LMFDB - Embedded newform 1740.2.bc.c.853.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1740,2,Mod(853,1740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1740.853"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1740, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1740.bc (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [30] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$13.8939699517$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			853.5
Character	$\chi$	$=$	1740.853
Dual form			1740.2.bc.c.1177.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{3} +(-1.37520 - 1.76319i) q^{5} +(0.501610 - 0.501610i) q^{7} -1.00000 q^{9} +(2.02083 + 2.02083i) q^{11} +(-4.80618 + 4.80618i) q^{13} +(1.76319 - 1.37520i) q^{15} +3.48181 q^{17} +(1.94489 - 1.94489i) q^{19} +(0.501610 + 0.501610i) q^{21} +(-1.96769 - 1.96769i) q^{23} +(-1.21766 + 4.84947i) q^{25} -1.00000i q^{27} +(-1.42694 - 5.19267i) q^{29} +(-3.14819 - 3.14819i) q^{31} +(-2.02083 + 2.02083i) q^{33} +(-1.57424 - 0.194618i) q^{35} -1.37567i q^{37} +(-4.80618 - 4.80618i) q^{39} +(-6.67274 + 6.67274i) q^{41} +6.60459i q^{43} +(1.37520 + 1.76319i) q^{45} +12.7543i q^{47} +6.49678i q^{49} +3.48181i q^{51} +(8.12769 + 8.12769i) q^{53} +(0.784058 - 6.34215i) q^{55} +(1.94489 + 1.94489i) q^{57} +6.18048i q^{59} +(1.97484 + 1.97484i) q^{61} +(-0.501610 + 0.501610i) q^{63} +(15.0837 + 1.86474i) q^{65} +(-7.83460 - 7.83460i) q^{67} +(1.96769 - 1.96769i) q^{69} -1.63417i q^{71} -11.5370 q^{73} +(-4.84947 - 1.21766i) q^{75} +2.02734 q^{77} +(-8.73698 + 8.73698i) q^{79} +1.00000 q^{81} +(8.37675 + 8.37675i) q^{83} +(-4.78818 - 6.13908i) q^{85} +(5.19267 - 1.42694i) q^{87} +(1.03678 - 1.03678i) q^{89} +4.82166i q^{91} +(3.14819 - 3.14819i) q^{93} +(-6.10382 - 0.754594i) q^{95} +15.3954i q^{97} +(-2.02083 - 2.02083i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 30 q^{9} + 4 q^{11} - 6 q^{13} - 6 q^{15} + 8 q^{19} - 6 q^{25} + 4 q^{29} - 4 q^{33} - 16 q^{35} - 6 q^{39} - 10 q^{41} - 6 q^{53} + 4 q^{55} + 8 q^{57} + 30 q^{61} - 2 q^{65} + 4 q^{67} + 12 q^{73}+ \cdots - 4 q^{99}+O(q^{100}) $ 30 * q - 30 * q^9 + 4 * q^11 - 6 * q^13 - 6 * q^15 + 8 * q^19 - 6 * q^25 + 4 * q^29 - 4 * q^33 - 16 * q^35 - 6 * q^39 - 10 * q^41 - 6 * q^53 + 4 * q^55 + 8 * q^57 + 30 * q^61 - 2 * q^65 + 4 * q^67 + 12 * q^73 + 8 * q^75 - 4 * q^77 - 4 * q^79 + 30 * q^81 - 28 * q^83 + 20 * q^85 + 10 * q^87 + 10 * q^89 + 20 * q^95 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1740\mathbb{Z}\right)^\times$.

$n$	$581$	$697$	$871$	$901$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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			0
$2$		0			0
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$		0			0
$5$	−1.37520	−	1.76319i	−0.615008	−	0.788521i
$5$	−1.37520	−	1.76319i	−0.615008	−	0.788521i
$6$		0			0
$7$	0.501610	−	0.501610i	0.189591	−	0.189591i	−0.605928	−	0.795519i	$-0.707198\pi$
$7$	0.501610	−	0.501610i	0.189591	−	0.189591i	0.795519	+	0.605928i	$0.207198\pi$
$8$		0			0
$9$	−1.00000			−0.333333
$10$		0			0
$11$	2.02083	+	2.02083i	0.609304	+	0.609304i	0.942764	−	0.333460i	$-0.108216\pi$
$11$	2.02083	+	2.02083i	0.609304	+	0.609304i	−0.333460	+	0.942764i	$0.608216\pi$
$12$		0			0
$13$	−4.80618	+	4.80618i	−1.33300	+	1.33300i	−0.430318	+	0.902677i	$0.641599\pi$
$13$	−4.80618	+	4.80618i	−1.33300	+	1.33300i	−0.902677	+	0.430318i	$0.858401\pi$
$14$		0			0
$15$	1.76319	−	1.37520i	0.455253	−	0.355075i
$16$		0			0
$17$	3.48181			0.844463			0.422231	−	0.906488i	$-0.361247\pi$
$17$	3.48181			0.844463			0.422231	+	0.906488i	$0.361247\pi$
$18$		0			0
$19$	1.94489	−	1.94489i	0.446189	−	0.446189i	−0.447897	−	0.894085i	$-0.647827\pi$
$19$	1.94489	−	1.94489i	0.446189	−	0.446189i	0.894085	+	0.447897i	$0.147827\pi$
$20$		0			0
$21$	0.501610	+	0.501610i	0.109460	+	0.109460i
$22$		0			0
$23$	−1.96769	−	1.96769i	−0.410291	−	0.410291i	0.471549	−	0.881840i	$-0.343695\pi$
$23$	−1.96769	−	1.96769i	−0.410291	−	0.410291i	−0.881840	+	0.471549i	$0.843695\pi$
$24$		0			0
$25$	−1.21766	+	4.84947i	−0.243531	+	0.969893i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−1.42694	−	5.19267i	−0.264976	−	0.964255i
$29$	−1.42694	−	5.19267i	−0.264976	−	0.964255i
$30$		0			0
$31$	−3.14819	−	3.14819i	−0.565432	−	0.565432i	0.365413	−	0.930845i	$-0.380928\pi$
$31$	−3.14819	−	3.14819i	−0.565432	−	0.565432i	−0.930845	+	0.365413i	$0.880928\pi$
$32$		0			0
$33$	−2.02083	+	2.02083i	−0.351782	+	0.351782i
$34$		0			0
$35$	−1.57424	−	0.194618i	−0.266096	−	0.0328965i
$36$		0			0
$37$		−	1.37567i		−	0.226159i	−0.993586	−	0.113080i	$-0.963928\pi$
$37$		−	1.37567i		−	0.226159i	0.993586	−	0.113080i	$-0.0360715\pi$
$38$		0			0
$39$	−4.80618	−	4.80618i	−0.769605	−	0.769605i
$40$		0			0
$41$	−6.67274	+	6.67274i	−1.04211	+	1.04211i	−0.0430338	+	0.999074i	$0.513702\pi$
$41$	−6.67274	+	6.67274i	−1.04211	+	1.04211i	−0.999074	+	0.0430338i	$0.986298\pi$
$42$		0			0
$43$			6.60459i			1.00719i	0.863940	+	0.503595i	$0.167990\pi$
$43$			6.60459i			1.00719i	−0.863940	+	0.503595i	$0.832010\pi$
$44$		0			0
$45$	1.37520	+	1.76319i	0.205003	+	0.262840i
$46$		0			0
$47$			12.7543i			1.86040i	0.367047	+	0.930202i	$0.380369\pi$
$47$			12.7543i			1.86040i	−0.367047	+	0.930202i	$0.619631\pi$
$48$		0			0
$49$			6.49678i			0.928111i
$50$		0			0
$51$			3.48181i			0.487551i
$52$		0			0
$53$	8.12769	+	8.12769i	1.11642	+	1.11642i	0.992262	+	0.124162i	$0.0396242\pi$
$53$	8.12769	+	8.12769i	1.11642	+	1.11642i	0.124162	+	0.992262i	$0.460376\pi$
$54$		0			0
$55$	0.784058	−	6.34215i	0.105722	−	0.855176i
$56$		0			0
$57$	1.94489	+	1.94489i	0.257607	+	0.257607i
$58$		0			0
$59$			6.18048i			0.804629i	0.915501	+	0.402315i	$0.131794\pi$
$59$			6.18048i			0.804629i	−0.915501	+	0.402315i	$0.868206\pi$
$60$		0			0
$61$	1.97484	+	1.97484i	0.252853	+	0.252853i	0.822139	−	0.569286i	$-0.192780\pi$
$61$	1.97484	+	1.97484i	0.252853	+	0.252853i	−0.569286	+	0.822139i	$0.692780\pi$
$62$		0			0
$63$	−0.501610	+	0.501610i	−0.0631969	+	0.0631969i
$64$		0			0
$65$	15.0837	+	1.86474i	1.87090	+	0.231293i
$66$		0			0
$67$	−7.83460	−	7.83460i	−0.957149	−	0.957149i	0.0419697	−	0.999119i	$-0.486637\pi$
$67$	−7.83460	−	7.83460i	−0.957149	−	0.957149i	−0.999119	+	0.0419697i	$0.986637\pi$
$68$		0			0
$69$	1.96769	−	1.96769i	0.236882	−	0.236882i
