LMFDB - Embedded newform 1050.2.bc.g.943.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(157,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("1050.157");

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.bc (of order $12$, degree $4$, 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			943.1
Root			$-1.09227 + 0.838128i$ of defining polynomial
Character	$\chi$	$=$	1050.943
Dual form			1050.2.bc.g.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(-0.153213 - 2.64131i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(-0.153213 - 2.64131i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(2.27722 + 3.94427i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(-1.77772 + 1.77772i) q^{13} +(-2.51166 + 0.831614i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.06747 - 3.98386i) q^{17} +(0.258819 - 0.965926i) q^{18} +(1.88956 - 3.27281i) q^{19} +(0.535629 - 2.59097i) q^{21} +(3.22048 - 3.22048i) q^{22} +(7.77857 - 2.08426i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.17725 + 1.25704i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.45334 + 2.21084i) q^{28} -1.55563i q^{29} +(3.37208 - 1.94687i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(1.17878 + 4.39926i) q^{33} -4.12440 q^{34} -1.00000 q^{36} +(2.95980 + 11.0461i) q^{37} +(-3.65035 - 0.978107i) q^{38} +(-2.17725 + 1.25704i) q^{39} -11.3796i q^{41} +(-2.64131 + 0.153213i) q^{42} +(-0.367260 - 0.367260i) q^{43} +(-3.94427 - 2.27722i) q^{44} +(-4.02648 - 6.97408i) q^{46} +(-4.87829 + 1.30713i) q^{47} +(0.707107 - 0.707107i) q^{48} +(-6.95305 + 0.809365i) q^{49} +(2.06220 - 3.57183i) q^{51} +(0.650691 - 2.42841i) q^{52} +(2.18307 - 8.14732i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.75935 - 1.97603i) q^{56} +(2.67224 - 2.67224i) q^{57} +(-1.50262 + 0.402626i) q^{58} +(-0.221511 - 0.383668i) q^{59} +(7.09442 + 4.09597i) q^{61} +(-2.75329 - 2.75329i) q^{62} +(1.18797 - 2.36405i) q^{63} +1.00000i q^{64} +(3.94427 - 2.27722i) q^{66} +(8.99808 + 2.41103i) q^{67} +(1.06747 + 3.98386i) q^{68} +8.05297 q^{69} -6.68403 q^{71} +(0.258819 + 0.965926i) q^{72} +(4.20080 + 1.12560i) q^{73} +(9.90370 - 5.71790i) q^{74} +3.77912i q^{76} +(10.0691 - 6.61917i) q^{77} +(1.77772 + 1.77772i) q^{78} +(-4.08283 - 2.35722i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-10.9919 + 2.94527i) q^{82} +(3.21718 - 3.21718i) q^{83} +(0.831614 + 2.51166i) q^{84} +(-0.259692 + 0.449799i) q^{86} +(0.402626 - 1.50262i) q^{87} +(-1.17878 + 4.39926i) q^{88} +(3.02425 - 5.23816i) q^{89} +(4.96788 + 4.42314i) q^{91} +(-5.69431 + 5.69431i) q^{92} +(3.76106 - 1.00777i) q^{93} +(2.52519 + 4.37376i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(-0.462652 - 0.462652i) q^{97} +(2.58137 + 6.50665i) q^{98} +4.55445i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{7}+O(q^{10}) $ 16 * q + 4 * q^7	$ 16 q + 4 q^{7} + 4 q^{11} - 16 q^{13} - 16 q^{14} + 8 q^{16} - 12 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{22} + 40 q^{23} + 8 q^{24} - 12 q^{26} + 4 q^{28} - 24 q^{31} - 4 q^{33} - 16 q^{34} - 16 q^{36} + 8 q^{37} + 20 q^{38} + 12 q^{39} - 8 q^{42} + 24 q^{43} - 4 q^{46} - 52 q^{49} + 8 q^{51} - 8 q^{52} + 28 q^{53} + 8 q^{54} + 8 q^{56} + 8 q^{57} + 12 q^{58} - 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 84 q^{67} - 12 q^{68} + 8 q^{69} - 32 q^{71} - 16 q^{73} + 24 q^{74} - 44 q^{77} + 16 q^{78} - 12 q^{79} + 8 q^{81} - 36 q^{82} - 16 q^{83} - 4 q^{84} - 8 q^{86} - 48 q^{87} + 4 q^{88} + 16 q^{89} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 8 q^{94} + 44 q^{97} - 24 q^{98}+O(q^{100}) $ 16 * q + 4 * q^7 + 4 * q^11 - 16 * q^13 - 16 * q^14 + 8 * q^16 - 12 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^22 + 40 * q^23 + 8 * q^24 - 12 * q^26 + 4 * q^28 - 24 * q^31 - 4 * q^33 - 16 * q^34 - 16 * q^36 + 8 * q^37 + 20 * q^38 + 12 * q^39 - 8 * q^42 + 24 * q^43 - 4 * q^46 - 52 * q^49 + 8 * q^51 - 8 * q^52 + 28 * q^53 + 8 * q^54 + 8 * q^56 + 8 * q^57 + 12 * q^58 - 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 84 * q^67 - 12 * q^68 + 8 * q^69 - 32 * q^71 - 16 * q^73 + 24 * q^74 - 44 * q^77 + 16 * q^78 - 12 * q^79 + 8 * q^81 - 36 * q^82 - 16 * q^83 - 4 * q^84 - 8 * q^86 - 48 * q^87 + 4 * q^88 + 16 * q^89 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 8 * q^94 + 44 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$		−	1.00000i		−	0.408248i
$7$	−0.153213	−	2.64131i	−0.0579090	−	0.998322i
$7$	−0.153213	−	2.64131i	−0.0579090	−	0.998322i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	2.27722	+	3.94427i	0.686609	+	1.18924i	0.972928	+	0.231107i	$0.0742348\pi$
$11$	2.27722	+	3.94427i	0.686609	+	1.18924i	−0.286319	+	0.958134i	$0.592432\pi$
$12$	−0.965926	+	0.258819i	−0.278839	+	0.0747146i
$13$	−1.77772	+	1.77772i	−0.493051	+	0.493051i	−0.909266	−	0.416215i	$-0.863356\pi$
$13$	−1.77772	+	1.77772i	−0.493051	+	0.493051i	0.416215	+	0.909266i	$0.363356\pi$
$14$	−2.51166	+	0.831614i	−0.671268	+	0.222258i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.06747	−	3.98386i	0.258900	−	0.966228i	−0.706979	−	0.707234i	$-0.749943\pi$
$17$	1.06747	−	3.98386i	0.258900	−	0.966228i	0.965879	−	0.258993i	$-0.0833908\pi$
$18$	0.258819	−	0.965926i	0.0610042	−	0.227671i
$19$	1.88956	−	3.27281i	0.433494	−	0.750834i	−0.563677	−	0.825995i	$-0.690614\pi$
$19$	1.88956	−	3.27281i	0.433494	−	0.750834i	0.997171	+	0.0751610i	$0.0239471\pi$
$20$		0			0
$21$	0.535629	−	2.59097i	0.116884	−	0.565395i
$22$	3.22048	−	3.22048i	0.686609	−	0.686609i
$23$	7.77857	−	2.08426i	1.62194	−	0.434599i	0.670372	−	0.742025i	$-0.266134\pi$
$23$	7.77857	−	2.08426i	1.62194	−	0.434599i	0.951572	+	0.307426i	$0.0994677\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	2.17725	+	1.25704i	0.426995	+	0.246525i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	1.45334	+	2.21084i	0.274656	+	0.417809i
$29$		−	1.55563i		−	0.288873i	−0.989514	−	0.144436i	$-0.953863\pi$
$29$		−	1.55563i		−	0.288873i	0.989514	−	0.144436i	$-0.0461369\pi$
$30$		0			0
$31$	3.37208	−	1.94687i	0.605643	−	0.349668i	−0.165615	−	0.986190i	$-0.552961\pi$
$31$	3.37208	−	1.94687i	0.605643	−	0.349668i	0.771258	+	0.636522i	$0.219628\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	1.17878	+	4.39926i	0.205199	+	0.765813i
$34$	−4.12440			−0.707328
$35$		0			0
$36$	−1.00000			−0.166667
$37$	2.95980	+	11.0461i	0.486589	+	1.81597i	0.572797	+	0.819697i	$0.305858\pi$
$37$	2.95980	+	11.0461i	0.486589	+	1.81597i	−0.0862078	+	0.996277i	$0.527475\pi$
$38$	−3.65035	−	0.978107i	−0.592164	−	0.158670i
$39$	−2.17725	+	1.25704i	−0.348640	+	0.201287i
$40$		0			0
$41$		−	11.3796i		−	1.77720i	−0.458682	−	0.888600i	$-0.651678\pi$
$41$		−	11.3796i		−	1.77720i	0.458682	−	0.888600i	$-0.348322\pi$
$42$	−2.64131	+	0.153213i	−0.407563	+	0.0236412i
$43$	−0.367260	−	0.367260i	−0.0560066	−	0.0560066i	0.678549	−	0.734555i	$-0.262609\pi$
$43$	−0.367260	−	0.367260i	−0.0560066	−	0.0560066i	−0.734555	+	0.678549i	$0.762609\pi$
$44$	−3.94427	−	2.27722i	−0.594621	−	0.343304i
$45$		0			0
$46$	−4.02648	−	6.97408i	−0.593673	−	1.02827i
$47$	−4.87829	+	1.30713i	−0.711572	+	0.190665i	−0.596408	−	0.802681i	$-0.703406\pi$
$47$	−4.87829	+	1.30713i	−0.711572	+	0.190665i	−0.115164	+	0.993347i	$0.536739\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$	−6.95305	+	0.809365i	−0.993293	+	0.115624i
$50$		0			0
$51$	2.06220	−	3.57183i	0.288765	−	0.500156i
$52$	0.650691	−	2.42841i	0.0902346	−	0.336760i
$53$	2.18307	−	8.14732i	0.299868	−	1.11912i	−0.637407	−	0.770528i	$-0.719993\pi$
$53$	2.18307	−	8.14732i	0.299868	−	1.11912i	0.937274	−	0.348593i	$-0.113341\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	1.75935	−	1.97603i	0.235103	−	0.264058i
$57$	2.67224	−	2.67224i	0.353947	−	0.353947i
$58$	−1.50262	+	0.402626i	−0.197304	+	0.0528674i
$59$	−0.221511	−	0.383668i	−0.0288383	−	0.0499493i	0.851246	−	0.524767i	$-0.175847\pi$
$59$	−0.221511	−	0.383668i	−0.0288383	−	0.0499493i	−0.880084	+	0.474817i	$0.842514\pi$
$60$		0			0
$61$	7.09442	+	4.09597i	0.908348	+	0.524435i	0.879899	−	0.475160i	$-0.157610\pi$
$61$	7.09442	+	4.09597i	0.908348	+	0.524435i	0.0284488	+	0.999595i	$0.490943\pi$
$62$	−2.75329	−	2.75329i	−0.349668	−	0.349668i
$63$	1.18797	−	2.36405i	0.149670	−	0.297842i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	3.94427	−	2.27722i	0.485506	−	0.280307i
$67$	8.99808	+	2.41103i	1.09929	+	0.294554i	0.762476	−	0.647017i	$-0.223984\pi$
$67$	8.99808	+	2.41103i	1.09929	+	0.294554i	0.336815	+	0.941571i	$0.390650\pi$
