LMFDB - Embedded newform 65.6.c.b.51.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,6,Mod(51,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("65.51");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	65.c (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:	$10.4249482878$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 227x^{12} + 16583x^{10} + 514217x^{8} + 6872896x^{6} + 35265600x^{4} + 63141120x^{2} + 26873856 $ x^14 + 227x^12 + 16583x^10 + 514217x^8 + 6872896x^6 + 35265600x^4 + 63141120x^2 + 26873856
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.8
Root			$-0.780788i$ of defining polynomial
Character	$\chi$	$=$	65.51
Dual form			65.6.c.b.51.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.21921i q^{2} -11.3769 q^{3} +30.5135 q^{4} -25.0000i q^{5} -13.8708i q^{6} +6.14028i q^{7} +76.2172i q^{8} -113.566 q^{9} +30.4803 q^{10} -391.252i q^{11} -347.149 q^{12} +(472.460 - 384.804i) q^{13} -7.48630 q^{14} +284.422i q^{15} +883.508 q^{16} +1547.69 q^{17} -138.461i q^{18} -3012.26i q^{19} -762.838i q^{20} -69.8572i q^{21} +477.019 q^{22} +921.321 q^{23} -867.115i q^{24} -625.000 q^{25} +(469.158 + 576.029i) q^{26} +4056.62 q^{27} +187.361i q^{28} -5248.50 q^{29} -346.771 q^{30} -1749.89i q^{31} +3516.13i q^{32} +4451.23i q^{33} +1886.96i q^{34} +153.507 q^{35} -3465.31 q^{36} -2782.37i q^{37} +3672.59 q^{38} +(-5375.13 + 4377.88i) q^{39} +1905.43 q^{40} -7301.71i q^{41} +85.1708 q^{42} -2464.65 q^{43} -11938.5i q^{44} +2839.16i q^{45} +1123.29i q^{46} +22645.6i q^{47} -10051.6 q^{48} +16769.3 q^{49} -762.007i q^{50} -17607.9 q^{51} +(14416.4 - 11741.7i) q^{52} -27383.4 q^{53} +4945.87i q^{54} -9781.30 q^{55} -467.995 q^{56} +34270.2i q^{57} -6399.03i q^{58} +47642.5i q^{59} +8678.73i q^{60} -25808.7 q^{61} +2133.49 q^{62} -697.329i q^{63} +23985.3 q^{64} +(-9620.11 - 11811.5i) q^{65} -5426.99 q^{66} -36207.0i q^{67} +47225.4 q^{68} -10481.8 q^{69} +187.157i q^{70} -25265.2i q^{71} -8655.71i q^{72} +60584.3i q^{73} +3392.30 q^{74} +7110.56 q^{75} -91914.8i q^{76} +2402.40 q^{77} +(-5337.56 - 6553.42i) q^{78} +87635.7 q^{79} -22087.7i q^{80} -18555.1 q^{81} +8902.33 q^{82} -82465.4i q^{83} -2131.59i q^{84} -38692.2i q^{85} -3004.93i q^{86} +59711.6 q^{87} +29820.1 q^{88} -26062.4i q^{89} -3461.54 q^{90} +(2362.80 + 2901.04i) q^{91} +28112.7 q^{92} +19908.3i q^{93} -27609.7 q^{94} -75306.6 q^{95} -40002.7i q^{96} +135691. i q^{97} +20445.3i q^{98} +44433.1i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 84 q^{3} - 38 q^{4} + 1118 q^{9} + 550 q^{10} + 168 q^{12} - 1132 q^{13} + 6440 q^{14} - 3434 q^{16} + 228 q^{17} + 2328 q^{22} + 8104 q^{23} - 8750 q^{25} - 142 q^{26} + 13680 q^{27} - 16700 q^{29}+ \cdots + 318800 q^{95}+O(q^{100}) $ 14 * q - 84 * q^3 - 38 * q^4 + 1118 * q^9 + 550 * q^10 + 168 * q^12 - 1132 * q^13 + 6440 * q^14 - 3434 * q^16 + 228 * q^17 + 2328 * q^22 + 8104 * q^23 - 8750 * q^25 - 142 * q^26 + 13680 * q^27 - 16700 * q^29 + 12700 * q^30 - 2000 * q^35 + 39970 * q^36 - 5652 * q^38 + 2416 * q^39 + 24750 * q^40 - 96836 * q^42 - 64948 * q^43 - 35932 * q^48 + 29010 * q^49 + 18632 * q^51 - 48972 * q^52 + 106232 * q^53 - 33400 * q^55 - 87808 * q^56 - 65252 * q^61 + 127744 * q^62 + 44754 * q^64 - 40550 * q^65 + 165768 * q^66 + 58536 * q^68 - 318208 * q^69 - 151892 * q^74 + 52500 * q^75 - 123736 * q^77 + 219028 * q^78 - 4336 * q^79 + 364406 * q^81 + 391092 * q^82 - 328560 * q^87 - 282548 * q^88 - 14750 * q^90 - 34376 * q^91 - 163604 * q^92 + 797896 * q^94 + 318800 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$-1$

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 $

$2$			1.21921i			0.215528i	0.994176	+	0.107764i	$0.0343691\pi$
$2$			1.21921i			0.215528i	−0.994176	+	0.107764i	$0.965631\pi$
$3$	−11.3769			−0.729828			−0.364914	−	0.931041i	$-0.618902\pi$
$3$	−11.3769			−0.729828			−0.364914	+	0.931041i	$0.618902\pi$
$4$	30.5135			0.953548
$5$		−	25.0000i		−	0.447214i
$5$		−	25.0000i		−	0.447214i
$6$		−	13.8708i		−	0.157298i
$7$			6.14028i			0.0473634i	0.999720	+	0.0236817i	$0.00753882\pi$
$7$			6.14028i			0.0473634i	−0.999720	+	0.0236817i	$0.992461\pi$
$8$			76.2172i			0.421045i
$9$	−113.566			−0.467351
$10$	30.4803			0.0963871
$11$		−	391.252i		−	0.974933i	−0.873142	−	0.487467i	$-0.837921\pi$
$11$		−	391.252i		−	0.974933i	0.873142	−	0.487467i	$-0.162079\pi$
$12$	−347.149			−0.695926
$13$	472.460	−	384.804i	0.775366	−	0.631512i
$13$	472.460	−	384.804i	0.775366	−	0.631512i
$14$	−7.48630			−0.0102081
$15$			284.422i			0.326389i
$16$	883.508			0.862801
$17$	1547.69			1.29886			0.649428	−	0.760423i	$-0.275009\pi$
$17$	1547.69			1.29886			0.649428	+	0.760423i	$0.275009\pi$
$18$		−	138.461i		−	0.100727i
$19$		−	3012.26i		−	1.91430i	−0.289601	−	0.957148i	$-0.593523\pi$
$19$		−	3012.26i		−	1.91430i	0.289601	−	0.957148i	$-0.406477\pi$
$20$		−	762.838i		−	0.426439i
$21$		−	69.8572i		−	0.0345671i
$22$	477.019			0.210126
$23$	921.321			0.363154			0.181577	−	0.983377i	$-0.441880\pi$
$23$	921.321			0.363154			0.181577	+	0.983377i	$0.441880\pi$
$24$		−	867.115i		−	0.307290i
$25$	−625.000			−0.200000
$26$	469.158	+	576.029i	0.136109	+	0.167113i
$27$	4056.62			1.07091
$28$			187.361i			0.0451632i
$29$	−5248.50			−1.15888			−0.579442	−	0.815013i	$-0.696730\pi$
$29$	−5248.50			−1.15888			−0.579442	+	0.815013i	$0.696730\pi$
$30$	−346.771			−0.0703460
$31$		−	1749.89i		−	0.327045i	−0.986540	−	0.163522i	$-0.947714\pi$
$31$		−	1749.89i		−	0.327045i	0.986540	−	0.163522i	$-0.0522856\pi$
$32$			3516.13i			0.607002i
$33$			4451.23i			0.711534i
$34$			1886.96i			0.279940i
$35$	153.507			0.0211816
$36$	−3465.31			−0.445642
$37$		−	2782.37i		−	0.334127i	−0.985946	−	0.167063i	$-0.946572\pi$
$37$		−	2782.37i		−	0.334127i	0.985946	−	0.167063i	$-0.0534284\pi$
$38$	3672.59			0.412585
$39$	−5375.13	+	4377.88i	−0.565884	+	0.460895i
$40$	1905.43			0.188297
$41$		−	7301.71i		−	0.678368i	−0.940720	−	0.339184i	$-0.889849\pi$
$41$		−	7301.71i		−	0.678368i	0.940720	−	0.339184i	$-0.110151\pi$
$42$	85.1708			0.00745019
$43$	−2464.65			−0.203275			−0.101638	−	0.994821i	$-0.532408\pi$
$43$	−2464.65			−0.203275			−0.101638	+	0.994821i	$0.532408\pi$
$44$		−	11938.5i		−	0.929645i
$45$			2839.16i			0.209006i
$46$			1123.29i			0.0782700i
$47$			22645.6i			1.49533i	0.664073	+	0.747667i	$0.268826\pi$
$47$			22645.6i			1.49533i	−0.664073	+	0.747667i	$0.731174\pi$
$48$	−10051.6			−0.629696
$49$	16769.3			0.997757
$50$		−	762.007i		−	0.0431056i
$51$	−17607.9			−0.947941
$52$	14416.4	−	11741.7i	0.739349	−	0.602177i
$53$	−27383.4			−1.33905			−0.669527	−	0.742788i	$-0.733503\pi$
$53$	−27383.4			−1.33905			−0.669527	+	0.742788i	$0.733503\pi$
$54$			4945.87i			0.230812i
$55$	−9781.30			−0.436004
$56$	−467.995			−0.0199421
$57$			34270.2i			1.39711i
$58$		−	6399.03i		−	0.249772i
$59$			47642.5i			1.78182i	0.454176	+	0.890912i	$0.349934\pi$
$59$			47642.5i			1.78182i	−0.454176	+	0.890912i	$0.650066\pi$
