LMFDB - Embedded newform 671.2.i.b.34.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(34,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("671.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.i (of order $5$, 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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$27$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			34.15
Character	$\chi$	$=$	671.34
Dual form			671.2.i.b.375.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.164681 - 0.119648i) q^{2} +(1.09278 - 0.793948i) q^{3} +(-0.605230 + 1.86271i) q^{4} +(-0.765842 + 2.35702i) q^{5} +(0.0849654 - 0.261497i) q^{6} +(-2.48994 - 1.80905i) q^{7} +(0.249004 + 0.766356i) q^{8} +(-0.363246 + 1.11796i) q^{9} +O(q^{10})$	\(q+(0.164681 - 0.119648i) q^{2} +(1.09278 - 0.793948i) q^{3} +(-0.605230 + 1.86271i) q^{4} +(-0.765842 + 2.35702i) q^{5} +(0.0849654 - 0.261497i) q^{6} +(-2.48994 - 1.80905i) q^{7} +(0.249004 + 0.766356i) q^{8} +(-0.363246 + 1.11796i) q^{9} +(0.155893 + 0.479788i) q^{10} -1.00000 q^{11} +(0.817511 + 2.51604i) q^{12} -5.07770 q^{13} -0.626496 q^{14} +(1.03446 + 3.18373i) q^{15} +(-3.03632 - 2.20602i) q^{16} +(1.77596 - 5.46584i) q^{17} +(0.0739413 + 0.227568i) q^{18} +(0.170076 - 0.123567i) q^{19} +(-3.92692 - 2.85308i) q^{20} -4.15724 q^{21} +(-0.164681 + 0.119648i) q^{22} +(-1.51548 + 4.66416i) q^{23} +(0.880552 + 0.639758i) q^{24} +(-0.923943 - 0.671284i) q^{25} +(-0.836202 + 0.607536i) q^{26} +(1.74286 + 5.36398i) q^{27} +(4.87671 - 3.54314i) q^{28} -8.26657 q^{29} +(0.551282 + 0.400530i) q^{30} +(-3.33270 - 2.42135i) q^{31} -2.37556 q^{32} +(-1.09278 + 0.793948i) q^{33} +(-0.361509 - 1.11261i) q^{34} +(6.17087 - 4.48340i) q^{35} +(-1.86257 - 1.35324i) q^{36} +(2.67841 + 1.94598i) q^{37} +(0.0132237 - 0.0406984i) q^{38} +(-5.54879 + 4.03143i) q^{39} -1.99701 q^{40} +(6.14977 + 4.46807i) q^{41} +(-0.684619 + 0.497405i) q^{42} +(0.799492 + 2.46058i) q^{43} +(0.605230 - 1.86271i) q^{44} +(-2.35685 - 1.71236i) q^{45} +(0.308486 + 0.949422i) q^{46} +2.79643 q^{47} -5.06949 q^{48} +(0.764037 + 2.35146i) q^{49} -0.232474 q^{50} +(-2.39887 - 7.38296i) q^{51} +(3.07318 - 9.45826i) q^{52} +(2.99856 + 9.22861i) q^{53} +(0.928805 + 0.674816i) q^{54} +(0.765842 - 2.35702i) q^{55} +(0.766369 - 2.35864i) q^{56} +(0.0877487 - 0.270063i) q^{57} +(-1.36135 + 0.989077i) q^{58} +(0.146575 - 0.106493i) q^{59} -6.55644 q^{60} +(-3.28145 - 7.08746i) q^{61} -0.838542 q^{62} +(2.92690 - 2.12652i) q^{63} +(5.68144 - 4.12781i) q^{64} +(3.88872 - 11.9682i) q^{65} +(-0.0849654 + 0.261497i) q^{66} +(-4.76398 + 14.6620i) q^{67} +(9.10639 + 6.61618i) q^{68} +(2.04702 + 6.30008i) q^{69} +(0.479797 - 1.47666i) q^{70} +(2.34485 + 7.21672i) q^{71} -0.947201 q^{72} +(1.11008 + 3.41646i) q^{73} +0.673915 q^{74} -1.54263 q^{75} +(0.127235 + 0.391588i) q^{76} +(2.48994 + 1.80905i) q^{77} +(-0.431429 + 1.32780i) q^{78} +(3.47680 + 10.7005i) q^{79} +(7.52498 - 5.46722i) q^{80} +(3.31031 + 2.40508i) q^{81} +1.54735 q^{82} +(-11.7213 + 8.51599i) q^{83} +(2.51609 - 7.74371i) q^{84} +(11.5230 + 8.37195i) q^{85} +(0.426065 + 0.309554i) q^{86} +(-9.03351 + 6.56323i) q^{87} +(-0.249004 - 0.766356i) q^{88} +(9.45984 - 6.87298i) q^{89} -0.593009 q^{90} +(12.6432 + 9.18582i) q^{91} +(-7.77074 - 5.64577i) q^{92} -5.56432 q^{93} +(0.460519 - 0.334587i) q^{94} +(0.160999 + 0.495505i) q^{95} +(-2.59595 + 1.88607i) q^{96} +(-2.15136 - 1.56306i) q^{97} +(0.407170 + 0.295827i) q^{98} +(0.363246 - 1.11796i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 2 q^{3} - 34 q^{4} + 4 q^{5} + 6 q^{6} + 10 q^{7} - 18 q^{8} - 25 q^{9}+O(q^{10}) $ 108 * q - 2 * q^3 - 34 * q^4 + 4 * q^5 + 6 * q^6 + 10 * q^7 - 18 * q^8 - 25 * q^9	\( 108 q - 2 q^{3} - 34 q^{4} + 4 q^{5} + 6 q^{6} + 10 q^{7} - 18 q^{8} - 25 q^{9} + 6 q^{10} - 108 q^{11} - 15 q^{12} - 26 q^{13} + 2 q^{14} + 8 q^{15} - 40 q^{16} + 4 q^{17} + 50 q^{18} + 8 q^{19} + 8 q^{20} - 64 q^{21} - 3 q^{23} + 71 q^{24} - 7 q^{25} + 29 q^{26} - 8 q^{27} + 42 q^{28} - 40 q^{29} - 36 q^{30} - 7 q^{31} - 6 q^{32} + 2 q^{33} - 4 q^{34} + 2 q^{35} + 30 q^{36} - 32 q^{37} - 3 q^{38} + 10 q^{39} - 154 q^{40} + 10 q^{41} - 36 q^{42} - 29 q^{43} + 34 q^{44} - 23 q^{45} + 45 q^{46} + 40 q^{47} + 140 q^{48} - 15 q^{49} + 6 q^{50} - 25 q^{51} - 7 q^{52} + 15 q^{53} - 2 q^{54} - 4 q^{55} + 35 q^{56} + 20 q^{57} + 77 q^{58} + 22 q^{59} + 72 q^{60} + 20 q^{61} + 80 q^{62} - 6 q^{63} - 30 q^{64} + 56 q^{65} - 6 q^{66} - 4 q^{67} - 109 q^{68} - 46 q^{69} + 41 q^{70} + 7 q^{71} - 264 q^{72} - 16 q^{73} - 44 q^{74} - 6 q^{75} + 22 q^{76} - 10 q^{77} - 60 q^{78} + 79 q^{79} + 57 q^{80} - 25 q^{81} - 28 q^{82} + 2 q^{83} + 87 q^{84} + 30 q^{85} - 10 q^{86} - 38 q^{87} + 18 q^{88} + 18 q^{89} + 62 q^{90} - 30 q^{91} - 6 q^{92} - 24 q^{93} - 16 q^{94} - 10 q^{95} + 65 q^{96} + 16 q^{97} + 9 q^{98} + 25 q^{99}+O(q^{100}) \) 108 * q - 2 * q^3 - 34 * q^4 + 4 * q^5 + 6 * q^6 + 10 * q^7 - 18 * q^8 - 25 * q^9 + 6 * q^10 - 108 * q^11 - 15 * q^12 - 26 * q^13 + 2 * q^14 + 8 * q^15 - 40 * q^16 + 4 * q^17 + 50 * q^18 + 8 * q^19 + 8 * q^20 - 64 * q^21 - 3 * q^23 + 71 * q^24 - 7 * q^25 + 29 * q^26 - 8 * q^27 + 42 * q^28 - 40 * q^29 - 36 * q^30 - 7 * q^31 - 6 * q^32 + 2 * q^33 - 4 * q^34 + 2 * q^35 + 30 * q^36 - 32 * q^37 - 3 * q^38 + 10 * q^39 - 154 * q^40 + 10 * q^41 - 36 * q^42 - 29 * q^43 + 34 * q^44 - 23 * q^45 + 45 * q^46 + 40 * q^47 + 140 * q^48 - 15 * q^49 + 6 * q^50 - 25 * q^51 - 7 * q^52 + 15 * q^53 - 2 * q^54 - 4 * q^55 + 35 * q^56 + 20 * q^57 + 77 * q^58 + 22 * q^59 + 72 * q^60 + 20 * q^61 + 80 * q^62 - 6 * q^63 - 30 * q^64 + 56 * q^65 - 6 * q^66 - 4 * q^67 - 109 * q^68 - 46 * q^69 + 41 * q^70 + 7 * q^71 - 264 * q^72 - 16 * q^73 - 44 * q^74 - 6 * q^75 + 22 * q^76 - 10 * q^77 - 60 * q^78 + 79 * q^79 + 57 * q^80 - 25 * q^81 - 28 * q^82 + 2 * q^83 + 87 * q^84 + 30 * q^85 - 10 * q^86 - 38 * q^87 + 18 * q^88 + 18 * q^89 + 62 * q^90 - 30 * q^91 - 6 * q^92 - 24 * q^93 - 16 * q^94 - 10 * q^95 + 65 * q^96 + 16 * q^97 + 9 * q^98 + 25 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/671\mathbb{Z}\right)^\times$.

$n$	$123$	$551$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.164681	−	0.119648i	0.116447	−	0.0846038i	−0.528037	−	0.849221i	$-0.677072\pi$
$2$	0.164681	−	0.119648i	0.116447	−	0.0846038i	0.644485	+	0.764617i	$0.277072\pi$
$3$	1.09278	−	0.793948i	0.630914	−	0.458386i	−0.225803	−	0.974173i	$-0.572500\pi$
$3$	1.09278	−	0.793948i	0.630914	−	0.458386i	0.856717	+	0.515787i	$0.172500\pi$
$4$	−0.605230	+	1.86271i	−0.302615	+	0.931353i
$5$	−0.765842	+	2.35702i	−0.342495	+	1.05409i	0.620416	+	0.784273i	$0.286964\pi$
$5$	−0.765842	+	2.35702i	−0.342495	+	1.05409i	−0.962911	+	0.269819i	$0.913036\pi$
$6$	0.0849654	−	0.261497i	0.0346870	−	0.106756i
$7$	−2.48994	−	1.80905i	−0.941110	−	0.683756i	0.00757760	−	0.999971i	$-0.497588\pi$
$7$	−2.48994	−	1.80905i	−0.941110	−	0.683756i	−0.948688	+	0.316215i	$0.897588\pi$
$8$	0.249004	+	0.766356i	0.0880362	+	0.270948i
$9$	−0.363246	+	1.11796i	−0.121082	+	0.372652i
$10$	0.155893	+	0.479788i	0.0492976	+	0.151722i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	0.817511	+	2.51604i	0.235995	+	0.726318i
$13$	−5.07770			−1.40830			−0.704151	−	0.710051i	$-0.748672\pi$
$13$	−5.07770			−1.40830			−0.704151	+	0.710051i	$0.748672\pi$
$14$	−0.626496			−0.167438
$15$	1.03446	+	3.18373i	0.267096	+	0.822036i
$16$	−3.03632	−	2.20602i	−0.759081	−	0.551505i
$17$	1.77596	−	5.46584i	0.430734	−	1.32566i	−0.466662	−	0.884436i	$-0.654544\pi$
$17$	1.77596	−	5.46584i	0.430734	−	1.32566i	0.897396	−	0.441226i	$-0.145456\pi$
$18$	0.0739413	+	0.227568i	0.0174281	+	0.0536382i
$19$	0.170076	−	0.123567i	0.0390181	−	0.0283483i	−0.568105	−	0.822956i	$-0.692323\pi$
$19$	0.170076	−	0.123567i	0.0390181	−	0.0283483i	0.607123	+	0.794608i	$0.292323\pi$
$20$	−3.92692	−	2.85308i	−0.878087	−	0.637967i
$21$	−4.15724			−0.907184
$22$	−0.164681	+	0.119648i	−0.0351101	+	0.0255090i
$23$	−1.51548	+	4.66416i	−0.315999	+	0.972544i	0.659343	+	0.751842i	$0.270835\pi$
$23$	−1.51548	+	4.66416i	−0.315999	+	0.972544i	−0.975341	+	0.220701i	$0.929165\pi$
$24$	0.880552	+	0.639758i	0.179742	+	0.130590i
$25$	−0.923943	−	0.671284i	−0.184789	−	0.134257i
$26$	−0.836202	+	0.607536i	−0.163993	+	0.119148i
$27$	1.74286	+	5.36398i	0.335414	+	1.03230i
$28$	4.87671	−	3.54314i	0.921612	−	0.669591i
$29$	−8.26657			−1.53506			−0.767532	−	0.641011i	$-0.778515\pi$
$29$	−8.26657			−1.53506			−0.767532	+	0.641011i	$0.778515\pi$
$30$	0.551282	+	0.400530i	0.100650	+	0.0731265i
$31$	−3.33270	−	2.42135i	−0.598571	−	0.434887i	0.246800	−	0.969066i	$-0.420621\pi$
$31$	−3.33270	−	2.42135i	−0.598571	−	0.434887i	−0.845371	+	0.534179i	$0.820621\pi$
$32$	−2.37556			−0.419943
$33$	−1.09278	+	0.793948i	−0.190228	+	0.138209i
$34$	−0.361509	−	1.11261i	−0.0619983	−	0.190811i
$35$	6.17087	−	4.48340i	1.04307	−	0.757833i
$36$	−1.86257	−	1.35324i	−0.310429	−	0.225540i
$37$	2.67841	+	1.94598i	0.440328	+	0.319917i	0.785765	−	0.618525i	$-0.212269\pi$
$37$	2.67841	+	1.94598i	0.440328	+	0.319917i	−0.345437	+	0.938442i	$0.612269\pi$
$38$	0.0132237	−	0.0406984i	0.00214517	−	0.00660216i
$39$	−5.54879	+	4.03143i	−0.888517	+	0.645546i
$40$	−1.99701			−0.315755
$41$	6.14977	+	4.46807i	0.960432	+	0.697795i	0.953251	−	0.302179i	$-0.0977141\pi$
$41$	6.14977	+	4.46807i	0.960432	+	0.697795i	0.00718123	+	0.999974i	$0.497714\pi$
$42$	−0.684619	+	0.497405i	−0.105639	+	0.0767512i
$43$	0.799492	+	2.46058i	0.121921	+	0.375235i	0.993328	−	0.115327i	$-0.0367915\pi$
