LMFDB - Embedded newform 69.7.b.a.47.11

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			47.11
Character	$\chi$	$=$	69.47
Dual form			69.7.b.a.47.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.52809i q^{2} +(-24.3830 + 11.5961i) q^{3} -26.7846 q^{4} -179.250i q^{5} +(110.488 + 232.324i) q^{6} -22.6651 q^{7} -354.592i q^{8} +(460.063 - 565.494i) q^{9} +O(q^{10})$	\(q-9.52809i q^{2} +(-24.3830 + 11.5961i) q^{3} -26.7846 q^{4} -179.250i q^{5} +(110.488 + 232.324i) q^{6} -22.6651 q^{7} -354.592i q^{8} +(460.063 - 565.494i) q^{9} -1707.91 q^{10} -1077.81i q^{11} +(653.089 - 310.596i) q^{12} -829.623 q^{13} +215.955i q^{14} +(2078.59 + 4370.66i) q^{15} -5092.80 q^{16} +6996.04i q^{17} +(-5388.08 - 4383.52i) q^{18} -3648.50 q^{19} +4801.14i q^{20} +(552.643 - 262.826i) q^{21} -10269.5 q^{22} -2536.99i q^{23} +(4111.87 + 8646.02i) q^{24} -16505.6 q^{25} +7904.73i q^{26} +(-4660.22 + 19123.4i) q^{27} +607.075 q^{28} +16187.7i q^{29} +(41644.0 - 19805.0i) q^{30} -3761.99 q^{31} +25830.8i q^{32} +(12498.4 + 26280.4i) q^{33} +66659.0 q^{34} +4062.72i q^{35} +(-12322.6 + 15146.5i) q^{36} +58209.4 q^{37} +34763.2i q^{38} +(20228.7 - 9620.36i) q^{39} -63560.6 q^{40} -3839.45i q^{41} +(-2504.23 - 5265.64i) q^{42} -144053. q^{43} +28868.8i q^{44} +(-101365. - 82466.3i) q^{45} -24172.7 q^{46} -9992.83i q^{47} +(124178. - 59056.4i) q^{48} -117135. q^{49} +157267. i q^{50} +(-81126.6 - 170585. i) q^{51} +22221.1 q^{52} -212996. i q^{53} +(182209. + 44403.0i) q^{54} -193198. q^{55} +8036.86i q^{56} +(88961.4 - 42308.2i) q^{57} +154238. q^{58} +66724.0i q^{59} +(-55674.3 - 117066. i) q^{60} +173578. q^{61} +35844.6i q^{62} +(-10427.4 + 12817.0i) q^{63} -79821.1 q^{64} +148710. i q^{65} +(250402. - 119086. i) q^{66} -397423. q^{67} -187386. i q^{68} +(29419.1 + 61859.6i) q^{69} +38710.0 q^{70} -397462. i q^{71} +(-200520. - 163135. i) q^{72} +582901. q^{73} -554625. i q^{74} +(402456. - 191400. i) q^{75} +97723.5 q^{76} +24428.8i q^{77} +(-91663.7 - 192741. i) q^{78} +289748. q^{79} +912884. i q^{80} +(-108125. - 520325. i) q^{81} -36582.7 q^{82} +536851. i q^{83} +(-14802.3 + 7039.68i) q^{84} +1.25404e6 q^{85} +1.37255e6i q^{86} +(-187713. - 394704. i) q^{87} -382184. q^{88} -158999. i q^{89} +(-785746. + 965813. i) q^{90} +18803.5 q^{91} +67952.3i q^{92} +(91728.7 - 43624.3i) q^{93} -95212.6 q^{94} +653993. i q^{95} +(-299535. - 629832. i) q^{96} +978817. q^{97} +1.11608e6i q^{98} +(-609497. - 495862. 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 $

$2$		−	9.52809i		−	1.19101i	−0.803351	−	0.595506i	$-0.796952\pi$
$2$		−	9.52809i		−	1.19101i	0.803351	−	0.595506i	$-0.203048\pi$
$3$	−24.3830	+	11.5961i	−0.903075	+	0.429484i
$3$	−24.3830	+	11.5961i	−0.903075	+	0.429484i
$4$	−26.7846			−0.418509
$5$		−	179.250i		−	1.43400i	−0.697073	−	0.717000i	$-0.745515\pi$
$5$		−	179.250i		−	1.43400i	0.697073	−	0.717000i	$-0.254485\pi$
$6$	110.488	+	232.324i	0.511520	+	1.07557i
$7$	−22.6651			−0.0660790			−0.0330395	−	0.999454i	$-0.510519\pi$
$7$	−22.6651			−0.0660790			−0.0330395	+	0.999454i	$0.510519\pi$
$8$		−	354.592i		−	0.692563i
$9$	460.063	−	565.494i	0.631087	−	0.775712i
$10$	−1707.91			−1.70791
$11$		−	1077.81i		−	0.809778i	−0.914366	−	0.404889i	$-0.867310\pi$
$11$		−	1077.81i		−	0.809778i	0.914366	−	0.404889i	$-0.132690\pi$
$12$	653.089	−	310.596i	0.377945	−	0.179743i
$13$	−829.623			−0.377616			−0.188808	−	0.982014i	$-0.560462\pi$
$13$	−829.623			−0.377616			−0.188808	+	0.982014i	$0.560462\pi$
$14$			215.955i			0.0787008i
$15$	2078.59	+	4370.66i	0.615880	+	1.29501i
$16$	−5092.80			−1.24336
$17$			6996.04i			1.42399i	0.702186	+	0.711993i	$0.252207\pi$
$17$			6996.04i			1.42399i	−0.702186	+	0.711993i	$0.747793\pi$
$18$	−5388.08	−	4383.52i	−0.923882	−	0.751633i
$19$	−3648.50			−0.531928			−0.265964	−	0.963983i	$-0.585690\pi$
$19$	−3648.50			−0.531928			−0.265964	+	0.963983i	$0.585690\pi$
$20$			4801.14i			0.600142i
$21$	552.643	−	262.826i	0.0596742	−	0.0283798i
$22$	−10269.5			−0.964455
$23$		−	2536.99i		−	0.208514i
$23$		−	2536.99i		−	0.208514i
$24$	4111.87	+	8646.02i	0.297444	+	0.625436i
$25$	−16505.6			−1.05636
$26$			7904.73i			0.449746i
$27$	−4660.22	+	19123.4i	−0.236764	+	0.971567i
$28$	607.075			0.0276546
$29$			16187.7i			0.663729i	0.943327	+	0.331864i	$0.107678\pi$
$29$			16187.7i			0.663729i	−0.943327	+	0.331864i	$0.892322\pi$
$30$	41644.0	−	19805.0i	1.54237	−	0.733520i
$31$	−3761.99			−0.126280			−0.0631398	−	0.998005i	$-0.520111\pi$
$31$	−3761.99			−0.126280			−0.0631398	+	0.998005i	$0.520111\pi$
$32$			25830.8i			0.788293i
$33$	12498.4	+	26280.4i	0.347786	+	0.731290i
$34$	66659.0			1.69598
$35$			4062.72i			0.0947573i
$36$	−12322.6	+	15146.5i	−0.264116	+	0.324642i
$37$	58209.4			1.14918			0.574590	−	0.818441i	$-0.305161\pi$
$37$	58209.4			1.14918			0.574590	+	0.818441i	$0.305161\pi$
$38$			34763.2i			0.633533i
$39$	20228.7	−	9620.36i	0.341016	−	0.162180i
$40$	−63560.6			−0.993135
$41$		−	3839.45i		−	0.0557080i	−0.999612	−	0.0278540i	$-0.991133\pi$
$41$		−	3839.45i		−	0.0557080i	0.999612	−	0.0278540i	$-0.00886735\pi$
$42$	−2504.23	−	5265.64i	−0.0338007	−	0.0710727i
$43$	−144053.			−1.81182			−0.905911	−	0.423469i	$-0.860812\pi$
$43$	−144053.			−1.81182			−0.905911	+	0.423469i	$0.860812\pi$
$44$			28868.8i			0.338899i
$45$	−101365.	−	82466.3i	−1.11237	−	0.904980i
$46$	−24172.7			−0.248343
$47$		−	9992.83i		−	0.0962487i	−0.998841	−	0.0481244i	$-0.984676\pi$
$47$		−	9992.83i		−	0.0962487i	0.998841	−	0.0481244i	$-0.0153244\pi$
$48$	124178.	−	59056.4i	1.12285	−	0.534003i
$49$	−117135.			−0.995634
$50$			157267.i			1.25813i
$51$	−81126.6	−	170585.i	−0.611579	−	1.28597i
$52$	22221.1			0.158036
$53$		−	212996.i		−	1.43069i	−0.698773	−	0.715344i	$-0.746270\pi$
$53$		−	212996.i		−	1.43069i	0.698773	−	0.715344i	$-0.253730\pi$
$54$	182209.	+	44403.0i	1.15715	+	0.281988i
$55$	−193198.			−1.16122
$56$			8036.86i			0.0457638i
$57$	88961.4	−	42308.2i	0.480371	−	0.228455i
$58$	154238.			0.790509
$59$			66724.0i			0.324882i	0.986718	+	0.162441i	$0.0519367\pi$
$59$			66724.0i			0.324882i	−0.986718	+	0.162441i	$0.948063\pi$
$60$	−55674.3	−	117066.i	−0.257751	−	0.541973i
$61$	173578.			0.764723			0.382362	−	0.924013i	$-0.375111\pi$
$61$	173578.			0.764723			0.382362	+	0.924013i	$0.375111\pi$
$62$			35844.6i			0.150400i
$63$	−10427.4	+	12817.0i	−0.0417016	+	0.0512582i
$64$	−79821.1			−0.304493
$65$			148710.i			0.541502i
$66$	250402.	−	119086.i	0.870975	−	0.414218i
$67$	−397423.			−1.32138			−0.660691	−	0.750658i	$-0.729736\pi$
$67$	−397423.			−1.32138			−0.660691	+	0.750658i	$0.729736\pi$
$68$		−	187386.i		−	0.595951i
$69$	29419.1	+	61859.6i	0.0895535	+	0.188304i
$70$	38710.0			0.112857
$71$		−	397462.i		−	1.11051i	−0.831682	−	0.555253i	$-0.812621\pi$
$71$		−	397462.i		−	1.11051i	0.831682	−	0.555253i	$-0.187379\pi$
$72$	−200520.	−	163135.i	−0.537229	−	0.437068i
$73$	582901.			1.49840			0.749198	−	0.662347i	$-0.230439\pi$
$73$	582901.			1.49840			0.749198	+	0.662347i	$0.230439\pi$
$74$		−	554625.i		−	1.36869i
$75$	402456.	−	191400.i	0.953969	−	0.453688i
$76$	97723.5			0.222617
$77$			24428.8i			0.0535093i
$78$	−91663.7	−	192741.i	−0.193158	−	0.406154i
$79$	289748.			0.587677			0.293839	−	0.955855i	$-0.405067\pi$
$79$	289748.			0.587677			0.293839	+	0.955855i	$0.405067\pi$
$80$			912884.i			1.78298i
$81$	−108125.	−	520325.i	−0.203457	−	0.979084i
$82$	−36582.7			−0.0663489
$83$			536851.i			0.938901i	0.882959	+	0.469451i	$0.155548\pi$
