LMFDB - Embedded newform 1456.2.cc.g.673.8

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			673.8
Character	$\chi$	$=$	1456.673
Dual form			1456.2.cc.g.225.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.509942 + 0.883245i) q^{3} +2.02001i q^{5} +(0.866025 + 0.500000i) q^{7} +(0.979919 - 1.69727i) q^{9} +(5.06414 - 2.92378i) q^{11} +(-2.41142 - 2.68049i) q^{13} +(-1.78417 + 1.03009i) q^{15} +(3.04158 - 5.26816i) q^{17} +(0.610163 + 0.352278i) q^{19} +1.01988i q^{21} +(2.48413 + 4.30265i) q^{23} +0.919550 q^{25} +5.05846 q^{27} +(-4.92645 - 8.53286i) q^{29} -4.81518i q^{31} +(5.16483 + 2.98192i) q^{33} +(-1.01001 + 1.74938i) q^{35} +(1.45284 - 0.838799i) q^{37} +(1.13785 - 3.49677i) q^{39} +(-1.89288 + 1.09285i) q^{41} +(-0.391141 + 0.677476i) q^{43} +(3.42850 + 1.97945i) q^{45} +5.26356i q^{47} +(0.500000 + 0.866025i) q^{49} +6.20411 q^{51} -10.0419 q^{53} +(5.90608 + 10.2296i) q^{55} +0.718565i q^{57} +(5.03891 + 2.90921i) q^{59} +(-3.48257 + 6.03200i) q^{61} +(1.69727 - 0.979919i) q^{63} +(5.41463 - 4.87110i) q^{65} +(-9.63479 + 5.56265i) q^{67} +(-2.53353 + 4.38820i) q^{69} +(10.7862 + 6.22739i) q^{71} +11.4541i q^{73} +(0.468917 + 0.812188i) q^{75} +5.84756 q^{77} -1.05083 q^{79} +(-0.360237 - 0.623949i) q^{81} -3.04409i q^{83} +(10.6418 + 6.14402i) q^{85} +(5.02440 - 8.70252i) q^{87} +(-1.34250 + 0.775094i) q^{89} +(-0.748104 - 3.52709i) q^{91} +(4.25299 - 2.45546i) q^{93} +(-0.711606 + 1.23254i) q^{95} +(1.33021 + 0.767994i) q^{97} -11.4603i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

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
$3$	0.509942	+	0.883245i	0.294415	+	0.509942i	0.974849	−	0.222868i	$-0.0715419\pi$
$3$	0.509942	+	0.883245i	0.294415	+	0.509942i	−0.680434	+	0.732810i	$0.738209\pi$
$4$		0			0
$5$			2.02001i			0.903377i	0.892176	+	0.451688i	$0.149178\pi$
$5$			2.02001i			0.903377i	−0.892176	+	0.451688i	$0.850822\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		0			0
$9$	0.979919	−	1.69727i	0.326640	−	0.565756i
$10$		0			0
$11$	5.06414	−	2.92378i	1.52690	−	0.881553i	0.527405	−	0.849614i	$-0.323165\pi$
$11$	5.06414	−	2.92378i	1.52690	−	0.881553i	0.999490	−	0.0319397i	$-0.0101684\pi$
$12$		0			0
$13$	−2.41142	−	2.68049i	−0.668808	−	0.743435i
$13$	−2.41142	−	2.68049i	−0.668808	−	0.743435i
$14$		0			0
$15$	−1.78417	+	1.03009i	−0.460670	+	0.265968i
$16$		0			0
$17$	3.04158	−	5.26816i	0.737690	−	1.27772i	−0.215842	−	0.976428i	$-0.569250\pi$
$17$	3.04158	−	5.26816i	0.737690	−	1.27772i	0.953533	−	0.301289i	$-0.0974169\pi$
$18$		0			0
$19$	0.610163	+	0.352278i	0.139981	+	0.0808181i	0.568355	−	0.822783i	$-0.307580\pi$
$19$	0.610163	+	0.352278i	0.139981	+	0.0808181i	−0.428374	+	0.903602i	$0.640913\pi$
$20$		0			0
$21$			1.01988i			0.222557i
$22$		0			0
$23$	2.48413	+	4.30265i	0.517978	+	0.897164i	0.999782	+	0.0208847i	$0.00664829\pi$
$23$	2.48413	+	4.30265i	0.517978	+	0.897164i	−0.481804	+	0.876279i	$0.660018\pi$
$24$		0			0
$25$	0.919550			0.183910
$26$		0			0
$27$	5.05846			0.973501
$28$		0			0
$29$	−4.92645	−	8.53286i	−0.914818	−	1.58451i	−0.807167	−	0.590323i	$-0.799000\pi$
$29$	−4.92645	−	8.53286i	−0.914818	−	1.58451i	−0.107651	−	0.994189i	$-0.534333\pi$
$30$		0			0
$31$		−	4.81518i		−	0.864833i	−0.901674	−	0.432416i	$-0.857661\pi$
$31$		−	4.81518i		−	0.864833i	0.901674	−	0.432416i	$-0.142339\pi$
$32$		0			0
$33$	5.16483	+	2.98192i	0.899082	+	0.519085i
$34$		0			0
$35$	−1.01001	+	1.74938i	−0.170722	+	0.295700i
$36$		0			0
$37$	1.45284	−	0.838799i	0.238846	−	0.137898i	−0.375800	−	0.926701i	$-0.622632\pi$
$37$	1.45284	−	0.838799i	0.238846	−	0.137898i	0.614646	+	0.788803i	$0.289299\pi$
$38$		0			0
$39$	1.13785	−	3.49677i	0.182202	−	0.559932i
$40$		0			0
$41$	−1.89288	+	1.09285i	−0.295618	+	0.170675i	−0.640473	−	0.767981i	$-0.721262\pi$
$41$	−1.89288	+	1.09285i	−0.295618	+	0.170675i	0.344855	+	0.938656i	$0.387928\pi$
$42$		0			0
$43$	−0.391141	+	0.677476i	−0.0596485	+	0.103314i	−0.894308	−	0.447453i	$-0.852331\pi$
$43$	−0.391141	+	0.677476i	−0.0596485	+	0.103314i	0.834659	+	0.550767i	$0.185665\pi$
$44$		0			0
$45$	3.42850	+	1.97945i	0.511091	+	0.295079i
$46$		0			0
$47$			5.26356i			0.767769i	0.923381	+	0.383885i	$0.125414\pi$
$47$			5.26356i			0.767769i	−0.923381	+	0.383885i	$0.874586\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$	6.20411			0.868749
$52$		0			0
$53$	−10.0419			−1.37936			−0.689681	−	0.724114i	$-0.742249\pi$
$53$	−10.0419			−1.37936			−0.689681	+	0.724114i	$0.742249\pi$
$54$		0			0
$55$	5.90608	+	10.2296i	0.796375	+	1.37936i
$56$		0			0
$57$			0.718565i			0.0951763i
$58$		0			0
$59$	5.03891	+	2.90921i	0.656010	+	0.378747i	0.790755	−	0.612133i	$-0.209688\pi$
$59$	5.03891	+	2.90921i	0.656010	+	0.378747i	−0.134745	+	0.990880i	$0.543022\pi$
$60$		0			0
$61$	−3.48257	+	6.03200i	−0.445898	+	0.772318i	−0.998114	−	0.0613829i	$-0.980449\pi$
$61$	−3.48257	+	6.03200i	−0.445898	+	0.772318i	0.552216	+	0.833701i	$0.313782\pi$
$62$		0			0
$63$	1.69727	−	0.979919i	0.213836	−	0.123458i
$64$		0			0
$65$	5.41463	−	4.87110i	0.671602	−	0.604186i
$66$		0			0
$67$	−9.63479	+	5.56265i	−1.17708	+	0.679586i	−0.955337	−	0.295520i	$-0.904507\pi$
$67$	−9.63479	+	5.56265i	−1.17708	+	0.679586i	−0.221740	+	0.975106i	$0.571174\pi$
$68$		0			0
$69$	−2.53353	+	4.38820i	−0.305001	+	0.528277i
$70$		0			0
$71$	10.7862	+	6.22739i	1.28008	+	0.739056i	0.976863	−	0.213865i	$-0.0686054\pi$
$71$	10.7862	+	6.22739i	1.28008	+	0.739056i	0.303219	+	0.952921i	$0.401939\pi$
$72$		0			0
$73$			11.4541i			1.34060i	0.742090	+	0.670301i	$0.233835\pi$
$73$			11.4541i			1.34060i	−0.742090	+	0.670301i	$0.766165\pi$
$74$		0			0
$75$	0.468917	+	0.812188i	0.0541459	+	0.0937834i
$76$		0			0
$77$	5.84756			0.666392
$78$		0			0
$79$	−1.05083			−0.118227			−0.0591136	−	0.998251i	$-0.518827\pi$
$79$	−1.05083			−0.118227			−0.0591136	+	0.998251i	$0.518827\pi$
$80$		0			0
$81$	−0.360237	−	0.623949i	−0.0400263	−	0.0693276i
$82$		0			0
$83$		−	3.04409i		−	0.334132i	−0.985946	−	0.167066i	$-0.946571\pi$
$83$		−	3.04409i		−	0.334132i	0.985946	−	0.167066i	$-0.0534293\pi$
$84$		0			0
$85$	10.6418	+	6.14402i	1.15426	+	0.666413i
$86$		0			0
$87$	5.02440	−	8.70252i	0.538673	−	0.933008i
$88$		0			0
$89$	−1.34250	+	0.775094i	−0.142305	+	0.0821598i	−0.569462	−	0.822018i	$-0.692848\pi$
