LMFDB - Embedded newform 69.7.b.a.47.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(47,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("69.47");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.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:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.6
Character	$\chi$	$=$	69.47
Dual form			69.7.b.a.47.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-13.1440i q^{2} +(26.0223 - 7.20015i) q^{3} -108.766 q^{4} -47.7180i q^{5} +(-94.6390 - 342.037i) q^{6} -438.649 q^{7} +588.401i q^{8} +(625.316 - 374.728i) q^{9} +O(q^{10})$	\(q-13.1440i q^{2} +(26.0223 - 7.20015i) q^{3} -108.766 q^{4} -47.7180i q^{5} +(-94.6390 - 342.037i) q^{6} -438.649 q^{7} +588.401i q^{8} +(625.316 - 374.728i) q^{9} -627.206 q^{10} +467.227i q^{11} +(-2830.33 + 783.129i) q^{12} -1755.12 q^{13} +5765.61i q^{14} +(-343.577 - 1241.73i) q^{15} +772.958 q^{16} -1383.78i q^{17} +(-4925.44 - 8219.17i) q^{18} -8702.22 q^{19} +5190.07i q^{20} +(-11414.6 + 3158.34i) q^{21} +6141.25 q^{22} +2536.99i q^{23} +(4236.57 + 15311.5i) q^{24} +13348.0 q^{25} +23069.3i q^{26} +(13574.0 - 14253.6i) q^{27} +47709.9 q^{28} -21709.1i q^{29} +(-16321.3 + 4515.98i) q^{30} +17128.7 q^{31} +27497.9i q^{32} +(3364.11 + 12158.3i) q^{33} -18188.5 q^{34} +20931.4i q^{35} +(-68012.8 + 40757.6i) q^{36} +35827.8 q^{37} +114382. i q^{38} +(-45672.1 + 12637.1i) q^{39} +28077.3 q^{40} -74536.0i q^{41} +(41513.3 + 150034. i) q^{42} -114261. q^{43} -50818.2i q^{44} +(-17881.3 - 29838.8i) q^{45} +33346.3 q^{46} -17798.5i q^{47} +(20114.1 - 5565.42i) q^{48} +74763.6 q^{49} -175447. i q^{50} +(-9963.46 - 36009.2i) q^{51} +190896. q^{52} -224205. i q^{53} +(-187350. - 178417. i) q^{54} +22295.1 q^{55} -258101. i q^{56} +(-226451. + 62657.3i) q^{57} -285346. q^{58} -252242. i q^{59} +(37369.3 + 135057. i) q^{60} +16777.2 q^{61} -225141. i q^{62} +(-274294. + 164374. i) q^{63} +410902. q^{64} +83750.5i q^{65} +(159809. - 44217.9i) q^{66} -200619. q^{67} +150508. i q^{68} +(18266.7 + 66018.3i) q^{69} +275123. q^{70} +563192. i q^{71} +(220490. + 367936. i) q^{72} -218791. q^{73} -470922. i q^{74} +(347345. - 96107.6i) q^{75} +946502. q^{76} -204948. i q^{77} +(166102. + 600315. i) q^{78} -627095. q^{79} -36884.0i q^{80} +(250598. - 468647. i) q^{81} -979703. q^{82} -327813. i q^{83} +(1.24152e6 - 343518. i) q^{84} -66031.4 q^{85} +1.50185e6i q^{86} +(-156309. - 564921. i) q^{87} -274917. q^{88} -965167. i q^{89} +(-392202. + 235032. i) q^{90} +769879. q^{91} -275938. i q^{92} +(445728. - 123329. i) q^{93} -233944. q^{94} +415252. i q^{95} +(197989. + 715556. i) q^{96} +410660. q^{97} -982695. i q^{98} +(175083. + 292164. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 20 q^{3} - 1408 q^{4} + 95 q^{6} + 568 q^{7} - 548 q^{9}+O(q^{10}) $ 44 * q + 20 * q^3 - 1408 * q^4 + 95 * q^6 + 568 * q^7 - 548 * q^9	$ 44 q + 20 q^{3} - 1408 q^{4} + 95 q^{6} + 568 q^{7} - 548 q^{9} + 1752 q^{10} + 4075 q^{12} + 808 q^{13} + 7696 q^{15} + 36776 q^{16} + 12149 q^{18} + 28936 q^{19} - 6416 q^{21} - 7764 q^{22} - 11792 q^{24} - 129172 q^{25} - 27172 q^{27} - 25988 q^{28} - 54658 q^{30} - 72248 q^{31} + 25968 q^{33} - 32100 q^{34} - 217125 q^{36} + 260968 q^{37} + 133440 q^{39} - 227880 q^{40} + 63332 q^{42} - 187304 q^{43} + 455472 q^{45} - 164849 q^{48} + 959652 q^{49} - 218832 q^{51} - 410102 q^{52} + 882504 q^{54} + 517392 q^{55} - 572600 q^{57} - 197334 q^{58} - 854196 q^{60} + 914248 q^{61} + 885136 q^{63} - 312634 q^{64} - 816874 q^{66} - 310856 q^{67} - 395040 q^{70} + 205764 q^{72} - 227912 q^{73} + 1167580 q^{75} - 1438412 q^{76} - 6065 q^{78} + 841384 q^{79} + 1019636 q^{81} - 291126 q^{82} - 2787738 q^{84} - 2823120 q^{85} - 2899120 q^{87} - 2657340 q^{88} + 1478966 q^{90} - 2848288 q^{91} - 1992952 q^{93} + 6985482 q^{94} + 1309665 q^{96} + 1079608 q^{97} + 3251880 q^{99}+O(q^{100}) $ 44 * q + 20 * q^3 - 1408 * q^4 + 95 * q^6 + 568 * q^7 - 548 * q^9 + 1752 * q^10 + 4075 * q^12 + 808 * q^13 + 7696 * q^15 + 36776 * q^16 + 12149 * q^18 + 28936 * q^19 - 6416 * q^21 - 7764 * q^22 - 11792 * q^24 - 129172 * q^25 - 27172 * q^27 - 25988 * q^28 - 54658 * q^30 - 72248 * q^31 + 25968 * q^33 - 32100 * q^34 - 217125 * q^36 + 260968 * q^37 + 133440 * q^39 - 227880 * q^40 + 63332 * q^42 - 187304 * q^43 + 455472 * q^45 - 164849 * q^48 + 959652 * q^49 - 218832 * q^51 - 410102 * q^52 + 882504 * q^54 + 517392 * q^55 - 572600 * q^57 - 197334 * q^58 - 854196 * q^60 + 914248 * q^61 + 885136 * q^63 - 312634 * q^64 - 816874 * q^66 - 310856 * q^67 - 395040 * q^70 + 205764 * q^72 - 227912 * q^73 + 1167580 * q^75 - 1438412 * q^76 - 6065 * q^78 + 841384 * q^79 + 1019636 * q^81 - 291126 * q^82 - 2787738 * q^84 - 2823120 * q^85 - 2899120 * q^87 - 2657340 * q^88 + 1478966 * q^90 - 2848288 * q^91 - 1992952 * q^93 + 6985482 * q^94 + 1309665 * q^96 + 1079608 * q^97 + 3251880 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	13.1440i		−	1.64300i	−0.570206	−	0.821502i	$-0.693136\pi$
$2$		−	13.1440i		−	1.64300i	0.570206	−	0.821502i	$-0.306864\pi$
$3$	26.0223	−	7.20015i	0.963787	−	0.266672i
$3$	26.0223	−	7.20015i	0.963787	−	0.266672i
$4$	−108.766			−1.69946
$5$		−	47.7180i		−	0.381744i	−0.981615	−	0.190872i	$-0.938869\pi$
$5$		−	47.7180i		−	0.381744i	0.981615	−	0.190872i	$-0.0611315\pi$
$6$	−94.6390	−	342.037i	−0.438144	−	1.58351i
$7$	−438.649			−1.27886			−0.639429	−	0.768850i	$-0.720829\pi$
$7$	−438.649			−1.27886			−0.639429	+	0.768850i	$0.720829\pi$
$8$			588.401i			1.14922i
$9$	625.316	−	374.728i	0.857772	−	0.514031i
$10$	−627.206			−0.627206
$11$			467.227i			0.351035i	0.984476	+	0.175517i	$0.0561598\pi$
$11$			467.227i			0.351035i	−0.984476	+	0.175517i	$0.943840\pi$
$12$	−2830.33	+	783.129i	−1.63792	+	0.453200i
$13$	−1755.12			−0.798869			−0.399434	−	0.916762i	$-0.630793\pi$
$13$	−1755.12			−0.798869			−0.399434	+	0.916762i	$0.630793\pi$
$14$			5765.61i			2.10117i
$15$	−343.577	−	1241.73i	−0.101800	−	0.367920i
$16$	772.958			0.188710
$17$		−	1383.78i		−	0.281658i	−0.990034	−	0.140829i	$-0.955023\pi$
$17$		−	1383.78i		−	0.281658i	0.990034	−	0.140829i	$-0.0449767\pi$
$18$	−4925.44	−	8219.17i	−0.844555	−	1.40932i
$19$	−8702.22			−1.26873			−0.634365	−	0.773034i	$-0.718738\pi$
$19$	−8702.22			−1.26873			−0.634365	+	0.773034i	$0.718738\pi$
$20$			5190.07i			0.648759i
$21$	−11414.6	+	3158.34i	−1.23255	+	0.341036i
$22$	6141.25			0.576751
$23$			2536.99i			0.208514i
$23$			2536.99i			0.208514i
$24$	4236.57	+	15311.5i	0.306465	+	1.10760i
$25$	13348.0			0.854272
$26$			23069.3i			1.31254i
$27$	13574.0	−	14253.6i	0.689632	−	0.724160i
$28$	47709.9			2.17337
$29$		−	21709.1i		−	0.890120i	−0.895501	−	0.445060i	$-0.853182\pi$
$29$		−	21709.1i		−	0.890120i	0.895501	−	0.445060i	$-0.146818\pi$
$30$	−16321.3	+	4515.98i	−0.604493	+	0.167259i
$31$	17128.7			0.574963			0.287482	−	0.957786i	$-0.407182\pi$
$31$	17128.7			0.574963			0.287482	+	0.957786i	$0.407182\pi$
$32$			27497.9i			0.839168i
$33$	3364.11	+	12158.3i	0.0936112	+	0.338323i
$34$	−18188.5			−0.462765
$35$			20931.4i			0.488196i
$36$	−68012.8	+	40757.6i	−1.45775	+	0.873576i
$37$	35827.8			0.707318			0.353659	−	0.935374i	$-0.384937\pi$
$37$	35827.8			0.707318			0.353659	+	0.935374i	$0.384937\pi$
$38$			114382.i			2.08453i
$39$	−45672.1	+	12637.1i	−0.769940	+	0.213036i
$40$	28077.3			0.438707
$41$		−	74536.0i		−	1.08147i	−0.841193	−	0.540735i	$-0.818146\pi$
$41$		−	74536.0i		−	1.08147i	0.841193	−	0.540735i	$-0.181854\pi$
$42$	41513.3	+	150034.i	0.560324	+	2.02508i
$43$	−114261.			−1.43711			−0.718557	−	0.695468i	$-0.755197\pi$
$43$	−114261.			−1.43711			−0.718557	+	0.695468i	$0.755197\pi$
$44$		−	50818.2i		−	0.596570i
$45$	−17881.3	−	29838.8i	−0.196228	−	0.327449i
$46$	33346.3			0.342590
$47$		−	17798.5i		−	0.171431i	−0.996320	−	0.0857155i	$-0.972682\pi$
$47$		−	17798.5i		−	0.171431i	0.996320	−	0.0857155i	$-0.0273176\pi$
$48$	20114.1	−	5565.42i	0.181877	−	0.0503239i
$49$	74763.6			0.635480
$50$		−	175447.i		−	1.40357i
$51$	−9963.46	−	36009.2i	−0.0751103	−	0.271458i
