LMFDB - Embedded newform 1456.2.cc.g.673.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(225,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("1456.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, degree $2$, not 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:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 728)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.11
Character	$\chi$	$=$	1456.673
Dual form			1456.2.cc.g.225.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45593 + 2.52174i) q^{3} +2.05353i q^{5} +(0.866025 + 0.500000i) q^{7} +(-2.73946 + 4.74488i) q^{9} +O(q^{10})$	\(q+(1.45593 + 2.52174i) q^{3} +2.05353i q^{5} +(0.866025 + 0.500000i) q^{7} +(-2.73946 + 4.74488i) q^{9} +(-0.911380 + 0.526186i) q^{11} +(0.832370 + 3.50816i) q^{13} +(-5.17847 + 2.98979i) q^{15} +(-0.611487 + 1.05913i) q^{17} +(0.0846661 + 0.0488820i) q^{19} +2.91186i q^{21} +(-3.88980 - 6.73733i) q^{23} +0.783030 q^{25} -7.21826 q^{27} +(0.0464789 + 0.0805039i) q^{29} -2.58105i q^{31} +(-2.65381 - 1.53218i) q^{33} +(-1.02676 + 1.77841i) q^{35} +(-1.41414 + 0.816456i) q^{37} +(-7.63480 + 7.20665i) q^{39} +(8.09611 - 4.67429i) q^{41} +(-3.41649 + 5.91753i) q^{43} +(-9.74374 - 5.62555i) q^{45} -1.47170i q^{47} +(0.500000 + 0.866025i) q^{49} -3.56112 q^{51} +10.6510 q^{53} +(-1.08054 - 1.87154i) q^{55} +0.284675i q^{57} +(9.53268 + 5.50370i) q^{59} +(-2.61553 + 4.53023i) q^{61} +(-4.74488 + 2.73946i) q^{63} +(-7.20409 + 1.70929i) q^{65} +(0.125626 - 0.0725300i) q^{67} +(11.3265 - 19.6181i) q^{69} +(-11.4660 - 6.61991i) q^{71} +14.9359i q^{73} +(1.14004 + 1.97460i) q^{75} -1.05237 q^{77} -3.92240 q^{79} +(-2.29090 - 3.96795i) q^{81} -15.6099i q^{83} +(-2.17494 - 1.25570i) q^{85} +(-0.135340 + 0.234416i) q^{87} +(2.23266 - 1.28903i) q^{89} +(-1.03322 + 3.45434i) q^{91} +(6.50875 - 3.75783i) q^{93} +(-0.100380 + 0.173864i) q^{95} +(-10.2946 - 5.94361i) q^{97} -5.76586i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} - 18 q^{9}+O(q^{10}) $ 24 * q + 2 * q^3 - 18 * q^9	$ 24 q + 2 q^{3} - 18 q^{9} - 12 q^{11} + 8 q^{17} + 12 q^{19} - 2 q^{23} - 28 q^{25} + 20 q^{27} + 2 q^{29} - 18 q^{33} + 8 q^{35} + 60 q^{37} - 18 q^{39} - 6 q^{41} - 24 q^{43} - 72 q^{45} + 12 q^{49} + 72 q^{51} - 48 q^{53} + 44 q^{55} + 12 q^{59} - 30 q^{61} - 12 q^{63} + 10 q^{65} - 78 q^{67} + 36 q^{69} + 36 q^{71} - 22 q^{75} + 4 q^{77} - 20 q^{79} - 40 q^{81} - 6 q^{85} + 20 q^{87} + 108 q^{89} - 6 q^{91} + 30 q^{93} - 18 q^{95} - 54 q^{97}+O(q^{100}) $ 24 * q + 2 * q^3 - 18 * q^9 - 12 * q^11 + 8 * q^17 + 12 * q^19 - 2 * q^23 - 28 * q^25 + 20 * q^27 + 2 * q^29 - 18 * q^33 + 8 * q^35 + 60 * q^37 - 18 * q^39 - 6 * q^41 - 24 * q^43 - 72 * q^45 + 12 * q^49 + 72 * q^51 - 48 * q^53 + 44 * q^55 + 12 * q^59 - 30 * q^61 - 12 * q^63 + 10 * q^65 - 78 * q^67 + 36 * q^69 + 36 * q^71 - 22 * q^75 + 4 * q^77 - 20 * q^79 - 40 * q^81 - 6 * q^85 + 20 * q^87 + 108 * q^89 - 6 * q^91 + 30 * q^93 - 18 * q^95 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	1.45593	+	2.52174i	0.840581	+	1.45593i	0.889404	+	0.457122i	$0.151120\pi$
$3$	1.45593	+	2.52174i	0.840581	+	1.45593i	−0.0488231	+	0.998807i	$0.515547\pi$
$4$		0			0
$5$			2.05353i			0.918365i	0.888342	+	0.459182i	$0.151858\pi$
$5$			2.05353i			0.918365i	−0.888342	+	0.459182i	$0.848142\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		0			0
$9$	−2.73946	+	4.74488i	−0.913153	+	1.58163i
$10$		0			0
$11$	−0.911380	+	0.526186i	−0.274792	+	0.158651i	−0.631063	−	0.775731i	$-0.717381\pi$
$11$	−0.911380	+	0.526186i	−0.274792	+	0.158651i	0.356272	+	0.934382i	$0.384048\pi$
$12$		0			0
$13$	0.832370	+	3.50816i	0.230858	+	0.972987i
$13$	0.832370	+	3.50816i	0.230858	+	0.972987i
$14$		0			0
$15$	−5.17847	+	2.98979i	−1.33707	+	0.771960i
$16$		0			0
$17$	−0.611487	+	1.05913i	−0.148307	+	0.256876i	−0.930602	−	0.366033i	$-0.880716\pi$
$17$	−0.611487	+	1.05913i	−0.148307	+	0.256876i	0.782295	+	0.622909i	$0.214049\pi$
$18$		0			0
$19$	0.0846661	+	0.0488820i	0.0194237	+	0.0112143i	0.509680	−	0.860364i	$-0.329764\pi$
$19$	0.0846661	+	0.0488820i	0.0194237	+	0.0112143i	−0.490257	+	0.871578i	$0.663097\pi$
$20$		0			0
$21$			2.91186i			0.635420i
$22$		0			0
$23$	−3.88980	−	6.73733i	−0.811079	−	1.40483i	−0.912110	−	0.409946i	$-0.865547\pi$
$23$	−3.88980	−	6.73733i	−0.811079	−	1.40483i	0.101031	−	0.994883i	$-0.467786\pi$
$24$		0			0
$25$	0.783030			0.156606
$26$		0			0
$27$	−7.21826			−1.38915
$28$		0			0
$29$	0.0464789	+	0.0805039i	0.00863092	+	0.0149492i	0.870309	−	0.492507i	$-0.163919\pi$
$29$	0.0464789	+	0.0805039i	0.00863092	+	0.0149492i	−0.861678	+	0.507456i	$0.830586\pi$
$30$		0			0
$31$		−	2.58105i		−	0.463570i	−0.972767	−	0.231785i	$-0.925543\pi$
$31$		−	2.58105i		−	0.463570i	0.972767	−	0.231785i	$-0.0744567\pi$
$32$		0			0
$33$	−2.65381	−	1.53218i	−0.461969	−	0.266718i
$34$		0			0
$35$	−1.02676	+	1.77841i	−0.173555	+	0.300605i
$36$		0			0
$37$	−1.41414	+	0.816456i	−0.232484	+	0.134224i	−0.611717	−	0.791076i	$-0.709521\pi$
$37$	−1.41414	+	0.816456i	−0.232484	+	0.134224i	0.379234	+	0.925301i	$0.376188\pi$
$38$		0			0
$39$	−7.63480	+	7.20665i	−1.22255	+	1.15399i
$40$		0			0
$41$	8.09611	−	4.67429i	1.26440	−	0.730002i	0.290478	−	0.956882i	$-0.406186\pi$
$41$	8.09611	−	4.67429i	1.26440	−	0.730002i	0.973923	+	0.226880i	$0.0728524\pi$
$42$		0			0
$43$	−3.41649	+	5.91753i	−0.521010	+	0.902415i	0.478692	+	0.877983i	$0.341111\pi$
$43$	−3.41649	+	5.91753i	−0.521010	+	0.902415i	−0.999701	+	0.0244323i	$0.992222\pi$
$44$		0			0
$45$	−9.74374	−	5.62555i	−1.45251	−	0.838608i
$46$		0			0
$47$		−	1.47170i		−	0.214670i	−0.994223	−	0.107335i	$-0.965768\pi$
$47$		−	1.47170i		−	0.214670i	0.994223	−	0.107335i	$-0.0342318\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$	−3.56112			−0.498657
$52$		0			0
$53$	10.6510			1.46302			0.731512	−	0.681829i	$-0.238815\pi$
$53$	10.6510			1.46302			0.731512	+	0.681829i	$0.238815\pi$
$54$		0			0
$55$	−1.08054	−	1.87154i	−0.145699	−	0.252359i
$56$		0			0
$57$			0.284675i			0.0377061i
$58$		0			0
$59$	9.53268	+	5.50370i	1.24105	+	0.716520i	0.969308	−	0.245850i	$-0.0790670\pi$
$59$	9.53268	+	5.50370i	1.24105	+	0.716520i	0.271742	+	0.962370i	$0.412400\pi$
$60$		0			0
$61$	−2.61553	+	4.53023i	−0.334884	+	0.580037i	−0.983463	−	0.181111i	$-0.942031\pi$
$61$	−2.61553	+	4.53023i	−0.334884	+	0.580037i	0.648578	+	0.761148i	$0.275364\pi$
$62$		0			0
$63$	−4.74488	+	2.73946i	−0.597799	+	0.345139i
$64$		0			0
$65$	−7.20409	+	1.70929i	−0.893558	+	0.212012i
$66$		0			0
$67$	0.125626	−	0.0725300i	0.0153476	−	0.00886094i	−0.492307	−	0.870422i	$-0.663846\pi$