$60$			8678.73i			0.311227i
$61$	−25808.7			−0.888059			−0.444030	−	0.896012i	$-0.646452\pi$
$61$	−25808.7			−0.888059			−0.444030	+	0.896012i	$0.646452\pi$
$62$	2133.49			0.0704873
$63$		−	697.329i		−	0.0221353i
$64$	23985.3			0.731974
$65$	−9620.11	−	11811.5i	−0.282421	−	0.346754i
$66$	−5426.99			−0.153356
$67$		−	36207.0i		−	0.985384i	−0.870204	−	0.492692i	$-0.836013\pi$
$67$		−	36207.0i		−	0.985384i	0.870204	−	0.492692i	$-0.163987\pi$
$68$	47225.4			1.23852
$69$	−10481.8			−0.265040
$70$			187.157i			0.00456522i
$71$		−	25265.2i		−	0.594809i	−0.954752	−	0.297404i	$-0.903879\pi$
$71$		−	25265.2i		−	0.594809i	0.954752	−	0.297404i	$-0.0961209\pi$
$72$		−	8655.71i		−	0.196776i
$73$			60584.3i			1.33062i	0.746568	+	0.665309i	$0.231700\pi$
$73$			60584.3i			1.33062i	−0.746568	+	0.665309i	$0.768300\pi$
$74$	3392.30			0.0720137
$75$	7110.56			0.145966
$76$		−	91914.8i		−	1.82537i
$77$	2402.40			0.0461762
$78$	−5337.56	−	6553.42i	−0.0993359	−	0.121964i
$79$	87635.7			1.57984			0.789920	−	0.613209i	$-0.210122\pi$
$79$	87635.7			1.57984			0.789920	+	0.613209i	$0.210122\pi$
$80$		−	22087.7i		−	0.385856i
$81$	−18555.1			−0.314232
$82$	8902.33			0.146207
$83$		−	82465.4i		−	1.31394i	−0.753915	−	0.656972i	$-0.771837\pi$
$83$		−	82465.4i		−	1.31394i	0.753915	−	0.656972i	$-0.228163\pi$
$84$		−	2131.59i		−	0.0329614i
$85$		−	38692.2i		−	0.580866i
$86$		−	3004.93i		−	0.0438116i
$87$	59711.6			0.845787
$88$	29820.1			0.410490
$89$		−	26062.4i		−	0.348771i	−0.984677	−	0.174385i	$-0.944206\pi$
$89$		−	26062.4i		−	0.348771i	0.984677	−	0.174385i	$-0.0557938\pi$
$90$	−3461.54			−0.0450467
$91$	2362.80	+	2901.04i	0.0299105	+	0.0367240i
$92$	28112.7			0.346285
$93$			19908.3i			0.238686i
$94$	−27609.7			−0.322287
$95$	−75306.6			−0.856099
$96$		−	40002.7i		−	0.443007i
$97$			135691.i			1.46427i	0.681159	+	0.732135i	$0.261476\pi$
$97$			135691.i			1.46427i	−0.681159	+	0.732135i	$0.738524\pi$
$98$			20445.3i			0.215045i
$99$			44433.1i			0.455636i
$100$	−19071.0			−0.190710
$101$	−144713.			−1.41157			−0.705787	−	0.708424i	$-0.749407\pi$
$101$	−144713.			−1.41157			−0.705787	+	0.708424i	$0.749407\pi$
$102$		−	21467.7i		−	0.204308i
$103$	−6472.89			−0.0601181			−0.0300590	−	0.999548i	$-0.509570\pi$
$103$	−6472.89			−0.0601181			−0.0300590	+	0.999548i	$0.509570\pi$
$104$	29328.7	+	36009.6i	0.265895	+	0.326464i
$105$	−1746.43			−0.0154589
$106$		−	33386.2i		−	0.288604i
$107$	89977.4			0.759755			0.379878	−	0.925037i	$-0.375966\pi$
$107$	89977.4			0.759755			0.379878	+	0.925037i	$0.375966\pi$
$108$	123782.			1.02117
$109$		−	36938.6i		−	0.297792i	−0.988853	−	0.148896i	$-0.952428\pi$
$109$		−	36938.6i		−	0.297792i	0.988853	−	0.148896i	$-0.0475720\pi$
$110$		−	11925.5i		−	0.0939711i
$111$			31654.8i			0.243855i
$112$			5424.98i			0.0408652i
$113$	27703.8			0.204100			0.102050	−	0.994779i	$-0.467460\pi$
$113$	27703.8			0.204100			0.102050	+	0.994779i	$0.467460\pi$
$114$	−41782.6			−0.301116
$115$		−	23033.0i		−	0.162408i
$116$	−160150.			−1.10505
$117$	−53655.6	+	43700.8i	−0.362368	+	0.295138i
$118$	−58086.3			−0.384033
$119$			9503.22i			0.0615182i
$120$	−21677.9			−0.137424
$121$	7972.79			0.0495047
$122$		−	31466.3i		−	0.191402i
$123$			83070.8i			0.495092i
$124$		−	53395.4i		−	0.311853i
$125$			15625.0i			0.0894427i
$126$	850.191			0.00477079
$127$	198569.			1.09245			0.546226	−	0.837638i	$-0.316064\pi$
$127$	198569.			1.09245			0.546226	+	0.837638i	$0.316064\pi$
$128$			141759.i			0.764764i
$129$	28040.1			0.148356
$130$	14400.7	−	11728.9i	0.0747353	−	0.0608696i
$131$	−102104.			−0.519834			−0.259917	−	0.965631i	$-0.583695\pi$
$131$	−102104.			−0.519834			−0.259917	+	0.965631i	$0.583695\pi$
$132$			135823.i			0.678481i
$133$	18496.1			0.0906675
$134$	44144.0			0.212378
$135$		−	101415.i		−	0.478927i
$136$			117960.i			0.546876i
$137$			388748.i			1.76957i	0.466001	+	0.884784i	$0.345694\pi$
$137$			388748.i			1.76957i	−0.466001	+	0.884784i	$0.654306\pi$
$138$		−	12779.5i		−	0.0571236i
$139$	−245256.			−1.07667			−0.538334	−	0.842732i	$-0.680946\pi$
$139$	−245256.			−1.07667			−0.538334	+	0.842732i	$0.680946\pi$
$140$	4684.04			0.0201976
$141$		−	257636.i		−	1.09134i
$142$	30803.7			0.128198
$143$	−150555.	−	184851.i	−0.615682	−	0.755930i
$144$	−100337.			−0.403231
$145$			131213.i			0.518269i
$146$	−73865.1			−0.286786
$147$	−190782.			−0.728191
$148$		−	84900.0i		−	0.318606i
$149$			455367.i			1.68034i	0.542327	+	0.840168i	$0.317543\pi$
$149$			455367.i			1.68034i	−0.542327	+	0.840168i	$0.682457\pi$
$150$			8669.27i			0.0314597i
$151$		−	265698.i		−	0.948301i	−0.880444	−	0.474150i	$-0.842755\pi$
$151$		−	265698.i		−	0.948301i	0.880444	−	0.474150i	$-0.157245\pi$
$152$	229586.			0.806004
$153$	−175765.			−0.607022
$154$			2929.03i			0.00995226i
$155$	−43747.3			−0.146259
$156$	−164014.	+	133584.i	−0.539597	+	0.439485i
$157$	160333.			0.519127			0.259564	−	0.965726i	$-0.416421\pi$
$157$	160333.			0.519127			0.259564	+	0.965726i	$0.416421\pi$
$158$			106846.i			0.340500i
$159$	311538.			0.977279
$160$	87903.3			0.271460
$161$			5657.16i			0.0172002i
$162$		−	22622.5i		−	0.0677258i
$163$		−	417031.i		−	1.22942i	−0.788755	−	0.614708i	$-0.789274\pi$
$163$		−	417031.i		−	1.22942i	0.788755	−	0.614708i	$-0.210726\pi$
$164$		−	222801.i		−	0.646856i
$165$	111281.			0.318208
$166$	100543.			0.283192
$167$		−	84930.5i		−	0.235653i	−0.993034	−	0.117826i	$-0.962407\pi$
$167$		−	84930.5i		−	0.235653i	0.993034	−	0.117826i	$-0.0375926\pi$
$168$	5324.32			0.0145543
$169$	75144.3	−	363609.i	0.202386	−	0.979306i
$170$	47173.9			0.125193
$171$			342092.i			0.894648i
$172$	−75205.2			−0.193833
$173$	−122126.			−0.310236			−0.155118	−	0.987896i	$-0.549576\pi$
$173$	−122126.			−0.310236			−0.155118	+	0.987896i	$0.549576\pi$
$174$			72801.1i			0.182291i
$175$		−	3837.67i		−	0.00947268i
$176$		−	345674.i		−	0.841173i
$177$		−	542024.i		−	1.30043i
$178$	31775.6			0.0751699
$179$	459412.			1.07169			0.535846	−	0.844316i	$-0.319993\pi$
$179$	459412.			1.07169			0.535846	+	0.844316i	$0.319993\pi$
$180$			86632.7i			0.199297i
$181$	334446.			0.758804			0.379402	−	0.925232i	$-0.376130\pi$
$181$	334446.			0.758804			0.379402	+	0.925232i	$0.376130\pi$
$182$	−3536.98	+	2880.76i	−0.00791505	+	0.00644657i
$183$	293623.			0.648130
$184$			70220.5i			0.152904i
$185$	−69559.3			−0.149426
$186$	−24272.5			−0.0514436
$187$		−	605536.i		−	1.26630i
$188$			690996.i			1.42587i
$189$			24908.7i			0.0507221i
$190$		−	91814.7i		−	0.184513i
$191$	−51647.5			−0.102439			−0.0512195	−	0.998687i	$-0.516311\pi$
$191$	−51647.5			−0.102439			−0.0512195	+	0.998687i	$0.516311\pi$
$192$	−272879.			−0.534215
$193$		−	661873.i		−	1.27903i	−0.768778	−	0.639516i	$-0.779135\pi$
$193$		−	661873.i		−	1.27903i	0.768778	−	0.639516i	$-0.220865\pi$
$194$	−165436.			−0.315592
$195$	109447.	+	134378.i	0.206118	+	0.253071i
$196$	511690.			0.951409
$197$			418033.i			0.767442i	0.923449	+	0.383721i	$0.125357\pi$
