LMFDB - Embedded newform 1456.2.r.o.625.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1456,2,Mod(417,1456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1456.417"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1456, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.r (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,3,0,1,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.856615824.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.4
Root			$2.33086i$ of defining polynomial
Character	$\chi$	$=$	1456.625
Dual form			1456.2.r.o.417.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.71646 + 2.97300i) q^{3} +(-0.459555 + 0.795973i) q^{5} +(1.51859 - 2.16654i) q^{7} +(-4.39248 + 7.60799i) q^{9} +(0.802125 + 1.38932i) q^{11} -1.00000 q^{13} -3.15524 q^{15} +(1.36116 + 2.35759i) q^{17} +(-1.05903 + 1.83430i) q^{19} +(9.04771 + 0.795973i) q^{21} +(2.71646 - 4.70505i) q^{23} +(2.07762 + 3.59854i) q^{25} -19.8593 q^{27} -6.50727 q^{29} +(2.83452 + 4.90954i) q^{31} +(-2.75363 + 4.76943i) q^{33} +(1.02663 + 2.20440i) q^{35} +(-4.71646 + 8.16915i) q^{37} +(-1.71646 - 2.97300i) q^{39} -2.35203 q^{41} +0.513812 q^{43} +(-4.03717 - 6.99259i) q^{45} +(2.31594 - 4.01132i) q^{47} +(-2.38779 - 6.58016i) q^{49} +(-4.67274 + 8.09343i) q^{51} +(-2.81486 - 4.87548i) q^{53} -1.47448 q^{55} -7.27114 q^{57} +(3.66797 + 6.35311i) q^{59} +(0.303203 - 0.525162i) q^{61} +(9.81267 + 21.0699i) q^{63} +(0.459555 - 0.795973i) q^{65} +(-5.72592 - 9.91759i) q^{67} +18.6508 q^{69} +15.3476 q^{71} +(5.09143 + 8.81861i) q^{73} +(-7.13230 + 12.3535i) q^{75} +(4.22812 + 0.371969i) q^{77} +(4.26276 - 7.38331i) q^{79} +(-20.9103 - 36.2177i) q^{81} +13.0561 q^{83} -2.50211 q^{85} +(-11.1695 - 19.3461i) q^{87} +(6.26529 - 10.8518i) q^{89} +(-1.51859 + 2.16654i) q^{91} +(-9.73070 + 16.8541i) q^{93} +(-0.973367 - 1.68592i) q^{95} -7.21788 q^{97} -14.0933 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{3} + q^{5} - q^{7} - 9 q^{9} + 4 q^{11} - 8 q^{13} + 18 q^{15} + 3 q^{21} + 11 q^{23} - 5 q^{25} - 54 q^{27} + 22 q^{29} - 5 q^{31} + 15 q^{33} + 25 q^{35} - 27 q^{37} - 3 q^{39} + 12 q^{41}+ \cdots + 6 q^{99}+O(q^{100}) $ 8 * q + 3 * q^3 + q^5 - q^7 - 9 * q^9 + 4 * q^11 - 8 * q^13 + 18 * q^15 + 3 * q^21 + 11 * q^23 - 5 * q^25 - 54 * q^27 + 22 * q^29 - 5 * q^31 + 15 * q^33 + 25 * q^35 - 27 * q^37 - 3 * q^39 + 12 * q^41 - 8 * q^43 - 6 * q^45 + 4 * q^47 - 25 * q^49 + 9 * q^51 - 18 * q^53 - 46 * q^55 - 18 * q^57 - 16 * q^59 - 10 * q^61 + 33 * q^63 - q^65 - 2 * q^67 + 54 * q^69 + 10 * q^71 + 7 * q^73 - 6 * q^75 + 31 * q^77 + 17 * q^79 - 24 * q^81 + 12 * q^83 - 30 * q^85 - 12 * q^87 + 21 * q^89 + q^91 - 33 * q^93 + 9 * q^95 + 16 * q^97 + 6 * q^99

Character values

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

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.71646	+	2.97300i	0.990999	+	1.71646i	0.611432	+	0.791297i	$0.290594\pi$
$3$	1.71646	+	2.97300i	0.990999	+	1.71646i	0.379567	+	0.925164i	$0.376073\pi$
$4$		0			0
$5$	−0.459555	+	0.795973i	−0.205519	+	0.355970i	−0.950298	−	0.311342i	$-0.899222\pi$
$5$	−0.459555	+	0.795973i	−0.205519	+	0.355970i	0.744779	+	0.667312i	$0.232555\pi$
$6$		0			0
$7$	1.51859	−	2.16654i	0.573972	−	0.818875i
$7$	1.51859	−	2.16654i	0.573972	−	0.818875i
$8$		0			0
$9$	−4.39248	+	7.60799i	−1.46416	+	2.53600i
$10$		0			0
$11$	0.802125	+	1.38932i	0.241850	+	0.418896i	0.961241	−	0.275709i	$-0.0889125\pi$
$11$	0.802125	+	1.38932i	0.241850	+	0.418896i	−0.719391	+	0.694605i	$0.755579\pi$
$12$		0			0
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	−3.15524			−0.814678
$16$		0			0
$17$	1.36116	+	2.35759i	0.330129	+	0.571800i	0.982537	−	0.186068i	$-0.0595744\pi$
$17$	1.36116	+	2.35759i	0.330129	+	0.571800i	−0.652408	+	0.757868i	$0.726241\pi$
$18$		0			0
$19$	−1.05903	+	1.83430i	−0.242958	+	0.420816i	−0.961556	−	0.274610i	$-0.911451\pi$
$19$	−1.05903	+	1.83430i	−0.242958	+	0.420816i	0.718597	+	0.695427i	$0.244785\pi$
$20$		0			0
$21$	9.04771	+	0.795973i	1.97437	+	0.173696i
$22$		0			0
$23$	2.71646	−	4.70505i	0.566421	−	0.981070i	−0.430495	−	0.902593i	$-0.641661\pi$
$23$	2.71646	−	4.70505i	0.566421	−	0.981070i	0.996916	−	0.0784773i	$-0.0250058\pi$
$24$		0			0
$25$	2.07762	+	3.59854i	0.415524	+	0.719708i
$26$		0			0
$27$	−19.8593			−3.82192
$28$		0			0
$29$	−6.50727			−1.20837			−0.604185	−	0.796844i	$-0.706501\pi$
$29$	−6.50727			−1.20837			−0.604185	+	0.796844i	$0.706501\pi$
$30$		0			0
$31$	2.83452	+	4.90954i	0.509095	+	0.881779i	0.999945	+	0.0105346i	$0.00335332\pi$
$31$	2.83452	+	4.90954i	0.509095	+	0.881779i	−0.490849	+	0.871245i	$0.663313\pi$
$32$		0			0
$33$	−2.75363	+	4.76943i	−0.479346	+	0.830252i
$34$		0			0
$35$	1.02663	+	2.20440i	0.173533	+	0.372611i
$36$		0			0
$37$	−4.71646	+	8.16915i	−0.775381	+	1.34300i	0.159198	+	0.987247i	$0.449109\pi$
$37$	−4.71646	+	8.16915i	−0.775381	+	1.34300i	−0.934580	+	0.355753i	$0.884224\pi$
$38$		0			0
$39$	−1.71646	−	2.97300i	−0.274854	−	0.476061i
$40$		0			0
$41$	−2.35203			−0.367326			−0.183663	−	0.982989i	$-0.558795\pi$
$41$	−2.35203			−0.367326			−0.183663	+	0.982989i	$0.558795\pi$
$42$		0			0
$43$	0.513812			0.0783555			0.0391778	−	0.999232i	$-0.487526\pi$
$43$	0.513812			0.0783555			0.0391778	+	0.999232i	$0.487526\pi$
$44$		0			0
$45$	−4.03717	−	6.99259i	−0.601826	−	1.04239i
$46$		0			0
$47$	2.31594	−	4.01132i	0.337814	−	0.585111i	−0.646207	−	0.763162i	$-0.723646\pi$
$47$	2.31594	−	4.01132i	0.337814	−	0.585111i	0.984021	+	0.178051i	$0.0569791\pi$
$48$		0			0
$49$	−2.38779	−	6.58016i	−0.341113	−	0.940022i
$50$		0			0
$51$	−4.67274	+	8.09343i	−0.654315	+	1.13331i
$52$		0			0
$53$	−2.81486	−	4.87548i	−0.386651	−	0.669699i	0.605346	−	0.795962i	$-0.293035\pi$
$53$	−2.81486	−	4.87548i	−0.386651	−	0.669699i	−0.991997	+	0.126264i	$0.959701\pi$
$54$		0			0
$55$	−1.47448			−0.198819
$56$		0			0
$57$	−7.27114			−0.963087
$58$		0			0
$59$	3.66797	+	6.35311i	0.477529	+	0.827105i	0.999668	−	0.0257557i	$-0.00819921\pi$
$59$	3.66797	+	6.35311i	0.477529	+	0.827105i	−0.522139	+	0.852860i	$0.674866\pi$
$60$		0			0
$61$	0.303203	−	0.525162i	0.0388211	−	0.0672401i	−0.845962	−	0.533243i	$-0.820973\pi$
$61$	0.303203	−	0.525162i	0.0388211	−	0.0672401i	0.884783	+	0.466003i	$0.154306\pi$
$62$		0			0
$63$	9.81267	+	21.0699i	1.23628	+	2.65455i
$64$		0			0
$65$	0.459555	−	0.795973i	0.0570008	−	0.0987283i
$66$		0			0
$67$	−5.72592	−	9.91759i	−0.699533	−	1.21163i	−0.968629	−	0.248513i	$-0.920058\pi$
$67$	−5.72592	−	9.91759i	−0.699533	−	1.21163i	0.269096	−	0.963113i	$-0.413275\pi$
