LMFDB - Embedded newform 6.7.b.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,7,Mod(5,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	6.b (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:	$1.38032450172$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-2}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 2 $ x^2 + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.2
Root			$1.41421i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.7.b.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.65685i q^{2} +(21.0000 + 16.9706i) q^{3} -32.0000 q^{4} -169.706i q^{5} +(-96.0000 + 118.794i) q^{6} +2.00000 q^{7} -181.019i q^{8} +(153.000 + 712.764i) q^{9} +O(q^{10})$	\(q+5.65685i q^{2} +(21.0000 + 16.9706i) q^{3} -32.0000 q^{4} -169.706i q^{5} +(-96.0000 + 118.794i) q^{6} +2.00000 q^{7} -181.019i q^{8} +(153.000 + 712.764i) q^{9} +960.000 q^{10} -33.9411i q^{11} +(-672.000 - 543.058i) q^{12} -2950.00 q^{13} +11.3137i q^{14} +(2880.00 - 3563.82i) q^{15} +1024.00 q^{16} +4480.23i q^{17} +(-4032.00 + 865.499i) q^{18} +5258.00 q^{19} +5430.58i q^{20} +(42.0000 + 33.9411i) q^{21} +192.000 q^{22} -10250.2i q^{23} +(3072.00 - 3801.41i) q^{24} -13175.0 q^{25} -16687.7i q^{26} +(-8883.00 + 17564.5i) q^{27} -64.0000 q^{28} +2206.17i q^{29} +(20160.0 + 16291.7i) q^{30} +22898.0 q^{31} +5792.62i q^{32} +(576.000 - 712.764i) q^{33} -25344.0 q^{34} -339.411i q^{35} +(-4896.00 - 22808.4i) q^{36} +34058.0 q^{37} +29743.7i q^{38} +(-61950.0 - 50063.2i) q^{39} -30720.0 q^{40} -16766.9i q^{41} +(-192.000 + 237.588i) q^{42} -6406.00 q^{43} +1086.12i q^{44} +(120960. - 25965.0i) q^{45} +57984.0 q^{46} +179888. i q^{47} +(21504.0 + 17377.9i) q^{48} -117645. q^{49} -74529.1i q^{50} +(-76032.0 + 94084.8i) q^{51} +94400.0 q^{52} -192548. i q^{53} +(-99360.0 - 50249.8i) q^{54} -5760.00 q^{55} -362.039i q^{56} +(110418. + 89231.2i) q^{57} -12480.0 q^{58} -326819. i q^{59} +(-92160.0 + 114042. i) q^{60} -62566.0 q^{61} +129531. i q^{62} +(306.000 + 1425.53i) q^{63} -32768.0 q^{64} +500632. i q^{65} +(4032.00 + 3258.35i) q^{66} +438698. q^{67} -143367. i q^{68} +(173952. - 215255. i) q^{69} +1920.00 q^{70} -68221.7i q^{71} +(129024. - 27696.0i) q^{72} -730510. q^{73} +192661. i q^{74} +(-276675. - 223587. i) q^{75} -168256. q^{76} -67.8823i q^{77} +(283200. - 350442. i) q^{78} +340562. q^{79} -173779. i q^{80} +(-484623. + 218106. i) q^{81} +94848.0 q^{82} +496253. i q^{83} +(-1344.00 - 1086.12i) q^{84} +760320. q^{85} -36237.8i q^{86} +(-37440.0 + 46329.6i) q^{87} -6144.00 q^{88} -386725. i q^{89} +(146880. + 684253. i) q^{90} -5900.00 q^{91} +328007. i q^{92} +(480858. + 388592. i) q^{93} -1.01760e6 q^{94} -892312. i q^{95} +(-98304.0 + 121645. i) q^{96} -281086. q^{97} -665501. i q^{98} +(24192.0 - 5192.99i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 42 q^{3} - 64 q^{4} - 192 q^{6} + 4 q^{7} + 306 q^{9}+O(q^{10}) $ 2 * q + 42 * q^3 - 64 * q^4 - 192 * q^6 + 4 * q^7 + 306 * q^9	$ 2 q + 42 q^{3} - 64 q^{4} - 192 q^{6} + 4 q^{7} + 306 q^{9} + 1920 q^{10} - 1344 q^{12} - 5900 q^{13} + 5760 q^{15} + 2048 q^{16} - 8064 q^{18} + 10516 q^{19} + 84 q^{21} + 384 q^{22} + 6144 q^{24} - 26350 q^{25} - 17766 q^{27} - 128 q^{28} + 40320 q^{30} + 45796 q^{31} + 1152 q^{33} - 50688 q^{34} - 9792 q^{36} + 68116 q^{37} - 123900 q^{39} - 61440 q^{40} - 384 q^{42} - 12812 q^{43} + 241920 q^{45} + 115968 q^{46} + 43008 q^{48} - 235290 q^{49} - 152064 q^{51} + 188800 q^{52} - 198720 q^{54} - 11520 q^{55} + 220836 q^{57} - 24960 q^{58} - 184320 q^{60} - 125132 q^{61} + 612 q^{63} - 65536 q^{64} + 8064 q^{66} + 877396 q^{67} + 347904 q^{69} + 3840 q^{70} + 258048 q^{72} - 1461020 q^{73} - 553350 q^{75} - 336512 q^{76} + 566400 q^{78} + 681124 q^{79} - 969246 q^{81} + 189696 q^{82} - 2688 q^{84} + 1520640 q^{85} - 74880 q^{87} - 12288 q^{88} + 293760 q^{90} - 11800 q^{91} + 961716 q^{93} - 2035200 q^{94} - 196608 q^{96} - 562172 q^{97} + 48384 q^{99}+O(q^{100}) $ 2 * q + 42 * q^3 - 64 * q^4 - 192 * q^6 + 4 * q^7 + 306 * q^9 + 1920 * q^10 - 1344 * q^12 - 5900 * q^13 + 5760 * q^15 + 2048 * q^16 - 8064 * q^18 + 10516 * q^19 + 84 * q^21 + 384 * q^22 + 6144 * q^24 - 26350 * q^25 - 17766 * q^27 - 128 * q^28 + 40320 * q^30 + 45796 * q^31 + 1152 * q^33 - 50688 * q^34 - 9792 * q^36 + 68116 * q^37 - 123900 * q^39 - 61440 * q^40 - 384 * q^42 - 12812 * q^43 + 241920 * q^45 + 115968 * q^46 + 43008 * q^48 - 235290 * q^49 - 152064 * q^51 + 188800 * q^52 - 198720 * q^54 - 11520 * q^55 + 220836 * q^57 - 24960 * q^58 - 184320 * q^60 - 125132 * q^61 + 612 * q^63 - 65536 * q^64 + 8064 * q^66 + 877396 * q^67 + 347904 * q^69 + 3840 * q^70 + 258048 * q^72 - 1461020 * q^73 - 553350 * q^75 - 336512 * q^76 + 566400 * q^78 + 681124 * q^79 - 969246 * q^81 + 189696 * q^82 - 2688 * q^84 + 1520640 * q^85 - 74880 * q^87 - 12288 * q^88 + 293760 * q^90 - 11800 * q^91 + 961716 * q^93 - 2035200 * q^94 - 196608 * q^96 - 562172 * q^97 + 48384 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/6\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$			5.65685i			0.707107i
$2$			5.65685i			0.707107i
$3$	21.0000	+	16.9706i	0.777778	+	0.628539i
$3$	21.0000	+	16.9706i	0.777778	+	0.628539i
$4$	−32.0000			−0.500000
$5$		−	169.706i		−	1.35765i	−0.734302	−	0.678823i	$-0.762491\pi$
$5$		−	169.706i		−	1.35765i	0.734302	−	0.678823i	$-0.237509\pi$
$6$	−96.0000	+	118.794i	−0.444444	+	0.549972i
$7$	2.00000			0.00583090			0.00291545	−	0.999996i	$-0.499072\pi$
$7$	2.00000			0.00583090			0.00291545	+	0.999996i	$0.499072\pi$
$8$		−	181.019i		−	0.353553i
$9$	153.000	+	712.764i	0.209877	+	0.977728i
$10$	960.000			0.960000
$11$		−	33.9411i		−	0.0255005i	−0.999919	−	0.0127502i	$-0.995941\pi$
$11$		−	33.9411i		−	0.0255005i	0.999919	−	0.0127502i	$-0.00405864\pi$
$12$	−672.000	−	543.058i	−0.388889	−	0.314270i
$13$	−2950.00			−1.34274			−0.671370	−	0.741122i	$-0.734294\pi$
$13$	−2950.00			−1.34274			−0.671370	+	0.741122i	$0.734294\pi$
$14$			11.3137i			0.00412307i
$15$	2880.00	−	3563.82i	0.853333	−	1.05595i
$16$	1024.00			0.250000
$17$			4480.23i			0.911913i	0.890002	+	0.455956i	$0.150703\pi$
$17$			4480.23i			0.911913i	−0.890002	+	0.455956i	$0.849297\pi$
$18$	−4032.00	+	865.499i	−0.691358	+	0.148405i
$19$	5258.00			0.766584			0.383292	−	0.923627i	$-0.374790\pi$
$19$	5258.00			0.766584			0.383292	+	0.923627i	$0.374790\pi$
$20$			5430.58i			0.678823i
$21$	42.0000	+	33.9411i	0.00453515	+	0.00366495i
$22$	192.000			0.0180316
$23$		−	10250.2i		−	0.842461i	−0.906954	−	0.421230i	$-0.861598\pi$
