LMFDB - Embedded newform 840.2.z.c.811.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(811,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.811"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.z (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,2,0,-2,-28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			811.11
Character	$\chi$	$=$	840.811
Dual form			840.2.z.c.811.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.135580 - 1.40770i) q^{2} -1.00000i q^{3} +(-1.96324 + 0.381712i) q^{4} -1.00000 q^{5} +(-1.40770 + 0.135580i) q^{6} +(2.43116 - 1.04376i) q^{7} +(0.803512 + 2.71189i) q^{8} -1.00000 q^{9} +(0.135580 + 1.40770i) q^{10} +5.54165 q^{11} +(0.381712 + 1.96324i) q^{12} +1.67913 q^{13} +(-1.79892 - 3.28083i) q^{14} +1.00000i q^{15} +(3.70859 - 1.49878i) q^{16} -5.50143i q^{17} +(0.135580 + 1.40770i) q^{18} -1.73478i q^{19} +(1.96324 - 0.381712i) q^{20} +(-1.04376 - 2.43116i) q^{21} +(-0.751337 - 7.80098i) q^{22} +3.54807i q^{23} +(2.71189 - 0.803512i) q^{24} +1.00000 q^{25} +(-0.227657 - 2.36371i) q^{26} +1.00000i q^{27} +(-4.37453 + 2.97716i) q^{28} -8.46101i q^{29} +(1.40770 - 0.135580i) q^{30} -7.31172 q^{31} +(-2.61265 - 5.01738i) q^{32} -5.54165i q^{33} +(-7.74436 + 0.745885i) q^{34} +(-2.43116 + 1.04376i) q^{35} +(1.96324 - 0.381712i) q^{36} +11.2477i q^{37} +(-2.44204 + 0.235201i) q^{38} -1.67913i q^{39} +(-0.803512 - 2.71189i) q^{40} +0.0892775i q^{41} +(-3.28083 + 1.79892i) q^{42} +8.68405 q^{43} +(-10.8796 + 2.11531i) q^{44} +1.00000 q^{45} +(4.99461 - 0.481048i) q^{46} -12.7949 q^{47} +(-1.49878 - 3.70859i) q^{48} +(4.82112 - 5.07512i) q^{49} +(-0.135580 - 1.40770i) q^{50} -5.50143 q^{51} +(-3.29653 + 0.640944i) q^{52} -1.26667i q^{53} +(1.40770 - 0.135580i) q^{54} -5.54165 q^{55} +(4.78404 + 5.75438i) q^{56} -1.73478 q^{57} +(-11.9106 + 1.14714i) q^{58} -13.0188i q^{59} +(-0.381712 - 1.96324i) q^{60} +2.49724 q^{61} +(0.991324 + 10.2927i) q^{62} +(-2.43116 + 1.04376i) q^{63} +(-6.70874 + 4.35808i) q^{64} -1.67913 q^{65} +(-7.80098 + 0.751337i) q^{66} +7.26352 q^{67} +(2.09996 + 10.8006i) q^{68} +3.54807 q^{69} +(1.79892 + 3.28083i) q^{70} -6.75026i q^{71} +(-0.803512 - 2.71189i) q^{72} +7.34731i q^{73} +(15.8334 - 1.52497i) q^{74} -1.00000i q^{75} +(0.662185 + 3.40578i) q^{76} +(13.4727 - 5.78417i) q^{77} +(-2.36371 + 0.227657i) q^{78} -1.15000i q^{79} +(-3.70859 + 1.49878i) q^{80} +1.00000 q^{81} +(0.125676 - 0.0121043i) q^{82} -9.14169i q^{83} +(2.97716 + 4.37453i) q^{84} +5.50143i q^{85} +(-1.17738 - 12.2245i) q^{86} -8.46101 q^{87} +(4.45278 + 15.0284i) q^{88} +4.16614i q^{89} +(-0.135580 - 1.40770i) q^{90} +(4.08224 - 1.75261i) q^{91} +(-1.35434 - 6.96569i) q^{92} +7.31172i q^{93} +(1.73474 + 18.0114i) q^{94} +1.73478i q^{95} +(-5.01738 + 2.61265i) q^{96} -4.20427i q^{97} +(-7.79789 - 6.09860i) q^{98} -5.54165 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} - 2 q^{4} - 28 q^{5} - 4 q^{6} - 4 q^{7} - 10 q^{8} - 28 q^{9} - 2 q^{10} + 8 q^{12} + 8 q^{13} + 6 q^{14} + 6 q^{16} - 2 q^{18} + 2 q^{20} + 4 q^{24} + 28 q^{25} - 16 q^{26} - 18 q^{28}+ \cdots - 54 q^{98}+O(q^{100}) $ 28 * q + 2 * q^2 - 2 * q^4 - 28 * q^5 - 4 * q^6 - 4 * q^7 - 10 * q^8 - 28 * q^9 - 2 * q^10 + 8 * q^12 + 8 * q^13 + 6 * q^14 + 6 * q^16 - 2 * q^18 + 2 * q^20 + 4 * q^24 + 28 * q^25 - 16 * q^26 - 18 * q^28 + 4 * q^30 - 24 * q^31 + 2 * q^32 - 8 * q^34 + 4 * q^35 + 2 * q^36 - 36 * q^38 + 10 * q^40 - 20 * q^42 + 24 * q^43 - 4 * q^44 + 28 * q^45 - 44 * q^46 + 24 * q^47 - 16 * q^48 + 28 * q^49 + 2 * q^50 - 16 * q^52 + 4 * q^54 - 34 * q^56 + 8 * q^57 - 12 * q^58 - 8 * q^60 + 16 * q^61 + 28 * q^62 + 4 * q^63 + 22 * q^64 - 8 * q^65 + 20 * q^66 - 8 * q^67 + 12 * q^68 + 24 * q^69 - 6 * q^70 + 10 * q^72 - 8 * q^74 + 16 * q^76 - 16 * q^77 + 20 * q^78 - 6 * q^80 + 28 * q^81 - 24 * q^82 + 16 * q^84 - 4 * q^86 - 16 * q^87 + 40 * q^88 + 2 * q^90 + 48 * q^91 + 40 * q^92 - 52 * q^94 + 16 * q^96 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$1$	$-1$	$-1$

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 $

$2$	−0.135580	−	1.40770i	−0.0958696	−	0.995394i
$2$	−0.135580	−	1.40770i	−0.0958696	−	0.995394i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.96324	+	0.381712i	−0.981618	+	0.190856i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.40770	+	0.135580i	−0.574691	+	0.0553504i
$7$	2.43116	−	1.04376i	0.918894	−	0.394505i
$7$	2.43116	−	1.04376i	0.918894	−	0.394505i
$8$	0.803512	+	2.71189i	0.284084	+	0.958799i
$9$	−1.00000			−0.333333
$10$	0.135580	+	1.40770i	0.0428742	+	0.445154i
$11$	5.54165			1.67087			0.835435	−	0.549589i	$-0.185216\pi$
$11$	5.54165			1.67087			0.835435	+	0.549589i	$0.185216\pi$
$12$	0.381712	+	1.96324i	0.110191	+	0.566737i
$13$	1.67913			0.465707			0.232853	−	0.972512i	$-0.425194\pi$
$13$	1.67913			0.465707			0.232853	+	0.972512i	$0.425194\pi$
$14$	−1.79892	−	3.28083i	−0.480782	−	0.876840i
$15$			1.00000i			0.258199i
$16$	3.70859	−	1.49878i	0.927148	−	0.374696i
$17$		−	5.50143i		−	1.33429i	−0.744926	−	0.667147i	$-0.767515\pi$
$17$		−	5.50143i		−	1.33429i	0.744926	−	0.667147i	$-0.232485\pi$
$18$	0.135580	+	1.40770i	0.0319565	+	0.331798i
$19$		−	1.73478i		−	0.397985i	−0.980001	−	0.198992i	$-0.936233\pi$
$19$		−	1.73478i		−	0.397985i	0.980001	−	0.198992i	$-0.0637669\pi$
$20$	1.96324	−	0.381712i	0.438993	−	0.0853535i
$21$	−1.04376	−	2.43116i	−0.227768	−	0.530523i
$22$	−0.751337	−	7.80098i	−0.160186	−	1.66317i
$23$			3.54807i			0.739823i	0.929067	+	0.369912i	$0.120612\pi$
$23$			3.54807i			0.739823i	−0.929067	+	0.369912i	$0.879388\pi$
$24$	2.71189	−	0.803512i	0.553563	−	0.164016i
$25$	1.00000			0.200000
$26$	−0.227657	−	2.36371i	−0.0446471	−	0.463562i
$27$			1.00000i			0.192450i
$28$	−4.37453	+	2.97716i	−0.826709	+	0.562630i
$29$		−	8.46101i		−	1.57117i	−0.618754	−	0.785585i	$-0.712362\pi$
$29$		−	8.46101i		−	1.57117i	0.618754	−	0.785585i	$-0.287638\pi$
$30$	1.40770	−	0.135580i	0.257010	−	0.0247534i
$31$	−7.31172			−1.31322			−0.656612	−	0.754229i	$-0.728011\pi$
$31$	−7.31172			−1.31322			−0.656612	+	0.754229i	$0.728011\pi$
$32$	−2.61265	−	5.01738i	−0.461855	−	0.886955i
$33$		−	5.54165i		−	0.964677i
$34$	−7.74436	+	0.745885i	−1.32815	+	0.127918i
$35$	−2.43116	+	1.04376i	−0.410942	+	0.176428i
$36$	1.96324	−	0.381712i	0.327206	−	0.0636187i
$37$			11.2477i			1.84912i	0.381039	+	0.924559i	$0.375567\pi$
$37$			11.2477i			1.84912i	−0.381039	+	0.924559i	$0.624433\pi$
$38$	−2.44204	+	0.235201i	−0.396152	+	0.0381547i
$39$		−	1.67913i		−	0.268876i
$40$	−0.803512	−	2.71189i	−0.127046	−	0.428788i
$41$			0.0892775i			0.0139428i	0.999976	+	0.00697140i	$0.00221908\pi$
$41$			0.0892775i			0.0139428i	−0.999976	+	0.00697140i	$0.997781\pi$
$42$	−3.28083	+	1.79892i	−0.506244	+	0.277580i
$43$	8.68405			1.32430			0.662152	−	0.749369i	$-0.269643\pi$
$43$	8.68405			1.32430			0.662152	+	0.749369i	$0.269643\pi$
$44$	−10.8796	+	2.11531i	−1.64016	+	0.318896i
$45$	1.00000			0.149071
$46$	4.99461	−	0.481048i	0.736416	−	0.0709266i
$47$	−12.7949			−1.86633			−0.933164	−	0.359450i	$-0.882964\pi$
$47$	−12.7949			−1.86633			−0.933164	+	0.359450i	$0.882964\pi$
$48$	−1.49878	−	3.70859i	−0.216331	−	0.535289i
$49$	4.82112	−	5.07512i	0.688731	−	0.725017i
$50$	−0.135580	−	1.40770i	−0.0191739	−	0.199079i
$51$	−5.50143			−0.770355
$52$	−3.29653	+	0.640944i	−0.457146	+	0.0888830i
$53$		−	1.26667i		−	0.173991i	−0.996209	−	0.0869955i	$-0.972273\pi$
$53$		−	1.26667i		−	0.173991i	0.996209	−	0.0869955i	$-0.0277266\pi$
$54$	1.40770	−	0.135580i	0.191564	−	0.0184501i
$55$	−5.54165			−0.747236
$56$	4.78404	+	5.75438i	0.639295	+	0.768962i
$57$	−1.73478			−0.229777
$58$	−11.9106	+	1.14714i	−1.56393	+	0.150628i
$59$		−	13.0188i		−	1.69490i	−0.530874	−	0.847451i	$-0.678136\pi$
$59$		−	13.0188i		−	1.69490i	0.530874	−	0.847451i	$-0.321864\pi$
$60$	−0.381712	−	1.96324i	−0.0492788	−	0.253453i
$61$	2.49724			0.319739			0.159869	−	0.987138i	$-0.448893\pi$
$61$	2.49724			0.319739			0.159869	+	0.987138i	$0.448893\pi$
$62$	0.991324	+	10.2927i	0.125898	+	1.30717i
$63$	−2.43116	+	1.04376i	−0.306298	+	0.131502i
$64$	−6.70874	+	4.35808i	−0.838592	+	0.544760i
$65$	−1.67913			−0.208270
$66$	−7.80098	+	0.751337i	−0.960234	+	0.0924833i
