LMFDB - Embedded newform 1232.2.bi.b.527.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(527,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 2, 3]))

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

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

chi := DirichletCharacter("1232.527");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.bi (of order $6$, degree $2$, 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:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			527.9
Character	$\chi$	$=$	1232.527
Dual form			1232.2.bi.b.879.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.378296 - 0.218409i) q^{3} +(1.77235 - 3.06979i) q^{5} +(-0.0782028 + 2.64460i) q^{7} +(-1.40459 + 2.43283i) q^{9} +O(q^{10})$	\(q+(0.378296 - 0.218409i) q^{3} +(1.77235 - 3.06979i) q^{5} +(-0.0782028 + 2.64460i) q^{7} +(-1.40459 + 2.43283i) q^{9} +(3.31216 + 0.172066i) q^{11} +1.73558i q^{13} -1.54839i q^{15} +(6.14033 - 3.54512i) q^{17} +(-2.82628 + 4.89526i) q^{19} +(0.548021 + 1.01752i) q^{21} +(4.11553 + 2.37610i) q^{23} +(-3.78242 - 6.55134i) q^{25} +2.53756i q^{27} +5.14195i q^{29} +(1.15290 - 0.665629i) q^{31} +(1.29056 - 0.658315i) q^{33} +(7.97976 + 4.92720i) q^{35} +(-1.31137 + 2.27137i) q^{37} +(0.379068 + 0.656564i) q^{39} -11.4272i q^{41} +7.18250 q^{43} +(4.97885 + 8.62363i) q^{45} +(-1.64006 - 0.946889i) q^{47} +(-6.98777 - 0.413630i) q^{49} +(1.54857 - 2.68221i) q^{51} +(-2.48267 - 4.30011i) q^{53} +(6.39850 - 9.86268i) q^{55} +2.46914i q^{57} +(11.8533 - 6.84353i) q^{59} +(-4.97094 - 2.86997i) q^{61} +(-6.32401 - 3.90484i) q^{63} +(5.32788 + 3.07605i) q^{65} +(-7.50181 + 4.33117i) q^{67} +2.07585 q^{69} -3.90229i q^{71} +(-1.27511 + 0.736187i) q^{73} +(-2.86175 - 1.65223i) q^{75} +(-0.714064 + 8.74586i) q^{77} +(0.136201 - 0.235908i) q^{79} +(-3.65956 - 6.33854i) q^{81} -0.829151 q^{83} -25.1327i q^{85} +(1.12305 + 1.94518i) q^{87} +(3.99274 - 6.91563i) q^{89} +(-4.58991 - 0.135727i) q^{91} +(0.290759 - 0.503610i) q^{93} +(10.0183 + 17.3522i) q^{95} +10.2837 q^{97} +(-5.07085 + 7.81623i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{5} + 12 q^{9}+O(q^{10}) $ 32 * q - 2 * q^5 + 12 * q^9	$ 32 q - 2 q^{5} + 12 q^{9} + 9 q^{11} + 18 q^{23} - 6 q^{25} + 5 q^{33} - 6 q^{37} - 10 q^{45} + 36 q^{47} - 32 q^{49} + 42 q^{59} + 18 q^{67} - 24 q^{69} + 78 q^{75} - 19 q^{77} - 24 q^{81} - 8 q^{89} + 18 q^{91} + 2 q^{93} + 12 q^{97}+O(q^{100}) $ 32 * q - 2 * q^5 + 12 * q^9 + 9 * q^11 + 18 * q^23 - 6 * q^25 + 5 * q^33 - 6 * q^37 - 10 * q^45 + 36 * q^47 - 32 * q^49 + 42 * q^59 + 18 * q^67 - 24 * q^69 + 78 * q^75 - 19 * q^77 - 24 * q^81 - 8 * q^89 + 18 * q^91 + 2 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

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
$3$	0.378296	−	0.218409i	0.218409	−	0.126099i	−0.386804	−	0.922162i	$-0.626421\pi$
$3$	0.378296	−	0.218409i	0.218409	−	0.126099i	0.605214	+	0.796063i	$0.293088\pi$
$4$		0			0
$5$	1.77235	−	3.06979i	0.792617	−	1.37285i	−0.131724	−	0.991286i	$-0.542051\pi$
$5$	1.77235	−	3.06979i	0.792617	−	1.37285i	0.924341	−	0.381567i	$-0.124615\pi$
$6$		0			0
$7$	−0.0782028	+	2.64460i	−0.0295579	+	0.999563i
$7$	−0.0782028	+	2.64460i	−0.0295579	+	0.999563i
$8$		0			0
$9$	−1.40459	+	2.43283i	−0.468198	+	0.810943i
$10$		0			0
$11$	3.31216	+	0.172066i	0.998653	+	0.0518798i
$11$	3.31216	+	0.172066i	0.998653	+	0.0518798i
$12$		0			0
$13$			1.73558i			0.481364i	0.970604	+	0.240682i	$0.0773711\pi$
$13$			1.73558i			0.481364i	−0.970604	+	0.240682i	$0.922629\pi$
$14$		0			0
$15$		−	1.54839i		−	0.399792i
$16$		0			0
$17$	6.14033	−	3.54512i	1.48925	−	0.859818i	0.489323	−	0.872103i	$-0.337244\pi$
$17$	6.14033	−	3.54512i	1.48925	−	0.859818i	0.999925	+	0.0122849i	$0.00391052\pi$
$18$		0			0
$19$	−2.82628	+	4.89526i	−0.648393	+	1.12305i	0.335114	+	0.942178i	$0.391225\pi$
$19$	−2.82628	+	4.89526i	−0.648393	+	1.12305i	−0.983507	+	0.180872i	$0.942108\pi$
$20$		0			0
$21$	0.548021	+	1.01752i	0.119588	+	0.222041i
$22$		0			0
$23$	4.11553	+	2.37610i	0.858147	+	0.495452i	0.863391	−	0.504535i	$-0.168336\pi$
$23$	4.11553	+	2.37610i	0.858147	+	0.495452i	−0.00524419	+	0.999986i	$0.501669\pi$
$24$		0			0
$25$	−3.78242	−	6.55134i	−0.756484	−	1.31027i
$26$		0			0
$27$			2.53756i			0.488354i
$28$		0			0
$29$			5.14195i			0.954836i	0.878676	+	0.477418i	$0.158427\pi$
$29$			5.14195i			0.954836i	−0.878676	+	0.477418i	$0.841573\pi$
$30$		0			0
$31$	1.15290	−	0.665629i	0.207067	−	0.119550i	−0.392880	−	0.919590i	$-0.628521\pi$
$31$	1.15290	−	0.665629i	0.207067	−	0.119550i	0.599948	+	0.800039i	$0.295188\pi$
$32$		0			0
$33$	1.29056	−	0.658315i	0.224657	−	0.114598i
$34$		0			0
$35$	7.97976	+	4.92720i	1.34883	+	0.832849i
$36$		0			0
$37$	−1.31137	+	2.27137i	−0.215589	+	0.373411i	−0.953455	−	0.301537i	$-0.902500\pi$
$37$	−1.31137	+	2.27137i	−0.215589	+	0.373411i	0.737866	+	0.674947i	$0.235834\pi$
$38$		0			0
$39$	0.379068	+	0.656564i	0.0606994	+	0.105134i
$40$		0			0
$41$		−	11.4272i		−	1.78462i	−0.451419	−	0.892312i	$-0.649082\pi$
$41$		−	11.4272i		−	1.78462i	0.451419	−	0.892312i	$-0.350918\pi$
$42$		0			0
$43$	7.18250			1.09532			0.547661	−	0.836701i	$-0.315518\pi$
$43$	7.18250			1.09532			0.547661	+	0.836701i	$0.315518\pi$
$44$		0			0
$45$	4.97885	+	8.62363i	0.742204	+	1.28553i
$46$		0			0
$47$	−1.64006	−	0.946889i	−0.239227	−	0.138118i	0.375594	−	0.926784i	$-0.377439\pi$
$47$	−1.64006	−	0.946889i	−0.239227	−	0.138118i	−0.614822	+	0.788666i	$0.710772\pi$
$48$		0			0
$49$	−6.98777	−	0.413630i	−0.998253	−	0.0590900i
$50$		0			0
$51$	1.54857	−	2.68221i	0.216844	−	0.375585i
$52$		0			0
$53$	−2.48267	−	4.30011i	−0.341021	−	0.590666i	0.643602	−	0.765361i	$-0.277439\pi$
$53$	−2.48267	−	4.30011i	−0.341021	−	0.590666i	−0.984623	+	0.174695i	$0.944106\pi$
$54$		0			0
$55$	6.39850	−	9.86268i	0.862773	−	1.32988i
$56$		0			0
$57$			2.46914i			0.327046i
$58$		0			0
$59$	11.8533	−	6.84353i	1.54317	−	0.890951i	0.544537	−	0.838737i	$-0.316706\pi$
$59$	11.8533	−	6.84353i	1.54317	−	0.890951i	0.998636	−	0.0522141i	$-0.0166278\pi$
$60$		0			0
$61$	−4.97094	−	2.86997i	−0.636463	−	0.367462i	0.146788	−	0.989168i	$-0.453107\pi$
$61$	−4.97094	−	2.86997i	−0.636463	−	0.367462i	−0.783251	+	0.621706i	$0.786440\pi$
$62$		0			0
$63$	−6.32401	−	3.90484i	−0.796750	−	0.491963i
$64$		0			0
$65$	5.32788	+	3.07605i	0.660842	+	0.381537i
$66$		0			0
$67$	−7.50181	+	4.33117i	−0.916492	+	0.529137i	−0.882514	−	0.470286i	$-0.844151\pi$
$67$	−7.50181	+	4.33117i	−0.916492	+	0.529137i	−0.0339777	+	0.999423i	$0.510818\pi$
$68$		0			0
$69$	2.07585			0.249903
$70$		0			0