$43$	0.799492	+	2.46058i	0.121921	+	0.375235i	−0.871406	+	0.490562i	$0.836791\pi$
$44$	0.605230	−	1.86271i	0.0912418	−	0.280813i
$45$	−2.35685	−	1.71236i	−0.351339	−	0.255263i
$46$	0.308486	+	0.949422i	0.0454838	+	0.139985i
$47$	2.79643			0.407901			0.203951	−	0.978981i	$-0.434622\pi$
$47$	2.79643			0.407901			0.203951	+	0.978981i	$0.434622\pi$
$48$	−5.06949			−0.731717
$49$	0.764037	+	2.35146i	0.109148	+	0.335924i
$50$	−0.232474			−0.0328767
$51$	−2.39887	−	7.38296i	−0.335909	−	1.03382i
$52$	3.07318	−	9.45826i	0.426173	−	1.31163i
$53$	2.99856	+	9.22861i	0.411884	+	1.26765i	0.915009	+	0.403434i	$0.132184\pi$
$53$	2.99856	+	9.22861i	0.411884	+	1.26765i	−0.503125	+	0.864214i	$0.667816\pi$
$54$	0.928805	+	0.674816i	0.126394	+	0.0918309i
$55$	0.765842	−	2.35702i	0.103266	−	0.317820i
$56$	0.766369	−	2.35864i	0.102410	−	0.315187i
$57$	0.0877487	−	0.270063i	0.0116226	−	0.0357707i
$58$	−1.36135	+	0.989077i	−0.178754	+	0.129872i
$59$	0.146575	−	0.106493i	0.0190825	−	0.0138642i	−0.578203	−	0.815893i	$-0.696246\pi$
$59$	0.146575	−	0.106493i	0.0190825	−	0.0138642i	0.597286	+	0.802029i	$0.296246\pi$
$60$	−6.55644			−0.846433
$61$	−3.28145	−	7.08746i	−0.420147	−	0.907456i
$61$	−3.28145	−	7.08746i	−0.420147	−	0.907456i
$62$	−0.838542			−0.106495
$63$	2.92690	−	2.12652i	0.368755	−	0.267916i
$64$	5.68144	−	4.12781i	0.710180	−	0.515976i
$65$	3.88872	−	11.9682i	0.482336	−	1.48448i
$66$	−0.0849654	+	0.261497i	−0.0104585	+	0.0321880i
$67$	−4.76398	+	14.6620i	−0.582013	+	1.79125i	0.0289367	+	0.999581i	$0.490788\pi$
$67$	−4.76398	+	14.6620i	−0.582013	+	1.79125i	−0.610949	+	0.791670i	$0.709212\pi$
$68$	9.10639	+	6.61618i	1.10431	+	0.802330i
$69$	2.04702	+	6.30008i	0.246432	+	0.758441i
$70$	0.479797	−	1.47666i	0.0573467	−	0.176495i
$71$	2.34485	+	7.21672i	0.278283	+	0.856467i	0.988332	+	0.152315i	$0.0486728\pi$
$71$	2.34485	+	7.21672i	0.278283	+	0.856467i	−0.710049	+	0.704152i	$0.751327\pi$
$72$	−0.947201			−0.111629
$73$	1.11008	+	3.41646i	0.129925	+	0.399867i	0.994766	−	0.102178i	$-0.0325812\pi$
$73$	1.11008	+	3.41646i	0.129925	+	0.399867i	−0.864842	+	0.502045i	$0.832581\pi$
$74$	0.673915			0.0783411
$75$	−1.54263			−0.178127
$76$	0.127235	+	0.391588i	0.0145948	+	0.0449182i
$77$	2.48994	+	1.80905i	0.283755	+	0.206160i
$78$	−0.431429	+	1.32780i	−0.0488497	+	0.150344i
$79$	3.47680	+	10.7005i	0.391171	+	1.20390i	0.931904	+	0.362705i	$0.118147\pi$
$79$	3.47680	+	10.7005i	0.391171	+	1.20390i	−0.540733	+	0.841194i	$0.681853\pi$
$80$	7.52498	−	5.46722i	0.841318	−	0.611253i
$81$	3.31031	+	2.40508i	0.367812	+	0.267231i
$82$	1.54735			0.170876
$83$	−11.7213	+	8.51599i	−1.28657	+	0.934751i	−0.999730	−	0.0232262i	$-0.992606\pi$
$83$	−11.7213	+	8.51599i	−1.28657	+	0.934751i	−0.286844	+	0.957977i	$0.592606\pi$
$84$	2.51609	−	7.74371i	0.274527	−	0.844909i
$85$	11.5230	+	8.37195i	1.24984	+	0.908065i
$86$	0.426065	+	0.309554i	0.0459437	+	0.0333801i
$87$	−9.03351	+	6.56323i	−0.968494	+	0.703652i
$88$	−0.249004	−	0.766356i	−0.0265439	−	0.0816938i
$89$	9.45984	−	6.87298i	1.00274	−	0.728534i	0.0400671	−	0.999197i	$-0.487243\pi$
$89$	9.45984	−	6.87298i	1.00274	−	0.728534i	0.962674	+	0.270663i	$0.0872428\pi$
$90$	−0.593009			−0.0625087
$91$	12.6432	+	9.18582i	1.32537	+	0.962935i
$92$	−7.77074	−	5.64577i	−0.810155	−	0.588612i
$93$	−5.56432			−0.576993
$94$	0.460519	−	0.334587i	0.0474990	−	0.0345100i
$95$	0.160999	+	0.495505i	0.0165182	+	0.0508378i
$96$	−2.59595	+	1.88607i	−0.264948	+	0.192496i
$97$	−2.15136	−	1.56306i	−0.218438	−	0.158704i	0.473185	−	0.880963i	$-0.343104\pi$
$97$	−2.15136	−	1.56306i	−0.218438	−	0.158704i	−0.691623	+	0.722259i	$0.743104\pi$
$98$	0.407170	+	0.295827i	0.0411304	+	0.0298830i
$99$	0.363246	−	1.11796i	0.0365076	−	0.112359i
$100$	1.80960	−	1.31475i	0.180960	−	0.131475i
$101$	4.21297			0.419206			0.209603	−	0.977787i	$-0.432783\pi$
$101$	4.21297			0.419206			0.209603	+	0.977787i	$0.432783\pi$
$102$	−1.27840	−	0.928815i	−0.126581	−	0.0919664i
$103$	−1.34172	+	0.974815i	−0.132203	+	0.0960513i	−0.651922	−	0.758286i	$-0.726037\pi$
$103$	−1.34172	+	0.974815i	−0.132203	+	0.0960513i	0.519718	+	0.854338i	$0.326037\pi$
$104$	−1.26437	−	3.89133i	−0.123982	−	0.381576i
$105$	3.18379	−	9.79870i	0.310706	−	0.956255i
$106$	1.59799	+	1.16101i	0.155211	+	0.112767i
$107$	−2.96969	−	9.13975i	−0.287090	−	0.883573i	−0.985764	−	0.168133i	$-0.946226\pi$
$107$	−2.96969	−	9.13975i	−0.287090	−	0.883573i	0.698674	−	0.715440i	$-0.253774\pi$
$108$	−11.0463			−1.06293
$109$	−5.60348			−0.536716			−0.268358	−	0.963319i	$-0.586481\pi$
$109$	−5.60348			−0.536716			−0.268358	+	0.963319i	$0.586481\pi$
$110$	−0.155893	−	0.479788i	−0.0148638	−	0.0457460i
$111$	4.47190			0.424454
$112$	3.56948	+	10.9857i	0.337284	+	1.03805i
$113$	3.32513	−	10.2337i	0.312802	−	0.962706i	−0.663848	−	0.747868i	$-0.731078\pi$
$113$	3.32513	−	10.2337i	0.312802	−	0.962706i	0.976650	−	0.214838i	$-0.0689223\pi$
$114$	−0.0178619	−	0.0549732i	−0.00167292	−	0.00514871i
$115$	−9.83289	−	7.14401i	−0.916922	−	0.666183i
$116$	5.00317	−	15.3982i	0.464533	−	1.42969i
$117$	1.84445	−	5.67665i	0.170520	−	0.524806i
$118$	0.0113965	−	0.0350748i	0.00104913	−	0.00322890i
$119$	−14.3100	+	10.3968i	−1.31180	+	0.953077i
$120$	−2.18229	+	1.58552i	−0.199215	+	0.144738i
$121$	1.00000			0.0909091
$122$	−1.38839	−	0.774553i	−0.125699	−	0.0701247i
$123$	10.2677			0.925810
$124$	6.52731	−	4.74237i	0.586170	−	0.425877i
$125$	−7.73518	+	5.61994i	−0.691856	+	0.502662i
$126$	0.227572	−	0.700394i	0.0202737	−	0.0623961i
$127$	−5.82955	+	17.9415i	−0.517289	+	1.59205i	0.261789	+	0.965125i	$0.415688\pi$
$127$	−5.82955	+	17.9415i	−0.517289	+	1.59205i	−0.779078	+	0.626927i	$0.784312\pi$
$128$	1.90992	−	5.87813i	0.168815	−	0.519558i
$129$	2.82724	+	2.05411i	0.248925	+	0.180854i
$130$	−0.791576	−	2.43622i	−0.0694258	−	0.213671i
$131$	3.22416	−	9.92293i	0.281696	−	0.866970i	−0.705674	−	0.708537i	$-0.749356\pi$
$131$	3.22416	−	9.92293i	0.281696	−	0.866970i	0.987370	−	0.158434i	$-0.0506444\pi$
$132$	−0.817511	−	2.51604i	−0.0711552	−	0.218993i
$133$	−0.647019			−0.0561036
$134$	0.969742	+	2.98456i	0.0837729	+	0.257827i
$135$	−13.9778			−1.20301
$136$	4.63100			0.397105
$137$	−6.65137	−	20.4708i	−0.568265	−	1.74894i	−0.658047	−	0.752977i	$-0.728617\pi$
$137$	−6.65137	−	20.4708i	−0.568265	−	1.74894i	0.0897822	−	0.995961i	$-0.471383\pi$
$138$	1.09090	+	0.792583i	0.0928634	+	0.0674692i
$139$	−0.836898	+	2.57571i	−0.0709848	+	0.218469i	−0.980255	−	0.197738i	$-0.936641\pi$
$139$	−0.836898	+	2.57571i	−0.0709848	+	0.218469i	0.909270	+	0.416206i	$0.136641\pi$
$140$	4.61646	+	14.2080i	0.390162	+	1.20079i
$141$	3.05587	−	2.22022i	0.257351	−	0.186976i
$142$	1.24962	+	0.907901i	0.104866	+	0.0761893i
$143$	5.07770			0.424619
$144$	3.56916	−	2.59315i	0.297430	−	0.216096i
$145$	6.33089	−	19.4845i	0.525752	−	1.61810i
$146$	0.591581	+	0.429809i	0.0489596	+	0.0355712i
$147$	2.70186	+	1.96302i	0.222846	+	0.161907i
$148$	−5.24584	+	3.81132i	−0.431205	+	0.313289i
$149$	−5.24389	−	16.1390i	−0.429597	−	1.32216i	−0.898524	−	0.438925i	$-0.855359\pi$
$149$	−5.24389	−	16.1390i	−0.429597	−	1.32216i	0.468927	−	0.883237i	$-0.344641\pi$
$150$	−0.254042	+	0.184572i	−0.0207424	+	0.0150702i
$151$	1.01108			0.0822804			0.0411402	−	0.999153i	$-0.486901\pi$
$151$	1.01108			0.0822804			0.0411402	+	0.999153i	$0.486901\pi$
$152$	0.137046	+	0.0995698i	0.0111159	+	0.00807618i
$153$	5.46546	+	3.97089i	0.441856	+	0.321027i
$154$	0.626496			0.0504845
$155$	8.25949	−	6.00087i	0.663418	−	0.482002i
$156$	−4.15108	−	12.7757i	−0.332352	−	1.02287i
$157$	14.9379	−	10.8530i	1.19217	−	0.866166i	0.198682	−	0.980064i	$-0.436334\pi$
$157$	14.9379	−	10.8530i	1.19217	−	0.866166i	0.993492	+	0.113898i	$0.0363338\pi$
$158$	1.85285	+	1.34618i	0.147405	+	0.107096i
$159$	10.6038	+	7.70411i	0.840935	+	0.610975i
$160$	1.81930	−	5.59924i	0.143829	−	0.442659i
$161$	12.2111	−	8.87191i	0.962372	−	0.699204i
$162$	0.832907			0.0654394
$163$	5.94613	+	4.32012i	0.465737	+	0.338378i	0.795778	−	0.605589i	$-0.207062\pi$
$163$	5.94613	+	4.32012i	0.465737	+	0.338378i	−0.330040	+	0.943967i	$0.607062\pi$
$164$	−12.0447	+	8.75100i	−0.940534	+	0.683338i
$165$	−1.03446	−	3.18373i	−0.0805324	−	0.247853i
$166$	−0.911349	+	2.80485i	−0.0707344	+	0.217698i
$167$	−8.74777	−	6.35563i	−0.676923	−	0.491813i	0.195413	−	0.980721i	$-0.437395\pi$
$167$	−8.74777	−	6.35563i	−0.676923	−	0.491813i	−0.872335	+	0.488908i	$0.837395\pi$
$168$	−1.03517	−	3.18592i	−0.0798651	−	0.245799i
$169$	12.7831			0.983312
$170$	2.89931			0.222367
$171$	0.0763635	+	0.235023i	0.00583966	+	0.0179726i
$172$	−5.06722			−0.386372
$173$	4.05600	+	12.4831i	0.308372	+	0.949071i	0.978397	+	0.206733i	$0.0662832\pi$
$173$	4.05600	+	12.4831i	0.308372	+	0.949071i	−0.670025	+	0.742338i	$0.733717\pi$
$174$	−0.702372	+	2.16168i	−0.0532467	+	0.163876i
$175$	1.08618	+	3.34292i	0.0821075	+	0.252701i
$176$	3.03632	+	2.20602i	0.228872	+	0.166285i
$177$	0.0756238	−	0.232746i	0.00568423	−	0.0174943i
$178$	0.735521	−	2.26370i	0.0551296	−	0.169671i
$179$	−2.21914	+	6.82980i	−0.165866	+	0.510484i	−0.999099	−	0.0424386i	$-0.986487\pi$
$179$	−2.21914	+	6.82980i	−0.165866	+	0.510484i	0.833233	+	0.552922i	$0.186487\pi$
$180$	4.61605	−	3.35376i	0.344060	−	0.249974i
$181$	−7.18729	+	5.22187i	−0.534227	+	0.388139i	−0.821937	−	0.569579i	$-0.807106\pi$
$181$	−7.18729	+	5.22187i	−0.534227	+	0.388139i	0.287709	+	0.957718i	$0.407106\pi$
$182$	3.18116			0.235803
$183$	−9.21296	−	5.13970i	−0.681042	−	0.379938i
$184$	−3.95176			−0.291328
