	2.09699e6i	−0.913792	−	0.171379i
$685$		−	8.46995e6i		−	0.689691i
$686$		0			0
$687$		−	1.13925e7i		−	0.920932i
$688$	7.53856e6	−	1.93909e7i	0.607179	−	1.56181i
$689$		−	2.83866e7i		−	2.27806i
$690$	1.70685e7	+	1.58674e6i	1.36481	+	0.126877i
$691$	2.17627e7			1.73387			0.866935	−	0.498421i	$-0.166086\pi$
$691$	2.17627e7			1.73387			0.866935	+	0.498421i	$0.166086\pi$
$692$	−2.63344e6	+	1.40415e7i	−0.209054	+	1.11468i
$693$		0			0
$694$	441473.	−	4.74892e6i	0.0347941	−	0.374280i
$695$			3.29672e6i			0.258893i
$696$	−8.02799e6	−	2.29189e6i	−0.628180	−	0.179337i
$697$	−5.90326e6			−0.460267
$698$	−1.87422e6	+	2.01610e7i	−0.145607	+	1.56629i
$699$	909372.			0.0703961
$700$		0			0
$701$	2.12560e7			1.63375			0.816877	−	0.576812i	$-0.195704\pi$
$701$	2.12560e7			1.63375			0.816877	+	0.576812i	$0.195704\pi$
$702$	−859731.	+	9.24812e6i	−0.0658446	+	0.708289i
$703$	−9.44046e6			−0.720452
$704$	4.88199e6	−	7.85342e6i	0.371249	−	0.597210i
$705$		−	1.04367e7i		−	0.790840i
$706$	−298667.	+	3.21276e6i	−0.0225515	+	0.242586i
$707$		0			0
$708$	2.40979e6	+	451948.i	0.180674	+	0.0338849i
$709$	6.01542e6			0.449418			0.224709	−	0.974426i	$-0.427857\pi$
$709$	6.01542e6			0.449418			0.224709	+	0.974426i	$0.427857\pi$
$710$	2.07238e7	+	1.92654e6i	1.54285	+	0.143428i
$711$		−	326448.i		−	0.0242181i
$712$	3.16901e6	−	1.11004e7i	0.234274	−	0.820613i
$713$		−	5.79460e6i		−	0.426874i
$714$		0			0
$715$			1.11550e7i			0.816024i
$716$	−2.47059e6	+	1.31732e7i	−0.180102	+	0.960306i
$717$			1.45355e6i			0.105592i
$718$	562892.	−	6.05502e6i	0.0407487	−	0.438333i
$719$	−3.75157e6			−0.270640			−0.135320	−	0.990802i	$-0.543206\pi$
$719$	−3.75157e6			−0.270640			−0.135320	+	0.990802i	$0.543206\pi$
$720$	−2.53184e6	+	6.51247e6i	−0.182014	+	0.468182i
$721$		0			0
$722$	−2.49758e7	−	2.32182e6i	−1.78310	−	0.165762i
$723$		−	1.01304e7i		−	0.720741i
$724$	3.05181e6	−	1.62723e7i	0.216377	−	1.15372i
$725$	1.37351e6			0.0970480
$726$	−8.91838e6	−	829078.i	−0.627978	−	0.0583786i
$727$	−6.68142e6			−0.468849			−0.234424	−	0.972134i	$-0.575321\pi$
$727$	−6.68142e6			−0.468849			−0.234424	+	0.972134i	$0.575321\pi$
$728$		0			0
$729$	−51873.8			−0.00361517
$730$	6.28078e6	+	583879.i	0.436221	+	0.0405523i
$731$	9.32981e6			0.645772
$732$	−2.67180e6	+	1.42461e7i	−0.184301	+	0.982694i
$733$			27872.1i			0.00191606i	1.00000		0.000958031i	$0.000304951\pi$
$733$			27872.1i			0.00191606i	−1.00000		0.000958031i	$0.999695\pi$
$734$	−1.40281e7	−	1.30409e6i	−0.961080	−	0.0893447i
$735$		0			0
