LMFDB - Embedded newform 1050.2.bc.h.493.4

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			493.4
Root			$-1.09227 - 0.838128i$ of defining polynomial
Character	$\chi$	$=$	1050.493
Dual form			1050.2.bc.h.607.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	2.64131	+	0.153213i	0.998322	+	0.0579090i
$7$	2.64131	+	0.153213i	0.998322	+	0.0579090i
$8$	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	−0.286319	−	0.958134i	$-0.592432\pi$
$11$	2.27722	−	3.94427i	0.686609	−	1.18924i	0.972928	−	0.231107i	$-0.0742348\pi$
$12$	−0.258819	+	0.965926i	−0.0747146	+	0.278839i
$13$	1.77772	−	1.77772i	0.493051	−	0.493051i	−0.416215	−	0.909266i	$-0.636644\pi$
$13$	1.77772	−	1.77772i	0.493051	−	0.493051i	0.909266	+	0.416215i	$0.136644\pi$
$14$	2.51166	+	0.831614i	0.671268	+	0.222258i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.98386	−	1.06747i	0.966228	−	0.258900i	0.258993	−	0.965879i	$-0.416609\pi$
$17$	3.98386	−	1.06747i	0.966228	−	0.258900i	0.707234	+	0.706979i	$0.249943\pi$
$18$	−0.965926	+	0.258819i	−0.227671	+	0.0610042i
$19$	−1.88956	−	3.27281i	−0.433494	−	0.750834i	0.563677	−	0.825995i	$-0.309386\pi$
$19$	−1.88956	−	3.27281i	−0.433494	−	0.750834i	−0.997171	+	0.0751610i	$0.976053\pi$
$20$		0			0
$21$	0.535629	+	2.59097i	0.116884	+	0.565395i
$22$	3.22048	−	3.22048i	0.686609	−	0.686609i
$23$	−2.08426	+	7.77857i	−0.434599	+	1.62194i	0.307426	+	0.951572i	$0.400532\pi$
$23$	−2.08426	+	7.77857i	−0.434599	+	1.62194i	−0.742025	+	0.670372i	$0.766134\pi$
$24$	−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
$28$	2.21084	+	1.45334i	0.417809	+	0.274656i
$29$		−	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	0.771258	−	0.636522i	$-0.219628\pi$
$31$	3.37208	+	1.94687i	0.605643	+	0.349668i	−0.165615	+	0.986190i	$0.552961\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	4.39926	+	1.17878i	0.765813	+	0.205199i
$34$	4.12440			0.707328
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−11.0461	−	2.95980i	−1.81597	−	0.486589i	−0.819697	−	0.572797i	$-0.805858\pi$
$37$	−11.0461	−	2.95980i	−1.81597	−	0.486589i	−0.996277	+	0.0862078i	$0.972525\pi$
$38$	−0.978107	−	3.65035i	−0.158670	−	0.592164i
$39$	2.17725	+	1.25704i	0.348640	+	0.201287i
$40$		0			0
$41$			11.3796i			1.77720i	0.458682	+	0.888600i	$0.348322\pi$
$41$			11.3796i			1.77720i	−0.458682	+	0.888600i	$0.651678\pi$
$42$	−0.153213	+	2.64131i	−0.0236412	+	0.407563i
$43$	−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
$47$	−1.30713	+	4.87829i	−0.190665	+	0.711572i	0.802681	+	0.596408i	$0.203406\pi$
$47$	−1.30713	+	4.87829i	−0.190665	+	0.711572i	−0.993347	+	0.115164i	$0.963261\pi$
$48$	−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
$52$	2.42841	−	0.650691i	0.336760	−	0.0902346i
$53$	−8.14732	+	2.18307i	−1.11912	+	0.299868i	−0.770528	−	0.637407i	$-0.780007\pi$
$53$	−8.14732	+	2.18307i	−1.11912	+	0.299868i	−0.348593	+	0.937274i	$0.613341\pi$
$54$	−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
$58$	0.402626	−	1.50262i	0.0528674	−	0.197304i
$59$	0.221511	−	0.383668i	0.0288383	−	0.0499493i	−0.851246	−	0.524767i	$-0.824153\pi$
$59$	0.221511	−	0.383668i	0.0288383	−	0.0499493i	0.880084	+	0.474817i	$0.157486\pi$
$60$		0			0
$61$	7.09442	−	4.09597i	0.908348	−	0.524435i	0.0284488	−	0.999595i	$-0.490943\pi$
$61$	7.09442	−	4.09597i	0.908348	−	0.524435i	0.879899	+	0.475160i	$0.157610\pi$
$62$	2.75329	+	2.75329i	0.349668	+	0.349668i
$63$	−2.36405	+	1.18797i	−0.297842	+	0.149670i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	3.94427	+	2.27722i	0.485506	+	0.280307i
$67$	−2.41103	−	8.99808i	−0.294554	−	1.09929i	−0.941571	−	0.336815i	$-0.890650\pi$
$67$	−2.41103	−	8.99808i	−0.294554	−	1.09929i	0.647017	−	0.762476i	$-0.276016\pi$
$68$	3.98386	+	1.06747i	0.483114	+	0.129450i
$69$	−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	$0.629818\pi$
$72$	−0.965926	−	0.258819i	−0.113835	−	0.0305021i
$73$	1.12560	+	4.20080i	0.131742	+	0.491666i	0.999990	−	0.00446349i	$-0.00142078\pi$
$73$	1.12560	+	4.20080i	0.131742	+	0.491666i	−0.868249	+	0.496130i	$0.834754\pi$
$74$	−9.90370	−	5.71790i	−1.15128	−	0.664693i
$75$		0			0
$76$		−	3.77912i		−	0.433494i
$77$	6.61917	−	10.0691i	0.754324	−	1.14748i
$78$	1.77772	+	1.77772i	0.201287	+	0.201287i
$79$	4.08283	−	2.35722i	0.459354	−	0.265208i	−0.252418	−	0.967618i	$-0.581226\pi$
$79$	4.08283	−	2.35722i	0.459354	−	0.265208i	0.711773	+	0.702410i	$0.247893\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−2.94527	+	10.9919i	−0.325250	+	1.21385i
$83$	−3.21718	+	3.21718i	−0.353131	+	0.353131i	−0.861273	−	0.508142i	$-0.830332\pi$
$83$	−3.21718	+	3.21718i	−0.353131	+	0.353131i	0.508142	+	0.861273i	$0.330332\pi$
$84$	−0.831614	+	2.51166i	−0.0907365	+	0.274044i
$85$		0			0
$86$	−0.259692	−	0.449799i	−0.0280033	−	0.0485031i
$87$	1.50262	−	0.402626i	0.161098	−	0.0431660i
$88$	4.39926	−	1.17878i	0.468963	−	0.125658i
$89$	−3.02425	−	5.23816i	−0.320570	−	0.555244i	0.660035	−	0.751234i	$-0.270541\pi$
$89$	−3.02425	−	5.23816i	−0.320570	−	0.555244i	−0.980606	+	0.195990i	$0.937208\pi$
$90$		0			0
$91$	4.96788	−	4.42314i	0.520775	−	0.463671i
$92$	−5.69431	+	5.69431i	−0.593673	+	0.593673i
$93$	−1.00777	+	3.76106i	−0.104501	+	0.390004i
$94$	−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	0.730204	−	0.683229i	$-0.239425\pi$
$97$	0.462652	+	0.462652i	0.0469752	+	0.0469752i	−0.683229	+	0.730204i	$0.739425\pi$
$98$	6.50665	+	2.58137i	0.657271	+	0.260758i
$99$			4.55445i			0.457739i
$100$		0			0
$101$	−4.85151	−	2.80102i	−0.482743	−	0.278712i	0.238816	−	0.971065i	$-0.423241\pi$
$101$	−4.85151	−	2.80102i	−0.482743	−	0.278712i	−0.721559	+	0.692353i	$0.756574\pi$
$102$	1.06747	+	3.98386i	0.105695	+	0.394461i
$103$	5.36863	+	1.43852i	0.528987	+	0.141742i	0.513420	−	0.858137i	$-0.328378\pi$
$103$	5.36863	+	1.43852i	0.528987	+	0.141742i	0.0155666	+	0.999879i	$0.495045\pi$
$104$	2.51408			0.246525
$105$		0			0
$106$	−8.43473			−0.819253
$107$	7.23514	+	1.93865i	0.699447	+	0.187416i	0.590983	−	0.806684i	$-0.298740\pi$
$107$	7.23514	+	1.93865i	0.699447	+	0.187416i	0.108464	+	0.994100i	$0.465407\pi$
$108$	−0.258819	−	0.965926i	−0.0249049	−	0.0929463i
