LMFDB - Embedded newform 429.2.m.b.109.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(109,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("429.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.m (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.5
Character	$\chi$	$=$	429.109
Dual form			429.2.m.b.307.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10479 - 1.10479i) q^{2} +1.00000 q^{3} +0.441107i q^{4} +(1.95513 - 1.95513i) q^{5} +(-1.10479 - 1.10479i) q^{6} +(1.11517 - 1.11517i) q^{7} +(-1.72224 + 1.72224i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.10479 - 1.10479i) q^{2} +1.00000 q^{3} +0.441107i q^{4} +(1.95513 - 1.95513i) q^{5} +(-1.10479 - 1.10479i) q^{6} +(1.11517 - 1.11517i) q^{7} +(-1.72224 + 1.72224i) q^{8} +1.00000 q^{9} -4.32001 q^{10} +(-2.92897 - 1.55601i) q^{11} +0.441107i q^{12} +(1.60847 - 3.22689i) q^{13} -2.46406 q^{14} +(1.95513 - 1.95513i) q^{15} +4.68764 q^{16} -0.0613854 q^{17} +(-1.10479 - 1.10479i) q^{18} +(1.53359 + 1.53359i) q^{19} +(0.862423 + 0.862423i) q^{20} +(1.11517 - 1.11517i) q^{21} +(1.51683 + 4.95494i) q^{22} +6.25724i q^{23} +(-1.72224 + 1.72224i) q^{24} -2.64508i q^{25} +(-5.34204 + 1.78801i) q^{26} +1.00000 q^{27} +(0.491911 + 0.491911i) q^{28} -5.40860i q^{29} -4.32001 q^{30} +(-1.00255 + 1.00255i) q^{31} +(-1.73435 - 1.73435i) q^{32} +(-2.92897 - 1.55601i) q^{33} +(0.0678178 + 0.0678178i) q^{34} -4.36062i q^{35} +0.441107i q^{36} +(-1.41877 - 1.41877i) q^{37} -3.38858i q^{38} +(1.60847 - 3.22689i) q^{39} +6.73443i q^{40} +(-6.30390 - 6.30390i) q^{41} -2.46406 q^{42} +6.96197 q^{43} +(0.686366 - 1.29199i) q^{44} +(1.95513 - 1.95513i) q^{45} +(6.91291 - 6.91291i) q^{46} +(-6.90374 - 6.90374i) q^{47} +4.68764 q^{48} +4.51278i q^{49} +(-2.92225 + 2.92225i) q^{50} -0.0613854 q^{51} +(1.42341 + 0.709509i) q^{52} -6.29470 q^{53} +(-1.10479 - 1.10479i) q^{54} +(-8.76871 + 2.68432i) q^{55} +3.84120i q^{56} +(1.53359 + 1.53359i) q^{57} +(-5.97535 + 5.97535i) q^{58} +(8.28019 + 8.28019i) q^{59} +(0.862423 + 0.862423i) q^{60} +9.57065i q^{61} +2.21521 q^{62} +(1.11517 - 1.11517i) q^{63} -5.54310i q^{64} +(-3.16422 - 9.45377i) q^{65} +(1.51683 + 4.95494i) q^{66} +(2.56219 - 2.56219i) q^{67} -0.0270776i q^{68} +6.25724i q^{69} +(-4.81755 + 4.81755i) q^{70} +(2.26887 - 2.26887i) q^{71} +(-1.72224 + 1.72224i) q^{72} +(3.20483 - 3.20483i) q^{73} +3.13487i q^{74} -2.64508i q^{75} +(-0.676477 + 0.676477i) q^{76} +(-5.00152 + 1.53109i) q^{77} +(-5.34204 + 1.78801i) q^{78} +7.07646i q^{79} +(9.16495 - 9.16495i) q^{80} +1.00000 q^{81} +13.9289i q^{82} +(9.65308 + 9.65308i) q^{83} +(0.491911 + 0.491911i) q^{84} +(-0.120017 + 0.120017i) q^{85} +(-7.69149 - 7.69149i) q^{86} -5.40860i q^{87} +(7.72422 - 2.36457i) q^{88} +(4.26632 + 4.26632i) q^{89} -4.32001 q^{90} +(-1.80482 - 5.39226i) q^{91} -2.76011 q^{92} +(-1.00255 + 1.00255i) q^{93} +15.2543i q^{94} +5.99673 q^{95} +(-1.73435 - 1.73435i) q^{96} +(9.43613 - 9.43613i) q^{97} +(4.98566 - 4.98566i) q^{98} +(-2.92897 - 1.55601i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9}+O(q^{10}) $ 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9	$ 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9} - 4 q^{15} - 20 q^{16} - 16 q^{20} - 8 q^{22} + 12 q^{26} + 28 q^{27} + 8 q^{31} - 32 q^{34} - 12 q^{37} + 36 q^{44} - 4 q^{45} - 40 q^{47} - 20 q^{48} + 8 q^{53} - 16 q^{55} + 16 q^{58} - 44 q^{59} - 16 q^{60} - 8 q^{66} - 20 q^{67} - 36 q^{70} - 60 q^{71} + 12 q^{78} - 8 q^{80} + 28 q^{81} + 48 q^{86} + 32 q^{89} + 4 q^{91} + 64 q^{92} + 8 q^{93} + 8 q^{97}+O(q^{100}) $ 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9 - 4 * q^15 - 20 * q^16 - 16 * q^20 - 8 * q^22 + 12 * q^26 + 28 * q^27 + 8 * q^31 - 32 * q^34 - 12 * q^37 + 36 * q^44 - 4 * q^45 - 40 * q^47 - 20 * q^48 + 8 * q^53 - 16 * q^55 + 16 * q^58 - 44 * q^59 - 16 * q^60 - 8 * q^66 - 20 * q^67 - 36 * q^70 - 60 * q^71 + 12 * q^78 - 8 * q^80 + 28 * q^81 + 48 * q^86 + 32 * q^89 + 4 * q^91 + 64 * q^92 + 8 * q^93 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.10479	−	1.10479i	−0.781202	−	0.781202i	0.198832	−	0.980034i	$-0.436285\pi$
$2$	−1.10479	−	1.10479i	−0.781202	−	0.781202i	−0.980034	+	0.198832i	$0.936285\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$			0.441107i			0.220554i
$5$	1.95513	−	1.95513i	0.874361	−	0.874361i	−0.118583	−	0.992944i	$-0.537835\pi$
$5$	1.95513	−	1.95513i	0.874361	−	0.874361i	0.992944	+	0.118583i	$0.0378351\pi$
$6$	−1.10479	−	1.10479i	−0.451027	−	0.451027i
$7$	1.11517	−	1.11517i	0.421496	−	0.421496i	−0.464223	−	0.885718i	$-0.653666\pi$
$7$	1.11517	−	1.11517i	0.421496	−	0.421496i	0.885718	+	0.464223i	$0.153666\pi$
$8$	−1.72224	+	1.72224i	−0.608905	+	0.608905i
$9$	1.00000			0.333333
$10$	−4.32001			−1.36611
$11$	−2.92897	−	1.55601i	−0.883117	−	0.469154i
$11$	−2.92897	−	1.55601i	−0.883117	−	0.469154i
$12$			0.441107i			0.127337i
$13$	1.60847	−	3.22689i	0.446110	−	0.894978i
$13$	1.60847	−	3.22689i	0.446110	−	0.894978i
$14$	−2.46406			−0.658547
$15$	1.95513	−	1.95513i	0.504813	−	0.504813i
$16$	4.68764			1.17191
$17$	−0.0613854			−0.0148881			−0.00744407	−	0.999972i	$-0.502370\pi$
$17$	−0.0613854			−0.0148881			−0.00744407	+	0.999972i	$0.502370\pi$
$18$	−1.10479	−	1.10479i	−0.260401	−	0.260401i
$19$	1.53359	+	1.53359i	0.351829	+	0.351829i	0.860790	−	0.508960i	$-0.169970\pi$
$19$	1.53359	+	1.53359i	0.351829	+	0.351829i	−0.508960	+	0.860790i	$0.669970\pi$
$20$	0.862423	+	0.862423i	0.192844	+	0.192844i
$21$	1.11517	−	1.11517i	0.243351	−	0.243351i
$22$	1.51683	+	4.95494i	0.323389	+	1.05640i
$23$			6.25724i			1.30472i	0.757907	+	0.652362i	$0.226222\pi$
$23$			6.25724i			1.30472i	−0.757907	+	0.652362i	$0.773778\pi$
$24$	−1.72224	+	1.72224i	−0.351552	+	0.351552i
$25$		−	2.64508i		−	0.529015i
$26$	−5.34204	+	1.78801i	−1.04766	+	0.350657i
$27$	1.00000			0.192450
$28$	0.491911	+	0.491911i	0.0929625	+	0.0929625i
$29$		−	5.40860i		−	1.00435i	−0.864765	−	0.502176i	$-0.832533\pi$
$29$		−	5.40860i		−	1.00435i	0.864765	−	0.502176i	$-0.167467\pi$
$30$	−4.32001			−0.788722
$31$	−1.00255	+	1.00255i	−0.180063	+	0.180063i	−0.791383	−	0.611320i	$-0.790639\pi$
$31$	−1.00255	+	1.00255i	−0.180063	+	0.180063i	0.611320	+	0.791383i	$0.290639\pi$
$32$	−1.73435	−	1.73435i	−0.306593	−	0.306593i
$33$	−2.92897	−	1.55601i	−0.509868	−	0.270866i
$34$	0.0678178	+	0.0678178i	0.0116307	+	0.0116307i
$35$		−	4.36062i		−	0.737079i
$36$			0.441107i			0.0735179i
$37$	−1.41877	−	1.41877i	−0.233244	−	0.233244i	0.580802	−	0.814045i	$-0.302739\pi$
$37$	−1.41877	−	1.41877i	−0.233244	−	0.233244i	−0.814045	+	0.580802i	$0.802739\pi$
$38$		−	3.38858i		−	0.549700i
$39$	1.60847	−	3.22689i	0.257562	−	0.516716i
$40$			6.73443i			1.06481i
$41$	−6.30390	−	6.30390i	−0.984504	−	0.984504i	0.0153779	−	0.999882i	$-0.495105\pi$
$41$	−6.30390	−	6.30390i	−0.984504	−	0.984504i	−0.999882	+	0.0153779i	$0.995105\pi$
$42$	−2.46406			−0.380212
$43$	6.96197			1.06169			0.530845	−	0.847469i	$-0.321875\pi$
$43$	6.96197			1.06169			0.530845	+	0.847469i	$0.321875\pi$
$44$	0.686366	−	1.29199i	0.103474	−	0.194775i
$45$	1.95513	−	1.95513i	0.291454	−	0.291454i
$46$	6.91291	−	6.91291i	1.01925	−	1.01925i
$47$	−6.90374	−	6.90374i	−1.00701	−	1.00701i	−0.999975	−	0.00703862i	$-0.997760\pi$
$47$	−6.90374	−	6.90374i	−1.00701	−	1.00701i	−0.00703862	−	0.999975i	$-0.502240\pi$
$48$	4.68764			0.676602
$49$			4.51278i			0.644683i
$50$	−2.92225	+	2.92225i	−0.413268	+	0.413268i
$51$	−0.0613854			−0.00859568
$52$	1.42341	+	0.709509i	0.197391	+	0.0983912i
$53$	−6.29470			−0.864644			−0.432322	−	0.901719i	$-0.642306\pi$
$53$	−6.29470			−0.864644			−0.432322	+	0.901719i	$0.642306\pi$
$54$	−1.10479	−	1.10479i	−0.150342	−	0.150342i
$55$	−8.76871	+	2.68432i	−1.18237	+	0.361953i
$56$			3.84120i			0.513302i
$57$	1.53359	+	1.53359i	0.203129	+	0.203129i
$58$	−5.97535	+	5.97535i	−0.784602	+	0.784602i
$59$	8.28019	+	8.28019i	1.07799	+	1.07799i	0.996690	+	0.0812986i	$0.0259067\pi$
$59$	8.28019	+	8.28019i	1.07799	+	1.07799i	0.0812986	+	0.996690i	$0.474093\pi$
$60$	0.862423	+	0.862423i	0.111338	+	0.111338i
$61$			9.57065i			1.22540i	0.790317	+	0.612698i	$0.209916\pi$
$61$			9.57065i			1.22540i	−0.790317	+	0.612698i	$0.790084\pi$
$62$	2.21521			0.281332
$63$	1.11517	−	1.11517i	0.140499	−	0.140499i
$64$		−	5.54310i		−	0.692887i
$65$	−3.16422	−	9.45377i	−0.392473	−	1.17260i
