LMFDB - Embedded newform 1020.2.bd.b.361.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1020,2,Mod(361,1020)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1020, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1020.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1020.bd (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.14474100617$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 20x^{10} + 152x^{8} + 558x^{6} + 1032x^{4} + 900x^{2} + 289 $ x^12 + 20x^10 + 152x^8 + 558x^6 + 1032x^4 + 900*x^2 + 289
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			361.5
Root			$2.70027i$ of defining polynomial
Character	$\chi$	$=$	1020.361
Dual form			1020.2.bd.b.421.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(0.707107 - 0.707107i) q^{5} +(-0.359550 - 0.359550i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(0.707107 - 0.707107i) q^{5} +(-0.359550 - 0.359550i) q^{7} -1.00000i q^{9} +(3.11829 + 3.11829i) q^{11} +4.06901 q^{13} -1.00000i q^{15} +(1.90270 + 3.65783i) q^{17} +5.29659i q^{19} -0.508480 q^{21} +(-5.51902 - 5.51902i) q^{23} -1.00000i q^{25} +(-0.707107 - 0.707107i) q^{27} +(3.66982 - 3.66982i) q^{29} +(6.01054 - 6.01054i) q^{31} +4.40993 q^{33} -0.508480 q^{35} +(-1.94133 + 1.94133i) q^{37} +(2.87723 - 2.87723i) q^{39} +(0.199882 + 0.199882i) q^{41} -6.34591i q^{43} +(-0.707107 - 0.707107i) q^{45} +7.52846 q^{47} -6.74145i q^{49} +(3.93189 + 1.24106i) q^{51} -2.19998i q^{53} +4.40993 q^{55} +(3.74526 + 3.74526i) q^{57} +14.4865i q^{59} +(-2.90025 - 2.90025i) q^{61} +(-0.359550 + 0.359550i) q^{63} +(2.87723 - 2.87723i) q^{65} -9.33057 q^{67} -7.80507 q^{69} +(-9.85010 + 9.85010i) q^{71} +(3.79216 - 3.79216i) q^{73} +(-0.707107 - 0.707107i) q^{75} -2.24236i q^{77} +(-5.22357 - 5.22357i) q^{79} -1.00000 q^{81} +0.961740i q^{83} +(3.93189 + 1.24106i) q^{85} -5.18991i q^{87} -0.0393607 q^{89} +(-1.46301 - 1.46301i) q^{91} -8.50019i q^{93} +(3.74526 + 3.74526i) q^{95} +(6.13331 - 6.13331i) q^{97} +(3.11829 - 3.11829i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{7}+O(q^{10}) $ 12 * q + 4 * q^7	$ 12 q + 4 q^{7} + 4 q^{11} - 8 q^{13} + 4 q^{17} + 4 q^{23} + 4 q^{29} + 8 q^{31} + 12 q^{37} + 4 q^{39} + 28 q^{41} + 24 q^{47} + 8 q^{51} - 8 q^{61} + 4 q^{63} + 4 q^{65} - 64 q^{67} - 8 q^{69} + 8 q^{71} - 12 q^{73} + 4 q^{79} - 12 q^{81} + 8 q^{85} - 4 q^{91} + 40 q^{97} + 4 q^{99}+O(q^{100}) $ 12 * q + 4 * q^7 + 4 * q^11 - 8 * q^13 + 4 * q^17 + 4 * q^23 + 4 * q^29 + 8 * q^31 + 12 * q^37 + 4 * q^39 + 28 * q^41 + 24 * q^47 + 8 * q^51 - 8 * q^61 + 4 * q^63 + 4 * q^65 - 64 * q^67 - 8 * q^69 + 8 * q^71 - 12 * q^73 + 4 * q^79 - 12 * q^81 + 8 * q^85 - 4 * q^91 + 40 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1020\mathbb{Z}\right)^\times$.

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$	−0.359550	−	0.359550i	−0.135897	−	0.135897i	0.635886	−	0.771783i	$-0.280635\pi$
$7$	−0.359550	−	0.359550i	−0.135897	−	0.135897i	−0.771783	+	0.635886i	$0.780635\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	3.11829	+	3.11829i	0.940200	+	0.940200i	0.998310	−	0.0581105i	$-0.0185076\pi$
$11$	3.11829	+	3.11829i	0.940200	+	0.940200i	−0.0581105	+	0.998310i	$0.518508\pi$
$12$		0			0
$13$	4.06901			1.12854			0.564271	−	0.825590i	$-0.309157\pi$
$13$	4.06901			1.12854			0.564271	+	0.825590i	$0.309157\pi$
$14$		0			0
$15$		−	1.00000i		−	0.258199i
$16$		0			0
$17$	1.90270	+	3.65783i	0.461473	+	0.887154i
$17$	1.90270	+	3.65783i	0.461473	+	0.887154i
$18$		0			0
$19$			5.29659i			1.21512i	0.794273	+	0.607561i	$0.207852\pi$
$19$			5.29659i			1.21512i	−0.794273	+	0.607561i	$0.792148\pi$
$20$		0			0
$21$	−0.508480			−0.110960
$22$		0			0
$23$	−5.51902	−	5.51902i	−1.15080	−	1.15080i	−0.986393	−	0.164402i	$-0.947431\pi$
$23$	−5.51902	−	5.51902i	−1.15080	−	1.15080i	−0.164402	−	0.986393i	$-0.552569\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$	3.66982	−	3.66982i	0.681469	−	0.681469i	−0.278862	−	0.960331i	$-0.589957\pi$
$29$	3.66982	−	3.66982i	0.681469	−	0.681469i	0.960331	+	0.278862i	$0.0899572\pi$
$30$		0			0
$31$	6.01054	−	6.01054i	1.07952	−	1.07952i	0.0829731	−	0.996552i	$-0.473558\pi$
$31$	6.01054	−	6.01054i	1.07952	−	1.07952i	0.996552	−	0.0829731i	$-0.0264416\pi$
$32$		0			0
$33$	4.40993			0.767670
$34$		0			0
$35$	−0.508480			−0.0859489
$36$		0			0
$37$	−1.94133	+	1.94133i	−0.319153	+	0.319153i	−0.848442	−	0.529289i	$-0.822459\pi$
$37$	−1.94133	+	1.94133i	−0.319153	+	0.319153i	0.529289	+	0.848442i	$0.322459\pi$
$38$		0			0
$39$	2.87723	−	2.87723i	0.460725	−	0.460725i
$40$		0			0
$41$	0.199882	+	0.199882i	0.0312163	+	0.0312163i	0.722543	−	0.691326i	$-0.242973\pi$
$41$	0.199882	+	0.199882i	0.0312163	+	0.0312163i	−0.691326	+	0.722543i	$0.742973\pi$
$42$		0			0
$43$		−	6.34591i		−	0.967742i	−0.875139	−	0.483871i	$-0.839230\pi$
$43$		−	6.34591i		−	0.967742i	0.875139	−	0.483871i	$-0.160770\pi$
$44$		0			0
$45$	−0.707107	−	0.707107i	−0.105409	−	0.105409i
$46$		0			0
$47$	7.52846			1.09814			0.549069	−	0.835777i	$-0.314982\pi$
$47$	7.52846			1.09814			0.549069	+	0.835777i	$0.314982\pi$
$48$		0			0
$49$		−	6.74145i		−	0.963064i
$50$		0			0
$51$	3.93189	+	1.24106i	0.550575	+	0.173784i
$52$		0			0
$53$		−	2.19998i		−	0.302191i	−0.988519	−	0.151095i	$-0.951720\pi$
$53$		−	2.19998i		−	0.302191i	0.988519	−	0.151095i	$-0.0482801\pi$
$54$		0			0
$55$	4.40993			0.594635
$56$		0			0
$57$	3.74526	+	3.74526i	0.496071	+	0.496071i
$58$		0			0
$59$			14.4865i			1.88598i	0.332817	+	0.942991i	$0.392001\pi$
$59$			14.4865i			1.88598i	−0.332817	+	0.942991i	$0.607999\pi$
$60$		0			0
$61$	−2.90025	−	2.90025i	−0.371339	−	0.371339i	0.496626	−	0.867965i	$-0.334572\pi$
$61$	−2.90025	−	2.90025i	−0.371339	−	0.371339i	−0.867965	+	0.496626i	$0.834572\pi$
$62$		0			0
$63$	−0.359550	+	0.359550i	−0.0452990	+	0.0452990i
$64$		0			0
$65$	2.87723	−	2.87723i	0.356876	−	0.356876i
$66$		0			0
$67$	−9.33057			−1.13991			−0.569955	−	0.821676i	$-0.693039\pi$
$67$	−9.33057			−1.13991			−0.569955	+	0.821676i	$0.693039\pi$
$68$		0			0
$69$	−7.80507			−0.939620
$70$		0			0
$71$	−9.85010	+	9.85010i	−1.16899	+	1.16899i	−0.186546	+	0.982446i	$0.559729\pi$
$71$	−9.85010	+	9.85010i	−1.16899	+	1.16899i	−0.982446	+	0.186546i	$0.940271\pi$