$68$		0			0
$69$	18.6508			2.24529
$70$		0			0
$71$	15.3476			1.82143			0.910715	−	0.413035i	$-0.135531\pi$
$71$	15.3476			1.82143			0.910715	+	0.413035i	$0.135531\pi$
$72$		0			0
$73$	5.09143	+	8.81861i	0.595907	+	1.03214i	0.993418	+	0.114544i	$0.0365405\pi$
$73$	5.09143	+	8.81861i	0.595907	+	1.03214i	−0.397511	+	0.917597i	$0.630126\pi$
$74$		0			0
$75$	−7.13230	+	12.3535i	−0.823567	+	1.42646i
$76$		0			0
$77$	4.22812	+	0.371969i	0.481839	+	0.0423898i
$78$		0			0
$79$	4.26276	−	7.38331i	0.479598	−	0.830688i	−0.520128	−	0.854088i	$-0.674116\pi$
$79$	4.26276	−	7.38331i	0.479598	−	0.830688i	0.999726	+	0.0234004i	$0.00744926\pi$
$80$		0			0
$81$	−20.9103	−	36.2177i	−2.32337	−	4.02419i
$82$		0			0
$83$	13.0561			1.43309			0.716547	−	0.697539i	$-0.245722\pi$
$83$	13.0561			1.43309			0.716547	+	0.697539i	$0.245722\pi$
$84$		0			0
$85$	−2.50211			−0.271392
$86$		0			0
$87$	−11.1695	−	19.3461i	−1.19749	−	2.07412i
$88$		0			0
$89$	6.26529	−	10.8518i	0.664120	−	1.15029i	−0.315404	−	0.948958i	$-0.602140\pi$
$89$	6.26529	−	10.8518i	0.664120	−	1.15029i	0.979523	−	0.201331i	$-0.0645268\pi$
$90$		0			0
$91$	−1.51859	+	2.16654i	−0.159191	+	0.227115i
$92$		0			0
$93$	−9.73070	+	16.8541i	−1.00903	+	1.74769i
$94$		0			0
$95$	−0.973367	−	1.68592i	−0.0998653	−	0.172972i
$96$		0			0
$97$	−7.21788			−0.732864			−0.366432	−	0.930445i	$-0.619421\pi$
$97$	−7.21788			−0.732864			−0.366432	+	0.930445i	$0.619421\pi$
$98$		0			0
$99$	−14.0933			−1.41643
$100$		0			0
$101$	−0.378666	−	0.655869i	−0.0376787	−	0.0652614i	0.846571	−	0.532276i	$-0.178663\pi$
$101$	−0.378666	−	0.655869i	−0.0376787	−	0.0652614i	−0.884250	+	0.467014i	$0.845330\pi$
$102$		0			0
$103$	−0.165476	+	0.286614i	−0.0163049	+	0.0282409i	−0.874063	−	0.485813i	$-0.838524\pi$
$103$	−0.165476	+	0.286614i	−0.0163049	+	0.0282409i	0.857758	+	0.514054i	$0.171857\pi$
$104$		0			0
$105$	−4.79150	+	6.83594i	−0.467602	+	0.667120i
$106$		0			0
$107$	−5.12645	+	8.87927i	−0.495592	+	0.858391i	−0.999987	−	0.00508195i	$-0.998382\pi$
$107$	−5.12645	+	8.87927i	−0.495592	+	0.858391i	0.504395	+	0.863473i	$0.331716\pi$
$108$		0			0
$109$	3.98760	+	6.90673i	0.381943	+	0.661545i	0.991340	−	0.131320i	$-0.0419216\pi$
$109$	3.98760	+	6.90673i	0.381943	+	0.661545i	−0.609397	+	0.792865i	$0.708588\pi$
$110$		0			0
$111$	−32.3825			−3.07361
$112$		0			0
$113$	14.8308			1.39517			0.697583	−	0.716504i	$-0.254259\pi$
$113$	14.8308			1.39517			0.697583	+	0.716504i	$0.254259\pi$
$114$		0			0
$115$	2.49673	+	4.32446i	0.232821	+	0.403258i
$116$		0			0
$117$	4.39248	−	7.60799i	0.406085	−	0.703359i
$118$		0			0
$119$	7.17485	+	0.631208i	0.657718	+	0.0578628i
$120$		0			0
$121$	4.21319	−	7.29746i	0.383017	−	0.663405i
$122$		0			0
$123$	−4.03717	−	6.99259i	−0.364020	−	0.630501i
$124$		0			0
$125$	−8.41467			−0.752631
$126$		0			0
$127$	−19.0102			−1.68688			−0.843442	−	0.537219i	$-0.819475\pi$
$127$	−19.0102			−1.68688			−0.843442	+	0.537219i	$0.819475\pi$
$128$		0			0
$129$	0.881938	+	1.52756i	0.0776503	+	0.134494i
$130$		0			0
$131$	6.89248	−	11.9381i	0.602199	−	1.04304i	−0.390289	−	0.920692i	$-0.627625\pi$
$131$	6.89248	−	11.9381i	0.602199	−	1.04304i	0.992487	−	0.122346i	$-0.0390418\pi$
$132$		0			0
$133$	2.36584	+	5.07997i	0.205145	+	0.440489i
$134$		0			0
$135$	9.12645	−	15.8075i	0.785480	−	1.36049i
$136$		0			0
$137$	−3.34149	−	5.78764i	−0.285483	−	0.494471i	0.687243	−	0.726427i	$-0.258821\pi$
$137$	−3.34149	−	5.78764i	−0.285483	−	0.494471i	−0.972726	+	0.231956i	$0.925487\pi$
$138$		0			0
$139$	1.25944			0.106824			0.0534121	−	0.998573i	$-0.482990\pi$
$139$	1.25944			0.106824			0.0534121	+	0.998573i	$0.482990\pi$
$140$		0			0
$141$	15.9009			1.33909
$142$		0			0
$143$	−0.802125	−	1.38932i	−0.0670771	−	0.116181i
$144$		0			0
$145$	2.99045	−	5.17961i	0.248343	−	0.430143i
$146$		0			0
$147$	15.4642	−	18.3935i	1.27547	−	1.51707i
$148$		0			0
$149$	−2.63088	+	4.55682i	−0.215530	+	0.373310i	−0.953437	−	0.301594i	$-0.902481\pi$
$149$	−2.63088	+	4.55682i	−0.215530	+	0.373310i	0.737906	+	0.674903i	$0.235815\pi$
$150$		0			0
$151$	6.88770	+	11.9299i	0.560513	+	0.970837i	0.997452	+	0.0713460i	$0.0227295\pi$
$151$	6.88770	+	11.9299i	0.560513	+	0.970837i	−0.436938	+	0.899491i	$0.643937\pi$
$152$		0			0
$153$	−23.9154			−1.93345
$154$		0			0
$155$	−5.21048			−0.418516
$156$		0			0
$157$	−0.613375	−	1.06240i	−0.0489526	−	0.0847884i	0.840511	−	0.541795i	$-0.182255\pi$
$157$	−0.613375	−	1.06240i	−0.0489526	−	0.0847884i	−0.889463	+	0.457006i	$0.848922\pi$
$158$		0			0
$159$	9.66319	−	16.7371i	0.766341	−	1.32734i
$160$		0			0
$161$	−6.06849	−	13.0303i	−0.478264	−	1.02694i
$162$		0			0
$163$	−7.72808	+	13.3854i	−0.605310	+	1.04843i	0.386693	+	0.922209i	$0.373617\pi$
$163$	−7.72808	+	13.3854i	−0.605310	+	1.04843i	−0.992002	+	0.126219i	$0.959716\pi$
$164$		0			0
$165$	−2.53089	−	4.38364i	−0.197030	−	0.341266i
$166$		0			0
$167$	23.7091			1.83466			0.917331	−	0.398126i	$-0.130339\pi$
$167$	23.7091			1.83466			0.917331	+	0.398126i	$0.130339\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	−9.30354	−	16.1142i	−0.711460	−	1.23228i
$172$		0			0
$173$	7.08816	−	12.2770i	0.538903	−	0.933407i	−0.460061	−	0.887887i	$-0.652172\pi$
$173$	7.08816	−	12.2770i	0.538903	−	0.933407i	0.998963	−	0.0455194i	$-0.0144943\pi$
$174$		0			0
$175$	10.9514	+	0.963452i	0.827850	+	0.0728301i
$176$		0			0
$177$	−12.5919	+	21.8097i	−0.946462	+	1.63932i
$178$		0			0
$179$	−3.23027	−	5.59500i	−0.241442	−	0.418190i	0.719683	−	0.694302i	$-0.244287\pi$
$179$	−3.23027	−	5.59500i	−0.241442	−	0.418190i	−0.961125	+	0.276113i	$0.910954\pi$
$180$		0			0
$181$	11.9476			0.888057			0.444029	−	0.896013i	$-0.353549\pi$
$181$	11.9476			0.888057			0.444029	+	0.896013i	$0.353549\pi$
$182$		0			0
$183$	2.08174			0.153887
$184$		0			0
$185$	−4.33495	−	7.50835i	−0.318712	−	0.552025i
$186$		0			0
$187$	−2.18364	+	3.78217i	−0.159683	+	0.276580i
$188$		0			0
$189$	−30.1581	+	43.0260i	−2.19368	+	3.12968i
$190$		0			0
$191$	1.08928	−	1.88668i	0.0788172	−	0.136515i	−0.823923	−	0.566702i	$-0.808219\pi$
$191$	1.08928	−	1.88668i	0.0788172	−	0.136515i	0.902740	+	0.430187i	$0.141552\pi$
$192$		0			0
$193$	10.1494	+	17.5792i	0.730569	+	1.26538i	0.956640	+	0.291271i	$0.0940782\pi$
$193$	10.1494	+	17.5792i	0.730569	+	1.26538i	−0.226072	+	0.974111i	$0.572588\pi$
$194$		0			0
$195$	3.15524			0.225951
$196$		0			0
$197$	−2.00938			−0.143162			−0.0715810	−	0.997435i	$-0.522804\pi$
$197$	−2.00938			−0.143162			−0.0715810	+	0.997435i	$0.522804\pi$
$198$		0			0
