LMFDB - Embedded newform 460.2.x.a.17.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(17,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 14]))

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

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

chi := DirichletCharacter("460.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.x (of order $44$, degree $20$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.8
Character	$\chi$	$=$	460.17
Dual form			460.2.x.a.433.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.483512 - 0.264018i) q^{3} +(-0.935821 + 2.03082i) q^{5} +(-1.13426 - 1.51520i) q^{7} +(-1.45784 + 2.26845i) q^{9} +O(q^{10})$	\(q+(0.483512 - 0.264018i) q^{3} +(-0.935821 + 2.03082i) q^{5} +(-1.13426 - 1.51520i) q^{7} +(-1.45784 + 2.26845i) q^{9} +(4.16231 - 1.90086i) q^{11} +(4.22795 + 3.16500i) q^{13} +(0.0836923 + 1.22900i) q^{15} +(0.464578 + 6.49564i) q^{17} +(1.69437 + 1.95541i) q^{19} +(-0.948468 - 0.433151i) q^{21} +(3.12510 + 3.63782i) q^{23} +(-3.24848 - 3.80097i) q^{25} +(-0.223877 + 3.13020i) q^{27} +(-3.01750 - 2.61468i) q^{29} +(-5.74187 + 1.68596i) q^{31} +(1.51067 - 2.01801i) q^{33} +(4.13856 - 0.885532i) q^{35} +(2.05546 - 0.447138i) q^{37} +(2.87988 + 0.414064i) q^{39} +(3.87576 - 2.49080i) q^{41} +(-2.26482 - 4.14771i) q^{43} +(-3.24254 - 5.08348i) q^{45} +(-0.444089 - 0.444089i) q^{47} +(0.962857 - 3.27919i) q^{49} +(1.93959 + 3.01807i) q^{51} +(-3.79001 + 2.83717i) q^{53} +(-0.0348596 + 10.2318i) q^{55} +(1.33551 + 0.498121i) q^{57} +(8.79290 - 1.26423i) q^{59} +(-0.556268 - 1.89448i) q^{61} +(5.09072 - 0.364096i) q^{63} +(-10.3842 + 5.62434i) q^{65} +(-0.961312 - 2.57738i) q^{67} +(2.47147 + 0.933850i) q^{69} +(2.87588 - 6.29730i) q^{71} +(-6.12778 - 0.438267i) q^{73} +(-2.57420 - 0.980160i) q^{75} +(-7.60133 - 4.15064i) q^{77} +(-1.46050 - 10.1580i) q^{79} +(-2.64233 - 5.78590i) q^{81} +(1.70088 + 7.81882i) q^{83} +(-13.6263 - 5.13528i) q^{85} +(-2.14932 - 0.467556i) q^{87} +(17.6468 + 5.18158i) q^{89} -9.99611i q^{91} +(-2.33114 + 2.33114i) q^{93} +(-5.55673 + 1.61106i) q^{95} +(1.71375 - 7.87800i) q^{97} +(-1.75599 + 12.2132i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3}+O(q^{10}) $ 240 * q + 4 * q^3	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{22}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.483512	−	0.264018i	0.279156	−	0.152431i	−0.333572	−	0.942725i	$-0.608254\pi$
$3$	0.483512	−	0.264018i	0.279156	−	0.152431i	0.612728	+	0.790294i	$0.290072\pi$
$4$		0			0
$5$	−0.935821	+	2.03082i	−0.418512	+	0.908211i
$5$	−0.935821	+	2.03082i	−0.418512	+	0.908211i
$6$		0			0
$7$	−1.13426	−	1.51520i	−0.428711	−	0.572690i	0.533223	−	0.845975i	$-0.320981\pi$
$7$	−1.13426	−	1.51520i	−0.428711	−	0.572690i	−0.961933	+	0.273285i	$0.911890\pi$
$8$		0			0
$9$	−1.45784	+	2.26845i	−0.485948	+	0.756150i
$10$		0			0
$11$	4.16231	−	1.90086i	1.25498	−	0.573132i	0.326744	−	0.945113i	$-0.394049\pi$
$11$	4.16231	−	1.90086i	1.25498	−	0.573132i	0.928240	+	0.371981i	$0.121321\pi$
$12$		0			0
$13$	4.22795	+	3.16500i	1.17262	+	0.877814i	0.994348	−	0.106167i	$-0.0338579\pi$
$13$	4.22795	+	3.16500i	1.17262	+	0.877814i	0.178273	+	0.983981i	$0.442949\pi$
$14$		0			0
$15$	0.0836923	+	1.22900i	0.0216093	+	0.317327i
$16$		0			0
$17$	0.464578	+	6.49564i	0.112677	+	1.57542i	0.668237	+	0.743949i	$0.267049\pi$
$17$	0.464578	+	6.49564i	0.112677	+	1.57542i	−0.555560	+	0.831476i	$0.687496\pi$
$18$		0			0
$19$	1.69437	+	1.95541i	0.388716	+	0.448602i	0.916055	−	0.401053i	$-0.131356\pi$
$19$	1.69437	+	1.95541i	0.388716	+	0.448602i	−0.527339	+	0.849655i	$0.676810\pi$
$20$		0			0
$21$	−0.948468	−	0.433151i	−0.206973	−	0.0945213i
$22$		0			0
$23$	3.12510	+	3.63782i	0.651628	+	0.758538i
$23$	3.12510	+	3.63782i	0.651628	+	0.758538i
$24$		0			0
$25$	−3.24848	−	3.80097i	−0.649696	−	0.760194i
$26$		0			0
$27$	−0.223877	+	3.13020i	−0.0430851	+	0.602408i
$28$		0			0
$29$	−3.01750	−	2.61468i	−0.560336	−	0.485533i	0.328032	−	0.944667i	$-0.393615\pi$
$29$	−3.01750	−	2.61468i	−0.560336	−	0.485533i	−0.888367	+	0.459133i	$0.848160\pi$
$30$		0			0
$31$	−5.74187	+	1.68596i	−1.03127	+	0.302808i	−0.753227	−	0.657761i	$-0.771504\pi$
$31$	−5.74187	+	1.68596i	−1.03127	+	0.302808i	−0.278043	+	0.960569i	$0.589686\pi$
$32$		0			0
$33$	1.51067	−	2.01801i	0.262973	−	0.351291i
$34$		0			0
$35$	4.13856	−	0.885532i	0.699545	−	0.149682i
$36$		0			0
$37$	2.05546	−	0.447138i	0.337916	−	0.0735091i	−0.0404057	−	0.999183i	$-0.512865\pi$
$37$	2.05546	−	0.447138i	0.337916	−	0.0735091i	0.378321	+	0.925674i	$0.376501\pi$
$38$		0			0
$39$	2.87988	+	0.414064i	0.461150	+	0.0663034i
$40$		0			0
$41$	3.87576	−	2.49080i	0.605292	−	0.388998i	−0.201797	−	0.979427i	$-0.564678\pi$
$41$	3.87576	−	2.49080i	0.605292	−	0.388998i	0.807089	+	0.590430i	$0.201042\pi$
$42$		0			0
$43$	−2.26482	−	4.14771i	−0.345382	−	0.632520i	0.646028	−	0.763314i	$-0.276429\pi$
$43$	−2.26482	−	4.14771i	−0.345382	−	0.632520i	−0.991410	+	0.130794i	$0.958247\pi$
$44$		0			0
$45$	−3.24254	−	5.08348i	−0.483369	−	0.757801i
$46$		0			0
$47$	−0.444089	−	0.444089i	−0.0647771	−	0.0647771i	0.673976	−	0.738753i	$-0.264585\pi$
$47$	−0.444089	−	0.444089i	−0.0647771	−	0.0647771i	−0.738753	+	0.673976i	$0.764585\pi$
$48$		0			0
$49$	0.962857	−	3.27919i	0.137551	−	0.468456i
$50$		0			0
$51$	1.93959	+	3.01807i	0.271597	+	0.422614i
$52$		0			0
$53$	−3.79001	+	2.83717i	−0.520599	+	0.389715i	−0.827013	−	0.562183i	$-0.809962\pi$
$53$	−3.79001	+	2.83717i	−0.520599	+	0.389715i	0.306414	+	0.951898i	$0.400871\pi$
$54$		0			0
$55$	−0.0348596	+	10.2318i	−0.00470047	+	1.37965i
$56$		0			0
$57$	1.33551	+	0.498121i	0.176893	+	0.0659777i
$58$		0			0
$59$	8.79290	−	1.26423i	1.14474	−	0.164589i	0.456261	−	0.889846i	$-0.349188\pi$
$59$	8.79290	−	1.26423i	1.14474	−	0.164589i	0.688478	+	0.725258i	$0.258279\pi$
$60$		0			0
$61$	−0.556268	−	1.89448i	−0.0712229	−	0.242563i	0.916186	−	0.400754i	$-0.131252\pi$
$61$	−0.556268	−	1.89448i	−0.0712229	−	0.242563i	−0.987408	+	0.158191i	$0.949434\pi$
$62$		0			0
$63$	5.09072	−	0.364096i	0.641371	−	0.0458717i
$64$		0			0
$65$	−10.3842	+	5.62434i	−1.28800	+	0.697613i
$66$		0			0
$67$	−0.961312	−	2.57738i	−0.117443	−	0.314877i	0.864906	−	0.501934i	$-0.167378\pi$
$67$	−0.961312	−	2.57738i	−0.117443	−	0.314877i	−0.982349	+	0.187057i	$0.940105\pi$
$68$		0			0
$69$	2.47147	+	0.933850i	0.297530	+	0.112422i
$70$		0			0
$71$	2.87588	−	6.29730i	0.341304	−	0.747352i	−0.658683	−	0.752421i	$-0.728886\pi$
$71$	2.87588	−	6.29730i	0.341304	−	0.747352i	0.999987	+	0.00506837i	$0.00161332\pi$
$72$		0			0
$73$	−6.12778	−	0.438267i	−0.717202	−	0.0512953i	−0.292032	−	0.956409i	$-0.594331\pi$
$73$	−6.12778	−	0.438267i	−0.717202	−	0.0512953i	−0.425170	+	0.905113i	$0.639786\pi$
$74$		0			0
$75$	−2.57420	−	0.980160i	−0.297243	−	0.113179i
$76$		0			0
$77$	−7.60133	−	4.15064i	−0.866252	−	0.473010i