$72$		0			0
$73$	3.79216	−	3.79216i	0.443838	−	0.443838i	−0.449461	−	0.893300i	$-0.648384\pi$
$73$	3.79216	−	3.79216i	0.443838	−	0.443838i	0.893300	+	0.449461i	$0.148384\pi$
$74$		0			0
$75$	−0.707107	−	0.707107i	−0.0816497	−	0.0816497i
$76$		0			0
$77$		−	2.24236i		−	0.255541i
$78$		0			0
$79$	−5.22357	−	5.22357i	−0.587698	−	0.587698i	0.349309	−	0.937007i	$-0.386416\pi$
$79$	−5.22357	−	5.22357i	−0.587698	−	0.587698i	−0.937007	+	0.349309i	$0.886416\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$			0.961740i			0.105565i	0.998606	+	0.0527824i	$0.0168090\pi$
$83$			0.961740i			0.105565i	−0.998606	+	0.0527824i	$0.983191\pi$
$84$		0			0
$85$	3.93189	+	1.24106i	0.426473	+	0.134612i
$86$		0			0
$87$		−	5.18991i		−	0.556417i
$88$		0			0
$89$	−0.0393607			−0.00417223			−0.00208612	−	0.999998i	$-0.500664\pi$
$89$	−0.0393607			−0.00417223			−0.00208612	+	0.999998i	$0.500664\pi$
$90$		0			0
$91$	−1.46301	−	1.46301i	−0.153365	−	0.153365i
$92$		0			0
$93$		−	8.50019i		−	0.881428i
$94$		0			0
$95$	3.74526	+	3.74526i	0.384255	+	0.384255i
$96$		0			0
$97$	6.13331	−	6.13331i	0.622744	−	0.622744i	−0.323488	−	0.946232i	$-0.604856\pi$
$97$	6.13331	−	6.13331i	0.622744	−	0.622744i	0.946232	+	0.323488i	$0.104856\pi$
$98$		0			0
$99$	3.11829	−	3.11829i	0.313400	−	0.313400i
$100$		0			0
$101$	7.48625			0.744909			0.372455	−	0.928050i	$-0.378516\pi$
$101$	7.48625			0.744909			0.372455	+	0.928050i	$0.378516\pi$
$102$		0			0
$103$	10.8237			1.06649			0.533247	−	0.845960i	$-0.320972\pi$
$103$	10.8237			1.06649			0.533247	+	0.845960i	$0.320972\pi$
$104$		0			0
$105$	−0.359550	+	0.359550i	−0.0350885	+	0.0350885i
$106$		0			0
$107$	−13.1741	+	13.1741i	−1.27358	+	1.27358i	−0.329390	+	0.944194i	$0.606843\pi$
$107$	−13.1741	+	13.1741i	−1.27358	+	1.27358i	−0.944194	+	0.329390i	$0.893157\pi$
$108$		0			0
$109$	12.1927	+	12.1927i	1.16784	+	1.16784i	0.982714	+	0.185130i	$0.0592708\pi$
$109$	12.1927	+	12.1927i	1.16784	+	1.16784i	0.185130	+	0.982714i	$0.440729\pi$
$110$		0			0
$111$			2.74545i			0.260587i
$112$		0			0
$113$	1.48937	+	1.48937i	0.140108	+	0.140108i	0.773682	−	0.633574i	$-0.218413\pi$
$113$	1.48937	+	1.48937i	0.140108	+	0.140108i	−0.633574	+	0.773682i	$0.718413\pi$
$114$		0			0
$115$	−7.80507			−0.727827
$116$		0			0
$117$		−	4.06901i		−	0.376180i
$118$		0			0
$119$	0.631056	−	1.99929i	0.0578488	−	0.183275i
$120$		0			0
$121$			8.44746i			0.767951i
$122$		0			0
$123$	0.282676			0.0254880
$124$		0			0
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$		−	8.28625i		−	0.735285i	−0.929967	−	0.367643i	$-0.880165\pi$
$127$		−	8.28625i		−	0.735285i	0.929967	−	0.367643i	$-0.119835\pi$
$128$		0			0
$129$	−4.48723	−	4.48723i	−0.395079	−	0.395079i
$130$		0			0
$131$	−4.87345	+	4.87345i	−0.425796	+	0.425796i	−0.887193	−	0.461398i	$-0.847348\pi$
$131$	−4.87345	+	4.87345i	−0.425796	+	0.425796i	0.461398	+	0.887193i	$0.347348\pi$
$132$		0			0
$133$	1.90439	−	1.90439i	0.165132	−	0.165132i
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	−20.4863			−1.75027			−0.875133	−	0.483882i	$-0.839226\pi$
$137$	−20.4863			−1.75027			−0.875133	+	0.483882i	$0.839226\pi$
$138$		0			0
$139$	7.61141	−	7.61141i	0.645592	−	0.645592i	−0.306333	−	0.951925i	$-0.599102\pi$
$139$	7.61141	−	7.61141i	0.645592	−	0.645592i	0.951925	+	0.306333i	$0.0991020\pi$
$140$		0			0
$141$	5.32342	−	5.32342i	0.448313	−	0.448313i
$142$		0			0
$143$	12.6884	+	12.6884i	1.06105	+	1.06105i
$144$		0			0
$145$		−	5.18991i		−	0.430999i
$146$		0			0
$147$	−4.76692	−	4.76692i	−0.393169	−	0.393169i
$148$		0			0
$149$	−12.8705			−1.05439			−0.527195	−	0.849744i	$-0.676756\pi$
$149$	−12.8705			−1.05439			−0.527195	+	0.849744i	$0.676756\pi$
$150$		0			0
$151$			21.1442i			1.72069i	0.509713	+	0.860345i	$0.329752\pi$
$151$			21.1442i			1.72069i	−0.509713	+	0.860345i	$0.670248\pi$
$152$		0			0
$153$	3.65783	−	1.90270i	0.295718	−	0.153824i
$154$		0			0
$155$		−	8.50019i		−	0.682751i
$156$		0			0
$157$	10.2280			0.816284			0.408142	−	0.912918i	$-0.366177\pi$
$157$	10.2280			0.816284			0.408142	+	0.912918i	$0.366177\pi$
$158$		0			0
$159$	−1.55562	−	1.55562i	−0.123369	−	0.123369i
$160$		0			0
$161$			3.96873i			0.312779i
$162$		0			0
$163$	−16.6845	−	16.6845i	−1.30683	−	1.30683i	−0.923690	−	0.383140i	$-0.874843\pi$
$163$	−16.6845	−	16.6845i	−1.30683	−	1.30683i	−0.383140	−	0.923690i	$-0.625157\pi$
$164$		0			0
$165$	3.11829	−	3.11829i	0.242759	−	0.242759i
$166$		0			0
$167$	−14.2094	+	14.2094i	−1.09956	+	1.09956i	−0.105095	+	0.994462i	$0.533515\pi$
$167$	−14.2094	+	14.2094i	−1.09956	+	1.09956i	−0.994462	+	0.105095i	$0.966485\pi$
$168$		0			0
$169$	3.55687			0.273605
$170$		0			0
$171$	5.29659			0.405041
$172$		0			0
$173$	0.954533	−	0.954533i	0.0725718	−	0.0725718i	−0.669889	−	0.742461i	$-0.733658\pi$
$173$	0.954533	−	0.954533i	0.0725718	−	0.0725718i	0.742461	+	0.669889i	$0.233658\pi$
$174$		0			0
$175$	−0.359550	+	0.359550i	−0.0271794	+	0.0271794i
$176$		0			0
$177$	10.2435	+	10.2435i	0.769949	+	0.769949i
$178$		0			0
$179$		−	4.70251i		−	0.351482i	−0.984436	−	0.175741i	$-0.943768\pi$
$179$		−	4.70251i		−	0.351482i	0.984436	−	0.175741i	$-0.0562322\pi$
$180$		0			0
$181$	−7.62378	−	7.62378i	−0.566671	−	0.566671i	0.364523	−	0.931194i	$-0.381232\pi$
$181$	−7.62378	−	7.62378i	−0.566671	−	0.566671i	−0.931194	+	0.364523i	$0.881232\pi$
$182$		0			0
$183$	−4.10157			−0.303197
$184$		0			0
$185$			2.74545i			0.201850i
$186$		0			0
$187$	−5.47300	+	17.3394i	−0.400225	+	1.26798i
$188$		0			0
$189$			0.508480i			0.0369865i
$190$		0			0
$191$	−9.63437			−0.697119			−0.348559	−	0.937287i	$-0.613329\pi$
$191$	−9.63437			−0.697119			−0.348559	+	0.937287i	$0.613329\pi$
$192$		0			0
$193$	−8.48941	−	8.48941i	−0.611081	−	0.611081i	0.332146	−	0.943228i	$-0.392227\pi$
$193$	−8.48941	−	8.48941i	−0.611081	−	0.611081i	−0.943228	+	0.332146i	$0.892227\pi$
$194$		0			0
$195$		−	4.06901i		−	0.291388i
$196$		0			0
$197$	11.1844	+	11.1844i	0.796853	+	0.796853i	0.982598	−	0.185745i	$-0.0594699\pi$
$197$	11.1844	+	11.1844i	0.796853	+	0.796853i	−0.185745	+	0.982598i	$0.559470\pi$
$198$		0			0
$199$	−13.5932	+	13.5932i	−0.963595	+	0.963595i	−0.999360	−	0.0357648i	$-0.988613\pi$