$23$		−	10250.2i		−	0.842461i	0.906954	−	0.421230i	$-0.138402\pi$
$24$	3072.00	−	3801.41i	0.222222	−	0.274986i
$25$	−13175.0			−0.843200
$26$		−	16687.7i		−	0.949461i
$27$	−8883.00	+	17564.5i	−0.451303	+	0.892371i
$28$	−64.0000			−0.00291545
$29$			2206.17i			0.0904577i	0.998977	+	0.0452289i	$0.0144017\pi$
$29$			2206.17i			0.0904577i	−0.998977	+	0.0452289i	$0.985598\pi$
$30$	20160.0	+	16291.7i	0.746667	+	0.603398i
$31$	22898.0			0.768621			0.384311	−	0.923204i	$-0.374439\pi$
$31$	22898.0			0.768621			0.384311	+	0.923204i	$0.374439\pi$
$32$			5792.62i			0.176777i
$33$	576.000	−	712.764i	0.0160280	−	0.0198337i
$34$	−25344.0			−0.644820
$35$		−	339.411i		−	0.00791630i
$36$	−4896.00	−	22808.4i	−0.104938	−	0.488864i
$37$	34058.0			0.672379			0.336189	−	0.941794i	$-0.390862\pi$
$37$	34058.0			0.672379			0.336189	+	0.941794i	$0.390862\pi$
$38$			29743.7i			0.542057i
$39$	−61950.0	−	50063.2i	−1.04435	−	0.843965i
$40$	−30720.0			−0.480000
$41$		−	16766.9i		−	0.243277i	−0.992574	−	0.121639i	$-0.961185\pi$
$41$		−	16766.9i		−	0.243277i	0.992574	−	0.121639i	$-0.0388149\pi$
$42$	−192.000	+	237.588i	−0.00259151	+	0.00320683i
$43$	−6406.00			−0.0805715			−0.0402858	−	0.999188i	$-0.512827\pi$
$43$	−6406.00			−0.0805715			−0.0402858	+	0.999188i	$0.512827\pi$
$44$			1086.12i			0.0127502i
$45$	120960.	−	25965.0i	1.32741	−	0.284938i
$46$	57984.0			0.595710
$47$			179888.i			1.73264i	0.499489	+	0.866320i	$0.333521\pi$
$47$			179888.i			1.73264i	−0.499489	+	0.866320i	$0.666479\pi$
$48$	21504.0	+	17377.9i	0.194444	+	0.157135i
$49$	−117645.			−0.999966
$50$		−	74529.1i		−	0.596232i
$51$	−76032.0	+	94084.8i	−0.573173	+	0.709266i
$52$	94400.0			0.671370
$53$		−	192548.i		−	1.29334i	−0.762772	−	0.646668i	$-0.776162\pi$
$53$		−	192548.i		−	1.29334i	0.762772	−	0.646668i	$-0.223838\pi$
$54$	−99360.0	−	50249.8i	−0.631001	−	0.319120i
$55$	−5760.00			−0.0346206
$56$		−	362.039i		−	0.00206154i
$57$	110418.	+	89231.2i	0.596232	+	0.481828i
$58$	−12480.0			−0.0639633
$59$		−	326819.i		−	1.59130i	−0.605758	−	0.795649i	$-0.707130\pi$
$59$		−	326819.i		−	1.59130i	0.605758	−	0.795649i	$-0.292870\pi$
$60$	−92160.0	+	114042.i	−0.426667	+	0.527973i
$61$	−62566.0			−0.275644			−0.137822	−	0.990457i	$-0.544010\pi$
$61$	−62566.0			−0.275644			−0.137822	+	0.990457i	$0.544010\pi$
$62$			129531.i			0.543497i
$63$	306.000	+	1425.53i	0.00122377	+	0.00570104i
$64$	−32768.0			−0.125000
$65$			500632.i			1.82296i
$66$	4032.00	+	3258.35i	0.0140245	+	0.0113335i
$67$	438698.			1.45862			0.729308	−	0.684185i	$-0.239842\pi$
$67$	438698.			1.45862			0.729308	+	0.684185i	$0.239842\pi$
$68$		−	143367.i		−	0.455956i
$69$	173952.	−	215255.i	0.529520	−	0.655247i
$70$	1920.00			0.00559767
$71$		−	68221.7i		−	0.190611i	−0.995448	−	0.0953053i	$-0.969617\pi$
$71$		−	68221.7i		−	0.190611i	0.995448	−	0.0953053i	$-0.0303827\pi$
$72$	129024.	−	27696.0i	0.345679	−	0.0742026i
$73$	−730510.			−1.87784			−0.938918	−	0.344141i	$-0.888170\pi$
$73$	−730510.			−1.87784			−0.938918	+	0.344141i	$0.888170\pi$
$74$			192661.i			0.475444i
$75$	−276675.	−	223587.i	−0.655822	−	0.529984i
$76$	−168256.			−0.383292
$77$		−	67.8823i		−	0.000148691i
$78$	283200.	−	350442.i	0.596773	−	0.738469i
$79$	340562.			0.690740			0.345370	−	0.938467i	$-0.387753\pi$
$79$	340562.			0.690740			0.345370	+	0.938467i	$0.387753\pi$
$80$		−	173779.i		−	0.339411i
$81$	−484623.	+	218106.i	−0.911904	+	0.410404i
$82$	94848.0			0.172023
$83$			496253.i			0.867899i	0.900937	+	0.433949i	$0.142880\pi$
$83$			496253.i			0.867899i	−0.900937	+	0.433949i	$0.857120\pi$
$84$	−1344.00	−	1086.12i	−0.00226757	−	0.00183248i
$85$	760320.			1.23805
$86$		−	36237.8i		−	0.0569727i
$87$	−37440.0	+	46329.6i	−0.0568562	+	0.0703560i
$88$	−6144.00			−0.00901578
$89$		−	386725.i		−	0.548570i	−0.961648	−	0.274285i	$-0.911559\pi$
$89$		−	386725.i		−	0.548570i	0.961648	−	0.274285i	$-0.0884412\pi$
$90$	146880.	+	684253.i	0.201481	+	0.938619i
$91$	−5900.00			−0.00782939
$92$			328007.i			0.421230i
$93$	480858.	+	388592.i	0.597817	+	0.483109i
$94$	−1.01760e6			−1.22516
$95$		−	892312.i		−	1.04075i
$96$	−98304.0	+	121645.i	−0.111111	+	0.137493i
$97$	−281086.			−0.307981			−0.153991	−	0.988072i	$-0.549213\pi$
$97$	−281086.			−0.307981			−0.153991	+	0.988072i	$0.549213\pi$
$98$		−	665501.i		−	0.707083i
$99$	24192.0	−	5192.99i	0.0249325	−	0.00535195i
$100$	421600.			0.421600
$101$		−	945362.i		−	0.917559i	−0.888550	−	0.458780i	$-0.848287\pi$
$101$		−	945362.i		−	0.917559i	0.888550	−	0.458780i	$-0.151713\pi$
$102$	−532224.	−	430102.i	−0.501527	−	0.405295i
$103$	−865726.			−0.792262			−0.396131	−	0.918194i	$-0.629647\pi$
$103$	−865726.			−0.792262			−0.396131	+	0.918194i	$0.629647\pi$
$104$			534007.i			0.474730i
$105$	5760.00	−	7127.64i	0.00497570	−	0.00615712i
$106$	1.08922e6			0.914527
$107$			1.47410e6i			1.20330i	0.798759	+	0.601651i	$0.205490\pi$
$107$			1.47410e6i			1.20330i	−0.798759	+	0.601651i	$0.794510\pi$
$108$	284256.	−	562065.i	0.225652	−	0.446185i
$109$	650810.			0.502545			0.251272	−	0.967916i	$-0.419151\pi$
$109$	650810.			0.502545			0.251272	+	0.967916i	$0.419151\pi$
$110$		−	32583.5i		−	0.0244805i
$111$	715218.	+	577983.i	0.522961	+	0.422616i
$112$	2048.00			0.00145773
$113$			1.74417e6i			1.20879i	0.796683	+	0.604397i	$0.206586\pi$
$113$			1.74417e6i			1.20879i	−0.796683	+	0.604397i	$0.793414\pi$
$114$	−504768.	+	624619.i	−0.340704	+	0.421600i
$115$	−1.73952e6			−1.14376
$116$		−	70597.5i		−	0.0452289i
$117$	−451350.	−	2.10265e6i	−0.281810	−	1.31283i
$118$	1.84877e6			1.12522
$119$			8960.46i			0.00531728i
$120$	−645120.	−	521336.i	−0.373333	−	0.301699i
$121$	1.77041e6			0.999350
$122$		−	353927.i		−	0.194910i
$123$	284544.	−	352105.i	0.152909	−	0.189216i
$124$	−732736.			−0.384311
$125$		−	415779.i		−	0.212879i
$126$	−8064.00	+	1731.00i	−0.00403124	+	0.000865336i
$127$	−2.28053e6			−1.11333			−0.556665	−	0.830737i	$-0.687919\pi$
$127$	−2.28053e6			−1.11333			−0.556665	+	0.830737i	$0.687919\pi$
$128$		−	185364.i		−	0.0883883i
$129$	−134526.	−	108713.i	−0.0626667	−	0.0506424i
$130$	−2.83200e6			−1.28903
$131$		−	1.07196e6i		−	0.476832i	−0.971163	−	0.238416i	$-0.923372\pi$
$131$		−	1.07196e6i		−	0.476832i	0.971163	−	0.238416i	$-0.0766282\pi$
$132$	−18432.0	+	22808.4i	−0.00801402	+	0.00991685i
$133$	10516.0			0.00446988
$134$			2.48165e6i			1.03140i
$135$	2.98080e6	+	1.50750e6i	1.21152	+	0.612709i
$136$	811008.			0.322410
$137$		−	2.78338e6i		−	1.08246i	−0.840876	−	0.541228i	$-0.817960\pi$
$137$		−	2.78338e6i		−	1.08246i	0.840876	−	0.541228i	$-0.182040\pi$