$736$	7.99724e6	−	1.60011e7i	0.544184	−	1.08882i
$737$	411146.			0.0278822
$738$	910320.	−	9.79230e6i	0.0615252	−	0.661826i
$739$		−	6.12009e6i		−	0.412237i	−0.978527	−	0.206118i	$-0.933917\pi$
$739$		−	6.12009e6i		−	0.412237i	0.978527	−	0.206118i	$-0.0660832\pi$
$740$	−1.06884e6	+	5.69905e6i	−0.0717517	+	0.382581i
$741$		−	4.00522e7i		−	2.67967i
$742$		0			0
$743$			1.23711e7i			0.822122i	0.911608	+	0.411061i	$0.134842\pi$
$743$			1.23711e7i			0.822122i	−0.911608	+	0.411061i	$0.865158\pi$
$744$	6.35218e6	+	1.81346e6i	0.420717	+	0.120109i
$745$			2.91340e6i			0.192313i
$746$	3.31105e6	+	307805.i	0.217831	+	0.0202502i
$747$	−3.01897e6			−0.197951
$748$	4.07579e6	+	764401.i	0.266353	+	0.0499536i
$749$		0			0
$750$	1.90329e6	−	2.04736e7i	0.123552	−	1.32905i
$751$		−	1.62554e7i		−	1.05172i	−0.850572	−	0.525858i	$-0.823744\pi$
$751$		−	1.62554e7i		−	1.05172i	0.850572	−	0.525858i	$-0.176256\pi$
$752$	−1.01508e7	−	3.94631e6i	−0.654572	−	0.254476i
$753$	2.37833e7			1.52857
$754$	972805.	−	1.04645e7i	0.0623157	−	0.670329i
$755$	1.79698e7			1.14730
$756$		0			0
$757$	1.63597e7			1.03761			0.518807	−	0.854891i	$-0.326376\pi$
$757$	1.63597e7			1.03761			0.518807	+	0.854891i	$0.326376\pi$
$758$	265876.	−	2.86002e6i	0.0168076	−	0.180799i
$759$	1.69486e7			1.06790
$760$	−6.59110e6	+	2.30872e7i	−0.413927	+	1.44990i
$761$		−	2.41632e7i		−	1.51249i	−0.654286	−	0.756247i	$-0.727031\pi$
$761$		−	2.41632e7i		−	1.51249i	0.654286	−	0.756247i	$-0.272969\pi$
$762$	3327.64	−	35795.4i	0.000207611	−	0.00223326i
$763$		0			0
$764$	265834.	−	1.41743e6i	0.0164770	−	0.0878555i
$765$	−3.13343e6			−0.193583
$766$	−2.59415e6	−	241160.i	−0.159744	−	0.0148502i
$767$			3.08639e6i			0.189436i
$768$	1.50380e7	+	1.37744e7i	0.919998	+	0.842695i
$769$		−	2.70890e6i		−	0.165188i	−0.996583	−	0.0825939i	$-0.973680\pi$
$769$		−	2.70890e6i		−	0.165188i	0.996583	−	0.0825939i	$-0.0263204\pi$
$770$		0			0
$771$		−	2.18361e7i		−	1.32294i
$772$	1.42365e6	+	267000.i	0.0859725	+	0.0161238i
$773$			4.56000e6i			0.274484i	0.990538	+	0.137242i	$0.0438237\pi$
$773$			4.56000e6i			0.274484i	−0.990538	+	0.137242i	$0.956176\pi$
$774$	−1.43872e6	+	1.54762e7i	−0.0863222	+	0.928567i
$775$	−1.08679e6			−0.0649970
$776$	3.52279e6	−	1.23396e7i	0.210006	−	0.735608i
$777$		0			0
$778$	−9.14956e6	−	850569.i	−0.541940	−	0.0503803i
$779$		−	3.37932e7i		−	1.99520i
$780$	−2.41788e7	−	4.53466e6i	−1.42298	−	0.266875i
$781$	2.05782e7			1.20720
$782$	7.98750e6	+	742541.i	0.467083	+	0.0434213i
$783$	−4.97009e6			−0.289707
$784$		0			0