$197$			418033.i			0.767442i	−0.923449	+	0.383721i	$0.874643\pi$
$198$	−54173.3			−0.0982025
$199$	846082.			1.51454			0.757268	−	0.653104i	$-0.226534\pi$
$199$	846082.			1.51454			0.757268	+	0.653104i	$0.226534\pi$
$200$		−	47635.8i		−	0.0842089i
$201$			411923.i			0.719161i
$202$		−	176436.i		−	0.304234i
$203$		−	32227.2i		−	0.0548887i
$204$	−537278.			−0.903907
$205$	−182543.			−0.303375
$206$		−	7891.82i		−	0.0129571i
$207$	−104631.			−0.169721
$208$	417422.	−	339978.i	0.668986	−	0.544869i
$209$	−1.17855e6			−1.86631
$210$		−	2129.27i		−	0.00333183i
$211$	469546.			0.726059			0.363029	−	0.931778i	$-0.381742\pi$
$211$	469546.			0.726059			0.363029	+	0.931778i	$0.381742\pi$
$212$	−835565.			−1.27685
$213$			287440.i			0.434108i
$214$			109701.i			0.163749i
$215$			61616.3i			0.0909075i
$216$			309184.i			0.450903i
$217$	10744.8			0.0154899
$218$	45035.9			0.0641827
$219$		−	689261.i		−	0.971122i
$220$	−298462.			−0.415750
$221$	731220.	−	595556.i	1.00709	−	0.820242i
$222$	−38593.8			−0.0525576
$223$			739991.i			0.996470i	0.867042	+	0.498235i	$0.166018\pi$
$223$			739991.i			0.996470i	−0.867042	+	0.498235i	$0.833982\pi$
$224$	−21590.0			−0.0287497
$225$	70979.0			0.0934703
$226$			33776.8i			0.0439894i
$227$			102602.i			0.132157i	0.997814	+	0.0660786i	$0.0210488\pi$
$227$			102602.i			0.132157i	−0.997814	+	0.0660786i	$0.978951\pi$
$228$			1.04570e6i			1.33221i
$229$		−	82633.6i		−	0.104128i	−0.998644	−	0.0520640i	$-0.983420\pi$
$229$		−	82633.6i		−	0.104128i	0.998644	−	0.0520640i	$-0.0165800\pi$
$230$	28082.1			0.0350034
$231$	−27331.8			−0.0337006
$232$		−	400026.i		−	0.487942i
$233$	−145160.			−0.175169			−0.0875846	−	0.996157i	$-0.527915\pi$
$233$	−145160.			−0.175169			−0.0875846	+	0.996157i	$0.527915\pi$
$234$	−53280.5	−	65417.5i	−0.0636105	−	0.0781006i
$235$	566139.			0.668734
$236$			1.45374e6i			1.69905i
$237$	−997022.			−1.15301
$238$	−11586.4			−0.0132589
$239$		−	305532.i		−	0.345989i	−0.984923	−	0.172994i	$-0.944656\pi$
$239$		−	305532.i		−	0.345989i	0.984923	−	0.172994i	$-0.0553442\pi$
$240$			251289.i			0.281609i
$241$			1.35283e6i			1.50037i	0.661226	+	0.750187i	$0.270037\pi$
$241$			1.35283e6i			1.50037i	−0.661226	+	0.750187i	$0.729963\pi$
$242$			9720.52i			0.0106697i
$243$	−774659.			−0.841579
$244$	−787515.			−0.846807
$245$		−	419232.i		−	0.446210i
$246$	−101281.			−0.106706
$247$	−1.15913e6	−	1.42317e6i	−1.20890	−	1.48428i
$248$	133372.			0.137700
$249$			938200.i			0.958952i
$250$	−19050.2			−0.0192774
$251$	275636.			0.276155			0.138077	−	0.990421i	$-0.455908\pi$
$251$	275636.			0.276155			0.138077	+	0.990421i	$0.455908\pi$
$252$		−	21278.0i		−	0.0211071i
$253$		−	360469.i		−	0.354051i
$254$			242098.i			0.235454i
$255$			440197.i			0.423932i
$256$	594696.			0.567146
$257$	611818.			0.577816			0.288908	−	0.957357i	$-0.406708\pi$
$257$	611818.			0.577816			0.288908	+	0.957357i	$0.406708\pi$
$258$			34186.8i			0.0319749i
$259$	17084.5			0.0158254
$260$	−293543.	−	360411.i	−0.269302	−	0.330647i
$261$	596053.			0.541606
$262$		−	124487.i		−	0.112039i
$263$	−505146.			−0.450327			−0.225163	−	0.974321i	$-0.572292\pi$
$263$	−505146.			−0.450327			−0.225163	+	0.974321i	$0.572292\pi$
$264$	−339261.			−0.299587
$265$			684586.i			0.598843i
$266$			22550.7i			0.0195414i
$267$			296509.i			0.254543i
$268$		−	1.10480e6i		−	0.939610i
$269$	325423.			0.274200			0.137100	−	0.990557i	$-0.456222\pi$
$269$	325423.			0.274200			0.137100	+	0.990557i	$0.456222\pi$
$270$	123647.			0.103222
$271$		−	314685.i		−	0.260288i	−0.991495	−	0.130144i	$-0.958456\pi$
$271$		−	314685.i		−	0.260288i	0.991495	−	0.130144i	$-0.0415439\pi$
$272$	1.36739e6			1.12065
$273$	−26881.4	−	33004.8i	−0.0218295	−	0.0268022i
$274$	−473967.			−0.381392
$275$			244533.i			0.194987i
$276$	−319836.			−0.252728
$277$	−1.70118e6			−1.33214			−0.666072	−	0.745887i	$-0.732026\pi$
$277$	−1.70118e6			−1.33214			−0.666072	+	0.745887i	$0.732026\pi$
$278$		−	299018.i		−	0.232052i
$279$			198729.i			0.152845i
$280$			11699.9i			0.00891838i
$281$			973161.i			0.735222i	0.929980	+	0.367611i	$0.119824\pi$
$281$			973161.i			0.735222i	−0.929980	+	0.367611i	$0.880176\pi$
$282$	314113.			0.235214
$283$	855504.			0.634974			0.317487	−	0.948263i	$-0.397161\pi$
$283$	855504.			0.634974			0.317487	+	0.948263i	$0.397161\pi$
$284$		−	770931.i		−	0.567178i
$285$	856755.			0.624805
$286$	225373.	−	183559.i	0.162924	−	0.132697i
$287$	44834.5			0.0321298
$288$		−	399315.i		−	0.283683i
$289$	975477.			0.687025
$290$	−159976.			−0.111702
$291$		−	1.54374e6i		−	1.06867i
$292$			1.84864e6i			1.26881i
$293$			434109.i			0.295413i	0.989031	+	0.147707i	$0.0471891\pi$
$293$			434109.i			0.295413i	−0.989031	+	0.147707i	$0.952811\pi$
$294$		−	232604.i		−	0.156946i
$295$	1.19106e6			0.796856
$296$	212065.			0.140682
$297$		−	1.58716e6i		−	1.04407i
$298$	−555189.			−0.362160
$299$	435287.	−	354528.i	0.281578	−	0.229336i
$300$	216968.			0.139185
$301$		−	15133.6i		−	0.00962781i
$302$	323942.			0.204386
$303$	1.64638e6			1.03021
$304$		−	2.66136e6i		−	1.65165i
$305$			645218.i			0.397152i
$306$		−	214295.i		−	0.130830i
$307$			1.33224e6i			0.806748i	0.915035	+	0.403374i	$0.132163\pi$
$307$			1.33224e6i			0.806748i	−0.915035	+	0.403374i	$0.867837\pi$
$308$	73305.6			0.0440312
$309$	73641.3			0.0438758
$310$		−	53337.2i		−	0.0315229i
$311$	−1.22090e6			−0.715781			−0.357891	−	0.933764i	$-0.616504\pi$
$311$	−1.22090e6			−0.715781			−0.357891	+	0.933764i	$0.616504\pi$
$312$	−333670.	−	409677.i	−0.194057	−	0.238262i
$313$	−3.36877e6			−1.94362			−0.971808	−	0.235772i	$-0.924238\pi$
$313$	−3.36877e6			−1.94362			−0.971808	+	0.235772i	$0.924238\pi$
$314$			195480.i			0.111887i
$315$	−17433.2			−0.00989922
$316$	2.67407e6			1.50645
$317$			181109.i			0.101226i	0.998718	+	0.0506131i	$0.0161175\pi$
$317$			181109.i			0.101226i	−0.998718	+	0.0506131i	$0.983882\pi$
$318$			379831.i			0.210631i
$319$			2.05349e6i			1.12984i
$320$		−	599633.i		−	0.327349i
$321$	−1.02366e6			−0.554491
$322$	−6897.28			−0.00370713
$323$		−	4.66204e6i		−	2.48639i
$324$	−566180.			−0.299635
$325$	−295288.	+	240503.i	−0.155073	+	0.126302i
$326$	508449.			0.264974
$327$			420246.i			0.217337i
$328$	556516.			0.285623
$329$	−139050.			−0.0708241
$330$			135675.i			0.0685827i
$331$			1.72873e6i			0.867277i	0.901087	+	0.433639i	$0.142771\pi$
$331$			1.72873e6i			0.867277i	−0.901087	+	0.433639i	$0.857229\pi$
$332$		−	2.51631e6i		−	1.25291i
$333$			315984.i			0.156154i
$334$	103548.			0.0507898
$335$	−905175.			−0.440677
$336$		−	61719.4i		−	0.0298245i
$337$	2.31320e6			1.10953			0.554764	−	0.832008i	$-0.312809\pi$
$337$	2.31320e6			1.10953			0.554764	+	0.832008i	$0.312809\pi$
$338$	443317.	+	91616.8i	0.211068	+	0.0436198i
$339$	−315183.			−0.148958
$340$		−	1.18063e6i		−	0.553883i
$341$	−684649.			−0.318847
$342$	−417082.			−0.192822
$343$			206168.i			0.0946205i
$344$		−	187849.i		−	0.0855880i
