LMFDB - Embedded newform 63.6.e.c.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-83})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 20x^{2} - 21x + 441 $ x^4 - x^3 - 20x^2 - 21x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.1
Root			$4.19493 + 1.84460i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.6.e.c.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.69493 - 8.13186i) q^{2} +(-28.0848 + 48.6443i) q^{4} +(-35.8645 - 62.1192i) q^{5} +(-87.5000 - 95.6596i) q^{7} +226.949 q^{8} +(-336.763 + 583.291i) q^{10} +(-280.305 + 485.503i) q^{11} +533.509 q^{13} +(-367.084 + 1160.65i) q^{14} +(-166.798 - 288.903i) q^{16} +(502.850 - 870.962i) q^{17} +(-684.263 - 1185.18i) q^{19} +4028.99 q^{20} +5264.05 q^{22} +(1614.04 + 2795.60i) q^{23} +(-1010.03 + 1749.42i) q^{25} +(-2504.79 - 4338.42i) q^{26} +(7110.71 - 1569.80i) q^{28} +753.456 q^{29} +(-4103.21 + 7106.97i) q^{31} +(2064.97 - 3576.64i) q^{32} -9443.39 q^{34} +(-2804.15 + 8866.21i) q^{35} +(1404.33 + 2432.37i) q^{37} +(-6425.14 + 11128.7i) q^{38} +(-8139.43 - 14097.9i) q^{40} -245.827 q^{41} -17504.5 q^{43} +(-15744.6 - 27270.5i) q^{44} +(15155.6 - 26250.3i) q^{46} +(-8172.74 - 14155.6i) q^{47} +(-1494.50 + 16740.4i) q^{49} +18968.1 q^{50} +(-14983.5 + 25952.2i) q^{52} +(-14820.8 + 25670.4i) q^{53} +40212.0 q^{55} +(-19858.1 - 21709.9i) q^{56} +(-3537.43 - 6127.00i) q^{58} +(-5178.05 + 8968.65i) q^{59} +(-477.089 - 826.343i) q^{61} +77057.2 q^{62} -49454.8 q^{64} +(-19134.0 - 33141.1i) q^{65} +(9907.60 - 17160.5i) q^{67} +(28244.9 + 48921.6i) q^{68} +(85264.1 - 18823.3i) q^{70} -62125.4 q^{71} +(-13554.8 + 23477.6i) q^{73} +(13186.5 - 22839.7i) q^{74} +76869.6 q^{76} +(70969.7 - 15667.6i) q^{77} +(-22343.7 - 38700.4i) q^{79} +(-11964.3 + 20722.8i) q^{80} +(1154.14 + 1999.03i) q^{82} -15606.6 q^{83} -72137.9 q^{85} +(82182.5 + 142344. i) q^{86} +(-63615.0 + 110184. i) q^{88} +(6817.66 + 11808.5i) q^{89} +(-46682.0 - 51035.2i) q^{91} -181320. q^{92} +(-76740.9 + 132919. i) q^{94} +(-49081.6 + 85011.8i) q^{95} -12919.5 q^{97} +(143147. - 66442.1i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 65 q^{4} - 33 q^{5} - 350 q^{7} + 750 q^{8} - 921 q^{10} - 1137 q^{11} + 1850 q^{13} - 2352 q^{14} + 895 q^{16} - 324 q^{17} - 2311 q^{19} + 7374 q^{20} + 3162 q^{22} + 1596 q^{23} - 395 q^{25}+ \cdots + 462021 q^{98}+O(q^{100}) $ 4 * q - 3 * q^2 - 65 * q^4 - 33 * q^5 - 350 * q^7 + 750 * q^8 - 921 * q^10 - 1137 * q^11 + 1850 * q^13 - 2352 * q^14 + 895 * q^16 - 324 * q^17 - 2311 * q^19 + 7374 * q^20 + 3162 * q^22 + 1596 * q^23 - 395 * q^25 - 2508 * q^26 + 13531 * q^28 + 4434 * q^29 - 4294 * q^31 + 1017 * q^32 - 35880 * q^34 - 15414 * q^35 + 19109 * q^37 - 6828 * q^38 - 10545 * q^40 + 25716 * q^41 - 5542 * q^43 - 36579 * q^44 + 40740 * q^46 - 23160 * q^47 - 5978 * q^49 + 58704 * q^50 - 33424 * q^52 - 31653 * q^53 + 35778 * q^55 - 65625 * q^56 + 2277 * q^58 + 41097 * q^59 - 42052 * q^61 + 204114 * q^62 - 60062 * q^64 - 23106 * q^65 - 30763 * q^67 + 44748 * q^68 + 151179 * q^70 - 204192 * q^71 + 28577 * q^73 - 77784 * q^74 + 170384 * q^76 + 96873 * q^77 + 18464 * q^79 - 71511 * q^80 + 86040 * q^82 - 122358 * q^83 - 247272 * q^85 + 258510 * q^86 - 212565 * q^88 + 29322 * q^89 - 161875 * q^91 - 333816 * q^92 - 109938 * q^94 - 61662 * q^95 - 19582 * q^97 + 462021 * q^98

Character values

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

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−4.69493	−	8.13186i	−0.829955	−	1.43752i	−0.898073	−	0.439847i	$-0.855033\pi$
$2$	−4.69493	−	8.13186i	−0.829955	−	1.43752i	0.0681181	−	0.997677i	$-0.478301\pi$
$3$		0			0
$3$		0			0
$4$	−28.0848	+	48.6443i	−0.877650	+	1.52013i
$5$	−35.8645	−	62.1192i	−0.641564	−	1.11122i	−0.985084	−	0.172076i	$-0.944952\pi$
$5$	−35.8645	−	62.1192i	−0.641564	−	1.11122i	0.343519	−	0.939146i	$-0.388381\pi$
$6$		0			0
$7$	−87.5000	−	95.6596i	−0.674937	−	0.737876i
$7$	−87.5000	−	95.6596i	−0.674937	−	0.737876i
$8$	226.949			1.25373
$9$		0			0
$10$	−336.763	+	583.291i	−1.06494	+	1.84453i
$11$	−280.305	+	485.503i	−0.698472	+	1.20979i	0.270524	+	0.962713i	$0.412803\pi$
$11$	−280.305	+	485.503i	−0.698472	+	1.20979i	−0.968996	+	0.247076i	$0.920530\pi$
$12$		0			0
$13$	533.509			0.875555			0.437777	−	0.899083i	$-0.355766\pi$
$13$	533.509			0.875555			0.437777	+	0.899083i	$0.355766\pi$
$14$	−367.084	+	1160.65i	−0.500547	+	1.58264i
$15$		0			0
$16$	−166.798	−	288.903i	−0.162889	−	0.282132i
$17$	502.850	−	870.962i	0.422004	−	0.730932i	−0.574132	−	0.818763i	$-0.694660\pi$
$17$	502.850	−	870.962i	0.422004	−	0.730932i	0.996135	+	0.0878311i	$0.0279936\pi$
$18$		0			0
$19$	−684.263	−	1185.18i	−0.434850	−	0.753182i	0.562434	−	0.826842i	$-0.309865\pi$
$19$	−684.263	−	1185.18i	−0.434850	−	0.753182i	−0.997283	+	0.0736606i	$0.976532\pi$
$20$	4028.99			2.25228
$21$		0			0
$22$	5264.05			2.31880
$23$	1614.04	+	2795.60i	0.636201	+	1.10193i	0.986259	+	0.165205i	$0.0528286\pi$
$23$	1614.04	+	2795.60i	0.636201	+	1.10193i	−0.350058	+	0.936728i	$0.613838\pi$
$24$		0			0
$25$	−1010.03	+	1749.42i	−0.323209	+	0.559815i
$26$	−2504.79	−	4338.42i	−0.726671	−	1.25863i
$27$		0			0
$28$	7110.71	−	1569.80i	1.71403	−	0.378398i
$29$	753.456			0.166365			0.0831827	−	0.996534i	$-0.473492\pi$
$29$	753.456			0.166365			0.0831827	+	0.996534i	$0.473492\pi$
$30$		0			0
$31$	−4103.21	+	7106.97i	−0.766866	+	1.32825i	0.172389	+	0.985029i	$0.444852\pi$
$31$	−4103.21	+	7106.97i	−0.766866	+	1.32825i	−0.939254	+	0.343222i	$0.888482\pi$
$32$	2064.97	−	3576.64i	0.356484	−	0.617448i
$33$		0			0
$34$	−9443.39			−1.40098
$35$	−2804.15	+	8866.21i	−0.386929	+	1.22340i
$36$		0			0
$37$	1404.33	+	2432.37i	0.168642	+	0.292096i	0.937943	−	0.346791i	$-0.112729\pi$
$37$	1404.33	+	2432.37i	0.168642	+	0.292096i	−0.769301	+	0.638887i	$0.779395\pi$
$38$	−6425.14	+	11128.7i	−0.721811	+	1.25021i
$39$		0			0
$40$	−8139.43	−	14097.9i	−0.804348	−	1.39317i
$41$	−245.827			−0.0228387			−0.0114193	−	0.999935i	$-0.503635\pi$
$41$	−245.827			−0.0228387			−0.0114193	+	0.999935i	$0.503635\pi$
$42$		0			0
$43$	−17504.5			−1.44371			−0.721853	−	0.692047i	$-0.756709\pi$
$43$	−17504.5			−1.44371			−0.721853	+	0.692047i	$0.756709\pi$
$44$	−15744.6	−	27270.5i	−1.22603	−	2.12354i
$45$		0			0
$46$	15155.6	−	26250.3i	1.05604	−	1.82911i
$47$	−8172.74	−	14155.6i	−0.539663	−	0.934725i	−0.998922	−	0.0464219i	$-0.985218\pi$
$47$	−8172.74	−	14155.6i	−0.539663	−	0.934725i	0.459258	−	0.888303i	$-0.348115\pi$
$48$		0			0
$49$	−1494.50	+	16740.4i	−0.0889213	+	0.996039i
$50$	18968.1			1.07300
$51$		0			0
$52$	−14983.5	+	25952.2i	−0.768430	+	1.33096i
$53$	−14820.8	+	25670.4i	−0.724741	+	1.25529i	0.234340	+	0.972155i	$0.424707\pi$
$53$	−14820.8	+	25670.4i	−0.724741	+	1.25529i	−0.959081	+	0.283133i	$0.908626\pi$
$54$		0			0
$55$	40212.0			1.79246
$56$	−19858.1	−	21709.9i	−0.846188	−	0.925097i
$57$		0			0
$58$	−3537.43	−	6127.00i	−0.138076	−	0.239154i
$59$	−5178.05	+	8968.65i	−0.193659	+	0.335426i	−0.946460	−	0.322821i	$-0.895369\pi$
$59$	−5178.05	+	8968.65i	−0.193659	+	0.335426i	0.752801	+	0.658248i	$0.228702\pi$
$60$		0			0
$61$	−477.089	−	826.343i	−0.0164163	−	0.0284339i	0.857701	−	0.514150i	$-0.171892\pi$
$61$	−477.089	−	826.343i	−0.0164163	−	0.0284339i	−0.874117	+	0.485716i	$0.838559\pi$
$62$	77057.2			2.54586
$63$		0			0
$64$	−49454.8			−1.50924
$65$	−19134.0	−	33141.1i	−0.561725	−	0.972935i
$66$		0			0
$67$	9907.60	−	17160.5i	0.269638	−	0.467027i	−0.699130	−	0.714994i	$-0.746429\pi$
$67$	9907.60	−	17160.5i	0.269638	−	0.467027i	0.968768	+	0.247967i	$0.0797626\pi$
