LMFDB - Embedded newform 1050.2.d.h.1049.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(1049,1050)]

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, 1, 1]))

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

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

chi := DirichletCharacter("1050.1049");

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.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.38429221223$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1049.9
Root			$-1.06864 - 1.36309i$ of defining polynomial
Character	$\chi$	$=$	1050.1049
Dual form			1050.2.d.h.1049.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.36309 - 1.06864i) q^{3} +1.00000 q^{4} +(1.36309 - 1.06864i) q^{6} +(0.294447 + 2.62932i) q^{7} +1.00000 q^{8} +(0.716015 - 2.91330i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.36309 - 1.06864i) q^{3} +1.00000 q^{4} +(1.36309 - 1.06864i) q^{6} +(0.294447 + 2.62932i) q^{7} +1.00000 q^{8} +(0.716015 - 2.91330i) q^{9} +1.43203i q^{11} +(1.36309 - 1.06864i) q^{12} +4.73625 q^{13} +(0.294447 + 2.62932i) q^{14} +1.00000 q^{16} -2.59897i q^{17} +(0.716015 - 2.91330i) q^{18} -2.72617i q^{19} +(3.21115 + 3.26933i) q^{21} +1.43203i q^{22} -2.82660 q^{23} +(1.36309 - 1.06864i) q^{24} +4.73625 q^{26} +(-2.13728 - 4.73625i) q^{27} +(0.294447 + 2.62932i) q^{28} +2.82660i q^{29} +5.91403i q^{31} +1.00000 q^{32} +(1.53032 + 1.95198i) q^{33} -2.59897i q^{34} +(0.716015 - 2.91330i) q^{36} +2.39457i q^{37} -2.72617i q^{38} +(6.45592 - 5.06134i) q^{39} +11.1481 q^{41} +(3.21115 + 3.26933i) q^{42} +0.432029i q^{43} +1.43203i q^{44} -2.82660 q^{46} -10.3158i q^{47} +(1.36309 - 1.06864i) q^{48} +(-6.82660 + 1.54839i) q^{49} +(-2.77736 - 3.54262i) q^{51} +4.73625 q^{52} -5.69066 q^{53} +(-2.13728 - 4.73625i) q^{54} +(0.294447 + 2.62932i) q^{56} +(-2.91330 - 3.71601i) q^{57} +2.82660i q^{58} -10.7775 q^{59} +1.05058i q^{61} +5.91403i q^{62} +(7.87082 + 1.02482i) q^{63} +1.00000 q^{64} +(1.53032 + 1.95198i) q^{66} -9.82660i q^{67} -2.59897i q^{68} +(-3.85291 + 3.02062i) q^{69} +13.2586i q^{71} +(0.716015 - 2.91330i) q^{72} +7.58963 q^{73} +2.39457i q^{74} -2.72617i q^{76} +(-3.76526 + 0.421657i) q^{77} +(6.45592 - 5.06134i) q^{78} -16.5173 q^{79} +(-7.97465 - 4.17193i) q^{81} +11.1481 q^{82} -12.9148i q^{83} +(3.21115 + 3.26933i) q^{84} +0.432029i q^{86} +(3.02062 + 3.85291i) q^{87} +1.43203i q^{88} -3.90396 q^{89} +(1.39457 + 12.4531i) q^{91} -2.82660 q^{92} +(6.31998 + 8.06134i) q^{93} -10.3158i q^{94} +(1.36309 - 1.06864i) q^{96} -14.0015 q^{97} +(-6.82660 + 1.54839i) q^{98} +(4.17193 + 1.02535i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{4} + 12 q^{8}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^4 + 12 * q^8	$ 12 q + 12 q^{2} + 12 q^{4} + 12 q^{8} + 12 q^{16} + 14 q^{21} + 20 q^{23} + 12 q^{32} - 12 q^{39} + 14 q^{42} + 20 q^{46} - 28 q^{49} + 28 q^{51} + 20 q^{53} - 8 q^{57} + 30 q^{63} + 12 q^{64} - 44 q^{77} - 12 q^{78} - 56 q^{79} - 16 q^{81} + 14 q^{84} - 20 q^{91} + 20 q^{92} - 48 q^{93} - 28 q^{98} - 48 q^{99}+O(q^{100}) $ 12 * q + 12 * q^2 + 12 * q^4 + 12 * q^8 + 12 * q^16 + 14 * q^21 + 20 * q^23 + 12 * q^32 - 12 * q^39 + 14 * q^42 + 20 * q^46 - 28 * q^49 + 28 * q^51 + 20 * q^53 - 8 * q^57 + 30 * q^63 + 12 * q^64 - 44 * q^77 - 12 * q^78 - 56 * q^79 - 16 * q^81 + 14 * q^84 - 20 * q^91 + 20 * q^92 - 48 * q^93 - 28 * q^98 - 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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.36309	−	1.06864i	0.786979	−	0.616980i
$3$	1.36309	−	1.06864i	0.786979	−	0.616980i
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$	1.36309	−	1.06864i	0.556478	−	0.436271i
$7$	0.294447	+	2.62932i	0.111290	+	0.993788i
$7$	0.294447	+	2.62932i	0.111290	+	0.993788i
$8$	1.00000			0.353553
$9$	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	$0.930736\pi$
$12$	1.36309	−	1.06864i	0.393489	−	0.308490i
$13$	4.73625			1.31360			0.656799	−	0.754066i	$-0.271910\pi$
$13$	4.73625			1.31360			0.656799	+	0.754066i	$0.271910\pi$
$14$	0.294447	+	2.62932i	0.0786942	+	0.702714i
$15$		0			0
$16$	1.00000			0.250000
$17$		−	2.59897i		−	0.630342i	−0.949035	−	0.315171i	$-0.897938\pi$
$17$		−	2.59897i		−	0.630342i	0.949035	−	0.315171i	$-0.102062\pi$
$18$	0.716015	−	2.91330i	0.168766	−	0.686672i
$19$		−	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
$21$	3.21115	+	3.26933i	0.700730	+	0.713426i
$22$			1.43203i			0.305310i
$23$	−2.82660			−0.589387			−0.294694	−	0.955592i	$-0.595218\pi$
$23$	−2.82660			−0.589387			−0.294694	+	0.955592i	$0.595218\pi$
$24$	1.36309	−	1.06864i	0.278239	−	0.218135i
$25$		0			0
$26$	4.73625			0.928854
$27$	−2.13728	−	4.73625i	−0.411320	−	0.911491i
$28$	0.294447	+	2.62932i	0.0556452	+	0.496894i
$29$			2.82660i			0.524887i	0.964947	+	0.262443i	$0.0845283\pi$
$29$			2.82660i			0.524887i	−0.964947	+	0.262443i	$0.915472\pi$
$30$		0			0
$31$			5.91403i			1.06219i	0.847312	+	0.531096i	$0.178220\pi$
$31$			5.91403i			1.06219i	−0.847312	+	0.531096i	$0.821780\pi$
$32$	1.00000			0.176777
$33$	1.53032	+	1.95198i	0.266395	+	0.339796i
$34$		−	2.59897i		−	0.445719i
$35$		0			0
$36$	0.716015	−	2.91330i	0.119336	−	0.485550i
$37$			2.39457i			0.393665i	0.980437	+	0.196833i	$0.0630656\pi$
$37$			2.39457i			0.393665i	−0.980437	+	0.196833i	$0.936934\pi$
$38$		−	2.72617i		−	0.442244i
$39$	6.45592	−	5.06134i	1.03377	−	0.810464i
$40$		0			0
$41$	11.1481			1.74104			0.870520	−	0.492134i	$-0.163783\pi$
$41$	11.1481			1.74104			0.870520	+	0.492134i	$0.163783\pi$
$42$	3.21115	+	3.26933i	0.495491	+	0.504468i
$43$			0.432029i			0.0658838i	0.999457	+	0.0329419i	$0.0104876\pi$
$43$			0.432029i			0.0658838i	−0.999457	+	0.0329419i	$0.989512\pi$
$44$			1.43203i			0.215887i
$45$		0			0
$46$	−2.82660			−0.416760
$47$		−	10.3158i		−	1.50471i	−0.658755	−	0.752357i	$-0.728917\pi$
$47$		−	10.3158i		−	1.50471i	0.658755	−	0.752357i	$-0.271083\pi$
$48$	1.36309	−	1.06864i	0.196745	−	0.154245i
$49$	−6.82660	+	1.54839i	−0.975229	+	0.221198i
$50$		0			0
$51$	−2.77736	−	3.54262i	−0.388908	−	0.496066i
$52$	4.73625			0.656799
$53$	−5.69066			−0.781672			−0.390836	−	0.920460i	$-0.627814\pi$
$53$	−5.69066			−0.781672			−0.390836	+	0.920460i	$0.627814\pi$
$54$	−2.13728	−	4.73625i	−0.290847	−	0.644521i
$55$		0			0
$56$	0.294447	+	2.62932i	0.0393471	+	0.351357i
$57$	−2.91330	−	3.71601i	−0.385876	−	0.492198i
$58$			2.82660i			0.371151i
$59$	−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	$0.0214245\pi$
