LMFDB - Embedded newform 675.2.u.a.349.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(49,675)]

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, 9]))

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

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

chi := DirichletCharacter("675.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not 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:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			349.2
Root			$0.642788 - 0.766044i$ of defining polynomial
Character	$\chi$	$=$	675.349
Dual form			675.2.u.a.499.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$-1$

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 $

$2$	1.32683	+	0.233956i	0.938209	+	0.165432i	0.621786	−	0.783187i	$-0.286407\pi$
$2$	1.32683	+	0.233956i	0.938209	+	0.165432i	0.316423	+	0.948618i	$0.397518\pi$
$3$	−0.300767	−	1.70574i	−0.173648	−	0.984808i
$3$	−0.300767	−	1.70574i	−0.173648	−	0.984808i
$4$	−0.173648	−	0.0632028i	−0.0868241	−	0.0316014i
$5$		0			0
$5$		0			0
$6$		−	2.33359i		−	0.952682i
$7$	0.237565	+	0.652704i	0.0897910	+	0.246699i	0.976457	−	0.215711i	$-0.0692070\pi$
$7$	0.237565	+	0.652704i	0.0897910	+	0.246699i	−0.886666	+	0.462410i	$0.846985\pi$
$8$	−2.54920	−	1.47178i	−0.901278	−	0.520353i
$9$	−2.81908	+	1.02606i	−0.939693	+	0.342020i
$10$		0			0
$11$	−3.52094	−	2.95442i	−1.06160	−	0.890792i	−0.0673390	−	0.997730i	$-0.521451\pi$
$11$	−3.52094	−	2.95442i	−1.06160	−	0.890792i	−0.994266	+	0.106938i	$0.965895\pi$
$12$	−0.0555796	+	0.315207i	−0.0160444	+	0.0909926i
$13$	−1.39003	+	0.245100i	−0.385525	+	0.0679785i	−0.363052	−	0.931769i	$-0.618265\pi$
$13$	−1.39003	+	0.245100i	−0.385525	+	0.0679785i	−0.0224733	+	0.999747i	$0.507154\pi$
$14$	0.162504	+	0.921605i	0.0434310	+	0.246309i
$15$		0			0
$16$	−2.75490	−	2.31164i	−0.688725	−	0.577909i
$17$	−3.35965	+	1.93969i	−0.814834	+	0.470445i	−0.848632	−	0.528984i	$-0.822573\pi$
$17$	−3.35965	+	1.93969i	−0.814834	+	0.470445i	0.0337978	+	0.999429i	$0.489240\pi$
$18$	−3.98048	+	0.701867i	−0.938209	+	0.165432i
$19$	3.53209	−	6.11776i	0.810317	−	1.40351i	−0.102326	−	0.994751i	$-0.532628\pi$
$19$	3.53209	−	6.11776i	0.810317	−	1.40351i	0.912642	−	0.408759i	$-0.134038\pi$
$20$		0			0
$21$	1.04189	−	0.601535i	0.227359	−	0.131266i
$22$	−3.98048	−	4.74376i	−0.848642	−	1.01137i
$23$	1.30753	−	3.59240i	0.272638	−	0.749066i	−0.725509	−	0.688213i	$-0.758396\pi$
$23$	1.30753	−	3.59240i	0.272638	−	0.749066i	0.998147	−	0.0608535i	$-0.0193823\pi$
$24$	−1.74376	+	4.79093i	−0.355943	+	0.977944i
$25$		0			0
$26$	−1.90167			−0.372949
$27$	2.59808	+	4.50000i	0.500000	+	0.866025i
$28$		−	0.128356i		−	0.0242569i
$29$	−0.851167	+	4.82721i	−0.158058	+	0.896390i	0.797879	+	0.602817i	$0.205955\pi$
$29$	−0.851167	+	4.82721i	−0.158058	+	0.896390i	−0.955937	+	0.293572i	$0.905156\pi$
$30$		0			0
$31$	0.786989	+	0.286441i	0.141347	+	0.0514462i	0.411725	−	0.911308i	$-0.364926\pi$
$31$	0.786989	+	0.286441i	0.141347	+	0.0514462i	−0.270378	+	0.962754i	$0.587149\pi$
$32$	0.669713	+	0.798133i	0.118390	+	0.141091i
$33$	−3.98048	+	6.89440i	−0.692913	+	1.20016i
$34$	−4.91147	+	1.78763i	−0.842311	+	0.306576i
$35$		0			0
$36$	0.554378			0.0923963
$37$	−6.91560	+	3.99273i	−1.13692	+	0.656400i	−0.945666	−	0.325141i	$-0.894588\pi$
$37$	−6.91560	+	3.99273i	−1.13692	+	0.656400i	−0.191253	+	0.981541i	$0.561255\pi$
$38$	6.11776	−	7.29086i	0.992431	−	1.18273i
$39$	0.836152	+	2.29731i	0.133891	+	0.367864i
$40$		0			0
$41$	−1.36571	−	7.74535i	−0.213289	−	1.20962i	−0.883851	−	0.467768i	$-0.845058\pi$
$41$	−1.36571	−	7.74535i	−0.213289	−	1.20962i	0.670563	−	0.741853i	$-0.266053\pi$
$42$	1.52314	−	0.554378i	0.235026	−	0.0855423i
$43$	−1.33618	+	1.59240i	−0.203765	+	0.242838i	−0.858243	−	0.513243i	$-0.828444\pi$
$43$	−1.33618	+	1.59240i	−0.203765	+	0.242838i	0.654478	+	0.756081i	$0.272888\pi$
$44$	0.424678	+	0.735564i	0.0640226	+	0.110890i
$45$		0			0
$46$	2.57532	−	4.46059i	0.379711	−	0.657678i
$47$	−2.35289	−	6.46451i	−0.343204	−	0.942945i	−0.984459	−	0.175617i	$-0.943808\pi$
$47$	−2.35289	−	6.46451i	−0.343204	−	0.942945i	0.641255	−	0.767328i	$-0.278414\pi$
$48$	−3.11446	+	5.39440i	−0.449533	+	0.778615i
$49$	4.99273	−	4.18939i	0.713247	−	0.598485i
$50$		0			0
$51$	4.31908	+	5.14728i	0.604792	+	0.720763i
$52$	0.256867	+	0.0452926i	0.0356211	+	0.00628096i
$53$		−	3.05644i		−	0.419834i	−0.977719	−	0.209917i	$-0.932681\pi$
$53$		−	3.05644i		−	0.419834i	0.977719	−	0.209917i	$-0.0673194\pi$
$54$	2.39440	+	6.57856i	0.325837	+	0.895229i
$55$		0			0
$56$	0.355037	−	2.01352i	0.0474438	−	0.269067i
$57$	−11.4976	−	4.18479i	−1.52290	−	0.554289i
$58$	−2.25870	+	6.20574i	−0.296582	+	0.814853i
$59$	6.82295	−	5.72513i	0.888272	−	0.745349i	−0.0795906	−	0.996828i	$-0.525361\pi$
$59$	6.82295	−	5.72513i	0.888272	−	0.745349i	0.967863	+	0.251479i	$0.0809169\pi$
$60$		0			0
$61$	8.12449	−	2.95707i	1.04023	−	0.378614i	0.235265	−	0.971931i	$-0.424404\pi$
$61$	8.12449	−	2.95707i	1.04023	−	0.378614i	0.804969	+	0.593317i	$0.202182\pi$
$62$	0.977185	+	0.564178i	0.124103	+	0.0716506i
$63$	−1.33943	−	1.59627i	−0.168752	−	0.201111i
$64$	4.29813	+	7.44459i	0.537267	+	0.930573i
$65$		0			0
$66$	−6.89440	+	8.21643i	−0.848642	+	1.01137i
$67$	−9.30975	+	1.64156i	−1.13737	+	0.200548i	−0.710453	−	0.703744i	$-0.751510\pi$
$67$	−9.30975	+	1.64156i	−1.13737	+	0.200548i	−0.426913	+	0.904293i	$0.640399\pi$
$68$	0.705990	−	0.124485i	0.0856139	−	0.0150960i
$69$	−6.52094	−	1.14982i	−0.785029	−	0.138422i
$70$		0			0
$71$	2.90033	+	5.02352i	0.344206	+	0.596182i	0.985209	−	0.171356i	$-0.0548149\pi$
$71$	2.90033	+	5.02352i	0.344206	+	0.596182i	−0.641003	+	0.767538i	$0.721482\pi$
$72$	8.69653	+	1.53343i	1.02490	+	0.180717i
$73$	4.68647	+	2.70574i	0.548510	+	0.316683i	0.748521	−	0.663111i	$-0.230764\pi$
$73$	4.68647	+	2.70574i	0.548510	+	0.316683i	−0.200011	+	0.979794i	$0.564098\pi$