$70$		0			0
$71$		−	1.63417i		−	0.193940i	−0.995287	−	0.0969702i	$-0.969085\pi$
$71$		−	1.63417i		−	0.193940i	0.995287	−	0.0969702i	$-0.0309152\pi$
$72$		0			0
$73$	−11.5370			−1.35031			−0.675153	−	0.737678i	$-0.735922\pi$
$73$	−11.5370			−1.35031			−0.675153	+	0.737678i	$0.735922\pi$
$74$		0			0
$75$	−4.84947	−	1.21766i	−0.559968	−	0.140603i
$76$		0			0
$77$	2.02734			0.231037
$78$		0			0
$79$	−8.73698	+	8.73698i	−0.982987	+	0.982987i	−0.999858	−	0.0168711i	$-0.994630\pi$
$79$	−8.73698	+	8.73698i	−0.982987	+	0.982987i	0.0168711	+	0.999858i	$0.494630\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	8.37675	+	8.37675i	0.919467	+	0.919467i	0.996991	−	0.0775233i	$-0.0247012\pi$
$83$	8.37675	+	8.37675i	0.919467	+	0.919467i	−0.0775233	+	0.996991i	$0.524701\pi$
$84$		0			0
$85$	−4.78818	−	6.13908i	−0.519351	−	0.665877i
$86$		0			0
$87$	5.19267	−	1.42694i	0.556713	−	0.152984i
$88$		0			0
$89$	1.03678	−	1.03678i	0.109898	−	0.109898i	−0.650020	−	0.759918i	$-0.725239\pi$
$89$	1.03678	−	1.03678i	0.109898	−	0.109898i	0.759918	+	0.650020i	$0.225239\pi$
$90$		0			0
$91$			4.82166i			0.505447i
$92$		0			0
$93$	3.14819	−	3.14819i	0.326452	−	0.326452i
$94$		0			0
$95$	−6.10382	−	0.754594i	−0.626238	−	0.0774197i
$96$		0			0
$97$			15.3954i			1.56317i	0.623798	+	0.781585i	$0.285589\pi$
$97$			15.3954i			1.56317i	−0.623798	+	0.781585i	$0.714411\pi$
$98$		0			0
$99$	−2.02083	−	2.02083i	−0.203101	−	0.203101i
$100$		0			0
$101$	4.50842	+	4.50842i	0.448604	+	0.448604i	0.894890	−	0.446286i	$-0.147254\pi$
$101$	4.50842	+	4.50842i	0.448604	+	0.448604i	−0.446286	+	0.894890i	$0.647254\pi$
$102$		0			0
$103$	−3.70204	−	3.70204i	−0.364772	−	0.364772i	0.500794	−	0.865566i	$-0.333041\pi$
$103$	−3.70204	−	3.70204i	−0.364772	−	0.364772i	−0.865566	+	0.500794i	$0.833041\pi$
$104$		0			0
$105$	0.194618	−	1.57424i	0.0189928	−	0.153631i
$106$		0			0
$107$	−11.4552	+	11.4552i	−1.10741	+	1.10741i	−0.113923	+	0.993490i	$0.536342\pi$
$107$	−11.4552	+	11.4552i	−1.10741	+	1.10741i	−0.993490	+	0.113923i	$0.963658\pi$
$108$		0			0
$109$	2.60487			0.249501			0.124751	−	0.992188i	$-0.460187\pi$
$109$	2.60487			0.249501			0.124751	+	0.992188i	$0.460187\pi$
$110$		0			0
$111$	1.37567			0.130573
$112$		0			0
$113$	1.95279			0.183703			0.0918515	−	0.995773i	$-0.470722\pi$
$113$	1.95279			0.183703			0.0918515	+	0.995773i	$0.470722\pi$
$114$		0			0
$115$	−0.763439	+	6.17536i	−0.0711910	+	0.575856i
$116$		0			0
$117$	4.80618	−	4.80618i	0.444332	−	0.444332i
$118$		0			0
$119$	1.74651	−	1.74651i	0.160102	−	0.160102i
$120$		0			0
$121$		−	2.83247i		−	0.257498i
$122$		0			0
$123$	−6.67274	−	6.67274i	−0.601661	−	0.601661i
$124$		0			0
$125$	10.2250	−	4.52203i	0.914555	−	0.404462i
$126$		0			0
$127$	−16.0596			−1.42506			−0.712531	−	0.701641i	$-0.752451\pi$
$127$	−16.0596			−1.42506			−0.712531	+	0.701641i	$0.752451\pi$
$128$		0			0
$129$	−6.60459			−0.581501
$130$		0			0
$131$	2.64207	−	2.64207i	0.230839	−	0.230839i	−0.582204	−	0.813043i	$-0.697809\pi$
$131$	2.64207	−	2.64207i	0.230839	−	0.230839i	0.813043	+	0.582204i	$0.197809\pi$
$132$		0			0
$133$		−	1.95115i		−	0.169186i
$134$		0			0
$135$	−1.76319	+	1.37520i	−0.151751	+	0.118358i
$136$		0			0
$137$	−9.24939			−0.790229			−0.395114	−	0.918632i	$-0.629295\pi$
$137$	−9.24939			−0.790229			−0.395114	+	0.918632i	$0.629295\pi$
$138$		0			0
$139$		−	6.62442i		−	0.561876i	−0.959726	−	0.280938i	$-0.909354\pi$
$139$		−	6.62442i		−	0.561876i	0.959726	−	0.280938i	$-0.0906456\pi$
$140$		0			0
$141$	−12.7543			−1.07411
$142$		0			0
$143$	−19.4250			−1.62440
$144$		0			0
$145$	−7.19333	+	9.65692i	−0.597373	+	0.801963i
$146$		0			0
$147$	−6.49678			−0.535845
$148$		0			0
$149$	−4.71805			−0.386517			−0.193259	−	0.981148i	$-0.561906\pi$
$149$	−4.71805			−0.386517			−0.193259	+	0.981148i	$0.561906\pi$
$150$		0			0
$151$			3.99628i			0.325213i	0.986691	+	0.162606i	$0.0519901\pi$
$151$			3.99628i			0.325213i	−0.986691	+	0.162606i	$0.948010\pi$
$152$		0			0
$153$	−3.48181			−0.281488
$154$		0			0
$155$	−1.22146	+	9.88024i	−0.0981101	+	0.793600i
$156$		0			0
$157$		−	23.2502i		−	1.85557i	−0.373115	−	0.927785i	$-0.621710\pi$
$157$		−	23.2502i		−	1.85557i	0.373115	−	0.927785i	$-0.378290\pi$
$158$		0			0
$159$	−8.12769	+	8.12769i	−0.644568	+	0.644568i
$160$		0			0
$161$	−1.97402			−0.155575
$162$		0			0
$163$	4.95520			0.388121			0.194061	−	0.980990i	$-0.437834\pi$
$163$	4.95520			0.388121			0.194061	+	0.980990i	$0.437834\pi$
$164$		0			0
$165$	6.34215	+	0.784058i	0.493736	+	0.0610389i
$166$		0			0
$167$	17.0407	+	17.0407i	1.31865	+	1.31865i	0.914845	+	0.403804i	$0.132312\pi$
$167$	17.0407	+	17.0407i	1.31865	+	1.31865i	0.403804	+	0.914845i	$0.367688\pi$
$168$		0			0
$169$		−	33.1988i		−	2.55375i
$170$		0			0
$171$	−1.94489	+	1.94489i	−0.148730	+	0.148730i
$172$		0			0
$173$	17.2301	−	17.2301i	1.30998	−	1.30998i	0.388548	−	0.921428i	$-0.372977\pi$
$173$	17.2301	−	17.2301i	1.30998	−	1.30998i	0.921428	−	0.388548i	$-0.127023\pi$
$174$		0			0
$175$	1.82175	+	3.04333i	0.137711	+	0.230054i
$176$		0			0
$177$	−6.18048			−0.464553
$178$		0			0
$179$	4.22671			0.315919			0.157959	−	0.987446i	$-0.449508\pi$
$179$	4.22671			0.315919			0.157959	+	0.987446i	$0.449508\pi$
$180$		0			0
$181$	−0.375464			−0.0279080			−0.0139540	−	0.999903i	$-0.504442\pi$
$181$	−0.375464			−0.0279080			−0.0139540	+	0.999903i	$0.504442\pi$
$182$		0			0
$183$	−1.97484	+	1.97484i	−0.145985	+	0.145985i
$184$		0			0
$185$	−2.42557	+	1.89182i	−0.178331	+	0.139090i
$186$		0			0
$187$	7.03615	+	7.03615i	0.514534	+	0.514534i
$188$		0			0
$189$	−0.501610	−	0.501610i	−0.0364867	−	0.0364867i
$190$		0			0
$191$	−18.1023	−	18.1023i	−1.30983	−	1.30983i	−0.921532	−	0.388301i	$-0.873062\pi$
$191$	−18.1023	−	18.1023i	−1.30983	−	1.30983i	−0.388301	−	0.921532i	$-0.626938\pi$
$192$		0			0
$193$			13.9942i			1.00733i	0.863900	+	0.503663i	$0.168015\pi$
$193$			13.9942i			1.00733i	−0.863900	+	0.503663i	$0.831985\pi$
$194$		0			0
$195$	−1.86474	+	15.0837i	−0.133537	+	1.08016i
$196$		0			0
$197$	15.1397	−	15.1397i	1.07866	−	1.07866i	0.0820262	−	0.996630i	$-0.473861\pi$
$197$	15.1397	−	15.1397i	1.07866	−	1.07866i	0.996630	−	0.0820262i	$-0.0261391\pi$
$198$		0			0
$199$			1.61172i			0.114252i	0.998367	+	0.0571258i	$0.0181936\pi$
$199$			1.61172i			0.114252i	−0.998367	+	0.0571258i	$0.981806\pi$