$67$	0.125626	−	0.0725300i	0.0153476	−	0.00886094i	0.507654	+	0.861561i	$0.330513\pi$
$68$		0			0
$69$	11.3265	−	19.6181i	1.36355	−	2.36175i
$70$		0			0
$71$	−11.4660	−	6.61991i	−1.36077	−	0.785639i	−0.371040	−	0.928617i	$-0.620999\pi$
$71$	−11.4660	−	6.61991i	−1.36077	−	0.785639i	−0.989726	+	0.142978i	$0.954332\pi$
$72$		0			0
$73$			14.9359i			1.74811i	0.485826	+	0.874056i	$0.338519\pi$
$73$			14.9359i			1.74811i	−0.485826	+	0.874056i	$0.661481\pi$
$74$		0			0
$75$	1.14004	+	1.97460i	0.131640	+	0.228007i
$76$		0			0
$77$	−1.05237			−0.119929
$78$		0			0
$79$	−3.92240			−0.441304			−0.220652	−	0.975353i	$-0.570819\pi$
$79$	−3.92240			−0.441304			−0.220652	+	0.975353i	$0.570819\pi$
$80$		0			0
$81$	−2.29090	−	3.96795i	−0.254544	−	0.440883i
$82$		0			0
$83$		−	15.6099i		−	1.71341i	−0.515808	−	0.856704i	$-0.672508\pi$
$83$		−	15.6099i		−	1.71341i	0.515808	−	0.856704i	$-0.327492\pi$
$84$		0			0
$85$	−2.17494	−	1.25570i	−0.235906	−	0.136200i
$86$		0			0
$87$	−0.135340	+	0.234416i	−0.0145100	+	0.0251320i
$88$		0			0
$89$	2.23266	−	1.28903i	0.236662	−	0.136637i	−0.376980	−	0.926222i	$-0.623037\pi$
$89$	2.23266	−	1.28903i	0.236662	−	0.136637i	0.613642	+	0.789585i	$0.289704\pi$
$90$		0			0
$91$	−1.03322	+	3.45434i	−0.108311	+	0.362113i
$92$		0			0
$93$	6.50875	−	3.75783i	0.674926	−	0.389669i
$94$		0			0
$95$	−0.100380	+	0.173864i	−0.0102988	+	0.0178381i
$96$		0			0
$97$	−10.2946	−	5.94361i	−1.04526	−	0.603482i	−0.123942	−	0.992289i	$-0.539554\pi$
$97$	−10.2946	−	5.94361i	−1.04526	−	0.603482i	−0.921319	+	0.388808i	$0.872887\pi$
$98$		0			0
$99$		−	5.76586i		−	0.579490i
$100$		0			0
$101$	−3.37173	−	5.84001i	−0.335500	−	0.581103i	0.648081	−	0.761572i	$-0.275572\pi$
$101$	−3.37173	−	5.84001i	−0.335500	−	0.581103i	−0.983581	+	0.180469i	$0.942239\pi$
$102$		0			0
$103$	12.5382			1.23542			0.617711	−	0.786405i	$-0.288060\pi$
$103$	12.5382			1.23542			0.617711	+	0.786405i	$0.288060\pi$
$104$		0			0
$105$	−5.97958			−0.583547
$106$		0			0
$107$	3.86830	+	6.70010i	0.373963	+	0.647723i	0.990171	−	0.139860i	$-0.0446654\pi$
$107$	3.86830	+	6.70010i	0.373963	+	0.647723i	−0.616208	+	0.787583i	$0.711332\pi$
$108$		0			0
$109$		−	3.78598i		−	0.362631i	−0.983425	−	0.181315i	$-0.941965\pi$
$109$		−	3.78598i		−	0.362631i	0.983425	−	0.181315i	$-0.0580355\pi$
$110$		0			0
$111$	−4.11778	−	2.37740i	−0.390843	−	0.225653i
$112$		0			0
$113$	−4.35346	+	7.54042i	−0.409539	+	0.709343i	−0.994838	−	0.101475i	$-0.967644\pi$
$113$	−4.35346	+	7.54042i	−0.409539	+	0.709343i	0.585299	+	0.810818i	$0.300977\pi$
$114$		0			0
$115$	13.8353	−	7.98780i	1.29015	−	0.744866i
$116$		0			0
$117$	−18.9260	−	5.66095i	−1.74971	−	0.523355i
$118$		0			0
$119$	−1.05913	+	0.611487i	−0.0970899	+	0.0560549i
$120$		0			0
$121$	−4.94626	+	8.56717i	−0.449660	+	0.778834i
$122$		0			0
$123$	23.5747	+	13.6109i	2.12566	+	1.22725i
$124$		0			0
$125$			11.8756i			1.06219i
$126$		0			0
$127$	−7.75910	−	13.4391i	−0.688508	−	1.19253i	−0.972320	−	0.233652i	$-0.924932\pi$
$127$	−7.75910	−	13.4391i	−0.688508	−	1.19253i	0.283812	−	0.958880i	$-0.408401\pi$
$128$		0			0
$129$	−19.8967			−1.75180
$130$		0			0
$131$	−2.28800			−0.199903			−0.0999516	−	0.994992i	$-0.531869\pi$
$131$	−2.28800			−0.199903			−0.0999516	+	0.994992i	$0.531869\pi$
$132$		0			0
$133$	0.0488820	+	0.0846661i	0.00423861	+	0.00734148i
$134$		0			0
$135$		−	14.8229i		−	1.27575i
$136$		0			0
$137$	13.5513	+	7.82386i	1.15777	+	0.668437i	0.950768	−	0.309904i	$-0.100297\pi$
$137$	13.5513	+	7.82386i	1.15777	+	0.668437i	0.206999	+	0.978341i	$0.433630\pi$
$138$		0			0
$139$	−1.61477	+	2.79686i	−0.136963	+	0.237226i	−0.926345	−	0.376675i	$-0.877067\pi$
$139$	−1.61477	+	2.79686i	−0.136963	+	0.237226i	0.789383	+	0.613901i	$0.210401\pi$
$140$		0			0
$141$	3.71126	−	2.14270i	0.312545	−	0.180448i
$142$		0			0
$143$	−2.60455	−	2.75928i	−0.217803	−	0.230743i
$144$		0			0
$145$	−0.165317	+	0.0954457i	−0.0137288	+	0.00792634i
$146$		0			0
$147$	−1.45593	+	2.52174i	−0.120083	+	0.207990i
$148$		0			0
$149$	7.39382	+	4.26882i	0.605725	+	0.349716i	0.771291	−	0.636483i	$-0.219612\pi$
$149$	7.39382	+	4.26882i	0.605725	+	0.349716i	−0.165565	+	0.986199i	$0.552945\pi$
$150$		0			0
$151$		−	22.5331i		−	1.83372i	−0.399210	−	0.916859i	$-0.630716\pi$
$151$		−	22.5331i		−	1.83372i	0.399210	−	0.916859i	$-0.369284\pi$
$152$		0			0
$153$	−3.35029	−	5.80286i	−0.270855	−	0.469134i
$154$		0			0
$155$	5.30026			0.425727
$156$		0			0
$157$	−20.9363			−1.67090			−0.835451	−	0.549565i	$-0.814794\pi$
$157$	−20.9363			−1.67090			−0.835451	+	0.549565i	$0.814794\pi$
$158$		0			0
$159$	15.5071	+	26.8590i	1.22979	+	2.13006i
$160$		0			0
$161$		−	7.77959i		−	0.613118i
$162$		0			0
$163$	2.45781	+	1.41902i	0.192511	+	0.111146i	0.593157	−	0.805087i	$-0.297881\pi$
$163$	2.45781	+	1.41902i	0.192511	+	0.111146i	−0.400647	+	0.916233i	$0.631215\pi$
$164$		0			0
$165$	3.14637	−	5.44967i	0.244944	−	0.424256i
$166$		0			0
$167$	18.2239	−	10.5216i	1.41020	−	0.814182i	0.414798	−	0.909914i	$-0.363852\pi$
$167$	18.2239	−	10.5216i	1.41020	−	0.814182i	0.995407	+	0.0957317i	$0.0305191\pi$
$168$		0			0
$169$	−11.6143	+	5.84017i	−0.893409	+	0.449244i
$170$		0			0
$171$	−0.463879	+	0.267820i	−0.0354737	+	0.0204807i
$172$		0			0
$173$	10.6492	−	18.4450i	0.809646	−	1.40235i	−0.103463	−	0.994633i	$-0.532992\pi$
$173$	10.6492	−	18.4450i	0.809646	−	1.40235i	0.913109	−	0.407715i	$-0.133674\pi$
$174$		0			0
$175$	0.678124	+	0.391515i	0.0512613	+	0.0295958i
$176$		0			0
$177$			32.0520i			2.40917i
$178$		0			0
$179$	5.48794	+	9.50539i	0.410188	+	0.710466i	0.994910	−	0.100767i	$-0.0321297\pi$
$179$	5.48794	+	9.50539i	0.410188	+	0.710466i	−0.584722	+	0.811234i	$0.698796\pi$
$180$		0			0
$181$	16.7011			1.24139			0.620693	−	0.784054i	$-0.286851\pi$
$181$	16.7011			1.24139			0.620693	+	0.784054i	$0.286851\pi$
$182$		0			0
$183$	−15.2321			−1.12599
$184$		0			0
$185$	−1.67661	−	2.90398i	−0.123267	−	0.213505i
$186$		0			0
$187$		−	1.28702i		−	0.0941164i
$188$		0			0
$189$	−6.25120	−	3.60913i	−0.454708	−	0.262526i
$190$		0			0
$191$	−8.79820	+	15.2389i	−0.636615	+	1.10265i	0.349555	+	0.936916i	$0.386333\pi$
$191$	−8.79820	+	15.2389i	−0.636615	+	1.10265i	−0.986170	+	0.165734i	$0.947001\pi$
$192$		0			0
$193$	−5.46949	+	3.15781i	−0.393703	+	0.227304i	−0.683763	−	0.729704i	$-0.739658\pi$
$193$	−5.46949	+	3.15781i	−0.393703	+	0.227304i	0.290060	+	0.957008i	$0.406325\pi$
$194$		0			0
$195$	−14.7990	−	15.6783i	−1.05978	−	1.12274i
$196$		0			0
$197$	2.72730	−	1.57461i	0.194312	−	0.112186i	−0.399687	−	0.916651i	$-0.630881\pi$
$197$	2.72730	−	1.57461i	0.194312	−	0.112186i	0.594000	+	0.804465i	$0.297548\pi$
