LMFDB - Embedded newform 65.6.c.b.51.10

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			51.10
Root			$5.90915i$ of defining polynomial
Character	$\chi$	$=$	65.51
Dual form			65.6.c.b.51.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.90915i q^{2} -14.1735 q^{3} +16.7186 q^{4} +25.0000i q^{5} -55.4063i q^{6} +16.6406i q^{7} +190.448i q^{8} -42.1117 q^{9} -97.7287 q^{10} +248.134i q^{11} -236.961 q^{12} +(-257.734 - 552.147i) q^{13} -65.0506 q^{14} -354.338i q^{15} -209.496 q^{16} -2183.42 q^{17} -164.621i q^{18} -1173.50i q^{19} +417.964i q^{20} -235.856i q^{21} -969.991 q^{22} -3181.60 q^{23} -2699.32i q^{24} -625.000 q^{25} +(2158.42 - 1007.52i) q^{26} +4041.03 q^{27} +278.207i q^{28} -531.446 q^{29} +1385.16 q^{30} -611.250i q^{31} +5275.39i q^{32} -3516.92i q^{33} -8535.32i q^{34} -416.015 q^{35} -704.047 q^{36} +15393.4i q^{37} +4587.37 q^{38} +(3653.00 + 7825.86i) q^{39} -4761.20 q^{40} +4360.29i q^{41} +921.994 q^{42} -17192.1 q^{43} +4148.44i q^{44} -1052.79i q^{45} -12437.3i q^{46} +1679.47i q^{47} +2969.29 q^{48} +16530.1 q^{49} -2443.22i q^{50} +30946.8 q^{51} +(-4308.94 - 9231.10i) q^{52} +16858.9 q^{53} +15797.0i q^{54} -6203.34 q^{55} -3169.17 q^{56} +16632.5i q^{57} -2077.50i q^{58} +16357.1i q^{59} -5924.02i q^{60} +37434.3 q^{61} +2389.47 q^{62} -700.764i q^{63} -27326.1 q^{64} +(13803.7 - 6443.35i) q^{65} +13748.2 q^{66} +19597.2i q^{67} -36503.7 q^{68} +45094.4 q^{69} -1626.26i q^{70} -47154.3i q^{71} -8020.09i q^{72} -62252.0i q^{73} -60175.2 q^{74} +8858.44 q^{75} -19619.1i q^{76} -4129.09 q^{77} +(-30592.4 + 14280.1i) q^{78} -85212.1 q^{79} -5237.39i q^{80} -47042.5 q^{81} -17045.0 q^{82} +80834.1i q^{83} -3943.17i q^{84} -54585.6i q^{85} -67206.4i q^{86} +7532.45 q^{87} -47256.6 q^{88} +123026. i q^{89} +4115.52 q^{90} +(9188.05 - 4288.85i) q^{91} -53191.8 q^{92} +8663.55i q^{93} -6565.28 q^{94} +29337.4 q^{95} -74770.8i q^{96} +5149.36i q^{97} +64618.6i q^{98} -10449.3i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			3.90915i			0.691046i	0.938410	+	0.345523i	$0.112299\pi$
$2$			3.90915i			0.691046i	−0.938410	+	0.345523i	$0.887701\pi$
$3$	−14.1735			−0.909231			−0.454615	−	0.890688i	$-0.650223\pi$
$3$	−14.1735			−0.909231			−0.454615	+	0.890688i	$0.650223\pi$
$4$	16.7186			0.522455
$5$			25.0000i			0.447214i
$5$			25.0000i			0.447214i
$6$		−	55.4063i		−	0.628321i
$7$			16.6406i			0.128358i	0.997938	+	0.0641791i	$0.0204429\pi$
$7$			16.6406i			0.128358i	−0.997938	+	0.0641791i	$0.979557\pi$
$8$			190.448i			1.05209i
$9$	−42.1117			−0.173299
$10$	−97.7287			−0.309045
$11$			248.134i			0.618307i	0.951012	+	0.309153i	$0.100046\pi$
$11$			248.134i			0.618307i	−0.951012	+	0.309153i	$0.899954\pi$
$12$	−236.961			−0.475032
$13$	−257.734	−	552.147i	−0.422974	−	0.906142i
$13$	−257.734	−	552.147i	−0.422974	−	0.906142i
$14$	−65.0506			−0.0887015
$15$		−	354.338i		−	0.406620i
$16$	−209.496			−0.204586
$17$	−2183.42			−1.83238			−0.916190	−	0.400744i	$-0.868752\pi$
$17$	−2183.42			−1.83238			−0.916190	+	0.400744i	$0.868752\pi$
$18$		−	164.621i		−	0.119758i
$19$		−	1173.50i		−	0.745757i	−0.927880	−	0.372878i	$-0.878371\pi$
$19$		−	1173.50i		−	0.745757i	0.927880	−	0.372878i	$-0.121629\pi$
$20$			417.964i			0.233649i
$21$		−	235.856i		−	0.116707i
$22$	−969.991			−0.427278
$23$	−3181.60			−1.25408			−0.627041	−	0.778986i	$-0.715734\pi$
$23$	−3181.60			−1.25408			−0.627041	+	0.778986i	$0.715734\pi$
$24$		−	2699.32i		−	0.956590i
$25$	−625.000			−0.200000
$26$	2158.42	−	1007.52i	0.626186	−	0.292294i
$27$	4041.03			1.06680
$28$			278.207i			0.0670614i
$29$	−531.446			−0.117345			−0.0586724	−	0.998277i	$-0.518687\pi$
$29$	−531.446			−0.117345			−0.0586724	+	0.998277i	$0.518687\pi$
$30$	1385.16			0.280994
$31$		−	611.250i		−	0.114239i	−0.998367	−	0.0571195i	$-0.981808\pi$
$31$		−	611.250i		−	0.114239i	0.998367	−	0.0571195i	$-0.0181916\pi$
$32$			5275.39i			0.910709i
$33$		−	3516.92i		−	0.562183i
$34$		−	8535.32i		−	1.26626i
$35$	−416.015			−0.0574036
$36$	−704.047			−0.0905410
$37$			15393.4i			1.84855i	0.381727	+	0.924275i	$0.375330\pi$
$37$			15393.4i			1.84855i	−0.381727	+	0.924275i	$0.624670\pi$
$38$	4587.37			0.515353
$39$	3653.00	+	7825.86i	0.384581	+	0.823892i
$40$	−4761.20			−0.470508
$41$			4360.29i			0.405094i	0.979273	+	0.202547i	$0.0649219\pi$
$41$			4360.29i			0.405094i	−0.979273	+	0.202547i	$0.935078\pi$
$42$	921.994			0.0806501
$43$	−17192.1			−1.41794			−0.708969	−	0.705240i	$-0.750839\pi$
$43$	−17192.1			−1.41794			−0.708969	+	0.705240i	$0.750839\pi$
$44$			4148.44i			0.323037i
$45$		−	1052.79i		−	0.0775018i
$46$		−	12437.3i		−	0.866629i
$47$			1679.47i			0.110899i	0.998461	+	0.0554494i	$0.0176591\pi$
$47$			1679.47i			0.110899i	−0.998461	+	0.0554494i	$0.982341\pi$
$48$	2969.29			0.186016
$49$	16530.1			0.983524
$50$		−	2443.22i		−	0.138209i
$51$	30946.8			1.66606
$52$	−4308.94	−	9231.10i	−0.220985	−	0.473418i
$53$	16858.9			0.824403			0.412202	−	0.911093i	$-0.364760\pi$
$53$	16858.9			0.824403			0.412202	+	0.911093i	$0.364760\pi$
$54$			15797.0i			0.737208i
$55$	−6203.34			−0.276515
$56$	−3169.17			−0.135044
$57$			16632.5i			0.678065i
$58$		−	2077.50i		−	0.0810907i
$59$			16357.1i			0.611754i	0.952071	+	0.305877i	$0.0989496\pi$
$59$			16357.1i			0.611754i	−0.952071	+	0.305877i	$0.901050\pi$
$60$		−	5924.02i		−	0.212441i
$61$	37434.3			1.28809			0.644043	−	0.764989i	$-0.277256\pi$
$61$	37434.3			1.28809			0.644043	+	0.764989i	$0.277256\pi$
$62$	2389.47			0.0789444
$63$		−	700.764i		−	0.0222444i
$64$	−27326.1			−0.833928
$65$	13803.7	−	6443.35i	0.405239	−	0.189160i
$66$	13748.2			0.388495
$67$			19597.2i			0.533344i	0.963787	+	0.266672i	$0.0859241\pi$
$67$			19597.2i			0.533344i	−0.963787	+	0.266672i	$0.914076\pi$
$68$	−36503.7			−0.957336
$69$	45094.4			1.14025
$70$		−	1626.26i		−	0.0396685i
$71$		−	47154.3i		−	1.11013i	−0.831806	−	0.555067i	$-0.812693\pi$
$71$		−	47154.3i		−	1.11013i	0.831806	−	0.555067i	$-0.187307\pi$
$72$		−	8020.09i		−	0.182326i
$73$		−	62252.0i		−	1.36724i	−0.729836	−	0.683622i	$-0.760404\pi$
$73$		−	62252.0i		−	1.36724i	0.729836	−	0.683622i	$-0.239596\pi$
$74$	−60175.2			−1.27743
$75$	8858.44			0.181846
$76$		−	19619.1i		−	0.389624i
$77$	−4129.09			−0.0793648
$78$	−30592.4	+	14280.1i	−0.569348	+	0.265763i
$79$	−85212.1			−1.53615			−0.768075	−	0.640360i	$-0.778785\pi$
$79$	−85212.1			−1.53615			−0.768075	+	0.640360i	$0.778785\pi$
$80$		−	5237.39i		−	0.0914935i
$81$	−47042.5			−0.796668
$82$	−17045.0			−0.279939
$83$			80834.1i			1.28795i	0.765046	+	0.643976i	$0.222716\pi$
$83$			80834.1i			1.28795i	−0.765046	+	0.643976i	$0.777284\pi$
