LMFDB - Embedded newform 630.2.bf.b.419.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(209,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.209"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-4,0,-4,6,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.856615824.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			419.4
Root			$0.385731i$ of defining polynomial
Character	$\chi$	$=$	630.419
Dual form			630.2.bf.b.209.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.73065 + 0.0696054i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.09155 + 0.790826i) q^{5} +(-0.805046 - 1.53359i) q^{6} +(-2.36975 - 1.17656i) q^{7} +1.00000 q^{8} +(2.99031 + 0.240925i) q^{9} +(-0.360902 - 2.20675i) q^{10} +(1.16595 - 0.673160i) q^{11} +(-0.925606 + 1.46399i) q^{12} +(1.23065 - 2.13155i) q^{13} +(0.165947 + 2.64054i) q^{14} +(3.56470 + 1.51423i) q^{15} +(-0.500000 - 0.866025i) q^{16} +0.246520i q^{17} +(-1.28651 - 2.71015i) q^{18} +1.47434i q^{19} +(-1.73065 + 1.41593i) q^{20} +(-4.01932 - 2.20116i) q^{21} +(-1.16595 - 0.673160i) q^{22} +(4.15626 - 7.19885i) q^{23} +(1.73065 + 0.0696054i) q^{24} +(3.74919 + 3.30811i) q^{25} -2.46130 q^{26} +(5.15842 + 0.625100i) q^{27} +(2.20380 - 1.46399i) q^{28} +(-4.56386 + 2.63495i) q^{29} +(-0.470993 - 3.84424i) q^{30} +(8.15842 + 4.71026i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.06470 - 1.08385i) q^{33} +(0.213493 - 0.123260i) q^{34} +(-4.02601 - 4.33489i) q^{35} +(-1.70380 + 2.46922i) q^{36} -1.87126i q^{37} +(1.27682 - 0.737171i) q^{38} +(2.27820 - 3.60331i) q^{39} +(2.09155 + 0.790826i) q^{40} +(-4.73065 + 8.19373i) q^{41} +(0.103401 + 4.58141i) q^{42} +(7.27682 - 4.20127i) q^{43} +1.34632i q^{44} +(6.06386 + 2.86872i) q^{45} -8.31252 q^{46} +(-8.27520 + 4.77769i) q^{47} +(-0.805046 - 1.53359i) q^{48} +(4.23143 + 5.57629i) q^{49} +(0.990310 - 4.90095i) q^{50} +(-0.0171591 + 0.426640i) q^{51} +(1.23065 + 2.13155i) q^{52} -8.10571 q^{53} +(-2.03786 - 4.77987i) q^{54} +(2.97099 - 0.485889i) q^{55} +(-2.36975 - 1.17656i) q^{56} +(-0.102622 + 2.55157i) q^{57} +(4.56386 + 2.63495i) q^{58} +(2.66673 - 4.61891i) q^{59} +(-3.09371 + 2.33001i) q^{60} +(-6.46877 + 3.73475i) q^{61} -9.42053i q^{62} +(-6.80283 - 4.08920i) q^{63} +1.00000 q^{64} +(4.25966 - 3.48502i) q^{65} +(-1.97099 - 1.24616i) q^{66} +(-1.74112 - 1.00524i) q^{67} +(-0.213493 - 0.123260i) q^{68} +(7.69411 - 12.1694i) q^{69} +(-1.74112 + 5.65407i) q^{70} -15.3040i q^{71} +(2.99031 + 0.240925i) q^{72} -5.92861 q^{73} +(-1.62056 + 0.935631i) q^{74} +(6.25828 + 5.98615i) q^{75} +(-1.27682 - 0.737171i) q^{76} +(-3.55501 + 0.223418i) q^{77} +(-4.25966 - 0.171320i) q^{78} +(0.270127 + 0.467874i) q^{79} +(-0.360902 - 2.20675i) q^{80} +(8.88391 + 1.44088i) q^{81} +9.46130 q^{82} +(-1.04539 + 0.603555i) q^{83} +(3.91592 - 2.38025i) q^{84} +(-0.194954 + 0.515610i) q^{85} +(-7.27682 - 4.20127i) q^{86} +(-8.08186 + 4.24251i) q^{87} +(1.16595 - 0.673160i) q^{88} -13.5043 q^{89} +(-0.547545 - 6.68582i) q^{90} +(-5.42423 + 3.60331i) q^{91} +(4.15626 + 7.19885i) q^{92} +(13.7915 + 8.71969i) q^{93} +(8.27520 + 4.77769i) q^{94} +(-1.16595 + 3.08366i) q^{95} +(-0.925606 + 1.46399i) q^{96} +(-5.12803 - 8.88201i) q^{97} +(2.71349 - 6.45267i) q^{98} +(3.64873 - 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 6 q^{5} - 3 q^{6} - 2 q^{7} + 8 q^{8} - 6 q^{10} + 9 q^{11} + 3 q^{12} - 4 q^{13} + q^{14} + 15 q^{15} - 4 q^{16} - 3 q^{18} - 12 q^{21} - 9 q^{22} + 9 q^{23} + 20 q^{25} + 8 q^{26}+ \cdots - 18 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 6 * q^5 - 3 * q^6 - 2 * q^7 + 8 * q^8 - 6 * q^10 + 9 * q^11 + 3 * q^12 - 4 * q^13 + q^14 + 15 * q^15 - 4 * q^16 - 3 * q^18 - 12 * q^21 - 9 * q^22 + 9 * q^23 + 20 * q^25 + 8 * q^26 + 18 * q^27 + q^28 + 21 * q^29 + 42 * q^31 - 4 * q^32 + 3 * q^33 + 9 * q^34 + 9 * q^35 + 3 * q^36 - 21 * q^38 + 12 * q^39 + 6 * q^40 - 24 * q^41 + 15 * q^42 + 27 * q^43 - 9 * q^45 - 18 * q^46 - 15 * q^47 - 3 * q^48 - 4 * q^49 - 16 * q^50 + 21 * q^51 - 4 * q^52 + 12 * q^53 + 20 * q^55 - 2 * q^56 - 39 * q^57 - 21 * q^58 - 3 * q^59 - 15 * q^60 + 21 * q^61 + 18 * q^63 + 8 * q^64 + 24 * q^65 - 12 * q^66 - 9 * q^68 + 21 * q^69 - 82 * q^73 - 6 * q^74 + 15 * q^75 + 21 * q^76 + 9 * q^77 - 24 * q^78 - 8 * q^79 - 6 * q^80 - 12 * q^81 + 48 * q^82 - 15 * q^83 - 3 * q^84 - 5 * q^85 - 27 * q^86 - 30 * q^87 + 9 * q^88 - 42 * q^89 - 12 * q^90 - 8 * q^91 + 9 * q^92 - 6 * q^93 + 15 * q^94 - 9 * q^95 + 3 * q^96 + 11 * q^97 + 29 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.73065	+	0.0696054i	0.999192	+	0.0401867i
$3$	1.73065	+	0.0696054i	0.999192	+	0.0401867i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.09155	+	0.790826i	0.935371	+	0.353668i
$5$	2.09155	+	0.790826i	0.935371	+	0.353668i
$6$	−0.805046	−	1.53359i	−0.328659	−	0.626086i
$7$	−2.36975	−	1.17656i	−0.895681	−	0.444696i
$7$	−2.36975	−	1.17656i	−0.895681	−	0.444696i
$8$	1.00000			0.353553
$9$	2.99031	+	0.240925i	0.996770	+	0.0803085i
$10$	−0.360902	−	2.20675i	−0.114127	−	0.697836i
$11$	1.16595	−	0.673160i	0.351546	−	0.202965i	−0.313820	−	0.949483i	$-0.601609\pi$
$11$	1.16595	−	0.673160i	0.351546	−	0.202965i	0.665366	+	0.746517i	$0.268275\pi$
$12$	−0.925606	+	1.46399i	−0.267199	+	0.422616i
$13$	1.23065	−	2.13155i	0.341321	−	0.591186i	−0.643357	−	0.765566i	$-0.722459\pi$
$13$	1.23065	−	2.13155i	0.341321	−	0.591186i	0.984678	+	0.174380i	$0.0557922\pi$
$14$	0.165947	+	2.64054i	0.0443513	+	0.705715i
$15$	3.56470	+	1.51423i	0.920403	+	0.390972i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$			0.246520i			0.0597899i	0.999553	+	0.0298949i	$0.00951727\pi$
$17$			0.246520i			0.0597899i	−0.999553	+	0.0298949i	$0.990483\pi$
$18$	−1.28651	−	2.71015i	−0.303233	−	0.638788i
$19$			1.47434i			0.338237i	0.985596	+	0.169119i	$0.0540921\pi$
$19$			1.47434i			0.338237i	−0.985596	+	0.169119i	$0.945908\pi$
$20$	−1.73065	+	1.41593i	−0.386985	+	0.316611i
$21$	−4.01932	−	2.20116i	−0.877087	−	0.480332i
$22$	−1.16595	−	0.673160i	−0.248581	−	0.143518i
$23$	4.15626	−	7.19885i	0.866640	−	1.50106i	0.00122971	−	0.999999i	$-0.499609\pi$
$23$	4.15626	−	7.19885i	0.866640	−	1.50106i	0.865410	−	0.501065i	$-0.167058\pi$
$24$	1.73065	+	0.0696054i	0.353268	+	0.0142081i
$25$	3.74919	+	3.30811i	0.749838	+	0.661621i
$26$	−2.46130			−0.482701
$27$	5.15842	+	0.625100i	0.992738	+	0.120301i
$28$	2.20380	−	1.46399i	0.416480	−	0.276667i
$29$	−4.56386	+	2.63495i	−0.847488	+	0.489297i	−0.859803	−	0.510627i	$-0.829413\pi$
$29$	−4.56386	+	2.63495i	−0.847488	+	0.489297i	0.0123145	+	0.999924i	$0.496080\pi$
$30$	−0.470993	−	3.84424i	−0.0859912	−	0.701859i
$31$	8.15842	+	4.71026i	1.46529	+	0.845988i	0.999248	−	0.0387719i	$-0.0123446\pi$
$31$	8.15842	+	4.71026i	1.46529	+	0.845988i	0.466047	+	0.884760i	$0.345678\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.06470	−	1.08385i	0.359419	−	0.188674i
$34$	0.213493	−	0.123260i	0.0366137	−	0.0211389i
$35$	−4.02601	−	4.33489i	−0.680519	−	0.732730i
$36$	−1.70380	+	2.46922i	−0.283967	+	0.411537i
$37$		−	1.87126i		−	0.307634i	−0.988099	−	0.153817i	$-0.950843\pi$
$37$		−	1.87126i		−	0.307634i	0.988099	−	0.153817i	$-0.0491565\pi$
$38$	1.27682	−	0.737171i	0.207127	−	0.119585i
$39$	2.27820	−	3.60331i	0.364803	−	0.576992i
$40$	2.09155	+	0.790826i	0.330704	+	0.125040i
$41$	−4.73065	+	8.19373i	−0.738804	+	1.27965i	0.214231	+	0.976783i	$0.431276\pi$
$41$	−4.73065	+	8.19373i	−0.738804	+	1.27965i	−0.953034	+	0.302862i	$0.902058\pi$
$42$	0.103401	+	4.58141i	0.0159551	+	0.706927i
$43$	7.27682	−	4.20127i	1.10970	−	0.640688i	0.170952	−	0.985279i	$-0.445316\pi$
$43$	7.27682	−	4.20127i	1.10970	−	0.640688i	0.938753	+	0.344591i	$0.111983\pi$
$44$			1.34632i			0.202965i
$45$	6.06386	+	2.86872i	0.903947	+	0.427644i
$46$	−8.31252			−1.22561
$47$	−8.27520	+	4.77769i	−1.20706	+	0.696897i	−0.962116	−	0.272640i	$-0.912103\pi$
$47$	−8.27520	+	4.77769i	−1.20706	+	0.696897i	−0.244945	+	0.969537i	$0.578770\pi$
$48$	−0.805046	−	1.53359i	−0.116198	−	0.221355i
$49$	4.23143	+	5.57629i	0.604490	+	0.796613i
$50$	0.990310	−	4.90095i	0.140051	−	0.693099i
$51$	−0.0171591	+	0.426640i	−0.00240276	+	0.0597416i
$52$	1.23065	+	2.13155i	0.170661	+	0.295593i
$53$	−8.10571			−1.11341			−0.556703	−	0.830712i	$-0.687934\pi$
$53$	−8.10571			−1.11341			−0.556703	+	0.830712i	$0.687934\pi$
$54$	−2.03786	−	4.77987i	−0.277317	−	0.650458i
$55$	2.97099	−	0.485889i	0.400609	−	0.0655173i
$56$	−2.36975	−	1.17656i	−0.316671	−	0.157224i
$57$	−0.102622	+	2.55157i	−0.0135926	+	0.337964i
$58$	4.56386	+	2.63495i	0.599265	+	0.345986i
$59$	2.66673	−	4.61891i	0.347178	−	0.601330i	−0.638569	−	0.769565i	$-0.720473\pi$
$59$	2.66673	−	4.61891i	0.347178	−	0.601330i	0.985747	+	0.168234i	$0.0538066\pi$
$60$	−3.09371	+	2.33001i	−0.399396	+	0.300803i
$61$	−6.46877	+	3.73475i	−0.828241	+	0.478185i	−0.853250	−	0.521502i	$-0.825372\pi$
$61$	−6.46877	+	3.73475i	−0.828241	+	0.478185i	0.0250087	+	0.999687i	$0.492039\pi$
$62$		−	9.42053i		−	1.19641i
$63$	−6.80283	−	4.08920i	−0.857075	−	0.515191i
$64$	1.00000			0.125000
$65$	4.25966	−	3.48502i	0.528346	−	0.432264i
$66$	−1.97099	−	1.24616i	−0.242612	−	0.153392i
$67$	−1.74112	−	1.00524i	−0.212712	−	0.122809i	0.389859	−	0.920874i	$-0.372524\pi$
$67$	−1.74112	−	1.00524i	−0.212712	−	0.122809i	−0.602571	+	0.798065i	$0.705857\pi$
