LMFDB - Embedded newform 61.2.g.a.52.4

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			52.4
Root			$1.46081i$ of defining polynomial
Character	$\chi$	$=$	61.52
Dual form			61.2.g.a.27.4

$q$-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 $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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	−0.389188	−	0.921159i	$-0.627244\pi$
$2$	0.858642	−	1.18182i	0.607152	−	0.835673i	0.996339	+	0.0854858i	$0.0272442\pi$
$3$	−1.89518	−	1.37693i	−1.09418	−	0.794968i	−0.114080	−	0.993472i	$-0.536392\pi$
$3$	−1.89518	−	1.37693i	−1.09418	−	0.794968i	−0.980100	+	0.198503i	$0.936392\pi$
$4$	−0.0413973	−	0.127408i	−0.0206986	−	0.0637039i
$5$	−0.701732	−	2.15971i	−0.313824	−	0.965851i	−0.976236	−	0.216711i	$-0.930467\pi$
$5$	−0.701732	−	2.15971i	−0.313824	−	0.965851i	0.662412	−	0.749140i	$-0.269533\pi$
$6$	−3.25455	+	1.05747i	−1.32867	+	0.431710i
$7$	2.88318	+	3.96835i	1.08974	+	1.49990i	0.848326	+	0.529474i	$0.177611\pi$
$7$	2.88318	+	3.96835i	1.08974	+	1.49990i	0.241412	+	0.970423i	$0.422389\pi$
$8$	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	$-0.957347\pi$
$11$		−	0.886190i		−	0.267196i	0.991036	−	0.133598i	$-0.0426532\pi$
$12$	−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	−0.845681	−	0.533688i	$-0.820806\pi$
$17$	−5.01435	+	1.62926i	−1.21616	+	0.395154i	−0.370477	+	0.928842i	$0.620806\pi$
$18$	3.45607	+	1.12295i	0.814603	+	0.264681i
$19$	2.88412	+	2.09543i	0.661662	+	0.480726i	0.867224	−	0.497918i	$-0.165902\pi$
$19$	2.88412	+	2.09543i	0.661662	+	0.480726i	−0.205562	+	0.978644i	$0.565902\pi$
$20$	−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	−0.402394	−	0.915467i	$-0.631822\pi$
$23$	−0.910439	+	0.295820i	−0.189840	+	0.0616827i	0.212554	+	0.977149i	$0.431822\pi$
$24$	−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	$0.00394510\pi$
$29$			0.133483i			0.0247872i	−0.999923	+	0.0123936i	$0.996055\pi$
$30$	4.56765	+	6.28683i	0.833935	+	1.14781i
$31$	−1.85187	−	2.54888i	−0.332605	−	0.457792i	0.609658	−	0.792664i	$-0.291307\pi$
$31$	−1.85187	−	2.54888i	−0.332605	−	0.457792i	−0.942263	+	0.334873i	$0.891307\pi$
$32$		−	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	−0.999719	−	0.0237001i	$-0.992455\pi$
$37$	−4.33901	−	5.97214i	−0.713329	−	0.981813i	0.286390	−	0.958113i	$-0.407545\pi$
$38$	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	−0.315414	−	0.948954i	$-0.602143\pi$
$41$	3.13514	−	2.27781i	0.489626	−	0.355734i	0.805041	+	0.593220i	$0.202143\pi$
$42$	−13.5799	−	9.86635i	−2.09542	−	1.52241i
$43$	−1.59245	−	0.517419i	−0.242847	−	0.0789056i	0.185065	−	0.982726i	$-0.440750\pi$
$43$	−1.59245	−	0.517419i	−0.242847	−	0.0789056i	−0.427911	+	0.903821i	$0.640750\pi$
$44$	−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	0.331953	−	0.943296i	$-0.392292\pi$
$53$	0.335279	+	0.108939i	0.0460541	+	0.0149639i	−0.285899	+	0.958260i	$0.592292\pi$
$54$	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	−0.849493	−	0.527600i	$-0.823092\pi$
$59$	−0.654495	+	0.900835i	−0.0852080	+	0.117279i	0.764285	+	0.644879i	$0.223092\pi$
$60$	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	−0.688644	−	0.725099i	$-0.741794\pi$
$67$	−6.70844	+	2.17970i	−0.819566	+	0.266293i	−0.130922	+	0.991393i	$0.541794\pi$
$68$	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	−0.759971	−	0.649957i	$-0.774787\pi$
$71$	−14.8034	−	4.80990i	−1.75684	−	0.570830i	−0.996865	+	0.0791270i	$0.974787\pi$
$72$			6.78104i			0.799153i
$73$	1.11393	−	3.42832i	0.130376	−	0.401255i	−0.864466	−	0.502691i	$-0.832344\pi$
$73$	1.11393	−	3.42832i	0.130376	−	0.401255i	0.994842	+	0.101435i	$0.0323435\pi$