$199$	−13.5932	+	13.5932i	−0.963595	+	0.963595i	0.0357648	+	0.999360i	$0.488613\pi$
$200$		0			0
$201$	−6.59771	+	6.59771i	−0.465366	+	0.465366i
$202$		0			0
$203$	−2.63897			−0.185219
$204$		0			0
$205$	0.282676			0.0197429
$206$		0			0
$207$	−5.51902	+	5.51902i	−0.383598	+	0.383598i
$208$		0			0
$209$	−16.5163	+	16.5163i	−1.14246	+	1.14246i
$210$		0			0
$211$	−2.45659	−	2.45659i	−0.169119	−	0.169119i	0.617473	−	0.786592i	$-0.288156\pi$
$211$	−2.45659	−	2.45659i	−0.169119	−	0.169119i	−0.786592	+	0.617473i	$0.788156\pi$
$212$		0			0
$213$			13.9301i			0.954478i
$214$		0			0
$215$	−4.48723	−	4.48723i	−0.306027	−	0.306027i
$216$		0			0
$217$	−4.32218			−0.293409
$218$		0			0
$219$		−	5.36292i		−	0.362393i
$220$		0			0
$221$	7.74212	+	14.8838i	0.520791	+	1.00119i
$222$		0			0
$223$		−	18.1646i		−	1.21639i	−0.793787	−	0.608196i	$-0.791894\pi$
$223$		−	18.1646i		−	1.21639i	0.793787	−	0.608196i	$-0.208106\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$		0			0
$227$	9.70783	+	9.70783i	0.644332	+	0.644332i	0.951617	−	0.307286i	$-0.0994207\pi$
$227$	9.70783	+	9.70783i	0.644332	+	0.644332i	−0.307286	+	0.951617i	$0.599421\pi$
$228$		0			0
$229$			25.3781i			1.67703i	0.544878	+	0.838515i	$0.316576\pi$
$229$			25.3781i			1.67703i	−0.544878	+	0.838515i	$0.683424\pi$
$230$		0			0
$231$	−1.58559	−	1.58559i	−0.104324	−	0.104324i
$232$		0			0
$233$	15.9179	−	15.9179i	1.04282	−	1.04282i	0.0437760	−	0.999041i	$-0.486061\pi$
$233$	15.9179	−	15.9179i	1.04282	−	1.04282i	0.999041	−	0.0437760i	$-0.0139388\pi$
$234$		0			0
$235$	5.32342	−	5.32342i	0.347262	−	0.347262i
$236$		0			0
$237$	−7.38725			−0.479853
$238$		0			0
$239$	2.24250			0.145055			0.0725277	−	0.997366i	$-0.476893\pi$
$239$	2.24250			0.145055			0.0725277	+	0.997366i	$0.476893\pi$
$240$		0			0
$241$	−0.932996	+	0.932996i	−0.0600996	+	0.0600996i	−0.736518	−	0.676418i	$-0.763531\pi$
$241$	−0.932996	+	0.932996i	−0.0600996	+	0.0600996i	0.676418	+	0.736518i	$0.263531\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−4.76692	−	4.76692i	−0.304548	−	0.304548i
$246$		0			0
$247$			21.5519i			1.37132i
$248$		0			0
$249$	0.680053	+	0.680053i	0.0430966	+	0.0430966i
$250$		0			0
$251$	−20.5641			−1.29800			−0.648998	−	0.760790i	$-0.724812\pi$
$251$	−20.5641			−1.29800			−0.648998	+	0.760790i	$0.724812\pi$
$252$		0			0
$253$		−	34.4198i		−	2.16395i
$254$		0			0
$255$	3.65783	−	1.90270i	0.229062	−	0.119152i
$256$		0			0
$257$		−	15.3859i		−	0.959746i	−0.877338	−	0.479873i	$-0.840683\pi$
$257$		−	15.3859i		−	0.959746i	0.877338	−	0.479873i	$-0.159317\pi$
$258$		0			0
$259$	1.39601			0.0867438
$260$		0			0
$261$	−3.66982	−	3.66982i	−0.227156	−	0.227156i
$262$		0			0
$263$			1.57461i			0.0970945i	0.998821	+	0.0485472i	$0.0154591\pi$
$263$			1.57461i			0.0970945i	−0.998821	+	0.0485472i	$0.984541\pi$
$264$		0			0
$265$	−1.55562	−	1.55562i	−0.0955611	−	0.0955611i
$266$		0			0
$267$	−0.0278322	+	0.0278322i	−0.00170331	+	0.00170331i
$268$		0			0
$269$	12.0653	−	12.0653i	0.735633	−	0.735633i	−0.236096	−	0.971730i	$-0.575868\pi$
$269$	12.0653	−	12.0653i	0.735633	−	0.735633i	0.971730	+	0.236096i	$0.0758681\pi$
$270$		0			0
$271$	−21.4562			−1.30337			−0.651686	−	0.758489i	$-0.725938\pi$
$271$	−21.4562			−1.30337			−0.651686	+	0.758489i	$0.725938\pi$
$272$		0			0
$273$	−2.06901			−0.125222
$274$		0			0
$275$	3.11829	−	3.11829i	0.188040	−	0.188040i
$276$		0			0
$277$	11.5656	−	11.5656i	0.694909	−	0.694909i	−0.268399	−	0.963308i	$-0.586495\pi$
$277$	11.5656	−	11.5656i	0.694909	−	0.694909i	0.963308	+	0.268399i	$0.0864945\pi$
$278$		0			0
$279$	−6.01054	−	6.01054i	−0.359842	−	0.359842i
$280$		0			0
$281$			31.2176i			1.86229i	0.364654	+	0.931143i	$0.381187\pi$
$281$			31.2176i			1.86229i	−0.364654	+	0.931143i	$0.618813\pi$
$282$		0			0
$283$	−13.0761	−	13.0761i	−0.777292	−	0.777292i	0.202078	−	0.979370i	$-0.435231\pi$
$283$	−13.0761	−	13.0761i	−0.777292	−	0.777292i	−0.979370	+	0.202078i	$0.935231\pi$
$284$		0			0
$285$	5.29659			0.313743
$286$		0			0
$287$		−	0.143735i		−	0.00848441i
$288$		0			0
$289$	−9.75945	+	13.9195i	−0.574085	+	0.818796i
$290$		0			0
$291$		−	8.67381i		−	0.508468i
$292$		0			0
$293$	−1.29575			−0.0756988			−0.0378494	−	0.999283i	$-0.512051\pi$
$293$	−1.29575			−0.0756988			−0.0378494	+	0.999283i	$0.512051\pi$
$294$		0			0
$295$	10.2435	+	10.2435i	0.596400	+	0.596400i
$296$		0			0
$297$		−	4.40993i		−	0.255890i
$298$		0			0
$299$	−22.4570	−	22.4570i	−1.29872	−	1.29872i
$300$		0			0
$301$	−2.28167	+	2.28167i	−0.131513	+	0.131513i
$302$		0			0
$303$	5.29357	−	5.29357i	0.304108	−	0.304108i
$304$		0			0
$305$	−4.10157			−0.234855
$306$		0			0
$307$	−1.12715			−0.0643299			−0.0321650	−	0.999483i	$-0.510240\pi$
$307$	−1.12715			−0.0643299			−0.0321650	+	0.999483i	$0.510240\pi$
$308$		0			0
$309$	7.65353	−	7.65353i	0.435394	−	0.435394i
$310$		0			0
$311$	−18.3491	+	18.3491i	−1.04048	+	1.04048i	−0.0413354	+	0.999145i	$0.513161\pi$
$311$	−18.3491	+	18.3491i	−1.04048	+	1.04048i	−0.999145	+	0.0413354i	$0.986839\pi$
$312$		0			0
$313$	−14.4763	−	14.4763i	−0.818248	−	0.818248i	0.167606	−	0.985854i	$-0.446396\pi$
$313$	−14.4763	−	14.4763i	−0.818248	−	0.818248i	−0.985854	+	0.167606i	$0.946396\pi$
$314$		0			0
$315$			0.508480i			0.0286496i
$316$		0			0
$317$	−6.45996	−	6.45996i	−0.362827	−	0.362827i	0.502025	−	0.864853i	$-0.332588\pi$
$317$	−6.45996	−	6.45996i	−0.362827	−	0.362827i	−0.864853	+	0.502025i	$0.832588\pi$
$318$		0			0
$319$	22.8871			1.28143
$320$		0			0
$321$			18.6309i			1.03988i
$322$		0			0
$323$	−19.3740	+	10.0778i	−1.07800	+	0.560746i
$324$		0			0
$325$		−	4.06901i		−	0.225708i
$326$		0			0
$327$	17.2430			0.953541
$328$		0			0
$329$	−2.70686	−	2.70686i	−0.149234	−	0.149234i
$330$		0			0
$331$			32.2775i			1.77413i	0.461645	+	0.887065i	$0.347259\pi$
$331$			32.2775i			1.77413i	−0.461645	+	0.887065i	$0.652741\pi$
$332$		0			0
$333$	1.94133	+	1.94133i	0.106384	+	0.106384i
$334$		0			0
$335$	−6.59771	+	6.59771i	−0.360471	+	0.360471i
$336$		0			0
$337$	−3.94515	+	3.94515i	−0.214906	+	0.214906i	−0.806348	−	0.591442i	$-0.798559\pi$
$337$	−3.94515	+	3.94515i	−0.214906	+	0.214906i	0.591442	+	0.806348i	$0.298559\pi$
$338$		0			0
$339$	2.10628			0.114398
$340$		0			0
$341$	37.4852			2.02994
$342$		0			0
