LMFDB - Embedded newform 123.2.e.a.91.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [123,2,Mod(73,123)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(123, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("123.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 123 = 3 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	123.e (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:	$0.982159944862$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} + 92x^{8} + 236x^{6} + 260x^{4} + 88x^{2} + 4 $ x^12 + 16x^10 + 92x^8 + 236x^6 + 260x^4 + 88*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			91.5
Root			$1.47985i$ of defining polynomial
Character	$\chi$	$=$	123.91
Dual form			123.2.e.a.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.47985i q^{2} +(0.707107 + 0.707107i) q^{3} -0.189944 q^{4} -1.46738i q^{5} +(-1.04641 + 1.04641i) q^{6} +(1.37066 + 1.37066i) q^{7} +2.67860i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.47985i q^{2} +(0.707107 + 0.707107i) q^{3} -0.189944 q^{4} -1.46738i q^{5} +(-1.04641 + 1.04641i) q^{6} +(1.37066 + 1.37066i) q^{7} +2.67860i q^{8} +1.00000i q^{9} +2.17150 q^{10} +(-4.55762 - 4.55762i) q^{11} +(-0.134310 - 0.134310i) q^{12} +(-1.32631 - 1.32631i) q^{13} +(-2.02837 + 2.02837i) q^{14} +(1.03759 - 1.03759i) q^{15} -4.34381 q^{16} +(-2.21208 + 2.21208i) q^{17} -1.47985 q^{18} +(3.06173 - 3.06173i) q^{19} +0.278719i q^{20} +1.93841i q^{21} +(6.74457 - 6.74457i) q^{22} +6.29636 q^{23} +(-1.89406 + 1.89406i) q^{24} +2.84680 q^{25} +(1.96274 - 1.96274i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.260349 - 0.260349i) q^{28} +(-3.32332 - 3.32332i) q^{29} +(1.53548 + 1.53548i) q^{30} -0.616624 q^{31} -1.07096i q^{32} -6.44544i q^{33} +(-3.27354 - 3.27354i) q^{34} +(2.01128 - 2.01128i) q^{35} -0.189944i q^{36} -10.2743 q^{37} +(4.53089 + 4.53089i) q^{38} -1.87569i q^{39} +3.93053 q^{40} +(2.23089 + 6.00193i) q^{41} -2.86855 q^{42} -2.62011i q^{43} +(0.865690 + 0.865690i) q^{44} +1.46738 q^{45} +9.31764i q^{46} +(2.93034 - 2.93034i) q^{47} +(-3.07154 - 3.07154i) q^{48} -3.24257i q^{49} +4.21282i q^{50} -3.12835 q^{51} +(0.251924 + 0.251924i) q^{52} +(2.78161 + 2.78161i) q^{53} +(-1.04641 - 1.04641i) q^{54} +(-6.68775 + 6.68775i) q^{55} +(-3.67146 + 3.67146i) q^{56} +4.32995 q^{57} +(4.91800 - 4.91800i) q^{58} -4.81080 q^{59} +(-0.197084 + 0.197084i) q^{60} +11.5896i q^{61} -0.912508i q^{62} +(-1.37066 + 1.37066i) q^{63} -7.10276 q^{64} +(-1.94620 + 1.94620i) q^{65} +9.53826 q^{66} +(-2.29029 + 2.29029i) q^{67} +(0.420170 - 0.420170i) q^{68} +(4.45220 + 4.45220i) q^{69} +(2.97639 + 2.97639i) q^{70} +(-1.46784 - 1.46784i) q^{71} -2.67860 q^{72} +14.4189i q^{73} -15.2043i q^{74} +(2.01299 + 2.01299i) q^{75} +(-0.581557 + 0.581557i) q^{76} -12.4939i q^{77} +2.77573 q^{78} +(-0.809869 - 0.809869i) q^{79} +6.37402i q^{80} -1.00000 q^{81} +(-8.88192 + 3.30138i) q^{82} -7.47123 q^{83} -0.368188i q^{84} +(3.24596 + 3.24596i) q^{85} +3.87736 q^{86} -4.69989i q^{87} +(12.2080 - 12.2080i) q^{88} +(7.27368 + 7.27368i) q^{89} +2.17150i q^{90} -3.63585i q^{91} -1.19595 q^{92} +(-0.436019 - 0.436019i) q^{93} +(4.33645 + 4.33645i) q^{94} +(-4.49272 - 4.49272i) q^{95} +(0.757282 - 0.757282i) q^{96} +(-2.25412 + 2.25412i) q^{97} +4.79850 q^{98} +(4.55762 - 4.55762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{4}+O(q^{10}) $ 12 * q - 8 * q^4	$ 12 q - 8 q^{4} - 24 q^{10} - 12 q^{11} + 8 q^{12} + 4 q^{13} + 20 q^{14} - 4 q^{15} + 8 q^{17} + 4 q^{19} + 12 q^{22} - 8 q^{23} + 12 q^{24} - 28 q^{25} - 20 q^{26} - 44 q^{28} + 12 q^{29} + 16 q^{30} + 12 q^{31} + 8 q^{34} + 36 q^{35} + 4 q^{37} + 20 q^{38} + 56 q^{40} - 20 q^{41} - 32 q^{42} + 20 q^{44} + 8 q^{45} - 40 q^{47} - 16 q^{48} - 12 q^{51} + 20 q^{52} - 12 q^{53} - 16 q^{55} - 40 q^{56} - 24 q^{57} + 36 q^{58} - 16 q^{59} - 4 q^{60} - 8 q^{64} + 4 q^{65} + 16 q^{66} + 16 q^{67} + 4 q^{68} - 36 q^{70} + 8 q^{71} - 24 q^{72} + 40 q^{75} - 52 q^{76} + 56 q^{78} - 12 q^{81} - 20 q^{82} + 40 q^{83} + 36 q^{85} + 48 q^{86} + 36 q^{88} - 24 q^{89} - 72 q^{92} - 8 q^{93} - 16 q^{94} + 28 q^{95} - 24 q^{96} + 40 q^{97} + 80 q^{98} + 12 q^{99}+O(q^{100}) $ 12 * q - 8 * q^4 - 24 * q^10 - 12 * q^11 + 8 * q^12 + 4 * q^13 + 20 * q^14 - 4 * q^15 + 8 * q^17 + 4 * q^19 + 12 * q^22 - 8 * q^23 + 12 * q^24 - 28 * q^25 - 20 * q^26 - 44 * q^28 + 12 * q^29 + 16 * q^30 + 12 * q^31 + 8 * q^34 + 36 * q^35 + 4 * q^37 + 20 * q^38 + 56 * q^40 - 20 * q^41 - 32 * q^42 + 20 * q^44 + 8 * q^45 - 40 * q^47 - 16 * q^48 - 12 * q^51 + 20 * q^52 - 12 * q^53 - 16 * q^55 - 40 * q^56 - 24 * q^57 + 36 * q^58 - 16 * q^59 - 4 * q^60 - 8 * q^64 + 4 * q^65 + 16 * q^66 + 16 * q^67 + 4 * q^68 - 36 * q^70 + 8 * q^71 - 24 * q^72 + 40 * q^75 - 52 * q^76 + 56 * q^78 - 12 * q^81 - 20 * q^82 + 40 * q^83 + 36 * q^85 + 48 * q^86 + 36 * q^88 - 24 * q^89 - 72 * q^92 - 8 * q^93 - 16 * q^94 + 28 * q^95 - 24 * q^96 + 40 * q^97 + 80 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/123\mathbb{Z}\right)^\times$.

$n$	$83$	$88$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$			1.47985i			1.04641i	0.852207	+	0.523204i	$0.175264\pi$
$2$			1.47985i			1.04641i	−0.852207	+	0.523204i	$0.824736\pi$
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−0.189944			−0.0949718
$5$		−	1.46738i		−	0.656232i	−0.944637	−	0.328116i	$-0.893586\pi$
$5$		−	1.46738i		−	0.656232i	0.944637	−	0.328116i	$-0.106414\pi$
$6$	−1.04641	+	1.04641i	−0.427195	+	0.427195i
$7$	1.37066	+	1.37066i	0.518062	+	0.518062i	0.916985	−	0.398923i	$-0.130616\pi$
$7$	1.37066	+	1.37066i	0.518062	+	0.518062i	−0.398923	+	0.916985i	$0.630616\pi$
$8$			2.67860i			0.947030i
$9$			1.00000i			0.333333i
$10$	2.17150			0.686687
$11$	−4.55762	−	4.55762i	−1.37417	−	1.37417i	−0.854156	−	0.520017i	$-0.825926\pi$
$11$	−4.55762	−	4.55762i	−1.37417	−	1.37417i	−0.520017	−	0.854156i	$-0.674074\pi$
$12$	−0.134310	−	0.134310i	−0.0387721	−	0.0387721i
$13$	−1.32631	−	1.32631i	−0.367853	−	0.367853i	0.498841	−	0.866694i	$-0.333759\pi$
$13$	−1.32631	−	1.32631i	−0.367853	−	0.367853i	−0.866694	+	0.498841i	$0.833759\pi$
$14$	−2.02837	+	2.02837i	−0.542105	+	0.542105i
$15$	1.03759	−	1.03759i	0.267906	−	0.267906i
$16$	−4.34381			−1.08595
$17$	−2.21208	+	2.21208i	−0.536508	+	0.536508i	−0.922502	−	0.385993i	$-0.873859\pi$
$17$	−2.21208	+	2.21208i	−0.536508	+	0.536508i	0.385993	+	0.922502i	$0.373859\pi$
$18$	−1.47985			−0.348803
$19$	3.06173	−	3.06173i	0.702410	−	0.702410i	−0.262517	−	0.964927i	$-0.584553\pi$
$19$	3.06173	−	3.06173i	0.702410	−	0.702410i	0.964927	+	0.262517i	$0.0845527\pi$
$20$			0.278719i			0.0623235i
$21$			1.93841i			0.422996i
$22$	6.74457	−	6.74457i	1.43795	−	1.43795i
$23$	6.29636			1.31288			0.656441	−	0.754378i	$-0.272061\pi$
$23$	6.29636			1.31288			0.656441	+	0.754378i	$0.272061\pi$
$24$	−1.89406	+	1.89406i	−0.386623	+	0.386623i
$25$	2.84680			0.569360
$26$	1.96274	−	1.96274i	0.384924	−	0.384924i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−0.260349	−	0.260349i	−0.0492013	−	0.0492013i
$29$	−3.32332	−	3.32332i	−0.617125	−	0.617125i	0.327668	−	0.944793i	$-0.393737\pi$
$29$	−3.32332	−	3.32332i	−0.617125	−	0.617125i	−0.944793	+	0.327668i	$0.893737\pi$
$30$	1.53548	+	1.53548i	0.280339	+	0.280339i
$31$	−0.616624			−0.110749			−0.0553744	−	0.998466i	$-0.517635\pi$
$31$	−0.616624			−0.110749			−0.0553744	+	0.998466i	$0.517635\pi$
$32$		−	1.07096i		−	0.189320i
$33$		−	6.44544i		−	1.12201i
$34$	−3.27354	−	3.27354i	−0.561407	−	0.561407i
$35$	2.01128	−	2.01128i	0.339969	−	0.339969i
$36$		−	0.189944i		−	0.0316573i
$37$	−10.2743			−1.68908			−0.844539	−	0.535494i	$-0.820125\pi$
$37$	−10.2743			−1.68908			−0.844539	+	0.535494i	$0.820125\pi$
$38$	4.53089	+	4.53089i	0.735008	+	0.735008i
$39$		−	1.87569i		−	0.300351i
$40$	3.93053			0.621471
$41$	2.23089	+	6.00193i	0.348407	+	0.937343i
$41$	2.23089	+	6.00193i	0.348407	+	0.937343i
$42$	−2.86855			−0.442627
$43$		−	2.62011i		−	0.399563i	−0.979840	−	0.199782i	$-0.935977\pi$
$43$		−	2.62011i		−	0.399563i	0.979840	−	0.199782i	$-0.0640233\pi$
$44$	0.865690	+	0.865690i	0.130508	+	0.130508i
$45$	1.46738			0.218744
$46$			9.31764i			1.37381i
$47$	2.93034	−	2.93034i	0.427434	−	0.427434i	−0.460320	−	0.887753i	$-0.652265\pi$
$47$	2.93034	−	2.93034i	0.427434	−	0.427434i	0.887753	+	0.460320i	$0.152265\pi$
$48$	−3.07154	−	3.07154i	−0.443338	−	0.443338i
$49$		−	3.24257i		−	0.463224i
$50$			4.21282i			0.595783i
$51$	−3.12835			−0.438057
