LMFDB - Embedded newform 61.2.g.a.27.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,2,Mod(3,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("61.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	61.g (of order $10$, 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:	$0.487087452330$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 17x^{14} + 111x^{12} + 361x^{10} + 624x^{8} + 558x^{6} + 229x^{4} + 34x^{2} + 1 $ x^16 + 17x^14 + 111x^12 + 361x^10 + 624x^8 + 558x^6 + 229x^4 + 34*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			27.4
Root			$-1.46081i$ of defining polynomial
Character	$\chi$	$=$	61.27
Dual form			61.2.g.a.52.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.858642 + 1.18182i) q^{2} +(-1.89518 + 1.37693i) q^{3} +(-0.0413973 + 0.127408i) q^{4} +(-0.701732 + 2.15971i) q^{5} +(-3.25455 - 1.05747i) q^{6} +(2.88318 - 3.96835i) q^{7} +(2.59251 - 0.842356i) q^{8} +(0.768714 - 2.36586i) q^{9} +O(q^{10})$	\(q+(0.858642 + 1.18182i) q^{2} +(-1.89518 + 1.37693i) q^{3} +(-0.0413973 + 0.127408i) q^{4} +(-0.701732 + 2.15971i) q^{5} +(-3.25455 - 1.05747i) q^{6} +(2.88318 - 3.96835i) q^{7} +(2.59251 - 0.842356i) q^{8} +(0.768714 - 2.36586i) q^{9} +(-3.15492 + 1.02510i) q^{10} +0.886190i q^{11} +(-0.0969759 - 0.298461i) q^{12} -4.51165 q^{13} +7.16550 q^{14} +(-1.64385 - 5.05926i) q^{15} +(3.43831 + 2.49808i) q^{16} +(-5.01435 - 1.62926i) q^{17} +(3.45607 - 1.12295i) q^{18} +(2.88412 - 2.09543i) q^{19} +(-0.246114 - 0.178812i) q^{20} +11.4906i q^{21} +(-1.04732 + 0.760921i) q^{22} +(-0.910439 - 0.295820i) q^{23} +(-3.75339 + 5.16610i) q^{24} +(-0.126831 - 0.0921481i) q^{25} +(-3.87389 - 5.33196i) q^{26} +(-0.370914 - 1.14156i) q^{27} +(0.386243 + 0.531618i) q^{28} -0.133483i q^{29} +(4.56765 - 6.28683i) q^{30} +(-1.85187 + 2.54888i) q^{31} +0.756570i q^{32} +(-1.22022 - 1.67949i) q^{33} +(-2.38004 - 7.32501i) q^{34} +(6.54727 + 9.01154i) q^{35} +(0.269606 + 0.195880i) q^{36} +(-4.33901 + 5.97214i) q^{37} +(4.95285 + 1.60928i) q^{38} +(8.55037 - 6.21221i) q^{39} +6.19017i q^{40} +(3.13514 + 2.27781i) q^{41} +(-13.5799 + 9.86635i) q^{42} +(-1.59245 + 0.517419i) q^{43} +(-0.112908 - 0.0366859i) q^{44} +(4.57014 + 3.32040i) q^{45} +(-0.432136 - 1.32998i) q^{46} +4.07030 q^{47} -9.95586 q^{48} +(-5.27200 - 16.2255i) q^{49} -0.229014i q^{50} +(11.7464 - 3.81665i) q^{51} +(0.186770 - 0.574819i) q^{52} +(0.335279 - 0.108939i) q^{53} +(1.03063 - 1.41854i) q^{54} +(-1.91391 - 0.621868i) q^{55} +(4.13189 - 12.7166i) q^{56} +(-2.58065 + 7.94243i) q^{57} +(0.157753 - 0.114614i) q^{58} +(-0.654495 - 0.900835i) q^{59} +0.712640 q^{60} +(6.44483 + 4.41182i) q^{61} -4.60241 q^{62} +(-7.17223 - 9.87172i) q^{63} +(5.98249 - 4.34653i) q^{64} +(3.16597 - 9.74386i) q^{65} +(0.937119 - 2.88416i) q^{66} +(-6.70844 - 2.17970i) q^{67} +(0.415161 - 0.571420i) q^{68} +(2.13276 - 0.692977i) q^{69} +(-5.02826 + 15.4754i) q^{70} +(-14.8034 + 4.80990i) q^{71} -6.78104i q^{72} +(1.11393 + 3.42832i) q^{73} -10.7836 q^{74} +0.367248 q^{75} +(0.147580 + 0.454204i) q^{76} +(3.51672 + 2.55504i) q^{77} +(14.6834 + 4.77093i) q^{78} +(1.13976 - 0.370331i) q^{79} +(-7.80789 + 5.67276i) q^{80} +(8.31234 + 6.03927i) q^{81} +5.66099i q^{82} +(1.81433 - 1.31819i) q^{83} +(-1.46400 - 0.475681i) q^{84} +(7.03746 - 9.68623i) q^{85} +(-1.97884 - 1.43771i) q^{86} +(0.183796 + 0.252974i) q^{87} +(0.746488 + 2.29745i) q^{88} +(8.54135 + 11.7562i) q^{89} +8.25211i q^{90} +(-13.0079 + 17.9038i) q^{91} +(0.0753794 - 0.103751i) q^{92} -7.38045i q^{93} +(3.49493 + 4.81036i) q^{94} +(2.50165 + 7.69929i) q^{95} +(-1.04174 - 1.43383i) q^{96} +(2.66713 + 1.93779i) q^{97} +(14.6489 - 20.1625i) q^{98} +(2.09660 + 0.681227i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9	$ 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9} - 5 q^{10} - 12 q^{13} - 18 q^{14} - 13 q^{15} + 19 q^{16} - 10 q^{18} + 3 q^{19} - 13 q^{20} + 19 q^{22} - 15 q^{23} + 10 q^{24} - 2 q^{25} + 10 q^{26} - 4 q^{27} + 35 q^{28} + 45 q^{30} - 15 q^{31} + 25 q^{33} - 14 q^{34} + 10 q^{35} + 37 q^{36} - 5 q^{37} - 15 q^{38} - 3 q^{39} + 12 q^{41} - 15 q^{42} - 25 q^{43} - 50 q^{44} + 36 q^{45} + 27 q^{46} + 6 q^{47} - 20 q^{48} - 30 q^{49} + 50 q^{51} - 46 q^{52} - 20 q^{53} - 20 q^{54} + 20 q^{55} - 28 q^{56} - 11 q^{57} - 41 q^{58} + 5 q^{59} + 14 q^{60} - 53 q^{61} + 16 q^{62} - 5 q^{63} + 17 q^{64} + 20 q^{65} + 13 q^{66} - 55 q^{67} + 80 q^{68} - 15 q^{69} - 17 q^{70} - 50 q^{71} - 11 q^{73} + 24 q^{74} - 88 q^{75} - 19 q^{76} + 63 q^{77} + 50 q^{78} + 40 q^{79} - 49 q^{80} - 19 q^{81} + 31 q^{83} - 25 q^{84} + 55 q^{85} + 35 q^{86} + 25 q^{87} + 27 q^{88} + 60 q^{89} - 15 q^{91} - 5 q^{92} + 65 q^{94} + 48 q^{95} - 25 q^{96} + 45 q^{97} + 10 q^{98} - 5 q^{99}+O(q^{100}) $ 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9 - 5 * q^10 - 12 * q^13 - 18 * q^14 - 13 * q^15 + 19 * q^16 - 10 * q^18 + 3 * q^19 - 13 * q^20 + 19 * q^22 - 15 * q^23 + 10 * q^24 - 2 * q^25 + 10 * q^26 - 4 * q^27 + 35 * q^28 + 45 * q^30 - 15 * q^31 + 25 * q^33 - 14 * q^34 + 10 * q^35 + 37 * q^36 - 5 * q^37 - 15 * q^38 - 3 * q^39 + 12 * q^41 - 15 * q^42 - 25 * q^43 - 50 * q^44 + 36 * q^45 + 27 * q^46 + 6 * q^47 - 20 * q^48 - 30 * q^49 + 50 * q^51 - 46 * q^52 - 20 * q^53 - 20 * q^54 + 20 * q^55 - 28 * q^56 - 11 * q^57 - 41 * q^58 + 5 * q^59 + 14 * q^60 - 53 * q^61 + 16 * q^62 - 5 * q^63 + 17 * q^64 + 20 * q^65 + 13 * q^66 - 55 * q^67 + 80 * q^68 - 15 * q^69 - 17 * q^70 - 50 * q^71 - 11 * q^73 + 24 * q^74 - 88 * q^75 - 19 * q^76 + 63 * q^77 + 50 * q^78 + 40 * q^79 - 49 * q^80 - 19 * q^81 + 31 * q^83 - 25 * q^84 + 55 * q^85 + 35 * q^86 + 25 * q^87 + 27 * q^88 + 60 * q^89 - 15 * q^91 - 5 * q^92 + 65 * q^94 + 48 * q^95 - 25 * q^96 + 45 * q^97 + 10 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.858642	+	1.18182i	0.607152	+	0.835673i	0.996339	−	0.0854858i	$-0.0272442\pi$
$2$	0.858642	+	1.18182i	0.607152	+	0.835673i	−0.389188	+	0.921159i	$0.627244\pi$
$3$	−1.89518	+	1.37693i	−1.09418	+	0.794968i	−0.980100	−	0.198503i	$-0.936392\pi$
$3$	−1.89518	+	1.37693i	−1.09418	+	0.794968i	−0.114080	+	0.993472i	$0.536392\pi$
$4$	−0.0413973	+	0.127408i	−0.0206986	+	0.0637039i
$5$	−0.701732	+	2.15971i	−0.313824	+	0.965851i	0.662412	+	0.749140i	$0.269533\pi$
$5$	−0.701732	+	2.15971i	−0.313824	+	0.965851i	−0.976236	+	0.216711i	$0.930467\pi$
$6$	−3.25455	−	1.05747i	−1.32867	−	0.431710i
$7$	2.88318	−	3.96835i	1.08974	−	1.49990i	0.241412	−	0.970423i	$-0.422389\pi$
$7$	2.88318	−	3.96835i	1.08974	−	1.49990i	0.848326	−	0.529474i	$-0.177611\pi$
$8$	2.59251	−	0.842356i	0.916589	−	0.297818i
$9$	0.768714	−	2.36586i	0.256238	−	0.788620i
$10$	−3.15492	+	1.02510i	−0.997674	+	0.324164i
$11$			0.886190i			0.267196i	0.991036	+	0.133598i	$0.0426532\pi$
$11$			0.886190i			0.267196i	−0.991036	+	0.133598i	$0.957347\pi$
$12$	−0.0969759	−	0.298461i	−0.0279945	−	0.0861583i
$13$	−4.51165			−1.25131			−0.625653	−	0.780101i	$-0.715168\pi$
$13$	−4.51165			−1.25131			−0.625653	+	0.780101i	$0.715168\pi$
$14$	7.16550			1.91506
$15$	−1.64385	−	5.05926i	−0.424441	−	1.30630i
$16$	3.43831	+	2.49808i	0.859577	+	0.624519i
$17$	−5.01435	−	1.62926i	−1.21616	−	0.395154i	−0.370477	−	0.928842i	$-0.620806\pi$
$17$	−5.01435	−	1.62926i	−1.21616	−	0.395154i	−0.845681	+	0.533688i	$0.820806\pi$
$18$	3.45607	−	1.12295i	0.814603	−	0.264681i
$19$	2.88412	−	2.09543i	0.661662	−	0.480726i	−0.205562	−	0.978644i	$-0.565902\pi$
$19$	2.88412	−	2.09543i	0.661662	−	0.480726i	0.867224	+	0.497918i	$0.165902\pi$
$20$	−0.246114	−	0.178812i	−0.0550327	−	0.0399836i
$21$			11.4906i			2.50746i
$22$	−1.04732	+	0.760921i	−0.223289	+	0.162229i
$23$	−0.910439	−	0.295820i	−0.189840	−	0.0616827i	0.212554	−	0.977149i	$-0.431822\pi$
$23$	−0.910439	−	0.295820i	−0.189840	−	0.0616827i	−0.402394	+	0.915467i	$0.631822\pi$
$24$	−3.75339	+	5.16610i	−0.766158	+	1.05453i
$25$	−0.126831	−	0.0921481i	−0.0253662	−	0.0184296i
$26$	−3.87389	−	5.33196i	−0.759733	−	1.04568i
$27$	−0.370914	−	1.14156i	−0.0713824	−	0.219693i
$28$	0.386243	+	0.531618i	0.0729931	+	0.100466i
$29$		−	0.133483i		−	0.0247872i	−0.999923	−	0.0123936i	$-0.996055\pi$
$29$		−	0.133483i		−	0.0247872i	0.999923	−	0.0123936i	$-0.00394510\pi$
$30$	4.56765	−	6.28683i	0.833935	−	1.14781i
$31$	−1.85187	+	2.54888i	−0.332605	+	0.457792i	−0.942263	−	0.334873i	$-0.891307\pi$
$31$	−1.85187	+	2.54888i	−0.332605	+	0.457792i	0.609658	+	0.792664i	$0.291307\pi$
$32$			0.756570i			0.133744i
$33$	−1.22022	−	1.67949i	−0.212413	−	0.292361i
$34$	−2.38004	−	7.32501i	−0.408173	−	1.25623i
$35$	6.54727	+	9.01154i	1.10669	+	1.52323i
$36$	0.269606	+	0.195880i	0.0449344	+	0.0326467i
$37$	−4.33901	+	5.97214i	−0.713329	+	0.981813i	0.286390	+	0.958113i	$0.407545\pi$
$37$	−4.33901	+	5.97214i	−0.713329	+	0.981813i	−0.999719	+	0.0237001i	$0.992455\pi$
$38$	4.95285	+	1.60928i	0.803459	+	0.261060i
$39$	8.55037	−	6.21221i	1.36915	−	0.994749i
$40$			6.19017i			0.978752i
$41$	3.13514	+	2.27781i	0.489626	+	0.355734i	0.805041	−	0.593220i	$-0.202143\pi$
$41$	3.13514	+	2.27781i	0.489626	+	0.355734i	−0.315414	+	0.948954i	$0.602143\pi$
$42$	−13.5799	+	9.86635i	−2.09542	+	1.52241i
$43$	−1.59245	+	0.517419i	−0.242847	+	0.0789056i	−0.427911	−	0.903821i	$-0.640750\pi$
$43$	−1.59245	+	0.517419i	−0.242847	+	0.0789056i	0.185065	+	0.982726i	$0.440750\pi$
$44$	−0.112908	−	0.0366859i	−0.0170215	−	0.00553060i
$45$	4.57014	+	3.32040i	0.681276	+	0.494976i
$46$	−0.432136	−	1.32998i	−0.0637150	−	0.196095i
$47$	4.07030			0.593714			0.296857	−	0.954922i	$-0.404062\pi$