$343$	−4.94074	+	4.94074i	−0.266775	+	0.266775i
$344$		0			0
$345$	−5.51902	+	5.51902i	−0.297134	+	0.297134i
$346$		0			0
$347$	9.94363	+	9.94363i	0.533802	+	0.533802i	0.921702	−	0.387899i	$-0.126799\pi$
$347$	9.94363	+	9.94363i	0.533802	+	0.533802i	−0.387899	+	0.921702i	$0.626799\pi$
$348$		0			0
$349$			24.1516i			1.29281i	0.762997	+	0.646403i	$0.223727\pi$
$349$			24.1516i			1.29281i	−0.762997	+	0.646403i	$0.776273\pi$
$350$		0			0
$351$	−2.87723	−	2.87723i	−0.153575	−	0.153575i
$352$		0			0
$353$	9.05616			0.482011			0.241005	−	0.970524i	$-0.422523\pi$
$353$	9.05616			0.482011			0.241005	+	0.970524i	$0.422523\pi$
$354$		0			0
$355$			13.9301i			0.739335i
$356$		0			0
$357$	−0.967487	−	1.85993i	−0.0512048	−	0.0984382i
$358$		0			0
$359$		−	1.75864i		−	0.0928177i	−0.998923	−	0.0464088i	$-0.985222\pi$
$359$		−	1.75864i		−	0.0928177i	0.998923	−	0.0464088i	$-0.0147777\pi$
$360$		0			0
$361$	−9.05390			−0.476521
$362$		0			0
$363$	5.97326	+	5.97326i	0.313515	+	0.313515i
$364$		0			0
$365$		−	5.36292i		−	0.280708i
$366$		0			0
$367$	−14.6953	−	14.6953i	−0.767088	−	0.767088i	0.210505	−	0.977593i	$-0.432489\pi$
$367$	−14.6953	−	14.6953i	−0.767088	−	0.767088i	−0.977593	+	0.210505i	$0.932489\pi$
$368$		0			0
$369$	0.199882	−	0.199882i	0.0104054	−	0.0104054i
$370$		0			0
$371$	−0.791003	+	0.791003i	−0.0410668	+	0.0410668i
$372$		0			0
$373$	18.2805			0.946528			0.473264	−	0.880921i	$-0.343076\pi$
$373$	18.2805			0.946528			0.473264	+	0.880921i	$0.343076\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	14.9326	−	14.9326i	0.769066	−	0.769066i
$378$		0			0
$379$	3.42866	−	3.42866i	0.176119	−	0.176119i	−0.613543	−	0.789661i	$-0.710256\pi$
$379$	3.42866	−	3.42866i	0.176119	−	0.176119i	0.789661	+	0.613543i	$0.210256\pi$
$380$		0			0
$381$	−5.85926	−	5.85926i	−0.300179	−	0.300179i
$382$		0			0
$383$			2.94624i			0.150546i	0.997163	+	0.0752730i	$0.0239828\pi$
$383$			2.94624i			0.150546i	−0.997163	+	0.0752730i	$0.976017\pi$
$384$		0			0
$385$	−1.58559	−	1.58559i	−0.0808091	−	0.0808091i
$386$		0			0
$387$	−6.34591			−0.322581
$388$		0			0
$389$		−	9.36701i		−	0.474926i	−0.971397	−	0.237463i	$-0.923684\pi$
$389$		−	9.36701i		−	0.474926i	0.971397	−	0.237463i	$-0.0763159\pi$
$390$		0			0
$391$	9.68659	−	30.6887i	0.489872	−	1.55199i
$392$		0			0
$393$			6.89211i			0.347661i
$394$		0			0
$395$	−7.38725			−0.371693
$396$		0			0
$397$	−17.1620	−	17.1620i	−0.861335	−	0.861335i	0.130158	−	0.991493i	$-0.458451\pi$
$397$	−17.1620	−	17.1620i	−0.861335	−	0.861335i	−0.991493	+	0.130158i	$0.958451\pi$
$398$		0			0
$399$		−	2.69321i		−	0.134829i
$400$		0			0
$401$	−3.58964	−	3.58964i	−0.179258	−	0.179258i	0.611774	−	0.791032i	$-0.290456\pi$
$401$	−3.58964	−	3.58964i	−0.179258	−	0.179258i	−0.791032	+	0.611774i	$0.790456\pi$
$402$		0			0
$403$	24.4570	−	24.4570i	1.21829	−	1.21829i
$404$		0			0
$405$	−0.707107	+	0.707107i	−0.0351364	+	0.0351364i
$406$		0			0
$407$	−12.1073			−0.600134
$408$		0			0
$409$	6.80512			0.336491			0.168246	−	0.985745i	$-0.446190\pi$
$409$	6.80512			0.336491			0.168246	+	0.985745i	$0.446190\pi$
$410$		0			0
$411$	−14.4860	+	14.4860i	−0.714543	+	0.714543i
$412$		0			0
$413$	5.20862	−	5.20862i	0.256300	−	0.256300i
$414$		0			0
$415$	0.680053	+	0.680053i	0.0333825	+	0.0333825i
$416$		0			0
$417$		−	10.7642i		−	0.527123i
$418$		0			0
$419$	−0.459245	−	0.459245i	−0.0224356	−	0.0224356i	0.695800	−	0.718236i	$-0.255050\pi$
$419$	−0.459245	−	0.459245i	−0.0224356	−	0.0224356i	−0.718236	+	0.695800i	$0.755050\pi$
$420$		0			0
$421$	−12.7173			−0.619801			−0.309901	−	0.950769i	$-0.600296\pi$
$421$	−12.7173			−0.619801			−0.309901	+	0.950769i	$0.600296\pi$
$422$		0			0
$423$		−	7.52846i		−	0.366046i
$424$		0			0
$425$	3.65783	−	1.90270i	0.177431	−	0.0922946i
$426$		0			0
$427$			2.08557i			0.100928i
$428$		0			0
$429$	17.9441			0.866347
$430$		0			0
$431$	5.50186	+	5.50186i	0.265015	+	0.265015i	0.827088	−	0.562073i	$-0.189996\pi$
$431$	5.50186	+	5.50186i	0.265015	+	0.265015i	−0.562073	+	0.827088i	$0.689996\pi$
$432$		0			0
$433$			33.9559i			1.63182i	0.578180	+	0.815909i	$0.303763\pi$
$433$			33.9559i			1.63182i	−0.578180	+	0.815909i	$0.696237\pi$
$434$		0			0
$435$	−3.66982	−	3.66982i	−0.175955	−	0.175955i
$436$		0			0
$437$	29.2320	−	29.2320i	1.39836	−	1.39836i
$438$		0			0
$439$	19.5401	−	19.5401i	0.932600	−	0.932600i	−0.0652677	−	0.997868i	$-0.520790\pi$
$439$	19.5401	−	19.5401i	0.932600	−	0.932600i	0.997868	+	0.0652677i	$0.0207901\pi$
$440$		0			0
$441$	−6.74145			−0.321021
$442$		0			0
$443$	26.0592			1.23811			0.619054	−	0.785348i	$-0.287516\pi$
$443$	26.0592			1.23811			0.619054	+	0.785348i	$0.287516\pi$
$444$		0			0
$445$	−0.0278322	+	0.0278322i	−0.00131938	+	0.00131938i
$446$		0			0
$447$	−9.10080	+	9.10080i	−0.430453	+	0.430453i
$448$		0			0
$449$	4.69769	+	4.69769i	0.221698	+	0.221698i	0.809213	−	0.587515i	$-0.199894\pi$
$449$	4.69769	+	4.69769i	0.221698	+	0.221698i	−0.587515	+	0.809213i	$0.699894\pi$
$450$		0			0
$451$			1.24658i			0.0586991i
$452$		0			0
$453$	14.9512	+	14.9512i	0.702468	+	0.702468i
$454$		0			0
$455$	−2.06901			−0.0969968
$456$		0			0
$457$			13.1492i			0.615093i	0.951533	+	0.307546i	$0.0995079\pi$
$457$			13.1492i			0.615093i	−0.951533	+	0.307546i	$0.900492\pi$
$458$		0			0
$459$	1.24106	−	3.93189i	0.0579279	−	0.183525i
$460$		0			0
$461$		−	33.5432i		−	1.56226i	−0.624367	−	0.781131i	$-0.714643\pi$
$461$		−	33.5432i		−	1.56226i	0.624367	−	0.781131i	$-0.285357\pi$
$462$		0			0
$463$	−11.3850			−0.529107			−0.264554	−	0.964371i	$-0.585225\pi$
$463$	−11.3850			−0.529107			−0.264554	+	0.964371i	$0.585225\pi$
$464$		0			0
$465$	−6.01054	−	6.01054i	−0.278732	−	0.278732i
$466$		0			0
$467$			21.8871i			1.01281i	0.862295	+	0.506406i	$0.169026\pi$
$467$			21.8871i			1.01281i	−0.862295	+	0.506406i	$0.830974\pi$
$468$		0			0
$469$	3.35480	+	3.35480i	0.154910	+	0.154910i
$470$		0			0
$471$	7.23229	−	7.23229i	0.333246	−	0.333246i
$472$		0			0
$473$	19.7884	−	19.7884i	0.909870	−	0.909870i
$474$		0			0
$475$	5.29659			0.243024
$476$		0			0
$477$	−2.19998			−0.100730
$478$		0			0
$479$	0.346633	−	0.346633i	0.0158381	−	0.0158381i	−0.699143	−	0.714981i	$-0.746435\pi$