$109$	−1.27034	−	0.733433i	−0.121677	−	0.0702501i	0.437926	−	0.899011i	$-0.355713\pi$
$109$	−1.27034	−	0.733433i	−0.121677	−	0.0702501i	−0.559603	+	0.828761i	$0.689046\pi$
$110$		0			0
$111$		−	11.4358i		−	1.08544i
$112$	1.18797	+	2.36405i	0.112253	+	0.223382i
$113$	−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
$117$	−0.650691	+	2.42841i	−0.0601564	+	0.224507i
$118$	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
$122$	7.91280	−	2.12023i	0.716391	−	0.191957i
$123$	−10.9919	+	2.94527i	−0.991105	+	0.265566i
$124$	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	$0.949182\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	0.259692	−	0.449799i	0.0228646	−	0.0396026i
$130$		0			0
$131$	0.323655	−	0.186862i	0.0282779	−	0.0163262i	−0.485794	−	0.874073i	$-0.661470\pi$
$131$	0.323655	−	0.186862i	0.0282779	−	0.0163262i	0.514072	+	0.857747i	$0.328136\pi$
$132$	3.22048	+	3.22048i	0.280307	+	0.280307i
$133$	−4.48947	−	8.93402i	−0.389287	−	0.774677i
$134$		−	9.31550i		−	0.804737i
$135$		0			0
$136$	3.57183	+	2.06220i	0.306282	+	0.176832i
$137$	0.688094	+	2.56800i	0.0587878	+	0.219399i	0.989070	−	0.147445i	$-0.0471049\pi$
$137$	0.688094	+	2.56800i	0.0587878	+	0.219399i	−0.930282	+	0.366844i	$0.880438\pi$
$138$	−7.77857	−	2.08426i	−0.662156	−	0.177424i
$139$	−4.58070			−0.388530			−0.194265	−	0.980949i	$-0.562232\pi$
$139$	−4.58070			−0.388530			−0.194265	+	0.980949i	$0.562232\pi$
$140$		0			0
$141$	−5.05038			−0.425319
$142$	−6.45627	−	1.72995i	−0.541798	−	0.145174i
$143$	−2.96354	−	11.0601i	−0.247823	−	0.924889i
$144$	−0.866025	−	0.500000i	−0.0721688	−	0.0416667i
$145$		0			0
$146$			4.34898i			0.359925i
$147$	1.01780	+	6.92561i	0.0839463	+	0.571215i
$148$	−8.08634	−	8.08634i	−0.664693	−	0.664693i
$149$	−14.9338	+	8.62203i	−1.22342	+	0.706344i	−0.965646	−	0.259860i	$-0.916324\pi$
$149$	−14.9338	+	8.62203i	−1.22342	+	0.706344i	−0.257778	+	0.966204i	$0.582990\pi$
$150$		0			0
$151$	2.78385	−	4.82177i	0.226546	−	0.392390i	−0.730236	−	0.683195i	$-0.760590\pi$
$151$	2.78385	−	4.82177i	0.226546	−	0.392390i	0.956782	+	0.290805i	$0.0939231\pi$
$152$	0.978107	−	3.65035i	0.0793350	−	0.296082i
$153$	−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
$157$	3.99014	−	1.06916i	0.318448	−	0.0853279i	−0.0960544	−	0.995376i	$-0.530622\pi$
$157$	3.99014	−	1.06916i	0.318448	−	0.0853279i	0.414503	+	0.910048i	$0.363956\pi$
$158$	4.55381	−	1.22019i	0.362281	−	0.0970730i
$159$	−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
$163$	5.62644	−	20.9982i	0.440697	−	1.64470i	−0.286357	−	0.958123i	$-0.592444\pi$
$163$	5.62644	−	20.9982i	0.440697	−	1.64470i	0.727054	−	0.686580i	$-0.240889\pi$
$164$	−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	$-0.843379\pi$
$167$	−17.4949	−	17.4949i	−1.35380	−	1.35380i	−0.472425	−	0.881371i	$-0.656621\pi$
$168$	−1.45334	+	2.21084i	−0.112128	+	0.170570i
$169$			6.67942i			0.513802i
$170$		0			0
$171$	3.27281	+	1.88956i	0.250278	+	0.144498i
$172$	−0.134426	−	0.501686i	−0.0102499	−	0.0382532i
$173$	16.0017	+	4.28763i	1.21658	+	0.325982i	0.809342	−	0.587338i	$-0.199824\pi$
$173$	16.0017	+	4.28763i	1.21658	+	0.325982i	0.407241	+	0.913321i	$0.366491\pi$
$174$	1.55563			0.117932
$175$		0			0
$176$	4.55445			0.343304
$177$	0.427926	+	0.114663i	0.0321649	+	0.00861856i
$178$	−1.56547	−	5.84241i	−0.117337	−	0.437907i
$179$	11.0222	+	6.36367i	0.823837	+	0.475643i	0.851738	−	0.523968i	$-0.175549\pi$
$179$	11.0222	+	6.36367i	0.823837	+	0.475643i	−0.0279007	+	0.999611i	$0.508882\pi$
$180$		0			0
$181$		−	9.09951i		−	0.676361i	−0.941081	−	0.338180i	$-0.890189\pi$
$181$		−	9.09951i		−	0.676361i	0.941081	−	0.338180i	$-0.109811\pi$
$182$	5.94340	−	2.98665i	0.440554	−	0.221385i
$183$	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
$187$	4.86175	−	18.1443i	0.355526	−	1.32684i
$188$	−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	−0.980959	−	0.194216i	$-0.937784\pi$
$191$	−9.10308	−	15.7670i	−0.658676	−	1.14086i	0.322283	−	0.946643i	$-0.395550\pi$
$192$	−0.965926	+	0.258819i	−0.0697097	+	0.0186787i
$193$	−9.72810	+	2.60664i	−0.700244	+	0.187630i	−0.591340	−	0.806422i	$-0.701401\pi$
$193$	−9.72810	+	2.60664i	−0.700244	+	0.187630i	−0.108904	+	0.994052i	$0.534734\pi$
$194$	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	$0.944886\pi$
$198$	−1.17878	+	4.39926i	−0.0837721	+	0.312642i
$199$	12.6984	−	21.9943i	0.900168	−	1.55914i	0.0728933	−	0.997340i	$-0.476777\pi$
$199$	12.6984	−	21.9943i	0.900168	−	1.55914i	0.827275	−	0.561797i	$-0.189890\pi$
$200$		0			0
$201$	8.06746	−	4.65775i	0.569035	−	0.328532i
$202$	−3.96124	−	3.96124i	−0.278712	−	0.278712i
$203$	0.238342	−	4.10890i	0.0167283	−	0.288388i
$204$			4.12440i			0.288765i
$205$		0			0
$206$	4.81338	+	2.77901i	0.335364	+	0.193623i
$207$	−2.08426	−	7.77857i	−0.144866	−	0.540648i
$208$	2.42841	+	0.650691i	0.168380	+	0.0451173i
$209$	−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	$0.655299\pi$
$212$	−8.14732	−	2.18307i	−0.559560	−	0.149934i
$213$	−1.72995	−	6.45627i	−0.118534	−	0.442377i
$214$	6.48684	+	3.74518i	0.443432	+	0.256015i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	8.60842	+	5.65893i	0.584378	+	0.384153i
$218$	−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
$222$	2.95980	−	11.0461i	0.198649	−	0.741369i
$223$	15.8412	−	15.8412i	1.06081	−	1.06081i	0.0627803	−	0.998027i	$-0.480003\pi$
$223$	15.8412	−	15.8412i	1.06081	−	1.06081i	0.998027	−	0.0627803i	$-0.0199968\pi$
$224$	0.535629	+	2.59097i	0.0357883	+	0.173116i
$225$		0			0
$226$	−5.01221	−	8.68141i	−0.333407	−	0.577479i
$227$	10.5795	−	2.83476i	0.702184	−	0.188150i	0.109976	−	0.993934i	$-0.464923\pi$
$227$	10.5795	−	2.83476i	0.702184	−	0.188150i	0.592209	+	0.805785i	$0.298256\pi$
$228$	3.65035	−	0.978107i	0.241750	−	0.0647767i
$229$	14.4722	+	25.0665i	0.956347	+	1.65644i	0.731255	+	0.682104i	$0.238935\pi$
$229$	14.4722	+	25.0665i	0.956347	+	1.65644i	0.225092	+	0.974338i	$0.427732\pi$
$230$		0			0
$231$	11.4392	+	3.78754i	0.752645	+	0.249202i
$232$	1.09999	−	1.09999i	0.0722182	−	0.0722182i
$233$	−0.365476	+	1.36397i	−0.0239431	+	0.0893569i	−0.976864	−	0.213864i	$-0.931395\pi$