$68$	−0.213493	−	0.123260i	−0.0258898	−	0.0149475i
$69$	7.69411	−	12.1694i	0.926262	−	1.46502i
$70$	−1.74112	+	5.65407i	−0.208104	+	0.675791i
$71$		−	15.3040i		−	1.81625i	−0.418697	−	0.908126i	$-0.637513\pi$
$71$		−	15.3040i		−	1.81625i	0.418697	−	0.908126i	$-0.362487\pi$
$72$	2.99031	+	0.240925i	0.352411	+	0.0283933i
$73$	−5.92861			−0.693891			−0.346945	−	0.937885i	$-0.612781\pi$
$73$	−5.92861			−0.693891			−0.346945	+	0.937885i	$0.612781\pi$
$74$	−1.62056	+	0.935631i	−0.188386	+	0.108765i
$75$	6.25828	+	5.98615i	0.722644	+	0.691221i
$76$	−1.27682	−	0.737171i	−0.146461	−	0.0845593i
$77$	−3.55501	+	0.223418i	−0.405131	+	0.0254609i
$78$	−4.25966	−	0.171320i	−0.482311	−	0.0193982i
$79$	0.270127	+	0.467874i	0.0303917	+	0.0526399i	0.880821	−	0.473449i	$-0.156991\pi$
$79$	0.270127	+	0.467874i	0.0303917	+	0.0526399i	−0.850430	+	0.526089i	$0.823658\pi$
$80$	−0.360902	−	2.20675i	−0.0403500	−	0.246722i
$81$	8.88391	+	1.44088i	0.987101	+	0.160098i
$82$	9.46130			1.04483
$83$	−1.04539	+	0.603555i	−0.114746	+	0.0662487i	−0.556275	−	0.830999i	$-0.687770\pi$
$83$	−1.04539	+	0.603555i	−0.114746	+	0.0662487i	0.441528	+	0.897247i	$0.354436\pi$
$84$	3.91592	−	2.38025i	0.427261	−	0.259707i
$85$	−0.194954	+	0.515610i	−0.0211458	+	0.0559257i
$86$	−7.27682	−	4.20127i	−0.784679	−	0.453035i
$87$	−8.08186	+	4.24251i	−0.866467	+	0.454844i
$88$	1.16595	−	0.673160i	0.124290	−	0.0717591i
$89$	−13.5043			−1.43145			−0.715724	−	0.698383i	$-0.753903\pi$
$89$	−13.5043			−1.43145			−0.715724	+	0.698383i	$0.753903\pi$
$90$	−0.547545	−	6.68582i	−0.0577163	−	0.704747i
$91$	−5.42423	+	3.60331i	−0.568613	+	0.377730i
$92$	4.15626	+	7.19885i	0.433320	+	0.750532i
$93$	13.7915	+	8.71969i	1.43011	+	0.904190i
$94$	8.27520	+	4.77769i	0.853521	+	0.492781i
$95$	−1.16595	+	3.08366i	−0.119624	+	0.316377i
$96$	−0.925606	+	1.46399i	−0.0944693	+	0.149417i
$97$	−5.12803	−	8.88201i	−0.520673	−	0.901831i	−0.999711	−	0.0240374i	$-0.992348\pi$
$97$	−5.12803	−	8.88201i	−0.520673	−	0.901831i	0.479039	−	0.877794i	$-0.340985\pi$
$98$	2.71349	−	6.45267i	0.274104	−	0.651818i
$99$	3.64873	−	1.73205i	0.366711	−	0.174078i
$100$	−4.73950	+	1.59284i	−0.473950	+	0.159284i
$101$	−0.702424	−	1.21663i	−0.0698938	−	0.121060i	0.828961	−	0.559307i	$-0.188933\pi$
$101$	−0.702424	−	1.21663i	−0.0698938	−	0.121060i	−0.898854	+	0.438247i	$0.855599\pi$
$102$	0.378061	−	0.198460i	0.0374336	−	0.0196504i
$103$	−4.86975	+	8.43465i	−0.479831	+	0.831091i	−0.999732	−	0.0231349i	$-0.992635\pi$
$103$	−4.86975	+	8.43465i	−0.479831	+	0.831091i	0.519902	+	0.854226i	$0.325969\pi$
$104$	1.23065	−	2.13155i	0.120675	−	0.209016i
$105$	−6.66588	−	7.78241i	−0.650524	−	0.759486i
$106$	4.05286	+	7.01975i	0.393648	+	0.681819i
$107$	−14.8538			−1.43598			−0.717988	−	0.696056i	$-0.754937\pi$
$107$	−14.8538			−1.43598			−0.717988	+	0.696056i	$0.754937\pi$
$108$	−3.12056	+	4.15477i	−0.300276	+	0.399793i
$109$	1.09233			0.104626			0.0523132	−	0.998631i	$-0.483341\pi$
$109$	1.09233			0.104626			0.0523132	+	0.998631i	$0.483341\pi$
$110$	−1.90629	−	2.33001i	−0.181758	−	0.222158i
$111$	0.130250	−	3.23850i	0.0123628	−	0.307385i
$112$	0.165947	+	2.64054i	0.0156806	+	0.249508i
$113$	4.00963	−	6.94488i	0.377194	−	0.653319i	−0.613459	−	0.789727i	$-0.710222\pi$
$113$	4.00963	−	6.94488i	0.377194	−	0.653319i	0.990653	+	0.136408i	$0.0435557\pi$
$114$	2.26104	−	1.18691i	0.211766	−	0.111165i
$115$	14.3861	−	11.7699i	1.34151	−	1.09755i
$116$		−	5.26989i		−	0.489297i
$117$	4.19358	−	6.07750i	0.387696	−	0.561865i
$118$	−5.33345			−0.490984
$119$	0.290045	−	0.584191i	0.0265883	−	0.0535527i
$120$	3.56470	+	1.51423i	0.325411	+	0.138229i
$121$	−4.59371	+	7.95654i	−0.417610	+	0.723322i
$122$	6.46877	+	3.73475i	0.585655	+	0.338128i
$123$	−8.75744	+	13.8512i	−0.789632	+	1.24892i
$124$	−8.15842	+	4.71026i	−0.732647	+	0.422994i
$125$	5.22549	+	9.88404i	0.467382	+	0.884055i
$126$	−0.139940	+	7.93602i	−0.0124668	+	0.706997i
$127$		−	6.14992i		−	0.545717i	−0.962054	−	0.272858i	$-0.912031\pi$
$127$		−	6.14992i		−	0.545717i	0.962054	−	0.272858i	$-0.0879690\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	12.8861	−	6.76443i	1.13456	−	0.595575i
$130$	−5.14795	−	1.94646i	−0.451505	−	0.170716i
$131$	−9.56170	+	16.5614i	−0.835410	+	1.44697i	0.0582861	+	0.998300i	$0.481436\pi$
$131$	−9.56170	+	16.5614i	−0.835410	+	1.44697i	−0.893696	+	0.448673i	$0.851897\pi$
$132$	−0.0937112	+	2.33001i	−0.00815651	+	0.202801i
$133$	1.73465	−	3.49382i	0.150413	−	0.302953i
$134$			2.01047i			0.173678i
$135$	10.2948	+	5.38684i	0.886031	+	0.463625i
$136$			0.246520i			0.0211389i
$137$	6.25828	+	10.8397i	0.534681	+	0.926094i	0.999179	+	0.0405202i	$0.0129015\pi$
$137$	6.25828	+	10.8397i	0.534681	+	0.926094i	−0.464498	+	0.885574i	$0.653765\pi$
$138$	−14.3861	−	0.578596i	−1.22462	−	0.0492534i
$139$	4.02870	+	2.32597i	0.341710	+	0.197286i	0.661028	−	0.750361i	$-0.270120\pi$
$139$	4.02870	+	2.32597i	0.341710	+	0.197286i	−0.319318	+	0.947648i	$0.603454\pi$
$140$	5.76713	−	1.31918i	0.487411	−	0.111491i
$141$	−14.6540	+	7.69251i	−1.23409	+	0.647827i
$142$	−13.2537	+	7.65200i	−1.11222	+	0.642142i
$143$		−	3.31370i		−	0.277106i
$144$	−1.28651	−	2.71015i	−0.107209	−	0.225846i
$145$	−11.6293	+	1.90191i	−0.965765	+	0.157945i
$146$	2.96430	+	5.13432i	0.245327	+	0.424920i
$147$	6.93499	+	9.94514i	0.571989	+	0.820262i
$148$	1.62056	+	0.935631i	0.133209	+	0.0769084i
$149$	−3.13672	−	1.81099i	−0.256970	−	0.148362i	0.365981	−	0.930622i	$-0.380733\pi$
$149$	−3.13672	−	1.81099i	−0.256970	−	0.148362i	−0.622952	+	0.782260i	$0.714067\pi$
$150$	2.05501	−	8.41290i	0.167791	−	0.686911i
$151$	−5.59071	−	9.68340i	−0.454966	−	0.788024i	0.543721	−	0.839266i	$-0.317015\pi$
$151$	−5.59071	−	9.68340i	−0.454966	−	0.788024i	−0.998686	+	0.0512427i	$0.983682\pi$
$152$			1.47434i			0.119585i
$153$	−0.0593929	+	0.737171i	−0.00480163	+	0.0595967i
$154$	1.97099	+	2.96702i	0.158827	+	0.239090i
$155$	13.3388	+	16.3036i	1.07140	+	1.30954i
$156$	1.98146	+	3.77463i	0.158644	+	0.302212i
$157$	−2.79836	+	4.84689i	−0.223333	+	0.386824i	−0.955818	−	0.293959i	$-0.905027\pi$
$157$	−2.79836	+	4.84689i	−0.223333	+	0.386824i	0.732485	+	0.680783i	$0.238360\pi$
$158$	0.270127	−	0.467874i	0.0214902	−	0.0372221i
$159$	−14.0282	−	0.564202i	−1.11251	−	0.0447441i
$160$	−1.73065	+	1.41593i	−0.136820	+	0.111939i
$161$	−18.3191	+	12.1694i	−1.44375	+	0.959083i
$162$	−3.19411	−	8.41413i	−0.250953	−	0.661077i
$163$			21.3334i			1.67096i	0.549522	+	0.835480i	$0.314810\pi$
$163$			21.3334i			1.67096i	−0.549522	+	0.835480i	$0.685190\pi$
$164$	−4.73065	−	8.19373i	−0.369402	−	0.639823i
$165$	5.17557	−	0.634107i	0.402918	−	0.0493652i
$166$	1.04539	+	0.603555i	0.0811378	+	0.0468449i
$167$	2.90007	+	1.67436i	0.224414	+	0.129566i	0.607993	−	0.793943i	$-0.291975\pi$
$167$	2.90007	+	1.67436i	0.224414	+	0.129566i	−0.383578	+	0.923508i	$0.625308\pi$
$168$	−4.01932	−	2.20116i	−0.310097	−	0.169823i
$169$	3.47099	+	6.01194i	0.266999	+	0.462457i
$170$	0.544008	−	0.0889694i	0.0417235	−	0.00682364i
$171$	−0.355207	+	4.40874i	−0.0271633	+	0.337145i
$172$			8.40255i			0.640688i
$173$	6.26050	−	3.61450i	0.475977	−	0.274805i	−0.242761	−	0.970086i	$-0.578053\pi$
$173$	6.26050	−	3.61450i	0.475977	−	0.274805i	0.718738	+	0.695281i	$0.244720\pi$
$174$	7.71505	+	4.87785i	0.584876	+	0.369789i
$175$	−4.99247	−	12.2505i	−0.377395	−	0.926052i
$176$	−1.16595	−	0.673160i	−0.0878866	−	0.0507413i
$177$	4.93667	−	7.80810i	0.371063	−	0.586893i
$178$	6.75213	+	11.6950i	0.506093	+	0.876579i
$179$			7.87760i			0.588800i	0.955682	+	0.294400i	$0.0951197\pi$
$179$			7.87760i			0.588800i	−0.955682	+	0.294400i	$0.904880\pi$
$180$	−5.51632	+	3.81710i	−0.411162	+	0.284510i
$181$			7.54179i			0.560577i	0.959916	+	0.280288i	$0.0904301\pi$
$181$			7.54179i			0.560577i	−0.959916	+	0.280288i	$0.909570\pi$
$182$	5.83267	+	2.89586i	0.432347	+	0.214656i
$183$	−11.4552	+	6.01329i	−0.846789	+	0.444515i
$184$	4.15626	−	7.19885i	0.306403	−	0.530706i
$185$	1.47984	−	3.91384i	0.108800	−	0.287751i
$186$	0.655720	−	16.3036i	0.0480797	−	1.19544i
$187$	0.165947	+	0.287429i	0.0121353	+	0.0210189i
$188$		−	9.55537i		−	0.696897i
$189$	−11.4887	−	7.55050i	−0.835679	−	0.549218i
$190$	3.25351	−	0.532092i	0.236034	−	0.0386020i
$191$	3.09884	−	1.78912i	0.224224	−	0.129456i	−0.383680	−	0.923466i	$-0.625344\pi$
$191$	3.09884	−	1.78912i	0.224224	−	0.129456i	0.607905	+	0.794010i	$0.292010\pi$
$192$	1.73065	+	0.0696054i	0.124899	+	0.00502334i
$193$	7.22120	+	4.16916i	0.519794	+	0.300103i	0.736850	−	0.676056i	$-0.236312\pi$
$193$	7.22120	+	4.16916i	0.519794	+	0.300103i	−0.217057	+	0.976159i	$0.569646\pi$
$194$	−5.12803	+	8.88201i	−0.368171	+	0.637691i
$195$	7.61456	−	5.73486i	0.545290	−	0.410682i
$196$	−6.94492	+	0.876382i	−0.496066	+	0.0625987i
$197$	−0.503178			−0.0358499			−0.0179250	−	0.999839i	$-0.505706\pi$
$197$	−0.503178			−0.0358499			−0.0179250	+	0.999839i	$0.505706\pi$
$198$	−3.32436	−	2.29386i	−0.236252	−	0.163018i
$199$		−	5.50523i		−	0.390255i	−0.980778	−	0.195128i	$-0.937488\pi$
$199$		−	5.50523i		−	0.390255i	0.980778	−	0.195128i	$-0.0625121\pi$
$200$	3.74919	+	3.30811i	0.265108	+	0.233919i
$201$	−2.94330	−	1.86091i	−0.207605	−	0.131258i
$202$	−0.702424	+	1.21663i	−0.0494223	+	0.0856020i
