LMFDB - Embedded newform 756.2.e.a.323.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("756.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.2
Character	$\chi$	$=$	756.323
Dual form			756.2.e.a.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40635 + 0.148963i) q^{2} +(1.95562 - 0.418986i) q^{4} -1.05610i q^{5} +1.00000i q^{7} +(-2.68787 + 0.880554i) q^{8} +O(q^{10})$	\(q+(-1.40635 + 0.148963i) q^{2} +(1.95562 - 0.418986i) q^{4} -1.05610i q^{5} +1.00000i q^{7} +(-2.68787 + 0.880554i) q^{8} +(0.157319 + 1.48524i) q^{10} -0.870034 q^{11} +2.65138 q^{13} +(-0.148963 - 1.40635i) q^{14} +(3.64890 - 1.63876i) q^{16} +1.50401i q^{17} +3.94077i q^{19} +(-0.442490 - 2.06532i) q^{20} +(1.22357 - 0.129603i) q^{22} +3.92908 q^{23} +3.88466 q^{25} +(-3.72876 + 0.394957i) q^{26} +(0.418986 + 1.95562i) q^{28} -0.285909i q^{29} +0.345489i q^{31} +(-4.88751 + 2.84821i) q^{32} +(-0.224042 - 2.11517i) q^{34} +1.05610 q^{35} +3.07212 q^{37} +(-0.587027 - 5.54208i) q^{38} +(0.929950 + 2.83864i) q^{40} -7.74051i q^{41} -8.68571i q^{43} +(-1.70146 + 0.364532i) q^{44} +(-5.52564 + 0.585286i) q^{46} +7.32132 q^{47} -1.00000 q^{49} +(-5.46318 + 0.578670i) q^{50} +(5.18510 - 1.11089i) q^{52} +14.4009i q^{53} +0.918840i q^{55} +(-0.880554 - 2.68787i) q^{56} +(0.0425898 + 0.402087i) q^{58} +10.7614 q^{59} -3.78816 q^{61} +(-0.0514650 - 0.485878i) q^{62} +(6.44925 - 4.73362i) q^{64} -2.80012i q^{65} +5.17110i q^{67} +(0.630161 + 2.94128i) q^{68} +(-1.48524 + 0.157319i) q^{70} +7.45460 q^{71} +5.01831 q^{73} +(-4.32047 + 0.457632i) q^{74} +(1.65113 + 7.70664i) q^{76} -0.870034i q^{77} -6.95925i q^{79} +(-1.73068 - 3.85359i) q^{80} +(1.15305 + 10.8858i) q^{82} +12.7140 q^{83} +1.58838 q^{85} +(1.29385 + 12.2151i) q^{86} +(2.33854 - 0.766112i) q^{88} +14.9938i q^{89} +2.65138i q^{91} +(7.68378 - 1.64623i) q^{92} +(-10.2963 + 1.09060i) q^{94} +4.16183 q^{95} +8.02538 q^{97} +(1.40635 - 0.148963i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{4}+O(q^{10}) $ 24 * q - 8 * q^4	$ 24 q - 8 q^{4} - 16 q^{10} + 8 q^{16} + 16 q^{22} - 24 q^{25} - 8 q^{28} - 8 q^{34} + 16 q^{37} - 8 q^{40} - 24 q^{49} - 8 q^{52} + 32 q^{58} - 80 q^{61} + 40 q^{64} - 24 q^{70} - 32 q^{82} + 56 q^{85} + 56 q^{88} + 72 q^{94}+O(q^{100}) $ 24 * q - 8 * q^4 - 16 * q^10 + 8 * q^16 + 16 * q^22 - 24 * q^25 - 8 * q^28 - 8 * q^34 + 16 * q^37 - 8 * q^40 - 24 * q^49 - 8 * q^52 + 32 * q^58 - 80 * q^61 + 40 * q^64 - 24 * q^70 - 32 * q^82 + 56 * q^85 + 56 * q^88 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.40635	+	0.148963i	−0.994437	+	0.105333i
$2$	−1.40635	+	0.148963i	−0.994437	+	0.105333i
$3$		0			0
$3$		0			0
$4$	1.95562	−	0.418986i	0.977810	−	0.209493i
$5$		−	1.05610i		−	0.472300i	−0.971717	−	0.236150i	$-0.924114\pi$
$5$		−	1.05610i		−	0.472300i	0.971717	−	0.236150i	$-0.0758858\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−2.68787	+	0.880554i	−0.950304	+	0.311323i
$9$		0			0
$10$	0.157319	+	1.48524i	0.0497486	+	0.469673i
$11$	−0.870034			−0.262325			−0.131163	−	0.991361i	$-0.541871\pi$
$11$	−0.870034			−0.262325			−0.131163	+	0.991361i	$0.541871\pi$
$12$		0			0
$13$	2.65138			0.735361			0.367681	−	0.929952i	$-0.380152\pi$
$13$	2.65138			0.735361			0.367681	+	0.929952i	$0.380152\pi$
$14$	−0.148963	−	1.40635i	−0.0398120	−	0.375862i
$15$		0			0
$16$	3.64890	−	1.63876i	0.912225	−	0.409689i
$17$			1.50401i			0.364777i	0.983227	+	0.182389i	$0.0583829\pi$
$17$			1.50401i			0.364777i	−0.983227	+	0.182389i	$0.941617\pi$
$18$		0			0
$19$			3.94077i			0.904074i	0.891999	+	0.452037i	$0.149302\pi$
$19$			3.94077i			0.904074i	−0.891999	+	0.452037i	$0.850698\pi$
$20$	−0.442490	−	2.06532i	−0.0989437	−	0.461820i
$21$		0			0
$22$	1.22357	−	0.129603i	0.260866	−	0.0276314i
$23$	3.92908			0.819269			0.409635	−	0.912250i	$-0.365656\pi$
$23$	3.92908			0.819269			0.409635	+	0.912250i	$0.365656\pi$
$24$		0			0
$25$	3.88466			0.776932
$26$	−3.72876	+	0.394957i	−0.731271	+	0.0774575i
$27$		0			0
$28$	0.418986	+	1.95562i	0.0791810	+	0.369577i
$29$		−	0.285909i		−	0.0530920i	−0.999648	−	0.0265460i	$-0.991549\pi$
$29$		−	0.285909i		−	0.0530920i	0.999648	−	0.0265460i	$-0.00845084\pi$
$30$		0			0
$31$			0.345489i			0.0620517i	0.999519	+	0.0310259i	$0.00987742\pi$
$31$			0.345489i			0.0620517i	−0.999519	+	0.0310259i	$0.990123\pi$
$32$	−4.88751	+	2.84821i	−0.863997	+	0.503497i
$33$		0			0
$34$	−0.224042	−	2.11517i	−0.0384229	−	0.362748i
$35$	1.05610			0.178513
$36$		0			0
$37$	3.07212			0.505054			0.252527	−	0.967590i	$-0.418738\pi$
$37$	3.07212			0.505054			0.252527	+	0.967590i	$0.418738\pi$
$38$	−0.587027	−	5.54208i	−0.0952284	−	0.899045i
$39$		0			0
$40$	0.929950	+	2.83864i	0.147038	+	0.448829i
$41$		−	7.74051i		−	1.20886i	−0.796657	−	0.604432i	$-0.793400\pi$
$41$		−	7.74051i		−	1.20886i	0.796657	−	0.604432i	$-0.206600\pi$
$42$		0			0
$43$		−	8.68571i		−	1.32456i	−0.749257	−	0.662279i	$-0.769589\pi$
$43$		−	8.68571i		−	1.32456i	0.749257	−	0.662279i	$-0.230411\pi$
$44$	−1.70146	+	0.364532i	−0.256504	+	0.0549553i
$45$		0			0
$46$	−5.52564	+	0.585286i	−0.814712	+	0.0862957i
$47$	7.32132			1.06792			0.533962	−	0.845508i	$-0.320702\pi$
$47$	7.32132			1.06792			0.533962	+	0.845508i	$0.320702\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−5.46318	+	0.578670i	−0.772610	+	0.0818362i
$51$		0			0
$52$	5.18510	−	1.11089i	0.719044	−	0.154053i
$53$			14.4009i			1.97811i	0.147544	+	0.989055i	$0.452863\pi$
$53$			14.4009i			1.97811i	−0.147544	+	0.989055i	$0.547137\pi$
$54$		0			0
$55$			0.918840i			0.123896i
$56$	−0.880554	−	2.68787i	−0.117669	−	0.359181i
$57$		0			0
$58$	0.0425898	+	0.402087i	0.00559231	+	0.0527966i
$59$	10.7614			1.40102			0.700509	−	0.713644i	$-0.252956\pi$
$59$	10.7614			1.40102			0.700509	+	0.713644i	$0.252956\pi$
$60$		0			0
$61$	−3.78816			−0.485024			−0.242512	−	0.970148i	$-0.577971\pi$
$61$	−3.78816			−0.485024			−0.242512	+	0.970148i	$0.577971\pi$
$62$	−0.0514650	−	0.485878i	−0.00653606	−	0.0617065i
$63$		0			0
$64$	6.44925	−	4.73362i	0.806156	−	0.591703i
$65$		−	2.80012i		−	0.347312i
$66$		0			0
$67$			5.17110i			0.631750i	0.948801	+	0.315875i	$0.102298\pi$
$67$			5.17110i			0.631750i	−0.948801	+	0.315875i	$0.897702\pi$
$68$	0.630161	+	2.94128i	0.0764183	+	0.356683i
$69$		0			0
$70$	−1.48524	+	0.157319i	−0.177520	+	0.0188032i
$71$	7.45460			0.884698			0.442349	−	0.896843i	$-0.354145\pi$
$71$	7.45460			0.884698			0.442349	+	0.896843i	$0.354145\pi$
$72$		0			0
$73$	5.01831			0.587348			0.293674	−	0.955906i	$-0.405122\pi$
$73$	5.01831			0.587348			0.293674	+	0.955906i	$0.405122\pi$