$78$		0			0
$79$	−1.46050	−	10.1580i	−0.164319	−	1.14287i	−0.890375	−	0.455229i	$-0.849557\pi$
$79$	−1.46050	−	10.1580i	−0.164319	−	1.14287i	0.726055	−	0.687636i	$-0.241352\pi$
$80$		0			0
$81$	−2.64233	−	5.78590i	−0.293592	−	0.642877i
$82$		0			0
$83$	1.70088	+	7.81882i	0.186696	+	0.858227i	0.971230	+	0.238142i	$0.0765384\pi$
$83$	1.70088	+	7.81882i	0.186696	+	0.858227i	−0.784534	+	0.620085i	$0.787098\pi$
$84$		0			0
$85$	−13.6263	−	5.13528i	−1.47798	−	0.557000i
$86$		0			0
$87$	−2.14932	−	0.467556i	−0.230431	−	0.0501272i
$88$		0			0
$89$	17.6468	+	5.18158i	1.87056	+	0.549246i	0.998172	+	0.0604322i	$0.0192479\pi$
$89$	17.6468	+	5.18158i	1.87056	+	0.549246i	0.872388	+	0.488814i	$0.162570\pi$
$90$		0			0
$91$		−	9.99611i		−	1.04788i
$92$		0			0
$93$	−2.33114	+	2.33114i	−0.241728	+	0.241728i
$94$		0			0
$95$	−5.55673	+	1.61106i	−0.570108	+	0.165291i
$96$		0			0
$97$	1.71375	−	7.87800i	0.174005	−	0.799889i	−0.804547	−	0.593889i	$-0.797592\pi$
$97$	1.71375	−	7.87800i	0.174005	−	0.799889i	0.978552	−	0.206000i	$-0.0660447\pi$
$98$		0			0
$99$	−1.75599	+	12.2132i	−0.176483	+	1.22747i
$100$		0			0
$101$	−16.7079	−	10.7375i	−1.66250	−	1.06842i	−0.914380	−	0.404858i	$-0.867321\pi$
$101$	−16.7079	−	10.7375i	−1.66250	−	1.06842i	−0.748119	−	0.663565i	$-0.769043\pi$
$102$		0			0
$103$	−5.04280	+	13.5203i	−0.496882	+	1.33219i	0.410490	+	0.911865i	$0.365358\pi$
$103$	−5.04280	+	13.5203i	−0.496882	+	1.33219i	−0.907372	+	0.420328i	$0.861915\pi$
$104$		0			0
$105$	1.76725	−	1.52082i	0.172466	−	0.148417i
$106$		0			0
$107$	4.31479	−	7.90194i	0.417126	−	0.763909i	−0.581646	−	0.813442i	$-0.697591\pi$
$107$	4.31479	−	7.90194i	0.417126	−	0.763909i	0.998773	+	0.0495323i	$0.0157731\pi$
$108$		0			0
$109$	−8.22247	+	9.48924i	−0.787570	+	0.908904i	−0.997632	−	0.0687838i	$-0.978088\pi$
$109$	−8.22247	+	9.48924i	−0.787570	+	0.908904i	0.210061	+	0.977688i	$0.432634\pi$
$110$		0			0
$111$	0.875788	−	0.758875i	0.0831262	−	0.0720292i
$112$		0			0
$113$	14.1533	−	5.27892i	1.33143	−	0.496599i	0.419806	−	0.907614i	$-0.362098\pi$
$113$	14.1533	−	5.27892i	1.33143	−	0.496599i	0.911629	+	0.411015i	$0.134825\pi$
$114$		0			0
$115$	−10.3123	+	2.94217i	−0.961627	+	0.274359i
$116$		0			0
$117$	−13.3433	+	4.97681i	−1.23359	+	0.460106i
$118$		0			0
$119$	9.31522	−	8.07169i	0.853925	−	0.739930i
$120$		0			0
$121$	6.50808	−	7.51072i	0.591643	−	0.682793i
$122$		0			0
$123$	1.21636	−	2.22760i	0.109676	−	0.200856i
$124$		0			0
$125$	10.7591	−	3.04006i	0.962322	−	0.271911i
$126$		0			0
$127$	−1.11041	+	2.97712i	−0.0985328	+	0.264177i	−0.976859	−	0.213886i	$-0.931388\pi$
$127$	−1.11041	+	2.97712i	−0.0985328	+	0.264177i	0.878326	+	0.478062i	$0.158661\pi$
$128$		0			0
$129$	−2.19014	−	1.40752i	−0.192831	−	0.123925i
$130$		0			0
$131$	0.559784	−	3.89339i	0.0489086	−	0.340167i	−0.950645	−	0.310281i	$-0.899577\pi$
$131$	0.559784	−	3.89339i	0.0489086	−	0.340167i	0.999553	−	0.0298853i	$-0.00951419\pi$
$132$		0			0
$133$	1.04097	−	4.78526i	0.0902635	−	0.414935i
$134$		0			0
$135$	−6.14738	−	3.38396i	−0.529082	−	0.291245i
$136$		0			0
$137$	−9.81495	+	9.81495i	−0.838548	+	0.838548i	−0.988668	−	0.150120i	$-0.952034\pi$
$137$	−9.81495	+	9.81495i	−0.838548	+	0.838548i	0.150120	+	0.988668i	$0.452034\pi$
$138$		0			0
$139$		−	10.3160i		−	0.874993i	−0.899220	−	0.437497i	$-0.855865\pi$
$139$		−	10.3160i		−	0.874993i	0.899220	−	0.437497i	$-0.144135\pi$
$140$		0			0
$141$	−0.331970	−	0.0974752i	−0.0279569	−	0.00820890i
$142$		0			0
$143$	23.6143	+	5.13697i	1.97472	+	0.429575i
$144$		0			0
$145$	8.13378	−	3.68114i	0.675474	−	0.305702i
$146$		0			0
$147$	−0.400211	−	1.83974i	−0.0330089	−	0.151739i
$148$		0			0
$149$	−1.00728	−	2.20564i	−0.0825199	−	0.180693i	0.863874	−	0.503708i	$-0.168031\pi$
$149$	−1.00728	−	2.20564i	−0.0825199	−	0.180693i	−0.946394	+	0.323014i	$0.895304\pi$
$150$		0			0
$151$	−2.90056	−	20.1738i	−0.236044	−	1.64172i	−0.671134	−	0.741336i	$-0.734192\pi$
$151$	−2.90056	−	20.1738i	−0.236044	−	1.64172i	0.435090	−	0.900387i	$-0.356717\pi$
$152$		0			0
$153$	−15.4123	−	8.41576i	−1.24601	−	0.680374i
$154$		0			0
$155$	1.94946	−	13.2385i	0.156585	−	1.06334i
$156$		0			0
$157$	−4.75815	−	0.340310i	−0.379742	−	0.0271597i	−0.119836	−	0.992794i	$-0.538237\pi$
$157$	−4.75815	−	0.340310i	−0.379742	−	0.0271597i	−0.259906	+	0.965634i	$0.583691\pi$
$158$		0			0
$159$	−1.08346	+	2.37244i	−0.0859236	+	0.188147i
$160$		0			0
$161$	1.96733	−	8.86138i	0.155048	−	0.698375i
$162$		0			0
$163$	8.33261	+	22.3406i	0.652660	+	1.74985i	0.661563	+	0.749890i	$0.269894\pi$
$163$	8.33261	+	22.3406i	0.652660	+	1.74985i	−0.00890215	+	0.999960i	$0.502834\pi$
$164$		0			0
$165$	2.68452	+	4.95640i	0.208989	+	0.385855i
$166$		0			0
$167$	14.6493	−	1.04774i	1.13360	−	0.0810766i	0.508098	−	0.861299i	$-0.330349\pi$
$167$	14.6493	−	1.04774i	1.13360	−	0.0810766i	0.625502	+	0.780223i	$0.284894\pi$
$168$		0			0
$169$	4.19578	+	14.2895i	0.322752	+	1.09919i
$170$		0			0
$171$	−6.90589	+	0.992917i	−0.528106	+	0.0759302i
$172$		0			0
$173$	−6.68438	−	2.49315i	−0.508204	−	0.189550i	0.0822651	−	0.996610i	$-0.473785\pi$
$173$	−6.68438	−	2.49315i	−0.508204	−	0.189550i	−0.590469	+	0.807060i	$0.701057\pi$
$174$		0			0
$175$	−2.07459	+	9.23338i	−0.156824	+	0.697978i
$176$		0			0
$177$	3.91770	−	2.93275i	0.294472	−	0.220439i
$178$		0			0
$179$	−10.4798	−	16.3069i	−0.783297	−	1.21883i	−0.971578	−	0.236719i	$-0.923928\pi$
$179$	−10.4798	−	16.3069i	−0.783297	−	1.21883i	0.188281	−	0.982115i	$-0.439708\pi$
$180$		0			0
$181$	−5.26614	+	17.9348i	−0.391429	+	1.33309i	0.494465	+	0.869198i	$0.335364\pi$
$181$	−5.26614	+	17.9348i	−0.391429	+	1.33309i	−0.885894	+	0.463888i	$0.846454\pi$
$182$		0			0
$183$	−0.769138	−	0.769138i	−0.0568563	−	0.0568563i
$184$		0			0
$185$	−1.01548	+	4.59272i	−0.0746599	+	0.337663i
$186$		0			0
$187$	14.2810	+	26.1538i	1.04433	+	1.91255i
$188$		0			0
$189$	4.99681	−	3.21126i	0.363465	−	0.233584i
$190$		0			0
$191$	14.7515	+	2.12094i	1.06738	+	0.153466i	0.653545	−	0.756887i	$-0.273281\pi$
$191$	14.7515	+	2.12094i	1.06738	+	0.153466i	0.413832	+	0.910353i	$0.364190\pi$
$192$		0			0
$193$	−11.9094	+	2.59074i	−0.857259	+	0.186485i	−0.619653	−	0.784876i	$-0.712727\pi$
$193$	−11.9094	+	2.59074i	−0.857259	+	0.186485i	−0.237607	+	0.971361i	$0.576363\pi$
$194$		0			0
$195$	−3.53594	+	5.46104i	−0.253214	+	0.391073i
$196$		0			0
$197$	−2.67495	+	3.57331i	−0.190582	+	0.254588i	−0.885647	−	0.464359i	$-0.846285\pi$
$197$	−2.67495	+	3.57331i	−0.190582	+	0.254588i	0.695065	+	0.718947i	$0.255376\pi$
$198$		0			0
$199$	−8.92953	+	2.62195i	−0.632997	+	0.185865i	−0.582463	−	0.812858i	$-0.697911\pi$
$199$	−8.92953	+	2.62195i	−0.632997	+	0.185865i	−0.0505347	+	0.998722i	$0.516093\pi$
$200$		0			0
$201$	−1.14528	−	0.992390i	−0.0807818	−	0.0699978i
$202$		0			0
$203$	−0.539117	+	7.53783i	−0.0378386	+	0.529052i
