LMFDB - Embedded newform 1380.2.p.b.91.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(91,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1380.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.p (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:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.9
Character	$\chi$	$=$	1380.91
Dual form			1380.2.p.b.91.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18761 - 0.767836i) q^{2} -1.00000i q^{3} +(0.820857 + 1.82379i) q^{4} +1.00000i q^{5} +(-0.767836 + 1.18761i) q^{6} -0.597446 q^{7} +(0.425506 - 2.79624i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.18761 - 0.767836i) q^{2} -1.00000i q^{3} +(0.820857 + 1.82379i) q^{4} +1.00000i q^{5} +(-0.767836 + 1.18761i) q^{6} -0.597446 q^{7} +(0.425506 - 2.79624i) q^{8} -1.00000 q^{9} +(0.767836 - 1.18761i) q^{10} +3.20657 q^{11} +(1.82379 - 0.820857i) q^{12} +3.38926 q^{13} +(0.709536 + 0.458740i) q^{14} +1.00000 q^{15} +(-2.65239 + 2.99413i) q^{16} +7.02799i q^{17} +(1.18761 + 0.767836i) q^{18} -5.07349 q^{19} +(-1.82379 + 0.820857i) q^{20} +0.597446i q^{21} +(-3.80816 - 2.46212i) q^{22} +(1.05397 + 4.67858i) q^{23} +(-2.79624 - 0.425506i) q^{24} -1.00000 q^{25} +(-4.02514 - 2.60240i) q^{26} +1.00000i q^{27} +(-0.490418 - 1.08961i) q^{28} -7.11039 q^{29} +(-1.18761 - 0.767836i) q^{30} -7.60264i q^{31} +(5.44902 - 1.51928i) q^{32} -3.20657i q^{33} +(5.39634 - 8.34654i) q^{34} -0.597446i q^{35} +(-0.820857 - 1.82379i) q^{36} +2.75487i q^{37} +(6.02535 + 3.89560i) q^{38} -3.38926i q^{39} +(2.79624 + 0.425506i) q^{40} +2.61478 q^{41} +(0.458740 - 0.709536i) q^{42} -1.14299 q^{43} +(2.63213 + 5.84809i) q^{44} -1.00000i q^{45} +(2.34067 - 6.36563i) q^{46} +5.36961i q^{47} +(2.99413 + 2.65239i) q^{48} -6.64306 q^{49} +(1.18761 + 0.767836i) q^{50} +7.02799 q^{51} +(2.78210 + 6.18129i) q^{52} +11.3626i q^{53} +(0.767836 - 1.18761i) q^{54} +3.20657i q^{55} +(-0.254217 + 1.67060i) q^{56} +5.07349i q^{57} +(8.44440 + 5.45961i) q^{58} +0.724850i q^{59} +(0.820857 + 1.82379i) q^{60} +7.28065i q^{61} +(-5.83758 + 9.02901i) q^{62} +0.597446 q^{63} +(-7.63789 - 2.37963i) q^{64} +3.38926i q^{65} +(-2.46212 + 3.80816i) q^{66} +2.69109 q^{67} +(-12.8175 + 5.76897i) q^{68} +(4.67858 - 1.05397i) q^{69} +(-0.458740 + 0.709536i) q^{70} -2.14641i q^{71} +(-0.425506 + 2.79624i) q^{72} +8.52225 q^{73} +(2.11528 - 3.27172i) q^{74} +1.00000i q^{75} +(-4.16461 - 9.25295i) q^{76} -1.91575 q^{77} +(-2.60240 + 4.02514i) q^{78} +10.5381 q^{79} +(-2.99413 - 2.65239i) q^{80} +1.00000 q^{81} +(-3.10535 - 2.00772i) q^{82} +0.284248 q^{83} +(-1.08961 + 0.490418i) q^{84} -7.02799 q^{85} +(1.35744 + 0.877631i) q^{86} +7.11039i q^{87} +(1.36441 - 8.96632i) q^{88} +13.8871i q^{89} +(-0.767836 + 1.18761i) q^{90} -2.02490 q^{91} +(-7.66757 + 5.76266i) q^{92} -7.60264 q^{93} +(4.12298 - 6.37703i) q^{94} -5.07349i q^{95} +(-1.51928 - 5.44902i) q^{96} -6.87156i q^{97} +(7.88939 + 5.10078i) q^{98} -3.20657 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} + 2 q^{10} - 20 q^{14} + 48 q^{15} - 6 q^{16} + 4 q^{18} - 16 q^{19} - 28 q^{22} - 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} - 4 q^{30} + 16 q^{32} + 28 q^{34} + 2 q^{36} - 2 q^{40} - 8 q^{41} + 26 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 16 q^{51} - 16 q^{52} + 2 q^{54} - 40 q^{56} - 8 q^{58} - 2 q^{60} + 24 q^{62} - 26 q^{64} + 48 q^{67} + 44 q^{68} - 8 q^{69} + 4 q^{72} - 20 q^{74} + 64 q^{76} + 32 q^{77} + 64 q^{79} - 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} + 40 q^{86} - 2 q^{90} - 28 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 + 2 * q^10 - 20 * q^14 + 48 * q^15 - 6 * q^16 + 4 * q^18 - 16 * q^19 - 28 * q^22 - 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 - 4 * q^30 + 16 * q^32 + 28 * q^34 + 2 * q^36 - 2 * q^40 - 8 * q^41 + 26 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 - 16 * q^51 - 16 * q^52 + 2 * q^54 - 40 * q^56 - 8 * q^58 - 2 * q^60 + 24 * q^62 - 26 * q^64 + 48 * q^67 + 44 * q^68 - 8 * q^69 + 4 * q^72 - 20 * q^74 + 64 * q^76 + 32 * q^77 + 64 * q^79 - 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 + 40 * q^86 - 2 * q^90 - 28 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$1$	$1$	$-1$	$-1$

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 $

$2$	−1.18761	−	0.767836i	−0.839770	−	0.542942i
$2$	−1.18761	−	0.767836i	−0.839770	−	0.542942i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.820857	+	1.82379i	0.410428	+	0.911893i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−0.767836	+	1.18761i	−0.313468	+	0.484842i
$7$	−0.597446			−0.225813			−0.112907	−	0.993606i	$-0.536016\pi$
$7$	−0.597446			−0.225813			−0.112907	+	0.993606i	$0.536016\pi$
$8$	0.425506	−	2.79624i	0.150439	−	0.988619i
$9$	−1.00000			−0.333333
$10$	0.767836	−	1.18761i	0.242811	−	0.375557i
$11$	3.20657			0.966816			0.483408	−	0.875395i	$-0.339399\pi$
$11$	3.20657			0.966816			0.483408	+	0.875395i	$0.339399\pi$
$12$	1.82379	−	0.820857i	0.526482	−	0.236961i
$13$	3.38926			0.940013			0.470006	−	0.882663i	$-0.344252\pi$
$13$	3.38926			0.940013			0.470006	+	0.882663i	$0.344252\pi$
$14$	0.709536	+	0.458740i	0.189631	+	0.122604i
$15$	1.00000			0.258199
$16$	−2.65239	+	2.99413i	−0.663097	+	0.748533i
$17$			7.02799i			1.70454i	0.523104	+	0.852269i	$0.324774\pi$
$17$			7.02799i			1.70454i	−0.523104	+	0.852269i	$0.675226\pi$
$18$	1.18761	+	0.767836i	0.279923	+	0.180981i
$19$	−5.07349			−1.16394			−0.581969	−	0.813211i	$-0.697717\pi$
$19$	−5.07349			−1.16394			−0.581969	+	0.813211i	$0.697717\pi$
$20$	−1.82379	+	0.820857i	−0.407811	+	0.183549i
$21$			0.597446i			0.130373i
$22$	−3.80816	−	2.46212i	−0.811903	−	0.524925i
$23$	1.05397	+	4.67858i	0.219768	+	0.975552i
$23$	1.05397	+	4.67858i	0.219768	+	0.975552i
$24$	−2.79624	−	0.425506i	−0.570780	−	0.0868561i
$25$	−1.00000			−0.200000
$26$	−4.02514	−	2.60240i	−0.789395	−	0.510372i
$27$			1.00000i			0.192450i
$28$	−0.490418	−	1.08961i	−0.0926802	−	0.205918i
$29$	−7.11039			−1.32037			−0.660183	−	0.751105i	$-0.729521\pi$
$29$	−7.11039			−1.32037			−0.660183	+	0.751105i	$0.729521\pi$
$30$	−1.18761	−	0.767836i	−0.216828	−	0.140187i
$31$		−	7.60264i		−	1.36547i	−0.730664	−	0.682737i	$-0.760789\pi$
$31$		−	7.60264i		−	1.36547i	0.730664	−	0.682737i	$-0.239211\pi$
$32$	5.44902	−	1.51928i	0.963259	−	0.268573i
$33$		−	3.20657i		−	0.558191i
$34$	5.39634	−	8.34654i	0.925465	−	1.43142i
$35$		−	0.597446i		−	0.100987i
$36$	−0.820857	−	1.82379i	−0.136809	−	0.303964i
$37$			2.75487i			0.452897i	0.974023	+	0.226449i	$0.0727115\pi$
$37$			2.75487i			0.452897i	−0.974023	+	0.226449i	$0.927288\pi$
$38$	6.02535	+	3.89560i	0.977440	+	0.631950i
$39$		−	3.38926i		−	0.542717i
$40$	2.79624	+	0.425506i	0.442124	+	0.0672785i
$41$	2.61478			0.408360			0.204180	−	0.978933i	$-0.434547\pi$
$41$	2.61478			0.408360			0.204180	+	0.978933i	$0.434547\pi$
$42$	0.458740	−	0.709536i	0.0707852	−	0.109484i
$43$	−1.14299			−0.174305			−0.0871524	−	0.996195i	$-0.527777\pi$
$43$	−1.14299			−0.174305			−0.0871524	+	0.996195i	$0.527777\pi$
$44$	2.63213	+	5.84809i	0.396809	+	0.881633i
$45$		−	1.00000i		−	0.149071i
$46$	2.34067	−	6.36563i	0.345113	−	0.938561i
$47$			5.36961i			0.783238i	0.920127	+	0.391619i	$0.128085\pi$
$47$			5.36961i			0.783238i	−0.920127	+	0.391619i	$0.871915\pi$
$48$	2.99413	+	2.65239i	0.432166	+	0.382839i
$49$	−6.64306			−0.949008
$50$	1.18761	+	0.767836i	0.167954	+	0.108588i
$51$	7.02799			0.984115
$52$	2.78210	+	6.18129i	0.385808	+	0.857191i
$53$			11.3626i			1.56078i	0.625295	+	0.780388i	$0.284979\pi$
$53$			11.3626i			1.56078i	−0.625295	+	0.780388i	$0.715021\pi$
$54$	0.767836	−	1.18761i	0.104489	−	0.161614i
$55$			3.20657i			0.432373i
$56$	−0.254217	+	1.67060i	−0.0339712	+	0.223243i
$57$			5.07349i			0.672000i
$58$	8.44440	+	5.45961i	1.10880	+	0.716882i
$59$			0.724850i			0.0943674i	0.998886	+	0.0471837i	$0.0150246\pi$
$59$			0.724850i			0.0943674i	−0.998886	+	0.0471837i	$0.984975\pi$
$60$	0.820857	+	1.82379i	0.105972	+	0.235450i
$61$			7.28065i			0.932192i	0.884734	+	0.466096i	$0.154340\pi$