$68$	1.06747	+	3.98386i	0.129450	+	0.483114i
$69$	8.05297			0.969464
$70$		0			0
$71$	−6.68403			−0.793248			−0.396624	−	0.917981i	$-0.629818\pi$
$71$	−6.68403			−0.793248			−0.396624	+	0.917981i	$0.629818\pi$
$72$	0.258819	+	0.965926i	0.0305021	+	0.113835i
$73$	4.20080	+	1.12560i	0.491666	+	0.131742i	0.496130	−	0.868249i	$-0.334754\pi$
$73$	4.20080	+	1.12560i	0.491666	+	0.131742i	−0.00446349	+	0.999990i	$0.501421\pi$
$74$	9.90370	−	5.71790i	1.15128	−	0.664693i
$75$		0			0
$76$			3.77912i			0.433494i
$77$	10.0691	−	6.61917i	1.14748	−	0.754324i
$78$	1.77772	+	1.77772i	0.201287	+	0.201287i
$79$	−4.08283	−	2.35722i	−0.459354	−	0.265208i	0.252418	−	0.967618i	$-0.418774\pi$
$79$	−4.08283	−	2.35722i	−0.459354	−	0.265208i	−0.711773	+	0.702410i	$0.752107\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−10.9919	+	2.94527i	−1.21385	+	0.325250i
$83$	3.21718	−	3.21718i	0.353131	−	0.353131i	−0.508142	−	0.861273i	$-0.669668\pi$
$83$	3.21718	−	3.21718i	0.353131	−	0.353131i	0.861273	+	0.508142i	$0.169668\pi$
$84$	0.831614	+	2.51166i	0.0907365	+	0.274044i
$85$		0			0
$86$	−0.259692	+	0.449799i	−0.0280033	+	0.0485031i
$87$	0.402626	−	1.50262i	0.0431660	−	0.161098i
$88$	−1.17878	+	4.39926i	−0.125658	+	0.468963i
$89$	3.02425	−	5.23816i	0.320570	−	0.555244i	−0.660035	−	0.751234i	$-0.729459\pi$
$89$	3.02425	−	5.23816i	0.320570	−	0.555244i	0.980606	+	0.195990i	$0.0627921\pi$
$90$		0			0
$91$	4.96788	+	4.42314i	0.520775	+	0.463671i
$92$	−5.69431	+	5.69431i	−0.593673	+	0.593673i
$93$	3.76106	−	1.00777i	0.390004	−	0.104501i
$94$	2.52519	+	4.37376i	0.260453	+	0.451118i
$95$		0			0
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	−0.462652	−	0.462652i	−0.0469752	−	0.0469752i	0.683229	−	0.730204i	$-0.260575\pi$
$97$	−0.462652	−	0.462652i	−0.0469752	−	0.0469752i	−0.730204	+	0.683229i	$0.760575\pi$
$98$	2.58137	+	6.50665i	0.260758	+	0.657271i
$99$			4.55445i			0.457739i
$100$		0			0
$101$	−4.85151	+	2.80102i	−0.482743	+	0.278712i	−0.721559	−	0.692353i	$-0.756574\pi$
$101$	−4.85151	+	2.80102i	−0.482743	+	0.278712i	0.238816	+	0.971065i	$0.423241\pi$
$102$	−3.98386	−	1.06747i	−0.394461	−	0.105695i
$103$	1.43852	+	5.36863i	0.141742	+	0.528987i	0.999879	+	0.0155666i	$0.00495519\pi$
$103$	1.43852	+	5.36863i	0.141742	+	0.528987i	−0.858137	+	0.513420i	$0.828378\pi$
$104$	−2.51408			−0.246525
$105$		0			0
$106$	−8.43473			−0.819253
$107$	−1.93865	−	7.23514i	−0.187416	−	0.699447i	−0.994100	−	0.108464i	$-0.965407\pi$
$107$	−1.93865	−	7.23514i	−0.187416	−	0.699447i	0.806684	−	0.590983i	$-0.201260\pi$
$108$	−0.965926	−	0.258819i	−0.0929463	−	0.0249049i
$109$	1.27034	−	0.733433i	0.121677	−	0.0702501i	−0.437926	−	0.899011i	$-0.644287\pi$
$109$	1.27034	−	0.733433i	0.121677	−	0.0702501i	0.559603	+	0.828761i	$0.310954\pi$
$110$		0			0
$111$			11.4358i			1.08544i
$112$	−2.36405	−	1.18797i	−0.223382	−	0.112253i
$113$	−7.08834	−	7.08834i	−0.666815	−	0.666815i	0.290163	−	0.956977i	$-0.406291\pi$
$113$	−7.08834	−	7.08834i	−0.666815	−	0.666815i	−0.956977	+	0.290163i	$0.906291\pi$
$114$	−3.27281	−	1.88956i	−0.306527	−	0.176973i
$115$		0			0
$116$	0.777814	+	1.34721i	0.0722182	+	0.125086i
$117$	−2.42841	+	0.650691i	−0.224507	+	0.0601564i
$118$	−0.313264	+	0.313264i	−0.0288383	+	0.0288383i
$119$	−10.6862	−	2.20915i	−0.979599	−	0.202512i
$120$		0			0
$121$	−4.87150	+	8.43768i	−0.442863	+	0.767062i
$122$	2.12023	−	7.91280i	0.191957	−	0.716391i
$123$	2.94527	−	10.9919i	0.265566	−	0.991105i
$124$	−1.94687	+	3.37208i	−0.174834	+	0.302821i
$125$		0			0
$126$	−2.59097	−	0.535629i	−0.230822	−	0.0477177i
$127$	−12.9176	+	12.9176i	−1.14625	+	1.14625i	−0.158971	+	0.987283i	$0.550818\pi$
$127$	−12.9176	+	12.9176i	−1.14625	+	1.14625i	−0.987283	+	0.158971i	$0.949182\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−0.259692	−	0.449799i	−0.0228646	−	0.0396026i
$130$		0			0
$131$	0.323655	+	0.186862i	0.0282779	+	0.0163262i	0.514072	−	0.857747i	$-0.328136\pi$
$131$	0.323655	+	0.186862i	0.0282779	+	0.0163262i	−0.485794	+	0.874073i	$0.661470\pi$
$132$	−3.22048	−	3.22048i	−0.280307	−	0.280307i
$133$	−8.93402	−	4.48947i	−0.774677	−	0.389287i
$134$		−	9.31550i		−	0.804737i
$135$		0			0
$136$	3.57183	−	2.06220i	0.306282	−	0.176832i
$137$	−2.56800	−	0.688094i	−0.219399	−	0.0587878i	0.147445	−	0.989070i	$-0.452895\pi$
$137$	−2.56800	−	0.688094i	−0.219399	−	0.0587878i	−0.366844	+	0.930282i	$0.619562\pi$
$138$	−2.08426	−	7.77857i	−0.177424	−	0.662156i
$139$	4.58070			0.388530			0.194265	−	0.980949i	$-0.437768\pi$
$139$	4.58070			0.388530			0.194265	+	0.980949i	$0.437768\pi$
$140$		0			0
$141$	−5.05038			−0.425319
$142$	1.72995	+	6.45627i	0.145174	+	0.541798i
$143$	−11.0601	−	2.96354i	−0.924889	−	0.247823i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$		0			0
$146$		−	4.34898i		−	0.359925i
$147$	−6.92561	−	1.01780i	−0.571215	−	0.0839463i
$148$	−8.08634	−	8.08634i	−0.664693	−	0.664693i
$149$	14.9338	+	8.62203i	1.22342	+	0.706344i	0.965646	−	0.259860i	$-0.0836764\pi$
$149$	14.9338	+	8.62203i	1.22342	+	0.706344i	0.257778	+	0.966204i	$0.417010\pi$
$150$		0			0
$151$	2.78385	+	4.82177i	0.226546	+	0.392390i	0.956782	−	0.290805i	$-0.0939231\pi$
$151$	2.78385	+	4.82177i	0.226546	+	0.392390i	−0.730236	+	0.683195i	$0.760590\pi$
$152$	3.65035	−	0.978107i	0.296082	−	0.0793350i
$153$	2.91639	−	2.91639i	0.235776	−	0.235776i
$154$	−8.99971	−	8.01287i	−0.725217	−	0.645696i
$155$		0			0
$156$	1.25704	−	2.17725i	0.100644	−	0.174320i
$157$	1.06916	−	3.99014i	0.0853279	−	0.318448i	−0.910048	−	0.414503i	$-0.863956\pi$
$157$	1.06916	−	3.99014i	0.0853279	−	0.318448i	0.995376	+	0.0960544i	$0.0306223\pi$
$158$	−1.22019	+	4.55381i	−0.0970730	+	0.362281i
$159$	4.21737	−	7.30469i	0.334459	−	0.579300i
$160$		0			0
$161$	−6.69696	−	20.2263i	−0.527795	−	1.59406i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−20.9982	+	5.62644i	−1.64470	+	0.440697i	−0.958123	−	0.286357i	$-0.907556\pi$
$163$	−20.9982	+	5.62644i	−1.64470	+	0.440697i	−0.686580	+	0.727054i	$0.740889\pi$
$164$	5.68982	+	9.85506i	0.444300	+	0.769551i
$165$		0			0
$166$	−3.94022	−	2.27489i	−0.305821	−	0.176566i
$167$	17.4949	+	17.4949i	1.35380	+	1.35380i	0.881371	+	0.472425i	$0.156621\pi$
$167$	17.4949	+	17.4949i	1.35380	+	1.35380i	0.472425	+	0.881371i	$0.343379\pi$
$168$	2.21084	−	1.45334i	0.170570	−	0.112128i
$169$			6.67942i			0.513802i
$170$		0			0
$171$	3.27281	−	1.88956i	0.250278	−	0.144498i
$172$	0.501686	+	0.134426i	0.0382532	+	0.0102499i
$173$	4.28763	+	16.0017i	0.325982	+	1.21658i	0.913321	+	0.407241i	$0.133509\pi$
$173$	4.28763	+	16.0017i	0.325982	+	1.21658i	−0.587338	+	0.809342i	$0.699824\pi$
$174$	−1.55563			−0.117932
$175$		0			0
$176$	4.55445			0.343304
$177$	−0.114663	−	0.427926i	−0.00861856	−	0.0321649i
$178$	−5.84241	−	1.56547i	−0.437907	−	0.117337i
$179$	−11.0222	+	6.36367i	−0.823837	+	0.475643i	−0.851738	−	0.523968i	$-0.824451\pi$
$179$	−11.0222	+	6.36367i	−0.823837	+	0.475643i	0.0279007	+	0.999611i	$0.491118\pi$
$180$		0			0
$181$			9.09951i			0.676361i	0.941081	+	0.338180i	$0.109811\pi$
$181$			9.09951i			0.676361i	−0.941081	+	0.338180i	$0.890189\pi$
$182$	2.98665	−	5.94340i	0.221385	−	0.440554i
$183$	5.79257	+	5.79257i	0.428199	+	0.428199i
$184$	6.97408	+	4.02648i	0.514136	+	0.296836i
$185$		0			0
$186$	−1.94687	−	3.37208i	−0.142751	−	0.247253i
$187$	18.1443	−	4.86175i	1.32684	−	0.355526i
$188$	3.57116	−	3.57116i	0.260453	−	0.260453i
$189$	1.75935	−	1.97603i	0.127974	−	0.143735i
$190$		0			0
$191$	−9.10308	+	15.7670i	−0.658676	+	1.14086i	0.322283	+	0.946643i	$0.395550\pi$
$191$	−9.10308	+	15.7670i	−0.658676	+	1.14086i	−0.980959	+	0.194216i	$0.937784\pi$
$192$	−0.258819	+	0.965926i	−0.0186787	+	0.0697097i
$193$	2.60664	−	9.72810i	0.187630	−	0.700244i	−0.806422	−	0.591340i	$-0.798599\pi$
$193$	2.60664	−	9.72810i	0.187630	−	0.700244i	0.994052	−	0.108904i	$-0.0347342\pi$
$194$	−0.327144	+	0.566631i	−0.0234876	+	0.0406817i
$195$		0			0
$196$	5.61684	−	4.17746i	0.401203	−	0.298390i
$197$	−16.2439	+	16.2439i	−1.15733	+	1.15733i	−0.172283	+	0.985048i	$0.555114\pi$
$197$	−16.2439	+	16.2439i	−1.15733	+	1.15733i	−0.985048	+	0.172283i	$0.944886\pi$
$198$	4.39926	−	1.17878i	0.312642	−	0.0837721i
$199$	−12.6984	−	21.9943i	−0.900168	−	1.55914i	−0.827275	−	0.561797i	$-0.810110\pi$
$199$	−12.6984	−	21.9943i	−0.900168	−	1.55914i	−0.0728933	−	0.997340i	$-0.523223\pi$
$200$		0			0
$201$	8.06746	+	4.65775i	0.569035	+	0.328532i
$202$	3.96124	+	3.96124i	0.278712	+	0.278712i
$203$	−4.10890	+	0.238342i	−0.288388	+	0.0167283i