$74$	−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	0.372431	−	0.928060i	$-0.378524\pi$
$79$	1.13976	+	0.370331i	0.128233	+	0.0416655i	−0.244197	+	0.969726i	$0.578524\pi$
$80$	−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	0.682890	−	0.730521i	$-0.260723\pi$
$83$	1.81433	+	1.31819i	0.199149	+	0.144690i	−0.483742	+	0.875211i	$0.660723\pi$
$84$	−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	−0.0633377	−	0.997992i	$-0.520175\pi$
$89$	8.54135	−	11.7562i	0.905382	−	1.24615i	0.968719	−	0.248159i	$-0.0798255\pi$
$90$		−	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	−0.444091	−	0.895982i	$-0.646473\pi$
$97$	2.66713	−	1.93779i	0.270806	−	0.196752i	0.714897	+	0.699229i	$0.246473\pi$
$98$	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	$0.114155\pi$
$101$			7.05481i			0.701980i	−0.936379	+	0.350990i	$0.885845\pi$
$102$	14.5966	−	10.6050i	1.44528	−	1.05005i
$103$	7.44971	+	5.41253i	0.734041	+	0.533312i	0.890839	−	0.454318i	$-0.150117\pi$
$103$	7.44971	+	5.41253i	0.734041	+	0.533312i	−0.156798	+	0.987631i	$0.550117\pi$
$104$	−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	0.597613	+	0.801784i	$0.296116\pi$
$107$	−3.69432	+	11.3699i	−0.357143	+	1.09917i	−0.954756	+	0.297389i	$0.903884\pi$
$108$	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	−0.913462	−	0.406924i	$-0.866601\pi$
$113$	−4.39705	−	13.5327i	−0.413640	−	1.27305i	0.499823	−	0.866128i	$-0.333399\pi$
$114$	−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	0.816971	−	0.576678i	$-0.195651\pi$
$127$	−2.06158	−	6.34488i	−0.182935	−	0.563017i	−0.999907	+	0.0136610i	$0.995651\pi$
$128$	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	0.994948	−	0.100391i	$-0.0320094\pi$
$131$	1.49948	+	4.61491i	0.131010	+	0.403207i	−0.863938	+	0.503598i	$0.832009\pi$
$132$	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	0.542655	+	0.839956i	$0.317419\pi$
$137$	−4.56572	+	14.0518i	−0.390076	+	1.20053i	−0.932731	+	0.360574i	$0.882581\pi$
$138$	2.65025	−	1.92552i	0.225605	−	0.163911i
$139$	20.4076	−	6.63082i	1.73095	−	0.562419i	0.737361	−	0.675498i	$-0.236071\pi$
$139$	20.4076	−	6.63082i	1.73095	−	0.562419i	0.993586	+	0.113079i	$0.0360715\pi$
$140$	−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	−0.783000	−	0.622022i	$-0.786311\pi$
$149$	2.63754	−	8.11751i	0.216076	−	0.665013i	0.999075	−	0.0429906i	$-0.0136886\pi$
$150$	0.315335	−	0.434021i	0.0257470	−	0.0354377i
$151$			12.5964i			1.02508i	0.858664	+	0.512539i	$0.171295\pi$
$151$			12.5964i			1.02508i	−0.858664	+	0.512539i	$0.828705\pi$
$152$	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	−0.222208	+	0.974999i	$0.571326\pi$
$157$	−13.5427	+	18.6399i	−1.08082	+	1.48762i	−0.858613	+	0.512624i	$0.828674\pi$
$158$	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	−0.144810	−	0.989460i	$-0.546257\pi$
$163$	9.59418	−	6.97058i	0.751474	−	0.545978i	0.896283	+	0.443482i	$0.146257\pi$
$164$	−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	−0.597133	−	0.802142i	$-0.703694\pi$
$167$	−0.242634	+	0.176284i	−0.0187756	+	0.0136413i	0.578358	+	0.815783i	$0.303694\pi$
$168$	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	0.152626	−	0.988284i	$-0.451227\pi$
$173$	−4.00896	−	1.30259i	−0.304796	−	0.0990342i	−0.457422	+	0.889250i	$0.651227\pi$
$174$	−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	0.972850	+	0.231435i	$0.0743419\pi$
$179$	4.30581	+	13.2519i	0.321832	+	0.990496i	−0.651019	+	0.759062i	$0.725658\pi$
$180$	−0.612236	−	0.444815i	−0.0456334	−	0.0331546i
$181$	−2.66221	+	3.66421i	−0.197880	+	0.272359i	−0.896413	−	0.443219i	$-0.853836\pi$