$61$			7.28065i			0.932192i	−0.884734	+	0.466096i	$0.845660\pi$
$62$	−5.83758	+	9.02901i	−0.741373	+	1.14669i
$63$	0.597446			0.0752711
$64$	−7.63789	−	2.37963i	−0.954736	−	0.297454i
$65$			3.38926i			0.420386i
$66$	−2.46212	+	3.80816i	−0.303065	+	0.468753i
$67$	2.69109			0.328769			0.164384	−	0.986396i	$-0.447436\pi$
$67$	2.69109			0.328769			0.164384	+	0.986396i	$0.447436\pi$
$68$	−12.8175	+	5.76897i	−1.55436	+	0.699590i
$69$	4.67858	−	1.05397i	0.563235	−	0.126883i
$70$	−0.458740	+	0.709536i	−0.0548300	+	0.0848057i
$71$		−	2.14641i		−	0.254732i	−0.991856	−	0.127366i	$-0.959348\pi$
$71$		−	2.14641i		−	0.254732i	0.991856	−	0.127366i	$-0.0406523\pi$
$72$	−0.425506	+	2.79624i	−0.0501464	+	0.329540i
$73$	8.52225			0.997454			0.498727	−	0.866759i	$-0.333801\pi$
$73$	8.52225			0.997454			0.498727	+	0.866759i	$0.333801\pi$
$74$	2.11528	−	3.27172i	0.245897	−	0.380330i
$75$			1.00000i			0.115470i
$76$	−4.16461	−	9.25295i	−0.477713	−	1.06139i
$77$	−1.91575			−0.218320
$78$	−2.60240	+	4.02514i	−0.294664	+	0.455757i
$79$	10.5381			1.18563			0.592815	−	0.805339i	$-0.298017\pi$
$79$	10.5381			1.18563			0.592815	+	0.805339i	$0.298017\pi$
$80$	−2.99413	−	2.65239i	−0.334754	−	0.296546i
$81$	1.00000			0.111111
$82$	−3.10535	−	2.00772i	−0.342928	−	0.221716i
$83$	0.284248			0.0312003			0.0156001	−	0.999878i	$-0.495034\pi$
$83$	0.284248			0.0312003			0.0156001	+	0.999878i	$0.495034\pi$
$84$	−1.08961	+	0.490418i	−0.118887	+	0.0535089i
$85$	−7.02799			−0.762292
$86$	1.35744	+	0.877631i	0.146376	+	0.0946374i
$87$			7.11039i			0.762314i
$88$	1.36441	−	8.96632i	0.145447	−	0.955813i
$89$			13.8871i			1.47203i	0.676967	+	0.736014i	$0.263294\pi$
$89$			13.8871i			1.47203i	−0.676967	+	0.736014i	$0.736706\pi$
$90$	−0.767836	+	1.18761i	−0.0809370	+	0.125186i
$91$	−2.02490			−0.212267
$92$	−7.66757	+	5.76266i	−0.799400	+	0.600799i
$93$	−7.60264			−0.788357
$94$	4.12298	−	6.37703i	0.425253	−	0.657740i
$95$		−	5.07349i		−	0.520529i
$96$	−1.51928	−	5.44902i	−0.155061	−	0.556138i
$97$		−	6.87156i		−	0.697701i	−0.937178	−	0.348850i	$-0.886572\pi$
$97$		−	6.87156i		−	0.697701i	0.937178	−	0.348850i	$-0.113428\pi$
$98$	7.88939	+	5.10078i	0.796949	+	0.515256i
$99$	−3.20657			−0.322272
$100$	−0.820857	−	1.82379i	−0.0820857	−	0.182379i
$101$	−3.13467			−0.311911			−0.155956	−	0.987764i	$-0.549846\pi$
$101$	−3.13467			−0.311911			−0.155956	+	0.987764i	$0.549846\pi$
$102$	−8.34654	−	5.39634i	−0.826431	−	0.534317i
$103$	12.6006			1.24157			0.620786	−	0.783980i	$-0.286813\pi$
$103$	12.6006			1.24157			0.620786	+	0.783980i	$0.286813\pi$
$104$	1.44215	−	9.47719i	0.141415	−	0.929315i
$105$	−0.597446			−0.0583048
$106$	8.72463	−	13.4944i	0.847411	−	1.31069i
$107$	14.7242			1.42344			0.711721	−	0.702462i	$-0.247916\pi$
$107$	14.7242			1.42344			0.711721	+	0.702462i	$0.247916\pi$
$108$	−1.82379	+	0.820857i	−0.175494	+	0.0789870i
$109$			7.47562i			0.716034i	0.933715	+	0.358017i	$0.116547\pi$
$109$			7.47562i			0.716034i	−0.933715	+	0.358017i	$0.883453\pi$
$110$	2.46212	−	3.80816i	0.234754	−	0.363094i
$111$	2.75487			0.261480
$112$	1.58466	−	1.78883i	0.149736	−	0.169029i
$113$			10.6577i			1.00260i	0.865275	+	0.501298i	$0.167144\pi$
$113$			10.6577i			1.00260i	−0.865275	+	0.501298i	$0.832856\pi$
$114$	3.89560	−	6.02535i	0.364857	−	0.564325i
$115$	−4.67858	+	1.05397i	−0.436280	+	0.0982833i
$116$	−5.83661	−	12.9678i	−0.541916	−	1.20403i
$117$	−3.38926			−0.313338
$118$	0.556566	−	0.860842i	0.0512360	−	0.0792470i
$119$		−	4.19884i		−	0.384907i
$120$	0.425506	−	2.79624i	0.0388432	−	0.255260i
$121$	−0.717935			−0.0652669
$122$	5.59034	−	8.64661i	0.506126	−	0.782827i
$123$		−	2.61478i		−	0.235767i
$124$	13.8656	−	6.24068i	1.24517	−	0.560430i
$125$		−	1.00000i		−	0.0894427i
$126$	−0.709536	−	0.458740i	−0.0632105	−	0.0408678i
$127$			14.4607i			1.28318i	0.767048	+	0.641590i	$0.221725\pi$
$127$			14.4607i			1.28318i	−0.767048	+	0.641590i	$0.778275\pi$
$128$	7.24370	+	8.69073i	0.640259	+	0.768159i
$129$			1.14299i			0.100635i
$130$	2.60240	−	4.02514i	0.228245	−	0.353028i
$131$			0.856508i			0.0748334i	0.999300	+	0.0374167i	$0.0119129\pi$
$131$			0.856508i			0.0748334i	−0.999300	+	0.0374167i	$0.988087\pi$
$132$	5.84809	−	2.63213i	0.509011	−	0.229098i
$133$	3.03113			0.262833
$134$	−3.19597	−	2.06631i	−0.276090	−	0.178502i
$135$	−1.00000			−0.0860663
$136$	19.6519	+	2.99045i	1.68514	+	0.256429i
$137$			1.07940i			0.0922197i	0.998936	+	0.0461098i	$0.0146824\pi$
$137$			1.07940i			0.0922197i	−0.998936	+	0.0461098i	$0.985318\pi$
$138$	−6.36563	−	2.34067i	−0.541878	−	0.199251i
$139$			11.9643i			1.01480i	0.861711	+	0.507400i	$0.169393\pi$
$139$			11.9643i			1.01480i	−0.861711	+	0.507400i	$0.830607\pi$
$140$	1.08961	−	0.490418i	0.0920891	−	0.0414478i
$141$	5.36961			0.452203
$142$	−1.64809	+	2.54911i	−0.138305	+	0.213916i
$143$	10.8679			0.908819
$144$	2.65239	−	2.99413i	0.221032	−	0.249511i
$145$		−	7.11039i		−	0.590486i
$146$	−10.1212	−	6.54369i	−0.837633	−	0.541560i
$147$			6.64306i			0.547910i
$148$	−5.02428	+	2.26135i	−0.412994	+	0.185882i
$149$		−	6.27286i		−	0.513892i	−0.966426	−	0.256946i	$-0.917284\pi$
$149$		−	6.27286i		−	0.513892i	0.966426	−	0.256946i	$-0.0827163\pi$
$150$	0.767836	−	1.18761i	0.0626935	−	0.0969683i
$151$		−	4.90117i		−	0.398852i	−0.979913	−	0.199426i	$-0.936092\pi$
$151$		−	4.90117i		−	0.398852i	0.979913	−	0.199426i	$-0.0639077\pi$
$152$	−2.15880	+	14.1867i	−0.175102	+	1.15069i
$153$		−	7.02799i		−	0.568179i
$154$	2.27517	+	1.47098i	0.183339	+	0.118535i
$155$	7.60264			0.610659
$156$	6.18129	−	2.78210i	0.494899	−	0.222746i
$157$		−	15.5294i		−	1.23938i	−0.784845	−	0.619692i	$-0.787258\pi$
$157$		−	15.5294i		−	1.23938i	0.784845	−	0.619692i	$-0.212742\pi$
$158$	−12.5152	−	8.09154i	−0.995657	−	0.643728i
$159$	11.3626			0.901115
$160$	1.51928	+	5.44902i	0.120109	+	0.430783i
$161$	−0.629691	−	2.79520i	−0.0496266	−	0.220293i
$162$	−1.18761	−	0.767836i	−0.0933078	−	0.0603269i
$163$		−	12.2541i		−	0.959817i	−0.877318	−	0.479909i	$-0.840670\pi$
$163$		−	12.2541i		−	0.959817i	0.877318	−	0.479909i	$-0.159330\pi$
$164$	2.14636	+	4.76879i	0.167602	+	0.372380i
$165$	3.20657			0.249631
$166$	−0.337577	−	0.218256i	−0.0262011	−	0.0169399i
$167$			6.07192i			0.469860i	0.972012	+	0.234930i	$0.0754860\pi$
$167$			6.07192i			0.469860i	−0.972012	+	0.234930i	$0.924514\pi$
$168$	1.67060	+	0.254217i	0.128890	+	0.0196133i
$169$	−1.51289			−0.116376
$170$	8.34654	+	5.39634i	0.640150	+	0.413880i
$171$	5.07349			0.387979
$172$	−0.938233	−	2.08457i	−0.0715396	−	0.158947i
$173$	12.8034			0.973424			0.486712	−	0.873562i	$-0.338196\pi$
$173$	12.8034			0.973424			0.486712	+	0.873562i	$0.338196\pi$
$174$	5.45961	−	8.44440i	0.413892	−	0.640169i
$175$	0.597446			0.0451627
$176$	−8.50506	+	9.60089i	−0.641093	+	0.723694i
$177$	0.724850			0.0544831
$178$	10.6630	−	16.4925i	0.799225	−	1.23616i
$179$			13.0723i			0.977068i	0.872545	+	0.488534i	$0.162468\pi$
$179$			13.0723i			0.977068i	−0.872545	+	0.488534i	$0.837532\pi$
$180$	1.82379	−	0.820857i	0.135937	−	0.0611830i
$181$			8.60430i			0.639552i	0.947493	+	0.319776i	$0.103608\pi$
$181$			8.60430i			0.639552i	−0.947493	+	0.319776i	$0.896392\pi$
$182$	2.40480	+	1.55479i	0.178256	+	0.115249i
$183$	7.28065			0.538201
$184$	13.5309	−	0.956386i	0.997511	−	0.0705057i
$185$	−2.75487			−0.202542
$186$	9.02901	+	5.83758i	0.662039	+	0.428032i
$187$			22.5357i			1.64797i
$188$	−9.79302	+	4.40768i	−0.714229	+	0.321463i
$189$		−	0.597446i		−	0.0434578i
$190$	−3.89560	+	6.02535i	−0.282617	+	0.437125i
$191$	7.02846			0.508561			0.254281	−	0.967130i	$-0.418161\pi$
$191$	7.02846			0.508561			0.254281	+	0.967130i	$0.418161\pi$
$192$	−2.37963	+	7.63789i	−0.171735	+	0.551217i
$193$	−12.6339			−0.909409			−0.454704	−	0.890642i	$-0.650255\pi$
$193$	−12.6339			−0.909409			−0.454704	+	0.890642i	$0.650255\pi$
$194$	−5.27623	+	8.16076i	−0.378811	+	0.585908i
$195$	3.38926			0.242710
$196$	−5.45300	−	12.1155i	−0.389500	−	0.865394i
$197$	−4.35505			−0.310284			−0.155142	−	0.987892i	$-0.549584\pi$
$197$	−4.35505			−0.310284			−0.155142	+	0.987892i	$0.549584\pi$