$68$	28244.9	+	48921.6i	0.740743	+	1.28300i
$69$		0			0
$70$	85264.1	−	18823.3i	2.07980	−	0.459147i
$71$	−62125.4			−1.46259			−0.731296	−	0.682060i	$-0.761084\pi$
$71$	−62125.4			−1.46259			−0.731296	+	0.682060i	$0.761084\pi$
$72$		0			0
$73$	−13554.8	+	23477.6i	−0.297705	+	0.515641i	−0.975611	−	0.219509i	$-0.929555\pi$
$73$	−13554.8	+	23477.6i	−0.297705	+	0.515641i	0.677905	+	0.735149i	$0.262888\pi$
$74$	13186.5	−	22839.7i	0.279930	−	0.484853i
$75$		0			0
$76$	76869.6			1.52658
$77$	70969.7	−	15667.6i	1.36410	−	0.301145i
$78$		0			0
$79$	−22343.7	−	38700.4i	−0.402798	−	0.697666i	0.591265	−	0.806477i	$-0.298629\pi$
$79$	−22343.7	−	38700.4i	−0.402798	−	0.697666i	−0.994062	+	0.108812i	$0.965295\pi$
$80$	−11964.3	+	20722.8i	−0.209008	+	0.362012i
$81$		0			0
$82$	1154.14	+	1999.03i	0.0189551	+	0.0328311i
$83$	−15606.6			−0.248665			−0.124332	−	0.992241i	$-0.539679\pi$
$83$	−15606.6			−0.248665			−0.124332	+	0.992241i	$0.539679\pi$
$84$		0			0
$85$	−72137.9			−1.08297
$86$	82182.5	+	142344.i	1.19821	+	2.07536i
$87$		0			0
$88$	−63615.0	+	110184.i	−0.875696	+	1.51675i
$89$	6817.66	+	11808.5i	0.0912347	+	0.158023i	0.908031	−	0.418903i	$-0.137585\pi$
$89$	6817.66	+	11808.5i	0.0912347	+	0.158023i	−0.816796	+	0.576926i	$0.804252\pi$
$90$		0			0
$91$	−46682.0	−	51035.2i	−0.590944	−	0.646050i
$92$	−181320.			−2.23345
$93$		0			0
$94$	−76740.9	+	132919.i	−0.895793	+	1.55156i
$95$	−49081.6	+	85011.8i	−0.557968	+	0.966429i
$96$		0			0
$97$	−12919.5			−0.139417			−0.0697086	−	0.997567i	$-0.522207\pi$
$97$	−12919.5			−0.139417			−0.0697086	+	0.997567i	$0.522207\pi$
$98$	143147.	−	66442.1i	1.50563	−	0.698841i
$99$		0			0
$100$	−56733.0	−	98264.4i	−0.567330	−	0.982644i
$101$	12571.5	−	21774.4i	0.122626	−	0.212394i	−0.798177	−	0.602424i	$-0.794202\pi$
$101$	12571.5	−	21774.4i	0.122626	−	0.212394i	0.920802	+	0.390029i	$0.127535\pi$
$102$		0			0
$103$	80376.6	+	139216.i	0.746511	+	1.29300i	0.949485	+	0.313811i	$0.101606\pi$
$103$	80376.6	+	139216.i	0.746511	+	1.29300i	−0.202974	+	0.979184i	$0.565061\pi$
$104$	121079.			1.09771
$105$		0			0
$106$	278331.			2.40601
$107$	−47187.8	−	81731.6i	−0.398446	−	0.690129i	0.595088	−	0.803661i	$-0.297117\pi$
$107$	−47187.8	−	81731.6i	−0.398446	−	0.690129i	−0.993534	+	0.113531i	$0.963784\pi$
$108$		0			0
$109$	41696.7	−	72220.9i	0.336152	−	0.582233i	−0.647553	−	0.762020i	$-0.724208\pi$
$109$	41696.7	−	72220.9i	0.336152	−	0.582233i	0.983705	+	0.179788i	$0.0575410\pi$
$110$	−188793.	−	326999.i	−1.48766	−	2.57670i
$111$		0			0
$112$	−13041.5	+	41234.9i	−0.0982387	+	0.310613i
$113$	179254.			1.32060			0.660301	−	0.751001i	$-0.270429\pi$
$113$	179254.			1.32060			0.660301	+	0.751001i	$0.270429\pi$
$114$		0			0
$115$	115774.	−	200526.i	0.816328	−	1.41392i
$116$	−21160.7	+	36651.3i	−0.146011	+	0.252898i
$117$		0			0
$118$	97242.5			0.642911
$119$	−127315.	+	28106.8i	−0.824163	+	0.181946i
$120$		0			0
$121$	−76616.4	−	132703.i	−0.475727	−	0.823984i
$122$	−4479.80	+	7759.25i	−0.0272496	+	0.0471976i
$123$		0			0
$124$	−230476.	−	399195.i	−1.34608	−	2.33148i
$125$	−79256.4			−0.453690
$126$		0			0
$127$	−143674.			−0.790440			−0.395220	−	0.918586i	$-0.629332\pi$
$127$	−143674.			−0.790440			−0.395220	+	0.918586i	$0.629332\pi$
$128$	166108.	+	287707.i	0.896117	+	1.55212i
$129$		0			0
$130$	−179666.	+	311191.i	−0.932412	+	1.61498i
$131$	26144.9	+	45284.3i	0.133110	+	0.230553i	0.924874	−	0.380274i	$-0.124170\pi$
$131$	26144.9	+	45284.3i	0.133110	+	0.230553i	−0.791764	+	0.610827i	$0.790837\pi$
$132$		0			0
$133$	−53500.6	+	169159.i	−0.262259	+	0.829215i
$134$	−186062.			−0.895150
$135$		0			0
$136$	114122.	−	197664.i	0.529079	−	0.916391i
$137$	4705.05	−	8149.39i	0.0214172	−	0.0370957i	−0.855118	−	0.518433i	$-0.826516\pi$
$137$	4705.05	−	8149.39i	0.0214172	−	0.0370957i	0.876535	+	0.481337i	$0.159849\pi$
$138$		0			0
$139$	183094.			0.803781			0.401890	−	0.915688i	$-0.368353\pi$
$139$	183094.			0.803781			0.401890	+	0.915688i	$0.368353\pi$
$140$	−352537.	−	385412.i	−1.52014	−	1.66190i
$141$		0			0
$142$	291674.	+	505195.i	1.21389	+	2.10251i
$143$	−149545.	+	259020.i	−0.611551	+	1.05924i
$144$		0			0
$145$	−27022.3	−	46804.1i	−0.106734	−	0.184869i
$146$	254556.			0.988328
$147$		0			0
$148$	−157762.			−0.592034
$149$	−83500.8	−	144628.i	−0.308123	−	0.533685i	0.669828	−	0.742516i	$-0.266368\pi$
$149$	−83500.8	−	144628.i	−0.308123	−	0.533685i	−0.977952	+	0.208830i	$0.933034\pi$
$150$		0			0
$151$	−188132.	+	325855.i	−0.671461	+	1.16300i	0.306029	+	0.952022i	$0.401000\pi$
$151$	−188132.	+	325855.i	−0.671461	+	1.16300i	−0.977490	+	0.210982i	$0.932334\pi$
$152$	−155293.	−	268976.i	−0.545184	−	0.944286i
$153$		0			0
$154$	−460605.	−	503557.i	−1.56504	−	1.71099i
$155$	588639.			1.96797
$156$		0			0
$157$	−19537.5	+	33840.0i	−0.0632587	+	0.109567i	−0.895920	−	0.444215i	$-0.853483\pi$
$157$	−19537.5	+	33840.0i	−0.0632587	+	0.109567i	0.832662	+	0.553782i	$0.186816\pi$
$158$	−209804.	+	363391.i	−0.668608	+	1.15806i
$159$		0			0
$160$	−296237.			−0.914829
$161$	126197.	−	399013.i	0.383694	−	1.21317i
$162$		0			0
$163$	238959.	+	413890.i	0.704458	+	1.22016i	0.966887	+	0.255206i	$0.0821433\pi$
$163$	238959.	+	413890.i	0.704458	+	1.22016i	−0.262428	+	0.964951i	$0.584523\pi$
$164$	6904.01	−	11958.1i	0.0200444	−	0.0347178i
$165$		0			0
$166$	73272.1	+	126911.i	0.206381	+	0.357462i
$167$	−39793.4			−0.110413			−0.0552064	−	0.998475i	$-0.517582\pi$
$167$	−39793.4			−0.110413			−0.0552064	+	0.998475i	$0.517582\pi$
$168$		0			0
$169$	−86661.4			−0.233404
$170$	338683.	+	586616.i	0.898816	+	1.55680i
$171$		0			0
$172$	491610.	−	851494.i	1.26707	−	2.19463i
$173$	24169.1	+	41862.1i	0.0613968	+	0.106342i	0.895090	−	0.445886i	$-0.147111\pi$
$173$	24169.1	+	41862.1i	0.0613968	+	0.106342i	−0.833693	+	0.552228i	$0.813778\pi$
$174$		0			0
$175$	255727.	−	56455.5i	0.631220	−	0.139351i
$176$	187018.			0.455094
$177$		0			0
$178$	64016.9	−	110881.i	0.151441	−	0.262304i
$179$	−71455.3	+	123764.i	−0.166687	+	0.288711i	−0.937253	−	0.348650i	$-0.886640\pi$
$179$	−71455.3	+	123764.i	−0.166687	+	0.288711i	0.770566	+	0.637360i	$0.219974\pi$
$180$		0			0
$181$	−77245.3			−0.175257			−0.0876285	−	0.996153i	$-0.527929\pi$
$181$	−77245.3			−0.175257			−0.0876285	+	0.996153i	$0.527929\pi$
$182$	−195842.	+	619219.i	−0.438256	+	1.38569i
$183$		0			0
$184$	366305.	+	634459.i	0.797625	+	1.38153i
$185$	100731.	−	174472.i	0.216389	−	0.374797i
$186$		0			0
$187$	281903.	+	488270.i	0.589516	+	1.02107i
$188$	918119.			1.89454
$189$		0			0
$190$	921739.			1.85235
$191$	136027.	+	235606.i	0.269800	+	0.467307i	0.968810	−	0.247805i	$-0.0797092\pi$
$191$	136027.	+	235606.i	0.269800	+	0.467307i	−0.699010	+	0.715112i	$0.746376\pi$
$192$		0			0
$193$	8016.89	−	13885.7i	0.0154922	−	0.0268333i	−0.858175	−	0.513357i	$-0.828402\pi$
$193$	8016.89	−	13885.7i	0.0154922	−	0.0268333i	0.873668	+	0.486523i	$0.161735\pi$
$194$	60656.2	+	105060.i	0.115710	+	0.200415i
$195$		0			0
$196$	−772353.	−	542850.i	−1.43607	−	1.00935i
$197$	−1.03228e6			−1.89510			−0.947552	−	0.319603i	$-0.896451\pi$
$197$	−1.03228e6			−1.89510			−0.947552	+	0.319603i	$0.896451\pi$
$198$		0			0
$199$	440868.	−	763606.i	0.789180	−	1.36690i	−0.137290	−	0.990531i	$-0.543839\pi$
$199$	440868.	−	763606.i	0.789180	−	1.36690i	0.926470	−	0.376369i	$-0.122827\pi$
$200$	−229226.	+	397030.i	−0.405217	+	0.701857i
$201$		0			0
$202$	−236089.			−0.407096
$203$	−65927.4	−	72075.3i	−0.112286	−	0.122757i
$204$		0			0