$199$	−1.32071	−	2.28754i	−0.0936228	−	0.162159i	0.815410	−	0.578884i	$-0.196511\pi$
$199$	−1.32071	−	2.28754i	−0.0936228	−	0.162159i	−0.909033	+	0.416724i	$0.863178\pi$
$200$		0			0
$201$	19.6567	−	34.0463i	1.38647	−	2.40144i
$202$		0			0
$203$	−9.88185	+	14.0983i	−0.693570	+	0.989504i
$204$		0			0
$205$	1.08089	−	1.87216i	0.0754926	−	0.130757i
$206$		0			0
$207$	23.8640	+	41.3336i	1.65866	+	2.87289i
$208$		0			0
$209$	−3.39790			−0.235038
$210$		0			0
$211$	−9.92194			−0.683055			−0.341527	−	0.939872i	$-0.610944\pi$
$211$	−9.92194			−0.683055			−0.341527	+	0.939872i	$0.610944\pi$
$212$		0			0
$213$	26.3436	+	45.6285i	1.80504	+	3.12641i
$214$		0			0
$215$	−0.236125	+	0.408980i	−0.0161036	+	0.0278922i
$216$		0			0
$217$	14.9412	+	1.31445i	1.01427	+	0.0892308i
$218$		0			0
$219$	−17.4785	+	30.2736i	−1.18109	+	2.04570i
$220$		0			0
$221$	−1.36116	−	2.35759i	−0.0915613	−	0.158589i
$222$		0			0
$223$	9.20402			0.616347			0.308173	−	0.951330i	$-0.400282\pi$
$223$	9.20402			0.616347			0.308173	+	0.951330i	$0.400282\pi$
$224$		0			0
$225$	−36.5036			−2.43357
$226$		0			0
$227$	−10.2674	−	17.7837i	−0.681474	−	1.18035i	−0.974531	−	0.224253i	$-0.928006\pi$
$227$	−10.2674	−	17.7837i	−0.681474	−	1.18035i	0.293057	−	0.956095i	$-0.405328\pi$
$228$		0			0
$229$	−0.897165	+	1.55394i	−0.0592864	+	0.102687i	−0.894145	−	0.447777i	$-0.852216\pi$
$229$	−0.897165	+	1.55394i	−0.0592864	+	0.102687i	0.834859	+	0.550464i	$0.185549\pi$
$230$		0			0
$231$	6.15154	+	13.2087i	0.404741	+	0.869066i
$232$		0			0
$233$	−10.9351	+	18.9401i	−0.716381	+	1.24081i	0.246044	+	0.969259i	$0.420869\pi$
$233$	−10.9351	+	18.9401i	−0.716381	+	1.24081i	−0.962425	+	0.271549i	$0.912464\pi$
$234$		0			0
$235$	2.12860	+	3.68685i	0.138855	+	0.240503i
$236$		0			0
$237$	29.2674			1.90112
$238$		0			0
$239$	−12.3468			−0.798648			−0.399324	−	0.916810i	$-0.630755\pi$
$239$	−12.3468			−0.798648			−0.399324	+	0.916810i	$0.630755\pi$
$240$		0			0
$241$	6.98976	+	12.1066i	0.450250	+	0.779856i	0.998401	−	0.0565234i	$-0.0180015\pi$
$241$	6.98976	+	12.1066i	0.450250	+	0.779856i	−0.548151	+	0.836379i	$0.684668\pi$
$242$		0			0
$243$	41.9944	−	72.7365i	2.69394	−	4.66605i
$244$		0			0
$245$	6.33495	+	1.12333i	0.404725	+	0.0717669i
$246$		0			0
$247$	1.05903	−	1.83430i	0.0673845	−	0.116713i
$248$		0			0
$249$	22.4103	+	38.8158i	1.42019	+	2.45985i
$250$		0			0
$251$	5.72231			0.361189			0.180595	−	0.983558i	$-0.442198\pi$
$251$	5.72231			0.361189			0.180595	+	0.983558i	$0.442198\pi$
$252$		0			0
$253$	8.71577			0.547956
$254$		0			0
$255$	−4.29477	−	7.43876i	−0.268949	−	0.465833i
$256$		0			0
$257$	4.44131	−	7.69257i	0.277041	−	0.479849i	−0.693607	−	0.720354i	$-0.743979\pi$
$257$	4.44131	−	7.69257i	0.277041	−	0.479849i	0.970648	+	0.240504i	$0.0773128\pi$
$258$		0			0
$259$	10.5364	+	22.6240i	0.654702	+	1.40578i
$260$		0			0
$261$	28.5830	−	49.5073i	1.76925	−	3.06442i
$262$		0			0
$263$	8.46209	+	14.6568i	0.521795	+	0.903775i	0.999679	+	0.0253520i	$0.00807065\pi$
$263$	8.46209	+	14.6568i	0.521795	+	0.903775i	−0.477884	+	0.878423i	$0.658596\pi$
$264$		0			0
$265$	5.17434			0.317857
$266$		0			0
$267$	43.0165			2.63257
$268$		0			0
$269$	0.947160	+	1.64053i	0.0577494	+	0.100025i	0.893455	−	0.449153i	$-0.148274\pi$
$269$	0.947160	+	1.64053i	0.0577494	+	0.100025i	−0.835705	+	0.549178i	$0.814941\pi$
$270$		0			0
$271$	−5.23319	+	9.06416i	−0.317894	+	0.550608i	−0.980048	−	0.198759i	$-0.936309\pi$
$271$	−5.23319	+	9.06416i	−0.317894	+	0.550608i	0.662155	+	0.749367i	$0.269642\pi$
$272$		0			0
$273$	−9.04771	−	0.795973i	−0.547593	−	0.0481745i
$274$		0			0
$275$	−3.33302	+	5.77296i	−0.200989	+	0.348123i
$276$		0			0
$277$	5.64353	+	9.77488i	0.339087	+	0.587316i	0.984261	−	0.176720i	$-0.0565486\pi$
$277$	5.64353	+	9.77488i	0.339087	+	0.587316i	−0.645174	+	0.764035i	$0.723215\pi$
$278$		0			0
$279$	−49.8023			−2.98159
$280$		0			0
$281$	14.5517			0.868079			0.434040	−	0.900894i	$-0.357088\pi$
$281$	14.5517			0.868079			0.434040	+	0.900894i	$0.357088\pi$
$282$		0			0
$283$	6.76787	+	11.7223i	0.402308	+	0.696818i	0.994004	−	0.109343i	$-0.0348747\pi$
$283$	6.76787	+	11.7223i	0.402308	+	0.696818i	−0.591696	+	0.806161i	$0.701541\pi$
$284$		0			0
$285$	3.34149	−	5.78764i	0.197933	−	0.342830i
$286$		0			0
$287$	−3.57177	+	5.09577i	−0.210835	+	0.300794i
$288$		0			0
$289$	4.79451	−	8.30433i	0.282030	−	0.488490i
$290$		0			0
$291$	−12.3892	−	21.4587i	−0.726268	−	1.25793i
$292$		0			0
$293$	14.4816			0.846026			0.423013	−	0.906124i	$-0.360973\pi$
$293$	14.4816			0.846026			0.423013	+	0.906124i	$0.360973\pi$
$294$		0			0
$295$	−6.74254			−0.392566
$296$		0			0
$297$	−15.9297	−	27.5910i	−0.924332	−	1.60099i
$298$		0			0
$299$	−2.71646	+	4.70505i	−0.157097	+	0.272100i
$300$		0			0
$301$	0.780267	−	1.11319i	0.0449739	−	0.0641634i
$302$		0			0
$303$	1.29993	−	2.25155i	0.0746791	−	0.129348i
$304$		0			0
$305$	0.278677	+	0.482682i	0.0159570	+	0.0276383i
$306$		0			0
$307$	14.6530			0.836288			0.418144	−	0.908381i	$-0.362681\pi$
$307$	14.6530			0.836288			0.418144	+	0.908381i	$0.362681\pi$
$308$		0			0
$309$	−1.13614			−0.0646325
$310$		0			0
$311$	−6.91326	−	11.9741i	−0.392015	−	0.678990i	0.600700	−	0.799474i	$-0.294889\pi$
$311$	−6.91326	−	11.9741i	−0.392015	−	0.678990i	−0.992715	+	0.120485i	$0.961555\pi$
$312$		0			0
$313$	−8.98292	+	15.5589i	−0.507744	+	0.879439i	0.492215	+	0.870473i	$0.336187\pi$
$313$	−8.98292	+	15.5589i	−0.507744	+	0.879439i	−0.999960	+	0.00896576i	$0.997146\pi$
$314$		0			0
$315$	−21.2805	−	1.87216i	−1.19902	−	0.105484i
$316$		0			0
$317$	−1.82029	+	3.15283i	−0.102237	+	0.177080i	−0.912606	−	0.408840i	$-0.865933\pi$
$317$	−1.82029	+	3.15283i	−0.102237	+	0.177080i	0.810369	+	0.585920i	$0.199267\pi$
$318$		0			0
$319$	−5.21965	−	9.04069i	−0.292244	−	0.506182i
$320$		0			0
$321$	−35.1974			−1.96453
$322$		0			0
$323$	−5.76603			−0.320830
$324$		0			0
$325$	−2.07762	−	3.59854i	−0.115245	−	0.199611i
$326$		0			0
$327$	−13.6891	+	23.7103i	−0.757011	+	1.31118i
$328$		0			0
$329$	−5.17373	−	11.1091i	−0.285237	−	0.612465i
$330$		0			0
$331$	6.78126	−	11.7455i	0.372732	−	0.645590i	−0.617253	−	0.786765i	$-0.711755\pi$
$331$	6.78126	−	11.7455i	0.372732	−	0.645590i	0.989985	+	0.141175i	$0.0450879\pi$
$332$		0			0
$333$	−41.4339	−	71.7656i	−2.27056	−	3.93273i
$334$		0			0
$335$	10.5255			0.575070
$336$		0			0
$337$	−16.1880			−0.881818			−0.440909	−	0.897552i	$-0.645344\pi$
$337$	−16.1880			−0.881818			−0.440909	+	0.897552i	$0.645344\pi$
$338$		0			0
$339$	25.4565	+	44.0920i	1.38261	+	2.39475i
$340$		0			0
