LMFDB - Embedded newform 2380.2.be.a.421.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2380,2,Mod(421,2380)] 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("2380.421"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2380, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2380 = 2^{2} \cdot 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2380.be (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4] 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:	$19.0043956811$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			421.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2380.421
Dual form			2380.2.be.a.701.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{3} +(-0.707107 - 0.707107i) q^{5} +(-0.707107 + 0.707107i) q^{7} -1.00000i q^{9} +(0.585786 - 0.585786i) q^{11} -0.171573 q^{13} -1.41421i q^{15} +(1.00000 - 4.00000i) q^{17} +1.41421i q^{19} -1.41421 q^{21} +(-0.707107 + 0.707107i) q^{23} +1.00000i q^{25} +(4.00000 - 4.00000i) q^{27} +(2.24264 + 2.24264i) q^{29} +(-6.12132 - 6.12132i) q^{31} +1.17157 q^{33} +1.00000 q^{35} +(3.29289 + 3.29289i) q^{37} +(-0.171573 - 0.171573i) q^{39} +(2.70711 - 2.70711i) q^{41} -11.4142i q^{43} +(-0.707107 + 0.707107i) q^{45} -7.00000 q^{47} -1.00000i q^{49} +(5.00000 - 3.00000i) q^{51} -8.24264i q^{53} -0.828427 q^{55} +(-1.41421 + 1.41421i) q^{57} -3.17157i q^{59} +(4.36396 - 4.36396i) q^{61} +(0.707107 + 0.707107i) q^{63} +(0.121320 + 0.121320i) q^{65} +0.343146 q^{67} -1.41421 q^{69} +(2.00000 + 2.00000i) q^{71} +(12.0711 + 12.0711i) q^{73} +(-1.00000 + 1.00000i) q^{75} +0.828427i q^{77} +(3.24264 - 3.24264i) q^{79} +5.00000 q^{81} -15.1421i q^{83} +(-3.53553 + 2.12132i) q^{85} +4.48528i q^{87} +11.0711 q^{89} +(0.121320 - 0.121320i) q^{91} -12.2426i q^{93} +(1.00000 - 1.00000i) q^{95} +(-12.8995 - 12.8995i) q^{97} +(-0.585786 - 0.585786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} + 8 q^{11} - 12 q^{13} + 4 q^{17} + 16 q^{27} - 8 q^{29} - 16 q^{31} + 16 q^{33} + 4 q^{35} + 16 q^{37} - 12 q^{39} + 8 q^{41} - 28 q^{47} + 20 q^{51} + 8 q^{55} - 8 q^{61} - 8 q^{65} + 24 q^{67}+ \cdots - 8 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 + 8 * q^11 - 12 * q^13 + 4 * q^17 + 16 * q^27 - 8 * q^29 - 16 * q^31 + 16 * q^33 + 4 * q^35 + 16 * q^37 - 12 * q^39 + 8 * q^41 - 28 * q^47 + 20 * q^51 + 8 * q^55 - 8 * q^61 - 8 * q^65 + 24 * q^67 + 8 * q^71 + 20 * q^73 - 4 * q^75 - 4 * q^79 + 20 * q^81 + 16 * q^89 - 8 * q^91 + 4 * q^95 - 12 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2380\mathbb{Z}\right)^\times$.

$n$	$477$	$1191$	$1261$	$1361$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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			0
$2$		0			0
$3$	1.00000	+	1.00000i	0.577350	+	0.577350i	0.934172	−	0.356822i	$-0.116140\pi$
$3$	1.00000	+	1.00000i	0.577350	+	0.577350i	−0.356822	+	0.934172i	$0.616140\pi$
$4$		0			0
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	0.585786	−	0.585786i	0.176621	−	0.176621i	−0.613260	−	0.789881i	$-0.710142\pi$
$11$	0.585786	−	0.585786i	0.176621	−	0.176621i	0.789881	+	0.613260i	$0.210142\pi$
$12$		0			0
$13$	−0.171573			−0.0475858			−0.0237929	−	0.999717i	$-0.507574\pi$
$13$	−0.171573			−0.0475858			−0.0237929	+	0.999717i	$0.507574\pi$
$14$		0			0
$15$		−	1.41421i		−	0.365148i
$16$		0			0
$17$	1.00000	−	4.00000i	0.242536	−	0.970143i
$17$	1.00000	−	4.00000i	0.242536	−	0.970143i
$18$		0			0
$19$			1.41421i			0.324443i	0.986754	+	0.162221i	$0.0518659\pi$
$19$			1.41421i			0.324443i	−0.986754	+	0.162221i	$0.948134\pi$
$20$		0			0
$21$	−1.41421			−0.308607
$22$		0			0
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i	−0.776974	−	0.629532i	$-0.783247\pi$
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i	0.629532	+	0.776974i	$0.283247\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	4.00000	−	4.00000i	0.769800	−	0.769800i
$28$		0			0
$29$	2.24264	+	2.24264i	0.416448	+	0.416448i	0.883977	−	0.467530i	$-0.154856\pi$
$29$	2.24264	+	2.24264i	0.416448	+	0.416448i	−0.467530	+	0.883977i	$0.654856\pi$
$30$		0			0
$31$	−6.12132	−	6.12132i	−1.09942	−	1.09942i	−0.994478	−	0.104943i	$-0.966534\pi$
$31$	−6.12132	−	6.12132i	−1.09942	−	1.09942i	−0.104943	−	0.994478i	$-0.533466\pi$
$32$		0			0
$33$	1.17157			0.203945
$34$		0			0
$35$	1.00000			0.169031
$36$		0			0
$37$	3.29289	+	3.29289i	0.541348	+	0.541348i	0.923924	−	0.382576i	$-0.124963\pi$
$37$	3.29289	+	3.29289i	0.541348	+	0.541348i	−0.382576	+	0.923924i	$0.624963\pi$
$38$		0			0
$39$	−0.171573	−	0.171573i	−0.0274736	−	0.0274736i
$40$		0			0
$41$	2.70711	−	2.70711i	0.422779	−	0.422779i	−0.463380	−	0.886159i	$-0.653364\pi$
$41$	2.70711	−	2.70711i	0.422779	−	0.422779i	0.886159	+	0.463380i	$0.153364\pi$
$42$		0			0
$43$		−	11.4142i		−	1.74065i	−0.492477	−	0.870326i	$-0.663908\pi$
$43$		−	11.4142i		−	1.74065i	0.492477	−	0.870326i	$-0.336092\pi$
$44$		0			0
$45$	−0.707107	+	0.707107i	−0.105409	+	0.105409i
$46$		0			0
$47$	−7.00000			−1.02105			−0.510527	−	0.859861i	$-0.670550\pi$
$47$	−7.00000			−1.02105			−0.510527	+	0.859861i	$0.670550\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	5.00000	−	3.00000i	0.700140	−	0.420084i
$52$		0			0
$53$		−	8.24264i		−	1.13221i	−0.824332	−	0.566107i	$-0.808449\pi$
$53$		−	8.24264i		−	1.13221i	0.824332	−	0.566107i	$-0.191551\pi$
$54$		0			0
$55$	−0.828427			−0.111705
$56$		0			0
$57$	−1.41421	+	1.41421i	−0.187317	+	0.187317i
$58$		0			0
$59$		−	3.17157i		−	0.412904i	−0.978457	−	0.206452i	$-0.933808\pi$
$59$		−	3.17157i		−	0.412904i	0.978457	−	0.206452i	$-0.0661917\pi$
$60$		0			0
$61$	4.36396	−	4.36396i	0.558748	−	0.558748i	−0.370203	−	0.928951i	$-0.620712\pi$
$61$	4.36396	−	4.36396i	0.558748	−	0.558748i	0.928951	+	0.370203i	$0.120712\pi$
$62$		0			0
$63$	0.707107	+	0.707107i	0.0890871	+	0.0890871i
$64$		0			0
$65$	0.121320	+	0.121320i	0.0150479	+	0.0150479i
$66$		0			0
$67$	0.343146			0.0419219			0.0209610	−	0.999780i	$-0.493327\pi$
$67$	0.343146			0.0419219			0.0209610	+	0.999780i	$0.493327\pi$
$68$		0			0
$69$	−1.41421			−0.170251
$70$		0			0
$71$	2.00000	+	2.00000i	0.237356	+	0.237356i	0.815755	−	0.578398i	$-0.196322\pi$
$71$	2.00000	+	2.00000i	0.237356	+	0.237356i	−0.578398	+	0.815755i	$0.696322\pi$