$204$			4.12440i			0.288765i
$205$		0			0
$206$	4.81338	−	2.77901i	0.335364	−	0.193623i
$207$	7.77857	+	2.08426i	0.540648	+	0.144866i
$208$	0.650691	+	2.42841i	0.0451173	+	0.168380i
$209$	17.2118			1.19056
$210$		0			0
$211$	−13.6182			−0.937517			−0.468759	−	0.883326i	$-0.655299\pi$
$211$	−13.6182			−0.937517			−0.468759	+	0.883326i	$0.655299\pi$
$212$	2.18307	+	8.14732i	0.149934	+	0.559560i
$213$	−6.45627	−	1.72995i	−0.442377	−	0.118534i
$214$	−6.48684	+	3.74518i	−0.443432	+	0.256015i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	−5.65893	−	8.60842i	−0.384153	−	0.584378i
$218$	−1.03723	−	1.03723i	−0.0702501	−	0.0702501i
$219$	3.76633	+	2.17449i	0.254505	+	0.146939i
$220$		0			0
$221$	5.18452	+	8.97985i	0.348749	+	0.604050i
$222$	11.0461	−	2.95980i	0.741369	−	0.198649i
$223$	−15.8412	+	15.8412i	−1.06081	+	1.06081i	−0.0627803	+	0.998027i	$0.519997\pi$
$223$	−15.8412	+	15.8412i	−1.06081	+	1.06081i	−0.998027	+	0.0627803i	$0.980003\pi$
$224$	−0.535629	+	2.59097i	−0.0357883	+	0.173116i
$225$		0			0
$226$	−5.01221	+	8.68141i	−0.333407	+	0.577479i
$227$	2.83476	−	10.5795i	0.188150	−	0.702184i	−0.805785	−	0.592209i	$-0.798256\pi$
$227$	2.83476	−	10.5795i	0.188150	−	0.702184i	0.993934	−	0.109976i	$-0.0350772\pi$
$228$	−0.978107	+	3.65035i	−0.0647767	+	0.241750i
$229$	−14.4722	+	25.0665i	−0.956347	+	1.65644i	−0.225092	+	0.974338i	$0.572268\pi$
$229$	−14.4722	+	25.0665i	−0.956347	+	1.65644i	−0.731255	+	0.682104i	$0.761065\pi$
$230$		0			0
$231$	11.4392	−	3.78754i	0.752645	−	0.249202i
$232$	1.09999	−	1.09999i	0.0722182	−	0.0722182i
$233$	1.36397	−	0.365476i	0.0893569	−	0.0239431i	−0.213864	−	0.976864i	$-0.568605\pi$
$233$	1.36397	−	0.365476i	0.0893569	−	0.0239431i	0.303220	+	0.952920i	$0.401938\pi$
$234$	1.25704	+	2.17725i	0.0821751	+	0.142332i
$235$		0			0
$236$	0.383668	+	0.221511i	0.0249747	+	0.0144191i
$237$	−3.33362	−	3.33362i	−0.216542	−	0.216542i
$238$	0.631910	+	10.8938i	0.0409606	+	0.706141i
$239$		−	4.36430i		−	0.282303i	−0.989988	−	0.141152i	$-0.954920\pi$
$239$		−	4.36430i		−	0.282303i	0.989988	−	0.141152i	$-0.0450805\pi$
$240$		0			0
$241$	−2.65862	+	1.53496i	−0.171257	+	0.0988752i	−0.583178	−	0.812344i	$-0.698191\pi$
$241$	−2.65862	+	1.53496i	−0.171257	+	0.0988752i	0.411922	+	0.911219i	$0.364858\pi$
$242$	9.41101	+	2.52167i	0.604963	+	0.162099i
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	−8.19194			−0.524435
$245$		0			0
$246$	−11.3796			−0.725539
$247$	2.45904	+	9.17725i	0.156465	+	0.583934i
$248$	3.76106	+	1.00777i	0.238828	+	0.0639937i
$249$	3.94022	−	2.27489i	0.249701	−	0.144165i
$250$		0			0
$251$		−	1.25355i		−	0.0791234i	−0.999217	−	0.0395617i	$-0.987404\pi$
$251$		−	1.25355i		−	0.0791234i	0.999217	−	0.0395617i	$-0.0125962\pi$
$252$	0.153213	+	2.64131i	0.00965150	+	0.166387i
$253$	25.9344	+	25.9344i	1.63048	+	1.63048i
$254$	15.8208	+	9.13414i	0.992685	+	0.573127i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.81783	+	1.82683i	−0.425285	+	0.113955i	−0.465112	−	0.885252i	$-0.653986\pi$
$257$	−6.81783	+	1.82683i	−0.425285	+	0.113955i	0.0398273	+	0.999207i	$0.487319\pi$
$258$	−0.367260	+	0.367260i	−0.0228646	+	0.0228646i
$259$	28.7228	−	9.51018i	1.78475	−	0.590934i
$260$		0			0
$261$	0.777814	−	1.34721i	0.0481455	−	0.0833904i
$262$	0.0967271	−	0.360990i	0.00597582	−	0.0223021i
$263$	1.47214	−	5.49409i	0.0907758	−	0.338780i	−0.905569	−	0.424198i	$-0.860556\pi$
$263$	1.47214	−	5.49409i	0.0907758	−	0.338780i	0.996345	+	0.0854182i	$0.0272226\pi$
$264$	−2.27722	+	3.94427i	−0.140153	+	0.242753i
$265$		0			0
$266$	−2.02421	+	9.79156i	−0.124112	+	0.600359i
$267$	4.27694	−	4.27694i	0.261745	−	0.261745i
$268$	−8.99808	+	2.41103i	−0.549645	+	0.147277i
$269$	3.85391	+	6.67517i	0.234977	+	0.406992i	0.959266	−	0.282504i	$-0.0911652\pi$
$269$	3.85391	+	6.67517i	0.234977	+	0.406992i	−0.724289	+	0.689496i	$0.757832\pi$
$270$		0			0
$271$	−15.4900	−	8.94316i	−0.940951	−	0.543258i	−0.0506925	−	0.998714i	$-0.516143\pi$
$271$	−15.4900	−	8.94316i	−0.940951	−	0.543258i	−0.890258	+	0.455456i	$0.849476\pi$
$272$	−2.91639	−	2.91639i	−0.176832	−	0.176832i
$273$	3.65381	+	5.55821i	0.221139	+	0.336398i
$274$			2.65859i			0.160611i
$275$		0			0
$276$	−6.97408	+	4.02648i	−0.419790	+	0.242366i
$277$	14.2439	+	3.81664i	0.855832	+	0.229319i	0.659951	−	0.751308i	$-0.270577\pi$
$277$	14.2439	+	3.81664i	0.855832	+	0.229319i	0.195881	+	0.980628i	$0.437244\pi$
$278$	−1.18557	−	4.42461i	−0.0711059	−	0.265371i
$279$	3.89374			0.233112
$280$		0			0
$281$	0.587402			0.0350415			0.0175207	−	0.999847i	$-0.494423\pi$
$281$	0.587402			0.0350415			0.0175207	+	0.999847i	$0.494423\pi$
$282$	1.30713	+	4.87829i	0.0778387	+	0.290498i
$283$	−17.9809	−	4.81795i	−1.06885	−	0.286398i	−0.318830	−	0.947812i	$-0.603290\pi$
$283$	−17.9809	−	4.81795i	−1.06885	−	0.286398i	−0.750021	+	0.661414i	$0.769957\pi$
$284$	5.78854	−	3.34201i	0.343486	−	0.198312i
$285$		0			0
$286$			11.4502i			0.677066i
$287$	−30.0572	+	1.74351i	−1.77422	+	0.102916i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$	−0.00921092	−	0.00531793i	−0.000541819	−	0.000312819i
$290$		0			0
$291$	−0.327144	−	0.566631i	−0.0191775	−	0.0332165i
$292$	−4.20080	+	1.12560i	−0.245833	+	0.0658708i
$293$	20.6736	−	20.6736i	1.20777	−	1.20777i	0.236018	−	0.971749i	$-0.424158\pi$
$293$	20.6736	−	20.6736i	1.20777	−	1.20777i	0.971749	−	0.236018i	$-0.0758423\pi$
$294$	0.809365	+	6.95305i	0.0472031	+	0.405510i
$295$		0			0
$296$	−5.71790	+	9.90370i	−0.332346	+	0.575641i
$297$	−1.17878	+	4.39926i	−0.0683996	+	0.255271i
$298$	4.46309	−	16.6565i	0.258540	−	0.964884i
$299$	−10.1229	+	17.5334i	−0.585422	+	1.01398i
$300$		0			0
$301$	−0.913778	+	1.02632i	−0.0526693	+	0.0591559i
$302$	3.93696	−	3.93696i	0.226546	−	0.226546i
$303$	−5.41115	+	1.44991i	−0.310863	+	0.0832954i
$304$	−1.88956	−	3.27281i	−0.108374	−	0.187709i
$305$		0			0
$306$	−3.57183	−	2.06220i	−0.204188	−	0.117888i
$307$	1.63464	+	1.63464i	0.0932937	+	0.0932937i	0.752213	−	0.658920i	$-0.228986\pi$
$307$	1.63464	+	1.63464i	0.0932937	+	0.0932937i	−0.658920	+	0.752213i	$0.728986\pi$
$308$	−5.41055	+	10.7669i	−0.308294	+	0.613503i
$309$			5.55802i			0.316185i
$310$		0			0
$311$	12.0239	−	6.94197i	0.681810	−	0.393643i	−0.118727	−	0.992927i	$-0.537881\pi$
$311$	12.0239	−	6.94197i	0.681810	−	0.393643i	0.800537	+	0.599284i	$0.204548\pi$
$312$	−2.42841	−	0.650691i	−0.137482	−	0.0368381i
$313$	−3.49157	−	13.0307i	−0.197355	−	0.736540i	−0.991645	−	0.129000i	$-0.958823\pi$
$313$	−3.49157	−	13.0307i	−0.197355	−	0.736540i	0.794289	−	0.607540i	$-0.207843\pi$
$314$	−4.13090			−0.233120
$315$		0			0
$316$	4.71445			0.265208
$317$	−3.55024	−	13.2497i	−0.199401	−	0.744175i	−0.991083	−	0.133242i	$-0.957461\pi$
$317$	−3.55024	−	13.2497i	−0.199401	−	0.744175i	0.791682	−	0.610933i	$-0.209206\pi$
$318$	−8.14732	−	2.18307i	−0.456879	−	0.122420i
$319$	6.13581	−	3.54251i	0.343539	−	0.198343i
$320$		0			0
$321$		−	7.49036i		−	0.418071i
$322$	−17.8038	+	11.7037i	−0.992167	+	0.652223i
$323$	−11.0214	−	11.0214i	−0.613245	−	0.613245i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$		0			0
$326$	10.8694	+	18.8264i	0.602003	+	1.04270i
$327$	1.41688	−	0.379653i	0.0783538	−	0.0209948i
$328$	8.04662	−	8.04662i	0.444300	−	0.444300i
$329$	4.19996	+	12.6848i	0.231552	+	0.699336i
$330$		0			0
$331$	−16.6194	+	28.7856i	−0.913483	+	1.58220i	−0.104375	+	0.994538i	$0.533284\pi$
$331$	−16.6194	+	28.7856i	−0.913483	+	1.58220i	−0.809108	+	0.587660i	$0.800049\pi$
$332$	−1.17757	+	4.39475i	−0.0646275	+	0.241193i
$333$	−2.95980	+	11.0461i	−0.162196	+	0.605325i
$334$	12.3708	−	21.4268i	0.676898	−	1.17242i
$335$		0			0
$336$	−1.97603	−	1.75935i	−0.107801	−	0.0959805i
$337$	17.0329	−	17.0329i	0.927842	−	0.927842i	−0.0697246	−	0.997566i	$-0.522212\pi$
$337$	17.0329	−	17.0329i	0.927842	−	0.927842i	0.997566	+	0.0697246i	$0.0222121\pi$
$338$	6.45183	−	1.72876i	0.350933	−	0.0940323i
$339$	−5.01221	−	8.68141i	−0.272226	−	0.471509i
$340$		0			0
$341$	15.3579	+	8.86691i	0.831679	+	0.480170i
$342$	−2.67224	−	2.67224i	−0.144498	−	0.144498i
$343$	3.20308	+	18.2412i	0.172950	+	0.984931i
$344$		−	0.519384i		−	0.0280033i
$345$		0			0
$346$	14.3467	−	8.28306i	0.771283	−	0.445300i
$347$	1.98700	+	0.532414i	0.106668	+	0.0285815i	0.311758	−	0.950162i	$-0.399082\pi$
$347$	1.98700	+	0.532414i	0.106668	+	0.0285815i	−0.205090	+	0.978743i	$0.565749\pi$
$348$	0.402626	+	1.50262i	0.0215830	+	0.0805489i
$349$	−11.7250			−0.627627			−0.313814	−	0.949485i	$-0.601607\pi$