$84$		−	3943.17i		−	0.0609743i
$85$		−	54585.6i		−	0.819465i
$86$		−	67206.4i		−	0.979861i
$87$	7532.45			0.106694
$88$	−47256.6			−0.650512
$89$			123026.i			1.64635i	0.567790	+	0.823173i	$0.307798\pi$
$89$			123026.i			1.64635i	−0.567790	+	0.823173i	$0.692202\pi$
$90$	4115.52			0.0535573
$91$	9188.05	−	4288.85i	0.116311	−	0.0542922i
$92$	−53191.8			−0.655202
$93$			8663.55i			0.103870i
$94$	−6565.28			−0.0766362
$95$	29337.4			0.333513
$96$		−	74770.8i		−	0.828044i
$97$			5149.36i			0.0555679i	0.999614	+	0.0277839i	$0.00884504\pi$
$97$			5149.36i			0.0555679i	−0.999614	+	0.0277839i	$0.991155\pi$
$98$			64618.6i			0.679661i
$99$		−	10449.3i		−	0.107152i
$100$	−10449.1			−0.104491
$101$	7268.27			0.0708970			0.0354485	−	0.999372i	$-0.488714\pi$
$101$	7268.27			0.0708970			0.0354485	+	0.999372i	$0.488714\pi$
$102$			120975.i			1.15132i
$103$	45138.8			0.419234			0.209617	−	0.977784i	$-0.432778\pi$
$103$	45138.8			0.419234			0.209617	+	0.977784i	$0.432778\pi$
$104$	105155.	−	49085.0i	0.953340	−	0.445005i
$105$	5896.39			0.0521931
$106$			65903.9i			0.569701i
$107$	−82937.0			−0.700307			−0.350154	−	0.936692i	$-0.613871\pi$
$107$	−82937.0			−0.700307			−0.350154	+	0.936692i	$0.613871\pi$
$108$	67560.3			0.557355
$109$			48125.6i			0.387981i	0.981003	+	0.193990i	$0.0621430\pi$
$109$			48125.6i			0.387981i	−0.981003	+	0.193990i	$0.937857\pi$
$110$		−	24249.8i		−	0.191085i
$111$		−	218179.i		−	1.68076i
$112$		−	3486.13i		−	0.0262603i
$113$	186846.			1.37653			0.688267	−	0.725457i	$-0.258372\pi$
$113$	186846.			1.37653			0.688267	+	0.725457i	$0.258372\pi$
$114$	−65019.1			−0.468574
$115$		−	79540.0i		−	0.560843i
$116$	−8885.01			−0.0613074
$117$	10853.6	+	23251.8i	0.0733010	+	0.157034i
$118$	−63942.4			−0.422750
$119$		−	36333.5i		−	0.235201i
$120$	67482.9			0.427800
$121$	99480.7			0.617697
$122$			146336.i			0.890127i
$123$		−	61800.6i		−	0.368324i
$124$		−	10219.2i		−	0.0596848i
$125$		−	15625.0i		−	0.0894427i
$126$	2739.39			0.0153719
$127$	−112462.			−0.618724			−0.309362	−	0.950944i	$-0.600115\pi$
$127$	−112462.			−0.618724			−0.309362	+	0.950944i	$0.600115\pi$
$128$			61990.5i			0.334426i
$129$	243672.			1.28923
$130$	25188.0	+	53960.6i	0.130718	+	0.280039i
$131$	−59428.8			−0.302565			−0.151282	−	0.988491i	$-0.548340\pi$
$131$	−59428.8			−0.302565			−0.151282	+	0.988491i	$0.548340\pi$
$132$		−	58797.9i		−	0.293716i
$133$	19527.7			0.0957240
$134$	−76608.5			−0.368566
$135$			101026.i			0.477087i
$136$		−	415829.i		−	1.92782i
$137$			386899.i			1.76115i	0.473907	+	0.880575i	$0.342843\pi$
$137$			386899.i			1.76115i	−0.473907	+	0.880575i	$0.657157\pi$
$138$			176281.i			0.787966i
$139$	−16270.2			−0.0714259			−0.0357130	−	0.999362i	$-0.511370\pi$
$139$	−16270.2			−0.0714259			−0.0357130	+	0.999362i	$0.511370\pi$
$140$	−6955.17			−0.0299908
$141$		−	23803.9i		−	0.100833i
$142$	184333.			0.767154
$143$	137006.	−	63952.5i	0.560274	−	0.261527i
$144$	8822.22			0.0354545
$145$		−	13286.1i		−	0.0524782i
$146$	243352.			0.944829
$147$	−234289.			−0.894251
$148$			257356.i			0.965785i
$149$		−	72218.6i		−	0.266491i	−0.991083	−	0.133246i	$-0.957460\pi$
$149$		−	72218.6i		−	0.266491i	0.991083	−	0.133246i	$-0.0425400\pi$
$150$			34629.0i			0.125664i
$151$			273395.i			0.975770i	0.872908	+	0.487885i	$0.162231\pi$
$151$			273395.i			0.975770i	−0.872908	+	0.487885i	$0.837769\pi$
$152$	223490.			0.784601
$153$	91947.7			0.317550
$154$		−	16141.2i		−	0.0548447i
$155$	15281.2			0.0510892
$156$	61072.8	+	130837.i	0.200926	+	0.430447i
$157$	−253530.			−0.820882			−0.410441	−	0.911887i	$-0.634625\pi$
$157$	−253530.			−0.820882			−0.410441	+	0.911887i	$0.634625\pi$
$158$		−	333107.i		−	1.06155i
$159$	−238950.			−0.749573
$160$	−131885.			−0.407281
$161$		−	52943.7i		−	0.160972i
$162$		−	183896.i		−	0.550535i
$163$		−	456348.i		−	1.34532i	−0.739950	−	0.672662i	$-0.765151\pi$
$163$		−	456348.i		−	1.34532i	0.739950	−	0.672662i	$-0.234849\pi$
$164$			72897.8i			0.211644i
$165$	87923.1			0.251416
$166$	−315993.			−0.890034
$167$			447758.i			1.24237i	0.783662	+	0.621187i	$0.213349\pi$
$167$			447758.i			1.24237i	−0.783662	+	0.621187i	$0.786651\pi$
$168$	44918.2			0.122786
$169$	−238439.	+	284614.i	−0.642186	+	0.766549i
$170$	213383.			0.566288
$171$			49417.9i			0.129239i
$172$	−287427.			−0.740809
$173$	125657.			0.319208			0.159604	−	0.987181i	$-0.448978\pi$
$173$	125657.			0.319208			0.159604	+	0.987181i	$0.448978\pi$
$174$			29445.5i			0.0737302i
$175$		−	10400.4i		−	0.0256717i
$176$		−	51982.9i		−	0.126497i
$177$		−	231838.i		−	0.556225i
$178$	−480926.			−1.13770
$179$	61098.5			0.142527			0.0712636	−	0.997458i	$-0.477297\pi$
$179$	61098.5			0.142527			0.0712636	+	0.997458i	$0.477297\pi$
$180$		−	17601.2i		−	0.0404912i
$181$	−212478.			−0.482078			−0.241039	−	0.970515i	$-0.577488\pi$
$181$	−212478.			−0.482078			−0.241039	+	0.970515i	$0.577488\pi$
$182$	16765.7	+	35917.5i	0.0375184	+	0.0803761i
$183$	−530575.			−1.17117
$184$		−	605930.i		−	1.31940i
$185$	−384836.			−0.826697
$186$	−33867.1			−0.0717787
$187$		−	541781.i		−	1.13297i
$188$			28078.3i			0.0579396i
$189$			67245.2i			0.136933i
$190$			114684.i			0.230473i
$191$	138109.			0.273929			0.136964	−	0.990576i	$-0.456265\pi$
$191$	138109.			0.273929			0.136964	+	0.990576i	$0.456265\pi$
$192$	387307.			0.758233
$193$			26646.6i			0.0514931i	0.999669	+	0.0257465i	$0.00819628\pi$
$193$			26646.6i			0.0514931i	−0.999669	+	0.0257465i	$0.991804\pi$
$194$	−20129.6			−0.0384000
$195$	−195646.	+	91324.9i	−0.368456	+	0.171990i
$196$	276359.			0.513847
$197$		−	966381.i		−	1.77412i	−0.461654	−	0.887060i	$-0.652744\pi$
$197$		−	966381.i		−	1.77412i	0.461654	−	0.887060i	$-0.347256\pi$
$198$	40848.0			0.0740470
$199$	−92606.7			−0.165771			−0.0828857	−	0.996559i	$-0.526414\pi$
$199$	−92606.7			−0.165771			−0.0828857	+	0.996559i	$0.526414\pi$
$200$		−	119030.i		−	0.210417i
$201$		−	277762.i		−	0.484933i
$202$			28412.7i			0.0489931i
$203$		−	8843.58i		−	0.0150622i
$204$	517385.			0.870440
$205$	−109007.			−0.181164
$206$			176454.i			0.289710i
$207$	133983.			0.217332
$208$	53994.2	+	115672.i	0.0865344	+	0.185384i
$209$	291184.			0.461106
$210$			23049.9i			0.0360678i
$211$	−987593.			−1.52712			−0.763558	−	0.645740i	$-0.776549\pi$
$211$	−987593.			−1.52712			−0.763558	+	0.645740i	$0.776549\pi$
$212$	281857.			0.430714
$213$			668342.i			1.00937i
$214$		−	324213.i		−	0.483945i
$215$		−	429802.i		−	0.634121i
$216$			769607.i			1.12237i
$217$	10171.6			0.0146635
$218$	−188130.			−0.268113
$219$			882329.i			1.24314i
$220$	−103711.			−0.144467
$221$	562743.	+	1.20557e6i	0.775049	+	1.66040i