$72$		0			0
$73$	12.0711	+	12.0711i	1.41281	+	1.41281i	0.737883	+	0.674928i	$0.235825\pi$
$73$	12.0711	+	12.0711i	1.41281	+	1.41281i	0.674928	+	0.737883i	$0.264175\pi$
$74$		0			0
$75$	−1.00000	+	1.00000i	−0.115470	+	0.115470i
$76$		0			0
$77$			0.828427i			0.0944080i
$78$		0			0
$79$	3.24264	−	3.24264i	0.364826	−	0.364826i	−0.500760	−	0.865586i	$-0.666946\pi$
$79$	3.24264	−	3.24264i	0.364826	−	0.364826i	0.865586	+	0.500760i	$0.166946\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$		0			0
$83$		−	15.1421i		−	1.66207i	−0.556224	−	0.831033i	$-0.687750\pi$
$83$		−	15.1421i		−	1.66207i	0.556224	−	0.831033i	$-0.312250\pi$
$84$		0			0
$85$	−3.53553	+	2.12132i	−0.383482	+	0.230089i
$86$		0			0
$87$			4.48528i			0.480873i
$88$		0			0
$89$	11.0711			1.17353			0.586765	−	0.809757i	$-0.300401\pi$
$89$	11.0711			1.17353			0.586765	+	0.809757i	$0.300401\pi$
$90$		0			0
$91$	0.121320	−	0.121320i	0.0127178	−	0.0127178i
$92$		0			0
$93$		−	12.2426i		−	1.26950i
$94$		0			0
$95$	1.00000	−	1.00000i	0.102598	−	0.102598i
$96$		0			0
$97$	−12.8995	−	12.8995i	−1.30975	−	1.30975i	−0.921597	−	0.388148i	$-0.873115\pi$
$97$	−12.8995	−	12.8995i	−1.30975	−	1.30975i	−0.388148	−	0.921597i	$-0.626885\pi$
$98$		0			0
$99$	−0.585786	−	0.585786i	−0.0588738	−	0.0588738i
$100$		0			0
$101$	11.6569			1.15990			0.579950	−	0.814652i	$-0.303072\pi$
$101$	11.6569			1.15990			0.579950	+	0.814652i	$0.303072\pi$
$102$		0			0
$103$	10.0000			0.985329			0.492665	−	0.870219i	$-0.336023\pi$
$103$	10.0000			0.985329			0.492665	+	0.870219i	$0.336023\pi$
$104$		0			0
$105$	1.00000	+	1.00000i	0.0975900	+	0.0975900i
$106$		0			0
$107$	−12.3640	−	12.3640i	−1.19527	−	1.19527i	−0.975567	−	0.219702i	$-0.929491\pi$
$107$	−12.3640	−	12.3640i	−1.19527	−	1.19527i	−0.219702	−	0.975567i	$-0.570509\pi$
$108$		0			0
$109$	−5.82843	+	5.82843i	−0.558262	+	0.558262i	−0.928812	−	0.370550i	$-0.879169\pi$
$109$	−5.82843	+	5.82843i	−0.558262	+	0.558262i	0.370550	+	0.928812i	$0.379169\pi$
$110$		0			0
$111$			6.58579i			0.625095i
$112$		0			0
$113$	3.17157	−	3.17157i	0.298356	−	0.298356i	−0.542013	−	0.840370i	$-0.682338\pi$
$113$	3.17157	−	3.17157i	0.298356	−	0.298356i	0.840370	+	0.542013i	$0.182338\pi$
$114$		0			0
$115$	1.00000			0.0932505
$116$		0			0
$117$			0.171573i			0.0158619i
$118$		0			0
$119$	2.12132	+	3.53553i	0.194461	+	0.324102i
$120$		0			0
$121$			10.3137i			0.937610i
$122$		0			0
$123$	5.41421			0.488183
$124$		0			0
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$		0			0
$127$			6.34315i			0.562863i	0.959581	+	0.281432i	$0.0908092\pi$
$127$			6.34315i			0.562863i	−0.959581	+	0.281432i	$0.909191\pi$
$128$		0			0
$129$	11.4142	−	11.4142i	1.00497	−	1.00497i
$130$		0			0
$131$	6.94975	+	6.94975i	0.607202	+	0.607202i	0.942214	−	0.335012i	$-0.108740\pi$
$131$	6.94975	+	6.94975i	0.607202	+	0.607202i	−0.335012	+	0.942214i	$0.608740\pi$
$132$		0			0
$133$	−1.00000	−	1.00000i	−0.0867110	−	0.0867110i
$134$		0			0
$135$	−5.65685			−0.486864
$136$		0			0
$137$	15.4142			1.31693			0.658463	−	0.752613i	$-0.271207\pi$
$137$	15.4142			1.31693			0.658463	+	0.752613i	$0.271207\pi$
$138$		0			0
$139$	−3.89949	−	3.89949i	−0.330751	−	0.330751i	0.522121	−	0.852872i	$-0.325141\pi$
$139$	−3.89949	−	3.89949i	−0.330751	−	0.330751i	−0.852872	+	0.522121i	$0.825141\pi$
$140$		0			0
$141$	−7.00000	−	7.00000i	−0.589506	−	0.589506i
$142$		0			0
$143$	−0.100505	+	0.100505i	−0.00840466	+	0.00840466i
$144$		0			0
$145$		−	3.17157i		−	0.263385i
$146$		0			0
$147$	1.00000	−	1.00000i	0.0824786	−	0.0824786i
$148$		0			0
$149$	−1.48528			−0.121679			−0.0608395	−	0.998148i	$-0.519378\pi$
$149$	−1.48528			−0.121679			−0.0608395	+	0.998148i	$0.519378\pi$
$150$		0			0
$151$			2.31371i			0.188287i	0.995559	+	0.0941435i	$0.0300112\pi$
$151$			2.31371i			0.188287i	−0.995559	+	0.0941435i	$0.969989\pi$
$152$		0			0
$153$	−4.00000	−	1.00000i	−0.323381	−	0.0808452i
$154$		0			0
$155$			8.65685i			0.695335i
$156$		0			0
$157$	−22.1421			−1.76713			−0.883567	−	0.468304i	$-0.844865\pi$
$157$	−22.1421			−1.76713			−0.883567	+	0.468304i	$0.844865\pi$
$158$		0			0
$159$	8.24264	−	8.24264i	0.653684	−	0.653684i
$160$		0			0
$161$		−	1.00000i		−	0.0788110i
$162$		0			0
$163$	−6.70711	+	6.70711i	−0.525341	+	0.525341i	−0.919180	−	0.393839i	$-0.871147\pi$
$163$	−6.70711	+	6.70711i	−0.525341	+	0.525341i	0.393839	+	0.919180i	$0.371147\pi$
$164$		0			0
$165$	−0.828427	−	0.828427i	−0.0644930	−	0.0644930i
$166$		0			0
$167$	−0.414214	−	0.414214i	−0.0320528	−	0.0320528i	0.690899	−	0.722952i	$-0.257215\pi$
$167$	−0.414214	−	0.414214i	−0.0320528	−	0.0320528i	−0.722952	+	0.690899i	$0.757215\pi$
$168$		0			0
$169$	−12.9706			−0.997736
$170$		0			0
$171$	1.41421			0.108148
$172$		0			0
$173$	14.3137	+	14.3137i	1.08825	+	1.08825i	0.995709	+	0.0925424i	$0.0294994\pi$
$173$	14.3137	+	14.3137i	1.08825	+	1.08825i	0.0925424	+	0.995709i	$0.470501\pi$
$174$		0			0
$175$	−0.707107	−	0.707107i	−0.0534522	−	0.0534522i
$176$		0			0
$177$	3.17157	−	3.17157i	0.238390	−	0.238390i
$178$		0			0
$179$			9.82843i			0.734611i	0.930100	+	0.367306i	$0.119720\pi$
$179$			9.82843i			0.734611i	−0.930100	+	0.367306i	$0.880280\pi$
$180$		0			0
$181$	15.1924	−	15.1924i	1.12924	−	1.12924i	0.138941	−	0.990301i	$-0.455630\pi$
$181$	15.1924	−	15.1924i	1.12924	−	1.12924i	0.990301	−	0.138941i	$-0.0443697\pi$
$182$		0			0
$183$	8.72792			0.645187
$184$		0			0
$185$		−	4.65685i		−	0.342379i
$186$		0			0
$187$	−1.75736	−	2.92893i	−0.128511	−	0.214185i
$188$		0			0
$189$			5.65685i			0.411476i
$190$		0			0
$191$	−4.31371			−0.312129			−0.156064	−	0.987747i	$-0.549881\pi$
$191$	−4.31371			−0.312129			−0.156064	+	0.987747i	$0.549881\pi$
$192$		0			0
$193$	2.36396	−	2.36396i	0.170162	−	0.170162i	−0.616889	−	0.787050i	$-0.711607\pi$
$193$	2.36396	−	2.36396i	0.170162	−	0.170162i	0.787050	+	0.616889i	$0.211607\pi$
$194$		0			0
$195$			0.242641i			0.0173759i
$196$		0			0
$197$	−6.48528	+	6.48528i	−0.462057	+	0.462057i	−0.899329	−	0.437272i	$-0.855945\pi$
$197$	−6.48528	+	6.48528i	−0.462057	+	0.462057i	0.437272	+	0.899329i	$0.355945\pi$
$198$		0			0
$199$	−0.585786	−	0.585786i	−0.0415253	−	0.0415253i	0.686039	−	0.727565i	$-0.259348\pi$
