LMFDB - Embedded newform 840.2.z.d.811.12

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			811.12
Character	$\chi$	$=$	840.811
Dual form			840.2.z.d.811.11

$q$-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} +(-1.13969 - 3.56386i) 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} +(5.17137 - 1.12115i) 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} +(-3.56386 + 1.13969i) 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} +(0.877106 + 7.43173i) 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} +(-1.13969 - 3.56386i) 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} +(-1.12115 - 5.17137i) 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} +(6.49060 + 7.47477i) 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} + 2 q^{14} + 6 q^{16} - 2 q^{18} - 2 q^{20} - 4 q^{24} + 28 q^{25} + 16 q^{26} + 10 q^{28}+ \cdots - 30 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 + 2 * q^14 + 6 * q^16 - 2 * q^18 - 2 * q^20 - 4 * q^24 + 28 * q^25 + 16 * q^26 + 10 * 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 + 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 - 22 * 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 + 2 * 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 - 12 * 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 - 30 * 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	$-0.574806\pi$
$13$	−1.67913			−0.465707			−0.232853	+	0.972512i	$0.574806\pi$
$14$	−1.13969	−	3.56386i	−0.304594	−	0.952482i
$15$		−	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	$-0.879388\pi$
$23$		−	3.54807i		−	0.739823i	0.929067	−	0.369912i	$-0.120612\pi$
$24$	−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
$28$	5.17137	−	1.12115i	0.977296	−	0.211877i
$29$			8.46101i			1.57117i	0.618754	+	0.785585i	$0.287638\pi$
$29$			8.46101i			1.57117i	−0.618754	+	0.785585i	$0.712362\pi$
$30$	1.40770	+	0.135580i	0.257010	+	0.0247534i
$31$	7.31172			1.31322			0.656612	−	0.754229i	$-0.271989\pi$
$31$	7.31172			1.31322			0.656612	+	0.754229i	$0.271989\pi$
$32$	−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	$-0.624433\pi$
$37$		−	11.2477i		−	1.84912i	0.381039	−	0.924559i	$-0.375567\pi$
$38$	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	$0.997781\pi$
$42$	−3.56386	+	1.13969i	−0.549916	+	0.175858i
$43$	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	$-0.117036\pi$
$47$	12.7949			1.86633			0.933164	+	0.359450i	$0.117036\pi$
$48$	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	$0.0277266\pi$
$53$			1.26667i			0.173991i	−0.996209	+	0.0869955i	$0.972273\pi$
$54$	−1.40770	−	0.135580i	−0.191564	−	0.0184501i
$55$	5.54165			0.747236
$56$	0.877106	+	7.43173i	0.117208	+	0.993107i
$57$	−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	$-0.551107\pi$
$61$	−2.49724			−0.319739			−0.159869	+	0.987138i	$0.551107\pi$
$62$	−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
$70$	−1.13969	−	3.56386i	−0.136219	−	0.425963i
$71$			6.75026i			0.801108i	0.916273	+	0.400554i	$0.131182\pi$
$71$			6.75026i			0.801108i	−0.916273	+	0.400554i	$0.868818\pi$
$72$	−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	$0.0206067\pi$
$79$			1.15000i			0.129386i	−0.997905	+	0.0646928i	$0.979393\pi$
$80$	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	$-0.167297\pi$
$84$	−1.12115	−	5.17137i	−0.122327	−	0.564242i
$85$		−	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	$-0.0684665\pi$
$98$	6.49060	+	7.47477i	0.655649	+	0.755066i
$99$	−5.54165			−0.556957
$100$	−1.96324	−	0.381712i	−0.196324	−	0.0381712i
$101$	−15.0071			−1.49326			−0.746629	−	0.665240i	$-0.768329\pi$
$101$	−15.0071			−1.49326			−0.746629	+	0.665240i	$0.768329\pi$
$102$	0.745885	−	7.74436i	0.0738536	−	0.766806i
$103$	−1.31225			−0.129300			−0.0646501	−	0.997908i	$-0.520593\pi$
$103$	−1.31225			−0.129300			−0.0646501	+	0.997908i	$0.520593\pi$