$222$	852894.			1.16148
$223$		−	830130.i		−	1.11785i	−0.829218	−	0.558925i	$-0.811214\pi$
$223$		−	830130.i		−	1.11785i	0.829218	−	0.558925i	$-0.188786\pi$
$224$	−87785.6			−0.116897
$225$	26319.8			0.0346598
$226$			730407.i			0.951249i
$227$		−	829852.i		−	1.06890i	−0.845201	−	0.534448i	$-0.820519\pi$
$227$		−	829852.i		−	1.06890i	0.845201	−	0.534448i	$-0.179481\pi$
$228$			278072.i			0.354259i
$229$			306303.i			0.385978i	0.981201	+	0.192989i	$0.0618182\pi$
$229$			306303.i			0.385978i	−0.981201	+	0.192989i	$0.938182\pi$
$230$	310934.			0.387568
$231$	58523.7			0.0721609
$232$		−	101213.i		−	0.123457i
$233$	−314863.			−0.379955			−0.189978	−	0.981788i	$-0.560842\pi$
$233$	−314863.			−0.379955			−0.189978	+	0.981788i	$0.560842\pi$
$234$	−90894.9	+	42428.4i	−0.108518	+	0.0506544i
$235$	−41986.7			−0.0495954
$236$			273467.i			0.319614i
$237$	1.20775e6			1.39672
$238$	142033.			0.162535
$239$		−	311949.i		−	0.353256i	−0.984278	−	0.176628i	$-0.943481\pi$
$239$		−	311949.i		−	0.353256i	0.984278	−	0.176628i	$-0.0565189\pi$
$240$			74232.2i			0.0831887i
$241$			509482.i			0.565049i	0.959260	+	0.282525i	$0.0911719\pi$
$241$			509482.i			0.565049i	−0.959260	+	0.282525i	$0.908828\pi$
$242$			388885.i			0.426857i
$243$	−315214.			−0.342445
$244$	625847.			0.672967
$245$			413252.i			0.439845i
$246$	241588.			0.254529
$247$	−647942.	+	302450.i	−0.675762	+	0.315436i
$248$	116411.			0.120189
$249$		−	1.14570e6i		−	1.17105i
$250$	61080.4			0.0618091
$251$	837701.			0.839276			0.419638	−	0.907692i	$-0.362157\pi$
$251$	837701.			0.839276			0.419638	+	0.907692i	$0.362157\pi$
$252$		−	11715.8i		−	0.0116217i
$253$		−	789462.i		−	0.775408i
$254$		−	439631.i		−	0.427567i
$255$			773669.i			0.745083i
$256$	−1.11677e6			−1.06503
$257$	915293.			0.864425			0.432213	−	0.901772i	$-0.357733\pi$
$257$	915293.			0.864425			0.432213	+	0.901772i	$0.357733\pi$
$258$			952550.i			0.890920i
$259$	−256156.			−0.237277
$260$	230778.	−	107724.i	0.211719	−	0.0988274i
$261$	22380.1			0.0203358
$262$		−	232316.i		−	0.209086i
$263$	276512.			0.246504			0.123252	−	0.992375i	$-0.460668\pi$
$263$	276512.			0.246504			0.123252	+	0.992375i	$0.460668\pi$
$264$	669791.			0.591466
$265$			421473.i			0.368684i
$266$			76336.5i			0.0661497i
$267$		−	1.74371e6i		−	1.49691i
$268$			327638.i			0.278649i
$269$	−1.05233e6			−0.886688			−0.443344	−	0.896351i	$-0.646208\pi$
$269$	−1.05233e6			−0.886688			−0.443344	+	0.896351i	$0.646208\pi$
$270$	−394925.			−0.329689
$271$			1.53935e6i			1.27325i	0.771174	+	0.636625i	$0.219670\pi$
$271$			1.53935e6i			1.27325i	−0.771174	+	0.636625i	$0.780330\pi$
$272$	457418.			0.374879
$273$	−130227.	+	60788.0i	−0.105753	+	0.0493641i
$274$	−1.51245e6			−1.21704
$275$		−	155083.i		−	0.123661i
$276$	753914.			0.595730
$277$	−2.10699e6			−1.64992			−0.824961	−	0.565190i	$-0.808803\pi$
$277$	−2.10699e6			−1.64992			−0.824961	+	0.565190i	$0.808803\pi$
$278$		−	63602.6i		−	0.0493586i
$279$			25740.8i			0.0197975i
$280$		−	79229.2i		−	0.0603935i
$281$		−	1.77967e6i		−	1.34454i	−0.740306	−	0.672270i	$-0.765319\pi$
$281$		−	1.77967e6i		−	1.34454i	0.740306	−	0.672270i	$-0.234681\pi$
$282$	93053.1			0.0696800
$283$	1.46715e6			1.08895			0.544477	−	0.838776i	$-0.316728\pi$
$283$	1.46715e6			1.08895			0.544477	+	0.838776i	$0.316728\pi$
$284$		−	788352.i		−	0.579995i
$285$	−415814.			−0.303240
$286$	250000.	+	535577.i	0.180728	+	0.387175i
$287$	−72557.9			−0.0519972
$288$		−	222156.i		−	0.157825i
$289$	3.34748e6			2.35762
$290$	51937.5			0.0362649
$291$		−	72984.5i		−	0.0505240i
$292$		−	1.04076e6i		−	0.714324i
$293$		−	2.26615e6i		−	1.54213i	−0.636758	−	0.771064i	$-0.719725\pi$
$293$		−	2.26615e6i		−	1.54213i	0.636758	−	0.771064i	$-0.280275\pi$
$294$		−	915872.i		−	0.617968i
$295$	−408928.			−0.273585
$296$	−2.93165e6			−1.94484
$297$			1.00272e6i			0.659609i
$298$	282313.			0.184158
$299$	820007.	+	1.75671e6i	0.530444	+	1.13638i
$300$	148100.			0.0950065
$301$		−	286086.i		−	0.182004i
$302$	−1.06874e6			−0.674302
$303$	−103017.			−0.0644617
$304$			245842.i			0.152571i
$305$			935857.i			0.576050i
$306$			359437.i			0.219442i
$307$		−	1.21393e6i		−	0.735099i	−0.930004	−	0.367550i	$-0.880197\pi$
$307$		−	1.21393e6i		−	0.735099i	0.930004	−	0.367550i	$-0.119803\pi$
$308$	−69032.5			−0.0414645
$309$	−639775.			−0.381181
$310$			59736.6i			0.0353050i
$311$	−3.21451e6			−1.88458			−0.942288	−	0.334804i	$-0.891330\pi$
$311$	−3.21451e6			−1.88458			−0.942288	+	0.334804i	$0.891330\pi$
$312$	−1.49042e6	+	695706.i	−0.866806	+	0.404612i
$313$	1.80819e6			1.04324			0.521618	−	0.853179i	$-0.325328\pi$
$313$	1.80819e6			1.04324			0.521618	+	0.853179i	$0.325328\pi$
$314$		−	991088.i		−	0.567268i
$315$	17519.1			0.00994799
$316$	−1.42462e6			−0.802570
$317$			2.46984e6i			1.38045i	0.723594	+	0.690226i	$0.242489\pi$
$317$			2.46984e6i			1.38045i	−0.723594	+	0.690226i	$0.757511\pi$
$318$		−	934090.i		−	0.517989i
$319$		−	131870.i		−	0.0725551i
$320$		−	683153.i		−	0.372944i
$321$	1.17551e6			0.636741
$322$	206965.			0.111239
$323$			2.56224e6i			1.36651i
$324$	−786482.			−0.416223
$325$	161084.	+	345092.i	0.0845948	+	0.181228i
$326$	1.78393e6			0.929681
$327$		−	682109.i		−	0.352764i
$328$	−830409.			−0.426194
$329$	−27947.3			−0.0142348
$330$			343704.i			0.173740i
$331$		−	2.60783e6i		−	1.30830i	−0.756363	−	0.654152i	$-0.773026\pi$
$331$		−	2.60783e6i		−	1.30830i	0.756363	−	0.654152i	$-0.226974\pi$
$332$			1.35143e6i			0.672897i
$333$		−	648244.i		−	0.320352i
$334$	−1.75035e6			−0.858538
$335$	−489931.			−0.238519
$336$			49410.7i			0.0238766i
$337$	1.78977e6			0.858464			0.429232	−	0.903194i	$-0.358784\pi$
$337$	1.78977e6			0.858464			0.429232	+	0.903194i	$0.358784\pi$
$338$	−1.11260e6	−	932095.i	−0.529721	−	0.443781i
$339$	−2.64826e6			−1.25159
$340$		−	912592.i		−	0.428134i
$341$	151672.			0.0706347
$342$	−193182.			−0.0893102
$343$			554749.i			0.254602i
$344$		−	3.27420e6i		−	1.49179i
$345$			1.12736e6i			0.509936i
$346$			491214.i			0.220587i
$347$	137940.			0.0614988			0.0307494	−	0.999527i	$-0.490211\pi$
$347$	137940.			0.0614988			0.0307494	+	0.999527i	$0.490211\pi$
$348$	125932.			0.0557426
$349$			1.33434e6i			0.586410i	0.956050	+	0.293205i	$0.0947219\pi$
$349$			1.33434e6i			0.586410i	−0.956050	+	0.293205i	$0.905278\pi$
$350$	40656.6			0.0177403
$351$	−1.04151e6	−	2.23124e6i	−0.451228	−	0.966672i
$352$	−1.30900e6			−0.563097
$353$			2.86186e6i			1.22239i	0.791479	+	0.611197i	$0.209312\pi$
$353$			2.86186e6i			1.22239i	−0.791479	+	0.611197i	$0.790688\pi$
$354$	906288.			0.384377
$355$	1.17886e6			0.496467
$356$			2.05681e6i			0.860142i
