LMFDB - Embedded newform 675.2.l.a.526.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(76,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 0]))

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

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

chi := DirichletCharacter("675.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, 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:	$5.38990213644$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			526.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	675.526
Dual form			675.2.l.a.376.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.233956 - 1.32683i) q^{2} +(-1.70574 - 0.300767i) q^{3} +(0.173648 - 0.0632028i) q^{4} +2.33359i q^{6} +(-0.652704 - 0.237565i) q^{7} +(-1.47178 - 2.54920i) q^{8} +(2.81908 + 1.02606i) q^{9} +O(q^{10})$	\(q+(-0.233956 - 1.32683i) q^{2} +(-1.70574 - 0.300767i) q^{3} +(0.173648 - 0.0632028i) q^{4} +2.33359i q^{6} +(-0.652704 - 0.237565i) q^{7} +(-1.47178 - 2.54920i) q^{8} +(2.81908 + 1.02606i) q^{9} +(-3.52094 + 2.95442i) q^{11} +(-0.315207 + 0.0555796i) q^{12} +(0.245100 - 1.39003i) q^{13} +(-0.162504 + 0.921605i) q^{14} +(-2.75490 + 2.31164i) q^{16} +(-1.93969 + 3.35965i) q^{17} +(0.701867 - 3.98048i) q^{18} +(-3.53209 - 6.11776i) q^{19} +(1.04189 + 0.601535i) q^{21} +(4.74376 + 3.98048i) q^{22} +(-3.59240 + 1.30753i) q^{23} +(1.74376 + 4.79093i) q^{24} -1.90167 q^{26} +(-4.50000 - 2.59808i) q^{27} -0.128356 q^{28} +(0.851167 + 4.82721i) q^{29} +(0.786989 - 0.286441i) q^{31} +(-0.798133 - 0.669713i) q^{32} +(6.89440 - 3.98048i) q^{33} +(4.91147 + 1.78763i) q^{34} +0.554378 q^{36} +(-3.99273 + 6.91560i) q^{37} +(-7.29086 + 6.11776i) q^{38} +(-0.836152 + 2.29731i) q^{39} +(-1.36571 + 7.74535i) q^{41} +(0.554378 - 1.52314i) q^{42} +(1.59240 - 1.33618i) q^{43} +(-0.424678 + 0.735564i) q^{44} +(2.57532 + 4.46059i) q^{46} +(6.46451 + 2.35289i) q^{47} +(5.39440 - 3.11446i) q^{48} +(-4.99273 - 4.18939i) q^{49} +(4.31908 - 5.14728i) q^{51} +(-0.0452926 - 0.256867i) q^{52} -3.05644 q^{53} +(-2.39440 + 6.57856i) q^{54} +(0.355037 + 2.01352i) q^{56} +(4.18479 + 11.4976i) q^{57} +(6.20574 - 2.25870i) q^{58} +(-6.82295 - 5.72513i) q^{59} +(8.12449 + 2.95707i) q^{61} +(-0.564178 - 0.977185i) q^{62} +(-1.59627 - 1.33943i) q^{63} +(-4.29813 + 7.44459i) q^{64} +(-6.89440 - 8.21643i) q^{66} +(-1.64156 + 9.30975i) q^{67} +(-0.124485 + 0.705990i) q^{68} +(6.52094 - 1.14982i) q^{69} +(2.90033 - 5.02352i) q^{71} +(-1.53343 - 8.69653i) q^{72} +(2.70574 + 4.68647i) q^{73} +(10.1099 + 3.67972i) q^{74} +(-1.00000 - 0.839100i) q^{76} +(3.00000 - 1.09191i) q^{77} +(3.24376 + 0.571962i) q^{78} +(-2.27584 - 12.9070i) q^{79} +(6.89440 + 5.78509i) q^{81} +10.5963 q^{82} +(0.197119 + 1.11792i) q^{83} +(0.218941 + 0.0386052i) q^{84} +(-2.14543 - 1.80023i) q^{86} -8.48995i q^{87} +(12.7135 + 4.62733i) q^{88} +(-0.368241 - 0.637812i) q^{89} +(-0.490200 + 0.849051i) q^{91} +(-0.541174 + 0.454099i) q^{92} +(-1.42855 + 0.251892i) q^{93} +(1.60947 - 9.12776i) q^{94} +(1.15998 + 1.38241i) q^{96} +(6.39440 - 5.36554i) q^{97} +(-4.39053 + 7.60462i) q^{98} +(-12.9572 + 4.71605i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 6 q^{7} + 6 q^{8}+O(q^{10}) $ 6 * q - 6 * q^2 - 6 * q^7 + 6 * q^8	$ 6 q - 6 q^{2} - 6 q^{7} + 6 q^{8} - 18 q^{11} - 9 q^{12} - 6 q^{14} - 18 q^{16} - 6 q^{17} + 18 q^{18} - 12 q^{19} + 36 q^{22} - 18 q^{23} + 18 q^{24} + 12 q^{26} - 27 q^{27} + 36 q^{28} - 21 q^{29} - 3 q^{31} + 9 q^{32} + 9 q^{34} - 18 q^{36} - 6 q^{37} - 12 q^{38} - 9 q^{39} - 18 q^{41} - 18 q^{42} + 6 q^{43} - 27 q^{44} - 9 q^{46} + 6 q^{47} - 9 q^{48} - 12 q^{49} + 9 q^{51} - 36 q^{52} - 48 q^{53} + 27 q^{54} - 48 q^{56} + 18 q^{57} + 27 q^{58} + 36 q^{61} + 15 q^{62} + 18 q^{63} - 12 q^{64} - 18 q^{67} + 12 q^{68} + 36 q^{69} + 3 q^{71} + 9 q^{72} + 6 q^{73} + 12 q^{74} - 6 q^{76} + 18 q^{77} + 27 q^{78} - 12 q^{79} + 36 q^{82} - 18 q^{83} + 36 q^{84} + 3 q^{86} + 18 q^{88} + 3 q^{89} + 63 q^{92} - 9 q^{93} + 27 q^{94} + 27 q^{96} - 3 q^{97} - 9 q^{98} - 27 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - 6 * q^7 + 6 * q^8 - 18 * q^11 - 9 * q^12 - 6 * q^14 - 18 * q^16 - 6 * q^17 + 18 * q^18 - 12 * q^19 + 36 * q^22 - 18 * q^23 + 18 * q^24 + 12 * q^26 - 27 * q^27 + 36 * q^28 - 21 * q^29 - 3 * q^31 + 9 * q^32 + 9 * q^34 - 18 * q^36 - 6 * q^37 - 12 * q^38 - 9 * q^39 - 18 * q^41 - 18 * q^42 + 6 * q^43 - 27 * q^44 - 9 * q^46 + 6 * q^47 - 9 * q^48 - 12 * q^49 + 9 * q^51 - 36 * q^52 - 48 * q^53 + 27 * q^54 - 48 * q^56 + 18 * q^57 + 27 * q^58 + 36 * q^61 + 15 * q^62 + 18 * q^63 - 12 * q^64 - 18 * q^67 + 12 * q^68 + 36 * q^69 + 3 * q^71 + 9 * q^72 + 6 * q^73 + 12 * q^74 - 6 * q^76 + 18 * q^77 + 27 * q^78 - 12 * q^79 + 36 * q^82 - 18 * q^83 + 36 * q^84 + 3 * q^86 + 18 * q^88 + 3 * q^89 + 63 * q^92 - 9 * q^93 + 27 * q^94 + 27 * q^96 - 3 * q^97 - 9 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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 $

$2$	−0.233956	−	1.32683i	−0.165432	−	0.938209i	−0.948618	−	0.316423i	$-0.897518\pi$
$2$	−0.233956	−	1.32683i	−0.165432	−	0.938209i	0.783187	−	0.621786i	$-0.213593\pi$
$3$	−1.70574	−	0.300767i	−0.984808	−	0.173648i
$3$	−1.70574	−	0.300767i	−0.984808	−	0.173648i
$4$	0.173648	−	0.0632028i	0.0868241	−	0.0316014i
$5$		0			0
$5$		0			0
$6$			2.33359i			0.952682i
$7$	−0.652704	−	0.237565i	−0.246699	−	0.0897910i	0.215711	−	0.976457i	$-0.430793\pi$
$7$	−0.652704	−	0.237565i	−0.246699	−	0.0897910i	−0.462410	+	0.886666i	$0.653015\pi$
$8$	−1.47178	−	2.54920i	−0.520353	−	0.901278i
$9$	2.81908	+	1.02606i	0.939693	+	0.342020i
$10$		0			0
$11$	−3.52094	+	2.95442i	−1.06160	+	0.890792i	−0.994266	−	0.106938i	$-0.965895\pi$
$11$	−3.52094	+	2.95442i	−1.06160	+	0.890792i	−0.0673390	+	0.997730i	$0.521451\pi$
$12$	−0.315207	+	0.0555796i	−0.0909926	+	0.0160444i
$13$	0.245100	−	1.39003i	0.0679785	−	0.385525i	−0.931769	−	0.363052i	$-0.881735\pi$
$13$	0.245100	−	1.39003i	0.0679785	−	0.385525i	0.999747	−	0.0224733i	$-0.00715409\pi$
$14$	−0.162504	+	0.921605i	−0.0434310	+	0.246309i
$15$		0			0
$16$	−2.75490	+	2.31164i	−0.688725	+	0.577909i
$17$	−1.93969	+	3.35965i	−0.470445	+	0.814834i	−0.999429	−	0.0337978i	$-0.989240\pi$
$17$	−1.93969	+	3.35965i	−0.470445	+	0.814834i	0.528984	+	0.848632i	$0.322573\pi$
$18$	0.701867	−	3.98048i	0.165432	−	0.938209i
$19$	−3.53209	−	6.11776i	−0.810317	−	1.40351i	−0.912642	−	0.408759i	$-0.865962\pi$
$19$	−3.53209	−	6.11776i	−0.810317	−	1.40351i	0.102326	−	0.994751i	$-0.467372\pi$
$20$		0			0
$21$	1.04189	+	0.601535i	0.227359	+	0.131266i
$22$	4.74376	+	3.98048i	1.01137	+	0.848642i
$23$	−3.59240	+	1.30753i	−0.749066	+	0.272638i	−0.688213	−	0.725509i	$-0.741604\pi$
$23$	−3.59240	+	1.30753i	−0.749066	+	0.272638i	−0.0608535	+	0.998147i	$0.519382\pi$
$24$	1.74376	+	4.79093i	0.355943	+	0.977944i
$25$		0			0
$26$	−1.90167			−0.372949
$27$	−4.50000	−	2.59808i	−0.866025	−	0.500000i
$28$	−0.128356			−0.0242569
