LMFDB - Embedded newform 52.3.b.d.51.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,3,Mod(51,52)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("52.51");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	52.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.41689737467$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1044287785216.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 28x^{4} + 16x^{2} + 256 $ x^8 + x^6 + 28x^4 + 16x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.2
Root			$-1.54609 + 1.26870i$ of defining polynomial
Character	$\chi$	$=$	52.51
Dual form			52.3.b.d.51.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54609 + 1.26870i) q^{2} +5.02456i q^{3} +(0.780776 - 3.92306i) q^{4} +0.712445i q^{5} +(-6.37468 - 7.76841i) q^{6} -7.05256 q^{7} +(3.77005 + 7.05597i) q^{8} -16.2462 q^{9} +O(q^{10})$	\(q+(-1.54609 + 1.26870i) q^{2} +5.02456i q^{3} +(0.780776 - 3.92306i) q^{4} +0.712445i q^{5} +(-6.37468 - 7.76841i) q^{6} -7.05256 q^{7} +(3.77005 + 7.05597i) q^{8} -16.2462 q^{9} +(-0.903882 - 1.10150i) q^{10} +15.8415 q^{11} +(19.7116 + 3.92306i) q^{12} +(-4.24621 + 12.2870i) q^{13} +(10.9039 - 8.94762i) q^{14} -3.57972 q^{15} +(-14.7808 - 6.12606i) q^{16} +15.4924 q^{17} +(25.1181 - 20.6116i) q^{18} +10.6323 q^{19} +(2.79496 + 0.556260i) q^{20} -35.4360i q^{21} +(-24.4924 + 20.0982i) q^{22} +21.3353i q^{23} +(-35.4531 + 18.9429i) q^{24} +24.4924 q^{25} +(-9.02352 - 24.3839i) q^{26} -36.4090i q^{27} +(-5.50647 + 27.6676i) q^{28} -2.24621 q^{29} +(5.53457 - 4.54161i) q^{30} -26.2601 q^{31} +(30.6245 - 9.28101i) q^{32} +79.5968i q^{33} +(-23.9526 + 19.6553i) q^{34} -5.02456i q^{35} +(-12.6847 + 63.7348i) q^{36} -42.5605i q^{37} +(-16.4384 + 13.4892i) q^{38} +(-61.7366 - 21.3353i) q^{39} +(-5.02699 + 2.68596i) q^{40} -33.2987i q^{41} +(44.9579 + 54.7872i) q^{42} -46.4582i q^{43} +(12.3687 - 62.1473i) q^{44} -11.5745i q^{45} +(-27.0683 - 32.9863i) q^{46} +47.4178 q^{47} +(30.7808 - 74.2669i) q^{48} +0.738634 q^{49} +(-37.8674 + 31.0737i) q^{50} +77.8426i q^{51} +(44.8872 + 26.2515i) q^{52} -24.7386 q^{53} +(46.1923 + 56.2916i) q^{54} +11.2862i q^{55} +(-26.5885 - 49.7627i) q^{56} +53.4226i q^{57} +(3.47284 - 2.84978i) q^{58} +44.2656 q^{59} +(-2.79496 + 14.0435i) q^{60} +91.2311 q^{61} +(40.6004 - 33.3163i) q^{62} +114.577 q^{63} +(-35.5734 + 53.2028i) q^{64} +(-8.75379 - 3.02519i) q^{65} +(-100.985 - 123.064i) q^{66} -70.7394 q^{67} +(12.0961 - 60.7777i) q^{68} -107.201 q^{69} +(6.37468 + 7.76841i) q^{70} -10.5254 q^{71} +(-61.2491 - 114.633i) q^{72} -52.1731i q^{73} +(53.9967 + 65.8022i) q^{74} +123.064i q^{75} +(8.30144 - 41.7111i) q^{76} -111.723 q^{77} +(122.519 - 45.3392i) q^{78} -12.5233i q^{79} +(4.36448 - 10.5305i) q^{80} +36.7235 q^{81} +(42.2462 + 51.4827i) q^{82} -21.4783 q^{83} +(-139.018 - 27.6676i) q^{84} +11.0375i q^{85} +(58.9417 + 71.8284i) q^{86} -11.2862i q^{87} +(59.7235 + 111.777i) q^{88} +137.469i q^{89} +(14.6847 + 17.8952i) q^{90} +(29.9467 - 86.6546i) q^{91} +(83.6998 + 16.6581i) q^{92} -131.945i q^{93} +(-73.3120 + 60.1591i) q^{94} +7.57491i q^{95} +(46.6330 + 153.875i) q^{96} +137.645i q^{97} +(-1.14199 + 0.937108i) q^{98} -257.365 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 64 q^{9}+O(q^{10}) $ 8 * q - 2 * q^4 - 64 * q^9	$ 8 q - 2 q^{4} - 64 q^{9} + 34 q^{10} + 34 q^{12} + 32 q^{13} + 46 q^{14} - 110 q^{16} - 8 q^{17} - 64 q^{22} + 64 q^{25} - 34 q^{26} + 48 q^{29} + 102 q^{30} - 52 q^{36} - 148 q^{38} + 34 q^{40} + 170 q^{42} + 238 q^{48} - 192 q^{49} - 76 q^{52} - 122 q^{56} + 400 q^{61} - 104 q^{62} + 70 q^{64} - 136 q^{65} - 544 q^{66} + 138 q^{68} - 170 q^{74} - 432 q^{77} + 442 q^{78} - 168 q^{81} + 272 q^{82} + 16 q^{88} + 68 q^{90} + 884 q^{92} - 34 q^{94}+O(q^{100}) $ 8 * q - 2 * q^4 - 64 * q^9 + 34 * q^10 + 34 * q^12 + 32 * q^13 + 46 * q^14 - 110 * q^16 - 8 * q^17 - 64 * q^22 + 64 * q^25 - 34 * q^26 + 48 * q^29 + 102 * q^30 - 52 * q^36 - 148 * q^38 + 34 * q^40 + 170 * q^42 + 238 * q^48 - 192 * q^49 - 76 * q^52 - 122 * q^56 + 400 * q^61 - 104 * q^62 + 70 * q^64 - 136 * q^65 - 544 * q^66 + 138 * q^68 - 170 * q^74 - 432 * q^77 + 442 * q^78 - 168 * q^81 + 272 * q^82 + 16 * q^88 + 68 * q^90 + 884 * q^92 - 34 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.54609	+	1.26870i	−0.773044	+	0.634352i
$2$	−1.54609	+	1.26870i	−0.773044	+	0.634352i
$3$			5.02456i			1.67485i	0.546549	+	0.837427i	$0.315941\pi$
$3$			5.02456i			1.67485i	−0.546549	+	0.837427i	$0.684059\pi$
$4$	0.780776	−	3.92306i	0.195194	−	0.980765i
$5$			0.712445i			0.142489i	0.997459	+	0.0712445i	$0.0226970\pi$
$5$			0.712445i			0.142489i	−0.997459	+	0.0712445i	$0.977303\pi$
$6$	−6.37468	−	7.76841i	−1.06245	−	1.29474i
$7$	−7.05256			−1.00751			−0.503754	−	0.863847i	$-0.668048\pi$
$7$	−7.05256			−1.00751			−0.503754	+	0.863847i	$0.668048\pi$
$8$	3.77005	+	7.05597i	0.471257	+	0.881996i
$9$	−16.2462			−1.80513
$10$	−0.903882	−	1.10150i	−0.0903882	−	0.110150i
$11$	15.8415			1.44014			0.720070	−	0.693901i	$-0.244110\pi$
$11$	15.8415			1.44014			0.720070	+	0.693901i	$0.244110\pi$
$12$	19.7116	+	3.92306i	1.64264	+	0.326922i
$13$	−4.24621	+	12.2870i	−0.326632	+	0.945152i
$13$	−4.24621	+	12.2870i	−0.326632	+	0.945152i
$14$	10.9039	−	8.94762i	0.778849	−	0.639116i
$15$	−3.57972			−0.238648
$16$	−14.7808	−	6.12606i	−0.923799	−	0.382879i
$17$	15.4924			0.911319			0.455659	−	0.890154i	$-0.349403\pi$
$17$	15.4924			0.911319			0.455659	+	0.890154i	$0.349403\pi$
$18$	25.1181	−	20.6116i	1.39545	−	1.14509i
$19$	10.6323			0.559594			0.279797	−	0.960059i	$-0.409733\pi$
$19$	10.6323			0.559594			0.279797	+	0.960059i	$0.409733\pi$
$20$	2.79496	+	0.556260i	0.139748	+	0.0278130i
$21$		−	35.4360i		−	1.68743i
$22$	−24.4924	+	20.0982i	−1.11329	+	0.913557i
$23$			21.3353i			0.927624i	0.885934	+	0.463812i	$0.153519\pi$
$23$			21.3353i			0.927624i	−0.885934	+	0.463812i	$0.846481\pi$
$24$	−35.4531	+	18.9429i	−1.47721	+	0.789286i
$25$	24.4924			0.979697
$26$	−9.02352	−	24.3839i	−0.347059	−	0.937843i
$27$		−	36.4090i		−	1.34848i
$28$	−5.50647	+	27.6676i	−0.196660	+	0.988129i
$29$	−2.24621			−0.0774556			−0.0387278	−	0.999250i	$-0.512331\pi$
$29$	−2.24621			−0.0774556			−0.0387278	+	0.999250i	$0.512331\pi$
$30$	5.53457	−	4.54161i	0.184486	−	0.151387i
$31$	−26.2601			−0.847099			−0.423549	−	0.905873i	$-0.639216\pi$
$31$	−26.2601			−0.847099			−0.423549	+	0.905873i	$0.639216\pi$
$32$	30.6245	−	9.28101i	0.957017	−	0.290032i
$33$			79.5968i			2.41202i
$34$	−23.9526	+	19.6553i	−0.704490	+	0.578097i
$35$		−	5.02456i		−	0.143559i
$36$	−12.6847	+	63.7348i	−0.352352	+	1.77041i
$37$		−	42.5605i		−	1.15028i	−0.818054	−	0.575142i	$-0.804947\pi$
$37$		−	42.5605i		−	1.15028i	0.818054	−	0.575142i	$-0.195053\pi$
$38$	−16.4384	+	13.4892i	−0.432591	+	0.354980i
$39$	−61.7366	−	21.3353i	−1.58299	−	0.547060i
$40$	−5.02699	+	2.68596i	−0.125675	+	0.0671489i
$41$		−	33.2987i		−	0.812163i	−0.913837	−	0.406082i	$-0.866895\pi$
$41$		−	33.2987i		−	0.812163i	0.913837	−	0.406082i	$-0.133105\pi$
$42$	44.9579	+	54.7872i	1.07043	+	1.30446i
$43$		−	46.4582i		−	1.08042i	−0.841530	−	0.540211i	$-0.818344\pi$
$43$		−	46.4582i		−	1.08042i	0.841530	−	0.540211i	$-0.181656\pi$
$44$	12.3687	−	62.1473i	0.281107	−	1.41244i
$45$		−	11.5745i		−	0.257212i
$46$	−27.0683	−	32.9863i	−0.588440	−	0.717094i
$47$	47.4178			1.00889			0.504444	−	0.863444i	$-0.331697\pi$
$47$	47.4178			1.00889			0.504444	+	0.863444i	$0.331697\pi$
$48$	30.7808	−	74.2669i	0.641266	−	1.54723i
$49$	0.738634			0.0150742
$50$	−37.8674	+	31.0737i	−0.757349	+	0.621473i
$51$			77.8426i			1.52633i
$52$	44.8872	+	26.2515i	0.863215	+	0.504837i
$53$	−24.7386			−0.466767			−0.233383	−	0.972385i	$-0.574980\pi$
$53$	−24.7386			−0.466767			−0.233383	+	0.972385i	$0.574980\pi$
$54$	46.1923	+	56.2916i	0.855413	+	1.04244i
$55$			11.2862i			0.205204i
$56$	−26.5885	−	49.7627i	−0.474795	−	0.888619i
$57$			53.4226i			0.937238i
$58$	3.47284	−	2.84978i	0.0598766	−	0.0491341i
$59$	44.2656			0.750264			0.375132	−	0.926971i	$-0.377597\pi$
$59$	44.2656			0.750264			0.375132	+	0.926971i	$0.377597\pi$