$74$	−4.32047	+	0.457632i	−0.502244	+	0.0531986i
$75$		0			0
$76$	1.65113	+	7.70664i	0.189397	+	0.884013i
$77$		−	0.870034i		−	0.0991496i
$78$		0			0
$79$		−	6.95925i		−	0.782977i	−0.920183	−	0.391489i	$-0.871960\pi$
$79$		−	6.95925i		−	0.782977i	0.920183	−	0.391489i	$-0.128040\pi$
$80$	−1.73068	−	3.85359i	−0.193496	−	0.430844i
$81$		0			0
$82$	1.15305	+	10.8858i	0.127333	+	1.20214i
$83$	12.7140			1.39554			0.697769	−	0.716323i	$-0.254176\pi$
$83$	12.7140			1.39554			0.697769	+	0.716323i	$0.254176\pi$
$84$		0			0
$85$	1.58838			0.172284
$86$	1.29385	+	12.2151i	0.139519	+	1.31719i
$87$		0			0
$88$	2.33854	−	0.766112i	0.249289	−	0.0816679i
$89$			14.9938i			1.58934i	0.607043	+	0.794669i	$0.292356\pi$
$89$			14.9938i			1.58934i	−0.607043	+	0.794669i	$0.707644\pi$
$90$		0			0
$91$			2.65138i			0.277940i
$92$	7.68378	−	1.64623i	0.801090	−	0.171631i
$93$		0			0
$94$	−10.2963	+	1.09060i	−1.06198	+	0.112487i
$95$	4.16183			0.426995
$96$		0			0
$97$	8.02538			0.814854			0.407427	−	0.913238i	$-0.366426\pi$
$97$	8.02538			0.814854			0.407427	+	0.913238i	$0.366426\pi$
$98$	1.40635	−	0.148963i	0.142062	−	0.0150475i
$99$		0			0
$100$	7.59692	−	1.62762i	0.759692	−	0.162762i
$101$			0.496004i			0.0493542i	0.999695	+	0.0246771i	$0.00785576\pi$
$101$			0.496004i			0.0493542i	−0.999695	+	0.0246771i	$0.992144\pi$
$102$		0			0
$103$			10.8982i			1.07383i	0.843635	+	0.536917i	$0.180411\pi$
$103$			10.8982i			1.07383i	−0.843635	+	0.536917i	$0.819589\pi$
$104$	−7.12656	+	2.33469i	−0.698817	+	0.228935i
$105$		0			0
$106$	−2.14519	−	20.2526i	−0.208359	−	1.96711i
$107$	5.82236			0.562869			0.281434	−	0.959580i	$-0.409190\pi$
$107$	5.82236			0.562869			0.281434	+	0.959580i	$0.409190\pi$
$108$		0			0
$109$	−8.42089			−0.806575			−0.403287	−	0.915073i	$-0.632132\pi$
$109$	−8.42089			−0.806575			−0.403287	+	0.915073i	$0.632132\pi$
$110$	−0.136873	−	1.29221i	−0.0130503	−	0.123207i
$111$		0			0
$112$	1.63876	+	3.64890i	0.154848	+	0.344789i
$113$		−	15.5050i		−	1.45859i	−0.684198	−	0.729296i	$-0.739848\pi$
$113$		−	15.5050i		−	1.45859i	0.684198	−	0.729296i	$-0.260152\pi$
$114$		0			0
$115$		−	4.14948i		−	0.386941i
$116$	−0.119792	−	0.559129i	−0.0111224	−	0.0519139i
$117$		0			0
$118$	−15.1343	+	1.60305i	−1.39322	+	0.147573i
$119$	−1.50401			−0.137873
$120$		0			0
$121$	−10.2430			−0.931186
$122$	5.32746	−	0.564294i	0.482326	−	0.0510888i
$123$		0			0
$124$	0.144755	+	0.675646i	0.0129994	+	0.0606748i
$125$		−	9.38306i		−	0.839246i
$126$		0			0
$127$		−	11.1094i		−	0.985799i	−0.870086	−	0.492900i	$-0.835937\pi$
$127$		−	11.1094i		−	0.985799i	0.870086	−	0.492900i	$-0.164063\pi$
$128$	−8.36474	+	7.61781i	−0.739346	+	0.673326i
$129$		0			0
$130$	0.417113	+	3.93793i	0.0365832	+	0.345379i
$131$	−11.0139			−0.962291			−0.481145	−	0.876641i	$-0.659779\pi$
$131$	−11.0139			−0.962291			−0.481145	+	0.876641i	$0.659779\pi$
$132$		0			0
$133$	−3.94077			−0.341708
$134$	−0.770301	−	7.27235i	−0.0665438	−	0.628236i
$135$		0			0
$136$	−1.32437	−	4.04259i	−0.113563	−	0.346649i
$137$			10.1565i			0.867732i	0.900977	+	0.433866i	$0.142851\pi$
$137$			10.1565i			0.867732i	−0.900977	+	0.433866i	$0.857149\pi$
$138$		0			0
$139$			9.01304i			0.764476i	0.924064	+	0.382238i	$0.124847\pi$
$139$			9.01304i			0.764476i	−0.924064	+	0.382238i	$0.875153\pi$
$140$	2.06532	−	0.442490i	0.174552	−	0.0373972i
$141$		0			0
$142$	−10.4837	+	1.11046i	−0.879776	+	0.0931875i
$143$	−2.30679			−0.192904
$144$		0			0
$145$	−0.301947			−0.0250754
$146$	−7.05748	+	0.747541i	−0.584081	+	0.0618669i
$147$		0			0
$148$	6.00791	−	1.28718i	0.493847	−	0.105805i
$149$		−	18.0769i		−	1.48092i	−0.672103	−	0.740458i	$-0.734609\pi$
$149$		−	18.0769i		−	1.48092i	0.672103	−	0.740458i	$-0.265391\pi$
$150$		0			0
$151$		−	15.9753i		−	1.30005i	−0.759913	−	0.650025i	$-0.774759\pi$
$151$		−	15.9753i		−	1.30005i	0.759913	−	0.650025i	$-0.225241\pi$
$152$	−3.47006	−	10.5923i	−0.281459	−	0.859145i
$153$		0			0
$154$	0.129603	+	1.22357i	0.0104437	+	0.0985980i
$155$	0.364870			0.0293071
$156$		0			0
$157$	−13.8789			−1.10766			−0.553829	−	0.832630i	$-0.686834\pi$
$157$	−13.8789			−1.10766			−0.553829	+	0.832630i	$0.686834\pi$
$158$	1.03667	+	9.78712i	0.0824730	+	0.778622i
$159$		0			0
$160$	3.00798	+	5.16167i	0.237802	+	0.408066i
$161$			3.92908i			0.309655i
$162$		0			0
$163$			17.0351i			1.33430i	0.744925	+	0.667148i	$0.232485\pi$
$163$			17.0351i			1.33430i	−0.744925	+	0.667148i	$0.767515\pi$
$164$	−3.24317	−	15.1375i	−0.253249	−	1.18204i
$165$		0			0
$166$	−17.8802	+	1.89390i	−1.38777	+	0.146996i
$167$	0.813720			0.0629676			0.0314838	−	0.999504i	$-0.489977\pi$
$167$	0.813720			0.0629676			0.0314838	+	0.999504i	$0.489977\pi$
$168$		0			0
$169$	−5.97017			−0.459244
$170$	−2.23382	+	0.236610i	−0.171326	+	0.0181472i
$171$		0			0
$172$	−3.63919	−	16.9859i	−0.277486	−	1.29517i
$173$			22.9734i			1.74663i	0.487154	+	0.873316i	$0.338035\pi$
$173$			22.9734i			1.74663i	−0.487154	+	0.873316i	$0.661965\pi$
$174$		0			0
$175$			3.88466i			0.293653i
$176$	−3.17467	+	1.42577i	−0.239300	+	0.107472i
$177$		0			0
$178$	−2.23351	−	21.0865i	−0.167409	−	1.58050i
$179$	−4.33924			−0.324330			−0.162165	−	0.986764i	$-0.551848\pi$
$179$	−4.33924			−0.324330			−0.162165	+	0.986764i	$0.551848\pi$
$180$		0			0
$181$	−22.9035			−1.70240			−0.851201	−	0.524840i	$-0.824125\pi$
$181$	−22.9035			−1.70240			−0.851201	+	0.524840i	$0.824125\pi$
$182$	−0.394957	−	3.72876i	−0.0292762	−	0.276394i
$183$		0			0
$184$	−10.5608	+	3.45977i	−0.778555	+	0.255057i
$185$		−	3.24446i		−	0.238537i
$186$		0			0
$187$		−	1.30854i		−	0.0956902i
$188$	14.3177	−	3.06753i	1.04423	−	0.223723i
$189$		0			0
$190$	−5.85297	+	0.619957i	−0.424619	+	0.0449764i
$191$	−15.0886			−1.09177			−0.545886	−	0.837860i	$-0.683807\pi$
$191$	−15.0886			−1.09177			−0.545886	+	0.837860i	$0.683807\pi$
$192$		0			0
$193$	12.4455			0.895844			0.447922	−	0.894073i	$-0.352164\pi$
$193$	12.4455			0.895844			0.447922	+	0.894073i	$0.352164\pi$
$194$	−11.2865	+	1.19548i	−0.810321	+	0.0858306i
$195$		0			0
$196$	−1.95562	+	0.418986i	−0.139687	+	0.0299276i
$197$		−	0.814174i		−	0.0580075i	−0.999579	−	0.0290038i	$-0.990767\pi$
$197$		−	0.814174i		−	0.0580075i	0.999579	−	0.0290038i	$-0.00923348\pi$
$198$		0			0
$199$		−	10.3338i		−	0.732545i	−0.930508	−	0.366272i	$-0.880634\pi$
$199$		−	10.3338i		−	0.732545i	0.930508	−	0.366272i	$-0.119366\pi$
$200$	−10.4414	+	3.42066i	−0.738322	+	0.241877i
$201$		0			0
$202$	−0.0738860	−	0.697553i	−0.00519860	−	0.0490797i
$203$	0.285909			0.0200669
$204$		0			0
$205$	−8.17472			−0.570947
