LMFDB - Embedded newform 756.2.bo.a.85.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(85,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("756.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bo (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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			85.7
Character	$\chi$	$=$	756.85
Dual form			756.2.bo.a.169.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33395 + 1.10480i) q^{3} +(-0.457942 + 2.59712i) q^{5} +(0.766044 - 0.642788i) q^{7} +(0.558836 + 2.94749i) q^{9} +O(q^{10})$	\(q+(1.33395 + 1.10480i) q^{3} +(-0.457942 + 2.59712i) q^{5} +(0.766044 - 0.642788i) q^{7} +(0.558836 + 2.94749i) q^{9} +(0.380345 + 2.15704i) q^{11} +(1.11857 - 0.407125i) q^{13} +(-3.48017 + 2.95849i) q^{15} +(-1.41307 + 2.44750i) q^{17} +(-2.24603 - 3.89024i) q^{19} +(1.73202 - 0.0111200i) q^{21} +(-0.274257 - 0.230129i) q^{23} +(-1.83685 - 0.668560i) q^{25} +(-2.51093 + 4.54920i) q^{27} +(-0.120542 - 0.0438737i) q^{29} +(1.76526 + 1.48123i) q^{31} +(-1.87574 + 3.29759i) q^{33} +(1.31859 + 2.28387i) q^{35} +(-3.45840 + 5.99012i) q^{37} +(1.94190 + 0.692708i) q^{39} +(8.33706 - 3.03444i) q^{41} +(-1.26458 - 7.17177i) q^{43} +(-7.91090 + 0.101584i) q^{45} +(-6.73636 + 5.65248i) q^{47} +(0.173648 - 0.984808i) q^{49} +(-4.58896 + 1.70369i) q^{51} +2.43522 q^{53} -5.77628 q^{55} +(1.30185 - 7.67079i) q^{57} +(-0.856916 + 4.85981i) q^{59} +(-2.91674 + 2.44743i) q^{61} +(2.32270 + 1.89870i) q^{63} +(0.545113 + 3.09149i) q^{65} +(10.6665 - 3.88227i) q^{67} +(-0.111598 - 0.609980i) q^{69} +(6.01954 - 10.4262i) q^{71} +(-4.57136 - 7.91783i) q^{73} +(-1.71164 - 2.92118i) q^{75} +(1.67788 + 1.40791i) q^{77} +(8.54611 + 3.11053i) q^{79} +(-8.37540 + 3.29433i) q^{81} +(8.41863 + 3.06413i) q^{83} +(-5.70935 - 4.79072i) q^{85} +(-0.112325 - 0.191700i) q^{87} +(0.196340 + 0.340072i) q^{89} +(0.595176 - 1.03088i) q^{91} +(0.718303 + 3.92613i) q^{93} +(11.1320 - 4.05171i) q^{95} +(1.08142 + 6.13303i) q^{97} +(-6.14532 + 2.32650i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9}+O(q^{10}) $ 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9	$ 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9} - 9 q^{13} + 3 q^{15} - 3 q^{21} - 45 q^{25} + 15 q^{27} + 6 q^{29} - 9 q^{31} + 6 q^{33} + 6 q^{35} + 30 q^{39} + 9 q^{41} + 9 q^{43} - 21 q^{45} - 27 q^{47} - 108 q^{51} - 84 q^{53} - 57 q^{57} - 66 q^{59} + 3 q^{63} + 30 q^{65} + 63 q^{67} + 42 q^{69} + 42 q^{71} + 3 q^{75} - 9 q^{77} + 36 q^{79} + 3 q^{81} + 12 q^{83} + 18 q^{85} + 39 q^{87} + 12 q^{89} + 21 q^{93} + 120 q^{95} + 18 q^{97} + 39 q^{99}+O(q^{100}) $ 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9 - 9 * q^13 + 3 * q^15 - 3 * q^21 - 45 * q^25 + 15 * q^27 + 6 * q^29 - 9 * q^31 + 6 * q^33 + 6 * q^35 + 30 * q^39 + 9 * q^41 + 9 * q^43 - 21 * q^45 - 27 * q^47 - 108 * q^51 - 84 * q^53 - 57 * q^57 - 66 * q^59 + 3 * q^63 + 30 * q^65 + 63 * q^67 + 42 * q^69 + 42 * q^71 + 3 * q^75 - 9 * q^77 + 36 * q^79 + 3 * q^81 + 12 * q^83 + 18 * q^85 + 39 * q^87 + 12 * q^89 + 21 * q^93 + 120 * q^95 + 18 * q^97 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.33395	+	1.10480i	0.770155	+	0.637856i
$3$	1.33395	+	1.10480i	0.770155	+	0.637856i
$4$		0			0
$5$	−0.457942	+	2.59712i	−0.204798	+	1.16147i	0.692959	+	0.720977i	$0.256307\pi$
$5$	−0.457942	+	2.59712i	−0.204798	+	1.16147i	−0.897757	+	0.440490i	$0.854805\pi$
$6$		0			0
$7$	0.766044	−	0.642788i	0.289538	−	0.242951i
$7$	0.766044	−	0.642788i	0.289538	−	0.242951i
$8$		0			0
$9$	0.558836	+	2.94749i	0.186279	+	0.982497i
$10$		0			0
$11$	0.380345	+	2.15704i	0.114678	+	0.650373i	0.986909	+	0.161278i	$0.0515617\pi$
$11$	0.380345	+	2.15704i	0.114678	+	0.650373i	−0.872231	+	0.489095i	$0.837327\pi$
$12$		0			0
$13$	1.11857	−	0.407125i	0.310234	−	0.112916i	−0.182211	−	0.983259i	$-0.558325\pi$
$13$	1.11857	−	0.407125i	0.310234	−	0.112916i	0.492445	+	0.870343i	$0.336103\pi$
$14$		0			0
$15$	−3.48017	+	2.95849i	−0.898575	+	0.763878i
$16$		0			0
$17$	−1.41307	+	2.44750i	−0.342719	+	0.593607i	−0.984937	−	0.172916i	$-0.944681\pi$
$17$	−1.41307	+	2.44750i	−0.342719	+	0.593607i	0.642218	+	0.766522i	$0.278015\pi$
$18$		0			0
$19$	−2.24603	−	3.89024i	−0.515275	−	0.892482i	−0.999843	−	0.0177286i	$-0.994357\pi$
$19$	−2.24603	−	3.89024i	−0.515275	−	0.892482i	0.484568	−	0.874754i	$-0.338977\pi$
$20$		0			0
$21$	1.73202	−	0.0111200i	0.377957	−	0.00242658i
$22$		0			0
$23$	−0.274257	−	0.230129i	−0.0571866	−	0.0479853i	0.613746	−	0.789503i	$-0.289662\pi$
$23$	−0.274257	−	0.230129i	−0.0571866	−	0.0479853i	−0.670933	+	0.741518i	$0.734106\pi$
$24$		0			0
$25$	−1.83685	−	0.668560i	−0.367371	−	0.133712i
$26$		0			0
$27$	−2.51093	+	4.54920i	−0.483228	+	0.875494i
$28$		0			0
$29$	−0.120542	−	0.0438737i	−0.0223841	−	0.00814715i	0.330804	−	0.943700i	$-0.392680\pi$
$29$	−0.120542	−	0.0438737i	−0.0223841	−	0.00814715i	−0.353188	+	0.935552i	$0.614902\pi$
$30$		0			0
$31$	1.76526	+	1.48123i	0.317050	+	0.266036i	0.787398	−	0.616444i	$-0.211427\pi$
$31$	1.76526	+	1.48123i	0.317050	+	0.266036i	−0.470349	+	0.882481i	$0.655872\pi$
$32$		0			0
$33$	−1.87574	+	3.29759i	−0.326524	+	0.574037i
$34$		0			0
$35$	1.31859	+	2.28387i	0.222883	+	0.386044i
$36$		0			0
$37$	−3.45840	+	5.99012i	−0.568557	+	0.984770i	0.428152	+	0.903707i	$0.359165\pi$
$37$	−3.45840	+	5.99012i	−0.568557	+	0.984770i	−0.996709	+	0.0810632i	$0.974168\pi$
$38$		0			0
$39$	1.94190	+	0.692708i	0.310953	+	0.110922i
$40$		0			0
$41$	8.33706	−	3.03444i	1.30203	−	0.473900i	0.404373	−	0.914594i	$-0.367490\pi$
$41$	8.33706	−	3.03444i	1.30203	−	0.473900i	0.897658	+	0.440694i	$0.145268\pi$
$42$		0			0
$43$	−1.26458	−	7.17177i	−0.192846	−	1.09369i	−0.915453	−	0.402426i	$-0.868167\pi$
$43$	−1.26458	−	7.17177i	−0.192846	−	1.09369i	0.722606	−	0.691260i	$-0.242944\pi$
$44$		0			0
$45$	−7.91090	+	0.101584i	−1.17929	+	0.0151433i
$46$		0			0
$47$	−6.73636	+	5.65248i	−0.982599	+	0.824499i	−0.984479	−	0.175500i	$-0.943846\pi$
$47$	−6.73636	+	5.65248i	−0.982599	+	0.824499i	0.00188033	+	0.999998i	$0.499401\pi$
$48$		0			0
$49$	0.173648	−	0.984808i	0.0248069	−	0.140687i
$50$		0			0
$51$	−4.58896	+	1.70369i	−0.642583	+	0.238564i
$52$		0			0
$53$	2.43522			0.334504			0.167252	−	0.985914i	$-0.446511\pi$
$53$	2.43522			0.334504			0.167252	+	0.985914i	$0.446511\pi$
$54$		0			0
$55$	−5.77628			−0.778873
$56$		0			0
$57$	1.30185	−	7.67079i	0.172434	−	1.01602i
$58$		0			0
$59$	−0.856916	+	4.85981i	−0.111561	+	0.632694i	0.876835	+	0.480792i	$0.159651\pi$
$59$	−0.856916	+	4.85981i	−0.111561	+	0.632694i	−0.988396	+	0.151902i	$0.951460\pi$
$60$		0			0
$61$	−2.91674	+	2.44743i	−0.373450	+	0.313362i	−0.810125	−	0.586258i	$-0.800601\pi$
$61$	−2.91674	+	2.44743i	−0.373450	+	0.313362i	0.436674	+	0.899620i	$0.356156\pi$
$62$		0			0
$63$	2.32270	+	1.89870i	0.292633	+	0.239213i
$64$		0			0
$65$	0.545113	+	3.09149i	0.0676129	+	0.383452i
$66$		0			0
$67$	10.6665	−	3.88227i	1.30311	−	0.474295i	0.405105	−	0.914270i	$-0.367235\pi$