$52$	190896.			1.35765
$53$		−	224205.i		−	1.50597i	−0.658036	−	0.752986i	$-0.728613\pi$
$53$		−	224205.i		−	1.50597i	0.658036	−	0.752986i	$-0.271387\pi$
$54$	−187350.	−	178417.i	−1.18980	−	1.13307i
$55$	22295.1			0.134005
$56$		−	258101.i		−	1.46969i
$57$	−226451.	+	62657.3i	−1.22279	+	0.338335i
$58$	−285346.			−1.46247
$59$		−	252242.i		−	1.22818i	−0.789237	−	0.614088i	$-0.789524\pi$
$59$		−	252242.i		−	1.22818i	0.789237	−	0.614088i	$-0.210476\pi$
$60$	37369.3	+	135057.i	0.173006	+	0.625266i
$61$	16777.2			0.0739145			0.0369572	−	0.999317i	$-0.488233\pi$
$61$	16777.2			0.0739145			0.0369572	+	0.999317i	$0.488233\pi$
$62$		−	225141.i		−	0.944667i
$63$	−274294.	+	164374.i	−1.09697	+	0.657373i
$64$	410902.			1.56747
$65$			83750.5i			0.304963i
$66$	159809.	−	44217.9i	0.555865	−	0.153804i
$67$	−200619.			−0.667032			−0.333516	−	0.942744i	$-0.608235\pi$
$67$	−200619.			−0.667032			−0.333516	+	0.942744i	$0.608235\pi$
$68$			150508.i			0.478667i
$69$	18266.7	+	66018.3i	0.0556050	+	0.200964i
$70$	275123.			0.802108
$71$			563192.i			1.57355i	0.617237	+	0.786777i	$0.288252\pi$
$71$			563192.i			1.57355i	−0.617237	+	0.786777i	$0.711748\pi$
$72$	220490.	+	367936.i	0.590734	+	0.985768i
$73$	−218791.			−0.562419			−0.281210	−	0.959646i	$-0.590736\pi$
$73$	−218791.			−0.562419			−0.281210	+	0.959646i	$0.590736\pi$
$74$		−	470922.i		−	1.16213i
$75$	347345.	−	96107.6i	0.823336	−	0.227811i
$76$	946502.			2.15616
$77$		−	204948.i		−	0.448924i
$78$	166102.	+	600315.i	0.350019	+	1.26501i
$79$	−627095.			−1.27190			−0.635948	−	0.771732i	$-0.719391\pi$
$79$	−627095.			−1.27190			−0.635948	+	0.771732i	$0.719391\pi$
$80$		−	36884.0i		−	0.0720390i
$81$	250598.	−	468647.i	0.471545	−	0.881842i
$82$	−979703.			−1.77686
$83$		−	327813.i		−	0.573312i	−0.958034	−	0.286656i	$-0.907456\pi$
$83$		−	327813.i		−	0.573312i	0.958034	−	0.286656i	$-0.0925437\pi$
$84$	1.24152e6	−	343518.i	2.09467	−	0.579578i
$85$	−66031.4			−0.107521
$86$			1.50185e6i			2.36118i
$87$	−156309.	−	564921.i	−0.237370	−	0.857886i
$88$	−274917.			−0.403416
$89$		−	965167.i		−	1.36909i	−0.728970	−	0.684546i	$-0.760001\pi$
$89$		−	965167.i		−	1.36909i	0.728970	−	0.684546i	$-0.239999\pi$
$90$	−392202.	+	235032.i	−0.538000	+	0.322403i
$91$	769879.			1.02164
$92$		−	275938.i		−	0.354362i
$93$	445728.	−	123329.i	0.554142	−	0.153327i
$94$	−233944.			−0.281662
$95$			415252.i			0.484329i
$96$	197989.	+	715556.i	0.223783	+	0.808779i
$97$	410660.			0.449953			0.224976	−	0.974364i	$-0.427770\pi$
$97$	410660.			0.449953			0.224976	+	0.974364i	$0.427770\pi$
$98$		−	982695.i		−	1.04410i
$99$	175083.	+	292164.i	0.180443	+	0.301107i
$100$	−1.45180e6			−1.45180
$101$			782678.i			0.759660i	0.925056	+	0.379830i	$0.124017\pi$
$101$			782678.i			0.759660i	−0.925056	+	0.379830i	$0.875983\pi$
$102$	−473306.	+	130960.i	−0.446007	+	0.123407i
$103$	1.04943e6			0.960373			0.480187	−	0.877166i	$-0.340569\pi$
$103$	1.04943e6			0.960373			0.480187	+	0.877166i	$0.340569\pi$
$104$		−	1.03271e6i		−	0.918076i
$105$	150709.	+	544683.i	0.130188	+	0.470517i
$106$	−2.94695e6			−2.47432
$107$		−	1.60297e6i		−	1.30850i	−0.756278	−	0.654251i	$-0.772984\pi$
$107$		−	1.60297e6i		−	1.30850i	0.756278	−	0.654251i	$-0.227016\pi$
$108$	−1.47639e6	+	1.55031e6i	−1.17200	+	1.23068i
$109$	−1.03170e6			−0.796658			−0.398329	−	0.917243i	$-0.630410\pi$
$109$	−1.03170e6			−0.796658			−0.398329	+	0.917243i	$0.630410\pi$
$110$		−	293048.i		−	0.220171i
$111$	932320.	−	257966.i	0.681704	−	0.188622i
$112$	−339057.			−0.241334
$113$			2.60011e6i			1.80200i	0.433815	+	0.901002i	$0.357167\pi$
$113$			2.60011e6i			1.80200i	−0.433815	+	0.901002i	$0.642833\pi$
$114$	823570.	+	2.97648e6i	0.555886	+	2.00904i
$115$	121060.			0.0795990
$116$			2.36121e6i			1.51273i
$117$	−1.09750e6	+	657691.i	−0.685247	+	0.410643i
$118$	−3.31547e6			−2.01790
$119$			606995.i			0.360200i
$120$	730634.	−	202161.i	0.422821	−	0.116991i
$121$	1.55326e6			0.876775
$122$		−	220520.i		−	0.121442i
$123$	−536670.	−	1.93959e6i	−0.288398	−	1.04231i
$124$	−1.86302e6			−0.977129
$125$		−	1.38253e6i		−	0.707856i
$126$	2.16054e6	+	3.60533e6i	1.08007	+	1.80232i
$127$	330659.			0.161425			0.0807123	−	0.996737i	$-0.474281\pi$
$127$	330659.			0.161425			0.0807123	+	0.996737i	$0.474281\pi$
$128$		−	3.64105e6i		−	1.73619i
$129$	−2.97332e6	+	822694.i	−1.38507	+	0.383239i
$130$	1.10082e6			0.501056
$131$		−	3.56316e6i		−	1.58497i	−0.609891	−	0.792485i	$-0.708787\pi$
$131$		−	3.56316e6i		−	1.58497i	0.609891	−	0.792485i	$-0.291213\pi$
$132$	−365899.	−	1.32240e6i	−0.159089	−	0.574967i
$133$	3.81722e6			1.62253
$134$			2.63694e6i			1.09594i
$135$	−680155.	−	647725.i	−0.276444	−	0.263263i
$136$	814220.			0.323687
$137$		−	1.43949e6i		−	0.559819i	−0.960026	−	0.279910i	$-0.909695\pi$
$137$		−	1.43949e6i		−	0.559819i	0.960026	−	0.279910i	$-0.0903045\pi$
$138$	867747.	−	240099.i	0.330184	−	0.0913593i
$139$	5.05611e6			1.88266			0.941331	−	0.337484i	$-0.109576\pi$
$139$	5.05611e6			1.88266			0.941331	+	0.337484i	$0.109576\pi$
$140$		−	2.27662e6i		−	0.829671i
$141$	−128152.	−	463157.i	−0.0457159	−	0.165223i
$142$	7.40262e6			2.58536
$143$		−	820037.i		−	0.280431i
$144$	483343.	−	289649.i	0.161871	−	0.0970030i
$145$	−1.03592e6			−0.339798
$146$			2.87579e6i			0.924057i
$147$	1.94552e6	−	538309.i	0.612468	−	0.169465i
$148$	−3.89683e6			−1.20206
$149$			4.37080e6i			1.32130i	0.750693	+	0.660651i	$0.229720\pi$
$149$			4.37080e6i			1.32130i	−0.750693	+	0.660651i	$0.770280\pi$
$150$	−1.26324e6	−	4.56551e6i	−0.374294	−	1.35274i
$151$	1.37902e6			0.400536			0.200268	−	0.979741i	$-0.435819\pi$
$151$	1.37902e6			0.400536			0.200268	+	0.979741i	$0.435819\pi$
$152$		−	5.12039e6i		−	1.45805i
$153$	−518543.	−	865302.i	−0.144781	−	0.241598i
$154$	−2.69385e6			−0.737583
$155$		−	817348.i		−	0.219489i
$156$	4.96755e6	−	1.37448e6i	1.30848	−	0.362047i
$157$	4.51533e6			1.16678			0.583392	−	0.812191i	$-0.301725\pi$
$157$	4.51533e6			1.16678			0.583392	+	0.812191i	$0.301725\pi$
$158$			8.24255e6i			2.08973i
$159$	−1.61431e6	−	5.83431e6i	−0.401601	−	1.45144i
$160$	1.31214e6			0.320347
$161$		−	1.11285e6i		−	0.266661i
$162$	−6.15991e6	−	3.29387e6i	−1.44887	−	0.774750i
$163$	5.06077e6			1.16857			0.584284	−	0.811550i	$-0.301376\pi$
$163$	5.06077e6			1.16857			0.584284	+	0.811550i	$0.301376\pi$
$164$			8.10695e6i			1.83792i
$165$	580169.	−	160528.i	0.129152	−	0.0357355i
$166$	−4.30878e6			−0.941955
$167$		−	1.02997e6i		−	0.221145i	−0.993868	−	0.110572i	$-0.964732\pi$
$167$		−	1.02997e6i		−	0.221145i	0.993868	−	0.110572i	$-0.0352684\pi$
$168$	−1.85837e6	−	6.71637e6i	−0.391926	−	1.41647i
$169$	−1.74638e6			−0.361808
$170$			867918.i			0.176658i
$171$	−5.44163e6	+	3.26097e6i	−1.08828	+	0.652166i
$172$	1.24276e7			2.44232
$173$			6.01110e6i			1.16096i	0.814276	+	0.580478i	$0.197134\pi$
$173$			6.01110e6i			1.16096i	−0.814276	+	0.580478i	$0.802866\pi$
$174$	−7.42534e6	+	2.05453e6i	−1.40951	+	0.390000i
$175$	−5.85508e6			−1.09249
$176$			361147.i			0.0662439i
$177$	−1.81618e6	−	6.56390e6i	−0.327521	−	1.18370i
$178$	−1.26862e7			−2.24942
$179$		−	4.79139e6i		−	0.835416i	−0.908581	−	0.417708i	$-0.862834\pi$
$179$		−	4.79139e6i		−	0.835416i	0.908581	−	0.417708i	$-0.137166\pi$
$180$	1.94487e6	+	3.24543e6i	0.333482	+	0.556487i
$181$	−4.50330e6			−0.759442			−0.379721	−	0.925101i	$-0.623980\pi$
$181$	−4.50330e6			−0.759442			−0.379721	+	0.925101i	$0.623980\pi$
$182$		−	1.01193e7i		−	1.67856i
$183$	436580.	−	120798.i	0.0712378	−	0.0197109i
$184$	−1.49277e6			−0.239629
$185$		−	1.70963e6i		−	0.270014i
$186$	−1.62105e6	−	5.85867e6i	−0.251917	−	0.910458i
$187$	646541.			0.0988716
$188$			1.93586e6i			0.291341i
$189$	−5.95423e6	+	6.25234e6i	−0.881942	+	0.926099i
$190$	5.45809e6			0.795755
$191$			1.13199e7i			1.62458i	0.583253	+	0.812290i	$0.301779\pi$
$191$			1.13199e7i			1.62458i	−0.583253	+	0.812290i	$0.698221\pi$
$192$	1.06926e7	−	2.95856e6i	1.51070	−	0.418000i
$193$	9.43706e6			1.31270			0.656349	−	0.754458i	$-0.272100\pi$