$66$	1.51683	+	4.95494i	0.186709	+	0.609911i
$67$	2.56219	−	2.56219i	0.313022	−	0.313022i	−0.533057	−	0.846079i	$-0.678957\pi$
$67$	2.56219	−	2.56219i	0.313022	−	0.313022i	0.846079	+	0.533057i	$0.178957\pi$
$68$		−	0.0270776i		−	0.00328364i
$69$			6.25724i			0.753283i
$70$	−4.81755	+	4.81755i	−0.575808	+	0.575808i
$71$	2.26887	−	2.26887i	0.269266	−	0.269266i	−0.559539	−	0.828804i	$-0.689022\pi$
$71$	2.26887	−	2.26887i	0.269266	−	0.269266i	0.828804	+	0.559539i	$0.189022\pi$
$72$	−1.72224	+	1.72224i	−0.202968	+	0.202968i
$73$	3.20483	−	3.20483i	0.375097	−	0.375097i	−0.494232	−	0.869330i	$-0.664551\pi$
$73$	3.20483	−	3.20483i	0.375097	−	0.375097i	0.869330	+	0.494232i	$0.164551\pi$
$74$			3.13487i			0.364421i
$75$		−	2.64508i		−	0.305427i
$76$	−0.676477	+	0.676477i	−0.0775973	+	0.0775973i
$77$	−5.00152	+	1.53109i	−0.569976	+	0.174484i
$78$	−5.34204	+	1.78801i	−0.604867	+	0.202452i
$79$			7.07646i			0.796164i	0.917350	+	0.398082i	$0.130324\pi$
$79$			7.07646i			0.796164i	−0.917350	+	0.398082i	$0.869676\pi$
$80$	9.16495	−	9.16495i	1.02467	−	1.02467i
$81$	1.00000			0.111111
$82$			13.9289i			1.53819i
$83$	9.65308	+	9.65308i	1.05956	+	1.05956i	0.998110	+	0.0614537i	$0.0195736\pi$
$83$	9.65308	+	9.65308i	1.05956	+	1.05956i	0.0614537	+	0.998110i	$0.480426\pi$
$84$	0.491911	+	0.491911i	0.0536719	+	0.0536719i
$85$	−0.120017	+	0.120017i	−0.0130176	+	0.0130176i
$86$	−7.69149	−	7.69149i	−0.829395	−	0.829395i
$87$		−	5.40860i		−	0.579863i
$88$	7.72422	−	2.36457i	0.823404	−	0.252064i
$89$	4.26632	+	4.26632i	0.452229	+	0.452229i	0.896094	−	0.443865i	$-0.146393\pi$
$89$	4.26632	+	4.26632i	0.452229	+	0.452229i	−0.443865	+	0.896094i	$0.646393\pi$
$90$	−4.32001			−0.455369
$91$	−1.80482	−	5.39226i	−0.189196	−	0.565263i
$92$	−2.76011			−0.287762
$93$	−1.00255	+	1.00255i	−0.103960	+	0.103960i
$94$			15.2543i			1.57336i
$95$	5.99673			0.615252
$96$	−1.73435	−	1.73435i	−0.177012	−	0.177012i
$97$	9.43613	−	9.43613i	0.958094	−	0.958094i	−0.0410627	−	0.999157i	$-0.513074\pi$
$97$	9.43613	−	9.43613i	0.958094	−	0.958094i	0.999157	+	0.0410627i	$0.0130743\pi$
$98$	4.98566	−	4.98566i	0.503627	−	0.503627i
$99$	−2.92897	−	1.55601i	−0.294372	−	0.156385i
$100$	1.16676			0.116676
$101$	5.84983			0.582080			0.291040	−	0.956711i	$-0.405999\pi$
$101$	5.84983			0.582080			0.291040	+	0.956711i	$0.405999\pi$
$102$	0.0678178	+	0.0678178i	0.00671496	+	0.00671496i
$103$		−	6.83706i		−	0.673675i	−0.941563	−	0.336838i	$-0.890643\pi$
$103$		−	6.83706i		−	0.673675i	0.941563	−	0.336838i	$-0.109357\pi$
$104$	2.78731	+	8.32767i	0.273318	+	0.816595i
$105$		−	4.36062i		−	0.425553i
$106$	6.95430	+	6.95430i	0.675461	+	0.675461i
$107$			16.6500i			1.60961i	0.593537	+	0.804806i	$0.297731\pi$
$107$			16.6500i			1.60961i	−0.593537	+	0.804806i	$0.702269\pi$
$108$			0.441107i			0.0424456i
$109$	−0.829101	−	0.829101i	−0.0794135	−	0.0794135i	0.666284	−	0.745698i	$-0.267884\pi$
$109$	−0.829101	−	0.829101i	−0.0794135	−	0.0794135i	−0.745698	+	0.666284i	$0.767884\pi$
$110$	12.6532	+	6.72196i	1.20643	+	0.640914i
$111$	−1.41877	−	1.41877i	−0.134663	−	0.134663i
$112$	5.22753	−	5.22753i	0.493955	−	0.493955i
$113$	9.59790			0.902895			0.451447	−	0.892298i	$-0.350908\pi$
$113$	9.59790			0.902895			0.451447	+	0.892298i	$0.350908\pi$
$114$		−	3.38858i		−	0.317369i
$115$	12.2337	+	12.2337i	1.14080	+	1.14080i
$116$	2.38577			0.221514
$117$	1.60847	−	3.22689i	0.148703	−	0.298326i
$118$		−	18.2957i		−	1.68425i
$119$	−0.0684553	+	0.0684553i	−0.00627529	+	0.00627529i
$120$			6.73443i			0.614766i
$121$	6.15769	+	9.11498i	0.559790	+	0.828635i
$122$	10.5735	−	10.5735i	0.957282	−	0.957282i
$123$	−6.30390	−	6.30390i	−0.568404	−	0.568404i
$124$	−0.442232	−	0.442232i	−0.0397136	−	0.0397136i
$125$	4.60418	+	4.60418i	0.411811	+	0.411811i
$126$	−2.46406			−0.219516
$127$	−2.39458			−0.212485			−0.106242	−	0.994340i	$-0.533882\pi$
$127$	−2.39458			−0.212485			−0.106242	+	0.994340i	$0.533882\pi$
$128$	−9.59265	+	9.59265i	−0.847878	+	0.847878i
$129$	6.96197			0.612967
$130$	−6.94861	+	13.9402i	−0.609433	+	1.22264i
$131$		−	10.3449i		−	0.903838i	−0.892059	−	0.451919i	$-0.850740\pi$
$131$		−	10.3449i		−	0.903838i	0.892059	−	0.451919i	$-0.149260\pi$
$132$	0.686366	−	1.29199i	0.0597405	−	0.112453i
$133$	3.42043			0.296589
$134$	−5.66135			−0.489066
$135$	1.95513	−	1.95513i	0.168271	−	0.168271i
$136$	0.105721	−	0.105721i	0.00906547	−	0.00906547i
$137$	5.12381	+	5.12381i	0.437757	+	0.437757i	0.891256	−	0.453500i	$-0.149825\pi$
$137$	5.12381	+	5.12381i	0.437757	+	0.437757i	−0.453500	+	0.891256i	$0.649825\pi$
$138$	6.91291	−	6.91291i	0.588466	−	0.588466i
$139$			14.8481i			1.25940i	0.776838	+	0.629701i	$0.216823\pi$
$139$			14.8481i			1.25940i	−0.776838	+	0.629701i	$0.783177\pi$
$140$	1.92350			0.162566
$141$	−6.90374	−	6.90374i	−0.581400	−	0.581400i
$142$	−5.01324			−0.420702
$143$	−9.73222	+	6.94866i	−0.813849	+	0.581076i
$144$	4.68764			0.390637
$145$	−10.5745	−	10.5745i	−0.878167	−	0.878167i
$146$	−7.08131			−0.586054
$147$			4.51278i			0.372208i
$148$	0.625828	−	0.625828i	0.0514428	−	0.0514428i
$149$	−1.39774	−	1.39774i	−0.114508	−	0.114508i	0.647531	−	0.762039i	$-0.275802\pi$
$149$	−1.39774	−	1.39774i	−0.114508	−	0.114508i	−0.762039	+	0.647531i	$0.775802\pi$
$150$	−2.92225	+	2.92225i	−0.238600	+	0.238600i
$151$	6.86639	−	6.86639i	0.558779	−	0.558779i	−0.370181	−	0.928960i	$-0.620704\pi$
$151$	6.86639	−	6.86639i	0.558779	−	0.558779i	0.928960	+	0.370181i	$0.120704\pi$
$152$	−5.28243			−0.428461
$153$	−0.0613854			−0.00496272
$154$	7.21714	+	3.83409i	0.581574	+	0.308960i
$155$			3.92023i			0.314881i
$156$	1.42341	+	0.709509i	0.113964	+	0.0568062i
$157$	−14.4384			−1.15231			−0.576155	−	0.817341i	$-0.695447\pi$
$157$	−14.4384			−1.15231			−0.576155	+	0.817341i	$0.695447\pi$
$158$	7.81798	−	7.81798i	0.621965	−	0.621965i
$159$	−6.29470			−0.499202
$160$	−6.78178			−0.536147
$161$	6.97790	+	6.97790i	0.549936	+	0.549936i
$162$	−1.10479	−	1.10479i	−0.0868002	−	0.0868002i
$163$	−12.8540	−	12.8540i	−1.00680	−	1.00680i	−0.999977	−	0.00682740i	$-0.997827\pi$
$163$	−12.8540	−	12.8540i	−1.00680	−	1.00680i	−0.00682740	−	0.999977i	$-0.502173\pi$
$164$	2.78070	−	2.78070i	0.217136	−	0.217136i
$165$	−8.76871	+	2.68432i	−0.682643	+	0.208974i
$166$		−	21.3292i		−	1.65547i
$167$	−3.54192	+	3.54192i	−0.274082	+	0.274082i	−0.830741	−	0.556659i	$-0.812083\pi$
$167$	−3.54192	+	3.54192i	−0.274082	+	0.274082i	0.556659	+	0.830741i	$0.312083\pi$
$168$			3.84120i			0.296355i
$169$	−7.82564	−	10.3807i	−0.601972	−	0.798517i
$170$	0.265185			0.0203388
$171$	1.53359	+	1.53359i	0.117276	+	0.117276i
$172$			3.07098i			0.234160i
$173$	19.6916			1.49712			0.748562	−	0.663065i	$-0.230745\pi$
$173$	19.6916			1.49712			0.748562	+	0.663065i	$0.230745\pi$
$174$	−5.97535	+	5.97535i	−0.452990	+	0.452990i
$175$	−2.94972	−	2.94972i	−0.222978	−	0.222978i
$176$	−13.7299	−	7.29400i	−1.03493	−	0.549806i
$177$	8.28019	+	8.28019i	0.622377	+	0.622377i
$178$		−	9.42676i		−	0.706565i
$179$			21.9857i			1.64329i	0.570002	+	0.821643i	$0.306942\pi$
$179$			21.9857i			1.64329i	−0.570002	+	0.821643i	$0.693058\pi$
$180$	0.862423	+	0.862423i	0.0642812	+	0.0642812i
$181$			3.45171i			0.256564i	0.991738	+	0.128282i	$0.0409462\pi$
$181$			3.45171i			0.256564i	−0.991738	+	0.128282i	$0.959054\pi$
$182$	−3.96337	+	7.95124i	−0.293784	+	0.589385i
$183$			9.57065i			0.707483i
$184$	−10.7765	−	10.7765i	−0.794453	−	0.794453i
$185$	−5.54775			−0.407879
$186$	2.21521			0.162427
$187$	0.179796	+	0.0955161i	0.0131480	+	0.00698483i
$188$	3.04529	−	3.04529i	0.222101	−	0.222101i
$189$	1.11517	−	1.11517i	0.0811169	−	0.0811169i
$190$	−6.62511	−	6.62511i	−0.480636	−	0.480636i
$191$	14.5678			1.05409			0.527046	−	0.849837i	$-0.323299\pi$
$191$	14.5678			1.05409			0.527046	+	0.849837i	$0.323299\pi$
$192$		−	5.54310i		−	0.400039i
$193$	−1.83845	+	1.83845i	−0.132334	+	0.132334i	−0.770171	−	0.637837i	$-0.779829\pi$
$193$	−1.83845	+	1.83845i	−0.132334	+	0.132334i	0.637837	+	0.770171i	$0.279829\pi$
$194$	−20.8498			−1.49693
$195$	−3.16422	−	9.45377i	−0.226595	−	0.676998i
$196$	−1.99062			−0.142187
$197$	−13.7414	−	13.7414i	−0.979036	−	0.979036i	0.0207491	−	0.999785i	$-0.493395\pi$
$197$	−13.7414	−	13.7414i	−0.979036	−	0.979036i	−0.999785	+	0.0207491i	$0.993395\pi$
$198$	1.51683	+	4.95494i	0.107796	+	0.352132i
$199$			20.9457i			1.48480i	0.669958	+	0.742399i	$0.266312\pi$