$29$	0.851167	+	4.82721i	0.158058	+	0.896390i	0.955937	+	0.293572i	$0.0948442\pi$
$29$	0.851167	+	4.82721i	0.158058	+	0.896390i	−0.797879	+	0.602817i	$0.794045\pi$
$30$		0			0
$31$	0.786989	−	0.286441i	0.141347	−	0.0514462i	−0.270378	−	0.962754i	$-0.587149\pi$
$31$	0.786989	−	0.286441i	0.141347	−	0.0514462i	0.411725	+	0.911308i	$0.364926\pi$
$32$	−0.798133	−	0.669713i	−0.141091	−	0.118390i
$33$	6.89440	−	3.98048i	1.20016	−	0.692913i
$34$	4.91147	+	1.78763i	0.842311	+	0.306576i
$35$		0			0
$36$	0.554378			0.0923963
$37$	−3.99273	+	6.91560i	−0.656400	+	1.13692i	0.325141	+	0.945666i	$0.394588\pi$
$37$	−3.99273	+	6.91560i	−0.656400	+	1.13692i	−0.981541	+	0.191253i	$0.938745\pi$
$38$	−7.29086	+	6.11776i	−1.18273	+	0.992431i
$39$	−0.836152	+	2.29731i	−0.133891	+	0.367864i
$40$		0			0
$41$	−1.36571	+	7.74535i	−0.213289	+	1.20962i	0.670563	+	0.741853i	$0.266053\pi$
$41$	−1.36571	+	7.74535i	−0.213289	+	1.20962i	−0.883851	+	0.467768i	$0.845058\pi$
$42$	0.554378	−	1.52314i	0.0855423	−	0.235026i
$43$	1.59240	−	1.33618i	0.242838	−	0.203765i	−0.513243	−	0.858243i	$-0.671556\pi$
$43$	1.59240	−	1.33618i	0.242838	−	0.203765i	0.756081	+	0.654478i	$0.227112\pi$
$44$	−0.424678	+	0.735564i	−0.0640226	+	0.110890i
$45$		0			0
$46$	2.57532	+	4.46059i	0.379711	+	0.657678i
$47$	6.46451	+	2.35289i	0.942945	+	0.343204i	0.767328	−	0.641255i	$-0.221586\pi$
$47$	6.46451	+	2.35289i	0.942945	+	0.343204i	0.175617	+	0.984459i	$0.443808\pi$
$48$	5.39440	−	3.11446i	0.778615	−	0.449533i
$49$	−4.99273	−	4.18939i	−0.713247	−	0.598485i
$50$		0			0
$51$	4.31908	−	5.14728i	0.604792	−	0.720763i
$52$	−0.0452926	−	0.256867i	−0.00628096	−	0.0356211i
$53$	−3.05644			−0.419834			−0.209917	−	0.977719i	$-0.567319\pi$
$53$	−3.05644			−0.419834			−0.209917	+	0.977719i	$0.567319\pi$
$54$	−2.39440	+	6.57856i	−0.325837	+	0.895229i
$55$		0			0
$56$	0.355037	+	2.01352i	0.0474438	+	0.269067i
$57$	4.18479	+	11.4976i	0.554289	+	1.52290i
$58$	6.20574	−	2.25870i	0.814853	−	0.296582i
$59$	−6.82295	−	5.72513i	−0.888272	−	0.745349i	0.0795906	−	0.996828i	$-0.474639\pi$
$59$	−6.82295	−	5.72513i	−0.888272	−	0.745349i	−0.967863	+	0.251479i	$0.919083\pi$
$60$		0			0
$61$	8.12449	+	2.95707i	1.04023	+	0.378614i	0.804969	−	0.593317i	$-0.202182\pi$
$61$	8.12449	+	2.95707i	1.04023	+	0.378614i	0.235265	+	0.971931i	$0.424404\pi$
$62$	−0.564178	−	0.977185i	−0.0716506	−	0.124103i
$63$	−1.59627	−	1.33943i	−0.201111	−	0.168752i
$64$	−4.29813	+	7.44459i	−0.537267	+	0.930573i
$65$		0			0
$66$	−6.89440	−	8.21643i	−0.848642	−	1.01137i
$67$	−1.64156	+	9.30975i	−0.200548	+	1.13737i	0.703744	+	0.710453i	$0.251510\pi$
$67$	−1.64156	+	9.30975i	−0.200548	+	1.13737i	−0.904293	+	0.426913i	$0.859601\pi$
$68$	−0.124485	+	0.705990i	−0.0150960	+	0.0856139i
$69$	6.52094	−	1.14982i	0.785029	−	0.138422i
$70$		0			0
$71$	2.90033	−	5.02352i	0.344206	−	0.596182i	−0.641003	−	0.767538i	$-0.721482\pi$
$71$	2.90033	−	5.02352i	0.344206	−	0.596182i	0.985209	+	0.171356i	$0.0548149\pi$
$72$	−1.53343	−	8.69653i	−0.180717	−	1.02490i
$73$	2.70574	+	4.68647i	0.316683	+	0.548510i	0.979794	−	0.200011i	$-0.0640977\pi$
$73$	2.70574	+	4.68647i	0.316683	+	0.548510i	−0.663111	+	0.748521i	$0.730764\pi$
$74$	10.1099	+	3.67972i	1.17526	+	0.427758i
$75$		0			0
$76$	−1.00000	−	0.839100i	−0.114708	−	0.0962513i
$77$	3.00000	−	1.09191i	0.341882	−	0.124435i
$78$	3.24376	+	0.571962i	0.367283	+	0.0647619i
$79$	−2.27584	−	12.9070i	−0.256053	−	1.45215i	−0.793356	−	0.608757i	$-0.791668\pi$
$79$	−2.27584	−	12.9070i	−0.256053	−	1.45215i	0.537304	−	0.843389i	$-0.319443\pi$
$80$		0			0
$81$	6.89440	+	5.78509i	0.766044	+	0.642788i
$82$	10.5963			1.17016
$83$	0.197119	+	1.11792i	0.0216366	+	0.122707i	0.993713	−	0.111957i	$-0.0357120\pi$
$83$	0.197119	+	1.11792i	0.0216366	+	0.122707i	−0.972076	+	0.234665i	$0.924601\pi$
$84$	0.218941	+	0.0386052i	0.0238884	+	0.00421217i
$85$		0			0
$86$	−2.14543	−	1.80023i	−0.231348	−	0.194124i
$87$		−	8.48995i		−	0.910218i
$88$	12.7135	+	4.62733i	1.35526	+	0.493275i
$89$	−0.368241	−	0.637812i	−0.0390335	−	0.0676079i	0.845849	−	0.533423i	$-0.179095\pi$
$89$	−0.368241	−	0.637812i	−0.0390335	−	0.0676079i	−0.884882	+	0.465815i	$0.845761\pi$
$90$		0			0
$91$	−0.490200	+	0.849051i	−0.0513869	+	0.0890047i
$92$	−0.541174	+	0.454099i	−0.0564213	+	0.0473431i
$93$	−1.42855	+	0.251892i	−0.148134	+	0.0261199i
$94$	1.60947	−	9.12776i	0.166004	−	0.941457i
$95$		0			0
$96$	1.15998	+	1.38241i	0.118390	+	0.141091i
$97$	6.39440	−	5.36554i	0.649253	−	0.544788i	−0.257591	−	0.966254i	$-0.582929\pi$
$97$	6.39440	−	5.36554i	0.649253	−	0.544788i	0.906844	+	0.421466i	$0.138484\pi$
$98$	−4.39053	+	7.60462i	−0.443510	+	0.768183i
$99$	−12.9572	+	4.71605i	−1.30225	+	0.473981i
$100$		0			0
$101$	−11.6099	−	4.22567i	−1.15523	−	0.420470i	−0.307840	−	0.951438i	$-0.599606\pi$
$101$	−11.6099	−	4.22567i	−1.15523	−	0.420470i	−0.847392	+	0.530968i	$0.821828\pi$
$102$	−7.84002	−	4.52644i	−0.776278	−	0.448184i
$103$	6.43763	+	5.40182i	0.634319	+	0.532257i	0.902268	−	0.431176i	$-0.141901\pi$
$103$	6.43763	+	5.40182i	0.634319	+	0.532257i	−0.267949	+	0.963433i	$0.586346\pi$
$104$	−3.90420	+	1.42101i	−0.382838	+	0.139342i
$105$		0			0
$106$	0.715070	+	4.05537i	0.0694538	+	0.393892i
$107$	−13.9581			−1.34938			−0.674691	−	0.738101i	$-0.735723\pi$
$107$	−13.9581			−1.34938			−0.674691	+	0.738101i	$0.735723\pi$
$108$	−0.945622	−	0.166739i	−0.0909926	−	0.0160444i
$109$	−15.5817			−1.49246			−0.746229	−	0.665689i	$-0.768138\pi$
$109$	−15.5817			−1.49246			−0.746229	+	0.665689i	$0.768138\pi$
$110$		0			0
$111$	8.89053	−	10.5953i	0.843852	−	1.00566i
$112$	2.34730	−	0.854346i	0.221799	−	0.0807281i
$113$	−13.1532	−	11.0368i	−1.23735	−	1.03826i	−0.997727	−	0.0673899i	$-0.978533\pi$
$113$	−13.1532	−	11.0368i	−1.23735	−	1.03826i	−0.239619	−	0.970867i	$-0.577023\pi$
$114$	14.2763	−	8.24243i	1.33710	−	0.771975i
$115$		0			0
$116$	0.452896	+	0.784440i	0.0420504	+	0.0728334i
$117$	2.11721	−	3.66712i	0.195736	−	0.339025i
$118$	−6.00000	+	10.3923i	−0.552345	+	0.956689i
$119$	2.06418	−	1.73205i	0.189223	−	0.158777i
$120$		0			0
$121$	1.75830	−	9.97184i	0.159846	−	0.906531i
$122$	2.02276	−	11.4716i	0.183132	−	1.03859i
$123$	4.65910	−	12.8008i	0.420097	−	1.15421i
$124$	0.118555	−	0.0994798i	0.0106466	−	0.00893355i
$125$		0			0
$126$	−1.40373	+	2.43134i	−0.125055	+	0.216601i
$127$	−11.1839	−	19.3711i	−0.992412	−	1.71891i	−0.602690	−	0.797975i	$-0.705904\pi$
$127$	−11.1839	−	19.3711i	−0.992412	−	1.71891i	−0.389722	−	0.920933i	$-0.627429\pi$
$128$	8.92514	+	3.24849i	0.788879	+	0.287128i
$129$	−3.11809	+	1.80023i	−0.274532	+	0.158501i
$130$		0			0
$131$	−13.9427	+	5.07472i	−1.21818	+	0.443381i	−0.869533	−	0.493874i	$-0.835580\pi$
$131$	−13.9427	+	5.07472i	−1.21818	+	0.443381i	−0.348645	+	0.937255i	$0.613358\pi$
$132$	0.945622	−	1.12695i	0.0823059	−	0.0980883i
$133$	0.852044	+	4.83218i	0.0738816	+	0.419003i
$134$	12.7365			1.10026
$135$		0			0
$136$	11.4192			0.979190
$137$	−2.22328	−	12.6088i	−0.189947	−	1.07725i	−0.919432	−	0.393249i	$-0.871351\pi$