$52$	0.251924	+	0.251924i	0.0349356	+	0.0349356i
$53$	2.78161	+	2.78161i	0.382083	+	0.382083i	0.871852	−	0.489769i	$-0.162919\pi$
$53$	2.78161	+	2.78161i	0.382083	+	0.382083i	−0.489769	+	0.871852i	$0.662919\pi$
$54$	−1.04641	−	1.04641i	−0.142398	−	0.142398i
$55$	−6.68775	+	6.68775i	−0.901776	+	0.901776i
$56$	−3.67146	+	3.67146i	−0.490620	+	0.490620i
$57$	4.32995			0.573515
$58$	4.91800	−	4.91800i	0.645765	−	0.645765i
$59$	−4.81080			−0.626312			−0.313156	−	0.949702i	$-0.601386\pi$
$59$	−4.81080			−0.626312			−0.313156	+	0.949702i	$0.601386\pi$
$60$	−0.197084	+	0.197084i	−0.0254435	+	0.0254435i
$61$			11.5896i			1.48390i	0.670455	+	0.741951i	$0.266099\pi$
$61$			11.5896i			1.48390i	−0.670455	+	0.741951i	$0.733901\pi$
$62$		−	0.912508i		−	0.115889i
$63$	−1.37066	+	1.37066i	−0.172687	+	0.172687i
$64$	−7.10276			−0.887846
$65$	−1.94620	+	1.94620i	−0.241397	+	0.241397i
$66$	9.53826			1.17408
$67$	−2.29029	+	2.29029i	−0.279804	+	0.279804i	−0.833031	−	0.553227i	$-0.813396\pi$
$67$	−2.29029	+	2.29029i	−0.279804	+	0.279804i	0.553227	+	0.833031i	$0.313396\pi$
$68$	0.420170	−	0.420170i	0.0509531	−	0.0509531i
$69$	4.45220	+	4.45220i	0.535982	+	0.535982i
$70$	2.97639	+	2.97639i	0.355746	+	0.355746i
$71$	−1.46784	−	1.46784i	−0.174201	−	0.174201i	0.614621	−	0.788822i	$-0.289309\pi$
$71$	−1.46784	−	1.46784i	−0.174201	−	0.174201i	−0.788822	+	0.614621i	$0.789309\pi$
$72$	−2.67860			−0.315677
$73$			14.4189i			1.68760i	0.536656	+	0.843801i	$0.319687\pi$
$73$			14.4189i			1.68760i	−0.536656	+	0.843801i	$0.680313\pi$
$74$		−	15.2043i		−	1.76747i
$75$	2.01299	+	2.01299i	0.232440	+	0.232440i
$76$	−0.581557	+	0.581557i	−0.0667091	+	0.0667091i
$77$		−	12.4939i		−	1.42381i
$78$	2.77573			0.314290
$79$	−0.809869	−	0.809869i	−0.0911174	−	0.0911174i	0.660079	−	0.751196i	$-0.270523\pi$
$79$	−0.809869	−	0.809869i	−0.0911174	−	0.0911174i	−0.751196	+	0.660079i	$0.770523\pi$
$80$			6.37402i			0.712637i
$81$	−1.00000			−0.111111
$82$	−8.88192	+	3.30138i	−0.980844	+	0.364576i
$83$	−7.47123			−0.820074			−0.410037	−	0.912069i	$-0.634484\pi$
$83$	−7.47123			−0.820074			−0.410037	+	0.912069i	$0.634484\pi$
$84$		−	0.368188i		−	0.0401727i
$85$	3.24596	+	3.24596i	0.352074	+	0.352074i
$86$	3.87736			0.418107
$87$		−	4.69989i		−	0.503881i
$88$	12.2080	−	12.2080i	1.30138	−	1.30138i
$89$	7.27368	+	7.27368i	0.771009	+	0.771009i	0.978283	−	0.207274i	$-0.0664592\pi$
$89$	7.27368	+	7.27368i	0.771009	+	0.771009i	−0.207274	+	0.978283i	$0.566459\pi$
$90$			2.17150i			0.228896i
$91$		−	3.63585i		−	0.381141i
$92$	−1.19595			−0.124687
$93$	−0.436019	−	0.436019i	−0.0452130	−	0.0452130i
$94$	4.33645	+	4.33645i	0.447270	+	0.447270i
$95$	−4.49272	−	4.49272i	−0.460944	−	0.460944i
$96$	0.757282	−	0.757282i	0.0772897	−	0.0772897i
$97$	−2.25412	+	2.25412i	−0.228871	+	0.228871i	−0.812221	−	0.583350i	$-0.801742\pi$
$97$	−2.25412	+	2.25412i	−0.228871	+	0.228871i	0.583350	+	0.812221i	$0.301742\pi$
$98$	4.79850			0.484722
$99$	4.55762	−	4.55762i	0.458058	−	0.458058i
$100$	−0.540731			−0.0540731
$101$	−1.03177	+	1.03177i	−0.102665	+	0.102665i	−0.756574	−	0.653909i	$-0.773128\pi$
$101$	−1.03177	+	1.03177i	−0.102665	+	0.102665i	0.653909	+	0.756574i	$0.273128\pi$
$102$		−	4.62948i		−	0.458387i
$103$		−	14.1269i		−	1.39196i	−0.718060	−	0.695981i	$-0.754970\pi$
$103$		−	14.1269i		−	1.39196i	0.718060	−	0.695981i	$-0.245030\pi$
$104$	3.55267	−	3.55267i	0.348368	−	0.348368i
$105$	2.84438			0.277583
$106$	−4.11635	+	4.11635i	−0.399815	+	0.399815i
$107$	17.6306			1.70442			0.852208	−	0.523204i	$-0.175263\pi$
$107$	17.6306			1.70442			0.852208	+	0.523204i	$0.175263\pi$
$108$	0.134310	−	0.134310i	0.0129240	−	0.0129240i
$109$	−2.82849	+	2.82849i	−0.270920	+	0.270920i	−0.829470	−	0.558551i	$-0.811358\pi$
$109$	−2.82849	+	2.82849i	−0.270920	+	0.270920i	0.558551	+	0.829470i	$0.311358\pi$
$110$	−9.89684	−	9.89684i	−0.943627	−	0.943627i
$111$	−7.26500	−	7.26500i	−0.689563	−	0.689563i
$112$	−5.95390	−	5.95390i	−0.562590	−	0.562590i
$113$	0.462477			0.0435062			0.0217531	−	0.999763i	$-0.493075\pi$
$113$	0.462477			0.0435062			0.0217531	+	0.999763i	$0.493075\pi$
$114$			6.40765i			0.600132i
$115$		−	9.23915i		−	0.861555i
$116$	0.631243	+	0.631243i	0.0586095	+	0.0586095i
$117$	1.32631	−	1.32631i	0.122618	−	0.122618i
$118$		−	7.11924i		−	0.655379i
$119$	−6.06403			−0.555889
$120$	2.77930	+	2.77930i	0.253715	+	0.253715i
$121$			30.5437i			2.77670i
$122$	−17.1509			−1.55277
$123$	−2.66652	+	5.82148i	−0.240432	+	0.524905i
$124$	0.117124			0.0105180
$125$		−	11.5142i		−	1.02986i
$126$	−2.02837	−	2.02837i	−0.180702	−	0.180702i
$127$	4.79628			0.425601			0.212801	−	0.977096i	$-0.431742\pi$
$127$	4.79628			0.425601			0.212801	+	0.977096i	$0.431742\pi$
$128$		−	12.6529i		−	1.11837i
$129$	1.85270	−	1.85270i	0.163121	−	0.163121i
$130$	−2.88008	−	2.88008i	−0.252600	−	0.252600i
$131$			19.1667i			1.67460i	0.546742	+	0.837301i	$0.315868\pi$
$131$			19.1667i			1.67460i	−0.546742	+	0.837301i	$0.684132\pi$
$132$			1.22427i			0.106559i
$133$	8.39321			0.727784
$134$	−3.38928	−	3.38928i	−0.292789	−	0.292789i
$135$	1.03759	+	1.03759i	0.0893019	+	0.0893019i
$136$	−5.92529	−	5.92529i	−0.508089	−	0.508089i
$137$	6.99304	−	6.99304i	0.597455	−	0.597455i	−0.342179	−	0.939635i	$-0.611165\pi$
$137$	6.99304	−	6.99304i	0.597455	−	0.597455i	0.939635	+	0.342179i	$0.111165\pi$
$138$	−6.58857	+	6.58857i	−0.560856	+	0.560856i
$139$	−1.87886			−0.159363			−0.0796816	−	0.996820i	$-0.525390\pi$
$139$	−1.87886			−0.159363			−0.0796816	+	0.996820i	$0.525390\pi$
$140$	−0.382030	+	0.382030i	−0.0322874	+	0.0322874i
$141$	4.14412			0.348998
$142$	2.17218	−	2.17218i	0.182285	−	0.182285i
$143$			12.0896i			1.01099i
$144$		−	4.34381i		−	0.361984i
$145$	−4.87657	+	4.87657i	−0.404977	+	0.404977i
$146$	−21.3377			−1.76592
$147$	2.29284	−	2.29284i	0.189110	−	0.189110i
$148$	1.95153			0.160415
$149$	8.37391	−	8.37391i	0.686017	−	0.686017i	−0.275332	−	0.961349i	$-0.588788\pi$
$149$	8.37391	−	8.37391i	0.686017	−	0.686017i	0.961349	+	0.275332i	$0.0887878\pi$
$150$	−2.97891	+	2.97891i	−0.243227	+	0.243227i
$151$	−14.2607	−	14.2607i	−1.16052	−	1.16052i	−0.984363	−	0.176154i	$-0.943634\pi$
$151$	−14.2607	−	14.2607i	−1.16052	−	1.16052i	−0.176154	−	0.984363i	$-0.556366\pi$
$152$	8.20117	+	8.20117i	0.665203	+	0.665203i
$153$	−2.21208	−	2.21208i	−0.178836	−	0.178836i
$154$	18.4891			1.48989
$155$			0.904821i			0.0726769i
$156$			0.356275i			0.0285248i
$157$	−9.35694	−	9.35694i	−0.746765	−	0.746765i	0.227105	−	0.973870i	$-0.427074\pi$
$157$	−9.35694	−	9.35694i	−0.746765	−	0.746765i	−0.973870	+	0.227105i	$0.927074\pi$
$158$	1.19848	−	1.19848i	0.0953460	−	0.0953460i
$159$			3.93379i			0.311970i
$160$	−1.57150			−0.124238
$161$	8.63019	+	8.63019i	0.680154	+	0.680154i
$162$		−	1.47985i		−	0.116268i
$163$	20.1607			1.57911			0.789553	−	0.613682i	$-0.210312\pi$
$163$	20.1607			1.57911			0.789553	+	0.613682i	$0.210312\pi$
$164$	−0.423744	−	1.14003i	−0.0330888	−	0.0890212i
$165$	−9.45791			−0.736297
$166$		−	11.0563i		−	0.858133i
$167$	3.00014	+	3.00014i	0.232157	+	0.232157i	0.813593	−	0.581435i	$-0.197509\pi$
$167$	3.00014	+	3.00014i	0.232157	+	0.232157i	−0.581435	+	0.813593i	$0.697509\pi$
$168$	−5.19223			−0.400590
$169$		−	9.48179i		−	0.729369i
$170$	−4.80352	+	4.80352i	−0.368413	+	0.368413i
$171$	3.06173	+	3.06173i	0.234137	+	0.234137i
$172$			0.497674i			0.0379473i
$173$			17.6687i			1.34332i	0.740858	+	0.671662i	$0.234419\pi$
$173$			17.6687i			1.34332i	−0.740858	+	0.671662i	$0.765581\pi$
$174$	6.95511			0.527265
$175$	3.90200	+	3.90200i	0.294963	+	0.294963i
$176$	19.7974	+	19.7974i	1.49229	+	1.49229i
$177$	−3.40175	−	3.40175i	−0.255691	−	0.255691i
$178$	−10.7639	+	10.7639i	−0.806790	+	0.806790i
$179$	−7.98389	+	7.98389i	−0.596744	+	0.596744i	−0.939445	−	0.342701i	$-0.888658\pi$
$179$	−7.98389	+	7.98389i	−0.596744	+	0.596744i	0.342701	+	0.939445i	$0.388658\pi$
$180$	−0.278719			−0.0207745
$181$	−3.52280	+	3.52280i	−0.261848	+	0.261848i	−0.825804	−	0.563957i	$-0.809278\pi$
$181$	−3.52280	+	3.52280i	−0.261848	+	0.261848i	0.563957	+	0.825804i	$0.309278\pi$
$182$	5.38050			0.398829
$183$	−8.19511	+	8.19511i	−0.605800	+	0.605800i
$184$			16.8655i			1.24334i
$185$			15.0762i			1.10843i
$186$	0.645240	−	0.645240i	0.0473113	−	0.0473113i
$187$	20.1636			1.47451
$188$	−0.556599	+	0.556599i	−0.0405941	+	0.0405941i
$189$	−1.93841			−0.140999
$190$	6.64854	−	6.64854i	0.482336	−	0.482336i