$203$	13.9154	−	0.874525i	0.976668	−	0.0613796i
$204$	−0.360902	−	0.228180i	−0.0252682	−	0.0159758i
$205$	−16.3742	+	13.3965i	−1.14363	+	0.935652i
$206$	9.73950			0.678583
$207$	14.1629	−	20.5254i	0.984389	−	1.42662i
$208$	−2.46130			−0.170661
$209$	0.992468	+	1.71901i	0.0686505	+	0.118906i
$210$	−3.40683	+	9.66403i	−0.235093	+	0.666882i
$211$	10.9269	−	18.9260i	0.752240	−	1.30292i	−0.194494	−	0.980904i	$-0.562307\pi$
$211$	10.9269	−	18.9260i	0.752240	−	1.30292i	0.946735	−	0.322015i	$-0.104360\pi$
$212$	4.05286	−	7.01975i	0.278351	−	0.482119i
$213$	1.06524	−	26.4859i	0.0729892	−	1.81478i
$214$	7.42692	+	12.8638i	0.507694	+	0.879352i
$215$	18.5423	−	3.03249i	1.26458	−	0.206814i
$216$	5.15842	+	0.625100i	0.350986	+	0.0425327i
$217$	−13.7915	−	20.7610i	−0.936229	−	1.40935i
$218$	−0.546166	−	0.945987i	−0.0369910	−	0.0640703i
$219$	−10.2604	−	0.412663i	−0.693330	−	0.0278852i
$220$	−1.06470	+	2.81590i	−0.0717823	+	0.189848i
$221$	0.525470	+	0.303380i	0.0353469	+	0.0204076i
$222$	−2.86975	+	1.50645i	−0.192605	+	0.101106i
$223$	3.85337	+	6.67423i	0.258041	+	0.446940i	0.965717	−	0.259597i	$-0.0835898\pi$
$223$	3.85337	+	6.67423i	0.258041	+	0.446940i	−0.707676	+	0.706537i	$0.750256\pi$
$224$	2.20380	−	1.46399i	0.147248	−	0.0978167i
$225$	10.4142	+	10.7955i	0.694282	+	0.719703i
$226$	−8.01925			−0.533433
$227$	−17.4828	+	10.0937i	−1.16037	+	0.669942i	−0.951393	−	0.307979i	$-0.900348\pi$
$227$	−17.4828	+	10.0937i	−1.16037	+	0.669942i	−0.208979	+	0.977920i	$0.567014\pi$
$228$	−2.15842	−	1.36466i	−0.142945	−	0.0903768i
$229$	−6.16057	−	3.55681i	−0.407102	−	0.235041i	0.282442	−	0.959284i	$-0.408856\pi$
$229$	−6.16057	−	3.55681i	−0.407102	−	0.235041i	−0.689544	+	0.724244i	$0.742189\pi$
$230$	−17.3861	−	6.57375i	−1.14640	−	0.433460i
$231$	−6.16804	+	0.139211i	−0.405827	+	0.00915940i
$232$	−4.56386	+	2.63495i	−0.299632	+	0.172993i
$233$	−22.8989			−1.50016			−0.750079	−	0.661349i	$-0.769984\pi$
$233$	−22.8989			−1.50016			−0.750079	+	0.661349i	$0.769984\pi$
$234$	−7.36006	−	0.592991i	−0.481142	−	0.0387650i
$235$	−21.0863	+	3.44855i	−1.37552	+	0.224959i
$236$	2.66673	+	4.61891i	0.173589	+	0.300665i
$237$	0.434929	+	0.828529i	0.0282517	+	0.0538188i
$238$	−0.650946	+	0.0409093i	−0.0421946	+	0.00265176i
$239$	−13.9049	−	8.02800i	−0.899434	−	0.519288i	−0.0224174	−	0.999749i	$-0.507136\pi$
$239$	−13.9049	−	8.02800i	−0.899434	−	0.519288i	−0.877016	+	0.480460i	$0.840470\pi$
$240$	−0.470993	−	3.84424i	−0.0304025	−	0.248144i
$241$	5.76122	−	3.32624i	0.371113	−	0.214262i	−0.302832	−	0.953044i	$-0.597932\pi$
$241$	5.76122	−	3.32624i	0.371113	−	0.214262i	0.673944	+	0.738782i	$0.264599\pi$
$242$	9.18742			0.590590
$243$	15.2747	+	3.11204i	0.979870	+	0.199637i
$244$		−	7.46950i		−	0.478185i
$245$	4.44039	+	15.0094i	0.283686	+	0.958917i
$246$	16.3742	+	0.658558i	1.04398	+	0.0419881i
$247$	3.14264	+	1.81440i	0.199961	+	0.115448i
$248$	8.15842	+	4.71026i	0.518060	+	0.299102i
$249$	−1.85121	+	0.971778i	−0.117316	+	0.0615839i
$250$	5.94708	−	9.46743i	0.376126	−	0.598773i
$251$	9.60841			0.606477			0.303239	−	0.952915i	$-0.401932\pi$
$251$	9.60841			0.606477			0.303239	+	0.952915i	$0.401932\pi$
$252$	6.94277	−	3.84682i	0.437353	−	0.242327i
$253$		−	11.1913i		−	0.703591i
$254$	−5.32598	+	3.07496i	−0.334182	+	0.192940i
$255$	−0.373287	+	0.878771i	−0.0233761	+	0.0550308i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.29727	+	3.05838i	0.330435	+	0.190777i	0.656034	−	0.754731i	$-0.272233\pi$
$257$	5.29727	+	3.05838i	0.330435	+	0.190777i	−0.325599	+	0.945508i	$0.605566\pi$
$258$	−12.3012	−	7.77745i	−0.765840	−	0.484203i
$259$	−2.20164	+	4.43442i	−0.136804	+	0.275542i
$260$	0.888288	+	5.43148i	0.0550893	+	0.336846i
$261$	−14.2822	+	6.77976i	−0.884045	+	0.419657i
$262$	19.1234			1.18145
$263$	−8.13556	−	14.0912i	−0.501660	−	0.868901i	−0.999998	−	0.00191810i	$-0.999389\pi$
$263$	−8.13556	−	14.0912i	−0.501660	−	0.868901i	0.498338	−	0.866983i	$-0.333944\pi$
$264$	2.06470	−	1.08385i	0.127074	−	0.0667063i
$265$	−16.9535	−	6.41020i	−1.04145	−	0.393776i
$266$	−3.89306	+	0.244663i	−0.238699	+	0.0150013i
$267$	−23.3712	−	0.939969i	−1.43029	−	0.0575252i
$268$	1.74112	−	1.00524i	0.106356	−	0.0614046i
$269$	7.72288			0.470872			0.235436	−	0.971890i	$-0.424348\pi$
$269$	7.72288			0.470872			0.235436	+	0.971890i	$0.424348\pi$
$270$	−0.482241	−	11.6089i	−0.0293482	−	0.706497i
$271$		−	7.62672i		−	0.463290i	−0.972800	−	0.231645i	$-0.925589\pi$
$271$		−	7.62672i		−	0.463290i	0.972800	−	0.231645i	$-0.0744108\pi$
$272$	0.213493	−	0.123260i	0.0129449	−	0.00747373i
$273$	−9.63826	+	5.85852i	−0.583334	+	0.354574i
$274$	6.25828	−	10.8397i	0.378076	−	0.654848i
$275$	6.59824	+	1.33327i	0.397889	+	0.0803995i
$276$	6.69195	+	12.7480i	0.402808	+	0.767339i
$277$	12.0531	−	6.95886i	0.724200	−	0.418117i	−0.0920966	−	0.995750i	$-0.529357\pi$
$277$	12.0531	−	6.95886i	0.724200	−	0.418117i	0.816297	+	0.577633i	$0.196024\pi$
$278$		−	4.65195i		−	0.279005i
$279$	23.2614	+	16.0507i	1.39262	+	0.960931i
$280$	−4.02601	−	4.33489i	−0.240600	−	0.259059i
$281$	−26.1618	+	15.1045i	−1.56068	+	0.901060i	−0.563494	+	0.826120i	$0.690543\pi$
$281$	−26.1618	+	15.1045i	−1.56068	+	0.901060i	−0.997188	+	0.0749404i	$0.976123\pi$
$282$	13.9889	+	8.84451i	0.833029	+	0.526683i
$283$	−3.80151	+	6.58441i	−0.225976	+	0.391402i	−0.956612	−	0.291365i	$-0.905891\pi$
$283$	−3.80151	+	6.58441i	−0.225976	+	0.391402i	0.730636	+	0.682768i	$0.239224\pi$
$284$	13.2537	+	7.65200i	0.786460	+	0.454063i
$285$	−2.23249	+	5.25559i	−0.132241	+	0.311314i
$286$	−2.86975	+	1.65685i	−0.169692	+	0.0979717i
$287$	20.8508	−	13.8512i	1.23079	−	0.817611i
$288$	−1.70380	+	2.46922i	−0.100398	+	0.145500i
$289$	16.9392			0.996425
$290$	7.46178	+	9.12035i	0.438171	+	0.535566i
$291$	−8.25660	−	15.7286i	−0.484010	−	0.922027i
$292$	2.96430	−	5.13432i	0.173473	−	0.300464i
$293$	26.8981	+	15.5296i	1.57140	+	0.907249i	0.995998	+	0.0893804i	$0.0284887\pi$
$293$	26.8981	+	15.5296i	1.57140	+	0.907249i	0.575404	+	0.817869i	$0.304845\pi$
$294$	5.14525	−	10.9785i	0.300077	−	0.640276i
$295$	9.23035	−	7.55177i	0.537412	−	0.439681i
$296$		−	1.87126i		−	0.108765i
$297$	6.43523	−	2.74361i	0.373410	−	0.159200i
$298$			3.62198i			0.209815i
$299$	−10.2298	−	17.7186i	−0.591605	−	1.02469i
$300$	−8.31329	+	2.42676i	−0.479968	+	0.140109i
$301$	−22.1873	+	1.39438i	−1.27885	+	0.0803707i
$302$	−5.59071	+	9.68340i	−0.321709	+	0.557217i
$303$	−1.13097	−	2.15446i	−0.0649723	−	0.123771i
$304$	1.27682	−	0.737171i	0.0732305	−	0.0422797i
$305$	−16.4833	+	2.69575i	−0.943832	+	0.154358i
$306$	0.668105	−	0.317150i	0.0381930	−	0.0181302i
$307$	25.2516			1.44119			0.720593	−	0.693358i	$-0.243870\pi$
$307$	25.2516			1.44119			0.720593	+	0.693358i	$0.243870\pi$
$308$	1.58402	−	3.19044i	0.0902580	−	0.181792i
$309$	−9.01494	+	14.2585i	−0.512842	+	0.811137i
$310$	7.44999	−	19.7035i	0.423131	−	1.11909i
$311$	14.0520	−	24.3388i	0.796817	−	1.38013i	−0.124863	−	0.992174i	$-0.539849\pi$
$311$	14.0520	−	24.3388i	0.796817	−	1.38013i	0.921679	−	0.387953i	$-0.126818\pi$
$312$	2.27820	−	3.60331i	0.128977	−	0.203997i
$313$	11.1704	+	19.3477i	0.631389	+	1.09360i	0.987268	+	0.159066i	$0.0508483\pi$
$313$	11.1704	+	19.3477i	0.631389	+	1.09360i	−0.355879	+	0.934532i	$0.615818\pi$
$314$	5.59671			0.315841
$315$	−10.9946	−	13.9326i	−0.619477	−	0.785015i
$316$	−0.540254			−0.0303917
$317$	−8.46214	−	14.6569i	−0.475281	−	0.823212i	0.524318	−	0.851523i	$-0.324320\pi$
$317$	−8.46214	−	14.6569i	−0.475281	−	0.823212i	−0.999599	+	0.0283112i	$0.990987\pi$
$318$	6.52547	+	12.4308i	0.365930	+	0.697087i
$319$	−3.54748	+	6.14442i	−0.198621	+	0.344021i
$320$	2.09155	+	0.790826i	0.116921	+	0.0442085i
$321$	−25.7068	−	1.03391i	−1.43482	−	0.0577071i
$322$	19.6986	+	9.78014i	1.09776	+	0.545026i
$323$	−0.363455			−0.0202232
$324$	−5.68980	+	6.97325i	−0.316100	+	0.387403i
$325$	11.6653	−	3.92046i	0.647077	−	0.217468i
$326$	18.4752	−	10.6667i	1.02325	−	0.590773i
$327$	1.89045	+	0.0760322i	0.104542	+	0.00420459i
$328$	−4.73065	+	8.19373i	−0.261207	+	0.452423i
$329$	25.2314	−	1.58569i	1.39105	−	0.0874219i
$330$	−3.13694	−	4.16513i	−0.172683	−	0.229283i
$331$	−4.73518	−	8.20158i	−0.260269	−	0.450800i	0.706044	−	0.708168i	$-0.250478\pi$
$331$	−4.73518	−	8.20158i	−0.260269	−	0.450800i	−0.966313	+	0.257368i	$0.917145\pi$
$332$		−	1.20711i		−	0.0662487i
$333$	0.450835	−	5.59565i	0.0247056	−	0.306640i
$334$		−	3.34872i		−	0.183234i
$335$	−2.84668	−	3.47943i	−0.155531	−	0.190101i
$336$	0.103401	+	4.58141i	0.00564099	+	0.249936i
$337$	−26.2388	−	15.1490i	−1.42932	−	0.825217i	−0.432250	−	0.901754i	$-0.642280\pi$
$337$	−26.2388	−	15.1490i	−1.42932	−	0.825217i	−0.997067	+	0.0765370i	$0.975614\pi$
$338$	3.47099	−	6.01194i	0.188797	−	0.327006i
$339$	7.42267	−	11.7401i	0.403144	−	0.637633i
$340$	−0.349054	−	0.426640i	−0.0189301	−	0.0231378i
$341$	12.6830			0.686825
$342$	3.99568	−	1.89675i	0.216062	−	0.102565i
$343$	−3.46661	−	18.1929i	−0.187180	−	0.982326i
$344$	7.27682	−	4.20127i	0.392340	−	0.226517i
$345$	25.7165	−	19.3683i	1.38453	−	1.04275i
$346$	−6.26050	−	3.61450i	−0.336567	−	0.194317i
$347$	8.26551	−	14.3163i	0.443716	−	0.768538i	−0.554246	−	0.832353i	$-0.686993\pi$
$347$	8.26551	−	14.3163i	0.443716	−	0.768538i	0.997962	+	0.0638147i	$0.0203267\pi$