$198$		0			0
$199$	−8.94865	+	15.4995i	−0.634353	+	1.09873i	0.352299	+	0.935887i	$0.385400\pi$
$199$	−8.94865	+	15.4995i	−0.634353	+	1.09873i	−0.986652	+	0.162844i	$0.947933\pi$
$200$		0			0
$201$	0.365804	+	0.211197i	0.0258018	+	0.0148967i
$202$		0			0
$203$			0.0929579i			0.00652436i
$204$		0			0
$205$	9.59878	+	16.6256i	0.670408	+	1.16118i
$206$		0			0
$207$	42.6238			2.96256
$208$		0			0
$209$	−0.102884			−0.00711664
$210$		0			0
$211$	12.1087	+	20.9729i	0.833596	+	1.44383i	0.895168	+	0.445729i	$0.147055\pi$
$211$	12.1087	+	20.9729i	0.833596	+	1.44383i	−0.0615718	+	0.998103i	$0.519611\pi$
$212$		0			0
$213$		−	38.5525i		−	2.64157i
$214$		0			0
$215$	−12.1518	−	7.01585i	−0.828747	−	0.478477i
$216$		0			0
$217$	1.29053	−	2.23526i	0.0876066	−	0.151739i
$218$		0			0
$219$	−37.6644	+	21.7456i	−2.54513	+	1.46943i
$220$		0			0
$221$	−4.22456	−	1.26361i	−0.284175	−	0.0849993i
$222$		0			0
$223$	12.8730	−	7.43226i	0.862043	−	0.497701i	−0.00265287	−	0.999996i	$-0.500844\pi$
$223$	12.8730	−	7.43226i	0.862043	−	0.497701i	0.864696	+	0.502296i	$0.167511\pi$
$224$		0			0
$225$	−2.14508	+	3.71539i	−0.143005	+	0.247692i
$226$		0			0
$227$	7.98601	+	4.61073i	0.530050	+	0.306025i	0.741037	−	0.671464i	$-0.234334\pi$
$227$	7.98601	+	4.61073i	0.530050	+	0.306025i	−0.210987	+	0.977489i	$0.567668\pi$
$228$		0			0
$229$		−	3.93967i		−	0.260341i	−0.991492	−	0.130170i	$-0.958448\pi$
$229$		−	3.93967i		−	0.260341i	0.991492	−	0.130170i	$-0.0415524\pi$
$230$		0			0
$231$	−1.53218	−	2.65381i	−0.100810	−	0.174608i
$232$		0			0
$233$	11.1894			0.733043			0.366521	−	0.930410i	$-0.380549\pi$
$233$	11.1894			0.733043			0.366521	+	0.930410i	$0.380549\pi$
$234$		0			0
$235$	3.02218			0.197146
$236$		0			0
$237$	−5.71073	−	9.89128i	−0.370952	−	0.642508i
$238$		0			0
$239$			16.7694i			1.08472i	0.840146	+	0.542360i	$0.182469\pi$
$239$			16.7694i			1.08472i	−0.840146	+	0.542360i	$0.817531\pi$
$240$		0			0
$241$	17.4032	+	10.0478i	1.12104	+	0.647233i	0.941666	−	0.336548i	$-0.109259\pi$
$241$	17.4032	+	10.0478i	1.12104	+	0.647233i	0.179375	+	0.983781i	$0.442593\pi$
$242$		0			0
$243$	−4.15662	+	7.19948i	−0.266648	+	0.461847i
$244$		0			0
$245$	−1.77841	+	1.02676i	−0.113618	+	0.0655975i
$246$		0			0
$247$	−0.101012	+	0.337710i	−0.00642725	+	0.0214880i
$248$		0			0
$249$	39.3641	−	22.7269i	2.49460	−	1.44026i
$250$		0			0
$251$	−4.44877	+	7.70550i	−0.280804	+	0.486367i	−0.971583	−	0.236699i	$-0.923934\pi$
$251$	−4.44877	+	7.70550i	−0.280804	+	0.486367i	0.690779	+	0.723066i	$0.257268\pi$
$252$		0			0
$253$	7.09017	+	4.09351i	0.445755	+	0.257357i
$254$		0			0
$255$		−	7.31286i		−	0.457949i
$256$		0			0
$257$	2.34561	+	4.06271i	0.146315	+	0.253425i	0.929863	−	0.367907i	$-0.119925\pi$
$257$	2.34561	+	4.06271i	0.146315	+	0.253425i	−0.783548	+	0.621331i	$0.786592\pi$
$258$		0			0
$259$	−1.63291			−0.101464
$260$		0			0
$261$	−0.509309			−0.0315254
$262$		0			0
$263$	11.6560	+	20.1888i	0.718741	+	1.24490i	0.961499	+	0.274809i	$0.0886147\pi$
$263$	11.6560	+	20.1888i	0.718741	+	1.24490i	−0.242757	+	0.970087i	$0.578052\pi$
$264$		0			0
$265$			21.8720i			1.34359i
$266$		0			0
$267$	6.50120	+	3.75347i	0.397867	+	0.229709i
$268$		0			0
$269$	5.90163	−	10.2219i	0.359829	−	0.623241i	−0.628103	−	0.778130i	$-0.716169\pi$
$269$	5.90163	−	10.2219i	0.359829	−	0.623241i	0.987932	+	0.154889i	$0.0495018\pi$
$270$		0			0
$271$	−10.9155	+	6.30207i	−0.663069	+	0.382823i	−0.793445	−	0.608641i	$-0.791715\pi$
$271$	−10.9155	+	6.30207i	−0.663069	+	0.382823i	0.130376	+	0.991465i	$0.458381\pi$
$272$		0			0
$273$	−10.2153	+	2.42374i	−0.618255	+	0.146692i
$274$		0			0
$275$	−0.713638	+	0.412019i	−0.0430340	+	0.0248457i
$276$		0			0
$277$	−13.3380	+	23.1022i	−0.801405	+	1.38807i	0.117287	+	0.993098i	$0.462580\pi$
$277$	−13.3380	+	23.1022i	−0.801405	+	1.38807i	−0.918692	+	0.394976i	$0.870753\pi$
$278$		0			0
$279$	12.2468	+	7.07068i	0.733196	+	0.423311i
$280$		0			0
$281$		−	22.5796i		−	1.34699i	−0.739193	−	0.673493i	$-0.764793\pi$
$281$		−	22.5796i		−	1.34699i	0.739193	−	0.673493i	$-0.235207\pi$
$282$		0			0
$283$	−4.55376	−	7.88734i	−0.270693	−	0.468853i	0.698347	−	0.715760i	$-0.253919\pi$
$283$	−4.55376	−	7.88734i	−0.270693	−	0.468853i	−0.969039	+	0.246906i	$0.920586\pi$
$284$		0			0
$285$	−0.584587			−0.0346280
$286$		0			0
$287$	9.34859			0.551830
$288$		0			0
$289$	7.75217	+	13.4271i	0.456010	+	0.789832i
$290$		0			0
$291$		−	34.6139i		−	2.02910i
$292$		0			0
$293$	4.68448	+	2.70459i	0.273670	+	0.158004i	0.630554	−	0.776145i	$-0.282828\pi$
$293$	4.68448	+	2.70459i	0.273670	+	0.158004i	−0.356884	+	0.934149i	$0.616161\pi$
$294$		0			0
$295$	−11.3020	+	19.5756i	−0.658027	+	1.13974i
$296$		0			0
$297$	6.57858	−	3.79814i	0.381728	−	0.220391i
$298$		0			0
$299$	20.3978	−	19.2540i	1.17964	−	1.11349i
$300$		0			0
$301$	−5.91753	+	3.41649i	−0.341081	+	0.196923i
$302$		0			0
$303$	9.81800	−	17.0053i	0.564030	−	0.976928i
$304$		0			0
$305$	−9.30295	−	5.37106i	−0.532685	−	0.307546i
$306$		0			0
$307$		−	24.1603i		−	1.37890i	−0.724333	−	0.689450i	$-0.757852\pi$
$307$		−	24.1603i		−	1.37890i	0.724333	−	0.689450i	$-0.242148\pi$
$308$		0			0
$309$	18.2547	+	31.6180i	1.03847	+	1.79869i
$310$		0			0
$311$	−19.4000			−1.10007			−0.550036	−	0.835141i	$-0.685386\pi$
$311$	−19.4000			−1.10007			−0.550036	+	0.835141i	$0.685386\pi$
$312$		0			0
$313$	14.3761			0.812587			0.406294	−	0.913743i	$-0.366821\pi$
$313$	14.3761			0.812587			0.406294	+	0.913743i	$0.366821\pi$
$314$		0			0
$315$	−5.62555	−	9.74374i	−0.316964	−	0.548998i
$316$		0			0
$317$		−	20.8516i		−	1.17115i	−0.810620	−	0.585573i	$-0.800870\pi$
$317$		−	20.8516i		−	1.17115i	0.810620	−	0.585573i	$-0.199130\pi$
$318$		0			0
$319$	−0.0847200	−	0.0489131i	−0.00474341	−	0.00273861i
$320$		0			0
$321$	−11.2639	+	19.5097i	−0.628692	+	1.08893i
$322$		0			0
$323$	−0.103544	+	0.0597814i	−0.00576136	+	0.00332632i
$324$		0			0
$325$	0.651771	+	2.74699i	0.0361537	+	0.152376i
$326$		0			0
$327$	9.54726	−	5.51211i	0.527965	−	0.304821i
$328$		0			0
$329$	0.735852	−	1.27453i	0.0405688	−	0.0702673i
$330$		0			0
$331$	5.75943	+	3.32521i	0.316567	+	0.182770i	0.649861	−	0.760053i	$-0.274827\pi$
$331$	5.75943	+	3.32521i	0.316567	+	0.182770i	−0.333294	+	0.942823i	$0.608160\pi$
$332$		0			0
$333$		−	8.94659i		−	0.490270i
$334$		0			0
$335$	0.148942	+	0.257975i	0.00813758	+	0.0140947i
$336$		0			0
$337$	−7.26103			−0.395533			−0.197767	−	0.980249i	$-0.563369\pi$
$337$	−7.26103			−0.395533			−0.197767	+	0.980249i	$0.563369\pi$
$338$		0			0
$339$	−25.3533			−1.37700
$340$		0			0