$104$	−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	$-0.962038\pi$
$109$		−	2.48432i		−	0.237955i	0.992897	−	0.118978i	$-0.0379616\pi$
$110$	−0.751337	+	7.80098i	−0.0716372	+	0.743794i
$111$	−11.2477			−1.06759
$112$	−10.5806	+	0.227106i	−0.999770	+	0.0214595i
$113$	−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
$126$	1.13969	+	3.56386i	0.101531	+	0.317494i
$127$		−	0.926602i		−	0.0822226i	−0.999155	−	0.0411113i	$-0.986910\pi$
$127$		−	0.926602i		−	0.0822226i	0.999155	−	0.0411113i	$-0.0130898\pi$
$128$	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	$0.828442\pi$
$140$	5.17137	−	1.12115i	0.437060	−	0.0947544i
$141$		−	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	$0.150400\pi$
$149$			11.1107i			0.910221i	−0.890435	+	0.455110i	$0.849600\pi$
$150$	1.40770	+	0.135580i	0.114938	+	0.0110701i
$151$		−	3.03195i		−	0.246737i	−0.992361	−	0.123368i	$-0.960630\pi$
$151$		−	3.03195i		−	0.246737i	0.992361	−	0.123368i	$-0.0393696\pi$
$152$	−4.70453	−	1.39391i	−0.381588	−	0.113061i
$153$			5.50143i			0.444764i
$154$	−6.31575	−	19.7497i	−0.508937	−	1.59147i
$155$	7.31172			0.587292
$156$	0.640944	−	3.29653i	0.0513166	−	0.263933i
$157$	−5.57251			−0.444735			−0.222367	−	0.974963i	$-0.571378\pi$
$157$	−5.57251			−0.444735			−0.222367	+	0.974963i	$0.571378\pi$
$158$	−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	$-0.571254\pi$
$167$	−5.73739			−0.443973			−0.221986	+	0.975050i	$0.571254\pi$
$168$	7.43173	−	0.877106i	0.573371	−	0.0676702i
$169$	−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	$-0.725618\pi$
$173$	−17.1231			−1.30185			−0.650923	+	0.759144i	$0.725618\pi$
$174$	−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	$-0.515207\pi$
$181$	−1.28496			−0.0955104			−0.0477552	+	0.998859i	$0.515207\pi$
$182$	1.91368	+	5.98419i	0.141852	+	0.443577i
$183$			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	$-0.893655\pi$
$191$		−	9.06371i		−	0.655827i	0.944708	−	0.327914i	$-0.106345\pi$
$192$	−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
$196$	−11.4022	+	8.12338i	−0.814445	+	0.580241i
$197$		−	13.1628i		−	0.937808i	−0.883249	−	0.468904i	$-0.844649\pi$
$197$		−	13.1628i		−	0.937808i	0.883249	−	0.468904i	$-0.155351\pi$
$198$	0.751337	−	7.80098i	0.0533952	−	0.554391i
$199$	−0.276416			−0.0195946			−0.00979732	−	0.999952i	$-0.503119\pi$
$199$	−0.276416			−0.0195946			−0.00979732	+	0.999952i	$0.503119\pi$
$200$	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
$210$	−3.56386	+	1.13969i	−0.245930	+	0.0786459i
$211$	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	$-0.296374\pi$
$223$	17.8291			1.19393			0.596963	+	0.802268i	$0.296374\pi$
$224$	1.11482	−	14.9251i	0.0744869	−	0.997222i
$225$	−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	$-0.536192\pi$
$229$	−3.43380			−0.226912			−0.113456	+	0.993543i	$0.536192\pi$
$230$	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
$238$	−19.6063	+	6.26991i	−1.27089	+	0.406418i
$239$		−	23.7708i		−	1.53761i	−0.639484	−	0.768804i	$-0.720852\pi$
$239$		−	23.7708i		−	1.53761i	0.639484	−	0.768804i	$-0.279148\pi$
$240$	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	$0.971953\pi$
$252$	−5.17137	+	1.12115i	−0.325765	+	0.0706257i
$253$		−	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	$0.0355238\pi$
$263$			3.61223i			0.222740i	−0.993779	+	0.111370i	$0.964476\pi$
$264$	−15.0284	−	4.45278i	−0.924932	−	0.274050i
$265$			1.26667i			0.0778111i
$266$	−6.18250	+	1.97710i	−0.379074	+	0.121224i
$267$	4.16614			0.254964
$268$	−14.2600	−	2.77258i	−0.871069	−	0.169362i
$269$	−8.64776			−0.527263			−0.263632	−	0.964623i	$-0.584920\pi$
$269$	−8.64776			−0.527263			−0.263632	+	0.964623i	$0.584920\pi$
$270$	−1.40770	−	0.135580i	−0.0856699	−	0.00825115i
$271$	3.09276			0.187872			0.0939358	−	0.995578i	$-0.470055\pi$
$271$	3.09276			0.187872			0.0939358	+	0.995578i	$0.470055\pi$