$233$	−0.365476	+	1.36397i	−0.0239431	+	0.0893569i	0.952920	+	0.303220i	$0.0980619\pi$
$234$	−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
$238$	10.8938	+	0.631910i	0.706141	+	0.0409606i
$239$		−	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	0.411922	−	0.911219i	$-0.364858\pi$
$241$	−2.65862	−	1.53496i	−0.171257	−	0.0988752i	−0.583178	+	0.812344i	$0.698191\pi$
$242$	−2.52167	−	9.41101i	−0.162099	−	0.604963i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	8.19194			0.524435
$245$		0			0
$246$	−11.3796			−0.725539
$247$	−9.17725	−	2.45904i	−0.583934	−	0.156465i
$248$	1.00777	+	3.76106i	0.0639937	+	0.238828i
$249$	−3.94022	−	2.27489i	−0.249701	−	0.144165i
$250$		0			0
$251$			1.25355i			0.0791234i	0.999217	+	0.0395617i	$0.0125962\pi$
$251$			1.25355i			0.0791234i	−0.999217	+	0.0395617i	$0.987404\pi$
$252$	−2.64131	−	0.153213i	−0.166387	−	0.00965150i
$253$	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
$257$	−1.82683	+	6.81783i	−0.113955	+	0.425285i	−0.999207	−	0.0398273i	$-0.987319\pi$
$257$	−1.82683	+	6.81783i	−0.113955	+	0.425285i	0.885252	+	0.465112i	$0.153986\pi$
$258$	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
$262$	0.360990	−	0.0967271i	0.0223021	−	0.00597582i
$263$	−5.49409	+	1.47214i	−0.338780	+	0.0907758i	−0.424198	−	0.905569i	$-0.639444\pi$
$263$	−5.49409	+	1.47214i	−0.338780	+	0.0907758i	0.0854182	+	0.996345i	$0.472777\pi$
$264$	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
$268$	2.41103	−	8.99808i	0.147277	−	0.549645i
$269$	−3.85391	+	6.67517i	−0.234977	+	0.406992i	−0.959266	−	0.282504i	$-0.908835\pi$
$269$	−3.85391	+	6.67517i	−0.234977	+	0.406992i	0.724289	+	0.689496i	$0.242168\pi$
$270$		0			0
$271$	−15.4900	+	8.94316i	−0.940951	+	0.543258i	−0.890258	−	0.455456i	$-0.849476\pi$
$271$	−15.4900	+	8.94316i	−0.940951	+	0.543258i	−0.0506925	+	0.998714i	$0.516143\pi$
$272$	2.91639	+	2.91639i	0.176832	+	0.176832i
$273$	5.55821	+	3.65381i	0.336398	+	0.221139i
$274$			2.65859i			0.160611i
$275$		0			0
$276$	−6.97408	−	4.02648i	−0.419790	−	0.242366i
$277$	−3.81664	−	14.2439i	−0.229319	−	0.855832i	−0.980628	−	0.195881i	$-0.937244\pi$
$277$	−3.81664	−	14.2439i	−0.229319	−	0.855832i	0.751308	−	0.659951i	$-0.229423\pi$
$278$	−4.42461	−	1.18557i	−0.265371	−	0.0711059i
$279$	−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	$0.494423\pi$
$282$	−4.87829	−	1.30713i	−0.290498	−	0.0778387i
$283$	−4.81795	−	17.9809i	−0.286398	−	1.06885i	−0.947812	−	0.318830i	$-0.896710\pi$
$283$	−4.81795	−	17.9809i	−0.286398	−	1.06885i	0.661414	−	0.750021i	$-0.269957\pi$
$284$	−5.78854	−	3.34201i	−0.343486	−	0.198312i
$285$		0			0
$286$		−	11.4502i		−	0.677066i
$287$	−1.74351	+	30.0572i	−0.102916	+	1.77422i
$288$	−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
$292$	−1.12560	+	4.20080i	−0.0658708	+	0.245833i
$293$	−20.6736	+	20.6736i	−1.20777	+	1.20777i	−0.236018	+	0.971749i	$0.575842\pi$
$293$	−20.6736	+	20.6736i	−1.20777	+	1.20777i	−0.971749	+	0.236018i	$0.924158\pi$
$294$	−0.809365	+	6.95305i	−0.0472031	+	0.405510i
$295$		0			0
$296$	−5.71790	−	9.90370i	−0.332346	−	0.575641i
$297$	−4.39926	+	1.17878i	−0.255271	+	0.0683996i
$298$	−16.6565	+	4.46309i	−0.964884	+	0.258540i
$299$	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
$303$	1.44991	−	5.41115i	0.0832954	−	0.310863i
$304$	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	0.658920	−	0.752213i	$-0.271014\pi$
$307$	−1.63464	−	1.63464i	−0.0932937	−	0.0932937i	−0.752213	+	0.658920i	$0.771014\pi$
$308$	10.7669	−	5.41055i	0.613503	−	0.308294i
$309$			5.55802i			0.316185i
$310$		0			0
$311$	12.0239	+	6.94197i	0.681810	+	0.393643i	0.800537	−	0.599284i	$-0.204548\pi$
$311$	12.0239	+	6.94197i	0.681810	+	0.393643i	−0.118727	+	0.992927i	$0.537881\pi$
$312$	0.650691	+	2.42841i	0.0368381	+	0.137482i
$313$	−13.0307	−	3.49157i	−0.736540	−	0.197355i	−0.129000	−	0.991645i	$-0.541177\pi$
$313$	−13.0307	−	3.49157i	−0.736540	−	0.197355i	−0.607540	+	0.794289i	$0.707843\pi$
$314$	4.13090			0.233120
$315$		0			0
$316$	4.71445			0.265208
$317$	13.2497	+	3.55024i	0.744175	+	0.199401i	0.610933	−	0.791682i	$-0.290794\pi$
$317$	13.2497	+	3.55024i	0.744175	+	0.199401i	0.133242	+	0.991083i	$0.457461\pi$
$318$	−2.18307	−	8.14732i	−0.122420	−	0.456879i
$319$	−6.13581	−	3.54251i	−0.343539	−	0.198343i
$320$		0			0
$321$			7.49036i			0.418071i
$322$	−11.7037	+	17.8038i	−0.652223	+	0.992167i
$323$	−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
$327$	0.379653	−	1.41688i	0.0209948	−	0.0783538i
$328$	−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	−0.809108	−	0.587660i	$-0.800049\pi$
$331$	−16.6194	−	28.7856i	−0.913483	−	1.58220i	−0.104375	−	0.994538i	$-0.533284\pi$
$332$	−4.39475	+	1.17757i	−0.241193	+	0.0646275i
$333$	11.0461	−	2.95980i	0.605325	−	0.162196i
$334$	−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	$0.0222121\pi$
$338$	−1.72876	+	6.45183i	−0.0940323	+	0.350933i
$339$	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
$343$	18.2412	+	3.20308i	0.984931	+	0.172950i
$344$		−	0.519384i		−	0.0280033i
$345$		0			0
$346$	14.3467	+	8.28306i	0.771283	+	0.445300i
$347$	−0.532414	−	1.98700i	−0.0285815	−	0.106668i	0.950162	−	0.311758i	$-0.100918\pi$
$347$	−0.532414	−	1.98700i	−0.0285815	−	0.106668i	−0.978743	+	0.205090i	$0.934251\pi$
$348$	1.50262	+	0.402626i	0.0805489	+	0.0215830i
$349$	11.7250			0.627627			0.313814	−	0.949485i	$-0.398393\pi$
$349$	11.7250			0.627627			0.313814	+	0.949485i	$0.398393\pi$
$350$		0			0
$351$	−2.51408			−0.134191
$352$	4.39926	+	1.17878i	0.234481	+	0.0628291i
$353$	2.95640	+	11.0334i	0.157353	+	0.587250i	0.998892	+	0.0470542i	$0.0149833\pi$
$353$	2.95640	+	11.0334i	0.157353	+	0.587250i	−0.841539	+	0.540196i	$0.818350\pi$
$354$	0.383668	+	0.221511i	0.0203917	+	0.0117732i
$355$		0			0
$356$		−	6.04851i		−	0.320570i
$357$	4.89966	+	9.75027i	0.259317	+	0.516039i
$358$	8.99958	+	8.99958i	0.475643	+	0.475643i
$359$	−2.08846	+	1.20577i	−0.110225	+	0.0636383i	−0.554099	−	0.832451i	$-0.686937\pi$
$359$	−2.08846	+	1.20577i	−0.110225	+	0.0636383i	0.443874	+	0.896089i	$0.353604\pi$
$360$		0			0
$361$	2.35914	−	4.08615i	0.124165	−	0.215061i
$362$	2.35513	−	8.78945i	0.123783	−	0.461963i