$200$		0			0
$201$	7.83460	−	7.83460i	0.552610	−	0.552610i
$202$		0			0
$203$	−3.32046	−	1.88893i	−0.233051	−	0.132577i
$204$		0			0
$205$	20.9416	+	2.58894i	1.46263	+	0.180820i
$206$		0			0
$207$	1.96769	+	1.96769i	0.136764	+	0.136764i
$208$		0			0
$209$	7.86060			0.543729
$210$		0			0
$211$	13.1359	−	13.1359i	0.904309	−	0.904309i	−0.0914961	−	0.995805i	$-0.529165\pi$
$211$	13.1359	−	13.1359i	0.904309	−	0.904309i	0.995805	+	0.0914961i	$0.0291649\pi$
$212$		0			0
$213$	1.63417			0.111972
$214$		0			0
$215$	11.6451	−	9.08262i	0.794190	−	0.619429i
$216$		0			0
$217$	−3.15833			−0.214401
$218$		0			0
$219$		−	11.5370i		−	0.779600i
$220$		0			0
$221$	−16.7342	+	16.7342i	−1.12566	+	1.12566i
$222$		0			0
$223$	12.9508	+	12.9508i	0.867251	+	0.867251i	0.992167	−	0.124916i	$-0.0398662\pi$
$223$	12.9508	+	12.9508i	0.867251	+	0.867251i	−0.124916	+	0.992167i	$0.539866\pi$
$224$		0			0
$225$	1.21766	−	4.84947i	0.0811770	−	0.323298i
$226$		0			0
$227$	−6.68951	+	6.68951i	−0.443998	+	0.443998i	−0.893353	−	0.449355i	$-0.851654\pi$
$227$	−6.68951	+	6.68951i	−0.443998	+	0.443998i	0.449355	+	0.893353i	$0.351654\pi$
$228$		0			0
$229$	−6.44176	−	6.44176i	−0.425684	−	0.425684i	0.461471	−	0.887155i	$-0.347322\pi$
$229$	−6.44176	−	6.44176i	−0.425684	−	0.425684i	−0.887155	+	0.461471i	$0.847322\pi$
$230$		0			0
$231$			2.02734i			0.133389i
$232$		0			0
$233$	11.5455	+	11.5455i	0.756369	+	0.756369i	0.975660	−	0.219290i	$-0.0703742\pi$
$233$	11.5455	+	11.5455i	0.756369	+	0.756369i	−0.219290	+	0.975660i	$0.570374\pi$
$234$		0			0
$235$	22.4882	−	17.5397i	1.46697	−	1.14416i
$236$		0			0
$237$	−8.73698	−	8.73698i	−0.567528	−	0.567528i
$238$		0			0
$239$		−	13.9588i		−	0.902920i	−0.892291	−	0.451460i	$-0.850903\pi$
$239$		−	13.9588i		−	0.902920i	0.892291	−	0.451460i	$-0.149097\pi$
$240$		0			0
$241$		−	7.52970i		−	0.485030i	−0.970148	−	0.242515i	$-0.922028\pi$
$241$		−	7.52970i		−	0.485030i	0.970148	−	0.242515i	$-0.0779724\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$		0			0
$245$	11.4550	−	8.93436i	0.731835	−	0.570795i
$246$		0			0
$247$			18.6950i			1.18953i
$248$		0			0
$249$	−8.37675	+	8.37675i	−0.530855	+	0.530855i
$250$		0			0
$251$	6.20891	+	6.20891i	0.391903	+	0.391903i	0.875365	−	0.483462i	$-0.160621\pi$
$251$	6.20891	+	6.20891i	0.391903	+	0.391903i	−0.483462	+	0.875365i	$0.660621\pi$
$252$		0			0
$253$		−	7.95273i		−	0.499984i
$254$		0			0
$255$	6.13908	−	4.78818i	0.384444	−	0.299847i
$256$		0			0
$257$	−10.2480	+	10.2480i	−0.639254	+	0.639254i	−0.950371	−	0.311118i	$-0.899297\pi$
$257$	−10.2480	+	10.2480i	−0.639254	+	0.639254i	0.311118	+	0.950371i	$0.399297\pi$
$258$		0			0
$259$	−0.690051	−	0.690051i	−0.0428777	−	0.0428777i
$260$		0			0
$261$	1.42694	+	5.19267i	0.0883253	+	0.321418i
$262$		0			0
$263$		−	9.97094i		−	0.614835i	−0.951575	−	0.307417i	$-0.900535\pi$
$263$		−	9.97094i		−	0.614835i	0.951575	−	0.307417i	$-0.0994647\pi$
$264$		0			0
$265$	3.15344	−	25.5078i	0.193715	−	1.56693i
$266$		0			0
$267$	1.03678	+	1.03678i	0.0634496	+	0.0634496i
$268$		0			0
$269$	9.63229	+	9.63229i	0.587291	+	0.587291i	0.936897	−	0.349606i	$-0.113684\pi$
$269$	9.63229	+	9.63229i	0.587291	+	0.587291i	−0.349606	+	0.936897i	$0.613684\pi$
$270$		0			0
$271$	−15.5653	+	15.5653i	−0.945525	+	0.945525i	−0.998591	−	0.0530663i	$-0.983101\pi$
$271$	−15.5653	+	15.5653i	−0.945525	+	0.945525i	0.0530663	+	0.998591i	$0.483101\pi$
$272$		0			0
$273$	−4.82166			−0.291820
$274$		0			0
$275$	−12.2606	+	7.33928i	−0.739344	+	0.442575i
$276$		0			0
$277$	−16.7440	+	16.7440i	−1.00605	+	1.00605i	−0.00606968	+	0.999982i	$0.501932\pi$
$277$	−16.7440	+	16.7440i	−1.00605	+	1.00605i	−0.999982	+	0.00606968i	$0.998068\pi$
$278$		0			0
$279$	3.14819	+	3.14819i	0.188477	+	0.188477i
$280$		0			0
$281$	24.0520			1.43482			0.717411	−	0.696650i	$-0.245327\pi$
$281$	24.0520			1.43482			0.717411	+	0.696650i	$0.245327\pi$
$282$		0			0
$283$	−9.33420	+	9.33420i	−0.554860	+	0.554860i	−0.927840	−	0.372979i	$-0.878336\pi$
$283$	−9.33420	+	9.33420i	−0.554860	+	0.554860i	0.372979	+	0.927840i	$0.378336\pi$
$284$		0			0
$285$	0.754594	−	6.10382i	0.0446983	−	0.361559i
$286$		0			0
$287$			6.69423i			0.395148i
$288$		0			0
$289$	−4.87701			−0.286883
$290$		0			0
$291$	−15.3954			−0.902497
$292$		0			0
$293$		−	3.20784i		−	0.187404i	−0.995600	−	0.0937020i	$-0.970130\pi$
$293$		−	3.20784i		−	0.187404i	0.995600	−	0.0937020i	$-0.0298701\pi$
$294$		0			0
$295$	10.8973	−	8.49938i	0.634467	−	0.494853i
$296$		0			0
$297$	2.02083	−	2.02083i	0.117261	−	0.117261i
$298$		0			0
$299$	18.9141			1.09383
$300$		0			0
$301$	3.31292	+	3.31292i	0.190954	+	0.190954i
$302$		0			0
$303$	−4.50842	+	4.50842i	−0.259002	+	0.259002i
$304$		0			0
$305$	0.766216	−	6.19782i	0.0438734	−	0.354886i
$306$		0			0
$307$	20.3426			1.16102			0.580508	−	0.814254i	$-0.302854\pi$
$307$	20.3426			1.16102			0.580508	+	0.814254i	$0.302854\pi$
$308$		0			0
$309$	3.70204	−	3.70204i	0.210601	−	0.210601i
$310$		0			0
$311$	−15.1136	−	15.1136i	−0.857013	−	0.857013i	0.133972	−	0.990985i	$-0.457227\pi$
$311$	−15.1136	−	15.1136i	−0.857013	−	0.857013i	−0.990985	+	0.133972i	$0.957227\pi$
$312$		0			0
$313$	12.6402	+	12.6402i	0.714465	+	0.714465i	0.967466	−	0.253001i	$-0.0814177\pi$
$313$	12.6402	+	12.6402i	0.714465	+	0.714465i	−0.253001	+	0.967466i	$0.581418\pi$
$314$		0			0
$315$	1.57424	+	0.194618i	0.0886987	+	0.0109655i
$316$		0			0
$317$			12.2398i			0.687458i	0.939069	+	0.343729i	$0.111690\pi$
$317$			12.2398i			0.687458i	−0.939069	+	0.343729i	$0.888310\pi$
$318$		0			0
$319$	7.60991	−	13.3771i	0.426073	−	0.748975i
$320$		0			0
$321$	−11.4552	−	11.4552i	−0.639365	−	0.639365i
$322$		0			0
$323$	6.77174	−	6.77174i	0.376790	−	0.376790i
$324$		0			0
$325$	−17.4551	−	29.1597i	−0.968237	−	1.61749i
$326$		0			0
$327$			2.60487i			0.144050i
$328$		0			0
$329$	6.39768	+	6.39768i	0.352715	+	0.352715i
$330$		0			0
$331$	−7.42276	+	7.42276i	−0.407992	+	0.407992i	−0.881038	−	0.473046i	$-0.843154\pi$
$331$	−7.42276	+	7.42276i	−0.407992	+	0.407992i	0.473046	+	0.881038i	$0.343154\pi$
$332$		0			0
$333$			1.37567i			0.0753864i
$334$		0			0
$335$	−3.03973	+	24.5880i	−0.166078	+	1.34339i
$336$		0			0
$337$		−	16.8587i		−	0.918351i	−0.888346	−	0.459176i	$-0.848145\pi$
$337$		−	16.8587i		−	0.918351i	0.888346	−	0.459176i	$-0.151855\pi$