$89$	−1.34250	+	0.775094i	−0.142305	+	0.0821598i	0.427157	+	0.904177i	$0.359515\pi$
$90$		0			0
$91$	−0.748104	−	3.52709i	−0.0784226	−	0.369739i
$92$		0			0
$93$	4.25299	−	2.45546i	0.441014	−	0.254620i
$94$		0			0
$95$	−0.711606	+	1.23254i	−0.0730092	+	0.126456i
$96$		0			0
$97$	1.33021	+	0.767994i	0.135062	+	0.0779780i	0.566008	−	0.824399i	$-0.308487\pi$
$97$	1.33021	+	0.767994i	0.135062	+	0.0779780i	−0.430947	+	0.902377i	$0.641820\pi$
$98$		0			0
$99$		−	11.4603i		−	1.15180i
$100$		0			0
$101$	7.88894	+	13.6640i	0.784978	+	1.35962i	0.929012	+	0.370050i	$0.120659\pi$
$101$	7.88894	+	13.6640i	0.784978	+	1.35962i	−0.144033	+	0.989573i	$0.546007\pi$
$102$		0			0
$103$	0.0661752			0.00652044			0.00326022	−	0.999995i	$-0.498962\pi$
$103$	0.0661752			0.00652044			0.00326022	+	0.999995i	$0.498962\pi$
$104$		0			0
$105$	−2.06018			−0.201053
$106$		0			0
$107$	−2.45244	−	4.24775i	−0.237087	−	0.410646i	0.722790	−	0.691067i	$-0.242859\pi$
$107$	−2.45244	−	4.24775i	−0.237087	−	0.410646i	−0.959877	+	0.280421i	$0.909526\pi$
$108$		0			0
$109$		−	13.7491i		−	1.31692i	−0.752614	−	0.658462i	$-0.771207\pi$
$109$		−	13.7491i		−	1.31692i	0.752614	−	0.658462i	$-0.228793\pi$
$110$		0			0
$111$	1.48173	+	0.855478i	0.140640	+	0.0811984i
$112$		0			0
$113$	1.46579	−	2.53882i	0.137890	−	0.238832i	−0.788808	−	0.614640i	$-0.789301\pi$
$113$	1.46579	−	2.53882i	0.137890	−	0.238832i	0.926698	+	0.375808i	$0.122635\pi$
$114$		0			0
$115$	−8.69140	+	5.01798i	−0.810477	+	0.467929i
$116$		0			0
$117$	−6.91252	+	1.46616i	−0.639062	+	0.135547i
$118$		0			0
$119$	5.26816	−	3.04158i	0.482932	−	0.278821i
$120$		0			0
$121$	11.5970	−	20.0866i	1.05427	−	1.82605i
$122$		0			0
$123$	−1.93052	−	1.11458i	−0.174069	−	0.100499i
$124$		0			0
$125$			11.9576i			1.06952i
$126$		0			0
$127$	2.86732	+	4.96634i	0.254433	+	0.440691i	0.964741	−	0.263200i	$-0.0847778\pi$
$127$	2.86732	+	4.96634i	0.254433	+	0.440691i	−0.710308	+	0.703891i	$0.751444\pi$
$128$		0			0
$129$	−0.797837			−0.0702456
$130$		0			0
$131$	−18.6052			−1.62554			−0.812772	−	0.582581i	$-0.802043\pi$
$131$	−18.6052			−1.62554			−0.812772	+	0.582581i	$0.802043\pi$
$132$		0			0
$133$	0.352278	+	0.610163i	0.0305464	+	0.0529079i
$134$		0			0
$135$			10.2181i			0.879438i
$136$		0			0
$137$	11.4279	+	6.59793i	0.976355	+	0.563699i	0.901168	−	0.433470i	$-0.142711\pi$
$137$	11.4279	+	6.59793i	0.976355	+	0.563699i	0.0751875	+	0.997169i	$0.476044\pi$
$138$		0			0
$139$	−6.03195	+	10.4476i	−0.511623	+	0.886158i	0.488286	+	0.872684i	$0.337622\pi$
$139$	−6.03195	+	10.4476i	−0.511623	+	0.886158i	−0.999909	+	0.0134739i	$0.995711\pi$
$140$		0			0
$141$	−4.64902	+	2.68411i	−0.391518	+	0.226043i
$142$		0			0
$143$	−20.0489	−	6.52393i	−1.67658	−	0.545558i
$144$		0			0
$145$	17.2365	−	9.95148i	1.43141	−	0.826426i
$146$		0			0
$147$	−0.509942	+	0.883245i	−0.0420593	+	0.0728488i
$148$		0			0
$149$	−20.5202	−	11.8473i	−1.68108	−	0.970571i	−0.960947	−	0.276734i	$-0.910748\pi$
$149$	−20.5202	−	11.8473i	−1.68108	−	0.970571i	−0.720132	−	0.693837i	$-0.755919\pi$
$150$		0			0
$151$		−	18.0151i		−	1.46605i	−0.680203	−	0.733024i	$-0.738108\pi$
$151$		−	18.0151i		−	1.46605i	0.680203	−	0.733024i	$-0.261892\pi$
$152$		0			0
$153$	−5.96099	−	10.3247i	−0.481918	−	0.834706i
$154$		0			0
$155$	9.72673			0.781270
$156$		0			0
$157$	13.3205			1.06309			0.531547	−	0.847028i	$-0.321611\pi$
$157$	13.3205			1.06309			0.531547	+	0.847028i	$0.321611\pi$
$158$		0			0
$159$	−5.12079	−	8.86946i	−0.406105	−	0.703394i
$160$		0			0
$161$			4.96827i			0.391554i
$162$		0			0
$163$	10.9382	+	6.31518i	0.856746	+	0.494643i	0.862921	−	0.505338i	$-0.168632\pi$
$163$	10.9382	+	6.31518i	0.856746	+	0.494643i	−0.00617502	+	0.999981i	$0.501966\pi$
$164$		0			0
$165$	−6.02351	+	10.4330i	−0.468930	+	0.812210i
$166$		0			0
$167$	−16.0968	+	9.29348i	−1.24561	+	0.719151i	−0.970230	−	0.242185i	$-0.922136\pi$
$167$	−16.0968	+	9.29348i	−1.24561	+	0.719151i	−0.275376	+	0.961336i	$0.588802\pi$
$168$		0			0
$169$	−1.37010	+	12.9276i	−0.105392	+	0.994431i
$170$		0			0
$171$	1.19582	−	0.690408i	0.0914467	−	0.0527968i
$172$		0			0
$173$	−3.60469	+	6.24350i	−0.274059	+	0.474685i	−0.969897	−	0.243514i	$-0.921700\pi$
$173$	−3.60469	+	6.24350i	−0.274059	+	0.474685i	0.695838	+	0.718199i	$0.255033\pi$
$174$		0			0
$175$	0.796354	+	0.459775i	0.0601987	+	0.0347557i
$176$		0			0
$177$			5.93412i			0.446036i
$178$		0			0
$179$	−10.3711	−	17.9632i	−0.775170	−	1.34263i	−0.934699	−	0.355440i	$-0.884331\pi$
$179$	−10.3711	−	17.9632i	−0.775170	−	1.34263i	0.159529	−	0.987193i	$-0.449002\pi$
$180$		0			0
$181$	15.2611			1.13435			0.567173	−	0.823599i	$-0.308037\pi$
$181$	15.2611			1.13435			0.567173	+	0.823599i	$0.308037\pi$
$182$		0			0
$183$	−7.10364			−0.525116
$184$		0			0
$185$	1.69439	+	2.93476i	0.124574	+	0.215768i
$186$		0			0
$187$		−	35.5716i		−	2.60125i
$188$		0			0
$189$	4.38075	+	2.52923i	0.318653	+	0.183974i
$190$		0			0
$191$	1.59564	−	2.76373i	0.115456	−	0.199976i	−0.802506	−	0.596645i	$-0.796500\pi$
$191$	1.59564	−	2.76373i	0.115456	−	0.199976i	0.917962	+	0.396668i	$0.129834\pi$
$192$		0			0
$193$	9.04430	−	5.22173i	0.651023	−	0.375868i	−0.137825	−	0.990457i	$-0.544011\pi$
$193$	9.04430	−	5.22173i	0.651023	−	0.375868i	0.788848	+	0.614588i	$0.210678\pi$
$194$		0			0
$195$	7.06352	+	2.29847i	0.505829	+	0.164597i
$196$		0			0
$197$	−2.98736	+	1.72476i	−0.212841	+	0.122884i	−0.602631	−	0.798020i	$-0.705881\pi$
$197$	−2.98736	+	1.72476i	−0.212841	+	0.122884i	0.389790	+	0.920904i	$0.372548\pi$
$198$		0			0
$199$	2.49808	−	4.32679i	0.177084	−	0.306718i	−0.763797	−	0.645457i	$-0.776667\pi$
$199$	2.49808	−	4.32679i	0.177084	−	0.306718i	0.940880	+	0.338739i	$0.110000\pi$
$200$		0			0
$201$	−9.82636	−	5.67325i	−0.693098	−	0.400161i
$202$		0			0
$203$		−	9.85289i		−	0.691538i
$204$		0			0
$205$	−2.20758	−	3.82364i	−0.154184	−	0.267054i
$206$		0			0
$207$	9.73699			0.676768
$208$		0			0
$209$	4.11994			0.284982
$210$		0			0
$211$	11.3510	+	19.6604i	0.781432	+	1.35348i	0.931108	+	0.364745i	$0.118844\pi$
$211$	11.3510	+	19.6604i	0.781432	+	1.35348i	−0.149676	+	0.988735i	$0.547823\pi$
$212$		0			0
$213$			12.7024i			0.870356i
$214$		0			0
$215$	−1.36851	−	0.790110i	−0.0933316	−	0.0538850i
$216$		0			0
$217$	2.40759	−	4.17007i	0.163438	−	0.283083i
$218$		0			0