$479$	0.346633	−	0.346633i	0.0158381	−	0.0158381i	0.714981	+	0.699143i	$0.246435\pi$
$480$		0			0
$481$	−7.89930	+	7.89930i	−0.360177	+	0.360177i
$482$		0			0
$483$	2.80631	+	2.80631i	0.127692	+	0.127692i
$484$		0			0
$485$		−	8.67381i		−	0.393858i
$486$		0			0
$487$	11.2796	+	11.2796i	0.511127	+	0.511127i	0.914872	−	0.403745i	$-0.132292\pi$
$487$	11.2796	+	11.2796i	0.511127	+	0.511127i	−0.403745	+	0.914872i	$0.632292\pi$
$488$		0			0
$489$	−23.5954			−1.06702
$490$		0			0
$491$		−	20.7710i		−	0.937383i	−0.883362	−	0.468691i	$-0.844726\pi$
$491$		−	20.7710i		−	0.937383i	0.883362	−	0.468691i	$-0.155274\pi$
$492$		0			0
$493$	20.4062	+	6.44101i	0.919048	+	0.290088i
$494$		0			0
$495$		−	4.40993i		−	0.198212i
$496$		0			0
$497$	7.08321			0.317725
$498$		0			0
$499$	9.02275	+	9.02275i	0.403914	+	0.403914i	0.879610	−	0.475696i	$-0.157804\pi$
$499$	9.02275	+	9.02275i	0.403914	+	0.403914i	−0.475696	+	0.879610i	$0.657804\pi$
$500$		0			0
$501$			20.0951i			0.897785i
$502$		0			0
$503$	2.95531	+	2.95531i	0.131771	+	0.131771i	0.769916	−	0.638145i	$-0.220298\pi$
$503$	2.95531	+	2.95531i	0.131771	+	0.131771i	−0.638145	+	0.769916i	$0.720298\pi$
$504$		0			0
$505$	5.29357	−	5.29357i	0.235561	−	0.235561i
$506$		0			0
$507$	2.51509	−	2.51509i	0.111699	−	0.111699i
$508$		0			0
$509$	−22.5805			−1.00086			−0.500432	−	0.865776i	$-0.666825\pi$
$509$	−22.5805			−1.00086			−0.500432	+	0.865776i	$0.666825\pi$
$510$		0			0
$511$	−2.72694			−0.120633
$512$		0			0
$513$	3.74526	−	3.74526i	0.165357	−	0.165357i
$514$		0			0
$515$	7.65353	−	7.65353i	0.337255	−	0.337255i
$516$		0			0
$517$	23.4759	+	23.4759i	1.03247	+	1.03247i
$518$		0			0
$519$		−	1.34991i		−	0.0592546i
$520$		0			0
$521$	−24.4738	−	24.4738i	−1.07222	−	1.07222i	−0.997181	−	0.0750363i	$-0.976093\pi$
$521$	−24.4738	−	24.4738i	−1.07222	−	1.07222i	−0.0750363	−	0.997181i	$-0.523907\pi$
$522$		0			0
$523$	−24.1073			−1.05414			−0.527070	−	0.849822i	$-0.676709\pi$
$523$	−24.1073			−1.05414			−0.527070	+	0.849822i	$0.676709\pi$
$524$		0			0
$525$			0.508480i			0.0221919i
$526$		0			0
$527$	33.4218	+	10.5493i	1.45588	+	0.459533i
$528$		0			0
$529$			37.9192i			1.64866i
$530$		0			0
$531$	14.4865			0.628661
$532$		0			0
$533$	0.813322	+	0.813322i	0.0352289	+	0.0352289i
$534$		0			0
$535$			18.6309i			0.805485i
$536$		0			0
$537$	−3.32518	−	3.32518i	−0.143492	−	0.143492i
$538$		0			0
$539$	21.0218	−	21.0218i	0.905472	−	0.905472i
$540$		0			0
$541$	30.7395	−	30.7395i	1.32159	−	1.32159i	0.409106	−	0.912487i	$-0.365841\pi$
$541$	30.7395	−	30.7395i	1.32159	−	1.32159i	0.912487	−	0.409106i	$-0.134159\pi$
$542$		0			0
$543$	−10.7817			−0.462685
$544$		0			0
$545$	17.2430			0.738610
$546$		0			0
$547$	13.8744	−	13.8744i	0.593226	−	0.593226i	−0.345276	−	0.938501i	$-0.612215\pi$
$547$	13.8744	−	13.8744i	0.593226	−	0.593226i	0.938501	+	0.345276i	$0.112215\pi$
$548$		0			0
$549$	−2.90025	+	2.90025i	−0.123780	+	0.123780i
$550$		0			0
$551$	19.4376	+	19.4376i	0.828068	+	0.828068i
$552$		0			0
$553$			3.75627i			0.159733i
$554$		0			0
$555$	1.94133	+	1.94133i	0.0824048	+	0.0824048i
$556$		0			0
$557$	−19.5866			−0.829913			−0.414956	−	0.909841i	$-0.636203\pi$
$557$	−19.5866			−0.829913			−0.414956	+	0.909841i	$0.636203\pi$
$558$		0			0
$559$		−	25.8216i		−	1.09214i
$560$		0			0
$561$	8.39078	+	16.1308i	0.354259	+	0.681042i
$562$		0			0
$563$		−	26.3012i		−	1.10846i	−0.832362	−	0.554232i	$-0.813012\pi$
$563$		−	26.3012i		−	1.10846i	0.832362	−	0.554232i	$-0.186988\pi$
$564$		0			0
$565$	2.10628			0.0886121
$566$		0			0
$567$	0.359550	+	0.359550i	0.0150997	+	0.0150997i
$568$		0			0
$569$		−	35.4417i		−	1.48579i	−0.669406	−	0.742897i	$-0.733451\pi$
$569$		−	35.4417i		−	1.48579i	0.669406	−	0.742897i	$-0.266549\pi$
$570$		0			0
$571$	−4.31474	−	4.31474i	−0.180566	−	0.180566i	0.611036	−	0.791603i	$-0.290753\pi$
$571$	−4.31474	−	4.31474i	−0.180566	−	0.180566i	−0.791603	+	0.611036i	$0.790753\pi$
$572$		0			0
$573$	−6.81253	+	6.81253i	−0.284598	+	0.284598i
$574$		0			0
$575$	−5.51902	+	5.51902i	−0.230159	+	0.230159i
$576$		0			0
$577$	−13.3828			−0.557133			−0.278567	−	0.960417i	$-0.589859\pi$
$577$	−13.3828			−0.557133			−0.278567	+	0.960417i	$0.589859\pi$
$578$		0			0
$579$	−12.0058			−0.498946
$580$		0			0
$581$	0.345794	−	0.345794i	0.0143459	−	0.0143459i
$582$		0			0
$583$	6.86018	−	6.86018i	0.284120	−	0.284120i
$584$		0			0
$585$	−2.87723	−	2.87723i	−0.118959	−	0.118959i
$586$		0			0
$587$		−	4.39320i		−	0.181327i	−0.995882	−	0.0906635i	$-0.971101\pi$
$587$		−	4.39320i		−	0.181327i	0.995882	−	0.0906635i	$-0.0288988\pi$
$588$		0			0
$589$	31.8354	+	31.8354i	1.31175	+	1.31175i
$590$		0			0
$591$	15.8171			0.650627
$592$		0			0
$593$			21.6374i			0.888541i	0.895893	+	0.444270i	$0.146537\pi$
$593$			21.6374i			0.888541i	−0.895893	+	0.444270i	$0.853463\pi$
$594$		0			0
$595$	−0.967487	−	1.85993i	−0.0396631	−	0.0762499i
$596$		0			0
$597$			19.2237i			0.786772i
$598$		0			0
$599$	40.4516			1.65281			0.826403	−	0.563079i	$-0.190383\pi$
$599$	40.4516			1.65281			0.826403	+	0.563079i	$0.190383\pi$
$600$		0			0
$601$	13.3394	+	13.3394i	0.544125	+	0.544125i	0.924735	−	0.380611i	$-0.124286\pi$
$601$	13.3394	+	13.3394i	0.544125	+	0.544125i	−0.380611	+	0.924735i	$0.624286\pi$
$602$		0			0
$603$			9.33057i			0.379970i
$604$		0			0
$605$	5.97326	+	5.97326i	0.242847	+	0.242847i
$606$		0			0
$607$	26.9515	−	26.9515i	1.09393	−	1.09393i	0.0988231	−	0.995105i	$-0.468492\pi$
$607$	26.9515	−	26.9515i	1.09393	−	1.09393i	0.995105	−	0.0988231i	$-0.0315078\pi$
$608$		0			0
$609$	−1.86603	+	1.86603i	−0.0756155	+	0.0756155i
$610$		0			0
$611$	30.6334			1.23929
$612$		0			0
$613$	−31.3231			−1.26513			−0.632564	−	0.774508i	$-0.717997\pi$
$613$	−31.3231			−1.26513			−0.632564	+	0.774508i	$0.717997\pi$
$614$		0			0
$615$	0.199882	−	0.199882i	0.00806001	−	0.00806001i
$616$		0			0
$617$	19.0726	−	19.0726i	0.767835	−	0.767835i	−0.209890	−	0.977725i	$-0.567311\pi$
$617$	19.0726	−	19.0726i	0.767835	−	0.767835i	0.977725	+	0.209890i	$0.0673106\pi$
$618$		0			0
$619$	1.02197	+	1.02197i	0.0410766	+	0.0410766i	0.727347	−	0.686270i	$-0.240753\pi$
$619$	1.02197	+	1.02197i	0.0410766	+	0.0410766i	−0.686270	+	0.727347i	$0.740753\pi$
$620$		0			0
$621$			7.80507i			0.313207i
