LMFDB - Embedded newform 756.2.e.b.323.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(323,756)]

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, 1, 0]))

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

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

chi := DirichletCharacter("756.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.e (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:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.13
Character	$\chi$	$=$	756.323
Dual form			756.2.e.b.323.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0572568 - 1.41305i) q^{2} +(-1.99344 - 0.161814i) q^{4} +0.386370i q^{5} -1.00000i q^{7} +(-0.342790 + 2.80758i) q^{8} +O(q^{10})$	\(q+(0.0572568 - 1.41305i) q^{2} +(-1.99344 - 0.161814i) q^{4} +0.386370i q^{5} -1.00000i q^{7} +(-0.342790 + 2.80758i) q^{8} +(0.545962 + 0.0221223i) q^{10} +3.49674 q^{11} +5.33247 q^{13} +(-1.41305 - 0.0572568i) q^{14} +(3.94763 + 0.645134i) q^{16} -4.58027i q^{17} +6.22605i q^{19} +(0.0625201 - 0.770207i) q^{20} +(0.200212 - 4.94108i) q^{22} -8.20171 q^{23} +4.85072 q^{25} +(0.305320 - 7.53507i) q^{26} +(-0.161814 + 1.99344i) q^{28} -6.76887i q^{29} -9.47346i q^{31} +(1.13764 - 5.54128i) q^{32} +(-6.47216 - 0.262251i) q^{34} +0.386370 q^{35} +4.41693 q^{37} +(8.79775 + 0.356484i) q^{38} +(-1.08476 - 0.132444i) q^{40} -4.43840i q^{41} -1.95948i q^{43} +(-6.97054 - 0.565820i) q^{44} +(-0.469604 + 11.5895i) q^{46} -0.996370 q^{47} -1.00000 q^{49} +(0.277737 - 6.85433i) q^{50} +(-10.6300 - 0.862868i) q^{52} +1.92203i q^{53} +1.35103i q^{55} +(2.80758 + 0.342790i) q^{56} +(-9.56478 - 0.387564i) q^{58} +5.78408 q^{59} +6.68946 q^{61} +(-13.3865 - 0.542420i) q^{62} +(-7.76499 - 1.92482i) q^{64} +2.06031i q^{65} +3.49626i q^{67} +(-0.741151 + 9.13050i) q^{68} +(0.0221223 - 0.545962i) q^{70} +12.0342 q^{71} +8.14330 q^{73} +(0.252899 - 6.24137i) q^{74} +(1.00746 - 12.4113i) q^{76} -3.49674i q^{77} +12.0625i q^{79} +(-0.249260 + 1.52525i) q^{80} +(-6.27170 - 0.254129i) q^{82} -11.4944 q^{83} +1.76968 q^{85} +(-2.76885 - 0.112194i) q^{86} +(-1.19865 + 9.81736i) q^{88} +0.206472i q^{89} -5.33247i q^{91} +(16.3496 + 1.32715i) q^{92} +(-0.0570490 + 1.40792i) q^{94} -2.40556 q^{95} -8.99826 q^{97} +(-0.0572568 + 1.41305i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4}+O(q^{10}) $ 24 * q + 4 * q^4	$ 24 q + 4 q^{4} + 20 q^{10} + 20 q^{16} - 8 q^{22} - 24 q^{25} - 8 q^{28} - 20 q^{34} + 16 q^{37} - 32 q^{40} + 36 q^{46} - 24 q^{49} + 16 q^{52} - 52 q^{58} + 16 q^{61} + 4 q^{64} + 12 q^{70} + 4 q^{82} - 64 q^{85} - 16 q^{88} + 12 q^{94}+O(q^{100}) $ 24 * q + 4 * q^4 + 20 * q^10 + 20 * q^16 - 8 * q^22 - 24 * q^25 - 8 * q^28 - 20 * q^34 + 16 * q^37 - 32 * q^40 + 36 * q^46 - 24 * q^49 + 16 * q^52 - 52 * q^58 + 16 * q^61 + 4 * q^64 + 12 * q^70 + 4 * q^82 - 64 * q^85 - 16 * q^88 + 12 * q^94

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 $

$2$	0.0572568	−	1.41305i	0.0404867	−	0.999180i
$2$	0.0572568	−	1.41305i	0.0404867	−	0.999180i
$3$		0			0
$3$		0			0
$4$	−1.99344	−	0.161814i	−0.996722	−	0.0809069i
$5$			0.386370i			0.172790i	0.996261	+	0.0863950i	$0.0275347\pi$
$5$			0.386370i			0.172790i	−0.996261	+	0.0863950i	$0.972465\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−0.342790	+	2.80758i	−0.121195	+	0.992629i
$9$		0			0
$10$	0.545962	+	0.0221223i	0.172648	+	0.00699569i
$11$	3.49674			1.05431			0.527153	−	0.849771i	$-0.323260\pi$
$11$	3.49674			1.05431			0.527153	+	0.849771i	$0.323260\pi$
$12$		0			0
$13$	5.33247			1.47896			0.739481	−	0.673178i	$-0.235071\pi$
$13$	5.33247			1.47896			0.739481	+	0.673178i	$0.235071\pi$
$14$	−1.41305	−	0.0572568i	−0.377655	−	0.0153025i
$15$		0			0
$16$	3.94763	+	0.645134i	0.986908	+	0.161283i
$17$		−	4.58027i		−	1.11088i	−0.831557	−	0.555439i	$-0.812550\pi$
$17$		−	4.58027i		−	1.11088i	0.831557	−	0.555439i	$-0.187450\pi$
$18$		0			0
$19$			6.22605i			1.42835i	0.699965	+	0.714177i	$0.253199\pi$
$19$			6.22605i			1.42835i	−0.699965	+	0.714177i	$0.746801\pi$
$20$	0.0625201	−	0.770207i	0.0139799	−	0.172224i
$21$		0			0
$22$	0.200212	−	4.94108i	0.0426853	−	1.05344i
$23$	−8.20171			−1.71017			−0.855087	−	0.518484i	$-0.826497\pi$
$23$	−8.20171			−1.71017			−0.855087	+	0.518484i	$0.826497\pi$
$24$		0			0
$25$	4.85072			0.970144
$26$	0.305320	−	7.53507i	0.0598782	−	1.47775i
$27$		0			0
$28$	−0.161814	+	1.99344i	−0.0305800	+	0.376725i
$29$		−	6.76887i		−	1.25695i	−0.777831	−	0.628474i	$-0.783680\pi$
$29$		−	6.76887i		−	1.25695i	0.777831	−	0.628474i	$-0.216320\pi$
$30$		0			0
$31$		−	9.47346i		−	1.70148i	−0.525584	−	0.850742i	$-0.676153\pi$
$31$		−	9.47346i		−	1.70148i	0.525584	−	0.850742i	$-0.323847\pi$
$32$	1.13764	−	5.54128i	0.201108	−	0.979569i
$33$		0			0
$34$	−6.47216	−	0.262251i	−1.10997	−	0.0449757i
$35$	0.386370			0.0653085
$36$		0			0
$37$	4.41693			0.726139			0.363070	−	0.931762i	$-0.381729\pi$
$37$	4.41693			0.726139			0.363070	+	0.931762i	$0.381729\pi$
$38$	8.79775	+	0.356484i	1.42718	+	0.0578293i
$39$		0			0
$40$	−1.08476	−	0.132444i	−0.171516	−	0.0209412i
$41$		−	4.43840i		−	0.693162i	−0.938020	−	0.346581i	$-0.887343\pi$
$41$		−	4.43840i		−	0.693162i	0.938020	−	0.346581i	$-0.112657\pi$
$42$		0			0
$43$		−	1.95948i		−	0.298818i	−0.988775	−	0.149409i	$-0.952263\pi$
$43$		−	1.95948i		−	0.298818i	0.988775	−	0.149409i	$-0.0477371\pi$
$44$	−6.97054	−	0.565820i	−1.05085	−	0.0853006i
$45$		0			0
$46$	−0.469604	+	11.5895i	−0.0692393	+	1.70877i
$47$	−0.996370			−0.145336			−0.0726678	−	0.997356i	$-0.523151\pi$
$47$	−0.996370			−0.145336			−0.0726678	+	0.997356i	$0.523151\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	0.277737	−	6.85433i	0.0392779	−	0.969348i
$51$		0			0
$52$	−10.6300	−	0.862868i	−1.47411	−	0.119658i
$53$			1.92203i			0.264011i	0.991249	+	0.132005i	$0.0421416\pi$
$53$			1.92203i			0.264011i	−0.991249	+	0.132005i	$0.957858\pi$
$54$		0			0
$55$			1.35103i			0.182173i
$56$	2.80758	+	0.342790i	0.375178	+	0.0458072i
$57$		0			0
$58$	−9.56478	−	0.387564i	−1.25592	−	0.0508896i
$59$	5.78408			0.753023			0.376512	−	0.926412i	$-0.377124\pi$
$59$	5.78408			0.753023			0.376512	+	0.926412i	$0.377124\pi$
$60$		0			0
$61$	6.68946			0.856498			0.428249	−	0.903661i	$-0.359131\pi$
$61$	6.68946			0.856498			0.428249	+	0.903661i	$0.359131\pi$
$62$	−13.3865	−	0.542420i	−1.70009	−	0.0688874i
$63$		0			0
$64$	−7.76499	−	1.92482i	−0.970624	−	0.240602i
$65$			2.06031i			0.255550i
$66$		0			0
$67$			3.49626i			0.427136i	0.976928	+	0.213568i	$0.0685085\pi$
$67$			3.49626i			0.427136i	−0.976928	+	0.213568i	$0.931491\pi$
$68$	−0.741151	+	9.13050i	−0.0898777	+	1.10724i
