LMFDB - Embedded newform 1050.2.b.d.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(251,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1050.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 4x^{8} - 30x^{6} + 36x^{4} + 729 $ x^12 + 4x^8 - 30x^6 + 36*x^4 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.2
Root			$-1.06864 + 1.36309i$ of defining polynomial
Character	$\chi$	$=$	1050.251
Dual form			1050.2.b.d.251.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.06864 - 1.36309i) q^{3} -1.00000 q^{4} +(-1.36309 + 1.06864i) q^{6} +(2.62932 + 0.294447i) q^{7} +1.00000i q^{8} +(-0.716015 + 2.91330i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.06864 - 1.36309i) q^{3} -1.00000 q^{4} +(-1.36309 + 1.06864i) q^{6} +(2.62932 + 0.294447i) q^{7} +1.00000i q^{8} +(-0.716015 + 2.91330i) q^{9} +1.43203i q^{11} +(1.06864 + 1.36309i) q^{12} -4.73625i q^{13} +(0.294447 - 2.62932i) q^{14} +1.00000 q^{16} +2.59897 q^{17} +(2.91330 + 0.716015i) q^{18} -2.72617i q^{19} +(-2.40844 - 3.89865i) q^{21} +1.43203 q^{22} -2.82660i q^{23} +(1.36309 - 1.06864i) q^{24} -4.73625 q^{26} +(4.73625 - 2.13728i) q^{27} +(-2.62932 - 0.294447i) q^{28} -2.82660i q^{29} -5.91403i q^{31} -1.00000i q^{32} +(1.95198 - 1.53032i) q^{33} -2.59897i q^{34} +(0.716015 - 2.91330i) q^{36} +2.39457 q^{37} -2.72617 q^{38} +(-6.45592 + 5.06134i) q^{39} -11.1481 q^{41} +(-3.89865 + 2.40844i) q^{42} -0.432029 q^{43} -1.43203i q^{44} -2.82660 q^{46} +10.3158 q^{47} +(-1.06864 - 1.36309i) q^{48} +(6.82660 + 1.54839i) q^{49} +(-2.77736 - 3.54262i) q^{51} +4.73625i q^{52} -5.69066i q^{53} +(-2.13728 - 4.73625i) q^{54} +(-0.294447 + 2.62932i) q^{56} +(-3.71601 + 2.91330i) q^{57} -2.82660 q^{58} -10.7775 q^{59} -1.05058i q^{61} -5.91403 q^{62} +(-2.74044 + 7.44916i) q^{63} -1.00000 q^{64} +(-1.53032 - 1.95198i) q^{66} -9.82660 q^{67} -2.59897 q^{68} +(-3.85291 + 3.02062i) q^{69} +13.2586i q^{71} +(-2.91330 - 0.716015i) q^{72} -7.58963i q^{73} -2.39457i q^{74} +2.72617i q^{76} +(-0.421657 + 3.76526i) q^{77} +(5.06134 + 6.45592i) q^{78} +16.5173 q^{79} +(-7.97465 - 4.17193i) q^{81} +11.1481i q^{82} -12.9148 q^{83} +(2.40844 + 3.89865i) q^{84} +0.432029i q^{86} +(-3.85291 + 3.02062i) q^{87} -1.43203 q^{88} -3.90396 q^{89} +(1.39457 - 12.4531i) q^{91} +2.82660i q^{92} +(-8.06134 + 6.31998i) q^{93} -10.3158i q^{94} +(-1.36309 + 1.06864i) q^{96} -14.0015i q^{97} +(1.54839 - 6.82660i) q^{98} +(-4.17193 - 1.02535i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 4 q^{7}+O(q^{10}) $ 12 * q - 12 * q^4 - 4 * q^7	$ 12 q - 12 q^{4} - 4 q^{7} + 12 q^{16} + 8 q^{18} + 14 q^{21} + 4 q^{28} - 8 q^{37} + 12 q^{39} + 14 q^{42} + 12 q^{43} + 20 q^{46} + 28 q^{49} + 28 q^{51} - 36 q^{57} + 20 q^{58} - 22 q^{63} - 12 q^{64} - 64 q^{67} - 8 q^{72} + 8 q^{78} + 56 q^{79} - 16 q^{81} - 14 q^{84} - 20 q^{91} - 44 q^{93} + 48 q^{99}+O(q^{100}) $ 12 * q - 12 * q^4 - 4 * q^7 + 12 * q^16 + 8 * q^18 + 14 * q^21 + 4 * q^28 - 8 * q^37 + 12 * q^39 + 14 * q^42 + 12 * q^43 + 20 * q^46 + 28 * q^49 + 28 * q^51 - 36 * q^57 + 20 * q^58 - 22 * q^63 - 12 * q^64 - 64 * q^67 - 8 * q^72 + 8 * q^78 + 56 * q^79 - 16 * q^81 - 14 * q^84 - 20 * q^91 - 44 * q^93 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.06864	−	1.36309i	−0.616980	−	0.786979i
$3$	−1.06864	−	1.36309i	−0.616980	−	0.786979i
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−1.36309	+	1.06864i	−0.556478	+	0.436271i
$7$	2.62932	+	0.294447i	0.993788	+	0.111290i
$7$	2.62932	+	0.294447i	0.993788	+	0.111290i
$8$			1.00000i			0.353553i
$9$	−0.716015	+	2.91330i	−0.238672	+	0.971100i
$10$		0			0
$11$			1.43203i			0.431773i	0.976418	+	0.215887i	$0.0692641\pi$
$11$			1.43203i			0.431773i	−0.976418	+	0.215887i	$0.930736\pi$
$12$	1.06864	+	1.36309i	0.308490	+	0.393489i
$13$		−	4.73625i		−	1.31360i	−0.754066	−	0.656799i	$-0.771910\pi$
$13$		−	4.73625i		−	1.31360i	0.754066	−	0.656799i	$-0.228090\pi$
$14$	0.294447	−	2.62932i	0.0786942	−	0.702714i
$15$		0			0
$16$	1.00000			0.250000
$17$	2.59897			0.630342			0.315171	−	0.949035i	$-0.397938\pi$
$17$	2.59897			0.630342			0.315171	+	0.949035i	$0.397938\pi$
$18$	2.91330	+	0.716015i	0.686672	+	0.168766i
$19$		−	2.72617i		−	0.625427i	−0.949847	−	0.312714i	$-0.898762\pi$
$19$		−	2.72617i		−	0.625427i	0.949847	−	0.312714i	$-0.101238\pi$
$20$		0			0
$21$	−2.40844	−	3.89865i	−0.525564	−	0.850754i
$22$	1.43203			0.305310
$23$		−	2.82660i		−	0.589387i	−0.955592	−	0.294694i	$-0.904782\pi$
$23$		−	2.82660i		−	0.589387i	0.955592	−	0.294694i	$-0.0952176\pi$
$24$	1.36309	−	1.06864i	0.278239	−	0.218135i
$25$		0			0
$26$	−4.73625			−0.928854
$27$	4.73625	−	2.13728i	0.911491	−	0.411320i
$28$	−2.62932	−	0.294447i	−0.496894	−	0.0556452i
$29$		−	2.82660i		−	0.524887i	−0.964947	−	0.262443i	$-0.915472\pi$
$29$		−	2.82660i		−	0.524887i	0.964947	−	0.262443i	$-0.0845283\pi$
$30$		0			0
$31$		−	5.91403i		−	1.06219i	−0.847312	−	0.531096i	$-0.821780\pi$
$31$		−	5.91403i		−	1.06219i	0.847312	−	0.531096i	$-0.178220\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.95198	−	1.53032i	0.339796	−	0.266395i
$34$		−	2.59897i		−	0.445719i
$35$		0			0
$36$	0.716015	−	2.91330i	0.119336	−	0.485550i
$37$	2.39457			0.393665			0.196833	−	0.980437i	$-0.436934\pi$
$37$	2.39457			0.393665			0.196833	+	0.980437i	$0.436934\pi$
$38$	−2.72617			−0.442244
$39$	−6.45592	+	5.06134i	−1.03377	+	0.810464i
$40$		0			0
$41$	−11.1481			−1.74104			−0.870520	−	0.492134i	$-0.836217\pi$
$41$	−11.1481			−1.74104			−0.870520	+	0.492134i	$0.836217\pi$
$42$	−3.89865	+	2.40844i	−0.601574	+	0.371630i
$43$	−0.432029			−0.0658838			−0.0329419	−	0.999457i	$-0.510488\pi$
$43$	−0.432029			−0.0658838			−0.0329419	+	0.999457i	$0.510488\pi$
$44$		−	1.43203i		−	0.215887i
$45$		0			0
$46$	−2.82660			−0.416760
$47$	10.3158			1.50471			0.752357	−	0.658755i	$-0.228917\pi$
$47$	10.3158			1.50471			0.752357	+	0.658755i	$0.228917\pi$
$48$	−1.06864	−	1.36309i	−0.154245	−	0.196745i
$49$	6.82660	+	1.54839i	0.975229	+	0.221198i
$50$		0			0
$51$	−2.77736	−	3.54262i	−0.388908	−	0.496066i
$52$			4.73625i			0.656799i
$53$		−	5.69066i		−	0.781672i	−0.920460	−	0.390836i	$-0.872186\pi$
$53$		−	5.69066i		−	0.781672i	0.920460	−	0.390836i	$-0.127814\pi$
$54$	−2.13728	−	4.73625i	−0.290847	−	0.644521i
$55$		0			0
$56$	−0.294447	+	2.62932i	−0.0393471	+	0.351357i
$57$	−3.71601	+	2.91330i	−0.492198	+	0.385876i
$58$	−2.82660			−0.371151
$59$	−10.7775			−1.40311			−0.701555	−	0.712615i	$-0.747510\pi$
$59$	−10.7775			−1.40311			−0.701555	+	0.712615i	$0.747510\pi$
$60$		0			0
$61$		−	1.05058i		−	0.134513i	−0.997736	−	0.0672563i	$-0.978575\pi$
$61$		−	1.05058i		−	0.134513i	0.997736	−	0.0672563i	$-0.0214245\pi$
$62$	−5.91403			−0.751083
$63$	−2.74044	+	7.44916i	−0.345263	+	0.938506i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−1.53032	−	1.95198i	−0.188370	−	0.240272i
$67$	−9.82660			−1.20051			−0.600255	−	0.799808i	$-0.704934\pi$
$67$	−9.82660			−1.20051			−0.600255	+	0.799808i	$0.704934\pi$
$68$	−2.59897			−0.315171
$69$	−3.85291	+	3.02062i	−0.463835	+	0.363640i
