LMFDB - Embedded newform 429.2.e.c.428.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(428,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("429.428");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.e (of order $2$, degree $1$, 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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 20x^{14} + 164x^{12} - 666x^{10} + 1300x^{8} - 924x^{6} + 273x^{4} + 404x^{2} + 64 $ x^16 - 20x^14 + 164x^12 - 666x^10 + 1300x^8 - 924x^6 + 273x^4 + 404*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			428.6
Root			$2.34517 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	429.428
Dual form			429.2.e.c.428.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.662153i q^{2} +(-1.28078 - 1.16602i) q^{3} +1.56155 q^{4} +2.33205 q^{5} +(-0.772087 + 0.848071i) q^{6} -2.35829i q^{8} +(0.280776 + 2.98683i) q^{9} +O(q^{10})$	\(q-0.662153i q^{2} +(-1.28078 - 1.16602i) q^{3} +1.56155 q^{4} +2.33205 q^{5} +(-0.772087 + 0.848071i) q^{6} -2.35829i q^{8} +(0.280776 + 2.98683i) q^{9} -1.54417i q^{10} +(2.33205 - 2.35829i) q^{11} +(-2.00000 - 1.82081i) q^{12} +(0.772087 + 3.52191i) q^{13} +(-2.98683 - 2.71922i) q^{15} +1.56155 q^{16} +6.41273 q^{17} +(1.97774 - 0.185917i) q^{18} -7.04383 q^{19} +3.64162 q^{20} +(-1.56155 - 1.54417i) q^{22} +2.33205i q^{23} +(-2.74983 + 3.02045i) q^{24} +0.438447 q^{25} +(2.33205 - 0.511240i) q^{26} +(3.12311 - 4.15286i) q^{27} -6.41273 q^{29} +(-1.80054 + 1.97774i) q^{30} -9.68466i q^{31} -5.75058i q^{32} +(-5.73666 + 0.301224i) q^{33} -4.24621i q^{34} +(0.438447 + 4.66410i) q^{36} +5.43845i q^{37} +4.66410i q^{38} +(3.11777 - 5.41106i) q^{39} -5.49966i q^{40} -4.34475i q^{41} +1.54417i q^{43} +(3.64162 - 3.68260i) q^{44} +(0.654784 + 6.96543i) q^{45} +1.54417 q^{46} +(-2.00000 - 1.82081i) q^{48} -7.00000 q^{49} -0.290319i q^{50} +(-8.21327 - 7.47740i) q^{51} +(1.20565 + 5.49966i) q^{52} -4.66410i q^{53} +(-2.74983 - 2.06798i) q^{54} +(5.43845 - 5.49966i) q^{55} +(9.02157 + 8.21327i) q^{57} +4.24621i q^{58} +1.30957 q^{59} +(-4.66410 - 4.24621i) q^{60} +7.04383i q^{61} -6.41273 q^{62} -0.684658 q^{64} +(1.80054 + 8.21327i) q^{65} +(0.199457 + 3.79855i) q^{66} +9.68466i q^{67} +10.0138 q^{68} +(2.71922 - 2.98683i) q^{69} -5.97366 q^{71} +(7.04383 - 0.662153i) q^{72} +8.58800 q^{73} +3.60109 q^{74} +(-0.561553 - 0.511240i) q^{75} -10.9993 q^{76} +(-3.58295 - 2.06444i) q^{78} +12.5435i q^{79} +3.64162 q^{80} +(-8.84233 + 1.67726i) q^{81} -2.87689 q^{82} +9.80501i q^{83} +14.9548 q^{85} +1.02248 q^{86} +(8.21327 + 7.47740i) q^{87} +(-5.56155 - 5.49966i) q^{88} -14.2794 q^{89} +(4.61219 - 0.433567i) q^{90} +3.64162i q^{92} +(-11.2925 + 12.4039i) q^{93} -16.4265 q^{95} +(-6.70531 + 7.36520i) q^{96} +13.9309i q^{97} +4.63507i q^{98} +(7.69861 + 6.30328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} - 8 q^{4} - 12 q^{9}+O(q^{10}) $ 16 * q - 4 * q^3 - 8 * q^4 - 12 * q^9	$ 16 q - 4 q^{3} - 8 q^{4} - 12 q^{9} - 32 q^{12} - 8 q^{16} + 8 q^{22} + 40 q^{25} - 16 q^{27} + 40 q^{36} - 32 q^{48} - 112 q^{49} + 120 q^{55} + 88 q^{64} + 32 q^{66} + 60 q^{69} + 24 q^{75} - 92 q^{78} - 92 q^{81} - 112 q^{82} - 56 q^{88}+O(q^{100}) $ 16 * q - 4 * q^3 - 8 * q^4 - 12 * q^9 - 32 * q^12 - 8 * q^16 + 8 * q^22 + 40 * q^25 - 16 * q^27 + 40 * q^36 - 32 * q^48 - 112 * q^49 + 120 * q^55 + 88 * q^64 + 32 * q^66 + 60 * q^69 + 24 * q^75 - 92 * q^78 - 92 * q^81 - 112 * q^82 - 56 * q^88

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	0.662153i		−	0.468213i	−0.972211	−	0.234107i	$-0.924784\pi$
$2$		−	0.662153i		−	0.468213i	0.972211	−	0.234107i	$-0.0752165\pi$
$3$	−1.28078	−	1.16602i	−0.739457	−	0.673204i
$3$	−1.28078	−	1.16602i	−0.739457	−	0.673204i
$4$	1.56155			0.780776
$5$	2.33205			1.04292			0.521462	−	0.853275i	$-0.325387\pi$
$5$	2.33205			1.04292			0.521462	+	0.853275i	$0.325387\pi$
$6$	−0.772087	+	0.848071i	−0.315203	+	0.346223i
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$		−	2.35829i		−	0.833783i
$9$	0.280776	+	2.98683i	0.0935921	+	0.995611i
$10$		−	1.54417i		−	0.488311i
$11$	2.33205	−	2.35829i	0.703139	−	0.711053i
$11$	2.33205	−	2.35829i	0.703139	−	0.711053i
$12$	−2.00000	−	1.82081i	−0.577350	−	0.525622i
$13$	0.772087	+	3.52191i	0.214138	+	0.976803i
$13$	0.772087	+	3.52191i	0.214138	+	0.976803i
$14$		0			0
$15$	−2.98683	−	2.71922i	−0.771197	−	0.702101i
$16$	1.56155			0.390388
$17$	6.41273			1.55532			0.777658	−	0.628688i	$-0.216408\pi$
$17$	6.41273			1.55532			0.777658	+	0.628688i	$0.216408\pi$
$18$	1.97774	−	0.185917i	0.466158	−	0.0438211i
$19$	−7.04383			−1.61597			−0.807983	−	0.589206i	$-0.799441\pi$
$19$	−7.04383			−1.61597			−0.807983	+	0.589206i	$0.799441\pi$
$20$	3.64162			0.814290
$21$		0			0
$22$	−1.56155	−	1.54417i	−0.332924	−	0.329219i
$23$			2.33205i			0.486266i	0.969993	+	0.243133i	$0.0781751\pi$
$23$			2.33205i			0.486266i	−0.969993	+	0.243133i	$0.921825\pi$
$24$	−2.74983	+	3.02045i	−0.561306	+	0.616546i
$25$	0.438447			0.0876894
$26$	2.33205	−	0.511240i	0.457352	−	0.100262i
$27$	3.12311	−	4.15286i	0.601042	−	0.799217i
$28$		0			0
$29$	−6.41273			−1.19081			−0.595407	−	0.803424i	$-0.703009\pi$
$29$	−6.41273			−1.19081			−0.595407	+	0.803424i	$0.703009\pi$
$30$	−1.80054	+	1.97774i	−0.328733	+	0.361084i
$31$		−	9.68466i		−	1.73942i	−0.493567	−	0.869708i	$-0.664307\pi$
$31$		−	9.68466i		−	1.73942i	0.493567	−	0.869708i	$-0.335693\pi$
$32$		−	5.75058i		−	1.01657i
$33$	−5.73666	+	0.301224i	−0.998624	+	0.0524364i
$34$		−	4.24621i		−	0.728219i
$35$		0			0
$36$	0.438447	+	4.66410i	0.0730745	+	0.777349i
$37$			5.43845i			0.894075i	0.894515	+	0.447038i	$0.147521\pi$
$37$			5.43845i			0.894075i	−0.894515	+	0.447038i	$0.852479\pi$
$38$			4.66410i			0.756616i
$39$	3.11777	−	5.41106i	0.499242	−	0.866463i
$40$		−	5.49966i		−	0.869572i
$41$		−	4.34475i		−	0.678537i	−0.940690	−	0.339268i	$-0.889821\pi$
$41$		−	4.34475i		−	0.678537i	0.940690	−	0.339268i	$-0.110179\pi$
$42$		0			0
$43$			1.54417i			0.235484i	0.993044	+	0.117742i	$0.0375656\pi$
$43$			1.54417i			0.235484i	−0.993044	+	0.117742i	$0.962434\pi$
$44$	3.64162	−	3.68260i	0.548994	−	0.555173i
$45$	0.654784	+	6.96543i	0.0976094	+	1.03835i
$46$	1.54417			0.227676
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	−2.00000	−	1.82081i	−0.288675	−	0.262811i
$49$	−7.00000			−1.00000
$50$		−	0.290319i		−	0.0410574i
$51$	−8.21327	−	7.47740i	−1.15009	−	1.04704i
$52$	1.20565	+	5.49966i	0.167194	+	0.762665i
$53$		−	4.66410i		−	0.640663i	−0.947306	−	0.320331i	$-0.896206\pi$
$53$		−	4.66410i		−	0.640663i	0.947306	−	0.320331i	$-0.103794\pi$
$54$	−2.74983	−	2.06798i	−0.374204	−	0.281416i
$55$	5.43845	−	5.49966i	0.733320	−	0.741573i
$56$		0			0
$57$	9.02157	+	8.21327i	1.19494	+	1.08787i
$58$			4.24621i			0.557555i
$59$	1.30957			0.170491			0.0852456	−	0.996360i	$-0.472833\pi$
$59$	1.30957			0.170491			0.0852456	+	0.996360i	$0.472833\pi$
$60$	−4.66410	−	4.24621i	−0.602132	−	0.548184i
$61$			7.04383i			0.901870i	0.892557	+	0.450935i	$0.148909\pi$
$61$			7.04383i			0.901870i	−0.892557	+	0.450935i	$0.851091\pi$
$62$	−6.41273			−0.814418
$63$		0			0
$64$	−0.684658			−0.0855823
$65$	1.80054	+	8.21327i	0.223330	+	1.01873i
$66$	0.199457	+	3.79855i	0.0245514	+	0.467569i