$341$	−4.54729	+	7.87613i	−0.246249	+	0.426516i
$342$		0			0
$343$	−17.8822	−	4.81930i	−0.965550	−	0.260218i
$344$		0			0
$345$	−8.57107	+	14.8455i	−0.461451	+	0.799257i
$346$		0			0
$347$	7.09612	+	12.2908i	0.380940	+	0.659807i	0.991197	−	0.132397i	$-0.0422673\pi$
$347$	7.09612	+	12.2908i	0.380940	+	0.659807i	−0.610257	+	0.792203i	$0.708934\pi$
$348$		0			0
$349$	−4.22675			−0.226253			−0.113126	−	0.993581i	$-0.536086\pi$
$349$	−4.22675			−0.226253			−0.113126	+	0.993581i	$0.536086\pi$
$350$		0			0
$351$	19.8593			1.06001
$352$		0			0
$353$	−14.6195	−	25.3217i	−0.778116	−	1.34774i	−0.933026	−	0.359808i	$-0.882842\pi$
$353$	−14.6195	−	25.3217i	−0.778116	−	1.34774i	0.154910	−	0.987929i	$-0.450491\pi$
$354$		0			0
$355$	−7.05309	+	12.2163i	−0.374339	+	0.648375i
$356$		0			0
$357$	10.4388	+	22.4143i	0.552479	+	1.18629i
$358$		0			0
$359$	4.14723	−	7.18321i	0.218882	−	0.379115i	−0.735584	−	0.677433i	$-0.763092\pi$
$359$	4.14723	−	7.18321i	0.218882	−	0.379115i	0.954467	+	0.298318i	$0.0964256\pi$
$360$		0			0
$361$	7.25691	+	12.5693i	0.381942	+	0.661544i
$362$		0			0
$363$	28.9271			1.51828
$364$		0			0
$365$	−9.35917			−0.489882
$366$		0			0
$367$	−12.3626	−	21.4126i	−0.645321	−	1.11773i	−0.984227	−	0.176909i	$-0.943390\pi$
$367$	−12.3626	−	21.4126i	−0.645321	−	1.11773i	0.338906	−	0.940820i	$-0.389943\pi$
$368$		0			0
$369$	10.3313	−	17.8943i	0.537823	−	0.931538i
$370$		0			0
$371$	−14.8375	−	1.30533i	−0.770326	−	0.0677695i
$372$		0			0
$373$	3.96541	−	6.86829i	0.205321	−	0.355626i	−0.744914	−	0.667161i	$-0.767509\pi$
$373$	3.96541	−	6.86829i	0.205321	−	0.355626i	0.950235	+	0.311534i	$0.100843\pi$
$374$		0			0
$375$	−14.4435	−	25.0168i	−0.745857	−	1.29186i
$376$		0			0
$377$	6.50727			0.335141
$378$		0			0
$379$	34.5050			1.77240			0.886202	−	0.463299i	$-0.153334\pi$
$379$	34.5050			1.77240			0.886202	+	0.463299i	$0.153334\pi$
$380$		0			0
$381$	−32.6303	−	56.5174i	−1.67170	−	2.89547i
$382$		0			0
$383$	7.96429	−	13.7946i	0.406956	−	0.704869i	−0.587591	−	0.809158i	$-0.699923\pi$
$383$	7.96429	−	13.7946i	0.406956	−	0.704869i	0.994547	+	0.104289i	$0.0332568\pi$
$384$		0			0
$385$	−2.23913	+	3.19453i	−0.114117	+	0.162808i
$386$		0			0
$387$	−2.25691	+	3.90908i	−0.114725	+	0.198709i
$388$		0			0
$389$	−4.04845	−	7.01212i	−0.205265	−	0.355529i	0.744952	−	0.667118i	$-0.232472\pi$
$389$	−4.04845	−	7.01212i	−0.205265	−	0.355529i	−0.950217	+	0.311589i	$0.899139\pi$
$390$		0			0
$391$	14.7901			0.747968
$392$		0			0
$393$	47.3227			2.38711
$394$		0			0
$395$	3.91795	+	6.78608i	0.197133	+	0.341445i
$396$		0			0
$397$	15.7955	−	27.3586i	0.792753	−	1.37309i	−0.131503	−	0.991316i	$-0.541980\pi$
$397$	15.7955	−	27.3586i	0.792753	−	1.37309i	0.924256	−	0.381773i	$-0.124686\pi$
$398$		0			0
$399$	−11.0419	+	15.7532i	−0.552784	+	0.788648i
$400$		0			0
$401$	−0.706911	+	1.22441i	−0.0353015	+	0.0611439i	−0.883136	−	0.469116i	$-0.844572\pi$
$401$	−0.706911	+	1.22441i	−0.0353015	+	0.0611439i	0.847835	+	0.530260i	$0.177906\pi$
$402$		0			0
$403$	−2.83452	−	4.90954i	−0.141198	−	0.244562i
$404$		0			0
$405$	38.4377			1.90999
$406$		0			0
$407$	−15.1328			−0.750104
$408$		0			0
$409$	−9.23496	−	15.9954i	−0.456639	−	0.790923i	0.542141	−	0.840287i	$-0.317614\pi$
$409$	−9.23496	−	15.9954i	−0.456639	−	0.790923i	−0.998781	+	0.0493646i	$0.984280\pi$
$410$		0			0
$411$	11.4711	−	19.8685i	0.565827	−	0.980041i
$412$		0			0
$413$	19.3344	+	1.70094i	0.951383	+	0.0836980i
$414$		0			0
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$		0			0
$417$	2.16178	+	3.74431i	0.105863	+	0.183360i
$418$		0			0
$419$	15.1529			0.740268			0.370134	−	0.928978i	$-0.379312\pi$
$419$	15.1529			0.740268			0.370134	+	0.928978i	$0.379312\pi$
$420$		0			0
$421$	15.8804			0.773962			0.386981	−	0.922088i	$-0.373518\pi$
$421$	15.8804			0.773962			0.386981	+	0.922088i	$0.373518\pi$
$422$		0			0
$423$	20.3454	+	35.2393i	0.989227	+	1.71339i
$424$		0			0
$425$	−5.65593	+	9.79635i	−0.274353	+	0.475193i
$426$		0			0
$427$	−0.677346	−	1.45440i	−0.0327791	−	0.0703836i
$428$		0			0
$429$	2.75363	−	4.76943i	0.132947	−	0.230270i
$430$		0			0
$431$	−7.50142	−	12.9928i	−0.361331	−	0.625843i	0.626850	−	0.779140i	$-0.284344\pi$
$431$	−7.50142	−	12.9928i	−0.361331	−	0.625843i	−0.988180	+	0.153298i	$0.951011\pi$
$432$		0			0
$433$	9.81258			0.471562			0.235781	−	0.971806i	$-0.424235\pi$
$433$	9.81258			0.471562			0.235781	+	0.971806i	$0.424235\pi$
$434$		0			0
$435$	20.5320			0.984432
$436$		0			0
$437$	5.75363	+	9.96559i	0.275234	+	0.476719i
$438$		0			0
$439$	0.702223	−	1.21629i	0.0335153	−	0.0580502i	−0.848781	−	0.528744i	$-0.822663\pi$
$439$	0.702223	−	1.21629i	0.0335153	−	0.0580502i	0.882297	+	0.470694i	$0.155996\pi$
$440$		0			0
$441$	60.5501	+	10.7369i	2.88334	+	0.511281i
$442$		0			0
$443$	14.6176	−	25.3185i	0.694504	−	1.20292i	−0.275843	−	0.961203i	$-0.588957\pi$
$443$	14.6176	−	25.3185i	0.694504	−	1.20292i	0.970348	−	0.241714i	$-0.0777096\pi$
$444$		0			0
$445$	5.75850	+	9.97401i	0.272979	+	0.472813i
$446$		0			0
$447$	−18.0632			−0.854362
$448$		0			0
$449$	9.13416			0.431067			0.215534	−	0.976496i	$-0.430851\pi$
$449$	9.13416			0.431067			0.215534	+	0.976496i	$0.430851\pi$
$450$		0			0
$451$	−1.88663	−	3.26773i	−0.0888377	−	0.153871i
$452$		0			0
$453$	−23.6449	+	40.9543i	−1.11094	+	1.92420i
$454$		0			0
$455$	−1.02663	−	2.20440i	−0.0481293	−	0.103344i
$456$		0			0
$457$	−20.4671	+	35.4500i	−0.957409	+	1.65828i	−0.228654	+	0.973508i	$0.573432\pi$
$457$	−20.4671	+	35.4500i	−0.957409	+	1.65828i	−0.728755	+	0.684774i	$0.759901\pi$
$458$		0			0
$459$	−27.0316	−	46.8201i	−1.26173	−	2.18538i
$460$		0			0
$461$	−33.4731			−1.55900			−0.779499	−	0.626404i	$-0.784526\pi$
$461$	−33.4731			−1.55900			−0.779499	+	0.626404i	$0.784526\pi$
$462$		0			0
$463$	6.94390			0.322710			0.161355	−	0.986896i	$-0.448414\pi$
$463$	6.94390			0.322710			0.161355	+	0.986896i	$0.448414\pi$
$464$		0			0
$465$	−8.94359	−	15.4908i	−0.414749	−	0.718366i
$466$		0			0
$467$	−6.09358	+	10.5544i	−0.281977	+	0.488399i	−0.971872	−	0.235511i	$-0.924324\pi$
$467$	−6.09358	+	10.5544i	−0.281977	+	0.488399i	0.689894	+	0.723910i	$0.257657\pi$
$468$		0			0
$469$	−30.1822	−	2.65528i	−1.39368	−	0.122609i
$470$		0			0
$471$	2.10567	−	3.64712i	0.0970240	−	0.168051i
$472$		0			0
$473$	0.412141	+	0.713850i	0.0189503	+	0.0328228i
$474$		0			0
$475$	−8.80105			−0.403820
$476$		0			0
$477$	49.4568			2.26447
$478$		0			0
$479$	4.04264	+	7.00206i	0.184713	+	0.319932i	0.943480	−	0.331430i	$-0.107531\pi$