$357$			514973.i			0.213852i
$358$			238843.i			0.0984929i
$359$			2.63309e6i			1.07827i	0.842218	+	0.539137i	$0.181249\pi$
$359$			2.63309e6i			1.07827i	−0.842218	+	0.539137i	$0.818751\pi$
$360$	200502.			0.0815386
$361$	1.09901e6			0.443847
$362$		−	830608.i		−	0.333138i
$363$	−1.40999e6			−0.561629
$364$	153611.	−	71703.4i	0.0607672	−	0.0283652i
$365$	1.55630e6			0.611450
$366$		−	2.07410e6i		−	0.809331i
$367$	1.32115e6			0.512019			0.256010	−	0.966674i	$-0.417592\pi$
$367$	1.32115e6			0.512019			0.256010	+	0.966674i	$0.417592\pi$
$368$	666532.			0.256567
$369$		−	183619.i		−	0.0702025i
$370$		−	1.50438e6i		−	0.571286i
$371$			280542.i			0.105819i
$372$			144842.i			0.0542672i
$373$	3.39609e6			1.26389			0.631943	−	0.775015i	$-0.282258\pi$
$373$	3.39609e6			1.26389			0.631943	+	0.775015i	$0.282258\pi$
$374$	2.11790e6			0.782937
$375$			221461.i			0.0813241i
$376$	−319851.			−0.116675
$377$	136972.	+	293436.i	0.0496338	+	0.106331i
$378$	−262871.			−0.0946267
$379$			2.80353e6i			1.00255i	0.865287	+	0.501276i	$0.167136\pi$
$379$			2.80353e6i			1.00255i	−0.865287	+	0.501276i	$0.832864\pi$
$380$	490479.			0.174245
$381$	1.59398e6			0.562563
$382$			539887.i			0.189297i
$383$		−	1.76078e6i		−	0.613351i	−0.951814	−	0.306676i	$-0.900783\pi$
$383$		−	1.76078e6i		−	0.613351i	0.951814	−	0.306676i	$-0.0992167\pi$
$384$		−	878623.i		−	0.304071i
$385$		−	103227.i		−	0.0354930i
$386$	−104166.			−0.0355841
$387$	723988.			0.245728
$388$			86089.9i			0.0290317i
$389$	128325.			0.0429968			0.0214984	−	0.999769i	$-0.493156\pi$
$389$	128325.			0.0429968			0.0214984	+	0.999769i	$0.493156\pi$
$390$	−357002.	−	764811.i	−0.118853	−	0.254620i
$391$	6.94678e6			2.29796
$392$			3.14812e6i			1.03475i
$393$	842314.			0.275101
$394$	3.77773e6			1.22600
$395$		−	2.13030e6i		−	0.686987i
$396$		−	174698.i		−	0.0559821i
$397$		−	2.18548e6i		−	0.695937i	−0.937506	−	0.347968i	$-0.886872\pi$
$397$		−	2.18548e6i		−	0.695937i	0.937506	−	0.347968i	$-0.113128\pi$
$398$		−	362013.i		−	0.114556i
$399$	−276775.			−0.0870353
$400$	130935.			0.0409171
$401$			2.30983e6i			0.717329i	0.933466	+	0.358665i	$0.116768\pi$
$401$			2.30983e6i			0.717329i	−0.933466	+	0.358665i	$0.883232\pi$
$402$	1.08581e6			0.335111
$403$	−337500.	+	157540.i	−0.103517	+	0.0483201i
$404$	121515.			0.0370405
$405$		−	1.17606e6i		−	0.356281i
$406$	34570.8			0.0104087
$407$	−3.81963e6			−1.14297
$408$			5.89375e6i			1.75284i
$409$			3.24428e6i			0.958980i	0.877547	+	0.479490i	$0.159178\pi$
$409$			3.24428e6i			0.958980i	−0.877547	+	0.479490i	$0.840822\pi$
$410$		−	426126.i		−	0.125192i
$411$		−	5.48372e6i		−	1.60129i
$412$	754656.			0.219031
$413$	−272192.			−0.0785236
$414$			523758.i			0.150186i
$415$	−2.02085e6			−0.575989
$416$	2.91279e6	−	1.35965e6i	0.825231	−	0.385206i
$417$	230606.			0.0649427
$418$			1.13828e6i			0.318646i
$419$	−4.93780e6			−1.37404			−0.687018	−	0.726640i	$-0.741081\pi$
$419$	−4.93780e6			−1.37404			−0.687018	+	0.726640i	$0.741081\pi$
$420$	98579.2			0.0272685
$421$		−	1.17016e6i		−	0.321767i	−0.986973	−	0.160884i	$-0.948566\pi$
$421$		−	1.17016e6i		−	0.321767i	0.986973	−	0.160884i	$-0.0514344\pi$
$422$		−	3.86065e6i		−	1.05531i
$423$		−	70725.2i		−	0.0192187i
$424$			3.21075e6i			0.867344i
$425$	1.36464e6			0.366476
$426$	−2.61265e6			−0.697520
$427$			622929.i			0.165337i
$428$	−1.38659e6			−0.365879
$429$	−1.94186e6	+	906431.i	−0.509418	+	0.237789i
$430$	1.68016e6			0.438207
$431$		−	2.34773e6i		−	0.608773i	−0.952549	−	0.304387i	$-0.901548\pi$
$431$		−	2.34773e6i		−	0.608773i	0.952549	−	0.304387i	$-0.0984515\pi$
$432$	−846579.			−0.218252
$433$	−317728.			−0.0814396			−0.0407198	−	0.999171i	$-0.512965\pi$
$433$	−317728.			−0.0814396			−0.0407198	+	0.999171i	$0.512965\pi$
$434$			39762.1i			0.0101332i
$435$			188311.i			0.0477148i
$436$			804591.i			0.202702i
$437$			3.73359e6i			0.935241i
$438$	−3.44916e6			−0.859068
$439$	2.20032e6			0.544909			0.272454	−	0.962169i	$-0.412165\pi$
$439$	2.20032e6			0.544909			0.272454	+	0.962169i	$0.412165\pi$
$440$		−	1.18141e6i		−	0.290918i
$441$	−696110.			−0.170444
$442$	−4.71275e6	+	2.19984e6i	−1.14741	+	0.535595i
$443$	−6.06565e6			−1.46848			−0.734240	−	0.678890i	$-0.762461\pi$
$443$	−6.06565e6			−1.46848			−0.734240	+	0.678890i	$0.762461\pi$
$444$		−	3.64764e6i		−	0.878121i
$445$	−3.07565e6			−0.736268
$446$	3.24510e6			0.772487
$447$			1.02359e6i			0.242302i
$448$		−	454723.i		−	0.107041i
$449$			384660.i			0.0900452i	0.998986	+	0.0450226i	$0.0143360\pi$
$449$			384660.i			0.0900452i	−0.998986	+	0.0450226i	$0.985664\pi$
$450$			102888.i			0.0239516i
$451$	−1.08194e6			−0.250472
$452$	3.12379e6			0.719177
$453$		−	3.87496e6i		−	0.887200i
$454$	3.24401e6			0.738657
$455$	107221.	+	229701.i	0.0242802	+	0.0520158i
$456$	−3.16764e6			−0.713383
$457$			5.94523e6i			1.33161i	0.746125	+	0.665806i	$0.231912\pi$
$457$			5.94523e6i			1.33161i	−0.746125	+	0.665806i	$0.768088\pi$
$458$	−1.19739e6			−0.266729
$459$	−8.82328e6			−1.95478
$460$		−	1.32979e6i		−	0.293015i
$461$			1.41278e6i			0.309615i	0.987945	+	0.154808i	$0.0494758\pi$
$461$			1.41278e6i			0.309615i	−0.987945	+	0.154808i	$0.950524\pi$
$462$			228778.i			0.0498665i
$463$		−	7.23589e6i		−	1.56870i	−0.620319	−	0.784349i	$-0.712997\pi$
$463$		−	7.23589e6i		−	1.56870i	0.620319	−	0.784349i	$-0.287003\pi$
$464$	111336.			0.0240071
$465$	−216589.			−0.0464519
$466$		−	1.23085e6i		−	0.262567i
$467$	4.05635e6			0.860683			0.430342	−	0.902666i	$-0.358393\pi$
$467$	4.05635e6			0.860683			0.430342	+	0.902666i	$0.358393\pi$
$468$	181457.	+	388737.i	0.0382965	+	0.0820430i
$469$	−326110.			−0.0684592
$470$		−	164132.i		−	0.0342727i
$471$	3.59341e6			0.746371
$472$	−3.11518e6			−0.643618
$473$		−	4.26593e6i		−	0.876720i
$474$			4.72129e6i			0.965195i
$475$			733434.i			0.149151i
$476$		−	607443.i		−	0.122882i
$477$	−709957.			−0.142868
$478$	1.21946e6			0.244116
$479$		−	3.88692e6i		−	0.774046i	−0.922070	−	0.387023i	$-0.873503\pi$
$479$		−	3.88692e6i		−	0.774046i	0.922070	−	0.387023i	$-0.126497\pi$
$480$	1.86927e6			0.370313
$481$	8.49944e6	−	3.96741e6i	1.67505	−	0.781888i
$482$	−1.99164e6			−0.390475
$483$			750398.i			0.146361i
$484$	1.66317e6			0.322719
$485$	−128734.			−0.0248507
$486$		−	1.23222e6i		−	0.236645i
$487$			4.21722e6i			0.805756i	0.915254	+	0.402878i	$0.131990\pi$
$487$			4.21722e6i			0.805756i	−0.915254	+	0.402878i	$0.868010\pi$
$488$			7.12929e6i			1.35518i
$489$			6.46805e6i			1.22321i
$490$	−1.61546e6			−0.303954
$491$	−1.02480e7			−1.91839			−0.959196	−	0.282743i	$-0.908756\pi$
$491$	−1.02480e7			−1.91839			−0.959196	+	0.282743i	$0.908756\pi$