$181$	−2.66221	+	3.66421i	−0.197880	+	0.272359i	0.698533	+	0.715578i	$0.253836\pi$
$182$	−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	−0.338546	−	0.940950i	$-0.609935\pi$
$191$	−16.1077	−	5.23371i	−1.16551	−	0.378698i	−0.826966	+	0.562252i	$0.809935\pi$
$192$	−5.35301	−	16.4749i	−0.386320	−	1.18897i
$193$	6.11799	+	1.98786i	0.440383	+	0.143089i	0.520812	−	0.853671i	$-0.325629\pi$
$193$	6.11799	+	1.98786i	0.440383	+	0.143089i	−0.0804294	+	0.996760i	$0.525629\pi$
$194$		−	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	−0.275562	−	0.961283i	$-0.588864\pi$
$199$	7.80834	−	5.67309i	0.553519	−	0.402155i	0.829081	+	0.559128i	$0.188864\pi$
$200$	−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	−0.545084	−	0.838381i	$-0.683502\pi$
$211$	6.11108	−	8.41118i	0.420704	−	0.579050i	0.965788	+	0.259332i	$0.0835023\pi$
$212$		−	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	$0.00915945\pi$
$223$			0.859294i			0.0575426i	−0.999586	+	0.0287713i	$0.990841\pi$
$224$	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	0.160532	−	0.987031i	$-0.448679\pi$
$227$	13.1164	−	4.26179i	0.870568	−	0.282865i	0.710035	+	0.704166i	$0.248679\pi$
$228$	−0.905095	+	0.657590i	−0.0599414	+	0.0435500i
$229$	−1.34271	+	4.13243i	−0.0887286	+	0.273078i	−0.985569	−	0.169277i	$-0.945857\pi$
$229$	−1.34271	+	4.13243i	−0.0887286	+	0.273078i	0.896840	+	0.442355i	$0.145857\pi$
$230$	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	$-0.852303\pi$
$233$		−	13.6626i		−	0.895066i	0.894268	−	0.447533i	$-0.147697\pi$
$234$	−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	0.917153	+	0.398535i	$0.130481\pi$
$239$	6.32938	+	19.4798i	0.409414	+	1.26005i	−0.507739	+	0.861511i	$0.669519\pi$
$240$	6.98635	+	21.5018i	0.450967	+	1.38793i
$241$	−1.14463	−	0.831621i	−0.0737320	−	0.0535694i	0.550309	−	0.834961i	$-0.314510\pi$
$241$	−1.14463	−	0.831621i	−0.0737320	−	0.0535694i	−0.624041	+	0.781392i	$0.714510\pi$
$242$	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	0.801231	−	0.598356i	$-0.204179\pi$
$251$	−0.244510	−	0.336539i	−0.0154333	−	0.0212422i	−0.816664	+	0.577114i	$0.804179\pi$
$252$	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	0.978655	−	0.205510i	$-0.0658855\pi$
$263$	17.6059	+	12.7914i	1.08562	+	0.788752i	0.106969	+	0.994262i	$0.465885\pi$
$264$	−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	−0.989566	−	0.144080i	$-0.953978\pi$
$269$	−18.9980	+	13.8029i	−1.15833	+	0.841577i	−0.168765	+	0.985656i	$0.553978\pi$
$270$	2.34041	−	3.22130i	0.142433	−	0.196042i
$271$	−5.91459	+	18.2032i	−0.359285	+	1.10577i	0.594197	+	0.804319i	$0.297470\pi$
$271$	−5.91459	+	18.2032i	−0.359285	+	1.10577i	−0.953483	+	0.301448i	$0.902530\pi$
$272$	−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	−0.951498	−	0.307654i	$-0.900456\pi$
$277$	−6.07270	+	8.35835i	−0.364873	+	0.502205i	0.586625	+	0.809859i	$0.300456\pi$
$278$	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	0.715794	−	0.698312i	$-0.246065\pi$
$281$	−2.84188	−	3.91151i	−0.169532	−	0.233341i	−0.885326	+	0.464970i	$0.846065\pi$
$282$	−13.2470	+	4.30421i	−0.788848	+	0.256312i
$283$	−17.3784	−	12.6262i	−1.03304	−	0.750548i	−0.0641261	−	0.997942i	$-0.520426\pi$
$283$	−17.3784	−	12.6262i	−1.03304	−	0.750548i	−0.968915	+	0.247393i	$0.920426\pi$
$284$			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	−0.570277	−	0.821453i	$-0.693164\pi$
$293$	6.40056	−	19.6989i	0.373925	−	1.15082i	0.944201	−	0.329369i	$-0.106836\pi$
$294$		−	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	−0.482783	−	0.875740i	$-0.660374\pi$
$307$	8.74815	−	12.0408i	0.499283	−	0.687204i	0.982066	+	0.188536i	$0.0603741\pi$