$785$	2.04061e7			1.18191
$786$	−1.03946e7	−	966315.i	−0.600140	−	0.0557908i
$787$	1.19341e7			0.686835			0.343418	−	0.939183i	$-0.388415\pi$
$787$	1.19341e7			0.686835			0.343418	+	0.939183i	$0.388415\pi$
$788$	1.03268e7	+	1.93676e6i	0.592451	+	0.111112i
$789$		−	2.95129e7i		−	1.68779i
$790$	−686020.	−	63774.4i	−0.0391083	−	0.00363562i
$791$		0			0
$792$	−1.89650e6	+	6.64303e6i	−0.107433	+	0.376317i
$793$	−1.82460e7			−1.03035
$794$	1.99504e6	−	2.14607e7i	0.112306	−	1.20807i
$795$		−	3.55560e7i		−	1.99524i
$796$	−3.51218e6	−	658696.i	−0.196469	−	0.0368470i
$797$		−	3.32514e6i		−	0.185423i	−0.995693	−	0.0927116i	$-0.970447\pi$
$797$		−	3.32514e6i		−	0.185423i	0.995693	−	0.0927116i	$-0.0295535\pi$
$798$		0			0
$799$		−	4.88401e6i		−	0.270651i
$800$	−3.00105e6	−	1.49991e6i	−0.165786	−	0.0828589i
$801$			8.62430e6i			0.474944i
$802$	−7.92411e6	−	736648.i	−0.435025	−	0.0404412i
$803$	6.23666e6			0.341321
$804$	−167137.	+	891175.i	−0.00911868	+	0.0486209i
$805$		0			0
$806$	−769736.	+	8.28004e6i	−0.0417353	+	0.448947i
$807$			1.32178e7i			0.714456i
$808$	209201.	−	732787.i	0.0112729	−	0.0394866i
$809$	−1.75356e7			−0.941996			−0.470998	−	0.882134i	$-0.656106\pi$
$809$	−1.75356e7			−0.941996			−0.470998	+	0.882134i	$0.656106\pi$
$810$	−1.94509e6	+	2.09233e7i	−0.104166	+	1.12052i
$811$	2.11367e7			1.12846			0.564230	−	0.825618i	$-0.309173\pi$
$811$	2.11367e7			1.12846			0.564230	+	0.825618i	$0.309173\pi$
$812$		0			0
$813$	2.74999e7			1.45917
$814$	−530664.	+	5.70835e6i	−0.0280711	+	0.301960i
$815$	−3.00434e7			−1.58436
$816$	−3.31374e6	+	8.52371e6i	−0.174218	+	0.448129i
$817$			5.34085e7i			2.79934i
$818$	555804.	−	5.97878e6i	0.0290428	−	0.312413i
$819$		0			0
$820$	−2.04004e7	−	3.82602e6i	−1.05951	−	0.198707i
$821$	5.13514e6			0.265885			0.132943	−	0.991124i	$-0.457557\pi$
$821$	5.13514e6			0.265885			0.132943	+	0.991124i	$0.457557\pi$
$822$	1.83889e7	+	1.70949e6i	0.949241	+	0.0882442i
$823$			1.31165e7i			0.675024i	0.941321	+	0.337512i	$0.109585\pi$
$823$			1.31165e7i			0.675024i	−0.941321	+	0.337512i	$0.890415\pi$
$824$	−2.25669e7	−	6.44254e6i	−1.15785	−	0.330551i
$825$		−	3.17877e6i		−	0.162601i
$826$		0			0
$827$			2.61032e7i			1.32718i	0.748097	+	0.663589i	$0.230968\pi$
$827$			2.61032e7i			1.32718i	−0.748097	+	0.663589i	$0.769032\pi$
$828$	−2.46345e6	+	1.31351e7i	−0.124873	+	0.665822i
$829$			3.56646e7i			1.80240i	0.433406	+	0.901199i	$0.357312\pi$
$829$			3.56646e7i			1.80240i	−0.433406	+	0.901199i	$0.642688\pi$
$830$	−589782.	+	6.34428e6i	−0.0297164	+	0.319659i