$185$	−6.63795	+	4.82275i	−0.488032	+	0.354576i
$186$	−0.916339	+	0.665759i	−0.0671892	+	0.0488158i
$187$	−1.77596	+	5.46584i	−0.129871	+	0.399702i
$188$	−1.69248	+	5.20893i	−0.123437	+	0.379900i
$189$	5.36407	−	16.5089i	0.390179	−	1.20085i
$190$	0.0857997	+	0.0623371i	0.00622457	+	0.00452241i
$191$	−5.06594	−	15.5914i	−0.366559	−	1.12815i	−0.948999	−	0.315279i	$-0.897902\pi$
$191$	−5.06594	−	15.5914i	−0.366559	−	1.12815i	0.582440	−	0.812873i	$-0.302098\pi$
$192$	2.93127	−	9.02154i	0.211547	−	0.651073i
$193$	8.01189	+	24.6580i	0.576708	+	1.77493i	0.630288	+	0.776362i	$0.282937\pi$
$193$	8.01189	+	24.6580i	0.576708	+	1.77493i	−0.0535797	+	0.998564i	$0.517063\pi$
$194$	−0.541305			−0.0388634
$195$	−5.25267	−	16.1660i	−0.376151	−	1.15767i
$196$	−4.84250			−0.345893
$197$	−17.8208			−1.26968			−0.634840	−	0.772644i	$-0.718934\pi$
$197$	−17.8208			−1.26968			−0.634840	+	0.772644i	$0.718934\pi$
$198$	−0.0739413	−	0.227568i	−0.00525478	−	0.0161725i
$199$	−4.50079	−	3.27002i	−0.319053	−	0.231805i	0.416718	−	0.909036i	$-0.363180\pi$
$199$	−4.50079	−	3.27002i	−0.319053	−	0.231805i	−0.735771	+	0.677230i	$0.763180\pi$
$200$	0.284377	−	0.875221i	0.0201085	−	0.0618875i
$201$	6.43492	+	19.8046i	0.453884	+	1.39691i
$202$	0.693796	−	0.504073i	0.0488153	−	0.0354664i
$203$	20.5833	+	14.9546i	1.44466	+	1.04961i
$204$	15.2041			1.06450
$205$	−15.2411	+	11.0733i	−1.06448	+	0.773392i
$206$	−0.104321	+	0.321067i	−0.00726839	+	0.0223698i
$207$	−4.66383	−	3.38847i	−0.324158	−	0.235515i
$208$	15.4176	+	11.2015i	1.06902	+	0.776685i
$209$	−0.170076	+	0.123567i	−0.0117644	+	0.00854733i
$210$	−0.648083	−	1.99459i	−0.0447220	−	0.137640i
$211$	14.3316	−	10.4125i	0.986630	−	0.716828i	0.0274493	−	0.999623i	$-0.491262\pi$
$211$	14.3316	−	10.4125i	0.986630	−	0.716828i	0.959180	+	0.282795i	$0.0912615\pi$
$212$	−19.0050			−1.30527
$213$	8.29210	+	6.02456i	0.568165	+	0.412796i
$214$	−1.58260	−	1.14983i	−0.108185	−	0.0786007i
$215$	−6.41193			−0.437290
$216$	−3.67673	+	2.67130i	−0.250170	+	0.181759i
$217$	3.91790	+	12.0580i	0.265964	+	0.818553i
$218$	−0.922787	+	0.670444i	−0.0624990	+	0.0454082i
$219$	3.92556	+	2.85208i	0.265265	+	0.192726i
$220$	3.92692	+	2.85308i	0.264753	+	0.192354i
$221$	−9.01780	+	27.7539i	−0.606603	+	1.86693i
$222$	0.736438	−	0.535054i	0.0494265	−	0.0359105i
$223$	26.7792			1.79327			0.896635	−	0.442770i	$-0.146004\pi$
$223$	26.7792			1.79327			0.896635	+	0.442770i	$0.146004\pi$
$224$	5.91501	+	4.29750i	0.395213	+	0.287139i
$225$	1.08608	−	0.789086i	0.0724056	−	0.0526058i
$226$	−0.676854	−	2.08314i	−0.0450237	−	0.138569i
$227$	−2.87649	+	8.85292i	−0.190919	+	0.587589i	−1.00000		0.000108473i	$-0.999965\pi$
$227$	−2.87649	+	8.85292i	−0.190919	+	0.587589i	0.809081	+	0.587697i	$0.199965\pi$
$228$	0.449939	+	0.326900i	0.0297980	+	0.0216495i
$229$	−4.06276	−	12.5039i	−0.268475	−	0.826280i	−0.990872	−	0.134803i	$-0.956960\pi$
$229$	−4.06276	−	12.5039i	−0.268475	−	0.826280i	0.722398	−	0.691478i	$-0.243040\pi$
$230$	−2.47406			−0.163135
$231$	4.15724			0.273526
$232$	−2.05841	−	6.33513i	−0.135141	−	0.415922i
$233$	17.7059			1.15995			0.579975	−	0.814634i	$-0.303062\pi$
$233$	17.7059			1.15995			0.579975	+	0.814634i	$0.303062\pi$
$234$	−0.375452	−	1.15552i	−0.0245440	−	0.0755388i
$235$	−2.14162	+	6.59124i	−0.139704	+	0.429965i
$236$	0.109654	+	0.337479i	0.00713784	+	0.0219680i
$237$	12.2950	+	8.93284i	0.798646	+	0.580250i
$238$	−1.11263	+	3.42433i	−0.0721212	+	0.221966i
$239$	3.68760	−	11.3493i	0.238531	−	0.734124i	−0.758102	−	0.652136i	$-0.773873\pi$
$239$	3.68760	−	11.3493i	0.238531	−	0.734124i	0.996633	−	0.0819877i	$-0.0261268\pi$
$240$	3.88243	−	11.9489i	0.250610	−	0.771297i
$241$	12.7089	−	9.23358i	0.818654	−	0.594787i	−0.0976724	−	0.995219i	$-0.531140\pi$
$241$	12.7089	−	9.23358i	0.818654	−	0.594787i	0.916327	+	0.400431i	$0.131140\pi$
$242$	0.164681	−	0.119648i	0.0105861	−	0.00769126i
$243$	−11.3931			−0.730870
$244$	15.1879	−	1.82283i	0.972304	−	0.116695i
$245$	−6.12758			−0.391477
$246$	1.69090	−	1.22851i	0.107808	−	0.0783271i
$247$	−0.863595	+	0.627438i	−0.0549492	+	0.0399229i
$248$	1.02576	−	3.15696i	0.0651357	−	0.200467i
$249$	−6.04745	+	18.6121i	−0.383241	+	1.17950i
$250$	−0.601425	+	1.85100i	−0.0380374	+	0.117067i
$251$	−12.2822	−	8.92352i	−0.775244	−	0.563248i	0.128304	−	0.991735i	$-0.459047\pi$
$251$	−12.2822	−	8.92352i	−0.775244	−	0.563248i	−0.903548	+	0.428487i	$0.859047\pi$
$252$	2.18963	+	6.73898i	0.137934	+	0.424516i
$253$	1.51548	−	4.66416i	0.0952772	−	0.293233i
$254$	1.18665	+	3.65212i	0.0744568	+	0.229155i
$255$	19.2389			1.20479
$256$	3.95146	+	12.1613i	0.246966	+	0.760083i
$257$	−16.6262			−1.03711			−0.518557	−	0.855043i	$-0.673531\pi$
$257$	−16.6262			−1.03711			−0.518557	+	0.855043i	$0.673531\pi$
$258$	0.711363			0.0442875
$259$	−3.14871	−	9.69075i	−0.195652	−	0.602154i
$260$	19.9397	+	14.4871i	1.23661	+	0.898450i
$261$	3.00280	−	9.24166i	0.185868	−	0.572044i
$262$	−0.656300	−	2.01988i	−0.0405463	−	0.124789i
$263$	−2.47266	+	1.79650i	−0.152471	+	0.110777i	−0.661405	−	0.750029i	$-0.730040\pi$
$263$	−2.47266	+	1.79650i	−0.152471	+	0.110777i	0.508934	+	0.860805i	$0.330040\pi$
$264$	−0.880552	−	0.639758i	−0.0541942	−	0.0393744i
$265$	−24.0485			−1.47728
$266$	−0.106552	+	0.0774144i	−0.00653311	+	0.00474658i
$267$	4.88070	−	15.0212i	0.298694	−	0.919285i
$268$	−24.4277	−	17.7478i	−1.49216	−	1.08412i
$269$	−4.93647	−	3.58655i	−0.300982	−	0.218676i	0.427035	−	0.904235i	$-0.359558\pi$
$269$	−4.93647	−	3.58655i	−0.300982	−	0.218676i	−0.728017	+	0.685559i	$0.759558\pi$
$270$	−2.30187	+	1.67241i	−0.140088	+	0.101780i
$271$	6.00743	+	18.4890i	0.364925	+	1.12312i	0.950028	+	0.312165i	$0.101054\pi$
$271$	6.00743	+	18.4890i	0.364925	+	1.12312i	−0.585103	+	0.810959i	$0.698946\pi$
$272$	−17.4501	+	12.6783i	−1.05807	+	0.768733i
$273$	21.1092			1.27759
$274$	−3.54464	−	2.57533i	−0.214140	−	0.155582i
$275$	0.923943	+	0.671284i	0.0557159	+	0.0404799i
$276$	−12.9741			−0.780950
$277$	−15.6340	+	11.3588i	−0.939356	+	0.682482i	−0.948265	−	0.317478i	$-0.897164\pi$
$277$	−15.6340	+	11.3588i	−0.939356	+	0.682482i	0.00890979	+	0.999960i	$0.497164\pi$
$278$	0.170357	+	0.524304i	0.0102173	+	0.0314456i
$279$	3.91755	−	2.84627i	0.234538	−	0.170402i
$280$	4.97245	+	3.61270i	0.297161	+	0.215900i
$281$	−2.30455	−	1.67435i	−0.137478	−	0.0998836i	0.516921	−	0.856033i	$-0.327078\pi$
$281$	−2.30455	−	1.67435i	−0.137478	−	0.0998836i	−0.654399	+	0.756150i	$0.727078\pi$
$282$	0.237600	−	0.731257i	0.0141489	−	0.0435457i
$283$	−11.2090	+	8.14378i	−0.666303	+	0.484098i	−0.868786	−	0.495188i	$-0.835099\pi$
$283$	−11.2090	+	8.14378i	−0.666303	+	0.484098i	0.202483	+	0.979286i	$0.435099\pi$
$284$	−14.8618			−0.881886
$285$	0.569342	+	0.413651i	0.0337249	+	0.0245026i
$286$	0.836202	−	0.607536i	0.0494457	−	0.0359244i
$287$	−7.22962	−	22.2505i	−0.426751	−	1.31340i
$288$	0.862912	−	2.65577i	0.0508476	−	0.156493i
$289$	−12.9681	−	9.42189i	−0.762831	−	0.554229i
$290$	−1.28870	−	3.96620i	−0.0756749	−	0.232903i
$291$	−3.59194			−0.210563
$292$	−7.03572			−0.411734
$293$	−2.47815	−	7.62696i	−0.144775	−	0.445572i	0.852207	−	0.523205i	$-0.175264\pi$
$293$	−2.47815	−	7.62696i	−0.144775	−	0.445572i	−0.996982	+	0.0776332i	$0.975264\pi$
$294$	0.679817			0.0396477
$295$	0.138753	+	0.427037i	0.00807851	+	0.0248631i
$296$	−0.824376	+	2.53717i	−0.0479159	+	0.147470i
$297$	−1.74286	−	5.36398i	−0.101131	−	0.311250i
$298$	−2.79457	−	2.03038i	−0.161885	−	0.117617i
$299$	7.69514	−	23.6832i	0.445021	−	1.36963i
$300$	0.933644	−	2.87346i	0.0539039	−	0.165899i
$301$	2.46063	−	7.57303i	0.141828	−	0.436502i
$302$	0.166506	−	0.120973i	0.00958132	−	0.00696123i
$303$	4.60383	−	3.34488i	0.264483	−	0.192158i
$304$	−0.788997			−0.0452521
$305$	19.2184	−	2.30657i	1.10044	−	0.132074i
$306$	1.37517			0.0786130
$307$	−18.4585	+	13.4109i	−1.05348	+	0.765400i	−0.972872	−	0.231346i	$-0.925687\pi$
$307$	−18.4585	+	13.4109i	−1.05348	+	0.765400i	−0.0806111	+	0.996746i	$0.525687\pi$
$308$	−4.87671	+	3.54314i	−0.277877	+	0.201889i
$309$	−0.692244	+	2.13051i	−0.0393804	+	0.121200i
$310$	0.642191	−	1.97646i	0.0364740	−	0.112255i
$311$	2.04164	−	6.28353i	0.115771	−	0.356306i	−0.876336	−	0.481700i	$-0.840019\pi$
$311$	2.04164	−	6.28353i	0.115771	−	0.356306i	0.992107	+	0.125394i	$0.0400195\pi$
$312$	−4.47118	−	3.24850i	−0.253131	−	0.183910i
$313$	5.14244	+	15.8268i	0.290668	+	0.894583i	0.984642	+	0.174584i	$0.0558580\pi$
$313$	5.14244	+	15.8268i	0.290668	+	0.894583i	−0.693975	+	0.719999i	$0.744142\pi$
$314$	1.16145	−	3.57458i	0.0655444	−	0.201725i
$315$	2.77070	+	8.52733i	0.156111	+	0.480461i
$316$	−22.0361			−1.23963
$317$	2.34137	+	7.20599i	0.131504	+	0.404728i	0.995030	−	0.0995764i	$-0.0317488\pi$
$317$	2.34137	+	7.20599i	0.131504	+	0.404728i	−0.863526	+	0.504305i	$0.831749\pi$
$318$	2.66802			0.149615
$319$	8.26657			0.462839
$320$	5.37824	+	16.5525i	0.300653	+	0.925314i
$321$	−10.5017	−	7.62992i	−0.586147	−	0.425861i
$322$	0.949439	−	2.92207i	0.0529102	−	0.162841i
$323$	−0.373352	−	1.14906i	−0.0207738	−	0.0639353i
$324$	−6.48345	+	4.71050i	−0.360192	+	0.261694i
$325$	4.69151	+	3.40858i	0.260238	+	0.189074i
$326$	1.49611			0.0828618
$327$	−6.12334	+	4.44887i	−0.338622	+	0.246023i
$328$	−1.89281	+	5.82548i	−0.104513	+	0.321658i
$329$	−6.96295	−	5.05888i	−0.383880	−	0.278905i
$330$	−0.551282	−	0.400530i	−0.0303471	−	0.0220485i
$331$	−21.2267	+	15.4221i	−1.16673	+	0.847677i	−0.990613	−	0.136693i	$-0.956352\pi$
$331$	−21.2267	+	15.4221i	−1.16673	+	0.847677i	−0.176113	+	0.984370i	$0.556352\pi$