$492$		−	1.03322e6i		−	0.192433i
$493$	1.16037e6			0.215020
$494$	−1.18232e6	−	2.53290e6i	−0.217981	−	0.466983i
$495$	261233.			0.0479198
$496$			128054.i			0.0233717i
$497$	784676.			0.142495
$498$	4.47872e6			0.809246
$499$		−	2.53309e6i		−	0.455407i	−0.973730	−	0.227704i	$-0.926878\pi$
$499$		−	2.53309e6i		−	0.455407i	0.973730	−	0.227704i	$-0.0731217\pi$
$500$		−	261228.i		−	0.0467298i
$501$		−	6.34631e6i		−	1.12961i
$502$			3.27470e6i			0.579978i
$503$	−5.44222e6			−0.959082			−0.479541	−	0.877519i	$-0.659197\pi$
$503$	−5.44222e6			−0.959082			−0.479541	+	0.877519i	$0.659197\pi$
$504$	133459.			0.0234030
$505$			181707.i			0.0317061i
$506$	3.08612e6			0.535842
$507$	3.37952e6	−	4.03398e6i	0.583896	−	0.696970i
$508$	−1.88020e6			−0.323255
$509$		−	7.33872e6i		−	1.25553i	−0.778404	−	0.627763i	$-0.783971\pi$
$509$		−	7.33872e6i		−	1.25553i	0.778404	−	0.627763i	$-0.216029\pi$
$510$	−3.02439e6			−0.514887
$511$	1.03591e6			0.175497
$512$		−	2.38191e6i		−	0.401560i
$513$		−	4.74213e6i		−	0.795573i
$514$			3.57802e6i			0.597358i
$515$			1.12847e6i			0.187487i
$516$	4.07385e6			0.673566
$517$	−416732.			−0.0685695
$518$		−	1.00135e6i		−	0.163969i
$519$	−1.78101e6			−0.290233
$520$	1.22712e6	+	2.62888e6i	0.199012	+	0.426347i
$521$	−2.58651e6			−0.417465			−0.208732	−	0.977973i	$-0.566934\pi$
$521$	−2.58651e6			−0.417465			−0.208732	+	0.977973i	$0.566934\pi$
$522$			87487.1i			0.0140530i
$523$	−844782.			−0.135049			−0.0675244	−	0.997718i	$-0.521510\pi$
$523$	−844782.			−0.135049			−0.0675244	+	0.997718i	$0.521510\pi$
$524$	−993564.			−0.158077
$525$			147410.i			0.0233415i
$526$			1.08092e6i			0.170346i
$527$			1.33462e6i			0.209329i
$528$			736780.i			0.115015i
$529$	3.68624e6			0.572723
$530$	−1.64760e6			−0.254778
$531$		−	688826.i		−	0.106016i
$532$	326474.			0.0500115
$533$	2.40752e6	−	1.12380e6i	0.367073	−	0.171344i
$534$	6.81641e6			1.03443
$535$		−	2.07342e6i		−	0.313187i
$536$	−3.73226e6			−0.561125
$537$	−865980.			−0.129590
$538$		−	4.11371e6i		−	0.612743i
$539$			4.10167e6i			0.608119i
$540$			1.68901e6i			0.249257i
$541$			6.68520e6i			0.982022i	0.871153	+	0.491011i	$0.163373\pi$
$541$			6.68520e6i			0.982022i	−0.871153	+	0.491011i	$0.836627\pi$
$542$	−6.01754e6			−0.879875
$543$	3.01156e6			0.438320
$544$		−	1.15184e7i		−	1.66876i
$545$	−1.20314e6			−0.173510
$546$	−237629.	−	509076.i	−0.0341129	−	0.0730805i
$547$	−8.21064e6			−1.17330			−0.586650	−	0.809841i	$-0.699553\pi$
$547$	−8.21064e6			−1.17330			−0.586650	+	0.809841i	$0.699553\pi$
$548$			6.46839e6i			0.920121i
$549$	−1.57642e6			−0.223224
$550$	606244.			0.0854557
$551$			623649.i			0.0875107i
$552$			8.58815e6i			1.19964i
$553$		−	1.41798e6i		−	0.197178i
$554$		−	8.23654e6i		−	1.14017i
$555$	5.45447e6			0.751658
$556$	−272014.			−0.0373168
$557$			1.89415e6i			0.258688i	0.991600	+	0.129344i	$0.0412871\pi$
$557$			1.89415e6i			0.258688i	−0.991600	+	0.129344i	$0.958713\pi$
$558$	−100624.			−0.0136810
$559$	4.43098e6	+	9.49255e6i	0.599751	+	1.28485i
$560$	87153.3			0.0117439
$561$			7.67893e6i			1.03013i
$562$	6.95699e6			0.929139
$563$	1.28391e7			1.70712			0.853560	−	0.520995i	$-0.174439\pi$
$563$	1.28391e7			1.70712			0.853560	+	0.520995i	$0.174439\pi$
$564$		−	397968.i		−	0.0526805i
$565$			4.67114e6i			0.615605i
$566$			5.73532e6i			0.752517i
$567$		−	782815.i		−	0.102259i
$568$	8.98044e6			1.16796
$569$	1.09378e6			0.141629			0.0708143	−	0.997490i	$-0.477440\pi$
$569$	1.09378e6			0.141629			0.0708143	+	0.997490i	$0.477440\pi$
$570$		−	1.62548e6i		−	0.209553i
$571$	−2.32467e6			−0.298380			−0.149190	−	0.988809i	$-0.547667\pi$
$571$	−2.32467e6			−0.298380			−0.149190	+	0.988809i	$0.547667\pi$
$572$	2.29055e6	−	1.06919e6i	0.292718	−	0.136636i
$573$	−1.95748e6			−0.249064
$574$		−	283640.i		−	0.0359325i
$575$	1.98850e6			0.250817
$576$	1.15075e6			0.144519
$577$		−	8.43797e6i		−	1.05511i	−0.849520	−	0.527556i	$-0.823109\pi$
$577$		−	8.43797e6i		−	1.05511i	0.849520	−	0.527556i	$-0.176891\pi$
$578$			1.30858e7i			1.62922i
$579$		−	377676.i		−	0.0468191i
$580$		−	222125.i		−	0.0274175i
$581$	−1.34513e6			−0.165319
$582$	285307.			0.0349145
$583$			4.18326e6i			0.509734i
$584$	1.18558e7			1.43846
$585$	−581296.	+	271341.i	−0.0702276	+	0.0327812i
$586$	8.85873e6			1.06568
$587$		−	9.49816e6i		−	1.13774i	−0.822427	−	0.568871i	$-0.807380\pi$
$587$		−	9.49816e6i		−	1.13774i	0.822427	−	0.568871i	$-0.192620\pi$
$588$	−3.91698e6			−0.467206
$589$	−717299.			−0.0851945
$590$		−	1.59856e6i		−	0.189060i
$591$			1.36970e7i			1.61308i
$592$		−	3.22486e6i		−	0.378187i
$593$		−	7.78092e6i		−	0.908645i	−0.890837	−	0.454323i	$-0.849881\pi$
$593$		−	7.78092e6i		−	0.908645i	0.890837	−	0.454323i	$-0.150119\pi$
$594$	−3.91977e6			−0.455821
$595$	908337.			0.105185
$596$		−	1.20739e6i		−	0.139230i
$597$	1.31256e6			0.150725
$598$	−6.86724e6	+	3.20553e6i	−0.785289	+	0.366561i
$599$	−8.31479e6			−0.946857			−0.473429	−	0.880832i	$-0.656984\pi$
$599$	−8.31479e6			−0.946857			−0.473429	+	0.880832i	$0.656984\pi$
$600$			1.68707e6i			0.191318i
$601$	−8.59965e6			−0.971168			−0.485584	−	0.874190i	$-0.661393\pi$
$601$	−8.59965e6			−0.971168			−0.485584	+	0.874190i	$0.661393\pi$
$602$	1.11835e6			0.125773
$603$		−	825273.i		−	0.0924282i
$604$			4.57076e6i			0.509796i
$605$			2.48702e6i			0.276242i
$606$		−	402708.i		−	0.0445460i
$607$	9.01035e6			0.992590			0.496295	−	0.868154i	$-0.334693\pi$
$607$	9.01035e6			0.992590			0.496295	+	0.868154i	$0.334693\pi$
$608$	6.19064e6			0.679167
$609$			125344.i			0.0136950i
$610$	−3.65840e6			−0.398077
$611$	927312.	−	432856.i	0.100490	−	0.0469073i
$612$	1.53723e6			0.165906
$613$			1.62035e7i			1.74164i	0.491605	+	0.870819i	$0.336411\pi$
$613$			1.62035e7i			1.74164i	−0.491605	+	0.870819i	$0.663589\pi$
$614$	4.74541e6			0.507988
$615$	1.54502e6			0.164720
$616$		−	786377.i		−	0.0834986i
$617$			3.77735e6i			0.399461i	0.979851	+	0.199731i	$0.0640067\pi$
$617$			3.77735e6i			0.399461i	−0.979851	+	0.199731i	$0.935993\pi$
$618$		−	2.50098e6i		−	0.263414i
$619$			1.58671e7i			1.66445i	0.554437	+	0.832225i	$0.312933\pi$
$619$			1.58671e7i			1.66445i	−0.554437	+	0.832225i	$0.687067\pi$
$620$	255480.			0.0266918
$621$	−1.28570e7			−1.33786
$622$		−	1.25660e7i		−	1.30233i
$623$	−2.04722e6			−0.211322
$624$	−765287.	−	1.63948e6i	−0.0786797	−	0.168557i
$625$	390625.			0.0400000
$626$			7.06848e6i			0.720925i
$627$	−4.12709e6			−0.419252
$628$	−4.23866e6			−0.428874
$629$		−	3.36104e7i		−	3.38725i
$630$			68484.7i			0.00687452i
$631$		−	8.27657e6i		−	0.827517i	−0.910387	−	0.413758i	$-0.864216\pi$
$631$		−	8.27657e6i		−	0.827517i	0.910387	−	0.413758i	$-0.135784\pi$
