LMFDB - Embedded newform 231.2.y.b.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (of order $15$, degree $8$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			25.3
Character	$\chi$	$=$	231.25
Dual form			231.2.y.b.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05983 - 0.471865i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.437687 - 0.486101i) q^{4} +(-0.113401 + 1.07894i) q^{5} +(0.938560 + 0.681904i) q^{6} +(1.82236 + 1.91807i) q^{7} +(0.951494 + 2.92840i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(-1.05983 - 0.471865i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.437687 - 0.486101i) q^{4} +(-0.113401 + 1.07894i) q^{5} +(0.938560 + 0.681904i) q^{6} +(1.82236 + 1.91807i) q^{7} +(0.951494 + 2.92840i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.629300 - 1.08998i) q^{10} +(-0.627333 - 3.25676i) q^{11} +(0.327057 + 0.566478i) q^{12} +(3.50880 - 2.54929i) q^{13} +(-1.02631 - 2.89273i) q^{14} +(0.335248 - 1.03179i) q^{15} +(0.236643 - 2.25151i) q^{16} +(0.697807 - 0.310684i) q^{17} +(-0.776274 - 0.862140i) q^{18} +(4.52489 - 5.02540i) q^{19} +(0.574108 - 0.417114i) q^{20} +(-1.38375 - 2.25505i) q^{21} +(-0.871885 + 3.74761i) q^{22} +(2.30506 + 3.99249i) q^{23} +(-0.321854 - 3.06223i) q^{24} +(3.73948 + 0.794852i) q^{25} +(-4.92163 + 1.04613i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.134754 - 1.72537i) q^{28} +(-2.38711 + 7.34675i) q^{29} +(-0.842168 + 0.935322i) q^{30} +(0.211274 + 2.01014i) q^{31} +(1.76589 - 3.05861i) q^{32} +(-0.0634935 + 3.31602i) q^{33} -0.886154 q^{34} +(-2.27615 + 1.74871i) q^{35} +(-0.202132 - 0.622098i) q^{36} +(7.88763 - 1.67657i) q^{37} +(-7.16691 + 3.19091i) q^{38} +(-3.96215 + 1.76406i) q^{39} +(-3.26747 + 0.694522i) q^{40} +(-0.592028 - 1.82207i) q^{41} +(0.402452 + 3.04290i) q^{42} -9.06103 q^{43} +(-1.30854 + 1.73039i) q^{44} +(-0.542442 + 0.939537i) q^{45} +(-0.559051 - 5.31902i) q^{46} +(7.01213 - 7.78776i) q^{47} +(-0.699587 + 2.15311i) q^{48} +(-0.358015 + 6.99084i) q^{49} +(-3.58814 - 2.60694i) q^{50} +(-0.747153 + 0.158812i) q^{51} +(-2.77497 - 0.589837i) q^{52} +(-0.0132578 - 0.126140i) q^{53} +(0.580062 + 1.00470i) q^{54} +(3.58499 - 0.307535i) q^{55} +(-3.88292 + 7.16163i) q^{56} +(-5.47085 + 3.97481i) q^{57} +(5.99659 - 6.65989i) q^{58} +(-3.90292 - 4.33463i) q^{59} +(-0.648285 + 0.288635i) q^{60} +(-1.19632 + 11.3823i) q^{61} +(0.724599 - 2.23009i) q^{62} +(0.884657 + 2.49347i) q^{63} +(-6.97787 + 5.06972i) q^{64} +(2.35263 + 4.07488i) q^{65} +(1.63200 - 3.48444i) q^{66} +(-1.51951 + 2.63186i) q^{67} +(-0.456445 - 0.203222i) q^{68} +(-1.42461 - 4.38449i) q^{69} +(3.23747 - 0.779290i) q^{70} +(8.54586 + 6.20893i) q^{71} +(-0.321854 + 3.06223i) q^{72} +(-0.702789 - 0.780526i) q^{73} +(-9.15062 - 1.94502i) q^{74} +(-3.49251 - 1.55497i) q^{75} -4.42334 q^{76} +(5.10347 - 7.13825i) q^{77} +5.03159 q^{78} +(-8.61373 - 3.83508i) q^{79} +(2.40241 + 0.510648i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.232326 + 2.21044i) q^{82} +(-7.03285 - 5.10966i) q^{83} +(-0.490533 + 1.65965i) q^{84} +(0.256077 + 0.788124i) q^{85} +(9.60311 + 4.27558i) q^{86} +(3.86242 - 6.68990i) q^{87} +(8.94017 - 4.93586i) q^{88} +(0.0262036 + 0.0453860i) q^{89} +(1.01823 - 0.739786i) q^{90} +(11.2840 + 2.08441i) q^{91} +(0.931854 - 2.86795i) q^{92} +(0.211274 - 2.01014i) q^{93} +(-11.1064 + 4.94489i) q^{94} +(4.90898 + 5.45198i) q^{95} +(-2.36322 + 2.62463i) q^{96} +(7.76672 - 5.64285i) q^{97} +(3.67816 - 7.24014i) q^{98} +(0.751545 - 3.23035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.05983	−	0.471865i	−0.749410	−	0.333659i	−0.00375667	−	0.999993i	$-0.501196\pi$
$2$	−1.05983	−	0.471865i	−0.749410	−	0.333659i	−0.745653	+	0.666334i	$0.767862\pi$
$3$	−0.978148	−	0.207912i	−0.564734	−	0.120038i
$3$	−0.978148	−	0.207912i	−0.564734	−	0.120038i
$4$	−0.437687	−	0.486101i	−0.218844	−	0.243050i
$5$	−0.113401	+	1.07894i	−0.0507146	+	0.482517i	0.939458	+	0.342665i	$0.111329\pi$
$5$	−0.113401	+	1.07894i	−0.0507146	+	0.482517i	−0.990172	+	0.139852i	$0.955337\pi$
$6$	0.938560	+	0.681904i	0.383165	+	0.278386i
$7$	1.82236	+	1.91807i	0.688787	+	0.724964i
$7$	1.82236	+	1.91807i	0.688787	+	0.724964i
$8$	0.951494	+	2.92840i	0.336404	+	1.03534i
$9$	0.913545	+	0.406737i	0.304515	+	0.135579i
$10$	0.629300	−	1.08998i	0.199002	−	0.344682i
$11$	−0.627333	−	3.25676i	−0.189148	−	0.981949i
$11$	−0.627333	−	3.25676i	−0.189148	−	0.981949i
$12$	0.327057	+	0.566478i	0.0944131	+	0.163528i
$13$	3.50880	−	2.54929i	0.973165	−	0.707046i	0.0169945	−	0.999856i	$-0.494590\pi$
$13$	3.50880	−	2.54929i	0.973165	−	0.707046i	0.956171	+	0.292810i	$0.0945902\pi$
$14$	−1.02631	−	2.89273i	−0.274293	−	0.773115i
$15$	0.335248	−	1.03179i	0.0865606	−	0.266406i
$16$	0.236643	−	2.25151i	0.0591608	−	0.562877i
$17$	0.697807	−	0.310684i	0.169243	−	0.0753518i	−0.320366	−	0.947294i	$-0.603806\pi$
$17$	0.697807	−	0.310684i	0.169243	−	0.0753518i	0.489609	+	0.871942i	$0.337139\pi$
$18$	−0.776274	−	0.862140i	−0.182970	−	0.203208i
$19$	4.52489	−	5.02540i	1.03808	−	1.15291i	0.0500357	−	0.998747i	$-0.484066\pi$
$19$	4.52489	−	5.02540i	1.03808	−	1.15291i	0.988046	−	0.154159i	$-0.0492668\pi$
$20$	0.574108	−	0.417114i	0.128374	−	0.0932695i
$21$	−1.38375	−	2.25505i	−0.301958	−	0.492092i
$22$	−0.871885	+	3.74761i	−0.185886	+	0.798993i
$23$	2.30506	+	3.99249i	0.480639	+	0.832491i	0.999753	−	0.0222140i	$-0.00707150\pi$
$23$	2.30506	+	3.99249i	0.480639	+	0.832491i	−0.519114	+	0.854705i	$0.673738\pi$