$831$	6.68520e6			0.335824
$832$	−1.35530e7	+	2.18020e7i	−0.678776	+	1.09191i
$833$		0			0
$834$	−7.15744e6	−	665376.i	−0.356322	−	0.0331247i
$835$		−	5.21879e6i		−	0.259032i
$836$	−4.37581e6	+	2.33319e7i	−0.216542	+	1.15461i
$837$	3.93260e6			0.194029
$838$	−6.61037e6	−	614519.i	−0.325174	−	0.0302291i
$839$	−2.91230e7			−1.42834			−0.714169	−	0.699973i	$-0.753195\pi$
$839$	−2.91230e7			−1.42834			−0.714169	+	0.699973i	$0.753195\pi$
$840$		0			0
$841$	−1.48874e7			−0.725819
$842$	−1.37861e7	−	1.28160e6i	−0.670133	−	0.0622975i
$843$	9.25582e6			0.448586
$844$	5.12129e6	−	2.73068e7i	0.247470	−	1.31951i
$845$		−	1.22335e7i		−	0.589400i
$846$	8.10157e6	+	753145.i	0.389173	+	0.0361787i
$847$		0			0
$848$	−3.45822e7	−	1.34444e7i	−1.65144	−	0.642027i
$849$	1.62967e7			0.775944
$850$	139266.	−	1.49808e6i	0.00661145	−	0.0711193i
$851$			1.10902e7i			0.524947i
$852$	−8.36536e6	+	4.46042e7i	−0.394808	+	2.10512i
$853$		−	2.35737e7i		−	1.10932i	−0.832078	−	0.554658i	$-0.812849\pi$
$853$		−	2.35737e7i		−	1.10932i	0.832078	−	0.554658i	$-0.187151\pi$
$854$		0			0
$855$		−	1.79373e7i		−	0.839156i
$856$	−5.32701e6	+	1.86594e7i	−0.248484	+	0.870388i
$857$		−	6.88392e6i		−	0.320172i	−0.987103	−	0.160086i	$-0.948823\pi$
$857$		−	6.88392e6i		−	0.320172i	0.987103	−	0.160086i	$-0.0511772\pi$
$858$	−2.42183e7	−	2.25140e6i	−1.12312	−	0.104408i
$859$	1.17091e7			0.541430			0.270715	−	0.962660i	$-0.412740\pi$
$859$	1.17091e7			0.541430			0.270715	+	0.962660i	$0.412740\pi$
$860$	3.22418e7	+	6.04683e6i	1.48653	+	0.278793i
$861$		0			0
$862$	−2.74722e6	+	2.95518e7i	−0.125929	+	1.35462i
$863$			3.42212e7i			1.56411i	0.623208	+	0.782056i	$0.285829\pi$
$863$			3.42212e7i			1.56411i	−0.623208	+	0.782056i	$0.714171\pi$
$864$	1.08594e7	+	5.42746e6i	0.494905	+	0.247350i
$865$	−2.25260e7			−1.02363
$866$	1.85802e6	−	1.99867e7i	0.0841892	−	0.905622i
$867$	2.35127e7			1.06232
$868$		0			0
$869$	−681201.			−0.0306003
$870$	1.21850e6	−	1.31074e7i	0.0545792	−	0.587107i
$871$	−1.14139e6			−0.0509787
$872$	−2.86753e7	−	8.18643e6i	−1.27708	−	0.364589i
$873$			9.58708e6i			0.425746i
$874$	−4.25067e6	+	4.57244e7i	−0.188226	+	2.02474i
$875$		0			0
$876$	−2.53529e6	+	1.35182e7i	−0.111627	+	0.595195i
$877$	−4.23145e7			−1.85776			−0.928882	−	0.370376i	$-0.879229\pi$
$877$	−4.23145e7			−1.85776			−0.928882	+	0.370376i	$0.879229\pi$
$878$	−8.19856e6	−	762162.i	−0.358923	−	0.0333665i
$879$			2.60750e7i			1.13829i
$880$	1.35896e7	+	5.28320e6i	0.591563	+	0.229980i
$881$			3.87794e7i			1.68330i	0.540024	+	0.841650i	$0.318415\pi$
