LMFDB - Embedded newform 605.2.e.b.362.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(362,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("605.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			362.4
Character	$\chi$	$=$	605.362
Dual form			605.2.e.b.483.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03659 + 1.03659i) q^{2} +(0.588647 - 0.588647i) q^{3} -0.149021i q^{4} +(-2.18706 + 0.465567i) q^{5} +1.22037i q^{6} +(2.98069 - 2.98069i) q^{7} +(-1.91870 - 1.91870i) q^{8} +2.30699i q^{9} +O(q^{10})$	\(q+(-1.03659 + 1.03659i) q^{2} +(0.588647 - 0.588647i) q^{3} -0.149021i q^{4} +(-2.18706 + 0.465567i) q^{5} +1.22037i q^{6} +(2.98069 - 2.98069i) q^{7} +(-1.91870 - 1.91870i) q^{8} +2.30699i q^{9} +(1.78448 - 2.74968i) q^{10} +(-0.0877208 - 0.0877208i) q^{12} +(-0.654555 - 0.654555i) q^{13} +6.17948i q^{14} +(-1.01335 + 1.56146i) q^{15} +4.27583 q^{16} +(1.36314 - 1.36314i) q^{17} +(-2.39139 - 2.39139i) q^{18} +5.43176 q^{19} +(0.0693793 + 0.325918i) q^{20} -3.50915i q^{21} +(1.95998 - 1.95998i) q^{23} -2.25887 q^{24} +(4.56649 - 2.03645i) q^{25} +1.35700 q^{26} +(3.12394 + 3.12394i) q^{27} +(-0.444185 - 0.444185i) q^{28} -1.00183 q^{29} +(-0.568163 - 2.66902i) q^{30} +0.423945 q^{31} +(-0.594873 + 0.594873i) q^{32} +2.82602i q^{34} +(-5.13124 + 7.90666i) q^{35} +0.343790 q^{36} +(3.48815 + 3.48815i) q^{37} +(-5.63049 + 5.63049i) q^{38} -0.770604 q^{39} +(5.08960 + 3.30303i) q^{40} -0.577469i q^{41} +(3.63753 + 3.63753i) q^{42} +(5.05373 + 5.05373i) q^{43} +(-1.07406 - 5.04553i) q^{45} +4.06339i q^{46} +(0.841173 + 0.841173i) q^{47} +(2.51696 - 2.51696i) q^{48} -10.7690i q^{49} +(-2.62261 + 6.84452i) q^{50} -1.60481i q^{51} +(-0.0975424 + 0.0975424i) q^{52} +(6.42164 - 6.42164i) q^{53} -6.47647 q^{54} -11.4381 q^{56} +(3.19739 - 3.19739i) q^{57} +(1.03848 - 1.03848i) q^{58} +9.30975i q^{59} +(0.232691 + 0.151011i) q^{60} -7.78179i q^{61} +(-0.439456 + 0.439456i) q^{62} +(6.87641 + 6.87641i) q^{63} +7.31840i q^{64} +(1.73629 + 1.12681i) q^{65} +(-3.05526 - 3.05526i) q^{67} +(-0.203136 - 0.203136i) q^{68} -2.30748i q^{69} +(-2.87696 - 13.5149i) q^{70} +8.59135 q^{71} +(4.42642 - 4.42642i) q^{72} +(3.86109 + 3.86109i) q^{73} -7.23154 q^{74} +(1.48930 - 3.88681i) q^{75} -0.809447i q^{76} +(0.798797 - 0.798797i) q^{78} -2.28422 q^{79} +(-9.35152 + 1.99069i) q^{80} -3.24316 q^{81} +(0.598596 + 0.598596i) q^{82} +(-1.40622 - 1.40622i) q^{83} -0.522937 q^{84} +(-2.34664 + 3.61590i) q^{85} -10.4773 q^{86} +(-0.589724 + 0.589724i) q^{87} +13.9313i q^{89} +(6.34348 + 4.11677i) q^{90} -3.90204 q^{91} +(-0.292079 - 0.292079i) q^{92} +(0.249554 - 0.249554i) q^{93} -1.74390 q^{94} +(-11.8796 + 2.52885i) q^{95} +0.700340i q^{96} +(-2.35066 - 2.35066i) q^{97} +(11.1630 + 11.1630i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} + 8 q^{5}+O(q^{10}) $ 32 * q - 4 * q^3 + 8 * q^5	$ 32 q - 4 q^{3} + 8 q^{5} + 12 q^{12} - 36 q^{15} - 8 q^{16} - 64 q^{20} - 24 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{31} + 24 q^{36} + 32 q^{37} - 40 q^{38} + 60 q^{42} - 28 q^{45} - 28 q^{47} + 56 q^{48} + 116 q^{53} - 80 q^{56} - 80 q^{58} + 104 q^{60} - 8 q^{67} - 80 q^{70} + 24 q^{71} - 76 q^{75} + 60 q^{78} + 8 q^{80} + 8 q^{81} - 20 q^{82} - 40 q^{86} + 80 q^{91} + 52 q^{92} + 32 q^{93} + 92 q^{97}+O(q^{100}) $ 32 * q - 4 * q^3 + 8 * q^5 + 12 * q^12 - 36 * q^15 - 8 * q^16 - 64 * q^20 - 24 * q^23 + 16 * q^25 - 16 * q^27 - 8 * q^31 + 24 * q^36 + 32 * q^37 - 40 * q^38 + 60 * q^42 - 28 * q^45 - 28 * q^47 + 56 * q^48 + 116 * q^53 - 80 * q^56 - 80 * q^58 + 104 * q^60 - 8 * q^67 - 80 * q^70 + 24 * q^71 - 76 * q^75 + 60 * q^78 + 8 * q^80 + 8 * q^81 - 20 * q^82 - 40 * q^86 + 80 * q^91 + 52 * q^92 + 32 * q^93 + 92 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.03659	+	1.03659i	−0.732977	+	0.732977i	−0.971208	−	0.238231i	$-0.923432\pi$
$2$	−1.03659	+	1.03659i	−0.732977	+	0.732977i	0.238231	+	0.971208i	$0.423432\pi$
$3$	0.588647	−	0.588647i	0.339856	−	0.339856i	−0.516457	−	0.856313i	$-0.672750\pi$
$3$	0.588647	−	0.588647i	0.339856	−	0.339856i	0.856313	+	0.516457i	$0.172750\pi$
$4$		−	0.149021i		−	0.0745105i
$5$	−2.18706	+	0.465567i	−0.978085	+	0.208208i
$5$	−2.18706	+	0.465567i	−0.978085	+	0.208208i
$6$			1.22037i			0.498213i
$7$	2.98069	−	2.98069i	1.12659	−	1.12659i	0.135866	−	0.990727i	$-0.456618\pi$
$7$	2.98069	−	2.98069i	1.12659	−	1.12659i	0.990727	−	0.135866i	$-0.0433818\pi$
$8$	−1.91870	−	1.91870i	−0.678362	−	0.678362i
$9$			2.30699i			0.768996i
$10$	1.78448	−	2.74968i	0.564302	−	0.869525i
$11$		0			0
$11$		0			0
$12$	−0.0877208	−	0.0877208i	−0.0253228	−	0.0253228i
$13$	−0.654555	−	0.654555i	−0.181541	−	0.181541i	0.610486	−	0.792027i	$-0.290974\pi$
$13$	−0.654555	−	0.654555i	−0.181541	−	0.181541i	−0.792027	+	0.610486i	$0.790974\pi$
$14$			6.17948i			1.65153i
$15$	−1.01335	+	1.56146i	−0.261647	+	0.403168i
$16$	4.27583			1.06896
$17$	1.36314	−	1.36314i	0.330609	−	0.330609i	−0.522209	−	0.852818i	$-0.674892\pi$
$17$	1.36314	−	1.36314i	0.330609	−	0.330609i	0.852818	+	0.522209i	$0.174892\pi$
$18$	−2.39139	−	2.39139i	−0.563657	−	0.563657i
$19$	5.43176			1.24613			0.623066	−	0.782170i	$-0.285887\pi$
$19$	5.43176			1.24613			0.623066	+	0.782170i	$0.285887\pi$
$20$	0.0693793	+	0.325918i	0.0155137	+	0.0728776i
$21$		−	3.50915i		−	0.765758i
$22$		0			0
$23$	1.95998	−	1.95998i	0.408685	−	0.408685i	−0.472595	−	0.881280i	$-0.656683\pi$
$23$	1.95998	−	1.95998i	0.408685	−	0.408685i	0.881280	+	0.472595i	$0.156683\pi$
$24$	−2.25887			−0.461091
$25$	4.56649	−	2.03645i	0.913299	−	0.407290i
$26$	1.35700			0.266130
$27$	3.12394	+	3.12394i	0.601203	+	0.601203i
$28$	−0.444185	−	0.444185i	−0.0839431	−	0.0839431i
$29$	−1.00183			−0.186035			−0.0930175	−	0.995664i	$-0.529651\pi$
$29$	−1.00183			−0.186035			−0.0930175	+	0.995664i	$0.529651\pi$
$30$	−0.568163	−	2.66902i	−0.103732	−	0.487294i
$31$	0.423945			0.0761428			0.0380714	−	0.999275i	$-0.487879\pi$
$31$	0.423945			0.0761428			0.0380714	+	0.999275i	$0.487879\pi$
$32$	−0.594873	+	0.594873i	−0.105160	+	0.105160i
$33$		0			0
$34$			2.82602i			0.484658i
$35$	−5.13124	+	7.90666i	−0.867338	+	1.33647i
$36$	0.343790			0.0572983
$37$	3.48815	+	3.48815i	0.573449	+	0.573449i	0.933091	−	0.359642i	$-0.117101\pi$
$37$	3.48815	+	3.48815i	0.573449	+	0.573449i	−0.359642	+	0.933091i	$0.617101\pi$
$38$	−5.63049	+	5.63049i	−0.913386	+	0.913386i
$39$	−0.770604			−0.123395
$40$	5.08960	+	3.30303i	0.804736	+	0.522255i
$41$		−	0.577469i		−	0.0901854i	−0.998983	−	0.0450927i	$-0.985642\pi$
$41$		−	0.577469i		−	0.0901854i	0.998983	−	0.0450927i	$-0.0143583\pi$
$42$	3.63753	+	3.63753i	0.561283	+	0.561283i
$43$	5.05373	+	5.05373i	0.770687	+	0.770687i	0.978227	−	0.207540i	$-0.0665456\pi$
$43$	5.05373	+	5.05373i	0.770687	+	0.770687i	−0.207540	+	0.978227i	$0.566546\pi$
$44$		0			0
$45$	−1.07406	−	5.04553i	−0.160111	−	0.752143i
$46$			4.06339i			0.599113i
$47$	0.841173	+	0.841173i	0.122698	+	0.122698i	0.765789	−	0.643092i	$-0.222349\pi$
$47$	0.841173	+	0.841173i	0.122698	+	0.122698i	−0.643092	+	0.765789i	$0.722349\pi$
$48$	2.51696	−	2.51696i	0.363292	−	0.363292i
$49$		−	10.7690i		−	1.53843i
$50$	−2.62261	+	6.84452i	−0.370893	+	0.967961i
$51$		−	1.60481i		−	0.224719i
$52$	−0.0975424	+	0.0975424i	−0.0135267	+	0.0135267i
$53$	6.42164	−	6.42164i	0.882080	−	0.882080i	−0.111666	−	0.993746i	$-0.535619\pi$
$53$	6.42164	−	6.42164i	0.882080	−	0.882080i	0.993746	+	0.111666i	$0.0356188\pi$
$54$	−6.47647			−0.881337
$55$		0			0
$56$	−11.4381			−1.52848
$57$	3.19739	−	3.19739i	0.423505	−	0.423505i
$58$	1.03848	−	1.03848i	0.136359	−	0.136359i
$59$			9.30975i			1.21203i	0.795455	+	0.606013i	$0.207232\pi$
$59$			9.30975i			1.21203i	−0.795455	+	0.606013i	$0.792768\pi$
$60$	0.232691	+	0.151011i	0.0300403	+	0.0194954i
$61$		−	7.78179i		−	0.996357i	−0.867075	−	0.498178i	$-0.834002\pi$
$61$		−	7.78179i		−	0.996357i	0.867075	−	0.498178i	$-0.165998\pi$
$62$	−0.439456	+	0.439456i	−0.0558109	+	0.0558109i
$63$	6.87641	+	6.87641i	0.866346	+	0.866346i
$64$			7.31840i			0.914800i
$65$	1.73629	+	1.12681i	0.215361	+	0.139764i
$66$		0			0
$67$	−3.05526	−	3.05526i	−0.373259	−	0.373259i	0.495404	−	0.868663i	$-0.335020\pi$
$67$	−3.05526	−	3.05526i	−0.373259	−	0.373259i	−0.868663	+	0.495404i	$0.835020\pi$
$68$	−0.203136	−	0.203136i	−0.0246339	−	0.0246339i