$74$	−10.1099	+	3.67972i	−1.17526	+	0.427758i
$75$		0			0
$76$	−1.00000	+	0.839100i	−0.114708	+	0.0962513i
$77$	1.09191	−	3.00000i	0.124435	−	0.341882i
$78$	0.571962	+	3.24376i	0.0647619	+	0.367283i
$79$	2.27584	−	12.9070i	0.256053	−	1.45215i	−0.537304	−	0.843389i	$-0.680557\pi$
$79$	2.27584	−	12.9070i	0.256053	−	1.45215i	0.793356	−	0.608757i	$-0.208332\pi$
$80$		0			0
$81$	6.89440	−	5.78509i	0.766044	−	0.642788i
$82$		−	10.5963i		−	1.17016i
$83$	1.11792	+	0.197119i	0.122707	+	0.0216366i	0.234665	−	0.972076i	$-0.424601\pi$
$83$	1.11792	+	0.197119i	0.122707	+	0.0216366i	−0.111957	+	0.993713i	$0.535712\pi$
$84$	−0.218941	+	0.0386052i	−0.0238884	+	0.00421217i
$85$		0			0
$86$	−2.14543	+	1.80023i	−0.231348	+	0.194124i
$87$	8.48995			0.910218
$88$	4.62733	+	12.7135i	0.493275	+	1.35526i
$89$	0.368241	−	0.637812i	0.0390335	−	0.0676079i	−0.845849	−	0.533423i	$-0.820905\pi$
$89$	0.368241	−	0.637812i	0.0390335	−	0.0676079i	0.884882	+	0.465815i	$0.154239\pi$
$90$		0			0
$91$	−0.490200	−	0.849051i	−0.0513869	−	0.0890047i
$92$	−0.454099	+	0.541174i	−0.0473431	+	0.0564213i
$93$	0.251892	−	1.42855i	0.0261199	−	0.148134i
$94$	−1.60947	−	9.12776i	−0.166004	−	0.941457i
$95$		0			0
$96$	1.15998	−	1.38241i	0.118390	−	0.141091i
$97$	5.36554	−	6.39440i	0.544788	−	0.649253i	−0.421466	−	0.906844i	$-0.638484\pi$
$97$	5.36554	−	6.39440i	0.544788	−	0.649253i	0.966254	+	0.257591i	$0.0829288\pi$
$98$	7.60462	−	4.39053i	0.768183	−	0.443510i
$99$	12.9572	+	4.71605i	1.30225	+	0.473981i
$100$		0			0
$101$	−11.6099	+	4.22567i	−1.15523	+	0.420470i	−0.847392	−	0.530968i	$-0.821828\pi$
$101$	−11.6099	+	4.22567i	−1.15523	+	0.420470i	−0.307840	+	0.951438i	$0.599606\pi$
$102$	4.52644	+	7.84002i	0.448184	+	0.776278i
$103$	5.40182	+	6.43763i	0.532257	+	0.634319i	0.963433	−	0.267949i	$-0.0863458\pi$
$103$	5.40182	+	6.43763i	0.532257	+	0.634319i	−0.431176	+	0.902268i	$0.641901\pi$
$104$	3.90420	+	1.42101i	0.382838	+	0.139342i
$105$		0			0
$106$	0.715070	−	4.05537i	0.0694538	−	0.393892i
$107$			13.9581i			1.34938i	0.738101	+	0.674691i	$0.235723\pi$
$107$			13.9581i			1.34938i	−0.738101	+	0.674691i	$0.764277\pi$
$108$	−0.166739	−	0.945622i	−0.0160444	−	0.0909926i
$109$	15.5817			1.49246			0.746229	−	0.665689i	$-0.231862\pi$
$109$	15.5817			1.49246			0.746229	+	0.665689i	$0.231862\pi$
$110$		0			0
$111$	8.89053	+	10.5953i	0.843852	+	1.00566i
$112$	0.854346	−	2.34730i	0.0807281	−	0.221799i
$113$	−11.0368	−	13.1532i	−1.03826	−	1.23735i	−0.970867	−	0.239619i	$-0.922977\pi$
$113$	−11.0368	−	13.1532i	−1.03826	−	1.23735i	−0.0673899	−	0.997727i	$-0.521467\pi$
$114$	−14.2763	−	8.24243i	−1.33710	−	0.771975i
$115$		0			0
$116$	0.452896	−	0.784440i	0.0420504	−	0.0728334i
$117$	3.66712	−	2.11721i	0.339025	−	0.195736i
$118$	10.3923	−	6.00000i	0.956689	−	0.552345i
$119$	−2.06418	−	1.73205i	−0.189223	−	0.158777i
$120$		0			0
$121$	1.75830	+	9.97184i	0.159846	+	0.906531i
$122$	11.4716	−	2.02276i	1.03859	−	0.183132i
$123$	−12.8008	+	4.65910i	−1.15421	+	0.420097i
$124$	−0.118555	−	0.0994798i	−0.0106466	−	0.00893355i
$125$		0			0
$126$	−1.40373	−	2.43134i	−0.125055	−	0.216601i
$127$	19.3711	+	11.1839i	1.71891	+	0.992412i	0.920933	+	0.389722i	$0.127429\pi$
$127$	19.3711	+	11.1839i	1.71891	+	0.992412i	0.797975	+	0.602690i	$0.205904\pi$
$128$	3.24849	+	8.92514i	0.287128	+	0.788879i
$129$	3.11809	+	1.80023i	0.274532	+	0.158501i
$130$		0			0
$131$	−13.9427	−	5.07472i	−1.21818	−	0.443381i	−0.348645	−	0.937255i	$-0.613358\pi$
$131$	−13.9427	−	5.07472i	−1.21818	−	0.443381i	−0.869533	+	0.493874i	$0.835580\pi$
$132$	1.12695	−	0.945622i	0.0980883	−	0.0823059i
$133$	4.83218	+	0.852044i	0.419003	+	0.0738816i
$134$	−12.7365			−1.10026
$135$		0			0
$136$	11.4192			0.979190
$137$	12.6088	+	2.22328i	1.07725	+	0.189947i	0.683997	−	0.729485i	$-0.260240\pi$
$137$	12.6088	+	2.22328i	1.07725	+	0.189947i	0.393249	+	0.919432i	$0.371351\pi$
$138$	−8.38316	−	3.05122i	−0.713622	−	0.259737i
$139$	−10.7258	−	3.90387i	−0.909751	−	0.331122i	−0.155597	−	0.987821i	$-0.549730\pi$
$139$	−10.7258	−	3.90387i	−0.909751	−	0.331122i	−0.754153	+	0.656698i	$0.771952\pi$
$140$		0			0
$141$	−10.3191	+	5.95772i	−0.869023	+	0.501731i
$142$	2.67296	+	7.34389i	0.224310	+	0.616286i
$143$	5.61835	+	3.24376i	0.469830	+	0.271256i
$144$	10.1382	+	3.68999i	0.844846	+	0.307499i
$145$		0			0
$146$	5.58512	+	4.68647i	0.462228	+	0.387855i
$147$	−8.64766	−	7.25624i	−0.713247	−	0.598485i
$148$	1.45323	−	0.256244i	0.119455	−	0.0210631i
$149$	−2.26352	−	12.8370i	−0.185435	−	1.05165i	−0.925396	−	0.379002i	$-0.876267\pi$
$149$	−2.26352	−	12.8370i	−0.185435	−	1.05165i	0.739961	−	0.672650i	$-0.234844\pi$
$150$		0			0
$151$	−1.56418	−	1.31250i	−0.127291	−	0.106810i	0.576920	−	0.816801i	$-0.304255\pi$
$151$	−1.56418	−	1.31250i	−0.127291	−	0.106810i	−0.704211	+	0.709991i	$0.748699\pi$
$152$	−18.0080	+	10.3969i	−1.46064	+	0.843302i
$153$	7.48086	−	8.91534i	0.604792	−	0.720763i
$154$	2.15064	−	3.72503i	0.173304	−	0.300171i
$155$		0			0
$156$		−	0.451771i		−	0.0361706i
$157$	−7.44956	−	8.87804i	−0.594540	−	0.708545i	0.381932	−	0.924190i	$-0.375259\pi$
$157$	−7.44956	−	8.87804i	−0.594540	−	0.708545i	−0.976472	+	0.215646i	$0.930814\pi$
$158$	6.03931	−	16.5929i	0.480462	−	1.32006i
$159$	−5.21348	+	0.919277i	−0.413456	+	0.0729034i
$160$		0			0
$161$	2.65539			0.209274
$162$	10.5011	−	6.06283i	0.825047	−	0.476341i
$163$		−	16.6382i		−	1.30320i	−0.758562	−	0.651600i	$-0.774098\pi$
$163$		−	16.6382i		−	1.30320i	0.758562	−	0.651600i	$-0.225902\pi$
$164$	−0.252374	+	1.43128i	−0.0197071	+	0.111764i
$165$		0			0
$166$	1.43717	+	0.523086i	0.111546	+	0.0405993i
$167$	−0.0681784	−	0.0812519i	−0.00527581	−	0.00628746i	0.763400	−	0.645926i	$-0.223529\pi$
$167$	−0.0681784	−	0.0812519i	−0.00527581	−	0.00628746i	−0.768676	+	0.639638i	$0.779084\pi$
$168$	−3.54131			−0.273218
$169$	−10.3439	+	3.76487i	−0.795684	+	0.289605i
$170$		0			0
$171$	−3.68004	+	20.8706i	−0.281420	+	1.59601i