$363$	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
$367$	−5.03135	+	1.34815i	−0.262635	+	0.0703727i	−0.387733	−	0.921772i	$-0.626742\pi$
$367$	−5.03135	+	1.34815i	−0.262635	+	0.0703727i	0.125099	+	0.992144i	$0.460075\pi$
$368$	−7.77857	+	2.08426i	−0.405486	+	0.108650i
$369$	−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
$373$	0.0379573	−	0.141659i	0.00196535	−	0.00733480i	−0.964936	−	0.262485i	$-0.915458\pi$
$373$	0.0379573	−	0.141659i	0.00196535	−	0.00733480i	0.966902	+	0.255150i	$0.0821248\pi$
$374$	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
$378$	−1.18797	−	2.36405i	−0.0611026	−	0.121594i
$379$			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
$382$	−4.71210	−	17.5858i	−0.241092	−	0.899768i
$383$	3.71843	+	0.996351i	0.190003	+	0.0509112i	0.352566	−	0.935787i	$-0.385309\pi$
$383$	3.71843	+	0.996351i	0.190003	+	0.0509112i	−0.162563	+	0.986698i	$0.551976\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−10.0713			−0.512614
$387$	0.501686	+	0.134426i	0.0255021	+	0.00683328i
$388$	0.169342	+	0.631994i	0.00859706	+	0.0320847i
$389$	15.4340	+	8.91085i	0.782537	+	0.451798i	0.837329	−	0.546700i	$-0.184116\pi$
$389$	15.4340	+	8.91085i	0.782537	+	0.451798i	−0.0547917	+	0.998498i	$0.517449\pi$
$390$		0			0
$391$			33.2136i			1.67969i
$392$	4.34424	+	5.48886i	0.219417	+	0.277229i
$393$	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
$397$	−6.63778	+	24.7725i	−0.333141	+	1.24330i	0.572730	+	0.819744i	$0.305884\pi$
$397$	−6.63778	+	24.7725i	−0.333141	+	1.24330i	−0.905871	+	0.423554i	$0.860782\pi$
$398$	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	0.924203	−	0.381901i	$-0.124730\pi$
$401$	2.63060	+	4.55632i	0.131366	+	0.227532i	−0.792838	+	0.609433i	$0.791397\pi$
$402$	8.99808	−	2.41103i	0.448784	−	0.120251i
$403$	9.45560	−	2.53362i	0.471017	−	0.126209i
$404$	−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
$408$	−1.06747	+	3.98386i	−0.0528477	+	0.197230i
$409$	4.18773	−	7.25336i	0.207070	−	0.358655i	−0.743720	−	0.668491i	$-0.766941\pi$
$409$	4.18773	−	7.25336i	0.207070	−	0.358655i	0.950790	+	0.309835i	$0.100274\pi$
$410$		0			0
$411$	−2.30241	+	1.32929i	−0.113569	+	0.0655693i
$412$	3.93011	+	3.93011i	0.193623	+	0.193623i
$413$	0.643862	−	0.979449i	0.0316824	−	0.0481955i
$414$		−	8.05297i		−	0.395782i
$415$		0			0
$416$	2.17725	+	1.25704i	0.106749	+	0.0616313i
$417$	−1.18557	−	4.42461i	−0.0580577	−	0.216674i
$418$	−16.6253	−	4.45474i	−0.813170	−	0.217888i
$419$	9.53078			0.465609			0.232805	−	0.972524i	$-0.425210\pi$
$419$	9.53078			0.465609			0.232805	+	0.972524i	$0.425210\pi$
$420$		0			0
$421$	16.8461			0.821027			0.410514	−	0.911854i	$-0.365349\pi$
$421$	16.8461			0.821027			0.410514	+	0.911854i	$0.365349\pi$
$422$	−13.1542	−	3.52466i	−0.640336	−	0.171578i
$423$	−1.30713	−	4.87829i	−0.0635550	−	0.237191i
$424$	−7.30469	−	4.21737i	−0.354747	−	0.204813i
$425$		0			0
$426$		−	6.68403i		−	0.323842i
$427$	19.3661	−	9.73177i	0.937193	−	0.470953i
$428$	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	0.480541	+	0.876972i	$0.340440\pi$
$431$	−10.7791	+	18.6699i	−0.519209	+	0.899297i	−0.999751	+	0.0223251i	$0.992893\pi$
$432$	0.258819	−	0.965926i	0.0124524	−	0.0464731i
$433$	−25.8823	+	25.8823i	−1.24382	+	1.24382i	−0.285422	+	0.958402i	$0.592134\pi$
$433$	−25.8823	+	25.8823i	−1.24382	+	1.24382i	−0.958402	+	0.285422i	$0.907866\pi$
$434$	6.85045	+	7.69413i	0.328832	+	0.369330i
$435$		0			0
$436$	−0.733433	−	1.27034i	−0.0351251	−	0.0608384i
$437$	29.3961	−	7.87667i	1.40621	−	0.376792i
$438$	−4.20080	+	1.12560i	−0.200722	+	0.0537832i
$439$	10.5899	+	18.3422i	0.505426	+	0.875424i	0.999980	+	0.00627716i	$0.00199809\pi$
$439$	10.5899	+	18.3422i	0.505426	+	0.875424i	−0.494554	+	0.869147i	$0.664669\pi$
$440$		0			0
$441$	−6.42620	+	2.77559i	−0.306010	+	0.132171i
$442$	7.33202	−	7.33202i	0.348749	−	0.348749i
$443$	1.07420	−	4.00895i	0.0510366	−	0.190471i	−0.935701	−	0.352794i	$-0.885232\pi$
$443$	1.07420	−	4.00895i	0.0510366	−	0.190471i	0.986738	+	0.162322i	$0.0518985\pi$
$444$	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
$448$	−0.153213	+	2.64131i	−0.00723862	+	0.124790i
$449$			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
$452$	−2.59451	−	9.68285i	−0.122036	−	0.455443i
$453$	5.37799	+	1.44103i	0.252680	+	0.0677053i
$454$	10.9527			0.514035
$455$		0			0
$456$	3.77912			0.176973
$457$	−0.455291	−	0.121995i	−0.0212976	−	0.00570668i	0.248155	−	0.968720i	$-0.420176\pi$
$457$	−0.455291	−	0.121995i	−0.0212976	−	0.00570668i	−0.269452	+	0.963014i	$0.586843\pi$
$458$	7.49134	+	27.9581i	0.350047	+	1.30639i
$459$	−3.57183	−	2.06220i	−0.166719	−	0.0962551i
$460$		0			0
$461$			26.3199i			1.22584i	0.790145	+	0.612920i	$0.210005\pi$
$461$			26.3199i			1.22584i	−0.790145	+	0.612920i	$0.789995\pi$
$462$	10.0691	+	6.61917i	0.468459	+	0.307952i
$463$	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
$467$	8.02693	−	29.9569i	0.371442	−	1.38624i	−0.487033	−	0.873384i	$-0.661921\pi$
$467$	8.02693	−	29.9569i	0.371442	−	1.38624i	0.858475	−	0.512856i	$-0.171413\pi$
$468$	−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
$472$	0.427926	−	0.114663i	0.0196969	−	0.00527777i
$473$	−2.28490	+	0.612238i	−0.105060	+	0.0281507i
$474$	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
$478$	1.12956	−	4.21559i	0.0516650	−	0.192817i
$479$	16.6760	−	28.8837i	0.761945	−	1.31973i	−0.179901	−	0.983685i	$-0.557578\pi$
$479$	16.6760	−	28.8837i	0.761945	−	1.31973i	0.941847	−	0.336043i	$-0.109089\pi$
$480$		0			0
$481$	−24.8987	+	14.3752i	−1.13528	+	0.655455i
$482$	−2.17075	−	2.17075i	−0.0988752	−	0.0988752i
$483$	−21.2704	−	1.23382i	−0.967837	−	0.0561407i
$484$		−	9.74299i		−	0.442863i
$485$		0			0
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	0.855056	+	3.19111i	0.0387463	+	0.144603i	0.982589	−	0.185791i	$-0.0594849\pi$
$487$	0.855056	+	3.19111i	0.0387463	+	0.144603i	−0.943843	+	0.330395i	$0.892818\pi$
$488$	7.91280	+	2.12023i	0.358196	+	0.0959783i
$489$	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	$0.473995\pi$
$492$	−10.9919	−	2.94527i	−0.495552	−	0.132783i
$493$	−1.66059	−	6.19740i	−0.0747891	−	0.279117i