$47$	4.07030			0.593714			0.296857	+	0.954922i	$0.404062\pi$
$48$	−9.95586			−1.43700
$49$	−5.27200	−	16.2255i	−0.753142	−	2.31793i
$50$		−	0.229014i		−	0.0323874i
$51$	11.7464	−	3.81665i	1.64483	−	0.534438i
$52$	0.186770	−	0.574819i	0.0259004	−	0.0797131i
$53$	0.335279	−	0.108939i	0.0460541	−	0.0149639i	−0.285899	−	0.958260i	$-0.592292\pi$
$53$	0.335279	−	0.108939i	0.0460541	−	0.0149639i	0.331953	+	0.943296i	$0.392292\pi$
$54$	1.03063	−	1.41854i	0.140251	−	0.193039i
$55$	−1.91391	−	0.621868i	−0.258072	−	0.0838527i
$56$	4.13189	−	12.7166i	0.552147	−	1.69933i
$57$	−2.58065	+	7.94243i	−0.341816	+	1.05200i
$58$	0.157753	−	0.114614i	0.0207140	−	0.0150496i
$59$	−0.654495	−	0.900835i	−0.0852080	−	0.117279i	0.764285	−	0.644879i	$-0.223092\pi$
$59$	−0.654495	−	0.900835i	−0.0852080	−	0.117279i	−0.849493	+	0.527600i	$0.823092\pi$
$60$	0.712640			0.0920014
$61$	6.44483	+	4.41182i	0.825176	+	0.564876i
$61$	6.44483	+	4.41182i	0.825176	+	0.564876i
$62$	−4.60241			−0.584506
$63$	−7.17223	−	9.87172i	−0.903615	−	1.24372i
$64$	5.98249	−	4.34653i	0.747811	−	0.543316i
$65$	3.16597	−	9.74386i	0.392690	−	1.20858i
$66$	0.937119	−	2.88416i	0.115351	−	0.355015i
$67$	−6.70844	−	2.17970i	−0.819566	−	0.266293i	−0.130922	−	0.991393i	$-0.541794\pi$
$67$	−6.70844	−	2.17970i	−0.819566	−	0.266293i	−0.688644	+	0.725099i	$0.741794\pi$
$68$	0.415161	−	0.571420i	0.0503456	−	0.0692948i
$69$	2.13276	−	0.692977i	0.256755	−	0.0834246i
$70$	−5.02826	+	15.4754i	−0.600992	+	1.84966i
$71$	−14.8034	+	4.80990i	−1.75684	+	0.570830i	−0.996865	−	0.0791270i	$-0.974787\pi$
$71$	−14.8034	+	4.80990i	−1.75684	+	0.570830i	−0.759971	+	0.649957i	$0.774787\pi$
$72$		−	6.78104i		−	0.799153i
$73$	1.11393	+	3.42832i	0.130376	+	0.401255i	0.994842	−	0.101435i	$-0.0323435\pi$
$73$	1.11393	+	3.42832i	0.130376	+	0.401255i	−0.864466	+	0.502691i	$0.832344\pi$
$74$	−10.7836			−1.25357
$75$	0.367248			0.0424062
$76$	0.147580	+	0.454204i	0.0169286	+	0.0521008i
$77$	3.51672	+	2.55504i	0.400767	+	0.291174i
$78$	14.6834	+	4.77093i	1.66257	+	0.540202i
$79$	1.13976	−	0.370331i	0.128233	−	0.0416655i	−0.244197	−	0.969726i	$-0.578524\pi$
$79$	1.13976	−	0.370331i	0.128233	−	0.0416655i	0.372431	+	0.928060i	$0.378524\pi$
$80$	−7.80789	+	5.67276i	−0.872949	+	0.634234i
$81$	8.31234	+	6.03927i	0.923594	+	0.671030i
$82$			5.66099i			0.625152i
$83$	1.81433	−	1.31819i	0.199149	−	0.144690i	−0.483742	−	0.875211i	$-0.660723\pi$
$83$	1.81433	−	1.31819i	0.199149	−	0.144690i	0.682890	+	0.730521i	$0.260723\pi$
$84$	−1.46400	−	0.475681i	−0.159735	−	0.0519011i
$85$	7.03746	−	9.68623i	0.763319	−	1.05062i
$86$	−1.97884	−	1.43771i	−0.213384	−	0.155033i
$87$	0.183796	+	0.252974i	0.0197050	+	0.0271216i
$88$	0.746488	+	2.29745i	0.0795759	+	0.244909i
$89$	8.54135	+	11.7562i	0.905382	+	1.24615i	0.968719	+	0.248159i	$0.0798255\pi$
$89$	8.54135	+	11.7562i	0.905382	+	1.24615i	−0.0633377	+	0.997992i	$0.520175\pi$
$90$			8.25211i			0.869849i
$91$	−13.0079	+	17.9038i	−1.36360	+	1.87683i
$92$	0.0753794	−	0.103751i	0.00785885	−	0.0108168i
$93$		−	7.38045i		−	0.765317i
$94$	3.49493	+	4.81036i	0.360474	+	0.496151i
$95$	2.50165	+	7.69929i	0.256664	+	0.789931i
$96$	−1.04174	−	1.43383i	−0.106322	−	0.146340i
$97$	2.66713	+	1.93779i	0.270806	+	0.196752i	0.714897	−	0.699229i	$-0.246473\pi$
$97$	2.66713	+	1.93779i	0.270806	+	0.196752i	−0.444091	+	0.895982i	$0.646473\pi$
$98$	14.6489	−	20.1625i	1.47976	−	2.03672i
$99$	2.09660	+	0.681227i	0.210716	+	0.0684659i
$100$	0.0169908	−	0.0123446i	0.00169908	−	0.00123446i
$101$		−	7.05481i		−	0.701980i	−0.936379	−	0.350990i	$-0.885845\pi$
$101$		−	7.05481i		−	0.701980i	0.936379	−	0.350990i	$-0.114155\pi$
$102$	14.5966	+	10.6050i	1.44528	+	1.05005i
$103$	7.44971	−	5.41253i	0.734041	−	0.533312i	−0.156798	−	0.987631i	$-0.550117\pi$
$103$	7.44971	−	5.41253i	0.734041	−	0.533312i	0.890839	+	0.454318i	$0.150117\pi$
$104$	−11.6965	+	3.80042i	−1.14693	+	0.372662i
$105$	−24.8164	−	8.06335i	−2.42184	−	0.786903i
$106$	0.416631	+	0.302700i	0.0404668	+	0.0294008i
$107$	−3.69432	−	11.3699i	−0.357143	−	1.09917i	−0.954756	−	0.297389i	$-0.903884\pi$
$107$	−3.69432	−	11.3699i	−0.357143	−	1.09917i	0.597613	−	0.801784i	$-0.296116\pi$
$108$	0.160798			0.0154728
$109$	−2.15211			−0.206135			−0.103068	−	0.994674i	$-0.532866\pi$
$109$	−2.15211			−0.206135			−0.103068	+	0.994674i	$0.532866\pi$
$110$	−0.908431	−	2.79586i	−0.0866155	−	0.266575i
$111$		−	17.2927i		−	1.64135i
$112$	19.8265	−	6.44202i	1.87343	−	0.608714i
$113$	−4.39705	+	13.5327i	−0.413640	+	1.27305i	0.499823	+	0.866128i	$0.333399\pi$
$113$	−4.39705	+	13.5327i	−0.413640	+	1.27305i	−0.913462	+	0.406924i	$0.866601\pi$
$114$	−11.6024	+	3.76984i	−1.08666	+	0.353078i
$115$	1.27777	−	1.75870i	0.119153	−	0.163999i
$116$	0.0170068	+	0.00552584i	0.00157904	+	0.000513061i
$117$	−3.46817	+	10.6739i	−0.320633	+	0.986805i
$118$	0.502648	−	1.54699i	0.0462725	−	0.142412i
$119$	−20.9227	+	15.2013i	−1.91798	+	1.39350i
$120$	−8.52340	−	11.7315i	−0.778076	−	1.07093i
$121$	10.2147			0.928606
$122$	0.319821	+	11.4048i	0.0289552	+	1.03254i
$123$	−9.07801			−0.818537
$124$	−0.248085	−	0.341459i	−0.0222786	−	0.0306639i
$125$	−8.89778	+	6.46461i	−0.795841	+	0.578213i
$126$	5.50822	−	16.9526i	0.490711	−	1.51025i
$127$	−2.06158	+	6.34488i	−0.182935	+	0.563017i	−0.999907	−	0.0136610i	$-0.995651\pi$
$127$	−2.06158	+	6.34488i	−0.182935	+	0.563017i	0.816971	+	0.576678i	$0.195651\pi$
$128$	11.7127	+	3.80569i	1.03527	+	0.336379i
$129$	2.30553	−	3.17329i	0.202990	−	0.279392i
$130$	14.2339	−	4.62488i	1.24840	−	0.405629i
$131$	1.49948	−	4.61491i	0.131010	−	0.403207i	−0.863938	−	0.503598i	$-0.832009\pi$
$131$	1.49948	−	4.61491i	0.131010	−	0.403207i	0.994948	+	0.100391i	$0.0320094\pi$
$132$	0.264493	−	0.0859391i	0.0230212	−	0.00748004i
$133$		−	17.4867i		−	1.51629i
$134$	−3.18413	−	9.79975i	−0.275067	−	0.846570i
$135$	2.72571			0.234592
$136$	−14.3721			−1.23240
$137$	−4.56572	−	14.0518i	−0.390076	−	1.20053i	−0.932731	−	0.360574i	$-0.882581\pi$
$137$	−4.56572	−	14.0518i	−0.390076	−	1.20053i	0.542655	−	0.839956i	$-0.317419\pi$
$138$	2.65025	+	1.92552i	0.225605	+	0.163911i
$139$	20.4076	+	6.63082i	1.73095	+	0.562419i	0.993586	−	0.113079i	$-0.0360715\pi$
$139$	20.4076	+	6.63082i	1.73095	+	0.562419i	0.737361	+	0.675498i	$0.236071\pi$
$140$	−1.41918	+	0.461120i	−0.119943	+	0.0389717i
$141$	−7.71393	+	5.60450i	−0.649630	+	0.471984i
$142$	−18.3952	−	13.3649i	−1.54369	−	1.12156i
$143$		−	3.99818i		−	0.334345i
$144$	8.55318	−	6.21425i	0.712765	−	0.517854i
$145$	0.288285	+	0.0936693i	0.0239407	+	0.00777882i
$146$	−3.09519	+	4.26017i	−0.256160	+	0.352574i
$147$	32.3327	+	23.4911i	2.66676	+	1.93751i
$148$	−0.581273	−	0.800054i	−0.0477804	−	0.0657640i
$149$	2.63754	+	8.11751i	0.216076	+	0.665013i	0.999075	+	0.0429906i	$0.0136886\pi$
$149$	2.63754	+	8.11751i	0.216076	+	0.665013i	−0.783000	+	0.622022i	$0.786311\pi$
$150$	0.315335	+	0.434021i	0.0257470	+	0.0354377i
$151$		−	12.5964i		−	1.02508i	−0.858664	−	0.512539i	$-0.828705\pi$
$151$		−	12.5964i		−	1.02508i	0.858664	−	0.512539i	$-0.171295\pi$
$152$	5.71199	−	7.86188i	0.463304	−	0.637683i
$153$	−7.70920	+	10.6108i	−0.623252	+	0.857833i
$154$			6.34999i			0.511697i
$155$	−4.20532	−	5.78813i	−0.337779	−	0.464913i
$156$	0.437521	+	1.34655i	0.0350297	+	0.107810i
$157$	−13.5427	−	18.6399i	−1.08082	−	1.48762i	−0.858613	−	0.512624i	$-0.828674\pi$
$157$	−13.5427	−	18.6399i	−1.08082	−	1.48762i	−0.222208	−	0.974999i	$-0.571326\pi$
$158$	1.41631	+	1.02901i	0.112676	+	0.0818637i
$159$	−0.485412	+	0.668112i	−0.0384957	+	0.0529848i
$160$	−1.63397	−	0.530909i	−0.129177	−	0.0419721i
$161$	−3.79887	+	2.76004i	−0.299393	+	0.217522i
$162$			15.0093i			1.17924i
$163$	9.59418	+	6.97058i	0.751474	+	0.545978i	0.896283	−	0.443482i	$-0.146257\pi$
$163$	9.59418	+	6.97058i	0.751474	+	0.545978i	−0.144810	+	0.989460i	$0.546257\pi$
$164$	−0.419997	+	0.305146i	−0.0327963	+	0.0238279i
$165$	4.48347	−	1.45677i	0.349037	−	0.113409i
$166$	3.11572	+	1.01236i	0.241827	+	0.0785744i
$167$	−0.242634	−	0.176284i	−0.0187756	−	0.0136413i	0.578358	−	0.815783i	$-0.303694\pi$
$167$	−0.242634	−	0.176284i	−0.0187756	−	0.0136413i	−0.597133	+	0.802142i	$0.703694\pi$
$168$	9.67922	+	29.7896i	0.746768	+	2.29831i
$169$	7.35500			0.565769
$170$	17.4900			1.34142
$171$	−2.74044	−	8.43421i	−0.209567	−	0.644980i
$172$		−	0.224310i		−	0.0171035i
$173$	−4.00896	+	1.30259i	−0.304796	+	0.0990342i	−0.457422	−	0.889250i	$-0.651227\pi$
$173$	−4.00896	+	1.30259i	−0.304796	+	0.0990342i	0.152626	+	0.988284i	$0.451227\pi$
$174$	−0.141154	+	0.434428i	−0.0107009	+	0.0329339i
$175$	−0.731353	+	0.237631i	−0.0552851	+	0.0179632i
$176$	−2.21377	+	3.04700i	−0.166869	+	0.229676i
$177$	2.48077	+	0.806050i	0.186466	+	0.0605864i
$178$	−6.55970	+	20.1887i	−0.491670	+	1.51321i
$179$	4.30581	−	13.2519i	0.321832	−	0.990496i	−0.651019	−	0.759062i	$-0.725658\pi$
$179$	4.30581	−	13.2519i	0.321832	−	0.990496i	0.972850	−	0.231435i	$-0.0743419\pi$
$180$	−0.612236	+	0.444815i	−0.0456334	+	0.0331546i
$181$	−2.66221	−	3.66421i	−0.197880	−	0.272359i	0.698533	−	0.715578i	$-0.253836\pi$
$181$	−2.66221	−	3.66421i	−0.197880	−	0.272359i	−0.896413	+	0.443219i	$0.853836\pi$
$182$	−32.3282			−2.39633
$183$	−18.2888	+	0.512867i	−1.35195	+	0.0379122i
$184$	−2.60951			−0.192375
$185$	−9.85326	−	13.5618i	−0.724426	−	0.997087i
$186$	8.72237	−	6.33717i	0.639555	−	0.464664i
$187$	1.44383	−	4.44367i	0.105584	−	0.324953i
$188$	−0.168499	+	0.518588i	−0.0122891	+	0.0378219i