$632$		−	1.62285e7i		−	1.61616i
$633$	1.39977e7			1.38850
$634$	−9.65498e6			−0.953956
$635$		−	2.81155e6i		−	0.276702i
$636$	−3.99490e6			−0.391618
$637$	−4.26037e6	−	9.12704e6i	−0.416005	−	0.891212i
$638$	515498.			0.0501389
$639$			1.98575e6i			0.192385i
$640$	−1.54976e6			−0.149560
$641$	−1.51762e7			−1.45888			−0.729439	−	0.684046i	$-0.760219\pi$
$641$	−1.51762e7			−1.45888			−0.729439	+	0.684046i	$0.760219\pi$
$642$			4.59523e6i			0.440018i
$643$		−	7.61038e6i		−	0.725903i	−0.931808	−	0.362952i	$-0.881769\pi$
$643$		−	7.61038e6i		−	0.725903i	0.931808	−	0.362952i	$-0.118231\pi$
$644$		−	885143.i		−	0.0841006i
$645$			6.09180e6i			0.576562i
$646$	−1.00162e7			−0.944322
$647$	1.32967e7			1.24878			0.624388	−	0.781114i	$-0.285348\pi$
$647$	1.32967e7			1.24878			0.624388	+	0.781114i	$0.285348\pi$
$648$		−	8.95915e6i		−	0.838164i
$649$	−4.05875e6			−0.378251
$650$	−1.34901e6	+	629700.i	−0.125237	+	0.0584589i
$651$	−144167.			−0.0133325
$652$		−	7.62948e6i		−	0.702872i
$653$	−1.73108e7			−1.58867			−0.794335	−	0.607480i	$-0.792181\pi$
$653$	−1.73108e7			−1.58867			−0.794335	+	0.607480i	$0.792181\pi$
$654$	2.66646e6			0.243776
$655$		−	1.48572e6i		−	0.135311i
$656$		−	913463.i		−	0.0828765i
$657$			2.62154e6i			0.236942i
$658$		−	109250.i		−	0.00983689i
$659$	6.97931e6			0.626036			0.313018	−	0.949747i	$-0.398660\pi$
$659$	6.97931e6			0.626036			0.313018	+	0.949747i	$0.398660\pi$
$660$	1.46995e6			0.131354
$661$		−	1.16481e7i		−	1.03693i	−0.855098	−	0.518467i	$-0.826503\pi$
$661$		−	1.16481e7i		−	1.03693i	0.855098	−	0.518467i	$-0.173497\pi$
$662$	1.01944e7			0.904099
$663$	−7.97603e6	−	1.70872e7i	−0.704698	−	1.50968i
$664$	−1.53947e7			−1.35504
$665$			488191.i			0.0428091i
$666$	2.53408e6			0.221378
$667$	1.69085e6			0.147160
$668$			7.48588e6i			0.649085i
$669$			1.17658e7i			1.01638i
$670$		−	1.91521e6i		−	0.164828i
$671$			9.28870e6i			0.796432i
$672$	1.24423e6			0.106286
$673$	5.43224e6			0.462318			0.231159	−	0.972916i	$-0.425748\pi$
$673$	5.43224e6			0.462318			0.231159	+	0.972916i	$0.425748\pi$
$674$			6.99647e6i			0.593238i
$675$	−2.52565e6			−0.213360
$676$	−3.98636e6	+	4.75834e6i	−0.335514	+	0.400487i
$677$	−5.56649e6			−0.466777			−0.233389	−	0.972384i	$-0.574981\pi$
$677$	−5.56649e6			−0.466777			−0.233389	+	0.972384i	$0.574981\pi$
$678$		−	1.03524e7i		−	0.864905i
$679$	−85688.4			−0.00713260
$680$	1.03957e7			0.862149
$681$			1.17619e7i			0.971874i
$682$			592907.i			0.0488119i
$683$			1.57905e7i			1.29522i	0.761971	+	0.647611i	$0.224232\pi$
$683$			1.57905e7i			1.29522i	−0.761971	+	0.647611i	$0.775768\pi$
$684$			826196.i			0.0675216i
$685$	−9.67247e6			−0.787610
$686$	−2.16860e6			−0.175942
$687$		−	4.34139e6i		−	0.350943i
$688$	3.60167e6			0.290090
$689$	−4.34511e6	−	9.30859e6i	−0.348701	−	0.747026i
$690$	−4.40702e6			−0.352389
$691$			2.21719e7i			1.76648i	0.468925	+	0.883238i	$0.344641\pi$
$691$			2.21719e7i			1.76648i	−0.468925	+	0.883238i	$0.655359\pi$
$692$	2.10081e6			0.166772
$693$	173883.			0.0137538
$694$			539228.i			0.0424985i
$695$		−	406755.i		−	0.0319427i
$696$			1.43454e6i			0.112251i
$697$		−	9.52037e6i		−	0.742287i
$698$	−5.21612e6			−0.405237
$699$	4.46272e6			0.345467
$700$		−	173879.i		−	0.0134123i
$701$	3.22961e6			0.248230			0.124115	−	0.992268i	$-0.460391\pi$
$701$	3.22961e6			0.248230			0.124115	+	0.992268i	$0.460391\pi$
$702$	8.72226e6	−	4.07142e6i	0.668015	−	0.311820i
$703$	1.80641e7			1.37857
$704$		−	6.78053e6i		−	0.515623i
$705$	595098.			0.0450937
$706$	−1.11874e7			−0.844731
$707$			120948.i			0.00910021i
$708$		−	3.87599e6i		−	0.290603i
$709$			1.30490e7i			0.974905i	0.873149	+	0.487453i	$0.162074\pi$
$709$			1.30490e7i			0.974905i	−0.873149	+	0.487453i	$0.837926\pi$
$710$			4.60833e6i			0.343082i
$711$	3.58843e6			0.266214
$712$	−2.34300e7			−1.73210
$713$			1.94475e6i			0.143265i
$714$	−2.01310e6			−0.147782
$715$	1.59881e6	+	3.42515e6i	0.116959	+	0.250562i
$716$	1.02148e6			0.0744641
$717$			4.42142e6i			0.321191i
$718$	−1.02931e7			−0.745137
$719$	1.16498e7			0.840420			0.420210	−	0.907427i	$-0.361956\pi$
$719$	1.16498e7			0.840420			0.420210	+	0.907427i	$0.361956\pi$
$720$			220556.i			0.0158557i
$721$			751137.i			0.0538122i
$722$			4.29619e6i			0.306719i
$723$		−	7.22114e6i		−	0.513760i
$724$	−3.55232e6			−0.251864
$725$	332154.			0.0234690
$726$		−	5.51186e6i		−	0.388112i
$727$	−2.06191e6			−0.144689			−0.0723443	−	0.997380i	$-0.523048\pi$
$727$	−2.06191e6			−0.144689			−0.0723443	+	0.997380i	$0.523048\pi$
$728$	816803.	+	1.74985e6i	0.0571201	+	0.122369i
$729$	1.58990e7			1.10803
$730$			6.08381e6i			0.422541i
$731$	3.75376e7			2.59820
$732$	−8.87045e6			−0.611883
$733$		−	6.87751e6i		−	0.472793i	−0.971657	−	0.236397i	$-0.924034\pi$
$733$		−	6.87751e6i		−	0.472793i	0.971657	−	0.236397i	$-0.0759664\pi$
$734$			5.16457e6i			0.353829i
$735$		−	5.85723e6i		−	0.399921i
$736$		−	1.67842e7i		−	1.14210i
$737$	−4.86273e6			−0.329770
$738$	717795.			0.0485132
$739$		−	1.18754e7i		−	0.799905i	−0.916536	−	0.399953i	$-0.869027\pi$
$739$		−	1.18754e7i		−	0.799905i	0.916536	−	0.399953i	$-0.130973\pi$
$740$	−6.43390e6			−0.431912
$741$	9.18360e6	−	4.28677e6i	0.614423	−	0.286804i
$742$	−1.09668e6			−0.0731258
$743$			2.73070e7i			1.81469i	0.420387	+	0.907345i	$0.361894\pi$
$743$			2.73070e7i			1.81469i	−0.420387	+	0.907345i	$0.638106\pi$
$744$	−1.64996e6			−0.109280
$745$	1.80546e6			0.119179
$746$			1.32758e7i			0.873403i
$747$		−	3.40406e6i		−	0.223201i
$748$		−	9.05779e6i		−	0.591927i
$749$		−	1.38012e6i		−	0.0898902i
$750$	−865724.			−0.0561987
$751$	6.34944e6			0.410805			0.205403	−	0.978678i	$-0.434150\pi$
$751$	6.34944e6			0.410805			0.205403	+	0.978678i	$0.434150\pi$
$752$		−	351841.i		−	0.0226883i
$753$	−1.18732e7			−0.763095
$754$	−1.14709e6	+	535443.i	−0.0734797	+	0.0342992i
$755$	−6.83486e6			−0.436378
$756$			1.12424e6i			0.0715411i
$757$	1.00625e7			0.638212			0.319106	−	0.947719i	$-0.396617\pi$
$757$	1.00625e7			0.638212			0.319106	+	0.947719i	$0.396617\pi$
$758$	−1.09594e7			−0.692810
$759$			1.11894e7i			0.705024i
$760$			5.58725e6i			0.350884i
$761$			9.34500e6i			0.584948i	0.956273	+	0.292474i	$0.0944785\pi$
$761$			9.34500e6i			0.584948i	−0.956273	+	0.292474i	$0.905521\pi$
$762$			6.23111e6i			0.388757i
$763$	−800839.			−0.0498005
$764$	2.30898e6			0.143115
$765$			2.29869e6i			0.142013i
$766$	6.88317e6			0.423854
$767$	9.03153e6	−	4.21579e6i	0.554336	−	0.258756i
$768$	1.58285e7			0.968360
$769$		−	1.62569e7i		−	0.991336i	−0.868512	−	0.495668i	$-0.834923\pi$
$769$		−	1.62569e7i		−	0.991336i	0.868512	−	0.495668i	$-0.165077\pi$