$137$	−2.22328	−	12.6088i	−0.189947	−	1.07725i	0.729485	−	0.683997i	$-0.239760\pi$
$138$	−3.05122	−	8.38316i	−0.259737	−	0.713622i
$139$	10.7258	−	3.90387i	0.909751	−	0.331122i	0.155597	−	0.987821i	$-0.450270\pi$
$139$	10.7258	−	3.90387i	0.909751	−	0.331122i	0.754153	+	0.656698i	$0.228048\pi$
$140$		0			0
$141$	−10.3191	−	5.95772i	−0.869023	−	0.501731i
$142$	−7.34389	−	2.67296i	−0.616286	−	0.224310i
$143$	3.24376	+	5.61835i	0.271256	+	0.469830i
$144$	−10.1382	+	3.68999i	−0.844846	+	0.307499i
$145$		0			0
$146$	5.58512	−	4.68647i	0.462228	−	0.387855i
$147$	7.25624	+	8.64766i	0.598485	+	0.713247i
$148$	−0.256244	+	1.45323i	−0.0210631	+	0.119455i
$149$	2.26352	−	12.8370i	0.185435	−	1.05165i	−0.739961	−	0.672650i	$-0.765156\pi$
$149$	2.26352	−	12.8370i	0.185435	−	1.05165i	0.925396	−	0.379002i	$-0.123733\pi$
$150$		0			0
$151$	−1.56418	+	1.31250i	−0.127291	+	0.106810i	−0.704211	−	0.709991i	$-0.748699\pi$
$151$	−1.56418	+	1.31250i	−0.127291	+	0.106810i	0.576920	+	0.816801i	$0.304255\pi$
$152$	−10.3969	+	18.0080i	−0.843302	+	1.46064i
$153$	−8.91534	+	7.48086i	−0.720763	+	0.604792i
$154$	−2.15064	−	3.72503i	−0.173304	−	0.300171i
$155$		0			0
$156$			0.451771i			0.0361706i
$157$	8.87804	+	7.44956i	0.708545	+	0.594540i	0.924190	−	0.381932i	$-0.124741\pi$
$157$	8.87804	+	7.44956i	0.708545	+	0.594540i	−0.215646	+	0.976472i	$0.569186\pi$
$158$	−16.5929	+	6.03931i	−1.32006	+	0.480462i
$159$	5.21348	+	0.919277i	0.413456	+	0.0729034i
$160$		0			0
$161$	2.65539			0.209274
$162$	6.06283	−	10.5011i	0.476341	−	0.825047i
$163$	−16.6382			−1.30320			−0.651600	−	0.758562i	$-0.725902\pi$
$163$	−16.6382			−1.30320			−0.651600	+	0.758562i	$0.725902\pi$
$164$	0.252374	+	1.43128i	0.0197071	+	0.111764i
$165$		0			0
$166$	1.43717	−	0.523086i	0.111546	−	0.0405993i
$167$	0.0812519	+	0.0681784i	0.00628746	+	0.00527581i	0.645926	−	0.763400i	$-0.276471\pi$
$167$	0.0812519	+	0.0681784i	0.00628746	+	0.00527581i	−0.639638	+	0.768676i	$0.720916\pi$
$168$		−	3.54131i		−	0.273218i
$169$	10.3439	+	3.76487i	0.795684	+	0.289605i
$170$		0			0
$171$	−3.68004	−	20.8706i	−0.281420	−	1.59601i
$172$	0.192066	−	0.332669i	0.0146449	−	0.0253658i
$173$	5.88532	−	4.93837i	0.447452	−	0.375457i	−0.391037	−	0.920375i	$-0.627884\pi$
$173$	5.88532	−	4.93837i	0.447452	−	0.375457i	0.838489	+	0.544918i	$0.183439\pi$
$174$	−11.2647	+	1.98627i	−0.853975	+	0.150579i
$175$		0			0
$176$	2.87030	−	16.2783i	0.216357	−	1.22702i
$177$	9.91622	+	11.8177i	0.745349	+	0.888272i
$178$	−0.760115	+	0.637812i	−0.0569730	+	0.0478060i
$179$	11.2515	−	19.4882i	0.840976	−	1.45661i	−0.0480938	−	0.998843i	$-0.515315\pi$
$179$	11.2515	−	19.4882i	0.840976	−	1.45661i	0.889070	−	0.457771i	$-0.151352\pi$
$180$		0			0
$181$	−10.8944	−	18.8697i	−0.809774	−	1.40257i	−0.913020	−	0.407914i	$-0.866256\pi$
$181$	−10.8944	−	18.8697i	−0.809774	−	1.40257i	0.103246	−	0.994656i	$-0.467077\pi$
$182$	1.24123	+	0.451771i	0.0920061	+	0.0334875i
$183$	−12.9688	−	7.48757i	−0.958685	−	0.553497i
$184$	8.62037	+	7.23335i	0.635502	+	0.533249i
$185$		0			0
$186$	0.668434	+	1.83651i	0.0490119	+	0.134659i
$187$	−3.09627	−	17.5598i	−0.226421	−	1.28410i
$188$	1.27126			0.0927161
$189$	2.31996	+	2.76481i	0.168752	+	0.201111i
$190$		0			0
$191$	1.81180	+	10.2753i	0.131098	+	0.743491i	0.977498	+	0.210944i	$0.0676539\pi$
$191$	1.81180	+	10.2753i	0.131098	+	0.743491i	−0.846401	+	0.532547i	$0.821235\pi$
$192$	9.57057	−	11.4058i	0.690697	−	0.823140i
$193$	−9.37211	+	3.41117i	−0.674619	+	0.245541i	−0.656536	−	0.754295i	$-0.727979\pi$
$193$	−9.37211	+	3.41117i	−0.674619	+	0.245541i	−0.0180838	+	0.999836i	$0.505757\pi$
$194$	−8.61515	−	7.22897i	−0.618532	−	0.519010i
$195$		0			0
$196$	−1.13176	−	0.411927i	−0.0808399	−	0.0294233i
$197$	8.38578	+	14.5246i	0.597462	+	1.03483i	0.993194	+	0.116469i	$0.0371575\pi$
$197$	8.38578	+	14.5246i	0.597462	+	1.03483i	−0.395732	+	0.918366i	$0.629509\pi$
$198$	9.28880	+	16.0887i	0.660126	+	1.14337i
$199$	−13.7981	+	23.8991i	−0.978124	+	1.69416i	−0.308908	+	0.951092i	$0.599963\pi$
$199$	−13.7981	+	23.8991i	−0.978124	+	1.69416i	−0.669216	+	0.743068i	$0.733370\pi$
$200$		0			0
$201$	5.60014	−	15.3863i	0.395003	−	1.08526i
$202$	−2.89053	+	16.3930i	−0.203377	+	1.15341i
$203$	0.591214	−	3.35294i	0.0414951	−	0.235330i
$204$	0.424678	−	1.16679i	0.0297334	−	0.0816918i
$205$		0			0
$206$	5.66116	−	9.80542i	0.394432	−	0.683176i
$207$	−11.4688			−0.797140
$208$	2.53802	+	4.39598i	0.175980	+	0.304806i
$209$	30.5107	+	11.1050i	2.11047	+	0.768149i
$210$		0			0
$211$	−6.10220	−	5.12035i	−0.420093	−	0.352499i	0.408106	−	0.912935i	$-0.366189\pi$
$211$	−6.10220	−	5.12035i	−0.420093	−	0.352499i	−0.828198	+	0.560435i	$0.810634\pi$
$212$	−0.530745	+	0.193175i	−0.0364517	+	0.0132673i
$213$	−6.45811	+	7.69648i	−0.442502	+	0.527354i
$214$	3.26558	+	18.5200i	0.223230	+	1.26600i
$215$		0			0
$216$			15.2952i			1.04071i
$217$	−0.581719			−0.0394896
$218$	3.64543	+	20.6743i	0.246900	+	1.40024i
$219$	−3.20574	−	8.80769i	−0.216624	−	0.595169i
$220$		0			0
$221$	4.19459	+	3.51968i	0.282159	+	0.236759i
$222$	−16.1382	−	9.31737i	−1.08312	−	0.625341i
$223$	19.5141	+	7.10257i	1.30676	+	0.475623i	0.899194	−	0.437551i	$-0.144154\pi$
$223$	19.5141	+	7.10257i	1.30676	+	0.475623i	0.407570	+	0.913174i	$0.366376\pi$
$224$	0.361844	+	0.626733i	0.0241767	+	0.0418753i
$225$		0			0
$226$	−11.5667	+	20.0341i	−0.769406	+	1.33265i
$227$	−1.23783	+	1.03866i	−0.0821574	+	0.0689382i	−0.682941	−	0.730473i	$-0.739300\pi$
$227$	−1.23783	+	1.03866i	−0.0821574	+	0.0689382i	0.600784	+	0.799411i	$0.294855\pi$
$228$	1.45336	+	1.73205i	0.0962513	+	0.114708i
$229$	1.76604	−	10.0157i	0.116704	−	0.661858i	−0.869189	−	0.494480i	$-0.835359\pi$
$229$	1.76604	−	10.0157i	0.116704	−	0.661858i	0.985893	−	0.167379i	$-0.0535303\pi$
$230$		0			0
$231$	−5.44562	+	0.960210i	−0.358296	+	0.0631772i
$232$	11.0528	−	9.27439i	0.725651	−	0.608893i
$233$	10.4966	−	18.1806i	0.687655	−	1.19105i	−0.284940	−	0.958545i	$-0.591974\pi$
$233$	10.4966	−	18.1806i	0.687655	−	1.19105i	0.972595	−	0.232508i	$-0.0746931\pi$
$234$	−5.36097	−	1.95123i	−0.350457	−	0.127556i
$235$		0			0
$236$	−1.54664	−	0.562930i	−0.100677	−	0.0366436i
$237$			22.7004i			1.47455i
$238$	−2.78106	−	2.33359i	−0.180269	−	0.151264i
$239$	−4.70574	+	1.71275i	−0.304389	+	0.110788i	−0.489699	−	0.871892i	$-0.662893\pi$
$239$	−4.70574	+	1.71275i	−0.304389	+	0.110788i	0.185310	+	0.982680i	$0.440671\pi$
$240$		0			0
$241$	3.95290	+	22.4180i	0.254628	+	1.44407i	0.797025	+	0.603947i	$0.206406\pi$
$241$	3.95290	+	22.4180i	0.254628	+	1.44407i	−0.542396	+	0.840123i	$0.682483\pi$
$242$	−13.6423			−0.876959
$243$	−10.0201	−	11.9415i	−0.642788	−	0.766044i
$244$	1.59770			0.102282
$245$		0			0
$246$	−18.0744	−	3.18701i	−1.15238	−	0.203196i
$247$	−9.36959	+	3.41025i	−0.596172	+	0.216989i
$248$	−1.88847	−	1.58461i	−0.119918	−	0.100623i
$249$		−	1.96616i		−	0.124600i
$250$		0			0
$251$	−7.30928	−	12.6600i	−0.461358	−	0.799095i	0.537671	−	0.843154i	$-0.319304\pi$