$479$	4.04264	+	7.00206i	0.184713	+	0.319932i	−0.758767	+	0.651362i	$0.774198\pi$
$480$		0			0
$481$	4.71646	−	8.16915i	0.215052	−	0.372481i
$482$		0			0
$483$	28.3229	−	40.4077i	1.28873	−	1.83861i
$484$		0			0
$485$	3.31701	−	5.74524i	0.150618	−	0.260878i
$486$		0			0
$487$	−13.2103	−	22.8808i	−0.598614	−	1.03683i	−0.993026	−	0.117896i	$-0.962385\pi$
$487$	−13.2103	−	22.8808i	−0.598614	−	1.03683i	0.394412	−	0.918934i	$-0.370948\pi$
$488$		0			0
$489$	−53.0598			−2.39945
$490$		0			0
$491$	−21.9504			−0.990609			−0.495304	−	0.868720i	$-0.664943\pi$
$491$	−21.9504			−0.990609			−0.495304	+	0.868720i	$0.664943\pi$
$492$		0			0
$493$	−8.85741	−	15.3415i	−0.398918	−	0.690946i
$494$		0			0
$495$	6.47664	−	11.2179i	0.291103	−	0.504206i
$496$		0			0
$497$	23.3067	−	33.2513i	1.04545	−	1.49152i
$498$		0			0
$499$	4.38335	−	7.59219i	0.196226	−	0.339873i	−0.751076	−	0.660216i	$-0.770465\pi$
$499$	4.38335	−	7.59219i	0.196226	−	0.339873i	0.947302	+	0.320343i	$0.103798\pi$
$500$		0			0
$501$	40.6957	+	70.4870i	1.81815	+	3.14913i
$502$		0			0
$503$	−19.7135			−0.878983			−0.439492	−	0.898247i	$-0.644841\pi$
$503$	−19.7135			−0.878983			−0.439492	+	0.898247i	$0.644841\pi$
$504$		0			0
$505$	0.696072			0.0309748
$506$		0			0
$507$	1.71646	+	2.97300i	0.0762307	+	0.132035i
$508$		0			0
$509$	−10.5547	+	18.2812i	−0.467828	+	0.810302i	−0.999324	−	0.0367587i	$-0.988297\pi$
$509$	−10.5547	+	18.2812i	−0.467828	+	0.810302i	0.531496	+	0.847061i	$0.321630\pi$
$510$		0			0
$511$	26.8377	+	2.36104i	1.18723	+	0.104446i
$512$		0			0
$513$	21.0316	−	36.4278i	0.928569	−	1.60833i
$514$		0			0
$515$	−0.152091	−	0.263430i	−0.00670194	−	0.0116081i
$516$		0			0
$517$	7.43069			0.326801
$518$		0			0
$519$	48.6662			2.13621
$520$		0			0
$521$	15.0740	+	26.1090i	0.660405	+	1.14386i	0.980509	+	0.196473i	$0.0629489\pi$
$521$	15.0740	+	26.1090i	0.660405	+	1.14386i	−0.320104	+	0.947382i	$0.603718\pi$
$522$		0			0
$523$	−0.140008	+	0.242500i	−0.00612211	+	0.0106038i	−0.869070	−	0.494689i	$-0.835282\pi$
$523$	−0.140008	+	0.242500i	−0.00612211	+	0.0106038i	0.862948	+	0.505293i	$0.168615\pi$
$524$		0			0
$525$	15.9333	+	34.2123i	0.695388	+	1.49315i
$526$		0			0
$527$	−7.71646	+	13.3653i	−0.336134	+	0.582202i
$528$		0			0
$529$	−3.25832	−	5.64358i	−0.141666	−	0.245373i
$530$		0			0
$531$	−64.4459			−2.79671
$532$		0			0
$533$	2.35203			0.101878
$534$		0			0
$535$	−4.71177	−	8.16103i	−0.203708	−	0.352832i
$536$		0			0
$537$	11.0893	−	19.2072i	0.478538	−	0.828851i
$538$		0			0
$539$	7.22665	−	8.59552i	0.311274	−	0.370235i
$540$		0			0
$541$	−5.28384	+	9.15188i	−0.227170	+	0.393470i	−0.956968	−	0.290193i	$-0.906281\pi$
$541$	−5.28384	+	9.15188i	−0.227170	+	0.393470i	0.729798	+	0.683663i	$0.239614\pi$
$542$		0			0
$543$	20.5076	+	35.5201i	0.880064	+	1.52432i
$544$		0			0
$545$	−7.33010			−0.313987
$546$		0			0
$547$	21.0940			0.901912			0.450956	−	0.892546i	$-0.351083\pi$
$547$	21.0940			0.901912			0.450956	+	0.892546i	$0.351083\pi$
$548$		0			0
$549$	2.66362	+	4.61353i	0.113681	+	0.196901i
$550$		0			0
$551$	6.89140	−	11.9363i	0.293584	−	0.508502i
$552$		0			0
$553$	−9.52288	−	20.4476i	−0.404954	−	0.869522i
$554$		0			0
$555$	14.8815	−	25.7756i	0.631686	−	1.09411i
$556$		0			0
$557$	−20.1847	−	34.9609i	−0.855253	−	1.48134i	−0.876410	−	0.481566i	$-0.840068\pi$
$557$	−20.1847	−	34.9609i	−0.855253	−	1.48134i	0.0211566	−	0.999776i	$-0.493265\pi$
$558$		0			0
$559$	−0.513812			−0.0217319
$560$		0			0
$561$	−14.9925			−0.632984
$562$		0			0
$563$	−15.4252	−	26.7173i	−0.650095	−	1.12600i	−0.983099	−	0.183073i	$-0.941396\pi$
$563$	−15.4252	−	26.7173i	−0.650095	−	1.12600i	0.333004	−	0.942925i	$-0.391938\pi$
$564$		0			0
$565$	−6.81559	+	11.8049i	−0.286734	+	0.496638i
$566$		0			0
$567$	−110.221	−	9.69671i	−4.62885	−	0.407224i
$568$		0			0
$569$	4.21276	−	7.29672i	0.176608	−	0.305894i	−0.764108	−	0.645088i	$-0.776821\pi$
$569$	4.21276	−	7.29672i	0.176608	−	0.305894i	0.940717	+	0.339193i	$0.110154\pi$
$570$		0			0
$571$	1.58015	+	2.73690i	0.0661273	+	0.114536i	0.897193	−	0.441638i	$-0.145602\pi$
$571$	1.58015	+	2.73690i	0.0661273	+	0.114536i	−0.831066	+	0.556173i	$0.812269\pi$
$572$		0			0
$573$	7.47879			0.312431
$574$		0			0
$575$	22.5751			0.941446
$576$		0			0
$577$	−7.96429	−	13.7946i	−0.331558	−	0.574275i	0.651260	−	0.758855i	$-0.274241\pi$
$577$	−7.96429	−	13.7946i	−0.331558	−	0.574275i	−0.982817	+	0.184580i	$0.940908\pi$
$578$		0			0
$579$	−34.8420	+	60.3482i	−1.44799	+	2.50799i
$580$		0			0
$581$	19.8268	−	28.2866i	0.822555	−	1.17352i
$582$		0			0
$583$	4.51574	−	7.82149i	0.187023	−	0.323933i
$584$		0			0
$585$	4.03717	+	6.99259i	0.166917	+	0.289108i
$586$		0			0
$587$	25.0415			1.03357			0.516786	−	0.856114i	$-0.327128\pi$
$587$	25.0415			1.03357			0.516786	+	0.856114i	$0.327128\pi$
$588$		0			0
$589$	−12.0074			−0.494756
$590$		0			0
$591$	−3.44902	−	5.97387i	−0.141874	−	0.245732i
$592$		0			0
$593$	−11.0987	+	19.2234i	−0.455767	+	0.789412i	−0.998732	−	0.0503438i	$-0.983968\pi$
$593$	−11.0987	+	19.2234i	−0.455767	+	0.789412i	0.542965	+	0.839755i	$0.317302\pi$
$594$		0			0
$595$	−3.79967	+	5.42092i	−0.155771	+	0.222236i
$596$		0			0
$597$	4.53390	−	7.85295i	0.185560	−	0.321400i
$598$		0			0
$599$	−18.2197	−	31.5575i	−0.744438	−	1.28940i	−0.950457	−	0.310856i	$-0.899384\pi$
$599$	−18.2197	−	31.5575i	−0.744438	−	1.28940i	0.206019	−	0.978548i	$-0.433949\pi$
$600$		0			0
$601$	−36.3090			−1.48107			−0.740537	−	0.672015i	$-0.765429\pi$
$601$	−36.3090			−1.48107			−0.740537	+	0.672015i	$0.765429\pi$
$602$		0			0
$603$	100.604			4.09691
$604$		0			0
$605$	3.87239	+	6.70717i	0.157435	+	0.272685i
$606$		0			0
$607$	−4.42521	+	7.66470i	−0.179614	+	0.311100i	−0.941748	−	0.336318i	$-0.890818\pi$
$607$	−4.42521	+	7.66470i	−0.179614	+	0.311100i	0.762134	+	0.647419i	$0.224152\pi$
$608$		0			0
$609$	−58.8759	−	5.17961i	−2.38577	−	0.209888i
$610$		0			0
$611$	−2.31594	+	4.01132i	−0.0936928	+	0.162281i
$612$		0			0
$613$	−10.4880	−	18.1658i	−0.423608	−	0.733710i	0.572682	−	0.819778i	$-0.305903\pi$
$613$	−10.4880	−	18.1658i	−0.423608	−	0.733710i	−0.996289	+	0.0860680i	$0.972570\pi$
$614$		0			0
$615$	7.42122			0.299252
$616$		0			0
$617$	−18.4816			−0.744042			−0.372021	−	0.928224i	$-0.621335\pi$
$617$	−18.4816			−0.744042			−0.372021	+	0.928224i	$0.621335\pi$
$618$		0			0
$619$	9.90672	+	17.1589i	0.398185	+	0.689676i	0.993502	−	0.113815i	$-0.0363070\pi$
$619$	9.90672	+	17.1589i	0.398185	+	0.689676i	−0.595317	+	0.803491i	$0.702974\pi$
$620$		0			0
$621$	−53.9470	+	93.4390i	−2.16482	+	3.74958i
$622$		0			0