$83$			536851.i			0.938901i	−0.882959	+	0.469451i	$0.844452\pi$
$84$	−14802.3	+	7039.68i	−0.0249742	+	0.0118772i
$85$	1.25404e6			2.04200
$86$			1.37255e6i			2.15790i
$87$	−187713.	−	394704.i	−0.285061	−	0.599397i
$88$	−382184.			−0.560822
$89$		−	158999.i		−	0.225541i	−0.993621	−	0.112770i	$-0.964028\pi$
$89$		−	158999.i		−	0.225541i	0.993621	−	0.112770i	$-0.0359725\pi$
$90$	−785746.	+	965813.i	−1.07784	+	1.32485i
$91$	18803.5			0.0249525
$92$			67952.3i			0.0872652i
$93$	91728.7	−	43624.3i	0.114040	−	0.0542350i
$94$	−95212.6			−0.114633
$95$			653993.i			0.762785i
$96$	−299535.	−	629832.i	−0.338559	−	0.711887i
$97$	978817.			1.07247			0.536236	−	0.844068i	$-0.319846\pi$
$97$	978817.			1.07247			0.536236	+	0.844068i	$0.319846\pi$
$98$			1.11608e6i			1.18581i
$99$	−609497.	−	495862.i	−0.628154	−	0.511041i
$100$	442095.			0.442095
$101$		−	1.65991e6i		−	1.61109i	−0.592532	−	0.805547i	$-0.701872\pi$
$101$		−	1.65991e6i		−	1.61109i	0.592532	−	0.805547i	$-0.298128\pi$
$102$	−1.62535e6	+	772981.i	−1.53160	+	0.728398i
$103$	−347135.			−0.317677			−0.158839	−	0.987305i	$-0.550775\pi$
$103$	−347135.			−0.317677			−0.158839	+	0.987305i	$0.550775\pi$
$104$			294178.i			0.261523i
$105$	−47111.5	−	99061.3i	−0.0406967	−	0.0855729i
$106$	−2.02945e6			−1.70397
$107$		−	1.14879e6i		−	0.937755i	−0.883263	−	0.468878i	$-0.844658\pi$
$107$		−	1.14879e6i		−	0.937755i	0.883263	−	0.468878i	$-0.155342\pi$
$108$	124822.	−	512211.i	0.0990877	−	0.406610i
$109$	−1.48843e6			−1.14934			−0.574672	−	0.818384i	$-0.694870\pi$
$109$	−1.48843e6			−1.14934			−0.574672	+	0.818384i	$0.694870\pi$
$110$			1.84081e6i			1.38303i
$111$	−1.41932e6	+	675000.i	−1.03780	+	0.493554i
$112$	115429.			0.0821599
$113$			2.47569e6i			1.71578i	0.513837	+	0.857888i	$0.328223\pi$
$113$			2.47569e6i			1.71578i	−0.513837	+	0.857888i	$0.671777\pi$
$114$	−403116.	−	847632.i	−0.272092	−	0.572128i
$115$	−454756.			−0.299010
$116$		−	433580.i		−	0.277776i
$117$	−381679.	+	469147.i	−0.238309	+	0.292921i
$118$	635752.			0.386938
$119$		−	158566.i		−	0.0940956i
$120$	1.54980e6	−	737053.i	0.896875	−	0.426535i
$121$	609877.			0.344260
$122$		−	1.65386e6i		−	0.910794i
$123$	44522.5	+	93617.4i	0.0239257	+	0.0503085i
$124$	100763.			0.0528491
$125$			157842.i			0.0808150i
$126$	122121.	+	99352.9i	0.0610492	+	0.0496671i
$127$	1.30693e6			0.638030			0.319015	−	0.947750i	$-0.396648\pi$
$127$	1.30693e6			0.638030			0.319015	+	0.947750i	$0.396648\pi$
$128$			2.41371e6i			1.15095i
$129$	3.51243e6	−	1.67044e6i	1.63621	−	0.778148i
$130$	1.41692e6			0.644935
$131$		−	2.32946e6i		−	1.03619i	−0.855322	−	0.518097i	$-0.826641\pi$
$131$		−	2.32946e6i		−	1.03619i	0.855322	−	0.518097i	$-0.173359\pi$
$132$	−334764.	−	703908.i	−0.145552	−	0.306051i
$133$	82693.5			0.0351493
$134$			3.78668e6i			1.57378i
$135$	3.42786e6	+	835344.i	1.39323	+	0.339519i
$136$	2.48074e6			0.986200
$137$			1.17952e6i			0.458715i	0.973342	+	0.229357i	$0.0736625\pi$
$137$			1.17952e6i			0.458715i	−0.973342	+	0.229357i	$0.926338\pi$
$138$	589404.	−	280308.i	0.224272	−	0.106659i
$139$	−4.65112e6			−1.73186			−0.865931	−	0.500164i	$-0.833273\pi$
$139$	−4.65112e6			−1.73186			−0.865931	+	0.500164i	$0.833273\pi$
$140$		−	108818.i		−	0.0396568i
$141$	115877.	+	243655.i	0.0413373	+	0.0869198i
$142$	−3.78706e6			−1.32263
$143$			894180.i			0.305785i
$144$	−2.34301e6	+	2.87995e6i	−0.784668	+	0.964488i
$145$	2.90164e6			0.951787
$146$		−	5.55394e6i		−	1.78461i
$147$	2.85611e6	−	1.35831e6i	0.899131	−	0.427608i
$148$	−1.55912e6			−0.480942
$149$		−	6.25750e6i		−	1.89166i	−0.324669	−	0.945828i	$-0.605253\pi$
$149$		−	6.25750e6i		−	1.89166i	0.324669	−	0.945828i	$-0.394747\pi$
$150$	−1.82367e6	−	3.83463e6i	−0.540348	−	1.13619i
$151$	−3.83790e6			−1.11471			−0.557356	−	0.830274i	$-0.688184\pi$
$151$	−3.83790e6			−1.11471			−0.557356	+	0.830274i	$0.688184\pi$
$152$			1.29373e6i			0.368394i
$153$	3.95622e6	+	3.21862e6i	1.10460	+	0.898660i
$154$	232760.			0.0637302
$155$			674337.i			0.181085i
$156$	−541818.	+	257677.i	−0.142718	+	0.0678738i
$157$	−3.65477e6			−0.944412			−0.472206	−	0.881488i	$-0.656542\pi$
$157$	−3.65477e6			−0.944412			−0.472206	+	0.881488i	$0.656542\pi$
$158$		−	2.76074e6i		−	0.699931i
$159$	2.46992e6	+	5.19349e6i	0.614457	+	1.29202i
$160$	4.63017e6			1.13041
$161$			57501.2i			0.0137784i
$162$	−4.95771e6	+	1.03023e6i	−1.16610	+	0.242320i
$163$	3.76240e6			0.868764			0.434382	−	0.900729i	$-0.356967\pi$
$163$	3.76240e6			0.868764			0.434382	+	0.900729i	$0.356967\pi$
$164$			102838.i			0.0233143i
$165$	4.71076e6	−	2.24034e6i	1.04867	−	0.498726i
$166$	5.11517e6			1.11824
$167$			739973.i			0.158879i	0.996840	+	0.0794395i	$0.0253130\pi$
$167$			739973.i			0.158879i	−0.996840	+	0.0794395i	$0.974687\pi$
$168$	−93195.9	−	195963.i	−0.0196548	−	0.0413281i
$169$	−4.13853e6			−0.857406
$170$		−	1.19486e7i		−	2.43204i
$171$	−1.67854e6	+	2.06320e6i	−0.335693	+	0.412623i
$172$	3.85839e6			0.758264
$173$		−	7.49776e6i		−	1.44808i	−0.689757	−	0.724041i	$-0.742283\pi$
$173$		−	7.49776e6i		−	1.44808i	0.689757	−	0.724041i	$-0.257717\pi$
$174$	−3.76078e6	+	1.78855e6i	−0.713888	+	0.339511i
$175$	374100.			0.0698029
$176$			5.48909e6i			1.00684i
$177$	−773735.	−	1.62693e6i	−0.139532	−	0.293393i
$178$	−1.51496e6			−0.268622
$179$			5.60300e6i			0.976925i	0.872585	+	0.488462i	$0.162442\pi$
$179$			5.60300e6i			0.976925i	−0.872585	+	0.488462i	$0.837558\pi$
$180$	2.71501e6	+	2.20882e6i	0.465537	+	0.378742i
$181$	−3.56472e6			−0.601160			−0.300580	−	0.953757i	$-0.597180\pi$
$181$	−3.56472e6			−0.601160			−0.300580	+	0.953757i	$0.597180\pi$
$182$		−	179161.i		−	0.0297187i
$183$	−4.23235e6	+	2.01282e6i	−0.690602	+	0.328436i
$184$	−899598.			−0.144409
$185$		−	1.04340e7i		−	1.64792i
$186$	−415656.	−	874000.i	−0.0645945	−	0.135823i
$187$	7.54044e6			1.15311
$188$			267654.i			0.0402810i
$189$	105624.	−	433433.i	0.0156451	−	0.0642002i
$190$	6.23131e6			0.908486
$191$		−	1.60332e6i		−	0.230102i	−0.993360	−	0.115051i	$-0.963297\pi$
$191$		−	1.60332e6i		−	0.230102i	0.993360	−	0.115051i	$-0.0367031\pi$
$192$	1.94628e6	−	925610.i	0.274980	−	0.130775i
$193$	−9.99694e6			−1.39058			−0.695289	−	0.718731i	$-0.744724\pi$
$193$	−9.99694e6			−1.39058			−0.695289	+	0.718731i	$0.744724\pi$
$194$		−	9.32626e6i		−	1.27733i
$195$	−1.72445e6	−	3.62600e6i	−0.232566	−	0.489017i
$196$	3.13742e6			0.416682
$197$		−	742241.i		−	0.0970837i	−0.998821	−	0.0485419i	$-0.984543\pi$
$197$		−	742241.i		−	0.0970837i	0.998821	−	0.0485419i	$-0.0154574\pi$
$198$	−4.72462e6	+	5.80735e6i	−0.608656	+	0.748139i
$199$	−1.52870e7			−1.93983			−0.969915	−	0.243444i	$-0.921723\pi$
$199$	−1.52870e7			−1.93983			−0.969915	+	0.243444i	$0.921723\pi$
$200$			5.85274e6i			0.731593i
$201$	9.69036e6	−	4.60854e6i	1.19331	−	0.567512i
$202$	−1.58158e7			−1.91883
$203$		−	366895.i		−	0.0438585i
$204$	2.17294e6	+	4.56904e6i	0.255951	+	0.538188i
$205$	−688222.			−0.0798853
$206$			3.30753e6i			0.378357i
$207$	−1.43465e6	−	1.16718e6i	−0.161747	−	0.131591i
$208$	4.22510e6			0.469513
$209$			3.93240e6i			0.430744i
$210$	−943865.	+	448883.i	−0.101918	+	0.0484702i
$211$	1.05631e6			0.112446			0.0562232	−	0.998418i	$-0.482094\pi$
$211$	1.05631e6			0.112446			0.0562232	+	0.998418i	$0.482094\pi$
$212$			5.70502e6i			0.598755i
$213$	4.60900e6	+	9.69133e6i	0.476944	+	1.00287i
$214$	−1.09458e7			−1.11688
$215$			2.58214e7i			2.59815i
$216$	6.78099e6	+	1.65248e6i	0.672871	+	0.163974i
$217$	85265.9			0.00834442