$198$	3.80816	+	2.46212i	0.270634	+	0.174975i
$199$	9.68856			0.686804			0.343402	−	0.939189i	$-0.388421\pi$
$199$	9.68856			0.686804			0.343402	+	0.939189i	$0.388421\pi$
$200$	−0.425506	+	2.79624i	−0.0300878	+	0.197724i
$201$		−	2.69109i		−	0.189815i
$202$	3.72278	+	2.40691i	0.261934	+	0.169350i
$203$	4.24807			0.298156
$204$	5.76897	+	12.8175i	0.403909	+	0.897408i
$205$			2.61478i			0.182624i
$206$	−14.9646	−	9.67518i	−1.04264	−	0.674102i
$207$	−1.05397	−	4.67858i	−0.0732560	−	0.325184i
$208$	−8.98965	+	10.1479i	−0.623320	+	0.703631i
$209$	−16.2685			−1.12531
$210$	0.709536	+	0.458740i	0.0489626	+	0.0316561i
$211$		−	17.7624i		−	1.22281i	−0.791317	−	0.611406i	$-0.790604\pi$
$211$		−	17.7624i		−	1.22281i	0.791317	−	0.611406i	$-0.209396\pi$
$212$	−20.7230	+	9.32709i	−1.42326	+	0.640587i
$213$	−2.14641			−0.147070
$214$	−17.4867	−	11.3058i	−1.19536	−	0.772846i
$215$		−	1.14299i		−	0.0779515i
$216$	2.79624	+	0.425506i	0.190260	+	0.0289520i
$217$			4.54217i			0.308342i
$218$	5.74005	−	8.87815i	0.388765	−	0.601304i
$219$		−	8.52225i		−	0.575881i
$220$	−5.84809	+	2.63213i	−0.394278	+	0.177458i
$221$			23.8197i			1.60229i
$222$	−3.27172	−	2.11528i	−0.219583	−	0.141969i
$223$		−	29.6580i		−	1.98605i	−0.117914	−	0.993024i	$-0.537621\pi$
$223$		−	29.6580i		−	1.98605i	0.117914	−	0.993024i	$-0.462379\pi$
$224$	−3.25549	+	0.907687i	−0.217517	+	0.0606474i
$225$	1.00000			0.0666667
$226$	8.18339	−	12.6573i	0.544351	−	0.841950i
$227$	−25.7926			−1.71191			−0.855957	−	0.517047i	$-0.827031\pi$
$227$	−25.7926			−1.71191			−0.855957	+	0.517047i	$0.827031\pi$
$228$	−9.25295	+	4.16461i	−0.612792	+	0.275808i
$229$		−	3.91484i		−	0.258700i	−0.991599	−	0.129350i	$-0.958711\pi$
$229$		−	3.91484i		−	0.258700i	0.991599	−	0.129350i	$-0.0412890\pi$
$230$	6.36563	+	2.34067i	0.419737	+	0.154339i
$231$			1.91575i			0.126047i
$232$	−3.02552	+	19.8823i	−0.198635	+	1.30534i
$233$	23.0683			1.51126			0.755628	−	0.655001i	$-0.227332\pi$
$233$	23.0683			1.51126			0.755628	+	0.655001i	$0.227332\pi$
$234$	4.02514	+	2.60240i	0.263132	+	0.170124i
$235$	−5.36961			−0.350275
$236$	−1.32197	+	0.594998i	−0.0860530	+	0.0387311i
$237$		−	10.5381i		−	0.684524i
$238$	−3.22402	+	4.98661i	−0.208982	+	0.323234i
$239$		−	21.4690i		−	1.38872i	−0.719630	−	0.694358i	$-0.755688\pi$
$239$		−	21.4690i		−	1.38872i	0.719630	−	0.694358i	$-0.244312\pi$
$240$	−2.65239	+	2.99413i	−0.171211	+	0.193270i
$241$		−	1.57916i		−	0.101723i	−0.998706	−	0.0508614i	$-0.983803\pi$
$241$		−	1.57916i		−	0.101723i	0.998706	−	0.0508614i	$-0.0161967\pi$
$242$	0.852631	+	0.551256i	0.0548092	+	0.0354361i
$243$		−	1.00000i		−	0.0641500i
$244$	−13.2783	+	5.97637i	−0.850059	+	0.382598i
$245$		−	6.64306i		−	0.424409i
$246$	−2.00772	+	3.10535i	−0.128008	+	0.197990i
$247$	−17.1954			−1.09412
$248$	−21.2588	−	3.23497i	−1.34993	−	0.205421i
$249$		−	0.284248i		−	0.0180135i
$250$	−0.767836	+	1.18761i	−0.0485622	+	0.0751113i
$251$	−8.94836			−0.564816			−0.282408	−	0.959294i	$-0.591133\pi$
$251$	−8.94836			−0.564816			−0.282408	+	0.959294i	$0.591133\pi$
$252$	0.490418	+	1.08961i	0.0308934	+	0.0686392i
$253$	3.37963	+	15.0022i	0.212475	+	0.943179i
$254$	11.1034	−	17.1738i	0.696692	−	1.07758i
$255$			7.02799i			0.440110i
$256$	−1.92967	−	15.8832i	−0.120604	−	0.992701i
$257$	−10.1016			−0.630118			−0.315059	−	0.949072i	$-0.602024\pi$
$257$	−10.1016			−0.630118			−0.315059	+	0.949072i	$0.602024\pi$
$258$	0.877631	−	1.35744i	0.0546389	−	0.0845102i
$259$		−	1.64588i		−	0.102270i
$260$	−6.18129	+	2.78210i	−0.383347	+	0.172539i
$261$	7.11039			0.440122
$262$	0.657657	−	1.01720i	0.0406302	−	0.0628429i
$263$	−19.8604			−1.22464			−0.612322	−	0.790608i	$-0.709764\pi$
$263$	−19.8604			−1.22464			−0.612322	+	0.790608i	$0.709764\pi$
$264$	−8.96632	−	1.36441i	−0.551839	−	0.0839739i
$265$	−11.3626			−0.698001
$266$	−3.59982	−	2.32741i	−0.220719	−	0.142703i
$267$	13.8871			0.849875
$268$	2.20900	+	4.90797i	0.134936	+	0.299802i
$269$	25.7428			1.56957			0.784784	−	0.619770i	$-0.212774\pi$
$269$	25.7428			1.56957			0.784784	+	0.619770i	$0.212774\pi$
$270$	1.18761	+	0.767836i	0.0722759	+	0.0467290i
$271$		−	11.7790i		−	0.715523i	−0.933813	−	0.357762i	$-0.883540\pi$
$271$		−	11.7790i		−	0.715523i	0.933813	−	0.357762i	$-0.116460\pi$
$272$	−21.0427	−	18.6410i	−1.27590	−	1.13027i
$273$			2.02490i			0.122553i
$274$	0.828804	−	1.28192i	0.0500699	−	0.0774433i
$275$	−3.20657			−0.193363
$276$	5.76266	+	7.66757i	0.346872	+	0.461534i
$277$	28.6106			1.71904			0.859522	−	0.511099i	$-0.170761\pi$
$277$	28.6106			1.71904			0.859522	+	0.511099i	$0.170761\pi$
$278$	9.18663	−	14.2090i	0.550978	−	0.852199i
$279$			7.60264i			0.455158i
$280$	−1.67060	−	0.254217i	−0.0998375	−	0.0151924i
$281$			11.6562i			0.695349i	0.937615	+	0.347674i	$0.113029\pi$
$281$			11.6562i			0.695349i	−0.937615	+	0.347674i	$0.886971\pi$
$282$	−6.37703	−	4.12298i	−0.379746	−	0.245520i
$283$	−29.7129			−1.76625			−0.883125	−	0.469138i	$-0.844565\pi$
$283$	−29.7129			−1.76625			−0.883125	+	0.469138i	$0.844565\pi$
$284$	3.91459	−	1.76189i	0.232288	−	0.104549i
$285$	−5.07349			−0.300527
$286$	−12.9069	−	8.34476i	−0.763199	−	0.493436i
$287$	−1.56219			−0.0922131
$288$	−5.44902	+	1.51928i	−0.321086	+	0.0895243i
$289$	−32.3926			−1.90545
$290$	−5.45961	+	8.44440i	−0.320599	+	0.495872i
$291$	−6.87156			−0.402818
$292$	6.99555	+	15.5428i	0.409384	+	0.909572i
$293$		−	23.5616i		−	1.37648i	−0.725481	−	0.688242i	$-0.758383\pi$
$293$		−	23.5616i		−	1.37648i	0.725481	−	0.688242i	$-0.241617\pi$
$294$	5.10078	−	7.88939i	0.297483	−	0.460119i
$295$	−0.724850			−0.0422024
$296$	7.70326	+	1.17221i	0.447743	+	0.0681335i
$297$			3.20657i			0.186064i
$298$	−4.81652	+	7.44974i	−0.279014	+	0.431552i
$299$	3.57219	+	15.8570i	0.206585	+	0.917031i
$300$	−1.82379	+	0.820857i	−0.105296	+	0.0473922i
$301$	0.682877			0.0393604
$302$	−3.76329	+	5.82070i	−0.216553	+	0.334944i
$303$			3.13467i			0.180082i
$304$	13.4569	−	15.1907i	0.771804	−	0.871246i
$305$	−7.28065			−0.416889
$306$	−5.39634	+	8.34654i	−0.308488	+	0.477140i
$307$			17.2091i			0.982178i	0.871110	+	0.491089i	$0.163401\pi$
$307$			17.2091i			0.982178i	−0.871110	+	0.491089i	$0.836599\pi$
$308$	−1.57256	−	3.49392i	−0.0896047	−	0.199084i
$309$		−	12.6006i		−	0.716822i
$310$	−9.02901	−	5.83758i	−0.512813	−	0.331552i
$311$			20.3547i			1.15421i	0.816669	+	0.577106i	$0.195818\pi$
$311$			20.3547i			1.15421i	−0.816669	+	0.577106i	$0.804182\pi$
$312$	−9.47719	−	1.44215i	−0.536540	−	0.0816459i
$313$			34.4686i			1.94828i	0.225939	+	0.974142i	$0.427455\pi$
$313$			34.4686i			1.94828i	−0.225939	+	0.974142i	$0.572545\pi$
$314$	−11.9241	+	18.4430i	−0.672913	+	1.04080i
$315$			0.597446i			0.0336623i
$316$	8.65028	+	19.2193i	0.486616	+	1.08117i
$317$	−23.3763			−1.31294			−0.656471	−	0.754351i	$-0.727952\pi$
$317$	−23.3763			−1.31294			−0.656471	+	0.754351i	$0.727952\pi$
$318$	−13.4944	−	8.72463i	−0.756730	−	0.489253i
$319$	−22.7999			−1.27655
$320$	2.37963	−	7.63789i	0.133026	−	0.426971i
$321$		−	14.7242i		−	0.821825i
$322$	−1.39843	+	3.80312i	−0.0779312	+	0.211940i
$323$		−	35.6564i		−	1.98398i
$324$	0.820857	+	1.82379i	0.0456032	+	0.101321i
$325$	−3.38926			−0.188003
$326$	−9.40916	+	14.5532i	−0.521125	+	0.806026i
$327$	7.47562			0.413403
$328$	1.11260	−	7.31154i	0.0614333	−	0.403712i
$329$		−	3.20805i		−	0.176866i
$330$	−3.80816	−	2.46212i	−0.209633	−	0.135535i
$331$			11.4719i			0.630554i	0.949000	+	0.315277i	$0.102097\pi$
$331$			11.4719i			0.630554i	−0.949000	+	0.315277i	$0.897903\pi$
$332$	0.233327	+	0.518408i	0.0128055	+	0.0284513i
$333$		−	2.75487i		−	0.150966i
$334$	4.66224	−	7.21111i	0.255106	−	0.394574i
$335$			2.69109i			0.147030i
$336$	−1.78883	−	1.58466i	−0.0975888	−	0.0864502i
$337$			33.9101i			1.84720i	0.383357	+	0.923600i	$0.374768\pi$
$337$			33.9101i			1.84720i	−0.383357	+	0.923600i	$0.625232\pi$
$338$	1.79673	+	1.16165i	0.0977292	+	0.0631854i
$339$	10.6577			0.578849
$340$	−5.76897	−	12.8175i	−0.312866	−	0.695129i
$341$		−	24.3784i		−	1.32016i