$67$			9.68466i			1.18317i	0.806243	+	0.591585i	$0.201497\pi$
$67$			9.68466i			1.18317i	−0.806243	+	0.591585i	$0.798503\pi$
$68$	10.0138			1.21435
$69$	2.71922	−	2.98683i	0.327356	−	0.359572i
$70$		0			0
$71$	−5.97366			−0.708943			−0.354472	−	0.935067i	$-0.615339\pi$
$71$	−5.97366			−0.708943			−0.354472	+	0.935067i	$0.615339\pi$
$72$	7.04383	−	0.662153i	0.830123	−	0.0780355i
$73$	8.58800			1.00515			0.502575	−	0.864534i	$-0.332386\pi$
$73$	8.58800			1.00515			0.502575	+	0.864534i	$0.332386\pi$
$74$	3.60109			0.418618
$75$	−0.561553	−	0.511240i	−0.0648425	−	0.0590329i
$76$	−10.9993			−1.26171
$77$		0			0
$78$	−3.58295	−	2.06444i	−0.405689	−	0.233752i
$79$			12.5435i			1.41125i	0.708584	+	0.705626i	$0.249334\pi$
$79$			12.5435i			1.41125i	−0.708584	+	0.705626i	$0.750666\pi$
$80$	3.64162			0.407145
$81$	−8.84233	+	1.67726i	−0.982481	+	0.186363i
$82$	−2.87689			−0.317700
$83$			9.80501i			1.07624i	0.842868	+	0.538120i	$0.180865\pi$
$83$			9.80501i			1.07624i	−0.842868	+	0.538120i	$0.819135\pi$
$84$		0			0
$85$	14.9548			1.62208
$86$	1.02248			0.110257
$87$	8.21327	+	7.47740i	0.880555	+	0.801661i
$88$	−5.56155	−	5.49966i	−0.592864	−	0.586265i
$89$	−14.2794			−1.51361			−0.756805	−	0.653640i	$-0.773241\pi$
$89$	−14.2794			−1.51361			−0.756805	+	0.653640i	$0.773241\pi$
$90$	4.61219	−	0.433567i	0.486167	−	0.0457020i
$91$		0			0
$92$			3.64162i			0.379665i
$93$	−11.2925	+	12.4039i	−1.17098	+	1.28622i
$94$		0			0
$95$	−16.4265			−1.68533
$96$	−6.70531	+	7.36520i	−0.684358	+	0.751708i
$97$			13.9309i			1.41447i	0.706981	+	0.707233i	$0.250057\pi$
$97$			13.9309i			1.41447i	−0.706981	+	0.707233i	$0.749943\pi$
$98$			4.63507i			0.468213i
$99$	7.69861	+	6.30328i	0.773740	+	0.633504i
$100$	0.684658			0.0684658
$101$	10.0138			0.996412			0.498206	−	0.867059i	$-0.333992\pi$
$101$	10.0138			0.996412			0.498206	+	0.867059i	$0.333992\pi$
$102$	−4.95118	+	5.43845i	−0.490240	+	0.538487i
$103$	5.12311			0.504795			0.252397	−	0.967624i	$-0.418781\pi$
$103$	5.12311			0.504795			0.252397	+	0.967624i	$0.418781\pi$
$104$	8.30571	−	1.82081i	0.814442	−	0.178545i
$105$		0			0
$106$	−3.08835			−0.299967
$107$	−3.60109			−0.348130			−0.174065	−	0.984734i	$-0.555690\pi$
$107$	−3.60109			−0.348130			−0.174065	+	0.984734i	$0.555690\pi$
$108$	4.87689	−	6.48490i	0.469279	−	0.624010i
$109$	15.6318			1.49726			0.748629	−	0.662989i	$-0.230712\pi$
$109$	15.6318			1.49726			0.748629	+	0.662989i	$0.230712\pi$
$110$	−3.64162	−	3.60109i	−0.347214	−	0.343350i
$111$	6.34136	−	6.96543i	0.601895	−	0.661130i
$112$		0			0
$113$		−	3.35453i		−	0.315567i	−0.987474	−	0.157784i	$-0.949565\pi$
$113$		−	3.35453i		−	0.315567i	0.987474	−	0.157784i	$-0.0504349\pi$
$114$	5.43845	−	5.97366i	0.509357	−	0.559485i
$115$			5.43845i			0.507138i
$116$	−10.0138			−0.929760
$117$	−10.3026	+	3.29496i	−0.952474	+	0.304620i
$118$		−	0.867135i		−	0.0798262i
$119$		0			0
$120$	−6.41273	+	7.04383i	−0.585399	+	0.643011i
$121$	−0.123106	−	10.9993i	−0.0111914	−	0.999937i
$122$	4.66410			0.422267
$123$	−5.06609	+	5.56466i	−0.456794	+	0.501748i
$124$		−	15.1231i		−	1.35809i
$125$	−10.6378			−0.951470
$126$		0			0
$127$			2.41131i			0.213969i	0.994261	+	0.106985i	$0.0341195\pi$
$127$			2.41131i			0.213969i	−0.994261	+	0.106985i	$0.965880\pi$
$128$		−	11.0478i		−	0.976497i
$129$	1.80054	−	1.97774i	0.158529	−	0.174130i
$130$	5.43845	−	1.19224i	0.476983	−	0.104566i
$131$	12.8255			1.12057			0.560283	−	0.828301i	$-0.310692\pi$
$131$	12.8255			1.12057			0.560283	+	0.828301i	$0.310692\pi$
$132$	−8.95810	+	0.470378i	−0.779702	+	0.0409411i
$133$		0			0
$134$	6.41273			0.553975
$135$	7.28323	−	9.68466i	0.626841	−	0.833523i
$136$		−	15.1231i		−	1.29680i
$137$	−2.33205			−0.199240			−0.0996201	−	0.995026i	$-0.531763\pi$
$137$	−2.33205			−0.199240			−0.0996201	+	0.995026i	$0.531763\pi$
$138$	−1.97774	−	1.80054i	−0.168356	−	0.153272i
$139$		−	16.4990i		−	1.39942i	−0.714425	−	0.699712i	$-0.753312\pi$
$139$		−	16.4990i		−	1.39942i	0.714425	−	0.699712i	$-0.246688\pi$
$140$		0			0
$141$		0			0
$142$			3.95548i			0.331937i
$143$	10.1063	+	6.39247i	0.845127	+	0.534565i
$144$	0.438447	+	4.66410i	0.0365373	+	0.388675i
$145$	−14.9548			−1.24193
$146$		−	5.68658i		−	0.470624i
$147$	8.96543	+	8.16217i	0.739457	+	0.673204i
$148$			8.49242i			0.698073i
$149$			2.64861i			0.216983i	0.994097	+	0.108491i	$0.0346020\pi$
$149$			2.64861i			0.216983i	−0.994097	+	0.108491i	$0.965398\pi$
$150$	−0.338519	+	0.371834i	−0.0276400	+	0.0303601i
$151$	−18.0431			−1.46833			−0.734165	−	0.678971i	$-0.762426\pi$
$151$	−18.0431			−1.46833			−0.734165	+	0.678971i	$0.762426\pi$
$152$			16.6114i			1.34736i
$153$	1.80054	+	19.1537i	0.145565	+	1.54849i
$154$		0			0
$155$		−	22.5851i		−	1.81408i
$156$	4.86856	−	8.44965i	0.389796	−	0.676513i
$157$	−3.43845			−0.274418			−0.137209	−	0.990542i	$-0.543813\pi$
$157$	−3.43845			−0.274418			−0.137209	+	0.990542i	$0.543813\pi$
$158$	8.30571			0.660767
$159$	−5.43845	+	5.97366i	−0.431297	+	0.473742i
$160$		−	13.4106i		−	1.06020i
$161$		0			0
$162$	1.11061	+	5.85498i	0.0872575	+	0.460011i
$163$		−	4.24621i		−	0.332589i	−0.986076	−	0.166294i	$-0.946820\pi$
$163$		−	4.24621i		−	0.332589i	0.986076	−	0.166294i	$-0.0531802\pi$
$164$		−	6.78456i		−	0.529785i
$165$	−13.3782	+	0.702470i	−1.04149	+	0.0546872i
$166$	6.49242			0.503910
$167$		−	17.5420i		−	1.35744i	−0.734395	−	0.678722i	$-0.762534\pi$
$167$		−	17.5420i		−	1.35744i	0.734395	−	0.678722i	$-0.237466\pi$
$168$		0			0
$169$	−11.8078	+	5.43845i	−0.908290	+	0.418342i
$170$		−	9.90237i		−	0.759477i
$171$	−1.97774	−	21.0387i	−0.151242	−	1.60887i
$172$			2.41131i			0.183861i
$173$	−6.41273			−0.487551			−0.243775	−	0.969832i	$-0.578386\pi$
$173$	−6.41273			−0.487551			−0.243775	+	0.969832i	$0.578386\pi$
$174$	4.95118	−	5.43845i	0.375348	−	0.412288i
$175$		0			0
$176$	3.64162	−	3.68260i	0.274497	−	0.277587i
$177$	−1.67726	−	1.52699i	−0.126071	−	0.114775i
$178$			9.45514i			0.708693i
$179$			18.9435i			1.41590i	0.706262	+	0.707951i	$0.250380\pi$
$179$			18.9435i			1.41590i	−0.706262	+	0.707951i	$0.749620\pi$
$180$	1.02248	+	10.8769i	0.0762111	+	0.810716i
$181$	14.8078			1.10065			0.550326	−	0.834950i	$-0.314503\pi$
$181$	14.8078			1.10065			0.550326	+	0.834950i	$0.314503\pi$
$182$		0			0
$183$	8.21327	−	9.02157i	0.607143	−	0.666894i
$184$	5.49966			0.405440
$185$			12.6827i			0.932452i
$186$	8.21327	+	7.47740i	0.602226	+	0.548269i
$187$	14.9548	−	15.1231i	1.09360	−	1.10591i
$188$		0			0
$189$		0			0
$190$			10.8769i			0.789093i
$191$			2.33205i			0.168741i	0.996434	+	0.0843705i	$0.0268879\pi$
$191$			2.33205i			0.168741i	−0.996434	+	0.0843705i	$0.973112\pi$
$192$	0.876894	+	0.798328i	0.0632844	+	0.0576144i
$193$	−5.49966			−0.395874			−0.197937	−	0.980215i	$-0.563424\pi$
$193$	−5.49966			−0.395874			−0.197937	+	0.980215i	$0.563424\pi$
$194$	9.22437			0.662271
$195$	7.27078	−	12.6188i	0.520671	−	0.903654i
$196$	−10.9309			−0.780776
$197$			24.9073i			1.77457i	0.461223	+	0.887284i	$0.347411\pi$
$197$			24.9073i			1.77457i	−0.461223	+	0.887284i	$0.652589\pi$
$198$	4.17374	−	5.09766i	0.296615	−	0.362275i
$199$	−15.3693			−1.08950			−0.544751	−	0.838598i	$-0.683376\pi$