$204$		0			0
$205$	1.43136	+	10.2019i	0.0999702	+	0.712533i
$206$		0			0
$207$	−12.8081	+	1.78575i	−0.890226	+	0.124118i
$208$		0			0
$209$	10.7695	+	4.91826i	0.744941	+	0.340203i
$210$		0			0
$211$	9.65256	+	11.1397i	0.664510	+	0.766885i	0.983507	−	0.180871i	$-0.0578915\pi$
$211$	9.65256	+	11.1397i	0.664510	+	0.766885i	−0.318997	+	0.947756i	$0.603346\pi$
$212$		0			0
$213$	−0.272075	−	3.80411i	−0.0186423	−	0.260653i
$214$		0			0
$215$	10.5427	−	0.717937i	0.719008	−	0.0489629i
$216$		0			0
$217$	9.06735	+	6.78773i	0.615532	+	0.460781i
$218$		0			0
$219$	−3.07857	+	1.40593i	−0.208030	+	0.0950042i
$220$		0			0
$221$	−18.5945	+	28.9336i	−1.25080	+	1.94629i
$222$		0			0
$223$	−10.8311	−	14.4687i	−0.725306	−	0.968895i	−0.999973	−	0.00735547i	$-0.997659\pi$
$223$	−10.8311	−	14.4687i	−0.725306	−	0.968895i	0.274667	−	0.961539i	$-0.411432\pi$
$224$		0			0
$225$	13.3581	−	1.82779i	0.890539	−	0.121853i
$226$		0			0
$227$	−9.90056	+	5.40611i	−0.657123	+	0.358816i	−0.772963	−	0.634452i	$-0.781226\pi$
$227$	−9.90056	+	5.40611i	−0.657123	+	0.358816i	0.115840	+	0.993268i	$0.463044\pi$
$228$		0			0
$229$	2.02531			0.133836			0.0669181	−	0.997758i	$-0.478683\pi$
$229$	2.02531			0.133836			0.0669181	+	0.997758i	$0.478683\pi$
$230$		0			0
$231$	−4.77118			−0.313921
$232$		0			0
$233$	18.5115	−	10.1080i	1.21273	−	0.662200i	0.259878	−	0.965641i	$-0.416318\pi$
$233$	18.5115	−	10.1080i	1.21273	−	0.662200i	0.952850	+	0.303442i	$0.0981358\pi$
$234$		0			0
$235$	1.31745	−	0.486279i	0.0859413	−	0.0317213i
$236$		0			0
$237$	−3.38806	−	4.52592i	−0.220078	−	0.293990i
$238$		0			0
$239$	−2.03229	+	3.16231i	−0.131458	+	0.204553i	−0.900742	−	0.434354i	$-0.856977\pi$
$239$	−2.03229	+	3.16231i	−0.131458	+	0.204553i	0.769284	+	0.638907i	$0.220613\pi$
$240$		0			0
$241$	16.0461	−	7.32801i	1.03362	−	0.472039i	0.174956	−	0.984576i	$-0.444022\pi$
$241$	16.0461	−	7.32801i	1.03362	−	0.472039i	0.858665	+	0.512537i	$0.171294\pi$
$242$		0			0
$243$	−10.3420	−	7.74189i	−0.663437	−	0.496643i
$244$		0			0
$245$	5.75839	+	5.02413i	0.367890	+	0.320980i
$246$		0			0
$247$	0.974843	+	13.6301i	0.0620277	+	0.867261i
$248$		0			0
$249$	2.88670	+	3.33143i	0.182937	+	0.211121i
$250$		0			0
$251$	12.2036	+	5.57320i	0.770285	+	0.351778i	0.761484	−	0.648184i	$-0.224471\pi$
$251$	12.2036	+	5.57320i	0.770285	+	0.351778i	0.00880137	+	0.999961i	$0.497198\pi$
$252$		0			0
$253$	19.9226	+	9.20136i	1.25253	+	0.578485i
$254$		0			0
$255$	−7.94427	+	1.11460i	−0.497489	+	0.0697990i
$256$		0			0
$257$	0.834769	−	11.6716i	0.0520714	−	0.728054i	−0.902617	−	0.430446i	$-0.858356\pi$
$257$	0.834769	−	11.6716i	0.0520714	−	0.728054i	0.954688	−	0.297608i	$-0.0961890\pi$
$258$		0			0
$259$	−3.00893	−	2.60726i	−0.186966	−	0.162007i
$260$		0			0
$261$	10.3303	−	3.03325i	0.639430	−	0.187754i
$262$		0			0
$263$	−4.66392	+	6.23027i	−0.287590	+	0.384175i	−0.920949	−	0.389683i	$-0.872585\pi$
$263$	−4.66392	+	6.23027i	−0.287590	+	0.384175i	0.633359	+	0.773858i	$0.281675\pi$
$264$		0			0
$265$	−2.21501	−	10.3519i	−0.136067	−	0.635914i
$266$		0			0
$267$	9.90049	−	2.15372i	0.605900	−	0.131805i
$268$		0			0
$269$	23.2754	+	3.34650i	1.41913	+	0.204040i	0.808788	−	0.588100i	$-0.200124\pi$
$269$	23.2754	+	3.34650i	1.41913	+	0.204040i	0.610339	+	0.792140i	$0.291033\pi$
$270$		0			0
$271$	22.7802	−	14.6399i	1.38380	−	0.889313i	0.384372	−	0.923178i	$-0.374418\pi$
$271$	22.7802	−	14.6399i	1.38380	−	0.889313i	0.999426	+	0.0338654i	$0.0107817\pi$
$272$		0			0
$273$	−2.63915	−	4.83324i	−0.159729	−	0.292521i
$274$		0			0
$275$	−20.7463	−	9.64590i	−1.25105	−	0.581670i
$276$		0			0
$277$	−0.551669	−	0.551669i	−0.0331466	−	0.0331466i	0.690339	−	0.723486i	$-0.257461\pi$
$277$	−0.551669	−	0.551669i	−0.0331466	−	0.0331466i	−0.723486	+	0.690339i	$0.757461\pi$
$278$		0			0
$279$	4.54622	−	15.4830i	0.272175	−	0.926943i
$280$		0			0
$281$	12.7924	+	19.9054i	0.763132	+	1.18746i	0.977548	+	0.210714i	$0.0675787\pi$
$281$	12.7924	+	19.9054i	0.763132	+	1.18746i	−0.214416	+	0.976742i	$0.568785\pi$
$282$		0			0
$283$	19.0422	−	14.2548i	1.13194	−	0.847360i	0.142144	−	0.989846i	$-0.454600\pi$
$283$	19.0422	−	14.2548i	1.13194	−	0.847360i	0.989797	+	0.142486i	$0.0455095\pi$
$284$		0			0
$285$	−2.26140	+	2.24604i	−0.133954	+	0.133044i
$286$		0			0
$287$	−8.17018	−	3.04732i	−0.482270	−	0.179878i
$288$		0			0
$289$	−25.1506	+	3.61611i	−1.47945	+	0.212712i
$290$		0			0
$291$	−1.25131	−	4.26157i	−0.0733531	−	0.249818i
$292$		0			0
$293$	15.7808	−	1.12866i	0.921921	−	0.0659371i	0.397696	−	0.917517i	$-0.369810\pi$
$293$	15.7808	−	1.12866i	0.921921	−	0.0659371i	0.524225	+	0.851580i	$0.324355\pi$
$294$		0			0
$295$	−5.66116	+	19.0399i	−0.329605	+	1.10855i
$296$		0			0
$297$	5.01825	+	13.4544i	0.291188	+	0.780706i
$298$		0			0
$299$	1.69904	+	25.2715i	0.0982581	+	1.46149i
$300$		0			0
$301$	−3.71570	+	8.13624i	−0.214169	+	0.468965i
$302$		0			0
$303$	−10.9134	−	0.780540i	−0.626957	−	0.0448408i
$304$		0			0
$305$	4.36791	+	0.643208i	0.250106	+	0.0368300i
$306$		0			0
$307$	−15.2749	−	8.34071i	−0.871783	−	0.476029i	−0.0199242	−	0.999801i	$-0.506342\pi$
$307$	−15.2749	−	8.34071i	−0.871783	−	0.476029i	−0.851858	+	0.523772i	$0.824524\pi$
$308$		0			0
$309$	1.13134	+	7.86861i	0.0643594	+	0.447630i
$310$		0			0
$311$	−2.04163	−	4.47055i	−0.115770	−	0.253502i	0.842873	−	0.538113i	$-0.180863\pi$
$311$	−2.04163	−	4.47055i	−0.115770	−	0.253502i	−0.958643	+	0.284611i	$0.908135\pi$
$312$		0			0
$313$	−1.21089	−	5.56636i	−0.0684434	−	0.314629i	0.930179	−	0.367107i	$-0.119652\pi$
$313$	−1.21089	−	5.56636i	−0.0684434	−	0.314629i	−0.998622	+	0.0524780i	$0.983288\pi$
$314$		0			0
$315$	−4.02459	+	10.6791i	−0.226760	+	0.601698i
$316$		0			0
$317$	−8.49414	−	1.84779i	−0.477079	−	0.103782i	−0.0324050	−	0.999475i	$-0.510317\pi$
$317$	−8.49414	−	1.84779i	−0.477079	−	0.103782i	−0.444673	+	0.895693i	$0.646680\pi$
$318$		0			0
$319$	−17.5299	−	5.14725i	−0.981487	−	0.288191i
$320$		0			0
$321$		−	4.95987i		−	0.276833i
$322$		0			0
$323$	−11.9145	+	11.9145i	−0.662940	+	0.662940i
$324$		0			0
$325$	−1.70432	−	26.3518i	−0.0945387	−	1.46173i
$326$		0			0
$327$	−1.47034	+	6.75904i	−0.0813100	+	0.373776i
$328$		0			0
$329$	−0.169169	+	1.17660i	−0.00932659	+	0.0648679i
$330$		0			0
$331$	−18.9448	−	12.1751i	−1.04130	−	0.669203i	−0.0959926	−	0.995382i	$-0.530603\pi$
$331$	−18.9448	−	12.1751i	−1.04130	−	0.669203i	−0.945308	+	0.326179i	$0.894239\pi$
$332$		0			0
$333$	−1.98223	+	5.31457i	−0.108626	+	0.291236i
$334$		0			0
$335$	6.13381	+	0.459709i	0.335126	+	0.0251166i
$336$		0			0
$337$	4.62678	−	8.47331i	0.252037	−	0.461571i	−0.720775	−	0.693169i	$-0.756214\pi$
$337$	4.62678	−	8.47331i	0.252037	−	0.461571i	0.972811	+	0.231599i	$0.0743956\pi$
$338$		0			0
$339$	5.44959	−	6.28916i	0.295981	−	0.341580i
$340$		0			0
$341$	−20.6946	+	17.9320i	−1.12068	+	0.971073i
$342$		0			0