$272$	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	$-0.775971\pi$
$277$		−	21.5406i		−	1.29425i	0.762384	−	0.647125i	$-0.224029\pi$
$278$	−17.0363	−	1.64082i	−1.02177	−	0.0984100i
$279$	−7.31172			−0.437741
$280$	0.877106	+	7.43173i	0.0524171	+	0.444131i
$281$	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	$-0.794063\pi$
$293$	−27.3161			−1.59583			−0.797913	+	0.602773i	$0.794063\pi$
$294$	7.47477	−	6.49060i	0.435937	−	0.378539i
$295$		−	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	$0.978248\pi$
$308$	28.6579	−	6.21301i	1.63293	−	0.354019i
$309$			1.31225i			0.0746515i
$310$	−0.991324	+	10.2927i	−0.0563034	+	0.584586i
$311$	24.3201			1.37907			0.689533	−	0.724255i	$-0.257816\pi$
$311$	24.3201			1.37907			0.689533	+	0.724255i	$0.257816\pi$
$312$	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	$-0.928468\pi$
$317$		−	7.93499i		−	0.445673i	0.974856	−	0.222837i	$-0.0715317\pi$
$318$	−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
$322$	−12.6448	+	4.04369i	−0.704669	+	0.225346i
$323$	−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
$336$	0.227106	+	10.5806i	0.0123897	+	0.577217i
$337$	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	$-0.462131\pi$
$349$	4.43452			0.237374			0.118687	+	0.992932i	$0.462131\pi$
$350$	−1.13969	−	3.56386i	−0.0609189	−	0.190496i
$351$		−	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	$0.137453\pi$
$359$			15.8598i			0.837049i	−0.908206	+	0.418525i	$0.862547\pi$
$360$	−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
$364$	−8.68339	+	1.88255i	−0.455133	+	0.0986727i
$365$			7.34731i			0.384576i
$366$	−3.51536	−	0.338576i	−0.183751	−	0.0176977i
$367$	20.7390			1.08257			0.541284	−	0.840840i	$-0.317938\pi$
$367$	20.7390			1.08257			0.541284	+	0.840840i	$0.317938\pi$
$368$	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	$0.123374\pi$
$373$			14.5992i			0.755920i	−0.925822	+	0.377960i	$0.876626\pi$
$374$	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
$378$	3.56386	−	1.13969i	0.183305	−	0.0586192i
$379$	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	$-0.523919\pi$
$383$	−2.93845			−0.150148			−0.0750739	+	0.997178i	$0.523919\pi$
$384$	−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	$0.272624\pi$
$389$			29.8030i			1.51107i	−0.655106	+	0.755537i	$0.727376\pi$
$390$	−2.36371	−	0.227657i	−0.119691	−	0.0115278i
$391$	−19.5195			−0.987141
$392$	−9.88936	−	17.1523i	−0.499488	−	0.866321i
$393$	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	$-0.329082\pi$
$397$	20.3840			1.02304			0.511521	+	0.859271i	$0.329082\pi$
$398$	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
$406$	30.1539	−	9.64291i	1.49651	−	0.478569i
$407$		−	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	$0.843984\pi$
$420$	−1.12115	−	5.17137i	−0.0547065	−	0.252337i
$421$		−	14.8800i		−	0.725206i	−0.931944	−	0.362603i	$-0.881888\pi$
$421$		−	14.8800i		−	0.725206i	0.931944	−	0.362603i	$-0.118112\pi$
$422$	−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	$-0.997841\pi$
$431$		−	0.281619i		−	0.0135651i	0.999977	−	0.00678255i	$-0.00215897\pi$
$432$	−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	$0.968823\pi$
$434$	−8.33308	−	26.0580i	−0.400001	−	1.25082i
$435$	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	$-0.644101\pi$
$439$	−18.3292			−0.874804			−0.437402	+	0.899266i	$0.644101\pi$
$440$	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
$448$	20.8588	+	3.59287i	0.985488	+	0.169747i
$449$	−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	$-0.362327\pi$
$461$	17.9992			0.838305			0.419153	+	0.907916i	$0.362327\pi$
$462$	−19.7497	+	6.31575i	−0.918838	+	0.293835i
$463$			22.6300i			1.05170i	0.850576	+	0.525852i	$0.176254\pi$
$463$			22.6300i			1.05170i	−0.850576	+	0.525852i	$0.823746\pi$
$464$	−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
$476$	−6.16792	−	28.4499i	−0.282706	−	1.30400i