$189$	−5.59951	−	1.81939i	−0.407304	−	0.132341i
$190$	−6.95115	+	9.56744i	−0.504289	+	0.694095i
$191$	−16.1077	+	5.23371i	−1.16551	+	0.378698i	−0.826966	−	0.562252i	$-0.809935\pi$
$191$	−16.1077	+	5.23371i	−1.16551	+	0.378698i	−0.338546	+	0.940950i	$0.609935\pi$
$192$	−5.35301	+	16.4749i	−0.386320	+	1.18897i
$193$	6.11799	−	1.98786i	0.440383	−	0.143089i	−0.0804294	−	0.996760i	$-0.525629\pi$
$193$	6.11799	−	1.98786i	0.440383	−	0.143089i	0.520812	+	0.853671i	$0.325629\pi$
$194$			4.81594i			0.345764i
$195$	7.41649	+	22.8256i	0.531106	+	1.63458i
$196$	2.28551			0.163250
$197$	4.29801			0.306220			0.153110	−	0.988209i	$-0.451071\pi$
$197$	4.29801			0.306220			0.153110	+	0.988209i	$0.451071\pi$
$198$	0.995143	+	3.06274i	0.0707217	+	0.217659i
$199$	7.80834	+	5.67309i	0.553519	+	0.402155i	0.829081	−	0.559128i	$-0.188864\pi$
$199$	7.80834	+	5.67309i	0.553519	+	0.402155i	−0.275562	+	0.961283i	$0.588864\pi$
$200$	−0.406432	−	0.132058i	−0.0287391	−	0.00933789i
$201$	15.7150	−	5.10610i	1.10845	−	0.360156i
$202$	8.33751	−	6.05756i	0.586625	−	0.426208i
$203$	−0.529708	−	0.384855i	−0.0371782	−	0.0270115i
$204$			1.65459i			0.115844i
$205$	−7.11944	+	5.17258i	−0.497243	+	0.361268i
$206$	12.7933	+	4.15678i	0.891349	+	0.289617i
$207$	−1.39974	+	1.92657i	−0.0972883	+	0.133906i
$208$	−15.5124	−	11.2705i	−1.07559	−	0.781465i
$209$	1.85695	+	2.55588i	0.128448	+	0.176794i
$210$	−11.7790	−	36.2521i	−0.812830	−	2.50163i
$211$	6.11108	+	8.41118i	0.420704	+	0.579050i	0.965788	−	0.259332i	$-0.0835023\pi$
$211$	6.11108	+	8.41118i	0.420704	+	0.579050i	−0.545084	+	0.838381i	$0.683502\pi$
$212$			0.0472269i			0.00324356i
$213$	21.4321	−	29.4987i	1.46850	−	2.02122i
$214$	10.2651	−	14.1287i	0.701709	−	0.965820i
$215$		−	3.80232i		−	0.259316i
$216$	−1.92319	−	2.64705i	−0.130857	−	0.180109i
$217$	4.77558	+	14.6977i	0.324188	+	0.997747i
$218$	−1.84790	−	2.54341i	−0.125155	−	0.172261i
$219$	−6.83164	−	4.96348i	−0.461639	−	0.335401i
$220$	0.158462	−	0.218104i	0.0106835	−	0.0147046i
$221$	22.6230	+	7.35066i	1.52179	+	0.494459i
$222$	20.4369	−	14.8483i	1.37163	−	0.996551i
$223$		−	0.859294i		−	0.0575426i	−0.999586	−	0.0287713i	$-0.990841\pi$
$223$		−	0.859294i		−	0.0575426i	0.999586	−	0.0287713i	$-0.00915945\pi$
$224$	3.00234	+	2.18132i	0.200602	+	0.145746i
$225$	−0.315506	+	0.229229i	−0.0210338	+	0.0152819i
$226$	−19.7687	+	6.42325i	−1.31500	+	0.427268i
$227$	13.1164	+	4.26179i	0.870568	+	0.282865i	0.710035	−	0.704166i	$-0.248679\pi$
$227$	13.1164	+	4.26179i	0.870568	+	0.282865i	0.160532	+	0.987031i	$0.448679\pi$
$228$	−0.905095	−	0.657590i	−0.0599414	−	0.0435500i
$229$	−1.34271	−	4.13243i	−0.0887286	−	0.273078i	0.896840	−	0.442355i	$-0.145857\pi$
$229$	−1.34271	−	4.13243i	−0.0887286	−	0.273078i	−0.985569	+	0.169277i	$0.945857\pi$
$230$	3.17561			0.209394
$231$	−10.1829			−0.669985
$232$	−0.112440	−	0.346056i	−0.00738207	−	0.0227197i
$233$			13.6626i			0.895066i	0.894268	+	0.447533i	$0.147697\pi$
$233$			13.6626i			0.895066i	−0.894268	+	0.447533i	$0.852303\pi$
$234$	−15.5926	+	5.06634i	−1.01932	+	0.331197i
$235$	−2.85626	+	8.79066i	−0.186322	+	0.573439i
$236$	0.141868	−	0.0460956i	0.00923481	−	0.00300057i
$237$	−1.65013	+	2.27121i	−0.107187	+	0.147531i
$238$	−35.9303	−	11.6745i	−2.32901	−	0.756743i
$239$	6.32938	−	19.4798i	0.409414	−	1.26005i	−0.507739	−	0.861511i	$-0.669519\pi$
$239$	6.32938	−	19.4798i	0.409414	−	1.26005i	0.917153	−	0.398535i	$-0.130481\pi$
$240$	6.98635	−	21.5018i	0.450967	−	1.38793i
$241$	−1.14463	+	0.831621i	−0.0737320	+	0.0535694i	−0.624041	−	0.781392i	$-0.714510\pi$
$241$	−1.14463	+	0.831621i	−0.0737320	+	0.0535694i	0.550309	+	0.834961i	$0.314510\pi$
$242$	8.77074	+	12.0719i	0.563805	+	0.776011i
$243$	−20.4681			−1.31303
$244$	−0.828899	+	0.638484i	−0.0530648	+	0.0408747i
$245$	38.7420			2.47513
$246$	−7.79477	−	10.7286i	−0.496976	−	0.684029i
$247$	−13.0121	+	9.45387i	−0.827942	+	0.601535i
$248$	−2.65392	+	8.16792i	−0.168524	+	0.518663i
$249$	−1.62343	+	4.99640i	−0.102881	+	0.316634i
$250$	−15.2800	−	4.96478i	−0.966393	−	0.314000i
$251$	−0.244510	+	0.336539i	−0.0154333	+	0.0212422i	−0.816664	−	0.577114i	$-0.804179\pi$
$251$	−0.244510	+	0.336539i	−0.0154333	+	0.0212422i	0.801231	+	0.598356i	$0.204179\pi$
$252$	1.55464	−	0.505135i	0.0979334	−	0.0318205i
$253$	0.262153	−	0.806823i	0.0164814	−	0.0507245i
$254$	−9.26867	+	3.01157i	−0.581568	+	0.188963i
$255$			28.0472i			1.75638i
$256$	0.989177	+	3.04437i	0.0618236	+	0.190273i
$257$	4.91227			0.306419			0.153210	−	0.988194i	$-0.451039\pi$
$257$	4.91227			0.306419			0.153210	+	0.988194i	$0.451039\pi$
$258$	5.72987			0.356726
$259$	11.1894	+	34.4375i	0.695276	+	2.13984i
$260$	1.11038	+	0.806738i	0.0688629	+	0.0500318i
$261$	−0.315802	−	0.102610i	−0.0195477	−	0.00635142i
$262$	6.74151	−	2.19045i	0.416492	−	0.135326i
$263$	17.6059	−	12.7914i	1.08562	−	0.788752i	0.106969	−	0.994262i	$-0.465885\pi$
$263$	17.6059	−	12.7914i	1.08562	−	0.788752i	0.978655	+	0.205510i	$0.0658855\pi$
$264$	−4.57815	−	3.32622i	−0.281766	−	0.204715i
$265$			0.800551i			0.0491775i
$266$	20.6661	−	15.0148i	1.26712	−	0.920618i
$267$	−32.3747	−	10.5192i	−1.98130	−	0.643764i
$268$	0.555422	−	0.764473i	0.0339278	−	0.0466976i
$269$	−18.9980	−	13.8029i	−1.15833	−	0.841577i	−0.168765	−	0.985656i	$-0.553978\pi$
$269$	−18.9980	−	13.8029i	−1.15833	−	0.841577i	−0.989566	+	0.144080i	$0.953978\pi$
$270$	2.34041	+	3.22130i	0.142433	+	0.196042i
$271$	−5.91459	−	18.2032i	−0.359285	−	1.10577i	−0.953483	−	0.301448i	$-0.902530\pi$
$271$	−5.91459	−	18.2032i	−0.359285	−	1.10577i	0.594197	−	0.804319i	$-0.297470\pi$
$272$	−13.1709	−	18.1281i	−0.798600	−	1.09918i
$273$		−	51.8418i		−	3.13761i
$274$	12.6864	−	17.4614i	0.766414	−	1.05488i
$275$	0.0816608	−	0.112396i	0.00492433	−	0.00677776i
$276$			0.300418i			0.0180830i
$277$	−6.07270	−	8.35835i	−0.364873	−	0.502205i	0.586625	−	0.809859i	$-0.300456\pi$
$277$	−6.07270	−	8.35835i	−0.364873	−	0.502205i	−0.951498	+	0.307654i	$0.900456\pi$
$278$	9.68637	+	29.8116i	0.580950	+	1.78798i
$279$	4.60673	+	6.34062i	0.275798	+	0.379603i
$280$	24.5648	+	17.8474i	1.46803	+	1.06658i
$281$	−2.84188	+	3.91151i	−0.169532	+	0.233341i	−0.885326	−	0.464970i	$-0.846065\pi$
$281$	−2.84188	+	3.91151i	−0.169532	+	0.233341i	0.715794	+	0.698312i	$0.246065\pi$
$282$	−13.2470	−	4.30421i	−0.788848	−	0.256312i
$283$	−17.3784	+	12.6262i	−1.03304	+	0.750548i	−0.968915	−	0.247393i	$-0.920426\pi$
$283$	−17.3784	+	12.6262i	−1.03304	+	0.750548i	−0.0641261	+	0.997942i	$0.520426\pi$
$284$		−	2.08518i		−	0.123733i
$285$	−15.3424	−	11.1469i	−0.908806	−	0.660286i
$286$	4.72513	−	3.43301i	0.279403	−	0.202998i
$287$	18.0783	−	5.87400i	1.06713	−	0.346731i
$288$	1.78994	+	0.581586i	0.105473	+	0.0342703i
$289$	8.73591	+	6.34701i	0.513877	+	0.373353i
$290$	0.136833	+	0.421129i	0.00803511	+	0.0247295i
$291$	−7.72287			−0.452723
$292$	−0.482909			−0.0282601
$293$	6.40056	+	19.6989i	0.373925	+	1.15082i	0.944201	+	0.329369i	$0.106836\pi$
$293$	6.40056	+	19.6989i	0.373925	+	1.15082i	−0.570277	+	0.821453i	$0.693164\pi$
$294$			58.3819i			3.40490i
$295$	2.40482	−	0.781374i	0.140014	−	0.0454934i
$296$	−6.21825	+	19.1378i	−0.361428	+	1.11236i
$297$	1.01164	−	0.328700i	0.0587011	−	0.0190731i
$298$	−7.32873	+	10.0871i	−0.424542	+	0.584332i
$299$	4.10758	+	1.33464i	0.237548	+	0.0771839i
$300$	−0.0152031	+	0.0467903i	−0.000877750	+	0.00270144i
$301$	−2.53802	+	7.81122i	−0.146289	+	0.450231i
$302$	14.8866	−	10.8158i	0.856630	−	0.622378i
$303$	9.71394	+	13.3701i	0.558052	+	0.768092i
$304$	15.1510			0.868972
$305$	−14.0508	+	10.8230i	−0.804546	+	0.619725i
$306$	−19.1595			−1.09528
$307$	8.74815	+	12.0408i	0.499283	+	0.687204i	0.982066	−	0.188536i	$-0.0603741\pi$
$307$	8.74815	+	12.0408i	0.499283	+	0.687204i	−0.482783	+	0.875740i	$0.660374\pi$
$308$	−0.471115	+	0.342285i	−0.0268443	+	0.0195035i
$309$	−6.66585	+	20.5154i	−0.379207	+	1.16708i
$310$	3.22966	−	9.93986i	0.183432	−	0.564546i
$311$	−24.2309	−	7.87309i	−1.37401	−	0.446442i	−0.473312	−	0.880895i	$-0.656942\pi$
$311$	−24.2309	−	7.87309i	−1.37401	−	0.446442i	−0.900695	+	0.434453i	$0.856942\pi$
$312$	16.9340	−	23.3076i	0.958699	−	1.31954i
$313$	−17.5894	+	5.71513i	−0.994210	+	0.323038i	−0.760550	−	0.649280i	$-0.775070\pi$
$313$	−17.5894	+	5.71513i	−0.994210	+	0.323038i	−0.233660	+	0.972318i	$0.575070\pi$
$314$	10.4007	−	32.0099i	0.586943	−	1.80643i
$315$	26.3530	−	8.56262i	1.48482	−	0.482449i
$316$			0.160545i			0.00903137i
$317$	0.484942	+	1.49250i	0.0272370	+	0.0838270i	0.963751	−	0.266803i	$-0.0859674\pi$
$317$	0.484942	+	1.49250i	0.0272370	+	0.0838270i	−0.936514	+	0.350630i	$0.885967\pi$
$318$	−1.20638			−0.0676506
$319$	0.118291			0.00662305
$320$	5.18914	+	15.9705i	0.290082	+	0.892780i
$321$	22.6569	+	16.4612i	1.26459	+	0.918776i
$322$	−6.52375	−	2.11969i	−0.363554	−	0.118126i
$323$	−17.8760	+	5.80826i	−0.994646	+	0.323180i
$324$	−1.11356	+	0.809048i	−0.0618644	+	0.0449471i
$325$	0.572217	+	0.415740i	0.0317409	+	0.0230611i
$326$			17.3238i			0.959478i
$327$	4.07863	−	2.96330i	0.225549	−	0.163871i
$328$	10.0466	+	3.26434i	0.554731	+	0.180243i
$329$	11.7354	−	16.1524i	0.646993	−	0.890509i
$330$	5.57133	+	4.04781i	0.306692	+	0.222825i
$331$	5.46662	+	7.52416i	0.300473	+	0.413565i	0.932381	−	0.361478i	$-0.117728\pi$
$331$	5.46662	+	7.52416i	0.300473	+	0.413565i	−0.631908	+	0.775044i	$0.717728\pi$
$332$	0.0928391	+	0.285729i	0.00509521	+	0.0156814i
$333$	10.7938	+	14.8564i	0.591495	+	0.814123i
$334$		−	0.438115i		−	0.0239726i
$335$	9.41505	−	12.9587i	0.514399	−	0.708010i