$191$	7.04986	−	7.04986i	0.510110	−	0.510110i	−0.404450	−	0.914560i	$-0.632537\pi$
$191$	7.04986	−	7.04986i	0.510110	−	0.510110i	0.914560	+	0.404450i	$0.132537\pi$
$192$	−5.02241	−	5.02241i	−0.362461	−	0.362461i
$193$	−10.4258	−	10.4258i	−0.750464	−	0.750464i	0.224102	−	0.974566i	$-0.428055\pi$
$193$	−10.4258	−	10.4258i	−0.750464	−	0.750464i	−0.974566	+	0.224102i	$0.928055\pi$
$194$	−3.33575	−	3.33575i	−0.239493	−	0.239493i
$195$	−2.75235			−0.197100
$196$			0.615905i			0.0439932i
$197$		−	7.35165i		−	0.523783i	−0.965097	−	0.261892i	$-0.915654\pi$
$197$		−	7.35165i		−	0.523783i	0.965097	−	0.261892i	$-0.0843463\pi$
$198$	6.74457	+	6.74457i	0.479316	+	0.479316i
$199$	17.4004	−	17.4004i	1.23348	−	1.23348i	0.270866	−	0.962617i	$-0.412690\pi$
$199$	17.4004	−	17.4004i	1.23348	−	1.23348i	0.962617	−	0.270866i	$-0.0873099\pi$
$200$			7.62545i			0.539200i
$201$	−3.23896			−0.228459
$202$	−1.52686	−	1.52686i	−0.107430	−	0.107430i
$203$		−	9.11031i		−	0.639418i
$204$	0.594211			0.0416031
$205$	8.80710	−	3.27357i	0.615115	−	0.228636i
$206$	20.9056			1.45656
$207$			6.29636i			0.437627i
$208$	5.76125	+	5.76125i	0.399471	+	0.399471i
$209$	−27.9084			−1.93047
$210$			4.20925i			0.290466i
$211$	−2.20494	+	2.20494i	−0.151794	+	0.151794i	−0.778919	−	0.627125i	$-0.784232\pi$
$211$	−2.20494	+	2.20494i	−0.151794	+	0.151794i	0.627125	+	0.778919i	$0.284232\pi$
$212$	−0.528349	−	0.528349i	−0.0362871	−	0.0362871i
$213$		−	2.07584i		−	0.142234i
$214$			26.0906i			1.78352i
$215$	−3.84470			−0.262206
$216$	−1.89406	−	1.89406i	−0.128874	−	0.128874i
$217$	−0.845183	−	0.845183i	−0.0573748	−	0.0573748i
$218$	−4.18572	−	4.18572i	−0.283493	−	0.283493i
$219$	−10.1957	+	10.1957i	−0.688961	+	0.688961i
$220$	1.27030	−	1.27030i	0.0856433	−	0.0856433i
$221$	5.86782			0.394712
$222$	10.7511	−	10.7511i	0.721565	−	0.721565i
$223$	−24.2193			−1.62185			−0.810923	−	0.585153i	$-0.801034\pi$
$223$	−24.2193			−1.62185			−0.810923	+	0.585153i	$0.801034\pi$
$224$	1.46792	−	1.46792i	0.0980797	−	0.0980797i
$225$			2.84680i			0.189787i
$226$			0.684395i			0.0455253i
$227$	2.19179	−	2.19179i	0.145475	−	0.145475i	−0.630618	−	0.776093i	$-0.717199\pi$
$227$	2.19179	−	2.19179i	0.145475	−	0.145475i	0.776093	+	0.630618i	$0.217199\pi$
$228$	−0.822445			−0.0544678
$229$	4.55514	−	4.55514i	0.301012	−	0.301012i	−0.540398	−	0.841410i	$-0.681726\pi$
$229$	4.55514	−	4.55514i	0.301012	−	0.301012i	0.841410	+	0.540398i	$0.181726\pi$
$230$	13.6725			0.901539
$231$	8.83453	−	8.83453i	0.581269	−	0.581269i
$232$	8.90186	−	8.90186i	0.584436	−	0.584436i
$233$	10.5546	+	10.5546i	0.691455	+	0.691455i	0.962552	−	0.271097i	$-0.0873864\pi$
$233$	10.5546	+	10.5546i	0.691455	+	0.691455i	−0.271097	+	0.962552i	$0.587386\pi$
$234$	1.96274	+	1.96274i	0.128308	+	0.128308i
$235$	−4.29992	−	4.29992i	−0.280496	−	0.280496i
$236$	0.913780			0.0594820
$237$		−	1.14533i		−	0.0743970i
$238$		−	8.97383i		−	0.581687i
$239$	−20.5206	−	20.5206i	−1.32736	−	1.32736i	−0.907662	−	0.419702i	$-0.862134\pi$
$239$	−20.5206	−	20.5206i	−1.32736	−	1.32736i	−0.419702	−	0.907662i	$-0.637866\pi$
$240$	−4.50711	+	4.50711i	−0.290933	+	0.290933i
$241$			14.4248i			0.929182i	0.885525	+	0.464591i	$0.153799\pi$
$241$			14.4248i			0.929182i	−0.885525	+	0.464591i	$0.846201\pi$
$242$	−45.2000			−2.90557
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		−	2.20138i		−	0.140929i
$245$	−4.75808			−0.303982
$246$	−8.61490	−	3.94604i	−0.549266	−	0.251590i
$247$	−8.12163			−0.516767
$248$		−	1.65169i		−	0.104882i
$249$	−5.28296	−	5.28296i	−0.334794	−	0.334794i
$250$	17.0393			1.07766
$251$			4.27434i			0.269794i	0.990860	+	0.134897i	$0.0430703\pi$
$251$			4.27434i			0.269794i	−0.990860	+	0.134897i	$0.956930\pi$
$252$	0.260349	−	0.260349i	0.0164004	−	0.0164004i
$253$	−28.6964	−	28.6964i	−1.80413	−	1.80413i
$254$			7.09776i			0.445353i
$255$			4.59048i			0.287467i
$256$	4.51883			0.282427
$257$	−10.0037	−	10.0037i	−0.624011	−	0.624011i	0.322544	−	0.946555i	$-0.395462\pi$
$257$	−10.0037	−	10.0037i	−0.624011	−	0.624011i	−0.946555	+	0.322544i	$0.895462\pi$
$258$	2.74171	+	2.74171i	0.170691	+	0.170691i
$259$	−14.0825	−	14.0825i	−0.875047	−	0.875047i
$260$	0.369669	−	0.369669i	0.0229259	−	0.0229259i
$261$	3.32332	−	3.32332i	0.205708	−	0.205708i
$262$	−28.3637			−1.75232
$263$	7.55483	−	7.55483i	0.465851	−	0.465851i	−0.434717	−	0.900567i	$-0.643151\pi$
$263$	7.55483	−	7.55483i	0.465851	−	0.465851i	0.900567	+	0.434717i	$0.143151\pi$
$264$	17.2648			1.06257
$265$	4.08168	−	4.08168i	0.250735	−	0.250735i
$266$			12.4207i			0.761559i
$267$			10.2865i			0.629526i
$268$	0.435026	−	0.435026i	0.0265735	−	0.0265735i
$269$	2.47737			0.151048			0.0755241	−	0.997144i	$-0.475937\pi$
$269$	2.47737			0.151048			0.0755241	+	0.997144i	$0.475937\pi$
$270$	−1.53548	+	1.53548i	−0.0934463	+	0.0934463i
$271$	18.1173			1.10055			0.550273	−	0.834985i	$-0.314524\pi$
$271$	18.1173			1.10055			0.550273	+	0.834985i	$0.314524\pi$
$272$	9.60885	−	9.60885i	0.582622	−	0.582622i
$273$	2.57094	−	2.57094i	0.155600	−	0.155600i
$274$	10.3486	+	10.3486i	0.625183	+	0.625183i
$275$	−12.9746	−	12.9746i	−0.782398	−	0.782398i
$276$	−0.845666	−	0.845666i	−0.0509031	−	0.0509031i
$277$	19.8816			1.19457			0.597284	−	0.802030i	$-0.296247\pi$
$277$	19.8816			1.19457			0.597284	+	0.802030i	$0.296247\pi$
$278$		−	2.78043i		−	0.166759i
$279$		−	0.616624i		−	0.0369163i
$280$	5.38743	+	5.38743i	0.321961	+	0.321961i
$281$	20.5646	−	20.5646i	1.22678	−	1.22678i	0.261610	−	0.965174i	$-0.415746\pi$
$281$	20.5646	−	20.5646i	1.22678	−	1.22678i	0.965174	−	0.261610i	$-0.0842536\pi$
$282$			6.13266i			0.365195i
$283$	29.3573			1.74511			0.872554	−	0.488518i	$-0.162462\pi$
$283$	29.3573			1.74511			0.872554	+	0.488518i	$0.162462\pi$
$284$	0.278807	+	0.278807i	0.0165442	+	0.0165442i
$285$		−	6.35367i		−	0.376359i
$286$	−17.8908			−1.05791
$287$	−5.16881	+	11.2844i	−0.305105	+	0.666098i
$288$	1.07096			0.0631068
$289$			7.21340i			0.424318i
$290$	−7.21658	−	7.21658i	−0.423772	−	0.423772i
$291$	−3.18781			−0.186873
$292$		−	2.73877i		−	0.160275i
$293$	−12.0274	+	12.0274i	−0.702647	+	0.702647i	−0.964978	−	0.262331i	$-0.915509\pi$
$293$	−12.0274	+	12.0274i	−0.702647	+	0.702647i	0.262331	+	0.964978i	$0.415509\pi$
$294$	3.39305	+	3.39305i	0.197887	+	0.197887i
$295$			7.05926i			0.411006i
$296$		−	27.5207i		−	1.59961i
$297$	6.44544			0.374002
$298$	12.3921	+	12.3921i	0.717854	+	0.717854i
$299$	−8.35094	−	8.35094i	−0.482947	−	0.482947i
$300$	−0.382354	−	0.382354i	−0.0220752	−	0.0220752i
$301$	3.59129	−	3.59129i	0.206999	−	0.206999i
$302$	21.1036	−	21.1036i	1.21438	−	1.21438i
$303$	−1.45914			−0.0838256
$304$	−13.2996	+	13.2996i	−0.762784	+	0.762784i
$305$	17.0064			0.973783
$306$	3.27354	−	3.27354i	0.187136	−	0.187136i
$307$		−	12.1713i		−	0.694651i	−0.937745	−	0.347326i	$-0.887090\pi$
$307$		−	12.1713i		−	0.694651i	0.937745	−	0.347326i	$-0.112910\pi$
$308$			2.37314i			0.135222i
$309$	9.98921	−	9.98921i	0.568266	−	0.568266i
$310$	−1.33900			−0.0760498
$311$	−1.44086	+	1.44086i	−0.0817035	+	0.0817035i	−0.746777	−	0.665074i	$-0.768400\pi$
$311$	−1.44086	+	1.44086i	−0.0817035	+	0.0817035i	0.665074	+	0.746777i	$0.268400\pi$
$312$	5.02423			0.284441
$313$	−7.80710	+	7.80710i	−0.441283	+	0.441283i	−0.892443	−	0.451160i	$-0.851010\pi$
$313$	−7.80710	+	7.80710i	−0.441283	+	0.441283i	0.451160	+	0.892443i	$0.351010\pi$
$314$	13.8468	−	13.8468i	0.781422	−	0.781422i
$315$	2.01128	+	2.01128i	0.113323	+	0.113323i
$316$	0.153829	+	0.153829i	0.00865358	+	0.00865358i
$317$	−12.5558	−	12.5558i	−0.705201	−	0.705201i	0.260321	−	0.965522i	$-0.416172\pi$
$317$	−12.5558	−	12.5558i	−0.705201	−	0.705201i	−0.965522	+	0.260321i	$0.916172\pi$
$318$	−5.82140			−0.326448
$319$			30.2928i			1.69607i
$320$			10.4225i			0.582633i
$321$	12.4667	+	12.4667i	0.695825	+	0.695825i
$322$	−12.7713	+	12.7713i	−0.711719	+	0.711719i
$323$			13.5456i			0.753697i
$324$	0.189944			0.0105524
$325$	−3.77574	−	3.77574i	−0.209441	−	0.209441i
$326$			29.8347i			1.65239i
$327$	−4.00008			−0.221205
$328$	−16.0768	+	5.97568i	−0.887692	+	0.329952i
$329$	8.03301			0.442874
$330$		−	13.9962i		−	0.770468i
$331$	15.2806	+	15.2806i	0.839896	+	0.839896i	0.988845	−	0.148949i	$-0.0475889\pi$
$331$	15.2806	+	15.2806i	0.839896	+	0.839896i	−0.148949	+	0.988845i	$0.547589\pi$
$332$	1.41911			0.0778839
$333$		−	10.2743i		−	0.563026i
$334$	−4.43974	+	4.43974i	−0.242932	+	0.242932i
$335$	3.36073	+	3.36073i	0.183616	+	0.183616i