$69$		0			0
$70$	0.0221223	−	0.545962i	0.00264412	−	0.0652549i
$71$	12.0342			1.42820			0.714100	−	0.700044i	$-0.246836\pi$
$71$	12.0342			1.42820			0.714100	+	0.700044i	$0.246836\pi$
$72$		0			0
$73$	8.14330			0.953101			0.476551	−	0.879147i	$-0.341887\pi$
$73$	8.14330			0.953101			0.476551	+	0.879147i	$0.341887\pi$
$74$	0.252899	−	6.24137i	0.0293990	−	0.725544i
$75$		0			0
$76$	1.00746	−	12.4113i	0.115564	−	1.42367i
$77$		−	3.49674i		−	0.398490i
$78$		0			0
$79$			12.0625i			1.35713i	0.734540	+	0.678566i	$0.237398\pi$
$79$			12.0625i			1.35713i	−0.734540	+	0.678566i	$0.762602\pi$
$80$	−0.249260	+	1.52525i	−0.0278682	+	0.170528i
$81$		0			0
$82$	−6.27170	−	0.254129i	−0.692593	−	0.0280638i
$83$	−11.4944			−1.26168			−0.630838	−	0.775915i	$-0.717289\pi$
$83$	−11.4944			−1.26168			−0.630838	+	0.775915i	$0.717289\pi$
$84$		0			0
$85$	1.76968			0.191949
$86$	−2.76885	−	0.112194i	−0.298573	−	0.0120981i
$87$		0			0
$88$	−1.19865	+	9.81736i	−0.127776	+	1.04653i
$89$			0.206472i			0.0218860i	0.999940	+	0.0109430i	$0.00348334\pi$
$89$			0.206472i			0.0218860i	−0.999940	+	0.0109430i	$0.996517\pi$
$90$		0			0
$91$		−	5.33247i		−	0.558995i
$92$	16.3496	+	1.32715i	1.70457	+	0.138365i
$93$		0			0
$94$	−0.0570490	+	1.40792i	−0.00588415	+	0.145216i
$95$	−2.40556			−0.246805
$96$		0			0
$97$	−8.99826			−0.913635			−0.456818	−	0.889560i	$-0.651011\pi$
$97$	−8.99826			−0.913635			−0.456818	+	0.889560i	$0.651011\pi$
$98$	−0.0572568	+	1.41305i	−0.00578381	+	0.142740i
$99$		0			0
$100$	−9.66963	−	0.784914i	−0.966963	−	0.0784914i
$101$			5.94651i			0.591700i	0.955234	+	0.295850i	$0.0956028\pi$
$101$			5.94651i			0.591700i	−0.955234	+	0.295850i	$0.904397\pi$
$102$		0			0
$103$		−	10.9130i		−	1.07529i	−0.843172	−	0.537644i	$-0.819314\pi$
$103$		−	10.9130i		−	1.07529i	0.843172	−	0.537644i	$-0.180686\pi$
$104$	−1.82792	+	14.9713i	−0.179242	+	1.46806i
$105$		0			0
$106$	2.71593	+	0.110049i	0.263794	+	0.0106889i
$107$	2.37293			0.229400			0.114700	−	0.993400i	$-0.463409\pi$
$107$	2.37293			0.229400			0.114700	+	0.993400i	$0.463409\pi$
$108$		0			0
$109$	−3.49012			−0.334293			−0.167146	−	0.985932i	$-0.553455\pi$
$109$	−3.49012			−0.334293			−0.167146	+	0.985932i	$0.553455\pi$
$110$	1.90908	+	0.0773559i	0.182024	+	0.00737560i
$111$		0			0
$112$	0.645134	−	3.94763i	0.0609594	−	0.373016i
$113$			19.0081i			1.78813i	0.447935	+	0.894066i	$0.352160\pi$
$113$			19.0081i			1.78813i	−0.447935	+	0.894066i	$0.647840\pi$
$114$		0			0
$115$		−	3.16890i		−	0.295501i
$116$	−1.09530	+	13.4934i	−0.101696	+	1.25283i
$117$		0			0
$118$	0.331178	−	8.17322i	0.0304874	−	0.752406i
$119$	−4.58027			−0.419872
$120$		0			0
$121$	1.22716			0.111560
$122$	0.383017	−	9.45257i	0.0346767	−	0.855795i
$123$		0			0
$124$	−1.53294	+	18.8848i	−0.137662	+	1.69591i
$125$			3.80602i			0.340421i
$126$		0			0
$127$			7.29024i			0.646904i	0.946245	+	0.323452i	$0.104843\pi$
$127$			7.29024i			0.646904i	−0.946245	+	0.323452i	$0.895157\pi$
$128$	−3.16447	+	10.8621i	−0.279702	+	0.960087i
$129$		0			0
$130$	2.91133	+	0.117967i	0.255340	+	0.0103464i
$131$	−13.1755			−1.15115			−0.575574	−	0.817749i	$-0.695222\pi$
$131$	−13.1755			−1.15115			−0.575574	+	0.817749i	$0.695222\pi$
$132$		0			0
$133$	6.22605			0.539867
$134$	4.94041	+	0.200185i	0.426786	+	0.0172933i
$135$		0			0
$136$	12.8595	+	1.57007i	1.10269	+	0.134632i
$137$			5.32595i			0.455027i	0.973775	+	0.227513i	$0.0730595\pi$
$137$			5.32595i			0.455027i	−0.973775	+	0.227513i	$0.926940\pi$
$138$		0			0
$139$		−	8.71810i		−	0.739459i	−0.929139	−	0.369730i	$-0.879450\pi$
$139$		−	8.71810i		−	0.739459i	0.929139	−	0.369730i	$-0.120550\pi$
$140$	−0.770207	−	0.0625201i	−0.0650944	−	0.00528391i
$141$		0			0
$142$	0.689041	−	17.0050i	0.0578231	−	1.42703i
$143$	18.6462			1.55928
$144$		0			0
$145$	2.61529			0.217188
$146$	0.466259	−	11.5069i	0.0385879	−	0.952320i
$147$		0			0
$148$	−8.80491	−	0.714721i	−0.723759	−	0.0587497i
$149$		−	5.27938i		−	0.432503i	−0.976338	−	0.216252i	$-0.930617\pi$
$149$		−	5.27938i		−	0.432503i	0.976338	−	0.216252i	$-0.0693832\pi$
$150$		0			0
$151$			15.0546i			1.22513i	0.790422	+	0.612563i	$0.209861\pi$
$151$			15.0546i			1.22513i	−0.790422	+	0.612563i	$0.790139\pi$
$152$	−17.4801	−	2.13423i	−1.41783	−	0.173109i
$153$		0			0
$154$	−4.94108	−	0.200212i	−0.398163	−	0.0161335i
$155$	3.66026			0.293999
$156$		0			0
$157$	−5.68524			−0.453732			−0.226866	−	0.973926i	$-0.572848\pi$
$157$	−5.68524			−0.453732			−0.226866	+	0.973926i	$0.572848\pi$
$158$	17.0449	+	0.690657i	1.35602	+	0.0549457i
$159$		0			0
$160$	2.14099	+	0.439549i	0.169260	+	0.0347494i
$161$			8.20171i			0.646385i
$162$		0			0
$163$			19.5536i			1.53156i	0.643103	+	0.765780i	$0.277647\pi$
$163$			19.5536i			1.53156i	−0.643103	+	0.765780i	$0.722353\pi$
$164$	−0.718195	+	8.84770i	−0.0560816	+	0.690889i
$165$		0			0
$166$	−0.658133	+	16.2422i	−0.0510810	+	1.26064i
$167$	−6.27919			−0.485899			−0.242949	−	0.970039i	$-0.578115\pi$
$167$	−6.27919			−0.485899			−0.242949	+	0.970039i	$0.578115\pi$
$168$		0			0
$169$	15.4353			1.18733
$170$	0.101326	−	2.50065i	0.00777136	−	0.191791i
$171$		0			0
$172$	−0.317071	+	3.90611i	−0.0241764	+	0.297838i
$173$		−	6.12181i		−	0.465433i	−0.972545	−	0.232716i	$-0.925239\pi$
$173$		−	6.12181i		−	0.465433i	0.972545	−	0.232716i	$-0.0747614\pi$
$174$		0			0
$175$		−	4.85072i		−	0.366680i
$176$	13.8038	+	2.25586i	1.04050	+	0.170042i
$177$		0			0
$178$	0.291757	+	0.0118220i	0.0218681	+	0.000886093i
$179$	18.1104			1.35363			0.676816	−	0.736152i	$-0.263359\pi$
$179$	18.1104			1.35363			0.676816	+	0.736152i	$0.263359\pi$
$180$		0			0
$181$	6.16529			0.458262			0.229131	−	0.973396i	$-0.426412\pi$
$181$	6.16529			0.458262			0.229131	+	0.973396i	$0.426412\pi$
$182$	−7.53507	−	0.305320i	−0.558537	−	0.0226318i
$183$		0			0
$184$	2.81146	−	23.0269i	0.207264	−	1.69757i
$185$			1.70657i			0.125470i
$186$		0			0
$187$		−	16.0160i		−	1.17120i
$188$	1.98621	+	0.161227i	0.144859	+	0.0117587i
$189$		0			0
$190$	−0.137735	+	3.39919i	−0.00999233	+	0.246603i
$191$	−17.9832			−1.30122			−0.650610	−	0.759412i	$-0.725487\pi$
$191$	−17.9832			−1.30122			−0.650610	+	0.759412i	$0.725487\pi$
$192$		0			0
$193$	15.5475			1.11913			0.559565	−	0.828786i	$-0.310968\pi$
$193$	15.5475			1.11913			0.559565	+	0.828786i	$0.310968\pi$
$194$	−0.515212	+	12.7150i	−0.0369900	+	0.912886i
$195$		0			0
$196$	1.99344	+	0.161814i	0.142389	+	0.0115581i
$197$		−	15.2391i		−	1.08574i	−0.839815	−	0.542872i	$-0.817337\pi$
$197$		−	15.2391i		−	1.08574i	0.839815	−	0.542872i	$-0.182663\pi$
$198$		0			0
$199$		−	21.5459i		−	1.52735i	−0.645601	−	0.763675i	$-0.723393\pi$