$70$		0			0
$71$			13.2586i			1.57351i	0.617265	+	0.786755i	$0.288240\pi$
$71$			13.2586i			1.57351i	−0.617265	+	0.786755i	$0.711760\pi$
$72$	−2.91330	−	0.716015i	−0.343336	−	0.0843831i
$73$		−	7.58963i		−	0.888299i	−0.895953	−	0.444150i	$-0.853506\pi$
$73$		−	7.58963i		−	0.888299i	0.895953	−	0.444150i	$-0.146494\pi$
$74$		−	2.39457i		−	0.278363i
$75$		0			0
$76$			2.72617i			0.312714i
$77$	−0.421657	+	3.76526i	−0.0480522	+	0.429091i
$78$	5.06134	+	6.45592i	0.573084	+	0.730989i
$79$	16.5173			1.85834			0.929169	−	0.369656i	$-0.120525\pi$
$79$	16.5173			1.85834			0.929169	+	0.369656i	$0.120525\pi$
$80$		0			0
$81$	−7.97465	−	4.17193i	−0.886072	−	0.463548i
$82$			11.1481i			1.23110i
$83$	−12.9148			−1.41758			−0.708790	−	0.705419i	$-0.750759\pi$
$83$	−12.9148			−1.41758			−0.708790	+	0.705419i	$0.750759\pi$
$84$	2.40844	+	3.89865i	0.262782	+	0.425377i
$85$		0			0
$86$			0.432029i			0.0465869i
$87$	−3.85291	+	3.02062i	−0.413075	+	0.323845i
$88$	−1.43203			−0.152655
$89$	−3.90396			−0.413819			−0.206910	−	0.978360i	$-0.566341\pi$
$89$	−3.90396			−0.413819			−0.206910	+	0.978360i	$0.566341\pi$
$90$		0			0
$91$	1.39457	−	12.4531i	0.146191	−	1.30544i
$92$			2.82660i			0.294694i
$93$	−8.06134	+	6.31998i	−0.835923	+	0.655351i
$94$		−	10.3158i		−	1.06399i
$95$		0			0
$96$	−1.36309	+	1.06864i	−0.139120	+	0.109068i
$97$		−	14.0015i		−	1.42163i	−0.703377	−	0.710817i	$-0.748325\pi$
$97$		−	14.0015i		−	1.42163i	0.703377	−	0.710817i	$-0.251675\pi$
$98$	1.54839	−	6.82660i	0.156411	−	0.689591i
$99$	−4.17193	−	1.02535i	−0.419295	−	0.103052i
$100$		0			0
$101$	10.3158			1.02646			0.513231	−	0.858251i	$-0.328449\pi$
$101$	10.3158			1.02646			0.513231	+	0.858251i	$0.328449\pi$
$102$	−3.54262	+	2.77736i	−0.350771	+	0.275000i
$103$			13.8743i			1.36707i	0.729917	+	0.683536i	$0.239559\pi$
$103$			13.8743i			1.36707i	−0.729917	+	0.683536i	$0.760441\pi$
$104$	4.73625			0.464427
$105$		0			0
$106$	−5.69066			−0.552726
$107$		−	15.9493i		−	1.54188i	−0.636910	−	0.770938i	$-0.719788\pi$
$107$		−	15.9493i		−	1.54188i	0.636910	−	0.770938i	$-0.280212\pi$
$108$	−4.73625	+	2.13728i	−0.455746	+	0.205660i
$109$	−10.7891			−1.03341			−0.516706	−	0.856163i	$-0.672842\pi$
$109$	−10.7891			−1.03341			−0.516706	+	0.856163i	$0.672842\pi$
$110$		0			0
$111$	−2.55894	−	3.26401i	−0.242884	−	0.309806i
$112$	2.62932	+	0.294447i	0.248447	+	0.0278226i
$113$		−	14.3439i		−	1.34936i	−0.738112	−	0.674679i	$-0.764282\pi$
$113$		−	14.3439i		−	1.34936i	0.738112	−	0.674679i	$-0.235718\pi$
$114$	2.91330	+	3.71601i	0.272856	+	0.348037i
$115$		0			0
$116$			2.82660i			0.262443i
$117$	13.7981	+	3.39122i	1.27564	+	0.313519i
$118$			10.7775i			0.992148i
$119$	6.83350	+	0.765257i	0.626426	+	0.0701510i
$120$		0			0
$121$	8.94929			0.813572
$122$	−1.05058			−0.0951148
$123$	11.9133	+	15.1958i	1.07419	+	1.37016i
$124$			5.91403i			0.531096i
$125$		0			0
$126$	7.44916	+	2.74044i	0.663624	+	0.244138i
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$			1.00000i			0.0883883i
$129$	0.461684	+	0.588894i	0.0406490	+	0.0518492i
$130$		0			0
$131$	17.2804			1.50980			0.754899	−	0.655842i	$-0.227686\pi$
$131$	17.2804			1.50980			0.754899	+	0.655842i	$0.227686\pi$
$132$	−1.95198	+	1.53032i	−0.169898	+	0.133198i
$133$	0.802714	−	7.16797i	0.0696041	−	0.621542i
$134$			9.82660i			0.848889i
$135$		0			0
$136$			2.59897i			0.222859i
$137$			3.03746i			0.259507i	0.991546	+	0.129754i	$0.0414187\pi$
$137$			3.03746i			0.259507i	−0.991546	+	0.129754i	$0.958581\pi$
$138$	3.02062	+	3.85291i	0.257132	+	0.327981i
$139$			20.7478i			1.75980i	0.475155	+	0.879902i	$0.342392\pi$
$139$			20.7478i			1.75980i	−0.475155	+	0.879902i	$0.657608\pi$
$140$		0			0
$141$	−11.0239	−	14.0613i	−0.928379	−	1.18418i
$142$	13.2586			1.11264
$143$	6.78244			0.567176
$144$	−0.716015	+	2.91330i	−0.0596679	+	0.242775i
$145$		0			0
$146$	−7.58963			−0.628122
$147$	−5.18460	−	10.9599i	−0.427618	−	0.903959i
$148$	−2.39457			−0.196833
$149$		−	18.9493i		−	1.55239i	−0.630495	−	0.776193i	$-0.717148\pi$
$149$		−	18.9493i		−	1.55239i	0.630495	−	0.776193i	$-0.282852\pi$
$150$		0			0
$151$	5.25863			0.427941			0.213971	−	0.976840i	$-0.431360\pi$
$151$	5.25863			0.427941			0.213971	+	0.976840i	$0.431360\pi$
$152$	2.72617			0.221122
$153$	−1.86090	+	7.57157i	−0.150445	+	0.612125i
$154$	3.76526	+	0.421657i	0.303413	+	0.0339781i
$155$		0			0
$156$	6.45592	−	5.06134i	0.516887	−	0.405232i
$157$			6.29566i			0.502449i	0.967929	+	0.251224i	$0.0808332\pi$
$157$			6.29566i			0.502449i	−0.967929	+	0.251224i	$0.919167\pi$
$158$		−	16.5173i		−	1.31404i
$159$	−7.75687	+	6.08127i	−0.615160	+	0.482276i
$160$		0			0
$161$	0.832284	−	7.43203i	0.0655932	−	0.585726i
$162$	−4.17193	+	7.97465i	−0.327778	+	0.626547i
$163$	0.605427			0.0474207			0.0237104	−	0.999719i	$-0.492452\pi$
$163$	0.605427			0.0474207			0.0237104	+	0.999719i	$0.492452\pi$
$164$	11.1481			0.870520
$165$		0			0
$166$			12.9148i			1.00238i
$167$	−12.0825			−0.934971			−0.467485	−	0.884001i	$-0.654840\pi$
$167$	−12.0825			−0.934971			−0.467485	+	0.884001i	$0.654840\pi$
$168$	3.89865	−	2.40844i	0.300787	−	0.185815i
$169$	−9.43203			−0.725541
$170$		0			0
$171$	7.94217	+	1.95198i	0.607353	+	0.149272i
$172$	0.432029			0.0329419
$173$	15.5137			1.17949			0.589744	−	0.807590i	$-0.299229\pi$
$173$	15.5137			1.17949			0.589744	+	0.807590i	$0.299229\pi$
$174$	3.02062	+	3.85291i	0.228993	+	0.292088i
$175$		0			0
$176$			1.43203i			0.107943i
$177$	11.5173	+	14.6907i	0.865690	+	1.10422i
$178$			3.90396i			0.292614i
$179$		−	4.56797i		−	0.341426i	−0.985321	−	0.170713i	$-0.945393\pi$
$179$		−	4.56797i		−	0.341426i	0.985321	−	0.170713i	$-0.0546071\pi$
$180$		0			0
$181$			7.80792i			0.580358i	0.956972	+	0.290179i	$0.0937149\pi$
$181$			7.80792i			0.580358i	−0.956972	+	0.290179i	$0.906285\pi$
$182$	−12.4531	−	1.39457i	−0.923084	−	0.103373i
$183$	−1.43203	+	1.12269i	−0.105859	+	0.0829916i
$184$	2.82660			0.208380
$185$		0			0
$186$	6.31998	+	8.06134i	0.463403	+	0.591086i
$187$			3.72179i			0.272165i
$188$	−10.3158			−0.752357
$189$	13.0824	−	4.22501i	0.951605	−	0.307325i
$190$		0			0
$191$			7.22117i			0.522506i	0.965270	+	0.261253i	$0.0841357\pi$
$191$			7.22117i			0.522506i	−0.965270	+	0.261253i	$0.915864\pi$
$192$	1.06864	+	1.36309i	0.0771225	+	0.0983724i
$193$	7.60250			0.547240			0.273620	−	0.961838i	$-0.411779\pi$
$193$	7.60250			0.547240			0.273620	+	0.961838i	$0.411779\pi$
$194$	−14.0015			−1.00525
$195$		0			0
$196$	−6.82660	−	1.54839i	−0.487614	−	0.110599i
$197$		−	21.7384i		−	1.54880i	−0.632697	−	0.774400i	$-0.718052\pi$
$197$		−	21.7384i		−	1.54880i	0.632697	−	0.774400i	$-0.281948\pi$
$198$	−1.02535	+	4.17193i	−0.0728687	+	0.296486i
$199$			6.04124i			0.428252i	0.976806	+	0.214126i	$0.0686904\pi$
$199$			6.04124i			0.428252i	−0.976806	+	0.214126i	$0.931310\pi$
$200$		0			0
$201$	10.5011	+	13.3945i	0.740691	+	0.944776i
$202$		−	10.3158i		−	0.725818i
$203$	0.832284	−	7.43203i	0.0584149	−	0.521626i
$204$	2.77736	+	3.54262i	0.194454	+	0.248033i
$205$		0			0
$206$	13.8743			0.966666