$622$		0			0
$623$	0.0141522	+	0.0141522i	0.000566994	+	0.000566994i
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$			23.3576i			0.932812i
$628$		0			0
$629$	−10.7948	−	3.40728i	−0.430418	−	0.135857i
$630$		0			0
$631$		−	45.7271i		−	1.82037i	−0.414207	−	0.910183i	$-0.635941\pi$
$631$		−	45.7271i		−	1.82037i	0.414207	−	0.910183i	$-0.364059\pi$
$632$		0			0
$633$	−3.47415			−0.138085
$634$		0			0
$635$	−5.85926	−	5.85926i	−0.232518	−	0.232518i
$636$		0			0
$637$		−	27.4310i		−	1.08686i
$638$		0			0
$639$	9.85010	+	9.85010i	0.389664	+	0.389664i
$640$		0			0
$641$	−23.1708	+	23.1708i	−0.915190	+	0.915190i	−0.996675	−	0.0814847i	$-0.974034\pi$
$641$	−23.1708	+	23.1708i	−0.915190	+	0.915190i	0.0814847	+	0.996675i	$0.474034\pi$
$642$		0			0
$643$	19.5506	−	19.5506i	0.771000	−	0.771000i	−0.207282	−	0.978281i	$-0.566462\pi$
$643$	19.5506	−	19.5506i	0.771000	−	0.771000i	0.978281	+	0.207282i	$0.0664616\pi$
$644$		0			0
$645$	−6.34591			−0.249870
$646$		0			0
$647$	−42.4433			−1.66862			−0.834310	−	0.551296i	$-0.814133\pi$
$647$	−42.4433			−1.66862			−0.834310	+	0.551296i	$0.814133\pi$
$648$		0			0
$649$	−45.1731	+	45.1731i	−1.77320	+	1.77320i
$650$		0			0
$651$	−3.05624	+	3.05624i	−0.119784	+	0.119784i
$652$		0			0
$653$	8.57322	+	8.57322i	0.335496	+	0.335496i	0.854669	−	0.519173i	$-0.173760\pi$
$653$	8.57322	+	8.57322i	0.335496	+	0.335496i	−0.519173	+	0.854669i	$0.673760\pi$
$654$		0			0
$655$			6.89211i			0.269297i
$656$		0			0
$657$	−3.79216	−	3.79216i	−0.147946	−	0.147946i
$658$		0			0
$659$	10.6924			0.416518			0.208259	−	0.978074i	$-0.433220\pi$
$659$	10.6924			0.416518			0.208259	+	0.978074i	$0.433220\pi$
$660$		0			0
$661$		−	21.6504i		−	0.842101i	−0.907037	−	0.421051i	$-0.861661\pi$
$661$		−	21.6504i		−	0.842101i	0.907037	−	0.421051i	$-0.138339\pi$
$662$		0			0
$663$	15.9989	+	5.04990i	0.621346	+	0.196122i
$664$		0			0
$665$		−	2.69321i		−	0.104438i
$666$		0			0
$667$	−40.5077			−1.56846
$668$		0			0
$669$	−12.8443	−	12.8443i	−0.496590	−	0.496590i
$670$		0			0
$671$		−	18.0876i		−	0.698265i
$672$		0			0
$673$	−14.2965	−	14.2965i	−0.551090	−	0.551090i	0.375665	−	0.926755i	$-0.377414\pi$
$673$	−14.2965	−	14.2965i	−0.551090	−	0.551090i	−0.926755	+	0.375665i	$0.877414\pi$
$674$		0			0
$675$	−0.707107	+	0.707107i	−0.0272166	+	0.0272166i
$676$		0			0
$677$	13.9428	−	13.9428i	0.535865	−	0.535865i	−0.386447	−	0.922312i	$-0.626298\pi$
$677$	13.9428	−	13.9428i	0.535865	−	0.535865i	0.922312	+	0.386447i	$0.126298\pi$
$678$		0			0
$679$	−4.41046			−0.169258
$680$		0			0
$681$	13.7289			0.526094
$682$		0			0
$683$	13.4616	−	13.4616i	0.515094	−	0.515094i	−0.400989	−	0.916083i	$-0.631333\pi$
$683$	13.4616	−	13.4616i	0.515094	−	0.515094i	0.916083	+	0.400989i	$0.131333\pi$
$684$		0			0
$685$	−14.4860	+	14.4860i	−0.553483	+	0.553483i
$686$		0			0
$687$	17.9450	+	17.9450i	0.684645	+	0.684645i
$688$		0			0
$689$		−	8.95176i		−	0.341035i
$690$		0			0
$691$	31.5638	+	31.5638i	1.20074	+	1.20074i	0.973940	+	0.226805i	$0.0728279\pi$
$691$	31.5638	+	31.5638i	1.20074	+	1.20074i	0.226805	+	0.973940i	$0.427172\pi$
$692$		0			0
$693$	−2.24236			−0.0851803
$694$		0			0
$695$		−	10.7642i		−	0.408308i
$696$		0			0
$697$	−0.350818	+	1.11145i	−0.0132882	+	0.0420991i
$698$		0			0
$699$		−	22.5113i		−	0.851457i
$700$		0			0
$701$	3.75559			0.141847			0.0709233	−	0.997482i	$-0.477405\pi$
$701$	3.75559			0.141847			0.0709233	+	0.997482i	$0.477405\pi$
$702$		0			0
$703$	−10.2824	−	10.2824i	−0.387809	−	0.387809i
$704$		0			0
$705$		−	7.52846i		−	0.283538i
$706$		0			0
$707$	−2.69168	−	2.69168i	−0.101231	−	0.101231i
$708$		0			0
$709$	22.9518	−	22.9518i	0.861974	−	0.861974i	−0.129593	−	0.991567i	$-0.541367\pi$
$709$	22.9518	−	22.9518i	0.861974	−	0.861974i	0.991567	+	0.129593i	$0.0413672\pi$
$710$		0			0
$711$	−5.22357	+	5.22357i	−0.195899	+	0.195899i
$712$		0			0
$713$	−66.3446			−2.48462
$714$		0			0
$715$	17.9441			0.671070
$716$		0			0
$717$	1.58569	−	1.58569i	0.0592187	−	0.0592187i
$718$		0			0
$719$	−1.98483	+	1.98483i	−0.0740216	+	0.0740216i	−0.743148	−	0.669127i	$-0.766668\pi$
$719$	−1.98483	+	1.98483i	−0.0740216	+	0.0740216i	0.669127	+	0.743148i	$0.266668\pi$
$720$		0			0
$721$	−3.89167	−	3.89167i	−0.144933	−	0.144933i
$722$		0			0
$723$			1.31946i			0.0490711i
$724$		0			0
$725$	−3.66982	−	3.66982i	−0.136294	−	0.136294i
$726$		0			0
$727$	2.67217			0.0991053			0.0495527	−	0.998772i	$-0.484220\pi$
$727$	2.67217			0.0991053			0.0495527	+	0.998772i	$0.484220\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	23.2123	−	12.0744i	0.858536	−	0.446587i
$732$		0			0
$733$			8.62422i			0.318543i	0.987235	+	0.159271i	$0.0509145\pi$
$733$			8.62422i			0.318543i	−0.987235	+	0.159271i	$0.949085\pi$
$734$		0			0
$735$	−6.74145			−0.248662
$736$		0			0
$737$	−29.0954	−	29.0954i	−1.07174	−	1.07174i
$738$		0			0
$739$			5.22140i			0.192072i	0.995378	+	0.0960361i	$0.0306164\pi$
$739$			5.22140i			0.192072i	−0.995378	+	0.0960361i	$0.969384\pi$
$740$		0			0
$741$	15.2395	+	15.2395i	0.559837	+	0.559837i
$742$		0			0
$743$	−24.1181	+	24.1181i	−0.884806	+	0.884806i	−0.994018	−	0.109212i	$-0.965167\pi$
$743$	−24.1181	+	24.1181i	−0.884806	+	0.884806i	0.109212	+	0.994018i	$0.465167\pi$
$744$		0			0
$745$	−9.10080	+	9.10080i	−0.333428	+	0.333428i
$746$		0			0
$747$	0.961740			0.0351882
$748$		0			0
$749$	9.47346			0.346153
$750$		0			0
$751$	14.1861	−	14.1861i	0.517660	−	0.517660i	−0.399203	−	0.916863i	$-0.630713\pi$
$751$	14.1861	−	14.1861i	0.517660	−	0.517660i	0.916863	+	0.399203i	$0.130713\pi$
$752$		0			0
$753$	−14.5410	+	14.5410i	−0.529904	+	0.529904i
$754$		0			0
$755$	14.9512	+	14.9512i	0.544130	+	0.544130i
$756$		0			0
$757$			28.0575i			1.01977i	0.860243	+	0.509884i	$0.170312\pi$
$757$			28.0575i			1.01977i	−0.860243	+	0.509884i	$0.829688\pi$
$758$		0			0
$759$	−24.3385	−	24.3385i	−0.883431	−	0.883431i
$760$		0			0
$761$	−21.0744			−0.763945			−0.381972	−	0.924174i	$-0.624755\pi$
$761$	−21.0744			−0.763945			−0.381972	+	0.924174i	$0.624755\pi$
$762$		0			0
$763$		−	8.76773i		−	0.317413i
$764$		0			0
$765$	1.24106	−	3.93189i	0.0448707	−	0.142158i
$766$		0			0
$767$			58.9458i			2.12841i
$768$		0			0
$769$	−30.9862			−1.11739			−0.558695	−	0.829373i	$-0.688698\pi$