$67$	10.6665	−	3.88227i	1.30311	−	0.474295i	0.898010	+	0.439975i	$0.145013\pi$
$68$		0			0
$69$	−0.111598	−	0.609980i	−0.0134349	−	0.0734330i
$70$		0			0
$71$	6.01954	−	10.4262i	0.714388	−	1.23736i	−0.248807	−	0.968553i	$-0.580038\pi$
$71$	6.01954	−	10.4262i	0.714388	−	1.23736i	0.963195	−	0.268804i	$-0.0866283\pi$
$72$		0			0
$73$	−4.57136	−	7.91783i	−0.535037	−	0.926711i	−0.999162	−	0.0409415i	$-0.986964\pi$
$73$	−4.57136	−	7.91783i	−0.535037	−	0.926711i	0.464124	−	0.885770i	$-0.346369\pi$
$74$		0			0
$75$	−1.71164	−	2.92118i	−0.197644	−	0.337309i
$76$		0			0
$77$	1.67788	+	1.40791i	0.191212	+	0.160446i
$78$		0			0
$79$	8.54611	+	3.11053i	0.961513	+	0.349962i	0.774626	−	0.632419i	$-0.217938\pi$
$79$	8.54611	+	3.11053i	0.961513	+	0.349962i	0.186887	+	0.982381i	$0.440160\pi$
$80$		0			0
$81$	−8.37540	+	3.29433i	−0.930600	+	0.366037i
$82$		0			0
$83$	8.41863	+	3.06413i	0.924064	+	0.336332i	0.759854	−	0.650094i	$-0.225270\pi$
$83$	8.41863	+	3.06413i	0.924064	+	0.336332i	0.164210	+	0.986425i	$0.447493\pi$
$84$		0			0
$85$	−5.70935	−	4.79072i	−0.619266	−	0.519626i
$86$		0			0
$87$	−0.112325	−	0.191700i	−0.0120425	−	0.0205524i
$88$		0			0
$89$	0.196340	+	0.340072i	0.0208120	+	0.0360475i	0.876244	−	0.481868i	$-0.160042\pi$
$89$	0.196340	+	0.340072i	0.0208120	+	0.0360475i	−0.855432	+	0.517915i	$0.826708\pi$
$90$		0			0
$91$	0.595176	−	1.03088i	0.0623914	−	0.108065i
$92$		0			0
$93$	0.718303	+	3.92613i	0.0744846	+	0.407121i
$94$		0			0
$95$	11.1320	−	4.05171i	1.14212	−	0.415696i
$96$		0			0
$97$	1.08142	+	6.13303i	0.109801	+	0.622715i	0.989193	+	0.146616i	$0.0468383\pi$
$97$	1.08142	+	6.13303i	0.109801	+	0.622715i	−0.879392	+	0.476099i	$0.842051\pi$
$98$		0			0
$99$	−6.14532	+	2.32650i	−0.617628	+	0.233822i
$100$		0			0
$101$	−3.69656	+	3.10178i	−0.367821	+	0.308639i	−0.807899	−	0.589321i	$-0.799395\pi$
$101$	−3.69656	+	3.10178i	−0.367821	+	0.308639i	0.440078	+	0.897960i	$0.354951\pi$
$102$		0			0
$103$	0.916799	−	5.19943i	0.0903349	−	0.512315i	−0.905742	−	0.423829i	$-0.860686\pi$
$103$	0.916799	−	5.19943i	0.0903349	−	0.512315i	0.996077	−	0.0884864i	$-0.0282030\pi$
$104$		0			0
$105$	−0.764283	+	4.50334i	−0.0745864	+	0.439481i
$106$		0			0
$107$	19.0567			1.84228			0.921139	−	0.389234i	$-0.127260\pi$
$107$	19.0567			1.84228			0.921139	+	0.389234i	$0.127260\pi$
$108$		0			0
$109$	−8.46797			−0.811084			−0.405542	−	0.914076i	$-0.632917\pi$
$109$	−8.46797			−0.811084			−0.405542	+	0.914076i	$0.632917\pi$
$110$		0			0
$111$	−11.2312	+	4.16968i	−1.06602	+	0.395768i
$112$		0			0
$113$	2.11410	−	11.9897i	0.198878	−	1.12789i	−0.707910	−	0.706303i	$-0.750362\pi$
$113$	2.11410	−	11.9897i	0.198878	−	1.12789i	0.906787	−	0.421588i	$-0.138527\pi$
$114$		0			0
$115$	0.723267	−	0.606893i	0.0674450	−	0.0565931i
$116$		0			0
$117$	1.82509	+	3.06945i	0.168730	+	0.283770i
$118$		0			0
$119$	0.490753	+	2.78320i	0.0449872	+	0.255135i
$120$		0			0
$121$	5.82844	−	2.12138i	0.529858	−	0.192853i
$122$		0			0
$123$	14.4737	+	5.16299i	1.30505	+	0.465531i
$124$		0			0
$125$	−4.01546	+	6.95498i	−0.359153	+	0.622072i
$126$		0			0
$127$	−8.15176	−	14.1193i	−0.723352	−	1.25288i	−0.959649	−	0.281201i	$-0.909267\pi$
$127$	−8.15176	−	14.1193i	−0.723352	−	1.25288i	0.236297	−	0.971681i	$-0.424066\pi$
$128$		0			0
$129$	6.23649	−	10.9639i	0.549092	−	0.965316i
$130$		0			0
$131$	1.26556	+	1.06193i	0.110572	+	0.0927812i	0.696398	−	0.717656i	$-0.254785\pi$
$131$	1.26556	+	1.06193i	0.110572	+	0.0927812i	−0.585825	+	0.810437i	$0.699230\pi$
$132$		0			0
$133$	−4.22116	−	1.53638i	−0.366021	−	0.133221i
$134$		0			0
$135$	−10.6650	−	8.60445i	−0.917894	−	0.740553i
$136$		0			0
$137$	3.53433	+	1.28639i	0.301958	+	0.109904i	0.488556	−	0.872533i	$-0.337524\pi$
$137$	3.53433	+	1.28639i	0.301958	+	0.109904i	−0.186598	+	0.982436i	$0.559746\pi$
$138$		0			0
$139$	14.0159	+	11.7607i	1.18881	+	0.997532i	0.999879	+	0.0155416i	$0.00494724\pi$
$139$	14.0159	+	11.7607i	1.18881	+	0.997532i	0.188933	+	0.981990i	$0.439497\pi$
$140$		0			0
$141$	−15.2308	+	0.0977858i	−1.28267	+	0.00823505i
$142$		0			0
$143$	1.30363	+	2.25795i	0.109015	+	0.188819i
$144$		0			0
$145$	0.169147	−	0.292971i	0.0140469	−	0.0243299i
$146$		0			0
$147$	1.31965	−	1.12184i	0.108843	−	0.0925275i
$148$		0			0
$149$	8.62044	−	3.13758i	0.706214	−	0.257041i	0.0361523	−	0.999346i	$-0.488490\pi$
$149$	8.62044	−	3.13758i	0.706214	−	0.257041i	0.670062	+	0.742305i	$0.266268\pi$
$150$		0			0
$151$	−2.83448	−	16.0751i	−0.230667	−	1.30818i	−0.851551	−	0.524273i	$-0.824337\pi$
$151$	−2.83448	−	16.0751i	−0.230667	−	1.30818i	0.620884	−	0.783903i	$-0.286774\pi$
$152$		0			0
$153$	−8.00367	−	2.79725i	−0.647058	−	0.226144i
$154$		0			0
$155$	−4.65531	+	3.90627i	−0.373923	+	0.313759i
$156$		0			0
$157$	0.153732	−	0.871859i	0.0122692	−	0.0695819i	−0.978058	−	0.208331i	$-0.933197\pi$
$157$	0.153732	−	0.871859i	0.0122692	−	0.0695819i	0.990328	+	0.138749i	$0.0443081\pi$
$158$		0			0
$159$	3.24846	+	2.69043i	0.257620	+	0.213365i
$160$		0			0
$161$	−0.358018			−0.0282157
$162$		0			0
$163$	18.5442			1.45250			0.726248	−	0.687433i	$-0.241262\pi$
$163$	18.5442			1.45250			0.726248	+	0.687433i	$0.241262\pi$
$164$		0			0
$165$	−7.70525	−	6.38163i	−0.599853	−	0.496809i
$166$		0			0
$167$	1.83559	−	10.4102i	0.142042	−	0.805563i	−0.827652	−	0.561242i	$-0.810324\pi$
$167$	1.83559	−	10.4102i	0.142042	−	0.805563i	0.969694	−	0.244321i	$-0.0785651\pi$
$168$		0			0
$169$	−8.87314	+	7.44545i	−0.682549	+	0.572727i
$170$		0			0
$171$	10.2113	−	8.79416i	0.780876	−	0.672506i
$172$		0			0
$173$	1.31893	+	7.48001i	0.100276	+	0.568694i	0.993002	+	0.118095i	$0.0376787\pi$
$173$	1.31893	+	7.48001i	0.100276	+	0.568694i	−0.892726	+	0.450600i	$0.851210\pi$
$174$		0			0
$175$	−1.83685	+	0.668560i	−0.138853	+	0.0505384i
$176$		0			0
$177$	−6.51220	+	5.53602i	−0.489487	+	0.416112i
$178$		0			0
$179$	−1.64868	+	2.85560i	−0.123228	+	0.213437i	−0.921039	−	0.389471i	$-0.872658\pi$
$179$	−1.64868	+	2.85560i	−0.123228	+	0.213437i	0.797811	+	0.602908i	$0.205991\pi$
$180$		0			0
$181$	−10.0546	−	17.4151i	−0.747355	−	1.29446i	−0.949087	−	0.315015i	$-0.897990\pi$
$181$	−10.0546	−	17.4151i	−0.747355	−	1.29446i	0.201732	−	0.979441i	$-0.435343\pi$
$182$		0			0
$183$	−6.59470	+	0.0423397i	−0.487494	+	0.00312984i
$184$		0			0
$185$	−13.9733	−	11.7250i	−1.02734	−	0.862039i
$186$		0			0
$187$	−5.81683	−	2.11715i	−0.425368	−	0.154821i
$188$		0			0
$189$	1.00069	+	5.09888i	0.0727894	+	0.370889i
$190$		0			0
$191$	−19.2235	−	6.99679i	−1.39096	−	0.506270i	−0.465481	−	0.885058i	$-0.654119\pi$
$191$	−19.2235	−	6.99679i	−1.39096	−	0.506270i	−0.925483	+	0.378788i	$0.876341\pi$
$192$		0			0
$193$	−6.15294	−	5.16293i	−0.442898	−	0.371636i	0.393894	−	0.919156i	$-0.371128\pi$
$193$	−6.15294	−	5.16293i	−0.442898	−	0.371636i	−0.836793	+	0.547520i	$0.815572\pi$
$194$		0			0
$195$	−2.68832	+	4.72613i	−0.192515	+	0.338445i
$196$		0			0
$197$	6.00180	+	10.3954i	0.427610	+	0.740643i	0.996660	−	0.0816600i	$-0.0260222\pi$