$345$			262044.i			0.118530i
$346$		−	148897.i		−	0.0668646i
$347$	1.45965e6			0.650766			0.325383	−	0.945582i	$-0.394507\pi$
$347$	1.45965e6			0.650766			0.325383	+	0.945582i	$0.394507\pi$
$348$	1.82201e6			0.806498
$349$		−	441041.i		−	0.193828i	−0.995293	−	0.0969138i	$-0.969103\pi$
$349$		−	441041.i		−	0.193828i	0.995293	−	0.0969138i	$-0.0308971\pi$
$350$	4678.93			0.00204163
$351$	1.91659e6	−	1.56100e6i	0.830350	−	0.676295i
$352$	1.37569e6			0.591787
$353$			1.75552e6i			0.749843i	0.927057	+	0.374921i	$0.122330\pi$
$353$			1.75552e6i			0.749843i	−0.927057	+	0.374921i	$0.877670\pi$
$354$	660842.			0.280278
$355$	−631631.			−0.266006
$356$		−	795257.i		−	0.332569i
$357$		−	108117.i		−	0.0448977i
$358$			560121.i			0.230980i
$359$			2.60457e6i			1.06659i	0.845928	+	0.533297i	$0.179047\pi$
$359$			2.60457e6i			1.06659i	−0.845928	+	0.533297i	$0.820953\pi$
$360$	−216393.			−0.0880008
$361$	−6.59763e6			−2.66453
$362$			407761.i			0.163544i
$363$	−90705.5			−0.0361299
$364$	72097.5	+	88520.8i	0.0285211	+	0.0350181i
$365$	1.51461e6			0.595070
$366$			357989.i			0.139690i
$367$	−1.40036e6			−0.542717			−0.271359	−	0.962478i	$-0.587473\pi$
$367$	−1.40036e6			−0.542717			−0.271359	+	0.962478i	$0.587473\pi$
$368$	813994.			0.313330
$369$			829229.i			0.317036i
$370$		−	84807.5i		−	0.0322055i
$371$		−	168142.i		−	0.0634221i
$372$			607473.i			0.227599i
$373$	−698420.			−0.259923			−0.129961	−	0.991519i	$-0.541485\pi$
$373$	−698420.			−0.259923			−0.129961	+	0.991519i	$0.541485\pi$
$374$	738276.			0.272923
$375$		−	177764.i		−	0.0652778i
$376$	−1.72598e6			−0.629603
$377$	−2.47971e6	+	2.01965e6i	−0.898560	+	0.731850i
$378$	−30369.0			−0.0109320
$379$		−	860183.i		−	0.307605i	−0.988102	−	0.153802i	$-0.950848\pi$
$379$		−	860183.i		−	0.307605i	0.988102	−	0.153802i	$-0.0491519\pi$
$380$	−2.29787e6			−0.816331
$381$	−2.25910e6			−0.797302
$382$		−	62969.2i		−	0.0220785i
$383$			3.53928e6i			1.23287i	0.787406	+	0.616435i	$0.211424\pi$
$383$			3.53928e6i			1.23287i	−0.787406	+	0.616435i	$0.788576\pi$
$384$		−	1.61278e6i		−	0.558146i
$385$		−	60059.9i		−	0.0206506i
$386$	806964.			0.275668
$387$	279902.			0.0950010
$388$			4.14041e6i			1.39625i
$389$	854347.			0.286260			0.143130	−	0.989704i	$-0.454283\pi$
$389$	854347.			0.286260			0.143130	+	0.989704i	$0.454283\pi$
$390$	−163835.	+	133439.i	−0.0545439	+	0.0444244i
$391$	1.42592e6			0.471685
$392$			1.27811e6i			0.420100i
$393$	1.16163e6			0.379390
$394$	−509671.			−0.165405
$395$		−	2.19089e6i		−	0.706526i
$396$			1.35581e6i			0.434471i
$397$			4.61900e6i			1.47086i	0.677601	+	0.735430i	$0.263020\pi$
$397$			4.61900e6i			1.47086i	−0.677601	+	0.735430i	$0.736980\pi$
$398$			1.03155e6i			0.326425i
$399$	−210428.			−0.0661717
$400$	−552192.			−0.172560
$401$		−	147425.i		−	0.0457835i	−0.999738	−	0.0228917i	$-0.992713\pi$
$401$		−	147425.i		−	0.0457835i	0.999738	−	0.0228917i	$-0.00728730\pi$
$402$	−502221.			−0.154999
$403$	−673366.	−	826754.i	−0.206533	−	0.253579i
$404$	−4.41570e6			−1.34600
$405$			463876.i			0.140529i
$406$	39291.8			0.0118301
$407$	−1.08861e6			−0.325751
$408$		−	1.34202e6i		−	0.399125i
$409$			5.88390e6i			1.73923i	0.493731	+	0.869615i	$0.335633\pi$
$409$			5.88390e6i			1.73923i	−0.493731	+	0.869615i	$0.664367\pi$
$410$		−	222558.i		−	0.0653859i
$411$		−	4.42275e6i		−	1.29148i
$412$	−197511.			−0.0573254
$413$	−292538.			−0.0843932
$414$		−	127567.i		−	0.0365796i
$415$	−2.06164e6			−0.587613
$416$	1.35302e6	+	1.66123e6i	0.383329	+	0.470649i
$417$	2.79025e6			0.785782
$418$		−	1.43691e6i		−	0.402243i
$419$	875261.			0.243558			0.121779	−	0.992557i	$-0.461140\pi$
$419$	875261.			0.243558			0.121779	+	0.992557i	$0.461140\pi$
$420$	−53289.8			−0.0147408
$421$			268396.i			0.0738025i	0.999319	+	0.0369012i	$0.0117487\pi$
$421$			268396.i			0.0738025i	−0.999319	+	0.0369012i	$0.988251\pi$
$422$			572475.i			0.156486i
$423$		−	2.57177e6i		−	0.698847i
$424$		−	2.08709e6i		−	0.563802i
$425$	−967304.			−0.259771
$426$	−350450.			−0.0935625
$427$		−	158473.i		−	0.0420615i
$428$	2.74553e6			0.724463
$429$	1.71285e6	+	2.10303e6i	0.449342	+	0.551699i
$430$	−75123.3			−0.0195931
$431$		−	5.07495e6i		−	1.31595i	−0.753041	−	0.657974i	$-0.771414\pi$
$431$		−	5.07495e6i		−	1.31595i	0.753041	−	0.657974i	$-0.228586\pi$
$432$	3.58405e6			0.923985
$433$	192569.			0.0493590			0.0246795	−	0.999695i	$-0.492143\pi$
$433$	192569.			0.0493590			0.0246795	+	0.999695i	$0.492143\pi$
$434$			13100.2i			0.00333852i
$435$		−	1.49279e6i		−	0.378247i
$436$		−	1.12713e6i		−	0.283959i
$437$		−	2.77526e6i		−	0.695185i
$438$	840356.			0.209304
$439$	7.75585e6			1.92074			0.960368	−	0.278734i	$-0.0899148\pi$
$439$	7.75585e6			1.92074			0.960368	+	0.278734i	$0.0899148\pi$
$440$		−	745504.i		−	0.183577i
$441$	−1.90443e6			−0.466303
$442$	726109.	+	891512.i	0.176785	+	0.217056i
$443$	−1.65318e6			−0.400230			−0.200115	−	0.979772i	$-0.564132\pi$
$443$	−1.65318e6			−0.400230			−0.200115	+	0.979772i	$0.564132\pi$
$444$			965898.i			0.232527i
$445$	−651561.			−0.155975
$446$	−902205.			−0.214767
$447$		−	5.18066e6i		−	1.22636i
$448$			147277.i			0.0346688i
$449$		−	4.12655e6i		−	0.965988i	−0.875624	−	0.482994i	$-0.839549\pi$
$449$		−	4.12655e6i		−	0.965988i	0.875624	−	0.482994i	$-0.160451\pi$
$450$			86538.4i			0.0201455i
$451$	−2.85681e6			−0.661363
$452$	845341.			0.194619
$453$			3.02282e6i			0.692096i
$454$	−125094.			−0.0284836
$455$	72525.9	−	59070.1i	0.0164235	−	0.0133764i
$456$	−2.61198e6			−0.588244
$457$			2.76471e6i			0.619239i	0.950861	+	0.309620i	$0.100202\pi$
$457$			2.76471e6i			0.619239i	−0.950861	+	0.309620i	$0.899798\pi$
$458$	100748.			0.0224425
$459$	6.27837e6			1.39096
$460$		−	702819.i		−	0.154863i
$461$		−	4.25293e6i		−	0.932043i	−0.884773	−	0.466022i	$-0.845687\pi$
$461$		−	4.25293e6i		−	0.932043i	0.884773	−	0.466022i	$-0.154313\pi$
$462$		−	33323.2i		−	0.00726344i
$463$		−	2.81006e6i		−	0.609204i	−0.952480	−	0.304602i	$-0.901477\pi$
$463$		−	2.81006e6i		−	0.609204i	0.952480	−	0.304602i	$-0.0985235\pi$
$464$	−4.63709e6			−0.999887
$465$	497708.			0.106744
$466$		−	176981.i		−	0.0377539i
$467$	8.91425e6			1.89144			0.945720	−	0.324982i	$-0.105358\pi$
$467$	8.91425e6			1.89144			0.945720	+	0.324982i	$0.105358\pi$
$468$	−1.63722e6	+	1.33347e6i	−0.345535	+	0.281428i
$469$	222321.			0.0466711
$470$			690243.i			0.144131i
$471$	−1.82409e6			−0.378873
$472$	−3.63118e6			−0.750228
$473$			964301.i			0.198180i
$474$		−	1.21558e6i		−	0.248507i
$475$			1.88266e6i			0.382859i
$476$			289977.i			0.0586605i
$477$	3.10984e6			0.625809
$478$	372508.			0.0745703
$479$		−	1.04773e6i		−	0.208647i	−0.994543	−	0.104323i	$-0.966732\pi$
$479$		−	1.04773e6i		−	0.208647i	0.994543	−	0.104323i	$-0.0332677\pi$
$480$	−1.00007e6			−0.198119
$481$	−1.07067e6	−	1.31456e6i	−0.211005	−	0.259070i
$482$	−1.64938e6			−0.323373
$483$		−	64360.9i		−	0.0125532i
$484$	243278.			0.0472051
$485$	3.39227e6			0.654842