$206$	−1.62343	−	15.3267i	−0.113110	−	1.06786i
$207$		0			0
$208$	9.67463	−	4.34497i	0.670815	−	0.301269i
$209$		−	3.42860i		−	0.237161i
$210$		0			0
$211$		−	20.2314i		−	1.39278i	−0.717661	−	0.696392i	$-0.754787\pi$
$211$		−	20.2314i		−	1.39278i	0.717661	−	0.696392i	$-0.245213\pi$
$212$	6.03376	+	28.1626i	0.414401	+	1.93422i
$213$		0			0
$214$	−8.18825	+	0.867314i	−0.559737	+	0.0592884i
$215$	−9.17294			−0.625589
$216$		0			0
$217$	−0.345489			−0.0234533
$218$	11.8427	−	1.25440i	0.802088	−	0.0849585i
$219$		0			0
$220$	0.384981	+	1.79690i	0.0259554	+	0.121147i
$221$			3.98772i			0.268243i
$222$		0			0
$223$			18.9294i			1.26761i	0.773494	+	0.633804i	$0.218507\pi$
$223$			18.9294i			1.26761i	−0.773494	+	0.633804i	$0.781493\pi$
$224$	−2.84821	−	4.88751i	−0.190304	−	0.326560i
$225$		0			0
$226$	2.30967	+	21.8055i	0.153637	+	1.45048i
$227$	−14.0163			−0.930293			−0.465146	−	0.885234i	$-0.653998\pi$
$227$	−14.0163			−0.930293			−0.465146	+	0.885234i	$0.653998\pi$
$228$		0			0
$229$	−13.6003			−0.898736			−0.449368	−	0.893347i	$-0.648351\pi$
$229$	−13.6003			−0.898736			−0.449368	+	0.893347i	$0.648351\pi$
$230$	0.618118	+	5.83561i	0.0407575	+	0.384789i
$231$		0			0
$232$	0.251758	+	0.768485i	0.0165287	+	0.0504535i
$233$		−	20.7949i		−	1.36232i	−0.732135	−	0.681160i	$-0.761476\pi$
$233$		−	20.7949i		−	1.36232i	0.732135	−	0.681160i	$-0.238524\pi$
$234$		0			0
$235$		−	7.73202i		−	0.504381i
$236$	21.0453	−	4.50889i	1.36993	−	0.293504i
$237$		0			0
$238$	2.11517	−	0.224042i	0.137106	−	0.0145225i
$239$	−4.17360			−0.269968			−0.134984	−	0.990848i	$-0.543098\pi$
$239$	−4.17360			−0.269968			−0.134984	+	0.990848i	$0.543098\pi$
$240$		0			0
$241$	20.0402			1.29091			0.645453	−	0.763800i	$-0.276669\pi$
$241$	20.0402			1.29091			0.645453	+	0.763800i	$0.276669\pi$
$242$	14.4053	−	1.52583i	0.926005	−	0.0980841i
$243$		0			0
$244$	−7.40820	+	1.58719i	−0.474261	+	0.101609i
$245$			1.05610i			0.0674715i
$246$		0			0
$247$			10.4485i			0.664821i
$248$	−0.304222	−	0.928629i	−0.0193181	−	0.0589680i
$249$		0			0
$250$	1.39773	+	13.1958i	0.0883999	+	0.834577i
$251$	−24.6372			−1.55509			−0.777543	−	0.628830i	$-0.783534\pi$
$251$	−24.6372			−1.55509			−0.777543	+	0.628830i	$0.783534\pi$
$252$		0			0
$253$	−3.41843			−0.214915
$254$	1.65489	+	15.6237i	0.103837	+	0.980315i
$255$		0			0
$256$	10.6290	−	11.9593i	0.664310	−	0.747457i
$257$		−	1.94314i		−	0.121210i	−0.998162	−	0.0606048i	$-0.980697\pi$
$257$		−	1.94314i		−	0.121210i	0.998162	−	0.0606048i	$-0.0193029\pi$
$258$		0			0
$259$			3.07212i			0.190892i
$260$	−1.17321	−	5.47596i	−0.0727594	−	0.339605i
$261$		0			0
$262$	15.4894	−	1.64066i	0.956938	−	0.101361i
$263$	−17.8338			−1.09968			−0.549840	−	0.835270i	$-0.685311\pi$
$263$	−17.8338			−1.09968			−0.549840	+	0.835270i	$0.685311\pi$
$264$		0			0
$265$	15.2087			0.934263
$266$	5.54208	−	0.587027i	0.339807	−	0.0359929i
$267$		0			0
$268$	2.16662	+	10.1127i	0.132347	+	0.617732i
$269$			24.2047i			1.47579i	0.674916	+	0.737894i	$0.264180\pi$
$269$			24.2047i			1.47579i	−0.674916	+	0.737894i	$0.735820\pi$
$270$		0			0
$271$			14.9540i			0.908390i	0.890902	+	0.454195i	$0.150073\pi$
$271$			14.9540i			0.908390i	−0.890902	+	0.454195i	$0.849927\pi$
$272$	2.46471	+	5.48800i	0.149445	+	0.332759i
$273$		0			0
$274$	−1.51295	−	14.2836i	−0.0914004	−	0.862905i
$275$	−3.37979			−0.203809
$276$		0			0
$277$	−6.84370			−0.411198			−0.205599	−	0.978636i	$-0.565914\pi$
$277$	−6.84370			−0.411198			−0.205599	+	0.978636i	$0.565914\pi$
$278$	−1.34261	−	12.6755i	−0.0805242	−	0.760223i
$279$		0			0
$280$	−2.83864	+	0.929950i	−0.169641	+	0.0555751i
$281$			4.72862i			0.282086i	0.990003	+	0.141043i	$0.0450455\pi$
$281$			4.72862i			0.282086i	−0.990003	+	0.141043i	$0.954954\pi$
$282$		0			0
$283$		−	26.5263i		−	1.57682i	−0.615148	−	0.788411i	$-0.710904\pi$
$283$		−	26.5263i		−	1.57682i	0.615148	−	0.788411i	$-0.289096\pi$
$284$	14.5784	−	3.12337i	0.865067	−	0.185338i
$285$		0			0
$286$	3.24415	−	0.343626i	0.191831	−	0.0203190i
$287$	7.74051			0.456908
$288$		0			0
$289$	14.7379			0.866938
$290$	0.424642	−	0.0449789i	0.0249359	−	0.00264125i
$291$		0			0
$292$	9.81390	−	2.10260i	0.574315	−	0.123045i
$293$		−	24.4807i		−	1.43018i	−0.699035	−	0.715088i	$-0.746387\pi$
$293$		−	24.4807i		−	1.43018i	0.699035	−	0.715088i	$-0.253613\pi$
$294$		0			0
$295$		−	11.3651i		−	0.661701i
$296$	−8.25746	+	2.70517i	−0.479955	+	0.157235i
$297$		0			0
$298$	2.69278	+	25.4224i	0.155989	+	1.47268i
$299$	10.4175			0.602459
$300$		0			0
$301$	8.68571			0.500636
$302$	2.37972	+	22.4668i	0.136937	+	1.29282i
$303$		0			0
$304$	6.45796	+	14.3795i	0.370389	+	0.824719i
$305$			4.00066i			0.229077i
$306$		0			0
$307$			2.17734i			0.124267i	0.998068	+	0.0621336i	$0.0197905\pi$
$307$			2.17734i			0.124267i	−0.998068	+	0.0621336i	$0.980209\pi$
$308$	−0.364532	−	1.70146i	−0.0207712	−	0.0969495i
$309$		0			0
$310$	−0.513133	+	0.0543520i	−0.0291440	+	0.00308699i
$311$	−16.4839			−0.934718			−0.467359	−	0.884068i	$-0.654794\pi$
$311$	−16.4839			−0.934718			−0.467359	+	0.884068i	$0.654794\pi$
$312$		0			0
$313$	9.41825			0.532351			0.266176	−	0.963925i	$-0.414240\pi$
$313$	9.41825			0.532351			0.266176	+	0.963925i	$0.414240\pi$
$314$	19.5186	−	2.06744i	1.10150	−	0.116672i
$315$		0			0
$316$	−2.91583	−	13.6097i	−0.164028	−	0.765603i
$317$		−	24.8108i		−	1.39351i	−0.717309	−	0.696755i	$-0.754626\pi$
$317$		−	24.8108i		−	1.39351i	0.717309	−	0.696755i	$-0.245374\pi$
$318$		0			0
$319$			0.248751i			0.0139274i
$320$	−4.99916	−	6.81103i	−0.279462	−	0.380748i
$321$		0			0
$322$	−0.585286	−	5.52564i	−0.0326167	−	0.307932i
$323$	−5.92697			−0.329785
$324$		0			0
$325$	10.2997			0.571326
$326$	−2.53760	−	23.9573i	−0.140545	−	1.32687i
$327$		0			0
$328$	6.81594	+	20.8054i	0.376347	+	1.14879i
$329$			7.32132i			0.403637i
$330$		0			0
$331$			25.6878i			1.41193i	0.708246	+	0.705965i	$0.249487\pi$
$331$			25.6878i			1.41193i	−0.708246	+	0.705965i	$0.750513\pi$
$332$	24.8637	−	5.32697i	1.36457	−	0.292356i
$333$		0			0
$334$	−1.14437	+	0.121214i	−0.0626173	+	0.00663253i
$335$	5.46118			0.298376
$336$		0			0
$337$	35.3953			1.92810			0.964052	−	0.265714i	$-0.0856075\pi$
$337$	35.3953			1.92810			0.964052	+	0.265714i	$0.0856075\pi$
$338$	8.39612	−	0.889332i	0.456689	−	0.0483733i
$339$		0			0
$340$	3.10628	−	0.665511i	0.168461	−	0.0360924i
$341$		−	0.300588i		−	0.0162777i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	7.64824	+	23.3460i	0.412365	+	1.25873i
$345$		0			0
$346$	−3.42217	−	32.3085i	−0.183977	−	1.73692i
