LMFDB - Embedded newform 429.2.m.b.109.7

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			109.7
Character	$\chi$	$=$	429.109
Dual form			429.2.m.b.307.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.290762 - 0.290762i) q^{2} +1.00000 q^{3} -1.83092i q^{4} +(1.55280 - 1.55280i) q^{5} +(-0.290762 - 0.290762i) q^{6} +(0.786011 - 0.786011i) q^{7} +(-1.11388 + 1.11388i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.290762 - 0.290762i) q^{2} +1.00000 q^{3} -1.83092i q^{4} +(1.55280 - 1.55280i) q^{5} +(-0.290762 - 0.290762i) q^{6} +(0.786011 - 0.786011i) q^{7} +(-1.11388 + 1.11388i) q^{8} +1.00000 q^{9} -0.902988 q^{10} +(2.98747 - 1.44050i) q^{11} -1.83092i q^{12} +(-2.05053 + 2.96569i) q^{13} -0.457084 q^{14} +(1.55280 - 1.55280i) q^{15} -3.01408 q^{16} -2.52854 q^{17} +(-0.290762 - 0.290762i) q^{18} +(1.03638 + 1.03638i) q^{19} +(-2.84304 - 2.84304i) q^{20} +(0.786011 - 0.786011i) q^{21} +(-1.28748 - 0.449801i) q^{22} -5.04613i q^{23} +(-1.11388 + 1.11388i) q^{24} +0.177649i q^{25} +(1.45853 - 0.266095i) q^{26} +1.00000 q^{27} +(-1.43912 - 1.43912i) q^{28} +0.703508i q^{29} -0.902988 q^{30} +(-2.73971 + 2.73971i) q^{31} +(3.10415 + 3.10415i) q^{32} +(2.98747 - 1.44050i) q^{33} +(0.735203 + 0.735203i) q^{34} -2.44103i q^{35} -1.83092i q^{36} +(1.75183 + 1.75183i) q^{37} -0.602682i q^{38} +(-2.05053 + 2.96569i) q^{39} +3.45927i q^{40} +(-7.42693 - 7.42693i) q^{41} -0.457084 q^{42} +9.78809 q^{43} +(-2.63743 - 5.46980i) q^{44} +(1.55280 - 1.55280i) q^{45} +(-1.46722 + 1.46722i) q^{46} +(2.29881 + 2.29881i) q^{47} -3.01408 q^{48} +5.76437i q^{49} +(0.0516537 - 0.0516537i) q^{50} -2.52854 q^{51} +(5.42993 + 3.75434i) q^{52} +13.3620 q^{53} +(-0.290762 - 0.290762i) q^{54} +(2.40213 - 6.87573i) q^{55} +1.75105i q^{56} +(1.03638 + 1.03638i) q^{57} +(0.204553 - 0.204553i) q^{58} +(-2.75813 - 2.75813i) q^{59} +(-2.84304 - 2.84304i) q^{60} -10.7355i q^{61} +1.59321 q^{62} +(0.786011 - 0.786011i) q^{63} +4.22302i q^{64} +(1.42107 + 7.78917i) q^{65} +(-1.28748 - 0.449801i) q^{66} +(-9.79511 + 9.79511i) q^{67} +4.62954i q^{68} -5.04613i q^{69} +(-0.709759 + 0.709759i) q^{70} +(-2.26225 + 2.26225i) q^{71} +(-1.11388 + 1.11388i) q^{72} +(0.116977 - 0.116977i) q^{73} -1.01873i q^{74} +0.177649i q^{75} +(1.89753 - 1.89753i) q^{76} +(1.21594 - 3.48043i) q^{77} +(1.45853 - 0.266095i) q^{78} +15.3785i q^{79} +(-4.68025 + 4.68025i) q^{80} +1.00000 q^{81} +4.31894i q^{82} +(-4.15034 - 4.15034i) q^{83} +(-1.43912 - 1.43912i) q^{84} +(-3.92631 + 3.92631i) q^{85} +(-2.84601 - 2.84601i) q^{86} +0.703508i q^{87} +(-1.72315 + 4.93224i) q^{88} +(-2.00196 - 2.00196i) q^{89} -0.902988 q^{90} +(0.719330 + 3.94281i) q^{91} -9.23904 q^{92} +(-2.73971 + 2.73971i) q^{93} -1.33681i q^{94} +3.21858 q^{95} +(3.10415 + 3.10415i) q^{96} +(-3.65886 + 3.65886i) q^{97} +(1.67606 - 1.67606i) q^{98} +(2.98747 - 1.44050i) 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 $

$2$	−0.290762	−	0.290762i	−0.205600	−	0.205600i	0.596794	−	0.802394i	$-0.296441\pi$
$2$	−0.290762	−	0.290762i	−0.205600	−	0.205600i	−0.802394	+	0.596794i	$0.796441\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		−	1.83092i		−	0.915458i
$5$	1.55280	−	1.55280i	0.694431	−	0.694431i	−0.268772	−	0.963204i	$-0.586618\pi$
$5$	1.55280	−	1.55280i	0.694431	−	0.694431i	0.963204	+	0.268772i	$0.0866179\pi$
$6$	−0.290762	−	0.290762i	−0.118703	−	0.118703i
$7$	0.786011	−	0.786011i	0.297084	−	0.297084i	−0.542786	−	0.839871i	$-0.682631\pi$
$7$	0.786011	−	0.786011i	0.297084	−	0.297084i	0.839871	+	0.542786i	$0.182631\pi$
$8$	−1.11388	+	1.11388i	−0.393818	+	0.393818i
$9$	1.00000			0.333333
$10$	−0.902988			−0.285550
$11$	2.98747	−	1.44050i	0.900756	−	0.434326i
$11$	2.98747	−	1.44050i	0.900756	−	0.434326i
$12$		−	1.83092i		−	0.528540i
$13$	−2.05053	+	2.96569i	−0.568714	+	0.822535i
$13$	−2.05053	+	2.96569i	−0.568714	+	0.822535i
$14$	−0.457084			−0.122161
$15$	1.55280	−	1.55280i	0.400930	−	0.400930i
$16$	−3.01408			−0.753520
$17$	−2.52854			−0.613261			−0.306631	−	0.951829i	$-0.599202\pi$
$17$	−2.52854			−0.613261			−0.306631	+	0.951829i	$0.599202\pi$
$18$	−0.290762	−	0.290762i	−0.0685332	−	0.0685332i
$19$	1.03638	+	1.03638i	0.237763	+	0.237763i	0.815923	−	0.578160i	$-0.196229\pi$
$19$	1.03638	+	1.03638i	0.237763	+	0.237763i	−0.578160	+	0.815923i	$0.696229\pi$
$20$	−2.84304	−	2.84304i	−0.635722	−	0.635722i
$21$	0.786011	−	0.786011i	0.171522	−	0.171522i
$22$	−1.28748	−	0.449801i	−0.274492	−	0.0958978i
$23$		−	5.04613i		−	1.05219i	−0.850425	−	0.526096i	$-0.823655\pi$
$23$		−	5.04613i		−	1.05219i	0.850425	−	0.526096i	$-0.176345\pi$
$24$	−1.11388	+	1.11388i	−0.227371	+	0.227371i
$25$			0.177649i			0.0355299i
$26$	1.45853	−	0.266095i	0.286040	−	0.0521856i
$27$	1.00000			0.192450
$28$	−1.43912	−	1.43912i	−0.271968	−	0.271968i
$29$			0.703508i			0.130638i	0.997864	+	0.0653191i	$0.0208065\pi$
$29$			0.703508i			0.130638i	−0.997864	+	0.0653191i	$0.979193\pi$
$30$	−0.902988			−0.164862
$31$	−2.73971	+	2.73971i	−0.492067	+	0.492067i	−0.908957	−	0.416890i	$-0.863120\pi$
$31$	−2.73971	+	2.73971i	−0.492067	+	0.492067i	0.416890	+	0.908957i	$0.363120\pi$
$32$	3.10415	+	3.10415i	0.548741	+	0.548741i
$33$	2.98747	−	1.44050i	0.520052	−	0.250758i
$34$	0.735203	+	0.735203i	0.126086	+	0.126086i
$35$		−	2.44103i		−	0.412609i
$36$		−	1.83092i		−	0.305153i
$37$	1.75183	+	1.75183i	0.288000	+	0.288000i	0.836289	−	0.548289i	$-0.184721\pi$
$37$	1.75183	+	1.75183i	0.288000	+	0.288000i	−0.548289	+	0.836289i	$0.684721\pi$
$38$		−	0.602682i		−	0.0977679i
$39$	−2.05053	+	2.96569i	−0.328347	+	0.474891i
$40$			3.45927i			0.546959i
$41$	−7.42693	−	7.42693i	−1.15989	−	1.15989i	−0.984498	−	0.175393i	$-0.943880\pi$
$41$	−7.42693	−	7.42693i	−1.15989	−	1.15989i	−0.175393	−	0.984498i	$-0.556120\pi$
$42$	−0.457084			−0.0705296
$43$	9.78809			1.49267			0.746335	−	0.665570i	$-0.231812\pi$
$43$	9.78809			1.49267			0.746335	+	0.665570i	$0.231812\pi$
$44$	−2.63743	−	5.46980i	−0.397607	−	0.824604i
$45$	1.55280	−	1.55280i	0.231477	−	0.231477i
$46$	−1.46722	+	1.46722i	−0.216330	+	0.216330i
$47$	2.29881	+	2.29881i	0.335315	+	0.335315i	0.854601	−	0.519286i	$-0.173802\pi$
$47$	2.29881	+	2.29881i	0.335315	+	0.335315i	−0.519286	+	0.854601i	$0.673802\pi$
$48$	−3.01408			−0.435045
$49$			5.76437i			0.823482i
$50$	0.0516537	−	0.0516537i	0.00730493	−	0.00730493i
$51$	−2.52854			−0.354066
$52$	5.42993	+	3.75434i	0.752996	+	0.520634i
$53$	13.3620			1.83541			0.917705	−	0.397263i	$-0.130040\pi$
$53$	13.3620			1.83541			0.917705	+	0.397263i	$0.130040\pi$
$54$	−0.290762	−	0.290762i	−0.0395677	−	0.0395677i
$55$	2.40213	−	6.87573i	0.323903	−	0.927123i
$56$			1.75105i			0.233994i
$57$	1.03638	+	1.03638i	0.137272	+	0.137272i
$58$	0.204553	−	0.204553i	0.0268592	−	0.0268592i
$59$	−2.75813	−	2.75813i	−0.359078	−	0.359078i	0.504395	−	0.863473i	$-0.331716\pi$
$59$	−2.75813	−	2.75813i	−0.359078	−	0.359078i	−0.863473	+	0.504395i	$0.831716\pi$
$60$	−2.84304	−	2.84304i	−0.367035	−	0.367035i
$61$		−	10.7355i		−	1.37453i	−0.726405	−	0.687267i	$-0.758810\pi$
$61$		−	10.7355i		−	1.37453i	0.726405	−	0.687267i	$-0.241190\pi$
$62$	1.59321			0.202338
$63$	0.786011	−	0.786011i	0.0990281	−	0.0990281i
$64$			4.22302i			0.527878i
$65$	1.42107	+	7.78917i	0.176261	+	0.966127i
$66$	−1.28748	−	0.449801i	−0.158478	−	0.0553666i
$67$	−9.79511	+	9.79511i	−1.19666	+	1.19666i	−0.221503	+	0.975160i	$0.571096\pi$
$67$	−9.79511	+	9.79511i	−1.19666	+	1.19666i	−0.975160	+	0.221503i	$0.928904\pi$
$68$			4.62954i			0.561414i
$69$		−	5.04613i		−	0.607483i
$70$	−0.709759	+	0.709759i	−0.0848324	+	0.0848324i
$71$	−2.26225	+	2.26225i	−0.268479	+	0.268479i	−0.828487	−	0.560008i	$-0.810798\pi$
$71$	−2.26225	+	2.26225i	−0.268479	+	0.268479i	0.560008	+	0.828487i	$0.310798\pi$
$72$	−1.11388	+	1.11388i	−0.131273	+	0.131273i
$73$	0.116977	−	0.116977i	0.0136911	−	0.0136911i	−0.700228	−	0.713919i	$-0.746918\pi$
$73$	0.116977	−	0.116977i	0.0136911	−	0.0136911i	0.713919	+	0.700228i	$0.246918\pi$
$74$		−	1.01873i		−	0.118425i
$75$			0.177649i			0.0205132i
$76$	1.89753	−	1.89753i	0.217662	−	0.217662i
$77$	1.21594	−	3.48043i	0.138569	−	0.396632i