$348$	0.366813	−	9.12035i	0.0196633	−	0.488902i
$349$	9.71689	−	5.61005i	0.520133	−	0.300299i	−0.216856	−	0.976204i	$-0.569580\pi$
$349$	9.71689	−	5.61005i	0.520133	−	0.300299i	0.736989	+	0.675905i	$0.236247\pi$
$350$	−8.11303	+	10.4489i	−0.433660	+	0.558515i
$351$	7.68064	−	10.2261i	0.409962	−	0.545831i
$352$			1.34632i			0.0717591i
$353$	11.0368	−	6.37208i	0.587428	−	0.339152i	−0.176652	−	0.984273i	$-0.556527\pi$
$353$	11.0368	−	6.37208i	0.587428	−	0.339152i	0.764080	+	0.645122i	$0.223193\pi$
$354$	−9.23035	−	0.371237i	−0.490587	−	0.0197310i
$355$	12.1028	−	32.0091i	0.642350	−	1.69887i
$356$	6.75213	−	11.6950i	0.357862	−	0.619835i
$357$	0.542629	−	0.990842i	0.0287190	−	0.0524409i
$358$	6.82220	−	3.93880i	0.360565	−	0.208172i
$359$		−	13.0046i		−	0.686355i	−0.939271	−	0.343178i	$-0.888497\pi$
$359$		−	13.0046i		−	0.686355i	0.939271	−	0.343178i	$-0.111503\pi$
$360$	6.06386	+	2.86872i	0.319594	+	0.151195i
$361$	16.8263			0.885596
$362$	6.53138	−	3.77089i	0.343282	−	0.198194i
$363$	−8.50393	+	13.4503i	−0.446341	+	0.705955i
$364$	−0.408447	−	6.49917i	−0.0214084	−	0.340649i
$365$	−12.4000	−	4.68849i	−0.649045	−	0.245407i
$366$	10.9352	+	6.91381i	0.571594	+	0.361391i
$367$	−15.1533	−	26.2462i	−0.790994	−	1.37004i	−0.925352	−	0.379108i	$-0.876231\pi$
$367$	−15.1533	−	26.2462i	−0.790994	−	1.37004i	0.134359	−	0.990933i	$-0.457103\pi$
$368$	−8.31252			−0.433320
$369$	−16.1202	+	23.3621i	−0.839184	+	1.21618i
$370$	−4.12941	+	0.675341i	−0.214678	+	0.0351093i
$371$	19.2085	+	9.53683i	0.997256	+	0.495127i
$372$	−14.4472	+	7.58396i	−0.749054	+	0.393210i
$373$	24.9505	+	14.4052i	1.29189	+	0.745872i	0.978989	−	0.203915i	$-0.0653666\pi$
$373$	24.9505	+	14.4052i	1.29189	+	0.745872i	0.312899	+	0.949786i	$0.398700\pi$
$374$	0.165947	−	0.287429i	0.00858093	−	0.0148626i
$375$	8.35553	+	17.4695i	0.431478	+	0.902124i
$376$	−8.27520	+	4.77769i	−0.426761	+	0.246390i
$377$			12.9708i			0.668031i
$378$	−0.794577	+	13.7247i	−0.0408686	+	0.705925i
$379$	34.4133			1.76769			0.883846	−	0.467777i	$-0.154945\pi$
$379$	34.4133			1.76769			0.883846	+	0.467777i	$0.154945\pi$
$380$	−2.08756	−	2.55157i	−0.107089	−	0.130893i
$381$	0.428067	−	10.6434i	0.0219306	−	0.545276i
$382$	−3.09884	−	1.78912i	−0.158551	−	0.0915393i
$383$	−9.86291	−	5.69435i	−0.503971	−	0.290968i	0.226381	−	0.974039i	$-0.427311\pi$
$383$	−9.86291	−	5.69435i	−0.503971	−	0.290968i	−0.730352	+	0.683071i	$0.760644\pi$
$384$	−0.805046	−	1.53359i	−0.0410823	−	0.0782607i
$385$	−7.61219	−	2.34411i	−0.387953	−	0.119467i
$386$		−	8.33833i		−	0.424410i
$387$	22.7721	−	10.8099i	1.15757	−	0.549500i
$388$	10.2561			0.520673
$389$	−10.6623	+	6.15591i	−0.540602	+	0.312117i	−0.745323	−	0.666703i	$-0.767705\pi$
$389$	−10.6623	+	6.15591i	−0.540602	+	0.312117i	0.204721	+	0.978820i	$0.434371\pi$
$390$	−8.77382	−	3.72697i	−0.444280	−	0.188723i
$391$	1.77466	+	1.02460i	0.0897484	+	0.0518163i
$392$	4.23143	+	5.57629i	0.213720	+	0.281645i
$393$	−17.7007	+	27.9964i	−0.892884	+	1.41223i
$394$	0.251589	+	0.435765i	0.0126749	+	0.0219535i
$395$	0.194979	+	1.19221i	0.00981044	+	0.0599864i
$396$	−0.324363	+	4.02591i	−0.0162998	+	0.202310i
$397$	−33.1711			−1.66481			−0.832405	−	0.554168i	$-0.813037\pi$
$397$	−33.1711			−1.66481			−0.832405	+	0.554168i	$0.813037\pi$
$398$	−4.76767	+	2.75261i	−0.238981	+	0.137976i
$399$	3.24526	−	5.92585i	0.162466	−	0.296663i
$400$	0.990310	−	4.90095i	0.0495155	−	0.245047i
$401$	11.4991	+	6.63899i	0.574236	+	0.331535i	0.758839	−	0.651278i	$-0.225767\pi$
$401$	11.4991	+	6.63899i	0.574236	+	0.331535i	−0.184603	+	0.982813i	$0.559100\pi$
$402$	−0.139940	+	3.47943i	−0.00697956	+	0.173538i
$403$	20.0803	−	11.5934i	1.00027	−	0.577508i
$404$	1.40485			0.0698938
$405$	17.4417	+	10.0393i	0.866684	+	0.498857i
$406$	−7.71505	−	11.6138i	−0.382892	−	0.576384i
$407$	−1.25966	−	2.18179i	−0.0624390	−	0.108147i
$408$	−0.0171591	+	0.426640i	−0.000849503	+	0.0211218i
$409$	−12.8060	−	7.39357i	−0.633218	−	0.365589i	0.148779	−	0.988870i	$-0.452466\pi$
$409$	−12.8060	−	7.39357i	−0.633218	−	0.365589i	−0.781997	+	0.623282i	$0.785799\pi$
$410$	19.7888	+	7.48224i	0.977300	+	0.369522i
$411$	10.0764	+	19.1953i	0.497032	+	0.946833i
$412$	−4.86975	−	8.43465i	−0.239915	−	0.415546i
$413$	−11.7539	+	7.80810i	−0.578370	+	0.384211i
$414$	−24.8570	−	2.00270i	−1.22165	−	0.0984272i
$415$	−2.66379	+	0.435648i	−0.130760	+	0.0213851i
$416$	1.23065	+	2.13155i	0.0603377	+	0.104508i
$417$	6.81038	+	4.30587i	0.333506	+	0.210859i
$418$	0.992468	−	1.71901i	0.0485432	−	0.0840793i
$419$	0.587083	−	1.01686i	0.0286809	−	0.0496768i	−0.851329	−	0.524633i	$-0.824203\pi$
$419$	0.587083	−	1.01686i	0.0286809	−	0.0496768i	0.880010	+	0.474956i	$0.157536\pi$
$420$	10.0727	−	1.88162i	0.491498	−	0.0918136i
$421$	−9.97171	−	17.2715i	−0.485991	−	0.841762i	0.513879	−	0.857863i	$-0.328208\pi$
$421$	−9.97171	−	17.2715i	−0.485991	−	0.841762i	−0.999870	+	0.0161009i	$0.994875\pi$
$422$	−21.8538			−1.06383
$423$	−25.8965	+	12.2931i	−1.25913	+	0.597709i
$424$	−8.10571			−0.393648
$425$	−0.815514	+	0.924250i	−0.0395583	+	0.0448327i
$426$	−23.4701	+	12.3204i	−1.13713	+	0.596927i
$427$	19.7235	−	1.23954i	0.954488	−	0.0599857i
$428$	7.42692	−	12.8638i	0.358994	−	0.621796i
$429$	0.230652	−	5.73486i	0.0111360	−	0.276882i
$430$	−11.8974	−	14.5419i	−0.573743	−	0.701272i
$431$			22.0124i			1.06030i	0.847903	+	0.530151i	$0.177865\pi$
$431$			22.0124i			1.06030i	−0.847903	+	0.530151i	$0.822135\pi$
$432$	−2.03786	−	4.77987i	−0.0980464	−	0.229972i
$433$	1.88985			0.0908202			0.0454101	−	0.998968i	$-0.485541\pi$
$433$	1.88985			0.0908202			0.0454101	+	0.998968i	$0.485541\pi$
$434$	−11.0838	+	22.3243i	−0.532038	+	1.07160i
$435$	−20.2587	+	2.48208i	−0.971332	+	0.119007i
$436$	−0.546166	+	0.945987i	−0.0261566	+	0.0453046i
$437$	10.6136	+	6.12775i	0.507716	+	0.293130i
$438$	4.77280	+	9.09206i	0.228053	+	0.434435i
$439$	−24.1785	+	13.9595i	−1.15398	+	0.666249i	−0.949853	−	0.312696i	$-0.898768\pi$
$439$	−24.1785	+	13.9595i	−1.15398	+	0.666249i	−0.204124	+	0.978945i	$0.565435\pi$
$440$	2.97099	−	0.485889i	0.141637	−	0.0231639i
$441$	11.3098	+	17.6943i	0.538563	+	0.842585i
$442$		−	0.606760i		−	0.0288606i
$443$	−16.8221	−	29.1368i	−0.799244	−	1.38433i	−0.920109	−	0.391662i	$-0.871900\pi$
$443$	−16.8221	−	29.1368i	−0.799244	−	1.38433i	0.120865	−	0.992669i	$-0.461433\pi$
$444$	2.73950	+	1.73205i	0.130011	+	0.0821995i
$445$	−28.2449	−	10.6795i	−1.33893	−	0.506257i
$446$	3.85337	−	6.67423i	0.182462	−	0.316034i
$447$	−5.30252	−	3.35252i	−0.250801	−	0.158569i
$448$	−2.36975	−	1.17656i	−0.111960	−	0.0555871i
$449$			14.3956i			0.679373i	0.940539	+	0.339686i	$0.110321\pi$
$449$			14.3956i			0.679373i	−0.940539	+	0.339686i	$0.889679\pi$
$450$	4.14210	−	14.4168i	0.195260	−	0.679613i
$451$			12.7379i			0.599806i
$452$	4.00963	+	6.94488i	0.188597	+	0.326660i
$453$	−9.00156	−	17.1477i	−0.422930	−	0.805671i
$454$	17.4828	+	10.0937i	0.820507	+	0.473720i
$455$	−14.1947	+	3.24690i	−0.665455	+	0.152217i
$456$	−0.102622	+	2.55157i	−0.00480573	+	0.119488i
$457$	−22.2454	+	12.8434i	−1.04060	+	0.600789i	−0.920002	−	0.391913i	$-0.871813\pi$
$457$	−22.2454	+	12.8434i	−1.04060	+	0.600789i	−0.120594	+	0.992702i	$0.538480\pi$
$458$			7.11362i			0.332398i
$459$	−0.154100	+	1.27165i	−0.00719275	+	0.0593556i
$460$	3.00000	+	18.3437i	0.139876	+	0.855277i
$461$	−12.2680	−	21.2487i	−0.571376	−	0.989653i	−0.996425	−	0.0844823i	$-0.973076\pi$
$461$	−12.2680	−	21.2487i	−0.571376	−	0.989653i	0.425049	−	0.905170i	$-0.360257\pi$
$462$	3.20458	+	5.27208i	0.149091	+	0.245279i
$463$	19.5138	+	11.2663i	0.906883	+	0.523589i	0.879427	−	0.476034i	$-0.157926\pi$
$463$	19.5138	+	11.2663i	0.906883	+	0.523589i	0.0274562	+	0.999623i	$0.491259\pi$
$464$	4.56386	+	2.63495i	0.211872	+	0.122324i
$465$	21.9499	+	29.1444i	1.01790	+	1.35154i
$466$	11.4495	+	19.8310i	0.530386	+	0.918655i
$467$		−	30.4040i		−	1.40693i	−0.710731	−	0.703464i	$-0.751635\pi$
$467$		−	30.4040i		−	1.40693i	0.710731	−	0.703464i	$-0.248365\pi$
$468$	3.16649	+	6.67049i	0.146371	+	0.308344i
$469$	2.94330	+	4.43068i	0.135909	+	0.204590i
$470$	13.5297	+	16.5370i	0.624078	+	0.762796i
$471$	−5.18035	+	8.19350i	−0.238698	+	0.377537i
$472$	2.66673	−	4.61891i	0.122746	−	0.212602i
$473$	5.65626	−	9.79693i	0.260075	−	0.450463i
$474$	0.500063	−	0.790925i	0.0229686	−	0.0363284i
$475$	−4.87728	+	5.52759i	−0.223785	+	0.253623i
$476$	0.360902	+	0.543281i	0.0165419	+	0.0249013i
$477$	−24.2386	−	1.95287i	−1.10981	−	0.0894159i
$478$			16.0560i			0.734385i
$479$	15.6602	+	27.1242i	0.715532	+	1.23934i	0.962754	+	0.270379i	$0.0871491\pi$
$479$	15.6602	+	27.1242i	0.715532	+	1.23934i	−0.247222	+	0.968959i	$0.579518\pi$
$480$	−3.09371	+	2.33001i	−0.141208	+	0.106350i
$481$	−3.98869	−	2.30287i	−0.181869	−	0.105002i
$482$	−5.76122	−	3.32624i	−0.262416	−	0.151506i
$483$	−32.5511	+	19.7859i	−1.48113	+	0.900289i
$484$	−4.59371	−	7.95654i	−0.208805	−	0.361661i
$485$	−3.70143	−	22.6326i	−0.168073	−	1.02769i
$486$	−4.94223	−	14.7843i	−0.224184	−	0.670628i
$487$			33.1308i			1.50130i	0.660700	+	0.750650i	$0.270259\pi$
$487$			33.1308i			1.50130i	−0.660700	+	0.750650i	$0.729741\pi$
$488$	−6.46877	+	3.73475i	−0.292828	+	0.169064i
$489$	−1.48492	+	36.9206i	−0.0671503	+	1.66961i
$490$	10.7784	−	11.3502i	0.486916	−	0.512750i