$60$	−2.79496	+	14.0435i	−0.0465827	+	0.234058i
$61$	91.2311			1.49559			0.747796	−	0.663929i	$-0.231112\pi$
$61$	91.2311			1.49559			0.747796	+	0.663929i	$0.231112\pi$
$62$	40.6004	−	33.3163i	0.654845	−	0.537359i
$63$	114.577			1.81869
$64$	−35.5734	+	53.2028i	−0.555834	+	0.831293i
$65$	−8.75379	−	3.02519i	−0.134674	−	0.0465414i
$66$	−100.985	−	123.064i	−1.53007	−	1.86460i
$67$	−70.7394			−1.05581			−0.527906	−	0.849303i	$-0.677023\pi$
$67$	−70.7394			−1.05581			−0.527906	+	0.849303i	$0.677023\pi$
$68$	12.0961	−	60.7777i	0.177884	−	0.893789i
$69$	−107.201			−1.55363
$70$	6.37468	+	7.76841i	0.0910669	+	0.110977i
$71$	−10.5254			−0.148245			−0.0741226	−	0.997249i	$-0.523616\pi$
$71$	−10.5254			−0.148245			−0.0741226	+	0.997249i	$0.523616\pi$
$72$	−61.2491	−	114.633i	−0.850682	−	1.59212i
$73$		−	52.1731i		−	0.714700i	−0.933971	−	0.357350i	$-0.883680\pi$
$73$		−	52.1731i		−	0.714700i	0.933971	−	0.357350i	$-0.116320\pi$
$74$	53.9967	+	65.8022i	0.729685	+	0.889219i
$75$			123.064i			1.64085i
$76$	8.30144	−	41.7111i	0.109229	−	0.548830i
$77$	−111.723			−1.45095
$78$	122.519	−	45.3392i	1.57075	−	0.581272i
$79$		−	12.5233i		−	0.158523i	−0.996854	−	0.0792616i	$-0.974744\pi$
$79$		−	12.5233i		−	0.158523i	0.996854	−	0.0792616i	$-0.0252562\pi$
$80$	4.36448	−	10.5305i	0.0545560	−	0.131631i
$81$	36.7235			0.453376
$82$	42.2462	+	51.4827i	0.515198	+	0.627838i
$83$	−21.4783			−0.258775			−0.129388	−	0.991594i	$-0.541301\pi$
$83$	−21.4783			−0.258775			−0.129388	+	0.991594i	$0.541301\pi$
$84$	−139.018	−	27.6676i	−1.65497	−	0.329376i
$85$			11.0375i			0.129853i
$86$	58.9417	+	71.8284i	0.685368	+	0.835214i
$87$		−	11.2862i		−	0.129727i
$88$	59.7235	+	111.777i	0.678676	+	1.27020i
$89$			137.469i			1.54460i	0.635258	+	0.772300i	$0.280894\pi$
$89$			137.469i			1.54460i	−0.635258	+	0.772300i	$0.719106\pi$
$90$	14.6847	+	17.8952i	0.163163	+	0.198836i
$91$	29.9467	−	86.6546i	0.329084	−	0.952249i
$92$	83.6998	+	16.6581i	0.909781	+	0.181067i
$93$		−	131.945i		−	1.41877i
$94$	−73.3120	+	60.1591i	−0.779915	+	0.639991i
$95$			7.57491i			0.0797359i
$96$	46.6330	+	153.875i	0.485760	+	1.60286i
$97$			137.645i			1.41902i	0.704696	+	0.709510i	$0.251083\pi$
$97$			137.645i			1.41902i	−0.704696	+	0.709510i	$0.748917\pi$
$98$	−1.14199	+	0.937108i	−0.0116530	+	0.00956233i
$99$	−257.365			−2.59965
$100$	19.1231	−	96.0852i	0.191231	−	0.960852i
$101$	112.492			1.11379			0.556893	−	0.830584i	$-0.311993\pi$
$101$	112.492			1.11379			0.556893	+	0.830584i	$0.311993\pi$
$102$	−98.7593	−	120.352i	−0.968228	−	1.17992i
$103$		−	27.6732i		−	0.268671i	−0.990936	−	0.134336i	$-0.957110\pi$
$103$		−	27.6732i		−	0.268671i	0.990936	−	0.134336i	$-0.0428901\pi$
$104$	−102.705	+	16.3614i	−0.987547	+	0.157321i
$105$	25.2462			0.240440
$106$	38.2481	−	31.3860i	0.360831	−	0.296095i
$107$			51.4827i			0.481147i	0.970631	+	0.240573i	$0.0773355\pi$
$107$			51.4827i			0.481147i	−0.970631	+	0.240573i	$0.922665\pi$
$108$	−142.835	−	28.4273i	−1.32254	−	0.263216i
$109$		−	72.8340i		−	0.668202i	−0.942537	−	0.334101i	$-0.891567\pi$
$109$		−	72.8340i		−	0.668202i	0.942537	−	0.334101i	$-0.108433\pi$
$110$	−14.3189	−	17.4495i	−0.130172	−	0.158632i
$111$	213.848			1.92656
$112$	104.242	+	43.2044i	0.930735	+	0.385754i
$113$	−147.477			−1.30511			−0.652554	−	0.757742i	$-0.726303\pi$
$113$	−147.477			−1.30511			−0.652554	+	0.757742i	$0.726303\pi$
$114$	−67.7775	−	82.5960i	−0.594539	−	0.724526i
$115$	−15.2003			−0.132176
$116$	−1.75379	+	8.81202i	−0.0151189	+	0.0759657i
$117$	68.9848	−	199.617i	0.589614	−	1.70613i
$118$	−68.4384	+	56.1599i	−0.579987	+	0.475932i
$119$	−109.261			−0.918162
$120$	−13.4957	−	25.2584i	−0.112465	−	0.210487i
$121$	129.955			1.07400
$122$	−141.051	+	115.745i	−1.15616	+	0.948732i
$123$	167.311			1.36025
$124$	−20.5032	+	103.020i	−0.165349	+	0.830805i
$125$			35.2606i			0.282085i
$126$	−177.147	+	145.365i	−1.40593	+	1.15369i
$127$		−	182.121i		−	1.43403i	−0.697060	−	0.717013i	$-0.745509\pi$
$127$		−	182.121i		−	1.43403i	0.697060	−	0.717013i	$-0.254491\pi$
$128$	−12.4990	−	127.388i	−0.0976486	−	0.995221i
$129$	233.432			1.80955
$130$	17.3722	−	6.42876i	0.133632	−	0.0494520i
$131$		−	154.524i		−	1.17957i	−0.807559	−	0.589787i	$-0.799212\pi$
$131$		−	154.524i		−	1.17957i	0.807559	−	0.589787i	$-0.200788\pi$
$132$	312.263	+	62.1473i	2.36563	+	0.470813i
$133$	−74.9848			−0.563796
$134$	109.369	−	89.7474i	0.816189	−	0.669757i
$135$	25.9394			0.192144
$136$	58.4073	+	109.314i	0.429465	+	0.803780i
$137$		−	83.5206i		−	0.609640i	−0.952410	−	0.304820i	$-0.901404\pi$
$137$		−	83.5206i		−	0.609640i	0.952410	−	0.304820i	$-0.0985963\pi$
$138$	165.742	−	136.006i	1.20103	−	0.985551i
$139$		−	5.02456i		−	0.0361479i	−0.999837	−	0.0180740i	$-0.994247\pi$
$139$		−	5.02456i		−	0.0361479i	0.999837	−	0.0180740i	$-0.00575343\pi$
$140$	−19.7116	−	3.92306i	−0.140797	−	0.0280218i
$141$			238.253i			1.68974i
$142$	16.2732	−	13.3536i	0.114600	−	0.0940396i
$143$	−67.2665	+	194.645i	−0.470395	+	1.36115i
$144$	240.132	+	99.5253i	1.66758	+	0.691148i
$145$		−	1.60030i		−	0.0110366i
$146$	66.1922	+	80.6642i	0.453371	+	0.552494i
$147$			3.71131i			0.0252470i
$148$	−166.967	−	33.2302i	−1.12816	−	0.224528i
$149$			33.1233i			0.222304i	0.993803	+	0.111152i	$0.0354540\pi$
$149$			33.1233i			0.222304i	−0.993803	+	0.111152i	$0.964546\pi$
$150$	−156.131	−	190.267i	−1.04088	−	1.26845i
$151$	−26.5807			−0.176031			−0.0880156	−	0.996119i	$-0.528053\pi$
$151$	−26.5807			−0.176031			−0.0880156	+	0.996119i	$0.528053\pi$
$152$	40.0843	+	75.0211i	0.263712	+	0.493560i
$153$	−251.693			−1.64505
$154$	172.734	−	141.744i	1.12165	−	0.920416i
$155$		−	18.7088i		−	0.120702i
$156$	−131.902	+	225.538i	−0.845528	+	1.44576i
$157$	−52.2462			−0.332778			−0.166389	−	0.986060i	$-0.553211\pi$
$157$	−52.2462			−0.332778			−0.166389	+	0.986060i	$0.553211\pi$
$158$	15.8884	+	19.3622i	0.100560	+	0.122545i
$159$		−	124.301i		−	0.781766i
$160$	6.61221	+	21.8183i	0.0413263	+	0.136364i
$161$		−	150.469i		−	0.934589i
$162$	−56.7777	+	46.5913i	−0.350480	+	0.287600i
$163$	213.100			1.30736			0.653680	−	0.756771i	$-0.273224\pi$
$163$	213.100			1.30736			0.653680	+	0.756771i	$0.273224\pi$
$164$	−130.633	−	25.9988i	−0.796541	−	0.158529i
$165$	−56.7083			−0.343687
$166$	33.2074	−	27.2497i	0.200045	−	0.164155i
$167$	−131.728			−0.788790			−0.394395	−	0.918941i	$-0.629046\pi$
$167$	−131.728			−0.788790			−0.394395	+	0.918941i	$0.629046\pi$
$168$	250.035	−	133.596i	1.48831	−	0.795213i
$169$	−132.939	−	104.346i	−0.786624	−	0.617433i
$170$	−14.0033	−	17.0649i	−0.0823725	−	0.100382i
$171$	−172.734			−1.01014
$172$	−182.258	−	36.2734i	−1.05964	−	0.210892i
$173$	183.417			1.06021			0.530106	−	0.847931i	$-0.322152\pi$
$173$	183.417			1.06021			0.530106	+	0.847931i	$0.322152\pi$
$174$	14.3189	+	17.4495i	0.0822925	+	0.100284i
$175$	−172.734			−0.987053
$176$	−234.150	−	97.0463i	−1.33040	−	0.551399i
$177$			222.415i			1.25658i
$178$	−174.408	−	212.540i	−0.979821	−	1.19404i
$179$			120.666i			0.674110i	0.941485	+	0.337055i	$0.109431\pi$
$179$			120.666i			0.674110i	−0.941485	+	0.337055i	$0.890569\pi$
$180$	−45.4075	−	9.03712i	−0.252264	−	0.0502062i
$181$	−87.4773			−0.483300			−0.241650	−	0.970363i	$-0.577689\pi$
$181$	−87.4773			−0.483300			−0.241650	+	0.970363i	$0.577689\pi$
$182$	63.6390	+	171.969i	0.349665	+	0.944886i
$183$			458.396i			2.50490i
$184$	−150.542	+	80.4354i	−0.818161	+	0.437149i
$185$	30.3220			0.163903
$186$	167.400	+	203.999i	0.899998	+	1.09677i
$187$	245.424			1.31243
$188$	37.0227	−	186.023i	0.196929	−	0.989482i
$189$			256.777i			1.35861i
$190$	−9.61033	−	11.7115i	−0.0505807	−	0.0616394i
$191$			116.726i			0.611130i	0.952171	+	0.305565i	$0.0988453\pi$
$191$			116.726i			0.611130i	−0.952171	+	0.305565i	$0.901155\pi$
$192$	−267.321	−	178.741i	−1.39229	−	0.930941i
$193$			29.9227i			0.155040i	0.996991	+	0.0775199i	$0.0247001\pi$
$193$			29.9227i			0.155040i	−0.996991	+	0.0775199i	$0.975300\pi$
$194$	−174.631	−	212.811i	−0.900158	−	1.09696i
$195$	15.2003	−	43.9839i	0.0779500	−	0.225559i
$196$	0.576708	−	2.89770i	0.00294239	−	0.0147842i
$197$			32.2354i			0.163632i	0.996647	+	0.0818158i	$0.0260719\pi$