$332$	−8.76873	−	26.9874i	−0.481246	−	1.48112i
$333$	−3.14844	+	2.28747i	−0.172533	+	0.125353i
$334$	−2.20103			−0.120435
$335$	−30.9102	−	22.4576i	−1.68881	−	1.22699i
$336$	12.6227	+	9.17095i	0.688626	+	0.500316i
$337$	5.43222			0.295912			0.147956	−	0.988994i	$-0.452731\pi$
$337$	5.43222			0.295912			0.147956	+	0.988994i	$0.452731\pi$
$338$	2.10513	−	1.52947i	0.114504	−	0.0831920i
$339$	−4.49140	−	13.8231i	−0.243940	−	0.750769i
$340$	−22.5685	+	16.3970i	−1.22395	+	0.889252i
$341$	3.33270	+	2.42135i	0.180476	+	0.131123i
$342$	0.0406956	+	0.0295671i	0.00220056	+	0.00159880i
$343$	−4.30601	+	13.2525i	−0.232503	+	0.715569i
$344$	−1.68660	+	1.22539i	−0.0909356	+	0.0660686i
$345$	−16.4171			−0.883868
$346$	2.16152	+	1.57044i	0.116204	+	0.0844272i
$347$	11.5196	−	8.36947i	0.618404	−	0.449297i	−0.233960	−	0.972246i	$-0.575168\pi$
$347$	11.5196	−	8.36947i	0.618404	−	0.449297i	0.852364	+	0.522949i	$0.175168\pi$
$348$	−6.75801	−	20.7990i	−0.362267	−	1.11494i
$349$	−0.780673	+	2.40267i	−0.0417885	+	0.128612i	−0.969774	−	0.244004i	$-0.921539\pi$
$349$	−0.780673	+	2.40267i	−0.0417885	+	0.128612i	0.927986	+	0.372616i	$0.121539\pi$
$350$	0.578846	+	0.420556i	0.0309406	+	0.0224797i
$351$	−8.84973	−	27.2367i	−0.472364	−	1.45379i
$352$	2.37556			0.126618
$353$	−4.06945			−0.216595			−0.108297	−	0.994119i	$-0.534540\pi$
$353$	−4.06945			−0.216595			−0.108297	+	0.994119i	$0.534540\pi$
$354$	−0.0153938	−	0.0473771i	−0.000818169	−	0.00251807i
$355$	−18.8057			−0.998105
$356$	7.07696	+	21.7806i	0.375078	+	1.15437i
$357$	−7.38309	+	22.7228i	−0.390755	+	1.20262i
$358$	0.451721	+	1.39026i	0.0238742	+	0.0734773i
$359$	6.74570	+	4.90104i	0.356025	+	0.258667i	0.751392	−	0.659856i	$-0.229383\pi$
$359$	6.74570	+	4.90104i	0.356025	+	0.258667i	−0.395368	+	0.918523i	$0.629383\pi$
$360$	0.725407	−	2.23257i	0.0382323	−	0.117667i
$361$	−5.85767	+	18.0280i	−0.308298	+	0.948844i
$362$	−0.558826	+	1.71989i	−0.0293712	+	0.0903953i
$363$	1.09278	−	0.793948i	0.0573558	−	0.0416715i
$364$	−24.7625	+	17.9910i	−1.29791	+	0.942985i
$365$	−8.90281			−0.465995
$366$	−2.13216	+	0.255899i	−0.111450	+	0.0133761i
$367$	26.6353			1.39035			0.695175	−	0.718840i	$-0.255327\pi$
$367$	26.6353			1.39035			0.695175	+	0.718840i	$0.255327\pi$
$368$	14.8907	−	10.8187i	0.776231	−	0.563965i
$369$	−7.22898	+	5.25216i	−0.376326	+	0.273417i
$370$	−0.516113	+	1.58843i	−0.0268314	+	0.0825787i
$371$	9.22878	−	28.4033i	0.479134	−	1.47462i
$372$	3.36769	−	10.3647i	0.174607	−	0.537384i
$373$	18.5337	+	13.4655i	0.959636	+	0.697216i	0.953066	−	0.302762i	$-0.0979087\pi$
$373$	18.5337	+	13.4655i	0.959636	+	0.697216i	0.00656995	+	0.999978i	$0.497909\pi$
$374$	0.361509	+	1.11261i	0.0186932	+	0.0575318i
$375$	−3.99088	+	12.2827i	−0.206088	+	0.634274i
$376$	0.696323	+	2.14306i	0.0359101	+	0.110520i
$377$	41.9752			2.16183
$378$	−1.09190	−	3.36051i	−0.0561610	−	0.172846i
$379$	−18.8635			−0.968955			−0.484478	−	0.874804i	$-0.660990\pi$
$379$	−18.8635			−0.968955			−0.484478	+	0.874804i	$0.660990\pi$
$380$	−1.02042			−0.0523465
$381$	7.87424	+	24.2344i	0.403409	+	1.24157i
$382$	−2.69974	−	1.96148i	−0.138131	−	0.100358i
$383$	−11.4878	+	35.3559i	−0.587001	+	1.80660i	0.00408077	+	0.999992i	$0.498701\pi$
$383$	−11.4878	+	35.3559i	−0.587001	+	1.80660i	−0.591082	+	0.806612i	$0.701299\pi$
$384$	−2.57981	−	7.93985i	−0.131651	−	0.405179i
$385$	−6.17087	+	4.48340i	−0.314497	+	0.228495i
$386$	4.26969	+	3.10211i	0.217321	+	0.157893i
$387$	−3.04123			−0.154595
$388$	4.21358	−	3.06134i	0.213912	−	0.155416i
$389$	6.30697	−	19.4109i	0.319776	−	0.984169i	−0.653968	−	0.756522i	$-0.726897\pi$
$389$	6.30697	−	19.4109i	0.319776	−	0.984169i	0.973744	−	0.227647i	$-0.0731032\pi$
$390$	−2.79925	−	2.03377i	−0.141745	−	0.102984i
$391$	22.8021	+	16.5667i	1.15315	+	0.837814i
$392$	−1.61181	+	1.17105i	−0.0814087	+	0.0591469i
$393$	−4.35501	−	13.4033i	−0.219681	−	0.676109i
$394$	−2.93475	+	2.13222i	−0.147851	+	0.107420i
$395$	−27.8840			−1.40299
$396$	1.86257	+	1.35324i	0.0935979	+	0.0680029i
$397$	−29.4245	−	21.3782i	−1.47677	−	1.07294i	−0.978578	−	0.205874i	$-0.933996\pi$
$397$	−29.4245	−	21.3782i	−1.47677	−	1.07294i	−0.498196	−	0.867065i	$-0.666004\pi$
$398$	−1.13245			−0.0567644
$399$	−0.707046	+	0.513699i	−0.0353966	+	0.0257171i
$400$	1.32453	+	4.07647i	0.0662263	+	0.203824i
$401$	−11.4922	+	8.34960i	−0.573895	+	0.416959i	−0.836518	−	0.547939i	$-0.815412\pi$
$401$	−11.4922	+	8.34960i	−0.573895	+	0.416959i	0.262623	+	0.964899i	$0.415412\pi$
$402$	3.42929	+	2.49153i	0.171038	+	0.124266i
$403$	16.9225	+	12.2949i	0.842968	+	0.612452i
$404$	−2.54981	+	7.84752i	−0.126858	+	0.390429i
$405$	−8.20399	+	5.96055i	−0.407659	+	0.296182i
$406$	5.17897			0.257028
$407$	−2.67841	−	1.94598i	−0.132764	−	0.0964585i
$408$	5.06064	−	3.67677i	0.250539	−	0.182027i
$409$	7.37821	+	22.7078i	0.364829	+	1.12283i	0.950088	+	0.311982i	$0.100993\pi$
$409$	7.37821	+	22.7078i	0.364829	+	1.12283i	−0.585259	+	0.810846i	$0.699007\pi$
$410$	−1.18502	+	3.64712i	−0.0585241	+	0.180119i
$411$	−23.5212	−	17.0892i	−1.16022	−	0.842946i
$412$	−1.00375	−	3.08921i	−0.0494510	−	0.152195i
$413$	−0.557615			−0.0274384
$414$	−1.17347			−0.0576728
$415$	−11.0957	−	34.1491i	−0.544668	−	1.67631i
$416$	12.0624			0.591407
$417$	1.13044	+	3.47912i	0.0553577	+	0.170373i
$418$	−0.0132237	+	0.0406984i	−0.000646793	+	0.00199062i
$419$	0.0696556	+	0.214378i	0.00340290	+	0.0104730i	0.952744	−	0.303776i	$-0.0982474\pi$
$419$	0.0696556	+	0.214378i	0.00340290	+	0.0104730i	−0.949341	+	0.314249i	$0.898247\pi$
$420$	16.3252	+	11.8609i	0.796586	+	0.578754i
$421$	5.96634	−	18.3625i	0.290782	−	0.894934i	−0.693824	−	0.720144i	$-0.744076\pi$
$421$	5.96634	−	18.3625i	0.290782	−	0.894934i	0.984606	−	0.174789i	$-0.0559245\pi$
$422$	1.11431	−	3.42950i	0.0542438	−	0.166945i
$423$	−1.01579	+	3.12629i	−0.0493895	+	0.152005i
$424$	−6.32575	+	4.59592i	−0.307205	+	0.223198i
$425$	−5.31002	+	3.85795i	−0.257574	+	0.187138i
$426$	2.08638			0.101085
$427$	−4.65094	+	23.5837i	−0.225075	+	1.14129i
$428$	18.8220			0.909796
$429$	5.54879	−	4.03143i	0.267898	−	0.194639i
$430$	−1.05592	+	0.767173i	−0.0509212	+	0.0369964i
$431$	−6.64474	+	20.4504i	−0.320066	+	0.985061i	0.653553	+	0.756881i	$0.273278\pi$
$431$	−6.64474	+	20.4504i	−0.320066	+	0.985061i	−0.973619	+	0.228181i	$0.926722\pi$
$432$	6.54114	−	20.1316i	0.314711	−	0.968580i
$433$	4.53741	−	13.9647i	0.218054	−	0.671102i	−0.780869	−	0.624695i	$-0.785223\pi$
$433$	4.53741	−	13.9647i	0.218054	−	0.671102i	0.998923	−	0.0464062i	$-0.0147769\pi$
$434$	2.08792	+	1.51696i	0.100223	+	0.0728166i
$435$	−8.55141	−	26.3185i	−0.410009	−	1.26188i
$436$	3.39139	−	10.4376i	0.162418	−	0.499872i
$437$	0.318591	+	0.980523i	0.0152403	+	0.0469048i
$438$	0.987711			0.0471947
$439$	−1.23967	−	3.81530i	−0.0591660	−	0.182094i	0.917105	−	0.398645i	$-0.130519\pi$
$439$	−1.23967	−	3.81530i	−0.0591660	−	0.182094i	−0.976271	+	0.216551i	$0.930519\pi$
$440$	1.99701			0.0952039
$441$	−2.90637			−0.138398
$442$	1.83564	+	5.64951i	0.0873123	+	0.268720i
$443$	9.85335	+	7.15888i	0.468147	+	0.340128i	0.796719	−	0.604351i	$-0.206567\pi$
$443$	9.85335	+	7.15888i	0.468147	+	0.340128i	−0.328572	+	0.944479i	$0.606567\pi$
$444$	−2.70653	+	8.32984i	−0.128446	+	0.395317i
$445$	8.95500	+	27.5607i	0.424508	+	1.30650i
$446$	4.41004	−	3.20408i	0.208821	−	0.151718i
$447$	−18.5440	−	13.4730i	−0.877099	−	0.637250i
$448$	−21.6139			−1.02116
$449$	−27.3199	+	19.8491i	−1.28931	+	0.936737i	−0.999791	−	0.0204363i	$-0.993494\pi$
$449$	−27.3199	+	19.8491i	−1.28931	+	0.936737i	−0.289516	+	0.957173i	$0.593494\pi$
$450$	0.0844451	−	0.259895i	0.00398078	−	0.0122516i
$451$	−6.14977	−	4.46807i	−0.289581	−	0.210393i
$452$	17.0499	+	12.3875i	0.801960	+	0.582658i
$453$	1.10488	−	0.802744i	0.0519119	−	0.0377162i
$454$	0.585530	+	1.80207i	0.0274803	+	0.0845756i
$455$	−31.3338	+	22.7654i	−1.46895	+	1.06726i
$456$	0.228814			0.0107152
$457$	33.7496	+	24.5205i	1.57874	+	1.14702i	0.918123	+	0.396295i	$0.129704\pi$
$457$	33.7496	+	24.5205i	1.57874	+	1.14702i	0.660615	+	0.750725i	$0.270296\pi$
$458$	−2.16512	−	1.57305i	−0.101170	−	0.0735040i
$459$	32.4139			1.51295
$460$	19.2584	−	13.9920i	0.897925	−	0.652381i
$461$	4.06536	+	12.5119i	0.189342	+	0.582736i	0.999996	−	0.00278975i	$-0.000888006\pi$
$461$	4.06536	+	12.5119i	0.189342	+	0.582736i	−0.810654	+	0.585526i	$0.800888\pi$
$462$	0.684619	−	0.497405i	0.0318514	−	0.0231414i
$463$	−11.6014	−	8.42892i	−0.539164	−	0.391725i	0.284611	−	0.958643i	$-0.408136\pi$
$463$	−11.6014	−	8.42892i	−0.539164	−	0.391725i	−0.823774	+	0.566918i	$0.808136\pi$
$464$	25.1000	+	18.2362i	1.16524	+	0.846595i
$465$	4.26139	−	13.1152i	0.197617	−	0.608203i
$466$	2.91582	−	2.11847i	0.135073	−	0.0981363i
$467$	19.1421			0.885791			0.442896	−	0.896573i	$-0.353951\pi$
$467$	19.1421			0.885791			0.442896	+	0.896573i	$0.353951\pi$
$468$	9.45760	+	6.87135i	0.437178	+	0.317628i
$469$	38.3864	−	27.8893i	1.77252	−	1.28781i
$470$	0.435943	+	1.34169i	0.0201085	+	0.0618877i
$471$	7.70704	−	23.7198i	0.355122	−	1.09295i
$472$	0.118109	+	0.0858115i	0.00543642	+	0.00394979i
$473$	−0.799492	−	2.46058i	−0.0367607	−	0.113138i
$474$	3.09355			0.142091
$475$	−0.240089			−0.0110160
$476$	−10.7054	−	32.9478i	−0.490681	−	1.51016i
$477$	−11.4064			−0.522263
$478$	−0.750638	−	2.31023i	−0.0343334	−	0.105667i
$479$	−2.02235	+	6.22415i	−0.0924034	+	0.284389i	−0.986568	−	0.163349i	$-0.947770\pi$
$479$	−2.02235	+	6.22415i	−0.0924034	+	0.284389i	0.894165	+	0.447738i	$0.147770\pi$