$336$		−	8.42008i		−	0.459353i
$337$			24.9051i			1.35667i	0.734753	+	0.678334i	$0.237298\pi$
$337$			24.9051i			1.35667i	−0.734753	+	0.678334i	$0.762702\pi$
$338$	14.0316			0.763218
$339$	0.327021	+	0.327021i	0.0177613	+	0.0177613i
$340$	−0.616549	−	0.616549i	−0.0334371	−	0.0334371i
$341$	2.81033	+	2.81033i	0.152188	+	0.152188i
$342$	−4.53089	+	4.53089i	−0.245003	+	0.245003i
$343$	14.0391	−	14.0391i	0.758040	−	0.758040i
$344$	7.01825			0.378398
$345$	6.53306	−	6.53306i	0.351728	−	0.351728i
$346$	−26.1469			−1.40567
$347$	−9.83198	+	9.83198i	−0.527808	+	0.527808i	−0.919918	−	0.392110i	$-0.871745\pi$
$347$	−9.83198	+	9.83198i	−0.527808	+	0.527808i	0.392110	+	0.919918i	$0.371745\pi$
$348$			0.892713i			0.0478544i
$349$		−	27.5028i		−	1.47219i	−0.676877	−	0.736096i	$-0.736667\pi$
$349$		−	27.5028i		−	1.47219i	0.676877	−	0.736096i	$-0.263333\pi$
$350$	−5.77436	+	5.77436i	−0.308652	+	0.308652i
$351$	1.87569			0.100117
$352$	−4.88101	+	4.88101i	−0.260159	+	0.260159i
$353$	−21.3441			−1.13603			−0.568016	−	0.823017i	$-0.692289\pi$
$353$	−21.3441			−1.13603			−0.568016	+	0.823017i	$0.692289\pi$
$354$	5.03406	−	5.03406i	0.267557	−	0.267557i
$355$	−2.15388	+	2.15388i	−0.114316	+	0.114316i
$356$	−1.38159	−	1.38159i	−0.0732241	−	0.0732241i
$357$	−4.28792	−	4.28792i	−0.226941	−	0.226941i
$358$	−11.8149	−	11.8149i	−0.624439	−	0.624439i
$359$	17.6782			0.933019			0.466509	−	0.884516i	$-0.345511\pi$
$359$	17.6782			0.933019			0.466509	+	0.884516i	$0.345511\pi$
$360$			3.93053i			0.207157i
$361$			0.251573i			0.0132407i
$362$	−5.21320	−	5.21320i	−0.274000	−	0.274000i
$363$	−21.5977	+	21.5977i	−1.13358	+	1.13358i
$364$			0.690607i			0.0361976i
$365$	21.1580			1.10746
$366$	−12.1275	−	12.1275i	−0.633915	−	0.633915i
$367$		−	3.10979i		−	0.162330i	−0.996701	−	0.0811648i	$-0.974136\pi$
$367$		−	3.10979i		−	0.162330i	0.996701	−	0.0811648i	$-0.0258640\pi$
$368$	−27.3502			−1.42573
$369$	−6.00193	+	2.23089i	−0.312448	+	0.116136i
$370$	−22.3105			−1.15987
$371$			7.62530i			0.395886i
$372$	0.0828189	+	0.0828189i	0.00429396	+	0.00429396i
$373$	−3.46343			−0.179330			−0.0896648	−	0.995972i	$-0.528580\pi$
$373$	−3.46343			−0.179330			−0.0896648	+	0.995972i	$0.528580\pi$
$374$			29.8390i			1.54294i
$375$	8.14179	−	8.14179i	0.420440	−	0.420440i
$376$	7.84921	+	7.84921i	0.404792	+	0.404792i
$377$			8.81552i			0.454023i
$378$		−	2.86855i		−	0.147542i
$379$	6.94555			0.356769			0.178384	−	0.983961i	$-0.442913\pi$
$379$	6.94555			0.356769			0.178384	+	0.983961i	$0.442913\pi$
$380$	0.853364	+	0.853364i	0.0437767	+	0.0437767i
$381$	3.39148	+	3.39148i	0.173751	+	0.173751i
$382$	10.4327	+	10.4327i	0.533784	+	0.533784i
$383$	−22.0903	+	22.0903i	−1.12876	+	1.12876i	−0.138382	+	0.990379i	$0.544190\pi$
$383$	−22.0903	+	22.0903i	−1.12876	+	1.12876i	−0.990379	+	0.138382i	$0.955810\pi$
$384$	8.94696	−	8.94696i	0.456573	−	0.456573i
$385$	−18.3333			−0.934352
$386$	15.4285	−	15.4285i	0.785292	−	0.785292i
$387$	2.62011			0.133188
$388$	0.428155	−	0.428155i	0.0217363	−	0.0217363i
$389$		−	31.2867i		−	1.58630i	−0.609026	−	0.793150i	$-0.708440\pi$
$389$		−	31.2867i		−	1.58630i	0.609026	−	0.793150i	$-0.291560\pi$
$390$		−	4.07305i		−	0.206247i
$391$	−13.9281	+	13.9281i	−0.704372	+	0.704372i
$392$	8.68555			0.438687
$393$	−13.5529	+	13.5529i	−0.683653	+	0.683653i
$394$	10.8793			0.548092
$395$	−1.18838	+	1.18838i	−0.0597941	+	0.0597941i
$396$	−0.865690	+	0.865690i	−0.0435025	+	0.0435025i
$397$	12.0457	+	12.0457i	0.604556	+	0.604556i	0.941518	−	0.336962i	$-0.109399\pi$
$397$	12.0457	+	12.0457i	0.604556	+	0.604556i	−0.336962	+	0.941518i	$0.609399\pi$
$398$	25.7499	+	25.7499i	1.29073	+	1.29073i
$399$	5.93490	+	5.93490i	0.297116	+	0.297116i
$400$	−12.3659			−0.618297
$401$		−	27.1170i		−	1.35416i	−0.735909	−	0.677080i	$-0.763245\pi$
$401$		−	27.1170i		−	1.35416i	0.735909	−	0.677080i	$-0.236755\pi$
$402$		−	4.79317i		−	0.239061i
$403$	0.817835	+	0.817835i	0.0407393	+	0.0407393i
$404$	0.195978	−	0.195978i	0.00975027	−	0.00975027i
$405$			1.46738i			0.0729147i
$406$	13.4818			0.669093
$407$	46.8261	+	46.8261i	2.32108	+	2.32108i
$408$		−	8.37962i		−	0.414853i
$409$	−29.6477			−1.46599			−0.732993	−	0.680237i	$-0.761877\pi$
$409$	−29.6477			−1.46599			−0.732993	+	0.680237i	$0.761877\pi$
$410$	4.84438	+	13.0332i	0.239247	+	0.643662i
$411$	9.88965			0.487820
$412$			2.68331i			0.132197i
$413$	−6.59398	−	6.59398i	−0.324469	−	0.324469i
$414$	−9.31764			−0.457937
$415$			10.9631i			0.538159i
$416$	−1.42042	+	1.42042i	−0.0696420	+	0.0696420i
$417$	−1.32856	−	1.32856i	−0.0650598	−	0.0650598i
$418$		−	41.3001i		−	2.02006i
$419$		−	23.6740i		−	1.15655i	−0.815842	−	0.578274i	$-0.803726\pi$
$419$		−	23.6740i		−	1.15655i	0.815842	−	0.578274i	$-0.196274\pi$
$420$	−0.540272			−0.0263626
$421$	−7.30013	−	7.30013i	−0.355786	−	0.355786i	0.506471	−	0.862257i	$-0.330950\pi$
$421$	−7.30013	−	7.30013i	−0.355786	−	0.355786i	−0.862257	+	0.506471i	$0.830950\pi$
$422$	−3.26297	−	3.26297i	−0.158839	−	0.158839i
$423$	2.93034	+	2.93034i	0.142478	+	0.142478i
$424$	−7.45083	+	7.45083i	−0.361844	+	0.361844i
$425$	−6.29734	+	6.29734i	−0.305466	+	0.305466i
$426$	3.07193			0.148835
$427$	−15.8855	+	15.8855i	−0.768753	+	0.768753i
$428$	−3.34882			−0.161871
$429$	−8.54867	+	8.54867i	−0.412734	+	0.412734i
$430$		−	5.68956i		−	0.274375i
$431$		−	3.68537i		−	0.177518i	−0.996053	−	0.0887591i	$-0.971710\pi$
$431$		−	3.68537i		−	0.177518i	0.996053	−	0.0887591i	$-0.0282901\pi$
$432$	3.07154	−	3.07154i	0.147779	−	0.147779i
$433$	12.5601			0.603601			0.301800	−	0.953371i	$-0.402412\pi$
$433$	12.5601			0.603601			0.301800	+	0.953371i	$0.402412\pi$
$434$	1.25074	−	1.25074i	0.0600375	−	0.0600375i
$435$	−6.89652			−0.330663
$436$	0.537253	−	0.537253i	0.0257297	−	0.0257297i
$437$	19.2778	−	19.2778i	0.922181	−	0.922181i
$438$	−15.0880	−	15.0880i	−0.720935	−	0.720935i
$439$	18.1065	+	18.1065i	0.864178	+	0.864178i	0.991820	−	0.127642i	$-0.0407409\pi$
$439$	18.1065	+	18.1065i	0.864178	+	0.864178i	−0.127642	+	0.991820i	$0.540741\pi$
$440$	−17.9138	−	17.9138i	−0.854009	−	0.854009i
$441$	3.24257			0.154408
$442$			8.68346i			0.413030i
$443$			11.8948i			0.565138i	0.959247	+	0.282569i	$0.0911866\pi$
$443$			11.8948i			0.565138i	−0.959247	+	0.282569i	$0.908813\pi$
$444$	1.37994	+	1.37994i	0.0654890	+	0.0654890i
$445$	10.6732	−	10.6732i	0.505961	−	0.505961i
$446$		−	35.8409i		−	1.69711i
$447$	11.8425			0.560131
$448$	−9.73550	−	9.73550i	−0.459959	−	0.459959i
$449$			5.86505i			0.276789i	0.990377	+	0.138394i	$0.0441942\pi$
$449$			5.86505i			0.276789i	−0.990377	+	0.138394i	$0.955806\pi$
$450$	−4.21282			−0.198594
$451$	17.1869	−	37.5220i	0.809300	−	1.76684i
$452$	−0.0878446			−0.00413186
$453$		−	20.1676i		−	0.947558i
$454$	3.24352	+	3.24352i	0.152226	+	0.152226i
$455$	−5.33518			−0.250117
$456$			11.5982i			0.543136i
$457$	23.4662	−	23.4662i	1.09770	−	1.09770i	0.103022	−	0.994679i	$-0.467149\pi$
$457$	23.4662	−	23.4662i	1.09770	−	1.09770i	0.994679	−	0.103022i	$-0.0328511\pi$
$458$	6.74091	+	6.74091i	0.314982	+	0.314982i
$459$		−	3.12835i		−	0.146019i
$460$			1.75492i			0.0818234i
$461$	−17.1222			−0.797460			−0.398730	−	0.917068i	$-0.630549\pi$
$461$	−17.1222			−0.797460			−0.398730	+	0.917068i	$0.630549\pi$
$462$	13.0737	+	13.0737i	0.608245	+	0.608245i
$463$	11.0674	+	11.0674i	0.514346	+	0.514346i	0.915855	−	0.401509i	$-0.131514\pi$
$463$	11.0674	+	11.0674i	0.514346	+	0.514346i	−0.401509	+	0.915855i	$0.631514\pi$
$464$	14.4359	+	14.4359i	0.670168	+	0.670168i
$465$	−0.639805	+	0.639805i	−0.0296702	+	0.0296702i
$466$	−15.6192	+	15.6192i	−0.723545	+	0.723545i
$467$	11.2455			0.520382			0.260191	−	0.965557i	$-0.416215\pi$
$467$	11.2455			0.520382			0.260191	+	0.965557i	$0.416215\pi$
$468$	−0.251924	+	0.251924i	−0.0116452	+	0.0116452i
$469$	−6.27844			−0.289911
$470$	6.36321	−	6.36321i	0.293513	−	0.293513i
$471$		−	13.2327i		−	0.609731i
$472$		−	12.8862i		−	0.593136i
$473$	−11.9415	+	11.9415i	−0.549069	+	0.549069i
$474$	1.69491			0.0778497
$475$	8.71614	−	8.71614i	0.399924	−	0.399924i
$476$	1.15182			0.0527938
$477$	−2.78161	+	2.78161i	−0.127361	+	0.127361i
$478$	30.3673	−	30.3673i	1.38897	−	1.38897i
$479$	0.574198	+	0.574198i	0.0262358	+	0.0262358i	0.720103	−	0.693867i	$-0.244095\pi$
$479$	0.574198	+	0.574198i	0.0262358	+	0.0262358i	−0.693867	+	0.720103i	$0.744095\pi$
$480$	−1.11122	−	1.11122i	−0.0507200	−	0.0507200i
$481$	13.6269	+	13.6269i	0.621332	+	0.621332i