$67$	7.26352			0.887381			0.443690	−	0.896180i	$-0.353669\pi$
$67$	7.26352			0.887381			0.443690	+	0.896180i	$0.353669\pi$
$68$	2.09996	+	10.8006i	0.254658	+	1.30977i
$69$	3.54807			0.427137
$70$	1.79892	+	3.28083i	0.215012	+	0.392135i
$71$		−	6.75026i		−	0.801108i	−0.916273	−	0.400554i	$-0.868818\pi$
$71$		−	6.75026i		−	0.801108i	0.916273	−	0.400554i	$-0.131182\pi$
$72$	−0.803512	−	2.71189i	−0.0946948	−	0.319600i
$73$			7.34731i			0.859938i	0.902844	+	0.429969i	$0.141475\pi$
$73$			7.34731i			0.859938i	−0.902844	+	0.429969i	$0.858525\pi$
$74$	15.8334	−	1.52497i	1.84060	−	0.177274i
$75$		−	1.00000i		−	0.115470i
$76$	0.662185	+	3.40578i	0.0759579	+	0.390669i
$77$	13.4727	−	5.78417i	1.53535	−	0.659167i
$78$	−2.36371	+	0.227657i	−0.267637	+	0.0257770i
$79$		−	1.15000i		−	0.129386i	−0.997905	−	0.0646928i	$-0.979393\pi$
$79$		−	1.15000i		−	0.129386i	0.997905	−	0.0646928i	$-0.0206067\pi$
$80$	−3.70859	+	1.49878i	−0.414633	+	0.167569i
$81$	1.00000			0.111111
$82$	0.125676	−	0.0121043i	0.0138786	−	0.00133669i
$83$		−	9.14169i		−	1.00343i	−0.865033	−	0.501715i	$-0.832703\pi$
$83$		−	9.14169i		−	1.00343i	0.865033	−	0.501715i	$-0.167297\pi$
$84$	2.97716	+	4.37453i	0.324835	+	0.477301i
$85$			5.50143i			0.596714i
$86$	−1.17738	−	12.2245i	−0.126961	−	1.31820i
$87$	−8.46101			−0.907115
$88$	4.45278	+	15.0284i	0.474668	+	1.60203i
$89$			4.16614i			0.441610i	0.975318	+	0.220805i	$0.0708685\pi$
$89$			4.16614i			0.441610i	−0.975318	+	0.220805i	$0.929132\pi$
$90$	−0.135580	−	1.40770i	−0.0142914	−	0.148385i
$91$	4.08224	−	1.75261i	0.427935	−	0.183724i
$92$	−1.35434	−	6.96569i	−0.141200	−	0.726224i
$93$			7.31172i			0.758190i
$94$	1.73474	+	18.0114i	0.178924	+	1.85773i
$95$			1.73478i			0.177984i
$96$	−5.01738	+	2.61265i	−0.512084	+	0.266652i
$97$		−	4.20427i		−	0.426878i	−0.976956	−	0.213439i	$-0.931533\pi$
$97$		−	4.20427i		−	0.426878i	0.976956	−	0.213439i	$-0.0684665\pi$
$98$	−7.79789	−	6.09860i	−0.787706	−	0.616051i
$99$	−5.54165			−0.556957
$100$	−1.96324	+	0.381712i	−0.196324	+	0.0381712i
$101$	15.0071			1.49326			0.746629	−	0.665240i	$-0.231671\pi$
$101$	15.0071			1.49326			0.746629	+	0.665240i	$0.231671\pi$
$102$	0.745885	+	7.74436i	0.0738536	+	0.766806i
$103$	1.31225			0.129300			0.0646501	−	0.997908i	$-0.479407\pi$
$103$	1.31225			0.129300			0.0646501	+	0.997908i	$0.479407\pi$
$104$	1.34920	+	4.55362i	0.132300	+	0.446519i
$105$	1.04376	+	2.43116i	0.101861	+	0.237257i
$106$	−1.78310	+	0.171736i	−0.173190	+	0.0166805i
$107$	−16.7713			−1.62134			−0.810672	−	0.585501i	$-0.800898\pi$
$107$	−16.7713			−1.62134			−0.810672	+	0.585501i	$0.800898\pi$
$108$	−0.381712	−	1.96324i	−0.0367303	−	0.188912i
$109$			2.48432i			0.237955i	0.992897	+	0.118978i	$0.0379616\pi$
$109$			2.48432i			0.237955i	−0.992897	+	0.118978i	$0.962038\pi$
$110$	0.751337	+	7.80098i	0.0716372	+	0.743794i
$111$	11.2477			1.06759
$112$	7.45182	−	7.51468i	0.704131	−	0.710070i
$113$	−10.7975			−1.01575			−0.507873	−	0.861432i	$-0.669568\pi$
$113$	−10.7975			−1.01575			−0.507873	+	0.861432i	$0.669568\pi$
$114$	0.235201	+	2.44204i	0.0220286	+	0.228718i
$115$		−	3.54807i		−	0.330859i
$116$	3.22967	+	16.6110i	0.299867	+	1.54229i
$117$	−1.67913			−0.155236
$118$	−18.3265	+	1.76509i	−1.68709	+	0.162490i
$119$	−5.74219	−	13.3749i	−0.526386	−	1.22607i
$120$	−2.71189	+	0.803512i	−0.247561	+	0.0733503i
$121$	19.7099			1.79181
$122$	−0.338576	−	3.51536i	−0.0306532	−	0.318266i
$123$	0.0892775			0.00804988
$124$	14.3546	−	2.79097i	1.28908	−	0.250637i
$125$	−1.00000			−0.0894427
$126$	1.79892	+	3.28083i	0.160261	+	0.292280i
$127$			0.926602i			0.0822226i	0.999155	+	0.0411113i	$0.0130898\pi$
$127$			0.926602i			0.0822226i	−0.999155	+	0.0411113i	$0.986910\pi$
$128$	7.04444	+	8.85302i	0.622646	+	0.782504i
$129$		−	8.68405i		−	0.764588i
$130$	0.227657	+	2.36371i	0.0199668	+	0.207311i
$131$			12.4963i			1.09181i	0.837847	+	0.545905i	$0.183814\pi$
$131$			12.4963i			1.09181i	−0.837847	+	0.545905i	$0.816186\pi$
$132$	2.11531	+	10.8796i	0.184115	+	0.946944i
$133$	−1.81070	−	4.21753i	−0.157007	−	0.365706i
$134$	−0.984790	−	10.2249i	−0.0850729	−	0.883293i
$135$		−	1.00000i		−	0.0860663i
$136$	14.9193	−	4.42047i	1.27932	−	0.379052i
$137$	3.53259			0.301810			0.150905	−	0.988548i	$-0.451781\pi$
$137$	3.53259			0.301810			0.150905	+	0.988548i	$0.451781\pi$
$138$	−0.481048	−	4.99461i	−0.0409495	−	0.425170i
$139$			12.1022i			1.02650i	0.858240	+	0.513249i	$0.171558\pi$
$139$			12.1022i			1.02650i	−0.858240	+	0.513249i	$0.828442\pi$
$140$	4.37453	−	2.97716i	0.369715	−	0.251616i
$141$			12.7949i			1.07753i
$142$	−9.50233	+	0.915201i	−0.797418	+	0.0768019i
$143$	9.30514			0.778135
$144$	−3.70859	+	1.49878i	−0.309049	+	0.124899i
$145$			8.46101i			0.702649i
$146$	10.3428	−	0.996150i	0.855977	−	0.0824419i
$147$	−5.07512	−	4.82112i	−0.418589	−	0.397639i
$148$	−4.29340	−	22.0820i	−0.352916	−	1.81513i
$149$		−	11.1107i		−	0.910221i	−0.890435	−	0.455110i	$-0.849600\pi$
$149$		−	11.1107i		−	0.910221i	0.890435	−	0.455110i	$-0.150400\pi$
$150$	−1.40770	+	0.135580i	−0.114938	+	0.0110701i
$151$			3.03195i			0.246737i	0.992361	+	0.123368i	$0.0393696\pi$
$151$			3.03195i			0.246737i	−0.992361	+	0.123368i	$0.960630\pi$
$152$	4.70453	−	1.39391i	0.381588	−	0.113061i
$153$			5.50143i			0.444764i
$154$	−9.96900	−	18.1812i	−0.803325	−	1.46509i
$155$	7.31172			0.587292
$156$	0.640944	+	3.29653i	0.0513166	+	0.263933i
$157$	5.57251			0.444735			0.222367	−	0.974963i	$-0.428622\pi$
$157$	5.57251			0.444735			0.222367	+	0.974963i	$0.428622\pi$
$158$	−1.61886	+	0.155918i	−0.128790	+	0.0124041i
$159$	−1.26667			−0.100454
$160$	2.61265	+	5.01738i	0.206548	+	0.396659i
$161$	3.70334	+	8.62593i	0.291864	+	0.679819i
$162$	−0.135580	−	1.40770i	−0.0106522	−	0.110599i
$163$	−20.9634			−1.64198			−0.820989	−	0.570944i	$-0.806577\pi$
$163$	−20.9634			−1.64198			−0.820989	+	0.570944i	$0.806577\pi$
$164$	−0.0340783	−	0.175273i	−0.00266107	−	0.0136865i
$165$			5.54165i			0.431417i
$166$	−12.8687	+	1.23943i	−0.998808	+	0.0961985i
$167$	5.73739			0.443973			0.221986	−	0.975050i	$-0.428746\pi$
$167$	5.73739			0.443973			0.221986	+	0.975050i	$0.428746\pi$
$168$	5.75438	−	4.78404i	0.443960	−	0.369097i
$169$	−10.1805			−0.783117
$170$	7.74436	−	0.745885i	0.593966	−	0.0572068i
$171$			1.73478i			0.132662i
$172$	−17.0488	+	3.31481i	−1.29996	+	0.252752i
$173$	17.1231			1.30185			0.650923	−	0.759144i	$-0.274382\pi$
$173$	17.1231			1.30185			0.650923	+	0.759144i	$0.274382\pi$
$174$	1.14714	+	11.9106i	0.0869648	+	0.902937i
$175$	2.43116	−	1.04376i	0.183779	−	0.0789011i
$176$	20.5517	−	8.30572i	1.54914	−	0.626068i
$177$	−13.0188			−0.978552
$178$	5.86468	−	0.564846i	0.439576	−	0.0423370i
$179$	14.4927			1.08324			0.541618	−	0.840625i	$-0.317812\pi$
$179$	14.4927			1.08324			0.541618	+	0.840625i	$0.317812\pi$
$180$	−1.96324	+	0.381712i	−0.146331	+	0.0284512i
$181$	1.28496			0.0955104			0.0477552	−	0.998859i	$-0.484793\pi$
$181$	1.28496			0.0955104			0.0477552	+	0.998859i	$0.484793\pi$
$182$	−3.02062	−	5.50895i	−0.223904	−	0.408350i
$183$		−	2.49724i		−	0.184601i
$184$	−9.62198	+	2.85092i	−0.709342	+	0.210172i
$185$		−	11.2477i		−	0.826951i
$186$	10.2927	−	0.991324i	0.754698	−	0.0726874i
$187$		−	30.4870i		−	2.22943i
$188$	25.1194	−	4.88397i	1.83202	−	0.356200i
$189$	1.04376	+	2.43116i	0.0759226	+	0.176841i
$190$	2.44204	−	0.235201i	0.177164	−	0.0170633i
$191$			9.06371i			0.655827i	0.944708	+	0.327914i	$0.106345\pi$
$191$			9.06371i			0.655827i	−0.944708	+	0.327914i	$0.893655\pi$
$192$	4.35808	+	6.70874i	0.314517	+	0.484161i
$193$	17.5065			1.26014			0.630072	−	0.776536i	$-0.283025\pi$
$193$	17.5065			1.26014			0.630072	+	0.776536i	$0.283025\pi$
$194$	−5.91834	+	0.570015i	−0.424912	+	0.0409247i
$195$			1.67913i			0.120245i
$196$	−7.52775	+	11.8039i	−0.537697	+	0.843138i
$197$			13.1628i			0.937808i	0.883249	+	0.468904i	$0.155351\pi$
$197$			13.1628i			0.937808i	−0.883249	+	0.468904i	$0.844649\pi$
$198$	0.751337	+	7.80098i	0.0533952	+	0.554391i
$199$	0.276416			0.0195946			0.00979732	−	0.999952i	$-0.496881\pi$
$199$	0.276416			0.0195946			0.00979732	+	0.999952i	$0.496881\pi$