$69$		−	2.30748i		−	0.277788i
$70$	−2.87696	−	13.5149i	−0.343863	−	1.61534i
$71$	8.59135			1.01961			0.509803	−	0.860291i	$-0.329718\pi$
$71$	8.59135			1.01961			0.509803	+	0.860291i	$0.329718\pi$
$72$	4.42642	−	4.42642i	0.521658	−	0.521658i
$73$	3.86109	+	3.86109i	0.451906	+	0.451906i	0.895987	−	0.444081i	$-0.146470\pi$
$73$	3.86109	+	3.86109i	0.451906	+	0.451906i	−0.444081	+	0.895987i	$0.646470\pi$
$74$	−7.23154			−0.840650
$75$	1.48930	−	3.88681i	0.171970	−	0.448810i
$76$		−	0.809447i		−	0.0928499i
$77$		0			0
$78$	0.798797	−	0.798797i	0.0904460	−	0.0904460i
$79$	−2.28422			−0.256994			−0.128497	−	0.991710i	$-0.541015\pi$
$79$	−2.28422			−0.256994			−0.128497	+	0.991710i	$0.541015\pi$
$80$	−9.35152	+	1.99069i	−1.04553	+	0.222566i
$81$	−3.24316			−0.360351
$82$	0.598596	+	0.598596i	0.0661039	+	0.0661039i
$83$	−1.40622	−	1.40622i	−0.154352	−	0.154352i	0.625706	−	0.780059i	$-0.284811\pi$
$83$	−1.40622	−	1.40622i	−0.154352	−	0.154352i	−0.780059	+	0.625706i	$0.784811\pi$
$84$	−0.522937			−0.0570571
$85$	−2.34664	+	3.61590i	−0.254528	+	0.392199i
$86$	−10.4773			−1.12979
$87$	−0.589724	+	0.589724i	−0.0632250	+	0.0632250i
$88$		0			0
$89$			13.9313i			1.47671i	0.674410	+	0.738357i	$0.264398\pi$
$89$			13.9313i			1.47671i	−0.674410	+	0.738357i	$0.735602\pi$
$90$	6.34348	+	4.11677i	0.668662	+	0.433946i
$91$	−3.90204			−0.409045
$92$	−0.292079	−	0.292079i	−0.0304513	−	0.0304513i
$93$	0.249554	−	0.249554i	0.0258776	−	0.0258776i
$94$	−1.74390			−0.179869
$95$	−11.8796	+	2.52885i	−1.21882	+	0.259454i
$96$			0.700340i			0.0714782i
$97$	−2.35066	−	2.35066i	−0.238673	−	0.238673i	0.577627	−	0.816301i	$-0.303979\pi$
$97$	−2.35066	−	2.35066i	−0.238673	−	0.238673i	−0.816301	+	0.577627i	$0.803979\pi$
$98$	11.1630	+	11.1630i	1.12763	+	1.12763i
$99$		0			0
$100$	−0.303474	−	0.680504i	−0.0303474	−	0.0680504i
$101$		−	13.2909i		−	1.32249i	−0.750168	−	0.661247i	$-0.770027\pi$
$101$		−	13.2909i		−	1.32249i	0.750168	−	0.661247i	$-0.229973\pi$
$102$	1.66353	+	1.66353i	0.164714	+	0.164714i
$103$	7.12932	−	7.12932i	0.702472	−	0.702472i	−0.262468	−	0.964941i	$-0.584536\pi$
$103$	7.12932	−	7.12932i	0.702472	−	0.702472i	0.964941	+	0.262468i	$0.0845365\pi$
$104$			2.51179i			0.246301i
$105$	1.63374	+	7.67473i	0.159437	+	0.748977i
$106$			13.3132i			1.29309i
$107$	−4.36050	+	4.36050i	−0.421546	+	0.421546i	−0.885736	−	0.464190i	$-0.846346\pi$
$107$	−4.36050	+	4.36050i	−0.421546	+	0.421546i	0.464190	+	0.885736i	$0.346346\pi$
$108$	0.465533	−	0.465533i	0.0447960	−	0.0447960i
$109$	−19.9193			−1.90793			−0.953964	−	0.299922i	$-0.903039\pi$
$109$	−19.9193			−1.90793			−0.953964	+	0.299922i	$0.903039\pi$
$110$		0			0
$111$	4.10659			0.389780
$112$	12.7449	−	12.7449i	1.20428	−	1.20428i
$113$	8.57166	−	8.57166i	0.806354	−	0.806354i	−0.177726	−	0.984080i	$-0.556874\pi$
$113$	8.57166	−	8.57166i	0.806354	−	0.806354i	0.984080	+	0.177726i	$0.0568741\pi$
$114$			6.62874i			0.620839i
$115$	−3.37411	+	5.19912i	−0.314637	+	0.484820i
$116$			0.149294i			0.0138616i
$117$	1.51005	−	1.51005i	0.139604	−	0.139604i
$118$	−9.65036	−	9.65036i	−0.888388	−	0.888388i
$119$		−	8.12617i		−	0.744925i
$120$	4.94030	−	1.05166i	0.450986	−	0.0960028i
$121$		0			0
$122$	8.06650	+	8.06650i	0.730306	+	0.730306i
$123$	−0.339925	−	0.339925i	−0.0306500	−	0.0306500i
$124$		−	0.0631767i		−	0.00567344i
$125$	−9.03911	+	6.57985i	−0.808483	+	0.588520i
$126$	−14.2560			−1.27002
$127$	−0.819912	+	0.819912i	−0.0727554	+	0.0727554i	−0.742548	−	0.669793i	$-0.766383\pi$
$127$	−0.819912	+	0.819912i	−0.0727554	+	0.0727554i	0.669793	+	0.742548i	$0.266383\pi$
$128$	−8.77589	−	8.77589i	−0.775687	−	0.775687i
$129$	5.94973			0.523845
$130$	−2.96786	+	0.631777i	−0.260298	+	0.0554105i
$131$		−	14.4532i		−	1.26278i	−0.775465	−	0.631390i	$-0.782485\pi$
$131$		−	14.4532i		−	1.26278i	0.775465	−	0.631390i	$-0.217515\pi$
$132$		0			0
$133$	16.1904	−	16.1904i	1.40388	−	1.40388i
$134$	6.33408			0.547181
$135$	−8.28667	−	5.37786i	−0.713203	−	0.462852i
$136$	−5.23090			−0.448546
$137$	−8.74810	−	8.74810i	−0.747401	−	0.747401i	0.226590	−	0.973990i	$-0.427242\pi$
$137$	−8.74810	−	8.74810i	−0.747401	−	0.747401i	−0.973990	+	0.226590i	$0.927242\pi$
$138$	2.39190	+	2.39190i	0.203612	+	0.203612i
$139$	1.00938			0.0856145			0.0428073	−	0.999083i	$-0.486370\pi$
$139$	1.00938			0.0856145			0.0428073	+	0.999083i	$0.486370\pi$
$140$	1.17826	+	0.764663i	0.0995810	+	0.0646258i
$141$	0.990308			0.0833990
$142$	−8.90567	+	8.90567i	−0.747347	+	0.747347i
$143$		0			0
$144$			9.86430i			0.822025i
$145$	2.19106	−	0.466419i	0.181958	−	0.0387340i
$146$	−8.00470			−0.662474
$147$	−6.33913	−	6.33913i	−0.522843	−	0.522843i
$148$	0.519808	−	0.519808i	0.0427280	−	0.0427280i
$149$	1.22057			0.0999930			0.0499965	−	0.998749i	$-0.484079\pi$
$149$	1.22057			0.0999930			0.0499965	+	0.998749i	$0.484079\pi$
$150$	2.48522	+	5.57280i	0.202917	+	0.455017i
$151$		−	1.58675i		−	0.129128i	−0.997914	−	0.0645639i	$-0.979434\pi$
$151$		−	1.58675i		−	0.129128i	0.997914	−	0.0645639i	$-0.0205656\pi$
$152$	−10.4219	−	10.4219i	−0.845329	−	0.845329i
$153$	3.14474	+	3.14474i	0.254237	+	0.254237i
$154$		0			0
$155$	−0.927195	+	0.197375i	−0.0744741	+	0.0158535i
$156$			0.114836i			0.00919425i
$157$	−5.24615	−	5.24615i	−0.418688	−	0.418688i	0.466063	−	0.884751i	$-0.345672\pi$
$157$	−5.24615	−	5.24615i	−0.418688	−	0.418688i	−0.884751	+	0.466063i	$0.845672\pi$
$158$	2.36779	−	2.36779i	0.188371	−	0.188371i
$159$		−	7.56016i		−	0.599560i
$160$	1.02407	−	1.57798i	0.0809599	−	0.124750i
$161$		−	11.6842i		−	0.920844i
$162$	3.36182	−	3.36182i	0.264129	−	0.264129i
$163$	−10.8957	+	10.8957i	−0.853416	+	0.853416i	−0.990552	−	0.137136i	$-0.956210\pi$
$163$	−10.8957	+	10.8957i	−0.853416	+	0.853416i	0.137136	+	0.990552i	$0.456210\pi$
$164$	−0.0860550			−0.00671976
$165$		0			0
$166$	2.91533			0.226273
$167$	2.93461	−	2.93461i	0.227087	−	0.227087i	−0.584388	−	0.811475i	$-0.698665\pi$
$167$	2.93461	−	2.93461i	0.227087	−	0.227087i	0.811475	+	0.584388i	$0.198665\pi$
$168$	−6.73299	+	6.73299i	−0.519462	+	0.519462i
$169$		−	12.1431i		−	0.934086i
$170$	−1.31570	−	6.18068i	−0.100910	−	0.474037i
$171$			12.5310i			0.958270i
$172$	0.753112	−	0.753112i	0.0574243	−	0.0574243i
$173$	3.06159	+	3.06159i	0.232768	+	0.232768i	0.813847	−	0.581079i	$-0.197369\pi$
$173$	3.06159	+	3.06159i	0.232768	+	0.232768i	−0.581079	+	0.813847i	$0.697369\pi$
$174$		−	1.22260i		−	0.0926850i
$175$	7.54127	−	19.6813i	0.570066	−	1.48777i
$176$		0			0
$177$	5.48016	+	5.48016i	0.411914	+	0.411914i
$178$	−14.4410	−	14.4410i	−1.08240	−	1.08240i
$179$			3.71960i			0.278016i	0.990291	+	0.139008i	$0.0443913\pi$
$179$			3.71960i			0.278016i	−0.990291	+	0.139008i	$0.955609\pi$
$180$	−0.751890	+	0.160057i	−0.0560426	+	0.0119300i
$181$	6.04656			0.449437			0.224719	−	0.974424i	$-0.427854\pi$
$181$	6.04656			0.449437			0.224719	+	0.974424i	$0.427854\pi$
$182$	4.04481	−	4.04481i	0.299821	−	0.299821i
$183$	−4.58073	−	4.58073i	−0.338617	−	0.338617i
$184$	−7.52124			−0.554473
$185$	−9.25279	−	6.00485i	−0.680278	−	0.441485i
$186$			0.517369i			0.0379353i
$187$		0			0
$188$	0.125352	−	0.125352i	0.00914227	−	0.00914227i
$189$	18.6230			1.35462
$190$	9.69286	−	14.9356i	0.703194	−	1.08354i
$191$	−16.5546			−1.19785			−0.598926	−	0.800805i	$-0.704405\pi$
$191$	−16.5546			−1.19785			−0.598926	+	0.800805i	$0.704405\pi$
$192$	4.30795	+	4.30795i	0.310900	+	0.310900i
$193$	−11.9954	−	11.9954i	−0.863451	−	0.863451i	0.128286	−	0.991737i	$-0.459052\pi$
$193$	−11.9954	−	11.9954i	−0.863451	−	0.863451i	−0.991737	+	0.128286i	$0.959052\pi$
$194$	4.87332			0.349884
$195$	1.68536	−	0.358768i	0.120691	−	0.0256919i
$196$	−1.60480			−0.114629
$197$	−9.63624	+	9.63624i	−0.686554	+	0.686554i	−0.961469	−	0.274915i	$-0.911350\pi$
$197$	−9.63624	+	9.63624i	−0.686554	+	0.686554i	0.274915	+	0.961469i	$0.411350\pi$
$198$		0			0
$199$		−	19.4166i		−	1.37640i	−0.725519	−	0.688202i	$-0.758400\pi$
$199$		−	19.4166i		−	1.37640i	0.725519	−	0.688202i	$-0.241600\pi$
$200$	−12.6691	−	4.85439i	−0.895838	−	0.343257i
$201$	−3.59694			−0.253709
$202$	13.7772	+	13.7772i	0.969358	+	0.969358i
$203$	−2.98614	+	2.98614i	−0.209586	+	0.209586i
$204$	−0.239151			−0.0167439
$205$	0.268850	+	1.26296i	0.0187773	+	0.0882090i
$206$			14.7803i			1.02979i
$207$	4.52166	+	4.52166i	0.314277	+	0.314277i