$482$	−21.3465			−0.972305
$483$			12.2049i			0.555343i
$484$		−	5.80158i		−	0.263708i
$485$	3.30765	+	3.30765i	0.150193	+	0.150193i
$486$	1.04641	−	1.04641i	0.0474661	−	0.0474661i
$487$			8.15754i			0.369654i	0.982771	+	0.184827i	$0.0591724\pi$
$487$			8.15754i			0.369654i	−0.982771	+	0.184827i	$0.940828\pi$
$488$	−31.0441			−1.40530
$489$	14.2558	+	14.2558i	0.644667	+	0.644667i
$490$		−	7.04122i		−	0.318090i
$491$	−29.5560			−1.33384			−0.666922	−	0.745127i	$-0.732389\pi$
$491$	−29.5560			−1.33384			−0.666922	+	0.745127i	$0.732389\pi$
$492$	0.506489	−	1.10575i	0.0228343	−	0.0498512i
$493$	14.7029			0.662186
$494$		−	12.0188i		−	0.540750i
$495$	−6.68775	−	6.68775i	−0.300592	−	0.300592i
$496$	2.67849			0.120268
$497$		−	4.02384i		−	0.180494i
$498$	7.81796	−	7.81796i	0.350331	−	0.350331i
$499$	−20.1209	−	20.1209i	−0.900735	−	0.900735i	0.0947646	−	0.995500i	$-0.469790\pi$
$499$	−20.1209	−	20.1209i	−0.900735	−	0.900735i	−0.995500	+	0.0947646i	$0.969790\pi$
$500$			2.18705i			0.0978080i
$501$			4.24283i			0.189556i
$502$	−6.32536			−0.282315
$503$	−0.789760	−	0.789760i	−0.0352137	−	0.0352137i	0.689281	−	0.724494i	$-0.257927\pi$
$503$	−0.789760	−	0.789760i	−0.0352137	−	0.0352137i	−0.724494	+	0.689281i	$0.757927\pi$
$504$	−3.67146	−	3.67146i	−0.163540	−	0.163540i
$505$	1.51400	+	1.51400i	0.0673720	+	0.0673720i
$506$	42.4662	−	42.4662i	1.88785	−	1.88785i
$507$	6.70464	−	6.70464i	0.297763	−	0.297763i
$508$	−0.911023			−0.0404201
$509$	−24.5121	+	24.5121i	−1.08648	+	1.08648i	−0.0905912	+	0.995888i	$0.528876\pi$
$509$	−24.5121	+	24.5121i	−1.08648	+	1.08648i	−0.995888	+	0.0905912i	$0.971124\pi$
$510$	−6.79320			−0.300808
$511$	−19.7634	+	19.7634i	−0.874283	+	0.874283i
$512$		−	18.6187i		−	0.822836i
$513$			4.32995i			0.191172i
$514$	14.8039	−	14.8039i	0.652970	−	0.652970i
$515$	−20.7295			−0.913451
$516$	−0.351908	+	0.351908i	−0.0154919	+	0.0154919i
$517$	−26.7107			−1.17474
$518$	20.8400	−	20.8400i	0.915657	−	0.915657i
$519$	−12.4936	+	12.4936i	−0.548410	+	0.548410i
$520$	−5.21311	−	5.21311i	−0.228610	−	0.228610i
$521$	−19.7272	−	19.7272i	−0.864265	−	0.864265i	0.127565	−	0.991830i	$-0.459284\pi$
$521$	−19.7272	−	19.7272i	−0.864265	−	0.864265i	−0.991830	+	0.127565i	$0.959284\pi$
$522$	4.91800	+	4.91800i	0.215255	+	0.215255i
$523$	−5.47241			−0.239292			−0.119646	−	0.992817i	$-0.538176\pi$
$523$	−5.47241			−0.239292			−0.119646	+	0.992817i	$0.538176\pi$
$524$		−	3.64059i		−	0.159040i
$525$			5.51826i			0.240837i
$526$	11.1800	+	11.1800i	0.487470	+	0.487470i
$527$	1.36402	−	1.36402i	0.0594177	−	0.0594177i
$528$			27.9978i			1.21845i
$529$	16.6441			0.723658
$530$	6.04025	+	6.04025i	0.262372	+	0.262372i
$531$		−	4.81080i		−	0.208771i
$532$	−1.59424			−0.0691189
$533$	5.00156	−	10.9193i	0.216642	−	0.472967i
$534$	−15.2225			−0.658742
$535$		−	25.8708i		−	1.11849i
$536$	−6.13479	−	6.13479i	−0.264983	−	0.264983i
$537$	−11.2909			−0.487240
$538$			3.66613i			0.158058i
$539$	−14.7784	+	14.7784i	−0.636549	+	0.636549i
$540$	−0.197084	−	0.197084i	−0.00848116	−	0.00848116i
$541$		−	4.93069i		−	0.211987i	−0.994367	−	0.105993i	$-0.966198\pi$
$541$		−	4.93069i		−	0.211987i	0.994367	−	0.105993i	$-0.0338023\pi$
$542$			26.8108i			1.15162i
$543$	−4.98199			−0.213798
$544$	2.36904	+	2.36904i	0.101572	+	0.101572i
$545$	4.15046	+	4.15046i	0.177786	+	0.177786i
$546$	3.80459	+	3.80459i	0.162821	+	0.162821i
$547$	−2.60816	+	2.60816i	−0.111517	+	0.111517i	−0.760663	−	0.649147i	$-0.775126\pi$
$547$	−2.60816	+	2.60816i	−0.111517	+	0.111517i	0.649147	+	0.760663i	$0.275126\pi$
$548$	−1.32828	+	1.32828i	−0.0567414	+	0.0567414i
$549$	−11.5896			−0.494634
$550$	19.2004	−	19.2004i	0.818709	−	0.818709i
$551$	−20.3502			−0.866950
$552$	−11.9257	+	11.9257i	−0.507591	+	0.507591i
$553$		−	2.22011i		−	0.0944089i
$554$			29.4217i			1.25001i
$555$	−10.6605	+	10.6605i	−0.452513	+	0.452513i
$556$	0.356878			0.0151350
$557$	−6.18224	+	6.18224i	−0.261950	+	0.261950i	−0.825846	−	0.563896i	$-0.809302\pi$
$557$	−6.18224	+	6.18224i	−0.261950	+	0.261950i	0.563896	+	0.825846i	$0.309302\pi$
$558$	0.912508			0.0386295
$559$	−3.47509	+	3.47509i	−0.146981	+	0.146981i
$560$	−8.73663	+	8.73663i	−0.369190	+	0.369190i
$561$	14.2578	+	14.2578i	0.601966	+	0.601966i
$562$	30.4325	+	30.4325i	1.28372	+	1.28372i
$563$	6.01639	+	6.01639i	0.253561	+	0.253561i	0.822429	−	0.568868i	$-0.192618\pi$
$563$	6.01639	+	6.01639i	0.253561	+	0.253561i	−0.568868	+	0.822429i	$0.692618\pi$
$564$	−0.787149			−0.0331450
$565$		−	0.678630i		−	0.0285502i
$566$			43.4442i			1.82610i
$567$	−1.37066	−	1.37066i	−0.0575624	−	0.0575624i
$568$	3.93177	−	3.93177i	0.164973	−	0.164973i
$569$		−	8.71956i		−	0.365543i	−0.983155	−	0.182771i	$-0.941493\pi$
$569$		−	8.71956i		−	0.365543i	0.983155	−	0.182771i	$-0.0585068\pi$
$570$	9.40246			0.393826
$571$	−6.28625	−	6.28625i	−0.263072	−	0.263072i	0.563229	−	0.826301i	$-0.309559\pi$
$571$	−6.28625	−	6.28625i	−0.263072	−	0.263072i	−0.826301	+	0.563229i	$0.809559\pi$
$572$		−	2.29635i		−	0.0960152i
$573$	9.97001			0.416503
$574$	−16.6992	−	7.64905i	−0.697011	−	0.319265i
$575$	17.9245			0.747502
$576$		−	7.10276i		−	0.295949i
$577$	0.0163177	+	0.0163177i	0.000679313	+	0.000679313i	0.707446	−	0.706767i	$-0.249847\pi$
$577$	0.0163177	+	0.0163177i	0.000679313	+	0.000679313i	−0.706767	+	0.707446i	$0.749847\pi$
$578$	−10.6747			−0.444010
$579$		−	14.7443i		−	0.612751i
$580$	0.926274	−	0.926274i	0.0384614	−	0.0384614i
$581$	−10.2405	−	10.2405i	−0.424849	−	0.424849i
$582$		−	4.71746i		−	0.195545i
$583$		−	25.3550i		−	1.05010i
$584$	−38.6225			−1.59821
$585$	−1.94620	−	1.94620i	−0.0804656	−	0.0804656i
$586$	−17.7987	−	17.7987i	−0.735256	−	0.735256i
$587$	25.8029	+	25.8029i	1.06500	+	1.06500i	0.997735	+	0.0672634i	$0.0214268\pi$
$587$	25.8029	+	25.8029i	1.06500	+	1.06500i	0.0672634	+	0.997735i	$0.478573\pi$
$588$	−0.435510	+	0.435510i	−0.0179601	+	0.0179601i
$589$	−1.88794	+	1.88794i	−0.0777911	+	0.0777911i
$590$	−10.4466			−0.430081
$591$	5.19840	−	5.19840i	0.213834	−	0.213834i
$592$	44.6294			1.83426
$593$	5.95775	−	5.95775i	0.244656	−	0.244656i	−0.574117	−	0.818773i	$-0.694655\pi$
$593$	5.95775	−	5.95775i	0.244656	−	0.244656i	0.818773	+	0.574117i	$0.194655\pi$
$594$			9.53826i			0.391360i
$595$			8.89824i			0.364792i
$596$	−1.59057	+	1.59057i	−0.0651523	+	0.0651523i
$597$	24.6079			1.00713
$598$	12.3581	−	12.3581i	0.505360	−	0.505360i
$599$	−3.26862			−0.133552			−0.0667762	−	0.997768i	$-0.521271\pi$
$599$	−3.26862			−0.133552			−0.0667762	+	0.997768i	$0.521271\pi$
$600$	−5.39200	+	5.39200i	−0.220128	+	0.220128i
$601$	−23.5642	+	23.5642i	−0.961206	+	0.961206i	−0.999275	−	0.0380694i	$-0.987879\pi$
$601$	−23.5642	+	23.5642i	−0.961206	+	0.961206i	0.0380694	+	0.999275i	$0.487879\pi$
$602$	5.31456	+	5.31456i	0.216605	+	0.216605i
$603$	−2.29029	−	2.29029i	−0.0932679	−	0.0932679i
$604$	2.70872	+	2.70872i	0.110216	+	0.110216i
$605$	44.8192			1.82216
$606$		−	2.15931i		−	0.0877158i
$607$			19.6850i			0.798989i	0.916735	+	0.399495i	$0.130814\pi$
$607$			19.6850i			0.798989i	−0.916735	+	0.399495i	$0.869186\pi$
$608$	−3.27899	−	3.27899i	−0.132981	−	0.132981i
$609$	6.44196	−	6.44196i	0.261041	−	0.261041i
$610$			25.1668i			1.01898i
$611$	−7.77308			−0.314465
$612$	0.420170	+	0.420170i	0.0169844	+	0.0169844i
$613$			26.5863i			1.07381i	0.843643	+	0.536905i	$0.180407\pi$
$613$			26.5863i			1.07381i	−0.843643	+	0.536905i	$0.819593\pi$
$614$	18.0116			0.726890
$615$	8.54232	+	3.91280i	0.344460	+	0.157779i
$616$	33.4662			1.34839
$617$			34.1561i			1.37507i	0.726149	+	0.687537i	$0.241308\pi$
$617$			34.1561i			1.37507i	−0.726149	+	0.687537i	$0.758692\pi$
$618$	14.7825	+	14.7825i	0.594639	+	0.594639i
$619$	14.8735			0.597817			0.298909	−	0.954282i	$-0.403377\pi$
$619$	14.8735			0.597817			0.298909	+	0.954282i	$0.403377\pi$
$620$		−	0.171865i		−	0.00690226i
$621$	−4.45220	+	4.45220i	−0.178661	+	0.178661i
$622$	−2.13225	−	2.13225i	−0.0854952	−	0.0854952i
$623$			19.9395i			0.798860i
$624$			8.14763i			0.326166i
$625$	−2.66175			−0.106470
$626$	−11.5533	−	11.5533i	−0.461763	−	0.461763i
$627$	−19.7342	−	19.7342i	−0.788109	−	0.788109i
$628$	1.77729	+	1.77729i	0.0709216	+	0.0709216i
$629$	22.7275	−	22.7275i	0.906204	−	0.906204i
$630$	−2.97639	+	2.97639i	−0.118582	+	0.118582i
$631$	−22.9858			−0.915049			−0.457524	−	0.889197i	$-0.651264\pi$
$631$	−22.9858			−0.915049			−0.457524	+	0.889197i	$0.651264\pi$