$480$	−2.45741	−	7.56314i	−0.112165	−	0.345209i
$481$	−13.6002	−	9.88110i	−0.620114	−	0.450539i
$482$	0.988143	−	3.04119i	0.0450087	−	0.138523i
$483$	6.30020	−	19.3900i	0.286669	−	0.882276i
$484$	−0.605230	+	1.86271i	−0.0275104	+	0.0846684i
$485$	5.33176	−	3.87375i	0.242103	−	0.175898i
$486$	−1.87623	+	1.36316i	−0.0851077	+	0.0618344i
$487$	−17.1088			−0.775274			−0.387637	−	0.921812i	$-0.626709\pi$
$487$	−17.1088			−0.775274			−0.387637	+	0.921812i	$0.626709\pi$
$488$	4.61442	−	4.27956i	0.208885	−	0.193727i
$489$	9.92774			0.448948
$490$	−1.00910	+	0.733152i	−0.0455864	+	0.0331204i
$491$	−3.01896	+	2.19340i	−0.136244	+	0.0989869i	−0.653820	−	0.756650i	$-0.726835\pi$
$491$	−3.01896	+	2.19340i	−0.136244	+	0.0989869i	0.517576	+	0.855637i	$0.326835\pi$
$492$	−6.21433	+	19.1258i	−0.280164	+	0.862256i
$493$	−14.6811	+	45.1838i	−0.661203	+	2.03498i
$494$	−0.0671461	+	0.206654i	−0.00302105	+	0.00929782i
$495$	2.35685	+	1.71236i	0.105933	+	0.0769646i
$496$	4.77762	+	14.7040i	0.214522	+	0.660229i
$497$	7.21685	−	22.2112i	0.323720	−	0.996308i
$498$	1.23100	+	3.78863i	0.0551625	+	0.169773i
$499$	38.4903			1.72306			0.861530	−	0.507706i	$-0.169506\pi$
$499$	38.4903			1.72306			0.861530	+	0.507706i	$0.169506\pi$
$500$	−5.78673	−	17.8097i	−0.258790	−	0.796475i
$501$	−14.6054			−0.652521
$502$	−3.09032			−0.137928
$503$	−4.06739	−	12.5181i	−0.181356	−	0.558156i	0.818511	−	0.574491i	$-0.194800\pi$
$503$	−4.06739	−	12.5181i	−0.181356	−	0.558156i	−0.999867	+	0.0163351i	$0.994800\pi$
$504$	2.35848	+	1.71353i	0.105055	+	0.0763269i
$505$	−3.22647	+	9.93005i	−0.143576	+	0.441881i
$506$	−0.308486	−	0.949422i	−0.0137139	−	0.0422070i
$507$	13.9690	−	10.1491i	0.620386	−	0.450737i
$508$	−29.8915	−	21.7175i	−1.32622	−	0.963557i
$509$	22.0543			0.977541			0.488771	−	0.872412i	$-0.337445\pi$
$509$	22.0543			0.977541			0.488771	+	0.872412i	$0.337445\pi$
$510$	3.16829	−	2.30190i	0.140294	−	0.101930i
$511$	3.41652	−	10.5150i	0.151138	−	0.465155i
$512$	12.1063	+	8.79572i	0.535027	+	0.388720i
$513$	0.959231	+	0.696922i	0.0423511	+	0.0307699i
$514$	−2.73802	+	1.98929i	−0.120769	+	0.0877438i
$515$	−1.27011	−	3.90901i	−0.0559679	−	0.172251i
$516$	−5.53733	+	4.02311i	−0.243767	+	0.177107i
$517$	−2.79643			−0.122987
$518$	−1.67801	−	1.21915i	−0.0737276	−	0.0535662i
$519$	14.3432	+	10.4210i	0.629597	+	0.457429i
$520$	10.1402			0.444679
$521$	−3.89064	+	2.82672i	−0.170452	+	0.123841i	−0.669741	−	0.742595i	$-0.733595\pi$
$521$	−3.89064	+	2.82672i	−0.170452	+	0.123841i	0.499289	+	0.866436i	$0.333595\pi$
$522$	−0.611241	−	1.88121i	−0.0267533	−	0.0823381i
$523$	−10.3128	+	7.49270i	−0.450948	+	0.327633i	−0.789970	−	0.613146i	$-0.789904\pi$
$523$	−10.3128	+	7.49270i	−0.450948	+	0.327633i	0.339022	+	0.940778i	$0.389904\pi$
$524$	16.5321	+	12.0113i	0.722210	+	0.524716i
$525$	3.84105	+	2.79069i	0.167637	+	0.121796i
$526$	−0.192254	+	0.591698i	−0.00838268	+	0.0257992i
$527$	−19.1535	+	13.9158i	−0.834338	+	0.606182i
$528$	5.06949			0.220621
$529$	−0.850285	−	0.617768i	−0.0369689	−	0.0268595i
$530$	−3.96033	+	2.87735i	−0.172026	+	0.124984i
$531$	0.0658117	+	0.202548i	0.00285599	+	0.00878982i
$532$	0.391595	−	1.20521i	0.0169778	−	0.0522523i
$533$	−31.2267	−	22.6875i	−1.35258	−	0.982706i
$534$	−0.993501	−	3.05768i	−0.0429930	−	0.132319i
$535$	23.8169			1.02969
$536$	−12.4226			−0.536573
$537$	2.99749	+	9.22532i	0.129351	+	0.398102i
$538$	−1.24207			−0.0535493
$539$	−0.764037	−	2.35146i	−0.0329094	−	0.101285i
$540$	8.45975	−	26.0364i	0.364050	−	1.12043i
$541$	−9.95327	−	30.6330i	−0.427924	−	1.31702i	−0.900166	−	0.435547i	$-0.856555\pi$
$541$	−9.95327	−	30.6330i	−0.427924	−	1.31702i	0.472242	−	0.881469i	$-0.343445\pi$
$542$	3.20147	+	2.32601i	0.137515	+	0.0999106i
$543$	−3.70820	+	11.4127i	−0.159134	+	0.489765i
$544$	−4.21890	+	12.9844i	−0.180884	+	0.556703i
$545$	4.29138	−	13.2075i	0.183822	−	0.565747i
$546$	3.47629	−	2.52567i	0.148772	−	0.108089i
$547$	−8.61472	+	6.25896i	−0.368339	+	0.267614i	−0.756522	−	0.653969i	$-0.773103\pi$
$547$	−8.61472	+	6.25896i	−0.368339	+	0.267614i	0.388183	+	0.921582i	$0.373103\pi$
$548$	42.1567			1.80084
$549$	9.11544	−	1.09403i	0.389037	−	0.0466919i
$550$	0.232474			0.00991271
$551$	−1.40594	+	1.02148i	−0.0598952	+	0.0435164i
$552$	−4.31839	+	3.13749i	−0.183803	+	0.133541i
$553$	10.7007	−	32.9333i	0.455039	−	1.40047i
$554$	−1.21557	+	3.74115i	−0.0516447	+	0.158946i
$555$	−3.42477	+	10.5404i	−0.145374	+	0.447414i
$556$	−4.29127	−	3.11779i	−0.181990	−	0.132224i
$557$	4.91640	+	15.1311i	0.208315	+	0.641127i	0.999561	+	0.0296291i	$0.00943262\pi$
$557$	4.91640	+	15.1311i	0.208315	+	0.641127i	−0.791246	+	0.611498i	$0.790567\pi$
$558$	0.304597	−	0.937453i	0.0128946	−	0.0396856i
$559$	−4.05958	−	12.4941i	−0.171702	−	0.528445i
$560$	−28.6272			−1.20972
$561$	2.39887	+	7.38296i	0.101280	+	0.311709i
$562$	−0.579849			−0.0244594
$563$	11.9002			0.501534			0.250767	−	0.968047i	$-0.419317\pi$
$563$	11.9002			0.501534			0.250767	+	0.968047i	$0.419317\pi$
$564$	2.28611	+	7.03593i	0.0962627	+	0.296266i
$565$	21.5745	+	15.6748i	0.907646	+	0.659444i
$566$	−0.871517	+	2.68225i	−0.0366326	+	0.112744i
$567$	−3.89157	−	11.9770i	−0.163431	−	0.502987i
$568$	−4.94669	+	3.59398i	−0.207559	+	0.150800i
$569$	−24.7459	−	17.9789i	−1.03740	−	0.753716i	−0.0676242	−	0.997711i	$-0.521542\pi$
$569$	−24.7459	−	17.9789i	−1.03740	−	0.753716i	−0.969776	+	0.243995i	$0.921542\pi$
$570$	0.143252			0.00600018
$571$	12.4084	−	9.01521i	0.519274	−	0.377275i	−0.297056	−	0.954860i	$-0.596005\pi$
$571$	12.4084	−	9.01521i	0.519274	−	0.377275i	0.816330	+	0.577585i	$0.196005\pi$
$572$	−3.07318	+	9.45826i	−0.128496	+	0.395470i
$573$	−17.9147	−	13.0158i	−0.748396	−	0.543742i
$574$	−3.85280	−	2.79922i	−0.160813	−	0.116837i
$575$	4.53119	−	3.29210i	0.188964	−	0.137290i
$576$	2.55095	+	7.85101i	0.106289	+	0.327125i
$577$	−25.5777	+	18.5833i	−1.06481	+	0.773632i	−0.974973	−	0.222324i	$-0.928636\pi$
$577$	−25.5777	+	18.5833i	−1.06481	+	0.773632i	−0.0898408	+	0.995956i	$0.528636\pi$
$578$	−3.26291			−0.135719
$579$	28.3324	+	20.5847i	1.17745	+	0.855471i
$580$	32.4622	+	23.5852i	1.34792	+	0.979320i
$581$	44.5911			1.84995
$582$	−0.591525	+	0.429768i	−0.0245195	+	0.0178145i
$583$	−2.99856	−	9.22861i	−0.124188	−	0.382210i
$584$	−2.34181	+	1.70143i	−0.0969049	+	0.0704055i
$585$	11.9674	+	8.69483i	0.494791	+	0.359487i
$586$	−1.32065	−	0.959511i	−0.0545557	−	0.0396370i
$587$	3.55034	−	10.9268i	0.146538	−	0.450998i	−0.850668	−	0.525704i	$-0.823802\pi$
$587$	3.55034	−	10.9268i	0.146538	−	0.450998i	0.997206	+	0.0747064i	$0.0238019\pi$
$588$	−5.29177	+	3.84470i	−0.218229	+	0.158553i
$589$	−0.866012			−0.0356834
$590$	0.0739441	+	0.0537235i	0.00304423	+	0.00221176i
$591$	−19.4741	+	14.1488i	−0.801059	+	0.582003i
$592$	−3.83965	−	11.8172i	−0.157809	−	0.485686i
$593$	11.7499	−	36.1623i	0.482509	−	1.48501i	−0.353048	−	0.935605i	$-0.614855\pi$
$593$	11.7499	−	36.1623i	0.482509	−	1.48501i	0.835557	−	0.549404i	$-0.185145\pi$
$594$	−0.928805	−	0.674816i	−0.0381093	−	0.0276880i
$595$	−13.5463	−	41.6913i	−0.555346	−	1.70918i
$596$	33.2361			1.36140
$597$	−7.51458			−0.307551
$598$	−1.56640	−	4.82088i	−0.0640548	−	0.197141i
$599$	18.7924			0.767838			0.383919	−	0.923367i	$-0.374574\pi$
$599$	18.7924			0.767838			0.383919	+	0.923367i	$0.374574\pi$
$600$	−0.384120	−	1.18220i	−0.0156816	−	0.0482631i
$601$	1.40078	−	4.31116i	0.0571391	−	0.175856i	−0.918414	−	0.395621i	$-0.870529\pi$
$601$	1.40078	−	4.31116i	0.0571391	−	0.175856i	0.975553	+	0.219766i	$0.0705292\pi$
$602$	−0.500878	−	1.54154i	−0.0204143	−	0.0628287i
$603$	−14.6610	−	10.6518i	−0.597042	−	0.433776i
$604$	−0.611935	+	1.88334i	−0.0248993	+	0.0766321i
$605$	−0.765842	+	2.35702i	−0.0311359	+	0.0958265i
$606$	0.357956	−	1.10168i	0.0145410	−	0.0447526i
$607$	−12.9047	+	9.37579i	−0.523784	+	0.380551i	−0.818028	−	0.575179i	$-0.804932\pi$
$607$	−12.9047	+	9.37579i	−0.523784	+	0.380551i	0.294243	+	0.955731i	$0.404932\pi$
$608$	−0.404025	+	0.293541i	−0.0163854	+	0.0119047i
$609$	34.3661			1.39259
$610$	2.88893	−	2.67928i	0.116969	−	0.108481i
$611$	−14.1994			−0.574448
$612$	−10.7045	+	7.77724i	−0.432702	+	0.314376i
$613$	−1.26491	+	0.919014i	−0.0510894	+	0.0371186i	−0.613037	−	0.790054i	$-0.710052\pi$
$613$	−1.26491	+	0.919014i	−0.0510894	+	0.0371186i	0.561947	+	0.827173i	$0.310052\pi$
$614$	−1.43518	+	4.41704i	−0.0579193	+	0.178257i
$615$	−7.86346	+	24.2012i	−0.317085	+	0.975888i
$616$	−0.766369	+	2.35864i	−0.0308779	+	0.0950324i
$617$	16.0778	+	11.6812i	0.647267	+	0.470267i	0.862339	−	0.506331i	$-0.168999\pi$
$617$	16.0778	+	11.6812i	0.647267	+	0.470267i	−0.215072	+	0.976598i	$0.568999\pi$
$618$	0.140911	+	0.433680i	0.00566828	+	0.0174452i
$619$	1.26514	−	3.89371i	0.0508504	−	0.156501i	−0.922407	−	0.386220i	$-0.873781\pi$
$619$	1.26514	−	3.89371i	0.0508504	−	0.156501i	0.973257	+	0.229719i	$0.0737806\pi$
$620$	6.17897	+	19.0169i	0.248153	+	0.763737i
$621$	−27.6597			−1.10995
$622$	−0.415591	−	1.27906i	−0.0166637	−	0.0512855i
$623$	−35.9880			−1.44183
$624$	25.7413			1.03048
$625$	−9.08695	−	27.9668i	−0.363478	−	1.11867i
$626$	2.74050	+	1.99109i	0.109533	+	0.0795801i
$627$	−0.0877487	+	0.270063i	−0.00350435	+	0.0107853i
$628$	11.1751	+	34.3935i	0.445936	+	1.37245i
$629$	15.3932	−	11.1838i	0.613765	−	0.445927i
$630$	1.47656	+	1.07278i	0.0588275	+	0.0427407i
$631$	−42.6029			−1.69600			−0.847998	−	0.529999i	$-0.822192\pi$
$631$	−42.6029			−1.69600			−0.847998	+	0.529999i	$0.822192\pi$