$24$	−0.321854	−	3.06223i	−0.0656981	−	0.625075i
$25$	3.73948	+	0.794852i	0.747897	+	0.158970i
$26$	−4.92163	+	1.04613i	−0.965212	+	0.205162i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	0.134754	−	1.72537i	0.0254661	−	0.326064i
$29$	−2.38711	+	7.34675i	−0.443274	+	1.36426i	0.441091	+	0.897462i	$0.354592\pi$
$29$	−2.38711	+	7.34675i	−0.443274	+	1.36426i	−0.884365	+	0.466796i	$0.845408\pi$
$30$	−0.842168	+	0.935322i	−0.153758	+	0.170766i
$31$	0.211274	+	2.01014i	0.0379459	+	0.361031i	0.996975	+	0.0777234i	$0.0247651\pi$
$31$	0.211274	+	2.01014i	0.0379459	+	0.361031i	−0.959029	+	0.283308i	$0.908568\pi$
$32$	1.76589	−	3.05861i	0.312168	−	0.540692i
$33$	−0.0634935	+	3.31602i	−0.0110528	+	0.577244i
$34$	−0.886154			−0.151974
$35$	−2.27615	+	1.74871i	−0.384739	+	0.295585i
$36$	−0.202132	−	0.622098i	−0.0336887	−	0.103683i
$37$	7.88763	−	1.67657i	1.29672	−	0.275626i	0.492683	−	0.870209i	$-0.336016\pi$
$37$	7.88763	−	1.67657i	1.29672	−	0.275626i	0.804034	+	0.594583i	$0.202683\pi$
$38$	−7.16691	+	3.19091i	−1.16263	+	0.517635i
$39$	−3.96215	+	1.76406i	−0.634452	+	0.282476i
$40$	−3.26747	+	0.694522i	−0.516632	+	0.109814i
$41$	−0.592028	−	1.82207i	−0.0924592	−	0.284560i	0.894124	−	0.447819i	$-0.147799\pi$
$41$	−0.592028	−	1.82207i	−0.0924592	−	0.284560i	−0.986583	+	0.163259i	$0.947799\pi$
$42$	0.402452	+	3.04290i	0.0620996	+	0.469530i
$43$	−9.06103			−1.38179			−0.690897	−	0.722953i	$-0.742784\pi$
$43$	−9.06103			−1.38179			−0.690897	+	0.722953i	$0.742784\pi$
$44$	−1.30854	+	1.73039i	−0.197269	+	0.260866i
$45$	−0.542442	+	0.939537i	−0.0808625	+	0.140058i
$46$	−0.559051	−	5.31902i	−0.0824276	−	0.784246i
$47$	7.01213	−	7.78776i	1.02282	−	1.13596i	0.0321821	−	0.999482i	$-0.489754\pi$
$47$	7.01213	−	7.78776i	1.02282	−	1.13596i	0.990643	−	0.136480i	$-0.0435790\pi$
$48$	−0.699587	+	2.15311i	−0.100977	+	0.310774i
$49$	−0.358015	+	6.99084i	−0.0511449	+	0.998691i
$50$	−3.58814	−	2.60694i	−0.507439	−	0.368676i
$51$	−0.747153	+	0.158812i	−0.104622	+	0.0222382i
$52$	−2.77497	−	0.589837i	−0.384819	−	0.0817957i
$53$	−0.0132578	−	0.126140i	−0.00182110	−	0.0173266i	0.993574	−	0.113188i	$-0.0361062\pi$
$53$	−0.0132578	−	0.126140i	−0.00182110	−	0.0173266i	−0.995395	+	0.0958612i	$0.969440\pi$
$54$	0.580062	+	1.00470i	0.0789364	+	0.136722i
$55$	3.58499	−	0.307535i	0.483399	−	0.0414680i
$56$	−3.88292	+	7.16163i	−0.518877	+	0.957013i
$57$	−5.47085	+	3.97481i	−0.724632	+	0.526476i
$58$	5.99659	−	6.65989i	0.787391	−	0.874486i
$59$	−3.90292	−	4.33463i	−0.508117	−	0.564321i	0.433437	−	0.901184i	$-0.357301\pi$
$59$	−3.90292	−	4.33463i	−0.508117	−	0.564321i	−0.941554	+	0.336863i	$0.890634\pi$
$60$	−0.648285	+	0.288635i	−0.0836933	+	0.0372627i
$61$	−1.19632	+	11.3823i	−0.153174	+	1.45735i	0.600249	+	0.799813i	$0.295068\pi$