$78$	1.45853	−	0.266095i	0.165146	−	0.0301294i
$79$			15.3785i			1.73021i	0.501589	+	0.865106i	$0.332749\pi$
$79$			15.3785i			1.73021i	−0.501589	+	0.865106i	$0.667251\pi$
$80$	−4.68025	+	4.68025i	−0.523268	+	0.523268i
$81$	1.00000			0.111111
$82$			4.31894i			0.476947i
$83$	−4.15034	−	4.15034i	−0.455559	−	0.455559i	0.441635	−	0.897195i	$-0.354399\pi$
$83$	−4.15034	−	4.15034i	−0.455559	−	0.455559i	−0.897195	+	0.441635i	$0.854399\pi$
$84$	−1.43912	−	1.43912i	−0.157021	−	0.157021i
$85$	−3.92631	+	3.92631i	−0.425868	+	0.425868i
$86$	−2.84601	−	2.84601i	−0.306893	−	0.306893i
$87$			0.703508i			0.0754239i
$88$	−1.72315	+	4.93224i	−0.183688	+	0.525779i
$89$	−2.00196	−	2.00196i	−0.212207	−	0.212207i	0.592997	−	0.805204i	$-0.297944\pi$
$89$	−2.00196	−	2.00196i	−0.212207	−	0.212207i	−0.805204	+	0.592997i	$0.797944\pi$
$90$	−0.902988			−0.0951833
$91$	0.719330	+	3.94281i	0.0754063	+	0.413318i
$92$	−9.23904			−0.963236
$93$	−2.73971	+	2.73971i	−0.284095	+	0.284095i
$94$		−	1.33681i		−	0.137881i
$95$	3.21858			0.330220
$96$	3.10415	+	3.10415i	0.316816	+	0.316816i
$97$	−3.65886	+	3.65886i	−0.371501	+	0.371501i	−0.868024	−	0.496523i	$-0.834610\pi$
$97$	−3.65886	+	3.65886i	−0.371501	+	0.371501i	0.496523	+	0.868024i	$0.334610\pi$
$98$	1.67606	−	1.67606i	0.169308	−	0.169308i
$99$	2.98747	−	1.44050i	0.300252	−	0.144775i
$100$	0.325261			0.0325261
$101$	13.1989			1.31334			0.656671	−	0.754177i	$-0.271964\pi$
$101$	13.1989			1.31334			0.656671	+	0.754177i	$0.271964\pi$
$102$	0.735203	+	0.735203i	0.0727960	+	0.0727960i
$103$			11.3192i			1.11531i	0.830071	+	0.557657i	$0.188300\pi$
$103$			11.3192i			1.11531i	−0.830071	+	0.557657i	$0.811700\pi$
$104$	−1.01939	−	5.58749i	−0.0999592	−	0.547898i
$105$		−	2.44103i		−	0.238220i
$106$	−3.88516	−	3.88516i	−0.377360	−	0.377360i
$107$			8.44953i			0.816847i	0.912793	+	0.408424i	$0.133921\pi$
$107$			8.44953i			0.816847i	−0.912793	+	0.408424i	$0.866079\pi$
$108$		−	1.83092i		−	0.176180i
$109$	4.26483	+	4.26483i	0.408497	+	0.408497i	0.881214	−	0.472717i	$-0.156727\pi$
$109$	4.26483	+	4.26483i	0.408497	+	0.408497i	−0.472717	+	0.881214i	$0.656727\pi$
$110$	−2.69765	+	1.30075i	−0.257211	+	0.124022i
$111$	1.75183	+	1.75183i	0.166277	+	0.166277i
$112$	−2.36910	+	2.36910i	−0.223859	+	0.223859i
$113$	1.09151			0.102681			0.0513404	−	0.998681i	$-0.483651\pi$
$113$	1.09151			0.102681			0.0513404	+	0.998681i	$0.483651\pi$
$114$		−	0.602682i		−	0.0564463i
$115$	−7.83561	−	7.83561i	−0.730675	−	0.730675i
$116$	1.28806			0.119594
$117$	−2.05053	+	2.96569i	−0.189571	+	0.274178i
$118$			1.60392i			0.147653i
$119$	−1.98746	+	1.98746i	−0.182190	+	0.182190i
$120$			3.45927i			0.315787i
$121$	6.84994	−	8.60688i	0.622722	−	0.782443i
$122$	−3.12146	+	3.12146i	−0.282604	+	0.282604i
$123$	−7.42693	−	7.42693i	−0.669664	−	0.669664i
$124$	5.01618	+	5.01618i	0.450466	+	0.450466i
$125$	8.03983	+	8.03983i	0.719105	+	0.719105i
$126$	−0.457084			−0.0407203
$127$	−2.00874			−0.178247			−0.0891234	−	0.996021i	$-0.528407\pi$
$127$	−2.00874			−0.178247			−0.0891234	+	0.996021i	$0.528407\pi$
$128$	7.43619	−	7.43619i	0.657273	−	0.657273i
$129$	9.78809			0.861794
$130$	1.85160	−	2.67799i	0.162396	−	0.234875i
$131$			21.0354i			1.83787i	0.394411	+	0.918934i	$0.370949\pi$
$131$			21.0354i			1.83787i	−0.394411	+	0.918934i	$0.629051\pi$
$132$	−2.63743	−	5.46980i	−0.229559	−	0.476085i
$133$	1.62922			0.141271
$134$	5.69609			0.492067
$135$	1.55280	−	1.55280i	0.133643	−	0.133643i
$136$	2.81650	−	2.81650i	0.241513	−	0.241513i
$137$	1.08115	+	1.08115i	0.0923693	+	0.0923693i	0.751782	−	0.659412i	$-0.229195\pi$
$137$	1.08115	+	1.08115i	0.0923693	+	0.0923693i	−0.659412	+	0.751782i	$0.729195\pi$
$138$	−1.46722	+	1.46722i	−0.124898	+	0.124898i
$139$		−	12.9897i		−	1.10177i	−0.834580	−	0.550886i	$-0.814290\pi$
$139$		−	12.9897i		−	1.10177i	0.834580	−	0.550886i	$-0.185710\pi$
$140$	−4.46932			−0.377726
$141$	2.29881	+	2.29881i	0.193594	+	0.193594i
$142$	1.31555			0.110399
$143$	−1.85382	+	11.8137i	−0.155024	+	0.987911i
$144$	−3.01408			−0.251173
$145$	1.09240	+	1.09240i	0.0907192	+	0.0907192i
$146$	−0.0680248			−0.00562977
$147$			5.76437i			0.475437i
$148$	3.20746	−	3.20746i	0.263651	−	0.263651i
$149$	−13.5402	−	13.5402i	−1.10926	−	1.10926i	−0.993248	−	0.116011i	$-0.962989\pi$
$149$	−13.5402	−	13.5402i	−1.10926	−	1.10926i	−0.116011	−	0.993248i	$-0.537011\pi$
$150$	0.0516537	−	0.0516537i	0.00421750	−	0.00421750i
$151$	−7.08302	+	7.08302i	−0.576408	+	0.576408i	−0.933912	−	0.357504i	$-0.883628\pi$
$151$	−7.08302	+	7.08302i	−0.576408	+	0.576408i	0.357504	+	0.933912i	$0.383628\pi$
$152$	−2.30882			−0.187270
$153$	−2.52854			−0.204420
$154$	−1.36552	+	0.658428i	−0.110037	+	0.0530577i
$155$			8.50843i			0.683413i
$156$	5.42993	+	3.75434i	0.434742	+	0.300588i
$157$	−7.78954			−0.621673			−0.310837	−	0.950463i	$-0.600609\pi$
$157$	−7.78954			−0.621673			−0.310837	+	0.950463i	$0.600609\pi$
$158$	4.47147	−	4.47147i	0.355731	−	0.355731i
$159$	13.3620			1.05967
$160$	9.64022			0.762126
$161$	−3.96632	−	3.96632i	−0.312589	−	0.312589i
$162$	−0.290762	−	0.290762i	−0.0228444	−	0.0228444i
$163$	3.76936	+	3.76936i	0.295239	+	0.295239i	0.839146	−	0.543907i	$-0.183056\pi$
$163$	3.76936	+	3.76936i	0.295239	+	0.295239i	−0.543907	+	0.839146i	$0.683056\pi$
$164$	−13.5981	+	13.5981i	−1.06183	+	1.06183i
$165$	2.40213	−	6.87573i	0.187006	−	0.535275i
$166$			2.41352i			0.187326i
$167$	5.38448	−	5.38448i	0.416664	−	0.416664i	−0.467388	−	0.884052i	$-0.654805\pi$
$167$	5.38448	−	5.38448i	0.416664	−	0.416664i	0.884052	+	0.467388i	$0.154805\pi$
$168$			1.75105i			0.135097i
$169$	−4.59067	−	12.1625i	−0.353129	−	0.935575i
$170$	2.28324			0.175117
$171$	1.03638	+	1.03638i	0.0792542	+	0.0792542i
$172$		−	17.9212i		−	1.36648i
$173$	2.36171			0.179558			0.0897788	−	0.995962i	$-0.471384\pi$
$173$	2.36171			0.179558			0.0897788	+	0.995962i	$0.471384\pi$
$174$	0.204553	−	0.204553i	0.0155071	−	0.0155071i
$175$	0.139634	+	0.139634i	0.0105554	+	0.0105554i
$176$	−9.00447	+	4.34177i	−0.678737	+	0.327273i
$177$	−2.75813	−	2.75813i	−0.207314	−	0.207314i
$178$			1.16419i			0.0872594i
$179$			0.0363645i			0.00271801i	0.999999	+	0.00135900i	$0.000432584\pi$
$179$			0.0363645i			0.00271801i	−0.999999	+	0.00135900i	$0.999567\pi$
$180$	−2.84304	−	2.84304i	−0.211907	−	0.211907i
$181$		−	19.2987i		−	1.43446i	−0.696836	−	0.717230i	$-0.745410\pi$
$181$		−	19.2987i		−	1.43446i	0.696836	−	0.717230i	$-0.254590\pi$
$182$	0.937264	−	1.35557i	0.0694746	−	0.100482i
$183$		−	10.7355i		−	0.793588i
$184$	5.62081	+	5.62081i	0.414371	+	0.414371i
$185$	5.44048			0.399992
$186$	1.59321			0.116820
$187$	−7.55393	+	3.64235i	−0.552398	+	0.266355i
$188$	4.20892	−	4.20892i	0.306967	−	0.306967i
$189$	0.786011	−	0.786011i	0.0571739	−	0.0571739i
$190$	−0.935842	−	0.935842i	−0.0678931	−	0.0678931i
$191$	−6.00243			−0.434321			−0.217160	−	0.976136i	$-0.569679\pi$
$191$	−6.00243			−0.434321			−0.217160	+	0.976136i	$0.569679\pi$
$192$			4.22302i			0.304770i
$193$	3.86066	−	3.86066i	0.277896	−	0.277896i	−0.554372	−	0.832269i	$-0.687042\pi$
$193$	3.86066	−	3.86066i	0.277896	−	0.277896i	0.832269	+	0.554372i	$0.187042\pi$
$194$	2.12772			0.152761
$195$	1.42107	+	7.78917i	0.101765	+	0.557794i
$196$	10.5541			0.753863
$197$	7.98406	+	7.98406i	0.568840	+	0.568840i	0.931804	−	0.362963i	$-0.118235\pi$
$197$	7.98406	+	7.98406i	0.568840	+	0.568840i	−0.362963	+	0.931804i	$0.618235\pi$
$198$	−1.28748	−	0.449801i	−0.0914975	−	0.0319659i
$199$		−	18.4604i		−	1.30862i	−0.756225	−	0.654312i	$-0.772958\pi$
$199$		−	18.4604i		−	1.30862i	0.756225	−	0.654312i	$-0.227042\pi$
$200$	−0.197881	−	0.197881i	−0.0139923	−	0.0139923i
$201$	−9.79511	+	9.79511i	−0.690894	+	0.690894i
$202$	−3.83775	−	3.83775i	−0.270023	−	0.270023i
$203$	0.552965	+	0.552965i	0.0388105	+	0.0388105i
$204$			4.62954i			0.324133i
$205$	−23.0650			−1.61093
$206$	3.29119	−	3.29119i	0.229308	−	0.229308i
$207$		−	5.04613i		−	0.350730i
$208$	6.18045	−	8.93884i	0.428537	−	0.619797i
$209$	4.58907	+	1.60326i	0.317433	+	0.110900i
$210$	−0.709759	+	0.709759i	−0.0489780	+	0.0489780i
$211$			4.79348i			0.329997i	0.986294	+	0.164998i	$0.0527619\pi$