$338$		0			0
$339$			1.95279i			0.106061i
$340$		0			0
$341$		−	12.7239i		−	0.689040i
$342$		0			0
$343$	6.77011	+	6.77011i	0.365552	+	0.365552i
$344$		0			0
$345$	−6.17536	−	0.763439i	−0.332470	−	0.0411022i
$346$		0			0
$347$	7.93765	+	7.93765i	0.426115	+	0.426115i	0.887303	−	0.461187i	$-0.152576\pi$
$347$	7.93765	+	7.93765i	0.426115	+	0.426115i	−0.461187	+	0.887303i	$0.652576\pi$
$348$		0			0
$349$		−	33.7672i		−	1.80752i	−0.428041	−	0.903759i	$-0.640796\pi$
$349$		−	33.7672i		−	1.80752i	0.428041	−	0.903759i	$-0.359204\pi$
$350$		0			0
$351$	4.80618	+	4.80618i	0.256535	+	0.256535i
$352$		0			0
$353$	6.26823	−	6.26823i	0.333624	−	0.333624i	−0.520337	−	0.853961i	$-0.674194\pi$
$353$	6.26823	−	6.26823i	0.333624	−	0.333624i	0.853961	+	0.520337i	$0.174194\pi$
$354$		0			0
$355$	−2.88135	+	2.24731i	−0.152926	+	0.119275i
$356$		0			0
$357$	1.74651	+	1.74651i	0.0924351	+	0.0924351i
$358$		0			0
$359$	8.79222	−	8.79222i	0.464036	−	0.464036i	−0.435940	−	0.899976i	$-0.643584\pi$
$359$	8.79222	−	8.79222i	0.464036	−	0.464036i	0.899976	+	0.435940i	$0.143584\pi$
$360$		0			0
$361$			11.4348i			0.601832i
$362$		0			0
$363$	2.83247			0.148666
$364$		0			0
$365$	15.8657	+	20.3419i	0.830449	+	1.06474i
$366$		0			0
$367$	−0.0871643			−0.00454994			−0.00227497	−	0.999997i	$-0.500724\pi$
$367$	−0.0871643			−0.00454994			−0.00227497	+	0.999997i	$0.500724\pi$
$368$		0			0
$369$	6.67274	−	6.67274i	0.347369	−	0.347369i
$370$		0			0
$371$	8.15386			0.423327
$372$		0			0
$373$	−13.3123	−	13.3123i	−0.689284	−	0.689284i	0.272790	−	0.962074i	$-0.412054\pi$
$373$	−13.3123	−	13.3123i	−0.689284	−	0.689284i	−0.962074	+	0.272790i	$0.912054\pi$
$374$		0			0
$375$	4.52203	+	10.2250i	0.233516	+	0.528018i
$376$		0			0
$377$	31.8151	+	18.0988i	1.63856	+	0.932136i
$378$		0			0
$379$	−6.06804	+	6.06804i	−0.311694	+	0.311694i	−0.845566	−	0.533871i	$-0.820737\pi$
$379$	−6.06804	+	6.06804i	−0.311694	+	0.311694i	0.533871	+	0.845566i	$0.320737\pi$
$380$		0			0
$381$		−	16.0596i		−	0.822760i
$382$		0			0
$383$	10.3792	−	10.3792i	0.530354	−	0.530354i	−0.390324	−	0.920678i	$-0.627637\pi$
$383$	10.3792	−	10.3792i	0.530354	−	0.530354i	0.920678	+	0.390324i	$0.127637\pi$
$384$		0			0
$385$	−2.78799	−	3.57458i	−0.142089	−	0.182177i
$386$		0			0
$387$		−	6.60459i		−	0.335730i
$388$		0			0
$389$	−3.47374	−	3.47374i	−0.176126	−	0.176126i	0.613539	−	0.789664i	$-0.289745\pi$
$389$	−3.47374	−	3.47374i	−0.176126	−	0.176126i	−0.789664	+	0.613539i	$0.789745\pi$
$390$		0			0
$391$	−6.85111	−	6.85111i	−0.346476	−	0.346476i
$392$		0			0
$393$	2.64207	+	2.64207i	0.133275	+	0.133275i
$394$		0			0
$395$	27.4200	+	3.38984i	1.37965	+	0.170561i
$396$		0			0
$397$	−20.7555	+	20.7555i	−1.04169	+	1.04169i	−0.0425988	+	0.999092i	$0.513564\pi$
$397$	−20.7555	+	20.7555i	−1.04169	+	1.04169i	−0.999092	+	0.0425988i	$0.986436\pi$
$398$		0			0
$399$	1.95115			0.0976798
$400$		0			0
$401$	9.97648			0.498202			0.249101	−	0.968478i	$-0.419865\pi$
$401$	9.97648			0.498202			0.249101	+	0.968478i	$0.419865\pi$
$402$		0			0
$403$	30.2616			1.50744
$404$		0			0
$405$	−1.37520	−	1.76319i	−0.0683342	−	0.0876135i
$406$		0			0
$407$	2.78000	−	2.78000i	0.137800	−	0.137800i
$408$		0			0
$409$	21.9619	−	21.9619i	1.08595	−	1.08595i	0.0900067	−	0.995941i	$-0.471311\pi$
$409$	21.9619	−	21.9619i	1.08595	−	1.08595i	0.995941	−	0.0900067i	$-0.0286889\pi$
$410$		0			0
$411$		−	9.24939i		−	0.456239i
$412$		0			0
$413$	3.10019	+	3.10019i	0.152550	+	0.152550i
$414$		0			0
$415$	3.25008	−	26.2895i	0.159540	−	1.29050i
$416$		0			0
$417$	6.62442			0.324399
$418$		0			0
$419$	−3.40385			−0.166289			−0.0831444	−	0.996538i	$-0.526496\pi$
$419$	−3.40385			−0.166289			−0.0831444	+	0.996538i	$0.526496\pi$
$420$		0			0
$421$	3.95762	−	3.95762i	0.192883	−	0.192883i	−0.604058	−	0.796940i	$-0.706450\pi$
$421$	3.95762	−	3.95762i	0.192883	−	0.192883i	0.796940	+	0.604058i	$0.206450\pi$
$422$		0			0
$423$		−	12.7543i		−	0.620135i
$424$		0			0
$425$	−4.23964	+	16.8849i	−0.205653	+	0.819038i
$426$		0			0
$427$	1.98120			0.0958771
$428$		0			0
$429$		−	19.4250i		−	0.937847i
$430$		0			0
$431$	−36.1403			−1.74082			−0.870408	−	0.492330i	$-0.836145\pi$
$431$	−36.1403			−1.74082			−0.870408	+	0.492330i	$0.836145\pi$
$432$		0			0
$433$	32.8987			1.58101			0.790505	−	0.612456i	$-0.209818\pi$
$433$	32.8987			1.58101			0.790505	+	0.612456i	$0.209818\pi$
$434$		0			0
$435$	−9.65692	−	7.19333i	−0.463014	−	0.344894i
$436$		0			0
$437$	−7.65387			−0.366134
$438$		0			0
$439$	−37.2286			−1.77682			−0.888412	−	0.459047i	$-0.848191\pi$
$439$	−37.2286			−1.77682			−0.888412	+	0.459047i	$0.848191\pi$
$440$		0			0
$441$		−	6.49678i		−	0.309370i
$442$		0			0
$443$	−5.36973			−0.255123			−0.127562	−	0.991831i	$-0.540715\pi$
$443$	−5.36973			−0.255123			−0.127562	+	0.991831i	$0.540715\pi$
$444$		0			0
$445$	−3.25380	−	0.402256i	−0.154245	−	0.0190688i
$446$		0			0
$447$		−	4.71805i		−	0.223156i
$448$		0			0
$449$	2.19153	−	2.19153i	0.103425	−	0.103425i	−0.653501	−	0.756926i	$-0.726700\pi$
$449$	2.19153	−	2.19153i	0.103425	−	0.103425i	0.756926	+	0.653501i	$0.226700\pi$
$450$		0			0
$451$	−26.9690			−1.26992
$452$		0			0
$453$	−3.99628			−0.187762
$454$		0			0
$455$	8.50148	−	6.63074i	0.398556	−	0.310854i
$456$		0			0
$457$	−6.08404	−	6.08404i	−0.284599	−	0.284599i	0.550341	−	0.834940i	$-0.314498\pi$
$457$	−6.08404	−	6.08404i	−0.284599	−	0.284599i	−0.834940	+	0.550341i	$0.814498\pi$
$458$		0			0
$459$		−	3.48181i		−	0.162517i
$460$		0			0
$461$	5.42871	−	5.42871i	0.252840	−	0.252840i	−0.569294	−	0.822134i	$-0.692783\pi$
$461$	5.42871	−	5.42871i	0.252840	−	0.252840i	0.822134	+	0.569294i	$0.192783\pi$
$462$		0			0
$463$	7.05481	−	7.05481i	0.327865	−	0.327865i	−0.523909	−	0.851774i	$-0.675527\pi$
$463$	7.05481	−	7.05481i	0.327865	−	0.327865i	0.851774	+	0.523909i	$0.175527\pi$
$464$		0			0
$465$	−9.88024	−	1.22146i	−0.458185	−	0.0566439i
$466$		0			0
$467$	−15.6186			−0.722744			−0.361372	−	0.932422i	$-0.617691\pi$
$467$	−15.6186			−0.722744			−0.361372	+	0.932422i	$0.617691\pi$
$468$		0			0
$469$	−7.85983			−0.362933
$470$		0			0
$471$	23.2502			1.07131
$472$		0			0
$473$	−13.3468	+	13.3468i	−0.613685	+	0.613685i
$474$		0			0
$475$	7.06347	+	11.7999i	0.324094	+	0.541416i
$476$		0			0
$477$	−8.12769	−	8.12769i	−0.372141	−	0.372141i