$208$	−2.79877	−	2.79877i	−0.194060	−	0.194060i
$209$		0			0
$210$	−9.64903	−	6.26200i	−0.665846	−	0.432119i
$211$			6.39095i			0.439971i	0.975503	+	0.219986i	$0.0706010\pi$
$211$			6.39095i			0.439971i	−0.975503	+	0.219986i	$0.929399\pi$
$212$	−0.956959	−	0.956959i	−0.0657242	−	0.0657242i
$213$	5.05727	−	5.05727i	0.346519	−	0.346519i
$214$		−	9.04007i		−	0.617967i
$215$	−13.4057	−	8.69998i	−0.914260	−	0.593334i
$216$		−	11.9878i		−	0.815668i
$217$	1.26365	−	1.26365i	0.0857820	−	0.0857820i
$218$	20.6481	−	20.6481i	1.39847	−	1.39847i
$219$	4.54564			0.307166
$220$		0			0
$221$	−1.78450			−0.120038
$222$	−4.25683	+	4.25683i	−0.285700	+	0.285700i
$223$	10.0373	−	10.0373i	0.672150	−	0.672150i	−0.286062	−	0.958211i	$-0.592346\pi$
$223$	10.0373	−	10.0373i	0.672150	−	0.672150i	0.958211	+	0.286062i	$0.0923462\pi$
$224$			3.54626i			0.236944i
$225$	4.69807	+	10.5349i	0.313204	+	0.702323i
$226$			17.7705i			1.18208i
$227$	−5.85353	+	5.85353i	−0.388512	+	0.388512i	−0.874156	−	0.485644i	$-0.838585\pi$
$227$	−5.85353	+	5.85353i	−0.388512	+	0.388512i	0.485644	+	0.874156i	$0.338585\pi$
$228$	−0.476479	−	0.476479i	−0.0315556	−	0.0315556i
$229$			19.5994i			1.29517i	0.761995	+	0.647583i	$0.224220\pi$
$229$			19.5994i			1.29517i	−0.761995	+	0.647583i	$0.775780\pi$
$230$	−1.89178	−	8.88688i	−0.124740	−	0.585984i
$231$		0			0
$232$	1.92221	+	1.92221i	0.126199	+	0.126199i
$233$	2.62559	+	2.62559i	0.172008	+	0.172008i	0.787861	−	0.615853i	$-0.211188\pi$
$233$	2.62559	+	2.62559i	0.172008	+	0.172008i	−0.615853	+	0.787861i	$0.711188\pi$
$234$			3.13059i			0.204653i
$235$	−2.23132	−	1.44808i	−0.145555	−	0.0944621i
$236$	1.38735			0.0903087
$237$	−1.34460	+	1.34460i	−0.0873410	+	0.0873410i
$238$	8.42347	+	8.42347i	0.546013	+	0.546013i
$239$	3.21291			0.207826			0.103913	−	0.994586i	$-0.466864\pi$
$239$	3.21291			0.207826			0.103913	+	0.994586i	$0.466864\pi$
$240$	−4.33294	+	6.67656i	−0.279690	+	0.430970i
$241$			25.4119i			1.63693i	0.574559	+	0.818463i	$0.305174\pi$
$241$			25.4119i			1.63693i	−0.574559	+	0.818463i	$0.694826\pi$
$242$		0			0
$243$	−11.2809	+	11.2809i	−0.723671	+	0.723671i
$244$	−1.15965			−0.0742390
$245$	5.01368	+	23.5524i	0.320313	+	1.50471i
$246$	0.704724			0.0449315
$247$	−3.55538	−	3.55538i	−0.226224	−	0.226224i
$248$	−0.813423	−	0.813423i	−0.0516524	−	0.0516524i
$249$	−1.65553			−0.104915
$250$	2.54923	−	16.1904i	0.161227	−	1.02397i
$251$	16.3055			1.02919			0.514596	−	0.857433i	$-0.327942\pi$
$251$	16.3055			1.02919			0.514596	+	0.857433i	$0.327942\pi$
$252$	1.02473	−	1.02473i	0.0645519	−	0.0645519i
$253$		0			0
$254$		−	1.69982i		−	0.106656i
$255$	0.747149	+	3.50983i	0.0467883	+	0.219794i
$256$	3.55714			0.222321
$257$	11.4580	+	11.4580i	0.714729	+	0.714729i	0.967521	−	0.252792i	$-0.0813487\pi$
$257$	11.4580	+	11.4580i	0.714729	+	0.714729i	−0.252792	+	0.967521i	$0.581349\pi$
$258$	−6.16741	+	6.16741i	−0.383966	+	0.383966i
$259$	20.7942			1.29209
$260$	0.167919	−	0.258744i	0.0104139	−	0.0160466i
$261$		−	2.31121i		−	0.143060i
$262$	14.9820	+	14.9820i	0.925589	+	0.925589i
$263$	−0.677874	−	0.677874i	−0.0417995	−	0.0417995i	0.685898	−	0.727698i	$-0.259410\pi$
$263$	−0.677874	−	0.677874i	−0.0417995	−	0.0417995i	−0.727698	+	0.685898i	$0.759410\pi$
$264$		0			0
$265$	−11.0548	+	17.0342i	−0.679092	+	1.04640i
$266$			33.5654i			2.05803i
$267$	8.20062	+	8.20062i	0.501870	+	0.501870i
$268$	−0.455298	+	0.455298i	−0.0278117	+	0.0278117i
$269$			28.4238i			1.73303i	0.499149	+	0.866516i	$0.333646\pi$
$269$			28.4238i			1.73303i	−0.499149	+	0.866516i	$0.666354\pi$
$270$	14.1645	−	3.01523i	0.862022	−	0.183501i
$271$			30.7500i			1.86793i	0.357369	+	0.933963i	$0.383674\pi$
$271$			30.7500i			1.86793i	−0.357369	+	0.933963i	$0.616326\pi$
$272$	5.82855	−	5.82855i	0.353408	−	0.353408i
$273$	−2.29693	+	2.29693i	−0.139016	+	0.139016i
$274$	18.1363			1.09565
$275$		0			0
$276$	−0.343863			−0.0206981
$277$	−21.3182	+	21.3182i	−1.28089	+	1.28089i	−0.340720	+	0.940165i	$0.610671\pi$
$277$	−21.3182	+	21.3182i	−1.28089	+	1.28089i	−0.940165	+	0.340720i	$0.889329\pi$
$278$	−1.04631	+	1.04631i	−0.0627535	+	0.0627535i
$279$			0.978036i			0.0585535i
$280$	25.0158	−	5.32519i	1.49498	−	0.318241i
$281$		−	8.51905i		−	0.508204i	−0.967177	−	0.254102i	$-0.918220\pi$
$281$		−	8.51905i		−	0.508204i	0.967177	−	0.254102i	$-0.0817799\pi$
$282$	−1.02654	+	1.02654i	−0.0611295	+	0.0611295i
$283$	−6.74707	−	6.74707i	−0.401071	−	0.401071i	0.477539	−	0.878611i	$-0.341529\pi$
$283$	−6.74707	−	6.74707i	−0.401071	−	0.401071i	−0.878611	+	0.477539i	$0.841529\pi$
$284$		−	1.28029i		−	0.0759713i
$285$	−5.50430	+	8.48150i	−0.326046	+	0.502401i
$286$		0			0
$287$	−1.72125	−	1.72125i	−0.101602	−	0.101602i
$288$	−1.37236	−	1.37236i	−0.0808674	−	0.0808674i
$289$			13.2837i			0.781395i
$290$	−1.78774	+	2.75471i	−0.104980	+	0.161762i
$291$	−2.76742			−0.162229
$292$	0.575383	−	0.575383i	0.0336718	−	0.0336718i
$293$	1.63161	+	1.63161i	0.0953199	+	0.0953199i	0.753159	−	0.657839i	$-0.228529\pi$
$293$	1.63161	+	1.63161i	0.0953199	+	0.0953199i	−0.657839	+	0.753159i	$0.728529\pi$
$294$	13.1421			0.766464
$295$	−4.33431	−	20.3610i	−0.252354	−	1.18546i
$296$		−	13.3854i		−	0.778013i
$297$		0			0
$298$	−1.26523	+	1.26523i	−0.0732926	+	0.0732926i
$299$	−2.56583			−0.148386
$300$	−0.579216	−	0.221938i	−0.0334410	−	0.0128136i
$301$	30.1272			1.73650
$302$	1.64480	+	1.64480i	0.0946478	+	0.0946478i
$303$	−7.82366	−	7.82366i	−0.449457	−	0.449457i
$304$	23.2253			1.33206
$305$	3.62295	+	17.0193i	0.207449	+	0.974521i
$306$	−6.51959			−0.372700
$307$	12.4635	−	12.4635i	0.711327	−	0.711327i	−0.255486	−	0.966813i	$-0.582235\pi$
$307$	12.4635	−	12.4635i	0.711327	−	0.711327i	0.966813	+	0.255486i	$0.0822353\pi$
$308$		0			0
$309$		−	8.39331i		−	0.477479i
$310$	0.756521	−	1.16571i	0.0429675	−	0.0662081i
$311$	15.1136			0.857011			0.428506	−	0.903539i	$-0.359040\pi$
$311$	15.1136			0.857011			0.428506	+	0.903539i	$0.359040\pi$
$312$	1.47856	+	1.47856i	0.0837068	+	0.0837068i
$313$	18.4669	−	18.4669i	1.04381	−	1.04381i	0.0448178	−	0.998995i	$-0.485729\pi$
$313$	18.4669	−	18.4669i	1.04381	−	1.04381i	0.998995	−	0.0448178i	$-0.0142707\pi$
$314$	10.8762			0.613777
$315$	−18.2406	−	11.8377i	−1.02774	−	0.666980i
$316$			0.340396i			0.0191488i
$317$	20.0304	+	20.0304i	1.12502	+	1.12502i	0.990975	+	0.134045i	$0.0427965\pi$
$317$	20.0304	+	20.0304i	1.12502	+	1.12502i	0.134045	+	0.990975i	$0.457203\pi$
$318$	7.83675	+	7.83675i	0.439463	+	0.439463i
$319$		0			0
$320$	−3.40720	−	16.0058i	−0.190469	−	0.894751i
$321$			5.13360i			0.286529i
$322$	12.1117	+	12.1117i	0.674957	+	0.674957i
$323$	7.40423	−	7.40423i	0.411983	−	0.411983i
$324$			0.483299i			0.0268500i
$325$	−4.32199	−	1.65605i	−0.239741	−	0.0918613i
$326$		−	22.5886i		−	1.25107i
$327$	−11.7255	+	11.7255i	−0.648420	+	0.648420i
$328$	−1.10799	+	1.10799i	−0.0611784	+	0.0611784i
$329$	5.01454			0.276461
$330$		0			0
$331$	−24.6455			−1.35464			−0.677319	−	0.735690i	$-0.736858\pi$
$331$	−24.6455			−1.35464			−0.677319	+	0.735690i	$0.736858\pi$
$332$	−0.209556	+	0.209556i	−0.0115009	+	0.0115009i
$333$	−8.04713	+	8.04713i	−0.440980	+	0.440980i
$334$			6.08395i			0.332899i
$335$	8.10448	+	5.25962i	0.442795	+	0.287364i
$336$		−	15.0045i		−	0.818564i
$337$	21.9315	−	21.9315i	1.19469	−	1.19469i	0.218949	−	0.975736i	$-0.429737\pi$
$337$	21.9315	−	21.9315i	1.19469	−	1.19469i	0.975736	−	0.218949i	$-0.0702628\pi$
$338$	12.5874	+	12.5874i	0.684663	+	0.684663i
$339$		−	10.0914i		−	0.548088i
$340$	0.538845	+	0.349698i	0.0292230	+	0.0189650i
$341$		0			0
$342$	−12.9895	−	12.9895i	−0.702390	−	0.702390i
$343$	−11.2342	−	11.2342i	−0.606587	−	0.606587i
$344$		−	19.3932i		−	1.04561i
$345$	1.07429	+	5.04660i	0.0578376	+	0.271700i
$346$	−6.34720			−0.341227
$347$	−21.3446	+	21.3446i	−1.14584	+	1.14584i	−0.158473	+	0.987363i	$0.550657\pi$
$347$	−21.3446	+	21.3446i	−1.14584	+	1.14584i	−0.987363	+	0.158473i	$0.949343\pi$
$348$	0.0878813	+	0.0878813i	0.00471093	+	0.00471093i
$349$	−21.3672			−1.14376			−0.571881	−	0.820336i	$-0.693786\pi$
$349$	−21.3672			−1.14376			−0.571881	+	0.820336i	$0.693786\pi$
$350$	12.5842	+	28.2185i	0.672653	+	1.50834i
$351$		−	4.08959i		−	0.218286i
$352$		0			0
$353$	−2.82626	+	2.82626i	−0.150427	+	0.150427i	−0.778309	−	0.627882i	$-0.783922\pi$