$138$	1.21766e6	+	984021.i	0.463330	+	0.374427i
$139$	4.57395e6			1.70313			0.851563	−	0.524253i	$-0.175655\pi$
$139$	4.57395e6			1.70313			0.851563	+	0.524253i	$0.175655\pi$
$140$			10861.2i			0.00395815i
$141$	−3.05280e6	+	3.77765e6i	−1.08903	+	1.34761i
$142$	385920.			0.134782
$143$			100126.i			0.0342405i
$144$	156672.	+	729870.i	0.0524691	+	0.244432i
$145$	374400.			0.122809
$146$		−	4.13239e6i		−	1.32783i
$147$	−2.47054e6	−	1.99650e6i	−0.777751	−	0.628518i
$148$	−1.08986e6			−0.336189
$149$			4.46010e6i			1.34830i	0.738595	+	0.674149i	$0.235489\pi$
$149$			4.46010e6i			1.34830i	−0.738595	+	0.674149i	$0.764511\pi$
$150$	1.26480e6	−	1.56511e6i	0.374756	−	0.463736i
$151$	−2.20809e6			−0.641338			−0.320669	−	0.947191i	$-0.603908\pi$
$151$	−2.20809e6			−0.641338			−0.320669	+	0.947191i	$0.603908\pi$
$152$		−	951800.i		−	0.271028i
$153$	−3.19334e6	+	685475.i	−0.891603	+	0.191389i
$154$	384.000			0.000105140
$155$		−	3.88592e6i		−	1.04352i
$156$	1.98240e6	+	1.60202e6i	0.522177	+	0.421983i
$157$	−1.28887e6			−0.333051			−0.166525	−	0.986037i	$-0.553255\pi$
$157$	−1.28887e6			−0.333051			−0.166525	+	0.986037i	$0.553255\pi$
$158$			1.92651e6i			0.488427i
$159$	3.26765e6	−	4.04351e6i	0.812913	−	1.00593i
$160$	983040.			0.240000
$161$		−	20500.4i		−	0.00491231i
$162$	−1.23379e6	−	2.74144e6i	−0.290200	−	0.644813i
$163$	879914.			0.203178			0.101589	−	0.994826i	$-0.467607\pi$
$163$	879914.			0.203178			0.101589	+	0.994826i	$0.467607\pi$
$164$			536541.i			0.121639i
$165$	−120960.	−	97750.4i	−0.0269271	−	0.0217604i
$166$	−2.80723e6			−0.613697
$167$			5.96760e6i			1.28130i	0.767834	+	0.640649i	$0.221335\pi$
$167$			5.96760e6i			1.28130i	−0.767834	+	0.640649i	$0.778665\pi$
$168$	6144.00	−	7602.81i	0.00129576	−	0.00160342i
$169$	3.87569e6			0.802951
$170$			4.30102e6i			0.875436i
$171$	804474.	+	3.74771e6i	0.160888	+	0.749511i
$172$	204992.			0.0402858
$173$			418867.i			0.0808981i	0.999182	+	0.0404490i	$0.0128788\pi$
$173$			418867.i			0.0808981i	−0.999182	+	0.0404490i	$0.987121\pi$
$174$	−262080.	−	211793.i	−0.0497492	−	0.0402034i
$175$	−26350.0			−0.00491662
$176$		−	34755.7i		−	0.00637512i
$177$	5.54630e6	−	6.86320e6i	1.00019	−	1.23768i
$178$	2.18765e6			0.387898
$179$			302110.i			0.0526752i	0.999653	+	0.0263376i	$0.00838448\pi$
$179$			302110.i			0.0526752i	−0.999653	+	0.0263376i	$0.991616\pi$
$180$	−3.87072e6	+	830879.i	−0.663704	+	0.142469i
$181$	−6.47618e6			−1.09215			−0.546076	−	0.837735i	$-0.683879\pi$
$181$	−6.47618e6			−1.09215			−0.546076	+	0.837735i	$0.683879\pi$
$182$		−	33375.4i		−	0.00553621i
$183$	−1.31389e6	−	1.06178e6i	−0.214390	−	0.173253i
$184$	−1.85549e6			−0.297855
$185$		−	5.77983e6i		−	0.912852i
$186$	−2.19821e6	+	2.72014e6i	−0.341610	+	0.422720i
$187$	152064.			0.0232542
$188$		−	5.75641e6i		−	0.866320i
$189$	−17766.0	+	35129.1i	−0.00263151	+	0.00520333i
$190$	5.04768e6			0.735921
$191$		−	5.02166e6i		−	0.720687i	−0.932820	−	0.360344i	$-0.882659\pi$
$191$		−	5.02166e6i		−	0.720687i	0.932820	−	0.360344i	$-0.117341\pi$
$192$	−688128.	−	556091.i	−0.0972222	−	0.0785674i
$193$	3.50093e6			0.486980			0.243490	−	0.969903i	$-0.421708\pi$
$193$	3.50093e6			0.486980			0.243490	+	0.969903i	$0.421708\pi$
$194$		−	1.59006e6i		−	0.217775i
$195$	−8.49600e6	+	1.05133e7i	−1.14580	+	1.41786i
$196$	3.76464e6			0.499983
$197$			4.85423e6i			0.634923i	0.948271	+	0.317462i	$0.102830\pi$
$197$			4.85423e6i			0.634923i	−0.948271	+	0.317462i	$0.897170\pi$
$198$	29376.0	+	136851.i	0.00378440	+	0.0176300i
$199$	−9.50976e6			−1.20673			−0.603365	−	0.797465i	$-0.706174\pi$
$199$	−9.50976e6			−1.20673			−0.603365	+	0.797465i	$0.706174\pi$
$200$			2.38493e6i			0.298116i
$201$	9.21266e6	+	7.44495e6i	1.13448	+	0.916798i
$202$	5.34778e6			0.648812
$203$			4412.35i			0.000527450i
$204$	2.43302e6	−	3.01071e6i	0.286587	−	0.354633i
$205$	−2.84544e6			−0.330284
$206$		−	4.89729e6i		−	0.560214i
$207$	7.30598e6	−	1.56828e6i	0.823697	−	0.176813i
$208$	−3.02080e6			−0.335685
$209$		−	178462.i		−	0.0195483i
$210$	40320.0	+	32583.5i	0.00435374	+	0.00351835i
$211$	7.06414e6			0.751990			0.375995	−	0.926622i	$-0.377301\pi$
$211$	7.06414e6			0.751990			0.375995	+	0.926622i	$0.377301\pi$
$212$			6.16154e6i			0.646668i
$213$	1.15776e6	−	1.43265e6i	0.119806	−	0.148253i
$214$	−8.33875e6			−0.850863
$215$			1.08713e6i			0.109388i
$216$	3.17952e6	+	1.60799e6i	0.315501	+	0.159560i
$217$	45796.0			0.00448176
$218$			3.68154e6i			0.355353i
$219$	−1.53407e7	−	1.23972e7i	−1.46054	−	1.18029i
$220$	184320.			0.0173103
$221$		−	1.32167e7i		−	1.22446i
$222$	−3.26957e6	+	4.04588e6i	−0.298835	+	0.369789i
$223$	4.66891e6			0.421019			0.210509	−	0.977592i	$-0.432488\pi$
$223$	4.66891e6			0.421019			0.210509	+	0.977592i	$0.432488\pi$
$224$			11585.2i			0.00103077i
$225$	−2.01578e6	−	9.39066e6i	−0.176968	−	0.824420i
$226$	−9.86650e6			−0.854747
$227$			1.96525e7i			1.68012i	0.542494	+	0.840059i	$0.317480\pi$
$227$			1.96525e7i			1.68012i	−0.542494	+	0.840059i	$0.682520\pi$
$228$	−3.53338e6	−	2.85540e6i	−0.298116	−	0.240914i
$229$	−4.48178e6			−0.373202			−0.186601	−	0.982436i	$-0.559747\pi$
$229$	−4.48178e6			−0.373202			−0.186601	+	0.982436i	$0.559747\pi$
$230$		−	9.84021e6i		−	0.808762i
$231$	1152.00	−	1425.53i	9.34580e−5	−	0.000115648i
$232$	399360.			0.0319816
$233$			2.29286e6i			0.181263i	0.995884	+	0.0906316i	$0.0288886\pi$
$233$			2.29286e6i			0.181263i	−0.995884	+	0.0906316i	$0.971111\pi$
$234$	1.18944e7	−	2.55322e6i	0.928314	−	0.199270i
$235$	3.05280e7			2.35231
$236$			1.04582e7i			0.795649i
$237$	7.15180e6	+	5.77953e6i	0.537243	+	0.434158i
$238$	−50688.0			−0.00375988
$239$		−	2.64564e6i		−	0.193793i	−0.995294	−	0.0968964i	$-0.969108\pi$
$239$		−	2.64564e6i		−	0.193793i	0.995294	−	0.0968964i	$-0.0308915\pi$
$240$	2.94912e6	−	3.64935e6i	0.213333	−	0.263987i
$241$	−6.99581e6			−0.499789			−0.249894	−	0.968273i	$-0.580396\pi$
$241$	−6.99581e6			−0.499789			−0.249894	+	0.968273i	$0.580396\pi$
$242$			1.00149e7i			0.706647i
$243$	−1.38785e7	−	3.64411e6i	−0.967214	−	0.253964i
$244$	2.00211e6			0.137822
$245$			1.99650e7i			1.35760i
$246$	1.99181e6	+	1.60962e6i	0.133796	+	0.108123i
$247$	−1.55111e7			−1.02932
$248$		−	4.14498e6i		−	0.271749i
$249$	−8.42170e6	+	1.04213e7i	−0.545508	+	0.675032i
$250$	2.35200e6			0.150528
$251$		−	2.84990e7i		−	1.80223i	−0.433585	−	0.901113i	$-0.642752\pi$
$251$		−	2.84990e7i		−	1.80223i	0.433585	−	0.901113i	$-0.357248\pi$
$252$	−9792.00	−	45616.9i	−0.000611885	−	0.00285052i
$253$	−347904.			−0.0214831
