LMFDB - Embedded newform 756.2.b.f.55.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(55,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("756.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.b (of order $2$, degree $1$, 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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} - 4x^{10} - 4x^{8} - 16x^{6} - 16x^{4} + 256 $ x^16 - x^12 - 4x^10 - 4x^8 - 16x^6 - 16x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.3
Root			$1.16433 - 0.802711i$ of defining polynomial
Character	$\chi$	$=$	756.55
Dual form			756.2.b.f.55.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16433 - 0.802711i) q^{2} +(0.711311 + 1.86923i) q^{4} +0.944421i q^{5} +(-2.59468 + 0.517335i) q^{7} +(0.672257 - 2.74738i) q^{8} +O(q^{10})$	\(q+(-1.16433 - 0.802711i) q^{2} +(0.711311 + 1.86923i) q^{4} +0.944421i q^{5} +(-2.59468 + 0.517335i) q^{7} +(0.672257 - 2.74738i) q^{8} +(0.758097 - 1.09961i) q^{10} -3.44501i q^{11} +2.04974i q^{13} +(3.43632 + 1.48043i) q^{14} +(-2.98807 + 2.65921i) q^{16} -4.37401i q^{17} +1.09657 q^{19} +(-1.76534 + 0.671777i) q^{20} +(-2.76534 + 4.01111i) q^{22} -3.80465i q^{23} +4.10807 q^{25} +(1.64535 - 2.38657i) q^{26} +(-2.81264 - 4.48208i) q^{28} +4.94141 q^{29} +4.40936 q^{31} +(5.61367 - 0.697633i) q^{32} +(-3.51106 + 5.09277i) q^{34} +(-0.488582 - 2.45047i) q^{35} +6.97615 q^{37} +(-1.27676 - 0.880227i) q^{38} +(2.59468 + 0.634894i) q^{40} +7.38669i q^{41} -4.99177i q^{43} +(6.43953 - 2.45047i) q^{44} +(-3.05403 + 4.42985i) q^{46} +9.82139 q^{47} +(6.46473 - 2.68464i) q^{49} +(-4.78313 - 3.29759i) q^{50} +(-3.83145 + 1.45800i) q^{52} +1.34451 q^{53} +3.25354 q^{55} +(-0.322978 + 7.47634i) q^{56} +(-5.75342 - 3.96653i) q^{58} -9.08422 q^{59} +9.06524i q^{61} +(-5.13393 - 3.53944i) q^{62} +(-7.09614 - 3.69388i) q^{64} -1.93582 q^{65} -11.7607i q^{67} +(8.17604 - 3.11128i) q^{68} +(-1.39815 + 3.24534i) q^{70} +0.593808i q^{71} -15.0018i q^{73} +(-8.12251 - 5.59983i) q^{74} +(0.780001 + 2.04974i) q^{76} +(1.78222 + 8.93869i) q^{77} -9.27553i q^{79} +(-2.51142 - 2.82200i) q^{80} +(5.92937 - 8.60052i) q^{82} +2.26282 q^{83} +4.13090 q^{85} +(-4.00695 + 5.81205i) q^{86} +(-9.46473 - 2.31593i) q^{88} -12.5590i q^{89} +(-1.06040 - 5.31843i) q^{91} +(7.11178 - 2.70629i) q^{92} +(-11.4353 - 7.88374i) q^{94} +1.03562i q^{95} +18.8330i q^{97} +(-9.68204 - 2.06352i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + q^{14} + 4 q^{16} + 26 q^{20} + 10 q^{22} - 20 q^{25} + 6 q^{26} - 11 q^{28} + 6 q^{35} + 8 q^{37} + 20 q^{38} - 6 q^{46} + 8 q^{47} - 14 q^{49} - 21 q^{56} + 14 q^{58} + 44 q^{59} - 48 q^{62} + 24 q^{64} + 2 q^{68} - 27 q^{70} - 54 q^{80} - 4 q^{83} + 8 q^{85} - 34 q^{88} + 47 q^{98}+O(q^{100}) $ 16 * q + q^14 + 4 * q^16 + 26 * q^20 + 10 * q^22 - 20 * q^25 + 6 * q^26 - 11 * q^28 + 6 * q^35 + 8 * q^37 + 20 * q^38 - 6 * q^46 + 8 * q^47 - 14 * q^49 - 21 * q^56 + 14 * q^58 + 44 * q^59 - 48 * q^62 + 24 * q^64 + 2 * q^68 - 27 * q^70 - 54 * q^80 - 4 * q^83 + 8 * q^85 - 34 * q^88 + 47 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.16433	−	0.802711i	−0.823303	−	0.567602i
$2$	−1.16433	−	0.802711i	−0.823303	−	0.567602i
$3$		0			0
$3$		0			0
$4$	0.711311	+	1.86923i	0.355655	+	0.934617i
$5$			0.944421i			0.422358i	0.977447	+	0.211179i	$0.0677303\pi$
$5$			0.944421i			0.422358i	−0.977447	+	0.211179i	$0.932270\pi$
$6$		0			0
$7$	−2.59468	+	0.517335i	−0.980697	+	0.195534i
$7$	−2.59468	+	0.517335i	−0.980697	+	0.195534i
$8$	0.672257	−	2.74738i	0.237679	−	0.971344i
$9$		0			0
$10$	0.758097	−	1.09961i	0.239731	−	0.347729i
$11$		−	3.44501i		−	1.03871i	−0.854559	−	0.519354i	$-0.826172\pi$
$11$		−	3.44501i		−	1.03871i	0.854559	−	0.519354i	$-0.173828\pi$
$12$		0			0
$13$			2.04974i			0.568496i	0.958751	+	0.284248i	$0.0917440\pi$
$13$			2.04974i			0.568496i	−0.958751	+	0.284248i	$0.908256\pi$
$14$	3.43632	+	1.48043i	0.918396	+	0.395662i
$15$		0			0
$16$	−2.98807	+	2.65921i	−0.747018	+	0.664803i
$17$		−	4.37401i		−	1.06085i	−0.847731	−	0.530426i	$-0.822032\pi$
$17$		−	4.37401i		−	1.06085i	0.847731	−	0.530426i	$-0.177968\pi$
$18$		0			0
$19$	1.09657			0.251570			0.125785	−	0.992058i	$-0.459855\pi$
$19$	1.09657			0.251570			0.125785	+	0.992058i	$0.459855\pi$
$20$	−1.76534	+	0.671777i	−0.394743	+	0.150214i
$21$		0			0
$22$	−2.76534	+	4.01111i	−0.589574	+	0.855172i
$23$		−	3.80465i		−	0.793325i	−0.917965	−	0.396662i	$-0.870168\pi$
$23$		−	3.80465i		−	0.793325i	0.917965	−	0.396662i	$-0.129832\pi$
$24$		0			0
$25$	4.10807			0.821614
$26$	1.64535	−	2.38657i	0.322680	−	0.468045i
$27$		0			0
$28$	−2.81264	−	4.48208i	−0.531540	−	0.847033i
$29$	4.94141			0.917598			0.458799	−	0.888540i	$-0.348280\pi$
$29$	4.94141			0.917598			0.458799	+	0.888540i	$0.348280\pi$
$30$		0			0
$31$	4.40936			0.791944			0.395972	−	0.918263i	$-0.370408\pi$
$31$	4.40936			0.791944			0.395972	+	0.918263i	$0.370408\pi$
$32$	5.61367	−	0.697633i	0.992366	−	0.123325i
$33$		0			0
$34$	−3.51106	+	5.09277i	−0.602142	+	0.873403i
$35$	−0.488582	−	2.45047i	−0.0825854	−	0.414205i
$36$		0			0
$37$	6.97615			1.14687			0.573436	−	0.819251i	$-0.305610\pi$
$37$	6.97615			1.14687			0.573436	+	0.819251i	$0.305610\pi$
$38$	−1.27676	−	0.880227i	−0.207118	−	0.142792i
$39$		0			0
$40$	2.59468	+	0.634894i	0.410255	+	0.100385i
$41$			7.38669i			1.15361i	0.816883	+	0.576804i	$0.195700\pi$
$41$			7.38669i			1.15361i	−0.816883	+	0.576804i	$0.804300\pi$
$42$		0			0
$43$		−	4.99177i		−	0.761239i	−0.924732	−	0.380619i	$-0.875711\pi$
$43$		−	4.99177i		−	0.761239i	0.924732	−	0.380619i	$-0.124289\pi$
$44$	6.43953	−	2.45047i	0.970795	−	0.369422i
$45$		0			0
$46$	−3.05403	+	4.42985i	−0.450293	+	0.653146i
$47$	9.82139			1.43260			0.716299	−	0.697794i	$-0.245835\pi$
$47$	9.82139			1.43260			0.716299	+	0.697794i	$0.245835\pi$
$48$		0			0
$49$	6.46473	−	2.68464i	0.923533	−	0.383519i
$50$	−4.78313	−	3.29759i	−0.676437	−	0.466350i
$51$		0			0
$52$	−3.83145	+	1.45800i	−0.531326	+	0.202189i
$53$	1.34451			0.184683			0.0923416	−	0.995727i	$-0.470565\pi$
$53$	1.34451			0.184683			0.0923416	+	0.995727i	$0.470565\pi$
$54$		0			0
$55$	3.25354			0.438707
$56$	−0.322978	+	7.47634i	−0.0431598	+	0.999068i
$57$		0			0
$58$	−5.75342	−	3.96653i	−0.755461	−	0.520831i
$59$	−9.08422			−1.18266			−0.591332	−	0.806428i	$-0.701398\pi$
$59$	−9.08422			−1.18266			−0.591332	+	0.806428i	$0.701398\pi$
$60$		0			0
$61$			9.06524i			1.16068i	0.814373	+	0.580342i	$0.197081\pi$
$61$			9.06524i			1.16068i	−0.814373	+	0.580342i	$0.802919\pi$
$62$	−5.13393	−	3.53944i	−0.652010	−	0.449509i
$63$		0			0
$64$	−7.09614	−	3.69388i	−0.887018	−	0.461735i
$65$	−1.93582			−0.240109
$66$		0			0
$67$		−	11.7607i		−	1.43680i	−0.695632	−	0.718399i	$-0.744875\pi$