$342$	−6.02535	−	3.89560i	−0.325813	−	0.210650i
$343$	8.15099			0.440112
$344$	−0.486351	+	3.19608i	−0.0262223	+	0.172321i
$345$	1.05397	+	4.67858i	0.0567439	+	0.251886i
$346$	−15.2055	−	9.83090i	−0.817453	−	0.528513i
$347$		−	7.57551i		−	0.406675i	−0.979109	−	0.203337i	$-0.934821\pi$
$347$		−	7.57551i		−	0.406675i	0.979109	−	0.203337i	$-0.0651788\pi$
$348$	−12.9678	+	5.83661i	−0.695149	+	0.312875i
$349$	21.7478			1.16413			0.582066	−	0.813142i	$-0.302245\pi$
$349$	21.7478			1.16413			0.582066	+	0.813142i	$0.302245\pi$
$350$	−0.709536	−	0.458740i	−0.0379263	−	0.0245207i
$351$			3.38926i			0.180906i
$352$	17.4726	−	4.87166i	0.931295	−	0.259661i
$353$	24.0890			1.28213			0.641065	−	0.767487i	$-0.278493\pi$
$353$	24.0890			1.28213			0.641065	+	0.767487i	$0.278493\pi$
$354$	−0.860842	−	0.556566i	−0.0457533	−	0.0295811i
$355$	2.14641			0.113920
$356$	−25.3271	+	11.3993i	−1.34233	+	0.604162i
$357$	−4.19884			−0.222226
$358$	10.0374	−	15.5248i	0.530491	−	0.820513i
$359$	10.9481			0.577819			0.288910	−	0.957356i	$-0.406707\pi$
$359$	10.9481			0.577819			0.288910	+	0.957356i	$0.406707\pi$
$360$	−2.79624	−	0.425506i	−0.147375	−	0.0224262i
$361$	6.74026			0.354751
$362$	6.60669	−	10.2186i	0.347240	−	0.537077i
$363$			0.717935i			0.0376818i
$364$	−1.66215	−	3.69299i	−0.0871206	−	0.193565i
$365$			8.52225i			0.446075i
$366$	−8.64661	−	5.59034i	−0.451965	−	0.292212i
$367$	−37.2487			−1.94436			−0.972182	−	0.234226i	$-0.924744\pi$
$367$	−37.2487			−1.94436			−0.972182	+	0.234226i	$0.924744\pi$
$368$	−16.8038	−	9.25369i	−0.875961	−	0.482382i
$369$	−2.61478			−0.136120
$370$	3.27172	+	2.11528i	0.170089	+	0.109968i
$371$		−	6.78856i		−	0.352444i
$372$	−6.24068	−	13.8656i	−0.323564	−	0.718897i
$373$		−	19.8958i		−	1.03016i	−0.857141	−	0.515082i	$-0.827762\pi$
$373$		−	19.8958i		−	1.03016i	0.857141	−	0.515082i	$-0.172238\pi$
$374$	17.3037	−	26.7637i	0.894754	−	1.38392i
$375$	−1.00000			−0.0516398
$376$	15.0147	+	2.28480i	0.774324	+	0.117830i
$377$	−24.0990			−1.24116
$378$	−0.458740	+	0.709536i	−0.0235951	+	0.0364946i
$379$	−33.6078			−1.72632			−0.863158	−	0.504933i	$-0.831517\pi$
$379$	−33.6078			−1.72632			−0.863158	+	0.504933i	$0.831517\pi$
$380$	9.25295	−	4.16461i	0.474666	−	0.213640i
$381$	14.4607			0.740845
$382$	−8.34710	−	5.39670i	−0.427075	−	0.276119i
$383$	3.78312			0.193308			0.0966542	−	0.995318i	$-0.469186\pi$
$383$	3.78312			0.193308			0.0966542	+	0.995318i	$0.469186\pi$
$384$	8.69073	−	7.24370i	0.443497	−	0.369654i
$385$		−	1.91575i		−	0.0976357i
$386$	15.0042	+	9.70076i	0.763694	+	0.493756i
$387$	1.14299			0.0581016
$388$	12.5322	−	5.64056i	0.636228	−	0.286356i
$389$		−	19.7742i		−	1.00259i	−0.865275	−	0.501297i	$-0.832856\pi$
$389$		−	19.7742i		−	1.00259i	0.865275	−	0.501297i	$-0.167144\pi$
$390$	−4.02514	−	2.60240i	−0.203821	−	0.131778i
$391$	−32.8810	+	7.40730i	−1.66287	+	0.374603i
$392$	−2.82666	+	18.5756i	−0.142768	+	0.938208i
$393$	0.856508			0.0432051
$394$	5.17212	+	3.34396i	0.260567	+	0.168466i
$395$			10.5381i			0.530230i
$396$	−2.63213	−	5.84809i	−0.132270	−	0.293878i
$397$	16.8524			0.845800			0.422900	−	0.906176i	$-0.361012\pi$
$397$	16.8524			0.845800			0.422900	+	0.906176i	$0.361012\pi$
$398$	−11.5063	−	7.43922i	−0.576758	−	0.372895i
$399$		−	3.03113i		−	0.151747i
$400$	2.65239	−	2.99413i	0.132619	−	0.149707i
$401$		−	16.6908i		−	0.833497i	−0.909022	−	0.416749i	$-0.863170\pi$
$401$		−	16.6908i		−	0.833497i	0.909022	−	0.416749i	$-0.136830\pi$
$402$	−2.06631	+	3.19597i	−0.103058	+	0.159401i
$403$		−	25.7674i		−	1.28356i
$404$	−2.57312	−	5.71697i	−0.128017	−	0.284430i
$405$			1.00000i			0.0496904i
$406$	−5.04507	−	3.26182i	−0.250383	−	0.161882i
$407$			8.83366i			0.437868i
$408$	2.99045	−	19.6519i	0.148050	−	0.972915i
$409$	2.27170			0.112328			0.0561642	−	0.998422i	$-0.482113\pi$
$409$	2.27170			0.112328			0.0561642	+	0.998422i	$0.482113\pi$
$410$	2.00772	−	3.10535i	0.0991542	−	0.153362i
$411$	1.07940			0.0532430
$412$	10.3433	+	22.9808i	0.509577	+	1.13218i
$413$		−	0.433059i		−	0.0213094i
$414$	−2.34067	+	6.36563i	−0.115038	+	0.312854i
$415$			0.284248i			0.0139532i
$416$	18.4682	−	5.14923i	0.905476	−	0.252462i
$417$	11.9643			0.585895
$418$	19.3207	+	12.4915i	0.945005	+	0.610980i
$419$	−17.3533			−0.847762			−0.423881	−	0.905718i	$-0.639333\pi$
$419$	−17.3533			−0.847762			−0.423881	+	0.905718i	$0.639333\pi$
$420$	−0.490418	−	1.08961i	−0.0239299	−	0.0531677i
$421$		−	28.7238i		−	1.39991i	−0.714185	−	0.699957i	$-0.753203\pi$
$421$		−	28.7238i		−	1.39991i	0.714185	−	0.699957i	$-0.246797\pi$
$422$	−13.6386	+	21.0949i	−0.663916	+	1.02688i
$423$		−	5.36961i		−	0.261079i
$424$	31.7726	+	4.83487i	1.54301	+	0.234802i
$425$		−	7.02799i		−	0.340907i
$426$	2.54911	+	1.64809i	0.123505	+	0.0798502i
$427$		−	4.34980i		−	0.210501i
$428$	12.0865	+	26.8538i	0.584221	+	1.29803i
$429$		−	10.8679i		−	0.524707i
$430$	−0.877631	+	1.35744i	−0.0423231	+	0.0654613i
$431$	−8.23520			−0.396676			−0.198338	−	0.980134i	$-0.563554\pi$
$431$	−8.23520			−0.396676			−0.198338	+	0.980134i	$0.563554\pi$
$432$	−2.99413	−	2.65239i	−0.144055	−	0.127613i
$433$			12.9393i			0.621823i	0.950439	+	0.310911i	$0.100634\pi$
$433$			12.9393i			0.621823i	−0.950439	+	0.310911i	$0.899366\pi$
$434$	3.48764	−	5.39434i	0.167412	−	0.258937i
$435$	−7.11039			−0.340917
$436$	−13.6339	+	6.13641i	−0.652946	+	0.293881i
$437$	−5.34731	−	23.7367i	−0.255796	−	1.13548i
$438$	−6.54369	+	10.1212i	−0.312670	+	0.483607i
$439$			7.74111i			0.369463i	0.982789	+	0.184732i	$0.0591416\pi$
$439$			7.74111i			0.369463i	−0.982789	+	0.184732i	$0.940858\pi$
$440$	8.96632	+	1.36441i	0.427453	+	0.0650459i
$441$	6.64306			0.316336
$442$	18.2896	−	28.2886i	0.869949	−	1.34555i
$443$		−	19.4137i		−	0.922375i	−0.887303	−	0.461187i	$-0.847424\pi$
$443$		−	19.4137i		−	0.922375i	0.887303	−	0.461187i	$-0.152576\pi$
$444$	2.26135	+	5.02428i	0.107319	+	0.238442i
$445$	−13.8871			−0.658311
$446$	−22.7725	+	35.2223i	−1.07831	+	1.66782i
$447$	−6.27286			−0.296696
$448$	4.56323	+	1.42170i	0.215592	+	0.0671691i
$449$	6.46413			0.305061			0.152531	−	0.988299i	$-0.451258\pi$
$449$	6.46413			0.305061			0.152531	+	0.988299i	$0.451258\pi$
$450$	−1.18761	−	0.767836i	−0.0559847	−	0.0361961i
$451$	8.38446			0.394809
$452$	−19.4374	+	8.74847i	−0.914259	+	0.411493i
$453$	−4.90117			−0.230277
$454$	30.6317	+	19.8045i	1.43761	+	0.929470i
$455$		−	2.02490i		−	0.0949289i
$456$	14.1867	+	2.15880i	0.664352	+	0.101095i
$457$			14.0511i			0.657281i	0.944455	+	0.328640i	$0.106590\pi$
$457$			14.0511i			0.657281i	−0.944455	+	0.328640i	$0.893410\pi$
$458$	−3.00595	+	4.64932i	−0.140459	+	0.217248i
$459$	−7.02799			−0.328038
$460$	−5.76266	−	7.66757i	−0.268686	−	0.357503i
$461$	11.1513			0.519368			0.259684	−	0.965694i	$-0.416382\pi$
$461$	11.1513			0.519368			0.259684	+	0.965694i	$0.416382\pi$
$462$	1.47098	−	2.27517i	0.0684362	−	0.105851i
$463$		−	7.29089i		−	0.338836i	−0.985544	−	0.169418i	$-0.945811\pi$
$463$		−	7.29089i		−	0.338836i	0.985544	−	0.169418i	$-0.0541888\pi$
$464$	18.8595	−	21.2895i	0.875531	−	0.988338i
$465$		−	7.60264i		−	0.352564i
$466$	−27.3963	−	17.7127i	−1.26911	−	0.820524i
$467$	−18.8832			−0.873808			−0.436904	−	0.899508i	$-0.643925\pi$
$467$	−18.8832			−0.873808			−0.436904	+	0.899508i	$0.643925\pi$
$468$	−2.78210	−	6.18129i	−0.128603	−	0.285730i
$469$	−1.60778			−0.0742403
$470$	6.37703	+	4.12298i	0.294150	+	0.190179i
$471$	−15.5294			−0.715559
$472$	2.02685	+	0.308428i	0.0932935	+	0.0141966i
$473$	−3.66508			−0.168521
$474$	−8.09154	+	12.5152i	−0.371657	+	0.574843i
$475$	5.07349			0.232788
$476$	7.65779	−	3.44665i	0.350994	−	0.157977i
$477$		−	11.3626i		−	0.520259i
$478$	−16.4847	+	25.4969i	−0.753992	+	1.16620i
$479$	10.7974			0.493344			0.246672	−	0.969099i	$-0.420663\pi$
$479$	10.7974			0.493344			0.246672	+	0.969099i	$0.420663\pi$
$480$	5.44902	−	1.51928i	0.248712	−	0.0693452i
$481$			9.33697i			0.425729i
$482$	−1.21254	+	1.87544i	−0.0552296	+	0.0854239i
$483$	−2.79520	+	0.629691i	−0.127186	+	0.0286519i
$484$	−0.589322	−	1.30936i	−0.0267874	−	0.0595164i
$485$	6.87156			0.312021