$193$	9.43706e6			1.31270			0.656349	+	0.754458i	$0.272100\pi$
$194$		−	5.39772e6i		−	0.739274i
$195$	603016.	+	2.17938e6i	0.0813252	+	0.293920i
$196$	−8.13171e6			−1.07997
$197$		−	1.11110e7i		−	1.45330i	−0.687007	−	0.726651i	$-0.741076\pi$
$197$		−	1.11110e7i		−	1.45330i	0.687007	−	0.726651i	$-0.258924\pi$
$198$	3.84022e6	−	2.30130e6i	0.494721	−	0.296468i
$199$	2.33462e6			0.296249			0.148125	−	0.988969i	$-0.452676\pi$
$199$	2.33462e6			0.296249			0.148125	+	0.988969i	$0.452676\pi$
$200$			7.85397e6i			0.981746i
$201$	−5.22055e6	+	1.44448e6i	−0.642877	+	0.177879i
$202$	1.02875e7			1.24812
$203$			9.52268e6i			1.13834i
$204$	1.08368e6	+	3.91656e6i	0.127647	+	0.461333i
$205$	−3.55670e6			−0.412844
$206$		−	1.37937e7i		−	1.57790i
$207$	950684.	+	1.58642e6i	0.107183	+	0.178858i
$208$	−1.35663e6			−0.150755
$209$		−	4.06591e6i		−	0.445368i
$210$	7.15933e6	−	1.98093e6i	0.773062	−	0.213900i
$211$	−1.24638e7			−1.32679			−0.663396	−	0.748268i	$-0.730886\pi$
$211$	−1.24638e7			−1.32679			−0.663396	+	0.748268i	$0.730886\pi$
$212$			2.43858e7i			2.55934i
$213$	4.05507e6	+	1.46555e7i	0.419623	+	1.51657i
$214$	−2.10695e7			−2.14987
$215$			5.45228e6i			0.548609i
$216$	8.38685e6	+	7.98696e6i	0.832219	+	0.792539i
$217$	−7.51350e6			−0.735297
$218$			1.35606e7i			1.30891i
$219$	−5.69342e6	+	1.57533e6i	−0.542052	+	0.149982i
$220$	−2.42494e6			−0.227737
$221$			2.42870e6i			0.225008i
$222$	−3.39071e6	−	1.22544e7i	−0.309907	−	1.12004i
$223$	−4.49582e6			−0.405410			−0.202705	−	0.979240i	$-0.564973\pi$
$223$	−4.49582e6			−0.405410			−0.202705	+	0.979240i	$0.564973\pi$
$224$		−	1.20619e7i		−	1.07318i
$225$	8.34671e6	−	5.00187e6i	0.732770	−	0.439122i
$226$	3.41759e7			2.96070
$227$			9.16978e6i			0.783937i	0.919979	+	0.391969i	$0.128206\pi$
$227$			9.16978e6i			0.783937i	−0.919979	+	0.391969i	$0.871794\pi$
$228$	2.46301e7	−	6.81496e6i	2.07808	−	0.574988i
$229$	−2.81166e6			−0.234130			−0.117065	−	0.993124i	$-0.537349\pi$
$229$	−2.81166e6			−0.234130			−0.117065	+	0.993124i	$0.537349\pi$
$230$		−	1.59122e6i		−	0.130782i
$231$	−1.47566e6	−	5.33322e6i	−0.119716	−	0.432667i
$232$	1.27737e7			1.02294
$233$		−	1.48516e7i		−	1.17410i	−0.809551	−	0.587050i	$-0.800289\pi$
$233$		−	1.48516e7i		−	1.17410i	0.809551	−	0.587050i	$-0.199711\pi$
$234$	8.64472e6	+	1.44256e7i	0.674688	+	1.12586i
$235$	−849307.			−0.0654427
$236$			2.74352e7i			2.08724i
$237$	−1.63184e7	+	4.51518e6i	−1.22584	+	0.339180i
$238$	7.97836e6			0.591811
$239$			1.99278e7i			1.45970i	0.683605	+	0.729852i	$0.260411\pi$
$239$			1.99278e7i			1.45970i	−0.683605	+	0.729852i	$0.739589\pi$
$240$	−265570.	−	959804.i	−0.0192108	−	0.0694303i
$241$	3.76495e6			0.268973			0.134486	−	0.990915i	$-0.457062\pi$
$241$	3.76495e6			0.268973			0.134486	+	0.990915i	$0.457062\pi$
$242$		−	2.04161e7i		−	1.44054i
$243$	3.14680e6	−	1.39996e7i	0.219306	−	0.975656i
$244$	−1.82478e6			−0.125615
$245$		−	3.56757e6i		−	0.242591i
$246$	−2.54941e7	+	7.05401e6i	−1.71251	+	0.473839i
$247$	1.52734e7			1.01355
$248$			1.00786e7i			0.660759i
$249$	−2.36030e6	−	8.53042e6i	−0.152887	−	0.552551i
$250$	−1.81720e7			−1.16301
$251$			2.12334e7i			1.34276i	0.741114	+	0.671379i	$0.234298\pi$
$251$			2.12334e7i			1.34276i	−0.741114	+	0.671379i	$0.765702\pi$
$252$	2.98337e7	−	1.78782e7i	1.86426	−	1.11718i
$253$	−1.18535e6			−0.0731958
$254$		−	4.34620e6i		−	0.265221i
$255$	−1.71828e6	+	475436.i	−0.103627	+	0.0286729i
$256$	−2.15603e7			−1.28509
$257$		−	1.79808e7i		−	1.05928i	−0.848223	−	0.529640i	$-0.822327\pi$
$257$		−	1.79808e7i		−	1.05928i	0.848223	−	0.529640i	$-0.177673\pi$
$258$	1.08135e7	+	3.90814e7i	0.629663	+	2.27568i
$259$	−1.57158e7			−0.904560
$260$		−	9.10917e6i		−	0.518273i
$261$	−8.13503e6	−	1.35751e7i	−0.457549	−	0.763520i
$262$	−4.68343e7			−2.60411
$263$			602396.i			0.0331143i	0.999863	+	0.0165571i	$0.00527054\pi$
$263$			602396.i			0.0331143i	−0.999863	+	0.0165571i	$0.994729\pi$
$264$	−7.15395e6	+	1.97944e6i	−0.388807	+	0.107580i
$265$	−1.06986e7			−0.574895
$266$		−	5.01736e7i		−	2.66582i
$267$	−6.94935e6	−	2.51158e7i	−0.365099	−	1.31951i
$268$	2.18204e7			1.13360
$269$			3.34553e7i			1.71873i	0.511360	+	0.859367i	$0.329142\pi$
$269$			3.34553e7i			1.71873i	−0.511360	+	0.859367i	$0.670858\pi$
$270$	−8.51371e6	+	8.93998e6i	−0.432541	+	0.454198i
$271$	−7.85369e6			−0.394608			−0.197304	−	0.980342i	$-0.563219\pi$
$271$	−7.85369e6			−0.394608			−0.197304	+	0.980342i	$0.563219\pi$
$272$		−	1.06961e6i		−	0.0531518i
$273$	2.00340e7	−	5.54324e6i	0.984644	−	0.272443i
$274$	−1.89207e7			−0.919785
$275$			6.23654e6i			0.299879i
$276$	−1.98679e6	−	7.18052e6i	−0.0944987	−	0.341530i
$277$	−2.20889e7			−1.03929			−0.519643	−	0.854384i	$-0.673935\pi$
$277$	−2.20889e7			−1.03929			−0.519643	+	0.854384i	$0.673935\pi$
$278$		−	6.64577e7i		−	3.09322i
$279$	1.07109e7	−	6.41862e6i	0.493187	−	0.295549i
$280$	−1.23161e7			−0.561045
$281$			2.53681e6i			0.114332i	0.998365	+	0.0571662i	$0.0182065\pi$
$281$			2.53681e6i			0.114332i	−0.998365	+	0.0571662i	$0.981794\pi$
$282$	−6.08775e6	+	1.68443e6i	−0.271462	+	0.0751114i
$283$	2.61532e7			1.15389			0.576947	−	0.816782i	$-0.304244\pi$
$283$	2.61532e7			1.15389			0.576947	+	0.816782i	$0.304244\pi$
$284$		−	6.12560e7i		−	2.67420i
$285$	2.98988e6	+	1.08058e7i	0.129157	+	0.466791i
$286$	−1.07786e7			−0.460749
$287$			3.26951e7i			1.38305i
$288$	1.03042e7	+	1.71948e7i	0.431358	+	0.719814i
$289$	2.22227e7			0.920669
$290$			1.36161e7i			0.558289i
$291$	1.06863e7	−	2.95681e6i	0.433659	−	0.119990i
$292$	2.37969e7			0.955810
$293$			1.89879e7i			0.754875i	0.926035	+	0.377437i	$0.123195\pi$
$293$			1.89879e7i			0.754875i	−0.926035	+	0.377437i	$0.876805\pi$
$294$	−7.07556e6	−	2.55720e7i	−0.278432	−	1.00629i
$295$	−1.20365e7			−0.468849
$296$			2.10811e7i			0.812864i
$297$	6.65969e6	+	6.34215e6i	0.254205	+	0.242085i
$298$	5.74499e7			2.17090
$299$		−	4.45272e6i		−	0.166576i
$300$	−3.77792e7	+	1.04532e7i	−1.39923	+	0.387156i
$301$	5.01203e7			1.83787
$302$		−	1.81259e7i		−	0.658082i
$303$	5.63540e6	+	2.03670e7i	0.202580	+	0.732150i
$304$	−6.72645e6			−0.239423
$305$		−	800573.i		−	0.0282164i
$306$	−1.13736e7	+	6.81575e6i	−0.396947	+	0.237875i
$307$	−1.27270e7			−0.439858			−0.219929	−	0.975516i	$-0.570583\pi$
$307$	−1.27270e7			−0.439858			−0.219929	+	0.975516i	$0.570583\pi$
$308$			2.22913e7i			0.762929i
$309$	2.73084e7	−	7.55602e6i	0.925595	−	0.256105i
$310$	−1.07432e7			−0.360621
$311$			2.96968e7i			0.987253i	0.869674	+	0.493626i	$0.164329\pi$
$311$			2.96968e7i			0.987253i	−0.869674	+	0.493626i	$0.835671\pi$
$312$	−7.43567e6	−	2.68735e7i	−0.244825	−	0.884830i
$313$	3.48981e7			1.13807			0.569035	−	0.822313i	$-0.307317\pi$
$313$	3.48981e7			1.13807			0.569035	+	0.822313i	$0.307317\pi$
$314$		−	5.93497e7i		−	1.91703i
$315$	7.84360e6	+	1.30887e7i	0.250948	+	0.418761i
$316$	6.82063e7			2.16154
$317$		−	6.16997e7i		−	1.93689i	−0.249222	−	0.968446i	$-0.580175\pi$
$317$		−	6.16997e7i		−	1.93689i	0.249222	−	0.968446i	$-0.419825\pi$
$318$	−7.66864e7	+	2.12185e7i	−2.38472	+	0.659832i
$319$	1.01431e7			0.312463
$320$		−	1.96074e7i		−	0.598370i
$321$	−1.15416e7	−	4.17129e7i	−0.348941	−	1.26112i
$322$	−1.46273e7			−0.438124
$323$			1.20420e7i			0.357348i
$324$	−2.72565e7	+	5.09727e7i	−0.801373	+	1.49866i
$325$	−2.34273e7			−0.682451
$326$		−	6.65189e7i		−	1.91996i
$327$	−2.68470e7	+	7.42836e6i	−0.767809	+	0.212447i
$328$	4.38570e7			1.24285
$329$			7.80728e6i			0.219236i
$330$	−2.10999e6	−	7.62576e6i	−0.0587135	−	0.212198i
$331$	−2.28258e7			−0.629421			−0.314711	−	0.949188i	$-0.601908\pi$
$331$	−2.28258e7			−0.629421			−0.314711	+	0.949188i	$0.601908\pi$
$332$			3.56547e7i			0.974323i
$333$	2.24037e7	−	1.34257e7i	0.606718	−	0.363583i
$334$	−1.35380e7			−0.363342
$335$			9.57311e6i			0.254635i
$336$	−8.82303e6	+	2.44126e6i	−0.232595	+	0.0643571i
$337$	4.51885e7			1.18070			0.590348	−	0.807149i	$-0.298991\pi$
$337$	4.51885e7			1.18070			0.590348	+	0.807149i	$0.298991\pi$
$338$			2.29545e7i			0.594453i
$339$	1.87212e7	+	6.76606e7i	0.480544	+	1.73675i