$341$	1.35811	+	2.35232i	0.0735459	+	0.127385i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$	40.2864	+	23.2593i	2.16894	+	1.25224i
$346$		0			0
$347$	10.7842	−	18.6787i	0.578924	−	1.00273i	−0.416679	−	0.909054i	$-0.636806\pi$
$347$	10.7842	−	18.6787i	0.578924	−	1.00273i	0.995603	−	0.0936719i	$-0.0298605\pi$
$348$		0			0
$349$	−24.2212	+	13.9841i	−1.29653	+	0.748552i	−0.979803	−	0.199965i	$-0.935917\pi$
$349$	−24.2212	+	13.9841i	−1.29653	+	0.748552i	−0.316727	+	0.948517i	$0.602584\pi$
$350$		0			0
$351$	−6.00826	−	25.3228i	−0.320697	−	1.35163i
$352$		0			0
$353$	3.45777	−	1.99635i	0.184039	−	0.106255i	−0.405150	−	0.914250i	$-0.632781\pi$
$353$	3.45777	−	1.99635i	0.184039	−	0.106255i	0.589189	+	0.807995i	$0.299447\pi$
$354$		0			0
$355$	13.5942	−	23.5458i	0.721503	−	1.24968i
$356$		0			0
$357$	−3.08402	−	1.78056i	−0.163224	−	0.0942374i
$358$		0			0
$359$			5.73178i			0.302512i	0.988495	+	0.151256i	$0.0483317\pi$
$359$			5.73178i			0.302512i	−0.988495	+	0.151256i	$0.951668\pi$
$360$		0			0
$361$	−9.49522	−	16.4462i	−0.499748	−	0.865590i
$362$		0			0
$363$	−28.8056			−1.51190
$364$		0			0
$365$	−30.6712			−1.60540
$366$		0			0
$367$	7.22834	+	12.5199i	0.377316	+	0.653531i	0.990671	−	0.136277i	$-0.0435136\pi$
$367$	7.22834	+	12.5199i	0.377316	+	0.653531i	−0.613354	+	0.789808i	$0.710180\pi$
$368$		0			0
$369$			51.2201i			2.66641i
$370$		0			0
$371$	9.22401	+	5.32549i	0.478887	+	0.276485i
$372$		0			0
$373$	6.70139	−	11.6071i	0.346985	−	0.600995i	−0.638727	−	0.769433i	$-0.720539\pi$
$373$	6.70139	−	11.6071i	0.346985	−	0.600995i	0.985712	+	0.168438i	$0.0538722\pi$
$374$		0			0
$375$	−29.9472	+	17.2900i	−1.54647	+	0.892854i
$376$		0			0
$377$	−0.243733	+	0.230064i	−0.0125529	+	0.0118489i
$378$		0			0
$379$	12.8824	−	7.43766i	0.661725	−	0.382047i	−0.131209	−	0.991355i	$-0.541886\pi$
$379$	12.8824	−	7.43766i	0.661725	−	0.382047i	0.792934	+	0.609308i	$0.208553\pi$
$380$		0			0
$381$	22.5934	−	39.1329i	1.15749	−	2.00484i
$382$		0			0
$383$	1.32428	+	0.764575i	0.0676677	+	0.0390679i	0.533452	−	0.845830i	$-0.320894\pi$
$383$	1.32428	+	0.764575i	0.0676677	+	0.0390679i	−0.465784	+	0.884898i	$0.654228\pi$
$384$		0			0
$385$		−	2.16107i		−	0.110138i
$386$		0			0
$387$	−18.7187	−	32.4217i	−0.951523	−	1.64809i
$388$		0			0
$389$	12.3489			0.626113			0.313057	−	0.949734i	$-0.398647\pi$
$389$	12.3489			0.626113			0.313057	+	0.949734i	$0.398647\pi$
$390$		0			0
$391$	9.51423			0.481156
$392$		0			0
$393$	−3.33116	−	5.76974i	−0.168035	−	0.291045i
$394$		0			0
$395$		−	8.05475i		−	0.405278i
$396$		0			0
$397$	−22.8725	−	13.2055i	−1.14794	−	0.662763i	−0.199556	−	0.979887i	$-0.563950\pi$
$397$	−22.8725	−	13.2055i	−1.14794	−	0.662763i	−0.948384	+	0.317123i	$0.897283\pi$
$398$		0			0
$399$	−0.142337	+	0.246536i	−0.00712578	+	0.0123422i
$400$		0			0
$401$	25.3714	−	14.6482i	1.26699	−	0.731495i	0.292569	−	0.956244i	$-0.405490\pi$
$401$	25.3714	−	14.6482i	1.26699	−	0.731495i	0.974416	+	0.224750i	$0.0721565\pi$
$402$		0			0
$403$	9.05473	−	2.14839i	0.451048	−	0.107019i
$404$		0			0
$405$	8.14829	−	4.70441i	0.404892	−	0.233764i
$406$		0			0
$407$	0.859214	−	1.48820i	0.0425897	−	0.0737675i
$408$		0			0
$409$	26.4780	+	15.2871i	1.30925	+	0.755898i	0.981972	−	0.189028i	$-0.0605338\pi$
$409$	26.4780	+	15.2871i	1.30925	+	0.755898i	0.327282	+	0.944927i	$0.393867\pi$
$410$		0			0
$411$			45.5639i			2.24750i
$412$		0			0
$413$	5.50370	+	9.53268i	0.270819	+	0.469073i
$414$		0			0
$415$	32.0553			1.57353
$416$		0			0
$417$	−9.40393			−0.460513
$418$		0			0
$419$	−2.04590	−	3.54360i	−0.0999487	−	0.173116i	0.811714	−	0.584054i	$-0.198535\pi$
$419$	−2.04590	−	3.54360i	−0.0999487	−	0.173116i	−0.911663	+	0.410938i	$0.865201\pi$
$420$		0			0
$421$		−	20.5931i		−	1.00365i	−0.864970	−	0.501823i	$-0.832663\pi$
$421$		−	20.5931i		−	1.00365i	0.864970	−	0.501823i	$-0.167337\pi$
$422$		0			0
$423$	6.98307	+	4.03167i	0.339528	+	0.196027i
$424$		0			0
$425$	−0.478812	+	0.829327i	−0.0232258	+	0.0402283i
$426$		0			0
$427$	−4.53023	+	2.61553i	−0.219233	+	0.126574i
$428$		0			0
$429$	3.16617	−	10.5853i	0.152864	−	0.511064i
$430$		0			0
$431$	19.8535	−	11.4624i	0.956309	−	0.552125i	0.0612740	−	0.998121i	$-0.480484\pi$
$431$	19.8535	−	11.4624i	0.956309	−	0.552125i	0.895035	+	0.445996i	$0.147150\pi$
$432$		0			0
$433$	18.6966	−	32.3834i	0.898499	−	1.55625i	0.0690855	−	0.997611i	$-0.477992\pi$
$433$	18.6966	−	32.3834i	0.898499	−	1.55625i	0.829413	−	0.558635i	$-0.188675\pi$
$434$		0			0
$435$	−0.481379	−	0.277924i	−0.0230804	−	0.0133255i
$436$		0			0
$437$		−	0.760564i		−	0.0363827i
$438$		0			0
$439$	13.5311	+	23.4365i	0.645802	+	1.11856i	0.984116	+	0.177529i	$0.0568103\pi$
$439$	13.5311	+	23.4365i	0.645802	+	1.11856i	−0.338313	+	0.941034i	$0.609856\pi$
$440$		0			0
$441$	−5.47892			−0.260901
$442$		0			0
$443$	4.22311			0.200646			0.100323	−	0.994955i	$-0.468012\pi$
$443$	4.22311			0.200646			0.100323	+	0.994955i	$0.468012\pi$
$444$		0			0
$445$	2.64706	+	4.58483i	0.125482	+	0.217342i
$446$		0			0
$447$			24.8604i			1.17586i
$448$		0			0
$449$	−13.8726	−	8.00933i	−0.654687	−	0.377984i	0.135562	−	0.990769i	$-0.456716\pi$
$449$	−13.8726	−	8.00933i	−0.654687	−	0.377984i	−0.790250	+	0.612785i	$0.790049\pi$
$450$		0			0
$451$	−4.91909	+	8.52012i	−0.231631	+	0.401197i
$452$		0			0
$453$	56.8227	−	32.8066i	2.66976	−	1.54139i
$454$		0			0
$455$	−7.09357	−	2.12175i	−0.332552	−	0.0994694i
$456$		0			0
$457$	12.8417	−	7.41414i	0.600708	−	0.346819i	−0.168612	−	0.985683i	$-0.553928\pi$
$457$	12.8417	−	7.41414i	0.600708	−	0.346819i	0.769320	+	0.638864i	$0.220595\pi$
$458$		0			0
$459$	4.41387	−	7.64505i	0.206022	−	0.356840i
$460$		0			0
$461$	−0.270392	−	0.156111i	−0.0125934	−	0.00727082i	0.493690	−	0.869638i	$-0.335648\pi$
$461$	−0.270392	−	0.156111i	−0.0125934	−	0.00727082i	−0.506284	+	0.862367i	$0.668981\pi$
$462$		0			0
$463$		−	27.3468i		−	1.27091i	−0.772137	−	0.635457i	$-0.780812\pi$
$463$		−	27.3468i		−	1.27091i	0.772137	−	0.635457i	$-0.219188\pi$
$464$		0			0
$465$	7.71680	+	13.3659i	0.357858	+	0.619828i
$466$		0			0
$467$	−30.8629			−1.42816			−0.714082	−	0.700062i	$-0.753156\pi$
$467$	−30.8629			−1.42816			−0.714082	+	0.700062i	$0.753156\pi$
$468$		0			0
$469$	0.145060			0.00669824
$470$		0			0
$471$	−30.4818	−	52.7961i	−1.40453	−	2.43272i
$472$		0			0
$473$		−	7.19083i		−	0.330635i
$474$		0			0
$475$	0.0662961	+	0.0382761i	0.00304187	+	0.00175623i
$476$		0			0
$477$	−29.1779	+	50.5376i	−1.33596	+	2.31396i
$478$		0			0
$479$	−12.1245	+	7.00007i	−0.553981	+	0.319841i	−0.750726	−	0.660613i	$-0.770296\pi$
$479$	−12.1245	+	7.00007i	−0.553981	+	0.319841i	0.196745	+	0.980455i	$0.436963\pi$
