LMFDB - Embedded newform 69.7.b.a.47.15

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			47.15
Character	$\chi$	$=$	69.47
Dual form			69.7.b.a.47.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.32520i q^{2} +(24.9999 - 10.1983i) q^{3} +23.9919 q^{4} +138.173i q^{5} +(-64.5060 - 158.129i) q^{6} -112.869 q^{7} -556.566i q^{8} +(520.991 - 509.911i) q^{9} +O(q^{10})$	\(q-6.32520i q^{2} +(24.9999 - 10.1983i) q^{3} +23.9919 q^{4} +138.173i q^{5} +(-64.5060 - 158.129i) q^{6} -112.869 q^{7} -556.566i q^{8} +(520.991 - 509.911i) q^{9} +873.969 q^{10} -88.8573i q^{11} +(599.795 - 244.676i) q^{12} +3829.52 q^{13} +713.918i q^{14} +(1409.12 + 3454.30i) q^{15} -1984.91 q^{16} -3733.08i q^{17} +(-3225.29 - 3295.37i) q^{18} +4068.78 q^{19} +3315.03i q^{20} +(-2821.71 + 1151.07i) q^{21} -562.040 q^{22} -2536.99i q^{23} +(-5676.01 - 13914.1i) q^{24} -3466.69 q^{25} -24222.5i q^{26} +(7824.51 - 18060.9i) q^{27} -2707.94 q^{28} +23573.7i q^{29} +(21849.2 - 8912.97i) q^{30} +22629.1 q^{31} -23065.3i q^{32} +(-906.190 - 2221.42i) q^{33} -23612.5 q^{34} -15595.4i q^{35} +(12499.6 - 12233.7i) q^{36} -93227.7 q^{37} -25735.8i q^{38} +(95737.6 - 39054.4i) q^{39} +76902.2 q^{40} -54403.0i q^{41} +(7280.73 + 17847.9i) q^{42} -108971. q^{43} -2131.86i q^{44} +(70455.8 + 71986.7i) q^{45} -16047.0 q^{46} +98535.9i q^{47} +(-49622.5 + 20242.6i) q^{48} -104910. q^{49} +21927.5i q^{50} +(-38070.9 - 93326.6i) q^{51} +91877.4 q^{52} +268606. i q^{53} +(-114239. - 49491.6i) q^{54} +12277.7 q^{55} +62819.0i q^{56} +(101719. - 41494.5i) q^{57} +149108. q^{58} +204138. i q^{59} +(33807.5 + 82875.3i) q^{60} +339459. q^{61} -143134. i q^{62} +(-58803.7 + 57553.2i) q^{63} -272927. q^{64} +529135. i q^{65} +(-14050.9 + 5731.83i) q^{66} -221900. q^{67} -89563.7i q^{68} +(-25872.9 - 63424.6i) q^{69} -98644.0 q^{70} -144907. i q^{71} +(-283799. - 289966. i) q^{72} +95201.2 q^{73} +589683. i q^{74} +(-86666.9 + 35354.2i) q^{75} +97617.7 q^{76} +10029.2i q^{77} +(-247027. - 605559. i) q^{78} -275214. q^{79} -274260. i q^{80} +(11422.0 - 531318. i) q^{81} -344110. q^{82} +83972.6i q^{83} +(-67698.3 + 27616.3i) q^{84} +515810. q^{85} +689264. i q^{86} +(240411. + 589341. i) q^{87} -49455.0 q^{88} +157806. i q^{89} +(455330. - 445647. i) q^{90} -432234. q^{91} -60867.3i q^{92} +(565726. - 230778. i) q^{93} +623259. q^{94} +562194. i q^{95} +(-235226. - 576630. i) q^{96} +21395.9 q^{97} +663574. i q^{98} +(-45309.3 - 46293.8i) 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 $

$2$		−	6.32520i		−	0.790649i	−0.918541	−	0.395325i	$-0.870632\pi$
$2$		−	6.32520i		−	0.790649i	0.918541	−	0.395325i	$-0.129368\pi$
$3$	24.9999	−	10.1983i	0.925923	−	0.377713i
$3$	24.9999	−	10.1983i	0.925923	−	0.377713i
$4$	23.9919			0.374873
$5$			138.173i			1.10538i	0.833386	+	0.552691i	$0.186399\pi$
$5$			138.173i			1.10538i	−0.833386	+	0.552691i	$0.813601\pi$
$6$	−64.5060	−	158.129i	−0.298639	−	0.732080i
$7$	−112.869			−0.329064			−0.164532	−	0.986372i	$-0.552611\pi$
$7$	−112.869			−0.329064			−0.164532	+	0.986372i	$0.552611\pi$
$8$		−	556.566i		−	1.08704i
$9$	520.991	−	509.911i	0.714665	−	0.699467i
$10$	873.969			0.873969
$11$		−	88.8573i		−	0.0667598i	−0.999443	−	0.0333799i	$-0.989373\pi$
$11$		−	88.8573i		−	0.0667598i	0.999443	−	0.0333799i	$-0.0106271\pi$
$12$	599.795	−	244.676i	0.347104	−	0.141595i
$13$	3829.52			1.74307			0.871534	−	0.490336i	$-0.163126\pi$
$13$	3829.52			1.74307			0.871534	+	0.490336i	$0.163126\pi$
$14$			713.918i			0.260174i
$15$	1409.12	+	3454.30i	0.417517	+	1.02350i
$16$	−1984.91			−0.484596
$17$		−	3733.08i		−	0.759837i	−0.925020	−	0.379919i	$-0.875952\pi$
$17$		−	3733.08i		−	0.759837i	0.925020	−	0.379919i	$-0.124048\pi$
$18$	−3225.29	−	3295.37i	−0.553033	−	0.565050i
$19$	4068.78			0.593203			0.296601	−	0.955001i	$-0.404147\pi$
$19$	4068.78			0.593203			0.296601	+	0.955001i	$0.404147\pi$
$20$			3315.03i			0.414378i
$21$	−2821.71	+	1151.07i	−0.304688	+	0.124292i
$22$	−562.040			−0.0527836
$23$		−	2536.99i		−	0.208514i
$23$		−	2536.99i		−	0.208514i
$24$	−5676.01	−	13914.1i	−0.410591	−	1.00652i
$25$	−3466.69			−0.221868
$26$		−	24222.5i		−	1.37816i
$27$	7824.51	−	18060.9i	0.397527	−	0.917591i
$28$	−2707.94			−0.123357
$29$			23573.7i			0.966572i	0.875462	+	0.483286i	$0.160557\pi$
$29$			23573.7i			0.966572i	−0.875462	+	0.483286i	$0.839443\pi$
$30$	21849.2	−	8912.97i	0.809228	−	0.330110i
$31$	22629.1			0.759595			0.379798	−	0.925070i	$-0.375994\pi$
$31$	22629.1			0.759595			0.379798	+	0.925070i	$0.375994\pi$
$32$		−	23065.3i		−	0.703897i
$33$	−906.190	−	2221.42i	−0.0252161	−	0.0618144i
$34$	−23612.5			−0.600765
$35$		−	15595.4i		−	0.363741i
$36$	12499.6	−	12233.7i	0.267909	−	0.262212i
$37$	−93227.7			−1.84052			−0.920258	−	0.391312i	$-0.872021\pi$
$37$	−93227.7			−1.84052			−0.920258	+	0.391312i	$0.872021\pi$
$38$		−	25735.8i		−	0.469016i
$39$	95737.6	−	39054.4i	1.61395	−	0.658380i
$40$	76902.2			1.20160
$41$		−	54403.0i		−	0.789353i	−0.918820	−	0.394677i	$-0.870857\pi$
$41$		−	54403.0i		−	0.789353i	0.918820	−	0.394677i	$-0.129143\pi$
$42$	7280.73	+	17847.9i	0.0982713	+	0.240901i
$43$	−108971.			−1.37059			−0.685293	−	0.728267i	$-0.740326\pi$
$43$	−108971.			−1.37059			−0.685293	+	0.728267i	$0.740326\pi$
$44$		−	2131.86i		−	0.0250265i
$45$	70455.8	+	71986.7i	0.773178	+	0.789978i
$46$	−16047.0			−0.164862
$47$			98535.9i			0.949075i	0.880235	+	0.474538i	$0.157385\pi$
$47$			98535.9i			0.949075i	−0.880235	+	0.474538i	$0.842615\pi$
$48$	−49622.5	+	20242.6i	−0.448699	+	0.183039i
$49$	−104910.			−0.891717
$50$			21927.5i			0.175420i
$51$	−38070.9	−	93326.6i	−0.287001	−	0.703550i
$52$	91877.4			0.653430
$53$			268606.i			1.80421i	0.431514	+	0.902106i	$0.357980\pi$
$53$			268606.i			1.80421i	−0.431514	+	0.902106i	$0.642020\pi$
$54$	−114239.	−	49491.6i	−0.725493	−	0.314304i
$55$	12277.7			0.0737951
$56$			62819.0i			0.357707i
$57$	101719.	−	41494.5i	0.549260	−	0.224061i
$58$	149108.			0.764220
$59$			204138.i			0.993959i	0.867762	+	0.496980i	$0.165558\pi$
$59$			204138.i			0.993959i	−0.867762	+	0.496980i	$0.834442\pi$
$60$	33807.5	+	82875.3i	0.156516	+	0.383682i
$61$	339459.			1.49554			0.747769	−	0.663959i	$-0.231125\pi$
$61$	339459.			1.49554			0.747769	+	0.663959i	$0.231125\pi$
$62$		−	143134.i		−	0.600574i
$63$	−58803.7	+	57553.2i	−0.235171	+	0.230169i
$64$	−272927.			−1.04113
$65$			529135.i			1.92675i
$66$	−14050.9	+	5731.83i	−0.0488735	+	0.0199371i
$67$	−221900.			−0.737789			−0.368895	−	0.929471i	$-0.620264\pi$
$67$	−221900.			−0.737789			−0.368895	+	0.929471i	$0.620264\pi$
$68$		−	89563.7i		−	0.284843i
$69$	−25872.9	−	63424.6i	−0.0787587	−	0.193068i
$70$	−98644.0			−0.287592
$71$		−	144907.i		−	0.404870i	−0.979296	−	0.202435i	$-0.935114\pi$
$71$		−	144907.i		−	0.404870i	0.979296	−	0.202435i	$-0.0648855\pi$
$72$	−283799.	−	289966.i	−0.760350	−	0.776872i
$73$	95201.2			0.244723			0.122361	−	0.992486i	$-0.460953\pi$
$73$	95201.2			0.244723			0.122361	+	0.992486i	$0.460953\pi$
$74$			589683.i			1.45520i
$75$	−86666.9	+	35354.2i	−0.205433	+	0.0838026i
$76$	97617.7			0.222376
$77$			10029.2i			0.0219683i
$78$	−247027.	−	605559.i	−0.520548	−	1.27607i
$79$	−275214.			−0.558199			−0.279099	−	0.960262i	$-0.590036\pi$
$79$	−275214.			−0.558199			−0.279099	+	0.960262i	$0.590036\pi$
$80$		−	274260.i		−	0.535664i
$81$	11422.0	−	531318.i	0.0214924	−	0.999769i
$82$	−344110.			−0.624102
$83$			83972.6i			0.146860i	0.997300	+	0.0734300i	$0.0233946\pi$