$61$			1.05058i			0.134513i	−0.997736	+	0.0672563i	$0.978575\pi$
$62$			5.91403i			0.751083i
$63$	7.87082	+	1.02482i	0.991630	+	0.129115i
$64$	1.00000			0.125000
$65$		0			0
$66$	1.53032	+	1.95198i	0.188370	+	0.240272i
$67$		−	9.82660i		−	1.20051i	−0.799808	−	0.600255i	$-0.795066\pi$
$67$		−	9.82660i		−	1.20051i	0.799808	−	0.600255i	$-0.204934\pi$
$68$		−	2.59897i		−	0.315171i
$69$	−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	$0.711760\pi$
$72$	0.716015	−	2.91330i	0.0843831	−	0.343336i
$73$	7.58963			0.888299			0.444150	−	0.895953i	$-0.353506\pi$
$73$	7.58963			0.888299			0.444150	+	0.895953i	$0.353506\pi$
$74$			2.39457i			0.278363i
$75$		0			0
$76$		−	2.72617i		−	0.312714i
$77$	−3.76526	+	0.421657i	−0.429091	+	0.0480522i
$78$	6.45592	−	5.06134i	0.730989	−	0.573084i
$79$	−16.5173			−1.85834			−0.929169	−	0.369656i	$-0.879475\pi$
$79$	−16.5173			−1.85834			−0.929169	+	0.369656i	$0.879475\pi$
$80$		0			0
$81$	−7.97465	−	4.17193i	−0.886072	−	0.463548i
$82$	11.1481			1.23110
$83$		−	12.9148i		−	1.41758i	−0.705419	−	0.708790i	$-0.749241\pi$
$83$		−	12.9148i		−	1.41758i	0.705419	−	0.708790i	$-0.250759\pi$
$84$	3.21115	+	3.26933i	0.350365	+	0.356713i
$85$		0			0
$86$			0.432029i			0.0465869i
$87$	3.02062	+	3.85291i	0.323845	+	0.413075i
$88$			1.43203i			0.152655i
$89$	−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
$92$	−2.82660			−0.294694
$93$	6.31998	+	8.06134i	0.655351	+	0.835923i
$94$		−	10.3158i		−	1.06399i
$95$		0			0
$96$	1.36309	−	1.06864i	0.139120	−	0.109068i
$97$	−14.0015			−1.42163			−0.710817	−	0.703377i	$-0.751675\pi$
$97$	−14.0015			−1.42163			−0.710817	+	0.703377i	$0.751675\pi$
$98$	−6.82660	+	1.54839i	−0.689591	+	0.156411i
$99$	4.17193	+	1.02535i	0.419295	+	0.103052i
$100$		0			0
$101$	−10.3158			−1.02646			−0.513231	−	0.858251i	$-0.671551\pi$
$101$	−10.3158			−1.02646			−0.513231	+	0.858251i	$0.671551\pi$
$102$	−2.77736	−	3.54262i	−0.275000	−	0.350771i
$103$	−13.8743			−1.36707			−0.683536	−	0.729917i	$-0.739559\pi$
$103$	−13.8743			−1.36707			−0.683536	+	0.729917i	$0.739559\pi$
$104$	4.73625			0.464427
$105$		0			0
$106$	−5.69066			−0.552726
$107$	15.9493			1.54188			0.770938	−	0.636910i	$-0.219788\pi$
$107$	15.9493			1.54188			0.770938	+	0.636910i	$0.219788\pi$
$108$	−2.13728	−	4.73625i	−0.205660	−	0.455746i
$109$	10.7891			1.03341			0.516706	−	0.856163i	$-0.327158\pi$
$109$	10.7891			1.03341			0.516706	+	0.856163i	$0.327158\pi$
$110$		0			0
$111$	2.55894	+	3.26401i	0.242884	+	0.309806i
$112$	0.294447	+	2.62932i	0.0278226	+	0.248447i
$113$	−14.3439			−1.34936			−0.674679	−	0.738112i	$-0.735718\pi$
$113$	−14.3439			−1.34936			−0.674679	+	0.738112i	$0.735718\pi$
$114$	−2.91330	−	3.71601i	−0.272856	−	0.348037i
$115$		0			0
$116$			2.82660i			0.262443i
$117$	3.39122	−	13.7981i	0.313519	−	1.27564i
$118$	−10.7775			−0.992148
$119$	6.83350	−	0.765257i	0.626426	−	0.0701510i
$120$		0			0
$121$	8.94929			0.813572
$122$			1.05058i			0.0951148i
$123$	15.1958	−	11.9133i	1.37016	−	1.07419i
$124$			5.91403i			0.531096i
$125$		0			0
$126$	7.87082	+	1.02482i	0.701188	+	0.0912979i
$127$			2.00000i			0.177471i	0.996055	+	0.0887357i	$0.0282826\pi$
$127$			2.00000i			0.177471i	−0.996055	+	0.0887357i	$0.971717\pi$
$128$	1.00000			0.0883883
$129$	0.461684	+	0.588894i	0.0406490	+	0.0518492i
$130$		0			0
$131$	−17.2804			−1.50980			−0.754899	−	0.655842i	$-0.772314\pi$
$131$	−17.2804			−1.50980			−0.754899	+	0.655842i	$0.772314\pi$
$132$	1.53032	+	1.95198i	0.133198	+	0.169898i
$133$	7.16797	−	0.802714i	0.621542	−	0.0696041i
$134$		−	9.82660i		−	0.848889i
$135$		0			0
$136$		−	2.59897i		−	0.222859i
$137$	−3.03746			−0.259507			−0.129754	−	0.991546i	$-0.541419\pi$
$137$	−3.03746			−0.259507			−0.129754	+	0.991546i	$0.541419\pi$
$138$	−3.85291	+	3.02062i	−0.327981	+	0.257132i
$139$			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
$142$			13.2586i			1.11264i
$143$			6.78244i			0.567176i
$144$	0.716015	−	2.91330i	0.0596679	−	0.242775i
$145$		0			0
$146$	7.58963			0.628122
$147$	−7.65059	+	9.40577i	−0.631010	+	0.775775i
$148$			2.39457i			0.196833i
$149$			18.9493i			1.55239i	0.630495	+	0.776193i	$0.282852\pi$
$149$			18.9493i			1.55239i	−0.630495	+	0.776193i	$0.717148\pi$
$150$		0			0
$151$	5.25863			0.427941			0.213971	−	0.976840i	$-0.431360\pi$
$151$	5.25863			0.427941			0.213971	+	0.976840i	$0.431360\pi$
$152$		−	2.72617i		−	0.221122i
$153$	−7.57157	−	1.86090i	−0.612125	−	0.150445i
$154$	−3.76526	+	0.421657i	−0.303413	+	0.0339781i
$155$		0			0
$156$	6.45592	−	5.06134i	0.516887	−	0.405232i
$157$	6.29566			0.502449			0.251224	−	0.967929i	$-0.419167\pi$
$157$	6.29566			0.502449			0.251224	+	0.967929i	$0.419167\pi$
$158$	−16.5173			−1.31404
$159$	−7.75687	+	6.08127i	−0.615160	+	0.482276i
$160$		0			0
$161$	−0.832284	−	7.43203i	−0.0655932	−	0.585726i
$162$	−7.97465	−	4.17193i	−0.626547	−	0.327778i
$163$		−	0.605427i		−	0.0474207i	−0.999719	−	0.0237104i	$-0.992452\pi$
$163$		−	0.605427i		−	0.0474207i	0.999719	−	0.0237104i	$-0.00754795\pi$
$164$	11.1481			0.870520
$165$		0			0
$166$		−	12.9148i		−	1.00238i
$167$			12.0825i			0.934971i	0.884001	+	0.467485i	$0.154840\pi$
$167$			12.0825i			0.934971i	−0.884001	+	0.467485i	$0.845160\pi$
$168$	3.21115	+	3.26933i	0.247746	+	0.252234i
$169$	9.43203			0.725541
$170$		0			0
$171$	−7.94217	−	1.95198i	−0.607353	−	0.149272i
$172$			0.432029i			0.0329419i
$173$			15.5137i			1.17949i	0.807590	+	0.589744i	$0.200771\pi$
$173$			15.5137i			1.17949i	−0.807590	+	0.589744i	$0.799229\pi$
$174$	3.02062	+	3.85291i	0.228993	+	0.292088i
$175$		0			0
$176$			1.43203i			0.107943i
$177$	−14.6907	+	11.5173i	−1.10422	+	0.865690i
$178$	−3.90396			−0.292614
$179$			4.56797i			0.341426i	0.985321	+	0.170713i	$0.0546071\pi$
$179$			4.56797i			0.341426i	−0.985321	+	0.170713i	$0.945393\pi$
$180$		0			0
$181$		−	7.80792i		−	0.580358i	−0.956972	−	0.290179i	$-0.906285\pi$
$181$		−	7.80792i		−	0.580358i	0.956972	−	0.290179i	$-0.0937149\pi$
$182$	1.39457	+	12.4531i	0.103373	+	0.923084i
$183$	1.12269	+	1.43203i	0.0829916	+	0.105859i
$184$	−2.82660			−0.208380
$185$		0			0
$186$	6.31998	+	8.06134i	0.463403	+	0.591086i
$187$	3.72179			0.272165
$188$		−	10.3158i		−	0.752357i
$189$	11.8238	−	7.01416i	0.860053	−	0.510205i
$190$		0			0
$191$			7.22117i			0.522506i	0.965270	+	0.261253i	$0.0841357\pi$
$191$			7.22117i			0.522506i	−0.965270	+	0.261253i	$0.915864\pi$
$192$	1.36309	−	1.06864i	0.0983724	−	0.0771225i
$193$		−	7.60250i		−	0.547240i	−0.961838	−	0.273620i	$-0.911779\pi$