$347$	8.03851			0.431530			0.215765	−	0.976445i	$-0.430775\pi$
$347$	8.03851			0.431530			0.215765	+	0.976445i	$0.430775\pi$
$348$		0			0
$349$	−15.2272			−0.815092			−0.407546	−	0.913185i	$-0.633615\pi$
$349$	−15.2272			−0.815092			−0.407546	+	0.913185i	$0.633615\pi$
$350$	−0.578670	−	5.46318i	−0.0309312	−	0.292019i
$351$		0			0
$352$	4.25230	−	2.47804i	0.226648	−	0.132080i
$353$			24.4132i			1.29938i	0.760197	+	0.649692i	$0.225102\pi$
$353$			24.4132i			1.29938i	−0.760197	+	0.649692i	$0.774898\pi$
$354$		0			0
$355$		−	7.87277i		−	0.417843i
$356$	6.28219	+	29.3222i	0.332955	+	1.55407i
$357$		0			0
$358$	6.10247	−	0.646385i	0.322526	−	0.0341625i
$359$	27.3591			1.44396			0.721979	−	0.691915i	$-0.243233\pi$
$359$	27.3591			1.44396			0.721979	+	0.691915i	$0.243233\pi$
$360$		0			0
$361$	3.47036			0.182650
$362$	32.2102	−	3.41176i	1.69293	−	0.179318i
$363$		0			0
$364$	1.11089	+	5.18510i	0.0582266	+	0.271773i
$365$		−	5.29981i		−	0.277405i
$366$		0			0
$367$			7.64374i			0.399000i	0.979898	+	0.199500i	$0.0639318\pi$
$367$			7.64374i			0.399000i	−0.979898	+	0.199500i	$0.936068\pi$
$368$	14.3368	−	6.43880i	0.747358	−	0.335646i
$369$		0			0
$370$	0.483303	+	4.56283i	0.0251257	+	0.237210i
$371$	−14.4009			−0.747656
$372$		0			0
$373$	−18.0932			−0.936832			−0.468416	−	0.883508i	$-0.655175\pi$
$373$	−18.0932			−0.936832			−0.468416	+	0.883508i	$0.655175\pi$
$374$	0.194924	+	1.84027i	0.0100793	+	0.0951579i
$375$		0			0
$376$	−19.6787	+	6.44682i	−1.01485	+	0.332469i
$377$		−	0.758054i		−	0.0390418i
$378$		0			0
$379$		−	5.57730i		−	0.286487i	−0.989688	−	0.143243i	$-0.954247\pi$
$379$		−	5.57730i		−	0.286487i	0.989688	−	0.143243i	$-0.0457531\pi$
$380$	8.13896	−	1.74375i	0.417520	−	0.0894524i
$381$		0			0
$382$	21.2198	−	2.24764i	1.08570	−	0.114999i
$383$	−19.0490			−0.973357			−0.486679	−	0.873581i	$-0.661792\pi$
$383$	−19.0490			−0.973357			−0.486679	+	0.873581i	$0.661792\pi$
$384$		0			0
$385$	−0.918840			−0.0468284
$386$	−17.5026	+	1.85391i	−0.890861	+	0.0943615i
$387$		0			0
$388$	15.6946	−	3.36252i	0.796772	−	0.170706i
$389$			9.01997i			0.457330i	0.973505	+	0.228665i	$0.0734361\pi$
$389$			9.01997i			0.457330i	−0.973505	+	0.228665i	$0.926564\pi$
$390$		0			0
$391$			5.90939i			0.298851i
$392$	2.68787	−	0.880554i	0.135758	−	0.0444747i
$393$		0			0
$394$	0.121282	+	1.14501i	0.00611008	+	0.0576848i
$395$	−7.34964			−0.369801
$396$		0			0
$397$	19.2163			0.964440			0.482220	−	0.876050i	$-0.339831\pi$
$397$	19.2163			0.964440			0.482220	+	0.876050i	$0.339831\pi$
$398$	1.53935	+	14.5329i	0.0771608	+	0.728470i
$399$		0			0
$400$	14.1747	−	6.36601i	0.708737	−	0.318301i
$401$		−	29.6675i		−	1.48152i	−0.671768	−	0.740762i	$-0.734465\pi$
$401$		−	29.6675i		−	1.48152i	0.671768	−	0.740762i	$-0.265535\pi$
$402$		0			0
$403$			0.916025i			0.0456304i
$404$	0.207819	+	0.969995i	0.0103394	+	0.0482590i
$405$		0			0
$406$	−0.402087	+	0.0425898i	−0.0199552	+	0.00211369i
$407$	−2.67285			−0.132488
$408$		0			0
$409$	−25.1744			−1.24480			−0.622398	−	0.782701i	$-0.713841\pi$
$409$	−25.1744			−1.24480			−0.622398	+	0.782701i	$0.713841\pi$
$410$	11.4965	−	1.21773i	0.567771	−	0.0601393i
$411$		0			0
$412$	4.56621	+	21.3128i	0.224961	+	1.05001i
$413$			10.7614i			0.529535i
$414$		0			0
$415$		−	13.4272i		−	0.659113i
$416$	−12.9586	+	7.55169i	−0.635350	+	0.370252i
$417$		0			0
$418$	0.510734	+	4.82180i	0.0249808	+	0.235842i
$419$	17.8596			0.872498			0.436249	−	0.899826i	$-0.356307\pi$
$419$	17.8596			0.872498			0.436249	+	0.899826i	$0.356307\pi$
$420$		0			0
$421$	−3.84615			−0.187450			−0.0937250	−	0.995598i	$-0.529877\pi$
$421$	−3.84615			−0.187450			−0.0937250	+	0.995598i	$0.529877\pi$
$422$	3.01372	+	28.4523i	0.146706	+	1.38504i
$423$		0			0
$424$	−12.6807	−	38.7076i	−0.615831	−	1.87981i
$425$			5.84259i			0.283407i
$426$		0			0
$427$		−	3.78816i		−	0.183322i
$428$	11.3863	−	2.43949i	0.550379	−	0.117917i
$429$		0			0
$430$	12.9003	−	1.36643i	0.622109	−	0.0658949i
$431$	−14.2748			−0.687594			−0.343797	−	0.939044i	$-0.611713\pi$
$431$	−14.2748			−0.687594			−0.343797	+	0.939044i	$0.611713\pi$
$432$		0			0
$433$	2.39529			0.115110			0.0575551	−	0.998342i	$-0.481670\pi$
$433$	2.39529			0.115110			0.0575551	+	0.998342i	$0.481670\pi$
$434$	0.485878	−	0.0514650i	0.0233229	−	0.00247040i
$435$		0			0
$436$	−16.4681	+	3.52824i	−0.788677	+	0.168972i
$437$			15.4836i			0.740680i
$438$		0			0
$439$			13.9944i			0.667916i	0.942588	+	0.333958i	$0.108384\pi$
$439$			13.9944i			0.667916i	−0.942588	+	0.333958i	$0.891616\pi$
$440$	−0.809088	−	2.46972i	−0.0385718	−	0.117739i
$441$		0			0
$442$	−0.594021	−	5.60811i	−0.0282547	−	0.266751i
$443$	−27.8526			−1.32332			−0.661659	−	0.749805i	$-0.730147\pi$
$443$	−27.8526			−1.32332			−0.661659	+	0.749805i	$0.730147\pi$
$444$		0			0
$445$	15.8349			0.750645
$446$	−2.81978	−	26.6213i	−0.133520	−	1.26056i
$447$		0			0
$448$	4.73362	+	6.44925i	0.223643	+	0.304698i
$449$		−	2.30063i		−	0.108573i	−0.998525	−	0.0542866i	$-0.982712\pi$
$449$		−	2.30063i		−	0.108573i	0.998525	−	0.0542866i	$-0.0172885\pi$
$450$		0			0
$451$			6.73451i			0.317115i
$452$	−6.49640	−	30.3220i	−0.305565	−	1.42623i
$453$		0			0
$454$	19.7117	−	2.08790i	0.925118	−	0.0979901i
$455$	2.80012			0.131271
$456$		0			0
$457$	26.7799			1.25271			0.626356	−	0.779538i	$-0.284546\pi$
$457$	26.7799			1.25271			0.626356	+	0.779538i	$0.284546\pi$
$458$	19.1268	−	2.02594i	0.893737	−	0.0946662i
$459$		0			0
$460$	−1.73858	−	8.11481i	−0.0810615	−	0.378355i
$461$		−	7.87462i		−	0.366758i	−0.983042	−	0.183379i	$-0.941296\pi$
$461$		−	7.87462i		−	0.366758i	0.983042	−	0.183379i	$-0.0587035\pi$
$462$		0			0
$463$			4.04912i			0.188179i	0.995564	+	0.0940894i	$0.0299939\pi$
$463$			4.04912i			0.188179i	−0.995564	+	0.0940894i	$0.970006\pi$
$464$	−0.468535	−	1.04325i	−0.0217512	−	0.0484318i
$465$		0			0
$466$	3.09766	+	29.2448i	0.143497	+	1.35474i
$467$	7.11546			0.329264			0.164632	−	0.986355i	$-0.447356\pi$
$467$	7.11546			0.329264			0.164632	+	0.986355i	$0.447356\pi$
$468$		0			0
$469$	−5.17110			−0.238779
$470$	1.15178	+	10.8739i	0.0531277	+	0.501575i
$471$		0			0
$472$	−28.9253	+	9.47601i	−1.33139	+	0.436169i
$473$			7.55686i			0.347465i
$474$		0			0
$475$			15.3085i			0.702404i
$476$	−2.94128	+	0.630161i	−0.134813	+	0.0288834i
$477$		0			0
$478$	5.86952	−	0.621710i	0.268466	−	0.0284364i
$479$	13.6522			0.623786			0.311893	−	0.950117i	$-0.399037\pi$
$479$	13.6522			0.623786			0.311893	+	0.950117i	$0.399037\pi$
$480$		0			0
$481$	8.14538			0.371397
$482$	−28.1835	+	2.98525i	−1.28372	+	0.135974i