$207$	8.23474	+	2.02389i	0.572354	+	0.140670i
$208$		−	4.73625i		−	0.328400i
$209$	3.90396			0.270043
$210$		0			0
$211$	16.7759			1.15490			0.577450	−	0.816426i	$-0.304048\pi$
$211$	16.7759			1.15490			0.577450	+	0.816426i	$0.304048\pi$
$212$			5.69066i			0.390836i
$213$	18.0727	−	14.1687i	1.23832	−	0.970824i
$214$	−15.9493			−1.09027
$215$		0			0
$216$	2.13728	+	4.73625i	0.145424	+	0.322261i
$217$	1.74137	−	15.5499i	0.118212	−	1.05559i
$218$			10.7891i			0.730733i
$219$	−10.3453	+	8.11059i	−0.699073	+	0.548063i
$220$		0			0
$221$		−	12.3093i		−	0.828016i
$222$	−3.26401	+	2.55894i	−0.219066	+	0.171745i
$223$			11.1120i			0.744112i	0.928210	+	0.372056i	$0.121347\pi$
$223$			11.1120i			0.744112i	−0.928210	+	0.372056i	$0.878653\pi$
$224$	0.294447	−	2.62932i	0.0196736	−	0.175679i
$225$		0			0
$226$	−14.3439			−0.954140
$227$	−7.24413			−0.480810			−0.240405	−	0.970673i	$-0.577280\pi$
$227$	−7.24413			−0.480810			−0.240405	+	0.970673i	$0.577280\pi$
$228$	3.71601	−	2.91330i	0.246099	−	0.192938i
$229$		−	27.1596i		−	1.79476i	−0.441259	−	0.897380i	$-0.645468\pi$
$229$		−	27.1596i		−	1.79476i	0.441259	−	0.897380i	$-0.354532\pi$
$230$		0			0
$231$	5.58297	−	3.44895i	0.367333	−	0.226924i
$232$	2.82660			0.185576
$233$		−	5.38132i		−	0.352542i	−0.984342	−	0.176271i	$-0.943596\pi$
$233$		−	5.38132i		−	0.352542i	0.984342	−	0.176271i	$-0.0564035\pi$
$234$	3.39122	−	13.7981i	0.221691	−	0.902011i
$235$		0			0
$236$	10.7775			0.701555
$237$	−17.6510	−	22.5145i	−1.14656	−	1.46247i
$238$	0.765257	−	6.83350i	0.0496043	−	0.442950i
$239$		−	2.51726i		−	0.162828i	−0.996680	−	0.0814141i	$-0.974056\pi$
$239$		−	2.51726i		−	0.162828i	0.996680	−	0.0814141i	$-0.0259436\pi$
$240$		0			0
$241$			16.8077i			1.08268i	0.840804	+	0.541340i	$0.182083\pi$
$241$			16.8077i			1.08268i	−0.840804	+	0.541340i	$0.817917\pi$
$242$		−	8.94929i		−	0.575282i
$243$	2.83532	+	15.3284i	0.181886	+	0.983320i
$244$			1.05058i			0.0672563i
$245$		0			0
$246$	15.1958	−	11.9133i	0.968850	−	0.759564i
$247$	−12.9118			−0.821560
$248$	5.91403			0.375542
$249$	13.8012	+	17.6040i	0.874619	+	1.11561i
$250$		0			0
$251$	1.75565			0.110816			0.0554079	−	0.998464i	$-0.482354\pi$
$251$	1.75565			0.110816			0.0554079	+	0.998464i	$0.482354\pi$
$252$	2.74044	−	7.44916i	0.172632	−	0.469253i
$253$	4.04778			0.254482
$254$		−	2.00000i		−	0.125491i
$255$		0			0
$256$	1.00000			0.0625000
$257$	21.9366			1.36837			0.684184	−	0.729309i	$-0.260159\pi$
$257$	21.9366			1.36837			0.684184	+	0.729309i	$0.260159\pi$
$258$	0.588894	−	0.461684i	0.0366629	−	0.0287432i
$259$	6.29609	+	0.705074i	0.391220	+	0.0438112i
$260$		0			0
$261$	8.23474	+	2.02389i	0.509718	+	0.125276i
$262$		−	17.2804i		−	1.06759i
$263$			4.08523i			0.251906i	0.992036	+	0.125953i	$0.0401989\pi$
$263$			4.08523i			0.251906i	−0.992036	+	0.125953i	$0.959801\pi$
$264$	1.53032	+	1.95198i	0.0941850	+	0.120136i
$265$		0			0
$266$	−7.16797	−	0.802714i	−0.439497	−	0.0492175i
$267$	4.17193	+	5.32144i	0.255318	+	0.325667i
$268$	9.82660			0.600255
$269$	6.96461			0.424640			0.212320	−	0.977200i	$-0.431898\pi$
$269$	6.96461			0.424640			0.212320	+	0.977200i	$0.431898\pi$
$270$		0			0
$271$			23.4740i			1.42594i	0.701194	+	0.712971i	$0.252651\pi$
$271$			23.4740i			1.42594i	−0.701194	+	0.712971i	$0.747349\pi$
$272$	2.59897			0.157585
$273$	−18.4649	+	11.4069i	−1.11755	+	0.690380i
$274$	3.03746			0.183499
$275$		0			0
$276$	3.85291	−	3.02062i	0.231918	−	0.181820i
$277$	−14.1227			−0.848550			−0.424275	−	0.905533i	$-0.639471\pi$
$277$	−14.1227			−0.848550			−0.424275	+	0.905533i	$0.639471\pi$
$278$	20.7478			1.24437
$279$	17.2294	+	4.23453i	1.03149	+	0.253515i
$280$		0			0
$281$			23.6532i			1.41103i	0.708694	+	0.705516i	$0.249285\pi$
$281$			23.6532i			1.41103i	−0.708694	+	0.705516i	$0.750715\pi$
$282$	−14.0613	+	11.0239i	−0.837341	+	0.656463i
$283$		−	0.807187i		−	0.0479823i	−0.999712	−	0.0239912i	$-0.992363\pi$
$283$		−	0.807187i		−	0.0479823i	0.999712	−	0.0239912i	$-0.00763735\pi$
$284$		−	13.2586i		−	0.786755i
$285$		0			0
$286$		−	6.78244i		−	0.401054i
$287$	−29.3118	−	3.28252i	−1.73022	−	0.193761i
$288$	2.91330	+	0.716015i	0.171668	+	0.0421916i
$289$	−10.2454			−0.602669
$290$		0			0
$291$	−19.0852	+	14.9625i	−1.11880	+	0.877120i
$292$			7.58963i			0.444150i
$293$	14.6704			0.857055			0.428528	−	0.903529i	$-0.359032\pi$
$293$	14.6704			0.857055			0.428528	+	0.903529i	$0.359032\pi$
$294$	−10.9599	+	5.18460i	−0.639196	+	0.302372i
$295$		0			0
$296$			2.39457i			0.139182i
$297$	3.06065	+	6.78244i	0.177597	+	0.393557i
$298$	−18.9493			−1.09770
$299$	−13.3875			−0.774218
$300$		0			0
$301$	−1.13594	−	0.127210i	−0.0654746	−	0.00733224i
$302$		−	5.25863i		−	0.302600i
$303$	−11.0239	−	14.0613i	−0.633306	−	0.807803i
$304$		−	2.72617i		−	0.156357i
$305$		0			0
$306$	7.57157	+	1.86090i	0.432838	+	0.106380i
$307$		−	10.0975i		−	0.576295i	−0.957586	−	0.288148i	$-0.906961\pi$
$307$		−	10.0975i		−	0.576295i	0.957586	−	0.288148i	$-0.0930394\pi$
$308$	0.421657	−	3.76526i	0.0240261	−	0.214545i
$309$	18.9118	−	14.8266i	1.07586	−	0.843456i
$310$		0			0
$311$	−4.27456			−0.242388			−0.121194	−	0.992629i	$-0.538672\pi$
$311$	−4.27456			−0.242388			−0.121194	+	0.992629i	$0.538672\pi$
$312$	−5.06134	−	6.45592i	−0.286542	−	0.365494i
$313$		−	0.923368i		−	0.0521918i	−0.999659	−	0.0260959i	$-0.991692\pi$
$313$		−	0.923368i		−	0.0521918i	0.999659	−	0.0260959i	$-0.00830753\pi$
$314$	6.29566			0.355285
$315$		0			0
$316$	−16.5173			−0.929169
$317$			15.7384i			0.883959i	0.897025	+	0.441979i	$0.145724\pi$
$317$			15.7384i			0.883959i	−0.897025	+	0.441979i	$0.854276\pi$
$318$	6.08127	+	7.75687i	0.341021	+	0.434984i
$319$	4.04778			0.226632
$320$		0			0
$321$	−21.7403	+	17.0441i	−1.21342	+	0.951307i
$322$	−7.43203	−	0.832284i	−0.414171	−	0.0463814i
$323$		−	7.08523i		−	0.394233i
$324$	7.97465	+	4.17193i	0.443036	+	0.231774i
$325$		0			0
$326$		−	0.605427i		−	0.0335315i
$327$	11.5297	+	14.7065i	0.637595	+	0.813274i
$328$		−	11.1481i		−	0.615550i
$329$	27.1235	+	3.03746i	1.49537	+	0.167460i
$330$		0			0
$331$	−12.6054			−0.692857			−0.346428	−	0.938076i	$-0.612606\pi$
$331$	−12.6054			−0.692857			−0.346428	+	0.938076i	$0.612606\pi$
$332$	12.9148			0.708790
$333$	−1.71455	+	6.97611i	−0.0939567	+	0.382289i
$334$			12.0825i			0.661124i
$335$		0			0
$336$	−2.40844	−	3.89865i	−0.131391	−	0.212689i
$337$	−18.8986			−1.02947			−0.514736	−	0.857349i	$-0.672110\pi$
$337$	−18.8986			−1.02947			−0.514736	+	0.857349i	$0.672110\pi$
$338$			9.43203i			0.513035i
$339$	−19.5519	+	15.3284i	−1.06192	+	0.832526i
$340$		0			0
$341$	8.46907			0.458626
$342$	1.95198	−	7.94217i	0.105551	−	0.429463i
$343$	17.4934	+	6.08127i	0.944553	+	0.328358i
$344$		−	0.432029i		−	0.0232935i
$345$		0			0
$346$		−	15.5137i		−	0.834024i
$347$			30.7384i			1.65013i	0.565041	+	0.825063i	$0.308860\pi$
$347$			30.7384i			1.65013i	−0.565041	+	0.825063i	$0.691140\pi$
$348$	3.85291	−	3.02062i	0.206537	−	0.161922i
$349$			0.970523i			0.0519509i	0.999663	+	0.0259754i	$0.00826917\pi$