$200$	0.803512	+	2.71189i	0.0568169	+	0.191760i
$201$		−	7.26352i		−	0.512329i
$202$	−2.03466	−	21.1254i	−0.143158	−	1.48638i
$203$	−8.83129	−	20.5701i	−0.619835	−	1.44374i
$204$	10.8006	−	2.09996i	0.756194	−	0.147027i
$205$		−	0.0892775i		−	0.00623541i
$206$	−0.177916	−	1.84726i	−0.0123960	−	0.128705i
$207$		−	3.54807i		−	0.246608i
$208$	6.22721	−	2.51665i	0.431779	−	0.174498i
$209$		−	9.61352i		−	0.664981i
$210$	3.28083	−	1.79892i	0.226399	−	0.124137i
$211$	12.0851			0.831973			0.415986	−	0.909371i	$-0.363436\pi$
$211$	12.0851			0.831973			0.415986	+	0.909371i	$0.363436\pi$
$212$	0.483505	+	2.48678i	0.0332072	+	0.170793i
$213$	−6.75026			−0.462520
$214$	2.27386	+	23.6090i	0.155438	+	1.61388i
$215$	−8.68405			−0.592247
$216$	−2.71189	+	0.803512i	−0.184521	+	0.0546721i
$217$	−17.7760	+	7.63171i	−1.20671	+	0.518074i
$218$	3.49718	−	0.336825i	0.236859	−	0.0228127i
$219$	7.34731			0.496485
$220$	10.8796	−	2.11531i	0.733500	−	0.142614i
$221$		−	9.23762i		−	0.621389i
$222$	−1.52497	−	15.8334i	−0.102349	−	1.06267i
$223$	−17.8291			−1.19393			−0.596963	−	0.802268i	$-0.703626\pi$
$223$	−17.8291			−1.19393			−0.596963	+	0.802268i	$0.703626\pi$
$224$	−11.5887	−	9.47108i	−0.774304	−	0.632813i
$225$	−1.00000			−0.0666667
$226$	1.46393	+	15.1997i	0.0973793	+	1.01107i
$227$			27.5789i			1.83048i	0.402911	+	0.915239i	$0.367999\pi$
$227$			27.5789i			1.83048i	−0.402911	+	0.915239i	$0.632001\pi$
$228$	3.40578	−	0.662185i	0.225553	−	0.0438543i
$229$	3.43380			0.226912			0.113456	−	0.993543i	$-0.463808\pi$
$229$	3.43380			0.226912			0.113456	+	0.993543i	$0.463808\pi$
$230$	−4.99461	+	0.481048i	−0.329335	+	0.0317193i
$231$	−5.78417	−	13.4727i	−0.380570	−	0.886436i
$232$	22.9454	−	6.79852i	1.50644	−	0.446345i
$233$	8.12381			0.532209			0.266104	−	0.963944i	$-0.414263\pi$
$233$	8.12381			0.532209			0.266104	+	0.963944i	$0.414263\pi$
$234$	0.227657	+	2.36371i	0.0148824	+	0.154521i
$235$	12.7949			0.834648
$236$	4.96943	+	25.5589i	0.323482	+	1.66375i
$237$	−1.15000			−0.0747008
$238$	−18.0493	+	9.89665i	−1.16996	+	0.641505i
$239$			23.7708i			1.53761i	0.639484	+	0.768804i	$0.279148\pi$
$239$			23.7708i			1.53761i	−0.639484	+	0.768804i	$0.720852\pi$
$240$	1.49878	+	3.70859i	0.0967460	+	0.239389i
$241$		−	13.8075i		−	0.889417i	−0.895675	−	0.444708i	$-0.853307\pi$
$241$		−	13.8075i		−	0.889417i	0.895675	−	0.444708i	$-0.146693\pi$
$242$	−2.67227	−	27.7456i	−0.171780	−	1.78355i
$243$		−	1.00000i		−	0.0641500i
$244$	−4.90267	+	0.953227i	−0.313861	+	0.0610241i
$245$	−4.82112	+	5.07512i	−0.308010	+	0.324238i
$246$	−0.0121043	−	0.125676i	−0.000771739	−	0.00801280i
$247$		−	2.91291i		−	0.185344i
$248$	−5.87506	−	19.8286i	−0.373066	−	1.25912i
$249$	−9.14169			−0.579331
$250$	0.135580	+	1.40770i	0.00857484	+	0.0890307i
$251$			2.78833i			0.175998i	0.996121	+	0.0879990i	$0.0280472\pi$
$251$			2.78833i			0.175998i	−0.996121	+	0.0879990i	$0.971953\pi$
$252$	4.37453	−	2.97716i	0.275570	−	0.187543i
$253$			19.6621i			1.23615i
$254$	1.30438	−	0.125629i	0.0818439	−	0.00788265i
$255$	5.50143			0.344513
$256$	11.5073	−	11.1167i	0.719206	−	0.694796i
$257$			3.21699i			0.200670i	0.994954	+	0.100335i	$0.0319915\pi$
$257$			3.21699i			0.200670i	−0.994954	+	0.100335i	$0.968009\pi$
$258$	−12.2245	+	1.17738i	−0.761066	+	0.0733007i
$259$	11.7400	+	27.3451i	0.729487	+	1.69914i
$260$	3.29653	−	0.640944i	0.204442	−	0.0397497i
$261$			8.46101i			0.523723i
$262$	17.5911	−	1.69426i	1.08678	−	0.104671i
$263$		−	3.61223i		−	0.222740i	−0.993779	−	0.111370i	$-0.964476\pi$
$263$		−	3.61223i		−	0.222740i	0.993779	−	0.111370i	$-0.0355238\pi$
$264$	15.0284	−	4.45278i	0.924932	−	0.274050i
$265$			1.26667i			0.0778111i
$266$	−5.69151	+	3.12073i	−0.348969	+	0.191344i
$267$	4.16614			0.254964
$268$	−14.2600	+	2.77258i	−0.871069	+	0.169362i
$269$	8.64776			0.527263			0.263632	−	0.964623i	$-0.415080\pi$
$269$	8.64776			0.527263			0.263632	+	0.964623i	$0.415080\pi$
$270$	−1.40770	+	0.135580i	−0.0856699	+	0.00825115i
$271$	−3.09276			−0.187872			−0.0939358	−	0.995578i	$-0.529945\pi$
$271$	−3.09276			−0.187872			−0.0939358	+	0.995578i	$0.529945\pi$
$272$	−8.24545	−	20.4026i	−0.499954	−	1.23709i
$273$	−1.75261	−	4.08224i	−0.106073	−	0.247068i
$274$	−0.478950	−	4.97283i	−0.0289344	−	0.300420i
$275$	5.54165			0.334174
$276$	−6.96569	+	1.35434i	−0.419286	+	0.0815217i
$277$			21.5406i			1.29425i	0.762384	+	0.647125i	$0.224029\pi$
$277$			21.5406i			1.29425i	−0.762384	+	0.647125i	$0.775971\pi$
$278$	17.0363	−	1.64082i	1.02177	−	0.0984100i
$279$	7.31172			0.437741
$280$	−4.78404	−	5.75438i	−0.285901	−	0.343890i
$281$	17.0871			1.01933			0.509664	−	0.860373i	$-0.329770\pi$
$281$	17.0871			1.01933			0.509664	+	0.860373i	$0.329770\pi$
$282$	18.0114	−	1.73474i	1.07256	−	0.103302i
$283$			25.9118i			1.54030i	0.637865	+	0.770148i	$0.279818\pi$
$283$			25.9118i			1.54030i	−0.637865	+	0.770148i	$0.720182\pi$
$284$	2.57666	+	13.2523i	0.152896	+	0.786382i
$285$	1.73478			0.102759
$286$	−1.26159	−	13.0988i	−0.0745996	−	0.774551i
$287$	0.0931846	+	0.217048i	0.00550051	+	0.0128120i
$288$	2.61265	+	5.01738i	0.153952	+	0.295652i
$289$	−13.2658			−0.780339
$290$	11.9106	−	1.14714i	0.699412	−	0.0673627i
$291$	−4.20427			−0.246458
$292$	−2.80456	−	14.4245i	−0.164124	−	0.844130i
$293$	27.3161			1.59583			0.797913	−	0.602773i	$-0.205937\pi$
$293$	27.3161			1.59583			0.797913	+	0.602773i	$0.205937\pi$
$294$	−6.09860	+	7.79789i	−0.355677	+	0.454782i
$295$			13.0188i			0.757983i
$296$	−30.5027	+	9.03770i	−1.77293	+	0.525306i
$297$			5.54165i			0.321559i
$298$	−15.6405	+	1.50638i	−0.906028	+	0.0872625i
$299$			5.95767i			0.344541i
$300$	0.381712	+	1.96324i	0.0220382	+	0.113347i
$301$	21.1123	−	9.06409i	1.21690	−	0.522445i
$302$	4.26807	−	0.411072i	0.245600	−	0.0236545i
$303$		−	15.0071i		−	0.862133i
$304$	−2.60005	−	6.43358i	−0.149123	−	0.368991i
$305$	−2.49724			−0.142991
$306$	7.74436	−	0.745885i	0.442716	−	0.0426394i
$307$			2.39283i			0.136566i	0.997666	+	0.0682831i	$0.0217521\pi$
$307$			2.39283i			0.136566i	−0.997666	+	0.0682831i	$0.978248\pi$
$308$	−24.2421	+	16.4984i	−1.38132	+	0.940082i
$309$		−	1.31225i		−	0.0746515i
$310$	−0.991324	−	10.2927i	−0.0563034	−	0.584586i
$311$	−24.3201			−1.37907			−0.689533	−	0.724255i	$-0.742184\pi$
$311$	−24.3201			−1.37907			−0.689533	+	0.724255i	$0.742184\pi$
$312$	4.55362	−	1.34920i	0.257798	−	0.0763834i
$313$			30.3185i			1.71370i	0.515562	+	0.856852i	$0.327583\pi$
$313$			30.3185i			1.71370i	−0.515562	+	0.856852i	$0.672417\pi$
$314$	−0.755522	−	7.84442i	−0.0426366	−	0.442686i
$315$	2.43116	−	1.04376i	0.136981	−	0.0588094i
$316$	0.438970	+	2.25773i	0.0246940	+	0.127007i
$317$			7.93499i			0.445673i	0.974856	+	0.222837i	$0.0715317\pi$
$317$			7.93499i			0.445673i	−0.974856	+	0.222837i	$0.928468\pi$
$318$	0.171736	+	1.78310i	0.00963047	+	0.0999910i
$319$		−	46.8879i		−	2.62522i
$320$	6.70874	−	4.35808i	0.375030	−	0.243624i
$321$			16.7713i			0.936083i
$322$	11.6406	−	6.38270i	0.648707	−	0.355694i
$323$	−9.54375			−0.531029
$324$	−1.96324	+	0.381712i	−0.109069	+	0.0212062i
$325$	1.67913			0.0931413
$326$	2.84222	+	29.5101i	0.157416	+	1.63441i
$327$	2.48432			0.137383
$328$	−0.242111	+	0.0717355i	−0.0133683	+	0.00396093i
$329$	−31.1065	+	13.3549i	−1.71496	+	0.736277i
$330$	7.80098	−	0.751337i	0.429430	−	0.0413598i
$331$	−14.2122			−0.781172			−0.390586	−	0.920566i	$-0.627728\pi$
$331$	−14.2122			−0.781172			−0.390586	+	0.920566i	$0.627728\pi$
$332$	3.48949	+	17.9473i	0.191511	+	0.984985i
$333$		−	11.2477i		−	0.616373i
$334$	−0.777876	−	8.07652i	−0.0425635	−	0.441928i
$335$	−7.26352			−0.396849
$336$	−7.51468	−	7.45182i	−0.409959	−	0.406530i
$337$	2.94854			0.160617			0.0803085	−	0.996770i	$-0.474409\pi$
$337$	2.94854			0.160617			0.0803085	+	0.996770i	$0.474409\pi$
$338$	1.38028	+	14.3311i	0.0750772	+	0.779510i
$339$			10.7975i			0.586442i
$340$	−2.09996	−	10.8006i	−0.113887	−	0.585745i
$341$	−40.5190			−2.19423
$342$	2.44204	−	0.235201i	0.132051	−	0.0127182i
$343$	6.42370	−	17.3706i	0.346847	−	0.937922i
$344$	6.97774	+	23.5502i	0.376214	+	1.26974i
$345$	−3.54807			−0.191022
$346$	−2.32155	−	24.1042i	−0.124808	−	1.29585i
$347$	−30.9749			−1.66282			−0.831410	−	0.555659i	$-0.812466\pi$