$486$		−	944473.i		−	0.181384i
$487$		−	2.64473e6i		−	0.505311i	−0.967556	−	0.252656i	$-0.918696\pi$
$487$		−	2.64473e6i		−	0.505311i	0.967556	−	0.252656i	$-0.0813039\pi$
$488$		−	1.96707e6i		−	0.373913i
$489$			4.74451e6i			0.897262i
$490$	511133.			0.0961709
$491$	−2.58589e6			−0.484069			−0.242034	−	0.970268i	$-0.577815\pi$
$491$	−2.58589e6			−0.484069			−0.242034	+	0.970268i	$0.577815\pi$
$492$			2.53478e6i			0.472093i
$493$	−8.12304e6			−1.50522
$494$	1.73515e6	−	1.41323e6i	0.319904	−	0.260552i
$495$	1.11083e6			0.203767
$496$		−	1.54604e6i		−	0.282174i
$497$	155135.			0.0281722
$498$	−1.14386e6			−0.206681
$499$			8.62141e6i			1.54998i	0.631972	+	0.774992i	$0.282246\pi$
$499$			8.62141e6i			1.54998i	−0.631972	+	0.774992i	$0.717754\pi$
$500$			476774.i			0.0852879i
$501$			966245.i			0.171986i
$502$			336059.i			0.0595191i
$503$	4.82702e6			0.850665			0.425333	−	0.905037i	$-0.360157\pi$
$503$	4.82702e6			0.850665			0.425333	+	0.905037i	$0.360157\pi$
$504$	53148.5			0.00931997
$505$			3.61782e6i			0.631275i
$506$	439488.			0.0763081
$507$	−854909.	+	4.13674e6i	−0.147707	+	0.714725i
$508$	6.05905e6			1.04171
$509$		−	7.34279e6i		−	1.25622i	−0.778124	−	0.628111i	$-0.783828\pi$
$509$		−	7.34279e6i		−	1.25622i	0.778124	−	0.628111i	$-0.216172\pi$
$510$	−536693.			−0.0913693
$511$	−372005.			−0.0630225
$512$			5.26136e6i			0.887000i
$513$		−	1.22196e7i		−	2.05005i
$514$			745936.i			0.124536i
$515$			161822.i			0.0268856i
$516$	855602.			0.141464
$517$	8.86012e6			1.45785
$518$			20829.7i			0.00341081i
$519$	1.38941e6			0.226419
$520$	900240.	−	733218.i	0.145999	−	0.118912i
$521$	1.06181e7			1.71377			0.856885	−	0.515508i	$-0.172397\pi$
$521$	1.06181e7			1.71377			0.856885	+	0.515508i	$0.172397\pi$
$522$			726715.i			0.116731i
$523$	−7.02911e6			−1.12369			−0.561844	−	0.827243i	$-0.689908\pi$
$523$	−7.02911e6			−1.12369			−0.561844	+	0.827243i	$0.689908\pi$
$524$	−3.11556e6			−0.495687
$525$			43660.8i			0.00691342i
$526$		−	615880.i		−	0.0970581i
$527$		−	2.70828e6i		−	0.424784i
$528$			3.93270e6i			0.613912i
$529$	−5.58751e6			−0.868119
$530$	−834655.			−0.129068
$531$		−	5.41059e6i		−	0.832738i
$532$	564382.			0.0864558
$533$	−2.80973e6	−	3.44977e6i	−0.428397	−	0.525983i
$534$	−361508.			−0.0548611
$535$		−	2.24943e6i		−	0.339773i
$536$	2.75960e6			0.414891
$537$	−5.22668e6			−0.782150
$538$			396760.i			0.0590979i
$539$		−	6.56102e6i		−	0.972746i
$540$		−	3.09454e6i		−	0.456680i
$541$		−	1.98960e6i		−	0.292263i	−0.989265	−	0.146131i	$-0.953318\pi$
$541$		−	1.98960e6i		−	0.292263i	0.989265	−	0.146131i	$-0.0466822\pi$
$542$	383668.			0.0560993
$543$	−3.80496e6			−0.553796
$544$			5.44187e6i			0.788408i
$545$	−923464.			−0.133177
$546$	40239.8	−	32774.1i	0.00577663	−	0.00470488i
$547$	−7.00138e6			−1.00050			−0.500248	−	0.865882i	$-0.666758\pi$
$547$	−7.00138e6			−1.00050			−0.500248	+	0.865882i	$0.666758\pi$
$548$			1.18621e7i			1.68737i
$549$	2.93100e6			0.415036
$550$	−298137.			−0.0420251
$551$			1.58099e7i			2.21845i
$552$		−	798891.i		−	0.111594i
$553$			538107.i			0.0748266i
$554$		−	2.07410e6i		−	0.287115i
$555$	791369.			0.109055
$556$	−7.48361e6			−1.02665
$557$			2.38525e6i			0.325759i	0.986646	+	0.162879i	$0.0520781\pi$
$557$			2.38525e6i			0.325759i	−0.986646	+	0.162879i	$0.947922\pi$
$558$	−242292.			−0.0329423
$559$	−1.16445e6	+	948409.i	−0.157613	+	0.128371i
$560$	135625.			0.0182755
$561$			6.88911e6i			0.924179i
$562$	−1.18649e6			−0.158461
$563$	1.10441e7			1.46845			0.734226	−	0.678905i	$-0.237545\pi$
$563$	1.10441e7			1.46845			0.734226	+	0.678905i	$0.237545\pi$
$564$		−	7.86138e6i		−	1.04064i
$565$		−	692595.i		−	0.0912764i
$566$			1.04304e6i			0.136855i
$567$		−	113933.i		−	0.0148831i
$568$	1.92564e6			0.250441
$569$	−1.05466e7			−1.36563			−0.682815	−	0.730591i	$-0.739245\pi$
$569$	−1.05466e7			−1.36563			−0.682815	+	0.730591i	$0.739245\pi$
$570$			1.04457e6i			0.134663i
$571$	−2.56217e6			−0.328865			−0.164433	−	0.986388i	$-0.552579\pi$
$571$	−2.56217e6			−0.328865			−0.164433	+	0.986388i	$0.552579\pi$
$572$	−4.59398e6	−	5.64046e6i	−0.587082	−	0.720816i
$573$	587588.			0.0747629
$574$			54662.8i			0.00692487i
$575$	−575826.			−0.0726309
$576$	−2.72393e6			−0.342089
$577$			1.48196e7i			1.85309i	0.376183	+	0.926545i	$0.377236\pi$
$577$			1.48196e7i			1.85309i	−0.376183	+	0.926545i	$0.622764\pi$
$578$			1.18931e6i			0.148073i
$579$			7.53006e6i			0.933474i
$580$			4.00376e6i			0.494194i
$581$	506360.			0.0622328
$582$	1.88215e6			0.230328
$583$			1.07138e7i			1.30549i
$584$	−4.61757e6			−0.560249
$585$	1.09252e6	+	1.34139e6i	0.131990	+	0.162056i
$586$	−529271.			−0.0636699
$587$		−	1.20402e7i		−	1.44224i	−0.692809	−	0.721121i	$-0.743627\pi$
$587$		−	1.20402e7i		−	1.44224i	0.692809	−	0.721121i	$-0.256373\pi$
$588$	−5.82145e6			−0.694364
$589$	−5.27113e6			−0.626060
$590$			1.45216e6i			0.171745i
$591$		−	4.75592e6i		−	0.560100i
$592$		−	2.45825e6i		−	0.288285i
$593$		−	2.36654e6i		−	0.276361i	−0.990407	−	0.138180i	$-0.955875\pi$
$593$		−	2.36654e6i		−	0.276361i	0.990407	−	0.138180i	$-0.0441254\pi$
$594$	1.93508e6			0.225026
$595$	237581.			0.0275118
$596$			1.38949e7i			1.60228i
$597$	−9.62578e6			−1.10535
$598$	432245.	+	530708.i	0.0494284	+	0.0606879i
$599$	−292768.			−0.0333392			−0.0166696	−	0.999861i	$-0.505306\pi$
$599$	−292768.			−0.0333392			−0.0166696	+	0.999861i	$0.505306\pi$
$600$			541947.i			0.0614580i
$601$	1.20438e7			1.36011			0.680057	−	0.733159i	$-0.261955\pi$
$601$	1.20438e7			1.36011			0.680057	+	0.733159i	$0.261955\pi$
$602$	18451.1			0.00207506
$603$			4.11190e6i			0.460520i
$604$		−	8.10738e6i		−	0.904250i
$605$		−	199320.i		−	0.0221392i
$606$			2.00729e6i			0.222039i
$607$	−1.05634e7			−1.16367			−0.581836	−	0.813306i	$-0.697666\pi$
$607$	−1.05634e7			−1.16367			−0.581836	+	0.813306i	$0.697666\pi$
$608$	1.05915e7			1.16198
$609$			366646.i			0.0400593i
$610$	−786657.			−0.0855975
$611$	8.71411e6	+	1.06991e7i	0.944322	+	1.15943i
$612$	−5.36321e6			−0.578824
$613$		−	1.72742e7i		−	1.85673i	−0.371675	−	0.928363i	$-0.621217\pi$
$613$		−	1.72742e7i		−	1.85673i	0.371675	−	0.928363i	$-0.378783\pi$
$614$	−1.62429e6			−0.173877
$615$	2.07677e6			0.221412
$616$			183104.i			0.0194422i
$617$		−	1.23381e7i		−	1.30477i	−0.757886	−	0.652387i	$-0.773768\pi$
$617$		−	1.23381e7i		−	1.30477i	0.757886	−	0.652387i	$-0.226232\pi$
$618$			89784.4i			0.00945648i
$619$		−	3.76541e6i		−	0.394990i	−0.980304	−	0.197495i	$-0.936719\pi$
$619$		−	3.76541e6i		−	0.394990i	0.980304	−	0.197495i	$-0.0632806\pi$
$620$	−1.33488e6			−0.139465
$621$	3.73745e6			0.388907
$622$		−	1.48854e6i		−	0.154271i
$623$	160031.			0.0165190
$624$	−4.74897e6	+	3.86789e6i	−0.488245	+	0.397660i
$625$	390625.			0.0400000
$626$		−	4.10724e6i		−	0.418904i
$627$	1.34083e7			1.36209
$628$	4.89232e6			0.495012
$629$		−	4.30624e6i		−	0.433982i
$630$		−	21254.8i		−	0.00213356i
$631$		−	4.25951e6i		−	0.425879i	−0.977065	−	0.212940i	$-0.931696\pi$