$770$	403531.			0.0245273
$771$	−1.29729e7			−0.785962
$772$			445493.i			0.0269028i
$773$			7.83583e6i			0.471668i	0.971793	+	0.235834i	$0.0757821\pi$
$773$			7.83583e6i			0.471668i	−0.971793	+	0.235834i	$0.924218\pi$
$774$			2.83018e6i			0.169809i
$775$			382031.i			0.0228478i
$776$	−980686.			−0.0584623
$777$	3.63063e6			0.215739
$778$			501640.i			0.0297128i
$779$	5.11678e6			0.302102
$780$	−3.27093e6	+	1.52682e6i	−0.192502	+	0.0898569i
$781$	1.17006e7			0.686403
$782$			2.71560e7i			1.58799i
$783$	−2.14759e6			−0.125183
$784$	−3.46298e6			−0.201215
$785$		−	6.33826e6i		−	0.367110i
$786$			3.29273e6i			0.190108i
$787$			1.75045e7i			1.00742i	0.863872	+	0.503712i	$0.168033\pi$
$787$			1.75045e7i			1.00742i	−0.863872	+	0.503712i	$0.831967\pi$
$788$		−	1.61565e7i		−	0.926898i
$789$	−3.91914e6			−0.224129
$790$	8.32767e6			0.474740
$791$			3.10922e6i			0.176689i
$792$	1.99005e6			0.112733
$793$	−9.64809e6	−	2.06692e7i	−0.544827	−	1.16719i
$794$	8.54335e6			0.480925
$795$		−	5.97374e6i		−	0.335219i
$796$	−1.54825e6			−0.0866081
$797$	4.11253e6			0.229331			0.114666	−	0.993404i	$-0.463420\pi$
$797$	4.11253e6			0.229331			0.114666	+	0.993404i	$0.463420\pi$
$798$		−	1.08196e6i		−	0.0601454i
$799$		−	3.66699e6i		−	0.203209i
$800$		−	3.29712e6i		−	0.182142i
$801$		−	5.18083e6i		−	0.285311i
$802$	−9.02946e6			−0.495708
$803$	1.54468e7			0.845376
$804$		−	4.64377e6i		−	0.253356i
$805$	1.32359e6			0.0719888
$806$	−615847.	−	1.31934e6i	−0.0333914	−	0.0715349i
$807$	1.49152e7			0.806204
$808$			1.38423e6i			0.0745898i
$809$	1.80079e7			0.967368			0.483684	−	0.875243i	$-0.339298\pi$
$809$	1.80079e7			0.967368			0.483684	+	0.875243i	$0.339298\pi$
$810$	4.59740e6			0.246207
$811$		−	2.66465e7i		−	1.42262i	−0.702879	−	0.711310i	$-0.748102\pi$
$811$		−	2.66465e7i		−	1.42262i	0.702879	−	0.711310i	$-0.251898\pi$
$812$		−	147852.i		−	0.00786931i
$813$		−	2.18180e7i		−	1.15768i
$814$		−	1.49315e7i		−	0.789846i
$815$	1.14087e7			0.601647
$816$	−6.48321e6			−0.340851
$817$			2.01748e7i			1.05744i
$818$	−1.26824e7			−0.662700
$819$	−386925.	+	180611.i	−0.0201566	+	0.00940879i
$820$	−1.82245e6			−0.0946499
$821$			2.13752e7i			1.10676i	0.832929	+	0.553379i	$0.186662\pi$
$821$			2.13752e7i			1.10676i	−0.832929	+	0.553379i	$0.813338\pi$
$822$	2.14367e7			1.10657
$823$	2.63422e7			1.35566			0.677832	−	0.735217i	$-0.262920\pi$
$823$	2.63422e7			1.35566			0.677832	+	0.735217i	$0.262920\pi$
$824$			8.59660e6i			0.441071i
$825$			2.19808e6i			0.112437i
$826$		−	1.06404e6i		−	0.0542635i
$827$			1.46357e7i			0.744133i	0.928206	+	0.372067i	$0.121351\pi$
$827$			1.46357e7i			0.744133i	−0.928206	+	0.372067i	$0.878649\pi$
$828$	2.24000e6			0.113546
$829$	−4.09806e6			−0.207106			−0.103553	−	0.994624i	$-0.533021\pi$
$829$	−4.09806e6			−0.207106			−0.103553	+	0.994624i	$0.533021\pi$
$830$		−	7.89981e6i		−	0.398035i
$831$	2.98635e7			1.50016
$832$	7.04288e6	+	1.50880e7i	0.352729	+	0.755657i
$833$	−3.60922e7			−1.80219
$834$			901472.i			0.0448784i
$835$	−1.11940e7			−0.555607
$836$	4.86817e6			0.240907
$837$		−	2.47008e6i		−	0.121870i
$838$		−	1.93026e7i		−	0.949523i
$839$		−	2.07513e7i		−	1.01775i	−0.860841	−	0.508874i	$-0.830062\pi$
$839$		−	2.07513e7i		−	1.01775i	0.860841	−	0.508874i	$-0.169938\pi$
$840$			1.12296e6i			0.0549117i
$841$	−2.02287e7			−0.986230
$842$	4.57435e6			0.222356
$843$			2.52242e7i			1.22250i
$844$	−1.65111e7			−0.797849
$845$	−7.11535e6	−	5.96098e6i	−0.342811	−	0.287194i
$846$	276475.			0.0132810
$847$			1.65542e6i			0.0792865i
$848$	−3.53187e6			−0.168661
$849$	−2.07947e7			−0.990110
$850$			5.33458e6i			0.253252i
$851$		−	4.89758e7i		−	2.31823i
$852$			1.11737e7i			0.527349i
$853$			3.48833e7i			1.64151i	0.571278	+	0.820757i	$0.306448\pi$
$853$			3.48833e7i			1.64151i	−0.571278	+	0.820757i	$0.693552\pi$
$854$	−2.43512e6			−0.114255
$855$	−1.23545e6			−0.0577975
$856$		−	1.57952e7i		−	0.736784i
$857$	−3.62552e7			−1.68623			−0.843117	−	0.537730i	$-0.819282\pi$
$857$	−3.62552e7			−1.68623			−0.843117	+	0.537730i	$0.819282\pi$
$858$	−3.54337e6	−	7.59101e6i	−0.164323	−	0.352031i
$859$	1.97684e7			0.914089			0.457044	−	0.889444i	$-0.348908\pi$
$859$	1.97684e7			0.914089			0.457044	+	0.889444i	$0.348908\pi$
$860$		−	7.18567e6i		−	0.331300i
$861$	1.02840e6			0.0472774
$862$	9.17764e6			0.420691
$863$			4.05134e7i			1.85171i	0.377883	+	0.925853i	$0.376652\pi$
$863$			4.05134e7i			1.85171i	−0.377883	+	0.925853i	$0.623348\pi$
$864$			2.13180e7i			0.971544i
$865$			3.14144e6i			0.142754i
$866$		−	1.24205e6i		−	0.0562785i
$867$	−4.74455e7			−2.14362
$868$	170054.			0.00766103
$869$		−	2.11440e7i		−	0.949812i
$870$	−736137.			−0.0329731
$871$	1.08206e7	−	5.05088e6i	0.483286	−	0.225591i
$872$	−9.16543e6			−0.408189
$873$		−	216848.i		−	0.00962987i
$874$	−1.45952e7			−0.646295
$875$	260009.			0.0114807
$876$			1.47513e7i			0.649485i
$877$		−	1.00077e7i		−	0.439376i	−0.975570	−	0.219688i	$-0.929496\pi$
$877$		−	1.00077e7i		−	0.439376i	0.975570	−	0.219688i	$-0.0705040\pi$
$878$			8.60136e6i			0.376557i
$879$			3.21193e7i			1.40215i
$880$	1.29957e6			0.0565710
$881$	2.79088e6			0.121144			0.0605718	−	0.998164i	$-0.480708\pi$
$881$	2.79088e6			0.121144			0.0605718	+	0.998164i	$0.480708\pi$
$882$		−	2.72120e6i		−	0.117785i
$883$	−4.31588e7			−1.86281			−0.931403	−	0.363989i	$-0.881415\pi$
$883$	−4.31588e7			−1.86281			−0.931403	+	0.363989i	$0.881415\pi$
$884$	9.40825e6	+	2.01554e7i	0.404928	+	0.867483i
$885$	5.79594e6			0.248752
$886$		−	2.37115e7i		−	1.01479i
$887$	5.93655e6			0.253352			0.126676	−	0.991944i	$-0.459569\pi$
$887$	5.93655e6			0.253352			0.126676	+	0.991944i	$0.459569\pi$
$888$	4.15518e7			1.76830
$889$		−	1.87144e6i		−	0.0794183i
$890$		−	1.20232e7i		−	0.508796i
$891$		−	1.16728e7i		−	0.492585i
$892$		−	1.38786e7i		−	0.584027i
$893$	1.97085e6			0.0827035
$894$	−4.00137e6			−0.167442
$895$			1.52746e6i			0.0637401i
$896$	−1.03156e6			−0.0429264
$897$	−1.16224e7	−	2.48988e7i	−0.482296	−	1.03323i
$898$	−1.50369e6			−0.0622254
$899$			324846.i			0.0134054i
$900$	440029.			0.0181082
$901$	−3.68101e7			−1.51062
$902$		−	4.22945e6i		−	0.173088i
$903$			4.05485e6i			0.165484i
$904$			3.55844e7i			1.44823i
$905$		−	5.31195e6i		−	0.215592i
$906$	1.51478e7			0.613096
$907$	−2.95996e7			−1.19473			−0.597363	−	0.801971i	$-0.703785\pi$
$907$	−2.95996e7			−1.19473			−0.597363	+	0.801971i	$0.703785\pi$
$908$		−	1.38739e7i		−	0.558451i
$909$	−306079.			−0.0122864
$910$	−897937.	+	419144.i	−0.0359453	+	0.0167787i
$911$	−4.06010e7			−1.62084			−0.810421	−	0.585847i	$-0.800762\pi$
$911$	−4.06010e7			−1.62084			−0.810421	+	0.585847i	$0.800762\pi$