$172$	0.332669	−	0.192066i	0.0253658	−	0.0146449i
$173$	−4.93837	+	5.88532i	−0.375457	+	0.447452i	−0.920375	−	0.391037i	$-0.872116\pi$
$173$	−4.93837	+	5.88532i	−0.375457	+	0.447452i	0.544918	+	0.838489i	$0.316561\pi$
$174$	11.2647	+	1.98627i	0.853975	+	0.150579i
$175$		0			0
$176$	2.87030	+	16.2783i	0.216357	+	1.22702i
$177$	−11.8177	−	9.91622i	−0.888272	−	0.745349i
$178$	0.637812	−	0.760115i	0.0478060	−	0.0569730i
$179$	−11.2515	−	19.4882i	−0.840976	−	1.45661i	−0.889070	−	0.457771i	$-0.848648\pi$
$179$	−11.2515	−	19.4882i	−0.840976	−	1.45661i	0.0480938	−	0.998843i	$-0.484685\pi$
$180$		0			0
$181$	−10.8944	+	18.8697i	−0.809774	+	1.40257i	0.103246	+	0.994656i	$0.467077\pi$
$181$	−10.8944	+	18.8697i	−0.809774	+	1.40257i	−0.913020	+	0.407914i	$0.866256\pi$
$182$	−0.451771	−	1.24123i	−0.0334875	−	0.0920061i
$183$	−7.48757	−	12.9688i	−0.553497	−	0.958685i
$184$	−8.62037	+	7.23335i	−0.635502	+	0.533249i
$185$		0			0
$186$	0.668434	−	1.83651i	0.0490119	−	0.134659i
$187$	17.5598	+	3.09627i	1.28410	+	0.226421i
$188$			1.27126i			0.0927161i
$189$	−2.31996	+	2.76481i	−0.168752	+	0.201111i
$190$		0			0
$191$	1.81180	−	10.2753i	0.131098	−	0.743491i	−0.846401	−	0.532547i	$-0.821235\pi$
$191$	1.81180	−	10.2753i	0.131098	−	0.743491i	0.977498	−	0.210944i	$-0.0676539\pi$
$192$	11.4058	−	9.57057i	0.823140	−	0.690697i
$193$	3.41117	−	9.37211i	0.245541	−	0.674619i	−0.754295	−	0.656536i	$-0.772021\pi$
$193$	3.41117	−	9.37211i	0.245541	−	0.674619i	0.999836	−	0.0180838i	$-0.00575657\pi$
$194$	8.61515	−	7.22897i	0.618532	−	0.519010i
$195$		0			0
$196$	−1.13176	+	0.411927i	−0.0808399	+	0.0294233i
$197$	−14.5246	−	8.38578i	−1.03483	−	0.597462i	−0.116469	−	0.993194i	$-0.537158\pi$
$197$	−14.5246	−	8.38578i	−1.03483	−	0.597462i	−0.918366	+	0.395732i	$0.870491\pi$
$198$	16.0887	+	9.28880i	1.14337	+	0.660126i
$199$	13.7981	+	23.8991i	0.978124	+	1.69416i	0.669216	+	0.743068i	$0.266630\pi$
$199$	13.7981	+	23.8991i	0.978124	+	1.69416i	0.308908	+	0.951092i	$0.400037\pi$
$200$		0			0
$201$	5.60014	+	15.3863i	0.395003	+	1.08526i
$202$	−16.3930	+	2.89053i	−1.15341	+	0.203377i
$203$	−3.35294	+	0.591214i	−0.235330	+	0.0414951i
$204$	−0.424678	−	1.16679i	−0.0297334	−	0.0816918i
$205$		0			0
$206$	5.66116	+	9.80542i	0.394432	+	0.683176i
$207$			11.4688i			0.797140i
$208$	4.39598	+	2.53802i	0.304806	+	0.175980i
$209$	−30.5107	+	11.1050i	−2.11047	+	0.768149i
$210$		0			0
$211$	−6.10220	+	5.12035i	−0.420093	+	0.352499i	−0.828198	−	0.560435i	$-0.810634\pi$
$211$	−6.10220	+	5.12035i	−0.420093	+	0.352499i	0.408106	+	0.912935i	$0.366189\pi$
$212$	−0.193175	+	0.530745i	−0.0132673	+	0.0364517i
$213$	7.69648	−	6.45811i	0.527354	−	0.442502i
$214$	−3.26558	+	18.5200i	−0.223230	+	1.26600i
$215$		0			0
$216$		−	15.2952i		−	1.04071i
$217$			0.581719i			0.0394896i
$218$	20.6743	+	3.64543i	1.40024	+	0.246900i
$219$	3.20574	−	8.80769i	0.216624	−	0.595169i
$220$		0			0
$221$	4.19459	−	3.51968i	0.282159	−	0.236759i
$222$	9.31737	+	16.1382i	0.625341	+	1.08312i
$223$	7.10257	+	19.5141i	0.475623	+	1.30676i	0.913174	+	0.407570i	$0.133624\pi$
$223$	7.10257	+	19.5141i	0.475623	+	1.30676i	−0.437551	+	0.899194i	$0.644154\pi$
$224$	−0.361844	+	0.626733i	−0.0241767	+	0.0418753i
$225$		0			0
$226$	−11.5667	−	20.0341i	−0.769406	−	1.33265i
$227$	−1.03866	+	1.23783i	−0.0689382	+	0.0821574i	−0.799411	−	0.600784i	$-0.794855\pi$
$227$	−1.03866	+	1.23783i	−0.0689382	+	0.0821574i	0.730473	+	0.682941i	$0.239300\pi$
$228$	1.73205	+	1.45336i	0.114708	+	0.0962513i
$229$	−1.76604	−	10.0157i	−0.116704	−	0.661858i	−0.985893	−	0.167379i	$-0.946470\pi$
$229$	−1.76604	−	10.0157i	−0.116704	−	0.661858i	0.869189	−	0.494480i	$-0.164641\pi$
$230$		0			0
$231$	−5.44562	−	0.960210i	−0.358296	−	0.0631772i
$232$	9.27439	−	11.0528i	0.608893	−	0.725651i
$233$	−18.1806	+	10.4966i	−1.19105	+	0.687655i	−0.958545	−	0.284940i	$-0.908026\pi$
$233$	−18.1806	+	10.4966i	−1.19105	+	0.687655i	−0.232508	+	0.972595i	$0.574693\pi$
$234$	5.36097	−	1.95123i	0.350457	−	0.127556i
$235$		0			0
$236$	−1.54664	+	0.562930i	−0.100677	+	0.0366436i
$237$	−22.7004			−1.47455
$238$	−2.33359	−	2.78106i	−0.151264	−	0.180269i
$239$	4.70574	+	1.71275i	0.304389	+	0.110788i	0.489699	−	0.871892i	$-0.337107\pi$
$239$	4.70574	+	1.71275i	0.304389	+	0.110788i	−0.185310	+	0.982680i	$0.559329\pi$
$240$		0			0
$241$	3.95290	−	22.4180i	0.254628	−	1.44407i	−0.542396	−	0.840123i	$-0.682483\pi$
$241$	3.95290	−	22.4180i	0.254628	−	1.44407i	0.797025	−	0.603947i	$-0.206406\pi$
$242$			13.6423i			0.876959i
$243$	−11.9415	−	10.0201i	−0.766044	−	0.642788i
$244$	−1.59770			−0.102282
$245$		0			0
$246$	−18.0744	+	3.18701i	−1.15238	+	0.203196i
$247$	−3.41025	+	9.36959i	−0.216989	+	0.596172i
$248$	−1.58461	−	1.88847i	−0.100623	−	0.119918i
$249$		−	1.96616i		−	0.124600i
$250$		0			0
$251$	−7.30928	+	12.6600i	−0.461358	+	0.799095i	−0.999029	−	0.0440598i	$-0.985971\pi$
$251$	−7.30928	+	12.6600i	−0.461358	+	0.799095i	0.537671	+	0.843154i	$0.319304\pi$
$252$	0.131701	+	0.361844i	0.00829635	+	0.0227940i
$253$	−15.2172	+	8.78564i	−0.956696	+	0.552349i
$254$	23.0856	+	19.3711i	1.44852	+	1.21545i
$255$		0			0
$256$	−0.763356	−	4.32921i	−0.0477098	−	0.270575i
$257$	−0.208911	+	0.0368366i	−0.0130315	+	0.00229781i	−0.180160	−	0.983637i	$-0.557662\pi$
$257$	−0.208911	+	0.0368366i	−0.0130315	+	0.00229781i	0.167129	+	0.985935i	$0.446550\pi$
$258$	3.71599	+	3.11809i	0.231348	+	0.194124i
$259$	−4.24897	−	3.56531i	−0.264018	−	0.221538i
$260$		0			0
$261$	−2.55350	−	14.4816i	−0.158058	−	0.896390i
$262$	−17.3123	−	9.99525i	−1.06956	−	0.617509i
$263$	−0.565258	−	1.55303i	−0.0348553	−	0.0957641i	0.921044	−	0.389458i	$-0.127338\pi$
$263$	−0.565258	−	1.55303i	−0.0348553	−	0.0957641i	−0.955900	+	0.293694i	$0.905115\pi$
$264$	20.2941	−	11.7168i	1.24902	−	0.721119i
$265$		0			0
$266$	6.21213	+	2.26103i	0.380890	+	0.138633i
$267$	−1.19869	−	0.436289i	−0.0733589	−	0.0267005i