$478$		0			0
$479$	3.01260	+	3.01260i	0.137649	+	0.137649i	0.772574	−	0.634925i	$-0.218969\pi$
$479$	3.01260	+	3.01260i	0.137649	+	0.137649i	−0.634925	+	0.772574i	$0.718969\pi$
$480$		0			0
$481$	6.61173	+	6.61173i	0.301469	+	0.301469i
$482$		0			0
$483$		−	1.97402i		−	0.0898211i
$484$		0			0
$485$	27.1451	−	21.1718i	1.23259	−	0.961362i
$486$		0			0
$487$	−29.3293	+	29.3293i	−1.32904	+	1.32904i	−0.422830	+	0.906209i	$0.638963\pi$
$487$	−29.3293	+	29.3293i	−1.32904	+	1.32904i	−0.906209	+	0.422830i	$0.861037\pi$
$488$		0			0
$489$			4.95520i			0.224082i
$490$		0			0
$491$	−24.7019	+	24.7019i	−1.11478	+	1.11478i	−0.122285	+	0.992495i	$0.539022\pi$
$491$	−24.7019	+	24.7019i	−1.11478	+	1.11478i	−0.992495	+	0.122285i	$0.960978\pi$
$492$		0			0
$493$	−4.96833	−	18.0799i	−0.223762	−	0.814277i
$494$		0			0
$495$	−0.784058	+	6.34215i	−0.0352408	+	0.285059i
$496$		0			0
$497$	−0.819716	−	0.819716i	−0.0367693	−	0.0367693i
$498$		0			0
$499$	6.46371			0.289355			0.144678	−	0.989479i	$-0.453785\pi$
$499$	6.46371			0.289355			0.144678	+	0.989479i	$0.453785\pi$
$500$		0			0
$501$	−17.0407	+	17.0407i	−0.761323	+	0.761323i
$502$		0			0
$503$	18.4269			0.821613			0.410806	−	0.911723i	$-0.365247\pi$
$503$	18.4269			0.821613			0.410806	+	0.911723i	$0.365247\pi$
$504$		0			0
$505$	1.74921	−	14.1492i	0.0778389	−	0.629629i
$506$		0			0
$507$	33.1988			1.47441
$508$		0			0
$509$		−	34.8282i		−	1.54373i	−0.635784	−	0.771867i	$-0.719323\pi$
$509$		−	34.8282i		−	1.54373i	0.635784	−	0.771867i	$-0.280677\pi$
$510$		0			0
$511$	−5.78708	+	5.78708i	−0.256005	+	0.256005i
$512$		0			0
$513$	−1.94489	−	1.94489i	−0.0858690	−	0.0858690i
$514$		0			0
$515$	−1.43634	+	11.6184i	−0.0632929	+	0.511969i
$516$		0			0
$517$	−25.7743	+	25.7743i	−1.13355	+	1.13355i
$518$		0			0
$519$	17.2301	+	17.2301i	0.756315	+	0.756315i
$520$		0			0
$521$			1.47444i			0.0645963i	0.999478	+	0.0322982i	$0.0102826\pi$
$521$			1.47444i			0.0645963i	−0.999478	+	0.0322982i	$0.989717\pi$
$522$		0			0
$523$	−5.29825	−	5.29825i	−0.231676	−	0.231676i	0.581716	−	0.813392i	$-0.302382\pi$
$523$	−5.29825	−	5.29825i	−0.231676	−	0.231676i	−0.813392	+	0.581716i	$0.802382\pi$
$524$		0			0
$525$	−3.04333	+	1.82175i	−0.132822	+	0.0795077i
$526$		0			0
$527$	−10.9614	−	10.9614i	−0.477486	−	0.477486i
$528$		0			0
$529$		−	15.2564i		−	0.663322i
$530$		0			0
$531$		−	6.18048i		−	0.268210i
$532$		0			0
$533$		−	64.1408i		−	2.77825i
$534$		0			0
$535$	35.9507	+	4.44447i	1.55429	+	0.192151i
$536$		0			0
$537$			4.22671i			0.182396i
$538$		0			0
$539$	−13.1289	+	13.1289i	−0.565501	+	0.565501i
$540$		0			0
$541$	18.7558	+	18.7558i	0.806376	+	0.806376i	0.984083	−	0.177708i	$-0.0568681\pi$
$541$	18.7558	+	18.7558i	0.806376	+	0.806376i	−0.177708	+	0.984083i	$0.556868\pi$
$542$		0			0
$543$		−	0.375464i		−	0.0161127i
$544$		0			0
$545$	−3.58222	−	4.59287i	−0.153445	−	0.196737i
$546$		0			0
$547$	3.07804	−	3.07804i	0.131607	−	0.131607i	−0.638235	−	0.769842i	$-0.720335\pi$
$547$	3.07804	−	3.07804i	0.131607	−	0.131607i	0.769842	+	0.638235i	$0.220335\pi$
$548$		0			0
$549$	−1.97484	−	1.97484i	−0.0842843	−	0.0842843i
$550$		0			0
$551$	−12.8744	−	7.32394i	−0.548469	−	0.312010i
$552$		0			0
$553$			8.76510i			0.372730i
$554$		0			0
$555$	−1.89182	−	2.42557i	−0.0803034	−	0.102960i
$556$		0			0
$557$	−12.6910	−	12.6910i	−0.537737	−	0.537737i	0.385127	−	0.922864i	$-0.374158\pi$
$557$	−12.6910	−	12.6910i	−0.537737	−	0.537737i	−0.922864	+	0.385127i	$0.874158\pi$
$558$		0			0
$559$	−31.7428	−	31.7428i	−1.34258	−	1.34258i
$560$		0			0
$561$	−7.03615	+	7.03615i	−0.297067	+	0.297067i
$562$		0			0
$563$	−5.96529			−0.251407			−0.125704	−	0.992068i	$-0.540119\pi$
$563$	−5.96529			−0.251407			−0.125704	+	0.992068i	$0.540119\pi$
$564$		0			0
$565$	−2.68547	−	3.44313i	−0.112979	−	0.144854i
$566$		0			0
$567$	0.501610	−	0.501610i	0.0210656	−	0.0210656i
$568$		0			0
$569$	−6.08615	−	6.08615i	−0.255145	−	0.255145i	0.567931	−	0.823076i	$-0.307744\pi$
$569$	−6.08615	−	6.08615i	−0.255145	−	0.255145i	−0.823076	+	0.567931i	$0.807744\pi$
$570$		0			0
$571$	−39.6194			−1.65802			−0.829011	−	0.559233i	$-0.811096\pi$
$571$	−39.6194			−1.65802			−0.829011	+	0.559233i	$0.811096\pi$
$572$		0			0
$573$	18.1023	−	18.1023i	0.756233	−	0.756233i
$574$		0			0
$575$	11.9382	−	7.14627i	0.497857	−	0.298020i
$576$		0			0
$577$			6.06967i			0.252684i	0.991987	+	0.126342i	$0.0403236\pi$
$577$			6.06967i			0.252684i	−0.991987	+	0.126342i	$0.959676\pi$
$578$		0			0
$579$	−13.9942			−0.581580
$580$		0			0
$581$	8.40371			0.348645
$582$		0			0
$583$			32.8494i			1.36048i
$584$		0			0
$585$	−15.0837	−	1.86474i	−0.623632	−	0.0770975i
$586$		0			0
$587$	32.0504	−	32.0504i	1.32286	−	1.32286i	0.411414	−	0.911448i	$-0.365035\pi$
$587$	32.0504	−	32.0504i	1.32286	−	1.32286i	0.911448	−	0.411414i	$-0.134965\pi$
$588$		0			0
$589$	−12.2458			−0.504579
$590$		0			0
$591$	15.1397	+	15.1397i	0.622763	+	0.622763i
$592$		0			0
$593$	−5.65238	+	5.65238i	−0.232115	+	0.232115i	−0.813575	−	0.581460i	$-0.802482\pi$
$593$	−5.65238	+	5.65238i	−0.232115	+	0.232115i	0.581460	+	0.813575i	$0.302482\pi$
$594$		0			0
$595$	−5.48122	−	0.677624i	−0.224708	−	0.0277799i
$596$		0			0
$597$	−1.61172			−0.0659632
$598$		0			0
$599$	17.0284	−	17.0284i	0.695763	−	0.695763i	−0.267731	−	0.963494i	$-0.586274\pi$
$599$	17.0284	−	17.0284i	0.695763	−	0.695763i	0.963494	+	0.267731i	$0.0862738\pi$
$600$		0			0
$601$	31.7974	+	31.7974i	1.29704	+	1.29704i	0.930336	+	0.366707i	$0.119515\pi$
$601$	31.7974	+	31.7974i	1.29704	+	1.29704i	0.366707	+	0.930336i	$0.380485\pi$
$602$		0			0
$603$	7.83460	+	7.83460i	0.319050	+	0.319050i
$604$		0			0
$605$	−4.99418	+	3.89521i	−0.203042	+	0.158363i
$606$		0			0
$607$			17.6894i			0.717993i	0.933339	+	0.358996i	$0.116881\pi$
$607$			17.6894i			0.717993i	−0.933339	+	0.358996i	$0.883119\pi$
$608$		0			0
$609$	1.88893	−	3.32046i	0.0765432	−	0.134552i
$610$		0			0
$611$	−61.2995	−	61.2995i	−2.47991	−	2.47991i
$612$		0			0
$613$	29.2411	−	29.2411i	1.18104	−	1.18104i	0.201562	−	0.979476i	$-0.435398\pi$
$613$	29.2411	−	29.2411i	1.18104	−	1.18104i	0.979476	−	0.201562i	$-0.0646017\pi$
$614$		0			0
$615$	−2.58894	+	20.9416i	−0.104396	+	0.844449i
$616$		0			0
$617$		−	33.9743i		−	1.36775i	−0.729597	−	0.683877i	$-0.760292\pi$
$617$		−	33.9743i		−	1.36775i	0.729597	−	0.683877i	$-0.239708\pi$