$71$		−	3.90229i		−	0.463116i	−0.972821	−	0.231558i	$-0.925618\pi$
$71$		−	3.90229i		−	0.463116i	0.972821	−	0.231558i	$-0.0743824\pi$
$72$		0			0
$73$	−1.27511	+	0.736187i	−0.149241	+	0.0861642i	−0.572761	−	0.819722i	$-0.694128\pi$
$73$	−1.27511	+	0.736187i	−0.149241	+	0.0861642i	0.423520	+	0.905887i	$0.360794\pi$
$74$		0			0
$75$	−2.86175	−	1.65223i	−0.330446	−	0.190783i
$76$		0			0
$77$	−0.714064	+	8.74586i	−0.0813752	+	0.996684i
$78$		0			0
$79$	0.136201	−	0.235908i	0.0153238	−	0.0265417i	−0.858262	−	0.513212i	$-0.828455\pi$
$79$	0.136201	−	0.235908i	0.0153238	−	0.0265417i	0.873586	+	0.486670i	$0.161789\pi$
$80$		0			0
$81$	−3.65956	−	6.33854i	−0.406617	−	0.704282i
$82$		0			0
$83$	−0.829151			−0.0910111			−0.0455056	−	0.998964i	$-0.514490\pi$
$83$	−0.829151			−0.0910111			−0.0455056	+	0.998964i	$0.514490\pi$
$84$		0			0
$85$		−	25.1327i		−	2.72602i
$86$		0			0
$87$	1.12305	+	1.94518i	0.120404	+	0.208545i
$88$		0			0
$89$	3.99274	−	6.91563i	0.423230	−	0.733056i	−0.573023	−	0.819539i	$-0.694230\pi$
$89$	3.99274	−	6.91563i	0.423230	−	0.733056i	0.996253	+	0.0864833i	$0.0275629\pi$
$90$		0			0
$91$	−4.58991	−	0.135727i	−0.481154	−	0.0142281i
$92$		0			0
$93$	0.290759	−	0.503610i	0.0301503	−	0.0522219i
$94$		0			0
$95$	10.0183	+	17.3522i	1.02785	+	1.78030i
$96$		0			0
$97$	10.2837			1.04415			0.522074	−	0.852900i	$-0.325159\pi$
$97$	10.2837			1.04415			0.522074	+	0.852900i	$0.325159\pi$
$98$		0			0
$99$	−5.07085	+	7.81623i	−0.509639	+	0.785561i
$100$		0			0
$101$	9.55063	−	5.51406i	0.950323	−	0.548669i	0.0571416	−	0.998366i	$-0.481801\pi$
$101$	9.55063	−	5.51406i	0.950323	−	0.548669i	0.893181	+	0.449697i	$0.148468\pi$
$102$		0			0
$103$	2.43645	+	1.40669i	0.240071	+	0.138605i	0.615209	−	0.788364i	$-0.289071\pi$
$103$	2.43645	+	1.40669i	0.240071	+	0.138605i	−0.375138	+	0.926969i	$0.622405\pi$
$104$		0			0
$105$	4.09486	+	0.121088i	0.399617	+	0.0118170i
$106$		0			0
$107$	−6.88822	+	11.9308i	−0.665910	+	1.15339i	0.313128	+	0.949711i	$0.398623\pi$
$107$	−6.88822	+	11.9308i	−0.665910	+	1.15339i	−0.979038	+	0.203679i	$0.934710\pi$
$108$		0			0
$109$	−14.0430	+	8.10776i	−1.34508	+	0.776582i	−0.987548	−	0.157318i	$-0.949715\pi$
$109$	−14.0430	+	8.10776i	−1.34508	+	0.776582i	−0.357532	+	0.933901i	$0.616382\pi$
$110$		0			0
$111$			1.14567i			0.108742i
$112$		0			0
$113$	2.80710			0.264069			0.132035	−	0.991245i	$-0.457849\pi$
$113$	2.80710			0.264069			0.132035	+	0.991245i	$0.457849\pi$
$114$		0			0
$115$	14.5883	−	8.42255i	1.36036	−	0.785407i
$116$		0			0
$117$	−4.22238	−	2.43779i	−0.390359	−	0.225374i
$118$		0			0
$119$	8.89521	+	16.5159i	0.815423	+	1.51401i
$120$		0			0
$121$	10.9408	+	1.13982i	0.994617	+	0.103620i
$122$		0			0
$123$	−2.49580	−	4.32286i	−0.225039	−	0.389779i
$124$		0			0
$125$	−9.09155			−0.813173
$126$		0			0
$127$	−8.13226			−0.721622			−0.360811	−	0.932639i	$-0.617500\pi$
$127$	−8.13226			−0.721622			−0.360811	+	0.932639i	$0.617500\pi$
$128$		0			0
$129$	2.71711	−	1.56873i	0.239228	−	0.138119i
$130$		0			0
$131$	−5.86312	+	10.1552i	−0.512263	+	0.887266i	0.487636	+	0.873047i	$0.337859\pi$
$131$	−5.86312	+	10.1552i	−0.512263	+	0.887266i	−0.999899	+	0.0142187i	$0.995474\pi$
$132$		0			0
$133$	−12.7250	−	7.85719i	−1.10339	−	0.681305i
$134$		0			0
$135$	7.78979	+	4.49744i	0.670439	+	0.387078i
$136$		0			0
$137$	3.56810	+	6.18014i	0.304844	+	0.528005i	0.977227	−	0.212199i	$-0.0680624\pi$
$137$	3.56810	+	6.18014i	0.304844	+	0.528005i	−0.672383	+	0.740204i	$0.734729\pi$
$138$		0			0
$139$	0.178761			0.0151623			0.00758115	−	0.999971i	$-0.497587\pi$
$139$	0.178761			0.0151623			0.00758115	+	0.999971i	$0.497587\pi$
$140$		0			0
$141$	−0.827238			−0.0696660
$142$		0			0
$143$	−0.298634	+	5.74852i	−0.0249730	+	0.480716i
$144$		0			0
$145$	15.7847	+	9.11331i	1.31085	+	0.756819i
$146$		0			0
$147$	−2.73379	+	1.36972i	−0.225479	+	0.112973i
$148$		0			0
$149$	6.32544	+	3.65199i	0.518200	+	0.299183i	0.736198	−	0.676766i	$-0.236619\pi$
$149$	6.32544	+	3.65199i	0.518200	+	0.299183i	−0.217998	+	0.975949i	$0.569953\pi$
$150$		0			0
$151$	−2.85561	−	4.94606i	−0.232386	−	0.402504i	0.726124	−	0.687564i	$-0.241320\pi$
$151$	−2.85561	−	4.94606i	−0.232386	−	0.402504i	−0.958510	+	0.285060i	$0.907987\pi$
$152$		0			0
$153$			19.9178i			1.61026i
$154$		0			0
$155$		−	4.71890i		−	0.379031i
$156$		0			0
$157$	9.56429	+	16.5658i	0.763313	+	1.32210i	0.941134	+	0.338035i	$0.109762\pi$
$157$	9.56429	+	16.5658i	0.763313	+	1.32210i	−0.177820	+	0.984063i	$0.556905\pi$
$158$		0			0
$159$	−1.87837	−	1.08448i	−0.148964	−	0.0860047i
$160$		0			0
$161$	−6.60567	+	10.6981i	−0.520600	+	0.843128i
$162$		0			0
$163$	−8.81090	−	5.08698i	−0.690123	−	0.398443i	0.113535	−	0.993534i	$-0.463783\pi$
$163$	−8.81090	−	5.08698i	−0.690123	−	0.398443i	−0.803658	+	0.595091i	$0.797116\pi$
$164$		0			0
$165$	0.266424	−	5.12851i	0.0207411	−	0.399254i
$166$		0			0
$167$	−13.1455			−1.01723			−0.508616	−	0.860993i	$-0.669843\pi$
$167$	−13.1455			−1.01723			−0.508616	+	0.860993i	$0.669843\pi$
$168$		0			0
$169$	9.98775			0.768289
$170$		0			0
$171$	−7.93955	−	13.7517i	−0.607153	−	1.05162i
$172$		0			0
$173$	−18.1603	−	10.4849i	−1.38071	−	0.797150i	−0.388462	−	0.921465i	$-0.626994\pi$
$173$	−18.1603	−	10.4849i	−1.38071	−	0.797150i	−0.992243	+	0.124314i	$0.960327\pi$
$174$		0			0
$175$	17.6214	−	9.49063i	1.33206	−	0.717424i
$176$		0			0
$177$	2.98938	−	5.17776i	0.224696	−	0.389184i
$178$		0			0
$179$	8.40739	−	4.85401i	0.628398	−	0.362806i	−0.151734	−	0.988421i	$-0.548486\pi$
$179$	8.40739	−	4.85401i	0.628398	−	0.362806i	0.780131	+	0.625616i	$0.215152\pi$
$180$		0			0
$181$	−11.8561			−0.881253			−0.440627	−	0.897690i	$-0.645244\pi$
$181$	−11.8561			−0.881253			−0.440627	+	0.897690i	$0.645244\pi$
$182$		0			0
$183$	−2.50732			−0.185346
$184$		0			0
$185$	4.64842	+	8.05130i	0.341759	+	0.591943i
$186$		0			0
$187$	20.9477	−	10.6855i	1.53185	−	0.781398i
$188$		0			0
$189$	−6.71083	−	0.198445i	−0.488141	−	0.0144347i
$190$		0			0
$191$	−20.9992	−	12.1239i	−1.51945	−	0.877255i	−0.999737	−	0.0229142i	$-0.992706\pi$
$191$	−20.9992	−	12.1239i	−1.51945	−	0.877255i	−0.519713	−	0.854341i	$-0.673961\pi$
$192$		0			0
$193$	8.26937	−	4.77432i	0.595242	−	0.343663i	−0.171925	−	0.985110i	$-0.554999\pi$
$193$	8.26937	−	4.77432i	0.595242	−	0.343663i	0.767168	+	0.641447i	$0.221665\pi$
$194$		0			0
$195$	2.68735			0.192445
$196$		0			0
$197$		−	3.78280i		−	0.269514i	−0.990879	−	0.134757i	$-0.956975\pi$
$197$		−	3.78280i		−	0.269514i	0.990879	−	0.134757i	$-0.0430253\pi$
$198$		0			0
$199$	−13.3875	+	7.72927i	−0.949014	+	0.547914i	−0.892775	−	0.450504i	$-0.851244\pi$