$199$	−0.585786	−	0.585786i	−0.0415253	−	0.0415253i	−0.727565	+	0.686039i	$0.759348\pi$
$200$		0			0
$201$	0.343146	+	0.343146i	0.0242036	+	0.0242036i
$202$		0			0
$203$	−3.17157			−0.222601
$204$		0			0
$205$	−3.82843			−0.267389
$206$		0			0
$207$	0.707107	+	0.707107i	0.0491473	+	0.0491473i
$208$		0			0
$209$	0.828427	+	0.828427i	0.0573035	+	0.0573035i
$210$		0			0
$211$	−2.58579	+	2.58579i	−0.178013	+	0.178013i	−0.790489	−	0.612476i	$-0.790174\pi$
$211$	−2.58579	+	2.58579i	−0.178013	+	0.178013i	0.612476	+	0.790489i	$0.290174\pi$
$212$		0			0
$213$			4.00000i			0.274075i
$214$		0			0
$215$	−8.07107	+	8.07107i	−0.550442	+	0.550442i
$216$		0			0
$217$	8.65685			0.587666
$218$		0			0
$219$			24.1421i			1.63137i
$220$		0			0
$221$	−0.171573	+	0.686292i	−0.0115412	+	0.0461650i
$222$		0			0
$223$		−	15.8284i		−	1.05995i	−0.848013	−	0.529975i	$-0.822201\pi$
$223$		−	15.8284i		−	1.05995i	0.848013	−	0.529975i	$-0.177799\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	10.7279	−	10.7279i	0.712037	−	0.712037i	−0.254924	−	0.966961i	$-0.582050\pi$
$227$	10.7279	−	10.7279i	0.712037	−	0.712037i	0.966961	+	0.254924i	$0.0820504\pi$
$228$		0			0
$229$			16.3848i			1.08274i	0.840786	+	0.541368i	$0.182094\pi$
$229$			16.3848i			1.08274i	−0.840786	+	0.541368i	$0.817906\pi$
$230$		0			0
$231$	−0.828427	+	0.828427i	−0.0545065	+	0.0545065i
$232$		0			0
$233$	0.807612	+	0.807612i	0.0529084	+	0.0529084i	0.733066	−	0.680158i	$-0.238089\pi$
$233$	0.807612	+	0.807612i	0.0529084	+	0.0529084i	−0.680158	+	0.733066i	$0.738089\pi$
$234$		0			0
$235$	4.94975	+	4.94975i	0.322886	+	0.322886i
$236$		0			0
$237$	6.48528			0.421264
$238$		0			0
$239$	7.82843			0.506379			0.253189	−	0.967417i	$-0.418520\pi$
$239$	7.82843			0.506379			0.253189	+	0.967417i	$0.418520\pi$
$240$		0			0
$241$	−0.464466	−	0.464466i	−0.0299189	−	0.0299189i	0.691989	−	0.721908i	$-0.256735\pi$
$241$	−0.464466	−	0.464466i	−0.0299189	−	0.0299189i	−0.721908	+	0.691989i	$0.756735\pi$
$242$		0			0
$243$	−7.00000	−	7.00000i	−0.449050	−	0.449050i
$244$		0			0
$245$	−0.707107	+	0.707107i	−0.0451754	+	0.0451754i
$246$		0			0
$247$		−	0.242641i		−	0.0154389i
$248$		0			0
$249$	15.1421	−	15.1421i	0.959594	−	0.959594i
$250$		0			0
$251$	−21.8995			−1.38228			−0.691142	−	0.722719i	$-0.742892\pi$
$251$	−21.8995			−1.38228			−0.691142	+	0.722719i	$0.742892\pi$
$252$		0			0
$253$			0.828427i			0.0520828i
$254$		0			0
$255$	−5.65685	−	1.41421i	−0.354246	−	0.0885615i
$256$		0			0
$257$			16.3137i			1.01762i	0.860878	+	0.508811i	$0.169915\pi$
$257$			16.3137i			1.01762i	−0.860878	+	0.508811i	$0.830085\pi$
$258$		0			0
$259$	−4.65685			−0.289363
$260$		0			0
$261$	2.24264	−	2.24264i	0.138816	−	0.138816i
$262$		0			0
$263$		−	1.31371i		−	0.0810067i	−0.999179	−	0.0405034i	$-0.987104\pi$
$263$		−	1.31371i		−	0.0810067i	0.999179	−	0.0405034i	$-0.0128962\pi$
$264$		0			0
$265$	−5.82843	+	5.82843i	−0.358037	+	0.358037i
$266$		0			0
$267$	11.0711	+	11.0711i	0.677538	+	0.677538i
$268$		0			0
$269$	16.1213	+	16.1213i	0.982934	+	0.982934i	0.999857	−	0.0169226i	$-0.00538687\pi$
$269$	16.1213	+	16.1213i	0.982934	+	0.982934i	−0.0169226	+	0.999857i	$0.505387\pi$
$270$		0			0
$271$	−3.41421			−0.207399			−0.103699	−	0.994609i	$-0.533068\pi$
$271$	−3.41421			−0.207399			−0.103699	+	0.994609i	$0.533068\pi$
$272$		0			0
$273$	0.242641			0.0146853
$274$		0			0
$275$	0.585786	+	0.585786i	0.0353243	+	0.0353243i
$276$		0			0
$277$	−6.36396	−	6.36396i	−0.382373	−	0.382373i	0.489583	−	0.871957i	$-0.337149\pi$
$277$	−6.36396	−	6.36396i	−0.382373	−	0.382373i	−0.871957	+	0.489583i	$0.837149\pi$
$278$		0			0
$279$	−6.12132	+	6.12132i	−0.366474	+	0.366474i
$280$		0			0
$281$		−	4.65685i		−	0.277805i	−0.990306	−	0.138902i	$-0.955643\pi$
$281$		−	4.65685i		−	0.277805i	0.990306	−	0.138902i	$-0.0443574\pi$
$282$		0			0
$283$	9.72792	−	9.72792i	0.578265	−	0.578265i	−0.356160	−	0.934425i	$-0.615914\pi$
$283$	9.72792	−	9.72792i	0.578265	−	0.578265i	0.934425	+	0.356160i	$0.115914\pi$
$284$		0			0
$285$	2.00000			0.118470
$286$		0			0
$287$			3.82843i			0.225985i
$288$		0			0
$289$	−15.0000	−	8.00000i	−0.882353	−	0.470588i
$290$		0			0
$291$		−	25.7990i		−	1.51236i
$292$		0			0
$293$	3.65685			0.213636			0.106818	−	0.994279i	$-0.465934\pi$
$293$	3.65685			0.213636			0.106818	+	0.994279i	$0.465934\pi$
$294$		0			0
$295$	−2.24264	+	2.24264i	−0.130572	+	0.130572i
$296$		0			0
$297$		−	4.68629i		−	0.271926i
$298$		0			0
$299$	0.121320	−	0.121320i	0.00701614	−	0.00701614i
$300$		0			0
$301$	8.07107	+	8.07107i	0.465209	+	0.465209i
$302$		0			0
$303$	11.6569	+	11.6569i	0.669669	+	0.669669i
$304$		0			0
$305$	−6.17157			−0.353383
$306$		0			0
$307$	−32.1421			−1.83445			−0.917224	−	0.398371i	$-0.869576\pi$
$307$	−32.1421			−1.83445			−0.917224	+	0.398371i	$0.869576\pi$
$308$		0			0
$309$	10.0000	+	10.0000i	0.568880	+	0.568880i
$310$		0			0
$311$	−4.70711	−	4.70711i	−0.266916	−	0.266916i	0.560941	−	0.827856i	$-0.310440\pi$
$311$	−4.70711	−	4.70711i	−0.266916	−	0.266916i	−0.827856	+	0.560941i	$0.810440\pi$
$312$		0			0
$313$	8.92893	−	8.92893i	0.504693	−	0.504693i	−0.408200	−	0.912893i	$-0.633843\pi$
$313$	8.92893	−	8.92893i	0.504693	−	0.504693i	0.912893	+	0.408200i	$0.133843\pi$
$314$		0			0
$315$		−	1.00000i		−	0.0563436i
$316$		0			0
$317$	−15.0919	+	15.0919i	−0.847645	+	0.847645i	−0.989839	−	0.142194i	$-0.954584\pi$
$317$	−15.0919	+	15.0919i	−0.847645	+	0.847645i	0.142194	+	0.989839i	$0.454584\pi$
$318$		0			0
$319$	2.62742			0.147107
$320$		0			0
$321$		−	24.7279i		−	1.38018i
$322$		0			0
$323$	5.65685	+	1.41421i	0.314756	+	0.0786889i
$324$		0			0
$325$		−	0.171573i		−	0.00951715i
$326$		0			0
$327$	−11.6569			−0.644626
$328$		0			0
$329$	4.94975	−	4.94975i	0.272888	−	0.272888i
$330$		0			0
$331$		−	0.857864i		−	0.0471525i	−0.999722	−	0.0235762i	$-0.992495\pi$
$331$		−	0.857864i		−	0.0471525i	0.999722	−	0.0235762i	$-0.00750525\pi$
$332$		0			0
$333$	3.29289	−	3.29289i	0.180449	−	0.180449i
$334$		0			0
$335$	−0.242641	−	0.242641i	−0.0132569	−	0.0132569i
$336$		0			0
$337$	−9.89949	−	9.89949i	−0.539260	−	0.539260i	0.384052	−	0.923312i	$-0.374528\pi$