$205$	8816.49	+	15270.6i	0.0146525	+	0.0253788i
$206$	754725.	−	1.30722e6i	1.23914	−	2.14626i
$207$		0			0
$208$	−88988.4	−	154132.i	−0.142618	−	0.247022i
$209$	767210.			1.21492
$210$		0			0
$211$	−372813.			−0.576480			−0.288240	−	0.957558i	$-0.593070\pi$
$211$	−372813.			−0.576480			−0.288240	+	0.957558i	$0.593070\pi$
$212$	−832480.	−	1.44190e6i	−1.27214	−	2.20341i
$213$		0			0
$214$	−443087.	+	767449.i	−0.661385	+	1.14555i
$215$	627791.	+	1.08737e6i	0.926230	+	1.60428i
$216$		0			0
$217$	1.03888e6	−	229348.i	1.49767	−	0.330633i
$218$	−783054.			−1.11596
$219$		0			0
$220$	−1.12935e6	+	1.95609e6i	−1.57315	+	2.72478i
$221$	268275.	−	464666.i	0.369487	−	0.639971i
$222$		0			0
$223$	−1.08205e6			−1.45708			−0.728541	−	0.685002i	$-0.759801\pi$
$223$	−1.08205e6			−1.45708			−0.728541	+	0.685002i	$0.759801\pi$
$224$	−522825.	+	115422.i	−0.696204	+	0.153697i
$225$		0			0
$226$	−841584.	−	1.45767e6i	−1.09604	−	1.89840i
$227$	276524.	−	478954.i	0.356179	−	0.616921i	−0.631140	−	0.775669i	$-0.717413\pi$
$227$	276524.	−	478954.i	0.356179	−	0.616921i	0.987319	+	0.158748i	$0.0507459\pi$
$228$		0			0
$229$	−261512.	−	452952.i	−0.329536	−	0.570773i	0.652884	−	0.757458i	$-0.273559\pi$
$229$	−261512.	−	452952.i	−0.329536	−	0.570773i	−0.982420	+	0.186685i	$0.940226\pi$
$230$	−2.17420e6			−2.71006
$231$		0			0
$232$	170996.			0.208577
$233$	−182090.	−	315390.i	−0.219734	−	0.380590i	0.734993	−	0.678075i	$-0.237186\pi$
$233$	−182090.	−	315390.i	−0.219734	−	0.380590i	−0.954727	+	0.297485i	$0.903852\pi$
$234$		0			0
$235$	−586223.	+	1.01537e6i	−0.692458	+	1.19937i
$236$	−290849.	−	503766.i	−0.339929	−	0.588774i
$237$		0			0
$238$	826297.	+	903351.i	0.945570	+	1.03375i
$239$	−371841.			−0.421078			−0.210539	−	0.977585i	$-0.567522\pi$
$239$	−371841.			−0.421078			−0.210539	+	0.977585i	$0.567522\pi$
$240$		0			0
$241$	855737.	−	1.48218e6i	0.949069	−	1.64384i	0.201678	−	0.979452i	$-0.435360\pi$
$241$	855737.	−	1.48218e6i	0.949069	−	1.64384i	0.747391	−	0.664384i	$-0.231306\pi$
$242$	−719417.	+	1.24607e6i	−0.789664	+	1.36774i
$243$		0			0
$244$	53595.8			0.0576310
$245$	1.09350e6	−	507550.i	1.16387	−	0.540212i
$246$		0			0
$247$	−365060.	−	632303.i	−0.380735	−	0.659452i
$248$	−931221.	+	1.61292e6i	−0.961443	+	1.66527i
$249$		0			0
$250$	372103.	+	644502.i	0.376542	+	0.652190i
$251$	−58134.1			−0.0582434			−0.0291217	−	0.999576i	$-0.509271\pi$
$251$	−58134.1			−0.0582434			−0.0291217	+	0.999576i	$0.509271\pi$
$252$		0			0
$253$	−1.80969e6			−1.77748
$254$	674540.	+	1.16834e6i	0.656030	+	1.13628i
$255$		0			0
$256$	768453.	−	1.33100e6i	0.732853	−	1.26934i
$257$	−155920.	−	270061.i	−0.147254	−	0.255052i	0.782957	−	0.622075i	$-0.213710\pi$
$257$	−155920.	−	270061.i	−0.147254	−	0.255052i	−0.930212	+	0.367023i	$0.880377\pi$
$258$		0			0
$259$	109801.	−	347171.i	0.101708	−	0.321583i
$260$	2.14950e6			1.97199
$261$		0			0
$262$	245497.	−	425214.i	0.220950	−	0.382696i
$263$	431983.	−	748216.i	0.385103	−	0.667018i	−0.606681	−	0.794946i	$-0.707499\pi$
$263$	431983.	−	748216.i	0.385103	−	0.667018i	0.991783	+	0.127928i	$0.0408326\pi$
$264$		0			0
$265$	2.12617e6			1.85987
$266$	1.62676e6	−	359133.i	1.40968	−	0.311208i
$267$		0			0
$268$	556506.	+	963896.i	0.473296	+	0.819773i
$269$	−560346.	+	970548.i	−0.472145	+	0.817779i	−0.999492	−	0.0318707i	$-0.989854\pi$
$269$	−560346.	+	970548.i	−0.472145	+	0.817779i	0.527347	+	0.849650i	$0.323187\pi$
$270$		0			0
$271$	−570058.	−	987369.i	−0.471515	−	0.816688i	0.527954	−	0.849273i	$-0.322959\pi$
$271$	−570058.	−	987369.i	−0.471515	−	0.816688i	−0.999469	+	0.0325848i	$0.989626\pi$
$272$	−335498.			−0.274959
$273$		0			0
$274$	−88359.6			−0.0711013
$275$	−566233.	−	980744.i	−0.451506	−	0.782031i
$276$		0			0
$277$	994005.	−	1.72167e6i	0.778375	−	1.34819i	−0.154502	−	0.987992i	$-0.549377\pi$
$277$	994005.	−	1.72167e6i	0.778375	−	1.34819i	0.932878	−	0.360193i	$-0.117289\pi$
$278$	−859615.	−	1.48890e6i	−0.667102	−	1.15545i
$279$		0			0
$280$	−636399.	+	2.01218e6i	−0.485104	+	1.53381i
$281$	−532321.			−0.402168			−0.201084	−	0.979574i	$-0.564446\pi$
$281$	−532321.			−0.402168			−0.201084	+	0.979574i	$0.564446\pi$
$282$		0			0
$283$	−1.31237e6	+	2.27308e6i	−0.974067	+	1.68713i	−0.291087	+	0.956697i	$0.594017\pi$
$283$	−1.31237e6	+	2.27308e6i	−0.974067	+	1.68713i	−0.682980	+	0.730437i	$0.739316\pi$
$284$	1.74478e6	−	3.02205e6i	1.28364	−	2.22334i
$285$		0			0
$286$	2.80842e6			2.03024
$287$	21509.9	+	23515.7i	0.0154146	+	0.0168521i
$288$		0			0
$289$	204212.	+	353705.i	0.143826	+	0.249113i
$290$	−253736.	+	439484.i	−0.177169	+	0.306866i
$291$		0			0
$292$	−761369.	−	1.31873e6i	−0.522562	−	0.905104i
$293$	−609962.			−0.415082			−0.207541	−	0.978226i	$-0.566546\pi$
$293$	−609962.			−0.415082			−0.207541	+	0.978226i	$0.566546\pi$
$294$		0			0
$295$	742834.			0.496978
$296$	318712.	+	552026.i	0.211431	+	0.366210i
$297$		0			0
$298$	−784061.	+	1.35803e6i	−0.511457	+	0.885870i
$299$	861104.	+	1.49148e6i	0.557029	+	0.964802i
$300$		0			0
$301$	1.53164e6	+	1.67447e6i	0.974409	+	1.06528i
$302$	3.53307e6			2.22913
$303$		0			0
$304$	−228268.	+	395372.i	−0.141665	+	0.245370i
$305$	−34221.2	+	59272.8i	−0.0210642	+	0.0364843i
$306$		0			0
$307$	−1.34843e6			−0.816551			−0.408275	−	0.912859i	$-0.633870\pi$
$307$	−1.34843e6			−0.816551			−0.408275	+	0.912859i	$0.633870\pi$
$308$	−1.23103e6	+	3.89229e6i	−0.739420	+	2.33791i
$309$		0			0
$310$	−2.76362e6	−	4.78673e6i	−1.63333	−	2.82901i
$311$	−1.66530e6	+	2.88439e6i	−0.976320	+	1.69104i	−0.300813	+	0.953683i	$0.597258\pi$
$311$	−1.66530e6	+	2.88439e6i	−0.976320	+	1.69104i	−0.675507	+	0.737353i	$0.736075\pi$
$312$		0			0
$313$	1.41835e6	+	2.45666e6i	0.818320	+	1.41737i	0.906919	+	0.421305i	$0.138428\pi$
$313$	1.41835e6	+	2.45666e6i	0.818320	+	1.41737i	−0.0885991	+	0.996067i	$0.528239\pi$
$314$	366909.			0.210007
$315$		0			0
$316$	2.51007e6			1.41406
$317$	−544195.	−	942574.i	−0.304163	−	0.526826i	0.672912	−	0.739723i	$-0.265043\pi$
$317$	−544195.	−	942574.i	−0.304163	−	0.526826i	−0.977075	+	0.212897i	$0.931710\pi$
$318$		0			0
$319$	−211198.	+	365805.i	−0.116202	+	0.201267i
$320$	1.77367e6	+	3.07209e6i	0.968274	+	1.67710i
$321$		0			0
$322$	−3.83721e6	+	847122.i	−2.06241	+	0.455309i
$323$	−1.37633e6			−0.734033
$324$		0			0
$325$	−538860.	+	933332.i	−0.282988	+	0.490149i
$326$	2.24380e6	−	3.88637e6i	1.16934	−	2.02535i
$327$		0			0
$328$	−55790.4			−0.0286335
$329$	−639004.	+	2.02042e6i	−0.325472	+	1.02908i
$330$		0			0
$331$	−652773.	−	1.13064e6i	−0.327485	−	0.567221i	0.654527	−	0.756039i	$-0.272868\pi$
$331$	−652773.	−	1.13064e6i	−0.327485	−	0.567221i	−0.982012	+	0.188817i	$0.939535\pi$
$332$	438309.	−	759174.i	0.218241	−	0.378004i
$333$		0			0
$334$	186827.	+	323594.i	0.0916376	+	0.158721i
$335$	−1.42133e6			−0.691961
$336$		0			0
$337$	−3.17016e6			−1.52057			−0.760285	−	0.649590i	$-0.774941\pi$
$337$	−3.17016e6			−1.52057			−0.760285	+	0.649590i	$0.774941\pi$
$338$	406869.	+	704718.i	0.193715	+	0.335524i
$339$		0			0
$340$	2.02598e6	−	3.50910e6i	0.950469	−	1.64626i
$341$	−2.30030e6	−	3.98424e6i	−1.07127	−	1.85549i
$342$		0			0
$343$	1.73215e6	−	1.32182e6i	0.794969	−	0.606650i
$344$	−3.97263e6			−1.81002
$345$		0			0
$346$	226945.	−	393080.i	0.101913	−	0.176519i
$347$	−857958.	+	1.48603e6i	−0.382510	+	0.662526i	−0.991420	−	0.130713i	$-0.958273\pi$
$347$	−857958.	+	1.48603e6i	−0.382510	+	0.662526i	0.608911	+	0.793239i	$0.291607\pi$
$348$		0			0
$349$	−2.95822e6			−1.30007			−0.650034	−	0.759905i	$-0.725245\pi$
$349$	−2.95822e6			−1.30007			−0.650034	+	0.759905i	$0.725245\pi$