$197$			32.2354i			0.163632i	−0.996647	+	0.0818158i	$0.973928\pi$
$198$	397.909	−	326.520i	2.00964	−	1.64909i
$199$			248.602i			1.24925i	0.780923	+	0.624627i	$0.214749\pi$
$199$			248.602i			1.24925i	−0.780923	+	0.624627i	$0.785251\pi$
$200$	92.3378	+	172.818i	0.461689	+	0.864089i
$201$		−	355.434i		−	1.76833i
$202$	−173.923	+	142.720i	−0.861006	+	0.706533i
$203$	15.8415			0.0780372
$204$	305.381	+	60.7777i	1.49697	+	0.297930i
$205$	23.7235			0.115724
$206$	35.1091	+	42.7851i	0.170432	+	0.207695i
$207$		−	346.619i		−	1.67449i
$208$	138.033	−	155.598i	0.663621	−	0.748069i
$209$	168.432			0.805894
$210$	−39.0329	+	32.0300i	−0.185871	+	0.152524i
$211$			61.6080i			0.291981i	0.989286	+	0.145990i	$0.0466369\pi$
$211$			61.6080i			0.291981i	−0.989286	+	0.145990i	$0.953363\pi$
$212$	−19.3153	+	97.0511i	−0.0911101	+	0.457788i
$213$		−	52.8855i		−	0.248289i
$214$	−65.3164	−	79.5968i	−0.305217	−	0.371948i
$215$	33.0989			0.153948
$216$	256.901	−	137.264i	1.18936	−	0.635482i
$217$	185.201			0.853460
$218$	92.4048	+	112.608i	0.423875	+	0.516549i
$219$	262.147			1.19702
$220$	44.2765	+	8.81202i	0.201257	+	0.0400546i
$221$	−65.7841	+	190.355i	−0.297666	+	0.861335i
$222$	−330.627	+	271.310i	−1.48931	+	1.22212i
$223$	−126.172			−0.565792			−0.282896	−	0.959151i	$-0.591295\pi$
$223$	−126.172			−0.565792			−0.282896	+	0.959151i	$0.591295\pi$
$224$	−215.982	+	65.4549i	−0.964203	+	0.292209i
$225$	−397.909			−1.76848
$226$	228.013	−	187.105i	1.00891	−	0.827899i
$227$	94.3817			0.415778			0.207889	−	0.978152i	$-0.433341\pi$
$227$	94.3817			0.415778			0.207889	+	0.978152i	$0.433341\pi$
$228$	209.580	+	41.7111i	0.919210	+	0.182943i
$229$		−	311.624i		−	1.36081i	−0.732839	−	0.680403i	$-0.761805\pi$
$229$		−	311.624i		−	1.36081i	0.732839	−	0.680403i	$-0.238195\pi$
$230$	23.5009	−	19.2846i	0.102178	−	0.0838462i
$231$		−	561.361i		−	2.43014i
$232$	−8.46834	−	15.8492i	−0.0365015	−	0.0683155i
$233$	−228.602			−0.981125			−0.490563	−	0.871406i	$-0.663209\pi$
$233$	−228.602			−0.981125			−0.490563	+	0.871406i	$0.663209\pi$
$234$	146.598	+	396.146i	0.626488	+	1.69293i
$235$			33.7825i			0.143755i
$236$	34.5615	−	173.656i	0.146447	−	0.735832i
$237$	62.9242			0.265503
$238$	168.928	−	138.620i	0.709780	−	0.582438i
$239$	−38.5219			−0.161179			−0.0805897	−	0.996747i	$-0.525680\pi$
$239$	−38.5219			−0.161179			−0.0805897	+	0.996747i	$0.525680\pi$
$240$	52.9111	+	21.9296i	0.220463	+	0.0913733i
$241$			120.371i			0.499464i	0.968315	+	0.249732i	$0.0803425\pi$
$241$			120.371i			0.499464i	−0.968315	+	0.249732i	$0.919658\pi$
$242$	−200.921	+	164.874i	−0.830253	+	0.681297i
$243$		−	143.162i		−	0.589144i
$244$	71.2311	−	357.905i	0.291931	−	1.46682i
$245$			0.526236i			0.00214790i
$246$	−258.678	+	212.269i	−1.05154	+	0.862881i
$247$	−45.1469	+	130.639i	−0.182781	+	0.528901i
$248$	−99.0019	−	185.290i	−0.399201	−	0.747138i
$249$		−	107.919i		−	0.433410i
$250$	−44.7353	−	54.5160i	−0.178941	−	0.218064i
$251$		−	332.858i		−	1.32613i	−0.748563	−	0.663064i	$-0.769256\pi$
$251$		−	332.858i		−	1.32613i	0.748563	−	0.663064i	$-0.230744\pi$
$252$	89.4593	−	449.494i	0.354997	−	1.78371i
$253$			337.985i			1.33591i
$254$	231.058	+	281.576i	0.909678	+	1.10857i
$255$	−55.4586			−0.217485
$256$	180.943	+	181.096i	0.706807	+	0.707406i
$257$	172.970			0.673034			0.336517	−	0.941677i	$-0.390751\pi$
$257$	172.970			0.673034			0.336517	+	0.941677i	$0.390751\pi$
$258$	−360.906	+	296.156i	−1.39886	+	1.14789i
$259$			300.160i			1.15892i
$260$	−18.7028	+	31.9796i	−0.0719337	+	0.122999i
$261$	36.4924			0.139818
$262$	196.046	+	238.908i	0.748266	+	0.911863i
$263$		−	252.465i		−	0.959944i	−0.877284	−	0.479972i	$-0.840647\pi$
$263$		−	252.465i		−	0.959944i	0.877284	−	0.479972i	$-0.159353\pi$
$264$	−561.633	+	300.084i	−2.12740	+	1.13668i
$265$		−	17.6249i		−	0.0665091i
$266$	115.933	−	95.1336i	0.435839	−	0.357645i
$267$	−690.724			−2.58698
$268$	−55.2316	+	277.515i	−0.206088	+	1.03550i
$269$	315.110			1.17141			0.585706	−	0.810524i	$-0.300817\pi$
$269$	315.110			1.17141			0.585706	+	0.810524i	$0.300817\pi$
$270$	−40.1046	+	32.9095i	−0.148536	+	0.121887i
$271$	−23.3216			−0.0860577			−0.0430288	−	0.999074i	$-0.513701\pi$
$271$	−23.3216			−0.0860577			−0.0430288	+	0.999074i	$0.513701\pi$
$272$	−228.990	−	94.9076i	−0.841875	−	0.348925i
$273$	435.401	+	150.469i	1.59488	+	0.551168i
$274$	105.963	+	129.130i	0.386726	+	0.471278i
$275$	387.998			1.41090
$276$	−83.6998	+	420.555i	−0.303260	+	1.52375i
$277$	152.277			0.549735			0.274867	−	0.961482i	$-0.411366\pi$
$277$	152.277			0.549735			0.274867	+	0.961482i	$0.411366\pi$
$278$	6.37468	+	7.76841i	0.0229305	+	0.0279439i
$279$	426.627			1.52913
$280$	35.4531	−	18.9429i	0.126618	−	0.0676531i
$281$		−	541.701i		−	1.92776i	−0.266335	−	0.963881i	$-0.585813\pi$
$281$		−	541.701i		−	1.92776i	0.266335	−	0.963881i	$-0.414187\pi$
$282$	−302.273	−	368.361i	−1.07189	−	1.30624i
$283$			121.979i			0.431021i	0.976502	+	0.215510i	$0.0691415\pi$
$283$			121.979i			0.431021i	−0.976502	+	0.215510i	$0.930858\pi$
$284$	−8.21799	+	41.2918i	−0.0289366	+	0.145394i
$285$	−38.0606			−0.133546
$286$	−142.947	−	386.279i	−0.499813	−	1.35063i
$287$			234.841i			0.818262i
$288$	−497.533	+	150.781i	−1.72754	+	0.523546i
$289$	−48.9848			−0.169498
$290$	2.03031	+	2.47421i	0.00700107	+	0.00853175i
$291$	−691.605			−2.37665
$292$	−204.678	−	40.7355i	−0.700952	−	0.139505i
$293$		−	107.010i		−	0.365221i	−0.983185	−	0.182610i	$-0.941545\pi$
$293$		−	107.010i		−	0.365221i	0.983185	−	0.182610i	$-0.0584547\pi$
$294$	−4.70856	−	5.73801i	−0.0160155	−	0.0195170i
$295$			31.5368i			0.106904i
$296$	300.305	−	160.455i	1.01455	−	0.542079i
$297$		−	576.775i		−	1.94200i
$298$	−42.0237	−	51.2115i	−0.141019	−	0.171851i
$299$	−262.147	−	90.5944i	−0.876745	−	0.302991i
$300$	482.786	+	96.0852i	1.60929	+	0.320284i
$301$			327.649i			1.08853i
$302$	41.0961	−	33.7231i	0.136080	−	0.111666i
$303$			565.225i			1.86543i
$304$	−157.153	−	65.1340i	−0.516952	−	0.214257i
$305$			64.9971i			0.213105i
$306$	389.140	−	319.324i	1.27170	−	1.04354i
$307$	412.762			1.34450			0.672250	−	0.740324i	$-0.265328\pi$
$307$	412.762			1.34450			0.672250	+	0.740324i	$0.265328\pi$
$308$	−87.2311	+	438.298i	−0.283218	+	1.42304i
$309$	139.045			0.449985
$310$	23.7360	+	28.9255i	0.0765677	+	0.0933081i
$311$		−	502.304i		−	1.61512i	−0.589782	−	0.807562i	$-0.700786\pi$
$311$		−	502.304i		−	1.61512i	0.589782	−	0.807562i	$-0.299214\pi$
$312$	−82.2089	−	516.047i	−0.263490	−	1.65400i
$313$	−283.617			−0.906126			−0.453063	−	0.891479i	$-0.649669\pi$
$313$	−283.617			−0.906126			−0.453063	+	0.891479i	$0.649669\pi$
$314$	80.7772	−	66.2850i	0.257252	−	0.211099i
$315$			81.6301i			0.259143i
$316$	−49.1298	−	9.77792i	−0.155474	−	0.0309428i
$317$			470.106i			1.48298i	0.670962	+	0.741491i	$0.265881\pi$
$317$			470.106i			1.48298i	−0.670962	+	0.741491i	$0.734119\pi$
$318$	157.701	+	192.180i	0.495915	+	0.604339i
$319$	−35.5835			−0.111547
$320$	−37.9040	−	25.3441i	−0.118450	−	0.0792002i
$321$	−258.678			−0.805851
$322$	190.901	+	232.638i	0.592859	+	0.722479i
$323$	164.720			0.509969
$324$	28.6728	−	144.068i	0.0884964	−	0.444655i
$325$	−104.000	+	300.938i	−0.320000	+	0.925962i
$326$	−329.471	+	270.360i	−1.01065	+	0.829326i
$327$	365.959			1.11914
$328$	234.955	−	125.538i	0.716325	−	0.382737i
$329$	−334.417			−1.01646
$330$	87.6761	−	71.9461i	0.265685	−	0.218019i
$331$	−572.647			−1.73005			−0.865026	−	0.501728i	$-0.832698\pi$
$331$	−572.647			−1.73005			−0.865026	+	0.501728i	$0.832698\pi$
$332$	−16.7698	+	84.2608i	−0.0505114	+	0.253797i
$333$			691.446i			2.07642i
$334$	203.663	−	167.124i	0.609769	−	0.500371i
$335$		−	50.3979i		−	0.150441i
$336$	−217.083	+	523.772i	−0.646081	+	1.55885i
$337$	−16.2614			−0.0482533			−0.0241267	−	0.999709i	$-0.507680\pi$
$337$	−16.2614			−0.0482533			−0.0241267	+	0.999709i	$0.507680\pi$
$338$	337.920	−	7.33248i	0.999765	−	0.0216937i
$339$		−	741.008i		−	2.18587i
$340$	43.3007	+	8.61782i	0.127355	+	0.0253465i
$341$	−416.000			−1.21994
$342$	267.062	−	219.149i	0.780884	−	0.640786i
$343$	340.366			0.992322