$347$	−30.9749			−1.66282			−0.831410	+	0.555659i	$0.812466\pi$
$348$	16.6110	−	3.22967i	0.890441	−	0.173129i
$349$	−4.43452			−0.237374			−0.118687	−	0.992932i	$-0.537869\pi$
$349$	−4.43452			−0.237374			−0.118687	+	0.992932i	$0.537869\pi$
$350$	−1.79892	−	3.28083i	−0.0961565	−	0.175368i
$351$			1.67913i			0.0896253i
$352$	−14.4784	−	27.8045i	−0.771700	−	1.48199i
$353$			25.5750i			1.36122i	0.732647	+	0.680609i	$0.238285\pi$
$353$			25.5750i			1.36122i	−0.732647	+	0.680609i	$0.761715\pi$
$354$	1.76509	+	18.3265i	0.0938134	+	0.974044i
$355$			6.75026i			0.358266i
$356$	−1.59027	−	8.17912i	−0.0842840	−	0.433493i
$357$	−13.3749	+	5.74219i	−0.707874	+	0.303909i
$358$	−1.96492	−	20.4014i	−0.103849	−	1.07825i
$359$		−	15.8598i		−	0.837049i	−0.908206	−	0.418525i	$-0.862547\pi$
$359$		−	15.8598i		−	0.837049i	0.908206	−	0.418525i	$-0.137453\pi$
$360$	0.803512	+	2.71189i	0.0423488	+	0.142929i
$361$	15.9906			0.841608
$362$	−0.174215	−	1.80884i	−0.00915655	−	0.0950705i
$363$		−	19.7099i		−	1.03450i
$364$	−7.34540	+	4.99904i	−0.385004	+	0.262021i
$365$		−	7.34731i		−	0.384576i
$366$	−3.51536	+	0.338576i	−0.183751	+	0.0176977i
$367$	−20.7390			−1.08257			−0.541284	−	0.840840i	$-0.682062\pi$
$367$	−20.7390			−1.08257			−0.541284	+	0.840840i	$0.682062\pi$
$368$	5.31778	+	13.1583i	0.277209	+	0.685926i
$369$		−	0.0892775i		−	0.00464760i
$370$	−15.8334	+	1.52497i	−0.823142	+	0.0792795i
$371$	−1.32211	−	3.07949i	−0.0686404	−	0.159879i
$372$	−2.79097	−	14.3546i	−0.144705	−	0.744253i
$373$		−	14.5992i		−	0.755920i	−0.925822	−	0.377960i	$-0.876626\pi$
$373$		−	14.5992i		−	0.755920i	0.925822	−	0.377960i	$-0.123374\pi$
$374$	−42.9165	+	4.13343i	−2.21916	+	0.213735i
$375$			1.00000i			0.0516398i
$376$	−10.2809	−	34.6984i	−0.530195	−	1.78943i
$377$		−	14.2071i		−	0.731704i
$378$	3.28083	−	1.79892i	0.168748	−	0.0925266i
$379$	35.0992			1.80292			0.901462	−	0.432859i	$-0.142495\pi$
$379$	35.0992			1.80292			0.901462	+	0.432859i	$0.142495\pi$
$380$	−0.662185	−	3.40578i	−0.0339694	−	0.174713i
$381$	0.926602			0.0474713
$382$	12.7590	−	1.22886i	0.652806	−	0.0628739i
$383$	2.93845			0.150148			0.0750739	−	0.997178i	$-0.476081\pi$
$383$	2.93845			0.150148			0.0750739	+	0.997178i	$0.476081\pi$
$384$	8.85302	−	7.04444i	0.451779	−	0.359485i
$385$	−13.4727	+	5.78417i	−0.686630	+	0.294789i
$386$	−2.37353	−	24.6439i	−0.120810	−	1.25434i
$387$	−8.68405			−0.441435
$388$	1.60482	+	8.25396i	0.0814724	+	0.419032i
$389$		−	29.8030i		−	1.51107i	−0.655106	−	0.755537i	$-0.727376\pi$
$389$		−	29.8030i		−	1.51107i	0.655106	−	0.755537i	$-0.272624\pi$
$390$	2.36371	−	0.227657i	0.119691	−	0.0115278i
$391$	19.5195			0.987141
$392$	17.6370	+	8.99644i	0.890804	+	0.454389i
$393$	12.4963			0.630357
$394$	18.5292	−	1.78461i	0.933488	−	0.0899073i
$395$			1.15000i			0.0578630i
$396$	10.8796	−	2.11531i	0.546719	−	0.106299i
$397$	−20.3840			−1.02304			−0.511521	−	0.859271i	$-0.670918\pi$
$397$	−20.3840			−1.02304			−0.511521	+	0.859271i	$0.670918\pi$
$398$	−0.0374766	−	0.389111i	−0.00187853	−	0.0195044i
$399$	−4.21753	+	1.81070i	−0.211140	+	0.0906482i
$400$	3.70859	−	1.49878i	0.185430	−	0.0749391i
$401$	−4.24845			−0.212157			−0.106079	−	0.994358i	$-0.533830\pi$
$401$	−4.24845			−0.212157			−0.106079	+	0.994358i	$0.533830\pi$
$402$	−10.2249	+	0.984790i	−0.509970	+	0.0491168i
$403$	−12.2773			−0.611577
$404$	−29.4624	+	5.72838i	−1.46581	+	0.284998i
$405$	−1.00000			−0.0496904
$406$	−27.7592	+	15.2207i	−1.37766	+	0.755391i
$407$			62.3311i			3.08964i
$408$	−4.42047	−	14.9193i	−0.218846	−	0.738615i
$409$		−	16.3835i		−	0.810113i	−0.914292	−	0.405057i	$-0.867252\pi$
$409$		−	16.3835i		−	0.810113i	0.914292	−	0.405057i	$-0.132748\pi$
$410$	−0.125676	+	0.0121043i	−0.00620669	+	0.000597787i
$411$		−	3.53259i		−	0.174250i
$412$	−2.57626	+	0.500903i	−0.126923	+	0.0246777i
$413$	−13.5885	−	31.6508i	−0.668648	−	1.55743i
$414$	−4.99461	+	0.481048i	−0.245472	+	0.0236422i
$415$			9.14169i			0.448748i
$416$	−4.38697	−	8.42483i	−0.215089	−	0.413061i
$417$	12.1022			0.592649
$418$	−13.5329	+	1.30340i	−0.661918	+	0.0637515i
$419$			19.2720i			0.941497i	0.882268	+	0.470748i	$0.156016\pi$
$419$			19.2720i			0.941497i	−0.882268	+	0.470748i	$0.843984\pi$
$420$	−2.97716	−	4.37453i	−0.145270	−	0.213455i
$421$			14.8800i			0.725206i	0.931944	+	0.362603i	$0.118112\pi$
$421$			14.8800i			0.725206i	−0.931944	+	0.362603i	$0.881888\pi$
$422$	−1.63850	−	17.0122i	−0.0797609	−	0.828141i
$423$	12.7949			0.622110
$424$	3.43508	−	1.01779i	0.166822	−	0.0494281i
$425$		−	5.50143i		−	0.266859i
$426$	0.915201	+	9.50233i	0.0443416	+	0.460389i
$427$	6.07120	−	2.60653i	0.293806	−	0.126139i
$428$	32.9260	−	6.40181i	1.59154	−	0.309443i
$429$		−	9.30514i		−	0.449257i
$430$	1.17738	+	12.2245i	0.0567785	+	0.589519i
$431$			0.281619i			0.0135651i	0.999977	+	0.00678255i	$0.00215897\pi$
$431$			0.281619i			0.0135651i	−0.999977	+	0.00678255i	$0.997841\pi$
$432$	1.49878	+	3.70859i	0.0721102	+	0.178430i
$433$			4.06965i			0.195575i	0.995207	+	0.0977874i	$0.0311765\pi$
$433$			4.06965i			0.195575i	−0.995207	+	0.0977874i	$0.968823\pi$
$434$	13.1532	+	23.9885i	0.631375	+	1.15149i
$435$	8.46101			0.405674
$436$	−0.948297	−	4.87731i	−0.0454152	−	0.233581i
$437$	6.15510			0.294439
$438$	−0.996150	−	10.3428i	−0.0475979	−	0.494198i
$439$	18.3292			0.874804			0.437402	−	0.899266i	$-0.355899\pi$
$439$	18.3292			0.874804			0.437402	+	0.899266i	$0.355899\pi$
$440$	−4.45278	−	15.0284i	−0.212278	−	0.716449i
$441$	−4.82112	+	5.07512i	−0.229577	+	0.241672i
$442$	−13.0038	+	1.25244i	−0.618527	+	0.0595724i
$443$	−16.2913			−0.774023			−0.387012	−	0.922075i	$-0.626493\pi$
$443$	−16.2913			−0.774023			−0.387012	+	0.922075i	$0.626493\pi$
$444$	−22.0820	+	4.29340i	−1.04796	+	0.203756i
$445$		−	4.16614i		−	0.197494i
$446$	2.41728	+	25.0981i	0.114461	+	1.18843i
$447$	−11.1107			−0.525516
$448$	−11.7612	+	17.5975i	−0.555666	+	0.831405i
$449$	−36.2809			−1.71220			−0.856101	−	0.516809i	$-0.827120\pi$
$449$	−36.2809			−1.71220			−0.856101	+	0.516809i	$0.827120\pi$
$450$	0.135580	+	1.40770i	0.00639131	+	0.0663596i
$451$			0.494744i			0.0232966i
$452$	21.1981	−	4.12155i	0.997075	−	0.193861i
$453$	3.03195			0.142453
$454$	38.8229	−	3.73916i	1.82205	−	0.175487i
$455$	−4.08224	+	1.75261i	−0.191378	+	0.0821638i
$456$	−1.39391	−	4.70453i	−0.0652760	−	0.220310i
$457$	21.7531			1.01757			0.508783	−	0.860895i	$-0.330096\pi$
$457$	21.7531			1.01757			0.508783	+	0.860895i	$0.330096\pi$
$458$	−0.465555	−	4.83375i	−0.0217539	−	0.225867i
$459$	5.50143			0.256785
$460$	1.35434	+	6.96569i	0.0631465	+	0.324777i
$461$	−17.9992			−0.838305			−0.419153	−	0.907916i	$-0.637673\pi$
$461$	−17.9992			−0.838305			−0.419153	+	0.907916i	$0.637673\pi$
$462$	−18.1812	+	9.96900i	−0.845867	+	0.463800i
$463$		−	22.6300i		−	1.05170i	−0.850576	−	0.525852i	$-0.823746\pi$
$463$		−	22.6300i		−	1.05170i	0.850576	−	0.525852i	$-0.176254\pi$
$464$	−12.6812	−	31.3784i	−0.588710	−	1.45671i
$465$		−	7.31172i		−	0.339073i
$466$	−1.10143	−	11.4359i	−0.0510227	−	0.529757i
$467$			11.6927i			0.541072i	0.962710	+	0.270536i	$0.0872009\pi$
$467$			11.6927i			0.541072i	−0.962710	+	0.270536i	$0.912799\pi$
$468$	3.29653	−	0.640944i	0.152382	−	0.0296277i
$469$	17.6588	−	7.58140i	0.815408	−	0.350077i
$470$	−1.73474	−	18.0114i	−0.0800174	−	0.830803i
$471$		−	5.57251i		−	0.256768i
$472$	35.3056	−	10.4607i	1.62507	−	0.481495i
$473$	48.1239			2.21274
$474$	0.155918	+	1.61886i	0.00716153	+	0.0743567i
$475$		−	1.73478i		−	0.0795970i
$476$	16.3786	+	24.0662i	0.750714	+	1.10307i
$477$			1.26667i			0.0579970i
$478$	33.4622	−	3.22286i	1.53053	−	0.147410i
$479$	−26.6487			−1.21761			−0.608805	−	0.793320i	$-0.708351\pi$
$479$	−26.6487			−1.21761			−0.608805	+	0.793320i	$0.708351\pi$
$480$	5.01738	−	2.61265i	0.229011	−	0.119250i
$481$			18.8864i			0.861147i
$482$	−19.4368	+	1.87202i	−0.885320	+	0.0852681i
$483$	8.62593	−	3.70334i	0.392494	−	0.168508i
$484$	−38.6951	+	7.52350i	−1.75887	+	0.341977i
$485$			4.20427i			0.190906i
$486$	−1.40770	+	0.135580i	−0.0638545	+	0.00615004i
$487$			9.67576i			0.438450i	0.975674	+	0.219225i	$0.0703530\pi$