$350$	−1.65971e6	−	1.81448e6i	−0.724205	−	0.791739i
$351$		0			0
$352$	1.15765e6	+	2.00510e6i	0.497988	+	0.862541i
$353$	1.88490e6	−	3.26474e6i	0.805103	−	1.39448i	−0.111119	−	0.993807i	$-0.535443\pi$
$353$	1.88490e6	−	3.26474e6i	0.805103	−	1.39448i	0.916222	−	0.400672i	$-0.131223\pi$
$354$		0			0
$355$	2.22810e6	+	3.85918e6i	0.938347	+	1.62526i
$356$	−765890.			−0.320289
$357$		0			0
$358$	1.34191e6			0.553371
$359$	964935.	+	1.67132e6i	0.395150	+	0.684420i	0.993120	−	0.117099i	$-0.0373593\pi$
$359$	964935.	+	1.67132e6i	0.395150	+	0.684420i	−0.597970	+	0.801518i	$0.704026\pi$
$360$		0			0
$361$	301617.	−	522416.i	0.121811	−	0.210984i
$362$	362662.	+	628148.i	0.145455	+	0.251936i
$363$		0			0
$364$	3.79363e6	−	837500.i	1.50073	−	0.331308i
$365$	1.94455e6			0.763988
$366$		0			0
$367$	−1.18371e6	+	2.05025e6i	−0.458754	+	0.794586i	−0.998895	−	0.0469885i	$-0.985038\pi$
$367$	−1.18371e6	+	2.05025e6i	−0.458754	+	0.794586i	0.540141	+	0.841575i	$0.318371\pi$
$368$	538438.	−	932603.i	0.207260	−	0.358986i
$369$		0			0
$370$	−1.89171e6			−0.718373
$371$	3.75244e6	−	828409.i	1.41540	−	0.312471i
$372$		0			0
$373$	−1.76914e6	−	3.06425e6i	−0.658402	−	1.14039i	−0.981029	−	0.193860i	$-0.937899\pi$
$373$	−1.76914e6	−	3.06425e6i	−0.658402	−	1.14039i	0.322627	−	0.946526i	$-0.395434\pi$
$374$	2.64703e6	−	4.58479e6i	0.978543	−	1.69489i
$375$		0			0
$376$	−1.85480e6	−	3.21260e6i	−0.676592	−	1.17189i
$377$	401975.			0.145662
$378$		0			0
$379$	1.79847e6			0.643139			0.321569	−	0.946886i	$-0.395790\pi$
$379$	1.79847e6			0.643139			0.321569	+	0.946886i	$0.395790\pi$
$380$	−2.75689e6	−	4.77508e6i	−0.979401	−	1.69637i
$381$		0			0
$382$	1.27728e6	−	2.21231e6i	0.447843	−	0.775687i
$383$	1.30407e6	+	2.25872e6i	0.454261	+	0.786802i	0.998645	−	0.0520333i	$-0.0165702\pi$
$383$	1.30407e6	+	2.25872e6i	0.454261	+	0.786802i	−0.544385	+	0.838836i	$0.683237\pi$
$384$		0			0
$385$	−3.51855e6	−	3.84667e6i	−1.20980	−	1.32261i
$386$	−150555.			−0.0514313
$387$		0			0
$388$	362841.	−	628460.i	0.122359	−	0.211933i
$389$	−1.41498e6	+	2.45081e6i	−0.474106	+	0.821175i	−0.999560	−	0.0296466i	$-0.990562\pi$
$389$	−1.41498e6	+	2.45081e6i	−0.474106	+	0.821175i	0.525455	+	0.850821i	$0.323895\pi$
$390$		0			0
$391$	3.24648e6			1.07392
$392$	−339176.	+	3.79923e6i	−0.111483	+	1.24876i
$393$		0			0
$394$	4.84650e6	+	8.39438e6i	1.57285	+	2.72426i
$395$	−1.60269e6	+	2.77594e6i	−0.516841	+	0.895195i
$396$		0			0
$397$	1.21531e6	+	2.10498e6i	0.387000	+	0.670303i	0.992044	−	0.125888i	$-0.0401781\pi$
$397$	1.21531e6	+	2.10498e6i	0.387000	+	0.670303i	−0.605045	+	0.796191i	$0.706845\pi$
$398$	−8.27939e6			−2.61993
$399$		0			0
$400$	673885.			0.210589
$401$	−1.21592e6	−	2.10604e6i	−0.377611	−	0.654041i	0.613103	−	0.790003i	$-0.289921\pi$
$401$	−1.21592e6	−	2.10604e6i	−0.377611	−	0.654041i	−0.990714	+	0.135962i	$0.956588\pi$
$402$		0			0
$403$	−2.18910e6	+	3.79163e6i	−0.671433	+	1.16296i
$404$	706134.	+	1.22306e6i	0.215245	+	0.372816i
$405$		0			0
$406$	−276581.	+	874501.i	−0.0832737	+	0.263297i
$407$	−1.57457e6			−0.471167
$408$		0			0
$409$	2.38733e6	−	4.13497e6i	0.705674	−	1.22226i	−0.260774	−	0.965400i	$-0.583978\pi$
$409$	2.38733e6	−	4.13497e6i	0.705674	−	1.22226i	0.966448	−	0.256863i	$-0.0826889\pi$
$410$	82785.6	−	143389.i	0.0243218	−	0.0421266i
$411$		0			0
$412$	−9.02944e6			−2.62070
$413$	1.31102e6	−	289427.i	0.378210	−	0.0834956i
$414$		0			0
$415$	559725.	+	969472.i	0.159534	+	0.276322i
$416$	1.10168e6	−	1.90817e6i	0.312121	−	0.540609i
$417$		0			0
$418$	−3.60200e6	−	6.23884e6i	−1.00833	−	1.74648i
$419$	457181.			0.127219			0.0636097	−	0.997975i	$-0.479739\pi$
$419$	457181.			0.127219			0.0636097	+	0.997975i	$0.479739\pi$
$420$		0			0
$421$	−1.82396e6			−0.501545			−0.250773	−	0.968046i	$-0.580685\pi$
$421$	−1.82396e6			−0.501545			−0.250773	+	0.968046i	$0.580685\pi$
$422$	1.75033e6	+	3.03166e6i	0.478453	+	0.828704i
$423$		0			0
$424$	−3.36358e6	+	5.82589e6i	−0.908629	+	1.57379i
$425$	1.01579e6	+	1.75939e6i	0.272791	+	0.472488i
$426$		0			0
$427$	−37302.3	+	117943.i	−0.00990069	+	0.0313042i
$428$	5.30104e6			1.39879
$429$		0			0
$430$	5.89487e6	−	1.02102e7i	1.53746	−	2.66295i
$431$	−1.69124e6	+	2.92932e6i	−0.438544	+	0.759580i	−0.997577	−	0.0695651i	$-0.977839\pi$
$431$	−1.69124e6	+	2.92932e6i	−0.438544	+	0.759580i	0.559034	+	0.829145i	$0.311172\pi$
$432$		0			0
$433$	−285266.			−0.0731190			−0.0365595	−	0.999331i	$-0.511640\pi$
$433$	−285266.			−0.0731190			−0.0365595	+	0.999331i	$0.511640\pi$
$434$	−6.74250e6	−	7.37125e6i	−1.71829	−	1.87853i
$435$		0			0
$436$	2.34209e6	+	4.05662e6i	0.590048	+	1.02199i
$437$	2.20886e6	−	3.82585e6i	0.553304	−	0.958351i
$438$		0			0
$439$	−2.17610e6	−	3.76911e6i	−0.538911	−	0.933421i	−0.998963	−	0.0455294i	$-0.985503\pi$
$439$	−2.17610e6	−	3.76911e6i	−0.538911	−	0.933421i	0.460052	−	0.887892i	$-0.347831\pi$
$440$	9.12610e6			2.24726
$441$		0			0
$442$	−5.03813e6			−1.22663
$443$	−2.55280e6	−	4.42158e6i	−0.618027	−	1.07045i	−0.989845	−	0.142148i	$-0.954599\pi$
$443$	−2.55280e6	−	4.42158e6i	−0.618027	−	1.07045i	0.371819	−	0.928305i	$-0.378734\pi$
$444$		0			0
$445$	489024.	−	847015.i	0.117066	−	0.202764i
$446$	5.08014e6	+	8.79906e6i	1.20931	+	2.09459i
$447$		0			0
$448$	4.32729e6	+	4.73082e6i	1.01864	+	1.11363i
$449$	−3.04163e6			−0.712016			−0.356008	−	0.934483i	$-0.615862\pi$
$449$	−3.04163e6			−0.712016			−0.356008	+	0.934483i	$0.615862\pi$
$450$		0			0
$451$	68906.7	−	119350.i	0.0159522	−	0.0276300i
$452$	−5.03430e6	+	8.71966e6i	−1.15903	+	2.00749i
$453$		0			0
$454$	−5.19305e6			−1.18245
$455$	−1.49604e6	+	4.73020e6i	−0.338777	+	1.07115i
$456$		0			0
$457$	872162.	+	1.51063e6i	0.195347	+	0.338351i	0.947014	−	0.321192i	$-0.104083\pi$
$457$	872162.	+	1.51063e6i	0.195347	+	0.338351i	−0.751667	+	0.659542i	$0.770750\pi$
$458$	−2.45556e6	+	4.25316e6i	−0.547000	+	0.947432i
$459$		0			0
$460$	6.50295e6	+	1.12634e7i	1.43290	+	2.48186i
$461$	6.85701e6			1.50273			0.751367	−	0.659884i	$-0.229395\pi$
$461$	6.85701e6			1.50273			0.751367	+	0.659884i	$0.229395\pi$
$462$		0			0
$463$	5.13844e6			1.11398			0.556992	−	0.830518i	$-0.311955\pi$
$463$	5.13844e6			1.11398			0.556992	+	0.830518i	$0.311955\pi$
$464$	−125675.	−	217676.i	−0.0270991	−	0.0469370i
$465$		0			0
$466$	−1.70980e6	+	2.96147e6i	−0.364738	+	0.631746i
$467$	−2.29085e6	−	3.96788e6i	−0.486077	−	0.841910i	0.513795	−	0.857913i	$-0.328239\pi$
$467$	−2.29085e6	−	3.96788e6i	−0.486077	−	0.841910i	−0.999872	+	0.0160029i	$0.994906\pi$
$468$		0			0
$469$	−2.50848e6	+	553784.i	−0.526597	+	0.116254i
$470$	1.10091e7			2.29883
$471$		0			0
$472$	−1.17516e6	+	2.03543e6i	−0.242795	+	0.420534i
$473$	4.90660e6	−	8.49848e6i	1.00839	−	1.74658i
$474$		0			0
$475$	2.76450e6			0.562190
$476$	2.20839e6	−	6.98253e6i	0.446743	−	1.41252i
$477$		0			0
$478$	1.74577e6	+	3.02376e6i	0.349476	+	0.605310i
$479$	−144261.	+	249868.i	−0.0287284	+	0.0497590i	−0.880032	−	0.474914i	$-0.842479\pi$
$479$	−144261.	+	249868.i	−0.0287284	+	0.0497590i	0.851304	+	0.524673i	$0.175812\pi$
$480$		0			0
$481$	749223.	+	1.29769e6i	0.147655	+	0.255746i
$482$	−1.60705e7			−3.15074
$483$		0			0
$484$	8.60702e6			1.67009
$485$	463352.	+	802549.i	0.0894451	+	0.154923i
$486$		0			0
$487$	3.90842e6	−	6.76959e6i	0.746757	−	1.29342i	−0.202613	−	0.979259i	$-0.564943\pi$
$487$	3.90842e6	−	6.76959e6i	0.746757	−	1.29342i	0.949369	−	0.314162i	$-0.101723\pi$
$488$	−108275.	−	187538.i	−0.0205816	−	0.0356484i
$489$		0			0
$490$	−9.26124e6	−	6.50929e6i	−1.74253	−	1.22474i