$480$		0			0
$481$	−4.04134	−	4.28144i	−0.184269	−	0.195217i
$482$		0			0
$483$	19.6181	−	11.3265i	0.892656	−	0.515375i
$484$		0			0
$485$	12.2054	−	21.1403i	0.554216	−	0.959931i
$486$		0			0
$487$	25.5444	+	14.7481i	1.15753	+	0.668299i	0.950710	−	0.310081i	$-0.100356\pi$
$487$	25.5444	+	14.7481i	1.15753	+	0.668299i	0.206817	+	0.978380i	$0.433690\pi$
$488$		0			0
$489$			8.26396i			0.373709i
$490$		0			0
$491$	−18.3776	−	31.8310i	−0.829370	−	1.43651i	−0.898533	−	0.438906i	$-0.855366\pi$
$491$	−18.3776	−	31.8310i	−0.829370	−	1.43651i	0.0691630	−	0.997605i	$-0.477967\pi$
$492$		0			0
$493$	−0.113685			−0.00512012
$494$		0			0
$495$	11.8403			0.532184
$496$		0			0
$497$	−6.61991	−	11.4660i	−0.296943	−	0.514321i
$498$		0			0
$499$			0.533994i			0.0239049i	0.999929	+	0.0119524i	$0.00380467\pi$
$499$			0.533994i			0.0239049i	−0.999929	+	0.0119524i	$0.996195\pi$
$500$		0			0
$501$	53.0653	+	30.6373i	2.37078	+	1.36877i
$502$		0			0
$503$	7.07690	−	12.2576i	0.315544	−	0.546538i	−0.664009	−	0.747724i	$-0.731146\pi$
$503$	7.07690	−	12.2576i	0.315544	−	0.546538i	0.979553	+	0.201187i	$0.0644798\pi$
$504$		0			0
$505$	11.9926	−	6.92394i	0.533664	−	0.308111i
$506$		0			0
$507$	−31.6370	−	20.7855i	−1.40505	−	0.923115i
$508$		0			0
$509$	20.8008	−	12.0094i	0.921981	−	0.532306i	0.0377147	−	0.999289i	$-0.487992\pi$
$509$	20.8008	−	12.0094i	0.921981	−	0.532306i	0.884267	+	0.466982i	$0.154659\pi$
$510$		0			0
$511$	−7.46794	+	12.9348i	−0.330362	+	0.572204i
$512$		0			0
$513$	−0.611142	−	0.352843i	−0.0269826	−	0.0155784i
$514$		0			0
$515$			25.7474i			1.13457i
$516$		0			0
$517$	0.774390	+	1.34128i	0.0340576	+	0.0589895i
$518$		0			0
$519$	62.0181			2.72229
$520$		0			0
$521$	−44.0076			−1.92801			−0.964004	−	0.265888i	$-0.914335\pi$
$521$	−44.0076			−1.92801			−0.964004	+	0.265888i	$0.914335\pi$
$522$		0			0
$523$	10.1341	+	17.5528i	0.443133	+	0.767528i	0.997920	−	0.0644638i	$-0.0205337\pi$
$523$	10.1341	+	17.5528i	0.443133	+	0.767528i	−0.554787	+	0.831992i	$0.687200\pi$
$524$		0			0
$525$			2.28007i			0.0995105i
$526$		0			0
$527$	2.73366	+	1.57828i	0.119080	+	0.0687509i
$528$		0			0
$529$	−18.7610	+	32.4951i	−0.815697	+	1.41283i
$530$		0			0
$531$	−52.2288	+	30.1543i	−2.26654	+	1.30859i
$532$		0			0
$533$	23.1371	+	24.5117i	1.00218	+	1.06172i
$534$		0			0
$535$	−13.7588	+	7.94366i	−0.594846	+	0.343434i
$536$		0			0
$537$	−15.9801	+	27.6784i	−0.689593	+	1.19441i
$538$		0			0
$539$	−0.911380	−	0.526186i	−0.0392559	−	0.0226644i
$540$		0			0
$541$			2.61640i			0.112488i	0.998417	+	0.0562438i	$0.0179124\pi$
$541$			2.61640i			0.112488i	−0.998417	+	0.0562438i	$0.982088\pi$
$542$		0			0
$543$	24.3157	+	42.1160i	1.04349	+	1.80737i
$544$		0			0
$545$	7.77460			0.333027
$546$		0			0
$547$	−13.4011			−0.572988			−0.286494	−	0.958082i	$-0.592490\pi$
$547$	−13.4011			−0.572988			−0.286494	+	0.958082i	$0.592490\pi$
$548$		0			0
$549$	−14.3303	−	24.8208i	−0.611601	−	1.05932i
$550$		0			0
$551$			0.00908793i			0.000387159i
$552$		0			0
$553$	−3.39690	−	1.96120i	−0.144451	−	0.0833987i
$554$		0			0
$555$	4.88206	−	8.45597i	0.207232	−	0.358936i
$556$		0			0
$557$	24.0732	−	13.8987i	1.02002	−	0.588907i	0.105907	−	0.994376i	$-0.466225\pi$
$557$	24.0732	−	13.8987i	1.02002	−	0.588907i	0.914109	+	0.405469i	$0.132892\pi$
$558$		0			0
$559$	−23.6034	−	7.06000i	−0.998318	−	0.298606i
$560$		0			0
$561$	3.24554	−	1.87381i	0.137027	−	0.0791124i
$562$		0			0
$563$	7.12553	−	12.3418i	0.300305	−	0.520144i	−0.675900	−	0.736994i	$-0.736245\pi$
$563$	7.12553	−	12.3418i	0.300305	−	0.520144i	0.976205	+	0.216850i	$0.0695781\pi$
$564$		0			0
$565$	−15.4845	−	8.93995i	−0.651436	−	0.376107i
$566$		0			0
$567$		−	4.58179i		−	0.192417i
$568$		0			0
$569$	−18.9357	−	32.7976i	−0.793827	−	1.37495i	−0.923581	−	0.383403i	$-0.874752\pi$
$569$	−18.9357	−	32.7976i	−0.793827	−	1.37495i	0.129754	−	0.991546i	$-0.458581\pi$
$570$		0			0
$571$	37.1372			1.55414			0.777071	−	0.629413i	$-0.216705\pi$
$571$	37.1372			1.55414			0.777071	+	0.629413i	$0.216705\pi$
$572$		0			0
$573$	−51.2382			−2.14051
$574$		0			0
$575$	−3.04583	−	5.27553i	−0.127020	−	0.220005i
$576$		0			0
$577$		−	12.0177i		−	0.500301i	−0.968207	−	0.250151i	$-0.919520\pi$
$577$		−	12.0177i		−	0.500301i	0.968207	−	0.250151i	$-0.0804802\pi$
$578$		0			0
$579$	−15.9264	−	9.19511i	−0.661878	−	0.382136i
$580$		0			0
$581$	7.80495	−	13.5186i	0.323804	−	0.560844i
$582$		0			0
$583$	−9.70709	+	5.60439i	−0.402026	+	0.232110i
$584$		0			0
$585$	11.6249	−	38.8651i	0.480631	−	1.60687i
$586$		0			0
$587$	−6.00908	+	3.46935i	−0.248021	+	0.143195i	−0.618858	−	0.785503i	$-0.712404\pi$
$587$	−6.00908	+	3.46935i	−0.248021	+	0.143195i	0.370837	+	0.928698i	$0.379071\pi$
$588$		0			0
$589$	0.126167	−	0.218527i	0.00519862	−	0.00900427i
$590$		0			0
$591$	7.94152	+	4.58504i	0.326670	+	0.188603i
$592$		0			0
$593$		−	30.2948i		−	1.24406i	−0.782994	−	0.622029i	$-0.786309\pi$
$593$		−	30.2948i		−	1.24406i	0.782994	−	0.622029i	$-0.213691\pi$
$594$		0			0
$595$	−1.25570	−	2.17494i	−0.0514788	−	0.0891640i
$596$		0			0
$597$	−52.1144			−2.13290
$598$		0			0
$599$	−36.2260			−1.48015			−0.740077	−	0.672522i	$-0.765211\pi$
$599$	−36.2260			−1.48015			−0.740077	+	0.672522i	$0.765211\pi$
$600$		0			0
$601$	−2.10804	−	3.65122i	−0.0859886	−	0.148937i	0.819823	−	0.572616i	$-0.194072\pi$
$601$	−2.10804	−	3.65122i	−0.0859886	−	0.148937i	−0.905812	+	0.423680i	$0.860738\pi$
$602$		0			0
$603$			0.794771i			0.0323656i
$604$		0			0
$605$	−17.5929	−	10.1573i	−0.715253	−	0.412952i
$606$		0			0
$607$	−13.9933	+	24.2372i	−0.567972	+	0.983756i	0.428794	+	0.903402i	$0.358938\pi$
$607$	−13.9933	+	24.2372i	−0.567972	+	0.983756i	−0.996766	+	0.0803542i	$0.974395\pi$
$608$		0			0
$609$	−0.234416	+	0.135340i	−0.00949901	+	0.00548426i
$610$		0			0
$611$	5.16297	−	1.22500i	0.208871	−	0.0495583i
$612$		0			0
$613$	−20.1232	+	11.6181i	−0.812767	+	0.469251i	−0.847916	−	0.530131i	$-0.822143\pi$
$613$	−20.1232	+	11.6181i	−0.812767	+	0.469251i	0.0351486	+	0.999382i	$0.488810\pi$
$614$		0			0
$615$	−27.9503	+	48.4113i	−1.12706	+	1.95213i
$616$		0			0
$617$	−5.41635	−	3.12713i	−0.218054	−	0.125894i	0.386995	−	0.922082i	$-0.373513\pi$
$617$	−5.41635	−	3.12713i	−0.218054	−	0.125894i	−0.605049	+	0.796188i	$0.706846\pi$
$618$		0			0
$619$			10.3848i			0.417400i	0.977980	+	0.208700i	$0.0669231\pi$
$619$			10.3848i			0.417400i	−0.977980	+	0.208700i	$0.933077\pi$
$620$		0			0
$621$	28.0776	+	48.6318i	1.12671	+	1.95153i
$622$		0			0
$623$	2.57806			0.103288
$624$		0			0
$625$	−20.4717			−0.818869
$626$		0			0