$199$		−	21.5459i		−	1.52735i	0.645601	−	0.763675i	$-0.276607\pi$
$200$	−1.66278	+	13.6188i	−0.117576	+	0.962992i
$201$		0			0
$202$	8.40274	+	0.340478i	0.591215	+	0.0239560i
$203$	−6.76887			−0.475082
$204$		0			0
$205$	1.71487			0.119771
$206$	−15.4206	−	0.624842i	−1.07441	−	0.0435348i
$207$		0			0
$208$	21.0506	+	3.44016i	1.45960	+	0.238532i
$209$			21.7709i			1.50592i
$210$		0			0
$211$		−	10.1173i		−	0.696503i	−0.937401	−	0.348251i	$-0.886776\pi$
$211$		−	10.1173i		−	0.696503i	0.937401	−	0.348251i	$-0.113224\pi$
$212$	0.311011	−	3.83145i	0.0213603	−	0.263145i
$213$		0			0
$214$	0.135866	−	3.35307i	0.00928762	−	0.229211i
$215$	0.757085			0.0516327
$216$		0			0
$217$	−9.47346			−0.643100
$218$	−0.199833	+	4.93173i	−0.0135344	+	0.334019i
$219$		0			0
$220$	0.218616	−	2.69321i	0.0147391	−	0.181576i
$221$		−	24.4241i		−	1.64295i
$222$		0			0
$223$			4.80598i			0.321832i	0.986968	+	0.160916i	$0.0514449\pi$
$223$			4.80598i			0.321832i	−0.986968	+	0.160916i	$0.948555\pi$
$224$	−5.54128	−	1.13764i	−0.370242	−	0.0760116i
$225$		0			0
$226$	26.8595	+	1.08834i	1.78667	+	0.0723955i
$227$	−2.62950			−0.174526			−0.0872630	−	0.996185i	$-0.527812\pi$
$227$	−2.62950			−0.174526			−0.0872630	+	0.996185i	$0.527812\pi$
$228$		0			0
$229$	−11.0616			−0.730973			−0.365487	−	0.930817i	$-0.619097\pi$
$229$	−11.0616			−0.730973			−0.365487	+	0.930817i	$0.619097\pi$
$230$	−4.47782	−	0.181441i	−0.295259	−	0.0119639i
$231$		0			0
$232$	19.0041	+	2.32030i	1.24768	+	0.152335i
$233$			20.8133i			1.36352i	0.731575	+	0.681761i	$0.238786\pi$
$233$			20.8133i			1.36352i	−0.731575	+	0.681761i	$0.761214\pi$
$234$		0			0
$235$		−	0.384968i		−	0.0251125i
$236$	−11.5302	−	0.935944i	−0.750554	−	0.0609248i
$237$		0			0
$238$	−0.262251	+	6.47216i	−0.0169992	+	0.419528i
$239$	26.4240			1.70923			0.854614	−	0.519263i	$-0.173794\pi$
$239$	26.4240			1.70923			0.854614	+	0.519263i	$0.173794\pi$
$240$		0			0
$241$	−21.4304			−1.38045			−0.690226	−	0.723594i	$-0.742489\pi$
$241$	−21.4304			−1.38045			−0.690226	+	0.723594i	$0.742489\pi$
$242$	0.0702631	−	1.73404i	0.00451668	−	0.111468i
$243$		0			0
$244$	−13.3351	−	1.08245i	−0.853690	−	0.0692966i
$245$		−	0.386370i		−	0.0246843i
$246$		0			0
$247$			33.2002i			2.11248i
$248$	26.5975	+	3.24741i	1.68894	+	0.206210i
$249$		0			0
$250$	5.37812	+	0.217921i	0.340142	+	0.0137825i
$251$	8.66366			0.546845			0.273423	−	0.961894i	$-0.411844\pi$
$251$	8.66366			0.546845			0.273423	+	0.961894i	$0.411844\pi$
$252$		0			0
$253$	−28.6792			−1.80305
$254$	10.3015	+	0.417416i	0.646374	+	0.0261910i
$255$		0			0
$256$	15.1676	+	5.09350i	0.947975	+	0.318344i
$257$			30.9680i			1.93173i	0.259049	+	0.965864i	$0.416591\pi$
$257$			30.9680i			1.93173i	−0.259049	+	0.965864i	$0.583409\pi$
$258$		0			0
$259$		−	4.41693i		−	0.274455i
$260$	0.333386	−	4.10711i	0.0206758	−	0.254712i
$261$		0			0
$262$	−0.754387	+	18.6177i	−0.0466062	+	1.15021i
$263$	−15.7715			−0.972514			−0.486257	−	0.873816i	$-0.661638\pi$
$263$	−15.7715			−0.972514			−0.486257	+	0.873816i	$0.661638\pi$
$264$		0			0
$265$	−0.742614			−0.0456184
$266$	0.356484	−	8.79775i	0.0218574	−	0.539425i
$267$		0			0
$268$	0.565744	−	6.96960i	0.0345583	−	0.425736i
$269$			5.55063i			0.338428i	0.985579	+	0.169214i	$0.0541229\pi$
$269$			5.55063i			0.338428i	−0.985579	+	0.169214i	$0.945877\pi$
$270$		0			0
$271$		−	9.57901i		−	0.581884i	−0.956741	−	0.290942i	$-0.906031\pi$
$271$		−	9.57901i		−	0.581884i	0.956741	−	0.290942i	$-0.0939686\pi$
$272$	2.95488	−	18.0812i	0.179166	−	1.09633i
$273$		0			0
$274$	7.52585	+	0.304947i	0.454653	+	0.0184225i
$275$	16.9617			1.02283
$276$		0			0
$277$	−23.8684			−1.43411			−0.717057	−	0.697015i	$-0.754511\pi$
$277$	−23.8684			−1.43411			−0.717057	+	0.697015i	$0.754511\pi$
$278$	−12.3191	−	0.499170i	−0.738853	−	0.0299382i
$279$		0			0
$280$	−0.132444	+	1.08476i	−0.00791503	+	0.0648271i
$281$		−	8.73238i		−	0.520930i	−0.965483	−	0.260465i	$-0.916124\pi$
$281$		−	8.73238i		−	0.520930i	0.965483	−	0.260465i	$-0.0838759\pi$
$282$		0			0
$283$			1.18895i			0.0706760i	0.999375	+	0.0353380i	$0.0112508\pi$
$283$			1.18895i			0.0706760i	−0.999375	+	0.0353380i	$0.988749\pi$
$284$	−23.9895	−	1.94730i	−1.42352	−	0.115551i
$285$		0			0
$286$	1.06762	−	26.3481i	0.0631299	−	1.55800i
$287$	−4.43840			−0.261990
$288$		0			0
$289$	−3.97884			−0.234049
$290$	0.149743	−	3.69555i	0.00879322	−	0.217010i
$291$		0			0
$292$	−16.2332	−	1.31770i	−0.949977	−	0.0771125i
$293$		−	5.50536i		−	0.321627i	−0.986985	−	0.160813i	$-0.948588\pi$
$293$		−	5.50536i		−	0.321627i	0.986985	−	0.160813i	$-0.0514117\pi$
$294$		0			0
$295$			2.23480i			0.130115i
$296$	−1.51408	+	12.4009i	−0.0880041	+	0.720787i
$297$		0			0
$298$	−7.46004	−	0.302280i	−0.432149	−	0.0175106i
$299$	−43.7354			−2.52928
$300$		0			0
$301$	−1.95948			−0.112943
$302$	21.2730	+	0.861978i	1.22412	+	0.0496013i
$303$		0			0
$304$	−4.01664	+	24.5782i	−0.230370	+	1.40965i
$305$			2.58461i			0.147994i
$306$		0			0
$307$			19.4222i			1.10849i	0.832355	+	0.554243i	$0.186992\pi$
$307$			19.4222i			1.10849i	−0.832355	+	0.554243i	$0.813008\pi$
$308$	−0.565820	+	6.97054i	−0.0322406	+	0.397184i
$309$		0			0
$310$	0.209575	−	5.17215i	0.0119031	−	0.293758i
$311$	−19.9681			−1.13229			−0.566143	−	0.824307i	$-0.691565\pi$
$311$	−19.9681			−1.13229			−0.566143	+	0.824307i	$0.691565\pi$
$312$		0			0
$313$	−20.6381			−1.16654			−0.583268	−	0.812280i	$-0.698226\pi$
$313$	−20.6381			−1.16654			−0.583268	+	0.812280i	$0.698226\pi$
$314$	−0.325519	+	8.03356i	−0.0183701	+	0.453360i
$315$		0			0
$316$	1.95187	−	24.0458i	0.109801	−	1.35268i
$317$		−	27.4374i		−	1.54104i	−0.637418	−	0.770518i	$-0.719997\pi$
$317$		−	27.4374i		−	1.54104i	0.637418	−	0.770518i	$-0.280003\pi$
$318$		0			0
$319$		−	23.6689i		−	1.32521i
$320$	0.743693	−	3.00016i	0.0415737	−	0.167714i
$321$		0			0
$322$	11.5895	+	0.469604i	0.645855	+	0.0261700i
$323$	28.5170			1.58673
$324$		0			0
$325$	25.8663			1.43481
$326$	27.6304	+	1.11958i	1.53030	+	0.0620078i
$327$		0			0
$328$	12.4612	+	1.52144i	0.688052	+	0.0840074i
$329$			0.996370i			0.0549317i
$330$		0			0
$331$			21.0348i			1.15618i	0.815975	+	0.578088i	$0.196201\pi$
$331$			21.0348i			1.15618i	−0.815975	+	0.578088i	$0.803799\pi$
$332$	22.9135	+	1.85996i	1.25754	+	0.102078i
$333$		0			0
$334$	−0.359527	+	8.87284i	−0.0196724	+	0.485500i
$335$	−1.35085			−0.0738049
$336$		0			0
$337$	−19.7637			−1.07660			−0.538298	−	0.842755i	$-0.680932\pi$
$337$	−19.7637			−1.07660			−0.538298	+	0.842755i	$0.680932\pi$
$338$	0.883773	−	21.8108i	0.0480709	−	1.18635i
$339$		0			0
$340$	−3.52775	−	0.286359i	−0.191319	−	0.0155300i