$268$	1.72037	+	0.303348i	0.105088	+	0.0185299i
$269$	3.03684			0.185159			0.0925796	−	0.995705i	$-0.470489\pi$
$269$	3.03684			0.185159			0.0925796	+	0.995705i	$0.470489\pi$
$270$		0			0
$271$	15.9145			0.966735			0.483368	−	0.875418i	$-0.339413\pi$
$271$	15.9145			0.966735			0.483368	+	0.875418i	$0.339413\pi$
$272$	13.7394	+	2.42262i	0.833071	+	0.146893i
$273$	−1.30082	+	1.09152i	−0.0787293	+	0.0660617i
$274$	16.2096	+	5.89981i	0.979258	+	0.356421i
$275$		0			0
$276$	1.05968	+	0.611806i	0.0637851	+	0.0368264i
$277$	6.02265	+	16.5471i	0.361866	+	0.994219i	0.978369	+	0.206867i	$0.0663266\pi$
$277$	6.02265	+	16.5471i	0.361866	+	0.994219i	−0.616503	+	0.787353i	$0.711451\pi$
$278$	−13.3180	−	7.68913i	−0.798758	−	0.461163i
$279$	−2.51249			−0.150419
$280$		0			0
$281$	6.72668	+	5.64436i	0.401280	+	0.336714i	0.820988	−	0.570945i	$-0.193423\pi$
$281$	6.72668	+	5.64436i	0.401280	+	0.336714i	−0.419708	+	0.907659i	$0.637868\pi$
$282$	−15.0855	+	5.49067i	−0.898327	+	0.326964i
$283$	−1.99157	+	0.351167i	−0.118386	+	0.0208747i	−0.232527	−	0.972590i	$-0.574700\pi$
$283$	−1.99157	+	0.351167i	−0.118386	+	0.0208747i	0.114141	+	0.993465i	$0.463588\pi$
$284$	−0.186137	−	1.05563i	−0.0110452	−	0.0626403i
$285$		0			0
$286$	6.69569	+	5.61835i	0.395924	+	0.332220i
$287$	4.73097	−	2.73143i	0.279261	−	0.161231i
$288$	−2.70691	−	1.56283i	−0.159506	−	0.0920909i
$289$	−0.975185	+	1.68907i	−0.0573638	+	0.0993571i
$290$		0			0
$291$	−12.5209	−	7.22897i	−0.733991	−	0.423770i
$292$	−0.642788	−	0.766044i	−0.0376163	−	0.0448294i
$293$	−6.69999	+	18.4081i	−0.391418	+	1.07541i	0.574937	+	0.818198i	$0.305027\pi$
$293$	−6.69999	+	18.4081i	−0.391418	+	1.07541i	−0.966355	+	0.257213i	$0.917196\pi$
$294$	−9.77631	−	11.6510i	−0.570166	−	0.679497i
$295$		0			0
$296$	23.5057			1.36624
$297$	4.14722	−	23.5201i	0.240646	−	1.36477i
$298$		−	17.5621i		−	1.01735i
$299$	−0.937004	+	5.31402i	−0.0541884	+	0.307317i
$300$		0			0
$301$	−1.35679	−	0.493832i	−0.0782042	−	0.0284640i
$302$	−1.76833	−	2.10741i	−0.101756	−	0.121268i
$303$	10.6998	+	18.5326i	0.614686	+	1.06467i
$304$	−23.8726	+	8.68891i	−1.36919	+	0.498343i
$305$		0			0
$306$	12.0116	−	10.0789i	0.686658	−	0.576175i
$307$	7.16079	−	4.13429i	0.408688	−	0.235956i	−0.281538	−	0.959550i	$-0.590845\pi$
$307$	7.16079	−	4.13429i	0.408688	−	0.235956i	0.690226	+	0.723594i	$0.257511\pi$
$308$	−0.379217	+	0.451933i	−0.0216079	+	0.0257513i
$309$	9.35622	−	11.1503i	0.532257	−	0.634319i
$310$		0			0
$311$	−4.79679	−	27.2039i	−0.272001	−	1.54259i	−0.748330	−	0.663327i	$-0.769144\pi$
$311$	−4.79679	−	27.2039i	−0.272001	−	1.54259i	0.476329	−	0.879267i	$-0.341967\pi$
$312$	1.24962	−	7.08693i	0.0707457	−	0.401219i
$313$	−1.63695	+	1.95084i	−0.0925257	+	0.110268i	−0.810321	−	0.585987i	$-0.800707\pi$
$313$	−1.63695	+	1.95084i	−0.0925257	+	0.110268i	0.717795	+	0.696255i	$0.245152\pi$
$314$	−7.80722	−	13.5225i	−0.440587	−	0.763119i
$315$		0			0
$316$	−1.21095	+	2.09743i	−0.0681214	+	0.117990i
$317$	−9.82115	−	26.9834i	−0.551611	−	1.51554i	−0.831510	−	0.555509i	$-0.812523\pi$
$317$	−9.82115	−	26.9834i	−0.551611	−	1.51554i	0.279900	−	0.960029i	$-0.409699\pi$
$318$	−7.13246			−0.399968
$319$	17.2585	−	14.4816i	0.966292	−	0.810815i
$320$		0			0
$321$	23.8089	−	4.19815i	1.32888	−	0.234318i
$322$	3.52325	+	0.621244i	0.196343	+	0.0346206i
$323$			27.4047i			1.52484i
$324$	−1.56283	+	0.568825i	−0.0868241	+	0.0316014i
$325$		0			0
$326$	3.89259	−	22.0760i	0.215591	−	1.22267i
$327$	−4.68647	−	26.5783i	−0.259163	−	1.46978i
$328$	−7.91799	+	21.7545i	−0.437198	+	1.20119i
$329$	3.66044	−	3.07148i	0.201807	−	0.169336i
$330$		0			0
$331$	7.92514	−	2.88452i	0.435605	−	0.158547i	−0.114904	−	0.993377i	$-0.536656\pi$
$331$	7.92514	−	2.88452i	0.435605	−	0.158547i	0.550509	+	0.834829i	$0.314434\pi$
$332$	−0.181666	−	0.104885i	−0.00997021	−	0.00575630i
$333$	15.3988	−	18.3516i	0.843852	−	1.00566i
$334$	−0.0714517	−	0.123758i	−0.00390966	−	0.00677174i
$335$		0			0
$336$	−4.26083	−	0.751299i	−0.232447	−	0.0409867i
$337$	15.9954	−	2.82042i	0.871325	−	0.153638i	0.279931	−	0.960020i	$-0.409689\pi$
$337$	15.9954	−	2.82042i	0.871325	−	0.153638i	0.591395	+	0.806382i	$0.298577\pi$
$338$	−14.6054	+	2.57532i	−0.794428	+	0.140079i
$339$	−19.1163	+	22.7820i	−1.03826	+	1.23735i
$340$		0			0
$341$	−1.92468	−	3.33364i	−0.104227	−	0.180527i
$342$	−9.76557	+	26.8307i	−0.528062	+	1.45084i
$343$	8.13127	+	4.69459i	0.439047	+	0.253484i
$344$	5.74985	−	2.09277i	0.310011	−	0.112835i
$345$		0			0
$346$	−7.92926	+	6.65344i	−0.426280	+	0.357691i
$347$	4.28715	−	11.7788i	0.230146	−	0.632321i	−0.769836	−	0.638241i	$-0.779662\pi$
$347$	4.28715	−	11.7788i	0.230146	−	0.632321i	0.999982	+	0.00592013i	$0.00188445\pi$
$348$	−1.47426	−	0.536588i	−0.0790288	−	0.0287641i
$349$	−5.70187	+	32.3369i	−0.305214	+	1.73095i	0.317282	+	0.948331i	$0.397230\pi$
$349$	−5.70187	+	32.3369i	−0.305214	+	1.73095i	−0.622496	+	0.782623i	$0.713881\pi$
$350$		0			0
$351$	−4.71436	−	5.61835i	−0.251634	−	0.299885i
$352$		−	4.78880i		−	0.255244i
$353$	−15.9515	−	2.81268i	−0.849013	−	0.149704i	−0.267819	−	0.963469i	$-0.586303\pi$
$353$	−15.9515	−	2.81268i	−0.849013	−	0.149704i	−0.581194	+	0.813765i	$0.697414\pi$
$354$	−13.3601	−	15.9219i	−0.710081	−	0.846241i
$355$		0			0
$356$	−0.104256	+	0.0874810i	−0.00552555	+	0.00463649i
$357$	−2.33359	+	4.04189i	−0.123506	+	0.213919i
$358$	−10.3694	−	28.4898i	−0.548042	−	1.50573i
$359$	6.13088	−	10.6190i	0.323576	−	0.560449i	−0.657647	−	0.753326i	$-0.728448\pi$
$359$	6.13088	−	10.6190i	0.323576	−	0.560449i	0.981223	+	0.192877i	$0.0617817\pi$
$360$		0			0
$361$	−15.4513	−	26.7624i	−0.813227	−	1.40855i
$362$	−18.8697	+	22.4880i	−0.991767	+	1.18194i
$363$	16.4805	−	5.99841i	0.865001	−	0.314835i
$364$	0.0314599	+	0.178418i	0.00164895	+	0.00935165i
$365$		0			0
$366$	−6.90058	−	18.9592i	−0.360699	−	0.991012i
