LMFDB - Embedded newform 756.2.bo.b.169.5

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			169.5
Character	$\chi$	$=$	756.169
Dual form			756.2.bo.b.85.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.368051 + 1.69249i) q^{3} +(-0.269336 - 1.52748i) q^{5} +(-0.766044 - 0.642788i) q^{7} +(-2.72908 - 1.24585i) q^{9} +O(q^{10})$	\(q+(-0.368051 + 1.69249i) q^{3} +(-0.269336 - 1.52748i) q^{5} +(-0.766044 - 0.642788i) q^{7} +(-2.72908 - 1.24585i) q^{9} +(0.264899 - 1.50232i) q^{11} +(4.53864 + 1.65193i) q^{13} +(2.68438 + 0.106341i) q^{15} +(2.11248 + 3.65892i) q^{17} +(2.93251 - 5.07925i) q^{19} +(1.36986 - 1.05995i) q^{21} +(-2.38034 + 1.99735i) q^{23} +(2.43781 - 0.887289i) q^{25} +(3.11303 - 4.16041i) q^{27} +(6.44544 - 2.34595i) q^{29} +(2.65459 - 2.22746i) q^{31} +(2.44517 + 1.00127i) q^{33} +(-0.775522 + 1.34324i) q^{35} +(3.33103 + 5.76951i) q^{37} +(-4.46633 + 7.07363i) q^{39} +(2.88306 + 1.04935i) q^{41} +(-0.427942 + 2.42698i) q^{43} +(-1.16797 + 4.50416i) q^{45} +(-6.83673 - 5.73670i) q^{47} +(0.173648 + 0.984808i) q^{49} +(-6.97021 + 2.22869i) q^{51} -2.09450 q^{53} -2.36611 q^{55} +(7.51730 + 6.83268i) q^{57} +(-0.513137 - 2.91014i) q^{59} +(3.83080 + 3.21443i) q^{61} +(1.28978 + 2.70859i) q^{63} +(1.30087 - 7.37760i) q^{65} +(10.8207 + 3.93842i) q^{67} +(-2.50441 - 4.76384i) q^{69} +(0.0775777 + 0.134369i) q^{71} +(-3.24631 + 5.62278i) q^{73} +(0.604496 + 4.45254i) q^{75} +(-1.16860 + 0.980569i) q^{77} +(6.52716 - 2.37569i) q^{79} +(5.89572 + 6.80003i) q^{81} +(-9.90258 + 3.60424i) q^{83} +(5.01997 - 4.21225i) q^{85} +(1.59826 + 11.7723i) q^{87} +(8.50356 - 14.7286i) q^{89} +(-2.41496 - 4.18283i) q^{91} +(2.79295 + 5.31270i) q^{93} +(-8.54829 - 3.11132i) q^{95} +(2.87124 - 16.2836i) q^{97} +(-2.59459 + 3.76992i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9}+O(q^{10}) $ 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9	$ 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9} + 9 q^{13} + 3 q^{15} + 3 q^{21} + 12 q^{23} + 27 q^{25} + 39 q^{27} + 30 q^{29} - 9 q^{31} - 6 q^{33} + 6 q^{35} - 18 q^{39} - 27 q^{41} + 9 q^{43} - 81 q^{45} + 9 q^{47} + 12 q^{53} - 21 q^{57} - 24 q^{59} - 3 q^{63} - 78 q^{65} - 9 q^{67} + 6 q^{69} - 30 q^{71} + 57 q^{75} + 9 q^{77} + 99 q^{81} + 78 q^{83} + 18 q^{85} + 21 q^{87} + 12 q^{89} - 51 q^{93} - 36 q^{95} + 36 q^{97} + 15 q^{99}+O(q^{100}) $ 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9 + 9 * q^13 + 3 * q^15 + 3 * q^21 + 12 * q^23 + 27 * q^25 + 39 * q^27 + 30 * q^29 - 9 * q^31 - 6 * q^33 + 6 * q^35 - 18 * q^39 - 27 * q^41 + 9 * q^43 - 81 * q^45 + 9 * q^47 + 12 * q^53 - 21 * q^57 - 24 * q^59 - 3 * q^63 - 78 * q^65 - 9 * q^67 + 6 * q^69 - 30 * q^71 + 57 * q^75 + 9 * q^77 + 99 * q^81 + 78 * q^83 + 18 * q^85 + 21 * q^87 + 12 * q^89 - 51 * q^93 - 36 * q^95 + 36 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$	$1$

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
$3$	−0.368051	+	1.69249i	−0.212494	+	0.977162i
$3$	−0.368051	+	1.69249i	−0.212494	+	0.977162i
$4$		0			0
$5$	−0.269336	−	1.52748i	−0.120451	−	0.683110i	−0.983906	−	0.178685i	$-0.942816\pi$
$5$	−0.269336	−	1.52748i	−0.120451	−	0.683110i	0.863456	−	0.504425i	$-0.168295\pi$
$6$		0			0
$7$	−0.766044	−	0.642788i	−0.289538	−	0.242951i
$7$	−0.766044	−	0.642788i	−0.289538	−	0.242951i
$8$		0			0
$9$	−2.72908	−	1.24585i	−0.909692	−	0.415283i
$10$		0			0
$11$	0.264899	−	1.50232i	0.0798702	−	0.452966i	−0.918476	−	0.395477i	$-0.870579\pi$
$11$	0.264899	−	1.50232i	0.0798702	−	0.452966i	0.998346	−	0.0574894i	$-0.0183095\pi$
$12$		0			0
$13$	4.53864	+	1.65193i	1.25879	+	0.458163i	0.883363	−	0.468689i	$-0.155273\pi$
$13$	4.53864	+	1.65193i	1.25879	+	0.458163i	0.375428	+	0.926852i	$0.377496\pi$
$14$		0			0
$15$	2.68438	+	0.106341i	0.693105	+	0.0274570i
$16$		0			0
$17$	2.11248	+	3.65892i	0.512352	+	0.887419i	0.999897	+	0.0143219i	$0.00455897\pi$
$17$	2.11248	+	3.65892i	0.512352	+	0.887419i	−0.487546	+	0.873098i	$0.662108\pi$
$18$		0			0
$19$	2.93251	−	5.07925i	0.672763	−	1.16526i	−0.304354	−	0.952559i	$-0.598441\pi$
$19$	2.93251	−	5.07925i	0.672763	−	1.16526i	0.977117	−	0.212701i	$-0.0682261\pi$
$20$		0			0
$21$	1.36986	−	1.05995i	0.298928	−	0.231300i
$22$		0			0
$23$	−2.38034	+	1.99735i	−0.496336	+	0.416475i	−0.856290	−	0.516495i	$-0.827237\pi$
$23$	−2.38034	+	1.99735i	−0.496336	+	0.416475i	0.359955	+	0.932970i	$0.382792\pi$
$24$		0			0
$25$	2.43781	−	0.887289i	0.487562	−	0.177458i
$26$		0			0
$27$	3.11303	−	4.16041i	0.599103	−	0.800672i
$28$		0			0
$29$	6.44544	−	2.34595i	1.19689	−	0.435632i	0.334751	−	0.942307i	$-0.391348\pi$
$29$	6.44544	−	2.34595i	1.19689	−	0.435632i	0.862137	+	0.506675i	$0.169125\pi$
$30$		0			0
$31$	2.65459	−	2.22746i	0.476778	−	0.400064i	−0.372482	−	0.928040i	$-0.621493\pi$
$31$	2.65459	−	2.22746i	0.476778	−	0.400064i	0.849260	+	0.527975i	$0.177049\pi$
$32$		0			0
$33$	2.44517	+	1.00127i	0.425650	+	0.174299i
$34$		0			0
$35$	−0.775522	+	1.34324i	−0.131087	+	0.227050i
$36$		0			0
$37$	3.33103	+	5.76951i	0.547618	+	0.948502i	0.998437	+	0.0558870i	$0.0177986\pi$
$37$	3.33103	+	5.76951i	0.547618	+	0.948502i	−0.450819	+	0.892615i	$0.648868\pi$
$38$		0			0
$39$	−4.46633	+	7.07363i	−0.715185	+	1.13269i
$40$		0			0
$41$	2.88306	+	1.04935i	0.450258	+	0.163881i	0.557189	−	0.830386i	$-0.311880\pi$
$41$	2.88306	+	1.04935i	0.450258	+	0.163881i	−0.106930	+	0.994267i	$0.534102\pi$
$42$		0			0
$43$	−0.427942	+	2.42698i	−0.0652606	+	0.370111i	0.934634	+	0.355610i	$0.115727\pi$
$43$	−0.427942	+	2.42698i	−0.0652606	+	0.370111i	−0.999895	+	0.0145007i	$0.995384\pi$
$44$		0			0
$45$	−1.16797	+	4.50416i	−0.174111	+	0.671441i
$46$		0			0
$47$	−6.83673	−	5.73670i	−0.997240	−	0.836783i	−0.0106399	−	0.999943i	$-0.503387\pi$
$47$	−6.83673	−	5.73670i	−0.997240	−	0.836783i	−0.986600	+	0.163160i	$0.947831\pi$
$48$		0			0
$49$	0.173648	+	0.984808i	0.0248069	+	0.140687i
$50$		0			0
$51$	−6.97021	+	2.22869i	−0.976025	+	0.312079i
$52$		0			0
$53$	−2.09450			−0.287701			−0.143851	−	0.989599i	$-0.545948\pi$
$53$	−2.09450			−0.287701			−0.143851	+	0.989599i	$0.545948\pi$
$54$		0			0
$55$	−2.36611			−0.319046
$56$		0			0
$57$	7.51730	+	6.83268i	0.995690	+	0.905010i
$58$		0			0
$59$	−0.513137	−	2.91014i	−0.0668047	−	0.378868i	−0.999819	−	0.0190289i	$-0.993943\pi$
$59$	−0.513137	−	2.91014i	−0.0668047	−	0.378868i	0.933014	−	0.359840i	$-0.117169\pi$
$60$		0			0
$61$	3.83080	+	3.21443i	0.490484	+	0.411565i	0.854200	−	0.519945i	$-0.174048\pi$
$61$	3.83080	+	3.21443i	0.490484	+	0.411565i	−0.363716	+	0.931510i	$0.618492\pi$
$62$		0			0
$63$	1.28978	+	2.70859i	0.162497	+	0.341251i
$64$		0			0
$65$	1.30087	−	7.37760i	0.161353	−	0.915079i
$66$		0			0
$67$	10.8207	+	3.93842i	1.32196	+	0.481155i	0.904087	−	0.427349i	$-0.140552\pi$
$67$	10.8207	+	3.93842i	1.32196	+	0.481155i	0.417876	+	0.908504i	$0.362775\pi$
$68$		0			0
$69$	−2.50441	−	4.76384i	−0.301495	−	0.573499i
$70$		0			0