$881$			3.87794e7i			1.68330i	−0.540024	+	0.841650i	$0.681585\pi$
$882$		0			0
$883$			3.05205e7i			1.31732i	0.752443	+	0.658658i	$0.228875\pi$
$883$			3.05205e7i			1.31732i	−0.752443	+	0.658658i	$0.771125\pi$
$884$	−1.13149e7	−	2.12207e6i	−0.486989	−	0.0913331i
$885$			3.86589e6i			0.165917i
$886$	3.14403e6	−	3.38203e7i	0.134556	−	1.44742i
$887$	1.77253e7			0.756457			0.378228	−	0.925712i	$-0.376533\pi$
$887$	1.77253e7			0.756457			0.378228	+	0.925712i	$0.376533\pi$
$888$	−1.21574e7	−	3.47076e6i	−0.517376	−	0.147704i
$889$		0			0
$890$	1.81237e7	+	1.68483e6i	0.766958	+	0.0712986i
$891$			2.07763e7i			0.876748i
$892$	2.45270e7	+	4.59995e6i	1.03213	+	0.193572i
$893$	2.79585e7			1.17323
$894$	−6.32522e6	−	588010.i	−0.264687	−	0.0246060i
$895$	−2.11330e7			−0.881870
$896$		0			0
$897$	−4.70514e7			−1.95250
$898$	4.29983e7	+	3.99725e6i	1.77935	+	0.165413i
$899$	−4.44982e6			−0.183630
$900$	2.46353e6	+	462027.i	0.101380	+	0.0190134i
$901$		−	1.66390e7i		−	0.682835i
$902$	−2.04337e7	−	1.89957e6i	−0.836238	−	0.0777391i
$903$		0			0
$904$	2.62201e7	+	7.48549e6i	1.06712	+	0.304649i
$905$	2.61047e7			1.05949
$906$	−3.62684e6	+	3.90139e7i	−0.146794	+	1.57906i
$907$		−	4.83735e6i		−	0.195249i	−0.995223	−	0.0976246i	$-0.968876\pi$
$907$		−	4.83735e6i		−	0.195249i	0.995223	−	0.0976246i	$-0.0311245\pi$
$908$	2.61256e7	+	4.89977e6i	1.05160	+	0.197225i
$909$			569329.i			0.0228535i
$910$		0			0
$911$		−	4.84024e7i		−	1.93228i	−0.258011	−	0.966142i	$-0.583067\pi$
$911$		−	4.84024e7i		−	1.93228i	0.258011	−	0.966142i	$-0.416933\pi$
$912$	−4.87939e7	−	1.89695e7i	−1.94258	−	0.755211i
$913$			6.29971e6i			0.250117i
$914$	1.29286e7	+	1.20188e6i	0.511902	+	0.0475878i
$915$	−2.28542e7			−0.902429
$916$	3.45533e6	−	1.84239e7i	0.136066	−	0.725508i
$917$		0			0
$918$	−503937.	+	5.42085e6i	−0.0197365	+	0.212305i
$919$			9.13239e6i			0.356694i	0.983968	+	0.178347i	$0.0570749\pi$
$919$			9.13239e6i			0.356694i	−0.983968	+	0.178347i	$0.942925\pi$
$920$	2.71218e7	+	7.74291e6i	1.05645	+	0.301602i
$921$	−4.66412e7			−1.81185
$922$	478981.	−	5.15239e6i	0.0185563	−	0.199609i
$923$	−5.71277e7			−2.20720
$924$		0			0
$925$	2.08000e6			0.0799299
$926$	961964.	−	1.03478e7i	0.0368664	−	0.396572i
$927$	1.75330e7			0.670127
$928$	−1.22877e7	−	6.14129e6i	−0.468381	−	0.234094i
$929$		−	1.64623e7i		−	0.625821i	−0.949783	−	0.312911i	$-0.898696\pi$
$929$		−	1.64623e7i		−	0.625821i	0.949783	−	0.312911i	$-0.101304\pi$
$930$	−964141.	+	1.03713e7i	−0.0365539	+	0.393209i
$931$		0			0