$340$	7.18194e6			0.182728
$341$			8.00301e6i			0.201832i
$342$	4.28623e7	+	7.15250e7i	1.07151	+	1.78805i
$343$	1.88116e7			0.466169
$344$		−	6.72310e7i		−	1.65156i
$345$	3.15026e6	−	871652.i	0.0767165	−	0.0212269i
$346$	7.90101e7			1.90745
$347$		−	3.74555e7i		−	0.896452i	−0.893920	−	0.448226i	$-0.852056\pi$
$347$		−	3.74555e7i		−	0.896452i	0.893920	−	0.448226i	$-0.147944\pi$
$348$	1.70011e7	+	6.14439e7i	0.403402	+	1.45795i
$349$	−5.13327e7			−1.20758			−0.603792	−	0.797142i	$-0.706344\pi$
$349$	−5.13327e7			−1.20758			−0.603792	+	0.797142i	$0.706344\pi$
$350$			7.69594e7i			1.79497i
$351$	−2.38240e7	+	2.50168e7i	−0.550925	+	0.578509i
$352$	−1.28477e7			−0.294577
$353$		−	4.23703e7i		−	0.963246i	−0.876378	−	0.481623i	$-0.840047\pi$
$353$		−	4.23703e7i		−	0.963246i	0.876378	−	0.481623i	$-0.159953\pi$
$354$	−8.62761e7	+	2.38719e7i	−1.94483	+	0.538118i
$355$	2.68744e7			0.600694
$356$			1.04977e8i			2.32672i
$357$	4.37046e6	+	1.57954e7i	0.0960555	+	0.347157i
$358$	−6.29782e7			−1.37259
$359$		−	4.71429e7i		−	1.01890i	−0.860499	−	0.509452i	$-0.829848\pi$
$359$		−	4.71429e7i		−	1.01890i	0.860499	−	0.509452i	$-0.170152\pi$
$360$	1.75572e7	−	1.05214e7i	0.376311	−	0.225509i
$361$	2.86827e7			0.609675
$362$			5.91915e7i			1.24777i
$363$	4.04193e7	−	1.11837e7i	0.845024	−	0.233812i
$364$	−8.37363e7			−1.73624
$365$			1.04402e7i			0.214700i
$366$	−1.58778e6	−	5.73842e6i	−0.0323852	−	0.117044i
$367$	−9.49477e7			−1.92082			−0.960409	−	0.278594i	$-0.910132\pi$
$367$	−9.49477e7			−1.92082			−0.960409	+	0.278594i	$0.910132\pi$
$368$			1.96099e6i			0.0393489i
$369$	−2.79307e7	−	4.66085e7i	−0.555909	−	0.927654i
$370$	−2.24714e7			−0.443634
$371$			9.83471e7i			1.92593i
$372$	−4.84799e7	+	1.34140e7i	−0.941744	+	0.260573i
$373$	−1.00834e7			−0.194304			−0.0971521	−	0.995270i	$-0.530973\pi$
$373$	−1.00834e7			−0.194304			−0.0971521	+	0.995270i	$0.530973\pi$
$374$		−	8.49816e6i		−	0.162446i
$375$	−9.95444e6	−	3.59766e7i	−0.188766	−	0.682223i
$376$	1.04726e7			0.197012
$377$			3.81020e7i			0.711089i
$378$	8.21810e7	+	7.82625e7i	1.52158	+	1.44903i
$379$	−9.91508e7			−1.82129			−0.910644	−	0.413192i	$-0.864414\pi$
$379$	−9.91508e7			−1.82129			−0.910644	+	0.413192i	$0.864414\pi$
$380$		−	4.51651e7i		−	0.823100i
$381$	8.60450e6	−	2.38080e6i	0.155579	−	0.0430475i
$382$	1.48789e8			2.66919
$383$		−	2.94040e7i		−	0.523372i	−0.965153	−	0.261686i	$-0.915721\pi$
$383$		−	2.94040e7i		−	0.523372i	0.965153	−	0.261686i	$-0.0842785\pi$
$384$	−2.62161e7	−	9.47483e7i	−0.462993	−	1.67331i
$385$	−9.77972e6			−0.171374
$386$		−	1.24041e8i		−	2.15677i
$387$	−7.14490e7	+	4.28167e7i	−1.23272	+	0.738721i
$388$	−4.46656e7			−0.764678
$389$		−	1.05494e8i		−	1.79217i	−0.443887	−	0.896083i	$-0.646401\pi$
$389$		−	1.05494e8i		−	1.79217i	0.443887	−	0.896083i	$-0.353599\pi$
$390$	2.86458e7	−	7.92607e6i	0.482911	−	0.133618i
$391$	3.51065e6			0.0587297
$392$			4.39910e7i			0.730307i
$393$	−2.56553e7	−	9.27214e7i	−0.422668	−	1.52757i
$394$	−1.46044e8			−2.38778
$395$			2.99237e7i			0.485538i
$396$	−1.90430e7	−	3.17774e7i	−0.306655	−	0.511721i
$397$	9.67517e7			1.54628			0.773138	−	0.634238i	$-0.218686\pi$
$397$	9.67517e7			1.54628			0.773138	+	0.634238i	$0.218686\pi$
$398$		−	3.06864e7i		−	0.486739i
$399$	9.93326e7	−	2.74845e7i	1.56377	−	0.432683i
$400$	1.03174e7			0.161210
$401$			1.94705e7i			0.301957i	0.988537	+	0.150978i	$0.0482424\pi$
$401$			1.94705e7i			0.301957i	−0.988537	+	0.150978i	$0.951758\pi$
$402$	1.89863e7	+	6.86191e7i	0.292256	+	1.05625i
$403$	−3.00629e7			−0.459320
$404$		−	8.51284e7i		−	1.29101i
$405$	−2.23629e7	−	1.19580e7i	−0.336638	−	0.180009i
$406$	1.25166e8			1.87029
$407$			1.67397e7i			0.248293i
$408$	2.11878e7	−	5.86250e6i	0.311965	−	0.0863183i
$409$	−6.68935e7			−0.977719			−0.488859	−	0.872363i	$-0.662587\pi$
$409$	−6.68935e7			−0.977719			−0.488859	+	0.872363i	$0.662587\pi$
$410$			4.67494e7i			0.678305i
$411$	−1.03646e7	−	3.74589e7i	−0.149288	−	0.539547i
$412$	−1.14141e8			−1.63212
$413$			1.10645e8i			1.57066i
$414$	2.08520e7	−	1.24958e7i	0.293864	−	0.176102i
$415$	−1.56425e7			−0.218858
$416$		−	4.82619e7i		−	0.670385i
$417$	1.31571e8	−	3.64048e7i	1.81449	−	0.502054i
$418$	−5.34425e7			−0.731741
$419$		−	4.68018e6i		−	0.0636239i	−0.999494	−	0.0318119i	$-0.989872\pi$
$419$		−	4.68018e6i		−	0.0636239i	0.999494	−	0.0318119i	$-0.0101278\pi$
$420$	−1.63920e7	−	5.92427e7i	−0.221250	−	0.799627i
$421$	−5.72930e7			−0.767813			−0.383907	−	0.923372i	$-0.625422\pi$
$421$	−5.72930e7			−0.767813			−0.383907	+	0.923372i	$0.625422\pi$
$422$			1.63825e8i			2.17993i
$423$	−6.66960e6	−	1.11297e7i	−0.0881208	−	0.147049i
$424$	1.31922e8			1.73069
$425$		−	1.84707e7i		−	0.240612i
$426$	1.92633e8	−	5.33000e7i	2.49173	−	0.689443i
$427$	−7.35929e6			−0.0945262
$428$			1.74348e8i			2.22375i
$429$	−5.90439e6	−	2.13392e7i	−0.0747831	−	0.270275i
$430$	7.16650e7			0.901367
$431$			8.59214e7i			1.07317i	0.843845	+	0.536586i	$0.180286\pi$
$431$			8.59214e7i			1.07317i	−0.843845	+	0.536586i	$0.819714\pi$
$432$	1.04922e7	−	1.10175e7i	0.130141	−	0.136657i
$433$	−8.35154e7			−1.02873			−0.514367	−	0.857570i	$-0.671973\pi$
$433$	−8.35154e7			−1.02873			−0.514367	+	0.857570i	$0.671973\pi$
$434$			9.87576e7i			1.20810i
$435$	−2.69569e7	+	7.45875e6i	−0.327493	+	0.0906146i
$436$	1.12213e8			1.35389
$437$		−	2.20775e7i		−	0.264548i
$438$	2.07061e7	+	7.48346e7i	0.246420	+	0.890594i
$439$	1.52785e8			1.80587			0.902937	−	0.429772i	$-0.141406\pi$
$439$	1.52785e8			1.80587			0.902937	+	0.429772i	$0.141406\pi$
$440$			1.31185e7i			0.154001i
$441$	4.67509e7	−	2.80161e7i	0.545097	−	0.326656i
$442$	3.19229e7			0.369688
$443$		−	3.98245e7i		−	0.458078i	−0.973417	−	0.229039i	$-0.926442\pi$
$443$		−	3.98245e7i		−	0.458078i	0.973417	−	0.229039i	$-0.0735583\pi$
$444$	−1.01404e8	+	2.80578e7i	−1.15853	+	0.320556i
$445$	−4.60558e7			−0.522642
$446$			5.90932e7i			0.666090i
$447$	3.14704e7	+	1.13738e8i	0.352355	+	1.27345i
$448$	−1.80242e8			−2.00457
$449$		−	7.81946e7i		−	0.863849i	−0.901910	−	0.431924i	$-0.857835\pi$
$449$		−	7.81946e7i		−	0.863849i	0.901910	−	0.431924i	$-0.142165\pi$
$450$	−6.57448e7	−	1.09709e8i	−0.721479	−	1.20394i
$451$	3.48252e7			0.379633
$452$		−	2.82802e8i		−	3.06244i
$453$	3.58853e7	−	9.92919e6i	0.386031	−	0.106812i
$454$	1.20528e8			1.28801
$455$		−	3.67370e7i		−	0.390005i
$456$	−3.68676e7	−	1.33244e8i	−0.388821	−	1.40525i
$457$	2.01962e7			0.211603			0.105801	−	0.994387i	$-0.466259\pi$
$457$	2.01962e7			0.211603			0.105801	+	0.994387i	$0.466259\pi$
$458$			3.69566e7i			0.384676i
$459$	−1.97240e7	−	1.87835e7i	−0.203965	−	0.194240i
$460$	−1.31672e7			−0.135276
$461$		−	4.83077e7i		−	0.493076i	−0.969133	−	0.246538i	$-0.920707\pi$
$461$		−	4.83077e7i		−	0.493076i	0.969133	−	0.246538i	$-0.0792929\pi$
$462$	−7.01000e7	+	1.93961e7i	−0.710873	+	0.196693i
$463$	−3.89946e7			−0.392882			−0.196441	−	0.980516i	$-0.562938\pi$
$463$	−3.89946e7			−0.392882			−0.196441	+	0.980516i	$0.562938\pi$
$464$		−	1.67803e7i		−	0.167975i
$465$	−5.88503e6	−	2.12692e7i	−0.0585315	−	0.211540i
$466$	−1.95210e8			−1.92905
$467$			1.04773e8i			1.02872i	0.857574	+	0.514360i	$0.171971\pi$
$467$			1.04773e8i			1.02872i	−0.857574	+	0.514360i	$0.828029\pi$
$468$	1.19370e8	−	7.15342e7i	1.16455	−	0.697873i
$469$	8.80011e7			0.853040
$470$			1.11633e7i			0.107523i
$471$	1.17499e8	−	3.25111e7i	1.12453	−	0.311149i
$472$	1.48419e8			1.41145
$473$		−	5.33857e7i		−	0.504477i
$474$	5.93476e7	+	2.14490e8i	0.557273	+	2.01406i
$475$	−1.16157e8			−1.08384
$476$		−	6.60202e7i		−	0.612147i
$477$	−8.40159e7	−	1.40199e8i	−0.774116	−	1.29178i
$478$	2.61931e8			2.39830
$479$		−	5.93897e7i		−	0.540386i	−0.962806	−	0.270193i	$-0.912912\pi$
$479$		−	5.93897e7i		−	0.540386i	0.962806	−	0.270193i	$-0.0870876\pi$
$480$	3.41449e7	−	9.44762e6i	0.308746	−	0.0854277i
$481$	−6.28819e7			−0.565054
$482$		−	4.94867e7i		−	0.441924i
$483$	−8.01268e6	−	2.89588e7i	−0.0711110	−	0.257004i
$484$	−1.68941e8			−1.49005
$485$		−	1.95958e7i		−	0.171767i