$349$			0.970523i			0.0519509i	−0.999663	+	0.0259754i	$0.991731\pi$
$350$		0			0
$351$	−10.1227	−	22.4320i	−0.540309	−	1.19733i
$352$	1.43203			0.0763274
$353$	16.3570			0.870598			0.435299	−	0.900286i	$-0.356643\pi$
$353$	16.3570			0.870598			0.435299	+	0.900286i	$0.356643\pi$
$354$	14.6907	−	11.5173i	0.780800	−	0.612136i
$355$		0			0
$356$	3.90396			0.206910
$357$	−6.25944	−	10.1324i	−0.331285	−	0.536266i
$358$	−4.56797			−0.241425
$359$			9.81335i			0.517929i	0.965887	+	0.258964i	$0.0833812\pi$
$359$			9.81335i			0.517929i	−0.965887	+	0.258964i	$0.916619\pi$
$360$		0			0
$361$	11.5680			0.608841
$362$	7.80792			0.410375
$363$	−9.56358	−	12.1987i	−0.501958	−	0.640264i
$364$	−1.39457	+	12.4531i	−0.0730955	+	0.652719i
$365$		0			0
$366$	1.12269	+	1.43203i	0.0586839	+	0.0748534i
$367$			33.9970i			1.77463i	0.461163	+	0.887315i	$0.347432\pi$
$367$			33.9970i			1.77463i	−0.461163	+	0.887315i	$0.652568\pi$
$368$		−	2.82660i		−	0.147347i
$369$	7.98220	−	32.4777i	0.415537	−	1.69072i
$370$		0			0
$371$	1.67560	−	14.9625i	0.0869927	−	0.776817i
$372$	8.06134	−	6.31998i	0.417961	−	0.327676i
$373$	26.5650			1.37549			0.687743	−	0.725954i	$-0.258602\pi$
$373$	26.5650			1.37549			0.687743	+	0.725954i	$0.258602\pi$
$374$	3.72179			0.192449
$375$		0			0
$376$			10.3158i			0.531997i
$377$	−13.3875			−0.689490
$378$	−4.22501	−	13.0824i	−0.217311	−	0.672886i
$379$	8.25863			0.424217			0.212109	−	0.977246i	$-0.431967\pi$
$379$	8.25863			0.424217			0.212109	+	0.977246i	$0.431967\pi$
$380$		0			0
$381$	−2.13728	−	2.72617i	−0.109496	−	0.139666i
$382$	7.22117			0.369467
$383$	−32.6920			−1.67049			−0.835243	−	0.549882i	$-0.814673\pi$
$383$	−32.6920			−1.67049			−0.835243	+	0.549882i	$0.814673\pi$
$384$	1.36309	−	1.06864i	0.0695598	−	0.0545338i
$385$		0			0
$386$		−	7.60250i		−	0.386957i
$387$	0.309339	−	1.25863i	0.0157246	−	0.0639798i
$388$			14.0015i			0.710817i
$389$		−	1.33354i		−	0.0676134i	−0.999428	−	0.0338067i	$-0.989237\pi$
$389$		−	1.33354i		−	0.0676134i	0.999428	−	0.0338067i	$-0.0107631\pi$
$390$		0			0
$391$		−	7.34624i		−	0.371515i
$392$	−1.54839	+	6.82660i	−0.0782054	+	0.344795i
$393$	−18.4666	−	23.5547i	−0.931514	−	1.18818i
$394$	−21.7384			−1.09517
$395$		0			0
$396$	4.17193	+	1.02535i	0.209647	+	0.0515260i
$397$			23.0123i			1.15495i	0.816407	+	0.577477i	$0.195963\pi$
$397$			23.0123i			1.15495i	−0.816407	+	0.577477i	$0.804037\pi$
$398$	6.04124			0.302820
$399$	−10.6284	+	6.56582i	−0.532085	+	0.328702i
$400$		0			0
$401$			17.5547i			0.876641i	0.898819	+	0.438320i	$0.144426\pi$
$401$			17.5547i			0.876641i	−0.898819	+	0.438320i	$0.855574\pi$
$402$	13.3945	−	10.5011i	0.668058	−	0.523748i
$403$	−28.0103			−1.39529
$404$	−10.3158			−0.513231
$405$		0			0
$406$	−7.43203	−	0.832284i	−0.368845	−	0.0413056i
$407$			3.42910i			0.169974i
$408$	3.54262	−	2.77736i	0.175386	−	0.137500i
$409$			9.94521i			0.491759i	0.969300	+	0.245879i	$0.0790767\pi$
$409$			9.94521i			0.491759i	−0.969300	+	0.245879i	$0.920923\pi$
$410$		0			0
$411$	4.14032	−	3.24595i	0.204227	−	0.160111i
$412$		−	13.8743i		−	0.683536i
$413$	−28.3374	−	3.17340i	−1.39439	−	0.156153i
$414$	2.02389	−	8.23474i	0.0994687	−	0.404716i
$415$		0			0
$416$	−4.73625			−0.232214
$417$	28.2811	−	22.1719i	1.38493	−	1.08576i
$418$		−	3.90396i		−	0.190949i
$419$	7.71684			0.376992			0.188496	−	0.982074i	$-0.439639\pi$
$419$	7.71684			0.376992			0.188496	+	0.982074i	$0.439639\pi$
$420$		0			0
$421$	11.2109			0.546384			0.273192	−	0.961960i	$-0.411921\pi$
$421$	11.2109			0.546384			0.273192	+	0.961960i	$0.411921\pi$
$422$		−	16.7759i		−	0.816638i
$423$	−7.38627	+	30.0530i	−0.359133	+	1.46123i
$424$	5.69066			0.276363
$425$		0			0
$426$	−14.1687	−	18.0727i	−0.686476	−	0.875624i
$427$	0.309339	−	2.76230i	0.0149700	−	0.133677i
$428$			15.9493i			0.770938i
$429$	−7.24799	−	9.24506i	−0.349936	−	0.446356i
$430$		0			0
$431$		−	26.2079i		−	1.26239i	−0.775624	−	0.631196i	$-0.782565\pi$
$431$		−	26.2079i		−	1.26239i	0.775624	−	0.631196i	$-0.217435\pi$
$432$	4.73625	−	2.13728i	0.227873	−	0.102830i
$433$		−	23.4378i		−	1.12635i	−0.826337	−	0.563175i	$-0.809580\pi$
$433$		−	23.4378i		−	1.12635i	0.826337	−	0.563175i	$-0.190420\pi$
$434$	−15.5499	−	1.74137i	−0.746417	−	0.0835884i
$435$		0			0
$436$	10.7891			0.516706
$437$	−7.70581			−0.368619
$438$	8.11059	+	10.3453i	0.387539	+	0.494319i
$439$		−	25.0334i		−	1.19478i	−0.801952	−	0.597389i	$-0.796205\pi$
$439$		−	25.0334i		−	1.19478i	0.801952	−	0.597389i	$-0.203795\pi$
$440$		0			0
$441$	−9.39887	+	18.7793i	−0.447565	+	0.894251i
$442$	−12.3093			−0.585496
$443$			18.4666i			0.877373i	0.898640	+	0.438686i	$0.144556\pi$
$443$			18.4666i			0.877373i	−0.898640	+	0.438686i	$0.855444\pi$
$444$	2.55894	+	3.26401i	0.121442	+	0.154903i
$445$		0			0
$446$	11.1120			0.526167
$447$	−25.8295	+	20.2500i	−1.22170	+	0.957791i
$448$	−2.62932	−	0.294447i	−0.124223	−	0.0139113i
$449$			32.3439i			1.52640i	0.646162	+	0.763201i	$0.276373\pi$
$449$			32.3439i			1.52640i	−0.646162	+	0.763201i	$0.723627\pi$
$450$		0			0
$451$		−	15.9644i		−	0.751734i
$452$			14.3439i			0.674679i
$453$	−5.61959	−	7.16797i	−0.264031	−	0.336781i
$454$			7.24413i			0.339984i
$455$		0			0
$456$	−2.91330	−	3.71601i	−0.136428	−	0.174018i
$457$	−10.9251			−0.511054			−0.255527	−	0.966802i	$-0.582249\pi$
$457$	−10.9251			−0.511054			−0.255527	+	0.966802i	$0.582249\pi$
$458$	−27.1596			−1.26909
$459$	12.3093	−	5.55472i	0.574551	−	0.259272i
$460$		0			0
$461$	−26.6729			−1.24228			−0.621139	−	0.783700i	$-0.713330\pi$
$461$	−26.6729			−1.24228			−0.621139	+	0.783700i	$0.713330\pi$
$462$	−3.44895	−	5.58297i	−0.160460	−	0.259743i
$463$	8.07491			0.375273			0.187637	−	0.982239i	$-0.439917\pi$
$463$	8.07491			0.375273			0.187637	+	0.982239i	$0.439917\pi$
$464$		−	2.82660i		−	0.131222i
$465$		0			0
$466$	−5.38132			−0.249285
$467$	41.6228			1.92607			0.963037	−	0.269371i	$-0.0868156\pi$
$467$	41.6228			1.92607			0.963037	+	0.269371i	$0.0868156\pi$
$468$	−13.7981	−	3.39122i	−0.637818	−	0.156759i
$469$	−25.8372	−	2.89341i	−1.19305	−	0.133605i
$470$		0			0
$471$	8.58154	−	6.72780i	0.395416	−	0.310001i
$472$		−	10.7775i		−	0.496074i
$473$		−	0.618679i		−	0.0284469i
$474$	−22.5145	+	17.6510i	−1.03412	+	0.810738i
$475$		0			0
$476$	−6.83350	−	0.765257i	−0.313213	−	0.0350755i
$477$	16.5786	+	4.07460i	0.759082	+	0.186563i
$478$	−2.51726			−0.115137
$479$	−21.3728			−0.976549			−0.488274	−	0.872690i	$-0.662373\pi$
$479$	−21.3728			−0.976549			−0.488274	+	0.872690i	$0.662373\pi$
$480$		0			0
$481$		−	11.3413i		−	0.517118i
$482$	16.8077			0.765570
$483$	−11.0199	+	6.80769i	−0.501424	+	0.309761i
$484$	−8.94929			−0.406786
$485$		0			0
$486$	15.3284	−	2.83532i	0.695312	−	0.128613i
$487$	27.1094			1.22845			0.614223	−	0.789133i	$-0.289470\pi$
$487$	27.1094			1.22845			0.614223	+	0.789133i	$0.289470\pi$
$488$	1.05058			0.0475574
$489$	−0.646984	−	0.825250i	−0.0292576	−	0.0373191i
$490$		0			0
$491$			30.0000i			1.35388i	0.736038	+	0.676941i	$0.236695\pi$
$491$			30.0000i			1.35388i	−0.736038	+	0.676941i	$0.763305\pi$