$193$		−	7.60250i		−	0.547240i	0.961838	−	0.273620i	$-0.0882210\pi$
$194$	−14.0015			−1.00525
$195$		0			0
$196$	−6.82660	+	1.54839i	−0.487614	+	0.110599i
$197$	21.7384			1.54880			0.774400	−	0.632697i	$-0.218052\pi$
$197$	21.7384			1.54880			0.774400	+	0.632697i	$0.218052\pi$
$198$	4.17193	+	1.02535i	0.296486	+	0.0728687i
$199$			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
$202$	−10.3158			−0.725818
$203$	−7.43203	+	0.832284i	−0.521626	+	0.0584149i
$204$	−2.77736	−	3.54262i	−0.194454	−	0.248033i
$205$		0			0
$206$	−13.8743			−0.966666
$207$	−2.02389	+	8.23474i	−0.140670	+	0.572354i
$208$	4.73625			0.328400
$209$	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	$0.304048\pi$
$212$	−5.69066			−0.390836
$213$	14.1687	+	18.0727i	0.970824	+	1.23832i
$214$	15.9493			1.09027
$215$		0			0
$216$	−2.13728	−	4.73625i	−0.145424	−	0.322261i
$217$	−15.5499	+	1.74137i	−1.05559	+	0.118212i
$218$	10.7891			0.730733
$219$	10.3453	−	8.11059i	0.699073	−	0.548063i
$220$		0			0
$221$		−	12.3093i		−	0.828016i
$222$	2.55894	+	3.26401i	0.171745	+	0.219066i
$223$	−11.1120			−0.744112			−0.372056	−	0.928210i	$-0.621347\pi$
$223$	−11.1120			−0.744112			−0.372056	+	0.928210i	$0.621347\pi$
$224$	0.294447	+	2.62932i	0.0196736	+	0.175679i
$225$		0			0
$226$	−14.3439			−0.954140
$227$			7.24413i			0.480810i	0.970673	+	0.240405i	$0.0772802\pi$
$227$			7.24413i			0.480810i	−0.970673	+	0.240405i	$0.922720\pi$
$228$	−2.91330	−	3.71601i	−0.192938	−	0.246099i
$229$		−	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
$231$	−4.68178	+	4.59846i	−0.308038	+	0.302557i
$232$			2.82660i			0.185576i
$233$	−5.38132			−0.352542			−0.176271	−	0.984342i	$-0.556404\pi$
$233$	−5.38132			−0.352542			−0.176271	+	0.984342i	$0.556404\pi$
$234$	3.39122	−	13.7981i	0.221691	−	0.902011i
$235$		0			0
$236$	−10.7775			−0.701555
$237$	−22.5145	+	17.6510i	−1.46247	+	1.14656i
$238$	6.83350	−	0.765257i	0.442950	−	0.0496043i
$239$			2.51726i			0.162828i	0.996680	+	0.0814141i	$0.0259436\pi$
$239$			2.51726i			0.162828i	−0.996680	+	0.0814141i	$0.974056\pi$
$240$		0			0
$241$		−	16.8077i		−	1.08268i	−0.840804	−	0.541340i	$-0.817917\pi$
$241$		−	16.8077i		−	1.08268i	0.840804	−	0.541340i	$-0.182083\pi$
$242$	8.94929			0.575282
$243$	−15.3284	+	2.83532i	−0.983320	+	0.181886i
$244$			1.05058i			0.0672563i
$245$		0			0
$246$	15.1958	−	11.9133i	0.968850	−	0.759564i
$247$		−	12.9118i		−	0.821560i
$248$			5.91403i			0.375542i
$249$	−13.8012	−	17.6040i	−0.874619	−	1.11561i
$250$		0			0
$251$	−1.75565			−0.110816			−0.0554079	−	0.998464i	$-0.517646\pi$
$251$	−1.75565			−0.110816			−0.0554079	+	0.998464i	$0.517646\pi$
$252$	7.87082	+	1.02482i	0.495815	+	0.0645574i
$253$		−	4.04778i		−	0.254482i
$254$			2.00000i			0.125491i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	21.9366i		−	1.36837i	−0.729309	−	0.684184i	$-0.760159\pi$
$257$		−	21.9366i		−	1.36837i	0.729309	−	0.684184i	$-0.239841\pi$
$258$	0.461684	+	0.588894i	0.0287432	+	0.0366629i
$259$	−6.29609	+	0.705074i	−0.391220	+	0.0438112i
$260$		0			0
$261$	8.23474	+	2.02389i	0.509718	+	0.125276i
$262$	−17.2804			−1.06759
$263$	4.08523			0.251906			0.125953	−	0.992036i	$-0.459801\pi$
$263$	4.08523			0.251906			0.125953	+	0.992036i	$0.459801\pi$
$264$	1.53032	+	1.95198i	0.0941850	+	0.120136i
$265$		0			0
$266$	7.16797	−	0.802714i	0.439497	−	0.0492175i
$267$	−5.32144	+	4.17193i	−0.325667	+	0.255318i
$268$		−	9.82660i		−	0.600255i
$269$	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	$-0.747349\pi$
$271$		−	23.4740i		−	1.42594i	0.701194	−	0.712971i	$-0.252651\pi$
$272$		−	2.59897i		−	0.157585i
$273$	15.2088	+	15.4843i	0.920478	+	0.937155i
$274$	−3.03746			−0.183499
$275$		0			0
$276$	−3.85291	+	3.02062i	−0.231918	+	0.181820i
$277$		−	14.1227i		−	0.848550i	−0.905533	−	0.424275i	$-0.860529\pi$
$277$		−	14.1227i		−	0.848550i	0.905533	−	0.424275i	$-0.139471\pi$
$278$			20.7478i			1.24437i
$279$	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	$0.750715\pi$
$282$	−11.0239	−	14.0613i	−0.656463	−	0.837341i
$283$	0.807187			0.0479823			0.0239912	−	0.999712i	$-0.492363\pi$
$283$	0.807187			0.0479823			0.0239912	+	0.999712i	$0.492363\pi$
$284$			13.2586i			0.786755i
$285$		0			0
$286$			6.78244i			0.401054i
$287$	3.28252	+	29.3118i	0.193761	+	1.73022i
$288$	0.716015	−	2.91330i	0.0421916	−	0.171668i
$289$	10.2454			0.602669
$290$		0			0
$291$	−19.0852	+	14.9625i	−1.11880	+	0.877120i
$292$	7.58963			0.444150
$293$			14.6704i			0.857055i	0.903529	+	0.428528i	$0.140968\pi$
$293$			14.6704i			0.857055i	−0.903529	+	0.428528i	$0.859032\pi$
$294$	−7.65059	+	9.40577i	−0.446191	+	0.548556i
$295$		0			0
$296$			2.39457i			0.139182i
$297$	6.78244	−	3.06065i	0.393557	−	0.177597i
$298$			18.9493i			1.09770i
$299$	−13.3875			−0.774218
$300$		0			0
$301$	−1.13594	+	0.127210i	−0.0654746	+	0.00733224i
$302$	5.25863			0.302600
$303$	−14.0613	+	11.0239i	−0.807803	+	0.633306i
$304$		−	2.72617i		−	0.156357i
$305$		0			0
$306$	−7.57157	−	1.86090i	−0.432838	−	0.106380i
$307$	−10.0975			−0.576295			−0.288148	−	0.957586i	$-0.593039\pi$
$307$	−10.0975			−0.576295			−0.288148	+	0.957586i	$0.593039\pi$
$308$	−3.76526	+	0.421657i	−0.214545	+	0.0240261i
$309$	−18.9118	+	14.8266i	−1.07586	+	0.843456i
$310$		0			0
$311$	4.27456			0.242388			0.121194	−	0.992629i	$-0.461328\pi$
$311$	4.27456			0.242388			0.121194	+	0.992629i	$0.461328\pi$
$312$	6.45592	−	5.06134i	0.365494	−	0.286542i
$313$	0.923368			0.0521918			0.0260959	−	0.999659i	$-0.491692\pi$
$313$	0.923368			0.0521918			0.0260959	+	0.999659i	$0.491692\pi$
$314$	6.29566			0.355285
$315$		0			0
$316$	−16.5173			−0.929169
$317$	−15.7384			−0.883959			−0.441979	−	0.897025i	$-0.645724\pi$
$317$	−15.7384			−0.883959			−0.441979	+	0.897025i	$0.645724\pi$
$318$	−7.75687	+	6.08127i	−0.434984	+	0.341021i
$319$	−4.04778			−0.226632
$320$		0			0
$321$	21.7403	−	17.0441i	1.21342	−	0.951307i
$322$	−0.832284	−	7.43203i	−0.0463814	−	0.414171i
$323$	−7.08523			−0.394233
$324$	−7.97465	−	4.17193i	−0.443036	−	0.231774i
$325$		0			0
$326$		−	0.605427i		−	0.0335315i
$327$	14.7065	−	11.5297i	0.813274	−	0.637595i
$328$	11.1481			0.615550
$329$	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	$0.612606\pi$
$332$		−	12.9148i		−	0.708790i
$333$	6.97611	+	1.71455i	0.382289	+	0.0939567i
$334$			12.0825i			0.661124i
$335$		0			0
$336$	3.21115	+	3.26933i	0.175183	+	0.178357i
$337$		−	18.8986i		−	1.02947i	−0.857349	−	0.514736i	$-0.827890\pi$
$337$		−	18.8986i		−	1.02947i	0.857349	−	0.514736i	$-0.172110\pi$