$483$		0			0
$484$	−20.0315	+	4.29169i	−0.910523	+	0.195077i
$485$		−	8.47557i		−	0.384856i
$486$		0			0
$487$			8.74705i			0.396367i	0.980165	+	0.198183i	$0.0635041\pi$
$487$			8.74705i			0.396367i	−0.980165	+	0.198183i	$0.936496\pi$
$488$	10.1821	−	3.33568i	0.460920	−	0.150999i
$489$		0			0
$490$	−0.157319	−	1.48524i	−0.00710694	−	0.0670962i
$491$	−28.9088			−1.30464			−0.652319	−	0.757945i	$-0.726204\pi$
$491$	−28.9088			−1.30464			−0.652319	+	0.757945i	$0.726204\pi$
$492$		0			0
$493$	0.430011			0.0193667
$494$	−1.55643	−	14.6942i	−0.0700273	−	0.661123i
$495$		0			0
$496$	0.566173	+	1.26066i	0.0254219	+	0.0566051i
$497$			7.45460i			0.334384i
$498$		0			0
$499$		−	4.93977i		−	0.221134i	−0.993869	−	0.110567i	$-0.964733\pi$
$499$		−	4.93977i		−	0.221134i	0.993869	−	0.110567i	$-0.0352667\pi$
$500$	−3.93137	−	18.3497i	−0.175816	−	0.820623i
$501$		0			0
$502$	34.6484	−	3.67002i	1.54643	−	0.163801i
$503$	−43.9724			−1.96063			−0.980317	−	0.197431i	$-0.936740\pi$
$503$	−43.9724			−1.96063			−0.980317	+	0.197431i	$0.936740\pi$
$504$		0			0
$505$	0.523828			0.0233100
$506$	4.80750	−	0.509219i	0.213719	−	0.0226375i
$507$		0			0
$508$	−4.65468	−	21.7258i	−0.206518	−	0.963925i
$509$			0.287660i			0.0127503i	0.999980	+	0.00637514i	$0.00202929\pi$
$509$			0.287660i			0.0127503i	−0.999980	+	0.00637514i	$0.997971\pi$
$510$		0			0
$511$			5.01831i			0.221997i
$512$	−13.1665	+	18.4023i	−0.581883	+	0.813273i
$513$		0			0
$514$	0.289455	+	2.73272i	0.0127673	+	0.120535i
$515$	11.5096			0.507172
$516$		0			0
$517$	−6.36980			−0.280143
$518$	−0.457632	−	4.32047i	−0.0201072	−	0.189831i
$519$		0			0
$520$	2.46565	+	7.52633i	0.108126	+	0.330052i
$521$			28.4414i			1.24604i	0.782205	+	0.623021i	$0.214095\pi$
$521$			28.4414i			1.24604i	−0.782205	+	0.623021i	$0.785905\pi$
$522$		0			0
$523$		−	11.0124i		−	0.481538i	−0.970582	−	0.240769i	$-0.922600\pi$
$523$		−	11.0124i		−	0.481538i	0.970582	−	0.240769i	$-0.0773996\pi$
$524$	−21.5390	+	4.61468i	−0.940938	+	0.201593i
$525$		0			0
$526$	25.0805	−	2.65657i	1.09356	−	0.115832i
$527$	−0.519621			−0.0226350
$528$		0			0
$529$	−7.56235			−0.328798
$530$	−21.3887	+	2.26553i	−0.929065	+	0.0984083i
$531$		0			0
$532$	−7.70664	+	1.65113i	−0.334125	+	0.0715854i
$533$		−	20.5230i		−	0.888952i
$534$		0			0
$535$		−	6.14897i		−	0.265843i
$536$	−4.55343	−	13.8992i	−0.196678	−	0.600355i
$537$		0			0
$538$	−3.60560	−	34.0402i	−0.155449	−	1.46758i
$539$	0.870034			0.0374750
$540$		0			0
$541$	4.81970			0.207215			0.103608	−	0.994618i	$-0.466961\pi$
$541$	4.81970			0.207215			0.103608	+	0.994618i	$0.466961\pi$
$542$	−2.22759	−	21.0305i	−0.0956830	−	0.903336i
$543$		0			0
$544$	−4.28375	−	7.35088i	−0.183664	−	0.315166i
$545$			8.89326i			0.380946i
$546$		0			0
$547$			19.2213i			0.821842i	0.911671	+	0.410921i	$0.134793\pi$
$547$			19.2213i			0.821842i	−0.911671	+	0.410921i	$0.865207\pi$
$548$	4.25545	+	19.8623i	0.181784	+	0.848477i
$549$		0			0
$550$	4.75315	−	0.503462i	0.202675	−	0.0214677i
$551$	1.12670			0.0479991
$552$		0			0
$553$	6.95925			0.295938
$554$	9.62461	−	1.01946i	0.408910	−	0.0433125i
$555$		0			0
$556$	3.77634	+	17.6261i	0.160152	+	0.747512i
$557$		−	26.3592i		−	1.11688i	−0.829546	−	0.558438i	$-0.811401\pi$
$557$		−	26.3592i		−	1.11688i	0.829546	−	0.558438i	$-0.188599\pi$
$558$		0			0
$559$		−	23.0291i		−	0.974029i
$560$	3.85359	−	1.73068i	0.162844	−	0.0731347i
$561$		0			0
$562$	−0.704387	−	6.65007i	−0.0297128	−	0.280516i
$563$	8.78897			0.370411			0.185206	−	0.982700i	$-0.440705\pi$
$563$	8.78897			0.370411			0.185206	+	0.982700i	$0.440705\pi$
$564$		0			0
$565$	−16.3748			−0.688894
$566$	3.95142	+	37.3051i	0.166091	+	1.56805i
$567$		0			0
$568$	−20.0370	+	6.56418i	−0.840732	+	0.275427i
$569$		−	40.4774i		−	1.69690i	−0.529275	−	0.848450i	$-0.677536\pi$
$569$		−	40.4774i		−	1.69690i	0.529275	−	0.848450i	$-0.322464\pi$
$570$		0			0
$571$		−	6.29103i		−	0.263272i	−0.991298	−	0.131636i	$-0.957977\pi$
$571$		−	6.29103i		−	0.263272i	0.991298	−	0.131636i	$-0.0420229\pi$
$572$	−4.51121	+	0.966515i	−0.188623	+	0.0404120i
$573$		0			0
$574$	−10.8858	+	1.15305i	−0.454366	+	0.0481272i
$575$	15.2631			0.636517
$576$		0			0
$577$	42.1989			1.75676			0.878381	−	0.477960i	$-0.158624\pi$
$577$	42.1989			1.75676			0.878381	+	0.477960i	$0.158624\pi$
$578$	−20.7266	+	2.19540i	−0.862115	+	0.0913167i
$579$		0			0
$580$	−0.590494	+	0.126512i	−0.0245189	+	0.00525312i
$581$			12.7140i			0.527464i
$582$		0			0
$583$		−	12.5292i		−	0.518908i
$584$	−13.4885	+	4.41889i	−0.558160	+	0.182855i
$585$		0			0
$586$	3.64671	+	34.4283i	0.150644	+	1.42222i
$587$	33.3101			1.37485			0.687427	−	0.726253i	$-0.258740\pi$
$587$	33.3101			1.37485			0.687427	+	0.726253i	$0.258740\pi$
$588$		0			0
$589$	−1.36149			−0.0560993
$590$	1.69297	+	15.9833i	0.0696987	+	0.658020i
$591$		0			0
$592$	11.2099	−	5.03446i	0.460723	−	0.206915i
$593$			9.29517i			0.381707i	0.981619	+	0.190853i	$0.0611255\pi$
$593$			9.29517i			0.381707i	−0.981619	+	0.190853i	$0.938874\pi$
$594$		0			0
$595$			1.58838i			0.0651174i
$596$	−7.57397	−	35.3515i	−0.310242	−	1.44805i
$597$		0			0
$598$	−14.6506	+	1.55182i	−0.599108	+	0.0634585i
$599$	27.5198			1.12443			0.562214	−	0.826992i	$-0.309950\pi$
$599$	27.5198			1.12443			0.562214	+	0.826992i	$0.309950\pi$
$600$		0			0
$601$	−12.1029			−0.493688			−0.246844	−	0.969055i	$-0.579393\pi$
$601$	−12.1029			−0.493688			−0.246844	+	0.969055i	$0.579393\pi$
$602$	−12.2151	+	1.29385i	−0.497851	+	0.0527332i
$603$		0			0
$604$	−6.69342	−	31.2416i	−0.272351	−	1.27120i
$605$			10.8176i			0.439799i
$606$		0			0
$607$			18.6748i			0.757987i	0.925399	+	0.378993i	$0.123730\pi$
$607$			18.6748i			0.757987i	−0.925399	+	0.378993i	$0.876270\pi$
$608$	−11.2241	−	19.2605i	−0.455198	−	0.781117i
$609$		0			0
$610$	−0.595949	−	5.62631i	−0.0241293	−	0.227803i
$611$	19.4116			0.785310
$612$		0			0
$613$	−46.5110			−1.87856			−0.939280	−	0.343152i	$-0.888505\pi$
$613$	−46.5110			−1.87856			−0.939280	+	0.343152i	$0.888505\pi$
$614$	−0.324342	−	3.06209i	−0.0130894	−	0.123576i
$615$		0			0
$616$	0.766112	+	2.33854i	0.0308675	+	0.0942223i
$617$			4.87667i			0.196327i	0.995170	+	0.0981636i	$0.0312968\pi$
$617$			4.87667i			0.196327i	−0.995170	+	0.0981636i	$0.968703\pi$
$618$		0			0
$619$			13.6028i			0.546741i	0.961909	+	0.273370i	$0.0881385\pi$
$619$			13.6028i			0.546741i	−0.961909	+	0.273370i	$0.911862\pi$
$620$	0.713547	−	0.152875i	0.0286567	−	0.00613963i
$621$		0			0
$622$	23.1821	−	2.45549i	0.929518	−	0.0984562i
$623$	−14.9938			−0.600713
$624$		0			0