$336$	−28.7045	+	39.5084i	−1.56596	+	2.15536i
$337$		−	8.83674i		−	0.481368i	−0.970604	−	0.240684i	$-0.922628\pi$
$337$		−	8.83674i		−	0.481368i	0.970604	−	0.240684i	$-0.0773717\pi$
$338$	6.31531	+	8.69228i	0.343508	+	0.472798i
$339$	−10.3004	−	31.7013i	−0.559439	−	1.72178i
$340$	0.942769	+	1.29761i	0.0511288	+	0.0703728i
$341$	−2.25879	−	1.64111i	−0.122320	−	0.0888710i
$342$	7.61466	−	10.4807i	0.411753	−	0.566730i
$343$	−46.9332	−	15.2495i	−2.53415	−	0.823396i
$344$	−3.69259	+	2.68282i	−0.199091	+	0.144648i
$345$			5.09243i			0.274167i
$346$	−4.98169	−	3.61941i	−0.267818	−	0.194581i
$347$	−0.336132	+	0.244214i	−0.0180445	+	0.0131101i	−0.596771	−	0.802412i	$-0.703550\pi$
$347$	−0.336132	+	0.244214i	−0.0180445	+	0.0131101i	0.578726	+	0.815522i	$0.303550\pi$
$348$	−0.0398395	+	0.0129446i	−0.00213562	+	0.000693905i
$349$	−31.5894	−	10.2640i	−1.69094	−	0.549421i	−0.703959	−	0.710241i	$-0.748586\pi$
$349$	−31.5894	−	10.2640i	−1.69094	−	0.549421i	−0.986984	+	0.160820i	$0.948586\pi$
$350$	−0.908807	−	0.660287i	−0.0485778	−	0.0352938i
$351$	1.67343	+	5.15030i	0.0893213	+	0.274903i
$352$	−0.670465			−0.0357359
$353$	27.0641			1.44048			0.720238	−	0.693727i	$-0.244033\pi$
$353$	27.0641			1.44048			0.720238	+	0.693727i	$0.244033\pi$
$354$	1.17749	+	3.62393i	0.0625826	+	0.192610i
$355$		−	35.3462i		−	1.87598i
$356$	−1.85142	+	0.601561i	−0.0981248	+	0.0318827i
$357$	18.7212	−	57.6181i	0.990834	−	3.04947i
$358$	19.3586	−	6.28998i	1.02313	−	0.332436i
$359$	−18.8516	+	25.9471i	−0.994951	+	1.36943i	−0.0665793	+	0.997781i	$0.521209\pi$
$359$	−18.8516	+	25.9471i	−0.994951	+	1.36943i	−0.928372	+	0.371652i	$0.878791\pi$
$360$	14.6451	+	4.75847i	0.771863	+	0.250793i
$361$	−1.94403	+	5.98311i	−0.102317	+	0.314900i
$362$	2.04456	−	6.29250i	0.107460	−	0.330726i
$363$	−19.3586	+	14.0648i	−1.01606	+	0.738212i
$364$	−1.74259	−	2.39848i	−0.0913368	−	0.125714i
$365$	−8.18586			−0.428468
$366$	−16.3097	−	21.1737i	−0.852521	−	1.10677i
$367$	35.2922			1.84224			0.921118	−	0.389283i	$-0.127277\pi$
$367$	35.2922			1.84224			0.921118	+	0.389283i	$0.127277\pi$
$368$	−2.39139	−	3.29147i	−0.124660	−	0.171580i
$369$	7.79901	−	5.66631i	0.406000	−	0.294976i
$370$	7.56723	−	23.2895i	0.393402	−	1.21077i
$371$	0.534361	−	1.64460i	0.0277427	−	0.0853831i
$372$	0.940327	+	0.305531i	0.0487537	+	0.0158410i
$373$	−10.0044	+	13.7699i	−0.518011	+	0.712980i	−0.985244	−	0.171153i	$-0.945251\pi$
$373$	−10.0044	+	13.7699i	−0.518011	+	0.712980i	0.467234	+	0.884134i	$0.345251\pi$
$374$	6.49135	−	2.10917i	0.335660	−	0.109062i
$375$	7.96156	−	24.5031i	0.411133	−	1.26534i
$376$	10.5523	−	3.42864i	0.544192	−	0.176819i
$377$			0.602229i			0.0310164i
$378$	−2.65778	−	8.17981i	−0.136702	−	0.420724i
$379$	−8.06156			−0.414095			−0.207047	−	0.978331i	$-0.566385\pi$
$379$	−8.06156			−0.414095			−0.207047	+	0.978331i	$0.566385\pi$
$380$	−1.08451			−0.0556342
$381$	−4.82938	−	14.8633i	−0.247417	−	0.761470i
$382$	−20.0160	−	14.5425i	−1.02411	−	0.744060i
$383$	−10.9726	−	3.56521i	−0.560673	−	0.182174i	0.0149507	−	0.999888i	$-0.495241\pi$
$383$	−10.9726	−	3.56521i	−0.560673	−	0.182174i	−0.575624	+	0.817714i	$0.695241\pi$
$384$	−27.4378	+	8.91508i	−1.40018	+	0.454946i
$385$	−7.98594	+	5.80213i	−0.407001	+	0.295704i
$386$	7.60246	+	5.52351i	0.386955	+	0.281139i
$387$			4.16526i			0.211732i
$388$	−0.357301	+	0.259594i	−0.0181392	+	0.0131789i
$389$	4.46377	+	1.45037i	0.226322	+	0.0735365i	0.419983	−	0.907532i	$-0.362036\pi$
$389$	4.46377	+	1.45037i	0.226322	+	0.0735365i	−0.193661	+	0.981069i	$0.562036\pi$
$390$	−20.6076	+	28.3640i	−1.04351	+	1.43627i
$391$	4.08329	+	2.96669i	0.206501	+	0.150032i
$392$	−27.3354	−	37.6239i	−1.38064	−	1.90029i
$393$	3.51262	+	10.8107i	0.177188	+	0.545329i
$394$	3.69045	+	5.07947i	0.185922	+	0.255900i
$395$			2.72143i			0.136930i
$396$	−0.173587	+	0.238922i	−0.00872309	+	0.0120063i
$397$	13.5303	−	18.6228i	0.679064	−	0.934652i	−0.320858	−	0.947127i	$-0.603971\pi$
$397$	13.5303	−	18.6228i	0.679064	−	0.934652i	0.999922	+	0.0124756i	$0.00397122\pi$
$398$			14.0992i			0.706730i
$399$	24.0779	+	33.1404i	1.20540	+	1.65909i
$400$	−0.205891	−	0.633667i	−0.0102946	−	0.0316834i
$401$	0.662992	+	0.912530i	0.0331082	+	0.0455696i	0.825250	−	0.564767i	$-0.191034\pi$
$401$	0.662992	+	0.912530i	0.0331082	+	0.0455696i	−0.792142	+	0.610337i	$0.791034\pi$
$402$	19.5280	+	14.1879i	0.973969	+	0.707630i
$403$	8.35498	−	11.4996i	0.416191	−	0.572838i
$404$	0.898837	+	0.292050i	0.0447188	+	0.0145300i
$405$	−18.8761	+	13.7143i	−0.937961	+	0.681469i
$406$		−	0.956472i		−	0.0474689i
$407$	−5.29245	−	3.84519i	−0.262337	−	0.190599i
$408$	27.2377	−	19.7894i	1.34847	−	0.979720i
$409$	−5.85995	+	1.90401i	−0.289756	+	0.0941474i	−0.450288	−	0.892883i	$-0.648679\pi$
$409$	−5.85995	+	1.90401i	−0.289756	+	0.0941474i	0.160533	+	0.987031i	$0.448679\pi$
$410$	−12.2261	−	3.97250i	−0.603804	−	0.196188i
$411$	28.0012	+	20.3440i	1.38120	+	1.00350i
$412$	0.381201	+	1.17321i	0.0187804	+	0.0578001i
$413$	−5.46186			−0.268761
$414$	−3.47873			−0.170970
$415$	1.57373	+	4.84344i	0.0772514	+	0.237755i
$416$		−	3.41338i		−	0.167355i
$417$	−47.8061	+	15.5331i	−2.34107	+	0.760661i
$418$	−1.42613	+	4.38917i	−0.0697542	+	0.214681i
$419$	−23.8004	+	7.73322i	−1.16273	+	0.377792i	−0.825923	−	0.563783i	$-0.809345\pi$
$419$	−23.8004	+	7.73322i	−1.16273	+	0.377792i	−0.336802	+	0.941575i	$0.609345\pi$
$420$	2.05467	−	2.82801i	0.100258	−	0.137993i
$421$	36.2759	+	11.7868i	1.76798	+	0.574452i	0.997976	−	0.0635870i	$-0.0202540\pi$
$421$	36.2759	+	11.7868i	1.76798	+	0.574452i	0.770004	+	0.638039i	$0.220254\pi$
$422$	−4.69327	+	14.4444i	−0.228465	+	0.703142i
$423$	3.12890	−	9.62975i	0.152132	−	0.468215i
$424$	0.777448	−	0.564849i	0.0377562	−	0.0274315i
$425$	0.485842	+	0.668704i	0.0235668	+	0.0324369i
$426$	53.2647			2.58068
$427$	36.0893	−	12.8553i	1.74648	−	0.622111i
$428$	1.60155			0.0774140
$429$	5.50520	+	7.57725i	0.265793	+	0.365833i
$430$	4.49366	−	3.26483i	0.216703	−	0.157444i
$431$	−3.33673	+	10.2694i	−0.160724	+	0.494659i	−0.998696	−	0.0510551i	$-0.983742\pi$
$431$	−3.33673	+	10.2694i	−0.160724	+	0.494659i	0.837971	+	0.545714i	$0.183742\pi$
$432$	1.57638	−	4.85159i	0.0758435	−	0.233422i
$433$	16.8381	+	5.47102i	0.809185	+	0.262920i	0.684253	−	0.729245i	$-0.260129\pi$
$433$	16.8381	+	5.47102i	0.809185	+	0.262920i	0.124933	+	0.992165i	$0.460129\pi$
$434$	−13.2696	+	18.2640i	−0.636959	+	0.876699i
$435$	−0.675325	+	0.219427i	−0.0323794	+	0.0105207i
$436$	0.0890917	−	0.274196i	0.00426672	−	0.0131316i
$437$	−3.24569	+	1.05459i	−0.155262	+	0.0504477i
$438$		−	12.3356i		−	0.589419i
$439$	2.00500	+	6.17076i	0.0956935	+	0.294514i	0.987434	−	0.158033i	$-0.0505153\pi$
$439$	2.00500	+	6.17076i	0.0956935	+	0.294514i	−0.891740	+	0.452547i	$0.850515\pi$
$440$	−5.48567			−0.261519
$441$	−42.4400			−2.02095
$442$	10.7379	+	33.0479i	0.510750	+	1.57193i
$443$	20.4826	+	14.8815i	0.973157	+	0.707040i	0.956169	−	0.292816i	$-0.0945922\pi$
$443$	20.4826	+	14.8815i	0.973157	+	0.707040i	0.0169883	+	0.999856i	$0.494592\pi$
$444$	2.20323	+	0.715873i	0.104561	+	0.0339738i
$445$	−31.3836	+	10.1972i	−1.48773	+	0.483392i
$446$	1.01553	−	0.737826i	0.0480868	−	0.0349371i
$447$	−16.1758	−	11.7524i	−0.765089	−	0.555870i
$448$		−	36.2724i		−	1.71371i
$449$	18.6173	−	13.5262i	0.878604	−	0.638343i	−0.0542781	−	0.998526i	$-0.517286\pi$
$449$	18.6173	−	13.5262i	0.878604	−	0.638343i	0.932882	+	0.360183i	$0.117286\pi$
$450$	−0.541814	−	0.176046i	−0.0255414	−	0.00829889i
$451$	−2.01857	+	2.77833i	−0.0950510	+	0.130826i
$452$	−1.54215	−	1.12044i	−0.0725366	−	0.0527009i
$453$	17.3443	+	23.8723i	0.814905	+	1.12162i
$454$	6.22566	+	19.1606i	0.292185	+	0.899252i
$455$	−29.5390	−	40.6569i	−1.38481	−	1.90603i
$456$			22.7646i			1.06605i
$457$	−7.07805	+	9.74211i	−0.331097	+	0.455717i	−0.941815	−	0.336132i	$-0.890881\pi$
$457$	−7.07805	+	9.74211i	−0.331097	+	0.455717i	0.610717	+	0.791849i	$0.290881\pi$
$458$	3.73088	−	5.13511i	0.174332	−	0.239948i
$459$			6.32847i			0.295388i
$460$	0.171176	+	0.235603i	0.00798110	+	0.0109850i
$461$	1.31166	+	4.03689i	0.0610903	+	0.188017i	0.976944	−	0.213495i	$-0.0684848\pi$
$461$	1.31166	+	4.03689i	0.0610903	+	0.188017i	−0.915854	+	0.401512i	$0.868485\pi$
$462$	−8.74347	−	12.0343i	−0.406783	−	0.559889i
$463$	−16.7160	−	12.1449i	−0.776858	−	0.564420i	0.127176	−	0.991880i	$-0.459409\pi$
$463$	−16.7160	−	12.1449i	−0.776858	−	0.564420i	−0.904034	+	0.427460i	$0.859409\pi$
$464$	0.333451	−	0.458956i	0.0154801	−	0.0213065i
$465$	15.9396	+	5.17910i	0.739183	+	0.240175i
$466$	−16.1467	+	11.7313i	−0.747982	+	0.543441i
$467$		−	34.2766i		−	1.58613i	−0.609136	−	0.793066i	$-0.708483\pi$
$467$		−	34.2766i		−	1.58613i	0.609136	−	0.793066i	$-0.291517\pi$
$468$	−1.21637	−	0.883744i	−0.0562267	−	0.0408511i
$469$	−27.9915	+	20.3370i	−1.29253	+	0.939075i
$470$	−12.8415	+	4.17245i	−0.592333	+	0.192461i
$471$	51.3314	+	16.6786i	2.36523	+	0.768508i
$472$	−2.45561	−	1.78410i	−0.113029	−	0.0821200i
$473$	−0.458532	−	1.41122i	−0.0210833	−	0.0648877i
$474$	−4.10103			−0.188367
$475$	−0.558886			−0.0256435
$476$	−1.07061	−	3.29501i	−0.0490715	−	0.151027i
$477$		−	0.876966i		−	0.0401535i
$478$	28.4563	−	9.24602i	1.30156	−	0.422903i
$479$	8.73495	−	26.8834i	0.399110	−	1.22833i	−0.526604	−	0.850111i	$-0.676535\pi$
$479$	8.73495	−	26.8834i	0.399110	−	1.22833i	0.925714	−	0.378224i	$-0.123465\pi$
$480$	3.82768	−	1.24369i	0.174709	−	0.0567664i
$481$	19.5761	−	26.9442i	0.892594	−	1.22855i