$308$	−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	−0.900695	−	0.434453i	$-0.856942\pi$
$311$	−24.2309	+	7.87309i	−1.37401	+	0.446442i	−0.473312	+	0.880895i	$0.656942\pi$
$312$	16.9340	+	23.3076i	0.958699	+	1.31954i
$313$	−17.5894	−	5.71513i	−0.994210	−	0.323038i	−0.233660	−	0.972318i	$-0.575070\pi$
$313$	−17.5894	−	5.71513i	−0.994210	−	0.323038i	−0.760550	+	0.649280i	$0.775070\pi$
$314$	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	−0.936514	−	0.350630i	$-0.885967\pi$
$317$	0.484942	−	1.49250i	0.0272370	−	0.0838270i	0.963751	+	0.266803i	$0.0859674\pi$
$318$	−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	−0.631908	−	0.775044i	$-0.717728\pi$
$331$	5.46662	−	7.52416i	0.300473	−	0.413565i	0.932381	+	0.361478i	$0.117728\pi$
$332$	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	$0.0773717\pi$
$337$			8.83674i			0.481368i	−0.970604	+	0.240684i	$0.922628\pi$
$338$	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	0.578726	−	0.815522i	$-0.303550\pi$
$347$	−0.336132	−	0.244214i	−0.0180445	−	0.0131101i	−0.596771	+	0.802412i	$0.703550\pi$
$348$	−0.0398395	−	0.0129446i	−0.00213562	−	0.000693905i
$349$	−31.5894	+	10.2640i	−1.69094	+	0.549421i	−0.986984	−	0.160820i	$-0.948586\pi$
$349$	−31.5894	+	10.2640i	−1.69094	+	0.549421i	−0.703959	+	0.710241i	$0.748586\pi$
$350$	−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	−0.928372	−	0.371652i	$-0.878791\pi$
$359$	−18.8516	−	25.9471i	−0.994951	−	1.36943i	−0.0665793	−	0.997781i	$-0.521209\pi$
$360$	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	0.467234	−	0.884134i	$-0.345251\pi$
$373$	−10.0044	−	13.7699i	−0.518011	−	0.712980i	−0.985244	+	0.171153i	$0.945251\pi$
$374$	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	−0.575624	−	0.817714i	$-0.695241\pi$
$383$	−10.9726	+	3.56521i	−0.560673	+	0.182174i	0.0149507	+	0.999888i	$0.495241\pi$
$384$	−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	−0.193661	−	0.981069i	$-0.562036\pi$
$389$	4.46377	−	1.45037i	0.226322	−	0.0735365i	0.419983	+	0.907532i	$0.362036\pi$
$390$	−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	0.999922	−	0.0124756i	$-0.00397122\pi$
$397$	13.5303	+	18.6228i	0.679064	+	0.934652i	−0.320858	+	0.947127i	$0.603971\pi$
$398$		−	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	−0.792142	−	0.610337i	$-0.791034\pi$
$401$	0.662992	−	0.912530i	0.0331082	−	0.0455696i	0.825250	+	0.564767i	$0.191034\pi$
$402$	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	0.160533	−	0.987031i	$-0.448679\pi$
$409$	−5.85995	−	1.90401i	−0.289756	−	0.0941474i	−0.450288	+	0.892883i	$0.648679\pi$
$410$	−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	−0.336802	−	0.941575i	$-0.609345\pi$
$419$	−23.8004	−	7.73322i	−1.16273	−	0.377792i	−0.825923	+	0.563783i	$0.809345\pi$
$420$	2.05467	+	2.82801i	0.100258	+	0.137993i
$421$	36.2759	−	11.7868i	1.76798	−	0.574452i	0.770004	−	0.638039i	$-0.220254\pi$
$421$	36.2759	−	11.7868i	1.76798	−	0.574452i	0.997976	+	0.0635870i	$0.0202540\pi$
$422$	−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	0.837971	−	0.545714i	$-0.183742\pi$
$431$	−3.33673	−	10.2694i	−0.160724	−	0.494659i	−0.998696	+	0.0510551i	$0.983742\pi$
$432$	1.57638	+	4.85159i	0.0758435	+	0.233422i
$433$	16.8381	−	5.47102i	0.809185	−	0.262920i	0.124933	−	0.992165i	$-0.460129\pi$
$433$	16.8381	−	5.47102i	0.809185	−	0.262920i	0.684253	+	0.729245i	$0.260129\pi$
$434$	−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	−0.891740	−	0.452547i	$-0.850515\pi$
$439$	2.00500	−	6.17076i	0.0956935	−	0.294514i	0.987434	+	0.158033i	$0.0505153\pi$