$67$		−	11.7607i		−	1.43680i	0.695632	−	0.718399i	$-0.255125\pi$
$68$	8.17604	−	3.11128i	0.991491	−	0.377298i
$69$		0			0
$70$	−1.39815	+	3.24534i	−0.167111	+	0.387892i
$71$			0.593808i			0.0704720i	0.999379	+	0.0352360i	$0.0112183\pi$
$71$			0.593808i			0.0704720i	−0.999379	+	0.0352360i	$0.988782\pi$
$72$		0			0
$73$		−	15.0018i		−	1.75583i	−0.478818	−	0.877914i	$-0.658935\pi$
$73$		−	15.0018i		−	1.75583i	0.478818	−	0.877914i	$-0.341065\pi$
$74$	−8.12251	−	5.59983i	−0.944223	−	0.650967i
$75$		0			0
$76$	0.780001	+	2.04974i	0.0894722	+	0.235122i
$77$	1.78222	+	8.93869i	0.203103	+	1.01866i
$78$		0			0
$79$		−	9.27553i		−	1.04358i	−0.853074	−	0.521789i	$-0.825265\pi$
$79$		−	9.27553i		−	1.04358i	0.853074	−	0.521789i	$-0.174735\pi$
$80$	−2.51142	−	2.82200i	−0.280785	−	0.315509i
$81$		0			0
$82$	5.92937	−	8.60052i	0.654790	−	0.949768i
$83$	2.26282			0.248377			0.124189	−	0.992259i	$-0.460367\pi$
$83$	2.26282			0.248377			0.124189	+	0.992259i	$0.460367\pi$
$84$		0			0
$85$	4.13090			0.448059
$86$	−4.00695	+	5.81205i	−0.432081	+	0.626730i
$87$		0			0
$88$	−9.46473	−	2.31593i	−1.00894	−	0.246879i
$89$		−	12.5590i		−	1.33125i	−0.746288	−	0.665624i	$-0.768166\pi$
$89$		−	12.5590i		−	1.33125i	0.746288	−	0.665624i	$-0.231834\pi$
$90$		0			0
$91$	−1.06040	−	5.31843i	−0.111160	−	0.557523i
$92$	7.11178	−	2.70629i	0.741455	−	0.282150i
$93$		0			0
$94$	−11.4353	−	7.88374i	−1.17946	−	0.813145i
$95$			1.03562i			0.106253i
$96$		0			0
$97$			18.8330i			1.91220i	0.293044	+	0.956099i	$0.405332\pi$
$97$			18.8330i			1.91220i	−0.293044	+	0.956099i	$0.594668\pi$
$98$	−9.68204	−	2.06352i	−0.978034	−	0.208447i
$99$		0			0
$100$	2.92211	+	7.67894i	0.292211	+	0.767894i
$101$		−	8.33111i		−	0.828976i	−0.910055	−	0.414488i	$-0.863961\pi$
$101$		−	8.33111i		−	0.828976i	0.910055	−	0.414488i	$-0.136039\pi$
$102$		0			0
$103$	−8.50215			−0.837742			−0.418871	−	0.908046i	$-0.637574\pi$
$103$	−8.50215			−0.837742			−0.418871	+	0.908046i	$0.637574\pi$
$104$	5.63141	+	1.37795i	0.552205	+	0.135119i
$105$		0			0
$106$	−1.56545	−	1.07926i	−0.152050	−	0.104827i
$107$		−	2.87772i		−	0.278199i	−0.990278	−	0.139100i	$-0.955579\pi$
$107$		−	2.87772i		−	0.278199i	0.990278	−	0.139100i	$-0.0444208\pi$
$108$		0			0
$109$	6.97615			0.668194			0.334097	−	0.942539i	$-0.391569\pi$
$109$	6.97615			0.668194			0.334097	+	0.942539i	$0.391569\pi$
$110$	−3.78818	−	2.61165i	−0.361189	−	0.249011i
$111$		0			0
$112$	6.37739	−	8.44564i	0.602607	−	0.798038i
$113$	−12.6043			−1.18571			−0.592857	−	0.805308i	$-0.702000\pi$
$113$	−12.6043			−1.18571			−0.592857	+	0.805308i	$0.702000\pi$
$114$		0			0
$115$	3.59319			0.335067
$116$	3.51488	+	9.23666i	0.326349	+	0.857603i
$117$		0			0
$118$	10.5770	+	7.29200i	0.973691	+	0.671283i
$119$	2.26282	+	11.3491i	0.207433	+	1.04037i
$120$		0			0
$121$	−0.868079			−0.0789163
$122$	7.27676	−	10.5549i	0.658807	−	0.955595i
$123$		0			0
$124$	3.13643	+	8.24213i	0.281659	+	0.740165i
$125$			8.60185i			0.769373i
$126$		0			0
$127$		−	7.80359i		−	0.692457i	−0.938150	−	0.346228i	$-0.887462\pi$
$127$		−	7.80359i		−	0.692457i	0.938150	−	0.346228i	$-0.112538\pi$
$128$	5.29710	+	9.99703i	0.468202	+	0.883621i
$129$		0			0
$130$	2.25393	+	1.55390i	0.197682	+	0.136286i
$131$	−4.28566			−0.374440			−0.187220	−	0.982318i	$-0.559948\pi$
$131$	−4.28566			−0.374440			−0.187220	+	0.982318i	$0.559948\pi$
$132$		0			0
$133$	−2.84524	+	0.567293i	−0.246714	+	0.0491905i
$134$	−9.44044	+	13.6933i	−0.815529	+	1.18292i
$135$		0			0
$136$	−12.0170	−	2.94045i	−1.03045	−	0.252142i
$137$	−7.31387			−0.624866			−0.312433	−	0.949940i	$-0.601144\pi$
$137$	−7.31387			−0.624866			−0.312433	+	0.949940i	$0.601144\pi$
$138$		0			0
$139$	8.44290			0.716117			0.358059	−	0.933699i	$-0.383439\pi$
$139$	8.44290			0.716117			0.358059	+	0.933699i	$0.383439\pi$
$140$	4.23297	−	2.65632i	0.357751	−	0.224500i
$141$		0			0
$142$	0.476656	−	0.691386i	0.0400001	−	0.0580198i
$143$	7.06138			0.590502
$144$		0			0
$145$			4.66678i			0.387555i
$146$	−12.0421	+	17.4670i	−0.996612	+	1.44558i
$147$		0			0
$148$	4.96221	+	13.0401i	0.407891	+	1.07189i
$149$	2.71211			0.222185			0.111093	−	0.993810i	$-0.464565\pi$
$149$	2.71211			0.222185			0.111093	+	0.993810i	$0.464565\pi$
$150$		0			0
$151$			15.2805i			1.24351i	0.783211	+	0.621756i	$0.213580\pi$
$151$			15.2805i			1.24351i	−0.783211	+	0.621756i	$0.786420\pi$
$152$	0.737175	−	3.01268i	0.0597928	−	0.244361i
$153$		0			0
$154$	5.10010	−	11.8382i	0.410978	−	0.953946i
$155$			4.16429i			0.334484i
$156$		0			0
$157$		−	11.6823i		−	0.932347i	−0.884693	−	0.466173i	$-0.845632\pi$
$157$		−	11.6823i		−	0.932347i	0.884693	−	0.466173i	$-0.154368\pi$
$158$	−7.44557	+	10.7997i	−0.592338	+	0.859182i
$159$		0			0
$160$	0.658859	+	5.30167i	0.0520874	+	0.419134i
$161$	1.96828	+	9.87185i	0.155122	+	0.778011i
$162$		0			0
$163$			8.15169i			0.638490i	0.947672	+	0.319245i	$0.103429\pi$
$163$			8.15169i			0.638490i	−0.947672	+	0.319245i	$0.896571\pi$
$164$	−13.8075	+	5.25423i	−1.07818	+	0.410287i
$165$		0			0
$166$	−2.63467	−	1.81639i	−0.204490	−	0.140980i
$167$	−22.8828			−1.77072			−0.885361	−	0.464904i	$-0.846089\pi$
$167$	−22.8828			−1.77072			−0.885361	+	0.464904i	$0.846089\pi$
$168$		0			0
$169$	8.79855			0.676812
$170$	−4.80972	−	3.31592i	−0.368889	−	0.254320i
$171$		0			0
$172$	9.33080	−	3.55070i	0.711467	−	0.270739i
$173$		−	21.2156i		−	1.61300i	−0.591237	−	0.806498i	$-0.701360\pi$
$173$		−	21.2156i		−	1.61300i	0.591237	−	0.806498i	$-0.298640\pi$
$174$		0			0
$175$	−10.6591	+	2.12525i	−0.805754	+	0.160654i
$176$	9.16101	+	10.2939i	0.690537	+	0.775935i
$177$		0			0
$178$	−10.0812	+	14.6227i	−0.755619	+	1.09602i
$179$			21.7448i			1.62529i	0.582762	+	0.812643i	$0.301972\pi$
$179$			21.7448i			1.62529i	−0.582762	+	0.812643i	$0.698028\pi$
$180$		0			0
$181$		−	7.31447i		−	0.543680i	−0.962342	−	0.271840i	$-0.912368\pi$
$181$		−	7.31447i		−	0.543680i	0.962342	−	0.271840i	$-0.0876322\pi$
$182$	−3.03450	+	7.04358i	−0.224932	+	0.522105i
$183$		0			0
$184$	−10.4528	−	2.55770i	−0.770591	−	0.188556i
$185$			6.58842i			0.484391i
$186$		0			0
$187$	−15.0685			−1.10192
$188$	6.98606	+	18.3585i	0.509511	+	1.33893i
$189$		0			0
$190$	0.831305	−	1.20580i	0.0603092	−	0.0874781i
$191$			15.0890i			1.09180i	0.837850	+	0.545900i	$0.183812\pi$
$191$			15.0890i			1.09180i	−0.837850	+	0.545900i	$0.816188\pi$
$192$		0			0
$193$	−4.37089			−0.314624			−0.157312	−	0.987549i	$-0.550283\pi$
$193$	−4.37089			−0.314624			−0.157312	+	0.987549i	$0.550283\pi$
$194$	15.1174	−	21.9277i	1.08537	−	1.57432i
$195$		0			0
$196$	9.61665	+	10.1745i	0.686903	+	0.726749i
$197$	15.6005			1.11149			0.555746	−	0.831352i	$-0.312433\pi$
$197$	15.6005			1.11149			0.555746	+	0.831352i	$0.312433\pi$
$198$		0			0
$199$	20.3171			1.44024			0.720120	−	0.693849i	$-0.244087\pi$