$71$	0.0775777	+	0.134369i	0.00920678	+	0.0159466i	0.870592	−	0.492006i	$-0.163736\pi$
$71$	0.0775777	+	0.134369i	0.00920678	+	0.0159466i	−0.861385	+	0.507952i	$0.830403\pi$
$72$		0			0
$73$	−3.24631	+	5.62278i	−0.379952	+	0.658096i	−0.991055	−	0.133455i	$-0.957393\pi$
$73$	−3.24631	+	5.62278i	−0.379952	+	0.658096i	0.611103	+	0.791551i	$0.290726\pi$
$74$		0			0
$75$	0.604496	+	4.45254i	0.0698011	+	0.514136i
$76$		0			0
$77$	−1.16860	+	0.980569i	−0.133174	+	0.111746i
$78$		0			0
$79$	6.52716	−	2.37569i	0.734363	−	0.267286i	0.0523524	−	0.998629i	$-0.483328\pi$
$79$	6.52716	−	2.37569i	0.734363	−	0.267286i	0.682010	+	0.731342i	$0.261106\pi$
$80$		0			0
$81$	5.89572	+	6.80003i	0.655080	+	0.755559i
$82$		0			0
$83$	−9.90258	+	3.60424i	−1.08695	+	0.395617i	−0.822490	−	0.568780i	$-0.807416\pi$
$83$	−9.90258	+	3.60424i	−1.08695	+	0.395617i	−0.264459	+	0.964397i	$0.585193\pi$
$84$		0			0
$85$	5.01997	−	4.21225i	0.544492	−	0.456883i
$86$		0			0
$87$	1.59826	+	11.7723i	0.171351	+	1.26212i
$88$		0			0
$89$	8.50356	−	14.7286i	0.901375	−	1.56123i	0.0756649	−	0.997133i	$-0.475892\pi$
$89$	8.50356	−	14.7286i	0.901375	−	1.56123i	0.825710	−	0.564094i	$-0.190775\pi$
$90$		0			0
$91$	−2.41496	−	4.18283i	−0.253156	−	0.438480i
$92$		0			0
$93$	2.79295	+	5.31270i	0.289615	+	0.550901i
$94$		0			0
$95$	−8.54829	−	3.11132i	−0.877036	−	0.319215i
$96$		0			0
$97$	2.87124	−	16.2836i	0.291530	−	1.65335i	−0.389451	−	0.921047i	$-0.627335\pi$
$97$	2.87124	−	16.2836i	0.291530	−	1.65335i	0.680981	−	0.732301i	$-0.261554\pi$
$98$		0			0
$99$	−2.59459	+	3.76992i	−0.260766	+	0.378891i
$100$		0			0
$101$	−9.99484	−	8.38667i	−0.994524	−	0.834505i	−0.00830766	−	0.999965i	$-0.502644\pi$
$101$	−9.99484	−	8.38667i	−0.994524	−	0.834505i	−0.986216	+	0.165461i	$0.947089\pi$
$102$		0			0
$103$	−0.309350	−	1.75441i	−0.0304812	−	0.172867i	0.965767	−	0.259412i	$-0.0835287\pi$
$103$	−0.309350	−	1.75441i	−0.0304812	−	0.172867i	−0.996248	+	0.0865444i	$0.972418\pi$
$104$		0			0
$105$	−1.98800	−	1.80695i	−0.194009	−	0.176340i
$106$		0			0
$107$	−5.46443			−0.528266			−0.264133	−	0.964486i	$-0.585086\pi$
$107$	−5.46443			−0.528266			−0.264133	+	0.964486i	$0.585086\pi$
$108$		0			0
$109$	−10.3244			−0.988902			−0.494451	−	0.869205i	$-0.664631\pi$
$109$	−10.3244			−0.988902			−0.494451	+	0.869205i	$0.664631\pi$
$110$		0			0
$111$	−10.9909	+	3.51428i	−1.04321	+	0.333560i
$112$		0			0
$113$	2.95349	+	16.7501i	0.277841	+	1.57572i	0.729790	+	0.683672i	$0.239618\pi$
$113$	2.95349	+	16.7501i	0.277841	+	1.57572i	−0.451948	+	0.892044i	$0.649271\pi$
$114$		0			0
$115$	3.69202	+	3.09797i	0.344282	+	0.288887i
$116$		0			0
$117$	−10.3282	−	10.1627i	−0.954846	−	0.939541i
$118$		0			0
$119$	0.733657	−	4.16078i	0.0672542	−	0.381418i
$120$		0			0
$121$	8.14983	+	2.96630i	0.740894	+	0.269663i
$122$		0			0
$123$	−2.83713	+	4.49335i	−0.255815	+	0.405152i
$124$		0			0
$125$	−5.88952	−	10.2009i	−0.526775	−	0.912400i
$126$		0			0
$127$	3.25320	−	5.63471i	0.288675	−	0.499999i	−0.684819	−	0.728713i	$-0.740119\pi$
$127$	3.25320	−	5.63471i	0.288675	−	0.499999i	0.973494	+	0.228714i	$0.0734521\pi$
$128$		0			0
$129$	−3.95015	−	1.61754i	−0.347791	−	0.142417i
$130$		0			0
$131$	−1.09870	+	0.921918i	−0.0959938	+	0.0805484i	−0.689522	−	0.724265i	$-0.742179\pi$
$131$	−1.09870	+	0.921918i	−0.0959938	+	0.0805484i	0.593528	+	0.804814i	$0.297735\pi$
$132$		0			0
$133$	−5.51131	+	2.00595i	−0.477891	+	0.173938i
$134$		0			0
$135$	−7.19340	−	3.63455i	−0.619110	−	0.312812i
$136$		0			0
$137$	5.21956	−	1.89976i	0.445937	−	0.162308i	−0.109284	−	0.994011i	$-0.534856\pi$
$137$	5.21956	−	1.89976i	0.445937	−	0.162308i	0.555221	+	0.831703i	$0.312634\pi$
$138$		0			0
$139$	−5.21809	+	4.37850i	−0.442593	+	0.371379i	−0.836679	−	0.547694i	$-0.815506\pi$
$139$	−5.21809	+	4.37850i	−0.442593	+	0.371379i	0.394086	+	0.919074i	$0.371061\pi$
$140$		0			0
$141$	12.2256	−	9.45973i	1.02958	−	0.796653i
$142$		0			0
$143$	3.68401	−	6.38088i	0.308072	−	0.533596i
$144$		0			0
$145$	−5.31938	−	9.21344i	−0.441751	−	0.765135i
$146$		0			0
$147$	−1.73069	−	0.0685607i	−0.142745	−	0.00565479i
$148$		0			0
$149$	−22.5472	−	8.20650i	−1.84714	−	0.672303i	−0.986656	−	0.162821i	$-0.947941\pi$
$149$	−22.5472	−	8.20650i	−1.84714	−	0.672303i	−0.860482	−	0.509482i	$-0.829837\pi$
$150$		0			0
$151$	1.90907	−	10.8269i	0.155358	−	0.881079i	−0.803100	−	0.595844i	$-0.796818\pi$
$151$	1.90907	−	10.8269i	0.155358	−	0.881079i	0.958458	−	0.285234i	$-0.0920714\pi$
$152$		0			0
$153$	−1.20666	−	12.6173i	−0.0975526	−	1.02005i
$154$		0			0
$155$	−4.11739	−	3.45490i	−0.330716	−	0.277504i
$156$		0			0
$157$	2.56606	+	14.5529i	0.204794	+	1.16144i	0.897764	+	0.440478i	$0.145191\pi$
$157$	2.56606	+	14.5529i	0.204794	+	1.16144i	−0.692969	+	0.720967i	$0.743698\pi$
$158$		0			0
$159$	0.770881	−	3.54492i	0.0611348	−	0.281131i
$160$		0			0
$161$	3.10732			0.244891
$162$		0			0
$163$	−12.8919			−1.00978			−0.504888	−	0.863185i	$-0.668466\pi$
$163$	−12.8919			−1.00978			−0.504888	+	0.863185i	$0.668466\pi$
$164$		0			0
$165$	0.870849	−	4.00463i	0.0677955	−	0.311760i
$166$		0			0
$167$	0.00280226	+	0.0158924i	0.000216845	+	0.00122979i	0.984916	−	0.173033i	$-0.0553568\pi$
$167$	0.00280226	+	0.0158924i	0.000216845	+	0.00122979i	−0.984699	+	0.174263i	$0.944246\pi$
$168$		0			0
$169$	7.91178	+	6.63877i	0.608598	+	0.510675i
$170$		0			0
$171$	−14.3310	+	10.2082i	−1.09592	+	0.780641i
$172$		0			0
$173$	1.81006	−	10.2654i	0.137616	−	0.780460i	−0.835386	−	0.549664i	$-0.814756\pi$
$173$	1.81006	−	10.2654i	0.137616	−	0.780460i	0.973002	−	0.230796i	$-0.0741331\pi$
$174$		0			0
$175$	−2.43781	−	0.887289i	−0.184281	−	0.0670728i
$176$		0			0
$177$	5.11426	+	0.202599i	0.384412	+	0.0152283i
$178$		0			0
$179$	8.78305	+	15.2127i	0.656476	+	1.13705i	0.981522	+	0.191351i	$0.0612869\pi$
$179$	8.78305	+	15.2127i	0.656476	+	1.13705i	−0.325046	+	0.945698i	$0.605380\pi$
$180$		0			0
$181$	2.70741	−	4.68938i	0.201240	−	0.348559i	−0.747688	−	0.664050i	$-0.768836\pi$
$181$	2.70741	−	4.68938i	0.201240	−	0.348559i	0.948928	+	0.315492i	$0.102169\pi$
$182$		0			0
$183$	−6.85033	+	5.30054i	−0.506391	+	0.391827i
$184$		0			0
$185$	7.91566	−	6.64202i	0.581971	−	0.488331i
$186$		0			0
$187$	6.05647	−	2.20437i	0.442893	−	0.161200i
$188$		0			0
$189$	−5.05898	+	1.18604i	−0.367987	+	0.0862720i
$190$		0			0
$191$	−1.64737	+	0.599593i	−0.119199	+	0.0433851i	−0.400931	−	0.916108i	$-0.631313\pi$
$191$	−1.64737	+	0.599593i	−0.119199	+	0.0433851i	0.281732	+	0.959493i	$0.409091\pi$
$192$		0			0
$193$	−13.2067	+	11.0818i	−0.950641	+	0.797682i	−0.979405	−	0.201904i	$-0.935287\pi$
$193$	−13.2067	+	11.0818i	−0.950641	+	0.797682i	0.0287644	+	0.999586i	$0.490843\pi$
$194$		0			0
$195$	12.0078	+	4.91705i	0.859894	+	0.352117i
$196$		0			0
$197$	−4.25126	+	7.36340i	−0.302890	+	0.524620i	−0.976789	−	0.214203i	$-0.931285\pi$
$197$	−4.25126	+	7.36340i	−0.302890	+	0.524620i	0.673900	+	0.738823i	$0.264618\pi$
