LMFDB - Embedded newform 680.2.l.a.101.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(101,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 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("680.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.l (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.18
Character	$\chi$	$=$	680.101
Dual form			680.2.l.a.101.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0976378 + 1.41084i) q^{2} -0.700054 q^{3} +(-1.98093 - 0.275503i) q^{4} +1.00000 q^{5} +(0.0683518 - 0.987663i) q^{6} -0.472369i q^{7} +(0.582104 - 2.76788i) q^{8} -2.50992 q^{9} +(-0.0976378 + 1.41084i) q^{10} +3.76587 q^{11} +(1.38676 + 0.192867i) q^{12} -2.08475i q^{13} +(0.666437 + 0.0461211i) q^{14} -0.700054 q^{15} +(3.84820 + 1.09150i) q^{16} +(3.62268 + 1.96881i) q^{17} +(0.245064 - 3.54110i) q^{18} -4.24061i q^{19} +(-1.98093 - 0.275503i) q^{20} +0.330684i q^{21} +(-0.367691 + 5.31304i) q^{22} +3.04244i q^{23} +(-0.407504 + 1.93766i) q^{24} +1.00000 q^{25} +(2.94124 + 0.203550i) q^{26} +3.85724 q^{27} +(-0.130139 + 0.935732i) q^{28} +8.44930 q^{29} +(0.0683518 - 0.987663i) q^{30} -1.89633i q^{31} +(-1.91567 + 5.32261i) q^{32} -2.63631 q^{33} +(-3.13138 + 4.91878i) q^{34} -0.472369i q^{35} +(4.97199 + 0.691491i) q^{36} +4.90602 q^{37} +(5.98282 + 0.414044i) q^{38} +1.45943i q^{39} +(0.582104 - 2.76788i) q^{40} +10.3105i q^{41} +(-0.466542 - 0.0322873i) q^{42} -8.18245i q^{43} +(-7.45994 - 1.03751i) q^{44} -2.50992 q^{45} +(-4.29240 - 0.297058i) q^{46} -5.56596 q^{47} +(-2.69394 - 0.764112i) q^{48} +6.77687 q^{49} +(-0.0976378 + 1.41084i) q^{50} +(-2.53607 - 1.37827i) q^{51} +(-0.574353 + 4.12975i) q^{52} +6.11891i q^{53} +(-0.376613 + 5.44195i) q^{54} +3.76587 q^{55} +(-1.30746 - 0.274968i) q^{56} +2.96866i q^{57} +(-0.824972 + 11.9206i) q^{58} -5.25557i q^{59} +(1.38676 + 0.192867i) q^{60} +4.08954 q^{61} +(2.67542 + 0.185154i) q^{62} +1.18561i q^{63} +(-7.32231 - 3.22239i) q^{64} -2.08475i q^{65} +(0.257404 - 3.71941i) q^{66} +14.0350i q^{67} +(-6.63387 - 4.89814i) q^{68} -2.12987i q^{69} +(0.666437 + 0.0461211i) q^{70} -14.4641i q^{71} +(-1.46104 + 6.94717i) q^{72} +11.7807i q^{73} +(-0.479013 + 6.92160i) q^{74} -0.700054 q^{75} +(-1.16830 + 8.40037i) q^{76} -1.77888i q^{77} +(-2.05903 - 0.142496i) q^{78} -14.2573i q^{79} +(3.84820 + 1.09150i) q^{80} +4.82950 q^{81} +(-14.5464 - 1.00669i) q^{82} +1.62221i q^{83} +(0.0911042 - 0.655063i) q^{84} +(3.62268 + 1.96881i) q^{85} +(11.5441 + 0.798916i) q^{86} -5.91497 q^{87} +(2.19213 - 10.4235i) q^{88} +4.13274 q^{89} +(0.245064 - 3.54110i) q^{90} -0.984770 q^{91} +(0.838201 - 6.02688i) q^{92} +1.32754i q^{93} +(0.543449 - 7.85268i) q^{94} -4.24061i q^{95} +(1.34107 - 3.72612i) q^{96} -1.51194i q^{97} +(-0.661679 + 9.56107i) q^{98} -9.45205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{3} + 2 q^{4} + 36 q^{5} + 36 q^{9} - 8 q^{11} - 2 q^{12} + 2 q^{14} - 4 q^{15} + 6 q^{16} - 10 q^{18} + 2 q^{20} + 26 q^{24} + 36 q^{25} + 6 q^{26} - 16 q^{27} + 14 q^{28} - 10 q^{32} - 8 q^{33}+ \cdots - 40 q^{99}+O(q^{100}) $ 36 * q - 4 * q^3 + 2 * q^4 + 36 * q^5 + 36 * q^9 - 8 * q^11 - 2 * q^12 + 2 * q^14 - 4 * q^15 + 6 * q^16 - 10 * q^18 + 2 * q^20 + 26 * q^24 + 36 * q^25 + 6 * q^26 - 16 * q^27 + 14 * q^28 - 10 * q^32 - 8 * q^33 - 24 * q^34 + 8 * q^36 - 20 * q^38 - 2 * q^42 + 6 * q^44 + 36 * q^45 + 24 * q^46 + 20 * q^47 - 4 * q^48 - 36 * q^49 + 6 * q^52 - 56 * q^54 - 8 * q^55 + 20 * q^56 - 18 * q^58 - 2 * q^60 - 24 * q^62 + 14 * q^64 - 16 * q^66 - 40 * q^68 + 2 * q^70 - 54 * q^72 + 6 * q^74 - 4 * q^75 + 2 * q^76 - 14 * q^78 + 6 * q^80 + 44 * q^81 + 22 * q^82 - 68 * q^84 - 36 * q^86 + 24 * q^87 - 58 * q^88 - 10 * q^90 - 56 * q^91 - 12 * q^92 + 14 * q^94 - 24 * q^96 + 10 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$1$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0976378	+	1.41084i	−0.0690404	+	0.997614i
$2$	−0.0976378	+	1.41084i	−0.0690404	+	0.997614i
$3$	−0.700054			−0.404176			−0.202088	−	0.979367i	$-0.564773\pi$
$3$	−0.700054			−0.404176			−0.202088	+	0.979367i	$0.564773\pi$
$4$	−1.98093	−	0.275503i	−0.990467	−	0.137751i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.0683518	−	0.987663i	0.0279045	−	0.403212i
$7$		−	0.472369i		−	0.178539i	−0.996008	−	0.0892694i	$-0.971547\pi$
$7$		−	0.472369i		−	0.178539i	0.996008	−	0.0892694i	$-0.0284532\pi$
$8$	0.582104	−	2.76788i	0.205805	−	0.978593i
$9$	−2.50992			−0.836642
$10$	−0.0976378	+	1.41084i	−0.0308758	+	0.446146i
$11$	3.76587			1.13545			0.567726	−	0.823217i	$-0.307823\pi$
$11$	3.76587			1.13545			0.567726	+	0.823217i	$0.307823\pi$
$12$	1.38676	+	0.192867i	0.400323	+	0.0556758i
$13$		−	2.08475i		−	0.578205i	−0.957298	−	0.289102i	$-0.906643\pi$
$13$		−	2.08475i		−	0.578205i	0.957298	−	0.289102i	$-0.0933568\pi$
$14$	0.666437	+	0.0461211i	0.178113	+	0.0123264i
$15$	−0.700054			−0.180753
$16$	3.84820	+	1.09150i	0.962049	+	0.272876i
$17$	3.62268	+	1.96881i	0.878628	+	0.477507i
$17$	3.62268	+	1.96881i	0.878628	+	0.477507i
$18$	0.245064	−	3.54110i	0.0577621	−	0.834645i
$19$		−	4.24061i		−	0.972863i	−0.873719	−	0.486432i	$-0.838298\pi$
$19$		−	4.24061i		−	0.972863i	0.873719	−	0.486432i	$-0.161702\pi$
$20$	−1.98093	−	0.275503i	−0.442950	−	0.0616042i
$21$			0.330684i			0.0721611i
$22$	−0.367691	+	5.31304i	−0.0783921	+	1.13274i
$23$			3.04244i			0.634393i	0.948360	+	0.317197i	$0.102741\pi$
$23$			3.04244i			0.634393i	−0.948360	+	0.317197i	$0.897259\pi$
$24$	−0.407504	+	1.93766i	−0.0831814	+	0.395524i
$25$	1.00000			0.200000
$26$	2.94124	+	0.203550i	0.576825	+	0.0399195i
$27$	3.85724			0.742327
$28$	−0.130139	+	0.935732i	−0.0245939	+	0.176837i
$29$	8.44930			1.56900			0.784498	−	0.620131i	$-0.212921\pi$
$29$	8.44930			1.56900			0.784498	+	0.620131i	$0.212921\pi$
$30$	0.0683518	−	0.987663i	0.0124793	−	0.180322i
$31$		−	1.89633i		−	0.340592i	−0.985393	−	0.170296i	$-0.945528\pi$
$31$		−	1.89633i		−	0.340592i	0.985393	−	0.170296i	$-0.0544723\pi$
$32$	−1.91567	+	5.32261i	−0.338645	+	0.940914i
$33$	−2.63631			−0.458923
$34$	−3.13138	+	4.91878i	−0.537028	+	0.843564i
$35$		−	0.472369i		−	0.0798449i
$36$	4.97199	+	0.691491i	0.828666	+	0.115248i
$37$	4.90602			0.806544			0.403272	−	0.915080i	$-0.367873\pi$
$37$	4.90602			0.806544			0.403272	+	0.915080i	$0.367873\pi$
$38$	5.98282	+	0.414044i	0.970542	+	0.0671669i
$39$			1.45943i			0.233697i
$40$	0.582104	−	2.76788i	0.0920387	−	0.437640i
$41$			10.3105i			1.61022i	0.593123	+	0.805112i	$0.297895\pi$
$41$			10.3105i			1.61022i	−0.593123	+	0.805112i	$0.702105\pi$
$42$	−0.466542	−	0.0322873i	−0.0719889	−	0.00498203i
$43$		−	8.18245i		−	1.24781i	−0.781500	−	0.623906i	$-0.785545\pi$
$43$		−	8.18245i		−	1.24781i	0.781500	−	0.623906i	$-0.214455\pi$
$44$	−7.45994	−	1.03751i	−1.12463	−	0.156410i
$45$	−2.50992			−0.374157
$46$	−4.29240	−	0.297058i	−0.632879	−	0.0437987i
$47$	−5.56596			−0.811879			−0.405940	−	0.913900i	$-0.633056\pi$
$47$	−5.56596			−0.811879			−0.405940	+	0.913900i	$0.633056\pi$
$48$	−2.69394	−	0.764112i	−0.388837	−	0.110290i
$49$	6.77687			0.968124
$50$	−0.0976378	+	1.41084i	−0.0138081	+	0.199523i
$51$	−2.53607	−	1.37827i	−0.355121	−	0.192997i
$52$	−0.574353	+	4.12975i	−0.0796484	+	0.572693i
$53$			6.11891i			0.840497i	0.907409	+	0.420249i	$0.138057\pi$
$53$			6.11891i			0.840497i	−0.907409	+	0.420249i	$0.861943\pi$
$54$	−0.376613	+	5.44195i	−0.0512505	+	0.740556i
$55$	3.76587			0.507790
$56$	−1.30746	−	0.274968i	−0.174717	−	0.0367441i
$57$			2.96866i			0.393208i
$58$	−0.824972	+	11.9206i	−0.108324	+	1.56525i
$59$		−	5.25557i		−	0.684217i	−0.939660	−	0.342109i	$-0.888859\pi$
$59$		−	5.25557i		−	0.684217i	0.939660	−	0.342109i	$-0.111141\pi$
$60$	1.38676	+	0.192867i	0.179030	+	0.0248990i
$61$	4.08954			0.523612			0.261806	−	0.965121i	$-0.415682\pi$
$61$	4.08954			0.523612			0.261806	+	0.965121i	$0.415682\pi$
$62$	2.67542	+	0.185154i	0.339779	+	0.0235146i
$63$			1.18561i			0.149373i
$64$	−7.32231	−	3.22239i	−0.915289	−	0.402798i
$65$		−	2.08475i		−	0.258581i
$66$	0.257404	−	3.71941i	0.0316842	−	0.457828i