$83$			83972.6i			0.146860i	−0.997300	+	0.0734300i	$0.976605\pi$
$84$	−67698.3	+	27616.3i	−0.114219	+	0.0465937i
$85$	515810.			0.839910
$86$			689264.i			1.08365i
$87$	240411.	+	589341.i	0.365087	+	0.894971i
$88$	−49455.0			−0.0725708
$89$			157806.i			0.223849i	0.993717	+	0.111924i	$0.0357014\pi$
$89$			157806.i			0.223849i	−0.993717	+	0.111924i	$0.964299\pi$
$90$	455330.	−	445647.i	0.624595	−	0.611312i
$91$	−432234.			−0.573581
$92$		−	60867.3i		−	0.0781665i
$93$	565726.	−	230778.i	0.703327	−	0.286909i
$94$	623259.			0.750386
$95$			562194.i			0.655716i
$96$	−235226.	−	576630.i	−0.265871	−	0.651754i
$97$	21395.9			0.0234431			0.0117216	−	0.999931i	$-0.496269\pi$
$97$	21395.9			0.0234431			0.0117216	+	0.999931i	$0.496269\pi$
$98$			663574.i			0.705035i
$99$	−45309.3	−	46293.8i	−0.0466963	−	0.0477109i
$100$	−83172.5			−0.0831725
$101$		−	928319.i		−	0.901017i	−0.892772	−	0.450509i	$-0.851243\pi$
$101$		−	928319.i		−	0.901017i	0.892772	−	0.450509i	$-0.148757\pi$
$102$	−590309.	+	240806.i	−0.556262	+	0.226917i
$103$	172198.			0.157585			0.0787927	−	0.996891i	$-0.474893\pi$
$103$	172198.			0.157585			0.0787927	+	0.996891i	$0.474893\pi$
$104$		−	2.13138e6i		−	1.89479i
$105$	−159046.	−	389884.i	−0.137390	−	0.336796i
$106$	1.69898e6			1.42650
$107$		−	340216.i		−	0.277718i	−0.990312	−	0.138859i	$-0.955657\pi$
$107$		−	340216.i		−	0.277718i	0.990312	−	0.138859i	$-0.0443435\pi$
$108$	187725.	−	433316.i	0.149022	−	0.343980i
$109$	−719387.			−0.555499			−0.277749	−	0.960654i	$-0.589588\pi$
$109$	−719387.			−0.555499			−0.277749	+	0.960654i	$0.589588\pi$
$110$		−	77658.6i		−	0.0583460i
$111$	−2.33068e6	+	950760.i	−1.70418	+	0.695188i
$112$	224034.			0.159463
$113$			1.69167e6i			1.17241i	0.810161	+	0.586207i	$0.199380\pi$
$113$			1.69167e6i			1.17241i	−0.810161	+	0.586207i	$0.800620\pi$
$114$	−262461.	−	643393.i	−0.177153	−	0.434272i
$115$	350543.			0.230488
$116$			565579.i			0.362342i
$117$	1.99514e6	−	1.95272e6i	1.24571	−	1.21922i
$118$	1.29122e6			0.785873
$119$			421349.i			0.250035i
$120$	1.92255e6	−	784269.i	1.11259	−	0.453859i
$121$	1.76367e6			0.995543
$122$		−	2.14714e6i		−	1.18245i
$123$	−554816.	−	1.36007e6i	−0.298149	−	0.730880i
$124$	542915.			0.284752
$125$			1.67995e6i			0.860132i
$126$	364035.	+	371945.i	0.181983	+	0.185938i
$127$	−1.15937e6			−0.565992			−0.282996	−	0.959121i	$-0.591328\pi$
$127$	−1.15937e6			−0.565992			−0.282996	+	0.959121i	$0.591328\pi$
$128$			250135.i			0.119274i
$129$	−2.72427e6	+	1.11132e6i	−1.26906	+	0.517689i
$130$	3.34688e6			1.52339
$131$		−	1.97726e6i		−	0.879527i	−0.898114	−	0.439763i	$-0.855062\pi$
$131$		−	1.97726e6i		−	0.879527i	0.898114	−	0.439763i	$-0.144938\pi$
$132$	−21741.2	−	53296.2i	−0.00945284	−	0.0231726i
$133$	−459239.			−0.195202
$134$			1.40356e6i			0.583333i
$135$	2.49553e6	+	1.08113e6i	1.01429	+	0.439418i
$136$	−2.07770e6			−0.825975
$137$		−	1.19005e6i		−	0.462811i	−0.972857	−	0.231405i	$-0.925668\pi$
$137$		−	1.19005e6i		−	0.462811i	0.972857	−	0.231405i	$-0.0743323\pi$
$138$	−401173.	+	163651.i	−0.152649	+	0.0622705i
$139$	−3.99314e6			−1.48686			−0.743430	−	0.668814i	$-0.766802\pi$
$139$	−3.99314e6			−1.48686			−0.743430	+	0.668814i	$0.766802\pi$
$140$		−	374163.i		−	0.136357i
$141$	1.00489e6	+	2.46339e6i	0.358479	+	0.878770i
$142$	−916568.			−0.320110
$143$		−	340281.i		−	0.116367i
$144$	−1.03412e6	+	1.01213e6i	−0.346324	+	0.338959i
$145$	−3.25725e6			−1.06843
$146$		−	602166.i		−	0.193490i
$147$	−2.62273e6	+	1.06990e6i	−0.825661	+	0.336813i
$148$	−2.23671e6			−0.689961
$149$			2.46284e6i			0.744523i	0.928128	+	0.372262i	$0.121418\pi$
$149$			2.46284e6i			0.744523i	−0.928128	+	0.372262i	$0.878582\pi$
$150$	223622.	+	548185.i	0.0662585	+	0.162425i
$151$	−3.81010e6			−1.10664			−0.553319	−	0.832969i	$-0.686639\pi$
$151$	−3.81010e6			−1.10664			−0.553319	+	0.832969i	$0.686639\pi$
$152$		−	2.26454e6i		−	0.644837i
$153$	−1.90354e6	−	1.94490e6i	−0.531481	−	0.543029i
$154$	63436.9			0.0173692
$155$			3.12672e6i			0.839643i
$156$	2.29693e6	−	936990.i	0.605025	−	0.246809i
$157$	−1.28528e6			−0.332123			−0.166061	−	0.986115i	$-0.553105\pi$
$157$	−1.28528e6			−0.332123			−0.166061	+	0.986115i	$0.553105\pi$
$158$			1.74078e6i			0.441339i
$159$	2.73931e6	+	6.71512e6i	0.681475	+	1.67056i
$160$	3.18699e6			0.778075
$161$			286348.i			0.0686146i
$162$	−3.36069e6	−	72246.1i	−0.790467	−	0.0169930i
$163$	−4.26371e6			−0.984520			−0.492260	−	0.870448i	$-0.663829\pi$
$163$	−4.26371e6			−0.984520			−0.492260	+	0.870448i	$0.663829\pi$
$164$		−	1.30523e6i		−	0.295907i
$165$	306940.	−	125211.i	0.0683285	−	0.0278734i
$166$	531143.			0.116115
$167$			8.79027e6i			1.88735i	0.330872	+	0.943676i	$0.392657\pi$
$167$			8.79027e6i			1.88735i	−0.330872	+	0.943676i	$0.607343\pi$
$168$	640645.	+	1.57047e6i	0.135111	+	0.331209i
$169$	9.83841e6			2.03828
$170$		−	3.26260e6i		−	0.664074i
$171$	2.11980e6	−	2.07472e6i	0.423941	−	0.414926i
$172$	−2.61443e6			−0.513796
$173$			3.26197e6i			0.630001i	0.949091	+	0.315001i	$0.102005\pi$
$173$			3.26197e6i			0.630001i	−0.949091	+	0.315001i	$0.897995\pi$
$174$	3.72770e6	−	1.52065e6i	0.707608	−	0.288656i
$175$	391282.			0.0730088
$176$			176374.i			0.0323516i
$177$	2.08186e6	+	5.10344e6i	0.375432	+	0.920329i
$178$	998156.			0.176986
$179$		−	2.85340e6i		−	0.497512i	−0.968566	−	0.248756i	$-0.919978\pi$
$179$		−	2.85340e6i		−	0.497512i	0.968566	−	0.248756i	$-0.0800218\pi$
$180$	1.69037e6	+	1.72710e6i	0.289844	+	0.296142i
$181$	−2.36232e6			−0.398384			−0.199192	−	0.979960i	$-0.563832\pi$
$181$	−2.36232e6			−0.398384			−0.199192	+	0.979960i	$0.563832\pi$
$182$			2.73396e6i			0.453501i
$183$	8.48643e6	−	3.46189e6i	1.38475	−	0.564885i
$184$	−1.41201e6			−0.226664
$185$		−	1.28815e7i		−	2.03447i
$186$	−1.45971e6	−	3.57833e6i	−0.226845	−	0.556085i
$187$	−331711.			−0.0507266
$188$			2.36406e6i			0.355783i
$189$	−883145.	+	2.03852e6i	−0.130812	+	0.301946i
$190$	3.55599e6			0.518441
$191$		−	1.32304e7i		−	1.89877i	−0.314116	−	0.949385i	$-0.601708\pi$
$191$		−	1.32304e7i		−	1.89877i	0.314116	−	0.949385i	$-0.398292\pi$
$192$	−6.82314e6	+	2.78338e6i	−0.964008	+	0.393250i
$193$	−2.90958e6			−0.404723			−0.202362	−	0.979311i	$-0.564862\pi$
$193$	−2.90958e6			−0.404723			−0.202362	+	0.979311i	$0.564862\pi$
$194$		−	135333.i		−	0.0185353i
$195$	5.39626e6	+	1.32283e7i	0.727761	+	1.78403i
$196$	−2.51698e6			−0.334281
$197$		−	9.81918e6i		−	1.28433i	−0.766566	−	0.642165i	$-0.778036\pi$
$197$		−	9.81918e6i		−	1.28433i	0.766566	−	0.642165i	$-0.221964\pi$
$198$	−292818.	+	286590.i	−0.0377226	+	0.0369204i
$199$	8.45304e6			1.07264			0.536319	−	0.844015i	$-0.319814\pi$
$199$	8.45304e6			1.07264			0.536319	+	0.844015i	$0.319814\pi$
$200$			1.92944e6i			0.241180i
$201$	−5.54747e6	+	2.26299e6i	−0.683136	+	0.278673i
$202$	−5.87180e6			−0.712389
$203$		−	2.66074e6i		−	0.318064i
$204$	−913394.	−	2.23908e6i	−0.107589	−	0.263742i
$205$	7.51701e6			0.872536
$206$		−	1.08918e6i		−	0.124595i
$207$	−1.29364e6	−	1.32175e6i	−0.145849	−	0.149018i
$208$	−7.60124e6			−0.844684
$209$		−	361541.i		−	0.0396021i
$210$	−2.46609e6	+	1.00600e6i	−0.266288	+	0.108627i
$211$	1.01210e7			1.07740			0.538700	−	0.842498i	$-0.318916\pi$
$211$	1.01210e7			1.07740			0.538700	+	0.842498i	$0.318916\pi$
$212$			6.44436e6i			0.676351i
$213$	−1.47780e6	−	3.62267e6i	−0.152925	−	0.374878i
$214$	−2.15194e6			−0.219578
$215$		−	1.50568e7i		−	1.51502i
$216$	−1.00521e7	−	4.35486e6i	−0.997460	−	0.432128i
$217$	−2.55412e6			−0.249956