$494$	−8.22809	−	4.75049i	−0.370199	−	0.213735i
$495$		0			0
$496$			3.89374i			0.174834i
$497$	−17.6546	−	1.02408i	−0.791917	−	0.0459362i
$498$	−3.21718	−	3.21718i	−0.144165	−	0.144165i
$499$	−0.561004	+	0.323896i	−0.0251140	+	0.0144996i	−0.512504	−	0.858685i	$-0.671282\pi$
$499$	−0.561004	+	0.323896i	−0.0251140	+	0.0144996i	0.487390	+	0.873184i	$0.337949\pi$
$500$		0			0
$501$	12.3708	−	21.4268i	0.552685	−	0.957278i
$502$	−0.324443	+	1.21084i	−0.0144806	+	0.0540423i
$503$	12.9189	−	12.9189i	0.576027	−	0.576027i	−0.357779	−	0.933806i	$-0.616466\pi$
$503$	12.9189	−	12.9189i	0.576027	−	0.576027i	0.933806	+	0.357779i	$0.116466\pi$
$504$	−2.51166	−	0.831614i	−0.111878	−	0.0370430i
$505$		0			0
$506$	18.3384	+	31.7631i	0.815242	+	1.41204i
$507$	−6.45183	+	1.72876i	−0.286536	+	0.0767770i
$508$	−17.6458	+	4.72818i	−0.782906	+	0.209779i
$509$	−10.1554	−	17.5896i	−0.450128	−	0.779645i	0.548265	−	0.836304i	$-0.315288\pi$
$509$	−10.1554	−	17.5896i	−0.450128	−	0.779645i	−0.998394	+	0.0566595i	$0.981955\pi$
$510$		0			0
$511$	2.32944	+	11.2681i	0.103049	+	0.498470i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−0.978107	+	3.65035i	−0.0431845	+	0.161167i
$514$	−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
$518$	−25.2827	−	16.6201i	−1.11086	−	0.730247i
$519$			16.5661i			0.727172i
$520$		0			0
$521$	1.07875	+	0.622814i	0.0472607	+	0.0272860i	0.523444	−	0.852060i	$-0.324647\pi$
$521$	1.07875	+	0.622814i	0.0472607	+	0.0272860i	−0.476183	+	0.879346i	$0.657980\pi$
$522$	0.402626	+	1.50262i	0.0176225	+	0.0657679i
$523$	−19.6016	−	5.25224i	−0.857119	−	0.229664i	−0.196609	−	0.980482i	$-0.562993\pi$
$523$	−19.6016	−	5.25224i	−0.857119	−	0.229664i	−0.660509	+	0.750818i	$0.729660\pi$
$524$	0.373725			0.0163262
$525$		0			0
$526$	−5.68790			−0.248004
$527$	15.5121	+	4.15646i	0.675718	+	0.181058i
$528$	1.17878	+	4.39926i	0.0512997	+	0.191453i
$529$	−36.2434	−	20.9252i	−1.57580	−	0.909790i
$530$		0			0
$531$			0.443022i			0.0192255i
$532$	0.579009	−	9.98182i	0.0251032	−	0.432767i
$533$	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
$537$	−3.29408	+	12.2937i	−0.142150	+	0.530510i
$538$	−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	0.956380	+	0.292126i	$0.0943625\pi$
$541$	17.0068	+	29.4566i	0.731178	+	1.26644i	−0.225202	+	0.974312i	$0.572304\pi$
$542$	−17.2769	+	4.62932i	−0.742104	+	0.198846i
$543$	8.78945	−	2.35513i	0.377191	−	0.101068i
$544$	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	$0.931959\pi$
$548$	−0.688094	+	2.56800i	−0.0293939	+	0.109700i
$549$	−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
$553$	11.1452	−	5.60062i	0.473941	−	0.238163i
$554$		−	14.7464i		−	0.626512i
$555$		0			0
$556$	−3.96700	−	2.29035i	−0.168238	−	0.0971324i
$557$	−0.365782	−	1.36512i	−0.0154987	−	0.0578419i	0.957743	−	0.287624i	$-0.0928653\pi$
$557$	−0.365782	−	1.36512i	−0.0154987	−	0.0578419i	−0.973242	+	0.229782i	$0.926199\pi$
$558$	−3.76106	−	1.00777i	−0.159218	−	0.0426625i
$559$	−1.30577			−0.0552282
$560$		0			0
$561$	18.7843			0.793076
$562$	0.567387	+	0.152031i	0.0239338	+	0.00641303i
$563$	−9.90152	−	36.9530i	−0.417299	−	1.55738i	−0.780185	−	0.625548i	$-0.784875\pi$
$563$	−9.90152	−	36.9530i	−0.417299	−	1.55738i	0.362886	−	0.931834i	$-0.381791\pi$
$564$	−4.37376	−	2.52519i	−0.184168	−	0.106330i
$565$		0			0
$566$		−	18.6151i		−	0.782453i
$567$	1.45334	−	2.21084i	0.0610346	−	0.0928464i
$568$	−4.72632	−	4.72632i	−0.198312	−	0.198312i
$569$	31.1820	−	18.0029i	1.30722	−	0.754723i	0.325587	−	0.945512i	$-0.394438\pi$
$569$	31.1820	−	18.0029i	1.30722	−	0.754723i	0.981631	+	0.190789i	$0.0611047\pi$
$570$		0			0
$571$	17.1990	−	29.7895i	0.719756	−	1.24665i	−0.241341	−	0.970440i	$-0.577587\pi$
$571$	17.1990	−	29.7895i	0.719756	−	1.24665i	0.961096	−	0.276213i	$-0.0890795\pi$
$572$	2.96354	−	11.0601i	0.123912	−	0.462445i
$573$	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
$577$	43.1900	−	11.5727i	1.79802	−	0.481779i	0.804355	−	0.594148i	$-0.202511\pi$
$577$	43.1900	−	11.5727i	1.79802	−	0.481779i	0.993666	+	0.112370i	$0.0358442\pi$
$578$	0.0102734	−	0.00275276i	0.000427319	−	0.000114500i
$579$	−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
$583$	−9.94267	+	37.1066i	−0.411783	+	1.53680i
$584$	−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	0.985210	−	0.171351i	$-0.0548132\pi$
$587$	19.7182	+	19.7182i	0.813859	+	0.813859i	−0.171351	+	0.985210i	$0.554813\pi$
$588$	−2.58137	+	6.50665i	−0.106454	+	0.268330i
$589$		−	14.7149i		−	0.606316i
$590$		0			0
$591$	−19.8946	−	11.4862i	−0.818356	−	0.472478i
$592$	−2.95980	−	11.0461i	−0.121647	−	0.453994i
$593$	9.62724	+	2.57961i	0.395343	+	0.105932i	0.451013	−	0.892517i	$-0.351063\pi$
$593$	9.62724	+	2.57961i	0.395343	+	0.105932i	−0.0556699	+	0.998449i	$0.517729\pi$
$594$	−4.55445			−0.186871
$595$		0			0
$596$	−17.2441			−0.706344
$597$	24.5315	+	6.57319i	1.00401	+	0.269023i
$598$	5.23999	+	19.5559i	0.214279	+	0.799701i
$599$	−14.2556	−	8.23048i	−0.582469	−	0.336288i	0.179645	−	0.983731i	$-0.442505\pi$
$599$	−14.2556	−	8.23048i	−0.582469	−	0.336288i	−0.762114	+	0.647443i	$0.775838\pi$
$600$		0			0
$601$		−	34.0216i		−	1.38777i	−0.720086	−	0.693885i	$-0.755898\pi$
$601$		−	34.0216i		−	1.38777i	0.720086	−	0.693885i	$-0.244102\pi$
$602$	−0.617012	−	1.22785i	−0.0251475	−	0.0500434i
$603$	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
$607$	−9.31678	+	34.7707i	−0.378156	+	1.41130i	0.470521	+	0.882389i	$0.344066\pi$
$607$	−9.31678	+	34.7707i	−0.378156	+	1.41130i	−0.848678	+	0.528910i	$0.822601\pi$
$608$	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
$612$	−3.98386	+	1.06747i	−0.161038	+	0.0431500i
$613$	−31.8017	+	8.52125i	−1.28446	+	0.344170i	−0.835554	−	0.549409i	$-0.814853\pi$
$613$	−31.8017	+	8.52125i	−1.28446	+	0.344170i	−0.448906	+	0.893579i	$0.648186\pi$
$614$	−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	$0.154608\pi$
$618$	−1.43852	+	5.36863i	−0.0578658	+	0.215958i
$619$	2.58828	−	4.48304i	0.104032	−	0.180188i	−0.809310	−	0.587381i	$-0.800159\pi$
$619$	2.58828	−	4.48304i	0.104032	−	0.180188i	0.913342	+	0.407193i	$0.133492\pi$
$620$		0			0
