LMFDB - Embedded newform 756.2.bo.b.85.2

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			85.2
Character	$\chi$	$=$	756.85
Dual form			756.2.bo.b.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46947 + 0.916867i) q^{3} +(-0.137580 + 0.780255i) q^{5} +(-0.766044 + 0.642788i) q^{7} +(1.31871 - 2.69462i) q^{9} +O(q^{10})$	\(q+(-1.46947 + 0.916867i) q^{3} +(-0.137580 + 0.780255i) q^{5} +(-0.766044 + 0.642788i) q^{7} +(1.31871 - 2.69462i) q^{9} +(-0.813230 - 4.61206i) q^{11} +(-2.16049 + 0.786356i) q^{13} +(-0.513219 - 1.27271i) q^{15} +(1.40573 - 2.43480i) q^{17} +(-2.40481 - 4.16525i) q^{19} +(0.536332 - 1.64692i) q^{21} +(5.62038 + 4.71606i) q^{23} +(4.10859 + 1.49541i) q^{25} +(0.532798 + 5.16876i) q^{27} +(1.69990 + 0.618713i) q^{29} +(-2.57845 - 2.16358i) q^{31} +(5.42366 + 6.03168i) q^{33} +(-0.396146 - 0.686145i) q^{35} +(3.77351 - 6.53591i) q^{37} +(2.45381 - 3.13642i) q^{39} +(7.25782 - 2.64163i) q^{41} +(-2.14462 - 12.1628i) q^{43} +(1.92107 + 1.39966i) q^{45} +(-4.85227 + 4.07154i) q^{47} +(0.173648 - 0.984808i) q^{49} +(0.166698 + 4.86674i) q^{51} +11.0374 q^{53} +3.71047 q^{55} +(7.35278 + 3.91584i) q^{57} +(2.27829 - 12.9209i) q^{59} +(-5.05371 + 4.24056i) q^{61} +(0.721879 + 2.91185i) q^{63} +(-0.316317 - 1.79392i) q^{65} +(9.23265 - 3.36041i) q^{67} +(-12.5830 - 1.77699i) q^{69} +(-1.99424 + 3.45413i) q^{71} +(-2.23812 - 3.87653i) q^{73} +(-7.40856 + 1.56957i) q^{75} +(3.58754 + 3.01031i) q^{77} +(-12.7928 - 4.65620i) q^{79} +(-5.52200 - 7.10686i) q^{81} +(0.490062 + 0.178368i) q^{83} +(1.70636 + 1.43181i) q^{85} +(-3.06524 + 0.649398i) q^{87} +(3.53294 + 6.11923i) q^{89} +(1.14958 - 1.99112i) q^{91} +(5.77269 + 0.815228i) q^{93} +(3.58081 - 1.30331i) q^{95} +(1.02804 + 5.83029i) q^{97} +(-13.5002 - 3.89062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

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

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
$3$	−1.46947	+	0.916867i	−0.848402	+	0.529353i
$3$	−1.46947	+	0.916867i	−0.848402	+	0.529353i
$4$		0			0
$5$	−0.137580	+	0.780255i	−0.0615276	+	0.348941i	0.938466	+	0.345372i	$0.112247\pi$
$5$	−0.137580	+	0.780255i	−0.0615276	+	0.348941i	−0.999994	+	0.00356894i	$0.998864\pi$
$6$		0			0
$7$	−0.766044	+	0.642788i	−0.289538	+	0.242951i
$7$	−0.766044	+	0.642788i	−0.289538	+	0.242951i
$8$		0			0
$9$	1.31871	−	2.69462i	0.439571	−	0.898208i
$10$		0			0
$11$	−0.813230	−	4.61206i	−0.245198	−	1.39059i	−0.820032	−	0.572318i	$-0.806044\pi$
$11$	−0.813230	−	4.61206i	−0.245198	−	1.39059i	0.574834	−	0.818270i	$-0.305067\pi$
$12$		0			0
$13$	−2.16049	+	0.786356i	−0.599213	+	0.218096i	−0.623777	−	0.781602i	$-0.714403\pi$
$13$	−2.16049	+	0.786356i	−0.599213	+	0.218096i	0.0245635	+	0.999698i	$0.492180\pi$
$14$		0			0
$15$	−0.513219	−	1.27271i	−0.132513	−	0.328612i
$16$		0			0
$17$	1.40573	−	2.43480i	0.340940	−	0.590525i	−0.643668	−	0.765305i	$-0.722588\pi$
$17$	1.40573	−	2.43480i	0.340940	−	0.590525i	0.984608	+	0.174780i	$0.0559214\pi$
$18$		0			0
$19$	−2.40481	−	4.16525i	−0.551701	−	0.955573i	−0.998152	−	0.0607655i	$-0.980646\pi$
$19$	−2.40481	−	4.16525i	−0.551701	−	0.955573i	0.446452	−	0.894808i	$-0.352688\pi$
$20$		0			0
$21$	0.536332	−	1.64692i	0.117037	−	0.359388i
$22$		0			0
$23$	5.62038	+	4.71606i	1.17193	+	0.983367i	0.999998	−	0.00174162i	$-0.000554376\pi$
$23$	5.62038	+	4.71606i	1.17193	+	0.983367i	0.171933	+	0.985109i	$0.444999\pi$
$24$		0			0
$25$	4.10859	+	1.49541i	0.821719	+	0.299081i
$26$		0			0
$27$	0.532798	+	5.16876i	0.102537	+	0.994729i
$28$		0			0
$29$	1.69990	+	0.618713i	0.315663	+	0.114892i	0.494993	−	0.868897i	$-0.335171\pi$
$29$	1.69990	+	0.618713i	0.315663	+	0.114892i	−0.179330	+	0.983789i	$0.557393\pi$
$30$		0			0
$31$	−2.57845	−	2.16358i	−0.463104	−	0.388590i	0.381168	−	0.924506i	$-0.375522\pi$
$31$	−2.57845	−	2.16358i	−0.463104	−	0.388590i	−0.844272	+	0.535916i	$0.819967\pi$
$32$		0			0
$33$	5.42366	+	6.03168i	0.944139	+	1.04998i
$34$		0			0
$35$	−0.396146	−	0.686145i	−0.0669609	−	0.115980i
$36$		0			0
$37$	3.77351	−	6.53591i	0.620361	−	1.07450i	−0.369057	−	0.929407i	$-0.620319\pi$
$37$	3.77351	−	6.53591i	0.620361	−	1.07450i	0.989418	−	0.145090i	$-0.0463473\pi$
$38$		0			0
$39$	2.45381	−	3.13642i	0.392924	−	0.502228i
$40$		0			0
$41$	7.25782	−	2.64163i	1.13348	−	0.412554i	0.293927	−	0.955828i	$-0.405038\pi$
$41$	7.25782	−	2.64163i	1.13348	−	0.412554i	0.839555	+	0.543274i	$0.182816\pi$
$42$		0			0
$43$	−2.14462	−	12.1628i	−0.327052	−	1.85480i	−0.494846	−	0.868981i	$-0.664775\pi$
$43$	−2.14462	−	12.1628i	−0.327052	−	1.85480i	0.167794	−	0.985822i	$-0.446336\pi$
$44$		0			0
$45$	1.92107	+	1.39966i	0.286376	+	0.208649i
$46$		0			0
$47$	−4.85227	+	4.07154i	−0.707777	+	0.593895i	−0.923974	−	0.382454i	$-0.875079\pi$
$47$	−4.85227	+	4.07154i	−0.707777	+	0.593895i	0.216198	+	0.976350i	$0.430634\pi$
$48$		0			0
$49$	0.173648	−	0.984808i	0.0248069	−	0.140687i
$50$		0			0
$51$	0.166698	+	4.86674i	0.0233424	+	0.681480i
$52$		0			0
$53$	11.0374			1.51610			0.758048	−	0.652198i	$-0.226153\pi$
$53$	11.0374			1.51610			0.758048	+	0.652198i	$0.226153\pi$
$54$		0			0
$55$	3.71047			0.500319
$56$		0			0
$57$	7.35278	+	3.91584i	0.973899	+	0.518666i
$58$		0			0
$59$	2.27829	−	12.9209i	0.296609	−	1.68215i	−0.363983	−	0.931406i	$-0.618583\pi$
$59$	2.27829	−	12.9209i	0.296609	−	1.68215i	0.660591	−	0.750746i	$-0.270306\pi$
$60$		0			0
$61$	−5.05371	+	4.24056i	−0.647061	+	0.542948i	−0.906177	−	0.422898i	$-0.861013\pi$
$61$	−5.05371	+	4.24056i	−0.647061	+	0.542948i	0.259117	+	0.965846i	$0.416569\pi$
$62$		0			0
$63$	0.721879	+	2.91185i	0.0909483	+	0.366859i
$64$		0			0
$65$	−0.316317	−	1.79392i	−0.0392343	−	0.222509i
$66$		0			0
$67$	9.23265	−	3.36041i	1.12795	−	0.410540i	0.290401	−	0.956905i	$-0.406211\pi$
$67$	9.23265	−	3.36041i	1.12795	−	0.410540i	0.837547	+	0.546365i	$0.183989\pi$
$68$		0			0
$69$	−12.5830	−	1.77699i	−1.51482	−	0.213925i
$70$		0			0
$71$	−1.99424	+	3.45413i	−0.236673	+	0.409930i	−0.959758	−	0.280830i	$-0.909390\pi$
$71$	−1.99424	+	3.45413i	−0.236673	+	0.409930i	0.723084	+	0.690760i	$0.242724\pi$
$72$		0			0
$73$	−2.23812	−	3.87653i	−0.261952	−	0.453714i	0.704809	−	0.709397i	$-0.251033\pi$
$73$	−2.23812	−	3.87653i	−0.261952	−	0.453714i	−0.966761	+	0.255684i	$0.917700\pi$
$74$		0			0
$75$	−7.40856	+	1.56957i	−0.855467	+	0.181238i
$76$		0			0
$77$	3.58754	+	3.01031i	0.408839	+	0.343056i
$78$		0			0
$79$	−12.7928	−	4.65620i	−1.43930	−	0.523863i	−0.499720	−	0.866187i	$-0.666564\pi$
$79$	−12.7928	−	4.65620i	−1.43930	−	0.523863i	−0.939582	+	0.342324i	$0.888786\pi$
$80$		0			0
$81$	−5.52200	−	7.10686i	−0.613556	−	0.789652i
$82$		0			0