$631$		−	4.25951e6i		−	0.425879i	0.977065	−	0.212940i	$-0.0683037\pi$
$632$			6.67935e6i			0.665183i
$633$	−5.34197e6			−0.529898
$634$	−220811.			−0.0218171
$635$		−	4.96423e6i		−	0.488560i
$636$	9.50613e6			0.931882
$637$	7.92283e6	−	6.45290e6i	0.773627	−	0.630095i
$638$	−2.50364e6			−0.243511
$639$			2.86928e6i			0.277985i
$640$	3.54399e6			0.342013
$641$	2.97347e6			0.285837			0.142918	−	0.989734i	$-0.454351\pi$
$641$	2.97347e6			0.285837			0.142918	+	0.989734i	$0.454351\pi$
$642$		−	1.24806e6i		−	0.119508i
$643$		−	9.08699e6i		−	0.866748i	−0.901214	−	0.433374i	$-0.857323\pi$
$643$		−	9.08699e6i		−	0.866748i	0.901214	−	0.433374i	$-0.142677\pi$
$644$			172620.i			0.0164012i
$645$		−	701002.i		−	0.0663468i
$646$	5.68401e6			0.535888
$647$	−1.70405e7			−1.60037			−0.800185	−	0.599753i	$-0.795266\pi$
$647$	−1.70405e7			−1.60037			−0.800185	+	0.599753i	$0.795266\pi$
$648$		−	1.41421e6i		−	0.132306i
$649$	1.86402e7			1.73716
$650$	−293224.	−	360018.i	−0.0272217	−	0.0334227i
$651$	−122243.			−0.0113050
$652$		−	1.27251e7i		−	1.17231i
$653$	33156.7			0.00304291			0.00152145	−	0.999999i	$-0.499516\pi$
$653$	33156.7			0.00304291			0.00152145	+	0.999999i	$0.499516\pi$
$654$	−512369.			−0.0468423
$655$			2.55260e6i			0.232477i
$656$		−	6.45112e6i		−	0.585296i
$657$		−	6.88034e6i		−	0.621866i
$658$		−	169531.i		−	0.0152646i
$659$	1.21273e7			1.08780			0.543902	−	0.839149i	$-0.316946\pi$
$659$	1.21273e7			1.08780			0.543902	+	0.839149i	$0.316946\pi$
$660$	3.39557e6			0.303426
$661$			7.42160e6i			0.660684i	0.943861	+	0.330342i	$0.107164\pi$
$661$			7.42160e6i			0.660684i	−0.943861	+	0.330342i	$0.892836\pi$
$662$	−2.10769e6			−0.186923
$663$	−8.31901e6	+	6.77558e6i	−0.735001	+	0.598636i
$664$	6.28528e6			0.553229
$665$		−	462403.i		−	0.0405477i
$666$	−385251.			−0.0336557
$667$	−4.83555e6			−0.420854
$668$		−	2.59153e6i		−	0.224706i
$669$		−	8.41879e6i		−	0.727251i
$670$		−	1.10360e6i		−	0.0949783i
$671$			1.00977e7i			0.865799i
$672$	245627.			0.0209823
$673$	1.24325e7			1.05809			0.529043	−	0.848595i	$-0.322551\pi$
$673$	1.24325e7			1.05809			0.529043	+	0.848595i	$0.322551\pi$
$674$			2.82028e6i			0.239135i
$675$	−2.53539e6			−0.214183
$676$	2.29292e6	−	1.10950e7i	0.192984	−	0.933815i
$677$	−8.45003e6			−0.708576			−0.354288	−	0.935136i	$-0.615277\pi$
$677$	−8.45003e6			−0.708576			−0.354288	+	0.935136i	$0.615277\pi$
$678$		−	384275.i		−	0.0321047i
$679$	−833179.			−0.0693528
$680$	2.94901e6			0.244570
$681$		−	1.16729e6i		−	0.0964520i
$682$		−	834732.i		−	0.0687205i
$683$			9.91289e6i			0.813108i	0.913627	+	0.406554i	$0.133270\pi$
$683$			9.91289e6i			0.813108i	−0.913627	+	0.406554i	$0.866730\pi$
$684$			1.04384e7i			0.853090i
$685$	9.71871e6			0.791375
$686$	−251362.			−0.0203934
$687$			940113.i			0.0759956i
$688$	−2.17754e6			−0.175386
$689$	−1.29376e7	+	1.05373e7i	−1.03826	+	0.845629i
$690$	−319487.			−0.0255465
$691$			3.01942e6i			0.240563i	0.992740	+	0.120281i	$0.0383796\pi$
$691$			3.01942e6i			0.240563i	−0.992740	+	0.120281i	$0.961620\pi$
$692$	−3.72649e6			−0.295825
$693$	−272831.			−0.0215805
$694$			1.77962e6i			0.140258i
$695$			6.13139e6i			0.481501i
$696$			4.55105e6i			0.356114i
$697$		−	1.13008e7i		−	0.881101i
$698$	537722.			0.0417753
$699$	1.65147e6			0.127843
$700$		−	117101.i		−	0.00903265i
$701$	7.55729e6			0.580859			0.290430	−	0.956896i	$-0.406202\pi$
$701$	7.55729e6			0.580859			0.290430	+	0.956896i	$0.406202\pi$
$702$	1.90319e6	+	2.33673e6i	0.145761	+	0.178964i
$703$	−8.38124e6			−0.639617
$704$		−	9.38431e6i		−	0.713626i
$705$	−6.44090e6			−0.488061
$706$	−2.14036e6			−0.161612
$707$		−	888577.i		−	0.0668570i
$708$		−	1.65391e7i		−	1.24002i
$709$		−	8.22641e6i		−	0.614603i	−0.951612	−	0.307302i	$-0.900574\pi$
$709$		−	8.22641e6i		−	0.614603i	0.951612	−	0.307302i	$-0.0994260\pi$
$710$		−	770091.i		−	0.0573319i
$711$	−9.95247e6			−0.738341
$712$	1.98641e6			0.146848
$713$		−	1.61221e6i		−	0.118768i
$714$	131818.			0.00967672
$715$	−4.62128e6	+	3.76389e6i	−0.338062	+	0.275341i
$716$	1.40183e7			1.02191
$717$			3.47600e6i			0.252512i
$718$	−3.17552e6			−0.229881
$719$	−2.42533e7			−1.74964			−0.874821	−	0.484446i	$-0.839021\pi$
$719$	−2.42533e7			−1.74964			−0.874821	+	0.484446i	$0.839021\pi$
$720$			2.50842e6i			0.180330i
$721$		−	39745.3i		−	0.00284740i
$722$		−	8.04391e6i		−	0.574280i
$723$		−	1.53910e7i		−	1.09501i
$724$	1.02051e7			0.723556
$725$	3.28031e6			0.231777
$726$		−	110589.i		−	0.00778702i
$727$	−4.40741e6			−0.309277			−0.154638	−	0.987971i	$-0.549421\pi$
$727$	−4.40741e6			−0.309277			−0.154638	+	0.987971i	$0.549421\pi$
$728$	−221109.	+	180086.i	−0.0154624	+	0.0125937i
$729$	1.33221e7			0.928439
$730$			1.84663e6i			0.128254i
$731$	−3.81451e6			−0.264025
$732$	8.95947e6			0.618023
$733$			1.70711e7i			1.17355i	0.809751	+	0.586774i	$0.199602\pi$
$733$			1.70711e7i			1.17355i	−0.809751	+	0.586774i	$0.800398\pi$
$734$		−	1.70733e6i		−	0.116971i
$735$			4.76956e6i			0.325657i
$736$			3.23949e6i			0.220436i
$737$	−1.41661e7			−0.960684
$738$	−1.01101e6			−0.0683302
$739$			6.86306e6i			0.462281i	0.972920	+	0.231141i	$0.0742458\pi$
$739$			6.86306e6i			0.462281i	−0.972920	+	0.231141i	$0.925754\pi$
$740$	−2.12250e6			−0.142485
$741$	1.31873e7	+	1.61913e7i	0.882289	+	1.08327i
$742$	205000.			0.0136693
$743$			7.82433e6i			0.519966i	0.965613	+	0.259983i	$0.0837170\pi$
$743$			7.82433e6i			0.519966i	−0.965613	+	0.259983i	$0.916283\pi$
$744$	−1.51736e6			−0.100498
$745$	1.13842e7			0.751469
$746$		−	851521.i		−	0.0560207i
$747$			9.36530e6i			0.614073i
$748$		−	1.84770e7i		−	1.20747i
$749$			552486.i			0.0359846i
$750$	216732.			0.0140692
$751$	−1.55733e7			−1.00758			−0.503790	−	0.863826i	$-0.668062\pi$
$751$	−1.55733e7			−1.00758			−0.503790	+	0.863826i	$0.668062\pi$
$752$			2.00075e7i			1.29018i
$753$	−3.13588e6			−0.201545
$754$	−2.46238e6	−	3.02329e6i	−0.157734	−	0.193665i
$755$	−6.64245e6			−0.424093
$756$			760053.i			0.0483659i
$757$	4.30381e6			0.272969			0.136485	−	0.990642i	$-0.456420\pi$
$757$	4.30381e6			0.272969			0.136485	+	0.990642i	$0.456420\pi$
$758$	1.04874e6			0.0662974
$759$			4.10101e6i			0.258397i
$760$		−	5.73966e6i		−	0.360456i
$761$		−	2.17549e7i		−	1.36174i	−0.732403	−	0.680871i	$-0.761601\pi$
$761$		−	2.17549e7i		−	1.36174i	0.732403	−	0.680871i	$-0.238399\pi$
$762$		−	2.75432e6i		−	0.171841i
$763$	226813.			0.0141045
$764$	−1.57595e6			−0.0976805
$765$			4.39413e6i			0.271468i
$766$	−4.31513e6			−0.265718
$767$	1.83331e7	+	2.25092e7i	1.12524	+	1.38157i
$768$	−6.76579e6			−0.413919
$769$		−	2.85348e7i		−	1.74004i	−0.493017	−	0.870020i	$-0.664106\pi$
$769$		−	2.85348e7i		−	1.74004i	0.493017	−	0.870020i	$-0.335894\pi$
$770$	73225.7			0.00445079
$771$	−6.96059e6			−0.421706
$772$		−	2.01961e7i		−	1.21962i
$773$			2.79269e7i			1.68102i	0.541795	+	0.840511i	$0.317745\pi$
$773$			2.79269e7i			1.68102i	−0.541795	+	0.840511i	$0.682255\pi$