$199$	20.3171			1.44024			0.720120	+	0.693849i	$0.244087\pi$
$200$	2.76168	−	11.2864i	0.195280	−	0.798069i
$201$		0			0
$202$	−6.68747	+	9.70013i	−0.470529	+	0.682499i
$203$	−12.8214	+	2.55637i	−0.899885	+	0.179422i
$204$		0			0
$205$	−6.97615			−0.487235
$206$	9.89928	+	6.82477i	0.689715	+	0.475504i
$207$		0			0
$208$	−5.45070	−	6.12478i	−0.377938	−	0.424677i
$209$		−	3.77769i		−	0.261308i
$210$		0			0
$211$			28.7839i			1.98157i	0.135459	+	0.990783i	$0.456749\pi$
$211$			28.7839i			1.98157i	−0.135459	+	0.990783i	$0.543251\pi$
$212$	0.956367	+	2.51321i	0.0656836	+	0.172608i
$213$		0			0
$214$	−2.30997	+	3.35060i	−0.157906	+	0.229042i
$215$	4.71434			0.321515
$216$		0			0
$217$	−11.4409	+	2.28111i	−0.776657	+	0.154852i
$218$	−8.12251	−	5.59983i	−0.550126	−	0.379268i
$219$		0			0
$220$	2.31428	+	6.08163i	0.156029	+	0.410023i
$221$	8.96558			0.603091
$222$		0			0
$223$	12.3145			0.824643			0.412321	−	0.911038i	$-0.364718\pi$
$223$	12.3145			0.824643			0.412321	+	0.911038i	$0.364718\pi$
$224$	−14.2048	+	4.71428i	−0.949096	+	0.314986i
$225$		0			0
$226$	14.6755	+	10.1176i	0.976202	+	0.673014i
$227$	24.9056			1.65304			0.826522	−	0.562905i	$-0.190316\pi$
$227$	24.9056			1.65304			0.826522	+	0.562905i	$0.190316\pi$
$228$		0			0
$229$			9.63253i			0.636535i	0.948001	+	0.318268i	$0.103101\pi$
$229$			9.63253i			0.636535i	−0.948001	+	0.318268i	$0.896899\pi$
$230$	−4.18365	−	2.88430i	−0.275862	−	0.190185i
$231$		0			0
$232$	3.32190	−	13.5759i	0.218093	−	0.891303i
$233$	−25.9431			−1.69959			−0.849794	−	0.527115i	$-0.823274\pi$
$233$	−25.9431			−1.69959			−0.849794	+	0.527115i	$0.823274\pi$
$234$		0			0
$235$			9.27553i			0.605069i
$236$	−6.46170	−	16.9805i	−0.420621	−	1.10534i
$237$		0			0
$238$	6.47541	−	15.0305i	0.419739	−	0.974283i
$239$			7.45731i			0.482373i	0.970479	+	0.241187i	$0.0775366\pi$
$239$			7.45731i			0.482373i	−0.970479	+	0.241187i	$0.922463\pi$
$240$		0			0
$241$		−	23.0962i		−	1.48776i	−0.668314	−	0.743879i	$-0.732984\pi$
$241$		−	23.0962i		−	1.48776i	0.668314	−	0.743879i	$-0.267016\pi$
$242$	1.01073	+	0.696817i	0.0649720	+	0.0447931i
$243$		0			0
$244$	−16.9451	+	6.44820i	−1.08480	+	0.412804i
$245$	2.53543	+	6.10543i	0.161983	+	0.390062i
$246$		0			0
$247$			2.24768i			0.143017i
$248$	2.96422	−	12.1142i	0.188228	−	0.769250i
$249$		0			0
$250$	6.90480	−	10.0154i	0.436698	−	0.633427i
$251$	1.28566			0.0811502			0.0405751	−	0.999176i	$-0.487081\pi$
$251$	1.28566			0.0811502			0.0405751	+	0.999176i	$0.487081\pi$
$252$		0			0
$253$	−13.1071			−0.824033
$254$	−6.26402	+	9.08592i	−0.393040	+	0.570101i
$255$		0			0
$256$	1.85717	−	15.8919i	0.116073	−	0.993241i
$257$		−	16.4054i		−	1.02334i	−0.859181	−	0.511672i	$-0.829026\pi$
$257$		−	16.4054i		−	1.02334i	0.859181	−	0.511672i	$-0.170974\pi$
$258$		0			0
$259$	−18.1009	+	3.60900i	−1.12473	+	0.224253i
$260$	−1.37697	−	3.61850i	−0.0853961	−	0.224410i
$261$		0			0
$262$	4.98991	+	3.44015i	0.308277	+	0.212533i
$263$		−	23.3095i		−	1.43732i	−0.695360	−	0.718661i	$-0.744755\pi$
$263$		−	23.3095i		−	1.43732i	0.695360	−	0.718661i	$-0.255245\pi$
$264$		0			0
$265$			1.26979i			0.0780024i
$266$	3.76816	+	1.62339i	0.231041	+	0.0995367i
$267$		0			0
$268$	21.9835	−	8.36551i	1.34286	−	0.511005i
$269$			14.6853i			0.895378i	0.894189	+	0.447689i	$0.147753\pi$
$269$			14.6853i			0.895378i	−0.894189	+	0.447689i	$0.852247\pi$
$270$		0			0
$271$	−19.4778			−1.18319			−0.591597	−	0.806234i	$-0.701502\pi$
$271$	−19.4778			−1.18319			−0.591597	+	0.806234i	$0.701502\pi$
$272$	11.6314	+	13.0698i	0.705258	+	0.792476i
$273$		0			0
$274$	8.51574	+	5.87093i	0.514454	+	0.354676i
$275$		−	14.1523i		−	0.853417i
$276$		0			0
$277$	−20.8828			−1.25472			−0.627362	−	0.778728i	$-0.715865\pi$
$277$	−20.8828			−1.25472			−0.627362	+	0.778728i	$0.715865\pi$
$278$	−9.83029	−	6.77721i	−0.589582	−	0.406470i
$279$		0			0
$280$	−7.06082	−	0.305028i	−0.421965	−	0.0182289i
$281$	−13.9070			−0.829622			−0.414811	−	0.909908i	$-0.636152\pi$
$281$	−13.9070			−0.829622			−0.414811	+	0.909908i	$0.636152\pi$
$282$		0			0
$283$	21.0609			1.25194			0.625971	−	0.779846i	$-0.284703\pi$
$283$	21.0609			1.25194			0.625971	+	0.779846i	$0.284703\pi$
$284$	−1.10997	+	0.422382i	−0.0658643	+	0.0250637i
$285$		0			0
$286$	−8.22175	−	5.66825i	−0.486162	−	0.335170i
$287$	−3.82139	−	19.1661i	−0.225570	−	1.13134i
$288$		0			0
$289$	−2.13192			−0.125407
$290$	3.74607	−	5.43365i	0.219977	−	0.319075i
$291$		0			0
$292$	28.0419	−	10.6709i	1.64103	−	0.624470i
$293$			16.9330i			0.989234i	0.869111	+	0.494617i	$0.164692\pi$
$293$			16.9330i			0.989234i	−0.869111	+	0.494617i	$0.835308\pi$
$294$		0			0
$295$		−	8.57933i		−	0.499508i
$296$	4.68976	−	19.1661i	0.272587	−	1.11401i
$297$		0			0
$298$	−3.15779	−	2.17704i	−0.182926	−	0.126113i
$299$	7.79855			0.451002
$300$		0			0
$301$	2.58242	+	12.9521i	0.148848	+	0.746544i
$302$	12.2658	−	17.7915i	0.705820	−	1.02379i
$303$		0			0
$304$	−3.27663	+	2.91601i	−0.187927	+	0.167245i
$305$	−8.56140			−0.490225
$306$		0			0
$307$	−7.41866			−0.423405			−0.211703	−	0.977334i	$-0.567901\pi$
$307$	−7.41866			−0.423405			−0.211703	+	0.977334i	$0.567901\pi$
$308$	−15.4408	+	9.68958i	−0.879821	+	0.552115i
$309$		0			0
$310$	3.34272	−	4.84860i	0.189854	−	0.275382i
$311$	−9.23999			−0.523952			−0.261976	−	0.965074i	$-0.584374\pi$
$311$	−9.23999			−0.523952			−0.261976	+	0.965074i	$0.584374\pi$
$312$		0			0
$313$			6.80283i			0.384519i	0.981344	+	0.192259i	$0.0615815\pi$
$313$			6.80283i			0.384519i	−0.981344	+	0.192259i	$0.938419\pi$
$314$	−9.37749	+	13.6020i	−0.529202	+	0.767604i
$315$		0			0
$316$	17.3381	−	6.59779i	0.975347	−	0.371154i
$317$	32.7972			1.84208			0.921038	−	0.389472i	$-0.127342\pi$
$317$	32.7972			1.84208			0.921038	+	0.389472i	$0.127342\pi$
$318$		0			0
$319$		−	17.0232i		−	0.953117i
$320$	3.48858	−	6.70175i	0.195018	−	0.374639i
$321$		0			0
$322$	5.63252	−	13.0740i	0.313888	−	0.728586i
$323$		−	4.79639i		−	0.266879i
$324$		0			0
$325$			8.42048i			0.467084i
$326$	6.54345	−	9.49123i	0.362408	−	0.525670i
$327$		0			0
$328$	20.2940	+	4.96575i	1.12055	+	0.274188i
$329$	−25.4834	+	5.08095i	−1.40494	+	0.280122i
$330$		0			0
$331$			8.58896i			0.472092i	0.971742	+	0.236046i	$0.0758516\pi$
$331$			8.58896i			0.472092i	−0.971742	+	0.236046i	$0.924148\pi$
$332$	1.60957	+	4.22975i	0.0883367	+	0.232138i
$333$		0			0
$334$	26.6430	+	18.3682i	1.45784	+	1.00507i
$335$	11.1071			0.606843
$336$		0			0
$337$	−26.4652			−1.44165			−0.720825	−	0.693117i	$-0.756237\pi$
$337$	−26.4652			−1.44165			−0.720825	+	0.693117i	$0.756237\pi$
$338$	−10.2444	−	7.06269i	−0.557221	−	0.384160i
$339$		0			0
$340$	2.93836	+	7.72163i	0.159355	+	0.418764i
$341$		−	15.1903i		−	0.822600i
$342$		0			0