$198$		0			0
$199$	4.15926	+	7.20405i	0.294842	+	0.510682i	0.974948	−	0.222432i	$-0.0713996\pi$
$199$	4.15926	+	7.20405i	0.294842	+	0.510682i	−0.680106	+	0.733114i	$0.738066\pi$
$200$		0			0
$201$	−10.6483	+	16.8645i	−0.751076	+	1.18953i
$202$		0			0
$203$	−6.44544	−	2.34595i	−0.452381	−	0.164653i
$204$		0			0
$205$	0.826347	−	4.68645i	0.0577146	−	0.327316i
$206$		0			0
$207$	8.98453	−	2.48536i	0.624468	−	0.172745i
$208$		0			0
$209$	−6.85384	−	5.75105i	−0.474090	−	0.397809i
$210$		0			0
$211$	3.31208	+	18.7837i	0.228013	+	1.29313i	0.856841	+	0.515581i	$0.172424\pi$
$211$	3.31208	+	18.7837i	0.228013	+	1.29313i	−0.628828	+	0.777544i	$0.716465\pi$
$212$		0			0
$213$	−0.255971	+	0.0818454i	−0.0175388	+	0.00560795i
$214$		0			0
$215$	3.82243			0.260687
$216$		0			0
$217$	−3.46532			−0.235241
$218$		0			0
$219$	−8.32171	−	7.56384i	−0.562329	−	0.511117i
$220$		0			0
$221$	3.54350	+	20.0962i	0.238362	+	1.35182i
$222$		0			0
$223$	−13.0272	−	10.9312i	−0.872369	−	0.732004i	0.0922267	−	0.995738i	$-0.470602\pi$
$223$	−13.0272	−	10.9312i	−0.872369	−	0.732004i	−0.964596	+	0.263734i	$0.915046\pi$
$224$		0			0
$225$	−7.75839	−	0.615657i	−0.517226	−	0.0410438i
$226$		0			0
$227$	2.39049	−	13.5572i	0.158663	−	0.899820i	−0.796698	−	0.604378i	$-0.793422\pi$
$227$	2.39049	−	13.5572i	0.158663	−	0.899820i	0.955361	−	0.295442i	$-0.0954670\pi$
$228$		0			0
$229$	−18.2720	−	6.65047i	−1.20745	−	0.439476i	−0.341631	−	0.939834i	$-0.610979\pi$
$229$	−18.2720	−	6.65047i	−1.20745	−	0.439476i	−0.865818	+	0.500359i	$0.833201\pi$
$230$		0			0
$231$	−1.22950	−	2.33874i	−0.0808955	−	0.153878i
$232$		0			0
$233$	3.94579	+	6.83430i	0.258497	+	0.447730i	0.965840	−	0.259141i	$-0.0834394\pi$
$233$	3.94579	+	6.83430i	0.258497	+	0.447730i	−0.707342	+	0.706871i	$0.750106\pi$
$234$		0			0
$235$	−6.92132	+	11.9881i	−0.451497	+	0.782016i
$236$		0			0
$237$	1.61852	+	11.9216i	0.105134	+	0.774389i
$238$		0			0
$239$	−11.7746	+	9.88005i	−0.761635	+	0.639087i	−0.938552	−	0.345138i	$-0.887832\pi$
$239$	−11.7746	+	9.88005i	−0.761635	+	0.639087i	0.176917	+	0.984226i	$0.443388\pi$
$240$		0			0
$241$	28.7105	−	10.4498i	1.84941	−	0.673129i	0.863860	−	0.503733i	$-0.168040\pi$
$241$	28.7105	−	10.4498i	1.84941	−	0.673129i	0.985548	−	0.169397i	$-0.0541819\pi$
$242$		0			0
$243$	−13.6789	+	7.47573i	−0.877505	+	0.479568i
$244$		0			0
$245$	1.45751	−	0.530488i	0.0931166	−	0.0338917i
$246$		0			0
$247$	21.7002	−	18.2086i	1.38075	−	1.15858i
$248$		0			0
$249$	−2.45551	−	18.0866i	−0.155612	−	1.14619i
$250$		0			0
$251$	−13.9785	+	24.2114i	−0.882313	+	1.52821i	−0.0335511	+	0.999437i	$0.510682\pi$
$251$	−13.9785	+	24.2114i	−0.882313	+	1.52821i	−0.848762	+	0.528775i	$0.822652\pi$
$252$		0			0
$253$	2.37010	+	4.10513i	0.149007	+	0.258087i
$254$		0			0
$255$	5.28161	+	10.0466i	0.330748	+	0.629142i
$256$		0			0
$257$	−11.0736	−	4.03048i	−0.690755	−	0.251414i	−0.0272965	−	0.999627i	$-0.508690\pi$
$257$	−11.0736	−	4.03048i	−0.690755	−	0.251414i	−0.663458	+	0.748213i	$0.730912\pi$
$258$		0			0
$259$	1.15685	−	6.56085i	0.0718835	−	0.407671i
$260$		0			0
$261$	−20.5128	−	1.62777i	−1.26971	−	0.100756i
$262$		0			0
$263$	−4.00025	−	3.35661i	−0.246666	−	0.206977i	0.511069	−	0.859540i	$-0.329250\pi$
$263$	−4.00025	−	3.35661i	−0.246666	−	0.206977i	−0.757735	+	0.652562i	$0.773694\pi$
$264$		0			0
$265$	0.564123	+	3.19930i	0.0346538	+	0.196532i
$266$		0			0
$267$	21.7983	+	19.8131i	1.33404	+	1.21254i
$268$		0			0
$269$	25.4580			1.55220			0.776100	−	0.630610i	$-0.217195\pi$
$269$	25.4580			1.55220			0.776100	+	0.630610i	$0.217195\pi$
$270$		0			0
$271$	−4.19246			−0.254674			−0.127337	−	0.991860i	$-0.540643\pi$
$271$	−4.19246			−0.254674			−0.127337	+	0.991860i	$0.540643\pi$
$272$		0			0
$273$	7.96825	−	2.54781i	0.482260	−	0.154200i
$274$		0			0
$275$	−0.687218	−	3.89741i	−0.0414408	−	0.235022i
$276$		0			0
$277$	−13.3554	−	11.2065i	−0.802450	−	0.673336i	0.146343	−	0.989234i	$-0.453250\pi$
$277$	−13.3554	−	11.2065i	−0.802450	−	0.673336i	−0.948793	+	0.315898i	$0.897694\pi$
$278$		0			0
$279$	−10.0197	+	2.77171i	−0.599861	+	0.165938i
$280$		0			0
$281$	−5.22111	+	29.6104i	−0.311465	+	1.76641i	0.279925	+	0.960022i	$0.409690\pi$
$281$	−5.22111	+	29.6104i	−0.311465	+	1.76641i	−0.591390	+	0.806385i	$0.701421\pi$
$282$		0			0
$283$	24.4347	+	8.89351i	1.45249	+	0.528664i	0.943287	−	0.331980i	$-0.107716\pi$
$283$	24.4347	+	8.89351i	1.45249	+	0.528664i	0.509207	+	0.860644i	$0.329939\pi$
$284$		0			0
$285$	8.41210	−	13.3228i	0.498290	−	0.789175i
$286$		0			0
$287$	−1.53404	−	2.65704i	−0.0905518	−	0.156840i
$288$		0			0
$289$	−0.425151	+	0.736383i	−0.0250089	+	0.0433167i
$290$		0			0
$291$	26.5031	+	10.8527i	1.55364	+	0.636199i
$292$		0			0
$293$	10.3354	−	8.67240i	0.603798	−	0.506647i	−0.288866	−	0.957370i	$-0.593278\pi$
$293$	10.3354	−	8.67240i	0.603798	−	0.506647i	0.892664	+	0.450723i	$0.148834\pi$
$294$		0			0
$295$	−4.30698	+	1.56761i	−0.250762	+	0.0912700i
$296$		0			0
$297$	−5.42563	−	5.77886i	−0.314827	−	0.335323i
$298$		0			0
$299$	−14.1030	+	5.13307i	−0.815597	+	0.296853i
$300$		0			0
$301$	1.88786	−	1.58410i	0.108814	−	0.0913060i
$302$		0			0
$303$	17.8730	−	13.8295i	1.02678	−	0.794484i
$304$		0			0
$305$	3.87820	−	6.71724i	0.222065	−	0.384628i
$306$		0			0
$307$	6.30677	+	10.9236i	0.359946	+	0.623446i	0.987952	−	0.154764i	$-0.0494616\pi$
$307$	6.30677	+	10.9236i	0.359946	+	0.623446i	−0.628005	+	0.778209i	$0.716128\pi$
$308$		0			0
$309$	3.08319	+	0.122139i	0.175397	+	0.00694826i
$310$		0			0
$311$	−17.8984	−	6.51449i	−1.01493	−	0.369403i	−0.219604	−	0.975589i	$-0.570476\pi$
$311$	−17.8984	−	6.51449i	−1.01493	−	0.369403i	−0.795323	+	0.606186i	$0.792699\pi$
$312$		0			0
$313$	−1.60629	+	9.10973i	−0.0907929	+	0.514912i	0.905163	+	0.425065i	$0.139749\pi$
$313$	−1.60629	+	9.10973i	−0.0907929	+	0.514912i	−0.995956	+	0.0898470i	$0.971362\pi$
$314$		0			0
$315$	3.78994	−	2.69963i	0.213539	−	0.152107i
$316$		0			0
$317$	14.3035	+	12.0020i	0.803364	+	0.674102i	0.949014	−	0.315234i	$-0.102083\pi$
$317$	14.3035	+	12.0020i	0.803364	+	0.674102i	−0.145650	+	0.989336i	$0.546527\pi$
$318$		0			0
$319$	−1.81697	−	10.3045i	−0.101731	−	0.576944i
$320$		0			0
$321$	2.01119	−	9.24852i	0.112254	−	0.516202i
$322$		0			0
$323$	24.7795			1.37877
$324$		0			0
$325$	12.5301			0.695043
$326$		0			0
$327$	3.79992	−	17.4741i	0.210136	−	0.966318i
$328$		0			0
$329$	1.54976	+	8.78913i	0.0854411	+	0.484560i
$330$		0			0
$331$	−8.35670	−	7.01211i	−0.459326	−	0.385420i	0.383557	−	0.923517i	$-0.374699\pi$
$331$	−8.35670	−	7.01211i	−0.459326	−	0.385420i	−0.842883	+	0.538097i	$0.819143\pi$
$332$		0			0
$333$	−1.90270	−	19.8954i	−0.104267	−	1.09026i
$334$		0			0
$335$	3.10145	−	17.5892i	0.169451	−	0.961002i
$336$		0			0
$337$	3.94105	+	1.43443i	0.214683	+	0.0781382i	0.447123	−	0.894473i	$-0.352449\pi$
$337$	3.94105	+	1.43443i	0.214683	+	0.0781382i	−0.232440	+	0.972611i	$0.574671\pi$
$338$		0			0