$61$	−1.19632	+	11.3823i	−0.153174	+	1.45735i	−0.753423	+	0.657536i	$0.771599\pi$
$62$	0.724599	−	2.23009i	0.0920242	−	0.283221i
$63$	0.884657	+	2.49347i	0.111456	+	0.314147i
$64$	−6.97787	+	5.06972i	−0.872234	+	0.633715i
$65$	2.35263	+	4.07488i	0.291808	+	0.505426i
$66$	1.63200	−	3.48444i	0.200886	−	0.428905i
$67$	−1.51951	+	2.63186i	−0.185637	+	0.321533i	−0.943791	−	0.330543i	$-0.892768\pi$
$67$	−1.51951	+	2.63186i	−0.185637	+	0.321533i	0.758154	+	0.652076i	$0.226102\pi$
$68$	−0.456445	−	0.203222i	−0.0553520	−	0.0246443i
$69$	−1.42461	−	4.38449i	−0.171503	−	0.527831i
$70$	3.23747	−	0.779290i	0.386952	−	0.0931430i
$71$	8.54586	+	6.20893i	1.01421	+	0.736864i	0.965087	−	0.261929i	$-0.0843585\pi$
$71$	8.54586	+	6.20893i	1.01421	+	0.736864i	0.0491195	+	0.998793i	$0.484358\pi$
$72$	−0.321854	+	3.06223i	−0.0379308	+	0.360887i
$73$	−0.702789	−	0.780526i	−0.0822552	−	0.0913537i	0.700612	−	0.713542i	$-0.252910\pi$
$73$	−0.702789	−	0.780526i	−0.0822552	−	0.0913537i	−0.782867	+	0.622189i	$0.786244\pi$
$74$	−9.15062	−	1.94502i	−1.06374	−	0.226105i
$75$	−3.49251	−	1.55497i	−0.403280	−	0.179552i
$76$	−4.42334			−0.507392
$77$	5.10347	−	7.13825i	0.581595	−	0.813479i
$78$	5.03159			0.569715
$79$	−8.61373	−	3.83508i	−0.969121	−	0.431480i	−0.139755	−	0.990186i	$-0.544631\pi$
$79$	−8.61373	−	3.83508i	−0.969121	−	0.431480i	−0.829366	+	0.558706i	$0.811298\pi$
$80$	2.40241	+	0.510648i	0.268597	+	0.0570922i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	−0.232326	+	2.21044i	−0.0256562	+	0.244102i
$83$	−7.03285	−	5.10966i	−0.771956	−	0.560859i	0.130598	−	0.991435i	$-0.458310\pi$
$83$	−7.03285	−	5.10966i	−0.771956	−	0.560859i	−0.902554	+	0.430577i	$0.858310\pi$
$84$	−0.490533	+	1.65965i	−0.0535216	+	0.181082i
$85$	0.256077	+	0.788124i	0.0277755	+	0.0854841i
$86$	9.60311	+	4.27558i	1.03553	+	0.461048i
$87$	3.86242	−	6.68990i	0.414095	−	0.717233i
$88$	8.94017	−	4.93586i	0.953025	−	0.526165i
$89$	0.0262036	+	0.0453860i	0.00277758	+	0.00481090i	0.867411	−	0.497593i	$-0.165783\pi$
$89$	0.0262036	+	0.0453860i	0.00277758	+	0.00481090i	−0.864633	+	0.502404i	$0.832449\pi$
$90$	1.01823	−	0.739786i	0.107331	−	0.0779803i
$91$	11.2840	+	2.08441i	1.18289	+	0.218506i
$92$	0.931854	−	2.86795i	0.0971525	−	0.299005i
$93$	0.211274	−	2.01014i	0.0219081	−	0.208441i
$94$	−11.1064	+	4.94489i	−1.14554	+	0.510027i
$95$	4.90898	+	5.45198i	0.503651	+	0.559361i
$96$	−2.36322	+	2.62463i	−0.241196	+	0.267875i
$97$	7.76672	−	5.64285i	0.788591	−	0.572945i	−0.118954	−	0.992900i	$-0.537954\pi$
$97$	7.76672	−	5.64285i	0.788591	−	0.572945i	0.907545	+	0.419955i	$0.137954\pi$
$98$	3.67816	−	7.24014i	0.371551	−	0.731364i
$99$	0.751545	−	3.23035i	0.0755331	−	0.324663i