$491$	−3.14467e6			−0.588669			−0.294335	−	0.955702i	$-0.595098\pi$
$491$	−3.14467e6			−0.588669			−0.294335	+	0.955702i	$0.595098\pi$
$492$		0			0
$493$	378875.	−	656232.i	0.0702068	−	0.121602i
$494$	−3.42787e6	+	5.93724e6i	−0.631985	+	1.09463i
$495$		0			0
$496$	2.73763e6			0.499656
$497$	5.43597e6	+	5.94289e6i	0.987157	+	1.07921i
$498$		0			0
$499$	−3.36281e6	−	5.82456e6i	−0.604577	−	1.04716i	−0.992118	−	0.125305i	$-0.960009\pi$
$499$	−3.36281e6	−	5.82456e6i	−0.604577	−	1.04716i	0.387541	−	0.921852i	$-0.373324\pi$
$500$	2.22590e6	−	3.85537e6i	0.398181	−	0.689670i
$501$		0			0
$502$	272936.	+	472738.i	0.0483394	+	0.0837262i
$503$	9.45056e6			1.66547			0.832737	−	0.553669i	$-0.186773\pi$
$503$	9.45056e6			1.66547			0.832737	+	0.553669i	$0.186773\pi$
$504$		0			0
$505$	−1.80348e6			−0.314690
$506$	8.49639e6	+	1.47162e7i	1.47522	+	2.55516i
$507$		0			0
$508$	4.03506e6	−	6.98892e6i	0.693730	−	1.20158i
$509$	−4.41851e6	−	7.65308e6i	−0.755930	−	1.30931i	−0.944911	−	0.327328i	$-0.893852\pi$
$509$	−4.41851e6	−	7.65308e6i	−0.755930	−	1.30931i	0.188981	−	0.981981i	$-0.439481\pi$
$510$		0			0
$511$	3.43191e6	−	757645.i	0.581411	−	0.128355i
$512$	−3.80044e6			−0.640707
$513$		0			0
$514$	−1.46406e6	+	2.53583e6i	−0.244429	+	0.423363i
$515$	5.76534e6	−	9.98585e6i	0.957870	−	1.65908i
$516$		0			0
$517$	9.16344e6			1.50776
$518$	−3.33865e6	+	737057.i	−0.546697	+	0.120692i
$519$		0			0
$520$	−4.34246e6	−	7.52136e6i	−0.704251	−	1.21980i
$521$	347492.	−	601874.i	0.0560855	−	0.0971430i	−0.836619	−	0.547784i	$-0.815471\pi$
$521$	347492.	−	601874.i	0.0560855	−	0.0971430i	0.892705	+	0.450641i	$0.148805\pi$
$522$		0			0
$523$	−1.79105e6	−	3.10219e6i	−0.286321	−	0.495923i	0.686607	−	0.727028i	$-0.259099\pi$
$523$	−1.79105e6	−	3.10219e6i	−0.286321	−	0.495923i	−0.972929	+	0.231105i	$0.925766\pi$
$524$	−2.93710e6			−0.467294
$525$		0			0
$526$	−8.11252e6			−1.27847
$527$	4.12660e6	+	7.14748e6i	0.647240	+	1.12105i
$528$		0			0
$529$	−1.99208e6	+	3.45038e6i	−0.309504	+	0.536077i
$530$	−9.98222e6	−	1.72897e7i	−1.54361	−	2.67361i
$531$		0			0
$532$	−6.72609e6	−	7.35331e6i	−1.03035	−	1.12643i
$533$	−131151.			−0.0199965
$534$		0			0
$535$	−3.38473e6	+	5.86253e6i	−0.511258	+	0.885525i
$536$	2.24852e6	−	3.89456e6i	0.338053	−	0.585526i
$537$		0			0
$538$	1.05231e7			1.56744
$539$	−7.70860e6	−	5.41801e6i	−1.14289	−	0.803282i
$540$		0			0
$541$	2.58423e6	+	4.47602e6i	0.379610	+	0.657504i	0.991005	−	0.133821i	$-0.0427248\pi$
$541$	2.58423e6	+	4.47602e6i	0.379610	+	0.657504i	−0.611395	+	0.791325i	$0.709391\pi$
$542$	−5.35277e6	+	9.27126e6i	−0.782673	+	1.35563i
$543$		0			0
$544$	−2.07675e6	−	3.59703e6i	−0.300875	−	0.521131i
$545$	−5.98174e6			−0.862653
$546$		0			0
$547$	8.47489e6			1.21106			0.605530	−	0.795822i	$-0.292961\pi$
$547$	8.47489e6			1.21106			0.605530	+	0.795822i	$0.292961\pi$
$548$	264281.	+	457748.i	0.0375936	+	0.0651141i
$549$		0			0
$550$	−5.31685e6	+	9.20906e6i	−0.749459	+	1.29810i
$551$	−515562.	−	892980.i	−0.0723439	−	0.125303i
$552$		0			0
$553$	−1.74699e6	+	5.52367e6i	−0.242928	+	0.768095i
$554$	−1.86671e7			−2.58407
$555$		0			0
$556$	−5.14217e6	+	8.90649e6i	−0.705438	+	1.22186i
$557$	−5.21063e6	+	9.02508e6i	−0.711627	+	1.23257i	0.252619	+	0.967566i	$0.418708\pi$
$557$	−5.21063e6	+	9.02508e6i	−0.711627	+	1.23257i	−0.964246	+	0.265009i	$0.914625\pi$
$558$		0			0
$559$	−9.33880e6			−1.26404
$560$	3.02921e6	−	668743.i	0.408187	−	0.0901134i
$561$		0			0
$562$	2.49921e6	+	4.32876e6i	0.333781	+	0.578126i
$563$	−3.62039e6	+	6.27069e6i	−0.481375	+	0.833767i	−0.999772	−	0.0213739i	$-0.993196\pi$
$563$	−3.62039e6	+	6.27069e6i	−0.481375	+	0.833767i	0.518396	+	0.855141i	$0.326529\pi$
$564$		0			0
$565$	−6.42885e6	−	1.11351e7i	−0.847251	−	1.46748i
$566$	2.46459e7			3.23373
$567$		0			0
$568$	−1.40993e7			−1.83369
$569$	458268.	+	793743.i	0.0593388	+	0.102778i	0.894169	−	0.447730i	$-0.147767\pi$
$569$	458268.	+	793743.i	0.0593388	+	0.102778i	−0.834830	+	0.550508i	$0.814434\pi$
$570$		0			0
$571$	−5.03538e6	+	8.72154e6i	−0.646312	+	1.11944i	0.337685	+	0.941259i	$0.390356\pi$
$571$	−5.03538e6	+	8.72154e6i	−0.646312	+	1.11944i	−0.983997	+	0.178186i	$0.942977\pi$
$572$	−8.39990e6	−	1.45490e7i	−1.07345	−	1.85928i
$573$		0			0
$574$	90239.2	−	285320.i	0.0114318	−	0.0361454i
$575$	−6.52091e6			−0.822505
$576$		0			0
$577$	−5.84987e6	+	1.01323e7i	−0.731488	+	1.26697i	0.224760	+	0.974414i	$0.427840\pi$
$577$	−5.84987e6	+	1.01323e7i	−0.731488	+	1.26697i	−0.956247	+	0.292560i	$0.905493\pi$
$578$	1.91752e6	−	3.32125e6i	0.238738	−	0.413506i
$579$		0			0
$580$	3.03567e6			0.374701
$581$	1.36558e6	+	1.49292e6i	0.167833	+	0.183484i
$582$		0			0
$583$	−8.30871e6	−	1.43911e7i	−1.01242	−	1.75357i
$584$	−3.07626e6	+	5.32823e6i	−0.373242	+	0.646474i
$585$		0			0
$586$	2.86373e6	+	4.96013e6i	0.344499	+	0.596690i
$587$	6.92367e6			0.829357			0.414678	−	0.909968i	$-0.363894\pi$
$587$	6.92367e6			0.829357			0.414678	+	0.909968i	$0.363894\pi$
$588$		0			0
$589$	1.12307e7			1.33389
$590$	−3.48756e6	−	6.04062e6i	−0.412469	−	0.714417i
$591$		0			0
$592$	468481.	−	811432.i	0.0549398	−	0.0951586i
$593$	7.88850e6	+	1.36633e7i	0.921208	+	1.59558i	0.797548	+	0.603255i	$0.206130\pi$
$593$	7.88850e6	+	1.36633e7i	0.921208	+	1.59558i	0.123660	+	0.992325i	$0.460537\pi$
$594$		0			0
$595$	6.31207e6	+	6.90068e6i	0.730936	+	0.799097i
$596$	9.38041e6			1.08170
$597$		0			0
$598$	8.08565e6	−	1.40048e7i	0.924618	−	1.60148i
$599$	7.13541e6	−	1.23589e7i	0.812553	−	1.40738i	−0.0985183	−	0.995135i	$-0.531410\pi$
$599$	7.13541e6	−	1.23589e7i	0.812553	−	1.40738i	0.911072	−	0.412248i	$-0.135256\pi$
$600$		0			0
$601$	7.63222e6			0.861916			0.430958	−	0.902372i	$-0.358176\pi$
$601$	7.63222e6			0.861916			0.430958	+	0.902372i	$0.358176\pi$
$602$	6.42562e6	−	2.03167e7i	0.722643	−	2.28487i
$603$		0			0
$604$	−1.05673e7	−	1.83031e7i	−1.17862	−	2.04142i
$605$	−5.49562e6	+	9.51869e6i	−0.610419	+	1.05728i
$606$		0			0
$607$	1.78017e6	+	3.08335e6i	0.196106	+	0.339665i	0.947262	−	0.320459i	$-0.103837\pi$
$607$	1.78017e6	+	3.08335e6i	0.196106	+	0.339665i	−0.751157	+	0.660124i	$0.770504\pi$
$608$	−5.65194e6			−0.620067
$609$		0			0
$610$	642664.			0.0699294
$611$	−4.36023e6	−	7.55214e6i	−0.472505	−	0.818402i
$612$		0			0
$613$	6.86420e6	−	1.18891e7i	0.737800	−	1.27791i	−0.215683	−	0.976463i	$-0.569198\pi$
$613$	6.86420e6	−	1.18891e7i	0.737800	−	1.27791i	0.953484	−	0.301445i	$-0.0974688\pi$
$614$	6.33080e6	+	1.09653e7i	0.677700	+	1.17381i
$615$		0			0
$616$	1.61065e7	−	3.55576e6i	1.71021	−	0.377555i
$617$	6.51173e6			0.688626			0.344313	−	0.938855i	$-0.388112\pi$
$617$	6.51173e6			0.688626			0.344313	+	0.938855i	$0.388112\pi$
$618$		0			0
$619$	−4.42555e6	+	7.66527e6i	−0.464238	+	0.804083i	−0.999167	−	0.0408136i	$-0.987005\pi$
$619$	−4.42555e6	+	7.66527e6i	−0.464238	+	0.804083i	0.534929	+	0.844897i	$0.320338\pi$
$620$	−1.65318e7	+	2.86339e7i	−1.72719	+	2.99159i
$621$		0			0
$622$	3.12739e7			3.24121
$623$	533054.	−	1.68542e6i	0.0550238	−	0.173976i
$624$		0			0
$625$	5.99884e6	+	1.03903e7i	0.614281	+	1.06397i
$626$	1.33181e7	−	2.30677e7i	1.35834	−	2.35271i
$627$		0			0
$628$	−1.09741e6	−	1.90078e6i	−0.111038	−	0.192323i
$629$	2.82467e6			0.284670
$630$		0			0
$631$	−6.89663e6			−0.689546			−0.344773	−	0.938686i	$-0.612044\pi$
$631$	−6.89663e6			−0.689546			−0.344773	+	0.938686i	$0.612044\pi$
$632$	−5.07088e6	−	8.78303e6i	−0.504999	−	0.874685i
$633$		0			0
$634$	−5.10992e6	+	8.85064e6i	−0.504883	+	0.874483i
$635$	5.15280e6	+	8.92492e6i	0.507118	+	0.878355i