$477$		−	1.26667i		−	0.0579970i
$478$	33.4622	+	3.22286i	1.53053	+	0.147410i
$479$	26.6487			1.21761			0.608805	−	0.793320i	$-0.291649\pi$
$479$	26.6487			1.21761			0.608805	+	0.793320i	$0.291649\pi$
$480$	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	$-0.929647\pi$
$487$		−	9.67576i		−	0.438450i	0.975674	−	0.219225i	$-0.0703530\pi$
$488$	−2.00656	+	6.77225i	−0.0908328	+	0.306565i
$489$			20.9634i			0.947996i
$490$	6.49060	+	7.47477i	0.293215	+	0.337676i
$491$	−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	$-0.459544\pi$
$503$	5.68562			0.253509			0.126755	+	0.991934i	$0.459544\pi$
$504$	−0.877106	−	7.43173i	−0.0390694	−	0.331036i
$505$	−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	$-0.485801\pi$
$509$	2.01211			0.0891852			0.0445926	+	0.999005i	$0.485801\pi$
$510$	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
$518$	−40.0854	+	12.8189i	−1.76125	+	0.563231i
$519$			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
$532$	−1.94494	−	8.97116i	−0.0843239	−	0.388949i
$533$		−	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	$-0.792072\pi$
$541$		−	28.2718i		−	1.21550i	0.794129	−	0.607749i	$-0.207928\pi$
$542$	−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
$546$	5.98419	−	1.91368i	0.256100	−	0.0818981i
$547$	−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	$0.113876\pi$
$557$			16.5286i			0.700340i	−0.936686	+	0.350170i	$0.886124\pi$
$558$	0.991324	−	10.2927i	0.0419661	−	0.435725i
$559$	−14.5816			−0.616738
$560$	−10.5806	+	0.227106i	−0.447111	+	0.00959699i
$561$	−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
$574$	0.318173	−	0.101748i	0.0132803	−	0.00424690i
$575$		−	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	$-0.0439632\pi$
$588$	8.12338	+	11.4022i	0.335003	+	0.470220i
$589$		−	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	$-0.772847\pi$
$599$		−	32.0409i		−	1.30915i	0.755995	−	0.654577i	$-0.227153\pi$
$600$	−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	$-0.187812\pi$
$602$	−9.89710	−	30.9487i	−0.403376	−	1.26138i
$603$	−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	$-0.705610\pi$
$607$	−29.6611			−1.20391			−0.601953	+	0.798532i	$0.705610\pi$
$608$	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	$0.115209\pi$
$613$			17.5337i			0.708180i	−0.935211	+	0.354090i	$0.884791\pi$
$614$	−3.36839	−	0.324421i	−0.135937	−	0.0130925i
$615$	0.0892775			0.00360002
$616$	4.86061	+	41.1841i	0.195840	+	1.65935i
$617$	−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
$630$	1.13969	+	3.56386i	0.0454062	+	0.141988i
$631$		−	1.55276i		−	0.0618145i	−0.999522	−	0.0309072i	$-0.990160\pi$
$631$		−	1.55276i		−	0.0618145i	0.999522	−	0.0309072i	$-0.00983964\pi$
$632$	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	$0.866833\pi$
$644$	−3.97791	−	18.3484i	−0.156752	−	0.723027i
$645$		−	8.68405i		−	0.341934i
$646$	1.29394	−	13.4347i	0.0509095	−	0.528583i
$647$	−35.8391			−1.40898			−0.704490	−	0.709714i	$-0.748824\pi$
$647$	−35.8391			−1.40898			−0.704490	+	0.709714i	$0.748824\pi$
$648$	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	$-0.985776\pi$
$653$		−	2.28298i		−	0.0893398i	0.999002	−	0.0446699i	$-0.0142236\pi$
$654$	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
$658$	−14.5822	−	45.5993i	−0.568473	−	1.77765i
$659$	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	$-0.696944\pi$
$661$	−29.8230			−1.15998			−0.579991	+	0.814623i	$0.696944\pi$
$662$	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
$672$	−14.9251	−	1.11482i	−0.575746	−	0.0430050i
$673$	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	$-0.665974\pi$
$677$	−25.9210			−0.996226			−0.498113	+	0.867112i	$0.665974\pi$
$678$	−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
$686$	−23.5816	−	11.3977i	−0.900349	−	0.435168i
$687$			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