$337$	−9.89949	−	9.89949i	−0.539260	−	0.539260i	−0.923312	+	0.384052i	$0.874528\pi$
$338$		0			0
$339$	6.34315			0.344512
$340$		0			0
$341$	−7.17157			−0.388362
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$		0			0
$345$	1.00000	+	1.00000i	0.0538382	+	0.0538382i
$346$		0			0
$347$	−20.9706	+	20.9706i	−1.12576	+	1.12576i	−0.134900	+	0.990859i	$0.543071\pi$
$347$	−20.9706	+	20.9706i	−1.12576	+	1.12576i	−0.990859	+	0.134900i	$0.956929\pi$
$348$		0			0
$349$		−	23.6569i		−	1.26632i	−0.774020	−	0.633161i	$-0.781757\pi$
$349$		−	23.6569i		−	1.26632i	0.774020	−	0.633161i	$-0.218243\pi$
$350$		0			0
$351$	−0.686292	+	0.686292i	−0.0366315	+	0.0366315i
$352$		0			0
$353$	−26.7990			−1.42637			−0.713183	−	0.700978i	$-0.752747\pi$
$353$	−26.7990			−1.42637			−0.713183	+	0.700978i	$0.752747\pi$
$354$		0			0
$355$		−	2.82843i		−	0.150117i
$356$		0			0
$357$	−1.41421	+	5.65685i	−0.0748481	+	0.299392i
$358$		0			0
$359$			0.514719i			0.0271658i	0.999908	+	0.0135829i	$0.00432371\pi$
$359$			0.514719i			0.0271658i	−0.999908	+	0.0135829i	$0.995676\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$		0			0
$363$	−10.3137	+	10.3137i	−0.541329	+	0.541329i
$364$		0			0
$365$		−	17.0711i		−	0.893541i
$366$		0			0
$367$	−12.4142	+	12.4142i	−0.648017	+	0.648017i	−0.952513	−	0.304497i	$-0.901512\pi$
$367$	−12.4142	+	12.4142i	−0.648017	+	0.648017i	0.304497	+	0.952513i	$0.401512\pi$
$368$		0			0
$369$	−2.70711	−	2.70711i	−0.140926	−	0.140926i
$370$		0			0
$371$	5.82843	+	5.82843i	0.302597	+	0.302597i
$372$		0			0
$373$	15.7990			0.818041			0.409020	−	0.912525i	$-0.365871\pi$
$373$	15.7990			0.818041			0.409020	+	0.912525i	$0.365871\pi$
$374$		0			0
$375$	1.41421			0.0730297
$376$		0			0
$377$	−0.384776	−	0.384776i	−0.0198170	−	0.0198170i
$378$		0			0
$379$	12.7279	+	12.7279i	0.653789	+	0.653789i	0.953903	−	0.300114i	$-0.0970247\pi$
$379$	12.7279	+	12.7279i	0.653789	+	0.653789i	−0.300114	+	0.953903i	$0.597025\pi$
$380$		0			0
$381$	−6.34315	+	6.34315i	−0.324969	+	0.324969i
$382$		0			0
$383$			30.9706i			1.58252i	0.611479	+	0.791261i	$0.290575\pi$
$383$			30.9706i			1.58252i	−0.611479	+	0.791261i	$0.709425\pi$
$384$		0			0
$385$	0.585786	−	0.585786i	0.0298544	−	0.0298544i
$386$		0			0
$387$	−11.4142			−0.580217
$388$		0			0
$389$		−	17.4853i		−	0.886539i	−0.896388	−	0.443269i	$-0.853818\pi$
$389$		−	17.4853i		−	0.886539i	0.896388	−	0.443269i	$-0.146182\pi$
$390$		0			0
$391$	2.12132	+	3.53553i	0.107280	+	0.178800i
$392$		0			0
$393$			13.8995i			0.701137i
$394$		0			0
$395$	−4.58579			−0.230736
$396$		0			0
$397$	−5.72792	+	5.72792i	−0.287476	+	0.287476i	−0.836081	−	0.548605i	$-0.815159\pi$
$397$	−5.72792	+	5.72792i	−0.287476	+	0.287476i	0.548605	+	0.836081i	$0.315159\pi$
$398$		0			0
$399$		−	2.00000i		−	0.100125i
$400$		0			0
$401$	8.65685	−	8.65685i	0.432303	−	0.432303i	−0.457108	−	0.889411i	$-0.651115\pi$
$401$	8.65685	−	8.65685i	0.432303	−	0.432303i	0.889411	+	0.457108i	$0.151115\pi$
$402$		0			0
$403$	1.05025	+	1.05025i	0.0523168	+	0.0523168i
$404$		0			0
$405$	−3.53553	−	3.53553i	−0.175682	−	0.175682i
$406$		0			0
$407$	3.85786			0.191227
$408$		0			0
$409$	8.14214			0.402603			0.201301	−	0.979529i	$-0.435483\pi$
$409$	8.14214			0.402603			0.201301	+	0.979529i	$0.435483\pi$
$410$		0			0
$411$	15.4142	+	15.4142i	0.760327	+	0.760327i
$412$		0			0
$413$	2.24264	+	2.24264i	0.110353	+	0.110353i
$414$		0			0
$415$	−10.7071	+	10.7071i	−0.525591	+	0.525591i
$416$		0			0
$417$		−	7.79899i		−	0.381918i
$418$		0			0
$419$	25.9203	−	25.9203i	1.26629	−	1.26629i	0.318300	−	0.947990i	$-0.396888\pi$
$419$	25.9203	−	25.9203i	1.26629	−	1.26629i	0.947990	−	0.318300i	$-0.103112\pi$
$420$		0			0
$421$	−8.65685			−0.421909			−0.210955	−	0.977496i	$-0.567657\pi$
$421$	−8.65685			−0.421909			−0.210955	+	0.977496i	$0.567657\pi$
$422$		0			0
$423$			7.00000i			0.340352i
$424$		0			0
$425$	4.00000	+	1.00000i	0.194029	+	0.0485071i
$426$		0			0
$427$			6.17157i			0.298663i
$428$		0			0
$429$	−0.201010			−0.00970486
$430$		0			0
$431$	−20.3137	+	20.3137i	−0.978477	+	0.978477i	−0.999773	−	0.0212963i	$-0.993221\pi$
$431$	−20.3137	+	20.3137i	−0.978477	+	0.978477i	0.0212963	+	0.999773i	$0.493221\pi$
$432$		0			0
$433$		−	36.1127i		−	1.73547i	−0.497031	−	0.867733i	$-0.665576\pi$
$433$		−	36.1127i		−	1.73547i	0.497031	−	0.867733i	$-0.334424\pi$
$434$		0			0
$435$	3.17157	−	3.17157i	0.152065	−	0.152065i
$436$		0			0
$437$	−1.00000	−	1.00000i	−0.0478365	−	0.0478365i
$438$		0			0
$439$	11.8995	+	11.8995i	0.567932	+	0.567932i	0.931549	−	0.363617i	$-0.118458\pi$
$439$	11.8995	+	11.8995i	0.567932	+	0.567932i	−0.363617	+	0.931549i	$0.618458\pi$
$440$		0			0
$441$	−1.00000			−0.0476190
$442$		0			0
$443$	33.0711			1.57125			0.785627	−	0.618701i	$-0.212341\pi$
$443$	33.0711			1.57125			0.785627	+	0.618701i	$0.212341\pi$
$444$		0			0
$445$	−7.82843	−	7.82843i	−0.371103	−	0.371103i
$446$		0			0
$447$	−1.48528	−	1.48528i	−0.0702514	−	0.0702514i
$448$		0			0
$449$	1.72792	−	1.72792i	0.0815457	−	0.0815457i	−0.665157	−	0.746703i	$-0.731636\pi$
$449$	1.72792	−	1.72792i	0.0815457	−	0.0815457i	0.746703	+	0.665157i	$0.231636\pi$
$450$		0			0
$451$		−	3.17157i		−	0.149344i
$452$		0			0
$453$	−2.31371	+	2.31371i	−0.108708	+	0.108708i
$454$		0			0
$455$	−0.171573			−0.00804346
$456$		0			0
$457$		−	10.6863i		−	0.499884i	−0.968261	−	0.249942i	$-0.919589\pi$
$457$		−	10.6863i		−	0.499884i	0.968261	−	0.249942i	$-0.0804115\pi$
$458$		0			0
$459$	−12.0000	−	20.0000i	−0.560112	−	0.933520i
$460$		0			0
$461$			14.6863i			0.684009i	0.939698	+	0.342004i	$0.111106\pi$
$461$			14.6863i			0.684009i	−0.939698	+	0.342004i	$0.888894\pi$
$462$		0			0
$463$	−35.3137			−1.64117			−0.820584	−	0.571527i	$-0.806351\pi$
$463$	−35.3137			−1.64117			−0.820584	+	0.571527i	$0.806351\pi$
$464$		0			0
$465$	−8.65685	+	8.65685i	−0.401452	+	0.401452i
$466$		0			0
$467$		−	14.3137i		−	0.662359i	−0.943568	−	0.331180i	$-0.892553\pi$
$467$		−	14.3137i		−	0.662359i	0.943568	−	0.331180i	$-0.107447\pi$
$468$		0			0
$469$	−0.242641	+	0.242641i	−0.0112041	+	0.0112041i
$470$		0			0
$471$	−22.1421	−	22.1421i	−1.02026	−	1.02026i
$472$		0			0
$473$	−6.68629	−	6.68629i	−0.307436	−	0.307436i
$474$		0			0
$475$	−1.41421			−0.0648886
