LMFDB - Embedded newform 152.2.c.b.77.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,2,Mod(77,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("152.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.c (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:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 4 x^{12} + 4 x^{11} - 10 x^{10} + 24 x^{9} - 40 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 4x^12 + 4x^11 - 10x^10 + 24x^9 - 40x^8 + 48x^7 - 40x^6 + 32x^5 + 64x^4 - 128x^3 + 192x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			77.5
Root			$1.14052 + 0.836196i$ of defining polynomial
Character	$\chi$	$=$	152.77
Dual form			152.2.c.b.77.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.836196 - 1.14052i) q^{2} +3.13611i q^{3} +(-0.601554 + 1.90739i) q^{4} -0.594041i q^{5} +(3.57679 - 2.62240i) q^{6} -3.48756 q^{7} +(2.67842 - 0.908869i) q^{8} -6.83520 q^{9} +O(q^{10})$	\(q+(-0.836196 - 1.14052i) q^{2} +3.13611i q^{3} +(-0.601554 + 1.90739i) q^{4} -0.594041i q^{5} +(3.57679 - 2.62240i) q^{6} -3.48756 q^{7} +(2.67842 - 0.908869i) q^{8} -6.83520 q^{9} +(-0.677513 + 0.496734i) q^{10} +4.83520i q^{11} +(-5.98179 - 1.88654i) q^{12} +0.215597i q^{13} +(2.91629 + 3.97762i) q^{14} +1.86298 q^{15} +(-3.27627 - 2.29479i) q^{16} +1.29720 q^{17} +(5.71556 + 7.79565i) q^{18} +1.00000i q^{19} +(1.13307 + 0.357348i) q^{20} -10.9374i q^{21} +(5.51462 - 4.04317i) q^{22} +4.52815 q^{23} +(2.85031 + 8.39984i) q^{24} +4.64712 q^{25} +(0.245891 - 0.180281i) q^{26} -12.0276i q^{27} +(2.09796 - 6.65214i) q^{28} +9.41093i q^{29} +(-1.55781 - 2.12476i) q^{30} -1.22031 q^{31} +(0.122350 + 5.65553i) q^{32} -15.1637 q^{33} +(-1.08471 - 1.47948i) q^{34} +2.07176i q^{35} +(4.11174 - 13.0374i) q^{36} -5.62653i q^{37} +(1.14052 - 0.836196i) q^{38} -0.676135 q^{39} +(-0.539905 - 1.59109i) q^{40} -0.450021 q^{41} +(-12.4743 + 9.14580i) q^{42} -0.794359i q^{43} +(-9.22260 - 2.90863i) q^{44} +4.06039i q^{45} +(-3.78642 - 5.16442i) q^{46} +12.1986 q^{47} +(7.19673 - 10.2747i) q^{48} +5.16310 q^{49} +(-3.88590 - 5.30011i) q^{50} +4.06817i q^{51} +(-0.411227 - 0.129693i) q^{52} -2.56409i q^{53} +(-13.7177 + 10.0574i) q^{54} +2.87231 q^{55} +(-9.34118 + 3.16974i) q^{56} -3.13611 q^{57} +(10.7333 - 7.86938i) q^{58} -2.75191i q^{59} +(-1.12068 + 3.55343i) q^{60} +7.76665i q^{61} +(1.02042 + 1.39178i) q^{62} +23.8382 q^{63} +(6.34792 - 4.86867i) q^{64} +0.128073 q^{65} +(12.6798 + 17.2945i) q^{66} -4.11631i q^{67} +(-0.780337 + 2.47427i) q^{68} +14.2008i q^{69} +(2.36287 - 1.73239i) q^{70} -7.82788 q^{71} +(-18.3076 + 6.21230i) q^{72} +3.08931 q^{73} +(-6.41714 + 4.70488i) q^{74} +14.5739i q^{75} +(-1.90739 - 0.601554i) q^{76} -16.8631i q^{77} +(0.565381 + 0.771143i) q^{78} -10.0731 q^{79} +(-1.36320 + 1.94624i) q^{80} +17.2143 q^{81} +(0.376306 + 0.513256i) q^{82} +11.6296i q^{83} +(20.8619 + 6.57943i) q^{84} -0.770591i q^{85} +(-0.905979 + 0.664240i) q^{86} -29.5137 q^{87} +(4.39456 + 12.9507i) q^{88} +13.7091 q^{89} +(4.63094 - 3.39528i) q^{90} -0.751907i q^{91} +(-2.72392 + 8.63694i) q^{92} -3.82703i q^{93} +(-10.2004 - 13.9127i) q^{94} +0.594041 q^{95} +(-17.7364 + 0.383702i) q^{96} +2.08846 q^{97} +(-4.31736 - 5.88860i) q^{98} -33.0495i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9	$ 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9} - 8 q^{10} + 4 q^{12} + 4 q^{14} + 2 q^{16} - 8 q^{17} + 20 q^{18} + 8 q^{20} + 20 q^{22} + 6 q^{24} - 24 q^{25} - 10 q^{26} - 14 q^{28} + 4 q^{30} + 16 q^{31} - 20 q^{32} + 8 q^{36} + 2 q^{38} + 8 q^{39} + 28 q^{40} + 16 q^{41} - 2 q^{42} - 28 q^{44} - 48 q^{46} + 24 q^{47} + 36 q^{48} + 24 q^{49} + 12 q^{50} + 8 q^{52} - 34 q^{54} + 16 q^{55} - 48 q^{56} + 38 q^{58} - 28 q^{60} - 16 q^{62} - 32 q^{63} + 14 q^{64} + 16 q^{65} - 24 q^{66} - 26 q^{68} - 32 q^{70} + 48 q^{71} - 20 q^{74} - 4 q^{76} + 56 q^{78} - 48 q^{79} + 4 q^{80} - 16 q^{81} - 12 q^{82} + 64 q^{84} + 48 q^{86} - 48 q^{87} + 40 q^{88} - 16 q^{89} + 12 q^{90} + 62 q^{92} - 36 q^{94} + 16 q^{95} - 70 q^{96} + 32 q^{97} - 48 q^{98}+O(q^{100}) $ 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9 - 8 * q^10 + 4 * q^12 + 4 * q^14 + 2 * q^16 - 8 * q^17 + 20 * q^18 + 8 * q^20 + 20 * q^22 + 6 * q^24 - 24 * q^25 - 10 * q^26 - 14 * q^28 + 4 * q^30 + 16 * q^31 - 20 * q^32 + 8 * q^36 + 2 * q^38 + 8 * q^39 + 28 * q^40 + 16 * q^41 - 2 * q^42 - 28 * q^44 - 48 * q^46 + 24 * q^47 + 36 * q^48 + 24 * q^49 + 12 * q^50 + 8 * q^52 - 34 * q^54 + 16 * q^55 - 48 * q^56 + 38 * q^58 - 28 * q^60 - 16 * q^62 - 32 * q^63 + 14 * q^64 + 16 * q^65 - 24 * q^66 - 26 * q^68 - 32 * q^70 + 48 * q^71 - 20 * q^74 - 4 * q^76 + 56 * q^78 - 48 * q^79 + 4 * q^80 - 16 * q^81 - 12 * q^82 + 64 * q^84 + 48 * q^86 - 48 * q^87 + 40 * q^88 - 16 * q^89 + 12 * q^90 + 62 * q^92 - 36 * q^94 + 16 * q^95 - 70 * q^96 + 32 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−0.836196	−	1.14052i	−0.591280	−	0.806467i
$2$	−0.836196	−	1.14052i	−0.591280	−	0.806467i
$3$			3.13611i			1.81063i	0.424735	+	0.905317i	$0.360367\pi$
$3$			3.13611i			1.81063i	−0.424735	+	0.905317i	$0.639633\pi$
$4$	−0.601554	+	1.90739i	−0.300777	+	0.953695i
$5$		−	0.594041i		−	0.265663i	−0.991139	−	0.132832i	$-0.957593\pi$
$5$		−	0.594041i		−	0.265663i	0.991139	−	0.132832i	$-0.0424069\pi$
$6$	3.57679	−	2.62240i	1.46022	−	1.07059i
$7$	−3.48756			−1.31818			−0.659088	−	0.752066i	$-0.729057\pi$
$7$	−3.48756			−1.31818			−0.659088	+	0.752066i	$0.729057\pi$
$8$	2.67842	−	0.908869i	0.946966	−	0.321334i
$9$	−6.83520			−2.27840
$10$	−0.677513	+	0.496734i	−0.214248	+	0.157081i
$11$			4.83520i			1.45787i	0.684585	+	0.728933i	$0.259984\pi$
$11$			4.83520i			1.45787i	−0.684585	+	0.728933i	$0.740016\pi$
$12$	−5.98179	−	1.88654i	−1.72679	−	0.544597i
$13$			0.215597i			0.0597957i	0.999553	+	0.0298979i	$0.00951821\pi$
$13$			0.215597i			0.0597957i	−0.999553	+	0.0298979i	$0.990482\pi$
$14$	2.91629	+	3.97762i	0.779410	+	1.06306i
$15$	1.86298			0.481019
$16$	−3.27627	−	2.29479i	−0.819067	−	0.573699i
$17$	1.29720			0.314618			0.157309	−	0.987549i	$-0.449718\pi$
$17$	1.29720			0.314618			0.157309	+	0.987549i	$0.449718\pi$
$18$	5.71556	+	7.79565i	1.34717	+	1.83745i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	1.13307	+	0.357348i	0.253362	+	0.0799053i
$21$		−	10.9374i		−	2.38673i
$22$	5.51462	−	4.04317i	1.17572	−	0.862007i
$23$	4.52815			0.944184			0.472092	−	0.881549i	$-0.343499\pi$
$23$	4.52815			0.944184			0.472092	+	0.881549i	$0.343499\pi$
$24$	2.85031	+	8.39984i	0.581818	+	1.71461i
$25$	4.64712			0.929423
$26$	0.245891	−	0.180281i	0.0482233	−	0.0353560i
$27$		−	12.0276i		−	2.31471i
$28$	2.09796	−	6.65214i	0.396477	−	1.25714i
$29$			9.41093i			1.74757i	0.486316	+	0.873783i	$0.338340\pi$
$29$			9.41093i			1.74757i	−0.486316	+	0.873783i	$0.661660\pi$
$30$	−1.55781	−	2.12476i	−0.284417	−	0.387926i
$31$	−1.22031			−0.219174			−0.109587	−	0.993977i	$-0.534953\pi$
$31$	−1.22031			−0.219174			−0.109587	+	0.993977i	$0.534953\pi$
$32$	0.122350	+	5.65553i	0.0216286	+	0.999766i
$33$	−15.1637			−2.63966
$34$	−1.08471	−	1.47948i	−0.186027	−	0.253729i
$35$			2.07176i			0.350191i
$36$	4.11174	−	13.0374i	0.685290	−	2.17290i
$37$		−	5.62653i		−	0.924995i	−0.886621	−	0.462498i	$-0.846953\pi$
$37$		−	5.62653i		−	0.924995i	0.886621	−	0.462498i	$-0.153047\pi$
$38$	1.14052	−	0.836196i	0.185016	−	0.135649i
$39$	−0.676135			−0.108268
$40$	−0.539905	−	1.59109i	−0.0853665	−	0.251574i
$41$	−0.450021			−0.0702815			−0.0351407	−	0.999382i	$-0.511188\pi$
$41$	−0.450021			−0.0702815			−0.0351407	+	0.999382i	$0.511188\pi$
$42$	−12.4743	+	9.14580i	−1.92482	+	1.41123i
$43$		−	0.794359i		−	0.121139i	−0.998164	−	0.0605693i	$-0.980708\pi$
$43$		−	0.794359i		−	0.121139i	0.998164	−	0.0605693i	$-0.0192916\pi$
$44$	−9.22260	−	2.90863i	−1.39036	−	0.438493i
$45$			4.06039i			0.605287i
$46$	−3.78642	−	5.16442i	−0.558277	−	0.761453i
$47$	12.1986			1.77935			0.889676	−	0.456593i	$-0.150930\pi$
$47$	12.1986			1.77935			0.889676	+	0.456593i	$0.150930\pi$
$48$	7.19673	−	10.2747i	1.03876	−	1.48303i
$49$	5.16310			0.737586
$50$	−3.88590	−	5.30011i	−0.549549	−	0.749549i
$51$			4.06817i			0.569658i