$211$			4.79348i			0.329997i	−0.986294	+	0.164998i	$0.947238\pi$
$212$		−	24.4647i		−	1.68024i
$213$	−2.26225	+	2.26225i	−0.155007	+	0.155007i
$214$	2.45680	−	2.45680i	0.167944	−	0.167944i
$215$	15.1989	−	15.1989i	1.03656	−	1.03656i
$216$	−1.11388	+	1.11388i	−0.0757902	+	0.0757902i
$217$			4.30689i			0.292371i
$218$		−	2.48010i		−	0.167974i
$219$	0.116977	−	0.116977i	0.00790456	−	0.00790456i
$220$	−12.5889	−	4.39810i	−0.848742	−	0.296520i
$221$	5.18484	−	7.49887i	0.348770	−	0.504429i
$222$		−	1.01873i		−	0.0683729i
$223$	16.4689	−	16.4689i	1.10284	−	1.10284i	0.108772	−	0.994067i	$-0.465308\pi$
$223$	16.4689	−	16.4689i	1.10284	−	1.10284i	0.994067	−	0.108772i	$-0.0346918\pi$
$224$	4.87979			0.326045
$225$			0.177649i			0.0118433i
$226$	−0.317370	−	0.317370i	−0.0211112	−	0.0211112i
$227$	−12.5040	−	12.5040i	−0.829918	−	0.829918i	0.157587	−	0.987505i	$-0.449629\pi$
$227$	−12.5040	−	12.5040i	−0.829918	−	0.829918i	−0.987505	+	0.157587i	$0.949629\pi$
$228$	1.89753	−	1.89753i	0.125667	−	0.125667i
$229$	−12.8441	−	12.8441i	−0.848763	−	0.848763i	0.141216	−	0.989979i	$-0.454899\pi$
$229$	−12.8441	−	12.8441i	−0.848763	−	0.848763i	−0.989979	+	0.141216i	$0.954899\pi$
$230$			4.55660i			0.300453i
$231$	1.21594	−	3.48043i	0.0800028	−	0.228995i
$232$	−0.783626	−	0.783626i	−0.0514476	−	0.0514476i
$233$	7.57025			0.495944			0.247972	−	0.968767i	$-0.420236\pi$
$233$	7.57025			0.495944			0.247972	+	0.968767i	$0.420236\pi$
$234$	1.45853	−	0.266095i	0.0953468	−	0.0173952i
$235$	7.13915			0.465707
$236$	−5.04991	+	5.04991i	−0.328721	+	0.328721i
$237$			15.3785i			0.998939i
$238$	1.15576			0.0749165
$239$	−17.6615	−	17.6615i	−1.14243	−	1.14243i	−0.988005	−	0.154422i	$-0.950649\pi$
$239$	−17.6615	−	17.6615i	−1.14243	−	1.14243i	−0.154422	−	0.988005i	$-0.549351\pi$
$240$	−4.68025	+	4.68025i	−0.302109	+	0.302109i
$241$	−21.7895	+	21.7895i	−1.40359	+	1.40359i	−0.615270	+	0.788316i	$0.710953\pi$
$241$	−21.7895	+	21.7895i	−1.40359	+	1.40359i	−0.788316	+	0.615270i	$0.789047\pi$
$242$	−4.49425	+	0.510851i	−0.288902	+	0.0328387i
$243$	1.00000			0.0641500
$244$	−19.6557			−1.25833
$245$	8.95090	+	8.95090i	0.571852	+	0.571852i
$246$			4.31894i			0.275365i
$247$	−5.19873	+	0.948462i	−0.330787	+	0.0603492i
$248$		−	6.10344i		−	0.387569i
$249$	−4.15034	−	4.15034i	−0.263017	−	0.263017i
$250$		−	4.67535i		−	0.295695i
$251$			2.74584i			0.173316i	0.996238	+	0.0866580i	$0.0276187\pi$
$251$			2.74584i			0.173316i	−0.996238	+	0.0866580i	$0.972381\pi$
$252$	−1.43912	−	1.43912i	−0.0906560	−	0.0906560i
$253$	−7.26894	−	15.0752i	−0.456994	−	0.947767i
$254$	0.584065	+	0.584065i	0.0366475	+	0.0366475i
$255$	−3.92631	+	3.92631i	−0.245875	+	0.245875i
$256$	4.12172			0.257608
$257$		−	16.5907i		−	1.03490i	−0.855714	−	0.517450i	$-0.826882\pi$
$257$		−	16.5907i		−	1.03490i	0.855714	−	0.517450i	$-0.173118\pi$
$258$	−2.84601	−	2.84601i	−0.177185	−	0.177185i
$259$	2.75392			0.171120
$260$	14.2613	−	2.60185i	0.884449	−	0.161360i
$261$			0.703508i			0.0435460i
$262$	6.11628	−	6.11628i	0.377865	−	0.377865i
$263$			24.2691i			1.49650i	0.663417	+	0.748250i	$0.269106\pi$
$263$			24.2691i			1.49650i	−0.663417	+	0.748250i	$0.730894\pi$
$264$	−1.72315	+	4.93224i	−0.106052	+	0.303558i
$265$	20.7484	−	20.7484i	1.27457	−	1.27457i
$266$	−0.473715	−	0.473715i	−0.0290453	−	0.0290453i
$267$	−2.00196	−	2.00196i	−0.122518	−	0.122518i
$268$	17.9340	+	17.9340i	1.09549	+	1.09549i
$269$	1.09926			0.0670232			0.0335116	−	0.999438i	$-0.489331\pi$
$269$	1.09926			0.0670232			0.0335116	+	0.999438i	$0.489331\pi$
$270$	−0.902988			−0.0549541
$271$	12.2500	−	12.2500i	0.744135	−	0.744135i	−0.229236	−	0.973371i	$-0.573623\pi$
$271$	12.2500	−	12.2500i	0.744135	−	0.744135i	0.973371	+	0.229236i	$0.0736228\pi$
$272$	7.62122			0.462104
$273$	0.719330	+	3.94281i	0.0435358	+	0.238629i
$274$		−	0.628717i		−	0.0379822i
$275$	0.255903	+	0.530722i	0.0154315	+	0.0320037i
$276$	−9.23904			−0.556125
$277$	15.9495			0.958312			0.479156	−	0.877730i	$-0.340943\pi$
$277$	15.9495			0.958312			0.479156	+	0.877730i	$0.340943\pi$
$278$	−3.77691	+	3.77691i	−0.226524	+	0.226524i
$279$	−2.73971	+	2.73971i	−0.164022	+	0.164022i
$280$	2.71902	+	2.71902i	0.162493	+	0.162493i
$281$	−2.09512	+	2.09512i	−0.124984	+	0.124984i	−0.766832	−	0.641848i	$-0.778168\pi$
$281$	−2.09512	+	2.09512i	−0.124984	+	0.124984i	0.641848	+	0.766832i	$0.278168\pi$
$282$		−	1.33681i		−	0.0796059i
$283$	9.26268			0.550609			0.275304	−	0.961357i	$-0.411221\pi$
$283$	9.26268			0.550609			0.275304	+	0.961357i	$0.411221\pi$
$284$	4.14198	+	4.14198i	0.245781	+	0.245781i
$285$	3.21858			0.190653
$286$	3.97399	−	2.89595i	0.234987	−	0.171241i
$287$	−11.6753			−0.689171
$288$	3.10415	+	3.10415i	0.182914	+	0.182914i
$289$	−10.6065			−0.623911
$290$		−	0.635259i		−	0.0373037i
$291$	−3.65886	+	3.65886i	−0.214486	+	0.214486i
$292$	−0.214175	−	0.214175i	−0.0125336	−	0.0125336i
$293$	3.44489	−	3.44489i	0.201253	−	0.201253i	−0.599284	−	0.800537i	$-0.704548\pi$
$293$	3.44489	−	3.44489i	0.201253	−	0.201253i	0.800537	+	0.599284i	$0.204548\pi$
$294$	1.67606	−	1.67606i	0.0977498	−	0.0977498i
$295$	−8.56563			−0.498710
$296$	−3.90268			−0.226839
$297$	2.98747	−	1.44050i	0.173351	−	0.0835861i
$298$			7.87397i			0.456127i
$299$	14.9653	+	10.3472i	0.865464	+	0.598396i
$300$	0.325261			0.0187789
$301$	7.69355	−	7.69355i	0.443449	−	0.443449i
$302$	4.11895			0.237019
$303$	13.1989			0.758259
$304$	−3.12374	−	3.12374i	−0.179159	−	0.179159i
$305$	−16.6700	−	16.6700i	−0.954520	−	0.954520i
$306$	0.735203	+	0.735203i	0.0420288	+	0.0420288i
$307$	−13.2434	+	13.2434i	−0.755840	+	0.755840i	−0.975562	−	0.219723i	$-0.929485\pi$
$307$	−13.2434	+	13.2434i	−0.755840	+	0.755840i	0.219723	+	0.975562i	$0.429485\pi$
$308$	−6.37237	−	2.22628i	−0.363100	−	0.126854i
$309$			11.3192i			0.643927i
$310$	2.47393	−	2.47393i	0.140510	−	0.140510i
$311$		−	7.20166i		−	0.408369i	−0.978932	−	0.204184i	$-0.934546\pi$
$311$		−	7.20166i		−	0.408369i	0.978932	−	0.204184i	$-0.0654542\pi$
$312$	−1.01939	−	5.58749i	−0.0577115	−	0.316329i
$313$	8.06822			0.456043			0.228021	−	0.973656i	$-0.426774\pi$
$313$	8.06822			0.456043			0.228021	+	0.973656i	$0.426774\pi$
$314$	2.26490	+	2.26490i	0.127816	+	0.127816i
$315$		−	2.44103i		−	0.137536i
$316$	28.1567			1.58394
$317$	−18.1528	+	18.1528i	−1.01956	+	1.01956i	−0.0197570	+	0.999805i	$0.506289\pi$
$317$	−18.1528	+	18.1528i	−1.01956	+	1.01956i	−0.999805	+	0.0197570i	$0.993711\pi$
$318$	−3.88516	−	3.88516i	−0.217869	−	0.217869i
$319$	1.01340	+	2.10171i	0.0567395	+	0.117673i
$320$	6.55749	+	6.55749i	0.366575	+	0.366575i
$321$			8.44953i			0.471607i
$322$			2.30651i			0.128537i
$323$	−2.62054	−	2.62054i	−0.145811	−	0.145811i
$324$		−	1.83092i		−	0.101718i
$325$	−0.526853	−	0.364275i	−0.0292246	−	0.0202063i
$326$		−	2.19197i		−	0.121402i
$327$	4.26483	+	4.26483i	0.235846	+	0.235846i
$328$	16.5455			0.913571
$329$	3.61377			0.199234
$330$	−2.69765	+	1.30075i	−0.148501	+	0.0716040i
$331$	−10.4471	+	10.4471i	−0.574224	+	0.574224i	−0.933306	−	0.359082i	$-0.883090\pi$
$331$	−10.4471	+	10.4471i	−0.574224	+	0.574224i	0.359082	+	0.933306i	$0.383090\pi$
$332$	−7.59893	+	7.59893i	−0.417045	+	0.417045i
$333$	1.75183	+	1.75183i	0.0959999	+	0.0959999i
$334$	−3.13121			−0.171332
$335$			30.4196i			1.66200i
$336$	−2.36910	+	2.36910i	−0.129245	+	0.129245i
$337$	−18.4702			−1.00614			−0.503069	−	0.864247i	$-0.667796\pi$
$337$	−18.4702			−1.00614			−0.503069	+	0.864247i	$0.667796\pi$
$338$	−2.20159	+	4.87118i	−0.119751	+	0.264957i
$339$	1.09151			0.0592828
$340$	7.18873	+	7.18873i	0.389864	+	0.389864i
$341$	−4.23826	+	12.1313i	−0.229514	+	0.656949i
$342$		−	0.602682i		−	0.0325893i
$343$	10.0329	+	10.0329i	0.541728	+	0.541728i
$344$	−10.9028	+	10.9028i	−0.587840	+	0.587840i
$345$	−7.83561	−	7.83561i	−0.421855	−	0.421855i
$346$	−0.686696	−	0.686696i	−0.0369170	−	0.0369170i
$347$		−	4.35560i		−	0.233821i	−0.993142	−	0.116910i	$-0.962701\pi$
$347$		−	4.35560i		−	0.233821i	0.993142	−	0.116910i	$-0.0372990\pi$
$348$	1.28806			0.0690474
$349$	1.75034	−	1.75034i	0.0936938	−	0.0936938i	−0.658706	−	0.752400i	$-0.728896\pi$