$618$		0			0
$619$	−7.50471	−	7.50471i	−0.301640	−	0.301640i	0.540015	−	0.841655i	$-0.318418\pi$
$619$	−7.50471	−	7.50471i	−0.301640	−	0.301640i	−0.841655	+	0.540015i	$0.818418\pi$
$620$		0			0
$621$	−1.96769	+	1.96769i	−0.0789606	+	0.0789606i
$622$		0			0
$623$		−	1.04011i		−	0.0416713i
$624$		0			0
$625$	−22.0346	−	11.8100i	−0.881385	−	0.472398i
$626$		0			0
$627$			7.86060i			0.313922i
$628$		0			0
$629$		−	4.78983i		−	0.190983i
$630$		0			0
$631$		−	28.8048i		−	1.14670i	−0.819310	−	0.573351i	$-0.805643\pi$
$631$		−	28.8048i		−	1.14670i	0.819310	−	0.573351i	$-0.194357\pi$
$632$		0			0
$633$	13.1359	+	13.1359i	0.522103	+	0.522103i
$634$		0			0
$635$	22.0852	+	28.3161i	0.876424	+	1.12369i
$636$		0			0
$637$	−31.2247	−	31.2247i	−1.23717	−	1.23717i
$638$		0			0
$639$			1.63417i			0.0646468i
$640$		0			0
$641$	24.2453	+	24.2453i	0.957630	+	0.957630i	0.999138	−	0.0415083i	$-0.0132163\pi$
$641$	24.2453	+	24.2453i	0.957630	+	0.957630i	−0.0415083	+	0.999138i	$0.513216\pi$
$642$		0			0
$643$	1.93849	−	1.93849i	0.0764467	−	0.0764467i	−0.667850	−	0.744296i	$-0.732785\pi$
$643$	1.93849	−	1.93849i	0.0764467	−	0.0764467i	0.744296	+	0.667850i	$0.232785\pi$
$644$		0			0
$645$	9.08262	+	11.6451i	0.357628	+	0.458526i
$646$		0			0
$647$	5.51236	+	5.51236i	0.216713	+	0.216713i	0.807112	−	0.590399i	$-0.201029\pi$
$647$	5.51236	+	5.51236i	0.216713	+	0.216713i	−0.590399	+	0.807112i	$0.701029\pi$
$648$		0			0
$649$	−12.4897	+	12.4897i	−0.490264	+	0.490264i
$650$		0			0
$651$		−	3.15833i		−	0.123785i
$652$		0			0
$653$	24.2573			0.949261			0.474630	−	0.880185i	$-0.342582\pi$
$653$	24.2573			0.949261			0.474630	+	0.880185i	$0.342582\pi$
$654$		0			0
$655$	−8.29185	−	1.02509i	−0.323989	−	0.0400537i
$656$		0			0
$657$	11.5370			0.450102
$658$		0			0
$659$	10.2321	−	10.2321i	0.398587	−	0.398587i	−0.479147	−	0.877735i	$-0.659054\pi$
$659$	10.2321	−	10.2321i	0.398587	−	0.398587i	0.877735	+	0.479147i	$0.159054\pi$
$660$		0			0
$661$	24.0210			0.934310			0.467155	−	0.884176i	$-0.345279\pi$
$661$	24.0210			0.934310			0.467155	+	0.884176i	$0.345279\pi$
$662$		0			0
$663$	−16.7342	−	16.7342i	−0.649903	−	0.649903i
$664$		0			0
$665$	−3.44025	+	2.68322i	−0.133407	+	0.104051i
$666$		0			0
$667$	−7.40979	+	13.0253i	−0.286908	+	0.504343i
$668$		0			0
$669$	−12.9508	+	12.9508i	−0.500708	+	0.500708i
$670$		0			0
$671$			7.98166i			0.308128i
$672$		0			0
$673$	−9.75214	+	9.75214i	−0.375917	+	0.375917i	−0.869627	−	0.493710i	$-0.835641\pi$
$673$	−9.75214	+	9.75214i	−0.375917	+	0.375917i	0.493710	+	0.869627i	$0.335641\pi$
$674$		0			0
$675$	4.84947	+	1.21766i	0.186656	+	0.0468676i
$676$		0			0
$677$			14.9141i			0.573196i	0.958051	+	0.286598i	$0.0925244\pi$
$677$			14.9141i			0.573196i	−0.958051	+	0.286598i	$0.907476\pi$
$678$		0			0
$679$	7.72251	+	7.72251i	0.296363	+	0.296363i
$680$		0			0
$681$	−6.68951	−	6.68951i	−0.256342	−	0.256342i
$682$		0			0
$683$	−0.412993	−	0.412993i	−0.0158027	−	0.0158027i	0.699161	−	0.714964i	$-0.253557\pi$
$683$	−0.412993	−	0.412993i	−0.0158027	−	0.0158027i	−0.714964	+	0.699161i	$0.753557\pi$
$684$		0			0
$685$	12.7198	+	16.3084i	0.485997	+	0.623112i
$686$		0			0
$687$	6.44176	−	6.44176i	0.245769	−	0.245769i
$688$		0			0
$689$	−78.1263			−2.97638
$690$		0			0
$691$	46.2229			1.75840			0.879200	−	0.476453i	$-0.158078\pi$
$691$	46.2229			1.75840			0.879200	+	0.476453i	$0.158078\pi$
$692$		0			0
$693$	−2.02734			−0.0770122
$694$		0			0
$695$	−11.6801	+	9.10990i	−0.443051	+	0.345558i
$696$		0			0
$697$	−23.2332	+	23.2332i	−0.880021	+	0.880021i
$698$		0			0
$699$	−11.5455	+	11.5455i	−0.436690	+	0.436690i
$700$		0			0
$701$			40.0544i			1.51283i	0.654091	+	0.756416i	$0.273051\pi$
$701$			40.0544i			1.51283i	−0.654091	+	0.756416i	$0.726949\pi$
$702$		0			0
$703$	−2.67553	−	2.67553i	−0.100910	−	0.100910i
$704$		0			0
$705$	17.5397	+	22.4882i	0.660583	+	0.846954i
$706$		0			0
$707$	4.52293			0.170102
$708$		0			0
$709$	27.8875			1.04734			0.523669	−	0.851922i	$-0.324563\pi$
$709$	27.8875			1.04734			0.523669	+	0.851922i	$0.324563\pi$
$710$		0			0
$711$	8.73698	−	8.73698i	0.327662	−	0.327662i
$712$		0			0
$713$			12.3893i			0.463984i
$714$		0			0
$715$	26.7132	+	34.2499i	0.999017	+	1.28087i
$716$		0			0
$717$	13.9588			0.521301
$718$		0			0
$719$			25.8847i			0.965336i	0.875803	+	0.482668i	$0.160332\pi$
$719$			25.8847i			0.965336i	−0.875803	+	0.482668i	$0.839668\pi$
$720$		0			0
$721$	−3.71395			−0.138315
$722$		0			0
$723$	7.52970			0.280032
$724$		0			0
$725$	26.9192	−	0.597007i	0.999754	−	0.0221723i
$726$		0			0
$727$	7.52196			0.278974			0.139487	−	0.990224i	$-0.455455\pi$
$727$	7.52196			0.278974			0.139487	+	0.990224i	$0.455455\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$			22.9959i			0.850534i
$732$		0			0
$733$	10.1827			0.376106			0.188053	−	0.982159i	$-0.439782\pi$
$733$	10.1827			0.376106			0.188053	+	0.982159i	$0.439782\pi$
$734$		0			0
$735$	8.93436	+	11.4550i	0.329549	+	0.422525i
$736$		0			0
$737$		−	31.6648i		−	1.16639i
$738$		0			0
$739$	−5.18433	+	5.18433i	−0.190709	+	0.190709i	−0.796002	−	0.605294i	$-0.793056\pi$
$739$	−5.18433	+	5.18433i	−0.190709	+	0.190709i	0.605294	+	0.796002i	$0.293056\pi$
$740$		0			0
$741$	−18.6950			−0.686778
$742$		0			0
$743$	−13.6079			−0.499226			−0.249613	−	0.968346i	$-0.580303\pi$
$743$	−13.6079			−0.499226			−0.249613	+	0.968346i	$0.580303\pi$
$744$		0			0
$745$	6.48825	+	8.31880i	0.237711	+	0.304777i
$746$		0			0
$747$	−8.37675	−	8.37675i	−0.306489	−	0.306489i
$748$		0			0
$749$			11.4920i			0.419910i
$750$		0			0
$751$	−24.7706	+	24.7706i	−0.903891	+	0.903891i	−0.995770	−	0.0918794i	$-0.970713\pi$
$751$	−24.7706	+	24.7706i	−0.903891	+	0.903891i	0.0918794	+	0.995770i	$0.470713\pi$
$752$		0			0
$753$	−6.20891	+	6.20891i	−0.226265	+	0.226265i
$754$		0			0
$755$	7.04619	−	5.49568i	0.256437	−	0.200008i
$756$		0			0
$757$	−27.2957			−0.992080			−0.496040	−	0.868300i	$-0.665213\pi$
$757$	−27.2957			−0.992080			−0.496040	+	0.868300i	$0.665213\pi$
$758$		0			0
$759$	7.95273			0.288666
$760$		0			0
$761$	−12.5202			−0.453857			−0.226928	−	0.973911i	$-0.572868\pi$
$761$	−12.5202			−0.453857			−0.226928	+	0.973911i	$0.572868\pi$
$762$		0			0
$763$	1.30663	−	1.30663i	0.0473031	−	0.0473031i
$764$		0			0
$765$	4.78818	+	6.13908i	0.173117	+	0.221959i