$52$	−0.411227	−	0.129693i	−0.0570269	−	0.0179852i
$53$		−	2.56409i		−	0.352205i	−0.984372	−	0.176103i	$-0.943651\pi$
$53$		−	2.56409i		−	0.352205i	0.984372	−	0.176103i	$-0.0563490\pi$
$54$	−13.7177	+	10.0574i	−1.86674	+	1.36864i
$55$	2.87231			0.387302
$56$	−9.34118	+	3.16974i	−1.24827	+	0.423574i
$57$	−3.13611			−0.415388
$58$	10.7333	−	7.86938i	1.40935	−	1.03330i
$59$		−	2.75191i		−	0.358268i	−0.983825	−	0.179134i	$-0.942670\pi$
$59$		−	2.75191i		−	0.358268i	0.983825	−	0.179134i	$-0.0573295\pi$
$60$	−1.12068	+	3.55343i	−0.144679	+	0.458745i
$61$			7.76665i			0.994417i	0.867631	+	0.497209i	$0.165642\pi$
$61$			7.76665i			0.994417i	−0.867631	+	0.497209i	$0.834358\pi$
$62$	1.02042	+	1.39178i	0.129593	+	0.176757i
$63$	23.8382			3.00333
$64$	6.34792	−	4.86867i	0.793489	−	0.608584i
$65$	0.128073			0.0158855
$66$	12.6798	+	17.2945i	1.56078	+	2.12880i
$67$		−	4.11631i		−	0.502887i	−0.967872	−	0.251443i	$-0.919095\pi$
$67$		−	4.11631i		−	0.502887i	0.967872	−	0.251443i	$-0.0809053\pi$
$68$	−0.780337	+	2.47427i	−0.0946297	+	0.300049i
$69$			14.2008i			1.70957i
$70$	2.36287	−	1.73239i	0.282417	−	0.207061i
$71$	−7.82788			−0.928999			−0.464499	−	0.885573i	$-0.653766\pi$
$71$	−7.82788			−0.928999			−0.464499	+	0.885573i	$0.653766\pi$
$72$	−18.3076	+	6.21230i	−2.15757	+	0.732126i
$73$	3.08931			0.361577			0.180788	−	0.983522i	$-0.442135\pi$
$73$	3.08931			0.361577			0.180788	+	0.983522i	$0.442135\pi$
$74$	−6.41714	+	4.70488i	−0.745978	+	0.546931i
$75$			14.5739i			1.68285i
$76$	−1.90739	−	0.601554i	−0.218793	−	0.0690030i
$77$		−	16.8631i		−	1.92172i
$78$	0.565381	+	0.771143i	0.0640168	+	0.0873147i
$79$	−10.0731			−1.13331			−0.566654	−	0.823956i	$-0.691763\pi$
$79$	−10.0731			−1.13331			−0.566654	+	0.823956i	$0.691763\pi$
$80$	−1.36320	+	1.94624i	−0.152411	+	0.217596i
$81$	17.2143			1.91270
$82$	0.376306	+	0.513256i	0.0415560	+	0.0566797i
$83$			11.6296i			1.27651i	0.769825	+	0.638255i	$0.220343\pi$
$83$			11.6296i			1.27651i	−0.769825	+	0.638255i	$0.779657\pi$
$84$	20.8619	+	6.57943i	2.27622	+	0.717875i
$85$		−	0.770591i		−	0.0835823i
$86$	−0.905979	+	0.664240i	−0.0976943	+	0.0716268i
$87$	−29.5137			−3.16420
$88$	4.39456	+	12.9507i	0.468462	+	1.38055i
$89$	13.7091			1.45317			0.726583	−	0.687079i	$-0.241107\pi$
$89$	13.7091			1.45317			0.726583	+	0.687079i	$0.241107\pi$
$90$	4.63094	−	3.39528i	0.488144	−	0.357894i
$91$		−	0.751907i		−	0.0788213i
$92$	−2.72392	+	8.63694i	−0.283989	+	0.900463i
$93$		−	3.82703i		−	0.396845i
$94$	−10.2004	−	13.9127i	−1.05209	−	1.43499i
$95$	0.594041			0.0609473
$96$	−17.7364	+	0.383702i	−1.81021	+	0.0391615i
$97$	2.08846			0.212051			0.106026	−	0.994363i	$-0.466187\pi$
$97$	2.08846			0.212051			0.106026	+	0.994363i	$0.466187\pi$
$98$	−4.31736	−	5.88860i	−0.436120	−	0.594839i
$99$		−	33.0495i		−	3.32160i
$100$	−2.79549	+	8.86386i	−0.279549	+	0.886386i
$101$		−	2.77074i		−	0.275699i	−0.990453	−	0.137849i	$-0.955981\pi$
$101$		−	2.77074i		−	0.275699i	0.990453	−	0.137849i	$-0.0440190\pi$
$102$	4.63981	−	3.40179i	0.459410	−	0.336827i
$103$	−14.3363			−1.41260			−0.706301	−	0.707912i	$-0.749637\pi$
$103$	−14.3363			−1.41260			−0.706301	+	0.707912i	$0.749637\pi$
$104$	0.195949	+	0.577459i	0.0192144	+	0.0566245i
$105$	−6.49726			−0.634067
$106$	−2.92439	+	2.14408i	−0.284042	+	0.208252i
$107$		−	2.42388i		−	0.234325i	−0.993113	−	0.117163i	$-0.962620\pi$
$107$		−	2.42388i		−	0.234325i	0.993113	−	0.117163i	$-0.0373799\pi$
$108$	22.9413	+	7.23525i	2.20753	+	0.696213i
$109$			0.00123810i			0.000118589i	1.00000		5.92945e-5i	$1.88740e-5\pi$
$109$			0.00123810i			0.000118589i	−1.00000		5.92945e-5i	$0.999981\pi$
$110$	−2.40181	−	3.27591i	−0.229003	−	0.312346i
$111$	17.6454			1.67483
$112$	11.4262	+	8.00324i	1.07967	+	0.756235i
$113$	1.81614			0.170848			0.0854242	−	0.996345i	$-0.472775\pi$
$113$	1.81614			0.170848			0.0854242	+	0.996345i	$0.472775\pi$
$114$	2.62240	+	3.57679i	0.245611	+	0.334997i
$115$		−	2.68990i		−	0.250835i
$116$	−17.9503	−	5.66118i	−1.66664	−	0.525627i
$117$		−	1.47365i		−	0.136239i
$118$	−3.13859	+	2.30113i	−0.288931	+	0.211836i
$119$	−4.52407			−0.414721
$120$	4.98985	−	1.69320i	0.455509	−	0.154568i
$121$	−12.3791			−1.12538
$122$	8.85798	−	6.49444i	0.801964	−	0.587979i
$123$		−	1.41132i		−	0.127254i
$124$	0.734083	−	2.32761i	0.0659226	−	0.209025i
$125$		−	5.73078i		−	0.512577i
$126$	−19.9334	−	27.1878i	−1.77581	−	2.42209i
$127$	−16.1269			−1.43103			−0.715517	−	0.698596i	$-0.753809\pi$
$127$	−16.1269			−1.43103			−0.715517	+	0.698596i	$0.753809\pi$
$128$	−10.8609	−	3.16874i	−0.959977	−	0.280079i
$129$	2.49120			0.219338
$130$	−0.107094	−	0.146070i	−0.00939279	−	0.0128111i
$131$			11.1477i			0.973983i	0.873407	+	0.486992i	$0.161906\pi$
$131$			11.1477i			0.973983i	−0.873407	+	0.486992i	$0.838094\pi$
$132$	9.12179	−	28.9231i	0.793950	−	2.51743i
$133$		−	3.48756i		−	0.302410i
$134$	−4.69471	+	3.44204i	−0.405562	+	0.297347i
$135$	−7.14489			−0.614934
$136$	3.47446	−	1.17899i	0.297932	−	0.101097i
$137$	11.1666			0.954025			0.477013	−	0.878896i	$-0.341720\pi$
$137$	11.1666			0.954025			0.477013	+	0.878896i	$0.341720\pi$
$138$	16.1962	−	11.8746i	1.37871	−	1.01084i
$139$			13.0534i			1.10718i	0.832790	+	0.553589i	$0.186742\pi$
$139$			13.0534i			1.10718i	−0.832790	+	0.553589i	$0.813258\pi$
$140$	−3.95164	−	1.24627i	−0.333975	−	0.105329i
$141$			38.2562i			3.22176i
$142$	6.54564	+	8.92783i	0.549298	+	0.749207i
$143$	−1.04245			−0.0871742
$144$	22.3939	+	15.6854i	1.86616	+	1.30711i
$145$	5.59048			0.464264
$146$	−2.58327	−	3.52341i	−0.213793	−	0.291600i
$147$			16.1921i			1.33550i
$148$	10.7320	+	3.38466i	0.882163	+	0.278217i
$149$		−	14.3811i		−	1.17814i	−0.808080	−	0.589072i	$-0.799493\pi$
$149$		−	14.3811i		−	1.17814i	0.808080	−	0.589072i	$-0.200507\pi$
$150$	16.6217	−	12.1866i	1.35716	−	0.995032i
$151$	17.3489			1.41184			0.705918	−	0.708293i	$-0.250535\pi$
$151$	17.3489			1.41184			0.705918	+	0.708293i	$0.250535\pi$
$152$	0.908869	+	2.67842i	0.0737190	+	0.217249i
$153$	−8.86663			−0.716825
$154$	−19.2326	+	14.1008i	−1.54981	+	1.13628i
$155$			0.724915i			0.0582266i
$156$	0.406732	−	1.28965i	0.0325646	−	0.103255i
$157$		−	9.63293i		−	0.768791i	−0.923168	−	0.384396i	$-0.874410\pi$
$157$		−	9.63293i		−	0.768791i	0.923168	−	0.384396i	$-0.125590\pi$
$158$	8.42306	+	11.4885i	0.670102	+	0.913976i
$159$	8.04128			0.637715
$160$	3.35962	−	0.0726808i	0.265601	−	0.00574592i
$161$	−15.7922			−1.24460
$162$	−14.3945	−	19.6332i	−1.13094	−	1.54253i
$163$		−	22.5365i		−	1.76520i	−0.470129	−	0.882598i	$-0.655793\pi$
$163$		−	22.5365i		−	1.76520i	0.470129	−	0.882598i	$-0.344207\pi$
$164$	0.270712	−	0.858365i	0.0211390	−	0.0670271i
$165$			9.00787i			0.701262i
$166$	13.2637	−	9.72458i	1.02946	−	0.754774i
$167$	16.5108			1.27765			0.638823	−	0.769353i	$-0.279421\pi$
$167$	16.5108			1.27765			0.638823	+	0.769353i	$0.279421\pi$
$168$	−9.94065	−	29.2950i	−0.766938	−	2.26016i
$169$	12.9535			0.996424
$170$	−0.878871	+	0.644365i	−0.0674064	+	0.0494205i
$171$		−	6.83520i		−	0.522701i
$172$	1.51515	+	0.477850i	0.115529	+	0.0364357i
$173$			5.14911i			0.391479i	0.980656	+	0.195740i	$0.0627108\pi$
$173$			5.14911i			0.391479i	−0.980656	+	0.195740i	$0.937289\pi$
$174$	24.6793	+	33.6609i	1.87093	+	2.55182i
$175$	−16.2071			−1.22514
$176$	11.0958	−	15.8414i	0.836376	−	1.19409i
$177$	8.63029			0.648692
$178$	−11.4635	−	15.6355i	−0.859227	−	1.17193i
$179$		−	9.31580i		−	0.696295i	−0.937440	−	0.348148i	$-0.886811\pi$
$179$		−	9.31580i		−	0.696295i	0.937440	−	0.348148i	$-0.113189\pi$
$180$	−7.74474	−	2.44254i	−0.577259	−	0.182056i
$181$			5.15517i			0.383180i	0.981475	+	0.191590i	$0.0613645\pi$
$181$			5.15517i			0.383180i	−0.981475	+	0.191590i	$0.938636\pi$
$182$	−0.857562	+	0.628741i	−0.0635667	+	0.0466054i
$183$	−24.3571			−1.80053
$184$	12.1283	−	4.11549i	0.894110	−	0.303398i
$185$	−3.34239			−0.245737
$186$	−4.36479	+	3.20015i	−0.320042	+	0.234646i
$187$			6.27223i			0.458671i
$188$	−7.33813	+	23.2675i	−0.535188	+	1.69696i
$189$			41.9471i			3.05120i
$190$	−0.496734	−	0.677513i	−0.0360369	−	0.0491520i
$191$	−14.8805			−1.07672			−0.538359	−	0.842715i	$-0.680956\pi$
$191$	−14.8805			−1.07672			−0.538359	+	0.842715i	$0.680956\pi$