$344$	327.807	−	175.150i	0.952928	−	0.509156i
$345$		−	76.3746i		−	0.221376i
$346$	−283.578	+	232.702i	−0.819590	+	0.672548i
$347$			306.346i			0.882841i	0.897300	+	0.441421i	$0.145525\pi$
$347$			306.346i			0.882841i	−0.897300	+	0.441421i	$0.854475\pi$
$348$	−44.2765	−	8.81202i	−0.127231	−	0.0253219i
$349$		−	629.639i		−	1.80412i	−0.431607	−	0.902062i	$-0.642053\pi$
$349$		−	629.639i		−	1.80412i	0.431607	−	0.902062i	$-0.357947\pi$
$350$	267.062	−	219.149i	0.763036	−	0.626140i
$351$	447.357	+	154.600i	1.27452	+	0.440457i
$352$	485.140	−	147.026i	1.37824	−	0.417686i
$353$		−	203.365i		−	0.576105i	−0.957615	−	0.288053i	$-0.906992\pi$
$353$		−	203.365i		−	0.576105i	0.957615	−	0.288053i	$-0.0930078\pi$
$354$	−282.179	−	343.873i	−0.797116	−	0.971393i
$355$		−	7.49877i		−	0.0211233i
$356$	539.301	+	107.333i	1.51489	+	0.301497i
$357$		−	548.990i		−	1.53779i
$358$	−153.089	−	186.560i	−0.427623	−	0.521116i
$359$	367.828			1.02459			0.512296	−	0.858809i	$-0.328795\pi$
$359$	367.828			1.02459			0.512296	+	0.858809i	$0.328795\pi$
$360$	81.6695	−	43.6366i	0.226860	−	0.121213i
$361$	−247.955			−0.686855
$362$	135.248	−	110.983i	0.373612	−	0.306582i
$363$			652.964i			1.79880i
$364$	−316.570	−	185.140i	−0.869697	−	0.508628i
$365$	37.1704			0.101837
$366$	−581.569	−	708.721i	−1.58899	−	1.93639i
$367$			170.683i			0.465076i	0.972587	+	0.232538i	$0.0747030\pi$
$367$			170.683i			0.465076i	−0.972587	+	0.232538i	$0.925297\pi$
$368$	130.702	−	315.353i	0.355168	−	0.856937i
$369$			540.978i			1.46606i
$370$	−46.8805	+	38.4696i	−0.126704	+	0.103972i
$371$	174.471			0.470272
$372$	−517.629	−	103.020i	−1.39148	−	0.276935i
$373$	−724.742			−1.94301			−0.971505	−	0.237021i	$-0.923829\pi$
$373$	−724.742			−1.94301			−0.971505	+	0.237021i	$0.923829\pi$
$374$	−379.447	+	311.370i	−1.01456	+	0.832541i
$375$	−177.169			−0.472451
$376$	178.767	+	334.578i	0.475445	+	0.889836i
$377$	9.53789	−	27.5991i	0.0252994	−	0.0732073i
$378$	−325.774	−	397.000i	−0.861836	−	1.05026i
$379$	41.2202			0.108761			0.0543803	−	0.998520i	$-0.482682\pi$
$379$	41.2202			0.108761			0.0543803	+	0.998520i	$0.482682\pi$
$380$	29.7168	+	5.91431i	0.0782022	+	0.0155640i
$381$	915.080			2.40178
$382$	−148.091	−	180.468i	−0.387672	−	0.472430i
$383$	−622.255			−1.62469			−0.812343	−	0.583179i	$-0.801808\pi$
$383$	−622.255			−1.62469			−0.812343	+	0.583179i	$0.801808\pi$
$384$	640.070	−	62.8021i	1.66685	−	0.163547i
$385$		−	79.5968i		−	0.206745i
$386$	−37.9630	−	46.2631i	−0.0983499	−	0.119853i
$387$			754.769i			1.95031i
$388$	539.989	+	107.470i	1.39172	+	0.276984i
$389$	563.080			1.44751			0.723753	−	0.690060i	$-0.242416\pi$
$389$	563.080			1.44751			0.723753	+	0.690060i	$0.242416\pi$
$390$	32.3017	+	87.2877i	0.0828249	+	0.223815i
$391$			330.536i			0.845361i
$392$	2.78469	+	5.21178i	0.00710380	+	0.0132953i
$393$	776.417			1.97561
$394$	−40.8972	−	49.8388i	−0.103800	−	0.126494i
$395$	8.92218			0.0225878
$396$	−200.945	+	1009.66i	−0.507436	+	2.54964i
$397$		−	348.661i		−	0.878239i	−0.898429	−	0.439119i	$-0.855291\pi$
$397$		−	348.661i		−	0.878239i	0.898429	−	0.439119i	$-0.144709\pi$
$398$	−315.402	−	384.360i	−0.792467	−	0.965728i
$399$		−	376.766i		−	0.944275i
$400$	−362.017	−	150.042i	−0.905043	−	0.375105i
$401$			358.109i			0.893039i	0.894774	+	0.446520i	$0.147337\pi$
$401$			358.109i			0.893039i	−0.894774	+	0.446520i	$0.852663\pi$
$402$	450.941	+	549.533i	1.12174	+	1.36700i
$403$	111.506	−	322.657i	0.276689	−	0.800637i
$404$	87.8314	−	441.314i	0.217405	−	1.09236i
$405$			26.1634i			0.0646011i
$406$	−24.4924	+	20.0982i	−0.0603262	+	0.0495031i
$407$		−	674.224i		−	1.65657i
$408$	−549.255	+	293.471i	−1.34621	+	0.719291i
$409$			413.658i			1.01139i	0.862713	+	0.505694i	$0.168764\pi$
$409$			413.658i			1.01139i	−0.862713	+	0.505694i	$0.831236\pi$
$410$	−36.6786	+	30.0981i	−0.0894600	+	0.0734100i
$411$	419.655			1.02106
$412$	−108.563	−	21.6065i	−0.263503	−	0.0524431i
$413$	−312.186			−0.755897
$414$	439.757	+	535.903i	1.06221	+	1.29445i
$415$		−	15.3021i		−	0.0368726i
$416$	−16.0028	+	415.692i	−0.0384683	+	0.999260i
$417$	25.2462			0.0605425
$418$	−260.410	+	213.690i	−0.622991	+	0.511221i
$419$			389.365i			0.929273i	0.885502	+	0.464637i	$0.153815\pi$
$419$			389.365i			0.929273i	−0.885502	+	0.464637i	$0.846185\pi$
$420$	19.7116	−	99.0424i	0.0469325	−	0.235815i
$421$			87.9599i			0.208931i	0.994529	+	0.104465i	$0.0333132\pi$
$421$			87.9599i			0.208931i	−0.994529	+	0.104465i	$0.966687\pi$
$422$	−78.1623	−	95.2514i	−0.185219	−	0.225714i
$423$	−770.359			−1.82118
$424$	−93.2660	−	174.555i	−0.219967	−	0.411686i
$425$	379.447			0.892816
$426$	67.0961	+	81.7657i	0.157503	+	0.191938i
$427$	−643.413			−1.50682
$428$	201.970	+	40.1965i	0.471892	+	0.0939170i
$429$	−978.004	−	337.985i	−2.27973	−	0.787843i
$430$	−51.1738	+	41.9927i	−0.119009	+	0.0976574i
$431$	184.970			0.429164			0.214582	−	0.976706i	$-0.431161\pi$
$431$	184.970			0.429164			0.214582	+	0.976706i	$0.431161\pi$
$432$	−223.044	+	538.154i	−0.516306	+	1.24573i
$433$	−305.367			−0.705237			−0.352618	−	0.935767i	$-0.614709\pi$
$433$	−305.367			−0.705237			−0.352618	+	0.935767i	$0.614709\pi$
$434$	−286.337	+	234.965i	−0.659762	+	0.541394i
$435$	8.04081			0.0184846
$436$	−285.732	−	56.8671i	−0.655349	−	0.130429i
$437$			226.843i			0.519093i
$438$	−405.302	+	332.587i	−0.925347	+	0.759331i
$439$		−	109.456i		−	0.249329i	−0.992199	−	0.124665i	$-0.960215\pi$
$439$		−	109.456i		−	0.249329i	0.992199	−	0.124665i	$-0.0397855\pi$
$440$	−79.6352	+	42.5497i	−0.180989	+	0.0967038i
$441$	−12.0000			−0.0272109
$442$	−139.796	−	377.766i	−0.316281	−	0.854675i
$443$		−	448.118i		−	1.01155i	−0.862664	−	0.505777i	$-0.831206\pi$
$443$		−	448.118i		−	1.01155i	0.862664	−	0.505777i	$-0.168794\pi$
$444$	166.967	−	838.937i	0.376052	−	1.88950i
$445$	−97.9394			−0.220088
$446$	195.072	−	160.075i	0.437382	−	0.358912i
$447$	−166.430			−0.372326
$448$	250.884	−	375.216i	0.560008	−	0.837535i
$449$		−	710.672i		−	1.58279i	−0.611307	−	0.791394i	$-0.709356\pi$
$449$		−	710.672i		−	1.58279i	0.611307	−	0.791394i	$-0.290644\pi$
$450$	615.202	−	504.829i	1.36712	−	1.12184i
$451$		−	527.503i		−	1.16963i
$452$	−115.147	+	578.562i	−0.254749	+	1.28000i
$453$		−	133.556i		−	0.294826i
$454$	−145.922	+	119.742i	−0.321415	+	0.263750i
$455$	61.7366	+	21.3353i	0.135685	+	0.0468909i
$456$	−376.948	+	201.406i	−0.826640	+	0.441680i
$457$			400.658i			0.876714i	0.898801	+	0.438357i	$0.144439\pi$
$457$			400.658i			0.876714i	−0.898801	+	0.438357i	$0.855561\pi$
$458$	395.359	+	481.799i	0.863230	+	1.05196i
$459$		−	564.064i		−	1.22890i
$460$	−11.8680	+	59.6315i	−0.0258000	+	0.129634i
$461$			103.458i			0.224421i	0.993684	+	0.112211i	$0.0357932\pi$
$461$			103.458i			0.224421i	−0.993684	+	0.112211i	$0.964207\pi$
$462$	712.202	+	867.914i	1.54156	+	1.87860i
$463$	−819.192			−1.76931			−0.884657	−	0.466242i	$-0.845607\pi$
$463$	−819.192			−1.76931			−0.884657	+	0.466242i	$0.845607\pi$
$464$	33.2007	+	13.7604i	0.0715533	+	0.0296561i
$465$	94.0037			0.202159
$466$	353.439	−	290.029i	0.758453	−	0.622379i
$467$		−	249.686i		−	0.534660i	−0.963605	−	0.267330i	$-0.913859\pi$
$467$		−	249.686i		−	0.534660i	0.963605	−	0.267330i	$-0.0861414\pi$
$468$	−729.246	−	426.488i	−1.55822	−	0.911298i
$469$	498.894			1.06374
$470$	−42.8601	−	52.2308i	−0.0911916	−	0.111129i
$471$		−	262.514i		−	0.557355i
$472$	166.884	+	312.336i	0.353567	+	0.661730i
$473$		−	735.969i		−	1.55596i
$474$	−97.2864	+	79.8323i	−0.205246	+	0.168422i
$475$	260.410			0.548232
$476$	−85.3086	+	428.638i	−0.179220	+	0.900501i
$477$	401.909			0.842577
$478$	59.5582	−	48.8729i	0.124599	−	0.102245i
$479$	−251.194			−0.524413			−0.262207	−	0.965012i	$-0.584450\pi$
$479$	−251.194			−0.524413			−0.262207	+	0.965012i	$0.584450\pi$
$480$	−109.627	+	33.2234i	−0.228390	+	0.0692155i
$481$	522.939	+	180.721i	1.08719	+	0.375719i
$482$	−152.715	−	186.104i	−0.316836	−	0.386107i
$483$	756.040			1.56530
$484$	101.465	−	509.819i	0.209639	−	1.05335i
$485$	−98.0644			−0.202195
$486$	181.630	+	221.341i	0.373725	+	0.455434i
$487$	713.725			1.46555			0.732777	−	0.680469i	$-0.238224\pi$