$627$	−0.149792	−	0.259447i	−0.00598211	−	0.0103613i
$628$		0			0
$629$		−	1.99701i		−	0.0796259i
$630$		0			0
$631$	−19.7277	−	11.3898i	−0.785348	−	0.453421i	0.0529740	−	0.998596i	$-0.483130\pi$
$631$	−19.7277	−	11.3898i	−0.785348	−	0.453421i	−0.838322	+	0.545175i	$0.816463\pi$
$632$		0			0
$633$	−35.2588	+	61.0700i	−1.40141	+	2.42731i
$634$		0			0
$635$	27.5976	−	15.9335i	1.09518	−	0.632302i
$636$		0			0
$637$	−2.62197	+	2.47493i	−0.103886	+	0.0980604i
$638$		0			0
$639$	62.8214	−	36.2699i	2.48518	−	1.43482i
$640$		0			0
$641$	−22.9810	+	39.8042i	−0.907694	+	1.57217i	−0.0904340	+	0.995902i	$0.528825\pi$
$641$	−22.9810	+	39.8042i	−0.907694	+	1.57217i	−0.817260	+	0.576269i	$0.804508\pi$
$642$		0			0
$643$	−24.7170	−	14.2704i	−0.974742	−	0.562768i	−0.0740637	−	0.997254i	$-0.523597\pi$
$643$	−24.7170	−	14.2704i	−0.974742	−	0.562768i	−0.900679	+	0.434486i	$0.856930\pi$
$644$		0			0
$645$		−	40.8583i		−	1.60880i
$646$		0			0
$647$	−0.0332482	−	0.0575875i	−0.00130712	−	0.00226400i	0.865371	−	0.501132i	$-0.167083\pi$
$647$	−0.0332482	−	0.0575875i	−0.00130712	−	0.00226400i	−0.866678	+	0.498868i	$0.833749\pi$
$648$		0			0
$649$	−11.5839			−0.454707
$650$		0			0
$651$	7.51566			0.294562
$652$		0			0
$653$	−15.7206	−	27.2288i	−0.615193	−	1.06555i	−0.990351	−	0.138584i	$-0.955745\pi$
$653$	−15.7206	−	27.2288i	−0.615193	−	1.06555i	0.375158	−	0.926961i	$-0.377589\pi$
$654$		0			0
$655$		−	4.69846i		−	0.183584i
$656$		0			0
$657$	−70.8690	−	40.9162i	−2.76486	−	1.59629i
$658$		0			0
$659$	−15.3139	+	26.5244i	−0.596544	+	1.03325i	0.396783	+	0.917913i	$0.370127\pi$
$659$	−15.3139	+	26.5244i	−0.596544	+	1.03325i	−0.993327	+	0.115333i	$0.963207\pi$
$660$		0			0
$661$	10.1687	−	5.87092i	0.395518	−	0.228352i	−0.289031	−	0.957320i	$-0.593333\pi$
$661$	10.1687	−	5.87092i	0.395518	−	0.228352i	0.684548	+	0.728968i	$0.260000\pi$
$662$		0			0
$663$	−2.96417	−	12.4930i	−0.115119	−	0.485187i
$664$		0			0
$665$	−0.173864	+	0.100380i	−0.00674216	+	0.00389259i
$666$		0			0
$667$	0.361587	−	0.626288i	0.0140007	−	0.0242500i
$668$		0			0
$669$	37.4845	+	21.6417i	1.44923	+	0.836716i
$670$		0			0
$671$		−	5.50502i		−	0.212519i
$672$		0			0
$673$	−14.0959	−	24.4148i	−0.543357	−	0.941122i	−0.998708	−	0.0508098i	$-0.983820\pi$
$673$	−14.0959	−	24.4148i	−0.543357	−	0.941122i	0.455352	−	0.890312i	$-0.349514\pi$
$674$		0			0
$675$	−5.65211			−0.217550
$676$		0			0
$677$	0.773962			0.0297458			0.0148729	−	0.999889i	$-0.495266\pi$
$677$	0.773962			0.0297458			0.0148729	+	0.999889i	$0.495266\pi$
$678$		0			0
$679$	−5.94361	−	10.2946i	−0.228095	−	0.395072i
$680$		0			0
$681$			26.8516i			1.02895i
$682$		0			0
$683$	−29.4503	−	17.0031i	−1.12688	−	0.650607i	−0.183735	−	0.982976i	$-0.558819\pi$
$683$	−29.4503	−	17.0031i	−1.12688	−	0.650607i	−0.943149	+	0.332369i	$0.892152\pi$
$684$		0			0
$685$	−16.0665	+	27.8280i	−0.613869	+	1.06325i
$686$		0			0
$687$	9.93483	−	5.73588i	0.379037	−	0.218837i
$688$		0			0
$689$	8.86555	+	37.3653i	0.337750	+	1.42350i
$690$		0			0
$691$	15.0801	−	8.70649i	0.573673	−	0.331210i	−0.184942	−	0.982749i	$-0.559210\pi$
$691$	15.0801	−	8.70649i	0.573673	−	0.331210i	0.758615	+	0.651539i	$0.225876\pi$
$692$		0			0
$693$	2.88293	−	4.99338i	0.109513	−	0.189683i
$694$		0			0
$695$	−5.74342	−	3.31596i	−0.217860	−	0.125782i
$696$		0			0
$697$			11.4331i			0.433058i
$698$		0			0
$699$	16.2910	+	28.2168i	0.616182	+	1.06726i
$700$		0			0
$701$	32.1250			1.21334			0.606672	−	0.794952i	$-0.292504\pi$
$701$	32.1250			1.21334			0.606672	+	0.794952i	$0.292504\pi$
$702$		0			0
$703$	−0.159640			−0.00602093
$704$		0			0
$705$	4.40009	+	7.62117i	0.165717	+	0.287030i
$706$		0			0
$707$		−	6.74346i		−	0.253614i
$708$		0			0
$709$	13.8327	+	7.98630i	0.519497	+	0.299932i	0.736729	−	0.676188i	$-0.236369\pi$
$709$	13.8327	+	7.98630i	0.519497	+	0.299932i	−0.217232	+	0.976120i	$0.569703\pi$
$710$		0			0
$711$	10.7452	−	18.6113i	0.402978	−	0.697979i
$712$		0			0
$713$	−17.3894	+	10.0398i	−0.651237	+	0.375992i
$714$		0			0
$715$	5.66626	−	5.34851i	0.211906	−	0.200023i
$716$		0			0
$717$	−42.2880	+	24.4150i	−1.57928	+	0.911795i
$718$		0			0
$719$	19.3930	−	33.5896i	0.723236	−	1.25268i	−0.236460	−	0.971641i	$-0.575987\pi$
$719$	19.3930	−	33.5896i	0.723236	−	1.25268i	0.959696	−	0.281040i	$-0.0906794\pi$
$720$		0			0
$721$	10.8584	+	6.26908i	0.404387	+	0.233473i
$722$		0			0
$723$			58.5153i			2.17621i
$724$		0			0
$725$	0.0363944	+	0.0630370i	0.00135165	+	0.00234113i
$726$		0			0
$727$	−28.6102			−1.06110			−0.530548	−	0.847655i	$-0.678014\pi$
$727$	−28.6102			−1.06110			−0.530548	+	0.847655i	$0.678014\pi$
$728$		0			0
$729$	−37.9524			−1.40564
$730$		0			0
$731$	−4.17828	−	7.23699i	−0.154539	−	0.267670i
$732$		0			0
$733$			9.72749i			0.359293i	0.983731	+	0.179646i	$0.0574954\pi$
$733$			9.72749i			0.359293i	−0.983731	+	0.179646i	$0.942505\pi$
$734$		0			0
$735$	−5.17847	−	2.98979i	−0.191011	−	0.110280i
$736$		0			0
$737$	−0.0763284	+	0.132205i	−0.00281159	+	0.00486982i
$738$		0			0
$739$	4.69878	−	2.71284i	0.172847	−	0.0997935i	−0.411080	−	0.911599i	$-0.634848\pi$
$739$	4.69878	−	2.71284i	0.172847	−	0.0997935i	0.583928	+	0.811806i	$0.301515\pi$
$740$		0			0
$741$	−0.998684	+	0.236955i	−0.0366876	+	0.00870475i
$742$		0			0
$743$	−12.0848	+	6.97719i	−0.443350	+	0.255968i	−0.705018	−	0.709190i	$-0.749061\pi$
$743$	−12.0848	+	6.97719i	−0.443350	+	0.255968i	0.261668	+	0.965158i	$0.415728\pi$
$744$		0			0
$745$	−8.76614	+	15.1834i	−0.321167	+	0.556277i
$746$		0			0
$747$	74.0671	+	42.7627i	2.70997	+	1.56460i
$748$		0			0
$749$			7.73660i			0.282689i
$750$		0			0
$751$	20.2525	+	35.0784i	0.739024	+	1.28003i	0.952935	+	0.303174i	$0.0980465\pi$
$751$	20.2525	+	35.0784i	0.739024	+	1.28003i	−0.213911	+	0.976853i	$0.568620\pi$
$752$		0			0
$753$	−25.9084			−0.944154
$754$		0			0
$755$	46.2723			1.68402
$756$		0			0
$757$	1.91470	+	3.31635i	0.0695909	+	0.120535i	0.898721	−	0.438520i	$-0.144497\pi$
$757$	1.91470	+	3.31635i	0.0695909	+	0.120535i	−0.829130	+	0.559055i	$0.811164\pi$
$758$		0			0
$759$			23.8394i			0.865317i
$760$		0			0
$761$	16.7056	+	9.64499i	0.605578	+	0.349631i	0.771233	−	0.636553i	$-0.219640\pi$
$761$	16.7056	+	9.64499i	0.605578	+	0.349631i	−0.165655	+	0.986184i	$0.552974\pi$
$762$		0			0
$763$	1.89299	−	3.27875i	0.0685308	−	0.118699i
$764$		0			0
$765$	11.9163	−	6.87990i	0.430836	−	0.248743i
$766$		0			0
$767$	−11.3731	+	38.0233i	−0.410659	+	1.37294i
$768$		0			0
$769$	−4.83549	+	2.79177i	−0.174372	+	0.100674i	−0.584646	−	0.811289i	$-0.698767\pi$
$769$	−4.83549	+	2.79177i	−0.174372	+	0.100674i	0.410274	+	0.911962i	$0.365433\pi$
$770$		0			0