$100$	−1.25035	−	2.16566i	−0.125035	−	0.216566i
$101$	−0.907129	−	8.63076i	−0.0902627	−	0.858792i	−0.942178	−	0.335113i	$-0.891226\pi$
$101$	−0.907129	−	8.63076i	−0.0902627	−	0.858792i	0.851915	−	0.523680i	$-0.175441\pi$
$102$	0.866790	+	0.184242i	0.0858250	+	0.0182427i
$103$	−13.1288	+	2.79061i	−1.29362	+	0.274967i	−0.802776	−	0.596281i	$-0.796644\pi$
$103$	−13.1288	+	2.79061i	−1.29362	+	0.274967i	−0.490843	+	0.871248i	$0.663311\pi$
$104$	10.8039	+	7.84952i	1.05941	+	0.769709i
$105$	2.58998	−	1.23726i	0.252756	−	0.120744i
$106$	−0.0454700	+	0.139942i	−0.00441643	+	0.0135924i
$107$	10.5404	−	11.7063i	1.01898	−	1.13169i	0.0277406	−	0.999615i	$-0.491169\pi$
$107$	10.5404	−	11.7063i	1.01898	−	1.13169i	0.991239	−	0.132077i	$-0.0421646\pi$
$108$	0.0683734	+	0.650530i	0.00657924	+	0.0625973i
$109$	−1.53239	+	2.65418i	−0.146776	+	0.254224i	−0.930034	−	0.367473i	$-0.880223\pi$
$109$	−1.53239	+	2.65418i	−0.146776	+	0.254224i	0.783258	+	0.621697i	$0.213556\pi$
$110$	−3.94458	−	1.36570i	−0.376101	−	0.130214i
$111$	−8.06384			−0.765386
$112$	4.74981	−	3.64916i	0.448815	−	0.344813i
$113$	2.48074	+	7.63493i	0.233368	+	0.718234i	0.997334	+	0.0729766i	$0.0232499\pi$
$113$	2.48074	+	7.63493i	0.233368	+	0.718234i	−0.763965	+	0.645257i	$0.776750\pi$
$114$	7.67372	−	1.63110i	0.718710	−	0.152767i
$115$	−4.56905	+	2.03427i	−0.426066	+	0.189697i
$116$	4.61607	−	2.05521i	0.428591	−	0.190821i
$117$	4.24234	−	0.901736i	0.392204	−	0.0833656i
$118$	2.09105	+	6.43560i	0.192497	+	0.592445i
$119$	1.86757	+	0.772268i	0.171200	+	0.0707937i
$120$	3.34047			0.304941
$121$	−10.2129	+	4.08614i	−0.928446	+	0.371467i
$122$	6.63878	−	11.4987i	0.601047	−	1.04104i
$123$	0.200260	+	1.90535i	0.0180568	+	0.171799i
$124$	0.884657	−	0.982511i	0.0794445	−	0.0882321i
$125$	−2.95790	+	9.10348i	−0.264562	+	0.814240i
$126$	0.238998	−	3.06008i	0.0212916	−	0.272614i
$127$	4.38980	+	3.18938i	0.389532	+	0.283011i	0.765264	−	0.643717i	$-0.222609\pi$
$127$	4.38980	+	3.18938i	0.389532	+	0.283011i	−0.375732	+	0.926728i	$0.622609\pi$
$128$	2.87834	−	0.611811i	0.254412	−	0.0540769i
$129$	8.86303	+	1.88389i	0.780346	+	0.165868i
$130$	−0.570588	−	5.42878i	−0.0500439	−	0.476136i
$131$	−9.56357	−	16.5646i	−0.835573	−	1.44726i	−0.893563	−	0.448938i	$-0.851802\pi$
$131$	−9.56357	−	16.5646i	−0.835573	−	1.44726i	0.0579898	−	0.998317i	$-0.481531\pi$
$132$	1.63971	−	1.42051i	0.142718	−	0.123640i
$133$	17.8851	−	0.479010i	1.55083	−	0.0415354i
$134$	2.85230	−	2.07231i	0.246401	−	0.179021i
$135$	0.725929	−	0.806226i	0.0624780	−	0.0693889i
$136$	1.57376	+	1.74784i	0.134949	+	0.149876i
$137$	−6.75275	+	3.00652i	−0.576926	+	0.256864i	−0.674390	−	0.738375i	$-0.735593\pi$
$137$	−6.75275	+	3.00652i	−0.576926	+	0.256864i	0.0974643	+	0.995239i	$0.468927\pi$