$349$	−11.7250			−0.627627			−0.313814	+	0.949485i	$0.601607\pi$
$350$		0			0
$351$	−2.51408			−0.134191
$352$	−1.17878	−	4.39926i	−0.0628291	−	0.234481i
$353$	11.0334	+	2.95640i	0.587250	+	0.157353i	0.540196	−	0.841539i	$-0.318350\pi$
$353$	11.0334	+	2.95640i	0.587250	+	0.157353i	0.0470542	+	0.998892i	$0.485017\pi$
$354$	−0.383668	+	0.221511i	−0.0203917	+	0.0117732i
$355$		0			0
$356$			6.04851i			0.320570i
$357$	−9.75027	−	4.89966i	−0.516039	−	0.259317i
$358$	8.99958	+	8.99958i	0.475643	+	0.475643i
$359$	2.08846	+	1.20577i	0.110225	+	0.0636383i	0.554099	−	0.832451i	$-0.313063\pi$
$359$	2.08846	+	1.20577i	0.110225	+	0.0636383i	−0.443874	+	0.896089i	$0.646396\pi$
$360$		0			0
$361$	2.35914	+	4.08615i	0.124165	+	0.215061i
$362$	8.78945	−	2.35513i	0.461963	−	0.123783i
$363$	−6.88934	+	6.88934i	−0.361596	+	0.361596i
$364$	−6.51388	−	1.34661i	−0.341420	−	0.0705817i
$365$		0			0
$366$	4.09597	−	7.09442i	0.214100	−	0.370832i
$367$	−1.34815	+	5.03135i	−0.0703727	+	0.262635i	−0.992144	−	0.125099i	$-0.960075\pi$
$367$	−1.34815	+	5.03135i	−0.0703727	+	0.262635i	0.921772	+	0.387733i	$0.126742\pi$
$368$	2.08426	−	7.77857i	0.108650	−	0.405486i
$369$	5.68982	−	9.85506i	0.296200	−	0.513034i
$370$		0			0
$371$	−21.8541	−	4.51789i	−1.13461	−	0.234557i
$372$	−2.75329	+	2.75329i	−0.142751	+	0.142751i
$373$	−0.141659	+	0.0379573i	−0.00733480	+	0.00196535i	−0.262485	−	0.964936i	$-0.584542\pi$
$373$	−0.141659	+	0.0379573i	−0.00733480	+	0.00196535i	0.255150	+	0.966902i	$0.417875\pi$
$374$	−9.39217	−	16.2677i	−0.485658	−	0.841184i
$375$		0			0
$376$	−4.37376	−	2.52519i	−0.225559	−	0.130227i
$377$	2.76547	+	2.76547i	0.142429	+	0.142429i
$378$	−2.36405	−	1.18797i	−0.121594	−	0.0611026i
$379$			18.5438i			0.952530i	0.879302	+	0.476265i	$0.158010\pi$
$379$			18.5438i			0.952530i	−0.879302	+	0.476265i	$0.841990\pi$
$380$		0			0
$381$	−15.8208	+	9.13414i	−0.810524	+	0.467956i
$382$	17.5858	+	4.71210i	0.899768	+	0.241092i
$383$	0.996351	+	3.71843i	0.0509112	+	0.190003i	0.986698	−	0.162563i	$-0.0519760\pi$
$383$	0.996351	+	3.71843i	0.0509112	+	0.190003i	−0.935787	+	0.352566i	$0.885309\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−10.0713			−0.512614
$387$	−0.134426	−	0.501686i	−0.00683328	−	0.0255021i
$388$	0.631994	+	0.169342i	0.0320847	+	0.00859706i
$389$	−15.4340	+	8.91085i	−0.782537	+	0.451798i	−0.837329	−	0.546700i	$-0.815884\pi$
$389$	−15.4340	+	8.91085i	−0.782537	+	0.451798i	0.0547917	+	0.998498i	$0.482551\pi$
$390$		0			0
$391$		−	33.2136i		−	1.67969i
$392$	−5.48886	−	4.34424i	−0.277229	−	0.219417i
$393$	0.264263	+	0.264263i	0.0133303	+	0.0133303i
$394$	19.8946	+	11.4862i	1.00228	+	0.578665i
$395$		0			0
$396$	−2.27722	−	3.94427i	−0.114435	−	0.198207i
$397$	−24.7725	+	6.63778i	−1.24330	+	0.333141i	−0.819744	−	0.572730i	$-0.805884\pi$
$397$	−24.7725	+	6.63778i	−1.24330	+	0.333141i	−0.423554	+	0.905871i	$0.639218\pi$
$398$	−17.9583	+	17.9583i	−0.900168	+	0.900168i
$399$	−7.46764	−	6.64879i	−0.373849	−	0.332856i
$400$		0			0
$401$	2.63060	−	4.55632i	0.131366	−	0.227532i	−0.792838	−	0.609433i	$-0.791397\pi$
$401$	2.63060	−	4.55632i	0.131366	−	0.227532i	0.924203	+	0.381901i	$0.124730\pi$
$402$	2.41103	−	8.99808i	0.120251	−	0.448784i
$403$	−2.53362	+	9.45560i	−0.126209	+	0.471017i
$404$	2.80102	−	4.85151i	0.139356	−	0.241371i
$405$		0			0
$406$	1.29368	+	3.90720i	0.0642043	+	0.193911i
$407$	−36.8288	+	36.8288i	−1.82554	+	1.82554i
$408$	3.98386	−	1.06747i	0.197230	−	0.0528477i
$409$	−4.18773	−	7.25336i	−0.207070	−	0.358655i	0.743720	−	0.668491i	$-0.233059\pi$
$409$	−4.18773	−	7.25336i	−0.207070	−	0.358655i	−0.950790	+	0.309835i	$0.899726\pi$
$410$		0			0
$411$	−2.30241	−	1.32929i	−0.113569	−	0.0655693i
$412$	−3.93011	−	3.93011i	−0.193623	−	0.193623i
$413$	−0.979449	+	0.643862i	−0.0481955	+	0.0316824i
$414$		−	8.05297i		−	0.395782i
$415$		0			0
$416$	2.17725	−	1.25704i	0.106749	−	0.0616313i
$417$	4.42461	+	1.18557i	0.216674	+	0.0580577i
$418$	−4.45474	−	16.6253i	−0.217888	−	0.813170i
$419$	−9.53078			−0.465609			−0.232805	−	0.972524i	$-0.574790\pi$
$419$	−9.53078			−0.465609			−0.232805	+	0.972524i	$0.574790\pi$
$420$		0			0
$421$	16.8461			0.821027			0.410514	−	0.911854i	$-0.365349\pi$
$421$	16.8461			0.821027			0.410514	+	0.911854i	$0.365349\pi$
$422$	3.52466	+	13.1542i	0.171578	+	0.640336i
$423$	−4.87829	−	1.30713i	−0.237191	−	0.0635550i
$424$	7.30469	−	4.21737i	0.354747	−	0.204813i
$425$		0			0
$426$			6.68403i			0.323842i
$427$	9.73177	−	19.3661i	0.470953	−	0.937193i
$428$	5.29649	+	5.29649i	0.256015	+	0.256015i
$429$	−9.91619	−	5.72511i	−0.478758	−	0.276411i
$430$		0			0
$431$	−10.7791	−	18.6699i	−0.519209	−	0.899297i	−0.999751	−	0.0223251i	$-0.992893\pi$
$431$	−10.7791	−	18.6699i	−0.519209	−	0.899297i	0.480541	−	0.876972i	$-0.340440\pi$
$432$	0.965926	−	0.258819i	0.0464731	−	0.0124524i
$433$	25.8823	−	25.8823i	1.24382	−	1.24382i	0.285422	−	0.958402i	$-0.407866\pi$
$433$	25.8823	−	25.8823i	1.24382	−	1.24382i	0.958402	−	0.285422i	$-0.0921338\pi$
$434$	−6.85045	+	7.69413i	−0.328832	+	0.369330i
$435$		0			0
$436$	−0.733433	+	1.27034i	−0.0351251	+	0.0608384i
$437$	7.87667	−	29.3961i	0.376792	−	1.40621i
$438$	1.12560	−	4.20080i	0.0537832	−	0.200722i
$439$	−10.5899	+	18.3422i	−0.505426	+	0.875424i	0.494554	+	0.869147i	$0.335331\pi$
$439$	−10.5899	+	18.3422i	−0.505426	+	0.875424i	−0.999980	+	0.00627716i	$0.998002\pi$
$440$		0			0
$441$	−6.42620	−	2.77559i	−0.306010	−	0.132171i
$442$	7.33202	−	7.33202i	0.348749	−	0.348749i
$443$	−4.00895	+	1.07420i	−0.190471	+	0.0510366i	−0.352794	−	0.935701i	$-0.614768\pi$
$443$	−4.00895	+	1.07420i	−0.190471	+	0.0510366i	0.162322	+	0.986738i	$0.448102\pi$
$444$	−5.71790	−	9.90370i	−0.271360	−	0.470009i
$445$		0			0
$446$	19.4015	+	11.2014i	0.918686	+	0.530404i
$447$	12.1934	+	12.1934i	0.576728	+	0.576728i
$448$	2.64131	−	0.153213i	0.124790	−	0.00723862i
$449$			29.3795i			1.38651i	0.720694	+	0.693253i	$0.243823\pi$
$449$			29.3795i			1.38651i	−0.720694	+	0.693253i	$0.756177\pi$
$450$		0			0
$451$	44.8843	−	25.9140i	2.11352	−	1.22024i
$452$	9.68285	+	2.59451i	0.455443	+	0.122036i
$453$	1.44103	+	5.37799i	0.0677053	+	0.252680i
$454$	−10.9527			−0.514035
$455$		0			0
$456$	3.77912			0.176973
$457$	0.121995	+	0.455291i	0.00570668	+	0.0212976i	0.968720	−	0.248155i	$-0.0798241\pi$
$457$	0.121995	+	0.455291i	0.00570668	+	0.0212976i	−0.963014	+	0.269452i	$0.913157\pi$
$458$	27.9581	+	7.49134i	1.30639	+	0.350047i
$459$	3.57183	−	2.06220i	0.166719	−	0.0962551i
$460$		0			0
$461$		−	26.3199i		−	1.22584i	−0.790145	−	0.612920i	$-0.789995\pi$
$461$		−	26.3199i		−	1.22584i	0.790145	−	0.612920i	$-0.210005\pi$
$462$	−6.61917	−	10.0691i	−0.307952	−	0.468459i
$463$	1.02619	+	1.02619i	0.0476909	+	0.0476909i	0.730550	−	0.682859i	$-0.239264\pi$
$463$	1.02619	+	1.02619i	0.0476909	+	0.0476909i	−0.682859	+	0.730550i	$0.739264\pi$
$464$	−1.34721	−	0.777814i	−0.0625428	−	0.0361091i
$465$		0			0
$466$	−0.706045	−	1.22291i	−0.0327069	−	0.0566500i
$467$	29.9569	−	8.02693i	1.38624	−	0.371442i	0.512856	−	0.858475i	$-0.328587\pi$
$467$	29.9569	−	8.02693i	1.38624	−	0.371442i	0.873384	+	0.487033i	$0.161921\pi$
$468$	1.77772	−	1.77772i	0.0821751	−	0.0821751i
$469$	4.98966	−	24.1361i	0.230401	−	1.11450i
$470$		0			0
$471$	2.06545	−	3.57747i	0.0951709	−	0.164841i
$472$	0.114663	−	0.427926i	0.00527777	−	0.0196969i
$473$	0.612238	−	2.28490i	0.0281507	−	0.105060i
$474$	−2.35722	+	4.08283i	−0.108271	+	0.187531i
$475$		0			0
$476$	10.3591	−	3.42990i	0.474807	−	0.157209i
$477$	5.96425	−	5.96425i	0.273084	−	0.273084i
$478$	−4.21559	+	1.12956i	−0.192817	+	0.0516650i
$479$	−16.6760	−	28.8837i	−0.761945	−	1.31973i	−0.941847	−	0.336043i	$-0.890911\pi$
$479$	−16.6760	−	28.8837i	−0.761945	−	1.31973i	0.179901	−	0.983685i	$-0.442422\pi$
$480$		0			0
$481$	−24.8987	−	14.3752i	−1.13528	−	0.655455i
$482$	2.17075	+	2.17075i	0.0988752	+	0.0988752i
$483$	−1.23382	−	21.2704i	−0.0561407	−	0.967837i
$484$		−	9.74299i		−	0.442863i
$485$		0			0
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	−3.19111	−	0.855056i	−0.144603	−	0.0387463i	0.185791	−	0.982589i	$-0.440515\pi$
$487$	−3.19111	−	0.855056i	−0.144603	−	0.0387463i	−0.330395	+	0.943843i	$0.607182\pi$
$488$	2.12023	+	7.91280i	0.0959783	+	0.358196i
$489$	−21.7389			−0.983067
$490$		0			0
$491$	3.61649			0.163210			0.0816051	−	0.996665i	$-0.473995\pi$
$491$	3.61649			0.163210			0.0816051	+	0.996665i	$0.473995\pi$
$492$	2.94527	+	10.9919i	0.132783	+	0.495552i
$493$	−6.19740	−	1.66059i	−0.279117	−	0.0747891i