$338$	9.43203			0.513035
$339$	−19.5519	+	15.3284i	−1.06192	+	0.832526i
$340$		0			0
$341$	−8.46907			−0.458626
$342$	−7.94217	−	1.95198i	−0.429463	−	0.105551i
$343$	−6.08127	−	17.4934i	−0.328358	−	0.944553i
$344$			0.432029i			0.0232935i
$345$		0			0
$346$			15.5137i			0.834024i
$347$	−30.7384			−1.65013			−0.825063	−	0.565041i	$-0.808860\pi$
$347$	−30.7384			−1.65013			−0.825063	+	0.565041i	$0.808860\pi$
$348$	3.02062	+	3.85291i	0.161922	+	0.206537i
$349$			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
$352$			1.43203i			0.0763274i
$353$			16.3570i			0.870598i	0.900286	+	0.435299i	$0.143357\pi$
$353$			16.3570i			0.870598i	−0.900286	+	0.435299i	$0.856643\pi$
$354$	−14.6907	+	11.5173i	−0.780800	+	0.612136i
$355$		0			0
$356$	−3.90396			−0.206910
$357$	8.49687	−	8.34567i	0.449702	−	0.441700i
$358$			4.56797i			0.241425i
$359$		−	9.81335i		−	0.517929i	−0.965887	−	0.258964i	$-0.916619\pi$
$359$		−	9.81335i		−	0.517929i	0.965887	−	0.258964i	$-0.0833812\pi$
$360$		0			0
$361$	11.5680			0.608841
$362$		−	7.80792i		−	0.410375i
$363$	12.1987	−	9.56358i	0.640264	−	0.501958i
$364$	1.39457	+	12.4531i	0.0730955	+	0.652719i
$365$		0			0
$366$	1.12269	+	1.43203i	0.0586839	+	0.0748534i
$367$	33.9970			1.77463			0.887315	−	0.461163i	$-0.152568\pi$
$367$	33.9970			1.77463			0.887315	+	0.461163i	$0.152568\pi$
$368$	−2.82660			−0.147347
$369$	7.98220	−	32.4777i	0.415537	−	1.69072i
$370$		0			0
$371$	−1.67560	−	14.9625i	−0.0869927	−	0.776817i
$372$	6.31998	+	8.06134i	0.327676	+	0.417961i
$373$		−	26.5650i		−	1.37549i	−0.725954	−	0.687743i	$-0.758602\pi$
$373$		−	26.5650i		−	1.37549i	0.725954	−	0.687743i	$-0.241398\pi$
$374$	3.72179			0.192449
$375$		0			0
$376$		−	10.3158i		−	0.531997i
$377$			13.3875i			0.689490i
$378$	11.8238	−	7.01416i	0.608149	−	0.360769i
$379$	−8.25863			−0.424217			−0.212109	−	0.977246i	$-0.568033\pi$
$379$	−8.25863			−0.424217			−0.212109	+	0.977246i	$0.568033\pi$
$380$		0			0
$381$	2.13728	+	2.72617i	0.109496	+	0.139666i
$382$			7.22117i			0.369467i
$383$		−	32.6920i		−	1.67049i	−0.549882	−	0.835243i	$-0.685327\pi$
$383$		−	32.6920i		−	1.67049i	0.549882	−	0.835243i	$-0.314673\pi$
$384$	1.36309	−	1.06864i	0.0695598	−	0.0545338i
$385$		0			0
$386$		−	7.60250i		−	0.386957i
$387$	1.25863	+	0.309339i	0.0639798	+	0.0157246i
$388$	−14.0015			−0.710817
$389$			1.33354i			0.0676134i	0.999428	+	0.0338067i	$0.0107631\pi$
$389$			1.33354i			0.0676134i	−0.999428	+	0.0338067i	$0.989237\pi$
$390$		0			0
$391$			7.34624i			0.371515i
$392$	−6.82660	+	1.54839i	−0.344795	+	0.0782054i
$393$	−23.5547	+	18.4666i	−1.18818	+	0.931514i
$394$	21.7384			1.09517
$395$		0			0
$396$	4.17193	+	1.02535i	0.209647	+	0.0515260i
$397$	23.0123			1.15495			0.577477	−	0.816407i	$-0.304037\pi$
$397$	23.0123			1.15495			0.577477	+	0.816407i	$0.304037\pi$
$398$			6.04124i			0.302820i
$399$	8.91276	−	8.75416i	0.446196	−	0.438256i
$400$		0			0
$401$			17.5547i			0.876641i	0.898819	+	0.438320i	$0.144426\pi$
$401$			17.5547i			0.876641i	−0.898819	+	0.438320i	$0.855574\pi$
$402$	−10.5011	−	13.3945i	−0.523748	−	0.668058i
$403$			28.0103i			1.39529i
$404$	−10.3158			−0.513231
$405$		0			0
$406$	−7.43203	+	0.832284i	−0.368845	+	0.0413056i
$407$	−3.42910			−0.169974
$408$	−2.77736	−	3.54262i	−0.137500	−	0.175386i
$409$			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
$412$	−13.8743			−0.683536
$413$	−3.17340	−	28.3374i	−0.156153	−	1.39439i
$414$	−2.02389	+	8.23474i	−0.0994687	+	0.404716i
$415$		0			0
$416$	4.73625			0.232214
$417$	22.1719	+	28.2811i	1.08576	+	1.38493i
$418$	3.90396			0.190949
$419$	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	$0.411921\pi$
$422$	16.7759			0.816638
$423$	−30.0530	−	7.38627i	−1.46123	−	0.359133i
$424$	−5.69066			−0.276363
$425$		0			0
$426$	14.1687	+	18.0727i	0.686476	+	0.875624i
$427$	−2.76230	+	0.309339i	−0.133677	+	0.0149700i
$428$	15.9493			0.770938
$429$	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	$-0.217435\pi$
$432$	−2.13728	−	4.73625i	−0.102830	−	0.227873i
$433$	23.4378			1.12635			0.563175	−	0.826337i	$-0.309580\pi$
$433$	23.4378			1.12635			0.563175	+	0.826337i	$0.309580\pi$
$434$	−15.5499	+	1.74137i	−0.746417	+	0.0835884i
$435$		0			0
$436$	10.7891			0.516706
$437$			7.70581i			0.368619i
$438$	10.3453	−	8.11059i	0.494319	−	0.387539i
$439$		−	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
$441$	−0.377028	+	20.9966i	−0.0179537	+	0.999839i
$442$		−	12.3093i		−	0.585496i
$443$	18.4666			0.877373			0.438686	−	0.898640i	$-0.355444\pi$
$443$	18.4666			0.877373			0.438686	+	0.898640i	$0.355444\pi$
$444$	2.55894	+	3.26401i	0.121442	+	0.154903i
$445$		0			0
$446$	−11.1120			−0.526167
$447$	20.2500	+	25.8295i	0.957791	+	1.22170i
$448$	0.294447	+	2.62932i	0.0139113	+	0.124223i
$449$		−	32.3439i		−	1.52640i	−0.646162	−	0.763201i	$-0.723627\pi$
$449$		−	32.3439i		−	1.52640i	0.646162	−	0.763201i	$-0.276373\pi$
$450$		0			0
$451$			15.9644i			0.751734i
$452$	−14.3439			−0.674679
$453$	7.16797	−	5.61959i	0.336781	−	0.264031i
$454$			7.24413i			0.339984i
$455$		0			0
$456$	−2.91330	−	3.71601i	−0.136428	−	0.174018i
$457$		−	10.9251i		−	0.511054i	−0.966802	−	0.255527i	$-0.917751\pi$
$457$		−	10.9251i		−	0.511054i	0.966802	−	0.255527i	$-0.0822490\pi$
$458$		−	27.1596i		−	1.26909i
$459$	−12.3093	+	5.55472i	−0.574551	+	0.259272i
$460$		0			0
$461$	26.6729			1.24228			0.621139	−	0.783700i	$-0.286670\pi$
$461$	26.6729			1.24228			0.621139	+	0.783700i	$0.286670\pi$
$462$	−4.68178	+	4.59846i	−0.217816	+	0.213940i
$463$		−	8.07491i		−	0.375273i	−0.982239	−	0.187637i	$-0.939917\pi$
$463$		−	8.07491i		−	0.375273i	0.982239	−	0.187637i	$-0.0600827\pi$
$464$			2.82660i			0.131222i
$465$		0			0
$466$	−5.38132			−0.249285
$467$		−	41.6228i		−	1.92607i	−0.269371	−	0.963037i	$-0.586816\pi$
$467$		−	41.6228i		−	1.92607i	0.269371	−	0.963037i	$-0.413184\pi$
$468$	3.39122	−	13.7981i	0.156759	−	0.637818i
$469$	25.8372	−	2.89341i	1.19305	−	0.133605i
$470$		0			0
$471$	8.58154	−	6.72780i	0.395416	−	0.310001i
$472$	−10.7775			−0.496074
$473$	−0.618679			−0.0284469
$474$	−22.5145	+	17.6510i	−1.03412	+	0.810738i
$475$		0			0
$476$	6.83350	−	0.765257i	0.313213	−	0.0350755i
$477$	−4.07460	+	16.5786i	−0.186563	+	0.759082i
$478$			2.51726i			0.115137i
$479$	−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
$482$		−	16.8077i		−	0.765570i
$483$	−9.07664	−	9.24109i	−0.413002	−	0.420484i
$484$	8.94929			0.406786
$485$		0			0
$486$	−15.3284	+	2.83532i	−0.695312	+	0.128613i