$199$	−13.3875	+	7.72927i	−0.949014	+	0.547914i	−0.0562398	+	0.998417i	$0.517911\pi$
$200$		0			0
$201$	−1.89194	+	3.27693i	−0.133447	+	0.231137i
$202$		0			0
$203$	−13.5984	−	0.402115i	−0.954418	−	0.0282229i
$204$		0			0
$205$	−35.0790	−	20.2529i	−2.45003	−	1.41452i
$206$		0			0
$207$	−11.5613	+	6.67492i	−0.803566	+	0.463939i
$208$		0			0
$209$	−10.2034	+	15.7276i	−0.705783	+	1.08790i
$210$		0			0
$211$	19.0966			1.31467			0.657333	−	0.753600i	$-0.271684\pi$
$211$	19.0966			1.31467			0.657333	+	0.753600i	$0.271684\pi$
$212$		0			0
$213$	−0.852297	−	1.47622i	−0.0583984	−	0.101149i
$214$		0			0
$215$	12.7299	−	22.0488i	0.868170	−	1.50372i
$216$		0			0
$217$	1.67016	+	3.10102i	0.113378	+	0.210511i
$218$		0			0
$219$	−0.321581	+	0.556994i	−0.0217304	+	0.0376382i
$220$		0			0
$221$	6.15285	+	10.6570i	0.413885	+	0.716870i
$222$		0			0
$223$			6.87289i			0.460243i	0.973162	+	0.230121i	$0.0739123\pi$
$223$			6.87289i			0.460243i	−0.973162	+	0.230121i	$0.926088\pi$
$224$		0			0
$225$	21.2511			1.41674
$226$		0			0
$227$	−14.2462	−	24.6751i	−0.945551	−	1.63774i	−0.754644	−	0.656134i	$-0.772190\pi$
$227$	−14.2462	−	24.6751i	−0.945551	−	1.63774i	−0.190907	−	0.981608i	$-0.561143\pi$
$228$		0			0
$229$	−5.86371	+	10.1562i	−0.387485	+	0.671143i	−0.992110	−	0.125367i	$-0.959989\pi$
$229$	−5.86371	+	10.1562i	−0.387485	+	0.671143i	0.604626	+	0.796510i	$0.293323\pi$
$230$		0			0
$231$	1.64005	+	3.46449i	0.107907	+	0.227946i
$232$		0			0
$233$	−11.4182	−	6.59229i	−0.748030	−	0.431875i	0.0769519	−	0.997035i	$-0.475481\pi$
$233$	−11.4182	−	6.59229i	−0.748030	−	0.431875i	−0.824982	+	0.565160i	$0.808815\pi$
$234$		0			0
$235$	−5.81351	+	3.35643i	−0.379231	+	0.218949i
$236$		0			0
$237$		−	0.118991i		−	0.00772927i
$238$		0			0
$239$	−20.0194			−1.29495			−0.647474	−	0.762088i	$-0.724174\pi$
$239$	−20.0194			−1.29495			−0.647474	+	0.762088i	$0.724174\pi$
$240$		0			0
$241$	−2.60101	+	1.50169i	−0.167546	+	0.0967325i	−0.581428	−	0.813598i	$-0.697506\pi$
$241$	−2.60101	+	1.50169i	−0.167546	+	0.0967325i	0.413882	+	0.910330i	$0.364172\pi$
$242$		0			0
$243$	−9.36158	−	5.40491i	−0.600545	−	0.346725i
$244$		0			0
$245$	−13.6545	+	20.7179i	−0.872354	+	1.32362i
$246$		0			0
$247$	−8.49613	−	4.90524i	−0.540596	−	0.312113i
$248$		0			0
$249$	−0.313665	+	0.181094i	−0.0198777	+	0.0114764i
$250$		0			0
$251$			15.9926i			1.00944i	0.863282	+	0.504722i	$0.168405\pi$
$251$			15.9926i			1.00944i	−0.863282	+	0.504722i	$0.831595\pi$
$252$		0			0
$253$	13.2224	+	8.57817i	0.831288	+	0.539305i
$254$		0			0
$255$	−5.48922	−	9.50761i	−0.343748	−	0.595389i
$256$		0			0
$257$	8.08219	−	13.9988i	0.504153	−	0.873219i	−0.495835	−	0.868417i	$-0.665138\pi$
$257$	8.08219	−	13.9988i	0.504153	−	0.873219i	0.999988	−	0.00480245i	$-0.00152867\pi$
$258$		0			0
$259$	−5.90430	−	3.64568i	−0.366875	−	0.226532i
$260$		0			0
$261$	−12.5095	−	7.22235i	−0.774317	−	0.447052i
$262$		0			0
$263$	−13.2745	−	22.9920i	−0.818539	−	1.41775i	−0.906759	−	0.421649i	$-0.861451\pi$
$263$	−13.2745	−	22.9920i	−0.818539	−	1.41775i	0.0882203	−	0.996101i	$-0.471882\pi$
$264$		0			0
$265$	−17.6006			−1.08120
$266$		0			0
$267$		−	3.48821i		−	0.213475i
$268$		0			0
$269$	−0.253915	−	0.439793i	−0.0154814	−	0.0268146i	0.858181	−	0.513347i	$-0.171595\pi$
$269$	−0.253915	−	0.439793i	−0.0154814	−	0.0268146i	−0.873662	+	0.486533i	$0.838261\pi$
$270$		0			0
$271$	−2.60492	+	4.51186i	−0.158238	+	0.274076i	−0.934233	−	0.356663i	$-0.883915\pi$
$271$	−2.60492	+	4.51186i	−0.158238	+	0.274076i	0.775995	+	0.630738i	$0.217248\pi$
$272$		0			0
$273$	−1.76599	+	0.951135i	−0.106883	+	0.0575653i
$274$		0			0
$275$	−11.4007	−	22.3499i	−0.687488	−	1.34775i
$276$		0			0
$277$	1.84819	−	1.06705i	0.111047	−	0.0641129i	−0.443448	−	0.896300i	$-0.646245\pi$
$277$	1.84819	−	1.06705i	0.111047	−	0.0641129i	0.554495	+	0.832187i	$0.312912\pi$
$278$		0			0
$279$			3.73975i			0.223893i
$280$		0			0
$281$			14.8854i			0.887991i	0.896029	+	0.443996i	$0.146439\pi$
$281$			14.8854i			0.887991i	−0.896029	+	0.443996i	$0.853561\pi$
$282$		0			0
$283$	5.49575	+	9.51892i	0.326689	+	0.565841i	0.981853	−	0.189645i	$-0.0607338\pi$
$283$	5.49575	+	9.51892i	0.326689	+	0.565841i	−0.655164	+	0.755487i	$0.727400\pi$
$284$		0			0
$285$	7.57976	+	4.37618i	0.448986	+	0.259222i
$286$		0			0
$287$	30.2202	+	0.893637i	1.78384	+	0.0527497i
$288$		0			0
$289$	16.6357	−	28.8139i	0.978573	−	1.69494i
$290$		0			0
$291$	3.89027	−	2.24605i	0.228052	−	0.131666i
$292$		0			0
$293$		−	9.80630i		−	0.572890i	−0.958097	−	0.286445i	$-0.907526\pi$
$293$		−	9.80630i		−	0.572890i	0.958097	−	0.286445i	$-0.0924736\pi$
$294$		0			0
$295$		−	48.5164i		−	2.82473i
$296$		0			0
$297$	−0.436628	+	8.40481i	−0.0253357	+	0.487697i
$298$		0			0
$299$	−4.12392	+	7.14284i	−0.238493	+	0.413081i
$300$		0			0
$301$	−0.561692	+	18.9948i	−0.0323754	+	1.09484i
$302$		0			0
$303$	2.40864	−	4.17189i	0.138373	−	0.239669i
$304$		0			0
$305$	−17.6204	+	10.1732i	−1.00894	+	0.582514i
$306$		0			0
$307$	−9.05744			−0.516936			−0.258468	−	0.966020i	$-0.583218\pi$
$307$	−9.05744			−0.516936			−0.258468	+	0.966020i	$0.583218\pi$
$308$		0			0
$309$	1.22894			0.0699117
$310$		0			0
$311$	−11.8191	+	6.82374i	−0.670198	+	0.386939i	−0.796152	−	0.605097i	$-0.793134\pi$
$311$	−11.8191	+	6.82374i	−0.670198	+	0.386939i	0.125954	+	0.992036i	$0.459801\pi$
$312$		0			0
$313$	−9.03626	+	15.6513i	−0.510760	+	0.884662i	0.489163	+	0.872193i	$0.337302\pi$
$313$	−9.03626	+	15.6513i	−0.510760	+	0.884662i	−0.999922	+	0.0124691i	$0.996031\pi$
$314$		0			0
$315$	−23.1954	+	12.4927i	−1.30691	+	0.703882i
$316$		0			0
$317$	15.4159	−	26.7011i	0.865844	−	1.49969i	−0.000363291	−	1.00000i	$-0.500116\pi$
$317$	15.4159	−	26.7011i	0.865844	−	1.49969i	0.866207	−	0.499685i	$-0.166551\pi$
$318$		0			0
$319$	−0.884753	+	17.0309i	−0.0495366	+	0.953550i
$320$		0			0
$321$			6.01781i			0.335882i
$322$		0			0
$323$			40.0780i			2.23000i
$324$		0			0
$325$	11.3704	−	6.56470i	0.630716	−	0.364144i
$326$		0			0
$327$	−3.54162	+	6.13427i	−0.195852	+	0.339226i
$328$		0			0
$329$	2.63240	−	4.26325i	0.145129	−	0.235040i
$330$		0			0
$331$	5.11477	+	2.95301i	0.281133	+	0.162312i	0.633936	−	0.773385i	$-0.281438\pi$
$331$	5.11477	+	2.95301i	0.281133	+	0.162312i	−0.352803	+	0.935698i	$0.614772\pi$
$332$		0			0
$333$	−3.68390	−	6.38070i	−0.201876	−	0.349660i
$334$		0			0
$335$			30.7053i			1.67761i
$336$		0			0
$337$		−	15.8442i		−	0.863087i	−0.902092	−	0.431544i	$-0.857969\pi$
$337$		−	15.8442i		−	0.863087i	0.902092	−	0.431544i	$-0.142031\pi$
$338$		0			0
$339$	1.06191	−	0.613096i	0.0576753	−	0.0332988i
$340$		0			0