$636$		0			0
$637$	−797329.	+	8.93116e6i	−0.0778554	+	0.872086i
$638$	3.96623e6			0.385768
$639$		0			0
$640$	1.19147e7	−	2.06369e7i	1.14983	−	1.99157i
$641$	−8.33473e6	+	1.44362e7i	−0.801210	+	1.38774i	0.117610	+	0.993060i	$0.462477\pi$
$641$	−8.33473e6	+	1.44362e7i	−0.801210	+	1.38774i	−0.918820	+	0.394677i	$0.870856\pi$
$642$		0			0
$643$	−1.28697e7			−1.22756			−0.613779	−	0.789478i	$-0.710351\pi$
$643$	−1.28697e7			−1.22756			−0.613779	+	0.789478i	$0.710351\pi$
$644$	1.58655e7	+	1.73450e7i	1.50744	+	1.64801i
$645$		0			0
$646$	6.46177e6	+	1.11921e7i	0.609214	+	1.05519i
$647$	−5.73656e6	+	9.93601e6i	−0.538754	+	0.933150i	0.460217	+	0.887806i	$0.347772\pi$
$647$	−5.73656e6	+	9.93601e6i	−0.538754	+	0.933150i	−0.998971	+	0.0453435i	$0.985562\pi$
$648$		0			0
$649$	−2.90287e6	−	5.02792e6i	−0.270530	−	0.468572i
$650$	1.01196e7			0.939467
$651$		0			0
$652$	−2.68445e7			−2.47307
$653$	−6.59005e6	−	1.14143e7i	−0.604791	−	1.04753i	−0.992084	−	0.125573i	$-0.959923\pi$
$653$	−6.59005e6	−	1.14143e7i	−0.604791	−	1.04753i	0.387293	−	0.921957i	$-0.373410\pi$
$654$		0			0
$655$	1.87535e6	−	3.24820e6i	0.170797	−	0.295829i
$656$	41003.6	+	71020.4i	0.00372017	+	0.00644352i
$657$		0			0
$658$	1.94298e7	−	4.28943e6i	1.74946	−	0.386220i
$659$	1.13068e7			1.01421			0.507104	−	0.861885i	$-0.330716\pi$
$659$	1.13068e7			1.01421			0.507104	+	0.861885i	$0.330716\pi$
$660$		0			0
$661$	−1.10160e6	+	1.90802e6i	−0.0980661	+	0.169856i	−0.910884	−	0.412662i	$-0.864599\pi$
$661$	−1.10160e6	+	1.90802e6i	−0.0980661	+	0.169856i	0.812818	+	0.582518i	$0.197932\pi$
$662$	−6.12945e6	+	1.06165e7i	−0.543596	+	0.941536i
$663$		0			0
$664$	−3.54192e6			−0.311758
$665$	1.24268e7	−	2.74341e6i	1.08970	−	0.240567i
$666$		0			0
$667$	1.21611e6	+	2.10636e6i	0.105842	+	0.183323i
$668$	1.11759e6	−	1.93572e6i	0.0969038	−	0.167842i
$669$		0			0
$670$	6.67303e6	+	1.15580e7i	0.574296	+	0.994710i
$671$	534922.			0.0458653
$672$		0			0
$673$	−1.89787e7			−1.61521			−0.807606	−	0.589723i	$-0.799237\pi$
$673$	−1.89787e7			−1.61521			−0.807606	+	0.589723i	$0.799237\pi$
$674$	1.48837e7	+	2.57793e7i	1.26200	+	2.18586i
$675$		0			0
$676$	2.43387e6	−	4.21558e6i	0.204847	−	0.354806i
$677$	−9.82377e6	−	1.70153e7i	−0.823771	−	1.42681i	−0.902855	−	0.429945i	$-0.858533\pi$
$677$	−9.82377e6	−	1.70153e7i	−0.823771	−	1.42681i	0.0790842	−	0.996868i	$-0.474800\pi$
$678$		0			0
$679$	1.13046e6	+	1.23587e6i	0.0940977	+	0.102873i
$680$	−1.63717e7			−1.35775
$681$		0			0
$682$	−2.15995e7	+	3.74115e7i	−1.77821	+	3.07995i
$683$	8.13523e6	−	1.40906e7i	0.667295	−	1.15579i	−0.311363	−	0.950291i	$-0.600785\pi$
$683$	8.13523e6	−	1.40906e7i	0.667295	−	1.15579i	0.978658	−	0.205498i	$-0.0658813\pi$
$684$		0			0
$685$	−674978.			−0.0549621
$686$	−1.88812e7	−	7.87973e6i	−1.53186	−	0.639295i
$687$		0			0
$688$	2.91972e6	+	5.05711e6i	0.235164	+	0.407316i
$689$	−7.90704e6	+	1.36954e7i	−0.634550	+	1.09907i
$690$		0			0
$691$	−9.72335e6	−	1.68413e7i	−0.774677	−	1.34178i	−0.934976	−	0.354712i	$-0.884579\pi$
$691$	−9.72335e6	−	1.68413e7i	−0.774677	−	1.34178i	0.160299	−	0.987069i	$-0.448754\pi$
$692$	−2.71514e6			−0.215539
$693$		0			0
$694$	1.61122e7			1.26986
$695$	−6.56659e6	−	1.13737e7i	−0.515677	−	0.893179i
$696$		0			0
$697$	−123614.	+	214106.i	−0.00963800	+	0.0166935i
$698$	1.38886e7	+	2.40558e7i	1.07900	+	1.86888i
$699$		0			0
$700$	−4.43579e6	+	1.40252e7i	−0.342157	+	1.08184i
$701$	−1.49625e7			−1.15003			−0.575014	−	0.818144i	$-0.695003\pi$
$701$	−1.49625e7			−1.15003			−0.575014	+	0.818144i	$0.695003\pi$
$702$		0			0
$703$	1.92187e6	−	3.32877e6i	0.146668	−	0.254036i
$704$	1.38624e7	−	2.40104e7i	1.05416	−	1.82586i
$705$		0			0
$706$	−3.53979e7			−2.67280
$707$	−3.18293e6	+	702680.i	−0.239485	+	0.0528700i
$708$		0			0
$709$	−793193.	−	1.37385e6i	−0.0592603	−	0.102642i	0.834873	−	0.550442i	$-0.185541\pi$
$709$	−793193.	−	1.37385e6i	−0.0592603	−	0.102642i	−0.894134	+	0.447800i	$0.852208\pi$
$710$	2.09215e7	−	3.62372e7i	1.55757	−	2.69779i
$711$		0			0
$712$	1.54726e6	+	2.67994e6i	0.114384	+	0.198118i
$713$	−2.64910e7			−1.95152
$714$		0			0
$715$	2.14535e7			1.56940
$716$	−4.01362e6	−	6.95179e6i	−0.292586	−	0.506774i
$717$		0			0
$718$	9.06061e6	−	1.56934e7i	0.655913	−	1.13607i
$719$	−9.08376e6	−	1.57335e7i	−0.655305	−	1.13502i	−0.981817	−	0.189829i	$-0.939207\pi$
$719$	−9.08376e6	−	1.57335e7i	−0.655305	−	1.13502i	0.326512	−	0.945193i	$-0.394127\pi$
$720$		0			0
$721$	6.28442e6	−	1.98702e7i	0.450222	−	1.42352i
$722$	−5.66429e6			−0.404392
$723$		0			0
$724$	2.16942e6	−	3.75754e6i	0.153814	−	0.266414i
$725$	−761013.	+	1.31811e6i	−0.0537709	+	0.0931339i
$726$		0			0
$727$	1.26903e7			0.890506			0.445253	−	0.895405i	$-0.353114\pi$
$727$	1.26903e7			0.890506			0.445253	+	0.895405i	$0.353114\pi$
$728$	−1.05945e7	−	1.15824e7i	−0.740884	−	0.809973i
$729$		0			0
$730$	−9.12953e6	−	1.58128e7i	−0.634076	−	1.09825i
$731$	−8.80214e6	+	1.52458e7i	−0.609249	+	1.05525i
$732$		0			0
$733$	1.55701e6	+	2.69681e6i	0.107036	+	0.185392i	0.914568	−	0.404432i	$-0.132531\pi$
$733$	1.55701e6	+	2.69681e6i	0.107036	+	0.185392i	−0.807532	+	0.589824i	$0.799197\pi$
$734$	2.22298e7			1.52298
$735$		0			0
$736$	1.33318e7			0.907182
$737$	5.55430e6	+	9.62033e6i	0.376670	+	0.652411i
$738$		0			0
$739$	−4.54950e6	+	7.87996e6i	−0.306445	+	0.530778i	−0.977582	−	0.210555i	$-0.932473\pi$
$739$	−4.54950e6	+	7.87996e6i	−0.306445	+	0.530778i	0.671137	+	0.741333i	$0.265806\pi$
$740$	5.65804e6	+	9.80002e6i	0.379828	+	0.657881i
$741$		0			0
$742$	−2.43540e7	−	2.66250e7i	−1.62390	−	1.77534i
$743$	8.79218e6			0.584285			0.292142	−	0.956375i	$-0.405632\pi$
$743$	8.79218e6			0.584285			0.292142	+	0.956375i	$0.405632\pi$
$744$		0			0
$745$	−5.98943e6	+	1.03740e7i	−0.395362	+	0.684787i
$746$	−1.66120e7	+	2.87729e7i	−1.09289	+	1.89294i
$747$		0			0
$748$	−3.16687e7			−2.06955
$749$	−3.68948e6	+	1.16655e7i	−0.240304	+	0.759798i
$750$		0			0
$751$	1.40459e7	+	2.43282e7i	0.908759	+	1.57402i	0.815790	+	0.578349i	$0.196303\pi$
$751$	1.40459e7	+	2.43282e7i	0.908759	+	1.57402i	0.0929698	+	0.995669i	$0.470364\pi$
$752$	−2.72640e6	+	4.72226e6i	−0.175811	+	0.304513i
$753$		0			0
$754$	−1.88725e6	−	3.26881e6i	−0.120893	−	0.209393i
$755$	2.69891e7			1.72314
$756$		0			0
$757$	−4.18815e6			−0.265634			−0.132817	−	0.991141i	$-0.542402\pi$
$757$	−4.18815e6			−0.265634			−0.132817	+	0.991141i	$0.542402\pi$
$758$	−8.44369e6	−	1.46249e7i	−0.533776	−	0.924527i
$759$		0			0
$760$	−1.11390e7	+	1.92934e7i	−0.699541	+	1.21164i
$761$	−196591.	−	340506.i	−0.0123056	−	0.0213139i	0.859807	−	0.510619i	$-0.170584\pi$
$761$	−196591.	−	340506.i	−0.0123056	−	0.0213139i	−0.872113	+	0.489305i	$0.837250\pi$
$762$		0			0
$763$	−1.05571e7	+	2.33063e6i	−0.656497	+	0.144932i
$764$	−1.52812e7			−0.947159
$765$		0			0
$766$	1.22451e7	−	2.12091e7i	0.754031	−	1.30602i
$767$	−2.76254e6	+	4.78486e6i	−0.169559	+	0.293684i
$768$		0			0
$769$	1.57517e7			0.960530			0.480265	−	0.877124i	$-0.340541\pi$
$769$	1.57517e7			0.960530			0.480265	+	0.877124i	$0.340541\pi$
$770$	−1.47612e7	+	4.66722e7i	−0.897211	+	2.83682i
$771$		0			0
$772$	450306.	+	779952.i	0.0271934	+	0.0471004i
$773$	1.44236e6	−	2.49824e6i	0.0868210	−	0.150378i	−0.819345	−	0.573301i	$-0.805663\pi$
$773$	1.44236e6	−	2.49824e6i	0.0868210	−	0.150378i	0.906166	+	0.422923i	$0.138996\pi$
$774$		0			0
$775$	−8.28873e6	−	1.43565e7i	−0.495717	−	0.858606i
$776$	−2.93207e6			−0.174791
$777$		0			0
$778$	2.65729e7			1.57394
$779$	168211.	+	291349.i	0.00993139	+	0.0172017i