$492$	−11.9133	−	15.1958i	−0.537093	−	0.685081i
$493$		−	7.34624i		−	0.330858i
$494$			12.9118i			0.580931i
$495$		0			0
$496$		−	5.91403i		−	0.265548i
$497$	−3.90396	+	34.8611i	−0.175117	+	1.56374i
$498$	17.6040	−	13.8012i	0.788852	−	0.618449i
$499$	8.50694			0.380823			0.190412	−	0.981704i	$-0.439018\pi$
$499$	8.50694			0.380823			0.190412	+	0.981704i	$0.439018\pi$
$500$		0			0
$501$	12.9118	+	16.4695i	0.576858	+	0.735802i
$502$		−	1.75565i		−	0.0783586i
$503$	−12.1625			−0.542301			−0.271150	−	0.962537i	$-0.587404\pi$
$503$	−12.1625			−0.542301			−0.271150	+	0.962537i	$0.587404\pi$
$504$	−7.44916	−	2.74044i	−0.331812	−	0.122069i
$505$		0			0
$506$		−	4.04778i		−	0.179946i
$507$	10.0794	+	12.8567i	0.447644	+	0.570985i
$508$	−2.00000			−0.0887357
$509$	−6.12130			−0.271322			−0.135661	−	0.990755i	$-0.543316\pi$
$509$	−6.12130			−0.271322			−0.135661	+	0.990755i	$0.543316\pi$
$510$		0			0
$511$	2.23474	−	19.9555i	0.0988592	−	0.882781i
$512$		−	1.00000i		−	0.0441942i
$513$	−5.82660	−	12.9118i	−0.257251	−	0.570071i
$514$		−	21.9366i		−	0.967582i
$515$		0			0
$516$	−0.461684	−	0.588894i	−0.0203245	−	0.0259246i
$517$			14.7725i			0.649695i
$518$	0.705074	−	6.29609i	0.0309792	−	0.276634i
$519$	−16.5786	−	21.1466i	−0.727720	−	0.928232i
$520$		0			0
$521$	−32.7031			−1.43275			−0.716374	−	0.697717i	$-0.754199\pi$
$521$	−32.7031			−1.43275			−0.716374	+	0.697717i	$0.754199\pi$
$522$	2.02389	−	8.23474i	0.0885832	−	0.360425i
$523$			28.5557i			1.24865i	0.781163	+	0.624327i	$0.214627\pi$
$523$			28.5557i			1.24865i	−0.781163	+	0.624327i	$0.785373\pi$
$524$	−17.2804			−0.754899
$525$		0			0
$526$	4.08523			0.178125
$527$		−	15.3704i		−	0.669544i
$528$	1.95198	−	1.53032i	0.0849491	−	0.0665988i
$529$	15.0103			0.652623
$530$		0			0
$531$	7.71684	−	31.3981i	0.334882	−	1.36256i
$532$	−0.802714	+	7.16797i	−0.0348020	+	0.310771i
$533$			52.8001i			2.28703i
$534$	5.32144	−	4.17193i	0.230281	−	0.180537i
$535$		0			0
$536$		−	9.82660i		−	0.424445i
$537$	−6.22654	+	4.88152i	−0.268695	+	0.210653i
$538$		−	6.96461i		−	0.300266i
$539$	−2.21734	+	9.77589i	−0.0955074	+	0.421078i
$540$		0			0
$541$	−34.2932			−1.47438			−0.737189	−	0.675687i	$-0.763847\pi$
$541$	−34.2932			−1.47438			−0.737189	+	0.675687i	$0.763847\pi$
$542$	23.4740			1.00829
$543$	10.6429	−	8.34386i	0.456730	−	0.358070i
$544$		−	2.59897i		−	0.111430i
$545$		0			0
$546$	11.4069	+	18.4649i	0.488172	+	0.790227i
$547$	26.7759			1.14485			0.572427	−	0.819955i	$-0.306002\pi$
$547$	26.7759			1.14485			0.572427	+	0.819955i	$0.306002\pi$
$548$		−	3.03746i		−	0.129754i
$549$	3.06065	+	0.752229i	0.130625	+	0.0321044i
$550$		0			0
$551$	−7.70581			−0.328279
$552$	−3.02062	−	3.85291i	−0.128566	−	0.163991i
$553$	43.4291	+	4.86346i	1.84679	+	0.206815i
$554$			14.1227i			0.600016i
$555$		0			0
$556$		−	20.7478i		−	0.879902i
$557$		−	40.4158i		−	1.71247i	−0.516583	−	0.856237i	$-0.672796\pi$
$557$		−	40.4158i		−	1.71247i	0.516583	−	0.856237i	$-0.327204\pi$
$558$	4.23453	−	17.2294i	0.179262	−	0.729377i
$559$			2.04620i			0.0865449i
$560$		0			0
$561$	5.07313	−	3.97726i	0.214188	−	0.167920i
$562$	23.6532			0.997750
$563$	−8.16750			−0.344219			−0.172109	−	0.985078i	$-0.555058\pi$
$563$	−8.16750			−0.344219			−0.172109	+	0.985078i	$0.555058\pi$
$564$	11.0239	+	14.0613i	0.464189	+	0.592089i
$565$		0			0
$566$	−0.807187			−0.0339286
$567$	−19.7394	−	13.3174i	−0.828979	−	0.559280i
$568$	−13.2586			−0.556320
$569$			15.0375i			0.630403i	0.949025	+	0.315201i	$0.102072\pi$
$569$			15.0375i			0.630403i	−0.949025	+	0.315201i	$0.897928\pi$
$570$		0			0
$571$	38.6025			1.61546			0.807732	−	0.589550i	$-0.200695\pi$
$571$	38.6025			1.61546			0.807732	+	0.589550i	$0.200695\pi$
$572$	−6.78244			−0.283588
$573$	9.84309	−	7.71684i	0.411201	−	0.322376i
$574$	−3.28252	+	29.3118i	−0.137010	+	1.22345i
$575$		0			0
$576$	0.716015	−	2.91330i	0.0298339	−	0.121388i
$577$			23.9467i			0.996913i	0.866915	+	0.498457i	$0.166100\pi$
$577$			23.9467i			0.996913i	−0.866915	+	0.498457i	$0.833900\pi$
$578$			10.2454i			0.426152i
$579$	−8.12434	−	10.3629i	−0.337636	−	0.430666i
$580$		0			0
$581$	−33.9570	−	3.80271i	−1.40877	−	0.157763i
$582$	14.9625	+	19.0852i	0.620217	+	0.791108i
$583$	8.14919			0.337505
$584$	7.58963			0.314061
$585$		0			0
$586$		−	14.6704i		−	0.606030i
$587$	−17.9305			−0.740072			−0.370036	−	0.929017i	$-0.620655\pi$
$587$	−17.9305			−0.740072			−0.370036	+	0.929017i	$0.620655\pi$
$588$	5.18460	+	10.9599i	0.213809	+	0.451980i
$589$	−16.1227			−0.664324
$590$		0			0
$591$	−29.6314	+	23.2306i	−1.21887	+	0.955578i
$592$	2.39457			0.0984163
$593$	18.5744			0.762759			0.381379	−	0.924419i	$-0.375449\pi$
$593$	18.5744			0.762759			0.381379	+	0.924419i	$0.375449\pi$
$594$	6.78244	−	3.06065i	0.278287	−	0.125580i
$595$		0			0
$596$			18.9493i			0.776193i
$597$	8.23474	−	6.45592i	0.337026	−	0.264223i
$598$			13.3875i			0.547455i
$599$		−	29.3439i		−	1.19896i	−0.800391	−	0.599479i	$-0.795375\pi$
$599$		−	29.3439i		−	1.19896i	0.800391	−	0.599479i	$-0.204625\pi$
$600$		0			0
$601$		−	22.5145i		−	0.918385i	−0.888337	−	0.459192i	$-0.848139\pi$
$601$		−	22.5145i		−	0.918385i	0.888337	−	0.459192i	$-0.151861\pi$
$602$	−0.127210	+	1.13594i	−0.00518468	+	0.0462975i
$603$	7.03599	−	28.6279i	0.286528	−	1.16582i
$604$	−5.25863			−0.213971
$605$		0			0
$606$	−14.0613	+	11.0239i	−0.571203	+	0.447815i
$607$			17.5128i			0.710822i	0.934710	+	0.355411i	$0.115659\pi$
$607$			17.5128i			0.710822i	−0.934710	+	0.355411i	$0.884341\pi$
$608$	−2.72617			−0.110561
$609$	−11.0199	+	6.80769i	−0.446550	+	0.275862i
$610$		0			0
$611$		−	48.8582i		−	1.97659i
$612$	1.86090	−	7.57157i	0.0752223	−	0.306062i
$613$	−32.7626			−1.32327			−0.661635	−	0.749826i	$-0.730137\pi$
$613$	−32.7626			−1.32327			−0.661635	+	0.749826i	$0.730137\pi$
$614$	−10.0975			−0.407502
$615$		0			0
$616$	−3.76526	−	0.421657i	−0.151707	−	0.0169890i
$617$		−	0.693592i		−	0.0279229i	−0.999903	−	0.0139615i	$-0.995556\pi$
$617$		−	0.693592i		−	0.0279229i	0.999903	−	0.0139615i	$-0.00444422\pi$
$618$	−14.8266	−	18.9118i	−0.596413	−	0.760746i
$619$			18.5305i			0.744802i	0.928072	+	0.372401i	$0.121465\pi$
$619$			18.5305i			0.744802i	−0.928072	+	0.372401i	$0.878535\pi$
$620$		0			0
$621$	−6.04124	−	13.3875i	−0.242427	−	0.537221i
$622$			4.27456i			0.171394i
$623$	−10.2647	−	1.14951i	−0.411248	−	0.0460541i
$624$	−6.45592	+	5.06134i	−0.258444	+	0.202616i
$625$		0			0
$626$	−0.923368			−0.0369052
$627$	−4.17193	−	5.32144i	−0.166611	−	0.212518i
$628$		−	6.29566i		−	0.251224i
$629$	6.22341			0.248144
$630$		0			0
$631$	−8.39457			−0.334183			−0.167091	−	0.985941i	$-0.553437\pi$
$631$	−8.39457			−0.334183			−0.167091	+	0.985941i	$0.553437\pi$
$632$			16.5173i			0.657021i
$633$	−17.9274	−	22.8670i	−0.712550	−	0.908882i
$634$	15.7384			0.625053
$635$		0			0
$636$	7.75687	−	6.08127i	0.307580	−	0.241138i
$637$	7.33354	−	32.3325i	0.290566	−	1.28106i
$638$		−	4.04778i		−	0.160253i
$639$	−38.6264	−	9.49337i	−1.52804	−	0.375552i
$640$		0			0
$641$		−	23.6532i		−	0.934245i	−0.884193	−	0.467123i	$-0.845291\pi$