$341$	3.93313	−	2.00629i	0.212991	−	0.108647i
$342$		0			0
$343$	1.64035	−	18.4475i	0.0885704	−	0.996070i
$344$		0			0
$345$	3.67913	−	6.37244i	0.198078	−	0.343080i
$346$		0			0
$347$	−9.60169	−	16.6306i	−0.515446	−	0.892778i	−0.999839	−	0.0179281i	$-0.994293\pi$
$347$	−9.60169	−	16.6306i	−0.515446	−	0.892778i	0.484393	−	0.874850i	$-0.339040\pi$
$348$		0			0
$349$			25.2245i			1.35024i	0.737710	+	0.675118i	$0.235907\pi$
$349$			25.2245i			1.35024i	−0.737710	+	0.675118i	$0.764093\pi$
$350$		0			0
$351$	−4.40415			−0.235076
$352$		0			0
$353$	11.1464	+	19.3061i	0.593261	+	1.02756i	0.993790	+	0.111275i	$0.0354933\pi$
$353$	11.1464	+	19.3061i	0.593261	+	1.02756i	−0.400528	+	0.916284i	$0.631173\pi$
$354$		0			0
$355$	−11.9792	−	6.91620i	−0.635791	−	0.367074i
$356$		0			0
$357$	6.97226	+	4.30511i	0.369011	+	0.227851i
$358$		0			0
$359$	−15.1135	+	26.1774i	−0.797663	+	1.38159i	0.123472	+	0.992348i	$0.460597\pi$
$359$	−15.1135	+	26.1774i	−0.797663	+	1.38159i	−0.921135	+	0.389244i	$0.872736\pi$
$360$		0			0
$361$	−6.47571	−	11.2163i	−0.340827	−	0.590330i
$362$		0			0
$363$	4.38781	−	1.95838i	0.230300	−	0.102788i
$364$		0			0
$365$			5.21911i			0.273181i
$366$		0			0
$367$	22.3456	−	12.9012i	1.16643	−	0.673439i	0.213593	−	0.976923i	$-0.431483\pi$
$367$	22.3456	−	12.9012i	1.16643	−	0.673439i	0.952837	+	0.303484i	$0.0981499\pi$
$368$		0			0
$369$	27.8004	+	16.0505i	1.44723	+	0.835558i
$370$		0			0
$371$	11.5662	−	6.22938i	0.600488	−	0.323413i
$372$		0			0
$373$	−28.9234	−	16.6990i	−1.49760	−	0.864639i	−0.497602	−	0.867405i	$-0.665786\pi$
$373$	−28.9234	−	16.6990i	−1.49760	−	0.864639i	−0.999996	+	0.00276631i	$0.999119\pi$
$374$		0			0
$375$	−3.43930	+	1.98568i	−0.177605	+	0.102540i
$376$		0			0
$377$	−8.92427			−0.459623
$378$		0			0
$379$			32.0259i			1.64506i	0.568723	+	0.822529i	$0.307438\pi$
$379$			32.0259i			1.64506i	−0.568723	+	0.822529i	$0.692562\pi$
$380$		0			0
$381$	−3.07640	+	1.77616i	−0.157609	+	0.0909956i
$382$		0			0
$383$	11.3457	+	6.55042i	0.579736	+	0.334711i	0.761029	−	0.648718i	$-0.224695\pi$
$383$	11.3457	+	6.55042i	0.579736	+	0.334711i	−0.181292	+	0.983429i	$0.558028\pi$
$384$		0			0
$385$	25.5824	+	17.6927i	1.30380	+	0.901705i
$386$		0			0
$387$	−10.0885	+	17.4738i	−0.512827	+	0.888243i
$388$		0			0
$389$	14.7794	+	25.5987i	0.749345	+	1.29790i	0.948137	+	0.317862i	$0.102965\pi$
$389$	14.7794	+	25.5987i	0.749345	+	1.29790i	−0.198792	+	0.980042i	$0.563702\pi$
$390$		0			0
$391$	33.6943			1.70399
$392$		0			0
$393$			5.12224i			0.258383i
$394$		0			0
$395$	−0.482791	−	0.836219i	−0.0242919	−	0.0420748i
$396$		0			0
$397$	−8.60451	+	14.9035i	−0.431848	+	0.747983i	−0.997032	−	0.0769818i	$-0.975472\pi$
$397$	−8.60451	+	14.9035i	−0.431848	+	0.747983i	0.565184	+	0.824965i	$0.308805\pi$
$398$		0			0
$399$	−6.52989	−	0.193094i	−0.326903	−	0.00966680i
$400$		0			0
$401$	10.7946	−	18.6968i	0.539058	−	0.933675i	−0.459897	−	0.887972i	$-0.652114\pi$
$401$	10.7946	−	18.6968i	0.539058	−	0.933675i	0.998955	−	0.0457032i	$-0.0145528\pi$
$402$		0			0
$403$	1.15525	+	2.00096i	0.0575473	+	0.0996748i
$404$		0			0
$405$	−25.9440			−1.28917
$406$		0			0
$407$	−4.73431	+	7.29749i	−0.234671	+	0.361723i
$408$		0			0
$409$	33.0999	−	19.1103i	1.63669	−	0.944941i	0.654723	−	0.755869i	$-0.272785\pi$
$409$	33.0999	−	19.1103i	1.63669	−	0.944941i	0.981963	−	0.189072i	$-0.0605479\pi$
$410$		0			0
$411$	2.69960	+	1.55862i	0.133161	+	0.0768808i
$412$		0			0
$413$	17.1714	+	31.8825i	0.844949	+	1.56883i
$414$		0			0
$415$	−1.46954	+	2.54532i	−0.0721370	+	0.124945i
$416$		0			0
$417$	0.0676245	−	0.0390430i	0.00331159	−	0.00191195i
$418$		0			0
$419$		−	2.12908i		−	0.104012i	−0.998647	−	0.0520062i	$-0.983438\pi$
$419$		−	2.12908i		−	0.104012i	0.998647	−	0.0520062i	$-0.0165616\pi$
$420$		0			0
$421$	−26.3749			−1.28544			−0.642718	−	0.766103i	$-0.722193\pi$
$421$	−26.3749			−1.28544			−0.642718	+	0.766103i	$0.722193\pi$
$422$		0			0
$423$	4.60724	−	2.65999i	0.224012	−	0.129333i
$424$		0			0
$425$	−46.4506	−	26.8182i	−2.25318	−	1.30088i
$426$		0			0
$427$	7.97866	−	12.9217i	0.386114	−	0.625324i
$428$		0			0
$429$	1.14256	+	2.23987i	0.0551633	+	0.108142i
$430$		0			0
$431$	−14.7292	−	25.5117i	−0.709479	−	1.22885i	−0.965051	−	0.262064i	$-0.915597\pi$
$431$	−14.7292	−	25.5117i	−0.709479	−	1.22885i	0.255572	−	0.966790i	$-0.417736\pi$
$432$		0			0
$433$	−23.1651			−1.11324			−0.556622	−	0.830766i	$-0.687903\pi$
$433$	−23.1651			−1.11324			−0.556622	+	0.830766i	$0.687903\pi$
$434$		0			0
$435$	7.96173			0.381736
$436$		0			0
$437$	−23.2633	+	13.4311i	−1.11283	+	0.642495i
$438$		0			0
$439$	−9.80656	+	16.9855i	−0.468041	+	0.810672i	−0.999333	−	0.0365175i	$-0.988374\pi$
$439$	−9.80656	+	16.9855i	−0.468041	+	0.810672i	0.531292	+	0.847189i	$0.321707\pi$
$440$		0			0
$441$	10.8213	−	16.4191i	0.515299	−	0.781860i
$442$		0			0
$443$	−8.72109	−	5.03512i	−0.414351	−	0.239226i	0.278306	−	0.960492i	$-0.410227\pi$
$443$	−8.72109	−	5.03512i	−0.414351	−	0.239226i	−0.692658	+	0.721266i	$0.743560\pi$
$444$		0			0
$445$	−14.1530	−	24.5138i	−0.670919	−	1.16206i
$446$		0			0
$447$	3.19052			0.150906
$448$		0			0
$449$	−22.6926			−1.07093			−0.535466	−	0.844557i	$-0.679864\pi$
$449$	−22.6926			−1.07093			−0.535466	+	0.844557i	$0.679864\pi$
$450$		0			0
$451$	1.96622	−	37.8486i	0.0925859	−	1.78222i
$452$		0			0
$453$	−2.16053	−	1.24738i	−0.101511	−	0.0586072i
$454$		0			0
$455$	−8.55157	+	13.8495i	−0.400904	+	0.649276i
$456$		0			0
$457$	2.16313	+	1.24888i	0.101187	+	0.0584204i	0.549740	−	0.835336i	$-0.314727\pi$
$457$	2.16313	+	1.24888i	0.101187	+	0.0584204i	−0.448553	+	0.893756i	$0.648060\pi$
$458$		0			0
$459$	8.99596	+	15.5815i	0.419896	+	0.727281i
$460$		0			0
$461$		−	7.48432i		−	0.348580i	−0.984694	−	0.174290i	$-0.944237\pi$
$461$		−	7.48432i		−	0.348580i	0.984694	−	0.174290i	$-0.0557630\pi$
$462$		0			0
$463$		−	41.7018i		−	1.93805i	−0.246971	−	0.969023i	$-0.579435\pi$
$463$		−	41.7018i		−	1.93805i	0.246971	−	0.969023i	$-0.420565\pi$
$464$		0			0
$465$	−1.03065	−	1.78514i	−0.0477953	−	0.0827839i
$466$		0			0
$467$	−27.1833	−	15.6943i	−1.25789	−	0.726244i	−0.285227	−	0.958460i	$-0.592069\pi$
$467$	−27.1833	−	15.6943i	−1.25789	−	0.726244i	−0.972664	+	0.232216i	$0.925402\pi$
$468$		0			0
$469$	−10.8675	−	20.1780i	−0.501816	−	0.931732i
$470$		0			0
$471$	7.23627	+	4.17786i	0.333430	+	0.192506i
$472$		0			0
$473$	23.7896	+	1.23586i	1.09385	+	0.0568250i
$474$		0			0
$475$	42.7607			1.96199
$476$		0			0
$477$	13.9486			0.638662
$478$		0			0
$479$	2.99420	+	5.18611i	0.136809	+	0.236959i	0.926287	−	0.376819i	$-0.122982\pi$