$199$			20.9457i			1.48480i	−0.669958	+	0.742399i	$0.733688\pi$
$200$	4.55547	+	4.55547i	0.322120	+	0.322120i
$201$	2.56219	−	2.56219i	0.180723	−	0.180723i
$202$	−6.46281	−	6.46281i	−0.454722	−	0.454722i
$203$	−6.03153	−	6.03153i	−0.423330	−	0.423330i
$204$		−	0.0270776i		−	0.00189581i
$205$	−24.6499			−1.72162
$206$	−7.55349	+	7.55349i	−0.526277	+	0.526277i
$207$			6.25724i			0.434908i
$208$	7.53993	−	15.1265i	0.522800	−	1.04883i
$209$	−2.10555	−	6.87810i	−0.145644	−	0.475768i
$210$	−4.81755	+	4.81755i	−0.332443	+	0.332443i
$211$		−	11.3777i		−	0.783273i	−0.920120	−	0.391637i	$-0.871909\pi$
$211$		−	11.3777i		−	0.783273i	0.920120	−	0.391637i	$-0.128091\pi$
$212$		−	2.77664i		−	0.190700i
$213$	2.26887	−	2.26887i	0.155461	−	0.155461i
$214$	18.3947	−	18.3947i	1.25743	−	1.25743i
$215$	13.6116	−	13.6116i	0.928301	−	0.928301i
$216$	−1.72224	+	1.72224i	−0.117184	+	0.117184i
$217$			2.23603i			0.151792i
$218$			1.83196i			0.124076i
$219$	3.20483	−	3.20483i	0.216563	−	0.216563i
$220$	−1.18407	−	3.86794i	−0.0798301	−	0.260777i
$221$	−0.0987367	+	0.198084i	−0.00664175	+	0.0133246i
$222$			3.13487i			0.210399i
$223$	5.12094	−	5.12094i	0.342923	−	0.342923i	−0.514542	−	0.857465i	$-0.672038\pi$
$223$	5.12094	−	5.12094i	0.342923	−	0.342923i	0.857465	+	0.514542i	$0.172038\pi$
$224$	−3.86821			−0.258456
$225$		−	2.64508i		−	0.176338i
$226$	−10.6036	−	10.6036i	−0.705343	−	0.705343i
$227$	13.8377	+	13.8377i	0.918442	+	0.918442i	0.996916	−	0.0784740i	$-0.0250047\pi$
$227$	13.8377	+	13.8377i	0.918442	+	0.918442i	−0.0784740	+	0.996916i	$0.525005\pi$
$228$	−0.676477	+	0.676477i	−0.0448008	+	0.0448008i
$229$	6.31750	+	6.31750i	0.417472	+	0.417472i	0.884332	−	0.466859i	$-0.154615\pi$
$229$	6.31750	+	6.31750i	0.417472	+	0.417472i	−0.466859	+	0.884332i	$0.654615\pi$
$230$		−	27.0313i		−	1.78239i
$231$	−5.00152	+	1.53109i	−0.329076	+	0.100738i
$232$	9.31493	+	9.31493i	0.611555	+	0.611555i
$233$	−19.2278			−1.25966			−0.629828	−	0.776735i	$-0.716874\pi$
$233$	−19.2278			−1.25966			−0.629828	+	0.776735i	$0.716874\pi$
$234$	−5.34204	+	1.78801i	−0.349220	+	0.116886i
$235$	−26.9954			−1.76099
$236$	−3.65245	+	3.65245i	−0.237754	+	0.237754i
$237$			7.07646i			0.459665i
$238$	0.151257			0.00980454
$239$	−9.18301	−	9.18301i	−0.594000	−	0.594000i	0.344710	−	0.938709i	$-0.387977\pi$
$239$	−9.18301	−	9.18301i	−0.594000	−	0.594000i	−0.938709	+	0.344710i	$0.887977\pi$
$240$	9.16495	−	9.16495i	0.591595	−	0.591595i
$241$	−19.0893	+	19.0893i	−1.22965	+	1.22965i	−0.265553	+	0.964096i	$0.585554\pi$
$241$	−19.0893	+	19.0893i	−1.22965	+	1.22965i	−0.964096	+	0.265553i	$0.914446\pi$
$242$	3.26718	−	16.8730i	0.210022	−	1.08464i
$243$	1.00000			0.0641500
$244$	−4.22168			−0.270266
$245$	8.82307	+	8.82307i	0.563686	+	0.563686i
$246$			13.9289i			0.888076i
$247$	7.41546	−	2.48199i	0.471834	−	0.157925i
$248$		−	3.45327i		−	0.219283i
$249$	9.65308	+	9.65308i	0.611739	+	0.611739i
$250$		−	10.1733i		−	0.643415i
$251$			0.127788i			0.00806589i	0.999992	+	0.00403294i	$0.00128373\pi$
$251$			0.127788i			0.00806589i	−0.999992	+	0.00403294i	$0.998716\pi$
$252$	0.491911	+	0.491911i	0.0309875	+	0.0309875i
$253$	9.73630	−	18.3272i	0.612116	−	1.15222i
$254$	2.64550	+	2.64550i	0.165993	+	0.165993i
$255$	−0.120017	+	0.120017i	−0.00751573	+	0.00751573i
$256$	10.1095			0.631842
$257$		−	26.4414i		−	1.64937i	−0.565594	−	0.824684i	$-0.691353\pi$
$257$		−	26.4414i		−	1.64937i	0.565594	−	0.824684i	$-0.308647\pi$
$258$	−7.69149	−	7.69149i	−0.478851	−	0.478851i
$259$	−3.16434			−0.196622
$260$	4.17013	−	1.39576i	0.258620	−	0.0865614i
$261$		−	5.40860i		−	0.334784i
$262$	−11.4289	+	11.4289i	−0.706080	+	0.706080i
$263$		−	30.5887i		−	1.88618i	−0.332540	−	0.943089i	$-0.607906\pi$
$263$		−	30.5887i		−	1.88618i	0.332540	−	0.943089i	$-0.392094\pi$
$264$	7.72422	−	2.36457i	0.475393	−	0.145529i
$265$	−12.3070	+	12.3070i	−0.756011	+	0.756011i
$266$	−3.77885	−	3.77885i	−0.231696	−	0.231696i
$267$	4.26632	+	4.26632i	0.261095	+	0.261095i
$268$	1.13020	+	1.13020i	0.0690381	+	0.0690381i
$269$	−11.9452			−0.728314			−0.364157	−	0.931338i	$-0.618643\pi$
$269$	−11.9452			−0.728314			−0.364157	+	0.931338i	$0.618643\pi$
$270$	−4.32001			−0.262907
$271$	−11.2716	+	11.2716i	−0.684702	+	0.684702i	−0.961056	−	0.276354i	$-0.910874\pi$
$271$	−11.2716	+	11.2716i	−0.684702	+	0.684702i	0.276354	+	0.961056i	$0.410874\pi$
$272$	−0.287753			−0.0174476
$273$	−1.80482	−	5.39226i	−0.109232	−	0.326355i
$274$		−	11.3214i		−	0.683953i
$275$	−4.11576	+	7.74734i	−0.248190	+	0.467182i
$276$	−2.76011			−0.166139
$277$	−25.8937			−1.55580			−0.777900	−	0.628388i	$-0.783715\pi$
$277$	−25.8937			−1.55580			−0.777900	+	0.628388i	$0.783715\pi$
$278$	16.4040	−	16.4040i	0.983847	−	0.983847i
$279$	−1.00255	+	1.00255i	−0.0600211	+	0.0600211i
$280$	7.51005	+	7.51005i	0.448811	+	0.448811i
$281$	−17.6396	+	17.6396i	−1.05229	+	1.05229i	−0.0537328	+	0.998555i	$0.517112\pi$
$281$	−17.6396	+	17.6396i	−1.05229	+	1.05229i	−0.998555	+	0.0537328i	$0.982888\pi$
$282$			15.2543i			0.908381i
$283$	15.4705			0.919627			0.459813	−	0.888016i	$-0.347916\pi$
$283$	15.4705			0.919627			0.459813	+	0.888016i	$0.347916\pi$
$284$	1.00082	+	1.00082i	0.0593875	+	0.0593875i
$285$	5.99673			0.355216
$286$	18.4288	+	3.07524i	1.08972	+	0.181843i
$287$	−14.0599			−0.829928
$288$	−1.73435	−	1.73435i	−0.102198	−	0.102198i
$289$	−16.9962			−0.999778
$290$			23.3652i			1.37205i
$291$	9.43613	−	9.43613i	0.553156	−	0.553156i
$292$	1.41368	+	1.41368i	0.0827291	+	0.0827291i
$293$	20.4082	−	20.4082i	1.19226	−	1.19226i	0.215827	−	0.976432i	$-0.430755\pi$
$293$	20.4082	−	20.4082i	1.19226	−	1.19226i	0.976432	−	0.215827i	$-0.0692448\pi$
$294$	4.98566	−	4.98566i	0.290769	−	0.290769i
$295$	32.3777			1.88510
$296$	4.88692			0.284047
$297$	−2.92897	−	1.55601i	−0.169956	−	0.0902887i
$298$			3.08842i			0.178907i
$299$	20.1914	+	10.0646i	1.16770	+	0.582050i
$300$	1.16676			0.0673631
$301$	7.76380	−	7.76380i	0.447498	−	0.447498i
$302$	−15.1718			−0.873039
$303$	5.84983			0.336064
$304$	7.18891	+	7.18891i	0.412312	+	0.412312i
$305$	18.7119	+	18.7119i	1.07144	+	1.07144i
$306$	0.0678178	+	0.0678178i	0.00387688	+	0.00387688i
$307$	−4.32779	+	4.32779i	−0.247000	+	0.247000i	−0.819738	−	0.572738i	$-0.805881\pi$
$307$	−4.32779	+	4.32779i	−0.247000	+	0.247000i	0.572738	+	0.819738i	$0.305881\pi$
$308$	−0.675374	−	2.20621i	−0.0384830	−	0.125710i
$309$		−	6.83706i		−	0.388947i
$310$	4.33102	−	4.33102i	0.245985	−	0.245985i
$311$			17.3127i			0.981711i	0.871241	+	0.490856i	$0.163316\pi$
$311$			17.3127i			0.981711i	−0.871241	+	0.490856i	$0.836684\pi$
$312$	2.78731	+	8.32767i	0.157800	+	0.471462i
$313$	13.4551			0.760530			0.380265	−	0.924878i	$-0.375833\pi$
$313$	13.4551			0.760530			0.380265	+	0.924878i	$0.375833\pi$
$314$	15.9514	+	15.9514i	0.900187	+	0.900187i
$315$		−	4.36062i		−	0.245693i
$316$	−3.12148			−0.175597
$317$	2.76581	−	2.76581i	0.155343	−	0.155343i	−0.625156	−	0.780500i	$-0.714965\pi$
$317$	2.76581	−	2.76581i	0.155343	−	0.155343i	0.780500	+	0.625156i	$0.214965\pi$
$318$	6.95430	+	6.95430i	0.389978	+	0.389978i
$319$	−8.41582	+	15.8416i	−0.471196	+	0.886960i
$320$	−10.8375	−	10.8375i	−0.605834	−	0.605834i
$321$			16.6500i			0.929310i
$322$		−	15.4182i		−	0.859222i
$323$	−0.0941400	−	0.0941400i	−0.00523809	−	0.00523809i
$324$			0.441107i			0.0245060i
$325$	−8.53537	−	4.25453i	−0.473457	−	0.235999i
$326$			28.4019i			1.57304i
$327$	−0.829101	−	0.829101i	−0.0458494	−	0.0458494i
$328$	21.7137			1.19894
$329$	−15.3977			−0.848904
$330$	12.6532	+	6.72196i	0.696533	+	0.370032i
$331$	3.50310	−	3.50310i	0.192548	−	0.192548i	−0.604248	−	0.796796i	$-0.706526\pi$
$331$	3.50310	−	3.50310i	0.192548	−	0.192548i	0.796796	+	0.604248i	$0.206526\pi$
$332$	−4.25805	+	4.25805i	−0.233691	+	0.233691i
$333$	−1.41877	−	1.41877i	−0.0777479	−	0.0777479i
$334$	7.82613			0.428227
$335$		−	10.0188i		−	0.547388i
$336$	5.22753	−	5.22753i	0.285185	−	0.285185i
$337$	10.2422			0.557930			0.278965	−	0.960301i	$-0.410009\pi$
$337$	10.2422			0.557930			0.278965	+	0.960301i	$0.410009\pi$
$338$	−2.82282	+	20.1141i	−0.153541	+	1.09407i
$339$	9.59790			0.521286
$340$	−0.0529402	−	0.0529402i	−0.00287108	−	0.00287108i
$341$	4.49641	−	1.37646i	0.243494	−	0.0745395i
$342$		−	3.38858i		−	0.183233i
$343$	12.8387	+	12.8387i	0.693227	+	0.693227i