$251$	−7.30928	−	12.6600i	−0.461358	−	0.799095i	−0.999029	+	0.0440598i	$0.985971\pi$
$252$	−0.361844	−	0.131701i	−0.0227940	−	0.00829635i
$253$	8.78564	−	15.2172i	0.552349	−	0.956696i
$254$	−23.0856	+	19.3711i	−1.44852	+	1.21545i
$255$		0			0
$256$	−0.763356	+	4.32921i	−0.0477098	+	0.270575i
$257$	−0.0368366	+	0.208911i	−0.00229781	+	0.0130315i	−0.985935	−	0.167129i	$-0.946550\pi$
$257$	−0.0368366	+	0.208911i	−0.00229781	+	0.0130315i	0.983637	+	0.180160i	$0.0576616\pi$
$258$	3.11809	+	3.71599i	0.194124	+	0.231348i
$259$	4.24897	−	3.56531i	0.264018	−	0.221538i
$260$		0			0
$261$	−2.55350	+	14.4816i	−0.158058	+	0.896390i
$262$	9.99525	+	17.3123i	0.617509	+	1.06956i
$263$	−1.55303	−	0.565258i	−0.0957641	−	0.0348553i	0.293694	−	0.955900i	$-0.405115\pi$
$263$	−1.55303	−	0.565258i	−0.0957641	−	0.0348553i	−0.389458	+	0.921044i	$0.627338\pi$
$264$	−20.2941	−	11.7168i	−1.24902	−	0.721119i
$265$		0			0
$266$	6.21213	−	2.26103i	0.380890	−	0.138633i
$267$	0.436289	+	1.19869i	0.0267005	+	0.0733589i
$268$	0.303348	+	1.72037i	0.0185299	+	0.105088i
$269$	−3.03684			−0.185159			−0.0925796	−	0.995705i	$-0.529511\pi$
$269$	−3.03684			−0.185159			−0.0925796	+	0.995705i	$0.529511\pi$
$270$		0			0
$271$	15.9145			0.966735			0.483368	−	0.875418i	$-0.339413\pi$
$271$	15.9145			0.966735			0.483368	+	0.875418i	$0.339413\pi$
$272$	−2.42262	−	13.7394i	−0.146893	−	0.833071i
$273$	1.09152	−	1.30082i	0.0660617	−	0.0787293i
$274$	−16.2096	+	5.89981i	−0.979258	+	0.356421i
$275$		0			0
$276$	1.05968	−	0.611806i	0.0637851	−	0.0368264i
$277$	−16.5471	−	6.02265i	−0.994219	−	0.361866i	−0.206867	−	0.978369i	$-0.566327\pi$
$277$	−16.5471	−	6.02265i	−0.994219	−	0.361866i	−0.787353	+	0.616503i	$0.788549\pi$
$278$	−7.68913	−	13.3180i	−0.461163	−	0.798758i
$279$	2.51249			0.150419
$280$		0			0
$281$	6.72668	−	5.64436i	0.401280	−	0.336714i	−0.419708	−	0.907659i	$-0.637868\pi$
$281$	6.72668	−	5.64436i	0.401280	−	0.336714i	0.820988	+	0.570945i	$0.193423\pi$
$282$	−5.49067	+	15.0855i	−0.326964	+	0.898327i
$283$	0.351167	−	1.99157i	0.0208747	−	0.118386i	−0.972590	−	0.232527i	$-0.925300\pi$
$283$	0.351167	−	1.99157i	0.0208747	−	0.118386i	0.993465	+	0.114141i	$0.0364116\pi$
$284$	0.186137	−	1.05563i	0.0110452	−	0.0626403i
$285$		0			0
$286$	6.69569	−	5.61835i	0.395924	−	0.332220i
$287$	2.73143	−	4.73097i	0.161231	−	0.279261i
$288$	−1.56283	−	2.70691i	−0.0920909	−	0.159506i
$289$	0.975185	+	1.68907i	0.0573638	+	0.0993571i
$290$		0			0
$291$	−12.5209	+	7.22897i	−0.733991	+	0.423770i
$292$	0.766044	+	0.642788i	0.0448294	+	0.0376163i
$293$	18.4081	−	6.69999i	1.07541	−	0.391418i	0.257213	−	0.966355i	$-0.417196\pi$
$293$	18.4081	−	6.69999i	1.07541	−	0.391418i	0.818198	+	0.574937i	$0.194973\pi$
$294$	9.77631	−	11.6510i	0.570166	−	0.679497i
$295$		0			0
$296$	23.5057			1.36624
$297$	23.5201	−	4.14722i	1.36477	−	0.240646i
$298$	−17.5621			−1.01735
$299$	0.937004	+	5.31402i	0.0541884	+	0.307317i
$300$		0			0
$301$	−1.35679	+	0.493832i	−0.0782042	+	0.0284640i
$302$	2.10741	+	1.76833i	0.121268	+	0.101756i
$303$	18.5326	+	10.6998i	1.06467	+	0.614686i
$304$	23.8726	+	8.68891i	1.36919	+	0.498343i
$305$		0			0
$306$	12.0116	+	10.0789i	0.686658	+	0.576175i
$307$	4.13429	−	7.16079i	0.235956	−	0.408688i	−0.723594	−	0.690226i	$-0.757511\pi$
$307$	4.13429	−	7.16079i	0.235956	−	0.408688i	0.959550	+	0.281538i	$0.0908445\pi$
$308$	0.451933	−	0.379217i	0.0257513	−	0.0216079i
$309$	−9.35622	−	11.1503i	−0.532257	−	0.634319i
$310$		0			0
$311$	−4.79679	+	27.2039i	−0.272001	+	1.54259i	0.476329	+	0.879267i	$0.341967\pi$
$311$	−4.79679	+	27.2039i	−0.272001	+	1.54259i	−0.748330	+	0.663327i	$0.769144\pi$
$312$	7.08693	−	1.24962i	0.401219	−	0.0707457i
$313$	1.95084	−	1.63695i	0.110268	−	0.0925257i	−0.585987	−	0.810321i	$-0.699293\pi$
$313$	1.95084	−	1.63695i	0.110268	−	0.0925257i	0.696255	+	0.717795i	$0.254848\pi$
$314$	7.80722	−	13.5225i	0.440587	−	0.763119i
$315$		0			0
$316$	−1.21095	−	2.09743i	−0.0681214	−	0.117990i
$317$	26.9834	+	9.82115i	1.51554	+	0.551611i	0.960029	−	0.279900i	$-0.0903012\pi$
$317$	26.9834	+	9.82115i	1.51554	+	0.551611i	0.555509	+	0.831510i	$0.312523\pi$
$318$		−	7.13246i		−	0.399968i
$319$	−17.2585	−	14.4816i	−0.966292	−	0.810815i
$320$		0			0
$321$	23.8089	+	4.19815i	1.32888	+	0.234318i
$322$	−0.621244	−	3.52325i	−0.0346206	−	0.196343i
$323$	27.4047			1.52484
$324$	1.56283	+	0.568825i	0.0868241	+	0.0316014i
$325$		0			0
$326$	3.89259	+	22.0760i	0.215591	+	1.22267i
$327$	26.5783	+	4.68647i	1.46978	+	0.259163i
$328$	21.7545	−	7.91799i	1.20119	−	0.437198i
$329$	−3.66044	−	3.07148i	−0.201807	−	0.169336i
$330$		0			0
$331$	7.92514	+	2.88452i	0.435605	+	0.158547i	0.550509	−	0.834829i	$-0.314434\pi$
$331$	7.92514	+	2.88452i	0.435605	+	0.158547i	−0.114904	+	0.993377i	$0.536656\pi$
$332$	0.104885	+	0.181666i	0.00575630	+	0.00997021i
$333$	−18.3516	+	15.3988i	−1.00566	+	0.843852i
$334$	0.0714517	−	0.123758i	0.00390966	−	0.00677174i
$335$		0			0
$336$	−4.26083	+	0.751299i	−0.232447	+	0.0409867i
$337$	2.82042	−	15.9954i	0.153638	−	0.871325i	−0.806382	−	0.591395i	$-0.798577\pi$
$337$	2.82042	−	15.9954i	0.153638	−	0.871325i	0.960020	−	0.279931i	$-0.0903114\pi$
$338$	2.57532	−	14.6054i	0.140079	−	0.794428i
$339$	19.1163	+	22.7820i	1.03826	+	1.23735i
$340$		0			0
$341$	−1.92468	+	3.33364i	−0.104227	+	0.180527i
$342$	−26.8307	+	9.76557i	−1.45084	+	0.528062i
$343$	4.69459	+	8.13127i	0.253484	+	0.439047i
$344$	−5.74985	−	2.09277i	−0.310011	−	0.112835i
$345$		0			0
$346$	−7.92926	−	6.65344i	−0.426280	−	0.357691i
$347$	11.7788	−	4.28715i	0.632321	−	0.230146i	−0.00592013	−	0.999982i	$-0.501884\pi$
$347$	11.7788	−	4.28715i	0.632321	−	0.230146i	0.638241	+	0.769836i	$0.279662\pi$
$348$	−0.536588	−	1.47426i	−0.0287641	−	0.0790288i
$349$	5.70187	+	32.3369i	0.305214	+	1.73095i	0.622496	+	0.782623i	$0.286119\pi$
$349$	5.70187	+	32.3369i	0.305214	+	1.73095i	−0.317282	+	0.948331i	$0.602770\pi$
$350$		0			0
$351$	−4.71436	+	5.61835i	−0.251634	+	0.299885i
$352$	4.78880			0.255244
$353$	−2.81268	−	15.9515i	−0.149704	−	0.849013i	−0.963469	−	0.267819i	$-0.913697\pi$
$353$	−2.81268	−	15.9515i	−0.149704	−	0.849013i	0.813765	−	0.581194i	$-0.197414\pi$
$354$	13.3601	−	15.9219i	0.710081	−	0.846241i
$355$		0			0
$356$	−0.104256	−	0.0874810i	−0.00552555	−	0.00463649i
$357$	−4.04189	+	2.33359i	−0.213919	+	0.123506i
$358$	−28.4898	−	10.3694i	−1.50573	−	0.548042i
$359$	−6.13088	−	10.6190i	−0.323576	−	0.560449i	0.657647	−	0.753326i	$-0.271552\pi$
$359$	−6.13088	−	10.6190i	−0.323576	−	0.560449i	−0.981223	+	0.192877i	$0.938218\pi$
$360$		0			0
$361$	−15.4513	+	26.7624i	−0.813227	+	1.40855i
$362$	−22.4880	+	18.8697i	−1.18194	+	0.991767i
$363$	−5.99841	+	16.4805i	−0.314835	+	0.865001i
$364$	−0.0314599	+	0.178418i	−0.00164895	+	0.00935165i
$365$		0			0
$366$	−6.90058	+	18.9592i	−0.360699	+	0.991012i
$367$	−24.2743	+	20.3685i	−1.26711	+	1.06323i	−0.272218	+	0.962235i	$0.587757\pi$