$494$	8.22809	−	4.75049i	0.370199	−	0.213735i
$495$		0			0
$496$		−	3.89374i		−	0.174834i
$497$	1.02408	+	17.6546i	0.0459362	+	0.791917i
$498$	−3.21718	−	3.21718i	−0.144165	−	0.144165i
$499$	0.561004	+	0.323896i	0.0251140	+	0.0144996i	0.512504	−	0.858685i	$-0.328718\pi$
$499$	0.561004	+	0.323896i	0.0251140	+	0.0144996i	−0.487390	+	0.873184i	$0.662051\pi$
$500$		0			0
$501$	12.3708	+	21.4268i	0.552685	+	0.957278i
$502$	−1.21084	+	0.324443i	−0.0540423	+	0.0144806i
$503$	−12.9189	+	12.9189i	−0.576027	+	0.576027i	−0.933806	−	0.357779i	$-0.883534\pi$
$503$	−12.9189	+	12.9189i	−0.576027	+	0.576027i	0.357779	+	0.933806i	$0.383534\pi$
$504$	2.51166	−	0.831614i	0.111878	−	0.0370430i
$505$		0			0
$506$	18.3384	−	31.7631i	0.815242	−	1.41204i
$507$	−1.72876	+	6.45183i	−0.0767770	+	0.286536i
$508$	4.72818	−	17.6458i	0.209779	−	0.782906i
$509$	10.1554	−	17.5896i	0.450128	−	0.779645i	−0.548265	−	0.836304i	$-0.684712\pi$
$509$	10.1554	−	17.5896i	0.450128	−	0.779645i	0.998394	+	0.0566595i	$0.0180449\pi$
$510$		0			0
$511$	2.32944	−	11.2681i	0.103049	−	0.498470i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	3.65035	−	0.978107i	0.161167	−	0.0431845i
$514$	3.52917	+	6.11270i	0.155665	+	0.269620i
$515$		0			0
$516$	0.449799	+	0.259692i	0.0198013	+	0.0114323i
$517$	−16.2646	−	16.2646i	−0.715318	−	0.715318i
$518$	−16.6201	−	25.2827i	−0.730247	−	1.11086i
$519$			16.5661i			0.727172i
$520$		0			0
$521$	1.07875	−	0.622814i	0.0472607	−	0.0272860i	−0.476183	−	0.879346i	$-0.657980\pi$
$521$	1.07875	−	0.622814i	0.0472607	−	0.0272860i	0.523444	+	0.852060i	$0.324647\pi$
$522$	−1.50262	−	0.402626i	−0.0657679	−	0.0176225i
$523$	−5.25224	−	19.6016i	−0.229664	−	0.857119i	−0.980482	−	0.196609i	$-0.937007\pi$
$523$	−5.25224	−	19.6016i	−0.229664	−	0.857119i	0.750818	−	0.660509i	$-0.229660\pi$
$524$	−0.373725			−0.0163262
$525$		0			0
$526$	−5.68790			−0.248004
$527$	−4.15646	−	15.5121i	−0.181058	−	0.675718i
$528$	4.39926	+	1.17878i	0.191453	+	0.0512997i
$529$	36.2434	−	20.9252i	1.57580	−	0.909790i
$530$		0			0
$531$		−	0.443022i		−	0.0192255i
$532$	9.98182	−	0.579009i	0.432767	−	0.0251032i
$533$	20.2298	+	20.2298i	0.876250	+	0.876250i
$534$	−5.23816	−	3.02425i	−0.226677	−	0.130872i
$535$		0			0
$536$	4.65775	+	8.06746i	0.201184	+	0.348461i
$537$	−12.2937	+	3.29408i	−0.530510	+	0.142150i
$538$	5.45025	−	5.45025i	0.234977	−	0.234977i
$539$	−19.0260	−	25.5816i	−0.819508	−	1.10188i
$540$		0			0
$541$	17.0068	−	29.4566i	0.731178	−	1.26644i	−0.225202	−	0.974312i	$-0.572304\pi$
$541$	17.0068	−	29.4566i	0.731178	−	1.26644i	0.956380	−	0.292126i	$-0.0943625\pi$
$542$	−4.62932	+	17.2769i	−0.198846	+	0.742104i
$543$	−2.35513	+	8.78945i	−0.101068	+	0.377191i
$544$	−2.06220	+	3.57183i	−0.0884160	+	0.153141i
$545$		0			0
$546$	4.42314	−	4.96788i	0.189293	−	0.212606i
$547$	−27.8171	+	27.8171i	−1.18937	+	1.18937i	−0.212132	+	0.977241i	$0.568041\pi$
$547$	−27.8171	+	27.8171i	−1.18937	+	1.18937i	−0.977241	+	0.212132i	$0.931959\pi$
$548$	2.56800	−	0.688094i	0.109700	−	0.0293939i
$549$	4.09597	+	7.09442i	0.174812	+	0.302783i
$550$		0			0
$551$	−5.09127	−	2.93945i	−0.216896	−	0.125225i
$552$	5.69431	+	5.69431i	0.242366	+	0.242366i
$553$	−5.60062	+	11.1452i	−0.238163	+	0.473941i
$554$		−	14.7464i		−	0.626512i
$555$		0			0
$556$	−3.96700	+	2.29035i	−0.168238	+	0.0971324i
$557$	1.36512	+	0.365782i	0.0578419	+	0.0154987i	0.287624	−	0.957743i	$-0.407135\pi$
$557$	1.36512	+	0.365782i	0.0578419	+	0.0154987i	−0.229782	+	0.973242i	$0.573801\pi$
$558$	−1.00777	−	3.76106i	−0.0426625	−	0.159218i
$559$	1.30577			0.0552282
$560$		0			0
$561$	18.7843			0.793076
$562$	−0.152031	−	0.567387i	−0.00641303	−	0.0239338i
$563$	−36.9530	−	9.90152i	−1.55738	−	0.417299i	−0.625548	−	0.780185i	$-0.715125\pi$
$563$	−36.9530	−	9.90152i	−1.55738	−	0.417299i	−0.931834	+	0.362886i	$0.881791\pi$
$564$	4.37376	−	2.52519i	0.184168	−	0.106330i
$565$		0			0
$566$			18.6151i			0.782453i
$567$	2.21084	−	1.45334i	0.0928464	−	0.0610346i
$568$	−4.72632	−	4.72632i	−0.198312	−	0.198312i
$569$	−31.1820	−	18.0029i	−1.30722	−	0.754723i	−0.325587	−	0.945512i	$-0.605562\pi$
$569$	−31.1820	−	18.0029i	−1.30722	−	0.754723i	−0.981631	+	0.190789i	$0.938895\pi$
$570$		0			0
$571$	17.1990	+	29.7895i	0.719756	+	1.24665i	0.961096	+	0.276213i	$0.0890795\pi$
$571$	17.1990	+	29.7895i	0.719756	+	1.24665i	−0.241341	+	0.970440i	$0.577587\pi$
$572$	11.0601	−	2.96354i	0.462445	−	0.123912i
$573$	−12.8737	+	12.8737i	−0.537806	+	0.537806i
$574$	9.46346	+	28.5817i	0.394997	+	1.19298i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	11.5727	−	43.1900i	0.481779	−	1.79802i	−0.112370	−	0.993666i	$-0.535844\pi$
$577$	11.5727	−	43.1900i	0.481779	−	1.79802i	0.594148	−	0.804355i	$-0.297489\pi$
$578$	−0.00275276	+	0.0102734i	−0.000114500	+	0.000427319i
$579$	5.03564	−	8.72198i	0.209274	−	0.362473i
$580$		0			0
$581$	−8.99048	−	8.00466i	−0.372988	−	0.332089i
$582$	−0.462652	+	0.462652i	−0.0191775	+	0.0191775i
$583$	37.1066	−	9.94267i	1.53680	−	0.411783i
$584$	2.17449	+	3.76633i	0.0899811	+	0.155852i
$585$		0			0
$586$	−25.3199	−	14.6185i	−1.04596	−	0.603883i
$587$	−19.7182	−	19.7182i	−0.813859	−	0.813859i	0.171351	−	0.985210i	$-0.445187\pi$
$587$	−19.7182	−	19.7182i	−0.813859	−	0.813859i	−0.985210	+	0.171351i	$0.945187\pi$
$588$	6.50665	−	2.58137i	0.268330	−	0.106454i
$589$		−	14.7149i		−	0.606316i
$590$		0			0
$591$	−19.8946	+	11.4862i	−0.818356	+	0.472478i
$592$	11.0461	+	2.95980i	0.453994	+	0.121647i
$593$	2.57961	+	9.62724i	0.105932	+	0.395343i	0.998449	−	0.0556699i	$-0.0177294\pi$
$593$	2.57961	+	9.62724i	0.105932	+	0.395343i	−0.892517	+	0.451013i	$0.851063\pi$
$594$	4.55445			0.186871
$595$		0			0
$596$	−17.2441			−0.706344
$597$	−6.57319	−	24.5315i	−0.269023	−	1.00401i
$598$	19.5559	+	5.23999i	0.799701	+	0.214279i
$599$	14.2556	−	8.23048i	0.582469	−	0.336288i	−0.179645	−	0.983731i	$-0.557495\pi$
$599$	14.2556	−	8.23048i	0.582469	−	0.336288i	0.762114	+	0.647443i	$0.224162\pi$
$600$		0			0
$601$			34.0216i			1.38777i	0.720086	+	0.693885i	$0.244102\pi$
$601$			34.0216i			1.38777i	−0.720086	+	0.693885i	$0.755898\pi$
$602$	1.22785	+	0.617012i	0.0500434	+	0.0251475i
$603$	6.58705	+	6.58705i	0.268246	+	0.268246i
$604$	−4.82177	−	2.78385i	−0.196195	−	0.113273i
$605$		0			0
$606$	2.80102	+	4.85151i	0.113784	+	0.197079i
$607$	−34.7707	+	9.31678i	−1.41130	+	0.378156i	−0.882389	−	0.470521i	$-0.844066\pi$
$607$	−34.7707	+	9.31678i	−1.41130	+	0.378156i	−0.528910	+	0.848678i	$0.677399\pi$
$608$	−2.67224	+	2.67224i	−0.108374	+	0.108374i
$609$	−4.03058	−	0.833240i	−0.163327	−	0.0337646i
$610$		0			0
$611$	6.34852	−	10.9960i	0.256833	−	0.444849i
$612$	−1.06747	+	3.98386i	−0.0431500	+	0.161038i
$613$	8.52125	−	31.8017i	0.344170	−	1.28446i	−0.549409	−	0.835554i	$-0.685147\pi$
$613$	8.52125	−	31.8017i	0.344170	−	1.28446i	0.893579	−	0.448906i	$-0.148186\pi$
$614$	1.15586	−	2.00201i	0.0466469	−	0.0807947i
$615$		0			0
$616$	11.8004	+	2.43950i	0.475452	+	0.0982901i
$617$	10.3705	−	10.3705i	0.417499	−	0.417499i	−0.466842	−	0.884341i	$-0.654608\pi$
$617$	10.3705	−	10.3705i	0.417499	−	0.417499i	0.884341	+	0.466842i	$0.154608\pi$
$618$	5.36863	−	1.43852i	0.215958	−	0.0578658i
$619$	−2.58828	−	4.48304i	−0.104032	−	0.180188i	0.809310	−	0.587381i	$-0.199841\pi$
$619$	−2.58828	−	4.48304i	−0.104032	−	0.180188i	−0.913342	+	0.407193i	$0.866508\pi$
$620$		0			0
$621$	6.97408	+	4.02648i	0.279860	+	0.161577i
$622$	−9.81743	−	9.81743i	−0.393643	−	0.393643i
$623$	−14.2990	−	7.18544i	−0.572876	−	0.287879i
$624$			2.51408i			0.100644i
$625$		0			0
$626$	−11.6830	+	6.74520i	−0.466948	+	0.269592i
$627$	16.6253	+	4.45474i	0.663951	+	0.177905i
$628$	1.06916	+	3.99014i	0.0426640	+	0.159224i
$629$	47.1658			1.88062
$630$		0			0
$631$	14.5385			0.578769			0.289384	−	0.957213i	$-0.406549\pi$
$631$	14.5385			0.578769			0.289384	+	0.957213i	$0.406549\pi$
$632$	−1.22019	−	4.55381i	−0.0485365	−	0.181141i
$633$	−13.1542	−	3.52466i	−0.522832	−	0.140093i
$634$	−11.8793	+	6.85853i	−0.471788	+	0.272387i
$635$		0			0
$636$			8.43473i			0.334459i
$637$	10.9218	−	13.7994i	0.432736	−	0.546752i
$638$	−5.00987	−	5.00987i	−0.198343	−	0.198343i
$639$	−5.78854	−	3.34201i	−0.228991	−	0.132208i
$640$		0			0
$641$	−20.8743	−	36.1553i	−0.824484	−	1.42805i	−0.902313	−	0.431082i	$-0.858132\pi$
$641$	−20.8743	−	36.1553i	−0.824484	−	1.42805i	0.0778281	−	0.996967i	$-0.475201\pi$
$642$	−7.23514	+	1.93865i	−0.285548	+	0.0765124i