$487$			27.1094i			1.22845i	0.789133	+	0.614223i	$0.210530\pi$
$487$			27.1094i			1.22845i	−0.789133	+	0.614223i	$0.789470\pi$
$488$			1.05058i			0.0475574i
$489$	−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	$0.763305\pi$
$492$	15.1958	−	11.9133i	0.685081	−	0.537093i
$493$	7.34624			0.330858
$494$		−	12.9118i		−	0.580931i
$495$		0			0
$496$			5.91403i			0.265548i
$497$	−34.8611	+	3.90396i	−1.56374	+	0.175117i
$498$	−13.8012	−	17.6040i	−0.618449	−	0.788852i
$499$	−8.50694			−0.380823			−0.190412	−	0.981704i	$-0.560982\pi$
$499$	−8.50694			−0.380823			−0.190412	+	0.981704i	$0.560982\pi$
$500$		0			0
$501$	12.9118	+	16.4695i	0.576858	+	0.735802i
$502$	−1.75565			−0.0783586
$503$		−	12.1625i		−	0.542301i	−0.962537	−	0.271150i	$-0.912596\pi$
$503$		−	12.1625i		−	0.542301i	0.962537	−	0.271150i	$-0.0874041\pi$
$504$	7.87082	+	1.02482i	0.350594	+	0.0456489i
$505$		0			0
$506$		−	4.04778i		−	0.179946i
$507$	12.8567	−	10.0794i	0.570985	−	0.447644i
$508$			2.00000i			0.0887357i
$509$	−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
$512$	1.00000			0.0441942
$513$	−12.9118	+	5.82660i	−0.570071	+	0.257251i
$514$		−	21.9366i		−	0.967582i
$515$		0			0
$516$	0.461684	+	0.588894i	0.0203245	+	0.0259246i
$517$	14.7725			0.649695
$518$	−6.29609	+	0.705074i	−0.276634	+	0.0309792i
$519$	16.5786	+	21.1466i	0.727720	+	0.928232i
$520$		0			0
$521$	32.7031			1.43275			0.716374	−	0.697717i	$-0.245801\pi$
$521$	32.7031			1.43275			0.716374	+	0.697717i	$0.245801\pi$
$522$	8.23474	+	2.02389i	0.360425	+	0.0885832i
$523$	−28.5557			−1.24865			−0.624327	−	0.781163i	$-0.714627\pi$
$523$	−28.5557			−1.24865			−0.624327	+	0.781163i	$0.714627\pi$
$524$	−17.2804			−0.754899
$525$		0			0
$526$	4.08523			0.178125
$527$	15.3704			0.669544
$528$	1.53032	+	1.95198i	0.0665988	+	0.0849491i
$529$	−15.0103			−0.652623
$530$		0			0
$531$	−7.71684	+	31.3981i	−0.334882	+	1.36256i
$532$	7.16797	−	0.802714i	0.310771	−	0.0348020i
$533$	52.8001			2.28703
$534$	−5.32144	+	4.17193i	−0.230281	+	0.180537i
$535$		0			0
$536$		−	9.82660i		−	0.424445i
$537$	4.88152	+	6.22654i	0.210653	+	0.268695i
$538$	6.96461			0.300266
$539$	−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	$0.763847\pi$
$542$		−	23.4740i		−	1.00829i
$543$	−8.34386	−	10.6429i	−0.358070	−	0.456730i
$544$		−	2.59897i		−	0.111430i
$545$		0			0
$546$	15.2088	+	15.4843i	0.650876	+	0.662669i
$547$			26.7759i			1.14485i	0.819955	+	0.572427i	$0.193998\pi$
$547$			26.7759i			1.14485i	−0.819955	+	0.572427i	$0.806002\pi$
$548$	−3.03746			−0.129754
$549$	3.06065	+	0.752229i	0.130625	+	0.0321044i
$550$		0			0
$551$	7.70581			0.328279
$552$	−3.85291	+	3.02062i	−0.163991	+	0.128566i
$553$	−4.86346	−	43.4291i	−0.206815	−	1.84679i
$554$		−	14.1227i		−	0.600016i
$555$		0			0
$556$			20.7478i			0.879902i
$557$	40.4158			1.71247			0.856237	−	0.516583i	$-0.172796\pi$
$557$	40.4158			1.71247			0.856237	+	0.516583i	$0.172796\pi$
$558$	17.2294	+	4.23453i	0.729377	+	0.179262i
$559$			2.04620i			0.0865449i
$560$		0			0
$561$	5.07313	−	3.97726i	0.214188	−	0.167920i
$562$			23.6532i			0.997750i
$563$		−	8.16750i		−	0.344219i	−0.985078	−	0.172109i	$-0.944942\pi$
$563$		−	8.16750i		−	0.344219i	0.985078	−	0.172109i	$-0.0550583\pi$
$564$	−11.0239	−	14.0613i	−0.464189	−	0.592089i
$565$		0			0
$566$	0.807187			0.0339286
$567$	8.62122	−	22.1963i	0.362057	−	0.932156i
$568$			13.2586i			0.556320i
$569$		−	15.0375i		−	0.630403i	−0.949025	−	0.315201i	$-0.897928\pi$
$569$		−	15.0375i		−	0.630403i	0.949025	−	0.315201i	$-0.102072\pi$
$570$		0			0
$571$	38.6025			1.61546			0.807732	−	0.589550i	$-0.200695\pi$
$571$	38.6025			1.61546			0.807732	+	0.589550i	$0.200695\pi$
$572$			6.78244i			0.283588i
$573$	7.71684	+	9.84309i	0.322376	+	0.411201i
$574$	3.28252	+	29.3118i	0.137010	+	1.22345i
$575$		0			0
$576$	0.716015	−	2.91330i	0.0298339	−	0.121388i
$577$	23.9467			0.996913			0.498457	−	0.866915i	$-0.333900\pi$
$577$	23.9467			0.996913			0.498457	+	0.866915i	$0.333900\pi$
$578$	10.2454			0.426152
$579$	−8.12434	−	10.3629i	−0.337636	−	0.430666i
$580$		0			0
$581$	33.9570	−	3.80271i	1.40877	−	0.157763i
$582$	−19.0852	+	14.9625i	−0.791108	+	0.620217i
$583$		−	8.14919i		−	0.337505i
$584$	7.58963			0.314061
$585$		0			0
$586$			14.6704i			0.606030i
$587$			17.9305i			0.740072i	0.929017	+	0.370036i	$0.120655\pi$
$587$			17.9305i			0.740072i	−0.929017	+	0.370036i	$0.879345\pi$
$588$	−7.65059	+	9.40577i	−0.315505	+	0.387887i
$589$	16.1227			0.664324
$590$		0			0
$591$	29.6314	−	23.2306i	1.21887	−	0.955578i
$592$			2.39457i			0.0984163i
$593$			18.5744i			0.762759i	0.924419	+	0.381379i	$0.124551\pi$
$593$			18.5744i			0.762759i	−0.924419	+	0.381379i	$0.875449\pi$
$594$	6.78244	−	3.06065i	0.278287	−	0.125580i
$595$		0			0
$596$			18.9493i			0.776193i
$597$	6.45592	+	8.23474i	0.264223	+	0.337026i
$598$	−13.3875			−0.547455
$599$			29.3439i			1.19896i	0.800391	+	0.599479i	$0.204625\pi$
$599$			29.3439i			1.19896i	−0.800391	+	0.599479i	$0.795375\pi$
$600$		0			0
$601$			22.5145i			0.918385i	0.888337	+	0.459192i	$0.151861\pi$
$601$			22.5145i			0.918385i	−0.888337	+	0.459192i	$0.848139\pi$
$602$	−1.13594	+	0.127210i	−0.0462975	+	0.00518468i
$603$	−28.6279	−	7.03599i	−1.16582	−	0.286528i
$604$	5.25863			0.213971
$605$		0			0
$606$	−14.0613	+	11.0239i	−0.571203	+	0.447815i
$607$	17.5128			0.710822			0.355411	−	0.934710i	$-0.384341\pi$
$607$	17.5128			0.710822			0.355411	+	0.934710i	$0.384341\pi$
$608$		−	2.72617i		−	0.110561i
$609$	−9.24109	+	9.07664i	−0.374468	+	0.367804i
$610$		0			0
$611$		−	48.8582i		−	1.97659i
$612$	−7.57157	−	1.86090i	−0.306062	−	0.0752223i
$613$			32.7626i			1.32327i	0.749826	+	0.661635i	$0.230137\pi$
$613$			32.7626i			1.32327i	−0.749826	+	0.661635i	$0.769863\pi$
$614$	−10.0975			−0.407502
$615$		0			0
$616$	−3.76526	+	0.421657i	−0.151707	+	0.0169890i
$617$	0.693592			0.0279229			0.0139615	−	0.999903i	$-0.495556\pi$
$617$	0.693592			0.0279229			0.0139615	+	0.999903i	$0.495556\pi$
$618$	−18.9118	+	14.8266i	−0.760746	+	0.596413i
$619$			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
$622$	4.27456			0.171394
$623$	−1.14951	−	10.2647i	−0.0460541	−	0.411248i
$624$	6.45592	−	5.06134i	0.258444	−	0.202616i
$625$		0			0
$626$	0.923368			0.0369052
$627$	5.32144	−	4.17193i	0.212518	−	0.166611i
$628$	6.29566			0.251224
$629$	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	$0.553437\pi$
$632$	−16.5173			−0.657021
$633$	22.8670	−	17.9274i	0.908882	−	0.712550i
$634$	−15.7384			−0.625053