$487$	713.725			1.46555			0.732777	+	0.680469i	$0.238224\pi$
$488$	343.946	+	643.723i	0.704807	+	1.31911i
$489$			1070.73i			2.18963i
$490$	−0.667638	−	0.813607i	−0.00136253	−	0.00166042i
$491$			744.491i			1.51628i	0.652094	+	0.758138i	$0.273891\pi$
$491$			744.491i			1.51628i	−0.652094	+	0.758138i	$0.726109\pi$
$492$	130.633	−	656.372i	0.265514	−	1.33409i
$493$	−34.7993			−0.0705867
$494$	−95.9407	−	259.257i	−0.194212	−	0.524811i
$495$		−	183.358i		−	0.370421i
$496$	388.144	+	160.871i	0.782549	+	0.324336i
$497$	74.2311			0.149358
$498$	136.918	+	166.853i	0.274935	+	0.335045i
$499$	597.411			1.19722			0.598608	−	0.801042i	$-0.295721\pi$
$499$	597.411			1.19722			0.598608	+	0.801042i	$0.295721\pi$
$500$	138.329	+	27.5307i	0.276659	+	0.0550613i
$501$		−	661.875i		−	1.32111i
$502$	422.299	+	514.628i	0.841232	+	1.02516i
$503$			959.310i			1.90718i	0.301112	+	0.953589i	$0.402642\pi$
$503$			959.310i			1.90718i	−0.301112	+	0.953589i	$0.597358\pi$
$504$	431.963	+	808.455i	0.857070	+	1.60408i
$505$			80.1446i			0.158702i
$506$	−428.803	−	522.554i	−0.847437	−	1.03272i
$507$	524.294	−	667.962i	1.03411	−	1.31748i
$508$	−714.472	−	142.196i	−1.40644	−	0.279913i
$509$			522.805i			1.02712i	0.858053	+	0.513561i	$0.171674\pi$
$509$			522.805i			1.02712i	−0.858053	+	0.513561i	$0.828326\pi$
$510$	85.7438	−	70.3605i	0.168125	−	0.137962i
$511$			367.954i			0.720066i
$512$	−509.511	−	50.4274i	−0.995138	−	0.0984910i
$513$		−	387.111i		−	0.754603i
$514$	−267.426	+	219.447i	−0.520285	+	0.426941i
$515$	19.7156			0.0382827
$516$	182.258	−	915.767i	0.353213	−	1.77474i
$517$	751.170			1.45294
$518$	−380.815	−	464.074i	−0.735164	−	0.895897i
$519$			921.588i			1.77570i
$520$	−11.6566	−	73.1716i	−0.0224165	−	0.140715i
$521$	−489.526			−0.939590			−0.469795	−	0.882776i	$-0.655672\pi$
$521$	−489.526			−0.939590			−0.469795	+	0.882776i	$0.655672\pi$
$522$	−56.4205	+	46.2981i	−0.108085	+	0.0886937i
$523$		−	398.101i		−	0.761188i	−0.924742	−	0.380594i	$-0.875720\pi$
$523$		−	398.101i		−	0.761188i	0.924742	−	0.380594i	$-0.124280\pi$
$524$	−606.208	−	120.649i	−1.15689	−	0.230246i
$525$		−	867.914i		−	1.65317i
$526$	320.304	+	390.333i	0.608942	+	0.742079i
$527$	−406.832			−0.771977
$528$	487.615	−	1176.50i	0.923513	−	2.22822i
$529$	73.8030			0.139514
$530$	22.3608	+	27.2497i	0.0421902	+	0.0514145i
$531$	−719.148			−1.35433
$532$	−58.5464	+	294.170i	−0.110050	+	0.552951i
$533$	409.140	+	141.393i	0.767617	+	0.265278i
$534$	1067.92	−	876.324i	1.99985	−	1.64106i
$535$	−36.6786			−0.0685581
$536$	−266.691	−	499.135i	−0.497558	−	0.931222i
$537$	−606.292			−1.12903
$538$	−487.188	+	399.781i	−0.905553	+	0.743088i
$539$	11.7011			0.0217089
$540$	20.2529	−	101.762i	0.0375053	−	0.188448i
$541$		−	872.704i		−	1.61313i	−0.591144	−	0.806566i	$-0.701324\pi$
$541$		−	872.704i		−	1.61313i	0.591144	−	0.806566i	$-0.298676\pi$
$542$	36.0573	−	29.5883i	0.0665264	−	0.0545909i
$543$		−	439.535i		−	0.809456i
$544$	474.448	−	143.785i	0.872148	−	0.264311i
$545$	51.8902			0.0952113
$546$	−864.070	+	319.758i	−1.58255	+	0.585637i
$547$		−	304.176i		−	0.556081i	−0.960569	−	0.278040i	$-0.910315\pi$
$547$		−	304.176i		−	0.556081i	0.960569	−	0.278040i	$-0.0896849\pi$
$548$	−327.656	−	65.2110i	−0.597913	−	0.118998i
$549$	−1482.16			−2.69974
$550$	−599.879	+	492.255i	−1.09069	+	0.895008i
$551$	−23.8824			−0.0433437
$552$	−404.153	−	756.405i	−0.732161	−	1.37030i
$553$			88.3216i			0.159713i
$554$	−235.433	+	193.194i	−0.424969	+	0.348726i
$555$			152.355i			0.274513i
$556$	−19.7116	−	3.92306i	−0.0354526	−	0.00705586i
$557$			883.073i			1.58541i	0.609606	+	0.792704i	$0.291327\pi$
$557$			883.073i			1.58541i	−0.609606	+	0.792704i	$0.708673\pi$
$558$	−659.602	+	541.263i	−1.18208	+	0.970006i
$559$	570.830	+	197.271i	1.02116	+	0.352900i
$560$	−30.7808	+	74.2669i	−0.0549657	+	0.132619i
$561$			1233.15i			2.19812i
$562$	687.258	+	837.517i	1.22288	+	1.49024i
$563$			88.1963i			0.156654i	0.996928	+	0.0783271i	$0.0249579\pi$
$563$			88.1963i			0.156654i	−0.996928	+	0.0783271i	$0.975042\pi$
$564$	934.682	+	186.023i	1.65724	+	0.329827i
$565$		−	105.069i		−	0.185964i
$566$	−154.755	−	188.590i	−0.273419	−	0.333198i
$567$	−258.995			−0.456781
$568$	−39.6813	−	74.2669i	−0.0698615	−	0.130752i
$569$	−325.030			−0.571231			−0.285615	−	0.958344i	$-0.592198\pi$
$569$	−325.030			−0.571231			−0.285615	+	0.958344i	$0.592198\pi$
$570$	58.8451	−	48.2877i	0.103237	−	0.0847152i
$571$			753.456i			1.31954i	0.751469	+	0.659769i	$0.229346\pi$
$571$			753.456i			1.31954i	−0.751469	+	0.659769i	$0.770654\pi$
$572$	711.082	+	415.865i	1.24315	+	0.727036i
$573$	−586.496			−1.02355
$574$	−297.944	−	363.085i	−0.519066	−	0.632552i
$575$			522.554i			0.908790i
$576$	577.933	−	864.343i	1.00336	−	1.50060i
$577$			137.623i			0.238515i	0.992863	+	0.119258i	$0.0380514\pi$
$577$			137.623i			0.238515i	−0.992863	+	0.119258i	$0.961949\pi$
$578$	75.7349	−	62.1473i	0.131029	−	0.107521i
$579$	−150.348			−0.259669
$580$	−6.27808	−	1.24948i	−0.0108243	−	0.00215427i
$581$	151.477			0.260718
$582$	1069.28	−	877.442i	1.83725	−	1.50763i
$583$	−391.898			−0.672210
$584$	368.132	−	196.695i	0.630362	−	0.336807i
$585$	142.216	+	49.1479i	0.243104	+	0.0840135i
$586$	135.764	+	165.446i	0.231679	+	0.282332i
$587$	−886.245			−1.50979			−0.754894	−	0.655847i	$-0.772312\pi$
$587$	−886.245			−1.50979			−0.754894	+	0.655847i	$0.772312\pi$
$588$	14.5597	+	2.89770i	0.0247614	+	0.00492807i
$589$	−279.204			−0.474031
$590$	−40.0108	−	48.7586i	−0.0678150	−	0.0826417i
$591$	−161.969			−0.274059
$592$	−260.728	+	629.077i	−0.440419	+	1.06263i
$593$			781.916i			1.31858i	0.751890	+	0.659288i	$0.229142\pi$
$593$			781.916i			1.31858i	−0.751890	+	0.659288i	$0.770858\pi$
$594$	731.758	+	891.745i	1.23192	+	1.50125i
$595$		−	77.8426i		−	0.130828i
$596$	129.945	+	25.8619i	0.218028	+	0.0433924i
$597$	−1249.11			−2.09232
$598$	520.240	−	192.520i	0.869966	−	0.321940i
$599$		−	21.0308i		−	0.0351098i	−0.999846	−	0.0175549i	$-0.994412\pi$
$599$		−	21.0308i		−	0.0351098i	0.999846	−	0.0175549i	$-0.00558818\pi$
$600$	−868.333	+	463.957i	−1.44722	+	0.773261i
$601$	1040.76			1.73171			0.865855	−	0.500295i	$-0.166775\pi$
$601$	1040.76			1.73171			0.865855	+	0.500295i	$0.166775\pi$
$602$	−415.690	−	506.574i	−0.690515	−	0.841485i
$603$	1149.25			1.90588
$604$	−20.7536	+	104.278i	−0.0343603	+	0.172645i
$605$			92.5854i			0.153034i
$606$	−717.104	−	873.888i	−1.18334	−	1.44206i
$607$		−	927.926i		−	1.52871i	−0.644797	−	0.764354i	$-0.723058\pi$
$607$		−	927.926i		−	1.52871i	0.644797	−	0.764354i	$-0.276942\pi$
$608$	325.609	−	98.6783i	0.535541	−	0.162300i
$609$			79.5968i			0.130701i
$610$	−82.4621	−	100.491i	−0.135184	−	0.164740i
$611$	−201.346	+	582.621i	−0.329535	+	0.953553i
$612$	−196.516	+	987.407i	−0.321105	+	1.61341i
$613$		−	1090.88i		−	1.77957i	−0.456379	−	0.889785i	$-0.650854\pi$
$613$		−	1090.88i		−	1.77957i	0.456379	−	0.889785i	$-0.349146\pi$
$614$	−638.166	+	523.673i	−1.03936	+	0.852887i
$615$			119.200i			0.193821i
$616$	−421.204	−	788.317i	−0.683772	−	1.27974i
$617$		−	406.336i		−	0.658568i	−0.944231	−	0.329284i	$-0.893193\pi$
$617$		−	406.336i		−	0.658568i	0.944231	−	0.329284i	$-0.106807\pi$
$618$	−214.977	+	176.408i	−0.347858	+	0.285449i
$619$	92.2440			0.149021			0.0745105	−	0.997220i	$-0.476261\pi$
$619$	92.2440			0.149021			0.0745105	+	0.997220i	$0.476261\pi$
$620$	−73.3959	−	14.6074i	−0.118380	−	0.0235604i
$621$	776.799			1.25088
$622$	637.275	+	776.606i	1.02456	+	1.24856i
$623$		−	969.512i		−	1.55620i
$624$	781.814	+	693.556i	1.25291	+	1.11147i
$625$	587.189			0.939503
$626$	438.497	−	359.827i	0.700475	−	0.574803i
$627$			846.296i			1.34975i
$628$	−40.7926	+	204.965i	−0.0649564	+	0.326377i
$629$		−	659.365i		−	1.04827i
$630$	−103.564	−	126.207i	−0.164388	−	0.200329i
$631$	383.964			0.608501			0.304251	−	0.952592i	$-0.401594\pi$
$631$	383.964			0.608501			0.304251	+	0.952592i	$0.401594\pi$
$632$	88.3642	−	47.2136i	0.139817	−	0.0747051i
$633$	−309.553			−0.489025
$634$	−596.425	−	726.825i	−0.940734	−	1.14641i
$635$	129.751			0.204333
$636$	−487.639	−	97.0511i	−0.766728	−	0.152596i