$479$	2.99420	+	5.18611i	0.136809	+	0.236959i	−0.789478	+	0.613778i	$0.789649\pi$
$480$		0			0
$481$	−3.94215	−	2.27600i	−0.179746	−	0.103777i
$482$		0			0
$483$	−0.162338	+	5.48979i	−0.00738661	+	0.249794i
$484$		0			0
$485$	18.2262	−	31.5687i	0.827609	−	1.43346i
$486$		0			0
$487$	14.2993	−	8.25573i	0.647965	−	0.374103i	−0.139711	−	0.990192i	$-0.544617\pi$
$487$	14.2993	−	8.25573i	0.647965	−	0.374103i	0.787676	+	0.616090i	$0.211284\pi$
$488$		0			0
$489$	−4.44418			−0.200973
$490$		0			0
$491$	−32.9798			−1.48836			−0.744180	−	0.667980i	$-0.767159\pi$
$491$	−32.9798			−1.48836			−0.744180	+	0.667980i	$0.767159\pi$
$492$		0			0
$493$	18.2288	+	31.5732i	0.820984	+	1.42199i
$494$		0			0
$495$	15.0069	+	29.4195i	0.674511	+	1.32231i
$496$		0			0
$497$	10.3200	+	0.305170i	0.462914	+	0.0136887i
$498$		0			0
$499$	−20.0030	−	11.5487i	−0.895457	−	0.516992i	−0.0197333	−	0.999805i	$-0.506282\pi$
$499$	−20.0030	−	11.5487i	−0.895457	−	0.516992i	−0.875723	+	0.482813i	$0.839615\pi$
$500$		0			0
$501$	−4.97291	+	2.87111i	−0.222173	+	0.128272i
$502$		0			0
$503$	9.27147			0.413394			0.206697	−	0.978405i	$-0.433729\pi$
$503$	9.27147			0.413394			0.206697	+	0.978405i	$0.433729\pi$
$504$		0			0
$505$		−	39.0913i		−	1.73954i
$506$		0			0
$507$	3.77833	−	2.18142i	0.167802	−	0.0968802i
$508$		0			0
$509$	17.2409	−	29.8621i	0.764190	−	1.32362i	−0.176484	−	0.984303i	$-0.556473\pi$
$509$	17.2409	−	29.8621i	0.764190	−	1.32362i	0.940674	−	0.339312i	$-0.110194\pi$
$510$		0			0
$511$	−1.84720	−	3.42973i	−0.0817153	−	0.151722i
$512$		0			0
$513$	−12.4220	−	7.17186i	−0.548446	−	0.316646i
$514$		0			0
$515$	8.63648	−	4.98627i	0.380569	−	0.219721i
$516$		0			0
$517$	−5.26921	−	3.41845i	−0.231740	−	0.150343i
$518$		0			0
$519$	−9.15998			−0.402079
$520$		0			0
$521$	8.78744	+	15.2203i	0.384985	+	0.666813i	0.991767	−	0.128055i	$-0.0408734\pi$
$521$	8.78744	+	15.2203i	0.384985	+	0.666813i	−0.606783	+	0.794868i	$0.707540\pi$
$522$		0			0
$523$	3.82111	−	6.61836i	0.167086	−	0.289401i	−0.770308	−	0.637672i	$-0.779898\pi$
$523$	3.82111	−	6.61836i	0.167086	−	0.289401i	0.937394	+	0.348271i	$0.113231\pi$
$524$		0			0
$525$	4.59328	−	7.43896i	0.200467	−	0.324663i
$526$		0			0
$527$	4.71947	−	8.17436i	0.205583	−	0.356081i
$528$		0			0
$529$	−0.208278	−	0.360749i	−0.00905558	−	0.0156847i
$530$		0			0
$531$			38.4495i			1.66857i
$532$		0			0
$533$	19.8328			0.859054
$534$		0			0
$535$	24.4166	+	42.2908i	1.05562	+	1.82839i
$536$		0			0
$537$	2.12032	−	3.67251i	0.0914986	−	0.158480i
$538$		0			0
$539$	−23.0734	−	2.57236i	−0.993843	−	0.110799i
$540$		0			0
$541$	32.0975	+	18.5315i	1.37998	+	0.796731i	0.992156	−	0.125004i	$-0.0398944\pi$
$541$	32.0975	+	18.5315i	1.37998	+	0.796731i	0.387822	+	0.921734i	$0.373228\pi$
$542$		0			0
$543$	−4.48510	+	2.58947i	−0.192474	+	0.111125i
$544$		0			0
$545$			57.4790i			2.46213i
$546$		0			0
$547$	39.4112			1.68510			0.842551	−	0.538616i	$-0.181053\pi$
$547$	39.4112			1.68510			0.842551	+	0.538616i	$0.181053\pi$
$548$		0			0
$549$	13.9643	−	8.06230i	0.595982	−	0.344090i
$550$		0			0
$551$	−25.1712	−	14.5326i	−1.07233	−	0.619109i
$552$		0			0
$553$	0.613229	+	0.378646i	0.0260771	+	0.0161017i
$554$		0			0
$555$	3.51696	+	2.03052i	0.149287	+	0.0861906i
$556$		0			0
$557$	2.04693	−	1.18180i	0.0867314	−	0.0500744i	−0.456007	−	0.889976i	$-0.650721\pi$
$557$	2.04693	−	1.18180i	0.0867314	−	0.0500744i	0.542738	+	0.839902i	$0.317387\pi$
$558$		0			0
$559$			12.4658i			0.527248i
$560$		0			0
$561$	5.59064	−	8.61745i	0.236037	−	0.363829i
$562$		0			0
$563$	7.06393	+	12.2351i	0.297709	+	0.515647i	0.975611	−	0.219505i	$-0.0704441\pi$
$563$	7.06393	+	12.2351i	0.297709	+	0.515647i	−0.677902	+	0.735152i	$0.737111\pi$
$564$		0			0
$565$	4.97515	−	8.61721i	0.209306	−	0.362529i
$566$		0			0
$567$	17.0491	−	9.18235i	0.715993	−	0.385623i
$568$		0			0
$569$	−11.5855	−	6.68889i	−0.485689	−	0.280413i	0.237095	−	0.971486i	$-0.423805\pi$
$569$	−11.5855	−	6.68889i	−0.485689	−	0.280413i	−0.722784	+	0.691074i	$0.757138\pi$
$570$		0			0
$571$	17.9533	+	31.0961i	0.751323	+	1.30133i	0.947182	+	0.320697i	$0.103917\pi$
$571$	17.9533	+	31.0961i	0.751323	+	1.30133i	−0.195859	+	0.980632i	$0.562749\pi$
$572$		0			0
$573$	−10.5919			−0.442483
$574$		0			0
$575$		−	35.9496i		−	1.49920i
$576$		0			0
$577$	2.86546	+	4.96311i	0.119290	+	0.206617i	0.919487	−	0.393121i	$-0.128605\pi$
$577$	2.86546	+	4.96311i	0.119290	+	0.206617i	−0.800196	+	0.599738i	$0.795271\pi$
$578$		0			0
$579$	2.08551	−	3.61222i	0.0866710	−	0.150119i
$580$		0			0
$581$	0.0648419	−	2.19277i	0.00269010	−	0.0909714i
$582$		0			0
$583$	−7.48310	−	14.6698i	−0.309918	−	0.607562i
$584$		0			0
$585$	−14.9670	+	8.64121i	−0.618810	+	0.357270i
$586$		0			0
$587$		−	28.1819i		−	1.16319i	−0.813477	−	0.581597i	$-0.802428\pi$
$587$		−	28.1819i		−	1.16319i	0.813477	−	0.581597i	$-0.197572\pi$
$588$		0			0
$589$			7.52501i			0.310063i
$590$		0			0
$591$	−0.826200	−	1.43102i	−0.0339853	−	0.0588643i
$592$		0			0
$593$	−8.47438	−	4.89269i	−0.348001	−	0.200919i	0.315803	−	0.948825i	$-0.397726\pi$
$593$	−8.47438	−	4.89269i	−0.348001	−	0.200919i	−0.663805	+	0.747906i	$0.731059\pi$
$594$		0			0
$595$	66.4658	+	1.96545i	2.72483	+	0.0805755i
$596$		0			0
$597$	−3.37629	+	5.84791i	−0.138182	+	0.239339i
$598$		0			0
$599$	23.9482	−	13.8265i	0.978498	−	0.564936i	0.0766815	−	0.997056i	$-0.475568\pi$
$599$	23.9482	−	13.8265i	0.978498	−	0.564936i	0.901816	+	0.432120i	$0.142234\pi$
$600$		0			0
$601$		−	34.7983i		−	1.41945i	−0.704478	−	0.709725i	$-0.748819\pi$
$601$		−	34.7983i		−	1.41945i	0.704478	−	0.709725i	$-0.251181\pi$
$602$		0			0
$603$		−	24.3342i		−	0.990964i
$604$		0			0
$605$	22.8899	−	31.5658i	0.930605	−	1.28333i
$606$		0			0
$607$	12.4011	−	21.4794i	0.503346	−	0.871821i	−0.496647	−	0.867953i	$-0.665435\pi$
$607$	12.4011	−	21.4794i	0.503346	−	0.871821i	0.999993	−	0.00386793i	$-0.00123120\pi$
$608$		0			0
$609$	−5.23204	+	2.81789i	−0.212013	+	0.114187i
$610$		0			0
$611$	1.64340	−	2.84646i	0.0664850	−	0.115155i
$612$		0			0
$613$	−9.12728	+	5.26964i	−0.368647	+	0.212839i	−0.672867	−	0.739763i	$-0.734938\pi$
$613$	−9.12728	+	5.26964i	−0.368647	+	0.212839i	0.304220	+	0.952602i	$0.401604\pi$
$614$		0			0
$615$	−17.6937			−0.713479
$616$		0			0
$617$	−39.7994			−1.60226			−0.801132	−	0.598487i	$-0.795769\pi$
$617$	−39.7994			−1.60226			−0.801132	+	0.598487i	$0.795769\pi$
$618$		0			0
$619$	30.2792	−	17.4817i	1.21703	−	0.702650i	0.252745	−	0.967533i	$-0.418667\pi$
$619$	30.2792	−	17.4817i	1.21703	−	0.702650i	0.964280	+	0.264883i	$0.0853334\pi$
$620$		0			0
$621$	−6.02951	+	10.4434i	−0.241956	+	0.419080i