$482$	−1.96565	−	0.638679i	−0.0895330	−	0.0290910i
$483$	3.39916	−	10.4615i	0.154667	−	0.476016i
$484$	−0.422860	+	1.30143i	−0.0192209	+	0.0591558i
$485$	−6.05667	+	4.40043i	−0.275019	+	0.199813i
$486$	−17.5747	−	24.1896i	−0.797207	−	1.09726i
$487$	−18.0469			−0.817782			−0.408891	−	0.912583i	$-0.634084\pi$
$487$	−18.0469			−0.817782			−0.408891	+	0.912583i	$0.634084\pi$
$488$	20.4246	+	6.00884i	0.924578	+	0.272007i
$489$	−27.7806			−1.25628
$490$	33.2655	+	45.7860i	1.50278	+	2.06840i
$491$	27.7172	−	20.1377i	1.25086	−	0.908803i	0.252589	−	0.967574i	$-0.418718\pi$
$491$	27.7172	−	20.1377i	1.25086	−	0.908803i	0.998272	+	0.0587707i	$0.0187181\pi$
$492$	0.375805	−	1.15661i	0.0169426	−	0.0521440i
$493$	−0.217479	+	0.669331i	−0.00979475	+	0.0301451i
$494$	−22.3455	−	7.26051i	−1.00537	−	0.326666i
$495$	−2.94251	+	4.05001i	−0.132256	+	0.182034i
$496$	−12.7346	+	4.13772i	−0.571800	+	0.185789i
$497$	−23.5933	+	72.6127i	−1.05830	+	3.25713i
$498$	−7.29878	+	2.37152i	−0.327066	+	0.106270i
$499$		−	12.2033i		−	0.546294i	−0.961972	−	0.273147i	$-0.911935\pi$
$499$		−	12.2033i		−	0.546294i	0.961972	−	0.273147i	$-0.0880645\pi$
$500$	−0.455298	−	1.40126i	−0.0203615	−	0.0626664i
$501$	0.702564			0.0313883
$502$	−0.607675			−0.0271219
$503$	−2.43288	−	7.48763i	−0.108477	−	0.333857i	0.882054	−	0.471148i	$-0.156160\pi$
$503$	−2.43288	−	7.48763i	−0.108477	−	0.333857i	−0.990531	+	0.137291i	$0.956160\pi$
$504$	−26.9095	−	19.5509i	−1.19865	−	0.870868i
$505$	15.2363	+	4.95059i	0.678008	+	0.220298i
$506$	1.17861	−	0.382955i	0.0523958	−	0.0170244i
$507$	−13.9390	+	10.1273i	−0.619053	+	0.449768i
$508$	−0.723044	−	0.525322i	−0.0320799	−	0.0233074i
$509$			15.1912i			0.673338i	0.941623	+	0.336669i	$0.109300\pi$
$509$			15.1912i			0.673338i	−0.941623	+	0.336669i	$0.890700\pi$
$510$	−33.1467	+	24.0825i	−1.46776	+	1.06639i
$511$	16.8165	+	5.46400i	0.743916	+	0.241713i
$512$	11.7292	−	16.1438i	0.518360	−	0.713462i
$513$	−3.46182	−	2.51516i	−0.152843	−	0.111047i
$514$	4.21788	+	5.80542i	0.186043	+	0.256066i
$515$	6.46179	+	19.8873i	0.284741	+	0.876341i
$516$	0.308859	+	0.425107i	0.0135967	+	0.0187143i
$517$			3.60706i			0.158638i
$518$	−31.0912	+	42.7933i	−1.36607	+	1.88023i
$519$	5.80412	−	7.98868i	0.254772	−	0.350664i
$520$		−	27.9279i		−	1.22472i
$521$	−22.0893	−	30.4033i	−0.967749	−	1.33199i	−0.943176	−	0.332294i	$-0.892178\pi$
$521$	−22.0893	−	30.4033i	−0.967749	−	1.33199i	−0.0245726	−	0.999698i	$-0.507822\pi$
$522$	−0.149894	−	0.461327i	−0.00656069	−	0.0201917i
$523$	−10.4972	−	14.4481i	−0.459009	−	0.631772i	0.515293	−	0.857014i	$-0.327683\pi$
$523$	−10.4972	−	14.4481i	−0.459009	−	0.631772i	−0.974303	+	0.225241i	$0.927683\pi$
$524$	0.525901	+	0.382090i	0.0229741	+	0.0166917i
$525$	1.05884	−	1.45737i	0.0462116	−	0.0636048i
$526$	30.2343	+	9.82371i	1.31828	+	0.428334i
$527$	13.4387	−	9.76379i	0.585399	−	0.425317i
$528$		−	8.82279i		−	0.383963i
$529$	−17.8660	−	12.9804i	−0.776783	−	0.564366i
$530$	−0.946107	+	0.687387i	−0.0410963	+	0.0298582i
$531$	−2.63437	+	0.855959i	−0.114322	+	0.0371454i
$532$	2.22794	+	0.723902i	0.0965936	+	0.0313852i
$533$	−14.1447	−	10.2767i	−0.612673	−	0.445133i
$534$	−15.3665	−	47.2933i	−0.664975	−	2.04658i
$535$	27.1482			1.17372
$536$	−19.2278			−0.830513
$537$	10.0867	+	31.0435i	0.435271	+	1.33963i
$538$		−	34.3040i		−	1.47895i
$539$	14.3789	−	4.67199i	0.619344	−	0.201237i
$540$	−0.112837	+	0.347277i	−0.00485573	+	0.0149444i
$541$	6.09689	−	1.98100i	0.262126	−	0.0851698i	−0.175006	−	0.984567i	$-0.555994\pi$
$541$	6.09689	−	1.98100i	0.262126	−	0.0851698i	0.437132	+	0.899398i	$0.355994\pi$
$542$	16.4344	−	22.6200i	0.705919	−	0.971614i
$543$	10.0907	+	3.27867i	0.433033	+	0.140701i
$544$	1.23265	−	3.79370i	0.0528494	−	0.162654i
$545$	1.51021	−	4.64794i	0.0646902	−	0.199096i
$546$	61.2676	−	44.5135i	2.62201	−	1.90500i
$547$	9.67853	+	13.3213i	0.413824	+	0.569580i	0.964146	−	0.265373i	$-0.0854950\pi$
$547$	9.67853	+	13.3213i	0.413824	+	0.569580i	−0.550322	+	0.834952i	$0.685495\pi$
$548$	1.97932			0.0845524
$549$	15.3920	−	11.8561i	0.656914	−	0.506007i
$550$	0.202950			0.00865381
$551$	−0.279705	−	0.384981i	−0.0119158	−	0.0164007i
$552$	4.94547	−	3.59309i	0.210493	−	0.152932i
$553$	1.81653	−	5.59071i	0.0772467	−	0.237741i
$554$	4.66379	−	14.3537i	0.198145	−	0.609829i
$555$	37.3473	+	12.1349i	1.58530	+	0.515097i
$556$	−1.68964	+	2.32558i	−0.0716565	+	0.0986268i
$557$	4.31204	−	1.40107i	0.182707	−	0.0593651i	−0.216235	−	0.976341i	$-0.569378\pi$
$557$	4.31204	−	1.40107i	0.182707	−	0.0593651i	0.398942	+	0.916976i	$0.369378\pi$
$558$	−3.53794	+	10.8886i	−0.149773	+	0.460953i
$559$	7.18459	−	2.33441i	0.303876	−	0.0987352i
$560$			47.3401i			2.00048i
$561$	3.38228	+	10.4096i	0.142800	+	0.439493i
$562$	−7.06286			−0.297929
$563$	−12.6919			−0.534898			−0.267449	−	0.963572i	$-0.586181\pi$
$563$	−12.6919			−0.534898			−0.267449	+	0.963572i	$0.586181\pi$
$564$	−0.394721	−	1.21483i	−0.0166207	−	0.0511534i
$565$	−26.1412	−	18.9927i	−1.09977	−	0.799029i
$566$	−29.8437	−	9.69682i	−1.25443	−	0.407588i
$567$	47.9319	−	15.5740i	2.01295	−	0.654048i
$568$	−34.3261	+	24.9394i	−1.44029	+	1.04643i
$569$	−10.4524	−	7.59408i	−0.438185	−	0.318360i	0.346728	−	0.937966i	$-0.387293\pi$
$569$	−10.4524	−	7.59408i	−0.438185	−	0.318360i	−0.784913	+	0.619605i	$0.787293\pi$
$570$		−	27.7032i		−	1.16036i
$571$	−23.1114	+	16.7914i	−0.967184	+	0.702700i	−0.954808	−	0.297223i	$-0.903939\pi$
$571$	−23.1114	+	16.7914i	−0.967184	+	0.702700i	−0.0123758	+	0.999923i	$0.503939\pi$
$572$	0.509399	+	0.165514i	0.0212991	+	0.00692048i
$573$	23.3205	−	32.0979i	0.974227	−	1.34091i
$574$	22.4648	+	16.3217i	0.937664	+	0.681253i
$575$	0.0882127	+	0.121414i	0.00367872	+	0.00506333i
$576$	−5.68446	−	17.4950i	−0.236852	−	0.728957i
$577$	24.0603	+	33.1162i	1.00164	+	1.37864i	0.924312	+	0.381639i	$0.124640\pi$
$577$	24.0603	+	33.1162i	1.00164	+	1.37864i	0.0773318	+	0.997005i	$0.475360\pi$
$578$			15.7741i			0.656115i
$579$	−8.85754	+	12.1914i	−0.368107	+	0.506655i
$580$	−0.0238684	+	0.0328520i	−0.000991081	+	0.00136411i
$581$		−	11.0005i		−	0.456377i
$582$	−6.63118	−	9.12704i	−0.274871	−	0.378328i
$583$	0.0965405	+	0.297121i	0.00399830	+	0.0123055i
$584$	5.77574	+	7.94963i	0.239002	+	0.328958i
$585$	−20.6189	−	14.9805i	−0.852485	−	0.619367i
$586$	−17.7847	+	24.4786i	−0.734681	+	1.01120i
$587$	−16.5864	−	5.38924i	−0.684593	−	0.222438i	−0.0539880	−	0.998542i	$-0.517193\pi$
$587$	−16.5864	−	5.38924i	−0.684593	−	0.222438i	−0.630605	+	0.776104i	$0.717193\pi$
$588$	−4.33143	+	3.14697i	−0.178625	+	0.129779i
$589$			11.2317i			0.462796i
$590$	2.98833	+	2.17115i	0.123027	+	0.0893847i
$591$	−8.14548	+	5.91804i	−0.335060	+	0.243436i
$592$	−29.8377	+	9.69486i	−1.22632	+	0.398456i
$593$	30.0364	+	9.75943i	1.23345	+	0.400772i	0.851963	−	0.523603i	$-0.175412\pi$
$593$	30.0364	+	9.75943i	1.23345	+	0.400772i	0.381486	+	0.924375i	$0.375412\pi$
$594$	1.25710	+	0.913335i	0.0515794	+	0.0374746i
$595$	−18.1481	−	55.8542i	−0.744001	−	2.28980i
$596$	−1.14342			−0.0468364
$597$	−22.6096			−0.925350
$598$	1.94965	+	6.00040i	0.0797270	+	0.245375i
$599$			25.5658i			1.04459i	0.852765	+	0.522295i	$0.174924\pi$
$599$			25.5658i			1.04459i	−0.852765	+	0.522295i	$0.825076\pi$
$600$	0.952093	−	0.309354i	0.0388690	−	0.0126293i
$601$	−9.56588	+	29.4408i	−0.390201	+	1.20091i	0.542436	+	0.840097i	$0.317502\pi$
$601$	−9.56588	+	29.4408i	−0.390201	+	1.20091i	−0.932637	+	0.360817i	$0.882498\pi$
$602$	−11.4107	+	3.70756i	−0.465066	+	0.151109i
$603$	−10.3137	+	14.1957i	−0.420008	+	0.578092i
$604$	1.60488	+	0.521456i	0.0653015	+	0.0212177i
$605$	−7.16796	+	22.0607i	−0.291419	+	0.896895i
$606$	−7.46024	+	22.9603i	−0.303052	+	0.932697i
$607$	−16.8950	+	12.2749i	−0.685747	+	0.498225i	−0.875259	−	0.483654i	$-0.839309\pi$
$607$	−16.8950	+	12.2749i	−0.685747	+	0.498225i	0.189512	+	0.981878i	$0.439309\pi$
$608$	1.58534	+	2.18204i	0.0642941	+	0.0884933i
$609$	1.53381			0.0621530
$610$	−24.8555	−	7.31240i	−1.00637	−	0.296070i
$611$	−18.3638			−0.742918
$612$	−1.03276	−	1.42147i	−0.0417468	−	0.0574596i
$613$	16.4844	−	11.9766i	0.665798	−	0.483731i	−0.202818	−	0.979217i	$-0.565010\pi$
$613$	16.4844	−	11.9766i	0.665798	−	0.483731i	0.868616	+	0.495486i	$0.165010\pi$
$614$	−6.71852	+	20.6775i	−0.271137	+	0.834475i
$615$	6.37033	−	19.6059i	0.256877	−	0.790585i
$616$	11.2694	+	3.66164i	0.454056	+	0.147532i
$617$	10.7154	−	14.7485i	0.431385	−	0.593751i	−0.536885	−	0.843655i	$-0.680399\pi$
$617$	10.7154	−	14.7485i	0.431385	−	0.593751i	0.968271	+	0.249904i	$0.0803992\pi$
$618$	−29.9691	+	9.73754i	−1.20553	+	0.391701i
$619$	−0.566325	+	1.74297i	−0.0227625	+	0.0700558i	−0.961793	−	0.273779i	$-0.911726\pi$
$619$	−0.566325	+	1.74297i	−0.0227625	+	0.0700558i	0.939030	+	0.343835i	$0.111726\pi$
$620$	0.911541	−	0.296178i	0.0366084	−	0.0118948i
$621$			1.14904i			0.0461094i
$622$	−11.5011	−	35.3967i	−0.461151	−	1.41928i
$623$	71.2788			2.85573
$624$	44.9174			1.79813
$625$	−7.96006	−	24.4985i	−0.318402	−	0.979941i
$626$	−21.8572	−	15.8802i	−0.873591	−	0.634701i
$627$	−7.03851	−	2.28695i	−0.281091	−	0.0913320i
$628$	2.93549	−	0.953799i	0.117139	−	0.0380607i
$629$	31.4875	−	22.8770i	1.25549	−	0.912165i
$630$	32.7473	+	23.7923i	1.30468	+	0.947908i
$631$		−	32.3139i		−	1.28640i	−0.765699	−	0.643199i	$-0.777607\pi$
$631$		−	32.3139i		−	1.28640i	0.765699	−	0.643199i	$-0.222393\pi$
$632$	2.64289	−	1.92017i	0.105128	−	0.0763803i
$633$	−23.1631	−	7.52616i	−0.920652	−	0.299138i
$634$	−1.34747	+	1.85464i	−0.0535149	+	0.0736570i