$623$	−13.9965	−	30.0534i	−0.560757	−	1.20406i
$624$		0			0
$625$	−6.52108	+	11.2948i	−0.260843	+	0.451794i
$626$		0			0
$627$	−5.83237	−	10.1020i	−0.232922	−	0.403433i
$628$		0			0
$629$	−25.6794			−1.02390
$630$		0			0
$631$	−8.40898			−0.334756			−0.167378	−	0.985893i	$-0.553530\pi$
$631$	−8.40898			−0.334756			−0.167378	+	0.985893i	$0.553530\pi$
$632$		0			0
$633$	−17.0306	−	29.4979i	−0.676907	−	1.17244i
$634$		0			0
$635$	8.73625	−	15.1316i	0.346688	−	0.600481i
$636$		0			0
$637$	2.38779	+	6.58016i	0.0946077	+	0.260715i
$638$		0			0
$639$	−67.4142	+	116.765i	−2.66686	+	4.61914i
$640$		0			0
$641$	15.0134	+	26.0039i	0.592993	+	1.02709i	0.993827	+	0.110943i	$0.0353870\pi$
$641$	15.0134	+	26.0039i	0.592993	+	1.02709i	−0.400834	+	0.916151i	$0.631280\pi$
$642$		0			0
$643$	11.1349			0.439119			0.219559	−	0.975599i	$-0.429538\pi$
$643$	11.1349			0.439119			0.219559	+	0.975599i	$0.429538\pi$
$644$		0			0
$645$	−1.62120			−0.0638346
$646$		0			0
$647$	−14.2263	−	24.6406i	−0.559292	−	0.968722i	−0.997556	−	0.0698759i	$-0.977740\pi$
$647$	−14.2263	−	24.6406i	−0.559292	−	0.968722i	0.438264	−	0.898847i	$-0.355594\pi$
$648$		0			0
$649$	−5.88434	+	10.1920i	−0.230981	+	0.400070i
$650$		0			0
$651$	21.7381	+	46.6763i	0.851983	+	1.82939i
$652$		0			0
$653$	−16.8305	+	29.1513i	−0.658629	+	1.14078i	0.322342	+	0.946623i	$0.395530\pi$
$653$	−16.8305	+	29.1513i	−0.658629	+	1.14078i	−0.980971	+	0.194155i	$0.937803\pi$
$654$		0			0
$655$	6.33495	+	10.9725i	0.247527	+	0.428729i
$656$		0			0
$657$	−89.4560			−3.49001
$658$		0			0
$659$	−17.2594			−0.672332			−0.336166	−	0.941803i	$-0.609130\pi$
$659$	−17.2594			−0.672332			−0.336166	+	0.941803i	$0.609130\pi$
$660$		0			0
$661$	12.4140	+	21.5017i	0.482848	+	0.836317i	0.999806	−	0.0196934i	$-0.00626902\pi$
$661$	12.4140	+	21.5017i	0.482848	+	0.836317i	−0.516958	+	0.856011i	$0.672936\pi$
$662$		0			0
$663$	4.67274	−	8.09343i	0.181474	−	0.314323i
$664$		0			0
$665$	−5.13076	−	0.451379i	−0.198962	−	0.0175037i
$666$		0			0
$667$	−17.6767	+	30.6170i	−0.684446	+	1.18550i
$668$		0			0
$669$	15.7983	+	27.3635i	0.610799	+	1.05794i
$670$		0			0
$671$	0.972826			0.0375555
$672$		0			0
$673$	−12.7567			−0.491735			−0.245867	−	0.969303i	$-0.579073\pi$
$673$	−12.7567			−0.491735			−0.245867	+	0.969303i	$0.579073\pi$
$674$		0			0
$675$	−41.2600	−	71.4645i	−1.58810	−	2.75067i
$676$		0			0
$677$	6.66461	−	11.5434i	0.256142	−	0.443651i	−0.709063	−	0.705145i	$-0.750882\pi$
$677$	6.66461	−	11.5434i	0.256142	−	0.443651i	0.965205	+	0.261494i	$0.0842153\pi$
$678$		0			0
$679$	−10.9610	+	15.6378i	−0.420643	+	0.600124i
$680$		0			0
$681$	35.2473	−	61.0502i	1.35068	−	2.33945i
$682$		0			0
$683$	−17.1588	−	29.7198i	−0.656562	−	1.13720i	−0.981500	−	0.191463i	$-0.938677\pi$
$683$	−17.1588	−	29.7198i	−0.656562	−	1.13720i	0.324938	−	0.945735i	$-0.394657\pi$
$684$		0			0
$685$	6.14240			0.234689
$686$		0			0
$687$	−6.15980			−0.235011
$688$		0			0
$689$	2.81486	+	4.87548i	0.107238	+	0.185741i
$690$		0			0
$691$	−3.82544	+	6.62586i	−0.145527	+	0.252059i	−0.929569	−	0.368647i	$-0.879821\pi$
$691$	−3.82544	+	6.62586i	−0.145527	+	0.252059i	0.784043	+	0.620707i	$0.213154\pi$
$692$		0			0
$693$	−21.4019	+	30.5336i	−0.812989	+	1.15988i
$694$		0			0
$695$	−0.578782	+	1.00248i	−0.0219545	+	0.0380262i
$696$		0			0
$697$	−3.20149	−	5.54514i	−0.121265	−	0.210037i
$698$		0			0
$699$	−75.0785			−2.83973
$700$		0			0
$701$	32.7331			1.23631			0.618157	−	0.786055i	$-0.287880\pi$
$701$	32.7331			1.23631			0.618157	+	0.786055i	$0.287880\pi$
$702$		0			0
$703$	−9.98976	−	17.3028i	−0.376771	−	0.652586i
$704$		0			0
$705$	−7.30733	+	12.6567i	−0.275210	+	0.476677i
$706$		0			0
$707$	−1.99600	−	0.175599i	−0.0750674	−	0.00660406i
$708$		0			0
$709$	−1.83939	+	3.18591i	−0.0690796	+	0.119649i	−0.898496	−	0.438981i	$-0.855340\pi$
$709$	−1.83939	+	3.18591i	−0.0690796	+	0.119649i	0.829417	+	0.558630i	$0.188673\pi$
$710$		0			0
$711$	37.4481	+	64.8621i	1.40441	+	2.43252i
$712$		0			0
$713$	30.7995			1.15345
$714$		0			0
$715$	1.47448			0.0551426
$716$		0			0
$717$	−21.1928	−	36.7070i	−0.791459	−	1.37085i
$718$		0			0
$719$	5.68884	−	9.85336i	0.212158	−	0.367468i	−0.740232	−	0.672352i	$-0.765284\pi$
$719$	5.68884	−	9.85336i	0.212158	−	0.367468i	0.952390	+	0.304884i	$0.0986176\pi$
$720$		0			0
$721$	0.369670	+	0.793759i	0.0137672	+	0.0295611i
$722$		0			0
$723$	−23.9953	+	41.5611i	−0.892395	+	1.54567i
$724$		0			0
$725$	−13.5196	−	23.4167i	−0.502106	−	0.869673i
$726$		0			0
$727$	42.4642			1.57491			0.787456	−	0.616371i	$-0.211398\pi$
$727$	42.4642			1.57491			0.787456	+	0.616371i	$0.211398\pi$
$728$		0			0
$729$	162.866			6.03206
$730$		0			0
$731$	0.699378	+	1.21136i	0.0258674	+	0.0448037i
$732$		0			0
$733$	0.688838	−	1.19310i	0.0254428	−	0.0440682i	−0.853024	−	0.521872i	$-0.825234\pi$
$733$	0.688838	−	1.19310i	0.0254428	−	0.0440682i	0.878466	+	0.477804i	$0.158567\pi$
$734$		0			0
$735$	7.53404	+	20.7619i	0.277897	+	0.765816i
$736$		0			0
$737$	9.18582	−	15.9103i	0.338364	−	0.586064i
$738$		0			0
$739$	4.33009	+	7.49993i	0.159285	+	0.275889i	0.934611	−	0.355672i	$-0.115748\pi$
$739$	4.33009	+	7.49993i	0.159285	+	0.275889i	−0.775326	+	0.631561i	$0.782415\pi$
$740$		0			0
$741$	7.27114			0.267112
$742$		0			0
$743$	−47.1952			−1.73143			−0.865713	−	0.500541i	$-0.833134\pi$
$743$	−47.1952			−1.73143			−0.865713	+	0.500541i	$0.833134\pi$
$744$		0			0
$745$	−2.41807	−	4.18823i	−0.0885914	−	0.153445i
$746$		0			0
$747$	−57.3486	+	99.3307i	−2.09828	+	3.63432i
$748$		0			0
$749$	11.4523	+	24.5906i	0.418459	+	0.898521i
$750$		0			0
$751$	8.22588	−	14.2476i	0.300167	−	0.519904i	−0.676007	−	0.736895i	$-0.736291\pi$
$751$	8.22588	−	14.2476i	0.300167	−	0.519904i	0.976174	+	0.216991i	$0.0696243\pi$
$752$		0			0
$753$	9.82213	+	17.0124i	0.357938	+	0.619967i
$754$		0			0
$755$	−12.6611			−0.460785
$756$		0			0
$757$	−11.4147			−0.414873			−0.207437	−	0.978248i	$-0.566512\pi$
$757$	−11.4147			−0.414873			−0.207437	+	0.978248i	$0.566512\pi$
$758$		0			0
$759$	14.9603	+	25.9120i	0.543024	+	0.940545i
$760$		0			0
$761$	5.15192	−	8.92338i	0.186757	−	0.323472i	−0.757410	−	0.652939i	$-0.773536\pi$
$761$	5.15192	−	8.92338i	0.186757	−	0.323472i	0.944167	+	0.329467i	$0.106869\pi$
$762$		0			0
$763$	21.0192	+	1.84917i	0.760947	+	0.0669444i
$764$		0			0
$765$	10.9905	−	19.0360i	0.397361	−	0.688249i
$766$		0			0
$767$	−3.66797	−	6.35311i	−0.132443	−	0.229398i
$768$		0			0
$769$	37.3716			1.34766			0.673828	−	0.738888i	$-0.264649\pi$