$486$	−1.84011e8	−	4.13617e7i	−1.60301	−	0.360321i
$487$	−1.72005e8			−1.48921			−0.744603	−	0.667508i	$-0.767361\pi$
$487$	−1.72005e8			−1.48921			−0.744603	+	0.667508i	$0.767361\pi$
$488$			9.87170e6i			0.0849440i
$489$	1.31693e8	−	3.64383e7i	1.12625	−	0.311625i
$490$	−4.68922e7			−0.398577
$491$			9.17685e7i			0.775263i	0.921814	+	0.387631i	$0.126707\pi$
$491$			9.17685e7i			0.775263i	−0.921814	+	0.387631i	$0.873293\pi$
$492$	5.83713e7	+	2.10961e8i	0.490122	+	1.77136i
$493$	−3.00408e7			−0.250709
$494$		−	2.00754e8i		−	1.66526i
$495$	1.39415e7	−	8.35461e6i	0.114946	−	0.0688828i
$496$	1.32398e7			0.108502
$497$		−	2.47044e8i		−	2.01235i
$498$	−1.12124e8	+	3.10239e7i	−0.907844	+	0.251193i
$499$	−1.43737e8			−1.15682			−0.578411	−	0.815745i	$-0.696327\pi$
$499$	−1.43737e8			−1.15682			−0.578411	+	0.815745i	$0.696327\pi$
$500$			1.50372e8i			1.20298i
$501$	−7.41597e6	−	2.68022e7i	−0.0589732	−	0.213137i
$502$	2.79092e8			2.20616
$503$		−	1.52303e7i		−	0.119675i	−0.998208	−	0.0598376i	$-0.980942\pi$
$503$		−	1.52303e7i		−	0.119675i	0.998208	−	0.0598376i	$-0.0190583\pi$
$504$	−9.67178e7	−	1.61395e8i	−0.755466	−	1.26066i
$505$	3.73478e7			0.289995
$506$			1.55803e7i			0.120261i
$507$	−4.54447e7	+	1.25742e7i	−0.348706	+	0.0964843i
$508$	−3.59644e7			−0.274335
$509$		−	8.28996e7i		−	0.628636i	−0.949318	−	0.314318i	$-0.898224\pi$
$509$		−	8.28996e7i		−	0.628636i	0.949318	−	0.314318i	$-0.101776\pi$
$510$	6.24914e6	+	2.25852e7i	0.0471097	+	0.170260i
$511$	9.59722e7			0.719255
$512$			5.03625e7i			0.375230i
$513$	−1.18124e8	+	1.24038e8i	−0.874956	+	0.918764i
$514$	−2.36341e8			−1.74040
$515$		−	5.00764e7i		−	0.366616i
$516$	3.23395e8	−	8.94808e7i	2.35388	−	0.651300i
$517$	8.31593e6			0.0601782
$518$			2.06569e8i			1.48620i
$519$	4.32808e7	+	1.56422e8i	0.309595	+	1.11891i
$520$	−4.92788e7			−0.350470
$521$			8.24421e7i			0.582956i	0.956577	+	0.291478i	$0.0941471\pi$
$521$			8.24421e7i			0.582956i	−0.956577	+	0.291478i	$0.905853\pi$
$522$	−1.78431e8	+	1.06927e8i	−1.25447	+	0.751755i
$523$	1.53801e8			1.07511			0.537557	−	0.843227i	$-0.319347\pi$
$523$	1.53801e8			1.07511			0.537557	+	0.843227i	$0.319347\pi$
$524$			3.87549e8i			2.69360i
$525$	−1.52362e8	+	4.21575e7i	−1.05293	+	0.291338i
$526$	7.91792e6			0.0544069
$527$		−	2.37025e7i		−	0.161943i
$528$	2.60031e6	+	9.39786e6i	0.0176654	+	0.0638450i
$529$	−6.43634e6			−0.0434783
$530$			1.40623e8i			0.944556i
$531$	−9.45221e7	−	1.57731e8i	−0.631321	−	1.05350i
$532$	−4.15182e8			−2.75742
$533$			1.30819e8i			0.863953i
$534$	−3.30123e8	+	9.13425e7i	−2.16796	+	0.599859i
$535$	−7.64905e7			−0.499512
$536$		−	1.18044e8i		−	0.766567i
$537$	−3.44987e7	−	1.24683e8i	−0.222782	−	0.805163i
$538$	4.39738e8			2.82389
$539$			3.49316e7i			0.223076i
$540$	7.39775e7	+	7.04501e7i	0.469805	+	0.447405i
$541$	4.09218e6			0.0258442			0.0129221	−	0.999917i	$-0.495887\pi$
$541$	4.09218e6			0.0258442			0.0129221	+	0.999917i	$0.495887\pi$
$542$			1.03229e8i			0.648342i
$543$	−1.17186e8	+	3.24244e7i	−0.731941	+	0.202522i
$544$	3.80511e7			0.236358
$545$			4.92304e7i			0.304119i
$546$	−7.28606e7	−	2.63327e8i	−0.447625	−	1.61777i
$547$	3.02740e8			1.84973			0.924865	−	0.380297i	$-0.124178\pi$
$547$	3.02740e8			1.84973			0.924865	+	0.380297i	$0.124178\pi$
$548$			1.56567e8i			0.951392i
$549$	1.04910e7	−	6.28689e6i	0.0634018	−	0.0379943i
$550$	8.19733e7			0.492702
$551$			1.88918e8i			1.12932i
$552$	−3.88452e7	+	1.07482e7i	−0.230951	+	0.0639024i
$553$	2.75074e8			1.62658
$554$			2.90337e8i			1.70755i
$555$	−1.23096e7	−	4.44884e7i	−0.0720053	−	0.260236i
$556$	−5.49931e8			−3.19951
$557$			8.02028e7i			0.464113i	0.972702	+	0.232056i	$0.0745454\pi$
$557$			8.02028e7i			0.464113i	−0.972702	+	0.232056i	$0.925455\pi$
$558$	−8.43666e7	−	1.40784e8i	−0.485588	−	0.810309i
$559$	2.00541e8			1.14807
$560$			1.61791e7i			0.0921278i
$561$	1.68245e7	−	4.65520e6i	0.0952912	−	0.0263663i
$562$	3.33440e7			0.187849
$563$			2.83697e7i			0.158976i	0.996836	+	0.0794878i	$0.0253285\pi$
$563$			2.83697e7i			0.158976i	−0.996836	+	0.0794878i	$0.974672\pi$
$564$	1.39385e7	+	5.03755e7i	0.0776925	+	0.280790i
$565$	1.24072e8			0.687903
$566$		−	3.43759e8i		−	1.89585i
$567$	−1.09925e8	+	2.05571e8i	−0.603039	+	1.12775i
$568$	−3.31383e8			−1.80836
$569$			6.78733e7i			0.368436i	0.982885	+	0.184218i	$0.0589752\pi$
$569$			6.78733e7i			0.368436i	−0.982885	+	0.184218i	$0.941025\pi$
$570$	1.42032e8	−	3.92991e7i	0.766939	−	0.212206i
$571$	2.43127e8			1.30595			0.652973	−	0.757381i	$-0.273521\pi$
$571$	2.43127e8			1.30595			0.652973	+	0.757381i	$0.273521\pi$
$572$			8.91918e7i			0.476581i
$573$	8.15048e7	+	2.94569e8i	0.433231	+	1.56575i
$574$	4.29745e8			2.27235
$575$			3.38638e7i			0.178128i
$576$	2.56943e8	−	1.53977e8i	1.34453	−	0.805726i
$577$	1.03787e8			0.540276			0.270138	−	0.962822i	$-0.412931\pi$
$577$	1.03787e8			0.540276			0.270138	+	0.962822i	$0.412931\pi$
$578$		−	2.92096e8i		−	1.51266i
$579$	2.45574e8	−	6.79483e7i	1.26516	−	0.350060i
$580$	1.12672e8			0.577473
$581$			1.43795e8i			0.733186i
$582$	−3.88644e7	−	1.40461e8i	−0.197144	−	0.712503i
$583$	1.04754e8			0.528648
$584$		−	1.28737e8i		−	0.646343i
$585$	3.13837e7	+	5.23705e7i	0.156760	+	0.261589i
$586$	2.49578e8			1.24026
$587$			3.17170e8i			1.56811i	0.620689	+	0.784057i	$0.286853\pi$
$587$			3.17170e8i			1.56811i	−0.620689	+	0.784057i	$0.713147\pi$
$588$	−2.11605e8	+	5.85496e7i	−1.04087	+	0.287999i
$589$	−1.49058e8			−0.729473
$590$			1.58208e8i			0.770320i
$591$	−8.00011e7	−	2.89134e8i	−0.387555	−	1.40067i
$592$	2.76934e7			0.133478
$593$			6.00909e6i			0.0288167i	0.999896	+	0.0144084i	$0.00458649\pi$
$593$			6.00909e6i			0.0288167i	−0.999896	+	0.0144084i	$0.995414\pi$
$594$	8.33614e7	−	8.75352e7i	0.397746	−	0.417660i
$595$	2.89646e7			0.137504
$596$		−	4.75393e8i		−	2.24550i
$597$	6.07521e7	−	1.68096e7i	0.285521	−	0.0790015i
$598$	−5.85267e7			−0.273685
$599$		−	8.48092e7i		−	0.394605i	−0.980343	−	0.197303i	$-0.936782\pi$
$599$		−	8.48092e7i		−	0.394605i	0.980343	−	0.197303i	$-0.0632181\pi$
$600$	5.65498e7	+	2.04378e8i	0.261805	+	0.946194i
$601$	−1.76865e8			−0.814739			−0.407369	−	0.913264i	$-0.633554\pi$
$601$	−1.76865e8			−0.814739			−0.407369	+	0.913264i	$0.633554\pi$
$602$		−	6.58783e8i		−	3.01962i
$603$	−1.25450e8	+	7.51775e7i	−0.572161	+	0.342875i
$604$	−1.49990e8			−0.680695
$605$		−	7.41184e7i		−	0.334703i
$606$	2.67705e8	−	7.40719e7i	1.20293	−	0.332840i
$607$	1.04600e8			0.467696			0.233848	−	0.972273i	$-0.424868\pi$
$607$	1.04600e8			0.467696			0.233848	+	0.972273i	$0.424868\pi$
$608$		−	2.39292e8i		−	1.06468i
$609$	6.85648e7	+	2.47802e8i	0.303563	+	1.09712i
$610$	−1.05228e7			−0.0463596
$611$			3.12384e7i			0.136951i
$612$	5.63997e7	+	9.41151e7i	0.246049	+	0.410587i
$613$	−2.15018e8			−0.933457			−0.466728	−	0.884401i	$-0.654567\pi$
$613$	−2.15018e8			−0.933457			−0.466728	+	0.884401i	$0.654567\pi$
$614$			1.67285e8i			0.722688i
$615$	−9.25535e7	+	2.56088e7i	−0.397894	+	0.110094i
$616$	1.20592e8			0.515912
$617$		−	3.41175e8i		−	1.45252i	−0.687421	−	0.726259i	$-0.741257\pi$
$617$		−	3.41175e8i		−	1.45252i	0.687421	−	0.726259i	$-0.258743\pi$
$618$	−9.93166e7	−	3.58943e8i	−0.420781	−	1.52076i
$619$	−3.67538e8			−1.54964			−0.774820	−	0.632182i	$-0.782160\pi$
$619$	−3.67538e8			−1.54964			−0.774820	+	0.632182i	$0.782160\pi$
$620$			8.88994e7i			0.373013i
$621$	3.61614e7	+	3.44372e7i	0.150998	+	0.143798i
$622$	3.90336e8			1.62206
$623$			4.23369e8i			1.75087i
$624$	−3.53026e7	+	9.76795e6i	−0.145296	+	0.0402022i
$625$	1.42591e8			0.584052
$626$		−	4.58702e8i		−	1.86985i
$627$	−2.92752e7	−	1.05804e8i	−0.118767	−	0.429240i
$628$	−4.91113e8			−1.98291
$629$		−	4.95779e7i		−	0.199222i
$630$	1.72039e8	−	1.03096e8i	0.688026	−	0.412308i
$631$	−1.51162e8			−0.601665			−0.300832	−	0.953677i	$-0.597265\pi$
$631$	−1.51162e8			−0.601665			−0.300832	+	0.953677i	$0.597265\pi$
$632$		−	3.68983e8i		−	1.46169i
$633$	−3.24336e8	+	8.97412e7i	−1.27875	+	0.353819i
$634$	−8.10983e8			−3.18232
$635$		−	1.57784e7i		−	0.0616228i