$192$	15.2687	+	19.9078i	1.10192	+	1.43672i
$193$	−21.2754			−1.53144			−0.765719	−	0.643175i	$-0.777617\pi$
$193$	−21.2754			−1.53144			−0.765719	+	0.643175i	$0.777617\pi$
$194$	−1.74636	−	2.38193i	−0.125382	−	0.171012i
$195$			0.401652i			0.0287629i
$196$	−3.10588	+	9.84805i	−0.221849	+	0.703432i
$197$			3.69169i			0.263022i	0.991315	+	0.131511i	$0.0419829\pi$
$197$			3.69169i			0.263022i	−0.991315	+	0.131511i	$0.958017\pi$
$198$	−37.6935	+	27.6359i	−2.67876	+	1.96400i
$199$	11.6857			0.828377			0.414188	−	0.910191i	$-0.364065\pi$
$199$	11.6857			0.828377			0.414188	+	0.910191i	$0.364065\pi$
$200$	12.4469	−	4.22362i	0.880132	−	0.298655i
$201$	12.9092			0.910545
$202$	−3.16007	+	2.31688i	−0.222342	+	0.163015i
$203$		−	32.8212i		−	2.30360i
$204$	−7.75958	−	2.44722i	−0.543279	−	0.171340i
$205$			0.267331i			0.0186712i
$206$	11.9880	+	16.3508i	0.835243	+	1.13922i
$207$	−30.9508			−2.15123
$208$	0.494750	−	0.706352i	0.0343047	−	0.0489767i
$209$	−4.83520			−0.334458
$210$	5.43298	+	7.41023i	0.374911	+	0.511354i
$211$		−	7.61611i		−	0.524315i	−0.965025	−	0.262157i	$-0.915566\pi$
$211$		−	7.61611i		−	0.524315i	0.965025	−	0.262157i	$-0.0844340\pi$
$212$	4.89072	+	1.54244i	0.335896	+	0.105935i
$213$		−	24.5491i		−	1.68208i
$214$	−2.76447	+	2.02684i	−0.188976	+	0.138552i
$215$	−0.471882			−0.0321821
$216$	−10.9315	−	32.2150i	−0.743795	−	2.19196i
$217$	4.25591			0.288910
$218$	0.00141208	−	0.00103530i	9.56380e−5	−	7.01192e-5i
$219$			9.68844i			0.654684i
$220$	−1.72785	+	5.47860i	−0.116491	+	0.369367i
$221$			0.279672i			0.0188128i
$222$	−14.7550	−	20.1249i	−0.990292	−	1.35069i
$223$	−1.95477			−0.130901			−0.0654505	−	0.997856i	$-0.520848\pi$
$223$	−1.95477			−0.130901			−0.0654505	+	0.997856i	$0.520848\pi$
$224$	−0.426703	−	19.7240i	−0.0285103	−	1.31787i
$225$	−31.7640			−2.11760
$226$	−1.51865	−	2.07134i	−0.101019	−	0.137784i
$227$		−	13.3709i		−	0.887461i	−0.896160	−	0.443730i	$-0.853655\pi$
$227$		−	13.3709i		−	0.887461i	0.896160	−	0.443730i	$-0.146345\pi$
$228$	1.88654	−	5.98179i	0.124939	−	0.396153i
$229$			11.5800i			0.765225i	0.923909	+	0.382613i	$0.124976\pi$
$229$			11.5800i			0.765225i	−0.923909	+	0.382613i	$0.875024\pi$
$230$	−3.06788	+	2.24929i	−0.202290	+	0.148314i
$231$	52.8844			3.47954
$232$	8.55330	+	25.2065i	0.561552	+	1.65489i
$233$	1.58872			0.104080			0.0520401	−	0.998645i	$-0.483428\pi$
$233$	1.58872			0.104080			0.0520401	+	0.998645i	$0.483428\pi$
$234$	−1.68072	+	1.23226i	−0.109872	+	0.0805551i
$235$		−	7.24648i		−	0.472708i
$236$	5.24896	+	1.65542i	0.341678	+	0.107759i
$237$		−	31.5903i		−	2.05201i
$238$	3.78301	+	5.15978i	0.245216	+	0.334459i
$239$	23.8219			1.54091			0.770455	−	0.637494i	$-0.220029\pi$
$239$	23.8219			1.54091			0.770455	+	0.637494i	$0.220029\pi$
$240$	−6.10361	−	4.27515i	−0.393987	−	0.275960i
$241$	22.8554			1.47225			0.736123	−	0.676848i	$-0.236654\pi$
$241$	22.8554			1.47225			0.736123	+	0.676848i	$0.236654\pi$
$242$	10.3514	+	14.1186i	0.665412	+	0.907578i
$243$			17.9032i			1.14849i
$244$	−14.8140	−	4.67206i	−0.948370	−	0.299098i
$245$		−	3.06710i		−	0.195950i
$246$	−1.60963	+	1.18014i	−0.102626	+	0.0752428i
$247$	−0.215597			−0.0137181
$248$	−3.26851	+	1.10910i	−0.207551	+	0.0704281i
$249$	−36.4716			−2.31129
$250$	−6.53605	+	4.79205i	−0.413376	+	0.303076i
$251$		−	2.63524i		−	0.166335i	−0.996536	−	0.0831676i	$-0.973496\pi$
$251$		−	2.63524i		−	0.166335i	0.996536	−	0.0831676i	$-0.0265037\pi$
$252$	−14.3400	+	45.4687i	−0.903332	+	2.86426i
$253$			21.8945i			1.37649i
$254$	13.4853	+	18.3930i	0.846141	+	1.15408i
$255$	2.41666			0.151337
$256$	5.46784	+	15.0367i	0.341740	+	0.939795i
$257$	20.0579			1.25118			0.625588	−	0.780153i	$-0.284859\pi$
$257$	20.0579			1.25118			0.625588	+	0.780153i	$0.284859\pi$
$258$	−2.08313	−	2.84125i	−0.129690	−	0.176889i
$259$			19.6229i			1.21931i
$260$	−0.0770429	+	0.244285i	−0.00477800	+	0.0151499i
$261$		−	64.3256i		−	3.98165i
$262$	12.7142	−	9.32170i	0.785485	−	0.575896i
$263$	4.03667			0.248912			0.124456	−	0.992225i	$-0.460282\pi$
$263$	4.03667			0.248912			0.124456	+	0.992225i	$0.460282\pi$
$264$	−40.6149	+	13.7818i	−2.49967	+	0.848213i
$265$	−1.52318			−0.0935679
$266$	−3.97762	+	2.91629i	−0.243884	+	0.178809i
$267$			42.9934i			2.63115i
$268$	7.85140	+	2.47618i	0.479601	+	0.151257i
$269$			14.3095i			0.872467i	0.899834	+	0.436233i	$0.143688\pi$
$269$			14.3095i			0.872467i	−0.899834	+	0.436233i	$0.856312\pi$
$270$	5.97453	+	8.14886i	0.363598	+	0.495924i
$271$	9.85034			0.598366			0.299183	−	0.954196i	$-0.403286\pi$
$271$	9.85034			0.598366			0.299183	+	0.954196i	$0.403286\pi$
$272$	−4.24998	−	2.97681i	−0.257693	−	0.180496i
$273$	2.35806			0.142717
$274$	−9.33745	−	12.7357i	−0.564096	−	0.769390i
$275$			22.4697i			1.35498i
$276$	−27.0864	−	8.54253i	−1.63041	−	0.514200i
$277$			16.9641i			1.01928i	0.860389	+	0.509638i	$0.170221\pi$
$277$			16.9641i			1.01928i	−0.860389	+	0.509638i	$0.829779\pi$
$278$	14.8877	−	10.9152i	0.892902	−	0.654652i
$279$	8.34107			0.499367
$280$	1.88295	+	5.54904i	0.112528	+	0.331619i
$281$	−10.2078			−0.608944			−0.304472	−	0.952521i	$-0.598480\pi$
$281$	−10.2078			−0.608944			−0.304472	+	0.952521i	$0.598480\pi$
$282$	43.6318	−	31.9897i	2.59824	−	1.90496i
$283$			18.7709i			1.11581i	0.829903	+	0.557907i	$0.188396\pi$
$283$			18.7709i			1.11581i	−0.829903	+	0.557907i	$0.811604\pi$
$284$	4.70889	−	14.9308i	0.279421	−	0.885981i
$285$			1.86298i			0.110353i
$286$	0.871694	+	1.18893i	0.0515443	+	0.0703031i
$287$	1.56948			0.0926433
$288$	−0.836285	−	38.6567i	−0.0492785	−	2.27787i
$289$	−15.3173			−0.901016
$290$	−4.67473	−	6.37603i	−0.274510	−	0.374413i
$291$			6.54966i			0.383948i
$292$	−1.85839	+	5.89253i	−0.108754	+	0.344834i
$293$		−	19.8271i		−	1.15831i	−0.815217	−	0.579155i	$-0.803382\pi$
$293$		−	19.8271i		−	1.15831i	0.815217	−	0.579155i	$-0.196618\pi$
$294$	18.4673	−	13.5397i	1.07704	−	0.789654i
$295$	−1.63475			−0.0951786
$296$	−5.11377	−	15.0702i	−0.297232	−	0.875939i
$297$	58.1559			3.37454
$298$	−16.4019	+	12.0254i	−0.950134	+	0.696613i
$299$			0.976253i			0.0564582i
$300$	−27.7980	−	8.76697i	−1.60492	−	0.506161i
$301$			2.77038i			0.159682i
$302$	−14.5071	−	19.7867i	−0.834790	−	1.13860i
$303$	8.68935			0.499190
$304$	2.29479	−	3.27627i	0.131615	−	0.187907i
$305$	4.61371			0.264180
$306$	7.41424	+	10.1125i	0.423844	+	0.578095i
$307$		−	18.3935i		−	1.04977i	−0.851173	−	0.524886i	$-0.824108\pi$
$307$		−	18.3935i		−	1.04977i	0.851173	−	0.524886i	$-0.175892\pi$
$308$	32.1644	+	10.1440i	1.83274	+	0.578010i
$309$		−	44.9604i		−	2.55771i
$310$	0.826777	−	0.606171i	0.0469578	−	0.0344282i
$311$	19.1747			1.08730			0.543648	−	0.839313i	$-0.317043\pi$
$311$	19.1747			1.08730			0.543648	+	0.839313i	$0.317043\pi$
$312$	−1.81098	+	0.614518i	−0.102526	+	0.0347902i
$313$	14.2274			0.804183			0.402091	−	0.915600i	$-0.368283\pi$
$313$	14.2274			0.804183			0.402091	+	0.915600i	$0.368283\pi$
$314$	−10.9865	+	8.05501i	−0.620004	+	0.454571i
$315$		−	14.1609i		−	0.797874i
$316$	6.05949	−	19.2133i	0.340873	−	1.08083i
$317$			0.777938i			0.0436934i	0.999761	+	0.0218467i	$0.00695457\pi$
$317$			0.777938i			0.0436934i	−0.999761	+	0.0218467i	$0.993045\pi$
$318$	−6.72408	−	9.17121i	−0.377068	−	0.514296i
$319$	−45.5037			−2.54772
$320$	−2.89219	−	3.77092i	−0.161678	−	0.210801i
$321$	7.60156			0.424278
$322$	13.2054	+	18.0113i	0.735906	+	1.00373i
$323$			1.29720i			0.0721782i
$324$	−10.3553	+	32.8344i	−0.575297	+	1.82413i
$325$			1.00190i			0.0555755i
$326$	−25.7033	+	18.8449i	−1.42357	+	1.04372i
$327$	−0.00388283			−0.000214721
$328$	−1.20535	+	0.409010i	−0.0665542	+	0.0225838i
$329$	−42.5435			−2.34550
$330$	10.2736	−	7.53234i	0.565544	−	0.414642i
$331$		−	16.3988i		−	0.901359i	−0.892686	−	0.450680i	$-0.851182\pi$
$331$		−	16.3988i		−	0.901359i	0.892686	−	0.450680i	$-0.148818\pi$
$332$	−22.1821	−	6.99580i	−1.21740	−	0.383945i
$333$			38.4584i			2.10751i
$334$	−13.8063	−	18.8309i	−0.755446	−	1.03038i
$335$	−2.44525			−0.133599
$336$	−25.0991	+	35.8338i	−1.36927	+	1.95489i
$337$	24.6109			1.34064			0.670320	−	0.742072i	$-0.266157\pi$
$337$	24.6109			1.34064			0.670320	+	0.742072i	$0.266157\pi$