$218$			4.55026e6i			0.439205i
$219$	2.38002e6	−	970887.i	0.226594	−	0.0924350i
$220$	294564.			0.0276638
$221$		−	1.42959e7i		−	1.32445i
$222$	6.01374e6	+	1.47420e7i	0.549650	+	1.34741i
$223$	−4.19344e6			−0.378143			−0.189071	−	0.981963i	$-0.560548\pi$
$223$	−4.19344e6			−0.378143			−0.189071	+	0.981963i	$0.560548\pi$
$224$			2.60336e6i			0.231627i
$225$	−1.80611e6	+	1.76770e6i	−0.158561	+	0.155189i
$226$	1.07002e7			0.926969
$227$			2.33421e6i			0.199555i	0.995010	+	0.0997774i	$0.0318131\pi$
$227$			2.33421e6i			0.199555i	−0.995010	+	0.0997774i	$0.968187\pi$
$228$	2.44043e6	−	995531.i	0.205903	−	0.0839944i
$229$	−7.10364e6			−0.591527			−0.295763	−	0.955261i	$-0.595574\pi$
$229$	−7.10364e6			−0.591527			−0.295763	+	0.955261i	$0.595574\pi$
$230$		−	2.21726e6i		−	0.182235i
$231$	102281.	+	250730.i	0.00829771	+	0.0203409i
$232$	1.31203e7			1.05071
$233$		−	2.80360e6i		−	0.221640i	−0.993840	−	0.110820i	$-0.964652\pi$
$233$		−	2.80360e6i		−	0.221640i	0.993840	−	0.110820i	$-0.0353477\pi$
$234$	−1.23513e7	−	1.26197e7i	−0.963974	−	0.984920i
$235$	−1.36150e7			−1.04909
$236$			4.89767e6i			0.372609i
$237$	−6.88032e6	+	2.80670e6i	−0.516849	+	0.210839i
$238$	2.66511e6			0.197690
$239$			1.92244e7i			1.40818i	0.710111	+	0.704090i	$0.248645\pi$
$239$			1.92244e7i			1.40818i	−0.710111	+	0.704090i	$0.751355\pi$
$240$	−2.79698e6	−	6.85647e6i	−0.202327	−	0.495983i
$241$	1.68287e7			1.20226			0.601132	−	0.799150i	$-0.294717\pi$
$241$	1.68287e7			1.20226			0.601132	+	0.799150i	$0.294717\pi$
$242$		−	1.11555e7i		−	0.787126i
$243$	−5.13298e6	−	1.33994e7i	−0.357726	−	0.933827i
$244$	8.14425e6			0.560637
$245$		−	1.44956e7i		−	0.985687i
$246$	−8.60271e6	+	3.50932e6i	−0.577870	+	0.235732i
$247$	1.55815e7			1.03399
$248$		−	1.25946e7i		−	0.825713i
$249$	856375.	+	2.09931e6i	0.0554710	+	0.135981i
$250$	1.06260e7			0.680063
$251$		−	2.68125e7i		−	1.69557i	−0.530337	−	0.847787i	$-0.677935\pi$
$251$		−	2.68125e7i		−	1.69557i	0.530337	−	0.847787i	$-0.322065\pi$
$252$	−1.41081e6	+	1.38081e6i	−0.0881592	+	0.0862844i
$253$	−225431.			−0.0139204
$254$			7.33324e6i			0.447502i
$255$	1.28952e7	−	5.26036e6i	0.777691	−	0.317245i
$256$	−1.58851e7			−0.946829
$257$			1.88441e7i			1.11014i	0.831805	+	0.555068i	$0.187308\pi$
$257$			1.88441e7i			1.11014i	−0.831805	+	0.555068i	$0.812692\pi$
$258$	7.02930e6	+	1.72315e7i	0.409310	+	1.00338i
$259$	1.05225e7			0.605648
$260$			1.26950e7i			0.722289i
$261$	1.20205e7	+	1.22817e7i	0.676085	+	0.690775i
$262$	−1.25065e7			−0.695397
$263$		−	1.50937e7i		−	0.829713i	−0.909887	−	0.414857i	$-0.863832\pi$
$263$		−	1.50937e7i		−	0.829713i	0.909887	−	0.414857i	$-0.136168\pi$
$264$	−1.23637e6	+	504355.i	−0.0671949	+	0.0274110i
$265$	−3.71140e7			−1.99434
$266$			2.90478e6i			0.154336i
$267$	1.60935e6	+	3.94514e6i	0.0845506	+	0.207266i
$268$	−5.32379e6			−0.276578
$269$			2.72642e7i			1.40067i	0.713815	+	0.700334i	$0.246966\pi$
$269$			2.72642e7i			1.40067i	−0.713815	+	0.700334i	$0.753034\pi$
$270$	6.83839e6	−	1.57847e7i	0.347426	−	0.801946i
$271$	3.75170e7			1.88504			0.942520	−	0.334150i	$-0.108449\pi$
$271$	3.75170e7			1.88504			0.942520	+	0.334150i	$0.108449\pi$
$272$			7.40982e6i			0.368214i
$273$	−1.08058e7	+	4.40803e6i	−0.531091	+	0.216649i
$274$	−7.52729e6			−0.365921
$275$			308041.i			0.0148119i
$276$	−620741.	−	1.52168e6i	−0.0295245	−	0.0723761i
$277$	1.00994e7			0.475180			0.237590	−	0.971366i	$-0.423643\pi$
$277$	1.00994e7			0.475180			0.237590	+	0.971366i	$0.423643\pi$
$278$			2.52574e7i			1.17558i
$279$	1.17896e7	−	1.15388e7i	0.542856	−	0.531312i
$280$	−8.67987e6			−0.395402
$281$			3.82323e7i			1.72310i	0.507669	+	0.861552i	$0.330507\pi$
$281$			3.82323e7i			1.72310i	−0.507669	+	0.861552i	$0.669493\pi$
$282$	1.55814e7	−	6.35616e6i	0.694799	−	0.283431i
$283$	−3.95781e7			−1.74621			−0.873104	−	0.487533i	$-0.837897\pi$
$283$	−3.95781e7			−1.74621			−0.873104	+	0.487533i	$0.837897\pi$
$284$		−	3.47661e6i		−	0.151775i
$285$	5.73340e6	+	1.40548e7i	0.247673	+	0.607142i
$286$	−2.15234e6			−0.0920054
$287$			6.14041e6i			0.259748i
$288$	−1.17613e7	−	1.20168e7i	−0.492353	−	0.503051i
$289$	1.02017e7			0.422648
$290$			2.06027e7i			0.844754i
$291$	534895.	−	218201.i	0.0217065	−	0.00885478i
$292$	2.28406e6			0.0917400
$293$		−	2.00143e7i		−	0.795678i	−0.917455	−	0.397839i	$-0.869760\pi$
$293$		−	2.00143e7i		−	0.795678i	0.917455	−	0.397839i	$-0.130240\pi$
$294$	6.76730e6	+	1.65893e7i	0.266301	+	0.652808i
$295$	−2.82063e7			−1.09870
$296$			5.18873e7i			2.00072i
$297$	−1.60485e6	−	695265.i	−0.0612582	−	0.0265388i
$298$	1.55780e7			0.588657
$299$		−	9.71547e6i		−	0.363455i
$300$	−2.07930e6	+	848215.i	−0.0770113	+	0.0314154i
$301$	1.22995e7			0.451011
$302$			2.40996e7i			0.874963i
$303$	−9.46724e6	−	2.32079e7i	−0.340326	−	0.834272i
$304$	−8.07615e6			−0.287464
$305$			4.69039e7i			1.65314i
$306$	−1.23019e7	+	1.20403e7i	−0.429346	+	0.420215i
$307$	−4.32938e7			−1.49627			−0.748137	−	0.663545i	$-0.769051\pi$
$307$	−4.32938e7			−1.49627			−0.748137	+	0.663545i	$0.769051\pi$
$308$			240620.i			0.00823532i
$309$	4.30493e6	−	1.75612e6i	0.145912	−	0.0595221i
$310$	1.97771e7			0.663863
$311$		−	1.19688e6i		−	0.0397895i	−0.999802	−	0.0198947i	$-0.993667\pi$
$311$		−	1.19688e6i		−	0.0397895i	0.999802	−	0.0198947i	$-0.00633311\pi$
$312$	−2.17364e7	−	5.32843e7i	−0.715687	−	1.75443i
$313$	−6.66011e6			−0.217194			−0.108597	−	0.994086i	$-0.534636\pi$
$313$	−6.66011e6			−0.217194			−0.108597	+	0.994086i	$0.534636\pi$
$314$			8.12965e6i			0.262593i
$315$	−7.95227e6	−	8.12507e6i	−0.254425	−	0.259953i
$316$	−6.60290e6			−0.209254
$317$		−	5.84084e7i		−	1.83357i	−0.399382	−	0.916784i	$-0.630775\pi$
$317$		−	5.84084e7i		−	1.83357i	0.399382	−	0.916784i	$-0.369225\pi$
$318$	4.24745e7	−	1.73267e7i	1.32083	−	0.538808i
$319$	2.09470e6			0.0645282
$320$		−	3.77110e7i		−	1.15085i
$321$	−3.46962e6	−	8.50538e6i	−0.104898	−	0.257145i
$322$	1.81121e6			0.0542501
$323$		−	1.51891e7i		−	0.450738i
$324$	274034.	−	1.27473e7i	0.00805694	−	0.374787i
$325$	−1.32758e7			−0.386731
$326$			2.69688e7i			0.778410i
$327$	−1.79846e7	+	7.33650e6i	−0.514349	+	0.209819i
$328$	−3.02789e7			−0.858061
$329$		−	1.11216e7i		−	0.312307i
$330$	−791982.	−	1.94146e6i	−0.0220381	−	0.0540239i
$331$	−1.47605e7			−0.407022			−0.203511	−	0.979073i	$-0.565235\pi$
$331$	−1.47605e7			−0.407022			−0.203511	+	0.979073i	$0.565235\pi$
$332$			2.01466e6i			0.0550539i
$333$	−4.85708e7	+	4.75378e7i	−1.31535	+	1.28738i
$334$	5.56002e7			1.49223
$335$		−	3.06605e7i		−	0.815538i
$336$	5.60084e6	−	2.28476e6i	0.147651	−	0.0602314i
$337$	4.01067e7			1.04792			0.523959	−	0.851743i	$-0.324454\pi$
$337$	4.01067e7			1.04792			0.523959	+	0.851743i	$0.324454\pi$
$338$		−	6.22299e7i		−	1.61157i
$339$	1.72521e7	+	4.22917e7i	0.442837	+	1.08556i
$340$	1.23753e7			0.314860
$341$		−	2.01076e6i		−	0.0507105i
$342$	−1.31230e7	−	1.34081e7i	−0.328061	−	0.335189i
$343$	2.51200e7			0.622496
$344$			6.06497e7i			1.48989i
$345$	8.76355e6	−	3.57493e6i	0.213414	−	0.0870584i
$346$	2.06326e7			0.498110
$347$		−	7.30166e6i		−	0.174756i	−0.996175	−	0.0873782i	$-0.972151\pi$
$347$		−	7.30166e6i		−	0.174756i	0.996175	−	0.0873782i	$-0.0278489\pi$
$348$	5.76792e6	+	1.41394e7i	0.136862	+	0.335501i
$349$	−2.53495e7			−0.596339			−0.298170	−	0.954513i	$-0.596376\pi$
$349$	−2.53495e7			−0.596339			−0.298170	+	0.954513i	$0.596376\pi$
$350$		−	2.47493e6i		−	0.0577244i
$351$	2.99641e7	−	6.91647e7i	0.692916	−	1.59942i
$352$	−2.04952e6			−0.0469920