$367$	−20.3685	+	24.2743i	−1.06323	+	1.26711i	−0.100992	+	0.994887i	$0.532202\pi$
$367$	−20.3685	+	24.2743i	−1.06323	+	1.26711i	−0.962235	+	0.272218i	$0.912243\pi$
$368$	−11.9064	+	6.87417i	−0.620665	+	0.358341i
$369$	11.7973	+	20.4334i	0.614141	+	1.06372i
$370$		0			0
$371$	1.99495	−	0.726102i	0.103573	−	0.0376973i
$372$	−0.134029	+	0.232145i	−0.00694907	+	0.0120361i
$373$	−23.2393	−	27.6955i	−1.20329	−	1.43402i	−0.871311	−	0.490732i	$-0.836729\pi$
$373$	−23.2393	−	27.6955i	−1.20329	−	1.43402i	−0.331975	−	0.943288i	$-0.607715\pi$
$374$	22.5744	+	8.21643i	1.16730	+	0.424861i
$375$		0			0
$376$	−3.51636	+	19.9423i	−0.181342	+	1.02844i
$377$		−	6.91859i		−	0.356325i
$378$	−3.72503	+	3.12567i	−0.191595	+	0.160767i
$379$	13.7237			0.704939			0.352469	−	0.935823i	$-0.385342\pi$
$379$	13.7237			0.704939			0.352469	+	0.935823i	$0.385342\pi$
$380$		0			0
$381$	13.2506	−	36.4058i	0.678850	−	1.86512i
$382$	4.80790	−	13.2096i	0.245994	−	0.675862i
$383$	14.7209	+	17.5437i	0.752203	+	0.896441i	0.997328	−	0.0730503i	$-0.0232734\pi$
$383$	14.7209	+	17.5437i	0.752203	+	0.896441i	−0.245125	+	0.969492i	$0.578829\pi$
$384$	14.2469	−	8.22546i	0.727035	−	0.419754i
$385$		0			0
$386$	6.71869	−	11.6371i	0.341972	−	0.592314i
$387$	2.13290	−	5.86009i	0.108421	−	0.297885i
$388$	−1.33586	+	0.771259i	−0.0678180	+	0.0391547i
$389$	8.87211	+	7.44459i	0.449834	+	0.377455i	0.839374	−	0.543554i	$-0.182922\pi$
$389$	8.87211	+	7.44459i	0.449834	+	0.377455i	−0.389540	+	0.921009i	$0.627366\pi$
$390$		0			0
$391$	2.57532	+	14.6054i	0.130240	+	0.738626i
$392$	−18.8933	+	3.33140i	−0.954257	+	0.168261i
$393$	−4.46264	+	25.3089i	−0.225110	+	1.27666i
$394$	−17.3097	−	14.5246i	−0.872052	−	0.731739i
$395$		0			0
$396$	−1.95193	−	1.63787i	−0.0980883	−	0.0823059i
$397$	11.3072	+	6.52822i	0.567492	+	0.327642i	0.756147	−	0.654402i	$-0.227079\pi$
$397$	11.3072	+	6.52822i	0.567492	+	0.327642i	−0.188655	+	0.982043i	$0.560413\pi$
$398$	12.7164	+	34.9381i	0.637417	+	1.75129i
$399$		−	8.49870i		−	0.425467i
$400$		0			0
$401$	0.932419	+	0.339373i	0.0465628	+	0.0169475i	0.365197	−	0.930930i	$-0.381002\pi$
$401$	0.932419	+	0.339373i	0.0465628	+	0.0169475i	−0.318634	+	0.947878i	$0.603224\pi$
$402$	3.83072	+	21.7251i	0.191059	+	1.08355i
$403$	−1.16415	−	0.205270i	−0.0579902	−	0.0102252i
$404$	2.28312			0.113589
$405$		0			0
$406$	−4.58710			−0.227654
$407$	36.1457	+	6.37346i	1.79167	+	0.315920i
$408$	−3.43453	−	19.4782i	−0.170034	−	0.964314i
$409$	−29.7999	−	10.8463i	−1.47351	−	0.536315i	−0.524461	−	0.851435i	$-0.675733\pi$
$409$	−29.7999	−	10.8463i	−1.47351	−	0.536315i	−0.949052	+	0.315120i	$0.897955\pi$
$410$		0			0
$411$		−	22.1760i		−	1.09386i
$412$	−0.531139	−	1.45929i	−0.0261674	−	0.0718942i
$413$	5.35771	+	3.09327i	0.263636	+	0.152210i
$414$	−2.68320	+	15.2172i	−0.131872	+	0.747884i
$415$		0			0
$416$	−1.12654	−	0.945283i	−0.0552334	−	0.0463463i
$417$	−3.43301	+	19.4696i	−0.168115	+	0.953428i
$418$	−43.0806	+	7.59627i	−2.10714	+	0.371546i
$419$	2.20708	+	12.5170i	0.107823	+	0.611494i	0.990055	+	0.140680i	$0.0449288\pi$
$419$	2.20708	+	12.5170i	0.107823	+	0.611494i	−0.882232	+	0.470815i	$0.843960\pi$
$420$		0			0
$421$	−2.83544	−	2.37921i	−0.138191	−	0.115956i	0.571072	−	0.820900i	$-0.306528\pi$
$421$	−2.83544	−	2.37921i	−0.138191	−	0.115956i	−0.709263	+	0.704944i	$0.750972\pi$
$422$	−9.29450	+	5.36618i	−0.452449	+	0.261222i
$423$	13.2660	+	15.8097i	0.645013	+	0.768696i
$424$	−4.49841	+	7.79147i	−0.218462	+	0.378387i
$425$		0			0
$426$	11.7228	−	6.76817i	0.567972	−	0.327919i
$427$	3.86018	+	4.60039i	0.186807	+	0.222628i
$428$	0.882191	−	2.42380i	0.0426423	−	0.117159i
$429$	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	$0.570825\pi$
$432$	3.24492	−	18.4029i	0.156121	−	0.885408i
$433$		−	29.7861i		−	1.43143i	−0.698393	−	0.715715i	$-0.746101\pi$
$433$		−	29.7861i		−	1.43143i	0.698393	−	0.715715i	$-0.253899\pi$
$434$	−0.136096	+	0.771841i	−0.00653283	+	0.0370495i
$435$		0			0
$436$	−2.70574	−	0.984808i	−0.129581	−	0.0471637i
$437$	−17.3591	−	20.6878i	−0.830399	−	0.989631i
$438$	6.31407	−	10.9363i	0.301698	−	0.522556i
$439$	11.2604	−	4.09846i	0.537430	−	0.195609i	−0.0590226	−	0.998257i	$-0.518798\pi$
$439$	11.2604	−	4.09846i	0.537430	−	0.195609i	0.596453	+	0.802648i	$0.296576\pi$
$440$		0			0
$441$	−9.77631	+	16.9331i	−0.465539	+	0.806337i
$442$	6.38895	−	3.68866i	0.303891	−	0.175452i
$443$	23.0804	−	27.5061i	1.09658	−	1.30686i	0.148472	−	0.988917i	$-0.452565\pi$
$443$	23.0804	−	27.5061i	1.09658	−	1.30686i	0.948111	−	0.317940i	$-0.102991\pi$
$444$	−0.874171	−	2.40176i	−0.0414863	−	0.113983i
$445$		0			0
$446$	4.85844	+	27.5536i	0.230054	+	1.30470i
$447$	−21.2158	+	7.72193i	−1.00347	+	0.365235i
$448$	−3.83802	+	4.57398i	−0.181330	+	0.216100i
$449$	16.2777	+	28.1937i	0.768190	+	1.33054i	0.938543	+	0.345161i	$0.112176\pi$
$449$	16.2777	+	28.1937i	0.768190	+	1.33054i	−0.170353	+	0.985383i	$0.554491\pi$
$450$		0			0
$451$	−18.0744	+	31.3059i	−0.851092	+	1.47414i
$452$	1.08521	+	2.98158i	0.0510438	+	0.140242i
$453$	−1.76833	+	3.06283i	−0.0830833	+	0.143904i
$454$	−1.66772	+	1.39938i	−0.0782699	+	0.0656762i
$455$		0			0
$456$	23.1506	+	27.5899i	1.08413	+	1.29201i
$457$	−14.1589	−	2.49660i	−0.662325	−	0.116786i	−0.167627	−	0.985850i	$-0.553610\pi$
$457$	−14.1589	−	2.49660i	−0.662325	−	0.116786i	−0.494699	+	0.869065i	$0.664722\pi$
$458$		−	13.7023i		−	0.640268i
$459$	−17.4572	−	10.0789i	−0.814834	−	0.470445i
$460$		0			0
$461$	2.09920	−	11.9052i	0.0977696	−	0.554479i	−0.896094	−	0.443865i	$-0.853607\pi$
$461$	2.09920	−	11.9052i	0.0977696	−	0.554479i	0.993863	−	0.110614i	$-0.0352819\pi$
$462$	−7.00076	−	2.54807i	−0.325705	−	0.118547i
$463$	4.62327	−	12.7023i	0.214862	−	0.590328i	−0.784702	−	0.619873i	$-0.787184\pi$
$463$	4.62327	−	12.7023i	0.214862	−	0.590328i	0.999563	+	0.0295460i	$0.00940614\pi$
$464$	13.5036	−	11.3309i	0.626890	−	0.526023i
$465$		0			0
$466$	−26.5783	+	9.67372i	−1.23122	+	0.448126i