$353$	−2.82626	+	2.82626i	−0.150427	+	0.150427i	0.627882	+	0.778309i	$0.283922\pi$
$354$	−11.3613			−0.603847
$355$	−18.7898	+	3.99985i	−0.997260	+	0.212290i
$356$	2.07606			0.110031
$357$	−4.78345	−	4.78345i	−0.253167	−	0.253167i
$358$	−3.85568	−	3.85568i	−0.203779	−	0.203779i
$359$	10.7403			0.566851			0.283425	−	0.958994i	$-0.408529\pi$
$359$	10.7403			0.566851			0.283425	+	0.958994i	$0.408529\pi$
$360$	−7.62006	+	11.7416i	−0.401612	+	0.618839i
$361$	10.5040			0.552843
$362$	−6.26778	+	6.26778i	−0.329427	+	0.329427i
$363$		0			0
$364$			0.581487i			0.0304782i
$365$	−10.2420	−	6.64685i	−0.536093	−	0.347912i
$366$	9.49665			0.496398
$367$	−24.4690	−	24.4690i	−1.27727	−	1.27727i	−0.942190	−	0.335079i	$-0.891237\pi$
$367$	−24.4690	−	24.4690i	−1.27727	−	1.27727i	−0.335079	−	0.942190i	$-0.608763\pi$
$368$	8.38057	−	8.38057i	0.436867	−	0.436867i
$369$	1.33221			0.0693523
$370$	15.8158	−	3.36677i	0.822227	−	0.175030i
$371$		−	38.2818i		−	1.98749i
$372$	−0.0371888	−	0.0371888i	−0.00192815	−	0.00192815i
$373$	−9.90454	−	9.90454i	−0.512838	−	0.512838i	0.402557	−	0.915395i	$-0.368121\pi$
$373$	−9.90454	−	9.90454i	−0.512838	−	0.512838i	−0.915395	+	0.402557i	$0.868121\pi$
$374$		0			0
$375$	−1.44763	+	9.19406i	−0.0747555	+	0.474779i
$376$		−	3.22791i		−	0.166467i
$377$	0.655752	+	0.655752i	0.0337729	+	0.0337729i
$378$	−19.3043	+	19.3043i	−0.992908	+	0.992908i
$379$			26.5008i			1.36125i	0.732630	+	0.680627i	$0.238292\pi$
$379$			26.5008i			1.36125i	−0.732630	+	0.680627i	$0.761708\pi$
$380$	0.376852	+	1.77031i	0.0193321	+	0.0908150i
$381$			0.965278i			0.0494527i
$382$	17.1603	−	17.1603i	0.877997	−	0.877997i
$383$	−16.9972	+	16.9972i	−0.868516	+	0.868516i	−0.992308	−	0.123792i	$-0.960495\pi$
$383$	−16.9972	+	16.9972i	−0.868516	+	0.868516i	0.123792	+	0.992308i	$0.460495\pi$
$384$	−10.3318			−0.527243
$385$		0			0
$386$	24.8686			1.26578
$387$	−11.6589	+	11.6589i	−0.592655	+	0.592655i
$388$	−0.350298	+	0.350298i	−0.0177837	+	0.0177837i
$389$			7.54543i			0.382569i	0.981535	+	0.191284i	$0.0612652\pi$
$389$			7.54543i			0.382569i	−0.981535	+	0.191284i	$0.938735\pi$
$390$	−1.37513	+	2.11891i	−0.0696322	+	0.107295i
$391$		−	5.34346i		−	0.270230i
$392$	−20.6624	+	20.6624i	−1.04361	+	1.04361i
$393$	−8.50783	−	8.50783i	−0.429163	−	0.429163i
$394$		−	19.9776i		−	1.00646i
$395$	4.99573	−	1.06346i	0.251362	−	0.0535083i
$396$		0			0
$397$	16.0995	+	16.0995i	0.808008	+	0.808008i	0.984332	−	0.176324i	$-0.0564206\pi$
$397$	16.0995	+	16.0995i	0.808008	+	0.808008i	−0.176324	+	0.984332i	$0.556421\pi$
$398$	20.1269	+	20.1269i	1.00887	+	1.00887i
$399$		−	19.0608i		−	0.954236i
$400$	19.5256	−	8.70752i	0.976279	−	0.435376i
$401$	−24.1420			−1.20560			−0.602798	−	0.797894i	$-0.705947\pi$
$401$	−24.1420			−1.20560			−0.602798	+	0.797894i	$0.705947\pi$
$402$	3.72854	−	3.72854i	0.185963	−	0.185963i
$403$	−0.277495	−	0.277495i	−0.0138230	−	0.0138230i
$404$	−1.98062			−0.0985397
$405$	7.09300	−	1.50991i	0.352454	−	0.0750280i
$406$		−	6.19078i		−	0.307243i
$407$		0			0
$408$	−3.07915	+	3.07915i	−0.152441	+	0.152441i
$409$	5.85586			0.289553			0.144777	−	0.989464i	$-0.453754\pi$
$409$	5.85586			0.289553			0.144777	+	0.989464i	$0.453754\pi$
$410$	−1.58785	−	1.03048i	−0.0784185	−	0.0508918i
$411$	−10.2991			−0.508017
$412$	−1.06242	−	1.06242i	−0.0523416	−	0.0523416i
$413$	27.7495	+	27.7495i	1.36546	+	1.36546i
$414$	−9.37418			−0.460716
$415$	3.73017	+	2.42079i	0.183107	+	0.118832i
$416$	0.778754			0.0381815
$417$	0.594169	−	0.594169i	0.0290966	−	0.0290966i
$418$		0			0
$419$		−	11.0599i		−	0.540311i	−0.962817	−	0.270155i	$-0.912925\pi$
$419$		−	11.0599i		−	0.540311i	0.962817	−	0.270155i	$-0.0870751\pi$
$420$	1.14370	−	0.243462i	0.0558066	−	0.0118797i
$421$	7.87306			0.383710			0.191855	−	0.981423i	$-0.438550\pi$
$421$	7.87306			0.383710			0.191855	+	0.981423i	$0.438550\pi$
$422$	−6.62477	−	6.62477i	−0.322489	−	0.322489i
$423$	−1.94058	+	1.94058i	−0.0943540	+	0.0943540i
$424$	−24.6424			−1.19674
$425$	3.44880	−	9.00072i	0.167291	−	0.436599i
$426$			10.4846i			0.507980i
$427$	−23.1951	−	23.1951i	−1.12249	−	1.12249i
$428$	0.649807	+	0.649807i	0.0314096	+	0.0314096i
$429$		0			0
$430$	22.9144	−	4.87787i	1.10503	−	0.235232i
$431$		−	7.30295i		−	0.351771i	−0.984411	−	0.175885i	$-0.943721\pi$
$431$		−	7.30295i		−	0.351771i	0.984411	−	0.175885i	$-0.0562788\pi$
$432$	13.3575	+	13.3575i	0.642662	+	0.642662i
$433$	−3.56913	+	3.56913i	−0.171521	+	0.171521i	−0.787647	−	0.616126i	$-0.788701\pi$
$433$	−3.56913	+	3.56913i	−0.171521	+	0.171521i	0.616126	+	0.787647i	$0.288701\pi$
$434$			2.61976i			0.125752i
$435$	1.01521	−	1.56432i	0.0486755	−	0.0750034i
$436$			2.96840i			0.142161i
$437$	10.6462	−	10.6462i	0.509275	−	0.509275i
$438$	−4.71194	+	4.71194i	−0.225145	+	0.225145i
$439$	1.29778			0.0619394			0.0309697	−	0.999520i	$-0.490140\pi$
$439$	1.29778			0.0619394			0.0309697	+	0.999520i	$0.490140\pi$
$440$		0			0
$441$	24.8439			1.18304
$442$	1.84978	−	1.84978i	0.0879852	−	0.0879852i
$443$	−10.8900	+	10.8900i	−0.517401	+	0.517401i	−0.916784	−	0.399383i	$-0.869224\pi$
$443$	−10.8900	+	10.8900i	−0.517401	+	0.517401i	0.399383	+	0.916784i	$0.369224\pi$
$444$		−	0.611968i		−	0.0290427i
$445$	−6.48595	−	30.4686i	−0.307464	−	1.44435i
$446$			20.8091i			0.985341i
$447$	0.718486	−	0.718486i	0.0339832	−	0.0339832i
$448$	21.8138	+	21.8138i	1.03061	+	1.03061i
$449$			12.1228i			0.572110i	0.958213	+	0.286055i	$0.0923440\pi$
$449$			12.1228i			0.572110i	−0.958213	+	0.286055i	$0.907656\pi$
$450$	−15.7902	−	6.05033i	−0.744359	−	0.285215i
$451$		0			0
$452$	−1.27736	−	1.27736i	−0.0600818	−	0.0600818i
$453$	−0.934036	−	0.934036i	−0.0438848	−	0.0438848i
$454$		−	12.1354i		−	0.569541i
$455$	8.53402	−	1.81666i	0.400081	−	0.0851665i
$456$	−12.2697			−0.574580
$457$	2.48245	−	2.48245i	0.116124	−	0.116124i	−0.646657	−	0.762781i	$-0.723833\pi$
$457$	2.48245	−	2.48245i	0.116124	−	0.116124i	0.762781	+	0.646657i	$0.223833\pi$
$458$	−20.3165	−	20.3165i	−0.949326	−	0.949326i
$459$	8.51673			0.397527
$460$	0.774778	+	0.502813i	0.0361242	+	0.0234438i
$461$			5.45336i			0.253988i	0.991903	+	0.126994i	$0.0405329\pi$
$461$			5.45336i			0.253988i	−0.991903	+	0.126994i	$0.959467\pi$
$462$		0			0
$463$	15.3996	−	15.3996i	0.715681	−	0.715681i	−0.252037	−	0.967718i	$-0.581100\pi$
$463$	15.3996	−	15.3996i	0.715681	−	0.715681i	0.967718	+	0.252037i	$0.0811005\pi$
$464$	−4.28365			−0.198864
$465$	−0.429607	+	0.661975i	−0.0199225	+	0.0306984i
$466$	−5.44330			−0.252156
$467$	−10.3830	−	10.3830i	−0.480470	−	0.480470i	0.424812	−	0.905282i	$-0.360340\pi$
$467$	−10.3830	−	10.3830i	−0.480470	−	0.480470i	−0.905282	+	0.424812i	$0.860340\pi$
$468$	−0.225029	−	0.225029i	−0.0104020	−	0.0104020i
$469$	−18.2135			−0.841023
$470$	3.81401	−	0.811900i	0.175927	−	0.0374502i
$471$	−6.17626			−0.284587
$472$	17.8626	−	17.8626i	0.822193	−	0.822193i
$473$		0			0
$474$		−	2.78758i		−	0.128038i
$475$	24.8041	−	11.0615i	1.13809	−	0.507537i
$476$	−1.21097			−0.0555047
$477$	14.8146	+	14.8146i	0.678316	+	0.678316i
$478$	−3.33046	+	3.33046i	−0.152332	+	0.152332i
$479$	4.91370			0.224513			0.112256	−	0.993679i	$-0.464192\pi$
$479$	4.91370			0.224513			0.112256	+	0.993679i	$0.464192\pi$
$480$	−0.326055	−	1.53169i	−0.0148823	−	0.0699117i
$481$		−	4.56638i		−	0.208209i
$482$	−26.3416	−	26.3416i	−1.19983	−	1.19983i
$483$	−6.87787	−	6.87787i	−0.312954	−	0.312954i
$484$		0			0
$485$	6.23543	+	4.04665i	0.283136	+	0.183749i
$486$		−	23.3873i		−	1.06087i
$487$	−7.59259	−	7.59259i	−0.344053	−	0.344053i	0.513836	−	0.857889i	$-0.328224\pi$
$487$	−7.59259	−	7.59259i	−0.344053	−	0.344053i	−0.857889	+	0.513836i	$0.828224\pi$
$488$	−14.9309	+	14.9309i	−0.675891	+	0.675891i
$489$			12.8274i			0.580077i
$490$	−29.6113	−	19.2170i	−1.33770	−	0.868137i
$491$			3.25606i			0.146944i	0.997297	+	0.0734720i	$0.0234080\pi$
$491$			3.25606i			0.146944i	−0.997297	+	0.0734720i	$0.976592\pi$
$492$	−0.0506560	+	0.0506560i	−0.00228375	+	0.00228375i
$493$	−1.36563	+	1.36563i	−0.0615049	+	0.0615049i
$494$	7.37092			0.331634
$495$		0			0
$496$	1.81272			0.0813935
$497$	25.6081	−	25.6081i	1.14868	−	1.14868i
$498$	1.71610	−	1.71610i	0.0769002	−	0.0769002i
$499$		−	8.94183i		−	0.400291i	−0.979766	−	0.200146i	$-0.935858\pi$
$499$		−	8.94183i		−	0.400291i	0.979766	−	0.200146i	$-0.0641416\pi$