$635$		0			0
$636$	−7.75687	+	6.08127i	−0.307580	+	0.241138i
$637$	−32.3325	+	7.33354i	−1.28106	+	0.290566i
$638$	−4.04778			−0.160253
$639$	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	$-0.154709\pi$
$642$	21.7403	−	17.0441i	0.858020	−	0.672675i
$643$	2.60999			0.102928			0.0514641	−	0.998675i	$-0.483611\pi$
$643$	2.60999			0.102928			0.0514641	+	0.998675i	$0.483611\pi$
$644$	−0.832284	−	7.43203i	−0.0327966	−	0.292863i
$645$		0			0
$646$	−7.08523			−0.278765
$647$			4.45673i			0.175212i	0.996155	+	0.0876061i	$0.0279217\pi$
$647$			4.45673i			0.175212i	−0.996155	+	0.0876061i	$0.972078\pi$
$648$	−7.97465	−	4.17193i	−0.313274	−	0.163889i
$649$		−	15.4337i		−	0.605825i
$650$		0			0
$651$	−19.3349	+	18.9909i	−0.757795	+	0.744310i
$652$		−	0.605427i		−	0.0237104i
$653$	30.9118			1.20967			0.604837	−	0.796349i	$-0.293238\pi$
$653$	30.9118			1.20967			0.604837	+	0.796349i	$0.293238\pi$
$654$	14.7065	−	11.5297i	0.575072	−	0.450848i
$655$		0			0
$656$	11.1481			0.435260
$657$	5.43429	−	22.1109i	0.212012	−	0.862628i
$658$	27.1235	−	3.03746i	1.05738	−	0.118412i
$659$			4.56797i			0.177943i	0.996034	+	0.0889714i	$0.0283580\pi$
$659$			4.56797i			0.177943i	−0.996034	+	0.0889714i	$0.971642\pi$
$660$		0			0
$661$		−	38.0643i		−	1.48053i	−0.672315	−	0.740266i	$-0.734700\pi$
$661$		−	38.0643i		−	1.48053i	0.672315	−	0.740266i	$-0.265300\pi$
$662$	−12.6054			−0.489924
$663$	−13.1543	−	16.7787i	−0.510869	−	0.651631i
$664$		−	12.9148i		−	0.501190i
$665$		0			0
$666$	6.97611	+	1.71455i	0.270319	+	0.0664374i
$667$		−	7.98968i		−	0.309362i
$668$			12.0825i			0.467485i
$669$	−15.1466	+	11.8747i	−0.585601	+	0.459102i
$670$		0			0
$671$	−1.50446			−0.0580790
$672$	3.21115	+	3.26933i	0.123873	+	0.126117i
$673$			21.2212i			0.818016i	0.912531	+	0.409008i	$0.134125\pi$
$673$			21.2212i			0.818016i	−0.912531	+	0.409008i	$0.865875\pi$
$674$		−	18.8986i		−	0.727946i
$675$		0			0
$676$	9.43203			0.362770
$677$		−	3.53336i		−	0.135798i	−0.997692	−	0.0678991i	$-0.978370\pi$
$677$		−	3.53336i		−	0.135798i	0.997692	−	0.0678991i	$-0.0216296\pi$
$678$	−19.5519	+	15.3284i	−0.750888	+	0.588685i
$679$	−4.12269	−	36.8143i	−0.158214	−	1.41280i
$680$		0			0
$681$	7.74137	+	9.87438i	0.296650	+	0.378387i
$682$	−8.46907			−0.324297
$683$	−1.70391			−0.0651984			−0.0325992	−	0.999469i	$-0.510378\pi$
$683$	−1.70391			−0.0651984			−0.0325992	+	0.999469i	$0.510378\pi$
$684$	−7.94217	−	1.95198i	−0.303676	−	0.0746359i
$685$		0			0
$686$	−6.08127	−	17.4934i	−0.232184	−	0.667900i
$687$	−29.0239	−	37.0210i	−1.10733	−	1.41244i
$688$			0.432029i			0.0164710i
$689$	−26.9524			−1.02680
$690$		0			0
$691$			2.21734i			0.0843514i	0.999110	+	0.0421757i	$0.0134289\pi$
$691$			2.21734i			0.0843514i	−0.999110	+	0.0421757i	$0.986571\pi$
$692$			15.5137i			0.589744i
$693$	−1.46757	+	11.2712i	−0.0557483	+	0.428159i
$694$	−30.7384			−1.16682
$695$		0			0
$696$	3.02062	+	3.85291i	0.114496	+	0.146044i
$697$		−	28.9735i		−	1.09745i
$698$			0.970523i			0.0367348i
$699$	−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	$-0.0187644\pi$
$702$	−10.1227	−	22.4320i	−0.382056	−	0.846642i
$703$	6.52802			0.246209
$704$			1.43203i			0.0539716i
$705$		0			0
$706$			16.3570i			0.615606i
$707$	−3.03746	−	27.1235i	−0.114235	−	1.02008i
$708$	−14.6907	+	11.5173i	−0.552109	+	0.432845i
$709$	−12.8641			−0.483120			−0.241560	−	0.970386i	$-0.577659\pi$
$709$	−12.8641			−0.483120			−0.241560	+	0.970386i	$0.577659\pi$
$710$		0			0
$711$	−11.8266	+	48.1198i	−0.443532	+	1.80463i
$712$	−3.90396			−0.146307
$713$		−	16.7166i		−	0.626042i
$714$	8.49687	−	8.34567i	0.317987	−	0.312329i
$715$		0			0
$716$			4.56797i			0.170713i
$717$	2.69005	+	3.43125i	0.100462	+	0.128142i
$718$		−	9.81335i		−	0.366231i
$719$	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
$722$	11.5680			0.430515
$723$	−17.9614	−	22.9104i	−0.667991	−	0.852046i
$724$		−	7.80792i		−	0.290179i
$725$		0			0
$726$	12.1987	−	9.56358i	0.452735	−	0.354938i
$727$	18.9921			0.704379			0.352190	−	0.935929i	$-0.385437\pi$
$727$	18.9921			0.704379			0.352190	+	0.935929i	$0.385437\pi$
$728$	1.39457	+	12.4531i	0.0516863	+	0.461542i
$729$	−17.8641	+	20.2454i	−0.661632	+	0.749829i
$730$		0			0
$731$	1.12283			0.0415293
$732$	1.12269	+	1.43203i	0.0414958	+	0.0529293i
$733$	27.1345			1.00224			0.501119	−	0.865379i	$-0.332922\pi$
$733$	27.1345			1.00224			0.501119	+	0.865379i	$0.332922\pi$
$734$	33.9970			1.25485
$735$		0			0
$736$	−2.82660			−0.104190
$737$	14.0720			0.518348
$738$	7.98220	−	32.4777i	0.293829	−	1.19552i
$739$	−8.67741			−0.319204			−0.159602	−	0.987181i	$-0.551021\pi$
$739$	−8.67741			−0.319204			−0.159602	+	0.987181i	$0.551021\pi$
$740$		0			0
$741$	−13.7981	−	17.6000i	−0.506886	−	0.646551i
$742$	−1.67560	−	14.9625i	−0.0615131	−	0.549292i
$743$	52.5754			1.92880			0.964401	−	0.264443i	$-0.0851879\pi$
$743$	52.5754			1.92880			0.964401	+	0.264443i	$0.0851879\pi$
$744$	6.31998	+	8.06134i	0.231702	+	0.295543i
$745$		0			0
$746$		−	26.5650i		−	0.972615i
$747$	−37.6246	−	9.24717i	−1.37661	−	0.338336i
$748$	3.72179			0.136082
$749$	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	$0.489684\pi$
$752$		−	10.3158i		−	0.376179i
$753$	−2.39311	+	1.87616i	−0.0872097	+	0.0683711i
$754$			13.3875i			0.487543i
$755$		0			0
$756$	11.8238	−	7.01416i	0.430026	−	0.255103i
$757$			4.63995i			0.168642i	0.996439	+	0.0843210i	$0.0268721\pi$
$757$			4.63995i			0.168642i	−0.996439	+	0.0843210i	$0.973128\pi$
$758$	−8.25863			−0.299967
$759$	−4.32562	−	5.51747i	−0.157010	−	0.200272i
$760$		0			0
$761$	−40.6884			−1.47495			−0.737477	−	0.675373i	$-0.763983\pi$
$761$	−40.6884			−1.47495			−0.737477	+	0.675373i	$0.763983\pi$
$762$	2.13728	+	2.72617i	0.0774255	+	0.0987589i
$763$	3.17683	+	28.3681i	0.115009	+	1.02699i
$764$			7.22117i			0.261253i
$765$		0			0
$766$		−	32.6920i		−	1.18121i
$767$	−51.0448			−1.84312
$768$	1.36309	−	1.06864i	0.0491862	−	0.0385612i
$769$		−	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
$772$		−	7.60250i		−	0.273620i
$773$			28.4175i			1.02211i	0.859549	+	0.511053i	$0.170744\pi$
$773$			28.4175i			1.02211i	−0.859549	+	0.511053i	$0.829256\pi$
$774$	1.25863	+	0.309339i	0.0452406	+	0.0111190i
$775$		0			0
$776$	−14.0015			−0.502624
$777$	−7.82865	+	7.68933i	−0.280851	+	0.275853i
$778$			1.33354i			0.0478099i
$779$		−	30.3916i		−	1.08889i
$780$		0			0
$781$	−18.9867			−0.679399
$782$			7.34624i			0.262701i
$783$	13.3875	−	6.04124i	0.478430	−	0.215896i
$784$	−6.82660	+	1.54839i	−0.243807	+	0.0552996i