$491$	28.8188	+	16.6385i	1.30057	+	0.750886i	0.980502	−	0.196507i	$-0.0629599\pi$
$491$	28.8188	+	16.6385i	1.30057	+	0.750886i	0.320071	+	0.947394i	$0.396293\pi$
$492$	−7.61678	−	14.5098i	−0.343391	−	0.654151i
$493$	−0.649567	−	1.12508i	−0.0292550	−	0.0506712i
$494$		−	3.62880i		−	0.163268i
$495$	9.00125	−	0.737171i	0.404576	−	0.0331334i
$496$		−	9.42053i		−	0.422994i
$497$	−18.0060	+	36.2667i	−0.807681	+	1.62678i
$498$	1.76719	+	1.11731i	0.0791897	+	0.0500677i
$499$	−11.1122	+	19.2470i	−0.497453	+	0.861613i	−0.999996	−	0.00293899i	$-0.999064\pi$
$499$	−11.1122	+	19.2470i	−0.497453	+	0.861613i	0.502543	+	0.864552i	$0.332398\pi$
$500$	−11.1726	−	0.416608i	−0.499653	−	0.0186313i
$501$	4.90247	+	3.09959i	0.219026	+	0.138480i
$502$	−4.80420	−	8.32113i	−0.214422	−	0.371390i
$503$		−	0.276757i		−	0.0123400i	−0.999981	−	0.00616999i	$-0.998036\pi$
$503$		−	0.276757i		−	0.0123400i	0.999981	−	0.00616999i	$-0.00196398\pi$
$504$	−6.80283	−	4.08920i	−0.303022	−	0.182148i
$505$	−0.507012	−	3.10015i	−0.0225617	−	0.137955i
$506$	−9.69195	+	5.59565i	−0.430860	+	0.248757i
$507$	5.58862	+	10.6462i	0.248199	+	0.472813i
$508$	5.32598	+	3.07496i	0.236302	+	0.136429i
$509$	0.741658	−	1.28459i	0.0328734	−	0.0569384i	−0.849121	−	0.528199i	$-0.822868\pi$
$509$	0.741658	−	1.28459i	0.0328734	−	0.0569384i	0.881994	+	0.471261i	$0.156201\pi$
$510$	0.947681	−	0.116109i	0.0419640	−	0.00514140i
$511$	14.0493	+	6.97534i	0.621505	+	0.308571i
$512$	1.00000			0.0441942
$513$	−0.921611	+	7.60527i	−0.0406901	+	0.335781i
$514$		−	6.11676i		−	0.269799i
$515$	−16.8557	+	13.7904i	−0.742750	+	0.607678i
$516$	−0.584863	+	14.5419i	−0.0257471	+	0.640171i
$517$	−6.43230	+	11.1411i	−0.282892	+	0.489983i
$518$	4.94114	−	0.310531i	0.217101	−	0.0136439i
$519$	11.0863	−	5.81968i	0.486636	−	0.255456i
$520$	4.25966	−	3.48502i	0.186798	−	0.152828i
$521$	0.400049			0.0175265			0.00876323	−	0.999962i	$-0.497211\pi$
$521$	0.400049			0.0175265			0.00876323	+	0.999962i	$0.497211\pi$
$522$	13.0125	+	8.97886i	0.569543	+	0.392994i
$523$	19.5235			0.853703			0.426852	−	0.904322i	$-0.359623\pi$
$523$	19.5235			0.853703			0.426852	+	0.904322i	$0.359623\pi$
$524$	−9.56170	−	16.5614i	−0.417705	−	0.723486i
$525$	−7.78752	−	21.5489i	−0.339875	−	0.940471i
$526$	−8.13556	+	14.0912i	−0.354727	+	0.614406i
$527$	−1.16117	+	2.01121i	−0.0505815	+	0.0876098i
$528$	−1.97099	−	1.24616i	−0.0857765	−	0.0542322i
$529$	−23.0490	−	39.9220i	−1.00213	−	1.73574i
$530$	2.92536	+	17.8873i	0.127070	+	0.776974i
$531$	9.08715	−	13.1695i	0.394349	−	0.571507i
$532$	2.15842	+	3.24916i	0.0935792	+	0.140869i
$533$	11.6436	+	20.1673i	0.504339	+	0.873541i
$534$	10.8715	+	20.7100i	0.470458	+	0.896209i
$535$	−31.0676	−	11.7468i	−1.34317	−	0.507858i
$536$	−1.74112	−	1.00524i	−0.0752049	−	0.0434196i
$537$	−0.548324	+	13.6334i	−0.0236619	+	0.588324i
$538$	−3.86144	−	6.68821i	−0.166478	−	0.288349i
$539$	8.68736	+	3.65323i	0.374191	+	0.157356i
$540$	−9.81252	+	6.22210i	−0.422263	+	0.267757i
$541$	14.1025			0.606315			0.303157	−	0.952941i	$-0.401959\pi$
$541$	14.1025			0.606315			0.303157	+	0.952941i	$0.401959\pi$
$542$	−6.60493	+	3.81336i	−0.283706	+	0.163798i
$543$	−0.524949	+	13.0522i	−0.0225277	+	0.560124i
$544$	−0.213493	−	0.123260i	−0.00915342	−	0.00528473i
$545$	2.28467	+	0.863844i	0.0978645	+	0.0370030i
$546$	9.89276	+	5.41771i	0.423371	+	0.231857i
$547$	−16.1937	+	9.34946i	−0.692395	+	0.399754i	−0.804508	−	0.593941i	$-0.797571\pi$
$547$	−16.1937	+	9.34946i	−0.692395	+	0.399754i	0.112114	+	0.993695i	$0.464238\pi$
$548$	−12.5166			−0.534681
$549$	−20.2434	+	9.60956i	−0.863969	+	0.410126i
$550$	−2.14447	−	6.38088i	−0.0914406	−	0.272082i
$551$	−3.88481	−	6.72869i	−0.165499	−	0.286652i
$552$	7.69411	−	12.1694i	0.327483	−	0.517964i
$553$	−0.0896538	−	1.42656i	−0.00381247	−	0.0606637i
$554$	−12.0531	−	6.95886i	−0.512087	−	0.295653i
$555$	2.83351	−	6.67049i	0.120276	−	0.283147i
$556$	−4.02870	+	2.32597i	−0.170855	+	0.0986432i
$557$	6.26944			0.265645			0.132822	−	0.991140i	$-0.457596\pi$
$557$	6.26944			0.265645			0.132822	+	0.991140i	$0.457596\pi$
$558$	2.26965	−	28.1703i	0.0960817	−	1.19254i
$559$		−	20.6812i		−	0.874722i
$560$	−1.74112	+	5.65407i	−0.0735758	+	0.238928i
$561$	0.267190	+	0.508991i	0.0112808	+	0.0214896i
$562$	26.1618	+	15.1045i	1.10357	+	0.637146i
$563$	−24.8154	−	14.3272i	−1.04584	−	0.603818i	−0.124361	−	0.992237i	$-0.539688\pi$
$563$	−24.8154	−	14.3272i	−1.04584	−	0.603818i	−0.921483	+	0.388419i	$0.873021\pi$
$564$	0.665106	−	16.5370i	0.0280060	−	0.696334i
$565$	13.8785	−	11.3547i	0.583874	−	0.477694i
$566$	7.60302			0.319579
$567$	−19.3574	−	13.8670i	−0.812933	−	0.582357i
$568$		−	15.3040i		−	0.642142i
$569$	21.8423	−	12.6106i	0.915676	−	0.528666i	0.0334229	−	0.999441i	$-0.489359\pi$
$569$	21.8423	−	12.6106i	0.915676	−	0.528666i	0.882253	+	0.470776i	$0.156026\pi$
$570$	5.66772	−	0.694405i	0.237395	−	0.0290854i
$571$	18.7083	−	32.4037i	0.782917	−	1.35605i	−0.147319	−	0.989089i	$-0.547064\pi$
$571$	18.7083	−	32.4037i	0.782917	−	1.35605i	0.930236	−	0.366963i	$-0.119602\pi$
$572$	2.86975	+	1.65685i	0.119990	+	0.0692764i
$573$	5.48755	−	2.88064i	0.229246	−	0.120341i
$574$	−22.4209	−	11.1318i	−0.935831	−	0.464631i
$575$	39.3972	−	13.2405i	1.64298	−	0.552167i
$576$	2.99031	+	0.240925i	0.124596	+	0.0100386i
$577$	−3.79307			−0.157908			−0.0789538	−	0.996878i	$-0.525158\pi$
$577$	−3.79307			−0.157908			−0.0789538	+	0.996878i	$0.525158\pi$
$578$	−8.46961	−	14.6698i	−0.352289	−	0.610183i
$579$	12.2072	+	7.71800i	0.507314	+	0.320749i
$580$	4.16757	−	11.0223i	0.173049	−	0.457675i
$581$	3.18742	−	0.200317i	0.132237	−	0.00831053i
$582$	−9.49307	+	15.0147i	−0.393500	+	0.622380i
$583$	−9.45083	+	5.45644i	−0.391414	+	0.225983i
$584$	−5.92861			−0.245327
$585$	13.5773	−	9.39504i	0.561354	−	0.388437i
$586$		−	31.0592i		−	1.28304i
$587$	−32.9062	+	18.9984i	−1.35818	+	0.784147i	−0.989379	−	0.145360i	$-0.953566\pi$
$587$	−32.9062	+	18.9984i	−1.35818	+	0.784147i	−0.368804	+	0.929507i	$0.620233\pi$
$588$	−12.0802	+	1.03331i	−0.498181	+	0.0426129i
$589$	−6.94454	+	12.0283i	−0.286145	+	0.495617i
$590$	−11.1552	−	4.21783i	−0.459252	−	0.173645i
$591$	−0.870826	−	0.0350239i	−0.0358210	−	0.00144069i
$592$	−1.62056	+	0.935631i	−0.0666046	+	0.0384542i
$593$			12.0771i			0.495949i	0.968767	+	0.247974i	$0.0797648\pi$
$593$			12.0771i			0.495949i	−0.968767	+	0.247974i	$0.920235\pi$
$594$	−5.59365	−	4.20127i	−0.229510	−	0.172380i
$595$	1.06864	−	0.992491i	0.0438098	−	0.0406882i
$596$	3.13672	−	1.81099i	0.128485	−	0.0741810i
$597$	0.383194	−	9.52763i	0.0156831	−	0.389940i
$598$	−10.2298	+	17.7186i	−0.418328	+	0.724565i
$599$	−5.14603	−	2.97106i	−0.210261	−	0.121394i	0.391172	−	0.920318i	$-0.372070\pi$
$599$	−5.14603	−	2.97106i	−0.210261	−	0.121394i	−0.601433	+	0.798923i	$0.705403\pi$
$600$	6.25828	+	5.98615i	0.255493	+	0.244383i
$601$	21.7479	−	12.5562i	0.887115	−	0.512176i	0.0141176	−	0.999900i	$-0.495506\pi$
$601$	21.7479	−	12.5562i	0.887115	−	0.512176i	0.872998	+	0.487724i	$0.162173\pi$
$602$	12.3012	+	18.5176i	0.501360	+	0.754719i
$603$	−4.96430	−	3.42545i	−0.202162	−	0.139495i
$604$	11.1814			0.454966
$605$	−15.9002	+	13.0087i	−0.646436	+	0.528879i
$606$	−1.30033	+	2.05668i	−0.0528225	+	0.0835467i
$607$	11.7612	−	20.3710i	0.477372	−	0.826833i	−0.522292	−	0.852767i	$-0.674923\pi$
$607$	11.7612	−	20.3710i	0.477372	−	0.826833i	0.999664	+	0.0259343i	$0.00825608\pi$
$608$	−1.27682	−	0.737171i	−0.0517818	−	0.0298962i
$609$	24.1435	−	0.544912i	0.978346	−	0.0220810i
$610$	10.5762	+	12.9271i	0.428220	+	0.523403i
$611$			23.5187i			0.951464i
$612$	−0.608712	−	0.420021i	−0.0246057	−	0.0169784i
$613$			24.0649i			0.971974i	0.873966	+	0.485987i	$0.161540\pi$
$613$			24.0649i			0.971974i	−0.873966	+	0.485987i	$0.838460\pi$
$614$	−12.6258	−	21.8685i	−0.509536	−	0.882543i
$615$	−29.2705	+	22.0449i	−1.18030	+	0.888938i
$616$	−3.55501	+	0.223418i	−0.143236	+	0.00900178i
$617$	−15.9989	+	27.7108i	−0.644090	+	1.11560i	0.340421	+	0.940273i	$0.389430\pi$
$617$	−15.9989	+	27.7108i	−0.644090	+	1.11560i	−0.984511	+	0.175323i	$0.943903\pi$
$618$	16.8557	+	0.677922i	0.678035	+	0.0272700i
$619$	−25.1177	+	14.5017i	−1.00956	+	0.582872i	−0.911064	−	0.412265i	$-0.864738\pi$
$619$	−25.1177	+	14.5017i	−1.00956	+	0.582872i	−0.0985003	+	0.995137i	$0.531405\pi$
$620$	−20.7888	+	3.39988i	−0.834897	+	0.136543i
$621$	25.9397	−	34.5366i	1.04092	−	1.38591i
$622$	−28.1040			−1.12687
$623$	32.0017	+	15.8885i	1.28212	+	0.636560i
$624$	−4.25966	−	0.171320i	−0.170523	−	0.00685829i
$625$	3.11285	+	24.8054i	0.124514	+	0.992218i
$626$	11.1704	−	19.3477i	0.446460	−	0.773291i
$627$	1.59796	+	3.04408i	0.0638166	+	0.121569i
$628$	−2.79836	−	4.84689i	−0.111667	−	0.193412i
$629$	0.461303			0.0183934
$630$	−6.56870	+	16.4879i	−0.261703	+	0.656895i
$631$	29.7780			1.18544			0.592722	−	0.805407i	$-0.298053\pi$
$631$	29.7780			1.18544			0.592722	+	0.805407i	$0.298053\pi$
$632$	0.270127	+	0.467874i	0.0107451	+	0.0186110i
$633$	20.2280	−	31.9937i	0.803993	−	1.27164i
$634$	−8.46214	+	14.6569i	−0.336075	+	0.582098i
$635$	4.86351	−	12.8629i	0.193003	−	0.510448i
$636$	7.50270	−	11.8666i	0.297501	−	0.470543i
$637$	17.0936	−	2.15704i	0.677272	−	0.0854651i
$638$	7.09497			0.280892
$639$	3.68713	−	45.7637i	0.145860	−	1.81039i