$197$	6.00180	+	10.3954i	0.427610	+	0.740643i	−0.569050	+	0.822303i	$0.692689\pi$
$198$		0			0
$199$	7.53985	−	13.0594i	0.534486	−	0.925756i	−0.464702	−	0.885467i	$-0.653839\pi$
$199$	7.53985	−	13.0594i	0.534486	−	0.925756i	0.999188	−	0.0402893i	$-0.0128280\pi$
$200$		0			0
$201$	18.5176	+	6.60554i	1.30613	+	0.465919i
$202$		0			0
$203$	−0.120542	+	0.0438737i	−0.00846040	+	0.00307933i
$204$		0			0
$205$	4.06292	+	23.0419i	0.283766	+	1.60932i
$206$		0			0
$207$	0.525039	−	0.936976i	0.0364927	−	0.0651243i
$208$		0			0
$209$	7.53715	−	6.32442i	0.521356	−	0.437469i
$210$		0			0
$211$	4.56600	−	25.8951i	0.314336	−	1.78269i	−0.261580	−	0.965182i	$-0.584243\pi$
$211$	4.56600	−	25.8951i	0.314336	−	1.78269i	0.575916	−	0.817509i	$-0.304645\pi$
$212$		0			0
$213$	19.5486	−	7.25756i	1.33945	−	0.497280i
$214$		0			0
$215$	19.2051			1.30977
$216$		0			0
$217$	2.30438			0.156431
$218$		0			0
$219$	2.64965	−	15.6124i	0.179047	−	1.05499i
$220$		0			0
$221$	−0.584169	+	3.31299i	−0.0392955	+	0.222856i
$222$		0			0
$223$	10.8777	−	9.12743i	0.728421	−	0.611218i	−0.201279	−	0.979534i	$-0.564510\pi$
$223$	10.8777	−	9.12743i	0.728421	−	0.611218i	0.929701	+	0.368316i	$0.120065\pi$
$224$		0			0
$225$	0.944074	−	5.78772i	0.0629383	−	0.385848i
$226$		0			0
$227$	−0.823616	−	4.67096i	−0.0546653	−	0.310022i	0.945199	−	0.326495i	$-0.105868\pi$
$227$	−0.823616	−	4.67096i	−0.0546653	−	0.310022i	−0.999864	+	0.0164723i	$0.994756\pi$
$228$		0			0
$229$	7.20666	−	2.62301i	0.476230	−	0.173333i	−0.0927426	−	0.995690i	$-0.529563\pi$
$229$	7.20666	−	2.62301i	0.476230	−	0.173333i	0.568972	+	0.822357i	$0.307341\pi$
$230$		0			0
$231$	0.682750	+	3.73180i	0.0449216	+	0.245535i
$232$		0			0
$233$	2.87543	−	4.98040i	0.188376	−	0.326277i	−0.756333	−	0.654187i	$-0.773011\pi$
$233$	2.87543	−	4.98040i	0.188376	−	0.326277i	0.944709	+	0.327910i	$0.106344\pi$
$234$		0			0
$235$	−11.5953	−	20.0836i	−0.756394	−	1.31011i
$236$		0			0
$237$	7.96356	+	13.5910i	0.517289	+	0.882832i
$238$		0			0
$239$	−9.20164	−	7.72109i	−0.595204	−	0.499436i	0.294696	−	0.955591i	$-0.404782\pi$
$239$	−9.20164	−	7.72109i	−0.595204	−	0.499436i	−0.889900	+	0.456155i	$0.849226\pi$
$240$		0			0
$241$	6.72549	+	2.44788i	0.433227	+	0.157682i	0.549422	−	0.835545i	$-0.314848\pi$
$241$	6.72549	+	2.44788i	0.433227	+	0.157682i	−0.116196	+	0.993226i	$0.537070\pi$
$242$		0			0
$243$	−14.8119	−	4.85868i	−0.950186	−	0.311684i
$244$		0			0
$245$	2.47814	+	0.901970i	0.158323	+	0.0576248i
$246$		0			0
$247$	−4.09615	−	3.43707i	−0.260632	−	0.218696i
$248$		0			0
$249$	7.84476	+	13.3883i	0.497142	+	0.848448i
$250$		0			0
$251$	13.8473	+	23.9841i	0.874031	+	1.51387i	0.857792	+	0.513998i	$0.171836\pi$
$251$	13.8473	+	23.9841i	0.874031	+	1.51387i	0.0162393	+	0.999868i	$0.494831\pi$
$252$		0			0
$253$	0.392087	−	0.679114i	0.0246503	−	0.0426955i
$254$		0			0
$255$	−2.32320	−	12.6983i	−0.145485	−	0.795196i
$256$		0			0
$257$	−11.2382	+	4.09036i	−0.701017	+	0.255149i	−0.667845	−	0.744300i	$-0.732783\pi$
$257$	−11.2382	+	4.09036i	−0.701017	+	0.255149i	−0.0331721	+	0.999450i	$0.510561\pi$
$258$		0			0
$259$	1.20109	+	6.81172i	0.0746321	+	0.423259i
$260$		0			0
$261$	0.0619541	−	0.379815i	0.00383486	−	0.0235100i
$262$		0			0
$263$	−4.34343	+	3.64457i	−0.267827	+	0.224734i	−0.766803	−	0.641882i	$-0.778154\pi$
$263$	−4.34343	+	3.64457i	−0.267827	+	0.224734i	0.498976	+	0.866616i	$0.333709\pi$
$264$		0			0
$265$	−1.11519	+	6.32457i	−0.0685057	+	0.388515i
$266$		0			0
$267$	−0.113803	+	0.670555i	−0.00696462	+	0.0410373i
$268$		0			0
$269$	−14.3141			−0.872747			−0.436374	−	0.899766i	$-0.643737\pi$
$269$	−14.3141			−0.872747			−0.436374	+	0.899766i	$0.643737\pi$
$270$		0			0
$271$	12.7721			0.775848			0.387924	−	0.921691i	$-0.373192\pi$
$271$	12.7721			0.775848			0.387924	+	0.921691i	$0.373192\pi$
$272$		0			0
$273$	1.93285	−	0.717584i	0.116981	−	0.0434302i
$274$		0			0
$275$	0.743475	−	4.21646i	0.0448332	−	0.254262i
$276$		0			0
$277$	−17.2041	+	14.4360i	−1.03370	+	0.867375i	−0.991286	−	0.131726i	$-0.957948\pi$
$277$	−17.2041	+	14.4360i	−1.03370	+	0.867375i	−0.0424106	+	0.999100i	$0.513504\pi$
$278$		0			0
$279$	−3.37941	+	6.03084i	−0.202320	+	0.361057i
$280$		0			0
$281$	−3.37587	−	19.1455i	−0.201387	−	1.14212i	−0.903024	−	0.429590i	$-0.858658\pi$
$281$	−3.37587	−	19.1455i	−0.201387	−	1.14212i	0.701637	−	0.712535i	$-0.252453\pi$
$282$		0			0
$283$	7.82584	−	2.84837i	0.465198	−	0.169318i	−0.0987778	−	0.995110i	$-0.531493\pi$
$283$	7.82584	−	2.84837i	0.465198	−	0.169318i	0.563976	+	0.825791i	$0.309271\pi$
$284$		0			0
$285$	19.3258	+	6.89383i	1.14476	+	0.408355i
$286$		0			0
$287$	4.43606	−	7.68348i	0.261852	−	0.453541i
$288$		0			0
$289$	4.50648	+	7.80546i	0.265087	+	0.459145i
$290$		0			0
$291$	−5.33321	+	9.37590i	−0.312638	+	0.549625i
$292$		0			0
$293$	−25.2047	−	21.1492i	−1.47247	−	1.23555i	−0.913802	−	0.406161i	$-0.866867\pi$
$293$	−25.2047	−	21.1492i	−1.47247	−	1.23555i	−0.558670	−	0.829390i	$-0.688688\pi$
$294$		0			0
$295$	−12.2291	−	4.45102i	−0.712005	−	0.259149i
$296$		0			0
$297$	−10.7678	−	3.68591i	−0.624814	−	0.213878i
$298$		0			0
$299$	−0.400466	−	0.145758i	−0.0231596	−	0.00842939i
$300$		0			0
$301$	−5.57865	−	4.68104i	−0.321548	−	0.269811i
$302$		0			0
$303$	−8.35786	+	0.0536597i	−0.480147	+	0.00308267i
$304$		0			0
$305$	−5.02058	−	8.69590i	−0.287478	−	0.497926i
$306$		0			0
$307$	−11.9768	+	20.7445i	−0.683554	+	1.18395i	0.290335	+	0.956925i	$0.406233\pi$
$307$	−11.9768	+	20.7445i	−0.683554	+	1.18395i	−0.973889	+	0.227025i	$0.927100\pi$
$308$		0			0
$309$	6.96729	−	5.92289i	0.396355	−	0.336941i
$310$		0			0
$311$	−12.9653	+	4.71897i	−0.735192	+	0.267588i	−0.682361	−	0.731015i	$-0.739047\pi$
$311$	−12.9653	+	4.71897i	−0.735192	+	0.267588i	−0.0528313	+	0.998603i	$0.516825\pi$
$312$		0			0
$313$	3.86063	+	21.8947i	0.218216	+	1.23756i	0.875238	+	0.483692i	$0.160705\pi$
$313$	3.86063	+	21.8947i	0.218216	+	1.23756i	−0.657022	+	0.753871i	$0.728184\pi$
$314$		0			0
$315$	−5.99480	+	5.16285i	−0.337769	+	0.290893i
$316$		0			0
$317$	−21.4034	+	17.9596i	−1.20214	+	1.00871i	−0.202571	+	0.979268i	$0.564930\pi$
$317$	−21.4034	+	17.9596i	−1.20214	+	1.00871i	−0.999566	+	0.0294455i	$0.990626\pi$
$318$		0			0
$319$	0.0487900	−	0.276702i	0.00273172	−	0.0154923i
$320$		0			0
$321$	25.4206	+	21.0538i	1.41884	+	1.17511i
$322$		0			0
$323$	12.6952			0.706378
$324$		0			0
$325$	−2.32683			−0.129069
$326$		0			0
$327$	−11.2958	−	9.35541i	−0.624661	−	0.517355i
$328$		0			0
$329$	−1.52701	+	8.66010i	−0.0841867	+	0.477447i
$330$		0			0
$331$	−14.1976	+	11.9132i	−0.780371	+	0.654809i	−0.943342	−	0.331822i	$-0.892337\pi$
$331$	−14.1976	+	11.9132i	−0.780371	+	0.654809i	0.162971	+	0.986631i	$0.447892\pi$
$332$		0			0
$333$	−19.5885	−	6.84610i	−1.07344	−	0.375164i
$334$		0			0
$335$	5.19810	+	29.4799i	0.284003	+	1.61066i
$336$		0			0
$337$	−4.68867	+	1.70654i	−0.255408	+	0.0929609i	−0.466551	−	0.884494i	$-0.654504\pi$