$83$	0.490062	+	0.178368i	0.0537913	+	0.0195784i	0.368776	−	0.929518i	$-0.379777\pi$
$83$	0.490062	+	0.178368i	0.0537913	+	0.0195784i	−0.314984	+	0.949097i	$0.601999\pi$
$84$		0			0
$85$	1.70636	+	1.43181i	0.185081	+	0.155301i
$86$		0			0
$87$	−3.06524	+	0.649398i	−0.328628	+	0.0696228i
$88$		0			0
$89$	3.53294	+	6.11923i	0.374491	+	0.648637i	0.990251	−	0.139297i	$-0.0444842\pi$
$89$	3.53294	+	6.11923i	0.374491	+	0.648637i	−0.615760	+	0.787934i	$0.711151\pi$
$90$		0			0
$91$	1.14958	−	1.99112i	0.120508	−	0.208726i
$92$		0			0
$93$	5.77269	+	0.815228i	0.598600	+	0.0845352i
$94$		0			0
$95$	3.58081	−	1.30331i	0.367383	−	0.133717i
$96$		0			0
$97$	1.02804	+	5.83029i	0.104381	+	0.591976i	0.991466	+	0.130369i	$0.0416161\pi$
$97$	1.02804	+	5.83029i	0.104381	+	0.591976i	−0.887084	+	0.461608i	$0.847273\pi$
$98$		0			0
$99$	−13.5002	−	3.89062i	−1.35682	−	0.391022i
$100$		0			0
$101$	12.0787	−	10.1352i	1.20187	−	1.00849i	0.202300	−	0.979324i	$-0.435158\pi$
$101$	12.0787	−	10.1352i	1.20187	−	1.00849i	0.999574	−	0.0291691i	$-0.00928613\pi$
$102$		0			0
$103$	−2.86912	+	16.2716i	−0.282703	+	1.60329i	0.430675	+	0.902507i	$0.358276\pi$
$103$	−2.86912	+	16.2716i	−0.282703	+	1.60329i	−0.713378	+	0.700780i	$0.752836\pi$
$104$		0			0
$105$	1.21123	+	0.645059i	0.118204	+	0.0629514i
$106$		0			0
$107$	1.82234			0.176172			0.0880862	−	0.996113i	$-0.471925\pi$
$107$	1.82234			0.176172			0.0880862	+	0.996113i	$0.471925\pi$
$108$		0			0
$109$	−10.9885			−1.05250			−0.526252	−	0.850329i	$-0.676403\pi$
$109$	−10.9885			−1.05250			−0.526252	+	0.850329i	$0.676403\pi$
$110$		0			0
$111$	0.447481	+	13.0642i	0.0424730	+	1.24000i
$112$		0			0
$113$	1.97645	−	11.2090i	0.185929	−	1.05445i	−0.738828	−	0.673894i	$-0.764620\pi$
$113$	1.97645	−	11.2090i	0.185929	−	1.05445i	0.924757	−	0.380559i	$-0.124268\pi$
$114$		0			0
$115$	−4.45298	+	3.73650i	−0.415243	+	0.348430i
$116$		0			0
$117$	−0.730136	+	6.85870i	−0.0675011	+	0.634087i
$118$		0			0
$119$	0.488205	+	2.76875i	0.0447537	+	0.253811i
$120$		0			0
$121$	−10.2731	+	3.73911i	−0.933920	+	0.339919i
$122$		0			0
$123$	−8.24317	+	10.5363i	−0.743261	+	0.950023i
$124$		0			0
$125$	−3.71279	+	6.43074i	−0.332082	+	0.575183i
$126$		0			0
$127$	−3.28128	−	5.68335i	−0.291167	−	0.504315i	0.682919	−	0.730494i	$-0.260710\pi$
$127$	−3.28128	−	5.68335i	−0.291167	−	0.504315i	−0.974086	+	0.226178i	$0.927377\pi$
$128$		0			0
$129$	14.3031	+	15.9065i	1.25932	+	1.40049i
$130$		0			0
$131$	4.86799	+	4.08473i	0.425319	+	0.356885i	0.830182	−	0.557492i	$-0.188236\pi$
$131$	4.86799	+	4.08473i	0.425319	+	0.356885i	−0.404863	+	0.914377i	$0.632681\pi$
$132$		0			0
$133$	4.51956	+	1.64498i	0.391895	+	0.142638i
$134$		0			0
$135$	−4.10626	−	0.295401i	−0.353410	−	0.0254240i
$136$		0			0
$137$	−15.3527	−	5.58794i	−1.31167	−	0.477410i	−0.410892	−	0.911684i	$-0.634783\pi$
$137$	−15.3527	−	5.58794i	−1.31167	−	0.477410i	−0.900781	+	0.434274i	$0.857005\pi$
$138$		0			0
$139$	−3.43462	−	2.88199i	−0.291320	−	0.244447i	0.485400	−	0.874292i	$-0.338674\pi$
$139$	−3.43462	−	2.88199i	−0.291320	−	0.244447i	−0.776721	+	0.629845i	$0.783118\pi$
$140$		0			0
$141$	3.39723	−	10.4319i	0.286099	−	0.878526i
$142$		0			0
$143$	5.38370	+	9.32484i	0.450208	+	0.779782i
$144$		0			0
$145$	−0.716626	+	1.24123i	−0.0595125	+	0.103079i
$146$		0			0
$147$	0.647766	+	1.60636i	0.0534268	+	0.132491i
$148$		0			0
$149$	−9.33233	+	3.39669i	−0.764534	+	0.278268i	−0.694708	−	0.719291i	$-0.744467\pi$
$149$	−9.33233	+	3.39669i	−0.764534	+	0.278268i	−0.0698260	+	0.997559i	$0.522244\pi$
$150$		0			0
$151$	−3.61007	−	20.4738i	−0.293784	−	1.66613i	−0.672105	−	0.740456i	$-0.734610\pi$
$151$	−3.61007	−	20.4738i	−0.293784	−	1.66613i	0.378321	−	0.925674i	$-0.376501\pi$
$152$		0			0
$153$	−4.70711	−	6.99871i	−0.380547	−	0.565813i
$154$		0			0
$155$	2.04289	−	1.71419i	0.164089	−	0.137687i
$156$		0			0
$157$	2.30526	−	13.0738i	0.183980	−	1.04340i	−0.743280	−	0.668980i	$-0.766731\pi$
$157$	2.30526	−	13.0738i	0.183980	−	1.04340i	0.927260	−	0.374419i	$-0.122158\pi$
$158$		0			0
$159$	−16.2191	+	10.1198i	−1.28626	+	0.802551i
$160$		0			0
$161$	−7.33689			−0.578228
$162$		0			0
$163$	−10.1643			−0.796126			−0.398063	−	0.917358i	$-0.630317\pi$
$163$	−10.1643			−0.796126			−0.398063	+	0.917358i	$0.630317\pi$
$164$		0			0
$165$	−5.45244	+	3.40200i	−0.424471	+	0.264845i
$166$		0			0
$167$	−0.496842	+	2.81773i	−0.0384468	+	0.218042i	−0.997978	−	0.0635596i	$-0.979755\pi$
$167$	−0.496842	+	2.81773i	−0.0384468	+	0.218042i	0.959531	+	0.281602i	$0.0908658\pi$
$168$		0			0
$169$	−5.90920	+	4.95840i	−0.454553	+	0.381416i
$170$		0			0
$171$	−14.3950	+	0.987291i	−1.10082	+	0.0755000i
$172$		0			0
$173$	−1.62656	−	9.22471i	−0.123665	−	0.701342i	−0.982092	−	0.188404i	$-0.939668\pi$
$173$	−1.62656	−	9.22471i	−0.123665	−	0.701342i	0.858426	−	0.512937i	$-0.171443\pi$
$174$		0			0
$175$	−4.10859	+	1.49541i	−0.310580	+	0.113042i
$176$		0			0
$177$	8.49880	+	21.0758i	0.638809	+	1.58415i
$178$		0			0
$179$	−8.36067	+	14.4811i	−0.624906	+	1.08237i	0.363653	+	0.931534i	$0.381529\pi$
$179$	−8.36067	+	14.4811i	−0.624906	+	1.08237i	−0.988559	+	0.150834i	$0.951804\pi$
$180$		0			0
$181$	3.87816	+	6.71717i	0.288262	+	0.499284i	0.973395	−	0.229134i	$-0.0735894\pi$
$181$	3.87816	+	6.71717i	0.288262	+	0.499284i	−0.685133	+	0.728418i	$0.740256\pi$
$182$		0			0
$183$	3.53826	−	10.8650i	0.261556	−	0.803162i
$184$		0			0
$185$	4.58052	+	3.84351i	0.336766	+	0.282581i
$186$		0			0
$187$	−12.3726	−	4.50326i	−0.904775	−	0.329311i
$188$		0			0
$189$	−3.73056	−	3.61703i	−0.271359	−	0.263100i
$190$		0			0
$191$	11.3326	+	4.12472i	0.819996	+	0.298454i	0.717746	−	0.696305i	$-0.245174\pi$
$191$	11.3326	+	4.12472i	0.819996	+	0.298454i	0.102249	+	0.994759i	$0.467396\pi$
$192$		0			0
$193$	17.6295	+	14.7929i	1.26900	+	1.06482i	0.994663	+	0.103181i	$0.0329022\pi$
$193$	17.6295	+	14.7929i	1.26900	+	1.06482i	0.274335	+	0.961634i	$0.411542\pi$
$194$		0			0
$195$	2.10961	+	2.34610i	0.151072	+	0.168008i
$196$		0			0
$197$	−2.61349	−	4.52669i	−0.186203	−	0.322514i	0.757778	−	0.652512i	$-0.226285\pi$
$197$	−2.61349	−	4.52669i	−0.186203	−	0.322514i	−0.943981	+	0.329999i	$0.892952\pi$
$198$		0			0
$199$	5.21166	−	9.02687i	0.369445	−	0.639898i	−0.620034	−	0.784575i	$-0.712881\pi$
$199$	5.21166	−	9.02687i	0.369445	−	0.639898i	0.989479	+	0.144677i	$0.0462145\pi$
$200$		0			0
$201$	−10.4861	+	13.4032i	−0.739633	+	0.945385i
$202$		0			0
$203$	−1.69990	+	0.618713i	−0.119310	+	0.0434251i
$204$		0			0
$205$	1.06262	+	6.02639i	0.0742163	+	0.420901i
$206$		0			0
$207$	20.1197	−	8.92570i	1.39841	−	0.620379i
$208$		0			0
$209$	−17.2547	+	14.4784i	−1.19353	+	1.00149i
$210$		0			0