$632$	2.16932	−	2.16932i	0.0862908	−	0.0862908i
$633$	−3.11825			−0.123939
$634$	18.5806	−	18.5806i	0.737929	−	0.737929i
$635$		−	7.03796i		−	0.279293i
$636$		−	0.747198i		−	0.0296283i
$637$	−4.30066	+	4.30066i	−0.170398	+	0.170398i
$638$	−44.8287			−1.77479
$639$	1.46784	−	1.46784i	0.0580670	−	0.0580670i
$640$	−18.5666			−0.733910
$641$	−2.73571	+	2.73571i	−0.108054	+	0.108054i	−0.759067	−	0.651013i	$-0.774344\pi$
$641$	−2.73571	+	2.73571i	−0.108054	+	0.108054i	0.651013	+	0.759067i	$0.274344\pi$
$642$	−18.4488	+	18.4488i	−0.728117	+	0.728117i
$643$	19.5838	+	19.5838i	0.772311	+	0.772311i	0.978510	−	0.206199i	$-0.0661095\pi$
$643$	19.5838	+	19.5838i	0.772311	+	0.772311i	−0.206199	+	0.978510i	$0.566110\pi$
$644$	−1.63925	−	1.63925i	−0.0645954	−	0.0645954i
$645$	−2.71861	−	2.71861i	−0.107045	−	0.107045i
$646$	−20.0454			−0.788676
$647$		−	33.6537i		−	1.32306i	−0.749918	−	0.661531i	$-0.769907\pi$
$647$		−	33.6537i		−	1.32306i	0.749918	−	0.661531i	$-0.230093\pi$
$648$		−	2.67860i		−	0.105226i
$649$	21.9258	+	21.9258i	0.860661	+	0.860661i
$650$	5.58752	−	5.58752i	0.219160	−	0.219160i
$651$		−	1.19527i		−	0.0468463i
$652$	−3.82939			−0.149971
$653$	4.17772	+	4.17772i	0.163487	+	0.163487i	0.784109	−	0.620623i	$-0.213120\pi$
$653$	4.17772	+	4.17772i	0.163487	+	0.163487i	−0.620623	+	0.784109i	$0.713120\pi$
$654$		−	5.91951i		−	0.231471i
$655$	28.1248			1.09893
$656$	−9.69058	−	26.0712i	−0.378353	−	1.01791i
$657$	−14.4189			−0.562534
$658$			11.8876i			0.463427i
$659$	20.9129	+	20.9129i	0.814649	+	0.814649i	0.985327	−	0.170678i	$-0.0545957\pi$
$659$	20.9129	+	20.9129i	0.814649	+	0.814649i	−0.170678	+	0.985327i	$0.554596\pi$
$660$	1.79647			0.0699274
$661$			4.81466i			0.187268i	0.995607	+	0.0936342i	$0.0298484\pi$
$661$			4.81466i			0.187268i	−0.995607	+	0.0936342i	$0.970152\pi$
$662$	−22.6129	+	22.6129i	−0.878875	+	0.878875i
$663$	4.14917	+	4.14917i	0.161141	+	0.161141i
$664$		−	20.0125i		−	0.776635i
$665$		−	12.3160i		−	0.477595i
$666$	15.2043			0.589155
$667$	−20.9248	−	20.9248i	−0.810212	−	0.810212i
$668$	−0.569856	−	0.569856i	−0.0220484	−	0.0220484i
$669$	−17.1256	−	17.1256i	−0.662116	−	0.662116i
$670$	−4.97336	+	4.97336i	−0.192138	+	0.192138i
$671$	52.8211	−	52.8211i	2.03914	−	2.03914i
$672$	2.07596			0.0800817
$673$	19.6930	−	19.6930i	0.759108	−	0.759108i	−0.217052	−	0.976160i	$-0.569644\pi$
$673$	19.6930	−	19.6930i	0.759108	−	0.759108i	0.976160	+	0.217052i	$0.0696442\pi$
$674$	−36.8557			−1.41963
$675$	−2.01299	+	2.01299i	−0.0774800	+	0.0774800i
$676$			1.80101i			0.0692694i
$677$			12.4907i			0.480055i	0.970766	+	0.240028i	$0.0771565\pi$
$677$			12.4907i			0.480055i	−0.970766	+	0.240028i	$0.922844\pi$
$678$	−0.483941	+	0.483941i	−0.0185856	+	0.0185856i
$679$	−6.17928			−0.237139
$680$	−8.69464	+	8.69464i	−0.333424	+	0.333424i
$681$	3.09967			0.118779
$682$	−4.15886	+	4.15886i	−0.159251	+	0.159251i
$683$	−0.412600	+	0.412600i	−0.0157877	+	0.0157877i	−0.714957	−	0.699169i	$-0.753554\pi$
$683$	−0.412600	+	0.412600i	−0.0157877	+	0.0157877i	0.699169	+	0.714957i	$0.253554\pi$
$684$	−0.581557	−	0.581557i	−0.0222364	−	0.0222364i
$685$	−10.2614	−	10.2614i	−0.392069	−	0.392069i
$686$	20.7757	+	20.7757i	0.793220	+	0.793220i
$687$	6.44194			0.245775
$688$			11.3813i			0.433907i
$689$		−	7.37856i		−	0.281101i
$690$	9.66793	+	9.66793i	0.368052	+	0.368052i
$691$	11.1491	−	11.1491i	0.424132	−	0.424132i	−0.462492	−	0.886623i	$-0.653045\pi$
$691$	11.1491	−	11.1491i	0.424132	−	0.424132i	0.886623	+	0.462492i	$0.153045\pi$
$692$		−	3.35605i		−	0.127578i
$693$	12.4939			0.474604
$694$	−14.5498	−	14.5498i	−0.552303	−	0.552303i
$695$			2.75701i			0.104579i
$696$	12.5891			0.477190
$697$	−18.2117	−	8.34182i	−0.689816	−	0.315969i
$698$	40.6999			1.54052
$699$			14.9265i			0.564571i
$700$	−0.741160	−	0.741160i	−0.0280132	−	0.0280132i
$701$	−13.2843			−0.501741			−0.250870	−	0.968021i	$-0.580717\pi$
$701$	−13.2843			−0.501741			−0.250870	+	0.968021i	$0.580717\pi$
$702$			2.77573i			0.104763i
$703$	−31.4570	+	31.4570i	−1.18643	+	1.18643i
$704$	32.3717	+	32.3717i	1.22005	+	1.22005i
$705$		−	6.08100i		−	0.229024i
$706$		−	31.5860i		−	1.18875i
$707$	−2.82842			−0.106374
$708$	0.646140	+	0.646140i	0.0242834	+	0.0242834i
$709$	−19.6015	−	19.6015i	−0.736149	−	0.736149i	0.235681	−	0.971830i	$-0.424268\pi$
$709$	−19.6015	−	19.6015i	−0.736149	−	0.736149i	−0.971830	+	0.235681i	$0.924268\pi$
$710$	−3.18741	−	3.18741i	−0.119622	−	0.119622i
$711$	0.809869	−	0.809869i	0.0303725	−	0.0303725i
$712$	−19.4833	+	19.4833i	−0.730168	+	0.730168i
$713$	−3.88248			−0.145400
$714$	6.34546	−	6.34546i	0.237473	−	0.237473i
$715$	17.7401			0.663442
$716$	1.51649	−	1.51649i	0.0566739	−	0.0566739i
$717$		−	29.0204i		−	1.08379i
$718$			26.1610i			0.976319i
$719$	−7.45826	+	7.45826i	−0.278146	+	0.278146i	−0.832369	−	0.554222i	$-0.813016\pi$
$719$	−7.45826	+	7.45826i	−0.278146	+	0.278146i	0.554222	+	0.832369i	$0.313016\pi$
$720$	−6.37402			−0.237546
$721$	19.3632	−	19.3632i	0.721123	−	0.721123i
$722$	−0.372289			−0.0138552
$723$	−10.1999	+	10.1999i	−0.379337	+	0.379337i
$724$	0.669133	−	0.669133i	0.0248681	−	0.0248681i
$725$	−9.46082	−	9.46082i	−0.351366	−	0.351366i
$726$	−31.9612	−	31.9612i	−1.18619	−	1.18619i
$727$	−8.53573	−	8.53573i	−0.316573	−	0.316573i	0.530877	−	0.847449i	$-0.321863\pi$
$727$	−8.53573	−	8.53573i	−0.316573	−	0.316573i	−0.847449	+	0.530877i	$0.821863\pi$
$728$	9.73901			0.360952
$729$		−	1.00000i		−	0.0370370i
$730$			31.3105i			1.15885i
$731$	5.79590	+	5.79590i	0.214369	+	0.214369i
$732$	1.55661	−	1.55661i	0.0575339	−	0.0575339i
$733$		−	6.04068i		−	0.223118i	−0.993758	−	0.111559i	$-0.964416\pi$
$733$		−	6.04068i		−	0.223118i	0.993758	−	0.111559i	$-0.0355844\pi$
$734$	4.60201			0.169863
$735$	−3.36447	−	3.36447i	−0.124100	−	0.124100i
$736$		−	6.74314i		−	0.248555i
$737$	20.8766			0.768998
$738$	−3.30138	−	8.88192i	−0.121525	−	0.326948i
$739$	−12.1221			−0.445918			−0.222959	−	0.974828i	$-0.571572\pi$
$739$	−12.1221			−0.445918			−0.222959	+	0.974828i	$0.571572\pi$
$740$		−	2.86363i		−	0.105269i
$741$	−5.74286	−	5.74286i	−0.210969	−	0.210969i
$742$	−11.2843			−0.414258
$743$		−	32.4857i		−	1.19178i	−0.803064	−	0.595892i	$-0.796798\pi$
$743$		−	32.4857i		−	1.19178i	0.803064	−	0.595892i	$-0.203202\pi$
$744$	1.16792	−	1.16792i	0.0428181	−	0.0428181i
$745$	−12.2877	−	12.2877i	−0.450186	−	0.450186i
$746$		−	5.12534i		−	0.187652i
$747$		−	7.47123i		−	0.273358i
$748$	−3.82995			−0.140037
$749$	24.1656	+	24.1656i	0.882993	+	0.882993i
$750$	12.0486	+	12.0486i	0.439952	+	0.439952i
$751$	−24.1004	−	24.1004i	−0.879438	−	0.879438i	0.114038	−	0.993476i	$-0.463621\pi$
$751$	−24.1004	−	24.1004i	−0.879438	−	0.879438i	−0.993476	+	0.114038i	$0.963621\pi$
$752$	−12.7288	+	12.7288i	−0.464172	+	0.464172i
$753$	−3.02241	+	3.02241i	−0.110143	+	0.110143i
$754$	−13.0456			−0.475093
$755$	−20.9258	+	20.9258i	−0.761568	+	0.761568i
$756$	0.368188			0.0133909
$757$	−29.6238	+	29.6238i	−1.07669	+	1.07669i	−0.0798899	+	0.996804i	$0.525457\pi$
$757$	−29.6238	+	29.6238i	−1.07669	+	1.07669i	−0.996804	+	0.0798899i	$0.974543\pi$
$758$			10.2783i			0.373326i
$759$		−	40.5828i		−	1.47306i
$760$	12.0342	−	12.0342i	0.436528	−	0.436528i
$761$	1.26133			0.0457233			0.0228616	−	0.999739i	$-0.492722\pi$
$761$	1.26133			0.0457233			0.0228616	+	0.999739i	$0.492722\pi$
$762$	−5.01887	+	5.01887i	−0.181815	+	0.181815i
$763$	−7.75380			−0.280707
$764$	−1.33908	+	1.33908i	−0.0484461	+	0.0484461i
$765$	−3.24596	+	3.24596i	−0.117358	+	0.117358i
$766$	−32.6902	−	32.6902i	−1.18115	−	1.18115i
$767$	6.38062	+	6.38062i	0.230391	+	0.230391i
$768$	3.19529	+	3.19529i	0.115300	+	0.115300i
$769$	−16.3960			−0.591257			−0.295628	−	0.955303i	$-0.595529\pi$
$769$	−16.3960			−0.591257			−0.295628	+	0.955303i	$0.595529\pi$
$770$		−	27.1305i		−	0.977714i
$771$		−	14.1473i		−	0.509503i
$772$	1.98031	+	1.98031i	0.0712729	+	0.0712729i
$773$	10.4458	−	10.4458i	0.375709	−	0.375709i	−0.493842	−	0.869551i	$-0.664408\pi$
$773$	10.4458	−	10.4458i	0.375709	−	0.375709i	0.869551	+	0.493842i	$0.164408\pi$
$774$			3.87736i			0.139369i
$775$	−1.75540			−0.0630559
$776$	−6.03789	−	6.03789i	−0.216748	−	0.216748i
$777$		−	19.9157i		−	0.714473i
$778$	46.2995			1.65992
$779$	25.2067	+	11.5459i	0.903124	+	0.413675i
$780$	0.522791			0.0187189
$781$			13.3797i			0.478764i
$782$	−20.6114	−	20.6114i	−0.737061	−	0.737061i
$783$	4.69989			0.167960
$784$			14.0851i			0.503039i