$254$		−	1.29006e7i		−	0.787243i
$255$	1.59667e7	+	1.29031e7i	0.962931	+	0.778166i
$256$	1.04858e6			0.0625000
$257$		−	186812.i		−	0.0110054i	−0.999985	−	0.00550269i	$-0.998248\pi$
$257$		−	186812.i		−	0.0110054i	0.999985	−	0.00550269i	$-0.00175157\pi$
$258$	614976.	−	760994.i	0.0358096	−	0.0443121i
$259$	68116.0			0.00392058
$260$		−	1.60202e7i		−	0.911482i
$261$	−1.57248e6	+	337544.i	−0.0884430	+	0.0189850i
$262$	6.06394e6			0.337171
$263$		−	8.61541e6i		−	0.473597i	−0.971559	−	0.236798i	$-0.923902\pi$
$263$		−	8.61541e6i		−	0.473597i	0.971559	−	0.236798i	$-0.0760981\pi$
$264$	−129024.	−	104267.i	−0.00701227	−	0.00566677i
$265$	−3.26765e7			−1.75589
$266$			59487.5i			0.00316068i
$267$	6.56294e6	−	8.12123e6i	0.344798	−	0.426666i
$268$	−1.40383e7			−0.729308
$269$		−	7.55132e6i		−	0.387941i	−0.981007	−	0.193971i	$-0.937863\pi$
$269$		−	7.55132e6i		−	0.387941i	0.981007	−	0.193971i	$-0.0621367\pi$
$270$	−8.52768e6	+	1.68620e7i	−0.433251	+	0.856676i
$271$	1.39445e7			0.700642			0.350321	−	0.936630i	$-0.386073\pi$
$271$	1.39445e7			0.700642			0.350321	+	0.936630i	$0.386073\pi$
$272$			4.58775e6i			0.227978i
$273$	−123900.	−	100126.i	−0.00608952	−	0.00492108i
$274$	1.57452e7			0.765412
$275$			447174.i			0.0215020i
$276$	−5.56646e6	+	6.88815e6i	−0.264760	+	0.327624i
$277$	2.81293e7			1.32349			0.661744	−	0.749730i	$-0.269817\pi$
$277$	2.81293e7			1.32349			0.661744	+	0.749730i	$0.269817\pi$
$278$			2.58741e7i			1.20429i
$279$	3.50339e6	+	1.63209e7i	0.161316	+	0.751503i
$280$	−61440.0			−0.00279883
$281$			2.23430e7i			1.00698i	0.864000	+	0.503491i	$0.167951\pi$
$281$			2.23430e7i			1.00698i	−0.864000	+	0.503491i	$0.832049\pi$
$282$	−2.13696e7	−	1.72692e7i	−0.952904	−	0.770063i
$283$	1.01418e7			0.447464			0.223732	−	0.974651i	$-0.428176\pi$
$283$	1.01418e7			0.447464			0.223732	+	0.974651i	$0.428176\pi$
$284$			2.18309e6i			0.0953053i
$285$	1.51430e7	−	1.87386e7i	0.654152	−	0.809471i
$286$	−566400.			−0.0242117
$287$		−	33533.8i		−	0.00141853i
$288$	−4.12877e6	+	886271.i	−0.172840	+	0.0371013i
$289$	4.06512e6			0.168415
$290$			2.11793e6i			0.0868394i
$291$	−5.90281e6	−	4.77019e6i	−0.239541	−	0.193578i
$292$	2.33763e7			0.938918
$293$		−	2.78468e7i		−	1.10706i	−0.832828	−	0.553532i	$-0.813280\pi$
$293$		−	2.78468e7i		−	1.10706i	0.832828	−	0.553532i	$-0.186720\pi$
$294$	1.12939e7	−	1.39755e7i	0.444429	−	0.549953i
$295$	−5.54630e7			−2.16042
$296$		−	6.16516e6i		−	0.237722i
$297$	596160.	+	301499.i	0.0227559	+	0.0115084i
$298$	−2.52301e7			−0.953391
$299$			3.02381e7i			1.13121i
$300$	8.85360e6	+	7.15479e6i	0.327911	+	0.264992i
$301$	−12812.0			−0.000469805
$302$		−	1.24909e7i		−	0.453494i
$303$	1.60433e7	−	1.98526e7i	0.576722	−	0.713657i
$304$	5.38419e6			0.191646
$305$			1.06178e7i			0.374227i
$306$	−3.87763e6	−	1.80643e7i	−0.135333	−	0.630458i
$307$	−3.63254e7			−1.25544			−0.627718	−	0.778440i	$-0.716011\pi$
$307$	−3.63254e7			−1.25544			−0.627718	+	0.778440i	$0.716011\pi$
$308$			2172.23i			7.43454e-5i
$309$	−1.81802e7	−	1.46919e7i	−0.616204	−	0.497968i
$310$	2.19821e7			0.737877
$311$			3.59921e7i			1.19654i	0.801296	+	0.598268i	$0.204144\pi$
$311$			3.59921e7i			1.19654i	−0.801296	+	0.598268i	$0.795856\pi$
$312$	−9.06240e6	+	1.12141e7i	−0.298387	+	0.369235i
$313$	4.01099e7			1.30803			0.654016	−	0.756480i	$-0.273083\pi$
$313$	4.01099e7			1.30803			0.654016	+	0.756480i	$0.273083\pi$
$314$		−	7.29095e6i		−	0.235502i
$315$	241920.	−	51929.9i	0.00773998	−	0.00166145i
$316$	−1.08980e7			−0.345370
$317$		−	3.94377e7i		−	1.23804i	−0.785377	−	0.619018i	$-0.787531\pi$
$317$		−	3.94377e7i		−	1.23804i	0.785377	−	0.619018i	$-0.212469\pi$
$318$	2.28735e7	+	1.84846e7i	0.711299	+	0.574816i
$319$	74880.0			0.00230671
$320$			5.56091e6i			0.169706i
$321$	−2.50163e7	+	3.09560e7i	−0.756323	+	0.935902i
$322$	115968.			0.00347353
$323$			2.35570e7i			0.699058i
$324$	1.55079e7	−	6.97938e6i	0.455952	−	0.205202i
$325$	3.88662e7			1.13220
$326$			4.97755e6i			0.143669i
$327$	1.36670e7	+	1.10446e7i	0.390868	+	0.315869i
$328$	−3.03514e6			−0.0860115
$329$			359776.i			0.0101029i
$330$	552960.	−	684253.i	0.0153869	−	0.0190404i
$331$	2.78363e7			0.767586			0.383793	−	0.923419i	$-0.374618\pi$
$331$	2.78363e7			0.767586			0.383793	+	0.923419i	$0.374618\pi$
$332$		−	1.58801e7i		−	0.433949i
$333$	5.21087e6	+	2.42753e7i	0.141117	+	0.657403i
$334$	−3.37578e7			−0.906014
$335$		−	7.44495e7i		−	1.98028i
$336$	43008.0	+	34755.7i	0.00113379	+	0.000916238i
$337$	−2.37897e7			−0.621582			−0.310791	−	0.950478i	$-0.600594\pi$
$337$	−2.37897e7			−0.621582			−0.310791	+	0.950478i	$0.600594\pi$
$338$			2.19242e7i			0.567772i
$339$	−2.95995e7	+	3.66275e7i	−0.759775	+	0.940174i
$340$	−2.43302e7			−0.619027
$341$		−	777184.i		−	0.0196002i
$342$	−2.12003e7	+	4.55079e6i	−0.529984	+	0.113765i
$343$	−470588.			−0.0116616
$344$			1.15961e6i			0.0284863i
$345$	−3.65299e7	−	2.95206e7i	−0.889593	−	0.718900i
$346$	−2.36947e6			−0.0572036
$347$		−	5.34078e7i		−	1.27825i	−0.769103	−	0.639125i	$-0.779297\pi$
$347$		−	5.34078e7i		−	1.27825i	0.769103	−	0.639125i	$-0.220703\pi$
$348$	1.19808e6	−	1.48255e6i	0.0284281	−	0.0351780i
$349$	4.71677e7			1.10961			0.554803	−	0.831982i	$-0.312794\pi$
$349$	4.71677e7			1.10961			0.554803	+	0.831982i	$0.312794\pi$
$350$		−	149058.i		−	0.00347657i
$351$	2.62048e7	−	5.18154e7i	0.605983	−	1.19822i
$352$	196608.			0.00450789
$353$		−	1.75443e7i		−	0.398852i	−0.979913	−	0.199426i	$-0.936092\pi$
$353$		−	1.75443e7i		−	0.398852i	0.979913	−	0.199426i	$-0.0639078\pi$
$354$	3.88241e7	+	3.13746e7i	0.875169	+	0.707243i
$355$	−1.15776e7			−0.258782
$356$			1.23752e7i			0.274285i
$357$	−152064.	+	188170.i	−0.00334212	+	0.00413566i
$358$	−1.70899e6			−0.0372470
$359$			6.18249e7i			1.33623i	0.744059	+	0.668113i	$0.232898\pi$
$359$			6.18249e7i			1.33623i	−0.744059	+	0.668113i	$0.767102\pi$
$360$	−4.70016e6	−	2.18961e7i	−0.100741	−	0.469309i
$361$	−1.93993e7			−0.412349
$362$		−	3.66348e7i		−	0.772269i
$363$	3.71786e7	+	3.00448e7i	0.777272	+	0.628131i
$364$	188800.			0.00391469
$365$			1.23972e8i			2.54943i
$366$	6.00634e6	−	7.43246e6i	0.122509	−	0.151597i
$367$	−3.40461e7			−0.688761			−0.344381	−	0.938830i	$-0.611911\pi$
$367$	−3.40461e7			−0.688761			−0.344381	+	0.938830i	$0.611911\pi$
$368$		−	1.04962e7i		−	0.210615i
$369$	1.19508e7	−	2.56534e6i	0.237859	−	0.0510582i
$370$	3.26957e7			0.645484
$371$		−	385096.i		−	0.00754132i
$372$	−1.53875e7	−	1.24349e7i	−0.298908	−	0.241554i
$373$	−5.15781e7			−0.993892			−0.496946	−	0.867782i	$-0.665545\pi$