$932$	1.47063e6	+	275811.i	0.0554578	+	0.0104009i
$933$	−498954.			−0.0187653
$934$	−4.23922e7	−	3.94090e6i	−1.59008	−	0.147818i
$935$			6.53856e6i			0.244598i
$936$	5.26490e6	−	1.84418e7i	0.196427	−	0.688042i
$937$			7.05278e6i			0.262429i	0.991354	+	0.131214i	$0.0418876\pi$
$937$			7.05278e6i			0.262429i	−0.991354	+	0.131214i	$0.958112\pi$
$938$		0			0
$939$		−	369609.i		−	0.0136798i
$940$	3.16542e6	−	1.68781e7i	0.116845	−	0.623021i
$941$		−	229639.i		−	0.00845419i	−0.999991	−	0.00422710i	$-0.998654\pi$
$941$		−	229639.i		−	0.00845419i	0.999991	−	0.00422710i	$-0.00134553\pi$
$942$	−4.11854e6	+	4.43031e7i	−0.151223	+	1.62670i
$943$	−3.96986e7			−1.45377
$944$	3.76002e6	+	1.46177e6i	0.137328	+	0.0533888i
$945$		0			0
$946$	3.22944e7	+	3.00218e6i	1.17327	+	0.109071i
$947$		−	1.47748e7i		−	0.535362i	−0.963508	−	0.267681i	$-0.913743\pi$
$947$		−	1.47748e7i		−	0.535362i	0.963508	−	0.267681i	$-0.0862573\pi$
$948$	276918.	−	1.47653e6i	0.0100076	−	0.0533607i
$949$	−1.73137e7			−0.624058
$950$	8.57575e6	+	797226.i	0.308293	+	0.0286598i
$951$	2.18741e7			0.784295
$952$		0			0
$953$	1.90342e7			0.678896			0.339448	−	0.940625i	$-0.389760\pi$
$953$	1.90342e7			0.678896			0.339448	+	0.940625i	$0.389760\pi$
$954$	2.76007e7	+	2.56584e6i	0.981860	+	0.0912765i
$955$	2.27390e6			0.0806796
$956$	−440858.	+	2.35066e6i	−0.0156011	+	0.0831850i
$957$		−	1.30153e7i		−	0.459382i
$958$	2.80513e7	+	2.60773e6i	0.987505	+	0.0918012i
$959$		0			0
$960$	−1.69759e7	+	2.73084e7i	−0.594505	+	0.956352i
$961$	−2.51082e7			−0.877016
$962$	1.47319e6	−	1.58471e7i	0.0513240	−	0.552091i
$963$		−	1.44972e7i		−	0.503753i
$964$	3.07252e6	−	1.63827e7i	0.106488	−	0.567798i
$965$			2.28388e6i			0.0789504i
$966$		0			0
$967$			2.82424e7i			0.971258i	0.874165	+	0.485629i	$0.161409\pi$
$967$			2.82424e7i			0.971258i	−0.874165	+	0.485629i	$0.838591\pi$
$968$	−1.41713e7	−	4.04571e6i	−0.486094	−	0.138773i
$969$		−	2.34769e7i		−	0.803213i
$970$	2.01470e7	+	1.87292e6i	0.687512	+	0.0639130i
$971$	−4.62312e7			−1.57357			−0.786787	−	0.617225i	$-0.788257\pi$
$971$	−4.62312e7			−1.57357			−0.786787	+	0.617225i	$0.788257\pi$
$972$	−2.90159e7	−	5.44182e6i	−0.985077	−	0.184748i
$973$		0			0
$974$	1.01049e6	−	1.08699e7i	0.0341300	−	0.367136i
$975$			8.82463e6i			0.297293i
$976$	−8.64163e6	+	2.22283e7i	−0.290383	+	0.746933i
$977$	−4.05521e7			−1.35918			−0.679591	−	0.733592i	$-0.737843\pi$
$977$	−4.05521e7			−1.35918			−0.679591	+	0.733592i	$0.737843\pi$
$978$	6.06364e6	−	6.52265e7i	0.202715	−	2.18060i