$621$	6.97408	−	4.02648i	0.279860	−	0.161577i
$622$	9.81743	+	9.81743i	0.393643	+	0.393643i
$623$	−7.18544	−	14.2990i	−0.287879	−	0.572876i
$624$			2.51408i			0.100644i
$625$		0			0
$626$	−11.6830	−	6.74520i	−0.466948	−	0.269592i
$627$	−4.45474	−	16.6253i	−0.177905	−	0.663951i
$628$	3.99014	+	1.06916i	0.159224	+	0.0426640i
$629$	−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	$0.406549\pi$
$632$	4.55381	+	1.22019i	0.181141	+	0.0485365i
$633$	−3.52466	−	13.1542i	−0.140093	−	0.522832i
$634$	11.8793	+	6.85853i	0.471788	+	0.272387i
$635$		0			0
$636$		−	8.43473i		−	0.334459i
$637$	13.7994	−	10.9218i	0.546752	−	0.432736i
$638$	−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	0.0778281	+	0.996967i	$0.475201\pi$
$641$	−20.8743	+	36.1553i	−0.824484	+	1.42805i	−0.902313	+	0.431082i	$0.858132\pi$
$642$	−1.93865	+	7.23514i	−0.0765124	+	0.285548i
$643$	−15.5128	+	15.5128i	−0.611766	+	0.611766i	−0.943406	−	0.331640i	$-0.892398\pi$
$643$	−15.5128	+	15.5128i	−0.611766	+	0.611766i	0.331640	+	0.943406i	$0.392398\pi$
$644$	−15.9129	+	14.1680i	−0.627056	+	0.558298i
$645$		0			0
$646$	−7.79328	−	13.4984i	−0.306623	−	0.531086i
$647$	13.8141	−	3.70148i	0.543089	−	0.145520i	0.0231633	−	0.999732i	$-0.492626\pi$
$647$	13.8141	−	3.70148i	0.543089	−	0.145520i	0.519926	+	0.854211i	$0.325960\pi$
$648$	0.965926	−	0.258819i	0.0379452	−	0.0101674i
$649$	−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
$653$	−3.95094	+	14.7451i	−0.154612	+	0.577021i	0.844526	+	0.535515i	$0.179882\pi$
$653$	−3.95094	+	14.7451i	−0.154612	+	0.577021i	−0.999138	+	0.0415062i	$0.986784\pi$
$654$	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
$658$	−7.33993	+	11.1656i	−0.286140	+	0.435279i
$659$			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	0.829881	−	0.557940i	$-0.188408\pi$
$661$	19.5815	+	11.3054i	0.761632	+	0.439728i	−0.0682495	+	0.997668i	$0.521741\pi$
$662$	−8.60281	−	32.1061i	−0.334358	−	1.24784i
$663$	10.0157	+	2.68371i	0.388979	+	0.104226i
$664$	−4.54978			−0.176566
$665$		0			0
$666$	11.4358			0.443129
$667$	12.1006	+	3.24233i	0.468535	+	0.125544i
$668$	−6.40358	−	23.8985i	−0.247762	−	0.924660i
$669$	19.4015	+	11.2014i	0.750104	+	0.433073i
$670$		0			0
$671$		−	37.3097i		−	1.44033i
$672$	−2.36405	+	1.18797i	−0.0911952	+	0.0458269i
$673$	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
$677$	−2.30402	+	8.59870i	−0.0885505	+	0.330475i	−0.995963	−	0.0897664i	$-0.971388\pi$
$677$	−2.30402	+	8.59870i	−0.0885505	+	0.330475i	0.907412	+	0.420241i	$0.138055\pi$
$678$	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
$682$	17.1296	−	4.58985i	0.655925	−	0.175755i
$683$	46.2697	−	12.3979i	1.77046	−	0.474394i	0.781669	−	0.623693i	$-0.214368\pi$
$683$	46.2697	−	12.3979i	1.77046	−	0.474394i	0.988792	+	0.149299i	$0.0477018\pi$
$684$	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
$688$	0.134426	−	0.501686i	0.00512496	−	0.0191266i
$689$	−10.6028	+	18.3645i	−0.403934	+	0.699633i
$690$		0			0
$691$	−22.3848	+	12.9239i	−0.851559	+	0.491648i	−0.861177	−	0.508306i	$-0.830272\pi$
$691$	−22.3848	+	12.9239i	−0.851559	+	0.491648i	0.00961738	+	0.999954i	$0.496939\pi$
$692$	11.7140	+	11.7140i	0.445300	+	0.445300i
$693$	−0.697800	+	12.0297i	−0.0265072	+	0.456971i
$694$		−	2.05709i		−	0.0780861i
$695$		0			0
$696$	1.34721	+	0.777814i	0.0510660	+	0.0294829i
$697$	12.1474	+	45.3349i	0.460117	+	1.71718i
$698$	11.3255	+	3.03467i	0.428677	+	0.114864i
$699$	−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	$0.476186\pi$
$702$	−2.42841	−	0.650691i	−0.0916544	−	0.0245587i
$703$	11.1854	+	41.7447i	0.421867	+	1.57443i
$704$	3.94427	+	2.27722i	0.148655	+	0.0858261i
$705$		0			0
$706$			11.4227i			0.429897i
$707$	−12.3852	−	8.14167i	−0.465793	−	0.306199i
$708$	0.313264	+	0.313264i	0.0117732	+	0.0117732i
$709$	25.1665	−	14.5299i	0.945148	−	0.545682i	0.0535778	−	0.998564i	$-0.482937\pi$
$709$	25.1665	−	14.5299i	0.945148	−	0.545682i	0.891570	+	0.452882i	$0.149604\pi$
$710$		0			0
$711$	−2.35722	+	4.08283i	−0.0884028	+	0.153118i
$712$	1.56547	−	5.84241i	0.0586684	−	0.218954i
$713$	−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
$717$	4.21559	−	1.12956i	0.157434	−	0.0421843i
$718$	−2.32938	+	0.624155i	−0.0869316	+	0.0232932i
$719$	10.1319	+	17.5490i	0.377857	+	0.654467i	0.990750	−	0.135699i	$-0.0433279\pi$
$719$	10.1319	+	17.5490i	0.377857	+	0.654467i	−0.612893	+	0.790166i	$0.709995\pi$
$720$		0			0
$721$	13.9598	+	4.62212i	0.519891	+	0.172137i
$722$	3.33633	−	3.33633i	0.124165	−	0.124165i
$723$	0.794551	−	2.96531i	0.0295497	−	0.110281i
$724$	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	0.653088	−	0.757282i	$-0.273473\pi$
$727$	−2.80940	−	2.80940i	−0.104195	−	0.104195i	−0.757282	+	0.653088i	$0.773473\pi$
$728$	6.64046	+	0.385189i	0.246112	+	0.0142760i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−1.85515	−	1.07107i	−0.0686152	−	0.0396150i
$732$	2.12023	+	7.91280i	0.0783659	+	0.292466i
$733$	1.68418	+	0.451275i	0.0622066	+	0.0166682i	0.289788	−	0.957091i	$-0.406415\pi$
$733$	1.68418	+	0.451275i	0.0622066	+	0.0166682i	−0.227582	+	0.973759i	$0.573082\pi$
$734$	−5.20884			−0.192262
$735$		0			0
$736$	−8.05297			−0.296836
$737$	−40.9813	−	10.9809i	−1.50957	−	0.404487i
$738$	−2.94527	−	10.9919i	−0.108417	−	0.404617i
$739$	20.2692	+	11.7024i	0.745615	+	0.430481i	0.824107	−	0.566434i	$-0.191677\pi$
$739$	20.2692	+	11.7024i	0.745615	+	0.430481i	−0.0784926	+	0.996915i	$0.525011\pi$
$740$		0			0
$741$		−	9.50098i		−	0.349027i
$742$	−22.2787	−	1.29231i	−0.817879	−	0.0474421i
$743$	−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
$747$	1.17757	−	4.39475i	0.0430850	−	0.160795i
$748$	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	−0.935858	−	0.352376i	$-0.885374\pi$
$751$	−21.1862	−	36.6956i	−0.773096	−	1.33904i	0.162762	−	0.986665i	$-0.447960\pi$
$752$	−4.87829	+	1.30713i	−0.177893	+	0.0476663i
$753$	−1.21084	+	0.324443i	−0.0441254	+	0.0118234i
$754$	−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	$0.334828\pi$
$758$	−4.79948	+	17.9119i	−0.174325	+	0.650590i
$759$	−18.3384	+	31.7631i	−0.665642	+	1.15293i
$760$		0			0
$761$	13.4082	−	7.74124i	0.486048	−	0.280620i	−0.236886	−	0.971538i	$-0.576127\pi$