$476$		0			0
$477$	−8.24264			−0.377405
$478$		0			0
$479$	6.70711	+	6.70711i	0.306456	+	0.306456i	0.843533	−	0.537077i	$-0.180472\pi$
$479$	6.70711	+	6.70711i	0.306456	+	0.306456i	−0.537077	+	0.843533i	$0.680472\pi$
$480$		0			0
$481$	−0.564971	−	0.564971i	−0.0257605	−	0.0257605i
$482$		0			0
$483$	1.00000	−	1.00000i	0.0455016	−	0.0455016i
$484$		0			0
$485$			18.2426i			0.828356i
$486$		0			0
$487$	1.29289	−	1.29289i	0.0585866	−	0.0585866i	−0.677206	−	0.735793i	$-0.736810\pi$
$487$	1.29289	−	1.29289i	0.0585866	−	0.0585866i	0.735793	+	0.677206i	$0.236810\pi$
$488$		0			0
$489$	−13.4142			−0.606612
$490$		0			0
$491$			38.5980i			1.74190i	0.491369	+	0.870951i	$0.336496\pi$
$491$			38.5980i			1.74190i	−0.491369	+	0.870951i	$0.663504\pi$
$492$		0			0
$493$	11.2132	−	6.72792i	0.505017	−	0.303010i
$494$		0			0
$495$			0.828427i			0.0372350i
$496$		0			0
$497$	−2.82843			−0.126872
$498$		0			0
$499$	−10.7574	+	10.7574i	−0.481566	+	0.481566i	−0.905631	−	0.424066i	$-0.860603\pi$
$499$	−10.7574	+	10.7574i	−0.481566	+	0.481566i	0.424066	+	0.905631i	$0.360603\pi$
$500$		0			0
$501$		−	0.828427i		−	0.0370114i
$502$		0			0
$503$	19.0711	−	19.0711i	0.850337	−	0.850337i	−0.139838	−	0.990174i	$-0.544658\pi$
$503$	19.0711	−	19.0711i	0.850337	−	0.850337i	0.990174	+	0.139838i	$0.0446580\pi$
$504$		0			0
$505$	−8.24264	−	8.24264i	−0.366793	−	0.366793i
$506$		0			0
$507$	−12.9706	−	12.9706i	−0.576043	−	0.576043i
$508$		0			0
$509$	2.14214			0.0949485			0.0474742	−	0.998872i	$-0.484883\pi$
$509$	2.14214			0.0949485			0.0474742	+	0.998872i	$0.484883\pi$
$510$		0			0
$511$	−17.0711			−0.755180
$512$		0			0
$513$	5.65685	+	5.65685i	0.249756	+	0.249756i
$514$		0			0
$515$	−7.07107	−	7.07107i	−0.311588	−	0.311588i
$516$		0			0
$517$	−4.10051	+	4.10051i	−0.180340	+	0.180340i
$518$		0			0
$519$			28.6274i			1.25660i
$520$		0			0
$521$	24.0000	−	24.0000i	1.05146	−	1.05146i	0.0528570	−	0.998602i	$-0.483167\pi$
$521$	24.0000	−	24.0000i	1.05146	−	1.05146i	0.998602	−	0.0528570i	$-0.0168327\pi$
$522$		0			0
$523$	−44.6569			−1.95271			−0.976354	−	0.216178i	$-0.930641\pi$
$523$	−44.6569			−1.95271			−0.976354	+	0.216178i	$0.930641\pi$
$524$		0			0
$525$		−	1.41421i		−	0.0617213i
$526$		0			0
$527$	−30.6066	+	18.3640i	−1.33324	+	0.799947i
$528$		0			0
$529$			22.0000i			0.956522i
$530$		0			0
$531$	−3.17157			−0.137635
$532$		0			0
$533$	−0.464466	+	0.464466i	−0.0201183	+	0.0201183i
$534$		0			0
$535$			17.4853i			0.755955i
$536$		0			0
$537$	−9.82843	+	9.82843i	−0.424128	+	0.424128i
$538$		0			0
$539$	−0.585786	−	0.585786i	−0.0252316	−	0.0252316i
$540$		0			0
$541$	−23.8995	−	23.8995i	−1.02752	−	1.02752i	−0.999610	−	0.0279091i	$-0.991115\pi$
$541$	−23.8995	−	23.8995i	−1.02752	−	1.02752i	−0.0279091	−	0.999610i	$-0.508885\pi$
$542$		0			0
$543$	30.3848			1.30394
$544$		0			0
$545$	8.24264			0.353076
$546$		0			0
$547$	12.8492	+	12.8492i	0.549394	+	0.549394i	0.926266	−	0.376872i	$-0.123000\pi$
$547$	12.8492	+	12.8492i	0.549394	+	0.549394i	−0.376872	+	0.926266i	$0.623000\pi$
$548$		0			0
$549$	−4.36396	−	4.36396i	−0.186249	−	0.186249i
$550$		0			0
$551$	−3.17157	+	3.17157i	−0.135114	+	0.135114i
$552$		0			0
$553$			4.58579i			0.195007i
$554$		0			0
$555$	4.65685	−	4.65685i	0.197672	−	0.197672i
$556$		0			0
$557$	−19.0711			−0.808067			−0.404034	−	0.914744i	$-0.632392\pi$
$557$	−19.0711			−0.808067			−0.404034	+	0.914744i	$0.632392\pi$
$558$		0			0
$559$			1.95837i			0.0828302i
$560$		0			0
$561$	1.17157	−	4.68629i	0.0494638	−	0.197855i
$562$		0			0
$563$			43.4853i			1.83269i	0.400394	+	0.916343i	$0.368873\pi$
$563$			43.4853i			1.83269i	−0.400394	+	0.916343i	$0.631127\pi$
$564$		0			0
$565$	−4.48528			−0.188697
$566$		0			0
$567$	−3.53553	+	3.53553i	−0.148478	+	0.148478i
$568$		0			0
$569$			43.2843i			1.81457i	0.420515	+	0.907286i	$0.361849\pi$
$569$			43.2843i			1.81457i	−0.420515	+	0.907286i	$0.638151\pi$
$570$		0			0
$571$	−21.0000	+	21.0000i	−0.878823	+	0.878823i	−0.993413	−	0.114590i	$-0.963445\pi$
$571$	−21.0000	+	21.0000i	−0.878823	+	0.878823i	0.114590	+	0.993413i	$0.463445\pi$
$572$		0			0
$573$	−4.31371	−	4.31371i	−0.180208	−	0.180208i
$574$		0			0
$575$	−0.707107	−	0.707107i	−0.0294884	−	0.0294884i
$576$		0			0
$577$	−24.9706			−1.03954			−0.519769	−	0.854307i	$-0.673982\pi$
$577$	−24.9706			−1.03954			−0.519769	+	0.854307i	$0.673982\pi$
$578$		0			0
$579$	4.72792			0.196486
$580$		0			0
$581$	10.7071	+	10.7071i	0.444206	+	0.444206i
$582$		0			0
$583$	−4.82843	−	4.82843i	−0.199973	−	0.199973i
$584$		0			0
$585$	0.121320	−	0.121320i	0.00501598	−	0.00501598i
$586$		0			0
$587$		−	16.1421i		−	0.666257i	−0.942881	−	0.333129i	$-0.891896\pi$
$587$		−	16.1421i		−	0.666257i	0.942881	−	0.333129i	$-0.108104\pi$
$588$		0			0
$589$	8.65685	−	8.65685i	0.356699	−	0.356699i
$590$		0			0
$591$	−12.9706			−0.533538
$592$		0			0
$593$		−	4.79899i		−	0.197071i	−0.995134	−	0.0985354i	$-0.968584\pi$
$593$		−	4.79899i		−	0.197071i	0.995134	−	0.0985354i	$-0.0314158\pi$
$594$		0			0
$595$	1.00000	−	4.00000i	0.0409960	−	0.163984i
$596$		0			0
$597$		−	1.17157i		−	0.0479493i
$598$		0			0
$599$	15.3137			0.625701			0.312851	−	0.949802i	$-0.398716\pi$
$599$	15.3137			0.625701			0.312851	+	0.949802i	$0.398716\pi$
$600$		0			0
$601$	9.89949	−	9.89949i	0.403809	−	0.403809i	−0.475764	−	0.879573i	$-0.657828\pi$
$601$	9.89949	−	9.89949i	0.403809	−	0.403809i	0.879573	+	0.475764i	$0.157828\pi$
$602$		0			0
$603$		−	0.343146i		−	0.0139740i
$604$		0			0
$605$	7.29289	−	7.29289i	0.296498	−	0.296498i
$606$		0			0
$607$	8.68629	+	8.68629i	0.352566	+	0.352566i	0.861063	−	0.508498i	$-0.169799\pi$
$607$	8.68629	+	8.68629i	0.352566	+	0.352566i	−0.508498	+	0.861063i	$0.669799\pi$
$608$		0			0
$609$	−3.17157	−	3.17157i	−0.128519	−	0.128519i
$610$		0			0
$611$	1.20101			0.0485877
$612$		0			0
$613$	−25.3553			−1.02409			−0.512046	−	0.858958i	$-0.671112\pi$
$613$	−25.3553			−1.02409			−0.512046	+	0.858958i	$0.671112\pi$
$614$		0			0
$615$	−3.82843	−	3.82843i	−0.154377	−	0.154377i
$616$		0			0
$617$	−4.70711	−	4.70711i	−0.189501	−	0.189501i	0.605979	−	0.795480i	$-0.292781\pi$
$617$	−4.70711	−	4.70711i	−0.189501	−	0.189501i	−0.795480	+	0.605979i	$0.792781\pi$