$343$	−15.3850	+	10.3102i	−0.830715	+	0.556699i
$344$	−13.7143	−	3.35575i	−0.739424	−	0.180930i
$345$		0			0
$346$	−17.0300	+	24.7019i	−0.915540	+	1.32798i
$347$		−	12.6572i		−	0.679475i	−0.940520	−	0.339738i	$-0.889662\pi$
$347$		−	12.6572i		−	0.679475i	0.940520	−	0.339738i	$-0.110338\pi$
$348$		0			0
$349$		−	27.0876i		−	1.44997i	−0.688767	−	0.724983i	$-0.741848\pi$
$349$		−	27.0876i		−	1.44997i	0.688767	−	0.724983i	$-0.258152\pi$
$350$	14.1167	+	6.08171i	0.754567	+	0.325081i
$351$		0			0
$352$	−2.40335	−	19.3391i	−0.128099	−	1.03078i
$353$		−	3.28343i		−	0.174759i	−0.996175	−	0.0873796i	$-0.972151\pi$
$353$		−	3.28343i		−	0.174759i	0.996175	−	0.0873796i	$-0.0278493\pi$
$354$		0			0
$355$	−0.560805			−0.0297644
$356$	23.4756	−	8.93332i	1.24421	−	0.473465i
$357$		0			0
$358$	17.4548	−	25.3181i	0.922516	−	1.33810i
$359$			3.16696i			0.167146i	0.996502	+	0.0835730i	$0.0266332\pi$
$359$			3.16696i			0.167146i	−0.996502	+	0.0835730i	$0.973367\pi$
$360$		0			0
$361$	−17.7975			−0.936713
$362$	−5.87140	+	8.51643i	−0.308594	+	0.447613i
$363$		0			0
$364$	9.18711	−	5.76520i	0.481535	−	0.302178i
$365$	14.1680			0.741588
$366$		0			0
$367$	23.1586			1.20887			0.604436	−	0.796654i	$-0.293399\pi$
$367$	23.1586			1.20887			0.604436	+	0.796654i	$0.293399\pi$
$368$	10.1174	+	11.3686i	0.527405	+	0.592628i
$369$		0			0
$370$	5.28860	−	7.67107i	0.274941	−	0.398800i
$371$	−3.48858	+	0.695563i	−0.181118	+	0.0361119i
$372$		0			0
$373$	−22.0375			−1.14106			−0.570530	−	0.821277i	$-0.693262\pi$
$373$	−22.0375			−1.14106			−0.570530	+	0.821277i	$0.693262\pi$
$374$	17.5446	+	12.0956i	0.907211	+	0.625450i
$375$		0			0
$376$	6.60250	−	26.9830i	0.340498	−	1.39154i
$377$			10.1286i			0.521651i
$378$		0			0
$379$		−	6.37455i		−	0.327438i	−0.986507	−	0.163719i	$-0.947651\pi$
$379$		−	6.37455i		−	0.327438i	0.986507	−	0.163719i	$-0.0523491\pi$
$380$	−1.93582	+	0.736649i	−0.0993055	+	0.0377893i
$381$		0			0
$382$	12.1121	−	17.5685i	0.619709	−	0.898883i
$383$	−8.34704			−0.426514			−0.213257	−	0.976996i	$-0.568407\pi$
$383$	−8.34704			−0.426514			−0.213257	+	0.976996i	$0.568407\pi$
$384$		0			0
$385$	−8.44189	+	1.68317i	−0.430239	+	0.0857822i
$386$	5.08915	+	3.50856i	0.259031	+	0.178581i
$387$		0			0
$388$	−35.2032	+	13.3961i	−1.78717	+	0.680084i
$389$	15.4480			0.783245			0.391623	−	0.920126i	$-0.371914\pi$
$389$	15.4480			0.783245			0.391623	+	0.920126i	$0.371914\pi$
$390$		0			0
$391$	−16.6416			−0.841600
$392$	−3.02975	−	19.5658i	−0.153025	−	0.988222i
$393$		0			0
$394$	−18.1641	−	12.5227i	−0.915095	−	0.630885i
$395$	8.76001			0.440764
$396$		0			0
$397$			1.43356i			0.0719482i	0.999353	+	0.0359741i	$0.0114534\pi$
$397$			1.43356i			0.0719482i	−0.999353	+	0.0359741i	$0.988547\pi$
$398$	−23.6557	−	16.3088i	−1.18575	−	0.817484i
$399$		0			0
$400$	−12.2752	+	10.9242i	−0.613761	+	0.546211i
$401$	21.1657			1.05697			0.528483	−	0.848944i	$-0.322761\pi$
$401$	21.1657			1.05697			0.528483	+	0.848944i	$0.322761\pi$
$402$		0			0
$403$			9.03805i			0.450217i
$404$	15.5728	−	5.92601i	0.774776	−	0.294830i
$405$		0			0
$406$	16.9803	+	7.31543i	0.842718	+	0.363058i
$407$		−	24.0329i		−	1.19127i
$408$		0			0
$409$		−	20.5348i		−	1.01538i	−0.861539	−	0.507691i	$-0.830499\pi$
$409$		−	20.5348i		−	1.01538i	0.861539	−	0.507691i	$-0.169501\pi$
$410$	8.12251	+	5.59983i	0.401142	+	0.276556i
$411$		0			0
$412$	−6.04767	−	15.8925i	−0.297947	−	0.782968i
$413$	23.5706	−	4.69958i	1.15984	−	0.231251i
$414$		0			0
$415$			2.13706i			0.104904i
$416$	1.42997	+	11.5066i	0.0701099	+	0.564157i
$417$		0			0
$418$	−3.03239	+	4.39846i	−0.148319	+	0.215136i
$419$	3.97716			0.194297			0.0971486	−	0.995270i	$-0.469028\pi$
$419$	3.97716			0.194297			0.0971486	+	0.995270i	$0.469028\pi$
$420$		0			0
$421$	2.31959			0.113050			0.0565250	−	0.998401i	$-0.481998\pi$
$421$	2.31959			0.113050			0.0565250	+	0.998401i	$0.481998\pi$
$422$	23.1052	−	33.5139i	1.12474	−	1.63143i
$423$		0			0
$424$	0.903858	−	3.69388i	0.0438952	−	0.179391i
$425$		−	17.9687i		−	0.871611i
$426$		0			0
$427$	−4.68976	−	23.5214i	−0.226953	−	1.13828i
$428$	5.37912	−	2.04695i	0.260010	−	0.0989431i
$429$		0			0
$430$	−5.48903	−	3.78425i	−0.264704	−	0.182493i
$431$			6.89002i			0.331880i	0.986136	+	0.165940i	$0.0530659\pi$
$431$			6.89002i			0.331880i	−0.986136	+	0.165940i	$0.946934\pi$
$432$		0			0
$433$		−	2.26241i		−	0.108724i	−0.998521	−	0.0543621i	$-0.982687\pi$
$433$		−	2.26241i		−	0.108724i	0.998521	−	0.0543621i	$-0.0173125\pi$
$434$	15.1520	+	6.52775i	0.727319	+	0.313342i
$435$		0			0
$436$	4.96221	+	13.0401i	0.237647	+	0.624505i
$437$		−	4.17206i		−	0.199577i
$438$		0			0
$439$	4.94512			0.236018			0.118009	−	0.993013i	$-0.462349\pi$
$439$	4.94512			0.236018			0.118009	+	0.993013i	$0.462349\pi$
$440$	2.18721	−	8.93869i	0.104271	−	0.426135i
$441$		0			0
$442$	−10.4389	−	7.19677i	−0.496526	−	0.342316i
$443$			11.1415i			0.529348i	0.964338	+	0.264674i	$0.0852644\pi$
$443$			11.1415i			0.529348i	−0.964338	+	0.264674i	$0.914736\pi$
$444$		0			0
$445$	11.8610			0.562263
$446$	−14.3381	−	9.88501i	−0.678931	−	0.468069i
$447$		0			0
$448$	20.3232	+	5.91336i	0.960181	+	0.279380i
$449$	4.12154			0.194508			0.0972538	−	0.995260i	$-0.468994\pi$
$449$	4.12154			0.194508			0.0972538	+	0.995260i	$0.468994\pi$
$450$		0			0
$451$	25.4472			1.19826
$452$	−8.96558	−	23.5604i	−0.421706	−	1.10819i
$453$		0			0
$454$	−28.9982	−	19.9920i	−1.36096	−	0.938271i
$455$	5.02284	−	1.00147i	0.235474	−	0.0469495i
$456$		0			0
$457$	5.45050			0.254964			0.127482	−	0.991841i	$-0.459311\pi$
$457$	5.45050			0.254964			0.127482	+	0.991841i	$0.459311\pi$
$458$	7.73213	−	11.2154i	0.361299	−	0.524061i
$459$		0			0
$460$	2.55588	+	6.71652i	0.119168	+	0.313159i
$461$			25.7035i			1.19713i	0.801074	+	0.598566i	$0.204262\pi$
$461$			25.7035i			1.19713i	−0.801074	+	0.598566i	$0.795738\pi$
$462$		0			0
$463$			28.6023i			1.32926i	0.747171	+	0.664632i	$0.231412\pi$
$463$			28.6023i			1.32926i	−0.747171	+	0.664632i	$0.768588\pi$
$464$	−14.7653	+	13.1403i	−0.685462	+	0.610022i
$465$		0			0
$466$	30.2062	+	20.8248i	1.39928	+	0.964690i
$467$	6.66562			0.308448			0.154224	−	0.988036i	$-0.450712\pi$
$467$	6.66562			0.308448			0.154224	+	0.988036i	$0.450712\pi$
$468$		0			0
$469$	6.08422	+	30.5152i	0.280943	+	1.40906i
$470$	7.44557	−	10.7997i	0.343439	−	0.498155i
$471$		0			0
$472$	−6.10692	+	24.9577i	−0.281094	+	1.14877i
$473$	−17.1967			−0.790705
$474$		0			0
$475$	4.50478			0.206693
$476$	−19.6046	+	12.3025i	−0.898577	+	0.563885i
$477$		0			0
$478$	5.98606	−	8.68274i	0.273796	−	0.397139i
$479$	−21.8214			−0.997045			−0.498522	−	0.866877i	$-0.666124\pi$
$479$	−21.8214			−0.997045			−0.498522	+	0.866877i	$0.666124\pi$
$480$		0			0
$481$			14.2993i			0.651992i
$482$	−18.5396	+	26.8915i	−0.844455	+	1.22488i