$643$	15.5128	−	15.5128i	0.611766	−	0.611766i	−0.331640	−	0.943406i	$-0.607602\pi$
$643$	15.5128	−	15.5128i	0.611766	−	0.611766i	0.943406	+	0.331640i	$0.107602\pi$
$644$	15.9129	+	14.1680i	0.627056	+	0.558298i
$645$		0			0
$646$	−7.79328	+	13.4984i	−0.306623	+	0.531086i
$647$	3.70148	−	13.8141i	0.145520	−	0.543089i	−0.854211	−	0.519926i	$-0.825960\pi$
$647$	3.70148	−	13.8141i	0.145520	−	0.543089i	0.999732	−	0.0231633i	$-0.00737377\pi$
$648$	−0.258819	+	0.965926i	−0.0101674	+	0.0379452i
$649$	1.00886	−	1.74740i	0.0396012	−	0.0685913i
$650$		0			0
$651$	−3.23809	−	9.77973i	−0.126911	−	0.383298i
$652$	15.3717	−	15.3717i	0.602003	−	0.602003i
$653$	14.7451	−	3.95094i	0.577021	−	0.154612i	0.0415062	−	0.999138i	$-0.486784\pi$
$653$	14.7451	−	3.95094i	0.577021	−	0.154612i	0.535515	+	0.844526i	$0.320118\pi$
$654$	−0.733433	−	1.27034i	−0.0286795	−	0.0496743i
$655$		0			0
$656$	−9.85506	−	5.68982i	−0.384775	−	0.222150i
$657$	3.07520	+	3.07520i	0.119975	+	0.119975i
$658$	11.1656	−	7.33993i	0.435279	−	0.286140i
$659$			18.9116i			0.736690i	0.929689	+	0.368345i	$0.120076\pi$
$659$			18.9116i			0.736690i	−0.929689	+	0.368345i	$0.879924\pi$
$660$		0			0
$661$	19.5815	−	11.3054i	0.761632	−	0.439728i	−0.0682495	−	0.997668i	$-0.521741\pi$
$661$	19.5815	−	11.3054i	0.761632	−	0.439728i	0.829881	+	0.557940i	$0.188408\pi$
$662$	32.1061	+	8.60281i	1.24784	+	0.334358i
$663$	2.68371	+	10.0157i	0.104226	+	0.388979i
$664$	4.54978			0.176566
$665$		0			0
$666$	11.4358			0.443129
$667$	−3.24233	−	12.1006i	−0.125544	−	0.468535i
$668$	−23.8985	−	6.40358i	−0.924660	−	0.247762i
$669$	−19.4015	+	11.2014i	−0.750104	+	0.433073i
$670$		0			0
$671$			37.3097i			1.44033i
$672$	−1.18797	+	2.36405i	−0.0458269	+	0.0911952i
$673$	24.2623	+	24.2623i	0.935243	+	0.935243i	0.998027	−	0.0627838i	$-0.0199978\pi$
$673$	24.2623	+	24.2623i	0.935243	+	0.935243i	−0.0627838	+	0.998027i	$0.519998\pi$
$674$	−20.8610	−	12.0441i	−0.803534	−	0.463921i
$675$		0			0
$676$	−3.33971	−	5.78455i	−0.128450	−	0.222483i
$677$	−8.59870	+	2.30402i	−0.330475	+	0.0885505i	−0.420241	−	0.907412i	$-0.638055\pi$
$677$	−8.59870	+	2.30402i	−0.330475	+	0.0885505i	0.0897664	+	0.995963i	$0.471388\pi$
$678$	−7.08834	+	7.08834i	−0.272226	+	0.272226i
$679$	−1.15112	+	1.29289i	−0.0441761	+	0.0496166i
$680$		0			0
$681$	5.47634	−	9.48530i	0.209854	−	0.363477i
$682$	4.58985	−	17.1296i	0.175755	−	0.655925i
$683$	−12.3979	+	46.2697i	−0.474394	+	1.77046i	0.149299	+	0.988792i	$0.452298\pi$
$683$	−12.3979	+	46.2697i	−0.474394	+	1.77046i	−0.623693	+	0.781669i	$0.714368\pi$
$684$	−1.88956	+	3.27281i	−0.0722491	+	0.125139i
$685$		0			0
$686$	16.7906	−	7.81510i	0.641068	−	0.298382i
$687$	−20.4667	+	20.4667i	−0.780854	+	0.780854i
$688$	−0.501686	+	0.134426i	−0.0191266	+	0.00512496i
$689$	10.6028	+	18.3645i	0.403934	+	0.699633i
$690$		0			0
$691$	−22.3848	−	12.9239i	−0.851559	−	0.491648i	0.00961738	−	0.999954i	$-0.496939\pi$
$691$	−22.3848	−	12.9239i	−0.851559	−	0.491648i	−0.861177	+	0.508306i	$0.830272\pi$
$692$	−11.7140	−	11.7140i	−0.445300	−	0.445300i
$693$	12.0297	−	0.697800i	0.456971	−	0.0265072i
$694$		−	2.05709i		−	0.0780861i
$695$		0			0
$696$	1.34721	−	0.777814i	0.0510660	−	0.0294829i
$697$	−45.3349	−	12.1474i	−1.71718	−	0.460117i
$698$	3.03467	+	11.3255i	0.114864	+	0.428677i
$699$	1.41209			0.0534102
$700$		0			0
$701$	3.95788			0.149487			0.0747435	−	0.997203i	$-0.476186\pi$
$701$	3.95788			0.149487			0.0747435	+	0.997203i	$0.476186\pi$
$702$	0.650691	+	2.42841i	0.0245587	+	0.0916544i
$703$	41.7447	+	11.1854i	1.57443	+	0.421867i
$704$	−3.94427	+	2.27722i	−0.148655	+	0.0858261i
$705$		0			0
$706$		−	11.4227i		−	0.429897i
$707$	8.14167	+	12.3852i	0.306199	+	0.465793i
$708$	0.313264	+	0.313264i	0.0117732	+	0.0117732i
$709$	−25.1665	−	14.5299i	−0.945148	−	0.545682i	−0.0535778	−	0.998564i	$-0.517063\pi$
$709$	−25.1665	−	14.5299i	−0.945148	−	0.545682i	−0.891570	+	0.452882i	$0.850396\pi$
$710$		0			0
$711$	−2.35722	−	4.08283i	−0.0884028	−	0.153118i
$712$	5.84241	−	1.56547i	0.218954	−	0.0586684i
$713$	22.1722	−	22.1722i	0.830354	−	0.830354i
$714$	−2.20915	+	10.6862i	−0.0826753	+	0.399920i
$715$		0			0
$716$	6.36367	−	11.0222i	0.237821	−	0.411919i
$717$	1.12956	−	4.21559i	0.0421843	−	0.157434i
$718$	0.624155	−	2.32938i	0.0232932	−	0.0869316i
$719$	−10.1319	+	17.5490i	−0.377857	+	0.654467i	−0.990750	−	0.135699i	$-0.956672\pi$
$719$	−10.1319	+	17.5490i	−0.377857	+	0.654467i	0.612893	+	0.790166i	$0.290005\pi$
$720$		0			0
$721$	13.9598	−	4.62212i	0.519891	−	0.172137i
$722$	3.33633	−	3.33633i	0.124165	−	0.124165i
$723$	−2.96531	+	0.794551i	−0.110281	+	0.0295497i
$724$	−4.54975	−	7.88040i	−0.169090	−	0.292873i
$725$		0			0
$726$	8.43768	+	4.87150i	0.313152	+	0.180798i
$727$	2.80940	+	2.80940i	0.104195	+	0.104195i	0.757282	−	0.653088i	$-0.226527\pi$
$727$	2.80940	+	2.80940i	0.104195	+	0.104195i	−0.653088	+	0.757282i	$0.726527\pi$
$728$	0.385189	+	6.64046i	0.0142760	+	0.246112i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−1.85515	+	1.07107i	−0.0686152	+	0.0396150i
$732$	−7.91280	−	2.12023i	−0.292466	−	0.0783659i
$733$	0.451275	+	1.68418i	0.0166682	+	0.0622066i	0.973759	−	0.227582i	$-0.0730818\pi$
$733$	0.451275	+	1.68418i	0.0166682	+	0.0622066i	−0.957091	+	0.289788i	$0.906415\pi$
$734$	5.20884			0.192262
$735$		0			0
$736$	−8.05297			−0.296836
$737$	10.9809	+	40.9813i	0.404487	+	1.50957i
$738$	−10.9919	−	2.94527i	−0.404617	−	0.108417i
$739$	−20.2692	+	11.7024i	−0.745615	+	0.430481i	−0.824107	−	0.566434i	$-0.808323\pi$
$739$	−20.2692	+	11.7024i	−0.745615	+	0.430481i	0.0784926	+	0.996915i	$0.474989\pi$
$740$		0			0
$741$			9.50098i			0.349027i
$742$	1.29231	+	22.2787i	0.0474421	+	0.817879i
$743$	−1.84057	−	1.84057i	−0.0675240	−	0.0675240i	0.672538	−	0.740062i	$-0.265204\pi$
$743$	−1.84057	−	1.84057i	−0.0675240	−	0.0675240i	−0.740062	+	0.672538i	$0.765204\pi$
$744$	3.37208	+	1.94687i	0.123626	+	0.0713757i
$745$		0			0
$746$	0.0733279	+	0.127008i	0.00268472	+	0.00465008i
$747$	4.39475	−	1.17757i	0.160795	−	0.0430850i
$748$	−13.2825	+	13.2825i	−0.485658	+	0.485658i
$749$	−18.8132	+	6.22909i	−0.687420	+	0.227606i
$750$		0			0
$751$	−21.1862	+	36.6956i	−0.773096	+	1.33904i	0.162762	+	0.986665i	$0.447960\pi$
$751$	−21.1862	+	36.6956i	−0.773096	+	1.33904i	−0.935858	+	0.352376i	$0.885374\pi$
$752$	−1.30713	+	4.87829i	−0.0476663	+	0.177893i
$753$	0.324443	−	1.21084i	0.0118234	−	0.0441254i
$754$	1.95548	−	3.38699i	0.0712145	−	0.123347i
$755$		0			0
$756$	−0.535629	+	2.59097i	−0.0194807	+	0.0942325i
$757$	−10.2470	+	10.2470i	−0.372434	+	0.372434i	−0.868363	−	0.495929i	$-0.834828\pi$
$757$	−10.2470	+	10.2470i	−0.372434	+	0.372434i	0.495929	+	0.868363i	$0.334828\pi$
$758$	17.9119	−	4.79948i	0.650590	−	0.174325i
$759$	18.3384	+	31.7631i	0.665642	+	1.15293i
$760$		0			0
$761$	13.4082	+	7.74124i	0.486048	+	0.280620i	0.722933	−	0.690918i	$-0.242793\pi$
$761$	13.4082	+	7.74124i	0.486048	+	0.280620i	−0.236886	+	0.971538i	$0.576127\pi$
$762$	12.9176	+	12.9176i	0.467956	+	0.467956i
$763$	−2.13186	−	3.24300i	−0.0771784	−	0.117404i
$764$		−	18.2062i		−	0.658676i
$765$		0			0
$766$	3.33386	−	1.92480i	0.120457	−	0.0695460i
$767$	1.07584	+	0.288270i	0.0388463	+	0.0104088i
$768$	−0.258819	−	0.965926i	−0.00933933	−	0.0348548i
$769$	15.9644			0.575691			0.287846	−	0.957677i	$-0.407061\pi$
$769$	15.9644			0.575691			0.287846	+	0.957677i	$0.407061\pi$
$770$		0			0
$771$	−7.05834			−0.254200
$772$	2.60664	+	9.72810i	0.0938149	+	0.350122i
$773$	−22.3797	−	5.99662i	−0.804941	−	0.215683i	−0.167189	−	0.985925i	$-0.553469\pi$
$773$	−22.3797	−	5.99662i	−0.804941	−	0.215683i	−0.637752	+	0.770241i	$0.720136\pi$
$774$	−0.449799	+	0.259692i	−0.0161677	+	0.00933443i
$775$		0			0
$776$		−	0.654289i		−	0.0234876i
$777$	30.2055	−	1.75211i	1.08362	−	0.0628567i
$778$	12.6018	+	12.6018i	0.451798	+	0.451798i
$779$	−37.2434	−	21.5025i	−1.33438	−	0.770406i
$780$		0			0
$781$	−15.2210	−	26.3636i	−0.544651	−	0.943363i
$782$	−32.0819	+	8.59632i	−1.14725	+	0.307404i
$783$	1.09999	−	1.09999i	0.0393106	−	0.0393106i
$784$	−2.77559	+	6.42620i	−0.0991284	+	0.229507i
$785$		0			0
$786$	0.186862	−	0.323655i	0.00666516	−	0.0115444i
$787$	0.544910	−	2.03363i	0.0194239	−	0.0724912i	−0.955534	−	0.294882i	$-0.904720\pi$
$787$	0.544910	−	2.03363i	0.0194239	−	0.0724912i	0.974958	+	0.222391i	$0.0713862\pi$
$788$	5.94568	−	22.1896i	0.211806	−	0.790471i
$789$	2.84395	−	4.92586i	0.101247	−	0.175365i
$790$		0			0
$791$	−17.6365	+	19.8085i	−0.627081	+	0.704310i
$792$	−3.22048	+	3.22048i	−0.114435	+	0.114435i