$636$	1.75581e8	+	6.34572e8i	0.682506	+	2.46666i
$637$	−1.31219e8			−0.507665
$638$		−	1.33321e8i		−	0.513378i
$639$	2.11044e8	+	3.52173e8i	0.808855	+	1.34975i
$640$	−1.73743e8			−0.662778
$641$		−	1.68399e8i		−	0.639391i	−0.947520	−	0.319696i	$-0.896419\pi$
$641$		−	1.68399e8i		−	0.639391i	0.947520	−	0.319696i	$-0.103581\pi$
$642$	−5.48276e8	+	1.51704e8i	−2.07202	+	0.573312i
$643$	2.32415e8			0.874241			0.437120	−	0.899403i	$-0.355998\pi$
$643$	2.32415e8			0.874241			0.437120	+	0.899403i	$0.355998\pi$
$644$			1.21040e8i			0.453180i
$645$	3.92573e7	+	1.41881e8i	0.146299	+	0.528743i
$646$	1.58280e8			0.587123
$647$		−	4.13125e8i		−	1.52535i	−0.646783	−	0.762674i	$-0.723886\pi$
$647$		−	4.13125e8i		−	1.52535i	0.646783	−	0.762674i	$-0.276114\pi$
$648$	2.75752e8	+	1.47452e8i	1.01343	+	0.541909i
$649$	1.17854e8			0.431132
$650$			3.07929e8i			1.12127i
$651$	−1.95518e8	+	5.40983e7i	−0.708670	+	0.196083i
$652$	−5.50438e8			−1.98594
$653$			8.11047e7i			0.291277i	0.989338	+	0.145639i	$0.0465237\pi$
$653$			8.11047e7i			0.291277i	−0.989338	+	0.145639i	$0.953476\pi$
$654$	9.76387e7	+	3.52878e8i	0.349051	+	1.26151i
$655$	−1.70027e8			−0.605052
$656$		−	5.76132e7i		−	0.204085i
$657$	−1.36813e8	+	8.19870e7i	−0.482427	+	0.289101i
$658$	1.02619e8			0.360206
$659$		−	9.51846e7i		−	0.332591i	−0.986076	−	0.166295i	$-0.946819\pi$
$659$		−	9.51846e7i		−	0.332591i	0.986076	−	0.166295i	$-0.0531805\pi$
$660$	−6.31024e7	+	1.74599e7i	−0.219490	+	0.0607311i
$661$	7.53072e7			0.260755			0.130377	−	0.991464i	$-0.458381\pi$
$661$	7.53072e7			0.260755			0.130377	+	0.991464i	$0.458381\pi$
$662$			3.00023e8i			1.03414i
$663$	1.74870e7	+	6.32003e7i	0.0600033	+	0.216859i
$664$	1.92885e8			0.658862
$665$		−	1.82150e8i		−	0.619389i
$666$	−1.76468e8	−	2.94475e8i	−0.597369	−	0.996839i
$667$	5.50760e7			0.185603
$668$			1.12026e8i			0.375827i
$669$	−1.16991e8	+	3.23706e7i	−0.390729	+	0.108112i
$670$	1.25829e8			0.418367
$671$			7.83875e6i			0.0259465i
$672$	−8.68475e7	−	3.13878e8i	−0.286187	−	1.03431i
$673$	1.93197e8			0.633804			0.316902	−	0.948458i	$-0.397357\pi$
$673$	1.93197e8			0.633804			0.316902	+	0.948458i	$0.397357\pi$
$674$		−	5.93959e8i		−	1.93989i
$675$	1.81186e8	−	1.90258e8i	0.589133	−	0.618630i
$676$	1.89946e8			0.614880
$677$		−	4.17072e8i		−	1.34414i	−0.740486	−	0.672071i	$-0.765405\pi$
$677$		−	4.17072e8i		−	1.34414i	0.740486	−	0.672071i	$-0.234595\pi$
$678$	8.89333e8	−	2.46071e8i	2.85348	−	0.789536i
$679$	−1.80135e8			−0.575426
$680$		−	3.88529e7i		−	0.123565i
$681$	6.60238e7	+	2.38618e8i	0.209054	+	0.755549i
$682$	1.05192e8			0.331611
$683$			1.19914e8i			0.376365i	0.982134	+	0.188182i	$0.0602596\pi$
$683$			1.19914e8i			0.376365i	−0.982134	+	0.188182i	$0.939740\pi$
$684$	5.91862e8	−	3.54681e8i	1.84949	−	1.10833i
$685$	−6.86897e7			−0.213707
$686$		−	2.47260e8i		−	0.765918i
$687$	−7.31658e7	+	2.02444e7i	−0.225651	+	0.0624360i
$688$	−8.83187e7			−0.271199
$689$			3.93505e8i			1.20307i
$690$	−1.14570e7	−	4.14071e7i	−0.0348758	−	0.126046i
$691$	−2.72661e8			−0.826398			−0.413199	−	0.910641i	$-0.635589\pi$
$691$	−2.72661e8			−0.826398			−0.413199	+	0.910641i	$0.635589\pi$
$692$		−	6.53801e8i		−	1.97300i
$693$	−7.68000e7	−	1.28157e8i	−0.230761	−	0.385074i
$694$	−4.92316e8			−1.47287
$695$		−	2.41267e8i		−	0.718694i
$696$	3.32400e8	−	9.19724e7i	0.985900	−	0.272791i
$697$	−1.03142e8			−0.304604
$698$			6.74719e8i			1.98407i
$699$	−1.06934e8	−	3.86471e8i	−0.313100	−	1.13158i
$700$	6.36831e8			1.85665
$701$		−	1.66698e8i		−	0.483923i	−0.970286	−	0.241961i	$-0.922209\pi$
$701$		−	1.66698e8i		−	0.483923i	0.970286	−	0.241961i	$-0.0777907\pi$
$702$	3.28822e8	+	3.13143e8i	0.950493	+	0.905173i
$703$	−3.11781e8			−0.897396
$704$			1.91984e8i			0.550235i
$705$	−2.21009e7	+	6.11514e6i	−0.0630729	+	0.0174518i
$706$	−5.56917e8			−1.58262
$707$		−	3.43321e8i		−	0.971497i
$708$	1.97538e8	+	7.13926e8i	0.556609	+	2.01166i
$709$	6.65594e8			1.86754			0.933771	−	0.357870i	$-0.116497\pi$
$709$	6.65594e8			1.86754			0.933771	+	0.357870i	$0.116497\pi$
$710$		−	3.53238e8i		−	0.986943i
$711$	−3.92132e8	+	2.34990e8i	−1.09100	+	0.653794i
$712$	5.67905e8			1.57339
$713$			4.34555e7i			0.119888i
$714$	2.07615e8	−	5.74454e7i	0.570380	−	0.157820i
$715$	−3.91305e7			−0.107053
$716$			5.21139e8i			1.41976i
$717$	1.43483e8	+	5.18565e8i	0.389263	+	1.40684i
$718$	−6.19648e8			−1.67406
$719$			1.92657e7i			0.0518319i	0.999664	+	0.0259160i	$0.00825023\pi$
$719$			1.92657e7i			0.0518319i	−0.999664	+	0.0259160i	$0.991750\pi$
$720$	−1.38215e7	−	2.30641e7i	−0.0370303	−	0.0617930i
$721$	−4.60329e8			−1.22818
$722$		−	3.77006e8i		−	1.00170i
$723$	9.79726e7	−	2.71082e7i	0.259233	−	0.0717276i
$724$	4.89804e8			1.29064
$725$		−	2.89773e8i		−	0.760404i
$726$	−1.46999e8	−	5.31273e8i	−0.384153	−	1.38838i
$727$	−9.45293e7			−0.246016			−0.123008	−	0.992406i	$-0.539254\pi$
$727$	−9.45293e7			−0.246016			−0.123008	+	0.992406i	$0.539254\pi$
$728$			4.52997e8i			1.17409i
$729$	−1.89124e7	−	3.86959e8i	−0.0488162	−	0.998808i
$730$	1.37227e8			0.352753
$731$			1.58112e8i			0.404774i
$732$	−4.74849e7	+	1.31387e7i	−0.121066	+	0.0334980i
$733$	−3.68891e8			−0.936670			−0.468335	−	0.883551i	$-0.655146\pi$
$733$	−3.68891e8			−0.936670			−0.468335	+	0.883551i	$0.655146\pi$
$734$			1.24800e9i			3.15591i
$735$	−2.56870e7	−	9.28361e7i	−0.0646922	−	0.233806i
$736$	−6.97619e7			−0.174979
$737$		−	9.37344e7i		−	0.234151i
$738$	−6.12624e8	+	3.67123e8i	−1.52414	+	0.913360i
$739$	2.23448e8			0.553660			0.276830	−	0.960919i	$-0.410716\pi$
$739$	2.23448e8			0.553660			0.276830	+	0.960919i	$0.410716\pi$
$740$			1.85949e8i			0.458879i
$741$	3.97448e8	−	1.09971e8i	0.976845	−	0.270285i
$742$	1.29268e9			3.16431
$743$			4.41555e8i			1.07651i	0.842782	+	0.538255i	$0.180916\pi$
$743$			4.41555e8i			1.07651i	−0.842782	+	0.538255i	$0.819084\pi$
$744$	7.25671e7	+	2.62267e8i	0.176206	+	0.636831i
$745$	2.08566e8			0.504398
$746$			1.32537e8i			0.319243i
$747$	−1.22841e8	−	2.04986e8i	−0.294700	−	0.491771i
$748$	−7.03215e7			−0.168029
$749$			7.03141e8i			1.67339i
$750$	−4.72878e8	+	1.30842e8i	−1.12090	+	0.310143i
$751$	4.94253e8			1.16689			0.583445	−	0.812153i	$-0.301704\pi$
$751$	4.94253e8			1.16689			0.583445	+	0.812153i	$0.301704\pi$
$752$		−	1.37575e7i		−	0.0323508i
$753$	1.52884e8	+	5.52540e8i	0.358077	+	1.29413i
$754$	5.00814e8			1.16832
$755$		−	6.58042e7i		−	0.152902i
$756$	6.47615e8	−	6.80040e8i	1.49883	−	1.57387i
$757$	−4.04593e8			−0.932675			−0.466338	−	0.884607i	$-0.654427\pi$
$757$	−4.04593e8			−0.932675			−0.466338	+	0.884607i	$0.654427\pi$
$758$			1.30324e9i			2.99238i
$759$	−3.08455e7	+	8.53472e6i	−0.0705451	+	0.0195193i
$760$	−2.44335e8			−0.556601
$761$			2.81422e8i			0.638563i	0.947660	+	0.319281i	$0.103441\pi$
$761$			2.81422e8i			0.638563i	−0.947660	+	0.319281i	$0.896559\pi$
$762$	−3.12933e7	−	1.13098e8i	−0.0707272	−	0.255617i
$763$	4.52552e8			1.01881
$764$		−	1.23121e9i		−	2.76091i
$765$	−4.12904e7	+	2.47438e7i	−0.0922285	+	0.0552691i
$766$	−3.86488e8			−0.859903
$767$			4.42713e8i			0.981152i
$768$	−5.61048e8	+	1.55238e8i	−1.23856	+	0.342699i
$769$	1.19887e8			0.263629			0.131815	−	0.991274i	$-0.457920\pi$
$769$	1.19887e8			0.263629			0.131815	+	0.991274i	$0.457920\pi$
$770$			1.28545e8i			0.281568i
$771$	−1.29465e8	−	4.67902e8i	−0.282481	−	1.02092i
$772$	−1.02643e9			−2.23088
$773$		−	3.25069e8i		−	0.703781i	−0.936041	−	0.351890i	$-0.885539\pi$
$773$		−	3.25069e8i		−	0.703781i	0.936041	−	0.351890i	$-0.114461\pi$
$774$	5.62784e8	+	9.39128e8i	1.21372	+	2.02536i
$775$	2.28634e8			0.491175
$776$			2.41632e8i			0.517094i
$777$	−4.08961e8	+	1.13156e8i	−0.871804	+	0.241221i
$778$	−1.38661e9			−2.94454
$779$			6.48628e8i			1.37209i
$780$	−6.55874e7	−	2.37041e8i	−0.138209	−	0.499505i
$781$	−2.63139e8			−0.552372
$782$		−	4.61441e7i		−	0.0964931i
$783$	−3.09434e8	−	2.94680e8i	−0.644590	−	0.613855i
$784$	5.77892e7			0.119922
$785$		−	2.15462e8i		−	0.445413i
$786$	−1.21873e9	+	3.37214e8i	−2.50981	+	0.694445i
$787$	5.71669e8			1.17279			0.586395	−	0.810025i	$-0.300546\pi$