$761$	13.4082	−	7.74124i	0.486048	−	0.280620i	0.722933	+	0.690918i	$0.242793\pi$
$762$	−12.9176	−	12.9176i	−0.467956	−	0.467956i
$763$	−3.24300	−	2.13186i	−0.117404	−	0.0771784i
$764$		−	18.2062i		−	0.658676i
$765$		0			0
$766$	3.33386	+	1.92480i	0.120457	+	0.0695460i
$767$	−0.288270	−	1.07584i	−0.0104088	−	0.0388463i
$768$	−0.965926	−	0.258819i	−0.0348548	−	0.00933933i
$769$	−15.9644			−0.575691			−0.287846	−	0.957677i	$-0.592939\pi$
$769$	−15.9644			−0.575691			−0.287846	+	0.957677i	$0.592939\pi$
$770$		0			0
$771$	−7.05834			−0.254200
$772$	−9.72810	−	2.60664i	−0.350122	−	0.0938149i
$773$	−5.99662	−	22.3797i	−0.215683	−	0.804941i	−0.985925	−	0.167189i	$-0.946531\pi$
$773$	−5.99662	−	22.3797i	−0.215683	−	0.804941i	0.770241	−	0.637752i	$-0.220136\pi$
$774$	0.449799	+	0.259692i	0.0161677	+	0.00933443i
$775$		0			0
$776$			0.654289i			0.0234876i
$777$	1.75211	−	30.2055i	0.0628567	−	1.08362i
$778$	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
$782$	−8.59632	+	32.0819i	−0.307404	+	1.14725i
$783$	−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
$787$	2.03363	−	0.544910i	0.0724912	−	0.0194239i	−0.222391	−	0.974958i	$-0.571386\pi$
$787$	2.03363	−	0.544910i	0.0724912	−	0.0194239i	0.294882	+	0.955534i	$0.404720\pi$
$788$	−22.1896	+	5.94568i	−0.790471	+	0.211806i
$789$	−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
$793$	5.33042	−	19.8934i	0.189289	−	0.706435i
$794$	−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	0.150038	−	0.988680i	$-0.452060\pi$
$797$	−23.6759	−	23.6759i	−0.838642	−	0.838642i	−0.988680	+	0.150038i	$0.952060\pi$
$798$	8.93402	−	4.48947i	0.316261	−	0.158926i
$799$			20.8298i			0.736904i
$800$		0			0
$801$	5.23816	+	3.02425i	0.185081	+	0.106857i
$802$	1.36170	+	5.08192i	0.0480832	+	0.179449i
$803$	19.1323	+	5.12649i	0.675164	+	0.180910i
$804$	9.31550			0.328532
$805$		0			0
$806$	9.78915			0.344808
$807$	−7.44518	−	1.99493i	−0.262083	−	0.0702249i
$808$	−1.44991	−	5.41115i	−0.0510078	−	0.190364i
$809$	−1.15441	−	0.666500i	−0.0405869	−	0.0234329i	0.479569	−	0.877504i	$-0.340793\pi$
$809$	−1.15441	−	0.666500i	−0.0405869	−	0.0234329i	−0.520156	+	0.854071i	$0.674126\pi$
$810$		0			0
$811$			41.6705i			1.46325i	0.681708	+	0.731624i	$0.261237\pi$
$811$			41.6705i			1.46325i	−0.681708	+	0.731624i	$0.738763\pi$
$812$	2.26086	−	3.43924i	0.0793406	−	0.120694i
$813$	−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
$817$	−0.508013	+	1.89593i	−0.0177731	+	0.0663302i
$818$	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	0.997382	+	0.0723083i	$0.0230366\pi$
$821$	16.0833	+	27.8571i	0.561312	+	0.972221i	−0.436070	+	0.899913i	$0.643630\pi$
$822$	−2.56800	+	0.688094i	−0.0895693	+	0.0240000i
$823$	14.2933	−	3.82988i	0.498233	−	0.133501i	−0.000946758	−	1.00000i	$-0.500301\pi$
$823$	14.2933	−	3.82988i	0.498233	−	0.133501i	0.499180	+	0.866498i	$0.333635\pi$
$824$	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	$-0.0689062\pi$
$828$	2.08426	−	7.77857i	0.0724331	−	0.270324i
$829$	−25.2456	+	43.7267i	−0.876817	+	1.51869i	−0.0220025	+	0.999758i	$0.507004\pi$
$829$	−25.2456	+	43.7267i	−0.876817	+	1.51869i	−0.854814	+	0.518934i	$0.826329\pi$
$830$		0			0
$831$	12.7707	−	7.37318i	0.443011	−	0.255773i
$832$	1.77772	+	1.77772i	0.0616313	+	0.0616313i
$833$	28.5640	−	4.19779i	0.989682	−	0.145445i
$834$		−	4.58070i		−	0.158617i
$835$		0			0
$836$	−14.9058	−	8.60589i	−0.515529	−	0.297641i
$837$	−1.00777	−	3.76106i	−0.0348338	−	0.130001i
$838$	9.20603	+	2.46675i	0.318017	+	0.0852124i
$839$	22.4313			0.774414			0.387207	−	0.921993i	$-0.373440\pi$
$839$	22.4313			0.774414			0.387207	+	0.921993i	$0.373440\pi$
$840$		0			0
$841$	26.5800			0.916553
$842$	16.2721	+	4.36008i	0.560772	+	0.150258i
$843$	0.152031	+	0.567387i	0.00523622	+	0.0195418i
$844$	−11.7937	−	6.80911i	−0.405957	−	0.234379i
$845$		0			0
$846$		−	5.05038i		−	0.173636i
$847$	−11.5744	−	23.0329i	−0.397700	−	0.791420i
$848$	−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
$852$	1.72995	−	6.45627i	0.0592672	−	0.221188i
$853$	24.4497	−	24.4497i	0.837140	−	0.837140i	−0.151341	−	0.988482i	$-0.548359\pi$
$853$	24.4497	−	24.4497i	0.837140	−	0.837140i	0.988482	+	0.151341i	$0.0483592\pi$
$854$	21.2250	−	4.38784i	0.726305	−	0.150149i
$855$		0			0
$856$	3.74518	+	6.48684i	0.128008	+	0.221716i
$857$	−14.0196	+	3.75655i	−0.478901	+	0.128321i	−0.490191	−	0.871615i	$-0.663073\pi$
$857$	−14.0196	+	3.75655i	−0.478901	+	0.128321i	0.0112896	+	0.999936i	$0.496406\pi$
$858$	11.0601	−	2.96354i	0.377585	−	0.101173i
$859$	−8.65502	−	14.9909i	−0.295306	−	0.511484i	0.679750	−	0.733444i	$-0.262088\pi$
$859$	−8.65502	−	14.9909i	−0.295306	−	0.511484i	−0.975056	+	0.221959i	$0.928755\pi$
$860$		0			0
$861$	−29.4842	+	6.09527i	−1.00482	+	0.207726i
$862$	−15.2439	+	15.2439i	−0.519209	+	0.519209i
$863$	2.42352	−	9.04469i	0.0824975	−	0.307885i	−0.912331	−	0.409453i	$-0.865719\pi$
$863$	2.42352	−	9.04469i	0.0824975	−	0.307885i	0.994829	+	0.101568i	$0.0323861\pi$
$864$	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
$868$	4.62564	+	9.20499i	0.157005	+	0.312438i
$869$		−	21.4717i		−	0.728378i
$870$		0			0
$871$	−20.2822	−	11.7099i	−0.687236	−	0.396776i
$872$	−0.379653	−	1.41688i	−0.0128567	−	0.0479817i
$873$	−0.631994	−	0.169342i	−0.0213898	−	0.00573137i
$874$	30.4331			1.02942
$875$		0			0
$876$	−4.34898			−0.146939
$877$	−36.1496	−	9.68626i	−1.22069	−	0.327082i	−0.409740	−	0.912202i	$-0.634381\pi$
$877$	−36.1496	−	9.68626i	−1.22069	−	0.327082i	−0.810946	+	0.585120i	$0.801047\pi$
$878$	5.48171	+	20.4580i	0.184999	+	0.690425i
$879$	−25.3199	−	14.6185i	−0.854020	−	0.493069i
$880$		0			0
$881$		−	49.1425i		−	1.65565i	−0.560984	−	0.827827i	$-0.689577\pi$
$881$		−	49.1425i		−	1.65565i	0.560984	−	0.827827i	$-0.310423\pi$
$882$	−6.92561	+	1.01780i	−0.233197	+	0.0342709i
$883$	−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
$887$	6.78961	−	25.3392i	0.227973	−	0.850806i	−0.753219	−	0.657770i	$-0.771500\pi$
$887$	6.78961	−	25.3392i	0.227973	−	0.850806i	0.981192	−	0.193036i	$-0.0618334\pi$
$888$	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
$892$	21.6395	−	5.79830i	0.724545	−	0.194141i