$785$		0			0
$786$	−23.5547	+	18.4666i	−0.840169	+	0.658680i
$787$	−41.6778			−1.48565			−0.742826	−	0.669485i	$-0.766515\pi$
$787$	−41.6778			−1.48565			−0.742826	+	0.669485i	$0.766515\pi$
$788$	21.7384			0.774400
$789$	5.56853	−	4.36565i	0.198245	−	0.155421i
$790$		0			0
$791$	−4.22351	−	37.7145i	−0.150171	−	1.34097i
$792$	4.17193	+	1.02535i	0.148243	+	0.0364344i
$793$			4.97579i			0.176696i
$794$	23.0123			0.816675
$795$		0			0
$796$			6.04124i			0.214126i
$797$			10.2137i			0.361788i	0.983503	+	0.180894i	$0.0578990\pi$
$797$			10.2137i			0.361788i	−0.983503	+	0.180894i	$0.942101\pi$
$798$	8.91276	−	8.75416i	0.315508	−	0.309894i
$799$	−26.8104			−0.948484
$800$		0			0
$801$	−2.79529	+	11.3734i	−0.0987669	+	0.401860i
$802$			17.5547i			0.619879i
$803$			10.8686i			0.383544i
$804$	−10.5011	−	13.3945i	−0.370345	−	0.472388i
$805$		0			0
$806$			28.0103i			0.986621i
$807$	9.49337	−	7.44267i	0.334183	−	0.261994i
$808$	−10.3158			−0.362909
$809$		−	40.0691i		−	1.40875i	−0.709827	−	0.704376i	$-0.751227\pi$
$809$		−	40.0691i		−	1.40875i	0.709827	−	0.704376i	$-0.248773\pi$
$810$		0			0
$811$			34.8875i			1.22507i	0.790445	+	0.612533i	$0.209849\pi$
$811$			34.8875i			1.22507i	−0.790445	+	0.612533i	$0.790151\pi$
$812$	−7.43203	+	0.832284i	−0.260813	+	0.0292074i
$813$	−25.0852	−	31.9971i	−0.879778	−	1.12219i
$814$	−3.42910			−0.120190
$815$		0			0
$816$	−2.77736	−	3.54262i	−0.0972270	−	0.124016i
$817$	1.17779			0.0412056
$818$			9.94521i			0.347726i
$819$	37.2781	+	4.85378i	1.30260	+	0.169605i
$820$		0			0
$821$			33.4291i			1.16668i	0.812227	+	0.583342i	$0.198255\pi$
$821$			33.4291i			1.16668i	−0.812227	+	0.583342i	$0.801745\pi$
$822$	−4.14032	+	3.24595i	−0.144410	+	0.113215i
$823$			20.7414i			0.722999i	0.932372	+	0.361499i	$0.117735\pi$
$823$			20.7414i			0.722999i	−0.932372	+	0.361499i	$0.882265\pi$
$824$	−13.8743			−0.483333
$825$		0			0
$826$	−3.17340	−	28.3374i	−0.110417	−	0.985985i
$827$	41.8479			1.45519			0.727597	−	0.686005i	$-0.240637\pi$
$827$	41.8479			1.45519			0.727597	+	0.686005i	$0.240637\pi$
$828$	−2.02389	+	8.23474i	−0.0703350	+	0.286177i
$829$			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
$832$	4.73625			0.164200
$833$	4.02421	+	17.7421i	0.139430	+	0.614727i
$834$	22.1719	+	28.2811i	0.767751	+	0.979293i
$835$		0			0
$836$	3.90396			0.135021
$837$	28.0103	−	12.6400i	0.968178	−	0.436901i
$838$	7.71684			0.266574
$839$	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
$842$	11.2109			0.386352
$843$	25.2768	+	32.2414i	0.870578	+	1.11045i
$844$	16.7759			0.577450
$845$		0			0
$846$	−30.0530	−	7.38627i	−1.03325	−	0.253945i
$847$	2.63509	+	23.5305i	0.0905428	+	0.808518i
$848$	−5.69066			−0.195418
$849$	1.10027	−	0.862593i	0.0377611	−	0.0296041i
$850$		0			0
$851$		−	6.76850i		−	0.232021i
$852$	14.1687	+	18.0727i	0.485412	+	0.619160i
$853$	−2.22837			−0.0762978			−0.0381489	−	0.999272i	$-0.512146\pi$
$853$	−2.22837			−0.0762978			−0.0381489	+	0.999272i	$0.512146\pi$
$854$	−2.76230	+	0.309339i	−0.0945240	+	0.0105854i
$855$		0			0
$856$	15.9493			0.545136
$857$		−	5.75070i		−	0.196440i	−0.995165	−	0.0982201i	$-0.968685\pi$
$857$		−	5.75070i		−	0.196440i	0.995165	−	0.0982201i	$-0.0313149\pi$
$858$	7.24799	+	9.24506i	0.247442	+	0.315621i
$859$			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
$861$	35.7982	+	36.4468i	1.22000	+	1.24210i
$862$		−	26.2079i		−	0.892645i
$863$	−17.5783			−0.598372			−0.299186	−	0.954195i	$-0.596715\pi$
$863$	−17.5783			−0.598372			−0.299186	+	0.954195i	$0.596715\pi$
$864$	−2.13728	−	4.73625i	−0.0727118	−	0.161130i
$865$		0			0
$866$	23.4378			0.796450
$867$	13.9653	−	10.9486i	0.474288	−	0.371835i
$868$	−15.5499	+	1.74137i	−0.527797	+	0.0591059i
$869$		−	23.6532i		−	0.802380i
$870$		0			0
$871$		−	46.5412i		−	1.57699i
$872$	10.7891			0.365367
$873$	−10.0253	+	40.7905i	−0.339304	+	1.38055i
$874$			7.70581i			0.260653i
$875$		0			0
$876$	10.3453	−	8.11059i	0.349536	−	0.274031i
$877$		−	41.8237i		−	1.41229i	−0.708070	−	0.706143i	$-0.750434\pi$
$877$		−	41.8237i		−	1.41229i	0.708070	−	0.706143i	$-0.249566\pi$
$878$		−	25.0334i		−	0.844836i
$879$	15.6774	+	19.9971i	0.528786	+	0.674484i
$880$		0			0
$881$	−27.8757			−0.939158			−0.469579	−	0.882891i	$-0.655594\pi$
$881$	−27.8757			−0.939158			−0.469579	+	0.882891i	$0.655594\pi$
$882$	−0.377028	+	20.9966i	−0.0126952	+	0.706993i
$883$			11.6400i			0.391716i	0.980632	+	0.195858i	$0.0627491\pi$
$883$			11.6400i			0.391716i	−0.980632	+	0.195858i	$0.937251\pi$
$884$		−	12.3093i		−	0.414008i
$885$		0			0
$886$	18.4666			0.620396
$887$			38.7333i			1.30054i	0.759705	+	0.650268i	$0.225343\pi$
$887$			38.7333i			1.30054i	−0.759705	+	0.650268i	$0.774657\pi$
$888$	2.55894	+	3.26401i	0.0858723	+	0.109533i
$889$	−5.25863	+	0.588894i	−0.176369	+	0.0197509i
$890$		0			0
$891$	5.97433	−	11.4199i	0.200148	−	0.382582i
$892$	−11.1120			−0.372056
$893$	−28.1227			−0.941090
$894$	20.2500	+	25.8295i	0.677261	+	0.863869i
$895$		0			0
$896$	0.294447	+	2.62932i	0.00983678	+	0.0878393i
$897$	−18.2483	+	14.3064i	−0.609293	+	0.477677i
$898$		−	32.3439i		−	1.07933i
$899$	−16.7166			−0.557530
$900$		0			0
$901$			14.7898i			0.492721i
$902$			15.9644i			0.531556i
$903$	−1.41245	+	1.38731i	−0.0470033	+	0.0461668i
$904$	−14.3439			−0.477070
$905$		0			0
$906$	7.16797	−	5.61959i	0.238140	−	0.186698i
$907$			18.7730i			0.623346i	0.950189	+	0.311673i	$0.100889\pi$
$907$			18.7730i			0.623346i	−0.950189	+	0.311673i	$0.899111\pi$
$908$			7.24413i			0.240405i
$909$	−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	$-0.0197255\pi$
$912$	−2.91330	−	3.71601i	−0.0964690	−	0.123050i
$913$	18.4943			0.612073
$914$		−	10.9251i		−	0.361370i
$915$		0			0
$916$		−	27.1596i		−	0.897380i
$917$	−5.08816	−	45.4357i	−0.168026	−	1.50042i
$918$	−12.3093	+	5.55472i	−0.406269	+	0.183333i
$919$	−24.4423			−0.806279			−0.403139	−	0.915139i	$-0.632081\pi$
$919$	−24.4423			−0.806279			−0.403139	+	0.915139i	$0.632081\pi$
$920$		0			0
$921$	−13.7638	+	10.7906i	−0.453532	+	0.355563i
$922$	26.6729			0.878424
$923$			62.7961i			2.06696i
$924$	−4.68178	+	4.59846i	−0.154019	+	0.151278i
$925$		0			0
$926$		−	8.07491i		−	0.265358i
$927$	−9.93418	+	40.4199i	−0.326281	+	1.32756i
$928$			2.82660i			0.0927878i
$929$	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
$932$	−5.38132			−0.176271
$933$	5.82660	−	4.56797i	0.190754	−	0.149549i
$934$		−	41.6228i		−	1.36194i
$935$		0			0
$936$	3.39122	−	13.7981i	0.110846	−	0.451005i