$769$	37.3716			1.34766			0.673828	+	0.738888i	$0.264649\pi$
$770$		0			0
$771$	30.4933			1.09819
$772$		0			0
$773$	−8.11504	−	14.0557i	−0.291878	−	0.505547i	0.682376	−	0.731001i	$-0.260947\pi$
$773$	−8.11504	−	14.0557i	−0.291878	−	0.505547i	−0.974254	+	0.225454i	$0.927613\pi$
$774$		0			0
$775$	−11.7781	+	20.4003i	−0.423082	+	0.732800i
$776$		0			0
$777$	−49.1756	+	70.1580i	−1.76417	+	2.51690i
$778$		0			0
$779$	2.49088	−	4.31432i	0.0892449	−	0.154577i
$780$		0			0
$781$	12.3107	+	21.3228i	0.440513	+	0.762990i
$782$		0			0
$783$	129.230			4.61830
$784$		0			0
$785$	1.12752			0.0402429
$786$		0			0
$787$	−1.06625	−	1.84680i	−0.0380078	−	0.0658314i	0.846396	−	0.532554i	$-0.178768\pi$
$787$	−1.06625	−	1.84680i	−0.0380078	−	0.0658314i	−0.884404	+	0.466723i	$0.845435\pi$
$788$		0			0
$789$	−29.0497	+	50.3155i	−1.03420	+	1.79128i
$790$		0			0
$791$	22.5219	−	32.1316i	0.800786	−	1.14247i
$792$		0			0
$793$	−0.303203	+	0.525162i	−0.0107670	+	0.0186491i
$794$		0			0
$795$	8.88155	+	15.3833i	0.314996	+	0.545589i
$796$		0			0
$797$	38.0248			1.34691			0.673453	−	0.739230i	$-0.264810\pi$
$797$	38.0248			1.34691			0.673453	+	0.739230i	$0.264810\pi$
$798$		0			0
$799$	12.6094			0.446089
$800$		0			0
$801$	55.0403	+	95.3326i	1.94475	+	3.36841i
$802$		0			0
$803$	−8.16793	+	14.1473i	−0.288240	+	0.499246i
$804$		0			0
$805$	13.1606	+	1.15781i	0.463851	+	0.0408073i
$806$		0			0
$807$	−3.25153	+	5.63181i	−0.114459	+	0.198249i
$808$		0			0
$809$	−16.2387	−	28.1263i	−0.570922	−	0.988867i	−0.996472	−	0.0839314i	$-0.973252\pi$
$809$	−16.2387	−	28.1263i	−0.570922	−	0.988867i	0.425549	−	0.904935i	$-0.360081\pi$
$810$		0			0
$811$	−12.0285			−0.422377			−0.211188	−	0.977445i	$-0.567733\pi$
$811$	−12.0285			−0.422377			−0.211188	+	0.977445i	$0.567733\pi$
$812$		0			0
$813$	−35.9303			−1.26013
$814$		0			0
$815$	−7.10296	−	12.3027i	−0.248806	−	0.430944i
$816$		0			0
$817$	−0.544142	+	0.942482i	−0.0190371	+	0.0329733i
$818$		0			0
$819$	−9.81267	−	21.0699i	−0.342882	−	0.736241i
$820$		0			0
$821$	−19.4295	+	33.6529i	−0.678095	+	1.17450i	0.297459	+	0.954735i	$0.403861\pi$
$821$	−19.4295	+	33.6529i	−0.678095	+	1.17450i	−0.975554	+	0.219760i	$0.929472\pi$
$822$		0			0
$823$	−8.79735	−	15.2375i	−0.306656	−	0.531144i	0.670972	−	0.741482i	$-0.265877\pi$
$823$	−8.79735	−	15.2375i	−0.306656	−	0.531144i	−0.977629	+	0.210338i	$0.932544\pi$
$824$		0			0
$825$	−22.8840			−0.796719
$826$		0			0
$827$	−30.5575			−1.06259			−0.531294	−	0.847187i	$-0.678294\pi$
$827$	−30.5575			−1.06259			−0.531294	+	0.847187i	$0.678294\pi$
$828$		0			0
$829$	−26.3082	−	45.5671i	−0.913721	−	1.58261i	−0.808763	−	0.588135i	$-0.799862\pi$
$829$	−26.3082	−	45.5671i	−0.913721	−	1.58261i	−0.104958	−	0.994477i	$-0.533471\pi$
$830$		0			0
$831$	−19.3738	+	33.5564i	−0.672070	+	1.16406i
$832$		0			0
$833$	12.2632	−	14.5861i	0.424894	−	0.505377i
$834$		0			0
$835$	−10.8956	+	18.8718i	−0.377059	+	0.653085i
$836$		0			0
$837$	−56.2917	−	97.5000i	−1.94572	−	3.37009i
$838$		0			0
$839$	19.6341			0.677845			0.338922	−	0.940814i	$-0.389938\pi$
$839$	19.6341			0.677845			0.338922	+	0.940814i	$0.389938\pi$
$840$		0			0
$841$	13.3445			0.460157
$842$		0			0
$843$	24.9774	+	43.2621i	0.860266	+	1.49002i
$844$		0			0
$845$	−0.459555	+	0.795973i	−0.0158092	+	0.0273823i
$846$		0			0
$847$	−9.41214	−	20.2099i	−0.323405	−	0.694419i
$848$		0			0
$849$	−23.2336	+	40.2417i	−0.797374	+	1.38109i
$850$		0			0
$851$	25.6242	+	44.3824i	0.878385	+	1.52141i
$852$		0			0
$853$	0.00430866			0.000147526			7.37629e−5	−	1.00000i	$-0.499977\pi$
$853$	0.00430866			0.000147526			7.37629e−5		1.00000i	$0.499977\pi$
$854$		0			0
$855$	17.1020			0.584875
$856$		0			0
$857$	−3.09986	−	5.36912i	−0.105889	−	0.183406i	0.808212	−	0.588892i	$-0.200436\pi$
$857$	−3.09986	−	5.36912i	−0.105889	−	0.183406i	−0.914101	+	0.405486i	$0.867102\pi$
$858$		0			0
$859$	−6.52520	+	11.3020i	−0.222637	+	0.385619i	−0.955608	−	0.294641i	$-0.904800\pi$
$859$	−6.52520	+	11.3020i	−0.222637	+	0.385619i	0.732971	+	0.680260i	$0.238133\pi$
$860$		0			0
$861$	−21.2805	−	1.87216i	−0.725238	−	0.0638029i
$862$		0			0
$863$	0.142162	−	0.246232i	0.00483925	−	0.00838183i	−0.863596	−	0.504185i	$-0.831793\pi$
$863$	0.142162	−	0.246232i	0.00483925	−	0.00838183i	0.868435	+	0.495803i	$0.165126\pi$
$864$		0			0
$865$	6.51480	+	11.2840i	0.221510	+	0.383666i
$866$		0			0
$867$	32.9183			1.11797
$868$		0			0
$869$	13.6771			0.463963
$870$		0			0
$871$	5.72592	+	9.91759i	0.194016	+	0.336045i
$872$		0			0
$873$	31.7044	−	54.9136i	1.07303	−	1.85854i
$874$		0			0
$875$	−12.7784	+	18.2307i	−0.431989	+	0.616311i
$876$		0			0
$877$	13.9970	−	24.2435i	0.472644	−	0.818644i	−0.526865	−	0.849949i	$-0.676633\pi$
$877$	13.9970	−	24.2435i	0.472644	−	0.818644i	0.999510	+	0.0313045i	$0.00996616\pi$
$878$		0			0
$879$	24.8571	+	43.0538i	0.838411	+	1.45217i
$880$		0			0
$881$	3.18975			0.107465			0.0537327	−	0.998555i	$-0.482888\pi$
$881$	3.18975			0.107465			0.0537327	+	0.998555i	$0.482888\pi$
$882$		0			0
$883$	−39.6084			−1.33293			−0.666464	−	0.745537i	$-0.732193\pi$
$883$	−39.6084			−1.33293			−0.666464	+	0.745537i	$0.732193\pi$
$884$		0			0
$885$	−11.5733	−	20.0456i	−0.389033	−	0.673824i
$886$		0			0
$887$	3.68884	−	6.38925i	0.123859	−	0.214530i	−0.797427	−	0.603415i	$-0.793806\pi$
$887$	3.68884	−	6.38925i	0.123859	−	0.214530i	0.921286	+	0.388885i	$0.127140\pi$
$888$		0			0
$889$	−28.8687	+	41.1864i	−0.968224	+	1.38135i
$890$		0			0
$891$	33.5453	−	58.1022i	1.12381	−	1.94650i
$892$		0			0
$893$	4.90530	+	8.49623i	0.164150	+	0.284315i
$894$		0			0
$895$	5.93796			0.198484
$896$		0			0
$897$	−18.6508			−0.622732
$898$		0			0
$899$	−18.4450	−	31.9477i	−0.615175	−	1.06552i
$900$		0			0
$901$	7.66293	−	13.2726i	0.255289	−	0.442174i
$902$		0			0
$903$	4.64882	+	0.408980i	0.154703	+	0.0136100i
$904$		0			0
$905$	−5.49058	+	9.50996i	−0.182513	+	0.316122i
$906$		0			0
$907$	1.14237	+	1.97864i	0.0379317	+	0.0656996i	0.884368	−	0.466790i	$-0.154590\pi$
$907$	1.14237	+	1.97864i	0.0379317	+	0.0656996i	−0.846436	+	0.532490i	$0.821256\pi$
$908$		0			0
$909$	6.65313			0.220670
$910$		0			0
$911$	2.47732			0.0820772			0.0410386	−	0.999158i	$-0.486933\pi$
$911$	2.47732			0.0820772			0.0410386	+	0.999158i	$0.486933\pi$
$912$		0			0
$913$	10.4726	+	18.1391i	0.346593	+	0.600317i
$914$		0			0
$915$	−0.956676	+	1.65701i	−0.0316267	+	0.0547791i
$916$		0			0
$917$	−15.3976	−	33.0619i	−0.508473	−	1.09180i
$918$		0			0
$919$	−19.1087	+	33.0972i	−0.630337	+	1.09178i	0.357146	+	0.934049i	$0.383750\pi$