$67$			14.0350i			1.71465i	0.514775	+	0.857325i	$0.327875\pi$
$67$			14.0350i			1.71465i	−0.514775	+	0.857325i	$0.672125\pi$
$68$	−6.63387	−	4.89814i	−0.804475	−	0.593987i
$69$		−	2.12987i		−	0.256407i
$70$	0.666437	+	0.0461211i	0.0796544	+	0.00551253i
$71$		−	14.4641i		−	1.71657i	−0.513171	−	0.858287i	$-0.671529\pi$
$71$		−	14.4641i		−	1.71657i	0.513171	−	0.858287i	$-0.328471\pi$
$72$	−1.46104	+	6.94717i	−0.172185	+	0.818732i
$73$			11.7807i			1.37883i	0.724368	+	0.689413i	$0.242132\pi$
$73$			11.7807i			1.37883i	−0.724368	+	0.689413i	$0.757868\pi$
$74$	−0.479013	+	6.92160i	−0.0556841	+	0.804620i
$75$	−0.700054			−0.0808353
$76$	−1.16830	+	8.40037i	−0.134013	+	0.963589i
$77$		−	1.77888i		−	0.202722i
$78$	−2.05903	−	0.142496i	−0.233139	−	0.0161345i
$79$		−	14.2573i		−	1.60408i	−0.597273	−	0.802038i	$-0.703749\pi$
$79$		−	14.2573i		−	1.60408i	0.597273	−	0.802038i	$-0.296251\pi$
$80$	3.84820	+	1.09150i	0.430241	+	0.122034i
$81$	4.82950			0.536611
$82$	−14.5464	−	1.00669i	−1.60638	−	0.111170i
$83$			1.62221i			0.178060i	0.996029	+	0.0890302i	$0.0283768\pi$
$83$			1.62221i			0.178060i	−0.996029	+	0.0890302i	$0.971623\pi$
$84$	0.0911042	−	0.655063i	0.00994029	−	0.0714732i
$85$	3.62268	+	1.96881i	0.392934	+	0.213547i
$86$	11.5441	+	0.798916i	1.24483	+	0.0861494i
$87$	−5.91497			−0.634151
$88$	2.19213	−	10.4235i	0.233682	−	1.11115i
$89$	4.13274			0.438070			0.219035	−	0.975717i	$-0.429709\pi$
$89$	4.13274			0.438070			0.219035	+	0.975717i	$0.429709\pi$
$90$	0.245064	−	3.54110i	0.0258320	−	0.373265i
$91$	−0.984770			−0.103232
$92$	0.838201	−	6.02688i	0.0873885	−	0.628345i
$93$			1.32754i			0.137659i
$94$	0.543449	−	7.85268i	0.0560525	−	0.809942i
$95$		−	4.24061i		−	0.435078i
$96$	1.34107	−	3.72612i	0.136872	−	0.380295i
$97$		−	1.51194i		−	0.153514i	−0.997050	−	0.0767570i	$-0.975543\pi$
$97$		−	1.51194i		−	0.153514i	0.997050	−	0.0767570i	$-0.0244566\pi$
$98$	−0.661679	+	9.56107i	−0.0668396	+	0.965814i
$99$	−9.45205			−0.949967
$100$	−1.98093	−	0.275503i	−0.198093	−	0.0275503i
$101$		−	15.9111i		−	1.58321i	−0.611032	−	0.791606i	$-0.709245\pi$
$101$		−	15.9111i		−	1.58321i	0.611032	−	0.791606i	$-0.290755\pi$
$102$	2.19214	−	3.44341i	0.217054	−	0.340949i
$103$	−14.9491			−1.47298			−0.736488	−	0.676451i	$-0.763517\pi$
$103$	−14.9491			−1.47298			−0.736488	+	0.676451i	$0.763517\pi$
$104$	−5.77033	−	1.21354i	−0.565827	−	0.118997i
$105$			0.330684i			0.0322714i
$106$	−8.63280	−	0.597437i	−0.838492	−	0.0580283i
$107$	15.6850			1.51633			0.758165	−	0.652063i	$-0.226096\pi$
$107$	15.6850			1.51633			0.758165	+	0.652063i	$0.226096\pi$
$108$	−7.64094	−	1.06268i	−0.735250	−	0.102256i
$109$	−16.0643			−1.53869			−0.769343	−	0.638836i	$-0.779416\pi$
$109$	−16.0643			−1.53869			−0.769343	+	0.638836i	$0.779416\pi$
$110$	−0.367691	+	5.31304i	−0.0350580	+	0.506578i
$111$	−3.43448			−0.325986
$112$	0.515593	−	1.81777i	0.0487190	−	0.171763i
$113$		−	7.80211i		−	0.733961i	−0.930229	−	0.366980i	$-0.880392\pi$
$113$		−	7.80211i		−	0.733961i	0.930229	−	0.366980i	$-0.119608\pi$
$114$	−4.18830	−	0.289853i	−0.392270	−	0.0271473i
$115$			3.04244i			0.283709i
$116$	−16.7375	−	2.32780i	−1.55404	−	0.216131i
$117$			5.23256i			0.483750i
$118$	7.41477	+	0.513143i	0.682585	+	0.0472386i
$119$	0.930005	−	1.71124i	0.0852534	−	0.156869i
$120$	−0.407504	+	1.93766i	−0.0371999	+	0.176884i
$121$	3.18178			0.289252
$122$	−0.399294	+	5.76968i	−0.0361503	+	0.522362i
$123$		−	7.21788i		−	0.650814i
$124$	−0.522445	+	3.75651i	−0.0469169	+	0.337345i
$125$	1.00000			0.0894427
$126$	−1.67271	−	0.115760i	−0.149016	−	0.0103128i
$127$	10.8800			0.965447			0.482724	−	0.875773i	$-0.339648\pi$
$127$	10.8800			0.965447			0.482724	+	0.875773i	$0.339648\pi$
$128$	5.26120	−	10.0160i	0.465029	−	0.885295i
$129$			5.72815i			0.504336i
$130$	2.94124	+	0.203550i	0.257964	+	0.0178525i
$131$	13.9563			1.21937			0.609685	−	0.792644i	$-0.291296\pi$
$131$	13.9563			1.21937			0.609685	+	0.792644i	$0.291296\pi$
$132$	5.22236	+	0.726311i	0.454548	+	0.0632172i
$133$	−2.00313			−0.173694
$134$	−19.8011	−	1.37035i	−1.71056	−	0.118380i
$135$	3.85724			0.331979
$136$	7.55820	−	8.88108i	0.648111	−	0.761546i
$137$	−16.2479			−1.38815			−0.694075	−	0.719903i	$-0.744186\pi$
$137$	−16.2479			−1.38815			−0.694075	+	0.719903i	$0.744186\pi$
$138$	3.00491	+	0.207956i	0.255795	+	0.0177024i
$139$	3.86189			0.327561			0.163780	−	0.986497i	$-0.447631\pi$
$139$	3.86189			0.327561			0.163780	+	0.986497i	$0.447631\pi$
$140$	−0.130139	+	0.935732i	−0.0109987	+	0.0790838i
$141$	3.89647			0.328142
$142$	20.4065	+	1.41224i	1.71248	+	0.118513i
$143$		−	7.85089i		−	0.656524i
$144$	−9.65868	−	2.73959i	−0.804890	−	0.228300i
$145$	8.44930			0.701676
$146$	−16.6207	−	1.15024i	−1.37554	−	0.0951947i
$147$	−4.74417			−0.391293
$148$	−9.71850	−	1.35162i	−0.798856	−	0.111103i
$149$		−	15.2325i		−	1.24789i	−0.781467	−	0.623946i	$-0.785528\pi$
$149$		−	15.2325i		−	1.24789i	0.781467	−	0.623946i	$-0.214472\pi$
$150$	0.0683518	−	0.987663i	0.00558090	−	0.0806424i
$151$	−1.45467			−0.118380			−0.0591899	−	0.998247i	$-0.518852\pi$
$151$	−1.45467			−0.118380			−0.0591899	+	0.998247i	$0.518852\pi$
$152$	−11.7375	−	2.46848i	−0.952037	−	0.200220i
$153$	−9.09265	−	4.94157i	−0.735097	−	0.399502i
$154$	2.50971	+	0.173686i	0.202239	+	0.0139960i
$155$		−	1.89633i		−	0.152317i
$156$	0.402078	−	2.89104i	0.0321920	−	0.231469i
$157$		−	2.38317i		−	0.190198i	−0.995468	−	0.0950989i	$-0.969683\pi$
$157$		−	2.38317i		−	0.190198i	0.995468	−	0.0950989i	$-0.0303167\pi$
$158$	20.1148	+	1.39206i	1.60025	+	0.110746i
$159$		−	4.28357i		−	0.339709i
$160$	−1.91567	+	5.32261i	−0.151447	+	0.420790i
$161$	1.43716			0.113264
$162$	−0.471542	+	6.81364i	−0.0370478	+	0.535330i
$163$	−10.0630			−0.788196			−0.394098	−	0.919068i	$-0.628943\pi$
$163$	−10.0630			−0.788196			−0.394098	+	0.919068i	$0.628943\pi$
$164$	2.84056	−	20.4243i	0.221810	−	1.59487i
$165$	−2.63631			−0.205237
$166$	−2.28867	−	0.158389i	−0.177635	−	0.0122934i
$167$		−	4.09470i		−	0.316857i	−0.987370	−	0.158429i	$-0.949357\pi$
$167$		−	4.09470i		−	0.316857i	0.987370	−	0.158429i	$-0.0506428\pi$
$168$	0.915293	+	0.192492i	0.0706164	+	0.0148511i
$169$	8.65383			0.665679
$170$	−3.13138	+	4.91878i	−0.240166	+	0.377253i
$171$			10.6436i			0.813938i
$172$	−2.25428	+	16.2089i	−0.171888	+	1.23592i
$173$	16.3781			1.24520			0.622601	−	0.782540i	$-0.286076\pi$
$173$	16.3781			1.24520			0.622601	+	0.782540i	$0.286076\pi$
$174$	0.577525	−	8.34507i	0.0437820	−	0.632638i
$175$		−	0.472369i		−	0.0357077i
$176$	14.4918	+	4.11046i	1.09236	+	0.309838i
$177$			3.67918i			0.276544i
$178$	−0.403512	+	5.83064i	−0.0302445	+	0.437025i
$179$			8.16713i			0.610440i	0.952282	+	0.305220i	$0.0987300\pi$
$179$			8.16713i			0.610440i	−0.952282	+	0.305220i	$0.901270\pi$
$180$	4.97199	+	0.691491i	0.370591	+	0.0515407i
$181$	−12.6490			−0.940190			−0.470095	−	0.882616i	$-0.655780\pi$
$181$	−12.6490			−0.940190			−0.470095	+	0.882616i	$0.655780\pi$
$182$	0.0961508	−	1.38935i	0.00712717	−	0.102986i
$183$	−2.86290			−0.211631
$184$	8.42111	+	1.77102i	0.620813	+	0.130561i
$185$	4.90602			0.360698
$186$	−1.87294	−	0.129618i	−0.137331	−	0.00950403i
$187$	13.6425	+	7.41428i	0.997641	+	0.542186i
$188$	11.0258	+	1.53344i	0.804140	+	0.111837i
$189$		−	1.82204i		−	0.132534i
$190$	5.98282	+	0.414044i	0.434040	+	0.0300379i
$191$	−9.84032			−0.712021			−0.356010	−	0.934482i	$-0.615863\pi$
$191$	−9.84032			−0.712021			−0.356010	+	0.934482i	$0.615863\pi$
$192$	5.12601	+	2.25584i	0.369938	+	0.162802i
$193$			19.3479i			1.39270i	0.717705	+	0.696348i	$0.245193\pi$
$193$			19.3479i			1.39270i	−0.717705	+	0.696348i	$0.754807\pi$
$194$	2.13310	+	0.147622i	0.153148	+	0.0105987i
$195$			1.45943i			0.104512i
$196$	−13.4245	−	1.86704i	−0.958895	−	0.133360i
$197$	2.53115			0.180337			0.0901685	−	0.995927i	$-0.471259\pi$
$197$	2.53115			0.180337			0.0901685	+	0.995927i	$0.471259\pi$
$198$	0.922878	−	13.3353i	0.0655861	−	0.947700i
$199$			7.75580i			0.549794i	0.961474	+	0.274897i	$0.0886437\pi$
$199$			7.75580i			0.549794i	−0.961474	+	0.274897i	$0.911356\pi$