$793$	−19.8934	+	5.33042i	−0.706435	+	0.189289i
$794$	12.8232	+	22.2105i	0.455079	+	0.788219i
$795$		0			0
$796$	21.9943	+	12.6984i	0.779569	+	0.450084i
$797$	23.6759	+	23.6759i	0.838642	+	0.838642i	0.988680	−	0.150038i	$-0.0479397\pi$
$797$	23.6759	+	23.6759i	0.838642	+	0.838642i	−0.150038	+	0.988680i	$0.547940\pi$
$798$	−4.48947	+	8.93402i	−0.158926	+	0.316261i
$799$			20.8298i			0.736904i
$800$		0			0
$801$	5.23816	−	3.02425i	0.185081	−	0.106857i
$802$	−5.08192	−	1.36170i	−0.179449	−	0.0480832i
$803$	5.12649	+	19.1323i	0.180910	+	0.675164i
$804$	−9.31550			−0.328532
$805$		0			0
$806$	9.78915			0.344808
$807$	1.99493	+	7.44518i	0.0702249	+	0.262083i
$808$	−5.41115	−	1.44991i	−0.190364	−	0.0510078i
$809$	1.15441	−	0.666500i	0.0405869	−	0.0234329i	−0.479569	−	0.877504i	$-0.659207\pi$
$809$	1.15441	−	0.666500i	0.0405869	−	0.0234329i	0.520156	+	0.854071i	$0.325874\pi$
$810$		0			0
$811$		−	41.6705i		−	1.46325i	−0.681708	−	0.731624i	$-0.738763\pi$
$811$		−	41.6705i		−	1.46325i	0.681708	−	0.731624i	$-0.261237\pi$
$812$	3.43924	−	2.26086i	0.120694	−	0.0793406i
$813$	−12.6475	−	12.6475i	−0.443568	−	0.443568i
$814$	45.1059	+	26.0419i	1.58096	+	0.912768i
$815$		0			0
$816$	−2.06220	−	3.57183i	−0.0721914	−	0.125039i
$817$	−1.89593	+	0.508013i	−0.0663302	+	0.0177731i
$818$	−5.92234	+	5.92234i	−0.207070	+	0.207070i
$819$	2.09074	+	6.31449i	0.0730564	+	0.220646i
$820$		0			0
$821$	16.0833	−	27.8571i	0.561312	−	0.972221i	−0.436070	−	0.899913i	$-0.643630\pi$
$821$	16.0833	−	27.8571i	0.561312	−	0.972221i	0.997382	−	0.0723083i	$-0.0230366\pi$
$822$	−0.688094	+	2.56800i	−0.0240000	+	0.0895693i
$823$	−3.82988	+	14.2933i	−0.133501	+	0.498233i	−1.00000		0.000946758i	$-0.999699\pi$
$823$	−3.82988	+	14.2933i	−0.133501	+	0.498233i	0.866498	+	0.499180i	$0.166365\pi$
$824$	−2.77901	+	4.81338i	−0.0968113	+	0.167682i
$825$		0			0
$826$	0.875423	+	0.779431i	0.0304599	+	0.0271199i
$827$	34.2632	−	34.2632i	1.19145	−	1.19145i	0.214788	−	0.976661i	$-0.431094\pi$
$827$	34.2632	−	34.2632i	1.19145	−	1.19145i	0.976661	−	0.214788i	$-0.0689062\pi$
$828$	−7.77857	+	2.08426i	−0.270324	+	0.0724331i
$829$	25.2456	+	43.7267i	0.876817	+	1.51869i	0.854814	+	0.518934i	$0.173671\pi$
$829$	25.2456	+	43.7267i	0.876817	+	1.51869i	0.0220025	+	0.999758i	$0.492996\pi$
$830$		0			0
$831$	12.7707	+	7.37318i	0.443011	+	0.255773i
$832$	−1.77772	−	1.77772i	−0.0616313	−	0.0616313i
$833$	−4.19779	+	28.5640i	−0.145445	+	0.989682i
$834$		−	4.58070i		−	0.158617i
$835$		0			0
$836$	−14.9058	+	8.60589i	−0.515529	+	0.297641i
$837$	3.76106	+	1.00777i	0.130001	+	0.0348338i
$838$	2.46675	+	9.20603i	0.0852124	+	0.318017i
$839$	−22.4313			−0.774414			−0.387207	−	0.921993i	$-0.626560\pi$
$839$	−22.4313			−0.774414			−0.387207	+	0.921993i	$0.626560\pi$
$840$		0			0
$841$	26.5800			0.916553
$842$	−4.36008	−	16.2721i	−0.150258	−	0.560772i
$843$	0.567387	+	0.152031i	0.0195418	+	0.00523622i
$844$	11.7937	−	6.80911i	0.405957	−	0.234379i
$845$		0			0
$846$			5.05038i			0.173636i
$847$	23.0329	+	11.5744i	0.791420	+	0.397700i
$848$	−5.96425	−	5.96425i	−0.204813	−	0.204813i
$849$	−16.1212	−	9.30757i	−0.553278	−	0.319435i
$850$		0			0
$851$	46.0461	+	79.7542i	1.57844	+	2.73394i
$852$	6.45627	−	1.72995i	0.221188	−	0.0592672i
$853$	−24.4497	+	24.4497i	−0.837140	+	0.837140i	−0.988482	−	0.151341i	$-0.951641\pi$
$853$	−24.4497	+	24.4497i	−0.837140	+	0.837140i	0.151341	+	0.988482i	$0.451641\pi$
$854$	−21.2250	−	4.38784i	−0.726305	−	0.150149i
$855$		0			0
$856$	3.74518	−	6.48684i	0.128008	−	0.221716i
$857$	−3.75655	+	14.0196i	−0.128321	+	0.478901i	−0.999936	−	0.0112896i	$-0.996406\pi$
$857$	−3.75655	+	14.0196i	−0.128321	+	0.478901i	0.871615	+	0.490191i	$0.163073\pi$
$858$	−2.96354	+	11.0601i	−0.101173	+	0.377585i
$859$	8.65502	−	14.9909i	0.295306	−	0.511484i	−0.679750	−	0.733444i	$-0.737912\pi$
$859$	8.65502	−	14.9909i	0.295306	−	0.511484i	0.975056	+	0.221959i	$0.0712452\pi$
$860$		0			0
$861$	−29.4842	−	6.09527i	−1.00482	−	0.207726i
$862$	−15.2439	+	15.2439i	−0.519209	+	0.519209i
$863$	−9.04469	+	2.42352i	−0.307885	+	0.0824975i	−0.409453	−	0.912331i	$-0.634281\pi$
$863$	−9.04469	+	2.42352i	−0.307885	+	0.0824975i	0.101568	+	0.994829i	$0.467614\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	−31.6992	−	18.3016i	−1.07718	−	0.621912i
$867$	−0.00752068	−	0.00752068i	−0.000255416	−	0.000255416i
$868$	9.20499	+	4.62564i	0.312438	+	0.157005i
$869$		−	21.4717i		−	0.728378i
$870$		0			0
$871$	−20.2822	+	11.7099i	−0.687236	+	0.396776i
$872$	1.41688	+	0.379653i	0.0479817	+	0.0128567i
$873$	−0.169342	−	0.631994i	−0.00573137	−	0.0213898i
$874$	−30.4331			−1.02942
$875$		0			0
$876$	−4.34898			−0.146939
$877$	9.68626	+	36.1496i	0.327082	+	1.22069i	0.912202	+	0.409740i	$0.134381\pi$
$877$	9.68626	+	36.1496i	0.327082	+	1.22069i	−0.585120	+	0.810946i	$0.698953\pi$
$878$	20.4580	+	5.48171i	0.690425	+	0.184999i
$879$	25.3199	−	14.6185i	0.854020	−	0.493069i
$880$		0			0
$881$			49.1425i			1.65565i	0.560984	+	0.827827i	$0.310423\pi$
$881$			49.1425i			1.65565i	−0.560984	+	0.827827i	$0.689577\pi$
$882$	−1.01780	+	6.92561i	−0.0342709	+	0.233197i
$883$	−22.9167	−	22.9167i	−0.771207	−	0.771207i	0.207110	−	0.978318i	$-0.433594\pi$
$883$	−22.9167	−	22.9167i	−0.771207	−	0.771207i	−0.978318	+	0.207110i	$0.933594\pi$
$884$	−8.97985	−	5.18452i	−0.302025	−	0.174374i
$885$		0			0
$886$	2.07519	+	3.59433i	0.0697173	+	0.120754i
$887$	25.3392	−	6.78961i	0.850806	−	0.227973i	0.193036	−	0.981192i	$-0.438167\pi$
$887$	25.3392	−	6.78961i	0.850806	−	0.227973i	0.657770	+	0.753219i	$0.271500\pi$
$888$	−8.08634	+	8.08634i	−0.271360	+	0.271360i
$889$	36.0986	+	32.1403i	1.21071	+	1.07795i
$890$		0			0
$891$	−2.27722	+	3.94427i	−0.0762899	+	0.132138i
$892$	5.79830	−	21.6395i	0.194141	−	0.724545i
$893$	−4.93981	+	18.4356i	−0.165304	+	0.616925i
$894$	8.62203	−	14.9338i	0.288364	−	0.499461i
$895$		0			0
$896$	−0.831614	−	2.51166i	−0.0277823	−	0.0839086i
$897$	−14.3159	+	14.3159i	−0.477995	+	0.477995i
$898$	28.3785	−	7.60399i	0.947002	−	0.253748i
$899$	−3.02860	−	5.24569i	−0.101010	−	0.174954i
$900$		0			0
$901$	−30.1274	−	17.3941i	−1.00369	−	0.579481i
$902$	−36.6479	−	36.6479i	−1.22024	−	1.22024i
$903$	−1.14827	+	0.754842i	−0.0382121	+	0.0251196i
$904$		−	10.0244i		−	0.333407i
$905$		0			0
$906$	4.82177	−	2.78385i	0.160193	−	0.0924872i
$907$	1.22193	+	0.327416i	0.0405736	+	0.0108717i	0.279049	−	0.960277i	$-0.409981\pi$
$907$	1.22193	+	0.327416i	0.0405736	+	0.0108717i	−0.238475	+	0.971149i	$0.576648\pi$
$908$	2.83476	+	10.5795i	0.0940749	+	0.351092i
$909$	−5.60204			−0.185808
$910$		0			0
$911$	−49.7996			−1.64993			−0.824967	−	0.565182i	$-0.808806\pi$
$911$	−49.7996			−1.64993			−0.824967	+	0.565182i	$0.808806\pi$
$912$	−0.978107	−	3.65035i	−0.0323884	−	0.120875i
$913$	20.0156	+	5.36318i	0.662421	+	0.177495i
$914$	0.408203	−	0.235676i	0.0135021	−	0.00779547i
$915$		0			0
$916$		−	28.9443i		−	0.956347i
$917$	0.443974	−	0.883504i	0.0146613	−	0.0291759i
$918$	−2.91639	−	2.91639i	−0.0962551	−	0.0962551i
$919$	43.6221	+	25.1852i	1.43896	+	0.830784i	0.997777	−	0.0666338i	$-0.0212259\pi$
$919$	43.6221	+	25.1852i	1.43896	+	0.830784i	0.441182	+	0.897418i	$0.354559\pi$
$920$		0			0
$921$	1.15586	+	2.00201i	0.0380870	+	0.0659686i
$922$	−25.4231	+	6.81209i	−0.837264	+	0.224344i
$923$	11.8823	−	11.8823i	0.391112	−	0.391112i
$924$	−8.01287	+	8.99971i	−0.263604	+	0.296069i
$925$		0			0
$926$	0.725623	−	1.25682i	0.0238455	−	0.0413015i
$927$	−1.43852	+	5.36863i	−0.0472472	+	0.176329i
$928$	−0.402626	+	1.50262i	−0.0132168	+	0.0493259i
$929$	11.4115	−	19.7652i	0.374398	−	0.648476i	−0.615839	−	0.787872i	$-0.711183\pi$
$929$	11.4115	−	19.7652i	0.374398	−	0.648476i	0.990237	+	0.139396i	$0.0445161\pi$
$930$		0			0
$931$	−10.4893	+	24.2854i	−0.343773	+	0.795921i
$932$	−0.998499	+	0.998499i	−0.0327069	+	0.0327069i
$933$	13.4109	−	3.59343i	0.439052	−	0.117644i
$934$	−15.5068	−	26.8586i	−0.507399	−	0.878841i
$935$		0			0
$936$	−2.17725	−	1.25704i	−0.0711658	−	0.0410876i
$937$	24.9461	+	24.9461i	0.814954	+	0.814954i	0.985372	−	0.170418i	$-0.0545117\pi$
$937$	24.9461	+	24.9461i	0.814954	+	0.814954i	−0.170418	+	0.985372i	$0.554512\pi$
$938$	−24.6051	+	1.42725i	−0.803386	+	0.0466015i
$939$		−	13.4904i		−	0.440242i
$940$		0			0
$941$	−16.1409	+	9.31896i	−0.526179	+	0.303789i	−0.739459	−	0.673202i	$-0.764919\pi$
$941$	−16.1409	+	9.31896i	−0.526179	+	0.303789i	0.213280	+	0.976991i	$0.431585\pi$
$942$	−3.99014	−	1.06916i	−0.130006	−	0.0348350i