$219$	−10.1168	+	5.84093i	−0.683629	+	0.394693i
$220$		0			0
$221$	−21.4558	+	4.55083i	−1.44327	+	0.306122i
$222$		0			0
$223$	7.64573	−	4.41426i	0.511996	−	0.295601i	−0.221658	−	0.975125i	$-0.571147\pi$
$223$	7.64573	−	4.41426i	0.511996	−	0.295601i	0.733654	+	0.679524i	$0.237813\pi$
$224$		0			0
$225$	0.901084	−	1.56072i	0.0600723	−	0.104048i
$226$		0			0
$227$	13.6744	+	7.89493i	0.907603	+	0.524005i	0.879659	−	0.475605i	$-0.157771\pi$
$227$	13.6744	+	7.89493i	0.907603	+	0.524005i	0.0279438	+	0.999609i	$0.491104\pi$
$228$		0			0
$229$			7.89653i			0.521818i	0.965363	+	0.260909i	$0.0840222\pi$
$229$			7.89653i			0.521818i	−0.965363	+	0.260909i	$0.915978\pi$
$230$		0			0
$231$	2.98192	+	5.16483i	0.196196	+	0.339821i
$232$		0			0
$233$	−12.8845			−0.844089			−0.422045	−	0.906575i	$-0.638687\pi$
$233$	−12.8845			−0.844089			−0.422045	+	0.906575i	$0.638687\pi$
$234$		0			0
$235$	−10.6325			−0.693585
$236$		0			0
$237$	−0.535860	−	0.928137i	−0.0348079	−	0.0602890i
$238$		0			0
$239$			15.9013i			1.02857i	0.857620	+	0.514283i	$0.171942\pi$
$239$			15.9013i			1.02857i	−0.857620	+	0.514283i	$0.828058\pi$
$240$		0			0
$241$	−20.9790	−	12.1122i	−1.35137	−	0.780216i	−0.362931	−	0.931816i	$-0.618224\pi$
$241$	−20.9790	−	12.1122i	−1.35137	−	0.780216i	−0.988442	+	0.151600i	$0.951557\pi$
$242$		0			0
$243$	7.95509	−	13.7786i	0.510319	−	0.883898i
$244$		0			0
$245$	−1.74938	+	1.01001i	−0.111764	+	0.0645269i
$246$		0			0
$247$	−0.527081	−	2.48503i	−0.0335374	−	0.158119i
$248$		0			0
$249$	2.68867	−	1.55231i	0.170388	−	0.0983735i
$250$		0			0
$251$	−11.8183	+	20.4699i	−0.745966	+	1.29205i	0.203777	+	0.979017i	$0.434678\pi$
$251$	−11.8183	+	20.4699i	−0.745966	+	1.29205i	−0.949742	+	0.313033i	$0.898655\pi$
$252$		0			0
$253$	25.1600	+	14.5261i	1.58180	+	0.913250i
$254$		0			0
$255$			12.5324i			0.784808i
$256$		0			0
$257$	4.36835	+	7.56620i	0.272490	+	0.471966i	0.969499	−	0.245096i	$-0.0788195\pi$
$257$	4.36835	+	7.56620i	0.272490	+	0.471966i	−0.697009	+	0.717063i	$0.745486\pi$
$258$		0			0
$259$	1.67760			0.104241
$260$		0			0
$261$	−19.3101			−1.19526
$262$		0			0
$263$	−3.71086	−	6.42740i	−0.228822	−	0.396330i	0.728638	−	0.684899i	$-0.240154\pi$
$263$	−3.71086	−	6.42740i	−0.228822	−	0.396330i	−0.957459	+	0.288569i	$0.906821\pi$
$264$		0			0
$265$		−	20.2848i		−	1.24608i
$266$		0			0
$267$	−1.36920	−	0.790505i	−0.0837934	−	0.0483782i
$268$		0			0
$269$	−14.1475	+	24.5042i	−0.862589	+	1.49405i	0.00683299	+	0.999977i	$0.497825\pi$
$269$	−14.1475	+	24.5042i	−0.862589	+	1.49405i	−0.869422	+	0.494071i	$0.835508\pi$
$270$		0			0
$271$	−10.2435	+	5.91408i	−0.622248	+	0.359255i	−0.777744	−	0.628582i	$-0.783636\pi$
$271$	−10.2435	+	5.91408i	−0.622248	+	0.359255i	0.155496	+	0.987837i	$0.450302\pi$
$272$		0			0
$273$	2.73379	−	2.45937i	0.165457	−	0.148848i
$274$		0			0
$275$	4.65673	−	2.68856i	0.280811	−	0.162126i
$276$		0			0
$277$	0.106240	−	0.184013i	0.00638335	−	0.0110563i	−0.862816	−	0.505518i	$-0.831301\pi$
$277$	0.106240	−	0.184013i	0.00638335	−	0.0110563i	0.869199	+	0.494462i	$0.164635\pi$
$278$		0			0
$279$	−8.17266	−	4.71849i	−0.489285	−	0.282489i
$280$		0			0
$281$		−	20.2326i		−	1.20698i	−0.797371	−	0.603489i	$-0.793777\pi$
$281$		−	20.2326i		−	1.20698i	0.797371	−	0.603489i	$-0.206223\pi$
$282$		0			0
$283$	−10.1574	−	17.5931i	−0.603793	−	1.04580i	−0.992241	−	0.124330i	$-0.960322\pi$
$283$	−10.1574	−	17.5931i	−0.603793	−	1.04580i	0.388448	−	0.921471i	$-0.373011\pi$
$284$		0			0
$285$	−1.45151			−0.0859801
$286$		0			0
$287$	−2.18571			−0.129018
$288$		0			0
$289$	−10.0024	−	17.3246i	−0.588374	−	1.01909i
$290$		0			0
$291$			1.56653i			0.0918316i
$292$		0			0
$293$	−11.8479	−	6.84038i	−0.692161	−	0.399619i	0.112260	−	0.993679i	$-0.464191\pi$
$293$	−11.8479	−	6.84038i	−0.692161	−	0.399619i	−0.804421	+	0.594059i	$0.797524\pi$
$294$		0			0
$295$	−5.87665	+	10.1787i	−0.342152	+	0.592624i
$296$		0			0
$297$	25.6167	−	14.7898i	1.48643	−	0.858193i
$298$		0			0
$299$	5.54293	−	17.0342i	0.320556	−	0.985113i
$300$		0			0
$301$	−0.677476	+	0.391141i	−0.0390491	+	0.0225450i
$302$		0			0
$303$	−8.04580	+	13.9357i	−0.462219	+	0.800587i
$304$		0			0
$305$	−12.1847	−	7.03484i	−0.697694	−	0.402814i
$306$		0			0
$307$			9.17060i			0.523394i	0.965150	+	0.261697i	$0.0842821\pi$
$307$			9.17060i			0.523394i	−0.965150	+	0.261697i	$0.915718\pi$
$308$		0			0
$309$	0.0337455	+	0.0584490i	0.00191972	+	0.00332505i
$310$		0			0
$311$	19.7022			1.11721			0.558604	−	0.829435i	$-0.311337\pi$
$311$	19.7022			1.11721			0.558604	+	0.829435i	$0.311337\pi$
$312$		0			0
$313$	−18.7782			−1.06141			−0.530703	−	0.847558i	$-0.678072\pi$
$313$	−18.7782			−1.06141			−0.530703	+	0.847558i	$0.678072\pi$
$314$		0			0
$315$	1.97945	+	3.42850i	0.111529	+	0.193174i
$316$		0			0
$317$			16.5701i			0.930667i	0.885135	+	0.465334i	$0.154066\pi$
$317$			16.5701i			0.930667i	−0.885135	+	0.465334i	$0.845934\pi$
$318$		0			0
$319$	−49.8964	−	28.8077i	−2.79366	−	1.61292i
$320$		0			0
$321$	2.50121	−	4.33222i	0.139604	−	0.241801i
$322$		0			0
$323$	3.71172	−	2.14296i	0.206525	−	0.119238i
$324$		0			0
$325$	−2.21742	−	2.46485i	−0.123000	−	0.136725i
$326$		0			0
$327$	12.1438	−	7.01124i	0.671555	−	0.387722i
$328$		0			0
$329$	−2.63178	+	4.55838i	−0.145095	+	0.251312i
$330$		0			0
$331$	16.7899	+	9.69363i	0.922854	+	0.532810i	0.884545	−	0.466456i	$-0.154469\pi$
$331$	16.7899	+	9.69363i	0.922854	+	0.532810i	0.0383097	+	0.999266i	$0.487803\pi$
$332$		0			0
$333$		−	3.28782i		−	0.180171i
$334$		0			0
$335$	−11.2366	−	19.4624i	−0.613922	−	1.06334i
$336$		0			0
$337$	4.37084			0.238095			0.119047	−	0.992889i	$-0.462016\pi$
$337$	4.37084			0.238095			0.119047	+	0.992889i	$0.462016\pi$
$338$		0			0
$339$	2.98987			0.162388
$340$		0			0
$341$	−14.0786	−	24.3848i	−0.762396	−	1.32051i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$	−8.86421	−	5.11776i	−0.477233	−	0.275531i
$346$		0			0
$347$	−10.7824	+	18.6756i	−0.578828	+	1.00256i	0.416786	+	0.909005i	$0.363156\pi$
$347$	−10.7824	+	18.6756i	−0.578828	+	1.00256i	−0.995614	+	0.0935548i	$0.970177\pi$
$348$		0			0
$349$	16.6767	−	9.62828i	0.892682	−	0.515390i	0.0178632	−	0.999840i	$-0.494314\pi$
$349$	16.6767	−	9.62828i	0.892682	−	0.515390i	0.874819	+	0.484450i	$0.160980\pi$
$350$		0			0
$351$	−12.1981	−	13.5592i	−0.651085	−	0.723735i