$641$		−	23.6532i		−	0.934245i	0.884193	−	0.467123i	$-0.154709\pi$
$642$	17.0441	+	21.7403i	0.672675	+	0.858020i
$643$		−	2.60999i		−	0.102928i	−0.998675	−	0.0514641i	$-0.983611\pi$
$643$		−	2.60999i		−	0.102928i	0.998675	−	0.0514641i	$-0.0163888\pi$
$644$	−0.832284	+	7.43203i	−0.0327966	+	0.292863i
$645$		0			0
$646$	−7.08523			−0.278765
$647$	−4.45673			−0.175212			−0.0876061	−	0.996155i	$-0.527922\pi$
$647$	−4.45673			−0.175212			−0.0876061	+	0.996155i	$0.527922\pi$
$648$	4.17193	−	7.97465i	0.163889	−	0.313274i
$649$		−	15.4337i		−	0.605825i
$650$		0			0
$651$	−23.0567	+	14.2436i	−0.903664	+	0.558250i
$652$	−0.605427			−0.0237104
$653$			30.9118i			1.20967i	0.796349	+	0.604837i	$0.206762\pi$
$653$			30.9118i			1.20967i	−0.796349	+	0.604837i	$0.793238\pi$
$654$	14.7065	−	11.5297i	0.575072	−	0.450848i
$655$		0			0
$656$	−11.1481			−0.435260
$657$	22.1109	+	5.43429i	0.862628	+	0.212012i
$658$	3.03746	−	27.1235i	0.118412	−	1.05738i
$659$		−	4.56797i		−	0.177943i	−0.996034	−	0.0889714i	$-0.971642\pi$
$659$		−	4.56797i		−	0.177943i	0.996034	−	0.0889714i	$-0.0283580\pi$
$660$		0			0
$661$			38.0643i			1.48053i	0.672315	+	0.740266i	$0.265300\pi$
$661$			38.0643i			1.48053i	−0.672315	+	0.740266i	$0.734700\pi$
$662$			12.6054i			0.489924i
$663$	−16.7787	+	13.1543i	−0.651631	+	0.510869i
$664$		−	12.9148i		−	0.501190i
$665$		0			0
$666$	6.97611	+	1.71455i	0.270319	+	0.0664374i
$667$	−7.98968			−0.309362
$668$	12.0825			0.467485
$669$	15.1466	−	11.8747i	0.585601	−	0.459102i
$670$		0			0
$671$	1.50446			0.0580790
$672$	−3.89865	+	2.40844i	−0.150393	+	0.0929075i
$673$	−21.2212			−0.818016			−0.409008	−	0.912531i	$-0.634125\pi$
$673$	−21.2212			−0.818016			−0.409008	+	0.912531i	$0.634125\pi$
$674$			18.8986i			0.727946i
$675$		0			0
$676$	9.43203			0.362770
$677$	3.53336			0.135798			0.0678991	−	0.997692i	$-0.478370\pi$
$677$	3.53336			0.135798			0.0678991	+	0.997692i	$0.478370\pi$
$678$	15.3284	+	19.5519i	0.588685	+	0.750888i
$679$	4.12269	−	36.8143i	0.158214	−	1.41280i
$680$		0			0
$681$	7.74137	+	9.87438i	0.296650	+	0.378387i
$682$		−	8.46907i		−	0.324297i
$683$		−	1.70391i		−	0.0651984i	−0.999469	−	0.0325992i	$-0.989622\pi$
$683$		−	1.70391i		−	0.0651984i	0.999469	−	0.0325992i	$-0.0103785\pi$
$684$	−7.94217	−	1.95198i	−0.303676	−	0.0746359i
$685$		0			0
$686$	6.08127	−	17.4934i	0.232184	−	0.667900i
$687$	−37.0210	+	29.0239i	−1.41244	+	1.10733i
$688$	−0.432029			−0.0164710
$689$	−26.9524			−1.02680
$690$		0			0
$691$		−	2.21734i		−	0.0843514i	−0.999110	−	0.0421757i	$-0.986571\pi$
$691$		−	2.21734i		−	0.0843514i	0.999110	−	0.0421757i	$-0.0134289\pi$
$692$	−15.5137			−0.589744
$693$	−10.6674	−	3.92439i	−0.405222	−	0.149075i
$694$	30.7384			1.16682
$695$		0			0
$696$	−3.02062	−	3.85291i	−0.114496	−	0.146044i
$697$	−28.9735			−1.09745
$698$	0.970523			0.0367348
$699$	−7.33521	+	5.75070i	−0.277443	+	0.217511i
$700$		0			0
$701$		−	3.11976i		−	0.117832i	−0.998263	−	0.0589158i	$-0.981236\pi$
$701$		−	3.11976i		−	0.117832i	0.998263	−	0.0589158i	$-0.0187644\pi$
$702$	−22.4320	+	10.1227i	−0.846642	+	0.382056i
$703$		−	6.52802i		−	0.246209i
$704$		−	1.43203i		−	0.0539716i
$705$		0			0
$706$		−	16.3570i		−	0.615606i
$707$	27.1235	+	3.03746i	1.02008	+	0.114235i
$708$	−11.5173	−	14.6907i	−0.432845	−	0.552109i
$709$	12.8641			0.483120			0.241560	−	0.970386i	$-0.422341\pi$
$709$	12.8641			0.483120			0.241560	+	0.970386i	$0.422341\pi$
$710$		0			0
$711$	−11.8266	+	48.1198i	−0.443532	+	1.80463i
$712$		−	3.90396i		−	0.146307i
$713$	−16.7166			−0.626042
$714$	−10.1324	+	6.25944i	−0.379197	+	0.234254i
$715$		0			0
$716$			4.56797i			0.170713i
$717$	−3.43125	+	2.69005i	−0.128142	+	0.100462i
$718$	9.81335			0.366231
$719$	28.5196			1.06360			0.531801	−	0.846870i	$-0.321516\pi$
$719$	28.5196			1.06360			0.531801	+	0.846870i	$0.321516\pi$
$720$		0			0
$721$	−4.08523	+	36.4798i	−0.152142	+	1.35858i
$722$		−	11.5680i		−	0.430515i
$723$	22.9104	−	17.9614i	0.852046	−	0.667991i
$724$		−	7.80792i		−	0.290179i
$725$		0			0
$726$	−12.1987	+	9.56358i	−0.452735	+	0.354938i
$727$			18.9921i			0.704379i	0.935929	+	0.352190i	$0.114563\pi$
$727$			18.9921i			0.704379i	−0.935929	+	0.352190i	$0.885437\pi$
$728$	12.4531	+	1.39457i	0.461542	+	0.0516863i
$729$	17.8641	−	20.2454i	0.661632	−	0.749829i
$730$		0			0
$731$	−1.12283			−0.0415293
$732$	1.43203	−	1.12269i	0.0529293	−	0.0414958i
$733$		−	27.1345i		−	1.00224i	−0.865379	−	0.501119i	$-0.832922\pi$
$733$		−	27.1345i		−	1.00224i	0.865379	−	0.501119i	$-0.167078\pi$
$734$	33.9970			1.25485
$735$		0			0
$736$	−2.82660			−0.104190
$737$		−	14.0720i		−	0.518348i
$738$	−32.4777	−	7.98220i	−1.19552	−	0.293829i
$739$	8.67741			0.319204			0.159602	−	0.987181i	$-0.448979\pi$
$739$	8.67741			0.319204			0.159602	+	0.987181i	$0.448979\pi$
$740$		0			0
$741$	13.7981	+	17.6000i	0.506886	+	0.646551i
$742$	−14.9625	−	1.67560i	−0.549292	−	0.0615131i
$743$			52.5754i			1.92880i	0.264443	+	0.964401i	$0.414812\pi$
$743$			52.5754i			1.92880i	−0.264443	+	0.964401i	$0.585188\pi$
$744$	−6.31998	−	8.06134i	−0.231702	−	0.295543i
$745$		0			0
$746$		−	26.5650i		−	0.972615i
$747$	9.24717	−	37.6246i	0.338336	−	1.37661i
$748$		−	3.72179i		−	0.136082i
$749$	4.69622	−	41.9357i	0.171596	−	1.53230i
$750$		0			0
$751$	1.77589			0.0648033			0.0324016	−	0.999475i	$-0.489684\pi$
$751$	1.77589			0.0648033			0.0324016	+	0.999475i	$0.489684\pi$
$752$	10.3158			0.376179
$753$	−1.87616	−	2.39311i	−0.0683711	−	0.0872097i
$754$			13.3875i			0.487543i
$755$		0			0
$756$	−13.0824	+	4.22501i	−0.475802	+	0.153662i
$757$	4.63995			0.168642			0.0843210	−	0.996439i	$-0.473128\pi$
$757$	4.63995			0.168642			0.0843210	+	0.996439i	$0.473128\pi$
$758$		−	8.25863i		−	0.299967i
$759$	−4.32562	−	5.51747i	−0.157010	−	0.200272i
$760$		0			0
$761$	40.6884			1.47495			0.737477	−	0.675373i	$-0.236017\pi$
$761$	40.6884			1.47495			0.737477	+	0.675373i	$0.236017\pi$
$762$	−2.72617	+	2.13728i	−0.0987589	+	0.0774255i
$763$	−28.3681	−	3.17683i	−1.02699	−	0.115009i
$764$		−	7.22117i		−	0.261253i
$765$		0			0
$766$			32.6920i			1.18121i
$767$			51.0448i			1.84312i
$768$	−1.06864	−	1.36309i	−0.0385612	−	0.0491862i
$769$		−	19.2355i		−	0.693651i	−0.937930	−	0.346825i	$-0.887260\pi$
$769$		−	19.2355i		−	0.693651i	0.937930	−	0.346825i	$-0.112740\pi$
$770$		0			0
$771$	−23.4423	−	29.9015i	−0.844256	−	1.07688i
$772$	−7.60250			−0.273620
$773$	28.4175			1.02211			0.511053	−	0.859549i	$-0.329256\pi$
$773$	28.4175			1.02211			0.511053	+	0.859549i	$0.329256\pi$
$774$	−1.25863	−	0.309339i	−0.0452406	−	0.0111190i
$775$		0			0
$776$	14.0015			0.502624
$777$	−5.76718	−	9.33559i	−0.206896	−	0.334912i
$778$	−1.33354			−0.0478099
$779$			30.3916i			1.08889i
$780$		0			0
$781$	−18.9867			−0.679399
$782$	−7.34624			−0.262701
$783$	−6.04124	−	13.3875i	−0.215896	−	0.478430i
$784$	6.82660	+	1.54839i	0.243807	+	0.0552996i
$785$		0			0
$786$	−23.5547	+	18.4666i	−0.840169	+	0.658680i
$787$		−	41.6778i		−	1.48565i	−0.669485	−	0.742826i	$-0.733485\pi$
$787$		−	41.6778i		−	1.48565i	0.669485	−	0.742826i	$-0.266515\pi$