$211$	−0.707503	+	4.01245i	−0.0487065	+	0.276228i	−0.999428	−	0.0338178i	$-0.989233\pi$
$211$	−0.707503	+	4.01245i	−0.0487065	+	0.276228i	0.950721	+	0.310046i	$0.100345\pi$
$212$		0			0
$213$	−0.236487	−	6.90421i	−0.0162038	−	0.473069i
$214$		0			0
$215$	9.78511			0.667339
$216$		0			0
$217$	3.36593			0.228494
$218$		0			0
$219$	6.84312	+	3.64441i	0.462415	+	0.246267i
$220$		0			0
$221$	−1.12246	+	6.36577i	−0.0755047	+	0.428208i
$222$		0			0
$223$	−7.97698	+	6.69348i	−0.534178	+	0.448228i	−0.869541	−	0.493860i	$-0.835585\pi$
$223$	−7.97698	+	6.69348i	−0.534178	+	0.448228i	0.335363	+	0.942089i	$0.391141\pi$
$224$		0			0
$225$	9.44761	−	9.09911i	0.629840	−	0.606607i
$226$		0			0
$227$	−3.18963	−	18.0893i	−0.211703	−	1.20063i	−0.886537	−	0.462658i	$-0.846896\pi$
$227$	−3.18963	−	18.0893i	−0.211703	−	1.20063i	0.674834	−	0.737970i	$-0.264215\pi$
$228$		0			0
$229$	13.2618	−	4.82691i	0.876367	−	0.318972i	0.135624	−	0.990760i	$-0.456696\pi$
$229$	13.2618	−	4.82691i	0.876367	−	0.318972i	0.740743	+	0.671789i	$0.234474\pi$
$230$		0			0
$231$	−8.03186	−	1.13427i	−0.528457	−	0.0746295i
$232$		0			0
$233$	5.23915	−	9.07448i	0.343228	−	0.594489i	−0.641802	−	0.766870i	$-0.721813\pi$
$233$	5.23915	−	9.07448i	0.343228	−	0.594489i	0.985030	+	0.172382i	$0.0551462\pi$
$234$		0			0
$235$	−2.50926	−	4.34617i	−0.163686	−	0.283513i
$236$		0			0
$237$	23.0678	−	4.88712i	1.49841	−	0.317453i
$238$		0			0
$239$	3.91262	+	3.28308i	0.253086	+	0.212365i	0.760500	−	0.649338i	$-0.224954\pi$
$239$	3.91262	+	3.28308i	0.253086	+	0.212365i	−0.507414	+	0.861703i	$0.669398\pi$
$240$		0			0
$241$	−24.7884	−	9.02222i	−1.59676	−	0.581172i	−0.617998	−	0.786180i	$-0.712056\pi$
$241$	−24.7884	−	9.02222i	−1.59676	−	0.581172i	−0.978760	+	0.205007i	$0.934278\pi$
$242$		0			0
$243$	14.6305	+	5.38042i	0.938546	+	0.345154i
$244$		0			0
$245$	0.744511	+	0.270980i	0.0475650	+	0.0173123i
$246$		0			0
$247$	8.47094	+	7.10796i	0.538993	+	0.452269i
$248$		0			0
$249$	−0.883673	+	0.187214i	−0.0560005	+	0.0118642i
$250$		0			0
$251$	8.74261	+	15.1426i	0.551829	+	0.955796i	0.998143	+	0.0609191i	$0.0194032\pi$
$251$	8.74261	+	15.1426i	0.551829	+	0.955796i	−0.446314	+	0.894876i	$0.647264\pi$
$252$		0			0
$253$	17.1801	−	29.7568i	1.08010	−	1.87079i
$254$		0			0
$255$	−3.82023	−	0.539499i	−0.239232	−	0.0337848i
$256$		0			0
$257$	10.6581	−	3.87925i	0.664837	−	0.241981i	0.0125137	−	0.999922i	$-0.496017\pi$
$257$	10.6581	−	3.87925i	0.664837	−	0.241981i	0.652323	+	0.757941i	$0.273794\pi$
$258$		0			0
$259$	1.31053	+	7.43236i	0.0814321	+	0.461825i
$260$		0			0
$261$	3.90888	−	3.76469i	0.241953	−	0.233028i
$262$		0			0
$263$	3.95289	−	3.31687i	0.243745	−	0.204527i	−0.512728	−	0.858551i	$-0.671365\pi$
$263$	3.95289	−	3.31687i	0.243745	−	0.204527i	0.756473	+	0.654024i	$0.226921\pi$
$264$		0			0
$265$	−1.51852	+	8.61195i	−0.0932819	+	0.529028i
$266$		0			0
$267$	−10.8021	−	5.75282i	−0.661077	−	0.352067i
$268$		0			0
$269$	−18.5168			−1.12899			−0.564495	−	0.825436i	$-0.690929\pi$
$269$	−18.5168			−1.12899			−0.564495	+	0.825436i	$0.690929\pi$
$270$		0			0
$271$	6.86445			0.416986			0.208493	−	0.978024i	$-0.433144\pi$
$271$	6.86445			0.416986			0.208493	+	0.978024i	$0.433144\pi$
$272$		0			0
$273$	0.136322	+	3.97991i	0.00825059	+	0.240875i
$274$		0			0
$275$	3.55567	−	20.1652i	0.214415	−	1.21601i
$276$		0			0
$277$	−6.54638	+	5.49306i	−0.393334	+	0.330046i	−0.817910	−	0.575346i	$-0.804867\pi$
$277$	−6.54638	+	5.49306i	−0.393334	+	0.330046i	0.424576	+	0.905392i	$0.360423\pi$
$278$		0			0
$279$	−9.23027	+	4.09483i	−0.552602	+	0.245151i
$280$		0			0
$281$	0.775821	+	4.39990i	0.0462816	+	0.262476i	0.999165	−	0.0408613i	$-0.0130102\pi$
$281$	0.775821	+	4.39990i	0.0462816	+	0.262476i	−0.952883	+	0.303337i	$0.901899\pi$
$282$		0			0
$283$	−14.7435	+	5.36620i	−0.876411	+	0.318987i	−0.740760	−	0.671769i	$-0.765535\pi$
$283$	−14.7435	+	5.36620i	−0.876411	+	0.318987i	−0.135650	+	0.990757i	$0.543312\pi$
$284$		0			0
$285$	−4.06695	+	5.19830i	−0.240905	+	0.307921i
$286$		0			0
$287$	−3.86181	+	6.68885i	−0.227955	+	0.394830i
$288$		0			0
$289$	4.54784	+	7.87709i	0.267520	+	0.463358i
$290$		0			0
$291$	−6.85627	−	7.62489i	−0.401922	−	0.446979i
$292$		0			0
$293$	−3.82915	−	3.21304i	−0.223702	−	0.187708i	0.524048	−	0.851689i	$-0.324421\pi$
$293$	−3.82915	−	3.21304i	−0.223702	−	0.187708i	−0.747750	+	0.663981i	$0.768866\pi$
$294$		0			0
$295$	9.76811	+	3.55530i	0.568721	+	0.206998i
$296$		0			0
$297$	23.4054	−	6.66069i	1.35812	−	0.386492i
$298$		0			0
$299$	−15.8513	−	5.76941i	−0.916705	−	0.333653i
$300$		0			0
$301$	9.46094	+	7.93868i	0.545320	+	0.457578i
$302$		0			0
$303$	−8.45668	+	25.9680i	−0.485824	+	1.49182i
$304$		0			0
$305$	−2.61343	−	4.52660i	−0.149645	−	0.259192i
$306$		0			0
$307$	7.41018	−	12.8348i	0.422921	−	0.732521i	−0.573303	−	0.819344i	$-0.694338\pi$
$307$	7.41018	−	12.8348i	0.422921	−	0.732521i	0.996224	+	0.0868229i	$0.0276714\pi$
$308$		0			0
$309$	−10.7028	−	26.5413i	−0.608859	−	1.50988i
$310$		0			0
$311$	32.5612	−	11.8513i	1.84638	−	0.672026i	0.859370	−	0.511355i	$-0.170856\pi$
$311$	32.5612	−	11.8513i	1.84638	−	0.672026i	0.987008	−	0.160672i	$-0.0513660\pi$
$312$		0			0
$313$	1.63140	+	9.25211i	0.0922120	+	0.522960i	0.995566	+	0.0940647i	$0.0299861\pi$
$313$	1.63140	+	9.25211i	0.0922120	+	0.522960i	−0.903354	+	0.428896i	$0.858903\pi$
$314$		0			0
$315$	−2.37130	+	0.162637i	−0.133608	+	0.00916357i
$316$		0			0
$317$	−6.30287	+	5.28874i	−0.354005	+	0.297045i	−0.802396	−	0.596792i	$-0.796442\pi$
$317$	−6.30287	+	5.28874i	−0.354005	+	0.297045i	0.448391	+	0.893837i	$0.351997\pi$
$318$		0			0
$319$	1.47113	−	8.34319i	0.0823675	−	0.467129i
$320$		0			0
$321$	−2.67789	+	1.67084i	−0.149465	+	0.0932574i
$322$		0			0
$323$	−13.5221			−0.752387
$324$		0			0
$325$	−10.0525			−0.557613
$326$		0			0
$327$	16.1473	−	10.0750i	0.892946	−	0.557146i
$328$		0			0
$329$	1.09992	−	6.23796i	0.0606406	−	0.343910i
$330$		0			0
$331$	6.37211	−	5.34684i	0.350243	−	0.293889i	−0.450645	−	0.892703i	$-0.648806\pi$
$331$	6.37211	−	5.34684i	0.350243	−	0.293889i	0.800888	+	0.598815i	$0.204361\pi$
$332$		0			0
$333$	−12.6357	−	18.7872i	−0.692429	−	1.02953i
$334$		0			0
$335$	1.35175	+	7.66615i	0.0738539	+	0.418846i
$336$		0			0
$337$	21.5103	−	7.82911i	1.17174	−	0.426479i	0.318463	−	0.947935i	$-0.396833\pi$
$337$	21.5103	−	7.82911i	1.17174	−	0.426479i	0.853278	+	0.521456i	$0.174611\pi$
$338$		0			0
$339$	7.37281	+	18.2835i	0.400436	+	0.993022i
$340$		0			0
$341$	−7.88168	+	13.6515i	−0.426817	+	0.739269i
$342$		0			0
$343$	0.500000	+	0.866025i	0.0269975	+	0.0467610i
$344$		0			0
$345$	3.11768	−	9.57348i	0.167850	−	0.515419i