$486$	−0.767836	+	1.18761i	−0.0348297	+	0.0538713i
$487$			19.1032i			0.865649i	0.901478	+	0.432825i	$0.142483\pi$
$487$			19.1032i			0.865649i	−0.901478	+	0.432825i	$0.857517\pi$
$488$	20.3584	+	3.09796i	0.921583	+	0.140238i
$489$	−12.2541			−0.554151
$490$	−5.10078	+	7.88939i	−0.230430	+	0.356406i
$491$		−	18.7244i		−	0.845020i	−0.906358	−	0.422510i	$-0.861149\pi$
$491$		−	18.7244i		−	0.845020i	0.906358	−	0.422510i	$-0.138851\pi$
$492$	4.76879	−	2.14636i	0.214994	−	0.0967653i
$493$		−	49.9717i		−	2.25061i
$494$	20.4215	+	13.2032i	0.918806	+	0.594041i
$495$		−	3.20657i		−	0.144124i
$496$	22.7633	+	20.1652i	1.02210	+	0.905442i
$497$			1.28236i			0.0575219i
$498$	−0.218256	+	0.337577i	−0.00978028	+	0.0151272i
$499$		−	19.3230i		−	0.865015i	−0.901630	−	0.432508i	$-0.857629\pi$
$499$		−	19.3230i		−	0.865015i	0.901630	−	0.432508i	$-0.142371\pi$
$500$	1.82379	−	0.820857i	0.0815622	−	0.0367098i
$501$	6.07192			0.271274
$502$	10.6272	+	6.87087i	0.474315	+	0.306662i
$503$	−14.0150			−0.624898			−0.312449	−	0.949935i	$-0.601149\pi$
$503$	−14.0150			−0.624898			−0.312449	+	0.949935i	$0.601149\pi$
$504$	0.254217	−	1.67060i	0.0113237	−	0.0744145i
$505$		−	3.13467i		−	0.139491i
$506$	7.50552	−	20.4118i	0.333661	−	0.907416i
$507$			1.51289i			0.0671898i
$508$	−26.3732	+	11.8702i	−1.17012	+	0.526654i
$509$	−21.5384			−0.954674			−0.477337	−	0.878720i	$-0.658398\pi$
$509$	−21.5384			−0.954674			−0.477337	+	0.878720i	$0.658398\pi$
$510$	5.39634	−	8.34654i	0.238954	−	0.369591i
$511$	−5.09159			−0.225239
$512$	−9.90399	+	20.3448i	−0.437699	+	0.899122i
$513$		−	5.07349i		−	0.224000i
$514$	11.9968	+	7.75634i	0.529154	+	0.342117i
$515$			12.6006i			0.555248i
$516$	−2.08457	+	0.938233i	−0.0917683	+	0.0413034i
$517$			17.2180i			0.757247i
$518$	−1.26377	+	1.95467i	−0.0555268	+	0.0858835i
$519$		−	12.8034i		−	0.562007i
$520$	9.47719	+	1.44215i	0.415602	+	0.0632426i
$521$			37.6407i			1.64907i	0.565813	+	0.824534i	$0.308563\pi$
$521$			37.6407i			1.64907i	−0.565813	+	0.824534i	$0.691437\pi$
$522$	−8.44440	−	5.45961i	−0.369601	−	0.238961i
$523$	20.8903			0.913471			0.456735	−	0.889603i	$-0.349019\pi$
$523$	20.8903			0.913471			0.456735	+	0.889603i	$0.349019\pi$
$524$	−1.56209	+	0.703070i	−0.0682401	+	0.0307138i
$525$		−	0.597446i		−	0.0260747i
$526$	23.5865	+	15.2495i	1.02842	+	0.664911i
$527$	53.4313			2.32750
$528$	9.60089	+	8.50506i	0.417825	+	0.370135i
$529$	−20.7783	+	9.86218i	−0.903404	+	0.428791i
$530$	13.4944	+	8.72463i	0.586160	+	0.378974i
$531$		−	0.724850i		−	0.0314558i
$532$	2.48813	+	5.52814i	0.107874	+	0.239675i
$533$	8.86217			0.383863
$534$	−16.4925	−	10.6630i	−0.713700	−	0.461433i
$535$			14.7242i			0.636583i
$536$	1.14507	−	7.52492i	0.0494597	−	0.325027i
$537$	13.0723			0.564110
$538$	−30.5725	−	19.7663i	−1.31808	−	0.852184i
$539$	−21.3014			−0.917516
$540$	−0.820857	−	1.82379i	−0.0353240	−	0.0784832i
$541$	−13.4360			−0.577658			−0.288829	−	0.957381i	$-0.593266\pi$
$541$	−13.4360			−0.577658			−0.288829	+	0.957381i	$0.593266\pi$
$542$	−9.04434	+	13.9889i	−0.388487	+	0.600875i
$543$	8.60430			0.369246
$544$	10.6775	+	38.2956i	0.457793	+	1.64191i
$545$	−7.47562			−0.320220
$546$	1.55479	−	2.40480i	0.0665390	−	0.102916i
$547$		−	23.4700i		−	1.00350i	−0.865011	−	0.501752i	$-0.832689\pi$
$547$		−	23.4700i		−	1.00350i	0.865011	−	0.501752i	$-0.167311\pi$
$548$	−1.96860	+	0.886036i	−0.0840944	+	0.0378496i
$549$		−	7.28065i		−	0.310731i
$550$	3.80816	+	2.46212i	0.162381	+	0.104985i
$551$	36.0745			1.53682
$552$	−0.956386	−	13.5309i	−0.0407065	−	0.575913i
$553$	−6.29595			−0.267731
$554$	−33.9783	−	21.9682i	−1.44360	−	0.933341i
$555$			2.75487i			0.116938i
$556$	−21.8204	+	9.82099i	−0.925389	+	0.416503i
$557$			13.4142i			0.568380i	0.958768	+	0.284190i	$0.0917246\pi$
$557$			13.4142i			0.568380i	−0.958768	+	0.284190i	$0.908275\pi$
$558$	5.83758	−	9.02901i	0.247124	−	0.382228i
$559$	−3.87390			−0.163849
$560$	1.78883	+	1.58466i	0.0755920	+	0.0669641i
$561$	22.5357			0.951458
$562$	8.95002	−	13.8430i	0.377534	−	0.583933i
$563$	17.3504			0.731231			0.365616	−	0.930766i	$-0.380858\pi$
$563$	17.3504			0.731231			0.365616	+	0.930766i	$0.380858\pi$
$564$	4.40768	+	9.79302i	0.185597	+	0.412360i
$565$	−10.6577			−0.448374
$566$	35.2875	+	22.8146i	1.48324	+	0.958971i
$567$	−0.597446			−0.0250904
$568$	−6.00187	−	0.913311i	−0.251833	−	0.0383217i
$569$		−	37.8528i		−	1.58687i	−0.608652	−	0.793437i	$-0.708290\pi$
$569$		−	37.8528i		−	1.58687i	0.608652	−	0.793437i	$-0.291710\pi$
$570$	6.02535	+	3.89560i	0.252374	+	0.163169i
$571$	7.85120			0.328562			0.164281	−	0.986414i	$-0.447470\pi$
$571$	7.85120			0.328562			0.164281	+	0.986414i	$0.447470\pi$
$572$	8.92099	+	19.8207i	0.373005	+	0.828746i
$573$		−	7.02846i		−	0.293618i
$574$	1.85528	+	1.19950i	0.0774378	+	0.0500663i
$575$	−1.05397	−	4.67858i	−0.0439536	−	0.195110i
$576$	7.63789	+	2.37963i	0.318245	+	0.0991514i
$577$	39.2629			1.63454			0.817268	−	0.576258i	$-0.195488\pi$
$577$	39.2629			1.63454			0.817268	+	0.576258i	$0.195488\pi$
$578$	38.4699	+	24.8722i	1.60014	+	1.03455i
$579$			12.6339i			0.525047i
$580$	12.9678	−	5.83661i	0.538460	−	0.242352i
$581$	−0.169823			−0.00704544
$582$	8.16076	+	5.27623i	0.338274	+	0.218707i
$583$			36.4350i			1.50898i
$584$	3.62627	−	23.8302i	0.150056	−	0.986103i
$585$		−	3.38926i		−	0.140129i
$586$	−18.0915	+	27.9821i	−0.747351	+	1.15593i
$587$			3.34988i			0.138264i	0.997608	+	0.0691321i	$0.0220230\pi$
$587$			3.34988i			0.138264i	−0.997608	+	0.0691321i	$0.977977\pi$
$588$	−12.1155	+	5.45300i	−0.499635	+	0.224878i
$589$			38.5719i			1.58933i
$590$	0.860842	+	0.556566i	0.0354403	+	0.0229134i
$591$			4.35505i			0.179143i
$592$	−8.24843	−	7.30697i	−0.339009	−	0.300315i
$593$	−26.3464			−1.08192			−0.540958	−	0.841049i	$-0.681938\pi$
$593$	−26.3464			−1.08192			−0.540958	+	0.841049i	$0.681938\pi$
$594$	2.46212	−	3.80816i	0.101022	−	0.156251i
$595$	4.19884			0.172136
$596$	11.4403	−	5.14912i	0.468615	−	0.210916i
$597$		−	9.68856i		−	0.396527i
$598$	7.93316	−	21.5748i	0.324411	−	0.882259i
$599$			20.8312i			0.851142i	0.904925	+	0.425571i	$0.139927\pi$
$599$			20.8312i			0.851142i	−0.904925	+	0.425571i	$0.860073\pi$
$600$	2.79624	+	0.425506i	0.114156	+	0.0173712i
$601$	8.55626			0.349017			0.174508	−	0.984656i	$-0.444166\pi$
$601$	8.55626			0.349017			0.174508	+	0.984656i	$0.444166\pi$
$602$	−0.810994	−	0.524337i	−0.0330537	−	0.0213704i
$603$	−2.69109			−0.109590
$604$	8.93868	−	4.02316i	0.363710	−	0.163700i
$605$		−	0.717935i		−	0.0291882i
$606$	2.40691	−	3.72278i	0.0977741	−	0.151228i
$607$			11.7713i			0.477782i	0.971046	+	0.238891i	$0.0767839\pi$
$607$			11.7713i			0.477782i	−0.971046	+	0.238891i	$0.923216\pi$
$608$	−27.6455	+	7.70804i	−1.12117	+	0.312602i
$609$		−	4.24807i		−	0.172141i
$610$	8.64661	+	5.59034i	0.350091	+	0.226346i
$611$			18.1990i			0.736254i
$612$	12.8175	−	5.76897i	0.518118	−	0.233197i
$613$		−	5.33734i		−	0.215573i	−0.994174	−	0.107787i	$-0.965624\pi$
$613$		−	5.33734i		−	0.215573i	0.994174	−	0.107787i	$-0.0343763\pi$
$614$	13.2138	−	20.4378i	0.533265	−	0.824804i
$615$	2.61478			0.105438
$616$	−0.815164	+	5.35689i	−0.0328439	+	0.215835i
$617$		−	36.5457i		−	1.47128i	−0.677375	−	0.735638i	$-0.736883\pi$
$617$		−	36.5457i		−	1.47128i	0.677375	−	0.735638i	$-0.263117\pi$
$618$	−9.67518	+	14.9646i	−0.389193	+	0.601966i
$619$	30.2554			1.21607			0.608034	−	0.793911i	$-0.291958\pi$
$619$	30.2554			1.21607			0.608034	+	0.793911i	$0.291958\pi$
$620$	6.24068	+	13.8656i	0.250632	+	0.556855i
$621$	−4.67858	+	1.05397i	−0.187745	+	0.0422944i
$622$	15.6291	−	24.1736i	0.626670	−	0.969273i
$623$		−	8.29678i		−	0.332403i
$624$	10.1479	+	8.98965i	0.406241	+	0.359874i
$625$	1.00000			0.0400000
$626$	26.4663	−	40.9355i	1.05780	−	1.63611i
$627$			16.2685i			0.649700i
$628$	28.3224	−	12.7474i	1.13019	−	0.508678i
$629$	−19.3612			−0.771980
$630$	0.458740	−	0.709536i	0.0182767	−	0.0282686i
$631$	28.2748			1.12560			0.562802	−	0.826592i	$-0.309723\pi$
$631$	28.2748			1.12560			0.562802	+	0.826592i	$0.309723\pi$