$337$	−4.68867	+	1.70654i	−0.255408	+	0.0929609i	0.211143	+	0.977455i	$0.432281\pi$
$338$		0			0
$339$	16.0663	−	13.6579i	0.872599	−	0.741796i
$340$		0			0
$341$	−2.52366	+	4.37111i	−0.136664	+	0.236709i
$342$		0			0
$343$	−0.500000	−	0.866025i	−0.0269975	−	0.0467610i
$344$		0			0
$345$	1.63530	−	0.0104990i	0.0880414	−	0.000565249i
$346$		0			0
$347$	−17.1810	−	14.4166i	−0.922323	−	0.773921i	0.0520998	−	0.998642i	$-0.483409\pi$
$347$	−17.1810	−	14.4166i	−0.922323	−	0.773921i	−0.974423	+	0.224721i	$0.927853\pi$
$348$		0			0
$349$	1.96549	+	0.715379i	0.105210	+	0.0382933i	0.394089	−	0.919072i	$-0.371060\pi$
$349$	1.96549	+	0.715379i	0.105210	+	0.0382933i	−0.288879	+	0.957366i	$0.593282\pi$
$350$		0			0
$351$	−0.956545	+	6.11084i	−0.0510566	+	0.326173i
$352$		0			0
$353$	−12.0440	−	4.38365i	−0.641037	−	0.233318i	0.000991147	−	1.00000i	$-0.499685\pi$
$353$	−12.0440	−	4.38365i	−0.641037	−	0.233318i	−0.642028	+	0.766681i	$0.721907\pi$
$354$		0			0
$355$	24.3214	+	20.4080i	1.29084	+	1.08315i
$356$		0			0
$357$	−2.42024	+	4.25483i	−0.128093	+	0.225189i
$358$		0			0
$359$	12.0617	+	20.8915i	0.636593	+	1.10261i	0.986175	+	0.165706i	$0.0529904\pi$
$359$	12.0617	+	20.8915i	0.636593	+	1.10261i	−0.349582	+	0.936906i	$0.613676\pi$
$360$		0			0
$361$	−0.589310	+	1.02071i	−0.0310163	+	0.0537218i
$362$		0			0
$363$	10.1185	+	3.60945i	0.531086	+	0.189447i
$364$		0			0
$365$	22.6570	−	8.24646i	1.18592	−	0.431639i
$366$		0			0
$367$	4.28205	+	24.2847i	0.223521	+	1.26765i	0.865492	+	0.500923i	$0.167006\pi$
$367$	4.28205	+	24.2847i	0.223521	+	1.26765i	−0.641971	+	0.766729i	$0.721883\pi$
$368$		0			0
$369$	13.6030	+	22.8777i	0.708146	+	1.19096i
$370$		0			0
$371$	1.86549	−	1.56533i	0.0968514	−	0.0812680i
$372$		0			0
$373$	1.54942	−	8.78720i	0.0802259	−	0.454984i	−0.918059	−	0.396443i	$-0.870244\pi$
$373$	1.54942	−	8.78720i	0.0802259	−	0.454984i	0.998285	−	0.0585403i	$-0.0186446\pi$
$374$		0			0
$375$	−13.0403	+	4.84130i	−0.673396	+	0.250004i
$376$		0			0
$377$	−0.152696			−0.00786426
$378$		0			0
$379$	−6.44566			−0.331092			−0.165546	−	0.986202i	$-0.552939\pi$
$379$	−6.44566			−0.331092			−0.165546	+	0.986202i	$0.552939\pi$
$380$		0			0
$381$	4.72493	−	27.8404i	0.242065	−	1.42631i
$382$		0			0
$383$	−3.71070	+	21.0444i	−0.189608	+	1.07532i	0.730283	+	0.683144i	$0.239388\pi$
$383$	−3.71070	+	21.0444i	−0.189608	+	1.07532i	−0.919891	+	0.392174i	$0.871723\pi$
$384$		0			0
$385$	−4.42488	+	3.71292i	−0.225513	+	0.189228i
$386$		0			0
$387$	20.4320	−	7.73518i	1.03862	−	0.393201i
$388$		0			0
$389$	−0.822442	−	4.66430i	−0.0416995	−	0.236489i	0.956833	−	0.290637i	$-0.0938671\pi$
$389$	−0.822442	−	4.66430i	−0.0416995	−	0.236489i	−0.998533	+	0.0541472i	$0.982756\pi$
$390$		0			0
$391$	0.950786	−	0.346058i	0.0480833	−	0.0175009i
$392$		0			0
$393$	0.514970	+	2.81475i	0.0259768	+	0.141985i
$394$		0			0
$395$	−11.9920	+	20.7708i	−0.603385	+	1.04509i
$396$		0			0
$397$	9.90022	+	17.1477i	0.496878	+	0.860617i	0.999994	−	0.00360162i	$-0.00114643\pi$
$397$	9.90022	+	17.1477i	0.496878	+	0.860617i	−0.503116	+	0.864219i	$0.667813\pi$
$398$		0			0
$399$	−3.93342	−	6.71298i	−0.196917	−	0.336069i
$400$		0			0
$401$	−14.7076	−	12.3411i	−0.734462	−	0.616287i	0.196882	−	0.980427i	$-0.436918\pi$
$401$	−14.7076	−	12.3411i	−0.734462	−	0.616287i	−0.931344	+	0.364141i	$0.881363\pi$
$402$		0			0
$403$	2.57760	+	0.938170i	0.128399	+	0.0467336i
$404$		0			0
$405$	−4.72032	−	23.2605i	−0.234554	−	1.15583i
$406$		0			0
$407$	−14.2363	−	5.18161i	−0.705669	−	0.256843i
$408$		0			0
$409$	22.5584	+	18.9287i	1.11544	+	0.935966i	0.998365	−	0.0571568i	$-0.0182035\pi$
$409$	22.5584	+	18.9287i	1.11544	+	0.935966i	0.117076	+	0.993123i	$0.462648\pi$
$410$		0			0
$411$	3.29341	+	5.62071i	0.162452	+	0.277249i
$412$		0			0
$413$	2.46739	+	4.27365i	0.121412	+	0.210292i
$414$		0			0
$415$	−11.8132	+	20.4610i	−0.579885	+	1.00439i
$416$		0			0
$417$	5.70323	+	31.1729i	0.279288	+	1.52655i
$418$		0			0
$419$	18.9924	−	6.91266i	0.927839	−	0.337706i	0.166486	−	0.986044i	$-0.446758\pi$
$419$	18.9924	−	6.91266i	0.927839	−	0.337706i	0.761352	+	0.648338i	$0.224536\pi$
$420$		0			0
$421$	5.93996	+	33.6872i	0.289496	+	1.64181i	0.688769	+	0.724981i	$0.258152\pi$
$421$	5.93996	+	33.6872i	0.289496	+	1.64181i	−0.399273	+	0.916832i	$0.630737\pi$
$422$		0			0
$423$	−20.4251	−	16.6966i	−0.993105	−	0.811814i
$424$		0			0
$425$	4.23190	−	3.55099i	0.205277	−	0.172248i
$426$		0			0
$427$	−0.661171	+	3.74969i	−0.0319963	+	0.181460i
$428$		0			0
$429$	−0.755609	+	4.45223i	−0.0364811	+	0.214956i
$430$		0			0
$431$	21.1941			1.02088			0.510441	−	0.859913i	$-0.329482\pi$
$431$	21.1941			1.02088			0.510441	+	0.859913i	$0.329482\pi$
$432$		0			0
$433$	−15.9185			−0.764993			−0.382497	−	0.923957i	$-0.624936\pi$
$433$	−15.9185			−0.764993			−0.382497	+	0.923957i	$0.624936\pi$
$434$		0			0
$435$	0.549307	−	0.203935i	0.0263372	−	0.00977791i
$436$		0			0
$437$	−0.279267	+	1.58380i	−0.0133592	+	0.0757636i
$438$		0			0
$439$	−26.1760	+	21.9643i	−1.24931	+	1.04830i	−0.252575	+	0.967577i	$0.581278\pi$
$439$	−26.1760	+	21.9643i	−1.24931	+	1.04830i	−0.996737	+	0.0807200i	$0.974278\pi$
$440$		0			0
$441$	2.99975	−	0.0385200i	0.142845	−	0.00183428i
$442$		0			0
$443$	−1.54068	−	8.73761i	−0.0731997	−	0.415136i	−0.999285	−	0.0378208i	$-0.987958\pi$
$443$	−1.54068	−	8.73761i	−0.0731997	−	0.415136i	0.926085	−	0.377315i	$-0.123153\pi$
$444$		0			0
$445$	−0.973119	+	0.354186i	−0.0461303	+	0.0167900i
$446$		0			0
$447$	14.9656	+	5.33848i	0.707850	+	0.252502i
$448$		0			0
$449$	14.9964	−	25.9744i	0.707722	−	1.22581i	−0.257979	−	0.966151i	$-0.583056\pi$
$449$	14.9964	−	25.9744i	0.707722	−	1.22581i	0.965700	−	0.259659i	$-0.0836102\pi$
$450$		0			0
$451$	9.71639	+	16.8293i	0.457527	+	0.792460i
$452$		0			0
$453$	13.9787	−	24.5749i	0.656779	−	1.15463i
$454$		0			0
$455$	2.40475	+	2.01783i	0.112736	+	0.0945971i
$456$		0			0
$457$	19.4936	+	7.09509i	0.911872	+	0.331894i	0.755000	−	0.655725i	$-0.227637\pi$
$457$	19.4936	+	7.09509i	0.911872	+	0.331894i	0.156872	+	0.987619i	$0.449859\pi$
$458$		0			0
$459$	−7.58608	−	12.5738i	−0.354088	−	0.586896i
$460$		0			0
$461$	3.72054	+	1.35417i	0.173283	+	0.0630698i	0.427205	−	0.904155i	$-0.359498\pi$
$461$	3.72054	+	1.35417i	0.173283	+	0.0630698i	−0.253922	+	0.967225i	$0.581721\pi$
$462$		0			0
$463$	−9.20567	−	7.72447i	−0.427824	−	0.358987i	0.403306	−	0.915065i	$-0.367861\pi$
$463$	−9.20567	−	7.72447i	−0.427824	−	0.358987i	−0.831130	+	0.556078i	$0.812305\pi$
$464$		0			0
$465$	−10.5256	+	0.0675770i	−0.488112	+	0.00313381i
$466$		0			0
$467$	−0.628179	−	1.08804i	−0.0290687	−	0.0503484i	0.851125	−	0.524963i	$-0.175921\pi$
$467$	−0.628179	−	1.08804i	−0.0290687	−	0.0503484i	−0.880194	+	0.474614i	$0.842587\pi$
$468$		0			0
$469$	5.67550	−	9.83026i	0.262070	−	0.453919i
$470$		0			0
$471$	1.16830	−	0.993171i	0.0538324	−	0.0457629i
$472$		0			0
$473$	14.9889	−	5.45550i	0.689188	−	0.250844i
$474$		0			0
$475$	1.52477	+	8.64741i	0.0699613	+	0.396770i