$338$	−10.8317	−	14.7737i	−0.589165	−	0.803583i
$339$			5.69563i			0.309344i
$340$	1.46982	+	0.463552i	0.0797120	+	0.0251396i
$341$		−	5.90045i		−	0.319527i
$342$	−7.79565	+	5.71556i	−0.421541	+	0.309062i
$343$	6.40629			0.345907
$344$	−0.721968	−	2.12763i	−0.0389259	−	0.114714i
$345$	8.43584			0.454170
$346$	5.87264	−	4.30566i	0.315715	−	0.231474i
$347$			13.4635i			0.722760i	0.932419	+	0.361380i	$0.117694\pi$
$347$			13.4635i			0.722760i	−0.932419	+	0.361380i	$0.882306\pi$
$348$	17.7541	−	56.2942i	0.951719	−	3.01768i
$349$		−	2.83422i		−	0.151712i	−0.997119	−	0.0758560i	$-0.975831\pi$
$349$		−	2.83422i		−	0.151712i	0.997119	−	0.0758560i	$-0.0241689\pi$
$350$	13.5523	+	18.4845i	0.724402	+	0.988037i
$351$	2.59311			0.138410
$352$	−27.3456	+	0.591585i	−1.45753	+	0.0315316i
$353$	−5.02227			−0.267308			−0.133654	−	0.991028i	$-0.542671\pi$
$353$	−5.02227			−0.267308			−0.133654	+	0.991028i	$0.542671\pi$
$354$	−7.21661	−	9.84298i	−0.383558	−	0.523149i
$355$			4.65008i			0.246801i
$356$	−8.24678	+	26.1487i	−0.437079	+	1.38588i
$357$		−	14.1880i		−	0.750909i
$358$	−10.6248	+	7.78983i	−0.561539	+	0.411705i
$359$	23.6898			1.25030			0.625149	−	0.780505i	$-0.285038\pi$
$359$	23.6898			1.25030			0.625149	+	0.780505i	$0.285038\pi$
$360$	3.69036	+	10.8754i	0.194499	+	0.573186i
$361$	−1.00000			−0.0526316
$362$	5.87955	−	4.31073i	0.309022	−	0.226567i
$363$		−	38.8223i		−	2.03764i
$364$	1.43418	+	0.452312i	0.0751714	+	0.0237076i
$365$		−	1.83518i		−	0.0960577i
$366$	20.3673	+	27.7796i	1.06461	+	1.45206i
$367$	−16.9338			−0.883938			−0.441969	−	0.897030i	$-0.645720\pi$
$367$	−16.9338			−0.883938			−0.441969	+	0.897030i	$0.645720\pi$
$368$	−14.8354	−	10.3912i	−0.773349	−	0.541677i
$369$	3.07598			0.160129
$370$	2.79489	+	3.81205i	0.145299	+	0.198179i
$371$			8.94244i			0.464268i
$372$	7.29964	+	2.30217i	0.378469	+	0.119362i
$373$			12.8599i			0.665860i	0.942952	+	0.332930i	$0.108037\pi$
$373$			12.8599i			0.665860i	−0.942952	+	0.332930i	$0.891963\pi$
$374$	7.15357	−	5.24481i	0.369903	−	0.271203i
$375$	17.9724			0.928089
$376$	32.6731	−	11.0869i	1.68499	−	0.571765i
$377$	−2.02896			−0.104497
$378$	47.8413	−	35.0759i	2.46069	−	1.80411i
$379$		−	20.7810i		−	1.06745i	−0.845659	−	0.533723i	$-0.820793\pi$
$379$		−	20.7810i		−	1.06745i	0.845659	−	0.533723i	$-0.179207\pi$
$380$	−0.357348	+	1.13307i	−0.0183315	+	0.0581251i
$381$		−	50.5758i		−	2.59108i
$382$	12.4430	+	16.9715i	0.636642	+	0.868338i
$383$	−15.6170			−0.797993			−0.398996	−	0.916953i	$-0.630641\pi$
$383$	−15.6170			−0.797993			−0.398996	+	0.916953i	$0.630641\pi$
$384$	9.93751	−	34.0610i	0.507122	−	1.73817i
$385$	−10.0173			−0.510531
$386$	17.7904	+	24.2650i	0.905508	+	1.23505i
$387$			5.42960i			0.276002i
$388$	−1.25632	+	3.98351i	−0.0637801	+	0.202232i
$389$			10.1133i			0.512764i	0.966576	+	0.256382i	$0.0825304\pi$
$389$			10.1133i			0.512764i	−0.966576	+	0.256382i	$0.917470\pi$
$390$	0.458090	−	0.335860i	0.0231963	−	0.0170069i
$391$	5.87392			0.297057
$392$	13.8290	−	4.69258i	0.698469	−	0.237011i
$393$	−34.9606			−1.76353
$394$	4.21043	−	3.08698i	0.212119	−	0.155520i
$395$			5.98381i			0.301078i
$396$	63.0383	+	19.8811i	3.16779	+	0.999061i
$397$			4.60677i			0.231207i	0.993295	+	0.115604i	$0.0368802\pi$
$397$			4.60677i			0.231207i	−0.993295	+	0.115604i	$0.963120\pi$
$398$	−9.77153	−	13.3277i	−0.489802	−	0.668058i
$399$	10.9374			0.547554
$400$	−15.2252	−	10.6642i	−0.761259	−	0.533209i
$401$	−4.00112			−0.199806			−0.0999032	−	0.994997i	$-0.531853\pi$
$401$	−4.00112			−0.199806			−0.0999032	+	0.994997i	$0.531853\pi$
$402$	−10.7946	−	14.7231i	−0.538386	−	0.734324i
$403$		−	0.263095i		−	0.0131057i
$404$	5.28488	+	1.66675i	0.262933	+	0.0829239i
$405$		−	10.2260i		−	0.508135i
$406$	−37.4331	+	27.4450i	−1.85778	+	1.36207i
$407$	27.2054			1.34852
$408$	3.69743	+	10.8963i	0.183050	+	0.539446i
$409$	−14.5111			−0.717529			−0.358765	−	0.933428i	$-0.616802\pi$
$409$	−14.5111			−0.717529			−0.358765	+	0.933428i	$0.616802\pi$
$410$	0.304895	−	0.223541i	0.0150577	−	0.0110399i
$411$			35.0196i			1.72739i
$412$	8.62408	−	27.3450i	0.424878	−	1.34719i
$413$			9.59745i			0.472260i
$414$	25.8809	+	35.2999i	1.27198	+	1.73489i
$415$	6.90843			0.339122
$416$	−1.21931	+	0.0263782i	−0.0597817	+	0.00129330i
$417$	−40.9370			−2.00470
$418$	4.04317	+	5.51462i	0.197758	+	0.269729i
$419$		−	5.02078i		−	0.245281i	−0.992451	−	0.122641i	$-0.960864\pi$
$419$		−	5.02078i		−	0.245281i	0.992451	−	0.122641i	$-0.0391362\pi$
$420$	3.90845	−	12.3928i	0.190713	−	0.604707i
$421$			4.10152i			0.199896i	0.994993	+	0.0999479i	$0.0318676\pi$
$421$			4.10152i			0.199896i	−0.994993	+	0.0999479i	$0.968132\pi$
$422$	−8.68630	+	6.36856i	−0.422842	+	0.310017i
$423$	−83.3800			−4.05407
$424$	−2.33042	−	6.86773i	−0.113175	−	0.333526i
$425$	6.02825			0.292413
$426$	−27.9987	+	20.5279i	−1.35654	+	0.994578i
$427$		−	27.0867i		−	1.31082i
$428$	4.62328	+	1.45809i	0.223475	+	0.0704797i
$429$		−	3.26925i		−	0.157841i
$430$	0.394585	+	0.538189i	0.0190286	+	0.0259538i
$431$	−16.2920			−0.784760			−0.392380	−	0.919803i	$-0.628348\pi$
$431$	−16.2920			−0.784760			−0.392380	+	0.919803i	$0.628348\pi$
$432$	−27.6009	+	39.4056i	−1.32795	+	1.89590i
$433$	7.44858			0.357956			0.178978	−	0.983853i	$-0.442721\pi$
$433$	7.44858			0.357956			0.178978	+	0.983853i	$0.442721\pi$
$434$	−3.55878	−	4.85394i	−0.170827	−	0.232997i
$435$			17.5324i			0.840612i
$436$	−0.00236155		0.000744786i	−0.000113098		3.56688e-5i
$437$			4.52815i			0.216611i
$438$	11.0498	−	8.10143i	0.527981	−	0.387101i
$439$	15.8898			0.758379			0.379189	−	0.925319i	$-0.376203\pi$
$439$	15.8898			0.758379			0.379189	+	0.925319i	$0.376203\pi$
$440$	7.69325	−	2.61055i	0.366761	−	0.124453i
$441$	−35.2908			−1.68052
$442$	0.318971	−	0.233861i	0.0151719	−	0.0111236i
$443$			15.1742i			0.720949i	0.932769	+	0.360474i	$0.117385\pi$
$443$			15.1742i			0.720949i	−0.932769	+	0.360474i	$0.882615\pi$
$444$	−10.6147	+	33.6567i	−0.503750	+	1.59728i
$445$		−	8.14379i		−	0.386053i
$446$	1.63457	+	2.22945i	0.0773991	+	0.105567i
$447$	45.1007			2.13319
$448$	−22.1388	+	16.9798i	−1.04596	+	0.802220i
$449$	−24.3909			−1.15108			−0.575538	−	0.817775i	$-0.695207\pi$
$449$	−24.3909			−1.15108			−0.575538	+	0.817775i	$0.695207\pi$
$450$	26.5609	+	36.2273i	1.25209	+	1.70777i
$451$		−	2.17594i		−	0.102461i
$452$	−1.09251	+	3.46409i	−0.0513872	+	0.162937i
$453$			54.4082i			2.55632i
$454$	−15.2498	+	11.1807i	−0.715708	+	0.524738i
$455$	−0.446664			−0.0209399
$456$	−8.39984	+	2.85031i	−0.393358	+	0.133478i
$457$	−10.6860			−0.499869			−0.249934	−	0.968263i	$-0.580409\pi$
$457$	−10.6860			−0.499869			−0.249934	+	0.968263i	$0.580409\pi$
$458$	13.2071	−	9.68311i	0.617129	−	0.452462i
$459$		−	15.6022i		−	0.728250i
$460$	5.13069	+	1.61812i	0.239220	+	0.0754453i
$461$			21.8232i			1.01641i	0.861236	+	0.508205i	$0.169691\pi$
$461$			21.8232i			1.01641i	−0.861236	+	0.508205i	$0.830309\pi$
$462$	−44.2217	−	60.3156i	−2.05738	−	2.80613i
$463$	0.0258442			0.00120108			0.000600541	−	1.00000i	$-0.499809\pi$
$463$	0.0258442			0.00120108			0.000600541		1.00000i	$0.499809\pi$
$464$	21.5961	−	30.8327i	1.00258	−	1.43137i
$465$	−2.27341			−0.105427
$466$	−1.32848	−	1.81196i	−0.0615405	−	0.0839372i
$467$			4.66985i			0.216095i	0.994146	+	0.108047i	$0.0344598\pi$
$467$			4.66985i			0.216095i	−0.994146	+	0.108047i	$0.965540\pi$
$468$	2.81081	+	0.886477i	0.129930	+	0.0409774i
$469$			14.3559i			0.662893i
$470$	−8.26473	+	6.05947i	−0.381223	+	0.279503i
$471$	30.2099			1.39200
$472$	−2.50112	−	7.37078i	−0.115123	−	0.339267i
$473$	3.84088			0.176604
$474$	−36.0292	+	26.4156i	−1.65488	+	1.21331i
$475$			4.64712i			0.213224i
$476$	2.72147	−	8.62917i	0.124739	−	0.395517i
$477$			17.5261i			0.802464i
$478$	−19.9198	−	27.1692i	−0.911109	−	1.24269i
$479$	−30.5428			−1.39554			−0.697768	−	0.716324i	$-0.745823\pi$
$479$	−30.5428			−1.39554			−0.697768	+	0.716324i	$0.745823\pi$
$480$	0.227935	+	10.5361i	0.0104038	+	0.480907i
$481$	1.21306			0.0553108
$482$	−19.1116	−	26.0670i	−0.870509	−	1.18732i
$483$		−	49.5261i		−	2.25352i
$484$	7.44671	−	23.6118i	0.338487	−	1.07326i
$485$		−	1.24063i		−	0.0563342i
$486$	20.4189	−	14.9706i	0.926222	−	0.679081i