$200$	0.582104	−	2.76788i	0.0411610	−	0.195719i
$201$		−	9.82527i		−	0.693021i
$202$	22.4480	+	1.55352i	1.57943	+	0.109306i
$203$		−	3.99119i		−	0.280127i
$204$	4.64407	+	3.42896i	0.325150	+	0.240075i
$205$			10.3105i			0.720114i
$206$	1.45959	−	21.0907i	0.101695	−	1.46946i
$207$		−	7.63630i		−	0.530760i
$208$	2.27551	−	8.02252i	0.157778	−	0.556261i
$209$		−	15.9696i		−	1.10464i
$210$	−0.466542	−	0.0322873i	−0.0321944	−	0.00222803i
$211$	−10.3268			−0.710923			−0.355462	−	0.934691i	$-0.615676\pi$
$211$	−10.3268			−0.710923			−0.355462	+	0.934691i	$0.615676\pi$
$212$	1.68578	−	12.1212i	0.115780	−	0.832485i
$213$			10.1257i			0.693798i
$214$	−1.53145	+	22.1291i	−0.104688	+	1.51271i
$215$		−	8.18245i		−	0.558038i
$216$	2.24532	−	10.6764i	0.152774	−	0.726436i
$217$	−0.895769			−0.0608088
$218$	1.56849	−	22.6642i	0.106231	−	1.53501i
$219$		−	8.24712i		−	0.557289i
$220$	−7.45994	−	1.03751i	−0.502949	−	0.0699487i
$221$	4.10447	−	7.55236i	0.276097	−	0.508027i
$222$	0.335335	−	4.84549i	0.0225062	−	0.325208i
$223$	0.853240			0.0571372			0.0285686	−	0.999592i	$-0.490905\pi$
$223$	0.853240			0.0571372			0.0285686	+	0.999592i	$0.490905\pi$
$224$	2.51424	+	0.904902i	0.167990	+	0.0604613i
$225$	−2.50992			−0.167328
$226$	11.0075	+	0.761781i	0.732209	+	0.0506729i
$227$	−21.4110			−1.42110			−0.710549	−	0.703648i	$-0.751553\pi$
$227$	−21.4110			−1.42110			−0.710549	+	0.703648i	$0.751553\pi$
$228$	0.817873	−	5.88071i	0.0541650	−	0.389460i
$229$			0.280780i			0.0185545i	0.999957	+	0.00927725i	$0.00295308\pi$
$229$			0.280780i			0.0185545i	−0.999957	+	0.00927725i	$0.997047\pi$
$230$	−4.29240	−	0.297058i	−0.283032	−	0.0195874i
$231$			1.24531i			0.0819355i
$232$	4.91837	−	23.3866i	0.322907	−	1.53541i
$233$		−	2.80188i		−	0.183557i	−0.995779	−	0.0917786i	$-0.970745\pi$
$233$		−	2.80188i		−	0.183557i	0.995779	−	0.0917786i	$-0.0292552\pi$
$234$	−7.38230	−	0.510896i	−0.482596	−	0.0333983i
$235$	−5.56596			−0.363083
$236$	−1.44792	+	10.4109i	−0.0942518	+	0.677695i
$237$			9.98091i			0.648329i
$238$	2.32348	+	1.47917i	0.150609	+	0.0958803i
$239$	7.25286			0.469148			0.234574	−	0.972098i	$-0.424630\pi$
$239$	7.25286			0.469148			0.234574	+	0.972098i	$0.424630\pi$
$240$	−2.69394	−	0.764112i	−0.173893	−	0.0493232i
$241$			21.7072i			1.39828i	0.714983	+	0.699142i	$0.246435\pi$
$241$			21.7072i			1.39828i	−0.714983	+	0.699142i	$0.753565\pi$
$242$	−0.310662	+	4.48898i	−0.0199701	+	0.288562i
$243$	−14.9526			−0.959212
$244$	−8.10110	−	1.12668i	−0.518620	−	0.0721282i
$245$	6.77687			0.432958
$246$	10.1833	+	0.704738i	0.649261	+	0.0449325i
$247$	−8.84060			−0.562514
$248$	−5.24882	−	1.10386i	−0.333301	−	0.0700954i
$249$		−	1.13563i		−	0.0719678i
$250$	−0.0976378	+	1.41084i	−0.00617516	+	0.0892293i
$251$			7.87719i			0.497204i	0.968606	+	0.248602i	$0.0799711\pi$
$251$			7.87719i			0.497204i	−0.968606	+	0.248602i	$0.920029\pi$
$252$	0.326639	−	2.34862i	0.0205763	−	0.147949i
$253$			11.4574i			0.720323i
$254$	−1.06230	+	15.3500i	−0.0666548	+	0.963143i
$255$	−2.53607	−	1.37827i	−0.158815	−	0.0863108i
$256$	13.6172	+	8.40065i	0.851077	+	0.525041i
$257$	6.86958			0.428513			0.214256	−	0.976777i	$-0.431267\pi$
$257$	6.86958			0.428513			0.214256	+	0.976777i	$0.431267\pi$
$258$	−8.08150	−	0.559285i	−0.503132	−	0.0348195i
$259$		−	2.31745i		−	0.143999i
$260$	−0.574353	+	4.12975i	−0.0356199	+	0.256116i
$261$	−21.2071			−1.31269
$262$	−1.36267	+	19.6901i	−0.0841857	+	1.21646i
$263$	−26.2544			−1.61891			−0.809457	−	0.587179i	$-0.800239\pi$
$263$	−26.2544			−1.61891			−0.809457	+	0.587179i	$0.800239\pi$
$264$	−1.53461	+	7.29699i	−0.0944486	+	0.449099i
$265$			6.11891i			0.375882i
$266$	0.195582	−	2.82610i	0.0119919	−	0.173279i
$267$	−2.89314			−0.177057
$268$	3.86668	−	27.8024i	0.236195	−	1.69830i
$269$	−19.7359			−1.20332			−0.601661	−	0.798752i	$-0.705494\pi$
$269$	−19.7359			−1.20332			−0.601661	+	0.798752i	$0.705494\pi$
$270$	−0.376613	+	5.44195i	−0.0229199	+	0.331187i
$271$	−9.82641			−0.596912			−0.298456	−	0.954423i	$-0.596472\pi$
$271$	−9.82641			−0.596912			−0.298456	+	0.954423i	$0.596472\pi$
$272$	11.7918	+	11.5305i	0.714983	+	0.699142i
$273$	0.689392			0.0417239
$274$	1.58641	−	22.9231i	0.0958384	−	1.38484i
$275$	3.76587			0.227091
$276$	−0.586786	+	4.21914i	−0.0353203	+	0.253962i
$277$	−7.12825			−0.428295			−0.214148	−	0.976801i	$-0.568697\pi$
$277$	−7.12825			−0.428295			−0.214148	+	0.976801i	$0.568697\pi$
$278$	−0.377066	+	5.44850i	−0.0226149	+	0.326779i
$279$			4.75966i			0.284953i
$280$	−1.30746	−	0.274968i	−0.0781357	−	0.0164325i
$281$	−19.5618			−1.16696			−0.583480	−	0.812127i	$-0.698309\pi$
$281$	−19.5618			−1.16696			−0.583480	+	0.812127i	$0.698309\pi$
$282$	−0.380443	+	5.49730i	−0.0226551	+	0.327359i
$283$	−8.55218			−0.508374			−0.254187	−	0.967155i	$-0.581808\pi$
$283$	−8.55218			−0.508374			−0.254187	+	0.967155i	$0.581808\pi$
$284$	−3.98490	+	28.6524i	−0.236460	+	1.70021i
$285$			2.96866i			0.175848i
$286$	11.0763	+	0.766544i	0.654957	+	0.0453267i
$287$	4.87034			0.287487
$288$	4.80818	−	13.3594i	0.283325	−	0.787208i
$289$	9.24757	+	14.2647i	0.543975	+	0.839102i
$290$	−0.824972	+	11.9206i	−0.0484440	+	0.700002i
$291$			1.05844i			0.0620467i
$292$	3.24561	−	23.3368i	0.189935	−	1.36568i
$293$			22.8881i			1.33714i	0.743649	+	0.668570i	$0.233093\pi$
$293$			22.8881i			1.33714i	−0.743649	+	0.668570i	$0.766907\pi$
$294$	0.463211	−	6.69326i	0.0270150	−	0.390359i
$295$		−	5.25557i		−	0.305991i
$296$	2.85581	−	13.5793i	0.165991	−	0.789279i
$297$	14.5259			0.842877
$298$	21.4906	+	1.48727i	1.24492	+	0.0861550i
$299$	6.34272			0.366809
$300$	1.38676	+	0.192867i	0.0800646	+	0.0111352i
$301$	−3.86513			−0.222783
$302$	0.142031	−	2.05231i	0.00817298	−	0.118097i
$303$			11.1386i			0.639897i
$304$	4.62865	−	16.3187i	0.265471	−	0.935942i
$305$	4.08954			0.234166
$306$	7.85954	−	12.3458i	0.449300	−	0.705761i
$307$			4.75160i			0.271188i	0.990764	+	0.135594i	$0.0432943\pi$
$307$			4.75160i			0.271188i	−0.990764	+	0.135594i	$0.956706\pi$
$308$	−0.490086	+	3.52384i	−0.0279252	+	0.200790i
$309$	10.4652			0.595342
$310$	2.67542	+	0.185154i	0.151954	+	0.0105160i
$311$			18.5567i			1.05225i	0.850407	+	0.526126i	$0.176356\pi$
$311$			18.5567i			1.05225i	−0.850407	+	0.526126i	$0.823644\pi$
$312$	4.03954	+	0.849543i	0.228694	+	0.0480959i
$313$			27.7728i			1.56981i	0.619614	+	0.784907i	$0.287289\pi$
$313$			27.7728i			1.56981i	−0.619614	+	0.784907i	$0.712711\pi$
$314$	3.36227	+	0.232688i	0.189744	+	0.0131313i
$315$			1.18561i			0.0668016i
$316$	−3.92793	+	28.2428i	−0.220964	+	1.58878i
$317$	−6.90582			−0.387869			−0.193935	−	0.981014i	$-0.562125\pi$
$317$	−6.90582			−0.387869			−0.193935	+	0.981014i	$0.562125\pi$
$318$	6.04343	+	0.418238i	0.338898	+	0.0234536i
$319$	31.8190			1.78152
$320$	−7.32231	−	3.22239i	−0.409330	−	0.180137i
$321$	−10.9804			−0.612864
$322$	−0.140321	+	2.02760i	−0.00781977	+	0.112993i
$323$	8.34896	−	15.3624i	0.464549	−	0.854785i
$324$	−9.56691	−	1.33054i	−0.531495	−	0.0739188i
$325$		−	2.08475i		−	0.115641i
$326$	0.982531	−	14.1973i	0.0544173	−	0.786315i
$327$	11.2459			0.621900
$328$	28.5381	+	6.00176i	1.57575	+	0.331392i
$329$			2.62919i			0.144952i
$330$	0.257404	−	3.71941i	0.0141696	−	0.204747i
$331$			17.7274i			0.974385i	0.873295	+	0.487193i	$0.161979\pi$
$331$			17.7274i			0.974385i	−0.873295	+	0.487193i	$0.838021\pi$
$332$	0.446922	−	3.21348i	0.0245280	−	0.176363i
$333$	−12.3137			−0.674789
$334$	5.77696	+	0.399798i	0.316101	+	0.0218759i
$335$			14.0350i			0.766815i
$336$	−0.360943	+	1.27254i	−0.0196910	+	0.0694225i
$337$		−	6.64499i		−	0.361975i	−0.983485	−	0.180988i	$-0.942071\pi$
$337$		−	6.64499i		−	0.361975i	0.983485	−	0.180988i	$-0.0579294\pi$
$338$	−0.844941	+	12.2092i	−0.0459588	+	0.664091i
$339$			5.46190i			0.296650i
$340$	−6.63387	−	4.89814i	−0.359772	−	0.265639i
$341$		−	7.14135i		−	0.386726i
$342$	−15.0164	−	1.03922i	−0.811996	−	0.0561946i
$343$		−	6.50777i		−	0.351386i
$344$	−22.6480	−	4.76303i	−1.22110	−	0.256806i
$345$		−	2.12987i		−	0.114669i