$349$	1.75034	−	1.75034i	0.0936938	−	0.0936938i	0.752400	+	0.658706i	$0.228896\pi$
$350$		−	0.0812007i		−	0.00434036i
$351$	−2.05053	+	2.96569i	−0.109449	+	0.158297i
$352$	13.7451	+	4.80203i	0.732614	+	0.255949i
$353$	−7.94401	+	7.94401i	−0.422817	+	0.422817i	−0.886172	−	0.463356i	$-0.846645\pi$
$353$	−7.94401	+	7.94401i	−0.422817	+	0.422817i	0.463356	+	0.886172i	$0.346645\pi$
$354$			1.60392i			0.0852474i
$355$			7.02561i			0.372881i
$356$	−3.66541	+	3.66541i	−0.194267	+	0.194267i
$357$	−1.98746	+	1.98746i	−0.105188	+	0.105188i
$358$	0.0105734	−	0.0105734i	0.000558822	−	0.000558822i
$359$	−14.3686	+	14.3686i	−0.758347	+	0.758347i	−0.976021	−	0.217675i	$-0.930153\pi$
$359$	−14.3686	+	14.3686i	−0.758347	+	0.758347i	0.217675	+	0.976021i	$0.430153\pi$
$360$			3.45927i			0.182320i
$361$		−	16.8518i		−	0.886938i
$362$	−5.61132	+	5.61132i	−0.294925	+	0.294925i
$363$	6.84994	−	8.60688i	0.359529	−	0.451744i
$364$	7.21894	−	1.31703i	0.378375	−	0.0690313i
$365$		−	0.363282i		−	0.0190151i
$366$	−3.12146	+	3.12146i	−0.163161	+	0.163161i
$367$	−9.12931			−0.476546			−0.238273	−	0.971198i	$-0.576581\pi$
$367$	−9.12931			−0.476546			−0.238273	+	0.971198i	$0.576581\pi$
$368$			15.2094i			0.792847i
$369$	−7.42693	−	7.42693i	−0.386631	−	0.386631i
$370$	−1.58188	−	1.58188i	−0.0822383	−	0.0822383i
$371$	10.5027	−	10.5027i	0.545271	−	0.545271i
$372$	5.01618	+	5.01618i	0.260077	+	0.260077i
$373$		−	28.5648i		−	1.47903i	−0.673140	−	0.739515i	$-0.735055\pi$
$373$		−	28.5648i		−	1.47903i	0.673140	−	0.739515i	$-0.264945\pi$
$374$	3.25545	+	1.13734i	0.168336	+	0.0588104i
$375$	8.03983	+	8.03983i	0.415175	+	0.415175i
$376$	−5.12121			−0.264106
$377$	−2.08639	−	1.44256i	−0.107454	−	0.0742957i
$378$	−0.457084			−0.0235099
$379$	−21.7815	+	21.7815i	−1.11884	+	1.11884i	−0.126928	+	0.991912i	$0.540512\pi$
$379$	−21.7815	+	21.7815i	−1.11884	+	1.11884i	−0.991912	+	0.126928i	$0.959488\pi$
$380$		−	5.89295i		−	0.302302i
$381$	−2.00874			−0.102911
$382$	1.74528	+	1.74528i	0.0892962	+	0.0892962i
$383$	1.37711	−	1.37711i	0.0703671	−	0.0703671i	−0.671047	−	0.741414i	$-0.734155\pi$
$383$	1.37711	−	1.37711i	0.0703671	−	0.0703671i	0.741414	+	0.671047i	$0.234155\pi$
$384$	7.43619	−	7.43619i	0.379477	−	0.379477i
$385$	−3.51630	−	7.29250i	−0.179207	−	0.371660i
$386$	−2.24507			−0.114271
$387$	9.78809			0.497557
$388$	6.69907	+	6.69907i	0.340094	+	0.340094i
$389$			16.2827i			0.825568i	0.910829	+	0.412784i	$0.135443\pi$
$389$			16.2827i			0.825568i	−0.910829	+	0.412784i	$0.864557\pi$
$390$	1.85160	−	2.67799i	0.0937595	−	0.135605i
$391$			12.7593i			0.645268i
$392$	−6.42084	−	6.42084i	−0.324302	−	0.324302i
$393$			21.0354i			1.06109i
$394$		−	4.64292i		−	0.233907i
$395$	23.8796	+	23.8796i	1.20151	+	1.20151i
$396$	−2.63743	−	5.46980i	−0.132536	−	0.274868i
$397$	−9.79013	−	9.79013i	−0.491352	−	0.491352i	0.417380	−	0.908732i	$-0.362948\pi$
$397$	−9.79013	−	9.79013i	−0.491352	−	0.491352i	−0.908732	+	0.417380i	$0.862948\pi$
$398$	−5.36759	+	5.36759i	−0.269053	+	0.269053i
$399$	1.62922			0.0815629
$400$		−	0.535449i		−	0.0267725i
$401$	−24.7830	−	24.7830i	−1.23760	−	1.23760i	−0.960978	−	0.276625i	$-0.910784\pi$
$401$	−24.7830	−	24.7830i	−1.23760	−	1.23760i	−0.276625	−	0.960978i	$-0.589216\pi$
$402$	5.69609			0.284095
$403$	−2.50729	−	13.7430i	−0.124897	−	0.684587i
$404$		−	24.1661i		−	1.20231i
$405$	1.55280	−	1.55280i	0.0771591	−	0.0771591i
$406$		−	0.321562i		−	0.0159589i
$407$	7.75706	+	2.71004i	0.384503	+	0.134332i
$408$	2.81650	−	2.81650i	0.139438	−	0.139438i
$409$	7.78771	+	7.78771i	0.385077	+	0.385077i	0.872927	−	0.487850i	$-0.162219\pi$
$409$	7.78771	+	7.78771i	0.385077	+	0.385077i	−0.487850	+	0.872927i	$0.662219\pi$
$410$	6.70643	+	6.70643i	0.331207	+	0.331207i
$411$	1.08115	+	1.08115i	0.0533294	+	0.0533294i
$412$	20.7245			1.02102
$413$	−4.33585			−0.213353
$414$	−1.46722	+	1.46722i	−0.0721101	+	0.0721101i
$415$	−12.8893			−0.632710
$416$	−15.5711	+	2.84081i	−0.763436	+	0.139282i
$417$		−	12.9897i		−	0.636109i
$418$	−0.868161	−	1.80049i	−0.0424632	−	0.0880650i
$419$	6.67053			0.325877			0.162938	−	0.986636i	$-0.447903\pi$
$419$	6.67053			0.325877			0.162938	+	0.986636i	$0.447903\pi$
$420$	−4.46932			−0.218080
$421$	17.2229	−	17.2229i	0.839392	−	0.839392i	−0.149387	−	0.988779i	$-0.547730\pi$
$421$	17.2229	−	17.2229i	0.839392	−	0.839392i	0.988779	+	0.149387i	$0.0477300\pi$
$422$	1.39376	−	1.39376i	0.0678473	−	0.0678473i
$423$	2.29881	+	2.29881i	0.111772	+	0.111772i
$424$	−14.8837	+	14.8837i	−0.722817	+	0.722817i
$425$		−	0.449193i		−	0.0217891i
$426$	1.31555			0.0637386
$427$	−8.43819	−	8.43819i	−0.408353	−	0.408353i
$428$	15.4704			0.747789
$429$	−1.85382	+	11.8137i	−0.0895031	+	0.570371i
$430$	−8.83853			−0.426232
$431$	−3.14518	−	3.14518i	−0.151498	−	0.151498i	0.627289	−	0.778787i	$-0.284165\pi$
$431$	−3.14518	−	3.14518i	−0.151498	−	0.151498i	−0.778787	+	0.627289i	$0.784165\pi$
$432$	−3.01408			−0.145015
$433$		−	5.36790i		−	0.257965i	−0.991647	−	0.128982i	$-0.958829\pi$
$433$		−	5.36790i		−	0.257965i	0.991647	−	0.128982i	$-0.0411711\pi$
$434$	1.25228	−	1.25228i	0.0601113	−	0.0601113i
$435$	1.09240	+	1.09240i	0.0523768	+	0.0523768i
$436$	7.80854	−	7.80854i	0.373961	−	0.373961i
$437$	5.22973	−	5.22973i	0.250172	−	0.250172i
$438$	−0.0680248			−0.00325035
$439$	1.58544			0.0756688			0.0378344	−	0.999284i	$-0.487954\pi$
$439$	1.58544			0.0756688			0.0378344	+	0.999284i	$0.487954\pi$
$440$	4.98307	+	10.3345i	0.237558	+	0.492676i
$441$			5.76437i			0.274494i
$442$	−3.68794	+	0.672833i	−0.175418	+	0.0320034i
$443$	−20.6323			−0.980271			−0.490136	−	0.871646i	$-0.663053\pi$
$443$	−20.6323			−0.980271			−0.490136	+	0.871646i	$0.663053\pi$
$444$	3.20746	−	3.20746i	0.152219	−	0.152219i
$445$	−6.21726			−0.294727
$446$	−9.57705			−0.453487
$447$	−13.5402	−	13.5402i	−0.640431	−	0.640431i
$448$	3.31934	+	3.31934i	0.156824	+	0.156824i
$449$	−12.5630	−	12.5630i	−0.592886	−	0.592886i	0.345524	−	0.938410i	$-0.387701\pi$
$449$	−12.5630	−	12.5630i	−0.592886	−	0.592886i	−0.938410	+	0.345524i	$0.887701\pi$
$450$	0.0516537	−	0.0516537i	0.00243498	−	0.00243498i
$451$	−32.8862	−	11.4893i	−1.54855	−	0.541008i
$452$		−	1.99847i		−	0.0939999i
$453$	−7.08302	+	7.08302i	−0.332789	+	0.332789i
$454$			7.27136i			0.341262i
$455$	7.23935	+	5.00540i	0.339386	+	0.234657i
$456$	−2.30882			−0.108121
$457$	8.59698	+	8.59698i	0.402150	+	0.402150i	0.878990	−	0.476840i	$-0.158218\pi$
$457$	8.59698	+	8.59698i	0.402150	+	0.402150i	−0.476840	+	0.878990i	$0.658218\pi$
$458$			7.46916i			0.349011i
$459$	−2.52854			−0.118022
$460$	−14.3463	+	14.3463i	−0.668902	+	0.668902i
$461$	1.66154	+	1.66154i	0.0773855	+	0.0773855i	0.744740	−	0.667355i	$-0.232573\pi$
$461$	1.66154	+	1.66154i	0.0773855	+	0.0773855i	−0.667355	+	0.744740i	$0.732573\pi$
$462$	−1.36552	+	0.658428i	−0.0635300	+	0.0306329i
$463$	23.8292	+	23.8292i	1.10744	+	1.10744i	0.993487	+	0.113949i	$0.0363500\pi$
$463$	23.8292	+	23.8292i	1.10744	+	1.10744i	0.113949	+	0.993487i	$0.463650\pi$
$464$		−	2.12043i		−	0.0984384i
$465$			8.50843i			0.394569i
$466$	−2.20114	−	2.20114i	−0.101966	−	0.101966i
$467$		−	11.8982i		−	0.550584i	−0.961361	−	0.275292i	$-0.911225\pi$
$467$		−	11.8982i		−	0.550584i	0.961361	−	0.275292i	$-0.0887745\pi$
$468$	5.42993	+	3.75434i	0.250999	+	0.173545i
$469$			15.3981i			0.711020i
$470$	−2.07579	−	2.07579i	−0.0957492	−	0.0957492i
$471$	−7.78954			−0.358923
$472$	6.14448			0.282823
$473$	29.2416	−	14.0997i	1.34453	−	0.648306i
$474$	4.47147	−	4.47147i	0.205382	−	0.205382i
$475$	−0.184113	+	0.184113i	−0.00844768	+	0.00844768i
$476$	3.63887	+	3.63887i	0.166787	+	0.166787i
$477$	13.3620			0.611803
$478$			10.2706i			0.469765i
$479$	5.19922	−	5.19922i	0.237559	−	0.237559i	−0.578280	−	0.815838i	$-0.696276\pi$
$479$	5.19922	−	5.19922i	0.237559	−	0.237559i	0.815838	+	0.578280i	$0.196276\pi$
$480$	9.64022			0.440014
$481$	−8.78759	+	1.60322i	−0.400679	+	0.0731004i
$482$	12.6711			0.577154
$483$	−3.96632	−	3.96632i	−0.180474	−	0.180474i
$484$	−15.7585	−	12.5417i	−0.716294	−	0.570075i
$485$			11.3629i			0.515964i
$486$	−0.290762	−	0.290762i	−0.0131892	−	0.0131892i