$346$		0			0
$347$	23.4379	+	19.6667i	1.25821	+	1.05576i	0.995870	+	0.0907878i	$0.0289385\pi$
$347$	23.4379	+	19.6667i	1.25821	+	1.05576i	0.262340	+	0.964976i	$0.415506\pi$
$348$		0			0
$349$	−14.9219	−	5.43112i	−0.798749	−	0.290721i	−0.0897813	−	0.995962i	$-0.528617\pi$
$349$	−14.9219	−	5.43112i	−0.798749	−	0.290721i	−0.708968	+	0.705240i	$0.750839\pi$
$350$		0			0
$351$	−5.21559	−	10.7481i	−0.278388	−	0.573692i
$352$		0			0
$353$	−12.5457	−	4.56627i	−0.667741	−	0.243038i	−0.0141660	−	0.999900i	$-0.504509\pi$
$353$	−12.5457	−	4.56627i	−0.667741	−	0.243038i	−0.653575	+	0.756862i	$0.726732\pi$
$354$		0			0
$355$	−2.42073	−	2.03124i	−0.128479	−	0.107807i
$356$		0			0
$357$	−3.25598	−	3.62099i	−0.172325	−	0.191643i
$358$		0			0
$359$	4.54035	+	7.86412i	0.239631	+	0.415052i	0.960608	−	0.277906i	$-0.0896404\pi$
$359$	4.54035	+	7.86412i	0.239631	+	0.415052i	−0.720978	+	0.692958i	$0.756307\pi$
$360$		0			0
$361$	−2.06619	+	3.57875i	−0.108747	+	0.188355i
$362$		0			0
$363$	11.6678	−	14.9136i	0.612402	−	0.782761i
$364$		0			0
$365$	3.33260	−	1.21297i	0.174437	−	0.0634897i
$366$		0			0
$367$	5.93783	+	33.6751i	0.309952	+	1.75783i	0.599227	+	0.800579i	$0.295475\pi$
$367$	5.93783	+	33.6751i	0.309952	+	1.75783i	−0.289275	+	0.957246i	$0.593414\pi$
$368$		0			0
$369$	2.45277	−	23.0407i	0.127686	−	1.19945i
$370$		0			0
$371$	−8.45510	+	7.09467i	−0.438967	+	0.368337i
$372$		0			0
$373$	−3.60392	+	20.4389i	−0.186604	+	1.05828i	0.737273	+	0.675595i	$0.236113\pi$
$373$	−3.60392	+	20.4389i	−0.186604	+	1.05828i	−0.923877	+	0.382689i	$0.874998\pi$
$374$		0			0
$375$	−0.440280	−	12.8539i	−0.0227360	−	0.663774i
$376$		0			0
$377$	−4.15915			−0.214207
$378$		0			0
$379$	31.7289			1.62981			0.814903	−	0.579598i	$-0.196790\pi$
$379$	31.7289			1.62981			0.814903	+	0.579598i	$0.196790\pi$
$380$		0			0
$381$	10.0326	+	5.34304i	0.513987	+	0.273732i
$382$		0			0
$383$	2.56158	−	14.5274i	0.130890	−	0.742317i	−0.846743	−	0.532002i	$-0.821440\pi$
$383$	2.56158	−	14.5274i	0.130890	−	0.742317i	0.977634	−	0.210315i	$-0.0674490\pi$
$384$		0			0
$385$	−2.84238	+	2.38504i	−0.144861	+	0.121553i
$386$		0			0
$387$	−35.6022	−	10.2602i	−1.80976	−	0.521556i
$388$		0			0
$389$	−2.33212	−	13.2261i	−0.118243	−	0.670592i	−0.985093	−	0.172022i	$-0.944970\pi$
$389$	−2.33212	−	13.2261i	−0.118243	−	0.670592i	0.866850	−	0.498570i	$-0.166141\pi$
$390$		0			0
$391$	19.3834	−	7.05499i	0.980261	−	0.356786i
$392$		0			0
$393$	−10.8985	−	1.53911i	−0.549759	−	0.0776378i
$394$		0			0
$395$	5.39305	−	9.34104i	0.271354	−	0.469999i
$396$		0			0
$397$	−2.92323	−	5.06319i	−0.146713	−	0.254114i	0.783298	−	0.621647i	$-0.213536\pi$
$397$	−2.92323	−	5.06319i	−0.146713	−	0.254114i	−0.930011	+	0.367532i	$0.880203\pi$
$398$		0			0
$399$	−8.14961	+	1.72657i	−0.407991	+	0.0864365i
$400$		0			0
$401$	5.24098	+	4.39770i	0.261722	+	0.219611i	0.764200	−	0.644979i	$-0.223134\pi$
$401$	5.24098	+	4.39770i	0.261722	+	0.219611i	−0.502478	+	0.864590i	$0.667578\pi$
$402$		0			0
$403$	7.27208	+	2.64682i	0.362248	+	0.131848i
$404$		0			0
$405$	6.30488	−	3.33081i	0.313292	−	0.165509i
$406$		0			0
$407$	−33.2127	−	12.0884i	−1.64629	−	0.599202i
$408$		0			0
$409$	1.06721	+	0.895494i	0.0527700	+	0.0442793i	0.668791	−	0.743450i	$-0.266812\pi$
$409$	1.06721	+	0.895494i	0.0527700	+	0.0442793i	−0.616021	+	0.787730i	$0.711256\pi$
$410$		0			0
$411$	27.6839	−	5.86508i	1.36554	−	0.289303i
$412$		0			0
$413$	6.56009	+	11.3624i	0.322801	+	0.559107i
$414$		0			0
$415$	−0.206595	+	0.357833i	−0.0101414	+	0.0175653i
$416$		0			0
$417$	7.68948	+	1.08592i	0.376555	+	0.0531777i
$418$		0			0
$419$	−37.2367	+	13.5531i	−1.81913	+	0.662110i	−0.823657	+	0.567089i	$0.808070\pi$
$419$	−37.2367	+	13.5531i	−1.81913	+	0.662110i	−0.995475	+	0.0950209i	$0.969708\pi$
$420$		0			0
$421$	1.60415	+	9.09760i	0.0781816	+	0.443390i	0.998621	+	0.0525038i	$0.0167202\pi$
$421$	1.60415	+	9.09760i	0.0781816	+	0.443390i	−0.920439	+	0.390886i	$0.872169\pi$
$422$		0			0
$423$	4.57252	+	18.4442i	0.222324	+	0.896790i
$424$		0			0
$425$	9.41659	−	7.90146i	0.456772	−	0.383277i
$426$		0			0
$427$	1.14558	−	6.49692i	0.0554386	−	0.314408i
$428$		0			0
$429$	−16.4608	−	8.76648i	−0.794737	−	0.423250i
$430$		0			0
$431$	4.74675			0.228643			0.114322	−	0.993444i	$-0.463531\pi$
$431$	4.74675			0.228643			0.114322	+	0.993444i	$0.463531\pi$
$432$		0			0
$433$	15.7195			0.755430			0.377715	−	0.925922i	$-0.376710\pi$
$433$	15.7195			0.755430			0.377715	+	0.925922i	$0.376710\pi$
$434$		0			0
$435$	−0.0849809	−	2.48101i	−0.00407452	−	0.118955i
$436$		0			0
$437$	6.12763	−	34.7515i	0.293124	−	1.66239i
$438$		0			0
$439$	10.6478	−	8.93457i	0.508192	−	0.426424i	−0.352300	−	0.935887i	$-0.614600\pi$
$439$	10.6478	−	8.93457i	0.508192	−	0.426424i	0.860492	+	0.509463i	$0.170156\pi$
$440$		0			0
$441$	−2.42469	−	1.76659i	−0.115462	−	0.0841235i
$442$		0			0
$443$	−0.559471	−	3.17291i	−0.0265812	−	0.150750i	0.968628	−	0.248514i	$-0.0799421\pi$
$443$	−0.559471	−	3.17291i	−0.0265812	−	0.150750i	−0.995210	+	0.0977639i	$0.968831\pi$
$444$		0			0
$445$	−5.26062	+	1.91471i	−0.249377	+	0.0907660i
$446$		0			0
$447$	10.5993	−	13.5479i	0.501330	−	0.640792i
$448$		0			0
$449$	8.52668	−	14.7686i	0.402399	−	0.696976i	−0.591616	−	0.806220i	$-0.701510\pi$
$449$	8.52668	−	14.7686i	0.402399	−	0.696976i	0.994015	+	0.109244i	$0.0348431\pi$
$450$		0			0
$451$	−18.0856	−	31.3253i	−0.851620	−	1.47505i
$452$		0			0
$453$	24.0766	+	26.7757i	1.13122	+	1.25803i
$454$		0			0
$455$	1.39542	+	1.17090i	0.0654185	+	0.0548927i
$456$		0			0
$457$	−9.71589	−	3.53630i	−0.454490	−	0.165421i	0.104623	−	0.994512i	$-0.466636\pi$
$457$	−9.71589	−	3.53630i	−0.454490	−	0.165421i	−0.559114	+	0.829091i	$0.688859\pi$
$458$		0			0
$459$	13.3339	+	5.96864i	0.622372	+	0.278592i
$460$		0			0
$461$	14.9151	+	5.42866i	0.694667	+	0.252838i	0.665132	−	0.746726i	$-0.268375\pi$
$461$	14.9151	+	5.42866i	0.694667	+	0.252838i	0.0295346	+	0.999564i	$0.490597\pi$
$462$		0			0
$463$	−0.239331	−	0.200822i	−0.0111226	−	0.00933300i	0.637209	−	0.770691i	$-0.280089\pi$
$463$	−0.239331	−	0.200822i	−0.0111226	−	0.00933300i	−0.648332	+	0.761358i	$0.724533\pi$
$464$		0			0
$465$	−1.43029	+	4.39201i	−0.0663282	+	0.203675i
$466$		0			0
$467$	2.60851	+	4.51808i	0.120708	+	0.209072i	0.920047	−	0.391808i	$-0.128150\pi$
$467$	2.60851	+	4.51808i	0.120708	+	0.209072i	−0.799339	+	0.600880i	$0.794817\pi$
$468$		0			0
$469$	−4.91259	+	8.50886i	−0.226842	+	0.392903i
$470$		0			0
$471$	8.59938	+	21.3252i	0.396238	+	0.982612i
$472$		0			0
$473$	−54.3513	+	19.7822i	−2.49907	+	0.909589i
$474$		0			0
$475$	−3.65164	−	20.7095i	−0.167549	−	0.950216i
$476$		0			0