$346$	−1.59912	+	23.1068i	−0.0859692	+	1.24223i
$347$	−6.94078			−0.372600			−0.186300	−	0.982493i	$-0.559650\pi$
$347$	−6.94078			−0.372600			−0.186300	+	0.982493i	$0.559650\pi$
$348$	11.7172	+	1.62959i	0.628106	+	0.0873551i
$349$		−	27.3230i		−	1.46257i	−0.682072	−	0.731285i	$-0.738921\pi$
$349$		−	27.3230i		−	1.46257i	0.682072	−	0.731285i	$-0.261079\pi$
$350$	0.666437	+	0.0461211i	0.0356225	+	0.00246528i
$351$		−	8.04138i		−	0.429217i
$352$	−7.21415	+	20.0443i	−0.384516	+	1.06836i
$353$	5.69659			0.303199			0.151599	−	0.988442i	$-0.451558\pi$
$353$	5.69659			0.303199			0.151599	+	0.988442i	$0.451558\pi$
$354$	−5.19074	−	0.359228i	−0.275885	−	0.0190927i
$355$		−	14.4641i		−	0.767675i
$356$	−8.18669	−	1.13858i	−0.433894	−	0.0603447i
$357$	−0.651054	+	1.19796i	−0.0344574	+	0.0634028i
$358$	−11.5225	−	0.797421i	−0.608983	−	0.0421450i
$359$	28.5022			1.50429			0.752143	−	0.659000i	$-0.229020\pi$
$359$	28.5022			1.50429			0.752143	+	0.659000i	$0.229020\pi$
$360$	−1.46104	+	6.94717i	−0.0770034	+	0.366148i
$361$	1.01720			0.0535367
$362$	1.23502	−	17.8457i	0.0649111	−	0.937947i
$363$	−2.22742			−0.116909
$364$	1.95076	+	0.271307i	0.102248	+	0.0142203i
$365$			11.7807i			0.616630i
$366$	0.279527	−	4.03909i	0.0146111	−	0.211126i
$367$			30.1453i			1.57357i	0.617227	+	0.786786i	$0.288256\pi$
$367$			30.1453i			1.57357i	−0.617227	+	0.786786i	$0.711744\pi$
$368$	−3.32084	+	11.7079i	−0.173111	+	0.610317i
$369$		−	25.8785i		−	1.34718i
$370$	−0.479013	+	6.92160i	−0.0249027	+	0.359837i
$371$	2.89038			0.150061
$372$	0.365740	−	2.62976i	0.0189627	−	0.136347i
$373$		−	8.99135i		−	0.465555i	−0.972530	−	0.232777i	$-0.925219\pi$
$373$		−	8.99135i		−	0.465555i	0.972530	−	0.232777i	$-0.0747813\pi$
$374$	−11.7924	+	18.5235i	−0.609770	+	0.957827i
$375$	−0.700054			−0.0361506
$376$	−3.23997	+	15.4059i	−0.167089	+	0.794499i
$377$		−	17.6147i		−	0.907201i
$378$	2.57061	+	0.177900i	0.132218	+	0.00915020i
$379$	−11.8768			−0.610068			−0.305034	−	0.952341i	$-0.598668\pi$
$379$	−11.8768			−0.610068			−0.305034	+	0.952341i	$0.598668\pi$
$380$	−1.16830	+	8.40037i	−0.0599325	+	0.430930i
$381$	−7.61661			−0.390211
$382$	0.960788	−	13.8831i	0.0491582	−	0.710322i
$383$	10.6980			0.546644			0.273322	−	0.961923i	$-0.411877\pi$
$383$	10.6980			0.546644			0.273322	+	0.961923i	$0.411877\pi$
$384$	−3.68313	+	7.01172i	−0.187954	+	0.357815i
$385$		−	1.77888i		−	0.0906601i
$386$	−27.2968	−	1.88909i	−1.38937	−	0.0961522i
$387$			20.5373i			1.04397i
$388$	−0.416543	+	2.99505i	−0.0211468	+	0.152051i
$389$			14.5550i			0.737970i	0.929435	+	0.368985i	$0.120295\pi$
$389$			14.5550i			0.737970i	−0.929435	+	0.368985i	$0.879705\pi$
$390$	−2.05903	−	0.142496i	−0.104263	−	0.00721557i
$391$	−5.98999	+	11.0218i	−0.302927	+	0.557396i
$392$	3.94484	−	18.7576i	0.199245	−	0.947399i
$393$	−9.77018			−0.492840
$394$	−0.247136	+	3.57105i	−0.0124505	+	0.179907i
$395$		−	14.2573i		−	0.717365i
$396$	18.7239	+	2.60406i	0.940911	+	0.130859i
$397$	−5.14070			−0.258004			−0.129002	−	0.991644i	$-0.541177\pi$
$397$	−5.14070			−0.258004			−0.129002	+	0.991644i	$0.541177\pi$
$398$	−10.9422	−	0.757259i	−0.548482	−	0.0379580i
$399$	1.40230			0.0702029
$400$	3.84820	+	1.09150i	0.192410	+	0.0545752i
$401$			14.8456i			0.741354i	0.928762	+	0.370677i	$0.120874\pi$
$401$			14.8456i			0.741354i	−0.928762	+	0.370677i	$0.879126\pi$
$402$	13.8619	+	0.959318i	0.691367	+	0.0478464i
$403$	−3.95338			−0.196932
$404$	−4.38354	+	31.5188i	−0.218089	+	1.56812i
$405$	4.82950			0.239980
$406$	5.63092	+	0.389691i	0.279458	+	0.0193400i
$407$	18.4754			0.915793
$408$	−5.29115	+	6.21723i	−0.261951	+	0.307799i
$409$	28.8169			1.42490			0.712451	−	0.701722i	$-0.247585\pi$
$409$	28.8169			1.42490			0.712451	+	0.701722i	$0.247585\pi$
$410$	−14.5464	−	1.00669i	−0.718396	−	0.0497170i
$411$	11.3744			0.561057
$412$	29.6131	+	4.11851i	1.45893	+	0.202904i
$413$	−2.48257			−0.122159
$414$	10.7736	+	0.745592i	0.529493	+	0.0366438i
$415$			1.62221i			0.0796310i
$416$	11.0963	+	3.99368i	0.544041	+	0.195806i
$417$	−2.70353			−0.132392
$418$	22.5305	+	1.55924i	1.10200	+	0.0762648i
$419$	−15.8132			−0.772525			−0.386263	−	0.922389i	$-0.626234\pi$
$419$	−15.8132			−0.772525			−0.386263	+	0.922389i	$0.626234\pi$
$420$	0.0911042	−	0.655063i	0.00444543	−	0.0319638i
$421$		−	0.972923i		−	0.0474174i	−0.999719	−	0.0237087i	$-0.992453\pi$
$421$		−	0.972923i		−	0.0474174i	0.999719	−	0.0237087i	$-0.00754742\pi$
$422$	1.00828	−	14.5694i	0.0490824	−	0.709227i
$423$	13.9702			0.679252
$424$	16.9364	+	3.56184i	0.822505	+	0.172978i
$425$	3.62268	+	1.96881i	0.175726	+	0.0955013i
$426$	−14.2857	−	0.988647i	−0.692143	−	0.0479001i
$427$		−	1.93177i		−	0.0934849i
$428$	−31.0710	−	4.32127i	−1.50187	−	0.208876i
$429$			5.49604i			0.265351i
$430$	11.5441	+	0.798916i	0.556707	+	0.0385272i
$431$			29.2081i			1.40690i	0.710744	+	0.703451i	$0.248359\pi$
$431$			29.2081i			1.40690i	−0.710744	+	0.703451i	$0.751641\pi$
$432$	14.8434	+	4.21020i	0.714155	+	0.202563i
$433$	−23.8697			−1.14710			−0.573552	−	0.819169i	$-0.694435\pi$
$433$	−23.8697			−1.14710			−0.573552	+	0.819169i	$0.694435\pi$
$434$	0.0874610	−	1.26379i	0.00419826	−	0.0606637i
$435$	−5.91497			−0.283601
$436$	31.8224	+	4.42577i	1.52402	+	0.211956i
$437$	12.9018			0.617178
$438$	11.6354	+	0.805232i	0.555959	+	0.0384754i
$439$		−	24.6752i		−	1.17768i	−0.808249	−	0.588841i	$-0.799585\pi$
$439$		−	24.6752i		−	1.17768i	0.808249	−	0.588841i	$-0.200415\pi$
$440$	2.19213	−	10.4235i	0.104506	−	0.496920i
$441$	−17.0094			−0.809973
$442$	10.2544	+	6.52814i	0.487753	+	0.310512i
$443$		−	6.58438i		−	0.312834i	−0.987691	−	0.156417i	$-0.950006\pi$
$443$		−	6.58438i		−	0.312834i	0.987691	−	0.156417i	$-0.0499943\pi$
$444$	6.80347	+	0.946207i	0.322878	+	0.0449050i
$445$	4.13274			0.195911
$446$	−0.0833085	+	1.20378i	−0.00394477	+	0.0570008i
$447$			10.6636i			0.504369i
$448$	−1.52216	+	3.45883i	−0.0719151	+	0.163414i
$449$		−	17.6917i		−	0.834925i	−0.908694	−	0.417462i	$-0.862920\pi$
$449$		−	17.6917i		−	0.834925i	0.908694	−	0.417462i	$-0.137080\pi$
$450$	0.245064	−	3.54110i	0.0115524	−	0.166929i
$451$			38.8279i			1.82833i
$452$	−2.14950	+	15.4555i	−0.101104	+	0.726964i
$453$	1.01835			0.0478463
$454$	2.09052	−	30.2075i	0.0981132	−	1.41771i
$455$	−0.984770			−0.0461667
$456$	8.21689	+	1.72807i	0.384791	+	0.0809242i
$457$	8.25279			0.386049			0.193025	−	0.981194i	$-0.438170\pi$
$457$	8.25279			0.386049			0.193025	+	0.981194i	$0.438170\pi$
$458$	−0.396136	−	0.0274148i	−0.0185102	−	0.00128101i
$459$	13.9735	+	7.59418i	0.652229	+	0.354466i
$460$	0.838201	−	6.02688i	0.0390813	−	0.281005i
$461$		−	8.12505i		−	0.378421i	−0.981937	−	0.189211i	$-0.939407\pi$
$461$		−	8.12505i		−	0.378421i	0.981937	−	0.189211i	$-0.0605929\pi$
$462$	−1.75693	−	0.121590i	−0.0817400	−	0.00565686i
$463$	−25.7721			−1.19773			−0.598864	−	0.800850i	$-0.704381\pi$
$463$	−25.7721			−1.19773			−0.598864	+	0.800850i	$0.704381\pi$
$464$	32.5146	+	9.22245i	1.50945	+	0.428142i
$465$			1.32754i			0.0615630i
$466$	3.95300	+	0.273570i	0.183119	+	0.0126729i
$467$		−	31.6325i		−	1.46378i	−0.681425	−	0.731888i	$-0.738639\pi$
$467$		−	31.6325i		−	1.46378i	0.681425	−	0.731888i	$-0.261361\pi$
$468$	1.44158	−	10.3653i	0.0666372	−	0.479138i
$469$	6.62971			0.306131
$470$	0.543449	−	7.85268i	0.0250674	−	0.362217i
$471$			1.66835i			0.0768734i
$472$	−14.5468	−	3.05929i	−0.669570	−	0.140815i
$473$		−	30.8140i		−	1.41683i
$474$	−14.0815	−	0.974514i	−0.646782	−	0.0447609i
$475$		−	4.24061i		−	0.194573i
$476$	−2.31373	+	3.13363i	−0.106050	+	0.143630i
$477$		−	15.3580i		−	0.703195i
$478$	−0.708153	+	10.2326i	−0.0323902	+	0.468029i
$479$		−	10.9120i		−	0.498584i	−0.968428	−	0.249292i	$-0.919802\pi$
$479$		−	10.9120i		−	0.498584i	0.968428	−	0.249292i	$-0.0801978\pi$
$480$	1.34107	−	3.72612i	0.0612112	−	0.170073i
$481$		−	10.2278i		−	0.466348i
$482$	−30.6254	−	2.11945i	−1.39495	−	0.0965381i
$483$	−1.00609			−0.0457785
$484$	−6.30289	−	0.876588i	−0.286495	−	0.0398449i
$485$		−	1.51194i		−	0.0686536i
$486$	1.45994	−	21.0958i	0.0662244	−	0.956923i