$618$		0			0
$619$	23.5563	−	23.5563i	0.946810	−	0.946810i	−0.0518455	−	0.998655i	$-0.516510\pi$
$619$	23.5563	−	23.5563i	0.946810	−	0.946810i	0.998655	+	0.0518455i	$0.0165103\pi$
$620$		0			0
$621$			5.65685i			0.227002i
$622$		0			0
$623$	−7.82843	+	7.82843i	−0.313639	+	0.313639i
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$			1.65685i			0.0661684i
$628$		0			0
$629$	16.4645	−	9.87868i	0.656481	−	0.393889i
$630$		0			0
$631$			42.4853i			1.69131i	0.533728	+	0.845656i	$0.320791\pi$
$631$			42.4853i			1.69131i	−0.533728	+	0.845656i	$0.679209\pi$
$632$		0			0
$633$	−5.17157			−0.205552
$634$		0			0
$635$	4.48528	−	4.48528i	0.177993	−	0.177993i
$636$		0			0
$637$			0.171573i			0.00679796i
$638$		0			0
$639$	2.00000	−	2.00000i	0.0791188	−	0.0791188i
$640$		0			0
$641$	25.0711	+	25.0711i	0.990248	+	0.990248i	0.999953	−	0.00970526i	$-0.00308933\pi$
$641$	25.0711	+	25.0711i	0.990248	+	0.990248i	−0.00970526	+	0.999953i	$0.503089\pi$
$642$		0			0
$643$	15.3137	+	15.3137i	0.603914	+	0.603914i	0.941349	−	0.337435i	$-0.109559\pi$
$643$	15.3137	+	15.3137i	0.603914	+	0.603914i	−0.337435	+	0.941349i	$0.609559\pi$
$644$		0			0
$645$	−16.1421			−0.635596
$646$		0			0
$647$	5.02944			0.197728			0.0988638	−	0.995101i	$-0.468479\pi$
$647$	5.02944			0.197728			0.0988638	+	0.995101i	$0.468479\pi$
$648$		0			0
$649$	−1.85786	−	1.85786i	−0.0729276	−	0.0729276i
$650$		0			0
$651$	8.65685	+	8.65685i	0.339289	+	0.339289i
$652$		0			0
$653$	−25.4350	+	25.4350i	−0.995350	+	0.995350i	−0.999989	−	0.00463964i	$-0.998523\pi$
$653$	−25.4350	+	25.4350i	−0.995350	+	0.995350i	0.00463964	+	0.999989i	$0.498523\pi$
$654$		0			0
$655$		−	9.82843i		−	0.384028i
$656$		0			0
$657$	12.0711	−	12.0711i	0.470937	−	0.470937i
$658$		0			0
$659$	−6.20101			−0.241557			−0.120779	−	0.992679i	$-0.538539\pi$
$659$	−6.20101			−0.241557			−0.120779	+	0.992679i	$0.538539\pi$
$660$		0			0
$661$		−	7.02944i		−	0.273413i	−0.990612	−	0.136707i	$-0.956348\pi$
$661$		−	7.02944i		−	0.273413i	0.990612	−	0.136707i	$-0.0436518\pi$
$662$		0			0
$663$	−0.857864	+	0.514719i	−0.0333167	+	0.0199900i
$664$		0			0
$665$			1.41421i			0.0548408i
$666$		0			0
$667$	−3.17157			−0.122804
$668$		0			0
$669$	15.8284	−	15.8284i	0.611962	−	0.611962i
$670$		0			0
$671$		−	5.11270i		−	0.197374i
$672$		0			0
$673$	11.3934	−	11.3934i	0.439183	−	0.439183i	−0.452554	−	0.891737i	$-0.649487\pi$
$673$	11.3934	−	11.3934i	0.439183	−	0.439183i	0.891737	+	0.452554i	$0.149487\pi$
$674$		0			0
$675$	4.00000	+	4.00000i	0.153960	+	0.153960i
$676$		0			0
$677$	6.34315	+	6.34315i	0.243787	+	0.243787i	0.818415	−	0.574628i	$-0.194853\pi$
$677$	6.34315	+	6.34315i	0.243787	+	0.243787i	−0.574628	+	0.818415i	$0.694853\pi$
$678$		0			0
$679$	18.2426			0.700088
$680$		0			0
$681$	21.4558			0.822190
$682$		0			0
$683$	−1.75736	−	1.75736i	−0.0672435	−	0.0672435i	0.672685	−	0.739929i	$-0.265141\pi$
$683$	−1.75736	−	1.75736i	−0.0672435	−	0.0672435i	−0.739929	+	0.672685i	$0.765141\pi$
$684$		0			0
$685$	−10.8995	−	10.8995i	−0.416448	−	0.416448i
$686$		0			0
$687$	−16.3848	+	16.3848i	−0.625118	+	0.625118i
$688$		0			0
$689$			1.41421i			0.0538772i
$690$		0			0
$691$	−25.9203	+	25.9203i	−0.986055	+	0.986055i	−0.999904	−	0.0138490i	$-0.995592\pi$
$691$	−25.9203	+	25.9203i	−0.986055	+	0.986055i	0.0138490	+	0.999904i	$0.495592\pi$
$692$		0			0
$693$	0.828427			0.0314693
$694$		0			0
$695$			5.51472i			0.209185i
$696$		0			0
$697$	−8.12132	−	13.5355i	−0.307617	−	0.512695i
$698$		0			0
$699$			1.61522i			0.0610934i
$700$		0			0
$701$	26.4558			0.999223			0.499612	−	0.866249i	$-0.333476\pi$
$701$	26.4558			0.999223			0.499612	+	0.866249i	$0.333476\pi$
$702$		0			0
$703$	−4.65685	+	4.65685i	−0.175637	+	0.175637i
$704$		0			0
$705$			9.89949i			0.372837i
$706$		0			0
$707$	−8.24264	+	8.24264i	−0.309996	+	0.309996i
$708$		0			0
$709$	29.9706	+	29.9706i	1.12557	+	1.12557i	0.990889	+	0.134679i	$0.0430003\pi$
$709$	29.9706	+	29.9706i	1.12557	+	1.12557i	0.134679	+	0.990889i	$0.457000\pi$
$710$		0			0
$711$	−3.24264	−	3.24264i	−0.121609	−	0.121609i
$712$		0			0
$713$	8.65685			0.324202
$714$		0			0
$715$	0.142136			0.00531557
$716$		0			0
$717$	7.82843	+	7.82843i	0.292358	+	0.292358i
$718$		0			0
$719$	−14.8492	−	14.8492i	−0.553783	−	0.553783i	0.373747	−	0.927531i	$-0.378073\pi$
$719$	−14.8492	−	14.8492i	−0.553783	−	0.553783i	−0.927531	+	0.373747i	$0.878073\pi$
$720$		0			0
$721$	−7.07107	+	7.07107i	−0.263340	+	0.263340i
$722$		0			0
$723$		−	0.928932i		−	0.0345474i
$724$		0			0
$725$	−2.24264	+	2.24264i	−0.0832896	+	0.0832896i
$726$		0			0
$727$	−24.4558			−0.907017			−0.453509	−	0.891252i	$-0.649828\pi$
$727$	−24.4558			−0.907017			−0.453509	+	0.891252i	$0.649828\pi$
$728$		0			0
$729$		−	29.0000i		−	1.07407i
$730$		0			0
$731$	−45.6569	−	11.4142i	−1.68868	−	0.422170i
$732$		0			0
$733$			23.3431i			0.862199i	0.902304	+	0.431099i	$0.141874\pi$
$733$			23.3431i			0.862199i	−0.902304	+	0.431099i	$0.858126\pi$
$734$		0			0
$735$	−1.41421			−0.0521641
$736$		0			0
$737$	0.201010	−	0.201010i	0.00740430	−	0.00740430i
$738$		0			0
$739$		−	24.2843i		−	0.893311i	−0.894706	−	0.446656i	$-0.852615\pi$
$739$		−	24.2843i		−	0.893311i	0.894706	−	0.446656i	$-0.147385\pi$
$740$		0			0
$741$	0.242641	−	0.242641i	0.00891363	−	0.00891363i
$742$		0			0
$743$	23.0919	+	23.0919i	0.847159	+	0.847159i	0.989778	−	0.142619i	$-0.0455523\pi$
$743$	23.0919	+	23.0919i	0.847159	+	0.847159i	−0.142619	+	0.989778i	$0.545552\pi$
$744$		0			0
$745$	1.05025	+	1.05025i	0.0384783	+	0.0384783i
$746$		0			0
$747$	−15.1421			−0.554022
$748$		0			0
$749$	17.4853			0.638898
$750$		0			0
$751$	31.0416	+	31.0416i	1.13273	+	1.13273i	0.989722	+	0.143003i	$0.0456758\pi$
$751$	31.0416	+	31.0416i	1.13273	+	1.13273i	0.143003	+	0.989722i	$0.454324\pi$
$752$		0			0
$753$	−21.8995	−	21.8995i	−0.798062	−	0.798062i
$754$		0			0
$755$	1.63604	−	1.63604i	0.0595416	−	0.0595416i
$756$		0			0
$757$			51.9411i			1.88783i	0.330185	+	0.943916i	$0.392889\pi$
$757$			51.9411i			1.88783i	−0.330185	+	0.943916i	$0.607111\pi$
$758$		0			0
$759$	−0.828427	+	0.828427i	−0.0300700	+	0.0300700i
$760$		0			0
$761$	41.4558			1.50277			0.751387	−	0.659862i	$-0.229385\pi$