$487$	−22.4171	+	22.4171i	−1.01582	+	1.01582i	−0.0159442	+	0.999873i	$0.505075\pi$
$487$	−22.4171	+	22.4171i	−1.01582	+	1.01582i	−0.999873	+	0.0159442i	$0.994925\pi$
$488$	11.9581	+	11.9581i	0.541316	+	0.541316i
$489$	3.76936	+	3.76936i	0.170456	+	0.170456i
$490$		−	5.20516i		−	0.235145i
$491$	−9.97288			−0.450070			−0.225035	−	0.974351i	$-0.572250\pi$
$491$	−9.97288			−0.450070			−0.225035	+	0.974351i	$0.572250\pi$
$492$	−13.5981	+	13.5981i	−0.613049	+	0.613049i
$493$		−	1.77885i		−	0.0801153i
$494$	1.78737	+	1.23582i	0.0804175	+	0.0556020i
$495$	2.40213	−	6.87573i	0.107968	−	0.309041i
$496$	8.25771	−	8.25771i	0.370782	−	0.370782i
$497$			3.55630i			0.159522i
$498$			2.41352i			0.108153i
$499$	−16.6471	+	16.6471i	−0.745228	+	0.745228i	−0.973579	−	0.228351i	$-0.926667\pi$
$499$	−16.6471	+	16.6471i	−0.745228	+	0.745228i	0.228351	+	0.973579i	$0.426667\pi$
$500$	14.7203	−	14.7203i	0.658310	−	0.658310i
$501$	5.38448	−	5.38448i	0.240561	−	0.240561i
$502$	0.798386	−	0.798386i	0.0356337	−	0.0356337i
$503$		−	21.0754i		−	0.939706i	−0.882745	−	0.469853i	$-0.844307\pi$
$503$		−	21.0754i		−	0.939706i	0.882745	−	0.469853i	$-0.155693\pi$
$504$			1.75105i			0.0779980i
$505$	20.4952	−	20.4952i	0.912026	−	0.912026i
$506$	−2.26975	+	6.49681i	−0.100903	+	0.288819i
$507$	−4.59067	−	12.1625i	−0.203879	−	0.540154i
$508$			3.67783i			0.163177i
$509$	18.1840	−	18.1840i	0.805993	−	0.805993i	−0.178032	−	0.984025i	$-0.556973\pi$
$509$	18.1840	−	18.1840i	0.805993	−	0.805993i	0.984025	+	0.178032i	$0.0569731\pi$
$510$	2.28324			0.101104
$511$		−	0.183890i		−	0.00813482i
$512$	−16.0708	−	16.0708i	−0.710237	−	0.710237i
$513$	1.03638	+	1.03638i	0.0457575	+	0.0457575i
$514$	−4.82394	+	4.82394i	−0.212775	+	0.212775i
$515$	17.5764	+	17.5764i	0.774510	+	0.774510i
$516$		−	17.9212i		−	0.788935i
$517$	10.1790	+	3.55619i	0.447673	+	0.156401i
$518$	−0.800736	−	0.800736i	−0.0351823	−	0.0351823i
$519$	2.36171			0.103668
$520$	−10.2591	−	7.09333i	−0.449893	−	0.311063i
$521$	−43.7602			−1.91717			−0.958584	−	0.284810i	$-0.908070\pi$
$521$	−43.7602			−1.91717			−0.958584	+	0.284810i	$0.908070\pi$
$522$	0.204553	−	0.204553i	0.00895305	−	0.00895305i
$523$			22.8324i			0.998389i	0.866490	+	0.499195i	$0.166371\pi$
$523$			22.8324i			0.998389i	−0.866490	+	0.499195i	$0.833629\pi$
$524$	38.5140			1.68249
$525$	0.139634	+	0.139634i	0.00609414	+	0.00609414i
$526$	7.05654	−	7.05654i	0.307680	−	0.307680i
$527$	6.92747	−	6.92747i	0.301765	−	0.301765i
$528$	−9.00447	+	4.34177i	−0.391869	+	0.188951i
$529$	−2.46344			−0.107106
$530$	−12.0657			−0.524101
$531$	−2.75813	−	2.75813i	−0.119693	−	0.119693i
$532$		−	2.98296i		−	0.129328i
$533$	37.2551	−	6.79687i	1.61370	−	0.294405i
$534$			1.16419i			0.0503793i
$535$	13.1204	+	13.1204i	0.567244	+	0.567244i
$536$		−	21.8212i		−	0.942534i
$537$			0.0363645i			0.00156924i
$538$	−0.319624	−	0.319624i	−0.0137800	−	0.0137800i
$539$	8.30356	+	17.2209i	0.357660	+	0.741756i
$540$	−2.84304	−	2.84304i	−0.122345	−	0.122345i
$541$	−6.22864	+	6.22864i	−0.267790	+	0.267790i	−0.828209	−	0.560419i	$-0.810640\pi$
$541$	−6.22864	+	6.22864i	−0.267790	+	0.267790i	0.560419	+	0.828209i	$0.310640\pi$
$542$	−7.12367			−0.305988
$543$		−	19.2987i		−	0.828186i
$544$	−7.84896	−	7.84896i	−0.336522	−	0.336522i
$545$	13.2448			0.567346
$546$	0.937264	−	1.35557i	0.0401112	−	0.0580131i
$547$			25.8483i			1.10519i	0.833449	+	0.552597i	$0.186363\pi$
$547$			25.8483i			1.10519i	−0.833449	+	0.552597i	$0.813637\pi$
$548$	1.97950	−	1.97950i	0.0845601	−	0.0845601i
$549$		−	10.7355i		−	0.458178i
$550$	0.0799068	−	0.228721i	0.00340724	−	0.00975268i
$551$	−0.729104	+	0.729104i	−0.0310609	+	0.0310609i
$552$	5.62081	+	5.62081i	0.239237	+	0.239237i
$553$	12.0876	+	12.0876i	0.514019	+	0.514019i
$554$	−4.63750	−	4.63750i	−0.197029	−	0.197029i
$555$	5.44048			0.230936
$556$	−23.7831			−1.00863
$557$	−22.0790	+	22.0790i	−0.935518	+	0.935518i	−0.998043	−	0.0625257i	$-0.980084\pi$
$557$	−22.0790	+	22.0790i	−0.935518	+	0.935518i	0.0625257	+	0.998043i	$0.480084\pi$
$558$	1.59321			0.0674459
$559$	−20.0708	+	29.0285i	−0.848903	+	1.22777i
$560$			7.35746i			0.310909i
$561$	−7.55393	+	3.64235i	−0.318927	+	0.153780i
$562$	1.21836			0.0513936
$563$	−31.0226			−1.30745			−0.653723	−	0.756734i	$-0.726794\pi$
$563$	−31.0226			−1.30745			−0.653723	+	0.756734i	$0.726794\pi$
$564$	4.20892	−	4.20892i	0.177227	−	0.177227i
$565$	1.69490	−	1.69490i	0.0713048	−	0.0713048i
$566$	−2.69323	−	2.69323i	−0.113205	−	0.113205i
$567$	0.786011	−	0.786011i	0.0330094	−	0.0330094i
$568$		−	5.03976i		−	0.211464i
$569$	−13.6586			−0.572600			−0.286300	−	0.958140i	$-0.592425\pi$
$569$	−13.6586			−0.572600			−0.286300	+	0.958140i	$0.592425\pi$
$570$	−0.935842	−	0.935842i	−0.0391981	−	0.0391981i
$571$	−35.4267			−1.48256			−0.741280	−	0.671196i	$-0.765781\pi$
$571$	−35.4267			−1.48256			−0.741280	+	0.671196i	$0.765781\pi$
$572$	21.6299	+	3.39418i	0.904390	+	0.141918i
$573$	−6.00243			−0.250755
$574$	3.39473	+	3.39473i	0.141693	+	0.141693i
$575$	0.896442			0.0373842
$576$			4.22302i			0.175959i
$577$	4.67205	−	4.67205i	0.194500	−	0.194500i	−0.603137	−	0.797637i	$-0.706083\pi$
$577$	4.67205	−	4.67205i	0.194500	−	0.194500i	0.797637	+	0.603137i	$0.206083\pi$
$578$	3.08396	+	3.08396i	0.128276	+	0.128276i
$579$	3.86066	−	3.86066i	0.160444	−	0.160444i
$580$	2.00010	−	2.00010i	0.0830496	−	0.0830496i
$581$	−6.52443			−0.270679
$582$	2.12772			0.0881967
$583$	39.9185	−	19.2479i	1.65326	−	0.797166i
$584$			0.260597i			0.0107836i
$585$	1.42107	+	7.78917i	0.0587538	+	0.322042i
$586$	−2.00329			−0.0827551
$587$	−3.05752	+	3.05752i	−0.126198	+	0.126198i	−0.767385	−	0.641187i	$-0.778442\pi$
$587$	−3.05752	+	3.05752i	−0.126198	+	0.126198i	0.641187	+	0.767385i	$0.278442\pi$
$588$	10.5541			0.435243
$589$	−5.67878			−0.233990
$590$	2.49056	+	2.49056i	0.102535	+	0.102535i
$591$	7.98406	+	7.98406i	0.328420	+	0.328420i
$592$	−5.28017	−	5.28017i	−0.217014	−	0.217014i
$593$	14.8001	−	14.8001i	0.607766	−	0.607766i	−0.334596	−	0.942362i	$-0.608600\pi$
$593$	14.8001	−	14.8001i	0.607766	−	0.607766i	0.942362	+	0.334596i	$0.108600\pi$
$594$	−1.28748	−	0.449801i	−0.0528261	−	0.0184555i
$595$			6.17224i			0.253037i
$596$	−24.7910	+	24.7910i	−1.01548	+	1.01548i
$597$		−	18.4604i		−	0.755534i
$598$	−1.34275	−	7.35991i	−0.0549092	−	0.300969i
$599$	36.3824			1.48655			0.743273	−	0.668989i	$-0.233273\pi$
$599$	36.3824			1.48655			0.743273	+	0.668989i	$0.233273\pi$
$600$	−0.197881	−	0.197881i	−0.00807845	−	0.00807845i
$601$			7.79047i			0.317780i	0.987296	+	0.158890i	$0.0507915\pi$
$601$			7.79047i			0.317780i	−0.987296	+	0.158890i	$0.949208\pi$
$602$	−4.47398			−0.182346
$603$	−9.79511	+	9.79511i	−0.398888	+	0.398888i
$604$	12.9684	+	12.9684i	0.527677	+	0.527677i
$605$	−2.72817	−	24.0013i	−0.110916	−	0.975791i
$606$	−3.83775	−	3.83775i	−0.155898	−	0.155898i
$607$		−	22.3940i		−	0.908943i	−0.890761	−	0.454472i	$-0.849828\pi$
$607$		−	22.3940i		−	0.908943i	0.890761	−	0.454472i	$-0.150172\pi$
$608$			6.43418i			0.260940i
$609$	0.552965	+	0.552965i	0.0224073	+	0.0224073i
$610$			9.69399i			0.392498i
$611$	−11.5313	+	2.10379i	−0.466507	+	0.0851101i
$612$			4.62954i			0.187138i
$613$	−19.1732	−	19.1732i	−0.774400	−	0.774400i	0.204472	−	0.978872i	$-0.434452\pi$
$613$	−19.1732	−	19.1732i	−0.774400	−	0.774400i	−0.978872	+	0.204472i	$0.934452\pi$
$614$	7.70134			0.310801
$615$	−23.0650			−0.930071
$616$	2.52238	+	5.23121i	0.101630	+	0.210771i
$617$	29.8063	−	29.8063i	1.19996	−	1.19996i	0.225778	−	0.974179i	$-0.427508\pi$
$617$	29.8063	−	29.8063i	1.19996	−	1.19996i	0.974179	−	0.225778i	$-0.0724923\pi$
$618$	3.29119	−	3.29119i	0.132391	−	0.132391i
$619$	−21.9599	−	21.9599i	−0.882642	−	0.882642i	0.111160	−	0.993802i	$-0.464543\pi$
$619$	−21.9599	−	21.9599i	−0.882642	−	0.882642i	−0.993802	+	0.111160i	$0.964543\pi$
$620$	15.5782			0.625636
$621$		−	5.04613i		−	0.202494i
$622$	−2.09397	+	2.09397i	−0.0839605	+	0.0839605i
$623$	−3.14712			−0.126087
$624$	6.18045	−	8.93884i	0.247416	−	0.357840i
$625$	24.0802			0.963208
$626$	−2.34593	−	2.34593i	−0.0937623	−	0.0937623i
$627$	4.58907	+	1.60326i	0.183270	+	0.0640279i