$339$	−29.4365	−	1.16611i	−1.59877	−	0.0633346i
$340$		0			0
$341$	−2.64316	−	4.57809i	−0.143135	−	0.247918i
$342$		0			0
$343$	0.500000	−	0.866025i	0.0269975	−	0.0467610i
$344$		0			0
$345$	−6.60215	+	5.10851i	−0.355448	+	0.275033i
$346$		0			0
$347$	−7.77628	+	6.52507i	−0.417453	+	0.350284i	−0.827193	−	0.561918i	$-0.810064\pi$
$347$	−7.77628	+	6.52507i	−0.417453	+	0.350284i	0.409740	+	0.912202i	$0.365619\pi$
$348$		0			0
$349$	−7.47519	+	2.72075i	−0.400138	+	0.145638i	−0.534247	−	0.845328i	$-0.679405\pi$
$349$	−7.47519	+	2.72075i	−0.400138	+	0.145638i	0.134109	+	0.990967i	$0.457183\pi$
$350$		0			0
$351$	21.0016	−	13.7401i	1.12098	−	0.733392i
$352$		0			0
$353$	25.9697	−	9.45220i	1.38223	−	0.503090i	0.459375	−	0.888242i	$-0.348073\pi$
$353$	25.9697	−	9.45220i	1.38223	−	0.503090i	0.922853	+	0.385152i	$0.125851\pi$
$354$		0			0
$355$	0.184351	−	0.154689i	0.00978433	−	0.00821002i
$356$		0			0
$357$	6.77207	+	2.77309i	0.358416	+	0.146767i
$358$		0			0
$359$	8.58661	−	14.8724i	0.453184	−	0.784937i	−0.545398	−	0.838177i	$-0.683621\pi$
$359$	8.58661	−	14.8724i	0.453184	−	0.784937i	0.998582	+	0.0532398i	$0.0169548\pi$
$360$		0			0
$361$	−7.69920	−	13.3354i	−0.405221	−	0.701864i
$362$		0			0
$363$	−8.01999	+	12.7018i	−0.420940	+	0.666671i
$364$		0			0
$365$	9.46303	+	3.44426i	0.495318	+	0.180281i
$366$		0			0
$367$	0.918573	−	5.20949i	0.0479491	−	0.271933i	−0.951402	−	0.307952i	$-0.900356\pi$
$367$	0.918573	−	5.20949i	0.0479491	−	0.271933i	0.999351	+	0.0360186i	$0.0114676\pi$
$368$		0			0
$369$	−6.56077	−	6.45561i	−0.341540	−	0.336066i
$370$		0			0
$371$	1.60448	+	1.34632i	0.0833003	+	0.0698972i
$372$		0			0
$373$	2.91203	+	16.5149i	0.150779	+	0.855111i	0.962544	+	0.271126i	$0.0873962\pi$
$373$	2.91203	+	16.5149i	0.150779	+	0.855111i	−0.811765	+	0.583985i	$0.801493\pi$
$374$		0			0
$375$	19.4327	−	6.21351i	1.00350	−	0.320864i
$376$		0			0
$377$	33.1289			1.70622
$378$		0			0
$379$	−32.2956			−1.65892			−0.829458	−	0.558569i	$-0.811351\pi$
$379$	−32.2956			−1.65892			−0.829458	+	0.558569i	$0.811351\pi$
$380$		0			0
$381$	8.33937	+	7.57988i	0.427239	+	0.388329i
$382$		0			0
$383$	5.39376	+	30.5896i	0.275609	+	1.56305i	0.737022	+	0.675868i	$0.236231\pi$
$383$	5.39376	+	30.5896i	0.275609	+	1.56305i	−0.461414	+	0.887185i	$0.652658\pi$
$384$		0			0
$385$	1.81255	+	1.52091i	0.0923759	+	0.0775126i
$386$		0			0
$387$	4.19154	−	6.09027i	0.213068	−	0.309586i
$388$		0			0
$389$	−2.81514	+	15.9655i	−0.142733	+	0.809482i	0.826426	+	0.563046i	$0.190371\pi$
$389$	−2.81514	+	15.9655i	−0.142733	+	0.809482i	−0.969159	+	0.246436i	$0.920741\pi$
$390$		0			0
$391$	−12.3366	−	4.49014i	−0.623887	−	0.227076i
$392$		0			0
$393$	−1.15596	−	2.19886i	−0.0583107	−	0.110918i
$394$		0			0
$395$	−5.38682	−	9.33025i	−0.271040	−	0.469456i
$396$		0			0
$397$	−8.96366	+	15.5255i	−0.449873	+	0.779203i	−0.998377	−	0.0569447i	$-0.981864\pi$
$397$	−8.96366	+	15.5255i	−0.449873	+	0.779203i	0.548504	+	0.836148i	$0.315197\pi$
$398$		0			0
$399$	−1.36662	−	10.0662i	−0.0684167	−	0.503938i
$400$		0			0
$401$	25.3981	−	21.3115i	1.26832	−	1.06425i	0.273575	−	0.961851i	$-0.411794\pi$
$401$	25.3981	−	21.3115i	1.26832	−	1.06425i	0.994744	−	0.102396i	$-0.0326508\pi$
$402$		0			0
$403$	15.7278	−	5.72446i	0.783459	−	0.285156i
$404$		0			0
$405$	8.79899	−	10.8371i	0.437225	−	0.538500i
$406$		0			0
$407$	9.55004	−	3.47593i	0.473378	−	0.172295i
$408$		0			0
$409$	−25.3123	+	21.2396i	−1.25161	+	1.05023i	−0.255090	+	0.966917i	$0.582105\pi$
$409$	−25.3123	+	21.2396i	−1.25161	+	1.05023i	−0.996524	+	0.0833112i	$0.973450\pi$
$410$		0			0
$411$	1.29428	+	9.53329i	0.0638420	+	0.470242i
$412$		0			0
$413$	−1.47752	+	2.55914i	−0.0727039	+	0.125927i
$414$		0			0
$415$	8.17253	+	14.1552i	0.401174	+	0.694854i
$416$		0			0
$417$	−5.49006	−	10.4431i	−0.268850	−	0.511401i
$418$		0			0
$419$	−21.4224	−	7.79712i	−1.04655	−	0.380914i	−0.239193	−	0.970972i	$-0.576883\pi$
$419$	−21.4224	−	7.79712i	−1.04655	−	0.380914i	−0.807361	+	0.590058i	$0.799105\pi$
$420$		0			0
$421$	2.06621	−	11.7180i	0.100701	−	0.571102i	−0.892150	−	0.451739i	$-0.850804\pi$
$421$	2.06621	−	11.7180i	0.100701	−	0.571102i	0.992851	−	0.119363i	$-0.0380851\pi$
$422$		0			0
$423$	11.5109	+	24.1734i	0.559680	+	1.17535i
$424$		0			0
$425$	8.39635	+	7.04537i	0.407283	+	0.341751i
$426$		0			0
$427$	−0.868373	−	4.92479i	−0.0420235	−	0.238327i
$428$		0			0
$429$	9.44371	+	8.58365i	0.455947	+	0.414423i
$430$		0			0
$431$	27.3252			1.31621			0.658105	−	0.752926i	$-0.271358\pi$
$431$	27.3252			1.31621			0.658105	+	0.752926i	$0.271358\pi$
$432$		0			0
$433$	−25.2285			−1.21240			−0.606201	−	0.795311i	$-0.707307\pi$
$433$	−25.2285			−1.21240			−0.606201	+	0.795311i	$0.707307\pi$
$434$		0			0
$435$	17.5515	−	5.61201i	0.841530	−	0.269075i
$436$		0			0
$437$	3.16464	+	17.9476i	0.151385	+	0.858550i
$438$		0			0
$439$	−5.67938	−	4.76556i	−0.271062	−	0.227448i	0.497117	−	0.867684i	$-0.334392\pi$
$439$	−5.67938	−	4.76556i	−0.271062	−	0.227448i	−0.768178	+	0.640236i	$0.778837\pi$
$440$		0			0
$441$	0.753022	−	2.90396i	0.0358582	−	0.138284i
$442$		0			0
$443$	2.23458	−	12.6729i	0.106168	−	0.602110i	−0.884579	−	0.466390i	$-0.845554\pi$
$443$	2.23458	−	12.6729i	0.106168	−	0.602110i	0.990747	−	0.135719i	$-0.0433346\pi$
$444$		0			0
$445$	−24.7880	−	9.02208i	−1.17506	−	0.427688i
$446$		0			0
$447$	22.1880	−	35.1406i	1.04946	−	1.66209i
$448$		0			0
$449$	10.6279	+	18.4081i	0.501562	+	0.868731i	0.999998	+	0.00180449i	$0.000574387\pi$
$449$	10.6279	+	18.4081i	0.501562	+	0.868731i	−0.498436	+	0.866926i	$0.666092\pi$
$450$		0			0
$451$	2.34018	−	4.05330i	0.110195	−	0.190863i
$452$		0			0
$453$	17.6218	+	7.21593i	0.827944	+	0.339034i
$454$		0			0
$455$	−5.73876	+	4.81539i	−0.269037	+	0.225749i
$456$		0			0
$457$	−12.0146	+	4.37296i	−0.562020	+	0.204559i	−0.607379	−	0.794412i	$-0.707779\pi$
$457$	−12.0146	+	4.37296i	−0.562020	+	0.204559i	0.0453589	+	0.998971i	$0.485557\pi$
$458$		0			0
$459$	21.7989	+	2.60155i	1.01748	+	0.121430i
$460$		0			0
$461$	−15.6075	+	5.68067i	−0.726914	+	0.264575i	−0.678858	−	0.734270i	$-0.737525\pi$
$461$	−15.6075	+	5.68067i	−0.726914	+	0.264575i	−0.0480560	+	0.998845i	$0.515303\pi$
$462$		0			0
$463$	−1.25731	+	1.05501i	−0.0584320	+	0.0490303i	−0.671536	−	0.740972i	$-0.734365\pi$
$463$	−1.25731	+	1.05501i	−0.0584320	+	0.0490303i	0.613104	+	0.790002i	$0.289921\pi$
$464$		0			0
$465$	7.36280	−	5.69708i	0.341442	−	0.264196i
$466$		0			0
$467$	4.01226	−	6.94943i	0.185665	−	0.321581i	−0.758135	−	0.652097i	$-0.773889\pi$
$467$	4.01226	−	6.94943i	0.185665	−	0.321581i	0.943800	+	0.330516i	$0.107223\pi$
$468$		0			0
$469$	−5.75759	−	9.97244i	−0.265861	−	0.460484i
$470$		0			0
$471$	−25.5751	−	1.01315i	−1.17844	−	0.0466833i
$472$		0			0
$473$	3.53274	+	1.28581i	0.162435	+	0.0591217i
$474$		0			0
$475$	2.64212	−	14.9842i	0.121229	−	0.687523i
$476$		0			0
$477$	5.71604	+	2.60942i	0.261719	+	0.119477i
$478$		0			0