$625$	9.51390			0.380556
$626$	−13.2453	+	1.40297i	−0.529390	+	0.0560739i
$627$		0			0
$628$	−27.1419	+	5.81507i	−1.08308	+	0.232047i
$629$			4.62052i			0.184232i
$630$		0			0
$631$		−	25.3007i		−	1.00720i	−0.863936	−	0.503602i	$-0.832008\pi$
$631$		−	25.3007i		−	1.00720i	0.863936	−	0.503602i	$-0.167992\pi$
$632$	6.12800	+	18.7055i	0.243759	+	0.744067i
$633$		0			0
$634$	3.69588	+	34.8925i	0.146782	+	1.38576i
$635$	−11.7326			−0.465594
$636$		0			0
$637$	−2.65138			−0.105052
$638$	−0.0370546	−	0.349829i	−0.00146700	−	0.0138499i
$639$		0			0
$640$	8.04514	+	8.83397i	0.318012	+	0.349193i
$641$		−	39.7748i		−	1.57101i	−0.618854	−	0.785506i	$-0.712403\pi$
$641$		−	39.7748i		−	1.57101i	0.618854	−	0.785506i	$-0.287597\pi$
$642$		0			0
$643$		−	28.5493i		−	1.12588i	−0.826499	−	0.562938i	$-0.809671\pi$
$643$		−	28.5493i		−	1.12588i	0.826499	−	0.562938i	$-0.190329\pi$
$644$	1.64623	+	7.68378i	0.0648705	+	0.302783i
$645$		0			0
$646$	8.33537	−	0.882898i	0.327951	−	0.0347371i
$647$	−7.06828			−0.277883			−0.138941	−	0.990301i	$-0.544370\pi$
$647$	−7.06828			−0.277883			−0.138941	+	0.990301i	$0.544370\pi$
$648$		0			0
$649$	−9.36280			−0.367522
$650$	−14.4850	+	1.53427i	−0.568148	+	0.0601792i
$651$		0			0
$652$	7.13749	+	33.3143i	0.279526	+	1.30469i
$653$		−	20.8683i		−	0.816642i	−0.912839	−	0.408321i	$-0.866114\pi$
$653$		−	20.8683i		−	0.816642i	0.912839	−	0.408321i	$-0.133886\pi$
$654$		0			0
$655$			11.6318i			0.454490i
$656$	−12.6848	−	28.2443i	−0.495258	−	1.10276i
$657$		0			0
$658$	−1.09060	−	10.2963i	−0.0425162	−	0.401392i
$659$	16.8250			0.655407			0.327704	−	0.944781i	$-0.393725\pi$
$659$	16.8250			0.655407			0.327704	+	0.944781i	$0.393725\pi$
$660$		0			0
$661$	−45.5430			−1.77142			−0.885709	−	0.464241i	$-0.846327\pi$
$661$	−45.5430			−1.77142			−0.885709	+	0.464241i	$0.846327\pi$
$662$	−3.82653	−	36.1260i	−0.148722	−	1.40408i
$663$		0			0
$664$	−34.1734	+	11.1953i	−1.32619	+	0.434463i
$665$			4.16183i			0.161389i
$666$		0			0
$667$		−	1.12336i		−	0.0434966i
$668$	1.59133	−	0.340938i	0.0615703	−	0.0131913i
$669$		0			0
$670$	−7.68030	+	0.813511i	−0.296716	+	0.0314287i
$671$	3.29583			0.127234
$672$		0			0
$673$	−4.10371			−0.158186			−0.0790931	−	0.996867i	$-0.525202\pi$
$673$	−4.10371			−0.158186			−0.0790931	+	0.996867i	$0.525202\pi$
$674$	−49.7780	+	5.27258i	−1.91738	+	0.203092i
$675$		0			0
$676$	−11.6754	+	2.50142i	−0.449053	+	0.0962084i
$677$			10.7247i			0.412184i	0.978533	+	0.206092i	$0.0660747\pi$
$677$			10.7247i			0.412184i	−0.978533	+	0.206092i	$0.933925\pi$
$678$		0			0
$679$			8.02538i			0.307986i
$680$	−4.26936	+	1.39866i	−0.163723	+	0.0536361i
$681$		0			0
$682$	0.0447763	+	0.422730i	0.00171457	+	0.0161872i
$683$	−16.7359			−0.640380			−0.320190	−	0.947353i	$-0.603747\pi$
$683$	−16.7359			−0.640380			−0.320190	+	0.947353i	$0.603747\pi$
$684$		0			0
$685$	10.7263			0.409830
$686$	0.148963	+	1.40635i	0.00568742	+	0.0536946i
$687$		0			0
$688$	−14.2338	−	31.6933i	−0.542657	−	1.20830i
$689$			38.1822i			1.45463i
$690$		0			0
$691$			3.77961i			0.143783i	0.997412	+	0.0718916i	$0.0229036\pi$
$691$			3.77961i			0.143783i	−0.997412	+	0.0718916i	$0.977096\pi$
$692$	9.62553	+	44.9272i	0.365908	+	1.70788i
$693$		0			0
$694$	−11.3049	+	1.19744i	−0.429130	+	0.0454542i
$695$	9.51863			0.361062
$696$		0			0
$697$	11.6418			0.440966
$698$	21.4147	−	2.26828i	0.810557	−	0.0858557i
$699$		0			0
$700$	1.62762	+	7.59692i	0.0615182	+	0.287137i
$701$			5.08149i			0.191925i	0.995385	+	0.0959626i	$0.0305929\pi$
$701$			5.08149i			0.191925i	−0.995385	+	0.0959626i	$0.969407\pi$
$702$		0			0
$703$			12.1065i			0.456606i
$704$	−5.61107	+	4.11841i	−0.211475	+	0.155219i
$705$		0			0
$706$	−3.63666	−	34.3334i	−0.136867	−	1.29216i
$707$	−0.496004			−0.0186541
$708$		0			0
$709$	−16.3954			−0.615742			−0.307871	−	0.951428i	$-0.599617\pi$
$709$	−16.3954			−0.615742			−0.307871	+	0.951428i	$0.599617\pi$
$710$	1.17275	+	11.0718i	0.0440125	+	0.415519i
$711$		0			0
$712$	−13.2028	−	40.3013i	−0.494797	−	1.51035i
$713$			1.35745i			0.0508371i
$714$		0			0
$715$			2.43620i			0.0911086i
$716$	−8.48591	+	1.81808i	−0.317133	+	0.0679449i
$717$		0			0
$718$	−38.4764	+	4.07548i	−1.43593	+	0.152096i
$719$	45.4774			1.69602			0.848011	−	0.529979i	$-0.177800\pi$
$719$	45.4774			1.69602			0.848011	+	0.529979i	$0.177800\pi$
$720$		0			0
$721$	−10.8982			−0.405871
$722$	−4.88052	+	0.516954i	−0.181634	+	0.0192390i
$723$		0			0
$724$	−44.7905	+	9.59624i	−1.66463	+	0.356642i
$725$		−	1.11066i		−	0.0412489i
$726$		0			0
$727$		−	40.7022i		−	1.50956i	−0.655977	−	0.754781i	$-0.727743\pi$
$727$		−	40.7022i		−	1.50956i	0.655977	−	0.754781i	$-0.272257\pi$
$728$	−2.33469	−	7.12656i	−0.0865293	−	0.264128i
$729$		0			0
$730$	0.789475	+	7.45337i	0.0292198	+	0.275862i
$731$	13.0634			0.483168
$732$		0			0
$733$	−26.7016			−0.986245			−0.493122	−	0.869960i	$-0.664144\pi$
$733$	−26.7016			−0.986245			−0.493122	+	0.869960i	$0.664144\pi$
$734$	−1.13863	−	10.7498i	−0.0420277	−	0.396781i
$735$		0			0
$736$	−19.2034	+	11.1908i	−0.707846	+	0.412500i
$737$		−	4.49903i		−	0.165724i
$738$		0			0
$739$		−	12.3234i		−	0.453322i	−0.973974	−	0.226661i	$-0.927219\pi$
$739$		−	12.3234i		−	0.453322i	0.973974	−	0.226661i	$-0.0727810\pi$
$740$	−1.35938	−	6.34493i	−0.0499719	−	0.233244i
$741$		0			0
$742$	20.2526	−	2.14519i	0.743496	−	0.0787525i
$743$	8.89340			0.326267			0.163134	−	0.986604i	$-0.447840\pi$
$743$	8.89340			0.326267			0.163134	+	0.986604i	$0.447840\pi$
$744$		0			0
$745$	−19.0909			−0.699437
$746$	25.4453	−	2.69522i	0.931620	−	0.0986789i
$747$		0			0
$748$	−0.548262	−	2.55902i	−0.0200464	−	0.0935669i
$749$			5.82236i			0.212744i
$750$		0			0
$751$		−	39.5818i		−	1.44436i	−0.691704	−	0.722181i	$-0.743140\pi$
$751$		−	39.5818i		−	1.44436i	0.691704	−	0.722181i	$-0.256860\pi$
$752$	26.7148	−	11.9979i	0.974187	−	0.437517i
$753$		0			0
$754$	0.112922	+	1.06609i	0.00411237	+	0.0388246i
$755$	−16.8714			−0.614014
$756$		0			0
$757$	−45.2648			−1.64518			−0.822589	−	0.568637i	$-0.807471\pi$
$757$	−45.2648			−1.64518			−0.822589	+	0.568637i	$0.807471\pi$
$758$	0.830809	+	7.84361i	0.0301763	+	0.284893i
$759$		0			0
$760$	−11.1864	+	3.66472i	−0.405775	+	0.132933i
$761$			26.1668i			0.948546i	0.880378	+	0.474273i	$0.157289\pi$
$761$			26.1668i			0.948546i	−0.880378	+	0.474273i	$0.842711\pi$
$762$		0			0
$763$		−	8.42089i		−	0.304857i
$764$	−29.5075	+	6.32191i	−1.06755	+	0.228719i
$765$		0			0
$766$	26.7895	−	2.83759i	0.967943	−	0.102526i
$767$	28.5326			1.03025
$768$		0			0
$769$	−0.920389			−0.0331901			−0.0165950	−	0.999862i	$-0.505283\pi$