$919$	−19.1087	+	33.0972i	−0.630337	+	1.09178i	−0.987483	+	0.157727i	$0.949583\pi$
$920$		0			0
$921$	25.1512	+	43.5632i	0.828761	+	1.43546i
$922$		0			0
$923$	−15.3476			−0.505174
$924$		0			0
$925$	−39.1960			−1.28876
$926$		0			0
$927$	−1.45370	−	2.51789i	−0.0477459	−	0.0826983i
$928$		0			0
$929$	−10.3214	+	17.8772i	−0.338634	+	0.586531i	−0.984176	−	0.177194i	$-0.943298\pi$
$929$	−10.3214	+	17.8772i	−0.338634	+	0.586531i	0.645542	+	0.763725i	$0.276631\pi$
$930$		0			0
$931$	14.5987	+	2.58868i	0.478453	+	0.0848405i
$932$		0			0
$933$	23.7327	−	41.1062i	0.776973	−	1.34576i
$934$		0			0
$935$	−2.00700	−	3.47623i	−0.0656360	−	0.113685i
$936$		0			0
$937$	−46.3418			−1.51392			−0.756960	−	0.653461i	$-0.773316\pi$
$937$	−46.3418			−1.51392			−0.756960	+	0.653461i	$0.773316\pi$
$938$		0			0
$939$	−61.6753			−2.01270
$940$		0			0
$941$	−16.3148	−	28.2581i	−0.531849	−	0.921189i	−0.999309	−	0.0371749i	$-0.988164\pi$
$941$	−16.3148	−	28.2581i	−0.531849	−	0.921189i	0.467460	−	0.884014i	$-0.345169\pi$
$942$		0			0
$943$	−6.38921	+	11.0664i	−0.208061	+	0.360373i
$944$		0			0
$945$	−20.3882	−	43.7778i	−0.663229	−	1.42409i
$946$		0			0
$947$	−8.60533	+	14.9049i	−0.279636	+	0.484343i	−0.971294	−	0.237882i	$-0.923547\pi$
$947$	−8.60533	+	14.9049i	−0.279636	+	0.484343i	0.691659	+	0.722225i	$0.256880\pi$
$948$		0			0
$949$	−5.09143	−	8.81861i	−0.165275	−	0.286264i
$950$		0			0
$951$	−12.4978			−0.405269
$952$		0			0
$953$	50.0504			1.62129			0.810646	−	0.585537i	$-0.199116\pi$
$953$	50.0504			1.62129			0.810646	+	0.585537i	$0.199116\pi$
$954$		0			0
$955$	1.00116	+	1.73407i	0.0323969	+	0.0561131i
$956$		0			0
$957$	17.9186	−	31.0360i	0.579227	−	1.00325i
$958$		0			0
$959$	−17.6135	−	1.54955i	−0.568769	−	0.0500375i
$960$		0			0
$961$	−0.569048	+	0.985619i	−0.0183564	+	0.0317942i
$962$		0			0
$963$	−45.0356	−	78.0040i	−1.45125	−	2.51364i
$964$		0			0
$965$	−18.6568			−0.600584
$966$		0			0
$967$	15.9540			0.513045			0.256522	−	0.966538i	$-0.417423\pi$
$967$	15.9540			0.513045			0.256522	+	0.966538i	$0.417423\pi$
$968$		0			0
$969$	−9.89717	−	17.1424i	−0.317943	−	0.550693i
$970$		0			0
$971$	2.54699	−	4.41151i	0.0817367	−	0.141572i	−0.822259	−	0.569113i	$-0.807287\pi$
$971$	2.54699	−	4.41151i	0.0817367	−	0.141572i	0.903996	+	0.427541i	$0.140620\pi$
$972$		0			0
$973$	1.91257	−	2.72863i	0.0613141	−	0.0874757i
$974$		0			0
$975$	7.13230	−	12.3535i	0.228416	−	0.395629i
$976$		0			0
$977$	−14.8925	−	25.7945i	−0.476453	−	0.825240i	0.523183	−	0.852220i	$-0.324744\pi$
$977$	−14.8925	−	25.7945i	−0.476453	−	0.825240i	−0.999636	+	0.0269801i	$0.991411\pi$
$978$		0			0
$979$	20.1022			0.642469
$980$		0			0
$981$	−70.0619			−2.23690
$982$		0			0
$983$	−12.8886	−	22.3236i	−0.411081	−	0.712013i	0.583927	−	0.811806i	$-0.301515\pi$
$983$	−12.8886	−	22.3236i	−0.411081	−	0.712013i	−0.995008	+	0.0997927i	$0.968182\pi$
$984$		0			0
$985$	0.923419	−	1.59941i	0.0294226	−	0.0509614i
$986$		0			0
$987$	24.1468	−	34.4499i	0.768602	−	1.09655i
$988$		0			0
$989$	1.39575	−	2.41751i	0.0443822	−	0.0768723i
$990$		0			0
$991$	−9.05764	−	15.6883i	−0.287725	−	0.498355i	0.685541	−	0.728034i	$-0.259566\pi$
$991$	−9.05764	−	15.6883i	−0.287725	−	0.498355i	−0.973266	+	0.229679i	$0.926232\pi$
$992$		0			0
$993$	46.5591			1.47751
$994$		0			0
$995$	2.42776			0.0769652
$996$		0			0
$997$	−7.34777	−	12.7267i	−0.232706	−	0.403059i	0.725897	−	0.687803i	$-0.241425\pi$
$997$	−7.34777	−	12.7267i	−0.232706	−	0.403059i	−0.958604	+	0.284744i	$0.908091\pi$
$998$		0			0
$999$	93.6656	−	162.234i	2.96345	−	5.13284i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.r.o.625.4		8
4.3	odd	2		364.2.j.e.261.1	yes	8
7.4	even	3	inner	1456.2.r.o.417.4		8
12.11	even	2		3276.2.r.j.2809.3		8
28.3	even	6		2548.2.j.q.1145.4		8
28.11	odd	6		364.2.j.e.53.1	✓	8
28.19	even	6		2548.2.a.p.1.1		4
28.23	odd	6		2548.2.a.q.1.4		4
28.27	even	2		2548.2.j.q.1353.4		8
84.11	even	6		3276.2.r.j.1873.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.j.e.53.1	✓	8	28.11	odd	6
364.2.j.e.261.1	yes	8	4.3	odd	2
1456.2.r.o.417.4		8	7.4	even	3	inner
1456.2.r.o.625.4		8	1.1	even	1	trivial
2548.2.a.p.1.1		4	28.19	even	6
2548.2.a.q.1.4		4	28.23	odd	6
2548.2.j.q.1145.4		8	28.3	even	6
2548.2.j.q.1353.4		8	28.27	even	2
3276.2.r.j.1873.3		8	84.11	even	6
3276.2.r.j.2809.3		8	12.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.71646 + 2.97300i) q^{3} +(-0.459555 + 0.795973i) q^{5} +(1.51859 - 2.16654i) q^{7} +(-4.39248 + 7.60799i) q^{9} +(0.802125 + 1.38932i) q^{11} -1.00000 q^{13} -3.15524 q^{15} +(1.36116 + 2.35759i) q^{17} +(-1.05903 + 1.83430i) q^{19} +(9.04771 + 0.795973i) q^{21} +(2.71646 - 4.70505i) q^{23} +(2.07762 + 3.59854i) q^{25} -19.8593 q^{27} -6.50727 q^{29} +(2.83452 + 4.90954i) q^{31} +(-2.75363 + 4.76943i) q^{33} +(1.02663 + 2.20440i) q^{35} +(-4.71646 + 8.16915i) q^{37} +(-1.71646 - 2.97300i) q^{39} -2.35203 q^{41} +0.513812 q^{43} +(-4.03717 - 6.99259i) q^{45} +(2.31594 - 4.01132i) q^{47} +(-2.38779 - 6.58016i) q^{49} +(-4.67274 + 8.09343i) q^{51} +(-2.81486 - 4.87548i) q^{53} -1.47448 q^{55} -7.27114 q^{57} +(3.66797 + 6.35311i) q^{59} +(0.303203 - 0.525162i) q^{61} +(9.81267 + 21.0699i) q^{63} +(0.459555 - 0.795973i) q^{65} +(-5.72592 - 9.91759i) q^{67} +18.6508 q^{69} +15.3476 q^{71} +(5.09143 + 8.81861i) q^{73} +(-7.13230 + 12.3535i) q^{75} +(4.22812 + 0.371969i) q^{77} +(4.26276 - 7.38331i) q^{79} +(-20.9103 - 36.2177i) q^{81} +13.0561 q^{83} -2.50211 q^{85} +(-11.1695 - 19.3461i) q^{87} +(6.26529 - 10.8518i) q^{89} +(-1.51859 + 2.16654i) q^{91} +(-9.73070 + 16.8541i) q^{93} +(-0.973367 - 1.68592i) q^{95} -7.21788 q^{97} -14.0933 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{3} + q^{5} - q^{7} - 9 q^{9} + 4 q^{11} - 8 q^{13} + 18 q^{15} + 3 q^{21} + 11 q^{23} - 5 q^{25} - 54 q^{27} + 22 q^{29} - 5 q^{31} + 15 q^{33} + 25 q^{35} - 27 q^{37} - 3 q^{39} + 12 q^{41}+ \cdots + 6 q^{99}+O(q^{100}) \) 8 * q + 3 * q^3 + q^5 - q^7 - 9 * q^9 + 4 * q^11 - 8 * q^13 + 18 * q^15 + 3 * q^21 + 11 * q^23 - 5 * q^25 - 54 * q^27 + 22 * q^29 - 5 * q^31 + 15 * q^33 + 25 * q^35 - 27 * q^37 - 3 * q^39 + 12 * q^41 - 8 * q^43 - 6 * q^45 + 4 * q^47 - 25 * q^49 + 9 * q^51 - 18 * q^53 - 46 * q^55 - 18 * q^57 - 16 * q^59 - 10 * q^61 + 33 * q^63 - q^65 - 2 * q^67 + 54 * q^69 + 10 * q^71 + 7 * q^73 - 6 * q^75 + 31 * q^77 + 17 * q^79 - 24 * q^81 + 12 * q^83 - 30 * q^85 - 12 * q^87 + 21 * q^89 + q^91 - 33 * q^93 + 9 * q^95 + 16 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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