$780$		0			0
$781$	1.74141e7	−	3.01620e7i	1.02158	−	1.76943i
$782$	−1.52420e7	−	2.63999e7i	−0.891303	−	1.54378i
$783$		0			0
$784$	5.08564e6	−	2.36051e6i	0.295499	−	0.137156i
$785$	2.80281e6			0.162338
$786$		0			0
$787$	1.48933e7	−	2.57960e7i	0.857145	−	1.48462i	−0.0174963	−	0.999847i	$-0.505570\pi$
$787$	1.48933e7	−	2.57960e7i	0.857145	−	1.48462i	0.874641	−	0.484771i	$-0.161097\pi$
$788$	2.89914e7	−	5.02146e7i	1.66324	−	2.88081i
$789$		0			0
$790$	3.00981e7			1.71582
$791$	−1.56847e7	−	1.71473e7i	−0.891322	−	0.974440i
$792$		0			0
$793$	−254531.	−	440861.i	−0.0143734	−	0.0248954i
$794$	1.14116e7	−	1.97655e7i	0.642385	−	1.11264i
$795$		0			0
$796$	2.47634e7	+	4.28914e7i	1.38525	+	2.39932i
$797$	−8.11321e6			−0.452425			−0.226213	−	0.974078i	$-0.572634\pi$
$797$	−8.11321e6			−0.452425			−0.226213	+	0.974078i	$0.572634\pi$
$798$		0			0
$799$	−1.64387e7			−0.910960
$800$	4.17137e6	+	7.22503e6i	0.230438	+	0.399130i
$801$		0			0
$802$	−1.14173e7	+	1.97754e7i	−0.626800	+	1.08565i
$803$	−7.59897e6	−	1.31618e7i	−0.415878	−	0.720321i
$804$		0			0
$805$	−2.93124e7	+	6.47115e6i	−1.59427	+	0.351959i
$806$	4.11107e7			2.22904
$807$		0			0
$808$	2.85308e6	−	4.94169e6i	0.153740	−	0.266285i
$809$	55798.5	−	96645.8i	0.00299744	−	0.00519173i	−0.864523	−	0.502594i	$-0.832379\pi$
$809$	55798.5	−	96645.8i	0.00299744	−	0.00519173i	0.867520	+	0.497402i	$0.165713\pi$
$810$		0			0
$811$	−209250.			−0.0111716			−0.00558578	−	0.999984i	$-0.501778\pi$
$811$	−209250.			−0.0111716			−0.00558578	+	0.999984i	$0.501778\pi$
$812$	5.35761e6	−	1.18277e6i	0.285155	−	0.0629523i
$813$		0			0
$814$	7.39248e6	+	1.28042e7i	0.391047	+	0.677314i
$815$	1.71403e7	−	2.96879e7i	0.903910	−	1.56562i
$816$		0			0
$817$	1.19777e7	+	2.07460e7i	0.627795	+	1.08737i
$818$	−4.48334e7			−2.34271
$819$		0			0
$820$	−990437.			−0.0514390
$821$	3.42307e6	+	5.92893e6i	0.177238	+	0.306986i	0.940934	−	0.338591i	$-0.109950\pi$
$821$	3.42307e6	+	5.92893e6i	0.177238	+	0.306986i	−0.763695	+	0.645577i	$0.776617\pi$
$822$		0			0
$823$	2.80605e6	−	4.86022e6i	0.144409	−	0.250125i	−0.784743	−	0.619821i	$-0.787205\pi$
$823$	2.80605e6	−	4.86022e6i	0.144409	−	0.250125i	0.929152	+	0.369697i	$0.120538\pi$
$824$	1.82414e7	+	3.15950e7i	0.935923	+	1.62107i
$825$		0			0
$826$	−8.50872e6	−	9.30217e6i	−0.433924	−	0.474389i
$827$	2.15868e7			1.09755			0.548776	−	0.835969i	$-0.315094\pi$
$827$	2.15868e7			1.09755			0.548776	+	0.835969i	$0.315094\pi$
$828$		0			0
$829$	−9.62135e6	+	1.66647e7i	−0.486239	+	0.842190i	−0.999875	−	0.0158177i	$-0.994965\pi$
$829$	−9.62135e6	+	1.66647e7i	−0.486239	+	0.842190i	0.513636	+	0.858008i	$0.328298\pi$
$830$	5.25574e6	−	9.10321e6i	0.264813	−	0.458669i
$831$		0			0
$832$	−2.63846e7			−1.32142
$833$	1.38288e7	+	9.71958e6i	0.690511	+	0.485327i
$834$		0			0
$835$	1.42717e6	+	2.47193e6i	0.0708369	+	0.122693i
$836$	−2.15469e7	+	3.73204e7i	−1.06628	+	1.84684i
$837$		0			0
$838$	−2.14644e6	−	3.71774e6i	−0.105586	−	0.182881i
$839$	−2.47678e7			−1.21474			−0.607369	−	0.794420i	$-0.707775\pi$
$839$	−2.47678e7			−1.21474			−0.607369	+	0.794420i	$0.707775\pi$
$840$		0			0
$841$	−1.99435e7			−0.972323
$842$	8.56337e6	+	1.48322e7i	0.416260	+	0.720983i
$843$		0			0
$844$	1.04704e7	−	1.81352e7i	0.505948	−	0.876328i
$845$	3.10807e6	+	5.38333e6i	0.149744	+	0.259364i
$846$		0			0
$847$	−5.99042e6	+	1.89406e7i	−0.286912	+	0.907165i
$848$	9.88836e6			0.472210
$849$		0			0
$850$	9.53811e6	−	1.65205e7i	0.452809	−	0.784288i
$851$	−4.53329e6	+	7.85190e6i	−0.214580	+	0.371664i
$852$		0			0
$853$	−2.91267e7			−1.37062			−0.685312	−	0.728250i	$-0.740334\pi$
$853$	−2.91267e7			−1.37062			−0.685312	+	0.728250i	$0.740334\pi$
$854$	1.13423e6	−	250398.i	0.0532177	−	0.0117486i
$855$		0			0
$856$	−1.07092e7	−	1.85489e7i	−0.499544	−	0.865236i
$857$	−1.61293e6	+	2.79367e6i	−0.0750175	+	0.129934i	−0.901094	−	0.433624i	$-0.857235\pi$
$857$	−1.61293e6	+	2.79367e6i	−0.0750175	+	0.129934i	0.826076	+	0.563558i	$0.190568\pi$
$858$		0			0
$859$	−1.32335e7	−	2.29212e7i	−0.611918	−	1.05987i	−0.990917	−	0.134476i	$-0.957065\pi$
$859$	−1.32335e7	−	2.29212e7i	−0.611918	−	1.05987i	0.378999	−	0.925397i	$-0.376268\pi$
$860$	−7.05255e7			−3.25162
$861$		0			0
$862$	3.17611e7			1.45589
$863$	7.92552e6	+	1.37274e7i	0.362243	+	0.627424i	0.988330	−	0.152330i	$-0.0486776\pi$
$863$	7.92552e6	+	1.37274e7i	0.362243	+	0.627424i	−0.626086	+	0.779754i	$0.715344\pi$
$864$		0			0
$865$	1.73363e6	−	3.00273e6i	0.0787799	−	0.136451i
$866$	1.33930e6	+	2.31974e6i	0.0606854	+	0.105110i
$867$		0			0
$868$	−1.80202e7	+	5.69768e7i	−0.811823	+	2.56684i
$869$	2.50522e7			1.12537
$870$		0			0
$871$	5.28579e6	−	9.15526e6i	0.236083	−	0.408908i
$872$	9.46305e6	−	1.63905e7i	0.421444	−	0.729962i
$873$		0			0
$874$	−4.14817e7			−1.83687
$875$	6.93493e6	+	7.58163e6i	0.306212	+	0.334767i
$876$		0			0
$877$	7.45659e6	+	1.29152e7i	0.327372	+	0.567024i	0.981989	−	0.188936i	$-0.0605037\pi$
$877$	7.45659e6	+	1.29152e7i	0.327372	+	0.567024i	−0.654618	+	0.755960i	$0.727170\pi$
$878$	−2.04333e7	+	3.53915e7i	−0.894544	+	1.54940i
$879$		0			0
$880$	−6.70730e6	−	1.16174e7i	−0.291972	−	0.505711i
$881$	3.70679e7			1.60901			0.804504	−	0.593947i	$-0.202431\pi$
$881$	3.70679e7			1.60901			0.804504	+	0.593947i	$0.202431\pi$
$882$		0			0
$883$	1.50440e7			0.649325			0.324663	−	0.945830i	$-0.394749\pi$
$883$	1.50440e7			0.649325			0.324663	+	0.945830i	$0.394749\pi$
$884$	1.50689e7	+	2.61001e7i	0.648561	+	1.12334i
$885$		0			0
$886$	−2.39704e7	+	4.15180e7i	−1.02587	+	1.77686i
$887$	8.90504e6	+	1.54240e7i	0.380038	+	0.658245i	0.991067	−	0.133363i	$-0.0425777\pi$
$887$	8.90504e6	+	1.54240e7i	0.380038	+	0.658245i	−0.611030	+	0.791608i	$0.709244\pi$
$888$		0			0
$889$	1.25715e7	+	1.37438e7i	0.533497	+	0.583247i
$890$	−9.18375e6			−0.388638
$891$		0			0
$892$	3.03891e7	−	5.26354e7i	1.27881	−	2.21496i
$893$	−1.11846e7	+	1.93723e7i	−0.469345	+	0.812929i
$894$		0			0
$895$	1.02508e7			0.427762
$896$	1.29875e7	−	4.10641e7i	0.540450	−	1.70881i
$897$		0			0
$898$	1.42802e7	+	2.47341e7i	0.590941	+	1.02354i
$899$	−3.09159e6	+	5.35479e6i	−0.127580	+	0.220975i
$900$		0			0
$901$	1.49053e7	+	2.58168e7i	0.611687	+	1.05947i
$902$	−1.29405e6			−0.0529583
$903$		0			0
$904$	4.06815e7			1.65568
$905$	2.77037e6	+	4.79842e6i	0.112439	+	0.194750i
$906$		0			0
$907$	584680.	−	1.01270e6i	0.0235993	−	0.0408753i	−0.853985	−	0.520298i	$-0.825821\pi$
$907$	584680.	−	1.01270e6i	0.0235993	−	0.0408753i	0.877584	+	0.479423i	$0.159154\pi$
$908$	1.55323e7	+	2.69027e7i	0.625202	+	1.08288i
$909$		0			0
$910$	4.54892e7	−	1.00424e7i	1.82098	−	0.402008i
$911$	−2.74389e7			−1.09539			−0.547697	−	0.836677i	$-0.684495\pi$
$911$	−2.74389e7			−1.09539			−0.547697	+	0.836677i	$0.684495\pi$
$912$		0			0
$913$	4.37462e6	−	7.57707e6i	0.173685	−	0.300832i
$914$	8.18948e6	−	1.41846e7i	0.324258	−	0.561632i
$915$		0			0
$916$	2.93781e7			1.15687
$917$	2.04420e6	−	6.46339e6i	0.0802786	−	0.253827i
$918$		0			0
$919$	−5.51091e6	−	9.54518e6i	−0.215246	−	0.372817i	0.738103	−	0.674688i	$-0.235722\pi$
$919$	−5.51091e6	−	9.54518e6i	−0.215246	−	0.372817i	−0.953349	+	0.301872i	$0.902389\pi$
$920$	2.62747e7	−	4.55092e7i	1.02345	−	1.77268i
$921$		0			0
$922$	−3.21932e7	−	5.57602e7i	−1.24720	−	2.16022i
$923$	−3.31444e7			−1.28058
$924$		0			0
$925$	−5.67367e6			−0.218027
$926$	−2.41246e7	−	4.17851e7i	−0.924557	−	1.60138i
$927$		0			0
$928$	1.55587e6	−	2.69484e6i	0.0593065	−	0.102722i
$929$	2.12526e6	+	3.68105e6i	0.0807927	+	0.139937i	0.903591	−	0.428397i	$-0.140921\pi$