$774$			341259.i			0.0204754i
$775$			1.09368e6i			0.0654089i
$776$	−1.03420e7			−0.616523
$777$	−194369.			−0.0115498
$778$			1.04163e6i			0.0616971i
$779$	−2.19947e7			−1.29860
$780$	3.33961e6	+	4.10035e6i	0.196544	+	0.241315i
$781$	−9.88507e6			−0.579899
$782$			1.73849e6i			0.101661i
$783$	−2.12912e7			−1.24107
$784$	1.48158e7			0.860865
$785$		−	4.00832e6i		−	0.232161i
$786$			1.41627e6i			0.0817692i
$787$			2.09367e7i			1.20496i	0.798136	+	0.602478i	$0.205820\pi$
$787$			2.09367e7i			1.20496i	−0.798136	+	0.602478i	$0.794180\pi$
$788$			1.27557e7i			0.731792i
$789$	5.74700e6			0.328661
$790$	2.67116e6			0.152276
$791$			170109.i			0.00966688i
$792$	−3.38657e6			−0.191843
$793$	−1.21936e7	+	9.93131e6i	−0.688571	+	0.560820i
$794$	−5.63153e6			−0.317012
$795$		−	7.78846e6i		−	0.437052i
$796$	2.58169e7			1.44418
$797$	1.45712e7			0.812549			0.406274	−	0.913751i	$-0.366828\pi$
$797$	1.45712e7			0.812549			0.406274	+	0.913751i	$0.366828\pi$
$798$		−	256557.i		−	0.0142619i
$799$			3.50482e7i			1.94222i
$800$		−	2.19758e6i		−	0.121400i
$801$			2.95982e6i			0.162998i
$802$	179742.			0.00986763
$803$	2.37037e7			1.29726
$804$			1.25692e7i			0.685754i
$805$	141429.			0.00769217
$806$	1.00799e6	−	820975.i	0.0546535	−	0.0445136i
$807$	−3.70231e6			−0.200119
$808$		−	1.10296e7i		−	0.594336i
$809$	−2.59047e7			−1.39158			−0.695789	−	0.718246i	$-0.744945\pi$
$809$	−2.59047e7			−1.39158			−0.695789	+	0.718246i	$0.744945\pi$
$810$	−565564.			−0.0302879
$811$		−	9.38778e6i		−	0.501200i	−0.968091	−	0.250600i	$-0.919372\pi$
$811$		−	9.38778e6i		−	0.501200i	0.968091	−	0.250600i	$-0.0806279\pi$
$812$		−	983367.i		−	0.0523390i
$813$			3.58014e6i			0.189965i
$814$		−	1.32725e6i		−	0.0702086i
$815$	−1.04258e7			−0.549812
$816$	−1.55567e7			−0.817884
$817$			7.42418e6i			0.389129i
$818$	−7.17372e6			−0.374853
$819$	−268335.	−	329460.i	−0.0139787	−	0.0171630i
$820$	−5.57002e6			−0.289283
$821$		−	7.37712e6i		−	0.381970i	−0.981593	−	0.190985i	$-0.938832\pi$
$821$		−	7.37712e6i		−	0.381970i	0.981593	−	0.190985i	$-0.0611681\pi$
$822$	5.39227e6			0.278350
$823$	2.13960e7			1.10111			0.550557	−	0.834798i	$-0.314416\pi$
$823$	2.13960e7			1.10111			0.550557	+	0.834798i	$0.314416\pi$
$824$		−	493345.i		−	0.0253124i
$825$		−	2.78202e6i		−	0.142307i
$826$		−	356666.i		−	0.0181891i
$827$			6.14027e6i			0.312194i	0.987742	+	0.156097i	$0.0498912\pi$
$827$			6.14027e6i			0.312194i	−0.987742	+	0.156097i	$0.950109\pi$
$828$	−3.19266e6			−0.161837
$829$	−1.46790e7			−0.741838			−0.370919	−	0.928665i	$-0.620957\pi$
$829$	−1.46790e7			−0.741838			−0.370919	+	0.928665i	$0.620957\pi$
$830$		−	2.51357e6i		−	0.126647i
$831$	1.93542e7			0.972237
$832$	1.13321e7	−	9.22966e6i	0.567548	−	0.462251i
$833$	2.59536e7			1.29594
$834$			3.40190e6i			0.169358i
$835$	−2.12326e6			−0.105387
$836$	−3.59618e7			−1.77962
$837$		−	7.09864e6i		−	0.350237i
$838$			1.06713e6i			0.0524937i
$839$		−	2.35783e7i		−	1.15640i	−0.815896	−	0.578198i	$-0.803756\pi$
$839$		−	2.35783e7i		−	1.15640i	0.815896	−	0.578198i	$-0.196244\pi$
$840$		−	133108.i		−	0.00650888i
$841$	7.03561e6			0.343014
$842$	−327232.			−0.0159065
$843$		−	1.10715e7i		−	0.536586i
$844$	1.43275e7			0.692331
$845$	−9.09024e6	−	1.87861e6i	−0.437959	−	0.0905096i
$846$	3.13554e6			0.150621
$847$			48955.1i			0.00234471i
$848$	−2.41935e7			−1.15534
$849$	−9.73298e6			−0.463422
$850$		−	1.17935e6i		−	0.0559880i
$851$		−	2.56346e6i		−	0.121340i
$852$			8.77080e6i			0.413943i
$853$		−	1.60837e7i		−	0.756856i	−0.925631	−	0.378428i	$-0.876465\pi$
$853$		−	1.60837e7i		−	0.756856i	0.925631	−	0.378428i	$-0.123535\pi$
$854$	193212.			0.00906544
$855$	8.55229e6			0.400099
$856$			6.85782e6i			0.319891i
$857$	2.45455e7			1.14162			0.570809	−	0.821083i	$-0.306630\pi$
$857$	2.45455e7			1.14162			0.570809	+	0.821083i	$0.306630\pi$
$858$	−2.56404e6	+	2.08833e6i	−0.118907	+	0.0968459i
$859$	2.36147e7			1.09194			0.545971	−	0.837804i	$-0.316161\pi$
$859$	2.36147e7			1.09194			0.545971	+	0.837804i	$0.316161\pi$
$860$			1.88013e6i			0.0866846i
$861$	−510077.			−0.0234492
$862$	6.18744e6			0.283624
$863$			2.10316e7i			0.961271i	0.876920	+	0.480635i	$0.159594\pi$
$863$			2.10316e7i			0.961271i	−0.876920	+	0.480635i	$0.840406\pi$
$864$			1.42636e7i			0.650047i
$865$			3.05314e6i			0.138742i
$866$			234782.i			0.0106383i
$867$	−1.10979e7			−0.501410
$868$	327862.			0.0147704
$869$		−	3.42876e7i		−	1.54024i
$870$	1.82003e6			0.0815229
$871$	−1.39326e7	−	1.71064e7i	−0.622282	−	0.764033i
$872$	2.81535e6			0.125384
$873$		−	1.54099e7i		−	0.684329i
$874$	3.38363e6			0.149832
$875$	−95941.8			−0.00423631
$876$		−	2.10318e7i		−	0.926011i
$877$		−	2.16451e7i		−	0.950298i	−0.879905	−	0.475149i	$-0.842394\pi$
$877$		−	2.16451e7i		−	0.950298i	0.879905	−	0.475149i	$-0.157606\pi$
$878$			9.45602e6i			0.413973i
$879$		−	4.93881e6i		−	0.215601i
$880$	−8.64186e6			−0.376184
$881$	1.25222e7			0.543552			0.271776	−	0.962360i	$-0.412389\pi$
$881$	1.25222e7			0.543552			0.271776	+	0.962360i	$0.412389\pi$
$882$		−	2.32190e6i		−	0.100501i
$883$	4.38601e6			0.189307			0.0946537	−	0.995510i	$-0.469826\pi$
$883$	4.38601e6			0.189307			0.0946537	+	0.995510i	$0.469826\pi$
$884$	2.23121e7	−	1.81725e7i	0.960307	−	0.782140i
$885$	−1.35506e7			−0.581568
$886$		−	2.01557e6i		−	0.0862609i
$887$	3.48074e7			1.48547			0.742733	−	0.669587i	$-0.233529\pi$
$887$	3.48074e7			1.48547			0.742733	+	0.669587i	$0.233529\pi$
$888$	−2.41264e6			−0.102674
$889$			1.21927e6i			0.0517423i
$890$		−	794391.i		−	0.0336170i
$891$			7.25971e6i			0.306355i
$892$			2.25797e7i			0.950181i
$893$	6.82144e7			2.86251
$894$	6.31632e6			0.264314
$895$		−	1.14853e7i		−	0.479275i
$896$	−870442.			−0.0362218
$897$	−4.95222e6	+	4.03343e6i	−0.205503	+	0.167376i
$898$	5.03114e6			0.208198
$899$			9.18431e6i			0.379007i
$900$	2.16582e6			0.0891283
$901$	−4.23810e7			−1.73924
$902$		−	3.48306e6i		−	0.142542i
$903$			172174.i			0.00702664i
$904$			2.11151e6i			0.0859353i
$905$		−	8.36115e6i		−	0.339347i
$906$	−3.68546e6			−0.149166
$907$	−8.74330e6			−0.352904			−0.176452	−	0.984309i	$-0.556462\pi$
$907$	−8.74330e6			−0.352904			−0.176452	+	0.984309i	$0.556462\pi$
$908$			3.13075e6i			0.126018i
$909$	1.64345e7			0.659701
$910$	72019.0	+	88424.4i	0.00288299	+	0.00353972i
$911$	−2.23703e7			−0.893048			−0.446524	−	0.894772i	$-0.647338\pi$
$911$	−2.23703e7			−0.893048			−0.446524	+	0.894772i	$0.647338\pi$
$912$			3.02780e7i			1.20542i
$913$	−3.22648e7			−1.28101
$914$	−3.37076e6			−0.133463
$915$		−	7.34058e6i		−	0.289853i
$916$		−	2.52144e6i		−	0.0992911i
$917$		−	626947.i		−	0.0246211i
$918$			7.65466e6i			0.299792i
$919$	−3.29243e6			−0.128596			−0.0642981	−	0.997931i	$-0.520481\pi$
$919$	−3.29243e6			−0.128596			−0.0642981	+	0.997931i	$0.520481\pi$
$920$	1.75551e6			0.0683808
$921$		−	1.51568e7i		−	0.588787i
$922$	5.18522e6			0.200882
$923$	−9.72217e6	−	1.19368e7i	−0.375629	−	0.461194i