$500$	0.980537	+	1.34702i	0.0438509	+	0.0602405i
$501$		−	3.45490i		−	0.154353i
$502$	−16.9020	+	16.9020i	−0.754374	+	0.754374i
$503$	−13.6708	−	13.6708i	−0.609550	−	0.609550i	0.333278	−	0.942828i	$-0.391845\pi$
$503$	−13.6708	−	13.6708i	−0.609550	−	0.609550i	−0.942828	+	0.333278i	$0.891845\pi$
$504$		−	26.3875i		−	1.17539i
$505$	6.18781	+	29.0681i	0.275354	+	1.29351i
$506$		0			0
$507$	−7.14801	−	7.14801i	−0.317454	−	0.317454i
$508$	0.122184	+	0.122184i	0.00542104	+	0.00542104i
$509$			2.82153i			0.125062i	0.998043	+	0.0625311i	$0.0199173\pi$
$509$			2.82153i			0.125062i	−0.998043	+	0.0625311i	$0.980083\pi$
$510$	−4.41272	−	2.86376i	−0.195399	−	0.126809i
$511$	23.0174			1.01823
$512$	13.8645	−	13.8645i	0.612730	−	0.612730i
$513$	16.9685	+	16.9685i	0.749178	+	0.749178i
$514$	−23.7544			−1.04776
$515$	−12.2731	+	18.9114i	−0.540817	+	0.833338i
$516$		−	0.886635i		−	0.0390319i
$517$		0			0
$518$	−21.5550	+	21.5550i	−0.947071	+	0.947071i
$519$	3.60439			0.158215
$520$	−1.16941	−	5.49344i	−0.0512818	−	0.240903i
$521$	9.50337			0.416350			0.208175	−	0.978092i	$-0.433248\pi$
$521$	9.50337			0.416350			0.208175	+	0.978092i	$0.433248\pi$
$522$	2.39577	+	2.39577i	0.104860	+	0.104860i
$523$	10.4910	+	10.4910i	0.458739	+	0.458739i	0.898241	−	0.439503i	$-0.144845\pi$
$523$	10.4910	+	10.4910i	0.458739	+	0.458739i	−0.439503	+	0.898241i	$0.644845\pi$
$524$	−2.15383			−0.0940904
$525$	−7.14620	−	16.0245i	−0.311886	−	0.699366i
$526$	1.40535			0.0612761
$527$	0.577895	−	0.577895i	0.0251735	−	0.0251735i
$528$		0			0
$529$			15.3169i			0.665953i
$530$	−6.19817	−	29.1167i	−0.269231	−	1.26475i
$531$	−21.4775			−0.932044
$532$	−2.41271	−	2.41271i	−0.104604	−	0.104604i
$533$	−0.377985	+	0.377985i	−0.0163723	+	0.0163723i
$534$	−17.0013			−0.735718
$535$	7.50659	−	11.5668i	0.324538	−	0.500077i
$536$			11.7242i			0.506410i
$537$	2.18953	+	2.18953i	0.0944853	+	0.0944853i
$538$	−29.4638	−	29.4638i	−1.27027	−	1.27027i
$539$		0			0
$540$	−0.801414	+	1.23489i	−0.0344874	+	0.0531411i
$541$		−	31.2654i		−	1.34420i	−0.740459	−	0.672101i	$-0.765392\pi$
$541$		−	31.2654i		−	1.34420i	0.740459	−	0.672101i	$-0.234608\pi$
$542$	−31.8750	−	31.8750i	−1.36915	−	1.36915i
$543$	3.55929	−	3.55929i	0.152744	−	0.152744i
$544$			1.62179i			0.0695335i
$545$	43.5649	−	9.27379i	1.86611	−	0.397246i
$546$		−	4.76193i		−	0.203792i
$547$	−22.3204	+	22.3204i	−0.954353	+	0.954353i	−0.999003	−	0.0446500i	$-0.985783\pi$
$547$	−22.3204	+	22.3204i	−0.954353	+	0.954353i	0.0446500	+	0.999003i	$0.485783\pi$
$548$	−1.30365	+	1.30365i	−0.0556892	+	0.0556892i
$549$	17.9525			0.766194
$550$		0			0
$551$	−5.44169			−0.231824
$552$	−4.42736	+	4.42736i	−0.188441	+	0.188441i
$553$	−6.80853	+	6.80853i	−0.289528	+	0.289528i
$554$		−	44.1962i		−	1.87772i
$555$	−8.98136	+	1.91189i	−0.381238	+	0.0811553i
$556$		−	0.150419i		−	0.00637918i
$557$	9.37798	−	9.37798i	0.397358	−	0.397358i	−0.479942	−	0.877300i	$-0.659342\pi$
$557$	9.37798	−	9.37798i	0.397358	−	0.397358i	0.877300	+	0.479942i	$0.159342\pi$
$558$	−1.01382	−	1.01382i	−0.0429184	−	0.0429184i
$559$		−	6.61589i		−	0.279822i
$560$	−21.9403	+	33.8076i	−0.927149	+	1.42863i
$561$		0			0
$562$	8.83073	+	8.83073i	0.372502	+	0.372502i
$563$	20.7685	+	20.7685i	0.875286	+	0.875286i	0.993043	−	0.117756i	$-0.0375702\pi$
$563$	20.7685	+	20.7685i	0.875286	+	0.875286i	−0.117756	+	0.993043i	$0.537570\pi$
$564$		−	0.147577i		−	0.00621410i
$565$	−14.7561	+	22.7374i	−0.620793	+	0.956572i
$566$	13.9878			0.587952
$567$	−9.66685	+	9.66685i	−0.405970	+	0.405970i
$568$	−16.4842	−	16.4842i	−0.691662	−	0.691662i
$569$	21.4507			0.899262			0.449631	−	0.893214i	$-0.351555\pi$
$569$	21.4507			0.899262			0.449631	+	0.893214i	$0.351555\pi$
$570$	−3.08612	−	14.4975i	−0.129264	−	0.607233i
$571$			28.7176i			1.20179i	0.799326	+	0.600897i	$0.205190\pi$
$571$			28.7176i			1.20179i	−0.799326	+	0.600897i	$0.794810\pi$
$572$		0			0
$573$	−9.74484	+	9.74484i	−0.407097	+	0.407097i
$574$	3.56845			0.148944
$575$	4.95885	−	12.9417i	0.206798	−	0.539705i
$576$	−16.8835			−0.703477
$577$	−4.73218	−	4.73218i	−0.197003	−	0.197003i	0.601711	−	0.798714i	$-0.294486\pi$
$577$	−4.73218	−	4.73218i	−0.197003	−	0.197003i	−0.798714	+	0.601711i	$0.794486\pi$
$578$	−13.7697	−	13.7697i	−0.572745	−	0.572745i
$579$	−14.1222			−0.586898
$580$	−0.0695062	−	0.326514i	−0.00288609	−	0.0135578i
$581$	−8.38297			−0.347784
$582$	2.86867	−	2.86867i	0.118910	−	0.118910i
$583$		0			0
$584$		−	14.8165i		−	0.613112i
$585$	−2.59955	+	4.00561i	−0.107478	+	0.165611i
$586$	−3.38262			−0.139735
$587$	−25.8079	−	25.8079i	−1.06520	−	1.06520i	−0.997720	−	0.0674846i	$-0.978503\pi$
$587$	−25.8079	−	25.8079i	−1.06520	−	1.06520i	−0.0674846	−	0.997720i	$-0.521497\pi$
$588$	−0.944664	+	0.944664i	−0.0389573	+	0.0389573i
$589$	2.30277			0.0948839
$590$	25.5988	+	16.6131i	1.05389	+	0.683949i
$591$			11.3447i			0.466659i
$592$	14.9148	+	14.9148i	0.612993	+	0.612993i
$593$	−26.6656	−	26.6656i	−1.09502	−	1.09502i	−0.994983	−	0.100040i	$-0.968103\pi$
$593$	−26.6656	−	26.6656i	−1.09502	−	1.09502i	−0.100040	−	0.994983i	$-0.531897\pi$
$594$		0			0
$595$	3.78328	+	17.7724i	0.155099	+	0.728599i
$596$		−	0.181891i		−	0.00745053i
$597$	−11.4295	−	11.4295i	−0.467779	−	0.467779i
$598$	2.65971	−	2.65971i	0.108764	−	0.108764i
$599$		−	38.6017i		−	1.57722i	−0.614892	−	0.788611i	$-0.710801\pi$
$599$		−	38.6017i		−	1.57722i	0.614892	−	0.788611i	$-0.289199\pi$
$600$	−10.3151	+	4.60008i	−0.421114	+	0.187798i
$601$			38.1177i			1.55485i	0.628974	+	0.777427i	$0.283475\pi$
$601$			38.1177i			1.55485i	−0.628974	+	0.777427i	$0.716525\pi$
$602$	−31.2294	+	31.2294i	−1.27282	+	1.27282i
$603$	7.04845	−	7.04845i	0.287035	−	0.287035i
$604$	−0.236459			−0.00962138
$605$		0			0
$606$	16.2198			0.658884
$607$	−25.6202	+	25.6202i	−1.03989	+	1.03989i	−0.0407231	+	0.999170i	$0.512966\pi$
$607$	−25.6202	+	25.6202i	−1.03989	+	1.03989i	−0.999170	+	0.0407231i	$0.987034\pi$
$608$	−3.23121	+	3.23121i	−0.131043	+	0.131043i
$609$			3.51556i			0.142458i
$610$	−21.3974	−	13.8864i	−0.866357	−	0.562246i
$611$		−	1.10119i		−	0.0445493i
$612$	0.468633	−	0.468633i	0.0189434	−	0.0189434i
$613$	−1.70361	−	1.70361i	−0.0688081	−	0.0688081i	0.671865	−	0.740673i	$-0.265493\pi$
$613$	−1.70361	−	1.70361i	−0.0688081	−	0.0688081i	−0.740673	+	0.671865i	$0.765493\pi$
$614$			25.8389i			1.04277i
$615$	0.901696	+	0.585180i	0.0363599	+	0.0235967i
$616$		0			0
$617$	−25.5598	−	25.5598i	−1.02900	−	1.02900i	−0.999567	−	0.0294325i	$-0.990630\pi$
$617$	−25.5598	−	25.5598i	−1.02900	−	1.02900i	−0.0294325	−	0.999567i	$-0.509370\pi$
$618$	8.70038	+	8.70038i	0.349981	+	0.349981i
$619$			0.913846i			0.0367306i	0.999831	+	0.0183653i	$0.00584618\pi$
$619$			0.913846i			0.0367306i	−0.999831	+	0.0183653i	$0.994154\pi$
$620$	0.0294130	+	0.138172i	0.00118125	+	0.00554910i
$621$	12.2458			0.491406
$622$	−15.6665	+	15.6665i	−0.628170	+	0.628170i
$623$	41.5248	+	41.5248i	1.66366	+	1.66366i
$624$	−3.29497			−0.131905
$625$	16.7057	−	18.5989i	0.668230	−	0.743955i
$626$			38.2851i			1.53018i
$627$		0			0
$628$	−0.781786	+	0.781786i	−0.0311967	+	0.0311967i
$629$	9.50966			0.379175
$630$	31.1787	−	6.63712i	1.24219	−	0.264429i
$631$	23.1071			0.919881			0.459940	−	0.887950i	$-0.347871\pi$
$631$	23.1071			0.919881			0.459940	+	0.887950i	$0.347871\pi$
$632$	4.38272	+	4.38272i	0.174335	+	0.174335i
$633$	3.76201	+	3.76201i	0.149527	+	0.149527i
$634$	−41.5265			−1.64923
$635$	1.41148	−	2.17492i	0.0560127	−	0.0863092i
$636$	−1.12662			−0.0446735
$637$	−7.04889	+	7.04889i	−0.279287	+	0.279287i
$638$		0			0
$639$			19.8201i			0.784072i
$640$	23.2792	+	15.1077i	0.920191	+	0.597183i
$641$	8.72877			0.344766			0.172383	−	0.985030i	$-0.444853\pi$
$641$	8.72877			0.344766			0.172383	+	0.985030i	$0.444853\pi$
$642$	−5.32141	−	5.32141i	−0.210019	−	0.210019i
$643$	−22.3017	+	22.3017i	−0.879494	+	0.879494i	−0.993482	−	0.113988i	$-0.963638\pi$
$643$	−22.3017	+	22.3017i	−0.879494	+	0.879494i	0.113988	+	0.993482i	$0.463638\pi$
$644$	−1.74119			−0.0686126
$645$	−13.0124	+	2.77000i	−0.512364	+	0.109069i
$646$			15.3503i			0.603948i
$647$	−9.71662	−	9.71662i	−0.382000	−	0.382000i	0.489823	−	0.871822i	$-0.337062\pi$
$647$	−9.71662	−	9.71662i	−0.382000	−	0.382000i	−0.871822	+	0.489823i	$0.837062\pi$
$648$	6.22265	+	6.22265i	0.244449	+	0.244449i