$637$	−3.13639	+	9.07557i	−0.00492370	+	0.0142474i
$638$	55.0152	−	45.1449i	0.0862307	−	0.0707600i
$639$	170.998			0.267602
$640$	90.7571	−	8.90486i	0.141808	−	0.0139138i
$641$	−291.417			−0.454628			−0.227314	−	0.973821i	$-0.572994\pi$
$641$	−291.417			−0.454628			−0.227314	+	0.973821i	$0.572994\pi$
$642$	399.939	−	328.186i	0.622958	−	0.511193i
$643$	−533.430			−0.829595			−0.414797	−	0.909914i	$-0.636148\pi$
$643$	−533.430			−0.829595			−0.414797	+	0.909914i	$0.636148\pi$
$644$	−590.298	−	117.483i	−0.916612	−	0.182426i
$645$			166.307i			0.257841i
$646$	−254.671	+	208.981i	−0.394228	+	0.323500i
$647$			367.954i			0.568708i	0.958719	+	0.284354i	$0.0917791\pi$
$647$			367.954i			0.568708i	−0.958719	+	0.284354i	$0.908221\pi$
$648$	138.449	+	259.120i	0.213657	+	0.399876i
$649$	701.235			1.08049
$650$	−221.008	−	597.222i	−0.340012	−	0.918802i
$651$			930.552i			1.42942i
$652$	166.383	−	836.002i	0.255189	−	1.28221i
$653$	853.053			1.30636			0.653180	−	0.757203i	$-0.273435\pi$
$653$	853.053			1.30636			0.653180	+	0.757203i	$0.273435\pi$
$654$	−565.804	+	464.294i	−0.865144	+	0.709929i
$655$	110.090			0.168076
$656$	−203.990	+	492.181i	−0.310960	+	0.750275i
$657$			847.615i			1.29013i
$658$	517.038	−	424.276i	0.785771	−	0.644796i
$659$		−	64.4629i		−	0.0978193i	−0.998803	−	0.0489097i	$-0.984425\pi$
$659$		−	64.4629i		−	0.0978193i	0.998803	−	0.0489097i	$-0.0155746\pi$
$660$	−44.2765	+	222.470i	−0.0670856	+	0.337076i
$661$		−	360.411i		−	0.545251i	−0.962120	−	0.272625i	$-0.912108\pi$
$661$		−	360.411i		−	0.545251i	0.962120	−	0.272625i	$-0.0878919\pi$
$662$	885.363	−	726.520i	1.33741	−	1.09746i
$663$	−956.450	−	330.536i	−1.44261	−	0.498546i
$664$	−80.9745	−	151.550i	−0.121950	−	0.228239i
$665$		−	53.4226i		−	0.0803347i
$666$	−877.241	−	1069.04i	−1.31718	−	1.60516i
$667$		−	47.9237i		−	0.0718496i
$668$	−102.850	+	516.776i	−0.153967	+	0.773617i
$669$		−	633.957i		−	0.947619i
$670$	63.9401	+	77.9196i	0.0954329	+	0.116298i
$671$	1445.24			2.15386
$672$	−328.882	−	1085.21i	−0.489408	−	1.61490i
$673$	−647.341			−0.961874			−0.480937	−	0.876755i	$-0.659703\pi$
$673$	−647.341			−0.961874			−0.480937	+	0.876755i	$0.659703\pi$
$674$	25.1415	−	20.6309i	0.0373019	−	0.0306096i
$675$		−	891.745i		−	1.32110i
$676$	−513.152	+	440.058i	−0.759101	+	0.650973i
$677$	−545.879			−0.806320			−0.403160	−	0.915129i	$-0.632088\pi$
$677$	−545.879			−0.806320			−0.403160	+	0.915129i	$0.632088\pi$
$678$	940.121	+	1145.66i	1.38661	+	1.68977i
$679$		−	970.749i		−	1.42967i
$680$	−77.8802	+	41.6120i	−0.114530	+	0.0611940i
$681$			474.226i			0.696368i
$682$	643.173	−	527.781i	0.943068	−	0.773873i
$683$	14.1051			0.0206517			0.0103259	−	0.999947i	$-0.496713\pi$
$683$	14.1051			0.0206517			0.0103259	+	0.999947i	$0.496713\pi$
$684$	−134.867	+	677.647i	−0.197174	+	0.990712i
$685$	59.5038			0.0868669
$686$	−526.236	+	431.824i	−0.767108	+	0.629482i
$687$	1565.78			2.27915
$688$	−284.606	+	686.688i	−0.413671	+	0.998092i
$689$	105.045	−	303.963i	0.152461	−	0.441165i
$690$	96.8968	+	118.082i	0.140430	+	0.171133i
$691$	−543.368			−0.786350			−0.393175	−	0.919464i	$-0.628623\pi$
$691$	−543.368			−0.786350			−0.393175	+	0.919464i	$0.628623\pi$
$692$	143.207	−	719.554i	0.206947	−	1.03982i
$693$	1815.08			2.61917
$694$	−388.663	−	473.638i	−0.560032	−	0.682475i
$695$	3.57972			0.00515068
$696$	79.6352	−	42.5497i	0.114418	−	0.0611346i
$697$		−	515.877i		−	0.740140i
$698$	798.826	+	973.478i	1.14445	+	1.39467i
$699$		−	1148.63i		−	1.64324i
$700$	−134.867	+	677.647i	−0.192667	+	0.968067i
$701$	−699.814			−0.998309			−0.499154	−	0.866513i	$-0.666356\pi$
$701$	−699.814			−0.998309			−0.499154	+	0.866513i	$0.666356\pi$
$702$	−887.795	+	328.538i	−1.26467	+	0.468002i
$703$		−	452.515i		−	0.643691i
$704$	−563.537	+	842.814i	−0.800479	+	1.19718i
$705$	−169.742			−0.240769
$706$	258.010	+	314.420i	0.365454	+	0.445355i
$707$	−793.360			−1.12215
$708$	872.547	+	173.656i	1.23241	+	0.245277i
$709$			879.292i			1.24019i	0.784528	+	0.620093i	$0.212905\pi$
$709$			879.292i			1.24019i	−0.784528	+	0.620093i	$0.787095\pi$
$710$	9.51372	+	11.5938i	0.0133996	+	0.0163292i
$711$			203.457i			0.286156i
$712$	−969.980	+	518.267i	−1.36233	+	0.727903i
$713$		−	560.268i		−	0.785789i
$714$	696.506	+	848.787i	0.975499	+	1.18878i
$715$	−138.674	−	47.9237i	−0.193949	−	0.0670261i
$716$	473.378	+	94.2129i	0.661143	+	0.131582i
$717$		−	193.556i		−	0.269952i
$718$	−568.695	+	466.666i	−0.792054	+	0.649952i
$719$			580.375i			0.807197i	0.914936	+	0.403599i	$0.132241\pi$
$719$			580.375i			0.807197i	−0.914936	+	0.403599i	$0.867759\pi$
$720$	−70.9063	+	171.081i	−0.0984810	+	0.237612i
$721$			195.167i			0.270689i
$722$	383.360	−	314.581i	0.530969	−	0.435708i
$723$	−604.810			−0.836529
$724$	−68.3002	+	343.178i	−0.0943373	+	0.474003i
$725$	−55.0152			−0.0758830
$726$	−828.419	−	1009.54i	−1.14107	−	1.39055i
$727$		−	467.988i		−	0.643725i	−0.946786	−	0.321863i	$-0.895691\pi$
$727$		−	467.988i		−	0.643725i	0.946786	−	0.321863i	$-0.104309\pi$
$728$	724.333	−	115.390i	0.994963	−	0.158503i
$729$	1049.84			1.44011
$730$	−57.4688	+	47.1583i	−0.0787243	+	0.0646004i
$731$		−	719.749i		−	0.984609i
$732$	1798.31	+	357.905i	2.45671	+	0.488941i
$733$			967.953i			1.32054i	0.751030	+	0.660268i	$0.229557\pi$
$733$			967.953i			1.32054i	−0.751030	+	0.660268i	$0.770443\pi$
$734$	−216.546	−	263.891i	−0.295022	−	0.359524i
$735$	−2.64410			−0.00359742
$736$	198.014	+	653.385i	0.269040	+	0.887752i
$737$	−1120.62			−1.52052
$738$	−686.341	−	836.399i	−0.930001	−	1.13333i
$739$	−1181.97			−1.59942			−0.799711	−	0.600385i	$-0.795014\pi$
$739$	−1181.97			−1.59942			−0.799711	+	0.600385i	$0.795014\pi$
$740$	23.6747	−	118.955i	0.0319928	−	0.160750i
$741$	−656.401	−	226.843i	−0.885832	−	0.306132i
$742$	−269.747	+	221.352i	−0.363541	+	0.298318i
$743$	812.406			1.09341			0.546707	−	0.837324i	$-0.315881\pi$
$743$	812.406			1.09341			0.546707	+	0.837324i	$0.315881\pi$
$744$	931.002	−	497.441i	1.25135	−	0.668603i
$745$	−23.5985			−0.0316758
$746$	1120.52	−	919.484i	1.50203	−	1.23255i
$747$	348.942			0.467124
$748$	191.621	−	962.812i	0.256178	−	1.28718i
$749$		−	363.085i		−	0.484760i
$750$	273.919	−	224.775i	0.365225	−	0.299700i
$751$			222.775i			0.296637i	0.988940	+	0.148319i	$0.0473861\pi$
$751$			222.775i			0.296637i	−0.988940	+	0.148319i	$0.952614\pi$
$752$	−700.871	−	290.484i	−0.932010	−	0.386282i
$753$	1672.47			2.22107
$754$	20.2687	+	54.7715i	0.0268816	+	0.0726412i
$755$		−	18.9373i		−	0.0250825i
$756$	1007.35	+	200.485i	1.33247	+	0.265192i
$757$	−591.814			−0.781789			−0.390895	−	0.920435i	$-0.627834\pi$
$757$	−591.814			−0.781789			−0.390895	+	0.920435i	$0.627834\pi$
$758$	−63.7301	+	52.2963i	−0.0840767	+	0.0689925i
$759$	−1698.23			−2.23745
$760$	−53.4484	+	28.5578i	−0.0703268	+	0.0375761i
$761$		−	212.419i		−	0.279132i	−0.990213	−	0.139566i	$-0.955429\pi$
$761$		−	212.419i		−	0.279132i	0.990213	−	0.139566i	$-0.0445707\pi$
$762$	−1414.79	+	1160.97i	−1.85668	+	1.52358i
$763$			513.666i			0.673219i
$764$	457.922	+	91.1368i	0.599375	+	0.119289i
$765$		−	179.317i		−	0.234402i
$766$	962.061	−	789.458i	1.25595	−	1.03062i
$767$	−187.961	+	543.890i	−0.245060	+	0.709113i
$768$	−909.928	+	909.158i	−1.18480	+	1.18380i
$769$		−	705.477i		−	0.917395i	−0.888592	−	0.458698i	$-0.848316\pi$
$769$		−	705.477i		−	0.917395i	0.888592	−	0.458698i	$-0.151684\pi$
$770$	100.985	+	123.064i	0.131149	+	0.159823i
$771$			869.097i			1.12723i
$772$	117.388	+	23.3629i	0.152058	+	0.0302629i
$773$			1201.26i			1.55403i	0.629484	+	0.777013i	$0.283266\pi$
$773$			1201.26i			1.55403i	−0.629484	+	0.777013i	$0.716734\pi$
$774$	−957.579	−	1166.94i	−1.23718	−	1.50767i
$775$	−643.173			−0.829900
$776$	−971.218	+	518.929i	−1.25157	+	0.668722i
$777$	−1508.17			−1.94102
$778$	−870.570	+	714.382i	−1.11899	+	0.918228i
$779$		−	354.041i		−	0.454482i
$780$	−160.684	−	93.9731i	−0.206005	−	0.120478i
$781$	−166.739			−0.213494
$782$	−419.353	−	511.038i	−0.536257	−	0.653501i
$783$			81.7824i			0.104447i
$784$	−10.9176	−	4.52492i	−0.0139255	−	0.00577158i
$785$		−	37.2225i		−	0.0474172i