$483$		0			0
$484$	−0.617474	−	1.62264i	−0.0280670	−	0.0737565i
$485$	−17.7863			−0.807632
$486$		0			0
$487$			7.03966i			0.318998i	0.987198	+	0.159499i	$0.0509878\pi$
$487$			7.03966i			0.318998i	−0.987198	+	0.159499i	$0.949012\pi$
$488$	24.9056	+	6.09417i	1.12742	+	0.275870i
$489$		0			0
$490$	1.94883	−	9.14393i	0.0880391	−	0.413080i
$491$		−	2.31042i		−	0.104268i	−0.998640	−	0.0521340i	$-0.983398\pi$
$491$		−	2.31042i		−	0.104268i	0.998640	−	0.0521340i	$-0.0166023\pi$
$492$		0			0
$493$		−	21.6138i		−	0.973435i
$494$	1.80424	−	2.61704i	0.0811765	−	0.117746i
$495$		0			0
$496$	−13.1755	+	11.7254i	−0.591597	+	0.526487i
$497$	−0.307197	−	1.54074i	−0.0137797	−	0.0691117i
$498$		0			0
$499$			11.1665i			0.499882i	0.968261	+	0.249941i	$0.0804113\pi$
$499$			11.1665i			0.499882i	−0.968261	+	0.249941i	$0.919589\pi$
$500$	−16.0789	+	6.11859i	−0.719069	+	0.273632i
$501$		0			0
$502$	−1.49693	−	1.03201i	−0.0668112	−	0.0460610i
$503$	−2.76001			−0.123063			−0.0615314	−	0.998105i	$-0.519598\pi$
$503$	−2.76001			−0.123063			−0.0615314	+	0.998105i	$0.519598\pi$
$504$		0			0
$505$	7.86808			0.350125
$506$	15.2609	+	10.5212i	0.678429	+	0.467723i
$507$		0			0
$508$	14.5867	−	5.55078i	0.647182	−	0.246276i
$509$			13.2133i			0.585671i	0.956163	+	0.292835i	$0.0945988\pi$
$509$			13.2133i			0.585671i	−0.956163	+	0.292835i	$0.905401\pi$
$510$		0			0
$511$	7.76095	+	38.9249i	0.343324	+	1.72194i
$512$	−14.9189	+	17.0125i	−0.659329	+	0.751855i
$513$		0			0
$514$	−13.1688	+	19.1013i	−0.580852	+	0.842522i
$515$		−	8.02961i		−	0.353827i
$516$		0			0
$517$		−	33.8348i		−	1.48805i
$518$	23.9723	+	10.3277i	1.05328	+	0.453773i
$519$		0			0
$520$	−1.30137	+	5.31843i	−0.0570688	+	0.233228i
$521$		−	39.7699i		−	1.74235i	−0.490970	−	0.871176i	$-0.663358\pi$
$521$		−	39.7699i		−	1.74235i	0.490970	−	0.871176i	$-0.336642\pi$
$522$		0			0
$523$	−30.6727			−1.34122			−0.670612	−	0.741808i	$-0.733969\pi$
$523$	−30.6727			−1.34122			−0.670612	+	0.741808i	$0.733969\pi$
$524$	−3.04844	−	8.01090i	−0.133172	−	0.349958i
$525$		0			0
$526$	−18.7108	+	27.1398i	−0.815828	+	1.18335i
$527$		−	19.2866i		−	0.840136i
$528$		0			0
$529$	8.52463			0.370636
$530$	1.01927	−	1.47845i	0.0442743	−	0.0642196i
$531$		0			0
$532$	−3.08426	−	4.91491i	−0.133719	−	0.213088i
$533$	−15.1408			−0.655821
$534$		0			0
$535$	2.71778			0.117500
$536$	−32.3110	−	7.90621i	−1.39562	−	0.341496i
$537$		0			0
$538$	11.7880	−	17.0985i	0.508218	−	0.737167i
$539$	−9.24859	−	22.2710i	−0.398365	−	0.959282i
$540$		0			0
$541$	0.132937			0.00571541			0.00285771	−	0.999996i	$-0.499090\pi$
$541$	0.132937			0.00571541			0.00285771	+	0.999996i	$0.499090\pi$
$542$	22.6786	+	15.6351i	0.974128	+	0.671584i
$543$		0			0
$544$	−3.05145	−	24.5542i	−0.130830	−	1.05275i
$545$			6.58842i			0.282217i
$546$		0			0
$547$		−	37.9144i		−	1.62110i	−0.585669	−	0.810550i	$-0.699168\pi$
$547$		−	37.9144i		−	1.62110i	0.585669	−	0.810550i	$-0.300832\pi$
$548$	−5.20244	−	13.6713i	−0.222237	−	0.584011i
$549$		0			0
$550$	−11.3602	+	16.4779i	−0.484402	+	0.702621i
$551$	5.41860			0.230840
$552$		0			0
$553$	4.79855	+	24.0670i	0.204055	+	1.02343i
$554$	24.3144	+	16.7628i	1.03302	+	0.712184i
$555$		0			0
$556$	6.00553	+	15.7818i	0.254691	+	0.669296i
$557$	23.1661			0.981578			0.490789	−	0.871279i	$-0.336709\pi$
$557$	23.1661			0.981578			0.490789	+	0.871279i	$0.336709\pi$
$558$		0			0
$559$	10.2319			0.432761
$560$	7.97625	+	6.02295i	0.337058	+	0.254516i
$561$		0			0
$562$	16.1923	+	11.1633i	0.683030	+	0.470895i
$563$	25.3014			1.06633			0.533163	−	0.846013i	$-0.321003\pi$
$563$	25.3014			1.06633			0.533163	+	0.846013i	$0.321003\pi$
$564$		0			0
$565$		−	11.9038i		−	0.500796i
$566$	−24.5218	−	16.9058i	−1.03073	−	0.710605i
$567$		0			0
$568$	1.63141	+	0.399191i	0.0684525	+	0.0167497i
$569$	−27.1120			−1.13659			−0.568297	−	0.822824i	$-0.692397\pi$
$569$	−27.1120			−1.13659			−0.568297	+	0.822824i	$0.692397\pi$
$570$		0			0
$571$			5.90401i			0.247075i	0.992340	+	0.123538i	$0.0394239\pi$
$571$			5.90401i			0.247075i	−0.992340	+	0.123538i	$0.960576\pi$
$572$	5.02284	+	13.1994i	0.210015	+	0.551894i
$573$		0			0
$574$	−10.9355	+	25.3831i	−0.456438	+	1.05947i
$575$		−	15.6298i		−	0.651806i
$576$		0			0
$577$			23.3360i			0.971489i	0.874101	+	0.485745i	$0.161452\pi$
$577$			23.3360i			0.971489i	−0.874101	+	0.485745i	$0.838548\pi$
$578$	2.48225	+	1.71132i	0.103248	+	0.0711813i
$579$		0			0
$580$	−8.72330	+	3.31953i	−0.362215	+	0.137836i
$581$	−5.87131	+	1.17064i	−0.243583	+	0.0485662i
$582$		0			0
$583$		−	4.63186i		−	0.191832i
$584$	−41.2156	−	10.0851i	−1.70551	−	0.417323i
$585$		0			0
$586$	13.5923	−	19.7155i	0.561492	−	0.814440i
$587$	−11.3470			−0.468342			−0.234171	−	0.972195i	$-0.575238\pi$
$587$	−11.3470			−0.468342			−0.234171	+	0.972195i	$0.575238\pi$
$588$		0			0
$589$	4.83516			0.199229
$590$	−6.88672	+	9.98914i	−0.283522	+	0.411246i
$591$		0			0
$592$	−20.8452	+	18.5511i	−0.856734	+	0.762444i
$593$			27.5698i			1.13216i	0.824351	+	0.566078i	$0.191540\pi$
$593$			27.5698i			1.13216i	−0.824351	+	0.566078i	$0.808460\pi$
$594$		0			0
$595$	−10.7184	+	2.13706i	−0.439411	+	0.0876109i
$596$	1.92916	+	5.06958i	0.0790213	+	0.207658i
$597$		0			0
$598$	−9.08006	−	6.25998i	−0.371311	−	0.255990i
$599$			29.6098i			1.20982i	0.796292	+	0.604912i	$0.206792\pi$
$599$			29.6098i			1.20982i	−0.796292	+	0.604912i	$0.793208\pi$
$600$		0			0
$601$		−	24.3660i		−	0.993910i	−0.867776	−	0.496955i	$-0.834451\pi$
$601$		−	24.3660i		−	0.993910i	0.867776	−	0.496955i	$-0.165549\pi$
$602$	7.38998	−	17.1534i	0.301193	−	0.699119i
$603$		0			0
$604$	−28.5629	+	10.8692i	−1.16221	+	0.442262i
$605$		−	0.819833i		−	0.0333309i
$606$		0			0
$607$	−37.7025			−1.53030			−0.765148	−	0.643854i	$-0.777334\pi$
$607$	−37.7025			−1.53030			−0.765148	+	0.643854i	$0.777334\pi$
$608$	6.15577	−	0.765002i	0.249650	−	0.0310249i
$609$		0			0
$610$	9.96827	+	6.87233i	0.403603	+	0.278253i
$611$			20.1313i			0.814426i
$612$		0			0
$613$	2.00000			0.0807792			0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000			0.0807792			0.0403896	+	0.999184i	$0.487140\pi$
$614$	8.63774	+	5.95504i	0.348591	+	0.240326i
$615$		0			0
$616$	25.7561	+	1.11266i	1.03774	+	0.0448305i
$617$	−39.0969			−1.57398			−0.786991	−	0.616965i	$-0.788362\pi$
$617$	−39.0969			−1.57398			−0.786991	+	0.616965i	$0.788362\pi$
$618$		0			0
$619$	23.0479			0.926375			0.463188	−	0.886260i	$-0.346706\pi$
$619$	23.0479			0.926375			0.463188	+	0.886260i	$0.346706\pi$
$620$	−7.78404	+	2.96211i	−0.312615	+	0.118961i
$621$		0			0
$622$	10.7584	+	7.41704i	0.431371	+	0.297396i
$623$	6.49719	+	32.5865i	0.260304	+	1.30555i
$624$		0			0
$625$	12.4166			0.496663
$626$	5.46071	−	7.92071i	0.218254	−	0.316575i
$627$		0			0