$632$	4.48403	−	29.4671i	0.178365	−	1.17214i
$633$	−17.7624			−0.705991
$634$	27.7620	+	17.9491i	1.10257	+	0.712852i
$635$	−14.4607			−0.573856
$636$	9.32709	+	20.7230i	0.369843	+	0.821720i
$637$	−22.5151			−0.892080
$638$	27.0775	+	17.5066i	1.07201	+	0.693093i
$639$			2.14641i			0.0849106i
$640$	−8.69073	+	7.24370i	−0.343531	+	0.286332i
$641$		−	5.02194i		−	0.198355i	−0.995070	−	0.0991774i	$-0.968379\pi$
$641$		−	5.02194i		−	0.198355i	0.995070	−	0.0991774i	$-0.0316211\pi$
$642$	−11.3058	+	17.4867i	−0.446203	+	0.690144i
$643$	−43.1085			−1.70003			−0.850016	−	0.526756i	$-0.823408\pi$
$643$	−43.1085			−1.70003			−0.850016	+	0.526756i	$0.823408\pi$
$644$	4.58096	−	3.44288i	0.180515	−	0.135669i
$645$	−1.14299			−0.0450053
$646$	−27.3783	+	42.3461i	−1.07718	+	1.66608i
$647$		−	46.2260i		−	1.81733i	−0.417525	−	0.908666i	$-0.637102\pi$
$647$		−	46.2260i		−	1.81733i	0.417525	−	0.908666i	$-0.362898\pi$
$648$	0.425506	−	2.79624i	0.0167155	−	0.109847i
$649$			2.32428i			0.0912359i
$650$	4.02514	+	2.60240i	0.157879	+	0.102074i
$651$	4.54217			0.178022
$652$	22.3489	−	10.0589i	0.875251	−	0.393936i
$653$	48.4090			1.89439			0.947195	−	0.320657i	$-0.103904\pi$
$653$	48.4090			1.89439			0.947195	+	0.320657i	$0.103904\pi$
$654$	−8.87815	−	5.74005i	−0.347163	−	0.224454i
$655$	−0.856508			−0.0334665
$656$	−6.93541	+	7.82899i	−0.270782	+	0.305671i
$657$	−8.52225			−0.332485
$658$	−2.46326	+	3.80993i	−0.0960278	+	0.148527i
$659$	6.77356			0.263860			0.131930	−	0.991259i	$-0.457883\pi$
$659$	6.77356			0.263860			0.131930	+	0.991259i	$0.457883\pi$
$660$	2.63213	+	5.84809i	0.102456	+	0.227637i
$661$			6.01776i			0.234064i	0.993128	+	0.117032i	$0.0373380\pi$
$661$			6.01776i			0.234064i	−0.993128	+	0.117032i	$0.962662\pi$
$662$	8.80855	−	13.6242i	0.342354	−	0.529520i
$663$	23.8197			0.925081
$664$	0.120949	−	0.794825i	0.00469375	−	0.0308452i
$665$			3.03113i			0.117542i
$666$	−2.11528	+	3.27172i	−0.0819656	+	0.126777i
$667$	−7.49415	−	33.2666i	−0.290174	−	1.28809i
$668$	−11.0739	+	4.98418i	−0.428462	+	0.192844i
$669$	−29.6580			−1.14665
$670$	2.06631	−	3.19597i	0.0798286	−	0.123471i
$671$			23.3459i			0.901258i
$672$	0.907687	+	3.25549i	0.0350148	+	0.125583i
$673$	16.3612			0.630676			0.315338	−	0.948979i	$-0.397882\pi$
$673$	16.3612			0.630676			0.315338	+	0.948979i	$0.397882\pi$
$674$	26.0374	−	40.2721i	1.00292	−	1.55122i
$675$		−	1.00000i		−	0.0384900i
$676$	−1.24187	−	2.75919i	−0.0477640	−	0.106123i
$677$		−	40.7204i		−	1.56501i	−0.622644	−	0.782505i	$-0.713942\pi$
$677$		−	40.7204i		−	1.56501i	0.622644	−	0.782505i	$-0.286058\pi$
$678$	−12.6573	−	8.18339i	−0.486100	−	0.314281i
$679$			4.10538i			0.157550i
$680$	−2.99045	+	19.6519i	−0.114679	+	0.753617i
$681$			25.7926i			0.988374i
$682$	−18.7186	+	28.9521i	−0.716772	+	1.10863i
$683$			23.5908i			0.902676i	0.892353	+	0.451338i	$0.149053\pi$
$683$			23.5908i			0.902676i	−0.892353	+	0.451338i	$0.850947\pi$
$684$	4.16461	+	9.25295i	0.159238	+	0.353795i
$685$	−1.07940			−0.0412419
$686$	−9.68024	−	6.25862i	−0.369593	−	0.238955i
$687$	−3.91484			−0.149360
$688$	3.03166	−	3.42227i	0.115581	−	0.130473i
$689$			38.5109i			1.46715i
$690$	2.34067	−	6.36563i	0.0891079	−	0.242335i
$691$		−	2.60133i		−	0.0989591i	−0.998775	−	0.0494796i	$-0.984244\pi$
$691$		−	2.60133i		−	0.0989591i	0.998775	−	0.0494796i	$-0.0157563\pi$
$692$	10.5098	+	23.3506i	0.399521	+	0.887658i
$693$	1.91575			0.0727733
$694$	−5.81675	+	8.99679i	−0.220801	+	0.341513i
$695$	−11.9643			−0.453833
$696$	19.8823	+	3.02552i	0.753638	+	0.114682i
$697$			18.3766i			0.696064i
$698$	−25.8280	−	16.6987i	−0.977603	−	0.632056i
$699$		−	23.0683i		−	0.872524i
$700$	0.490418	+	1.08961i	0.0185360	+	0.0411835i
$701$		−	33.6821i		−	1.27215i	−0.771626	−	0.636077i	$-0.780556\pi$
$701$		−	33.6821i		−	1.27215i	0.771626	−	0.636077i	$-0.219444\pi$
$702$	2.60240	−	4.02514i	0.0982212	−	0.151919i
$703$		−	13.9768i		−	0.527144i
$704$	−24.4914	−	7.63045i	−0.923054	−	0.287583i
$705$			5.36961i			0.202231i
$706$	−28.6085	−	18.4964i	−1.07669	−	0.696122i
$707$	1.87280			0.0704338
$708$	0.594998	+	1.32197i	0.0223614	+	0.0496827i
$709$		−	44.3750i		−	1.66654i	−0.552869	−	0.833268i	$-0.686467\pi$
$709$		−	44.3750i		−	1.66654i	0.552869	−	0.833268i	$-0.313533\pi$
$710$	−2.54911	−	1.64809i	−0.0956663	−	0.0618517i
$711$	−10.5381			−0.395210
$712$	38.8316	+	5.90904i	1.45527	+	0.221451i
$713$	35.5696	−	8.01296i	1.33209	−	0.300088i
$714$	4.98661	+	3.22402i	0.186619	+	0.120656i
$715$			10.8679i			0.406436i
$716$	−23.8410	+	10.7305i	−0.890981	+	0.401016i
$717$	−21.4690			−0.801776
$718$	−13.0021	−	8.40635i	−0.485235	−	0.313722i
$719$			48.2655i			1.80000i	0.435889	+	0.900000i	$0.356434\pi$
$719$			48.2655i			1.80000i	−0.435889	+	0.900000i	$0.643566\pi$
$720$	2.99413	+	2.65239i	0.111585	+	0.0988487i
$721$	−7.52817			−0.280364
$722$	−8.00483	−	5.17541i	−0.297909	−	0.192609i
$723$	−1.57916			−0.0587297
$724$	−15.6924	+	7.06290i	−0.583203	+	0.262490i
$725$	7.11039			0.264073
$726$	0.551256	−	0.852631i	0.0204590	−	0.0316441i
$727$	1.10811			0.0410976			0.0205488	−	0.999789i	$-0.493459\pi$
$727$	1.10811			0.0410976			0.0205488	+	0.999789i	$0.493459\pi$
$728$	−0.861609	+	5.66211i	−0.0319333	+	0.209852i
$729$	−1.00000			−0.0370370
$730$	6.54369	−	10.1212i	0.242193	−	0.374601i
$731$		−	8.03294i		−	0.297109i
$732$	5.97637	+	13.2783i	0.220893	+	0.490782i
$733$			34.5996i			1.27796i	0.769221	+	0.638982i	$0.220644\pi$
$733$			34.5996i			1.27796i	−0.769221	+	0.638982i	$0.779356\pi$
$734$	44.2371	+	28.6009i	1.63282	+	1.05568i
$735$	−6.64306			−0.245033
$736$	12.8512	+	23.8924i	0.473701	+	0.880686i
$737$	8.62915			0.317859
$738$	3.10535	+	2.00772i	0.114309	+	0.0739052i
$739$		−	16.5908i		−	0.610301i	−0.952304	−	0.305150i	$-0.901293\pi$
$739$		−	16.5908i		−	0.610301i	0.952304	−	0.305150i	$-0.0987067\pi$
$740$	−2.26135	−	5.02428i	−0.0831289	−	0.184696i
$741$			17.1954i			0.631688i
$742$	−5.21250	+	8.06219i	−0.191357	+	0.295972i
$743$	40.5959			1.48932			0.744660	−	0.667444i	$-0.232612\pi$
$743$	40.5959			1.48932			0.744660	+	0.667444i	$0.232612\pi$
$744$	−3.23497	+	21.2588i	−0.118600	+	0.779385i
$745$	6.27286			0.229820
$746$	−15.2767	+	23.6285i	−0.559319	+	0.865101i
$747$	−0.284248			−0.0104001
$748$	−41.1003	+	18.4986i	−1.50278	+	0.676375i
$749$	−8.79692			−0.321432
$750$	1.18761	+	0.767836i	0.0433656	+	0.0280374i
$751$	−23.6313			−0.862317			−0.431158	−	0.902276i	$-0.641895\pi$
$751$	−23.6313			−0.862317			−0.431158	+	0.902276i	$0.641895\pi$
$752$	−16.0773	−	14.2423i	−0.586280	−	0.519363i
$753$			8.94836i			0.326096i
$754$	28.6203	+	18.5041i	1.04229	+	0.673878i
$755$	4.90117			0.178372
$756$	1.08961	−	0.490418i	0.0396289	−	0.0178363i
$757$		−	40.0525i		−	1.45573i	−0.685720	−	0.727866i	$-0.740512\pi$
$757$		−	40.0525i		−	1.45573i	0.685720	−	0.727866i	$-0.259488\pi$
$758$	39.9131	+	25.8053i	1.44971	+	0.937290i
$759$	15.0022	−	3.37963i	0.544545	−	0.122673i
$760$	−14.1867	−	2.15880i	−0.514605	−	0.0783079i
$761$	18.1806			0.659048			0.329524	−	0.944147i	$-0.393112\pi$
$761$	18.1806			0.659048			0.329524	+	0.944147i	$0.393112\pi$
$762$	−17.1738	−	11.1034i	−0.622139	−	0.402236i
$763$		−	4.46628i		−	0.161690i
$764$	5.76936	+	12.8184i	0.208728	+	0.463753i
$765$	7.02799			0.254097
$766$	−4.49289	−	2.90481i	−0.162335	−	0.104955i
$767$			2.45671i			0.0887066i
$768$	−15.8832	+	1.92967i	−0.573136	+	0.0696310i
$769$		−	11.2962i		−	0.407353i	−0.979038	−	0.203676i	$-0.934711\pi$
$769$		−	11.2962i		−	0.407353i	0.979038	−	0.203676i	$-0.0652890\pi$
$770$	−1.47098	+	2.27517i	−0.0530105	+	0.0819915i
$771$			10.1016i			0.363799i
$772$	−10.3706	−	23.0415i	−0.373247	−	0.829283i
$773$			45.1433i			1.62369i	0.583872	+	0.811846i	$0.301537\pi$
$773$			45.1433i			1.62369i	−0.583872	+	0.811846i	$0.698463\pi$
$774$	−1.35744	−	0.877631i	−0.0487920	−	0.0315458i
$775$			7.60264i			0.273095i
$776$	−19.2145	−	2.92389i	−0.689761	−	0.104962i
$777$	−1.64588			−0.0590457
$778$	−15.1834	+	23.4842i	−0.544350	+	0.841948i
$779$	−13.2660			−0.475305
$780$	2.78210	+	6.18129i	0.0996152	+	0.221326i