$373$	−5.15781e7			−0.993892			−0.496946	+	0.867782i	$0.665545\pi$
$374$			860204.i			0.0164432i
$375$	7.05600e6	−	8.73135e6i	0.133803	−	0.165572i
$376$	3.25632e7			0.612581
$377$		−	6.50821e6i		−	0.121461i
$378$	−198720.	−	100500.i	−0.00367931	−	0.00186076i
$379$	4.28828e7			0.787709			0.393855	−	0.919173i	$-0.371141\pi$
$379$	4.28828e7			0.787709			0.393855	+	0.919173i	$0.371141\pi$
$380$			2.85540e7i			0.520375i
$381$	−4.78910e7	−	3.87018e7i	−0.865923	−	0.699772i
$382$	2.84068e7			0.509603
$383$			1.51307e7i			0.269316i	0.990892	+	0.134658i	$0.0429936\pi$
$383$			1.51307e7i			0.269316i	−0.990892	+	0.134658i	$0.957006\pi$
$384$	3.14573e6	−	3.89264e6i	0.0555556	−	0.0687465i
$385$	−11520.0			−0.000201869
$386$			1.98043e7i			0.344347i
$387$	−980118.	−	4.56596e6i	−0.0169101	−	0.0787770i
$388$	8.99475e6			0.153991
$389$		−	6.15319e7i		−	1.04533i	−0.852540	−	0.522663i	$-0.824939\pi$
$389$		−	6.15319e7i		−	1.04533i	0.852540	−	0.522663i	$-0.175061\pi$
$390$	−5.94720e7	−	4.80606e7i	−1.00258	−	0.810206i
$391$	4.59233e7			0.768251
$392$			2.12960e7i			0.353541i
$393$	1.81918e7	−	2.25112e7i	0.299708	−	0.370870i
$394$	−2.74596e7			−0.448959
$395$		−	5.77953e7i		−	0.937780i
$396$	−774144.	+	166176.i	−0.0124663	+	0.00267598i
$397$	−8.55816e7			−1.36776			−0.683878	−	0.729596i	$-0.739708\pi$
$397$	−8.55816e7			−1.36776			−0.683878	+	0.729596i	$0.739708\pi$
$398$		−	5.37953e7i		−	0.853287i
$399$	220836.	+	178462.i	0.00347657	+	0.00280949i
$400$	−1.34912e7			−0.210800
$401$			4.09739e7i			0.635439i	0.948185	+	0.317719i	$0.102917\pi$
$401$			4.09739e7i			0.635439i	−0.948185	+	0.317719i	$0.897083\pi$
$402$	−4.21150e7	+	5.21147e7i	−0.648274	+	0.802198i
$403$	−6.75491e7			−1.03206
$404$			3.02516e7i			0.458780i
$405$	3.70138e7	+	8.22433e7i	0.557183	+	1.23804i
$406$	−24960.0			−0.000372964
$407$		−	1.15597e6i		−	0.0171460i
$408$	1.70312e7	+	1.37633e7i	0.250763	+	0.202647i
$409$	6.10556e7			0.892391			0.446196	−	0.894935i	$-0.352779\pi$
$409$	6.10556e7			0.892391			0.446196	+	0.894935i	$0.352779\pi$
$410$		−	1.60962e7i		−	0.233546i
$411$	4.72355e7	−	5.84509e7i	0.680366	−	0.841910i
$412$	2.77032e7			0.396131
$413$		−	653638.i		−	0.00927870i
$414$	8.87155e6	+	4.13289e7i	0.125025	+	0.582442i
$415$	8.42170e7			1.17830
$416$		−	1.70882e7i		−	0.237365i
$417$	9.60529e7	+	7.76224e7i	1.32465	+	1.07048i
$418$	1.00954e6			0.0138227
$419$		−	3.38860e7i		−	0.460657i	−0.973113	−	0.230329i	$-0.926020\pi$
$419$		−	3.38860e7i		−	0.460657i	0.973113	−	0.230329i	$-0.0739801\pi$
$420$	−184320.	+	228084.i	−0.00248785	+	0.00307856i
$421$	−1.96156e7			−0.262879			−0.131439	−	0.991324i	$-0.541960\pi$
$421$	−1.96156e7			−0.262879			−0.131439	+	0.991324i	$0.541960\pi$
$422$			3.99608e7i			0.531737i
$423$	−1.28218e8	+	2.75229e7i	−1.69405	+	0.363641i
$424$	−3.48549e7			−0.457263
$425$		−	5.90270e7i		−	0.768925i
$426$	8.10432e6	+	6.54928e6i	0.104831	+	0.0847159i
$427$	−125132.			−0.00160725
$428$		−	4.71711e7i		−	0.601651i
$429$	−1.69920e6	+	2.10265e6i	−0.0215215	+	0.0266315i
$430$	−6.14976e6			−0.0773487
$431$			4.01587e7i			0.501589i	0.968040	+	0.250795i	$0.0806919\pi$
$431$			4.01587e7i			0.501589i	−0.968040	+	0.250795i	$0.919308\pi$
$432$	−9.09619e6	+	1.79861e7i	−0.112826	+	0.223093i
$433$	−845854.			−0.0104191			−0.00520957	−	0.999986i	$-0.501658\pi$
$433$	−845854.			−0.0104191			−0.00520957	+	0.999986i	$0.501658\pi$
$434$			259061.i			0.00316908i
$435$	7.86240e6	+	6.35378e6i	0.0955185	+	0.0771906i
$436$	−2.08259e7			−0.251272
$437$		−	5.38957e7i		−	0.645817i
$438$	7.01290e7	−	8.67802e7i	0.834594	−	1.03276i
$439$	−7.48204e7			−0.884354			−0.442177	−	0.896928i	$-0.645794\pi$
$439$	−7.48204e7			−0.884354			−0.442177	+	0.896928i	$0.645794\pi$
$440$			1.04267e6i			0.0122402i
$441$	−1.79997e7	−	8.38531e7i	−0.209869	−	0.977695i
$442$	7.47648e7			0.865825
$443$			1.25246e8i			1.44063i	0.693649	+	0.720313i	$0.256002\pi$
$443$			1.25246e8i			1.44063i	−0.693649	+	0.720313i	$0.743998\pi$
$444$	−2.28870e7	−	1.84955e7i	−0.261481	−	0.211308i
$445$	−6.56294e7			−0.744764
$446$			2.64114e7i			0.297705i
$447$	−7.56904e7	+	9.36621e7i	−0.847458	+	1.04868i
$448$	−65536.0			−0.000728863
$449$		−	1.12812e8i		−	1.24628i	−0.782109	−	0.623142i	$-0.785856\pi$
$449$		−	1.12812e8i		−	1.24628i	0.782109	−	0.623142i	$-0.214144\pi$
$450$	5.31216e7	−	1.14029e7i	0.582953	−	0.125135i
$451$	−569088.			−0.00620369
$452$		−	5.58133e7i		−	0.604397i
$453$	−4.63700e7	−	3.74726e7i	−0.498818	−	0.403106i
$454$	−1.11171e8			−1.18802
$455$			1.00126e6i			0.0106295i
$456$	1.61526e7	−	1.99878e7i	0.170352	−	0.210800i
$457$	1.57358e8			1.64870			0.824350	−	0.566081i	$-0.191541\pi$
$457$	1.57358e8			1.64870			0.824350	+	0.566081i	$0.191541\pi$
$458$		−	2.53528e7i		−	0.263894i
$459$	−7.86931e7	−	3.97979e7i	−0.813764	−	0.411549i
$460$	5.56646e7			0.571881
$461$			1.83107e8i			1.86897i	0.356002	+	0.934485i	$0.384140\pi$
$461$			1.83107e8i			1.86897i	−0.356002	+	0.934485i	$0.615860\pi$
$462$	8064.00	+	6516.70i	8.17758e−5	+	6.60848e-5i
$463$	1.77978e8			1.79318			0.896588	−	0.442866i	$-0.146038\pi$
$463$	1.77978e8			1.79318			0.896588	+	0.442866i	$0.146038\pi$
$464$			2.25912e6i			0.0226144i
$465$	6.59462e7	−	8.16043e7i	0.655890	−	0.811623i
$466$	−1.29704e7			−0.128172
$467$			9.35797e7i			0.918821i	0.888224	+	0.459410i	$0.151939\pi$
$467$			9.35797e7i			0.918821i	−0.888224	+	0.459410i	$0.848061\pi$
$468$	1.44432e7	+	6.72849e7i	0.140905	+	0.656417i
$469$	877396.			0.00850505
$470$			1.72692e8i			1.66334i
$471$	−2.70663e7	−	2.18728e7i	−0.259039	−	0.209335i
$472$	−5.91606e7			−0.562609
$473$			217427.i			0.00205461i
$474$	−3.26940e7	+	4.04567e7i	−0.306996	+	0.379888i
$475$	−6.92742e7			−0.646384
$476$		−	286735.i		−	0.00265864i
$477$	1.37241e8	−	2.94598e7i	1.26453	−	0.271441i
$478$	1.49660e7			0.137032
$479$		−	1.07662e8i		−	0.979617i	−0.871830	−	0.489808i	$-0.837067\pi$
$479$		−	1.07662e8i		−	0.979617i	0.871830	−	0.489808i	$-0.162933\pi$
$480$	2.06438e7	+	1.66827e7i	0.186667	+	0.150849i
$481$	−1.00471e8			−0.902830
$482$		−	3.95743e7i		−	0.353404i
$483$	347904.	−	430509.i	0.00308758	−	0.00382068i
$484$	−5.66531e7			−0.499675
$485$			4.77019e7i			0.418129i
$486$	2.06142e7	−	7.85084e7i	0.179580	−	0.683923i
$487$	−4.14432e6			−0.0358811			−0.0179406	−	0.999839i	$-0.505711\pi$
$487$	−4.14432e6			−0.0358811			−0.0179406	+	0.999839i	$0.505711\pi$
$488$			1.13257e7i			0.0974549i
$489$	1.84782e7	+	1.49326e7i	0.158028	+	0.127706i
$490$	−1.12939e8			−0.959967
$491$		−	1.19347e8i		−	1.00824i	−0.863633	−	0.504122i	$-0.831816\pi$