$352$		0			0
$353$	7.66898	−	4.42769i	0.408179	−	0.235662i	−0.281828	−	0.959465i	$-0.590941\pi$
$353$	7.66898	−	4.42769i	0.408179	−	0.235662i	0.690007	+	0.723803i	$0.257607\pi$
$354$		0			0
$355$	−12.5794	+	21.7882i	−0.667646	+	1.15640i
$356$		0			0
$357$	5.37291	+	3.10205i	0.284365	+	0.164178i
$358$		0			0
$359$			24.2377i			1.27922i	0.768700	+	0.639609i	$0.220904\pi$
$359$			24.2377i			1.27922i	−0.768700	+	0.639609i	$0.779096\pi$
$360$		0			0
$361$	−9.25180	−	16.0246i	−0.486937	−	0.843399i
$362$		0			0
$363$	23.6552			1.24158
$364$		0			0
$365$	−23.1374			−1.21107
$366$		0			0
$367$	1.12828	+	1.95423i	0.0588955	+	0.102010i	0.893970	−	0.448127i	$-0.147909\pi$
$367$	1.12828	+	1.95423i	0.0588955	+	0.102010i	−0.835074	+	0.550137i	$0.814575\pi$
$368$		0			0
$369$			4.28363i			0.222997i
$370$		0			0
$371$	−8.69654	−	5.02095i	−0.451502	−	0.260675i
$372$		0			0
$373$	−1.00315	+	1.73750i	−0.0519409	+	0.0899643i	−0.890827	−	0.454343i	$-0.849874\pi$
$373$	−1.00315	+	1.73750i	−0.0519409	+	0.0899643i	0.838886	+	0.544307i	$0.183207\pi$
$374$		0			0
$375$	−10.5615	+	6.09766i	−0.545392	+	0.314882i
$376$		0			0
$377$	−10.9925	+	33.7816i	−0.566145	+	1.73984i
$378$		0			0
$379$	−4.46530	+	2.57804i	−0.229367	+	0.132425i	−0.610280	−	0.792186i	$-0.708943\pi$
$379$	−4.46530	+	2.57804i	−0.229367	+	0.132425i	0.380913	+	0.924611i	$0.375610\pi$
$380$		0			0
$381$	−2.92433	+	5.06509i	−0.149818	+	0.259492i
$382$		0			0
$383$	18.5542	+	10.7123i	0.948077	+	0.547373i	0.892483	−	0.451081i	$-0.148961\pi$
$383$	18.5542	+	10.7123i	0.948077	+	0.547373i	0.0555943	+	0.998453i	$0.482295\pi$
$384$		0			0
$385$			11.8122i			0.602003i
$386$		0			0
$387$	0.766573	+	1.32774i	0.0389671	+	0.0674930i
$388$		0			0
$389$	−24.3103			−1.23258			−0.616291	−	0.787518i	$-0.711366\pi$
$389$	−24.3103			−1.23258			−0.616291	+	0.787518i	$0.711366\pi$
$390$		0			0
$391$	30.2227			1.52843
$392$		0			0
$393$	−9.48757	−	16.4330i	−0.478585	−	0.828933i
$394$		0			0
$395$		−	2.12268i		−	0.106804i
$396$		0			0
$397$	1.43301	+	0.827347i	0.0719206	+	0.0415234i	0.535529	−	0.844517i	$-0.320112\pi$
$397$	1.43301	+	0.827347i	0.0719206	+	0.0415234i	−0.463608	+	0.886040i	$0.653446\pi$
$398$		0			0
$399$	−0.359283	+	0.622296i	−0.0179866	+	0.0311538i
$400$		0			0
$401$	3.33602	−	1.92605i	0.166593	−	0.0961825i	−0.414385	−	0.910102i	$-0.636003\pi$
$401$	3.33602	−	1.92605i	0.166593	−	0.0961825i	0.580978	+	0.813919i	$0.302670\pi$
$402$		0			0
$403$	−12.9071	+	11.6114i	−0.642947	+	0.578407i
$404$		0			0
$405$	1.26038	−	0.727683i	0.0626290	−	0.0361589i
$406$		0			0
$407$	4.90493	−	8.49559i	0.243129	−	0.421111i
$408$		0			0
$409$	20.7527	+	11.9816i	1.02615	+	0.592450i	0.915880	−	0.401451i	$-0.131494\pi$
$409$	20.7527	+	11.9816i	1.02615	+	0.592450i	0.110273	+	0.993901i	$0.464827\pi$
$410$		0			0
$411$			13.4582i			0.663846i
$412$		0			0
$413$	2.90921	+	5.03891i	0.143153	+	0.247948i
$414$		0			0
$415$	6.14909			0.301847
$416$		0			0
$417$	−12.3038			−0.602518
$418$		0			0
$419$	16.9634	+	29.3815i	0.828717	+	1.43538i	0.899045	+	0.437856i	$0.144262\pi$
$419$	16.9634	+	29.3815i	0.828717	+	1.43538i	−0.0703279	+	0.997524i	$0.522405\pi$
$420$		0			0
$421$		−	32.0785i		−	1.56341i	−0.623648	−	0.781705i	$-0.714350\pi$
$421$		−	32.0785i		−	1.56341i	0.623648	−	0.781705i	$-0.285650\pi$
$422$		0			0
$423$	8.93368	+	5.15786i	0.434370	+	0.250784i
$424$		0			0
$425$	2.79688	−	4.84434i	0.135669	−	0.234985i
$426$		0			0
$427$	−6.03200	+	3.48257i	−0.291909	+	0.168534i
$428$		0			0
$429$	−4.46157	−	21.0350i	−0.215407	−	1.01558i
$430$		0			0
$431$	4.66521	−	2.69346i	0.224715	−	0.129739i	−0.383416	−	0.923576i	$-0.625253\pi$
$431$	4.66521	−	2.69346i	0.224715	−	0.129739i	0.608132	+	0.793836i	$0.291919\pi$
$432$		0			0
$433$	−2.29422	+	3.97371i	−0.110253	+	0.190964i	−0.915872	−	0.401470i	$-0.868500\pi$
$433$	−2.29422	+	3.97371i	−0.110253	+	0.190964i	0.805619	+	0.592434i	$0.201833\pi$
$434$		0			0
$435$	17.5792	+	10.1494i	0.842858	+	0.486624i
$436$		0			0
$437$			3.50042i			0.167448i
$438$		0			0
$439$	−9.95016	−	17.2342i	−0.474895	−	0.822542i	0.524692	−	0.851292i	$-0.324181\pi$
$439$	−9.95016	−	17.2342i	−0.474895	−	0.822542i	−0.999587	+	0.0287501i	$0.990847\pi$
$440$		0			0
$441$	1.95984			0.0933256
$442$		0			0
$443$	−12.3708			−0.587757			−0.293878	−	0.955843i	$-0.594946\pi$
$443$	−12.3708			−0.587757			−0.293878	+	0.955843i	$0.594946\pi$
$444$		0			0
$445$	−1.56570	−	2.71187i	−0.0742213	−	0.128555i
$446$		0			0
$447$		−	24.1658i		−	1.14300i
$448$		0			0
$449$	15.8252	+	9.13666i	0.746835	+	0.431186i	0.824549	−	0.565790i	$-0.191429\pi$
$449$	15.8252	+	9.13666i	0.746835	+	0.431186i	−0.0777140	+	0.996976i	$0.524762\pi$
$450$		0			0
$451$	−6.39053	+	11.0687i	−0.300918	+	0.521206i
$452$		0			0
$453$	15.9117	−	9.18665i	0.747599	−	0.431627i
$454$		0			0
$455$	7.12476	−	1.51118i	0.334014	−	0.0708452i
$456$		0			0
$457$	23.4033	−	13.5119i	1.09476	−	0.632060i	0.159921	−	0.987130i	$-0.448876\pi$
$457$	23.4033	−	13.5119i	1.09476	−	0.632060i	0.934840	+	0.355069i	$0.115543\pi$
$458$		0			0
$459$	15.3857	−	26.6488i	0.718142	−	1.24386i
$460$		0			0
$461$	−18.4766	−	10.6675i	−0.860540	−	0.496833i	0.00365309	−	0.999993i	$-0.498837\pi$
$461$	−18.4766	−	10.6675i	−0.860540	−	0.496833i	−0.864193	+	0.503160i	$0.832171\pi$
$462$		0			0
$463$		−	22.2481i		−	1.03396i	−0.855998	−	0.516979i	$-0.827057\pi$
$463$		−	22.2481i		−	1.03396i	0.855998	−	0.516979i	$-0.172943\pi$
$464$		0			0
$465$	4.96007	+	8.59109i	0.230018	+	0.398402i
$466$		0			0
$467$	−39.4841			−1.82711			−0.913553	−	0.406719i	$-0.866673\pi$
$467$	−39.4841			−1.82711			−0.913553	+	0.406719i	$0.866673\pi$
$468$		0			0
$469$	−11.1253			−0.513718
$470$		0			0
$471$	6.79270	+	11.7653i	0.312991	+	0.542117i
$472$		0			0
$473$			4.57444i			0.210333i
$474$		0			0
$475$	0.561076	+	0.323937i	0.0257439	+	0.0148633i
$476$		0			0
$477$	−9.84025	+	17.0438i	−0.450554	+	0.780382i
$478$		0			0
$479$	32.4927	−	18.7597i	1.48463	−	0.857151i	0.484782	−	0.874635i	$-0.338899\pi$
$479$	32.4927	−	18.7597i	1.48463	−	0.857151i	0.999847	+	0.0174844i	$0.00556573\pi$
$480$		0			0
$481$	−5.75181	−	1.87164i	−0.262260	−	0.0853394i
$482$		0			0
$483$	−4.38820	+	2.53353i	−0.199670	+	0.115279i
$484$		0			0
$485$	−1.55136	+	2.68703i	−0.0704436	+	0.122012i
$486$		0			0