$943$	−23.7181	−	88.5173i	−0.772369	−	2.88252i
$944$	−0.443022			−0.0144191
$945$		0			0
$946$	−2.36551			−0.0769092
$947$	−0.657006	−	2.45198i	−0.0213498	−	0.0796786i	0.954429	−	0.298438i	$-0.0964656\pi$
$947$	−0.657006	−	2.45198i	−0.0213498	−	0.0796786i	−0.975779	+	0.218760i	$0.929799\pi$
$948$	4.55381	+	1.22019i	0.147901	+	0.0396299i
$949$	−9.46884	+	5.46684i	−0.307372	+	0.177461i
$950$		0			0
$951$		−	13.7171i		−	0.444806i
$952$	−5.99416	−	9.11836i	−0.194272	−	0.295528i
$953$	−31.1031	−	31.1031i	−1.00753	−	1.00753i	−0.999971	−	0.00755624i	$-0.997595\pi$
$953$	−31.1031	−	31.1031i	−1.00753	−	1.00753i	−0.00755624	−	0.999971i	$-0.502405\pi$
$954$	−7.30469	−	4.21737i	−0.236498	−	0.136542i
$955$		0			0
$956$	2.18215	+	3.77959i	0.0705758	+	0.122241i
$957$	6.84361	−	1.83374i	0.221222	−	0.0592764i
$958$	−23.5834	+	23.5834i	−0.761945	+	0.761945i
$959$	−1.42402	+	6.88831i	−0.0459840	+	0.222435i
$960$		0			0
$961$	−7.91940	+	13.7168i	−0.255465	+	0.442477i
$962$	−7.44117	+	27.7708i	−0.239913	+	0.895368i
$963$	1.93865	−	7.23514i	0.0624721	−	0.233149i
$964$	1.53496	−	2.65862i	0.0494376	−	0.0856284i
$965$		0			0
$966$	−20.2263	+	6.69696i	−0.650770	+	0.215471i
$967$	14.7707	−	14.7707i	0.474993	−	0.474993i	−0.428533	−	0.903526i	$-0.640969\pi$
$967$	14.7707	−	14.7707i	0.474993	−	0.474993i	0.903526	+	0.428533i	$0.140969\pi$
$968$	−9.41101	+	2.52167i	−0.302481	+	0.0810496i
$969$	−7.79328	−	13.4984i	−0.250356	−	0.433630i
$970$		0			0
$971$	9.39194	+	5.42244i	0.301402	+	0.174014i	0.643072	−	0.765805i	$-0.277659\pi$
$971$	9.39194	+	5.42244i	0.301402	+	0.174014i	−0.341671	+	0.939820i	$0.610993\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	−0.701821	−	12.0990i	−0.0224994	−	0.387878i
$974$			3.30368i			0.105857i
$975$		0			0
$976$	7.09442	−	4.09597i	0.227087	−	0.131109i
$977$	16.5560	+	4.43616i	0.529673	+	0.141925i	0.513737	−	0.857948i	$-0.328261\pi$
$977$	16.5560	+	4.43616i	0.529673	+	0.141925i	0.0159356	+	0.999873i	$0.494927\pi$
$978$	5.62644	+	20.9982i	0.179914	+	0.671447i
$979$	27.5476			0.880426
$980$		0			0
$981$	1.46687			0.0468334
$982$	−0.936018	−	3.49327i	−0.0298695	−	0.111475i
$983$	1.62331	+	0.434966i	0.0517757	+	0.0138732i	0.284614	−	0.958642i	$-0.408135\pi$
$983$	1.62331	+	0.434966i	0.0517757	+	0.0138732i	−0.232838	+	0.972515i	$0.574801\pi$
$984$	9.85506	−	5.68982i	0.314168	−	0.181385i
$985$		0			0
$986$			6.41602i			0.204328i
$987$	0.773782	+	13.3396i	0.0246298	+	0.424605i
$988$	−6.71821	−	6.71821i	−0.213735	−	0.213735i
$989$	−3.62222	−	2.09129i	−0.115180	−	0.0664992i
$990$		0			0
$991$	8.40392	+	14.5560i	0.266959	+	0.462387i	0.968075	−	0.250660i	$-0.0806478\pi$
$991$	8.40392	+	14.5560i	0.266959	+	0.462387i	−0.701116	+	0.713047i	$0.747314\pi$
$992$	−3.76106	+	1.00777i	−0.119414	+	0.0319968i
$993$	−23.5033	+	23.5033i	−0.745855	+	0.745855i
$994$	16.7880	−	5.55853i	0.532482	−	0.176306i
$995$		0			0
$996$	−2.27489	+	3.94022i	−0.0720826	+	0.124851i
$997$	−4.51978	+	16.8680i	−0.143143	+	0.534216i	0.856688	+	0.515835i	$0.172518\pi$
$997$	−4.51978	+	16.8680i	−0.143143	+	0.534216i	−0.999831	+	0.0183818i	$0.994149\pi$
$998$	0.167661	−	0.625718i	0.00530721	−	0.0198068i
$999$	−5.71790	+	9.90370i	−0.180906	+	0.313339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.g.943.1		16
5.2	odd	4		1050.2.bc.h.607.4		16
5.3	odd	4		210.2.u.a.187.2	yes	16
5.4	even	2		210.2.u.b.103.4	yes	16
7.3	odd	6		1050.2.bc.h.493.4		16
15.8	even	4		630.2.bv.a.397.3		16
15.14	odd	2		630.2.bv.b.523.1		16
35.3	even	12		210.2.u.b.157.4	yes	16
35.9	even	6		1470.2.m.e.1273.5		16
35.17	even	12	inner	1050.2.bc.g.157.1		16
35.19	odd	6		1470.2.m.d.1273.8		16
35.23	odd	12		1470.2.m.d.97.8		16
35.24	odd	6		210.2.u.a.73.2	✓	16
35.33	even	12		1470.2.m.e.97.5		16
105.38	odd	12		630.2.bv.b.577.1		16
105.59	even	6		630.2.bv.a.73.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.2	✓	16	35.24	odd	6
210.2.u.a.187.2	yes	16	5.3	odd	4
210.2.u.b.103.4	yes	16	5.4	even	2
210.2.u.b.157.4	yes	16	35.3	even	12
630.2.bv.a.73.3		16	105.59	even	6
630.2.bv.a.397.3		16	15.8	even	4
630.2.bv.b.523.1		16	15.14	odd	2
630.2.bv.b.577.1		16	105.38	odd	12
1050.2.bc.g.157.1		16	35.17	even	12	inner
1050.2.bc.g.943.1		16	1.1	even	1	trivial
1050.2.bc.h.493.4		16	7.3	odd	6
1050.2.bc.h.607.4		16	5.2	odd	4
1470.2.m.d.97.8		16	35.23	odd	12
1470.2.m.d.1273.8		16	35.19	odd	6
1470.2.m.e.97.5		16	35.33	even	12
1470.2.m.e.1273.5		16	35.9	even	6

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.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(-0.153213 - 2.64131i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(-0.153213 - 2.64131i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(2.27722 + 3.94427i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(-1.77772 + 1.77772i) q^{13} +(-2.51166 + 0.831614i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.06747 - 3.98386i) q^{17} +(0.258819 - 0.965926i) q^{18} +(1.88956 - 3.27281i) q^{19} +(0.535629 - 2.59097i) q^{21} +(3.22048 - 3.22048i) q^{22} +(7.77857 - 2.08426i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.17725 + 1.25704i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.45334 + 2.21084i) q^{28} -1.55563i q^{29} +(3.37208 - 1.94687i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(1.17878 + 4.39926i) q^{33} -4.12440 q^{34} -1.00000 q^{36} +(2.95980 + 11.0461i) q^{37} +(-3.65035 - 0.978107i) q^{38} +(-2.17725 + 1.25704i) q^{39} -11.3796i q^{41} +(-2.64131 + 0.153213i) q^{42} +(-0.367260 - 0.367260i) q^{43} +(-3.94427 - 2.27722i) q^{44} +(-4.02648 - 6.97408i) q^{46} +(-4.87829 + 1.30713i) q^{47} +(0.707107 - 0.707107i) q^{48} +(-6.95305 + 0.809365i) q^{49} +(2.06220 - 3.57183i) q^{51} +(0.650691 - 2.42841i) q^{52} +(2.18307 - 8.14732i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.75935 - 1.97603i) q^{56} +(2.67224 - 2.67224i) q^{57} +(-1.50262 + 0.402626i) q^{58} +(-0.221511 - 0.383668i) q^{59} +(7.09442 + 4.09597i) q^{61} +(-2.75329 - 2.75329i) q^{62} +(1.18797 - 2.36405i) q^{63} +1.00000i q^{64} +(3.94427 - 2.27722i) q^{66} +(8.99808 + 2.41103i) q^{67} +(1.06747 + 3.98386i) q^{68} +8.05297 q^{69} -6.68403 q^{71} +(0.258819 + 0.965926i) q^{72} +(4.20080 + 1.12560i) q^{73} +(9.90370 - 5.71790i) q^{74} +3.77912i q^{76} +(10.0691 - 6.61917i) q^{77} +(1.77772 + 1.77772i) q^{78} +(-4.08283 - 2.35722i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-10.9919 + 2.94527i) q^{82} +(3.21718 - 3.21718i) q^{83} +(0.831614 + 2.51166i) q^{84} +(-0.259692 + 0.449799i) q^{86} +(0.402626 - 1.50262i) q^{87} +(-1.17878 + 4.39926i) q^{88} +(3.02425 - 5.23816i) q^{89} +(4.96788 + 4.42314i) q^{91} +(-5.69431 + 5.69431i) q^{92} +(3.76106 - 1.00777i) q^{93} +(2.52519 + 4.37376i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(-0.462652 - 0.462652i) q^{97} +(2.58137 + 6.50665i) q^{98} +4.55445i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{7}+O(q^{10}) \) 16 * q + 4 * q^7	\( 16 q + 4 q^{7} + 4 q^{11} - 16 q^{13} - 16 q^{14} + 8 q^{16} - 12 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{22} + 40 q^{23} + 8 q^{24} - 12 q^{26} + 4 q^{28} - 24 q^{31} - 4 q^{33} - 16 q^{34} - 16 q^{36} + 8 q^{37} + 20 q^{38} + 12 q^{39} - 8 q^{42} + 24 q^{43} - 4 q^{46} - 52 q^{49} + 8 q^{51} - 8 q^{52} + 28 q^{53} + 8 q^{54} + 8 q^{56} + 8 q^{57} + 12 q^{58} - 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 84 q^{67} - 12 q^{68} + 8 q^{69} - 32 q^{71} - 16 q^{73} + 24 q^{74} - 44 q^{77} + 16 q^{78} - 12 q^{79} + 8 q^{81} - 36 q^{82} - 16 q^{83} - 4 q^{84} - 8 q^{86} - 48 q^{87} + 4 q^{88} + 16 q^{89} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 8 q^{94} + 44 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q + 4 * q^7 + 4 * q^11 - 16 * q^13 - 16 * q^14 + 8 * q^16 - 12 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^22 + 40 * q^23 + 8 * q^24 - 12 * q^26 + 4 * q^28 - 24 * q^31 - 4 * q^33 - 16 * q^34 - 16 * q^36 + 8 * q^37 + 20 * q^38 + 12 * q^39 - 8 * q^42 + 24 * q^43 - 4 * q^46 - 52 * q^49 + 8 * q^51 - 8 * q^52 + 28 * q^53 + 8 * q^54 + 8 * q^56 + 8 * q^57 + 12 * q^58 - 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 84 * q^67 - 12 * q^68 + 8 * q^69 - 32 * q^71 - 16 * q^73 + 24 * q^74 - 44 * q^77 + 16 * q^78 - 12 * q^79 + 8 * q^81 - 36 * q^82 - 16 * q^83 - 4 * q^84 - 8 * q^86 - 48 * q^87 + 4 * q^88 + 16 * q^89 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 8 * q^94 + 44 * q^97 - 24 * q^98

Introduction

L-functions

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