$353$			9.13972e6i			0.207782i	0.994589	+	0.103891i	$0.0331294\pi$
$353$			9.13972e6i			0.207782i	−0.994589	+	0.103891i	$0.966871\pi$
$354$	3.22803e7	−	1.31682e7i	0.727658	−	0.296835i
$355$	2.00223e7			0.447536
$356$			3.78607e6i			0.0839149i
$357$	4.29703e6	+	1.05337e7i	0.0944416	+	0.231513i
$358$	−1.80483e7			−0.393358
$359$		−	3.75800e7i		−	0.812219i	−0.913824	−	0.406109i	$-0.866885\pi$
$359$		−	3.75800e7i		−	0.812219i	0.913824	−	0.406109i	$-0.133115\pi$
$360$	4.00654e7	−	3.92133e7i	0.858740	−	0.840477i
$361$	−3.04909e7			−0.648110
$362$			1.49421e7i			0.314982i
$363$	4.40915e7	−	1.79863e7i	0.921796	−	0.376030i
$364$	−1.03701e7			−0.215020
$365$			1.31542e7i			0.270512i
$366$	−2.18971e7	−	5.36783e7i	−0.446626	−	1.09485i
$367$	6.76632e7			1.36885			0.684423	−	0.729085i	$-0.260054\pi$
$367$	6.76632e7			1.36885			0.684423	+	0.729085i	$0.260054\pi$
$368$			5.03570e6i			0.101045i
$369$	−2.77407e7	−	2.83435e7i	−0.552126	−	0.564123i
$370$	−8.14781e7			−1.60855
$371$		−	3.03173e7i		−	0.593702i
$372$	1.35728e7	−	5.53679e6i	0.263658	−	0.107555i
$373$	5.95078e6			0.114669			0.0573347	−	0.998355i	$-0.481740\pi$
$373$	5.95078e6			0.114669			0.0573347	+	0.998355i	$0.481740\pi$
$374$			2.09814e6i			0.0401069i
$375$	1.71325e7	+	4.19985e7i	0.324884	+	0.796416i
$376$	5.48417e7			1.03169
$377$			9.02760e7i			1.68480i
$378$	1.28940e7	+	5.58606e6i	0.238734	+	0.103426i
$379$	7.30729e6			0.134227			0.0671133	−	0.997745i	$-0.478621\pi$
$379$	7.30729e6			0.134227			0.0671133	+	0.997745i	$0.478621\pi$
$380$			1.34881e7i			0.245810i
$381$	−2.89841e7	+	1.18236e7i	−0.524065	+	0.213783i
$382$	−8.36847e7			−1.50126
$383$		−	8.03828e7i		−	1.43076i	−0.698735	−	0.715380i	$-0.746253\pi$
$383$		−	8.03828e7i		−	1.43076i	0.698735	−	0.715380i	$-0.253747\pi$
$384$	2.55094e6	+	6.25335e6i	0.0450513	+	0.110438i
$385$	−1.38577e6			−0.0242833
$386$			1.84037e7i			0.319994i
$387$	−5.67730e7	+	5.55656e7i	−0.979510	+	0.958680i
$388$	513328.			0.00878820
$389$			3.57957e7i			0.608111i	0.952654	+	0.304055i	$0.0983408\pi$
$389$			3.57957e7i			0.608111i	−0.952654	+	0.304055i	$0.901659\pi$
$390$	8.36717e7	−	3.41324e7i	1.41054	−	0.575404i
$391$	−9.47080e6			−0.158437
$392$			5.83891e7i			0.969335i
$393$	−2.01646e7	−	4.94312e7i	−0.332209	−	0.814373i
$394$	−6.21083e7			−1.01546
$395$		−	3.80270e7i		−	0.617022i
$396$	−1.08706e6	−	1.11068e6i	−0.0175052	−	0.0178856i
$397$	2.21929e7			0.354685			0.177343	−	0.984149i	$-0.443250\pi$
$397$	2.21929e7			0.354685			0.177343	+	0.984149i	$0.443250\pi$
$398$		−	5.34671e7i		−	0.848081i
$399$	−1.14809e7	+	4.68344e6i	−0.180742	+	0.0737303i
$400$	6.88106e6			0.107517
$401$			1.15454e8i			1.79051i	0.445551	+	0.895257i	$0.353008\pi$
$401$			1.15454e8i			1.79051i	−0.445551	+	0.895257i	$0.646992\pi$
$402$	1.43139e7	+	3.50888e7i	0.220333	+	0.540121i
$403$	8.66586e7			1.32403
$404$		−	2.22721e7i		−	0.337767i
$405$	7.34137e7	+	1.57820e6i	1.10513	+	0.0237573i
$406$	−1.68297e7			−0.251477
$407$			8.28396e6i			0.122873i
$408$	−5.19424e7	+	2.11890e7i	−0.764789	+	0.311982i
$409$	6.14099e7			0.897570			0.448785	−	0.893640i	$-0.351857\pi$
$409$	6.14099e7			0.897570			0.448785	+	0.893640i	$0.351857\pi$
$410$		−	4.75465e7i		−	0.689870i
$411$	−1.21364e7	−	2.97511e7i	−0.174810	−	0.428527i
$412$	4.13135e6			0.0590745
$413$		−	2.30409e7i		−	0.327076i
$414$	−8.36033e6	+	8.18254e6i	−0.117821	+	0.115315i
$415$	−1.16027e7			−0.162336
$416$		−	8.83290e7i		−	1.22694i
$417$	−9.98281e7	+	4.07231e7i	−1.37672	+	0.561607i
$418$	−2.28682e6			−0.0313114
$419$		−	5.45273e7i		−	0.741262i	−0.928780	−	0.370631i	$-0.879141\pi$
$419$		−	5.45273e7i		−	0.741262i	0.928780	−	0.370631i	$-0.120859\pi$
$420$	−3.81582e6	−	9.35405e6i	−0.0515039	−	0.126256i
$421$	1.84684e7			0.247505			0.123752	−	0.992313i	$-0.460507\pi$
$421$	1.84684e7			0.247505			0.123752	+	0.992313i	$0.460507\pi$
$422$		−	6.40174e7i		−	0.851846i
$423$	5.02445e7	+	5.13363e7i	0.663847	+	0.678271i
$424$	1.49497e8			1.96126
$425$			1.29414e7i			0.168584i
$426$	−2.29141e7	+	9.34740e6i	−0.296397	+	0.120910i
$427$	−3.83143e7			−0.492128
$428$		−	8.16244e6i		−	0.104109i
$429$	−3.47027e6	−	8.50699e6i	−0.0439533	−	0.107747i
$430$	−9.52375e7			−1.19785
$431$			3.75312e7i			0.468771i	0.972144	+	0.234386i	$0.0753079\pi$
$431$			3.75312e7i			0.468771i	−0.972144	+	0.234386i	$0.924692\pi$
$432$	−1.55309e7	+	3.58493e7i	−0.192640	+	0.444661i
$433$	−5.13815e7			−0.632912			−0.316456	−	0.948607i	$-0.602493\pi$
$433$	−5.13815e7			−0.632912			−0.316456	+	0.948607i	$0.602493\pi$
$434$			1.61553e7i			0.197627i
$435$	−8.14308e7	+	3.32182e7i	−0.989284	+	0.403561i
$436$	−1.72595e7			−0.208242
$437$		−	1.03225e7i		−	0.123691i
$438$	−6.14105e6	−	1.50541e7i	−0.0730837	−	0.179157i
$439$	1.53939e8			1.81951			0.909755	−	0.415146i	$-0.136270\pi$
$439$	1.53939e8			1.81951			0.909755	+	0.415146i	$0.136270\pi$
$440$		−	6.83332e6i		−	0.0802184i
$441$	−5.46569e7	+	5.34946e7i	−0.637279	+	0.623726i
$442$	−9.04244e7			−1.04717
$443$		−	9.36334e6i		−	0.107701i	−0.998549	−	0.0538505i	$-0.982851\pi$
$443$		−	9.36334e6i		−	0.107701i	0.998549	−	0.0538505i	$-0.0171494\pi$
$444$	−5.59175e7	+	2.28105e7i	−0.638850	+	0.260607i
$445$	−2.18045e7			−0.247438
$446$			2.65243e7i			0.298978i
$447$	2.51167e7	+	6.15709e7i	0.281216	+	0.689371i
$448$	3.08049e7			0.342599
$449$			1.03287e8i			1.14105i	0.821279	+	0.570526i	$0.193261\pi$
$449$			1.03287e8i			1.14105i	−0.821279	+	0.570526i	$0.806739\pi$
$450$	1.11811e7	+	1.14240e7i	0.122700	+	0.125367i
$451$	−4.83410e6			−0.0526971
$452$			4.05864e7i			0.439507i
$453$	−9.52522e7	+	3.88564e7i	−1.02466	+	0.417992i
$454$	1.47643e7			0.157778
$455$		−	5.97229e7i		−	0.634026i
$456$	−2.30944e7	−	5.66134e7i	−0.243564	−	0.597069i
$457$	2.01329e7			0.210939			0.105469	−	0.994423i	$-0.466365\pi$
$457$	2.01329e7			0.210939			0.105469	+	0.994423i	$0.466365\pi$
$458$			4.49319e7i			0.467690i
$459$	−6.74229e7	−	2.92095e7i	−0.697219	−	0.302055i
$460$	8.41020e6			0.0864038
$461$			1.36316e8i			1.39138i	0.718343	+	0.695689i	$0.244901\pi$
$461$			1.36316e8i			1.39138i	−0.718343	+	0.695689i	$0.755099\pi$
$462$	1.58592e6	−	646946.i	0.0160825	−	0.00656058i
$463$	−4.57862e7			−0.461309			−0.230654	−	0.973036i	$-0.574087\pi$
$463$	−4.57862e7			−0.461309			−0.230654	+	0.973036i	$0.574087\pi$
$464$		−	4.67917e7i		−	0.468397i
$465$	3.18872e7	+	7.81678e7i	0.317144	+	0.777444i
$466$	−1.77333e7			−0.175240
$467$		−	1.76351e8i		−	1.73152i	−0.500461	−	0.865759i	$-0.666836\pi$
$467$		−	1.76351e8i		−	1.73152i	0.500461	−	0.865759i	$-0.333164\pi$
$468$	4.78673e7	−	4.68493e7i	0.466983	−	0.457052i
$469$	2.50456e7			0.242780
$470$			8.61173e7i			0.829463i
$471$	−3.21319e7	+	1.31076e7i	−0.307520	+	0.125447i
$472$	1.13616e8			1.08048
$473$			9.68289e6i			0.0915001i
$474$	1.77529e7	+	4.35193e7i	0.166700	+	0.408646i
$475$	−1.41052e7			−0.131613
$476$			1.01090e7i			0.0937315i
$477$	1.36965e8	+	1.39941e8i	1.26199	+	1.28941i
$478$	1.21598e8			1.11338
$479$			1.27693e8i			1.16188i	0.813945	+	0.580941i	$0.197315\pi$
$479$			1.27693e8i			1.16188i	−0.813945	+	0.580941i	$0.802685\pi$
$480$	7.96746e7	−	3.25018e7i	0.720437	−	0.293889i
$481$	−3.57017e8			−3.20814
$482$		−	1.06445e8i		−	0.950569i
$483$	2.92025e6	+	7.15867e6i	0.0259167	+	0.0635318i
$484$	4.23137e7			0.373203
$485$			2.95633e6i			0.0259136i
$486$	−8.47538e7	+	3.24671e7i	−0.738330	+	0.282836i
$487$	−1.20842e8			−1.04624			−0.523119	−	0.852260i	$-0.675232\pi$
$487$	−1.20842e8			−1.04624			−0.523119	+	0.852260i	$0.675232\pi$