$367$	−24.2743	+	20.3685i	−1.26711	+	1.06323i	−0.994887	+	0.100992i	$0.967798\pi$
$368$	6.87417	−	11.9064i	0.358341	−	0.620665i
$369$	−11.7973	+	20.4334i	−0.614141	+	1.06372i
$370$		0			0
$371$	1.99495	+	0.726102i	0.103573	+	0.0376973i
$372$	−0.232145	+	0.134029i	−0.0120361	+	0.00694907i
$373$	−27.6955	−	23.2393i	−1.43402	−	1.20329i	−0.943288	−	0.331975i	$-0.892285\pi$
$373$	−27.6955	−	23.2393i	−1.43402	−	1.20329i	−0.490732	−	0.871311i	$-0.663271\pi$
$374$	−22.5744	+	8.21643i	−1.16730	+	0.424861i
$375$		0			0
$376$	−3.51636	−	19.9423i	−0.181342	−	1.02844i
$377$	6.91859			0.356325
$378$	3.12567	−	3.72503i	0.160767	−	0.191595i
$379$	−13.7237			−0.704939			−0.352469	−	0.935823i	$-0.614658\pi$
$379$	−13.7237			−0.704939			−0.352469	+	0.935823i	$0.614658\pi$
$380$		0			0
$381$	13.2506	+	36.4058i	0.678850	+	1.86512i
$382$	13.2096	−	4.80790i	0.675862	−	0.245994i
$383$	17.5437	+	14.7209i	0.896441	+	0.752203i	0.969492	−	0.245125i	$-0.0788289\pi$
$383$	17.5437	+	14.7209i	0.896441	+	0.752203i	−0.0730503	+	0.997328i	$0.523273\pi$
$384$	−14.2469	−	8.22546i	−0.727035	−	0.419754i
$385$		0			0
$386$	6.71869	+	11.6371i	0.341972	+	0.592314i
$387$	5.86009	−	2.13290i	0.297885	−	0.108421i
$388$	0.771259	−	1.33586i	0.0391547	−	0.0678180i
$389$	−8.87211	+	7.44459i	−0.449834	+	0.377455i	−0.839374	−	0.543554i	$-0.817078\pi$
$389$	−8.87211	+	7.44459i	−0.449834	+	0.377455i	0.389540	+	0.921009i	$0.372634\pi$
$390$		0			0
$391$	2.57532	−	14.6054i	0.130240	−	0.738626i
$392$	−3.33140	+	18.8933i	−0.168261	+	0.954257i
$393$	25.3089	−	4.46264i	1.27666	−	0.225110i
$394$	17.3097	−	14.5246i	0.872052	−	0.731739i
$395$		0			0
$396$	−1.95193	+	1.63787i	−0.0980883	+	0.0823059i
$397$	−6.52822	−	11.3072i	−0.327642	−	0.567492i	0.654402	−	0.756147i	$-0.272921\pi$
$397$	−6.52822	−	11.3072i	−0.327642	−	0.567492i	−0.982043	+	0.188655i	$0.939587\pi$
$398$	34.9381	+	12.7164i	1.75129	+	0.637417i
$399$		−	8.49870i		−	0.425467i
$400$		0			0
$401$	0.932419	−	0.339373i	0.0465628	−	0.0169475i	−0.318634	−	0.947878i	$-0.603224\pi$
$401$	0.932419	−	0.339373i	0.0465628	−	0.0169475i	0.365197	+	0.930930i	$0.381002\pi$
$402$	−21.7251	−	3.83072i	−1.08355	−	0.191059i
$403$	−0.205270	−	1.16415i	−0.0102252	−	0.0579902i
$404$	−2.28312			−0.113589
$405$		0			0
$406$	−4.58710			−0.227654
$407$	−6.37346	−	36.1457i	−0.315920	−	1.79167i
$408$	−19.4782	−	3.43453i	−0.964314	−	0.170034i
$409$	29.7999	−	10.8463i	1.47351	−	0.536315i	0.524461	−	0.851435i	$-0.324267\pi$
$409$	29.7999	−	10.8463i	1.47351	−	0.536315i	0.949052	+	0.315120i	$0.102045\pi$
$410$		0			0
$411$			22.1760i			1.09386i
$412$	1.45929	+	0.531139i	0.0718942	+	0.0261674i
$413$	3.09327	+	5.35771i	0.152210	+	0.263636i
$414$	2.68320	+	15.2172i	0.131872	+	0.747884i
$415$		0			0
$416$	−1.12654	+	0.945283i	−0.0552334	+	0.0463463i
$417$	−19.4696	+	3.43301i	−0.953428	+	0.168115i
$418$	7.59627	−	43.0806i	0.371546	−	2.10714i
$419$	−2.20708	+	12.5170i	−0.107823	+	0.611494i	0.882232	+	0.470815i	$0.156040\pi$
$419$	−2.20708	+	12.5170i	−0.107823	+	0.611494i	−0.990055	+	0.140680i	$0.955071\pi$
$420$		0			0
$421$	−2.83544	+	2.37921i	−0.138191	+	0.115956i	−0.709263	−	0.704944i	$-0.750972\pi$
$421$	−2.83544	+	2.37921i	−0.138191	+	0.115956i	0.571072	+	0.820900i	$0.306528\pi$
$422$	−5.36618	+	9.29450i	−0.261222	+	0.452449i
$423$	15.8097	+	13.2660i	0.768696	+	0.645013i
$424$	4.49841	+	7.79147i	0.218462	+	0.378387i
$425$		0			0
$426$	11.7228	+	6.76817i	0.567972	+	0.327919i
$427$	−4.60039	−	3.86018i	−0.222628	−	0.186807i
$428$	−2.42380	+	0.882191i	−0.117159	+	0.0426423i
$429$	−3.84318	−	10.5590i	−0.185550	−	0.509795i
$430$		0			0
$431$	−9.16250			−0.441342			−0.220671	−	0.975348i	$-0.570825\pi$
$431$	−9.16250			−0.441342			−0.220671	+	0.975348i	$0.570825\pi$
$432$	18.4029	−	3.24492i	0.885408	−	0.156121i
$433$	−29.7861			−1.43143			−0.715715	−	0.698393i	$-0.753899\pi$
$433$	−29.7861			−1.43143			−0.715715	+	0.698393i	$0.753899\pi$
$434$	0.136096	+	0.771841i	0.00653283	+	0.0370495i
$435$		0			0
$436$	−2.70574	+	0.984808i	−0.129581	+	0.0471637i
$437$	20.6878	+	17.3591i	0.989631	+	0.830399i
$438$	−10.9363	+	6.31407i	−0.522556	+	0.301698i
$439$	−11.2604	−	4.09846i	−0.537430	−	0.195609i	0.0590226	−	0.998257i	$-0.481202\pi$
$439$	−11.2604	−	4.09846i	−0.537430	−	0.195609i	−0.596453	+	0.802648i	$0.703424\pi$
$440$		0			0
$441$	−9.77631	−	16.9331i	−0.465539	−	0.806337i
$442$	3.68866	−	6.38895i	0.175452	−	0.303891i
$443$	−27.5061	+	23.0804i	−1.30686	+	1.09658i	−0.317940	+	0.948111i	$0.602991\pi$
$443$	−27.5061	+	23.0804i	−1.30686	+	1.09658i	−0.988917	+	0.148472i	$0.952565\pi$
$444$	0.874171	−	2.40176i	0.0414863	−	0.113983i
$445$		0			0
$446$	4.85844	−	27.5536i	0.230054	−	1.30470i
$447$	−7.72193	+	21.2158i	−0.365235	+	1.00347i
$448$	4.57398	−	3.83802i	0.216100	−	0.181330i
$449$	−16.2777	+	28.1937i	−0.768190	+	1.33054i	0.170353	+	0.985383i	$0.445509\pi$
$449$	−16.2777	+	28.1937i	−0.768190	+	1.33054i	−0.938543	+	0.345161i	$0.887824\pi$
$450$		0			0
$451$	−18.0744	−	31.3059i	−0.851092	−	1.47414i
$452$	−2.98158	−	1.08521i	−0.140242	−	0.0510438i
$453$	3.06283	−	1.76833i	0.143904	−	0.0830833i
$454$	1.66772	+	1.39938i	0.0782699	+	0.0656762i
$455$		0			0
$456$	23.1506	−	27.5899i	1.08413	−	1.29201i
$457$	2.49660	+	14.1589i	0.116786	+	0.662325i	0.985850	+	0.167627i	$0.0536104\pi$
$457$	2.49660	+	14.1589i	0.116786	+	0.662325i	−0.869065	+	0.494699i	$0.835278\pi$
$458$	−13.7023			−0.640268
$459$	17.4572	−	10.0789i	0.814834	−	0.470445i
$460$		0			0
$461$	2.09920	+	11.9052i	0.0977696	+	0.554479i	0.993863	+	0.110614i	$0.0352819\pi$
$461$	2.09920	+	11.9052i	0.0977696	+	0.554479i	−0.896094	+	0.443865i	$0.853607\pi$
$462$	2.54807	+	7.00076i	0.118547	+	0.325705i
$463$	−12.7023	+	4.62327i	−0.590328	+	0.214862i	−0.619873	−	0.784702i	$-0.712816\pi$
$463$	−12.7023	+	4.62327i	−0.590328	+	0.214862i	0.0295460	+	0.999563i	$0.490594\pi$
$464$	−13.5036	−	11.3309i	−0.626890	−	0.526023i
$465$		0			0
$466$	−26.5783	−	9.67372i	−1.23122	−	0.448126i
$467$	−8.68257	−	15.0387i	−0.401781	−	0.695906i	0.592160	−	0.805821i	$-0.298276\pi$
$467$	−8.68257	−	15.0387i	−0.401781	−	0.695906i	−0.993941	+	0.109915i	$0.964942\pi$
$468$	0.135878	−	0.770602i	0.00628096	−	0.0356211i
$469$	3.28312	−	5.68653i	0.151600	−	0.262579i
$470$		0			0
$471$	−12.9030	−	15.3772i	−0.594540	−	0.708545i
$472$	−4.55262	+	25.8192i	−0.209551	+	1.18843i
$473$	−1.65910	+	9.40923i	−0.0762855	+	0.432637i
$474$	30.1195	−	5.31088i	1.38343	−	0.243937i
$475$		0			0
$476$	0.248970	−	0.431229i	0.0114115	−	0.0197654i
$477$	−8.61633	−	3.13609i	−0.394515	−	0.143592i
$478$	3.37346	+	5.84300i	0.154298	+	0.267252i
$479$	6.75150	+	2.45734i	0.308484	+	0.112279i	0.491623	−	0.870808i	$-0.336404\pi$
$479$	6.75150	+	2.45734i	0.308484	+	0.112279i	−0.183139	+	0.983087i	$0.558626\pi$
$480$		0			0
$481$	8.63429	+	7.24503i	0.393690	+	0.330345i
$482$	28.8200	−	10.4896i	1.31272	−	0.477789i
$483$	−4.52940	−	0.798656i	−0.206095	−	0.0363401i
$484$	−0.324921	−	1.84272i	−0.0147692	−	0.0837600i
$485$		0			0