$341$		−	33.1262i		−	1.79388i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	5.50139	+	0.671690i	0.296615	+	0.0362151i
$345$		0			0
$346$	−8.65045	−	0.350515i	−0.465051	−	0.0188438i
$347$	0.272222			0.0146136			0.00730682	−	0.999973i	$-0.497674\pi$
$347$	0.272222			0.0146136			0.00730682	+	0.999973i	$0.497674\pi$
$348$		0			0
$349$	4.92498			0.263628			0.131814	−	0.991274i	$-0.457920\pi$
$349$	4.92498			0.263628			0.131814	+	0.991274i	$0.457920\pi$
$350$	−6.85433	−	0.277737i	−0.366379	−	0.0148456i
$351$		0			0
$352$	3.97802	−	19.3764i	0.212029	−	1.03276i
$353$			2.99080i			0.159184i	0.996828	+	0.0795922i	$0.0253618\pi$
$353$			2.99080i			0.159184i	−0.996828	+	0.0795922i	$0.974638\pi$
$354$		0			0
$355$			4.64967i			0.246779i
$356$	0.0334101	−	0.411591i	0.00177073	−	0.0218143i
$357$		0			0
$358$	1.03694	−	25.5909i	0.0548040	−	1.35252i
$359$	9.86716			0.520769			0.260385	−	0.965505i	$-0.416151\pi$
$359$	9.86716			0.520769			0.260385	+	0.965505i	$0.416151\pi$
$360$		0			0
$361$	−19.7637			−1.04020
$362$	0.353004	−	8.71188i	0.0185535	−	0.457886i
$363$		0			0
$364$	−0.862868	+	10.6300i	−0.0452266	+	0.557162i
$365$			3.14633i			0.164686i
$366$		0			0
$367$		−	23.8605i		−	1.24551i	−0.782418	−	0.622754i	$-0.786014\pi$
$367$		−	23.8605i		−	1.24551i	0.782418	−	0.622754i	$-0.213986\pi$
$368$	−32.3773	−	5.29120i	−1.68779	−	0.275823i
$369$		0			0
$370$	2.41148	+	0.0977128i	0.125367	+	0.00507985i
$371$	1.92203			0.0997867
$372$		0			0
$373$	−28.4683			−1.47403			−0.737016	−	0.675876i	$-0.763766\pi$
$373$	−28.4683			−1.47403			−0.737016	+	0.675876i	$0.763766\pi$
$374$	−22.6314	−	0.917024i	−1.17024	−	0.0474182i
$375$		0			0
$376$	0.341546	−	2.79739i	0.0176139	−	0.144264i
$377$		−	36.0948i		−	1.85898i
$378$		0			0
$379$			11.0145i			0.565779i	0.959153	+	0.282889i	$0.0912929\pi$
$379$			11.0145i			0.565779i	−0.959153	+	0.282889i	$0.908707\pi$
$380$	4.79535	+	0.389253i	0.245996	+	0.0199683i
$381$		0			0
$382$	−1.02966	+	25.4113i	−0.0526821	+	1.30015i
$383$	12.6616			0.646976			0.323488	−	0.946232i	$-0.395144\pi$
$383$	12.6616			0.646976			0.323488	+	0.946232i	$0.395144\pi$
$384$		0			0
$385$	1.35103			0.0688551
$386$	0.890198	−	21.9694i	0.0453099	−	1.11821i
$387$		0			0
$388$	17.9375	+	1.45604i	0.910640	+	0.0739194i
$389$			21.5099i			1.09060i	0.838242	+	0.545298i	$0.183584\pi$
$389$			21.5099i			1.09060i	−0.838242	+	0.545298i	$0.816416\pi$
$390$		0			0
$391$			37.5660i			1.89980i
$392$	0.342790	−	2.80758i	0.0173135	−	0.141804i
$393$		0			0
$394$	−21.5337	−	0.872545i	−1.08485	−	0.0439582i
$395$	−4.66057			−0.234499
$396$		0			0
$397$	−1.09412			−0.0549124			−0.0274562	−	0.999623i	$-0.508741\pi$
$397$	−1.09412			−0.0549124			−0.0274562	+	0.999623i	$0.508741\pi$
$398$	−30.4455	−	1.23365i	−1.52610	−	0.0618373i
$399$		0			0
$400$	19.1489	+	3.12936i	0.957443	+	0.156468i
$401$		−	2.97516i		−	0.148573i	−0.997237	−	0.0742863i	$-0.976332\pi$
$401$		−	2.97516i		−	0.148573i	0.997237	−	0.0742863i	$-0.0236679\pi$
$402$		0			0
$403$		−	50.5169i		−	2.51643i
$404$	0.962228	−	11.8540i	0.0478726	−	0.589760i
$405$		0			0
$406$	−0.387564	+	9.56478i	−0.0192345	+	0.474692i
$407$	15.4448			0.765573
$408$		0			0
$409$	−19.9391			−0.985923			−0.492962	−	0.870051i	$-0.664086\pi$
$409$	−19.9391			−0.985923			−0.492962	+	0.870051i	$0.664086\pi$
$410$	0.0981877	−	2.42320i	0.00484914	−	0.119673i
$411$		0			0
$412$	−1.76587	+	21.7544i	−0.0869983	+	1.07176i
$413$		−	5.78408i		−	0.284616i
$414$		0			0
$415$		−	4.44110i		−	0.218005i
$416$	6.06642	−	29.5487i	0.297431	−	1.44875i
$417$		0			0
$418$	30.7634	+	1.24653i	1.50469	+	0.0609698i
$419$	−27.5046			−1.34369			−0.671845	−	0.740692i	$-0.734498\pi$
$419$	−27.5046			−1.34369			−0.671845	+	0.740692i	$0.734498\pi$
$420$		0			0
$421$	13.4219			0.654142			0.327071	−	0.945000i	$-0.393938\pi$
$421$	13.4219			0.654142			0.327071	+	0.945000i	$0.393938\pi$
$422$	−14.2963	−	0.579284i	−0.695932	−	0.0281991i
$423$		0			0
$424$	−5.39624	−	0.658852i	−0.262065	−	0.0319967i
$425$		−	22.2176i		−	1.07771i
$426$		0			0
$427$		−	6.68946i		−	0.323726i
$428$	−4.73030	−	0.383973i	−0.228647	−	0.0185600i
$429$		0			0
$430$	0.0433482	−	1.06980i	0.00209044	−	0.0515904i
$431$	5.42483			0.261305			0.130652	−	0.991428i	$-0.458293\pi$
$431$	5.42483			0.261305			0.130652	+	0.991428i	$0.458293\pi$
$432$		0			0
$433$	−34.2723			−1.64702			−0.823511	−	0.567300i	$-0.807988\pi$
$433$	−34.2723			−1.64702			−0.823511	+	0.567300i	$0.807988\pi$
$434$	−0.542420	+	13.3865i	−0.0260370	+	0.642573i
$435$		0			0
$436$	6.95735	+	0.564750i	0.333197	+	0.0270466i
$437$		−	51.0643i		−	2.44274i
$438$		0			0
$439$			3.87818i			0.185096i	0.995708	+	0.0925478i	$0.0295011\pi$
$439$			3.87818i			0.185096i	−0.995708	+	0.0925478i	$0.970499\pi$
$440$	−3.79313	−	0.463121i	−0.180831	−	0.0220784i
$441$		0			0
$442$	−34.5126	−	1.39845i	−1.64160	−	0.0665174i
$443$	9.48942			0.450856			0.225428	−	0.974260i	$-0.427622\pi$
$443$	9.48942			0.450856			0.225428	+	0.974260i	$0.427622\pi$
$444$		0			0
$445$	−0.0797748			−0.00378169
$446$	6.79111	+	0.275175i	0.321568	+	0.0130299i
$447$		0			0
$448$	−1.92482	+	7.76499i	−0.0909392	+	0.366861i
$449$			18.2662i			0.862038i	0.902343	+	0.431019i	$0.141846\pi$
$449$			18.2662i			0.862038i	−0.902343	+	0.431019i	$0.858154\pi$
$450$		0			0
$451$		−	15.5199i		−	0.730804i
$452$	3.07578	−	37.8916i	0.144672	−	1.78227i
$453$		0			0
$454$	−0.150557	+	3.71563i	−0.00706598	+	0.174383i
$455$	2.06031			0.0965887
$456$		0			0
$457$	−3.62419			−0.169533			−0.0847663	−	0.996401i	$-0.527014\pi$
$457$	−3.62419			−0.169533			−0.0847663	+	0.996401i	$0.527014\pi$
$458$	−0.633353	+	15.6307i	−0.0295947	+	0.730374i
$459$		0			0
$460$	−0.512771	+	6.31702i	−0.0239081	+	0.294532i
$461$			9.53162i			0.443932i	0.975054	+	0.221966i	$0.0712473\pi$
$461$			9.53162i			0.443932i	−0.975054	+	0.221966i	$0.928753\pi$
$462$		0			0
$463$			41.9466i			1.94943i	0.223461	+	0.974713i	$0.428265\pi$
$463$			41.9466i			1.94943i	−0.223461	+	0.974713i	$0.571735\pi$
$464$	4.36683	−	26.7210i	0.202725	−	1.24049i
$465$		0			0
$466$	29.4103	+	1.19170i	1.36240	+	0.0552045i
$467$	−8.02448			−0.371329			−0.185664	−	0.982613i	$-0.559444\pi$
$467$	−8.02448			−0.371329			−0.185664	+	0.982613i	$0.559444\pi$
$468$		0			0
$469$	3.49626			0.161442
$470$	−0.543980	−	0.0220420i	−0.0250919	−	0.00101672i
$471$		0			0
$472$	−1.98272	+	16.2393i	−0.0912623	+	0.747472i
$473$		−	6.85178i		−	0.315045i
$474$		0			0
$475$			30.2008i			1.38571i
$476$	9.13050	+	0.741151i	0.418496	+	0.0339706i
$477$		0			0
$478$	1.51296	−	37.3386i	0.0692010	−	1.70783i
$479$	17.1710			0.784563			0.392281	−	0.919845i	$-0.371686\pi$