$635$	−12.2564	−	8.90482i	−0.486382	−	0.353377i
$636$	−0.0650280	−	0.0895033i	−0.00257853	−	0.00354904i
$637$	23.7854	+	73.2039i	0.942412	+	2.90045i
$638$	0.101570	+	0.139799i	0.00402119	+	0.00553470i
$639$			38.7201i			1.53174i
$640$	−16.4384	+	22.6255i	−0.649784	+	0.894351i
$641$	19.3948	−	26.6946i	0.766047	−	1.05437i	−0.230640	−	0.973039i	$-0.574082\pi$
$641$	19.3948	−	26.6946i	0.766047	−	1.05437i	0.996687	−	0.0813339i	$-0.0259180\pi$
$642$			40.9107i			1.61462i
$643$	1.12897	+	1.55389i	0.0445220	+	0.0612793i	0.830698	−	0.556724i	$-0.187942\pi$
$643$	1.12897	+	1.55389i	0.0445220	+	0.0612793i	−0.786176	+	0.618003i	$0.787942\pi$
$644$	−0.194388	−	0.598264i	−0.00765996	−	0.0235749i
$645$	5.23551	+	7.20606i	0.206148	+	0.283739i
$646$	−22.2134	−	16.1390i	−0.873974	−	0.634979i
$647$	−29.5214	+	40.6328i	−1.16061	+	1.59744i	−0.451635	+	0.892203i	$0.649159\pi$
$647$	−29.5214	+	40.6328i	−1.16061	+	1.59744i	−0.708973	+	0.705236i	$0.750841\pi$
$648$	26.6370	+	8.65489i	1.04640	+	0.339996i
$649$	0.798312	−	0.580007i	0.0313365	−	0.0227673i
$650$			1.03323i			0.0405266i
$651$	−29.2882	−	21.2792i	−1.14790	−	0.833996i
$652$	−1.28528	+	0.933809i	−0.0503354	+	0.0365708i
$653$	22.5456	−	7.32552i	0.882279	−	0.286670i	0.167376	−	0.985893i	$-0.446471\pi$
$653$	22.5456	−	7.32552i	0.882279	−	0.286670i	0.714903	+	0.699223i	$0.246471\pi$
$654$	7.00417	+	2.27579i	0.273885	+	0.0889906i
$655$	8.91464	+	6.47686i	0.348324	+	0.253072i
$656$	5.08942	+	15.6636i	0.198709	+	0.611562i
$657$	8.96723			0.349845
$658$	29.1657			1.13700
$659$	−14.7882	−	45.5133i	−0.576066	−	1.77295i	−0.632522	−	0.774543i	$-0.717980\pi$
$659$	−14.7882	−	45.5133i	−0.576066	−	1.77295i	0.0564558	−	0.998405i	$-0.482020\pi$
$660$			0.631535i			0.0245825i
$661$	−27.5233	+	8.94286i	−1.07053	+	0.347837i	−0.790695	−	0.612211i	$-0.790280\pi$
$661$	−27.5233	+	8.94286i	−1.07053	+	0.347837i	−0.279837	+	0.960048i	$0.590280\pi$
$662$	−4.19833	+	12.9211i	−0.163173	+	0.502194i
$663$	−52.9958	+	17.2194i	−2.05819	+	0.668746i
$664$	3.59328	−	4.94573i	0.139446	−	0.191931i
$665$	37.7662	+	12.2710i	1.46451	+	0.475848i
$666$	−8.28954	+	25.5126i	−0.321213	+	0.988593i
$667$	−0.0394869	+	0.121528i	−0.00152894	+	0.00470559i
$668$	0.0325044	−	0.0236158i	0.00125763	−	0.000913723i
$669$	1.18318	+	1.62851i	0.0457445	+	0.0629620i
$670$	23.3990			0.903983
$671$	−3.90972	+	5.71134i	−0.150933	+	0.220484i
$672$	−8.69347			−0.335358
$673$	3.60406	+	4.96057i	0.138926	+	0.191216i	0.872811	−	0.488058i	$-0.162295\pi$
$673$	3.60406	+	4.96057i	0.138926	+	0.191216i	−0.733885	+	0.679274i	$0.762295\pi$
$674$	10.4434	−	7.58760i	0.402266	−	0.292263i
$675$	−0.0581489	+	0.178964i	−0.00223815	+	0.00688832i
$676$	−0.304477	+	0.937084i	−0.0117107	+	0.0360417i
$677$	40.0042	+	12.9982i	1.53749	+	0.499560i	0.950682	−	0.310168i	$-0.100385\pi$
$677$	40.0042	+	12.9982i	1.53749	+	0.499560i	0.586805	+	0.809728i	$0.300385\pi$
$678$	28.6209	−	39.3933i	1.09918	−	1.51289i
$679$	15.3796	−	4.99715i	0.590216	−	0.191773i
$680$	10.0854	−	31.0397i	0.386757	−	1.19032i
$681$	−30.7261	+	9.98351i	−1.17743	+	0.382569i
$682$		−	4.07861i		−	0.156178i
$683$	−7.56000	−	23.2673i	−0.289275	−	0.890297i	−0.985085	−	0.172071i	$-0.944954\pi$
$683$	−7.56000	−	23.2673i	−0.289275	−	0.890297i	0.695809	−	0.718226i	$-0.255046\pi$
$684$	1.18803			0.0454255
$685$	33.5518			1.28195
$686$	−22.2766	−	68.5604i	−0.850526	−	2.61765i
$687$	8.23471	+	5.98286i	0.314174	+	0.228261i
$688$	−6.76789	−	2.19902i	−0.258023	−	0.0838369i
$689$	−1.51266	+	0.491494i	−0.0576278	+	0.0187244i
$690$	−6.01834	+	4.37258i	−0.229114	+	0.166461i
$691$	11.0969	+	8.06234i	0.422144	+	0.306706i	0.778500	−	0.627645i	$-0.215981\pi$
$691$	11.0969	+	8.06234i	0.422144	+	0.306706i	−0.356356	+	0.934350i	$0.615981\pi$
$692$		−	0.564697i		−	0.0214666i
$693$	8.74822	−	6.35596i	0.332318	−	0.241443i
$694$	−0.577235	−	0.187555i	−0.0219115	−	0.00711949i
$695$	−28.6413	+	39.4214i	−1.08643	+	1.49534i
$696$	0.689587	+	0.501014i	0.0261387	+	0.0189909i
$697$	−12.0095	−	16.5297i	−0.454893	−	0.626107i
$698$	−14.9938	−	46.1461i	−0.567523	−	1.74666i
$699$	−18.8124	−	25.8930i	−0.711549	−	0.979363i
$700$		−	0.103017i		−	0.00389369i
$701$	−23.5782	+	32.4525i	−0.890534	+	1.22572i	0.0828557	+	0.996562i	$0.473596\pi$
$701$	−23.5782	+	32.4525i	−0.890534	+	1.22572i	−0.973390	+	0.229154i	$0.926404\pi$
$702$	−4.64985	+	6.39997i	−0.175497	+	0.241551i
$703$			26.3165i			0.992544i
$704$	3.85185	+	5.30162i	0.145172	+	0.199812i
$705$	−6.69097	−	20.5927i	−0.251997	−	0.775566i
$706$	23.2384	+	31.9849i	0.874587	+	1.20377i
$707$	−27.9960	−	20.3403i	−1.05290	−	0.764974i
$708$	−0.205394	+	0.282701i	−0.00771918	+	0.0106245i
$709$	−9.08689	−	2.95251i	−0.341265	−	0.110884i	0.133370	−	0.991066i	$-0.457420\pi$
$709$	−9.08689	−	2.95251i	−0.341265	−	0.110884i	−0.474635	+	0.880183i	$0.657420\pi$
$710$	41.7728	−	30.3497i	1.56771	−	1.13901i
$711$		−	2.98119i		−	0.111804i
$712$	32.0464	+	23.2831i	1.20099	+	0.872570i
$713$	2.44002	−	1.77278i	0.0913795	−	0.0663911i
$714$	84.1690	−	27.3482i	3.14995	−	1.02348i
$715$	8.63491	+	2.80565i	0.322927	+	0.104925i
$716$	1.51015	+	1.09719i	0.0564370	+	0.0410039i
$717$	14.8270	+	45.6328i	0.553724	+	1.70419i
$718$	−46.8516			−1.74848
$719$	−28.9777			−1.08069			−0.540344	−	0.841444i	$-0.681706\pi$
$719$	−28.9777			−1.08069			−0.540344	+	0.841444i	$0.681706\pi$
$720$	7.41893	+	22.8331i	0.276487	+	0.850940i
$721$		−	45.1683i		−	1.68216i
$722$	−8.74018	+	2.83986i	−0.325276	+	0.105689i
$723$	1.02419	−	3.15213i	0.0380901	−	0.117229i
$724$	0.577057	−	0.187497i	0.0214462	−	0.00696828i
$725$	−0.0123002	+	0.0169298i	−0.000456819	+	0.000628757i
$726$	−33.2442	−	10.8017i	−1.23381	−	0.400888i
$727$	4.33471	−	13.3409i	0.160766	−	0.494785i	−0.837934	−	0.545772i	$-0.816237\pi$
$727$	4.33471	−	13.3409i	0.160766	−	0.494785i	0.998699	+	0.0509865i	$0.0162365\pi$
$728$	−18.6416	+	57.3731i	−0.690905	+	2.12639i
$729$	13.8535	−	10.0652i	0.513094	−	0.372784i
$730$	−7.02873	−	9.67422i	−0.260145	−	0.358059i
$731$	8.82812			0.326520
$732$	0.691765	−	2.35137i	0.0255684	−	0.0869091i
$733$	−39.4018			−1.45534			−0.727670	−	0.685927i	$-0.759397\pi$
$733$	−39.4018			−1.45534			−0.727670	+	0.685927i	$0.759397\pi$
$734$	30.3034	+	41.7090i	1.11852	+	1.53951i
$735$	−73.4228	+	53.3448i	−2.70824	+	1.96765i
$736$	0.223808	−	0.688811i	0.00824968	−	0.0253899i
$737$	1.93163	−	5.94495i	0.0711526	−	0.218985i
$738$	13.3931	+	4.35169i	0.493007	+	0.160188i
$739$	−0.905094	+	1.24575i	−0.0332944	+	0.0458258i	−0.825340	−	0.564637i	$-0.809016\pi$
$739$	−0.905094	+	1.24575i	−0.0332944	+	0.0458258i	0.792045	+	0.610462i	$0.209016\pi$
$740$	2.13578	−	0.693958i	0.0785129	−	0.0255104i
$741$	11.6430	−	35.8335i	0.427716	−	1.31638i
$742$	2.40244	−	0.780600i	0.0881964	−	0.0286567i
$743$		−	24.9170i		−	0.914116i	−0.889437	−	0.457058i	$-0.848903\pi$
$743$		−	24.9170i		−	0.914116i	0.889437	−	0.457058i	$-0.151097\pi$
$744$	−6.21697	−	19.1339i	−0.227925	−	0.701482i
$745$	−19.3823			−0.710113
$746$	−24.8638			−0.910329
$747$	−1.72395	−	5.30576i	−0.0630759	−	0.194128i
$748$	0.506387	+	0.367912i	0.0185153	+	0.0134522i
$749$	−55.7713	−	18.1212i	−2.03784	−	0.662134i
$750$	35.7944	−	11.6303i	1.30703	−	0.424679i
$751$	6.34897	−	4.61280i	0.231677	−	0.168323i	−0.465890	−	0.884843i	$-0.654266\pi$
$751$	6.34897	−	4.61280i	0.231677	−	0.168323i	0.697567	+	0.716519i	$0.254266\pi$
$752$	13.9949	+	10.1679i	0.510343	+	0.370786i
$753$		−	0.974473i		−	0.0355118i
$754$	−0.711726	+	0.517099i	−0.0259195	+	0.0188316i
$755$	27.2045	+	8.83928i	0.990073	+	0.321694i
$756$	0.463609	−	0.638103i	0.0168613	−	0.0232076i
$757$	−11.1212	−	8.08003i	−0.404207	−	0.293674i	0.367045	−	0.930203i	$-0.380369\pi$
$757$	−11.1212	−	8.08003i	−0.404207	−	0.293674i	−0.771253	+	0.636529i	$0.780369\pi$
$758$	−6.92200	−	9.52731i	−0.251418	−	0.346048i
$759$	0.614109	+	1.89003i	0.0222908	+	0.0686039i
$760$	12.9711	+	17.8532i	0.470511	+	0.647603i
$761$		−	36.9006i		−	1.33765i	−0.743421	−	0.668823i	$-0.766798\pi$
$761$		−	36.9006i		−	1.33765i	0.743421	−	0.668823i	$-0.233202\pi$
$762$	13.4190	−	18.4697i	0.486120	−	0.669087i
$763$	−6.20492	+	8.54035i	−0.224633	+	0.309181i
$764$		−	2.26891i		−	0.0820862i
$765$	−17.5065	−	24.0956i	−0.632947	−	0.871177i
$766$	−5.20810	−	16.0289i	−0.188176	−	0.579147i
$767$	2.95285	+	4.06426i	0.106621	+	0.146752i
$768$	−6.06654	−	4.40760i	−0.218907	−	0.159045i
$769$	30.6266	−	42.1539i	1.10442	−	1.52011i	0.275036	−	0.961434i	$-0.411310\pi$
$769$	30.6266	−	42.1539i	1.10442	−	1.52011i	0.829387	−	0.558674i	$-0.188690\pi$
$770$	−13.7141	−	4.45599i	−0.494223	−	0.160583i
$771$	−9.30962	+	6.76383i	−0.335278	+	0.243593i
$772$			0.861772i			0.0310158i
$773$	−9.27690	−	6.74006i	−0.333667	−	0.242423i	0.408318	−	0.912840i	$-0.366115\pi$
$773$	−9.27690	−	6.74006i	−0.333667	−	0.242423i	−0.741985	+	0.670417i	$0.766115\pi$
$774$	−4.92259	+	3.57647i	−0.176939	+	0.128554i
$775$	0.469749	−	0.152631i	0.0168739	−	0.00548265i
$776$	8.54687	+	2.77705i	0.306815	+	0.0996901i
$777$	−68.6237	−	49.8580i	−2.46186	−	1.78865i
$778$	2.11871	+	6.52072i	0.0759594	+	0.233779i
$779$	13.8151			0.494978
$780$	−3.21518			−0.115122
$781$	−4.26249	−	13.1186i	−0.152524	−	0.469420i
$782$			7.37304i			0.263659i
$783$	−0.152378	+	0.0495107i	−0.00544556	+	0.00176937i
$784$	22.4059	−	68.9582i	0.800210	−	2.46279i
$785$	49.7600	−	16.1680i	1.77601	−	0.577061i
$786$	−9.76025	+	13.4338i	−0.348137	+	0.479169i
$787$	−15.9503	−	5.18255i	−0.568565	−	0.184738i	0.0106062	−	0.999944i	$-0.496624\pi$