$487$			9.67576i			0.438450i	−0.975674	+	0.219225i	$0.929647\pi$
$488$	2.00656	+	6.77225i	0.0908328	+	0.306565i
$489$			20.9634i			0.947996i
$490$	7.79789	+	6.09860i	0.352273	+	0.275507i
$491$	−21.3834			−0.965021			−0.482511	−	0.875890i	$-0.660275\pi$
$491$	−21.3834			−0.965021			−0.482511	+	0.875890i	$0.660275\pi$
$492$	−0.175273	+	0.0340783i	−0.00790191	+	0.00153637i
$493$	−46.5477			−2.09640
$494$	−4.10051	+	0.394933i	−0.184491	+	0.0177689i
$495$	5.54165			0.249079
$496$	−27.1162	+	10.9587i	−1.21755	+	0.492059i
$497$	−7.04567	−	16.4110i	−0.316041	−	0.736133i
$498$	1.23943	+	12.8687i	0.0555402	+	0.576662i
$499$	−12.1520			−0.543997			−0.271998	−	0.962298i	$-0.587685\pi$
$499$	−12.1520			−0.543997			−0.271998	+	0.962298i	$0.587685\pi$
$500$	1.96324	−	0.381712i	0.0877986	−	0.0170707i
$501$		−	5.73739i		−	0.256328i
$502$	3.92513	−	0.378042i	0.175187	−	0.0168729i
$503$	−5.68562			−0.253509			−0.126755	−	0.991934i	$-0.540456\pi$
$503$	−5.68562			−0.253509			−0.126755	+	0.991934i	$0.540456\pi$
$504$	−4.78404	−	5.75438i	−0.213098	−	0.256321i
$505$	−15.0071			−0.667806
$506$	27.6784	−	2.66580i	1.23045	−	0.118509i
$507$			10.1805i			0.452133i
$508$	−0.353695	−	1.81914i	−0.0156927	−	0.0807112i
$509$	−2.01211			−0.0891852			−0.0445926	−	0.999005i	$-0.514199\pi$
$509$	−2.01211			−0.0891852			−0.0445926	+	0.999005i	$0.514199\pi$
$510$	−0.745885	−	7.74436i	−0.0330283	−	0.342926i
$511$	7.66886	+	17.8625i	0.339250	+	0.790191i
$512$	−17.2092	−	14.6916i	−0.760546	−	0.649284i
$513$	1.73478			0.0765922
$514$	4.52855	−	0.436160i	0.199746	−	0.0192382i
$515$	−1.31225			−0.0578248
$516$	3.31481	+	17.0488i	0.145926	+	0.750533i
$517$	−70.9049			−3.11839
$518$	36.9020	−	20.2338i	1.62138	−	0.889023i
$519$		−	17.1231i		−	0.751621i
$520$	−1.34920	−	4.55362i	−0.0591664	−	0.199689i
$521$		−	4.06826i		−	0.178234i	−0.996021	−	0.0891168i	$-0.971596\pi$
$521$		−	4.06826i		−	0.178234i	0.996021	−	0.0891168i	$-0.0284045\pi$
$522$	11.9106	−	1.14714i	0.521311	−	0.0502092i
$523$		−	23.4857i		−	1.02696i	−0.858102	−	0.513479i	$-0.828356\pi$
$523$		−	23.4857i		−	1.02696i	0.858102	−	0.513479i	$-0.171644\pi$
$524$	−4.77001	−	24.5333i	−0.208379	−	1.07174i
$525$	−1.04376	−	2.43116i	−0.0455536	−	0.106105i
$526$	−5.08494	+	0.489747i	−0.221714	+	0.0213540i
$527$			40.2249i			1.75223i
$528$	−8.30572	−	20.5517i	−0.361460	−	0.894398i
$529$	10.4112			0.452661
$530$	1.78310	−	0.171736i	0.0774527	−	0.00745973i
$531$			13.0188i			0.564967i
$532$	5.16470	+	7.58883i	0.223918	+	0.329018i
$533$			0.149908i			0.00649326i
$534$	−0.564846	−	5.86468i	−0.0244433	−	0.253789i
$535$	16.7713			0.725087
$536$	5.83633	+	19.6979i	0.252091	+	0.850820i
$537$		−	14.4927i		−	0.625407i
$538$	−1.17247	−	12.1735i	−0.0505486	−	0.524835i
$539$	26.7169	−	28.1245i	1.15078	−	1.21141i
$540$	0.381712	+	1.96324i	0.0164263	+	0.0844842i
$541$			28.2718i			1.21550i	0.794129	+	0.607749i	$0.207928\pi$
$541$			28.2718i			1.21550i	−0.794129	+	0.607749i	$0.792072\pi$
$542$	0.419317	+	4.35367i	0.0180112	+	0.187006i
$543$		−	1.28496i		−	0.0551430i
$544$	−27.6028	+	14.3733i	−1.18346	+	0.616250i
$545$		−	2.48432i		−	0.106417i
$546$	−5.50895	+	3.02062i	−0.235761	+	0.129271i
$547$	−29.7498			−1.27201			−0.636004	−	0.771685i	$-0.719414\pi$
$547$	−29.7498			−1.27201			−0.636004	+	0.771685i	$0.719414\pi$
$548$	−6.93532	+	1.34843i	−0.296262	+	0.0576023i
$549$	−2.49724			−0.106580
$550$	−0.751337	−	7.80098i	−0.0320371	−	0.332635i
$551$	−14.6780			−0.625302
$552$	2.85092	+	9.62198i	0.121343	+	0.409539i
$553$	−1.20033	−	2.79585i	−0.0510433	−	0.118892i
$554$	30.3227	−	2.92048i	1.28829	−	0.124079i
$555$	−11.2477			−0.477440
$556$	−4.61957	−	23.7595i	−0.195914	−	1.00763i
$557$		−	16.5286i		−	0.700340i	−0.936686	−	0.350170i	$-0.886124\pi$
$557$		−	16.5286i		−	0.700340i	0.936686	−	0.350170i	$-0.113876\pi$
$558$	−0.991324	−	10.2927i	−0.0419661	−	0.435725i
$559$	14.5816			0.616738
$560$	−7.45182	+	7.51468i	−0.314897	+	0.317553i
$561$	−30.4870			−1.28716
$562$	−2.31667	−	24.0535i	−0.0977227	−	1.01463i
$563$		−	15.9112i		−	0.670578i	−0.942115	−	0.335289i	$-0.891166\pi$
$563$		−	15.9112i		−	0.670578i	0.942115	−	0.335289i	$-0.108834\pi$
$564$	−4.88397	−	25.1194i	−0.205652	−	1.05772i
$565$	10.7975			0.454256
$566$	36.4760	−	3.51313i	1.53320	−	0.147668i
$567$	2.43116	−	1.04376i	0.102099	−	0.0438339i
$568$	18.3060	−	5.42391i	0.768102	−	0.227582i
$569$	13.2684			0.556239			0.278120	−	0.960546i	$-0.410289\pi$
$569$	13.2684			0.556239			0.278120	+	0.960546i	$0.410289\pi$
$570$	−0.235201	−	2.44204i	−0.00985149	−	0.102286i
$571$	−8.34007			−0.349021			−0.174511	−	0.984655i	$-0.555834\pi$
$571$	−8.34007			−0.349021			−0.174511	+	0.984655i	$0.555834\pi$
$572$	−18.2682	+	3.55189i	−0.763832	+	0.148512i
$573$	9.06371			0.378642
$574$	0.292905	−	0.160603i	0.0122256	−	0.00670345i
$575$			3.54807i			0.147965i
$576$	6.70874	−	4.35808i	0.279531	−	0.181587i
$577$			23.6242i			0.983487i	0.870740	+	0.491743i	$0.163640\pi$
$577$			23.6242i			0.983487i	−0.870740	+	0.491743i	$0.836360\pi$
$578$	1.79857	+	18.6742i	0.0748108	+	0.776744i
$579$		−	17.5065i		−	0.727545i
$580$	−3.22967	−	16.6110i	−0.134105	−	0.689732i
$581$	−9.54176	−	22.2249i	−0.395859	−	0.922046i
$582$	0.570015	+	5.91834i	0.0236279	+	0.245323i
$583$		−	7.01946i		−	0.290716i
$584$	−19.9251	+	5.90365i	−0.824508	+	0.244295i
$585$	1.67913			0.0694235
$586$	−3.70353	−	38.4529i	−0.152991	−	1.58848i
$587$		−	6.67124i		−	0.275351i	−0.990477	−	0.137676i	$-0.956037\pi$
$587$		−	6.67124i		−	0.275351i	0.990477	−	0.137676i	$-0.0439632\pi$
$588$	11.8039	+	7.52775i	0.486786	+	0.310439i
$589$			12.6842i			0.522643i
$590$	18.3265	−	1.76509i	0.754491	−	0.0726675i
$591$	13.1628			0.541444
$592$	16.8579	+	41.7133i	0.692857	+	1.71441i
$593$			25.3635i			1.04155i	0.853693	+	0.520776i	$0.174358\pi$
$593$			25.3635i			1.04155i	−0.853693	+	0.520776i	$0.825642\pi$
$594$	7.80098	−	0.751337i	0.320078	−	0.0308278i
$595$	5.74219	+	13.3749i	0.235407	+	0.548317i
$596$	4.24107	+	21.8128i	0.173721	+	0.893489i
$597$		−	0.276416i		−	0.0113130i
$598$	8.38660	−	0.807741i	0.342954	−	0.0330310i
$599$			32.0409i			1.30915i	0.755995	+	0.654577i	$0.227153\pi$
$599$			32.0409i			1.30915i	−0.755995	+	0.654577i	$0.772847\pi$
$600$	2.71189	−	0.803512i	0.110713	−	0.0328032i
$601$		−	27.2798i		−	1.11277i	−0.830925	−	0.556384i	$-0.812188\pi$
$601$		−	27.2798i		−	1.11277i	0.830925	−	0.556384i	$-0.187812\pi$
$602$	−15.6219	−	28.4909i	−0.636702	−	1.16120i
$603$	−7.26352			−0.295794
$604$	−1.15733	−	5.95243i	−0.0470912	−	0.242201i
$605$	−19.7099			−0.801320
$606$	−21.1254	+	2.03466i	−0.858162	+	0.0826524i
$607$	29.6611			1.20391			0.601953	−	0.798532i	$-0.294390\pi$
$607$	29.6611			1.20391			0.601953	+	0.798532i	$0.294390\pi$
$608$	−8.70403	+	4.53236i	−0.352995	+	0.183811i
$609$	−20.5701	+	8.83129i	−0.833542	+	0.357862i
$610$	0.338576	+	3.51536i	0.0137085	+	0.142333i
$611$	−21.4843			−0.869162
$612$	−2.09996	−	10.8006i	−0.0848860	−	0.436589i
$613$		−	17.5337i		−	0.708180i	−0.935211	−	0.354090i	$-0.884791\pi$
$613$		−	17.5337i		−	0.708180i	0.935211	−	0.354090i	$-0.115209\pi$
$614$	3.36839	−	0.324421i	0.135937	−	0.0130925i
$615$	−0.0892775			−0.00360002
$616$	26.5115	+	31.8888i	1.06818	+	1.28483i
$617$	−19.9979			−0.805085			−0.402543	−	0.915401i	$-0.631873\pi$
$617$	−19.9979			−0.805085			−0.402543	+	0.915401i	$0.631873\pi$
$618$	−1.84726	+	0.177916i	−0.0743076	+	0.00715681i
$619$			10.3616i			0.416466i	0.978079	+	0.208233i	$0.0667713\pi$
$619$			10.3616i			0.416466i	−0.978079	+	0.208233i	$0.933229\pi$
$620$	−14.3546	+	2.79097i	−0.576496	+	0.112088i
$621$	−3.54807			−0.142379
$622$	3.29732	+	34.2354i	0.132210	+	1.37271i
$623$	4.34847	+	10.1286i	0.174218	+	0.405793i
$624$	−2.51665	−	6.22721i	−0.100747	−	0.249288i
$625$	1.00000			0.0400000
$626$	42.6794	−	4.11059i	1.70581	−	0.164292i
$627$	−9.61352			−0.383927
$628$	−10.9402	+	2.12710i	−0.436560	+	0.0848804i
$629$	61.8787			2.46727
$630$	−1.79892	−	3.28083i	−0.0716708	−	0.130712i
$631$			1.55276i			0.0618145i	0.999522	+	0.0309072i	$0.00983964\pi$
$631$			1.55276i			0.0618145i	−0.999522	+	0.0309072i	$0.990160\pi$
$632$	3.11869	−	0.924042i	0.124055	−	0.0367564i
$633$		−	12.0851i		−	0.480340i