$479$	17.1710			0.784563			0.392281	+	0.919845i	$0.371686\pi$
$480$		0			0
$481$	23.5532			1.07393
$482$	−1.22703	+	30.2823i	−0.0558899	+	1.37932i
$483$		0			0
$484$	−2.44627	−	0.198571i	−0.111194	−	0.00902596i
$485$		−	3.47666i		−	0.157867i
$486$		0			0
$487$		−	31.5764i		−	1.43086i	−0.698682	−	0.715432i	$-0.746230\pi$
$487$		−	31.5764i		−	1.43086i	0.698682	−	0.715432i	$-0.253770\pi$
$488$	−2.29308	+	18.7812i	−0.103803	+	0.850184i
$489$		0			0
$490$	−0.545962	−	0.0221223i	−0.0246640	−	0.000999385i
$491$	−16.0782			−0.725599			−0.362800	−	0.931867i	$-0.618179\pi$
$491$	−16.0782			−0.725599			−0.362800	+	0.931867i	$0.618179\pi$
$492$		0			0
$493$	−31.0032			−1.39631
$494$	46.9137	+	1.90094i	2.11075	+	0.0855273i
$495$		0			0
$496$	6.11165	−	37.3977i	0.274421	−	1.67921i
$497$		−	12.0342i		−	0.539809i
$498$		0			0
$499$			16.6396i			0.744889i	0.928054	+	0.372445i	$0.121480\pi$
$499$			16.6396i			0.744889i	−0.928054	+	0.372445i	$0.878520\pi$
$500$	0.615868	−	7.58709i	0.0275424	−	0.339305i
$501$		0			0
$502$	0.496053	−	12.2422i	0.0221399	−	0.546397i
$503$	−20.1267			−0.897407			−0.448704	−	0.893681i	$-0.648114\pi$
$503$	−20.1267			−0.897407			−0.448704	+	0.893681i	$0.648114\pi$
$504$		0			0
$505$	−2.29755			−0.102240
$506$	−1.64208	+	40.5253i	−0.0729993	+	1.80157i
$507$		0			0
$508$	1.17966	−	14.5327i	0.0523391	−	0.644784i
$509$			37.6363i			1.66820i	0.551612	+	0.834101i	$0.314013\pi$
$509$			37.6363i			1.66820i	−0.551612	+	0.834101i	$0.685987\pi$
$510$		0			0
$511$		−	8.14330i		−	0.360238i
$512$	8.06584	−	21.1410i	0.356463	−	0.934309i
$513$		0			0
$514$	43.7594	+	1.77313i	1.93014	+	0.0782092i
$515$	4.21645			0.185799
$516$		0			0
$517$	−3.48404			−0.153228
$518$	−6.24137	−	0.252899i	−0.274230	−	0.0111118i
$519$		0			0
$520$	−5.78448	−	0.706253i	−0.253666	−	0.0309712i
$521$			36.2014i			1.58601i	0.609213	+	0.793007i	$0.291485\pi$
$521$			36.2014i			1.58601i	−0.609213	+	0.793007i	$0.708515\pi$
$522$		0			0
$523$		−	43.8379i		−	1.91690i	−0.285268	−	0.958448i	$-0.592083\pi$
$523$		−	43.8379i		−	1.91690i	0.285268	−	0.958448i	$-0.407917\pi$
$524$	26.2646	+	2.13198i	1.14738	+	0.0931359i
$525$		0			0
$526$	−0.903027	+	22.2860i	−0.0393739	+	0.971717i
$527$	−43.3910			−1.89014
$528$		0			0
$529$	44.2681			1.92470
$530$	−0.0425197	+	1.04935i	−0.00184694	+	0.0455810i
$531$		0			0
$532$	−12.4113	−	1.00746i	−0.538097	−	0.0436790i
$533$		−	23.6676i		−	1.02516i
$534$		0			0
$535$			0.916828i			0.0396379i
$536$	−9.81603	−	1.19848i	−0.423988	−	0.0517666i
$537$		0			0
$538$	7.84334	+	0.317811i	0.338150	+	0.0137018i
$539$	−3.49674			−0.150615
$540$		0			0
$541$	30.6236			1.31661			0.658307	−	0.752750i	$-0.271273\pi$
$541$	30.6236			1.31661			0.658307	+	0.752750i	$0.271273\pi$
$542$	−13.5357	−	0.548464i	−0.581407	−	0.0235585i
$543$		0			0
$544$	−25.3805	−	5.21068i	−1.08818	−	0.223406i
$545$		−	1.34848i		−	0.0577624i
$546$		0			0
$547$			21.4353i			0.916507i	0.888822	+	0.458254i	$0.151525\pi$
$547$			21.4353i			0.916507i	−0.888822	+	0.458254i	$0.848475\pi$
$548$	0.861813	−	10.6170i	0.0368148	−	0.453535i
$549$		0			0
$550$	0.971171	−	23.9678i	0.0414109	−	1.02199i
$551$	42.1433			1.79537
$552$		0			0
$553$	12.0625			0.512948
$554$	−1.36663	+	33.7273i	−0.0580625	+	1.43294i
$555$		0			0
$556$	−1.41071	+	17.3790i	−0.0598274	+	0.737035i
$557$			4.24025i			0.179665i	0.995957	+	0.0898326i	$0.0286332\pi$
$557$			4.24025i			0.179665i	−0.995957	+	0.0898326i	$0.971367\pi$
$558$		0			0
$559$		−	10.4489i		−	0.441940i
$560$	1.52525	+	0.249260i	0.0644535	+	0.0105332i
$561$		0			0
$562$	−12.3393	−	0.499988i	−0.520503	−	0.0210907i
$563$	31.5890			1.33132			0.665658	−	0.746257i	$-0.268151\pi$
$563$	31.5890			1.33132			0.665658	+	0.746257i	$0.268151\pi$
$564$		0			0
$565$	−7.34417			−0.308971
$566$	1.68006	+	0.0680757i	0.0706181	+	0.00286144i
$567$		0			0
$568$	−4.12521	+	33.7870i	−0.173090	+	1.41767i
$569$			12.1710i			0.510234i	0.966910	+	0.255117i	$0.0821141\pi$
$569$			12.1710i			0.510234i	−0.966910	+	0.255117i	$0.917886\pi$
$570$		0			0
$571$			3.04693i			0.127510i	0.997966	+	0.0637551i	$0.0203076\pi$
$571$			3.04693i			0.127510i	−0.997966	+	0.0637551i	$0.979692\pi$
$572$	−37.1702	−	3.01722i	−1.55417	−	0.126156i
$573$		0			0
$574$	−0.254129	+	6.27170i	−0.0106071	+	0.261776i
$575$	−39.7842			−1.65912
$576$		0			0
$577$	38.1633			1.58876			0.794381	−	0.607420i	$-0.207796\pi$
$577$	38.1633			1.58876			0.794381	+	0.607420i	$0.207796\pi$
$578$	−0.227815	+	5.62231i	−0.00947587	+	0.233857i
$579$		0			0
$580$	−5.21343	−	0.423190i	−0.216476	−	0.0175720i
$581$			11.4944i			0.476868i
$582$		0			0
$583$			6.72082i			0.278348i
$584$	−2.79144	+	22.8630i	−0.115511	+	0.946076i
$585$		0			0
$586$	−7.77938	−	0.315220i	−0.321363	−	0.0130216i
$587$	21.5383			0.888982			0.444491	−	0.895783i	$-0.353384\pi$
$587$	21.5383			0.888982			0.444491	+	0.895783i	$0.353384\pi$
$588$		0			0
$589$	58.9822			2.43032
$590$	3.15789	+	0.127957i	0.130008	+	0.00526792i
$591$		0			0
$592$	17.4364	+	2.84951i	0.716633	+	0.117114i
$593$			23.8264i			0.978434i	0.872162	+	0.489217i	$0.162717\pi$
$593$			23.8264i			0.978434i	−0.872162	+	0.489217i	$0.837283\pi$
$594$		0			0
$595$		−	1.76968i		−	0.0725497i
$596$	−0.854276	+	10.5241i	−0.0349925	+	0.431085i
$597$		0			0
$598$	−2.50415	+	61.8005i	−0.102402	+	2.52721i
$599$	17.2409			0.704446			0.352223	−	0.935916i	$-0.385426\pi$
$599$	17.2409			0.704446			0.352223	+	0.935916i	$0.385426\pi$
$600$		0			0
$601$	35.3544			1.44214			0.721068	−	0.692864i	$-0.243651\pi$
$601$	35.3544			1.44214			0.721068	+	0.692864i	$0.243651\pi$
$602$	−0.112194	+	2.76885i	−0.00457267	+	0.112850i
$603$		0			0
$604$	2.43604	−	30.0105i	0.0991212	−	1.22111i
$605$			0.474137i			0.0192764i
$606$		0			0
$607$		−	16.0905i		−	0.653091i	−0.945181	−	0.326546i	$-0.894115\pi$
$607$		−	16.0905i		−	0.653091i	0.945181	−	0.326546i	$-0.105885\pi$
$608$	34.5003	+	7.08299i	1.39917	+	0.287253i
$609$		0			0
$610$	3.65219	+	0.147986i	0.147873	+	0.00599179i
$611$	−5.31312			−0.214946
$612$		0			0
$613$	−31.2454			−1.26199			−0.630995	−	0.775787i	$-0.717353\pi$
$613$	−31.2454			−1.26199			−0.630995	+	0.775787i	$0.717353\pi$
$614$	27.4447	+	1.11205i	1.10758	+	0.0448789i
$615$		0			0
$616$	9.81736	+	1.19865i	0.395553	+	0.0482948i
$617$		−	13.4327i		−	0.540782i	−0.962751	−	0.270391i	$-0.912847\pi$
$617$		−	13.4327i		−	0.540782i	0.962751	−	0.270391i	$-0.0871529\pi$
$618$		0			0
$619$			0.489134i			0.0196599i	0.999952	+	0.00982997i	$0.00312903\pi$
$619$			0.489134i			0.0196599i	−0.999952	+	0.00982997i	$0.996871\pi$
$620$	−7.29652	−	0.592281i	−0.293035	−	0.0237866i
$621$		0			0