$476$		0			0
$477$	1.36089	+	7.17780i	0.0623110	+	0.328649i
$478$		0			0
$479$	−20.3666	+	17.0896i	−0.930575	+	0.780845i	−0.975921	−	0.218126i	$-0.930006\pi$
$479$	−20.3666	+	17.0896i	−0.930575	+	0.780845i	0.0453455	+	0.998971i	$0.485561\pi$
$480$		0			0
$481$	−1.42972	+	8.10835i	−0.0651896	+	0.369709i
$482$		0			0
$483$	−0.477577	−	0.395538i	−0.0217305	−	0.0179976i
$484$		0			0
$485$	−16.4234			−0.745750
$486$		0			0
$487$	−10.3782			−0.470280			−0.235140	−	0.971962i	$-0.575555\pi$
$487$	−10.3782			−0.470280			−0.235140	+	0.971962i	$0.575555\pi$
$488$		0			0
$489$	24.7370	+	20.4877i	1.11865	+	0.926484i
$490$		0			0
$491$	−3.78287	+	21.4537i	−0.170718	+	0.968192i	0.772252	+	0.635316i	$0.219130\pi$
$491$	−3.78287	+	21.4537i	−0.170718	+	0.968192i	−0.942971	+	0.332876i	$0.891981\pi$
$492$		0			0
$493$	0.277715	−	0.233031i	0.0125077	−	0.0104952i
$494$		0			0
$495$	−3.22799	−	17.0255i	−0.145088	−	0.765240i
$496$		0			0
$497$	−2.09057	−	11.8562i	−0.0937747	−	0.531823i
$498$		0			0
$499$	11.8565	−	4.31542i	0.530771	−	0.193185i	−0.0627117	−	0.998032i	$-0.519975\pi$
$499$	11.8565	−	4.31542i	0.530771	−	0.193185i	0.593482	+	0.804847i	$0.297753\pi$
$500$		0			0
$501$	13.9497	−	11.8587i	0.623228	−	0.529806i
$502$		0			0
$503$	−3.65222	+	6.32583i	−0.162844	+	0.282055i	−0.935888	−	0.352299i	$-0.885400\pi$
$503$	−3.65222	+	6.32583i	−0.162844	+	0.282055i	0.773043	+	0.634353i	$0.218734\pi$
$504$		0			0
$505$	−6.36288	−	11.0208i	−0.283145	−	0.490421i
$506$		0			0
$507$	−20.0620	+	0.128804i	−0.890986	+	0.00572036i
$508$		0			0
$509$	−0.213462	−	0.179116i	−0.00946152	−	0.00793916i	0.638045	−	0.769999i	$-0.279744\pi$
$509$	−0.213462	−	0.179116i	−0.00946152	−	0.00793916i	−0.647506	+	0.762060i	$0.724188\pi$
$510$		0			0
$511$	−8.59134	−	3.12699i	−0.380059	−	0.138330i
$512$		0			0
$513$	23.3371	−	0.449540i	1.03036	−	0.0198477i
$514$		0			0
$515$	13.0837	+	4.76208i	0.576536	+	0.209842i
$516$		0			0
$517$	−14.7548	−	12.3807i	−0.648915	−	0.544504i
$518$		0			0
$519$	−6.50453	+	11.4351i	−0.285517	+	0.501945i
$520$		0			0
$521$	−15.0420	−	26.0536i	−0.659004	−	1.14143i	−0.980874	−	0.194644i	$-0.937645\pi$
$521$	−15.0420	−	26.0536i	−0.659004	−	1.14143i	0.321870	−	0.946784i	$-0.395688\pi$
$522$		0			0
$523$	13.7871	−	23.8800i	0.602870	−	1.04420i	−0.389515	−	0.921020i	$-0.627357\pi$
$523$	13.7871	−	23.8800i	0.602870	−	1.04420i	0.992384	−	0.123180i	$-0.0393094\pi$
$524$		0			0
$525$	−3.18889	−	1.13753i	−0.139175	−	0.0496459i
$526$		0			0
$527$	−6.11973	+	2.22740i	−0.266580	+	0.0970271i
$528$		0			0
$529$	−3.97165	−	22.5243i	−0.172680	−	0.979320i
$530$		0			0
$531$	−14.8031	+	0.190088i	−0.642401	+	0.00824910i
$532$		0			0
$533$	8.09016	−	6.78845i	0.350424	−	0.294040i
$534$		0			0
$535$	−8.72685	+	49.4924i	−0.377295	+	2.13975i
$536$		0			0
$537$	−5.35412	+	1.98776i	−0.231047	+	0.0857781i
$538$		0			0
$539$	2.19032			0.0943438
$540$		0			0
$541$	−23.1045			−0.993341			−0.496671	−	0.867939i	$-0.665444\pi$
$541$	−23.1045			−0.993341			−0.496671	+	0.867939i	$0.665444\pi$
$542$		0			0
$543$	5.82787	−	34.3392i	0.250098	−	1.47364i
$544$		0			0
$545$	3.87784	−	21.9923i	0.166108	−	0.942048i
$546$		0			0
$547$	11.9883	−	10.0593i	0.512581	−	0.430106i	−0.349456	−	0.936953i	$-0.613633\pi$
$547$	11.9883	−	10.0593i	0.512581	−	0.430106i	0.862036	+	0.506847i	$0.169189\pi$
$548$		0			0
$549$	−8.84377	−	7.22935i	−0.377443	−	0.308541i
$550$		0			0
$551$	0.100062	+	0.567479i	0.00426278	+	0.0241754i
$552$		0			0
$553$	8.54611	−	3.11053i	0.363418	−	0.132273i
$554$		0			0
$555$	−5.68590	−	31.0783i	−0.241353	−	1.31920i
$556$		0			0
$557$	−9.69852	+	16.7983i	−0.410940	+	0.711768i	−0.994993	−	0.0999471i	$-0.968133\pi$
$557$	−9.69852	+	16.7983i	−0.410940	+	0.711768i	0.584053	+	0.811715i	$0.301466\pi$
$558$		0			0
$559$	−4.33432	−	7.50726i	−0.183322	−	0.317523i
$560$		0			0
$561$	−5.42032	−	9.25060i	−0.228846	−	0.390560i
$562$		0			0
$563$	−32.2409	−	27.0533i	−1.35879	−	1.14016i	−0.976353	−	0.216182i	$-0.930639\pi$
$563$	−32.2409	−	27.0533i	−1.35879	−	1.14016i	−0.382440	−	0.923980i	$-0.624916\pi$
$564$		0			0
$565$	30.1704	+	10.9811i	1.26928	+	0.461980i
$566$		0			0
$567$	−4.29838	+	7.90721i	−0.180515	+	0.332072i
$568$		0			0
$569$	−37.6737	−	13.7121i	−1.57937	−	0.574842i	−0.604299	−	0.796757i	$-0.706547\pi$
$569$	−37.6737	−	13.7121i	−1.57937	−	0.574842i	−0.975066	+	0.221915i	$0.928769\pi$
$570$		0			0
$571$	19.4184	+	16.2940i	0.812637	+	0.681883i	0.951236	−	0.308465i	$-0.0998154\pi$
$571$	19.4184	+	16.2940i	0.812637	+	0.681883i	−0.138599	+	0.990349i	$0.544260\pi$
$572$		0			0
$573$	−17.9131	−	30.5715i	−0.748332	−	1.27714i
$574$		0			0
$575$	0.349915	+	0.606071i	0.0145925	+	0.0252749i
$576$		0			0
$577$	−14.2152	+	24.6214i	−0.591786	+	1.02500i	0.402205	+	0.915549i	$0.368244\pi$
$577$	−14.2152	+	24.6214i	−0.591786	+	1.02500i	−0.993992	+	0.109455i	$0.965090\pi$
$578$		0			0
$579$	−2.50370	−	13.6848i	−0.104050	−	0.568723i
$580$		0			0
$581$	8.41863	−	3.06413i	0.349263	−	0.127122i
$582$		0			0
$583$	0.926226	+	5.25289i	0.0383603	+	0.217552i
$584$		0			0
$585$	−8.80750	+	3.33435i	−0.364145	+	0.137858i
$586$		0			0
$587$	−17.7819	+	14.9208i	−0.733939	+	0.615848i	−0.931202	−	0.364503i	$-0.881239\pi$
$587$	−17.7819	+	14.9208i	−0.733939	+	0.615848i	0.197263	+	0.980351i	$0.436795\pi$
$588$		0			0
$589$	1.79750	−	10.1942i	0.0740649	−	0.420043i
$590$		0			0
$591$	−3.47877	+	20.4977i	−0.143097	+	0.843164i
$592$		0			0
$593$	−39.5016			−1.62213			−0.811067	−	0.584953i	$-0.801113\pi$
$593$	−39.5016			−1.62213			−0.811067	+	0.584953i	$0.801113\pi$
$594$		0			0
$595$	−7.45303			−0.305545
$596$		0			0
$597$	24.4858	−	9.09054i	1.00214	−	0.372051i
$598$		0			0
$599$	3.41974	−	19.3943i	0.139727	−	0.792429i	−0.831724	−	0.555189i	$-0.812646\pi$
$599$	3.41974	−	19.3943i	0.139727	−	0.792429i	0.971451	−	0.237240i	$-0.0762429\pi$
$600$		0			0
$601$	35.9009	−	30.1245i	1.46443	−	1.22880i	0.543305	−	0.839535i	$-0.317173\pi$
$601$	35.9009	−	30.1245i	1.46443	−	1.22880i	0.921125	−	0.389267i	$-0.127272\pi$
$602$		0			0
$603$	17.4038	+	29.2697i	0.708736	+	1.19196i
$604$		0			0
$605$	2.84039	+	16.1086i	0.115478	+	0.654909i
$606$		0			0
$607$	−10.4026	+	3.78622i	−0.422227	+	0.153678i	−0.544390	−	0.838832i	$-0.683239\pi$
$607$	−10.4026	+	3.78622i	−0.422227	+	0.153678i	0.122164	+	0.992510i	$0.461017\pi$
$608$		0			0
$609$	−0.209269	−	0.0746496i	−0.00847999	−	0.00302495i
$610$		0			0
$611$	−5.23380	+	9.06521i	−0.211737	+	0.366739i
$612$		0			0
$613$	1.65024	+	2.85830i	0.0666525	+	0.115446i	0.897426	−	0.441165i	$-0.145435\pi$
$613$	1.65024	+	2.85830i	0.0666525	+	0.115446i	−0.830773	+	0.556611i	$0.812101\pi$
$614$		0			0
$615$	−20.0370	+	35.2255i	−0.807970	+	1.42043i
$616$		0			0
$617$	−5.14839	−	4.32001i	−0.207266	−	0.173917i	0.533245	−	0.845961i	$-0.320972\pi$
$617$	−5.14839	−	4.32001i	−0.207266	−	0.173917i	−0.740512	+	0.672044i	$0.765417\pi$
$618$		0			0
$619$	−20.6281	−	7.50803i	−0.829115	−	0.301773i	−0.107620	−	0.994192i	$-0.534323\pi$