$199$	−15.3693			−1.08950			−0.544751	+	0.838598i	$0.683376\pi$
$200$		−	1.03399i		−	0.0731140i
$201$	11.2925	−	12.4039i	0.796515	−	0.874902i
$202$		−	6.63068i		−	0.466533i
$203$		0			0
$204$	−12.8255	−	11.6763i	−0.897962	−	0.817508i
$205$		−	10.1322i		−	0.707662i
$206$		−	3.39228i		−	0.236351i
$207$	−6.96543	+	0.654784i	−0.484131	+	0.0455106i
$208$	1.20565	+	5.49966i	0.0835971	+	0.381333i
$209$	−16.4265	+	16.6114i	−1.13625	+	1.14904i
$210$		0			0
$211$			13.4106i			0.923225i	0.887082	+	0.461613i	$0.152729\pi$
$211$			13.4106i			0.923225i	−0.887082	+	0.461613i	$0.847271\pi$
$212$		−	7.28323i		−	0.500214i
$213$	7.65093	+	6.96543i	0.524233	+	0.477264i
$214$			2.38447i			0.162999i
$215$			3.60109i			0.245592i
$216$	−9.79366	−	7.36520i	−0.666374	−	0.501139i
$217$		0			0
$218$		−	10.3507i		−	0.701036i
$219$	−10.9993	−	10.0138i	−0.743265	−	0.676671i
$220$	8.49242	−	8.58800i	0.572559	−	0.579003i
$221$	4.95118	+	22.5851i	0.333053	+	1.51924i
$222$	−4.61219	−	4.19895i	−0.309550	−	0.281815i
$223$		−	9.68466i		−	0.648533i	−0.945966	−	0.324266i	$-0.894883\pi$
$223$		−	9.68466i		−	0.648533i	0.945966	−	0.324266i	$-0.105117\pi$
$224$		0			0
$225$	0.123106	+	1.30957i	0.00820704	+	0.0873045i
$226$	−2.22121			−0.147753
$227$		−	9.06134i		−	0.601423i	−0.953715	−	0.300711i	$-0.902776\pi$
$227$		−	9.06134i		−	0.601423i	0.953715	−	0.300711i	$-0.0972240\pi$
$228$	14.0877	+	12.8255i	0.932978	+	0.849387i
$229$			5.43845i			0.359383i	0.983723	+	0.179691i	$0.0575099\pi$
$229$			5.43845i			0.359383i	−0.983723	+	0.179691i	$0.942490\pi$
$230$	3.60109			0.237449
$231$		0			0
$232$			15.1231i			0.992881i
$233$	−10.0138			−0.656027			−0.328013	−	0.944673i	$-0.606379\pi$
$233$	−10.0138			−0.656027			−0.328013	+	0.944673i	$0.606379\pi$
$234$	2.18177	+	6.82189i	0.142627	+	0.445961i
$235$		0			0
$236$	2.04496			0.133116
$237$	14.6260	−	16.0654i	0.950061	−	1.04356i
$238$		0			0
$239$			6.62153i			0.428311i	0.976800	+	0.214156i	$0.0687000\pi$
$239$			6.62153i			0.428311i	−0.976800	+	0.214156i	$0.931300\pi$
$240$	−4.66410	−	4.24621i	−0.301066	−	0.274092i
$241$	−9.45514			−0.609059			−0.304529	−	0.952503i	$-0.598499\pi$
$241$	−9.45514			−0.609059			−0.304529	+	0.952503i	$0.598499\pi$
$242$	−7.28323	+	0.0815148i	−0.468184	+	0.00523997i
$243$	13.2808	+	8.16217i	0.851962	+	0.523603i
$244$			10.9993i			0.704159i
$245$	−16.3243			−1.04292
$246$	3.68466	+	3.35453i	0.234925	+	0.213877i
$247$	−5.43845	−	24.8078i	−0.346040	−	1.57848i
$248$	−22.8393			−1.45030
$249$	11.4329	−	12.5580i	0.724529	−	0.795833i
$250$			7.04383i			0.445491i
$251$		−	16.8985i		−	1.06662i	−0.845918	−	0.533312i	$-0.820947\pi$
$251$		−	16.8985i		−	1.06662i	0.845918	−	0.533312i	$-0.179053\pi$
$252$		0			0
$253$	5.49966	+	5.43845i	0.345760	+	0.341912i
$254$	1.59666			0.100183
$255$	−19.1537	−	17.4376i	−1.19945	−	1.09199i
$256$	−8.68466			−0.542791
$257$		−	30.6037i		−	1.90901i	−0.298200	−	0.954503i	$-0.596386\pi$
$257$		−	30.6037i		−	1.90901i	0.298200	−	0.954503i	$-0.403614\pi$
$258$	−1.30957	−	1.19224i	−0.0815301	−	0.0742254i
$259$		0			0
$260$	2.81164	+	12.8255i	0.174371	+	0.795401i
$261$	−1.80054	−	19.1537i	−0.111451	−	1.18559i
$262$		−	8.49242i		−	0.524664i
$263$	25.6509			1.58170			0.790852	−	0.612008i	$-0.209638\pi$
$263$	25.6509			1.58170			0.790852	+	0.612008i	$0.209638\pi$
$264$	0.710376	+	13.5287i	0.0437206	+	0.832636i
$265$		−	10.8769i		−	0.668162i
$266$		0			0
$267$	18.2887	+	16.6501i	1.11925	+	1.01897i
$268$			15.1231i			0.923791i
$269$		−	19.2306i		−	1.17251i	−0.810127	−	0.586254i	$-0.800602\pi$
$269$		−	19.2306i		−	1.17251i	0.810127	−	0.586254i	$-0.199398\pi$
$270$	−6.41273	−	4.82262i	−0.390266	−	0.293495i
$271$	−14.0877			−0.855764			−0.427882	−	0.903835i	$-0.640740\pi$
$271$	−14.0877			−0.855764			−0.427882	+	0.903835i	$0.640740\pi$
$272$	10.0138			0.607177
$273$		0			0
$274$			1.54417i			0.0932869i
$275$	1.02248	−	1.03399i	0.0616579	−	0.0623518i
$276$	4.24621	−	4.66410i	0.255592	−	0.280746i
$277$			3.08835i			0.185561i	0.995687	+	0.0927804i	$0.0295755\pi$
$277$			3.08835i			0.185561i	−0.995687	+	0.0927804i	$0.970425\pi$
$278$	−10.9248			−0.655229
$279$	28.9264	−	2.71922i	1.73178	−	0.162796i
$280$		0			0
$281$		−	8.68951i		−	0.518373i	−0.965827	−	0.259186i	$-0.916546\pi$
$281$		−	8.68951i		−	0.518373i	0.965827	−	0.259186i	$-0.0834544\pi$
$282$		0			0
$283$			1.54417i			0.0917916i	0.998946	+	0.0458958i	$0.0146142\pi$
$283$			1.54417i			0.0917916i	−0.998946	+	0.0458958i	$0.985386\pi$
$284$	−9.32819			−0.553526
$285$	21.0387	+	19.1537i	1.24623	+	1.13457i
$286$	4.23279	−	6.69189i	0.250290	−	0.395700i
$287$		0			0
$288$	17.1760	−	1.61463i	1.01211	−	0.0951428i
$289$	24.1231			1.41901
$290$			9.90237i			0.581487i
$291$	16.2437	−	17.8423i	0.952224	−	1.04594i
$292$	13.4106			0.784797
$293$			3.18348i			0.185981i	0.995667	+	0.0929904i	$0.0296426\pi$
$293$			3.18348i			0.185981i	−0.995667	+	0.0929904i	$0.970357\pi$
$294$	5.40461	−	5.93649i	0.315203	−	0.346223i
$295$	3.05398			0.177809
$296$	12.8255			0.745465
$297$	−2.51043	−	17.0499i	−0.145670	−	0.989333i
$298$	1.75379			0.101594
$299$	−8.21327	+	1.80054i	−0.474986	+	0.104128i
$300$	−0.876894	−	0.798328i	−0.0506275	−	0.0460915i
$301$		0			0
$302$			11.9473i			0.687491i
$303$	−12.8255	−	11.6763i	−0.736803	−	0.670789i
$304$	−10.9993			−0.630854
$305$			16.4265i			0.940581i
$306$	12.6827	−	1.19224i	0.725023	−	0.0681556i
$307$	−17.1760			−0.980286			−0.490143	−	0.871642i	$-0.663056\pi$
$307$	−17.1760			−0.980286			−0.490143	+	0.871642i	$0.663056\pi$
$308$		0			0
$309$	−6.56155	−	5.97366i	−0.373274	−	0.339830i
$310$	−14.9548			−0.849375
$311$			10.9248i			0.619491i	0.950819	+	0.309746i	$0.100244\pi$
$311$			10.9248i			0.619491i	−0.950819	+	0.309746i	$0.899756\pi$
$312$	−12.7609	−	7.35261i	−0.722442	−	0.416260i
$313$	14.3153			0.809151			0.404575	−	0.914505i	$-0.367419\pi$
$313$	14.3153			0.809151			0.404575	+	0.914505i	$0.367419\pi$
$314$			2.27678i			0.128486i
$315$		0			0
$316$			19.5873i			1.10187i
$317$	23.6076			1.32593			0.662967	−	0.748649i	$-0.269297\pi$
$317$	23.6076			1.32593			0.662967	+	0.748649i	$0.269297\pi$
$318$	3.95548	+	3.60109i	0.221812	+	0.201939i
$319$	−14.9548	+	15.1231i	−0.837308	+	0.846731i
$320$	−1.59666			−0.0892558
$321$	4.61219	+	4.19895i	0.257427	+	0.234363i
$322$		0			0
$323$	−45.1702			−2.51334
$324$	−13.8078	+	2.61914i	−0.767098	+	0.145508i
$325$	0.338519	+	1.54417i	0.0187777	+	0.0856553i
$326$	−2.81164			−0.155723
$327$	−20.0209	−	18.2271i	−1.10716	−	1.00796i
$328$	−10.2462			−0.565752
$329$		0			0
$330$	0.465143	+	8.85840i	0.0256053	+	0.487639i
$331$		−	29.0540i		−	1.59695i	−0.602027	−	0.798475i	$-0.705640\pi$
$331$		−	29.0540i		−	1.59695i	0.602027	−	0.798475i	$-0.294360\pi$
$332$			15.3110i			0.840303i
$333$	−16.2437	+	1.52699i	−0.890151	+	0.0836784i
$334$	−11.6155			−0.635573
$335$			22.5851i			1.23396i
$336$		0			0
$337$		−	18.0431i		−	0.982872i	−0.870914	−	0.491436i	$-0.836472\pi$
$337$		−	18.0431i		−	0.982872i	0.870914	−	0.491436i	$-0.163528\pi$
$338$	3.60109	+	7.81855i	0.195873	+	0.425273i
$339$	−3.91146	+	4.29640i	−0.212441	+	0.233348i
$340$	23.3527			1.26648
$341$	−22.8393	−	22.5851i	−1.23682	−	1.22305i
$342$	−13.9309	+	1.30957i	−0.753295	+	0.0708133i
$343$		0			0