$477$	14.5551	−	29.7415i	0.666432	−	1.36177i
$478$		0			0
$479$	−2.17071	+	1.82144i	−0.0991823	+	0.0832238i	−0.691030	−	0.722826i	$-0.742843\pi$
$479$	−2.17071	+	1.82144i	−0.0991823	+	0.0832238i	0.591848	+	0.806049i	$0.298399\pi$
$480$		0			0
$481$	−3.01310	+	17.0881i	−0.137385	+	0.779151i
$482$		0			0
$483$	10.7814	−	6.72695i	0.490570	−	0.306087i
$484$		0			0
$485$	−4.69055			−0.212987
$486$		0			0
$487$	41.8689			1.89726			0.948629	−	0.316389i	$-0.102471\pi$
$487$	41.8689			1.89726			0.948629	+	0.316389i	$0.102471\pi$
$488$		0			0
$489$	14.9361	−	9.31927i	0.675434	−	0.421432i
$490$		0			0
$491$	2.09263	−	11.8679i	0.0944391	−	0.535591i	−0.900479	−	0.434900i	$-0.856784\pi$
$491$	2.09263	−	11.8679i	0.0944391	−	0.535591i	0.994918	−	0.100691i	$-0.0321052\pi$
$492$		0			0
$493$	3.89604	−	3.26917i	0.175469	−	0.147236i
$494$		0			0
$495$	4.89303	−	9.99831i	0.219926	−	0.449391i
$496$		0			0
$497$	−0.692593	−	3.92789i	−0.0310671	−	0.176190i
$498$		0			0
$499$	−37.4229	+	13.6208i	−1.67528	+	0.609752i	−0.992651	−	0.121014i	$-0.961385\pi$
$499$	−37.4229	+	13.6208i	−1.67528	+	0.609752i	−0.682628	+	0.730766i	$0.739163\pi$
$500$		0			0
$501$	−1.85339	−	4.59612i	−0.0828032	−	0.205340i
$502$		0			0
$503$	−13.2280	+	22.9116i	−0.589808	+	1.02158i	0.404449	+	0.914561i	$0.367463\pi$
$503$	−13.2280	+	22.9116i	−0.589808	+	1.02158i	−0.994257	+	0.107017i	$0.965870\pi$
$504$		0			0
$505$	6.24627	+	10.8189i	0.277956	+	0.481433i
$506$		0			0
$507$	4.13722	−	12.7042i	0.183740	−	0.564213i
$508$		0			0
$509$	6.88069	+	5.77358i	0.304981	+	0.255909i	0.782414	−	0.622759i	$-0.213988\pi$
$509$	6.88069	+	5.77358i	0.304981	+	0.255909i	−0.477433	+	0.878668i	$0.658433\pi$
$510$		0			0
$511$	4.20629	+	1.53096i	0.186075	+	0.0677258i
$512$		0			0
$513$	20.2479	−	14.6491i	0.893967	−	0.646774i
$514$		0			0
$515$	−12.3013	−	4.47729i	−0.542058	−	0.197293i
$516$		0			0
$517$	22.7242	+	19.0679i	0.999409	+	0.838604i
$518$		0			0
$519$	10.8480	+	12.0641i	0.476175	+	0.529557i
$520$		0			0
$521$	−5.86161	−	10.1526i	−0.256802	−	0.444794i	0.708581	−	0.705629i	$-0.249335\pi$
$521$	−5.86161	−	10.1526i	−0.256802	−	0.444794i	−0.965383	+	0.260835i	$0.916002\pi$
$522$		0			0
$523$	−6.14985	+	10.6519i	−0.268914	+	0.465773i	−0.968582	−	0.248695i	$-0.919998\pi$
$523$	−6.14985	+	10.6519i	−0.268914	+	0.465773i	0.699667	+	0.714469i	$0.253331\pi$
$524$		0			0
$525$	4.66639	−	5.96449i	0.203658	−	0.260312i
$526$		0			0
$527$	−8.89250	+	3.23660i	−0.387363	+	0.140989i
$528$		0			0
$529$	5.35357	+	30.3616i	0.232764	+	1.32007i
$530$		0			0
$531$	−31.8124	−	23.1780i	−1.38054	−	1.00584i
$532$		0			0
$533$	−13.6032	+	11.4145i	−0.589221	+	0.494415i
$534$		0			0
$535$	−0.250718	+	1.42189i	−0.0108395	+	0.0614737i
$536$		0			0
$537$	−0.991448	−	28.9452i	−0.0427841	−	1.24908i
$538$		0			0
$539$	−4.68321			−0.201720
$540$		0			0
$541$	21.8811			0.940742			0.470371	−	0.882469i	$-0.344120\pi$
$541$	21.8811			0.940742			0.470371	+	0.882469i	$0.344120\pi$
$542$		0			0
$543$	−11.8576	−	6.31496i	−0.508859	−	0.271001i
$544$		0			0
$545$	1.51179	−	8.57380i	0.0647581	−	0.367261i
$546$		0			0
$547$	15.4014	−	12.9233i	0.658518	−	0.552562i	−0.251124	−	0.967955i	$-0.580800\pi$
$547$	15.4014	−	12.9233i	0.658518	−	0.552562i	0.909642	+	0.415393i	$0.136356\pi$
$548$		0			0
$549$	4.76234	+	19.2099i	0.203252	+	0.819859i
$550$		0			0
$551$	−1.51084	−	8.56839i	−0.0643639	−	0.365026i
$552$		0			0
$553$	12.7928	−	4.65620i	0.544005	−	0.198002i
$554$		0			0
$555$	−10.2549	−	1.44822i	−0.435298	−	0.0614734i
$556$		0			0
$557$	−23.4708	+	40.6527i	−0.994491	+	1.72251i	−0.406467	+	0.913665i	$0.633239\pi$
$557$	−23.4708	+	40.6527i	−0.994491	+	1.72251i	−0.588024	+	0.808843i	$0.700094\pi$
$558$		0			0
$559$	14.1977	+	24.5911i	0.600499	+	1.04009i
$560$		0			0
$561$	22.3101	−	4.72660i	0.941935	−	0.199557i
$562$		0			0
$563$	20.0930	+	16.8600i	0.846817	+	0.710564i	0.959086	−	0.283114i	$-0.0913674\pi$
$563$	20.0930	+	16.8600i	0.846817	+	0.710564i	−0.112269	+	0.993678i	$0.535812\pi$
$564$		0			0
$565$	8.47395	+	3.08427i	0.356502	+	0.129756i
$566$		0			0
$567$	8.79830	+	1.89470i	0.369494	+	0.0795700i
$568$		0			0
$569$	−4.65471	−	1.69418i	−0.195136	−	0.0710236i	0.242604	−	0.970125i	$-0.421999\pi$
$569$	−4.65471	−	1.69418i	−0.195136	−	0.0710236i	−0.437739	+	0.899102i	$0.644221\pi$
$570$		0			0
$571$	15.7832	+	13.2437i	0.660508	+	0.554232i	0.910239	−	0.414083i	$-0.135898\pi$
$571$	15.7832	+	13.2437i	0.660508	+	0.554232i	−0.249731	+	0.968315i	$0.580342\pi$
$572$		0			0
$573$	−20.4347	+	4.32928i	−0.853673	+	0.180858i
$574$		0			0
$575$	16.0394	+	27.7811i	0.668891	+	1.15855i
$576$		0			0
$577$	−17.9974	+	31.1725i	−0.749243	+	1.29773i	0.198944	+	0.980011i	$0.436249\pi$
$577$	−17.9974	+	31.1725i	−0.749243	+	1.29773i	−0.948186	+	0.317715i	$0.897084\pi$
$578$		0			0
$579$	−39.4692	−	5.57390i	−1.64028	−	0.231643i
$580$		0			0
$581$	−0.490062	+	0.178368i	−0.0203312	+	0.00739995i
$582$		0			0
$583$	−8.97591	−	50.9049i	−0.371744	−	2.10827i
$584$		0			0
$585$	−5.25108	−	1.51331i	−0.217105	−	0.0625678i
$586$		0			0
$587$	24.0642	−	20.1923i	0.993236	−	0.833424i	0.00720289	−	0.999974i	$-0.497707\pi$
$587$	24.0642	−	20.1923i	0.993236	−	0.833424i	0.986033	+	0.166550i	$0.0532628\pi$
$588$		0			0
$589$	−2.81116	+	15.9429i	−0.115832	+	0.656915i
$590$		0			0
$591$	7.99083	+	4.25564i	0.328699	+	0.175054i
$592$		0			0
$593$	−23.1529			−0.950777			−0.475389	−	0.879776i	$-0.657692\pi$
$593$	−23.1529			−0.950777			−0.475389	+	0.879776i	$0.657692\pi$
$594$		0			0
$595$	−2.22750			−0.0913185
$596$		0			0
$597$	0.618024	+	18.0432i	0.0252940	+	0.738457i
$598$		0			0
$599$	5.63222	−	31.9419i	0.230126	−	1.30511i	−0.622513	−	0.782610i	$-0.713888\pi$
$599$	5.63222	−	31.9419i	0.230126	−	1.30511i	0.852639	−	0.522501i	$-0.175001\pi$
$600$		0			0
$601$	2.03282	−	1.70574i	0.0829204	−	0.0695785i	−0.600385	−	0.799711i	$-0.704986\pi$
$601$	2.03282	−	1.70574i	0.0829204	−	0.0695785i	0.683306	+	0.730132i	$0.260542\pi$
$602$		0			0
$603$	3.12016	−	29.3099i	0.127063	−	1.19359i
$604$		0			0
$605$	−1.50408	−	8.53008i	−0.0611497	−	0.346797i
$606$		0			0
$607$	33.0980	−	12.0467i	1.34341	−	0.488960i	0.432523	−	0.901623i	$-0.357623\pi$
$607$	33.0980	−	12.0467i	1.34341	−	0.488960i	0.910884	+	0.412663i	$0.135401\pi$
$608$		0			0
$609$	1.93068	−	2.46776i	0.0782352	−	0.0999988i
$610$		0			0
$611$	7.28163	−	12.6122i	0.294583	−	0.510233i
$612$		0			0
$613$	2.13370	+	3.69568i	0.0861795	+	0.149267i	0.905893	−	0.423506i	$-0.139201\pi$
$613$	2.13370	+	3.69568i	0.0861795	+	0.149267i	−0.819714	+	0.572773i	$0.805867\pi$
$614$		0			0
$615$	−7.08688	−	7.88135i	−0.285771	−	0.317807i
$616$		0			0