$761$	41.4558			1.50277			0.751387	+	0.659862i	$0.229385\pi$
$762$		0			0
$763$		−	8.24264i		−	0.298404i
$764$		0			0
$765$	2.12132	+	3.53553i	0.0766965	+	0.127827i
$766$		0			0
$767$			0.544156i			0.0196483i
$768$		0			0
$769$	4.72792			0.170493			0.0852466	−	0.996360i	$-0.472832\pi$
$769$	4.72792			0.170493			0.0852466	+	0.996360i	$0.472832\pi$
$770$		0			0
$771$	−16.3137	+	16.3137i	−0.587524	+	0.587524i
$772$		0			0
$773$			49.2843i			1.77263i	0.463081	+	0.886316i	$0.346744\pi$
$773$			49.2843i			1.77263i	−0.463081	+	0.886316i	$0.653256\pi$
$774$		0			0
$775$	6.12132	−	6.12132i	0.219884	−	0.219884i
$776$		0			0
$777$	−4.65685	−	4.65685i	−0.167064	−	0.167064i
$778$		0			0
$779$	3.82843	+	3.82843i	0.137168	+	0.137168i
$780$		0			0
$781$	2.34315			0.0838443
$782$		0			0
$783$	17.9411			0.641164
$784$		0			0
$785$	15.6569	+	15.6569i	0.558817	+	0.558817i
$786$		0			0
$787$	−12.0711	−	12.0711i	−0.430287	−	0.430287i	0.458439	−	0.888726i	$-0.348409\pi$
$787$	−12.0711	−	12.0711i	−0.430287	−	0.430287i	−0.888726	+	0.458439i	$0.848409\pi$
$788$		0			0
$789$	1.31371	−	1.31371i	0.0467693	−	0.0467693i
$790$		0			0
$791$			4.48528i			0.159478i
$792$		0			0
$793$	−0.748737	+	0.748737i	−0.0265884	+	0.0265884i
$794$		0			0
$795$	−11.6569			−0.413426
$796$		0			0
$797$			27.7696i			0.983648i	0.870695	+	0.491824i	$0.163670\pi$
$797$			27.7696i			0.983648i	−0.870695	+	0.491824i	$0.836330\pi$
$798$		0			0
$799$	−7.00000	+	28.0000i	−0.247642	+	0.990569i
$800$		0			0
$801$		−	11.0711i		−	0.391177i
$802$		0			0
$803$	14.1421			0.499065
$804$		0			0
$805$	−0.707107	+	0.707107i	−0.0249222	+	0.0249222i
$806$		0			0
$807$			32.2426i			1.13499i
$808$		0			0
$809$	20.0000	−	20.0000i	0.703163	−	0.703163i	−0.261926	−	0.965088i	$-0.584357\pi$
$809$	20.0000	−	20.0000i	0.703163	−	0.703163i	0.965088	+	0.261926i	$0.0843575\pi$
$810$		0			0
$811$	0.807612	+	0.807612i	0.0283591	+	0.0283591i	0.721144	−	0.692785i	$-0.243617\pi$
$811$	0.807612	+	0.807612i	0.0283591	+	0.0283591i	−0.692785	+	0.721144i	$0.743617\pi$
$812$		0			0
$813$	−3.41421	−	3.41421i	−0.119742	−	0.119742i
$814$		0			0
$815$	9.48528			0.332255
$816$		0			0
$817$	16.1421			0.564742
$818$		0			0
$819$	−0.121320	−	0.121320i	−0.00423928	−	0.00423928i
$820$		0			0
$821$	23.1421	+	23.1421i	0.807666	+	0.807666i	0.984280	−	0.176614i	$-0.0565145\pi$
$821$	23.1421	+	23.1421i	0.807666	+	0.807666i	−0.176614	+	0.984280i	$0.556514\pi$
$822$		0			0
$823$	14.6066	−	14.6066i	0.509154	−	0.509154i	−0.405113	−	0.914267i	$-0.632768\pi$
$823$	14.6066	−	14.6066i	0.509154	−	0.509154i	0.914267	+	0.405113i	$0.132768\pi$
$824$		0			0
$825$			1.17157i			0.0407889i
$826$		0			0
$827$	−10.1213	+	10.1213i	−0.351953	+	0.351953i	−0.860836	−	0.508883i	$-0.830059\pi$
$827$	−10.1213	+	10.1213i	−0.351953	+	0.351953i	0.508883	+	0.860836i	$0.330059\pi$
$828$		0			0
$829$	5.65685			0.196471			0.0982353	−	0.995163i	$-0.468680\pi$
$829$	5.65685			0.196471			0.0982353	+	0.995163i	$0.468680\pi$
$830$		0			0
$831$		−	12.7279i		−	0.441527i
$832$		0			0
$833$	−4.00000	−	1.00000i	−0.138592	−	0.0346479i
$834$		0			0
$835$			0.585786i			0.0202720i
$836$		0			0
$837$	−48.9706			−1.69267
$838$		0			0
$839$	−35.0711	+	35.0711i	−1.21079	+	1.21079i	−0.240020	+	0.970768i	$0.577154\pi$
$839$	−35.0711	+	35.0711i	−1.21079	+	1.21079i	−0.970768	+	0.240020i	$0.922846\pi$
$840$		0			0
$841$		−	18.9411i		−	0.653142i
$842$		0			0
$843$	4.65685	−	4.65685i	0.160391	−	0.160391i
$844$		0			0
$845$	9.17157	+	9.17157i	0.315512	+	0.315512i
$846$		0			0
$847$	−7.29289	−	7.29289i	−0.250587	−	0.250587i
$848$		0			0
$849$	19.4558			0.667723
$850$		0			0
$851$	−4.65685			−0.159635
$852$		0			0
$853$	−37.7990	−	37.7990i	−1.29421	−	1.29421i	−0.932156	−	0.362057i	$-0.882075\pi$
$853$	−37.7990	−	37.7990i	−1.29421	−	1.29421i	−0.362057	−	0.932156i	$-0.617925\pi$
$854$		0			0
$855$	−1.00000	−	1.00000i	−0.0341993	−	0.0341993i
$856$		0			0
$857$	11.5563	−	11.5563i	0.394757	−	0.394757i	−0.481622	−	0.876379i	$-0.659952\pi$
$857$	11.5563	−	11.5563i	0.394757	−	0.394757i	0.876379	+	0.481622i	$0.159952\pi$
$858$		0			0
$859$		−	25.9411i		−	0.885100i	−0.896744	−	0.442550i	$-0.854074\pi$
$859$		−	25.9411i		−	0.885100i	0.896744	−	0.442550i	$-0.145926\pi$
$860$		0			0
$861$	−3.82843	+	3.82843i	−0.130472	+	0.130472i
$862$		0			0
$863$	18.9706			0.645765			0.322883	−	0.946439i	$-0.395348\pi$
$863$	18.9706			0.645765			0.322883	+	0.946439i	$0.395348\pi$
$864$		0			0
$865$		−	20.2426i		−	0.688270i
$866$		0			0
$867$	−7.00000	−	23.0000i	−0.237732	−	0.781121i
$868$		0			0
$869$		−	3.79899i		−	0.128872i
$870$		0			0
$871$	−0.0588745			−0.00199489
$872$		0			0
$873$	−12.8995	+	12.8995i	−0.436582	+	0.436582i
$874$		0			0
$875$			1.00000i			0.0338062i
$876$		0			0
$877$	10.4853	−	10.4853i	0.354063	−	0.354063i	−0.507556	−	0.861619i	$-0.669451\pi$
$877$	10.4853	−	10.4853i	0.354063	−	0.354063i	0.861619	+	0.507556i	$0.169451\pi$
$878$		0			0
$879$	3.65685	+	3.65685i	0.123343	+	0.123343i
$880$		0			0
$881$	−4.82843	−	4.82843i	−0.162674	−	0.162674i	0.621076	−	0.783750i	$-0.286696\pi$
$881$	−4.82843	−	4.82843i	−0.162674	−	0.162674i	−0.783750	+	0.621076i	$0.786696\pi$
$882$		0			0
$883$	35.9411			1.20952			0.604758	−	0.796410i	$-0.293270\pi$
$883$	35.9411			1.20952			0.604758	+	0.796410i	$0.293270\pi$
$884$		0			0
$885$	−4.48528			−0.150771
$886$		0			0
$887$	−22.1421	−	22.1421i	−0.743460	−	0.743460i	0.229782	−	0.973242i	$-0.426199\pi$
$887$	−22.1421	−	22.1421i	−0.743460	−	0.743460i	−0.973242	+	0.229782i	$0.926199\pi$
$888$		0			0
$889$	−4.48528	−	4.48528i	−0.150432	−	0.150432i
$890$		0			0
$891$	2.92893	−	2.92893i	0.0981229	−	0.0981229i
$892$		0			0
$893$		−	9.89949i		−	0.331274i
$894$		0			0
$895$	6.94975	−	6.94975i	0.232304	−	0.232304i
$896$		0			0
$897$	0.242641			0.00810154
$898$		0			0
$899$		−	27.4558i		−	0.915704i
$900$		0			0
$901$	−32.9706	−	8.24264i	−1.09841	−	0.274602i
$902$		0			0
$903$			16.1421i			0.537177i
$904$		0			0
$905$	−21.4853			−0.714195
$906$		0			0
$907$	−12.2426	+	12.2426i	−0.406510	+	0.406510i	−0.880520	−	0.474010i	$-0.842806\pi$
$907$	−12.2426	+	12.2426i	−0.406510	+	0.406510i	0.474010	+	0.880520i	$0.342806\pi$
$908$		0			0