$138$	−0.559051	+	5.31902i	−0.0475896	+	0.452785i
$139$	4.80738	−	14.7956i	0.407756	−	1.25494i	−0.510815	−	0.859690i	$-0.670656\pi$
$139$	4.80738	−	14.7956i	0.407756	−	1.25494i	0.918572	−	0.395254i	$-0.129344\pi$
$140$	1.84629	+	0.341050i	0.156040	+	0.0288240i
$141$	−8.47807	+	6.15968i	−0.713982	+	0.518738i
$142$	−6.12735	−	10.6129i	−0.514195	−	0.890613i
$143$	−10.5036	−	9.82804i	−0.878355	−	0.821862i
$144$	1.13196	−	1.96060i	0.0943296	−	0.163384i
$145$	−7.65601	−	3.40868i	−0.635797	−	0.283075i
$146$	0.376531	+	1.15884i	0.0311619	+	0.0959066i
$147$	1.80367	−	6.76364i	0.148764	−	0.557855i
$148$	−4.26729	−	3.10037i	−0.350769	−	0.254849i
$149$	−1.57440	+	14.9794i	−0.128980	+	1.22716i	0.718192	+	0.695845i	$0.244970\pi$
$149$	−1.57440	+	14.9794i	−0.128980	+	1.22716i	−0.847172	+	0.531319i	$0.821697\pi$
$150$	2.96772	+	3.29598i	0.242313	+	0.269116i
$151$	−20.8705	−	4.43616i	−1.69842	−	0.361009i	−0.746031	−	0.665911i	$-0.768043\pi$
$151$	−20.8705	−	4.43616i	−1.69842	−	0.361009i	−0.952384	+	0.304902i	$0.901376\pi$
$152$	19.0218	+	8.46905i	1.54287	+	0.686930i
$153$	0.763845			0.0617532
$154$	−8.77708	+	5.15715i	−0.707277	+	0.415575i
$155$	−2.19278			−0.176128
$156$	2.59169	+	1.15390i	0.207502	+	0.0923856i
$157$	2.77714	+	0.590300i	0.221640	+	0.0471111i	0.317393	−	0.948294i	$-0.397193\pi$
$157$	2.77714	+	0.590300i	0.221640	+	0.0471111i	−0.0957529	+	0.995405i	$0.530526\pi$
$158$	7.31942	+	8.12904i	0.582302	+	0.646711i
$159$	−0.0132578	+	0.126140i	−0.00105141	+	0.0100035i
$160$	3.09981	+	2.25214i	0.245061	+	0.178048i
$161$	−3.45723	+	11.6970i	−0.272468	+	0.921855i
$162$	−0.358498	−	1.10334i	−0.0281663	−	0.0866868i
$163$	3.72654	+	1.65916i	0.291885	+	0.129956i	0.547456	−	0.836835i	$-0.315597\pi$
$163$	3.72654	+	1.65916i	0.291885	+	0.129956i	−0.255570	+	0.966791i	$0.582263\pi$
$164$	−0.626588	+	1.08528i	−0.0489283	+	0.0847464i
$165$	−3.57059	−	0.444546i	−0.277970	−	0.0346079i
$166$	5.04252	+	8.73391i	0.391376	+	0.677883i
$167$	−4.00525	+	2.90999i	−0.309936	+	0.225182i	−0.731869	−	0.681445i	$-0.761352\pi$
$167$	−4.00525	+	2.90999i	−0.309936	+	0.225182i	0.421933	+	0.906627i	$0.361352\pi$
$168$	5.28705	−	6.19782i	0.407905	−	0.478173i
$169$	1.79556	−	5.52615i	0.138120	−	0.425089i
$170$	0.100491	−	0.956108i	0.00770731	−	0.0733301i
$171$	6.17771	−	2.75049i	0.472421	−	0.210336i
$172$	3.96590	+	4.40457i	0.302397	+	0.335846i
$173$	−0.890789	+	0.989321i	−0.0677254	+	0.0752167i	−0.776055	−	0.630665i	$-0.782782\pi$
$173$	−0.890789	+	0.989321i	−0.0677254	+	0.0752167i	0.708330	+	0.705882i	$0.249449\pi$
$174$	−7.25022	+	5.26759i	−0.549638	+	0.399335i
$175$	5.29010	+	8.62111i	0.399894	+	0.651695i
$176$	−7.48106	+	0.641756i	−0.563906	+	0.0483742i
$177$	2.91641	+	5.05137i	0.219211	+	0.379684i