$467$	15.0387	+	8.68257i	0.695906	+	0.401781i	0.805821	−	0.592160i	$-0.201724\pi$
$467$	15.0387	+	8.68257i	0.695906	+	0.401781i	−0.109915	+	0.993941i	$0.535058\pi$
$468$	−0.770602	+	0.135878i	−0.0356211	+	0.00628096i
$469$	−3.28312	−	5.68653i	−0.151600	−	0.262579i
$470$		0			0
$471$	−12.9030	+	15.3772i	−0.594540	+	0.708545i
$472$	−25.8192	+	4.55262i	−1.18843	+	0.209551i
$473$	9.40923	−	1.65910i	0.432637	−	0.0762855i
$474$	−30.1195	−	5.31088i	−1.38343	−	0.243937i
$475$		0			0
$476$	0.248970	+	0.431229i	0.0114115	+	0.0197654i
$477$	3.13609	+	8.61633i	0.143592	+	0.394515i
$478$	5.84300	+	3.37346i	0.267252	+	0.154298i
$479$	−6.75150	+	2.45734i	−0.308484	+	0.112279i	−0.491623	−	0.870808i	$-0.663596\pi$
$479$	−6.75150	+	2.45734i	−0.308484	+	0.112279i	0.183139	+	0.983087i	$0.441374\pi$
$480$		0			0
$481$	8.63429	−	7.24503i	0.393690	−	0.330345i
$482$	10.4896	−	28.8200i	0.477789	−	1.31272i
$483$	−0.798656	−	4.52940i	−0.0363401	−	0.206095i
$484$	0.324921	−	1.84272i	0.0147692	−	0.0837600i
$485$		0			0
$486$	−13.5000	−	16.0887i	−0.612372	−	0.729797i
$487$		−	13.9394i		−	0.631657i	−0.948816	−	0.315828i	$-0.897718\pi$
$487$		−	13.9394i		−	0.631657i	0.948816	−	0.315828i	$-0.102282\pi$
$488$	−25.0631	−	4.41930i	−1.13455	−	0.200052i
$489$	−28.3803	+	5.00422i	−1.28340	+	0.226298i
$490$		0			0
$491$	−16.6291	+	13.9534i	−0.750459	+	0.629710i	−0.935624	−	0.352997i	$-0.885163\pi$
$491$	−16.6291	+	13.9534i	−0.750459	+	0.629710i	0.185165	+	0.982707i	$0.440718\pi$
$492$	2.51730			0.113489
$493$	−6.50368	−	17.8687i	−0.292911	−	0.804766i
$494$	−6.71688	+	11.6340i	−0.302207	+	0.523438i
$495$		0			0
$496$	−1.50593	−	2.60835i	−0.0676182	−	0.117118i
$497$	−2.58985	+	3.08647i	−0.116171	+	0.138447i
$498$	0.459994	−	2.60876i	0.0206128	−	0.116901i
$499$	−0.726377	−	4.11949i	−0.0325171	−	0.184414i	0.964223	−	0.265092i	$-0.0854024\pi$
$499$	−0.726377	−	4.11949i	−0.0325171	−	0.184414i	−0.996740	+	0.0806786i	$0.974291\pi$
$500$		0			0
$501$	−0.118089	+	0.140732i	−0.00527581	+	0.00628746i
$502$	−12.6600	+	15.0876i	−0.565045	+	0.673395i
$503$	−20.6439	+	11.9187i	−0.920465	+	0.531431i	−0.883783	−	0.467896i	$-0.845012\pi$
$503$	−20.6439	+	11.9187i	−0.920465	+	0.531431i	−0.0366816	+	0.999327i	$0.511679\pi$
$504$	1.06511	+	6.04055i	0.0474438	+	0.269067i
$505$		0			0
$506$	−22.2460	+	8.09689i	−0.988957	+	0.359951i
$507$	9.53298	+	16.5116i	0.423375	+	0.733306i
$508$	−2.65690	−	3.16637i	−0.117881	−	0.140485i
$509$	20.8773	+	7.59873i	0.925371	+	0.336808i	0.760373	−	0.649486i	$-0.225016\pi$
$509$	20.8773	+	7.59873i	0.925371	+	0.336808i	0.164998	+	0.986294i	$0.447238\pi$
$510$		0			0
$511$	−0.652704	+	3.70167i	−0.0288739	+	0.163752i
$512$		−	24.9186i		−	1.10126i
$513$	36.7065			1.62063
$514$	−0.285807			−0.0126064
$515$		0			0
$516$	−0.427671	−	0.509678i	−0.0188272	−	0.0224373i
$517$	−10.8145	+	29.7126i	−0.475621	+	1.30676i
$518$	−4.80353	−	5.72462i	−0.211055	−	0.251525i
$519$	11.5241	+	6.65344i	0.505852	+	0.292054i
$520$		0			0
$521$	6.59358	−	11.4204i	0.288870	−	0.500337i	−0.684670	−	0.728853i	$-0.740054\pi$
$521$	6.59358	−	11.4204i	0.288870	−	0.500337i	0.973540	+	0.228515i	$0.0733872\pi$
$522$		−	19.8120i		−	0.867149i
$523$	−15.4351	+	8.91147i	−0.674931	+	0.389672i	−0.797942	−	0.602734i	$-0.794078\pi$
$523$	−15.4351	+	8.91147i	−0.674931	+	0.389672i	0.123011	+	0.992405i	$0.460745\pi$
$524$	2.10039	+	1.76243i	0.0917558	+	0.0769922i
$525$		0			0
$526$	−0.386659	−	2.19285i	−0.0168591	−	0.0956129i
$527$	−3.19961	+	0.564178i	−0.139377	+	0.0245760i
$528$	26.9032	−	9.79196i	1.17081	−	0.426140i
$529$	6.42333	+	5.38982i	0.279275	+	0.234340i
$530$		0			0
$531$	−13.3601	+	23.1404i	−0.579779	+	1.00421i
$532$	−0.785248	−	0.453363i	−0.0340448	−	0.0196558i
$533$	3.79677	+	10.4315i	0.164456	+	0.451840i
$534$	−1.48839	−	0.859322i	−0.0644089	−	0.0371865i
$535$		0			0
$536$	26.1484	+	9.51725i	1.12944	+	0.411082i
$537$	−29.8576	+	25.0535i	−1.28845	+	1.08114i
$538$	4.02936	+	0.710485i	0.173718	+	0.0306312i
$539$	−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	$0.439533\pi$
$542$	21.1158	+	3.72328i	0.907000	+	0.159928i
$543$	35.4633	+	12.9076i	1.52188	+	0.553918i
$544$	−3.79813	−	1.38241i	−0.162844	−	0.0592702i
$545$		0			0
$546$	−1.98133	+	1.14392i	−0.0847932	+	0.0489554i
$547$	−7.62689	−	20.9547i	−0.326102	−	0.895959i	−0.989088	−	0.147326i	$-0.952933\pi$
$547$	−7.62689	−	20.9547i	−0.326102	−	0.895959i	0.662986	−	0.748632i	$-0.269289\pi$
$548$	−2.04898	−	1.18298i	−0.0875283	−	0.0505345i
$549$	−19.8694	+	16.6724i	−0.848006	+	0.711562i
$550$		0			0
$551$	26.5253	+	22.2574i	1.13001	+	0.948195i
$552$	14.9309	+	12.5285i	0.635502	+	0.533249i
$553$	8.96508	−	1.58079i	0.381234	−	0.0672218i
$554$	4.11974	+	23.3642i	0.175031	+	0.992649i
$555$		0			0
$556$	1.61578	+	1.35580i	0.0685244	+	0.0574988i
$557$	32.8328	−	18.9561i	1.39117	−	0.803194i	0.397727	−	0.917504i	$-0.369799\pi$
$557$	32.8328	−	18.9561i	1.39117	−	0.803194i	0.993445	+	0.114310i	$0.0364657\pi$
$558$	−3.33364	−	0.587811i	−0.141124	−	0.0248840i
$559$	1.46703	−	2.54098i	0.0620489	−	0.107472i
$560$		0			0
$561$		−	30.8837i		−	1.30391i
$562$	7.60462	+	9.06283i	0.320782	+	0.382293i
$563$	12.5134	−	34.3803i	0.527377	−	1.44896i	−0.334770	−	0.942300i	$-0.608659\pi$
$563$	12.5134	−	34.3803i	0.527377	−	1.44896i	0.862147	−	0.506658i	$-0.169119\pi$
$564$	2.16843	−	0.382353i	0.0913075	−	0.0161000i
$565$		0			0
$566$	−2.72462			−0.114524
$567$	5.41381	+	3.12567i	0.227359	+	0.131266i
$568$		−	17.0746i		−	0.716435i
$569$	0.440103	−	2.49595i	0.0184501	−	0.104636i	−0.974192	−	0.225721i	$-0.927526\pi$
$569$	0.440103	−	2.49595i	0.0184501	−	0.104636i	0.992642	+	0.121085i	$0.0386374\pi$
$570$		0			0
$571$	20.5205	+	7.46886i	0.858758	+	0.312562i	0.733606	−	0.679575i	$-0.237836\pi$
$571$	20.5205	+	7.46886i	0.858758	+	0.312562i	0.125152	+	0.992138i	$0.460058\pi$
$572$	−0.770602	−	0.918368i	−0.0322205	−	0.0383989i