$486$	−13.5000	+	16.0887i	−0.612372	+	0.729797i
$487$	13.9394			0.631657			0.315828	−	0.948816i	$-0.397718\pi$
$487$	13.9394			0.631657			0.315828	+	0.948816i	$0.397718\pi$
$488$	−4.41930	−	25.0631i	−0.200052	−	1.13455i
$489$	28.3803	+	5.00422i	1.28340	+	0.226298i
$490$		0			0
$491$	−16.6291	−	13.9534i	−0.750459	−	0.629710i	0.185165	−	0.982707i	$-0.440718\pi$
$491$	−16.6291	−	13.9534i	−0.750459	−	0.629710i	−0.935624	+	0.352997i	$0.885163\pi$
$492$		−	2.51730i		−	0.113489i
$493$	−17.8687	−	6.50368i	−0.804766	−	0.292911i
$494$	6.71688	+	11.6340i	0.302207	+	0.523438i
$495$		0			0
$496$	−1.50593	+	2.60835i	−0.0676182	+	0.117118i
$497$	−3.08647	+	2.58985i	−0.138447	+	0.116171i
$498$	−2.60876	+	0.459994i	−0.116901	+	0.0206128i
$499$	0.726377	−	4.11949i	0.0325171	−	0.184414i	−0.964223	−	0.265092i	$-0.914598\pi$
$499$	0.726377	−	4.11949i	0.0325171	−	0.184414i	0.996740	+	0.0806786i	$0.0257087\pi$
$500$		0			0
$501$	−0.118089	−	0.140732i	−0.00527581	−	0.00628746i
$502$	−15.0876	+	12.6600i	−0.673395	+	0.565045i
$503$	11.9187	−	20.6439i	0.531431	−	0.920465i	−0.467896	−	0.883783i	$-0.654988\pi$
$503$	11.9187	−	20.6439i	0.531431	−	0.920465i	0.999327	−	0.0366816i	$-0.0116787\pi$
$504$	−1.06511	+	6.04055i	−0.0474438	+	0.269067i
$505$		0			0
$506$	−22.2460	−	8.09689i	−0.988957	−	0.359951i
$507$	−16.5116	−	9.53298i	−0.733306	−	0.423375i
$508$	−3.16637	−	2.65690i	−0.140485	−	0.117881i
$509$	−20.8773	+	7.59873i	−0.925371	+	0.336808i	−0.760373	−	0.649486i	$-0.774984\pi$
$509$	−20.8773	+	7.59873i	−0.925371	+	0.336808i	−0.164998	+	0.986294i	$0.552762\pi$
$510$		0			0
$511$	−0.652704	−	3.70167i	−0.0288739	−	0.163752i
$512$	24.9186			1.10126
$513$			36.7065i			1.62063i
$514$	0.285807			0.0126064
$515$		0			0
$516$	−0.427671	+	0.509678i	−0.0188272	+	0.0224373i
$517$	−29.7126	+	10.8145i	−1.30676	+	0.475621i
$518$	−5.72462	−	4.80353i	−0.251525	−	0.211055i
$519$	−11.5241	+	6.65344i	−0.505852	+	0.292054i
$520$		0			0
$521$	6.59358	+	11.4204i	0.288870	+	0.500337i	0.973540	−	0.228515i	$-0.0733872\pi$
$521$	6.59358	+	11.4204i	0.288870	+	0.500337i	−0.684670	+	0.728853i	$0.740054\pi$
$522$	19.8120			0.867149
$523$	8.91147	−	15.4351i	0.389672	−	0.674931i	−0.602734	−	0.797942i	$-0.705922\pi$
$523$	8.91147	−	15.4351i	0.389672	−	0.674931i	0.992405	+	0.123011i	$0.0392552\pi$
$524$	−2.10039	+	1.76243i	−0.0917558	+	0.0769922i
$525$		0			0
$526$	−0.386659	+	2.19285i	−0.0168591	+	0.0956129i
$527$	−0.564178	+	3.19961i	−0.0245760	+	0.139377i
$528$	−9.79196	+	26.9032i	−0.426140	+	1.17081i
$529$	−6.42333	+	5.38982i	−0.279275	+	0.234340i
$530$		0			0
$531$	−13.3601	−	23.1404i	−0.579779	−	1.00421i
$532$	0.453363	+	0.785248i	0.0196558	+	0.0340448i
$533$	10.4315	+	3.79677i	0.451840	+	0.164456i
$534$	1.48839	−	0.859322i	0.0644089	−	0.0371865i
$535$		0			0
$536$	26.1484	−	9.51725i	1.12944	−	0.411082i
$537$	−25.0535	+	29.8576i	−1.08114	+	1.28845i
$538$	0.710485	+	4.02936i	0.0306312	+	0.173718i
$539$	29.9564			1.29031
$540$		0			0
$541$	8.78375			0.377643			0.188821	−	0.982011i	$-0.439533\pi$
$541$	8.78375			0.377643			0.188821	+	0.982011i	$0.439533\pi$
$542$	−3.72328	−	21.1158i	−0.159928	−	0.907000i
$543$	12.9076	+	35.4633i	0.553918	+	1.52188i
$544$	3.79813	−	1.38241i	0.162844	−	0.0592702i
$545$		0			0
$546$	−1.98133	−	1.14392i	−0.0847932	−	0.0489554i
$547$	20.9547	+	7.62689i	0.895959	+	0.326102i	0.748632	−	0.662986i	$-0.230711\pi$
$547$	20.9547	+	7.62689i	0.895959	+	0.326102i	0.147326	+	0.989088i	$0.452933\pi$
$548$	−1.18298	−	2.04898i	−0.0505345	−	0.0875283i
$549$	19.8694	+	16.6724i	0.848006	+	0.711562i
$550$		0			0
$551$	26.5253	−	22.2574i	1.13001	−	0.948195i
$552$	−12.5285	−	14.9309i	−0.533249	−	0.635502i
$553$	−1.58079	+	8.96508i	−0.0672218	+	0.381234i
$554$	−4.11974	+	23.3642i	−0.175031	+	0.992649i
$555$		0			0
$556$	1.61578	−	1.35580i	0.0685244	−	0.0574988i
$557$	18.9561	−	32.8328i	0.803194	−	1.39117i	−0.114310	−	0.993445i	$-0.536466\pi$
$557$	18.9561	−	32.8328i	0.803194	−	1.39117i	0.917504	−	0.397727i	$-0.130201\pi$
$558$	−0.587811	−	3.33364i	−0.0248840	−	0.141124i
$559$	−1.46703	−	2.54098i	−0.0620489	−	0.107472i
$560$		0			0
$561$			30.8837i			1.30391i
$562$	−9.06283	−	7.60462i	−0.382293	−	0.320782i
$563$	−34.3803	+	12.5134i	−1.44896	+	0.527377i	−0.942300	−	0.334770i	$-0.891341\pi$
$563$	−34.3803	+	12.5134i	−1.44896	+	0.527377i	−0.506658	+	0.862147i	$0.669119\pi$
$564$	−2.16843	−	0.382353i	−0.0913075	−	0.0161000i
$565$		0			0
$566$	−2.72462			−0.114524
$567$	−3.12567	−	5.41381i	−0.131266	−	0.227359i
$568$	−17.0746			−0.716435
$569$	−0.440103	−	2.49595i	−0.0184501	−	0.104636i	0.974192	−	0.225721i	$-0.0724737\pi$
$569$	−0.440103	−	2.49595i	−0.0184501	−	0.104636i	−0.992642	+	0.121085i	$0.961363\pi$
$570$		0			0
$571$	20.5205	−	7.46886i	0.858758	−	0.312562i	0.125152	−	0.992138i	$-0.460058\pi$
$571$	20.5205	−	7.46886i	0.858758	−	0.312562i	0.733606	+	0.679575i	$0.237836\pi$
$572$	0.918368	+	0.770602i	0.0383989	+	0.0322205i
$573$		−	18.0718i		−	0.754961i
$574$	−6.91622	−	2.51730i	−0.288678	−	0.105070i
$575$		0			0
$576$	−19.7554	+	16.5767i	−0.823140	+	0.690697i
$577$	−5.02481	+	8.70323i	−0.209186	+	0.362320i	−0.951458	−	0.307778i	$-0.900415\pi$
$577$	−5.02481	+	8.70323i	−0.209186	+	0.362320i	0.742272	+	0.670098i	$0.233748\pi$
$578$	2.01296	−	1.68907i	0.0837279	−	0.0702561i
$579$	17.0123	−	2.99973i	0.707008	−	0.124665i
$580$		0			0
$581$	0.136917	−	0.776497i	0.00568029	−	0.0322145i
$582$	12.5209	+	14.9219i	0.519010	+	0.618532i
$583$	10.7615	−	9.03001i	0.445698	−	0.373985i
$584$	7.96451	−	13.7949i	0.329574	−	0.570838i
$585$		0			0
$586$	−13.1964	−	22.8568i	−0.545138	−	0.944207i
$587$	5.79726	+	2.11003i	0.239278	+	0.0870902i	0.458876	−	0.888500i	$-0.348252\pi$
$587$	5.79726	+	2.11003i	0.239278	+	0.0870902i	−0.219598	+	0.975591i	$0.570474\pi$
$588$	1.80659	+	1.04303i	0.0745025	+	0.0430140i
$589$	−4.53209	−	3.80287i	−0.186741	−	0.156695i
$590$		0			0
$591$	−9.93541	−	27.2973i	−0.408688	−	1.12286i
$592$	−4.98680	−	28.2815i	−0.204956	−	1.16236i
$593$	21.7965			0.895077			0.447538	−	0.894265i	$-0.352301\pi$
$593$	21.7965			0.895077			0.447538	+	0.894265i	$0.352301\pi$
$594$	−11.0053	−	30.2368i	−0.451553	−	1.24063i
$595$		0			0
$596$	−0.418281	−	2.37219i	−0.0171335	−	0.0971687i
$597$	30.7240	−	36.6155i	1.25745	−	1.49857i
$598$	6.83157	−	2.48649i	0.279364	−	0.101680i
$599$	−9.54395	−	8.00832i	−0.389955	−	0.327211i	0.426641	−	0.904421i	$-0.359697\pi$
$599$	−9.54395	−	8.00832i	−0.389955	−	0.327211i	−0.816596	+	0.577210i	$0.804141\pi$
$600$		0			0
$601$	14.9162	+	5.42906i	0.608445	+	0.221456i	0.627823	−	0.778356i	$-0.283946\pi$
$601$	14.9162	+	5.42906i	0.608445	+	0.221456i	−0.0193775	+	0.999812i	$0.506168\pi$
$602$	0.972659	+	1.68469i	0.0396426	+	0.0686630i
$603$	−14.1800	+	24.5606i	−0.577456	+	1.00018i
$604$	−0.188663	+	0.326774i	−0.00767659	+	0.0132962i
$605$		0			0
$606$	9.86097	−	27.0928i	0.400574	−	1.10057i
$607$	6.89811	−	39.1211i	0.279986	−	1.58788i	−0.442680	−	0.896680i	$-0.645972\pi$