$622$		0			0
$623$	17.9768	+	11.1000i	0.720226	+	0.444713i
$624$		0			0
$625$	2.79872	−	4.84752i	0.111949	−	0.193901i
$626$		0			0
$627$	−0.424855	+	8.17820i	−0.0169671	+	0.326606i
$628$		0			0
$629$			18.5959i			0.741468i
$630$		0			0
$631$			28.6326i			1.13984i	0.821699	+	0.569922i	$0.193027\pi$
$631$			28.6326i			1.13984i	−0.821699	+	0.569922i	$0.806973\pi$
$632$		0			0
$633$	7.22419	−	4.17089i	0.287136	−	0.165778i
$634$		0			0
$635$	−14.4132	+	24.9644i	−0.571970	+	0.990681i
$636$		0			0
$637$	0.717888	−	12.1278i	0.0284438	−	0.480523i
$638$		0			0
$639$	9.49360	+	5.48113i	0.375561	+	0.216830i
$640$		0			0
$641$	5.30932	+	9.19601i	0.209706	+	0.363221i	0.951622	−	0.307272i	$-0.0994161\pi$
$641$	5.30932	+	9.19601i	0.209706	+	0.363221i	−0.741916	+	0.670493i	$0.766083\pi$
$642$		0			0
$643$		−	19.7549i		−	0.779056i	−0.921015	−	0.389528i	$-0.872638\pi$
$643$		−	19.7549i		−	0.779056i	0.921015	−	0.389528i	$-0.127362\pi$
$644$		0			0
$645$		−	11.1213i		−	0.437901i
$646$		0			0
$647$	−41.3997	+	23.9021i	−1.62759	+	0.939690i	−0.642782	+	0.766050i	$0.722220\pi$
$647$	−41.3997	+	23.9021i	−1.62759	+	0.939690i	−0.984809	+	0.173640i	$0.944447\pi$
$648$		0			0
$649$	40.4377	−	20.6273i	1.58732	−	0.809692i
$650$		0			0
$651$	1.30911	+	0.808324i	0.0513079	+	0.0316807i
$652$		0			0
$653$	−7.89009	+	13.6660i	−0.308763	+	0.534794i	−0.978092	−	0.208173i	$-0.933248\pi$
$653$	−7.89009	+	13.6660i	−0.308763	+	0.534794i	0.669329	+	0.742966i	$0.266582\pi$
$654$		0			0
$655$	20.7830	+	35.9971i	0.812057	+	1.40652i
$656$		0			0
$657$		−	4.13618i		−	0.161368i
$658$		0			0
$659$	−24.6612			−0.960663			−0.480331	−	0.877087i	$-0.659484\pi$
$659$	−24.6612			−0.960663			−0.480331	+	0.877087i	$0.659484\pi$
$660$		0			0
$661$	4.26697	+	7.39061i	0.165966	+	0.287461i	0.936998	−	0.349335i	$-0.113593\pi$
$661$	4.26697	+	7.39061i	0.165966	+	0.287461i	−0.771032	+	0.636796i	$0.780259\pi$
$662$		0			0
$663$	4.65520	+	2.68768i	0.180793	+	0.104381i
$664$		0			0
$665$	−46.6730	+	25.1373i	−1.80990	+	0.974784i
$666$		0			0
$667$	−12.2178	+	21.1618i	−0.473075	+	0.819390i
$668$		0			0
$669$	1.50110	+	2.59999i	0.0580360	+	0.100521i
$670$		0			0
$671$	−15.9707	−	10.3611i	−0.616542	−	0.399987i
$672$		0			0
$673$			21.6375i			0.834063i	0.908892	+	0.417032i	$0.136930\pi$
$673$			21.6375i			0.834063i	−0.908892	+	0.417032i	$0.863070\pi$
$674$		0			0
$675$	16.6244	−	9.59813i	0.639875	−	0.369432i
$676$		0			0
$677$	40.8768	+	23.6002i	1.57102	+	0.907030i	0.996044	+	0.0888618i	$0.0283229\pi$
$677$	40.8768	+	23.6002i	1.57102	+	0.907030i	0.574979	+	0.818168i	$0.305010\pi$
$678$		0			0
$679$	−0.804211	+	27.1961i	−0.0308628	+	1.04369i
$680$		0			0
$681$	−10.7785	−	6.22299i	−0.413035	−	0.238466i
$682$		0			0
$683$	−30.7690	+	17.7645i	−1.17734	+	0.679739i	−0.955398	−	0.295320i	$-0.904574\pi$
$683$	−30.7690	+	17.7645i	−1.17734	+	0.679739i	−0.221945	+	0.975059i	$0.571240\pi$
$684$		0			0
$685$	25.2957			0.966497
$686$		0			0
$687$			5.12276i			0.195445i
$688$		0			0
$689$	7.46320	−	4.30888i	0.284325	−	0.164155i
$690$		0			0
$691$	6.68050	+	3.85699i	0.254138	+	0.146727i	0.621658	−	0.783289i	$-0.286460\pi$
$691$	6.68050	+	3.85699i	0.254138	+	0.146727i	−0.367519	+	0.930016i	$0.619793\pi$
$692$		0			0
$693$	−20.2742	−	14.0216i	−0.770154	−	0.532636i
$694$		0			0
$695$	0.316826	−	0.548759i	0.0120179	−	0.0208156i
$696$		0			0
$697$	−40.5107	−	70.1666i	−1.53445	−	2.65775i
$698$		0			0
$699$	−5.75927			−0.217836
$700$		0			0
$701$			19.9403i			0.753135i	0.926389	+	0.376567i	$0.122896\pi$
$701$			19.9403i			0.753135i	−0.926389	+	0.376567i	$0.877104\pi$
$702$		0			0
$703$	−7.41262	−	12.8390i	−0.279572	−	0.484234i
$704$		0			0
$705$	−1.46615	+	2.53945i	−0.0552185	+	0.0956412i
$706$		0			0
$707$	13.8356	+	25.6888i	0.520340	+	0.966125i
$708$		0			0
$709$	1.63331	−	2.82898i	0.0613404	−	0.106245i	−0.833724	−	0.552181i	$-0.813796\pi$
$709$	1.63331	−	2.82898i	0.0613404	−	0.106245i	0.895065	+	0.445936i	$0.147129\pi$
$710$		0			0
$711$	0.382615	+	0.662709i	0.0143492	+	0.0248535i
$712$		0			0
$713$	6.32641			0.236926
$714$		0			0
$715$	17.1175	+	11.1051i	0.640158	+	0.415308i
$716$		0			0
$717$	−7.57326	+	4.37243i	−0.282829	+	0.163291i
$718$		0			0
$719$	41.4824	+	23.9499i	1.54703	+	0.893179i	0.998366	+	0.0571372i	$0.0181973\pi$
$719$	41.4824	+	23.9499i	1.54703	+	0.893179i	0.548665	+	0.836042i	$0.315136\pi$
$720$		0			0
$721$	−3.91066	+	6.33343i	−0.145640	+	0.235869i
$722$		0			0
$723$	−0.655968	+	1.13617i	−0.0243957	+	0.0422546i
$724$		0			0
$725$	33.6866	−	19.4490i	1.25109	−	0.722318i
$726$		0			0
$727$			6.28704i			0.233173i	0.993181	+	0.116587i	$0.0371953\pi$
$727$			6.28704i			0.233173i	−0.993181	+	0.116587i	$0.962805\pi$
$728$		0			0
$729$	17.2354			0.638348
$730$		0			0
$731$	44.1029	−	25.4628i	1.63120	−	0.941776i
$732$		0			0
$733$	−9.67223	−	5.58426i	−0.357252	−	0.206259i	0.310623	−	0.950533i	$-0.399462\pi$
$733$	−9.67223	−	5.58426i	−0.357252	−	0.206259i	−0.667875	+	0.744274i	$0.732796\pi$
$734$		0			0
$735$	−0.640459	+	10.8198i	−0.0236237	+	0.399093i
$736$		0			0
$737$	−25.5924	+	13.0547i	−0.942709	+	0.480877i
$738$		0			0
$739$	18.6047	+	32.2243i	0.684385	+	1.18539i	0.973630	+	0.228135i	$0.0732627\pi$
$739$	18.6047	+	32.2243i	0.684385	+	1.18539i	−0.289244	+	0.957255i	$0.593404\pi$
$740$		0			0
$741$	−4.28540			−0.157428
$742$		0			0
$743$	42.3569			1.55392			0.776962	−	0.629547i	$-0.216760\pi$
$743$	42.3569			1.55392			0.776962	+	0.629547i	$0.216760\pi$
$744$		0			0
$745$	22.4217	−	12.9452i	0.821469	−	0.474275i
$746$		0			0
$747$	1.16462	−	2.01718i	0.0426112	−	0.0738048i
$748$		0			0
$749$	−31.0133	−	19.1496i	−1.13320	−	0.699711i
$750$		0			0
$751$	−0.276361	−	0.159557i	−0.0100845	−	0.00582231i	0.494949	−	0.868922i	$-0.335187\pi$
$751$	−0.276361	−	0.159557i	−0.0100845	−	0.00582231i	−0.505034	+	0.863100i	$0.668520\pi$
$752$		0			0
$753$	3.49293	+	6.04994i	0.127290	+	0.220472i
$754$		0			0
$755$	−20.2445			−0.736772
$756$		0			0
$757$	−6.03413			−0.219314			−0.109657	−	0.993969i	$-0.534975\pi$
$757$	−6.03413			−0.219314			−0.109657	+	0.993969i	$0.534975\pi$
$758$		0			0
$759$	6.87555	+	0.357183i	0.249567	+	0.0129649i
$760$		0			0
$761$	2.41626	+	1.39503i	0.0875895	+	0.0505698i	0.543155	−	0.839632i	$-0.317230\pi$
$761$	2.41626	+	1.39503i	0.0875895	+	0.0505698i	−0.455566	+	0.890202i	$0.650563\pi$
$762$		0			0
$763$	−20.3435	−	37.7722i	−0.736485	−	1.36745i
$764$		0			0
$765$	61.1436	+	35.3013i	2.21065	+	1.27632i
$766$		0			0
$767$	11.8775	+	20.5724i	0.428872	+	0.742828i
$768$		0			0
$769$		−	36.7974i		−	1.32695i	−0.748199	−	0.663475i	$-0.769081\pi$