$487$			8.42188i			0.381632i	0.981626	+	0.190816i	$0.0611134\pi$
$487$			8.42188i			0.381632i	−0.981626	+	0.190816i	$0.938887\pi$
$488$	2.38054	−	11.3193i	0.107762	−	0.512403i
$489$	7.04465			0.318570
$490$	−0.661679	+	9.56107i	−0.0298916	+	0.431925i
$491$		−	1.68337i		−	0.0759696i	−0.999278	−	0.0379848i	$-0.987906\pi$
$491$		−	1.68337i		−	0.0759696i	0.999278	−	0.0379848i	$-0.0120938\pi$
$492$	−1.98854	+	14.2981i	−0.0896505	+	0.644610i
$493$	30.6091	+	16.6351i	1.37856	+	0.749206i
$494$	0.863178	−	12.4727i	0.0388362	−	0.561172i
$495$	−9.45205			−0.424838
$496$	2.06986	−	7.29747i	0.0929393	−	0.327666i
$497$	−6.83239			−0.306475
$498$	1.60219	+	0.110881i	0.0717960	+	0.00496868i
$499$	−2.69995			−0.120866			−0.0604331	−	0.998172i	$-0.519248\pi$
$499$	−2.69995			−0.120866			−0.0604331	+	0.998172i	$0.519248\pi$
$500$	−1.98093	−	0.275503i	−0.0885900	−	0.0123208i
$501$			2.86651i			0.128066i
$502$	−11.1134	−	0.769112i	−0.496018	−	0.0343271i
$503$			41.6996i			1.85929i	0.368452	+	0.929647i	$0.379888\pi$
$503$			41.6996i			1.85929i	−0.368452	+	0.929647i	$0.620112\pi$
$504$	3.28163	+	0.690149i	0.146175	+	0.0307417i
$505$		−	15.9111i		−	0.708034i
$506$	−16.1646	−	1.11868i	−0.718604	−	0.0497314i
$507$	−6.05815			−0.269052
$508$	−21.5526	−	2.99748i	−0.956243	−	0.132992i
$509$			21.3267i			0.945291i	0.881253	+	0.472646i	$0.156701\pi$
$509$			21.3267i			0.945291i	−0.881253	+	0.472646i	$0.843299\pi$
$510$	2.19214	−	3.44341i	0.0970695	−	0.152477i
$511$	5.56484			0.246174
$512$	−13.1815	+	18.3915i	−0.582546	+	0.812797i
$513$		−	16.3571i		−	0.722183i
$514$	−0.670731	+	9.69187i	−0.0295847	+	0.427490i
$515$	−14.9491			−0.658735
$516$	1.57812	−	11.3471i	0.0694729	−	0.499528i
$517$	−20.9607			−0.921850
$518$	3.26955	+	0.226271i	0.143656	+	0.00994177i
$519$	−11.4655			−0.503281
$520$	−5.77033	−	1.21354i	−0.253046	−	0.0532172i
$521$		−	5.58565i		−	0.244712i	−0.992486	−	0.122356i	$-0.960955\pi$
$521$		−	5.58565i		−	0.244712i	0.992486	−	0.122356i	$-0.0390449\pi$
$522$	2.07062	−	29.9198i	0.0906284	−	1.30955i
$523$		−	30.3049i		−	1.32514i	−0.748999	−	0.662571i	$-0.769465\pi$
$523$		−	30.3049i		−	1.32514i	0.748999	−	0.662571i	$-0.230535\pi$
$524$	−27.6466	−	3.84500i	−1.20775	−	0.167970i
$525$			0.330684i			0.0144322i
$526$	2.56342	−	37.0407i	0.111770	−	1.61505i
$527$	3.73352	−	6.86981i	0.162635	−	0.299253i
$528$	−10.1450	−	2.87755i	−0.441506	−	0.125229i
$529$	13.7435			0.597545
$530$	−8.63280	−	0.597437i	−0.374985	−	0.0259510i
$531$			13.1911i			0.572445i
$532$	3.96808	+	0.551869i	0.172038	+	0.0239265i
$533$	21.4947			0.931039
$534$	0.282480	−	4.08176i	0.0122241	−	0.176635i
$535$	15.6850			0.678123
$536$	38.8472	+	8.16984i	1.67794	+	0.352883i
$537$		−	5.71743i		−	0.246725i
$538$	1.92697	−	27.8442i	0.0830777	−	1.20045i
$539$	25.5208			1.09926
$540$	−7.64094	−	1.06268i	−0.328814	−	0.0457305i
$541$	5.91685			0.254385			0.127193	−	0.991878i	$-0.459403\pi$
$541$	5.91685			0.254385			0.127193	+	0.991878i	$0.459403\pi$
$542$	0.959429	−	13.8635i	0.0412110	−	0.595487i
$543$	8.85496			0.380003
$544$	−17.4191	+	15.5105i	−0.746836	+	0.665008i
$545$	−16.0643			−0.688121
$546$	−0.0673107	+	0.972621i	−0.00288063	+	0.0416243i
$547$	39.6019			1.69325			0.846627	−	0.532187i	$-0.178629\pi$
$547$	39.6019			1.69325			0.846627	+	0.532187i	$0.178629\pi$
$548$	32.1860	+	4.47633i	1.37492	+	0.191219i
$549$	−10.2644			−0.438075
$550$	−0.367691	+	5.31304i	−0.0156784	+	0.226549i
$551$		−	35.8302i		−	1.52642i
$552$	−5.89523	−	1.23981i	−0.250918	−	0.0527697i
$553$	−6.73473			−0.286390
$554$	0.695987	−	10.0568i	0.0295697	−	0.427273i
$555$	−3.43448			−0.145785
$556$	−7.65014	−	1.06396i	−0.324438	−	0.0451219i
$557$		−	23.3121i		−	0.987763i	−0.869529	−	0.493882i	$-0.835578\pi$
$557$		−	23.3121i		−	0.987763i	0.869529	−	0.493882i	$-0.164422\pi$
$558$	−6.71511	−	0.464723i	−0.284273	−	0.0196733i
$559$	−17.0583			−0.721490
$560$	0.515593	−	1.81777i	0.0217878	−	0.0768148i
$561$	−9.55051	−	5.19040i	−0.403223	−	0.219139i
$562$	1.90997	−	27.5986i	0.0805674	−	1.16418i
$563$		−	8.22003i		−	0.346433i	−0.984884	−	0.173216i	$-0.944584\pi$
$563$		−	8.22003i		−	0.346433i	0.984884	−	0.173216i	$-0.0554160\pi$
$564$	−7.71866	−	1.07349i	−0.325014	−	0.0452020i
$565$		−	7.80211i		−	0.328237i
$566$	0.835016	−	12.0657i	0.0350983	−	0.507161i
$567$		−	2.28130i		−	0.0958058i
$568$	−40.0349	−	8.41961i	−1.67983	−	0.353279i
$569$	−42.0664			−1.76352			−0.881758	−	0.471703i	$-0.843639\pi$
$569$	−42.0664			−1.76352			−0.881758	+	0.471703i	$0.843639\pi$
$570$	−4.18830	−	0.289853i	−0.175429	−	0.0121406i
$571$	45.1866			1.89100			0.945500	−	0.325623i	$-0.105574\pi$
$571$	45.1866			1.89100			0.945500	+	0.325623i	$0.105574\pi$
$572$	−2.16294	+	15.5521i	−0.0904370	+	0.650265i
$573$	6.88876			0.287782
$574$	−0.475530	+	6.87127i	−0.0198482	+	0.286801i
$575$			3.04244i			0.126879i
$576$	18.3784	+	8.08795i	0.765769	+	0.336998i
$577$	−9.00464			−0.374868			−0.187434	−	0.982277i	$-0.560017\pi$
$577$	−9.00464			−0.374868			−0.187434	+	0.982277i	$0.560017\pi$
$578$	−21.0281	+	11.6541i	−0.874656	+	0.484745i
$579$		−	13.5446i		−	0.562894i
$580$	−16.7375	−	2.32780i	−0.694987	−	0.0966568i
$581$	0.766280			0.0317907
$582$	−1.49329	−	0.103344i	−0.0618987	−	0.00428373i
$583$			23.0430i			0.954345i
$584$	32.6076	+	6.85759i	1.34931	+	0.283769i
$585$			5.23256i			0.216340i
$586$	−32.2915	−	2.23475i	−1.33395	−	0.0923166i
$587$		−	19.0434i		−	0.786005i	−0.919537	−	0.393002i	$-0.871436\pi$
$587$		−	19.0434i		−	0.786005i	0.919537	−	0.393002i	$-0.128564\pi$
$588$	9.39789	+	1.30703i	0.387562	+	0.0539011i
$589$	−8.04162			−0.331349
$590$	7.41477	+	0.513143i	0.305261	+	0.0211258i
$591$	−1.77194			−0.0728879
$592$	18.8793	+	5.35494i	0.775935	+	0.220087i
$593$	−15.4544			−0.634636			−0.317318	−	0.948319i	$-0.602782\pi$
$593$	−15.4544			−0.634636			−0.317318	+	0.948319i	$0.602782\pi$
$594$	−1.41828	+	20.4937i	−0.0581926	+	0.840866i
$595$	0.930005	−	1.71124i	0.0381265	−	0.0701540i
$596$	−4.19659	+	30.1745i	−0.171899	+	1.23600i
$597$		−	5.42948i		−	0.222214i
$598$	−0.619290	+	8.94856i	−0.0253246	+	0.365934i
$599$	9.04450			0.369548			0.184774	−	0.982781i	$-0.440845\pi$
$599$	9.04450			0.369548			0.184774	+	0.982781i	$0.440845\pi$
$600$	−0.407504	+	1.93766i	−0.0166363	+	0.0791048i
$601$			19.6183i			0.800246i	0.916461	+	0.400123i	$0.131033\pi$
$601$			19.6183i			0.800246i	−0.916461	+	0.400123i	$0.868967\pi$
$602$	0.377383	−	5.45308i	0.0153810	−	0.222251i
$603$		−	35.2268i		−	1.43455i
$604$	2.88161	+	0.400767i	0.117251	+	0.0163070i
$605$	3.18178			0.129358
$606$	−15.7148	−	1.08755i	−0.638370	−	0.0441787i
$607$		−	25.1180i		−	1.01951i	−0.860320	−	0.509754i	$-0.829736\pi$
$607$		−	25.1180i		−	1.01951i	0.860320	−	0.509754i	$-0.170264\pi$
$608$	22.5711	+	8.12360i	0.915381	+	0.329456i
$609$			2.79405i			0.113220i
$610$	−0.399294	+	5.76968i	−0.0161669	+	0.233607i
$611$			11.6036i			0.469432i
$612$	16.6505	+	12.2940i	0.673057	+	0.496954i
$613$			5.63031i			0.227406i	0.993515	+	0.113703i	$0.0362712\pi$
$613$			5.63031i			0.227406i	−0.993515	+	0.113703i	$0.963729\pi$
$614$	−6.70375	−	0.463936i	−0.270541	−	0.0187229i
$615$		−	7.21788i		−	0.291053i
$616$	−4.92373	−	1.03549i	−0.198383	−	0.0417212i
$617$		−	14.6134i		−	0.588314i	−0.955757	−	0.294157i	$-0.904961\pi$
$617$		−	14.6134i		−	0.588314i	0.955757	−	0.294157i	$-0.0950389\pi$
$618$	−1.02179	+	14.7646i	−0.0411026	+	0.593921i
$619$	−10.0040			−0.402095			−0.201048	−	0.979581i	$-0.564435\pi$
$619$	−10.0040			−0.402095			−0.201048	+	0.979581i	$0.564435\pi$
$620$	−0.522445	+	3.75651i	−0.0209819	+	0.150865i
$621$			11.7354i			0.470927i
$622$	−26.1805	−	1.81183i	−1.04974	−	0.0726479i
$623$		−	1.95218i		−	0.0782124i
$624$	−1.59298	+	5.61619i	−0.0637702	+	0.224828i
$625$	1.00000			0.0400000
$626$	−39.1830	−	2.71168i	−1.56607	−	0.108380i
$627$			11.1796i			0.446469i
$628$	−0.656570	+	4.72091i	−0.0262000	+	0.188385i
$629$	17.7729	+	9.65902i	0.708653	+	0.385130i
$630$	−1.67271	−	0.115760i	−0.0666422	−	0.00461201i
$631$	13.4572			0.535722			0.267861	−	0.963458i	$-0.413683\pi$