$344$	3.64162			0.196343
$345$	6.34136	−	6.96543i	0.341407	−	0.375006i
$346$			4.24621i			0.228278i
$347$	−3.60109			−0.193316			−0.0966582	−	0.995318i	$-0.530815\pi$
$347$	−3.60109			−0.193316			−0.0966582	+	0.995318i	$0.530815\pi$
$348$	12.8255	+	11.6763i	0.687517	+	0.625918i
$349$	9.45514			0.506122			0.253061	−	0.967450i	$-0.418563\pi$
$349$	9.45514			0.506122			0.253061	+	0.967450i	$0.418563\pi$
$350$		0			0
$351$	17.0373	+	7.79295i	0.909384	+	0.415957i
$352$	−13.5616	−	13.4106i	−0.722833	−	0.714788i
$353$	−4.95118			−0.263525			−0.131762	−	0.991281i	$-0.542064\pi$
$353$	−4.95118			−0.263525			−0.131762	+	0.991281i	$0.542064\pi$
$354$	−1.01110	+	1.11061i	−0.0537394	+	0.0590280i
$355$	−13.9309			−0.739374
$356$	−22.2980			−1.18179
$357$		0			0
$358$	12.5435			0.662944
$359$			10.5487i			0.556738i	0.960474	+	0.278369i	$0.0897938\pi$
$359$			10.5487i			0.556738i	−0.960474	+	0.278369i	$0.910206\pi$
$360$	16.4265	−	1.54417i	0.865755	−	0.0813851i
$361$	30.6155			1.61134
$362$		−	9.80501i		−	0.515340i
$363$	−12.6678	+	14.2312i	−0.664886	+	0.746944i
$364$		0			0
$365$	20.0276			1.04829
$366$	−5.97366	−	5.43845i	−0.312248	−	0.284272i
$367$	11.0540			0.577013			0.288506	−	0.957478i	$-0.406841\pi$
$367$	11.0540			0.577013			0.288506	+	0.957478i	$0.406841\pi$
$368$			3.64162i			0.189832i
$369$	12.9771	−	1.21990i	0.675558	−	0.0635057i
$370$	8.39791			0.436586
$371$		0			0
$372$	−17.6339	+	19.3693i	−0.914275	+	1.00425i
$373$			3.08835i			0.159909i	0.996799	+	0.0799543i	$0.0254774\pi$
$373$			3.08835i			0.159909i	−0.996799	+	0.0799543i	$0.974523\pi$
$374$	−10.0138	−	9.90237i	−0.517802	−	0.512039i
$375$	13.6246	+	12.4039i	0.703571	+	0.640534i
$376$		0			0
$377$	−4.95118	−	22.5851i	−0.254999	−	1.16319i
$378$		0			0
$379$			20.5616i			1.05618i	0.849190	+	0.528088i	$0.177091\pi$
$379$			20.5616i			1.05618i	−0.849190	+	0.528088i	$0.822909\pi$
$380$	−25.6509			−1.31586
$381$	2.81164	−	3.08835i	0.144045	−	0.158221i
$382$	1.54417			0.0790068
$383$	−8.59280			−0.439072			−0.219536	−	0.975604i	$-0.570454\pi$
$383$	−8.59280			−0.439072			−0.219536	+	0.975604i	$0.570454\pi$
$384$	−12.8820	+	14.1498i	−0.657382	+	0.722077i
$385$		0			0
$386$			3.64162i			0.185353i
$387$	−4.61219	+	0.433567i	−0.234451	+	0.0220395i
$388$			21.7538i			1.10438i
$389$			10.6378i			0.539356i	0.962951	+	0.269678i	$0.0869172\pi$
$389$			10.6378i			0.539356i	−0.962951	+	0.269678i	$0.913083\pi$
$390$	−8.35561	−	4.81437i	−0.423103	−	0.243785i
$391$			14.9548i			0.756296i
$392$			16.5081i			0.833783i
$393$	−16.4265	−	14.9548i	−0.828610	−	0.754370i
$394$	16.4924			0.830876
$395$			29.2520i			1.47183i
$396$	12.0218	+	9.84291i	0.604118	+	0.494625i
$397$			8.49242i			0.426222i	0.977028	+	0.213111i	$0.0683597\pi$
$397$			8.49242i			0.426222i	−0.977028	+	0.213111i	$0.931640\pi$
$398$			10.1768i			0.510119i
$399$		0			0
$400$	0.684658			0.0342329
$401$	15.5889			0.778475			0.389237	−	0.921137i	$-0.372739\pi$
$401$	15.5889			0.778475			0.389237	+	0.921137i	$0.372739\pi$
$402$	−8.21327	−	7.47740i	−0.409641	−	0.372939i
$403$	34.1085	−	7.47740i	1.69907	−	0.372476i
$404$	15.6371			0.777975
$405$	−20.6207	+	3.91146i	−1.02465	+	0.194362i
$406$		0			0
$407$	12.8255	+	12.6827i	0.635734	+	0.628659i
$408$	−17.6339	+	19.3693i	−0.873008	+	0.958924i
$409$	16.4990			0.815821			0.407911	−	0.913022i	$-0.366257\pi$
$409$	16.4990			0.815821			0.407911	+	0.913022i	$0.366257\pi$
$410$	−6.70906			−0.331337
$411$	2.98683	+	2.71922i	0.147330	+	0.134129i
$412$	8.00000			0.394132
$413$		0			0
$414$	0.433567	+	4.61219i	0.0213087	+	0.226677i
$415$			22.8658i			1.12244i
$416$	20.2530	−	4.43994i	0.992987	−	0.217686i
$417$	−19.2382	+	21.1315i	−0.942098	+	1.03481i
$418$	10.9993	+	10.8769i	0.537994	+	0.532006i
$419$		−	15.0148i		−	0.733519i	−0.930316	−	0.366760i	$-0.880467\pi$
$419$		−	15.0148i		−	0.733519i	0.930316	−	0.366760i	$-0.119533\pi$
$420$		0			0
$421$			19.3693i			0.944003i	0.881598	+	0.472001i	$0.156468\pi$
$421$			19.3693i			0.944003i	−0.881598	+	0.472001i	$0.843532\pi$
$422$	8.87989			0.432266
$423$		0			0
$424$	−10.9993			−0.534174
$425$	2.81164			0.136385
$426$	4.61219	−	5.06609i	0.223461	−	0.245453i
$427$		0			0
$428$	−5.62329			−0.271812
$429$	−5.49009	−	19.9715i	−0.265064	−	0.964231i
$430$	2.38447			0.114989
$431$			14.3586i			0.691628i	0.938303	+	0.345814i	$0.112397\pi$
$431$			14.3586i			0.691628i	−0.938303	+	0.345814i	$0.887603\pi$
$432$	4.87689	−	6.48490i	0.234640	−	0.312005i
$433$	2.80776			0.134933			0.0674663	−	0.997722i	$-0.478508\pi$
$433$	2.80776			0.134933			0.0674663	+	0.997722i	$0.478508\pi$
$434$		0			0
$435$	19.1537	+	17.4376i	0.918352	+	0.836071i
$436$	24.4099			1.16902
$437$		−	16.4265i		−	0.785788i
$438$	−6.63068	+	7.28323i	−0.316826	+	0.348006i
$439$		−	21.8085i		−	1.04086i	−0.853903	−	0.520432i	$-0.825771\pi$
$439$		−	21.8085i		−	1.04086i	0.853903	−	0.520432i	$-0.174229\pi$
$440$	−12.9698	−	12.8255i	−0.618311	−	0.611430i
$441$	−1.96543	−	20.9078i	−0.0935921	−	0.995611i
$442$	14.9548	−	3.27844i	0.711327	−	0.155940i
$443$		−	23.6076i		−	1.12163i	−0.827941	−	0.560815i	$-0.810488\pi$
$443$		−	23.6076i		−	1.12163i	0.827941	−	0.560815i	$-0.189512\pi$
$444$	9.90237	−	10.8769i	0.469946	−	0.516195i
$445$	−33.3002			−1.57858
$446$	−6.41273			−0.303652
$447$	3.08835	−	3.39228i	0.146074	−	0.160449i
$448$		0			0
$449$	−35.5549			−1.67794			−0.838970	−	0.544178i	$-0.816842\pi$
$449$	−35.5549			−1.67794			−0.838970	+	0.544178i	$0.816842\pi$
$450$	0.867135	−	0.0815148i	0.0408771	−	0.00384265i
$451$	−10.2462	−	10.1322i	−0.482475	−	0.477106i
$452$		−	5.23827i		−	0.246388i
$453$	23.1092	+	21.0387i	1.08577	+	0.988486i
$454$	−6.00000			−0.281594
$455$		0			0
$456$	19.3693	−	21.2755i	0.907051	−	0.996317i
$457$	−33.6750			−1.57525			−0.787624	−	0.616156i	$-0.788689\pi$
$457$	−33.6750			−1.57525			−0.787624	+	0.616156i	$0.788689\pi$
$458$	3.60109			0.168268
$459$	20.0276	−	26.6311i	0.934810	−	1.24304i
$460$			8.49242i			0.395961i
$461$		−	13.7779i		−	0.641702i	−0.947130	−	0.320851i	$-0.896031\pi$
$461$		−	13.7779i		−	0.641702i	0.947130	−	0.320851i	$-0.103969\pi$
$462$		0			0
$463$			18.1771i			0.844761i	0.906419	+	0.422380i	$0.138805\pi$
$463$			18.1771i			0.844761i	−0.906419	+	0.422380i	$0.861195\pi$
$464$	−10.0138			−0.464880
$465$	−26.3348	+	28.9264i	−1.22124	+	1.34143i
$466$			6.63068i			0.307160i
$467$			18.9435i			0.876599i	0.898829	+	0.438300i	$0.144419\pi$
$467$			18.9435i			0.876599i	−0.898829	+	0.438300i	$0.855581\pi$
$468$	−16.0880	+	5.14526i	−0.743669	+	0.237840i
$469$		0			0
$470$		0			0
$471$	4.40388	+	4.00931i	0.202920	+	0.184739i
$472$		−	3.08835i		−	0.142153i
$473$	3.64162	+	3.60109i	0.167442	+	0.165578i
$474$	−10.6378	−	9.68466i	−0.488608	−	0.444831i
$475$	−3.08835			−0.141703
$476$		0			0
$477$	13.9309	−	1.30957i	0.637851	−	0.0599610i
$478$	4.38447			0.200541
$479$		−	17.5420i		−	0.801517i	−0.916184	−	0.400758i	$-0.868747\pi$
$479$		−	17.5420i		−	0.801517i	0.916184	−	0.400758i	$-0.131253\pi$
$480$	−15.6371	+	17.1760i	−0.713733	+	0.783974i
$481$	−19.1537	+	4.19895i	−0.873336	+	0.191456i
$482$			6.26075i			0.285169i
$483$		0			0
$484$	−0.192236	−	17.1760i	−0.00873800	−	0.780728i
$485$			32.4875i			1.47518i