$617$	4.44889	+	3.73307i	0.179106	+	0.150288i	0.727933	−	0.685648i	$-0.240481\pi$
$617$	4.44889	+	3.73307i	0.179106	+	0.150288i	−0.548827	+	0.835936i	$0.684926\pi$
$618$		0			0
$619$	−39.9092	−	14.5258i	−1.60409	−	0.583840i	−0.623830	−	0.781560i	$-0.714424\pi$
$619$	−39.9092	−	14.5258i	−1.60409	−	0.583840i	−0.980259	+	0.197720i	$0.936646\pi$
$620$		0			0
$621$	−21.3817	+	31.5632i	−0.858018	+	1.26659i
$622$		0			0
$623$	−6.63976	−	2.41667i	−0.266016	−	0.0968220i
$624$		0			0
$625$	12.2400	+	10.2706i	0.489599	+	0.410822i
$626$		0			0
$627$	12.0806	−	37.0959i	0.482452	−	1.48147i
$628$		0			0
$629$	−10.6091	−	18.3755i	−0.423012	−	0.732678i
$630$		0			0
$631$	−4.40058	+	7.62202i	−0.175184	+	0.303428i	−0.940225	−	0.340554i	$-0.889385\pi$
$631$	−4.40058	+	7.62202i	−0.175184	+	0.303428i	0.765041	+	0.643982i	$0.222719\pi$
$632$		0			0
$633$	−2.63922	−	6.54488i	−0.104900	−	0.260136i
$634$		0			0
$635$	4.88590	−	1.77832i	0.193891	−	0.0705705i
$636$		0			0
$637$	0.399243	+	2.26422i	0.0158186	+	0.0897117i
$638$		0			0
$639$	6.67775	+	9.92874i	0.264168	+	0.392775i
$640$		0			0
$641$	−29.3441	+	24.6226i	−1.15902	+	0.972534i	−0.999892	−	0.0147241i	$-0.995313\pi$
$641$	−29.3441	+	24.6226i	−1.15902	+	0.972534i	−0.159129	+	0.987258i	$0.550869\pi$
$642$		0			0
$643$	−7.53395	+	42.7271i	−0.297110	+	1.68499i	0.361392	+	0.932414i	$0.382302\pi$
$643$	−7.53395	+	42.7271i	−0.297110	+	1.68499i	−0.658501	+	0.752579i	$0.728809\pi$
$644$		0			0
$645$	−14.3790	+	8.97164i	−0.566171	+	0.353258i
$646$		0			0
$647$	46.5297			1.82927			0.914635	−	0.404281i	$-0.132478\pi$
$647$	46.5297			1.82927			0.914635	+	0.404281i	$0.132478\pi$
$648$		0			0
$649$	−61.4445			−2.41191
$650$		0			0
$651$	−4.94615	+	3.08611i	−0.193855	+	0.120954i
$652$		0			0
$653$	−0.0610495	+	0.346229i	−0.00238905	+	0.0135490i	−0.985979	−	0.166870i	$-0.946634\pi$
$653$	−0.0610495	+	0.346229i	−0.00238905	+	0.0135490i	0.983590	+	0.180419i	$0.0577452\pi$
$654$		0			0
$655$	−3.85687	+	3.23630i	−0.150700	+	0.126453i
$656$		0			0
$657$	−13.3972	+	0.918857i	−0.522676	+	0.0358480i
$658$		0			0
$659$	5.97004	+	33.8578i	0.232560	+	1.31891i	0.847693	+	0.530488i	$0.177991\pi$
$659$	5.97004	+	33.8578i	0.232560	+	1.31891i	−0.615133	+	0.788423i	$0.710898\pi$
$660$		0			0
$661$	8.27345	−	3.01129i	0.321800	−	0.117126i	−0.176069	−	0.984378i	$-0.556338\pi$
$661$	8.27345	−	3.01129i	0.321800	−	0.117126i	0.497869	+	0.867252i	$0.334116\pi$
$662$		0			0
$663$	−4.18714	−	10.3835i	−0.162615	−	0.403261i
$664$		0			0
$665$	−1.90531	+	3.30009i	−0.0738847	+	0.127972i
$666$		0			0
$667$	6.63620	+	11.4942i	0.256955	+	0.445059i
$668$		0			0
$669$	5.58494	−	17.1497i	0.215926	−	0.663046i
$670$		0			0
$671$	23.6675	+	19.8594i	0.913675	+	0.766665i
$672$		0			0
$673$	20.5548	+	7.48134i	0.792330	+	0.288384i	0.706304	−	0.707909i	$-0.250361\pi$
$673$	20.5548	+	7.48134i	0.792330	+	0.288384i	0.0860254	+	0.996293i	$0.472583\pi$
$674$		0			0
$675$	−5.54035	+	22.0331i	−0.213248	+	0.848054i
$676$		0			0
$677$	12.5002	+	4.54971i	0.480423	+	0.174860i	0.570868	−	0.821042i	$-0.306607\pi$
$677$	12.5002	+	4.54971i	0.480423	+	0.174860i	−0.0904454	+	0.995901i	$0.528829\pi$
$678$		0			0
$679$	−4.53516	−	3.80545i	−0.174044	−	0.146040i
$680$		0			0
$681$	21.2725	+	23.6573i	0.815165	+	0.906548i
$682$		0			0
$683$	2.20436	+	3.81806i	0.0843475	+	0.146094i	0.905113	−	0.425171i	$-0.139786\pi$
$683$	2.20436	+	3.81806i	0.0843475	+	0.146094i	−0.820765	+	0.571265i	$0.806453\pi$
$684$		0			0
$685$	6.47225	−	11.2103i	0.247292	−	0.428322i
$686$		0			0
$687$	−15.0623	+	19.2524i	−0.574663	+	0.734524i
$688$		0			0
$689$	−23.8461	+	8.67929i	−0.908466	+	0.330654i
$690$		0			0
$691$	2.44751	+	13.8805i	0.0931076	+	0.528040i	0.995311	+	0.0967284i	$0.0308378\pi$
$691$	2.44751	+	13.8805i	0.0931076	+	0.528040i	−0.902203	+	0.431311i	$0.858051\pi$
$692$		0			0
$693$	12.8426	−	5.69736i	0.487849	−	0.216425i
$694$		0			0
$695$	2.72122	−	2.28337i	0.103222	−	0.0866133i
$696$		0			0
$697$	3.77071	−	21.3848i	0.142826	−	0.810006i
$698$		0			0
$699$	0.621284	+	18.1383i	0.0234991	+	0.686054i
$700$		0			0
$701$	−26.0482			−0.983826			−0.491913	−	0.870644i	$-0.663702\pi$
$701$	−26.0482			−0.983826			−0.491913	+	0.870644i	$0.663702\pi$
$702$		0			0
$703$	−36.2982			−1.36901
$704$		0			0
$705$	7.67216	+	4.08593i	0.288950	+	0.153885i
$706$		0			0
$707$	−2.73802	+	15.5281i	−0.102974	+	0.583993i
$708$		0			0
$709$	−23.9414	+	20.0892i	−0.899139	+	0.754467i	−0.970022	−	0.243018i	$-0.921863\pi$
$709$	−23.9414	+	20.0892i	−0.899139	+	0.754467i	0.0708832	+	0.997485i	$0.477418\pi$
$710$		0			0
$711$	−29.4167	+	28.3316i	−1.10321	+	1.06252i
$712$		0			0
$713$	−4.28833	−	24.3203i	−0.160599	−	0.910803i
$714$		0			0
$715$	−8.01644	+	2.91775i	−0.299798	+	0.109118i
$716$		0			0
$717$	−8.75964	−	1.23705i	−0.327135	−	0.0461985i
$718$		0			0
$719$	−10.0746	+	17.4498i	−0.375720	+	0.650766i	−0.990435	−	0.137983i	$-0.955938\pi$
$719$	−10.0746	+	17.4498i	−0.375720	+	0.650766i	0.614714	+	0.788750i	$0.289271\pi$
$720$		0			0
$721$	−8.26130	−	14.3090i	−0.307667	−	0.532895i
$722$		0			0
$723$	44.6980	−	9.46968i	1.66234	−	0.352181i
$724$		0			0
$725$	6.05897	+	5.08408i	0.225024	+	0.188818i
$726$		0			0
$727$	11.6641	+	4.24540i	0.432599	+	0.157453i	0.549136	−	0.835733i	$-0.314957\pi$
$727$	11.6641	+	4.24540i	0.432599	+	0.157453i	−0.116536	+	0.993186i	$0.537179\pi$
$728$		0			0
$729$	−26.4323	+	5.50781i	−0.978972	+	0.203993i
$730$		0			0
$731$	−32.6286	−	11.8758i	−1.20681	−	0.439244i
$732$		0			0
$733$	−26.5473	−	22.2758i	−0.980545	−	0.822775i	0.00362630	−	0.999993i	$-0.498846\pi$
$733$	−26.5473	−	22.2758i	−0.980545	−	0.822775i	−0.984172	+	0.177218i	$0.943290\pi$
$734$		0			0
$735$	−1.34249	+	0.284419i	−0.0495186	+	0.0104910i
$736$		0			0
$737$	−23.0067	−	39.8487i	−0.847462	−	1.46785i
$738$		0			0
$739$	13.4450	−	23.2874i	0.494581	−	0.856639i	−0.505400	−	0.862885i	$-0.668655\pi$
$739$	13.4450	−	23.2874i	0.494581	−	0.856639i	0.999980	+	0.00624609i	$0.00198821\pi$
$740$		0			0
$741$	−18.9649	−	2.67825i	−0.696692	−	0.0983880i
$742$		0			0
$743$	−40.3434	+	14.6838i	−1.48006	+	0.538696i	−0.950811	−	0.309773i	$-0.899747\pi$
$743$	−40.3434	+	14.6838i	−1.48006	+	0.538696i	−0.529245	+	0.848469i	$0.677525\pi$
$744$		0			0
$745$	−1.36634	−	7.74892i	−0.0500589	−	0.283898i
$746$		0			0
$747$	1.12688	−	1.08532i	0.0412306	−	0.0397097i
$748$		0			0
$749$	−1.39599	+	1.17138i	−0.0510085	+	0.0428012i
$750$		0			0
$751$	1.53261	−	8.69186i	0.0559257	−	0.317170i	−0.943992	−	0.329967i	$-0.892962\pi$
$751$	1.53261	−	8.69186i	0.0559257	−	0.317170i	0.999918	+	0.0127968i	$0.00407345\pi$
$752$		0			0
$753$	−26.7308	−	14.2359i	−0.974126	−	0.518786i
$754$		0			0
$755$	16.4714			0.599456