$344$	−11.9902	+	11.9902i	−0.646469	+	0.646469i
$345$	12.2337	+	12.2337i	0.658641	+	0.658641i
$346$	−21.7550	−	21.7550i	−1.16956	−	1.16956i
$347$			21.5177i			1.15513i	0.816345	+	0.577564i	$0.195997\pi$
$347$			21.5177i			1.15513i	−0.816345	+	0.577564i	$0.804003\pi$
$348$	2.38577			0.127891
$349$	−14.9645	+	14.9645i	−0.801030	+	0.801030i	−0.983257	−	0.182227i	$-0.941670\pi$
$349$	−14.9645	+	14.9645i	−0.801030	+	0.801030i	0.182227	+	0.983257i	$0.441670\pi$
$350$			6.51762i			0.348381i
$351$	1.60847	−	3.22689i	0.0858539	−	0.172239i
$352$	2.38120	+	7.77853i	0.126918	+	0.414597i
$353$	3.29937	−	3.29937i	0.175608	−	0.175608i	−0.613830	−	0.789438i	$-0.710372\pi$
$353$	3.29937	−	3.29937i	0.175608	−	0.175608i	0.789438	+	0.613830i	$0.210372\pi$
$354$		−	18.2957i		−	0.972404i
$355$		−	8.87189i		−	0.470871i
$356$	−1.88191	+	1.88191i	−0.0997409	+	0.0997409i
$357$	−0.0684553	+	0.0684553i	−0.00362304	+	0.00362304i
$358$	24.2895	−	24.2895i	1.28374	−	1.28374i
$359$	−8.10953	+	8.10953i	−0.428004	+	0.428004i	−0.887948	−	0.459944i	$-0.847870\pi$
$359$	−8.10953	+	8.10953i	−0.428004	+	0.428004i	0.459944	+	0.887948i	$0.347870\pi$
$360$			6.73443i			0.354935i
$361$		−	14.2962i		−	0.752432i
$362$	3.81341	−	3.81341i	0.200428	−	0.200428i
$363$	6.15769	+	9.11498i	0.323195	+	0.478413i
$364$	2.37857	−	0.796118i	0.124671	−	0.0417279i
$365$		−	12.5317i		−	0.655941i
$366$	10.5735	−	10.5735i	0.552687	−	0.552687i
$367$	−18.1752			−0.948738			−0.474369	−	0.880326i	$-0.657324\pi$
$367$	−18.1752			−0.948738			−0.474369	+	0.880326i	$0.657324\pi$
$368$			29.3317i			1.52902i
$369$	−6.30390	−	6.30390i	−0.328168	−	0.328168i
$370$	6.12908	+	6.12908i	0.318636	+	0.318636i
$371$	−7.01968	+	7.01968i	−0.364444	+	0.364444i
$372$	−0.442232	−	0.442232i	−0.0229287	−	0.0229287i
$373$		−	17.3652i		−	0.899137i	−0.893246	−	0.449568i	$-0.851578\pi$
$373$		−	17.3652i		−	0.899137i	0.893246	−	0.449568i	$-0.148422\pi$
$374$	−0.0931111	−	0.304161i	−0.00481466	−	0.0157278i
$375$	4.60418	+	4.60418i	0.237759	+	0.237759i
$376$	23.7798			1.22635
$377$	−17.4530	−	8.69958i	−0.898873	−	0.448051i
$378$	−2.46406			−0.126737
$379$	−7.46016	+	7.46016i	−0.383203	+	0.383203i	−0.872255	−	0.489052i	$-0.837343\pi$
$379$	−7.46016	+	7.46016i	−0.383203	+	0.383203i	0.489052	+	0.872255i	$0.337343\pi$
$380$			2.64520i			0.135696i
$381$	−2.39458			−0.122678
$382$	−16.0944	−	16.0944i	−0.823459	−	0.823459i
$383$	13.4351	−	13.4351i	0.686500	−	0.686500i	−0.274957	−	0.961457i	$-0.588664\pi$
$383$	13.4351	−	13.4351i	0.686500	−	0.686500i	0.961457	+	0.274957i	$0.0886636\pi$
$384$	−9.59265	+	9.59265i	−0.489523	+	0.489523i
$385$	−6.78515	+	12.7721i	−0.345803	+	0.650927i
$386$	4.06219			0.206760
$387$	6.96197			0.353897
$388$	4.16235	+	4.16235i	0.211311	+	0.211311i
$389$			19.0707i			0.966924i	0.875365	+	0.483462i	$0.160621\pi$
$389$			19.0707i			0.966924i	−0.875365	+	0.483462i	$0.839379\pi$
$390$	−6.94861	+	13.9402i	−0.351856	+	0.705889i
$391$		−	0.384103i		−	0.0194249i
$392$	−7.77211	−	7.77211i	−0.392551	−	0.392551i
$393$		−	10.3449i		−	0.521831i
$394$			30.3627i			1.52965i
$395$	13.8354	+	13.8354i	0.696135	+	0.696135i
$396$	0.686366	−	1.29199i	0.0344912	−	0.0649249i
$397$	−12.8046	−	12.8046i	−0.642644	−	0.642644i	0.308560	−	0.951205i	$-0.400153\pi$
$397$	−12.8046	−	12.8046i	−0.642644	−	0.642644i	−0.951205	+	0.308560i	$0.900153\pi$
$398$	23.1405	−	23.1405i	1.15993	−	1.15993i
$399$	3.42043			0.171236
$400$		−	12.3992i		−	0.619958i
$401$	−10.9789	−	10.9789i	−0.548259	−	0.548259i	0.377678	−	0.925937i	$-0.376723\pi$
$401$	−10.9789	−	10.9789i	−0.548259	−	0.548259i	−0.925937	+	0.377678i	$0.876723\pi$
$402$	−5.66135			−0.282363
$403$	1.62254	+	4.84769i	0.0808247	+	0.241481i
$404$			2.58040i			0.128380i
$405$	1.95513	−	1.95513i	0.0971513	−	0.0971513i
$406$			13.3271i			0.661413i
$407$	1.94791	+	6.36313i	0.0965542	+	0.315409i
$408$	0.105721	−	0.105721i	0.00523395	−	0.00523395i
$409$	−26.1575	−	26.1575i	−1.29340	−	1.29340i	−0.932668	−	0.360736i	$-0.882526\pi$
$409$	−26.1575	−	26.1575i	−1.29340	−	1.29340i	−0.360736	−	0.932668i	$-0.617474\pi$
$410$	27.2329	+	27.2329i	1.34494	+	1.34494i
$411$	5.12381	+	5.12381i	0.252739	+	0.252739i
$412$	3.01588			0.148582
$413$	18.4677			0.908735
$414$	6.91291	−	6.91291i	0.339751	−	0.339751i
$415$	37.7461			1.85288
$416$	−8.38623	+	2.80691i	−0.411169	+	0.137620i
$417$			14.8481i			0.727116i
$418$	−5.27265	+	9.92503i	−0.257894	+	0.485449i
$419$	−25.4107			−1.24140			−0.620698	−	0.784050i	$-0.713151\pi$
$419$	−25.4107			−1.24140			−0.620698	+	0.784050i	$0.713151\pi$
$420$	1.92350			0.0938573
$421$	−1.05483	+	1.05483i	−0.0514091	+	0.0514091i	−0.732344	−	0.680935i	$-0.761574\pi$
$421$	−1.05483	+	1.05483i	−0.0514091	+	0.0514091i	0.680935	+	0.732344i	$0.261574\pi$
$422$	−12.5699	+	12.5699i	−0.611895	+	0.611895i
$423$	−6.90374	−	6.90374i	−0.335671	−	0.335671i
$424$	10.8410	−	10.8410i	0.526486	−	0.526486i
$425$			0.162369i			0.00787606i
$426$	−5.01324			−0.242892
$427$	10.6729	+	10.6729i	0.516499	+	0.516499i
$428$	−7.34442			−0.355006
$429$	−9.73222	+	6.94866i	−0.469876	+	0.335484i
$430$	−30.0758			−1.45038
$431$	−1.88372	−	1.88372i	−0.0907355	−	0.0907355i	0.660282	−	0.751018i	$-0.270437\pi$
$431$	−1.88372	−	1.88372i	−0.0907355	−	0.0907355i	−0.751018	+	0.660282i	$0.770437\pi$
$432$	4.68764			0.225534
$433$		−	17.0563i		−	0.819672i	−0.912159	−	0.409836i	$-0.865586\pi$
$433$		−	17.0563i		−	0.819672i	0.912159	−	0.409836i	$-0.134414\pi$
$434$	2.47034	−	2.47034i	0.118580	−	0.118580i
$435$	−10.5745	−	10.5745i	−0.507010	−	0.507010i
$436$	0.365723	−	0.365723i	0.0175149	−	0.0175149i
$437$	−9.59603	+	9.59603i	−0.459040	+	0.459040i
$438$	−7.08131			−0.338358
$439$	23.9189			1.14159			0.570793	−	0.821094i	$-0.306636\pi$
$439$	23.9189			1.14159			0.570793	+	0.821094i	$0.306636\pi$
$440$	10.4788	−	19.7249i	0.499558	−	0.940348i
$441$			4.51278i			0.214894i
$442$	0.327923	−	0.109758i	0.0155977	−	0.00522063i
$443$	−22.0082			−1.04564			−0.522820	−	0.852443i	$-0.675120\pi$
$443$	−22.0082			−1.04564			−0.522820	+	0.852443i	$0.675120\pi$
$444$	0.625828	−	0.625828i	0.0297005	−	0.0297005i
$445$	16.6824			0.790824
$446$	−11.3151			−0.535785
$447$	−1.39774	−	1.39774i	−0.0661111	−	0.0661111i
$448$	−6.18151	−	6.18151i	−0.292049	−	0.292049i
$449$	8.33968	+	8.33968i	0.393574	+	0.393574i	0.875959	−	0.482385i	$-0.160229\pi$
$449$	8.33968	+	8.33968i	0.393574	+	0.393574i	−0.482385	+	0.875959i	$0.660229\pi$
$450$	−2.92225	+	2.92225i	−0.137756	+	0.137756i
$451$	8.65500	+	28.2728i	0.407548	+	1.33132i
$452$			4.23371i			0.199137i
$453$	6.86639	−	6.86639i	0.322611	−	0.322611i
$454$		−	30.5755i		−	1.43498i
$455$	−14.0712	−	7.01393i	−0.659670	−	0.328818i
$456$	−5.28243			−0.247372
$457$	−0.210437	−	0.210437i	−0.00984381	−	0.00984381i	0.702168	−	0.712012i	$-0.252216\pi$
$457$	−0.210437	−	0.210437i	−0.00984381	−	0.00984381i	−0.712012	+	0.702168i	$0.752216\pi$
$458$		−	13.9590i		−	0.652260i
$459$	−0.0613854			−0.00286523
$460$	−5.39638	+	5.39638i	−0.251608	+	0.251608i
$461$	14.7879	+	14.7879i	0.688740	+	0.688740i	0.961954	−	0.273213i	$-0.0880865\pi$
$461$	14.7879	+	14.7879i	0.688740	+	0.688740i	−0.273213	+	0.961954i	$0.588086\pi$
$462$	7.21714	+	3.83409i	0.335772	+	0.178378i
$463$	−18.9327	−	18.9327i	−0.879879	−	0.879879i	0.113642	−	0.993522i	$-0.463748\pi$
$463$	−18.9327	−	18.9327i	−0.879879	−	0.879879i	−0.993522	+	0.113642i	$0.963748\pi$
$464$		−	25.3536i		−	1.17701i
$465$			3.92023i			0.181796i
$466$	21.2426	+	21.2426i	0.984045	+	0.984045i
$467$		−	41.4505i		−	1.91810i	−0.283232	−	0.959051i	$-0.591407\pi$
$467$		−	41.4505i		−	1.91810i	0.283232	−	0.959051i	$-0.408593\pi$
$468$	1.42341	+	0.709509i	0.0657969	+	0.0327971i
$469$		−	5.71457i		−	0.263875i
$470$	29.8242	+	29.8242i	1.37569	+	1.37569i
$471$	−14.4384			−0.665286
$472$	−28.5210			−1.31279
$473$	−20.3914	−	10.8329i	−0.937596	−	0.498096i
$474$	7.81798	−	7.81798i	0.359092	−	0.359092i
$475$	4.05646	−	4.05646i	0.186123	−	0.186123i
$476$	−0.0301962	−	0.0301962i	−0.00138404	−	0.00138404i
$477$	−6.29470			−0.288215
$478$			20.2905i			0.928068i
$479$	−11.5264	+	11.5264i	−0.526657	+	0.526657i	−0.919574	−	0.392917i	$-0.871466\pi$
$479$	−11.5264	+	11.5264i	−0.526657	+	0.526657i	0.392917	+	0.919574i	$0.371466\pi$
$480$	−6.78178			−0.309544
$481$	−6.86025	+	2.29616i	−0.312800	+	0.104696i
$482$	42.1792			1.92121
$483$	6.97790	+	6.97790i	0.317506	+	0.317506i