$632$	−7.33464	+	5.32893i	−0.291756	+	0.211973i
$633$	7.39424	−	22.7571i	0.293895	−	0.904515i
$634$	1.24776	+	0.906550i	0.0495549	+	0.0360037i
$635$	−37.8240	−	27.4807i	−1.50100	−	1.09054i
$636$	−20.7682	+	15.0890i	−0.823513	+	0.598317i
$637$	−3.87955	−	11.9400i	−0.153714	−	0.473082i
$638$	1.36135	−	0.989077i	0.0538963	−	0.0391580i
$639$	−8.91973			−0.352859
$640$	12.3922	+	9.00343i	0.489843	+	0.355892i
$641$	28.0864	+	20.4060i	1.10935	+	0.805988i	0.982561	−	0.185942i	$-0.0595336\pi$
$641$	28.0864	+	20.4060i	1.10935	+	0.805988i	0.126787	+	0.991930i	$0.459534\pi$
$642$	−2.64233			−0.104285
$643$	11.7601	−	8.54424i	0.463774	−	0.336952i	−0.331236	−	0.943548i	$-0.607466\pi$
$643$	11.7601	−	8.54424i	0.463774	−	0.336952i	0.795010	+	0.606596i	$0.207466\pi$
$644$	9.13521	+	28.1153i	0.359978	+	1.10790i
$645$	−7.00680	+	5.09074i	−0.275892	+	0.200448i
$646$	−0.198966	−	0.144558i	−0.00782823	−	0.00568754i
$647$	−9.04313	−	6.57022i	−0.355522	−	0.258302i	0.395660	−	0.918397i	$-0.370516\pi$
$647$	−9.04313	−	6.57022i	−0.355522	−	0.258302i	−0.751182	+	0.660095i	$0.770516\pi$
$648$	−1.01887	+	3.13575i	−0.0400248	+	0.123184i
$649$	−0.146575	+	0.106493i	−0.00575358	+	0.00418022i
$650$	1.18043			0.0463004
$651$	13.8548	+	10.0661i	0.543014	+	0.394523i
$652$	−11.6459	+	8.46123i	−0.456088	+	0.331367i
$653$	12.1577	+	37.4176i	0.475768	+	1.46426i	0.844919	+	0.534894i	$0.179649\pi$
$653$	12.1577	+	37.4176i	0.475768	+	1.46426i	−0.369151	+	0.929370i	$0.620351\pi$
$654$	−0.476102	+	1.46529i	−0.0186170	+	0.0572974i
$655$	20.9193	+	15.1988i	0.817387	+	0.593866i
$656$	−8.81605	−	27.1330i	−0.344209	−	1.05937i
$657$	−4.22268			−0.164743
$658$	−1.75195			−0.0682982
$659$	−7.83801	−	24.1229i	−0.305325	−	0.939695i	−0.979556	−	0.201174i	$-0.935524\pi$
$659$	−7.83801	−	24.1229i	−0.305325	−	0.939695i	0.674230	−	0.738521i	$-0.264476\pi$
$660$	6.55644			0.255209
$661$	1.10269	+	3.39372i	0.0428895	+	0.132000i	0.970208	−	0.242272i	$-0.0778926\pi$
$661$	1.10269	+	3.39372i	0.0428895	+	0.132000i	−0.927319	+	0.374272i	$0.877893\pi$
$662$	−1.65042	+	5.07947i	−0.0641453	+	0.197419i
$663$	12.1807	+	37.4885i	0.473061	+	1.45593i
$664$	−9.44491	−	6.86213i	−0.366534	−	0.266302i
$665$	0.495514	−	1.52504i	0.0192152	−	0.0591383i
$666$	−0.244797	+	0.753408i	−0.00948569	+	0.0291940i
$667$	12.5278	−	38.5566i	0.485078	−	1.49292i
$668$	17.1331	−	12.4479i	0.662899	−	0.481624i
$669$	29.2637	−	21.2613i	1.13140	−	0.822010i
$670$	−7.77733			−0.300465
$671$	3.28145	+	7.08746i	0.126679	+	0.273608i
$672$	9.87577			0.380966
$673$	−4.76241	+	3.46010i	−0.183578	+	0.133377i	−0.675779	−	0.737105i	$-0.736192\pi$
$673$	−4.76241	+	3.46010i	−0.183578	+	0.133377i	0.492201	+	0.870482i	$0.336192\pi$
$674$	0.894584	−	0.649954i	0.0344581	−	0.0250353i
$675$	1.99045	−	6.12597i	0.0766123	−	0.235789i
$676$	−7.73669	+	23.8111i	−0.297565	+	0.915811i
$677$	7.59250	−	23.3673i	0.291803	−	0.898079i	−0.692473	−	0.721444i	$-0.743479\pi$
$677$	7.59250	−	23.3673i	0.291803	−	0.898079i	0.984276	−	0.176635i	$-0.0565212\pi$
$678$	−2.39356	−	1.73902i	−0.0919240	−	0.0667867i
$679$	2.52912	+	7.78384i	0.0970588	+	0.298716i
$680$	−3.54662	+	10.9154i	−0.136006	+	0.418585i
$681$	3.88540	+	11.9580i	0.148889	+	0.458233i
$682$	0.838542			0.0321094
$683$	−4.61923	−	14.2165i	−0.176750	−	0.543980i	0.822959	−	0.568100i	$-0.192322\pi$
$683$	−4.61923	−	14.2165i	−0.176750	−	0.543980i	−0.999709	+	0.0241204i	$0.992322\pi$
$684$	−0.483995			−0.0185060
$685$	53.3440			2.03817
$686$	0.876519	+	2.69765i	0.0334656	+	0.102997i
$687$	−14.3671	−	10.4383i	−0.548140	−	0.398247i
$688$	3.00058	−	9.23482i	0.114396	−	0.352074i
$689$	−15.2258	−	46.8602i	−0.580056	−	1.78523i
$690$	−2.70359	+	1.96427i	−0.102924	+	0.0747786i
$691$	−22.6638	−	16.4662i	−0.862173	−	0.626405i	0.0663023	−	0.997800i	$-0.478880\pi$
$691$	−22.6638	−	16.4662i	−0.862173	−	0.626405i	−0.928475	+	0.371394i	$0.878880\pi$
$692$	−25.7071			−0.977238
$693$	−2.92690	+	2.12652i	−0.111184	+	0.0807797i
$694$	0.895670	−	2.75659i	0.0339992	−	0.104639i
$695$	−5.43006	−	3.94517i	−0.205974	−	0.149649i
$696$	−7.27914	−	5.28861i	−0.275915	−	0.200464i
$697$	35.3435	−	25.6786i	1.33873	−	0.972645i
$698$	0.158912	+	0.489080i	0.00601489	+	0.0185119i
$699$	19.3486	−	14.0575i	0.731830	−	0.531705i
$700$	−6.88426			−0.260201
$701$	−4.56291	−	3.31515i	−0.172339	−	0.125211i	0.498272	−	0.867021i	$-0.333968\pi$
$701$	−4.56291	−	3.31515i	−0.172339	−	0.125211i	−0.670611	+	0.741809i	$0.733968\pi$
$702$	−4.71619	−	3.42652i	−0.178001	−	0.129326i
$703$	0.695992			0.0262498
$704$	−5.68144	+	4.12781i	−0.214127	+	0.155573i
$705$	2.89279	+	8.90309i	0.108949	+	0.335310i
$706$	−0.670161	+	0.486900i	−0.0252218	+	0.0183247i
$707$	−10.4901	−	7.62147i	−0.394519	−	0.286635i
$708$	0.387768	+	0.281730i	0.0145732	+	0.0105881i
$709$	6.49662	−	19.9946i	0.243986	−	0.750911i	−0.751816	−	0.659373i	$-0.770822\pi$
$709$	6.49662	−	19.9946i	0.243986	−	0.750911i	0.995802	−	0.0915380i	$-0.0291783\pi$
$710$	−3.09695	+	2.25007i	−0.116226	+	0.0844435i
$711$	−13.2256			−0.495999
$712$	7.62268	+	5.53820i	0.285672	+	0.207553i
$713$	16.3442	−	11.8747i	0.612094	−	0.444713i
$714$	1.50288	+	4.62539i	0.0562439	+	0.173101i
$715$	−3.88872	+	11.9682i	−0.145430	+	0.447587i
$716$	−11.3788	−	8.26720i	−0.425247	−	0.308960i
$717$	−4.98101	−	15.3300i	−0.186019	−	0.572508i
$718$	1.69729			0.0633423
$719$	50.3624			1.87820			0.939101	−	0.343642i	$-0.111661\pi$
$719$	50.3624			1.87820			0.939101	+	0.343642i	$0.111661\pi$
$720$	3.37869	+	10.3985i	0.125916	+	0.387530i
$721$	5.10429			0.190094
$722$	1.19237	+	3.66974i	0.0443754	+	0.136573i
$723$	6.55703	−	20.1805i	0.243859	−	0.750519i
$724$	−5.37685	−	16.5482i	−0.199829	−	0.615011i
$725$	7.63784	+	5.54922i	0.283662	+	0.206093i
$726$	0.0849654	−	0.261497i	0.00315336	−	0.00970505i
$727$	9.23048	−	28.4085i	0.342340	−	1.05361i	−0.620653	−	0.784085i	$-0.713132\pi$
$727$	9.23048	−	28.4085i	0.342340	−	1.05361i	0.962993	−	0.269528i	$-0.0868676\pi$
$728$	−3.89140	+	11.9765i	−0.144225	+	0.443878i
$729$	−22.3811	+	16.2608i	−0.828928	+	0.602251i
$730$	−1.46613	+	1.06520i	−0.0542637	+	0.0394249i
$731$	14.8690			0.549951
$732$	15.1497	−	14.0503i	0.559949	−	0.519315i
$733$	−9.39324			−0.346947			−0.173474	−	0.984839i	$-0.555499\pi$
$733$	−9.39324			−0.346947			−0.173474	+	0.984839i	$0.555499\pi$
$734$	4.38633	−	3.18686i	0.161902	−	0.117629i
$735$	−6.69607	+	4.86498i	−0.246988	+	0.179448i
$736$	3.60010	−	11.0800i	0.132702	−	0.408413i
$737$	4.76398	−	14.6620i	0.175483	−	0.540082i
$738$	−0.562067	+	1.72986i	−0.0206900	+	0.0636772i
$739$	−15.8466	−	11.5132i	−0.582926	−	0.423520i	0.256852	−	0.966451i	$-0.417315\pi$
$739$	−15.8466	−	11.5132i	−0.582926	−	0.423520i	−0.839778	+	0.542931i	$0.817315\pi$
$740$	−4.96588	−	15.2834i	−0.182549	−	0.561829i
$741$	−0.445562	+	1.37130i	−0.0163681	+	0.0503759i
$742$	−1.87858	−	5.78169i	−0.0689650	−	0.212252i
$743$	3.01533			0.110622			0.0553108	−	0.998469i	$-0.482385\pi$
$743$	3.01533			0.110622			0.0553108	+	0.998469i	$0.482385\pi$
$744$	−1.38554	−	4.26425i	−0.0507963	−	0.156335i
$745$	42.0560			1.54081
$746$	4.66326			0.170734
$747$	−5.26280	−	16.1972i	−0.192556	−	0.592626i
$748$	−9.10639	−	6.61618i	−0.332963	−	0.241912i
$749$	−9.13992	+	28.1298i	−0.333965	+	1.02784i
$750$	0.812372	+	2.50022i	0.0296636	+	0.0912952i
$751$	−11.4193	+	8.29660i	−0.416696	+	0.302747i	−0.776307	−	0.630355i	$-0.782909\pi$
$751$	−11.4193	+	8.29660i	−0.416696	+	0.302747i	0.359611	+	0.933102i	$0.382909\pi$
$752$	−8.49087	−	6.16898i	−0.309630	−	0.224960i
$753$	−20.5065			−0.747298
$754$	6.91252	−	5.02224i	0.251739	−	0.182899i
$755$	−0.774326	+	2.38313i	−0.0281806	+	0.0867310i
$756$	27.5048	+	19.9834i	1.00034	+	0.726788i
$757$	34.3829	+	24.9807i	1.24967	+	0.907938i	0.998203	−	0.0599286i	$-0.0190873\pi$
$757$	34.3829	+	24.9807i	1.24967	+	0.907938i	0.251466	+	0.967866i	$0.419087\pi$
$758$	−3.10647	+	2.25698i	−0.112832	+	0.0819773i
$759$	−2.04702	−	6.30008i	−0.0743022	−	0.228679i
$760$	−0.339644	+	0.246766i	−0.0123202	+	0.00895113i
$761$	−0.0218266			−0.000791214			−0.000395607	−	1.00000i	$-0.500126\pi$
$761$	−0.0218266			−0.000791214			−0.000395607		1.00000i	$0.500126\pi$
$762$	4.19633	+	3.04882i	0.152017	+	0.110447i
$763$	13.9523	+	10.1370i	0.505109	+	0.366983i
$764$	32.1082			1.16163
$765$	−13.5451	+	9.84112i	−0.489726	+	0.355807i
$766$	2.33843	+	7.19695i	0.0844909	+	0.260036i
$767$	−0.744265	+	0.540740i	−0.0268739	+	0.0195250i
$768$	13.9735	+	10.1524i	0.504226	+	0.366342i
$769$	1.18560	+	0.861389i	0.0427538	+	0.0310625i	0.608957	−	0.793203i	$-0.291588\pi$
$769$	1.18560	+	0.861389i	0.0427538	+	0.0310625i	−0.566203	+	0.824266i	$0.691588\pi$
$770$	−0.479797	+	1.47666i	−0.0172907	+	0.0532152i
$771$	−18.1687	+	13.2003i	−0.654330	+	0.475398i
$772$	−50.7797			−1.82760
$773$	19.5724	+	14.2202i	0.703969	+	0.511464i	0.881223	−	0.472702i	$-0.156721\pi$
$773$	19.5724	+	14.2202i	0.703969	+	0.511464i	−0.177253	+	0.984165i	$0.556721\pi$
$774$	−0.500834	+	0.363877i	−0.0180021	+	0.0130793i
$775$	1.45381	+	4.47438i	0.0522225	+	0.160724i
$776$	0.662159	−	2.03791i	0.0237701	−	0.0731569i
$777$	−11.1348	−	8.08990i	−0.399458	−	0.290223i
$778$	−1.28383	−	3.95122i	−0.0460275	−	0.141658i
$779$	1.59803			0.0572555
$780$	33.2917			1.19203
$781$	−2.34485	−	7.21672i	−0.0839055	−	0.258235i
$782$	5.73725			0.205164
$783$	−14.4075	−	44.3417i	−0.514882	−	1.58464i
$784$	2.86751	−	8.82529i	0.102411	−	0.315189i
$785$	14.1407	+	43.5206i	0.504704	+	1.55332i
$786$	−2.32087	−	1.68621i	−0.0827827	−	0.0601451i