$607$	6.89811	−	39.1211i	0.279986	−	1.58788i	0.722666	−	0.691198i	$-0.242917\pi$
$608$	−1.27807	+	7.24827i	−0.0518324	+	0.293956i
$609$	−2.01691	+	5.54142i	−0.0817294	+	0.224550i
$610$		0			0
$611$	4.85504	−	8.40917i	0.196414	−	0.340199i
$612$	−1.07532	+	1.86251i	−0.0434673	+	0.0752876i
$613$	−9.88666	−	17.1242i	−0.399318	−	0.691640i	0.594324	−	0.804226i	$-0.297420\pi$
$613$	−9.88666	−	17.1242i	−0.399318	−	0.691640i	−0.993642	+	0.112586i	$0.964087\pi$
$614$	−10.4684	−	3.81018i	−0.422469	−	0.153766i
$615$		0			0
$616$	−7.19884	−	6.04055i	−0.290050	−	0.243381i
$617$	−16.0449	+	5.83986i	−0.645943	+	0.235104i	−0.644156	−	0.764895i	$-0.722791\pi$
$617$	−16.0449	+	5.83986i	−0.645943	+	0.235104i	−0.00178707	+	0.999998i	$0.500569\pi$
$618$	−12.6056	+	15.0228i	−0.507072	+	0.604304i
$619$	0.835847	+	4.74033i	0.0335955	+	0.190530i	0.996987	−	0.0775689i	$-0.0247158\pi$
$619$	0.835847	+	4.74033i	0.0335955	+	0.190530i	−0.963391	+	0.268099i	$0.913605\pi$
$620$		0			0
$621$	19.5628	+	3.44946i	0.785029	+	0.138422i
$622$	37.2172			1.49227
$623$	0.0888306	+	0.503783i	0.00355892	+	0.0201836i
$624$	−3.00703	−	8.26173i	−0.120377	−	0.330734i
$625$		0			0
$626$	−2.62836	−	2.20545i	−0.105050	−	0.0881476i
$627$	−48.7033	−	28.1188i	−1.94502	−	1.12296i
$628$	2.01249	+	0.732486i	0.0803070	+	0.0292294i
$629$	−15.4893	−	26.8283i	−0.617600	−	1.06971i
$630$		0			0
$631$	−11.9277	+	20.6593i	−0.474833	+	0.822435i	−0.999585	−	0.0288204i	$-0.990825\pi$
$631$	−11.9277	+	20.6593i	−0.474833	+	0.822435i	0.524752	+	0.851255i	$0.324158\pi$
$632$	−29.5529	+	24.7978i	−1.17555	+	0.986404i
$633$	8.86871	+	10.5693i	0.352499	+	0.420093i
$634$	6.71806	−	38.1000i	0.266808	−	1.51315i
$635$		0			0
$636$	0.963412	−	0.169875i	0.0382018	−	0.00673600i
$637$	−7.04710	+	5.91322i	−0.279216	+	0.234290i
$638$	−15.1769	+	26.2871i	−0.600859	+	1.04072i
$639$	13.3307	−	11.1858i	0.527354	−	0.442502i
$640$		0			0
$641$	41.6159	+	15.1470i	1.64373	+	0.598269i	0.987685	−	0.156453i	$-0.0500060\pi$
$641$	41.6159	+	15.1470i	1.64373	+	0.598269i	0.656045	+	0.754722i	$0.272228\pi$
$642$		−	32.5724i		−	1.28553i
$643$	5.55484	+	4.66107i	0.219062	+	0.183815i	0.745714	−	0.666266i	$-0.232109\pi$
$643$	5.55484	+	4.66107i	0.219062	+	0.183815i	−0.526652	+	0.850081i	$0.676553\pi$
$644$	0.461104	−	0.167828i	0.0181700	−	0.00661335i
$645$		0			0
$646$	−6.41147	−	36.3613i	−0.252256	−	1.43062i
$647$	26.8239			1.05456			0.527278	−	0.849693i	$-0.323213\pi$
$647$	26.8239			1.05456			0.527278	+	0.849693i	$0.323213\pi$
$648$	4.60030	−	26.0896i	0.180717	−	1.02490i
$649$	40.9377			1.60694
$650$		0			0
$651$	0.992259	+	0.174962i	0.0388897	+	0.00685730i
$652$	−2.88919	+	1.05158i	−0.113149	+	0.0411830i
$653$	−6.07604	−	5.09840i	−0.237774	−	0.199516i	0.516113	−	0.856521i	$-0.327379\pi$
$653$	−6.07604	−	5.09840i	−0.237774	−	0.199516i	−0.753886	+	0.657005i	$0.771823\pi$
$654$		−	36.3613i		−	1.42184i
$655$		0			0
$656$	−14.1420	−	24.4947i	−0.552153	−	0.956358i
$657$	2.81908	+	15.9878i	0.109983	+	0.623743i
$658$	−3.21894	+	5.57537i	−0.125487	+	0.217351i
$659$	−33.9302	+	28.4708i	−1.32173	+	1.10907i	−0.335798	+	0.941934i	$0.609006\pi$
$659$	−33.9302	+	28.4708i	−1.32173	+	1.10907i	−0.985935	+	0.167132i	$0.946550\pi$
$660$		0			0
$661$	−0.707796	+	4.01411i	−0.0275301	+	0.156131i	−0.995474	−	0.0950363i	$-0.969703\pi$
$661$	−0.707796	+	4.01411i	−0.0275301	+	0.156131i	0.967944	+	0.251167i	$0.0808144\pi$
$662$	1.97313	−	11.1902i	0.0766877	−	0.434918i
$663$	−6.09627	−	7.26525i	−0.236759	−	0.282159i
$664$	2.55968	−	2.14783i	0.0993348	−	0.0833518i
$665$		0			0
$666$	24.7251	+	20.7468i	0.958078	+	0.803923i
$667$	−9.36942	−	16.2283i	−0.362786	−	0.628363i
$668$	0.0184183	+	0.00670372i	0.000712626	+	0.000259375i
$669$	−31.1498	−	17.9843i	−1.20432	−	0.695314i
$670$		0			0
$671$	−37.3423	+	13.5915i	−1.44158	+	0.524693i
$672$	−0.428710	−	1.17787i	−0.0165379	−	0.0454374i
$673$	1.09863	+	6.23064i	0.0423491	+	0.240174i	0.998633	−	0.0522655i	$-0.0166442\pi$
$673$	1.09863	+	6.23064i	0.0423491	+	0.240174i	−0.956284	+	0.292439i	$0.905533\pi$
$674$	−21.8830			−0.842902
$675$		0			0
$676$	2.03415			0.0782365
$677$	−6.81252	−	38.6357i	−0.261826	−	1.48489i	−0.777922	−	0.628360i	$-0.783726\pi$
$677$	−6.81252	−	38.6357i	−0.261826	−	1.48489i	0.516096	−	0.856531i	$-0.327385\pi$
$678$	25.7554	−	30.6941i	0.989129	−	1.17880i
$679$	−5.44831	+	1.98302i	−0.209087	+	0.0761014i
$680$		0			0
$681$	2.42380	−	1.39938i	0.0928802	−	0.0536244i
$682$	4.87346	+	1.77379i	0.186614	+	0.0679220i
$683$	17.2533	+	29.8836i	0.660179	+	1.14346i	0.980568	+	0.196178i	$0.0628531\pi$
$683$	17.2533	+	29.8836i	0.660179	+	1.14346i	−0.320389	+	0.947286i	$0.603814\pi$
$684$	−1.95811	−	3.39155i	−0.0748702	−	0.129679i
$685$		0			0
$686$	9.69047	−	8.13127i	0.369984	−	0.310453i
$687$	−6.02481	+	16.5530i	−0.229861	+	0.631538i
$688$	−1.29813	+	7.36208i	−0.0494909	+	0.280677i
$689$	−0.749132	+	4.24854i	−0.0285397	+	0.161857i
$690$		0			0
$691$	23.2704	−	19.5262i	0.885247	−	0.742810i	−0.0820040	−	0.996632i	$-0.526132\pi$
$691$	23.2704	−	19.5262i	0.885247	−	0.742810i	0.967251	+	0.253822i	$0.0816876\pi$
$692$	0.709856	−	1.22951i	0.0269847	−	0.0467388i
$693$	9.57760			0.363823
$694$	−8.44403	−	14.6255i	−0.320531	−	0.555176i
$695$		0			0
$696$	−21.6426	+	12.4953i	−0.820360	+	0.473635i
$697$	−23.3726	−	19.6119i	−0.885300	−	0.742855i
$698$	41.5715	−	15.1308i	1.57350	−	0.572709i
$699$	−23.3726	+	27.8544i	−0.884032	+	1.05355i
$700$		0			0
$701$	−14.3952			−0.543698			−0.271849	−	0.962340i	$-0.587635\pi$
$701$	−14.3952			−0.543698			−0.271849	+	0.962340i	$0.587635\pi$
$702$	8.55753	+	4.94069i	0.322983	+	0.186474i
$703$	56.4107			2.12757
$704$	−6.86097	−	38.9105i	−0.258582	−	1.46649i
$705$		0			0
$706$	−20.5069	+	7.46389i	−0.771786	+	0.280907i
$707$	6.57398	+	5.51622i	0.247240	+	0.207459i
$708$	2.46884	+	1.42539i	0.0927849	+	0.0535694i
$709$	−14.1001	−	5.13203i	−0.529542	−	0.192737i	0.0633920	−	0.997989i	$-0.479808\pi$
$709$	−14.1001	−	5.13203i	−0.529542	−	0.192737i	−0.592934	+	0.805251i	$0.702030\pi$
$710$		0			0
$711$	6.82753	−	38.7209i	0.256053	−	1.45215i
$712$	−1.08394	+	1.87744i	−0.0406224	+	0.0703600i
$713$	−2.45265	+	2.05802i	−0.0918524	+	0.0770733i
$714$	4.04189	+	4.81694i	0.151264	+	0.180269i
$715$		0			0
$716$	0.722096	−	4.09521i	0.0269860	−	0.153045i
$717$	8.54189	−	1.50617i	0.319003	−	0.0562488i
$718$	−12.6552	+	10.6190i	−0.472289	+	0.396298i
$719$	10.2943	−	17.8302i	0.383911	−	0.664954i	−0.607706	−	0.794162i	$-0.707910\pi$
$719$	10.2943	−	17.8302i	0.383911	−	0.664954i	0.991617	+	0.129208i	$0.0412435\pi$
$720$		0			0
$721$	−2.91859	−	5.05514i	−0.108694	−	0.188263i
$722$	39.1241	+	14.2400i	1.45605	+	0.529958i
$723$		−	39.4281i		−	1.46635i
$724$	−3.08441	−	2.58812i	−0.114631	−	0.0961869i
$725$		0			0
$726$	23.2701	+	4.10315i	0.863636	+	0.152282i
$727$	5.55644	+	31.5121i	0.206077	+	1.16872i	0.895736	+	0.444586i	$0.146649\pi$
$727$	5.55644	+	31.5121i	0.206077	+	1.16872i	−0.689659	+	0.724134i	$0.742240\pi$