$781$		−	6.88260i		−	0.246279i
$782$	44.7376	+	16.4502i	1.59981	+	0.588258i
$783$		−	7.11039i		−	0.254105i
$784$	17.6200	−	19.8902i	0.629285	−	0.710364i
$785$	15.5294			0.554269
$786$	−1.01720	−	0.657657i	−0.0362824	−	0.0234579i
$787$	23.3916			0.833821			0.416910	−	0.908948i	$-0.363113\pi$
$787$	23.3916			0.833821			0.416910	+	0.908948i	$0.363113\pi$
$788$	−3.57487	−	7.94267i	−0.127349	−	0.282946i
$789$			19.8604i			0.707049i
$790$	8.09154	−	12.5152i	0.287884	−	0.445271i
$791$		−	6.36742i		−	0.226399i
$792$	−1.36441	+	8.96632i	−0.0484823	+	0.318604i
$793$			24.6760i			0.876272i
$794$	−20.0142	−	12.9399i	−0.710278	−	0.459220i
$795$			11.3626i			0.402991i
$796$	7.95292	+	17.6699i	0.281884	+	0.626292i
$797$		−	12.6987i		−	0.449809i	−0.974381	−	0.224905i	$-0.927793\pi$
$797$		−	12.6987i		−	0.449809i	0.974381	−	0.224905i	$-0.0722071\pi$
$798$	−2.32741	+	3.59982i	−0.0823895	+	0.127432i
$799$	−37.7376			−1.33506
$800$	−5.44902	+	1.51928i	−0.192652	+	0.0537146i
$801$		−	13.8871i		−	0.490676i
$802$	−12.8158	+	19.8222i	−0.452541	+	0.699946i
$803$	27.3272			0.964355
$804$	4.90797	−	2.20900i	0.173091	−	0.0779053i
$805$	2.79520	−	0.629691i	0.0985179	−	0.0221937i
$806$	−19.7851	+	30.6017i	−0.696900	+	1.07790i
$807$		−	25.7428i		−	0.906190i
$808$	−1.33382	+	8.76529i	−0.0469237	+	0.308362i
$809$	−4.05783			−0.142666			−0.0713329	−	0.997453i	$-0.522725\pi$
$809$	−4.05783			−0.142666			−0.0713329	+	0.997453i	$0.522725\pi$
$810$	0.767836	−	1.18761i	0.0269790	−	0.0417285i
$811$		−	51.0830i		−	1.79377i	−0.442268	−	0.896883i	$-0.645826\pi$
$811$		−	51.0830i		−	1.79377i	0.442268	−	0.896883i	$-0.354174\pi$
$812$	3.48706	+	7.74758i	0.122372	+	0.271887i
$813$	−11.7790			−0.413108
$814$	6.78280	−	10.4910i	0.237737	−	0.367709i
$815$	12.2541			0.429243
$816$	−18.6410	+	21.0427i	−0.652564	+	0.736643i
$817$	5.79896			0.202880
$818$	−2.69791	−	1.74429i	−0.0943301	−	0.0609878i
$819$	2.02490			0.0707558
$820$	−4.76879	+	2.14636i	−0.166533	+	0.0749541i
$821$	26.2817			0.917238			0.458619	−	0.888633i	$-0.348344\pi$
$821$	26.2817			0.917238			0.458619	+	0.888633i	$0.348344\pi$
$822$	−1.28192	−	0.828804i	−0.0447119	−	0.0289079i
$823$			6.12583i			0.213533i	0.994284	+	0.106767i	$0.0340497\pi$
$823$			6.12583i			0.213533i	−0.994284	+	0.106767i	$0.965950\pi$
$824$	5.36163	−	35.2342i	0.186781	−	1.22744i
$825$			3.20657i			0.111638i
$826$	−0.332518	+	0.514307i	−0.0115698	+	0.0178950i
$827$	33.9322			1.17994			0.589969	−	0.807426i	$-0.299140\pi$
$827$	33.9322			1.17994			0.589969	+	0.807426i	$0.299140\pi$
$828$	7.66757	−	5.76266i	0.266467	−	0.200266i
$829$	−29.4626			−1.02328			−0.511639	−	0.859200i	$-0.670962\pi$
$829$	−29.4626			−1.02328			−0.511639	+	0.859200i	$0.670962\pi$
$830$	0.218256	−	0.337577i	0.00757577	−	0.0117175i
$831$		−	28.6106i		−	0.992490i
$832$	−25.8868	−	8.06521i	−0.897464	−	0.279611i
$833$		−	46.6873i		−	1.61762i
$834$	−14.2090	−	9.18663i	−0.492017	−	0.318107i
$835$	−6.07192			−0.210128
$836$	−13.3541	−	29.6702i	−0.461861	−	1.02617i
$837$	7.60264			0.262786
$838$	20.6090	+	13.3244i	0.711925	+	0.460285i
$839$	36.2959			1.25307			0.626536	−	0.779392i	$-0.284472\pi$
$839$	36.2959			1.25307			0.626536	+	0.779392i	$0.284472\pi$
$840$	−0.254217	+	1.67060i	−0.00877132	+	0.0576412i
$841$	21.5576			0.743367
$842$	−22.0552	+	34.1128i	−0.760071	+	1.17561i
$843$	11.6562			0.401460
$844$	32.3948	−	14.5804i	1.11507	−	0.501877i
$845$		−	1.51289i		−	0.0520450i
$846$	−4.12298	+	6.37703i	−0.141751	+	0.219247i
$847$	0.428928			0.0147381
$848$	−34.0212	−	30.1381i	−1.16829	−	1.03495i
$849$			29.7129i			1.01974i
$850$	−5.39634	+	8.34654i	−0.185093	+	0.286284i
$851$	−12.8889	+	2.90355i	−0.441825	+	0.0995323i
$852$	−1.76189	−	3.91459i	−0.0603615	−	0.134112i
$853$	45.6348			1.56251			0.781253	−	0.624214i	$-0.214581\pi$
$853$	45.6348			1.56251			0.781253	+	0.624214i	$0.214581\pi$
$854$	−3.33993	+	5.16588i	−0.114290	+	0.176773i
$855$			5.07349i			0.173510i
$856$	6.26524	−	41.1724i	0.214142	−	1.40724i
$857$	7.66479			0.261824			0.130912	−	0.991394i	$-0.458209\pi$
$857$	7.66479			0.261824			0.130912	+	0.991394i	$0.458209\pi$
$858$	−8.34476	+	12.9069i	−0.284885	+	0.440633i
$859$		−	9.74044i		−	0.332339i	−0.986097	−	0.166170i	$-0.946860\pi$
$859$		−	9.74044i		−	0.332339i	0.986097	−	0.166170i	$-0.0531400\pi$
$860$	2.08457	−	0.938233i	0.0710834	−	0.0319935i
$861$			1.56219i			0.0532392i
$862$	9.78024	+	6.32328i	0.333116	+	0.215372i
$863$			15.3947i			0.524042i	0.965062	+	0.262021i	$0.0843889\pi$
$863$			15.3947i			0.524042i	−0.965062	+	0.262021i	$0.915611\pi$
$864$	1.51928	+	5.44902i	0.0516869	+	0.185379i
$865$			12.8034i			0.435328i
$866$	9.93525	−	15.3669i	0.337613	−	0.522188i
$867$			32.3926i			1.10011i
$868$	−8.28394	+	3.72847i	−0.281175	+	0.126552i
$869$	33.7911			1.14629
$870$	8.44440	+	5.45961i	0.286292	+	0.185098i
$871$	9.12080			0.309047
$872$	20.9036	+	3.18092i	0.707885	+	0.107720i
$873$			6.87156i			0.232567i
$874$	−11.8754	+	32.2959i	−0.401690	+	1.09243i
$875$			0.597446i			0.0201974i
$876$	15.5428	−	6.99555i	0.525141	−	0.236358i
$877$	−19.8160			−0.669139			−0.334569	−	0.942371i	$-0.608591\pi$
$877$	−19.8160			−0.669139			−0.334569	+	0.942371i	$0.608591\pi$
$878$	5.94390	−	9.19346i	0.200597	−	0.310264i
$879$	−23.5616			−0.794714
$880$	−9.60089	−	8.50506i	−0.323646	−	0.286705i
$881$		−	0.153404i		−	0.00516830i	−0.999997	−	0.00258415i	$-0.999177\pi$
$881$		−	0.153404i		−	0.00516830i	0.999997	−	0.00258415i	$-0.000822561\pi$
$882$	−7.88939	−	5.10078i	−0.265650	−	0.171752i
$883$			18.2475i			0.614077i	0.951697	+	0.307038i	$0.0993380\pi$
$883$			18.2475i			0.614077i	−0.951697	+	0.307038i	$0.900662\pi$
$884$	−43.4420	+	19.5526i	−1.46111	+	0.657624i
$885$			0.724850i			0.0243656i
$886$	−14.9066	+	23.0560i	−0.500796	+	0.774583i
$887$		−	32.8807i		−	1.10402i	−0.833836	−	0.552012i	$-0.813860\pi$
$887$		−	32.8807i		−	1.10402i	0.833836	−	0.552012i	$-0.186140\pi$
$888$	1.17221	−	7.70326i	0.0393369	−	0.258504i
$889$		−	8.63949i		−	0.289759i
$890$	16.4925	+	10.6630i	0.552830	+	0.357424i
$891$	3.20657			0.107424
$892$	54.0899	−	24.3450i	1.81106	−	0.815130i
$893$		−	27.2426i		−	0.911640i
$894$	7.44974	+	4.81652i	0.249156	+	0.161089i
$895$	−13.0723			−0.436958
$896$	−4.32772	−	5.19224i	−0.144579	−	0.173461i
$897$	15.8570	−	3.57219i	0.529448	−	0.119272i
$898$	−7.67690	−	4.96339i	−0.256181	−	0.165630i
$899$			54.0577i			1.80293i
$900$	0.820857	+	1.82379i	0.0273619	+	0.0607929i
$901$	−79.8564			−2.66040
$902$	−9.95750	−	6.43788i	−0.331549	−	0.214358i
$903$		−	0.682877i		−	0.0227247i
$904$	29.8016	+	4.53493i	0.991185	+	0.150830i
$905$	−8.60430			−0.286017
$906$	5.82070	+	3.76329i	0.193380	+	0.125027i
$907$	−20.3129			−0.674479			−0.337240	−	0.941419i	$-0.609493\pi$
$907$	−20.3129			−0.674479			−0.337240	+	0.941419i	$0.609493\pi$
$908$	−21.1720	−	47.0402i	−0.702618	−	1.56108i
$909$	3.13467			0.103970
$910$	−1.55479	+	2.40480i	−0.0515409	+	0.0797185i
$911$	−21.3021			−0.705769			−0.352884	−	0.935667i	$-0.614799\pi$
$911$	−21.3021			−0.705769			−0.352884	+	0.935667i	$0.614799\pi$
$912$	−15.1907	−	13.4569i	−0.503014	−	0.445601i
$913$	0.911460			0.0301649
$914$	10.7889	−	16.6872i	0.356865	−	0.551965i
$915$			7.28065i			0.240691i
$916$	7.13983	−	3.21352i	0.235906	−	0.106178i
$917$		−	0.511717i		−	0.0168984i
$918$	8.34654	+	5.39634i	0.275477	+	0.178106i
$919$	17.0118			0.561166			0.280583	−	0.959830i	$-0.409472\pi$
$919$	17.0118			0.561166			0.280583	+	0.959830i	$0.409472\pi$
$920$	0.956386	+	13.5309i	0.0315311	+	0.446101i
$921$	17.2091			0.567060
$922$	−13.2434	−	8.56236i	−0.436150	−	0.281986i
$923$		−	7.27475i		−	0.239451i
$924$	−3.49392	+	1.57256i	−0.114941	+	0.0517333i
$925$		−	2.75487i		−	0.0905794i
$926$	−5.59820	+	8.65876i	−0.183968	+	0.284545i
$927$	−12.6006			−0.413858
$928$	−38.7446	+	10.8027i	−1.27186	+	0.354615i
$929$	−17.3862			−0.570421			−0.285211	−	0.958465i	$-0.592064\pi$
$929$	−17.3862			−0.570421			−0.285211	+	0.958465i	$0.592064\pi$
$930$	−5.83758	+	9.02901i	−0.191422	+	0.296073i
$931$	33.7035			1.10459
$932$	18.9358	+	42.0717i	0.620262	+	1.37810i