$440$	−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	0.0169883	−	0.999856i	$-0.494592\pi$
$443$	20.4826	−	14.8815i	0.973157	−	0.707040i	0.956169	+	0.292816i	$0.0945922\pi$
$444$	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	0.932882	−	0.360183i	$-0.117286\pi$
$449$	18.6173	+	13.5262i	0.878604	+	0.638343i	−0.0542781	+	0.998526i	$0.517286\pi$
$450$	−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	0.610717	−	0.791849i	$-0.290881\pi$
$457$	−7.07805	−	9.74211i	−0.331097	−	0.455717i	−0.941815	+	0.336132i	$0.890881\pi$
$458$	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	−0.915854	−	0.401512i	$-0.868485\pi$
$461$	1.31166	−	4.03689i	0.0610903	−	0.188017i	0.976944	+	0.213495i	$0.0684848\pi$
$462$	−8.74347	+	12.0343i	−0.406783	+	0.559889i
$463$	−16.7160	+	12.1449i	−0.776858	+	0.564420i	−0.904034	−	0.427460i	$-0.859409\pi$
$463$	−16.7160	+	12.1449i	−0.776858	+	0.564420i	0.127176	+	0.991880i	$0.459409\pi$
$464$	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	$0.291517\pi$
$467$			34.2766i			1.58613i	−0.609136	+	0.793066i	$0.708483\pi$
$468$	−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	0.925714	+	0.378224i	$0.123465\pi$
$479$	8.73495	+	26.8834i	0.399110	+	1.22833i	−0.526604	+	0.850111i	$0.676535\pi$
$480$	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	0.998272	−	0.0587707i	$-0.0187181\pi$
$491$	27.7172	+	20.1377i	1.25086	+	0.908803i	0.252589	+	0.967574i	$0.418718\pi$
$492$	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	$0.0880645\pi$
$499$			12.2033i			0.546294i	−0.961972	+	0.273147i	$0.911935\pi$
$500$	−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	−0.990531	−	0.137291i	$-0.956160\pi$
$503$	−2.43288	+	7.48763i	−0.108477	+	0.333857i	0.882054	+	0.471148i	$0.156160\pi$
$504$	−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	$-0.890700\pi$
$509$		−	15.1912i		−	0.673338i	0.941623	−	0.336669i	$-0.109300\pi$
$510$	−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	−0.0245726	+	0.999698i	$0.507822\pi$
$521$	−22.0893	+	30.4033i	−0.967749	+	1.33199i	−0.943176	+	0.332294i	$0.892178\pi$
$522$	−0.149894	+	0.461327i	−0.00656069	+	0.0201917i
$523$	−10.4972	+	14.4481i	−0.459009	+	0.631772i	−0.974303	−	0.225241i	$-0.927683\pi$
$523$	−10.4972	+	14.4481i	−0.459009	+	0.631772i	0.515293	+	0.857014i	$0.327683\pi$
$524$	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	0.437132	−	0.899398i	$-0.355994\pi$
$541$	6.09689	+	1.98100i	0.262126	+	0.0851698i	−0.175006	+	0.984567i	$0.555994\pi$
$542$	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	−0.550322	−	0.834952i	$-0.685495\pi$
$547$	9.67853	−	13.3213i	0.413824	−	0.569580i	0.964146	+	0.265373i	$0.0854950\pi$
$548$	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	0.398942	−	0.916976i	$-0.369378\pi$
$557$	4.31204	+	1.40107i	0.182707	+	0.0593651i	−0.216235	+	0.976341i	$0.569378\pi$
$558$	−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	−0.784913	−	0.619605i	$-0.787293\pi$
$569$	−10.4524	+	7.59408i	−0.438185	+	0.318360i	0.346728	+	0.937966i	$0.387293\pi$
$570$			27.7032i			1.16036i
$571$	−23.1114	−	16.7914i	−0.967184	−	0.702700i	−0.0123758	−	0.999923i	$-0.503939\pi$
$571$	−23.1114	−	16.7914i	−0.967184	−	0.702700i	−0.954808	+	0.297223i	$0.903939\pi$
$572$	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	0.0773318	−	0.997005i	$-0.475360\pi$
$577$	24.0603	−	33.1162i	1.00164	−	1.37864i	0.924312	−	0.381639i	$-0.124640\pi$
$578$		−	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	−0.630605	−	0.776104i	$-0.717193\pi$
$587$	−16.5864	+	5.38924i	−0.684593	+	0.222438i	−0.0539880	+	0.998542i	$0.517193\pi$