$343$	−18.4744	+	6.89060i	−0.997524	+	0.372057i
$344$		0			0
$345$	−4.20934	+	4.14521i	−0.226623	+	0.223170i
$346$		0			0
$347$	30.3148	−	11.3068i	1.62738	−	0.606983i	0.640435	−	0.768012i	$-0.278754\pi$
$347$	30.3148	−	11.3068i	1.62738	−	0.606983i	0.986950	+	0.161029i	$0.0514814\pi$
$348$		0			0
$349$	4.47921	−	3.88125i	0.239766	−	0.207759i	−0.526686	−	0.850060i	$-0.676566\pi$
$349$	4.47921	−	3.88125i	0.239766	−	0.207759i	0.766452	+	0.642301i	$0.222020\pi$
$350$		0			0
$351$	−10.8536	+	12.5258i	−0.579325	+	0.668576i
$352$		0			0
$353$	−3.92577	+	7.18952i	−0.208948	+	0.382659i	−0.961045	−	0.276393i	$-0.910861\pi$
$353$	−3.92577	+	7.18952i	−0.208948	+	0.382659i	0.752097	+	0.659053i	$0.229043\pi$
$354$		0			0
$355$	10.0974	+	11.7336i	0.535914	+	0.622752i
$356$		0			0
$357$	2.37296	−	6.36214i	0.125590	−	0.336720i
$358$		0			0
$359$	−9.17371	−	5.89559i	−0.484170	−	0.311157i	0.275687	−	0.961247i	$-0.411095\pi$
$359$	−9.17371	−	5.89559i	−0.484170	−	0.311157i	−0.759857	+	0.650090i	$0.774731\pi$
$360$		0			0
$361$	1.75125	−	12.1802i	0.0921710	−	0.641063i
$362$		0			0
$363$	1.16377	−	5.34977i	0.0610822	−	0.280790i
$364$		0			0
$365$	6.62454	−	12.0343i	0.346744	−	0.629903i
$366$		0			0
$367$	22.6419	−	22.6419i	1.18190	−	1.18190i	0.202648	−	0.979252i	$-0.435045\pi$
$367$	22.6419	−	22.6419i	1.18190	−	1.18190i	0.979252	−	0.202648i	$-0.0649546\pi$
$368$		0			0
$369$			12.4232i			0.646724i
$370$		0			0
$371$	8.59774	+	2.52452i	0.446372	+	0.131067i
$372$		0			0
$373$	15.2196	+	3.31082i	0.788040	+	0.171428i	0.588538	−	0.808470i	$-0.299704\pi$
$373$	15.2196	+	3.31082i	0.788040	+	0.171428i	0.199502	+	0.979897i	$0.436068\pi$
$374$		0			0
$375$	4.39952	−	4.31050i	0.227190	−	0.222593i
$376$		0			0
$377$	−4.48237	−	20.6051i	−0.230854	−	1.06122i
$378$		0			0
$379$	−8.12010	−	17.7805i	−0.417102	−	0.913325i	−0.995246	−	0.0973909i	$-0.968950\pi$
$379$	−8.12010	−	17.7805i	−0.417102	−	0.913325i	0.578145	−	0.815934i	$-0.303777\pi$
$380$		0			0
$381$	0.249116	+	1.73264i	0.0127626	+	0.0887659i
$382$		0			0
$383$	−23.7991	−	12.9953i	−1.21608	−	0.664028i	−0.262428	−	0.964951i	$-0.584523\pi$
$383$	−23.7991	−	12.9953i	−1.21608	−	0.664028i	−0.953648	+	0.300923i	$0.902705\pi$
$384$		0			0
$385$	15.5427	−	11.5527i	0.792129	−	0.588780i
$386$		0			0
$387$	12.7106	+	0.909082i	0.646117	+	0.0462112i
$388$		0			0
$389$	3.84257	−	8.41405i	0.194826	−	0.426609i	−0.786856	−	0.617137i	$-0.788293\pi$
$389$	3.84257	−	8.41405i	0.194826	−	0.426609i	0.981682	+	0.190527i	$0.0610198\pi$
$390$		0			0
$391$	−22.1781	+	21.9896i	−1.12160	+	1.11206i
$392$		0			0
$393$	−0.757260	−	2.03029i	−0.0381987	−	0.102415i
$394$		0			0
$395$	21.9959	+	6.54005i	1.10673	+	0.329066i
$396$		0			0
$397$	−15.6835	+	1.12171i	−0.787132	+	0.0562968i	−0.459117	−	0.888376i	$-0.651834\pi$
$397$	−15.6835	+	1.12171i	−0.787132	+	0.0562968i	−0.328015	+	0.944673i	$0.606380\pi$
$398$		0			0
$399$	−0.760072	−	2.58857i	−0.0380512	−	0.129590i
$400$		0			0
$401$	−11.9594	+	1.71951i	−0.597226	+	0.0858682i	−0.434297	−	0.900770i	$-0.643003\pi$
$401$	−11.9594	+	1.71951i	−0.597226	+	0.0858682i	−0.162929	+	0.986638i	$0.552094\pi$
$402$		0			0
$403$	−29.6124	−	11.0448i	−1.47510	−	0.550183i
$404$		0			0
$405$	14.2229	+	0.0484573i	0.706740	+	0.00240786i
$406$		0			0
$407$	7.70552	−	5.76828i	0.381948	−	0.285923i
$408$		0			0
$409$	−10.0595	−	15.6529i	−0.497411	−	0.773986i	0.498251	−	0.867033i	$-0.333976\pi$
$409$	−10.0595	−	15.6529i	−0.497411	−	0.773986i	−0.995662	+	0.0930465i	$0.970339\pi$
$410$		0			0
$411$	−2.15433	+	7.33697i	−0.106265	+	0.361906i
$412$		0			0
$413$	−11.8890	−	11.8890i	−0.585020	−	0.585020i
$414$		0			0
$415$	−17.4704	−	3.86283i	−0.857586	−	0.189619i
$416$		0			0
$417$	−2.72361	−	4.98792i	−0.133376	−	0.244260i
$418$		0			0
$419$	−16.5750	+	10.6521i	−0.809739	+	0.520388i	−0.878781	−	0.477226i	$-0.841642\pi$
$419$	−16.5750	+	10.6521i	−0.809739	+	0.520388i	0.0690413	+	0.997614i	$0.478006\pi$
$420$		0			0
$421$	−25.9646	−	3.73314i	−1.26544	−	0.181942i	−0.523275	−	0.852164i	$-0.675290\pi$
$421$	−25.9646	−	3.73314i	−1.26544	−	0.181942i	−0.742161	+	0.670222i	$0.766199\pi$
$422$		0			0
$423$	1.65481	−	0.359981i	0.0804595	−	0.0175029i
$424$		0			0
$425$	23.1806	−	22.8668i	1.12442	−	1.10920i
$426$		0			0
$427$	−2.23955	+	2.99169i	−0.108379	+	0.144778i
$428$		0			0
$429$	12.7740	−	3.75080i	0.616736	−	0.181090i
$430$		0			0
$431$	20.7052	+	17.9412i	0.997336	+	0.864197i	0.990739	−	0.135781i	$-0.0433545\pi$
$431$	20.7052	+	17.9412i	0.997336	+	0.864197i	0.00659747	+	0.999978i	$0.497900\pi$
$432$		0			0
$433$	−2.32694	+	32.5349i	−0.111826	+	1.56353i	0.563568	+	0.826070i	$0.309428\pi$
$433$	−2.32694	+	32.5349i	−0.111826	+	1.56353i	−0.675394	+	0.737457i	$0.736026\pi$
$434$		0			0
$435$	2.96090	−	3.92734i	0.141964	−	0.188301i
$436$		0			0
$437$	−1.81835	+	12.2747i	−0.0869837	+	0.587178i
$438$		0			0
$439$	−11.3732	−	5.19399i	−0.542815	−	0.247895i	0.125085	−	0.992146i	$-0.460080\pi$
$439$	−11.3732	−	5.19399i	−0.542815	−	0.247895i	−0.667901	+	0.744251i	$0.732807\pi$
$440$		0			0
$441$	6.03498	+	6.96474i	0.287380	+	0.331654i
$442$		0			0
$443$	−0.572344	−	8.00242i	−0.0271929	−	0.380207i	−0.992765	−	0.120072i	$-0.961688\pi$
$443$	−0.572344	−	8.00242i	−0.0271929	−	0.380207i	0.965572	−	0.260135i	$-0.0837670\pi$
$444$		0			0
$445$	−27.0371	+	30.9886i	−1.28168	+	1.46900i
$446$		0			0
$447$	−1.06936	−	0.800515i	−0.0505791	−	0.0378631i
$448$		0			0
$449$	4.25992	−	1.94544i	0.201038	−	0.0918110i	−0.312352	−	0.949966i	$-0.601117\pi$
$449$	4.25992	−	1.94544i	0.201038	−	0.0918110i	0.513390	+	0.858156i	$0.328389\pi$
$450$		0			0
$451$	11.3974	−	17.7348i	0.536685	−	0.835098i
$452$		0			0
$453$	−6.72870	−	8.98850i	−0.316142	−	0.422316i
$454$		0			0
$455$	20.3003	+	9.35457i	0.951694	+	0.438549i
$456$		0			0
$457$	26.1018	−	14.2527i	1.22099	−	0.666712i	0.266181	−	0.963923i	$-0.414238\pi$
$457$	26.1018	−	14.2527i	1.22099	−	0.666712i	0.954812	+	0.297211i	$0.0960564\pi$
$458$		0			0
$459$	−20.4367			−0.953904
$460$		0			0
$461$	−15.5985			−0.726495			−0.363247	−	0.931693i	$-0.618332\pi$
$461$	−15.5985			−0.726495			−0.363247	+	0.931693i	$0.618332\pi$
$462$		0			0
$463$	27.8497	−	15.2071i	1.29428	−	0.706733i	0.323395	−	0.946264i	$-0.395176\pi$
$463$	27.8497	−	15.2071i	1.29428	−	0.706733i	0.970889	+	0.239531i	$0.0769938\pi$
$464$		0			0
$465$	−2.55260	−	6.91566i	−0.118374	−	0.320706i
$466$		0			0
$467$	−11.6572	−	15.5721i	−0.539429	−	0.720592i	0.445165	−	0.895448i	$-0.353145\pi$
$467$	−11.6572	−	15.5721i	−0.539429	−	0.720592i	−0.984594	+	0.174856i	$0.944054\pi$
$468$		0			0
$469$	−2.81485	+	4.38000i	−0.129978	+	0.202250i
$470$		0			0
$471$	−2.39047	+	1.09169i	−0.110147	+	0.0503025i
$472$		0			0
$473$	−17.3111	−	12.9589i	−0.795966	−	0.595853i
$474$		0			0
$475$	1.92832	−	12.7924i	0.0884776	−	0.586955i
$476$		0			0