$649$		0			0
$650$	6.19675	−	2.76347i	0.243057	−	0.108392i
$651$		−	1.48769i		−	0.0583070i
$652$	1.62369	+	1.62369i	0.0635885	+	0.0635885i
$653$	3.84746	−	3.84746i	0.150563	−	0.150563i	−0.627807	−	0.778369i	$-0.716047\pi$
$653$	3.84746	−	3.84746i	0.150563	−	0.150563i	0.778369	+	0.627807i	$0.216047\pi$
$654$		−	24.3089i		−	0.950554i
$655$	6.72893	+	31.6100i	0.262921	+	1.23511i
$656$		−	2.46916i		−	0.0964045i
$657$	−8.90749	+	8.90749i	−0.347514	+	0.347514i
$658$	−5.19801	+	5.19801i	−0.202639	+	0.202639i
$659$	42.1160			1.64061			0.820304	−	0.571928i	$-0.193805\pi$
$659$	42.1160			1.64061			0.820304	+	0.571928i	$0.193805\pi$
$660$		0			0
$661$	−19.5844			−0.761745			−0.380872	−	0.924628i	$-0.624376\pi$
$661$	−19.5844			−0.761745			−0.380872	+	0.924628i	$0.624376\pi$
$662$	25.5472	−	25.5472i	0.992918	−	0.992918i
$663$	−1.05044	+	1.05044i	−0.0407957	+	0.0407957i
$664$			5.39621i			0.209413i
$665$	−27.8717	+	42.9471i	−1.08082	+	1.66542i
$666$		−	16.6831i		−	0.646457i
$667$	−1.96357	+	1.96357i	−0.0760297	+	0.0760297i
$668$	−0.437318	−	0.437318i	−0.0169204	−	0.0169204i
$669$		−	11.8169i		−	0.456868i
$670$	−13.8530	+	2.94894i	−0.535189	+	0.113927i
$671$		0			0
$672$	2.08750	+	2.08750i	0.0805269	+	0.0805269i
$673$	−3.92182	−	3.92182i	−0.151175	−	0.151175i	0.627468	−	0.778643i	$-0.284092\pi$
$673$	−3.92182	−	3.92182i	−0.151175	−	0.151175i	−0.778643	+	0.627468i	$0.784092\pi$
$674$			45.4678i			1.75135i
$675$	20.6272	+	7.90372i	0.793943	+	0.304214i
$676$	−1.80958			−0.0695992
$677$	−1.64985	+	1.64985i	−0.0634089	+	0.0634089i	−0.738100	−	0.674691i	$-0.764277\pi$
$677$	−1.64985	+	1.64985i	−0.0634089	+	0.0634089i	0.674691	+	0.738100i	$0.264277\pi$
$678$	10.4606	+	10.4606i	0.401736	+	0.401736i
$679$	−14.0132			−0.537776
$680$	11.4403	−	2.43533i	0.438716	−	0.0933908i
$681$			6.89132i			0.264076i
$682$		0			0
$683$	−25.0400	+	25.0400i	−0.958127	+	0.958127i	−0.999158	−	0.0410307i	$-0.986936\pi$
$683$	−25.0400	+	25.0400i	−0.958127	+	0.958127i	0.0410307	+	0.999158i	$0.486936\pi$
$684$	1.86738			0.0714012
$685$	23.2055	+	15.0598i	0.886636	+	0.575406i
$686$	23.2903			0.889229
$687$	11.5371	+	11.5371i	0.440169	+	0.440169i
$688$	21.6089	+	21.6089i	0.823832	+	0.823832i
$689$	−8.40662			−0.320267
$690$	−6.34483	−	4.11765i	−0.241544	−	0.156756i
$691$	−1.79981			−0.0684681			−0.0342340	−	0.999414i	$-0.510899\pi$
$691$	−1.79981			−0.0684681			−0.0342340	+	0.999414i	$0.510899\pi$
$692$	0.456241	−	0.456241i	0.0173437	−	0.0173437i
$693$		0			0
$694$		−	44.2510i		−	1.67974i
$695$	−2.20758	+	0.469934i	−0.0837382	+	0.0178256i
$696$	2.26301			0.0857790
$697$	−0.787169	−	0.787169i	−0.0298161	−	0.0298161i
$698$	22.1490	−	22.1490i	0.838351	−	0.838351i
$699$	3.09109			0.116916
$700$	−2.93293	−	1.12381i	−0.110854	−	0.0424759i
$701$		−	17.8151i		−	0.672869i	−0.941707	−	0.336434i	$-0.890779\pi$
$701$		−	17.8151i		−	0.672869i	0.941707	−	0.336434i	$-0.109221\pi$
$702$	4.23921	+	4.23921i	0.159999	+	0.159999i
$703$	18.9468	+	18.9468i	0.714593	+	0.714593i
$704$		0			0
$705$	−2.16587	+	0.461055i	−0.0815713	+	0.0173643i
$706$		−	5.85933i		−	0.220519i
$707$	−39.6160	−	39.6160i	−1.48991	−	1.48991i
$708$	0.816659	−	0.816659i	0.0306919	−	0.0306919i
$709$		−	10.0474i		−	0.377339i	−0.982041	−	0.188670i	$-0.939583\pi$
$709$		−	10.0474i		−	0.377339i	0.982041	−	0.188670i	$-0.0604175\pi$
$710$	15.3311	−	23.6234i	0.575365	−	0.886572i
$711$		−	5.26966i		−	0.197628i
$712$	26.7300	−	26.7300i	1.00175	−	1.00175i
$713$	0.830926	−	0.830926i	0.0311184	−	0.0311184i
$714$	9.91691			0.371131
$715$		0			0
$716$	0.554298			0.0207151
$717$	1.89127	−	1.89127i	0.0706309	−	0.0706309i
$718$	−11.1332	+	11.1332i	−0.415489	+	0.415489i
$719$		−	6.85933i		−	0.255810i	−0.991786	−	0.127905i	$-0.959175\pi$
$719$		−	6.85933i		−	0.255810i	0.991786	−	0.127905i	$-0.0408252\pi$
$720$	−4.59249	−	21.5739i	−0.171152	−	0.804010i
$721$		−	42.5005i		−	1.58280i
$722$	−10.8883	+	10.8883i	−0.405221	+	0.405221i
$723$	14.9587	+	14.9587i	0.556319	+	0.556319i
$724$		−	0.901065i		−	0.0334878i
$725$	−4.57485	+	2.04017i	−0.169906	+	0.0757702i
$726$		0			0
$727$	−25.2212	−	25.2212i	−0.935401	−	0.935401i	0.0626351	−	0.998036i	$-0.480050\pi$
$727$	−25.2212	−	25.2212i	−0.935401	−	0.935401i	−0.998036	+	0.0626351i	$0.980050\pi$
$728$	7.48685	+	7.48685i	0.277481	+	0.277481i
$729$			3.55147i			0.131536i
$730$	17.5068	−	3.72672i	0.647955	−	0.137932i
$731$	13.7779			0.509592
$732$	−0.682625	+	0.682625i	−0.0252306	+	0.0252306i
$733$	−5.45218	−	5.45218i	−0.201381	−	0.201381i	0.599211	−	0.800591i	$-0.295481\pi$
$733$	−5.45218	−	5.45218i	−0.201381	−	0.201381i	−0.800591	+	0.599211i	$0.795481\pi$
$734$	50.7284			1.87242
$735$	16.8154	+	10.9128i	0.620245	+	0.402525i
$736$			2.33188i			0.0859543i
$737$		0			0
$738$	−1.38095	+	1.38095i	−0.0508336	+	0.0508336i
$739$	−40.8032			−1.50097			−0.750485	−	0.660887i	$-0.770180\pi$
$739$	−40.8032			−1.50097			−0.750485	+	0.660887i	$0.770180\pi$
$740$	−0.894848	+	1.37886i	−0.0328953	+	0.0506879i
$741$	−4.18574			−0.153767
$742$	39.6823	+	39.6823i	1.45678	+	1.45678i
$743$	−31.3704	−	31.3704i	−1.15087	−	1.15087i	−0.986379	−	0.164491i	$-0.947402\pi$
$743$	−31.3704	−	31.3704i	−1.15087	−	1.15087i	−0.164491	−	0.986379i	$-0.552598\pi$
$744$	−0.957638			−0.0351087
$745$	−2.66947	+	0.568258i	−0.0978017	+	0.0208193i
$746$	20.5338			0.751796
$747$	3.24412	−	3.24412i	0.118696	−	0.118696i
$748$		0			0
$749$			25.9946i			0.949821i
$750$	−8.02984	−	11.0310i	−0.293208	−	0.402796i
$751$	−13.1663			−0.480445			−0.240223	−	0.970718i	$-0.577220\pi$
$751$	−13.1663			−0.480445			−0.240223	+	0.970718i	$0.577220\pi$
$752$	3.59672	+	3.59672i	0.131159	+	0.131159i
$753$	9.59817	−	9.59817i	0.349777	−	0.349777i
$754$	−1.35949			−0.0495096
$755$	0.738739	+	3.47032i	0.0268854	+	0.126298i
$756$		−	2.77522i		−	0.100934i
$757$	−14.0516	−	14.0516i	−0.510713	−	0.510713i	0.404032	−	0.914745i	$-0.367608\pi$
$757$	−14.0516	−	14.0516i	−0.510713	−	0.510713i	−0.914745	+	0.404032i	$0.867608\pi$
$758$	−27.4703	−	27.4703i	−0.997768	−	0.997768i
$759$		0			0
$760$	27.6455	+	17.9413i	1.00281	+	0.650799i
$761$			17.7388i			0.643030i	0.946904	+	0.321515i	$0.104192\pi$
$761$			17.7388i			0.643030i	−0.946904	+	0.321515i	$0.895808\pi$
$762$	−1.00059	−	1.00059i	−0.0362477	−	0.0362477i
$763$	−59.3733	+	59.3733i	−2.14946	+	2.14946i
$764$			2.46699i			0.0892525i
$765$	−8.34184	−	5.41366i	−0.301600	−	0.195731i
$766$		−	35.2381i		−	1.27321i
$767$	6.09374	−	6.09374i	0.220032	−	0.220032i
$768$	2.09390	−	2.09390i	0.0755572	−	0.0755572i
$769$	−33.4001			−1.20444			−0.602218	−	0.798331i	$-0.705716\pi$
$769$	−33.4001			−1.20444			−0.602218	+	0.798331i	$0.705716\pi$
$770$		0			0
$771$	13.4894			0.485810
$772$	−1.78757	+	1.78757i	−0.0643362	+	0.0643362i
$773$	26.9841	−	26.9841i	0.970551	−	0.970551i	−0.0290274	−	0.999579i	$-0.509241\pi$
$773$	26.9841	−	26.9841i	0.970551	−	0.970551i	0.999579	+	0.0290274i	$0.00924101\pi$
$774$		−	24.1709i		−	0.868805i
$775$	1.93594	−	0.863343i	0.0695411	−	0.0310122i
$776$			9.02042i			0.323814i
$777$	12.2404	−	12.2404i	0.439123	−	0.439123i
$778$	−7.82149	−	7.82149i	−0.280414	−	0.280414i
$779$		−	3.13667i		−	0.112383i
$780$	−0.0534639	−	0.251154i	−0.00191432	−	0.00899276i
$781$		0			0
$782$	5.53895	+	5.53895i	0.198072	+	0.198072i
$783$	−3.12966	−	3.12966i	−0.111845	−	0.111845i
$784$		−	46.0464i		−	1.64451i
$785$	13.9161	+	9.03122i	0.496687	+	0.322338i
$786$	17.6382			0.629133
$787$	25.9828	−	25.9828i	0.926187	−	0.926187i	−0.0712698	−	0.997457i	$-0.522705\pi$
$787$	25.9828	−	25.9828i	0.926187	−	0.926187i	0.997457	+	0.0712698i	$0.0227051\pi$
$788$	1.43600	+	1.43600i	0.0511555	+	0.0511555i
$789$	−0.798057			−0.0284116
$790$	−4.07614	+	6.28086i	−0.145022	+	0.223463i
$791$		−	51.0989i		−	1.81687i
$792$		0			0
$793$	−5.09361	+	5.09361i	−0.180879	+	0.180879i
$794$	−33.3769			−1.18450
$795$	3.51976	+	16.5345i	0.124833	+	0.586420i
$796$	−2.89348			−0.102557
$797$	14.2420	+	14.2420i	0.504479	+	0.504479i	0.912827	−	0.408348i	$-0.133895\pi$
$797$	14.2420	+	14.2420i	0.504479	+	0.504479i	−0.408348	+	0.912827i	$0.633895\pi$
$798$	19.7582	+	19.7582i	0.699433	+	0.699433i
$799$	2.29327			0.0811300
$800$	−1.50505	+	3.92791i	−0.0532117	+	0.138873i
$801$	−32.1393			−1.13559
$802$	25.0253	−	25.0253i	0.883674	−	0.883674i
$803$		0			0