$484$	−4.02069	+	2.71620i	−0.182758	+	0.123464i
$485$		−	36.8977i		−	1.67544i
$486$	−1.10479	−	1.10479i	−0.0501141	−	0.0501141i
$487$	−15.5671	+	15.5671i	−0.705415	+	0.705415i	−0.965567	−	0.260153i	$-0.916227\pi$
$487$	−15.5671	+	15.5671i	−0.705415	+	0.705415i	0.260153	+	0.965567i	$0.416227\pi$
$488$	−16.4830	−	16.4830i	−0.746150	−	0.746150i
$489$	−12.8540	−	12.8540i	−0.581279	−	0.581279i
$490$		−	19.4952i		−	0.880705i
$491$	−3.62535			−0.163610			−0.0818049	−	0.996648i	$-0.526068\pi$
$491$	−3.62535			−0.163610			−0.0818049	+	0.996648i	$0.526068\pi$
$492$	2.78070	−	2.78070i	0.125364	−	0.125364i
$493$			0.332009i			0.0149529i
$494$	−10.9346	−	5.45043i	−0.491969	−	0.245226i
$495$	−8.76871	+	2.68432i	−0.394124	+	0.120651i
$496$	−4.69959	+	4.69959i	−0.211018	+	0.211018i
$497$		−	5.06037i		−	0.226989i
$498$		−	21.3292i		−	0.955784i
$499$	−13.9432	+	13.9432i	−0.624185	+	0.624185i	−0.946599	−	0.322414i	$-0.895506\pi$
$499$	−13.9432	+	13.9432i	−0.624185	+	0.624185i	0.322414	+	0.946599i	$0.395506\pi$
$500$	−2.03094	+	2.03094i	−0.0908264	+	0.0908264i
$501$	−3.54192	+	3.54192i	−0.158241	+	0.158241i
$502$	0.141178	−	0.141178i	0.00630109	−	0.00630109i
$503$			0.278315i			0.0124094i	0.999981	+	0.00620472i	$0.00197504\pi$
$503$			0.278315i			0.0124094i	−0.999981	+	0.00620472i	$0.998025\pi$
$504$			3.84120i			0.171101i
$505$	11.4372	−	11.4372i	0.508948	−	0.508948i
$506$	−31.0042	+	9.49115i	−1.37831	+	0.421933i
$507$	−7.82564	−	10.3807i	−0.347549	−	0.461024i
$508$		−	1.05627i		−	0.0468643i
$509$	−6.42539	+	6.42539i	−0.284800	+	0.284800i	−0.835020	−	0.550220i	$-0.814544\pi$
$509$	−6.42539	+	6.42539i	−0.284800	+	0.284800i	0.550220	+	0.835020i	$0.314544\pi$
$510$	0.265185			0.0117426
$511$		−	7.14789i		−	0.316204i
$512$	8.01649	+	8.01649i	0.354282	+	0.354282i
$513$	1.53359	+	1.53359i	0.0677096	+	0.0677096i
$514$	−29.2121	+	29.2121i	−1.28849	+	1.28849i
$515$	−13.3673	−	13.3673i	−0.589036	−	0.589036i
$516$			3.07098i			0.135192i
$517$	9.47855	+	30.9631i	0.416866	+	1.36175i
$518$	3.49592	+	3.49592i	0.153602	+	0.153602i
$519$	19.6916			0.864365
$520$	21.7313	+	10.8321i	0.952978	+	0.475020i
$521$	26.8395			1.17586			0.587930	−	0.808912i	$-0.299943\pi$
$521$	26.8395			1.17586			0.587930	+	0.808912i	$0.299943\pi$
$522$	−5.97535	+	5.97535i	−0.261534	+	0.261534i
$523$			3.90944i			0.170948i	0.996340	+	0.0854740i	$0.0272405\pi$
$523$			3.90944i			0.170948i	−0.996340	+	0.0854740i	$0.972760\pi$
$524$	4.56321			0.199345
$525$	−2.94972	−	2.94972i	−0.128736	−	0.128736i
$526$	−33.7940	+	33.7940i	−1.47349	+	1.47349i
$527$	0.0615419	−	0.0615419i	0.00268081	−	0.00268081i
$528$	−13.7299	−	7.29400i	−0.597519	−	0.317431i
$529$	−16.1530			−0.702305
$530$	27.1931			1.18119
$531$	8.28019	+	8.28019i	0.359329	+	0.359329i
$532$			1.50878i			0.0654138i
$533$	−30.4816	+	10.2023i	−1.32031	+	0.441913i
$534$		−	9.42676i		−	0.407936i
$535$	32.5529	+	32.5529i	1.40738	+	1.40738i
$536$			8.82544i			0.381201i
$537$			21.9857i			0.948752i
$538$	13.1969	+	13.1969i	0.568960	+	0.568960i
$539$	7.02191	−	13.2178i	0.302455	−	0.569330i
$540$	0.862423	+	0.862423i	0.0371128	+	0.0371128i
$541$	−15.9739	+	15.9739i	−0.686771	+	0.686771i	−0.961517	−	0.274746i	$-0.911406\pi$
$541$	−15.9739	+	15.9739i	−0.686771	+	0.686771i	0.274746	+	0.961517i	$0.411406\pi$
$542$	24.9055			1.06978
$543$			3.45171i			0.148127i
$544$	0.106464	+	0.106464i	0.00456461	+	0.00456461i
$545$	−3.24200			−0.138872
$546$	−3.96337	+	7.95124i	−0.169616	+	0.340282i
$547$			13.0544i			0.558165i	0.960267	+	0.279082i	$0.0900303\pi$
$547$			13.0544i			0.558165i	−0.960267	+	0.279082i	$0.909970\pi$
$548$	−2.26015	+	2.26015i	−0.0965489	+	0.0965489i
$549$			9.57065i			0.408465i
$550$	13.1062	−	4.01213i	0.558850	−	0.171078i
$551$	8.29457	−	8.29457i	0.353361	−	0.353361i
$552$	−10.7765	−	10.7765i	−0.458678	−	0.458678i
$553$	7.89147	+	7.89147i	0.335580	+	0.335580i
$554$	28.6070	+	28.6070i	1.21539	+	1.21539i
$555$	−5.54775			−0.235489
$556$	−6.54962			−0.277766
$557$	29.1662	−	29.1662i	1.23581	−	1.23581i	0.274116	−	0.961697i	$-0.411615\pi$
$557$	29.1662	−	29.1662i	1.23581	−	1.23581i	0.961697	−	0.274116i	$-0.0883851\pi$
$558$	2.21521			0.0937772
$559$	11.1981	−	22.4655i	0.473631	−	0.950190i
$560$		−	20.4410i		−	0.863790i
$561$	0.179796	+	0.0955161i	0.00759098	+	0.00403269i
$562$	38.9759			1.64410
$563$	−42.8889			−1.80755			−0.903775	−	0.428008i	$-0.859216\pi$
$563$	−42.8889			−1.80755			−0.903775	+	0.428008i	$0.859216\pi$
$564$	3.04529	−	3.04529i	0.128230	−	0.128230i
$565$	18.7652	−	18.7652i	0.789456	−	0.789456i
$566$	−17.0916	−	17.0916i	−0.718414	−	0.718414i
$567$	1.11517	−	1.11517i	0.0468329	−	0.0468329i
$568$			7.81510i			0.327915i
$569$	−7.63743			−0.320178			−0.160089	−	0.987103i	$-0.551178\pi$
$569$	−7.63743			−0.320178			−0.160089	+	0.987103i	$0.551178\pi$
$570$	−6.62511	−	6.62511i	−0.277495	−	0.277495i
$571$	23.1911			0.970516			0.485258	−	0.874371i	$-0.338726\pi$
$571$	23.1911			0.970516			0.485258	+	0.874371i	$0.338726\pi$
$572$	−3.06510	−	4.29296i	−0.128158	−	0.179497i
$573$	14.5678			0.608581
$574$	15.5332	+	15.5332i	0.648342	+	0.648342i
$575$	16.5509			0.690219
$576$		−	5.54310i		−	0.230962i
$577$	−27.7928	+	27.7928i	−1.15703	+	1.15703i	−0.171917	+	0.985112i	$0.554996\pi$
$577$	−27.7928	+	27.7928i	−1.15703	+	1.15703i	−0.985112	+	0.171917i	$0.945004\pi$
$578$	18.7772	+	18.7772i	0.781029	+	0.781029i
$579$	−1.83845	+	1.83845i	−0.0764034	+	0.0764034i
$580$	4.66450	−	4.66450i	0.193683	−	0.193683i
$581$	21.5297			0.893203
$582$	−20.8498			−0.864253
$583$	18.4370	+	9.79460i	0.763581	+	0.405651i
$584$			11.0390i			0.456797i
$585$	−3.16422	−	9.45377i	−0.130824	−	0.390865i
$586$	−45.0934			−1.86279
$587$	20.8177	−	20.8177i	0.859239	−	0.859239i	−0.132009	−	0.991249i	$-0.542143\pi$
$587$	20.8177	−	20.8177i	0.859239	−	0.859239i	0.991249	+	0.132009i	$0.0421428\pi$
$588$	−1.99062			−0.0820918
$589$	−3.07500			−0.126703
$590$	−35.7705	−	35.7705i	−1.47265	−	1.47265i
$591$	−13.7414	−	13.7414i	−0.565246	−	0.565246i
$592$	−6.65066	−	6.65066i	−0.273341	−	0.273341i
$593$	−31.5370	+	31.5370i	−1.29507	+	1.29507i	−0.363460	+	0.931610i	$0.618405\pi$
$593$	−31.5370	+	31.5370i	−1.29507	+	1.29507i	−0.931610	+	0.363460i	$0.881595\pi$
$594$	1.51683	+	4.95494i	0.0622362	+	0.203304i
$595$			0.267678i			0.0109737i
$596$	0.616556	−	0.616556i	0.0252551	−	0.0252551i
$597$			20.9457i			0.857248i
$598$	−11.1880	−	33.4264i	−0.457511	−	1.36691i
$599$	41.6993			1.70379			0.851893	−	0.523715i	$-0.175455\pi$
$599$	41.6993			1.70379			0.851893	+	0.523715i	$0.175455\pi$
$600$	4.55547	+	4.55547i	0.185976	+	0.185976i
$601$		−	37.0381i		−	1.51082i	−0.655254	−	0.755409i	$-0.727438\pi$
$601$		−	37.0381i		−	1.51082i	0.655254	−	0.755409i	$-0.272562\pi$
$602$	−17.1547			−0.699173
$603$	2.56219	−	2.56219i	0.104341	−	0.104341i
$604$	3.02882	+	3.02882i	0.123241	+	0.123241i
$605$	29.8601	+	5.78191i	1.21398	+	0.235068i
$606$	−6.46281	−	6.46281i	−0.262534	−	0.262534i
$607$			6.20213i			0.251737i	0.992047	+	0.125868i	$0.0401717\pi$
$607$			6.20213i			0.251737i	−0.992047	+	0.125868i	$0.959828\pi$
$608$		−	5.31957i		−	0.215737i
$609$	−6.03153	−	6.03153i	−0.244410	−	0.244410i
$610$		−	41.3453i		−	1.67402i
$611$	−33.3821	+	11.1731i	−1.35049	+	0.452017i
$612$		−	0.0270776i		−	0.00109455i
$613$	−23.5743	−	23.5743i	−0.952157	−	0.952157i	0.0467496	−	0.998907i	$-0.485114\pi$
$613$	−23.5743	−	23.5743i	−0.952157	−	0.952157i	−0.998907	+	0.0467496i	$0.985114\pi$
$614$	9.56258			0.385914
$615$	−24.6499			−0.993980
$616$	5.97693	−	11.2507i	0.240817	−	0.453305i
$617$	2.36799	−	2.36799i	0.0953319	−	0.0953319i	−0.657832	−	0.753164i	$-0.728527\pi$
$617$	2.36799	−	2.36799i	0.0953319	−	0.0953319i	0.753164	+	0.657832i	$0.228527\pi$
$618$	−7.55349	+	7.55349i	−0.303846	+	0.303846i
$619$	2.02438	+	2.02438i	0.0813666	+	0.0813666i	0.746619	−	0.665252i	$-0.231676\pi$
$619$	2.02438	+	2.02438i	0.0813666	+	0.0813666i	−0.665252	+	0.746619i	$0.731676\pi$
$620$	−1.72924			−0.0694481
$621$			6.25724i			0.251094i
$622$	19.1268	−	19.1268i	0.766915	−	0.766915i
$623$	9.51538			0.381226
$624$	7.53993	−	15.1265i	0.301839	−	0.605544i
$625$	31.2290			1.24916
$626$	−14.8651	−	14.8651i	−0.594128	−	0.594128i
$627$	−2.10555	−	6.87810i	−0.0840878	−	0.274685i
$628$		−	6.36888i		−	0.254146i
$629$	0.0870915	+	0.0870915i	0.00347257	+	0.00347257i