$786$	−1200.41	+	985.044i	−1.52724	+	1.25324i
$787$	617.768			0.784965			0.392483	−	0.919759i	$-0.371616\pi$
$787$	617.768			0.784965			0.392483	+	0.919759i	$0.371616\pi$
$788$	126.461	+	25.1687i	0.160484	+	0.0319399i
$789$	1268.53			1.60776
$790$	−13.7945	+	11.3196i	−0.0174614	+	0.0143286i
$791$	1040.09			1.31491
$792$	−970.280	−	1815.96i	−1.22510	−	2.29288i
$793$	−387.386	+	1120.95i	−0.488507	+	1.41356i
$794$	442.348	+	539.060i	0.557113	+	0.678917i
$795$	88.5574			0.111393
$796$	975.278	+	194.102i	1.22522	+	0.243847i
$797$	186.061			0.233451			0.116726	−	0.993164i	$-0.462760\pi$
$797$	186.061			0.233451			0.116726	+	0.993164i	$0.462760\pi$
$798$	478.005	+	582.513i	0.599003	+	0.729967i
$799$	734.616			0.919419
$800$	750.069	−	227.314i	0.937587	−	0.284143i
$801$		−	2233.36i		−	2.78821i
$802$	−454.334	−	553.668i	−0.566502	−	0.690359i
$803$		−	826.502i		−	1.02927i
$804$	−1394.39	−	277.515i	−1.73432	−	0.345168i
$805$	107.201			0.133169
$806$	236.958	+	640.324i	0.293993	+	0.794446i
$807$			1583.29i			1.96194i
$808$	424.103	+	793.743i	0.524879	+	0.982355i
$809$	341.981			0.422721			0.211360	−	0.977408i	$-0.432211\pi$
$809$	341.981			0.422721			0.211360	+	0.977408i	$0.432211\pi$
$810$	−33.1937	−	40.4510i	−0.0409799	−	0.0499395i
$811$	−247.854			−0.305616			−0.152808	−	0.988256i	$-0.548832\pi$
$811$	−247.854			−0.305616			−0.152808	+	0.988256i	$0.548832\pi$
$812$	12.3687	−	62.1473i	0.0152324	−	0.0765361i
$813$		−	117.181i		−	0.144134i
$814$	855.391	+	1042.41i	1.05085	+	1.28060i
$815$			151.822i			0.186284i
$816$	476.869	−	1150.57i	0.584398	−	1.41002i
$817$		−	493.956i		−	0.604598i
$818$	−524.810	−	639.551i	−0.641577	−	0.781848i
$819$	−486.520	+	1407.81i	−0.594041	+	1.71894i
$820$	18.5227	−	93.0686i	0.0225887	−	0.113498i
$821$			361.496i			0.440311i	0.975465	+	0.220156i	$0.0706565\pi$
$821$			361.496i			0.440311i	−0.975465	+	0.220156i	$0.929343\pi$
$822$	−648.823	+	532.418i	−0.789322	+	0.647710i
$823$		−	1086.85i		−	1.32059i	−0.751006	−	0.660296i	$-0.770431\pi$
$823$		−	1086.85i		−	1.32059i	0.751006	−	0.660296i	$-0.229569\pi$
$824$	195.261	−	104.329i	0.236967	−	0.126613i
$825$			1949.52i			2.36305i
$826$	482.666	−	396.071i	0.584342	−	0.479505i
$827$	−737.955			−0.892328			−0.446164	−	0.894951i	$-0.647210\pi$
$827$	−737.955			−0.892328			−0.446164	+	0.894951i	$0.647210\pi$
$828$	−1359.80	−	270.632i	−1.64228	−	0.326850i
$829$	−56.6817			−0.0683736			−0.0341868	−	0.999415i	$-0.510884\pi$
$829$	−56.6817			−0.0683736			−0.0341868	+	0.999415i	$0.510884\pi$
$830$	19.4139	+	23.6584i	0.0233902	+	0.0285041i
$831$			765.123i			0.920725i
$832$	−502.649	−	662.999i	−0.604145	−	0.796874i
$833$	11.4432			0.0137374
$834$	−39.0329	+	32.0300i	−0.0468020	+	0.0384053i
$835$		−	93.8488i		−	0.112394i
$836$	131.508	−	660.768i	0.157306	−	0.790392i
$837$			956.103i			1.14230i
$838$	−493.990	−	601.993i	−0.589487	−	0.718369i
$839$	−40.6316			−0.0484286			−0.0242143	−	0.999707i	$-0.507708\pi$
$839$	−40.6316			−0.0484286			−0.0242143	+	0.999707i	$0.507708\pi$
$840$	95.1796	+	178.136i	0.113309	+	0.212067i
$841$	−835.955			−0.994001
$842$	−111.595	−	135.994i	−0.132536	−	0.161513i
$843$	2721.81			3.22872
$844$	241.692	+	48.1021i	0.286365	+	0.0569930i
$845$	74.3409	−	94.7120i	0.0879774	−	0.112085i
$846$	1191.04	−	977.358i	1.40785	−	1.15527i
$847$	−916.512			−1.08207
$848$	365.656	+	151.550i	0.431198	+	0.178715i
$849$	−612.890			−0.721897
$850$	−586.658	+	481.406i	−0.690186	+	0.566360i
$851$	908.042			1.06703
$852$	−207.473	−	41.2918i	−0.243513	−	0.0484645i
$853$			484.738i			0.568274i	0.958784	+	0.284137i	$0.0917070\pi$
$853$			484.738i			0.568274i	−0.958784	+	0.284137i	$0.908293\pi$
$854$	994.773	−	816.301i	1.16484	−	0.955856i
$855$		−	123.064i		−	0.143934i
$856$	−363.260	+	194.093i	−0.424370	+	0.226744i
$857$	576.462			0.672651			0.336326	−	0.941746i	$-0.390816\pi$
$857$	576.462			0.672651			0.336326	+	0.941746i	$0.390816\pi$
$858$	1940.88	−	718.244i	2.26210	−	0.837114i
$859$			1697.06i			1.97563i	0.155639	+	0.987814i	$0.450256\pi$
$859$			1697.06i			1.97563i	−0.155639	+	0.987814i	$0.549744\pi$
$860$	25.8428	−	129.849i	0.0300498	−	0.150987i
$861$	−1179.97			−1.37047
$862$	−285.980	+	234.672i	−0.331763	+	0.272241i
$863$	43.1162			0.0499608			0.0249804	−	0.999688i	$-0.492048\pi$
$863$	43.1162			0.0499608			0.0249804	+	0.999688i	$0.492048\pi$
$864$	−337.913	−	1115.01i	−0.391102	−	1.29052i
$865$			130.674i			0.151068i
$866$	472.125	−	387.421i	0.545179	−	0.447369i
$867$		−	246.127i		−	0.283884i
$868$	144.600	−	726.553i	0.166590	−	0.837043i
$869$		−	198.389i		−	0.228296i
$870$	−12.4318	+	10.2014i	−0.0142894	+	0.0117258i
$871$	300.374	−	869.173i	0.344862	−	0.997902i
$872$	513.914	−	274.588i	0.589351	−	0.314895i
$873$		−	2236.21i		−	2.56152i
$874$	−287.797	−	350.720i	−0.329288	−	0.401281i
$875$		−	248.678i		−	0.284203i
$876$	204.678	−	1028.42i	0.233651	−	1.17399i
$877$		−	934.522i		−	1.06559i	−0.846244	−	0.532795i	$-0.821142\pi$
$877$		−	934.522i		−	1.06559i	0.846244	−	0.532795i	$-0.178858\pi$
$878$	138.867	+	169.228i	0.158163	+	0.192742i
$879$	537.677			0.611692
$880$	69.1401	−	166.819i	0.0785683	−	0.189567i
$881$	−279.583			−0.317348			−0.158674	−	0.987331i	$-0.550722\pi$
$881$	−279.583			−0.317348			−0.158674	+	0.987331i	$0.550722\pi$
$882$	18.5531	−	15.2245i	0.0210352	−	0.0172613i
$883$		−	184.824i		−	0.209314i	−0.994508	−	0.104657i	$-0.966626\pi$
$883$		−	184.824i		−	0.209314i	0.994508	−	0.104657i	$-0.0333744\pi$
$884$	695.411	+	406.700i	0.786664	+	0.460067i
$885$	−158.458			−0.179049
$886$	568.530	+	692.831i	0.641682	+	0.781976i
$887$			538.484i			0.607085i	0.952818	+	0.303542i	$0.0981694\pi$
$887$			538.484i			0.607085i	−0.952818	+	0.303542i	$0.901831\pi$
$888$	806.217	+	1508.90i	0.907902	+	1.69921i
$889$			1284.42i			1.44479i
$890$	151.423	−	124.256i	0.170138	−	0.139614i
$891$	581.757			0.652926
$892$	−98.5118	+	494.979i	−0.110439	+	0.554909i
$893$	504.159			0.564568
$894$	257.315	−	211.150i	0.287825	−	0.236186i
$895$	−85.9676			−0.0960532
$896$	88.1501	+	898.414i	0.0983818	+	1.00269i
$897$	455.197	−	1317.17i	0.507466	−	1.46842i
$898$	901.633	+	1098.76i	1.00405	+	1.22356i
$899$	58.9857			0.0656125
$900$	−310.678	+	1561.02i	−0.345198	+	1.73447i
$901$	−383.261			−0.425373
$902$	669.245	+	815.566i	0.741957	+	0.904175i
$903$	−1646.29			−1.82314
$904$	−555.997	−	1040.59i	−0.615041	−	1.15110i
$905$		−	62.3227i		−	0.0688649i
$906$	169.444	+	206.490i	0.187024	+	0.227914i
$907$		−	1068.99i		−	1.17860i	−0.807913	−	0.589302i	$-0.799403\pi$
$907$		−	1068.99i		−	1.17860i	0.807913	−	0.589302i	$-0.200597\pi$
$908$	73.6910	−	370.265i	0.0811575	−	0.407781i
$909$	−1827.58			−2.01053
$910$	−122.519	+	45.3392i	−0.134636	+	0.0498233i
$911$		−	1674.49i		−	1.83808i	−0.394163	−	0.919041i	$-0.628965\pi$
$911$		−	1674.49i		−	1.83808i	0.394163	−	0.919041i	$-0.371035\pi$
$912$	327.270	−	789.627i	0.358849	−	0.865819i
$913$	−340.250			−0.372672
$914$	−508.317	−	619.453i	−0.556146	−	0.677739i
$915$	−326.582			−0.356920
$916$	−1222.52	−	243.309i	−1.33463	−	0.265621i
$917$			1089.79i			1.18843i
$918$	715.631	+	872.093i	0.779554	+	0.949992i
$919$			864.224i			0.940397i	0.882561	+	0.470198i	$0.155818\pi$
$919$			864.224i			0.940397i	−0.882561	+	0.470198i	$0.844182\pi$
$920$	−57.3058	−	107.253i	−0.0622889	−	0.116579i
$921$			2073.95i			2.25184i
$922$	−131.258	−	159.956i	−0.142362	−	0.173488i
$923$	44.6931	−	129.325i	0.0484215	−	0.140114i
$924$	−2202.25	−	438.298i	−2.38339	−	0.474348i
$925$		−	1042.41i		−	1.12693i
$926$	1266.54	−	1039.31i	1.36776	−	1.12237i
$927$			449.584i			0.484988i
$928$	−68.7892	+	20.8471i	−0.0741263	+	0.0224646i
$929$		−	434.527i		−	0.467736i	−0.972268	−	0.233868i	$-0.924862\pi$
$929$		−	434.527i		−	0.467736i	0.972268	−	0.233868i	$-0.0751383\pi$
$930$	−145.338	+	119.263i	−0.156277	+	0.128240i
$931$	7.85336			0.00843541
$932$	−178.487	+	896.820i	−0.191510	+	0.962253i
$933$	2523.86			2.70510
$934$	316.778	+	386.037i	0.339163	+	0.413316i
$935$			174.851i			0.187006i
$936$	1668.57	−	265.811i	1.78266	−	0.283986i
$937$	481.508			0.513882			0.256941	−	0.966427i	$-0.417285\pi$