$787$	5.71669e8			1.17279			0.586395	+	0.810025i	$0.300546\pi$
$788$			1.20850e9i			2.46983i
$789$	4.33735e6	+	1.56757e7i	0.00883066	+	0.0319151i
$790$	3.93318e8			0.797742
$791$		−	1.14053e9i		−	2.30451i
$792$	−1.71910e8	+	1.03019e8i	−0.346039	+	0.207368i
$793$	−2.94459e7			−0.0590480
$794$		−	1.27171e9i		−	2.54054i
$795$	−2.78401e8	+	7.70315e7i	−0.554077	+	0.153309i
$796$	−2.53927e8			−0.503465
$797$		−	8.06138e8i		−	1.59234i	−0.605076	−	0.796168i	$-0.706857\pi$
$797$		−	8.06138e8i		−	1.59234i	0.605076	−	0.796168i	$-0.293143\pi$
$798$	−3.61258e8	−	1.30563e9i	−0.710900	−	2.56928i
$799$	−2.46293e7			−0.0482849
$800$			3.67041e8i			0.716877i
$801$	−3.61675e8	−	6.03534e8i	−0.703755	−	1.17437i
$802$	2.55921e8			0.496116
$803$		−	1.02225e8i		−	0.197428i
$804$	5.67816e8	−	1.57110e8i	1.09255	−	0.302299i
$805$	−5.31029e7			−0.101796
$806$			3.95148e8i			0.754665i
$807$	2.40883e8	+	8.70583e8i	0.458339	+	1.65649i
$808$	−4.60528e8			−0.873016
$809$		−	4.61773e8i		−	0.872134i	−0.899914	−	0.436067i	$-0.856371\pi$
$809$		−	4.61773e8i		−	0.872134i	0.899914	−	0.436067i	$-0.143629\pi$
$810$	−1.57177e8	+	2.93938e8i	−0.295756	+	0.553097i
$811$	−4.48371e8			−0.840572			−0.420286	−	0.907392i	$-0.638070\pi$
$811$	−4.48371e8			−0.840572			−0.420286	+	0.907392i	$0.638070\pi$
$812$		−	1.03574e9i		−	1.93456i
$813$	−2.04371e8	+	5.65477e7i	−0.380318	+	0.105231i
$814$	2.20027e8			0.407947
$815$		−	2.41490e8i		−	0.446093i
$816$	−7.70134e6	−	2.78336e7i	−0.0141741	−	0.0512270i
$817$	9.94321e8			1.82331
$818$			8.79250e8i			1.60640i
$819$	4.81417e8	−	2.88495e8i	0.876335	−	0.525155i
$820$	3.86847e8			0.701613
$821$		−	1.03690e8i		−	0.187373i	−0.995602	−	0.0936866i	$-0.970135\pi$
$821$		−	1.03690e8i		−	0.187373i	0.995602	−	0.0936866i	$-0.0298652\pi$
$822$	−4.92360e8	+	1.36232e8i	−0.886477	+	0.245281i
$823$	−3.43017e8			−0.615341			−0.307670	−	0.951493i	$-0.599549\pi$
$823$	−3.43017e8			−0.615341			−0.307670	+	0.951493i	$0.599549\pi$
$824$			6.17483e8i			1.10368i
$825$	4.49041e7	+	1.62289e8i	0.0799694	+	0.289019i
$826$	1.45433e9			2.58061
$827$			6.88470e8i			1.21722i	0.793470	+	0.608609i	$0.208272\pi$
$827$			6.88470e8i			1.21722i	−0.793470	+	0.608609i	$0.791728\pi$
$828$	−1.03402e8	−	1.72548e8i	−0.182153	−	0.303962i
$829$	−4.69708e8			−0.824451			−0.412225	−	0.911082i	$-0.635248\pi$
$829$	−4.69708e8			−0.824451			−0.412225	+	0.911082i	$0.635248\pi$
$830$			2.05606e8i			0.359585i
$831$	−5.74803e8	+	1.59043e8i	−1.00165	+	0.277149i
$832$	−7.21180e8			−1.25220
$833$		−	1.03457e8i		−	0.178988i
$834$	−4.78506e8	−	1.72938e9i	−0.824877	−	2.98121i
$835$	−4.91482e7			−0.0844206
$836$			4.42231e8i			0.756886i
$837$	2.32506e8	−	2.44147e8i	0.396513	−	0.416366i
$838$	−6.15164e7			−0.104534
$839$		−	1.62289e8i		−	0.274792i	−0.990516	−	0.137396i	$-0.956127\pi$
$839$		−	1.62289e8i		−	0.274792i	0.990516	−	0.137396i	$-0.0438733\pi$
$840$	−3.20492e8	+	8.86775e7i	−0.540728	+	0.149615i
$841$	1.23537e8			0.207686
$842$			7.53062e8i			1.26152i
$843$	1.82654e7	+	6.60136e7i	0.0304893	+	0.110192i
$844$	1.35563e9			2.25483
$845$			8.33337e7i			0.138118i
$846$	−1.46289e8	+	8.76654e7i	−0.241602	+	0.144783i
$847$	−6.81335e8			−1.12127
$848$		−	1.73301e8i		−	0.284193i
$849$	6.80566e8	−	1.88307e8i	1.11211	−	0.307711i
$850$	−2.42780e8			−0.395327
$851$			9.08949e7i			0.147486i
$852$	−4.41052e8	−	1.59402e9i	−0.713134	−	2.57736i
$853$	−2.37056e7			−0.0381948			−0.0190974	−	0.999818i	$-0.506079\pi$
$853$	−2.37056e7			−0.0381948			−0.0190974	+	0.999818i	$0.506079\pi$
$854$			9.67307e7i			0.155307i
$855$	1.55607e8	+	2.59664e8i	0.248960	+	0.415444i
$856$	9.43189e8			1.50376
$857$		−	9.85633e8i		−	1.56593i	−0.622065	−	0.782965i	$-0.713706\pi$
$857$		−	9.85633e8i		−	1.56593i	0.622065	−	0.782965i	$-0.286294\pi$
$858$	−2.80483e8	+	7.76075e7i	−0.444064	+	0.122869i
$859$	1.92332e8			0.303440			0.151720	−	0.988424i	$-0.451519\pi$
$859$	1.92332e8			0.303440			0.151720	+	0.988424i	$0.451519\pi$
$860$		−	5.93021e8i		−	0.932341i
$861$	2.35410e8	+	8.50800e8i	0.368820	+	1.33296i
$862$	1.12935e9			1.76323
$863$		−	2.25340e8i		−	0.350595i	−0.984516	−	0.175297i	$-0.943911\pi$
$863$		−	2.25340e8i		−	0.350595i	0.984516	−	0.175297i	$-0.0560887\pi$
$864$	3.91945e8	+	3.73256e8i	0.607692	+	0.578717i
$865$	2.86837e8			0.443187
$866$			1.09773e9i			1.69021i
$867$	5.78285e8	−	1.60007e8i	0.887329	−	0.245517i
$868$	8.17210e8			1.24961
$869$		−	2.92995e8i		−	0.446480i
$870$	9.80381e7	+	3.54322e8i	0.148880	+	0.538072i
$871$	3.52109e8			0.532871
$872$		−	6.07050e8i		−	0.915535i
$873$	2.56792e8	−	1.53886e8i	0.385957	−	0.231289i
$874$	−2.90187e8			−0.434654
$875$			6.06446e8i			0.905249i
$876$	6.19249e8	−	1.71341e8i	0.921198	−	0.254888i
$877$	1.38759e8			0.205713			0.102857	−	0.994696i	$-0.467202\pi$
$877$	1.38759e8			0.205713			0.102857	+	0.994696i	$0.467202\pi$
$878$		−	2.00821e9i		−	2.96706i
$879$	1.36716e8	+	4.94109e8i	0.201304	+	0.727538i
$880$	1.72332e7			0.0252882
$881$		−	6.99820e8i		−	1.02343i	−0.859155	−	0.511716i	$-0.829010\pi$
$881$		−	6.99820e8i		−	1.02343i	0.859155	−	0.511716i	$-0.170990\pi$
$882$	−3.68244e8	−	6.14495e8i	−0.536698	−	0.895597i
$883$	−1.15606e9			−1.67919			−0.839595	−	0.543212i	$-0.817208\pi$
$883$	−1.15606e9			−1.67919			−0.839595	+	0.543212i	$0.817208\pi$
$884$		−	2.64159e8i		−	0.382392i
$885$	−3.13216e8	+	8.66643e7i	−0.451870	+	0.125029i
$886$	−5.23455e8			−0.752624
$887$			6.38591e8i			0.915064i	0.889193	+	0.457532i	$0.151267\pi$
$887$			6.38591e8i			0.915064i	−0.889193	+	0.457532i	$0.848733\pi$
$888$	1.51787e8	+	5.48578e8i	0.216768	+	0.783428i
$889$	−1.45043e8			−0.206439
$890$			6.05359e8i			0.858703i
$891$	2.18965e8	+	1.17086e8i	0.309557	+	0.165528i
$892$	4.88990e8			0.688978
$893$			1.54886e8i			0.217500i
$894$	1.49498e9	−	4.13648e8i	2.09229	−	0.578920i
$895$	−2.28635e8			−0.318915
$896$			1.59714e9i			2.22034i
$897$	−3.20602e7	−	1.15870e8i	−0.0444211	−	0.160544i
$898$	−1.02779e9			−1.41931
$899$		−	3.71850e8i		−	0.511786i
$900$	−9.07835e8	+	5.44032e8i	−1.24532	+	0.746271i
$901$	−3.10251e8			−0.424169
$902$		−	4.57744e8i		−	0.623739i
$903$	1.30424e9	−	3.60874e8i	1.77131	−	0.490108i
$904$	−1.52990e9			−2.07090
$905$			2.14888e8i			0.289912i
$906$	−1.30510e8	−	4.71678e8i	−0.175492	−	0.634251i
$907$	8.59272e8			1.15162			0.575810	−	0.817584i	$-0.304687\pi$
$907$	8.59272e8			1.15162			0.575810	+	0.817584i	$0.304687\pi$
$908$		−	9.97356e8i		−	1.33227i
$909$	2.93292e8	+	4.89421e8i	0.390488	+	0.651615i
$910$	−4.82873e8			−0.640780
$911$		−	5.70761e8i		−	0.754917i	−0.926026	−	0.377459i	$-0.876798\pi$
$911$		−	5.70761e8i		−	0.754917i	0.926026	−	0.377459i	$-0.123202\pi$
$912$	−1.75037e8	+	4.84315e7i	−0.230752	+	0.0638474i
$913$	1.53163e8			0.201252
$914$		−	2.65460e8i		−	0.347665i
$915$	−5.76425e6	−	2.08327e7i	−0.00752453	−	0.0271946i
$916$	3.05812e8			0.397895
$917$			1.56297e9i			2.02695i
$918$	−2.46891e8	+	2.59253e8i	−0.319137	+	0.335116i
$919$	−1.24445e8			−0.160337			−0.0801683	−	0.996781i	$-0.525546\pi$
$919$	−1.24445e8			−0.160337			−0.0801683	+	0.996781i	$0.525546\pi$
$920$			7.12319e7i			0.0914768i
$921$	−3.31186e8	+	9.16366e7i	−0.423929	+	0.117298i
$922$	−6.34958e8			−0.810125
$923$		−	9.88467e8i		−	1.25706i
$924$	1.60501e8	+	5.80071e8i	0.203452	+	0.735301i
$925$	4.78229e8			0.604242
$926$			5.12547e8i			0.645506i
$927$	6.56222e8	−	3.93250e8i	0.823781	−	0.493661i
$928$	5.96955e8			0.746960
$929$		−	3.60163e8i		−	0.449212i	−0.974450	−	0.224606i	$-0.927890\pi$
$929$		−	3.60163e8i		−	0.449212i	0.974450	−	0.224606i	$-0.0721095\pi$
$930$	−2.79564e8	+	7.73530e7i	−0.347562	+	0.0961675i
$931$	−6.50609e8			−0.806253
$932$			1.61534e9i			1.99534i
$933$	2.13821e8	+	7.72778e8i	0.263273	+	0.951502i
$934$	1.37714e9			1.69019
$935$		−	3.08516e7i		−	0.0377436i
$936$	−3.86986e8	−	6.45770e8i	−0.471919	−	0.787500i
$937$	1.04784e9			1.27373			0.636864	−	0.770976i	$-0.280231\pi$
$937$	1.04784e9			1.27373			0.636864	+	0.770976i	$0.280231\pi$
$938$		−	1.15669e9i		−	1.40155i
$939$	9.08127e8	−	2.51272e8i	1.09686	−	0.303492i