$628$			14.2620i			0.569115i
$629$	−4.42958	−	4.42958i	−0.176619	−	0.176619i
$630$	−0.709759	+	0.709759i	−0.0282775	+	0.0282775i
$631$	19.4707	+	19.4707i	0.775118	+	0.775118i	0.978996	−	0.203878i	$-0.0653547\pi$
$631$	19.4707	+	19.4707i	0.775118	+	0.775118i	−0.203878	+	0.978996i	$0.565355\pi$
$632$	−17.1298	−	17.1298i	−0.681388	−	0.681388i
$633$			4.79348i			0.190524i
$634$	10.5563			0.419243
$635$	−3.11916	+	3.11916i	−0.123780	+	0.123780i
$636$		−	24.4647i		−	0.970087i
$637$	−17.0954	−	11.8200i	−0.677343	−	0.468326i
$638$	0.316438	−	0.905755i	0.0125279	−	0.0358592i
$639$	−2.26225	+	2.26225i	−0.0894931	+	0.0894931i
$640$		−	23.0938i		−	0.912862i
$641$		−	13.5135i		−	0.533752i	−0.963731	−	0.266876i	$-0.914009\pi$
$641$		−	13.5135i		−	0.533752i	0.963731	−	0.266876i	$-0.0859914\pi$
$642$	2.45680	−	2.45680i	0.0969623	−	0.0969623i
$643$	17.4592	−	17.4592i	0.688525	−	0.688525i	−0.273381	−	0.961906i	$-0.588142\pi$
$643$	17.4592	−	17.4592i	0.688525	−	0.688525i	0.961906	+	0.273381i	$0.0881420\pi$
$644$	−7.26199	+	7.26199i	−0.286162	+	0.286162i
$645$	15.1989	−	15.1989i	0.598457	−	0.598457i
$646$			1.52391i			0.0599572i
$647$		−	41.2539i		−	1.62186i	−0.585144	−	0.810929i	$-0.698962\pi$
$647$		−	41.2539i		−	1.62186i	0.585144	−	0.810929i	$-0.301038\pi$
$648$	−1.11388	+	1.11388i	−0.0437575	+	0.0437575i
$649$	−12.2129	−	4.26675i	−0.479399	−	0.167485i
$650$	0.0472716	+	0.259106i	0.00185415	+	0.0101630i
$651$			4.30689i			0.168800i
$652$	6.90137	−	6.90137i	0.270279	−	0.270279i
$653$	15.4516			0.604666			0.302333	−	0.953202i	$-0.402235\pi$
$653$	15.4516			0.604666			0.302333	+	0.953202i	$0.402235\pi$
$654$		−	2.48010i		−	0.0969796i
$655$	32.6636	+	32.6636i	1.27627	+	1.27627i
$656$	22.3854	+	22.3854i	0.874001	+	0.874001i
$657$	0.116977	−	0.116977i	0.00456370	−	0.00456370i
$658$	−1.05075	−	1.05075i	−0.0409624	−	0.0409624i
$659$			16.6262i			0.647664i	0.946115	+	0.323832i	$0.104971\pi$
$659$			16.6262i			0.647664i	−0.946115	+	0.323832i	$0.895029\pi$
$660$	−12.5889	−	4.39810i	−0.490021	−	0.171196i
$661$	−24.1354	−	24.1354i	−0.938758	−	0.938758i	0.0594718	−	0.998230i	$-0.481058\pi$
$661$	−24.1354	−	24.1354i	−0.938758	−	0.938758i	−0.998230	+	0.0594718i	$0.981058\pi$
$662$	6.07523			0.236121
$663$	5.18484	−	7.49887i	0.201363	−	0.291232i
$664$	9.24601			0.358815
$665$	2.52984	−	2.52984i	0.0981031	−	0.0981031i
$666$		−	1.01873i		−	0.0394751i
$667$	3.54999			0.137456
$668$	−9.85853	−	9.85853i	−0.381438	−	0.381438i
$669$	16.4689	−	16.4689i	0.636724	−	0.636724i
$670$	8.84486	−	8.84486i	0.341707	−	0.341707i
$671$	−15.4644	−	32.0718i	−0.596996	−	1.23812i
$672$	4.87979			0.188242
$673$	33.8599			1.30520			0.652602	−	0.757701i	$-0.273677\pi$
$673$	33.8599			1.30520			0.652602	+	0.757701i	$0.273677\pi$
$674$	5.37044	+	5.37044i	0.206861	+	0.206861i
$675$			0.177649i			0.00683773i
$676$	−22.2685	+	8.40513i	−0.856479	+	0.323274i
$677$		−	49.9662i		−	1.92036i	−0.279388	−	0.960178i	$-0.590132\pi$
$677$		−	49.9662i		−	1.92036i	0.279388	−	0.960178i	$-0.409868\pi$
$678$	−0.317370	−	0.317370i	−0.0121885	−	0.0121885i
$679$			5.75181i			0.220734i
$680$		−	8.74690i		−	0.335428i
$681$	−12.5040	−	12.5040i	−0.479153	−	0.479153i
$682$	4.75966	−	2.29501i	0.182257	−	0.0878805i
$683$	−17.7267	−	17.7267i	−0.678292	−	0.678292i	0.281322	−	0.959614i	$-0.409227\pi$
$683$	−17.7267	−	17.7267i	−0.678292	−	0.678292i	−0.959614	+	0.281322i	$0.909227\pi$
$684$	1.89753	−	1.89753i	0.0725539	−	0.0725539i
$685$	3.35762			0.128288
$686$		−	5.83439i		−	0.222758i
$687$	−12.8441	−	12.8441i	−0.490034	−	0.490034i
$688$	−29.5021			−1.12476
$689$	−27.3991	+	39.6275i	−1.04382	+	1.50969i
$690$			4.55660i			0.173467i
$691$	−0.0455174	+	0.0455174i	−0.00173156	+	0.00173156i	−0.707972	−	0.706240i	$-0.750390\pi$
$691$	−0.0455174	+	0.0455174i	−0.00173156	+	0.00173156i	0.706240	+	0.707972i	$0.250390\pi$
$692$		−	4.32409i		−	0.164377i
$693$	1.21594	−	3.48043i	0.0461896	−	0.132211i
$694$	−1.26644	+	1.26644i	−0.0480735	+	0.0480735i
$695$	−20.1704	−	20.1704i	−0.765106	−	0.765106i
$696$	−0.783626	−	0.783626i	−0.0297033	−	0.0297033i
$697$	18.7793	+	18.7793i	0.711316	+	0.711316i
$698$	−1.01787			−0.0385268
$699$	7.57025			0.286333
$700$	0.255659	−	0.255659i	0.00966299	−	0.00966299i
$701$	7.51392			0.283797			0.141898	−	0.989881i	$-0.454679\pi$
$701$	7.51392			0.283797			0.141898	+	0.989881i	$0.454679\pi$
$702$	1.45853	−	0.266095i	0.0550485	−	0.0100431i
$703$			3.63114i			0.136951i
$704$	6.08325	+	12.6162i	0.229271	+	0.475489i
$705$	7.13915			0.268876
$706$	4.61963			0.173862
$707$	10.3745	−	10.3745i	0.390173	−	0.390173i
$708$	−5.04991	+	5.04991i	−0.189787	+	0.189787i
$709$	−0.868011	−	0.868011i	−0.0325989	−	0.0325989i	0.690619	−	0.723218i	$-0.257338\pi$
$709$	−0.868011	−	0.868011i	−0.0325989	−	0.0325989i	−0.723218	+	0.690619i	$0.757338\pi$
$710$	2.04278	−	2.04278i	0.0766642	−	0.0766642i
$711$			15.3785i			0.576738i
$712$	4.45990			0.167142
$713$	13.8249	+	13.8249i	0.517748	+	0.517748i
$714$	1.15576			0.0432531
$715$	15.4657	+	21.2229i	0.578383	+	0.793690i
$716$	0.0665802			0.00248822
$717$	−17.6615	−	17.6615i	−0.659580	−	0.659580i
$718$	8.35570			0.311832
$719$		−	18.9135i		−	0.705356i	−0.935745	−	0.352678i	$-0.885271\pi$
$719$		−	18.9135i		−	0.705356i	0.935745	−	0.352678i	$-0.114729\pi$
$720$	−4.68025	+	4.68025i	−0.174423	+	0.174423i
$721$	8.89702	+	8.89702i	0.331342	+	0.331342i
$722$	−4.89987	+	4.89987i	−0.182354	+	0.182354i
$723$	−21.7895	+	21.7895i	−0.810361	+	0.810361i
$724$	−35.3343			−1.31319
$725$	−0.124978			−0.00464155
$726$	−4.49425	+	0.510851i	−0.166797	+	0.0189595i
$727$			27.1206i			1.00585i	0.864330	+	0.502924i	$0.167743\pi$
$727$			27.1206i			1.00585i	−0.864330	+	0.502924i	$0.832257\pi$
$728$	−5.19308	−	3.59058i	−0.192468	−	0.133076i
$729$	1.00000			0.0370370
$730$	−0.105629	+	0.105629i	−0.00390949	+	0.00390949i
$731$	−24.7496			−0.915397
$732$	−19.6557			−0.726496
$733$	19.5263	+	19.5263i	0.721220	+	0.721220i	0.968854	−	0.247633i	$-0.0796528\pi$
$733$	19.5263	+	19.5263i	0.721220	+	0.721220i	−0.247633	+	0.968854i	$0.579653\pi$
$734$	2.65445	+	2.65445i	0.0979777	+	0.0979777i
$735$	8.95090	+	8.95090i	0.330159	+	0.330159i
$736$	15.6639	−	15.6639i	0.577380	−	0.577380i
$737$	−15.1528	+	43.3724i	−0.558159	+	1.59764i
$738$			4.31894i			0.158982i
$739$	27.4768	−	27.4768i	1.01075	−	1.01075i	0.0108093	−	0.999942i	$-0.496559\pi$
$739$	27.4768	−	27.4768i	1.01075	−	1.01075i	0.999942	−	0.0108093i	$-0.00344078\pi$
$740$		−	9.96106i		−	0.366176i
$741$	−5.19873	+	0.948462i	−0.190980	+	0.0348426i
$742$	−6.10755			−0.224215
$743$	−24.4082	−	24.4082i	−0.895449	−	0.895449i	0.0995806	−	0.995030i	$-0.468250\pi$
$743$	−24.4082	−	24.4082i	−0.895449	−	0.895449i	−0.995030	+	0.0995806i	$0.968250\pi$
$744$		−	6.10344i		−	0.223763i
$745$	−42.0504			−1.54061
$746$	−8.30556	+	8.30556i	−0.304088	+	0.304088i
$747$	−4.15034	−	4.15034i	−0.151853	−	0.151853i
$748$	6.66884	+	13.8306i	0.243837	+	0.505697i
$749$	6.64143	+	6.64143i	0.242672	+	0.242672i
$750$		−	4.67535i		−	0.170720i
$751$			12.0719i			0.440509i	0.975442	+	0.220254i	$0.0706887\pi$
$751$			12.0719i			0.440509i	−0.975442	+	0.220254i	$0.929311\pi$
$752$	−6.92878	−	6.92878i	−0.252667	−	0.252667i
$753$			2.74584i			0.100064i
$754$	0.187200	+	1.02608i	0.00681742	+	0.0373678i
$755$			21.9970i			0.800552i
$756$	−1.43912	−	1.43912i	−0.0523403	−	0.0523403i
$757$	29.2281			1.06231			0.531157	−	0.847273i	$-0.321757\pi$
$757$	29.2281			1.06231			0.531157	+	0.847273i	$0.321757\pi$
$758$	12.6665			0.460067
$759$	−7.26894	−	15.0752i	−0.263846	−	0.547194i
$760$	−3.58513	+	3.58513i	−0.130046	+	0.130046i
$761$	0.436192	−	0.436192i	0.0158119	−	0.0158119i	−0.699157	−	0.714969i	$-0.746441\pi$
$761$	0.436192	−	0.436192i	0.0158119	−	0.0158119i	0.714969	+	0.699157i	$0.246441\pi$
$762$	0.584065	+	0.584065i	0.0211584	+	0.0211584i
$763$	6.70441			0.242716
$764$			10.9899i			0.397602i
$765$	−3.92631	+	3.92631i	−0.141956	+	0.141956i
$766$	−0.800823			−0.0289349
$767$	13.8354	−	2.52415i	0.499567	−	0.0911417i
$768$	4.12172			0.148730
$769$	−24.6185	−	24.6185i	−0.887765	−	0.887765i	0.106543	−	0.994308i	$-0.466022\pi$