$804$			0.536020i			0.0189040i
$805$	5.43978	+	25.5541i	0.191727	+	0.900663i
$806$	0.575295			0.0202639
$807$	16.7316	+	16.7316i	0.588981	+	0.588981i
$808$	−25.5012	+	25.5012i	−0.897131	+	0.897131i
$809$	−51.9338			−1.82590			−0.912948	−	0.408076i	$-0.866200\pi$
$809$	−51.9338			−1.82590			−0.912948	+	0.408076i	$0.866200\pi$
$810$	−5.78736	+	8.91766i	−0.203347	+	0.313335i
$811$			39.1727i			1.37554i	0.725928	+	0.687770i	$0.241410\pi$
$811$			39.1727i			1.37554i	−0.725928	+	0.687770i	$0.758590\pi$
$812$	0.444997	+	0.444997i	0.0156163	+	0.0156163i
$813$	18.1009	+	18.1009i	0.634826	+	0.634826i
$814$		0			0
$815$	18.7569	−	28.9022i	0.657025	−	1.01240i
$816$		−	6.86192i		−	0.240215i
$817$	27.4507	+	27.4507i	0.960377	+	0.960377i
$818$	−6.07010	+	6.07010i	−0.212236	+	0.212236i
$819$		−	9.00197i		−	0.314554i
$820$	0.188208	−	0.0400644i	0.00657250	−	0.00139911i
$821$		−	24.9965i		−	0.872384i	−0.899854	−	0.436192i	$-0.856327\pi$
$821$		−	24.9965i		−	0.872384i	0.899854	−	0.436192i	$-0.143673\pi$
$822$	10.6759	−	10.6759i	0.372365	−	0.372365i
$823$	−16.2466	+	16.2466i	−0.566321	+	0.566321i	−0.931096	−	0.364775i	$-0.881146\pi$
$823$	−16.2466	+	16.2466i	−0.566321	+	0.566321i	0.364775	+	0.931096i	$0.381146\pi$
$824$	−27.3580			−0.953062
$825$		0			0
$826$	−57.5294			−2.00170
$827$	3.91550	−	3.91550i	0.136155	−	0.136155i	−0.635744	−	0.771900i	$-0.719307\pi$
$827$	3.91550	−	3.91550i	0.136155	−	0.136155i	0.771900	+	0.635744i	$0.219307\pi$
$828$	0.673823	−	0.673823i	0.0234170	−	0.0234170i
$829$			14.9736i			0.520054i	0.965601	+	0.260027i	$0.0837315\pi$
$829$			14.9736i			0.520054i	−0.965601	+	0.260027i	$0.916268\pi$
$830$	−6.37600	+	1.35728i	−0.221314	+	0.0471119i
$831$			25.0978i			0.870632i
$832$	4.79029	−	4.79029i	0.166073	−	0.166073i
$833$	−14.6796	−	14.6796i	−0.508618	−	0.508618i
$834$			1.23181i			0.0426542i
$835$	−5.05192	+	7.78443i	−0.174829	+	0.269391i
$836$		0			0
$837$	1.32438	+	1.32438i	0.0457773	+	0.0457773i
$838$	11.4645	+	11.4645i	0.396035	+	0.396035i
$839$			12.5957i			0.434851i	0.976077	+	0.217426i	$0.0697660\pi$
$839$			12.5957i			0.434851i	−0.976077	+	0.217426i	$0.930234\pi$
$840$	11.5908	−	17.8601i	0.399922	−	0.616234i
$841$	−27.9963			−0.965391
$842$	−8.16111	+	8.16111i	−0.281250	+	0.281250i
$843$	−5.01472	−	5.01472i	−0.172716	−	0.172716i
$844$	0.952386			0.0327825
$845$	5.65344	+	26.5578i	0.194484	+	0.913615i
$846$		−	4.02315i		−	0.138319i
$847$		0			0
$848$	27.4579	−	27.4579i	0.942907	−	0.942907i
$849$	−7.94329			−0.272613
$850$	5.75504	+	12.9050i	0.197396	+	0.442638i
$851$	13.6735			0.468720
$852$	−0.753640	−	0.753640i	−0.0258193	−	0.0258193i
$853$	35.1948	+	35.1948i	1.20505	+	1.20505i	0.972611	+	0.232437i	$0.0746700\pi$
$853$	35.1948	+	35.1948i	1.20505	+	1.20505i	0.232437	+	0.972611i	$0.425330\pi$
$854$	48.0874			1.64552
$855$	−5.83403	−	27.4061i	−0.199519	−	0.937269i
$856$	16.7330			0.571922
$857$	21.2860	−	21.2860i	0.727117	−	0.727117i	−0.242927	−	0.970044i	$-0.578108\pi$
$857$	21.2860	−	21.2860i	0.727117	−	0.727117i	0.970044	+	0.242927i	$0.0781077\pi$
$858$		0			0
$859$		−	9.31402i		−	0.317790i	−0.987295	−	0.158895i	$-0.949207\pi$
$859$		−	9.31402i		−	0.317790i	0.987295	−	0.158895i	$-0.0507932\pi$
$860$	−1.29648	+	1.99773i	−0.0442096	+	0.0681220i
$861$	−2.02642			−0.0690603
$862$	7.57014	+	7.57014i	0.257840	+	0.257840i
$863$	25.0239	−	25.0239i	0.851825	−	0.851825i	−0.138533	−	0.990358i	$-0.544239\pi$
$863$	25.0239	−	25.0239i	0.851825	−	0.851825i	0.990358	+	0.138533i	$0.0442387\pi$
$864$	−3.71670			−0.126445
$865$	−8.12126	−	5.27051i	−0.276131	−	0.179203i
$866$		−	7.39941i		−	0.251442i
$867$	7.81942	+	7.81942i	0.265562	+	0.265562i
$868$	−0.188310	−	0.188310i	−0.00639166	−	0.00639166i
$869$		0			0
$870$	0.569202	+	2.67390i	0.0192978	+	0.0906538i
$871$			3.99967i			0.135524i
$872$	38.2192	+	38.2192i	1.29427	+	1.29427i
$873$	5.42295	−	5.42295i	0.183539	−	0.183539i
$874$			22.0713i			0.746574i
$875$	−7.33027	+	46.5552i	−0.247808	+	1.57385i
$876$		−	0.677396i		−	0.0228871i
$877$	15.4569	−	15.4569i	0.521941	−	0.521941i	−0.396216	−	0.918157i	$-0.629677\pi$
$877$	15.4569	−	15.4569i	0.521941	−	0.521941i	0.918157	+	0.396216i	$0.129677\pi$
$878$	−1.34526	+	1.34526i	−0.0454002	+	0.0454002i
$879$	1.92089			0.0647901
$880$		0			0
$881$	46.4810			1.56599			0.782993	−	0.622031i	$-0.213692\pi$
$881$	46.4810			1.56599			0.782993	+	0.622031i	$0.213692\pi$
$882$	−25.7529	+	25.7529i	−0.867144	+	0.867144i
$883$	−19.7450	+	19.7450i	−0.664471	+	0.664471i	−0.956431	−	0.291959i	$-0.905693\pi$
$883$	−19.7450	+	19.7450i	−0.664471	+	0.664471i	0.291959	+	0.956431i	$0.405693\pi$
$884$			0.265927i			0.00894411i
$885$	−14.5368	−	9.43408i	−0.488651	−	0.317123i
$886$		−	22.5769i		−	0.758486i
$887$	4.97816	−	4.97816i	0.167150	−	0.167150i	−0.618575	−	0.785726i	$-0.712290\pi$
$887$	4.97816	−	4.97816i	0.167150	−	0.167150i	0.785726	+	0.618575i	$0.212290\pi$
$888$	−7.87930	−	7.87930i	−0.264412	−	0.264412i
$889$			4.88780i			0.163932i
$890$	38.3066	+	24.8601i	1.28404	+	0.833313i
$891$		0			0
$892$	−1.49577	−	1.49577i	−0.0500822	−	0.0500822i
$893$	4.56905	+	4.56905i	0.152897	+	0.152897i
$894$			1.48954i			0.0498178i
$895$	−1.73172	−	8.13500i	−0.0578851	−	0.271923i
$896$	−52.3164			−1.74777
$897$	−1.51037	+	1.51037i	−0.0504298	+	0.0504298i
$898$	−12.5663	−	12.5663i	−0.419344	−	0.419344i
$899$	−0.424720			−0.0141652
$900$	1.56991	−	0.700111i	0.0523305	−	0.0233370i
$901$		−	17.5071i		−	0.583247i
$902$		0			0
$903$	17.7343	−	17.7343i	0.590160	−	0.590160i
$904$	−32.8929			−1.09400
$905$	−13.2242	+	2.81508i	−0.439588	+	0.0935764i
$906$	1.93642			0.0643332
$907$	−20.8941	−	20.8941i	−0.693777	−	0.693777i	0.269283	−	0.963061i	$-0.413213\pi$
$907$	−20.8941	−	20.8941i	−0.693777	−	0.693777i	−0.963061	+	0.269283i	$0.913213\pi$
$908$	0.872298	+	0.872298i	0.0289482	+	0.0289482i
$909$	30.6620			1.01699
$910$	−6.96312	+	10.7294i	−0.230825	+	0.355675i
$911$	16.9533			0.561689			0.280844	−	0.959753i	$-0.409386\pi$
$911$	16.9533			0.561689			0.280844	+	0.959753i	$0.409386\pi$
$912$	13.6715	−	13.6715i	0.452709	−	0.452709i
$913$		0			0
$914$			5.14655i			0.170233i
$915$	12.1510	+	7.88571i	0.401699	+	0.260694i
$916$	2.92072			0.0965034
$917$	−43.0804	−	43.0804i	−1.42264	−	1.42264i
$918$	−8.82832	+	8.82832i	−0.291378	+	0.291378i
$919$	−5.02309			−0.165697			−0.0828483	−	0.996562i	$-0.526402\pi$
$919$	−5.02309			−0.165697			−0.0828483	+	0.996562i	$0.526402\pi$
$920$	16.4494	−	3.50164i	0.542322	−	0.115446i
$921$		−	14.6732i		−	0.483497i
$922$	−5.65287	−	5.65287i	−0.186167	−	0.186167i
$923$	−5.62351	−	5.62351i	−0.185100	−	0.185100i
$924$		0			0
$925$	23.0321	+	8.82519i	0.757290	+	0.290170i
$926$			31.9260i			1.04915i
$927$	16.4473	+	16.4473i	0.540199	+	0.540199i
$928$	0.595961	−	0.595961i	0.0195634	−	0.0195634i
$929$		−	11.8130i		−	0.387572i	−0.981044	−	0.193786i	$-0.937923\pi$
$929$		−	11.8130i		−	0.387572i	0.981044	−	0.193786i	$-0.0620767\pi$
$930$	−0.240870	−	1.13152i	−0.00789843	−	0.0371039i
$931$		−	58.4945i		−	1.91708i
$932$	0.391268	−	0.391268i	0.0128164	−	0.0128164i
$933$	8.89656	−	8.89656i	0.291260	−	0.291260i
$934$	21.5258			0.704346
$935$		0			0
$936$	−5.79466			−0.189405
$937$	1.62077	−	1.62077i	0.0529483	−	0.0529483i	−0.680137	−	0.733085i	$-0.738080\pi$
$937$	1.62077	−	1.62077i	0.0529483	−	0.0529483i	0.733085	+	0.680137i	$0.238080\pi$
$938$	18.8799	−	18.8799i	0.616451	−	0.616451i
$939$		−	21.7410i		−	0.709492i
$940$	−0.215794	+	0.332514i	−0.00703842	+	0.0108454i
$941$		−	1.77332i		−	0.0578087i	−0.999582	−	0.0289044i	$-0.990798\pi$
$941$		−	1.77332i		−	0.0578087i	0.999582	−	0.0289044i	$-0.00920183\pi$
$942$	6.40223	−	6.40223i	0.208596	−	0.208596i
$943$	−1.13183	−	1.13183i	−0.0368574	−	0.0368574i
$944$			39.8070i			1.29561i
$945$	−40.7297	+	8.67026i	−1.32494	+	0.282043i
$946$		0			0
$947$	−8.63289	−	8.63289i	−0.280531	−	0.280531i	0.552790	−	0.833321i	$-0.313563\pi$
$947$	−8.63289	−	8.63289i	−0.280531	−	0.280531i	−0.833321	+	0.552790i	$0.813563\pi$
$948$	0.200373	+	0.200373i	0.00650782	+	0.00650782i
$949$		−	5.05459i		−	0.164079i
$950$	−14.2454	+	37.1778i	−0.462181	+	1.20621i
$951$	23.5817			0.764689
$952$	−15.5917	+	15.5917i	−0.505329	+	0.505329i
$953$	−13.0350	−	13.0350i	−0.422246	−	0.422246i	0.463730	−	0.885976i	$-0.346511\pi$
$953$	−13.0350	−	13.0350i	−0.422246	−	0.422246i	−0.885976	+	0.463730i	$0.846511\pi$