$631$	13.4572			0.535722			0.267861	+	0.963458i	$0.413683\pi$
$632$	−39.4626	−	8.29925i	−1.56974	−	0.330127i
$633$	7.22929			0.287338
$634$	0.674269	−	9.74299i	0.0267786	−	0.386944i
$635$	10.8800			0.431761
$636$	−1.18013	+	8.48546i	−0.0467954	+	0.336471i
$637$		−	14.1281i		−	0.559774i
$638$	−3.10674	+	44.8914i	−0.122997	+	1.77727i
$639$			36.3038i			1.43616i
$640$	5.26120	−	10.0160i	0.207967	−	0.395916i
$641$		−	42.8148i		−	1.69108i	−0.533909	−	0.845542i	$-0.679278\pi$
$641$		−	42.8148i		−	1.69108i	0.533909	−	0.845542i	$-0.320722\pi$
$642$	1.07210	−	15.4915i	0.0423124	−	0.611402i
$643$	−22.4425			−0.885044			−0.442522	−	0.896758i	$-0.645916\pi$
$643$	−22.4425			−0.885044			−0.442522	+	0.896758i	$0.645916\pi$
$644$	−2.84691	−	0.395940i	−0.112184	−	0.0156022i
$645$			5.72815i			0.225546i
$646$	20.8587	+	13.2790i	0.820673	+	0.522455i
$647$	−31.4314			−1.23570			−0.617849	−	0.786297i	$-0.711996\pi$
$647$	−31.4314			−1.23570			−0.617849	+	0.786297i	$0.711996\pi$
$648$	2.81127	−	13.3675i	0.110437	−	0.525123i
$649$		−	19.7918i		−	0.776896i
$650$	2.94124	+	0.203550i	0.115365	+	0.00798389i
$651$	0.627087			0.0245775
$652$	19.9342	+	2.77239i	0.780682	+	0.108575i
$653$	24.8465			0.972318			0.486159	−	0.873871i	$-0.338398\pi$
$653$	24.8465			0.972318			0.486159	+	0.873871i	$0.338398\pi$
$654$	−1.09803	+	15.8662i	−0.0429362	+	0.620416i
$655$	13.9563			0.545319
$656$	−11.2539	+	39.6767i	−0.439392	+	1.54911i
$657$		−	29.5687i		−	1.15358i
$658$	−3.70936	−	0.256708i	−0.144606	−	0.0100075i
$659$			36.5507i			1.42381i	0.702273	+	0.711907i	$0.252168\pi$
$659$			36.5507i			1.42381i	−0.702273	+	0.711907i	$0.747832\pi$
$660$	5.22236	+	0.726311i	0.203280	+	0.0282716i
$661$		−	17.4285i		−	0.677889i	−0.940806	−	0.338944i	$-0.889930\pi$
$661$		−	17.4285i		−	0.677889i	0.940806	−	0.338944i	$-0.110070\pi$
$662$	−25.0105	−	1.73086i	−0.972060	−	0.0672719i
$663$	−2.87335	+	5.28706i	−0.111592	+	0.205332i
$664$	4.49007	+	0.944293i	0.174249	+	0.0366457i
$665$	−2.00313			−0.0776782
$666$	1.20229	−	17.3727i	0.0465877	−	0.673178i
$667$			25.7065i			0.995360i
$668$	−1.12810	+	8.11133i	−0.0436475	+	0.313837i
$669$	−0.597314			−0.0230935
$670$	−19.8011	−	1.37035i	−0.764985	−	0.0529412i
$671$	15.4007			0.594536
$672$	−1.76010	−	0.633480i	−0.0678974	−	0.0244370i
$673$		−	26.9124i		−	1.03740i	−0.854957	−	0.518699i	$-0.826417\pi$
$673$		−	26.9124i		−	1.03740i	0.854957	−	0.518699i	$-0.173583\pi$
$674$	9.37500	+	0.648802i	0.361112	+	0.0249909i
$675$	3.85724			0.148465
$676$	−17.1427	−	2.38415i	−0.659333	−	0.0916982i
$677$	−15.5242			−0.596642			−0.298321	−	0.954466i	$-0.596427\pi$
$677$	−15.5242			−0.596642			−0.298321	+	0.954466i	$0.596427\pi$
$678$	−7.70586	−	0.533288i	−0.295942	−	0.0204808i
$679$	−0.714193			−0.0274082
$680$	7.55820	−	8.88108i	0.289844	−	0.340574i
$681$	14.9889			0.574374
$682$	10.0753	+	0.697266i	0.385803	+	0.0266997i
$683$	32.9726			1.26166			0.630830	−	0.775921i	$-0.282715\pi$
$683$	32.9726			1.26166			0.630830	+	0.775921i	$0.282715\pi$
$684$	2.93234	−	21.0843i	0.112121	−	0.806179i
$685$	−16.2479			−0.620799
$686$	9.18141	+	0.635404i	0.350548	+	0.0242598i
$687$		−	0.196561i		−	0.00749929i
$688$	8.93118	−	31.4877i	0.340498	−	1.20046i
$689$	12.7564			0.485979
$690$	3.00491	+	0.207956i	0.114395	+	0.00791676i
$691$	−38.9502			−1.48174			−0.740869	−	0.671650i	$-0.765586\pi$
$691$	−38.9502			−1.48174			−0.740869	+	0.671650i	$0.765586\pi$
$692$	−32.4439	−	4.51220i	−1.23333	−	0.171528i
$693$			4.46486i			0.169606i
$694$	0.677682	−	9.79232i	0.0257245	−	0.371711i
$695$	3.86189			0.146490
$696$	−3.44312	+	16.3719i	−0.130511	+	0.620576i
$697$	−20.2993	+	37.3515i	−0.768893	+	1.41479i
$698$	38.5484	+	2.66776i	1.45908	+	0.100976i
$699$			1.96147i			0.0741895i
$700$	−0.130139	+	0.935732i	−0.00491879	+	0.0353673i
$701$		−	39.7185i		−	1.50015i	−0.661354	−	0.750074i	$-0.730018\pi$
$701$		−	39.7185i		−	1.50015i	0.661354	−	0.750074i	$-0.269982\pi$
$702$	11.3451	+	0.785143i	0.428193	+	0.0296333i
$703$		−	20.8045i		−	0.784658i
$704$	−27.5749	−	12.1351i	−1.03927	−	0.457358i
$705$	3.89647			0.146750
$706$	−0.556203	+	8.03697i	−0.0209330	+	0.302475i
$707$	−7.51590			−0.282665
$708$	1.01362	−	7.28822i	0.0380943	−	0.273908i
$709$	−0.684050			−0.0256901			−0.0128450	−	0.999917i	$-0.504089\pi$
$709$	−0.684050			−0.0256901			−0.0128450	+	0.999917i	$0.504089\pi$
$710$	20.4065	+	1.41224i	0.765843	+	0.0530006i
$711$			35.7848i			1.34204i
$712$	2.40569	−	11.4389i	0.0901569	−	0.428692i
$713$	5.76949			0.216069
$714$	−1.62656	−	1.03550i	−0.0608725	−	0.0387525i
$715$		−	7.85089i		−	0.293606i
$716$	2.25006	−	16.1785i	0.0840889	−	0.604620i
$717$	−5.07739			−0.189619
$718$	−2.78289	+	40.2120i	−0.103857	+	1.50070i
$719$			38.6497i			1.44139i	0.693252	+	0.720695i	$0.256177\pi$
$719$			38.6497i			1.44139i	−0.693252	+	0.720695i	$0.743823\pi$
$720$	−9.65868	−	2.73959i	−0.359958	−	0.102099i
$721$			7.06148i			0.262983i
$722$	−0.0993170	+	1.43510i	−0.00369620	+	0.0534090i
$723$		−	15.1962i		−	0.565153i
$724$	25.0568	+	3.48482i	0.931227	+	0.129512i
$725$	8.44930			0.313799
$726$	0.217480	−	3.14252i	0.00807144	−	0.116630i
$727$	−25.3357			−0.939651			−0.469825	−	0.882759i	$-0.655683\pi$
$727$	−25.3357			−0.939651			−0.469825	+	0.882759i	$0.655683\pi$
$728$	−0.573238	+	2.72572i	−0.0212456	+	0.101022i
$729$	−4.02083			−0.148920
$730$	−16.6207	−	1.15024i	−0.615159	−	0.0425724i
$731$	16.1097	−	29.6424i	0.595838	−	1.09636i
$732$	5.67121	+	0.788735i	0.209614	+	0.0291525i
$733$			53.4938i			1.97584i	0.154968	+	0.987920i	$0.450473\pi$
$733$			53.4938i			1.97584i	−0.154968	+	0.987920i	$0.549527\pi$
$734$	−42.5301	−	2.94332i	−1.56982	−	0.108640i
$735$	−4.74417			−0.174991
$736$	−16.1937	−	5.82831i	−0.596909	−	0.214834i
$737$			52.8540i			1.94690i
$738$	36.5104	+	2.52672i	1.34397	+	0.0930098i
$739$			10.7854i			0.396746i	0.980127	+	0.198373i	$0.0635658\pi$
$739$			10.7854i			0.396746i	−0.980127	+	0.198373i	$0.936434\pi$
$740$	−9.71850	−	1.35162i	−0.357259	−	0.0496866i
$741$	6.18890			0.227355
$742$	−0.282211	+	4.07787i	−0.0103603	+	0.149703i
$743$			10.8676i			0.398694i	0.979929	+	0.199347i	$0.0638821\pi$
$743$			10.8676i			0.398694i	−0.979929	+	0.199347i	$0.936118\pi$
$744$	3.67446	+	0.772764i	0.134712	+	0.0283309i
$745$		−	15.2325i		−	0.558075i
$746$	12.6854	+	0.877896i	0.464444	+	0.0321421i
$747$		−	4.07162i		−	0.148973i
$748$	−24.9823	−	18.4458i	−0.913443	−	0.674444i
$749$		−	7.40912i		−	0.270724i
$750$	0.0683518	−	0.987663i	0.00249585	−	0.0360644i
$751$		−	43.1284i		−	1.57378i	−0.617095	−	0.786889i	$-0.711691\pi$
$751$		−	43.1284i		−	1.57378i	0.617095	−	0.786889i	$-0.288309\pi$
$752$	−21.4189	−	6.07528i	−0.781068	−	0.221543i
$753$		−	5.51446i		−	0.200958i
$754$	24.8514	+	1.71986i	0.905036	+	0.0626335i
$755$	−1.45467			−0.0529410
$756$	−0.501977	+	3.60935i	−0.0182567	+	0.131271i
$757$		−	22.5791i		−	0.820652i	−0.911939	−	0.410326i	$-0.865415\pi$
$757$		−	22.5791i		−	0.820652i	0.911939	−	0.410326i	$-0.134585\pi$
$758$	1.15962	−	16.7562i	0.0421194	−	0.608613i
$759$		−	8.02083i		−	0.291138i
$760$	−11.7375	−	2.46848i	−0.425764	−	0.0895411i
$761$	−10.4373			−0.378353			−0.189177	−	0.981943i	$-0.560582\pi$
$761$	−10.4373			−0.378353			−0.189177	+	0.981943i	$0.560582\pi$
$762$	0.743670	−	10.7458i	0.0269403	−	0.389280i
$763$			7.58830i			0.274715i
$764$	19.4930	+	2.71103i	0.705233	+	0.0980818i
$765$	−9.09265	−	4.94157i	−0.328745	−	0.178663i
$766$	−1.04453	+	15.0932i	−0.0377405	+	0.545340i
$767$	−10.9565			−0.395618
$768$	−9.53280	−	5.88091i	−0.343985	−	0.212209i
$769$	−30.5474			−1.10157			−0.550784	−	0.834648i	$-0.685671\pi$
$769$	−30.5474			−1.10157			−0.550784	+	0.834648i	$0.685671\pi$
$770$	2.50971	+	0.173686i	0.0904438	+	0.00625921i
$771$	−4.80908			−0.173195
$772$	5.33041	−	38.3270i	0.191846	−	1.37942i
$773$			40.8348i			1.46873i	0.678756	+	0.734364i	$0.262519\pi$
$773$			40.8348i			1.46873i	−0.678756	+	0.734364i	$0.737481\pi$
$774$	−28.9749	−	2.00522i	−1.04148	−	0.0720761i
$775$		−	1.89633i		−	0.0681183i
$776$	−4.18486	−	0.880105i	−0.150228	−	0.0315939i