$893$	18.4356	−	4.93981i	0.616925	−	0.165304i
$894$	−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
$898$	−7.60399	+	28.3785i	−0.253748	+	0.947002i
$899$	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
$903$	0.754842	−	1.14827i	0.0251196	−	0.0382121i
$904$		−	10.0244i		−	0.333407i
$905$		0			0
$906$	4.82177	+	2.78385i	0.160193	+	0.0924872i
$907$	−0.327416	−	1.22193i	−0.0108717	−	0.0405736i	0.960277	−	0.279049i	$-0.0900191\pi$
$907$	−0.327416	−	1.22193i	−0.0108717	−	0.0405736i	−0.971149	+	0.238475i	$0.923352\pi$
$908$	10.5795	+	2.83476i	0.351092	+	0.0940749i
$909$	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	$0.808806\pi$
$912$	3.65035	+	0.978107i	0.120875	+	0.0323884i
$913$	5.36318	+	20.0156i	0.177495	+	0.662421i
$914$	−0.408203	−	0.235676i	−0.0135021	−	0.00779547i
$915$		0			0
$916$			28.9443i			0.956347i
$917$	0.883504	−	0.443974i	0.0291759	−	0.0146613i
$918$	−2.91639	−	2.91639i	−0.0962551	−	0.0962551i
$919$	−43.6221	+	25.1852i	−1.43896	+	0.830784i	−0.997777	−	0.0666338i	$-0.978774\pi$
$919$	−43.6221	+	25.1852i	−1.43896	+	0.830784i	−0.441182	+	0.897418i	$0.645441\pi$
$920$		0			0
$921$	1.15586	−	2.00201i	0.0380870	−	0.0659686i
$922$	−6.81209	+	25.4231i	−0.224344	+	0.837264i
$923$	−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
$927$	−5.36863	+	1.43852i	−0.176329	+	0.0472472i
$928$	1.50262	−	0.402626i	0.0493259	−	0.0132168i
$929$	−11.4115	−	19.7652i	−0.374398	−	0.648476i	0.615839	−	0.787872i	$-0.288817\pi$
$929$	−11.4115	−	19.7652i	−0.374398	−	0.648476i	−0.990237	+	0.139396i	$0.955484\pi$
$930$		0			0
$931$	−10.4893	−	24.2854i	−0.343773	−	0.795921i
$932$	−0.998499	+	0.998499i	−0.0327069	+	0.0327069i
$933$	−3.59343	+	13.4109i	−0.117644	+	0.439052i
$934$	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	0.170418	−	0.985372i	$-0.445488\pi$
$937$	−24.9461	−	24.9461i	−0.814954	−	0.814954i	−0.985372	+	0.170418i	$0.945488\pi$
$938$	1.42725	−	24.6051i	0.0466015	−	0.803386i
$939$		−	13.4904i		−	0.440242i
$940$		0			0
$941$	−16.1409	−	9.31896i	−0.526179	−	0.303789i	0.213280	−	0.976991i	$-0.431585\pi$
$941$	−16.1409	−	9.31896i	−0.526179	−	0.303789i	−0.739459	+	0.673202i	$0.764919\pi$
$942$	1.06916	+	3.99014i	0.0348350	+	0.130006i
$943$	−88.5173	−	23.7181i	−2.88252	−	0.772369i
$944$	0.443022			0.0144191
$945$		0			0
$946$	−2.36551			−0.0769092
$947$	2.45198	+	0.657006i	0.0796786	+	0.0213498i	0.298438	−	0.954429i	$-0.403534\pi$
$947$	2.45198	+	0.657006i	0.0796786	+	0.0213498i	−0.218760	+	0.975779i	$0.570201\pi$
$948$	1.22019	+	4.55381i	0.0396299	+	0.147901i
$949$	9.46884	+	5.46684i	0.307372	+	0.177461i
$950$		0			0
$951$			13.7171i			0.444806i
$952$	9.11836	+	5.99416i	0.295528	+	0.194272i
$953$	−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
$957$	1.83374	−	6.84361i	0.0592764	−	0.221222i
$958$	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
$962$	−27.7708	+	7.44117i	−0.895368	+	0.239913i
$963$	−7.23514	+	1.93865i	−0.233149	+	0.0624721i
$964$	−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	$0.140969\pi$
$968$	2.52167	−	9.41101i	0.0810496	−	0.302481i
$969$	7.79328	−	13.4984i	0.250356	−	0.433630i
$970$		0			0
$971$	9.39194	−	5.42244i	0.301402	−	0.174014i	−0.341671	−	0.939820i	$-0.610993\pi$
$971$	9.39194	−	5.42244i	0.301402	−	0.174014i	0.643072	+	0.765805i	$0.277659\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	−12.0990	−	0.701821i	−0.387878	−	0.0224994i
$974$			3.30368i			0.105857i
$975$		0			0
$976$	7.09442	+	4.09597i	0.227087	+	0.131109i
$977$	−4.43616	−	16.5560i	−0.141925	−	0.529673i	−0.999873	−	0.0159356i	$-0.994927\pi$
$977$	−4.43616	−	16.5560i	−0.141925	−	0.529673i	0.857948	−	0.513737i	$-0.171739\pi$
$978$	20.9982	+	5.62644i	0.671447	+	0.179914i
$979$	−27.5476			−0.880426
$980$		0			0
$981$	1.46687			0.0468334
$982$	3.49327	+	0.936018i	0.111475	+	0.0298695i
$983$	0.434966	+	1.62331i	0.0138732	+	0.0517757i	0.972515	−	0.232838i	$-0.0748013\pi$
$983$	0.434966	+	1.62331i	0.0138732	+	0.0517757i	−0.958642	+	0.284614i	$0.908135\pi$
$984$	−9.85506	−	5.68982i	−0.314168	−	0.181385i
$985$		0			0
$986$		−	6.41602i		−	0.204328i
$987$	−13.3396	−	0.773782i	−0.424605	−	0.0246298i
$988$	−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	−0.701116	−	0.713047i	$-0.747314\pi$
$991$	8.40392	−	14.5560i	0.266959	−	0.462387i	0.968075	+	0.250660i	$0.0806478\pi$
$992$	−1.00777	+	3.76106i	−0.0319968	+	0.119414i
$993$	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
$997$	−16.8680	+	4.51978i	−0.534216	+	0.143143i	−0.515835	−	0.856688i	$-0.672518\pi$
$997$	−16.8680	+	4.51978i	−0.534216	+	0.143143i	−0.0183818	+	0.999831i	$0.505851\pi$
$998$	−0.625718	+	0.167661i	−0.0198068	+	0.00530721i
$999$	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.h.493.4		16
5.2	odd	4		1050.2.bc.g.157.1		16
5.3	odd	4		210.2.u.b.157.4	yes	16
5.4	even	2		210.2.u.a.73.2	✓	16
7.5	odd	6		1050.2.bc.g.943.1		16
15.8	even	4		630.2.bv.b.577.1		16
15.14	odd	2		630.2.bv.a.73.3		16
35.3	even	12		1470.2.m.d.97.8		16
35.4	even	6		1470.2.m.d.1273.8		16
35.12	even	12	inner	1050.2.bc.h.607.4		16
35.18	odd	12		1470.2.m.e.97.5		16
35.19	odd	6		210.2.u.b.103.4	yes	16
35.24	odd	6		1470.2.m.e.1273.5		16
35.33	even	12		210.2.u.a.187.2	yes	16
105.68	odd	12		630.2.bv.a.397.3		16
105.89	even	6		630.2.bv.b.523.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.2	✓	16	5.4	even	2
210.2.u.a.187.2	yes	16	35.33	even	12
210.2.u.b.103.4	yes	16	35.19	odd	6
210.2.u.b.157.4	yes	16	5.3	odd	4
630.2.bv.a.73.3		16	15.14	odd	2
630.2.bv.a.397.3		16	105.68	odd	12
630.2.bv.b.523.1		16	105.89	even	6
630.2.bv.b.577.1		16	15.8	even	4
1050.2.bc.g.157.1		16	5.2	odd	4
1050.2.bc.g.943.1		16	7.5	odd	6
1050.2.bc.h.493.4		16	1.1	even	1	trivial
1050.2.bc.h.607.4		16	35.12	even	12	inner
1470.2.m.d.97.8		16	35.3	even	12
1470.2.m.d.1273.8		16	35.4	even	6
1470.2.m.e.97.5		16	35.18	odd	12
1470.2.m.e.1273.5		16	35.24	odd	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)

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

Introduction

L-functions

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Database

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