$487$	−2.37133			−0.107455			−0.0537277	−	0.998556i	$-0.517110\pi$
$487$	−2.37133			−0.107455			−0.0537277	+	0.998556i	$0.517110\pi$
$488$	7.05886	+	20.8024i	0.319540	+	0.941679i
$489$	70.6770			3.19613
$490$	−3.49807	+	2.56469i	−0.158027	+	0.115861i
$491$		−	41.3206i		−	1.86477i	−0.361466	−	0.932385i	$-0.617724\pi$
$491$		−	41.3206i		−	1.86477i	0.361466	−	0.932385i	$-0.382276\pi$
$492$	2.69193	+	0.848983i	0.121362	+	0.0382751i
$493$			12.2079i			0.549815i
$494$	0.180281	+	0.245891i	0.00811122	+	0.0110632i
$495$	−19.6328			−0.882427
$496$	3.99807	+	2.80036i	0.179518	+	0.125740i
$497$	27.3002			1.22458
$498$	30.4974	+	41.5964i	1.36662	+	1.86398i
$499$			15.8610i			0.710035i	0.934860	+	0.355018i	$0.115525\pi$
$499$			15.8610i			0.710035i	−0.934860	+	0.355018i	$0.884475\pi$
$500$	10.9308	+	3.44737i	0.488842	+	0.154171i
$501$			51.7798i			2.31335i
$502$	−3.00554	+	2.20358i	−0.134144	+	0.0983506i
$503$	−18.6879			−0.833254			−0.416627	−	0.909078i	$-0.636788\pi$
$503$	−18.6879			−0.833254			−0.416627	+	0.909078i	$0.636788\pi$
$504$	63.8488	−	21.6658i	2.84405	−	0.965071i
$505$	−1.64593			−0.0732431
$506$	24.9710	−	18.3081i	1.11010	−	0.813893i
$507$			40.6237i			1.80416i
$508$	9.70121	−	30.7603i	0.430422	−	1.36477i
$509$			33.2172i			1.47233i	0.676804	+	0.736163i	$0.263364\pi$
$509$			33.2172i			1.47233i	−0.676804	+	0.736163i	$0.736636\pi$
$510$	−2.02080	−	2.75624i	−0.0894825	−	0.122048i
$511$	−10.7742			−0.476622
$512$	12.5774	−	18.8098i	0.555849	−	0.831283i
$513$	12.0276			0.531032
$514$	−16.7723	−	22.8763i	−0.739795	−	1.00903i
$515$			8.51637i			0.375276i
$516$	−1.49859	+	4.75169i	−0.0659717	+	0.209181i
$517$			58.9827i			2.59406i
$518$	22.3802	−	16.4086i	0.983330	−	0.720951i
$519$	−16.1482			−0.708826
$520$	0.343034	−	0.116402i	0.0150431	−	0.00510455i
$521$	−10.9831			−0.481178			−0.240589	−	0.970627i	$-0.577341\pi$
$521$	−10.9831			−0.481178			−0.240589	+	0.970627i	$0.577341\pi$
$522$	−73.3643	+	53.7888i	−3.21107	+	2.35427i
$523$		−	8.00433i		−	0.350005i	−0.984568	−	0.175002i	$-0.944007\pi$
$523$		−	8.00433i		−	0.350005i	0.984568	−	0.175002i	$-0.0559933\pi$
$524$	−21.2631	−	6.70597i	−0.928882	−	0.292952i
$525$		−	50.8273i		−	2.21829i
$526$	−3.37544	−	4.60388i	−0.147176	−	0.200739i
$527$	−1.58299			−0.0689561
$528$	49.6804	+	34.7976i	2.16206	+	1.51437i
$529$	−2.49589			−0.108517
$530$	1.27367	+	1.73721i	0.0553248	+	0.0754594i
$531$			18.8098i			0.816277i
$532$	6.65214	+	2.09796i	0.288407	+	0.0909580i
$533$		−	0.0970230i		−	0.00420253i
$534$	49.0346	−	35.9509i	2.12194	−	1.55575i
$535$	−1.43988			−0.0622516
$536$	−3.74118	−	11.0252i	−0.161594	−	0.476217i
$537$	29.2154			1.26074
$538$	16.3202	−	11.9656i	0.703615	−	0.515872i
$539$			24.9646i			1.07530i
$540$	4.29804	−	13.6281i	0.184958	−	0.586460i
$541$		−	24.4359i		−	1.05058i	−0.850923	−	0.525291i	$-0.823956\pi$
$541$		−	24.4359i		−	1.05058i	0.850923	−	0.525291i	$-0.176044\pi$
$542$	−8.23681	−	11.2345i	−0.353801	−	0.482562i
$543$	−16.1672			−0.693800
$544$	0.158712	+	7.33636i	0.00680473	+	0.314544i
$545$	0.000735485	0		3.15047e−5	0
$546$	−1.97180	−	2.68941i	−0.0843854	−	0.115096i
$547$			5.25284i			0.224595i	0.993675	+	0.112298i	$0.0358210\pi$
$547$			5.25284i			0.224595i	−0.993675	+	0.112298i	$0.964179\pi$
$548$	−6.71730	+	21.2990i	−0.286949	+	0.909849i
$549$		−	53.0866i		−	2.26568i
$550$	25.6271	−	18.7891i	1.09274	−	0.801169i
$551$	−9.41093			−0.400919
$552$	12.9066	+	38.0357i	0.549343	+	1.61891i
$553$	35.1305			1.49390
$554$	19.3479	−	14.1853i	0.822012	−	0.602677i
$555$		−	10.4821i		−	0.444940i
$556$	−24.8980	−	7.85234i	−1.05591	−	0.333014i
$557$		−	3.56791i		−	0.151177i	−0.997139	−	0.0755886i	$-0.975916\pi$
$557$		−	3.56791i		−	0.151177i	0.997139	−	0.0755886i	$-0.0240836\pi$
$558$	−6.97477	−	9.51312i	−0.295265	−	0.402723i
$559$	0.171261			0.00724357
$560$	4.75425	−	6.78762i	0.200904	−	0.286829i
$561$	−19.6704			−0.830485
$562$	8.53568	+	11.6421i	0.360056	+	0.491093i
$563$			17.0555i			0.718805i	0.933183	+	0.359403i	$0.117020\pi$
$563$			17.0555i			0.718805i	−0.933183	+	0.359403i	$0.882980\pi$
$564$	−72.9695	−	23.0132i	−3.07257	−	0.969030i
$565$		−	1.07886i		−	0.0453881i
$566$	21.4085	−	15.6961i	0.899867	−	0.659758i
$567$	−60.0361			−2.52128
$568$	−20.9664	+	7.11452i	−0.879731	+	0.298519i
$569$	−0.858816			−0.0360034			−0.0180017	−	0.999838i	$-0.505730\pi$
$569$	−0.858816			−0.0360034			−0.0180017	+	0.999838i	$0.505730\pi$
$570$	2.12476	−	1.55781i	0.0889963	−	0.0652497i
$571$		−	40.5440i		−	1.69671i	−0.529426	−	0.848356i	$-0.677593\pi$
$571$		−	40.5440i		−	1.69671i	0.529426	−	0.848356i	$-0.322407\pi$
$572$	0.627091	−	1.98836i	0.0262200	−	0.0831376i
$573$		−	46.6671i		−	1.94954i
$574$	−1.31239	−	1.79001i	−0.0547781	−	0.0747138i
$575$	21.0428			0.877546
$576$	−43.3893	+	33.2783i	−1.80789	+	1.38660i
$577$	36.5405			1.52120			0.760600	−	0.649220i	$-0.224905\pi$
$577$	36.5405			1.52120			0.760600	+	0.649220i	$0.224905\pi$
$578$	12.8082	+	17.4696i	0.532752	+	0.726639i
$579$		−	66.7221i		−	2.77288i
$580$	−3.36297	+	10.6632i	−0.139640	+	0.442766i
$581$		−	40.5588i		−	1.68266i
$582$	7.46999	−	5.47679i	0.309641	−	0.227020i
$583$	12.3979			0.513468
$584$	8.27450	−	2.80778i	0.342401	−	0.116187i
$585$	−0.875406			−0.0361936
$586$	−22.6131	+	16.5793i	−0.934139	+	0.684885i
$587$		−	30.4022i		−	1.25483i	−0.778684	−	0.627416i	$-0.784113\pi$
$587$		−	30.4022i		−	1.25483i	0.778684	−	0.627416i	$-0.215887\pi$
$588$	−30.8846	−	9.74040i	−1.27366	−	0.401687i
$589$		−	1.22031i		−	0.0502821i
$590$	1.36697	+	1.86445i	0.0562771	+	0.0767583i
$591$	−11.5776			−0.476237
$592$	−12.9117	+	18.4340i	−0.530668	+	0.757633i
$593$	−16.3814			−0.672703			−0.336351	−	0.941737i	$-0.609193\pi$
$593$	−16.3814			−0.672703			−0.336351	+	0.941737i	$0.609193\pi$
$594$	−48.6297	−	66.3277i	−1.99530	−	2.72146i
$595$			2.68749i			0.110176i
$596$	27.4303	+	8.65100i	1.12359	+	0.354359i
$597$			36.6476i			1.49989i
$598$	1.11343	−	0.816338i	0.0455316	−	0.0333826i
$599$	−2.24749			−0.0918298			−0.0459149	−	0.998945i	$-0.514620\pi$
$599$	−2.24749			−0.0918298			−0.0459149	+	0.998945i	$0.514620\pi$
$600$	13.2457	+	39.0350i	0.540755	+	1.59360i
$601$	−33.1805			−1.35346			−0.676730	−	0.736231i	$-0.736604\pi$
$601$	−33.1805			−1.35346			−0.676730	+	0.736231i	$0.736604\pi$
$602$	3.15966	−	2.31658i	0.128778	−	0.0944167i
$603$			28.1358i			1.14578i
$604$	−10.4363	+	33.0912i	−0.424648	+	1.34646i
$605$			7.35371i			0.298971i
$606$	−7.26600	−	9.91035i	−0.295161	−	0.402580i
$607$	35.7847			1.45246			0.726228	−	0.687454i	$-0.241272\pi$
$607$	35.7847			1.45246			0.726228	+	0.687454i	$0.241272\pi$
$608$	−5.65553	+	0.122350i	−0.229362	+	0.00496194i
$609$	102.931			4.17098
$610$	−3.85796	−	5.26201i	−0.156204	−	0.213052i
$611$			2.62998i			0.106398i
$612$	5.33375	−	16.9121i	0.215604	−	0.683632i
$613$		−	42.2856i		−	1.70790i	−0.520355	−	0.853950i	$-0.674200\pi$
$613$		−	42.2856i		−	1.70790i	0.520355	−	0.853950i	$-0.325800\pi$
$614$	−20.9781	+	15.3806i	−0.846606	+	0.620709i
$615$	−0.838380			−0.0338067
$616$	−15.3263	−	45.1664i	−0.617515	−	1.81981i
$617$	−26.2079			−1.05509			−0.527545	−	0.849527i	$-0.676887\pi$
$617$	−26.2079			−1.05509			−0.527545	+	0.849527i	$0.676887\pi$
$618$	−51.2780	+	37.5957i	−2.06270	+	1.51232i
$619$			40.7494i			1.63786i	0.573896	+	0.818929i	$0.305432\pi$
$619$			40.7494i			1.63786i	−0.573896	+	0.818929i	$0.694568\pi$
$620$	−1.38269	−	0.436075i	−0.0555304	−	0.0175132i
$621$		−	54.4628i		−	2.18552i
$622$	−16.0338	−	21.8690i	−0.642896	−	0.876868i
$623$	−47.8115			−1.91553
$624$	2.21520	+	1.55159i	0.0886789	+	0.0621133i
$625$	19.8313			0.793250
$626$	−11.8969	−	16.2266i	−0.475497	−	0.648546i
$627$		−	15.1637i		−	0.605581i
$628$	18.3737	+	5.79472i	0.733192	+	0.231235i
$629$		−	7.29874i		−	0.291020i
$630$	−16.1507	+	11.8412i	−0.643459	+	0.471767i
$631$	42.3804			1.68714			0.843569	−	0.537021i	$-0.180450\pi$
$631$	42.3804			1.68714			0.843569	+	0.537021i	$0.180450\pi$
$632$	−26.9800	+	9.15510i	−1.07320	+	0.364170i
$633$	23.8850			0.949343
$634$	0.887251	−	0.650509i	0.0352372	−	0.0258350i
$635$			9.58005i			0.380173i
$636$	−4.83726	+	15.3378i	−0.191810	+	0.608185i
$637$			1.11315i			0.0441045i