$487$	−4.59317	−	2.65187i	−0.208136	−	0.120168i	0.392309	−	0.919834i	$-0.371677\pi$
$487$	−4.59317	−	2.65187i	−0.208136	−	0.120168i	−0.600445	+	0.799666i	$0.705010\pi$
$488$		0			0
$489$			12.8815i			0.582521i
$490$		0			0
$491$	−16.3430	−	28.3069i	−0.737550	−	1.27747i	−0.953596	−	0.301090i	$-0.902649\pi$
$491$	−16.3430	−	28.3069i	−0.737550	−	1.27747i	0.216046	−	0.976383i	$-0.430684\pi$
$492$		0			0
$493$	−59.9366			−2.69941
$494$		0			0
$495$	23.1499			1.04051
$496$		0			0
$497$	6.22739	+	10.7862i	0.279337	+	0.483825i
$498$		0			0
$499$		−	11.9976i		−	0.537086i	−0.963268	−	0.268543i	$-0.913458\pi$
$499$		−	11.9976i		−	0.537086i	0.963268	−	0.268543i	$-0.0865421\pi$
$500$		0			0
$501$	−16.4168	−	9.47827i	−0.733451	−	0.423458i
$502$		0			0
$503$	−18.0640	+	31.2878i	−0.805435	+	1.39505i	0.110563	+	0.993869i	$0.464735\pi$
$503$	−18.0640	+	31.2878i	−0.805435	+	1.39505i	−0.915997	+	0.401184i	$0.868599\pi$
$504$		0			0
$505$	−27.6015	+	15.9357i	−1.22825	+	0.709131i
$506$		0			0
$507$	−12.1169	+	5.38219i	−0.538131	+	0.239031i
$508$		0			0
$509$	−7.09320	+	4.09526i	−0.314401	+	0.181519i	−0.648894	−	0.760879i	$-0.724768\pi$
$509$	−7.09320	+	4.09526i	−0.314401	+	0.181519i	0.334493	+	0.942398i	$0.391435\pi$
$510$		0			0
$511$	−5.72705	+	9.91954i	−0.253350	+	0.438815i
$512$		0			0
$513$	3.08649	+	1.78198i	0.136272	+	0.0786765i
$514$		0			0
$515$			0.133675i			0.00589042i
$516$		0			0
$517$	15.3895	+	26.6554i	0.676830	+	1.17230i
$518$		0			0
$519$	−7.35272			−0.322749
$520$		0			0
$521$	−22.0138			−0.964442			−0.482221	−	0.876050i	$-0.660170\pi$
$521$	−22.0138			−0.964442			−0.482221	+	0.876050i	$0.660170\pi$
$522$		0			0
$523$	−3.45843	−	5.99017i	−0.151226	−	0.261932i	0.780452	−	0.625215i	$-0.214989\pi$
$523$	−3.45843	−	5.99017i	−0.151226	−	0.261932i	−0.931679	+	0.363284i	$0.881656\pi$
$524$		0			0
$525$			0.937834i			0.0409304i
$526$		0			0
$527$	−25.3672	−	14.6457i	−1.10501	−	0.637979i
$528$		0			0
$529$	−0.841838	+	1.45811i	−0.0366016	+	0.0633959i
$530$		0			0
$531$	9.87544	−	5.70159i	0.428557	−	0.247428i
$532$		0			0
$533$	7.49391	+	2.43852i	0.324597	+	0.105624i
$534$		0			0
$535$	8.58052	−	4.95396i	0.370968	−	0.214179i
$536$		0			0
$537$	10.5773	−	18.3204i	0.456443	−	0.790583i
$538$		0			0
$539$	5.06414	+	2.92378i	0.218128	+	0.125936i
$540$		0			0
$541$			15.6696i			0.673690i	0.941560	+	0.336845i	$0.109360\pi$
$541$			15.6696i			0.673690i	−0.941560	+	0.336845i	$0.890640\pi$
$542$		0			0
$543$	7.78225	+	13.4793i	0.333968	+	0.578450i
$544$		0			0
$545$	27.7733			1.18968
$546$		0			0
$547$	−8.28824			−0.354379			−0.177190	−	0.984177i	$-0.556701\pi$
$547$	−8.28824			−0.354379			−0.177190	+	0.984177i	$0.556701\pi$
$548$		0			0
$549$	6.82528	+	11.8217i	0.291296	+	0.504539i
$550$		0			0
$551$		−	6.94192i		−	0.295736i
$552$		0			0
$553$	−0.910042	−	0.525413i	−0.0386989	−	0.0223428i
$554$		0			0
$555$	−1.72808	+	2.99312i	−0.0733527	+	0.127051i
$556$		0			0
$557$	33.9659	−	19.6102i	1.43918	−	0.830911i	0.441387	−	0.897317i	$-0.354486\pi$
$557$	33.9659	−	19.6102i	1.43918	−	0.830911i	0.997793	+	0.0664056i	$0.0211531\pi$
$558$		0			0
$559$	2.75918	−	0.585229i	0.116701	−	0.0247525i
$560$		0			0
$561$	31.4185	−	18.1395i	1.32649	−	0.765848i
$562$		0			0
$563$	−14.4692	+	25.0613i	−0.609803	+	1.05621i	0.381470	+	0.924381i	$0.375418\pi$
$563$	−14.4692	+	25.0613i	−0.609803	+	1.05621i	−0.991273	+	0.131828i	$0.957915\pi$
$564$		0			0
$565$	5.12845	+	2.96091i	0.215756	+	0.124567i
$566$		0			0
$567$		−	0.720474i		−	0.0302571i
$568$		0			0
$569$	−14.8904	−	25.7910i	−0.624240	−	1.08122i	−0.988687	−	0.149991i	$-0.952075\pi$
$569$	−14.8904	−	25.7910i	−0.624240	−	1.08122i	0.364448	−	0.931224i	$-0.381258\pi$
$570$		0			0
$571$	2.44165			0.102180			0.0510900	−	0.998694i	$-0.483730\pi$
$571$	2.44165			0.102180			0.0510900	+	0.998694i	$0.483730\pi$
$572$		0			0
$573$	3.25473			0.135968
$574$		0			0
$575$	2.28429	+	3.95650i	0.0952613	+	0.164997i
$576$		0			0
$577$		−	27.7941i		−	1.15708i	−0.815652	−	0.578542i	$-0.803622\pi$
$577$		−	27.7941i		−	1.15708i	0.815652	−	0.578542i	$-0.196378\pi$
$578$		0			0
$579$	9.22414	+	5.32556i	0.383342	+	0.221323i
$580$		0			0
$581$	1.52204	−	2.63626i	0.0631450	−	0.109370i
$582$		0			0
$583$	−50.8536	+	29.3603i	−2.10614	+	1.21598i
$584$		0			0
$585$	−2.96167	−	13.9634i	−0.122450	−	0.577314i
$586$		0			0
$587$	18.2317	−	10.5261i	0.752502	−	0.434457i	−0.0740954	−	0.997251i	$-0.523607\pi$
$587$	18.2317	−	10.5261i	0.752502	−	0.434457i	0.826597	+	0.562794i	$0.190274\pi$
$588$		0			0
$589$	1.69628	−	2.93805i	0.0698942	−	0.121060i
$590$		0			0
$591$	−3.04676	−	1.75905i	−0.125327	−	0.0723576i
$592$		0			0
$593$			8.12990i			0.333855i	0.985969	+	0.166927i	$0.0533846\pi$
$593$			8.12990i			0.333855i	−0.985969	+	0.166927i	$0.946615\pi$
$594$		0			0
$595$	6.14402	+	10.6418i	0.251880	+	0.436269i
$596$		0			0
$597$	5.09549			0.208545
$598$		0			0
$599$	18.1382			0.741105			0.370552	−	0.928812i	$-0.379168\pi$
$599$	18.1382			0.741105			0.370552	+	0.928812i	$0.379168\pi$
$600$		0			0
$601$	8.72037	+	15.1041i	0.355711	+	0.616110i	0.987239	−	0.159243i	$-0.0509053\pi$
$601$	8.72037	+	15.1041i	0.355711	+	0.616110i	−0.631528	+	0.775353i	$0.717572\pi$
$602$		0			0
$603$			21.8038i			0.887918i
$604$		0			0
$605$	40.5752	+	23.4261i	1.64962	+	0.952406i
$606$		0			0
$607$	3.03573	−	5.25803i	0.123216	−	0.213417i	−0.797818	−	0.602898i	$-0.794012\pi$
$607$	3.03573	−	5.25803i	0.123216	−	0.213417i	0.921034	+	0.389481i	$0.127346\pi$
$608$		0			0
$609$	8.70252	−	5.02440i	0.352644	−	0.203599i
$610$		0			0
$611$	14.1090	−	12.6927i	0.570787	−	0.513490i
$612$		0			0
$613$	−12.3808	+	7.14804i	−0.500054	+	0.288707i	−0.728736	−	0.684795i	$-0.759892\pi$
$613$	−12.3808	+	7.14804i	−0.500054	+	0.288707i	0.228682	+	0.973501i	$0.426559\pi$
$614$		0			0
$615$	2.25147	−	3.89967i	0.0907882	−	0.157250i
$616$		0			0
$617$	28.5296	+	16.4716i	1.14856	+	0.663120i	0.948535	−	0.316672i	$-0.102565\pi$
$617$	28.5296	+	16.4716i	1.14856	+	0.663120i	0.200022	+	0.979791i	$0.435899\pi$
$618$		0			0
$619$		−	14.2687i		−	0.573506i	−0.958005	−	0.286753i	$-0.907424\pi$
$619$		−	14.2687i		−	0.573506i	0.958005	−	0.286753i	$-0.0925759\pi$
$620$		0			0
$621$	12.5659	+	21.7647i	0.504251	+	0.873389i
$622$		0			0
$623$	−1.55019			−0.0621070
$624$		0			0