$479$	−28.6248	−	24.0191i	−1.30790	−	1.09746i	−0.988722	−	0.149766i	$-0.952148\pi$
$479$	−28.6248	−	24.0191i	−1.30790	−	1.09746i	−0.319180	−	0.947694i	$-0.603407\pi$
$480$		0			0
$481$	5.58751	+	31.6884i	0.254769	+	1.44486i
$482$		0			0
$483$	−1.14365	+	5.25912i	−0.0520379	+	0.239298i
$484$		0			0
$485$	−25.6462			−1.16453
$486$		0			0
$487$	12.6775			0.574472			0.287236	−	0.957860i	$-0.407264\pi$
$487$	12.6775			0.574472			0.287236	+	0.957860i	$0.407264\pi$
$488$		0			0
$489$	4.74489	−	21.8196i	0.214571	−	0.986714i
$490$		0			0
$491$	3.92161	+	22.2405i	0.176980	+	1.00370i	0.935834	+	0.352441i	$0.114648\pi$
$491$	3.92161	+	22.2405i	0.176980	+	1.00370i	−0.758854	+	0.651260i	$0.774241\pi$
$492$		0			0
$493$	22.1995	+	18.6276i	0.999816	+	0.838945i
$494$		0			0
$495$	6.45730	+	2.94781i	0.290234	+	0.132494i
$496$		0			0
$497$	0.0269425	−	0.152798i	0.00120853	−	0.00685394i
$498$		0			0
$499$	39.0821	+	14.2247i	1.74955	+	0.636786i	0.999692	−	0.0248084i	$-0.00789758\pi$
$499$	39.0821	+	14.2247i	1.74955	+	0.636786i	0.749862	+	0.661594i	$0.230120\pi$
$500$		0			0
$501$	−0.0279292	−	0.00110640i	−0.00124778	−	4.94304e-5i
$502$		0			0
$503$	17.3586	+	30.0660i	0.773982	+	1.34058i	0.935365	+	0.353684i	$0.115071\pi$
$503$	17.3586	+	30.0660i	0.773982	+	1.34058i	−0.161383	+	0.986892i	$0.551595\pi$
$504$		0			0
$505$	−10.1185	+	17.5258i	−0.450268	+	0.779886i
$506$		0			0
$507$	−14.1480	+	10.9472i	−0.628336	+	0.486184i
$508$		0			0
$509$	−19.6337	+	16.4746i	−0.870248	+	0.730225i	−0.964150	−	0.265357i	$-0.914510\pi$
$509$	−19.6337	+	16.4746i	−0.870248	+	0.730225i	0.0939025	+	0.995581i	$0.470066\pi$
$510$		0			0
$511$	6.10107	−	2.22061i	0.269896	−	0.0982339i
$512$		0			0
$513$	−12.0028	−	28.0123i	−0.529937	−	1.23677i
$514$		0			0
$515$	−2.59651	+	0.945053i	−0.114416	+	0.0416440i
$516$		0			0
$517$	−10.4294	+	8.75130i	−0.458684	+	0.384882i
$518$		0			0
$519$	16.7079	+	6.84169i	0.733394	+	0.300317i
$520$		0			0
$521$	0.226053	−	0.391535i	0.00990355	−	0.0171535i	−0.861031	−	0.508552i	$-0.830181\pi$
$521$	0.226053	−	0.391535i	0.00990355	−	0.0171535i	0.870935	+	0.491399i	$0.163514\pi$
$522$		0			0
$523$	−7.44343	−	12.8924i	−0.325478	−	0.563745i	0.656131	−	0.754647i	$-0.272192\pi$
$523$	−7.44343	−	12.8924i	−0.325478	−	0.563745i	−0.981609	+	0.190902i	$0.938859\pi$
$524$		0			0
$525$	2.39897	−	3.79941i	0.104700	−	0.165820i
$526$		0			0
$527$	13.7579	+	5.00746i	0.599303	+	0.218128i
$528$		0			0
$529$	−2.31726	+	13.1418i	−0.100751	+	0.571385i
$530$		0			0
$531$	−2.22521	+	8.58130i	−0.0965658	+	0.372397i
$532$		0			0
$533$	11.3517	+	9.52522i	0.491697	+	0.412583i
$534$		0			0
$535$	1.47177	+	8.34681i	0.0636301	+	0.360864i
$536$		0			0
$537$	−28.9800	+	9.26622i	−1.25058	+	0.399867i
$538$		0			0
$539$	1.52549			0.0657077
$540$		0			0
$541$	−34.5651			−1.48607			−0.743036	−	0.669252i	$-0.766615\pi$
$541$	−34.5651			−1.48607			−0.743036	+	0.669252i	$0.766615\pi$
$542$		0			0
$543$	6.94028	+	6.30821i	0.297836	+	0.270711i
$544$		0			0
$545$	2.78075	+	15.7704i	0.119114	+	0.675529i
$546$		0			0
$547$	−27.6797	−	23.2260i	−1.18350	−	0.993074i	−0.999949	−	0.0100636i	$-0.996797\pi$
$547$	−27.6797	−	23.2260i	−1.18350	−	0.993074i	−0.183550	−	0.983010i	$-0.558759\pi$
$548$		0			0
$549$	−6.44987	−	13.5450i	−0.275274	−	0.578087i
$550$		0			0
$551$	6.98564	−	39.6175i	0.297598	−	1.68776i
$552$		0			0
$553$	−6.52716	−	2.37569i	−0.277563	−	0.101025i
$554$		0			0
$555$	8.32823	+	15.8418i	0.353514	+	0.672447i
$556$		0			0
$557$	17.0671	+	29.5612i	0.723158	+	1.25255i	0.959728	+	0.280932i	$0.0906435\pi$
$557$	17.0671	+	29.5612i	0.723158	+	1.25255i	−0.236570	+	0.971615i	$0.576023\pi$
$558$		0			0
$559$	−5.95147	+	10.3083i	−0.251721	+	0.435993i
$560$		0			0
$561$	1.50180	+	11.0619i	0.0634062	+	0.467032i
$562$		0			0
$563$	−1.16621	+	0.978562i	−0.0491497	+	0.0412415i	−0.667032	−	0.745029i	$-0.732435\pi$
$563$	−1.16621	+	0.978562i	−0.0491497	+	0.0412415i	0.617882	+	0.786271i	$0.287991\pi$
$564$		0			0
$565$	24.7900	−	9.02281i	1.04292	−	0.379592i
$566$		0			0
$567$	−0.145411	−	8.99883i	−0.00610667	−	0.377915i
$568$		0			0
$569$	13.2604	−	4.82641i	0.555907	−	0.202333i	−0.0487623	−	0.998810i	$-0.515528\pi$
$569$	13.2604	−	4.82641i	0.555907	−	0.202333i	0.604669	+	0.796477i	$0.293305\pi$
$570$		0			0
$571$	1.89291	−	1.58834i	0.0792160	−	0.0664701i	−0.602320	−	0.798255i	$-0.705757\pi$
$571$	1.89291	−	1.58834i	0.0792160	−	0.0664701i	0.681536	+	0.731785i	$0.261312\pi$
$572$		0			0
$573$	−0.408493	−	3.00884i	−0.0170650	−	0.125696i
$574$		0			0
$575$	−4.03060	+	6.98120i	−0.168087	+	0.291136i
$576$		0			0
$577$	−6.54967	−	11.3444i	−0.272666	−	0.472272i	0.696877	−	0.717190i	$-0.254572\pi$
$577$	−6.54967	−	11.3444i	−0.272666	−	0.472272i	−0.969544	+	0.244918i	$0.921239\pi$
$578$		0			0
$579$	−13.8951	−	26.4310i	−0.577460	−	1.09843i
$580$		0			0
$581$	9.90258	+	3.60424i	0.410828	+	0.149529i
$582$		0			0
$583$	−0.554830	+	3.14660i	−0.0229787	+	0.130319i
$584$		0			0
$585$	−12.7416	+	18.5134i	−0.526798	+	0.765433i
$586$		0			0
$587$	22.2529	+	18.6724i	0.918476	+	0.770693i	0.973712	−	0.227781i	$-0.0731470\pi$
$587$	22.2529	+	18.6724i	0.918476	+	0.770693i	−0.0552369	+	0.998473i	$0.517591\pi$
$588$		0			0
$589$	−3.52925	−	20.0154i	−0.145420	−	0.824719i
$590$		0			0
$591$	−10.8978	−	9.90534i	−0.448277	−	0.407451i
$592$		0			0
$593$	−12.7166			−0.522207			−0.261104	−	0.965311i	$-0.584086\pi$
$593$	−12.7166			−0.522207			−0.261104	+	0.965311i	$0.584086\pi$
$594$		0			0
$595$	−6.55310			−0.268651
$596$		0			0
$597$	−13.7236	+	4.38807i	−0.561671	+	0.179592i
$598$		0			0
$599$	2.78607	+	15.8006i	0.113836	+	0.645593i	0.987320	+	0.158742i	$0.0507437\pi$
$599$	2.78607	+	15.8006i	0.113836	+	0.645593i	−0.873485	+	0.486852i	$0.838145\pi$
$600$		0			0
$601$	4.17077	+	3.49969i	0.170129	+	0.142755i	0.723877	−	0.689929i	$-0.242358\pi$
$601$	4.17077	+	3.49969i	0.170129	+	0.142755i	−0.553748	+	0.832684i	$0.686803\pi$
$602$		0			0
$603$	−24.6239	−	24.2293i	−1.00276	−	0.986691i
$604$		0			0
$605$	2.33592	−	13.2476i	0.0949685	−	0.538593i
$606$		0			0
$607$	26.8402	+	9.76904i	1.08941	+	0.396513i	0.823402	−	0.567458i	$-0.192073\pi$
$607$	26.8402	+	9.76904i	1.08941	+	0.396513i	0.266008	+	0.963971i	$0.414295\pi$
$608$		0			0
$609$	6.34276	−	10.0454i	0.257021	−	0.407062i
$610$		0			0
$611$	−21.5528	−	37.3306i	−0.871934	−	1.51023i
$612$		0			0
$613$	7.92708	−	13.7301i	0.320172	−	0.554554i	−0.660352	−	0.750957i	$-0.729593\pi$
$613$	7.92708	−	13.7301i	0.320172	−	0.554554i	0.980523	+	0.196403i	$0.0629261\pi$
$614$		0			0
$615$	7.62765	+	3.12344i	0.307576	+	0.125949i
$616$		0			0
$617$	20.2021	−	16.9516i	0.813305	−	0.682444i	−0.138089	−	0.990420i	$-0.544096\pi$
$617$	20.2021	−	16.9516i	0.813305	−	0.682444i	0.951394	+	0.307976i	$0.0996516\pi$
$618$		0			0
$619$	−25.7126	+	9.35863i	−1.03348	+	0.376155i	−0.802404	−	0.596781i	$-0.796446\pi$
$619$	−25.7126	+	9.35863i	−1.03348	+	0.376155i	−0.231074	+	0.972936i	$0.574224\pi$