$634$	11.1701	−	1.07583i	0.443621	−	0.0427265i
$635$		−	0.926602i		−	0.0367711i
$636$	2.48678	−	0.483505i	0.0986072	−	0.0191722i
$637$	8.09528	−	8.52178i	0.320747	−	0.337645i
$638$	−66.0041	+	6.35707i	−2.61313	+	0.251679i
$639$			6.75026i			0.267036i
$640$	−7.04444	−	8.85302i	−0.278456	−	0.349946i
$641$	−13.3311			−0.526546			−0.263273	−	0.964721i	$-0.584802\pi$
$641$	−13.3311			−0.526546			−0.263273	+	0.964721i	$0.584802\pi$
$642$	23.6090	−	2.27386i	0.931771	−	0.0897419i
$643$			20.6034i			0.812520i	0.913758	+	0.406260i	$0.133167\pi$
$643$			20.6034i			0.812520i	−0.913758	+	0.406260i	$0.866833\pi$
$644$	−10.5632	−	15.5211i	−0.416247	−	0.611618i
$645$			8.68405i			0.341934i
$646$	1.29394	+	13.4347i	0.0509095	+	0.528583i
$647$	35.8391			1.40898			0.704490	−	0.709714i	$-0.251176\pi$
$647$	35.8391			1.40898			0.704490	+	0.709714i	$0.251176\pi$
$648$	0.803512	+	2.71189i	0.0315649	+	0.106533i
$649$		−	72.1455i		−	2.83196i
$650$	−0.227657	−	2.36371i	−0.00892943	−	0.0927123i
$651$	7.63171	+	17.7760i	0.299110	+	0.696696i
$652$	41.1560	−	8.00197i	1.61179	−	0.313381i
$653$			2.28298i			0.0893398i	0.999002	+	0.0446699i	$0.0142236\pi$
$653$			2.28298i			0.0893398i	−0.999002	+	0.0446699i	$0.985776\pi$
$654$	−0.336825	−	3.49718i	−0.0131709	−	0.136751i
$655$		−	12.4963i		−	0.488272i
$656$	0.133808	+	0.331094i	0.00522431	+	0.0129270i
$657$		−	7.34731i		−	0.286646i
$658$	23.0170	+	41.9780i	0.897298	+	1.63647i
$659$	18.0400			0.702737			0.351369	−	0.936237i	$-0.385716\pi$
$659$	18.0400			0.702737			0.351369	+	0.936237i	$0.385716\pi$
$660$	−2.11531	−	10.8796i	−0.0823385	−	0.423486i
$661$	29.8230			1.15998			0.579991	−	0.814623i	$-0.303056\pi$
$661$	29.8230			1.15998			0.579991	+	0.814623i	$0.303056\pi$
$662$	1.92689	+	20.0065i	0.0748907	+	0.777574i
$663$	−9.23762			−0.358759
$664$	24.7913	−	7.34545i	0.962088	−	0.285059i
$665$	1.81070	+	4.21753i	0.0702158	+	0.163549i
$666$	−15.8334	+	1.52497i	−0.613534	+	0.0590914i
$667$	30.0202			1.16239
$668$	−11.2639	+	2.19003i	−0.435811	+	0.0847349i
$669$			17.8291i			0.689314i
$670$	0.984790	+	10.2249i	0.0380457	+	0.395021i
$671$	13.8388			0.534242
$672$	−9.47108	+	11.5887i	−0.365355	+	0.447045i
$673$	29.2670			1.12816			0.564080	−	0.825720i	$-0.309231\pi$
$673$	29.2670			1.12816			0.564080	+	0.825720i	$0.309231\pi$
$674$	−0.399763	−	4.15065i	−0.0153983	−	0.159877i
$675$			1.00000i			0.0384900i
$676$	19.9868	−	3.88603i	0.768722	−	0.149463i
$677$	25.9210			0.996226			0.498113	−	0.867112i	$-0.334026\pi$
$677$	25.9210			0.996226			0.498113	+	0.867112i	$0.334026\pi$
$678$	15.1997	−	1.46393i	0.583740	−	0.0562220i
$679$	−4.38826	−	10.2213i	−0.168406	−	0.392256i
$680$	−14.9193	+	4.42047i	−0.572129	+	0.169517i
$681$	27.5789			1.05683
$682$	5.49357	+	57.0386i	0.210360	+	2.18412i
$683$	22.5472			0.862745			0.431373	−	0.902174i	$-0.358029\pi$
$683$	22.5472			0.862745			0.431373	+	0.902174i	$0.358029\pi$
$684$	−0.662185	−	3.40578i	−0.0253193	−	0.130223i
$685$	−3.53259			−0.134973
$686$	−25.3234	−	6.68754i	−0.966854	−	0.255331i
$687$		−	3.43380i		−	0.131008i
$688$	32.2056	−	13.0155i	1.22783	−	0.496211i
$689$		−	2.12691i		−	0.0810288i
$690$	0.481048	+	4.99461i	0.0183132	+	0.190142i
$691$			8.74160i			0.332546i	0.986080	+	0.166273i	$0.0531733\pi$
$691$			8.74160i			0.332546i	−0.986080	+	0.166273i	$0.946827\pi$
$692$	−33.6167	+	6.53610i	−1.27792	+	0.248465i
$693$	−13.4727	+	5.78417i	−0.511784	+	0.219722i
$694$	4.19958	+	43.6034i	0.159414	+	1.65516i
$695$		−	12.1022i		−	0.459064i
$696$	−6.79852	−	22.9454i	−0.257697	−	0.869742i
$697$	0.491154			0.0186038
$698$	0.601233	+	6.24247i	0.0227570	+	0.236281i
$699$		−	8.12381i		−	0.307271i
$700$	−4.37453	+	2.97716i	−0.165342	+	0.112526i
$701$			14.5041i			0.547811i	0.961757	+	0.273906i	$0.0883156\pi$
$701$			14.5041i			0.547811i	−0.961757	+	0.273906i	$0.911684\pi$
$702$	2.36371	−	0.227657i	0.0892125	−	0.00859235i
$703$	19.5123			0.735921
$704$	−37.1775	+	24.1509i	−1.40118	+	0.910223i
$705$		−	12.7949i		−	0.481884i
$706$	36.0019	−	3.46746i	1.35495	−	0.130500i
$707$	36.4846	−	15.6638i	1.37215	−	0.589099i
$708$	25.5589	−	4.96943i	0.960564	−	0.186763i
$709$		−	27.9863i		−	1.05105i	−0.850779	−	0.525523i	$-0.823870\pi$
$709$		−	27.9863i		−	1.05105i	0.850779	−	0.525523i	$-0.176130\pi$
$710$	9.50233	−	0.915201i	0.356616	−	0.0343469i
$711$			1.15000i			0.0431285i
$712$	−11.2981	+	3.34755i	−0.423416	+	0.125455i
$713$		−	25.9425i		−	0.971554i
$714$	9.89665	+	18.0493i	0.370373	+	0.675478i
$715$	−9.30514			−0.347993
$716$	−28.4526	+	5.53205i	−1.06332	+	0.206742i
$717$	23.7708			0.887739
$718$	−22.3259	+	2.15028i	−0.833193	+	0.0802476i
$719$	31.9104			1.19006			0.595029	−	0.803704i	$-0.297141\pi$
$719$	31.9104			1.19006			0.595029	+	0.803704i	$0.297141\pi$
$720$	3.70859	−	1.49878i	0.138211	−	0.0558563i
$721$	3.19030	−	1.36968i	0.118813	−	0.0510096i
$722$	−2.16800	−	22.5099i	−0.0806847	−	0.837731i
$723$	−13.8075			−0.513505
$724$	−2.52268	+	0.490485i	−0.0937547	+	0.0182287i
$725$		−	8.46101i		−	0.314234i
$726$	−27.7456	+	2.67227i	−1.02973	+	0.0991771i
$727$	−37.3223			−1.38421			−0.692104	−	0.721798i	$-0.743316\pi$
$727$	−37.3223			−1.38421			−0.692104	+	0.721798i	$0.743316\pi$
$728$	8.03303	+	9.66235i	0.297724	+	0.358111i
$729$	−1.00000			−0.0370370
$730$	−10.3428	+	0.996150i	−0.382804	+	0.0368692i
$731$		−	47.7747i		−	1.76701i
$732$	0.953227	+	4.90267i	0.0352323	+	0.181208i
$733$	31.5170			1.16411			0.582053	−	0.813151i	$-0.302250\pi$
$733$	31.5170			1.16411			0.582053	+	0.813151i	$0.302250\pi$
$734$	2.81180	+	29.1943i	0.103785	+	1.07758i
$735$	5.07512	+	4.82112i	0.187199	+	0.177830i
$736$	17.8020	−	9.26985i	0.656190	−	0.341691i
$737$	40.2519			1.48270
$738$	−0.125676	+	0.0121043i	−0.00462619	+	0.000445564i
$739$	4.86962			0.179132			0.0895659	−	0.995981i	$-0.471452\pi$
$739$	4.86962			0.179132			0.0895659	+	0.995981i	$0.471452\pi$
$740$	4.29340	+	22.0820i	0.157829	+	0.811750i
$741$	−2.91291			−0.107009
$742$	−4.15575	+	2.27865i	−0.152562	+	0.0836518i
$743$			24.0338i			0.881714i	0.897577	+	0.440857i	$0.145325\pi$
$743$			24.0338i			0.881714i	−0.897577	+	0.440857i	$0.854675\pi$
$744$	−19.8286	+	5.87506i	−0.726952	+	0.215390i
$745$			11.1107i			0.407063i
$746$	−20.5513	+	1.97937i	−0.752438	+	0.0724698i
$747$			9.14169i			0.334477i
$748$	11.6373	+	59.8532i	0.425500	+	2.18845i
$749$	−40.7738	+	17.5053i	−1.48984	+	0.639629i
$750$	1.40770	−	0.135580i	0.0514019	−	0.00495069i
$751$		−	1.33007i		−	0.0485348i	−0.999706	−	0.0242674i	$-0.992275\pi$
$751$		−	1.33007i		−	0.0485348i	0.999706	−	0.0242674i	$-0.00772531\pi$
$752$	−47.4511	+	19.1768i	−1.73036	+	0.699305i
$753$	2.78833			0.101612
$754$	−19.9994	+	1.92620i	−0.728334	+	0.0701482i
$755$		−	3.03195i		−	0.110344i
$756$	−2.97716	−	4.37453i	−0.108278	−	0.159100i
$757$			12.9373i			0.470213i	0.971970	+	0.235106i	$0.0755439\pi$
$757$			12.9373i			0.470213i	−0.971970	+	0.235106i	$0.924456\pi$
$758$	−4.75875	−	49.4091i	−0.172846	−	1.79462i
$759$	19.6621			0.713691
$760$	−4.70453	+	1.39391i	−0.170651	+	0.0505626i
$761$			35.0635i			1.27105i	0.772079	+	0.635526i	$0.219217\pi$
$761$			35.0635i			1.27105i	−0.772079	+	0.635526i	$0.780783\pi$
$762$	−0.125629	−	1.30438i	−0.00455105	−	0.0472526i
$763$	2.59305	+	6.03980i	0.0938746	+	0.218655i
$764$	−3.45973	−	17.7942i	−0.125169	−	0.643772i
$765$		−	5.50143i		−	0.198905i
$766$	−0.398395	−	4.13645i	−0.0143946	−	0.149456i
$767$		−	21.8602i		−	0.789327i
$768$	−11.1167	−	11.5073i	−0.401141	−	0.415234i
$769$			18.6210i			0.671491i	0.941953	+	0.335746i	$0.108988\pi$
$769$			18.6210i			0.671491i	−0.941953	+	0.335746i	$0.891012\pi$
$770$	9.96900	+	18.1812i	0.359258	+	0.655206i
$771$	3.21699			0.115857
$772$	−34.3694	+	6.68244i	−1.23698	+	0.240506i
$773$	−26.4130			−0.950010			−0.475005	−	0.879983i	$-0.657554\pi$
$773$	−26.4130			−0.950010			−0.475005	+	0.879983i	$0.657554\pi$
$774$	1.17738	+	12.2245i	0.0423202	+	0.439402i
$775$	−7.31172			−0.262645
$776$	11.4015	−	3.37818i	0.409291	−	0.121270i
$777$	27.3451	−	11.7400i	0.981001	−	0.421170i
$778$	−41.9537	+	4.04070i	−1.50411	+	0.144866i
$779$	0.154876			0.00554903
$780$	−0.640944	−	3.29653i	−0.0229495	−	0.118035i