$937$	−13.2241			−0.432014			−0.216007	−	0.976392i	$-0.569303\pi$
$937$	−13.2241			−0.432014			−0.216007	+	0.976392i	$0.569303\pi$
$938$	25.8372	−	2.89341i	0.843616	−	0.0944733i
$939$	1.25863	−	0.986749i	0.0410739	−	0.0322013i
$940$		0			0
$941$	−29.3408			−0.956484			−0.478242	−	0.878228i	$-0.658726\pi$
$941$	−29.3408			−0.956484			−0.478242	+	0.878228i	$0.658726\pi$
$942$	8.58154	−	6.72780i	0.279602	−	0.219204i
$943$	−31.5112			−1.02615
$944$	−10.7775			−0.350777
$945$		0			0
$946$	−0.618679			−0.0201150
$947$	−47.1094			−1.53085			−0.765426	−	0.643524i	$-0.777471\pi$
$947$	−47.1094			−1.53085			−0.765426	+	0.643524i	$0.777471\pi$
$948$	−22.5145	+	17.6510i	−0.731236	+	0.573278i
$949$	35.9464			1.16687
$950$		0			0
$951$	−21.4529	+	16.8187i	−0.695657	+	0.545385i
$952$	6.83350	−	0.765257i	0.221475	−	0.0248021i
$953$	20.8876			0.676617			0.338308	−	0.941035i	$-0.390145\pi$
$953$	20.8876			0.676617			0.338308	+	0.941035i	$0.390145\pi$
$954$	−4.07460	+	16.5786i	−0.131920	+	0.536752i
$955$		0			0
$956$			2.51726i			0.0814141i
$957$	−5.51747	+	4.32562i	−0.178355	+	0.139827i
$958$	−21.3728			−0.690524
$959$	−0.894369	−	7.98643i	−0.0288807	−	0.257895i
$960$		0			0
$961$	−3.97579			−0.128251
$962$			11.3413i			0.365658i
$963$	11.4199	−	46.4651i	0.368002	−	1.49732i
$964$		−	16.8077i		−	0.541340i
$965$		0			0
$966$	−9.07664	−	9.24109i	−0.292036	−	0.297327i
$967$			27.3335i			0.878988i	0.898246	+	0.439494i	$0.144842\pi$
$967$			27.3335i			0.878988i	−0.898246	+	0.439494i	$0.855158\pi$
$968$	8.94929			0.287641
$969$	−9.65779	+	7.57157i	−0.310253	+	0.243234i
$970$		0			0
$971$	24.4555			0.784815			0.392407	−	0.919791i	$-0.371642\pi$
$971$	24.4555			0.784815			0.392407	+	0.919791i	$0.371642\pi$
$972$	−15.3284	+	2.83532i	−0.491660	+	0.0909430i
$973$	−54.5525	+	6.10912i	−1.74887	+	0.195849i
$974$			27.1094i			0.868642i
$975$		0			0
$976$			1.05058i			0.0336282i
$977$	−15.1124			−0.483488			−0.241744	−	0.970340i	$-0.577719\pi$
$977$	−15.1124			−0.483488			−0.241744	+	0.970340i	$0.577719\pi$
$978$	−0.646984	−	0.825250i	−0.0206883	−	0.0263886i
$979$		−	5.59059i		−	0.178676i
$980$		0			0
$981$	7.72519	−	31.4320i	0.246646	−	1.00355i
$982$			30.0000i			0.957338i
$983$		−	13.6670i		−	0.435910i	−0.975959	−	0.217955i	$-0.930061\pi$
$983$		−	13.6670i		−	0.435910i	0.975959	−	0.217955i	$-0.0699385\pi$
$984$	15.1958	−	11.9133i	0.484425	−	0.379782i
$985$		0			0
$986$	7.34624			0.233952
$987$	33.7258	−	33.1256i	1.07350	−	1.05440i
$988$		−	12.9118i		−	0.410780i
$989$		−	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	$0.517479\pi$
$992$			5.91403i			0.187771i
$993$	−17.1823	+	13.4707i	−0.545264	+	0.427479i
$994$	−34.8611	+	3.90396i	−1.10573	+	0.123826i
$995$		0			0
$996$	−13.8012	−	17.6040i	−0.437309	−	0.557803i
$997$	−40.4199			−1.28011			−0.640056	−	0.768329i	$-0.721089\pi$
$997$	−40.4199			−1.28011			−0.640056	+	0.768329i	$0.721089\pi$
$998$	−8.50694			−0.269283
$999$	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.d.h.1049.9		12
3.2	odd	2		1050.2.d.g.1049.10		12
5.2	odd	4		1050.2.b.e.251.8	yes	12
5.3	odd	4		1050.2.b.d.251.5	yes	12
5.4	even	2		1050.2.d.g.1049.4		12
7.6	odd	2	inner	1050.2.d.h.1049.4		12
15.2	even	4		1050.2.b.e.251.5	yes	12
15.8	even	4		1050.2.b.d.251.8	yes	12
15.14	odd	2	inner	1050.2.d.h.1049.3		12
21.20	even	2		1050.2.d.g.1049.3		12
35.13	even	4		1050.2.b.d.251.2	✓	12
35.27	even	4		1050.2.b.e.251.11	yes	12
35.34	odd	2		1050.2.d.g.1049.9		12
105.62	odd	4		1050.2.b.e.251.2	yes	12
105.83	odd	4		1050.2.b.d.251.11	yes	12
105.104	even	2	inner	1050.2.d.h.1049.10		12

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.36309 - 1.06864i) q^{3} +1.00000 q^{4} +(1.36309 - 1.06864i) q^{6} +(0.294447 + 2.62932i) q^{7} +1.00000 q^{8} +(0.716015 - 2.91330i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.36309 - 1.06864i) q^{3} +1.00000 q^{4} +(1.36309 - 1.06864i) q^{6} +(0.294447 + 2.62932i) q^{7} +1.00000 q^{8} +(0.716015 - 2.91330i) q^{9} +1.43203i q^{11} +(1.36309 - 1.06864i) q^{12} +4.73625 q^{13} +(0.294447 + 2.62932i) q^{14} +1.00000 q^{16} -2.59897i q^{17} +(0.716015 - 2.91330i) q^{18} -2.72617i q^{19} +(3.21115 + 3.26933i) q^{21} +1.43203i q^{22} -2.82660 q^{23} +(1.36309 - 1.06864i) q^{24} +4.73625 q^{26} +(-2.13728 - 4.73625i) q^{27} +(0.294447 + 2.62932i) q^{28} +2.82660i q^{29} +5.91403i q^{31} +1.00000 q^{32} +(1.53032 + 1.95198i) q^{33} -2.59897i q^{34} +(0.716015 - 2.91330i) q^{36} +2.39457i q^{37} -2.72617i q^{38} +(6.45592 - 5.06134i) q^{39} +11.1481 q^{41} +(3.21115 + 3.26933i) q^{42} +0.432029i q^{43} +1.43203i q^{44} -2.82660 q^{46} -10.3158i q^{47} +(1.36309 - 1.06864i) q^{48} +(-6.82660 + 1.54839i) q^{49} +(-2.77736 - 3.54262i) q^{51} +4.73625 q^{52} -5.69066 q^{53} +(-2.13728 - 4.73625i) q^{54} +(0.294447 + 2.62932i) q^{56} +(-2.91330 - 3.71601i) q^{57} +2.82660i q^{58} -10.7775 q^{59} +1.05058i q^{61} +5.91403i q^{62} +(7.87082 + 1.02482i) q^{63} +1.00000 q^{64} +(1.53032 + 1.95198i) q^{66} -9.82660i q^{67} -2.59897i q^{68} +(-3.85291 + 3.02062i) q^{69} +13.2586i q^{71} +(0.716015 - 2.91330i) q^{72} +7.58963 q^{73} +2.39457i q^{74} -2.72617i q^{76} +(-3.76526 + 0.421657i) q^{77} +(6.45592 - 5.06134i) q^{78} -16.5173 q^{79} +(-7.97465 - 4.17193i) q^{81} +11.1481 q^{82} -12.9148i q^{83} +(3.21115 + 3.26933i) q^{84} +0.432029i q^{86} +(3.02062 + 3.85291i) q^{87} +1.43203i q^{88} -3.90396 q^{89} +(1.39457 + 12.4531i) q^{91} -2.82660 q^{92} +(6.31998 + 8.06134i) q^{93} -10.3158i q^{94} +(1.36309 - 1.06864i) q^{96} -14.0015 q^{97} +(-6.82660 + 1.54839i) q^{98} +(4.17193 + 1.02535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{4} + 12 q^{8}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^4 + 12 * q^8	\( 12 q + 12 q^{2} + 12 q^{4} + 12 q^{8} + 12 q^{16} + 14 q^{21} + 20 q^{23} + 12 q^{32} - 12 q^{39} + 14 q^{42} + 20 q^{46} - 28 q^{49} + 28 q^{51} + 20 q^{53} - 8 q^{57} + 30 q^{63} + 12 q^{64} - 44 q^{77} - 12 q^{78} - 56 q^{79} - 16 q^{81} + 14 q^{84} - 20 q^{91} + 20 q^{92} - 48 q^{93} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^4 + 12 * q^8 + 12 * q^16 + 14 * q^21 + 20 * q^23 + 12 * q^32 - 12 * q^39 + 14 * q^42 + 20 * q^46 - 28 * q^49 + 28 * q^51 + 20 * q^53 - 8 * q^57 + 30 * q^63 + 12 * q^64 - 44 * q^77 - 12 * q^78 - 56 * q^79 - 16 * q^81 + 14 * q^84 - 20 * q^91 + 20 * q^92 - 48 * q^93 - 28 * q^98 - 48 * q^99

Introduction

L-functions

Modular forms

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Database

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