$218$			1.41819e7i			1.36888i
$219$	−1.42129e7	+	6.75936e6i	−1.35316	+	0.643536i
$220$	5.17473e6			0.485982
$221$		−	5.80408e6i		−	0.537721i
$222$	6.43146e6	+	1.35234e7i	0.587829	+	1.23603i
$223$	1.51199e7			1.36344			0.681719	−	0.731614i	$-0.261233\pi$
$223$	1.51199e7			1.36344			0.681719	+	0.731614i	$0.261233\pi$
$224$		−	585457.i		−	0.0520896i
$225$	−7.59360e6	+	9.33380e6i	−0.666653	+	0.819428i
$226$	2.35886e7			2.04351
$227$		−	8.92592e6i		−	0.763089i	−0.924350	−	0.381545i	$-0.875392\pi$
$227$		−	8.92592e6i		−	0.763089i	0.924350	−	0.381545i	$-0.124608\pi$
$228$	−2.38279e6	+	1.13321e6i	−0.201040	+	0.0956103i
$229$	−5.20955e6			−0.433804			−0.216902	−	0.976193i	$-0.569595\pi$
$229$	−5.20955e6			−0.433804			−0.216902	+	0.976193i	$0.569595\pi$
$230$			4.33296e6i			0.356124i
$231$	−283277.	−	595647.i	−0.0229814	−	0.0483229i
$232$	5.74002e6			0.459674
$233$		−	1.58679e7i		−	1.25445i	−0.778839	−	0.627224i	$-0.784191\pi$
$233$		−	1.58679e7i		−	1.25445i	0.778839	−	0.627224i	$-0.215809\pi$
$234$	4.47007e6	+	3.63667e6i	0.348873	+	0.283829i
$235$	−1.79122e6			−0.138021
$236$		−	1.78717e6i		−	0.135966i
$237$	−7.06493e6	+	3.35993e6i	−0.530717	+	0.252398i
$238$	−1.51083e6			−0.112069
$239$		−	1.89002e7i		−	1.38443i	−0.721690	−	0.692217i	$-0.756634\pi$
$239$		−	1.89002e7i		−	1.38443i	0.721690	−	0.692217i	$-0.243366\pi$
$240$	−1.05859e7	−	2.22589e7i	−0.765760	−	1.61016i
$241$	2.03823e7			1.45613			0.728066	−	0.685507i	$-0.240419\pi$
$241$	2.03823e7			1.45613			0.728066	+	0.685507i	$0.240419\pi$
$242$		−	5.81096e6i		−	0.410017i
$243$	8.67015e6	+	1.14333e7i	0.604238	+	0.796804i
$244$	−4.64920e6			−0.320043
$245$			2.09965e7i			1.42774i
$246$	891996.	−	424215.i	0.0599180	−	0.0284958i
$247$	3.02688e6			0.200865
$248$			1.33397e6i			0.0874565i
$249$	−6.22536e6	−	1.30901e7i	−0.403243	−	0.847898i
$250$	1.50393e6			0.0962516
$251$		−	1.52575e6i		−	0.0964855i	−0.998836	−	0.0482427i	$-0.984638\pi$
$251$		−	1.52575e6i		−	0.0964855i	0.998836	−	0.0482427i	$-0.0153621\pi$
$252$	279292.	−	343297.i	0.0174525	−	0.0214520i
$253$	−2.73441e6			−0.168850
$254$		−	1.24525e7i		−	0.759901i
$255$	−3.05773e7	+	1.45419e7i	−1.84408	+	0.877004i
$256$	1.78895e7			1.06630
$257$			1.66664e7i			0.981843i	0.871204	+	0.490922i	$0.163340\pi$
$257$			1.66664e7i			0.981843i	−0.871204	+	0.490922i	$0.836660\pi$
$258$	−1.59161e7	−	3.34668e7i	−0.926783	−	1.94875i
$259$	−1.31932e6			−0.0759367
$260$		−	3.98313e6i		−	0.226623i
$261$	9.15403e6	+	7.44735e6i	0.514862	+	0.418871i
$262$	−2.21953e7			−1.23412
$263$		−	1.89605e7i		−	1.04227i	−0.853473	−	0.521137i	$-0.825508\pi$
$263$		−	1.89605e7i		−	1.04227i	0.853473	−	0.521137i	$-0.174492\pi$
$264$	9.31881e6	−	4.43183e6i	0.506464	−	0.240864i
$265$	−3.81796e7			−2.05161
$266$		−	787912.i		−	0.0418632i
$267$	1.84377e6	+	3.87688e6i	0.0968662	+	0.203680i
$268$	1.06448e7			0.553010
$269$			4.06049e6i			0.208603i	0.994546	+	0.104302i	$0.0332607\pi$
$269$			4.06049e6i			0.208603i	−0.994546	+	0.104302i	$0.966739\pi$
$270$	7.95924e6	−	3.26610e7i	0.404371	−	1.65935i
$271$	1.41614e7			0.711537			0.355768	−	0.934574i	$-0.384219\pi$
$271$	1.41614e7			0.711537			0.355768	+	0.934574i	$0.384219\pi$
$272$		−	3.56295e7i		−	1.77053i
$273$	−458486.	+	218046.i	−0.0225340	+	0.0107167i
$274$	1.12386e7			0.546335
$275$			1.77899e7i			0.855414i
$276$	−787979.	−	1.65688e6i	−0.0374790	−	0.0788070i
$277$	2.65370e7			1.24857			0.624285	−	0.781197i	$-0.285390\pi$
$277$	2.65370e7			1.24857			0.624285	+	0.781197i	$0.285390\pi$
$278$			4.43163e7i			2.06267i
$279$	−1.73075e6	+	2.12738e6i	−0.0796934	+	0.0979565i
$280$	1.44061e6			0.0656253
$281$		−	9.22643e6i		−	0.415829i	−0.978147	−	0.207914i	$-0.933332\pi$
$281$		−	9.22643e6i		−	0.415829i	0.978147	−	0.207914i	$-0.0666675\pi$
$282$	2.32157e6	−	1.10409e6i	0.103522	−	0.0492332i
$283$	1.22509e7			0.540517			0.270258	−	0.962788i	$-0.412891\pi$
$283$	1.22509e7			0.540517			0.270258	+	0.962788i	$0.412891\pi$
$284$			1.06459e7i			0.464757i
$285$	−7.58374e6	−	1.59463e7i	−0.327604	−	0.688852i
$286$	8.51983e6			0.364194
$287$			87021.5i			0.00368113i
$288$	1.46071e7	+	1.18838e7i	0.611488	+	0.497482i
$289$	−2.48071e7			−1.02774
$290$		−	2.76471e7i		−	1.13359i
$291$	−2.38665e7	+	1.13504e7i	−0.968523	+	0.460610i
$292$	−1.56128e7			−0.627092
$293$		−	1.91758e7i		−	0.762345i	−0.924504	−	0.381172i	$-0.875520\pi$
$293$		−	1.91758e7i		−	0.762345i	0.924504	−	0.381172i	$-0.124480\pi$
$294$	−1.29421e7	−	2.72133e7i	−0.509287	−	1.07088i
$295$	1.19603e7			0.465881
$296$		−	2.06406e7i		−	0.795879i
$297$	2.06114e7	+	5.02285e6i	0.786754	+	0.191726i
$298$	−5.96220e7			−2.25298
$299$			2.10475e6i			0.0787385i
$300$	−1.07796e7	+	5.12656e6i	−0.399244	+	0.189872i
$301$	3.26496e6			0.119723
$302$			3.65679e7i			1.32763i
$303$	1.92484e7	+	4.04736e7i	0.691938	+	1.45494i
$304$	1.85811e7			0.661378
$305$		−	3.11138e7i		−	1.09661i
$306$	3.06673e7	−	3.76952e7i	1.07031	−	1.31559i
$307$	−3.00485e7			−1.03850			−0.519251	−	0.854622i	$-0.673789\pi$
$307$	−3.00485e7			−1.03850			−0.519251	+	0.854622i	$0.673789\pi$
$308$		−	654314.i		−	0.0223941i
$309$	8.46419e6	−	4.02539e6i	0.286886	−	0.136437i
$310$	6.42515e6			0.215674
$311$			7.04351e6i			0.234157i	0.993123	+	0.117079i	$0.0373530\pi$
$311$			7.04351e6i			0.234157i	−0.993123	+	0.117079i	$0.962647\pi$
$312$	−3.41130e6	−	7.17294e6i	−0.112320	−	0.236175i
$313$	−728230.			−0.0237485			−0.0118742	−	0.999929i	$-0.503780\pi$
$313$	−728230.			−0.0237485			−0.0118742	+	0.999929i	$0.503780\pi$
$314$			3.48230e7i			1.12481i
$315$	2.29744e6	+	1.86910e6i	0.0735043	+	0.0598001i
$316$	−7.76077e6			−0.245948
$317$			4.09372e7i			1.28511i	0.766240	+	0.642555i	$0.222126\pi$
$317$			4.09372e7i			1.28511i	−0.766240	+	0.642555i	$0.777874\pi$
$318$	4.94841e7	−	2.35336e7i	1.53881	−	0.731825i
$319$	1.74473e7			0.537473
$320$			1.43079e7i			0.436643i
$321$	1.33214e7	+	2.80110e7i	0.402751	+	0.846863i
$322$	547877.			0.0164103
$323$		−	2.55251e7i		−	0.757459i
$324$	2.89609e6	+	1.39367e7i	0.0851487	+	0.409755i
$325$	1.36934e7			0.398897
$326$		−	3.58485e7i		−	1.03471i
$327$	3.62925e7	−	1.72600e7i	1.03794	−	0.493625i
$328$	−1.36144e6			−0.0385813
$329$			226488.i			0.00636002i
$330$	−2.13462e7	−	4.48845e7i	−0.593988	−	1.24898i
$331$	5.99694e7			1.65366			0.826829	−	0.562453i	$-0.190142\pi$
$331$	5.99694e7			1.65366			0.826829	+	0.562453i	$0.190142\pi$
$332$		−	1.43793e7i		−	0.392939i
$333$	2.67800e7	−	3.29171e7i	0.725233	−	0.891433i
$334$	7.05053e6			0.189227
$335$			7.12380e7i			1.89486i
$336$	−2.81450e6	+	1.33852e6i	−0.0741965	+	0.0352863i
$337$	−4.23518e7			−1.10658			−0.553289	−	0.832989i	$-0.686627\pi$
$337$	−4.23518e7			−1.10658			−0.553289	+	0.832989i	$0.686627\pi$
$338$			3.94323e7i			1.02118i
$339$	−2.87082e7	−	6.03647e7i	−0.736897	−	1.54947i
$340$	−3.35890e7			−0.854594
$341$			4.05473e6i			0.102258i
$342$	1.96584e7	+	1.59933e7i	0.491439	+	0.399815i
$343$	5.32141e6			0.131869
$344$			5.10799e7i			1.25480i
$345$	1.10883e7	−	5.27338e6i	0.270028	−	0.128420i
$346$	−7.14393e7			−1.72468
$347$			2.52884e7i			0.605247i	0.953110	+	0.302624i	$0.0978625\pi$
$347$			2.52884e7i			0.605247i	−0.953110	+	0.302624i	$0.902137\pi$
$348$	5.02782e6	+	1.05720e7i	0.119300	+	0.250853i
$349$	2.45837e7			0.578324			0.289162	−	0.957280i	$-0.406623\pi$
$349$	2.45837e7			0.578324			0.289162	+	0.957280i	$0.406623\pi$
$350$		−	3.56446e6i		−	0.0831361i
$351$	3.86622e6	−	1.58652e7i	0.0894058	−	0.366880i
$352$	2.78408e7			0.638342