$588$	−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	0.381486	−	0.924375i	$-0.375412\pi$
$593$	30.0364	−	9.75943i	1.23345	−	0.400772i	0.851963	+	0.523603i	$0.175412\pi$
$594$	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	$-0.825076\pi$
$599$		−	25.5658i		−	1.04459i	0.852765	−	0.522295i	$-0.174924\pi$
$600$	0.952093	+	0.309354i	0.0388690	+	0.0126293i
$601$	−9.56588	−	29.4408i	−0.390201	−	1.20091i	−0.932637	−	0.360817i	$-0.882498\pi$
$601$	−9.56588	−	29.4408i	−0.390201	−	1.20091i	0.542436	−	0.840097i	$-0.317502\pi$
$602$	−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	0.189512	−	0.981878i	$-0.439309\pi$
$607$	−16.8950	−	12.2749i	−0.685747	−	0.498225i	−0.875259	+	0.483654i	$0.839309\pi$
$608$	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	0.868616	−	0.495486i	$-0.165010\pi$
$613$	16.4844	+	11.9766i	0.665798	+	0.483731i	−0.202818	+	0.979217i	$0.565010\pi$
$614$	−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	0.968271	−	0.249904i	$-0.0803992\pi$
$617$	10.7154	+	14.7485i	0.431385	+	0.593751i	−0.536885	+	0.843655i	$0.680399\pi$
$618$	−29.9691	−	9.73754i	−1.20553	−	0.391701i
$619$	−0.566325	−	1.74297i	−0.0227625	−	0.0700558i	0.939030	−	0.343835i	$-0.111726\pi$
$619$	−0.566325	−	1.74297i	−0.0227625	−	0.0700558i	−0.961793	+	0.273779i	$0.911726\pi$
$620$	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	$0.222393\pi$
$631$			32.3139i			1.28640i	−0.765699	+	0.643199i	$0.777607\pi$
$632$	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	0.996687	+	0.0813339i	$0.0259180\pi$
$641$	19.3948	+	26.6946i	0.766047	+	1.05437i	−0.230640	+	0.973039i	$0.574082\pi$
$642$		−	40.9107i		−	1.61462i
$643$	1.12897	−	1.55389i	0.0445220	−	0.0612793i	−0.786176	−	0.618003i	$-0.787942\pi$
$643$	1.12897	−	1.55389i	0.0445220	−	0.0612793i	0.830698	+	0.556724i	$0.187942\pi$
$644$	−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	−0.708973	−	0.705236i	$-0.750841\pi$
$647$	−29.5214	−	40.6328i	−1.16061	−	1.59744i	−0.451635	−	0.892203i	$-0.649159\pi$
$648$	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	0.714903	−	0.699223i	$-0.246471\pi$
$653$	22.5456	+	7.32552i	0.882279	+	0.286670i	0.167376	+	0.985893i	$0.446471\pi$
$654$	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	0.0564558	+	0.998405i	$0.482020\pi$
$659$	−14.7882	+	45.5133i	−0.576066	+	1.77295i	−0.632522	+	0.774543i	$0.717980\pi$
$660$		−	0.631535i		−	0.0245825i
$661$	−27.5233	−	8.94286i	−1.07053	−	0.347837i	−0.279837	−	0.960048i	$-0.590280\pi$
$661$	−27.5233	−	8.94286i	−1.07053	−	0.347837i	−0.790695	+	0.612211i	$0.790280\pi$
$662$	−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	−0.733885	−	0.679274i	$-0.762295\pi$
$673$	3.60406	−	4.96057i	0.138926	−	0.191216i	0.872811	+	0.488058i	$0.162295\pi$
$674$	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	0.586805	−	0.809728i	$-0.300385\pi$
$677$	40.0042	−	12.9982i	1.53749	−	0.499560i	0.950682	+	0.310168i	$0.100385\pi$
$678$	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	0.695809	+	0.718226i	$0.255046\pi$
$683$	−7.56000	+	23.2673i	−0.289275	+	0.890297i	−0.985085	+	0.172071i	$0.944954\pi$
$684$	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	−0.356356	−	0.934350i	$-0.615981\pi$
$691$	11.0969	−	8.06234i	0.422144	−	0.306706i	0.778500	+	0.627645i	$0.215981\pi$
$692$			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	−0.973390	−	0.229154i	$-0.926404\pi$
$701$	−23.5782	−	32.4525i	−0.890534	−	1.22572i	0.0828557	−	0.996562i	$-0.473596\pi$
$702$	−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	−0.474635	−	0.880183i	$-0.657420\pi$
$709$	−9.08689	+	2.95251i	−0.341265	+	0.110884i	0.133370	+	0.991066i	$0.457420\pi$