$486$	5.40461	−	8.79391i	0.245158	−	0.398900i
$487$		−	20.5616i		−	0.931733i	−0.884855	−	0.465866i	$-0.845743\pi$
$487$		−	20.5616i		−	0.931733i	0.884855	−	0.465866i	$-0.154257\pi$
$488$	16.6114			0.751964
$489$	−4.95118	+	5.43845i	−0.223900	+	0.245935i
$490$			10.8092i			0.488311i
$491$	−12.8255			−0.578805			−0.289402	−	0.957208i	$-0.593457\pi$
$491$	−12.8255			−0.578805			−0.289402	+	0.957208i	$0.593457\pi$
$492$	−7.91096	+	8.68951i	−0.356654	+	0.391753i
$493$	−41.1231			−1.85209
$494$	−16.4265	+	3.60109i	−0.739065	+	0.162021i
$495$	17.9535	+	14.6996i	0.806951	+	0.660696i
$496$		−	15.1231i		−	0.679047i
$497$		0			0
$498$	−8.31534	−	7.57032i	−0.372619	−	0.339234i
$499$		−	4.24621i		−	0.190087i	−0.995473	−	0.0950433i	$-0.969701\pi$
$499$		−	4.24621i		−	0.190087i	0.995473	−	0.0950433i	$-0.0302989\pi$
$500$	−16.6114			−0.742885
$501$	−20.4544	+	22.4674i	−0.913837	+	1.00377i
$502$	−11.1894			−0.499408
$503$	−7.20217			−0.321129			−0.160565	−	0.987025i	$-0.551331\pi$
$503$	−7.20217			−0.321129			−0.160565	+	0.987025i	$0.551331\pi$
$504$		0			0
$505$	23.3527			1.03918
$506$	3.60109	−	3.64162i	0.160088	−	0.161890i
$507$	21.4645	+	6.80270i	0.953270	+	0.302119i
$508$			3.76539i			0.167062i
$509$	23.6076			1.04639			0.523193	−	0.852214i	$-0.324741\pi$
$509$	23.6076			1.04639			0.523193	+	0.852214i	$0.324741\pi$
$510$	−11.5464	+	12.6827i	−0.511283	+	0.561600i
$511$		0			0
$512$		−	16.3450i		−	0.722355i
$513$	−21.9986	+	29.2520i	−0.971263	+	1.29151i
$514$	−20.2644			−0.893822
$515$	11.9473			0.526462
$516$	2.81164	−	3.08835i	0.123776	−	0.135957i
$517$		0			0
$518$		0			0
$519$	8.21327	+	7.47740i	0.360523	+	0.328221i
$520$	19.3693	−	4.24621i	0.849401	−	0.186209i
$521$			17.9210i			0.785133i	0.919724	+	0.392566i	$0.128413\pi$
$521$			17.9210i			0.785133i	−0.919724	+	0.392566i	$0.871587\pi$
$522$	−12.6827	+	1.19224i	−0.555108	+	0.0521827i
$523$			21.8085i			0.953620i	0.879006	+	0.476810i	$0.158207\pi$
$523$			21.8085i			0.953620i	−0.879006	+	0.476810i	$0.841793\pi$
$524$	20.0276			0.874911
$525$		0			0
$526$		−	16.9848i		−	0.740574i
$527$		−	62.1051i		−	2.70534i
$528$	−8.95810	+	0.470378i	−0.389851	+	0.0204706i
$529$	17.5616			0.763546
$530$	−7.20217			−0.312842
$531$	0.367696	+	3.91146i	0.0159566	+	0.169743i
$532$		0			0
$533$	15.3019	−	3.35453i	0.662797	−	0.145301i
$534$	11.0249	−	12.1099i	0.477095	−	0.524047i
$535$	−8.39791			−0.363073
$536$	22.8393			0.986506
$537$	22.0885	−	24.2624i	0.953191	−	1.04700i
$538$	−12.7336			−0.548984
$539$	−16.3243	+	16.5081i	−0.703139	+	0.711053i
$540$	11.3732	−	15.1231i	0.489422	−	0.650795i
$541$	9.45514			0.406508			0.203254	−	0.979126i	$-0.434848\pi$
$541$	9.45514			0.406508			0.203254	+	0.979126i	$0.434848\pi$
$542$			9.32819i			0.400680i
$543$	−18.9654	−	17.2662i	−0.813885	−	0.740964i
$544$		−	36.8769i		−	1.58108i
$545$	36.4542			1.56153
$546$		0			0
$547$			33.6750i			1.43984i	0.694058	+	0.719919i	$0.255821\pi$
$547$			33.6750i			1.43984i	−0.694058	+	0.719919i	$0.744179\pi$
$548$	−3.64162			−0.155562
$549$	−21.0387	+	1.97774i	−0.897911	+	0.0844079i
$550$	−0.684658	−	0.677039i	−0.0291939	−	0.0288690i
$551$	45.1702			1.92431
$552$	−7.04383	−	6.41273i	−0.299805	−	0.272944i
$553$		0			0
$554$	2.04496			0.0868820
$555$	14.7884	−	16.2437i	0.627731	−	0.689508i
$556$		−	25.7640i		−	1.09264i
$557$		−	27.3471i		−	1.15873i	−0.815067	−	0.579366i	$-0.803300\pi$
$557$		−	27.3471i		−	1.15873i	0.815067	−	0.579366i	$-0.196700\pi$
$558$	−1.80054	−	19.1537i	−0.0762231	−	0.810843i
$559$	−5.43845	+	1.19224i	−0.230022	+	0.0504262i
$560$		0			0
$561$	−36.7876	+	1.93167i	−1.55318	+	0.0815552i
$562$	−5.75379			−0.242709
$563$	3.60109			0.151768			0.0758839	−	0.997117i	$-0.475822\pi$
$563$	3.60109			0.151768			0.0758839	+	0.997117i	$0.475822\pi$
$564$		0			0
$565$		−	7.82292i		−	0.329113i
$566$	1.02248			0.0429780
$567$		0			0
$568$			14.0877i			0.591105i
$569$	−10.0138			−0.419801			−0.209901	−	0.977723i	$-0.567314\pi$
$569$	−10.0138			−0.419801			−0.209901	+	0.977723i	$0.567314\pi$
$570$	12.6827	−	13.9309i	0.531221	−	0.583500i
$571$		−	36.7633i		−	1.53850i	−0.638950	−	0.769249i	$-0.720631\pi$
$571$		−	36.7633i		−	1.53850i	0.638950	−	0.769249i	$-0.279369\pi$
$572$	15.7815	+	9.98217i	0.659856	+	0.417376i
$573$	2.71922	−	2.98683i	0.113597	−	0.124777i
$574$		0			0
$575$			1.02248i			0.0426404i
$576$	−0.192236	−	2.04496i	−0.00800983	−	0.0852067i
$577$		−	35.6847i		−	1.48557i	−0.669529	−	0.742786i	$-0.733504\pi$
$577$		−	35.6847i		−	1.48557i	0.669529	−	0.742786i	$-0.266496\pi$
$578$		−	15.9732i		−	0.664397i
$579$	7.04383	+	6.41273i	0.292732	+	0.266504i
$580$	−23.3527			−0.969668
$581$		0			0
$582$	−11.8144	−	10.7558i	−0.489721	−	0.445844i
$583$	−10.9993	−	10.8769i	−0.455545	−	0.450475i
$584$		−	20.2530i		−	0.838077i
$585$	−24.0261	+	7.68401i	−0.993358	+	0.317695i
$586$	2.10795			0.0870786
$587$	35.2678			1.45566			0.727829	−	0.685759i	$-0.240529\pi$
$587$	35.2678			1.45566			0.727829	+	0.685759i	$0.240529\pi$
$588$	14.0000	+	12.7457i	0.577350	+	0.525622i
$589$			68.2171i			2.81084i
$590$		−	2.02220i		−	0.0832527i
$591$	29.0425	−	31.9006i	1.19465	−	1.31222i
$592$			8.49242i			0.349036i
$593$		−	1.48734i		−	0.0610776i	−0.999534	−	0.0305388i	$-0.990278\pi$
$593$		−	1.48734i		−	0.0610776i	0.999534	−	0.0305388i	$-0.00972231\pi$
$594$	−11.2896	+	1.66229i	−0.463219	+	0.0682044i
$595$		0			0
$596$			4.13595i			0.169415i
$597$	19.6847	+	17.9210i	0.805639	+	0.733457i
$598$	1.19224	+	5.43845i	0.0487542	+	0.222395i
$599$		−	27.5363i		−	1.12510i	−0.826763	−	0.562551i	$-0.809820\pi$
$599$		−	27.5363i		−	1.12510i	0.826763	−	0.562551i	$-0.190180\pi$
$600$	−1.20565	+	1.32431i	−0.0492206	+	0.0540646i
$601$		−	21.9986i		−	0.897343i	−0.893697	−	0.448671i	$-0.851897\pi$
$601$		−	21.9986i		−	0.897343i	0.893697	−	0.448671i	$-0.148103\pi$
$602$		0			0
$603$	−28.9264	+	2.71922i	−1.17798	+	0.110735i
$604$	−28.1753			−1.14644
$605$	−0.287088	−	25.6509i	−0.0116718	−	1.04286i
$606$	−7.73154	+	8.49242i	−0.314072	+	0.344981i
$607$		−	33.6750i		−	1.36682i	−0.730032	−	0.683412i	$-0.760495\pi$
$607$		−	33.6750i		−	1.36682i	0.730032	−	0.683412i	$-0.239505\pi$
$608$			40.5061i			1.64274i
$609$		0			0
$610$	10.8769			0.440393
$611$		0			0
$612$	2.81164	+	29.9096i	0.113654	+	1.20902i
$613$	1.54417			0.0623686			0.0311843	−	0.999514i	$-0.490072\pi$
$613$	1.54417			0.0623686			0.0311843	+	0.999514i	$0.490072\pi$
$614$			11.3732i			0.458983i
$615$	−11.8144	+	12.9771i	−0.476401	+	0.523285i
$616$		0			0
$617$	24.9171			1.00313			0.501563	−	0.865121i	$-0.332759\pi$
$617$	24.9171			1.00313			0.501563	+	0.865121i	$0.332759\pi$
$618$	−3.95548	+	4.34475i	−0.159113	+	0.174772i
$619$		−	1.19224i		−	0.0479200i	−0.999713	−	0.0239600i	$-0.992373\pi$
$619$		−	1.19224i		−	0.0479200i	0.999713	−	0.0239600i	$-0.00762744\pi$
$620$		−	35.2678i		−	1.41639i
$621$	9.68466	+	7.28323i	0.388632	+	0.292266i
$622$	7.23393			0.290054
$623$		0			0
$624$	4.86856	−	8.44965i	0.194898	−	0.338257i
$625$	−27.0000			−1.08000
$626$		−	9.47895i		−	0.378855i
$627$	40.4081	−	2.12177i	1.61374	−	0.0847354i
$628$	−5.36932			−0.214259
$629$			34.8753i			1.39057i
$630$		0			0
$631$			1.19224i			0.0474622i	0.999718	+	0.0237311i	$0.00755455\pi$