$700$	5.17137	−	1.12115i	0.195459	−	0.0423754i
$701$		−	14.5041i		−	0.547811i	−0.961757	−	0.273906i	$-0.911684\pi$
$701$		−	14.5041i		−	0.547811i	0.961757	−	0.273906i	$-0.0883156\pi$
$702$	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	$0.176130\pi$
$709$			27.9863i			1.05105i	−0.850779	+	0.525523i	$0.823870\pi$
$710$	−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
$714$	6.26991	+	19.6063i	0.234646	+	0.733749i
$715$	−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	$-0.702859\pi$
$719$	−31.9104			−1.19006			−0.595029	+	0.803704i	$0.702859\pi$
$720$	−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	$-0.256684\pi$
$727$	37.3223			1.38421			0.692104	+	0.721798i	$0.256684\pi$
$728$	−1.47277	−	12.4788i	−0.0545847	−	0.462497i
$729$	−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	$-0.697750\pi$
$733$	−31.5170			−1.16411			−0.582053	+	0.813151i	$0.697750\pi$
$734$	−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
$742$	4.51425	−	1.44361i	0.165723	−	0.0529967i
$743$		−	24.0338i		−	0.881714i	−0.897577	−	0.440857i	$-0.854675\pi$
$743$		−	24.0338i		−	0.881714i	0.897577	−	0.440857i	$-0.145325\pi$
$744$	−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	$0.00772531\pi$
$751$			1.33007i			0.0485348i	−0.999706	+	0.0242674i	$0.992275\pi$
$752$	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
$756$	1.12115	+	5.17137i	0.0407758	+	0.188081i
$757$		−	12.9373i		−	0.470213i	−0.971970	−	0.235106i	$-0.924456\pi$
$757$		−	12.9373i		−	0.470213i	0.971970	−	0.235106i	$-0.0755439\pi$
$758$	−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	$0.891012\pi$
$770$	−6.31575	−	19.7497i	−0.227604	−	0.711729i
$771$	3.21699			0.115857
$772$	−34.3694	−	6.68244i	−1.23698	−	0.240506i
$773$	26.4130			0.950010			0.475005	−	0.879983i	$-0.342446\pi$
$773$	26.4130			0.950010			0.475005	+	0.879983i	$0.342446\pi$
$774$	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
$784$	25.4861	−	11.5957i	0.910216	−	0.414134i
$785$	−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	$-0.404861\pi$
$797$	16.6258			0.588917			0.294458	+	0.955664i	$0.404861\pi$
$798$	1.97710	+	6.18250i	0.0699887	+	0.218858i
$799$		−	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	$-0.336459\pi$
$812$	9.48605	+	43.7550i	0.332895	+	1.53550i
$813$		−	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	$0.299397\pi$
$821$			46.2978i			1.61580i	−0.589317	+	0.807902i	$0.700603\pi$
$822$	4.97283	+	0.478950i	0.173447	+	0.0167053i
$823$		−	5.51492i		−	0.192238i	−0.995370	−	0.0961191i	$-0.969357\pi$
$823$		−	5.51492i		−	0.192238i	0.995370	−	0.0961191i	$-0.0306430\pi$
$824$	−1.05441	+	3.55869i	−0.0367322	+	0.123973i
$825$		−	5.54165i		−	0.192935i
$826$	−46.3971	+	14.8373i	−1.61436	+	0.516257i
$827$	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	$-0.217097\pi$
$829$	44.7027			1.55259			0.776295	+	0.630370i	$0.217097\pi$
$830$	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	$-0.781843\pi$
$839$	−44.8497			−1.54838			−0.774191	+	0.632952i	$0.781843\pi$
$840$	7.43173	−	0.877106i	0.256419	−	0.0302630i
$841$	−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	$-0.500211\pi$
$853$	−0.0388026			−0.00132858			−0.000664288		1.00000i	$0.500211\pi$
$854$	2.84607	+	8.89982i	0.0973906	+	0.304545i
$855$			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	$-0.790632\pi$
$863$		−	35.9183i		−	1.22267i	0.791371	−	0.611337i	$-0.209368\pi$
$864$	−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
$868$	37.8116	−	8.19753i	1.28341	−	0.278242i
$869$			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	$0.110098\pi$
$877$			20.0801i			0.678057i	−0.940776	+	0.339028i	$0.889902\pi$
$878$	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	$-0.214553\pi$
$882$	−6.49060	−	7.47477i	−0.218550	−	0.251689i
$883$	−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	$-0.476120\pi$