$630$	−4.81755	+	4.81755i	−0.191936	+	0.191936i
$631$	−8.81311	−	8.81311i	−0.350845	−	0.350845i	0.509579	−	0.860424i	$-0.329801\pi$
$631$	−8.81311	−	8.81311i	−0.350845	−	0.350845i	−0.860424	+	0.509579i	$0.829801\pi$
$632$	−12.1874	−	12.1874i	−0.484788	−	0.484788i
$633$		−	11.3777i		−	0.452223i
$634$	−6.11126			−0.242709
$635$	−4.68172	+	4.68172i	−0.185788	+	0.185788i
$636$		−	2.77664i		−	0.110101i
$637$	14.5622	+	7.25868i	0.576977	+	0.287599i
$638$	26.7993	−	8.20391i	1.06099	−	0.324796i
$639$	2.26887	−	2.26887i	0.0897552	−	0.0897552i
$640$			37.5098i			1.48270i
$641$		−	11.7377i		−	0.463609i	−0.972762	−	0.231805i	$-0.925537\pi$
$641$		−	11.7377i		−	0.463609i	0.972762	−	0.231805i	$-0.0744630\pi$
$642$	18.3947	−	18.3947i	0.725979	−	0.725979i
$643$	−32.6595	+	32.6595i	−1.28796	+	1.28796i	−0.351943	+	0.936022i	$0.614479\pi$
$643$	−32.6595	+	32.6595i	−1.28796	+	1.28796i	−0.936022	+	0.351943i	$0.885521\pi$
$644$	−3.07800	+	3.07800i	−0.121290	+	0.121290i
$645$	13.6116	−	13.6116i	0.535955	−	0.535955i
$646$			0.208009i			0.00818401i
$647$			13.4261i			0.527834i	0.964545	+	0.263917i	$0.0850145\pi$
$647$			13.4261i			0.527834i	−0.964545	+	0.263917i	$0.914986\pi$
$648$	−1.72224	+	1.72224i	−0.0676561	+	0.0676561i
$649$	−11.3684	−	37.1364i	−0.446247	−	1.45773i
$650$	4.72942	+	14.1301i	0.185503	+	0.554229i
$651$			2.23603i			0.0876370i
$652$	5.67000	−	5.67000i	0.222054	−	0.222054i
$653$	12.4808			0.488412			0.244206	−	0.969723i	$-0.421473\pi$
$653$	12.4808			0.488412			0.244206	+	0.969723i	$0.421473\pi$
$654$			1.83196i			0.0716353i
$655$	−20.2256	−	20.2256i	−0.790281	−	0.790281i
$656$	−29.5504	−	29.5504i	−1.15375	−	1.15375i
$657$	3.20483	−	3.20483i	0.125032	−	0.125032i
$658$	17.0112	+	17.0112i	0.663166	+	0.663166i
$659$		−	46.5898i		−	1.81488i	−0.420182	−	0.907440i	$-0.638034\pi$
$659$		−	46.5898i		−	1.81488i	0.420182	−	0.907440i	$-0.361966\pi$
$660$	−1.18407	−	3.86794i	−0.0460899	−	0.150559i
$661$	−7.70328	−	7.70328i	−0.299623	−	0.299623i	0.541243	−	0.840866i	$-0.317954\pi$
$661$	−7.70328	−	7.70328i	−0.299623	−	0.299623i	−0.840866	+	0.541243i	$0.817954\pi$
$662$	−7.74037			−0.300838
$663$	−0.0987367	+	0.198084i	−0.00383462	+	0.00769294i
$664$	−33.2499			−1.29035
$665$	6.68740	−	6.68740i	0.259326	−	0.259326i
$666$			3.13487i			0.121474i
$667$	33.8429			1.31040
$668$	−1.56237	−	1.56237i	−0.0604498	−	0.0604498i
$669$	5.12094	−	5.12094i	0.197987	−	0.197987i
$670$	−11.0687	+	11.0687i	−0.427621	+	0.427621i
$671$	14.8920	−	28.0321i	0.574899	−	1.08217i
$672$	−3.86821			−0.149219
$673$	10.1580			0.391563			0.195781	−	0.980648i	$-0.437276\pi$
$673$	10.1580			0.391563			0.195781	+	0.980648i	$0.437276\pi$
$674$	−11.3155	−	11.3155i	−0.435856	−	0.435856i
$675$		−	2.64508i		−	0.101809i
$676$	4.57901	−	3.45195i	0.176116	−	0.132767i
$677$			0.385664i			0.0148223i	0.999973	+	0.00741113i	$0.00235906\pi$
$677$			0.385664i			0.0148223i	−0.999973	+	0.00741113i	$0.997641\pi$
$678$	−10.6036	−	10.6036i	−0.407230	−	0.407230i
$679$		−	21.0458i		−	0.807665i
$680$		−	0.413395i		−	0.0158530i
$681$	13.8377	+	13.8377i	0.530263	+	0.530263i
$682$	−6.48826	−	3.44688i	−0.248449	−	0.131988i
$683$	24.2330	+	24.2330i	0.927251	+	0.927251i	0.997528	−	0.0702761i	$-0.0223880\pi$
$683$	24.2330	+	24.2330i	0.927251	+	0.927251i	−0.0702761	+	0.997528i	$0.522388\pi$
$684$	−0.676477	+	0.676477i	−0.0258658	+	0.0258658i
$685$	20.0355			0.765515
$686$		−	28.3681i		−	1.08310i
$687$	6.31750	+	6.31750i	0.241028	+	0.241028i
$688$	32.6352			1.24421
$689$	−10.1248	+	20.3123i	−0.385726	+	0.773837i
$690$		−	27.0313i		−	1.02906i
$691$	−19.5269	+	19.5269i	−0.742839	+	0.742839i	−0.973123	−	0.230284i	$-0.926034\pi$
$691$	−19.5269	+	19.5269i	−0.742839	+	0.742839i	0.230284	+	0.973123i	$0.426034\pi$
$692$			8.68610i			0.330196i
$693$	−5.00152	+	1.53109i	−0.189992	+	0.0581612i
$694$	23.7724	−	23.7724i	0.902389	−	0.902389i
$695$	29.0300	+	29.0300i	1.10117	+	1.10117i
$696$	9.31493	+	9.31493i	0.353082	+	0.353082i
$697$	0.386967	+	0.386967i	0.0146574	+	0.0146574i
$698$	33.0651			1.25153
$699$	−19.2278			−0.727262
$700$	1.30114	−	1.30114i	0.0491786	−	0.0491786i
$701$	−3.35999			−0.126905			−0.0634525	−	0.997985i	$-0.520211\pi$
$701$	−3.35999			−0.126905			−0.0634525	+	0.997985i	$0.520211\pi$
$702$	−5.34204	+	1.78801i	−0.201622	+	0.0674840i
$703$		−	4.35161i		−	0.164124i
$704$	−8.62510	+	16.2355i	−0.325071	+	0.611900i
$705$	−26.9954			−1.01671
$706$	−7.29020			−0.274370
$707$	6.52357	−	6.52357i	0.245344	−	0.245344i
$708$	−3.65245	+	3.65245i	−0.137268	+	0.137268i
$709$	−17.0861	−	17.0861i	−0.641682	−	0.641682i	0.309287	−	0.950969i	$-0.399910\pi$
$709$	−17.0861	−	17.0861i	−0.641682	−	0.641682i	−0.950969	+	0.309287i	$0.899910\pi$
$710$	−9.80155	+	9.80155i	−0.367845	+	0.367845i
$711$			7.07646i			0.265388i
$712$	−14.6953			−0.550730
$713$	−6.27319	−	6.27319i	−0.234933	−	0.234933i
$714$	0.151257			0.00566066
$715$	−5.44223	+	32.6133i	−0.203528	+	1.21967i
$716$	−9.69804			−0.362433
$717$	−9.18301	−	9.18301i	−0.342946	−	0.342946i
$718$	17.9186			0.668716
$719$			0.915497i			0.0341423i	0.999854	+	0.0170711i	$0.00543418\pi$
$719$			0.915497i			0.0341423i	−0.999854	+	0.0170711i	$0.994566\pi$
$720$	9.16495	−	9.16495i	0.341558	−	0.341558i
$721$	−7.62450	−	7.62450i	−0.283951	−	0.283951i
$722$	−15.7943	+	15.7943i	−0.587802	+	0.587802i
$723$	−19.0893	+	19.0893i	−0.709938	+	0.709938i
$724$	−1.52258			−0.0565861
$725$	−14.3062			−0.531318
$726$	3.26718	−	16.8730i	0.121257	−	0.626217i
$727$			21.6047i			0.801274i	0.916237	+	0.400637i	$0.131211\pi$
$727$			21.6047i			0.801274i	−0.916237	+	0.400637i	$0.868789\pi$
$728$	12.3951	+	6.17846i	0.459394	+	0.228989i
$729$	1.00000			0.0370370
$730$	−13.8449	+	13.8449i	−0.512423	+	0.512423i
$731$	−0.427363			−0.0158066
$732$	−4.22168			−0.156038
$733$	−31.6890	−	31.6890i	−1.17046	−	1.17046i	−0.982100	−	0.188361i	$-0.939683\pi$
$733$	−31.6890	−	31.6890i	−1.17046	−	1.17046i	−0.188361	−	0.982100i	$-0.560317\pi$
$734$	20.0797	+	20.0797i	0.741156	+	0.741156i
$735$	8.82307	+	8.82307i	0.325444	+	0.325444i
$736$	10.8523	−	10.8523i	0.400020	−	0.400020i
$737$	−11.4914	+	3.51779i	−0.423290	+	0.129579i
$738$			13.9289i			0.512731i
$739$	−24.4743	+	24.4743i	−0.900303	+	0.900303i	−0.995462	−	0.0951593i	$-0.969664\pi$
$739$	−24.4743	+	24.4743i	−0.900303	+	0.900303i	0.0951593	+	0.995462i	$0.469664\pi$
$740$		−	2.44715i		−	0.0899591i
$741$	7.41546	−	2.48199i	0.272414	−	0.0911781i
$742$	15.5105			0.569408
$743$	−17.7092	−	17.7092i	−0.649689	−	0.649689i	0.303229	−	0.952918i	$-0.401935\pi$
$743$	−17.7092	−	17.7092i	−0.649689	−	0.649689i	−0.952918	+	0.303229i	$0.901935\pi$
$744$		−	3.45327i		−	0.126603i
$745$	−5.46555			−0.200242
$746$	−19.1849	+	19.1849i	−0.702408	+	0.702408i
$747$	9.65308	+	9.65308i	0.353188	+	0.353188i
$748$	−0.0421329	+	0.0793092i	−0.00154053	+	0.00289983i
$749$	18.5676	+	18.5676i	0.678445	+	0.678445i
$750$		−	10.1733i		−	0.371476i
$751$			36.8240i			1.34373i	0.740675	+	0.671863i	$0.234506\pi$
$751$			36.8240i			1.34373i	−0.740675	+	0.671863i	$0.765494\pi$
$752$	−32.3622	−	32.3622i	−1.18013	−	1.18013i
$753$			0.127788i			0.00465684i
$754$	9.67062	+	28.8930i	0.352183	+	1.05222i
$755$		−	26.8494i		−	0.977149i
$756$	0.491911	+	0.491911i	0.0178906	+	0.0178906i
$757$	11.8368			0.430216			0.215108	−	0.976590i	$-0.430990\pi$
$757$	11.8368			0.430216			0.215108	+	0.976590i	$0.430990\pi$
$758$	16.4838			0.598718
$759$	9.73630	−	18.3272i	0.353405	−	0.665236i
$760$	−10.3278	+	10.3278i	−0.374630	+	0.374630i
$761$	−33.2186	+	33.2186i	−1.20417	+	1.20417i	−0.231286	+	0.972886i	$0.574293\pi$
$761$	−33.2186	+	33.2186i	−1.20417	+	1.20417i	−0.972886	+	0.231286i	$0.925707\pi$
$762$	2.64550	+	2.64550i	0.0958363	+	0.0958363i
$763$	−1.84918			−0.0669449
$764$			6.42599i			0.232484i
$765$	−0.120017	+	0.120017i	−0.00433921	+	0.00433921i
$766$	−29.6858			−1.07259
$767$	40.0377	−	13.4008i	1.44568	−	0.483875i
$768$	10.1095			0.364794
$769$	31.3537	+	31.3537i	1.13064	+	1.13064i	0.990070	+	0.140573i	$0.0448943\pi$
$769$	31.3537	+	31.3537i	1.13064	+	1.13064i	0.140573	+	0.990070i	$0.455106\pi$
$770$	21.6066	−	6.61431i	0.778648	−	0.238363i
$771$		−	26.4414i		−	0.952263i
$772$	−0.810954	−	0.810954i	−0.0291869	−	0.0291869i
$773$	2.11611	−	2.11611i	0.0761111	−	0.0761111i	−0.668026	−	0.744138i	$-0.732861\pi$
$773$	2.11611	−	2.11611i	0.0761111	−	0.0761111i	0.744138	+	0.668026i	$0.232861\pi$