$781$		−	37.4075i		−	1.33855i
$782$	−2.64645	−	27.4775i	−0.0946369	−	0.982594i
$783$	8.46101			0.302372
$784$	10.2730	−	26.0474i	0.366895	−	0.930263i
$785$	−5.57251			−0.198892
$786$	−1.69426	−	17.5911i	−0.0604321	−	0.627453i
$787$		−	18.3513i		−	0.654153i	−0.944998	−	0.327077i	$-0.893936\pi$
$787$		−	18.3513i		−	0.654153i	0.944998	−	0.327077i	$-0.106064\pi$
$788$	−5.02439	−	25.8416i	−0.178986	−	0.920569i
$789$	−3.61223			−0.128599
$790$	1.61886	−	0.155918i	0.0575964	−	0.00554730i
$791$	−26.2506	+	11.2701i	−0.933363	+	0.400718i
$792$	−4.45278	−	15.0284i	−0.158223	−	0.534010i
$793$	4.19319			0.148904
$794$	2.76366	+	28.6945i	0.0980786	+	1.01833i
$795$	1.26667			0.0449243
$796$	−0.542671	+	0.105512i	−0.0192344	+	0.00373976i
$797$	−16.6258			−0.588917			−0.294458	−	0.955664i	$-0.595139\pi$
$797$	−16.6258			−0.588917			−0.294458	+	0.955664i	$0.595139\pi$
$798$	3.12073	+	5.69151i	0.110473	+	0.201477i
$799$			70.3903i			2.49023i
$800$	−2.61265	−	5.01738i	−0.0923710	−	0.177391i
$801$		−	4.16614i		−	0.147203i
$802$	0.576006	+	5.98054i	0.0203395	+	0.211180i
$803$			40.7162i			1.43684i
$804$	2.77258	+	14.2600i	0.0977812	+	0.502912i
$805$	−3.70334	−	8.62593i	−0.130526	−	0.304024i
$806$	1.66456	+	17.2828i	0.0586317	+	0.608760i
$807$		−	8.64776i		−	0.304416i
$808$	12.0584	+	40.6976i	0.424211	+	1.43174i
$809$	6.95098			0.244383			0.122192	−	0.992507i	$-0.461008\pi$
$809$	6.95098			0.244383			0.122192	+	0.992507i	$0.461008\pi$
$810$	0.135580	+	1.40770i	0.00476380	+	0.0494615i
$811$		−	49.6027i		−	1.74179i	−0.491471	−	0.870894i	$-0.663541\pi$
$811$		−	49.6027i		−	1.74179i	0.491471	−	0.870894i	$-0.336459\pi$
$812$	25.1898	+	37.0129i	0.883988	+	1.29890i
$813$			3.09276i			0.108468i
$814$	87.7434	−	8.45085i	3.07540	−	0.296202i
$815$	20.9634			0.734315
$816$	−20.4026	+	8.24545i	−0.714233	+	0.288648i
$817$		−	15.0649i		−	0.527053i
$818$	−23.0631	+	2.22128i	−0.806382	+	0.0776653i
$819$	−4.08224	+	1.75261i	−0.142645	+	0.0612413i
$820$	0.0340783	+	0.175273i	0.00119007	+	0.00612079i
$821$		−	46.2978i		−	1.61580i	−0.589317	−	0.807902i	$-0.700603\pi$
$821$		−	46.2978i		−	1.61580i	0.589317	−	0.807902i	$-0.299397\pi$
$822$	−4.97283	+	0.478950i	−0.173447	+	0.0167053i
$823$			5.51492i			0.192238i	0.995370	+	0.0961191i	$0.0306430\pi$
$823$			5.51492i			0.192238i	−0.995370	+	0.0961191i	$0.969357\pi$
$824$	1.05441	+	3.55869i	0.0367322	+	0.123973i
$825$		−	5.54165i		−	0.192935i
$826$	−42.7125	+	23.4198i	−1.48616	+	0.814879i
$827$	56.0706			1.94976			0.974882	−	0.222720i	$-0.0714937\pi$
$827$	56.0706			1.94976			0.974882	+	0.222720i	$0.0714937\pi$
$828$	1.35434	+	6.96569i	0.0470666	+	0.242075i
$829$	−44.7027			−1.55259			−0.776295	−	0.630370i	$-0.782903\pi$
$829$	−44.7027			−1.55259			−0.776295	+	0.630370i	$0.782903\pi$
$830$	12.8687	−	1.23943i	0.446681	−	0.0430213i
$831$	21.5406			0.747236
$832$	−11.2648	+	7.31778i	−0.390538	+	0.253698i
$833$	−27.9204	−	26.5230i	−0.967386	−	0.918969i
$834$	−1.64082	−	17.0363i	−0.0568171	−	0.589919i
$835$	−5.73739			−0.198551
$836$	3.66960	+	18.8736i	0.126916	+	0.652757i
$837$		−	7.31172i		−	0.252730i
$838$	27.1291	−	2.61289i	0.937160	−	0.0902610i
$839$	44.8497			1.54838			0.774191	−	0.632952i	$-0.218157\pi$
$839$	44.8497			1.54838			0.774191	+	0.632952i	$0.218157\pi$
$840$	−5.75438	+	4.78404i	−0.198545	+	0.165065i
$841$	−42.5887			−1.46857
$842$	20.9465	−	2.01743i	0.721865	−	0.0695252i
$843$		−	17.0871i		−	0.588510i
$844$	−23.7259	+	4.61303i	−0.816680	+	0.158787i
$845$	10.1805			0.350221
$846$	−1.73474	−	18.0114i	−0.0596414	−	0.619244i
$847$	47.9179	−	20.5724i	1.64648	−	0.706877i
$848$	−1.89847	−	4.69757i	−0.0651937	−	0.161315i
$849$	25.9118			0.889290
$850$	−7.74436	+	0.745885i	−0.265629	+	0.0255836i
$851$	−39.9078			−1.36802
$852$	13.2523	−	2.57666i	0.454018	−	0.0882747i
$853$	0.0388026			0.00132858			0.000664288	−	1.00000i	$-0.499789\pi$
$853$	0.0388026			0.00132858			0.000664288		1.00000i	$0.499789\pi$
$854$	−4.49234	−	8.19303i	−0.153725	−	0.280360i
$855$		−	1.73478i		−	0.0593281i
$856$	−13.4759	−	45.4820i	−0.460598	−	1.55454i
$857$			57.0186i			1.94772i	0.227154	+	0.973859i	$0.427058\pi$
$857$			57.0186i			1.94772i	−0.227154	+	0.973859i	$0.572942\pi$
$858$	−13.0988	+	1.26159i	−0.447187	+	0.0430701i
$859$		−	9.67639i		−	0.330154i	−0.986281	−	0.165077i	$-0.947213\pi$
$859$		−	9.67639i		−	0.330154i	0.986281	−	0.165077i	$-0.0527873\pi$
$860$	17.0488	−	3.31481i	0.581360	−	0.113034i
$861$	0.217048	−	0.0931846i	0.00739698	−	0.00317572i
$862$	0.396435	−	0.0381819i	0.0135026	−	0.00130048i
$863$			35.9183i			1.22267i	0.791371	+	0.611337i	$0.209368\pi$
$863$			35.9183i			1.22267i	−0.791371	+	0.611337i	$0.790632\pi$
$864$	5.01738	−	2.61265i	0.170695	−	0.0888840i
$865$	−17.1231			−0.582203
$866$	5.72884	−	0.551763i	0.194674	−	0.0187497i
$867$			13.2658i			0.450529i
$868$	31.9854	−	21.7682i	1.08565	−	0.738859i
$869$		−	6.37291i		−	0.216186i
$870$	−1.14714	−	11.9106i	−0.0388919	−	0.403806i
$871$	12.1964			0.413259
$872$	−6.73722	+	1.99618i	−0.228151	+	0.0675993i
$873$			4.20427i			0.142293i
$874$	−0.834510	−	8.66454i	−0.0282277	−	0.293082i
$875$	−2.43116	+	1.04376i	−0.0821883	+	0.0352856i
$876$	−14.4245	+	2.80456i	−0.487359	+	0.0947573i
$877$		−	20.0801i		−	0.678057i	−0.940776	−	0.339028i	$-0.889902\pi$
$877$		−	20.0801i		−	0.678057i	0.940776	−	0.339028i	$-0.110098\pi$
$878$	−2.48507	−	25.8020i	−0.0838671	−	0.870774i
$879$		−	27.3161i		−	0.921350i
$880$	−20.5517	+	8.30572i	−0.692798	+	0.279986i
$881$		−	37.0514i		−	1.24829i	−0.781307	−	0.624147i	$-0.785447\pi$
$881$		−	37.0514i		−	1.24829i	0.781307	−	0.624147i	$-0.214553\pi$
$882$	7.79789	+	6.09860i	0.262569	+	0.205350i
$883$	−13.3489			−0.449225			−0.224613	−	0.974448i	$-0.572112\pi$
$883$	−13.3489			−0.449225			−0.224613	+	0.974448i	$0.572112\pi$
$884$	3.52611	+	18.1356i	0.118596	+	0.609967i
$885$	13.0188			0.437622
$886$	2.20878	+	22.9333i	0.0742053	+	0.770458i
$887$	−4.46449			−0.149903			−0.0749515	−	0.997187i	$-0.523880\pi$
$887$	−4.46449			−0.149903			−0.0749515	+	0.997187i	$0.523880\pi$
$888$	9.03770	+	30.5027i	0.303285	+	1.02360i
$889$	0.967153	+	2.25272i	0.0324373	+	0.0755539i
$890$	−5.86468	+	0.564846i	−0.196584	+	0.0189337i
$891$	5.54165			0.185652
$892$	35.0028	−	6.80560i	1.17198	−	0.227868i
$893$			22.1963i			0.742771i
$894$	1.50638	+	15.6405i	0.0503810	+	0.523096i
$895$	−14.4927			−0.484438
$896$	26.3666	+	14.1704i	0.880847	+	0.473400i
$897$	5.95767			0.198921
$898$	4.91897	+	51.0726i	0.164148	+	1.70432i
$899$			61.8645i			2.06330i
$900$	1.96324	−	0.381712i	0.0654412	−	0.0127237i
$901$	−6.96852			−0.232155
$902$	0.696452	−	0.0670775i	0.0231893	−	0.00223344i
$903$	−9.06409	−	21.1123i	−0.301634	−	0.702575i
$904$	−8.67595	−	29.2818i	−0.288558	−	0.973897i
$905$	−1.28496			−0.0427135
$906$	−0.411072	−	4.26807i	−0.0136570	−	0.141797i
$907$	17.0639			0.566598			0.283299	−	0.959032i	$-0.408571\pi$
$907$	17.0639			0.566598			0.283299	+	0.959032i	$0.408571\pi$
$908$	−10.5272	−	54.1440i	−0.349358	−	1.79683i
$909$	−15.0071			−0.497753
$910$	3.02062	+	5.50895i	0.100133	+	0.182620i
$911$			0.534170i			0.0176978i	0.999961	+	0.00884891i	$0.00281673\pi$
$911$			0.534170i			0.0176978i	−0.999961	+	0.00884891i	$0.997183\pi$
$912$	−6.43358	+	2.60005i	−0.213037	+	0.0860963i
$913$		−	50.6600i		−	1.67660i
$914$	−2.94928	−	30.6218i	−0.0975536	−	1.01288i
$915$			2.49724i			0.0825562i
$916$	−6.74135	+	1.31072i	−0.222741	+	0.0433075i
$917$	13.0432	+	30.3806i	0.430725	+	1.00326i
$918$	−0.745885	−	7.74436i	−0.0246179	−	0.255602i
$919$		−	7.87145i		−	0.259655i	−0.991537	−	0.129828i	$-0.958558\pi$
$919$		−	7.87145i		−	0.259655i	0.991537	−	0.129828i	$-0.0414424\pi$
$920$	9.62198	−	2.85092i	0.317227	−	0.0939919i
$921$	2.39283			0.0788465
$922$	2.44033	+	25.3374i	0.0803680	+	0.834444i
$923$		−	11.3346i		−	0.373081i
$924$	16.4984	+	24.2421i	0.542756	+	0.797507i
$925$			11.2477i			0.369824i
$926$	−31.8562	+	3.06818i	−1.04686	+	0.100827i
$927$	−1.31225			−0.0431001
$928$	−42.4521	+	22.1056i	−1.39356	+	0.725653i
$929$		−	29.4442i		−	0.966034i	−0.875611	−	0.483017i	$-0.839541\pi$
$929$		−	29.4442i		−	0.966034i	0.875611	−	0.483017i	$-0.160459\pi$
$930$	−10.2927	+	0.991324i	−0.337511	+	0.0325068i