$619$	−20.6281	−	7.50803i	−0.829115	−	0.301773i	−0.721496	+	0.692419i	$0.756545\pi$
$620$		0			0
$621$	1.73554	−	0.669814i	0.0696450	−	0.0268787i
$622$		0			0
$623$	0.368999	+	0.134305i	0.0147836	+	0.00538081i
$624$		0			0
$625$	−23.7111	−	19.8960i	−0.948445	−	0.795840i
$626$		0			0
$627$	17.0414	−	0.109410i	0.680567	−	0.00436942i
$628$		0			0
$629$	−9.77390	−	16.9289i	−0.389711	−	0.674999i
$630$		0			0
$631$	11.9004	−	20.6121i	0.473747	−	0.820553i	−0.525802	−	0.850607i	$-0.676235\pi$
$631$	11.9004	−	20.6121i	0.473747	−	0.820553i	0.999548	+	0.0300540i	$0.00956793\pi$
$632$		0			0
$633$	34.6997	−	29.4982i	1.37919	−	1.17245i
$634$		0			0
$635$	40.4024	−	14.7053i	1.60332	−	0.583561i
$636$		0			0
$637$	−0.206703	−	1.17227i	−0.00818985	−	0.0464470i
$638$		0			0
$639$	34.0949	+	11.9160i	1.34877	+	0.471391i
$640$		0			0
$641$	26.9458	−	22.6102i	1.06430	−	0.893050i	0.0697717	−	0.997563i	$-0.477773\pi$
$641$	26.9458	−	22.6102i	1.06430	−	0.893050i	0.994523	+	0.104513i	$0.0333285\pi$
$642$		0			0
$643$	0.658632	−	3.73529i	0.0259739	−	0.147305i	−0.969063	−	0.246815i	$-0.920616\pi$
$643$	0.658632	−	3.73529i	0.0259739	−	0.147305i	0.995037	+	0.0995091i	$0.0317272\pi$
$644$		0			0
$645$	25.6186	+	21.2177i	1.00873	+	0.835447i
$646$		0			0
$647$	−42.7869			−1.68213			−0.841064	−	0.540936i	$-0.818070\pi$
$647$	−42.7869			−1.68213			−0.841064	+	0.540936i	$0.818070\pi$
$648$		0			0
$649$	−10.8087			−0.424281
$650$		0			0
$651$	3.07392	+	2.54588i	0.120477	+	0.0997808i
$652$		0			0
$653$	−6.34418	+	35.9797i	−0.248267	+	1.40799i	0.564514	+	0.825423i	$0.309064\pi$
$653$	−6.34418	+	35.9797i	−0.248267	+	1.40799i	−0.812781	+	0.582569i	$0.802048\pi$
$654$		0			0
$655$	−3.33751	+	2.80050i	−0.130407	+	0.109425i
$656$		0			0
$657$	20.7831	−	17.8988i	0.810825	−	0.698299i
$658$		0			0
$659$	2.33467	+	13.2406i	0.0909458	+	0.515779i	0.995915	+	0.0903010i	$0.0287829\pi$
$659$	2.33467	+	13.2406i	0.0909458	+	0.515779i	−0.904969	+	0.425478i	$0.860106\pi$
$660$		0			0
$661$	45.3706	−	16.5135i	1.76471	−	0.642302i	0.764713	−	0.644371i	$-0.222881\pi$
$661$	45.3706	−	16.5135i	1.76471	−	0.642302i	0.999998	+	0.00206890i	$0.000658553\pi$
$662$		0			0
$663$	−4.43944	+	3.77396i	−0.172414	+	0.146569i
$664$		0			0
$665$	5.92320	−	10.2593i	0.229692	−	0.397838i
$666$		0			0
$667$	0.0229629	+	0.0397730i	0.000889128	+	0.00154002i
$668$		0			0
$669$	24.5942	−	0.157901i	0.950867	−	0.00610482i
$670$		0			0
$671$	−6.38859	−	5.36066i	−0.246629	−	0.206946i
$672$		0			0
$673$	−19.8443	−	7.22273i	−0.764941	−	0.278416i	−0.0700624	−	0.997543i	$-0.522320\pi$
$673$	−19.8443	−	7.22273i	−0.764941	−	0.278416i	−0.694879	+	0.719127i	$0.744542\pi$
$674$		0			0
$675$	7.65362	−	6.67751i	0.294588	−	0.257018i
$676$		0			0
$677$	−39.4158	−	14.3462i	−1.51487	−	0.551368i	−0.555010	−	0.831844i	$-0.687286\pi$
$677$	−39.4158	−	14.3462i	−1.51487	−	0.551368i	−0.959861	+	0.280476i	$0.909508\pi$
$678$		0			0
$679$	4.77065	+	4.00305i	0.183081	+	0.153623i
$680$		0			0
$681$	4.06181	−	7.14075i	0.155649	−	0.273634i
$682$		0			0
$683$	−17.2911	−	29.9490i	−0.661624	−	1.14597i	−0.980189	−	0.198065i	$-0.936534\pi$
$683$	−17.2911	−	29.9490i	−0.661624	−	1.14597i	0.318565	−	0.947901i	$-0.396799\pi$
$684$		0			0
$685$	−4.95943	+	8.58998i	−0.189490	+	0.328206i
$686$		0			0
$687$	12.5112	+	4.46296i	0.477333	+	0.170272i
$688$		0			0
$689$	2.72396	−	0.991440i	0.103775	−	0.0377709i
$690$		0			0
$691$	−4.62454	−	26.2271i	−0.175926	−	0.997726i	−0.937070	−	0.349142i	$-0.886473\pi$
$691$	−4.62454	−	26.2271i	−0.175926	−	0.997726i	0.761144	−	0.648583i	$-0.224638\pi$
$692$		0			0
$693$	−3.21214	+	5.73233i	−0.122019	+	0.217753i
$694$		0			0
$695$	−36.9625	+	31.0152i	−1.40207	+	1.17647i
$696$		0			0
$697$	−4.35402	+	24.6929i	−0.164920	+	0.935309i
$698$		0			0
$699$	9.33802	−	3.46681i	0.353196	−	0.131127i
$700$		0			0
$701$	18.8084			0.710384			0.355192	−	0.934793i	$-0.384416\pi$
$701$	18.8084			0.710384			0.355192	+	0.934793i	$0.384416\pi$
$702$		0			0
$703$	31.0707			1.17185
$704$		0			0
$705$	6.72087	−	39.6010i	0.253123	−	1.49146i
$706$		0			0
$707$	−0.837942	+	4.75220i	−0.0315140	+	0.178725i
$708$		0			0
$709$	19.9154	−	16.7110i	0.747937	−	0.627594i	−0.187019	−	0.982356i	$-0.559883\pi$
$709$	19.9154	−	16.7110i	0.747937	−	0.627594i	0.934957	+	0.354762i	$0.115438\pi$
$710$		0			0
$711$	−4.39238	+	26.9279i	−0.164727	+	1.00987i
$712$		0			0
$713$	−0.143261	−	0.812475i	−0.00536517	−	0.0304274i
$714$		0			0
$715$	−6.46114	+	2.35166i	−0.241633	+	0.0879473i
$716$		0			0
$717$	−3.74425	−	20.4655i	−0.139832	−	0.764298i
$718$		0			0
$719$	14.1793	−	24.5592i	0.528798	−	0.915904i	−0.470639	−	0.882326i	$-0.655976\pi$
$719$	14.1793	−	24.5592i	0.528798	−	0.915904i	0.999436	−	0.0335781i	$-0.0106902\pi$
$720$		0			0
$721$	−2.63982	−	4.57230i	−0.0983120	−	0.170281i
$722$		0			0
$723$	6.26704	+	10.6957i	0.233074	+	0.397776i
$724$		0			0
$725$	0.192086	+	0.161179i	0.00713389	+	0.00598605i
$726$		0			0
$727$	−14.1740	−	5.15891i	−0.525684	−	0.191333i	0.0655262	−	0.997851i	$-0.479127\pi$
$727$	−14.1740	−	5.15891i	−0.525684	−	0.191333i	−0.591210	+	0.806518i	$0.701350\pi$
$728$		0			0
$729$	−14.3905	−	22.8454i	−0.532981	−	0.846127i
$730$		0			0
$731$	19.3399	+	7.03914i	0.715311	+	0.260352i
$732$		0			0
$733$	15.1209	+	12.6879i	0.558502	+	0.468639i	0.877808	−	0.479013i	$-0.159005\pi$
$733$	15.1209	+	12.6879i	0.558502	+	0.468639i	−0.319306	+	0.947652i	$0.603450\pi$
$734$		0			0
$735$	2.30922	+	3.94103i	0.0851768	+	0.145367i
$736$		0			0
$737$	12.4312	+	21.5314i	0.457908	+	0.793120i
$738$		0			0
$739$	12.9770	−	22.4768i	0.477366	−	0.826823i	−0.522297	−	0.852764i	$-0.674925\pi$
$739$	12.9770	−	22.4768i	0.477366	−	0.826823i	0.999663	+	0.0259408i	$0.00825815\pi$
$740$		0			0
$741$	−1.66677	−	9.11030i	−0.0612303	−	0.334675i
$742$		0			0
$743$	22.0781	−	8.03576i	0.809965	−	0.294803i	0.0963558	−	0.995347i	$-0.469281\pi$
$743$	22.0781	−	8.03576i	0.809965	−	0.294803i	0.713610	+	0.700544i	$0.247059\pi$
$744$		0			0
$745$	4.20102	+	23.8251i	0.153913	+	0.872886i
$746$		0			0
$747$	−4.32686	+	26.5262i	−0.158311	+	0.970542i
$748$		0			0
$749$	14.5983	−	12.2494i	0.533409	−	0.447583i
$750$		0			0
$751$	5.93847	−	33.6787i	0.216698	−	1.22895i	−0.661238	−	0.750176i	$-0.729969\pi$
$751$	5.93847	−	33.6787i	0.216698	−	1.22895i	0.877936	−	0.478778i	$-0.158920\pi$
$752$		0			0
$753$	−8.02615	+	47.2920i	−0.292489	+	1.72342i
$754$		0			0
$755$	43.0470			1.56664
$756$		0			0
$757$	−18.1325			−0.659037			−0.329518	−	0.944149i	$-0.606886\pi$
$757$	−18.1325			−0.659037			−0.329518	+	0.944149i	$0.606886\pi$
$758$		0			0
$759$	1.27331	−	0.472726i	0.0462181	−	0.0171589i
$760$		0			0
$761$	−3.54135	+	20.0840i	−0.128374	+	0.728044i	0.850873	+	0.525372i	$0.176074\pi$
$761$	−3.54135	+	20.0840i	−0.128374	+	0.728044i	−0.979247	+	0.202672i	$0.935037\pi$
$762$		0			0
$763$	−6.48684	+	5.44311i	−0.234839	+	0.197054i
$764$		0			0
$765$	10.9300	−	19.5055i	0.395175	−	0.705223i
$766$		0			0