$488$		−	1.88931e8i		−	1.62571i
$489$	−1.06592e8	+	4.34824e7i	−0.911589	+	0.371866i
$490$	−9.16878e7			−0.779333
$491$		−	4.74273e7i		−	0.400668i	−0.979728	−	0.200334i	$-0.935797\pi$
$491$		−	4.74273e7i		−	0.400668i	0.979728	−	0.200334i	$-0.0642027\pi$
$492$	−1.33111e7	−	3.26307e7i	−0.111768	−	0.273987i
$493$	8.80026e7			0.734437
$494$		−	9.85558e7i		−	0.817526i
$495$	6.39655e6	−	6.26051e6i	0.0527388	−	0.0516172i
$496$	−4.49167e7			−0.368097
$497$			1.63556e7i			0.133228i
$498$	1.32785e7	−	5.41674e6i	0.107513	−	0.0438581i
$499$	1.26048e8			1.01446			0.507228	−	0.861812i	$-0.330670\pi$
$499$	1.26048e8			1.01446			0.507228	+	0.861812i	$0.330670\pi$
$500$			4.03051e7i			0.322441i
$501$	8.96455e7	+	2.19756e8i	0.712878	+	1.74754i
$502$	−1.69595e8			−1.34060
$503$			1.13443e8i			0.891403i	0.895182	+	0.445702i	$0.147046\pi$
$503$			1.13443e8i			0.891403i	−0.895182	+	0.445702i	$0.852954\pi$
$504$	3.20321e7	+	3.27281e7i	0.250204	+	0.255641i
$505$	1.28268e8			0.995968
$506$			1.42589e6i			0.0110061i
$507$	2.45959e8	−	1.00335e8i	1.88729	−	0.769887i
$508$	−2.78155e7			−0.212175
$509$		−	2.00389e8i		−	1.51957i	−0.650173	−	0.759786i	$-0.725304\pi$
$509$		−	2.00389e8i		−	1.51957i	0.650173	−	0.759786i	$-0.274696\pi$
$510$	−3.32728e7	−	8.15646e7i	−0.250830	−	0.614881i
$511$	−1.07453e7			−0.0805294
$512$			1.16485e8i			0.867883i
$513$	3.18362e7	−	7.34860e7i	0.235814	−	0.544317i
$514$	1.19193e8			0.877728
$515$			2.37930e7i			0.174192i
$516$	−6.53604e7	+	2.66626e7i	−0.475736	+	0.194068i
$517$	8.75563e6			0.0633601
$518$		−	6.65569e7i		−	0.478855i
$519$	3.32664e7	+	8.15489e7i	0.237960	+	0.583332i
$520$	2.94499e8			2.09446
$521$		−	2.15076e8i		−	1.52082i	−0.649440	−	0.760412i	$-0.724997\pi$
$521$		−	2.15076e8i		−	1.52082i	0.649440	−	0.760412i	$-0.275003\pi$
$522$	7.76841e7	−	7.60321e7i	0.546161	−	0.534546i
$523$	7.20727e6			0.0503809			0.0251904	−	0.999683i	$-0.491981\pi$
$523$	7.20727e6			0.0503809			0.0251904	+	0.999683i	$0.491981\pi$
$524$		−	4.74381e7i		−	0.329711i
$525$	9.78201e6	−	3.99039e6i	0.0676005	−	0.0275764i
$526$	−9.54705e7			−0.656012
$527$		−	8.44762e7i		−	0.577169i
$528$	1.79870e6	+	4.40932e6i	0.0122196	+	0.0299550i
$529$	−6.43634e6			−0.0434783
$530$			2.34753e8i			1.57683i
$531$	1.04092e8	+	1.06354e8i	0.695241	+	0.710348i
$532$	−1.10180e7			−0.0731760
$533$		−	2.08337e8i		−	1.37590i
$534$	2.49538e7	−	1.01795e7i	0.163875	−	0.0668499i
$535$	4.70086e7			0.306984
$536$			1.23502e8i			0.802008i
$537$	−2.90997e7	−	7.13348e7i	−0.187917	−	0.460658i
$538$	1.72451e8			1.10744
$539$			9.32199e6i			0.0595309i
$540$	5.98725e7	+	2.59385e7i	0.380230	+	0.164726i
$541$	−1.69199e8			−1.06858			−0.534290	−	0.845301i	$-0.679421\pi$
$541$	−1.69199e8			−1.06858			−0.534290	+	0.845301i	$0.679421\pi$
$542$		−	2.37303e8i		−	1.49041i
$543$	−5.90577e7	+	2.40915e7i	−0.368873	+	0.150475i
$544$	−8.61046e7			−0.534847
$545$		−	9.93996e7i		−	0.614038i
$546$	2.78817e7	+	6.83488e7i	0.171294	+	0.419907i
$547$	3.19774e6			0.0195381			0.00976904	−	0.999952i	$-0.496890\pi$
$547$	3.19774e6			0.0195381			0.00976904	+	0.999952i	$0.496890\pi$
$548$		−	2.85515e7i		−	0.173495i
$549$	1.76855e8	−	1.73094e8i	1.06881	−	1.04608i
$550$	1.94842e6			0.0117110
$551$			9.59163e7i			0.573373i
$552$	−3.53000e7	+	1.44000e7i	−0.209873	+	0.0856141i
$553$	3.10631e7			0.183683
$554$		−	6.38809e7i		−	0.375701i
$555$	−1.31369e8	−	3.22037e8i	−0.768448	−	1.88376i
$556$	−9.58030e7			−0.557384
$557$			1.10496e8i			0.639410i	0.947517	+	0.319705i	$0.103584\pi$
$557$			1.10496e8i			0.639410i	−0.947517	+	0.319705i	$0.896416\pi$
$558$	−7.29854e7	−	7.45713e7i	−0.420081	−	0.429209i
$559$	−4.17307e8			−2.38902
$560$			3.09554e7i			0.176268i
$561$	−8.29275e6	+	3.38288e6i	−0.0469689	+	0.0191601i
$562$	2.41827e8			1.36237
$563$		−	3.04717e8i		−	1.70754i	−0.520650	−	0.853770i	$-0.674310\pi$
$563$		−	3.04717e8i		−	1.70754i	0.520650	−	0.853770i	$-0.325690\pi$
$564$	2.41093e7	+	5.91013e7i	0.134384	+	0.329428i
$565$	−2.33743e8			−1.29596
$566$			2.50340e8i			1.38064i
$567$	−1.28918e6	+	5.99693e7i	−0.00707238	+	0.328988i
$568$	−8.06506e7			−0.440111
$569$		−	1.60516e8i		−	0.871327i	−0.900110	−	0.435664i	$-0.856514\pi$
$569$		−	1.60516e8i		−	0.871327i	0.900110	−	0.435664i	$-0.143486\pi$
$570$	8.88994e7	−	3.62649e7i	0.480036	−	0.195822i
$571$	9.98727e7			0.536462			0.268231	−	0.963355i	$-0.413561\pi$
$571$	9.98727e7			0.536462			0.268231	+	0.963355i	$0.413561\pi$
$572$		−	8.16398e6i		−	0.0436228i
$573$	−1.34927e8	−	3.30758e8i	−0.717191	−	1.75811i
$574$	3.88393e7			0.205369
$575$			8.79498e6i			0.0462627i
$576$	−1.42192e8	+	1.39168e8i	−0.744061	+	0.728237i
$577$	−8.45151e7			−0.439954			−0.219977	−	0.975505i	$-0.570598\pi$
$577$	−8.45151e7			−0.439954			−0.219977	+	0.975505i	$0.570598\pi$
$578$		−	6.45277e7i		−	0.334166i
$579$	−7.27392e7	+	2.96727e7i	−0.374742	+	0.152869i
$580$	−7.81475e7			−0.400526
$581$		−	9.47791e6i		−	0.0483263i
$582$	−1.38016e6	−	3.38332e6i	−0.00700103	−	0.0171622i
$583$	2.38676e7			0.120449
$584$		−	5.29858e7i		−	0.266024i
$585$	2.69812e8	+	2.75674e8i	1.34770	+	1.37698i
$586$	−1.26594e8			−0.629102
$587$			1.69713e8i			0.839075i	0.907738	+	0.419537i	$0.137808\pi$
$587$			1.69713e8i			0.839075i	−0.907738	+	0.419537i	$0.862192\pi$
$588$	−6.29243e7	+	2.56688e7i	−0.309518	+	0.126262i
$589$	9.20728e7			0.450594
$590$			1.78411e8i			0.868690i
$591$	−1.00139e8	−	2.45479e8i	−0.485109	−	1.18919i
$592$	1.85048e8			0.891908
$593$			3.55856e8i			1.70651i	0.521490	+	0.853257i	$0.325376\pi$
$593$			3.55856e8i			1.70651i	−0.521490	+	0.853257i	$0.674624\pi$
$594$	−4.39769e6	+	1.01510e7i	−0.0209829	+	0.0484338i
$595$	−5.82189e7			−0.276384
$596$			5.90883e7i			0.279102i
$597$	2.11325e8	−	8.62063e7i	0.993180	−	0.405150i
$598$	−6.14523e7			−0.287365
$599$		−	3.37887e8i		−	1.57214i	−0.618137	−	0.786070i	$-0.712113\pi$
$599$		−	3.37887e8i		−	1.57214i	0.618137	−	0.786070i	$-0.287887\pi$
$600$	1.96770e7	+	4.82359e7i	0.0910970	+	0.223314i
$601$	−1.35895e7			−0.0626007			−0.0313004	−	0.999510i	$-0.509965\pi$
$601$	−1.35895e7			−0.0626007			−0.0313004	+	0.999510i	$0.509965\pi$
$602$		−	7.77965e7i		−	0.356591i
$603$	−1.15608e8	+	1.13149e8i	−0.527272	+	0.516059i
$604$	−9.14116e7			−0.414849
$605$			2.43690e8i			1.10045i
$606$	−1.46794e8	+	5.98822e7i	−0.659617	+	0.269079i
$607$	2.05202e8			0.917519			0.458759	−	0.888561i	$-0.348294\pi$
$607$	2.05202e8			0.917519			0.458759	+	0.888561i	$0.348294\pi$
$608$		−	9.38476e7i		−	0.417554i
$609$	−2.71350e7	−	6.65183e7i	−0.120137	−	0.294503i
$610$	2.96676e8			1.30705
$611$			3.77345e8i			1.65430i
$612$	−4.56695e7	−	4.66618e7i	−0.199238	−	0.203567i
$613$	2.44606e8			1.06191			0.530953	−	0.847402i	$-0.321834\pi$
$613$	2.44606e8			1.06191			0.530953	+	0.847402i	$0.321834\pi$
$614$			2.73842e8i			1.18303i
$615$	1.87925e8	−	7.66604e7i	0.807901	−	0.329569i
$616$	5.58193e6			0.0238804
$617$		−	6.47392e7i		−	0.275621i	−0.990459	−	0.137810i	$-0.955994\pi$
$617$		−	6.47392e7i		−	0.275621i	0.990459	−	0.137810i	$-0.0440064\pi$
$618$	−1.11078e7	−	2.72295e7i	−0.0470611	−	0.115365i
$619$	9.93529e7			0.418898			0.209449	−	0.977820i	$-0.432833\pi$
$619$	9.93529e7			0.418898			0.209449	+	0.977820i	$0.432833\pi$
$620$			7.50161e7i			0.314760i
$621$	−4.58205e7	−	1.98508e7i	−0.191331	−	0.0828900i
$622$	−7.57047e6			−0.0314595
$623$		−	1.78114e7i		−	0.0736605i
$624$	−1.90030e8	+	7.75194e7i	−0.782112	+	0.319049i
$625$	−2.86290e8			−1.17264
$626$			4.21265e7i			0.171725i