$769$	−30.9862			−1.11739			−0.558695	+	0.829373i	$0.688698\pi$
$770$		0			0
$771$	−10.8795	−	10.8795i	−0.391815	−	0.391815i
$772$		0			0
$773$			0.0951915i			0.00342380i	0.999999	+	0.00171190i	$0.000544915\pi$
$773$			0.0951915i			0.00342380i	−0.999999	+	0.00171190i	$0.999455\pi$
$774$		0			0
$775$	−6.01054	−	6.01054i	−0.215905	−	0.215905i
$776$		0			0
$777$	0.987128	−	0.987128i	0.0354130	−	0.0354130i
$778$		0			0
$779$	−1.05869	+	1.05869i	−0.0379316	+	0.0379316i
$780$		0			0
$781$	−61.4309			−2.19817
$782$		0			0
$783$	−5.18991			−0.185472
$784$		0			0
$785$	7.23229	−	7.23229i	0.258132	−	0.258132i
$786$		0			0
$787$	−18.0682	+	18.0682i	−0.644060	+	0.644060i	−0.951551	−	0.307491i	$-0.900511\pi$
$787$	−18.0682	+	18.0682i	−0.644060	+	0.644060i	0.307491	+	0.951551i	$0.400511\pi$
$788$		0			0
$789$	1.11342	+	1.11342i	0.0396387	+	0.0396387i
$790$		0			0
$791$		−	1.07100i		−	0.0380805i
$792$		0			0
$793$	−11.8012	−	11.8012i	−0.419071	−	0.419071i
$794$		0			0
$795$	−2.19998			−0.0780253
$796$		0			0
$797$		−	18.7821i		−	0.665295i	−0.943051	−	0.332648i	$-0.892058\pi$
$797$		−	18.7821i		−	0.665295i	0.943051	−	0.332648i	$-0.107942\pi$
$798$		0			0
$799$	14.3244	+	27.5378i	0.506762	+	0.974218i
$800$		0			0
$801$			0.0393607i			0.00139074i
$802$		0			0
$803$	23.6501			0.834593
$804$		0			0
$805$	2.80631	+	2.80631i	0.0989096	+	0.0989096i
$806$		0			0
$807$		−	17.0629i		−	0.600642i
$808$		0			0
$809$	17.1275	+	17.1275i	0.602172	+	0.602172i	0.940888	−	0.338717i	$-0.109993\pi$
$809$	17.1275	+	17.1275i	0.602172	+	0.602172i	−0.338717	+	0.940888i	$0.609993\pi$
$810$		0			0
$811$	−23.9663	+	23.9663i	−0.841570	+	0.841570i	−0.989063	−	0.147493i	$-0.952879\pi$
$811$	−23.9663	+	23.9663i	−0.841570	+	0.841570i	0.147493	+	0.989063i	$0.452879\pi$
$812$		0			0
$813$	−15.1718	+	15.1718i	−0.532099	+	0.532099i
$814$		0			0
$815$	−23.5954			−0.826512
$816$		0			0
$817$	33.6117			1.17592
$818$		0			0
$819$	−1.46301	+	1.46301i	−0.0511218	+	0.0511218i
$820$		0			0
$821$	33.5032	−	33.5032i	1.16927	−	1.16927i	0.186890	−	0.982381i	$-0.440159\pi$
$821$	33.5032	−	33.5032i	1.16927	−	1.16927i	0.982381	−	0.186890i	$-0.0598408\pi$
$822$		0			0
$823$	38.6851	+	38.6851i	1.34848	+	1.34848i	0.887318	+	0.461158i	$0.152566\pi$
$823$	38.6851	+	38.6851i	1.34848	+	1.34848i	0.461158	+	0.887318i	$0.347434\pi$
$824$		0			0
$825$		−	4.40993i		−	0.153534i
$826$		0			0
$827$	−33.8806	−	33.8806i	−1.17814	−	1.17814i	−0.980217	−	0.197928i	$-0.936579\pi$
$827$	−33.8806	−	33.8806i	−1.17814	−	1.17814i	−0.197928	−	0.980217i	$-0.563421\pi$
$828$		0			0
$829$	−23.4503			−0.814463			−0.407232	−	0.913325i	$-0.633506\pi$
$829$	−23.4503			−0.814463			−0.407232	+	0.913325i	$0.633506\pi$
$830$		0			0
$831$		−	16.3562i		−	0.567391i
$832$		0			0
$833$	24.6591	−	12.8270i	0.854386	−	0.444428i
$834$		0			0
$835$			20.0951i			0.695421i
$836$		0			0
$837$	−8.50019			−0.293809
$838$		0			0
$839$	−13.2563	−	13.2563i	−0.457658	−	0.457658i	0.440228	−	0.897886i	$-0.354897\pi$
$839$	−13.2563	−	13.2563i	−0.457658	−	0.457658i	−0.897886	+	0.440228i	$0.854897\pi$
$840$		0			0
$841$			2.06479i			0.0711997i
$842$		0			0
$843$	22.0742	+	22.0742i	0.760275	+	0.760275i
$844$		0			0
$845$	2.51509	−	2.51509i	0.0865216	−	0.0865216i
$846$		0			0
$847$	3.03728	−	3.03728i	0.104362	−	0.104362i
$848$		0			0
$849$	−18.4924			−0.634656
$850$		0			0
$851$	21.4285			0.734559
$852$		0			0
$853$	−36.4751	+	36.4751i	−1.24888	+	1.24888i	−0.292670	+	0.956213i	$0.594544\pi$
$853$	−36.4751	+	36.4751i	−1.24888	+	1.24888i	−0.956213	+	0.292670i	$0.905456\pi$
$854$		0			0
$855$	3.74526	−	3.74526i	0.128085	−	0.128085i
$856$		0			0
$857$	−9.01980	−	9.01980i	−0.308111	−	0.308111i	0.536066	−	0.844176i	$-0.319910\pi$
$857$	−9.01980	−	9.01980i	−0.308111	−	0.308111i	−0.844176	+	0.536066i	$0.819910\pi$
$858$		0			0
$859$			53.0361i			1.80957i	0.425870	+	0.904784i	$0.359968\pi$
$859$			53.0361i			1.80957i	−0.425870	+	0.904784i	$0.640032\pi$
$860$		0			0
$861$	−0.101636	−	0.101636i	−0.00346374	−	0.00346374i
$862$		0			0
$863$	3.91357			0.133220			0.0666098	−	0.997779i	$-0.478782\pi$
$863$	3.91357			0.133220			0.0666098	+	0.997779i	$0.478782\pi$
$864$		0			0
$865$		−	1.34991i		−	0.0458984i
$866$		0			0
$867$	2.94162	+	16.7436i	0.0999027	+	0.568641i
$868$		0			0
$869$		−	32.5772i		−	1.10511i
$870$		0			0
$871$	−37.9662			−1.28644
$872$		0			0
$873$	−6.13331	−	6.13331i	−0.207581	−	0.207581i
$874$		0			0
$875$			0.508480i			0.0171898i
$876$		0			0
$877$	−22.9892	−	22.9892i	−0.776289	−	0.776289i	0.202909	−	0.979198i	$-0.434961\pi$
$877$	−22.9892	−	22.9892i	−0.776289	−	0.776289i	−0.979198	+	0.202909i	$0.934961\pi$
$878$		0			0
$879$	−0.916237	+	0.916237i	−0.0309039	+	0.0309039i
$880$		0			0
$881$	0.0437347	−	0.0437347i	0.00147346	−	0.00147346i	−0.706370	−	0.707843i	$-0.749668\pi$
$881$	0.0437347	−	0.0437347i	0.00147346	−	0.00147346i	0.707843	+	0.706370i	$0.249668\pi$
$882$		0			0
$883$	7.91219			0.266266			0.133133	−	0.991098i	$-0.457496\pi$
$883$	7.91219			0.266266			0.133133	+	0.991098i	$0.457496\pi$
$884$		0			0
$885$	14.4865			0.486959
$886$		0			0
$887$	12.3440	−	12.3440i	0.414471	−	0.414471i	−0.468822	−	0.883293i	$-0.655321\pi$
$887$	12.3440	−	12.3440i	0.414471	−	0.414471i	0.883293	+	0.468822i	$0.155321\pi$
$888$		0			0
$889$	−2.97932	+	2.97932i	−0.0999231	+	0.0999231i
$890$		0			0
$891$	−3.11829	−	3.11829i	−0.104467	−	0.104467i
$892$		0			0
$893$			39.8752i			1.33437i
$894$		0			0
$895$	−3.32518	−	3.32518i	−0.111148	−	0.111148i
$896$		0			0
$897$	−31.7589			−1.06040
$898$		0			0
$899$		−	44.1152i		−	1.47133i
$900$		0			0
$901$	8.04716	−	4.18591i	0.268090	−	0.139453i
$902$		0			0
$903$			3.22677i			0.107380i
$904$		0			0
$905$	−10.7817			−0.358394
$906$		0			0
$907$	17.2069	+	17.2069i	0.571346	+	0.571346i	0.932504	−	0.361159i	$-0.117619\pi$
$907$	17.2069	+	17.2069i	0.571346	+	0.571346i	−0.361159	+	0.932504i	$0.617619\pi$
$908$		0			0
$909$		−	7.48625i		−	0.248303i
$910$		0			0
$911$	−17.5419	−	17.5419i	−0.581189	−	0.581189i	0.354041	−	0.935230i	$-0.384807\pi$
$911$	−17.5419	−	17.5419i	−0.581189	−	0.581189i	−0.935230	+	0.354041i	$0.884807\pi$
$912$		0			0
$913$	−2.99899	+	2.99899i	−0.0992519	+	0.0992519i