$777$			1.62234i			0.0582011i
$778$	−20.5348	−	1.42112i	−0.736209	−	0.0509497i
$779$	43.7227			1.56653
$780$	0.402078	−	2.89104i	0.0143967	−	0.103516i
$781$		−	54.4699i		−	1.94909i
$782$	−14.9651	−	9.52706i	−0.535151	−	0.340687i
$783$	32.5910			1.16471
$784$	26.0787	+	7.39698i	0.931383	+	0.264178i
$785$		−	2.38317i		−	0.0850590i
$786$	0.953939	−	13.7841i	0.0340259	−	0.491664i
$787$	−40.1369			−1.43073			−0.715363	−	0.698753i	$-0.753739\pi$
$787$	−40.1369			−1.43073			−0.715363	+	0.698753i	$0.753739\pi$
$788$	−5.01404	−	0.697338i	−0.178618	−	0.0248416i
$789$	18.3795			0.654327
$790$	20.1148	+	1.39206i	0.715653	+	0.0495271i
$791$	−3.68547			−0.131040
$792$	−5.50208	+	26.1621i	−0.195508	+	0.929631i
$793$		−	8.52565i		−	0.302755i
$794$	0.501927	−	7.25270i	0.0178127	−	0.257389i
$795$		−	4.28357i		−	0.151923i
$796$	2.13674	−	15.3637i	0.0757348	−	0.544553i
$797$		−	36.6352i		−	1.29768i	−0.760923	−	0.648842i	$-0.775254\pi$
$797$		−	36.6352i		−	1.29768i	0.760923	−	0.648842i	$-0.224746\pi$
$798$	−0.136918	+	1.97842i	−0.00484684	+	0.0700354i
$799$	−20.1637	−	10.9583i	−0.713340	−	0.387678i
$800$	−1.91567	+	5.32261i	−0.0677291	+	0.188183i
$801$	−10.3729			−0.366507
$802$	−20.9448	−	1.44949i	−0.739585	−	0.0511834i
$803$			44.3646i			1.56559i
$804$	−2.70689	+	19.4632i	−0.0954645	+	0.686414i
$805$	1.43716			0.0506531
$806$	0.385999	−	5.57758i	0.0135962	−	0.196462i
$807$	13.8162			0.486354
$808$	−44.0399	−	9.26190i	−1.54932	−	0.325833i
$809$		−	31.5268i		−	1.10842i	−0.832376	−	0.554212i	$-0.813020\pi$
$809$		−	31.5268i		−	1.10842i	0.832376	−	0.554212i	$-0.186980\pi$
$810$	−0.471542	+	6.81364i	−0.0165683	+	0.239407i
$811$	−2.16993			−0.0761965			−0.0380982	−	0.999274i	$-0.512130\pi$
$811$	−2.16993			−0.0761965			−0.0380982	+	0.999274i	$0.512130\pi$
$812$	−1.09958	+	7.90628i	−0.0385878	+	0.277456i
$813$	6.87901			0.241258
$814$	−1.80390	+	26.0659i	−0.0632267	+	0.913608i
$815$	−10.0630			−0.352492
$816$	−8.25490	−	8.07200i	−0.288979	−	0.282576i
$817$	−34.6986			−1.21395
$818$	−2.81362	+	40.6560i	−0.0983758	+	1.42150i
$819$	2.47170			0.0863681
$820$	2.84056	−	20.4243i	0.0991966	−	0.713249i
$821$	−43.9566			−1.53410			−0.767048	−	0.641590i	$-0.778275\pi$
$821$	−43.9566			−1.53410			−0.767048	+	0.641590i	$0.778275\pi$
$822$	−1.11057	+	16.0474i	−0.0387356	+	0.559718i
$823$		−	4.32095i		−	0.150619i	−0.997160	−	0.0753094i	$-0.976006\pi$
$823$		−	4.32095i		−	0.150619i	0.997160	−	0.0753094i	$-0.0239945\pi$
$824$	−8.70191	+	41.3772i	−0.303145	+	1.44144i
$825$	−2.63631			−0.0917846
$826$	0.242393	−	3.50251i	0.00843392	−	0.121868i
$827$	13.4583			0.467990			0.233995	−	0.972238i	$-0.424820\pi$
$827$	13.4583			0.467990			0.233995	+	0.972238i	$0.424820\pi$
$828$	−2.10382	+	15.1270i	−0.0731128	+	0.525700i
$829$			36.3519i			1.26255i	0.775558	+	0.631277i	$0.217469\pi$
$829$			36.3519i			1.26255i	−0.775558	+	0.631277i	$0.782531\pi$
$830$	−2.28867	−	0.158389i	−0.0794410	−	0.00549776i
$831$	4.99016			0.173107
$832$	−6.71786	+	15.2652i	−0.232900	+	0.529224i
$833$	24.5504	+	13.3424i	0.850621	+	0.462286i
$834$	0.263967	−	3.81424i	0.00914042	−	0.132076i
$835$		−	4.09470i		−	0.141703i
$836$	−4.39967	+	31.6347i	−0.152166	+	1.09411i
$837$		−	7.31462i		−	0.252830i
$838$	1.54397	−	22.3099i	0.0533354	−	0.770682i
$839$		−	10.1963i		−	0.352016i	−0.984389	−	0.176008i	$-0.943682\pi$
$839$		−	10.1963i		−	0.352016i	0.984389	−	0.176008i	$-0.0563185\pi$
$840$	0.915293	+	0.192492i	0.0315806	+	0.00664162i
$841$	42.3907			1.46175
$842$	1.37264	+	0.0949941i	0.0473042	+	0.00327371i
$843$	13.6943			0.471658
$844$	20.4566	+	2.84505i	0.704146	+	0.0979306i
$845$	8.65383			0.297701
$846$	−1.36402	+	19.7096i	−0.0468958	+	0.677631i
$847$		−	1.50297i		−	0.0516428i
$848$	−6.67882	+	23.5468i	−0.229352	+	0.808600i
$849$	5.98698			0.205473
$850$	−3.13138	+	4.91878i	−0.107406	+	0.168713i
$851$			14.9263i			0.511666i
$852$	2.78964	−	20.0582i	0.0955716	−	0.687184i
$853$	19.0192			0.651205			0.325602	−	0.945507i	$-0.394433\pi$
$853$	19.0192			0.651205			0.325602	+	0.945507i	$0.394433\pi$
$854$	2.72542	+	0.188614i	0.0932619	+	0.00645423i
$855$			10.6436i			0.364004i
$856$	9.13032	−	43.4143i	0.312068	−	1.48387i
$857$		−	15.6163i		−	0.533443i	−0.963774	−	0.266721i	$-0.914060\pi$
$857$		−	15.6163i		−	0.533443i	0.963774	−	0.266721i	$-0.0859404\pi$
$858$	−7.75403	−	0.536622i	−0.264718	−	0.0183200i
$859$			8.33388i			0.284348i	0.989842	+	0.142174i	$0.0454093\pi$
$859$			8.33388i			0.284348i	−0.989842	+	0.142174i	$0.954591\pi$
$860$	−2.25428	+	16.2089i	−0.0768705	+	0.552718i
$861$	−3.40950			−0.116196
$862$	−41.2079	−	2.85181i	−1.40355	−	0.0971331i
$863$	5.60477			0.190789			0.0953943	−	0.995440i	$-0.469589\pi$
$863$	5.60477			0.190789			0.0953943	+	0.995440i	$0.469589\pi$
$864$	−7.38920	+	20.5306i	−0.251386	+	0.698466i
$865$	16.3781			0.556871
$866$	2.33059	−	33.6763i	0.0791966	−	1.14437i
$867$	−6.47380	−	9.98608i	−0.219862	−	0.339145i
$868$	1.77446	+	0.246787i	0.0602291	+	0.00837649i
$869$		−	53.6913i		−	1.82135i
$870$	0.577525	−	8.34507i	0.0195799	−	0.282924i
$871$	29.2595			0.991419
$872$	−9.35112	+	44.4642i	−0.316669	+	1.50575i
$873$			3.79485i			0.128436i
$874$	−1.25971	+	18.2024i	−0.0426102	+	0.615705i
$875$		−	0.472369i		−	0.0159690i
$876$	−2.27210	+	16.3370i	−0.0767673	+	0.551976i
$877$	27.8925			0.941864			0.470932	−	0.882169i	$-0.343918\pi$
$877$	27.8925			0.941864			0.470932	+	0.882169i	$0.343918\pi$
$878$	34.8127	+	2.40923i	1.17487	+	0.0813076i
$879$		−	16.0229i		−	0.540440i
$880$	14.4918	+	4.11046i	0.488519	+	0.138564i
$881$		−	31.1567i		−	1.04969i	−0.851196	−	0.524847i	$-0.824122\pi$
$881$		−	31.1567i		−	1.04969i	0.851196	−	0.524847i	$-0.175878\pi$
$882$	1.66076	−	23.9976i	0.0559208	−	0.808040i
$883$		−	26.5634i		−	0.893931i	−0.894551	−	0.446965i	$-0.852505\pi$
$883$		−	26.5634i		−	0.893931i	0.894551	−	0.446965i	$-0.147495\pi$
$884$	−10.2114	+	13.8299i	−0.343446	+	0.465151i
$885$			3.67918i			0.123674i
$886$	9.28951	+	0.642885i	0.312087	+	0.0215981i
$887$			25.6641i			0.861717i	0.902419	+	0.430859i	$0.141789\pi$
$887$			25.6641i			0.861717i	−0.902419	+	0.430859i	$0.858211\pi$
$888$	−1.99922	+	9.50622i	−0.0670895	+	0.319008i
$889$		−	5.13939i		−	0.172370i
$890$	−0.403512	+	5.83064i	−0.0135258	+	0.195443i
$891$	18.1873			0.609296
$892$	−1.69021	−	0.235070i	−0.0565925	−	0.00787072i
$893$			23.6031i			0.789848i
$894$	−15.0446	−	1.04117i	−0.503165	−	0.0348218i
$895$			8.16713i			0.272997i
$896$	−4.73124	−	2.48523i	−0.158059	−	0.0830257i
$897$	−4.44025			−0.148256
$898$	24.9602	+	1.72738i	0.832932	+	0.0576435i
$899$		−	16.0227i		−	0.534387i
$900$	4.97199	+	0.691491i	0.165733	+	0.0230497i
$901$	−12.0470	+	22.1668i	−0.401343	+	0.738485i
$902$	−54.7799	−	3.79107i	−1.82397	−	0.126229i
$903$	2.70580			0.0900435
$904$	−21.5953	−	4.54164i	−0.718249	−	0.151053i
$905$	−12.6490			−0.420466
$906$	−0.0994296	+	1.43673i	−0.00330333	+	0.0477321i
$907$	20.5456			0.682206			0.341103	−	0.940026i	$-0.389200\pi$
$907$	20.5456			0.682206			0.341103	+	0.940026i	$0.389200\pi$
$908$	42.4138	+	5.89879i	1.40755	+	0.195758i
$909$			39.9356i			1.32458i
$910$	0.0961508	−	1.38935i	0.00318737	−	0.0460566i
$911$			34.5273i			1.14394i	0.820274	+	0.571970i	$0.193821\pi$
$911$			34.5273i			1.14394i	−0.820274	+	0.571970i	$0.806179\pi$
$912$	−3.24030	+	11.4240i	−0.107297	+	0.378286i
$913$			6.10902i			0.202179i
$914$	−0.805785	+	11.6434i	−0.0266530	+	0.385128i
$915$	−2.86290			−0.0946444
$916$	0.0773557	−	0.556207i	0.00255591	−	0.0183776i
$917$		−	6.59253i		−	0.217705i
$918$	−12.0785	+	18.9729i	−0.398650	+	0.626201i
$919$	18.5422			0.611650			0.305825	−	0.952088i	$-0.401068\pi$
$919$	18.5422			0.611650			0.305825	+	0.952088i	$0.401068\pi$
$920$	8.42111	+	1.77102i	0.277636	+	0.0583887i
$921$		−	3.32638i		−	0.109608i
$922$	11.4631	+	0.793312i	0.377518	+	0.0261263i
$923$	−30.1540			−0.992531
$924$	0.343087	−	2.46688i	0.0112867	−	0.0811544i
$925$	4.90602			0.161309
$926$	2.51633	−	36.3602i	0.0826917	−	1.19487i
$927$	37.5210			1.23235
$928$	−16.1860	+	44.9724i	−0.531333	+	1.47629i