$787$	−15.9503	−	5.18255i	−0.568565	−	0.184738i	−0.579172	+	0.815206i	$0.696624\pi$
$788$	−0.177926	+	0.547600i	−0.00633835	+	0.0195074i
$789$	−15.7534	+	48.4839i	−0.560835	+	1.72607i
$790$	−3.21624	+	2.33673i	−0.114429	+	0.0831372i
$791$	41.0252	+	56.4663i	1.45869	+	2.00771i
$792$	6.00929			0.213531
$793$	−29.0768	−	19.9046i	−1.03255	−	0.706834i
$794$	33.6264			1.19336
$795$	−1.10230	−	1.51718i	−0.0390945	−	0.0538090i
$796$	−1.04604	+	0.759993i	−0.0370759	+	0.0269372i
$797$	−11.9620	+	36.8153i	−0.423716	+	1.30406i	0.480502	+	0.876994i	$0.340454\pi$
$797$	−11.9620	+	36.8153i	−0.423716	+	1.30406i	−0.904218	+	0.427071i	$0.859546\pi$
$798$	−18.4917	+	56.9115i	−0.654597	+	2.01464i
$799$	−20.4099	−	6.63157i	−0.722050	−	0.234608i
$800$	0.0697165	−	0.0959565i	0.00246485	−	0.00339258i
$801$	34.3793	−	11.1705i	1.21473	−	0.394691i
$802$	−0.509173	+	1.56707i	−0.0179795	+	0.0553353i
$803$	−3.03815	+	0.987154i	−0.107214	+	0.0348359i
$804$			2.21359i			0.0780672i
$805$	−3.29510	−	10.1413i	−0.116137	−	0.357433i
$806$	20.7645			0.731397
$807$	55.0101			1.93645
$808$	−5.94266	−	18.2896i	−0.209062	−	0.643427i
$809$	23.4761	+	17.0564i	0.825377	+	0.599671i	0.918248	−	0.396007i	$-0.129604\pi$
$809$	23.4761	+	17.0564i	0.825377	+	0.599671i	−0.0928707	+	0.995678i	$0.529604\pi$
$810$	−32.4157	−	10.5325i	−1.13897	−	0.370074i
$811$	−1.18241	+	0.384187i	−0.0415199	+	0.0134906i	−0.329703	−	0.944085i	$-0.606949\pi$
$811$	−1.18241	+	0.384187i	−0.0415199	+	0.0134906i	0.288183	+	0.957575i	$0.406949\pi$
$812$	0.0709620	−	0.0515569i	0.00249028	−	0.00180929i
$813$	36.2737	+	26.3544i	1.27217	+	0.924287i
$814$		−	9.55636i		−	0.334950i
$815$	−21.7870	+	15.8292i	−0.763164	+	0.554471i
$816$	49.9222	+	16.2207i	1.74762	+	0.567838i
$817$	−3.50860	+	4.82918i	−0.122750	+	0.168951i
$818$	−7.28180	−	5.29054i	−0.254602	−	0.184979i
$819$	32.3586	+	44.5378i	1.13070	+	1.55628i
$820$	−0.364301	−	1.12120i	−0.0127219	−	0.0391541i
$821$	−12.6234	−	17.3747i	−0.440561	−	0.606380i	0.529776	−	0.848138i	$-0.322276\pi$
$821$	−12.6234	−	17.3747i	−0.440561	−	0.606380i	−0.970337	+	0.241758i	$0.922276\pi$
$822$			50.5606i			1.76350i
$823$	−12.4047	+	17.0736i	−0.432400	+	0.595148i	−0.968502	−	0.249006i	$-0.919896\pi$
$823$	−12.4047	+	17.0736i	−0.432400	+	0.595148i	0.536102	+	0.844153i	$0.319896\pi$
$824$	14.7541	−	20.3073i	0.513985	−	0.707439i
$825$			0.325452i			0.0113308i
$826$	−4.68978	−	6.45493i	−0.163178	−	0.224596i
$827$	−11.5898	−	35.6697i	−0.403016	−	1.24036i	−0.922541	−	0.385900i	$-0.873891\pi$
$827$	−11.5898	−	35.6697i	−0.403016	−	1.24036i	0.519525	−	0.854455i	$-0.326109\pi$
$828$	−0.187515	−	0.258092i	−0.00651659	−	0.00896932i
$829$	45.2541	+	32.8791i	1.57174	+	1.14194i	0.925465	+	0.378833i	$0.123674\pi$
$829$	45.2541	+	32.8791i	1.57174	+	1.14194i	0.646276	+	0.763104i	$0.276326\pi$
$830$	−4.37281	+	6.01865i	−0.151782	+	0.208910i
$831$	23.0177	+	7.47889i	0.798474	+	0.259440i
$832$	−26.9909	+	19.6100i	−0.935741	+	0.679856i
$833$			89.9499i			3.11658i
$834$	−59.4057	−	43.1607i	−2.05705	−	1.49453i
$835$	0.550987	−	0.400315i	0.0190677	−	0.0138535i
$836$	−0.402512	+	0.130784i	−0.0139212	+	0.00452326i
$837$	3.59657	+	1.16860i	0.124316	+	0.0403926i
$838$	−29.5753	−	21.4877i	−1.02166	−	0.742280i
$839$	6.87681	+	21.1647i	0.237414	+	0.730685i	0.996792	+	0.0800353i	$0.0255033\pi$
$839$	6.87681	+	21.1647i	0.237414	+	0.730685i	−0.759378	+	0.650650i	$0.774497\pi$
$840$	−71.1290			−2.45418
$841$	28.9822			0.999386
$842$	17.2182	+	52.9922i	0.593379	+	1.82623i
$843$		−	11.3261i		−	0.390090i
$844$	−1.32463	+	0.430399i	−0.0455957	+	0.0148150i
$845$	−5.16124	+	15.8847i	−0.177552	+	0.546449i
$846$	14.0672	−	4.57072i	0.483641	−	0.157145i
$847$	29.4507	−	40.5354i	1.01194	−	1.39281i
$848$	1.42493	+	0.462988i	0.0489323	+	0.0158991i
$849$	15.5499	−	47.8576i	0.533671	−	1.64247i
$850$	−0.373123	+	1.14835i	−0.0127980	+	0.0393882i
$851$	5.71708	−	4.15370i	0.195979	−	0.142387i
$852$	2.87114	+	3.95178i	0.0983635	+	0.135386i
$853$	14.7935			0.506521			0.253260	−	0.967398i	$-0.418497\pi$
$853$	14.7935			0.506521			0.253260	+	0.967398i	$0.418497\pi$
$854$	46.1804	+	31.6129i	1.58026	+	1.08177i
$855$	20.1385			0.688722
$856$	−19.1551	−	26.3647i	−0.654707	−	0.901127i
$857$	−14.5794	+	10.5926i	−0.498023	+	0.361835i	−0.808261	−	0.588824i	$-0.799591\pi$
$857$	−14.5794	+	10.5926i	−0.498023	+	0.361835i	0.310238	+	0.950659i	$0.399591\pi$
$858$	−4.22795	+	13.0123i	−0.144340	+	0.444233i
$859$	−9.46974	+	29.1449i	−0.323103	+	0.994410i	0.649186	+	0.760629i	$0.275110\pi$
$859$	−9.46974	+	29.1449i	−0.323103	+	0.994410i	−0.972290	+	0.233780i	$0.924890\pi$
$860$	0.484445	+	0.157406i	0.0165194	+	0.00536749i
$861$	−26.1735	+	36.0248i	−0.891991	+	1.22772i
$862$	−15.0016	+	4.87432i	−0.510957	+	0.166020i
$863$	7.73779	−	23.8145i	0.263397	−	0.810654i	−0.728661	−	0.684875i	$-0.759857\pi$
$863$	7.73779	−	23.8145i	0.263397	−	0.810654i	0.992058	−	0.125779i	$-0.0401430\pi$
$864$	0.863667	−	0.280622i	0.0293825	−	0.00954697i
$865$		−	9.57227i		−	0.325467i
$866$	7.99211	+	24.5972i	0.271583	+	0.835847i
$867$	−25.2954			−0.859078
$868$	−2.07030			−0.0702706
$869$	0.328184	+	1.01005i	0.0111329	+	0.0342634i
$870$	−0.839186	−	0.609704i	−0.0284511	−	0.0206709i
$871$	30.2661	+	9.83406i	1.02553	+	0.333215i
$872$	−5.57937	+	1.81285i	−0.188941	+	0.0613907i
$873$	6.63479	−	4.82046i	0.224554	−	0.163148i
$874$	−4.03321	−	2.93030i	−0.136426	−	0.0991189i
$875$			53.9481i			1.82378i
$876$	0.915197	−	0.664929i	0.0309216	−	0.0224659i
$877$	−31.7025	−	10.3008i	−1.07052	−	0.347832i	−0.279828	−	0.960050i	$-0.590277\pi$
$877$	−31.7025	−	10.3008i	−1.07052	−	0.347832i	−0.790689	+	0.612218i	$0.790277\pi$
$878$	−5.57115	+	7.66803i	−0.188017	+	0.258783i
$879$	−39.2541	−	28.5198i	−1.32401	−	0.961948i
$880$	−5.02715	−	6.91928i	−0.169465	−	0.233249i
$881$	−7.03117	−	21.6397i	−0.236886	−	0.729061i	−0.996866	−	0.0791137i	$-0.974791\pi$
$881$	−7.03117	−	21.6397i	−0.236886	−	0.729061i	0.759979	−	0.649947i	$-0.225209\pi$
$882$	−36.4408	−	50.1564i	−1.22702	−	1.68885i
$883$			36.2807i			1.22094i	0.792038	+	0.610472i	$0.209020\pi$
$883$			36.2807i			1.22094i	−0.792038	+	0.610472i	$0.790980\pi$
$884$	−1.87306	+	2.57805i	−0.0629979	+	0.0867091i
$885$	−3.48167	+	4.79210i	−0.117035	+	0.161085i
$886$			36.9846i			1.24252i
$887$	17.6008	+	24.2255i	0.590978	+	0.813412i	0.994845	−	0.101406i	$-0.0323341\pi$
$887$	17.6008	+	24.2255i	0.590978	+	0.813412i	−0.403867	+	0.914818i	$0.632334\pi$
$888$	−14.5666	−	44.8315i	−0.488825	−	1.50445i
$889$	19.2348	+	26.4745i	0.645116	+	0.887926i
$890$	−38.9985	−	28.3341i	−1.30723	−	0.949761i
$891$	−5.35194	+	7.36632i	−0.179297	+	0.246781i
$892$	0.109481	+	0.0355725i	0.00366569	+	0.00119105i
$893$	11.7392	−	8.52904i	0.392838	−	0.285414i
$894$		−	29.2080i		−	0.976862i
$895$	25.5988	+	18.5986i	0.855673	+	0.621683i
$896$	48.8722	−	35.5077i	1.63270	−	1.18623i
$897$	−9.62228	+	3.12647i	−0.321279	+	0.104390i
$898$	31.9712	+	10.3881i	1.06689	+	0.346654i
$899$	0.340232	+	0.247193i	0.0113474	+	0.00824435i
$900$	−0.0161444	−	0.0496874i	−0.000538147	−	0.00165625i
$901$	−1.85870			−0.0619221
$902$	−5.01672			−0.167038
$903$	−5.94547	−	18.2983i	−0.197853	−	0.608929i
$904$			38.7876i			1.29005i
$905$	9.78179	−	3.17830i	0.325158	−	0.105650i
$906$	−13.3203	+	40.9956i	−0.442536	+	1.36199i
$907$	10.2402	−	3.32724i	0.340020	−	0.110479i	−0.134029	−	0.990977i	$-0.542792\pi$
$907$	10.2402	−	3.32724i	0.340020	−	0.110479i	0.474050	+	0.880498i	$0.342792\pi$
$908$	−1.08597	+	1.49471i	−0.0360392	+	0.0496036i
$909$	−16.6907	−	5.42313i	−0.553595	−	0.179874i
$910$	22.6857	−	69.8195i	0.752025	−	2.31450i
$911$	12.3338	−	37.9595i	0.408636	−	1.25765i	−0.509184	−	0.860657i	$-0.670053\pi$
$911$	12.3338	−	37.9595i	0.408636	−	1.25765i	0.917821	−	0.396995i	$-0.129947\pi$
$912$	−28.7139	+	20.8619i	−0.950812	+	0.690805i
$913$	1.16817	+	1.60784i	0.0386607	+	0.0532118i
$914$	−17.5909			−0.581856
$915$	11.7262	−	39.8584i	0.387657	−	1.31768i
$916$	0.582088			0.0192327
$917$	−13.9903	−	19.2561i	−0.462002	−	0.635891i
$918$	−7.47912	+	5.43390i	−0.246848	+	0.179345i
$919$	−9.91870	+	30.5266i	−0.327188	+	1.00698i	0.643256	+	0.765651i	$0.277583\pi$
$919$	−9.91870	+	30.5266i	−0.327188	+	1.00698i	−0.970443	+	0.241329i	$0.922417\pi$
$920$	1.83117	−	5.63577i	0.0603720	−	0.185806i
$921$	−33.1585	−	10.7739i	−1.09261	−	0.355011i
$922$	−3.64462	+	5.01639i	−0.120029	+	0.165206i
$923$	66.7876	−	21.7006i	2.19834	−	0.714284i
$924$	0.421544	−	1.29738i	0.0138678	−	0.0426807i
$925$	1.10064	−	0.357620i	0.0361889	−	0.0117585i
$926$		−	30.1834i		−	0.991888i
$927$	−7.07859	−	21.7856i	−0.232491	−	0.715535i
$928$	0.100989			0.00331513
$929$	−22.7068			−0.744986			−0.372493	−	0.928035i	$-0.621497\pi$
$929$	−22.7068			−0.744986			−0.372493	+	0.928035i	$0.621497\pi$
$930$	7.56568	+	23.2848i	0.248088	+	0.763538i
$931$	−49.2046	−	35.7492i	−1.61262	−	1.17163i
$932$	−1.74072	−	0.565594i	−0.0570192	−	0.0185266i
$933$	56.7624	−	18.4432i	1.85832	−	0.603804i
$934$	40.5088	−	29.4313i	1.32549	−	0.963023i
$935$	8.58384	+	6.23653i	0.280722	+	0.203956i
$936$			30.5937i			0.999985i
$937$	−10.0142	+	7.27577i	−0.327151	+	0.237689i	−0.739221	−	0.673463i	$-0.764806\pi$
$937$	−10.0142	+	7.27577i	−0.327151	+	0.237689i	0.412070	+	0.911152i	$0.364806\pi$
$938$	−48.0693	−	15.6187i	−1.56952	−	0.509967i
$939$	25.4656	−	35.0504i	0.831039	−	1.14383i
$940$	−1.00176	−	0.727819i	−0.0326737	−	0.0237388i
$941$	−11.9517	−	16.4501i	−0.389615	−	0.536259i	0.568485	−	0.822694i	$-0.307530\pi$