$769$	−24.6185	−	24.6185i	−0.887765	−	0.887765i	−0.994308	+	0.106543i	$0.966022\pi$
$770$	−1.09798	+	3.14279i	−0.0395683	+	0.113258i
$771$		−	16.5907i		−	0.597499i
$772$	−7.06854	−	7.06854i	−0.254402	−	0.254402i
$773$	−18.7921	+	18.7921i	−0.675906	+	0.675906i	−0.959071	−	0.283165i	$-0.908616\pi$
$773$	−18.7921	+	18.7921i	−0.675906	+	0.675906i	0.283165	+	0.959071i	$0.408616\pi$
$774$	−2.84601	−	2.84601i	−0.102298	−	0.102298i
$775$	−0.486708	−	0.486708i	−0.0174831	−	0.0174831i
$776$		−	8.15110i		−	0.292607i
$777$	2.75392			0.0987964
$778$	4.73440	−	4.73440i	0.169736	−	0.169736i
$779$		−	15.3943i		−	0.551558i
$780$	14.2613	−	2.60185i	0.510637	−	0.0931612i
$781$	−3.49963	+	10.0171i	−0.125227	+	0.358442i
$782$	3.70993	−	3.70993i	0.132667	−	0.132667i
$783$			0.703508i			0.0251413i
$784$		−	17.3743i		−	0.620510i
$785$	−12.0956	+	12.0956i	−0.431709	+	0.431709i
$786$	6.11628	−	6.11628i	0.218161	−	0.218161i
$787$	−0.939086	+	0.939086i	−0.0334748	+	0.0334748i	−0.723646	−	0.690171i	$-0.757535\pi$
$787$	−0.939086	+	0.939086i	−0.0334748	+	0.0334748i	0.690171	+	0.723646i	$0.257535\pi$
$788$	14.6181	−	14.6181i	0.520749	−	0.520749i
$789$			24.2691i			0.864004i
$790$		−	13.8866i		−	0.494062i
$791$	0.857941	−	0.857941i	0.0305049	−	0.0305049i
$792$	−1.72315	+	4.93224i	−0.0612294	+	0.175260i
$793$	31.8381	+	22.0134i	1.13060	+	0.781717i
$794$			5.69319i			0.202044i
$795$	20.7484	−	20.7484i	0.735871	−	0.735871i
$796$	−33.7994			−1.19799
$797$			52.4691i			1.85855i	0.369389	+	0.929275i	$0.379567\pi$
$797$			52.4691i			1.85855i	−0.369389	+	0.929275i	$0.620433\pi$
$798$	−0.473715	−	0.473715i	−0.0167693	−	0.0167693i
$799$	−5.81262	−	5.81262i	−0.205636	−	0.205636i
$800$	−0.551450	+	0.551450i	−0.0194967	+	0.0194967i
$801$	−2.00196	−	2.00196i	−0.0707357	−	0.0707357i
$802$			14.4119i			0.508902i
$803$	0.180960	−	0.517969i	0.00638593	−	0.0182787i
$804$	17.9340	+	17.9340i	0.632484	+	0.632484i
$805$	−12.3178			−0.434144
$806$	−3.26692	+	4.72496i	−0.115072	+	0.166430i
$807$	1.09926			0.0386959
$808$	−14.7021	+	14.7021i	−0.517217	+	0.517217i
$809$		−	18.0194i		−	0.633528i	−0.948504	−	0.316764i	$-0.897404\pi$
$809$		−	18.0194i		−	0.633528i	0.948504	−	0.316764i	$-0.102596\pi$
$810$	−0.902988			−0.0317278
$811$	28.7923	+	28.7923i	1.01103	+	1.01103i	0.999938	+	0.0110947i	$0.00353164\pi$
$811$	28.7923	+	28.7923i	1.01103	+	1.01103i	0.0110947	+	0.999938i	$0.496468\pi$
$812$	1.01243	−	1.01243i	0.0355294	−	0.0355294i
$813$	12.2500	−	12.2500i	0.429626	−	0.429626i
$814$	−1.46748	−	3.04343i	−0.0514352	−	0.106672i
$815$	11.7061			0.410046
$816$	7.62122			0.266796
$817$	10.1442	+	10.1442i	0.354901	+	0.354901i
$818$		−	4.52874i		−	0.158344i
$819$	0.719330	+	3.94281i	0.0251354	+	0.137773i
$820$			42.2301i			1.47474i
$821$	18.3751	+	18.3751i	0.641296	+	0.641296i	0.950874	−	0.309578i	$-0.100188\pi$
$821$	18.3751	+	18.3751i	0.641296	+	0.641296i	−0.309578	+	0.950874i	$0.600188\pi$
$822$		−	0.628717i		−	0.0219290i
$823$			53.5933i			1.86815i	0.357081	+	0.934073i	$0.383772\pi$
$823$			53.5933i			1.86815i	−0.357081	+	0.934073i	$0.616228\pi$
$824$	−12.6083	−	12.6083i	−0.439230	−	0.439230i
$825$	0.255903	+	0.530722i	0.00890941	+	0.0184774i
$826$	1.26070	+	1.26070i	0.0438653	+	0.0438653i
$827$	34.3151	−	34.3151i	1.19325	−	1.19325i	0.217103	−	0.976149i	$-0.430339\pi$
$827$	34.3151	−	34.3151i	1.19325	−	1.19325i	0.976149	−	0.217103i	$-0.0696608\pi$
$828$	−9.23904			−0.321079
$829$		−	24.5521i		−	0.852729i	−0.904551	−	0.426365i	$-0.859794\pi$
$829$		−	24.5521i		−	0.852729i	0.904551	−	0.426365i	$-0.140206\pi$
$830$	3.74771	+	3.74771i	0.130085	+	0.130085i
$831$	15.9495			0.553282
$832$	−12.5242	−	8.65943i	−0.434198	−	0.300212i
$833$		−	14.5754i		−	0.505009i
$834$	−3.77691	+	3.77691i	−0.130784	+	0.130784i
$835$		−	16.7220i		−	0.578689i
$836$	2.93543	−	8.40220i	0.101524	−	0.290596i
$837$	−2.73971	+	2.73971i	−0.0946983	+	0.0946983i
$838$	−1.93954	−	1.93954i	−0.0670002	−	0.0670002i
$839$	25.6017	+	25.6017i	0.883868	+	0.883868i	0.993925	−	0.110057i	$-0.0351033\pi$
$839$	25.6017	+	25.6017i	0.883868	+	0.883868i	−0.110057	+	0.993925i	$0.535103\pi$
$840$	2.71902	+	2.71902i	0.0938153	+	0.0938153i
$841$	28.5051			0.982934
$842$	−10.0155			−0.345157
$843$	−2.09512	+	2.09512i	−0.0721598	+	0.0721598i
$844$	8.77646			0.302098
$845$	−26.0142	−	11.7575i	−0.894916	−	0.404469i
$846$		−	1.33681i		−	0.0459605i
$847$	−1.38097	−	12.1492i	−0.0474508	−	0.417452i
$848$	−40.2741			−1.38302
$849$	9.26268			0.317894
$850$	−0.130608	+	0.130608i	−0.00447983	+	0.00447983i
$851$	8.83998	−	8.83998i	0.303031	−	0.303031i
$852$	4.14198	+	4.14198i	0.141902	+	0.141902i
$853$	24.0360	−	24.0360i	0.822978	−	0.822978i	−0.163556	−	0.986534i	$-0.552296\pi$
$853$	24.0360	−	24.0360i	0.822978	−	0.822978i	0.986534	+	0.163556i	$0.0522963\pi$
$854$			4.90701i			0.167914i
$855$	3.21858			0.110073
$856$	−9.41180	−	9.41180i	−0.321689	−	0.321689i
$857$	29.9012			1.02141			0.510703	−	0.859757i	$-0.329385\pi$
$857$	29.9012			1.02141			0.510703	+	0.859757i	$0.329385\pi$
$858$	3.97399	−	2.89595i	0.135670	−	0.0988662i
$859$	−42.5355			−1.45129			−0.725646	−	0.688068i	$-0.758459\pi$
$859$	−42.5355			−1.45129			−0.725646	+	0.688068i	$0.758459\pi$
$860$	−27.8279	−	27.8279i	−0.948924	−	0.948924i
$861$	−11.6753			−0.397893
$862$			1.82900i			0.0622959i
$863$	5.76722	−	5.76722i	0.196319	−	0.196319i	−0.602101	−	0.798420i	$-0.705670\pi$
$863$	5.76722	−	5.76722i	0.196319	−	0.196319i	0.798420	+	0.602101i	$0.205670\pi$
$864$	3.10415	+	3.10415i	0.105605	+	0.105605i
$865$	3.66726	−	3.66726i	0.124690	−	0.124690i
$866$	−1.56078	+	1.56078i	−0.0530375	+	0.0530375i
$867$	−10.6065			−0.360215
$868$	7.88554			0.267653
$869$	22.1526	+	45.9427i	0.751477	+	1.55850i
$870$		−	0.635259i		−	0.0215373i
$871$	−8.96414	−	49.1344i	−0.303738	−	1.66486i
$872$	−9.50106			−0.321746
$873$	−3.65886	+	3.65886i	−0.123834	+	0.123834i
$874$	−3.04121			−0.102871
$875$	12.6388			0.427269
$876$	−0.214175	−	0.214175i	−0.00723629	−	0.00723629i
$877$	21.6841	+	21.6841i	0.732220	+	0.732220i	0.971059	−	0.238839i	$-0.0767668\pi$
$877$	21.6841	+	21.6841i	0.732220	+	0.732220i	−0.238839	+	0.971059i	$0.576767\pi$
$878$	−0.460985	−	0.460985i	−0.0155575	−	0.0155575i
$879$	3.44489	−	3.44489i	0.116193	−	0.116193i
$880$	−7.24022	+	20.7240i	−0.244068	+	0.698606i
$881$			50.2389i			1.69259i	0.532712	+	0.846296i	$0.321173\pi$
$881$			50.2389i			1.69259i	−0.532712	+	0.846296i	$0.678827\pi$
$882$	1.67606	−	1.67606i	0.0564359	−	0.0564359i
$883$			14.4407i			0.485968i	0.970030	+	0.242984i	$0.0781263\pi$
$883$			14.4407i			0.485968i	−0.970030	+	0.242984i	$0.921874\pi$
$884$	−13.7298	−	9.49301i	−0.461783	−	0.319284i
$885$	−8.56563			−0.287931
$886$	5.99909	+	5.99909i	0.201544	+	0.201544i
$887$			16.8328i			0.565191i	0.959239	+	0.282596i	$0.0911954\pi$
$887$			16.8328i			0.565191i	−0.959239	+	0.282596i	$0.908805\pi$
$888$	−3.90268			−0.130965
$889$	−1.57889	+	1.57889i	−0.0529543	+	0.0529543i
$890$	1.80774	+	1.80774i	0.0605957	+	0.0605957i
$891$	2.98747	−	1.44050i	0.100084	−	0.0482585i
$892$	−30.1531	−	30.1531i	−1.00960	−	1.00960i
$893$			4.76489i			0.159451i
$894$			7.87397i			0.263345i
$895$	0.0564666	+	0.0564666i	0.00188747	+	0.00188747i
$896$		−	11.6899i		−	0.390531i
$897$	14.9653	+	10.3472i	0.499676	+	0.345484i
$898$			7.30570i			0.243795i
$899$	−1.92741	−	1.92741i	−0.0642827	−	0.0642827i
$900$	0.325261			0.0108420
$901$	−33.7863			−1.12559
$902$	6.22141	+	12.9027i	0.207150	+	0.429613i
$903$	7.69355	−	7.69355i	0.256025	−	0.256025i
$904$	−1.21582	+	1.21582i	−0.0404375	+	0.0404375i
$905$	−29.9669	−	29.9669i	−0.996134	−	0.996134i
$906$	4.11895			0.136843
$907$			17.0850i			0.567297i	0.958928	+	0.283648i	$0.0915448\pi$
$907$			17.0850i			0.567297i	−0.958928	+	0.283648i	$0.908455\pi$
$908$	−22.8937	+	22.8937i	−0.759755	+	0.759755i
$909$	13.1989			0.437781
$910$	−0.649546	−	3.56031i	−0.0215323	−	0.118023i
$911$	51.4525			1.70470			0.852349	−	0.522974i	$-0.175178\pi$
$911$	51.4525			1.70470			0.852349	+	0.522974i	$0.175178\pi$
$912$	−3.12374	−	3.12374i	−0.103437	−	0.103437i
$913$	−18.3776	−	6.42047i	−0.608209	−	0.212486i
$914$		−	4.99935i		−	0.165364i