$767$	1.02003	+	5.78489i	0.0368312	+	0.208880i
$768$		0			0
$769$	−5.09704	+	1.85517i	−0.183804	+	0.0668992i	−0.432283	−	0.901738i	$-0.642292\pi$
$769$	−5.09704	+	1.85517i	−0.183804	+	0.0668992i	0.248479	+	0.968637i	$0.420069\pi$
$770$		0			0
$771$	−19.5101	−	6.95959i	−0.702641	−	0.250644i
$772$		0			0
$773$	18.7192	−	32.4226i	0.673283	−	1.16616i	−0.303684	−	0.952773i	$-0.598217\pi$
$773$	18.7192	−	32.4226i	0.673283	−	1.16616i	0.976967	−	0.213388i	$-0.0684499\pi$
$774$		0			0
$775$	−2.25223	−	3.90098i	−0.0809025	−	0.140127i
$776$		0			0
$777$	−5.92339	+	10.4134i	−0.212500	+	0.373580i
$778$		0			0
$779$	−30.5300	−	25.6177i	−1.09385	−	0.917850i
$780$		0			0
$781$	24.7792	+	9.01888i	0.886669	+	0.322721i
$782$		0			0
$783$	0.502263	−	0.438207i	0.0179494	−	0.0156602i
$784$		0			0
$785$	2.19392	+	0.798522i	0.0783044	+	0.0285005i
$786$		0			0
$787$	35.4470	+	29.7436i	1.26355	+	1.06024i	0.995295	+	0.0968958i	$0.0308914\pi$
$787$	35.4470	+	29.7436i	1.26355	+	1.06024i	0.268255	+	0.963348i	$0.413553\pi$
$788$		0			0
$789$	−9.82042	+	0.0630497i	−0.349616	+	0.00224463i
$790$		0			0
$791$	−6.08730	−	10.5435i	−0.216440	−	0.374884i
$792$		0			0
$793$	−2.26615	+	3.92509i	−0.0804735	+	0.139384i
$794$		0			0
$795$	−8.47499	+	7.20458i	−0.300577	+	0.255520i
$796$		0			0
$797$	15.4373	−	5.61872i	0.546817	−	0.199025i	−0.0538147	−	0.998551i	$-0.517138\pi$
$797$	15.4373	−	5.61872i	0.546817	−	0.199025i	0.600632	+	0.799526i	$0.294916\pi$
$798$		0			0
$799$	−4.31553	−	24.4746i	−0.152673	−	0.865849i
$800$		0			0
$801$	−0.892635	+	0.768756i	−0.0315397	+	0.0271626i
$802$		0			0
$803$	15.3404	−	12.8721i	0.541351	−	0.454248i
$804$		0			0
$805$	0.163951	−	0.929814i	0.00577853	−	0.0327716i
$806$		0			0
$807$	−19.0943	−	15.8142i	−0.672151	−	0.556687i
$808$		0			0
$809$	24.6205			0.865611			0.432806	−	0.901487i	$-0.357524\pi$
$809$	24.6205			0.865611			0.432806	+	0.901487i	$0.357524\pi$
$810$		0			0
$811$	−45.6157			−1.60178			−0.800892	−	0.598809i	$-0.795641\pi$
$811$	−45.6157			−1.60178			−0.800892	+	0.598809i	$0.795641\pi$
$812$		0			0
$813$	17.0373	+	14.1106i	0.597524	+	0.494880i
$814$		0			0
$815$	−8.49218	+	48.1616i	−0.297468	+	1.68703i
$816$		0			0
$817$	−25.0596	+	21.0275i	−0.876726	+	0.735660i
$818$		0			0
$819$	3.37110	+	1.17819i	0.117796	+	0.0411692i
$820$		0			0
$821$	5.66432	+	32.1240i	0.197686	+	1.12113i	0.908541	+	0.417795i	$0.137197\pi$
$821$	5.66432	+	32.1240i	0.197686	+	1.12113i	−0.710855	+	0.703339i	$0.751692\pi$
$822$		0			0
$823$	−25.9265	+	9.43647i	−0.903741	+	0.328935i	−0.751751	−	0.659447i	$-0.770790\pi$
$823$	−25.9265	+	9.43647i	−0.903741	+	0.328935i	−0.151990	+	0.988382i	$0.548568\pi$
$824$		0			0
$825$	5.65010	−	4.80315i	0.196711	−	0.167224i
$826$		0			0
$827$	−8.23536	+	14.2641i	−0.286372	+	0.496010i	−0.972941	−	0.231054i	$-0.925783\pi$
$827$	−8.23536	+	14.2641i	−0.286372	+	0.496010i	0.686569	+	0.727064i	$0.259116\pi$
$828$		0			0
$829$	16.7905	+	29.0820i	0.583158	+	1.01006i	0.995102	+	0.0988498i	$0.0315163\pi$
$829$	16.7905	+	29.0820i	0.583158	+	1.01006i	−0.411945	+	0.911209i	$0.635150\pi$
$830$		0			0
$831$	−38.8983	+	0.249737i	−1.34937	+	0.00866329i
$832$		0			0
$833$	2.16494	+	1.81660i	0.0750109	+	0.0629416i
$834$		0			0
$835$	26.1958	+	9.53451i	0.906545	+	0.329955i
$836$		0			0
$837$	−11.1708	+	4.31126i	−0.386120	+	0.149019i
$838$		0			0
$839$	−6.44181	−	2.34463i	−0.222396	−	0.0809455i	0.228419	−	0.973563i	$-0.426644\pi$
$839$	−6.44181	−	2.34463i	−0.222396	−	0.0809455i	−0.450815	+	0.892617i	$0.648867\pi$
$840$		0			0
$841$	−22.2027	−	18.6303i	−0.765610	−	0.642423i
$842$		0			0
$843$	16.6487	−	29.2688i	0.573412	−	1.00807i
$844$		0			0
$845$	−15.2733	−	26.4542i	−0.525419	−	0.910052i
$846$		0			0
$847$	3.10125	−	5.37152i	0.106560	−	0.184568i
$848$		0			0
$849$	13.5862	+	4.84640i	0.466276	+	0.166328i
$850$		0			0
$851$	2.32699	−	0.846957i	0.0797683	−	0.0290333i
$852$		0			0
$853$	−6.87462	−	38.9879i	−0.235383	−	1.33492i	−0.841807	−	0.539779i	$-0.818508\pi$
$853$	−6.87462	−	38.9879i	−0.235383	−	1.33492i	0.606424	−	0.795141i	$-0.292603\pi$
$854$		0			0
$855$	18.1633	+	30.5471i	0.621172	+	1.04469i
$856$		0			0
$857$	23.6798	−	19.8697i	0.808885	−	0.678735i	−0.141456	−	0.989945i	$-0.545178\pi$
$857$	23.6798	−	19.8697i	0.808885	−	0.678735i	0.950341	+	0.311209i	$0.100734\pi$
$858$		0			0
$859$	4.41649	−	25.0472i	0.150689	−	0.854598i	−0.811933	−	0.583750i	$-0.801585\pi$
$859$	4.41649	−	25.0472i	0.150689	−	0.854598i	0.962622	−	0.270848i	$-0.0873041\pi$
$860$		0			0
$861$	14.4062	−	5.34841i	0.490961	−	0.182273i
$862$		0			0
$863$	−3.09871			−0.105481			−0.0527406	−	0.998608i	$-0.516796\pi$
$863$	−3.09871			−0.105481			−0.0527406	+	0.998608i	$0.516796\pi$
$864$		0			0
$865$	−20.0305			−0.681056
$866$		0			0
$867$	−2.61205	+	15.3908i	−0.0887099	+	0.522700i
$868$		0			0
$869$	−3.45908	+	19.6174i	−0.117341	+	0.665475i
$870$		0			0
$871$	10.3506	−	8.68515i	0.350715	−	0.294285i
$872$		0			0
$873$	−17.4727	+	6.61483i	−0.591362	+	0.223878i
$874$		0			0
$875$	1.39455	+	7.90891i	0.0471445	+	0.267370i
$876$		0			0
$877$	15.5328	−	5.65349i	0.524506	−	0.190905i	−0.0661774	−	0.997808i	$-0.521080\pi$
$877$	15.5328	−	5.65349i	0.524506	−	0.190905i	0.590684	+	0.806903i	$0.298858\pi$
$878$		0			0
$879$	−10.2561	−	56.0581i	−0.345929	−	1.89079i
$880$		0			0
$881$	−16.7762	+	29.0572i	−0.565204	+	0.978963i	0.431826	+	0.901957i	$0.357869\pi$
$881$	−16.7762	+	29.0572i	−0.565204	+	0.978963i	−0.997031	+	0.0770058i	$0.975464\pi$
$882$		0			0
$883$	17.8006	+	30.8316i	0.599038	+	1.03756i	0.992963	+	0.118422i	$0.0377837\pi$
$883$	17.8006	+	30.8316i	0.599038	+	1.03756i	−0.393925	+	0.919143i	$0.628883\pi$
$884$		0			0
$885$	−11.3955	−	19.4481i	−0.383055	−	0.653742i
$886$		0			0
$887$	−33.2314	−	27.8845i	−1.11580	−	0.936270i	−0.117418	−	0.993083i	$-0.537462\pi$
$887$	−33.2314	−	27.8845i	−1.11580	−	0.936270i	−0.998385	+	0.0568130i	$0.981906\pi$
$888$		0			0
$889$	−15.3203	−	5.57613i	−0.513826	−	0.187017i
$890$		0			0
$891$	−10.2916	−	16.8131i	−0.344780	−	0.563261i
$892$		0			0
$893$	37.1196	+	13.5104i	1.24216	+	0.452109i
$894$		0			0
$895$	−6.66133	−	5.58952i	−0.222664	−	0.186837i
$896$		0			0
$897$	−0.373168	−	0.636868i	−0.0124597	−	0.0212644i
$898$		0			0
$899$	−0.147801	−	0.255999i	−0.00492944	−	0.00853803i
$900$		0			0
$901$	−3.44113	+	5.96022i	−0.114641	+	0.198564i
$902$		0			0
$903$	−2.27002	−	12.4076i	−0.0755414	−	0.412898i
$904$		0			0
$905$	49.8336	−	18.1379i	1.65652	−	0.602926i
$906$		0			0
$907$	−4.88511	−	27.7049i	−0.162208	−	0.919925i	−0.951897	−	0.306418i	$-0.900869\pi$
$907$	−4.88511	−	27.7049i	−0.162208	−	0.919925i	0.789690	−	0.613507i	$-0.210242\pi$
$908$		0			0
$909$	−11.2082	−	9.16218i	−0.371754	−	0.303890i
$910$		0			0
$911$	−30.9685	+	25.9856i	−1.02603	+	0.860943i	−0.990373	−	0.138421i	$-0.955797\pi$
$911$	−30.9685	+	25.9856i	−1.02603	+	0.860943i	−0.0356580	+	0.999364i	$0.511353\pi$
$912$		0			0
$913$	−3.40748	+	19.3248i	−0.112771	+	0.639557i
$914$		0			0