$631$			1.19224i			0.0474622i	−0.999718	+	0.0237311i	$0.992445\pi$
$632$	29.5812			1.17668
$633$	15.6371	−	17.1760i	0.621519	−	0.682685i
$634$		−	15.6318i		−	0.620819i
$635$			5.62329i			0.223153i
$636$	−8.49242	+	9.32819i	−0.336746	+	0.369887i
$637$	−5.40461	−	24.6534i	−0.214138	−	0.976803i
$638$	10.0138	+	9.90237i	0.396451	+	0.392038i
$639$	−1.67726	−	17.8423i	−0.0663515	−	0.705832i
$640$		−	25.7640i		−	1.01841i
$641$		−	8.59280i		−	0.339395i	−0.985496	−	0.169698i	$-0.945721\pi$
$641$		−	8.59280i		−	0.339395i	0.985496	−	0.169698i	$-0.0542791\pi$
$642$	2.78035	−	3.05398i	0.109732	−	0.120531i
$643$			37.5464i			1.48069i	0.672230	+	0.740343i	$0.265337\pi$
$643$			37.5464i			1.48069i	−0.672230	+	0.740343i	$0.734663\pi$
$644$		0			0
$645$	4.19895	−	4.61219i	0.165334	−	0.181605i
$646$			29.9096i			1.17678i
$647$		−	0.287088i		−	0.0112866i	−0.999984	−	0.00564330i	$-0.998204\pi$
$647$		−	0.287088i		−	0.0112866i	0.999984	−	0.00564330i	$-0.00179633\pi$
$648$	3.95548	+	20.8528i	0.155386	+	0.819176i
$649$	3.05398	−	3.08835i	0.119879	−	0.121228i
$650$	1.02248	−	0.224152i	0.0401050	−	0.00879195i
$651$		0			0
$652$		−	6.63068i		−	0.259678i
$653$			19.9660i			0.781328i	0.920533	+	0.390664i	$0.127755\pi$
$653$			19.9660i			0.781328i	−0.920533	+	0.390664i	$0.872245\pi$
$654$	−12.0691	+	13.2569i	−0.471940	+	0.518386i
$655$	29.9096			1.16866
$656$		−	6.78456i		−	0.264893i
$657$	2.41131	+	25.6509i	0.0940741	+	1.00074i
$658$		0			0
$659$	−29.2520			−1.13950			−0.569748	−	0.821819i	$-0.692959\pi$
$659$	−29.2520			−1.13950			−0.569748	+	0.821819i	$0.692959\pi$
$660$	−20.8907	+	1.09694i	−0.813170	+	0.0426985i
$661$		−	22.4233i		−	0.872165i	−0.899907	−	0.436082i	$-0.856366\pi$
$661$		−	22.4233i		−	0.872165i	0.899907	−	0.436082i	$-0.143634\pi$
$662$	−19.2382			−0.747713
$663$	19.9934	−	34.6996i	0.776479	−	1.34762i
$664$	23.1231			0.897351
$665$		0			0
$666$	1.01110	+	10.7558i	0.0391793	+	0.416780i
$667$		−	14.9548i		−	0.579052i
$668$		−	27.3928i		−	1.05986i
$669$	−11.2925	+	12.4039i	−0.436595	+	0.479562i
$670$	14.9548			0.577754
$671$	16.6114	+	16.4265i	0.641277	+	0.634140i
$672$		0			0
$673$			2.22121i			0.0856214i	0.999083	+	0.0428107i	$0.0136312\pi$
$673$			2.22121i			0.0856214i	−0.999083	+	0.0428107i	$0.986369\pi$
$674$	−11.9473			−0.460194
$675$	1.36932	−	1.82081i	0.0527050	−	0.0700829i
$676$	−18.4384	+	8.49242i	−0.709171	+	0.326632i
$677$	42.8669			1.64751			0.823755	−	0.566947i	$-0.191875\pi$
$677$	42.8669			1.64751			0.823755	+	0.566947i	$0.191875\pi$
$678$	2.84488	+	2.58999i	0.109257	+	0.0994678i
$679$		0			0
$680$		−	35.2678i		−	1.35246i
$681$	−10.5657	+	11.6056i	−0.404880	+	0.444726i
$682$	−14.9548	+	15.1231i	−0.572649	+	0.579094i
$683$	−44.5960			−1.70642			−0.853209	−	0.521569i	$-0.825347\pi$
$683$	−44.5960			−1.70642			−0.853209	+	0.521569i	$0.825347\pi$
$684$	−3.08835	−	32.8531i	−0.118086	−	1.25617i
$685$	−5.43845			−0.207792
$686$		0			0
$687$	6.34136	−	6.96543i	0.241938	−	0.265748i
$688$			2.41131i			0.0919303i
$689$	16.4265	−	3.60109i	0.625802	−	0.137190i
$690$	−4.61219	−	4.19895i	−0.175583	−	0.159851i
$691$			37.5464i			1.42833i	0.699976	+	0.714166i	$0.253194\pi$
$691$			37.5464i			1.42833i	−0.699976	+	0.714166i	$0.746806\pi$
$692$	−10.0138			−0.380668
$693$		0			0
$694$			2.38447i			0.0905133i
$695$		−	38.4764i		−	1.45949i
$696$	17.6339	−	19.3693i	0.668411	−	0.734192i
$697$		−	27.8617i		−	1.05534i
$698$		−	6.26075i		−	0.236973i
$699$	12.8255	+	11.6763i	0.485103	+	0.441640i
$700$		0			0
$701$	−15.6371			−0.590605			−0.295303	−	0.955404i	$-0.595420\pi$
$701$	−15.6371			−0.590605			−0.295303	+	0.955404i	$0.595420\pi$
$702$	5.16013	−	11.2813i	0.194756	−	0.425786i
$703$		−	38.3075i		−	1.44479i
$704$	−1.59666	+	1.61463i	−0.0601762	+	0.0608535i
$705$		0			0
$706$			3.27844i			0.123386i
$707$		0			0
$708$	−2.61914	−	2.38447i	−0.0984332	−	0.0896139i
$709$			5.43845i			0.204245i	0.994772	+	0.102123i	$0.0325634\pi$
$709$			5.43845i			0.204245i	−0.994772	+	0.102123i	$0.967437\pi$
$710$			9.22437i			0.346185i
$711$	−37.4653	+	3.52191i	−1.40506	+	0.132082i
$712$			33.6750i			1.26202i
$713$	22.5851			0.845818
$714$		0			0
$715$	23.5683	+	14.9075i	0.881403	+	0.557510i
$716$			29.5812i			1.10550i
$717$	7.72087	−	8.48071i	0.288341	−	0.316718i
$718$	6.98485			0.260672
$719$		−	16.3243i		−	0.608795i	−0.952545	−	0.304397i	$-0.901545\pi$
$719$		−	16.3243i		−	0.608795i	0.952545	−	0.304397i	$-0.0984551\pi$
$720$	1.02248	+	10.8769i	0.0381056	+	0.405358i
$721$		0			0
$722$		−	20.2722i		−	0.754452i
$723$	12.1099	+	11.0249i	0.450373	+	0.410021i
$724$	23.1231			0.859363
$725$	−2.81164			−0.104422
$726$	9.42324	+	8.38802i	0.349729	+	0.311309i
$727$	8.80776			0.326662			0.163331	−	0.986571i	$-0.447776\pi$
$727$	8.80776			0.326662			0.163331	+	0.986571i	$0.447776\pi$
$728$		0			0
$729$	−7.49242	−	25.9396i	−0.277497	−	0.960726i
$730$		−	13.2614i		−	0.490825i
$731$			9.90237i			0.366252i
$732$	12.8255	−	14.0877i	0.474043	−	0.520695i
$733$	−32.8078			−1.21179			−0.605893	−	0.795546i	$-0.707184\pi$
$733$	−32.8078			−1.21179			−0.605893	+	0.795546i	$0.707184\pi$
$734$		−	7.31943i		−	0.270165i
$735$	20.9078	+	19.0346i	0.771197	+	0.702101i
$736$	13.4106			0.494322
$737$	22.8393	+	22.5851i	0.841296	+	0.831932i
$738$	−0.807764	−	8.59280i	−0.0297342	−	0.316305i
$739$	10.9993			0.404616			0.202308	−	0.979322i	$-0.435156\pi$
$739$	10.9993			0.404616			0.202308	+	0.979322i	$0.435156\pi$
$740$			19.8047i			0.728037i
$741$	−21.9610	+	38.1146i	−0.806758	+	1.40017i
$742$		0			0
$743$			7.15640i			0.262543i	0.991346	+	0.131271i	$0.0419059\pi$
$743$			7.15640i			0.262543i	−0.991346	+	0.131271i	$0.958094\pi$
$744$	29.2520	+	26.6311i	1.07243	+	0.976345i
$745$			6.17669i			0.226297i
$746$	2.04496			0.0748713
$747$	−29.2859	+	2.75302i	−1.07152	+	0.100728i
$748$	23.3527	−	23.6155i	0.853859	−	0.863469i
$749$		0			0
$750$	8.21327	−	9.02157i	0.299906	−	0.329421i
$751$	−21.3002			−0.777255			−0.388627	−	0.921395i	$-0.627051\pi$
$751$	−21.3002			−0.777255			−0.388627	+	0.921395i	$0.627051\pi$
$752$		0			0
$753$	−19.7041	+	21.6432i	−0.718056	+	0.788723i
$754$	−14.9548	+	3.27844i	−0.544621	+	0.119394i
$755$	−42.0775			−1.53136
$756$		0			0
$757$	−24.1080			−0.876218			−0.438109	−	0.898922i	$-0.644352\pi$
$757$	−24.1080			−0.876218			−0.438109	+	0.898922i	$0.644352\pi$
$758$	13.6149			0.494516
$759$	−0.702470	−	13.3782i	−0.0254980	−	0.485597i
$760$			38.7386i			1.40520i
$761$		−	30.4133i		−	1.10248i	−0.834347	−	0.551240i	$-0.814155\pi$
$761$		−	30.4133i		−	1.10248i	0.834347	−	0.551240i	$-0.185845\pi$
$762$	−2.04496	−	1.86174i	−0.0740811	−	0.0674437i
$763$		0			0
$764$			3.64162i			0.131749i
$765$	4.19895	+	44.6675i	0.151813	+	1.61496i
$766$			5.68975i			0.205579i
$767$	1.01110	+	4.61219i	0.0365087	+	0.166536i
$768$	11.1231	+	10.1265i	0.401371	+	0.365409i
$769$	28.8524			1.04044			0.520221	−	0.854032i	$-0.325849\pi$
$769$	28.8524			1.04044			0.520221	+	0.854032i	$0.325849\pi$
$770$		0			0
$771$	−35.6847	+	39.1965i	−1.28515	+	1.41163i
$772$	−8.58800			−0.309089
$773$	22.8722			0.822655			0.411327	−	0.911488i	$-0.365065\pi$
$773$	22.8722			0.822655			0.411327	+	0.911488i	$0.365065\pi$
$774$	0.287088	+	3.05398i	0.0103192	+	0.109773i