$766$		0			0
$767$	−29.7045	−	29.7045i	−1.07257	−	1.07257i
$768$		0			0
$769$	22.3383	+	22.3383i	0.805539	+	0.805539i	0.983955	−	0.178416i	$-0.0570974\pi$
$769$	22.3383	+	22.3383i	0.805539	+	0.805539i	−0.178416	+	0.983955i	$0.557097\pi$
$770$		0			0
$771$	−10.2480	−	10.2480i	−0.369073	−	0.369073i
$772$		0			0
$773$			51.9016i			1.86677i	0.358878	+	0.933385i	$0.383160\pi$
$773$			51.9016i			1.86677i	−0.358878	+	0.933385i	$0.616840\pi$
$774$		0			0
$775$	19.1005	−	11.4336i	0.686109	−	0.410708i
$776$		0			0
$777$	0.690051	−	0.690051i	0.0247554	−	0.0247554i
$778$		0			0
$779$			25.9555i			0.929953i
$780$		0			0
$781$	3.30239	−	3.30239i	0.118169	−	0.118169i
$782$		0			0
$783$	−5.19267	+	1.42694i	−0.185571	+	0.0509946i
$784$		0			0
$785$	−40.9945	+	31.9737i	−1.46316	+	1.14119i
$786$		0			0
$787$	−6.54700	−	6.54700i	−0.233375	−	0.233375i	0.580725	−	0.814100i	$-0.302769\pi$
$787$	−6.54700	−	6.54700i	−0.233375	−	0.233375i	−0.814100	+	0.580725i	$0.802769\pi$
$788$		0			0
$789$	9.97094			0.354975
$790$		0			0
$791$	0.979538	−	0.979538i	0.0348284	−	0.0348284i
$792$		0			0
$793$	−18.9829			−0.674103
$794$		0			0
$795$	25.5078	+	3.15344i	0.904669	+	0.111841i
$796$		0			0
$797$	20.9268			0.741267			0.370633	−	0.928779i	$-0.379141\pi$
$797$	20.9268			0.741267			0.370633	+	0.928779i	$0.379141\pi$
$798$		0			0
$799$			44.4080i			1.57104i
$800$		0			0
$801$	−1.03678	+	1.03678i	−0.0366327	+	0.0366327i
$802$		0			0
$803$	−23.3144	−	23.3144i	−0.822747	−	0.822747i
$804$		0			0
$805$	2.71467	+	3.48057i	0.0956797	+	0.122674i
$806$		0			0
$807$	−9.63229	+	9.63229i	−0.339073	+	0.339073i
$808$		0			0
$809$	13.0558	+	13.0558i	0.459018	+	0.459018i	0.898333	−	0.439315i	$-0.144779\pi$
$809$	13.0558	+	13.0558i	0.459018	+	0.459018i	−0.439315	+	0.898333i	$0.644779\pi$
$810$		0			0
$811$		−	10.7784i		−	0.378480i	−0.981931	−	0.189240i	$-0.939398\pi$
$811$		−	10.7784i		−	0.378480i	0.981931	−	0.189240i	$-0.0606025\pi$
$812$		0			0
$813$	−15.5653	−	15.5653i	−0.545899	−	0.545899i
$814$		0			0
$815$	−6.81439	−	8.73695i	−0.238698	−	0.306042i
$816$		0			0
$817$	12.8452	+	12.8452i	0.449397	+	0.449397i
$818$		0			0
$819$		−	4.82166i		−	0.168482i
$820$		0			0
$821$			10.9264i			0.381334i	0.981655	+	0.190667i	$0.0610651\pi$
$821$			10.9264i			0.381334i	−0.981655	+	0.190667i	$0.938935\pi$
$822$		0			0
$823$			47.5372i			1.65704i	0.559959	+	0.828521i	$0.310817\pi$
$823$			47.5372i			1.65704i	−0.559959	+	0.828521i	$0.689183\pi$
$824$		0			0
$825$	−7.33928	−	12.2606i	−0.255521	−	0.426860i
$826$		0			0
$827$			9.55325i			0.332199i	0.986109	+	0.166099i	$0.0531173\pi$
$827$			9.55325i			0.332199i	−0.986109	+	0.166099i	$0.946883\pi$
$828$		0			0
$829$	35.0883	−	35.0883i	1.21867	−	1.21867i	0.250570	−	0.968099i	$-0.419382\pi$
$829$	35.0883	−	35.0883i	1.21867	−	1.21867i	0.968099	−	0.250570i	$-0.0806179\pi$
$830$		0			0
$831$	−16.7440	−	16.7440i	−0.580844	−	0.580844i
$832$		0			0
$833$			22.6205i			0.783755i
$834$		0			0
$835$	6.61159	−	53.4803i	0.228803	−	1.85076i
$836$		0			0
$837$	−3.14819	+	3.14819i	−0.108817	+	0.108817i
$838$		0			0
$839$	−28.5131	−	28.5131i	−0.984382	−	0.984382i	0.0154976	−	0.999880i	$-0.495067\pi$
$839$	−28.5131	−	28.5131i	−0.984382	−	0.984382i	−0.999880	+	0.0154976i	$0.995067\pi$
$840$		0			0
$841$	−24.9277	+	14.8193i	−0.859575	+	0.511009i
$842$		0			0
$843$			24.0520i			0.828395i
$844$		0			0
$845$	−58.5357	+	45.6549i	−2.01369	+	1.57058i
$846$		0			0
$847$	−1.42080	−	1.42080i	−0.0488191	−	0.0488191i
$848$		0			0
$849$	−9.33420	−	9.33420i	−0.320349	−	0.320349i
$850$		0			0
$851$	−2.70689	+	2.70689i	−0.0927911	+	0.0927911i
$852$		0			0
$853$	2.67881			0.0917207			0.0458604	−	0.998948i	$-0.485397\pi$
$853$	2.67881			0.0917207			0.0458604	+	0.998948i	$0.485397\pi$
$854$		0			0
$855$	6.10382	+	0.754594i	0.208746	+	0.0258066i
$856$		0			0
$857$	−18.1060	+	18.1060i	−0.618490	+	0.618490i	−0.945144	−	0.326654i	$-0.894079\pi$
$857$	−18.1060	+	18.1060i	−0.618490	+	0.618490i	0.326654	+	0.945144i	$0.394079\pi$
$858$		0			0
$859$	5.09077	+	5.09077i	0.173695	+	0.173695i	0.788601	−	0.614906i	$-0.210806\pi$
$859$	5.09077	+	5.09077i	0.173695	+	0.173695i	−0.614906	+	0.788601i	$0.710806\pi$
$860$		0			0
$861$	−6.69423			−0.228139
$862$		0			0
$863$	−28.1965	+	28.1965i	−0.959821	+	0.959821i	−0.999223	−	0.0394021i	$-0.987455\pi$
$863$	−28.1965	+	28.1965i	−0.959821	+	0.959821i	0.0394021	+	0.999223i	$0.487455\pi$
$864$		0			0
$865$	−54.0746	−	6.68505i	−1.83859	−	0.227299i
$866$		0			0
$867$		−	4.87701i		−	0.165632i
$868$		0			0
$869$	−35.3119			−1.19788
$870$		0			0
$871$	75.3091			2.55175
$872$		0			0
$873$		−	15.3954i		−	0.521057i
$874$		0			0
$875$	2.86068	−	7.39727i	0.0967088	−	0.250073i
$876$		0			0
$877$	−7.46600	+	7.46600i	−0.252109	+	0.252109i	−0.821835	−	0.569726i	$-0.807049\pi$
$877$	−7.46600	+	7.46600i	−0.252109	+	0.252109i	0.569726	+	0.821835i	$0.307049\pi$
$878$		0			0
$879$	3.20784			0.108198
$880$		0			0
$881$	10.9206	+	10.9206i	0.367924	+	0.367924i	0.866720	−	0.498796i	$-0.166224\pi$
$881$	10.9206	+	10.9206i	0.367924	+	0.367924i	−0.498796	+	0.866720i	$0.666224\pi$
$882$		0			0
$883$	−34.6279	+	34.6279i	−1.16532	+	1.16532i	−0.182029	+	0.983293i	$0.558266\pi$
$883$	−34.6279	+	34.6279i	−1.16532	+	1.16532i	−0.983293	+	0.182029i	$0.941734\pi$
$884$		0			0
$885$	8.49938	+	10.8973i	0.285704	+	0.366310i
$886$		0			0
$887$	15.4692			0.519406			0.259703	−	0.965688i	$-0.416375\pi$
$887$	15.4692			0.519406			0.259703	+	0.965688i	$0.416375\pi$
$888$		0			0
$889$	−8.05567	+	8.05567i	−0.270178	+	0.270178i
$890$		0			0
$891$	2.02083	+	2.02083i	0.0677004	+	0.0677004i
$892$		0			0
$893$	24.8057	+	24.8057i	0.830091	+	0.830091i
$894$		0			0
$895$	−5.81256	−	7.45248i	−0.194293	−	0.249109i
$896$		0			0
$897$			18.9141i			0.631524i
$898$		0			0
$899$	−11.8553	+	20.8398i	−0.395395	+	0.695047i
$900$		0			0
$901$	28.2991	+	28.2991i	0.942778	+	0.942778i
$902$		0			0
$903$	−3.31292	+	3.31292i	−0.110247	+	0.110247i
$904$		0			0
$905$	0.516338	+	0.662014i	0.0171637	+	0.0220061i
$906$		0			0
$907$		−	53.1165i		−	1.76371i	−0.471525	−	0.881853i	$-0.656296\pi$
$907$		−	53.1165i		−	1.76371i	0.471525	−	0.881853i	$-0.343704\pi$
$908$		0			0
$909$	−4.50842	−	4.50842i	−0.149535	−	0.149535i
$910$		0			0
$911$	22.8730	−	22.8730i	0.757818	−	0.757818i	−0.218107	−	0.975925i	$-0.569988\pi$