$622$	−1.14331	+	28.2160i	−0.0458425	+	1.13136i
$623$	0.206472			0.00827214
$624$		0			0
$625$	22.7831			0.911322
$626$	−1.18167	+	29.1628i	−0.0472291	+	1.16558i
$627$		0			0
$628$	11.3332	+	0.919951i	0.452244	+	0.0367101i
$629$		−	20.2307i		−	0.806652i
$630$		0			0
$631$		−	24.6454i		−	0.981118i	−0.871408	−	0.490559i	$-0.836793\pi$
$631$		−	24.6454i		−	0.981118i	0.871408	−	0.490559i	$-0.163207\pi$
$632$	−33.8663	−	4.13489i	−1.34713	−	0.164477i
$633$		0			0
$634$	−38.7705	−	1.57098i	−1.53977	−	0.0623915i
$635$	−2.81673			−0.111779
$636$		0			0
$637$	−5.33247			−0.211280
$638$	−33.4455	−	1.35521i	−1.32412	−	0.0536532i
$639$		0			0
$640$	−4.19681	−	1.22266i	−0.165893	−	0.0483298i
$641$			34.9422i			1.38014i	0.723745	+	0.690068i	$0.242419\pi$
$641$			34.9422i			1.38014i	−0.723745	+	0.690068i	$0.757581\pi$
$642$		0			0
$643$			16.2972i			0.642701i	0.946960	+	0.321350i	$0.104137\pi$
$643$			16.2972i			0.642701i	−0.946960	+	0.321350i	$0.895863\pi$
$644$	1.32715	−	16.3496i	0.0522971	−	0.644266i
$645$		0			0
$646$	1.63279	−	40.2960i	0.0642413	−	1.58543i
$647$	7.61731			0.299467			0.149734	−	0.988726i	$-0.452158\pi$
$647$	7.61731			0.299467			0.149734	+	0.988726i	$0.452158\pi$
$648$		0			0
$649$	20.2254			0.793916
$650$	1.48102	−	36.5505i	0.0580905	−	1.43363i
$651$		0			0
$652$	3.16405	−	38.9791i	0.123914	−	1.52654i
$653$			38.8914i			1.52194i	0.648788	+	0.760969i	$0.275276\pi$
$653$			38.8914i			1.52194i	−0.648788	+	0.760969i	$0.724724\pi$
$654$		0			0
$655$		−	5.09062i		−	0.198907i
$656$	2.86336	−	17.5212i	0.111795	−	0.684087i
$657$		0			0
$658$	1.40792	+	0.0570490i	0.0548866	+	0.00222400i
$659$	−2.21194			−0.0861648			−0.0430824	−	0.999072i	$-0.513718\pi$
$659$	−2.21194			−0.0861648			−0.0430824	+	0.999072i	$0.513718\pi$
$660$		0			0
$661$	17.0793			0.664308			0.332154	−	0.943225i	$-0.392225\pi$
$661$	17.0793			0.664308			0.332154	+	0.943225i	$0.392225\pi$
$662$	29.7233	+	1.20438i	1.15523	+	0.0468097i
$663$		0			0
$664$	3.94017	−	32.2715i	0.152908	−	1.25238i
$665$			2.40556i			0.0932837i
$666$		0			0
$667$			55.5163i			2.14960i
$668$	12.5172	+	1.01606i	0.484306	+	0.0393126i
$669$		0			0
$670$	−0.0773454	+	1.90883i	−0.00298811	+	0.0737444i
$671$	23.3913			0.903010
$672$		0			0
$673$	−14.8342			−0.571818			−0.285909	−	0.958257i	$-0.592295\pi$
$673$	−14.8342			−0.571818			−0.285909	+	0.958257i	$0.592295\pi$
$674$	−1.13160	+	27.9271i	−0.0435878	+	1.07571i
$675$		0			0
$676$	−30.7693	−	2.49764i	−1.18343	−	0.0960630i
$677$		−	30.8678i		−	1.18634i	−0.805076	−	0.593172i	$-0.797875\pi$
$677$		−	30.8678i		−	1.18634i	0.805076	−	0.593172i	$-0.202125\pi$
$678$		0			0
$679$			8.99826i			0.345322i
$680$	−0.606628	+	4.96851i	−0.0232631	+	0.190534i
$681$		0			0
$682$	−46.8091	−	1.89670i	−1.79241	−	0.0726283i
$683$	−39.6035			−1.51539			−0.757694	−	0.652611i	$-0.773674\pi$
$683$	−39.6035			−1.51539			−0.757694	+	0.652611i	$0.773674\pi$
$684$		0			0
$685$	−2.05779			−0.0786240
$686$	1.41305	+	0.0572568i	0.0539507	+	0.00218607i
$687$		0			0
$688$	1.26413	−	7.73531i	0.0481944	−	0.294906i
$689$			10.2492i			0.390462i
$690$		0			0
$691$		−	31.9714i		−	1.21625i	−0.793841	−	0.608125i	$-0.791922\pi$
$691$		−	31.9714i		−	1.21625i	0.793841	−	0.608125i	$-0.208078\pi$
$692$	−0.990594	+	12.2035i	−0.0376567	+	0.463907i
$693$		0			0
$694$	0.0155866	−	0.384664i	0.000591658	−	0.0146017i
$695$	3.36841			0.127771
$696$		0			0
$697$	−20.3290			−0.770018
$698$	0.281989	−	6.95927i	0.0106734	−	0.263412i
$699$		0			0
$700$	−0.784914	+	9.66963i	−0.0296669	+	0.365478i
$701$			19.3239i			0.729852i	0.931037	+	0.364926i	$0.118906\pi$
$701$			19.3239i			0.729852i	−0.931037	+	0.364926i	$0.881094\pi$
$702$		0			0
$703$			27.5001i			1.03718i
$704$	−27.1521	−	6.73058i	−1.02333	−	0.253668i
$705$		0			0
$706$	4.22617	+	0.171244i	0.159054	+	0.00644485i
$707$	5.94651			0.223642
$708$		0			0
$709$	−17.0015			−0.638503			−0.319252	−	0.947670i	$-0.603432\pi$
$709$	−17.0015			−0.638503			−0.319252	+	0.947670i	$0.603432\pi$
$710$	6.57023	+	0.266225i	0.246576	+	0.00999125i
$711$		0			0
$712$	−0.579688	−	0.0707767i	−0.0217247	−	0.00265247i
$713$			77.6986i			2.90983i
$714$		0			0
$715$			7.20435i			0.269427i
$716$	−36.1020	−	2.93051i	−1.34919	−	0.109518i
$717$		0			0
$718$	0.564962	−	13.9428i	0.0210842	−	0.520342i
$719$	−5.89884			−0.219990			−0.109995	−	0.993932i	$-0.535083\pi$
$719$	−5.89884			−0.219990			−0.109995	+	0.993932i	$0.535083\pi$
$720$		0			0
$721$	−10.9130			−0.406421
$722$	−1.13161	+	27.9272i	−0.0421141	+	1.03934i
$723$		0			0
$724$	−12.2901	−	0.997629i	−0.456760	−	0.0370766i
$725$		−	32.8339i		−	1.21942i
$726$		0			0
$727$		−	13.8081i		−	0.512112i	−0.966662	−	0.256056i	$-0.917577\pi$
$727$		−	13.8081i		−	0.512112i	0.966662	−	0.256056i	$-0.0824232\pi$
$728$	14.9713	+	1.82792i	0.554874	+	0.0677471i
$729$		0			0
$730$	4.44593	+	0.180149i	0.164551	+	0.00666760i
$731$	−8.97494			−0.331950
$732$		0			0
$733$	−27.4952			−1.01556			−0.507779	−	0.861488i	$-0.669533\pi$
$733$	−27.4952			−1.01556			−0.507779	+	0.861488i	$0.669533\pi$
$734$	−33.7162	−	1.36618i	−1.24449	−	0.0504265i
$735$		0			0
$736$	−9.33057	+	45.4480i	−0.343929	+	1.67523i
$737$			12.2255i			0.450332i
$738$		0			0
$739$			12.9652i			0.476931i	0.971151	+	0.238465i	$0.0766444\pi$
$739$			12.9652i			0.476931i	−0.971151	+	0.238465i	$0.923356\pi$
$740$	0.276147	−	3.40195i	0.0101514	−	0.125058i
$741$		0			0
$742$	0.110049	−	2.71593i	0.00404003	−	0.0997049i
$743$	−16.0988			−0.590608			−0.295304	−	0.955403i	$-0.595421\pi$
$743$	−16.0988			−0.590608			−0.295304	+	0.955403i	$0.595421\pi$
$744$		0			0
$745$	2.03979			0.0747323
$746$	−1.63000	+	40.2272i	−0.0596786	+	1.47282i
$747$		0			0
$748$	−2.59161	+	31.9269i	−0.0947586	+	1.16736i
$749$		−	2.37293i		−	0.0867049i
$750$		0			0
$751$			6.94450i			0.253409i	0.991941	+	0.126704i	$0.0404399\pi$
$751$			6.94450i			0.253409i	−0.991941	+	0.126704i	$0.959560\pi$
$752$	−3.93330	−	0.642792i	−0.143433	−	0.0234402i
$753$		0			0
$754$	−51.0039	−	2.06667i	−1.85745	−	0.0752638i
$755$	−5.81665			−0.211689
$756$		0			0
$757$	−16.5620			−0.601956			−0.300978	−	0.953631i	$-0.597313\pi$
$757$	−16.5620			−0.601956			−0.300978	+	0.953631i	$0.597313\pi$
$758$	15.5641	+	0.630657i	0.565315	+	0.0229065i
$759$		0			0
$760$	0.824602	−	6.75380i	0.0299115	−	0.244986i
$761$			20.2273i			0.733238i	0.930371	+	0.366619i	$0.119485\pi$
$761$			20.2273i			0.733238i	−0.930371	+	0.366619i	$0.880515\pi$
$762$		0			0
$763$			3.49012i			0.126351i
$764$	35.8485	+	2.90993i	1.29695	+	0.105278i
$765$		0			0
$766$	0.724961	−	17.8915i	0.0261939	−	0.646446i
$767$	30.8434			1.11369
$768$		0			0