$638$	38.0500	+	51.8977i	1.50641	+	2.05465i
$639$	53.5051			2.11663
$640$	−1.88236	+	6.45182i	−0.0744068	+	0.255030i
$641$	−40.0356			−1.58131			−0.790656	−	0.612261i	$-0.790260\pi$
$641$	−40.0356			−1.58131			−0.790656	+	0.612261i	$0.790260\pi$
$642$	−6.35639	−	8.66970i	−0.250867	−	0.342166i
$643$			2.25369i			0.0888767i	0.999012	+	0.0444384i	$0.0141498\pi$
$643$			2.25369i			0.0888767i	−0.999012	+	0.0444384i	$0.985850\pi$
$644$	9.49986	−	30.1219i	0.374347	−	1.18697i
$645$		−	1.47987i		−	0.0582700i
$646$	1.47948	−	1.08471i	0.0582093	−	0.0426775i
$647$	−6.89272			−0.270981			−0.135490	−	0.990779i	$-0.543261\pi$
$647$	−6.89272			−0.270981			−0.135490	+	0.990779i	$0.543261\pi$
$648$	46.1073	−	15.6456i	1.81127	−	0.614616i
$649$	13.3060			0.522307
$650$	1.14269	−	0.837786i	0.0448198	−	0.0328607i
$651$			13.3470i			0.523111i
$652$	42.9859	+	13.5569i	1.68346	+	0.530930i
$653$		−	5.75398i		−	0.225170i	−0.993642	−	0.112585i	$-0.964087\pi$
$653$		−	5.75398i		−	0.225170i	0.993642	−	0.112585i	$-0.0359131\pi$
$654$	0.00324681	+	0.00442843i	0.000126960	+	0.000173165i
$655$	6.62222			0.258751
$656$	1.47439	+	1.03271i	0.0575652	+	0.0403204i
$657$	−21.1161			−0.823817
$658$	35.5747	+	48.5215i	1.38684	+	1.89157i
$659$		−	34.1024i		−	1.32844i	−0.747537	−	0.664220i	$-0.768764\pi$
$659$		−	34.1024i		−	1.32844i	0.747537	−	0.664220i	$-0.231236\pi$
$660$	−17.1815	−	5.41872i	−0.668789	−	0.210923i
$661$		−	46.3767i		−	1.80384i	−0.431900	−	0.901922i	$-0.642157\pi$
$661$		−	46.3767i		−	1.80384i	0.431900	−	0.901922i	$-0.357843\pi$
$662$	−18.7031	+	13.7126i	−0.726916	+	0.532955i
$663$	−0.877084			−0.0340631
$664$	10.5697	+	31.1489i	0.410185	+	1.20881i
$665$	−2.07176			−0.0803392
$666$	43.8624	−	32.1588i	1.69964	−	1.24613i
$667$			42.6141i			1.65002i
$668$	−9.93215	+	31.4926i	−0.384287	+	1.21848i
$669$		−	6.13038i		−	0.237014i
$670$	2.04471	+	2.78885i	0.0789941	+	0.107743i
$671$	−37.5533			−1.44973
$672$	61.8568	−	1.33819i	2.38618	−	0.0516217i
$673$	−29.1579			−1.12395			−0.561977	−	0.827153i	$-0.689959\pi$
$673$	−29.1579			−1.12395			−0.561977	+	0.827153i	$0.689959\pi$
$674$	−20.5795	−	28.0691i	−0.792693	−	1.08118i
$675$		−	55.8937i		−	2.15135i
$676$	−7.79224	+	24.7074i	−0.299701	+	0.950285i
$677$			10.0436i			0.386006i	0.981198	+	0.193003i	$0.0618228\pi$
$677$			10.0436i			0.386006i	−0.981198	+	0.193003i	$0.938177\pi$
$678$	6.49595	−	4.76266i	0.249476	−	0.182909i
$679$	−7.28365			−0.279521
$680$	−0.700366	−	2.06397i	−0.0268578	−	0.0791496i
$681$	41.9328			1.60687
$682$	−6.72955	+	4.93393i	−0.257688	+	0.188930i
$683$			25.5866i			0.979042i	0.871991	+	0.489521i	$0.162828\pi$
$683$			25.5866i			0.979042i	−0.871991	+	0.489521i	$0.837172\pi$
$684$	13.0374	+	4.11174i	0.498497	+	0.157216i
$685$		−	6.63341i		−	0.253449i
$686$	−5.35691	−	7.30648i	−0.204528	−	0.278963i
$687$	−36.3161			−1.38554
$688$	−1.82289	+	2.60253i	−0.0694970	+	0.0992206i
$689$	0.552809			0.0210604
$690$	−7.05401	−	9.62121i	−0.268542	−	0.366273i
$691$		−	42.2386i		−	1.60683i	−0.595417	−	0.803417i	$-0.703013\pi$
$691$		−	42.2386i		−	1.60683i	0.595417	−	0.803417i	$-0.296987\pi$
$692$	−9.82135	−	3.09746i	−0.373352	−	0.117748i
$693$			115.262i			4.37845i
$694$	15.3554	−	11.2581i	0.582882	−	0.427353i
$695$	7.75428			0.294136
$696$	−79.0503	+	26.8241i	−2.99639	+	1.01676i
$697$	−0.583768			−0.0221118
$698$	−3.23247	+	2.36996i	−0.122351	+	0.0897043i
$699$			4.98239i			0.188451i
$700$	9.74945	−	30.9133i	0.368495	−	1.16841i
$701$			43.9811i			1.66114i	0.556911	+	0.830572i	$0.311986\pi$
$701$			43.9811i			1.66114i	−0.556911	+	0.830572i	$0.688014\pi$
$702$	−2.16835	−	2.95748i	−0.0818390	−	0.111623i
$703$	5.62653			0.212208
$704$	23.5410	+	30.6934i	0.887234	+	1.15680i
$705$	22.7258			0.855902
$706$	4.19960	+	5.72798i	0.158054	+	0.215575i
$707$			9.66314i			0.363420i
$708$	−5.19158	+	16.4613i	−0.195112	+	0.618654i
$709$			11.1307i			0.418023i	0.977913	+	0.209012i	$0.0670246\pi$
$709$			11.1307i			0.418023i	−0.977913	+	0.209012i	$0.932975\pi$
$710$	5.30350	−	3.88838i	0.199037	−	0.145928i
$711$	68.8514			2.58213
$712$	36.7189	−	12.4598i	1.37610	−	0.466951i
$713$	−5.52575			−0.206941
$714$	−16.1816	+	11.8639i	−0.605583	+	0.443997i
$715$			0.619259i			0.0231590i
$716$	17.7688	+	5.60395i	0.664053	+	0.209430i
$717$			74.7081i			2.79003i
$718$	−19.8093	−	27.0186i	−0.739276	−	1.00832i
$719$	17.8961			0.667413			0.333706	−	0.942677i	$-0.391701\pi$
$719$	17.8961			0.667413			0.333706	+	0.942677i	$0.391701\pi$
$720$	9.31775	−	13.3029i	0.347252	−	0.495770i
$721$	49.9989			1.86206
$722$	0.836196	+	1.14052i	0.0311200	+	0.0424456i
$723$			71.6771i			2.66570i
$724$	−9.83291	−	3.10111i	−0.365437	−	0.115252i
$725$			43.7337i			1.62423i
$726$	−44.2775	+	32.4631i	−1.64329	+	1.20482i
$727$	−35.8772			−1.33061			−0.665306	−	0.746571i	$-0.731699\pi$
$727$	−35.8772			−1.33061			−0.665306	+	0.746571i	$0.731699\pi$
$728$	−0.683385	−	2.01393i	−0.0253279	−	0.0746411i
$729$	−4.50357			−0.166799
$730$	−2.09305	+	1.53457i	−0.0774673	+	0.0567970i
$731$		−	1.03044i		−	0.0381123i
$732$	14.6521	−	46.4584i	0.541557	−	1.71715i
$733$		−	24.4618i		−	0.903516i	−0.892141	−	0.451758i	$-0.850797\pi$
$733$		−	24.4618i		−	0.903516i	0.892141	−	0.451758i	$-0.149203\pi$
$734$	14.1600	+	19.3133i	0.522655	+	0.712867i
$735$	9.61875			0.354793
$736$	0.554018	+	25.6091i	0.0204214	+	0.943963i
$737$	19.9032			0.733142
$738$	−2.57212	−	3.50821i	−0.0946812	−	0.129139i
$739$		−	26.7820i		−	0.985193i	−0.870258	−	0.492596i	$-0.836048\pi$
$739$		−	26.7820i		−	0.985193i	0.870258	−	0.492596i	$-0.163952\pi$
$740$	2.01063	−	6.37523i	0.0739121	−	0.234358i
$741$		−	0.676135i		−	0.0248384i
$742$	10.1990	−	7.47763i	0.374417	−	0.274512i
$743$	23.7835			0.872534			0.436267	−	0.899817i	$-0.356300\pi$
$743$	23.7835			0.872534			0.436267	+	0.899817i	$0.356300\pi$
$744$	−3.47827	−	10.2504i	−0.127520	−	0.375799i
$745$	−8.54295			−0.312990
$746$	14.6669	−	10.7534i	0.536994	−	0.393710i
$747$		−	79.4903i		−	2.90840i
$748$	−11.9636	−	3.77308i	−0.437432	−	0.137958i
$749$			8.45344i			0.308882i
$750$	−15.0284	−	20.4978i	−0.548760	−	0.748473i
$751$	22.4303			0.818494			0.409247	−	0.912424i	$-0.365791\pi$
$751$	22.4303			0.818494			0.409247	+	0.912424i	$0.365791\pi$
$752$	−39.9659	−	27.9933i	−1.45741	−	1.02081i
$753$	8.26442			0.301172
$754$	1.69661	+	2.31407i	0.0617869	+	0.0842733i
$755$		−	10.3060i		−	0.375073i
$756$	−80.0093	−	25.2334i	−2.90991	−	0.917730i
$757$		−	32.2421i		−	1.17186i	−0.810362	−	0.585930i	$-0.800729\pi$
$757$		−	32.2421i		−	1.17186i	0.810362	−	0.585930i	$-0.199271\pi$
$758$	−23.7010	+	17.3769i	−0.860859	+	0.631159i
$759$	−68.6635			−2.49233
$760$	1.59109	−	0.539905i	0.0577150	−	0.0195844i
$761$	16.3559			0.592902			0.296451	−	0.955048i	$-0.404197\pi$
$761$	16.3559			0.592902			0.296451	+	0.955048i	$0.404197\pi$
$762$	−57.6826	+	42.2913i	−2.08962	+	1.53205i
$763$		−	0.00431797i		−	0.000156321i
$764$	8.95145	−	28.3830i	0.323852	−	1.02686i
$765$			5.26714i			0.190434i
$766$	13.0589	+	17.8115i	0.471837	+	0.643554i
$767$	0.593302			0.0214229
$768$	−47.1568	+	17.1478i	−1.70162	+	0.618766i
$769$	−19.6832			−0.709794			−0.354897	−	0.934905i	$-0.615484\pi$
$769$	−19.6832			−0.709794			−0.354897	+	0.934905i	$0.615484\pi$
$770$	8.37646	+	11.4249i	0.301867	+	0.411727i
$771$			62.9038i			2.26542i
$772$	12.7983	−	40.5805i	0.460621	−	1.46052i
$773$		−	33.0819i		−	1.18987i	−0.803773	−	0.594936i	$-0.797177\pi$
$773$		−	33.0819i		−	1.18987i	0.803773	−	0.594936i	$-0.202823\pi$
$774$	6.19255	−	4.54021i	0.222586	−	0.163194i
$775$	−5.67093			−0.203706
$776$	5.59379	−	1.89814i	0.200805	−	0.0681392i
$777$	−61.5395			−2.20772
$778$	11.5344	−	8.45668i	0.413527	−	0.303187i
$779$		−	0.450021i		−	0.0161237i
$780$	−0.766106	−	0.241615i	−0.0274310	−	0.00865121i
$781$		−	37.8494i		−	1.35436i
$782$	−4.91175	−	6.69930i	−0.175644	−	0.239566i
$783$	113.191			4.04512
$784$	−16.9157	−	11.8483i	−0.604132	−	0.423152i
$785$	−5.72235			−0.204240
$786$	29.2339	+	39.8731i	1.04274	+	1.42223i
$787$			35.1617i			1.25338i	0.779269	+	0.626690i	$0.215591\pi$
$787$			35.1617i			1.25338i	−0.779269	+	0.626690i	$0.784409\pi$
$788$	−7.04149	−	2.22075i	−0.250843	−	0.0791110i