$573$	−18.0718			−0.754961
$574$	6.91622	−	2.51730i	0.288678	−	0.105070i
$575$		0			0
$576$	−19.7554	−	16.5767i	−0.823140	−	0.690697i
$577$	−8.70323	+	5.02481i	−0.362320	+	0.209186i	−0.670098	−	0.742272i	$-0.733748\pi$
$577$	−8.70323	+	5.02481i	−0.362320	+	0.209186i	0.307778	+	0.951458i	$0.400415\pi$
$578$	−1.68907	+	2.01296i	−0.0702561	+	0.0837279i
$579$	−17.0123	−	2.99973i	−0.707008	−	0.124665i
$580$		0			0
$581$	0.136917	+	0.776497i	0.00568029	+	0.0322145i
$582$	−14.9219	−	12.5209i	−0.618532	−	0.519010i
$583$	−9.03001	+	10.7615i	−0.373985	+	0.445698i
$584$	−7.96451	−	13.7949i	−0.329574	−	0.570838i
$585$		0			0
$586$	−13.1964	+	22.8568i	−0.545138	+	0.944207i
$587$	−2.11003	−	5.79726i	−0.0870902	−	0.239278i	0.888500	−	0.458876i	$-0.151748\pi$
$587$	−2.11003	−	5.79726i	−0.0870902	−	0.239278i	−0.975591	+	0.219598i	$0.929526\pi$
$588$	1.04303	+	1.80659i	0.0430140	+	0.0745025i
$589$	4.53209	−	3.80287i	0.186741	−	0.156695i
$590$		0			0
$591$	−9.93541	+	27.2973i	−0.408688	+	1.12286i
$592$	28.2815	+	4.98680i	1.16236	+	0.204956i
$593$			21.7965i			0.895077i	0.894265	+	0.447538i	$0.147699\pi$
$593$			21.7965i			0.895077i	−0.894265	+	0.447538i	$0.852301\pi$
$594$	11.0053	−	30.2368i	0.451553	−	1.24063i
$595$		0			0
$596$	−0.418281	+	2.37219i	−0.0171335	+	0.0971687i
$597$	36.6155	−	30.7240i	1.49857	−	1.25745i
$598$	−2.48649	+	6.83157i	−0.101680	+	0.279364i
$599$	9.54395	−	8.00832i	0.389955	−	0.327211i	−0.426641	−	0.904421i	$-0.640303\pi$
$599$	9.54395	−	8.00832i	0.389955	−	0.327211i	0.816596	+	0.577210i	$0.195859\pi$
$600$		0			0
$601$	14.9162	−	5.42906i	0.608445	−	0.221456i	−0.0193775	−	0.999812i	$-0.506168\pi$
$601$	14.9162	−	5.42906i	0.608445	−	0.221456i	0.627823	+	0.778356i	$0.283946\pi$
$602$	−1.68469	−	0.972659i	−0.0686630	−	0.0396426i
$603$	24.5606	−	14.1800i	1.00018	−	0.577456i
$604$	0.188663	+	0.326774i	0.00767659	+	0.0132962i
$605$		0			0
$606$	9.86097	+	27.0928i	0.400574	+	1.10057i
$607$	39.1211	−	6.89811i	1.58788	−	0.279986i	0.691198	−	0.722666i	$-0.257083\pi$
$607$	39.1211	−	6.89811i	1.58788	−	0.279986i	0.896680	+	0.442680i	$0.145972\pi$
$608$	7.24827	−	1.27807i	0.293956	−	0.0518324i
$609$	2.01691	+	5.54142i	0.0817294	+	0.224550i
$610$		0			0
$611$	4.85504	+	8.40917i	0.196414	+	0.340199i
$612$	−1.86251	+	1.07532i	−0.0752876	+	0.0434673i
$613$	−17.1242	−	9.88666i	−0.691640	−	0.399318i	0.112586	−	0.993642i	$-0.464087\pi$
$613$	−17.1242	−	9.88666i	−0.691640	−	0.399318i	−0.804226	+	0.594324i	$0.797420\pi$
$614$	10.4684	−	3.81018i	0.422469	−	0.153766i
$615$		0			0
$616$	−7.19884	+	6.04055i	−0.290050	+	0.243381i
$617$	−5.83986	+	16.0449i	−0.235104	+	0.645943i	0.764895	+	0.644156i	$0.222791\pi$
$617$	−5.83986	+	16.0449i	−0.235104	+	0.645943i	−0.999998	+	0.00178707i	$0.999431\pi$
$618$	15.0228	−	12.6056i	0.604304	−	0.507072i
$619$	−0.835847	+	4.74033i	−0.0335955	+	0.190530i	−0.996987	−	0.0775689i	$-0.975284\pi$
$619$	−0.835847	+	4.74033i	−0.0335955	+	0.190530i	0.963391	+	0.268099i	$0.0863953\pi$
$620$		0			0
$621$	19.5628	−	3.44946i	0.785029	−	0.138422i
$622$		−	37.2172i		−	1.49227i
$623$	0.503783	+	0.0888306i	0.0201836	+	0.00355892i
$624$	3.00703	−	8.26173i	0.120377	−	0.330734i
$625$		0			0
$626$	−2.62836	+	2.20545i	−0.105050	+	0.0881476i
$627$	28.1188	+	48.7033i	1.12296	+	1.94502i
$628$	0.732486	+	2.01249i	0.0292294	+	0.0803070i
$629$	15.4893	−	26.8283i	0.617600	−	1.06971i
$630$		0			0
$631$	−11.9277	−	20.6593i	−0.474833	−	0.822435i	0.524752	−	0.851255i	$-0.324158\pi$
$631$	−11.9277	−	20.6593i	−0.474833	−	0.822435i	−0.999585	+	0.0288204i	$0.990825\pi$
$632$	−24.7978	+	29.5529i	−0.986404	+	1.17555i
$633$	10.5693	+	8.86871i	0.420093	+	0.352499i
$634$	−6.71806	−	38.1000i	−0.266808	−	1.51315i
$635$		0			0
$636$	0.963412	+	0.169875i	0.0382018	+	0.00673600i
$637$	−5.91322	+	7.04710i	−0.234290	+	0.279216i
$638$	26.2871	−	15.1769i	1.04072	−	0.600859i
$639$	−13.3307	−	11.1858i	−0.527354	−	0.442502i
$640$		0			0
$641$	41.6159	−	15.1470i	1.64373	−	0.598269i	0.656045	−	0.754722i	$-0.272228\pi$
$641$	41.6159	−	15.1470i	1.64373	−	0.598269i	0.987685	+	0.156453i	$0.0500060\pi$
$642$	32.5724			1.28553
$643$	4.66107	+	5.55484i	0.183815	+	0.219062i	0.850081	−	0.526652i	$-0.176553\pi$
$643$	4.66107	+	5.55484i	0.183815	+	0.219062i	−0.666266	+	0.745714i	$0.732109\pi$
$644$	−0.461104	−	0.167828i	−0.0181700	−	0.00661335i
$645$		0			0
$646$	−6.41147	+	36.3613i	−0.252256	+	1.43062i
$647$		−	26.8239i		−	1.05456i	−0.849693	−	0.527278i	$-0.823213\pi$
$647$		−	26.8239i		−	1.05456i	0.849693	−	0.527278i	$-0.176787\pi$
$648$	−26.0896	+	4.60030i	−1.02490	+	0.180717i
$649$	−40.9377			−1.60694
$650$		0			0
$651$	0.992259	−	0.174962i	0.0388897	−	0.00685730i
$652$	−1.05158	+	2.88919i	−0.0411830	+	0.113149i
$653$	−5.09840	−	6.07604i	−0.199516	−	0.237774i	0.657005	−	0.753886i	$-0.271823\pi$
$653$	−5.09840	−	6.07604i	−0.199516	−	0.237774i	−0.856521	+	0.516113i	$0.827379\pi$
$654$		−	36.3613i		−	1.42184i
$655$		0			0
$656$	−14.1420	+	24.4947i	−0.552153	+	0.956358i
$657$	−15.9878	−	2.81908i	−0.623743	−	0.109983i
$658$	5.57537	−	3.21894i	0.217351	−	0.125487i
$659$	33.9302	+	28.4708i	1.32173	+	1.10907i	0.985935	+	0.167132i	$0.0534505\pi$
$659$	33.9302	+	28.4708i	1.32173	+	1.10907i	0.335798	+	0.941934i	$0.390994\pi$
$660$		0			0
$661$	−0.707796	−	4.01411i	−0.0275301	−	0.156131i	0.967944	−	0.251167i	$-0.0808144\pi$
$661$	−0.707796	−	4.01411i	−0.0275301	−	0.156131i	−0.995474	+	0.0950363i	$0.969703\pi$
$662$	11.1902	−	1.97313i	0.434918	−	0.0766877i
$663$	−7.26525	−	6.09627i	−0.282159	−	0.236759i
$664$	−2.55968	−	2.14783i	−0.0993348	−	0.0833518i
$665$		0			0
$666$	24.7251	−	20.7468i	0.958078	−	0.803923i
$667$	16.2283	+	9.36942i	0.628363	+	0.362786i
$668$	0.00670372	+	0.0184183i	0.000259375	+	0.000712626i
$669$	31.1498	−	17.9843i	1.20432	−	0.695314i
$670$		0			0
$671$	−37.3423	−	13.5915i	−1.44158	−	0.524693i
$672$	1.17787	+	0.428710i	0.0454374	+	0.0165379i