$771$	−6.83007	+	11.8300i	−0.245979	+	0.426048i
$772$		0			0
$773$	9.58739	+	5.53528i	0.344834	+	0.199090i	0.662408	−	0.749143i	$-0.269535\pi$
$773$	9.58739	+	5.53528i	0.344834	+	0.199090i	−0.317573	+	0.948234i	$0.602868\pi$
$774$		0			0
$775$		−	2.02104i		−	0.0725979i
$776$		0			0
$777$	−2.37740	−	4.11778i	−0.0852888	−	0.147725i
$778$		0			0
$779$	0.913955			0.0327458
$780$		0			0
$781$	13.9332			0.498569
$782$		0			0
$783$	−0.335497	−	0.581098i	−0.0119897	−	0.0207667i
$784$		0			0
$785$		−	42.9933i		−	1.53450i
$786$		0			0
$787$	11.6843	+	6.74595i	0.416501	+	0.240467i	0.693579	−	0.720380i	$-0.256033\pi$
$787$	11.6843	+	6.74595i	0.416501	+	0.240467i	−0.277078	+	0.960847i	$0.589366\pi$
$788$		0			0
$789$	−33.9407	+	58.7870i	−1.20832	+	2.09287i
$790$		0			0
$791$	−7.54042	+	4.35346i	−0.268106	+	0.154791i
$792$		0			0
$793$	−18.0698	−	5.40486i	−0.641679	−	0.191932i
$794$		0			0
$795$	−55.1557	+	31.8442i	−1.95617	+	1.12940i
$796$		0			0
$797$	−21.5544	+	37.3333i	−0.763495	+	1.32241i	0.177544	+	0.984113i	$0.443185\pi$
$797$	−21.5544	+	37.3333i	−0.763495	+	1.32241i	−0.941039	+	0.338299i	$0.890148\pi$
$798$		0			0
$799$	1.55872	+	0.899928i	0.0551436	+	0.0318372i
$800$		0			0
$801$			14.1250i			0.499081i
$802$		0			0
$803$	−7.85904	−	13.6123i	−0.277340	−	0.480366i
$804$		0			0
$805$	15.9756			0.563066
$806$		0			0
$807$	34.3694			1.20986
$808$		0			0
$809$	−11.2343	−	19.4584i	−0.394978	−	0.684121i	0.598121	−	0.801406i	$-0.295914\pi$
$809$	−11.2343	−	19.4584i	−0.394978	−	0.684121i	−0.993098	+	0.117285i	$0.962581\pi$
$810$		0			0
$811$			20.1452i			0.707392i	0.935360	+	0.353696i	$0.115075\pi$
$811$			20.1452i			0.707392i	−0.935360	+	0.353696i	$0.884925\pi$
$812$		0			0
$813$	−31.7844	−	18.3507i	−1.11473	−	0.643588i
$814$		0			0
$815$	−2.91399	+	5.04718i	−0.102073	+	0.176795i
$816$		0			0
$817$	−0.578522	+	0.334010i	−0.0202399	+	0.0116855i
$818$		0			0
$819$	−13.5599	−	14.3655i	−0.473823	−	0.501973i
$820$		0			0
$821$	−32.8314	+	18.9552i	−1.14583	+	0.661543i	−0.947866	−	0.318668i	$-0.896765\pi$
$821$	−32.8314	+	18.9552i	−1.14583	+	0.661543i	−0.197959	+	0.980210i	$0.563431\pi$
$822$		0			0
$823$	3.23524	−	5.60360i	0.112773	−	0.195329i	−0.804114	−	0.594475i	$-0.797360\pi$
$823$	3.23524	−	5.60360i	0.112773	−	0.195329i	0.916887	+	0.399146i	$0.130693\pi$
$824$		0			0
$825$	−2.07801	−	1.19974i	−0.0723471	−	0.0417696i
$826$		0			0
$827$			11.4148i			0.396931i	0.980108	+	0.198465i	$0.0635958\pi$
$827$			11.4148i			0.396931i	−0.980108	+	0.198465i	$0.936404\pi$
$828$		0			0
$829$	−4.07774	−	7.06286i	−0.141626	−	0.245303i	0.786483	−	0.617612i	$-0.211900\pi$
$829$	−4.07774	−	7.06286i	−0.141626	−	0.245303i	−0.928109	+	0.372309i	$0.878566\pi$
$830$		0			0
$831$	−77.6769			−2.69458
$832$		0			0
$833$	−1.22297			−0.0423735
$834$		0			0
$835$	21.6063	+	37.4232i	0.747716	+	1.29508i
$836$		0			0
$837$			18.6307i			0.643971i
$838$		0			0
$839$	−37.4586	−	21.6267i	−1.29321	−	0.746637i	−0.313991	−	0.949426i	$-0.601666\pi$
$839$	−37.4586	−	21.6267i	−1.29321	−	0.746637i	−0.979223	+	0.202789i	$0.935000\pi$
$840$		0			0
$841$	14.4957	−	25.1073i	0.499851	−	0.865767i
$842$		0			0
$843$	56.9400	−	32.8743i	1.96112	−	1.13225i
$844$		0			0
$845$	−11.9929	−	23.8503i	−0.412570	−	0.820476i
$846$		0			0
$847$	−8.56717	+	4.94626i	−0.294371	+	0.169955i
$848$		0			0
$849$	13.2599	−	22.9668i	0.455078	−	0.788219i
$850$		0			0
$851$	11.0015	+	6.35169i	0.377125	+	0.217733i
$852$		0			0
$853$			43.2702i			1.48154i	0.671757	+	0.740771i	$0.265540\pi$
$853$			43.2702i			1.48154i	−0.671757	+	0.740771i	$0.734460\pi$
$854$		0			0
$855$	−0.549976	−	0.952587i	−0.0188088	−	0.0325778i
$856$		0			0
$857$	1.48158			0.0506096			0.0253048	−	0.999680i	$-0.491944\pi$
$857$	1.48158			0.0506096			0.0253048	+	0.999680i	$0.491944\pi$
$858$		0			0
$859$	36.7330			1.25331			0.626657	−	0.779295i	$-0.284423\pi$
$859$	36.7330			1.25331			0.626657	+	0.779295i	$0.284423\pi$
$860$		0			0
$861$	13.6109	+	23.5747i	0.463858	+	0.803425i
$862$		0			0
$863$		−	34.4055i		−	1.17118i	−0.810608	−	0.585589i	$-0.800863\pi$
$863$		−	34.4055i		−	1.17118i	0.810608	−	0.585589i	$-0.199137\pi$
$864$		0			0
$865$	37.8773	+	21.8685i	1.28787	+	0.743550i
$866$		0			0
$867$	−22.5732	+	39.0980i	−0.766627	+	1.32784i
$868$		0			0
$869$	3.57480	−	2.06391i	0.121267	−	0.0700133i
$870$		0			0
$871$	0.359013	+	0.380342i	0.0121647	+	0.0128874i
$872$		0			0
$873$	56.4034	−	32.5645i	1.90897	−	1.10214i
$874$		0			0
$875$	−5.93780	+	10.2846i	−0.200734	+	0.347682i
$876$		0			0
$877$	−10.8716	−	6.27674i	−0.367109	−	0.211951i	0.305086	−	0.952325i	$-0.401315\pi$
$877$	−10.8716	−	6.27674i	−0.367109	−	0.211951i	−0.672195	+	0.740374i	$0.734648\pi$
$878$		0			0
$879$			15.7507i			0.531259i
$880$		0			0
$881$	−7.12702	−	12.3444i	−0.240116	−	0.415892i	0.720631	−	0.693318i	$-0.243852\pi$
$881$	−7.12702	−	12.3444i	−0.240116	−	0.415892i	−0.960747	+	0.277426i	$0.910519\pi$
$882$		0			0
$883$	−44.0943			−1.48389			−0.741946	−	0.670460i	$-0.766097\pi$
$883$	−44.0943			−1.48389			−0.741946	+	0.670460i	$0.766097\pi$
$884$		0			0
$885$	−65.8196			−2.21250
$886$		0			0
$887$	−21.1173	−	36.5762i	−0.709050	−	1.22811i	−0.965210	−	0.261476i	$-0.915791\pi$
$887$	−21.1173	−	36.5762i	−0.709050	−	1.22811i	0.256160	−	0.966634i	$-0.417542\pi$
$888$		0			0
$889$		−	15.5182i		−	0.520464i
$890$		0			0
$891$	4.17576	+	2.41087i	0.139893	+	0.0807673i
$892$		0			0
$893$	0.0719398	−	0.124603i	0.00240737	−	0.00416970i
$894$		0			0
$895$	−19.5196	+	11.2696i	−0.652467	+	0.376702i
$896$		0			0
$897$	78.2514	+	23.4057i	2.61274	+	0.781494i
$898$		0			0
$899$	0.207785	−	0.119965i	0.00693001	−	0.00400104i
$900$		0			0
$901$	−6.51293	+	11.2807i	−0.216977	+	0.375815i
$902$		0			0
$903$	−17.2310	−	9.94833i	−0.573412	−	0.331060i
$904$		0			0
$905$			34.2962i			1.14004i
$906$		0			0
$907$	−2.13555	−	3.69888i	−0.0709098	−	0.122819i	0.828391	−	0.560151i	$-0.189257\pi$
$907$	−2.13555	−	3.69888i	−0.0709098	−	0.122819i	−0.899300	+	0.437332i	$0.855924\pi$
$908$		0			0
$909$	36.9469			1.22545
$910$		0			0
$911$	5.37725			0.178156			0.0890781	−	0.996025i	$-0.471608\pi$
$911$	5.37725			0.178156			0.0890781	+	0.996025i	$0.471608\pi$
$912$		0			0
$913$	8.21370	+	14.2265i	0.271834	+	0.470830i
$914$		0			0
$915$		−	31.2795i		−	1.03407i
$916$		0			0
$917$	−1.98146	−	1.14400i	−0.0654337	−	0.0377782i
$918$		0			0
$919$	−6.34104	+	10.9830i	−0.209172	+	0.362296i	−0.951454	−	0.307791i	$-0.900410\pi$
$919$	−6.34104	+	10.9830i	−0.209172	+	0.362296i	0.742282	+	0.670087i	$0.233743\pi$
$920$		0			0
$921$	60.9260	−	35.1757i	2.00758	−	1.15908i
$922$		0			0