$628$	21.8369	−	8.30973i	0.871387	−	0.331594i
$629$		−	30.5137i		−	1.21666i
$630$		0			0
$631$			11.2224i			0.446758i	0.974732	+	0.223379i	$0.0717088\pi$
$631$			11.2224i			0.446758i	−0.974732	+	0.223379i	$0.928291\pi$
$632$	−25.4834	−	6.23554i	−1.01367	−	0.248036i
$633$		0			0
$634$	−38.1867	−	26.3267i	−1.51659	−	1.04557i
$635$	7.36988			0.292465
$636$		0			0
$637$	5.50281	+	13.2510i	0.218029	+	0.525025i
$638$	−13.6647	+	19.8206i	−0.540991	+	0.784704i
$639$		0			0
$640$	−9.44141	+	5.00270i	−0.373205	+	0.197749i
$641$	−19.9506			−0.788003			−0.394002	−	0.919110i	$-0.628910\pi$
$641$	−19.9506			−0.788003			−0.394002	+	0.919110i	$0.628910\pi$
$642$		0			0
$643$	27.4554			1.08273			0.541367	−	0.840787i	$-0.317907\pi$
$643$	27.4554			1.08273			0.541367	+	0.840787i	$0.317907\pi$
$644$	−17.0527	+	10.7011i	−0.671972	+	0.421684i
$645$		0			0
$646$	−3.85012	+	5.58457i	−0.151481	+	0.219722i
$647$	−43.2298			−1.69954			−0.849770	−	0.527154i	$-0.823259\pi$
$647$	−43.2298			−1.69954			−0.849770	+	0.527154i	$0.823259\pi$
$648$		0			0
$649$			31.2952i			1.22844i
$650$	6.75921	−	9.80419i	0.265118	−	0.384552i
$651$		0			0
$652$	−15.2374	+	5.79839i	−0.596743	+	0.227082i
$653$	48.4533			1.89613			0.948063	−	0.318084i	$-0.103039\pi$
$653$	48.4533			1.89613			0.948063	+	0.318084i	$0.103039\pi$
$654$		0			0
$655$		−	4.04747i		−	0.158148i
$656$	−19.6428	−	22.0720i	−0.766922	−	0.861766i
$657$		0			0
$658$	33.7495	+	14.5399i	1.31569	+	0.566824i
$659$			22.6111i			0.880804i	0.897801	+	0.440402i	$0.145164\pi$
$659$			22.6111i			0.880804i	−0.897801	+	0.440402i	$0.854836\pi$
$660$		0			0
$661$			24.2022i			0.941358i	0.882305	+	0.470679i	$0.155991\pi$
$661$			24.2022i			0.941358i	−0.882305	+	0.470679i	$0.844009\pi$
$662$	6.89445	−	10.0004i	0.267961	−	0.388675i
$663$		0			0
$664$	1.52120	−	6.21683i	0.0590340	−	0.241260i
$665$	−0.535763	−	2.68711i	−0.0207760	−	0.104202i
$666$		0			0
$667$		−	18.8004i		−	0.727953i
$668$	−16.2768	−	42.7733i	−0.629767	−	1.65495i
$669$		0			0
$670$	−12.9322	−	8.91575i	−0.499616	−	0.344445i
$671$	31.2298			1.20561
$672$		0			0
$673$	5.45050			0.210101			0.105051	−	0.994467i	$-0.466500\pi$
$673$	5.45050			0.210101			0.105051	+	0.994467i	$0.466500\pi$
$674$	30.8141	+	21.2439i	1.18692	+	0.818284i
$675$		0			0
$676$	6.25851	+	16.4466i	0.240712	+	0.632560i
$677$			36.8454i			1.41608i	0.706171	+	0.708041i	$0.250421\pi$
$677$			36.8454i			1.41608i	−0.706171	+	0.708041i	$0.749579\pi$
$678$		0			0
$679$	−9.74295	−	48.8655i	−0.373900	−	1.87529i
$680$	2.77703	−	11.3491i	0.106494	−	0.435220i
$681$		0			0
$682$	−12.1934	+	17.6864i	−0.466909	+	0.677249i
$683$			34.0857i			1.30425i	0.758110	+	0.652127i	$0.226123\pi$
$683$			34.0857i			1.30425i	−0.758110	+	0.652127i	$0.773877\pi$
$684$		0			0
$685$		−	6.90738i		−	0.263917i
$686$	26.1893	+	0.345307i	0.999913	+	0.0131839i
$687$		0			0
$688$	13.2742	+	14.9158i	0.506074	+	0.568659i
$689$			2.75591i			0.104992i
$690$		0			0
$691$	−36.6652			−1.39481			−0.697405	−	0.716678i	$-0.745662\pi$
$691$	−36.6652			−1.39481			−0.697405	+	0.716678i	$0.745662\pi$
$692$	39.6570	−	15.0909i	1.50753	−	0.573671i
$693$		0			0
$694$	−10.1601	+	14.7371i	−0.385672	+	0.559414i
$695$			7.97366i			0.302458i
$696$		0			0
$697$	32.3094			1.22381
$698$	−21.7435	+	31.5388i	−0.823004	+	1.19376i
$699$		0			0
$700$	−11.5545	−	18.4127i	−0.436720	−	0.695934i
$701$	36.2856			1.37049			0.685245	−	0.728313i	$-0.259695\pi$
$701$	36.2856			1.37049			0.685245	+	0.728313i	$0.259695\pi$
$702$		0			0
$703$	7.64982			0.288518
$704$	−12.7255	+	24.4463i	−0.479609	+	0.921353i
$705$		0			0
$706$	−2.63564	+	3.82298i	−0.0991937	+	0.143880i
$707$	4.30997	+	21.6166i	0.162093	+	0.812975i
$708$		0			0
$709$	38.2060			1.43485			0.717427	−	0.696633i	$-0.245319\pi$
$709$	38.2060			1.43485			0.717427	+	0.696633i	$0.245319\pi$
$710$	0.652960	+	0.450164i	0.0245051	+	0.0168944i
$711$		0			0
$712$	−34.5042	−	8.44284i	−1.29310	−	0.316409i
$713$		−	16.7761i		−	0.628269i
$714$		0			0
$715$			6.66892i			0.249403i
$716$	−40.6462	+	15.4673i	−1.51902	+	0.578042i
$717$		0			0
$718$	2.54216	−	3.68738i	0.0948724	−	0.137612i
$719$	14.3470			0.535054			0.267527	−	0.963550i	$-0.413793\pi$
$719$	14.3470			0.535054			0.267527	+	0.963550i	$0.413793\pi$
$720$		0			0
$721$	22.0604	−	4.39846i	0.821571	−	0.163807i
$722$	20.7221	+	14.2863i	0.771198	+	0.531680i
$723$		0			0
$724$	13.6725	−	5.20286i	0.508133	−	0.193363i
$725$	20.2997			0.753911
$726$		0			0
$727$	11.7557			0.435994			0.217997	−	0.975949i	$-0.430048\pi$
$727$	11.7557			0.435994			0.217997	+	0.975949i	$0.430048\pi$
$728$	−15.3246	−	0.662022i	−0.567967	−	0.0245362i
$729$		0			0
$730$	−16.4962	−	11.3728i	−0.610552	−	0.420927i
$731$	−21.8340			−0.807561
$732$		0			0
$733$		−	6.71652i		−	0.248080i	−0.992277	−	0.124040i	$-0.960415\pi$
$733$		−	6.71652i		−	0.248080i	0.992277	−	0.124040i	$-0.0395852\pi$
$734$	−26.9642	−	18.5897i	−0.995268	−	0.686158i
$735$		0			0
$736$	−2.65425	−	21.3581i	−0.0978369	−	0.787269i
$737$	−40.5157			−1.49241
$738$		0			0
$739$		−	29.1879i		−	1.07369i	−0.843679	−	0.536847i	$-0.819615\pi$
$739$		−	29.1879i		−	1.07369i	0.843679	−	0.536847i	$-0.180385\pi$
$740$	−12.3153	+	4.68642i	−0.452720	+	0.172276i
$741$		0			0
$742$	4.62018	+	1.99046i	0.169612	+	0.0730721i
$743$			40.8022i			1.49689i	0.663197	+	0.748445i	$0.269199\pi$
$743$			40.8022i			1.49689i	−0.663197	+	0.748445i	$0.730801\pi$
$744$		0			0
$745$			2.56138i			0.0938416i
$746$	25.6589	+	17.6898i	0.939438	+	0.647668i
$747$		0			0
$748$	−10.7184	−	28.1665i	−0.391903	−	1.02987i
$749$	1.48874	+	7.46675i	0.0543974	+	0.272829i
$750$		0			0
$751$		−	11.2771i		−	0.411509i	−0.978604	−	0.205755i	$-0.934035\pi$
$751$		−	11.2771i		−	0.411509i	0.978604	−	0.205755i	$-0.0659648\pi$
$752$	−29.3470	+	26.1172i	−1.07018	+	0.952395i
$753$		0			0
$754$	8.13036	−	11.7930i	0.296090	−	0.429477i
$755$	−14.4313			−0.525207
$756$		0			0
$757$	19.1446			0.695822			0.347911	−	0.937528i	$-0.386891\pi$
$757$	19.1446			0.695822			0.347911	+	0.937528i	$0.386891\pi$
$758$	−5.11692	+	7.42205i	−0.185855	+	0.269581i
$759$		0			0
$760$	2.84524	+	0.696204i	0.103208	+	0.0252540i
$761$			3.93458i			0.142628i	0.997454	+	0.0713142i	$0.0227193\pi$
$761$			3.93458i			0.142628i	−0.997454	+	0.0713142i	$0.977281\pi$
$762$		0			0
$763$	−18.1009	+	3.60900i	−0.655296	+	0.130655i
$764$	−28.2049	+	10.7330i	−1.02042	+	0.388305i
$765$		0			0
$766$	9.71868	+	6.70026i	0.351150	+	0.242090i
$767$		−	18.6203i		−	0.672340i
$768$		0			0
$769$			3.12867i			0.112823i	0.998408	+	0.0564114i	$0.0179658\pi$
$769$			3.12867i			0.112823i	−0.998408	+	0.0564114i	$0.982034\pi$
$770$	11.1802	+	4.81664i	0.402907	+	0.173580i
$771$		0			0
$772$	−3.10906	−	8.17022i	−0.111898	−	0.294053i
$773$			24.0844i			0.866257i	0.901332	+	0.433129i	$0.142590\pi$