$788$			21.7384i			0.774400i
$789$	5.56853	−	4.36565i	0.198245	−	0.155421i
$790$		0			0
$791$	4.22351	−	37.7145i	0.150171	−	1.34097i
$792$	1.02535	−	4.17193i	0.0364344	−	0.148243i
$793$	−4.97579			−0.176696
$794$	23.0123			0.816675
$795$		0			0
$796$		−	6.04124i		−	0.214126i
$797$	−10.2137			−0.361788			−0.180894	−	0.983503i	$-0.557899\pi$
$797$	−10.2137			−0.361788			−0.180894	+	0.983503i	$0.557899\pi$
$798$	6.56582	+	10.6284i	0.232427	+	0.376241i
$799$	26.8104			0.948484
$800$		0			0
$801$	2.79529	−	11.3734i	0.0987669	−	0.401860i
$802$	17.5547			0.619879
$803$	10.8686			0.383544
$804$	−10.5011	−	13.3945i	−0.370345	−	0.472388i
$805$		0			0
$806$			28.0103i			0.986621i
$807$	−7.44267	−	9.49337i	−0.261994	−	0.334183i
$808$			10.3158i			0.362909i
$809$			40.0691i			1.40875i	0.709827	+	0.704376i	$0.248773\pi$
$809$			40.0691i			1.40875i	−0.709827	+	0.704376i	$0.751227\pi$
$810$		0			0
$811$		−	34.8875i		−	1.22507i	−0.790445	−	0.612533i	$-0.790151\pi$
$811$		−	34.8875i		−	1.22507i	0.790445	−	0.612533i	$-0.209849\pi$
$812$	−0.832284	+	7.43203i	−0.0292074	+	0.260813i
$813$	31.9971	−	25.0852i	1.12219	−	0.879778i
$814$	3.42910			0.120190
$815$		0			0
$816$	−2.77736	−	3.54262i	−0.0972270	−	0.124016i
$817$			1.17779i			0.0412056i
$818$	9.94521			0.347726
$819$	35.2811	+	12.9794i	1.23282	+	0.453537i
$820$		0			0
$821$			33.4291i			1.16668i	0.812227	+	0.583342i	$0.198255\pi$
$821$			33.4291i			1.16668i	−0.812227	+	0.583342i	$0.801745\pi$
$822$	−3.24595	−	4.14032i	−0.113215	−	0.144410i
$823$	−20.7414			−0.722999			−0.361499	−	0.932372i	$-0.617735\pi$
$823$	−20.7414			−0.722999			−0.361499	+	0.932372i	$0.617735\pi$
$824$	−13.8743			−0.483333
$825$		0			0
$826$	−3.17340	+	28.3374i	−0.110417	+	0.985985i
$827$		−	41.8479i		−	1.45519i	−0.686005	−	0.727597i	$-0.740637\pi$
$827$		−	41.8479i		−	1.45519i	0.686005	−	0.727597i	$-0.259363\pi$
$828$	−8.23474	−	2.02389i	−0.286177	−	0.0703350i
$829$			19.7632i			0.686404i	0.939262	+	0.343202i	$0.111512\pi$
$829$			19.7632i			0.686404i	−0.939262	+	0.343202i	$0.888488\pi$
$830$		0			0
$831$	15.0921	+	19.2505i	0.523538	+	0.667791i
$832$			4.73625i			0.164200i
$833$	17.7421	+	4.02421i	0.614727	+	0.139430i
$834$	−22.1719	−	28.2811i	−0.767751	−	0.979293i
$835$		0			0
$836$	−3.90396			−0.135021
$837$	−12.6400	−	28.0103i	−0.436901	−	0.968178i
$838$		−	7.71684i		−	0.266574i
$839$	6.78244			0.234156			0.117078	−	0.993123i	$-0.462647\pi$
$839$	6.78244			0.234156			0.117078	+	0.993123i	$0.462647\pi$
$840$		0			0
$841$	21.0103			0.724494
$842$		−	11.2109i		−	0.386352i
$843$	32.2414	−	25.2768i	1.11045	−	0.870578i
$844$	−16.7759			−0.577450
$845$		0			0
$846$	30.0530	+	7.38627i	1.03325	+	0.253945i
$847$	23.5305	+	2.63509i	0.808518	+	0.0905428i
$848$		−	5.69066i		−	0.195418i
$849$	−1.10027	+	0.862593i	−0.0377611	+	0.0296041i
$850$		0			0
$851$		−	6.76850i		−	0.232021i
$852$	−18.0727	+	14.1687i	−0.619160	+	0.485412i
$853$			2.22837i			0.0762978i	0.999272	+	0.0381489i	$0.0121461\pi$
$853$			2.22837i			0.0762978i	−0.999272	+	0.0381489i	$0.987854\pi$
$854$	−2.76230	−	0.309339i	−0.0945240	−	0.0105854i
$855$		0			0
$856$	15.9493			0.545136
$857$	5.75070			0.196440			0.0982201	−	0.995165i	$-0.468685\pi$
$857$	5.75070			0.196440			0.0982201	+	0.995165i	$0.468685\pi$
$858$	−9.24506	+	7.24799i	−0.315621	+	0.247442i
$859$			46.1407i			1.57430i	0.616760	+	0.787151i	$0.288445\pi$
$859$			46.1407i			1.57430i	−0.616760	+	0.787151i	$0.711555\pi$
$860$		0			0
$861$	26.8495	+	43.4624i	0.915027	+	1.48120i
$862$	−26.2079			−0.892645
$863$		−	17.5783i		−	0.598372i	−0.954195	−	0.299186i	$-0.903285\pi$
$863$		−	17.5783i		−	0.598372i	0.954195	−	0.299186i	$-0.0967151\pi$
$864$	−2.13728	−	4.73625i	−0.0727118	−	0.161130i
$865$		0			0
$866$	−23.4378			−0.796450
$867$	10.9486	+	13.9653i	0.371835	+	0.474288i
$868$	−1.74137	+	15.5499i	−0.0591059	+	0.527797i
$869$			23.6532i			0.802380i
$870$		0			0
$871$			46.5412i			1.57699i
$872$		−	10.7891i		−	0.365367i
$873$	40.7905	+	10.0253i	1.38055	+	0.339304i
$874$			7.70581i			0.260653i
$875$		0			0
$876$	10.3453	−	8.11059i	0.349536	−	0.274031i
$877$	−41.8237			−1.41229			−0.706143	−	0.708070i	$-0.749566\pi$
$877$	−41.8237			−1.41229			−0.706143	+	0.708070i	$0.749566\pi$
$878$	−25.0334			−0.844836
$879$	−15.6774	−	19.9971i	−0.528786	−	0.674484i
$880$		0			0
$881$	27.8757			0.939158			0.469579	−	0.882891i	$-0.344406\pi$
$881$	27.8757			0.939158			0.469579	+	0.882891i	$0.344406\pi$
$882$	18.7793	+	9.39887i	0.632331	+	0.316476i
$883$	−11.6400			−0.391716			−0.195858	−	0.980632i	$-0.562749\pi$
$883$	−11.6400			−0.391716			−0.195858	+	0.980632i	$0.562749\pi$
$884$			12.3093i			0.414008i
$885$		0			0
$886$	18.4666			0.620396
$887$	−38.7333			−1.30054			−0.650268	−	0.759705i	$-0.725343\pi$
$887$	−38.7333			−1.30054			−0.650268	+	0.759705i	$0.725343\pi$
$888$	3.26401	−	2.55894i	0.109533	−	0.0858723i
$889$	5.25863	+	0.588894i	0.176369	+	0.0197509i
$890$		0			0
$891$	5.97433	−	11.4199i	0.200148	−	0.382582i
$892$		−	11.1120i		−	0.372056i
$893$		−	28.1227i		−	0.941090i
$894$	20.2500	+	25.8295i	0.677261	+	0.863869i
$895$		0			0
$896$	−0.294447	+	2.62932i	−0.00983678	+	0.0878393i
$897$	14.3064	+	18.2483i	0.477677	+	0.609293i
$898$	32.3439			1.07933
$899$	−16.7166			−0.557530
$900$		0			0
$901$		−	14.7898i		−	0.492721i
$902$	−15.9644			−0.531556
$903$	1.04052	+	1.68433i	0.0346262	+	0.0560510i
$904$	14.3439			0.477070
$905$		0			0
$906$	−7.16797	+	5.61959i	−0.238140	+	0.186698i
$907$	18.7730			0.623346			0.311673	−	0.950189i	$-0.399111\pi$
$907$	18.7730			0.623346			0.311673	+	0.950189i	$0.399111\pi$
$908$	7.24413			0.240405
$909$	−7.38627	+	30.0530i	−0.244987	+	0.996797i
$910$		0			0
$911$		−	3.73844i		−	0.123860i	−0.998080	−	0.0619300i	$-0.980274\pi$
$911$		−	3.73844i		−	0.123860i	0.998080	−	0.0619300i	$-0.0197255\pi$
$912$	−3.71601	+	2.91330i	−0.123050	+	0.0964690i
$913$		−	18.4943i		−	0.612073i
$914$			10.9251i			0.361370i
$915$		0			0
$916$			27.1596i			0.897380i
$917$	45.4357	+	5.08816i	1.50042	+	0.168026i
$918$	−5.55472	−	12.3093i	−0.183333	−	0.406269i
$919$	24.4423			0.806279			0.403139	−	0.915139i	$-0.367919\pi$
$919$	24.4423			0.806279			0.403139	+	0.915139i	$0.367919\pi$
$920$		0			0
$921$	−13.7638	+	10.7906i	−0.453532	+	0.355563i
$922$			26.6729i			0.878424i
$923$	62.7961			2.06696
$924$	−5.58297	+	3.44895i	−0.183666	+	0.113462i
$925$		0			0
$926$		−	8.07491i		−	0.265358i
$927$	−40.4199	−	9.93418i	−1.32756	−	0.326281i
$928$	−2.82660			−0.0927878
$929$	45.8974			1.50584			0.752922	−	0.658110i	$-0.228644\pi$
$929$	45.8974			1.50584			0.752922	+	0.658110i	$0.228644\pi$
$930$		0			0
$931$	4.22117	−	18.6105i	0.138343	−	0.609935i
$932$			5.38132i			0.176271i
$933$	4.56797	+	5.82660i	0.149549	+	0.190754i
$934$		−	41.6228i		−	1.36194i
$935$		0			0
$936$	−3.39122	+	13.7981i	−0.110846	+	0.451005i
$937$		−	13.2241i		−	0.432014i	−0.976392	−	0.216007i	$-0.930697\pi$
$937$		−	13.2241i		−	0.432014i	0.976392	−	0.216007i	$-0.0693034\pi$
$938$	−2.89341	+	25.8372i	−0.0944733	+	0.843616i