$620$		0			0
$621$	0.899700	+	16.1210i	0.0361037	+	0.646914i
$622$		0			0
$623$	−15.9815	+	5.81678i	−0.640284	+	0.233044i
$624$		0			0
$625$	−4.05889	+	3.40582i	−0.162356	+	0.136233i
$626$		0			0
$627$	12.2562	−	9.48340i	0.489465	−	0.378731i
$628$		0			0
$629$	−14.0735	+	24.3760i	−0.561146	+	0.971934i
$630$		0			0
$631$	−13.2330	−	22.9202i	−0.526797	−	0.912439i	−0.999512	−	0.0312239i	$-0.990059\pi$
$631$	−13.2330	−	22.9202i	−0.526797	−	0.912439i	0.472715	−	0.881215i	$-0.343274\pi$
$632$		0			0
$633$	−33.0104	−	1.30769i	−1.31204	−	0.0519761i
$634$		0			0
$635$	−9.48311	−	3.45157i	−0.376326	−	0.136971i
$636$		0			0
$637$	−0.838706	+	4.75654i	−0.0332308	+	0.188461i
$638$		0			0
$639$	−0.0443127	−	0.463352i	−0.00175299	−	0.0183299i
$640$		0			0
$641$	−23.4161	−	19.6485i	−0.924882	−	0.776068i	0.0500098	−	0.998749i	$-0.484075\pi$
$641$	−23.4161	−	19.6485i	−0.924882	−	0.776068i	−0.974891	+	0.222681i	$0.928519\pi$
$642$		0			0
$643$	−6.21074	−	35.2229i	−0.244928	−	1.38905i	−0.820660	−	0.571416i	$-0.806394\pi$
$643$	−6.21074	−	35.2229i	−0.244928	−	1.38905i	0.575733	−	0.817638i	$-0.304717\pi$
$644$		0			0
$645$	−1.40685	+	6.46944i	−0.0553946	+	0.254734i
$646$		0			0
$647$	20.1378			0.791699			0.395850	−	0.918315i	$-0.370450\pi$
$647$	20.1378			0.791699			0.395850	+	0.918315i	$0.370450\pi$
$648$		0			0
$649$	−4.50789			−0.176950
$650$		0			0
$651$	1.27541	−	5.86503i	0.0499874	−	0.229869i
$652$		0			0
$653$	1.28286	+	7.27546i	0.0502022	+	0.284711i	0.999566	−	0.0294690i	$-0.00938165\pi$
$653$	1.28286	+	7.27546i	0.0502022	+	0.284711i	−0.949364	+	0.314180i	$0.898271\pi$
$654$		0			0
$655$	1.70413	+	1.42994i	0.0665859	+	0.0558722i
$656$		0			0
$657$	15.8646	−	11.3006i	0.618936	−	0.440878i
$658$		0			0
$659$	−3.49979	+	19.8483i	−0.136332	+	0.773180i	0.837590	+	0.546299i	$0.183964\pi$
$659$	−3.49979	+	19.8483i	−0.136332	+	0.773180i	−0.973923	+	0.226881i	$0.927147\pi$
$660$		0			0
$661$	9.20871	+	3.35170i	0.358177	+	0.130366i	0.514840	−	0.857286i	$-0.327851\pi$
$661$	9.20871	+	3.35170i	0.358177	+	0.130366i	−0.156663	+	0.987652i	$0.550074\pi$
$662$		0			0
$663$	−35.3169	−	1.39906i	−1.37159	−	0.0543351i
$664$		0			0
$665$	4.54845	+	7.87815i	0.176381	+	0.305501i
$666$		0			0
$667$	−10.6567	+	18.4579i	−0.412629	+	0.714694i
$668$		0			0
$669$	23.2956	−	18.0253i	0.900660	−	0.696899i
$670$		0			0
$671$	5.84387	−	4.90359i	0.225600	−	0.189301i
$672$		0			0
$673$	−31.6012	+	11.5019i	−1.21814	+	0.443366i	−0.869519	−	0.493899i	$-0.835571\pi$
$673$	−31.6012	+	11.5019i	−1.21814	+	0.443366i	−0.348618	+	0.937265i	$0.613349\pi$
$674$		0			0
$675$	3.89748	−	12.9044i	0.150014	−	0.496692i
$676$		0			0
$677$	−2.31670	+	0.843212i	−0.0890382	+	0.0324073i	−0.386155	−	0.922434i	$-0.626197\pi$
$677$	−2.31670	+	0.843212i	−0.0890382	+	0.0324073i	0.297117	+	0.954841i	$0.403975\pi$
$678$		0			0
$679$	−12.6664	+	10.6284i	−0.486091	+	0.407879i
$680$		0			0
$681$	22.0656	+	9.03562i	0.845555	+	0.346246i
$682$		0			0
$683$	−8.35720	+	14.4751i	−0.319779	+	0.553874i	−0.980442	−	0.196809i	$-0.936942\pi$
$683$	−8.35720	+	14.4751i	−0.319779	+	0.553874i	0.660662	+	0.750683i	$0.270275\pi$
$684$		0			0
$685$	−4.30767	−	7.46110i	−0.164588	−	0.285074i
$686$		0			0
$687$	17.9809	−	28.4776i	0.686015	−	1.08649i
$688$		0			0
$689$	−9.50615	−	3.45996i	−0.362156	−	0.131814i
$690$		0			0
$691$	−0.583770	+	3.31072i	−0.0222077	+	0.125946i	−0.993896	−	0.110320i	$-0.964812\pi$
$691$	−0.583770	+	3.31072i	−0.0222077	+	0.125946i	0.971688	+	0.236266i	$0.0759236\pi$
$692$		0			0
$693$	4.41083	−	1.22015i	0.167554	−	0.0463498i
$694$		0			0
$695$	8.09349	+	6.79125i	0.307004	+	0.257607i
$696$		0			0
$697$	2.25092	+	12.7656i	0.0852599	+	0.483533i
$698$		0			0
$699$	−13.0193	+	4.16285i	−0.492434	+	0.157454i
$700$		0			0
$701$	−43.8430			−1.65593			−0.827963	−	0.560783i	$-0.810500\pi$
$701$	−43.8430			−1.65593			−0.827963	+	0.560783i	$0.810500\pi$
$702$		0			0
$703$	39.0731			1.47367
$704$		0			0
$705$	−17.7424	−	16.1265i	−0.668216	−	0.607360i
$706$		0			0
$707$	2.26565	+	12.8491i	0.0852084	+	0.483241i
$708$		0			0
$709$	−26.2776	−	22.0495i	−0.986875	−	0.828087i	−0.00176280	−	0.999998i	$-0.500561\pi$
$709$	−26.2776	−	22.0495i	−0.986875	−	0.828087i	−0.985112	+	0.171912i	$0.945006\pi$
$710$		0			0
$711$	−20.7729	−	1.64840i	−0.779044	−	0.0618200i
$712$		0			0
$713$	−1.86982	+	10.6043i	−0.0700252	+	0.397133i
$714$		0			0
$715$	−10.7389	−	3.90865i	−0.401613	−	0.146175i
$716$		0			0
$717$	−12.3883	−	23.5648i	−0.462649	−	0.880043i
$718$		0			0
$719$	19.6322	+	34.0040i	0.732157	+	1.26813i	0.955959	+	0.293499i	$0.0948197\pi$
$719$	19.6322	+	34.0040i	0.732157	+	1.26813i	−0.223802	+	0.974635i	$0.571847\pi$
$720$		0			0
$721$	−0.890738	+	1.54280i	−0.0331728	+	0.0574570i
$722$		0			0
$723$	7.11926	+	52.4385i	0.264768	+	1.95021i
$724$		0			0
$725$	13.6312	−	11.4379i	0.506251	−	0.424795i
$726$		0			0
$727$	−28.8036	+	10.4836i	−1.06826	+	0.388817i	−0.815528	−	0.578718i	$-0.803553\pi$
$727$	−28.8036	+	10.4836i	−1.06826	+	0.388817i	−0.252737	+	0.967535i	$0.581331\pi$
$728$		0			0
$729$	−7.61808	−	25.9030i	−0.282151	−	0.959370i
$730$		0			0
$731$	−9.78416	+	3.56114i	−0.361880	+	0.131714i
$732$		0			0
$733$	15.0760	−	12.6503i	0.556846	−	0.467249i	−0.320405	−	0.947281i	$-0.603819\pi$
$733$	15.0760	−	12.6503i	0.556846	−	0.467249i	0.877251	+	0.480031i	$0.159375\pi$
$734$		0			0
$735$	0.361413	+	2.66207i	0.0133309	+	0.0981918i
$736$		0			0
$737$	8.78317	−	15.2129i	0.323532	−	0.560374i
$738$		0			0
$739$	−2.02441	−	3.50638i	−0.0744691	−	0.128984i	0.826386	−	0.563104i	$-0.190393\pi$
$739$	−2.02441	−	3.50638i	−0.0744691	−	0.128984i	−0.900855	+	0.434120i	$0.857060\pi$
$740$		0			0
$741$	22.8312	+	43.4291i	0.838724	+	1.59541i
$742$		0			0
$743$	−46.8697	−	17.0592i	−1.71948	−	0.625841i	−0.721689	−	0.692218i	$-0.756634\pi$
$743$	−46.8697	−	17.0592i	−1.71948	−	0.625841i	−0.997795	+	0.0663769i	$0.978856\pi$
$744$		0			0
$745$	−6.46251	+	36.6507i	−0.236768	+	1.34278i
$746$		0			0
$747$	31.5152	+	2.50085i	1.15308	+	0.0915013i
$748$		0			0
$749$	4.18599	+	3.51247i	0.152953	+	0.128343i
$750$		0			0
$751$	−6.68230	−	37.8972i	−0.243841	−	1.38289i	−0.823170	−	0.567795i	$-0.807797\pi$
$751$	−6.68230	−	37.8972i	−0.243841	−	1.38289i	0.579330	−	0.815093i	$-0.303314\pi$
$752$		0			0
$753$	−35.8329	−	32.5695i	−1.30582	−	1.18690i
$754$		0			0
$755$	−17.0520			−0.620587
$756$		0			0
$757$	−2.89777			−0.105321			−0.0526607	−	0.998612i	$-0.516770\pi$
$757$	−2.89777			−0.105321			−0.0526607	+	0.998612i	$0.516770\pi$
$758$		0			0
$759$	−7.82023	+	2.50048i	−0.283856	+	0.0907617i
$760$		0			0
$761$	−2.98113	−	16.9068i	−0.108066	−	0.612871i	−0.989951	−	0.141408i	$-0.954837\pi$
$761$	−2.98113	−	16.9068i	−0.108066	−	0.612871i	0.881886	−	0.471463i	$-0.156274\pi$
$762$		0			0
$763$	7.90898	+	6.63642i	0.286324	+	0.240255i
$764$		0			0
$765$	−18.9477	+	5.24145i	−0.685056	+	0.189505i
$766$		0			0
$767$	2.47841	−	14.0558i	0.0894901	−	0.507524i