$912$		−	3.48445e6i		−	0.138722i
$913$	−2.00577e7			−0.796349
$914$	−2.32408e7			−0.920206
$915$		−	1.32644e7i		−	0.523762i
$916$			5.12095e6i			0.201656i
$917$		−	988930.i		−	0.0388367i
$918$		−	3.44915e7i		−	1.35085i
$919$	2.48347e7			0.969997			0.484999	−	0.874515i	$-0.338820\pi$
$919$	2.48347e7			0.969997			0.484999	+	0.874515i	$0.338820\pi$
$920$	1.51482e7			0.590055
$921$			1.72056e7i			0.668375i
$922$	−5.52277e6			−0.213959
$923$	−2.60361e7	+	1.21533e7i	−1.00594	+	0.469558i
$924$	978432.			0.0377008
$925$		−	9.62090e6i		−	0.369710i
$926$	2.82862e7			1.08404
$927$	−1.90087e6			−0.0726530
$928$		−	2.80358e6i		−	0.106867i
$929$		−	1.35407e7i		−	0.514756i	−0.966311	−	0.257378i	$-0.917141\pi$
$929$		−	1.35407e7i		−	0.514756i	0.966311	−	0.257378i	$-0.0828585\pi$
$930$		−	846678.i		−	0.0321004i
$931$		−	1.93980e7i		−	0.733470i
$932$	−5.26406e6			−0.198510
$933$	4.55608e7			1.71351
$934$			1.58569e7i			0.594772i
$935$	1.35445e7			0.506681
$936$	−4.42827e6	+	2.06705e6i	−0.165213	+	0.0771190i
$937$	5.80240e6			0.215903			0.107952	−	0.994156i	$-0.465571\pi$
$937$	5.80240e6			0.215903			0.107952	+	0.994156i	$0.465571\pi$
$938$		−	1.27481e6i		−	0.0473085i
$939$	−2.56284e7			−0.948543
$940$	−701957.			−0.0259114
$941$		−	1.78326e7i		−	0.656509i	−0.944589	−	0.328255i	$-0.893540\pi$
$941$		−	1.78326e7i		−	0.656509i	0.944589	−	0.328255i	$-0.106460\pi$
$942$			1.40472e7i			0.515777i
$943$		−	1.38727e7i		−	0.508022i
$944$		−	3.42675e6i		−	0.125156i
$945$	−1.68113e6			−0.0612381
$946$	1.66762e7			0.605854
$947$			2.72249e7i			0.986486i	0.869891	+	0.493243i	$0.164189\pi$
$947$			2.72249e7i			0.986486i	−0.869891	+	0.493243i	$0.835811\pi$
$948$	2.01919e7			0.729721
$949$	−3.43723e7	+	1.60445e7i	−1.23892	+	0.578309i
$950$	−2.86710e6			−0.103071
$951$		−	3.50063e7i		−	1.25515i
$952$	6.91964e6			0.247452
$953$	4.28116e7			1.52697			0.763483	−	0.645829i	$-0.223488\pi$
$953$	4.28116e7			1.52697			0.763483	+	0.645829i	$0.223488\pi$
$954$		−	2.77533e6i		−	0.0987287i
$955$			3.45272e6i			0.122505i
$956$		−	5.21535e6i		−	0.184560i
$957$			1.86905e6i			0.0659693i
$958$	1.51945e7			0.534902
$959$	−6.43823e6			−0.226058
$960$			9.68268e6i			0.339092i
$961$	2.82555e7			0.986949
$962$	1.55092e7	+	3.32256e7i	0.540321	+	1.15754i
$963$	3.49262e6			0.121363
$964$			8.51780e6i			0.295213i
$965$	−666165.			−0.0230284
$966$	−2.93342e6			−0.101142
$967$		−	174109.i		−	0.00598763i	−0.999996	−	0.00299382i	$-0.999047\pi$
$967$		−	174109.i		−	0.00598763i	0.999996	−	0.00299382i	$-0.000952963\pi$
$968$			1.89459e7i			0.649871i
$969$		−	3.63159e7i		−	1.24247i
$970$		−	503240.i		−	0.0171730i
$971$	−2.07727e7			−0.707040			−0.353520	−	0.935427i	$-0.615015\pi$
$971$	−2.07727e7			−0.707040			−0.353520	+	0.935427i	$0.615015\pi$
$972$	−5.26993e6			−0.178912
$973$		−	270746.i		−	0.00916811i
$974$	−1.64857e7			−0.556815
$975$	−2.28312e6	−	4.89116e6i	−0.0769162	−	0.164778i
$976$	−7.84232e6			−0.263524
$977$		−	7.25350e6i		−	0.243115i	−0.992584	−	0.121557i	$-0.961211\pi$
$977$		−	7.25350e6i		−	0.243115i	0.992584	−	0.121557i	$-0.0387888\pi$
$978$	−2.52846e7			−0.845295
$979$	−3.05268e7			−1.01795
$980$			6.90898e6i			0.229799i
$981$		−	2.02665e6i		−	0.0672367i
$982$		−	4.00611e7i		−	1.32570i
$983$			2.65029e7i			0.874803i	0.899266	+	0.437401i	$0.144101\pi$
$983$			2.65029e7i			0.874803i	−0.899266	+	0.437401i	$0.855899\pi$
$984$	1.17698e7			0.387509
$985$	2.41595e7			0.793411
$986$			4.53606e6i			0.148589i
$987$	396112.			0.0129427
$988$	−1.08327e7	+	5.05652e6i	−0.353055	+	0.164801i
$989$	5.46983e7			1.77821
$990$			1.02120e6i			0.0331148i
$991$	5.31052e7			1.71772			0.858861	−	0.512209i	$-0.171173\pi$
$991$	5.31052e7			1.71772			0.858861	+	0.512209i	$0.171173\pi$
$992$	3.22458e6			0.104038
$993$			3.69620e7i			1.18955i
$994$			3.06741e6i			0.0984705i
$995$		−	2.31517e6i		−	0.0741353i
$996$		−	1.91545e7i		−	0.611818i
$997$	5.86777e7			1.86954			0.934772	−	0.355249i	$-0.115604\pi$
$997$	5.86777e7			1.86954			0.934772	+	0.355249i	$0.115604\pi$
$998$	9.90224e6			0.314707
$999$			6.22054e7i			1.97203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.6.c.b.51.10	yes	14
13.5	odd	4		845.6.a.i.1.6		7
13.8	odd	4		845.6.a.j.1.2		7
13.12	even	2	inner	65.6.c.b.51.5	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.6.c.b.51.5	✓	14	13.12	even	2	inner
65.6.c.b.51.10	yes	14	1.1	even	1	trivial
845.6.a.i.1.6		7	13.5	odd	4
845.6.a.j.1.2		7	13.8	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)

\(f(q)\)	\(=\)	\(q+3.90915i q^{2} -14.1735 q^{3} +16.7186 q^{4} +25.0000i q^{5} -55.4063i q^{6} +16.6406i q^{7} +190.448i q^{8} -42.1117 q^{9} -97.7287 q^{10} +248.134i q^{11} -236.961 q^{12} +(-257.734 - 552.147i) q^{13} -65.0506 q^{14} -354.338i q^{15} -209.496 q^{16} -2183.42 q^{17} -164.621i q^{18} -1173.50i q^{19} +417.964i q^{20} -235.856i q^{21} -969.991 q^{22} -3181.60 q^{23} -2699.32i q^{24} -625.000 q^{25} +(2158.42 - 1007.52i) q^{26} +4041.03 q^{27} +278.207i q^{28} -531.446 q^{29} +1385.16 q^{30} -611.250i q^{31} +5275.39i q^{32} -3516.92i q^{33} -8535.32i q^{34} -416.015 q^{35} -704.047 q^{36} +15393.4i q^{37} +4587.37 q^{38} +(3653.00 + 7825.86i) q^{39} -4761.20 q^{40} +4360.29i q^{41} +921.994 q^{42} -17192.1 q^{43} +4148.44i q^{44} -1052.79i q^{45} -12437.3i q^{46} +1679.47i q^{47} +2969.29 q^{48} +16530.1 q^{49} -2443.22i q^{50} +30946.8 q^{51} +(-4308.94 - 9231.10i) q^{52} +16858.9 q^{53} +15797.0i q^{54} -6203.34 q^{55} -3169.17 q^{56} +16632.5i q^{57} -2077.50i q^{58} +16357.1i q^{59} -5924.02i q^{60} +37434.3 q^{61} +2389.47 q^{62} -700.764i q^{63} -27326.1 q^{64} +(13803.7 - 6443.35i) q^{65} +13748.2 q^{66} +19597.2i q^{67} -36503.7 q^{68} +45094.4 q^{69} -1626.26i q^{70} -47154.3i q^{71} -8020.09i q^{72} -62252.0i q^{73} -60175.2 q^{74} +8858.44 q^{75} -19619.1i q^{76} -4129.09 q^{77} +(-30592.4 + 14280.1i) q^{78} -85212.1 q^{79} -5237.39i q^{80} -47042.5 q^{81} -17045.0 q^{82} +80834.1i q^{83} -3943.17i q^{84} -54585.6i q^{85} -67206.4i q^{86} +7532.45 q^{87} -47256.6 q^{88} +123026. i q^{89} +4115.52 q^{90} +(9188.05 - 4288.85i) q^{91} -53191.8 q^{92} +8663.55i q^{93} -6565.28 q^{94} +29337.4 q^{95} -74770.8i q^{96} +5149.36i q^{97} +64618.6i q^{98} -10449.3i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 84 q^{3} - 38 q^{4} + 1118 q^{9} + 550 q^{10} + 168 q^{12} - 1132 q^{13} + 6440 q^{14} - 3434 q^{16} + 228 q^{17} + 2328 q^{22} + 8104 q^{23} - 8750 q^{25} - 142 q^{26} + 13680 q^{27} - 16700 q^{29}+ \cdots + 318800 q^{95}+O(q^{100}) \) 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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