$914$		0			0
$915$	−2.90025	+	2.90025i	−0.0958793	+	0.0958793i
$916$		0			0
$917$	3.50450			0.115729
$918$		0			0
$919$	9.20251			0.303563			0.151781	−	0.988414i	$-0.451499\pi$
$919$	9.20251			0.303563			0.151781	+	0.988414i	$0.451499\pi$
$920$		0			0
$921$	−0.797016	+	0.797016i	−0.0262626	+	0.0262626i
$922$		0			0
$923$	−40.0802	+	40.0802i	−1.31926	+	1.31926i
$924$		0			0
$925$	1.94133	+	1.94133i	0.0638305	+	0.0638305i
$926$		0			0
$927$		−	10.8237i		−	0.355498i
$928$		0			0
$929$	−2.82911	−	2.82911i	−0.0928202	−	0.0928202i	0.659172	−	0.751992i	$-0.270907\pi$
$929$	−2.82911	−	2.82911i	−0.0928202	−	0.0928202i	−0.751992	+	0.659172i	$0.770907\pi$
$930$		0			0
$931$	35.7067			1.17024
$932$		0			0
$933$			25.9495i			0.849549i
$934$		0			0
$935$	8.39078	+	16.1308i	0.274408	+	0.527532i
$936$		0			0
$937$			47.4218i			1.54920i	0.632450	+	0.774601i	$0.282049\pi$
$937$			47.4218i			1.54920i	−0.632450	+	0.774601i	$0.717951\pi$
$938$		0			0
$939$	−20.4725			−0.668096
$940$		0			0
$941$	11.4132	+	11.4132i	0.372059	+	0.372059i	0.868227	−	0.496168i	$-0.165260\pi$
$941$	11.4132	+	11.4132i	0.372059	+	0.372059i	−0.496168	+	0.868227i	$0.665260\pi$
$942$		0			0
$943$		−	2.20630i		−	0.0718471i
$944$		0			0
$945$	0.359550	+	0.359550i	0.0116962	+	0.0116962i
$946$		0			0
$947$	10.6694	−	10.6694i	0.346708	−	0.346708i	−0.512174	−	0.858882i	$-0.671160\pi$
$947$	10.6694	−	10.6694i	0.346708	−	0.346708i	0.858882	+	0.512174i	$0.171160\pi$
$948$		0			0
$949$	15.4303	−	15.4303i	0.500890	−	0.500890i
$950$		0			0
$951$	−9.13576			−0.296247
$952$		0			0
$953$	−53.7977			−1.74268			−0.871339	−	0.490682i	$-0.836748\pi$
$953$	−53.7977			−1.74268			−0.871339	+	0.490682i	$0.836748\pi$
$954$		0			0
$955$	−6.81253	+	6.81253i	−0.220448	+	0.220448i
$956$		0			0
$957$	16.1837	−	16.1837i	0.523143	−	0.523143i
$958$		0			0
$959$	7.36586	+	7.36586i	0.237856	+	0.237856i
$960$		0			0
$961$		−	41.2532i		−	1.33075i
$962$		0			0
$963$	13.1741	+	13.1741i	0.424528	+	0.424528i
$964$		0			0
$965$	−12.0058			−0.386482
$966$		0			0
$967$		−	44.3271i		−	1.42546i	−0.701437	−	0.712731i	$-0.747458\pi$
$967$		−	44.3271i		−	1.42546i	0.701437	−	0.712731i	$-0.252542\pi$
$968$		0			0
$969$	−6.57341	+	20.8256i	−0.211168	+	0.669015i
$970$		0			0
$971$		−	23.1392i		−	0.742571i	−0.928519	−	0.371285i	$-0.878917\pi$
$971$		−	23.1392i		−	0.742571i	0.928519	−	0.371285i	$-0.121083\pi$
$972$		0			0
$973$	−5.47337			−0.175468
$974$		0			0
$975$	−2.87723	−	2.87723i	−0.0921450	−	0.0921450i
$976$		0			0
$977$			28.0530i			0.897496i	0.893658	+	0.448748i	$0.148130\pi$
$977$			28.0530i			0.897496i	−0.893658	+	0.448748i	$0.851870\pi$
$978$		0			0
$979$	−0.122738	−	0.122738i	−0.00392273	−	0.00392273i
$980$		0			0
$981$	12.1927	−	12.1927i	0.389281	−	0.389281i
$982$		0			0
$983$	5.76605	−	5.76605i	0.183908	−	0.183908i	−0.609148	−	0.793057i	$-0.708488\pi$
$983$	5.76605	−	5.76605i	0.183908	−	0.183908i	0.793057	+	0.609148i	$0.208488\pi$
$984$		0			0
$985$	15.8171			0.503974
$986$		0			0
$987$	−3.82807			−0.121849
$988$		0			0
$989$	−35.0232	+	35.0232i	−1.11367	+	1.11367i
$990$		0			0
$991$	−3.04832	+	3.04832i	−0.0968331	+	0.0968331i	−0.753864	−	0.657031i	$-0.771812\pi$
$991$	−3.04832	+	3.04832i	−0.0968331	+	0.0968331i	0.657031	+	0.753864i	$0.271812\pi$
$992$		0			0
$993$	22.8236	+	22.8236i	0.724285	+	0.724285i
$994$		0			0
$995$			19.2237i			0.609431i
$996$		0			0
$997$	−14.1435	−	14.1435i	−0.447930	−	0.447930i	0.446736	−	0.894666i	$-0.352586\pi$
$997$	−14.1435	−	14.1435i	−0.447930	−	0.447930i	−0.894666	+	0.446736i	$0.852586\pi$
$998$		0			0
$999$	2.74545			0.0868623

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1020.2.bd.b.361.5	✓	12
3.2	odd	2		3060.2.be.c.361.2		12
17.13	even	4	inner	1020.2.bd.b.421.5	yes	12
51.47	odd	4		3060.2.be.c.1441.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1020.2.bd.b.361.5	✓	12	1.1	even	1	trivial
1020.2.bd.b.421.5	yes	12	17.13	even	4	inner
3060.2.be.c.361.2		12	3.2	odd	2
3060.2.be.c.1441.2		12	51.47	odd	4

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1020.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(0.707107 - 0.707107i) q^{5} +(-0.359550 - 0.359550i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(0.707107 - 0.707107i) q^{5} +(-0.359550 - 0.359550i) q^{7} -1.00000i q^{9} +(3.11829 + 3.11829i) q^{11} +4.06901 q^{13} -1.00000i q^{15} +(1.90270 + 3.65783i) q^{17} +5.29659i q^{19} -0.508480 q^{21} +(-5.51902 - 5.51902i) q^{23} -1.00000i q^{25} +(-0.707107 - 0.707107i) q^{27} +(3.66982 - 3.66982i) q^{29} +(6.01054 - 6.01054i) q^{31} +4.40993 q^{33} -0.508480 q^{35} +(-1.94133 + 1.94133i) q^{37} +(2.87723 - 2.87723i) q^{39} +(0.199882 + 0.199882i) q^{41} -6.34591i q^{43} +(-0.707107 - 0.707107i) q^{45} +7.52846 q^{47} -6.74145i q^{49} +(3.93189 + 1.24106i) q^{51} -2.19998i q^{53} +4.40993 q^{55} +(3.74526 + 3.74526i) q^{57} +14.4865i q^{59} +(-2.90025 - 2.90025i) q^{61} +(-0.359550 + 0.359550i) q^{63} +(2.87723 - 2.87723i) q^{65} -9.33057 q^{67} -7.80507 q^{69} +(-9.85010 + 9.85010i) q^{71} +(3.79216 - 3.79216i) q^{73} +(-0.707107 - 0.707107i) q^{75} -2.24236i q^{77} +(-5.22357 - 5.22357i) q^{79} -1.00000 q^{81} +0.961740i q^{83} +(3.93189 + 1.24106i) q^{85} -5.18991i q^{87} -0.0393607 q^{89} +(-1.46301 - 1.46301i) q^{91} -8.50019i q^{93} +(3.74526 + 3.74526i) q^{95} +(6.13331 - 6.13331i) q^{97} +(3.11829 - 3.11829i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{7}+O(q^{10}) \) 12 * q + 4 * q^7	\( 12 q + 4 q^{7} + 4 q^{11} - 8 q^{13} + 4 q^{17} + 4 q^{23} + 4 q^{29} + 8 q^{31} + 12 q^{37} + 4 q^{39} + 28 q^{41} + 24 q^{47} + 8 q^{51} - 8 q^{61} + 4 q^{63} + 4 q^{65} - 64 q^{67} - 8 q^{69} + 8 q^{71} - 12 q^{73} + 4 q^{79} - 12 q^{81} + 8 q^{85} - 4 q^{91} + 40 q^{97} + 4 q^{99}+O(q^{100}) \) 12 * q + 4 * q^7 + 4 * q^11 - 8 * q^13 + 4 * q^17 + 4 * q^23 + 4 * q^29 + 8 * q^31 + 12 * q^37 + 4 * q^39 + 28 * q^41 + 24 * q^47 + 8 * q^51 - 8 * q^61 + 4 * q^63 + 4 * q^65 - 64 * q^67 - 8 * q^69 + 8 * q^71 - 12 * q^73 + 4 * q^79 - 12 * q^81 + 8 * q^85 - 4 * q^91 + 40 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

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Database

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