$640$	−0.360902	−	2.20675i	−0.0142659	−	0.0872295i
$641$	25.6437	−	14.8054i	1.01286	−	0.584777i	0.100835	−	0.994903i	$-0.467849\pi$
$641$	25.6437	−	14.8054i	1.01286	−	0.584777i	0.912029	+	0.410126i	$0.134515\pi$
$642$	11.9580	+	22.7797i	0.471946	+	0.899044i
$643$	−6.37830	+	11.0475i	−0.251536	+	0.435673i	−0.963949	−	0.266088i	$-0.914269\pi$
$643$	−6.37830	+	11.0475i	−0.251536	+	0.435673i	0.712413	+	0.701760i	$0.247602\pi$
$644$	−1.37944	−	21.9495i	−0.0543575	−	0.864933i
$645$	32.3014	−	3.95754i	1.27187	−	0.155828i
$646$	0.181727	+	0.314761i	0.00714997	+	0.0123841i
$647$		−	17.0272i		−	0.669408i	−0.942323	−	0.334704i	$-0.891364\pi$
$647$		−	17.0272i		−	0.669408i	0.942323	−	0.334704i	$-0.108636\pi$
$648$	8.88391	+	1.44088i	0.348993	+	0.0566033i
$649$		−	7.18053i		−	0.281861i
$650$	−9.22789	−	8.14226i	−0.361948	−	0.319366i
$651$	−22.4232	−	36.8900i	−0.878836	−	1.44583i
$652$	−18.4752	−	10.6667i	−0.723546	−	0.417740i
$653$	4.92585	−	8.53182i	0.192763	−	0.333876i	−0.753402	−	0.657561i	$-0.771588\pi$
$653$	4.92585	−	8.53182i	0.192763	−	0.333876i	0.946165	+	0.323685i	$0.104922\pi$
$654$	−0.879377	−	1.67519i	−0.0343864	−	0.0655051i
$655$	−33.0960	+	27.0773i	−1.29317	+	1.05800i
$656$	9.46130			0.369402
$657$	−17.7284	−	1.42835i	−0.691650	−	0.0557253i
$658$	−13.9889	−	21.0582i	−0.545345	−	0.820933i
$659$	−3.23356	+	1.86690i	−0.125962	+	0.0727241i	−0.561657	−	0.827370i	$-0.689836\pi$
$659$	−3.23356	+	1.86690i	−0.125962	+	0.0727241i	0.435695	+	0.900094i	$0.356503\pi$
$660$	−2.03863	+	4.79923i	−0.0793537	+	0.186810i
$661$	13.3928	+	7.73237i	0.520921	+	0.300754i	0.737312	−	0.675553i	$-0.236095\pi$
$661$	13.3928	+	7.73237i	0.520921	+	0.300754i	−0.216390	+	0.976307i	$0.569428\pi$
$662$	−4.73518	+	8.20158i	−0.184038	+	0.318763i
$663$	0.888288	+	0.561621i	0.0344983	+	0.0218115i
$664$	−1.04539	+	0.603555i	−0.0405689	+	0.0234225i
$665$	6.39111	−	5.93571i	0.247837	−	0.230177i
$666$	−5.07139	+	2.40739i	−0.196513	+	0.0932846i
$667$			43.8061i			1.69618i
$668$	−2.90007	+	1.67436i	−0.112207	+	0.0647829i
$669$	6.20428	+	11.8190i	0.239871	+	0.456948i
$670$	−1.58993	+	4.20501i	−0.0614245	+	0.162454i
$671$	−5.02817	+	8.70904i	−0.194110	+	0.336209i
$672$	3.91592	−	2.38025i	0.151060	−	0.0918202i
$673$	43.3347	−	25.0193i	1.67043	−	0.964423i	0.703034	−	0.711156i	$-0.251828\pi$
$673$	43.3347	−	25.0193i	1.67043	−	0.964423i	0.967396	−	0.253267i	$-0.0815052\pi$
$674$			30.2979i			1.16703i
$675$	17.2720	+	19.4082i	0.664799	+	0.747022i
$676$	−6.94199			−0.266999
$677$	7.34767	−	4.24218i	0.282394	−	0.163040i	−0.352113	−	0.935958i	$-0.614537\pi$
$677$	7.34767	−	4.24218i	0.282394	−	0.163040i	0.634507	+	0.772917i	$0.281203\pi$
$678$	−13.8785	−	0.558184i	−0.533002	−	0.0214369i
$679$	1.70197	+	27.0816i	0.0653155	+	1.03929i
$680$	−0.194954	+	0.515610i	−0.00747615	+	0.0197727i
$681$	−30.9592	+	16.2518i	−1.18636	+	0.622769i
$682$	−6.34152	−	10.9838i	−0.242829	−	0.420593i
$683$	−14.5396			−0.556344			−0.278172	−	0.960531i	$-0.589729\pi$
$683$	−14.5396			−0.556344			−0.278172	+	0.960531i	$0.589729\pi$
$684$	−3.64048	−	2.51199i	−0.139197	−	0.0960483i
$685$	4.51725	+	27.6209i	0.172595	+	1.05534i
$686$	−14.0222	+	12.0986i	−0.535371	+	0.461928i
$687$	−10.4142	−	6.58441i	−0.397328	−	0.251211i
$688$	−7.27682	−	4.20127i	−0.277426	−	0.160172i
$689$	−9.97531	+	17.2777i	−0.380029	+	0.658230i
$690$	−29.6317	−	12.5870i	−1.12806	−	0.479180i
$691$	40.3430	−	23.2920i	1.53472	−	0.886071i	0.535585	−	0.844482i	$-0.320091\pi$
$691$	40.3430	−	23.2920i	1.53472	−	0.886071i	0.999135	−	0.0415892i	$-0.0132421\pi$
$692$			7.22900i			0.274805i
$693$	−10.6844	−	0.188404i	−0.405868	−	0.00715687i
$694$	−16.5310			−0.627509
$695$	6.58681	+	8.05090i	0.249852	+	0.305388i
$696$	−8.08186	+	4.24251i	−0.306342	+	0.160812i
$697$	−2.01992	−	1.16620i	−0.0765098	−	0.0441730i
$698$	−9.71689	−	5.61005i	−0.367790	−	0.212343i
$699$	−39.6300	−	1.59389i	−1.49895	−	0.0602864i
$700$	13.1055	+	1.80166i	0.495341	+	0.0680962i
$701$		−	0.630803i		−	0.0238251i	−0.999929	−	0.0119125i	$-0.996208\pi$
$701$		−	0.630803i		−	0.0238251i	0.999929	−	0.0119125i	$-0.00379197\pi$
$702$	−12.6964	−	1.53856i	−0.479196	−	0.0580692i
$703$	2.75888			0.104053
$704$	1.16595	−	0.673160i	0.0439433	−	0.0253707i
$705$	−36.7331	+	4.50052i	−1.38345	+	0.169499i
$706$	−11.0368	−	6.37208i	−0.415374	−	0.239817i
$707$	0.233131	+	3.70956i	0.00876778	+	0.139512i
$708$	4.29367	+	8.17933i	0.161366	+	0.307398i
$709$	−24.6555	−	42.7046i	−0.925957	−	1.60380i	−0.790015	−	0.613088i	$-0.789927\pi$
$709$	−24.6555	−	42.7046i	−0.925957	−	1.60380i	−0.135942	−	0.990717i	$-0.543406\pi$
$710$	−33.7721	+	5.52324i	−1.26745	+	0.207284i
$711$	0.695041	+	1.46417i	0.0260661	+	0.0549106i
$712$	−13.5043			−0.506093
$713$	67.8170	−	39.1541i	2.53976	−	1.46633i
$714$	−1.12941	+	0.0254904i	−0.0422671	+	0.000953955i
$715$	2.62056	−	6.93078i	0.0980034	−	0.259197i
$716$	−6.82220	−	3.93880i	−0.254958	−	0.147200i
$717$	−23.5058	−	14.8615i	−0.877839	−	0.555014i
$718$	−11.2623	+	6.50229i	−0.420305	+	0.242663i
$719$	30.6621			1.14350			0.571752	−	0.820427i	$-0.306264\pi$
$719$	30.6621			1.14350			0.571752	+	0.820427i	$0.306264\pi$
$720$	−0.547545	−	6.68582i	−0.0204058	−	0.249166i
$721$	21.4639	−	14.2585i	0.799359	−	0.531014i
$722$	−8.41316	−	14.5720i	−0.313105	−	0.542314i
$723$	10.2022	−	5.35555i	0.379423	−	0.199175i
$724$	−6.53138	−	3.77089i	−0.242737	−	0.140144i
$725$	−25.8275	−	5.21883i	−0.959208	−	0.193823i
$726$	15.9002	+	0.639494i	0.590113	+	0.0237339i
$727$	24.9478	+	43.2108i	0.925262	+	1.60260i	0.791140	+	0.611635i	$0.209488\pi$
$727$	24.9478	+	43.2108i	0.925262	+	1.60260i	0.134122	+	0.990965i	$0.457179\pi$
$728$	−5.42423	+	3.60331i	−0.201035	+	0.133548i
$729$	26.2185	+	6.44905i	0.971056	+	0.238854i
$730$	2.13964	+	13.0830i	0.0791917	+	0.484222i
$731$	1.03570	+	1.79388i	0.0383067	+	0.0663491i
$732$	0.519917	−	12.9271i	0.0192167	−	0.477799i
$733$	−8.12326	+	14.0699i	−0.300039	+	0.519683i	−0.976145	−	0.217122i	$-0.930333\pi$
$733$	−8.12326	+	14.0699i	−0.300039	+	0.519683i	0.676105	+	0.736805i	$0.263666\pi$
$734$	−15.1533	+	26.2462i	−0.559317	+	0.968765i
$735$	6.64003	+	26.2852i	0.244921	+	0.969543i
$736$	4.15626	+	7.19885i	0.153202	+	0.265353i
$737$	−2.70674			−0.0997040
$738$	28.2922	+	2.27947i	1.04145	+	0.0839084i
$739$	2.60884			0.0959678			0.0479839	−	0.998848i	$-0.484720\pi$
$739$	2.60884			0.0959678			0.0479839	+	0.998848i	$0.484720\pi$
$740$	2.64957	+	3.23850i	0.0974000	+	0.119050i
$741$	5.31252	+	3.35884i	0.195160	+	0.123390i
$742$	−1.34512	−	21.4035i	−0.0493810	−	0.785746i
$743$	12.6044	−	21.8315i	0.462411	−	0.800920i	−0.536669	−	0.843793i	$-0.680318\pi$
$743$	12.6044	−	21.8315i	0.462411	−	0.800920i	0.999081	+	0.0428731i	$0.0136511\pi$
$744$	13.7915	+	8.71969i	0.505621	+	0.319680i
$745$	−5.12845	−	6.26838i	−0.187892	−	0.229656i
$746$		−	28.8103i		−	1.05482i
$747$	−3.27144	+	1.55296i	−0.119696	+	0.0568197i
$748$	−0.331895			−0.0121353
$749$	35.1999	+	17.4764i	1.28618	+	0.638573i
$750$	10.9513	−	15.9709i	0.399885	−	0.583174i
$751$	−4.53086	+	7.84768i	−0.165333	+	0.286366i	−0.936774	−	0.349936i	$-0.886203\pi$
$751$	−4.53086	+	7.84768i	−0.165333	+	0.286366i	0.771440	+	0.636302i	$0.219537\pi$
$752$	8.27520	+	4.77769i	0.301765	+	0.174224i
$753$	16.6288	+	0.668797i	0.605987	+	0.0243723i
$754$	11.2331	−	6.48540i	0.409084	−	0.236185i
$755$	−4.03539	−	24.6746i	−0.146863	−	0.898001i
$756$	12.2833	−	6.17425i	0.446738	−	0.224555i
$757$		−	26.8628i		−	0.976346i	−0.872747	−	0.488173i	$-0.837663\pi$
$757$		−	26.8628i		−	0.976346i	0.872747	−	0.488173i	$-0.162337\pi$
$758$	−17.2067	−	29.8028i	−0.624974	−	1.08249i
$759$	0.778976	−	19.3683i	0.0282750	−	0.703023i
$760$	−1.16595	+	3.08366i	−0.0422934	+	0.111856i
$761$	−8.91154	+	15.4352i	−0.323043	+	0.559527i	−0.981114	−	0.193429i	$-0.938039\pi$
$761$	−8.91154	+	15.4352i	−0.323043	+	0.559527i	0.658071	+	0.752956i	$0.271373\pi$
$762$	−9.43145	+	4.95096i	−0.341666	+	0.179354i
$763$	−2.58855	−	1.28519i	−0.0937119	−	0.0465270i
$764$			3.57824i			0.129456i
$765$	−0.707197	+	1.49486i	−0.0255688	+	0.0540469i
$766$			11.3887i			0.411491i
$767$	−6.56362	−	11.3685i	−0.236999	−	0.410494i
$768$	−0.925606	+	1.46399i	−0.0333999	+	0.0528270i
$769$	11.7940	+	6.80929i	0.425304	+	0.245549i	0.697344	−	0.716737i	$-0.254365\pi$
$769$	11.7940	+	6.80929i	0.425304	+	0.245549i	−0.272040	+	0.962286i	$0.587698\pi$
$770$	1.77604	+	7.76440i	0.0640040	+	0.279810i
$771$	8.95485	+	5.66171i	0.322501	+	0.203902i
$772$	−7.22120	+	4.16916i	−0.259897	+	0.150051i
$773$		−	24.9560i		−	0.897603i	−0.893631	−	0.448802i	$-0.851851\pi$
$773$		−	24.9560i		−	0.897603i	0.893631	−	0.448802i	$-0.148149\pi$
$774$	−20.7477	−	14.3163i	−0.745762	−	0.514588i
$775$	15.0054	+	44.6486i	0.539010	+	1.60382i
$776$	−5.12803	−	8.88201i	−0.184086	−	0.318845i
$777$	−4.11894	+	7.52119i	−0.147766	+	0.269821i
$778$	10.6623	+	6.15591i	0.382264	+	0.220700i
$779$	−12.0804	−	6.97460i	−0.432824	−	0.249891i
$780$	1.15926	+	9.46184i	0.0415081	+	0.338788i
$781$	−10.3020	−	17.8437i	−0.368636	−	0.638497i
$782$		−	2.04920i		−	0.0732793i
$783$	−25.1894	+	10.7393i	−0.900196	+	0.383791i
$784$	2.71349	−	6.45267i	0.0969104	−	0.230453i
$785$	−9.68596	+	7.92452i	−0.345707	+	0.282838i
$786$	33.0960	+	1.33109i	1.18049	+	0.0474785i