$979$	1.79964e7			0.600107
$980$		0			0
$981$	2.22789e7			0.739132
$982$	−865656.	+	9.31185e6i	−0.0286462	+	0.308147i
$983$	−4.65269e7			−1.53575			−0.767875	−	0.640600i	$-0.778686\pi$
$983$	−4.65269e7			−1.53575			−0.767875	+	0.640600i	$0.778686\pi$
$984$	1.24240e7	−	4.35186e7i	0.409047	−	1.43281i
$985$			1.65668e7i			0.544061i
$986$	570216.	−	6.13381e6i	0.0186787	−	0.200927i
$987$		0			0
$988$	1.21478e7	−	6.47720e7i	0.395917	−	2.11103i
$989$	6.27417e7			2.03970
$990$	−1.08461e7	−	1.00829e6i	−0.351712	−	0.0326961i
$991$			4.32291e7i			1.39827i	0.714988	+	0.699136i	$0.246432\pi$
$991$			4.32291e7i			1.39827i	−0.714988	+	0.699136i	$0.753568\pi$
$992$	9.72266e6	+	4.85932e6i	0.313694	+	0.156782i
$993$			6.23621e7i			2.00700i
$994$		0			0
$995$		−	5.63438e6i		−	0.180422i
$996$	−1.36549e7	−	2.56092e6i	−0.436154	−	0.0817991i
$997$			2.98768e7i			0.951912i	0.879469	+	0.475956i	$0.157898\pi$
$997$			2.98768e7i			0.951912i	−0.879469	+	0.475956i	$0.842102\pi$
$998$	−1.75176e6	+	1.88437e7i	−0.0556735	+	0.598880i
$999$	−7.52655e6			−0.238607

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.6.d.b.195.2		36
4.3	odd	2	inner	196.6.d.b.195.3		36
7.2	even	3		28.6.f.a.3.12	✓	36
7.3	odd	6		28.6.f.a.19.13	yes	36
7.6	odd	2	inner	196.6.d.b.195.1		36
28.3	even	6		28.6.f.a.19.12	yes	36
28.23	odd	6		28.6.f.a.3.13	yes	36
28.27	even	2	inner	196.6.d.b.195.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.6.f.a.3.12	✓	36	7.2	even	3
28.6.f.a.3.13	yes	36	28.23	odd	6
28.6.f.a.19.12	yes	36	28.3	even	6
28.6.f.a.19.13	yes	36	7.3	odd	6
196.6.d.b.195.1		36	7.6	odd	2	inner
196.6.d.b.195.2		36	1.1	even	1	trivial
196.6.d.b.195.3		36	4.3	odd	2	inner
196.6.d.b.195.4		36	28.27	even	2	inner

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	196.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.63257 - 0.523620i) q^{2} +19.4483 q^{3} +(31.4516 + 5.89865i) q^{4} +50.4561i q^{5} +(-109.544 - 10.1835i) q^{6} +(-174.065 - 49.6932i) q^{8} +135.237 q^{9} +O(q^{10})\)	\(q+(-5.63257 - 0.523620i) q^{2} +19.4483 q^{3} +(31.4516 + 5.89865i) q^{4} +50.4561i q^{5} +(-109.544 - 10.1835i) q^{6} +(-174.065 - 49.6932i) q^{8} +135.237 q^{9} +(26.4198 - 284.197i) q^{10} -282.201i q^{11} +(611.682 + 114.719i) q^{12} +783.423i q^{13} +981.286i q^{15} +(954.412 + 371.044i) q^{16} +459.209i q^{17} +(-761.734 - 70.8129i) q^{18} -2628.74 q^{19} +(-297.622 + 1586.93i) q^{20} +(-147.766 + 1589.52i) q^{22} +3088.12i q^{23} +(-3385.27 - 966.450i) q^{24} +579.186 q^{25} +(410.216 - 4412.68i) q^{26} -2095.80 