$775$		−	4.24621i		−	0.152528i
$776$	32.8531			1.17936
$777$		0			0
$778$	7.04383			0.252534
$779$			30.6037i			1.09649i
$780$	11.3537	−	19.7050i	0.406528	−	0.705552i
$781$	−13.9309	+	14.0877i	−0.498486	+	0.504096i
$782$	9.90237			0.354108
$783$	−20.0276	+	26.6311i	−0.715729	+	0.951719i
$784$	−10.9309			−0.390388
$785$	−8.01862			−0.286197
$786$	−9.90237	+	10.8769i	−0.353206	+	0.387966i
$787$	−40.9089			−1.45824			−0.729122	−	0.684383i	$-0.760071\pi$
$787$	−40.9089			−1.45824			−0.729122	+	0.684383i	$0.760071\pi$
$788$			38.8940i			1.38554i
$789$	−32.8531	−	29.9096i	−1.16960	−	1.06481i
$790$	19.3693			0.689129
$791$		0			0
$792$	14.8650	−	18.1556i	0.528205	−	0.645131i
$793$	−24.8078	+	5.43845i	−0.880950	+	0.193125i
$794$	5.62329			0.199563
$795$	−12.6827	+	13.9309i	−0.449810	+	0.494077i
$796$	−24.0000			−0.850657
$797$		−	5.39949i		−	0.191260i	−0.995417	−	0.0956298i	$-0.969513\pi$
$797$		−	5.39949i		−	0.191260i	0.995417	−	0.0956298i	$-0.0304865\pi$
$798$		0			0
$799$		0			0
$800$		−	2.52132i		−	0.0891423i
$801$	−4.00931	−	42.6501i	−0.141662	−	1.50697i
$802$		−	10.3223i		−	0.364492i
$803$	20.0276	−	20.2530i	0.706760	−	0.714714i
$804$	17.6339	−	19.3693i	0.621900	−	0.683103i
$805$		0			0
$806$	−4.95118	−	22.5851i	−0.174398	−	0.795526i
$807$	−22.4233	+	24.6300i	−0.789337	+	0.867019i
$808$		−	23.6155i		−	0.830791i
$809$	22.8393			0.802986			0.401493	−	0.915862i	$-0.368491\pi$
$809$	22.8393			0.802986			0.401493	+	0.915862i	$0.368491\pi$
$810$	2.58999	+	13.6541i	0.0910028	+	0.479756i
$811$	27.3082			0.958920			0.479460	−	0.877564i	$-0.340833\pi$
$811$	27.3082			0.958920			0.479460	+	0.877564i	$0.340833\pi$
$812$		0			0
$813$	18.0431	+	16.4265i	0.632801	+	0.576104i
$814$	8.39791	−	8.49242i	0.294346	−	0.297659i
$815$		−	9.90237i		−	0.346865i
$816$	−12.8255	−	11.6763i	−0.448981	−	0.408754i
$817$		−	10.8769i		−	0.380534i
$818$		−	10.9248i		−	0.381978i
$819$		0			0
$820$		−	15.8219i		−	0.552526i
$821$		−	50.0233i		−	1.74583i	−0.487876	−	0.872913i	$-0.662228\pi$
$821$		−	50.0233i		−	1.74583i	0.487876	−	0.872913i	$-0.337772\pi$
$822$	1.80054	−	1.97774i	0.0628012	−	0.0689816i
$823$	51.0540			1.77963			0.889815	−	0.456322i	$-0.150833\pi$
$823$	51.0540			1.77963			0.889815	+	0.456322i	$0.150833\pi$
$824$		−	12.0818i		−	0.420889i
$825$	−2.51522	+	0.132071i	−0.0875688	+	0.00459812i
$826$		0			0
$827$			22.3044i			0.775600i	0.921743	+	0.387800i	$0.126765\pi$
$827$			22.3044i			0.775600i	−0.921743	+	0.387800i	$0.873235\pi$
$828$	−10.8769	+	1.02248i	−0.377998	+	0.0355336i
$829$	41.0540			1.42586			0.712932	−	0.701233i	$-0.247367\pi$
$829$	41.0540			1.42586			0.712932	+	0.701233i	$0.247367\pi$
$830$	15.1406			0.525539
$831$	3.60109	−	3.95548i	0.124920	−	0.137214i
$832$	−0.528616	−	2.41131i	−0.0183265	−	0.0835971i
$833$	−44.8891			−1.55532
$834$	13.9923	+	12.7386i	0.484513	+	0.441103i
$835$		−	40.9089i		−	1.41571i
$836$	−25.6509	+	25.9396i	−0.887156	+	0.897140i
$837$	−40.2190	−	30.2462i	−1.39017	−	1.04546i
$838$	−9.94208			−0.343443
$839$	−41.8156			−1.44364			−0.721818	−	0.692083i	$-0.756693\pi$
$839$	−41.8156			−1.44364			−0.721818	+	0.692083i	$0.756693\pi$
$840$		0			0
$841$	12.1231			0.418038
$842$	12.8255			0.441995
$843$	−10.1322	+	11.1293i	−0.348971	+	0.383314i
$844$			20.9414i			0.720832i
$845$	−27.5363	+	12.6827i	−0.947277	+	0.436299i
$846$		0			0
$847$		0			0
$848$		−	7.28323i		−	0.250107i
$849$	1.80054	−	1.97774i	0.0617945	−	0.0678759i
$850$		−	1.86174i		−	0.0638571i
$851$	−12.6827			−0.434758
$852$	11.9473	+	10.8769i	0.409309	+	0.372636i
$853$	41.5859			1.42388			0.711938	−	0.702243i	$-0.247818\pi$
$853$	41.5859			1.42388			0.711938	+	0.702243i	$0.247818\pi$
$854$		0			0
$855$	−4.61219	−	49.0633i	−0.157733	−	1.67793i
$856$			8.49242i			0.290265i
$857$	−42.8669			−1.46431			−0.732153	−	0.681140i	$-0.761484\pi$
$857$	−42.8669			−1.46431			−0.732153	+	0.681140i	$0.761484\pi$
$858$	−13.2242	+	3.63528i	−0.451466	+	0.124106i
$859$	18.5616			0.633312			0.316656	−	0.948540i	$-0.397440\pi$
$859$	18.5616			0.633312			0.316656	+	0.948540i	$0.397440\pi$
$860$			5.62329i			0.191752i
$861$		0			0
$862$	9.50758			0.323829
$863$	23.8947			0.813384			0.406692	−	0.913565i	$-0.366682\pi$
$863$	23.8947			0.813384			0.406692	+	0.913565i	$0.366682\pi$
$864$	−23.8813	−	17.9597i	−0.812459	−	0.611000i
$865$	−14.9548			−0.508478
$866$		−	1.85917i		−	0.0631772i
$867$	−30.8963	−	28.1281i	−1.04929	−	0.955281i
$868$		0			0
$869$	29.5812	+	29.2520i	1.00347	+	0.992306i
$870$	11.5464	−	12.6827i	0.391460	−	0.429984i
$871$	−34.1085	+	7.47740i	−1.15572	+	0.253362i
$872$		−	36.8645i		−	1.24839i
$873$	−41.6092	+	3.91146i	−1.40826	+	0.132383i
$874$	−10.8769			−0.367916
$875$		0			0
$876$	−17.1760	−	15.6371i	−0.580323	−	0.528329i
$877$	−18.7202			−0.632136			−0.316068	−	0.948737i	$-0.602363\pi$
$877$	−18.7202			−0.632136			−0.316068	+	0.948737i	$0.602363\pi$
$878$	−14.4406			−0.487346
$879$	3.71201	−	4.07732i	0.125203	−	0.137525i
$880$	8.49242	−	8.58800i	0.286280	−	0.289502i
$881$		−	45.9056i		−	1.54660i	−0.634042	−	0.773299i	$-0.718605\pi$
$881$		−	45.9056i		−	1.54660i	0.634042	−	0.773299i	$-0.281395\pi$
$882$	−13.8442	+	1.30142i	−0.466158	+	0.0438211i
$883$	−3.36932			−0.113387			−0.0566933	−	0.998392i	$-0.518056\pi$
$883$	−3.36932			−0.113387			−0.0566933	+	0.998392i	$0.518056\pi$
$884$	7.73154	+	35.2678i	0.260040	+	1.18618i
$885$	−3.91146	−	3.56101i	−0.131482	−	0.119702i
$886$	−15.6318			−0.525162
$887$	−16.4265			−0.551549			−0.275775	−	0.961222i	$-0.588934\pi$
$887$	−16.4265			−0.551549			−0.275775	+	0.961222i	$0.588934\pi$
$888$	−16.4265	−	14.9548i	−0.551239	−	0.501850i
$889$		0			0
$890$			22.0498i			0.739112i
$891$	−16.6653	+	24.7643i	−0.558307	+	0.829634i
$892$		−	15.1231i		−	0.506359i
$893$		0			0
$894$	−2.24621	−	2.04496i	−0.0751245	−	0.0683937i
$895$			44.1771i			1.47668i
$896$		0			0
$897$	12.6188	+	7.27078i	0.421331	+	0.242764i
$898$			23.5428i			0.785633i
$899$			62.1051i			2.07132i
$900$	0.192236	+	2.04496i	0.00640786	+	0.0681653i
$901$		−	29.9096i		−	0.996433i
$902$	−6.70906	+	6.78456i	−0.223387	+	0.225901i
$903$		0			0
$904$	−7.91096			−0.263115
$905$	34.5324			1.14790
$906$	13.9309	−	15.3019i	0.462822	−	0.508370i
$907$	−9.75379			−0.323869			−0.161935	−	0.986801i	$-0.551773\pi$
$907$	−9.75379			−0.323869			−0.161935	+	0.986801i	$0.551773\pi$
$908$		−	14.1498i		−	0.469577i
$909$	2.81164	+	29.9096i	0.0932563	+	0.992038i
$910$		0			0
$911$			29.5812i			0.980070i	0.871703	+	0.490035i	$0.163016\pi$
$911$			29.5812i			0.980070i	−0.871703	+	0.490035i	$0.836984\pi$
$912$	14.0877	+	12.8255i	0.466489	+	0.424693i
$913$	23.1231	+	22.8658i	0.765263	+	0.756746i
$914$			22.2980i			0.737552i
$915$	19.1537	−	21.0387i	0.633203	−	0.695519i
$916$			8.49242i			0.280598i
$917$		0			0
$918$	−17.6339	−	13.2614i	−0.582006	−	0.437690i
$919$			10.8092i			0.356563i	0.983980	+	0.178282i	$0.0570538\pi$
$919$			10.8092i			0.356563i	−0.983980	+	0.178282i	$0.942946\pi$
$920$	12.8255			0.422843
$921$	21.9986	+	20.0276i	0.724879	+	0.659933i
$922$	−9.12311			−0.300453
$923$	−4.61219	−	21.0387i	−0.151812	−	0.692498i
$924$		0			0
$925$			2.38447i			0.0784010i
$926$	12.0360			0.395528
$927$	1.43845	+	15.3019i	0.0472448	+	0.502579i