$477$	−0.910725	−	12.7336i	−0.0416993	−	0.583032i
$478$		0			0
$479$	8.06294	+	9.30513i	0.368405	+	0.425162i	0.909438	−	0.415839i	$-0.136512\pi$
$479$	8.06294	+	9.30513i	0.368405	+	0.425162i	−0.541033	+	0.841001i	$0.681967\pi$
$480$		0			0
$481$	10.1056	+	4.61506i	0.460775	+	0.210429i
$482$		0			0
$483$	−1.38833	−	4.80400i	−0.0631713	−	0.218590i
$484$		0			0
$485$	14.3950	+	10.8527i	0.653645	+	0.492797i
$486$		0			0
$487$	0.389408	−	5.44463i	0.0176457	−	0.246720i	−0.980972	−	0.194151i	$-0.937805\pi$
$487$	0.389408	−	5.44463i	0.0176457	−	0.246720i	0.998617	−	0.0525684i	$-0.0167408\pi$
$488$		0			0
$489$	9.92723	+	8.60200i	0.448925	+	0.388996i
$490$		0			0
$491$	−24.1260	+	7.08403i	−1.08879	+	0.319698i	−0.776390	−	0.630253i	$-0.782951\pi$
$491$	−24.1260	+	7.08403i	−1.08879	+	0.319698i	−0.312401	+	0.949950i	$0.601133\pi$
$492$		0			0
$493$	15.5822	−	20.8153i	0.701785	−	0.937475i
$494$		0			0
$495$	−23.1595	−	14.9954i	−1.04094	−	0.673994i
$496$		0			0
$497$	−12.8037	+	2.78527i	−0.574322	+	0.124936i
$498$		0			0
$499$	−43.1398	−	6.20256i	−1.93120	−	0.277665i	−0.934310	−	0.356461i	$-0.883983\pi$
$499$	−43.1398	−	6.20256i	−1.93120	−	0.277665i	−0.996891	+	0.0787964i	$0.974892\pi$
$500$		0			0
$501$	6.80651	−	4.37428i	0.304093	−	0.195428i
$502$		0			0
$503$	−1.83815	−	3.36632i	−0.0819592	−	0.150097i	0.833485	−	0.552542i	$-0.186342\pi$
$503$	−1.83815	−	3.36632i	−0.0819592	−	0.150097i	−0.915444	+	0.402445i	$0.868160\pi$
$504$		0			0
$505$	37.4416	−	23.8824i	1.66613	−	1.06275i
$506$		0			0
$507$	5.80140	+	5.80140i	0.257649	+	0.257649i
$508$		0			0
$509$	−2.58959	+	8.81933i	−0.114782	+	0.390910i	−0.996765	−	0.0803701i	$-0.974390\pi$
$509$	−2.58959	+	8.81933i	−0.114782	+	0.390910i	0.881984	+	0.471280i	$0.156208\pi$
$510$		0			0
$511$	6.28644	+	9.78190i	0.278096	+	0.432726i
$512$		0			0
$513$	−6.50017	+	4.86597i	−0.286990	+	0.214838i
$514$		0			0
$515$	−22.7381	−	22.8936i	−1.00196	−	1.00881i
$516$		0			0
$517$	−2.69259	−	1.00428i	−0.118420	−	0.0441684i
$518$		0			0
$519$	−3.89022	+	0.559329i	−0.170761	+	0.0245518i
$520$		0			0
$521$	4.55332	+	15.5072i	0.199485	+	0.679382i	0.997092	+	0.0762053i	$0.0242804\pi$
$521$	4.55332	+	15.5072i	0.199485	+	0.679382i	−0.797608	+	0.603177i	$0.793901\pi$
$522$		0			0
$523$	2.15198	−	0.153913i	0.0940995	−	0.00673013i	−0.0242100	−	0.999707i	$-0.507707\pi$
$523$	2.15198	−	0.153913i	0.0940995	−	0.00673013i	0.118310	+	0.992977i	$0.462252\pi$
$524$		0			0
$525$	1.43469	+	5.01218i	0.0626148	+	0.218750i
$526$		0			0
$527$	−13.6190	−	36.5138i	−0.593251	−	1.59057i
$528$		0			0
$529$	−3.46751	+	22.7371i	−0.150761	+	0.988570i
$530$		0			0
$531$	−9.95084	+	21.7893i	−0.431830	+	0.945575i
$532$		0			0
$533$	24.2699	+	1.73582i	1.05125	+	0.0751866i
$534$		0			0
$535$	12.0096	+	16.1574i	0.519219	+	0.698544i
$536$		0			0
$537$	−9.37242	−	5.11773i	−0.404450	−	0.220846i
$538$		0			0
$539$	−2.22558	−	15.4793i	−0.0958627	−	0.666739i
$540$		0			0
$541$	5.97692	+	13.0876i	0.256968	+	0.562681i	0.993514	−	0.113706i	$-0.0362721\pi$
$541$	5.97692	+	13.0876i	0.256968	+	0.562681i	−0.736547	+	0.676387i	$0.763545\pi$
$542$		0			0
$543$	2.18887	+	10.0621i	0.0939333	+	0.431805i
$544$		0			0
$545$	−11.5762	−	25.5786i	−0.495870	−	1.09567i
$546$		0			0
$547$	23.1452	+	5.03493i	0.989618	+	0.215278i	0.678106	−	0.734964i	$-0.262801\pi$
$547$	23.1452	+	5.03493i	0.989618	+	0.215278i	0.311512	+	0.950242i	$0.399165\pi$
$548$		0			0
$549$	5.10848	+	1.49998i	0.218024	+	0.0640177i
$550$		0			0
$551$		−	10.3307i		−	0.440103i
$552$		0			0
$553$	−13.7348	+	13.7348i	−0.584063	+	0.584063i
$554$		0			0
$555$	0.721560	+	2.48874i	0.0306285	+	0.105641i
$556$		0			0
$557$	−8.92019	+	41.0054i	−0.377960	+	1.73746i	0.258376	+	0.966044i	$0.416813\pi$
$557$	−8.92019	+	41.0054i	−0.377960	+	1.73746i	−0.636336	+	0.771412i	$0.719551\pi$
$558$		0			0
$559$	3.55197	−	24.7045i	0.150232	−	1.04489i
$560$		0			0
$561$	13.8101	+	8.87523i	0.583064	+	0.374712i
$562$		0			0
$563$	2.44309	−	6.55018i	0.102964	−	0.276057i	−0.875245	−	0.483680i	$-0.839300\pi$
$563$	2.44309	−	6.55018i	0.102964	−	0.276057i	0.978209	+	0.207623i	$0.0665727\pi$
$564$		0			0
$565$	−2.52443	+	33.6831i	−0.106204	+	1.41706i
$566$		0			0
$567$	−5.76968	+	10.5664i	−0.242304	+	0.443746i
$568$		0			0
$569$	8.50781	−	9.81854i	0.356666	−	0.411615i	−0.548854	−	0.835918i	$-0.684936\pi$
$569$	8.50781	−	9.81854i	0.356666	−	0.411615i	0.905520	+	0.424304i	$0.139481\pi$
$570$		0			0
$571$	−13.7751	+	11.9362i	−0.576470	+	0.499514i	−0.893598	−	0.448869i	$-0.851827\pi$
$571$	−13.7751	+	11.9362i	−0.576470	+	0.499514i	0.317128	+	0.948383i	$0.397282\pi$
$572$		0			0
$573$	7.69247	−	2.86914i	0.321358	−	0.119860i
$574$		0			0
$575$	3.67544	−	23.6958i	0.153276	−	0.988183i
$576$		0			0
$577$	12.5418	−	4.67786i	0.522123	−	0.194742i	−0.0745632	−	0.997216i	$-0.523756\pi$
$577$	12.5418	−	4.67786i	0.522123	−	0.194742i	0.596687	+	0.802474i	$0.296484\pi$
$578$		0			0
$579$	−5.07435	+	4.39695i	−0.210883	+	0.182731i
$580$		0			0
$581$	9.91781	−	11.4458i	0.411460	−	0.474850i
$582$		0			0
$583$	−10.3821	+	19.0135i	−0.429985	+	0.787458i
$584$		0			0
$585$	2.37996	−	31.7553i	0.0983991	−	1.31292i
$586$		0			0
$587$	−5.73594	+	15.3786i	−0.236747	+	0.634744i	−0.999935	−	0.0114331i	$-0.996361\pi$
$587$	−5.73594	+	15.3786i	−0.236747	+	0.634744i	0.763187	+	0.646177i	$0.223633\pi$
$588$		0			0
$589$	−13.0256	−	8.37106i	−0.536712	−	0.344924i
$590$		0			0
$591$	−0.349953	+	2.43397i	−0.0143951	+	0.100120i
$592$		0			0
$593$	0.382024	−	1.75614i	0.0156879	−	0.0721159i	−0.968637	−	0.248478i	$-0.920069\pi$
$593$	0.382024	−	1.75614i	0.0156879	−	0.0721159i	0.984325	+	0.176363i	$0.0564331\pi$
$594$		0			0
$595$	7.67479	+	26.4712i	0.314636	+	1.08521i
$596$		0			0
$597$	−3.62530	+	3.62530i	−0.148373	+	0.148373i
$598$		0			0
$599$			46.7821i			1.91146i	0.294239	+	0.955732i	$0.404934\pi$
$599$			46.7821i			1.91146i	−0.294239	+	0.955732i	$0.595066\pi$
$600$		0			0
$601$	23.6851	+	6.95457i	0.966135	+	0.283683i	0.726489	−	0.687178i	$-0.241151\pi$
$601$	23.6851	+	6.95457i	0.966135	+	0.283683i	0.239646	+	0.970860i	$0.422969\pi$
$602$		0			0
$603$	7.24809	+	1.57673i	0.295165	+	0.0642092i
$604$		0			0
$605$	9.16255	+	20.2454i	0.372511	+	0.823094i
$606$		0			0
$607$	5.70685	+	26.2339i	0.231634	+	1.06480i	0.935185	+	0.354159i	$0.115233\pi$
$607$	5.70685	+	26.2339i	0.231634	+	1.06480i	−0.703552	+	0.710644i	$0.748404\pi$
$608$		0			0
$609$	1.72945	+	3.78697i	0.0700809	+	0.153456i
$610$		0			0
$611$	−0.472043	−	3.28313i	−0.0190968	−	0.132821i
$612$		0			0
$613$	−28.4745	−	15.5482i	−1.15007	−	0.627988i	−0.212977	−	0.977057i	$-0.568316\pi$
$613$	−28.4745	−	15.5482i	−1.15007	−	0.627988i	−0.937097	+	0.349070i	$0.886498\pi$
$614$		0			0
$615$	3.38557	+	4.55485i	0.136519	+	0.183669i
$616$		0			0
$617$	−17.4933	−	1.25115i	−0.704255	−	0.0503693i	−0.285382	−	0.958414i	$-0.592120\pi$