$909$		−	11.6569i		−	0.386633i
$910$		0			0
$911$	17.1005	−	17.1005i	0.566565	−	0.566565i	−0.364599	−	0.931164i	$-0.618794\pi$
$911$	17.1005	−	17.1005i	0.566565	−	0.566565i	0.931164	+	0.364599i	$0.118794\pi$
$912$		0			0
$913$	−8.87006	−	8.87006i	−0.293556	−	0.293556i
$914$		0			0
$915$	−6.17157	−	6.17157i	−0.204026	−	0.204026i
$916$		0			0
$917$	−9.82843			−0.324563
$918$		0			0
$919$	−7.17157			−0.236568			−0.118284	−	0.992980i	$-0.537739\pi$
$919$	−7.17157			−0.236568			−0.118284	+	0.992980i	$0.537739\pi$
$920$		0			0
$921$	−32.1421	−	32.1421i	−1.05912	−	1.05912i
$922$		0			0
$923$	−0.343146	−	0.343146i	−0.0112948	−	0.0112948i
$924$		0			0
$925$	−3.29289	+	3.29289i	−0.108270	+	0.108270i
$926$		0			0
$927$		−	10.0000i		−	0.328443i
$928$		0			0
$929$	41.5355	−	41.5355i	1.36274	−	1.36274i	0.492325	−	0.870411i	$-0.336147\pi$
$929$	41.5355	−	41.5355i	1.36274	−	1.36274i	0.870411	−	0.492325i	$-0.163853\pi$
$930$		0			0
$931$	1.41421			0.0463490
$932$		0			0
$933$		−	9.41421i		−	0.308208i
$934$		0			0
$935$	−0.828427	+	3.31371i	−0.0270925	+	0.108370i
$936$		0			0
$937$		−	8.31371i		−	0.271597i	−0.990736	−	0.135799i	$-0.956640\pi$
$937$		−	8.31371i		−	0.271597i	0.990736	−	0.135799i	$-0.0433600\pi$
$938$		0			0
$939$	17.8579			0.582769
$940$		0			0
$941$	6.70711	−	6.70711i	0.218645	−	0.218645i	−0.589282	−	0.807927i	$-0.700589\pi$
$941$	6.70711	−	6.70711i	0.218645	−	0.218645i	0.807927	+	0.589282i	$0.200589\pi$
$942$		0			0
$943$			3.82843i			0.124671i
$944$		0			0
$945$	4.00000	−	4.00000i	0.130120	−	0.130120i
$946$		0			0
$947$	26.7487	+	26.7487i	0.869217	+	0.869217i	0.992386	−	0.123169i	$-0.0393056\pi$
$947$	26.7487	+	26.7487i	0.869217	+	0.869217i	−0.123169	+	0.992386i	$0.539306\pi$
$948$		0			0
$949$	−2.07107	−	2.07107i	−0.0672297	−	0.0672297i
$950$		0			0
$951$	−30.1838			−0.978776
$952$		0			0
$953$	12.4437			0.403089			0.201545	−	0.979479i	$-0.435404\pi$
$953$	12.4437			0.403089			0.201545	+	0.979479i	$0.435404\pi$
$954$		0			0
$955$	3.05025	+	3.05025i	0.0987039	+	0.0987039i
$956$		0			0
$957$	2.62742	+	2.62742i	0.0849323	+	0.0849323i
$958$		0			0
$959$	−10.8995	+	10.8995i	−0.351963	+	0.351963i
$960$		0			0
$961$			43.9411i			1.41746i
$962$		0			0
$963$	−12.3640	+	12.3640i	−0.398423	+	0.398423i
$964$		0			0
$965$	−3.34315			−0.107620
$966$		0			0
$967$		−	11.5147i		−	0.370288i	−0.982711	−	0.185144i	$-0.940725\pi$
$967$		−	11.5147i		−	0.370288i	0.982711	−	0.185144i	$-0.0592752\pi$
$968$		0			0
$969$	4.24264	+	7.07107i	0.136293	+	0.227155i
$970$		0			0
$971$			9.55635i			0.306678i	0.988174	+	0.153339i	$0.0490026\pi$
$971$			9.55635i			0.306678i	−0.988174	+	0.153339i	$0.950997\pi$
$972$		0			0
$973$	5.51472			0.176794
$974$		0			0
$975$	0.171573	−	0.171573i	0.00549473	−	0.00549473i
$976$		0			0
$977$		−	10.8284i		−	0.346432i	−0.984884	−	0.173216i	$-0.944584\pi$
$977$		−	10.8284i		−	0.346432i	0.984884	−	0.173216i	$-0.0554159\pi$
$978$		0			0
$979$	6.48528	−	6.48528i	0.207270	−	0.207270i
$980$		0			0
$981$	5.82843	+	5.82843i	0.186087	+	0.186087i
$982$		0			0
$983$	−0.313708	−	0.313708i	−0.0100057	−	0.0100057i	0.702086	−	0.712092i	$-0.252252\pi$
$983$	−0.313708	−	0.313708i	−0.0100057	−	0.0100057i	−0.712092	+	0.702086i	$0.752252\pi$
$984$		0			0
$985$	9.17157			0.292231
$986$		0			0
$987$	9.89949			0.315104
$988$		0			0
$989$	8.07107	+	8.07107i	0.256645	+	0.256645i
$990$		0			0
$991$	18.6985	+	18.6985i	0.593977	+	0.593977i	0.938703	−	0.344726i	$-0.112028\pi$
$991$	18.6985	+	18.6985i	0.593977	+	0.593977i	−0.344726	+	0.938703i	$0.612028\pi$
$992$		0			0
$993$	0.857864	−	0.857864i	0.0272235	−	0.0272235i
$994$		0			0
$995$			0.828427i			0.0262629i
$996$		0			0
$997$	28.1421	−	28.1421i	0.891270	−	0.891270i	−0.103372	−	0.994643i	$-0.532963\pi$
$997$	28.1421	−	28.1421i	0.891270	−	0.891270i	0.994643	+	0.103372i	$0.0329633\pi$
$998$		0			0
$999$	26.3431			0.833460

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2380.2.be.a.421.1	✓	4
17.4	even	4	inner	2380.2.be.a.701.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2380.2.be.a.421.1	✓	4	1.1	even	1	trivial
2380.2.be.a.701.1	yes	4	17.4	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:	\( N \)	\(=\)	\( 2380 = 2^{2} \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2380.be (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{3} +(-0.707107 - 0.707107i) q^{5} +(-0.707107 + 0.707107i) q^{7} -1.00000i q^{9} +(0.585786 - 0.585786i) q^{11} -0.171573 q^{13} -1.41421i q^{15} +(1.00000 - 4.00000i) q^{17} +1.41421i q^{19} -1.41421 q^{21} +(-0.707107 + 0.707107i) q^{23} +1.00000i q^{25} +(4.00000 - 4.00000i) q^{27} +(2.24264 + 2.24264i) q^{29} +(-6.12132 - 6.12132i) q^{31} +1.17157 q^{33} +1.00000 q^{35} +(3.29289 + 3.29289i) q^{37} +(-0.171573 - 0.171573i) q^{39} +(2.70711 - 2.70711i) q^{41} -11.4142i q^{43} +(-0.707107 + 0.707107i) q^{45} -7.00000 q^{47} -1.00000i q^{49} +(5.00000 - 3.00000i) q^{51} -8.24264i q^{53} -0.828427 q^{55} +(-1.41421 + 1.41421i) q^{57} -3.17157i q^{59} +(4.36396 - 4.36396i) q^{61} +(0.707107 + 0.707107i) q^{63} +(0.121320 + 0.121320i) q^{65} +0.343146 q^{67} -1.41421 q^{69} +(2.00000 + 2.00000i) q^{71} +(12.0711 + 12.0711i) q^{73} +(-1.00000 + 1.00000i) q^{75} +0.828427i q^{77} +(3.24264 - 3.24264i) q^{79} +5.00000 q^{81} -15.1421i q^{83} +(-3.53553 + 2.12132i) q^{85} +4.48528i q^{87} +11.0711 q^{89} +(0.121320 - 0.121320i) q^{91} -12.2426i q^{93} +(1.00000 - 1.00000i) q^{95} +(-12.8995 - 12.8995i) q^{97} +(-0.585786 - 0.585786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} + 8 q^{11} - 12 q^{13} + 4 q^{17} + 16 q^{27} - 8 q^{29} - 16 q^{31} + 16 q^{33} + 4 q^{35} + 16 q^{37} - 12 q^{39} + 8 q^{41} - 28 q^{47} + 20 q^{51} + 8 q^{55} - 8 q^{61} - 8 q^{65} + 24 q^{67}+ \cdots - 8 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 + 8 * q^11 - 12 * q^13 + 4 * q^17 + 16 * q^27 - 8 * q^29 - 16 * q^31 + 16 * q^33 + 4 * q^35 + 16 * q^37 - 12 * q^39 + 8 * q^41 - 28 * q^47 + 20 * q^51 + 8 * q^55 - 8 * q^61 - 8 * q^65 + 24 * q^67 + 8 * q^71 + 20 * q^73 - 4 * q^75 - 4 * q^79 + 20 * q^81 + 16 * q^89 - 8 * q^91 + 4 * q^95 - 12 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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