q^{27} +2371.45 q^{29} +(513.820 - 5527.16i) q^{30} -1876.42 q^{31} +(-5181.50 - 2589.68i) q^{32} -5488.34i q^{33} +(240.451 - 2586.53i) q^{34} +(4253.44 + 797.717i) q^{36} +3591.25 q^{37} +(14806.6 + 1376.46i) q^{38} +15236.3i q^{39} +(2507.32 - 8782.63i) q^{40} +12855.3i q^{41} -20317.1i q^{43} +(1664.60 - 8875.68i) q^{44} +6823.55i q^{45} +(1617.00 - 17394.0i) q^{46} -10635.7 q^{47} +(18561.7 + 7216.19i) q^{48} +(-3262.30 - 303.273i) q^{50} +8930.84i q^{51} +(-4621.14 + 24640.0i) q^{52} -36234.1 q^{53} +(11804.8 + 1097.40i) q^{54} +14238.7 q^{55} -51124.6 q^{57} +(-13357.3 - 1241.74i) q^{58} +3939.62 q^{59} +(-5788.26 + 30863.1i) q^{60} +23290.0i q^{61} +(10569.0 + 982.528i) q^{62} +(27829.2 + 17299.7i) q^{64} -39528.5 q^{65} +(-2873.80 + 30913.4i) q^{66} +1456.93i q^{67} +(-2708.71 + 14442.9i) q^{68} +60058.7i q^{69} +72920.6i q^{71} +(-23540.1 - 6720.38i) q^{72} +22100.1i q^{73} +(-20228.0 - 1880.45i) q^{74} +11264.2 q^{75} +(-82678.2 - 15506.0i) q^{76} +(7978.01 - 85819.3i) q^{78} -2413.89i q^{79} +(-18721.4 + 48155.9i) q^{80} -73622.5 q^{81} +(6731.27 - 72408.2i) q^{82} -22323.5 q^{83} -23169.9 q^{85} +(-10638.4 + 114438. i) q^{86} +46120.7 q^{87} +(-14023.5 + 49121.3i) q^{88} +63771.6i q^{89} +(3572.94 - 38434.1i) q^{90} +(-18215.7 + 97126.4i) q^{92} -36493.2 q^{93} +(59906.3 + 5569.06i) q^{94} -132636. i q^{95} +(-100772. - 50364.9i) q^{96} +70890.8i q^{97} -38164.1i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 24 q^{4} - 72 q^{8} + 2272 q^{9}+O(q^{10}) \) 36 * q + 24 * q^4 - 72 * q^8 + 2272 * q^9	\( 36 q + 24 q^{4} - 72 q^{8} + 2272 q^{9} - 1328 q^{16} + 3560 q^{18} + 13768 q^{22} - 15224 q^{25} + 176 q^{29} + 11672 q^{30} - 2320 q^{32} - 27920 q^{36} - 23444 q^{37} - 18192 q^{44} + 2080 q^{46} - 51168 q^{50} + 66972 q^{53} - 1668 q^{57} + 96872 q^{58} - 28624 q^{60} + 44544 q^{64} - 30712 q^{65} - 296128 q^{72} - 34304 q^{74} + 127704 q^{78} - 320804 q^{81} + 71212 q^{85} + 504992 q^{86} - 110536 q^{88} - 190176 q^{92} + 330324 q^{93}+O(q^{100}) \) 36 * q + 24 * q^4 - 72 * q^8 + 2272 * q^9 - 1328 * q^16 + 3560 * q^18 + 13768 * q^22 - 15224 * q^25 + 176 * q^29 + 11672 * q^30 - 2320 * q^32 - 27920 * q^36 - 23444 * q^37 - 18192 * q^44 + 2080 * q^46 - 51168 * q^50 + 66972 * q^53 - 1668 * q^57 + 96872 * q^58 - 28624 * q^60 + 44544 * q^64 - 30712 * q^65 - 296128 * q^72 - 34304 * q^74 + 127704 * q^78 - 320804 * q^81 + 71212 * q^85 + 504992 * q^86 - 110536 * q^88 - 190176 * q^92 + 330324 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more