$915$	−16.6700	−	16.6700i	−0.551092	−	0.551092i
$916$	−23.5165	+	23.5165i	−0.777007	+	0.777007i
$917$	16.5340	+	16.5340i	0.546002	+	0.546002i
$918$	0.735203	+	0.735203i	0.0242653	+	0.0242653i
$919$			26.0694i			0.859949i	0.902841	+	0.429974i	$0.141477\pi$
$919$			26.0694i			0.859949i	−0.902841	+	0.429974i	$0.858523\pi$
$920$	17.4559			0.575505
$921$	−13.2434	+	13.2434i	−0.436384	+	0.436384i
$922$		−	0.966223i		−	0.0318209i
$923$	−2.07033	−	11.3479i	−0.0681457	−	0.373522i
$924$	−6.37237	−	2.22628i	−0.209636	−	0.0732392i
$925$	−0.311212	+	0.311212i	−0.0102326	+	0.0102326i
$926$		−	13.8572i		−	0.455377i
$927$			11.3192i			0.371772i
$928$	−2.18379	+	2.18379i	−0.0716865	+	0.0716865i
$929$	−28.5905	+	28.5905i	−0.938023	+	0.938023i	−0.998188	−	0.0601656i	$-0.980837\pi$
$929$	−28.5905	+	28.5905i	−0.938023	+	0.938023i	0.0601656	+	0.998188i	$0.480837\pi$
$930$	2.47393	−	2.47393i	0.0811232	−	0.0811232i
$931$	−5.97410	+	5.97410i	−0.195793	+	0.195793i
$932$		−	13.8605i		−	0.454015i
$933$		−	7.20166i		−	0.235772i
$934$	−3.45955	+	3.45955i	−0.113200	+	0.113200i
$935$	−6.07389	+	17.3856i	−0.198637	+	0.568568i
$936$	−1.01939	−	5.58749i	−0.0333197	−	0.182633i
$937$		−	58.2402i		−	1.90262i	−0.308229	−	0.951312i	$-0.599736\pi$
$937$		−	58.2402i		−	1.90262i	0.308229	−	0.951312i	$-0.400264\pi$
$938$	4.47719	−	4.47719i	0.146185	−	0.146185i
$939$	8.06822			0.263296
$940$		−	13.0712i		−	0.426335i
$941$	15.1802	+	15.1802i	0.494859	+	0.494859i	0.909833	−	0.414974i	$-0.136209\pi$
$941$	15.1802	+	15.1802i	0.494859	+	0.494859i	−0.414974	+	0.909833i	$0.636209\pi$
$942$	2.26490	+	2.26490i	0.0737945	+	0.0737945i
$943$	−37.4773	+	37.4773i	−1.22043	+	1.22043i
$944$	8.31323	+	8.31323i	0.270573	+	0.270573i
$945$		−	2.44103i		−	0.0794067i
$946$	−12.6020	−	4.40269i	−0.409727	−	0.143144i
$947$	0.210436	+	0.210436i	0.00683824	+	0.00683824i	0.710518	−	0.703679i	$-0.248461\pi$
$947$	0.210436	+	0.210436i	0.00683824	+	0.00683824i	−0.703679	+	0.710518i	$0.748461\pi$
$948$	28.1567			0.914486
$949$	0.107053	+	0.586781i	0.00347509	+	0.0190477i
$950$	0.107066			0.00347368
$951$	−18.1528	+	18.1528i	−0.588644	+	0.588644i
$952$		−	4.42760i		−	0.143499i
$953$	−43.0122			−1.39330			−0.696652	−	0.717410i	$-0.745328\pi$
$953$	−43.0122			−1.39330			−0.696652	+	0.717410i	$0.745328\pi$
$954$	−3.88516	−	3.88516i	−0.125787	−	0.125787i
$955$	−9.32055	+	9.32055i	−0.301606	+	0.301606i
$956$	−32.3367	+	32.3367i	−1.04584	+	1.04584i
$957$	1.01340	+	2.10171i	0.0327586	+	0.0679385i
$958$	−3.02347			−0.0976840
$959$	1.69960			0.0548829
$960$	6.55749	+	6.55749i	0.211642	+	0.211642i
$961$			15.9880i			0.515741i
$962$	3.02125	+	2.08894i	0.0974090	+	0.0673501i
$963$			8.44953i			0.272282i
$964$	39.8948	+	39.8948i	1.28492	+	1.28492i
$965$		−	11.9896i		−	0.385960i
$966$			2.30651i			0.0742106i
$967$	8.31042	+	8.31042i	0.267245	+	0.267245i	0.827989	−	0.560744i	$-0.189485\pi$
$967$	8.31042	+	8.31042i	0.267245	+	0.267245i	−0.560744	+	0.827989i	$0.689485\pi$
$968$	1.95703	+	17.2171i	0.0629012	+	0.553379i
$969$	−2.62054	−	2.62054i	−0.0841838	−	0.0841838i
$970$	3.30391	−	3.30391i	0.106082	−	0.106082i
$971$	16.3567			0.524911			0.262456	−	0.964944i	$-0.415468\pi$
$971$	16.3567			0.524911			0.262456	+	0.964944i	$0.415468\pi$
$972$		−	1.83092i		−	0.0587266i
$973$	−10.2101	−	10.2101i	−0.327319	−	0.327319i
$974$	13.0361			0.417703
$975$	−0.526853	−	0.364275i	−0.0168728	−	0.0116661i
$976$			32.3575i			1.03574i
$977$	−21.6303	+	21.6303i	−0.692016	+	0.692016i	−0.962675	−	0.270659i	$-0.912758\pi$
$977$	−21.6303	+	21.6303i	−0.692016	+	0.692016i	0.270659	+	0.962675i	$0.412758\pi$
$978$		−	2.19197i		−	0.0700915i
$979$	−8.86460	−	3.09697i	−0.283314	−	0.0989797i
$980$	16.3883	−	16.3883i	0.523506	−	0.523506i
$981$	4.26483	+	4.26483i	0.136166	+	0.136166i
$982$	2.89973	+	2.89973i	0.0925342	+	0.0925342i
$983$	22.0064	+	22.0064i	0.701895	+	0.701895i	0.964817	−	0.262922i	$-0.0846861\pi$
$983$	22.0064	+	22.0064i	0.701895	+	0.701895i	−0.262922	+	0.964817i	$0.584686\pi$
$984$	16.5455			0.527451
$985$	24.7952			0.790041
$986$	−0.517221	+	0.517221i	−0.0164717	+	0.0164717i
$987$	3.61377			0.115028
$988$	1.73655	+	9.51843i	0.0552471	+	0.302822i
$989$		−	49.3920i		−	1.57057i
$990$	−2.69765	+	1.30075i	−0.0857369	+	0.0413406i
$991$	26.8579			0.853171			0.426585	−	0.904447i	$-0.359716\pi$
$991$	26.8579			0.853171			0.426585	+	0.904447i	$0.359716\pi$
$992$	−17.0089			−0.540034
$993$	−10.4471	+	10.4471i	−0.331528	+	0.331528i
$994$	1.03404	−	1.03404i	0.0327977	−	0.0327977i
$995$	−28.6653	−	28.6653i	−0.908750	−	0.908750i
$996$	−7.59893	+	7.59893i	−0.240781	+	0.240781i
$997$			46.5773i			1.47512i	0.675282	+	0.737560i	$0.264022\pi$
$997$			46.5773i			1.47512i	−0.675282	+	0.737560i	$0.735978\pi$
$998$	9.68071			0.306437
$999$	1.75183	+	1.75183i	0.0554256	+	0.0554256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.m.b.109.7	✓	28
11.10	odd	2	inner	429.2.m.b.109.8	yes	28
13.8	odd	4	inner	429.2.m.b.307.8	yes	28
143.21	even	4	inner	429.2.m.b.307.7	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.m.b.109.7	✓	28	1.1	even	1	trivial
429.2.m.b.109.8	yes	28	11.10	odd	2	inner
429.2.m.b.307.7	yes	28	143.21	even	4	inner
429.2.m.b.307.8	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)

\(f(q)\)	\(=\)	\(q+(-0.290762 - 0.290762i) q^{2} +1.00000 q^{3} -1.83092i q^{4} +(1.55280 - 1.55280i) q^{5} +(-0.290762 - 0.290762i) q^{6} +(0.786011 - 0.786011i) q^{7} +(-1.11388 + 1.11388i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.290762 - 0.290762i) q^{2} +1.00000 q^{3} -1.83092i q^{4} +(1.55280 - 1.55280i) q^{5} +(-0.290762 - 0.290762i) q^{6} +(0.786011 - 0.786011i) q^{7} +(-1.11388 + 1.11388i) q^{8} +1.00000 q^{9} -0.902988 q^{10} +(2.98747 - 1.44050i) q^{11} -1.83092i q^{12} +(-2.05053 + 2.96569i) q^{13} -0.457084 q^{14} +(1.55280 - 1.55280i) q^{15} -3.01408 q^{16} -2.52854 q^{17} +(-0.290762 - 0.290762i) q^{18} +(1.03638 + 1.03638i) q^{19} +(-2.84304 - 2.84304i) q^{20} +(0.786011 - 0.786011i) q^{21} +(-1.28748 - 0.449801i) q^{22} -5.04613i q^{23} +(-1.11388 + 1.11388i) q^{24} +0.177649i q^{25} +(1.45853 - 0.266095i) q^{26} +1.00000 q^{27} +(-1.43912 - 1.43912i) q^{28} +0.703508i q^{29} -0.902988 q^{30} +(-2.73971 + 2.73971i) q^{31} +(3.10415 + 3.10415i) q^{32} +(2.98747 - 1.44050i) q^{33} +(0.735203 + 0.735203i) q^{34} -2.44103i q^{35} -1.83092i q^{36} +(1.75183 + 1.75183i) q^{37} -0.602682i q^{38} +(-2.05053 + 2.96569i) q^{39} +3.45927i q^{40} +(-7.42693 - 7.42693i) q^{41} -0.457084 q^{42} +9.78809 q^{43} +(-2.63743 - 5.46980i) q^{44} +(1.55280 - 1.55280i) q^{45} +(-1.46722 + 1.46722i) q^{46} +(2.29881 + 2.29881i) q^{47} -3.01408 q^{48} +5.76437i q^{49} +(0.0516537 - 0.0516537i) q^{50} -2.52854 q^{51} +(5.42993 + 3.75434i) q^{52} +13.3620 q^{53} +(-0.290762 - 0.290762i) q^{54} +(2.40213 - 6.87573i) q^{55} +1.75105i q^{56} +(1.03638 + 1.03638i) q^{57} +(0.204553 - 0.204553i) q^{58} +(-2.75813 - 2.75813i) q^{59} +(-2.84304 - 2.84304i) q^{60} -10.7355i q^{61} +1.59321 q^{62} +(0.786011 - 0.786011i) q^{63} +4.22302i q^{64} +(1.42107 + 7.78917i) q^{65} +(-1.28748 - 0.449801i) q^{66} +(-9.79511 + 9.79511i) q^{67} +4.62954i q^{68} -5.04613i q^{69} +(-0.709759 + 0.709759i) q^{70} +(-2.26225 + 2.26225i) q^{71} +(-1.11388 + 1.11388i) q^{72} +(0.116977 - 0.116977i) q^{73} -1.01873i q^{74} +0.177649i q^{75} +(1.89753 - 1.89753i) q^{76} +(1.21594 - 3.48043i) q^{77} +(1.45853 - 0.266095i) q^{78} +15.3785i q^{79} +(-4.68025 + 4.68025i) q^{80} +1.00000 q^{81} +4.31894i q^{82} +(-4.15034 - 4.15034i) q^{83} +(-1.43912 - 1.43912i) q^{84} +(-3.92631 + 3.92631i) q^{85} +(-2.84601 - 2.84601i) q^{86} +0.703508i q^{87} +(-1.72315 + 4.93224i) q^{88} +(-2.00196 - 2.00196i) q^{89} -0.902988 q^{90} +(0.719330 + 3.94281i) q^{91} -9.23904 q^{92} +(-2.73971 + 2.73971i) q^{93} -1.33681i q^{94} +3.21858 q^{95} +(3.10415 + 3.10415i) q^{96} +(-3.65886 + 3.65886i) q^{97} +(1.67606 - 1.67606i) q^{98} +(2.98747 - 1.44050i) 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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Representations

Groups

Database

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