$785$	−13.7302	+	13.7302i	−0.490051	+	0.490051i
$786$	−20.0562	−	20.0562i	−0.715381	−	0.715381i
$787$			0.965027i			0.0343995i	0.999852	+	0.0171998i	$0.00547512\pi$
$787$			0.965027i			0.0343995i	−0.999852	+	0.0171998i	$0.994525\pi$
$788$			1.39640i			0.0497446i
$789$	10.6841			0.380366
$790$	−1.75863	−	1.75863i	−0.0625691	−	0.0625691i
$791$	0.633901	+	0.633901i	0.0225389	+	0.0225389i
$792$	12.2080	+	12.2080i	0.433794	+	0.433794i
$793$	15.3715	−	15.3715i	0.545857	−	0.545857i
$794$	−17.8258	+	17.8258i	−0.632613	+	0.632613i
$795$	5.77236			0.204725
$796$	−3.30510	+	3.30510i	−0.117146	+	0.117146i
$797$	6.25973			0.221731			0.110866	−	0.993835i	$-0.464638\pi$
$797$	6.25973			0.221731			0.110866	+	0.993835i	$0.464638\pi$
$798$	−8.78273	+	8.78273i	−0.310905	+	0.310905i
$799$			12.9643i			0.458643i
$800$		−	3.04880i		−	0.107791i
$801$	−7.27368	+	7.27368i	−0.257003	+	0.257003i
$802$	40.1290			1.41701
$803$	65.7157	−	65.7157i	2.31906	−	2.31906i
$804$	0.615220			0.0216971
$805$	12.6638	−	12.6638i	0.446339	−	0.446339i
$806$	−1.21027	+	1.21027i	−0.0426299	+	0.0426299i
$807$	1.75177	+	1.75177i	0.0616652	+	0.0616652i
$808$	−2.76370	−	2.76370i	−0.0972267	−	0.0972267i
$809$	14.9449	+	14.9449i	0.525434	+	0.525434i	0.919207	−	0.393774i	$-0.128831\pi$
$809$	14.9449	+	14.9449i	0.525434	+	0.525434i	−0.393774	+	0.919207i	$0.628831\pi$
$810$	−2.17150			−0.0762986
$811$			11.1120i			0.390193i	0.980784	+	0.195097i	$0.0625021\pi$
$811$			11.1120i			0.390193i	−0.980784	+	0.195097i	$0.937498\pi$
$812$			1.73044i			0.0607267i
$813$	12.8109	+	12.8109i	0.449296	+	0.449296i
$814$	−69.2954	+	69.2954i	−2.42880	+	2.42880i
$815$		−	29.5834i		−	1.03626i
$816$	13.5890			0.475709
$817$	−8.02209	−	8.02209i	−0.280657	−	0.280657i
$818$		−	43.8740i		−	1.53402i
$819$	3.63585			0.127047
$820$	−1.67285	+	0.621793i	−0.0584185	+	0.0217140i
$821$	−43.0904			−1.50387			−0.751933	−	0.659240i	$-0.770878\pi$
$821$	−43.0904			−1.50387			−0.751933	+	0.659240i	$0.770878\pi$
$822$			14.6352i			0.510460i
$823$	−6.56864	−	6.56864i	−0.228968	−	0.228968i	0.583293	−	0.812262i	$-0.301764\pi$
$823$	−6.56864	−	6.56864i	−0.228968	−	0.228968i	−0.812262	+	0.583293i	$0.801764\pi$
$824$	37.8403			1.31823
$825$		−	18.3489i		−	0.638826i
$826$	9.75807	−	9.75807i	0.339527	−	0.339527i
$827$	−14.2625	−	14.2625i	−0.495956	−	0.495956i	0.414221	−	0.910176i	$-0.364054\pi$
$827$	−14.2625	−	14.2625i	−0.495956	−	0.495956i	−0.910176	+	0.414221i	$0.864054\pi$
$828$		−	1.19595i		−	0.0415622i
$829$			7.31256i			0.253976i	0.991904	+	0.126988i	$0.0405309\pi$
$829$			7.31256i			0.253976i	−0.991904	+	0.126988i	$0.959469\pi$
$830$	−16.2237			−0.563134
$831$	14.0584	+	14.0584i	0.487680	+	0.487680i
$832$	9.42048	+	9.42048i	0.326596	+	0.326596i
$833$	7.17282	+	7.17282i	0.248523	+	0.248523i
$834$	1.96606	−	1.96606i	0.0680791	−	0.0680791i
$835$	4.40234	−	4.40234i	0.152349	−	0.152349i
$836$	5.30102			0.183340
$837$	0.436019	−	0.436019i	0.0150710	−	0.0150710i
$838$	35.0338			1.21022
$839$	1.23883	−	1.23883i	0.0427692	−	0.0427692i	−0.685399	−	0.728168i	$-0.740372\pi$
$839$	1.23883	−	1.23883i	0.0427692	−	0.0427692i	0.728168	+	0.685399i	$0.240372\pi$
$840$			7.61898i			0.262880i
$841$		−	6.91107i		−	0.238313i
$842$	10.8031	−	10.8031i	0.372298	−	0.372298i
$843$	29.0828			1.00166
$844$	0.418814	−	0.418814i	0.0144162	−	0.0144162i
$845$	−13.9134			−0.478635
$846$	−4.33645	+	4.33645i	−0.149090	+	0.149090i
$847$	−41.8651	+	41.8651i	−1.43850	+	1.43850i
$848$	−12.0828	−	12.0828i	−0.414924	−	0.414924i
$849$	20.7587	+	20.7587i	0.712437	+	0.712437i
$850$	−9.31910	−	9.31910i	−0.319642	−	0.319642i
$851$	−64.6904			−2.21756
$852$			0.394293i			0.0135083i
$853$			31.9544i			1.09410i	0.837101	+	0.547049i	$0.184249\pi$
$853$			31.9544i			1.09410i	−0.837101	+	0.547049i	$0.815751\pi$
$854$	−23.5081	−	23.5081i	−0.804430	−	0.804430i
$855$	4.49272	−	4.49272i	0.153648	−	0.153648i
$856$			47.2254i			1.61413i
$857$	24.1873			0.826224			0.413112	−	0.910680i	$-0.364442\pi$
$857$	24.1873			0.826224			0.413112	+	0.910680i	$0.364442\pi$
$858$	−12.6507	−	12.6507i	−0.431888	−	0.431888i
$859$		−	45.8683i		−	1.56500i	−0.622647	−	0.782502i	$-0.713943\pi$
$859$		−	45.8683i		−	1.56500i	0.622647	−	0.782502i	$-0.286057\pi$
$860$	0.730276			0.0249022
$861$	−11.6342	+	4.32439i	−0.396492	+	0.147375i
$862$	5.45379			0.185757
$863$		−	8.33608i		−	0.283764i	−0.989884	−	0.141882i	$-0.954685\pi$
$863$		−	8.33608i		−	0.283764i	0.989884	−	0.141882i	$-0.0453153\pi$
$864$	0.757282	+	0.757282i	0.0257632	+	0.0257632i
$865$	25.9266			0.881532
$866$			18.5870i			0.631613i
$867$	−5.10065	+	5.10065i	−0.173227	+	0.173227i
$868$	0.160537	+	0.160537i	0.00544898	+	0.00544898i
$869$			7.38214i			0.250422i
$870$		−	10.2058i		−	0.346008i
$871$	6.07529			0.205853
$872$	−7.57640	−	7.57640i	−0.256569	−	0.256569i
$873$	−2.25412	−	2.25412i	−0.0762904	−	0.0762904i
$874$	28.5281	+	28.5281i	0.964979	+	0.964979i
$875$	15.7821	−	15.7821i	0.533533	−	0.533533i
$876$	1.93661	−	1.93661i	0.0654318	−	0.0654318i
$877$	38.4643			1.29885			0.649424	−	0.760426i	$-0.275010\pi$
$877$	38.4643			1.29885			0.649424	+	0.760426i	$0.275010\pi$
$878$	−26.7949	+	26.7949i	−0.904284	+	0.904284i
$879$	−17.0093			−0.573709
$880$	29.0503	−	29.0503i	0.979286	−	0.979286i
$881$			28.1037i			0.946839i	0.880837	+	0.473420i	$0.156981\pi$
$881$			28.1037i			0.946839i	−0.880837	+	0.473420i	$0.843019\pi$
$882$			4.79850i			0.161574i
$883$	−0.556638	+	0.556638i	−0.0187324	+	0.0187324i	−0.716411	−	0.697679i	$-0.754216\pi$
$883$	−0.556638	+	0.556638i	−0.0187324	+	0.0187324i	0.697679	+	0.716411i	$0.254216\pi$
$884$	−1.11455			−0.0374865
$885$	−4.99165	+	4.99165i	−0.167793	+	0.167793i
$886$	−17.6024			−0.591365
$887$	−34.6799	+	34.6799i	−1.16444	+	1.16444i	−0.180944	+	0.983493i	$0.557915\pi$
$887$	−34.6799	+	34.6799i	−1.16444	+	1.16444i	−0.983493	+	0.180944i	$0.942085\pi$
$888$	19.4601	−	19.4601i	0.653037	−	0.653037i
$889$	6.57408	+	6.57408i	0.220488	+	0.220488i
$890$	15.7948	+	15.7948i	0.529442	+	0.529442i
$891$	4.55762	+	4.55762i	0.152686	+	0.152686i
$892$	4.60030			0.154030
$893$		−	17.9438i		−	0.600467i
$894$			17.5251i			0.586126i
$895$	11.7154	+	11.7154i	0.391603	+	0.391603i
$896$	17.3429	−	17.3429i	0.579385	−	0.579385i
$897$		−	11.8100i		−	0.394325i
$898$	−8.67937			−0.289634
$899$	2.04924	+	2.04924i	0.0683459	+	0.0683459i
$900$		−	0.540731i		−	0.0180244i
$901$	−12.3063			−0.409982
$902$	55.5268	+	25.4340i	1.84884	+	0.846859i
$903$	5.07885			0.169014
$904$			1.23879i			0.0412017i
$905$	5.16928	+	5.16928i	0.171833	+	0.171833i
$906$	29.8450			0.991533
$907$			27.0172i			0.897090i	0.893760	+	0.448545i	$0.148058\pi$
$907$			27.0172i			0.897090i	−0.893760	+	0.448545i	$0.851942\pi$
$908$	−0.416317	+	0.416317i	−0.0138160	+	0.0138160i
$909$	−1.03177	−	1.03177i	−0.0342216	−	0.0342216i
$910$		−	7.89524i		−	0.261725i
$911$		−	27.1675i		−	0.900099i	−0.893004	−	0.450050i	$-0.851406\pi$
$911$		−	27.1675i		−	0.900099i	0.893004	−	0.450050i	$-0.148594\pi$
$912$	−18.8085			−0.622810
$913$	34.0510	+	34.0510i	1.12692	+	1.12692i
$914$	34.7263	+	34.7263i	1.14864	+	1.14864i
$915$	12.0253	+	12.0253i	0.397545	+	0.397545i
$916$	−0.865220	+	0.865220i	−0.0285877	+	0.0285877i
$917$	−26.2711	+	26.2711i	−0.867547	+	0.867547i
$918$	4.62948			0.152796
$919$	−21.3553	+	21.3553i	−0.704446	+	0.704446i	−0.965362	−	0.260916i	$-0.915976\pi$
$919$	−21.3553	+	21.3553i	−0.704446	+	0.704446i	0.260916	+	0.965362i	$0.415976\pi$
$920$	24.7480			0.815918
$921$	8.60639	−	8.60639i	0.283590	−	0.283590i
$922$		−	25.3382i		−	0.834470i
$923$			3.89364i			0.128161i
$924$	−1.67806	+	1.67806i	−0.0552042	+	0.0552042i
$925$	−29.2487			−0.961693
$926$	−16.3781	+	16.3781i	−0.538216	+	0.538216i
$927$	14.1269			0.463988
$928$	−3.55914	+	3.55914i	−0.116834	+	0.116834i
$929$	6.88826	−	6.88826i	0.225996	−	0.225996i	−0.585021	−	0.811018i	$-0.698914\pi$
$929$	6.88826	−	6.88826i	0.225996	−	0.225996i	0.811018	+	0.585021i	$0.198914\pi$
$930$	−0.946812	−	0.946812i	−0.0310472	−	0.0310472i
$931$	−9.92788	−	9.92788i	−0.325373	−	0.325373i
$932$	−2.00478	−	2.00478i	−0.0656687	−	0.0656687i
$933$	−2.03768			−0.0667106
$934$			16.6417i			0.544532i
$935$		−	29.5877i		−	0.967621i
$936$	3.55267	+	3.55267i	0.116123	+	0.116123i
$937$	−28.5369	+	28.5369i	−0.932261	+	0.932261i	−0.997847	−	0.0655856i	$-0.979108\pi$
$937$	−28.5369	+	28.5369i	−0.932261	+	0.932261i	0.0655856	+	0.997847i	$0.479108\pi$
$938$		−	9.29112i		−	0.303366i
$939$	−11.0409			−0.360306