$627$	−3.68709e6	−	9.03849e6i	−0.0149583	−	0.0366685i
$628$	−3.08363e7			−0.124504
$629$			3.48026e8i			1.39849i
$630$	−5.13926e7	+	5.02997e7i	−0.205532	+	0.201161i
$631$	3.22644e8			1.28421			0.642105	−	0.766617i	$-0.278061\pi$
$631$	3.22644e8			1.28421			0.642105	+	0.766617i	$0.278061\pi$
$632$			1.53175e8i			0.606786i
$633$	2.53025e8	−	1.03217e8i	0.997589	−	0.406948i
$634$	−3.69444e8			−1.44971
$635$		−	1.60193e8i		−	0.625637i
$636$	6.57213e7	+	1.61108e8i	0.255467	+	0.626249i
$637$	−4.01753e8			−1.55432
$638$		−	1.32494e7i		−	0.0510192i
$639$	−7.38900e7	−	7.54955e7i	−0.283193	−	0.289347i
$640$	−3.45618e7			−0.131843
$641$			2.30025e8i			0.873375i	0.899613	+	0.436688i	$0.143848\pi$
$641$			2.30025e8i			0.873375i	−0.899613	+	0.436688i	$0.856152\pi$
$642$	−5.37982e7	+	2.19460e7i	−0.203312	+	0.0829374i
$643$	1.83229e8			0.689227			0.344614	−	0.938745i	$-0.388010\pi$
$643$	1.83229e8			0.689227			0.344614	+	0.938745i	$0.388010\pi$
$644$			6.87003e6i			0.0257218i
$645$	−1.53554e8	−	3.76420e8i	−0.572244	−	1.40279i
$646$	−9.60739e7			−0.356375
$647$			7.12157e7i			0.262944i	0.991320	+	0.131472i	$0.0419703\pi$
$647$			7.12157e7i			0.262944i	−0.991320	+	0.131472i	$0.958030\pi$
$648$	−2.95714e8	−	6.35707e6i	−1.08679	−	0.0233632i
$649$	1.81392e7			0.0663565
$650$			8.39718e7i			0.305769i
$651$	−6.38529e7	+	2.60476e7i	−0.231439	+	0.0944116i
$652$	−1.02294e8			−0.369070
$653$		−	4.00003e8i		−	1.43656i	−0.695755	−	0.718280i	$-0.744930\pi$
$653$		−	4.00003e8i		−	1.43656i	0.695755	−	0.718280i	$-0.255070\pi$
$654$	4.64048e7	+	1.13756e8i	0.165893	+	0.406669i
$655$	2.73203e8			0.972212
$656$			1.07985e8i			0.382518i
$657$	4.95990e7	−	4.85442e7i	0.174895	−	0.171175i
$658$	−7.03466e7			−0.246925
$659$			3.73034e8i			1.30344i	0.758458	+	0.651722i	$0.225953\pi$
$659$			3.73034e8i			1.30344i	−0.758458	+	0.651722i	$0.774047\pi$
$660$	7.36408e6	−	3.00404e6i	0.0256145	−	0.0104490i
$661$	5.35274e8			1.85341			0.926706	−	0.375787i	$-0.122627\pi$
$661$	5.35274e8			1.85341			0.926706	+	0.375787i	$0.122627\pi$
$662$			9.33632e7i			0.321812i
$663$	−1.45793e8	−	3.57396e8i	−0.500261	−	1.22634i
$664$	4.67363e7			0.159643
$665$		−	6.34543e7i		−	0.215772i
$666$	3.00686e8	+	3.07220e8i	1.01787	+	1.03998i
$667$	5.98064e7			0.201544
$668$			2.10895e8i			0.707518i
$669$	−1.04836e8	+	4.27658e7i	−0.350131	+	0.142830i
$670$	−1.93933e8			−0.644805
$671$		−	3.01634e7i		−	0.0998418i
$672$	2.65497e7	+	6.50837e7i	0.0874887	+	0.214469i
$673$	4.02319e8			1.31985			0.659926	−	0.751330i	$-0.270587\pi$
$673$	4.02319e8			1.31985			0.659926	+	0.751330i	$0.270587\pi$
$674$		−	2.53683e8i		−	0.828536i
$675$	−2.71252e7	+	6.26117e7i	−0.0881985	+	0.203584i
$676$	2.36042e8			0.764098
$677$		−	1.45002e8i		−	0.467312i	−0.972319	−	0.233656i	$-0.924931\pi$
$677$		−	1.45002e8i		−	0.467312i	0.972319	−	0.233656i	$-0.0750690\pi$
$678$	2.67503e8	−	1.09123e8i	0.858301	−	0.350129i
$679$	−2.41493e6			−0.00771429
$680$		−	2.87082e8i		−	0.913018i
$681$	2.38049e7	+	5.83550e7i	0.0753746	+	0.184772i
$682$	−1.27185e7			−0.0400942
$683$		−	2.22556e7i		−	0.0698517i	−0.999390	−	0.0349259i	$-0.988880\pi$
$683$		−	2.22556e7i		−	0.0698517i	0.999390	−	0.0349259i	$-0.0111195\pi$
$684$	5.08579e7	−	4.97764e7i	0.158924	−	0.155545i
$685$	1.64432e8			0.511582
$686$		−	1.58889e8i		−	0.492176i
$687$	−1.77590e8	+	7.24448e7i	−0.547708	+	0.223428i
$688$	2.16298e8			0.664181
$689$			1.02863e9i			3.14486i
$690$	−2.26122e7	−	5.54312e7i	−0.0688327	−	0.168736i
$691$	−5.36362e8			−1.62564			−0.812820	−	0.582516i	$-0.802069\pi$
$691$	−5.36362e8			−1.62564			−0.812820	+	0.582516i	$0.802069\pi$
$692$			7.82608e7i			0.236171i
$693$	5.11402e6	+	5.22514e6i	0.0153661	+	0.0156999i
$694$	−4.61844e7			−0.138171
$695$		−	5.51743e8i		−	1.64355i
$696$	3.28007e8	−	1.33805e8i	0.972872	−	0.396866i
$697$	−2.03091e8			−0.599780
$698$			1.60341e8i			0.471495i
$699$	−2.85919e7	−	7.00898e7i	−0.0837165	−	0.205222i
$700$	9.38759e6			0.0273691
$701$			1.89958e8i			0.551446i	0.961237	+	0.275723i	$0.0889172\pi$
$701$			1.89958e8i			0.551446i	−0.961237	+	0.275723i	$0.911083\pi$
$702$	−4.37480e8	−	1.89529e8i	−1.26458	−	0.547853i
$703$	−3.79323e8			−1.09180
$704$			2.42515e7i			0.0695058i
$705$	−3.40373e8	+	1.38849e8i	−0.971376	+	0.396256i
$706$	5.78105e7			0.164283
$707$			1.04778e8i			0.296492i
$708$	4.99477e7	+	1.22441e8i	0.140739	+	0.345007i
$709$	−4.80450e8			−1.34806			−0.674030	−	0.738704i	$-0.735438\pi$
$709$	−4.80450e8			−1.34806			−0.674030	+	0.738704i	$0.735438\pi$
$710$		−	1.26645e8i		−	0.353844i
$711$	−1.43384e8	+	1.40335e8i	−0.398925	+	0.390441i
$712$	8.78296e7			0.243333
$713$		−	5.74099e7i		−	0.158387i
$714$	6.66276e7	−	2.71795e7i	0.183046	−	0.0746702i
$715$	4.70175e7			0.128630
$716$		−	6.84585e7i		−	0.186504i
$717$	1.96055e8	+	4.80607e8i	0.531888	+	1.30387i
$718$	−2.37701e8			−0.642180
$719$		−	5.96184e7i		−	0.160396i	−0.996779	−	0.0801980i	$-0.974445\pi$
$719$		−	5.96184e7i		−	0.160396i	0.996779	−	0.0801980i	$-0.0255553\pi$
$720$	−1.39848e8	−	1.42887e8i	−0.374679	−	0.382820i
$721$	−1.94358e7			−0.0518557
$722$			1.92861e8i			0.512428i
$723$	4.20716e8	−	1.71624e8i	1.11320	−	0.454111i
$724$	−5.66764e7			−0.149344
$725$		−	8.17228e7i		−	0.214452i
$726$	−1.13767e8	−	2.78887e8i	−0.297308	−	0.728817i
$727$	−1.38855e8			−0.361374			−0.180687	−	0.983541i	$-0.557832\pi$
$727$	−1.38855e8			−0.361374			−0.180687	+	0.983541i	$0.557832\pi$
$728$			2.40567e8i			0.623507i
$729$	−2.64974e8	−	2.82636e8i	−0.683945	−	0.729533i
$730$	8.32030e7			0.213880
$731$			4.06798e8i			1.04142i
$732$	2.03606e8	−	8.30573e7i	0.519107	−	0.211760i
$733$	7.54927e8			1.91687			0.958436	−	0.285307i	$-0.0920957\pi$
$733$	7.54927e8			1.91687			0.958436	+	0.285307i	$0.0920957\pi$
$734$		−	4.27983e8i		−	1.08228i
$735$	−1.47830e8	−	3.62390e8i	−0.372307	−	0.912670i
$736$	−5.85165e7			−0.146773
$737$			1.97174e7i			0.0492547i
$738$	−1.79278e8	+	1.75465e8i	−0.446024	+	0.436538i
$739$	−2.06675e8			−0.512100			−0.256050	−	0.966664i	$-0.582421\pi$
$739$	−2.06675e8			−0.512100			−0.256050	+	0.966664i	$0.582421\pi$
$740$		−	3.09052e8i		−	0.762670i
$741$	3.89535e8	−	1.58904e8i	0.957397	−	0.390553i
$742$	−1.91763e8			−0.469410
$743$		−	7.25196e8i		−	1.76803i	−0.467460	−	0.884014i	$-0.654831\pi$
$743$		−	7.25196e8i		−	1.76803i	0.467460	−	0.884014i	$-0.345169\pi$
$744$	−1.28443e8	−	3.14864e8i	−0.311883	−	0.764546i
$745$	−3.40298e8			−0.822982
$746$		−	3.76399e7i		−	0.0906633i
$747$	4.28186e7	+	4.37490e7i	0.102724	+	0.104956i
$748$	−7.95839e6			−0.0190160
$749$			3.83999e7i			0.0913870i
$750$	2.65649e8	−	1.08367e8i	0.629686	−	0.256869i
$751$	2.29113e8			0.540917			0.270458	−	0.962732i	$-0.412825\pi$
$751$	2.29113e8			0.540917			0.270458	+	0.962732i	$0.412825\pi$
$752$		−	1.95585e8i		−	0.459919i
$753$	−2.73441e8	−	6.70311e8i	−0.640441	−	1.56997i
$754$	5.71014e8			1.33209
$755$		−	5.26452e8i		−	1.22326i
$756$	−2.11883e7	+	4.89080e7i	−0.0490378	+	0.113192i
$757$	−5.39486e8			−1.24363			−0.621817	−	0.783163i	$-0.713605\pi$
$757$	−5.39486e8			−1.24363			−0.621817	+	0.783163i	$0.713605\pi$
$758$		−	4.62200e7i		−	0.106126i
$759$	−5.63574e6	+	2.29900e6i	−0.0128892	+	0.00525792i
$760$	3.12898e8			0.712791
$761$			5.30857e8i			1.20455i	0.798290	+	0.602273i	$0.205738\pi$
$761$			5.30857e8i			1.20455i	−0.798290	+	0.602273i	$0.794262\pi$
$762$	7.47863e7	+	1.83330e8i	0.169027	+	0.414352i
$763$	8.11964e7			0.182795
$764$		−	3.17422e8i		−	0.711798i
$765$	2.68732e8	−	2.63017e8i	0.600254	−	0.587489i