$617$	−17.4933	−	1.25115i	−0.704255	−	0.0503693i	−0.418873	+	0.908045i	$0.637575\pi$
$618$		0			0
$619$	14.8119	−	32.4336i	0.595342	−	1.30362i	−0.336818	−	0.941570i	$-0.609351\pi$
$619$	14.8119	−	32.4336i	0.595342	−	1.30362i	0.932160	−	0.362047i	$-0.117922\pi$
$620$		0			0
$621$	−12.0868	+	8.96778i	−0.485025	+	0.359865i
$622$		0			0
$623$	−12.1650	−	32.6157i	−0.487381	−	1.30672i
$624$		0			0
$625$	−3.89476	+	24.6948i	−0.155790	+	0.987790i
$626$		0			0
$627$	6.50569	−	0.465296i	0.259812	−	0.0185821i
$628$		0			0
$629$	3.85937	+	13.1438i	0.153883	+	0.524078i
$630$		0			0
$631$	35.3074	−	5.07644i	1.40557	−	0.202090i	0.602567	−	0.798068i	$-0.294145\pi$
$631$	35.3074	−	5.07644i	1.40557	−	0.202090i	0.803000	+	0.595978i	$0.203236\pi$
$632$		0			0
$633$	7.60820	+	2.83771i	0.302399	+	0.112789i
$634$		0			0
$635$	−5.00686	−	5.04109i	−0.198691	−	0.200050i
$636$		0			0
$637$	14.4496	−	10.8168i	0.572512	−	0.428577i
$638$		0			0
$639$	10.0925	+	15.7043i	0.399254	+	0.621252i
$640$		0			0
$641$	0.200361	−	0.682368i	0.00791380	−	0.0269519i	−0.955441	−	0.295181i	$-0.904620\pi$
$641$	0.200361	−	0.682368i	0.00791380	−	0.0269519i	0.963355	+	0.268229i	$0.0864383\pi$
$642$		0			0
$643$	20.0376	+	20.0376i	0.790205	+	0.790205i	0.981527	−	0.191322i	$-0.0612775\pi$
$643$	20.0376	+	20.0376i	0.790205	+	0.790205i	−0.191322	+	0.981527i	$0.561277\pi$
$644$		0			0
$645$	4.90799	−	3.13060i	0.193252	−	0.123267i
$646$		0			0
$647$	10.1200	+	18.5335i	0.397859	+	0.728625i	0.997426	−	0.0716996i	$-0.0228423\pi$
$647$	10.1200	+	18.5335i	0.397859	+	0.728625i	−0.599567	+	0.800325i	$0.704660\pi$
$648$		0			0
$649$	34.1957	−	21.9762i	1.34230	−	0.862642i
$650$		0			0
$651$	6.17625	+	0.888011i	0.242067	+	0.0348039i
$652$		0			0
$653$	−39.2055	+	8.52864i	−1.53423	+	0.333751i	−0.898783	−	0.438393i	$-0.855548\pi$
$653$	−39.2055	+	8.52864i	−1.53423	+	0.333751i	−0.635447	+	0.772145i	$0.719184\pi$
$654$		0			0
$655$	7.38292	+	4.78033i	0.288474	+	0.186783i
$656$		0			0
$657$	9.92753	−	13.2616i	0.387310	−	0.517385i
$658$		0			0
$659$	19.1101	−	5.61122i	0.744423	−	0.218582i	0.112541	−	0.993647i	$-0.464101\pi$
$659$	19.1101	−	5.61122i	0.744423	−	0.218582i	0.631882	+	0.775065i	$0.282283\pi$
$660$		0			0
$661$	−7.39848	−	6.41082i	−0.287767	−	0.249352i	0.498999	−	0.866602i	$-0.333701\pi$
$661$	−7.39848	−	6.41082i	−0.287767	−	0.249352i	−0.786767	+	0.617251i	$0.788247\pi$
$662$		0			0
$663$	−1.35169	+	18.8990i	−0.0524952	+	0.733978i
$664$		0			0
$665$	8.74385	+	6.59217i	0.339072	+	0.255633i
$666$		0			0
$667$	0.0817492	−	19.1483i	0.00316534	−	0.741423i
$668$		0			0
$669$	−9.05697	−	4.13618i	−0.350163	−	0.159914i
$670$		0			0
$671$	−5.91650	−	6.82801i	−0.228404	−	0.263592i
$672$		0			0
$673$	0.172267	+	2.40861i	0.00664042	+	0.0928452i	0.999691	−	0.0248393i	$-0.00790740\pi$
$673$	0.172267	+	2.40861i	0.00664042	+	0.0928452i	−0.993051	+	0.117684i	$0.962453\pi$
$674$		0			0
$675$	12.6251	−	9.31746i	0.485939	−	0.358629i
$676$		0			0
$677$	2.90633	+	2.17565i	0.111699	+	0.0836172i	0.653667	−	0.756782i	$-0.273230\pi$
$677$	2.90633	+	2.17565i	0.111699	+	0.0836172i	−0.541968	+	0.840399i	$0.682321\pi$
$678$		0			0
$679$	−13.8806	+	6.33904i	−0.532687	+	0.243270i
$680$		0			0
$681$	−3.35973	+	5.22784i	−0.128745	+	0.200331i
$682$		0			0
$683$	−19.2201	−	25.6751i	−0.735438	−	0.982430i	−0.999838	−	0.0180170i	$-0.994265\pi$
$683$	−19.2201	−	25.6751i	−0.735438	−	0.982430i	0.264400	−	0.964413i	$-0.414826\pi$
$684$		0			0
$685$	−10.7474	−	29.1174i	−0.410637	−	1.11252i
$686$		0			0
$687$	0.979262	−	0.534717i	0.0373612	−	0.0204007i
$688$		0			0
$689$	−25.0036			−0.952563
$690$		0			0
$691$	9.23395			0.351276			0.175638	−	0.984455i	$-0.443801\pi$
$691$	9.23395			0.351276			0.175638	+	0.984455i	$0.443801\pi$
$692$		0			0
$693$	20.4971	−	11.1922i	0.778619	−	0.425158i
$694$		0			0
$695$	20.9500	+	9.65394i	0.794679	+	0.366195i
$696$		0			0
$697$	17.9799	+	24.0184i	0.681039	+	0.909761i
$698$		0			0
$699$	6.28183	−	9.77472i	0.237601	−	0.369714i
$700$		0			0
$701$	−36.6061	+	16.7174i	−1.38259	+	0.631408i	−0.961297	−	0.275515i	$-0.911151\pi$
$701$	−36.6061	+	16.7174i	−1.38259	+	0.631408i	−0.421295	+	0.906924i	$0.638424\pi$
$702$		0			0
$703$	4.35706	+	3.26165i	0.164330	+	0.123016i
$704$		0			0
$705$	0.508619	−	0.582953i	0.0191557	−	0.0219553i
$706$		0			0
$707$	2.68169	+	37.4949i	0.100855	+	1.41014i
$708$		0			0
$709$	−10.5481	−	12.1732i	−0.396142	−	0.457172i	0.522280	−	0.852774i	$-0.325082\pi$
$709$	−10.5481	−	12.1732i	−0.396142	−	0.457172i	−0.918422	+	0.395602i	$0.870536\pi$
$710$		0			0
$711$	25.1721	+	11.4957i	0.944028	+	0.431123i
$712$		0			0
$713$	−24.0771	−	15.6191i	−0.901696	−	0.584939i
$714$		0			0
$715$	−32.5310	+	43.1491i	−1.21659	+	1.61369i
$716$		0			0
$717$	−0.147733	+	2.06557i	−0.00551718	+	0.0771403i
$718$		0			0
$719$	−29.8342	−	25.8515i	−1.11263	−	0.964097i	−0.113062	−	0.993588i	$-0.536066\pi$
$719$	−29.8342	−	25.8515i	−1.11263	−	0.964097i	−0.999565	+	0.0294910i	$0.990611\pi$
$720$		0			0
$721$	26.2057	−	7.69470i	0.975953	−	0.286566i
$722$		0			0
$723$	5.82377	−	7.77964i	0.216588	−	0.289328i
$724$		0			0
$725$	−0.136030	+	19.9632i	−0.00505204	+	0.741413i
$726$		0			0
$727$	−12.7393	+	2.77127i	−0.472475	+	0.102781i	−0.442497	−	0.896770i	$-0.645907\pi$
$727$	−12.7393	+	2.77127i	−0.472475	+	0.102781i	−0.0299776	+	0.999551i	$0.509544\pi$
$728$		0			0
$729$	11.8434	+	1.70283i	0.438645	+	0.0630676i
$730$		0			0
$731$	25.8899	−	16.6384i	0.957571	−	0.615394i
$732$		0			0
$733$	−12.8116	−	23.4626i	−0.473206	−	0.866612i	−0.999863	−	0.0165340i	$-0.994737\pi$
$733$	−12.8116	−	23.4626i	−0.473206	−	0.866612i	0.526658	−	0.850078i	$-0.323445\pi$
$734$		0			0
$735$	4.11071	+	0.908909i	0.151626	+	0.0335256i
$736$		0			0
$737$	−8.90052	−	8.90052i	−0.327855	−	0.327855i
$738$		0			0
$739$	−8.76515	+	29.8513i	−0.322431	+	1.09810i	0.625659	+	0.780097i	$0.284830\pi$
$739$	−8.76515	+	29.8513i	−0.322431	+	1.09810i	−0.948090	+	0.318003i	$0.896988\pi$
$740$		0			0
$741$	4.06993	+	6.33294i	0.149513	+	0.232646i
$742$		0			0
$743$	16.8961	−	12.6483i	0.619859	−	0.464021i	−0.242614	−	0.970123i	$-0.578005\pi$
$743$	16.8961	−	12.6483i	0.619859	−	0.464021i	0.862474	+	0.506102i	$0.168914\pi$
$744$		0			0
$745$	5.42191	+	0.0184724i	0.198643	+	0.000676777i
$746$		0			0
$747$	−20.2162	−	7.54026i	−0.739673	−	0.275884i
$748$		0			0
$749$	−16.8671	+	2.42512i	−0.616310	+	0.0886120i
$750$		0			0
$751$	8.01318	+	27.2904i	0.292405	+	0.995840i	0.966387	+	0.257092i	$0.0827644\pi$
$751$	8.01318	+	27.2904i	0.292405	+	0.995840i	−0.673982	+	0.738748i	$0.735417\pi$
$752$		0			0
$753$	7.37202	−	0.527257i	0.268651	−	0.0192143i
$754$		0			0
$755$	43.6839	+	12.9886i	1.58982	+	0.472702i
$756$		0			0
$757$	0.589526	+	1.58058i	0.0214267	+	0.0574472i	0.947223	−	0.320576i	$-0.103877\pi$
$757$	0.589526	+	1.58058i	0.0214267	+	0.0574472i	−0.925796	+	0.378024i	$0.876604\pi$