$787$	−4.69967	+	14.4641i	−0.167525	+	0.515589i	−0.999213	−	0.0396535i	$-0.987375\pi$
$787$	−4.69967	+	14.4641i	−0.167525	+	0.515589i	0.831688	+	0.555243i	$0.187375\pi$
$788$	10.7857	−	33.1949i	0.384224	−	1.18252i
$789$	−1.27574	+	3.92633i	−0.0454176	+	0.139781i
$790$	−4.59196	+	3.33626i	−0.163375	+	0.118699i
$791$	−26.7927	+	19.4660i	−0.952637	+	0.692131i
$792$	0.947201			0.0336573
$793$	16.6622	+	35.9880i	0.591693	+	1.27797i
$794$	−7.40351			−0.262741
$795$	−26.2796	+	19.0932i	−0.932040	+	0.677167i
$796$	8.81510	−	6.40454i	0.312443	−	0.227003i
$797$	11.1104	−	34.1942i	0.393550	−	1.21122i	−0.536536	−	0.843878i	$-0.680267\pi$
$797$	11.1104	−	34.1942i	0.393550	−	1.21122i	0.930085	−	0.367344i	$-0.119733\pi$
$798$	−0.0549742	+	0.169193i	−0.00194606	+	0.00598937i
$799$	4.96635	−	15.2849i	0.175697	−	0.540739i
$800$	2.19488	+	1.59467i	0.0776008	+	0.0563803i
$801$	4.24744	+	13.0723i	0.150076	+	0.461886i
$802$	−0.893543	+	2.75004i	−0.0315521	+	0.0971074i
$803$	−1.11008	−	3.41646i	−0.0391737	−	0.120564i
$804$	−40.7848			−1.43837
$805$	11.5595	+	35.5764i	0.407418	+	1.25390i
$806$	4.25787			0.149977
$807$	−8.24199			−0.290132
$808$	1.04905	+	3.22863i	0.0369053	+	0.113583i
$809$	−15.1445	−	11.0031i	−0.532452	−	0.386849i	0.288822	−	0.957383i	$-0.406736\pi$
$809$	−15.1445	−	11.0031i	−0.532452	−	0.386849i	−0.821274	+	0.570534i	$0.806736\pi$
$810$	−0.637876	+	1.96318i	−0.0224127	+	0.0689791i
$811$	3.41018	+	10.4954i	0.119748	+	0.368545i	0.992908	−	0.118889i	$-0.0379331\pi$
$811$	3.41018	+	10.4954i	0.119748	+	0.368545i	−0.873160	+	0.487434i	$0.837933\pi$
$812$	−40.3137	+	29.2896i	−1.41473	+	1.02786i
$813$	21.2440	+	15.4347i	0.745061	+	0.541319i
$814$	−0.673915			−0.0236207
$815$	−14.7364	+	10.7066i	−0.516194	+	0.375037i
$816$	−9.00321	+	27.7090i	−0.315175	+	0.970010i
$817$	0.440022	+	0.319695i	0.0153944	+	0.0111847i
$818$	3.93199	+	2.85676i	0.137479	+	0.0998842i
$819$	−14.8619	+	10.7978i	−0.519317	+	0.377306i
$820$	−11.4019	−	35.0915i	−0.398173	−	1.22545i
$821$	−34.6591	+	25.1813i	−1.20961	+	0.878835i	−0.995196	−	0.0979074i	$-0.968785\pi$
$821$	−34.6591	+	25.1813i	−1.20961	+	0.878835i	−0.214417	+	0.976742i	$0.568785\pi$
$822$	−5.91818			−0.206420
$823$	20.6406	+	14.9963i	0.719487	+	0.522738i	0.886220	−	0.463264i	$-0.153322\pi$
$823$	20.6406	+	14.9963i	0.719487	+	0.522738i	−0.166733	+	0.986002i	$0.553322\pi$
$824$	−1.08115	−	0.785500i	−0.0376636	−	0.0273642i
$825$	1.54263			0.0537074
$826$	−0.0918287	+	0.0667175i	−0.00319513	+	0.00232140i
$827$	11.2720	+	34.6916i	0.391965	+	1.20635i	0.931300	+	0.364254i	$0.118676\pi$
$827$	11.2720	+	34.6916i	0.391965	+	1.20635i	−0.539335	+	0.842092i	$0.681324\pi$
$828$	9.13441	−	6.63654i	0.317443	−	0.230636i
$829$	21.8774	+	15.8948i	0.759833	+	0.552051i	0.898859	−	0.438238i	$-0.144397\pi$
$829$	21.8774	+	15.8948i	0.759833	+	0.552051i	−0.139026	+	0.990289i	$0.544397\pi$
$830$	−5.91313	−	4.29614i	−0.205248	−	0.149121i
$831$	−8.06618	+	24.8252i	−0.279813	+	0.861175i
$832$	−28.8487	+	20.9598i	−1.00015	+	0.726650i
$833$	14.2096			0.492335
$834$	0.602431	+	0.437692i	0.0208605	+	0.0151560i
$835$	21.6798	−	15.7513i	0.750259	−	0.545095i
$836$	−0.127235	−	0.391588i	−0.00440050	−	0.0135433i
$837$	7.17962	−	22.0966i	0.248164	−	0.763771i
$838$	0.0371208	+	0.0269699i	0.00128232	+	0.000931658i
$839$	12.4328	+	38.2642i	0.429227	+	1.32103i	0.898888	+	0.438179i	$0.144376\pi$
$839$	12.4328	+	38.2642i	0.429227	+	1.32103i	−0.469660	+	0.882847i	$0.655624\pi$
$840$	8.30206			0.286448
$841$	39.3362			1.35642
$842$	−1.21449	−	3.73782i	−0.0418541	−	0.128814i
$843$	−3.84771			−0.132522
$844$	10.7216	+	32.9976i	0.369051	+	1.13582i
$845$	−9.78981	+	30.1299i	−0.336780	+	1.03650i
$846$	0.206772	+	0.636378i	0.00710896	+	0.0218791i
$847$	−2.48994	−	1.80905i	−0.0855555	−	0.0621597i
$848$	11.2539	−	34.6360i	0.386461	−	1.18940i
$849$	−5.78313	+	17.7986i	−0.198477	+	0.610848i
$850$	−0.412864	+	1.27066i	−0.0141611	+	0.0435834i
$851$	−13.1354	+	9.54343i	−0.450276	+	0.327145i
$852$	−16.2406	+	11.7995i	−0.556394	+	0.404244i
$853$	−32.5447			−1.11431			−0.557155	−	0.830408i	$-0.688107\pi$
$853$	−32.5447			−1.11431			−0.557155	+	0.830408i	$0.688107\pi$
$854$	2.05581	+	4.44026i	0.0703485	+	0.151943i
$855$	−0.612435			−0.0209448
$856$	6.26484	−	4.55167i	0.214128	−	0.155573i
$857$	17.0544	−	12.3908i	0.582569	−	0.423261i	−0.257081	−	0.966390i	$-0.582761\pi$
$857$	17.0544	−	12.3908i	0.582569	−	0.423261i	0.839649	+	0.543129i	$0.182761\pi$
$858$	0.431429	−	1.32780i	0.0147287	−	0.0453304i
$859$	0.225228	−	0.693180i	0.00768468	−	0.0236510i	−0.947141	−	0.320819i	$-0.896042\pi$
$859$	0.225228	−	0.693180i	0.00768468	−	0.0236510i	0.954825	+	0.297168i	$0.0960420\pi$
$860$	3.88069	−	11.9435i	0.132330	−	0.407271i
$861$	−25.5661	−	18.5748i	−0.871289	−	0.633029i
$862$	1.35258	+	4.16283i	0.0460692	+	0.141786i
$863$	13.4648	−	41.4405i	0.458348	−	1.41065i	−0.408810	−	0.912619i	$-0.634056\pi$
$863$	13.4648	−	41.4405i	0.458348	−	1.41065i	0.867159	−	0.498032i	$-0.165944\pi$
$864$	−4.14027	−	12.7424i	−0.140855	−	0.433507i
$865$	−32.5291			−1.10602
$866$	−0.923623	−	2.84262i	−0.0313860	−	0.0965961i
$867$	−21.6517			−0.735332
$868$	−24.8318			−0.842847
$869$	−3.47680	−	10.7005i	−0.117942	−	0.362989i
$870$	−4.55721	−	3.31101i	−0.154504	−	0.112254i
$871$	24.1901	−	74.4494i	0.819649	−	2.52262i
$872$	−1.39529	−	4.29426i	−0.0472504	−	0.145422i
$873$	2.52890	−	1.83735i	0.0855903	−	0.0621850i
$874$	0.169784	+	0.123355i	0.00574301	+	0.00417254i
$875$	29.4269			0.994811
$876$	−7.68846	+	5.58599i	−0.259769	+	0.188733i
$877$	17.0954	−	52.6143i	0.577272	−	1.77666i	−0.0510388	−	0.998697i	$-0.516253\pi$
$877$	17.0954	−	52.6143i	0.577272	−	1.77666i	0.628310	−	0.777963i	$-0.283747\pi$
$878$	−0.660642	−	0.479985i	−0.0222956	−	0.0161987i
$879$	−8.76347	−	6.36703i	−0.295584	−	0.214755i
$880$	−7.52498	+	5.46722i	−0.253667	+	0.184300i
$881$	17.8336	+	54.8863i	0.600830	+	1.84917i	0.523251	+	0.852179i	$0.324719\pi$
$881$	17.8336	+	54.8863i	0.600830	+	1.84917i	0.0775795	+	0.996986i	$0.475281\pi$
$882$	−0.478624	+	0.347741i	−0.0161161	+	0.0117090i
$883$	−55.1722			−1.85669			−0.928346	−	0.371716i	$-0.878770\pi$
$883$	−55.1722			−1.85669			−0.928346	+	0.371716i	$0.878770\pi$
$884$	−46.2396	−	33.5950i	−1.55520	−	1.12992i
$885$	0.490671	+	0.356494i	0.0164937	+	0.0119834i
$886$	2.47920			0.0832905
$887$	8.06539	−	5.85985i	0.270809	−	0.196754i	−0.444089	−	0.895982i	$-0.646473\pi$
$887$	8.06539	−	5.85985i	0.270809	−	0.196754i	0.714899	+	0.699228i	$0.246473\pi$
$888$	1.11352	+	3.42707i	0.0373674	+	0.115005i
$889$	46.9723	−	34.1274i	1.57540	−	1.14460i
$890$	4.77229	+	3.46727i	0.159968	+	0.116223i
$891$	−3.31031	−	2.40508i	−0.110899	−	0.0805732i
$892$	−16.2076	+	49.8818i	−0.542670	+	1.67017i
$893$	0.475605	−	0.345548i	0.0159155	−	0.0115633i
$894$	−4.66585			−0.156049
$895$	−14.3985	−	10.4611i	−0.481288	−	0.349676i
$896$	−15.3894	+	11.1811i	−0.514124	+	0.373533i
$897$	−10.3942	−	31.9900i	−0.347051	−	1.06811i
$898$	−2.12418	+	6.53754i	−0.0708847	+	0.218161i
$899$	27.5500	+	20.0163i	0.918844	+	0.667579i
$900$	0.812505	+	2.50063i	0.0270835	+	0.0833544i
$901$	55.7675			1.85788
$902$	−1.54735			−0.0515210
$903$	−3.32368	−	10.2292i	−0.110605	−	0.340408i
$904$	8.67062			0.288381
$905$	−6.80373	−	20.9397i	−0.226164	−	0.696060i
$906$	0.0859066	−	0.264393i	0.00285406	−	0.00878388i
$907$	5.53902	+	17.0474i	0.183920	+	0.566048i	0.999928	−	0.0119927i	$-0.00381748\pi$
$907$	5.53902	+	17.0474i	0.183920	+	0.566048i	−0.816008	+	0.578041i	$0.803817\pi$
$908$	−14.7494	−	10.7161i	−0.489478	−	0.355626i
$909$	−1.53034	+	4.70991i	−0.0507583	+	0.156218i
$910$	−2.43627	+	7.49805i	−0.0807614	+	0.248558i
$911$	16.4348	−	50.5812i	0.544510	−	1.67583i	−0.177642	−	0.984095i	$-0.556847\pi$
$911$	16.4348	−	50.5812i	0.544510	−	1.67583i	0.722152	−	0.691735i	$-0.243153\pi$
$912$	−0.862197	+	0.626423i	−0.0285502	+	0.0207429i
$913$	11.7213	−	8.51599i	0.387917	−	0.281838i
$914$	8.49174			0.280882
$915$	19.1701	−	17.7789i	0.633743	−	0.587753i
$916$	25.7500			0.850803
$917$	−25.9790	+	18.8749i	−0.857903	+	0.623303i
$918$	5.33796	−	3.87826i	0.176179	−	0.128001i
$919$	−15.3356	+	47.1982i	−0.505875	+	1.55692i	0.293419	+	0.955984i	$0.405207\pi$
$919$	−15.3356	+	47.1982i	−0.505875	+	1.55692i	−0.799294	+	0.600940i	$0.794793\pi$
$920$	3.02642	−	9.31438i	0.0997783	−	0.307086i
$921$	−9.52346	+	29.3102i	−0.313809	+	0.965804i
$922$	2.16651	+	1.57406i	0.0713501	+	0.0518389i
$923$	−11.9065	−	36.6444i	−0.391906	−	1.20616i
$924$	−2.51609	+	7.74371i	−0.0827731	+	0.254749i
$925$	−1.16839	−	3.59595i	−0.0384165	−	0.118234i
$926$	−2.91904			−0.0959255
$927$	−0.602426	−	1.85408i	−0.0197863	−	0.0608959i
$928$	19.6377			0.644640
$929$	21.7588			0.713884			0.356942	−	0.934127i	$-0.383819\pi$
$929$	21.7588			0.713884			0.356942	+	0.934127i	$0.383819\pi$
$930$	−0.867436	−	2.66969i	−0.0284444	−	0.0875427i
$931$	0.420509	+	0.305517i	0.0137816	+	0.0100129i
$932$	−10.7161	+	32.9808i	−0.351018	+	1.08032i
$933$	−2.75774	−	8.48744i	−0.0902842	−	0.277866i
$934$	3.15234	−	2.29031i	0.103148	−	0.0749413i
$935$	−11.5230	−	8.37195i	−0.376842	−	0.273792i
$936$	4.80961			0.157207
$937$	36.7636	−	26.7103i	1.20101	−	0.872588i	0.206630	−	0.978419i	$-0.433750\pi$
$937$	36.7636	−	26.7103i	1.20101	−	0.872588i	0.994384	+	0.105832i	$0.0337505\pi$
$938$	2.98461	−	9.18569i	0.0974510	−	0.299923i
$939$	18.1852	+	13.2123i	0.593451	+	0.431167i
$940$	−10.9814	−	7.97843i	−0.358173	−	0.260228i
$941$	−15.8341	+	11.5042i	−0.516177	+	0.375025i	−0.815162	−	0.579233i	$-0.803352\pi$