$491$		−	1.19347e8i		−	1.00824i	0.863633	−	0.504122i	$-0.168184\pi$
$492$	−9.10541e6	+	1.12674e7i	−0.0764547	+	0.0946078i
$493$	−9.88416e6			−0.0824896
$494$		−	8.77440e7i		−	0.727841i
$495$	−881280.	−	4.10552e6i	−0.00726605	−	0.0338495i
$496$	2.34476e7			0.192155
$497$		−	136443.i		−	0.00111143i
$498$	−5.89519e7	−	4.76403e7i	−0.477320	−	0.385733i
$499$	1.17436e8			0.945144			0.472572	−	0.881292i	$-0.343326\pi$
$499$	1.17436e8			0.945144			0.472572	+	0.881292i	$0.343326\pi$
$500$			1.33049e7i			0.106439i
$501$	−1.01273e8	+	1.25320e8i	−0.805346	+	0.996565i
$502$	1.61215e8			1.27437
$503$		−	1.99753e8i		−	1.56960i	−0.619747	−	0.784802i	$-0.712765\pi$
$503$		−	1.99753e8i		−	1.56960i	0.619747	−	0.784802i	$-0.287235\pi$
$504$	258048.	−	55391.9i	0.00201562	−	0.000432668i
$505$	−1.60433e8			−1.24572
$506$		−	1.96804e6i		−	0.0151909i
$507$	8.13895e7	+	6.57727e7i	0.624517	+	0.504686i
$508$	7.29768e7			0.556665
$509$		−	1.12725e8i		−	0.854804i	−0.904062	−	0.427402i	$-0.859429\pi$
$509$		−	1.12725e8i		−	0.854804i	0.904062	−	0.427402i	$-0.140571\pi$
$510$	−7.29907e7	+	9.03214e7i	−0.550246	+	0.680895i
$511$	−1.46102e6			−0.0109495
$512$			5.93164e6i			0.0441942i
$513$	−4.67068e7	+	9.23543e7i	−0.345962	+	0.684077i
$514$	1.05677e6			0.00778198
$515$			1.46919e8i			1.07561i
$516$	4.30483e6	+	3.47883e6i	0.0313334	+	0.0253212i
$517$	6.10560e6			0.0441832
$518$			385322.i			0.00277227i
$519$	−7.10842e6	+	8.79622e6i	−0.0508476	+	0.0629207i
$520$	9.06240e7			0.644515
$521$			1.14581e8i			0.810215i	0.914269	+	0.405108i	$0.132766\pi$
$521$			1.14581e8i			0.810215i	−0.914269	+	0.405108i	$0.867234\pi$
$522$	−1.90944e6	−	8.89529e6i	−0.0134244	−	0.0625387i
$523$	−1.49806e8			−1.04719			−0.523594	−	0.851968i	$-0.675409\pi$
$523$	−1.49806e8			−1.04719			−0.523594	+	0.851968i	$0.675409\pi$
$524$			3.43028e7i			0.238416i
$525$	−553350.	−	447174.i	−0.00382404	−	0.00309029i
$526$	4.87361e7			0.334884
$527$			1.02588e8i			0.700916i
$528$	589824.	−	729870.i	0.00400701	−	0.00495842i
$529$	4.29689e7			0.290260
$530$		−	1.84846e8i		−	1.24160i
$531$	2.32945e8	−	5.00033e7i	1.55586	−	0.333976i
$532$	−336512.			−0.00223494
$533$			4.94624e7i			0.326658i
$534$	4.59406e7	+	3.71256e7i	0.301698	+	0.243809i
$535$	2.50163e8			1.63366
$536$		−	7.94128e7i		−	0.515699i
$537$	−5.12698e6	+	6.34431e6i	−0.0331084	+	0.0409696i
$538$	4.27167e7			0.274316
$539$			3.99300e6i			0.0254996i
$540$	−9.53856e7	−	4.82398e7i	−0.605761	−	0.306355i
$541$	−1.57017e8			−0.991644			−0.495822	−	0.868424i	$-0.665133\pi$
$541$	−1.57017e8			−0.991644			−0.495822	+	0.868424i	$0.665133\pi$
$542$			7.88822e7i			0.495429i
$543$	−1.36000e8	−	1.09904e8i	−0.849452	−	0.686461i
$544$	−2.59523e7			−0.161205
$545$		−	1.10446e8i		−	0.682277i
$546$	566400.	−	700884.i	0.00347973	−	0.00430594i
$547$	−2.79469e8			−1.70754			−0.853770	−	0.520650i	$-0.825690\pi$
$547$	−2.79469e8			−1.70754			−0.853770	+	0.520650i	$0.825690\pi$
$548$			8.90680e7i			0.541228i
$549$	−9.57260e6	−	4.45948e7i	−0.0578513	−	0.269505i
$550$	−2.52960e6			−0.0152042
$551$			1.16001e7i			0.0693434i
$552$	−3.89652e7	−	3.14887e7i	−0.231665	−	0.187213i
$553$	681124.			0.00402764
$554$			1.59123e8i			0.935847i
$555$	9.80870e7	−	1.21377e8i	0.573763	−	0.709996i
$556$	−1.46366e8			−0.851563
$557$		−	1.50294e8i		−	0.869712i	−0.900500	−	0.434856i	$-0.856799\pi$
$557$		−	1.50294e8i		−	0.869712i	0.900500	−	0.434856i	$-0.143201\pi$
$558$	−9.23247e7	+	1.98182e7i	−0.531393	+	0.114067i
$559$	1.88977e7			0.108187
$560$		−	347557.i		−	0.00197907i
$561$	3.19334e6	+	2.58061e6i	0.0180866	+	0.0146162i
$562$	−1.26391e8			−0.712044
$563$		−	8.27836e7i		−	0.463894i	−0.972728	−	0.231947i	$-0.925490\pi$
$563$		−	8.27836e7i		−	0.463894i	0.972728	−	0.231947i	$-0.0745097\pi$
$564$	9.76896e7	−	1.20885e8i	0.544516	−	0.673805i
$565$	2.95995e8			1.64111
$566$			5.73710e7i			0.316405i
$567$	−969246.	+	436211.i	−0.00531722	+	0.00239303i
$568$	−1.23494e7			−0.0673911
$569$			2.57230e8i			1.39632i	0.715942	+	0.698160i	$0.245997\pi$
$569$			2.57230e8i			1.39632i	−0.715942	+	0.698160i	$0.754003\pi$
$570$	1.06001e8	+	8.56620e7i	0.572383	+	0.462555i
$571$	2.84039e7			0.152570			0.0762852	−	0.997086i	$-0.475694\pi$
$571$	2.84039e7			0.152570			0.0762852	+	0.997086i	$0.475694\pi$
$572$		−	3.20404e6i		−	0.0171203i
$573$	8.52204e7	−	1.05455e8i	0.452980	−	0.560535i
$574$	189696.			0.00100305
$575$			1.35047e8i			0.710363i
$576$	−5.01350e6	−	2.33558e7i	−0.0262346	−	0.122216i
$577$	6.52476e7			0.339654			0.169827	−	0.985474i	$-0.445679\pi$
$577$	6.52476e7			0.339654			0.169827	+	0.985474i	$0.445679\pi$
$578$			2.29958e7i			0.119087i
$579$	7.35195e7	+	5.94128e7i	0.378763	+	0.306086i
$580$	−1.19808e7			−0.0614047
$581$			992506.i			0.00506063i
$582$	2.69843e7	−	3.33913e7i	0.136880	−	0.169381i
$583$	−6.53530e6			−0.0329807
$584$			1.32236e8i			0.663915i
$585$	−3.56832e8	+	7.65966e7i	−1.78236	+	0.382597i
$586$	1.57525e8			0.782813
$587$		−	6.66740e7i		−	0.329642i	−0.986324	−	0.164821i	$-0.947295\pi$
$587$		−	6.66740e7i		−	0.329642i	0.986324	−	0.164821i	$-0.0527046\pi$
$588$	7.90574e7	+	6.38881e7i	0.388876	+	0.314259i
$589$	1.20398e8			0.589213
$590$		−	3.13746e8i		−	1.52765i
$591$	−8.23789e7	+	1.01939e8i	−0.399074	+	0.493829i
$592$	3.48754e7			0.168095
$593$			1.53324e8i			0.735271i	0.929970	+	0.367635i	$0.119833\pi$
$593$			1.53324e8i			0.735271i	−0.929970	+	0.367635i	$0.880167\pi$
$594$	−1.70554e6	+	3.37239e6i	−0.00813770	+	0.0160908i
$595$	1.52064e6			0.00721897
$596$		−	1.42723e8i		−	0.674149i
$597$	−1.99705e8	−	1.61386e8i	−0.938568	−	0.758478i
$598$	−1.71053e8			−0.799883
$599$			2.18294e8i			1.01569i	0.861448	+	0.507846i	$0.169558\pi$
$599$			2.18294e8i			1.01569i	−0.861448	+	0.507846i	$0.830442\pi$
$600$	−4.04736e7	+	5.00835e7i	−0.187378	+	0.231868i
$601$	1.08478e8			0.499709			0.249854	−	0.968283i	$-0.419617\pi$
$601$	1.08478e8			0.499709			0.249854	+	0.968283i	$0.419617\pi$
$602$		−	72475.6i		−	0.000332202i
$603$	6.71208e7	+	3.12688e8i	0.306129	+	1.42613i
$604$	7.06590e7			0.320669
$605$		−	3.00448e8i		−	1.35676i
$606$	1.12303e8	+	9.07548e7i	0.504632	+	0.407804i
$607$	−3.43321e8			−1.53509			−0.767547	−	0.640993i	$-0.778523\pi$
$607$	−3.43321e8			−1.53509			−0.767547	+	0.640993i	$0.778523\pi$
$608$			3.04576e7i			0.135514i
$609$	−74880.0	+	92659.3i	−0.000331523	+	0.000410239i
$610$	−6.00634e7			−0.264618
$611$		−	5.30669e8i		−	2.32649i
$612$	1.02187e8	−	2.19352e7i	0.445801	−	0.0956946i
$613$	2.96325e8			1.28643			0.643216	−	0.765685i	$-0.277600\pi$