$954$	−30.7133			−0.994380
$955$	36.2060	−	7.70729i	1.17160	−	0.249402i
$956$		−	0.478792i		−	0.0154852i
$957$		0			0
$958$	−5.09348	+	5.09348i	−0.164563	+	0.164563i
$959$	−52.1507			−1.68403
$960$	−11.4274	−	7.41613i	−0.368818	−	0.239355i
$961$	−30.8203			−0.994202
$962$	4.73344	+	4.73344i	0.152612	+	0.152612i
$963$	−10.0596	−	10.0596i	−0.324167	−	0.324167i
$964$	3.78691			0.121968
$965$	31.8195	+	20.6501i	1.02431	+	0.664751i
$966$	14.2590			0.458776
$967$	9.49113	−	9.49113i	0.305214	−	0.305214i	−0.537836	−	0.843050i	$-0.680758\pi$
$967$	9.49113	−	9.49113i	0.305214	−	0.305214i	0.843050	+	0.537836i	$0.180758\pi$
$968$		0			0
$969$		−	8.71697i		−	0.280029i
$970$	−10.6583	+	2.26886i	−0.342216	+	0.0728487i
$971$	51.2201			1.64373			0.821865	−	0.569682i	$-0.192933\pi$
$971$	51.2201			1.64373			0.821865	+	0.569682i	$0.192933\pi$
$972$	1.68109	+	1.68109i	0.0539211	+	0.0539211i
$973$	3.00865	−	3.00865i	0.0964527	−	0.0964527i
$974$	15.7408			0.504366
$975$	−3.51896	+	1.56930i	−0.112697	+	0.0502577i
$976$		−	33.2737i		−	1.06506i
$977$	10.2391	+	10.2391i	0.327578	+	0.327578i	0.851665	−	0.524087i	$-0.175593\pi$
$977$	10.2391	+	10.2391i	0.327578	+	0.327578i	−0.524087	+	0.851665i	$0.675593\pi$
$978$	−13.2967	−	13.2967i	−0.425183	−	0.425183i
$979$		0			0
$980$	3.50981	−	0.747144i	0.112117	−	0.0238666i
$981$		−	45.9537i		−	1.46719i
$982$	−3.37519	−	3.37519i	−0.107707	−	0.107707i
$983$	40.6921	−	40.6921i	1.29788	−	1.29788i	0.368083	−	0.929793i	$-0.380014\pi$
$983$	40.6921	−	40.6921i	1.29788	−	1.29788i	0.929793	−	0.368083i	$-0.119986\pi$
$984$			1.30443i			0.0415837i
$985$	16.5888	−	25.5614i	0.528562	−	0.814454i
$986$		−	2.83119i		−	0.0901633i
$987$	2.95180	−	2.95180i	0.0939568	−	0.0939568i
$988$	−0.529827	+	0.529827i	−0.0168560	+	0.0168560i
$989$	19.8105			0.629936
$990$		0			0
$991$	13.1102			0.416458			0.208229	−	0.978080i	$-0.433230\pi$
$991$	13.1102			0.416458			0.208229	+	0.978080i	$0.433230\pi$
$992$	−0.252193	+	0.252193i	−0.00800715	+	0.00800715i
$993$	−14.5075	+	14.5075i	−0.460381	+	0.460381i
$994$			53.0900i			1.68391i
$995$	9.03971	+	42.4653i	0.286578	+	1.34624i
$996$			0.246709i			0.00781726i
$997$	−1.59446	+	1.59446i	−0.0504969	+	0.0504969i	−0.731904	−	0.681407i	$-0.761368\pi$
$997$	−1.59446	+	1.59446i	−0.0504969	+	0.0504969i	0.681407	+	0.731904i	$0.261368\pi$
$998$	9.26898	+	9.26898i	0.293404	+	0.293404i
$999$			21.7936i			0.689519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.b.362.4		32
5.3	odd	4	inner	605.2.e.b.483.13		32
11.2	odd	10		605.2.m.c.282.1		32
11.3	even	5		55.2.l.a.2.4	✓	32
11.4	even	5		605.2.m.e.457.1		32
11.5	even	5		605.2.m.c.602.4		32
11.6	odd	10		605.2.m.d.602.1		32
11.7	odd	10		55.2.l.a.17.4	yes	32
11.8	odd	10		605.2.m.e.112.1		32
11.9	even	5		605.2.m.d.282.4		32
11.10	odd	2	inner	605.2.e.b.362.13		32
33.14	odd	10		495.2.bj.a.442.1		32
33.29	even	10		495.2.bj.a.127.1		32
44.3	odd	10		880.2.cm.a.497.3		32
44.7	even	10		880.2.cm.a.17.3		32
55.3	odd	20		55.2.l.a.13.4	yes	32
55.7	even	20		275.2.bm.b.193.1		32
55.8	even	20		605.2.m.e.233.1		32
55.13	even	20		605.2.m.c.403.4		32
55.14	even	10		275.2.bm.b.57.1		32
55.18	even	20		55.2.l.a.28.4	yes	32
55.28	even	20		605.2.m.d.118.4		32
55.29	odd	10		275.2.bm.b.182.1		32
55.38	odd	20		605.2.m.c.118.1		32
55.43	even	4	inner	605.2.e.b.483.4		32
55.47	odd	20		275.2.bm.b.68.1		32
55.48	odd	20		605.2.m.e.578.1		32
55.53	odd	20		605.2.m.d.403.1		32
165.113	even	20		495.2.bj.a.343.1		32
165.128	odd	20		495.2.bj.a.28.1		32
220.3	even	20		880.2.cm.a.673.3		32
220.183	odd	20		880.2.cm.a.193.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.2.4	✓	32	11.3	even	5
55.2.l.a.13.4	yes	32	55.3	odd	20
55.2.l.a.17.4	yes	32	11.7	odd	10
55.2.l.a.28.4	yes	32	55.18	even	20
275.2.bm.b.57.1		32	55.14	even	10
275.2.bm.b.68.1		32	55.47	odd	20
275.2.bm.b.182.1		32	55.29	odd	10
275.2.bm.b.193.1		32	55.7	even	20
495.2.bj.a.28.1		32	165.128	odd	20
495.2.bj.a.127.1		32	33.29	even	10
495.2.bj.a.343.1		32	165.113	even	20
495.2.bj.a.442.1		32	33.14	odd	10
605.2.e.b.362.4		32	1.1	even	1	trivial
605.2.e.b.362.13		32	11.10	odd	2	inner
605.2.e.b.483.4		32	55.43	even	4	inner
605.2.e.b.483.13		32	5.3	odd	4	inner
605.2.m.c.118.1		32	55.38	odd	20
605.2.m.c.282.1		32	11.2	odd	10
605.2.m.c.403.4		32	55.13	even	20
605.2.m.c.602.4		32	11.5	even	5
605.2.m.d.118.4		32	55.28	even	20
605.2.m.d.282.4		32	11.9	even	5
605.2.m.d.403.1		32	55.53	odd	20
605.2.m.d.602.1		32	11.6	odd	10
605.2.m.e.112.1		32	11.8	odd	10
605.2.m.e.233.1		32	55.8	even	20
605.2.m.e.457.1		32	11.4	even	5
605.2.m.e.578.1		32	55.48	odd	20
880.2.cm.a.17.3		32	44.7	even	10
880.2.cm.a.193.3		32	220.183	odd	20
880.2.cm.a.497.3		32	44.3	odd	10
880.2.cm.a.673.3		32	220.3	even	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03659 + 1.03659i) q^{2} +(0.588647 - 0.588647i) q^{3} -0.149021i q^{4} +(-2.18706 + 0.465567i) q^{5} +1.22037i q^{6} +(2.98069 - 2.98069i) q^{7} +(-1.91870 - 1.91870i) q^{8} +2.30699i q^{9} +O(q^{10})\)	\(q+(-1.03659 + 1.03659i) q^{2} +(0.588647 - 0.588647i) q^{3} -0.149021i q^{4} +(-2.18706 + 0.465567i) q^{5} +1.22037i q^{6} +(2.98069 - 2.98069i) q^{7} +(-1.91870 - 1.91870i) q^{8} +2.30699i q^{9} +(1.78448 - 2.74968i) q^{10} +(-0.0877208 - 0.0877208i) q^{12} +(-0.654555 - 0.654555i) q^{13} +6.17948i q^{14} +(-1.01335 + 1.56146i) q^{15} +4.27583 q^{16} +(1.36314 - 1.36314i) q^{17} +(-2.39139 - 2.39139i) q^{18} +5.43176 q^{19} +(0.0693793 + 0.325918i) q^{20} -3.50915i q^{21} +(1.95998 - 1.95998i) q^{23} -2.25887 q^{24} +(4.56649 - 2.03645i) q^{25} +1.35700 q^{26} +(3.12394 + 3.12394i) q^{27} +(-0.444185 - 0.444185i) q^{28} -1.00183 q^{29} +(-0.568163 - 2.66902i) q^{30} +0.423945 q^{31} +(-0.594873 + 0.594873i) q^{32} +2.82602i q^{34} +(-5.13124 + 7.90666i) q^{35} +0.343790 q^{36} +(3.48815 + 3.48815i) q^{37} +(-5.63049 + 5.63049i) q^{38} -0.770604 q^{39} +(5.08960 + 3.30303i) q^{40} -0.577469i q^{41} +(3.63753 + 3.63753i) q^{42} +(5.05373 + 5.05373i) q^{43} +(-1.07406 - 5.04553i) q^{45} +4.06339i q^{46} +(0.841173 + 0.841173i) q^{47} +(2.51696 - 2.51696i) q^{48} -10.7690i q^{49} +(-2.62261 + 6.84452i) q^{50} -1.60481i q^{51} +(-0.0975424 + 0.0975424i) q^{52} +(6.42164 - 6.42164i) q^{53} -6.47647 q^{54} -11.4381 q^{56} +(3.19739 - 3.19739i) q^{57} +(1.03848 - 1.03848i) q^{58} +9.30975i q^{59} +(0.232691 + 0.151011i) q^{60} -7.78179i q^{61} +(-0.439456 + 0.439456i) q^{62} +(6.87641 + 6.87641i) q^{63} +7.31840i q^{64} +(1.73629 + 1.12681i) q^{65} +(-3.05526 - 3.05526i) q^{67} +(-0.203136 - 0.203136i) q^{68} -2.30748i q^{69} +(-2.87696 - 13.5149i) q^{70} +8.59135 q^{71} +(4.42642 - 4.42642i) q^{72} +(3.86109 + 3.86109i) q^{73} -7.23154 q^{74} +(1.48930 - 3.88681i) q^{75} -0.809447i q^{76} +(0.798797 - 0.798797i) q^{78} -2.28422 q^{79} +(-9.35152 + 1.99069i) q^{80} -3.24316 q^{81} +(0.598596 + 0.598596i) q^{82} +(-1.40622 - 1.40622i) q^{83} -0.522937 q^{84} +(-2.34664 + 3.61590i) q^{85} -10.4773 q^{86} +(-0.589724 + 0.589724i) q^{87} +13.9313i q^{89} +(6.34348 + 4.11677i) q^{90} -3.90204 q^{91} +(-0.292079 - 0.292079i) q^{92} +(0.249554 - 0.249554i) q^{93} -1.74390 q^{94} +(-11.8796 + 2.52885i) q^{95} +0.700340i q^{96} +(-2.35066 - 2.35066i) q^{97} +(11.1630 + 11.1630i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} + 8 q^{5}+O(q^{10}) \) 32 * q - 4 * q^3 + 8 * q^5	\( 32 q - 4 q^{3} + 8 q^{5} + 12 q^{12} - 36 q^{15} - 8 q^{16} - 64 q^{20} - 24 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{31} + 24 q^{36} + 32 q^{37} - 40 q^{38} + 60 q^{42} - 28 q^{45} - 28 q^{47} + 56 q^{48} + 116 q^{53} - 80 q^{56} - 80 q^{58} + 104 q^{60} - 8 q^{67} - 80 q^{70} + 24 q^{71} - 76 q^{75} + 60 q^{78} + 8 q^{80} + 8 q^{81} - 20 q^{82} - 40 q^{86} + 80 q^{91} + 52 q^{92} + 32 q^{93} + 92 q^{97}+O(q^{100}) \) 32 * q - 4 * q^3 + 8 * q^5 + 12 * q^12 - 36 * q^15 - 8 * q^16 - 64 * q^20 - 24 * q^23 + 16 * q^25 - 16 * q^27 - 8 * q^31 + 24 * q^36 + 32 * q^37 - 40 * q^38 + 60 * q^42 - 28 * q^45 - 28 * q^47 + 56 * q^48 + 116 * q^53 - 80 * q^56 - 80 * q^58 + 104 * q^60 - 8 * q^67 - 80 * q^70 + 24 * q^71 - 76 * q^75 + 60 * q^78 + 8 * q^80 + 8 * q^81 - 20 * q^82 - 40 * q^86 + 80 * q^91 + 52 * q^92 + 32 * q^93 + 92 * q^97

Introduction

L-functions

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