$710$	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	0.998699	−	0.0509865i	$-0.0162365\pi$
$727$	4.33471	+	13.3409i	0.160766	+	0.494785i	−0.837934	+	0.545772i	$0.816237\pi$
$728$	−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	0.792045	−	0.610462i	$-0.209016\pi$
$739$	−0.905094	−	1.24575i	−0.0332944	−	0.0458258i	−0.825340	+	0.564637i	$0.809016\pi$
$740$	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	$0.151097\pi$
$743$			24.9170i			0.914116i	−0.889437	+	0.457058i	$0.848903\pi$
$744$	−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	0.697567	−	0.716519i	$-0.254266\pi$
$751$	6.34897	+	4.61280i	0.231677	+	0.168323i	−0.465890	+	0.884843i	$0.654266\pi$
$752$	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	−0.771253	−	0.636529i	$-0.780369\pi$
$757$	−11.1212	+	8.08003i	−0.404207	+	0.293674i	0.367045	+	0.930203i	$0.380369\pi$
$758$	−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	$0.233202\pi$
$761$			36.9006i			1.33765i	−0.743421	+	0.668823i	$0.766798\pi$
$762$	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	0.829387	+	0.558674i	$0.188690\pi$
$769$	30.6266	+	42.1539i	1.10442	+	1.52011i	0.275036	+	0.961434i	$0.411310\pi$
$770$	−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	−0.741985	−	0.670417i	$-0.766115\pi$
$773$	−9.27690	+	6.74006i	−0.333667	+	0.242423i	0.408318	+	0.912840i	$0.366115\pi$
$774$	−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	−0.579172	−	0.815206i	$-0.696624\pi$
$787$	−15.9503	+	5.18255i	−0.568565	+	0.184738i	0.0106062	+	0.999944i	$0.496624\pi$
$788$	−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	−0.904218	−	0.427071i	$-0.859546\pi$
$797$	−11.9620	−	36.8153i	−0.423716	−	1.30406i	0.480502	−	0.876994i	$-0.340454\pi$
$798$	−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	−0.0928707	−	0.995678i	$-0.529604\pi$
$809$	23.4761	−	17.0564i	0.825377	−	0.599671i	0.918248	+	0.396007i	$0.129604\pi$
$810$	−32.4157	+	10.5325i	−1.13897	+	0.370074i
$811$	−1.18241	−	0.384187i	−0.0415199	−	0.0134906i	0.288183	−	0.957575i	$-0.406949\pi$
$811$	−1.18241	−	0.384187i	−0.0415199	−	0.0134906i	−0.329703	+	0.944085i	$0.606949\pi$
$812$	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	−0.970337	−	0.241758i	$-0.922276\pi$
$821$	−12.6234	+	17.3747i	−0.440561	+	0.606380i	0.529776	+	0.848138i	$0.322276\pi$
$822$		−	50.5606i		−	1.76350i
$823$	−12.4047	−	17.0736i	−0.432400	−	0.595148i	0.536102	−	0.844153i	$-0.319896\pi$
$823$	−12.4047	−	17.0736i	−0.432400	−	0.595148i	−0.968502	+	0.249006i	$0.919896\pi$
$824$	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	0.519525	+	0.854455i	$0.326109\pi$
$827$	−11.5898	+	35.6697i	−0.403016	+	1.24036i	−0.922541	+	0.385900i	$0.873891\pi$
$828$	−0.187515	+	0.258092i	−0.00651659	+	0.00896932i
$829$	45.2541	−	32.8791i	1.57174	−	1.14194i	0.646276	−	0.763104i	$-0.276326\pi$
$829$	45.2541	−	32.8791i	1.57174	−	1.14194i	0.925465	−	0.378833i	$-0.123674\pi$
$830$	−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	−0.759378	−	0.650650i	$-0.774497\pi$
$839$	6.87681	−	21.1647i	0.237414	−	0.730685i	0.996792	−	0.0800353i	$-0.0255033\pi$
$840$	−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	0.310238	−	0.950659i	$-0.399591\pi$
$857$	−14.5794	−	10.5926i	−0.498023	−	0.361835i	−0.808261	+	0.588824i	$0.799591\pi$
$858$	−4.22795	−	13.0123i	−0.144340	−	0.444233i
$859$	−9.46974	−	29.1449i	−0.323103	−	0.994410i	−0.972290	−	0.233780i	$-0.924890\pi$
$859$	−9.46974	−	29.1449i	−0.323103	−	0.994410i	0.649186	−	0.760629i	$-0.275110\pi$
$860$	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	0.992058	+	0.125779i	$0.0401430\pi$