$758$		0			0
$759$	12.0622	−	0.810959i	0.437829	−	0.0294359i
$760$		0			0
$761$	−22.0673	+	48.3207i	−0.799941	+	1.75163i	−0.154242	+	0.988033i	$0.549294\pi$
$761$	−22.0673	+	48.3207i	−0.799941	+	1.75163i	−0.645698	+	0.763593i	$0.723434\pi$
$762$		0			0
$763$	23.7045	+	1.69538i	0.858161	+	0.0613769i
$764$		0			0
$765$	31.5141	−	23.4240i	1.13939	−	0.846898i
$766$		0			0
$767$	41.1772	+	22.4845i	1.48682	+	0.811867i
$768$		0			0
$769$	6.50551	+	45.2468i	0.234595	+	1.63164i	0.677817	+	0.735231i	$0.262926\pi$
$769$	6.50551	+	45.2468i	0.234595	+	1.63164i	−0.443222	+	0.896412i	$0.646165\pi$
$770$		0			0
$771$	−2.67789	−	5.86375i	−0.0964417	−	0.211178i
$772$		0			0
$773$	10.7864	+	49.5843i	0.387960	+	1.78342i	0.593564	+	0.804787i	$0.297720\pi$
$773$	10.7864	+	49.5843i	0.387960	+	1.78342i	−0.205604	+	0.978635i	$0.565916\pi$
$774$		0			0
$775$	25.0606	+	16.3478i	0.900205	+	0.587232i
$776$		0			0
$777$	−2.14322	−	0.466229i	−0.0768875	−	0.0167259i
$778$		0			0
$779$	11.4375	+	3.35836i	0.409792	+	0.120326i
$780$		0			0
$781$		−	31.6780i		−	1.13353i
$782$		0			0
$783$	8.86003	−	8.86003i	0.316631	−	0.316631i
$784$		0			0
$785$	5.14389	−	9.34449i	0.183593	−	0.333519i
$786$		0			0
$787$	2.40889	−	11.0735i	0.0858676	−	0.394727i	−0.914074	−	0.405548i	$-0.867081\pi$
$787$	2.40889	−	11.0735i	0.0858676	−	0.394727i	0.999941	+	0.0108208i	$0.00344444\pi$
$788$		0			0
$789$	−0.610162	+	4.24377i	−0.0217223	+	0.151082i
$790$		0			0
$791$	−24.0522	−	15.4574i	−0.855198	−	0.549602i
$792$		0			0
$793$	3.64415	−	9.77034i	0.129407	−	0.346955i
$794$		0			0
$795$	−3.80408	−	4.42048i	−0.134917	−	0.156778i
$796$		0			0
$797$	−1.73077	+	3.16967i	−0.0613070	+	0.112275i	−0.906535	−	0.422130i	$-0.861283\pi$
$797$	−1.73077	+	3.16967i	−0.0613070	+	0.112275i	0.845228	+	0.534405i	$0.179464\pi$
$798$		0			0
$799$	2.67833	−	3.09096i	0.0947526	−	0.109350i
$800$		0			0
$801$	−37.4805	+	32.4770i	−1.32431	+	1.14752i
$802$		0			0
$803$	−26.3388	+	9.82386i	−0.929476	+	0.346677i
$804$		0			0
$805$	16.1548	+	12.2880i	0.569383	+	0.433094i
$806$		0			0
$807$	12.1375	−	4.52705i	0.427260	−	0.159360i
$808$		0			0
$809$	−40.9733	+	35.5035i	−1.44054	+	1.24824i	−0.521983	+	0.852956i	$0.674808\pi$
$809$	−40.9733	+	35.5035i	−1.44054	+	1.24824i	−0.918560	+	0.395282i	$0.870647\pi$
$810$		0			0
$811$	0.505776	−	0.583697i	0.0177602	−	0.0204964i	−0.746800	−	0.665049i	$-0.768411\pi$
$811$	0.505776	−	0.583697i	0.0177602	−	0.0204964i	0.764560	+	0.644552i	$0.222956\pi$
$812$		0			0
$813$	7.14930	−	13.0930i	0.250737	−	0.459190i
$814$		0			0
$815$	−53.1676	−	3.98474i	−1.86238	−	0.139579i
$816$		0			0
$817$	4.27303	−	11.4564i	0.149494	−	0.400810i
$818$		0			0
$819$	22.6757	+	14.5728i	0.792352	+	0.509214i
$820$		0			0
$821$	3.80317	−	26.4516i	0.132732	−	0.923168i	−0.809241	−	0.587477i	$-0.800121\pi$
$821$	3.80317	−	26.4516i	0.132732	−	0.923168i	0.941972	−	0.335691i	$-0.108970\pi$
$822$		0			0
$823$	−3.57230	+	16.4216i	−0.124522	+	0.572420i	0.872030	+	0.489453i	$0.162803\pi$
$823$	−3.57230	+	16.4216i	−0.124522	+	0.572420i	−0.996552	+	0.0829676i	$0.973560\pi$
$824$		0			0
$825$	−12.5778	+	0.813479i	−0.437902	+	0.0283217i
$826$		0			0
$827$	−15.0751	+	15.0751i	−0.524211	+	0.524211i	−0.918841	−	0.394629i	$-0.870873\pi$
$827$	−15.0751	+	15.0751i	−0.524211	+	0.524211i	0.394629	+	0.918841i	$0.370873\pi$
$828$		0			0
$829$			4.79511i			0.166541i	0.996527	+	0.0832705i	$0.0265366\pi$
$829$			4.79511i			0.166541i	−0.996527	+	0.0832705i	$0.973463\pi$
$830$		0			0
$831$	−0.412389	−	0.121088i	−0.0143056	−	0.00420051i
$832$		0			0
$833$	21.7478	+	4.73094i	0.753516	+	0.163917i
$834$		0			0
$835$	−11.5814	+	30.7307i	−0.400790	+	1.06348i
$836$		0			0
$837$	−3.99194	−	18.3507i	−0.137982	−	0.634292i
$838$		0			0
$839$	1.89871	+	4.15759i	0.0655507	+	0.143536i	0.939572	−	0.342352i	$-0.111224\pi$
$839$	1.89871	+	4.15759i	0.0655507	+	0.143536i	−0.874021	+	0.485888i	$0.838496\pi$
$840$		0			0
$841$	−1.85837	−	12.9252i	−0.0640817	−	0.445698i
$842$		0			0
$843$	11.4407	+	6.24708i	0.394037	+	0.215161i
$844$		0			0
$845$	−32.9460	−	4.85154i	−1.13338	−	0.166898i
$846$		0			0
$847$	−18.7621	−	1.34189i	−0.644673	−	0.0461079i
$848$		0			0
$849$	5.44361	−	11.9198i	0.186824	−	0.409088i
$850$		0			0
$851$	8.05013	+	6.08005i	0.275955	+	0.208422i
$852$		0			0
$853$	−15.8939	−	42.6132i	−0.544197	−	1.45905i	−0.860034	−	0.510236i	$-0.829558\pi$
$853$	−15.8939	−	42.6132i	−0.544197	−	1.45905i	0.315837	−	0.948813i	$-0.397715\pi$
$854$		0			0
$855$	4.44623	−	14.9538i	0.152058	−	0.511410i
$856$		0			0
$857$	−31.9935	+	2.28822i	−1.09288	+	0.0781642i	−0.606121	−	0.795373i	$-0.707275\pi$
$857$	−31.9935	+	2.28822i	−1.09288	+	0.0781642i	−0.486758	+	0.873537i	$0.661821\pi$
$858$		0			0
$859$	−10.6138	−	36.1473i	−0.362138	−	1.23333i	−0.916155	−	0.400824i	$-0.868724\pi$
$859$	−10.6138	−	36.1473i	−0.362138	−	1.23333i	0.554017	−	0.832505i	$-0.313094\pi$
$860$		0			0
$861$	−4.75493	+	0.683655i	−0.162047	+	0.0232989i
$862$		0			0
$863$	−0.314369	−	0.117254i	−0.0107013	−	0.00399136i	0.344108	−	0.938930i	$-0.388181\pi$
$863$	−0.314369	−	0.117254i	−0.0107013	−	0.00399136i	−0.354809	+	0.934939i	$0.615454\pi$
$864$		0			0
$865$	11.3185	−	11.2417i	0.384841	−	0.382228i
$866$		0			0
$867$	−11.2059	+	8.38863i	−0.380572	+	0.284893i
$868$		0			0
$869$	−25.3880	−	39.5046i	−0.861230	−	1.34010i
$870$		0			0
$871$	4.09303	−	13.9396i	0.138687	−	0.472324i
$872$		0			0
$873$	15.3724	+	15.3724i	0.520278	+	0.520278i
$874$		0			0
$875$	−16.8099	−	12.8539i	−0.568279	−	0.434542i
$876$		0			0
$877$	−0.933829	−	1.71018i	−0.0315332	−	0.0577487i	0.861437	−	0.507864i	$-0.169565\pi$
$877$	−0.933829	−	1.71018i	−0.0315332	−	0.0577487i	−0.892970	+	0.450115i	$0.851383\pi$
$878$		0			0
$879$	7.33220	−	4.71212i	0.247309	−	0.158936i
$880$		0			0
$881$	31.6363	+	4.54861i	1.06585	+	0.153247i	0.652854	−	0.757484i	$-0.273572\pi$
$881$	31.6363	+	4.54861i	1.06585	+	0.153247i	0.413001	+	0.910731i	$0.364481\pi$
$882$		0			0
$883$	−44.5155	+	9.68376i	−1.49807	+	0.325885i	−0.885539	−	0.464564i	$-0.846211\pi$
$883$	−44.5155	+	9.68376i	−1.49807	+	0.325885i	−0.612528	+	0.790449i	$0.709847\pi$
$884$		0			0
$885$	2.28964	+	10.7007i	0.0769653	+	0.359699i
$886$		0			0
$887$	30.4714	−	40.7050i	1.02313	−	1.36674i	0.0945846	−	0.995517i	$-0.469848\pi$
$887$	30.4714	−	40.7050i	1.02313	−	1.36674i	0.928544	−	0.371223i	$-0.121061\pi$
$888$		0			0
$889$	5.77041	−	1.69435i	0.193533	−	0.0568266i
$890$		0			0
$891$	−21.9964	−	19.0600i	−0.736907	−	0.638534i
$892$		0			0
$893$	0.115924	−	1.62083i	0.00387925	−	0.0542391i
$894$		0			0
$895$	42.9236	−	6.02229i	1.43478	−	0.201303i
$896$		0			0
$897$	7.49362	+	11.7705i	0.250205	+	0.393005i
$898$		0			0
$899$	21.7343	+	9.92573i	0.724880	+	0.331042i
$900$		0			0
$901$	−20.1900	−	23.3005i	−0.672626	−	0.776252i
$902$		0			0