$789$			12.6594i			0.450688i
$790$	6.82464	−	5.00364i	0.242810	−	0.178022i
$791$	−6.33392			−0.225208
$792$	−30.0377	−	88.5207i	−1.06734	−	3.14544i
$793$	−1.67446			−0.0594619
$794$	5.25410	−	3.85216i	0.186461	−	0.136708i
$795$		−	4.77685i		−	0.169417i
$796$	−7.02957	+	22.2892i	−0.249157	+	0.790019i
$797$			3.75101i			0.132868i	0.997791	+	0.0664338i	$0.0211621\pi$
$797$			3.75101i			0.132868i	−0.997791	+	0.0664338i	$0.978838\pi$
$798$	−9.14580	−	12.4743i	−0.323758	−	0.441584i
$799$	15.8241			0.559815
$800$	0.568573	+	26.2819i	0.0201021	+	0.929206i
$801$	−93.7046			−3.31089
$802$	3.34572	+	4.56334i	0.118141	+	0.161137i
$803$			14.9374i			0.527131i
$804$	−7.76558	+	24.6229i	−0.273871	+	0.868381i
$805$			9.38121i			0.330644i
$806$	−0.300064	+	0.219999i	−0.0105693	+	0.00774913i
$807$	−44.8763			−1.57972
$808$	−2.51824	−	7.42122i	−0.0885913	−	0.261078i
$809$	23.9158			0.840836			0.420418	−	0.907331i	$-0.361883\pi$
$809$	23.9158			0.840836			0.420418	+	0.907331i	$0.361883\pi$
$810$	−11.6629	+	8.55095i	−0.409794	+	0.300450i
$811$			52.0538i			1.82785i	0.405878	+	0.913927i	$0.366966\pi$
$811$			52.0538i			1.82785i	−0.405878	+	0.913927i	$0.633034\pi$
$812$	62.6028	+	19.7437i	2.19693	+	0.692869i
$813$			30.8918i			1.08342i
$814$	−22.7490	−	31.0282i	−0.797352	−	1.08754i
$815$	−13.3876			−0.468947
$816$	9.33561	−	13.3284i	0.326812	−	0.466588i
$817$	0.794359			0.0277911
$818$	12.1341	+	16.5502i	0.424260	+	0.578663i
$819$			5.13943i			0.179586i
$820$	−0.509904	−	0.160814i	−0.0178066	−	0.00561587i
$821$			0.703590i			0.0245555i	0.999925	+	0.0122777i	$0.00390822\pi$
$821$			0.703590i			0.0245555i	−0.999925	+	0.0122777i	$0.996092\pi$
$822$	39.9405	−	29.2833i	1.39308	−	1.02137i
$823$	23.4559			0.817622			0.408811	−	0.912619i	$-0.365943\pi$
$823$	23.4559			0.817622			0.408811	+	0.912619i	$0.365943\pi$
$824$	−38.3988	+	13.0299i	−1.33769	+	0.453916i
$825$	−70.4676			−2.45337
$826$	10.9460	−	8.02535i	0.380862	−	0.279238i
$827$		−	29.5282i		−	1.02680i	−0.858150	−	0.513399i	$-0.828386\pi$
$827$		−	29.5282i		−	1.02680i	0.858150	−	0.513399i	$-0.171614\pi$
$828$	18.6186	−	59.0352i	0.647039	−	2.05161i
$829$		−	4.42946i		−	0.153841i	−0.997037	−	0.0769207i	$-0.975491\pi$
$829$		−	4.42946i		−	0.153841i	0.997037	−	0.0769207i	$-0.0245088\pi$
$830$	−5.77680	−	7.87918i	−0.200516	−	0.273490i
$831$	−53.2014			−1.84554
$832$	1.04967	+	1.36859i	0.0363907	+	0.0474473i
$833$	6.69759			0.232058
$834$	34.2314	+	46.6893i	1.18534	+	1.61672i
$835$		−	9.80811i		−	0.339424i
$836$	2.90863	−	9.22260i	0.100597	−	0.318970i
$837$			14.6774i			0.507326i
$838$	−5.72628	+	4.19835i	−0.197811	+	0.145030i
$839$	−36.4506			−1.25841			−0.629207	−	0.777237i	$-0.716620\pi$
$839$	−36.4506			−1.25841			−0.629207	+	0.777237i	$0.716620\pi$
$840$	−17.4024	+	5.90515i	−0.600440	+	0.203747i
$841$	−59.5656			−2.05399
$842$	4.67785	−	3.42967i	0.161209	−	0.118194i
$843$		−	32.0127i		−	1.10257i
$844$	14.5269	+	4.58150i	0.500036	+	0.157702i
$845$		−	7.69492i		−	0.264713i
$846$	69.7220	+	95.0962i	2.39709	+	3.26947i
$847$	43.1730			1.48344
$848$	−5.88406	+	8.40065i	−0.202060	+	0.288479i
$849$	−58.8677			−2.02033
$850$	−5.04079	−	6.87531i	−0.172898	−	0.235821i
$851$		−	25.4777i		−	0.873366i
$852$	46.8247	+	14.7676i	1.60419	+	0.505930i
$853$		−	52.7043i		−	1.80456i	−0.431149	−	0.902281i	$-0.641892\pi$
$853$		−	52.7043i		−	1.80456i	0.431149	−	0.902281i	$-0.358108\pi$
$854$	−30.8928	+	22.6498i	−1.05713	+	0.775059i
$855$	−4.06039			−0.138862
$856$	−2.20299	−	6.49218i	−0.0752966	−	0.221898i
$857$	13.7199			0.468662			0.234331	−	0.972157i	$-0.424710\pi$
$857$	13.7199			0.468662			0.234331	+	0.972157i	$0.424710\pi$
$858$	−3.72863	+	2.73373i	−0.127293	+	0.0933280i
$859$		−	55.0757i		−	1.87916i	−0.342330	−	0.939580i	$-0.611216\pi$
$859$		−	55.0757i		−	1.87916i	0.342330	−	0.939580i	$-0.388784\pi$
$860$	0.283862	−	0.900062i	0.00967962	−	0.0306919i
$861$			4.92206i			0.167743i
$862$	13.6233	+	18.5813i	0.464013	+	0.632883i
$863$	38.3384			1.30505			0.652527	−	0.757766i	$-0.273709\pi$
$863$	38.3384			1.30505			0.652527	+	0.757766i	$0.273709\pi$
$864$	68.0225	−	1.47157i	2.31417	−	0.0500640i
$865$	3.05878			0.104002
$866$	−6.22847	−	8.49523i	−0.211652	−	0.288680i
$867$		−	48.0367i		−	1.63141i
$868$	−2.56016	+	8.11768i	−0.0868975	+	0.275532i
$869$		−	48.7053i		−	1.65221i
$870$	19.9959	−	14.6605i	0.677926	−	0.497037i
$871$	0.887462			0.0300705
$872$	0.00112527	+	0.00331617i	3.81066e−5	+	0.000112300i
$873$	−14.2751			−0.483138
$874$	5.16442	−	3.78642i	0.174689	−	0.128077i
$875$			19.9865i			0.675666i
$876$	−18.4796	−	5.82812i	−0.624368	−	0.196914i
$877$			21.4788i			0.725288i	0.931928	+	0.362644i	$0.118126\pi$
$877$			21.4788i			0.725288i	−0.931928	+	0.362644i	$0.881874\pi$
$878$	−13.2870	−	18.1226i	−0.448414	−	0.611607i
$879$	62.1800			2.09728
$880$	−9.41044	−	6.59135i	−0.317226	−	0.222194i
$881$	−11.2383			−0.378629			−0.189314	−	0.981917i	$-0.560627\pi$
$881$	−11.2383			−0.378629			−0.189314	+	0.981917i	$0.560627\pi$
$882$	29.5100	+	40.2498i	0.993655	+	1.35528i
$883$			15.7137i			0.528809i	0.964412	+	0.264405i	$0.0851755\pi$
$883$			15.7137i			0.528809i	−0.964412	+	0.264405i	$0.914825\pi$
$884$	−0.533444	−	0.168238i	−0.0179417	−	0.00565845i
$885$		−	5.12674i		−	0.172334i
$886$	17.3064	−	12.6886i	0.581421	−	0.426282i
$887$	4.48008			0.150426			0.0752131	−	0.997167i	$-0.476036\pi$
$887$	4.48008			0.150426			0.0752131	+	0.997167i	$0.476036\pi$
$888$	47.2619	−	16.0374i	1.58601	−	0.538179i
$889$	56.2437			1.88635
$890$	−9.28812	+	6.80980i	−0.311338	+	0.228265i
$891$			83.2347i			2.78847i
$892$	1.17590	−	3.72851i	0.0393720	−	0.124840i
$893$			12.1986i			0.408211i
$894$	−37.7130	−	51.4381i	−1.26131	−	1.72035i
$895$	−5.53396			−0.184980
$896$	37.8781	+	11.0512i	1.26542	+	0.369194i
$897$	−3.06164			−0.102225
$898$	20.3955	+	27.8182i	0.680608	+	0.928305i
$899$		−	11.4843i		−	0.383022i
$900$	19.1077	−	60.5862i	0.636924	−	2.01954i
$901$		−	3.32614i		−	0.110810i
$902$	−2.48170	+	1.81951i	−0.0826314	+	0.0605831i
$903$	−8.68822			−0.289126
$904$	4.86440	−	1.65064i	0.161788	−	0.0548993i
$905$	3.06238			0.101797
$906$	62.0534	−	45.4959i	2.06159	−	1.51150i
$907$		−	6.37021i		−	0.211519i	−0.994392	−	0.105760i	$-0.966273\pi$
$907$		−	6.37021i		−	0.211519i	0.994392	−	0.105760i	$-0.0337274\pi$
$908$	25.5036	+	8.04334i	0.846367	+	0.266928i
$909$			18.9386i			0.628152i
$910$	0.373498	+	0.509427i	0.0123813	+	0.0168873i
$911$	−30.5275			−1.01142			−0.505711	−	0.862703i	$-0.668770\pi$
$911$	−30.5275			−1.01142			−0.505711	+	0.862703i	$0.668770\pi$
$912$	10.2747	+	7.19673i	0.340231	+	0.238308i
$913$	−56.2312			−1.86098
$914$	8.93556	+	12.1875i	0.295562	+	0.403127i
$915$			14.4691i			0.478334i
$916$	−22.0875	−	6.96597i	−0.729791	−	0.230162i
$917$		−	38.8785i		−	1.28388i
$918$	−17.7946	+	13.0465i	−0.587309	+	0.430599i
$919$	−48.0650			−1.58552			−0.792758	−	0.609536i	$-0.791356\pi$
$919$	−48.0650			−1.58552			−0.792758	+	0.609536i	$0.791356\pi$
$920$	−2.44477	−	7.20471i	−0.0806017	−	0.237532i
$921$	57.6840			1.90075
$922$	24.8898	−	18.2485i	0.819700	−	0.600982i
$923$		−	1.68767i		−	0.0555502i
$924$	−31.8128	+	100.871i	−1.04657	+	3.31842i
$925$		−	26.1471i		−	0.859712i
$926$	−0.0216108	−	0.0294757i	−0.000710175	−	0.000968632i
$927$	97.9917			3.21847
$928$	−53.2238	+	1.15142i	−1.74716	+	0.0377974i
$929$	47.2953			1.55171			0.775854	−	0.630912i	$-0.217319\pi$
$929$	47.2953			1.55171			0.775854	+	0.630912i	$0.217319\pi$
$930$	1.90102	+	2.59287i	0.0623369	+	0.0850234i
$931$			5.16310i			0.169214i
$932$	−0.955698	+	3.03030i	−0.0313049	+	0.0992607i
$933$			60.1339i			1.96870i
$934$	5.32604	−	3.90491i	0.174273	−	0.127773i
$935$	3.72596			0.121852
$936$	−1.33935	−	3.94705i	−0.0437780	−	0.129013i
$937$	−8.30237			−0.271227			−0.135613	−	0.990762i	$-0.543301\pi$
$937$	−8.30237			−0.271227			−0.135613	+	0.990762i	$0.543301\pi$
$938$	16.3731	−	12.0043i	0.534601	−	0.391955i
$939$			44.6189i			1.45608i
$940$	13.8219	+	4.35915i	0.450819	+	0.142180i
$941$		−	31.3955i		−	1.02347i	−0.859145	−	0.511733i	$-0.829004\pi$
$941$		−	31.3955i		−	1.02347i	0.859145	−	0.511733i	$-0.170996\pi$
$942$	−25.2614	−	34.4549i	−0.823061	−	1.12260i