$756$		0			0
$757$	−21.0050			−0.763439			−0.381719	−	0.924278i	$-0.624668\pi$
$757$	−21.0050			−0.763439			−0.381719	+	0.924278i	$0.624668\pi$
$758$		0			0
$759$	2.03730	+	59.4787i	0.0739492	+	2.15894i
$760$		0			0
$761$	3.36253	−	19.0699i	0.121892	−	0.691283i	−0.861214	−	0.508243i	$-0.830295\pi$
$761$	3.36253	−	19.0699i	0.121892	−	0.691283i	0.983106	−	0.183040i	$-0.0585937\pi$
$762$		0			0
$763$	8.41765	−	7.06325i	0.304739	−	0.255707i
$764$		0			0
$765$	6.10839	−	2.70986i	0.220849	−	0.0979754i
$766$		0			0
$767$	5.23814	+	29.7070i	0.189138	+	1.07266i
$768$		0			0
$769$	4.48742	−	1.63329i	0.161820	−	0.0588978i	−0.259840	−	0.965652i	$-0.583670\pi$
$769$	4.48742	−	1.63329i	0.161820	−	0.0588978i	0.421660	+	0.906754i	$0.361448\pi$
$770$		0			0
$771$	−12.1051	+	15.4726i	−0.435955	+	0.557231i
$772$		0			0
$773$	−1.89623	+	3.28437i	−0.0682027	+	0.118131i	−0.898110	−	0.439770i	$-0.855060\pi$
$773$	−1.89623	+	3.28437i	−0.0682027	+	0.118131i	0.829907	+	0.557901i	$0.188393\pi$
$774$		0			0
$775$	−7.35839	−	12.7451i	−0.264321	−	0.457818i
$776$		0			0
$777$	−8.74027	−	9.72009i	−0.313555	−	0.348706i
$778$		0			0
$779$	−28.4567	−	23.8780i	−1.01957	−	0.855519i
$780$		0			0
$781$	17.5524	+	6.38856i	0.628075	+	0.228601i
$782$		0			0
$783$	−2.29228	+	9.11603i	−0.0819194	+	0.325780i
$784$		0			0
$785$	9.88371	+	3.59738i	0.352765	+	0.128396i
$786$		0			0
$787$	−2.59683	−	2.17900i	−0.0925672	−	0.0776731i	0.595330	−	0.803481i	$-0.297021\pi$
$787$	−2.59683	−	2.17900i	−0.0925672	−	0.0776731i	−0.687897	+	0.725808i	$0.741466\pi$
$788$		0			0
$789$	−2.76754	+	8.49832i	−0.0985272	+	0.302548i
$790$		0			0
$791$	5.69095	+	9.85702i	0.202347	+	0.350475i
$792$		0			0
$793$	7.58391	−	13.1357i	0.269313	−	0.466463i
$794$		0			0
$795$	−5.66458	−	14.0473i	−0.200902	−	0.498207i
$796$		0			0
$797$	−46.9995	+	17.1064i	−1.66481	+	0.605940i	−0.991107	−	0.133065i	$-0.957518\pi$
$797$	−46.9995	+	17.1064i	−1.66481	+	0.605940i	−0.673700	+	0.739005i	$0.735296\pi$
$798$		0			0
$799$	3.09239	+	17.5378i	0.109401	+	0.620443i
$800$		0			0
$801$	21.1480	−	1.45044i	0.747226	−	0.0512489i
$802$		0			0
$803$	−16.0587	+	13.4748i	−0.566699	+	0.475517i
$804$		0			0
$805$	1.00941	−	5.72465i	0.0355770	−	0.201767i
$806$		0			0
$807$	27.2100	−	16.9774i	0.957837	−	0.597634i
$808$		0			0
$809$	−28.4111			−0.998882			−0.499441	−	0.866348i	$-0.666461\pi$
$809$	−28.4111			−0.998882			−0.499441	+	0.866348i	$0.666461\pi$
$810$		0			0
$811$	15.3001			0.537260			0.268630	−	0.963243i	$-0.413429\pi$
$811$	15.3001			0.537260			0.268630	+	0.963243i	$0.413429\pi$
$812$		0			0
$813$	−10.0871	+	6.29379i	−0.353772	+	0.220733i
$814$		0			0
$815$	1.39840	−	7.93071i	0.0489838	−	0.277801i
$816$		0			0
$817$	−45.5035	+	38.1820i	−1.59197	+	1.33582i
$818$		0			0
$819$	−3.84937	−	5.72339i	−0.134508	−	0.199991i
$820$		0			0
$821$	6.93674	+	39.3402i	0.242094	+	1.37298i	0.827146	+	0.561987i	$0.189963\pi$
$821$	6.93674	+	39.3402i	0.242094	+	1.37298i	−0.585053	+	0.810995i	$0.698926\pi$
$822$		0			0
$823$	−6.96760	+	2.53600i	−0.242875	+	0.0883994i	−0.460590	−	0.887613i	$-0.652362\pi$
$823$	−6.96760	+	2.53600i	−0.242875	+	0.0883994i	0.217714	+	0.976013i	$0.430140\pi$
$824$		0			0
$825$	13.2638	+	32.8923i	0.461787	+	1.14516i
$826$		0			0
$827$	−11.7859	+	20.4137i	−0.409834	+	0.709854i	−0.994871	−	0.101153i	$-0.967747\pi$
$827$	−11.7859	+	20.4137i	−0.409834	+	0.709854i	0.585037	+	0.811007i	$0.301080\pi$
$828$		0			0
$829$	−9.08283	−	15.7319i	−0.315460	−	0.546393i	0.664075	−	0.747666i	$-0.268825\pi$
$829$	−9.08283	−	15.7319i	−0.315460	−	0.546393i	−0.979535	+	0.201273i	$0.935492\pi$
$830$		0			0
$831$	4.58333	−	14.0741i	0.158994	−	0.488224i
$832$		0			0
$833$	−2.15371	−	1.80717i	−0.0746215	−	0.0626149i
$834$		0			0
$835$	−2.13019	−	0.775327i	−0.0737183	−	0.0268313i
$836$		0			0
$837$	9.80924	−	14.4802i	0.339057	−	0.500508i
$838$		0			0
$839$	−30.8337	−	11.2226i	−1.06450	−	0.387446i	−0.250382	−	0.968147i	$-0.580556\pi$
$839$	−30.8337	−	11.2226i	−1.06450	−	0.387446i	−0.814117	+	0.580701i	$0.802778\pi$
$840$		0			0
$841$	−19.7084	−	16.5373i	−0.679601	−	0.570253i
$842$		0			0
$843$	−5.17417	−	5.75422i	−0.178208	−	0.198186i
$844$		0			0
$845$	−3.05583	−	5.29286i	−0.105124	−	0.182080i
$846$		0			0
$847$	5.46621	−	9.46776i	0.187821	−	0.325316i
$848$		0			0
$849$	16.7451	−	21.4033i	0.574691	−	0.734560i
$850$		0			0
$851$	52.0323	−	18.9382i	1.78365	−	0.649194i
$852$		0			0
$853$	0.880675	+	4.99455i	0.0301537	+	0.171010i	0.996166	−	0.0874873i	$-0.0278837\pi$
$853$	0.880675	+	4.99455i	0.0301537	+	0.171010i	−0.966012	+	0.258498i	$0.916773\pi$
$854$		0			0
$855$	1.21013	−	11.3676i	0.0413855	−	0.388764i
$856$		0			0
$857$	39.2868	−	32.9656i	1.34201	−	1.12608i	0.360909	−	0.932601i	$-0.382467\pi$
$857$	39.2868	−	32.9656i	1.34201	−	1.12608i	0.981104	−	0.193481i	$-0.0619779\pi$
$858$		0			0
$859$	3.33805	−	18.9310i	0.113893	−	0.645918i	−0.873400	−	0.487004i	$-0.838090\pi$
$859$	3.33805	−	18.9310i	0.113893	−	0.645918i	0.987292	−	0.158914i	$-0.0507992\pi$
$860$		0			0
$861$	−0.457951	−	13.3699i	−0.0156069	−	0.455643i
$862$		0			0
$863$	40.1010			1.36505			0.682527	−	0.730860i	$-0.260881\pi$
$863$	40.1010			1.36505			0.682527	+	0.730860i	$0.260881\pi$
$864$		0			0
$865$	7.42141			0.252335
$866$		0			0
$867$	−13.9052	−	7.40542i	−0.472244	−	0.251501i
$868$		0			0
$869$	−11.0712	+	62.7877i	−0.375563	+	2.12993i
$870$		0			0
$871$	−17.3046	+	14.5203i	−0.586345	+	0.492002i
$872$		0			0
$873$	17.0661	+	4.91830i	0.577601	+	0.166459i
$874$		0			0
$875$	−1.28944	−	7.31276i	−0.0435909	−	0.247217i
$876$		0			0
$877$	−39.9136	+	14.5274i	−1.34779	+	0.490554i	−0.912256	−	0.409620i	$-0.865661\pi$
$877$	−39.9136	+	14.5274i	−1.34779	+	0.490554i	−0.435530	+	0.900174i	$0.643439\pi$
$878$		0			0
$879$	8.57278	+	1.21066i	0.289153	+	0.0408346i
$880$		0			0
$881$	29.0803	−	50.3685i	0.979739	−	1.69696i	0.316421	−	0.948619i	$-0.397519\pi$
$881$	29.0803	−	50.3685i	0.979739	−	1.69696i	0.663317	−	0.748338i	$-0.269148\pi$
$882$		0			0
$883$	16.5357	+	28.6407i	0.556471	+	0.963836i	0.997787	+	0.0664842i	$0.0211782\pi$
$883$	16.5357	+	28.6407i	0.556471	+	0.963836i	−0.441317	+	0.897351i	$0.645488\pi$
$884$		0			0
$885$	−17.6137	+	3.73163i	−0.592079	+	0.125437i
$886$		0			0
$887$	34.6012	+	29.0338i	1.16179	+	0.974860i	0.999929	−	0.0119530i	$-0.00380484\pi$
$887$	34.6012	+	29.0338i	1.16179	+	0.974860i	0.161864	+	0.986813i	$0.448249\pi$
$888$		0			0
$889$	6.16679	+	2.24453i	0.206828	+	0.0752791i
$890$		0			0
$891$	−28.2866	+	31.2473i	−0.947637	+	1.04682i
$892$		0			0
$893$	28.6278	+	10.4197i	0.957991	+	0.348680i
$894$		0			0
$895$	−10.1487	−	8.51576i	−0.339233	−	0.284651i
$896$		0			0