$929$			18.2002i			0.597130i	0.954389	+	0.298565i	$0.0965080\pi$
$929$			18.2002i			0.597130i	−0.954389	+	0.298565i	$0.903492\pi$
$930$	−1.87294	−	0.129618i	−0.0614161	−	0.00425033i
$931$		−	28.7381i		−	0.941852i
$932$	−0.771925	+	5.55034i	−0.0252852	+	0.181807i
$933$		−	12.9907i		−	0.425295i
$934$	44.6283	+	3.08853i	1.46028	+	0.101060i
$935$	13.6425	+	7.41428i	0.446158	+	0.242473i
$936$	14.4831	+	3.04589i	0.473394	+	0.0995581i
$937$	−35.1844			−1.14942			−0.574711	−	0.818356i	$-0.694886\pi$
$937$	−35.1844			−1.14942			−0.574711	+	0.818356i	$0.694886\pi$
$938$	−0.647310	+	9.35345i	−0.0211354	+	0.305401i
$939$		−	19.4425i		−	0.634481i
$940$	11.0258	+	1.53344i	0.359622	+	0.0500152i
$941$	−6.97595			−0.227409			−0.113705	−	0.993515i	$-0.536272\pi$
$941$	−6.97595			−0.227409			−0.113705	+	0.993515i	$0.536272\pi$
$942$	−2.35377	−	0.162894i	−0.0766900	−	0.00530737i
$943$	−31.3690			−1.02152
$944$	5.73648	−	20.2245i	0.186707	−	0.658251i
$945$		−	1.82204i		−	0.0592710i
$946$	43.4736	+	3.00862i	1.41345	+	0.0978185i
$947$	51.4262			1.67113			0.835564	−	0.549394i	$-0.185141\pi$
$947$	51.4262			1.67113			0.835564	+	0.549394i	$0.185141\pi$
$948$	2.74977	−	19.7715i	0.0893082	−	0.642149i
$949$	24.5598			0.797244
$950$	5.98282	+	0.414044i	0.194108	+	0.0134334i
$951$	4.83444			0.156768
$952$	−4.19515	−	3.57026i	−0.135965	−	0.115713i
$953$	2.19024			0.0709487			0.0354743	−	0.999371i	$-0.488706\pi$
$953$	2.19024			0.0709487			0.0354743	+	0.999371i	$0.488706\pi$
$954$	21.6677	+	1.49952i	0.701517	+	0.0485488i
$955$	−9.84032			−0.318425
$956$	−14.3674	−	1.99818i	−0.464676	−	0.0646258i
$957$	−22.2750			−0.720048
$958$	15.3951	+	1.06543i	0.497394	+	0.0344224i
$959$			7.67499i			0.247838i
$960$	5.12601	+	2.25584i	0.165441	+	0.0728071i
$961$	27.4039			0.883997
$962$	14.4298	+	0.998621i	0.465235	+	0.0321968i
$963$	−39.3683			−1.26862
$964$	5.98039	−	43.0005i	0.192615	−	1.38495i
$965$			19.3479i			0.622832i
$966$	0.0982321	−	1.41943i	0.00316057	−	0.0456693i
$967$	−23.0610			−0.741592			−0.370796	−	0.928714i	$-0.620915\pi$
$967$	−23.0610			−0.741592			−0.370796	+	0.928714i	$0.620915\pi$
$968$	1.85212	−	8.80677i	0.0595296	−	0.283060i
$969$	−5.84472	+	10.7545i	−0.187760	+	0.345484i
$970$	2.13310	+	0.147622i	0.0684897	+	0.00473987i
$971$			24.4595i			0.784944i	0.919764	+	0.392472i	$0.128380\pi$
$971$			24.4595i			0.784944i	−0.919764	+	0.392472i	$0.871620\pi$
$972$	29.6202	+	4.11949i	0.950068	+	0.132133i
$973$		−	1.82423i		−	0.0584823i
$974$	−11.8819	−	0.822295i	−0.380721	−	0.0263480i
$975$			1.45943i			0.0467393i
$976$	15.7373	+	4.46375i	0.503740	+	0.142881i
$977$	59.5006			1.90359			0.951797	−	0.306730i	$-0.0992347\pi$
$977$	59.5006			1.90359			0.951797	+	0.306730i	$0.0992347\pi$
$978$	−0.687824	+	9.93887i	−0.0219942	+	0.317810i
$979$	15.5634			0.497408
$980$	−13.4245	−	1.86704i	−0.428831	−	0.0596405i
$981$	40.3203			1.28733
$982$	2.37497	+	0.164361i	0.0757883	+	0.00524497i
$983$		−	45.4634i		−	1.45006i	−0.688718	−	0.725029i	$-0.741826\pi$
$983$		−	45.4634i		−	1.45006i	0.688718	−	0.725029i	$-0.258174\pi$
$984$	−19.9782	−	4.20156i	−0.636882	−	0.133941i
$985$	2.53115			0.0806491
$986$	−26.4580	+	41.5603i	−0.842595	+	1.32355i
$987$		−	1.84057i		−	0.0585861i
$988$	17.5127	+	2.43561i	0.557152	+	0.0774871i
$989$	24.8946			0.791603
$990$	0.922878	−	13.3353i	0.0293310	−	0.423824i
$991$			3.88975i			0.123562i	0.998090	+	0.0617809i	$0.0196780\pi$
$991$			3.88975i			0.123562i	−0.998090	+	0.0617809i	$0.980322\pi$
$992$	10.0935	+	3.63274i	0.320467	+	0.115340i
$993$		−	12.4101i		−	0.393823i
$994$	0.667100	−	9.63941i	0.0211591	−	0.305743i
$995$			7.75580i			0.245875i
$996$	−0.312870	+	2.24961i	−0.00991365	+	0.0712817i
$997$	−32.4838			−1.02877			−0.514385	−	0.857559i	$-0.671980\pi$
$997$	−32.4838			−1.02877			−0.514385	+	0.857559i	$0.671980\pi$
$998$	0.263617	−	3.80919i	0.00834465	−	0.120578i
$999$	18.9237			0.598720

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.l.a.101.18	yes	36
4.3	odd	2		2720.2.l.b.2481.21		36
8.3	odd	2		2720.2.l.a.2481.15		36
8.5	even	2		680.2.l.b.101.17	yes	36
17.16	even	2		680.2.l.b.101.18	yes	36
68.67	odd	2		2720.2.l.a.2481.16		36
136.67	odd	2		2720.2.l.b.2481.22		36
136.101	even	2	inner	680.2.l.a.101.17	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.l.a.101.17	✓	36	136.101	even	2	inner
680.2.l.a.101.18	yes	36	1.1	even	1	trivial
680.2.l.b.101.17	yes	36	8.5	even	2
680.2.l.b.101.18	yes	36	17.16	even	2
2720.2.l.a.2481.15		36	8.3	odd	2
2720.2.l.a.2481.16		36	68.67	odd	2
2720.2.l.b.2481.21		36	4.3	odd	2
2720.2.l.b.2481.22		36	136.67	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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0976378 + 1.41084i) q^{2} -0.700054 q^{3} +(-1.98093 - 0.275503i) q^{4} +1.00000 q^{5} +(0.0683518 - 0.987663i) q^{6} -0.472369i q^{7} +(0.582104 - 2.76788i) q^{8} -2.50992 q^{9} +(-0.0976378 + 1.41084i) q^{10} +3.76587 q^{11} +(1.38676 + 0.192867i) q^{12} -2.08475i q^{13} +(0.666437 + 0.0461211i) q^{14} -0.700054 q^{15} +(3.84820 + 1.09150i) q^{16} +(3.62268 + 1.96881i) q^{17} +(0.245064 - 3.54110i) q^{18} -4.24061i q^{19} +(-1.98093 - 0.275503i) q^{20} +0.330684i q^{21} +(-0.367691 + 5.31304i) q^{22} +3.04244i q^{23} +(-0.407504 + 1.93766i) q^{24} +1.00000 q^{25} +(2.94124 + 0.203550i) q^{26} +3.85724 q^{27} +(-0.130139 + 0.935732i) q^{28} +8.44930 q^{29} +(0.0683518 - 0.987663i) q^{30} -1.89633i q^{31} +(-1.91567 + 5.32261i) q^{32} -2.63631 q^{33} +(-3.13138 + 4.91878i) q^{34} -0.472369i q^{35} +(4.97199 + 0.691491i) q^{36} +4.90602 q^{37} +(5.98282 + 0.414044i) q^{38} +1.45943i q^{39} +(0.582104 - 2.76788i) q^{40} +10.3105i q^{41} +(-0.466542 - 0.0322873i) q^{42} -8.18245i q^{43} +(-7.45994 - 1.03751i) q^{44} -2.50992 q^{45} +(-4.29240 - 0.297058i) q^{46} -5.56596 q^{47} +(-2.69394 - 0.764112i) q^{48} +6.77687 q^{49} +(-0.0976378 + 1.41084i) q^{50} +(-2.53607 - 1.37827i) q^{51} +(-0.574353 + 4.12975i) q^{52} +6.11891i q^{53} +(-0.376613 + 5.44195i) q^{54} +3.76587 q^{55} +(-1.30746 - 0.274968i) q^{56} +2.96866i q^{57} +(-0.824972 + 11.9206i) q^{58} -5.25557i q^{59} +(1.38676 + 0.192867i) q^{60} +4.08954 q^{61} +(2.67542 + 0.185154i) q^{62} +1.18561i q^{63} +(-7.32231 - 3.22239i) q^{64} -2.08475i q^{65} +(0.257404 - 3.71941i) q^{66} +14.0350i q^{67} +(-6.63387 - 4.89814i) q^{68} -2.12987i q^{69} +(0.666437 + 0.0461211i) q^{70} -14.4641i q^{71} +(-1.46104 + 6.94717i) q^{72} +11.7807i q^{73} +(-0.479013 + 6.92160i) q^{74} -0.700054 q^{75} +(-1.16830 + 8.40037i) q^{76} -1.77888i q^{77} +(-2.05903 - 0.142496i) q^{78} -14.2573i q^{79} +(3.84820 + 1.09150i) q^{80} +4.82950 q^{81} +(-14.5464 - 1.00669i) q^{82} +1.62221i q^{83} +(0.0911042 - 0.655063i) q^{84} +(3.62268 + 1.96881i) q^{85} +(11.5441 + 0.798916i) q^{86} -5.91497 q^{87} +(2.19213 - 10.4235i) q^{88} +4.13274 q^{89} +(0.245064 - 3.54110i) q^{90} -0.984770 q^{91} +(0.838201 - 6.02688i) q^{92} +1.32754i q^{93} +(0.543449 - 7.85268i) q^{94} -4.24061i q^{95} +(1.34107 - 3.72612i) q^{96} -1.51194i q^{97} +(-0.661679 + 9.56107i) q^{98} -9.45205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{3} + 2 q^{4} + 36 q^{5} + 36 q^{9} - 8 q^{11} - 2 q^{12} + 2 q^{14} - 4 q^{15} + 6 q^{16} - 10 q^{18} + 2 q^{20} + 26 q^{24} + 36 q^{25} + 6 q^{26} - 16 q^{27} + 14 q^{28} - 10 q^{32} - 8 q^{33}+ \cdots - 40 q^{99}+O(q^{100}) \) 36 * q - 4 * q^3 + 2 * q^4 + 36 * q^5 + 36 * q^9 - 8 * q^11 - 2 * q^12 + 2 * q^14 - 4 * q^15 + 6 * q^16 - 10 * q^18 + 2 * q^20 + 26 * q^24 + 36 * q^25 + 6 * q^26 - 16 * q^27 + 14 * q^28 - 10 * q^32 - 8 * q^33 - 24 * q^34 + 8 * q^36 - 20 * q^38 - 2 * q^42 + 6 * q^44 + 36 * q^45 + 24 * q^46 + 20 * q^47 - 4 * q^48 - 36 * q^49 + 6 * q^52 - 56 * q^54 - 8 * q^55 + 20 * q^56 - 18 * q^58 - 2 * q^60 - 24 * q^62 + 14 * q^64 - 16 * q^66 - 40 * q^68 + 2 * q^70 - 54 * q^72 + 6 * q^74 - 4 * q^75 + 2 * q^76 - 14 * q^78 + 6 * q^80 + 44 * q^81 + 22 * q^82 - 68 * q^84 - 36 * q^86 + 24 * q^87 - 58 * q^88 - 10 * q^90 - 56 * q^91 - 12 * q^92 + 14 * q^94 - 24 * q^96 + 10 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more