$937$	481.508			0.513882			0.256941	+	0.966427i	$0.417285\pi$
$938$	−771.334	+	632.949i	−0.822318	+	0.674786i
$939$		−	1425.05i		−	1.51763i
$940$	132.531	+	26.3766i	0.140990	+	0.0280602i
$941$			594.411i			0.631680i	0.948812	+	0.315840i	$0.102286\pi$
$941$			594.411i			0.631680i	−0.948812	+	0.315840i	$0.897714\pi$
$942$	333.053	+	405.870i	0.353560	+	0.430860i
$943$	710.439			0.753382
$944$	−654.279	−	271.174i	−0.693092	−	0.287260i
$945$	−182.939			−0.193587
$946$	933.727	+	1137.87i	0.987027	+	1.20283i
$947$	1342.53			1.41766			0.708831	−	0.705378i	$-0.249223\pi$
$947$	1342.53			1.41766			0.708831	+	0.705378i	$0.249223\pi$
$948$	49.1298	−	246.855i	0.0518246	−	0.260396i
$949$	641.049	+	221.538i	0.675500	+	0.233444i
$950$	−402.617	+	330.384i	−0.423808	+	0.347773i
$951$	−2362.07			−2.48378
$952$	−411.921	−	770.944i	−0.432690	−	0.809815i
$953$	−851.864			−0.893876			−0.446938	−	0.894565i	$-0.647486\pi$
$953$	−851.864			−0.893876			−0.446938	+	0.894565i	$0.647486\pi$
$954$	−621.387	+	509.904i	−0.651349	+	0.534491i
$955$	−83.1607			−0.0870793
$956$	−30.0770	+	151.124i	−0.0314613	+	0.158079i
$957$		−	178.791i		−	0.186825i
$958$	388.368	−	318.691i	0.405394	−	0.332663i
$959$			589.035i			0.614217i
$960$	127.343	−	190.451i	0.132649	−	0.198387i
$961$	−271.409			−0.282423
$962$	−1037.79	+	384.045i	−1.07879	+	0.399216i
$963$		−	836.399i		−	0.868535i
$964$	472.222	+	93.9827i	0.489856	+	0.0974924i
$965$	−21.3183			−0.0220915
$966$	−1168.90	+	959.191i	−1.21005	+	0.992952i
$967$	710.332			0.734573			0.367287	−	0.930108i	$-0.380287\pi$
$967$	710.332			0.734573			0.367287	+	0.930108i	$0.380287\pi$
$968$	489.936	+	916.955i	0.506132	+	0.947268i
$969$			827.645i			0.854123i
$970$	151.616	−	124.415i	0.156305	−	0.128263i
$971$			410.853i			0.423124i	0.977365	+	0.211562i	$0.0678550\pi$
$971$			410.853i			0.423124i	−0.977365	+	0.211562i	$0.932145\pi$
$972$	−561.633	−	111.777i	−0.577811	−	0.114997i
$973$			35.4360i			0.0364194i
$974$	−1103.48	+	905.506i	−1.13294	+	0.929677i
$975$	−1512.08	−	522.554i	−1.55085	−	0.535953i
$976$	−1348.47	−	558.887i	−1.38162	−	0.572630i
$977$		−	378.934i		−	0.387855i	−0.981016	−	0.193927i	$-0.937877\pi$
$977$		−	378.934i		−	0.387855i	0.981016	−	0.193927i	$-0.0621226\pi$
$978$	−1358.44	−	1655.45i	−1.38900	−	1.69268i
$979$			2177.73i			2.22444i
$980$	2.06445	+	0.410872i	0.00210659	+	0.000419258i
$981$			1183.28i			1.20619i
$982$	−944.540	−	1151.05i	−0.961853	−	1.17215i
$983$	−325.271			−0.330897			−0.165448	−	0.986218i	$-0.552907\pi$
$983$	−325.271			−0.330897			−0.165448	+	0.986218i	$0.552907\pi$
$984$	630.773	+	1180.54i	0.641029	+	1.19974i
$985$	−22.9660			−0.0233157
$986$	53.8027	−	44.1500i	0.0545666	−	0.0447769i
$987$		−	1680.30i		−	1.70243i
$988$	477.253	+	279.114i	0.483050	+	0.282504i
$989$	991.201			1.00223
$990$	232.628	+	283.488i	0.234977	+	0.286352i
$991$			1640.48i			1.65538i	0.561186	+	0.827690i	$0.310345\pi$
$991$			1640.48i			1.65538i	−0.561186	+	0.827690i	$0.689655\pi$
$992$	−804.203	+	243.720i	−0.810688	+	0.245685i
$993$		−	2877.30i		−	2.89758i
$994$	−114.768	+	94.1773i	−0.115461	+	0.0947458i
$995$	−177.115			−0.178005
$996$	−423.373	−	84.2608i	−0.425074	−	0.0845991i
$997$	1358.81			1.36290			0.681448	−	0.731867i	$-0.261351\pi$
$997$	1358.81			1.36290			0.681448	+	0.731867i	$0.261351\pi$
$998$	−923.650	+	757.938i	−0.925501	+	0.759457i
$999$	−1549.59			−1.55114

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	52.3.b.d.51.2	yes	8
3.2	odd	2		468.3.e.k.415.7		8
4.3	odd	2	inner	52.3.b.d.51.8	yes	8
8.3	odd	2		832.3.c.f.831.7		8
8.5	even	2		832.3.c.f.831.1		8
12.11	even	2		468.3.e.k.415.1		8
13.12	even	2	inner	52.3.b.d.51.7	yes	8
39.38	odd	2		468.3.e.k.415.2		8
52.51	odd	2	inner	52.3.b.d.51.1	✓	8
104.51	odd	2		832.3.c.f.831.8		8
104.77	even	2		832.3.c.f.831.2		8
156.155	even	2		468.3.e.k.415.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.3.b.d.51.1	✓	8	52.51	odd	2	inner
52.3.b.d.51.2	yes	8	1.1	even	1	trivial
52.3.b.d.51.7	yes	8	13.12	even	2	inner
52.3.b.d.51.8	yes	8	4.3	odd	2	inner
468.3.e.k.415.1		8	12.11	even	2
468.3.e.k.415.2		8	39.38	odd	2
468.3.e.k.415.7		8	3.2	odd	2
468.3.e.k.415.8		8	156.155	even	2
832.3.c.f.831.1		8	8.5	even	2
832.3.c.f.831.2		8	104.77	even	2
832.3.c.f.831.7		8	8.3	odd	2
832.3.c.f.831.8		8	104.51	odd	2

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:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	52.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54609 + 1.26870i) q^{2} +5.02456i q^{3} +(0.780776 - 3.92306i) q^{4} +0.712445i q^{5} +(-6.37468 - 7.76841i) q^{6} -7.05256 q^{7} +(3.77005 + 7.05597i) q^{8} -16.2462 q^{9} +O(q^{10})\)	\(q+(-1.54609 + 1.26870i) q^{2} +5.02456i q^{3} +(0.780776 - 3.92306i) q^{4} +0.712445i q^{5} +(-6.37468 - 7.76841i) q^{6} -7.05256 q^{7} +(3.77005 + 7.05597i) q^{8} -16.2462 q^{9} +(-0.903882 - 1.10150i) q^{10} +15.8415 q^{11} +(19.7116 + 3.92306i) q^{12} +(-4.24621 + 12.2870i) q^{13} +(10.9039 - 8.94762i) q^{14} -3.57972 q^{15} +(-14.7808 - 6.12606i) q^{16} +15.4924 q^{17} +(25.1181 - 20.6116i) q^{18} +10.6323 q^{19} +(2.79496 + 0.556260i) q^{20} -35.4360i q^{21} +(-24.4924 + 20.0982i) q^{22} +21.3353i q^{23} +(-35.4531 + 18.9429i) q^{24} +24.4924 q^{25} +(-9.02352 - 24.3839i) q^{26} -36.4090i q^{27} +(-5.50647 + 27.6676i) q^{28} -2.24621 q^{29} +(5.53457 - 4.54161i) q^{30} -26.2601 q^{31} +(30.6245 - 9.28101i) q^{32} +79.5968i q^{33} +(-23.9526 + 19.6553i) q^{34} -5.02456i q^{35} +(-12.6847 + 63.7348i) q^{36} -42.5605i q^{37} +(-16.4384 + 13.4892i) q^{38} +(-61.7366 - 21.3353i) q^{39} +(-5.02699 + 2.68596i) q^{40} -33.2987i q^{41} +(44.9579 + 54.7872i) q^{42} -46.4582i q^{43} +(12.3687 - 62.1473i) q^{44} -11.5745i q^{45} +(-27.0683 - 32.9863i) q^{46} +47.4178 q^{47} +(30.7808 - 74.2669i) q^{48} +0.738634 q^{49} +(-37.8674 + 31.0737i) q^{50} +77.8426i q^{51} +(44.8872 + 26.2515i) q^{52} -24.7386 q^{53} +(46.1923 + 56.2916i) q^{54} +11.2862i q^{55} +(-26.5885 - 49.7627i) q^{56} +53.4226i q^{57} +(3.47284 - 2.84978i) q^{58} +44.2656 q^{59} +(-2.79496 + 14.0435i) q^{60} +91.2311 q^{61} +(40.6004 - 33.3163i) q^{62} +114.577 q^{63} +(-35.5734 + 53.2028i) q^{64} +(-8.75379 - 3.02519i) q^{65} +(-100.985 - 123.064i) q^{66} -70.7394 q^{67} +(12.0961 - 60.7777i) q^{68} -107.201 q^{69} +(6.37468 + 7.76841i) q^{70} -10.5254 q^{71} +(-61.2491 - 114.633i) q^{72} -52.1731i q^{73} +(53.9967 + 65.8022i) q^{74} +123.064i q^{75} +(8.30144 - 41.7111i) q^{76} -111.723 q^{77} +(122.519 - 45.3392i) q^{78} -12.5233i q^{79} +(4.36448 - 10.5305i) q^{80} +36.7235 q^{81} +(42.2462 + 51.4827i) q^{82} -21.4783 q^{83} +(-139.018 - 27.6676i) q^{84} +11.0375i q^{85} +(58.9417 + 71.8284i) q^{86} -11.2862i q^{87} +(59.7235 + 111.777i) q^{88} +137.469i q^{89} +(14.6847 + 17.8952i) q^{90} +(29.9467 - 86.6546i) q^{91} +(83.6998 + 16.6581i) q^{92} -131.945i q^{93} +(-73.3120 + 60.1591i) q^{94} +7.57491i q^{95} +(46.6330 + 153.875i) q^{96} +137.645i q^{97} +(-1.14199 + 0.937108i) q^{98} -257.365 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 64 q^{9}+O(q^{10}) \) 8 * q - 2 * q^4 - 64 * q^9	\( 8 q - 2 q^{4} - 64 q^{9} + 34 q^{10} + 34 q^{12} + 32 q^{13} + 46 q^{14} - 110 q^{16} - 8 q^{17} - 64 q^{22} + 64 q^{25} - 34 q^{26} + 48 q^{29} + 102 q^{30} - 52 q^{36} - 148 q^{38} + 34 q^{40} + 170 q^{42} + 238 q^{48} - 192 q^{49} - 76 q^{52} - 122 q^{56} + 400 q^{61} - 104 q^{62} + 70 q^{64} - 136 q^{65} - 544 q^{66} + 138 q^{68} - 170 q^{74} - 432 q^{77} + 442 q^{78} - 168 q^{81} + 272 q^{82} + 16 q^{88} + 68 q^{90} + 884 q^{92} - 34 q^{94}+O(q^{100}) \) 8 * q - 2 * q^4 - 64 * q^9 + 34 * q^10 + 34 * q^12 + 32 * q^13 + 46 * q^14 - 110 * q^16 - 8 * q^17 - 64 * q^22 + 64 * q^25 - 34 * q^26 + 48 * q^29 + 102 * q^30 - 52 * q^36 - 148 * q^38 + 34 * q^40 + 170 * q^42 + 238 * q^48 - 192 * q^49 - 76 * q^52 - 122 * q^56 + 400 * q^61 - 104 * q^62 + 70 * q^64 - 136 * q^65 - 544 * q^66 + 138 * q^68 - 170 * q^74 - 432 * q^77 + 442 * q^78 - 168 * q^81 + 272 * q^82 + 16 * q^88 + 68 * q^90 + 884 * q^92 - 34 * q^94

Introduction

L-functions

Modular forms

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