$769$		−	36.7974i		−	1.32695i	0.748199	−	0.663475i	$-0.230919\pi$
$770$		0			0
$771$		−	7.06091i		−	0.254292i
$772$		0			0
$773$	2.94044	+	5.09298i	0.105760	+	0.183182i	0.914049	−	0.405605i	$-0.132939\pi$
$773$	2.94044	+	5.09298i	0.105760	+	0.183182i	−0.808288	+	0.588787i	$0.799606\pi$
$774$		0			0
$775$	−8.72152	−	5.03537i	−0.313286	−	0.180876i
$776$		0			0
$777$	−3.02982	−	0.0895944i	−0.108694	−	0.00321418i
$778$		0			0
$779$	55.9390	+	32.2964i	2.00422	+	1.15714i
$780$		0			0
$781$	0.671450	−	12.9250i	0.0240264	−	0.462493i
$782$		0			0
$783$	−13.0480			−0.466298
$784$		0			0
$785$	67.8049			2.42006
$786$		0			0
$787$	−3.59357	−	6.22425i	−0.128097	−	0.221871i	0.794842	−	0.606816i	$-0.207554\pi$
$787$	−3.59357	−	6.22425i	−0.128097	−	0.221871i	−0.922939	+	0.384945i	$0.874220\pi$
$788$		0			0
$789$	−10.0434	−	5.79854i	−0.357553	−	0.206433i
$790$		0			0
$791$	−0.219523	+	7.42364i	−0.00780534	+	0.263954i
$792$		0			0
$793$	4.98107	−	8.62747i	0.176883	−	0.306371i
$794$		0			0
$795$	−6.65824	+	3.84414i	−0.236143	+	0.136338i
$796$		0			0
$797$	31.9733			1.13255			0.566277	−	0.824215i	$-0.308383\pi$
$797$	31.9733			1.13255			0.566277	+	0.824215i	$0.308383\pi$
$798$		0			0
$799$	−13.4273			−0.475025
$800$		0			0
$801$	11.2164	+	19.4273i	0.396311	+	0.686431i
$802$		0			0
$803$	−4.35005	+	2.21897i	−0.153510	+	0.0783056i
$804$		0			0
$805$	21.1334	+	39.2388i	0.744854	+	1.38298i
$806$		0			0
$807$	−0.192110	−	0.110915i	−0.00676259	−	0.00390438i
$808$		0			0
$809$	30.2537	−	17.4670i	1.06366	−	0.614106i	0.137220	−	0.990541i	$-0.456183\pi$
$809$	30.2537	−	17.4670i	1.06366	−	0.614106i	0.926443	+	0.376435i	$0.122850\pi$
$810$		0			0
$811$	−17.0242			−0.597802			−0.298901	−	0.954284i	$-0.596620\pi$
$811$	−17.0242			−0.597802			−0.298901	+	0.954284i	$0.596620\pi$
$812$		0			0
$813$			2.27576i			0.0798143i
$814$		0			0
$815$	−31.2319	+	18.0318i	−1.09401	+	0.631625i
$816$		0			0
$817$	−20.2998	+	35.1602i	−0.710199	+	1.23010i
$818$		0			0
$819$	6.77717	−	10.9758i	0.236813	−	0.383527i
$820$		0			0
$821$	−20.5949	−	11.8905i	−0.718766	−	0.414980i	0.0955321	−	0.995426i	$-0.469545\pi$
$821$	−20.5949	−	11.8905i	−0.718766	−	0.414980i	−0.814298	+	0.580446i	$0.802878\pi$
$822$		0			0
$823$	19.4739	−	11.2433i	0.678818	−	0.391916i	−0.120592	−	0.992702i	$-0.538479\pi$
$823$	19.4739	−	11.2433i	0.678818	−	0.391916i	0.799409	+	0.600787i	$0.205146\pi$
$824$		0			0
$825$	−9.19427	−	5.96486i	−0.320104	−	0.207670i
$826$		0			0
$827$	30.7671			1.06988			0.534939	−	0.844891i	$-0.320335\pi$
$827$	30.7671			1.06988			0.534939	+	0.844891i	$0.320335\pi$
$828$		0			0
$829$	−12.1543	−	21.0518i	−0.422136	−	0.731160i	0.574013	−	0.818846i	$-0.305386\pi$
$829$	−12.1543	−	21.0518i	−0.422136	−	0.731160i	−0.996148	+	0.0876863i	$0.972053\pi$
$830$		0			0
$831$	0.466108	−	0.807323i	0.0161691	−	0.0280057i
$832$		0			0
$833$	−44.3735	+	22.2326i	−1.53745	+	0.770316i
$834$		0			0
$835$	−23.2984	+	40.3541i	−0.806275	+	1.39651i
$836$		0			0
$837$	1.68908	+	2.92556i	0.0583830	+	0.101122i
$838$		0			0
$839$		−	2.34812i		−	0.0810661i	−0.999178	−	0.0405330i	$-0.987094\pi$
$839$		−	2.34812i		−	0.0810661i	0.999178	−	0.0405330i	$-0.0129056\pi$
$840$		0			0
$841$	2.56038			0.0882888
$842$		0			0
$843$	3.25112	+	5.63111i	0.111975	+	0.193946i
$844$		0			0
$845$	17.7018	−	30.6603i	0.608959	−	1.05475i
$846$		0			0
$847$	−3.86996	+	28.8448i	−0.132973	+	0.991120i
$848$		0			0
$849$	4.15805	+	2.40065i	0.142704	+	0.0823900i
$850$		0			0
$851$	−10.7940	+	6.23192i	−0.370014	+	0.213628i
$852$		0			0
$853$		−	34.1777i		−	1.17022i	−0.810953	−	0.585111i	$-0.801051\pi$
$853$		−	34.1777i		−	1.17022i	0.810953	−	0.585111i	$-0.198949\pi$
$854$		0			0
$855$	−56.2865			−1.92496
$856$		0			0
$857$	23.9300	−	13.8160i	0.817433	−	0.471945i	−0.0320974	−	0.999485i	$-0.510219\pi$
$857$	23.9300	−	13.8160i	0.817433	−	0.471945i	0.849530	+	0.527540i	$0.176885\pi$
$858$		0			0
$859$	−23.3926	−	13.5057i	−0.798146	−	0.460810i	0.0446762	−	0.999002i	$-0.485774\pi$
$859$	−23.3926	−	13.5057i	−0.798146	−	0.460810i	−0.842823	+	0.538191i	$0.819108\pi$
$860$		0			0
$861$	11.6274	−	6.26233i	0.396260	−	0.213420i
$862$		0			0
$863$	5.77439	+	3.33385i	0.196562	+	0.113485i	0.595051	−	0.803688i	$-0.297132\pi$
$863$	5.77439	+	3.33385i	0.196562	+	0.113485i	−0.398489	+	0.917173i	$0.630465\pi$
$864$		0			0
$865$	−64.3728	+	37.1657i	−2.18874	+	1.26367i
$866$		0			0
$867$		−	14.5336i		−	0.493587i
$868$		0			0
$869$	0.491712	−	0.757928i	0.0166802	−	0.0257109i
$870$		0			0
$871$	−7.51711	−	13.0200i	−0.254707	−	0.441166i
$872$		0			0
$873$	−14.4444	+	25.0184i	−0.488868	+	0.846744i
$874$		0			0
$875$	0.710985	−	24.0435i	0.0240357	−	0.812818i
$876$		0			0
$877$	−28.4775	−	16.4415i	−0.961618	−	0.555190i	−0.0649472	−	0.997889i	$-0.520688\pi$
$877$	−28.4775	−	16.4415i	−0.961618	−	0.555190i	−0.896671	+	0.442698i	$0.854021\pi$
$878$		0			0
$879$	−2.14179	−	3.70969i	−0.0722408	−	0.125125i
$880$		0			0
$881$	40.2033			1.35448			0.677241	−	0.735761i	$-0.263175\pi$
$881$	40.2033			1.35448			0.677241	+	0.735761i	$0.263175\pi$
$882$		0			0
$883$		−	25.0056i		−	0.841504i	−0.907176	−	0.420752i	$-0.861766\pi$
$883$		−	25.0056i		−	0.841504i	0.907176	−	0.420752i	$-0.138234\pi$
$884$		0			0
$885$	−10.5964	−	18.3536i	−0.356195	−	0.616948i
$886$		0			0
$887$	−17.8439	+	30.9065i	−0.599138	+	1.03774i	0.393810	+	0.919192i	$0.371157\pi$
$887$	−17.8439	+	30.9065i	−0.599138	+	1.03774i	−0.992949	+	0.118546i	$0.962177\pi$
$888$		0			0
$889$	0.635966	−	21.5065i	0.0213296	−	0.721306i
$890$		0			0
$891$	−11.0304	−	21.6239i	−0.369532	−	0.724429i
$892$		0			0
$893$	9.27054	−	5.35235i	0.310227	−	0.179109i
$894$		0			0
$895$		−	34.4119i		−	1.15026i
$896$		0			0
$897$			3.60281i			0.120294i
$898$		0			0
$899$	3.42263	+	5.92817i	0.114151	+	0.197715i
$900$		0			0
$901$	−30.4888	−	17.6027i	−1.01573	−	0.586432i
$902$		0			0
$903$	3.93616	+	7.30834i	0.130987	+	0.243206i
$904$		0			0
$905$	−21.0130	+	36.3956i	−0.698496	+	1.20983i
$906$		0			0
$907$	−46.4312	+	26.8070i	−1.54172	+	0.890113i	−0.542991	+	0.839738i	$0.682708\pi$
$907$	−46.4312	+	26.8070i	−1.54172	+	0.890113i	−0.998730	+	0.0503750i	$0.983958\pi$
$908$		0			0
$909$			30.9801i			1.02754i
$910$		0			0
$911$		−	41.3552i		−	1.37016i	−0.728468	−	0.685080i	$-0.759767\pi$
$911$		−	41.3552i		−	1.37016i	0.728468	−	0.685080i	$-0.240233\pi$
$912$		0			0
$913$	−2.74628	−	0.142668i	−0.0908886	−	0.00472164i
$914$		0			0
$915$	−4.44383	+	7.69694i	−0.146909	+	0.254453i
$916$		0			0
$917$	−26.3979	−	16.2997i	−0.871737	−	0.538265i
$918$		0			0
$919$	16.6893	−	28.9068i	0.550530	−	0.953546i	−0.447706	−	0.894181i	$-0.647759\pi$