$923$	13.6797	−	45.7348i	0.450273	−	1.50538i
$924$		0			0
$925$	−1.10732	+	0.639309i	−0.0364083	+	0.0210204i
$926$		0			0
$927$	−34.3478	+	59.4921i	−1.12813	+	1.95398i
$928$		0			0
$929$	−50.5622	−	29.1921i	−1.65889	−	0.957762i	−0.973227	−	0.229846i	$-0.926178\pi$
$929$	−50.5622	−	29.1921i	−1.65889	−	0.957762i	−0.685666	−	0.727917i	$-0.740489\pi$
$930$		0			0
$931$			0.0977640i			0.00320408i
$932$		0			0
$933$	−28.2450	−	48.9217i	−0.924699	−	1.60163i
$934$		0			0
$935$	2.64293			0.0864332
$936$		0			0
$937$	20.6731			0.675360			0.337680	−	0.941261i	$-0.390358\pi$
$937$	20.6731			0.675360			0.337680	+	0.941261i	$0.390358\pi$
$938$		0			0
$939$	20.9306	+	36.2529i	0.683046	+	1.18307i
$940$		0			0
$941$		−	4.59948i		−	0.149939i	−0.997186	−	0.0749693i	$-0.976114\pi$
$941$		−	4.59948i		−	0.149939i	0.997186	−	0.0749693i	$-0.0238859\pi$
$942$		0			0
$943$	−62.9845	−	36.3641i	−2.05106	−	1.18418i
$944$		0			0
$945$	7.41144	−	12.8370i	0.241094	−	0.417587i
$946$		0			0
$947$	18.8455	−	10.8805i	0.612397	−	0.353567i	−0.161506	−	0.986872i	$-0.551635\pi$
$947$	18.8455	−	10.8805i	0.612397	−	0.353567i	0.773903	+	0.633304i	$0.218302\pi$
$948$		0			0
$949$	−52.3974	+	12.4322i	−1.70089	+	0.403565i
$950$		0			0
$951$	52.5825	−	30.3585i	1.70510	−	0.984442i
$952$		0			0
$953$	−3.06194	+	5.30343i	−0.0991859	+	0.171795i	−0.911348	−	0.411637i	$-0.864957\pi$
$953$	−3.06194	+	5.30343i	−0.0991859	+	0.171795i	0.812162	+	0.583432i	$0.198291\pi$
$954$		0			0
$955$	−31.2935	−	18.0673i	−1.01263	−	0.584645i
$956$		0			0
$957$		−	0.284856i		−	0.00920809i
$958$		0			0
$959$	7.82386	+	13.5513i	0.252646	+	0.437595i
$960$		0			0
$961$	24.3382			0.785102
$962$		0			0
$963$	−42.3882			−1.36594
$964$		0			0
$965$	−6.48465	−	11.2318i	−0.208748	−	0.361563i
$966$		0			0
$967$			24.7451i			0.795747i	0.917440	+	0.397874i	$0.130252\pi$
$967$			24.7451i			0.795747i	−0.917440	+	0.397874i	$0.869748\pi$
$968$		0			0
$969$	−0.301506	−	0.174075i	−0.00968578	−	0.00559209i
$970$		0			0
$971$	6.94926	−	12.0365i	0.223013	−	0.386269i	−0.732709	−	0.680542i	$-0.761744\pi$
$971$	6.94926	−	12.0365i	0.223013	−	0.386269i	0.955721	+	0.294273i	$0.0950776\pi$
$972$		0			0
$973$	−2.79686	+	1.61477i	−0.0896631	+	0.0517670i
$974$		0			0
$975$	−5.97828	+	5.64302i	−0.191458	+	0.180721i
$976$		0			0
$977$	0.903344	−	0.521546i	0.0289005	−	0.0166857i	−0.485480	−	0.874248i	$-0.661355\pi$
$977$	0.903344	−	0.521546i	0.0289005	−	0.0166857i	0.514381	+	0.857562i	$0.328022\pi$
$978$		0			0
$979$	−1.35654	+	2.34959i	−0.0433551	+	0.0750933i
$980$		0			0
$981$	17.9640	+	10.3715i	0.573547	+	0.331137i
$982$		0			0
$983$		−	31.3913i		−	1.00123i	−0.865671	−	0.500614i	$-0.833108\pi$
$983$		−	31.3913i		−	1.00123i	0.865671	−	0.500614i	$-0.166892\pi$
$984$		0			0
$985$	3.23350	+	5.60059i	0.103028	+	0.178450i
$986$		0			0
$987$	4.28539			0.136406
$988$		0			0
$989$	53.1578			1.69032
$990$		0			0
$991$	−4.28959	−	7.42978i	−0.136263	−	0.236015i	0.789816	−	0.613344i	$-0.210176\pi$
$991$	−4.28959	−	7.42978i	−0.136263	−	0.236015i	−0.926079	+	0.377329i	$0.876843\pi$
$992$		0			0
$993$			19.3651i			0.614532i
$994$		0			0
$995$	−31.8286	−	18.3763i	−1.00904	−	0.582567i
$996$		0			0
$997$	21.2274	−	36.7669i	0.672277	−	1.16442i	−0.304979	−	0.952359i	$-0.598650\pi$
$997$	21.2274	−	36.7669i	0.672277	−	1.16442i	0.977257	−	0.212060i	$-0.0680171\pi$
$998$		0			0
$999$	10.2076	−	5.89339i	0.322956	−	0.186459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.g.673.11		24
4.3	odd	2		728.2.bm.c.673.2	yes	24
13.4	even	6	inner	1456.2.cc.g.225.11		24
52.11	even	12		9464.2.a.bm.1.11		12
52.15	even	12		9464.2.a.bl.1.11		12
52.43	odd	6		728.2.bm.c.225.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.bm.c.225.2	✓	24	52.43	odd	6
728.2.bm.c.673.2	yes	24	4.3	odd	2
1456.2.cc.g.225.11		24	13.4	even	6	inner
1456.2.cc.g.673.11		24	1.1	even	1	trivial
9464.2.a.bl.1.11		12	52.15	even	12
9464.2.a.bm.1.11		12	52.11	even	12

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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.45593 + 2.52174i) q^{3} +2.05353i q^{5} +(0.866025 + 0.500000i) q^{7} +(-2.73946 + 4.74488i) q^{9} +O(q^{10})\)	\(q+(1.45593 + 2.52174i) q^{3} +2.05353i q^{5} +(0.866025 + 0.500000i) q^{7} +(-2.73946 + 4.74488i) q^{9} +(-0.911380 + 0.526186i) q^{11} +(0.832370 + 3.50816i) q^{13} +(-5.17847 + 2.98979i) q^{15} +(-0.611487 + 1.05913i) q^{17} +(0.0846661 + 0.0488820i) q^{19} +2.91186i q^{21} +(-3.88980 - 6.73733i) q^{23} +0.783030 q^{25} -7.21826 q^{27} +(0.0464789 + 0.0805039i) q^{29} -2.58105i q^{31} +(-2.65381 - 1.53218i) q^{33} +(-1.02676 + 1.77841i) q^{35} +(-1.41414 + 0.816456i) q^{37} +(-7.63480 + 7.20665i) q^{39} +(8.09611 - 4.67429i) q^{41} +(-3.41649 + 5.91753i) q^{43} +(-9.74374 - 5.62555i) q^{45} -1.47170i q^{47} +(0.500000 + 0.866025i) q^{49} -3.56112 q^{51} +10.6510 q^{53} +(-1.08054 - 1.87154i) q^{55} +0.284675i q^{57} +(9.53268 + 5.50370i) q^{59} +(-2.61553 + 4.53023i) q^{61} +(-4.74488 + 2.73946i) q^{63} +(-7.20409 + 1.70929i) q^{65} +(0.125626 - 0.0725300i) q^{67} +(11.3265 - 19.6181i) q^{69} +(-11.4660 - 6.61991i) q^{71} +14.9359i q^{73} +(1.14004 + 1.97460i) q^{75} -1.05237 q^{77} -3.92240 q^{79} +(-2.29090 - 3.96795i) q^{81} -15.6099i q^{83} +(-2.17494 - 1.25570i) q^{85} +(-0.135340 + 0.234416i) q^{87} +(2.23266 - 1.28903i) q^{89} +(-1.03322 + 3.45434i) q^{91} +(6.50875 - 3.75783i) q^{93} +(-0.100380 + 0.173864i) q^{95} +(-10.2946 - 5.94361i) q^{97} -5.76586i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} - 18 q^{9}+O(q^{10}) \) 24 * q + 2 * q^3 - 18 * q^9	\( 24 q + 2 q^{3} - 18 q^{9} - 12 q^{11} + 8 q^{17} + 12 q^{19} - 2 q^{23} - 28 q^{25} + 20 q^{27} + 2 q^{29} - 18 q^{33} + 8 q^{35} + 60 q^{37} - 18 q^{39} - 6 q^{41} - 24 q^{43} - 72 q^{45} + 12 q^{49} + 72 q^{51} - 48 q^{53} + 44 q^{55} + 12 q^{59} - 30 q^{61} - 12 q^{63} + 10 q^{65} - 78 q^{67} + 36 q^{69} + 36 q^{71} - 22 q^{75} + 4 q^{77} - 20 q^{79} - 40 q^{81} - 6 q^{85} + 20 q^{87} + 108 q^{89} - 6 q^{91} + 30 q^{93} - 18 q^{95} - 54 q^{97}+O(q^{100}) \) 24 * q + 2 * q^3 - 18 * q^9 - 12 * q^11 + 8 * q^17 + 12 * q^19 - 2 * q^23 - 28 * q^25 + 20 * q^27 + 2 * q^29 - 18 * q^33 + 8 * q^35 + 60 * q^37 - 18 * q^39 - 6 * q^41 - 24 * q^43 - 72 * q^45 + 12 * q^49 + 72 * q^51 - 48 * q^53 + 44 * q^55 + 12 * q^59 - 30 * q^61 - 12 * q^63 + 10 * q^65 - 78 * q^67 + 36 * q^69 + 36 * q^71 - 22 * q^75 + 4 * q^77 - 20 * q^79 - 40 * q^81 - 6 * q^85 + 20 * q^87 + 108 * q^89 - 6 * q^91 + 30 * q^93 - 18 * q^95 - 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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