$931$	−8.80420	−	8.36356i	−0.288546	−	0.274105i
$932$	−15.9490	+	3.10096i	−0.522426	+	0.101575i
$933$			24.3201i			0.796204i
$934$	16.4598	−	1.58529i	0.538580	−	0.0518724i
$935$			30.4870i			0.997032i
$936$	−1.34920	−	4.55362i	−0.0441000	−	0.148840i
$937$			47.0734i			1.53782i	0.639357	+	0.768910i	$0.279201\pi$
$937$			47.0734i			1.53782i	−0.639357	+	0.768910i	$0.720799\pi$
$938$	−13.0665	−	23.8304i	−0.426637	−	0.778091i
$939$	30.3185			0.989407
$940$	−25.1194	+	4.88397i	−0.819305	+	0.159298i
$941$	−7.55709			−0.246354			−0.123177	−	0.992385i	$-0.539308\pi$
$941$	−7.55709			−0.246354			−0.123177	+	0.992385i	$0.539308\pi$
$942$	−7.84442	+	0.755522i	−0.255585	+	0.0246162i
$943$	−0.316763			−0.0103152
$944$	−19.5123	−	48.2813i	−0.635072	−	1.57142i
$945$	−1.04376	−	2.43116i	−0.0339536	−	0.0790858i
$946$	−6.52465	−	67.7440i	−0.212135	−	2.20255i
$947$	−35.7888			−1.16298			−0.581490	−	0.813554i	$-0.697530\pi$
$947$	−35.7888			−1.16298			−0.581490	+	0.813554i	$0.697530\pi$
$948$	2.25773	−	0.438970i	0.0733276	−	0.0142571i
$949$			12.3371i			0.400479i
$950$	−2.44204	+	0.235201i	−0.0792304	+	0.00763094i
$951$	7.93499			0.257310
$952$	31.6573	−	26.3191i	1.02602	−	0.853007i
$953$	−0.983354			−0.0318540			−0.0159270	−	0.999873i	$-0.505070\pi$
$953$	−0.983354			−0.0318540			−0.0159270	+	0.999873i	$0.505070\pi$
$954$	1.78310	−	0.171736i	0.0577299	−	0.00556015i
$955$		−	9.06371i		−	0.293295i
$956$	−9.07362	−	46.6678i	−0.293462	−	1.50934i
$957$	−46.8879			−1.51567
$958$	3.61304	+	37.5134i	0.116732	+	1.21200i
$959$	8.58831	−	3.68719i	0.277331	−	0.119066i
$960$	−4.35808	−	6.70874i	−0.140656	−	0.216524i
$961$	22.4613			0.724557
$962$	26.5864	−	2.56062i	0.857180	−	0.0825578i
$963$	16.7713			0.540448
$964$	5.27048	+	27.1073i	0.169751	+	0.873067i
$965$	−17.5065			−0.563554
$966$	−6.38270	−	11.6406i	−0.205360	−	0.374531i
$967$			18.3924i			0.591459i	0.955272	+	0.295730i	$0.0955627\pi$
$967$			18.3924i			0.591459i	−0.955272	+	0.295730i	$0.904437\pi$
$968$	15.8371	+	53.4511i	0.509024	+	1.71798i
$969$			9.54375i			0.306590i
$970$	5.91834	−	0.570015i	0.190027	−	0.0183021i
$971$			1.49104i			0.0478497i	0.999714	+	0.0239248i	$0.00761624\pi$
$971$			1.49104i			0.0478497i	−0.999714	+	0.0239248i	$0.992384\pi$
$972$	0.381712	+	1.96324i	0.0122434	+	0.0629708i
$973$	12.6319	+	29.4225i	0.404959	+	0.943243i
$974$	13.6206	−	1.31184i	0.436431	−	0.0420341i
$975$		−	1.67913i		−	0.0537752i
$976$	9.26124	−	3.74282i	0.296445	−	0.119805i
$977$	−24.8612			−0.795382			−0.397691	−	0.917519i	$-0.630188\pi$
$977$	−24.8612			−0.795382			−0.397691	+	0.917519i	$0.630188\pi$
$978$	29.5101	−	2.84222i	0.943630	−	0.0908841i
$979$			23.0873i			0.737873i
$980$	7.52775	−	11.8039i	0.240465	−	0.377063i
$981$		−	2.48432i		−	0.0793183i
$982$	2.89917	+	30.1015i	0.0925162	+	0.960576i
$983$	33.5242			1.06925			0.534627	−	0.845088i	$-0.320452\pi$
$983$	33.5242			1.06925			0.534627	+	0.845088i	$0.320452\pi$
$984$	0.0717355	+	0.242111i	0.00228685	+	0.00771822i
$985$		−	13.1628i		−	0.419400i
$986$	6.31094	+	65.5251i	0.200981	+	2.08675i
$987$	13.3549	+	31.1065i	0.425090	+	0.990131i
$988$	1.11189	+	5.71874i	0.0353741	+	0.181937i
$989$			30.8116i			0.979751i
$990$	−0.751337	−	7.80098i	−0.0238791	−	0.247931i
$991$		−	32.3140i		−	1.02649i	−0.858243	−	0.513244i	$-0.828443\pi$
$991$		−	32.3140i		−	1.02649i	0.858243	−	0.513244i	$-0.171557\pi$
$992$	19.1029	+	36.6857i	0.606519	+	1.16477i
$993$			14.2122i			0.451010i
$994$	−22.1465	+	12.1432i	−0.702443	+	0.385159i
$995$	−0.276416			−0.00876299
$996$	17.9473	−	3.48949i	0.568682	−	0.110569i
$997$	2.00398			0.0634665			0.0317333	−	0.999496i	$-0.489897\pi$
$997$	2.00398			0.0634665			0.0317333	+	0.999496i	$0.489897\pi$
$998$	1.64757	+	17.1063i	0.0521528	+	0.541491i
$999$	−11.2477			−0.355863

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.z.c.811.11	✓	28
4.3	odd	2		3360.2.z.c.1231.4		28
7.6	odd	2		840.2.z.d.811.11	yes	28
8.3	odd	2		840.2.z.d.811.12	yes	28
8.5	even	2		3360.2.z.d.1231.26		28
28.27	even	2		3360.2.z.d.1231.25		28
56.13	odd	2		3360.2.z.c.1231.3		28
56.27	even	2	inner	840.2.z.c.811.12	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.z.c.811.11	✓	28	1.1	even	1	trivial
840.2.z.c.811.12	yes	28	56.27	even	2	inner
840.2.z.d.811.11	yes	28	7.6	odd	2
840.2.z.d.811.12	yes	28	8.3	odd	2
3360.2.z.c.1231.3		28	56.13	odd	2
3360.2.z.c.1231.4		28	4.3	odd	2
3360.2.z.d.1231.25		28	28.27	even	2
3360.2.z.d.1231.26		28	8.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.z (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.135580 - 1.40770i) q^{2} -1.00000i q^{3} +(-1.96324 + 0.381712i) q^{4} -1.00000 q^{5} +(-1.40770 + 0.135580i) q^{6} +(2.43116 - 1.04376i) q^{7} +(0.803512 + 2.71189i) q^{8} -1.00000 q^{9} +(0.135580 + 1.40770i) q^{10} +5.54165 q^{11} +(0.381712 + 1.96324i) q^{12} +1.67913 q^{13} +(-1.79892 - 3.28083i) q^{14} +1.00000i q^{15} +(3.70859 - 1.49878i) q^{16} -5.50143i q^{17} +(0.135580 + 1.40770i) q^{18} -1.73478i q^{19} +(1.96324 - 0.381712i) q^{20} +(-1.04376 - 2.43116i) q^{21} +(-0.751337 - 7.80098i) q^{22} +3.54807i q^{23} +(2.71189 - 0.803512i) q^{24} +1.00000 q^{25} +(-0.227657 - 2.36371i) q^{26} +1.00000i q^{27} +(-4.37453 + 2.97716i) q^{28} -8.46101i q^{29} +(1.40770 - 0.135580i) q^{30} -7.31172 q^{31} +(-2.61265 - 5.01738i) q^{32} -5.54165i q^{33} +(-7.74436 + 0.745885i) q^{34} +(-2.43116 + 1.04376i) q^{35} +(1.96324 - 0.381712i) q^{36} +11.2477i q^{37} +(-2.44204 + 0.235201i) q^{38} -1.67913i q^{39} +(-0.803512 - 2.71189i) q^{40} +0.0892775i q^{41} +(-3.28083 + 1.79892i) q^{42} +8.68405 q^{43} +(-10.8796 + 2.11531i) q^{44} +1.00000 q^{45} +(4.99461 - 0.481048i) q^{46} -12.7949 q^{47} +(-1.49878 - 3.70859i) q^{48} +(4.82112 - 5.07512i) q^{49} +(-0.135580 - 1.40770i) q^{50} -5.50143 q^{51} +(-3.29653 + 0.640944i) q^{52} -1.26667i q^{53} +(1.40770 - 0.135580i) q^{54} -5.54165 q^{55} +(4.78404 + 5.75438i) q^{56} -1.73478 q^{57} +(-11.9106 + 1.14714i) q^{58} -13.0188i q^{59} +(-0.381712 - 1.96324i) q^{60} +2.49724 q^{61} +(0.991324 + 10.2927i) q^{62} +(-2.43116 + 1.04376i) q^{63} +(-6.70874 + 4.35808i) q^{64} -1.67913 q^{65} +(-7.80098 + 0.751337i) q^{66} +7.26352 q^{67} +(2.09996 + 10.8006i) q^{68} +3.54807 q^{69} +(1.79892 + 3.28083i) q^{70} -6.75026i q^{71} +(-0.803512 - 2.71189i) q^{72} +7.34731i q^{73} +(15.8334 - 1.52497i) q^{74} -1.00000i q^{75} +(0.662185 + 3.40578i) q^{76} +(13.4727 - 5.78417i) q^{77} +(-2.36371 + 0.227657i) q^{78} -1.15000i q^{79} +(-3.70859 + 1.49878i) q^{80} +1.00000 q^{81} +(0.125676 - 0.0121043i) q^{82} -9.14169i q^{83} +(2.97716 + 4.37453i) q^{84} +5.50143i q^{85} +(-1.17738 - 12.2245i) q^{86} -8.46101 q^{87} +(4.45278 + 15.0284i) q^{88} +4.16614i q^{89} +(-0.135580 - 1.40770i) q^{90} +(4.08224 - 1.75261i) q^{91} +(-1.35434 - 6.96569i) q^{92} +7.31172i q^{93} +(1.73474 + 18.0114i) q^{94} +1.73478i q^{95} +(-5.01738 + 2.61265i) q^{96} -4.20427i q^{97} +(-7.79789 - 6.09860i) q^{98} -5.54165 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 2 q^{4} - 28 q^{5} - 4 q^{6} - 4 q^{7} - 10 q^{8} - 28 q^{9} - 2 q^{10} + 8 q^{12} + 8 q^{13} + 6 q^{14} + 6 q^{16} - 2 q^{18} + 2 q^{20} + 4 q^{24} + 28 q^{25} - 16 q^{26} - 18 q^{28}+ \cdots - 54 q^{98}+O(q^{100}) \) 28 * q + 2 * q^2 - 2 * q^4 - 28 * q^5 - 4 * q^6 - 4 * q^7 - 10 * q^8 - 28 * q^9 - 2 * q^10 + 8 * q^12 + 8 * q^13 + 6 * q^14 + 6 * q^16 - 2 * q^18 + 2 * q^20 + 4 * q^24 + 28 * q^25 - 16 * q^26 - 18 * q^28 + 4 * q^30 - 24 * q^31 + 2 * q^32 - 8 * q^34 + 4 * q^35 + 2 * q^36 - 36 * q^38 + 10 * q^40 - 20 * q^42 + 24 * q^43 - 4 * q^44 + 28 * q^45 - 44 * q^46 + 24 * q^47 - 16 * q^48 + 28 * q^49 + 2 * q^50 - 16 * q^52 + 4 * q^54 - 34 * q^56 + 8 * q^57 - 12 * q^58 - 8 * q^60 + 16 * q^61 + 28 * q^62 + 4 * q^63 + 22 * q^64 - 8 * q^65 + 20 * q^66 - 8 * q^67 + 12 * q^68 + 24 * q^69 - 6 * q^70 + 10 * q^72 - 8 * q^74 + 16 * q^76 - 16 * q^77 + 20 * q^78 - 6 * q^80 + 28 * q^81 - 24 * q^82 + 16 * q^84 - 4 * q^86 - 16 * q^87 + 40 * q^88 + 2 * q^90 + 48 * q^91 + 40 * q^92 - 52 * q^94 + 16 * q^96 - 54 * q^98

Introduction

L-functions

Modular forms

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