$924$	−833989.			−0.0321352
$925$			1.73898e6i			0.0668253i
$926$	3.42606e6			0.131301
$927$	735102.			0.0280963
$928$		−	1.84544e7i		−	0.703446i
$929$		−	2.50376e7i		−	0.951817i	−0.879495	−	0.475908i	$-0.842119\pi$
$929$		−	2.50376e7i		−	0.951817i	0.879495	−	0.475908i	$-0.157881\pi$
$930$			606812.i			0.0230063i
$931$		−	5.05135e7i		−	1.91000i
$932$	−4.42935e6			−0.167032
$933$	1.38901e7			0.522397
$934$			1.08684e7i			0.407659i
$935$	−1.51384e7			−0.566305
$936$	−3.33075e6	−	4.08948e6i	−0.124266	−	0.152573i
$937$	−4.64120e6			−0.172696			−0.0863478	−	0.996265i	$-0.527520\pi$
$937$	−4.64120e6			−0.172696			−0.0863478	+	0.996265i	$0.527520\pi$
$938$			271056.i			0.0100589i
$939$	3.83261e7			1.41851
$940$	1.72749e7			0.637670
$941$			1.62911e7i			0.599760i	0.953977	+	0.299880i	$0.0969467\pi$
$941$			1.62911e7i			0.599760i	−0.953977	+	0.299880i	$0.903053\pi$
$942$		−	2.22395e6i		−	0.0816579i
$943$		−	6.72722e6i		−	0.246352i
$944$			4.20926e7i			1.53736i
$945$	622719.			0.0226836
$946$	−1.17569e6			−0.0427134
$947$		−	2.98948e7i		−	1.08323i	−0.840627	−	0.541614i	$-0.817813\pi$
$947$		−	2.98948e7i		−	1.08323i	0.840627	−	0.541614i	$-0.182187\pi$
$948$	−3.04226e7			−1.09945
$949$	2.33131e7	+	2.86237e7i	0.840301	+	1.03172i
$950$	−2.29537e6			−0.0825169
$951$		−	2.06046e6i		−	0.0738777i
$952$	−724309.			−0.0259019
$953$	4.34693e7			1.55043			0.775213	−	0.631700i	$-0.217643\pi$
$953$	4.34693e7			1.55043			0.775213	+	0.631700i	$0.217643\pi$
$954$			3.79155e6i			0.134879i
$955$			1.29119e6i			0.0458122i
$956$		−	9.32286e6i		−	0.329917i
$957$		−	2.33623e7i		−	0.824586i
$958$	1.27741e6			0.0449692
$959$	−2.38702e6			−0.0838127
$960$			6.82196e6i			0.238908i
$961$	2.55670e7			0.893042
$962$	1.60273e6	−	1.30537e6i	0.0558370	−	0.0454775i
$963$	−1.02184e7			−0.355073
$964$			4.12795e7i			1.43068i
$965$	−1.65468e7			−0.572001
$966$	78469.6			0.00270557
$967$			2.94293e7i			1.01208i	0.862510	+	0.506039i	$0.168891\pi$
$967$			2.94293e7i			1.01208i	−0.862510	+	0.506039i	$0.831109\pi$
$968$			607664.i			0.0208437i
$969$			5.30395e7i			1.81464i
$970$			4.13590e6i			0.141137i
$971$	−3.14967e7			−1.07205			−0.536027	−	0.844201i	$-0.680076\pi$
$971$	−3.14967e7			−1.07205			−0.536027	+	0.844201i	$0.680076\pi$
$972$	−2.36376e7			−0.802486
$973$		−	1.50594e6i		−	0.0509947i
$974$	3.22448e6			0.108909
$975$	3.35946e6	−	2.73617e6i	0.113177	−	0.0921790i
$976$	−2.28022e7			−0.766218
$977$			5.67335e6i			0.190153i	0.995470	+	0.0950764i	$0.0303096\pi$
$977$			5.67335e6i			0.190153i	−0.995470	+	0.0950764i	$0.969690\pi$
$978$	−5.78457e6			−0.193385
$979$	−1.01970e7			−0.340028
$980$		−	1.27923e7i		−	0.425483i
$981$			4.19498e6i			0.139174i
$982$		−	3.15275e6i		−	0.104330i
$983$			1.96686e7i			0.649217i	0.945848	+	0.324609i	$0.105233\pi$
$983$			1.96686e7i			0.649217i	−0.945848	+	0.324609i	$0.894767\pi$
$984$	−6.33142e6			−0.208456
$985$	1.04508e7			0.343210
$986$		−	9.90370e6i		−	0.324418i
$987$	1.58196e6			0.0516894
$988$	−3.53692e7	−	4.34261e7i	−1.15274	−	1.41533i
$989$	−2.27074e6			−0.0738203
$990$			1.35433e6i			0.0439175i
$991$	3.75674e7			1.21514			0.607571	−	0.794266i	$-0.292144\pi$
$991$	3.75674e7			1.21514			0.607571	+	0.794266i	$0.292144\pi$
$992$	6.15285e6			0.198517
$993$		−	1.96676e7i		−	0.632963i
$994$			189143.i			0.00607189i
$995$		−	2.11520e7i		−	0.677321i
$996$			2.86278e7i			0.914407i
$997$	−6.54052e6			−0.208389			−0.104194	−	0.994557i	$-0.533226\pi$
$997$	−6.54052e6			−0.208389			−0.104194	+	0.994557i	$0.533226\pi$
$998$	−1.05113e7			−0.334065
$999$		−	1.12870e7i		−	0.357821i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.6.c.b.51.8	yes	14
13.5	odd	4		845.6.a.j.1.3		7
13.8	odd	4		845.6.a.i.1.5		7
13.12	even	2	inner	65.6.c.b.51.7	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.6.c.b.51.7	✓	14	13.12	even	2	inner
65.6.c.b.51.8	yes	14	1.1	even	1	trivial
845.6.a.i.1.5		7	13.8	odd	4
845.6.a.j.1.3		7	13.5	odd	4

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	65.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.21921i q^{2} -11.3769 q^{3} +30.5135 q^{4} -25.0000i q^{5} -13.8708i q^{6} +6.14028i q^{7} +76.2172i q^{8} -113.566 q^{9} +30.4803 q^{10} -391.252i q^{11} -347.149 q^{12} +(472.460 - 384.804i) q^{13} -7.48630 q^{14} +284.422i q^{15} +883.508 q^{16} +1547.69 q^{17} -138.461i q^{18} -3012.26i q^{19} -762.838i q^{20} -69.8572i q^{21} +477.019 q^{22} +921.321 q^{23} -867.115i q^{24} -625.000 q^{25} +(469.158 + 576.029i) q^{26} +4056.62 q^{27} +187.361i q^{28} -5248.50 q^{29} -346.771 q^{30} -1749.89i q^{31} +3516.13i q^{32} +4451.23i q^{33} +1886.96i q^{34} +153.507 q^{35} -3465.31 q^{36} -2782.37i q^{37} +3672.59 q^{38} +(-5375.13 + 4377.88i) q^{39} +1905.43 q^{40} -7301.71i q^{41} +85.1708 q^{42} -2464.65 q^{43} -11938.5i q^{44} +2839.16i q^{45} +1123.29i q^{46} +22645.6i q^{47} -10051.6 q^{48} +16769.3 q^{49} -762.007i q^{50} -17607.9 q^{51} +(14416.4 - 11741.7i) q^{52} -27383.4 q^{53} +4945.87i q^{54} -9781.30 q^{55} -467.995 q^{56} +34270.2i q^{57} -6399.03i q^{58} +47642.5i q^{59} +8678.73i q^{60} -25808.7 q^{61} +2133.49 q^{62} -697.329i q^{63} +23985.3 q^{64} +(-9620.11 - 11811.5i) q^{65} -5426.99 q^{66} -36207.0i q^{67} +47225.4 q^{68} -10481.8 q^{69} +187.157i q^{70} -25265.2i q^{71} -8655.71i q^{72} +60584.3i q^{73} +3392.30 q^{74} +7110.56 q^{75} -91914.8i q^{76} +2402.40 q^{77} +(-5337.56 - 6553.42i) q^{78} +87635.7 q^{79} -22087.7i q^{80} -18555.1 q^{81} +8902.33 q^{82} -82465.4i q^{83} -2131.59i q^{84} -38692.2i q^{85} -3004.93i q^{86} +59711.6 q^{87} +29820.1 q^{88} -26062.4i q^{89} -3461.54 q^{90} +(2362.80 + 2901.04i) q^{91} +28112.7 q^{92} +19908.3i q^{93} -27609.7 q^{94} -75306.6 q^{95} -40002.7i q^{96} +135691. i q^{97} +20445.3i q^{98} +44433.1i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 84 q^{3} - 38 q^{4} + 1118 q^{9} + 550 q^{10} + 168 q^{12} - 1132 q^{13} + 6440 q^{14} - 3434 q^{16} + 228 q^{17} + 2328 q^{22} + 8104 q^{23} - 8750 q^{25} - 142 q^{26} + 13680 q^{27} - 16700 q^{29}+ \cdots + 318800 q^{95}+O(q^{100}) \) 14 * q - 84 * q^3 - 38 * q^4 + 1118 * q^9 + 550 * q^10 + 168 * q^12 - 1132 * q^13 + 6440 * q^14 - 3434 * q^16 + 228 * q^17 + 2328 * q^22 + 8104 * q^23 - 8750 * q^25 - 142 * q^26 + 13680 * q^27 - 16700 * q^29 + 12700 * q^30 - 2000 * q^35 + 39970 * q^36 - 5652 * q^38 + 2416 * q^39 + 24750 * q^40 - 96836 * q^42 - 64948 * q^43 - 35932 * q^48 + 29010 * q^49 + 18632 * q^51 - 48972 * q^52 + 106232 * q^53 - 33400 * q^55 - 87808 * q^56 - 65252 * q^61 + 127744 * q^62 + 44754 * q^64 - 40550 * q^65 + 165768 * q^66 + 58536 * q^68 - 318208 * q^69 - 151892 * q^74 + 52500 * q^75 - 123736 * q^77 + 219028 * q^78 - 4336 * q^79 + 364406 * q^81 + 391092 * q^82 - 328560 * q^87 - 282548 * q^88 - 14750 * q^90 - 34376 * q^91 - 163604 * q^92 + 797896 * q^94 + 318800 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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