$728$	2.88587			0.106957
$729$	13.5000	+	23.3827i	0.500000	+	0.866025i
$730$		0			0
$731$	1.40033	+	7.94166i	0.0517931	+	0.293733i
$732$	−2.72525	−	0.480535i	−0.100728	−	0.0177611i
$733$	−38.8105	+	14.1259i	−1.43350	+	0.521751i	−0.937932	−	0.346819i	$-0.887262\pi$
$733$	−38.8105	+	14.1259i	−1.43350	+	0.521751i	−0.495567	+	0.868570i	$0.665040\pi$
$734$	32.7046	+	27.4424i	1.20715	+	1.01292i
$735$		0			0
$736$	3.74288	+	1.36230i	0.137964	+	0.0502149i
$737$	−21.7251	−	37.6290i	−0.800254	−	1.38608i
$738$	29.8717	+	10.8724i	1.09959	+	0.400219i
$739$	−12.1755	+	21.0885i	−0.447882	+	0.775754i	−0.998248	−	0.0591697i	$-0.981155\pi$
$739$	−12.1755	+	21.0885i	−0.447882	+	0.775754i	0.550366	+	0.834923i	$0.314488\pi$
$740$		0			0
$741$	17.0077	−	2.99892i	0.624795	−	0.110168i
$742$	0.496683	−	2.81683i	0.0182338	−	0.103409i
$743$	−2.54870	+	14.4544i	−0.0935026	+	0.530280i	0.901693	+	0.432376i	$0.142325\pi$
$743$	−2.54870	+	14.4544i	−0.0935026	+	0.530280i	−0.995196	+	0.0979034i	$0.968786\pi$
$744$	2.74463	+	3.27093i	0.100623	+	0.119918i
$745$		0			0
$746$	−24.3550	+	42.1842i	−0.891701	+	1.54447i
$747$	−0.591357	+	3.35375i	−0.0216366	+	0.122707i
$748$	−1.64749	−	2.85353i	−0.0602382	−	0.104336i
$749$	9.11051	+	3.31595i	0.332891	+	0.121162i
$750$		0			0
$751$	6.54260	+	5.48990i	0.238743	+	0.200329i	0.754307	−	0.656522i	$-0.227973\pi$
$751$	6.54260	+	5.48990i	0.238743	+	0.200329i	−0.515564	+	0.856851i	$0.672418\pi$
$752$	−23.2481	+	8.46161i	−0.847771	+	0.308563i
$753$	8.65998	+	23.7931i	0.315587	+	0.867069i
$754$	−1.61864	−	9.17977i	−0.0589475	−	0.334308i
$755$		0			0
$756$	0.577600	+	0.333477i	0.0210071	+	0.0121285i
$757$	17.3337			0.630003			0.315002	−	0.949091i	$-0.397995\pi$
$757$	17.3337			0.630003			0.315002	+	0.949091i	$0.397995\pi$
$758$	3.21073	+	18.2090i	0.116619	+	0.661380i
$759$	−19.5628	+	23.3141i	−0.710086	+	0.846247i
$760$		0			0
$761$	3.14227	+	2.63668i	0.113907	+	0.0955796i	0.697962	−	0.716135i	$-0.254090\pi$
$761$	3.14227	+	2.63668i	0.113907	+	0.0955796i	−0.584055	+	0.811714i	$0.698535\pi$
$762$	45.2041	−	26.0986i	1.63757	−	0.945453i
$763$	10.1702	+	3.70167i	0.368188	+	0.134009i
$764$	0.964041	+	1.66977i	0.0348778	+	0.0604101i
$765$		0			0
$766$	15.4277	−	26.7215i	0.557424	−	0.965487i
$767$	−9.63041	+	8.08088i	−0.347734	+	0.291784i
$768$	2.60417	−	7.15490i	0.0939699	−	0.258180i
$769$	−0.930770	+	5.27866i	−0.0335644	+	0.190353i	−0.996980	−	0.0776587i	$-0.975256\pi$
$769$	−0.930770	+	5.27866i	−0.0335644	+	0.190353i	0.963416	+	0.268012i	$0.0863667\pi$
$770$		0			0
$771$	0.125667	−	0.345268i	0.00452579	−	0.0124345i
$772$	−1.41185	+	1.18469i	−0.0508138	+	0.0426378i
$773$

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.233956 - 1.32683i) q^{2} +(-1.70574 - 0.300767i) q^{3} +(0.173648 - 0.0632028i) q^{4} +2.33359i q^{6} +(-0.652704 - 0.237565i) q^{7} +(-1.47178 - 2.54920i) q^{8} +(2.81908 + 1.02606i) q^{9} +O(q^{10})\)	\(q+(-0.233956 - 1.32683i) q^{2} +(-1.70574 - 0.300767i) q^{3} +(0.173648 - 0.0632028i) q^{4} +2.33359i q^{6} +(-0.652704 - 0.237565i) q^{7} +(-1.47178 - 2.54920i) q^{8} +(2.81908 + 1.02606i) q^{9} +(-3.52094 + 2.95442i) q^{11} +(-0.315207 + 0.0555796i) q^{12} +(0.245100 - 1.39003i) q^{13} +(-0.162504 + 0.921605i) q^{14} +(-2.75490 + 2.31164i) q^{16} +(-1.93969 + 3.35965i) q^{17} +(0.701867 - 3.98048i) q^{18} +(-3.53209 - 6.11776i) q^{19} +(1.04189 + 0.601535i) q^{21} +(4.74376 + 3.98048i) q^{22} +(-3.59240 + 1.30753i) q^{23} +(1.74376 + 4.79093i) q^{24} -1.90167 q^{26} +(-4.50000 - 2.59808i) q^{27} -0.128356 q^{28} +(0.851167 + 4.82721i) q^{29} +(0.786989 - 0.286441i) q^{31} +(-0.798133 - 0.669713i) q^{32} +(6.89440 - 3.98048i) q^{33} +(4.91147 + 1.78763i) q^{34} +0.554378 q^{36} +(-3.99273 + 6.91560i) q^{37} +(-7.29086 + 6.11776i) q^{38} +(-0.836152 + 2.29731i) q^{39} +(-1.36571 + 7.74535i) q^{41} +(0.554378 - 1.52314i) q^{42} +(1.59240 - 1.33618i) q^{43} +(-0.424678 + 0.735564i) q^{44} +(2.57532 + 4.46059i) q^{46} +(6.46451 + 2.35289i) q^{47} +(5.39440 - 3.11446i) q^{48} +(-4.99273 - 4.18939i) q^{49} +(4.31908 - 5.14728i) q^{51} +(-0.0452926 - 0.256867i) q^{52} -3.05644 q^{53} +(-2.39440 + 6.57856i) q^{54} +(0.355037 + 2.01352i) q^{56} +(4.18479 + 11.4976i) q^{57} +(6.20574 - 2.25870i) q^{58} +(-6.82295 - 5.72513i) q^{59} +(8.12449 + 2.95707i) q^{61} +(-0.564178 - 0.977185i) q^{62} +(-1.59627 - 1.33943i) q^{63} +(-4.29813 + 7.44459i) q^{64} +(-6.89440 - 8.21643i) q^{66} +(-1.64156 + 9.30975i) q^{67} +(-0.124485 + 0.705990i) q^{68} +(6.52094 - 1.14982i) q^{69} +(2.90033 - 5.02352i) q^{71} +(-1.53343 - 8.69653i) q^{72} +(2.70574 + 4.68647i) q^{73} +(10.1099 + 3.67972i) q^{74} +(-1.00000 - 0.839100i) q^{76} +(3.00000 - 1.09191i) q^{77} +(3.24376 + 0.571962i) q^{78} +(-2.27584 - 12.9070i) q^{79} +(6.89440 + 5.78509i) q^{81} +10.5963 q^{82} +(0.197119 + 1.11792i) q^{83} +(0.218941 + 0.0386052i) q^{84} +(-2.14543 - 1.80023i) q^{86} -8.48995i q^{87} +(12.7135 + 4.62733i) q^{88} +(-0.368241 - 0.637812i) q^{89} +(-0.490200 + 0.849051i) q^{91} +(-0.541174 + 0.454099i) q^{92} +(-1.42855 + 0.251892i) q^{93} +(1.60947 - 9.12776i) q^{94} +(1.15998 + 1.38241i) q^{96} +(6.39440 - 5.36554i) q^{97} +(-4.39053 + 7.60462i) q^{98} +(-12.9572 + 4.71605i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 6 * q - 6 * q^2 - 6 * q^7 + 6 * q^8	\( 6 q - 6 q^{2} - 6 q^{7} + 6 q^{8} - 18 q^{11} - 9 q^{12} - 6 q^{14} - 18 q^{16} - 6 q^{17} + 18 q^{18} - 12 q^{19} + 36 q^{22} - 18 q^{23} + 18 q^{24} + 12 q^{26} - 27 q^{27} + 36 q^{28} - 21 q^{29} - 3 q^{31} + 9 q^{32} + 9 q^{34} - 18 q^{36} - 6 q^{37} - 12 q^{38} - 9 q^{39} - 18 q^{41} - 18 q^{42} + 6 q^{43} - 27 q^{44} - 9 q^{46} + 6 q^{47} - 9 q^{48} - 12 q^{49} + 9 q^{51} - 36 q^{52} - 48 q^{53} + 27 q^{54} - 48 q^{56} + 18 q^{57} + 27 q^{58} + 36 q^{61} + 15 q^{62} + 18 q^{63} - 12 q^{64} - 18 q^{67} + 12 q^{68} + 36 q^{69} + 3 q^{71} + 9 q^{72} + 6 q^{73} + 12 q^{74} - 6 q^{76} + 18 q^{77} + 27 q^{78} - 12 q^{79} + 36 q^{82} - 18 q^{83} + 36 q^{84} + 3 q^{86} + 18 q^{88} + 3 q^{89} + 63 q^{92} - 9 q^{93} + 27 q^{94} + 27 q^{96} - 3 q^{97} - 9 q^{98} - 27 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^7 + 6 * q^8 - 18 * q^11 - 9 * q^12 - 6 * q^14 - 18 * q^16 - 6 * q^17 + 18 * q^18 - 12 * q^19 + 36 * q^22 - 18 * q^23 + 18 * q^24 + 12 * q^26 - 27 * q^27 + 36 * q^28 - 21 * q^29 - 3 * q^31 + 9 * q^32 + 9 * q^34 - 18 * q^36 - 6 * q^37 - 12 * q^38 - 9 * q^39 - 18 * q^41 - 18 * q^42 + 6 * q^43 - 27 * q^44 - 9 * q^46 + 6 * q^47 - 9 * q^48 - 12 * q^49 + 9 * q^51 - 36 * q^52 - 48 * q^53 + 27 * q^54 - 48 * q^56 + 18 * q^57 + 27 * q^58 + 36 * q^61 + 15 * q^62 + 18 * q^63 - 12 * q^64 - 18 * q^67 + 12 * q^68 + 36 * q^69 + 3 * q^71 + 9 * q^72 + 6 * q^73 + 12 * q^74 - 6 * q^76 + 18 * q^77 + 27 * q^78 - 12 * q^79 + 36 * q^82 - 18 * q^83 + 36 * q^84 + 3 * q^86 + 18 * q^88 + 3 * q^89 + 63 * q^92 - 9 * q^93 + 27 * q^94 + 27 * q^96 - 3 * q^97 - 9 * q^98 - 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more