$766$	−5.08437e8			−1.13123
$767$			7.81752e8i			1.73254i
$768$	−3.97127e8	+	1.62001e8i	−0.876690	+	0.357630i
$769$	2.86097e7			0.0629121			0.0314560	−	0.999505i	$-0.489986\pi$
$769$	2.86097e7			0.0629121			0.0314560	+	0.999505i	$0.489986\pi$
$770$			8.76524e6i			0.0191996i
$771$	1.92177e8	+	4.71101e8i	0.419313	+	1.02790i
$772$	−6.98063e7			−0.151720
$773$		−	1.53758e8i		−	0.332888i	−0.986051	−	0.166444i	$-0.946771\pi$
$773$		−	1.53758e8i		−	0.332888i	0.986051	−	0.166444i	$-0.0532285\pi$
$774$	3.51464e8	+	3.59100e8i	0.757980	+	0.774449i
$775$	−7.84481e7			−0.168530
$776$		−	1.19082e7i		−	0.0254837i
$777$	2.63062e8	−	1.07311e8i	0.560783	−	0.228761i
$778$	2.26415e8			0.480802
$779$		−	2.21354e8i		−	0.468247i
$780$	1.29466e8	+	3.17373e8i	0.272818	+	0.668784i
$781$	−1.28761e7			−0.0270291
$782$			5.99047e7i			0.125268i
$783$	4.25764e8	+	1.84453e8i	0.886918	+	0.384238i
$784$	2.08236e8			0.432123
$785$		−	1.77591e8i		−	0.367122i
$786$	−3.12662e8	+	1.27545e8i	−0.643884	+	0.262661i
$787$	5.13423e8			1.05330			0.526649	−	0.850083i	$-0.323448\pi$
$787$	5.13423e8			1.05330			0.526649	+	0.850083i	$0.323448\pi$
$788$		−	2.35581e8i		−	0.481461i
$789$	−1.53929e8	−	3.77341e8i	−0.313394	−	0.768250i
$790$	−2.40528e8			−0.487848
$791$		−	1.90937e8i		−	0.385799i
$792$	−2.57656e7	+	2.52176e7i	−0.0518638	+	0.0507609i
$793$	1.29996e9			2.60682
$794$		−	1.40375e8i		−	0.280432i
$795$	−9.27846e8	+	3.78498e8i	−1.84661	+	0.753290i
$796$	2.02804e8			0.402104
$797$		−	7.37302e8i		−	1.45637i	−0.685383	−	0.728183i	$-0.740365\pi$
$797$		−	7.37302e8i		−	1.45637i	0.685383	−	0.728183i	$-0.259635\pi$
$798$	2.96237e7	+	7.26191e7i	0.0582948	+	0.142903i
$799$	3.67842e8			0.721143
$800$			7.99602e7i			0.156172i
$801$	8.04672e7	+	8.22157e7i	0.156575	+	0.159977i
$802$	7.30272e8			1.41567
$803$		−	8.45933e6i		−	0.0163376i
$804$	−1.33094e8	+	5.42935e7i	−0.256089	+	0.104467i
$805$	−3.95655e7			−0.0758453
$806$		−	5.48133e8i		−	1.04684i
$807$	2.78047e8	+	6.81602e8i	0.529051	+	1.29691i
$808$	−5.16671e8			−0.979445
$809$		−	1.36100e8i		−	0.257048i	−0.991706	−	0.128524i	$-0.958976\pi$
$809$		−	1.36100e8i		−	0.257048i	0.991706	−	0.128524i	$-0.0410239\pi$
$810$	9.98243e6	−	4.64356e8i	0.0187837	−	0.873767i
$811$	4.97197e8			0.932108			0.466054	−	0.884756i	$-0.345675\pi$
$811$	4.97197e8			0.932108			0.466054	+	0.884756i	$0.345675\pi$
$812$		−	6.38363e7i		−	0.119234i
$813$	9.37922e8	−	3.82609e8i	1.74540	−	0.712005i
$814$	5.23977e7			0.0971491
$815$		−	5.89128e8i		−	1.08827i
$816$	7.55673e7	+	1.85245e8i	0.139080	+	0.340938i
$817$	−4.43380e8			−0.813036
$818$		−	3.88429e8i		−	0.709663i
$819$	−2.25190e8	+	2.20401e8i	−0.409918	+	0.401201i
$820$	1.80347e8			0.327091
$821$			4.46150e8i			0.806216i	0.915152	+	0.403108i	$0.132070\pi$
$821$			4.46150e8i			0.806216i	−0.915152	+	0.403108i	$0.867930\pi$
$822$	−1.88182e8	+	7.67653e7i	−0.338814	+	0.138213i
$823$	2.22190e8			0.398590			0.199295	−	0.979940i	$-0.436135\pi$
$823$	2.22190e8			0.398590			0.199295	+	0.979940i	$0.436135\pi$
$824$		−	9.58394e7i		−	0.171302i
$825$	3.14148e6	+	7.70099e6i	0.00559465	+	0.0137147i
$826$	−1.45738e8			−0.258603
$827$			7.10113e8i			1.25548i	0.778422	+	0.627741i	$0.216020\pi$
$827$			7.10113e8i			1.25548i	−0.778422	+	0.627741i	$0.783980\pi$
$828$	−3.10369e7	−	3.17113e7i	−0.0546749	−	0.0558629i
$829$	−9.98895e7			−0.175330			−0.0876650	−	0.996150i	$-0.527940\pi$
$829$	−9.98895e7			−0.175330			−0.0876650	+	0.996150i	$0.527940\pi$
$830$			7.33895e7i			0.128351i
$831$	2.52485e8	−	1.02997e8i	0.439980	−	0.179482i
$832$	−1.04518e9			−1.81476
$833$			3.91636e8i			0.677559i
$834$	2.57581e8	+	6.31432e8i	0.444034	+	1.08850i
$835$	−1.21458e9			−2.08624
$836$		−	8.67405e6i		−	0.0148458i
$837$	1.77062e8	−	4.08703e8i	0.301959	−	0.696998i
$838$	−3.44896e8			−0.586079
$839$			7.97495e8i			1.35034i	0.737664	+	0.675168i	$0.235929\pi$
$839$			7.97495e8i			1.35034i	−0.737664	+	0.675168i	$0.764071\pi$
$840$	−2.16996e8	+	8.85196e7i	−0.366112	+	0.149349i
$841$	3.91027e7			0.0657383
$842$		−	1.16816e8i		−	0.195690i
$843$	3.89903e8	+	9.55804e8i	0.650840	+	1.59546i
$844$	2.42823e8			0.403889
$845$			1.35940e9i			2.25308i
$846$	3.24712e8	−	3.17807e8i	0.536275	−	0.524870i
$847$	−1.99063e8			−0.327597
$848$		−	5.33158e8i		−	0.874315i
$849$	−9.89450e8	+	4.03628e8i	−1.61685	+	0.659566i
$850$	8.18571e7			0.133291
$851$			2.36518e8i			0.383774i
$852$	−3.54553e7	−	8.69148e7i	−0.0573275	−	0.140532i
$853$	−8.56955e8			−1.38074			−0.690368	−	0.723458i	$-0.742551\pi$
$853$	−8.56955e8			−1.38074			−0.690368	+	0.723458i	$0.742551\pi$
$854$			2.42346e8i			0.389100i
$855$	2.86669e8	+	2.92898e8i	0.458651	+	0.468617i
$856$	−1.89353e8			−0.301891
$857$			2.49978e8i			0.397155i	0.980085	+	0.198577i	$0.0636321\pi$
$857$			2.49978e8i			0.397155i	−0.980085	+	0.198577i	$0.936368\pi$
$858$	−5.38084e7	+	2.19502e7i	−0.0851899	+	0.0347517i
$859$	−1.01245e9			−1.59733			−0.798666	−	0.601774i	$-0.794461\pi$
$859$	−1.01245e9			−1.59733			−0.798666	+	0.601774i	$0.794461\pi$
$860$		−	3.61242e8i		−	0.567941i
$861$	6.26215e7	+	1.53510e8i	0.0981102	+	0.240506i
$862$	2.37392e8			0.370634
$863$		−	9.52313e8i		−	1.48166i	−0.671695	−	0.740828i	$-0.734433\pi$
$863$		−	9.52313e8i		−	1.48166i	0.671695	−	0.740828i	$-0.265567\pi$
$864$	−4.16581e8	−	1.80475e8i	−0.645889	−	0.279818i
$865$	−4.50715e8			−0.696392
$866$			3.24998e8i			0.500412i
$867$	2.55041e8	−	1.04040e8i	0.391339	−	0.159640i
$868$	−6.12783e7			−0.0937017
$869$			2.44547e7i			0.0372652i
$870$	2.10112e8	+	5.15066e8i	0.319075	+	0.782177i
$871$	−8.49769e8			−1.28602
$872$			4.00386e8i			0.603851i
$873$	1.11471e7	−	1.09100e7i	0.0167540	−	0.0163977i
$874$	−6.52917e7			−0.0977965
$875$		−	1.89614e8i		−	0.283039i
$876$	5.71013e7	−	2.32934e7i	0.0849441	−	0.0346514i
$877$	−1.17632e9			−1.74392			−0.871960	−	0.489578i	$-0.837151\pi$
$877$	−1.17632e9			−1.74392			−0.871960	+	0.489578i	$0.837151\pi$
$878$		−	9.73692e8i		−	1.43859i
$879$	−2.04111e8	−	5.00356e8i	−0.300538	−	0.736736i
$880$	−2.43700e7			−0.0357608
$881$		−	3.05565e8i		−	0.446865i	−0.974719	−	0.223432i	$-0.928274\pi$
$881$		−	3.05565e8i		−	0.446865i	0.974719	−	0.223432i	$-0.0717262\pi$
$882$	3.38364e8	+	3.45716e8i	0.493149	+	0.503864i
$883$	3.38288e8			0.491365			0.245683	−	0.969350i	$-0.420988\pi$
$883$	3.38288e8			0.491365			0.245683	+	0.969350i	$0.420988\pi$
$884$		−	3.42986e8i		−	0.496500i
$885$	−7.05156e8	+	2.87656e8i	−1.01731	+	0.414995i
$886$	−5.92250e7			−0.0851537
$887$			2.08934e8i			0.299391i	0.988732	+	0.149695i	$0.0478293\pi$
$887$			2.08934e8i			0.299391i	−0.988732	+	0.149695i	$0.952171\pi$
$888$	5.29161e8	+	1.29718e9i	0.755699	+	1.85251i
$889$	1.30857e8			0.186248
$890$			1.37918e8i			0.195637i
$891$	−4.72115e7	−	1.01492e6i	−0.0667444	−	0.00143483i
$892$	−1.00609e8			−0.141756
$893$			4.00921e8i			0.562994i
$894$	3.89448e8	−	1.58868e8i	0.545051	−	0.222344i
$895$	3.94262e8			0.549941
$896$		−	2.82325e7i		−	0.0392487i
$897$	−9.90809e7	−	2.42886e8i	−0.137282	−	0.336531i
$898$	6.53309e8			0.902173
$899$			5.33452e8i			0.734204i
$900$	−4.33321e7	+	4.24106e7i	−0.0594405	+	0.0581764i
$901$	1.00273e9			1.37091
$902$			3.05767e7i			0.0416649i
$903$	3.07486e8	−	1.25433e8i	0.417601	−	0.170353i
$904$	9.41528e8			1.27446
$905$		−	3.26407e8i		−	0.440367i
$906$	2.45775e8	+	6.02489e8i	0.330485	+	0.810148i
$907$	3.11333e8			0.417257			0.208629	−	0.977995i	$-0.433100\pi$
$907$	3.11333e8			0.417257			0.208629	+	0.977995i	$0.433100\pi$
$908$			5.60021e7i			0.0748078i