$863$	7.73779	+	23.8145i	0.263397	+	0.810654i	−0.728661	+	0.684875i	$0.759857\pi$
$864$	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	−0.790689	−	0.612218i	$-0.790277\pi$
$877$	−31.7025	+	10.3008i	−1.07052	+	0.347832i	−0.279828	+	0.960050i	$0.590277\pi$
$878$	−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	0.759979	+	0.649947i	$0.225209\pi$
$881$	−7.03117	+	21.6397i	−0.236886	+	0.729061i	−0.996866	+	0.0791137i	$0.974791\pi$
$882$	−36.4408	+	50.1564i	−1.22702	+	1.68885i
$883$		−	36.2807i		−	1.22094i	−0.792038	−	0.610472i	$-0.790980\pi$
$883$		−	36.2807i		−	1.22094i	0.792038	−	0.610472i	$-0.209020\pi$
$884$	−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	−0.403867	−	0.914818i	$-0.632334\pi$
$887$	17.6008	−	24.2255i	0.590978	−	0.813412i	0.994845	+	0.101406i	$0.0323341\pi$
$888$	−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	0.474050	−	0.880498i	$-0.342792\pi$
$907$	10.2402	+	3.32724i	0.340020	+	0.110479i	−0.134029	+	0.990977i	$0.542792\pi$
$908$	−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	0.917821	+	0.396995i	$0.129947\pi$
$911$	12.3338	+	37.9595i	0.408636	+	1.25765i	−0.509184	+	0.860657i	$0.670053\pi$
$912$	−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	−0.970443	−	0.241329i	$-0.922417\pi$
$919$	−9.91870	−	30.5266i	−0.327188	−	1.00698i	0.643256	−	0.765651i	$-0.277583\pi$
$920$	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	0.412070	−	0.911152i	$-0.364806\pi$
$937$	−10.0142	−	7.27577i	−0.327151	−	0.237689i	−0.739221	+	0.673463i	$0.764806\pi$
$938$	−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	−0.958100	−	0.286434i	$-0.907530\pi$
$941$	−11.9517	+	16.4501i	−0.389615	+	0.536259i	0.568485	+	0.822694i	$0.307530\pi$
$942$	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	$0.0771253\pi$
$947$			14.7671i			0.479865i	−0.970790	+	0.239932i	$0.922875\pi$
$948$	−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	−0.524523	−	0.851396i	$-0.675756\pi$
$953$	−13.8434	+	4.49801i	−0.448433	+	0.145705i	0.0760901	+	0.997101i	$0.475756\pi$
$954$	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	−0.744509	−	0.667613i	$-0.767316\pi$
$967$	−16.6243	−	51.1643i	−0.534602	−	1.64533i	0.209907	−	0.977721i	$-0.432684\pi$
$968$	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	0.999421	+	0.0340160i	$0.0108297\pi$
$971$	6.57079	+	20.2228i	0.210867	+	0.648981i	−0.788555	+	0.614965i	$0.789170\pi$
$972$	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	0.741253	−	0.671225i	$-0.234232\pi$
$983$	−3.95609	−	5.44508i	−0.126180	−	0.173671i	−0.867433	+	0.497554i	$0.834232\pi$
$984$	−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	−0.327437	−	0.944873i	$-0.606185\pi$
$991$	15.5149	−	47.7500i	0.492847	−	1.51683i	0.820285	−	0.571956i	$-0.193815\pi$
$992$	−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	$0.0704408\pi$
$997$			13.8612i			0.438989i	−0.975614	+	0.219494i	$0.929559\pi$
$998$	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.52.4	yes	16
3.2	odd	2		549.2.y.b.235.1		16
4.3	odd	2		976.2.bd.b.113.4		16
61.24	odd	20		3721.2.a.k.1.13		16
61.27	even	10	inner	61.2.g.a.27.4	✓	16
61.37	odd	20		3721.2.a.k.1.4		16
183.149	odd	10		549.2.y.b.271.1		16
244.27	odd	10		976.2.bd.b.881.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.g.a.27.4	✓	16	61.27	even	10	inner
61.2.g.a.52.4	yes	16	1.1	even	1	trivial
549.2.y.b.235.1		16	3.2	odd	2
549.2.y.b.271.1		16	183.149	odd	10
976.2.bd.b.113.4		16	4.3	odd	2
976.2.bd.b.881.4		16	244.27	odd	10
3721.2.a.k.1.4		16	61.37	odd	20
3721.2.a.k.1.13		16	61.24	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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