$919$	16.6893	−	28.9068i	0.550530	−	0.953546i	0.998236	−	0.0593653i	$-0.0189077\pi$
$920$		0			0
$921$	−3.42640	+	1.97823i	−0.112904	+	0.0651849i
$922$		0			0
$923$	6.77274			0.222928
$924$		0			0
$925$	19.8407			0.652357
$926$		0			0
$927$	−6.84446	+	3.95165i	−0.224802	+	0.129789i
$928$		0			0
$929$	4.95722	−	8.58616i	0.162641	−	0.281703i	−0.773174	−	0.634194i	$-0.781332\pi$
$929$	4.95722	−	8.58616i	0.162641	−	0.281703i	0.935815	+	0.352491i	$0.114665\pi$
$930$		0			0
$931$	21.7742	−	33.0379i	0.713621	−	1.08277i
$932$		0			0
$933$	−2.98074	+	5.16279i	−0.0975850	+	0.169022i
$934$		0			0
$935$	4.32448	−	83.2435i	0.141425	−	2.72235i
$936$		0			0
$937$		−	0.804679i		−	0.0262877i	−0.999914	−	0.0131439i	$-0.995816\pi$
$937$		−	0.804679i		−	0.0262877i	0.999914	−	0.0131439i	$-0.00418394\pi$
$938$		0			0
$939$			7.89442i			0.257625i
$940$		0			0
$941$	3.36591	−	1.94331i	0.109726	−	0.0633501i	−0.444133	−	0.895961i	$-0.646488\pi$
$941$	3.36591	−	1.94331i	0.109726	−	0.0633501i	0.553858	+	0.832611i	$0.313155\pi$
$942$		0			0
$943$	27.1521	−	47.0289i	0.884195	−	1.53147i
$944$		0			0
$945$	−12.5031	+	20.2491i	−0.406726	+	0.658705i
$946$		0			0
$947$	19.8993	+	11.4889i	0.646642	+	0.373339i	0.787168	−	0.616738i	$-0.211546\pi$
$947$	19.8993	+	11.4889i	0.646642	+	0.373339i	−0.140527	+	0.990077i	$0.544880\pi$
$948$		0			0
$949$	−1.27771	−	2.21307i	−0.0414764	−	0.0718392i
$950$		0			0
$951$		−	13.4679i		−	0.436727i
$952$		0			0
$953$		−	51.7367i		−	1.67592i	−0.545735	−	0.837958i	$-0.683750\pi$
$953$		−	51.7367i		−	1.67592i	0.545735	−	0.837958i	$-0.316250\pi$
$954$		0			0
$955$	−74.4358	+	42.9755i	−2.40868	+	1.39065i
$956$		0			0
$957$	3.38502	+	6.63598i	0.109422	+	0.214511i
$958$		0			0
$959$	−16.6230	+	8.95289i	−0.536785	+	0.289104i
$960$		0			0
$961$	−14.6139	+	25.3120i	−0.471415	+	0.816515i
$962$		0			0
$963$	−19.3503	−	33.5157i	−0.623556	−	1.08003i
$964$		0			0
$965$		−	33.8470i		−	1.08957i
$966$		0			0
$967$	15.0271			0.483238			0.241619	−	0.970371i	$-0.422322\pi$
$967$	15.0271			0.483238			0.241619	+	0.970371i	$0.422322\pi$
$968$		0			0
$969$	8.75341	+	15.1614i	0.281200	+	0.487053i
$970$		0			0
$971$	−23.7363	−	13.7041i	−0.761733	−	0.439787i	0.0681848	−	0.997673i	$-0.478279\pi$
$971$	−23.7363	−	13.7041i	−0.761733	−	0.439787i	−0.829917	+	0.557886i	$0.811613\pi$
$972$		0			0
$973$	−0.0139796	+	0.472750i	−0.000448166	+	0.0151557i
$974$		0			0
$975$	2.86758	−	4.96680i	0.0918362	−	0.159065i
$976$		0			0
$977$	2.53240	+	4.38625i	0.0810188	+	0.140329i	0.903688	−	0.428192i	$-0.140849\pi$
$977$	2.53240	+	4.38625i	0.0810188	+	0.140329i	−0.822669	+	0.568521i	$0.807516\pi$
$978$		0			0
$979$	14.4145	−	22.2187i	0.460691	−	0.710111i
$980$		0			0
$981$		−	45.5525i		−	1.45438i
$982$		0			0
$983$	22.0974	−	12.7579i	0.704796	−	0.406914i	−0.104335	−	0.994542i	$-0.533271\pi$
$983$	22.0974	−	12.7579i	0.704796	−	0.406914i	0.809131	+	0.587628i	$0.199938\pi$
$984$		0			0
$985$	−11.6124	−	6.70443i	−0.370002	−	0.213621i
$986$		0			0
$987$	0.0646924	−	2.18771i	0.00205918	−	0.0696356i
$988$		0			0
$989$	29.5598	+	17.0664i	0.939947	+	0.542679i
$990$		0			0
$991$	−40.2219	+	23.2221i	−1.27769	+	0.737676i	−0.976423	−	0.215864i	$-0.930743\pi$
$991$	−40.2219	+	23.2221i	−1.27769	+	0.737676i	−0.301268	+	0.953539i	$0.597410\pi$
$992$		0			0
$993$	2.57986			0.0818695
$994$		0			0
$995$			54.7958i			1.73714i
$996$		0			0
$997$	−17.6156	+	10.1703i	−0.557890	+	0.322098i	−0.752298	−	0.658823i	$-0.771055\pi$
$997$	−17.6156	+	10.1703i	−0.557890	+	0.322098i	0.194408	+	0.980921i	$0.437721\pi$
$998$		0			0
$999$	−5.76374	−	3.32770i	−0.182357	−	0.105284i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.bi.b.527.9	yes	32
4.3	odd	2		1232.2.bi.a.527.8	yes	32
7.4	even	3		1232.2.bi.a.879.7	yes	32
11.10	odd	2	inner	1232.2.bi.b.527.10	yes	32
28.11	odd	6	inner	1232.2.bi.b.879.10	yes	32
44.43	even	2		1232.2.bi.a.527.7	✓	32
77.32	odd	6		1232.2.bi.a.879.8	yes	32
308.263	even	6	inner	1232.2.bi.b.879.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1232.2.bi.a.527.7	✓	32	44.43	even	2
1232.2.bi.a.527.8	yes	32	4.3	odd	2
1232.2.bi.a.879.7	yes	32	7.4	even	3
1232.2.bi.a.879.8	yes	32	77.32	odd	6
1232.2.bi.b.527.9	yes	32	1.1	even	1	trivial
1232.2.bi.b.527.10	yes	32	11.10	odd	2	inner
1232.2.bi.b.879.9	yes	32	308.263	even	6	inner
1232.2.bi.b.879.10	yes	32	28.11	odd	6	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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.378296 - 0.218409i) q^{3} +(1.77235 - 3.06979i) q^{5} +(-0.0782028 + 2.64460i) q^{7} +(-1.40459 + 2.43283i) q^{9} +O(q^{10})\)	\(q+(0.378296 - 0.218409i) q^{3} +(1.77235 - 3.06979i) q^{5} +(-0.0782028 + 2.64460i) q^{7} +(-1.40459 + 2.43283i) q^{9} +(3.31216 + 0.172066i) q^{11} +1.73558i q^{13} -1.54839i q^{15} +(6.14033 - 3.54512i) q^{17} +(-2.82628 + 4.89526i) q^{19} +(0.548021 + 1.01752i) q^{21} +(4.11553 + 2.37610i) q^{23} +(-3.78242 - 6.55134i) q^{25} +2.53756i q^{27} +5.14195i q^{29} +(1.15290 - 0.665629i) q^{31} +(1.29056 - 0.658315i) q^{33} +(7.97976 + 4.92720i) q^{35} +(-1.31137 + 2.27137i) q^{37} +(0.379068 + 0.656564i) q^{39} -11.4272i q^{41} +7.18250 q^{43} +(4.97885 + 8.62363i) q^{45} +(-1.64006 - 0.946889i) q^{47} +(-6.98777 - 0.413630i) q^{49} +(1.54857 - 2.68221i) q^{51} +(-2.48267 - 4.30011i) q^{53} +(6.39850 - 9.86268i) q^{55} +2.46914i q^{57} +(11.8533 - 6.84353i) q^{59} +(-4.97094 - 2.86997i) q^{61} +(-6.32401 - 3.90484i) q^{63} +(5.32788 + 3.07605i) q^{65} +(-7.50181 + 4.33117i) q^{67} +2.07585 q^{69} -3.90229i q^{71} +(-1.27511 + 0.736187i) q^{73} +(-2.86175 - 1.65223i) q^{75} +(-0.714064 + 8.74586i) q^{77} +(0.136201 - 0.235908i) q^{79} +(-3.65956 - 6.33854i) q^{81} -0.829151 q^{83} -25.1327i q^{85} +(1.12305 + 1.94518i) q^{87} +(3.99274 - 6.91563i) q^{89} +(-4.58991 - 0.135727i) q^{91} +(0.290759 - 0.503610i) q^{93} +(10.0183 + 17.3522i) q^{95} +10.2837 q^{97} +(-5.07085 + 7.81623i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{5} + 12 q^{9}+O(q^{10}) \) 32 * q - 2 * q^5 + 12 * q^9	\( 32 q - 2 q^{5} + 12 q^{9} + 9 q^{11} + 18 q^{23} - 6 q^{25} + 5 q^{33} - 6 q^{37} - 10 q^{45} + 36 q^{47} - 32 q^{49} + 42 q^{59} + 18 q^{67} - 24 q^{69} + 78 q^{75} - 19 q^{77} - 24 q^{81} - 8 q^{89} + 18 q^{91} + 2 q^{93} + 12 q^{97}+O(q^{100}) \) 32 * q - 2 * q^5 + 12 * q^9 + 9 * q^11 + 18 * q^23 - 6 * q^25 + 5 * q^33 - 6 * q^37 - 10 * q^45 + 36 * q^47 - 32 * q^49 + 42 * q^59 + 18 * q^67 - 24 * q^69 + 78 * q^75 - 19 * q^77 - 24 * q^81 - 8 * q^89 + 18 * q^91 + 2 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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