$774$	−7.69149	−	7.69149i	−0.276465	−	0.276465i
$775$	2.65182	+	2.65182i	0.0952562	+	0.0952562i
$776$			32.5026i			1.16678i
$777$	−3.16434			−0.113520
$778$	21.0691	−	21.0691i	0.755363	−	0.755363i
$779$		−	19.3352i		−	0.692755i
$780$	4.17013	−	1.39576i	0.149314	−	0.0499763i
$781$	−10.1758	+	3.11507i	−0.364120	+	0.111466i
$782$	−0.424352	+	0.424352i	−0.0151748	+	0.0151748i
$783$		−	5.40860i		−	0.193288i
$784$			21.1543i			0.755510i
$785$	−28.2290	+	28.2290i	−1.00754	+	1.00754i
$786$	−11.4289	+	11.4289i	−0.407655	+	0.407655i
$787$	−3.96631	+	3.96631i	−0.141384	+	0.141384i	−0.774256	−	0.632872i	$-0.781876\pi$
$787$	−3.96631	+	3.96631i	−0.141384	+	0.141384i	0.632872	+	0.774256i	$0.281876\pi$
$788$	6.06144	−	6.06144i	0.215930	−	0.215930i
$789$		−	30.5887i		−	1.08899i
$790$		−	30.5703i		−	1.08764i
$791$	10.7033	−	10.7033i	0.380566	−	0.380566i
$792$	7.72422	−	2.36457i	0.274468	−	0.0840214i
$793$	30.8834	+	15.3941i	1.09670	+	0.546661i
$794$			28.2927i			1.00407i
$795$	−12.3070	+	12.3070i	−0.436483	+	0.436483i
$796$	−9.23928			−0.327478
$797$		−	26.0987i		−	0.924463i	−0.886759	−	0.462232i	$-0.847049\pi$
$797$		−	26.0987i		−	0.924463i	0.886759	−	0.462232i	$-0.152951\pi$
$798$	−3.77885	−	3.77885i	−0.133770	−	0.133770i
$799$	0.423789	+	0.423789i	0.0149926	+	0.0149926i
$800$	−4.58750	+	4.58750i	−0.162193	+	0.162193i
$801$	4.26632	+	4.26632i	0.150743	+	0.150743i
$802$			24.2586i			0.856602i
$803$	−14.3736	+	4.40011i	−0.507233	+	0.155276i
$804$	1.13020	+	1.13020i	0.0398591	+	0.0398591i
$805$	27.2854			0.961685
$806$	3.56310	−	7.14823i	0.125505	−	0.251786i
$807$	−11.9452			−0.420492
$808$	−10.0748	+	10.0748i	−0.354431	+	0.354431i
$809$		−	25.8829i		−	0.909996i	−0.890492	−	0.454998i	$-0.849640\pi$
$809$		−	25.8829i		−	0.909996i	0.890492	−	0.454998i	$-0.150360\pi$
$810$	−4.32001			−0.151790
$811$	11.6326	+	11.6326i	0.408477	+	0.408477i	0.881207	−	0.472730i	$-0.156731\pi$
$811$	11.6326	+	11.6326i	0.408477	+	0.408477i	−0.472730	+	0.881207i	$0.656731\pi$
$812$	2.66055	−	2.66055i	0.0933670	−	0.0933670i
$813$	−11.2716	+	11.2716i	−0.395313	+	0.395313i
$814$	4.87788	−	9.18192i	0.170969	−	0.321826i
$815$	−50.2626			−1.76062
$816$	−0.287753			−0.0100734
$817$	10.6768	+	10.6768i	0.373534	+	0.373534i
$818$			57.7969i			2.02082i
$819$	−1.80482	−	5.39226i	−0.0630654	−	0.188421i
$820$		−	10.8733i		−	0.379711i
$821$	13.3474	+	13.3474i	0.465828	+	0.465828i	0.900560	−	0.434732i	$-0.143157\pi$
$821$	13.3474	+	13.3474i	0.465828	+	0.465828i	−0.434732	+	0.900560i	$0.643157\pi$
$822$		−	11.3214i		−	0.394881i
$823$			22.8687i			0.797154i	0.917135	+	0.398577i	$0.130496\pi$
$823$			22.8687i			0.797154i	−0.917135	+	0.398577i	$0.869504\pi$
$824$	11.7751	+	11.7751i	0.410204	+	0.410204i
$825$	−4.11576	+	7.74734i	−0.143292	+	0.269728i
$826$	−20.4028	−	20.4028i	−0.709906	−	0.709906i
$827$	−17.8869	+	17.8869i	−0.621988	+	0.621988i	−0.946040	−	0.324051i	$-0.894955\pi$
$827$	−17.8869	+	17.8869i	−0.621988	+	0.621988i	0.324051	+	0.946040i	$0.394955\pi$
$828$	−2.76011			−0.0959206
$829$		−	12.9152i		−	0.448564i	−0.974524	−	0.224282i	$-0.927996\pi$
$829$		−	12.9152i		−	0.448564i	0.974524	−	0.224282i	$-0.0720037\pi$
$830$	−41.7014	−	41.7014i	−1.44748	−	1.44748i
$831$	−25.8937			−0.898242
$832$	−17.8870	−	8.91591i	−0.620119	−	0.309104i
$833$		−	0.277019i		−	0.00959813i
$834$	16.4040	−	16.4040i	0.568025	−	0.568025i
$835$			13.8498i			0.479293i
$836$	3.03398	−	0.928776i	0.104932	−	0.0321224i
$837$	−1.00255	+	1.00255i	−0.0346532	+	0.0346532i
$838$	28.0734	+	28.0734i	0.969781	+	0.969781i
$839$	−15.2070	−	15.2070i	−0.525005	−	0.525005i	0.394074	−	0.919079i	$-0.371065\pi$
$839$	−15.2070	−	15.2070i	−0.525005	−	0.525005i	−0.919079	+	0.394074i	$0.871065\pi$
$840$	7.51005	+	7.51005i	0.259121	+	0.259121i
$841$	−0.252976			−0.00872332
$842$	2.33072			0.0803218
$843$	−17.6396	+	17.6396i	−0.607539	+	0.607539i
$844$	5.01879			0.172754
$845$	−35.5958	−	4.99553i	−1.22453	−	0.171851i
$846$			15.2543i			0.524454i
$847$	17.0317	+	3.29790i	0.585215	+	0.113317i
$848$	−29.5073			−1.01328
$849$	15.4705			0.530947
$850$	0.179383	−	0.179383i	0.00615280	−	0.00615280i
$851$	8.87756	−	8.87756i	0.304319	−	0.304319i
$852$	1.00082	+	1.00082i	0.0342874	+	0.0342874i
$853$	26.3412	−	26.3412i	0.901906	−	0.901906i	−0.0936950	−	0.995601i	$-0.529868\pi$
$853$	26.3412	−	26.3412i	0.901906	−	0.901906i	0.995601	+	0.0936950i	$0.0298678\pi$
$854$		−	23.5826i		−	0.806981i
$855$	5.99673			0.205084
$856$	−28.6753	−	28.6753i	−0.980102	−	0.980102i
$857$	37.8235			1.29203			0.646013	−	0.763326i	$-0.276435\pi$
$857$	37.8235			1.29203			0.646013	+	0.763326i	$0.276435\pi$
$858$	18.4288	+	3.07524i	0.629149	+	0.104987i
$859$	−22.4989			−0.767651			−0.383825	−	0.923406i	$-0.625394\pi$
$859$	−22.4989			−0.767651			−0.383825	+	0.923406i	$0.625394\pi$
$860$	6.00416	+	6.00416i	0.204740	+	0.204740i
$861$	−14.0599			−0.479159
$862$			4.16221i			0.141766i
$863$	−33.5505	+	33.5505i	−1.14207	+	1.14207i	−0.154004	+	0.988070i	$0.549217\pi$
$863$	−33.5505	+	33.5505i	−1.14207	+	1.14207i	−0.988070	+	0.154004i	$0.950783\pi$
$864$	−1.73435	−	1.73435i	−0.0590039	−	0.0590039i
$865$	38.4996	−	38.4996i	1.30903	−	1.30903i
$866$	−18.8435	+	18.8435i	−0.640330	+	0.640330i
$867$	−16.9962			−0.577222
$868$	−0.986330			−0.0334782
$869$	11.0110	−	20.7267i	0.373523	−	0.703105i
$870$			23.3652i			0.792154i
$871$	−4.14670	−	12.3891i	−0.140506	−	0.419789i
$872$	2.85583			0.0967105
$873$	9.43613	−	9.43613i	0.319365	−	0.319365i
$874$	21.2031			0.717207
$875$	10.2689			0.347153
$876$	1.41368	+	1.41368i	0.0477637	+	0.0477637i
$877$	7.42962	+	7.42962i	0.250880	+	0.250880i	0.821332	−	0.570451i	$-0.193232\pi$
$877$	7.42962	+	7.42962i	0.250880	+	0.250880i	−0.570451	+	0.821332i	$0.693232\pi$
$878$	−26.4253	−	26.4253i	−0.891809	−	0.891809i
$879$	20.4082	−	20.4082i	0.688351	−	0.688351i
$880$	−41.1046	+	12.5831i	−1.38563	+	0.424176i
$881$			10.6331i			0.358239i	0.983827	+	0.179120i	$0.0573249\pi$
$881$			10.6331i			0.358239i	−0.983827	+	0.179120i	$0.942675\pi$
$882$	4.98566	−	4.98566i	0.167876	−	0.167876i
$883$		−	16.5526i		−	0.557038i	−0.960431	−	0.278519i	$-0.910157\pi$
$883$		−	16.5526i		−	0.557038i	0.960431	−	0.278519i	$-0.0898435\pi$
$884$	−0.0873763	−	0.0435535i	−0.00293878	−	0.00146486i
$885$	32.3777			1.08836
$886$	24.3144	+	24.3144i	0.816857	+	0.816857i
$887$		−	42.0124i		−	1.41064i	−0.708890	−	0.705319i	$-0.750804\pi$
$887$		−	42.0124i		−	1.41064i	0.708890	−	0.705319i	$-0.249196\pi$
$888$	4.88692			0.163994
$889$	−2.67037	+	2.67037i	−0.0895613	+	0.0895613i
$890$	−18.4305	−	18.4305i	−0.617793	−	0.617793i
$891$	−2.92897	−	1.55601i	−0.0981241	−	0.0521282i
$892$	2.25888	+	2.25888i	0.0756330	+	0.0756330i
$893$		−	21.1750i		−	0.708594i
$894$			3.08842i			0.103292i
$895$	42.9849	+	42.9849i	1.43683	+	1.43683i
$896$			21.3949i			0.714754i
$897$	20.1914	+	10.0646i	0.674172	+	0.336047i
$898$		−	18.4271i		−	0.614922i
$899$	5.42239	+	5.42239i	0.180847	+	0.180847i
$900$	1.16676			0.0388921
$901$	0.386403			0.0128729
$902$	21.6735	−	40.7974i	0.721649	−	1.35840i
$903$	7.76380	−	7.76380i	0.258363	−	0.258363i
$904$	−16.5299	+	16.5299i	−0.549777	+	0.549777i
$905$	6.74855	+	6.74855i	0.224329	+	0.224329i
$906$	−15.1718			−0.504049
$907$			17.3593i			0.576406i	0.957569	+	0.288203i	$0.0930579\pi$
$907$			17.3593i			0.576406i	−0.957569	+	0.288203i	$0.906942\pi$
$908$	−6.10392	+	6.10392i	−0.202566	+	0.202566i
$909$	5.84983			0.194027
$910$	7.79682	+	23.2946i	0.258462	+	0.772209i
$911$	14.1173			0.467726			0.233863	−	0.972270i	$-0.424863\pi$
$911$	14.1173			0.467726			0.233863	+	0.972270i	$0.424863\pi$
$912$	7.18891	+	7.18891i	0.238049	+	0.238049i
$913$	−13.2533	−	43.2938i	−0.438620	−	1.43282i
$914$			0.464975i			0.0153800i
$915$	18.7119	+	18.7119i	0.618596	+	0.618596i
$916$	−2.78670	+	2.78670i	−0.0920750	+	0.0920750i
$917$	−11.5363	−	11.5363i	−0.380964	−	0.380964i
$918$	0.0678178	+	0.0678178i	0.00223832	+	0.00223832i
$919$		−	20.9959i		−	0.692591i	−0.938125	−	0.346296i	$-0.887439\pi$
$919$		−	20.9959i		−	0.692591i	0.938125	−	0.346296i	$-0.112561\pi$
$920$	−42.1389			−1.38928
$921$	−4.32779	+	4.32779i	−0.142606	+	0.142606i
$922$		−	32.6749i		−	1.07609i
$923$	−3.67199	−	10.9708i	−0.120865	−	0.361109i
$924$	−0.675374	−	2.20621i	−0.0222182	−	0.0725789i
$925$	−3.75275	+	3.75275i	−0.123390	+	0.123390i
$926$			41.8333i			1.37473i