$903$	0.351526	+	4.91498i	0.0116981	+	0.163560i
$904$		0			0
$905$	−31.4943	−	27.4784i	−1.04691	−	0.913412i
$906$		0			0
$907$	10.2450	+	7.66932i	0.340180	+	0.254656i	0.755685	−	0.654935i	$-0.227304\pi$
$907$	10.2450	+	7.66932i	0.340180	+	0.254656i	−0.415505	+	0.909591i	$0.636395\pi$
$908$		0			0
$909$	48.7150	−	22.2474i	1.61578	−	0.737900i
$910$		0			0
$911$	12.2995	−	19.1384i	0.407501	−	0.634085i	−0.575474	−	0.817820i	$-0.695183\pi$
$911$	12.2995	−	19.1384i	0.407501	−	0.634085i	0.982976	+	0.183735i	$0.0588189\pi$
$912$		0			0
$913$	21.9421	+	29.3112i	0.726178	+	0.970060i
$914$		0			0
$915$	2.28176	−	0.842207i	0.0754326	−	0.0278425i
$916$		0			0
$917$	−6.53419	+	3.56794i	−0.215778	+	0.117824i
$918$		0			0
$919$	−25.5482			−0.842756			−0.421378	−	0.906885i	$-0.638454\pi$
$919$	−25.5482			−0.842756			−0.421378	+	0.906885i	$0.638454\pi$
$920$		0			0
$921$	−9.58768			−0.315925
$922$		0			0
$923$	32.0901	−	17.5225i	1.05626	−	0.576760i
$924$		0			0
$925$	−8.37668	−	6.36023i	−0.275424	−	0.209123i
$926$		0			0
$927$	−23.3184	−	31.1498i	−0.765878	−	1.02309i
$928$		0			0
$929$	−19.4099	+	30.2024i	−0.636819	+	0.990909i	0.361467	+	0.932385i	$0.382276\pi$
$929$	−19.4099	+	30.2024i	−0.636819	+	0.990909i	−0.998286	+	0.0585243i	$0.981360\pi$
$930$		0			0
$931$	8.04361	−	3.67339i	0.263619	−	0.120391i
$932$		0			0
$933$	−2.16746	−	1.62254i	−0.0709595	−	0.0531196i
$934$		0			0
$935$	−66.4782	+	4.52702i	−2.17407	+	0.148049i
$936$		0			0
$937$	−2.73891	−	38.2950i	−0.0894763	−	1.25104i	−0.821677	−	0.569953i	$-0.806961\pi$
$937$	−2.73891	−	38.2950i	−0.0894763	−	1.25104i	0.732201	−	0.681089i	$-0.238493\pi$
$938$		0			0
$939$	−2.05509	−	2.37171i	−0.0670655	−	0.0773977i
$940$		0			0
$941$	11.1181	+	5.07747i	0.362440	+	0.165521i	0.588308	−	0.808637i	$-0.299794\pi$
$941$	11.1181	+	5.07747i	0.362440	+	0.165521i	−0.225868	+	0.974158i	$0.572522\pi$
$942$		0			0
$943$	21.1732	+	6.31533i	0.689495	+	0.205655i
$944$		0			0
$945$	1.84537	+	13.1528i	0.0600299	+	0.427860i
$946$		0			0
$947$	−2.77463	+	38.7944i	−0.0901634	+	1.26065i	0.727966	+	0.685614i	$0.240466\pi$
$947$	−2.77463	+	38.7944i	−0.0901634	+	1.26065i	−0.818129	+	0.575035i	$0.804989\pi$
$948$		0			0
$949$	−24.5208	−	21.2474i	−0.795979	−	0.689720i
$950$		0			0
$951$	−4.59487	+	1.34918i	−0.148999	+	0.0437500i
$952$		0			0
$953$	8.02828	−	10.7245i	0.260062	−	0.347402i	−0.651439	−	0.758701i	$-0.725834\pi$
$953$	8.02828	−	10.7245i	0.260062	−	0.347402i	0.911500	+	0.411300i	$0.134925\pi$
$954$		0			0
$955$	−18.1120	+	27.9728i	−0.586089	+	0.905177i
$956$		0			0
$957$	−9.83489	+	2.13945i	−0.317917	+	0.0691586i
$958$		0			0
$959$	26.0043	+	3.73885i	0.839723	+	0.120734i
$960$		0			0
$961$	4.04769	−	2.60129i	0.130571	−	0.0839126i
$962$		0			0
$963$	11.6349	+	21.3077i	0.374928	+	0.686630i
$964$		0			0
$965$	5.88376	−	26.6104i	0.189405	−	0.856619i
$966$		0			0
$967$	−16.8844	−	16.8844i	−0.542967	−	0.542967i	0.381430	−	0.924398i	$-0.375432\pi$
$967$	−16.8844	−	16.8844i	−0.542967	−	0.542967i	−0.924398	+	0.381430i	$0.875432\pi$
$968$		0			0
$969$	−2.61517	+	8.90644i	−0.0840113	+	0.286116i
$970$		0			0
$971$	−20.5702	−	32.0078i	−0.660128	−	1.02718i	−0.996347	−	0.0853956i	$-0.972785\pi$
$971$	−20.5702	−	32.0078i	−0.660128	−	1.02718i	0.336219	−	0.941784i	$-0.390852\pi$
$972$		0			0
$973$	−15.6308	+	11.7011i	−0.501100	+	0.375119i
$974$		0			0
$975$	−7.78139	−	12.2914i	−0.249204	−	0.393641i
$976$		0			0
$977$	−14.6986	−	5.48229i	−0.470250	−	0.175394i	0.103157	−	0.994665i	$-0.467106\pi$
$977$	−14.6986	−	5.48229i	−0.470250	−	0.175394i	−0.573407	+	0.819271i	$0.694378\pi$
$978$		0			0
$979$	83.3011	−	11.9769i	2.66231	−	0.382783i
$980$		0			0
$981$	−9.53878	−	32.4861i	−0.304550	−	1.03720i
$982$		0			0
$983$	−47.4711	+	3.39520i	−1.51409	+	0.108290i	−0.803496	−	0.595311i	$-0.797029\pi$
$983$	−47.4711	+	3.39520i	−1.51409	+	0.108290i	−0.710596	+	0.703601i	$0.751574\pi$
$984$		0			0
$985$	−4.75349	−	8.77632i	−0.151459	−	0.279637i
$986$		0			0
$987$	0.228847	+	0.613563i	0.00728428	+	0.0195299i
$988$		0			0
$989$	8.01084	−	21.2010i	0.254730	−	0.674153i
$990$		0			0
$991$	0.773687	−	1.69414i	0.0245770	−	0.0538160i	−0.896945	−	0.442141i	$-0.854219\pi$
$991$	0.773687	−	1.69414i	0.0245770	−	0.0538160i	0.921522	+	0.388325i	$0.126946\pi$
$992$		0			0
$993$	−12.3745	−	0.885041i	−0.392692	−	0.0280859i
$994$		0			0
$995$	3.03173	−	20.5880i	0.0961123	−	0.652682i
$996$		0			0
$997$	18.5444	+	10.1260i	0.587307	+	0.320694i	0.745282	−	0.666749i	$-0.232315\pi$
$997$	18.5444	+	10.1260i	0.587307	+	0.320694i	−0.157975	+	0.987443i	$0.550497\pi$
$998$		0			0
$999$	0.939465	+	6.53412i	0.0297233	+	0.206730i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.17.8	✓	240
5.3	odd	4	inner	460.2.x.a.293.8	yes	240
23.19	odd	22	inner	460.2.x.a.157.8	yes	240
115.88	even	44	inner	460.2.x.a.433.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.17.8	✓	240	1.1	even	1	trivial
460.2.x.a.157.8	yes	240	23.19	odd	22	inner
460.2.x.a.293.8	yes	240	5.3	odd	4	inner
460.2.x.a.433.8	yes	240	115.88	even	44	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.483512 - 0.264018i) q^{3} +(-0.935821 + 2.03082i) q^{5} +(-1.13426 - 1.51520i) q^{7} +(-1.45784 + 2.26845i) q^{9} +O(q^{10})\)	\(q+(0.483512 - 0.264018i) q^{3} +(-0.935821 + 2.03082i) q^{5} +(-1.13426 - 1.51520i) q^{7} +(-1.45784 + 2.26845i) q^{9} +(4.16231 - 1.90086i) q^{11} +(4.22795 + 3.16500i) q^{13} +(0.0836923 + 1.22900i) q^{15} +(0.464578 + 6.49564i) q^{17} +(1.69437 + 1.95541i) q^{19} +(-0.948468 - 0.433151i) q^{21} +(3.12510 + 3.63782i) q^{23} +(-3.24848 - 3.80097i) q^{25} +(-0.223877 + 3.13020i) q^{27} +(-3.01750 - 2.61468i) q^{29} +(-5.74187 + 1.68596i) q^{31} +(1.51067 - 2.01801i) q^{33} +(4.13856 - 0.885532i) q^{35} +(2.05546 - 0.447138i) q^{37} +(2.87988 + 0.414064i) q^{39} +(3.87576 - 2.49080i) q^{41} +(-2.26482 - 4.14771i) q^{43} +(-3.24254 - 5.08348i) q^{45} +(-0.444089 - 0.444089i) q^{47} +(0.962857 - 3.27919i) q^{49} +(1.93959 + 3.01807i) q^{51} +(-3.79001 + 2.83717i) q^{53} +(-0.0348596 + 10.2318i) q^{55} +(1.33551 + 0.498121i) q^{57} +(8.79290 - 1.26423i) q^{59} +(-0.556268 - 1.89448i) q^{61} +(5.09072 - 0.364096i) q^{63} +(-10.3842 + 5.62434i) q^{65} +(-0.961312 - 2.57738i) q^{67} +(2.47147 + 0.933850i) q^{69} +(2.87588 - 6.29730i) q^{71} +(-6.12778 - 0.438267i) q^{73} +(-2.57420 - 0.980160i) q^{75} +(-7.60133 - 4.15064i) q^{77} +(-1.46050 - 10.1580i) q^{79} +(-2.64233 - 5.78590i) q^{81} +(1.70088 + 7.81882i) q^{83} +(-13.6263 - 5.13528i) q^{85} +(-2.14932 - 0.467556i) q^{87} +(17.6468 + 5.18158i) q^{89} -9.99611i q^{91} +(-2.33114 + 2.33114i) q^{93} +(-5.55673 + 1.61106i) q^{95} +(1.71375 - 7.87800i) q^{97} +(-1.75599 + 12.2132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 240 * q + 4 * q^3	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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