$673$	6.23064	+	1.09863i	0.240174	+	0.0423491i	0.292439	−	0.956284i	$-0.405533\pi$
$673$	6.23064	+	1.09863i	0.240174	+	0.0423491i	−0.0522655	+	0.998633i	$0.516644\pi$
$674$	21.8830			0.842902
$675$		0			0
$676$	2.03415			0.0782365
$677$	38.6357	+	6.81252i	1.48489	+	0.261826i	0.856531	−	0.516096i	$-0.172615\pi$
$677$	38.6357	+	6.81252i	1.48489	+	0.261826i	0.628360	+	0.777922i	$0.283726\pi$
$678$	−30.6941	+	25.7554i	−1.17880	+	0.989129i
$679$	5.44831	+	1.98302i	0.209087	+	0.0761014i
$680$		0			0
$681$	2.42380	+	1.39938i	0.0928802	+	0.0536244i
$682$	−1.77379	−	4.87346i	−0.0679220	−	0.186614i
$683$	29.8836	+	17.2533i	1.14346	+	0.660179i	0.947286	−	0.320389i	$-0.103814\pi$
$683$	29.8836	+	17.2533i	1.14346	+	0.660179i	0.196178	+	0.980568i	$0.437147\pi$
$684$	1.95811	−	3.39155i	0.0748702	−	0.129679i
$685$		0			0
$686$	9.69047	+	8.13127i	0.369984	+	0.310453i
$687$	−16.5530	+	6.02481i	−0.631538	+	0.229861i
$688$	7.36208	−	1.29813i	0.280677	−	0.0494909i
$689$	0.749132	+	4.24854i	0.0285397	+	0.161857i
$690$		0			0
$691$	23.2704	+	19.5262i	0.885247	+	0.742810i	0.967251	−	0.253822i	$-0.0816876\pi$
$691$	23.2704	+	19.5262i	0.885247	+	0.742810i	−0.0820040	+	0.996632i	$0.526132\pi$
$692$	1.22951	−	0.709856i	0.0467388	−	0.0269847i
$693$			9.57760i			0.363823i
$694$	8.44403	−	14.6255i	0.320531	−	0.555176i
$695$		0			0
$696$	−21.6426	−	12.4953i	−0.820360	−	0.473635i
$697$	19.6119	+	23.3726i	0.742855	+	0.885300i
$698$	−15.1308	+	41.5715i	−0.572709	+	1.57350i
$699$	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	$0.587635\pi$
$702$	−4.94069	−	8.55753i	−0.186474	−	0.322983i
$703$			56.4107i			2.12757i
$704$	6.86097	−	38.9105i	0.258582	−	1.46649i
$705$		0			0
$706$	−20.5069	−	7.46389i	−0.771786	−	0.280907i
$707$	−5.51622	−	6.57398i	−0.207459	−	0.247240i
$708$	1.42539	+	2.46884i	0.0535694	+	0.0927849i
$709$	14.1001	−	5.13203i	0.529542	−	0.192737i	−0.0633920	−	0.997989i	$-0.520192\pi$
$709$	14.1001	−	5.13203i	0.529542	−	0.192737i	0.592934	+	0.805251i	$0.297970\pi$
$710$		0			0
$711$	6.82753	+	38.7209i	0.256053	+	1.45215i
$712$	−1.87744	+	1.08394i	−0.0703600	+	0.0406224i
$713$	2.05802	−	2.45265i	0.0770733	−	0.0918524i
$714$	−4.04189	+	4.81694i	−0.151264	+	0.180269i
$715$		0			0
$716$	0.722096	+	4.09521i	0.0269860	+	0.153045i
$717$	1.50617	−	8.54189i	0.0562488	−	0.319003i
$718$	10.6190	−	12.6552i	0.396298	−	0.472289i
$719$	−10.2943	−	17.8302i	−0.383911	−	0.664954i	0.607706	−	0.794162i	$-0.292090\pi$
$719$	−10.2943	−	17.8302i	−0.383911	−	0.664954i	−0.991617	+	0.129208i	$0.958756\pi$
$720$		0			0
$721$	−2.91859	+	5.05514i	−0.108694	+	0.188263i
$722$	−14.2400	−	39.1241i	−0.529958	−	1.45605i
$723$	−39.4281			−1.46635
$724$	3.08441	−	2.58812i	0.114631	−	0.0961869i
$725$		0			0
$726$	23.2701	−	4.10315i	0.863636	−	0.152282i
$727$	−31.5121	−	5.55644i	−1.16872	−	0.206077i	−0.444586	−	0.895736i	$-0.646649\pi$
$727$	−31.5121	−	5.55644i	−1.16872	−	0.206077i	−0.724134	+	0.689659i	$0.757760\pi$
$728$			2.88587i			0.106957i
$729$	−13.5000	+	23.3827i	−0.500000	+	0.866025i
$730$		0			0
$731$	1.40033	−	7.94166i	0.0517931	−	0.293733i
$732$	0.480535	+	2.72525i	0.0177611	+	0.100728i
$733$	14.1259	−	38.8105i	0.521751	−	1.43350i	−0.346819	−	0.937932i	$-0.612738\pi$
$733$	14.1259	−	38.8105i	0.521751	−	1.43350i	0.868570	−	0.495567i	$-0.165040\pi$
$734$	−32.7046	+	27.4424i	−1.20715	+	1.01292i
$735$		0			0
$736$	3.74288	−	1.36230i	0.137964	−	0.0502149i
$737$	37.6290	+	21.7251i	1.38608	+	0.800254i
$738$	10.8724	+	29.8717i	0.400219	+	1.09959i
$739$	12.1755	+	21.0885i	0.447882	+	0.775754i	0.998248	−	0.0591697i	$-0.0188453\pi$
$739$	12.1755	+	21.0885i	0.447882	+	0.775754i	−0.550366	+	0.834923i	$0.685512\pi$
$740$		0			0
$741$	17.0077	+	2.99892i	0.624795	+	0.110168i
$742$	2.81683	−	0.496683i	0.103409	−	0.0182338i
$743$	14.4544	−	2.54870i	0.530280	−	0.0935026i	0.0979034	−	0.995196i	$-0.468786\pi$
$743$	14.4544	−	2.54870i	0.530280	−	0.0935026i	0.432376	+	0.901693i	$0.357675\pi$
$744$	−2.74463	+	3.27093i	−0.100623	+	0.119918i
$745$		0			0
$746$	−24.3550	−	42.1842i	−0.891701	−	1.54447i
$747$	−3.35375	+	0.591357i	−0.122707	+	0.0216366i
$748$	−2.85353	−	1.64749i	−0.104336	−	0.0602382i
$749$	−9.11051	+	3.31595i	−0.332891	+	0.121162i
$750$		0			0
$751$	6.54260	−	5.48990i	0.238743	−	0.200329i	−0.515564	−	0.856851i	$-0.672418\pi$
$751$	6.54260	−	5.48990i	0.238743	−	0.200329i	0.754307	+	0.656522i	$0.227973\pi$
$752$	−8.46161	+	23.2481i	−0.308563	+	0.847771i
$753$	23.7931	+	8.65998i	0.867069	+	0.315587i
$754$	1.61864	−	9.17977i	0.0589475	−	0.334308i
$755$		0			0
$756$	0.577600	−	0.333477i	0.0210071	−	0.0121285i
$757$		−	17.3337i		−	0.630003i	−0.949091	−	0.315002i	$-0.897995\pi$
$757$		−	17.3337i		−	0.630003i	0.949091	−	0.315002i	$-0.102005\pi$
$758$	18.2090	+	3.21073i	0.661380	+	0.116619i
$759$	19.5628	+	23.3141i	0.710086	+	0.846247i
$760$		0			0
$761$	3.14227	−	2.63668i	0.113907	−	0.0955796i	−0.584055	−	0.811714i	$-0.698535\pi$
$761$	3.14227	−	2.63668i	0.113907	−	0.0955796i	0.697962	+	0.716135i	$0.254090\pi$
$762$	26.0986	−	45.2041i	0.945453	−	1.63757i
$763$	3.70167	+	10.1702i	0.134009	+	0.368188i
$764$	−0.964041	+	1.66977i	−0.0348778	+	0.0604101i
$765$		0			0
$766$	15.4277	+	26.7215i	0.557424	+	0.965487i
$767$	−8.08088	+	9.63041i	−0.291784	+	0.347734i
$768$	−7.15490	+	2.60417i	−0.258180	+	0.0939699i
$769$	0.930770	+	5.27866i	0.0335644	+	0.190353i	0.996980	−	0.0776587i	$-0.0247444\pi$
$769$	0.930770	+	5.27866i	0.0335644	+	0.190353i	−0.963416	+	0.268012i	$0.913633\pi$
$770$		0			0
$771$	0.125667	+	0.345268i	0.00452579	+	0.0124345i
$772$	−1.18469	+	1.41185i	−0.0426378	+	0.0508138i
$773$	5.32196	−	3.07263i	0.191418	−	0.110515i	−0.401228	−	0.915978i	$-0.631417\pi$

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.u (of order \(18\), degree \(6\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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