$787$	1.89429	−	3.28100i	0.0675240	−	0.116955i	−0.830287	−	0.557336i	$-0.811823\pi$
$787$	1.89429	−	3.28100i	0.0675240	−	0.116955i	0.897811	+	0.440381i	$0.145157\pi$
$788$	0.251589	−	0.435765i	0.00896248	−	0.0155235i
$789$	−13.0990	−	24.9532i	−0.466337	−	0.888359i
$790$	0.934992	−	0.764960i	0.0332655	−	0.0272161i
$791$	−17.6729	+	11.7401i	−0.628374	+	0.417429i
$792$	3.64873	−	1.73205i	0.129652	−	0.0615457i
$793$			18.3847i			0.652860i
$794$	16.5856	+	28.7270i	0.588599	+	1.01948i
$795$	−28.8945	−	12.2739i	−1.02478	−	0.435310i
$796$	4.76767	+	2.75261i	0.168985	+	0.0975638i
$797$	3.98925	+	2.30320i	0.141307	+	0.0815834i	0.568987	−	0.822347i	$-0.307336\pi$
$797$	3.98925	+	2.30320i	0.141307	+	0.0815834i	−0.427680	+	0.903930i	$0.640669\pi$
$798$	−6.75456	+	0.152448i	−0.239109	+	0.00539662i
$799$	−1.17780	−	2.04000i	−0.0416674	−	0.0721700i
$800$	−4.73950	+	1.59284i	−0.167567	+	0.0563154i
$801$	−40.3819	−	3.25352i	−1.42682	−	0.114957i
$802$		−	13.2780i		−	0.468862i
$803$	−6.91244	+	3.99090i	−0.243935	+	0.140836i
$804$	3.08324	−	1.61852i	0.108738	−	0.0570809i
$805$	−47.9393	+	10.9657i	−1.68964	+	0.386490i
$806$	−20.0803	−	11.5934i	−0.707300	−	0.408360i
$807$	13.3656	+	0.537554i	0.470492	+	0.0189228i
$808$	−0.702424	−	1.21663i	−0.0247112	−	0.0428010i
$809$		−	10.5959i		−	0.372533i	−0.982499	−	0.186266i	$-0.940361\pi$
$809$		−	10.5959i		−	0.372533i	0.982499	−	0.186266i	$-0.0596387\pi$
$810$	−0.0265453	−	20.1246i	−0.000932707	−	0.707106i
$811$			39.4452i			1.38511i	0.721366	+	0.692554i	$0.243515\pi$
$811$			39.4452i			1.38511i	−0.721366	+	0.692554i	$0.756485\pi$
$812$	−6.20033	+	12.4883i	−0.217589	+	0.438255i
$813$	0.530861	−	13.1992i	0.0186181	−	0.462916i
$814$	−1.25966	+	2.18179i	−0.0441510	+	0.0764718i
$815$	−16.8710	+	44.6199i	−0.590965	+	1.56297i
$816$	0.378061	−	0.198460i	0.0132348	−	0.00694748i
$817$	6.19411	+	10.7285i	0.216705	+	0.375343i
$818$			14.7871i			0.517020i
$819$	−17.0883	+	9.46819i	−0.597112	+	0.330845i
$820$	−3.41460	−	20.8787i	−0.119243	−	0.729117i
$821$	−7.29853	+	4.21381i	−0.254721	+	0.147063i	−0.621924	−	0.783078i	$-0.713649\pi$
$821$	−7.29853	+	4.21381i	−0.254721	+	0.147063i	0.367203	+	0.930141i	$0.380315\pi$
$822$	11.5854	−	18.3241i	0.404087	−	0.639125i
$823$	−13.8355	−	7.98791i	−0.482274	−	0.278441i	0.239090	−	0.970998i	$-0.423151\pi$
$823$	−13.8355	−	7.98791i	−0.482274	−	0.278441i	−0.721364	+	0.692556i	$0.756484\pi$
$824$	−4.86975	+	8.43465i	−0.169646	+	0.293835i
$825$	11.3265	+	2.76671i	0.394337	+	0.0963244i
$826$	12.6389	+	6.27511i	0.439765	+	0.218339i
$827$	13.4764			0.468619			0.234310	−	0.972162i	$-0.424717\pi$
$827$	13.4764			0.468619			0.234310	+	0.972162i	$0.424717\pi$
$828$	10.6941	+	22.5281i	0.371646	+	0.782907i
$829$		−	0.478552i		−	0.0166208i	−0.999965	−	0.00831040i	$-0.997355\pi$
$829$		−	0.478552i		−	0.0166208i	0.999965	−	0.00831040i	$-0.00264531\pi$
$830$	1.70918	+	2.08909i	0.0593264	+	0.0725132i
$831$	21.3441	−	11.2044i	0.740418	−	0.388676i
$832$	1.23065	−	2.13155i	0.0426652	−	0.0738982i
$833$	−1.37467	+	1.04313i	−0.0476294	+	0.0361424i
$834$	0.323801	−	8.05090i	0.0112123	−	0.278780i
$835$	4.74153	+	5.79546i	0.164088	+	0.200560i
$836$	−1.98494			−0.0686505
$837$	39.1401	+	29.3973i	1.35288	+	1.01612i
$838$	−1.17417			−0.0405609
$839$	−19.6086	−	33.9630i	−0.676963	−	1.17253i	−0.975891	−	0.218258i	$-0.929962\pi$
$839$	−19.6086	−	33.9630i	−0.676963	−	1.17253i	0.298928	−	0.954276i	$-0.403371\pi$
$840$	−6.66588	−	7.78241i	−0.229995	−	0.268519i
$841$	−0.614104	+	1.06366i	−0.0211760	+	0.0366779i
$842$	−9.97171	+	17.2715i	−0.343648	+	0.595215i
$843$	−46.3283	+	24.3197i	−1.59563	+	0.837614i
$844$	10.9269	+	18.9260i	0.376120	+	0.651459i
$845$	2.50537	+	15.3192i	0.0861875	+	0.526998i
$846$	23.5943	+	16.2805i	0.811190	+	0.559734i
$847$	20.2473	−	13.4503i	0.695704	−	0.462156i
$848$	4.05286	+	7.01975i	0.139176	+	0.241059i
$849$	−7.03740	+	11.1307i	−0.241523	+	0.382005i
$850$	1.20818	+	0.244131i	0.0414403	+	0.00837363i
$851$	−13.4709	−	7.77745i	−0.461778	−	0.266607i
$852$	22.4048	+	14.1655i	0.767577	+	0.485301i
$853$	−18.8538	−	32.6557i	−0.645541	−	1.11811i	−0.984176	−	0.177192i	$-0.943299\pi$
$853$	−18.8538	−	32.6557i	−0.645541	−	1.11811i	0.338636	−	0.940918i	$-0.390035\pi$
$854$	−10.9352	−	16.4613i	−0.374196	−	0.563294i
$855$	−4.22948	+	8.94021i	−0.144645	+	0.305749i
$856$	−14.8538			−0.507694
$857$	40.6733	−	23.4827i	1.38937	−	0.802155i	0.396129	−	0.918195i	$-0.370353\pi$
$857$	40.6733	−	23.4827i	1.38937	−	0.802155i	0.993245	+	0.116040i	$0.0370201\pi$
$858$	−5.08186	+	2.66768i	−0.173492	+	0.0910731i
$859$	28.5039	+	16.4568i	0.972542	+	0.561498i	0.900010	−	0.435869i	$-0.143559\pi$
$859$	28.5039	+	16.4568i	0.972542	+	0.561498i	0.0725319	+	0.997366i	$0.476892\pi$
$860$	−6.64495	+	17.5744i	−0.226591	+	0.599281i
$861$	37.0497	−	22.5203i	1.26265	−	0.767489i
$862$	19.0633	−	11.0062i	0.649299	−	0.374873i
$863$	−16.5085			−0.561957			−0.280978	−	0.959714i	$-0.590659\pi$
$863$	−16.5085			−0.561957			−0.280978	+	0.959714i	$0.590659\pi$
$864$	−3.12056	+	4.15477i	−0.106164	+	0.141348i
$865$	15.9526	−	2.60896i	0.542405	−	0.0887073i
$866$	−0.944923	−	1.63665i	−0.0321098	−	0.0556158i
$867$	29.3159	+	1.17906i	0.995620	+	0.0400431i
$868$	24.8753	−	1.56331i	0.844323	−	0.0530622i
$869$	0.629908	+	0.363678i	0.0213682	+	0.0123369i
$870$	12.2789	+	16.3035i	0.416294	+	0.552742i
$871$	−4.28543	+	2.47419i	−0.145206	+	0.0838348i
$872$	1.09233			0.0369910
$873$	−13.1945	−	27.7954i	−0.446566	−	0.940733i
$874$		−	12.2555i		−	0.414548i
$875$	−0.753988	−	29.5708i	−0.0254894	−	0.999675i
$876$	5.48755	−	8.67939i	0.185407	−	0.293249i
$877$	−21.8550	−	12.6180i	−0.737991	−	0.426079i	0.0833476	−	0.996521i	$-0.473439\pi$
$877$	−21.8550	−	12.6180i	−0.737991	−	0.426079i	−0.821338	+	0.570441i	$0.806772\pi$
$878$	24.1785	+	13.9595i	0.815985	+	0.471109i
$879$	45.4702	+	28.7486i	1.53367	+	0.969666i
$880$	−1.90629	−	2.33001i	−0.0642610	−	0.0785447i
$881$	19.1314			0.644553			0.322277	−	0.946646i	$-0.395552\pi$
$881$	19.1314			0.644553			0.322277	+	0.946646i	$0.395552\pi$
$882$	9.66880	−	18.6417i	0.325565	−	0.627700i
$883$		−	6.39685i		−	0.215271i	−0.994190	−	0.107636i	$-0.965672\pi$
$883$		−	6.39685i		−	0.215271i	0.994190	−	0.107636i	$-0.0343280\pi$
$884$	−0.525470	+	0.303380i	−0.0176735	+	0.0102038i
$885$	16.5002	−	12.4270i	0.554647	−	0.417729i
$886$	−16.8221	+	29.1368i	−0.565151	+	0.978870i
$887$	22.3665	+	12.9133i	0.750993	+	0.433586i	0.826053	−	0.563593i	$-0.190581\pi$
$887$	22.3665	+	12.9133i	0.750993	+	0.433586i	−0.0750597	+	0.997179i	$0.523915\pi$
$888$	0.130250	−	3.23850i	0.00437090	−	0.108677i
$889$	−7.23572	+	14.5738i	−0.242678	+	0.488788i
$890$	4.87371	+	29.8005i	0.163367	+	0.998916i
$891$	11.3281	−	4.30030i	0.379506	−	0.144065i
$892$	−7.70674			−0.258041
$893$	−7.04395	−	12.2005i	−0.235717	−	0.408273i
$894$	−0.252109	+	6.26838i	−0.00843179	+	0.209646i
$895$	−6.22981	+	16.4764i	−0.208240	+	0.550746i
$896$	0.165947	+	2.64054i	0.00554391	+	0.0882143i
$897$	−16.4709	−	31.3767i	−0.549948	−	1.04764i
$898$	12.4670	−	7.19782i	0.416029	−	0.240195i
$899$	−49.6452			−1.65576
$900$	−14.5563	+	3.62122i	−0.485211	+	0.120707i
$901$		−	1.99822i		−	0.0665704i
$902$	11.0314	−	6.36897i	0.367305	−	0.212064i
$903$	−38.4955	+	0.868832i	−1.28105	+	0.0289129i
$904$	4.00963	−	6.94488i	0.133358	−	0.230983i
$905$	−5.96424	+	15.7741i	−0.198258	+	0.524347i
$906$	−10.3496	+	16.3694i	−0.343842	+	0.543838i
$907$	18.8255	−	10.8689i	0.625089	−	0.360895i	−0.153759	−	0.988108i	$-0.549138\pi$
$907$	18.8255	−	10.8689i	0.625089	−	0.360895i	0.778848	+	0.627213i	$0.215804\pi$
$908$		−	20.1874i		−	0.669942i
$909$	−1.80735	−	3.80734i	−0.0599459	−	0.126282i
$910$	9.90923	+	10.6695i	0.328488	+	0.353690i
$911$	5.89807	−	3.40525i	0.195412	−	0.112821i	−0.399102	−	0.916907i	$-0.630678\pi$
$911$	5.89807	−	3.40525i	0.195412	−	0.112821i	0.594514	+	0.804086i	$0.297345\pi$
$912$	2.26104	−	1.18691i	0.0748704	−	0.0393026i
$913$	−0.812578	+	1.40743i	−0.0268924	+	0.0465790i
$914$	22.2454	+	12.8434i	0.735813	+	0.424822i
$915$	−28.7145	+	3.51808i	−0.949273	+	0.116304i
$916$	6.16057	−	3.55681i	0.203551	−	0.117520i
$917$	42.1442	−	27.9964i	1.39172	−	0.924522i
$918$	1.17833	−	0.502372i	0.0388908	−	0.0165807i
$919$	−51.1270			−1.68652			−0.843262	−	0.537503i	$-0.819368\pi$
$919$	−51.1270			−1.68652			−0.843262	+	0.537503i	$0.819368\pi$
$920$	14.3861	−	11.7699i	0.474295	−	0.388042i
$921$	43.7018	+	1.75765i	1.44002	+	0.0579165i
$922$	−12.2680	+	21.2487i	−0.404024	+	0.699790i
$923$	−32.6213	−	18.8339i	−1.07374	−	0.619925i
$924$	2.96346	−	5.41129i	0.0974907	−	0.178018i
$925$	6.19033	−	7.01572i	0.203537	−	0.230675i
$926$		−	22.5326i		−	0.740467i
$927$	−16.5942	+	24.0490i	−0.545025	+	0.789872i
$928$		−	5.26989i		−	0.172993i
$929$	10.0757	+	17.4516i	0.330573	+	0.572570i	0.982624	−	0.185605i	$-0.0594246\pi$
$929$	10.0757	+	17.4516i	0.330573	+	0.572570i	−0.652051	+	0.758175i	$0.726091\pi$
$930$	14.2648	−	33.5814i	0.467762	−	1.10118i
$931$	−8.22136	+	6.23858i	−0.269444	+	0.204461i
$932$	11.4495	−	19.8310i	0.375039	−	0.649587i
$933$	26.0133	−	41.1439i	0.851636	−	1.34699i
$934$	−26.3306	+	15.2020i	−0.861564	+	0.497424i
$935$	0.119781	+	0.732409i	0.00391727	+	0.0239523i
$936$	4.19358	−	6.07750i	0.137071	−	0.198649i
$937$	20.0761			0.655859			0.327930	−	0.944702i	$-0.393649\pi$