$941$	−15.8341	+	11.5042i	−0.516177	+	0.375025i	0.298985	+	0.954258i	$0.403352\pi$
$942$	−1.56882	−	4.82834i	−0.0511150	−	0.157316i
$943$	−30.1596	+	21.9122i	−0.982131	+	0.713560i
$944$	−0.679976			−0.0221313
$945$	34.8038	+	25.2865i	1.13217	+	0.822568i
$946$	−0.426065	−	0.309554i	−0.0138526	−	0.0100645i
$947$	−38.3222			−1.24531			−0.622653	−	0.782498i	$-0.713945\pi$
$947$	−38.3222			−1.24531			−0.622653	+	0.782498i	$0.713945\pi$
$948$	−24.0805	+	17.4955i	−0.782100	+	0.568229i
$949$	−5.63664	−	17.3478i	−0.182973	−	0.563133i
$950$	−0.0395382	+	0.0287262i	−0.00128279	+	0.000932000i
$951$	8.27977	+	6.01560i	0.268490	+	0.195069i
$952$	−11.5309	−	8.37771i	−0.373720	−	0.271523i
$953$	0.561768	−	1.72894i	0.0181975	−	0.0560060i	−0.941545	−	0.336886i	$-0.890626\pi$
$953$	0.561768	−	1.72894i	0.0181975	−	0.0560060i	0.959743	+	0.280880i	$0.0906263\pi$
$954$	−1.87842	+	1.36475i	−0.0608160	+	0.0441854i
$955$	40.6289			1.31472
$956$	18.9085	+	13.7378i	0.611545	+	0.444313i
$957$	9.03351	−	6.56323i	0.292012	−	0.212159i
$958$	0.411663	+	1.26697i	0.0133002	+	0.0409339i
$959$	−20.4712	+	63.0038i	−0.661049	+	2.03450i
$960$	19.0190	+	13.8181i	0.613837	+	0.445979i
$961$	−4.33556	−	13.3435i	−0.139857	−	0.430435i
$962$	−3.42194			−0.110328
$963$	11.2966			0.364027
$964$	9.50762	+	29.2614i	0.306220	+	0.942447i
$965$	−64.2553			−2.06845
$966$	−1.28245	−	3.94697i	−0.0412621	−	0.126992i
$967$	−14.1471	+	43.5404i	−0.454942	+	1.40017i	0.416262	+	0.909245i	$0.363340\pi$
$967$	−14.1471	+	43.5404i	−0.454942	+	1.40017i	−0.871204	+	0.490922i	$0.836660\pi$
$968$	0.249004	+	0.766356i	0.00800329	+	0.0246316i
$969$	−1.32028	−	0.959241i	−0.0424136	−	0.0308153i
$970$	0.414554	−	1.27587i	0.0133105	−	0.0409656i
$971$	−17.1817	+	52.8798i	−0.551387	+	1.69699i	0.153913	+	0.988084i	$0.450812\pi$
$971$	−17.1817	+	52.8798i	−0.551387	+	1.69699i	−0.705300	+	0.708909i	$0.749188\pi$
$972$	6.89546	−	21.2220i	0.221172	−	0.680697i
$973$	6.74341	−	4.89938i	0.216184	−	0.157067i
$974$	−2.81750	+	2.04703i	−0.0902785	+	0.0655912i
$975$	7.83300			0.250857
$976$	−5.67152	+	28.7588i	−0.181541	+	0.920546i
$977$	−46.0158			−1.47217			−0.736087	−	0.676886i	$-0.763329\pi$
$977$	−46.0158			−1.47217			−0.736087	+	0.676886i	$0.763329\pi$
$978$	1.63491	−	1.18783i	0.0522787	−	0.0379827i
$979$	−9.45984	+	6.87298i	−0.302338	+	0.219661i
$980$	3.70859	−	11.4139i	0.118467	−	0.364603i
$981$	2.03544	−	6.26444i	0.0649866	−	0.200008i
$982$	−0.234730	+	0.722424i	−0.00749053	+	0.0230535i
$983$	−19.7530	−	14.3514i	−0.630022	−	0.457738i	0.226386	−	0.974038i	$-0.427309\pi$
$983$	−19.7530	−	14.3514i	−0.630022	−	0.457738i	−0.856408	+	0.516300i	$0.827309\pi$
$984$	2.55671	+	7.86873i	0.0815048	+	0.250846i
$985$	13.6479	−	42.0040i	0.434859	−	1.33836i
$986$	2.98844	+	9.19748i	0.0951714	+	0.292907i
$987$	−11.6254			−0.370042
$988$	−0.646059	−	1.98837i	−0.0205539	−	0.0632584i
$989$	−12.6882			−0.403460
$990$	0.593009			0.0188471
$991$	1.72243	+	5.30111i	0.0547149	+	0.168395i	0.974680	−	0.223606i	$-0.0717829\pi$
$991$	1.72243	+	5.30111i	0.0547149	+	0.168395i	−0.919965	+	0.392001i	$0.871783\pi$
$992$	7.91703	+	5.75206i	0.251366	+	0.182628i
$993$	−10.9517	+	33.7058i	−0.347541	+	1.06962i
$994$	−1.46904	−	4.52124i	−0.0465951	−	0.143405i
$995$	11.1544	−	8.10414i	0.353618	−	0.256919i
$996$	−31.0088	−	22.5292i	−0.982552	−	0.713866i
$997$	30.9015			0.978661			0.489330	−	0.872098i	$-0.337241\pi$
$997$	30.9015			0.978661			0.489330	+	0.872098i	$0.337241\pi$
$998$	6.33862	−	4.60528i	0.200646	−	0.145778i
$999$	−5.77008	+	17.7585i	−0.182557	+	0.561854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.i.b.34.15	✓	108
61.9	even	5	inner	671.2.i.b.375.15	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.i.b.34.15	✓	108	1.1	even	1	trivial
671.2.i.b.375.15	yes	108	61.9	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.i (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.164681 - 0.119648i) q^{2} +(1.09278 - 0.793948i) q^{3} +(-0.605230 + 1.86271i) q^{4} +(-0.765842 + 2.35702i) q^{5} +(0.0849654 - 0.261497i) q^{6} +(-2.48994 - 1.80905i) q^{7} +(0.249004 + 0.766356i) q^{8} +(-0.363246 + 1.11796i) q^{9} +O(q^{10})\)	\(q+(0.164681 - 0.119648i) q^{2} +(1.09278 - 0.793948i) q^{3} +(-0.605230 + 1.86271i) q^{4} +(-0.765842 + 2.35702i) q^{5} +(0.0849654 - 0.261497i) q^{6} +(-2.48994 - 1.80905i) q^{7} +(0.249004 + 0.766356i) q^{8} +(-0.363246 + 1.11796i) q^{9} +(0.155893 + 0.479788i) q^{10} -1.00000 q^{11} +(0.817511 + 2.51604i) q^{12} -5.07770 q^{13} -0.626496 q^{14} +(1.03446 + 3.18373i) q^{15} +(-3.03632 - 2.20602i) q^{16} +(1.77596 - 5.46584i) q^{17} +(0.0739413 + 0.227568i) q^{18} +(0.170076 - 0.123567i) q^{19} +(-3.92692 - 2.85308i) q^{20} -4.15724 q^{21} +(-0.164681 + 0.119648i) q^{22} +(-1.51548 + 4.66416i) q^{23} +(0.880552 + 0.639758i) q^{24} +(-0.923943 - 0.671284i) q^{25} +(-0.836202 + 0.607536i) q^{26} +(1.74286 + 5.36398i) q^{27} +(4.87671 - 3.54314i) q^{28} -8.26657 q^{29} +(0.551282 + 0.400530i) q^{30} +(-3.33270 - 2.42135i) q^{31} -2.37556 q^{32} +(-1.09278 + 0.793948i) q^{33} +(-0.361509 - 1.11261i) q^{34} +(6.17087 - 4.48340i) q^{35} +(-1.86257 - 1.35324i) q^{36} +(2.67841 + 1.94598i) q^{37} +(0.0132237 - 0.0406984i) q^{38} +(-5.54879 + 4.03143i) q^{39} -1.99701 q^{40} +(6.14977 + 4.46807i) q^{41} +(-0.684619 + 0.497405i) q^{42} +(0.799492 + 2.46058i) q^{43} +(0.605230 - 1.86271i) q^{44} +(-2.35685 - 1.71236i) q^{45} +(0.308486 + 0.949422i) q^{46} +2.79643 q^{47} -5.06949 q^{48} +(0.764037 + 2.35146i) q^{49} -0.232474 q^{50} +(-2.39887 - 7.38296i) q^{51} +(3.07318 - 9.45826i) q^{52} +(2.99856 + 9.22861i) q^{53} +(0.928805 + 0.674816i) q^{54} +(0.765842 - 2.35702i) q^{55} +(0.766369 - 2.35864i) q^{56} +(0.0877487 - 0.270063i) q^{57} +(-1.36135 + 0.989077i) q^{58} +(0.146575 - 0.106493i) q^{59} -6.55644 q^{60} +(-3.28145 - 7.08746i) q^{61} -0.838542 q^{62} +(2.92690 - 2.12652i) q^{63} +(5.68144 - 4.12781i) q^{64} +(3.88872 - 11.9682i) q^{65} +(-0.0849654 + 0.261497i) q^{66} +(-4.76398 + 14.6620i) q^{67} +(9.10639 + 6.61618i) q^{68} +(2.04702 + 6.30008i) q^{69} +(0.479797 - 1.47666i) q^{70} +(2.34485 + 7.21672i) q^{71} -0.947201 q^{72} +(1.11008 + 3.41646i) q^{73} +0.673915 q^{74} -1.54263 q^{75} +(0.127235 + 0.391588i) q^{76} +(2.48994 + 1.80905i) q^{77} +(-0.431429 + 1.32780i) q^{78} +(3.47680 + 10.7005i) q^{79} +(7.52498 - 5.46722i) q^{80} +(3.31031 + 2.40508i) q^{81} +1.54735 q^{82} +(-11.7213 + 8.51599i) q^{83} +(2.51609 - 7.74371i) q^{84} +(11.5230 + 8.37195i) q^{85} +(0.426065 + 0.309554i) q^{86} +(-9.03351 + 6.56323i) q^{87} +(-0.249004 - 0.766356i) q^{88} +(9.45984 - 6.87298i) q^{89} -0.593009 q^{90} +(12.6432 + 9.18582i) q^{91} +(-7.77074 - 5.64577i) q^{92} -5.56432 q^{93} +(0.460519 - 0.334587i) q^{94} +(0.160999 + 0.495505i) q^{95} +(-2.59595 + 1.88607i) q^{96} +(-2.15136 - 1.56306i) q^{97} +(0.407170 + 0.295827i) q^{98} +(0.363246 - 1.11796i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 2 q^{3} - 34 q^{4} + 4 q^{5} + 6 q^{6} + 10 q^{7} - 18 q^{8} - 25 q^{9}+O(q^{10}) \) 108 * q - 2 * q^3 - 34 * q^4 + 4 * q^5 + 6 * q^6 + 10 * q^7 - 18 * q^8 - 25 * q^9	\( 108 q - 2 q^{3} - 34 q^{4} + 4 q^{5} + 6 q^{6} + 10 q^{7} - 18 q^{8} - 25 q^{9} + 6 q^{10} - 108 q^{11} - 15 q^{12} - 26 q^{13} + 2 q^{14} + 8 q^{15} - 40 q^{16} + 4 q^{17} + 50 q^{18} + 8 q^{19} + 8 q^{20} - 64 q^{21} - 3 q^{23} + 71 q^{24} - 7 q^{25} + 29 q^{26} - 8 q^{27} + 42 q^{28} - 40 q^{29} - 36 q^{30} - 7 q^{31} - 6 q^{32} + 2 q^{33} - 4 q^{34} + 2 q^{35} + 30 q^{36} - 32 q^{37} - 3 q^{38} + 10 q^{39} - 154 q^{40} + 10 q^{41} - 36 q^{42} - 29 q^{43} + 34 q^{44} - 23 q^{45} + 45 q^{46} + 40 q^{47} + 140 q^{48} - 15 q^{49} + 6 q^{50} - 25 q^{51} - 7 q^{52} + 15 q^{53} - 2 q^{54} - 4 q^{55} + 35 q^{56} + 20 q^{57} + 77 q^{58} + 22 q^{59} + 72 q^{60} + 20 q^{61} + 80 q^{62} - 6 q^{63} - 30 q^{64} + 56 q^{65} - 6 q^{66} - 4 q^{67} - 109 q^{68} - 46 q^{69} + 41 q^{70} + 7 q^{71} - 264 q^{72} - 16 q^{73} - 44 q^{74} - 6 q^{75} + 22 q^{76} - 10 q^{77} - 60 q^{78} + 79 q^{79} + 57 q^{80} - 25 q^{81} - 28 q^{82} + 2 q^{83} + 87 q^{84} + 30 q^{85} - 10 q^{86} - 38 q^{87} + 18 q^{88} + 18 q^{89} + 62 q^{90} - 30 q^{91} - 6 q^{92} - 24 q^{93} - 16 q^{94} - 10 q^{95} + 65 q^{96} + 16 q^{97} + 9 q^{98} + 25 q^{99}+O(q^{100}) \) 108 * q - 2 * q^3 - 34 * q^4 + 4 * q^5 + 6 * q^6 + 10 * q^7 - 18 * q^8 - 25 * q^9 + 6 * q^10 - 108 * q^11 - 15 * q^12 - 26 * q^13 + 2 * q^14 + 8 * q^15 - 40 * q^16 + 4 * q^17 + 50 * q^18 + 8 * q^19 + 8 * q^20 - 64 * q^21 - 3 * q^23 + 71 * q^24 - 7 * q^25 + 29 * q^26 - 8 * q^27 + 42 * q^28 - 40 * q^29 - 36 * q^30 - 7 * q^31 - 6 * q^32 + 2 * q^33 - 4 * q^34 + 2 * q^35 + 30 * q^36 - 32 * q^37 - 3 * q^38 + 10 * q^39 - 154 * q^40 + 10 * q^41 - 36 * q^42 - 29 * q^43 + 34 * q^44 - 23 * q^45 + 45 * q^46 + 40 * q^47 + 140 * q^48 - 15 * q^49 + 6 * q^50 - 25 * q^51 - 7 * q^52 + 15 * q^53 - 2 * q^54 - 4 * q^55 + 35 * q^56 + 20 * q^57 + 77 * q^58 + 22 * q^59 + 72 * q^60 + 20 * q^61 + 80 * q^62 - 6 * q^63 - 30 * q^64 + 56 * q^65 - 6 * q^66 - 4 * q^67 - 109 * q^68 - 46 * q^69 + 41 * q^70 + 7 * q^71 - 264 * q^72 - 16 * q^73 - 44 * q^74 - 6 * q^75 + 22 * q^76 - 10 * q^77 - 60 * q^78 + 79 * q^79 + 57 * q^80 - 25 * q^81 - 28 * q^82 + 2 * q^83 + 87 * q^84 + 30 * q^85 - 10 * q^86 - 38 * q^87 + 18 * q^88 + 18 * q^89 + 62 * q^90 - 30 * q^91 - 6 * q^92 - 24 * q^93 - 16 * q^94 - 10 * q^95 + 65 * q^96 + 16 * q^97 + 9 * q^98 + 25 * q^99

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