$911$	22.8730	−	22.8730i	0.757818	−	0.757818i	0.975925	+	0.218107i	$0.0699882\pi$
$912$		0			0
$913$			33.8560i			1.12047i
$914$		0			0
$915$	6.19782	+	0.766216i	0.204894	+	0.0253303i
$916$		0			0
$917$		−	2.65058i		−	0.0875299i
$918$		0			0
$919$		−	53.4073i		−	1.76175i	−0.473353	−	0.880873i	$-0.656957\pi$
$919$		−	53.4073i		−	1.76175i	0.473353	−	0.880873i	$-0.343043\pi$
$920$		0			0
$921$			20.3426i			0.670313i
$922$		0			0
$923$	7.85412	+	7.85412i	0.258522	+	0.258522i
$924$		0			0
$925$	6.67128	+	1.67510i	0.219350	+	0.0550768i
$926$		0			0
$927$	3.70204	+	3.70204i	0.121591	+	0.121591i
$928$		0			0
$929$		−	11.0480i		−	0.362472i	−0.983440	−	0.181236i	$-0.941990\pi$
$929$		−	11.0480i		−	0.362472i	0.983440	−	0.181236i	$-0.0580098\pi$
$930$		0			0
$931$	12.6355	+	12.6355i	0.414112	+	0.414112i
$932$		0			0
$933$	15.1136	−	15.1136i	0.494797	−	0.494797i
$934$		0			0
$935$	2.72994	−	22.0822i	0.0892786	−	0.722164i
$936$		0			0
$937$	12.7857	+	12.7857i	0.417692	+	0.417692i	0.884407	−	0.466716i	$-0.154563\pi$
$937$	12.7857	+	12.7857i	0.417692	+	0.417692i	−0.466716	+	0.884407i	$0.654563\pi$
$938$		0			0
$939$	−12.6402	+	12.6402i	−0.412496	+	0.412496i
$940$		0			0
$941$		−	28.7450i		−	0.937060i	−0.883448	−	0.468530i	$-0.844784\pi$
$941$		−	28.7450i		−	0.937060i	0.883448	−	0.468530i	$-0.155216\pi$
$942$		0			0
$943$	26.2597			0.855135
$944$		0			0
$945$	−0.194618	+	1.57424i	−0.00633094	+	0.0512102i
$946$		0			0
$947$	13.6797			0.444530			0.222265	−	0.974986i	$-0.428655\pi$
$947$	13.6797			0.444530			0.222265	+	0.974986i	$0.428655\pi$
$948$		0			0
$949$	55.4490	−	55.4490i	1.79995	−	1.79995i
$950$		0			0
$951$	−12.2398			−0.396904
$952$		0			0
$953$	−7.34774	−	7.34774i	−0.238017	−	0.238017i	0.578012	−	0.816028i	$-0.303829\pi$
$953$	−7.34774	−	7.34774i	−0.238017	−	0.238017i	−0.816028	+	0.578012i	$0.803829\pi$
$954$		0			0
$955$	−7.02346	+	56.8119i	−0.227274	+	1.83839i
$956$		0			0
$957$	13.3771	+	7.60991i	0.432421	+	0.245994i
$958$		0			0
$959$	−4.63958	+	4.63958i	−0.149820	+	0.149820i
$960$		0			0
$961$		−	11.1778i		−	0.360573i
$962$		0			0
$963$	11.4552	−	11.4552i	0.369138	−	0.369138i
$964$		0			0
$965$	24.6744	−	19.2449i	0.794298	−	0.619514i
$966$		0			0
$967$			36.7626i			1.18220i	0.806597	+	0.591102i	$0.201307\pi$
$967$			36.7626i			1.18220i	−0.806597	+	0.591102i	$0.798693\pi$
$968$		0			0
$969$	6.77174	+	6.77174i	0.217540	+	0.217540i
$970$		0			0
$971$	−13.6273	−	13.6273i	−0.437322	−	0.437322i	0.453788	−	0.891110i	$-0.350072\pi$
$971$	−13.6273	−	13.6273i	−0.437322	−	0.437322i	−0.891110	+	0.453788i	$0.850072\pi$
$972$		0			0
$973$	−3.32288	−	3.32288i	−0.106527	−	0.106527i
$974$		0			0
$975$	29.1597	−	17.4551i	0.933858	−	0.559012i
$976$		0			0
$977$	31.0283	−	31.0283i	0.992682	−	0.992682i	−0.00729114	−	0.999973i	$-0.502321\pi$
$977$	31.0283	−	31.0283i	0.992682	−	0.992682i	0.999973	+	0.00729114i	$0.00232086\pi$
$978$		0			0
$979$	4.19030			0.133923
$980$		0			0
$981$	−2.60487			−0.0831671
$982$		0			0
$983$	−20.8489			−0.664978			−0.332489	−	0.943107i	$-0.607888\pi$
$983$	−20.8489			−0.664978			−0.332489	+	0.943107i	$0.607888\pi$
$984$		0			0
$985$	−47.5141	−	5.87401i	−1.51393	−	0.187161i
$986$		0			0
$987$	−6.39768	+	6.39768i	−0.203640	+	0.203640i
$988$		0			0
$989$	12.9958	−	12.9958i	0.413241	−	0.413241i
$990$		0			0
$991$		−	21.4607i		−	0.681720i	−0.940114	−	0.340860i	$-0.889282\pi$
$991$		−	21.4607i		−	0.681720i	0.940114	−	0.340860i	$-0.110718\pi$
$992$		0			0
$993$	−7.42276	−	7.42276i	−0.235554	−	0.235554i
$994$		0			0
$995$	2.84176	−	2.21643i	0.0900899	−	0.0702657i
$996$		0			0
$997$	17.7245			0.561342			0.280671	−	0.959804i	$-0.409443\pi$
$997$	17.7245			0.561342			0.280671	+	0.959804i	$0.409443\pi$
$998$		0			0
$999$	−1.37567			−0.0435244

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1740.2.bc.c.853.5	yes	30
5.2	odd	4		1740.2.bb.c.157.11	yes	30
29.17	odd	4		1740.2.bb.c.133.11	✓	30
145.17	even	4	inner	1740.2.bc.c.1177.5	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1740.2.bb.c.133.11	✓	30	29.17	odd	4
1740.2.bb.c.157.11	yes	30	5.2	odd	4
1740.2.bc.c.853.5	yes	30	1.1	even	1	trivial
1740.2.bc.c.1177.5	yes	30	145.17	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1740.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{3} +(-1.37520 - 1.76319i) q^{5} +(0.501610 - 0.501610i) q^{7} -1.00000 q^{9} +(2.02083 + 2.02083i) q^{11} +(-4.80618 + 4.80618i) q^{13} +(1.76319 - 1.37520i) q^{15} +3.48181 q^{17} +(1.94489 - 1.94489i) q^{19} +(0.501610 + 0.501610i) q^{21} +(-1.96769 - 1.96769i) q^{23} +(-1.21766 + 4.84947i) q^{25} -1.00000i q^{27} +(-1.42694 - 5.19267i) q^{29} +(-3.14819 - 3.14819i) q^{31} +(-2.02083 + 2.02083i) q^{33} +(-1.57424 - 0.194618i) q^{35} -1.37567i q^{37} +(-4.80618 - 4.80618i) q^{39} +(-6.67274 + 6.67274i) q^{41} +6.60459i q^{43} +(1.37520 + 1.76319i) q^{45} +12.7543i q^{47} +6.49678i q^{49} +3.48181i q^{51} +(8.12769 + 8.12769i) q^{53} +(0.784058 - 6.34215i) q^{55} +(1.94489 + 1.94489i) q^{57} +6.18048i q^{59} +(1.97484 + 1.97484i) q^{61} +(-0.501610 + 0.501610i) q^{63} +(15.0837 + 1.86474i) q^{65} +(-7.83460 - 7.83460i) q^{67} +(1.96769 - 1.96769i) q^{69} -1.63417i q^{71} -11.5370 q^{73} +(-4.84947 - 1.21766i) q^{75} +2.02734 q^{77} +(-8.73698 + 8.73698i) q^{79} +1.00000 q^{81} +(8.37675 + 8.37675i) q^{83} +(-4.78818 - 6.13908i) q^{85} +(5.19267 - 1.42694i) q^{87} +(1.03678 - 1.03678i) q^{89} +4.82166i q^{91} +(3.14819 - 3.14819i) q^{93} +(-6.10382 - 0.754594i) q^{95} +15.3954i q^{97} +(-2.02083 - 2.02083i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 30 q^{9} + 4 q^{11} - 6 q^{13} - 6 q^{15} + 8 q^{19} - 6 q^{25} + 4 q^{29} - 4 q^{33} - 16 q^{35} - 6 q^{39} - 10 q^{41} - 6 q^{53} + 4 q^{55} + 8 q^{57} + 30 q^{61} - 2 q^{65} + 4 q^{67} + 12 q^{73}+ \cdots - 4 q^{99}+O(q^{100}) \) 30 * q - 30 * q^9 + 4 * q^11 - 6 * q^13 - 6 * q^15 + 8 * q^19 - 6 * q^25 + 4 * q^29 - 4 * q^33 - 16 * q^35 - 6 * q^39 - 10 * q^41 - 6 * q^53 + 4 * q^55 + 8 * q^57 + 30 * q^61 - 2 * q^65 + 4 * q^67 + 12 * q^73 + 8 * q^75 - 4 * q^77 - 4 * q^79 + 30 * q^81 - 28 * q^83 + 20 * q^85 + 10 * q^87 + 10 * q^89 + 20 * q^95 - 4 * q^99

Introduction

L-functions

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Database

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