$769$	24.2180			0.873322			0.436661	−	0.899626i	$-0.356161\pi$
$769$	24.2180			0.873322			0.436661	+	0.899626i	$0.356161\pi$
$770$	0.0773559	−	1.90908i	0.00278771	−	0.0687986i
$771$		0			0
$772$	−30.9930	−	2.51580i	−1.11546	−	0.0905455i
$773$		−	43.4363i		−	1.56230i	−0.624346	−	0.781148i	$-0.714635\pi$
$773$		−	43.4363i		−	1.56230i	0.624346	−	0.781148i	$-0.285365\pi$
$774$		0			0
$775$		−	45.9531i		−	1.65068i
$776$	3.08451	−	25.2633i	0.110728	−	0.906900i
$777$		0			0
$778$	30.3947	+	1.23159i	1.08970	+	0.0441546i
$779$	27.6337			0.990080
$780$		0			0
$781$	42.0805			1.50576
$782$	53.0828	+	2.15091i	1.89824	+	0.0769164i
$783$		0			0
$784$	−3.94763	−	0.645134i	−0.140987	−	0.0230405i
$785$		−	2.19661i		−	0.0784003i
$786$		0			0
$787$		−	42.0714i		−	1.49968i	−0.661617	−	0.749842i	$-0.730130\pi$
$787$		−	42.0714i		−	1.49968i	0.661617	−	0.749842i	$-0.269870\pi$
$788$	−2.46591	+	30.3784i	−0.0878443	+	1.08218i
$789$		0			0
$790$	−0.266849	+	6.58564i	−0.00949408	+	0.234307i
$791$	19.0081			0.675850
$792$		0			0
$793$	35.6714			1.26673
$794$	−0.0626459	+	1.54605i	−0.00222322	+	0.0548674i
$795$		0			0
$796$	−3.48643	+	42.9506i	−0.123573	+	1.52234i
$797$		−	39.4905i		−	1.39883i	−0.714718	−	0.699413i	$-0.753445\pi$
$797$		−	39.4905i		−	1.39883i	0.714718	−	0.699413i	$-0.246555\pi$
$798$		0			0
$799$			4.56364i			0.161450i
$800$	5.51836	−	26.8792i	0.195103	−	0.950323i
$801$		0			0
$802$	−4.20407	−	0.170348i	−0.148451	−	0.00601521i
$803$	28.4750			1.00486
$804$		0			0
$805$	−3.16890			−0.111689
$806$	−71.3832	−	2.89244i	−2.51436	−	0.101882i
$807$		0			0
$808$	−16.6953	−	2.03840i	−0.587338	−	0.0717108i
$809$		−	5.57369i		−	0.195960i	−0.995188	−	0.0979802i	$-0.968762\pi$
$809$		−	5.57369i		−	0.195960i	0.995188	−	0.0979802i	$-0.0312382\pi$
$810$		0			0
$811$			28.0725i			0.985757i	0.870098	+	0.492879i	$0.164055\pi$
$811$			28.0725i			0.985757i	−0.870098	+	0.492879i	$0.835945\pi$
$812$	13.4934	+	1.09530i	0.473524	+	0.0384374i
$813$		0			0
$814$	0.884323	−	21.8244i	0.0309955	−	0.764945i
$815$	−7.55495			−0.264638
$816$		0			0
$817$	12.1998			0.426818
$818$	−1.14165	+	28.1750i	−0.0399167	+	0.985115i
$819$		0			0
$820$	−3.41849	−	0.277489i	−0.119379	−	0.00969034i
$821$		−	55.1825i		−	1.92588i	−0.269709	−	0.962942i	$-0.586928\pi$
$821$		−	55.1825i		−	1.92588i	0.269709	−	0.962942i	$-0.413072\pi$
$822$		0			0
$823$		−	10.0505i		−	0.350340i	−0.984538	−	0.175170i	$-0.943953\pi$
$823$		−	10.0505i		−	0.350340i	0.984538	−	0.175170i	$-0.0560475\pi$
$824$	30.6390	+	3.74086i	1.06736	+	0.130319i
$825$		0			0
$826$	−8.17322	−	0.331178i	−0.284383	−	0.0115232i
$827$	1.70986			0.0594577			0.0297288	−	0.999558i	$-0.490536\pi$
$827$	1.70986			0.0594577			0.0297288	+	0.999558i	$0.490536\pi$
$828$		0			0
$829$	34.6507			1.20347			0.601734	−	0.798697i	$-0.294477\pi$
$829$	34.6507			1.20347			0.601734	+	0.798697i	$0.294477\pi$
$830$	−6.27551	−	0.254283i	−0.217826	−	0.00882629i
$831$		0			0
$832$	−41.4066	−	10.2640i	−1.43552	−	0.355842i
$833$			4.58027i			0.158697i
$834$		0			0
$835$		−	2.42609i		−	0.0839584i
$836$	3.52283	−	43.3990i	0.121840	−	1.50098i
$837$		0			0
$838$	−1.57483	+	38.8655i	−0.0544015	+	1.34259i
$839$	−28.4935			−0.983707			−0.491853	−	0.870678i	$-0.663680\pi$
$839$	−28.4935			−0.983707			−0.491853	+	0.870678i	$0.663680\pi$
$840$		0			0
$841$	−16.8176			−0.579917
$842$	0.768494	−	18.9658i	0.0264840	−	0.653606i
$843$		0			0
$844$	−1.63712	+	20.1682i	−0.0563519	+	0.694220i
$845$			5.96372i			0.205158i
$846$		0			0
$847$		−	1.22716i		−	0.0421656i
$848$	−1.23996	+	7.58746i	−0.0425806	+	0.260554i
$849$		0			0
$850$	−31.3946	−	1.27211i	−1.07683	−	0.0436329i
$851$	−36.2264			−1.24183
$852$		0			0
$853$	25.2012			0.862874			0.431437	−	0.902143i	$-0.358007\pi$
$853$	25.2012			0.862874			0.431437	+	0.902143i	$0.358007\pi$
$854$	−9.45257	−	0.383017i	−0.323460	−	0.0131066i
$855$		0			0
$856$	−0.813416	+	6.66218i	−0.0278020	+	0.227709i
$857$			40.0177i			1.36698i	0.729961	+	0.683489i	$0.239538\pi$
$857$			40.0177i			1.36698i	−0.729961	+	0.683489i	$0.760462\pi$
$858$		0			0
$859$		−	21.4904i		−	0.733242i	−0.930370	−	0.366621i	$-0.880515\pi$
$859$		−	21.4904i		−	0.733242i	0.930370	−	0.366621i	$-0.119485\pi$
$860$	−1.50921	−	0.122507i	−0.0514635	−	0.00417745i
$861$		0			0
$862$	0.310608	−	7.66558i	0.0105794	−	0.261091i
$863$	−34.6137			−1.17827			−0.589133	−	0.808036i	$-0.700530\pi$
$863$	−34.6137			−1.17827			−0.589133	+	0.808036i	$0.700530\pi$
$864$		0			0
$865$	2.36528			0.0804221
$866$	−1.96232	+	48.4286i	−0.0666825	+	1.64567i
$867$		0			0
$868$	18.8848	+	1.53294i	0.640992	+	0.0520313i
$869$			42.1792i			1.43083i
$870$		0			0
$871$			18.6437i			0.631718i
$872$	1.19638	−	9.79878i	0.0405145	−	0.331829i
$873$		0			0
$874$	−72.1566	−	2.92378i	−2.44073	−	0.0988982i
$875$	3.80602			0.128667
$876$		0			0
$877$	7.62230			0.257387			0.128693	−	0.991684i	$-0.458922\pi$
$877$	7.62230			0.257387			0.128693	+	0.991684i	$0.458922\pi$
$878$	5.48008	+	0.222052i	0.184944	+	0.00749390i
$879$		0			0
$880$	−0.871598	+	5.33339i	−0.0293816	+	0.179788i
$881$			32.5174i			1.09554i	0.836629	+	0.547769i	$0.184523\pi$
$881$			32.5174i			1.09554i	−0.836629	+	0.547769i	$0.815477\pi$
$882$		0			0
$883$			16.9931i			0.571864i	0.958250	+	0.285932i	$0.0923032\pi$
$883$			16.9931i			0.571864i	−0.958250	+	0.285932i	$0.907697\pi$
$884$	−3.95216	+	48.6881i	−0.132926	+	1.63756i
$885$		0			0
$886$	0.543334	−	13.4091i	0.0182536	−	0.450486i
$887$	12.9685			0.435439			0.217719	−	0.976011i	$-0.430138\pi$
$887$	12.9685			0.435439			0.217719	+	0.976011i	$0.430138\pi$
$888$		0			0
$889$	7.29024			0.244507
$890$	−0.00456765	+	0.112726i	−0.000153108	+	0.00377859i
$891$		0			0
$892$	0.777675	−	9.58045i	0.0260385	−	0.320777i
$893$		−	6.20345i		−	0.207591i
$894$		0			0
$895$			6.99730i			0.233894i
$896$	10.8621	+	3.16447i	0.362879	+	0.105718i
$897$		0			0
$898$	25.8112	+	1.04587i	0.861331	+	0.0349010i
$899$	−64.1246			−2.13867
$900$		0			0
$901$	8.80340			0.293284
$902$	−21.9305	−	0.888620i	−0.730205	−	0.0295878i
$903$		0			0
$904$	−53.3667	−	6.51579i	−1.77495	−	0.216712i
$905$			2.38208i			0.0791831i
$906$		0			0
$907$		−	17.6698i		−	0.586718i	−0.956002	−	0.293359i	$-0.905227\pi$
$907$		−	17.6698i		−	0.586718i	0.956002	−	0.293359i	$-0.0947731\pi$
$908$	5.24176	+	0.425490i	0.173954	+	0.0141204i
$909$		0			0
$910$	0.117967	−	2.91133i	0.00391056	−	0.0965095i
$911$	−30.2405			−1.00191			−0.500957	−	0.865472i	$-0.667018\pi$
$911$	−30.2405			−1.00191			−0.500957	+	0.865472i	$0.667018\pi$
$912$		0			0
$913$	−40.1929			−1.33019
$914$	−0.207510	+	5.12118i	−0.00686381	+	0.169394i
$915$		0			0