$625$	−19.5567			−0.782267
$626$		0			0
$627$	2.10093	+	3.63891i	0.0839030	+	0.145324i
$628$		0			0
$629$		−	10.2051i		−	0.406903i
$630$		0			0
$631$	20.4636	+	11.8147i	0.814644	+	0.470335i	0.848566	−	0.529090i	$-0.177466\pi$
$631$	20.4636	+	11.8147i	0.814644	+	0.470335i	−0.0339220	+	0.999424i	$0.510800\pi$
$632$		0			0
$633$	−11.5767	+	20.0514i	−0.460131	+	0.796970i
$634$		0			0
$635$	−10.0321	+	5.79202i	−0.398110	+	0.229849i
$636$		0			0
$637$	1.11567	−	3.42860i	0.0442043	−	0.135846i
$638$		0			0
$639$	21.1391	−	12.2047i	0.836251	−	0.482810i
$640$		0			0
$641$	−18.5168	+	32.0720i	−0.731368	+	1.26677i	0.224931	+	0.974375i	$0.427784\pi$
$641$	−18.5168	+	32.0720i	−0.731368	+	1.26677i	−0.956299	+	0.292392i	$0.905549\pi$
$642$		0			0
$643$	28.9127	+	16.6927i	1.14021	+	0.658298i	0.946481	−	0.322758i	$-0.104610\pi$
$643$	28.9127	+	16.6927i	1.14021	+	0.658298i	0.193724	+	0.981056i	$0.437943\pi$
$644$		0			0
$645$		−	1.61164i		−	0.0634583i
$646$		0			0
$647$	12.1505	+	21.0454i	0.477687	+	0.827379i	0.999673	−	0.0255756i	$-0.00814184\pi$
$647$	12.1505	+	21.0454i	0.477687	+	0.827379i	−0.521986	+	0.852954i	$0.674809\pi$
$648$		0			0
$649$	34.0236			1.33554
$650$		0			0
$651$	4.91093			0.192474
$652$		0			0
$653$	2.73619	+	4.73922i	0.107075	+	0.185460i	0.914584	−	0.404395i	$-0.132518\pi$
$653$	2.73619	+	4.73922i	0.107075	+	0.185460i	−0.807509	+	0.589856i	$0.799185\pi$
$654$		0			0
$655$		−	37.5828i		−	1.46848i
$656$		0			0
$657$	19.4407	+	11.2241i	0.758454	+	0.437893i
$658$		0			0
$659$	0.668430	−	1.15775i	0.0260383	−	0.0450997i	−0.852713	−	0.522380i	$-0.825044\pi$
$659$	0.668430	−	1.15775i	0.0260383	−	0.0450997i	0.878751	+	0.477281i	$0.158377\pi$
$660$		0			0
$661$	36.5902	−	21.1254i	1.42319	−	0.821682i	0.426624	−	0.904429i	$-0.359703\pi$
$661$	36.5902	−	21.1254i	1.42319	−	0.821682i	0.996571	+	0.0827471i	$0.0263694\pi$
$662$		0			0
$663$	−14.9607	−	16.6301i	−0.581026	−	0.645859i
$664$		0			0
$665$	−1.23254	+	0.711606i	−0.0477958	+	0.0275949i
$666$		0			0
$667$	24.4759	−	42.3935i	0.947711	−	1.64148i
$668$		0			0
$669$	7.79775	+	4.50204i	0.301479	+	0.174059i
$670$		0			0
$671$			40.7292i			1.57233i
$672$		0			0
$673$	−1.50029	−	2.59858i	−0.0578320	−	0.100168i	0.835660	−	0.549247i	$-0.185085\pi$
$673$	−1.50029	−	2.59858i	−0.0578320	−	0.100168i	−0.893492	+	0.449079i	$0.851752\pi$
$674$		0			0
$675$	4.65150			0.179036
$676$		0			0
$677$	−8.36881			−0.321639			−0.160820	−	0.986984i	$-0.551414\pi$
$677$	−8.36881			−0.321639			−0.160820	+	0.986984i	$0.551414\pi$
$678$		0			0
$679$	0.767994	+	1.33021i	0.0294729	+	0.0510486i
$680$		0			0
$681$			16.1038i			0.617100i
$682$		0			0
$683$	−27.4304	−	15.8369i	−1.04959	−	0.605984i	−0.127059	−	0.991895i	$-0.540554\pi$
$683$	−27.4304	−	15.8369i	−1.04959	−	0.605984i	−0.922536	+	0.385911i	$0.873887\pi$
$684$		0			0
$685$	−13.3279	+	23.0846i	−0.509233	+	0.882017i
$686$		0			0
$687$	−6.97457	+	4.02677i	−0.266097	+	0.153631i
$688$		0			0
$689$	24.2153	+	26.9173i	0.922528	+	1.02547i
$690$		0			0
$691$	−9.92153	+	5.72820i	−0.377433	+	0.217911i	−0.676701	−	0.736258i	$-0.736591\pi$
$691$	−9.92153	+	5.72820i	−0.377433	+	0.217911i	0.299268	+	0.954169i	$0.403258\pi$
$692$		0			0
$693$	5.73014	−	9.92489i	0.217670	−	0.377015i
$694$		0			0
$695$	−21.1044	−	12.1846i	−0.800534	−	0.462189i
$696$		0			0
$697$			13.2960i			0.503622i
$698$		0			0
$699$	−6.57033	−	11.3801i	−0.248513	−	0.430436i
$700$		0			0
$701$	34.2672			1.29426			0.647128	−	0.762382i	$-0.275970\pi$
$701$	34.2672			1.29426			0.647128	+	0.762382i	$0.275970\pi$
$702$		0			0
$703$	1.18196			0.0445786
$704$		0			0
$705$	−5.42194	−	9.39107i	−0.204202	−	0.353688i
$706$		0			0
$707$			15.7779i			0.593388i
$708$		0			0
$709$	33.3838	+	19.2742i	1.25376	+	0.723857i	0.971853	−	0.235586i	$-0.0757010\pi$
$709$	33.3838	+	19.2742i	1.25376	+	0.723857i	0.281903	+	0.959443i	$0.409034\pi$
$710$		0			0
$711$	−1.02972	+	1.78353i	−0.0386177	+	0.0668878i
$712$		0			0
$713$	20.7180	−	11.9616i	0.775896	−	0.447964i
$714$		0			0
$715$	13.1784	−	40.4991i	0.492845	−	1.51458i
$716$		0			0
$717$	−14.0447	+	8.10872i	−0.524509	+	0.302826i
$718$		0			0
$719$	16.6621	−	28.8596i	0.621392	−	1.07628i	−0.367834	−	0.929891i	$-0.619901\pi$
$719$	16.6621	−	28.8596i	0.621392	−	1.07628i	0.989227	−	0.146392i	$-0.0467660\pi$
$720$		0			0
$721$	0.0573094	+	0.0330876i	0.00213432	+	0.00123225i
$722$		0			0
$723$		−	24.7061i		−	0.918829i
$724$		0			0
$725$	−4.53011	−	7.84639i	−0.168244	−	0.291408i
$726$		0			0
$727$	−1.38332			−0.0513045			−0.0256523	−	0.999671i	$-0.508166\pi$
$727$	−1.38332			−0.0513045			−0.0256523	+	0.999671i	$0.508166\pi$
$728$		0			0
$729$	14.0651			0.520930
$730$		0			0
$731$	2.37937	+	4.12119i	0.0880042	+	0.152428i
$732$		0			0
$733$		−	1.82716i		−	0.0674877i	−0.999431	−	0.0337439i	$-0.989257\pi$
$733$		−	1.82716i		−	0.0674877i	0.999431	−	0.0337439i	$-0.0107430\pi$
$734$		0			0
$735$	−1.78417	−	1.03009i	−0.0658100	−	0.0379954i
$736$		0			0
$737$	−32.5279	+	56.3400i	−1.19818	+	2.07531i
$738$		0			0
$739$	−6.76651	+	3.90665i	−0.248910	+	0.143708i	−0.619265	−	0.785182i	$-0.712569\pi$
$739$	−6.76651	+	3.90665i	−0.248910	+	0.143708i	0.370355	+	0.928890i	$0.379236\pi$
$740$		0			0
$741$	1.92611	−	1.73276i	0.0707574	−	0.0636546i
$742$		0			0
$743$	−14.3038	+	8.25828i	−0.524754	+	0.302967i	−0.738878	−	0.673840i	$-0.764644\pi$
$743$	−14.3038	+	8.25828i	−0.524754	+	0.302967i	0.214123	+	0.976807i	$0.431311\pi$
$744$		0			0
$745$	23.9318	−	41.4510i	0.876792	−	1.51865i
$746$		0			0
$747$	−5.16663	−	2.98296i	−0.189037	−	0.109141i
$748$		0			0
$749$		−	4.90488i		−	0.179221i
$750$		0			0
$751$	−3.63615	−	6.29801i	−0.132685	−	0.229817i	0.792026	−	0.610488i	$-0.209027\pi$
$751$	−3.63615	−	6.29801i	−0.132685	−	0.229817i	−0.924711	+	0.380670i	$0.875693\pi$
$752$		0			0
$753$	−24.1066			−0.878494
$754$		0			0
$755$	36.3907			1.32439
$756$		0			0
$757$	−10.0239	−	17.3618i	−0.364324	−	0.631027i	0.624344	−	0.781150i	$-0.285366\pi$
$757$	−10.0239	−	17.3618i	−0.364324	−	0.631027i	−0.988667	+	0.150123i	$0.952033\pi$
$758$		0			0
$759$			29.6299i			1.07550i
$760$		0			0
$761$	−36.2244	−	20.9142i	−1.31313	−	0.758138i	−0.330520	−	0.943799i	$-0.607224\pi$
$761$	−36.2244	−	20.9142i	−1.31313	−	0.758138i	−0.982614	+	0.185661i	$0.940557\pi$
$762$		0			0
$763$	6.87455	−	11.9071i	0.248875	−	0.431065i