$897$	28.5829	−	6.05554i	0.954355	−	0.202189i
$898$		0			0
$899$	−3.04448	−	5.27319i	−0.101539	−	0.175871i
$900$		0			0
$901$	15.5156	−	26.8737i	0.516898	−	0.895294i
$902$		0			0
$903$	−21.1813	−	2.99126i	−0.704870	−	0.0995429i
$904$		0			0
$905$	−5.77467	+	2.10181i	−0.191956	+	0.0698664i
$906$		0			0
$907$	1.77486	+	10.0657i	0.0589332	+	0.334227i	0.999992	−	0.00401626i	$-0.00127842\pi$
$907$	1.77486	+	10.0657i	0.0589332	+	0.334227i	−0.941059	+	0.338243i	$0.890167\pi$
$908$		0			0
$909$	−11.3823	−	45.9130i	−0.377528	−	1.52284i
$910$		0			0
$911$	3.98969	−	3.34775i	0.132184	−	0.110916i	−0.574299	−	0.818646i	$-0.694725\pi$
$911$	3.98969	−	3.34775i	0.132184	−	0.110916i	0.706483	+	0.707730i	$0.250281\pi$
$912$		0			0
$913$	0.424110	−	2.40525i	0.0140360	−	0.0796021i
$914$		0			0
$915$	7.99065	+	4.25555i	0.264163	+	0.140684i
$916$		0			0
$917$	−6.35472			−0.209851
$918$		0			0
$919$	20.3145			0.670113			0.335057	−	0.942198i	$-0.391245\pi$
$919$	20.3145			0.670113			0.335057	+	0.942198i	$0.391245\pi$
$920$		0			0
$921$	0.878734	+	25.6546i	0.0289553	+	0.845346i
$922$		0			0
$923$	1.59238	−	9.03082i	0.0524137	−	0.297253i
$924$		0			0
$925$	25.2777	−	21.2105i	0.831124	−	0.697396i
$926$		0			0
$927$	40.0623	+	29.1887i	1.31582	+	0.958683i
$928$		0			0
$929$	−4.08360	−	23.1592i	−0.133979	−	0.759830i	−0.975566	−	0.219709i	$-0.929489\pi$
$929$	−4.08360	−	23.1592i	−0.133979	−	0.759830i	0.841587	−	0.540122i	$-0.181622\pi$
$930$		0			0
$931$	−4.51956	+	1.64498i	−0.148123	+	0.0539122i
$932$		0			0
$933$	−36.9818	+	47.2695i	−1.21073	+	1.54753i
$934$		0			0
$935$	5.21592	−	9.03424i	0.170579	−	0.295451i
$936$		0			0
$937$	−4.90683	−	8.49888i	−0.160299	−	0.277646i	0.774677	−	0.632357i	$-0.217913\pi$
$937$	−4.90683	−	8.49888i	−0.160299	−	0.277646i	−0.934976	+	0.354711i	$0.884579\pi$
$938$		0			0
$939$	−10.8802	−	12.1000i	−0.355063	−	0.394868i
$940$		0			0
$941$	29.0451	+	24.3717i	0.946844	+	0.794496i	0.978763	−	0.204994i	$-0.0657176\pi$
$941$	29.0451	+	24.3717i	0.946844	+	0.794496i	−0.0319194	+	0.999490i	$0.510162\pi$
$942$		0			0
$943$	53.2499	+	19.3814i	1.73405	+	0.631144i
$944$		0			0
$945$	3.33545	−	2.41316i	0.108502	−	0.0785001i
$946$		0			0
$947$	47.0477	+	17.1239i	1.52884	+	0.556453i	0.963338	−	0.268291i	$-0.0864589\pi$
$947$	47.0477	+	17.1239i	1.52884	+	0.556453i	0.565505	+	0.824745i	$0.308681\pi$
$948$		0			0
$949$	7.88378	+	6.61527i	0.255918	+	0.214741i
$950$		0			0
$951$	4.41285	−	13.5506i	0.143096	−	0.439407i
$952$		0			0
$953$	8.45343	+	14.6418i	0.273834	+	0.474294i	0.969840	−	0.243742i	$-0.0783749\pi$
$953$	8.45343	+	14.6418i	0.273834	+	0.474294i	−0.696007	+	0.718035i	$0.745042\pi$
$954$		0			0
$955$	−4.77747	+	8.27481i	−0.154595	+	0.267767i
$956$		0			0
$957$	5.48781	+	13.6089i	0.177396	+	0.439914i
$958$		0			0
$959$	15.3527	−	5.58794i	0.495766	−	0.180444i
$960$		0			0
$961$	−3.41575	−	19.3717i	−0.110185	−	0.624892i
$962$		0			0
$963$	2.40314	−	4.91053i	0.0774402	−	0.158240i
$964$		0			0
$965$	−13.9677	+	11.7203i	−0.449636	+	0.377289i
$966$		0			0
$967$	−6.01414	+	34.1079i	−0.193402	+	1.09684i	0.721275	+	0.692649i	$0.243556\pi$
$967$	−6.01414	+	34.1079i	−0.193402	+	1.09684i	−0.914677	+	0.404186i	$0.867555\pi$
$968$		0			0
$969$	19.8703	−	12.3979i	0.638326	−	0.398278i
$970$		0			0
$971$	−23.2443			−0.745944			−0.372972	−	0.927843i	$-0.621661\pi$
$971$	−23.2443			−0.745944			−0.372972	+	0.927843i	$0.621661\pi$
$972$		0			0
$973$	4.48358			0.143737
$974$		0			0
$975$	14.7719	−	9.21682i	0.473080	−	0.295174i
$976$		0			0
$977$	2.32633	−	13.1933i	0.0744260	−	0.422091i	−0.924715	−	0.380659i	$-0.875697\pi$
$977$	2.32633	−	13.1933i	0.0744260	−	0.422091i	0.999141	−	0.0414314i	$-0.0131918\pi$
$978$		0			0
$979$	25.3492	−	21.2705i	0.810163	−	0.679807i
$980$		0			0
$981$	−14.4906	+	29.6098i	−0.462649	+	0.945367i
$982$		0			0
$983$	−5.71456	−	32.4089i	−0.182266	−	1.03368i	−0.929418	−	0.369030i	$-0.879690\pi$
$983$	−5.71456	−	32.4089i	−0.182266	−	1.03368i	0.747151	−	0.664654i	$-0.231421\pi$
$984$		0			0
$985$	3.89154	−	1.41640i	0.123995	−	0.0451304i
$986$		0			0
$987$	4.10307	+	10.1750i	0.130602	+	0.323874i
$988$		0			0
$989$	45.3067	−	78.4735i	1.44067	−	2.49531i
$990$		0			0
$991$	0.492680	+	0.853347i	0.0156505	+	0.0271075i	0.873745	−	0.486385i	$-0.161685\pi$
$991$	0.492680	+	0.853347i	0.0156505	+	0.0271075i	−0.858094	+	0.513492i	$0.828351\pi$
$992$		0			0
$993$	−4.46132	+	13.6994i	−0.141576	+	0.434738i
$994$		0			0
$995$	6.32624	+	5.30834i	0.200555	+	0.168286i
$996$		0			0
$997$	43.6879	+	15.9011i	1.38361	+	0.503593i	0.923270	−	0.384151i	$-0.125506\pi$
$997$	43.6879	+	15.9011i	1.38361	+	0.503593i	0.460339	+	0.887743i	$0.347728\pi$
$998$		0			0
$999$	35.7931	+	16.0221i	1.13244	+	0.506916i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bo.b.85.2	✓	54
27.7	even	9	inner	756.2.bo.b.169.2	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bo.b.85.2	✓	54	1.1	even	1	trivial
756.2.bo.b.169.2	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)

\(f(q)\)	\(=\)	\(q+(-1.46947 + 0.916867i) q^{3} +(-0.137580 + 0.780255i) q^{5} +(-0.766044 + 0.642788i) q^{7} +(1.31871 - 2.69462i) q^{9} +O(q^{10})\)	\(q+(-1.46947 + 0.916867i) q^{3} +(-0.137580 + 0.780255i) q^{5} +(-0.766044 + 0.642788i) q^{7} +(1.31871 - 2.69462i) q^{9} +(-0.813230 - 4.61206i) q^{11} +(-2.16049 + 0.786356i) q^{13} +(-0.513219 - 1.27271i) q^{15} +(1.40573 - 2.43480i) q^{17} +(-2.40481 - 4.16525i) q^{19} +(0.536332 - 1.64692i) q^{21} +(5.62038 + 4.71606i) q^{23} +(4.10859 + 1.49541i) q^{25} +(0.532798 + 5.16876i) q^{27} +(1.69990 + 0.618713i) q^{29} +(-2.57845 - 2.16358i) q^{31} +(5.42366 + 6.03168i) q^{33} +(-0.396146 - 0.686145i) q^{35} +(3.77351 - 6.53591i) q^{37} +(2.45381 - 3.13642i) q^{39} +(7.25782 - 2.64163i) q^{41} +(-2.14462 - 12.1628i) q^{43} +(1.92107 + 1.39966i) q^{45} +(-4.85227 + 4.07154i) q^{47} +(0.173648 - 0.984808i) q^{49} +(0.166698 + 4.86674i) q^{51} +11.0374 q^{53} +3.71047 q^{55} +(7.35278 + 3.91584i) q^{57} +(2.27829 - 12.9209i) q^{59} +(-5.05371 + 4.24056i) q^{61} +(0.721879 + 2.91185i) q^{63} +(-0.316317 - 1.79392i) q^{65} +(9.23265 - 3.36041i) q^{67} +(-12.5830 - 1.77699i) q^{69} +(-1.99424 + 3.45413i) q^{71} +(-2.23812 - 3.87653i) q^{73} +(-7.40856 + 1.56957i) q^{75} +(3.58754 + 3.01031i) q^{77} +(-12.7928 - 4.65620i) q^{79} +(-5.52200 - 7.10686i) q^{81} +(0.490062 + 0.178368i) q^{83} +(1.70636 + 1.43181i) q^{85} +(-3.06524 + 0.649398i) q^{87} +(3.53294 + 6.11923i) q^{89} +(1.14958 - 1.99112i) q^{91} +(5.77269 + 0.815228i) q^{93} +(3.58081 - 1.30331i) q^{95} +(1.02804 + 5.83029i) q^{97} +(-13.5002 - 3.89062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more