$768$		0			0
$769$	−13.3754	−	4.86826i	−0.482331	−	0.175554i	0.0893991	−	0.995996i	$-0.471505\pi$
$769$	−13.3754	−	4.86826i	−0.482331	−	0.175554i	−0.571730	+	0.820442i	$0.693728\pi$
$770$		0			0
$771$	10.8972	−	17.2587i	0.392454	−	0.621556i
$772$		0			0
$773$	−19.4400	−	33.6711i	−0.699210	−	1.21107i	−0.968741	−	0.248075i	$-0.920202\pi$
$773$	−19.4400	−	33.6711i	−0.699210	−	1.21107i	0.269531	−	0.962992i	$-0.413131\pi$
$774$		0			0
$775$	4.49497	−	7.78552i	0.161464	−	0.279664i
$776$		0			0
$777$	10.6784	+	4.37270i	0.383086	+	0.156870i
$778$		0			0
$779$	13.7845	−	11.5666i	0.493881	−	0.414415i
$780$		0			0
$781$	0.222415	−	0.0809523i	0.00795862	−	0.00289670i
$782$		0			0
$783$	10.3047	−	34.1187i	0.368261	−	1.21930i
$784$		0			0
$785$	21.5381	−	7.83922i	0.768727	−	0.279794i
$786$		0			0
$787$	8.53640	−	7.16289i	0.304290	−	0.255329i	−0.477837	−	0.878448i	$-0.658579\pi$
$787$	8.53640	−	7.16289i	0.304290	−	0.255329i	0.782127	+	0.623119i	$0.214135\pi$
$788$		0			0
$789$	7.15334	−	5.53500i	0.254666	−	0.197051i
$790$		0			0
$791$	8.50424	−	14.7298i	0.302376	−	0.523731i
$792$		0			0
$793$	12.0766	+	20.9173i	0.428854	+	0.742796i
$794$		0			0
$795$	−5.62243	−	0.222730i	−0.199407	−	0.00789942i
$796$		0			0
$797$	7.05074	+	2.56626i	0.249750	+	0.0909016i	0.463862	−	0.885908i	$-0.346463\pi$
$797$	7.05074	+	2.56626i	0.249750	+	0.0909016i	−0.214112	+	0.976809i	$0.568686\pi$
$798$		0			0
$799$	6.54768	−	37.1337i	0.231640	−	1.31370i
$800$		0			0
$801$	−41.5565	+	29.6013i	−1.46833	+	1.04591i
$802$		0			0
$803$	7.58726	+	6.36647i	0.267749	+	0.224668i
$804$		0			0
$805$	−0.836913	−	4.74637i	−0.0294973	−	0.167287i
$806$		0			0
$807$	−9.36982	+	43.0875i	−0.329833	+	1.51675i
$808$		0			0
$809$	−36.4169			−1.28035			−0.640175	−	0.768229i	$-0.721138\pi$
$809$	−36.4169			−1.28035			−0.640175	+	0.768229i	$0.721138\pi$
$810$		0			0
$811$	28.7481			1.00948			0.504741	−	0.863271i	$-0.331588\pi$
$811$	28.7481			1.00948			0.504741	+	0.863271i	$0.331588\pi$
$812$		0			0
$813$	1.54304	−	7.09571i	0.0541167	−	0.248857i
$814$		0			0
$815$	3.47227	+	19.6922i	0.121628	+	0.689788i
$816$		0			0
$817$	11.0723	+	9.29077i	0.387371	+	0.325043i
$818$		0			0
$819$	1.37944	+	14.4239i	0.0482014	+	0.504013i
$820$		0			0
$821$	−5.42958	+	30.7927i	−0.189493	+	1.07467i	0.730551	+	0.682858i	$0.239263\pi$
$821$	−5.42958	+	30.7927i	−0.189493	+	1.07467i	−0.920045	+	0.391813i	$0.871848\pi$
$822$		0			0
$823$	−32.7511	−	11.9204i	−1.14163	−	0.415520i	−0.299129	−	0.954213i	$-0.596696\pi$
$823$	−32.7511	−	11.9204i	−1.14163	−	0.415520i	−0.842502	+	0.538693i	$0.818918\pi$
$824$		0			0
$825$	6.84927	+	0.271331i	0.238461	+	0.00944653i
$826$		0			0
$827$	8.42032	+	14.5844i	0.292803	+	0.507150i	0.974471	−	0.224511i	$-0.0720786\pi$
$827$	8.42032	+	14.5844i	0.292803	+	0.507150i	−0.681668	+	0.731661i	$0.738745\pi$
$828$		0			0
$829$	14.8511	−	25.7228i	0.515799	−	0.893391i	−0.484032	−	0.875050i	$-0.660828\pi$
$829$	14.8511	−	25.7228i	0.515799	−	0.893391i	0.999832	−	0.0183407i	$-0.00583836\pi$
$830$		0			0
$831$	23.8825	−	18.4794i	0.828474	−	0.641044i
$832$		0			0
$833$	−3.23651	+	2.71575i	−0.112138	+	0.0940953i
$834$		0			0
$835$	0.0235206	−	0.00856079i	0.000813963	−	0.000296258i
$836$		0			0
$837$	−1.00336	−	17.9784i	−0.0346811	−	0.621423i
$838$		0			0
$839$	7.60062	−	2.76640i	0.262402	−	0.0955067i	−0.207469	−	0.978242i	$-0.566523\pi$
$839$	7.60062	−	2.76640i	0.262402	−	0.0955067i	0.469871	+	0.882735i	$0.344300\pi$
$840$		0			0
$841$	13.8250	−	11.6005i	0.476723	−	0.400018i
$842$		0			0
$843$	−48.1938	−	19.7348i	−1.65988	−	0.679704i
$844$		0			0
$845$	8.00967	−	13.8732i	0.275541	−	0.477251i
$846$		0			0
$847$	−4.33643	−	7.51092i	−0.149002	−	0.258078i
$848$		0			0
$849$	−24.0454	+	38.0824i	−0.825238	+	1.30698i
$850$		0			0
$851$	−19.4527	−	7.08021i	−0.666830	−	0.242706i
$852$		0			0
$853$	5.16566	−	29.2959i	0.176869	−	1.00307i	−0.759096	−	0.650979i	$-0.774359\pi$
$853$	5.16566	−	29.2959i	0.176869	−	1.00307i	0.935965	−	0.352094i	$-0.114530\pi$
$854$		0			0
$855$	19.4527	+	19.1409i	0.665269	+	0.654605i
$856$		0			0
$857$	−7.68078	−	6.44494i	−0.262371	−	0.220155i	0.502107	−	0.864806i	$-0.332558\pi$
$857$	−7.68078	−	6.44494i	−0.262371	−	0.220155i	−0.764477	+	0.644651i	$0.777003\pi$
$858$		0			0
$859$	2.86481	+	16.2471i	0.0977459	+	0.554345i	0.993871	+	0.110544i	$0.0352592\pi$
$859$	2.86481	+	16.2471i	0.0977459	+	0.554345i	−0.896125	+	0.443801i	$0.853630\pi$
$860$		0			0
$861$	5.06164	−	1.61844i	0.172500	−	0.0551561i
$862$		0			0
$863$	−34.6971			−1.18110			−0.590551	−	0.807000i	$-0.701090\pi$
$863$	−34.6971			−1.18110			−0.590551	+	0.807000i	$0.701090\pi$
$864$		0			0
$865$	−16.1676			−0.549716
$866$		0			0
$867$	−1.08985	−	0.990592i	−0.0370132	−	0.0336423i
$868$		0			0
$869$	−1.84001	−	10.4352i	−0.0624179	−	0.353990i
$870$		0			0
$871$	42.6054	+	35.7502i	1.44363	+	1.21135i
$872$		0			0
$873$	−28.1227	+	40.8621i	−0.951810	+	1.38297i
$874$		0			0
$875$	−2.04541	+	11.6001i	−0.0691474	+	0.392155i
$876$		0			0
$877$	0.778063	+	0.283192i	0.0262733	+	0.00956271i	0.355123	−	0.934819i	$-0.384439\pi$
$877$	0.778063	+	0.283192i	0.0262733	+	0.00956271i	−0.328850	+	0.944382i	$0.606661\pi$
$878$		0			0
$879$	10.8740	+	20.6844i	0.366773	+	0.697668i
$880$		0			0
$881$	−15.7066	−	27.2047i	−0.529170	−	0.916549i	−0.999421	−	0.0340168i	$-0.989170\pi$
$881$	−15.7066	−	27.2047i	−0.529170	−	0.916549i	0.470251	−	0.882533i	$-0.344163\pi$
$882$		0			0
$883$	−18.2230	+	31.5631i	−0.613252	+	1.06218i	0.377436	+	0.926036i	$0.376806\pi$
$883$	−18.2230	+	31.5631i	−0.613252	+	1.06218i	−0.990688	+	0.136148i	$0.956528\pi$
$884$		0			0
$885$	−1.06799	−	7.86651i	−0.0359001	−	0.264430i
$886$		0			0
$887$	35.0185	−	29.3840i	1.17580	−	0.986617i	0.175807	−	0.984425i	$-0.443747\pi$
$887$	35.0185	−	29.3840i	1.17580	−	0.986617i	0.999998	−	0.00219248i	$-0.000697889\pi$
$888$		0			0
$889$	−6.11401	+	2.22532i	−0.205057	+	0.0746348i
$890$		0			0
$891$	11.7776	−	7.05593i	0.394564	−	0.236383i
$892$		0			0
$893$	−49.1869	+	17.9026i	−1.64598	+	0.599087i
$894$		0			0
$895$	20.8715	−	17.5133i	0.697657	−	0.585404i
$896$		0			0
$897$	−3.49707	−	25.7585i	−0.116764	−	0.860050i
$898$		0			0
$899$	11.8845	−	20.5845i	0.396370	−	0.686532i
$900$		0			0
$901$	−4.42458	−	7.66360i	−0.147404	−	0.255312i
$902$		0			0
$903$	1.98625	+	3.77822i	0.0660984	+	0.125731i
$904$		0			0
$905$	−7.89213	−	2.87250i	−0.262343	−	0.0954852i
$906$		0			0
$907$	−6.02959	+	34.1955i	−0.200209	+	1.13544i	0.704594	+	0.709611i	$0.251129\pi$
$907$	−6.02959	+	34.1955i	−0.200209	+	1.13544i	−0.904803	+	0.425831i	$0.859982\pi$
$908$		0			0
$909$	16.8282	+	35.3399i	0.558156	+	1.17215i
$910$		0			0
$911$	−14.9695	−	12.5609i	−0.495960	−	0.416160i	0.360196	−	0.932877i	$-0.382710\pi$
$911$	−14.9695	−	12.5609i	−0.495960	−	0.416160i	−0.856157	+	0.516716i	$0.827154\pi$
$912$		0			0
$913$	2.79154	+	15.8316i	0.0923864	+	0.523949i
$914$		0			0