$353$			8.45279e7i			1.92166i	0.277143	+	0.960829i	$0.410612\pi$
$353$			8.45279e7i			1.92166i	−0.277143	+	0.960829i	$0.589388\pi$
$354$	−1.55016e7	+	7.37222e6i	−0.349434	+	0.166184i
$355$	−7.12451e7			−1.59247
$356$			4.25873e6i			0.0943909i
$357$	1.83874e6	+	3.86632e6i	0.0404125	+	0.0849753i
$358$	5.33859e7			1.16353
$359$			1.69615e7i			0.366591i	0.983058	+	0.183295i	$0.0586765\pi$
$359$			1.69615e7i			0.366591i	−0.983058	+	0.183295i	$0.941324\pi$
$360$	−2.92419e7	+	3.59431e7i	−0.626755	+	0.770386i
$361$	−3.37343e7			−0.717052
$362$			3.39650e7i			0.715989i
$363$	−1.48706e7	+	7.07217e6i	−0.310892	+	0.147854i
$364$	−503643.			−0.0104428
$365$		−	1.04485e8i		−	2.14870i
$366$	1.91783e7	+	4.03262e7i	0.391171	+	0.822515i
$367$	5.36269e6			0.108489			0.0542444	−	0.998528i	$-0.482725\pi$
$367$	5.36269e6			0.108489			0.0542444	+	0.998528i	$0.482725\pi$
$368$			1.29204e7i			0.259258i
$369$	−2.17119e6	−	1.76639e6i	−0.0432134	−	0.0351566i
$370$	−9.94165e7			−1.96270
$371$			4.82758e6i			0.0945383i
$372$	−2.45692e6	+	1.16846e6i	−0.0477267	+	0.0226978i
$373$	8.17809e7			1.57589			0.787944	−	0.615747i	$-0.211146\pi$
$373$	8.17809e7			1.57589			0.787944	+	0.615747i	$0.211146\pi$
$374$		−	7.18460e7i		−	1.37337i
$375$	−1.83034e6	−	3.84866e6i	−0.0347087	−	0.0729820i
$376$	−3.54338e6			−0.0666583
$377$		−	1.34297e7i		−	0.250635i
$378$	−4.12979e6	−	1.00640e6i	−0.0764632	−	0.0186335i
$379$	−1.07375e8			−1.97235			−0.986174	−	0.165713i	$-0.947007\pi$
$379$	−1.07375e8			−1.97235			−0.986174	+	0.165713i	$0.947007\pi$
$380$		−	1.75169e7i		−	0.319233i
$381$	−3.18669e7	+	1.51552e7i	−0.576189	+	0.274023i
$382$	−1.52766e7			−0.274054
$383$		−	3.04488e7i		−	0.541968i	−0.962584	−	0.270984i	$-0.912651\pi$
$383$		−	3.04488e7i		−	0.541968i	0.962584	−	0.270984i	$-0.0873491\pi$
$384$	−2.79896e7	−	5.88536e7i	−0.494313	−	1.03939i
$385$	4.37886e6			0.0767323
$386$			9.52518e7i			1.65619i
$387$	−6.62732e7	+	8.14608e7i	−1.14342	+	1.40545i
$388$	−2.62172e7			−0.448840
$389$		−	1.89327e7i		−	0.321636i	−0.986984	−	0.160818i	$-0.948587\pi$
$389$		−	1.89327e7i		−	0.321636i	0.986984	−	0.160818i	$-0.0514132\pi$
$390$	−3.45488e7	+	1.64307e7i	−0.582425	+	0.276989i
$391$	1.77489e7			0.296922
$392$			4.15352e7i			0.689539i
$393$	2.70126e7	+	5.67993e7i	0.445029	+	0.935761i
$394$	−7.07215e6			−0.115628
$395$		−	5.19373e7i		−	0.842729i
$396$	1.63251e7	+	1.32815e7i	0.262888	+	0.213875i
$397$	6.13037e7			0.979750			0.489875	−	0.871793i	$-0.337042\pi$
$397$	6.13037e7			0.979750			0.489875	+	0.871793i	$0.337042\pi$
$398$			1.45656e8i			2.31036i
$399$	−2.01632e6	+	958919.i	−0.0317424	+	0.0150960i
$400$	8.40595e7			1.31343
$401$		−	1.13119e8i		−	1.75429i	−0.480226	−	0.877145i	$-0.659445\pi$
$401$		−	1.13119e8i		−	1.75429i	0.480226	−	0.877145i	$-0.340555\pi$
$402$	−4.39106e7	−	9.23307e7i	−0.675913	−	1.42124i
$403$	3.12104e6			0.0476852
$404$			4.44600e7i			0.674257i
$405$	−9.32683e7	+	1.93815e7i	−1.40401	+	0.291758i
$406$	−3.49581e6			−0.0522360
$407$		−	6.27390e7i		−	0.930581i
$408$	−6.04880e7	+	2.87668e7i	−0.890612	+	0.423557i
$409$	−3.18247e7			−0.465152			−0.232576	−	0.972578i	$-0.574715\pi$
$409$	−3.18247e7			−0.465152			−0.232576	+	0.972578i	$0.574715\pi$
$410$			6.55744e6i			0.0951443i
$411$	−1.36778e7	−	2.87602e7i	−0.197011	−	0.414254i
$412$	9.29785e6			0.132951
$413$		−	1.51230e6i		−	0.0214679i
$414$	−1.11210e7	+	1.36695e7i	−0.156726	+	0.192643i
$415$	9.62306e7			1.34638
$416$		−	2.14298e7i		−	0.297672i
$417$	1.13408e8	−	5.39347e7i	1.56400	−	0.743806i
$418$	3.74683e7			0.513021
$419$		−	1.33066e8i		−	1.80894i	−0.426535	−	0.904471i	$-0.640266\pi$
$419$		−	1.33066e8i		−	1.80894i	0.426535	−	0.904471i	$-0.359734\pi$
$420$	1.26186e6	+	2.65331e6i	0.0170319	+	0.0358130i
$421$	9.05686e7			1.21376			0.606878	−	0.794795i	$-0.292422\pi$
$421$	9.05686e7			1.21376			0.606878	+	0.794795i	$0.292422\pi$
$422$		−	1.00647e7i		−	0.133925i
$423$	−5.65088e6	−	4.59733e6i	−0.0746613	−	0.0607414i
$424$	−7.55268e7			−0.990840
$425$		−	1.15474e8i		−	1.50424i
$426$	9.23399e7	−	4.39149e7i	1.19443	−	0.568046i
$427$	−3.93415e6			−0.0505321
$428$			3.07699e7i			0.392459i
$429$	−1.03690e7	−	2.18028e7i	−0.131330	−	0.276147i
$430$	2.46029e8			3.09443
$431$			6.59695e7i			0.823971i	0.911191	+	0.411985i	$0.135164\pi$
$431$			6.59695e7i			0.823971i	−0.911191	+	0.411985i	$0.864836\pi$
$432$	2.37336e7	−	9.73914e7i	0.294382	−	1.20801i
$433$	8.92979e7			1.09996			0.549981	−	0.835177i	$-0.314635\pi$
$433$	8.92979e7			1.09996			0.549981	+	0.835177i	$0.314635\pi$
$434$		−	812422.i		−	0.00993830i
$435$	−7.07508e7	+	3.36476e7i	−0.859535	+	0.408777i
$436$	3.98671e7			0.481011
$437$			9.25622e6i			0.110915i
$438$	6.44038e7	+	1.35422e8i	0.766459	+	1.61163i
$439$	2.30142e7			0.272020			0.136010	−	0.990707i	$-0.456572\pi$
$439$	2.30142e7			0.272020			0.136010	+	0.990707i	$0.456572\pi$
$440$			6.85066e7i			0.804219i
$441$	−5.38896e7	+	6.62393e7i	−0.628332	+	0.772325i
$442$	−5.53018e7			−0.640432
$443$			2.00964e7i			0.231157i	0.993298	+	0.115578i	$0.0368722\pi$
$443$			2.00964e7i			0.231157i	−0.993298	+	0.115578i	$0.963128\pi$
$444$	3.80159e7	−	1.80796e7i	0.434327	−	0.206557i
$445$	−2.85006e7			−0.323426
$446$		−	1.44064e8i		−	1.62387i
$447$	7.25623e7	+	1.52577e8i	0.812435	+	1.70831i
$448$	1.80915e6			0.0201206
$449$		−	6.99811e7i		−	0.773110i	−0.922266	−	0.386555i	$-0.873665\pi$
$449$		−	6.99811e7i		−	0.773110i	0.922266	−	0.386555i	$-0.126335\pi$
$450$	8.89333e7	+	7.23525e7i	0.975948	+	0.793992i
$451$	−4.13822e6			−0.0451111
$452$		−	6.63102e7i		−	0.718067i
$453$	9.35795e7	−	4.45045e7i	1.00667	−	0.478751i
$454$	−8.50470e7			−0.908848
$455$		−	3.37052e6i		−	0.0357819i
$456$	−1.50021e7	−	3.15450e7i	−0.158219	−	0.332687i
$457$	5.39940e7			0.565714			0.282857	−	0.959162i	$-0.408718\pi$
$457$	5.39940e7			0.565714			0.282857	+	0.959162i	$0.408718\pi$
$458$			4.96370e7i			0.516666i
$459$	−1.33788e8	−	3.26031e7i	−1.38350	−	0.337148i
$460$	1.21805e7			0.125138
$461$		−	1.24331e8i		−	1.26904i	−0.772904	−	0.634522i	$-0.781197\pi$
$461$		−	1.24331e8i		−	1.26904i	0.772904	−	0.634522i	$-0.218803\pi$
$462$	−5.67538e6	+	2.69909e6i	−0.0575531	+	0.0273711i
$463$	−8.63382e7			−0.869882			−0.434941	−	0.900459i	$-0.643231\pi$
$463$	−8.63382e7			−0.869882			−0.434941	+	0.900459i	$0.643231\pi$
$464$		−	8.24406e7i		−	0.825253i
$465$	−7.81966e6	−	1.64424e7i	−0.0777730	−	0.163533i
$466$	−1.51191e8			−1.49406
$467$			2.10005e7i			0.206196i	0.994671	+	0.103098i	$0.0328755\pi$
$467$			2.10005e7i			0.206196i	−0.994671	+	0.103098i	$0.967125\pi$
$468$	1.02231e7	−	1.25659e7i	0.0997344	−	0.122590i
$469$	9.00762e6			0.0873155
$470$			1.70669e7i			0.164384i
$471$	8.91144e7	−	4.23810e7i	0.852874	−	0.405609i
$472$	2.36598e7			0.225001
$473$			1.55262e8i			1.46717i
$474$	3.20138e7	+	6.73153e7i	0.300609	+	0.632090i
$475$	6.02205e7			0.561906
$476$			4.24712e6i			0.0393798i
$477$	−1.20448e8	−	9.79917e7i	−1.10980	−	0.902889i
$478$	−1.80083e8			−1.64888
$479$			1.29979e8i			1.18268i	0.806424	+	0.591338i	$0.201400\pi$
$479$			1.29979e8i			1.18268i	−0.806424	+	0.591338i	$0.798600\pi$
$480$	−1.12897e8	+	5.36917e7i	−1.02085	+	0.485494i
$481$	−4.82919e7			−0.433949
$482$		−	1.94204e8i		−	1.73427i
$483$	−666787.	−	1.40205e6i	−0.00591761	−	0.0124429i
$484$	−1.63353e7			−0.144076
$485$		−	1.75453e8i		−	1.53793i
$486$	1.08937e8	−	8.26100e7i	0.949003	−	0.719654i
$487$	1.19130e8			1.03141			0.515707	−	0.856765i	$-0.327529\pi$
$487$	1.19130e8			1.03141			0.515707	+	0.856765i	$0.327529\pi$