$941$	−11.9517	−	16.4501i	−0.389615	−	0.536259i	−0.958100	+	0.286434i	$0.907530\pi$
$942$	24.3642	+	74.9854i	0.793829	+	2.44316i
$943$	−2.18053	−	3.00125i	−0.0710079	−	0.0977340i
$944$		−	4.73233i		−	0.154024i
$945$	7.85871	−	10.8166i	0.255644	−	0.351864i
$946$	1.27409	−	1.75363i	0.0414241	−	0.0570154i
$947$		−	14.7671i		−	0.479865i	−0.970790	−	0.239932i	$-0.922875\pi$
$947$		−	14.7671i		−	0.479865i	0.970790	−	0.239932i	$-0.0771253\pi$
$948$	−0.221059	−	0.304261i	−0.00717965	−	0.00988194i
$949$	−5.02566	−	15.4674i	−0.163140	−	0.502093i
$950$	−0.479883	−	0.660503i	−0.0155695	−	0.0214295i
$951$	−2.97411	−	2.16082i	−0.0964420	−	0.0700692i
$952$	−41.4374	+	57.0338i	−1.34300	+	1.84847i
$953$	−13.8434	−	4.49801i	−0.448433	−	0.145705i	0.0760901	−	0.997101i	$-0.475756\pi$
$953$	−13.8434	−	4.49801i	−0.448433	−	0.145705i	−0.524523	+	0.851396i	$0.675756\pi$
$954$	1.03642	−	0.753000i	0.0335552	−	0.0243793i
$955$		−	38.4606i		−	1.24456i
$956$	2.21986	+	1.61282i	0.0717955	+	0.0521625i
$957$	−0.224183	+	0.162878i	−0.00724680	+	0.00526511i
$958$	39.2715	−	12.7601i	1.26881	−	0.412260i
$959$	−68.9264	−	22.3955i	−2.22575	−	0.723190i
$960$	−31.8246	−	23.1219i	−1.02713	−	0.746256i
$961$	6.51216	+	20.0424i	0.210070	+	0.646528i
$962$	48.6521			1.56861
$963$	−29.7395			−0.958343
$964$	−0.0585705	−	0.180261i	−0.00188643	−	0.00580583i
$965$			14.6080i			0.470249i
$966$	15.2823	−	4.96552i	0.491700	−	0.159763i
$967$	−16.6243	+	51.1643i	−0.534602	+	1.64533i	0.209907	+	0.977721i	$0.432684\pi$
$967$	−16.6243	+	51.1643i	−0.534602	+	1.64533i	−0.744509	+	0.667613i	$0.767316\pi$
$968$	26.4816	−	8.60439i	0.851150	−	0.276556i
$969$	25.8806	−	35.6216i	0.831404	−	1.14433i
$970$	−10.4010	−	3.37950i	−0.333957	−	0.108509i
$971$	6.57079	−	20.2228i	0.210867	−	0.648981i	−0.788555	−	0.614965i	$-0.789170\pi$
$971$	6.57079	−	20.2228i	0.210867	−	0.648981i	0.999421	−	0.0340160i	$-0.0108297\pi$
$972$	0.847322	−	2.60779i	0.0271779	−	0.0836449i
$973$	85.1521	−	61.8666i	2.72985	−	1.98335i
$974$	−15.4958	−	21.3282i	−0.496518	−	0.683398i
$975$	−1.65690			−0.0530631
$976$	11.1382	+	31.2689i	0.356526	+	1.00089i
$977$	16.3154			0.521976			0.260988	−	0.965342i	$-0.415952\pi$
$977$	16.3154			0.521976			0.260988	+	0.965342i	$0.415952\pi$
$978$	−23.8536	−	32.8317i	−0.762754	−	1.04984i
$979$	−10.4182	+	7.56926i	−0.332967	+	0.241915i
$980$	−1.60381	+	4.93603i	−0.0512319	+	0.157676i
$981$	−1.65436	+	5.09160i	−0.0528197	+	0.162562i
$982$	47.5983	+	15.4656i	1.51892	+	0.493528i
$983$	−3.95609	+	5.44508i	−0.126180	+	0.173671i	−0.867433	−	0.497554i	$-0.834232\pi$
$983$	−3.95609	+	5.44508i	−0.126180	+	0.173671i	0.741253	+	0.671225i	$0.234232\pi$
$984$	−23.5348	+	7.64692i	−0.750262	+	0.243775i
$985$	−3.01605	+	9.28245i	−0.0960994	+	0.295763i
$986$	−0.977764	+	0.317695i	−0.0311384	+	0.0101175i
$987$			46.7703i			1.48872i
$988$	−0.665829	−	2.04921i	−0.0211829	−	0.0651941i
$989$	1.60289			0.0509690
$990$	−7.31294			−0.232421
$991$	15.5149	+	47.7500i	0.492847	+	1.51683i	0.820285	+	0.571956i	$0.193815\pi$
$991$	15.5149	+	47.7500i	0.492847	+	1.51683i	−0.327437	+	0.944873i	$0.606185\pi$
$992$	−1.92840	−	1.40107i	−0.0612269	−	0.0444839i
$993$	−20.7204	−	6.73247i	−0.657543	−	0.213649i
$994$	−106.073	+	34.4653i	−3.36444	+	1.09317i
$995$	−17.7316	+	12.8828i	−0.562129	+	0.408411i
$996$	−0.569374	−	0.413675i	−0.0180413	−	0.0131078i
$997$		−	13.8612i		−	0.438989i	−0.975614	−	0.219494i	$-0.929559\pi$
$997$		−	13.8612i		−	0.438989i	0.975614	−	0.219494i	$-0.0704408\pi$
$998$	14.4221	−	10.4783i	0.456523	−	0.331683i
$999$	8.42693	+	2.73808i	0.266616	+	0.0866289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.2.g.a.27.4	✓	16
3.2	odd	2		549.2.y.b.271.1		16
4.3	odd	2		976.2.bd.b.881.4		16
61.28	odd	20		3721.2.a.k.1.13		16
61.33	odd	20		3721.2.a.k.1.4		16
61.52	even	10	inner	61.2.g.a.52.4	yes	16
183.113	odd	10		549.2.y.b.235.1		16
244.235	odd	10		976.2.bd.b.113.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.g.a.27.4	✓	16	1.1	even	1	trivial
61.2.g.a.52.4	yes	16	61.52	even	10	inner
549.2.y.b.235.1		16	183.113	odd	10
549.2.y.b.271.1		16	3.2	odd	2
976.2.bd.b.113.4		16	244.235	odd	10
976.2.bd.b.881.4		16	4.3	odd	2
3721.2.a.k.1.4		16	61.33	odd	20
3721.2.a.k.1.13		16	61.28	odd	20

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:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	61.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.858642 + 1.18182i) q^{2} +(-1.89518 + 1.37693i) q^{3} +(-0.0413973 + 0.127408i) q^{4} +(-0.701732 + 2.15971i) q^{5} +(-3.25455 - 1.05747i) q^{6} +(2.88318 - 3.96835i) q^{7} +(2.59251 - 0.842356i) q^{8} +(0.768714 - 2.36586i) q^{9} +O(q^{10})\)	\(q+(0.858642 + 1.18182i) q^{2} +(-1.89518 + 1.37693i) q^{3} +(-0.0413973 + 0.127408i) q^{4} +(-0.701732 + 2.15971i) q^{5} +(-3.25455 - 1.05747i) q^{6} +(2.88318 - 3.96835i) q^{7} +(2.59251 - 0.842356i) q^{8} +(0.768714 - 2.36586i) q^{9} +(-3.15492 + 1.02510i) q^{10} +0.886190i q^{11} +(-0.0969759 - 0.298461i) q^{12} -4.51165 q^{13} +7.16550 q^{14} +(-1.64385 - 5.05926i) q^{15} +(3.43831 + 2.49808i) q^{16} +(-5.01435 - 1.62926i) q^{17} +(3.45607 - 1.12295i) q^{18} +(2.88412 - 2.09543i) q^{19} +(-0.246114 - 0.178812i) q^{20} +11.4906i q^{21} +(-1.04732 + 0.760921i) q^{22} +(-0.910439 - 0.295820i) q^{23} +(-3.75339 + 5.16610i) q^{24} +(-0.126831 - 0.0921481i) q^{25} +(-3.87389 - 5.33196i) q^{26} +(-0.370914 - 1.14156i) q^{27} +(0.386243 + 0.531618i) q^{28} -0.133483i q^{29} +(4.56765 - 6.28683i) q^{30} +(-1.85187 + 2.54888i) q^{31} +0.756570i q^{32} +(-1.22022 - 1.67949i) q^{33} +(-2.38004 - 7.32501i) q^{34} +(6.54727 + 9.01154i) q^{35} +(0.269606 + 0.195880i) q^{36} +(-4.33901 + 5.97214i) q^{37} +(4.95285 + 1.60928i) q^{38} +(8.55037 - 6.21221i) q^{39} +6.19017i q^{40} +(3.13514 + 2.27781i) q^{41} +(-13.5799 + 9.86635i) q^{42} +(-1.59245 + 0.517419i) q^{43} +(-0.112908 - 0.0366859i) q^{44} +(4.57014 + 3.32040i) q^{45} +(-0.432136 - 1.32998i) q^{46} +4.07030 q^{47} -9.95586 q^{48} +(-5.27200 - 16.2255i) q^{49} -0.229014i q^{50} +(11.7464 - 3.81665i) q^{51} +(0.186770 - 0.574819i) q^{52} +(0.335279 - 0.108939i) q^{53} +(1.03063 - 1.41854i) q^{54} +(-1.91391 - 0.621868i) q^{55} +(4.13189 - 12.7166i) q^{56} +(-2.58065 + 7.94243i) q^{57} +(0.157753 - 0.114614i) q^{58} +(-0.654495 - 0.900835i) q^{59} +0.712640 q^{60} +(6.44483 + 4.41182i) q^{61} -4.60241 q^{62} +(-7.17223 - 9.87172i) q^{63} +(5.98249 - 4.34653i) q^{64} +(3.16597 - 9.74386i) q^{65} +(0.937119 - 2.88416i) q^{66} +(-6.70844 - 2.17970i) q^{67} +(0.415161 - 0.571420i) q^{68} +(2.13276 - 0.692977i) q^{69} +(-5.02826 + 15.4754i) q^{70} +(-14.8034 + 4.80990i) q^{71} -6.78104i q^{72} +(1.11393 + 3.42832i) q^{73} -10.7836 q^{74} +0.367248 q^{75} +(0.147580 + 0.454204i) q^{76} +(3.51672 + 2.55504i) q^{77} +(14.6834 + 4.77093i) q^{78} +(1.13976 - 0.370331i) q^{79} +(-7.80789 + 5.67276i) q^{80} +(8.31234 + 6.03927i) q^{81} +5.66099i q^{82} +(1.81433 - 1.31819i) q^{83} +(-1.46400 - 0.475681i) q^{84} +(7.03746 - 9.68623i) q^{85} +(-1.97884 - 1.43771i) q^{86} +(0.183796 + 0.252974i) q^{87} +(0.746488 + 2.29745i) q^{88} +(8.54135 + 11.7562i) q^{89} +8.25211i q^{90} +(-13.0079 + 17.9038i) q^{91} +(0.0753794 - 0.103751i) q^{92} -7.38045i q^{93} +(3.49493 + 4.81036i) q^{94} +(2.50165 + 7.69929i) q^{95} +(-1.04174 - 1.43383i) q^{96} +(2.66713 + 1.93779i) q^{97} +(14.6489 - 20.1625i) q^{98} +(2.09660 + 0.681227i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9	\( 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9} - 5 q^{10} - 12 q^{13} - 18 q^{14} - 13 q^{15} + 19 q^{16} - 10 q^{18} + 3 q^{19} - 13 q^{20} + 19 q^{22} - 15 q^{23} + 10 q^{24} - 2 q^{25} + 10 q^{26} - 4 q^{27} + 35 q^{28} + 45 q^{30} - 15 q^{31} + 25 q^{33} - 14 q^{34} + 10 q^{35} + 37 q^{36} - 5 q^{37} - 15 q^{38} - 3 q^{39} + 12 q^{41} - 15 q^{42} - 25 q^{43} - 50 q^{44} + 36 q^{45} + 27 q^{46} + 6 q^{47} - 20 q^{48} - 30 q^{49} + 50 q^{51} - 46 q^{52} - 20 q^{53} - 20 q^{54} + 20 q^{55} - 28 q^{56} - 11 q^{57} - 41 q^{58} + 5 q^{59} + 14 q^{60} - 53 q^{61} + 16 q^{62} - 5 q^{63} + 17 q^{64} + 20 q^{65} + 13 q^{66} - 55 q^{67} + 80 q^{68} - 15 q^{69} - 17 q^{70} - 50 q^{71} - 11 q^{73} + 24 q^{74} - 88 q^{75} - 19 q^{76} + 63 q^{77} + 50 q^{78} + 40 q^{79} - 49 q^{80} - 19 q^{81} + 31 q^{83} - 25 q^{84} + 55 q^{85} + 35 q^{86} + 25 q^{87} + 27 q^{88} + 60 q^{89} - 15 q^{91} - 5 q^{92} + 65 q^{94} + 48 q^{95} - 25 q^{96} + 45 q^{97} + 10 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9 - 5 * q^10 - 12 * q^13 - 18 * q^14 - 13 * q^15 + 19 * q^16 - 10 * q^18 + 3 * q^19 - 13 * q^20 + 19 * q^22 - 15 * q^23 + 10 * q^24 - 2 * q^25 + 10 * q^26 - 4 * q^27 + 35 * q^28 + 45 * q^30 - 15 * q^31 + 25 * q^33 - 14 * q^34 + 10 * q^35 + 37 * q^36 - 5 * q^37 - 15 * q^38 - 3 * q^39 + 12 * q^41 - 15 * q^42 - 25 * q^43 - 50 * q^44 + 36 * q^45 + 27 * q^46 + 6 * q^47 - 20 * q^48 - 30 * q^49 + 50 * q^51 - 46 * q^52 - 20 * q^53 - 20 * q^54 + 20 * q^55 - 28 * q^56 - 11 * q^57 - 41 * q^58 + 5 * q^59 + 14 * q^60 - 53 * q^61 + 16 * q^62 - 5 * q^63 + 17 * q^64 + 20 * q^65 + 13 * q^66 - 55 * q^67 + 80 * q^68 - 15 * q^69 - 17 * q^70 - 50 * q^71 - 11 * q^73 + 24 * q^74 - 88 * q^75 - 19 * q^76 + 63 * q^77 + 50 * q^78 + 40 * q^79 - 49 * q^80 - 19 * q^81 + 31 * q^83 - 25 * q^84 + 55 * q^85 + 35 * q^86 + 25 * q^87 + 27 * q^88 + 60 * q^89 - 15 * q^91 - 5 * q^92 + 65 * q^94 + 48 * q^95 - 25 * q^96 + 45 * q^97 + 10 * q^98 - 5 * q^99

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