$915$	9.94152	+	9.03612i	0.328656	+	0.298725i
$916$		0			0
$917$	1.43425			0.0473631
$918$		0			0
$919$	55.6107			1.83443			0.917214	−	0.398395i	$-0.130433\pi$
$919$	55.6107			1.83443			0.917214	+	0.398395i	$0.130433\pi$
$920$		0			0
$921$	−20.8094	+	6.65372i	−0.685694	+	0.219248i
$922$		0			0
$923$	0.130130	+	0.738003i	0.00428327	+	0.0242917i
$924$		0			0
$925$	13.2396	+	11.1094i	0.435317	+	0.365274i
$926$		0			0
$927$	−1.34149	+	5.17333i	−0.0440603	+	0.169914i
$928$		0			0
$929$	2.64675	−	15.0105i	0.0868370	−	0.492477i	−0.910108	−	0.414371i	$-0.864002\pi$
$929$	2.64675	−	15.0105i	0.0868370	−	0.492477i	0.996945	−	0.0781061i	$-0.0248873\pi$
$930$		0			0
$931$	5.51131	+	2.00595i	0.180626	+	0.0657425i
$932$		0			0
$933$	17.6133	−	27.8953i	0.576633	−	0.913252i
$934$		0			0
$935$	−4.99836	−	8.65742i	−0.163464	−	0.283128i
$936$		0			0
$937$	−18.8333	+	32.6203i	−0.615258	+	1.06566i	0.375081	+	0.926992i	$0.377615\pi$
$937$	−18.8333	+	32.6203i	−0.615258	+	1.06566i	−0.990339	+	0.138667i	$0.955718\pi$
$938$		0			0
$939$	−14.8270	−	6.07148i	−0.483860	−	0.198135i
$940$		0			0
$941$	13.9332	−	11.6914i	0.454210	−	0.381127i	−0.386786	−	0.922170i	$-0.626415\pi$
$941$	13.9332	−	11.6914i	0.454210	−	0.381127i	0.840995	+	0.541042i	$0.181970\pi$
$942$		0			0
$943$	−8.95858	+	3.26066i	−0.291732	+	0.106182i
$944$		0			0
$945$	3.17423	+	7.40805i	0.103258	+	0.240984i
$946$		0			0
$947$	15.4701	−	5.63067i	0.502712	−	0.182972i	−0.0782015	−	0.996938i	$-0.524918\pi$
$947$	15.4701	−	5.63067i	0.502712	−	0.182972i	0.580913	+	0.813965i	$0.302696\pi$
$948$		0			0
$949$	−24.0223	+	20.1571i	−0.779796	+	0.654326i
$950$		0			0
$951$	−25.5778	+	19.7912i	−0.829417	+	0.641774i
$952$		0			0
$953$	8.37953	−	14.5138i	0.271440	−	0.470147i	−0.697791	−	0.716301i	$-0.745834\pi$
$953$	8.37953	−	14.5138i	0.271440	−	0.470147i	0.969231	+	0.246154i	$0.0791669\pi$
$954$		0			0
$955$	1.35956	+	2.35483i	0.0439944	+	0.0762006i
$956$		0			0
$957$	18.1091	+	0.717386i	0.585385	+	0.0231898i
$958$		0			0
$959$	−5.21956	−	1.89976i	−0.168548	−	0.0613466i
$960$		0			0
$961$	−3.29785	+	18.7030i	−0.106382	+	0.603324i
$962$		0			0
$963$	14.9128	+	6.80785i	0.480560	+	0.219380i
$964$		0			0
$965$	20.4842	+	17.1883i	0.659410	+	0.553311i
$966$		0			0
$967$	−6.44651	−	36.5600i	−0.207306	−	1.17569i	−0.893770	−	0.448525i	$-0.851949\pi$
$967$	−6.44651	−	36.5600i	−0.207306	−	1.17569i	0.686464	−	0.727163i	$-0.259162\pi$
$968$		0			0
$969$	−9.12010	+	41.9391i	−0.292980	+	1.34728i
$970$		0			0
$971$	37.1146			1.19106			0.595532	−	0.803331i	$-0.296941\pi$
$971$	37.1146			1.19106			0.595532	+	0.803331i	$0.296941\pi$
$972$		0			0
$973$	6.81173			0.218374
$974$		0			0
$975$	−4.61170	+	21.2071i	−0.147693	+	0.679170i
$976$		0			0
$977$	8.86803	+	50.2931i	0.283713	+	1.60902i	0.709845	+	0.704358i	$0.248765\pi$
$977$	8.86803	+	50.2931i	0.283713	+	1.60902i	−0.426132	+	0.904661i	$0.640124\pi$
$978$		0			0
$979$	−19.8745	−	16.6766i	−0.635190	−	0.532988i
$980$		0			0
$981$	28.1762	+	12.8627i	0.899597	+	0.410674i
$982$		0			0
$983$	9.67075	−	54.8455i	0.308449	−	1.74930i	−0.298360	−	0.954453i	$-0.596440\pi$
$983$	9.67075	−	54.8455i	0.308449	−	1.74930i	0.606809	−	0.794848i	$-0.292449\pi$
$984$		0			0
$985$	12.3925	+	4.51049i	0.394857	+	0.143716i
$986$		0			0
$987$	−15.4459	−	0.611885i	−0.491650	−	0.0194765i
$988$		0			0
$989$	−3.82887	−	6.63180i	−0.121751	−	0.210879i
$990$		0			0
$991$	20.8100	−	36.0440i	0.661053	−	1.14498i	−0.319287	−	0.947658i	$-0.603443\pi$
$991$	20.8100	−	36.0440i	0.661053	−	1.14498i	0.980339	−	0.197319i	$-0.0632233\pi$
$992$		0			0
$993$	14.9436	−	11.5629i	0.474222	−	0.366936i
$994$		0			0
$995$	9.88381	−	8.29350i	0.313338	−	0.262922i
$996$		0			0
$997$	37.7045	−	13.7233i	1.19411	−	0.434621i	0.332947	−	0.942946i	$-0.391957\pi$
$997$	37.7045	−	13.7233i	1.19411	−	0.434621i	0.861166	+	0.508324i	$0.169735\pi$
$998$		0			0
$999$	34.3732	+	4.10221i	1.08752	+	0.129788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bo.b.169.5	yes	54
27.4	even	9	inner	756.2.bo.b.85.5	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bo.b.85.5	✓	54	27.4	even	9	inner
756.2.bo.b.169.5	yes	54	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.368051 + 1.69249i) q^{3} +(-0.269336 - 1.52748i) q^{5} +(-0.766044 - 0.642788i) q^{7} +(-2.72908 - 1.24585i) q^{9} +O(q^{10})\)	\(q+(-0.368051 + 1.69249i) q^{3} +(-0.269336 - 1.52748i) q^{5} +(-0.766044 - 0.642788i) q^{7} +(-2.72908 - 1.24585i) q^{9} +(0.264899 - 1.50232i) q^{11} +(4.53864 + 1.65193i) q^{13} +(2.68438 + 0.106341i) q^{15} +(2.11248 + 3.65892i) q^{17} +(2.93251 - 5.07925i) q^{19} +(1.36986 - 1.05995i) q^{21} +(-2.38034 + 1.99735i) q^{23} +(2.43781 - 0.887289i) q^{25} +(3.11303 - 4.16041i) q^{27} +(6.44544 - 2.34595i) q^{29} +(2.65459 - 2.22746i) q^{31} +(2.44517 + 1.00127i) q^{33} +(-0.775522 + 1.34324i) q^{35} +(3.33103 + 5.76951i) q^{37} +(-4.46633 + 7.07363i) q^{39} +(2.88306 + 1.04935i) q^{41} +(-0.427942 + 2.42698i) q^{43} +(-1.16797 + 4.50416i) q^{45} +(-6.83673 - 5.73670i) q^{47} +(0.173648 + 0.984808i) q^{49} +(-6.97021 + 2.22869i) q^{51} -2.09450 q^{53} -2.36611 q^{55} +(7.51730 + 6.83268i) q^{57} +(-0.513137 - 2.91014i) q^{59} +(3.83080 + 3.21443i) q^{61} +(1.28978 + 2.70859i) q^{63} +(1.30087 - 7.37760i) q^{65} +(10.8207 + 3.93842i) q^{67} +(-2.50441 - 4.76384i) q^{69} +(0.0775777 + 0.134369i) q^{71} +(-3.24631 + 5.62278i) q^{73} +(0.604496 + 4.45254i) q^{75} +(-1.16860 + 0.980569i) q^{77} +(6.52716 - 2.37569i) q^{79} +(5.89572 + 6.80003i) q^{81} +(-9.90258 + 3.60424i) q^{83} +(5.01997 - 4.21225i) q^{85} +(1.59826 + 11.7723i) q^{87} +(8.50356 - 14.7286i) q^{89} +(-2.41496 - 4.18283i) q^{91} +(2.79295 + 5.31270i) q^{93} +(-8.54829 - 3.11132i) q^{95} +(2.87124 - 16.2836i) q^{97} +(-2.59459 + 3.76992i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9}+O(q^{10}) \) 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9	\( 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9} + 9 q^{13} + 3 q^{15} + 3 q^{21} + 12 q^{23} + 27 q^{25} + 39 q^{27} + 30 q^{29} - 9 q^{31} - 6 q^{33} + 6 q^{35} - 18 q^{39} - 27 q^{41} + 9 q^{43} - 81 q^{45} + 9 q^{47} + 12 q^{53} - 21 q^{57} - 24 q^{59} - 3 q^{63} - 78 q^{65} - 9 q^{67} + 6 q^{69} - 30 q^{71} + 57 q^{75} + 9 q^{77} + 99 q^{81} + 78 q^{83} + 18 q^{85} + 21 q^{87} + 12 q^{89} - 51 q^{93} - 36 q^{95} + 36 q^{97} + 15 q^{99}+O(q^{100}) \) 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9 + 9 * q^13 + 3 * q^15 + 3 * q^21 + 12 * q^23 + 27 * q^25 + 39 * q^27 + 30 * q^29 - 9 * q^31 - 6 * q^33 + 6 * q^35 - 18 * q^39 - 27 * q^41 + 9 * q^43 - 81 * q^45 + 9 * q^47 + 12 * q^53 - 21 * q^57 - 24 * q^59 - 3 * q^63 - 78 * q^65 - 9 * q^67 + 6 * q^69 - 30 * q^71 + 57 * q^75 + 9 * q^77 + 99 * q^81 + 78 * q^83 + 18 * q^85 + 21 * q^87 + 12 * q^89 - 51 * q^93 - 36 * q^95 + 36 * q^97 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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