$940$	9.23754e7			0.111217
$941$			7.79093e8i			0.935019i	0.883988	+	0.467510i	$0.154849\pi$
$941$			7.79093e8i			0.935019i	−0.883988	+	0.467510i	$0.845151\pi$
$942$	−4.27327e8	−	1.54441e9i	−0.511219	−	1.84761i
$943$	1.89097e8			0.225502
$944$		−	1.94972e8i		−	0.231770i
$945$	2.98349e8	+	2.84123e8i	0.353532	+	0.336676i
$946$	−7.01703e8			−0.828857
$947$		−	4.69199e8i		−	0.552468i	−0.961090	−	0.276234i	$-0.910914\pi$
$947$		−	4.69199e8i		−	0.552468i	0.961090	−	0.276234i	$-0.0890864\pi$
$948$	1.77488e9	−	4.91096e8i	2.08327	−	0.576423i
$949$	3.84003e8			0.449299
$950$			1.52677e9i			1.78075i
$951$	−4.44248e8	−	1.60557e9i	−0.516516	−	1.86675i
$952$	−3.57156e8			−0.413950
$953$		−	9.62658e8i		−	1.11223i	−0.831106	−	0.556114i	$-0.812292\pi$
$953$		−	9.62658e8i		−	1.11223i	0.831106	−	0.556114i	$-0.187708\pi$
$954$	−1.84278e9	+	1.10431e9i	−2.12240	+	1.27188i
$955$	5.40161e8			0.620173
$956$		−	2.16746e9i		−	2.48071i
$957$	2.63946e8	−	7.30318e7i	0.301148	−	0.0833252i
$958$	−7.80620e8			−0.887857
$959$			6.31432e8i			0.715930i
$960$	−1.41176e8	−	5.10229e8i	−0.159569	−	0.576702i
$961$	−5.94110e8			−0.669417
$962$			8.26522e8i			0.928387i
$963$	−6.00679e8	−	1.00236e9i	−0.672610	−	1.12240i
$964$	−4.09497e8			−0.457109
$965$		−	4.50317e8i		−	0.501114i
$966$	−3.80636e8	+	1.05319e8i	−0.422259	+	0.116836i
$967$	−8.54062e8			−0.944518			−0.472259	−	0.881460i	$-0.656561\pi$
$967$	−8.54062e8			−0.944518			−0.472259	+	0.881460i	$0.656561\pi$
$968$			9.13939e8i			1.00761i
$969$	8.67042e7	+	3.13360e8i	0.0952947	+	0.344407i
$970$	−2.57568e8			−0.282213
$971$		−	1.50964e8i		−	0.164899i	−0.996595	−	0.0824493i	$-0.973726\pi$
$971$		−	1.50964e8i		−	0.164899i	0.996595	−	0.0824493i	$-0.0262742\pi$
$972$	−3.42264e8	+	1.52267e9i	−0.372702	+	1.65809i
$973$	−2.21786e9			−2.40766
$974$			2.26084e9i			2.44677i
$975$	−6.09630e8	+	1.68680e8i	−0.657738	+	0.181991i
$976$	1.29681e7			0.0139484
$977$			9.24430e8i			0.991266i	0.868532	+	0.495633i	$0.165064\pi$
$977$			9.24430e8i			0.991266i	−0.868532	+	0.495633i	$0.834936\pi$
$978$	−4.78946e8	−	1.73097e9i	−0.512000	−	1.85043i
$979$	4.50952e8			0.480598
$980$			3.88029e8i			0.412274i
$981$	−6.45135e8	+	3.86606e8i	−0.683351	+	0.409507i
$982$	1.20621e9			1.27376
$983$			4.02848e8i			0.424112i	0.977258	+	0.212056i	$0.0680159\pi$
$983$			4.02848e8i			0.424112i	−0.977258	+	0.212056i	$0.931984\pi$
$984$	1.14126e9	−	3.15777e8i	1.19784	−	0.331433i
$985$	−5.30196e8			−0.554789
$986$			3.94857e8i			0.411916i
$987$	5.62136e7	+	2.03163e8i	0.0584642	+	0.211297i
$988$	−1.66122e9			−1.72249
$989$		−	2.89879e8i		−	0.299659i
$990$	−1.09813e8	−	1.83247e8i	−0.113175	−	0.188857i
$991$	2.91744e8			0.299765			0.149883	−	0.988704i	$-0.452110\pi$
$991$	2.91744e8			0.299765			0.149883	+	0.988704i	$0.452110\pi$
$992$			4.71003e8i			0.482491i
$993$	−5.93978e8	+	1.64349e8i	−0.606628	+	0.167849i
$994$	−3.24715e9			−3.30631
$995$		−	1.11403e8i		−	0.113091i
$996$	2.56719e8	+	9.27816e8i	0.259825	+	0.939040i
$997$	5.14453e8			0.519111			0.259556	−	0.965728i	$-0.416424\pi$
$997$	5.14453e8			0.519111			0.259556	+	0.965728i	$0.416424\pi$
$998$			1.88928e9i			1.90066i
$999$	4.86327e8	−	5.10677e8i	0.487789	−	0.512212i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.b.a.47.6	✓	44
3.2	odd	2	inner	69.7.b.a.47.39	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.b.a.47.6	✓	44	1.1	even	1	trivial
69.7.b.a.47.39	yes	44	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-13.1440i q^{2} +(26.0223 - 7.20015i) q^{3} -108.766 q^{4} -47.7180i q^{5} +(-94.6390 - 342.037i) q^{6} -438.649 q^{7} +588.401i q^{8} +(625.316 - 374.728i) q^{9} +O(q^{10})\)	\(q-13.1440i q^{2} +(26.0223 - 7.20015i) q^{3} -108.766 q^{4} -47.7180i q^{5} +(-94.6390 - 342.037i) q^{6} -438.649 q^{7} +588.401i q^{8} +(625.316 - 374.728i) q^{9} -627.206 q^{10} +467.227i q^{11} +(-2830.33 + 783.129i) q^{12} -1755.12 q^{13} +5765.61i q^{14} +(-343.577 - 1241.73i) q^{15} +772.958 q^{16} -1383.78i q^{17} +(-4925.44 - 8219.17i) q^{18} -8702.22 q^{19} +5190.07i q^{20} +(-11414.6 + 3158.34i) q^{21} +6141.25 q^{22} +2536.99i q^{23} +(4236.57 + 15311.5i) q^{24} +13348.0 q^{25} +23069.3i q^{26} +(13574.0 - 14253.6i) q^{27} +47709.9 q^{28} -21709.1i q^{29} +(-16321.3 + 4515.98i) q^{30} +17128.7 q^{31} +27497.9i q^{32} +(3364.11 + 12158.3i) q^{33} -18188.5 q^{34} +20931.4i q^{35} +(-68012.8 + 40757.6i) q^{36} +35827.8 q^{37} +114382. i q^{38} +(-45672.1 + 12637.1i) q^{39} +28077.3 q^{40} -74536.0i q^{41} +(41513.3 + 150034. i) q^{42} -114261. q^{43} -50818.2i q^{44} +(-17881.3 - 29838.8i) q^{45} +33346.3 q^{46} -17798.5i q^{47} +(20114.1 - 5565.42i) q^{48} +74763.6 q^{49} -175447. i q^{50} +(-9963.46 - 36009.2i) q^{51} +190896. q^{52} -224205. i q^{53} +(-187350. - 178417. i) q^{54} +22295.1 q^{55} -258101. i q^{56} +(-226451. + 62657.3i) q^{57} -285346. q^{58} -252242. i q^{59} +(37369.3 + 135057. i) q^{60} +16777.2 q^{61} -225141. i q^{62} +(-274294. + 164374. i) q^{63} +410902. q^{64} +83750.5i q^{65} +(159809. - 44217.9i) q^{66} -200619. q^{67} +150508. i q^{68} +(18266.7 + 66018.3i) q^{69} +275123. q^{70} +563192. i q^{71} +(220490. + 367936. i) q^{72} -218791. q^{73} -470922. i q^{74} +(347345. - 96107.6i) q^{75} +946502. q^{76} -204948. i q^{77} +(166102. + 600315. i) q^{78} -627095. q^{79} -36884.0i q^{80} +(250598. - 468647. i) q^{81} -979703. q^{82} -327813. i q^{83} +(1.24152e6 - 343518. i) q^{84} -66031.4 q^{85} +1.50185e6i q^{86} +(-156309. - 564921. i) q^{87} -274917. q^{88} -965167. i q^{89} +(-392202. + 235032. i) q^{90} +769879. q^{91} -275938. i q^{92} +(445728. - 123329. i) q^{93} -233944. q^{94} +415252. i q^{95} +(197989. + 715556. i) q^{96} +410660. q^{97} -982695. i q^{98} +(175083. + 292164. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 20 q^{3} - 1408 q^{4} + 95 q^{6} + 568 q^{7} - 548 q^{9}+O(q^{10}) \) 44 * q + 20 * q^3 - 1408 * q^4 + 95 * q^6 + 568 * q^7 - 548 * q^9	\( 44 q + 20 q^{3} - 1408 q^{4} + 95 q^{6} + 568 q^{7} - 548 q^{9} + 1752 q^{10} + 4075 q^{12} + 808 q^{13} + 7696 q^{15} + 36776 q^{16} + 12149 q^{18} + 28936 q^{19} - 6416 q^{21} - 7764 q^{22} - 11792 q^{24} - 129172 q^{25} - 27172 q^{27} - 25988 q^{28} - 54658 q^{30} - 72248 q^{31} + 25968 q^{33} - 32100 q^{34} - 217125 q^{36} + 260968 q^{37} + 133440 q^{39} - 227880 q^{40} + 63332 q^{42} - 187304 q^{43} + 455472 q^{45} - 164849 q^{48} + 959652 q^{49} - 218832 q^{51} - 410102 q^{52} + 882504 q^{54} + 517392 q^{55} - 572600 q^{57} - 197334 q^{58} - 854196 q^{60} + 914248 q^{61} + 885136 q^{63} - 312634 q^{64} - 816874 q^{66} - 310856 q^{67} - 395040 q^{70} + 205764 q^{72} - 227912 q^{73} + 1167580 q^{75} - 1438412 q^{76} - 6065 q^{78} + 841384 q^{79} + 1019636 q^{81} - 291126 q^{82} - 2787738 q^{84} - 2823120 q^{85} - 2899120 q^{87} - 2657340 q^{88} + 1478966 q^{90} - 2848288 q^{91} - 1992952 q^{93} + 6985482 q^{94} + 1309665 q^{96} + 1079608 q^{97} + 3251880 q^{99}+O(q^{100}) \) 44 * q + 20 * q^3 - 1408 * q^4 + 95 * q^6 + 568 * q^7 - 548 * q^9 + 1752 * q^10 + 4075 * q^12 + 808 * q^13 + 7696 * q^15 + 36776 * q^16 + 12149 * q^18 + 28936 * q^19 - 6416 * q^21 - 7764 * q^22 - 11792 * q^24 - 129172 * q^25 - 27172 * q^27 - 25988 * q^28 - 54658 * q^30 - 72248 * q^31 + 25968 * q^33 - 32100 * q^34 - 217125 * q^36 + 260968 * q^37 + 133440 * q^39 - 227880 * q^40 + 63332 * q^42 - 187304 * q^43 + 455472 * q^45 - 164849 * q^48 + 959652 * q^49 - 218832 * q^51 - 410102 * q^52 + 882504 * q^54 + 517392 * q^55 - 572600 * q^57 - 197334 * q^58 - 854196 * q^60 + 914248 * q^61 + 885136 * q^63 - 312634 * q^64 - 816874 * q^66 - 310856 * q^67 - 395040 * q^70 + 205764 * q^72 - 227912 * q^73 + 1167580 * q^75 - 1438412 * q^76 - 6065 * q^78 + 841384 * q^79 + 1019636 * q^81 - 291126 * q^82 - 2787738 * q^84 - 2823120 * q^85 - 2899120 * q^87 - 2657340 * q^88 + 1478966 * q^90 - 2848288 * q^91 - 1992952 * q^93 + 6985482 * q^94 + 1309665 * q^96 + 1079608 * q^97 + 3251880 * q^99

Introduction

L-functions

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