$769$	−0.920389			−0.0331901			−0.0165950	+	0.999862i	$0.505283\pi$
$770$	1.29221	−	0.136873i	0.0465679	−	0.00493255i
$771$		0			0
$772$	24.3386	−	5.21448i	0.875965	−	0.187673i
$773$		−	32.5444i		−	1.17054i	−0.810838	−	0.585270i	$-0.800989\pi$
$773$		−	32.5444i		−	1.17054i	0.810838	−	0.585270i	$-0.199011\pi$
$774$		0			0
$775$			1.34211i			0.0482100i
$776$	−21.5711	+	7.06678i	−0.774359	+	0.253683i
$777$		0			0
$778$	−1.34364	−	12.6852i	−0.0481718	−	0.454786i
$779$	30.5035			1.09290
$780$		0			0
$781$	−6.48575			−0.232079
$782$	−0.880279	−	8.31065i	−0.0314787	−	0.297188i
$783$		0			0
$784$	−3.64890	+	1.63876i	−0.130318	+	0.0585270i
$785$			14.6575i			0.523147i
$786$		0			0
$787$			2.95012i			0.105161i	0.998617	+	0.0525803i	$0.0167445\pi$
$787$			2.95012i			0.105161i	−0.998617	+	0.0525803i	$0.983255\pi$
$788$	−0.341128	−	1.59222i	−0.0121522	−	0.0567203i
$789$		0			0
$790$	10.3361	−	1.09482i	0.367743	−	0.0389520i
$791$	15.5050			0.551296
$792$		0			0
$793$	−10.0439			−0.356668
$794$	−27.0248	+	2.86252i	−0.959075	+	0.101587i
$795$		0			0
$796$	−4.32973	−	20.2090i	−0.153463	−	0.716290i
$797$			39.7071i			1.40650i	0.710943	+	0.703250i	$0.248268\pi$
$797$			39.7071i			1.40650i	−0.710943	+	0.703250i	$0.751732\pi$
$798$		0			0
$799$			11.0114i			0.389554i
$800$	−18.9863	+	11.0643i	−0.671267	+	0.391183i
$801$		0			0
$802$	4.41935	+	41.7228i	0.156053	+	1.47328i
$803$	−4.36610			−0.154076
$804$		0			0
$805$	4.14948			0.146250
$806$	−0.136453	−	1.28825i	−0.00480637	−	0.0453766i
$807$		0			0
$808$	−0.436758	−	1.33319i	−0.0153651	−	0.0469015i
$809$			16.9633i			0.596399i	0.954504	+	0.298199i	$0.0963860\pi$
$809$			16.9633i			0.596399i	−0.954504	+	0.298199i	$0.903614\pi$
$810$		0			0
$811$			45.1091i			1.58399i	0.610525	+	0.791997i	$0.290958\pi$
$811$			45.1091i			1.58399i	−0.610525	+	0.791997i	$0.709042\pi$
$812$	0.559129	−	0.119792i	0.0196216	−	0.00420387i
$813$		0			0
$814$	3.75896	−	0.398155i	0.131751	−	0.0139553i
$815$	17.9907			0.630188
$816$		0			0
$817$	34.2283			1.19750
$818$	35.4040	−	3.75005i	1.23787	−	0.131118i
$819$		0			0
$820$	−15.9866	+	3.42509i	−0.558278	+	0.119609i
$821$		−	21.9667i		−	0.766642i	−0.923615	−	0.383321i	$-0.874780\pi$
$821$		−	21.9667i		−	0.766642i	0.923615	−	0.383321i	$-0.125220\pi$
$822$		0			0
$823$			33.4205i			1.16497i	0.812843	+	0.582483i	$0.197919\pi$
$823$			33.4205i			1.16497i	−0.812843	+	0.582483i	$0.802081\pi$
$824$	−9.59648	−	29.2930i	−0.334309	−	1.02047i
$825$		0			0
$826$	−1.60305	−	15.1343i	−0.0557772	−	0.526589i
$827$	47.5356			1.65297			0.826487	−	0.562956i	$-0.190336\pi$
$827$	47.5356			1.65297			0.826487	+	0.562956i	$0.190336\pi$
$828$		0			0
$829$	−0.682765			−0.0237134			−0.0118567	−	0.999930i	$-0.503774\pi$
$829$	−0.682765			−0.0237134			−0.0118567	+	0.999930i	$0.503774\pi$
$830$	2.00015	+	18.8832i	0.0694261	+	0.655447i
$831$		0			0
$832$	17.0994	−	12.5507i	0.592816	−	0.435116i
$833$		−	1.50401i		−	0.0521110i
$834$		0			0
$835$		−	0.859367i		−	0.0297396i
$836$	−1.43654	−	6.70504i	−0.0496837	−	0.231899i
$837$		0			0
$838$	−25.1168	+	2.66041i	−0.867645	+	0.0919025i
$839$	38.4072			1.32596			0.662982	−	0.748635i	$-0.269291\pi$
$839$	38.4072			1.32596			0.662982	+	0.748635i	$0.269291\pi$
$840$		0			0
$841$	28.9183			0.997181
$842$	5.40902	−	0.572933i	0.186407	−	0.0197446i
$843$		0			0
$844$	−8.47667	−	39.5649i	−0.291779	−	1.36188i
$845$			6.30507i			0.216901i
$846$		0			0
$847$		−	10.2430i		−	0.351955i
$848$	23.5995	+	52.5473i	0.810410	+	1.80448i
$849$		0			0
$850$	−0.870328	−	8.21670i	−0.0298520	−	0.281831i
$851$	12.0706			0.413775
$852$		0			0
$853$	−10.0891			−0.345445			−0.172722	−	0.984971i	$-0.555256\pi$
$853$	−10.0891			−0.345445			−0.172722	+	0.984971i	$0.555256\pi$
$854$	0.564294	+	5.32746i	0.0193097	+	0.182302i
$855$		0			0
$856$	−15.6497	+	5.12690i	−0.534896	+	0.175234i
$857$			4.14820i			0.141700i	0.997487	+	0.0708498i	$0.0225711\pi$
$857$			4.14820i			0.141700i	−0.997487	+	0.0708498i	$0.977429\pi$
$858$		0			0
$859$		−	47.7259i		−	1.62839i	−0.580593	−	0.814194i	$-0.697179\pi$
$859$		−	47.7259i		−	1.62839i	0.580593	−	0.814194i	$-0.302821\pi$
$860$	−17.9388	+	3.84334i	−0.611708	+	0.131057i
$861$		0			0
$862$	20.0753	−	2.12642i	0.683769	−	0.0724260i
$863$	41.9443			1.42780			0.713900	−	0.700248i	$-0.246927\pi$
$863$	41.9443			1.42780			0.713900	+	0.700248i	$0.246927\pi$
$864$		0			0
$865$	24.2621			0.824935
$866$	−3.36860	+	0.356808i	−0.114470	+	0.0121248i
$867$		0			0
$868$	−0.675646	+	0.144755i	−0.0229329	+	0.00491331i
$869$			6.05479i			0.205395i
$870$		0			0
$871$			13.7106i			0.464565i
$872$	22.6342	−	7.41505i	0.766491	−	0.251105i
$873$		0			0
$874$	−2.30648	−	21.7753i	−0.0780177	−	0.736560i
$875$	9.38306			0.317205
$876$		0			0
$877$	−3.87160			−0.130735			−0.0653674	−	0.997861i	$-0.520822\pi$
$877$	−3.87160			−0.130735			−0.0653674	+	0.997861i	$0.520822\pi$
$878$	−2.08464	−	19.6810i	−0.0703533	−	0.664201i
$879$		0			0
$880$	1.50575	+	3.35275i	0.0507590	+	0.113021i
$881$		−	54.3752i		−	1.83195i	−0.401239	−	0.915973i	$-0.631420\pi$
$881$		−	54.3752i		−	1.83195i	0.401239	−	0.915973i	$-0.368580\pi$
$882$		0			0
$883$			48.4006i			1.62881i	0.580297	+	0.814405i	$0.302936\pi$
$883$			48.4006i			1.62881i	−0.580297	+	0.814405i	$0.697064\pi$
$884$	1.67080	+	7.79846i	0.0561951	+	0.262291i
$885$		0			0
$886$	39.1704	−	4.14900i	1.31596	−	0.139388i
$887$	18.5182			0.621779			0.310890	−	0.950446i	$-0.399373\pi$
$887$	18.5182			0.621779			0.310890	+	0.950446i	$0.399373\pi$
$888$		0			0
$889$	11.1094			0.372597
$890$	−22.2693	+	2.35881i	−0.746469	+	0.0790674i
$891$		0			0
$892$	7.93117	+	37.0188i	0.265555	+	1.23948i
$893$			28.8516i			0.965482i
$894$		0			0
$895$			4.58265i			0.153181i
$896$	−7.61781	−	8.36474i	−0.254493	−	0.279446i
$897$		0			0
$898$	0.342707	+	3.23548i	0.0114363	+	0.107969i
$899$	0.0987785			0.00329445
$900$		0			0
$901$	−21.6591			−0.721570
$902$	−1.00319	−	9.47105i	−0.0334026	−	0.315351i
$903$		0			0
$904$	13.6530	+	41.6755i	0.454093	+	1.38611i
$905$			24.1883i			0.804045i
$906$		0			0
$907$			2.26206i			0.0751105i	0.999295	+	0.0375552i	$0.0119570\pi$
$907$			2.26206i			0.0751105i	−0.999295	+	0.0375552i	$0.988043\pi$
$908$	−27.4105	+	5.87263i	−0.909650	+	0.194890i
$909$		0			0
$910$	−3.93793	+	0.417113i	−0.130541	+	0.0138272i
$911$	−24.8598			−0.823641			−0.411820	−	0.911265i	$-0.635107\pi$
$911$	−24.8598			−0.823641			−0.411820	+	0.911265i	$0.635107\pi$
$912$		0			0
$913$	−11.0616			−0.366085
$914$	−37.6618	+	3.98921i	−1.24574	+	0.131951i
$915$		0			0