$764$		0			0
$765$	20.8561	−	12.0413i	0.754054	−	0.435353i
$766$		0			0
$767$	−4.35279	−	20.5221i	−0.157170	−	0.741010i
$768$		0			0
$769$	12.4644	−	7.19634i	0.449479	−	0.259507i	−0.258131	−	0.966110i	$-0.583107\pi$
$769$	12.4644	−	7.19634i	0.449479	−	0.259507i	0.707610	+	0.706603i	$0.249773\pi$
$770$		0			0
$771$	−4.45521	+	7.71664i	−0.160450	+	0.277908i
$772$		0			0
$773$	−0.184965	−	0.106790i	−0.00665272	−	0.00384095i	0.496670	−	0.867939i	$-0.334556\pi$
$773$	−0.184965	−	0.106790i	−0.00665272	−	0.00384095i	−0.503323	+	0.864099i	$0.667889\pi$
$774$		0			0
$775$		−	4.42780i		−	0.159051i
$776$		0			0
$777$	0.855478	+	1.48173i	0.0306901	+	0.0531568i
$778$		0			0
$779$	−1.53995			−0.0551746
$780$		0			0
$781$	72.8302			2.60607
$782$		0			0
$783$	−24.9202	−	43.1631i	−0.890576	−	1.54252i
$784$		0			0
$785$			26.9077i			0.960376i
$786$		0			0
$787$	−11.5580	−	6.67299i	−0.411996	−	0.237866i	0.279651	−	0.960102i	$-0.409781\pi$
$787$	−11.5580	−	6.67299i	−0.411996	−	0.237866i	−0.691647	+	0.722236i	$0.743115\pi$
$788$		0			0
$789$	3.78465	−	6.55520i	0.134737	−	0.233371i
$790$		0			0
$791$	2.53882	−	1.46579i	0.0902702	−	0.0521175i
$792$		0			0
$793$	24.5667	−	5.21066i	0.872389	−	0.185036i
$794$		0			0
$795$	17.9164	−	10.3441i	0.635430	−	0.366866i
$796$		0			0
$797$	21.3259	−	36.9376i	0.755403	−	1.30840i	−0.189770	−	0.981829i	$-0.560774\pi$
$797$	21.3259	−	36.9376i	0.755403	−	1.30840i	0.945174	−	0.326569i	$-0.105892\pi$
$798$		0			0
$799$	27.7293	+	16.0095i	0.980992	+	0.566376i
$800$		0			0
$801$			3.03812i			0.107347i
$802$		0			0
$803$	33.4893	+	58.0052i	1.18181	+	2.04696i
$804$		0			0
$805$	−10.0360			−0.353721
$806$		0			0
$807$	−28.8576			−1.01584
$808$		0			0
$809$	−19.1725	−	33.2077i	−0.674067	−	1.16752i	−0.976741	−	0.214425i	$-0.931212\pi$
$809$	−19.1725	−	33.2077i	−0.674067	−	1.16752i	0.302673	−	0.953094i	$-0.402121\pi$
$810$		0			0
$811$		−	16.6127i		−	0.583352i	−0.956517	−	0.291676i	$-0.905787\pi$
$811$		−	16.6127i		−	0.583352i	0.956517	−	0.291676i	$-0.0942129\pi$
$812$		0			0
$813$	−10.4472	−	6.03167i	−0.366398	−	0.211540i
$814$		0			0
$815$	−12.7567	+	22.0953i	−0.446849	+	0.773965i
$816$		0			0
$817$	−0.477320	+	0.275581i	−0.0166993	+	0.00964135i
$818$		0			0
$819$	−6.71950	−	2.18652i	−0.234798	−	0.0764033i
$820$		0			0
$821$	−14.8271	+	8.56041i	−0.517468	+	0.298760i	−0.735898	−	0.677092i	$-0.763240\pi$
$821$	−14.8271	+	8.56041i	−0.517468	+	0.298760i	0.218430	+	0.975853i	$0.429906\pi$
$822$		0			0
$823$	−18.9613	+	32.8419i	−0.660948	+	1.14480i	0.319419	+	0.947614i	$0.396512\pi$
$823$	−18.9613	+	32.8419i	−0.660948	+	1.14480i	−0.980367	+	0.197182i	$0.936821\pi$
$824$		0			0
$825$	4.74932	+	2.74202i	0.165350	+	0.0954650i
$826$		0			0
$827$			45.5918i			1.58538i	0.609624	+	0.792691i	$0.291321\pi$
$827$			45.5918i			1.58538i	−0.609624	+	0.792691i	$0.708679\pi$
$828$		0			0
$829$	−1.04770	−	1.81467i	−0.0363882	−	0.0630262i	0.847258	−	0.531182i	$-0.178252\pi$
$829$	−1.04770	−	1.81467i	−0.0363882	−	0.0630262i	−0.883646	+	0.468156i	$0.844919\pi$
$830$		0			0
$831$	0.216705			0.00751742
$832$		0			0
$833$	6.08315			0.210769
$834$		0			0
$835$	−18.7729	−	32.5157i	−0.649665	−	1.12525i
$836$		0			0
$837$		−	24.3574i		−	0.841915i
$838$		0			0
$839$	−14.3831	−	8.30408i	−0.496560	−	0.286689i	0.230732	−	0.973017i	$-0.425888\pi$
$839$	−14.3831	−	8.30408i	−0.496560	−	0.286689i	−0.727292	+	0.686329i	$0.759221\pi$
$840$		0			0
$841$	−34.0398	+	58.9586i	−1.17378	+	2.03305i
$842$		0			0
$843$	17.8704	−	10.3175i	0.615489	−	0.355353i
$844$		0			0
$845$	−26.1139	−	2.76762i	−0.898346	−	0.0952091i
$846$		0			0
$847$	20.0866	−	11.5970i	0.690184	−	0.398478i
$848$		0			0
$849$	10.3593	−	17.9429i	0.355532	−	0.615799i
$850$		0			0
$851$	7.21811	+	4.16738i	0.247434	+	0.142856i
$852$		0			0
$853$			12.2314i			0.418795i	0.977831	+	0.209397i	$0.0671502\pi$
$853$			12.2314i			0.418795i	−0.977831	+	0.209397i	$0.932850\pi$
$854$		0			0
$855$	1.39463	+	2.41557i	0.0476954	+	0.0826109i
$856$		0			0
$857$	50.3302			1.71925			0.859623	−	0.510929i	$-0.170699\pi$
$857$	50.3302			1.71925			0.859623	+	0.510929i	$0.170699\pi$
$858$		0			0
$859$	−51.4997			−1.75715			−0.878573	−	0.477608i	$-0.841504\pi$
$859$	−51.4997			−1.75715			−0.878573	+	0.477608i	$0.841504\pi$
$860$		0			0
$861$	−1.11458	−	1.93052i	−0.0379849	−	0.0657918i
$862$		0			0
$863$			2.82545i			0.0961793i	0.998843	+	0.0480896i	$0.0153133\pi$
$863$			2.82545i			0.0961793i	−0.998843	+	0.0480896i	$0.984687\pi$
$864$		0			0
$865$	−12.6120	−	7.28151i	−0.428819	−	0.247579i
$866$		0			0
$867$	10.2012	−	17.6691i	0.346453	−	0.600073i
$868$		0			0
$869$	−5.32153	+	3.07239i	−0.180520	+	0.104224i
$870$		0			0
$871$	38.1442	+	12.4121i	1.29247	+	0.420569i
$872$		0			0
$873$	2.60699	−	1.50514i	0.0882331	−	0.0509414i
$874$		0			0
$875$	−5.97878	+	10.3556i	−0.202120	+	0.350082i
$876$		0			0
$877$	9.67508	+	5.58591i	0.326704	+	0.188623i	0.654377	−	0.756169i	$-0.272931\pi$
$877$	9.67508	+	5.58591i	0.326704	+	0.188623i	−0.327673	+	0.944791i	$0.606264\pi$
$878$		0			0
$879$		−	13.9528i		−	0.470616i
$880$		0			0
$881$	−10.8598	−	18.8098i	−0.365877	−	0.633718i	0.623039	−	0.782190i	$-0.285898\pi$
$881$	−10.8598	−	18.8098i	−0.365877	−	0.633718i	−0.988916	+	0.148473i	$0.952564\pi$
$882$		0			0
$883$	48.0644			1.61750			0.808748	−	0.588155i	$-0.200146\pi$
$883$	48.0644			1.61750			0.808748	+	0.588155i	$0.200146\pi$
$884$		0			0
$885$	−11.9870			−0.402938
$886$		0			0
$887$	16.6014	+	28.7544i	0.557420	+	0.965480i	0.997711	+	0.0676244i	$0.0215419\pi$
$887$	16.6014	+	28.7544i	0.557420	+	0.965480i	−0.440291	+	0.897855i	$0.645125\pi$
$888$		0			0
$889$			5.73463i			0.192333i
$890$		0			0
$891$	−3.64858	−	2.10651i	−0.122232	−	0.0705707i
$892$		0			0
$893$	−1.85424	+	3.21163i	−0.0620497	+	0.107473i
$894$		0			0
$895$	36.2859	−	20.9497i	1.21290	−	0.700271i
$896$		0			0
$897$	17.8719	−	3.79068i	0.596727	−	0.126567i
$898$		0			0
$899$	−41.0873	+	23.7218i	−1.37034	+	0.791165i
$900$		0			0
$901$	−30.5432	+	52.9024i	−1.01754	+	1.76243i
$902$		0			0
$903$	−0.690947	−	0.398918i	−0.0229933	−	0.0132752i
$904$		0			0
$905$			30.8275i			1.02474i
$906$		0			0
$907$	8.44403	+	14.6255i	0.280379	+	0.485631i	0.971478	−	0.237129i	$-0.0762064\pi$
$907$	8.44403	+	14.6255i	0.280379	+	0.485631i	−0.691099	+	0.722760i	$0.742873\pi$