$916$	22.0507	+	1.78993i	0.728577	+	0.0591408i
$917$			13.1755i			0.435093i
$918$		0			0
$919$			17.1414i			0.565441i	0.959202	+	0.282721i	$0.0912370\pi$
$919$			17.1414i			0.565441i	−0.959202	+	0.282721i	$0.908763\pi$
$920$	8.89692	+	1.08627i	0.293323	+	0.0358131i
$921$		0			0
$922$	13.4687	+	0.545750i	0.443568	+	0.0179733i
$923$	64.1722			2.11225
$924$		0			0
$925$	21.4253			0.704460
$926$	59.2729	+	2.40173i	1.94783	+	0.0789258i
$927$		0			0
$928$	−37.5082	−	7.70052i	−1.23127	−	0.252782i
$929$		−	19.9342i		−	0.654021i	−0.945021	−	0.327011i	$-0.893959\pi$
$929$		−	19.9342i		−	0.654021i	0.945021	−	0.327011i	$-0.106041\pi$
$930$		0			0
$931$		−	6.22605i		−	0.204051i
$932$	3.36787	−	41.4901i	0.110318	−	1.35905i
$933$		0			0
$934$	−0.459456	+	11.3390i	−0.0150339	+	0.371024i
$935$	6.18810			0.202372
$936$		0			0
$937$	10.1107			0.330303			0.165152	−	0.986268i	$-0.447189\pi$
$937$	10.1107			0.330303			0.165152	+	0.986268i	$0.447189\pi$
$938$	0.200185	−	4.94041i	0.00653626	−	0.161310i
$939$		0			0
$940$	−0.0622931	+	0.767411i	−0.00203178	+	0.0250302i
$941$			40.1540i			1.30898i	0.756069	+	0.654492i	$0.227117\pi$
$941$			40.1540i			1.30898i	−0.756069	+	0.654492i	$0.772883\pi$
$942$		0			0
$943$			36.4025i			1.18543i
$944$	22.8334	+	3.73150i	0.743165	+	0.121450i
$945$		0			0
$946$	−9.68194	−	0.392311i	−0.314787	−	0.0127551i
$947$	28.7212			0.933312			0.466656	−	0.884439i	$-0.345459\pi$
$947$	28.7212			0.933312			0.466656	+	0.884439i	$0.345459\pi$
$948$		0			0
$949$	43.4239			1.40960
$950$	42.6754	+	1.72920i	1.38457	+	0.0561027i
$951$		0			0
$952$	1.57007	−	12.8595i	0.0508862	−	0.416777i
$953$			3.42678i			0.111004i	0.998459	+	0.0555022i	$0.0176760\pi$
$953$			3.42678i			0.111004i	−0.998459	+	0.0555022i	$0.982324\pi$
$954$		0			0
$955$		−	6.94818i		−	0.224838i
$956$	−52.6748	−	4.27578i	−1.70363	−	0.138288i
$957$		0			0
$958$	0.983156	−	24.2635i	0.0317643	−	0.783920i
$959$	5.32595			0.171984
$960$		0			0
$961$	−58.7464			−1.89504
$962$	1.34858	−	33.2819i	0.0434799	−	1.07305i
$963$		0			0
$964$	42.7202	+	3.46773i	1.37593	+	0.111688i
$965$			6.00708i			0.193375i
$966$		0			0
$967$		−	31.4049i		−	1.00991i	−0.863145	−	0.504956i	$-0.831509\pi$
$967$		−	31.4049i		−	1.00991i	0.863145	−	0.504956i	$-0.168491\pi$
$968$	−0.420657	+	3.44534i	−0.0135204	+	0.110737i
$969$		0			0
$970$	−4.91271	−	0.199062i	−0.157738	−	0.00639151i
$971$	20.9930			0.673696			0.336848	−	0.941559i	$-0.390639\pi$
$971$	20.9930			0.673696			0.336848	+	0.941559i	$0.390639\pi$
$972$		0			0
$973$	−8.71810			−0.279489
$974$	−44.6192	−	1.80797i	−1.42969	−	0.0579309i
$975$		0			0
$976$	26.4075	+	4.31560i	0.845284	+	0.138139i
$977$		−	1.40360i		−	0.0449052i	−0.999748	−	0.0224526i	$-0.992853\pi$
$977$		−	1.40360i		−	0.0449052i	0.999748	−	0.0224526i	$-0.00714748\pi$
$978$		0			0
$979$			0.721979i			0.0230746i
$980$	−0.0625201	+	0.770207i	−0.00199713	+	0.0246034i
$981$		0			0
$982$	−0.920586	+	22.7194i	−0.0293771	+	0.725004i
$983$	−8.34663			−0.266216			−0.133108	−	0.991102i	$-0.542496\pi$
$983$	−8.34663			−0.266216			−0.133108	+	0.991102i	$0.542496\pi$
$984$		0			0
$985$	5.88795			0.187606
$986$	−1.77515	+	43.8092i	−0.0565321	+	1.39517i
$987$		0			0
$988$	5.37226	−	66.1828i	0.170914	−	2.10556i
$989$			16.0711i			0.511031i
$990$		0			0
$991$		−	10.5476i		−	0.335056i	−0.985867	−	0.167528i	$-0.946421\pi$
$991$		−	10.5476i		−	0.335056i	0.985867	−	0.167528i	$-0.0535785\pi$
$992$	−52.4951	−	10.7774i	−1.66672	−	0.342182i
$993$		0			0
$994$	−17.0050	−	0.689041i	−0.539366	−	0.0218551i
$995$	8.32470			0.263911
$996$		0			0
$997$	1.14520			0.0362688			0.0181344	−	0.999836i	$-0.494227\pi$
$997$	1.14520			0.0362688			0.0181344	+	0.999836i	$0.494227\pi$
$998$	23.5126	+	0.952728i	0.744279	+	0.0301581i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.e.b.323.13	yes	24
3.2	odd	2	inner	756.2.e.b.323.12	yes	24
4.3	odd	2	inner	756.2.e.b.323.11	✓	24
12.11	even	2	inner	756.2.e.b.323.14	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.e.b.323.11	✓	24	4.3	odd	2	inner
756.2.e.b.323.12	yes	24	3.2	odd	2	inner
756.2.e.b.323.13	yes	24	1.1	even	1	trivial
756.2.e.b.323.14	yes	24	12.11	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.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0572568 - 1.41305i) q^{2} +(-1.99344 - 0.161814i) q^{4} +0.386370i q^{5} -1.00000i q^{7} +(-0.342790 + 2.80758i) q^{8} +O(q^{10})\)	\(q+(0.0572568 - 1.41305i) q^{2} +(-1.99344 - 0.161814i) q^{4} +0.386370i q^{5} -1.00000i q^{7} +(-0.342790 + 2.80758i) q^{8} +(0.545962 + 0.0221223i) q^{10} +3.49674 q^{11} +5.33247 q^{13} +(-1.41305 - 0.0572568i) q^{14} +(3.94763 + 0.645134i) q^{16} -4.58027i q^{17} +6.22605i q^{19} +(0.0625201 - 0.770207i) q^{20} +(0.200212 - 4.94108i) q^{22} -8.20171 q^{23} +4.85072 q^{25} +(0.305320 - 7.53507i) q^{26} +(-0.161814 + 1.99344i) q^{28} -6.76887i q^{29} -9.47346i q^{31} +(1.13764 - 5.54128i) q^{32} +(-6.47216 - 0.262251i) q^{34} +0.386370 q^{35} +4.41693 q^{37} +(8.79775 + 0.356484i) q^{38} +(-1.08476 - 0.132444i) q^{40} -4.43840i q^{41} -1.95948i q^{43} +(-6.97054 - 0.565820i) q^{44} +(-0.469604 + 11.5895i) q^{46} -0.996370 q^{47} -1.00000 q^{49} +(0.277737 - 6.85433i) q^{50} +(-10.6300 - 0.862868i) q^{52} +1.92203i q^{53} +1.35103i q^{55} +(2.80758 + 0.342790i) q^{56} +(-9.56478 - 0.387564i) q^{58} +5.78408 q^{59} +6.68946 q^{61} +(-13.3865 - 0.542420i) q^{62} +(-7.76499 - 1.92482i) q^{64} +2.06031i q^{65} +3.49626i q^{67} +(-0.741151 + 9.13050i) q^{68} +(0.0221223 - 0.545962i) q^{70} +12.0342 q^{71} +8.14330 q^{73} +(0.252899 - 6.24137i) q^{74} +(1.00746 - 12.4113i) q^{76} -3.49674i q^{77} +12.0625i q^{79} +(-0.249260 + 1.52525i) q^{80} +(-6.27170 - 0.254129i) q^{82} -11.4944 q^{83} +1.76968 q^{85} +(-2.76885 - 0.112194i) q^{86} +(-1.19865 + 9.81736i) q^{88} +0.206472i q^{89} -5.33247i q^{91} +(16.3496 + 1.32715i) q^{92} +(-0.0570490 + 1.40792i) q^{94} -2.40556 q^{95} -8.99826 q^{97} +(-0.0572568 + 1.41305i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4}+O(q^{10}) \) 24 * q + 4 * q^4	\( 24 q + 4 q^{4} + 20 q^{10} + 20 q^{16} - 8 q^{22} - 24 q^{25} - 8 q^{28} - 20 q^{34} + 16 q^{37} - 32 q^{40} + 36 q^{46} - 24 q^{49} + 16 q^{52} - 52 q^{58} + 16 q^{61} + 4 q^{64} + 12 q^{70} + 4 q^{82} - 64 q^{85} - 16 q^{88} + 12 q^{94}+O(q^{100}) \) 24 * q + 4 * q^4 + 20 * q^10 + 20 * q^16 - 8 * q^22 - 24 * q^25 - 8 * q^28 - 20 * q^34 + 16 * q^37 - 32 * q^40 + 36 * q^46 - 24 * q^49 + 16 * q^52 - 52 * q^58 + 16 * q^61 + 4 * q^64 + 12 * q^70 + 4 * q^82 - 64 * q^85 - 16 * q^88 + 12 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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