$940$	0.816741	+	0.816741i	0.0266392	+	0.0266392i
$941$		−	5.17931i		−	0.168841i	−0.996430	−	0.0844204i	$-0.973096\pi$
$941$		−	5.17931i		−	0.168841i	0.996430	−	0.0844204i	$-0.0269039\pi$
$942$	19.5824			0.638028
$943$	14.0465	+	37.7903i	0.457417	+	1.23062i
$944$	20.8972			0.680145
$945$			2.84438i			0.0925278i
$946$	−17.6715	−	17.6715i	−0.574551	−	0.574551i
$947$	−37.8810			−1.23097			−0.615483	−	0.788150i	$-0.711039\pi$
$947$	−37.8810			−1.23097			−0.615483	+	0.788150i	$0.711039\pi$
$948$			0.217548i			0.00706562i
$949$	19.1239	−	19.1239i	0.620789	−	0.620789i
$950$	12.8985	+	12.8985i	0.418484	+	0.418484i
$951$		−	17.7565i		−	0.575794i
$952$		−	16.2431i		−	0.526443i
$953$	−5.67251			−0.183751			−0.0918753	−	0.995771i	$-0.529286\pi$
$953$	−5.67251			−0.183751			−0.0918753	+	0.995771i	$0.529286\pi$
$954$	−4.11635	−	4.11635i	−0.133272	−	0.133272i
$955$	−10.3448	−	10.3448i	−0.334751	−	0.334751i
$956$	3.89775	+	3.89775i	0.126062	+	0.126062i
$957$	−21.4203	+	21.4203i	−0.692419	+	0.692419i
$958$	−0.849725	+	0.849725i	−0.0274534	+	0.0274534i
$959$	19.1702			0.619038
$960$	−7.36979	+	7.36979i	−0.237859	+	0.237859i
$961$	−30.6198			−0.987735
$962$	−20.1657	+	20.1657i	−0.650167	+	0.650167i
$963$			17.6306i			0.568138i
$964$		−	2.73990i		−	0.0882461i
$965$	−15.2986	+	15.2986i	−0.492478	+	0.492478i
$966$	−18.0614			−0.581116
$967$	−29.6025	+	29.6025i	−0.951951	+	0.951951i	−0.998897	−	0.0469463i	$-0.985051\pi$
$967$	−29.6025	+	29.6025i	−0.951951	+	0.951951i	0.0469463	+	0.998897i	$0.485051\pi$
$968$	−81.8145			−2.62962
$969$	−9.57819	+	9.57819i	−0.307696	+	0.307696i
$970$	−4.89481	+	4.89481i	−0.157163	+	0.157163i
$971$	14.9928	+	14.9928i	0.481141	+	0.481141i	0.905496	−	0.424355i	$-0.139499\pi$
$971$	14.9928	+	14.9928i	0.481141	+	0.481141i	−0.424355	+	0.905496i	$0.639499\pi$
$972$	0.134310	+	0.134310i	0.00430801	+	0.00430801i
$973$	−2.57529	−	2.57529i	−0.0825600	−	0.0825600i
$974$	−12.0719			−0.386809
$975$		−	5.33971i		−	0.171007i
$976$		−	50.3432i		−	1.61145i
$977$	−29.3725	−	29.3725i	−0.939710	−	0.939710i	0.0585730	−	0.998283i	$-0.481345\pi$
$977$	−29.3725	−	29.3725i	−0.939710	−	0.939710i	−0.998283	+	0.0585730i	$0.981345\pi$
$978$	−21.0963	+	21.0963i	−0.674586	+	0.674586i
$979$		−	66.3013i		−	2.11900i
$980$	0.903766			0.0288697
$981$	−2.82849	−	2.82849i	−0.0903066	−	0.0903066i
$982$		−	43.7384i		−	1.39575i
$983$	−35.3854			−1.12862			−0.564310	−	0.825563i	$-0.690858\pi$
$983$	−35.3854			−1.12862			−0.564310	+	0.825563i	$0.690858\pi$
$984$	−15.5934	−	7.14256i	−0.497101	−	0.227696i
$985$	−10.7877			−0.343723
$986$			21.7580i			0.692917i
$987$	5.68019	+	5.68019i	0.180803	+	0.180803i
$988$	1.54265			0.0490783
$989$		−	16.4972i		−	0.524580i
$990$	9.89684	−	9.89684i	0.314542	−	0.314542i
$991$	41.6717	+	41.6717i	1.32374	+	1.32374i	0.910720	+	0.413025i	$0.135528\pi$
$991$	41.6717	+	41.6717i	1.32374	+	1.32374i	0.413025	+	0.910720i	$0.364472\pi$
$992$			0.660378i			0.0209670i
$993$			21.6100i			0.685772i
$994$	5.95466			0.188870
$995$	−25.5330	−	25.5330i	−0.809451	−	0.809451i
$996$	1.00346	+	1.00346i	0.0317960	+	0.0317960i
$997$	20.8110	+	20.8110i	0.659092	+	0.659092i	0.955165	−	0.296073i	$-0.0956772\pi$
$997$	20.8110	+	20.8110i	0.659092	+	0.659092i	−0.296073	+	0.955165i	$0.595677\pi$
$998$	29.7758	−	29.7758i	0.942537	−	0.942537i
$999$	7.26500	−	7.26500i	0.229854	−	0.229854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	123.2.e.a.91.5	yes	12
3.2	odd	2		369.2.f.e.91.2		12
4.3	odd	2		1968.2.t.d.337.1		12
41.14	odd	8		5043.2.a.s.1.2		6
41.27	odd	8		5043.2.a.t.1.2		6
41.32	even	4	inner	123.2.e.a.73.2	✓	12
123.32	odd	4		369.2.f.e.73.5		12
164.155	odd	4		1968.2.t.d.1057.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
123.2.e.a.73.2	✓	12	41.32	even	4	inner
123.2.e.a.91.5	yes	12	1.1	even	1	trivial
369.2.f.e.73.5		12	123.32	odd	4
369.2.f.e.91.2		12	3.2	odd	2
1968.2.t.d.337.1		12	4.3	odd	2
1968.2.t.d.1057.3		12	164.155	odd	4
5043.2.a.s.1.2		6	41.14	odd	8
5043.2.a.t.1.2		6	41.27	odd	8

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:	\( N \)	\(=\)	\( 123 = 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	123.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.47985i q^{2} +(0.707107 + 0.707107i) q^{3} -0.189944 q^{4} -1.46738i q^{5} +(-1.04641 + 1.04641i) q^{6} +(1.37066 + 1.37066i) q^{7} +2.67860i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.47985i q^{2} +(0.707107 + 0.707107i) q^{3} -0.189944 q^{4} -1.46738i q^{5} +(-1.04641 + 1.04641i) q^{6} +(1.37066 + 1.37066i) q^{7} +2.67860i q^{8} +1.00000i q^{9} +2.17150 q^{10} +(-4.55762 - 4.55762i) q^{11} +(-0.134310 - 0.134310i) q^{12} +(-1.32631 - 1.32631i) q^{13} +(-2.02837 + 2.02837i) q^{14} +(1.03759 - 1.03759i) q^{15} -4.34381 q^{16} +(-2.21208 + 2.21208i) q^{17} -1.47985 q^{18} +(3.06173 - 3.06173i) q^{19} +0.278719i q^{20} +1.93841i q^{21} +(6.74457 - 6.74457i) q^{22} +6.29636 q^{23} +(-1.89406 + 1.89406i) q^{24} +2.84680 q^{25} +(1.96274 - 1.96274i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.260349 - 0.260349i) q^{28} +(-3.32332 - 3.32332i) q^{29} +(1.53548 + 1.53548i) q^{30} -0.616624 q^{31} -1.07096i q^{32} -6.44544i q^{33} +(-3.27354 - 3.27354i) q^{34} +(2.01128 - 2.01128i) q^{35} -0.189944i q^{36} -10.2743 q^{37} +(4.53089 + 4.53089i) q^{38} -1.87569i q^{39} +3.93053 q^{40} +(2.23089 + 6.00193i) q^{41} -2.86855 q^{42} -2.62011i q^{43} +(0.865690 + 0.865690i) q^{44} +1.46738 q^{45} +9.31764i q^{46} +(2.93034 - 2.93034i) q^{47} +(-3.07154 - 3.07154i) q^{48} -3.24257i q^{49} +4.21282i q^{50} -3.12835 q^{51} +(0.251924 + 0.251924i) q^{52} +(2.78161 + 2.78161i) q^{53} +(-1.04641 - 1.04641i) q^{54} +(-6.68775 + 6.68775i) q^{55} +(-3.67146 + 3.67146i) q^{56} +4.32995 q^{57} +(4.91800 - 4.91800i) q^{58} -4.81080 q^{59} +(-0.197084 + 0.197084i) q^{60} +11.5896i q^{61} -0.912508i q^{62} +(-1.37066 + 1.37066i) q^{63} -7.10276 q^{64} +(-1.94620 + 1.94620i) q^{65} +9.53826 q^{66} +(-2.29029 + 2.29029i) q^{67} +(0.420170 - 0.420170i) q^{68} +(4.45220 + 4.45220i) q^{69} +(2.97639 + 2.97639i) q^{70} +(-1.46784 - 1.46784i) q^{71} -2.67860 q^{72} +14.4189i q^{73} -15.2043i q^{74} +(2.01299 + 2.01299i) q^{75} +(-0.581557 + 0.581557i) q^{76} -12.4939i q^{77} +2.77573 q^{78} +(-0.809869 - 0.809869i) q^{79} +6.37402i q^{80} -1.00000 q^{81} +(-8.88192 + 3.30138i) q^{82} -7.47123 q^{83} -0.368188i q^{84} +(3.24596 + 3.24596i) q^{85} +3.87736 q^{86} -4.69989i q^{87} +(12.2080 - 12.2080i) q^{88} +(7.27368 + 7.27368i) q^{89} +2.17150i q^{90} -3.63585i q^{91} -1.19595 q^{92} +(-0.436019 - 0.436019i) q^{93} +(4.33645 + 4.33645i) q^{94} +(-4.49272 - 4.49272i) q^{95} +(0.757282 - 0.757282i) q^{96} +(-2.25412 + 2.25412i) q^{97} +4.79850 q^{98} +(4.55762 - 4.55762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4}+O(q^{10}) \) 12 * q - 8 * q^4	\( 12 q - 8 q^{4} - 24 q^{10} - 12 q^{11} + 8 q^{12} + 4 q^{13} + 20 q^{14} - 4 q^{15} + 8 q^{17} + 4 q^{19} + 12 q^{22} - 8 q^{23} + 12 q^{24} - 28 q^{25} - 20 q^{26} - 44 q^{28} + 12 q^{29} + 16 q^{30} + 12 q^{31} + 8 q^{34} + 36 q^{35} + 4 q^{37} + 20 q^{38} + 56 q^{40} - 20 q^{41} - 32 q^{42} + 20 q^{44} + 8 q^{45} - 40 q^{47} - 16 q^{48} - 12 q^{51} + 20 q^{52} - 12 q^{53} - 16 q^{55} - 40 q^{56} - 24 q^{57} + 36 q^{58} - 16 q^{59} - 4 q^{60} - 8 q^{64} + 4 q^{65} + 16 q^{66} + 16 q^{67} + 4 q^{68} - 36 q^{70} + 8 q^{71} - 24 q^{72} + 40 q^{75} - 52 q^{76} + 56 q^{78} - 12 q^{81} - 20 q^{82} + 40 q^{83} + 36 q^{85} + 48 q^{86} + 36 q^{88} - 24 q^{89} - 72 q^{92} - 8 q^{93} - 16 q^{94} + 28 q^{95} - 24 q^{96} + 40 q^{97} + 80 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 8 * q^4 - 24 * q^10 - 12 * q^11 + 8 * q^12 + 4 * q^13 + 20 * q^14 - 4 * q^15 + 8 * q^17 + 4 * q^19 + 12 * q^22 - 8 * q^23 + 12 * q^24 - 28 * q^25 - 20 * q^26 - 44 * q^28 + 12 * q^29 + 16 * q^30 + 12 * q^31 + 8 * q^34 + 36 * q^35 + 4 * q^37 + 20 * q^38 + 56 * q^40 - 20 * q^41 - 32 * q^42 + 20 * q^44 + 8 * q^45 - 40 * q^47 - 16 * q^48 - 12 * q^51 + 20 * q^52 - 12 * q^53 - 16 * q^55 - 40 * q^56 - 24 * q^57 + 36 * q^58 - 16 * q^59 - 4 * q^60 - 8 * q^64 + 4 * q^65 + 16 * q^66 + 16 * q^67 + 4 * q^68 - 36 * q^70 + 8 * q^71 - 24 * q^72 + 40 * q^75 - 52 * q^76 + 56 * q^78 - 12 * q^81 - 20 * q^82 + 40 * q^83 + 36 * q^85 + 48 * q^86 + 36 * q^88 - 24 * q^89 - 72 * q^92 - 8 * q^93 - 16 * q^94 + 28 * q^95 - 24 * q^96 + 40 * q^97 + 80 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more