$908$		0			0
$909$	30.9221			1.02562
$910$		0			0
$911$	−3.77644			−0.125119			−0.0625595	−	0.998041i	$-0.519926\pi$
$911$	−3.77644			−0.125119			−0.0625595	+	0.998041i	$0.519926\pi$
$912$		0			0
$913$	−8.90024	−	15.4157i	−0.294555	−	0.510184i
$914$		0			0
$915$		−	14.3494i		−	0.474378i
$916$		0			0
$917$	−16.1126	−	9.30260i	−0.532084	−	0.307199i
$918$		0			0
$919$	−24.8491	+	43.0399i	−0.819696	+	1.41976i	0.0862102	+	0.996277i	$0.472524\pi$
$919$	−24.8491	+	43.0399i	−0.819696	+	1.41976i	−0.905906	+	0.423478i	$0.860809\pi$
$920$		0			0
$921$	−8.09989	+	4.67647i	−0.266900	+	0.154095i
$922$		0			0
$923$	−9.31748	−	43.9291i	−0.306689	−	1.44594i
$924$		0			0
$925$	1.33596	−	0.771318i	0.0439262	−	0.0253608i
$926$		0			0
$927$	0.0648464	−	0.112317i	0.00212983	−	0.00368898i
$928$		0			0
$929$	−35.5455	−	20.5222i	−1.16621	−	0.673311i	−0.213425	−	0.976959i	$-0.568462\pi$
$929$	−35.5455	−	20.5222i	−1.16621	−	0.673311i	−0.952784	+	0.303648i	$0.901795\pi$
$930$		0			0
$931$			0.704556i			0.0230909i
$932$		0			0
$933$	10.0470	+	17.4018i	0.328923	+	0.569711i
$934$		0			0
$935$	71.8551			2.34991
$936$		0			0
$937$	24.0211			0.784735			0.392368	−	0.919808i	$-0.371656\pi$
$937$	24.0211			0.784735			0.392368	+	0.919808i	$0.371656\pi$
$938$		0			0
$939$	−9.57579	−	16.5857i	−0.312494	−	0.541255i
$940$		0			0
$941$		−	30.9571i		−	1.00917i	−0.863361	−	0.504586i	$-0.831645\pi$
$941$		−	30.9571i		−	1.00917i	0.863361	−	0.504586i	$-0.168355\pi$
$942$		0			0
$943$	−9.40433	−	5.42959i	−0.306247	−	0.176812i
$944$		0			0
$945$	−5.10907	+	8.84917i	−0.166198	+	0.287864i
$946$		0			0
$947$	49.4060	−	28.5246i	1.60548	−	0.926924i	0.615115	−	0.788437i	$-0.289109\pi$
$947$	49.4060	−	28.5246i	1.60548	−	0.926924i	0.990364	−	0.138487i	$-0.0442239\pi$
$948$		0			0
$949$	30.7027	−	27.6207i	0.996650	−	0.896604i
$950$		0			0
$951$	−14.6354	+	8.44977i	−0.474586	+	0.274002i
$952$		0			0
$953$	−21.7078	+	37.5989i	−0.703183	+	1.21795i	0.264160	+	0.964479i	$0.414905\pi$
$953$	−21.7078	+	37.5989i	−0.703183	+	1.21795i	−0.967343	+	0.253470i	$0.918428\pi$
$954$		0			0
$955$	5.58277	+	3.22321i	0.180654	+	0.104301i
$956$		0			0
$957$		−	58.7610i		−	1.89947i
$958$		0			0
$959$	6.59793	+	11.4279i	0.213058	+	0.369028i
$960$		0			0
$961$	7.81399			0.252064
$962$		0			0
$963$	−9.61278			−0.309767
$964$		0			0
$965$	10.5480	+	18.2696i	0.339551	+	0.588119i
$966$		0			0
$967$			26.4842i			0.851675i	0.904800	+	0.425837i	$0.140020\pi$
$967$			26.4842i			0.851675i	−0.904800	+	0.425837i	$0.859980\pi$
$968$		0			0
$969$	3.78552	+	2.18557i	0.121608	+	0.0702106i
$970$		0			0
$971$	−0.686676	+	1.18936i	−0.0220365	+	0.0381683i	−0.876833	−	0.480794i	$-0.840348\pi$
$971$	−0.686676	+	1.18936i	−0.0220365	+	0.0381683i	0.854797	+	0.518963i	$0.173682\pi$
$972$		0			0
$973$	−10.4476	+	6.03195i	−0.334936	+	0.193375i
$974$		0			0
$975$	1.04631	−	3.21546i	0.0335087	−	0.102977i
$976$		0			0
$977$	5.57241	−	3.21723i	0.178277	−	0.102928i	−0.408206	−	0.912890i	$-0.633845\pi$
$977$	5.57241	−	3.21723i	0.178277	−	0.102928i	0.586483	+	0.809962i	$0.300512\pi$
$978$		0			0
$979$	−4.53241	+	7.85036i	−0.144856	+	0.250899i
$980$		0			0
$981$	−23.3359	−	13.4730i	−0.745058	−	0.430159i
$982$		0			0
$983$		−	25.2739i		−	0.806113i	−0.915175	−	0.403056i	$-0.867948\pi$
$983$		−	25.2739i		−	0.806113i	0.915175	−	0.403056i	$-0.132052\pi$
$984$		0			0
$985$	−3.48403	−	6.03451i	−0.111010	−	0.192276i
$986$		0			0
$987$	−5.36822			−0.170872
$988$		0			0
$989$	−3.88659			−0.123586
$990$		0			0
$991$	24.2738	+	42.0434i	0.771082	+	1.33555i	0.936970	+	0.349409i	$0.113618\pi$
$991$	24.2738	+	42.0434i	0.771082	+	1.33555i	−0.165888	+	0.986145i	$0.553049\pi$
$992$		0			0
$993$			19.7728i			0.627469i
$994$		0			0
$995$	8.74018	+	5.04614i	0.277082	+	0.159973i
$996$		0			0
$997$	9.21146	−	15.9547i	0.291730	−	0.505291i	−0.682489	−	0.730896i	$-0.739102\pi$
$997$	9.21146	−	15.9547i	0.291730	−	0.505291i	0.974219	+	0.225605i	$0.0724358\pi$
$998$		0			0
$999$	7.34915	−	4.24303i	0.232517	−	0.134244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.g.673.8		24
4.3	odd	2		728.2.bm.c.673.5	yes	24
13.4	even	6	inner	1456.2.cc.g.225.8		24
52.11	even	12		9464.2.a.bm.1.8		12
52.15	even	12		9464.2.a.bl.1.8		12
52.43	odd	6		728.2.bm.c.225.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.bm.c.225.5	✓	24	52.43	odd	6
728.2.bm.c.673.5	yes	24	4.3	odd	2
1456.2.cc.g.225.8		24	13.4	even	6	inner
1456.2.cc.g.673.8		24	1.1	even	1	trivial
9464.2.a.bl.1.8		12	52.15	even	12
9464.2.a.bm.1.8		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)

\(f(q)\)	\(=\)	\(q+(0.509942 + 0.883245i) q^{3} +2.02001i q^{5} +(0.866025 + 0.500000i) q^{7} +(0.979919 - 1.69727i) q^{9} +(5.06414 - 2.92378i) q^{11} +(-2.41142 - 2.68049i) q^{13} +(-1.78417 + 1.03009i) q^{15} +(3.04158 - 5.26816i) q^{17} +(0.610163 + 0.352278i) q^{19} +1.01988i q^{21} +(2.48413 + 4.30265i) q^{23} +0.919550 q^{25} +5.05846 q^{27} +(-4.92645 - 8.53286i) q^{29} -4.81518i q^{31} +(5.16483 + 2.98192i) q^{33} +(-1.01001 + 1.74938i) q^{35} +(1.45284 - 0.838799i) q^{37} +(1.13785 - 3.49677i) q^{39} +(-1.89288 + 1.09285i) q^{41} +(-0.391141 + 0.677476i) q^{43} +(3.42850 + 1.97945i) q^{45} +5.26356i q^{47} +(0.500000 + 0.866025i) q^{49} +6.20411 q^{51} -10.0419 q^{53} +(5.90608 + 10.2296i) q^{55} +0.718565i q^{57} +(5.03891 + 2.90921i) q^{59} +(-3.48257 + 6.03200i) q^{61} +(1.69727 - 0.979919i) q^{63} +(5.41463 - 4.87110i) q^{65} +(-9.63479 + 5.56265i) q^{67} +(-2.53353 + 4.38820i) q^{69} +(10.7862 + 6.22739i) q^{71} +11.4541i q^{73} +(0.468917 + 0.812188i) q^{75} +5.84756 q^{77} -1.05083 q^{79} +(-0.360237 - 0.623949i) q^{81} -3.04409i q^{83} +(10.6418 + 6.14402i) q^{85} +(5.02440 - 8.70252i) q^{87} +(-1.34250 + 0.775094i) q^{89} +(-0.748104 - 3.52709i) q^{91} +(4.25299 - 2.45546i) q^{93} +(-0.711606 + 1.23254i) q^{95} +(1.33021 + 0.767994i) q^{97} -11.4603i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} - 18 q^{9} - 12 q^{11} + 8 q^{17} + 12 q^{19} - 2 q^{23} - 28 q^{25} + 20 q^{27} + 2 q^{29} - 18 q^{33} + 8 q^{35} + 60 q^{37} - 18 q^{39} - 6 q^{41} - 24 q^{43} - 72 q^{45} + 12 q^{49} + 72 q^{51}+ \cdots - 54 q^{97}+O(q^{100}) \) 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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