$933$	20.3547			0.666384
$934$	22.4259	+	14.4992i	0.733798	+	0.474427i
$935$	−22.5357			−0.736996
$936$	−1.44215	+	9.47719i	−0.0471383	+	0.309772i
$937$			23.8029i			0.777608i	0.921321	+	0.388804i	$0.127112\pi$
$937$			23.8029i			0.777608i	−0.921321	+	0.388804i	$0.872888\pi$
$938$	1.90942	+	1.23451i	0.0623448	+	0.0403082i
$939$	34.4686			1.12484
$940$	−4.40768	−	9.79302i	−0.143763	−	0.319413i
$941$		−	54.7134i		−	1.78361i	−0.452424	−	0.891803i	$-0.649441\pi$
$941$		−	54.7134i		−	1.78361i	0.452424	−	0.891803i	$-0.350559\pi$
$942$	18.4430	+	11.9241i	0.600905	+	0.388507i
$943$	2.75590	+	12.2335i	0.0897444	+	0.398376i
$944$	−2.17030	−	1.92258i	−0.0706372	−	0.0625748i
$945$	0.597446			0.0194349
$946$	4.35270	+	2.81418i	0.141519	+	0.0914969i
$947$		−	30.6931i		−	0.997390i	−0.866777	−	0.498695i	$-0.833813\pi$
$947$		−	30.6931i		−	0.997390i	0.866777	−	0.498695i	$-0.166187\pi$
$948$	19.2193	−	8.65028i	0.624212	−	0.280948i
$949$	28.8842			0.937620
$950$	−6.02535	−	3.89560i	−0.195488	−	0.126390i
$951$			23.3763i			0.758028i
$952$	−11.7410	−	1.78663i	−0.380527	−	0.0579052i
$953$			40.6312i			1.31617i	0.752942	+	0.658087i	$0.228634\pi$
$953$			40.6312i			1.31617i	−0.752942	+	0.658087i	$0.771366\pi$
$954$	−8.72463	+	13.4944i	−0.282470	+	0.436898i
$955$			7.02846i			0.227435i
$956$	39.1549	−	17.6230i	1.26636	−	0.569968i
$957$			22.7999i			0.737017i
$958$	−12.8231	−	8.29061i	−0.414296	−	0.267857i
$959$		−	0.644885i		−	0.0208244i
$960$	−7.63789	−	2.37963i	−0.246512	−	0.0768023i
$961$	−26.8002			−0.864521
$962$	7.16926	−	11.0887i	0.231146	−	0.357515i
$963$	−14.7242			−0.474481
$964$	2.88006	−	1.29627i	0.0927604	−	0.0417500i
$965$		−	12.6339i		−	0.406700i
$966$	3.80312	+	1.39843i	0.122363	+	0.0449936i
$967$		−	3.58163i		−	0.115177i	−0.998340	−	0.0575887i	$-0.981659\pi$
$967$		−	3.58163i		−	0.115177i	0.998340	−	0.0575887i	$-0.0183412\pi$
$968$	−0.305486	+	2.00752i	−0.00981870	+	0.0645241i
$969$	−35.6564			−1.14545
$970$	−8.16076	−	5.27623i	−0.262026	−	0.169409i
$971$	−44.3454			−1.42311			−0.711555	−	0.702630i	$-0.752009\pi$
$971$	−44.3454			−1.42311			−0.711555	+	0.702630i	$0.752009\pi$
$972$	1.82379	−	0.820857i	0.0584980	−	0.0263290i
$973$		−	7.14804i		−	0.229156i
$974$	14.6681	−	22.6873i	0.469997	−	0.726946i
$975$			3.38926i			0.108543i
$976$	−21.7992	−	19.3111i	−0.697777	−	0.618134i
$977$			25.8851i			0.828138i	0.910245	+	0.414069i	$0.135893\pi$
$977$			25.8851i			0.828138i	−0.910245	+	0.414069i	$0.864107\pi$
$978$	14.5532	+	9.40916i	0.465359	+	0.300872i
$979$			44.5298i			1.42318i
$980$	12.1155	−	5.45300i	0.387016	−	0.174190i
$981$		−	7.47562i		−	0.238678i
$982$	−14.3773	+	22.2374i	−0.458797	+	0.709623i
$983$	−57.9266			−1.84757			−0.923786	−	0.382909i	$-0.874922\pi$
$983$	−57.9266			−1.84757			−0.923786	+	0.382909i	$0.874922\pi$
$984$	−7.31154	−	1.11260i	−0.233083	−	0.0354685i
$985$		−	4.35505i		−	0.138763i
$986$	−38.3701	+	59.3472i	−1.22195	+	1.89000i
$987$	−3.20805			−0.102113
$988$	−14.1149	−	31.3607i	−0.449056	−	0.997717i
$989$	−1.20468	−	5.34759i	−0.0383066	−	0.170043i
$990$	−2.46212	+	3.80816i	−0.0782512	+	0.121031i
$991$		−	26.8433i		−	0.852704i	−0.904557	−	0.426352i	$-0.859798\pi$
$991$		−	26.8433i		−	0.852704i	0.904557	−	0.426352i	$-0.140202\pi$
$992$	−11.5505	−	41.4269i	−0.366730	−	1.31531i
$993$	11.4719			0.364050
$994$	0.984644	−	1.52295i	0.0312310	−	0.0483051i
$995$			9.68856i			0.307148i
$996$	0.518408	−	0.233327i	0.0164264	−	0.00739325i
$997$	−0.203706			−0.00645143			−0.00322571	−	0.999995i	$-0.501027\pi$
$997$	−0.203706			−0.00645143			−0.00322571	+	0.999995i	$0.501027\pi$
$998$	−14.8369	+	22.9482i	−0.469653	+	0.726414i
$999$	−2.75487			−0.0871601

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.p.b.91.9	yes	48
4.3	odd	2		1380.2.p.a.91.10	yes	48
23.22	odd	2		1380.2.p.a.91.9	✓	48
92.91	even	2	inner	1380.2.p.b.91.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.p.a.91.9	✓	48	23.22	odd	2
1380.2.p.a.91.10	yes	48	4.3	odd	2
1380.2.p.b.91.9	yes	48	1.1	even	1	trivial
1380.2.p.b.91.10	yes	48	92.91	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18761 - 0.767836i) q^{2} -1.00000i q^{3} +(0.820857 + 1.82379i) q^{4} +1.00000i q^{5} +(-0.767836 + 1.18761i) q^{6} -0.597446 q^{7} +(0.425506 - 2.79624i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.18761 - 0.767836i) q^{2} -1.00000i q^{3} +(0.820857 + 1.82379i) q^{4} +1.00000i q^{5} +(-0.767836 + 1.18761i) q^{6} -0.597446 q^{7} +(0.425506 - 2.79624i) q^{8} -1.00000 q^{9} +(0.767836 - 1.18761i) q^{10} +3.20657 q^{11} +(1.82379 - 0.820857i) q^{12} +3.38926 q^{13} +(0.709536 + 0.458740i) q^{14} +1.00000 q^{15} +(-2.65239 + 2.99413i) q^{16} +7.02799i q^{17} +(1.18761 + 0.767836i) q^{18} -5.07349 q^{19} +(-1.82379 + 0.820857i) q^{20} +0.597446i q^{21} +(-3.80816 - 2.46212i) q^{22} +(1.05397 + 4.67858i) q^{23} +(-2.79624 - 0.425506i) q^{24} -1.00000 q^{25} +(-4.02514 - 2.60240i) q^{26} +1.00000i q^{27} +(-0.490418 - 1.08961i) q^{28} -7.11039 q^{29} +(-1.18761 - 0.767836i) q^{30} -7.60264i q^{31} +(5.44902 - 1.51928i) q^{32} -3.20657i q^{33} +(5.39634 - 8.34654i) q^{34} -0.597446i q^{35} +(-0.820857 - 1.82379i) q^{36} +2.75487i q^{37} +(6.02535 + 3.89560i) q^{38} -3.38926i q^{39} +(2.79624 + 0.425506i) q^{40} +2.61478 q^{41} +(0.458740 - 0.709536i) q^{42} -1.14299 q^{43} +(2.63213 + 5.84809i) q^{44} -1.00000i q^{45} +(2.34067 - 6.36563i) q^{46} +5.36961i q^{47} +(2.99413 + 2.65239i) q^{48} -6.64306 q^{49} +(1.18761 + 0.767836i) q^{50} +7.02799 q^{51} +(2.78210 + 6.18129i) q^{52} +11.3626i q^{53} +(0.767836 - 1.18761i) q^{54} +3.20657i q^{55} +(-0.254217 + 1.67060i) q^{56} +5.07349i q^{57} +(8.44440 + 5.45961i) q^{58} +0.724850i q^{59} +(0.820857 + 1.82379i) q^{60} +7.28065i q^{61} +(-5.83758 + 9.02901i) q^{62} +0.597446 q^{63} +(-7.63789 - 2.37963i) q^{64} +3.38926i q^{65} +(-2.46212 + 3.80816i) q^{66} +2.69109 q^{67} +(-12.8175 + 5.76897i) q^{68} +(4.67858 - 1.05397i) q^{69} +(-0.458740 + 0.709536i) q^{70} -2.14641i q^{71} +(-0.425506 + 2.79624i) q^{72} +8.52225 q^{73} +(2.11528 - 3.27172i) q^{74} +1.00000i q^{75} +(-4.16461 - 9.25295i) q^{76} -1.91575 q^{77} +(-2.60240 + 4.02514i) q^{78} +10.5381 q^{79} +(-2.99413 - 2.65239i) q^{80} +1.00000 q^{81} +(-3.10535 - 2.00772i) q^{82} +0.284248 q^{83} +(-1.08961 + 0.490418i) q^{84} -7.02799 q^{85} +(1.35744 + 0.877631i) q^{86} +7.11039i q^{87} +(1.36441 - 8.96632i) q^{88} +13.8871i q^{89} +(-0.767836 + 1.18761i) q^{90} -2.02490 q^{91} +(-7.66757 + 5.76266i) q^{92} -7.60264 q^{93} +(4.12298 - 6.37703i) q^{94} -5.07349i q^{95} +(-1.51928 - 5.44902i) q^{96} -6.87156i q^{97} +(7.88939 + 5.10078i) q^{98} -3.20657 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} + 2 q^{10} - 20 q^{14} + 48 q^{15} - 6 q^{16} + 4 q^{18} - 16 q^{19} - 28 q^{22} - 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} - 4 q^{30} + 16 q^{32} + 28 q^{34} + 2 q^{36} - 2 q^{40} - 8 q^{41} + 26 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 16 q^{51} - 16 q^{52} + 2 q^{54} - 40 q^{56} - 8 q^{58} - 2 q^{60} + 24 q^{62} - 26 q^{64} + 48 q^{67} + 44 q^{68} - 8 q^{69} + 4 q^{72} - 20 q^{74} + 64 q^{76} + 32 q^{77} + 64 q^{79} - 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} + 40 q^{86} - 2 q^{90} - 28 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 + 2 * q^10 - 20 * q^14 + 48 * q^15 - 6 * q^16 + 4 * q^18 - 16 * q^19 - 28 * q^22 - 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 - 4 * q^30 + 16 * q^32 + 28 * q^34 + 2 * q^36 - 2 * q^40 - 8 * q^41 + 26 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 - 16 * q^51 - 16 * q^52 + 2 * q^54 - 40 * q^56 - 8 * q^58 - 2 * q^60 + 24 * q^62 - 26 * q^64 + 48 * q^67 + 44 * q^68 - 8 * q^69 + 4 * q^72 - 20 * q^74 + 64 * q^76 + 32 * q^77 + 64 * q^79 - 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 + 40 * q^86 - 2 * q^90 - 28 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Introduction

L-functions

Modular forms

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Database

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