$929$	2.12526e6	+	3.68105e6i	0.0807927	+	0.139937i	−0.822798	+	0.568334i	$0.807588\pi$
$930$		0			0
$931$	2.08630e7	−	9.68361e6i	0.788866	−	0.366153i
$932$	2.04559e7			0.771398
$933$		0			0
$934$	−2.15108e7	+	3.72578e7i	−0.806844	+	1.39749i
$935$	2.02206e7	−	3.50232e7i	0.756425	−	1.31017i
$936$		0			0
$937$	3.75738e7			1.39809			0.699046	−	0.715077i	$-0.253608\pi$
$937$	3.75738e7			1.39809			0.699046	+	0.715077i	$0.253608\pi$
$938$	1.62804e7	+	1.77986e7i	0.604169	+	0.660509i
$939$		0			0
$940$	−3.29279e7	−	5.70328e7i	−1.21547	−	2.10526i
$941$	3.43521e6	−	5.94997e6i	0.126468	−	0.219049i	−0.795838	−	0.605510i	$-0.792969\pi$
$941$	3.43521e6	−	5.94997e6i	0.126468	−	0.219049i	0.922306	+	0.386461i	$0.126303\pi$
$942$		0			0
$943$	−396775.	−	687235.i	−0.0145300	−	0.0251667i
$944$	3.45476e6			0.126179
$945$		0			0
$946$	−9.21446e7			−3.34767
$947$	−1.15462e7	−	1.99985e7i	−0.418372	−	0.724641i	0.577404	−	0.816459i	$-0.304066\pi$
$947$	−1.15462e7	−	1.99985e7i	−0.418372	−	0.724641i	−0.995776	+	0.0918172i	$0.970732\pi$
$948$		0			0
$949$	−7.23161e6	+	1.25255e7i	−0.260657	+	0.451471i
$950$	−1.29792e7	−	2.24806e7i	−0.466592	−	0.808162i
$951$		0			0
$952$	−2.88941e7	+	6.37881e6i	−1.03328	+	0.228112i
$953$	2.95399e7			1.05360			0.526802	−	0.849988i	$-0.323391\pi$
$953$	2.95399e7			1.05360			0.526802	+	0.849988i	$0.323391\pi$
$954$		0			0
$955$	9.75709e6	−	1.68998e7i	0.346188	−	0.599615i
$956$	1.04431e7	−	1.80880e7i	0.369559	−	0.640096i
$957$		0			0
$958$	2.70919e6			0.0953730
$959$	−1.19126e6	+	262988.i	−0.0418273	+	0.00923400i
$960$		0			0
$961$	−1.93581e7	−	3.35292e7i	−0.676166	−	1.17115i
$962$	7.03511e6	−	1.21852e7i	0.245094	−	0.424516i
$963$		0			0
$964$	4.80664e7	+	8.32535e7i	1.66590	+	2.88543i
$965$	−1.15009e6			−0.0397569
$966$		0			0
$967$	1.49151e7			0.512931			0.256466	−	0.966553i	$-0.417442\pi$
$967$	1.49151e7			0.512931			0.256466	+	0.966553i	$0.417442\pi$
$968$	−1.73880e7	−	3.01170e7i	−0.596434	−	1.03305i
$969$		0			0
$970$	4.35081e6	−	7.53582e6i	0.148471	−	0.257159i
$971$	7.74150e6	+	1.34087e7i	0.263498	+	0.456391i	0.967169	−	0.254134i	$-0.0817905\pi$
$971$	7.74150e6	+	1.34087e7i	0.263498	+	0.456391i	−0.703671	+	0.710526i	$0.748457\pi$
$972$		0			0
$973$	−1.60207e7	−	1.75147e7i	−0.542501	−	0.593091i
$974$	−7.33992e7			−2.47910
$975$		0			0
$976$	−159155.	+	275665.i	−0.00534807	+	0.00926313i
$977$	−1.41714e7	+	2.45455e7i	−0.474980	+	0.822690i	−0.999589	−	0.0286531i	$-0.990878\pi$
$977$	−1.41714e7	+	2.45455e7i	−0.474980	+	0.822690i	0.524609	+	0.851343i	$0.324212\pi$
$978$		0			0
$979$	−7.64410e6			−0.254900
$980$	−6.02133e6	+	6.74470e7i	−0.200275	+	2.24335i
$981$		0			0
$982$	1.47640e7	+	2.55720e7i	0.488569	+	0.846226i
$983$	1.28497e7	−	2.22563e7i	0.424139	−	0.734630i	−0.572201	−	0.820114i	$-0.693910\pi$
$983$	1.28497e7	−	2.22563e7i	0.424139	−	0.734630i	0.996340	+	0.0854834i	$0.0272434\pi$
$984$		0			0
$985$	3.70223e7	+	6.41245e7i	1.21583	+	2.10588i
$986$	−7.11518e6			−0.233074
$987$		0			0
$988$	4.10106e7			1.33661
$989$	−2.82530e7	−	4.89355e7i	−0.918487	−	1.59087i
$990$		0			0
$991$	−2.23202e7	+	3.86598e7i	−0.721962	+	1.25048i	0.238250	+	0.971204i	$0.423426\pi$
$991$	−2.23202e7	+	3.86598e7i	−0.721962	+	1.25048i	−0.960212	+	0.279271i	$0.909907\pi$
$992$	1.69460e7	+	2.93514e7i	0.546750	+	0.947000i
$993$		0			0
$994$	2.28052e7	−	7.21060e7i	0.732096	−	2.31476i
$995$	−6.32461e7			−2.02524
$996$		0			0
$997$	−1.15277e7	+	1.99665e7i	−0.367286	+	0.636158i	−0.989140	−	0.146975i	$-0.953046\pi$
$997$	−1.15277e7	+	1.99665e7i	−0.367286	+	0.636158i	0.621854	+	0.783133i	$0.286380\pi$
$998$	−3.15764e7	+	5.46919e7i	−1.00354	+	1.73819i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.e.c.46.1		4
3.2	odd	2		21.6.e.b.4.2	✓	4
7.2	even	3	inner	63.6.e.c.37.1		4
7.3	odd	6		441.6.a.s.1.2		2
7.4	even	3		441.6.a.t.1.2		2
12.11	even	2		336.6.q.e.193.2		4
21.2	odd	6		21.6.e.b.16.2	yes	4
21.5	even	6		147.6.e.l.79.2		4
21.11	odd	6		147.6.a.i.1.1		2
21.17	even	6		147.6.a.k.1.1		2
21.20	even	2		147.6.e.l.67.2		4
84.23	even	6		336.6.q.e.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.b.4.2	✓	4	3.2	odd	2
21.6.e.b.16.2	yes	4	21.2	odd	6
63.6.e.c.37.1		4	7.2	even	3	inner
63.6.e.c.46.1		4	1.1	even	1	trivial
147.6.a.i.1.1		2	21.11	odd	6
147.6.a.k.1.1		2	21.17	even	6
147.6.e.l.67.2		4	21.20	even	2
147.6.e.l.79.2		4	21.5	even	6
336.6.q.e.193.2		4	12.11	even	2
336.6.q.e.289.2		4	84.23	even	6
441.6.a.s.1.2		2	7.3	odd	6
441.6.a.t.1.2		2	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.69493 - 8.13186i) q^{2} +(-28.0848 + 48.6443i) q^{4} +(-35.8645 - 62.1192i) q^{5} +(-87.5000 - 95.6596i) q^{7} +226.949 q^{8} +(-336.763 + 583.291i) q^{10} +(-280.305 + 485.503i) q^{11} +533.509 q^{13} +(-367.084 + 1160.65i) q^{14} +(-166.798 - 288.903i) q^{16} +(502.850 - 870.962i) q^{17} +(-684.263 - 1185.18i) q^{19} +4028.99 q^{20} +5264.05 q^{22} +(1614.04 + 2795.60i) q^{23} +(-1010.03 + 1749.42i) q^{25} +(-2504.79 - 4338.42i) q^{26} +(7110.71 - 1569.80i) q^{28} +753.456 q^{29} +(-4103.21 + 7106.97i) q^{31} +(2064.97 - 3576.64i) q^{32} -9443.39 q^{34} +(-2804.15 + 8866.21i) q^{35} +(1404.33 + 2432.37i) q^{37} +(-6425.14 + 11128.7i) q^{38} +(-8139.43 - 14097.9i) q^{40} -245.827 q^{41} -17504.5 q^{43} +(-15744.6 - 27270.5i) q^{44} +(15155.6 - 26250.3i) q^{46} +(-8172.74 - 14155.6i) q^{47} +(-1494.50 + 16740.4i) q^{49} +18968.1 q^{50} +(-14983.5 + 25952.2i) q^{52} +(-14820.8 + 25670.4i) q^{53} +40212.0 q^{55} +(-19858.1 - 21709.9i) q^{56} +(-3537.43 - 6127.00i) q^{58} +(-5178.05 + 8968.65i) q^{59} +(-477.089 - 826.343i) q^{61} +77057.2 q^{62} -49454.8 q^{64} +(-19134.0 - 33141.1i) q^{65} +(9907.60 - 17160.5i) q^{67} +(28244.9 + 48921.6i) q^{68} +(85264.1 - 18823.3i) q^{70} -62125.4 q^{71} +(-13554.8 + 23477.6i) q^{73} +(13186.5 - 22839.7i) q^{74} +76869.6 q^{76} +(70969.7 - 15667.6i) q^{77} +(-22343.7 - 38700.4i) q^{79} +(-11964.3 + 20722.8i) q^{80} +(1154.14 + 1999.03i) q^{82} -15606.6 q^{83} -72137.9 q^{85} +(82182.5 + 142344. i) q^{86} +(-63615.0 + 110184. i) q^{88} +(6817.66 + 11808.5i) q^{89} +(-46682.0 - 51035.2i) q^{91} -181320. q^{92} +(-76740.9 + 132919. i) q^{94} +(-49081.6 + 85011.8i) q^{95} -12919.5 q^{97} +(143147. - 66442.1i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 65 q^{4} - 33 q^{5} - 350 q^{7} + 750 q^{8} - 921 q^{10} - 1137 q^{11} + 1850 q^{13} - 2352 q^{14} + 895 q^{16} - 324 q^{17} - 2311 q^{19} + 7374 q^{20} + 3162 q^{22} + 1596 q^{23} - 395 q^{25}+ \cdots + 462021 q^{98}+O(q^{100}) \) 4 * q - 3 * q^2 - 65 * q^4 - 33 * q^5 - 350 * q^7 + 750 * q^8 - 921 * q^10 - 1137 * q^11 + 1850 * q^13 - 2352 * q^14 + 895 * q^16 - 324 * q^17 - 2311 * q^19 + 7374 * q^20 + 3162 * q^22 + 1596 * q^23 - 395 * q^25 - 2508 * q^26 + 13531 * q^28 + 4434 * q^29 - 4294 * q^31 + 1017 * q^32 - 35880 * q^34 - 15414 * q^35 + 19109 * q^37 - 6828 * q^38 - 10545 * q^40 + 25716 * q^41 - 5542 * q^43 - 36579 * q^44 + 40740 * q^46 - 23160 * q^47 - 5978 * q^49 + 58704 * q^50 - 33424 * q^52 - 31653 * q^53 + 35778 * q^55 - 65625 * q^56 + 2277 * q^58 + 41097 * q^59 - 42052 * q^61 + 204114 * q^62 - 60062 * q^64 - 23106 * q^65 - 30763 * q^67 + 44748 * q^68 + 151179 * q^70 - 204192 * q^71 + 28577 * q^73 - 77784 * q^74 + 170384 * q^76 + 96873 * q^77 + 18464 * q^79 - 71511 * q^80 + 86040 * q^82 - 122358 * q^83 - 247272 * q^85 + 258510 * q^86 - 212565 * q^88 + 29322 * q^89 - 161875 * q^91 - 333816 * q^92 - 109938 * q^94 - 61662 * q^95 - 19582 * q^97 + 462021 * q^98

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