$773$			24.0844i			0.866257i	−0.901332	+	0.433129i	$0.857410\pi$
$774$		0			0
$775$	18.1139			0.650672
$776$	51.7412	+	12.6606i	1.85740	+	0.454489i
$777$		0			0
$778$	−17.9865	−	12.4003i	−0.644848	−	0.444572i
$779$			8.10001i			0.290213i
$780$		0			0
$781$	2.04567			0.0731999
$782$	19.3762	+	13.3584i	0.692892	+	0.477694i
$783$		0			0
$784$	−12.1781	+	25.2130i	−0.434931	+	0.900464i
$785$	11.0330			0.393784
$786$		0			0
$787$	49.4943			1.76428			0.882141	−	0.470985i	$-0.156101\pi$
$787$	49.4943			1.76428			0.882141	+	0.470985i	$0.156101\pi$
$788$	11.0968	+	29.1611i	0.395308	+	1.03882i
$789$		0			0
$790$	−10.1995	−	7.03176i	−0.362882	−	0.250179i
$791$	32.7042	−	6.52065i	1.16283	−	0.231848i
$792$		0			0
$793$	−18.5814			−0.659845
$794$	1.15073	−	1.66913i	0.0408380	−	0.0592352i
$795$		0			0
$796$	14.4518	+	37.9774i	0.512229	+	1.34607i
$797$		−	45.8276i		−	1.62330i	−0.584146	−	0.811649i	$-0.698570\pi$
$797$		−	45.8276i		−	1.62330i	0.584146	−	0.811649i	$-0.301430\pi$
$798$		0			0
$799$		−	42.9588i		−	1.51977i
$800$	23.0613	−	2.86592i	0.815342	−	0.101326i
$801$		0			0
$802$	−24.6438	−	16.9899i	−0.870203	−	0.599936i
$803$	−51.6813			−1.82379
$804$		0			0
$805$	−9.32319	+	1.85888i	−0.328599	+	0.0655170i
$806$	7.25494	−	10.5232i	0.255544	−	0.370665i
$807$		0			0
$808$	−22.8887	−	5.60064i	−0.805221	−	0.197030i
$809$	−37.1473			−1.30603			−0.653016	−	0.757344i	$-0.726496\pi$
$809$	−37.1473			−1.30603			−0.653016	+	0.757344i	$0.726496\pi$
$810$		0			0
$811$	−4.84971			−0.170296			−0.0851481	−	0.996368i	$-0.527136\pi$
$811$	−4.84971			−0.170296			−0.0851481	+	0.996368i	$0.527136\pi$
$812$	−13.8984	−	22.1478i	−0.487740	−	0.777236i
$813$		0			0
$814$	−19.2915	+	27.9821i	−0.676165	+	0.980773i
$815$	−7.69863			−0.269671
$816$		0			0
$817$		−	5.47382i		−	0.191505i
$818$	−16.4835	+	23.9093i	−0.576334	+	0.835968i
$819$		0			0
$820$	−4.96221	−	13.0401i	−0.173288	−	0.455378i
$821$	−2.21993			−0.0774761			−0.0387381	−	0.999249i	$-0.512334\pi$
$821$	−2.21993			−0.0774761			−0.0387381	+	0.999249i	$0.512334\pi$
$822$		0			0
$823$		−	26.5018i		−	0.923794i	−0.886934	−	0.461897i	$-0.847169\pi$
$823$		−	26.5018i		−	0.923794i	0.886934	−	0.461897i	$-0.152831\pi$
$824$	−5.71563	+	23.3586i	−0.199113	+	0.813735i
$825$		0			0
$826$	−31.2163	−	13.4486i	−1.08615	−	0.467935i
$827$		−	29.2189i		−	1.01604i	−0.861345	−	0.508021i	$-0.830377\pi$
$827$		−	29.2189i		−	1.01604i	0.861345	−	0.508021i	$-0.169623\pi$
$828$		0			0
$829$		−	46.0069i		−	1.59788i	−0.601408	−	0.798942i	$-0.705393\pi$
$829$		−	46.0069i		−	1.59788i	0.601408	−	0.798942i	$-0.294607\pi$
$830$	1.71544	−	2.48824i	0.0595438	−	0.0863679i
$831$		0			0
$832$	7.57151	−	14.5453i	0.262495	−	0.504266i
$833$	−11.7426	−	28.2768i	−0.406857	−	0.979732i
$834$		0			0
$835$		−	21.6110i		−	0.747879i
$836$	7.06138	−	2.68711i	0.244223	−	0.0929356i
$837$		0			0
$838$	−4.63072	−	3.19251i	−0.159965	−	0.110284i
$839$	−24.3927			−0.842130			−0.421065	−	0.907030i	$-0.638344\pi$
$839$	−24.3927			−0.842130			−0.421065	+	0.907030i	$0.638344\pi$
$840$		0			0
$841$	−4.58242			−0.158014
$842$	−2.70076	−	1.86196i	−0.0930745	−	0.0641675i
$843$		0			0
$844$	−53.8039	+	20.4743i	−1.85201	+	0.704755i
$845$			8.30954i			0.285857i
$846$		0			0
$847$	2.25239	−	0.449088i	0.0773930	−	0.0154308i
$848$	−4.01751	+	3.57535i	−0.137962	+	0.122778i
$849$		0			0
$850$	−14.4237	+	20.9214i	−0.494728	+	0.717599i
$851$		−	26.5418i		−	0.909841i
$852$		0			0
$853$			19.1876i			0.656971i	0.944509	+	0.328485i	$0.106538\pi$
$853$			19.1876i			0.656971i	−0.944509	+	0.328485i	$0.893462\pi$
$854$	−13.4205	+	31.1511i	−0.459239	+	1.06597i
$855$		0			0
$856$	−7.90616	−	1.93456i	−0.270227	−	0.0661220i
$857$			23.1818i			0.791877i	0.918277	+	0.395938i	$0.129581\pi$
$857$			23.1818i			0.791877i	−0.918277	+	0.395938i	$0.870419\pi$
$858$		0			0
$859$	19.0789			0.650965			0.325482	−	0.945548i	$-0.394473\pi$
$859$	19.0789			0.650965			0.325482	+	0.945548i	$0.394473\pi$
$860$	3.35336	+	8.81220i	0.114349	+	0.300494i
$861$		0			0
$862$	5.53069	−	8.02223i	0.188376	−	0.273238i
$863$			41.0656i			1.39789i	0.715177	+	0.698944i	$0.246346\pi$
$863$			41.0656i			1.39789i	−0.715177	+	0.698944i	$0.753654\pi$
$864$		0			0
$865$	20.0365			0.681262
$866$	−1.81606	+	2.63418i	−0.0617121	+	0.0895130i
$867$		0			0
$868$	−12.4020	−	19.7631i	−0.420950	−	0.670803i
$869$	−31.9543			−1.08397
$870$		0			0
$871$	24.1064			0.816814
$872$	4.68976	−	19.1661i	0.158815	−	0.649046i
$873$		0			0
$874$	−3.34896	+	4.85764i	−0.113280	+	0.164312i
$875$	−4.45004	−	22.3191i	−0.150439	−	0.754522i
$876$		0			0
$877$	20.8807			0.705092			0.352546	−	0.935794i	$-0.385316\pi$
$877$	20.8807			0.705092			0.352546	+	0.935794i	$0.385316\pi$
$878$	−5.75774	−	3.96950i	−0.194314	−	0.133964i
$879$		0			0
$880$	−9.72182	+	8.65185i	−0.327722	+	0.291654i
$881$		−	5.65474i		−	0.190513i	−0.995453	−	0.0952565i	$-0.969633\pi$
$881$		−	5.65474i		−	0.190513i	0.995453	−	0.0952565i	$-0.0303671\pi$
$882$		0			0
$883$		−	16.0230i		−	0.539217i	−0.962970	−	0.269608i	$-0.913106\pi$
$883$		−	16.0230i		−	0.539217i	0.962970	−	0.269608i	$-0.0868943\pi$
$884$	6.37732	+	16.7588i	0.214492	+	0.563659i
$885$		0			0
$886$	8.94340	−	12.9723i	0.300459	−	0.435814i
$887$	54.5611			1.83198			0.915992	−	0.401197i	$-0.131406\pi$
$887$	54.5611			1.83198			0.915992	+	0.401197i	$0.131406\pi$
$888$		0			0
$889$	4.03707	+	20.2478i	0.135399	+	0.679090i
$890$	−13.8100	−	9.52091i	−0.462913	−	0.319142i
$891$		0			0
$892$	8.75947	+	23.0188i	0.293289	+	0.770725i
$893$	10.7698			0.360398
$894$		0			0
$895$	−20.5363			−0.686452
$896$	−18.9161	−	23.1987i	−0.631943	−	0.775015i
$897$		0			0
$898$	−4.79882	−	3.30841i	−0.160139	−	0.110403i
$899$	21.7885			0.726686
$900$		0			0
$901$		−	5.88091i		−	0.195921i
$902$	−29.6288	−	20.4267i	−0.986533	−	0.680136i
$903$		0			0
$904$	−8.47333	+	34.6288i	−0.281819	+	1.15174i
$905$	6.90794			0.229628
$906$		0			0
$907$			33.0129i			1.09618i	0.836420	+	0.548089i	$0.184644\pi$
$907$			33.0129i			1.09618i	−0.836420	+	0.548089i	$0.815356\pi$
$908$	17.7156	+	46.5544i	0.587914	+	1.54496i
$909$		0			0
$910$	−6.65211	−	2.86585i	−0.220515	−	0.0950020i
$911$			10.4172i			0.345137i	0.984998	+	0.172569i	$0.0552066\pi$
$911$			10.4172i			0.345137i	−0.984998	+	0.172569i	$0.944793\pi$
$912$		0			0
$913$		−	7.79545i		−	0.257992i
$914$	−6.34616	−	4.37517i	−0.209912	−	0.144718i
$915$		0			0
$916$	−18.0055	+	6.85172i	−0.594917	+	0.226387i
$917$	11.1199	−	2.21712i	0.367212	−	0.0732158i
$918$		0			0
$919$		−	45.5590i		−	1.50285i	−0.659817	−	0.751427i	$-0.729366\pi$
$919$		−	45.5590i		−	1.50285i	0.659817	−	0.751427i	$-0.270634\pi$
$920$	2.41555	−	9.87185i	0.0796383	−	0.325465i
$921$		0			0
$922$	20.6325	−	29.9273i	0.679494	−	0.985602i