$613$	2.96325e8			1.28643			0.643216	+	0.765685i	$0.277600\pi$
$614$		−	2.05487e8i		−	0.887728i
$615$	−5.97542e7	−	4.82887e7i	−0.256888	−	0.207597i
$616$	−12288.0			−5.25701e−5
$617$		−	1.32676e8i		−	0.564853i	−0.959289	−	0.282426i	$-0.908861\pi$
$617$		−	1.32676e8i		−	0.564853i	0.959289	−	0.282426i	$-0.0911393\pi$
$618$	8.31097e7	−	1.02843e8i	0.352116	−	0.435722i
$619$	−4.14773e8			−1.74879			−0.874397	−	0.485211i	$-0.838743\pi$
$619$	−4.14773e8			−1.74879			−0.874397	+	0.485211i	$0.838743\pi$
$620$			1.24349e8i			0.521758i
$621$	1.80040e8	+	9.10527e7i	0.751787	+	0.380205i
$622$	−2.03602e8			−0.846078
$623$		−	773450.i		−	0.00319866i
$624$	−6.34368e7	−	5.12647e7i	−0.261088	−	0.210991i
$625$	−2.76419e8			−1.13221
$626$			2.26896e8i			0.924919i
$627$	3.02861e6	−	3.74771e6i	0.0122868	−	0.0152042i
$628$	4.12438e7			0.166525
$629$			1.52588e8i			0.613151i
$630$	293760.	+	1.36851e6i	0.00117482	+	0.00547300i
$631$	3.03858e8			1.20944			0.604718	−	0.796440i	$-0.293286\pi$
$631$	3.03858e8			1.20944			0.604718	+	0.796440i	$0.293286\pi$
$632$		−	6.16483e7i		−	0.244214i
$633$	1.48347e8	+	1.19882e8i	0.584881	+	0.472655i
$634$	2.23093e8			0.875424
$635$			3.87018e8i			1.51151i
$636$	−1.04565e8	+	1.29392e8i	−0.406456	+	0.502964i
$637$	3.47053e8			1.34269
$638$			423585.i			0.00163109i
$639$	4.86259e7	−	1.04379e7i	0.186365	−	0.0400047i
$640$	−3.14573e7			−0.120000
$641$		−	1.81629e8i		−	0.689622i	−0.938672	−	0.344811i	$-0.887943\pi$
$641$		−	1.81629e8i		−	0.689622i	0.938672	−	0.344811i	$-0.112057\pi$
$642$	−1.75114e8	−	1.41513e8i	−0.661782	−	0.534801i
$643$	1.73811e8			0.653798			0.326899	−	0.945059i	$-0.393996\pi$
$643$	1.73811e8			0.653798			0.326899	+	0.945059i	$0.393996\pi$
$644$			656014.i			0.00245615i
$645$	−1.84493e7	+	2.28298e7i	−0.0687544	+	0.0850792i
$646$	−1.33259e8			−0.494309
$647$			2.43137e8i			0.897713i	0.893604	+	0.448856i	$0.148168\pi$
$647$			2.43137e8i			0.897713i	−0.893604	+	0.448856i	$0.851832\pi$
$648$	3.94813e7	+	8.77261e7i	0.145100	+	0.322407i
$649$	−1.10926e7			−0.0405788
$650$			2.19861e8i			0.800585i
$651$	961716.	+	777184.i	0.00348581	+	0.00281696i
$652$	−2.81572e7			−0.101589
$653$		−	4.47562e7i		−	0.160736i	−0.996765	−	0.0803681i	$-0.974390\pi$
$653$		−	4.47562e7i		−	0.160736i	0.996765	−	0.0803681i	$-0.0256096\pi$
$654$	−6.24778e7	+	7.73123e7i	−0.223353	+	0.276386i
$655$	−1.81918e8			−0.647369
$656$		−	1.71693e7i		−	0.0608193i
$657$	−1.11768e8	−	5.20681e8i	−0.394114	−	1.83601i
$658$	−2.03520e6			−0.00714380
$659$		−	1.13574e8i		−	0.396845i	−0.980117	−	0.198423i	$-0.936418\pi$
$659$		−	1.13574e8i		−	0.396845i	0.980117	−	0.198423i	$-0.0635819\pi$
$660$	3.87072e6	+	3.12801e6i	0.0134636	+	0.0108802i
$661$	−9.93464e7			−0.343992			−0.171996	−	0.985098i	$-0.555022\pi$
$661$	−9.93464e7			−0.343992			−0.171996	+	0.985098i	$0.555022\pi$
$662$			1.57466e8i			0.542766i
$663$	2.24294e8	−	2.77550e8i	0.769623	−	0.952359i
$664$	8.98314e7			0.306849
$665$		−	1.78462e6i		−	0.00606851i
$666$	−1.37322e8	+	2.94772e7i	−0.464854	+	0.0997845i
$667$	2.26138e7			0.0762071
$668$		−	1.90963e8i		−	0.640649i
$669$	9.80472e7	+	7.92341e7i	0.327459	+	0.264627i
$670$	4.21150e8			1.40027
$671$			2.12356e6i			0.00702906i
$672$	−196608.	+	243290.i	−0.000647878	+	0.000801708i
$673$	−2.79412e8			−0.916642			−0.458321	−	0.888787i	$-0.651549\pi$
$673$	−2.79412e8			−0.916642			−0.458321	+	0.888787i	$0.651549\pi$
$674$		−	1.34575e8i		−	0.439525i
$675$	1.17034e8	−	2.31413e8i	0.380539	−	0.752447i
$676$	−1.24022e8			−0.401475
$677$			4.09293e7i			0.131907i	0.997823	+	0.0659536i	$0.0210089\pi$
$677$			4.09293e7i			0.131907i	−0.997823	+	0.0659536i	$0.978991\pi$
$678$	−2.07196e8	−	1.67440e8i	−0.664803	−	0.537242i
$679$	−562172.			−0.00179581
$680$		−	1.37633e8i		−	0.437718i
$681$	−3.33514e8	+	4.12702e8i	−1.05602	+	1.30676i
$682$	4.39642e6			0.0138594
$683$			3.74260e8i			1.17466i	0.809348	+	0.587329i	$0.199820\pi$
$683$			3.74260e8i			1.17466i	−0.809348	+	0.587329i	$0.800180\pi$
$684$	−2.57432e7	−	1.19927e8i	−0.0804440	−	0.374755i
$685$	−4.72355e8			−1.46959
$686$		−	2.66205e6i		−	0.00824600i
$687$	−9.41174e7	−	7.60584e7i	−0.290268	−	0.234572i
$688$	−6.55974e6			−0.0201429
$689$			5.68017e8i			1.73661i
$690$	1.66994e8	−	2.06644e8i	0.508339	−	0.629037i
$691$	1.15164e8			0.349047			0.174524	−	0.984653i	$-0.444161\pi$
$691$	1.15164e8			0.349047			0.174524	+	0.984653i	$0.444161\pi$
$692$		−	1.34038e7i		−	0.0404490i
$693$	48384.0	−	10386.0i	0.000145379	−	3.12067e-5i
$694$	3.02120e8			0.903859
$695$		−	7.76224e8i		−	2.31224i
$696$	8.38656e6	+	6.77736e6i	0.0248746	+	0.0201017i
$697$	7.51196e7			0.221848
$698$			2.66821e8i			0.784609i
$699$	−3.89111e7	+	4.81500e7i	−0.113931	+	0.140982i
$700$	843200.			0.00245831
$701$			5.65717e7i			0.164227i	0.996623	+	0.0821137i	$0.0261671\pi$
$701$			5.65717e7i			0.164227i	−0.996623	+	0.0821137i	$0.973833\pi$
$702$	2.93112e8	+	1.48237e8i	0.847271	+	0.428495i
$703$	1.79077e8			0.515435
$704$			1.11218e6i			0.00318756i
$705$	6.41088e8	+	5.18077e8i	1.82958	+	1.47852i
$706$	9.92456e7			0.282031
$707$		−	1.89072e6i		−	0.00535020i
$708$	−1.77482e8	+	2.19622e8i	−0.500097	+	0.618838i
$709$	−1.28652e8			−0.360975			−0.180488	−	0.983577i	$-0.557768\pi$
$709$	−1.28652e8			−0.360975			−0.180488	+	0.983577i	$0.557768\pi$
$710$		−	6.54928e7i		−	0.182986i
$711$	5.21060e7	+	2.42740e8i	0.144970	+	0.675356i
$712$	−7.00047e7			−0.193949
$713$		−	2.34710e8i		−	0.647533i
$714$	−1.06445e6	−	860204.i	−0.00292435	−	0.00236323i
$715$	1.69920e7			0.0464864
$716$		−	9.66752e6i		−	0.0263376i
$717$	4.48980e7	−	5.55585e7i	0.121806	−	0.150728i
$718$	−3.49735e8			−0.944855
$719$		−	2.01053e8i		−	0.540908i	−0.962733	−	0.270454i	$-0.912826\pi$
$719$		−	2.01053e8i		−	0.540908i	0.962733	−	0.270454i	$-0.0871738\pi$
$720$	1.23863e8	−	2.65881e7i	0.331852	−	0.0712345i
$721$	−1.73145e6			−0.00461960
$722$		−	1.09739e8i		−	0.291575i
$723$	−1.46912e8	−	1.18723e8i	−0.388725	−	0.314137i
$724$	2.07238e8			0.546076
$725$		−	2.90663e7i		−	0.0762739i
$726$	−1.69959e8	+	2.10314e8i	−0.444155	+	0.549614i
$727$	5.23208e8			1.36167			0.680833	−	0.732438i	$-0.261618\pi$
$727$	5.23208e8			1.36167			0.680833	+	0.732438i	$0.261618\pi$
$728$			1.06801e6i			0.00276811i
$729$	−2.29605e8	−	3.12051e8i	−0.592651	−	0.805459i
$730$	−7.01290e8			−1.80272
$731$		−	2.87003e7i		−	0.0734742i
$732$	4.20444e7	+	3.39770e7i	0.107195	+	0.0866266i
$733$	−6.57372e8			−1.66917			−0.834583	−	0.550882i	$-0.814291\pi$
$733$	−6.57372e8			−1.66917			−0.834583	+	0.550882i	$0.814291\pi$