$909$	−4.73360e8	−	4.83646e8i	−0.630232	−	0.643926i
$910$	−3.77759e8			−0.501292
$911$		−	9.53602e8i		−	1.26128i	−0.776075	−	0.630641i	$-0.782792\pi$
$911$		−	9.53602e8i		−	1.26128i	0.776075	−	0.630641i	$-0.217208\pi$
$912$	−2.01903e8	+	8.23627e7i	−0.266169	+	0.108579i
$913$	7.46158e6			0.00980435
$914$		−	1.27344e8i		−	0.166779i
$915$	4.78338e8	+	1.17259e9i	0.624413	+	1.53068i
$916$	−1.70430e8			−0.221748
$917$			2.23171e8i			0.289421i
$918$	−1.84756e8	+	4.26463e8i	−0.238820	+	0.551256i
$919$	6.11137e8			0.787394			0.393697	−	0.919240i	$-0.371196\pi$
$919$	6.11137e8			0.787394			0.393697	+	0.919240i	$0.371196\pi$
$920$		−	1.95101e8i		−	0.250550i
$921$	−1.08234e9	+	4.41522e8i	−1.38543	+	0.565163i
$922$	8.62228e8			1.10009
$923$		−	5.54926e8i		−	0.705716i
$924$	2.45391e6	+	6.01549e6i	0.00311059	+	0.00762526i
$925$	3.23191e8			0.408352
$926$			2.89607e8i			0.364734i
$927$	8.97134e7	−	8.78056e7i	0.112621	−	0.110226i
$928$	5.43735e8			0.680367
$929$		−	2.96553e8i		−	0.369875i	−0.982750	−	0.184937i	$-0.940792\pi$
$929$		−	2.96553e8i		−	0.369875i	0.982750	−	0.184937i	$-0.0592083\pi$
$930$	4.94427e8	−	2.01693e8i	0.614686	−	0.250750i
$931$	−4.26854e8			−0.528969
$932$		−	6.72637e7i		−	0.0830870i
$933$	−1.22061e7	−	2.99218e7i	−0.0150290	−	0.0368420i
$934$	−1.11545e9			−1.36902
$935$		−	4.58335e7i		−	0.0560722i
$936$	−1.08681e9	−	1.11043e9i	−1.32534	−	1.35414i
$937$	−3.54882e8			−0.431385			−0.215693	−	0.976461i	$-0.569201\pi$
$937$	−3.54882e8			−0.431385			−0.215693	+	0.976461i	$0.569201\pi$
$938$		−	1.58418e8i		−	0.191954i
$939$	−1.66502e8	+	6.79216e7i	−0.201105	+	0.0820372i
$940$	−3.26649e8			−0.393276
$941$		−	1.61313e8i		−	0.193598i	−0.995304	−	0.0967989i	$-0.969140\pi$
$941$		−	1.61313e8i		−	0.193598i	0.995304	−	0.0967989i	$-0.0308604\pi$
$942$	8.29083e7	+	2.03240e8i	0.0991848	+	0.243141i
$943$	−1.38020e8			−0.164591
$944$		−	4.05196e8i		−	0.481669i
$945$	−2.81668e8	−	1.22026e8i	−0.333766	−	0.144597i
$946$	6.12462e7			0.0723445
$947$		−	3.13889e8i		−	0.369596i	−0.982777	−	0.184798i	$-0.940837\pi$
$947$		−	3.13889e8i		−	0.369596i	0.982777	−	0.184798i	$-0.0591630\pi$
$948$	−1.65072e8	+	6.73381e7i	−0.193753	+	0.0790380i
$949$	3.64575e8			0.426568
$950$			8.92181e7i			0.104060i
$951$	−5.95664e8	−	1.46020e9i	−0.692564	−	1.69774i
$952$	2.34508e8			0.271799
$953$			2.28303e8i			0.263775i	0.991265	+	0.131888i	$0.0421038\pi$
$953$			2.28303e8i			0.263775i	−0.991265	+	0.131888i	$0.957896\pi$
$954$	8.85155e8	−	8.66331e8i	1.01947	−	0.997789i
$955$	1.82808e9			2.09886
$956$			4.61229e8i			0.527889i
$957$	5.23673e7	−	2.13623e7i	0.0597481	−	0.0243732i
$958$	8.07686e8			0.918642
$959$			1.34320e8i			0.152294i
$960$	−3.84587e8	−	9.42771e8i	−0.434691	−	1.06560i
$961$	−3.75427e8			−0.423015
$962$			2.25820e9i			2.53652i
$963$	−1.73480e8	−	1.77250e8i	−0.194254	−	0.198475i
$964$	4.03753e8			0.450697
$965$		−	4.02024e8i		−	0.447374i
$966$	4.52800e7	−	1.84712e7i	0.0502314	−	0.0204910i
$967$	−1.59288e9			−1.76158			−0.880792	−	0.473503i	$-0.842989\pi$
$967$	−1.59288e9			−1.76158			−0.880792	+	0.473503i	$0.842989\pi$
$968$		−	9.81596e8i		−	1.08220i
$969$	−1.54902e8	−	3.79725e8i	−0.170250	−	0.417348i
$970$	1.86994e7			0.0204886
$971$			7.94583e8i			0.867924i	0.900931	+	0.433962i	$0.142885\pi$
$971$			7.94583e8i			0.867924i	−0.900931	+	0.433962i	$0.857115\pi$
$972$	−1.23150e8	−	3.21477e8i	−0.134102	−	0.350067i
$973$	4.50701e8			0.489272
$974$			7.64348e8i			0.827207i
$975$	−3.31893e8	+	1.35390e8i	−0.358083	+	0.146074i
$976$	−6.73794e8			−0.724732
$977$		−	1.16822e9i		−	1.25268i	−0.779550	−	0.626340i	$-0.784552\pi$
$977$		−	1.16822e9i		−	1.25268i	0.779550	−	0.626340i	$-0.215448\pi$
$978$	2.75035e8	+	6.74217e8i	0.294016	+	0.720748i
$979$	1.40222e7			0.0149441
$980$		−	3.47778e8i		−	0.369508i
$981$	−3.74794e8	+	3.66823e8i	−0.396995	+	0.388553i
$982$	−2.99987e8			−0.316788
$983$			8.81529e8i			0.928060i	0.885819	+	0.464030i	$0.153597\pi$
$983$			8.81529e8i			0.928060i	−0.885819	+	0.464030i	$0.846403\pi$
$984$	−7.56969e8	+	3.08792e8i	−0.794498	+	0.324101i
$985$	1.35674e9			1.41967
$986$		−	5.56634e8i		−	0.580682i
$987$	−1.13421e8	−	2.78040e8i	−0.117962	−	0.289172i
$988$	3.73829e8			0.387616
$989$			2.76459e8i			0.285787i
$990$	−3.95990e7	−	4.04594e7i	−0.0408111	−	0.0416979i
$991$	1.57191e9			1.61513			0.807563	−	0.589781i	$-0.200786\pi$
$991$	1.57191e9			1.61513			0.807563	+	0.589781i	$0.200786\pi$
$992$		−	5.21947e8i		−	0.534677i
$993$	−3.69012e8	+	1.50532e8i	−0.376871	+	0.153738i
$994$	1.03452e8			0.105337
$995$			1.16798e9i			1.18567i
$996$	2.05461e7	+	5.03664e7i	0.0207946	+	0.0509757i
$997$	4.27775e8			0.431648			0.215824	−	0.976432i	$-0.430756\pi$
$997$	4.27775e8			0.431648			0.215824	+	0.976432i	$0.430756\pi$
$998$		−	7.97276e8i		−	0.802079i
$999$	−7.29461e8	+	1.68378e9i	−0.731654	+	1.68884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.b.a.47.15	✓	44
3.2	odd	2	inner	69.7.b.a.47.30	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.b.a.47.15	✓	44	1.1	even	1	trivial
69.7.b.a.47.30	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)

\(f(q)\)	\(=\)	\(q-6.32520i q^{2} +(24.9999 - 10.1983i) q^{3} +23.9919 q^{4} +138.173i q^{5} +(-64.5060 - 158.129i) q^{6} -112.869 q^{7} -556.566i q^{8} +(520.991 - 509.911i) q^{9} +O(q^{10})\)	\(q-6.32520i q^{2} +(24.9999 - 10.1983i) q^{3} +23.9919 q^{4} +138.173i q^{5} +(-64.5060 - 158.129i) q^{6} -112.869 q^{7} -556.566i q^{8} +(520.991 - 509.911i) q^{9} +873.969 q^{10} -88.8573i q^{11} +(599.795 - 244.676i) q^{12} +3829.52 q^{13} +713.918i q^{14} +(1409.12 + 3454.30i) q^{15} -1984.91 q^{16} -3733.08i q^{17} +(-3225.29 - 3295.37i) q^{18} +4068.78 q^{19} +3315.03i q^{20} +(-2821.71 + 1151.07i) q^{21} -562.040 q^{22} -2536.99i q^{23} +(-5676.01 - 13914.1i) q^{24} -3466.69 q^{25} -24222.5i q^{26} +(7824.51 - 18060.9i) q^{27} -2707.94 q^{28} +23573.7i q^{29} +(21849.2 - 8912.97i) q^{30} +22629.1 q^{31} -23065.3i q^{32} +(-906.190 - 2221.42i) q^{33} -23612.5 q^{34} -15595.4i q^{35} +(12499.6 - 12233.7i) q^{36} -93227.7 q^{37} -25735.8i q^{38} +(95737.6 - 39054.4i) q^{39} +76902.2 q^{40} -54403.0i q^{41} +(7280.73 + 17847.9i) q^{42} -108971. q^{43} -2131.86i q^{44} +(70455.8 + 71986.7i) q^{45} -16047.0 q^{46} +98535.9i q^{47} +(-49622.5 + 20242.6i) q^{48} -104910. q^{49} +21927.5i q^{50} +(-38070.9 - 93326.6i) q^{51} +91877.4 q^{52} +268606. i q^{53} +(-114239. - 49491.6i) q^{54} +12277.7 q^{55} +62819.0i q^{56} +(101719. - 41494.5i) q^{57} +149108. q^{58} +204138. i q^{59} +(33807.5 + 82875.3i) q^{60} +339459. q^{61} -143134. i q^{62} +(-58803.7 + 57553.2i) q^{63} -272927. q^{64} +529135. i q^{65} +(-14050.9 + 5731.83i) q^{66} -221900. q^{67} -89563.7i q^{68} +(-25872.9 - 63424.6i) q^{69} -98644.0 q^{70} -144907. i q^{71} +(-283799. - 289966. i) q^{72} +95201.2 q^{73} +589683. i q^{74} +(-86666.9 + 35354.2i) q^{75} +97617.7 q^{76} +10029.2i q^{77} +(-247027. - 605559. i) q^{78} -275214. q^{79} -274260. i q^{80} +(11422.0 - 531318. i) q^{81} -344110. q^{82} +83972.6i q^{83} +(-67698.3 + 27616.3i) q^{84} +515810. q^{85} +689264. i q^{86} +(240411. + 589341. i) q^{87} -49455.0 q^{88} +157806. i q^{89} +(455330. - 445647. i) q^{90} -432234. q^{91} -60867.3i q^{92} +(565726. - 230778. i) q^{93} +623259. q^{94} +562194. i q^{95} +(-235226. - 576630. i) q^{96} +21395.9 q^{97} +663574. i q^{98} +(-45309.3 - 46293.8i) 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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