$923$	−1.21715			−0.0400631
$924$		0			0
$925$	28.6585			0.942285
$926$	22.9594	−	33.3024i	0.754493	−	1.09439i
$927$		0			0
$928$	27.7395	−	3.44729i	0.910593	−	0.113163i
$929$			21.9033i			0.718624i	0.933218	+	0.359312i	$0.116989\pi$
$929$			21.9033i			0.718624i	−0.933218	+	0.359312i	$0.883011\pi$
$930$		0			0
$931$	7.08902	−	2.94389i	0.232333	−	0.0964820i
$932$	−18.4536	−	48.4937i	−0.604468	−	1.58846i
$933$		0			0
$934$	−7.76095	−	5.35056i	−0.253946	−	0.175076i
$935$		−	14.2310i		−	0.465403i
$936$		0			0
$937$		−	19.9676i		−	0.652312i	−0.945316	−	0.326156i	$-0.894247\pi$
$937$		−	19.9676i		−	0.652312i	0.945316	−	0.326156i	$-0.105753\pi$
$938$	17.4109	−	40.4136i	0.568486	−	1.31955i
$939$		0			0
$940$	−17.3381	+	6.59779i	−0.565508	+	0.215196i
$941$		−	31.5818i		−	1.02954i	−0.857330	−	0.514768i	$-0.827878\pi$
$941$		−	31.5818i		−	1.02954i	0.857330	−	0.514768i	$-0.172122\pi$
$942$		0			0
$943$	28.1038			0.915185
$944$	27.1443	−	24.1569i	0.883472	−	0.786239i
$945$		0			0
$946$	20.0226	+	13.8040i	0.650990	+	0.448806i
$947$		−	50.1762i		−	1.63051i	−0.579104	−	0.815253i	$-0.696598\pi$
$947$		−	50.1762i		−	1.63051i	0.579104	−	0.815253i	$-0.303402\pi$
$948$		0			0
$949$	30.7498			0.998182
$950$	−5.24503	−	3.61603i	−0.170171	−	0.117320i
$951$		0			0
$952$	32.7016	+	1.41271i	1.05986	+	0.0457862i
$953$	21.7989			0.706134			0.353067	−	0.935598i	$-0.385139\pi$
$953$	21.7989			0.706134			0.353067	+	0.935598i	$0.385139\pi$
$954$		0			0
$955$	−14.2504			−0.461131
$956$	−13.9395	+	5.30446i	−0.450834	+	0.171559i
$957$		0			0
$958$	25.4072	+	17.5163i	0.820870	+	0.565925i
$959$	18.9772	−	3.78372i	0.612805	−	0.122183i
$960$		0			0
$961$	−11.5575			−0.372824
$962$	11.4782	−	16.6491i	0.370072	−	0.536787i
$963$		0			0
$964$	43.1723	−	16.4286i	1.39048	−	0.529129i
$965$		−	4.12796i		−	0.132884i
$966$		0			0
$967$			43.5444i			1.40029i	0.713999	+	0.700147i	$0.246882\pi$
$967$			43.5444i			1.40029i	−0.713999	+	0.700147i	$0.753118\pi$
$968$	−0.583572	+	2.38494i	−0.0187567	+	0.0766549i
$969$		0			0
$970$	20.7090	+	14.2772i	0.664926	+	0.458414i
$971$	−53.3926			−1.71345			−0.856725	−	0.515773i	$-0.827505\pi$
$971$	−53.3926			−1.71345			−0.856725	+	0.515773i	$0.827505\pi$
$972$		0			0
$973$	−21.9066	+	4.36781i	−0.702294	+	0.140025i
$974$	5.65081	−	8.19646i	0.181064	−	0.262632i
$975$		0			0
$976$	−24.1064	−	27.0876i	−0.771627	−	0.867053i
$977$	29.8010			0.953419			0.476710	−	0.879061i	$-0.341829\pi$
$977$	29.8010			0.953419			0.476710	+	0.879061i	$0.341829\pi$
$978$		0			0
$979$	−43.2657			−1.38278
$980$	−9.60900	+	9.08217i	−0.306948	+	0.290119i
$981$		0			0
$982$	−1.85460	+	2.69009i	−0.0591827	+	0.0858441i
$983$	5.46417			0.174280			0.0871400	−	0.996196i	$-0.472227\pi$
$983$	5.46417			0.174280			0.0871400	+	0.996196i	$0.472227\pi$
$984$		0			0
$985$			14.7335i			0.469448i
$986$	−17.3496	+	25.1655i	−0.552524	+	0.801432i
$987$		0			0
$988$	−4.20145	+	1.59880i	−0.133666	+	0.0508646i
$989$	−18.9920			−0.603909
$990$		0			0
$991$		−	1.95872i		−	0.0622207i	−0.999516	−	0.0311103i	$-0.990096\pi$
$991$		−	1.95872i		−	0.0622207i	0.999516	−	0.0311103i	$-0.00990433\pi$
$992$	24.7527	−	3.07611i	0.785899	−	0.0976667i
$993$		0			0
$994$	−0.879091	+	2.04052i	−0.0278831	+	0.0647212i
$995$			19.1879i			0.608297i
$996$		0			0
$997$			31.2177i			0.988676i	0.869270	+	0.494338i	$0.164589\pi$
$997$			31.2177i			0.988676i	−0.869270	+	0.494338i	$0.835411\pi$
$998$	8.96349	−	13.0015i	0.283734	−	0.411555i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.b.f.55.3	yes	16
3.2	odd	2		756.2.b.e.55.14	yes	16
4.3	odd	2		756.2.b.e.55.4	yes	16
7.6	odd	2		756.2.b.e.55.3	✓	16
12.11	even	2	inner	756.2.b.f.55.13	yes	16
21.20	even	2	inner	756.2.b.f.55.14	yes	16
28.27	even	2	inner	756.2.b.f.55.4	yes	16
84.83	odd	2		756.2.b.e.55.13	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.b.e.55.3	✓	16	7.6	odd	2
756.2.b.e.55.4	yes	16	4.3	odd	2
756.2.b.e.55.13	yes	16	84.83	odd	2
756.2.b.e.55.14	yes	16	3.2	odd	2
756.2.b.f.55.3	yes	16	1.1	even	1	trivial
756.2.b.f.55.4	yes	16	28.27	even	2	inner
756.2.b.f.55.13	yes	16	12.11	even	2	inner
756.2.b.f.55.14	yes	16	21.20	even	2	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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16433 - 0.802711i) q^{2} +(0.711311 + 1.86923i) q^{4} +0.944421i q^{5} +(-2.59468 + 0.517335i) q^{7} +(0.672257 - 2.74738i) q^{8} +O(q^{10})\)	\(q+(-1.16433 - 0.802711i) q^{2} +(0.711311 + 1.86923i) q^{4} +0.944421i q^{5} +(-2.59468 + 0.517335i) q^{7} +(0.672257 - 2.74738i) q^{8} +(0.758097 - 1.09961i) q^{10} -3.44501i q^{11} +2.04974i q^{13} +(3.43632 + 1.48043i) q^{14} +(-2.98807 + 2.65921i) q^{16} -4.37401i q^{17} +1.09657 q^{19} +(-1.76534 + 0.671777i) q^{20} +(-2.76534 + 4.01111i) q^{22} -3.80465i q^{23} +4.10807 q^{25} +(1.64535 - 2.38657i) q^{26} +(-2.81264 - 4.48208i) q^{28} +4.94141 q^{29} +4.40936 q^{31} +(5.61367 - 0.697633i) q^{32} +(-3.51106 + 5.09277i) q^{34} +(-0.488582 - 2.45047i) q^{35} +6.97615 q^{37} +(-1.27676 - 0.880227i) q^{38} +(2.59468 + 0.634894i) q^{40} +7.38669i q^{41} -4.99177i q^{43} +(6.43953 - 2.45047i) q^{44} +(-3.05403 + 4.42985i) q^{46} +9.82139 q^{47} +(6.46473 - 2.68464i) q^{49} +(-4.78313 - 3.29759i) q^{50} +(-3.83145 + 1.45800i) q^{52} +1.34451 q^{53} +3.25354 q^{55} +(-0.322978 + 7.47634i) q^{56} +(-5.75342 - 3.96653i) q^{58} -9.08422 q^{59} +9.06524i q^{61} +(-5.13393 - 3.53944i) q^{62} +(-7.09614 - 3.69388i) q^{64} -1.93582 q^{65} -11.7607i q^{67} +(8.17604 - 3.11128i) q^{68} +(-1.39815 + 3.24534i) q^{70} +0.593808i q^{71} -15.0018i q^{73} +(-8.12251 - 5.59983i) q^{74} +(0.780001 + 2.04974i) q^{76} +(1.78222 + 8.93869i) q^{77} -9.27553i q^{79} +(-2.51142 - 2.82200i) q^{80} +(5.92937 - 8.60052i) q^{82} +2.26282 q^{83} +4.13090 q^{85} +(-4.00695 + 5.81205i) q^{86} +(-9.46473 - 2.31593i) q^{88} -12.5590i q^{89} +(-1.06040 - 5.31843i) q^{91} +(7.11178 - 2.70629i) q^{92} +(-11.4353 - 7.88374i) q^{94} +1.03562i q^{95} +18.8330i q^{97} +(-9.68204 - 2.06352i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + q^{14} + 4 q^{16} + 26 q^{20} + 10 q^{22} - 20 q^{25} + 6 q^{26} - 11 q^{28} + 6 q^{35} + 8 q^{37} + 20 q^{38} - 6 q^{46} + 8 q^{47} - 14 q^{49} - 21 q^{56} + 14 q^{58} + 44 q^{59} - 48 q^{62} + 24 q^{64} + 2 q^{68} - 27 q^{70} - 54 q^{80} - 4 q^{83} + 8 q^{85} - 34 q^{88} + 47 q^{98}+O(q^{100}) \) 16 * q + q^14 + 4 * q^16 + 26 * q^20 + 10 * q^22 - 20 * q^25 + 6 * q^26 - 11 * q^28 + 6 * q^35 + 8 * q^37 + 20 * q^38 - 6 * q^46 + 8 * q^47 - 14 * q^49 - 21 * q^56 + 14 * q^58 + 44 * q^59 - 48 * q^62 + 24 * q^64 + 2 * q^68 - 27 * q^70 - 54 * q^80 - 4 * q^83 + 8 * q^85 - 34 * q^88 + 47 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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