$734$		−	1.92594e8i		−	0.487028i
$735$	−3.38818e8	+	4.19265e8i	−0.853304	+	1.05591i
$736$	5.93756e7			0.148927
$737$		−	1.48899e7i		−	0.0371954i
$738$	1.45117e7	+	6.76042e7i	0.0361036	+	0.168192i
$739$	3.50495e8			0.868458			0.434229	−	0.900803i	$-0.357021\pi$
$739$	3.50495e8			0.868458			0.434229	+	0.900803i	$0.357021\pi$
$740$			1.84955e8i			0.456426i
$741$	−3.25733e8	−	2.63232e8i	−0.800585	−	0.646970i
$742$	2.17843e6			0.00533252
$743$		−	4.66667e8i		−	1.13773i	−0.822429	−	0.568867i	$-0.807382\pi$
$743$		−	4.66667e8i		−	1.13773i	0.822429	−	0.568867i	$-0.192618\pi$
$744$	7.03427e7	−	8.70446e7i	0.170805	−	0.211360i
$745$	7.56904e8			1.83051
$746$		−	2.91770e8i		−	0.702788i
$747$	−3.53711e8	+	7.59267e7i	−0.848569	+	0.182152i
$748$	−4.86605e6			−0.0116271
$749$			2.94819e6i			0.00701634i
$750$	4.93920e7	+	3.99148e7i	0.117077	+	0.0946128i
$751$	−3.36993e7			−0.0795612			−0.0397806	−	0.999208i	$-0.512666\pi$
$751$	−3.36993e7			−0.0795612			−0.0397806	+	0.999208i	$0.512666\pi$
$752$			1.84205e8i			0.433160i
$753$	4.83645e8	−	5.98480e8i	1.13277	−	1.40173i
$754$	3.68160e7			0.0858860
$755$			3.74726e8i			0.870709i
$756$	568512.	−	1.12413e6i	0.00131575	−	0.00260166i
$757$	2.98552e8			0.688227			0.344113	−	0.938928i	$-0.388180\pi$
$757$	2.98552e8			0.688227			0.344113	+	0.938928i	$0.388180\pi$
$758$			2.42582e8i			0.556995i
$759$	−7.30598e6	−	5.90413e6i	−0.0167091	−	0.0135030i
$760$	−1.61526e8			−0.367960
$761$		−	3.98702e8i		−	0.904679i	−0.891846	−	0.452340i	$-0.850590\pi$
$761$		−	3.98702e8i		−	0.904679i	0.891846	−	0.452340i	$-0.149410\pi$
$762$	2.18930e8	−	2.70913e8i	0.494813	−	0.612300i
$763$	1.30162e6			0.00293029
$764$			1.60693e8i			0.360344i
$765$	1.16329e8	+	5.41928e8i	0.259839	+	1.21048i
$766$	−8.55921e7			−0.190435
$767$			9.64116e8i			2.13670i
$768$	2.20201e7	+	1.77949e7i	0.0486111	+	0.0392837i
$769$	−5.17372e8			−1.13769			−0.568845	−	0.822444i	$-0.692610\pi$

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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+5.65685i q^{2} +(21.0000 + 16.9706i) q^{3} -32.0000 q^{4} -169.706i q^{5} +(-96.0000 + 118.794i) q^{6} +2.00000 q^{7} -181.019i q^{8} +(153.000 + 712.764i) q^{9} +O(q^{10})\)	\(q+5.65685i q^{2} +(21.0000 + 16.9706i) q^{3} -32.0000 q^{4} -169.706i q^{5} +(-96.0000 + 118.794i) q^{6} +2.00000 q^{7} -181.019i q^{8} +(153.000 + 712.764i) q^{9} +960.000 q^{10} -33.9411i q^{11} +(-672.000 - 543.058i) q^{12} -2950.00 q^{13} +11.3137i q^{14} +(2880.00 - 3563.82i) q^{15} +1024.00 q^{16} +4480.23i q^{17} +(-4032.00 + 865.499i) q^{18} +5258.00 q^{19} +5430.58i q^{20} +(42.0000 + 33.9411i) q^{21} +192.000 q^{22} -10250.2i q^{23} +(3072.00 - 3801.41i) q^{24} -13175.0 q^{25} -16687.7i q^{26} +(-8883.00 + 17564.5i) q^{27} -64.0000 q^{28} +2206.17i q^{29} +(20160.0 + 16291.7i) q^{30} +22898.0 q^{31} +5792.62i q^{32} +(576.000 - 712.764i) q^{33} -25344.0 q^{34} -339.411i q^{35} +(-4896.00 - 22808.4i) q^{36} +34058.0 q^{37} +29743.7i q^{38} +(-61950.0 - 50063.2i) q^{39} -30720.0 q^{40} -16766.9i q^{41} +(-192.000 + 237.588i) q^{42} -6406.00 q^{43} +1086.12i q^{44} +(120960. - 25965.0i) q^{45} +57984.0 q^{46} +179888. i q^{47} +(21504.0 + 17377.9i) q^{48} -117645. q^{49} -74529.1i q^{50} +(-76032.0 + 94084.8i) q^{51} +94400.0 q^{52} -192548. i q^{53} +(-99360.0 - 50249.8i) q^{54} -5760.00 q^{55} -362.039i q^{56} +(110418. + 89231.2i) q^{57} -12480.0 q^{58} -326819. i q^{59} +(-92160.0 + 114042. i) q^{60} -62566.0 q^{61} +129531. i q^{62} +(306.000 + 1425.53i) q^{63} -32768.0 q^{64} +500632. i q^{65} +(4032.00 + 3258.35i) q^{66} +438698. q^{67} -143367. i q^{68} +(173952. - 215255. i) q^{69} +1920.00 q^{70} -68221.7i q^{71} +(129024. - 27696.0i) q^{72} -730510. q^{73} +192661. i q^{74} +(-276675. - 223587. i) q^{75} -168256. q^{76} -67.8823i q^{77} +(283200. - 350442. i) q^{78} +340562. q^{79} -173779. i q^{80} +(-484623. + 218106. i) q^{81} +94848.0 q^{82} +496253. i q^{83} +(-1344.00 - 1086.12i) q^{84} +760320. q^{85} -36237.8i q^{86} +(-37440.0 + 46329.6i) q^{87} -6144.00 q^{88} -386725. i q^{89} +(146880. + 684253. i) q^{90} -5900.00 q^{91} +328007. i q^{92} +(480858. + 388592. i) q^{93} -1.01760e6 q^{94} -892312. i q^{95} +(-98304.0 + 121645. i) q^{96} -281086. q^{97} -665501. i q^{98} +(24192.0 - 5192.99i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 42 q^{3} - 64 q^{4} - 192 q^{6} + 4 q^{7} + 306 q^{9}+O(q^{10}) \) 2 * q + 42 * q^3 - 64 * q^4 - 192 * q^6 + 4 * q^7 + 306 * q^9	\( 2 q + 42 q^{3} - 64 q^{4} - 192 q^{6} + 4 q^{7} + 306 q^{9} + 1920 q^{10} - 1344 q^{12} - 5900 q^{13} + 5760 q^{15} + 2048 q^{16} - 8064 q^{18} + 10516 q^{19} + 84 q^{21} + 384 q^{22} + 6144 q^{24} - 26350 q^{25} - 17766 q^{27} - 128 q^{28} + 40320 q^{30} + 45796 q^{31} + 1152 q^{33} - 50688 q^{34} - 9792 q^{36} + 68116 q^{37} - 123900 q^{39} - 61440 q^{40} - 384 q^{42} - 12812 q^{43} + 241920 q^{45} + 115968 q^{46} + 43008 q^{48} - 235290 q^{49} - 152064 q^{51} + 188800 q^{52} - 198720 q^{54} - 11520 q^{55} + 220836 q^{57} - 24960 q^{58} - 184320 q^{60} - 125132 q^{61} + 612 q^{63} - 65536 q^{64} + 8064 q^{66} + 877396 q^{67} + 347904 q^{69} + 3840 q^{70} + 258048 q^{72} - 1461020 q^{73} - 553350 q^{75} - 336512 q^{76} + 566400 q^{78} + 681124 q^{79} - 969246 q^{81} + 189696 q^{82} - 2688 q^{84} + 1520640 q^{85} - 74880 q^{87} - 12288 q^{88} + 293760 q^{90} - 11800 q^{91} + 961716 q^{93} - 2035200 q^{94} - 196608 q^{96} - 562172 q^{97} + 48384 q^{99}+O(q^{100}) \) 2 * q + 42 * q^3 - 64 * q^4 - 192 * q^6 + 4 * q^7 + 306 * q^9 + 1920 * q^10 - 1344 * q^12 - 5900 * q^13 + 5760 * q^15 + 2048 * q^16 - 8064 * q^18 + 10516 * q^19 + 84 * q^21 + 384 * q^22 + 6144 * q^24 - 26350 * q^25 - 17766 * q^27 - 128 * q^28 + 40320 * q^30 + 45796 * q^31 + 1152 * q^33 - 50688 * q^34 - 9792 * q^36 + 68116 * q^37 - 123900 * q^39 - 61440 * q^40 - 384 * q^42 - 12812 * q^43 + 241920 * q^45 + 115968 * q^46 + 43008 * q^48 - 235290 * q^49 - 152064 * q^51 + 188800 * q^52 - 198720 * q^54 - 11520 * q^55 + 220836 * q^57 - 24960 * q^58 - 184320 * q^60 - 125132 * q^61 + 612 * q^63 - 65536 * q^64 + 8064 * q^66 + 877396 * q^67 + 347904 * q^69 + 3840 * q^70 + 258048 * q^72 - 1461020 * q^73 - 553350 * q^75 - 336512 * q^76 + 566400 * q^78 + 681124 * q^79 - 969246 * q^81 + 189696 * q^82 - 2688 * q^84 + 1520640 * q^85 - 74880 * q^87 - 12288 * q^88 + 293760 * q^90 - 11800 * q^91 + 961716 * q^93 - 2035200 * q^94 - 196608 * q^96 - 562172 * q^97 + 48384 * q^99

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