$488$		−	6.15492e7i		−	0.529619i
$489$	−9.17386e7	+	4.36290e7i	−0.784559	+	0.373120i
$490$	2.00057e8			1.70045
$491$			3.46686e7i			0.292881i	0.989219	+	0.146441i	$0.0467817\pi$
$491$			3.46686e7i			0.292881i	−0.989219	+	0.146441i	$0.953218\pi$
$492$	−1.19252e6	−	2.50750e6i	−0.0100131	−	0.0210546i
$493$	−1.13250e8			−0.945141
$494$		−	2.88404e7i		−	0.239232i
$495$	−8.88833e7	+	1.09252e8i	−0.732833	+	0.900773i
$496$	1.91591e7			0.157011
$497$			9.00852e6i			0.0733811i
$498$	−1.24723e8	+	5.93158e7i	−1.00986	+	0.480267i
$499$	−5.22092e7			−0.420190			−0.210095	−	0.977681i	$-0.567377\pi$
$499$	−5.22092e7			−0.420190			−0.210095	+	0.977681i	$0.567377\pi$
$500$		−	4.22773e6i		−	0.0338218i
$501$	−8.58077e6	−	1.80428e7i	−0.0682359	−	0.143480i
$502$	−1.45375e7			−0.114915
$503$			4.23745e7i			0.332967i	0.986044	+	0.166483i	$0.0532412\pi$
$503$			4.23745e7i			0.332967i	−0.986044	+	0.166483i	$0.946759\pi$
$504$	4.54479e6	+	3.69746e6i	0.0354995	+	0.0288810i
$505$	−2.97539e8			−2.31031
$506$			2.60537e7i			0.201103i
$507$	1.00910e8	−	4.79907e7i	0.774301	−	0.368242i
$508$	−3.50056e7			−0.267021
$509$		−	1.75517e8i		−	1.33096i	−0.746415	−	0.665481i	$-0.768226\pi$
$509$		−	1.75517e8i		−	1.33096i	0.746415	−	0.665481i	$-0.231774\pi$
$510$	1.38557e8	+	2.91343e8i	1.04452	+	2.19632i
$511$	−1.32115e7			−0.0990124
$512$		−	1.59755e7i		−	0.119027i
$513$	1.70028e7	−	6.97715e7i	0.125941	−	0.516804i
$514$	1.58799e8			1.16939
$515$			6.22239e7i			0.455549i
$516$	−9.40791e7	+	4.47421e7i	−0.684769	+	0.325662i
$517$	−1.07704e7			−0.0779401
$518$			1.25706e7i			0.0904415i
$519$	8.69444e7	+	1.82818e8i	0.621927	+	1.30773i
$520$	5.27314e7			0.375024
$521$		−	1.38273e8i		−	0.977742i	−0.872356	−	0.488871i	$-0.837409\pi$
$521$		−	1.38273e8i		−	0.977742i	0.872356	−	0.488871i	$-0.162591\pi$
$522$	7.09591e7	−	8.72205e7i	0.498880	−	0.613207i
$523$	2.08840e8			1.45985			0.729925	−	0.683527i	$-0.239555\pi$
$523$	2.08840e8			1.45985			0.729925	+	0.683527i	$0.239555\pi$
$524$			6.23936e7i			0.433657i
$525$	−9.12169e6	+	4.33809e6i	−0.0630373	+	0.0299792i
$526$	−1.80657e8			−1.24136
$527$		−	2.63191e7i		−	0.179820i
$528$	−6.36519e7	−	1.33841e8i	−0.432423	−	0.909256i
$529$	−6.43634e6			−0.0434783
$530$			3.63779e8i			2.44349i
$531$	3.77320e7	+	3.06972e7i	0.252015	+	0.205029i
$532$	−2.21491e6			−0.0147103
$533$			3.18530e6i			0.0210363i
$534$	3.69393e7	−	1.75676e7i	0.242586	−	0.115369i
$535$	−2.05921e8			−1.34474
$536$			1.40923e8i			0.915139i
$537$	−6.49727e7	−	1.36618e8i	−0.419573	−	0.882236i
$538$	3.86887e7			0.248449
$539$			1.26250e8i			0.806242i
$540$	−9.18138e7	−	2.23743e7i	−0.583078	−	0.142092i
$541$	8.63675e7			0.545455			0.272727	−	0.962091i	$-0.412074\pi$
$541$	8.63675e7			0.545455			0.272727	+	0.962091i	$0.412074\pi$
$542$		−	1.34931e8i		−	0.847448i
$543$	8.69187e7	−	4.13367e7i	0.542892	−	0.258188i
$544$	−1.80713e8			−1.12252
$545$			2.66802e8i			1.64816i
$546$	2.07757e6	+	4.36849e6i	0.0127637	+	0.0268382i
$547$	−2.75469e8			−1.68310			−0.841552	−	0.540176i	$-0.818358\pi$
$547$	−2.75469e8			−1.68310			−0.841552	+	0.540176i	$0.818358\pi$
$548$		−	3.15929e7i		−	0.191976i
$549$	7.98566e7	−	9.81571e7i	0.482607	−	0.593205i
$550$	1.69504e8			1.01881
$551$		−	5.90607e7i		−	0.353056i
$552$	2.19349e7	−	1.04318e7i	0.130412	−	0.0620214i
$553$	−6.56716e6			−0.0388331
$554$		−	2.52847e8i		−	1.48706i
$555$	1.20994e8	+	2.54413e8i	0.707757	+	1.48820i
$556$	1.24578e8			0.724800
$557$			1.45565e8i			0.842348i	0.906980	+	0.421174i	$0.138382\pi$
$557$			1.45565e8i			0.842348i	−0.906980	+	0.421174i	$0.861618\pi$
$558$	2.02699e7	+	1.64908e7i	0.116667	+	0.0949158i
$559$	1.19509e8			0.684173
$560$		−	2.06906e7i		−	0.117817i
$561$	−1.83859e8	+	8.74394e7i	−1.04135	+	0.495243i
$562$	−8.79103e7			−0.495257
$563$			1.08529e8i			0.608161i	0.952646	+	0.304081i	$0.0983492\pi$
$563$			1.08529e8i			0.608161i	−0.952646	+	0.304081i	$0.901651\pi$
$564$	−3.10373e6	−	6.52621e6i	−0.0173000	−	0.0363767i
$565$	4.43767e8			2.46042
$566$		−	1.16728e8i		−	0.643762i
$567$	2.45067e6	+	1.17932e7i	0.0134442	+	0.0646969i
$568$	−1.40937e8			−0.769095
$569$			1.77666e7i			0.0964423i	0.998837	+	0.0482211i	$0.0153552\pi$
$569$			1.77666e7i			0.0964423i	−0.998837	+	0.0482211i	$0.984645\pi$
$570$	−1.51938e8	+	7.22586e7i	−0.820431	+	0.390180i
$571$	−1.94381e8			−1.04411			−0.522055	−	0.852912i	$-0.674834\pi$
$571$	−1.94381e8			−1.04411			−0.522055	+	0.852912i	$0.674834\pi$
$572$		−	2.39502e7i		−	0.127974i
$573$	1.85922e7	+	3.90938e7i	0.0988251	+	0.207799i
$574$	829149.			0.00438427
$575$			4.18745e7i			0.220266i
$576$	−3.67227e7	+	4.51383e7i	−0.192162	+	0.236199i
$577$	3.15025e8			1.63990			0.819951	−	0.572433i	$-0.194000\pi$
$577$	3.15025e8			1.63990			0.819951	+	0.572433i	$0.194000\pi$
$578$			2.36364e8i			1.22405i
$579$	2.43756e8	−	1.15925e8i	1.25580	−	0.597230i
$580$	−7.77193e7			−0.398332
$581$		−	1.21678e7i		−	0.0620416i
$582$	1.08148e8	+	2.27402e8i	0.548591	+	1.15352i
$583$	−2.29571e8			−1.15854
$584$		−	2.06692e8i		−	1.03773i
$585$	8.40946e7	+	6.84159e7i	0.420049	+	0.341735i
$586$	−1.82709e8			−0.907962
$587$			3.01662e8i			1.49144i	0.666260	+	0.745720i	$0.267894\pi$
$587$			3.01662e8i			1.49144i	−0.666260	+	0.745720i	$0.732106\pi$
$588$	−7.64997e7	+	3.63817e7i	−0.376295	+	0.178958i
$589$	1.37256e7			0.0671717
$590$		−	1.13959e8i		−	0.554870i
$591$	8.60708e6	+	1.80981e7i	0.0416959	+	0.0876739i
$592$	−2.96449e8			−1.42884
$593$		−	1.61136e8i		−	0.772731i	−0.922346	−	0.386365i	$-0.873730\pi$
$593$		−	1.61136e8i		−	0.772731i	0.922346	−	0.386365i	$-0.126270\pi$
$594$	4.78582e7	−	1.96388e8i	0.228348	−	0.937033i
$595$	−2.84230e7			−0.134933
$596$			1.67604e8i			0.791675i
$597$	3.72744e8	−	1.77269e8i	1.75181	−	0.833125i
$598$	2.00543e7			0.0937784
$599$		−	4.69256e7i		−	0.218338i	−0.994023	−	0.109169i	$-0.965181\pi$
$599$		−	4.69256e7i		−	0.218338i	0.994023	−	0.109169i	$-0.0348190\pi$
$600$	−6.78688e7	−	1.42708e8i	−0.314207	−	0.660683i
$601$	4.10662e8			1.89174			0.945869	−	0.324548i	$-0.105212\pi$
$601$	4.10662e8			1.89174			0.945869	+	0.324548i	$0.105212\pi$
$602$		−	3.11089e7i		−	0.142592i
$603$	−1.82839e8	+	2.24740e8i	−0.833907	+	1.02501i
$604$	1.02796e8			0.466517
$605$		−	1.09320e8i		−	0.493668i
$606$	3.85637e8	−	1.83401e8i	1.73285	−	0.824107i
$607$	−2.32824e8			−1.04103			−0.520513	−	0.853853i	$-0.674259\pi$
$607$	−2.32824e8			−1.04103			−0.520513	+	0.853853i	$0.674259\pi$
$608$		−	9.42435e7i		−	0.419315i
$609$	4.25454e6	+	8.94601e6i	0.0188365	+	0.0396075i
$610$	−2.96455e8			−1.30608
$611$			8.29028e6i			0.0363451i
$612$	−1.05966e8	−	8.62094e7i	−0.462286	−	0.376097i
$613$	−3.22017e7			−0.139797			−0.0698984	−	0.997554i	$-0.522268\pi$
$613$	−3.22017e7			−0.139797			−0.0698984	+	0.997554i	$0.522268\pi$
$614$			2.86305e8i			1.23687i
$615$	1.67809e7	−	7.98066e6i	0.0721424	−	0.0343094i
$616$	8.66224e6			0.0370585
$617$		−	3.49638e7i		−	0.148855i	−0.997226	−	0.0744274i	$-0.976287\pi$
$617$		−	3.49638e7i		−	0.148855i	0.997226	−	0.0744274i	$-0.0237129\pi$
$618$	−3.83543e7	−	8.06476e7i	−0.162498	−	0.341685i
$619$	1.16588e8			0.491568			0.245784	−	0.969325i	$-0.420955\pi$
$619$	1.16588e8			0.491568			0.245784	+	0.969325i	$0.420955\pi$
$620$		−	1.80618e7i		−	0.0757856i
$621$	4.85159e7	+	1.18229e7i	0.202586	+	0.0493686i
$622$	6.71112e7			0.278884
$623$			3.60374e6i			0.0149035i
$624$	−1.03021e8	+	4.89946e7i	−0.424005	+	0.201648i
$625$	−2.29606e8			−0.940468
$626$			6.93864e6i			0.0282847i
$627$	−4.56004e7	−	9.58838e7i	−0.184998	−	0.388994i