$939$	−1.25863	+	0.986749i	−0.0410739	+	0.0322013i
$940$		0			0
$941$	29.3408			0.956484			0.478242	−	0.878228i	$-0.341274\pi$
$941$	29.3408			0.956484			0.478242	+	0.878228i	$0.341274\pi$
$942$	−6.72780	−	8.58154i	−0.219204	−	0.279602i
$943$			31.5112i			1.02615i
$944$	−10.7775			−0.350777
$945$		0			0
$946$	−0.618679			−0.0201150
$947$			47.1094i			1.53085i	0.643524	+	0.765426i	$0.277471\pi$
$947$			47.1094i			1.53085i	−0.643524	+	0.765426i	$0.722529\pi$
$948$	17.6510	+	22.5145i	0.573278	+	0.731236i
$949$	−35.9464			−1.16687
$950$		0			0
$951$	21.4529	−	16.8187i	0.695657	−	0.545385i
$952$	−0.765257	+	6.83350i	−0.0248021	+	0.221475i
$953$			20.8876i			0.676617i	0.941035	+	0.338308i	$0.109855\pi$
$953$			20.8876i			0.676617i	−0.941035	+	0.338308i	$0.890145\pi$
$954$	4.07460	−	16.5786i	0.131920	−	0.536752i
$955$		0			0
$956$			2.51726i			0.0814141i
$957$	−4.32562	−	5.51747i	−0.139827	−	0.178355i
$958$			21.3728i			0.690524i
$959$	−0.894369	+	7.98643i	−0.0288807	+	0.257895i
$960$		0			0
$961$	−3.97579			−0.128251
$962$	−11.3413			−0.365658
$963$	46.4651	+	11.4199i	1.49732	+	0.368002i
$964$		−	16.8077i		−	0.541340i
$965$		0			0
$966$	6.80769	+	11.0199i	0.219034	+	0.354560i
$967$	27.3335			0.878988			0.439494	−	0.898246i	$-0.355158\pi$
$967$	27.3335			0.878988			0.439494	+	0.898246i	$0.355158\pi$
$968$			8.94929i			0.287641i
$969$	−9.65779	+	7.57157i	−0.310253	+	0.243234i
$970$		0			0
$971$	−24.4555			−0.784815			−0.392407	−	0.919791i	$-0.628358\pi$
$971$	−24.4555			−0.784815			−0.392407	+	0.919791i	$0.628358\pi$
$972$	−2.83532	−	15.3284i	−0.0909430	−	0.491660i
$973$	−6.10912	+	54.5525i	−0.195849	+	1.74887i
$974$		−	27.1094i		−	0.868642i
$975$		0			0
$976$		−	1.05058i		−	0.0336282i
$977$			15.1124i			0.483488i	0.970340	+	0.241744i	$0.0777193\pi$
$977$			15.1124i			0.483488i	−0.970340	+	0.241744i	$0.922281\pi$
$978$	−0.825250	+	0.646984i	−0.0263886	+	0.0206883i
$979$		−	5.59059i		−	0.178676i
$980$		0			0
$981$	7.72519	−	31.4320i	0.246646	−	1.00355i
$982$	30.0000			0.957338
$983$	−13.6670			−0.435910			−0.217955	−	0.975959i	$-0.569939\pi$
$983$	−13.6670			−0.435910			−0.217955	+	0.975959i	$0.569939\pi$
$984$	−15.1958	+	11.9133i	−0.484425	+	0.379782i
$985$		0			0
$986$	−7.34624			−0.233952
$987$	−24.8450	−	40.2177i	−0.790824	−	1.28014i
$988$	12.9118			0.410780
$989$			1.22117i			0.0388311i
$990$		0			0
$991$	−3.45560			−0.109771			−0.0548854	−	0.998493i	$-0.517479\pi$
$991$	−3.45560			−0.109771			−0.0548854	+	0.998493i	$0.517479\pi$
$992$	−5.91403			−0.187771
$993$	13.4707	+	17.1823i	0.427479	+	0.545264i
$994$	34.8611	+	3.90396i	1.10573	+	0.123826i
$995$		0			0
$996$	−13.8012	−	17.6040i	−0.437309	−	0.557803i
$997$		−	40.4199i		−	1.28011i	−0.768329	−	0.640056i	$-0.778911\pi$
$997$		−	40.4199i		−	1.28011i	0.768329	−	0.640056i	$-0.221089\pi$
$998$		−	8.50694i		−	0.269283i
$999$	11.3413	−	5.11788i	0.358822	−	0.161922i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.b.d.251.2	✓	12
3.2	odd	2	inner	1050.2.b.d.251.11	yes	12
5.2	odd	4		1050.2.d.h.1049.4		12
5.3	odd	4		1050.2.d.g.1049.9		12
5.4	even	2		1050.2.b.e.251.11	yes	12
7.6	odd	2	inner	1050.2.b.d.251.5	yes	12
15.2	even	4		1050.2.d.g.1049.3		12
15.8	even	4		1050.2.d.h.1049.10		12
15.14	odd	2		1050.2.b.e.251.2	yes	12
21.20	even	2	inner	1050.2.b.d.251.8	yes	12
35.13	even	4		1050.2.d.g.1049.4		12
35.27	even	4		1050.2.d.h.1049.9		12
35.34	odd	2		1050.2.b.e.251.8	yes	12
105.62	odd	4		1050.2.d.g.1049.10		12
105.83	odd	4		1050.2.d.h.1049.3		12
105.104	even	2		1050.2.b.e.251.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.b.d.251.2	✓	12	1.1	even	1	trivial
1050.2.b.d.251.5	yes	12	7.6	odd	2	inner
1050.2.b.d.251.8	yes	12	21.20	even	2	inner
1050.2.b.d.251.11	yes	12	3.2	odd	2	inner
1050.2.b.e.251.2	yes	12	15.14	odd	2
1050.2.b.e.251.5	yes	12	105.104	even	2
1050.2.b.e.251.8	yes	12	35.34	odd	2
1050.2.b.e.251.11	yes	12	5.4	even	2
1050.2.d.g.1049.3		12	15.2	even	4
1050.2.d.g.1049.4		12	35.13	even	4
1050.2.d.g.1049.9		12	5.3	odd	4
1050.2.d.g.1049.10		12	105.62	odd	4
1050.2.d.h.1049.3		12	105.83	odd	4
1050.2.d.h.1049.4		12	5.2	odd	4
1050.2.d.h.1049.9		12	35.27	even	4
1050.2.d.h.1049.10		12	15.8	even	4

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.06864 - 1.36309i) q^{3} -1.00000 q^{4} +(-1.36309 + 1.06864i) q^{6} +(2.62932 + 0.294447i) q^{7} +1.00000i q^{8} +(-0.716015 + 2.91330i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.06864 - 1.36309i) q^{3} -1.00000 q^{4} +(-1.36309 + 1.06864i) q^{6} +(2.62932 + 0.294447i) q^{7} +1.00000i q^{8} +(-0.716015 + 2.91330i) q^{9} +1.43203i q^{11} +(1.06864 + 1.36309i) q^{12} -4.73625i q^{13} +(0.294447 - 2.62932i) q^{14} +1.00000 q^{16} +2.59897 q^{17} +(2.91330 + 0.716015i) q^{18} -2.72617i q^{19} +(-2.40844 - 3.89865i) q^{21} +1.43203 q^{22} -2.82660i q^{23} +(1.36309 - 1.06864i) q^{24} -4.73625 q^{26} +(4.73625 - 2.13728i) q^{27} +(-2.62932 - 0.294447i) q^{28} -2.82660i q^{29} -5.91403i q^{31} -1.00000i q^{32} +(1.95198 - 1.53032i) q^{33} -2.59897i q^{34} +(0.716015 - 2.91330i) q^{36} +2.39457 q^{37} -2.72617 q^{38} +(-6.45592 + 5.06134i) q^{39} -11.1481 q^{41} +(-3.89865 + 2.40844i) q^{42} -0.432029 q^{43} -1.43203i q^{44} -2.82660 q^{46} +10.3158 q^{47} +(-1.06864 - 1.36309i) q^{48} +(6.82660 + 1.54839i) q^{49} +(-2.77736 - 3.54262i) q^{51} +4.73625i q^{52} -5.69066i q^{53} +(-2.13728 - 4.73625i) q^{54} +(-0.294447 + 2.62932i) q^{56} +(-3.71601 + 2.91330i) q^{57} -2.82660 q^{58} -10.7775 q^{59} -1.05058i q^{61} -5.91403 q^{62} +(-2.74044 + 7.44916i) q^{63} -1.00000 q^{64} +(-1.53032 - 1.95198i) q^{66} -9.82660 q^{67} -2.59897 q^{68} +(-3.85291 + 3.02062i) q^{69} +13.2586i q^{71} +(-2.91330 - 0.716015i) q^{72} -7.58963i q^{73} -2.39457i q^{74} +2.72617i q^{76} +(-0.421657 + 3.76526i) q^{77} +(5.06134 + 6.45592i) q^{78} +16.5173 q^{79} +(-7.97465 - 4.17193i) q^{81} +11.1481i q^{82} -12.9148 q^{83} +(2.40844 + 3.89865i) q^{84} +0.432029i q^{86} +(-3.85291 + 3.02062i) q^{87} -1.43203 q^{88} -3.90396 q^{89} +(1.39457 - 12.4531i) q^{91} +2.82660i q^{92} +(-8.06134 + 6.31998i) q^{93} -10.3158i q^{94} +(-1.36309 + 1.06864i) q^{96} -14.0015i q^{97} +(1.54839 - 6.82660i) q^{98} +(-4.17193 - 1.02535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 4 q^{7}+O(q^{10}) \) 12 * q - 12 * q^4 - 4 * q^7	\( 12 q - 12 q^{4} - 4 q^{7} + 12 q^{16} + 8 q^{18} + 14 q^{21} + 4 q^{28} - 8 q^{37} + 12 q^{39} + 14 q^{42} + 12 q^{43} + 20 q^{46} + 28 q^{49} + 28 q^{51} - 36 q^{57} + 20 q^{58} - 22 q^{63} - 12 q^{64} - 64 q^{67} - 8 q^{72} + 8 q^{78} + 56 q^{79} - 16 q^{81} - 14 q^{84} - 20 q^{91} - 44 q^{93} + 48 q^{99}+O(q^{100}) \) 12 * q - 12 * q^4 - 4 * q^7 + 12 * q^16 + 8 * q^18 + 14 * q^21 + 4 * q^28 - 8 * q^37 + 12 * q^39 + 14 * q^42 + 12 * q^43 + 20 * q^46 + 28 * q^49 + 28 * q^51 - 36 * q^57 + 20 * q^58 - 22 * q^63 - 12 * q^64 - 64 * q^67 - 8 * q^72 + 8 * q^78 + 56 * q^79 - 16 * q^81 - 14 * q^84 - 20 * q^91 - 44 * q^93 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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