$927$		−	6.83706i		−	0.224558i
$928$	−9.38043	+	9.38043i	−0.307928	+	0.307928i
$929$	6.63320	−	6.63320i	0.217628	−	0.217628i	−0.589870	−	0.807498i	$-0.700821\pi$
$929$	6.63320	−	6.63320i	0.217628	−	0.217628i	0.807498	+	0.589870i	$0.200821\pi$
$930$	4.33102	−	4.33102i	0.142020	−	0.142020i
$931$	−6.92075	+	6.92075i	−0.226818	+	0.226818i
$932$		−	8.48152i		−	0.277822i
$933$			17.3127i			0.566791i
$934$	−45.7940	+	45.7940i	−1.49843	+	1.49843i
$935$	0.538271	−	0.164778i	0.0176033	−	0.00538881i
$936$	2.78731	+	8.32767i	0.0911061	+	0.272198i
$937$		−	30.3714i		−	0.992192i	−0.868268	−	0.496096i	$-0.834766\pi$
$937$		−	30.3714i		−	0.992192i	0.868268	−	0.496096i	$-0.165234\pi$
$938$	−6.31339	+	6.31339i	−0.206139	+	0.206139i
$939$	13.4551			0.439092
$940$		−	11.9079i		−	0.388392i
$941$	22.3934	+	22.3934i	0.730004	+	0.730004i	0.970620	−	0.240616i	$-0.0773494\pi$
$941$	22.3934	+	22.3934i	0.730004	+	0.730004i	−0.240616	+	0.970620i	$0.577349\pi$
$942$	15.9514	+	15.9514i	0.519723	+	0.519723i
$943$	39.4450	−	39.4450i	1.28451	−	1.28451i
$944$	38.8145	+	38.8145i	1.26331	+	1.26331i
$945$		−	4.36062i		−	0.141851i
$946$	10.5601	+	34.4961i	0.343339	+	1.12157i
$947$	27.5316	+	27.5316i	0.894657	+	0.894657i	0.994957	−	0.100300i	$-0.0319802\pi$
$947$	27.5316	+	27.5316i	0.894657	+	0.894657i	−0.100300	+	0.994957i	$0.531980\pi$
$948$	−3.12148			−0.101381
$949$	−5.18676	−	15.4965i	−0.168369	−	0.503039i
$950$	−8.96305			−0.290800
$951$	2.76581	−	2.76581i	0.0896875	−	0.0896875i
$952$		−	0.235794i		−	0.00764211i
$953$	45.7687			1.48259			0.741296	−	0.671178i	$-0.234211\pi$
$953$	45.7687			1.48259			0.741296	+	0.671178i	$0.234211\pi$
$954$	6.95430	+	6.95430i	0.225154	+	0.225154i
$955$	28.4821	−	28.4821i	0.921658	−	0.921658i
$956$	4.05069	−	4.05069i	0.131009	−	0.131009i
$957$	−8.41582	+	15.8416i	−0.272045	+	0.512087i
$958$	25.4685			0.822851
$959$	11.4279			0.369025
$960$	−10.8375	−	10.8375i	−0.349778	−	0.349778i
$961$			28.9898i			0.935154i
$962$	10.1159	+	5.04235i	0.326149	+	0.162572i
$963$			16.6500i			0.536538i
$964$	−8.42042	−	8.42042i	−0.271204	−	0.271204i
$965$			7.18882i			0.231416i
$966$		−	15.4182i		−	0.496072i
$967$	28.7750	+	28.7750i	0.925341	+	0.925341i	0.997400	−	0.0720598i	$-0.0229572\pi$
$967$	28.7750	+	28.7750i	0.925341	+	0.925341i	−0.0720598	+	0.997400i	$0.522957\pi$
$968$	−26.3033	−	5.09319i	−0.845419	−	0.163701i
$969$	−0.0941400	−	0.0941400i	−0.00302421	−	0.00302421i
$970$	−40.7641	+	40.7641i	−1.30886	+	1.30886i
$971$	−41.6907			−1.33792			−0.668959	−	0.743299i	$-0.733260\pi$
$971$	−41.6907			−1.33792			−0.668959	+	0.743299i	$0.733260\pi$
$972$			0.441107i			0.0141485i
$973$	16.5582	+	16.5582i	0.530832	+	0.530832i
$974$	34.3968			1.10214
$975$	−8.53537	−	4.25453i	−0.273351	−	0.136254i
$976$			44.8638i			1.43605i
$977$	−22.6588	+	22.6588i	−0.724918	+	0.724918i	−0.969603	−	0.244684i	$-0.921316\pi$
$977$	−22.6588	+	22.6588i	−0.724918	+	0.724918i	0.244684	+	0.969603i	$0.421316\pi$
$978$			28.4019i			0.908192i
$979$	−5.85749	−	19.1343i	−0.187206	−	0.611536i
$980$	−3.89192	+	3.89192i	−0.124323	+	0.124323i
$981$	−0.829101	−	0.829101i	−0.0264712	−	0.0264712i
$982$	4.00524	+	4.00524i	0.127812	+	0.127812i
$983$	21.9261	+	21.9261i	0.699333	+	0.699333i	0.964267	−	0.264934i	$-0.0853501\pi$
$983$	21.9261	+	21.9261i	0.699333	+	0.699333i	−0.264934	+	0.964267i	$0.585350\pi$
$984$	21.7137			0.692208
$985$	−53.7326			−1.71206
$986$	0.366799	−	0.366799i	0.0116813	−	0.0116813i
$987$	−15.3977			−0.490115
$988$	1.09482	+	3.27101i	0.0348310	+	0.104065i
$989$			43.5627i			1.38521i
$990$	12.6532	+	6.72196i	0.402144	+	0.213638i
$991$	35.6424			1.13222			0.566109	−	0.824331i	$-0.308448\pi$
$991$	35.6424			1.13222			0.566109	+	0.824331i	$0.308448\pi$
$992$	3.47755			0.110412
$993$	3.50310	−	3.50310i	0.111168	−	0.111168i
$994$	−5.59063	+	5.59063i	−0.177324	+	0.177324i
$995$	40.9515	+	40.9515i	1.29825	+	1.29825i
$996$	−4.25805	+	4.25805i	−0.134921	+	0.134921i
$997$			33.0655i			1.04719i	0.851966	+	0.523597i	$0.175410\pi$
$997$			33.0655i			1.04719i	−0.851966	+	0.523597i	$0.824590\pi$
$998$	30.8086			0.975229
$999$	−1.41877	−	1.41877i	−0.0448878	−	0.0448878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.m.b.109.5	✓	28
11.10	odd	2	inner	429.2.m.b.109.10	yes	28
13.8	odd	4	inner	429.2.m.b.307.10	yes	28
143.21	even	4	inner	429.2.m.b.307.5	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.m.b.109.5	✓	28	1.1	even	1	trivial
429.2.m.b.109.10	yes	28	11.10	odd	2	inner
429.2.m.b.307.5	yes	28	143.21	even	4	inner
429.2.m.b.307.10	yes	28	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.10479 - 1.10479i) q^{2} +1.00000 q^{3} +0.441107i q^{4} +(1.95513 - 1.95513i) q^{5} +(-1.10479 - 1.10479i) q^{6} +(1.11517 - 1.11517i) q^{7} +(-1.72224 + 1.72224i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.10479 - 1.10479i) q^{2} +1.00000 q^{3} +0.441107i q^{4} +(1.95513 - 1.95513i) q^{5} +(-1.10479 - 1.10479i) q^{6} +(1.11517 - 1.11517i) q^{7} +(-1.72224 + 1.72224i) q^{8} +1.00000 q^{9} -4.32001 q^{10} +(-2.92897 - 1.55601i) q^{11} +0.441107i q^{12} +(1.60847 - 3.22689i) q^{13} -2.46406 q^{14} +(1.95513 - 1.95513i) q^{15} +4.68764 q^{16} -0.0613854 q^{17} +(-1.10479 - 1.10479i) q^{18} +(1.53359 + 1.53359i) q^{19} +(0.862423 + 0.862423i) q^{20} +(1.11517 - 1.11517i) q^{21} +(1.51683 + 4.95494i) q^{22} +6.25724i q^{23} +(-1.72224 + 1.72224i) q^{24} -2.64508i q^{25} +(-5.34204 + 1.78801i) q^{26} +1.00000 q^{27} +(0.491911 + 0.491911i) q^{28} -5.40860i q^{29} -4.32001 q^{30} +(-1.00255 + 1.00255i) q^{31} +(-1.73435 - 1.73435i) q^{32} +(-2.92897 - 1.55601i) q^{33} +(0.0678178 + 0.0678178i) q^{34} -4.36062i q^{35} +0.441107i q^{36} +(-1.41877 - 1.41877i) q^{37} -3.38858i q^{38} +(1.60847 - 3.22689i) q^{39} +6.73443i q^{40} +(-6.30390 - 6.30390i) q^{41} -2.46406 q^{42} +6.96197 q^{43} +(0.686366 - 1.29199i) q^{44} +(1.95513 - 1.95513i) q^{45} +(6.91291 - 6.91291i) q^{46} +(-6.90374 - 6.90374i) q^{47} +4.68764 q^{48} +4.51278i q^{49} +(-2.92225 + 2.92225i) q^{50} -0.0613854 q^{51} +(1.42341 + 0.709509i) q^{52} -6.29470 q^{53} +(-1.10479 - 1.10479i) q^{54} +(-8.76871 + 2.68432i) q^{55} +3.84120i q^{56} +(1.53359 + 1.53359i) q^{57} +(-5.97535 + 5.97535i) q^{58} +(8.28019 + 8.28019i) q^{59} +(0.862423 + 0.862423i) q^{60} +9.57065i q^{61} +2.21521 q^{62} +(1.11517 - 1.11517i) q^{63} -5.54310i q^{64} +(-3.16422 - 9.45377i) q^{65} +(1.51683 + 4.95494i) q^{66} +(2.56219 - 2.56219i) q^{67} -0.0270776i q^{68} +6.25724i q^{69} +(-4.81755 + 4.81755i) q^{70} +(2.26887 - 2.26887i) q^{71} +(-1.72224 + 1.72224i) q^{72} +(3.20483 - 3.20483i) q^{73} +3.13487i q^{74} -2.64508i q^{75} +(-0.676477 + 0.676477i) q^{76} +(-5.00152 + 1.53109i) q^{77} +(-5.34204 + 1.78801i) q^{78} +7.07646i q^{79} +(9.16495 - 9.16495i) q^{80} +1.00000 q^{81} +13.9289i q^{82} +(9.65308 + 9.65308i) q^{83} +(0.491911 + 0.491911i) q^{84} +(-0.120017 + 0.120017i) q^{85} +(-7.69149 - 7.69149i) q^{86} -5.40860i q^{87} +(7.72422 - 2.36457i) q^{88} +(4.26632 + 4.26632i) q^{89} -4.32001 q^{90} +(-1.80482 - 5.39226i) q^{91} -2.76011 q^{92} +(-1.00255 + 1.00255i) q^{93} +15.2543i q^{94} +5.99673 q^{95} +(-1.73435 - 1.73435i) q^{96} +(9.43613 - 9.43613i) q^{97} +(4.98566 - 4.98566i) q^{98} +(-2.92897 - 1.55601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9}+O(q^{10}) \) 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9	\( 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9} - 4 q^{15} - 20 q^{16} - 16 q^{20} - 8 q^{22} + 12 q^{26} + 28 q^{27} + 8 q^{31} - 32 q^{34} - 12 q^{37} + 36 q^{44} - 4 q^{45} - 40 q^{47} - 20 q^{48} + 8 q^{53} - 16 q^{55} + 16 q^{58} - 44 q^{59} - 16 q^{60} - 8 q^{66} - 20 q^{67} - 36 q^{70} - 60 q^{71} + 12 q^{78} - 8 q^{80} + 28 q^{81} + 48 q^{86} + 32 q^{89} + 4 q^{91} + 64 q^{92} + 8 q^{93} + 8 q^{97}+O(q^{100}) \) 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9 - 4 * q^15 - 20 * q^16 - 16 * q^20 - 8 * q^22 + 12 * q^26 + 28 * q^27 + 8 * q^31 - 32 * q^34 - 12 * q^37 + 36 * q^44 - 4 * q^45 - 40 * q^47 - 20 * q^48 + 8 * q^53 - 16 * q^55 + 16 * q^58 - 44 * q^59 - 16 * q^60 - 8 * q^66 - 20 * q^67 - 36 * q^70 - 60 * q^71 + 12 * q^78 - 8 * q^80 + 28 * q^81 + 48 * q^86 + 32 * q^89 + 4 * q^91 + 64 * q^92 + 8 * q^93 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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