$628$	9.78915e7			0.395245
$629$			4.07236e8i			1.63642i
$630$	1.78090e7	−	2.18902e7i	0.0712226	−	0.0875445i
$631$	−2.29768e8			−0.914536			−0.457268	−	0.889329i	$-0.651172\pi$
$631$	−2.29768e8			−0.914536			−0.457268	+	0.889329i	$0.651172\pi$
$632$		−	1.02742e8i		−	0.407003i
$633$	−2.57561e7	+	1.22491e7i	−0.101548	+	0.0482939i
$634$	3.90053e8			1.53058
$635$		−	2.34267e8i		−	0.914935i
$636$	−6.61557e7	−	1.39106e8i	−0.257156	−	0.540721i
$637$	9.71782e7			0.375968
$638$		−	1.66240e8i		−	0.640137i
$639$	−2.24762e8	−	1.82858e8i	−0.861432	−	0.700826i
$640$	4.32658e8			1.65046
$641$			1.11754e8i			0.424314i	0.977236	+	0.212157i	$0.0680489\pi$
$641$			1.11754e8i			0.424314i	−0.977236	+	0.212157i	$0.931951\pi$
$642$	2.66891e8	−	1.26928e8i	1.00862	−	0.479681i
$643$	1.83633e7			0.0690744			0.0345372	−	0.999403i	$-0.489004\pi$
$643$	1.83633e7			0.0690744			0.0345372	+	0.999403i	$0.489004\pi$
$644$		−	1.54015e6i		−	0.00576639i
$645$	−2.99427e8	−	6.29604e8i	−1.11586	−	2.34633i
$646$	−2.43205e8			−0.902142
$647$			1.25223e8i			0.462352i	0.972912	+	0.231176i	$0.0742573\pi$
$647$			1.25223e8i			0.462352i	−0.972912	+	0.231176i	$0.925743\pi$
$648$	−1.84503e8	+	3.83404e7i	−0.678077	+	0.140907i
$649$	7.19160e7			0.263082
$650$		−	1.30472e8i		−	0.475092i
$651$	−2.07904e6	+	988749.i	−0.00753564	+	0.00358379i
$652$	−1.00774e8			−0.363586
$653$			4.68675e8i			1.68319i	0.540112	+	0.841593i	$0.318382\pi$
$653$			4.68675e8i			1.68319i	−0.540112	+	0.841593i	$0.681618\pi$
$654$	−1.64455e8	−	3.45798e8i	−0.587913	−	1.23620i
$655$	−4.17556e8			−1.48590
$656$			1.95536e7i			0.0692651i
$657$	2.68171e8	−	3.29627e8i	0.945618	−	1.16232i
$658$	2.15800e6			0.00757485
$659$		−	3.42115e8i		−	1.19541i	−0.801717	−	0.597703i	$-0.796080\pi$
$659$		−	3.42115e8i		−	1.19541i	0.801717	−	0.597703i	$-0.203920\pi$
$660$	−1.26176e8	+	6.00065e7i	−0.438878	+	0.208721i
$661$	1.49073e8			0.516173			0.258087	−	0.966122i	$-0.416908\pi$
$661$	1.49073e8			0.516173			0.258087	+	0.966122i	$0.416908\pi$
$662$		−	5.71394e8i		−	1.96953i
$663$	6.73045e7	+	1.41521e8i	0.230942	+	0.485602i
$664$	1.90363e8			0.650248
$665$		−	1.48228e7i		−	0.0504041i
$666$	−3.13637e8	−	2.55162e8i	−1.06171	−	0.863761i
$667$	4.10681e7			0.138397
$668$		−	1.98199e7i		−	0.0664923i
$669$	−3.68670e8	+	1.75332e8i	−1.23129	+	0.585574i
$670$	6.78762e8			2.25680
$671$		−	1.87084e8i		−	0.619256i
$672$	6.78899e6	+	1.42752e7i	0.0223716	+	0.0470408i
$673$	−2.91733e8			−0.957063			−0.478532	−	0.878070i	$-0.658831\pi$
$673$	−2.91733e8			−0.957063			−0.478532	+	0.878070i	$0.658831\pi$
$674$			4.03532e8i			1.31795i
$675$	7.69195e7	−	3.15642e8i	0.250107	−	1.02632i
$676$	1.10849e8			0.358832
$677$		−	3.91823e8i		−	1.26277i	−0.775470	−	0.631385i	$-0.782487\pi$
$677$		−	3.91823e8i		−	1.26277i	0.775470	−	0.631385i	$-0.217513\pi$
$678$	−5.75161e8	+	2.73535e8i	−1.84544	+	0.877654i
$679$	−2.21850e7			−0.0708679
$680$		−	4.44673e8i		−	1.41421i
$681$	1.03505e8	+	2.17641e8i	0.327734	+	0.689126i
$682$	3.86339e7			0.121791
$683$			3.31802e8i			1.04140i	0.853740	+	0.520700i	$0.174329\pi$
$683$			3.31802e8i			1.04140i	−0.853740	+	0.520700i	$0.825671\pi$
$684$	4.49589e7	−	5.52620e7i	0.140491	−	0.172686i
$685$	2.11429e8			0.657797
$686$		−	5.07029e7i		−	0.157058i
$687$	1.27024e8	−	6.04102e7i	0.391757	−	0.186312i
$688$	7.33630e8			2.25275
$689$			1.76707e8i			0.540251i
$690$	−5.02453e7	−	1.05651e8i	−0.152949	−	0.321607i
$691$	−1.93570e8			−0.586683			−0.293341	−	0.956008i	$-0.594767\pi$
$691$	−1.93570e8			−0.586683			−0.293341	+	0.956008i	$0.594767\pi$
$692$			2.00824e8i			0.606035i
$693$	1.38143e7	+	1.12388e7i	0.0415078	+	0.0337690i
$694$	2.40950e8			0.720857
$695$			8.33714e8i			2.48349i
$696$	−1.39959e8	+	6.65617e7i	−0.415120	+	0.197422i
$697$	2.68610e7			0.0793275
$698$		−	2.34236e8i		−	0.688791i
$699$	1.84005e8	+	3.86908e8i	0.538765	+	1.13286i
$700$	−1.00201e7			−0.0292132
$701$			2.15841e7i			0.0626586i	0.999509	+	0.0313293i	$0.00997406\pi$
$701$			2.15841e7i			0.0626586i	−0.999509	+	0.0313293i	$0.990026\pi$
$702$	−1.51165e8	−	3.68377e7i	−0.436958	−	0.106483i
$703$	−2.12377e8			−0.611282
$704$			8.60323e7i			0.246572i
$705$	4.36752e7	−	2.07710e7i	0.124643	−	0.0592776i
$706$	8.05390e8			2.28872
$707$			3.76220e7i			0.106459i
$708$	2.07242e7	+	4.35767e7i	0.0583952	+	0.122788i
$709$	2.08836e8			0.585959			0.292980	−	0.956119i	$-0.405353\pi$
$709$	2.08836e8			0.585959			0.292980	+	0.956119i	$0.405353\pi$
$710$			6.78830e8i			1.89665i
$711$	1.33302e8	−	1.63851e8i	0.370876	−	0.455868i
$712$	−5.63799e7			−0.156201
$713$			9.54416e6i			0.0263311i
$714$	3.68386e7	−	1.75197e7i	0.101207	−	0.0481318i
$715$	1.60282e8			0.438496
$716$		−	1.50074e8i		−	0.408852i
$717$	2.19167e8	+	4.60843e8i	0.594591	+	1.25025i
$718$	1.61611e8			0.436614
$719$			6.88758e8i			1.85302i	0.376272	+	0.926509i	$0.377206\pi$
$719$			6.88758e8i			1.85302i	−0.376272	+	0.926509i	$0.622794\pi$
$720$	5.16230e8	+	4.19984e8i	1.38308	+	1.12521i
$721$	7.86784e6			0.0209918
$722$			3.21424e8i			0.854017i
$723$	−4.96981e8	+	2.36354e8i	−1.31500	+	0.625385i
$724$	9.54796e7			0.251591
$725$		−	2.67187e8i		−	0.701134i
$726$	6.73843e7	+	1.41689e8i	0.176096	+	0.370276i
$727$	−3.99994e8			−1.04100			−0.520499	−	0.853862i	$-0.674254\pi$
$727$	−3.99994e8			−1.04100			−0.520499	+	0.853862i	$0.674254\pi$
$728$		−	6.66756e6i		−	0.0172812i
$729$	−3.43985e8	−	1.78238e8i	−0.887886	−	0.460063i
$730$	−9.95543e8			−2.55913
$731$		−	1.00780e9i		−	2.58001i
$732$	1.13362e8	−	5.39124e7i	0.289023	−	0.137453i
$733$	−5.46637e8			−1.38799			−0.693997	−	0.719978i	$-0.744152\pi$
$733$	−5.46637e8			−1.38799			−0.693997	+	0.719978i	$0.744152\pi$
$734$		−	5.10963e7i		−	0.129211i
$735$	−2.43477e8	−	5.11958e8i	−0.613190	−	1.28935i
$736$	6.55326e7			0.164370
$737$			4.28348e8i			1.07003i
$738$	−1.68303e7	+	2.06873e7i	−0.0418720	+	0.0514676i
$739$	2.98267e8			0.739046			0.369523	−	0.929222i	$-0.379521\pi$
$739$	2.98267e8			0.739046			0.369523	+	0.929222i	$0.379521\pi$
$740$			2.79471e8i			0.689671i
$741$	−7.38044e7	+	3.50999e7i	−0.181396	+	0.0862682i
$742$	4.59977e7			0.112596
$743$		−	5.06876e8i		−	1.23576i	−0.786271	−	0.617882i	$-0.787991\pi$
$743$		−	5.06876e8i		−	1.23576i	0.786271	−	0.617882i	$-0.212009\pi$
$744$	−1.54688e7	−	3.25263e7i	−0.0375611	−	0.0789797i
$745$	−1.12166e9			−2.71263
$746$		−	7.79216e8i		−	1.87690i
$747$	3.03586e8	+	2.46985e8i	0.728317	+	0.592529i
$748$	−2.01967e8			−0.482588
$749$			2.60374e7i			0.0619659i
$750$	−3.66704e7	+	1.74397e7i	−0.0869224	+	0.0413385i
$751$	−1.13798e8			−0.268667			−0.134333	−	0.990936i	$-0.542889\pi$
$751$	−1.13798e8			−0.268667			−0.134333	+	0.990936i	$0.542889\pi$
$752$			5.08915e7i			0.119672i
$753$	1.76927e7	+	3.72024e7i	0.0414389	+	0.0871336i
$754$	−1.27959e8			−0.298509
$755$			6.87943e8i			1.59850i
$756$	−2.82910e6	+	1.16093e7i	−0.00654761	+	0.0268683i
$757$	8.18254e7			0.188626			0.0943128	−	0.995543i	$-0.469935\pi$
$757$	8.18254e7			0.188626			0.0943128	+	0.995543i	$0.469935\pi$
$758$			1.02307e9i			2.34909i
$759$	6.66732e7	−	3.17084e7i	0.152484	−	0.0725185i
$760$	2.31901e8			0.528277
$761$			2.23329e8i			0.506747i	0.967368	+	0.253374i	$0.0815402\pi$
$761$			2.23329e8i			0.506747i	−0.967368	+	0.253374i	$0.918460\pi$
$762$	1.44400e8	+	3.03631e8i	0.326365	+	0.686247i
$763$	3.37355e7			0.0759475
$764$			4.29443e7i			0.0962998i
$765$	5.76938e8	−	7.09153e8i	1.28868	−	1.58400i
$766$	−2.90119e8			−0.645491
$767$		−	5.53557e7i		−	0.122681i