$915$	2.91003	−	17.1466i	0.0962027	−	0.566850i
$916$		0			0
$917$	1.65207			0.0545561
$918$		0			0
$919$	18.9389			0.624737			0.312368	−	0.949961i	$-0.398878\pi$
$919$	18.9389			0.624737			0.312368	+	0.949961i	$0.398878\pi$
$920$		0			0
$921$	−38.8950	+	14.4401i	−1.28163	+	0.475817i
$922$		0			0
$923$	2.48851	−	14.1130i	0.0819103	−	0.464536i
$924$		0			0
$925$	10.3573	−	8.69083i	0.340547	−	0.285753i
$926$		0			0
$927$	15.8376	−	0.203372i	0.520175	−	0.00667960i
$928$		0			0
$929$	−4.89711	−	27.7729i	−0.160669	−	0.911199i	−0.953418	−	0.301651i	$-0.902462\pi$
$929$	−4.89711	−	27.7729i	−0.160669	−	0.911199i	0.792749	−	0.609548i	$-0.208649\pi$
$930$		0			0
$931$	−4.22116	+	1.53638i	−0.138343	+	0.0503527i
$932$		0			0
$933$	−22.5085	−	8.02915i	−0.736895	−	0.262863i
$934$		0			0
$935$	8.16226	−	14.1375i	0.266935	−	0.462344i
$936$		0			0
$937$	14.5876	+	25.2665i	0.476557	+	0.825420i	0.999639	−	0.0268618i	$-0.00855142\pi$
$937$	14.5876	+	25.2665i	0.476557	+	0.825420i	−0.523083	+	0.852282i	$0.675218\pi$
$938$		0			0
$939$	−19.0394	+	33.4717i	−0.621327	+	1.09231i
$940$		0			0
$941$	38.6776	+	32.4544i	1.26085	+	1.05798i	0.995591	+	0.0938059i	$0.0299033\pi$
$941$	38.6776	+	32.4544i	1.26085	+	1.05798i	0.265263	+	0.964176i	$0.414541\pi$
$942$		0			0
$943$	−2.98482	−	1.08638i	−0.0971990	−	0.0353775i
$944$		0			0
$945$	−13.7007	+	0.263915i	−0.445683	+	0.00858514i
$946$		0			0
$947$	−13.5776	−	4.94184i	−0.441212	−	0.160588i	0.111855	−	0.993724i	$-0.464321\pi$
$947$	−13.5776	−	4.94184i	−0.441212	−	0.160588i	−0.553068	+	0.833136i	$0.686543\pi$
$948$		0			0
$949$	−8.33691	−	6.99550i	−0.270627	−	0.227083i
$950$		0			0
$951$	−48.3929	+	0.310695i	−1.56925	+	0.0100750i
$952$		0			0
$953$	12.8566	+	22.2682i	0.416465	+	0.721339i	0.995581	−	0.0939063i	$-0.0299354\pi$
$953$	12.8566	+	22.2682i	0.416465	+	0.721339i	−0.579116	+	0.815245i	$0.696602\pi$
$954$		0			0
$955$	26.9747	−	46.7216i	0.872882	−	1.51188i
$956$		0			0
$957$	0.370783	−	0.315203i	0.0119857	−	0.0101891i
$958$		0			0
$959$	3.53433	−	1.28639i	0.114129	−	0.0415397i
$960$		0			0
$961$	−4.46099	−	25.2995i	−0.143903	−	0.816114i
$962$		0			0
$963$	10.6496	+	56.1694i	0.343177	+	1.81003i
$964$		0			0
$965$	16.2264	−	13.6156i	0.522347	−	0.438301i
$966$		0			0
$967$	−2.17176	+	12.3167i	−0.0698391	+	0.396077i	0.929771	+	0.368139i	$0.120005\pi$
$967$	−2.17176	+	12.3167i	−0.0698391	+	0.396077i	−0.999610	+	0.0279377i	$0.991106\pi$
$968$		0			0
$969$	16.9347	+	14.0256i	0.544021	+	0.450568i
$970$		0			0
$971$	−17.3852			−0.557917			−0.278958	−	0.960303i	$-0.589989\pi$
$971$	−17.3852			−0.557917			−0.278958	+	0.960303i	$0.589989\pi$
$972$		0			0
$973$	18.2964			0.586557
$974$		0			0
$975$	−3.10387	−	2.57068i	−0.0994034	−	0.0823276i
$976$		0			0
$977$	−8.19655	+	46.4850i	−0.262231	+	1.48719i	0.514575	+	0.857445i	$0.327950\pi$
$977$	−8.19655	+	46.4850i	−0.262231	+	1.48719i	−0.776806	+	0.629740i	$0.783161\pi$
$978$		0			0
$979$	−0.658872	+	0.552859i	−0.0210576	+	0.0176695i
$980$		0			0
$981$	−4.73221	−	24.9593i	−0.151088	−	0.796888i
$982$		0			0
$983$	−1.92249	−	10.9030i	−0.0613180	−	0.347752i	−0.999996	−	0.00295555i	$-0.999059\pi$
$983$	−1.92249	−	10.9030i	−0.0613180	−	0.347752i	0.938678	−	0.344796i	$-0.112052\pi$
$984$		0			0
$985$	−29.7466	+	10.8269i	−0.947806	+	0.344973i
$986$		0			0
$987$	−11.6046	+	9.86508i	−0.369379	+	0.314009i
$988$		0			0
$989$	−1.30362	+	2.25793i	−0.0414526	+	0.0717979i
$990$		0			0
$991$	−5.05470	−	8.75500i	−0.160568	−	0.278112i	0.774505	−	0.632568i	$-0.217999\pi$
$991$	−5.05470	−	8.75500i	−0.160568	−	0.278112i	−0.935072	+	0.354457i	$0.884666\pi$
$992$		0			0
$993$	−32.1006	+	0.206094i	−1.01868	+	0.00654020i
$994$		0			0
$995$	30.4640	+	25.5623i	0.965774	+	0.810380i
$996$		0			0
$997$	−8.94166	−	3.25450i	−0.283185	−	0.103071i	0.196523	−	0.980499i	$-0.437035\pi$
$997$	−8.94166	−	3.25450i	−0.283185	−	0.103071i	−0.479708	+	0.877428i	$0.659257\pi$
$998$		0			0
$999$	−18.5665	−	30.7737i	−0.587418	−	0.973637i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bo.a.85.7	✓	54
27.7	even	9	inner	756.2.bo.a.169.7	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bo.a.85.7	✓	54	1.1	even	1	trivial
756.2.bo.a.169.7	yes	54	27.7	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33395 + 1.10480i) q^{3} +(-0.457942 + 2.59712i) q^{5} +(0.766044 - 0.642788i) q^{7} +(0.558836 + 2.94749i) q^{9} +O(q^{10})\)	\(q+(1.33395 + 1.10480i) q^{3} +(-0.457942 + 2.59712i) q^{5} +(0.766044 - 0.642788i) q^{7} +(0.558836 + 2.94749i) q^{9} +(0.380345 + 2.15704i) q^{11} +(1.11857 - 0.407125i) q^{13} +(-3.48017 + 2.95849i) q^{15} +(-1.41307 + 2.44750i) q^{17} +(-2.24603 - 3.89024i) q^{19} +(1.73202 - 0.0111200i) q^{21} +(-0.274257 - 0.230129i) q^{23} +(-1.83685 - 0.668560i) q^{25} +(-2.51093 + 4.54920i) q^{27} +(-0.120542 - 0.0438737i) q^{29} +(1.76526 + 1.48123i) q^{31} +(-1.87574 + 3.29759i) q^{33} +(1.31859 + 2.28387i) q^{35} +(-3.45840 + 5.99012i) q^{37} +(1.94190 + 0.692708i) q^{39} +(8.33706 - 3.03444i) q^{41} +(-1.26458 - 7.17177i) q^{43} +(-7.91090 + 0.101584i) q^{45} +(-6.73636 + 5.65248i) q^{47} +(0.173648 - 0.984808i) q^{49} +(-4.58896 + 1.70369i) q^{51} +2.43522 q^{53} -5.77628 q^{55} +(1.30185 - 7.67079i) q^{57} +(-0.856916 + 4.85981i) q^{59} +(-2.91674 + 2.44743i) q^{61} +(2.32270 + 1.89870i) q^{63} +(0.545113 + 3.09149i) q^{65} +(10.6665 - 3.88227i) q^{67} +(-0.111598 - 0.609980i) q^{69} +(6.01954 - 10.4262i) q^{71} +(-4.57136 - 7.91783i) q^{73} +(-1.71164 - 2.92118i) q^{75} +(1.67788 + 1.40791i) q^{77} +(8.54611 + 3.11053i) q^{79} +(-8.37540 + 3.29433i) q^{81} +(8.41863 + 3.06413i) q^{83} +(-5.70935 - 4.79072i) q^{85} +(-0.112325 - 0.191700i) q^{87} +(0.196340 + 0.340072i) q^{89} +(0.595176 - 1.03088i) q^{91} +(0.718303 + 3.92613i) q^{93} +(11.1320 - 4.05171i) q^{95} +(1.08142 + 6.13303i) q^{97} +(-6.14532 + 2.32650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9}+O(q^{10}) \) 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9	\( 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9} - 9 q^{13} + 3 q^{15} - 3 q^{21} - 45 q^{25} + 15 q^{27} + 6 q^{29} - 9 q^{31} + 6 q^{33} + 6 q^{35} + 30 q^{39} + 9 q^{41} + 9 q^{43} - 21 q^{45} - 27 q^{47} - 108 q^{51} - 84 q^{53} - 57 q^{57} - 66 q^{59} + 3 q^{63} + 30 q^{65} + 63 q^{67} + 42 q^{69} + 42 q^{71} + 3 q^{75} - 9 q^{77} + 36 q^{79} + 3 q^{81} + 12 q^{83} + 18 q^{85} + 39 q^{87} + 12 q^{89} + 21 q^{93} + 120 q^{95} + 18 q^{97} + 39 q^{99}+O(q^{100}) \) 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9 - 9 * q^13 + 3 * q^15 - 3 * q^21 - 45 * q^25 + 15 * q^27 + 6 * q^29 - 9 * q^31 + 6 * q^33 + 6 * q^35 + 30 * q^39 + 9 * q^41 + 9 * q^43 - 21 * q^45 - 27 * q^47 - 108 * q^51 - 84 * q^53 - 57 * q^57 - 66 * q^59 + 3 * q^63 + 30 * q^65 + 63 * q^67 + 42 * q^69 + 42 * q^71 + 3 * q^75 - 9 * q^77 + 36 * q^79 + 3 * q^81 + 12 * q^83 + 18 * q^85 + 39 * q^87 + 12 * q^89 + 21 * q^93 + 120 * q^95 + 18 * q^97 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more