$887$	4.46449			0.149903			0.0749515	+	0.997187i	$0.476120\pi$
$888$	−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
$896$	−7.88573	+	28.8759i	−0.263444	+	0.964675i
$897$	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
$910$	1.91368	+	5.98419i	0.0634380	+	0.198374i
$911$		−	0.534170i		−	0.0176978i	−0.999961	−	0.00884891i	$-0.997183\pi$
$911$		−	0.534170i		−	0.0176978i	0.999961	−	0.00884891i	$-0.00281673\pi$
$912$	−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	$0.0414424\pi$
$919$			7.87145i			0.259655i	−0.991537	+	0.129828i	$0.958558\pi$
$920$	−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
$924$	−6.21301	−	28.6579i	−0.204393	−	0.942775i
$925$		−	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	$0.720799\pi$
$938$	−8.27815	−	25.8862i	−0.270291	−	0.845214i
$939$	30.3185			0.989407
$940$	−25.1194	−	4.88397i	−0.819305	−	0.159298i
$941$	7.55709			0.246354			0.123177	−	0.992385i	$-0.460692\pi$
$941$	7.55709			0.246354			0.123177	+	0.992385i	$0.460692\pi$
$942$	−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
$952$	40.8852	−	4.82534i	1.32510	−	0.156390i
$953$	−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
$966$	4.04369	+	12.6448i	0.130104	+	0.406841i
$967$		−	18.3924i		−	0.591459i	−0.955272	−	0.295730i	$-0.904437\pi$
$967$		−	18.3924i		−	0.591459i	0.955272	−	0.295730i	$-0.0955627\pi$
$968$	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
$980$	−11.4022	+	8.12338i	−0.364231	+	0.259492i
$981$			2.48432i			0.0793183i
$982$	2.89917	−	30.1015i	0.0925162	−	0.960576i
$983$	−33.5242			−1.06925			−0.534627	−	0.845088i	$-0.679548\pi$
$983$	−33.5242			−1.06925			−0.534627	+	0.845088i	$0.679548\pi$
$984$	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	$0.171557\pi$
$991$			32.3140i			1.02649i	−0.858243	+	0.513244i	$0.828443\pi$
$992$	−19.1029	+	36.6857i	−0.606519	+	1.16477i
$993$			14.2122i			0.451010i
$994$	24.0570	−	7.69318i	0.763041	−	0.244013i
$995$	−0.276416			−0.00876299
$996$	17.9473	+	3.48949i	0.568682	+	0.110569i
$997$	−2.00398			−0.0634665			−0.0317333	−	0.999496i	$-0.510103\pi$
$997$	−2.00398			−0.0634665			−0.0317333	+	0.999496i	$0.510103\pi$
$998$	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.d.811.12	yes	28
4.3	odd	2		3360.2.z.d.1231.26		28
7.6	odd	2		840.2.z.c.811.12	yes	28
8.3	odd	2		840.2.z.c.811.11	✓	28
8.5	even	2		3360.2.z.c.1231.4		28
28.27	even	2		3360.2.z.c.1231.3		28
56.13	odd	2		3360.2.z.d.1231.25		28
56.27	even	2	inner	840.2.z.d.811.11	yes	28

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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} +(-1.13969 - 3.56386i) 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} +(5.17137 - 1.12115i) 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} +(-3.56386 + 1.13969i) 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} +(0.877106 + 7.43173i) 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} +(-1.13969 - 3.56386i) 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} +(-1.12115 - 5.17137i) 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} +(6.49060 + 7.47477i) q^{98} -5.54165 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 2 q^{4} + 28 q^{5} + 4 q^{6} + 4 q^{7} - 10 q^{8} - 28 q^{9} + 2 q^{10} - 8 q^{12} - 8 q^{13} + 2 q^{14} + 6 q^{16} - 2 q^{18} - 2 q^{20} - 4 q^{24} + 28 q^{25} + 16 q^{26} + 10 q^{28}+ \cdots - 30 q^{98}+O(q^{100}) \) 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 + 2 * q^14 + 6 * q^16 - 2 * q^18 - 2 * q^20 - 4 * q^24 + 28 * q^25 + 16 * q^26 + 10 * 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 + 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 - 22 * 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 + 2 * 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 - 12 * 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 - 30 * q^98

Introduction

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