$768$	−4.36201e8	+	2.07448e8i	−0.962948	+	0.457958i
$769$	−9.49025e7			−0.208689			−0.104344	−	0.994541i	$-0.533274\pi$
$769$	−9.49025e7			−0.208689			−0.104344	+	0.994541i	$0.533274\pi$
$770$		−	4.17221e7i		−	0.0913891i
$771$	−1.93264e8	−	4.06377e8i	−0.421686	−	0.886678i
$772$	2.67764e8			0.581969
$773$			8.96641e7i			0.194124i	0.995278	+	0.0970622i	$0.0309446\pi$
$773$			8.96641e7i			0.194124i	−0.995278	+	0.0970622i	$0.969055\pi$
$774$	7.76166e8	+	6.31457e8i	1.67391	+	1.36182i
$775$	6.20938e7			0.133396
$776$		−	3.47081e8i		−	0.742755i
$777$	3.21690e7	−	1.52989e7i	0.0685765	−	0.0326136i
$778$	−1.80393e8			−0.383072
$779$			1.40082e7i			0.0296327i
$780$	4.61887e7	+	9.71208e7i	0.0973311	+	0.204658i
$781$	−4.28391e8			−0.899263
$782$		−	1.69113e8i		−	0.353637i
$783$	−3.09563e8	−	7.54381e7i	−0.644857	−	0.157147i
$784$	5.96547e8			1.23793
$785$			6.55118e8i			1.35429i
$786$	5.41189e8	−	2.57378e8i	1.11450	−	0.530034i
$787$	1.46185e8			0.299902			0.149951	−	0.988693i	$-0.452088\pi$
$787$	1.46185e8			0.299902			0.149951	+	0.988693i	$0.452088\pi$
$788$			1.98806e7i			0.0406304i
$789$	2.19867e8	+	4.62313e8i	0.447640	+	0.941251i
$790$	−4.94864e8			−1.00370
$791$		−	5.61117e7i		−	0.113377i
$792$	−1.75829e8	+	2.16123e8i	−0.353928	+	0.435036i
$793$	−1.44004e8			−0.288772
$794$		−	5.84108e8i		−	1.16689i
$795$	9.30934e8	−	4.42733e8i	1.85275	−	0.881131i
$796$	4.09456e8			0.811836
$797$		−	5.84725e8i		−	1.15499i	−0.816396	−	0.577493i	$-0.804031\pi$
$797$		−	5.84725e8i		−	1.15499i	0.816396	−	0.577493i	$-0.195969\pi$
$798$	9.13667e6	+	1.92117e7i	0.0179796	+	0.0378056i
$799$	6.99103e7			0.137057
$800$		−	4.26352e8i		−	0.832718i
$801$	−8.99132e7	−	7.31497e7i	−0.174955	−	0.142336i
$802$	−1.07781e9			−2.08938
$803$		−	6.28259e8i		−	1.21337i
$804$	−2.59552e8	+	1.23438e8i	−0.499409	+	0.237509i
$805$	1.03071e7			0.0197583
$806$		−	2.97375e7i		−	0.0567937i
$807$	−4.70856e7	−	9.90069e7i	−0.0895917	−	0.188384i
$808$	−5.88591e8			−1.11578
$809$			7.26785e8i			1.37265i	0.727294	+	0.686326i	$0.240778\pi$
$809$			7.26785e8i			1.37265i	−0.727294	+	0.686326i	$0.759222\pi$
$810$	1.84669e8	+	8.88669e8i	0.347487	+	1.67219i
$811$	6.60128e8			1.23756			0.618779	−	0.785565i	$-0.287628\pi$
$811$	6.60128e8			1.23756			0.618779	+	0.785565i	$0.287628\pi$
$812$			9.82713e6i			0.0183552i
$813$	−3.45297e8	+	1.64216e8i	−0.642571	+	0.305593i
$814$	−5.97783e8			−1.10833
$815$		−	6.74410e8i		−	1.24581i
$816$	4.13161e8	+	8.68753e8i	0.760412	+	1.59892i
$817$	5.25575e8			0.963759
$818$			3.03229e8i			0.554001i
$819$	8.65078e6	−	1.06333e7i	0.0157472	−	0.0193559i
$820$	1.84337e7			0.0334327
$821$			3.15803e8i			0.570671i	0.958428	+	0.285336i	$0.0921051\pi$
$821$			3.15803e8i			0.570671i	−0.958428	+	0.285336i	$0.907895\pi$
$822$	−2.74030e8	+	1.30323e8i	−0.493381	+	0.234642i
$823$	−1.67348e7			−0.0300206			−0.0150103	−	0.999887i	$-0.504778\pi$
$823$	−1.67348e7			−0.0300206			−0.0150103	+	0.999887i	$0.504778\pi$
$824$			1.23091e8i			0.220011i
$825$	−2.06293e8	−	4.33772e8i	−0.367386	−	0.772503i
$826$	−1.44094e7			−0.0255685
$827$		−	1.03006e9i		−	1.82116i	−0.413335	−	0.910579i	$-0.635636\pi$
$827$		−	1.03006e9i		−	1.82116i	0.413335	−	0.910579i	$-0.364364\pi$
$828$	3.84266e7	+	3.12623e7i	0.0676926	+	0.0550720i
$829$	3.58178e8			0.628688			0.314344	−	0.949309i	$-0.398216\pi$
$829$	3.58178e8			0.628688			0.314344	+	0.949309i	$0.398216\pi$
$830$		−	9.16894e8i		−	1.60356i
$831$	−6.47053e8	+	3.07725e8i	−1.12755	+	0.536241i
$832$	6.62214e7			0.114982
$833$		−	8.19484e8i		−	1.41777i
$834$	−5.13895e8	−	1.08057e9i	−0.885882	−	1.86274i
$835$	1.32640e8			0.227832
$836$		−	1.05328e8i		−	0.180270i
$837$	1.75317e7	−	7.19420e7i	0.0298984	−	0.122689i
$838$	−1.26786e9			−2.15447
$839$			3.10532e8i			0.525799i	0.964823	+	0.262900i	$0.0846788\pi$
$839$			3.10532e8i			0.525799i	−0.964823	+	0.262900i	$0.915321\pi$
$840$	−3.51263e7	+	1.67054e7i	−0.0592646	+	0.0281850i
$841$	3.32782e8			0.559464
$842$		−	8.62946e8i		−	1.44560i
$843$	1.06990e8	+	2.24968e8i	0.178592	+	0.375524i
$844$	−2.82929e7			−0.0470599
$845$			7.41832e8i			1.22952i
$846$	−4.38038e7	+	5.38422e7i	−0.0723437	+	0.0889224i
$847$	−1.38229e7			−0.0227483
$848$			1.08475e9i			1.77886i
$849$	−2.98714e8	+	1.42062e8i	−0.488127	+	0.232143i
$850$	−1.10024e9			−1.79156
$851$		−	1.47677e8i		−	0.239621i
$852$	−1.23450e8	−	2.59578e8i	−0.199605	−	0.419710i
$853$	6.61872e8			1.06642			0.533209	−	0.845984i	$-0.320986\pi$
$853$	6.61872e8			1.06642			0.533209	+	0.845984i	$0.320986\pi$
$854$			3.74850e7i			0.0601843i
$855$	3.69829e8	+	3.00878e8i	0.591702	+	0.481384i
$856$	−4.07352e8			−0.649454
$857$			8.91027e8i			1.41563i	0.706400	+	0.707813i	$0.250318\pi$
$857$			8.91027e8i			1.41563i	−0.706400	+	0.707813i	$0.749682\pi$
$858$	−2.07739e8	+	9.87965e7i	−0.328894	+	0.156415i
$859$	9.13886e8			1.44183			0.720913	−	0.693026i	$-0.243723\pi$
$859$	9.13886e8			1.44183			0.720913	+	0.693026i	$0.243723\pi$
$860$		−	6.91616e8i		−	1.08735i
$861$	−1.00911e6	−	2.12185e6i	−0.00158098	−	0.00332433i
$862$	6.28564e8			0.981359
$863$		−	2.95333e8i		−	0.459494i	−0.973250	−	0.229747i	$-0.926210\pi$
$863$		−	2.95333e8i		−	0.459494i	0.973250	−	0.229747i	$-0.0737898\pi$
$864$	−4.93971e8	−	1.20377e8i	−0.765880	−	0.186639i
$865$	−1.34397e9			−2.07655
$866$		−	8.50839e8i		−	1.31007i
$867$	6.04871e8	−	2.87664e8i	0.928123	−	0.441396i
$868$	−2.28381e6			−0.00349222
$869$		−	3.12294e8i		−	0.475888i
$870$	3.20598e8	+	6.74120e8i	0.486858	+	1.02372i
$871$	3.29711e8			0.498975
$872$			5.27787e8i			0.795993i
$873$	4.50317e8	−	5.53515e8i	0.676824	−	0.831930i
$874$	8.81941e7			0.132101
$875$		−	3.57750e6i		−	0.00534017i
$876$	3.80686e8	−	1.81047e8i	0.566311	−	0.269326i
$877$	−3.11433e8			−0.461706			−0.230853	−	0.972989i	$-0.574152\pi$
$877$	−3.11433e8			−0.461706			−0.230853	+	0.972989i	$0.574152\pi$
$878$		−	2.19281e8i		−	0.323980i
$879$	2.22364e8	+	4.67565e8i	0.327415	+	0.688454i
$880$	9.83920e8			1.44382
$881$		−	4.69407e8i		−	0.686471i	−0.939249	−	0.343235i	$-0.888477\pi$
$881$		−	4.69407e8i		−	0.686471i	0.939249	−	0.343235i	$-0.111523\pi$
$882$	6.31134e8	+	5.13465e8i	0.919848	+	0.748351i
$883$	1.28864e9			1.87175			0.935875	−	0.352331i	$-0.114611\pi$
$883$	1.28864e9			1.87175			0.935875	+	0.352331i	$0.114611\pi$
$884$			1.55460e8i			0.225041i
$885$	−2.91627e8	+	1.38692e8i	−0.420725	+	0.200088i
$886$	1.91480e8			0.275311
$887$		−	3.31556e8i		−	0.475102i	−0.971375	−	0.237551i	$-0.923655\pi$
$887$		−	3.31556e8i		−	0.475102i	0.971375	−	0.237551i	$-0.0763447\pi$
$888$	2.39350e8	+	5.03280e8i	0.341817	+	0.718738i
$889$	−2.96217e7			−0.0421604
$890$			2.71557e8i			0.385204i
$891$	−5.60814e8	+	1.16539e8i	−0.792841	+	0.164755i
$892$	−4.04981e8			−0.570611
$893$			3.64588e7i			0.0511974i
$894$	1.45377e9	−	6.91381e8i	2.03461	−	0.967620i
$895$	1.00434e9			1.40091
$896$		−	5.47070e7i		−	0.0760534i
$897$	−2.44068e7	−	5.13201e7i	−0.0338169	−	0.0711067i
$898$	−6.66786e8			−0.920784
$899$		−	6.08980e7i		−	0.0838154i
$900$	2.03391e8	−	2.50002e8i	0.279000	−	0.342938i
$901$	1.49013e9			2.03728
$902$			3.94293e7i			0.0537279i
$903$	−7.96096e7	+	3.78607e7i	−0.108119	+	0.0514192i
$904$	8.77859e8			1.18828
$905$			6.38977e8i			0.862063i
$906$	−4.24043e8	−	8.91634e8i	−0.570197	−	1.19895i
$907$	−3.75459e7			−0.0503200			−0.0251600	−	0.999683i	$-0.508010\pi$
$907$	−3.75459e7			−0.0503200			−0.0251600	+	0.999683i	$0.508010\pi$
$908$			2.39077e8i			0.319360i
$909$	−9.38669e8	−	7.63663e8i	−1.24974	−	1.01674i