$928$			36.8769i			1.21054i
$929$	−38.9094			−1.27658			−0.638288	−	0.769797i	$-0.720357\pi$
$929$	−38.9094			−1.27658			−0.638288	+	0.769797i	$0.720357\pi$
$930$	19.1537	+	17.4376i	0.628076	+	0.571803i
$931$	49.3068			1.61597
$932$	−15.6371			−0.512210
$933$	12.7386	−	13.9923i	0.417044	−	0.458087i
$934$	12.5435			0.410435
$935$	34.8753	−	35.2678i	1.14054	−	1.15338i
$936$	7.77050	+	24.2965i	0.253987	+	0.794157i
$937$		−	42.2630i		−	1.38067i	−0.723489	−	0.690336i	$-0.757463\pi$
$937$		−	42.2630i		−	1.38067i	0.723489	−	0.690336i	$-0.242537\pi$
$938$		0			0
$939$	−18.3348	−	16.6920i	−0.598332	−	0.544724i
$940$		0			0
$941$		−	18.6576i		−	0.608219i	−0.952637	−	0.304109i	$-0.901641\pi$
$941$		−	18.6576i		−	0.608219i	0.952637	−	0.304109i	$-0.0983588\pi$
$942$	2.65478	−	2.91605i	0.0864974	−	0.0950099i
$943$	10.1322			0.329949
$944$	2.04496			0.0665578
$945$		0			0
$946$	2.38447	−	2.41131i	0.0775259	−	0.0783984i
$947$	−31.9133			−1.03704			−0.518521	−	0.855065i	$-0.673517\pi$
$947$	−31.9133			−1.03704			−0.518521	+	0.855065i	$0.673517\pi$
$948$	22.8393	−	25.0870i	0.741785	−	0.814787i
$949$	6.63068	+	30.2462i	0.215241	+	0.981834i
$950$			2.04496i			0.0663473i
$951$	−30.2360	−	27.5270i	−0.980470	−	0.892624i
$952$		0			0
$953$	22.8393			0.739837			0.369918	−	0.929064i	$-0.379386\pi$
$953$	22.8393			0.739837			0.369918	+	0.929064i	$0.379386\pi$
$954$	−0.867135	−	9.22437i	−0.0280745	−	0.298650i
$955$			5.43845i			0.175984i
$956$			10.3399i			0.334415i
$957$	36.7876	−	1.93167i	1.18918	−	0.0624420i
$958$	−11.6155			−0.375281
$959$		0			0
$960$	2.04496	+	1.86174i	0.0660008	+	0.0600874i
$961$	−62.7926			−2.02557
$962$	2.78035	+	12.6827i	0.0896421	+	0.408907i
$963$	−1.01110	−	10.7558i	−0.0325822	−	0.346602i
$964$	−14.7647			−0.475539
$965$	−12.8255			−0.412866
$966$		0			0
$967$	20.2644			0.651658			0.325829	−	0.945429i	$-0.394357\pi$
$967$	20.2644			0.651658			0.325829	+	0.945429i	$0.394357\pi$
$968$	−25.9396	+	0.290319i	−0.833731	+	0.00933122i
$969$	57.8529	+	52.6695i	1.85850	+	1.69199i
$970$	21.5117			0.690698
$971$			34.9807i			1.12258i	0.827618	+	0.561292i	$0.189696\pi$
$971$			34.9807i			1.12258i	−0.827618	+	0.561292i	$0.810304\pi$
$972$	20.7386	+	12.7457i	0.665192	+	0.408817i
$973$		0			0
$974$	−13.6149			−0.436250
$975$	1.36698	−	2.37246i	0.0437783	−	0.0759796i
$976$			10.9993i			0.352079i
$977$	1.75787			0.0562393			0.0281196	−	0.999605i	$-0.491048\pi$
$977$	1.75787			0.0562393			0.0281196	+	0.999605i	$0.491048\pi$
$978$	3.60109	+	3.27844i	0.115150	+	0.104833i
$979$	−33.3002	+	33.6750i	−1.06428	+	1.07626i
$980$	−25.4913			−0.814290
$981$	4.38905	+	46.6897i	0.140132	+	1.49069i
$982$			8.49242i			0.271004i
$983$	17.9210			0.571591			0.285795	−	0.958291i	$-0.407742\pi$
$983$	17.9210			0.571591			0.285795	+	0.958291i	$0.407742\pi$
$984$	13.1231	+	11.9473i	0.418349	+	0.380867i
$985$			58.0849i			1.85074i
$986$			27.2298i			0.867174i
$987$		0			0
$988$	−8.49242	−	38.7386i	−0.270180	−	1.23244i
$989$	−3.60109			−0.114508
$990$	9.73336	−	11.8880i	0.309346	−	0.377825i
$991$	30.7386			0.976445			0.488222	−	0.872719i	$-0.337645\pi$
$991$	30.7386			0.976445			0.488222	+	0.872719i	$0.337645\pi$
$992$	−55.6924			−1.76823
$993$	−33.8776	+	37.2116i	−1.07507	+	1.18088i
$994$		0			0
$995$	−35.8420			−1.13627
$996$	17.8530	−	19.6100i	0.565695	−	0.621367i
$997$			26.8212i			0.849437i	0.905325	+	0.424719i	$0.139627\pi$
$997$			26.8212i			0.849437i	−0.905325	+	0.424719i	$0.860373\pi$
$998$	−2.81164			−0.0890010
$999$	22.5851	+	16.9848i	0.714561	+	0.537377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.e.c.428.6	yes	16
3.2	odd	2	inner	429.2.e.c.428.11	yes	16
11.10	odd	2	inner	429.2.e.c.428.10	yes	16
13.12	even	2	inner	429.2.e.c.428.9	yes	16
33.32	even	2	inner	429.2.e.c.428.7	yes	16
39.38	odd	2	inner	429.2.e.c.428.8	yes	16
143.142	odd	2	inner	429.2.e.c.428.5	✓	16
429.428	even	2	inner	429.2.e.c.428.12	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.e.c.428.5	✓	16	143.142	odd	2	inner
429.2.e.c.428.6	yes	16	1.1	even	1	trivial
429.2.e.c.428.7	yes	16	33.32	even	2	inner
429.2.e.c.428.8	yes	16	39.38	odd	2	inner
429.2.e.c.428.9	yes	16	13.12	even	2	inner
429.2.e.c.428.10	yes	16	11.10	odd	2	inner
429.2.e.c.428.11	yes	16	3.2	odd	2	inner
429.2.e.c.428.12	yes	16	429.428	even	2	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.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.662153i q^{2} +(-1.28078 - 1.16602i) q^{3} +1.56155 q^{4} +2.33205 q^{5} +(-0.772087 + 0.848071i) q^{6} -2.35829i q^{8} +(0.280776 + 2.98683i) q^{9} +O(q^{10})\)	\(q-0.662153i q^{2} +(-1.28078 - 1.16602i) q^{3} +1.56155 q^{4} +2.33205 q^{5} +(-0.772087 + 0.848071i) q^{6} -2.35829i q^{8} +(0.280776 + 2.98683i) q^{9} -1.54417i q^{10} +(2.33205 - 2.35829i) q^{11} +(-2.00000 - 1.82081i) q^{12} +(0.772087 + 3.52191i) q^{13} +(-2.98683 - 2.71922i) q^{15} +1.56155 q^{16} +6.41273 q^{17} +(1.97774 - 0.185917i) q^{18} -7.04383 q^{19} +3.64162 q^{20} +(-1.56155 - 1.54417i) q^{22} +2.33205i q^{23} +(-2.74983 + 3.02045i) q^{24} +0.438447 q^{25} +(2.33205 - 0.511240i) q^{26} +(3.12311 - 4.15286i) q^{27} -6.41273 q^{29} +(-1.80054 + 1.97774i) q^{30} -9.68466i q^{31} -5.75058i q^{32} +(-5.73666 + 0.301224i) q^{33} -4.24621i q^{34} +(0.438447 + 4.66410i) q^{36} +5.43845i q^{37} +4.66410i q^{38} +(3.11777 - 5.41106i) q^{39} -5.49966i q^{40} -4.34475i q^{41} +1.54417i q^{43} +(3.64162 - 3.68260i) q^{44} +(0.654784 + 6.96543i) q^{45} +1.54417 q^{46} +(-2.00000 - 1.82081i) q^{48} -7.00000 q^{49} -0.290319i q^{50} +(-8.21327 - 7.47740i) q^{51} +(1.20565 + 5.49966i) q^{52} -4.66410i q^{53} +(-2.74983 - 2.06798i) q^{54} +(5.43845 - 5.49966i) q^{55} +(9.02157 + 8.21327i) q^{57} +4.24621i q^{58} +1.30957 q^{59} +(-4.66410 - 4.24621i) q^{60} +7.04383i q^{61} -6.41273 q^{62} -0.684658 q^{64} +(1.80054 + 8.21327i) q^{65} +(0.199457 + 3.79855i) q^{66} +9.68466i q^{67} +10.0138 q^{68} +(2.71922 - 2.98683i) q^{69} -5.97366 q^{71} +(7.04383 - 0.662153i) q^{72} +8.58800 q^{73} +3.60109 q^{74} +(-0.561553 - 0.511240i) q^{75} -10.9993 q^{76} +(-3.58295 - 2.06444i) q^{78} +12.5435i q^{79} +3.64162 q^{80} +(-8.84233 + 1.67726i) q^{81} -2.87689 q^{82} +9.80501i q^{83} +14.9548 q^{85} +1.02248 q^{86} +(8.21327 + 7.47740i) q^{87} +(-5.56155 - 5.49966i) q^{88} -14.2794 q^{89} +(4.61219 - 0.433567i) q^{90} +3.64162i q^{92} +(-11.2925 + 12.4039i) q^{93} -16.4265 q^{95} +(-6.70531 + 7.36520i) q^{96} +13.9309i q^{97} +4.63507i q^{98} +(7.69861 + 6.30328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} - 8 q^{4} - 12 q^{9}+O(q^{10}) \) 16 * q - 4 * q^3 - 8 * q^4 - 12 * q^9	\( 16 q - 4 q^{3} - 8 q^{4} - 12 q^{9} - 32 q^{12} - 8 q^{16} + 8 q^{22} + 40 q^{25} - 16 q^{27} + 40 q^{36} - 32 q^{48} - 112 q^{49} + 120 q^{55} + 88 q^{64} + 32 q^{66} + 60 q^{69} + 24 q^{75} - 92 q^{78} - 92 q^{81} - 112 q^{82} - 56 q^{88}+O(q^{100}) \) 16 * q - 4 * q^3 - 8 * q^4 - 12 * q^9 - 32 * q^12 - 8 * q^16 + 8 * q^22 + 40 * q^25 - 16 * q^27 + 40 * q^36 - 32 * q^48 - 112 * q^49 + 120 * q^55 + 88 * q^64 + 32 * q^66 + 60 * q^69 + 24 * q^75 - 92 * q^78 - 92 * q^81 - 112 * q^82 - 56 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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