$937$	20.0761			0.655859			0.327930	+	0.944702i	$0.393649\pi$
$938$	2.36543	−	4.76432i	0.0772342	−	0.155560i
$939$	17.9854	+	34.2617i	0.586931	+	1.11809i
$940$	7.55663	−	19.9856i	0.246470	−	0.651858i
$941$	11.0888	−	19.2063i	0.361484	−	0.626108i	−0.626722	−	0.779243i	$-0.715604\pi$
$941$	11.0888	−	19.2063i	0.361484	−	0.626108i	0.988205	+	0.153135i	$0.0489370\pi$
$942$	9.68596	+	0.389561i	0.315586	+	0.0126926i
$943$	39.3236	+	68.1105i	1.28055	+	2.21798i
$944$	−5.33345			−0.173589
$945$	−18.0581	−	24.8778i	−0.587429	−	0.809275i
$946$	−11.3125			−0.367802
$947$	−20.7581	−	35.9541i	−0.674549	−	1.16835i	−0.976601	−	0.215061i	$-0.931005\pi$
$947$	−20.7581	−	35.9541i	−0.674549	−	1.16835i	0.302052	−	0.953291i	$-0.402328\pi$
$948$	−0.934992	−	0.0376046i	−0.0303671	−	0.00122134i
$949$	−7.29605	+	12.6371i	−0.236840	+	0.410218i
$950$	7.22567	+	1.46006i	0.234432	+	0.0473705i
$951$	−13.6248	−	25.9549i	−0.441815	−	0.841647i
$952$	0.290045	−	0.584191i	0.00940040	−	0.0189337i
$953$	54.9073			1.77862			0.889311	−	0.457303i	$-0.151185\pi$
$953$	54.9073			1.77862			0.889311	+	0.457303i	$0.151185\pi$
$954$	10.4281	+	21.9677i	0.337621	+	0.711230i
$955$	7.89628	−	1.29139i	0.255518	−	0.0417884i
$956$	13.9049	−	8.02800i	0.449717	−	0.259644i
$957$	−6.56714	+	10.3869i	−0.212286	+	0.335762i
$958$	15.6602	−	27.1242i	0.505958	−	0.876345i
$959$	−2.07709	−	33.0505i	−0.0670727	−	1.06726i
$960$	3.56470	+	1.51423i	0.115050	+	0.0488715i
$961$	28.8732	+	50.0098i	0.931392	+	1.61322i
$962$			4.60574i			0.148495i
$963$	−44.4176	−	3.57867i	−1.43134	−	0.115321i
$964$			6.65248i			0.214262i
$965$	11.8064	+	14.4307i	0.380063	+	0.464542i
$966$	33.4106	+	18.2971i	1.07497	+	0.588701i
$967$	−30.0780	−	17.3656i	−0.967244	−	0.558439i	−0.0688491	−	0.997627i	$-0.521933\pi$
$967$	−30.0780	−	17.3656i	−0.967244	−	0.558439i	−0.898395	+	0.439189i	$0.855266\pi$
$968$	−4.59371	+	7.95654i	−0.147647	+	0.255733i
$969$	−0.629013	−	0.0252984i	−0.0202068	−	0.000812702i
$970$	−17.7497	+	14.5218i	−0.569907	+	0.466267i
$971$	−39.1395			−1.25605			−0.628024	−	0.778194i	$-0.716136\pi$
$971$	−39.1395			−1.25605			−0.628024	+	0.778194i	$0.716136\pi$
$972$	−10.3324	+	11.6722i	−0.331413	+	0.374387i
$973$	−6.81038	−	10.2520i	−0.218331	−	0.328663i
$974$	28.6921	−	16.5654i	0.919354	−	0.530790i
$975$	20.4615	−	5.97298i	0.655294	−	0.191289i
$976$	6.46877	+	3.73475i	0.207060	+	0.119546i
$977$	1.99898	−	3.46234i	0.0639530	−	0.110770i	−0.832276	−	0.554361i	$-0.812963\pi$
$977$	1.99898	−	3.46234i	0.0639530	−	0.110770i	0.896229	+	0.443591i	$0.146296\pi$
$978$	32.7167	−	17.1743i	1.04616	−	0.549175i
$979$	−15.7452	+	9.09052i	−0.503220	+	0.290534i
$980$	−15.2187	−	3.65922i	−0.486145	−	0.116890i
$981$	3.26641	+	0.263171i	0.104288	+	0.00840239i
$982$		−	33.2771i		−	1.06191i
$983$	−9.34495	+	5.39531i	−0.298058	+	0.172084i	−0.641570	−	0.767064i	$-0.721717\pi$
$983$	−9.34495	+	5.39531i	−0.298058	+	0.172084i	0.343512	+	0.939148i	$0.388383\pi$
$984$	−8.75744	+	13.8512i	−0.279177	+	0.441560i
$985$	−1.05242	−	0.397926i	−0.0335330	−	0.0126790i
$986$	−0.649567	+	1.12508i	−0.0206864	+	0.0358299i
$987$	43.7771	−	0.988035i	1.39344	−	0.0314495i
$988$	−3.14264	+	1.81440i	−0.0999806	+	0.0577238i
$989$		−	69.8463i		−	2.22098i
$990$	−5.13904	−	7.42673i	−0.163329	−	0.236037i
$991$	−7.10079			−0.225564			−0.112782	−	0.993620i	$-0.535976\pi$
$991$	−7.10079			−0.225564			−0.112782	+	0.993620i	$0.535976\pi$
$992$	−8.15842	+	4.71026i	−0.259030	+	0.149551i
$993$	−7.62408	−	14.5237i	−0.241943	−	0.460895i
$994$	40.4109	−	2.53966i	1.28176	−	0.0805531i
$995$	4.35367	−	11.5145i	0.138021	−	0.365033i
$996$	0.0840213	−	2.08909i	0.00266232	−	0.0661952i
$997$	18.5660	+	32.1573i	0.587992	+	1.01843i	0.994495	+	0.104782i	$0.0334146\pi$
$997$	18.5660	+	32.1573i	0.587992	+	1.01843i	−0.406503	+	0.913649i	$0.633252\pi$
$998$	22.2245			0.703504
$999$	1.16973	−	9.65275i	0.0370085	−	0.305399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bf.b.419.4	yes	8
3.2	odd	2		1890.2.bf.c.1259.2		8
5.4	even	2		630.2.bf.c.419.1	yes	8
7.6	odd	2		630.2.bf.a.419.1	yes	8
9.2	odd	6		630.2.bf.d.209.4	yes	8
9.7	even	3		1890.2.bf.a.629.1		8
15.14	odd	2		1890.2.bf.b.1259.4		8
21.20	even	2		1890.2.bf.d.1259.3		8
35.34	odd	2		630.2.bf.d.419.4	yes	8
45.29	odd	6		630.2.bf.a.209.1	✓	8
45.34	even	6		1890.2.bf.d.629.3		8
63.20	even	6		630.2.bf.c.209.1	yes	8
63.34	odd	6		1890.2.bf.b.629.4		8
105.104	even	2		1890.2.bf.a.1259.1		8
315.34	odd	6		1890.2.bf.c.629.2		8
315.209	even	6	inner	630.2.bf.b.209.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bf.a.209.1	✓	8	45.29	odd	6
630.2.bf.a.419.1	yes	8	7.6	odd	2
630.2.bf.b.209.4	yes	8	315.209	even	6	inner
630.2.bf.b.419.4	yes	8	1.1	even	1	trivial
630.2.bf.c.209.1	yes	8	63.20	even	6
630.2.bf.c.419.1	yes	8	5.4	even	2
630.2.bf.d.209.4	yes	8	9.2	odd	6
630.2.bf.d.419.4	yes	8	35.34	odd	2
1890.2.bf.a.629.1		8	9.7	even	3
1890.2.bf.a.1259.1		8	105.104	even	2
1890.2.bf.b.629.4		8	63.34	odd	6
1890.2.bf.b.1259.4		8	15.14	odd	2
1890.2.bf.c.629.2		8	315.34	odd	6
1890.2.bf.c.1259.2		8	3.2	odd	2
1890.2.bf.d.629.3		8	45.34	even	6
1890.2.bf.d.1259.3		8	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.73065 + 0.0696054i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.09155 + 0.790826i) q^{5} +(-0.805046 - 1.53359i) q^{6} +(-2.36975 - 1.17656i) q^{7} +1.00000 q^{8} +(2.99031 + 0.240925i) q^{9} +(-0.360902 - 2.20675i) q^{10} +(1.16595 - 0.673160i) q^{11} +(-0.925606 + 1.46399i) q^{12} +(1.23065 - 2.13155i) q^{13} +(0.165947 + 2.64054i) q^{14} +(3.56470 + 1.51423i) q^{15} +(-0.500000 - 0.866025i) q^{16} +0.246520i q^{17} +(-1.28651 - 2.71015i) q^{18} +1.47434i q^{19} +(-1.73065 + 1.41593i) q^{20} +(-4.01932 - 2.20116i) q^{21} +(-1.16595 - 0.673160i) q^{22} +(4.15626 - 7.19885i) q^{23} +(1.73065 + 0.0696054i) q^{24} +(3.74919 + 3.30811i) q^{25} -2.46130 q^{26} +(5.15842 + 0.625100i) q^{27} +(2.20380 - 1.46399i) q^{28} +(-4.56386 + 2.63495i) q^{29} +(-0.470993 - 3.84424i) q^{30} +(8.15842 + 4.71026i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.06470 - 1.08385i) q^{33} +(0.213493 - 0.123260i) q^{34} +(-4.02601 - 4.33489i) q^{35} +(-1.70380 + 2.46922i) q^{36} -1.87126i q^{37} +(1.27682 - 0.737171i) q^{38} +(2.27820 - 3.60331i) q^{39} +(2.09155 + 0.790826i) q^{40} +(-4.73065 + 8.19373i) q^{41} +(0.103401 + 4.58141i) q^{42} +(7.27682 - 4.20127i) q^{43} +1.34632i q^{44} +(6.06386 + 2.86872i) q^{45} -8.31252 q^{46} +(-8.27520 + 4.77769i) q^{47} +(-0.805046 - 1.53359i) q^{48} +(4.23143 + 5.57629i) q^{49} +(0.990310 - 4.90095i) q^{50} +(-0.0171591 + 0.426640i) q^{51} +(1.23065 + 2.13155i) q^{52} -8.10571 q^{53} +(-2.03786 - 4.77987i) q^{54} +(2.97099 - 0.485889i) q^{55} +(-2.36975 - 1.17656i) q^{56} +(-0.102622 + 2.55157i) q^{57} +(4.56386 + 2.63495i) q^{58} +(2.66673 - 4.61891i) q^{59} +(-3.09371 + 2.33001i) q^{60} +(-6.46877 + 3.73475i) q^{61} -9.42053i q^{62} +(-6.80283 - 4.08920i) q^{63} +1.00000 q^{64} +(4.25966 - 3.48502i) q^{65} +(-1.97099 - 1.24616i) q^{66} +(-1.74112 - 1.00524i) q^{67} +(-0.213493 - 0.123260i) q^{68} +(7.69411 - 12.1694i) q^{69} +(-1.74112 + 5.65407i) q^{70} -15.3040i q^{71} +(2.99031 + 0.240925i) q^{72} -5.92861 q^{73} +(-1.62056 + 0.935631i) q^{74} +(6.25828 + 5.98615i) q^{75} +(-1.27682 - 0.737171i) q^{76} +(-3.55501 + 0.223418i) q^{77} +(-4.25966 - 0.171320i) q^{78} +(0.270127 + 0.467874i) q^{79} +(-0.360902 - 2.20675i) q^{80} +(8.88391 + 1.44088i) q^{81} +9.46130 q^{82} +(-1.04539 + 0.603555i) q^{83} +(3.91592 - 2.38025i) q^{84} +(-0.194954 + 0.515610i) q^{85} +(-7.27682 - 4.20127i) q^{86} +(-8.08186 + 4.24251i) q^{87} +(1.16595 - 0.673160i) q^{88} -13.5043 q^{89} +(-0.547545 - 6.68582i) q^{90} +(-5.42423 + 3.60331i) q^{91} +(4.15626 + 7.19885i) q^{92} +(13.7915 + 8.71969i) q^{93} +(8.27520 + 4.77769i) q^{94} +(-1.16595 + 3.08366i) q^{95} +(-0.925606 + 1.46399i) q^{96} +(-5.12803 - 8.88201i) q^{97} +(2.71349 - 6.45267i) q^{98} +(3.64873 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 6 q^{5} - 3 q^{6} - 2 q^{7} + 8 q^{8} - 6 q^{10} + 9 q^{11} + 3 q^{12} - 4 q^{13} + q^{14} + 15 q^{15} - 4 q^{16} - 3 q^{18} - 12 q^{21} - 9 q^{22} + 9 q^{23} + 20 q^{25} + 8 q^{26}+ \cdots - 18 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 6 * q^5 - 3 * q^6 - 2 * q^7 + 8 * q^8 - 6 * q^10 + 9 * q^11 + 3 * q^12 - 4 * q^13 + q^14 + 15 * q^15 - 4 * q^16 - 3 * q^18 - 12 * q^21 - 9 * q^22 + 9 * q^23 + 20 * q^25 + 8 * q^26 + 18 * q^27 + q^28 + 21 * q^29 + 42 * q^31 - 4 * q^32 + 3 * q^33 + 9 * q^34 + 9 * q^35 + 3 * q^36 - 21 * q^38 + 12 * q^39 + 6 * q^40 - 24 * q^41 + 15 * q^42 + 27 * q^43 - 9 * q^45 - 18 * q^46 - 15 * q^47 - 3 * q^48 - 4 * q^49 - 16 * q^50 + 21 * q^51 - 4 * q^52 + 12 * q^53 + 20 * q^55 - 2 * q^56 - 39 * q^57 - 21 * q^58 - 3 * q^59 - 15 * q^60 + 21 * q^61 + 18 * q^63 + 8 * q^64 + 24 * q^65 - 12 * q^66 - 9 * q^68 + 21 * q^69 - 82 * q^73 - 6 * q^74 + 15 * q^75 + 21 * q^76 + 9 * q^77 - 24 * q^78 - 8 * q^79 - 6 * q^80 - 12 * q^81 + 48 * q^82 - 15 * q^83 - 3 * q^84 - 5 * q^85 - 27 * q^86 - 30 * q^87 + 9 * q^88 - 42 * q^89 - 12 * q^90 - 8 * q^91 + 9 * q^92 - 6 * q^93 + 15 * q^94 - 9 * q^95 + 3 * q^96 + 11 * q^97 + 29 * q^98 - 18 * q^99

Introduction

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