$916$	−26.5971	+	5.69836i	−0.878793	+	0.188279i
$917$		−	11.0139i		−	0.363712i
$918$		0			0
$919$		−	20.9532i		−	0.691183i	−0.938385	−	0.345592i	$-0.887678\pi$
$919$		−	20.9532i		−	0.691183i	0.938385	−	0.345592i	$-0.112322\pi$
$920$	3.65385	+	11.1533i	0.120464	+	0.367712i
$921$		0			0
$922$	1.17302	+	11.0744i	0.0386315	+	0.364717i
$923$	19.7650			0.650573
$924$		0			0
$925$	11.9342			0.392393
$926$	−0.603168	−	5.69447i	−0.0198213	−	0.187132i
$927$		0			0
$928$	0.814328	+	1.39738i	0.0267316	+	0.0458713i
$929$		−	7.62114i		−	0.250042i	−0.992154	−	0.125021i	$-0.960100\pi$
$929$		−	7.62114i		−	0.250042i	0.992154	−	0.125021i	$-0.0398998\pi$
$930$		0			0
$931$		−	3.94077i		−	0.129153i
$932$	−8.71278	−	40.6669i	−0.285397	−	1.33209i
$933$		0			0
$934$	−10.0068	+	1.05994i	−0.327433	+	0.0346822i
$935$	−1.38195			−0.0451945
$936$		0			0
$937$	22.5243			0.735837			0.367918	−	0.929858i	$-0.380071\pi$
$937$	22.5243			0.735837			0.367918	+	0.929858i	$0.380071\pi$
$938$	7.27235	−	0.770301i	0.237451	−	0.0251512i
$939$		0			0
$940$	−3.23961	−	15.1209i	−0.105664	−	0.493189i
$941$			31.3730i			1.02273i	0.859363	+	0.511366i	$0.170860\pi$
$941$			31.3730i			1.02273i	−0.859363	+	0.511366i	$0.829140\pi$
$942$		0			0
$943$		−	30.4130i		−	0.990385i
$944$	39.2674	−	17.6353i	1.27804	−	0.573982i
$945$		0			0
$946$	−1.12569	−	10.6276i	−0.0365994	−	0.345532i
$947$	−36.2883			−1.17921			−0.589606	−	0.807691i	$-0.700717\pi$
$947$	−36.2883			−1.17921			−0.589606	+	0.807691i	$0.700717\pi$
$948$		0			0
$949$	13.3055			0.431913
$950$	−2.28040	−	21.5291i	−0.0739860	−	0.698497i
$951$		0			0
$952$	4.04259	−	1.32437i	0.131021	−	0.0429230i
$953$		−	18.3398i		−	0.594084i	−0.954864	−	0.297042i	$-0.904000\pi$
$953$		−	18.3398i		−	0.594084i	0.954864	−	0.297042i	$-0.0960002\pi$
$954$		0			0
$955$			15.9350i			0.515644i
$956$	−8.16197	+	1.74868i	−0.263977	+	0.0565564i
$957$		0			0
$958$	−19.1998	+	2.03367i	−0.620316	+	0.0657050i
$959$	−10.1565			−0.327972
$960$		0			0
$961$	30.8806			0.996150
$962$	−11.4552	+	1.21336i	−0.369331	+	0.0391202i
$963$		0			0
$964$	39.1911	−	8.39659i	1.26226	−	0.270436i
$965$		−	13.1436i		−	0.423108i
$966$		0			0
$967$			57.0916i			1.83594i	0.396647	+	0.917971i	$0.370174\pi$
$967$			57.0916i			1.83594i	−0.396647	+	0.917971i	$0.629826\pi$
$968$	27.5319	−	9.01955i	0.884909	−	0.289899i
$969$		0			0
$970$	1.26254	+	11.9196i	0.0405379	+	0.382715i
$971$	2.03867			0.0654240			0.0327120	−	0.999465i	$-0.489586\pi$
$971$	2.03867			0.0654240			0.0327120	+	0.999465i	$0.489586\pi$
$972$		0			0
$973$	−9.01304			−0.288945
$974$	−1.30298	−	12.3014i	−0.0417503	−	0.394162i
$975$		0			0
$976$	−13.8226	+	6.20786i	−0.442451	+	0.198709i
$977$			24.0990i			0.770994i	0.922709	+	0.385497i	$0.125970\pi$
$977$			24.0990i			0.770994i	−0.922709	+	0.385497i	$0.874030\pi$
$978$		0			0
$979$		−	13.0451i		−	0.416923i
$980$	0.442490	+	2.06532i	0.0141348	+	0.0659743i
$981$		0			0
$982$	40.6558	−	4.30634i	1.29738	−	0.137421i
$983$	−16.2601			−0.518616			−0.259308	−	0.965795i	$-0.583494\pi$
$983$	−16.2601			−0.518616			−0.259308	+	0.965795i	$0.583494\pi$
$984$		0			0
$985$	−0.859846			−0.0273970
$986$	−0.604745	+	0.0640556i	−0.0192590	+	0.00203995i
$987$		0			0
$988$	4.37777	+	20.4333i	0.139275	+	0.650069i
$989$		−	34.1268i		−	1.08517i
$990$		0			0
$991$			12.6547i			0.401991i	0.979592	+	0.200995i	$0.0644176\pi$
$991$			12.6547i			0.401991i	−0.979592	+	0.200995i	$0.935582\pi$
$992$	−0.984026	−	1.68858i	−0.0312428	−	0.0536125i
$993$		0			0
$994$	−1.11046	−	10.4837i	−0.0352216	−	0.332524i
$995$	−10.9135			−0.345981
$996$		0			0
$997$	29.6658			0.939525			0.469763	−	0.882793i	$-0.344339\pi$
$997$	29.6658			0.939525			0.469763	+	0.882793i	$0.344339\pi$
$998$	0.735841	+	6.94702i	0.0232926	+	0.219904i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.e.a.323.2	yes	24
3.2	odd	2	inner	756.2.e.a.323.23	yes	24
4.3	odd	2	inner	756.2.e.a.323.24	yes	24
12.11	even	2	inner	756.2.e.a.323.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.e.a.323.1	✓	24	12.11	even	2	inner
756.2.e.a.323.2	yes	24	1.1	even	1	trivial
756.2.e.a.323.23	yes	24	3.2	odd	2	inner
756.2.e.a.323.24	yes	24	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40635 + 0.148963i) q^{2} +(1.95562 - 0.418986i) q^{4} -1.05610i q^{5} +1.00000i q^{7} +(-2.68787 + 0.880554i) q^{8} +O(q^{10})\)	\(q+(-1.40635 + 0.148963i) q^{2} +(1.95562 - 0.418986i) q^{4} -1.05610i q^{5} +1.00000i q^{7} +(-2.68787 + 0.880554i) q^{8} +(0.157319 + 1.48524i) q^{10} -0.870034 q^{11} +2.65138 q^{13} +(-0.148963 - 1.40635i) q^{14} +(3.64890 - 1.63876i) q^{16} +1.50401i q^{17} +3.94077i q^{19} +(-0.442490 - 2.06532i) q^{20} +(1.22357 - 0.129603i) q^{22} +3.92908 q^{23} +3.88466 q^{25} +(-3.72876 + 0.394957i) q^{26} +(0.418986 + 1.95562i) q^{28} -0.285909i q^{29} +0.345489i q^{31} +(-4.88751 + 2.84821i) q^{32} +(-0.224042 - 2.11517i) q^{34} +1.05610 q^{35} +3.07212 q^{37} +(-0.587027 - 5.54208i) q^{38} +(0.929950 + 2.83864i) q^{40} -7.74051i q^{41} -8.68571i q^{43} +(-1.70146 + 0.364532i) q^{44} +(-5.52564 + 0.585286i) q^{46} +7.32132 q^{47} -1.00000 q^{49} +(-5.46318 + 0.578670i) q^{50} +(5.18510 - 1.11089i) q^{52} +14.4009i q^{53} +0.918840i q^{55} +(-0.880554 - 2.68787i) q^{56} +(0.0425898 + 0.402087i) q^{58} +10.7614 q^{59} -3.78816 q^{61} +(-0.0514650 - 0.485878i) q^{62} +(6.44925 - 4.73362i) q^{64} -2.80012i q^{65} +5.17110i q^{67} +(0.630161 + 2.94128i) q^{68} +(-1.48524 + 0.157319i) q^{70} +7.45460 q^{71} +5.01831 q^{73} +(-4.32047 + 0.457632i) q^{74} +(1.65113 + 7.70664i) q^{76} -0.870034i q^{77} -6.95925i q^{79} +(-1.73068 - 3.85359i) q^{80} +(1.15305 + 10.8858i) q^{82} +12.7140 q^{83} +1.58838 q^{85} +(1.29385 + 12.2151i) q^{86} +(2.33854 - 0.766112i) q^{88} +14.9938i q^{89} +2.65138i q^{91} +(7.68378 - 1.64623i) q^{92} +(-10.2963 + 1.09060i) q^{94} +4.16183 q^{95} +8.02538 q^{97} +(1.40635 - 0.148963i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{4}+O(q^{10}) \) 24 * q - 8 * q^4	\( 24 q - 8 q^{4} - 16 q^{10} + 8 q^{16} + 16 q^{22} - 24 q^{25} - 8 q^{28} - 8 q^{34} + 16 q^{37} - 8 q^{40} - 24 q^{49} - 8 q^{52} + 32 q^{58} - 80 q^{61} + 40 q^{64} - 24 q^{70} - 32 q^{82} + 56 q^{85} + 56 q^{88} + 72 q^{94}+O(q^{100}) \) 24 * q - 8 * q^4 - 16 * q^10 + 8 * q^16 + 16 * q^22 - 24 * q^25 - 8 * q^28 - 8 * q^34 + 16 * q^37 - 8 * q^40 - 24 * q^49 - 8 * q^52 + 32 * q^58 - 80 * q^61 + 40 * q^64 - 24 * q^70 - 32 * q^82 + 56 * q^85 + 56 * q^88 + 72 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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