$943$	−2.03776			−0.0663586
$944$	−6.31506	+	9.01598i	−0.205538	+	0.293445i
$945$	24.9183			0.810591
$946$	−3.21173	−	4.38059i	−0.104422	−	0.142425i
$947$			2.14805i			0.0698024i	0.999391	+	0.0349012i	$0.0111117\pi$
$947$			2.14805i			0.0698024i	−0.999391	+	0.0349012i	$0.988888\pi$
$948$	60.2549	+	19.0032i	1.95699	+	0.617197i
$949$			0.666046i			0.0216208i
$950$	5.30011	−	3.88590i	0.171958	−	0.126075i
$951$	−2.43970			−0.0791127
$952$	−12.1174	+	4.11179i	−0.392727	+	0.133264i
$953$	25.3661			0.821689			0.410844	−	0.911705i	$-0.365234\pi$
$953$	25.3661			0.821689			0.410844	+	0.911705i	$0.365234\pi$
$954$	19.9888	−	14.6552i	0.647160	−	0.474480i
$955$			8.83965i			0.286044i
$956$	−14.3301	+	45.4376i	−0.463470	+	1.46956i
$957$		−	142.705i		−	4.61299i
$958$	25.5398	+	34.8346i	0.825152	+	1.12545i
$959$	−38.9442			−1.25757
$960$	11.8260	−	9.07023i	0.381684	−	0.292741i
$961$	−29.5108			−0.951963
$962$	−1.01436	−	1.38351i	−0.0327041	−	0.0446063i
$963$			16.5677i			0.533887i
$964$	−13.7488	+	43.5942i	−0.442818	+	1.40407i
$965$			12.6385i			0.406847i
$966$	−56.4853	+	41.4135i	−1.81739	+	1.33246i
$967$	−12.8395			−0.412892			−0.206446	−	0.978458i	$-0.566190\pi$
$967$	−12.8395			−0.412892			−0.206446	+	0.978458i	$0.566190\pi$
$968$	−33.1566	+	11.2510i	−1.06569	+	0.361621i
$969$	−4.06817			−0.130688
$970$	−1.41496	+	1.03741i	−0.0454317	+	0.0333093i
$971$			8.77909i			0.281734i	0.990028	+	0.140867i	$0.0449891\pi$
$971$			8.77909i			0.281734i	−0.990028	+	0.140867i	$0.955011\pi$
$972$	−34.1484	−	10.7698i	−1.09531	−	0.345440i
$973$		−	45.5247i		−	1.45945i
$974$	1.98290	+	2.70454i	0.0635362	+	0.0866592i
$975$	−3.14208			−0.100627
$976$	17.8229	−	25.4456i	0.570496	−	0.814494i
$977$	−45.9701			−1.47071			−0.735357	−	0.677680i	$-0.762986\pi$
$977$	−45.9701			−1.47071			−0.735357	+	0.677680i	$0.762986\pi$
$978$	−59.0998	−	80.6083i	−1.88980	−	2.57757i
$979$			66.2864i			2.11852i
$980$	5.85014	+	1.84502i	0.186876	+	0.0589371i
$981$		−	0.00846269i		−	0.000270193i
$982$	−47.1268	+	34.5521i	−1.50388	+	1.10260i
$983$	−51.4992			−1.64257			−0.821284	−	0.570519i	$-0.806742\pi$
$983$	−51.4992			−1.64257			−0.821284	+	0.570519i	$0.806742\pi$
$984$	−1.28270	−	3.78011i	−0.0408910	−	0.120505i
$985$	2.19302			0.0698753
$986$	13.9233	−	10.2082i	0.443407	−	0.325094i
$987$		−	133.421i		−	4.24684i
$988$	0.129693	−	0.411227i	0.00412608	−	0.0130829i
$989$		−	3.59697i		−	0.114377i
$990$	16.4168	+	22.3915i	0.521761	+	0.711648i
$991$	−29.4762			−0.936343			−0.468171	−	0.883638i	$-0.655087\pi$
$991$	−29.4762			−0.936343			−0.468171	+	0.883638i	$0.655087\pi$
$992$	−0.149305	−	6.90151i	−0.00474043	−	0.219123i
$993$	51.4284			1.63203
$994$	−22.8283	−	31.1364i	−0.724071	−	0.987586i
$995$		−	6.94178i		−	0.220069i
$996$	21.9396	−	69.5655i	0.695184	−	2.20427i
$997$			54.3591i			1.72157i	0.508968	+	0.860786i	$0.330027\pi$
$997$			54.3591i			1.72157i	−0.508968	+	0.860786i	$0.669973\pi$
$998$	18.0897	−	13.2629i	0.572620	−	0.419829i
$999$	−67.6737			−2.14110

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.c.b.77.5	✓	16
3.2	odd	2		1368.2.g.b.685.12		16
4.3	odd	2		608.2.c.b.305.1		16
8.3	odd	2		608.2.c.b.305.16		16
8.5	even	2	inner	152.2.c.b.77.6	yes	16
12.11	even	2		5472.2.g.b.2737.9		16
16.3	odd	4		4864.2.a.bn.1.8		8
16.5	even	4		4864.2.a.bq.1.8		8
16.11	odd	4		4864.2.a.bp.1.1		8
16.13	even	4		4864.2.a.bo.1.1		8
24.5	odd	2		1368.2.g.b.685.11		16
24.11	even	2		5472.2.g.b.2737.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.c.b.77.5	✓	16	1.1	even	1	trivial
152.2.c.b.77.6	yes	16	8.5	even	2	inner
608.2.c.b.305.1		16	4.3	odd	2
608.2.c.b.305.16		16	8.3	odd	2
1368.2.g.b.685.11		16	24.5	odd	2
1368.2.g.b.685.12		16	3.2	odd	2
4864.2.a.bn.1.8		8	16.3	odd	4
4864.2.a.bo.1.1		8	16.13	even	4
4864.2.a.bp.1.1		8	16.11	odd	4
4864.2.a.bq.1.8		8	16.5	even	4
5472.2.g.b.2737.8		16	24.11	even	2
5472.2.g.b.2737.9		16	12.11	even	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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.836196 - 1.14052i) q^{2} +3.13611i q^{3} +(-0.601554 + 1.90739i) q^{4} -0.594041i q^{5} +(3.57679 - 2.62240i) q^{6} -3.48756 q^{7} +(2.67842 - 0.908869i) q^{8} -6.83520 q^{9} +O(q^{10})\)	\(q+(-0.836196 - 1.14052i) q^{2} +3.13611i q^{3} +(-0.601554 + 1.90739i) q^{4} -0.594041i q^{5} +(3.57679 - 2.62240i) q^{6} -3.48756 q^{7} +(2.67842 - 0.908869i) q^{8} -6.83520 q^{9} +(-0.677513 + 0.496734i) q^{10} +4.83520i q^{11} +(-5.98179 - 1.88654i) q^{12} +0.215597i q^{13} +(2.91629 + 3.97762i) q^{14} +1.86298 q^{15} +(-3.27627 - 2.29479i) q^{16} +1.29720 q^{17} +(5.71556 + 7.79565i) q^{18} +1.00000i q^{19} +(1.13307 + 0.357348i) q^{20} -10.9374i q^{21} +(5.51462 - 4.04317i) q^{22} +4.52815 q^{23} +(2.85031 + 8.39984i) q^{24} +4.64712 q^{25} +(0.245891 - 0.180281i) q^{26} -12.0276i q^{27} +(2.09796 - 6.65214i) q^{28} +9.41093i q^{29} +(-1.55781 - 2.12476i) q^{30} -1.22031 q^{31} +(0.122350 + 5.65553i) q^{32} -15.1637 q^{33} +(-1.08471 - 1.47948i) q^{34} +2.07176i q^{35} +(4.11174 - 13.0374i) q^{36} -5.62653i q^{37} +(1.14052 - 0.836196i) q^{38} -0.676135 q^{39} +(-0.539905 - 1.59109i) q^{40} -0.450021 q^{41} +(-12.4743 + 9.14580i) q^{42} -0.794359i q^{43} +(-9.22260 - 2.90863i) q^{44} +4.06039i q^{45} +(-3.78642 - 5.16442i) q^{46} +12.1986 q^{47} +(7.19673 - 10.2747i) q^{48} +5.16310 q^{49} +(-3.88590 - 5.30011i) q^{50} +4.06817i q^{51} +(-0.411227 - 0.129693i) q^{52} -2.56409i q^{53} +(-13.7177 + 10.0574i) q^{54} +2.87231 q^{55} +(-9.34118 + 3.16974i) q^{56} -3.13611 q^{57} +(10.7333 - 7.86938i) q^{58} -2.75191i q^{59} +(-1.12068 + 3.55343i) q^{60} +7.76665i q^{61} +(1.02042 + 1.39178i) q^{62} +23.8382 q^{63} +(6.34792 - 4.86867i) q^{64} +0.128073 q^{65} +(12.6798 + 17.2945i) q^{66} -4.11631i q^{67} +(-0.780337 + 2.47427i) q^{68} +14.2008i q^{69} +(2.36287 - 1.73239i) q^{70} -7.82788 q^{71} +(-18.3076 + 6.21230i) q^{72} +3.08931 q^{73} +(-6.41714 + 4.70488i) q^{74} +14.5739i q^{75} +(-1.90739 - 0.601554i) q^{76} -16.8631i q^{77} +(0.565381 + 0.771143i) q^{78} -10.0731 q^{79} +(-1.36320 + 1.94624i) q^{80} +17.2143 q^{81} +(0.376306 + 0.513256i) q^{82} +11.6296i q^{83} +(20.8619 + 6.57943i) q^{84} -0.770591i q^{85} +(-0.905979 + 0.664240i) q^{86} -29.5137 q^{87} +(4.39456 + 12.9507i) q^{88} +13.7091 q^{89} +(4.63094 - 3.39528i) q^{90} -0.751907i q^{91} +(-2.72392 + 8.63694i) q^{92} -3.82703i q^{93} +(-10.2004 - 13.9127i) q^{94} +0.594041 q^{95} +(-17.7364 + 0.383702i) q^{96} +2.08846 q^{97} +(-4.31736 - 5.88860i) q^{98} -33.0495i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9	\( 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9} - 8 q^{10} + 4 q^{12} + 4 q^{14} + 2 q^{16} - 8 q^{17} + 20 q^{18} + 8 q^{20} + 20 q^{22} + 6 q^{24} - 24 q^{25} - 10 q^{26} - 14 q^{28} + 4 q^{30} + 16 q^{31} - 20 q^{32} + 8 q^{36} + 2 q^{38} + 8 q^{39} + 28 q^{40} + 16 q^{41} - 2 q^{42} - 28 q^{44} - 48 q^{46} + 24 q^{47} + 36 q^{48} + 24 q^{49} + 12 q^{50} + 8 q^{52} - 34 q^{54} + 16 q^{55} - 48 q^{56} + 38 q^{58} - 28 q^{60} - 16 q^{62} - 32 q^{63} + 14 q^{64} + 16 q^{65} - 24 q^{66} - 26 q^{68} - 32 q^{70} + 48 q^{71} - 20 q^{74} - 4 q^{76} + 56 q^{78} - 48 q^{79} + 4 q^{80} - 16 q^{81} - 12 q^{82} + 64 q^{84} + 48 q^{86} - 48 q^{87} + 40 q^{88} - 16 q^{89} + 12 q^{90} + 62 q^{92} - 36 q^{94} + 16 q^{95} - 70 q^{96} + 32 q^{97} - 48 q^{98}+O(q^{100}) \) 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9 - 8 * q^10 + 4 * q^12 + 4 * q^14 + 2 * q^16 - 8 * q^17 + 20 * q^18 + 8 * q^20 + 20 * q^22 + 6 * q^24 - 24 * q^25 - 10 * q^26 - 14 * q^28 + 4 * q^30 + 16 * q^31 - 20 * q^32 + 8 * q^36 + 2 * q^38 + 8 * q^39 + 28 * q^40 + 16 * q^41 - 2 * q^42 - 28 * q^44 - 48 * q^46 + 24 * q^47 + 36 * q^48 + 24 * q^49 + 12 * q^50 + 8 * q^52 - 34 * q^54 + 16 * q^55 - 48 * q^56 + 38 * q^58 - 28 * q^60 - 16 * q^62 - 32 * q^63 + 14 * q^64 + 16 * q^65 - 24 * q^66 - 26 * q^68 - 32 * q^70 + 48 * q^71 - 20 * q^74 - 4 * q^76 + 56 * q^78 - 48 * q^79 + 4 * q^80 - 16 * q^81 - 12 * q^82 + 64 * q^84 + 48 * q^86 - 48 * q^87 + 40 * q^88 - 16 * q^89 + 12 * q^90 + 62 * q^92 - 36 * q^94 + 16 * q^95 - 70 * q^96 + 32 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more