$910$	−3.21147e7			−0.0426167
$911$		−	9.55810e8i		−	1.26420i	−0.774886	−	0.632101i	$-0.782193\pi$
$911$		−	9.55810e8i		−	1.26420i	0.774886	−	0.632101i	$-0.217807\pi$
$912$	−4.53062e8	+	2.15467e8i	−0.597274	+	0.284051i
$913$	5.78626e8			0.760301
$914$		−	5.14460e8i		−	0.673772i
$915$	3.60797e8	+	7.58648e8i	0.470977	+	0.990323i
$916$	1.39535e8			0.181551
$917$			5.27974e7i			0.0684707i
$918$	−3.10645e8	+	1.27474e9i	−0.401547	+	1.64776i
$919$	1.38780e9			1.78805			0.894027	−	0.448013i	$-0.147868\pi$
$919$	1.38780e9			1.78805			0.894027	+	0.448013i	$0.147868\pi$
$920$			1.61253e8i			0.207083i
$921$	7.32672e8	−	3.48444e8i	0.937844	−	0.446020i
$922$	−1.18464e9			−1.51145
$923$			3.29744e8i			0.419345i
$924$	7.58746e6	+	1.59541e7i	0.00961791	+	0.0202236i
$925$	−9.60780e8			−1.21394
$926$			8.22639e8i			1.03604i
$927$	−1.59704e8	+	1.96302e8i	−0.200482	+	0.246426i
$928$	−4.18140e8			−0.523213
$929$		−	4.76408e7i		−	0.0594199i	−0.999559	−	0.0297099i	$-0.990542\pi$
$929$		−	4.76408e7i		−	0.0594199i	0.999559	−	0.0297099i	$-0.00945836\pi$
$930$	−1.56665e8	+	7.45064e7i	−0.194770	+	0.0926286i
$931$	4.27368e8			0.529606
$932$			4.25016e8i			0.524998i
$933$	−8.16769e7	−	1.71742e8i	−0.100567	−	0.211462i
$934$	2.00095e8			0.245581
$935$		−	1.35162e9i		−	1.65356i
$936$	1.66356e8	+	1.35340e8i	0.202866	+	0.165044i
$937$	−7.63514e8			−0.928107			−0.464053	−	0.885807i	$-0.653605\pi$
$937$	−7.63514e8			−0.928107			−0.464053	+	0.885807i	$0.653605\pi$
$938$		−	8.58254e7i		−	0.103994i
$939$	1.77564e7	−	8.44460e6i	0.0214466	−	0.0101996i
$940$	4.79769e7			0.0577629
$941$		−	1.27145e9i		−	1.52591i	−0.646449	−	0.762957i	$-0.723747\pi$
$941$		−	1.27145e9i		−	1.52591i	0.646449	−	0.762957i	$-0.276253\pi$
$942$	−4.03810e8	−	8.49090e8i	−0.483086	−	1.01578i
$943$	−9.74067e6			−0.0116159
$944$		−	3.39812e8i		−	0.403945i
$945$	−7.76928e7	−	1.89331e7i	−0.0920630	−	0.0224351i
$946$	1.47935e9			1.74742
$947$		−	4.45751e8i		−	0.524859i	−0.964951	−	0.262429i	$-0.915476\pi$
$947$		−	4.45751e8i		−	0.524859i	0.964951	−	0.262429i	$-0.0845237\pi$
$948$	1.89231e8	−	8.99944e7i	0.222110	−	0.105631i
$949$	−4.83588e8			−0.565819
$950$		−	5.73787e8i		−	0.669237i
$951$	−4.74710e8	−	9.98172e8i	−0.551934	−	1.16055i
$952$	−5.62262e7			−0.0651671
$953$			4.17255e8i			0.482084i	0.970515	+	0.241042i	$0.0774891\pi$
$953$			4.17255e8i			0.482084i	−0.970515	+	0.241042i	$0.922511\pi$
$954$	−9.33674e8	+	1.14764e9i	−1.07535	+	1.32179i
$955$	−2.87395e8			−0.329966
$956$			5.06233e8i			0.579398i
$957$	−4.25418e8	+	2.02320e8i	−0.485378	+	0.230836i
$958$	1.23845e9			1.40858
$959$		−	2.67339e7i		−	0.0303114i
$960$	−1.65916e8	−	3.48870e8i	−0.187531	−	0.394321i
$961$	−8.73351e8			−0.984053
$962$			4.60130e8i			0.516839i
$963$	−6.49634e8	−	5.28516e8i	−0.727428	−	0.591806i
$964$	−5.45930e8			−0.609405
$965$			1.79195e9i			1.99409i
$966$	−1.33589e7	+	6.35321e6i	−0.0148197	+	0.00704794i
$967$	−9.03538e8			−0.999234			−0.499617	−	0.866246i	$-0.666526\pi$
$967$	−9.03538e8			−0.999234			−0.499617	+	0.866246i	$0.666526\pi$
$968$		−	2.16257e8i		−	0.238421i
$969$	2.95990e8	+	6.22378e8i	0.325316	+	0.684042i
$970$	−1.67173e9			−1.83169
$971$		−	1.35585e9i		−	1.48099i	−0.672059	−	0.740497i	$-0.734590\pi$
$971$		−	1.35585e9i		−	1.48099i	0.672059	−	0.740497i	$-0.265410\pi$
$972$	−2.32226e8	−	3.06235e8i	−0.252879	−	0.333470i
$973$	1.05418e8			0.114440
$974$		−	1.13508e9i		−	1.22843i
$975$	−3.33886e8	+	1.58790e8i	−0.360234	+	0.171320i
$976$	−8.83996e8			−0.950825
$977$		−	9.31323e8i		−	0.998658i	−0.866413	−	0.499329i	$-0.833580\pi$
$977$		−	9.31323e8i		−	0.998658i	0.866413	−	0.499329i	$-0.166420\pi$
$978$	4.15701e8	+	8.74094e8i	0.444390	+	0.934419i
$979$	−1.71372e8			−0.182638
$980$		−	5.62382e8i		−	0.597521i
$981$	−6.84773e8	+	8.41700e8i	−0.725337	+	0.891560i
$982$	3.30326e8			0.348825
$983$		−	6.67455e7i		−	0.0702686i	−0.999383	−	0.0351343i	$-0.988814\pi$
$983$		−	6.67455e7i		−	0.0702686i	0.999383	−	0.0351343i	$-0.0111859\pi$
$984$	3.31960e7	−	1.57873e7i	0.0348418	−	0.0165700i
$985$	−1.33047e8			−0.139218
$986$			1.07905e9i			1.12567i
$987$	−2.62637e6	−	5.52247e6i	−0.00273152	−	0.00574357i
$988$	−8.10736e7			−0.0840638
$989$			3.65460e8i			0.377791i
$990$	1.04097e9	+	8.46889e8i	1.07283	+	0.872812i
$991$	−6.54081e8			−0.672064			−0.336032	−	0.941851i	$-0.609085\pi$
$991$	−6.54081e8			−0.672064			−0.336032	+	0.941851i	$0.609085\pi$
$992$		−	9.71752e7i		−	0.0995453i
$993$	−1.46224e9	+	6.95409e8i	−1.49338	+	0.710220i
$994$	8.58340e7			0.0873977
$995$			2.74020e9i			2.78172i
$996$	1.66744e8	+	3.50612e8i	0.168761	+	0.354853i
$997$	−4.72616e7			−0.0476895			−0.0238447	−	0.999716i	$-0.507591\pi$
$997$	−4.72616e7			−0.0476895			−0.0238447	+	0.999716i	$0.507591\pi$
$998$			4.97454e8i			0.500451i
$999$	−2.71269e8	+	1.11316e9i	−0.272084	+	1.11651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.b.a.47.11	✓	44
3.2	odd	2	inner	69.7.b.a.47.34	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.b.a.47.11	✓	44	1.1	even	1	trivial
69.7.b.a.47.34	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)

\(f(q)\)	\(=\)	\(q-9.52809i q^{2} +(-24.3830 + 11.5961i) q^{3} -26.7846 q^{4} -179.250i q^{5} +(110.488 + 232.324i) q^{6} -22.6651 q^{7} -354.592i q^{8} +(460.063 - 565.494i) q^{9} +O(q^{10})\)	\(q-9.52809i q^{2} +(-24.3830 + 11.5961i) q^{3} -26.7846 q^{4} -179.250i q^{5} +(110.488 + 232.324i) q^{6} -22.6651 q^{7} -354.592i q^{8} +(460.063 - 565.494i) q^{9} -1707.91 q^{10} -1077.81i q^{11} +(653.089 - 310.596i) q^{12} -829.623 q^{13} +215.955i q^{14} +(2078.59 + 4370.66i) q^{15} -5092.80 q^{16} +6996.04i q^{17} +(-5388.08 - 4383.52i) q^{18} -3648.50 q^{19} +4801.14i q^{20} +(552.643 - 262.826i) q^{21} -10269.5 q^{22} -2536.99i q^{23} +(4111.87 + 8646.02i) q^{24} -16505.6 q^{25} +7904.73i q^{26} +(-4660.22 + 19123.4i) q^{27} +607.075 q^{28} +16187.7i q^{29} +(41644.0 - 19805.0i) q^{30} -3761.99 q^{31} +25830.8i q^{32} +(12498.4 + 26280.4i) q^{33} +66659.0 q^{34} +4062.72i q^{35} +(-12322.6 + 15146.5i) q^{36} +58209.4 q^{37} +34763.2i q^{38} +(20228.7 - 9620.36i) q^{39} -63560.6 q^{40} -3839.45i q^{41} +(-2504.23 - 5265.64i) q^{42} -144053. q^{43} +28868.8i q^{44} +(-101365. - 82466.3i) q^{45} -24172.7 q^{46} -9992.83i q^{47} +(124178. - 59056.4i) q^{48} -117135. q^{49} +157267. i q^{50} +(-81126.6 - 170585. i) q^{51} +22221.1 q^{52} -212996. i q^{53} +(182209. + 44403.0i) q^{54} -193198. q^{55} +8036.86i q^{56} +(88961.4 - 42308.2i) q^{57} +154238. q^{58} +66724.0i q^{59} +(-55674.3 - 117066. i) q^{60} +173578. q^{61} +35844.6i q^{62} +(-10427.4 + 12817.0i) q^{63} -79821.1 q^{64} +148710. i q^{65} +(250402. - 119086. i) q^{66} -397423. q^{67} -187386. i q^{68} +(29419.1 + 61859.6i) q^{69} +38710.0 q^{70} -397462. i q^{71} +(-200520. - 163135. i) q^{72} +582901. q^{73} -554625. i q^{74} +(402456. - 191400. i) q^{75} +97723.5 q^{76} +24428.8i q^{77} +(-91663.7 - 192741. i) q^{78} +289748. q^{79} +912884. i q^{80} +(-108125. - 520325. i) q^{81} -36582.7 q^{82} +536851. i q^{83} +(-14802.3 + 7039.68i) q^{84} +1.25404e6 q^{85} +1.37255e6i q^{86} +(-187713. - 394704. i) q^{87} -382184. q^{88} -158999. i q^{89} +(-785746. + 965813. i) q^{90} +18803.5 q^{91} +67952.3i q^{92} +(91728.7 - 43624.3i) q^{93} -95212.6 q^{94} +653993. i q^{95} +(-299535. - 629832. i) q^{96} +978817. q^{97} +1.11608e6i q^{98} +(-609497. - 495862. 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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