$178$	−0.00635521	−	0.0604658i	−0.000476343	−	0.00453210i
$179$	6.98782	+	1.48531i	0.522294	+	0.111017i	0.461512	−	0.887134i	$-0.347307\pi$
$179$	6.98782	+	1.48531i	0.522294	+	0.111017i	0.0607821	+	0.998151i	$0.480641\pi$
$180$	0.694129	−	0.147542i	0.0517374	−	0.0109971i
$181$	−2.59407	−	1.88470i	−0.192815	−	0.140089i	0.487189	−	0.873296i	$-0.338022\pi$
$181$	−2.59407	−	1.88470i	−0.192815	−	0.140089i	−0.680005	+	0.733208i	$0.738022\pi$
$182$	−10.9755	−	7.53364i	−0.813561	−	0.558431i
$183$	3.53669	−	10.8848i	0.261439	−	0.804628i
$184$	−9.49833	+	10.5490i	−0.700226	+	0.777680i
$185$	0.914450	+	8.70041i	0.0672317	+	0.639667i
$186$	−1.17243	+	2.03070i	−0.0859665	+	0.148898i
$187$	−1.44958	−	2.07768i	−0.106004	−	0.151935i
$188$	−6.85476			−0.499935
$189$	−0.346904	−	2.62291i	−0.0252336	−	0.190789i
$190$	−2.63007	−	8.09453i	−0.190805	−	0.587239i
$191$	−18.6858	+	3.97178i	−1.35206	+	0.287388i	−0.826292	−	0.563243i	$-0.809554\pi$
$191$	−18.6858	+	3.97178i	−1.35206	+	0.287388i	−0.525764	+	0.850631i	$0.676220\pi$
$192$	7.87944	−	3.50815i	0.568650	−	0.253179i
$193$	−3.75830	+	1.67330i	−0.270528	+	0.120447i	−0.537517	−	0.843253i	$-0.680638\pi$
$193$	−3.75830	+	1.67330i	−0.270528	+	0.120447i	0.266989	+	0.963699i	$0.413971\pi$
$194$	−10.8940	+	2.31560i	−0.782146	+	0.166250i
$195$	−1.45401	−	4.47497i	−0.104124	−	0.320459i
$196$	3.55495	−	2.88577i	0.253925	−	0.206126i
$197$	22.7631			1.62180			0.810902	−	0.585182i	$-0.198977\pi$
$197$	22.7631			1.62180			0.810902	+	0.585182i	$0.198977\pi$
$198$	−2.32080	+	3.06898i	−0.164932	+	0.218103i
$199$	−2.85056	+	4.93732i	−0.202071	+	0.349997i	−0.949196	−	0.314687i	$-0.898100\pi$
$199$	−2.85056	+	4.93732i	−0.202071	+	0.349997i	0.747125	+	0.664684i	$0.231434\pi$
$200$	1.23045	+	11.7070i	0.0870063	+	0.827809i
$201$	2.03350	−	2.25843i	0.143432	−	0.159297i
$202$	−3.11115	+	9.57514i	−0.218900	+	0.673704i
$203$	−18.4418	+	8.80978i	−1.29436	+	0.618325i
$204$	0.404218	+	0.293681i	0.0283009	+	0.0205618i
$205$	2.03305	−	0.432137i	0.141994	−	0.0301818i
$206$	15.2310	+	3.23745i	1.06120	+	0.225564i
$207$	0.481889	+	4.58487i	0.0334936	+	0.318671i
$208$	−4.90942	−	8.50336i	−0.340407	−	0.589602i
$209$	−19.2051	−	11.5839i	−1.32845	−	0.801273i
$210$	−3.32875	+	0.0891527i	−0.229705	+	0.00615212i
$211$	−2.99858	+	2.17859i	−0.206430	+	0.149980i	−0.686197	−	0.727416i	$-0.740721\pi$
$211$	−2.99858	+	2.17859i	−0.206430	+	0.149980i	0.479767	+	0.877396i	$0.340721\pi$
$212$	−0.0555139	+	0.0616544i	−0.00381271	+	0.00423444i
$213$	−7.06820	−	7.85003i	−0.484305	−	0.537875i
$214$	−16.6948	+	7.43300i	−1.14123	+	0.508110i
$215$	1.02753	−	9.77632i	0.0700771	−	0.666739i
$216$	0.951494	−	2.92840i	0.0647410	−	0.199252i
$217$	−3.47057	+	4.06843i	−0.235598	+	0.276183i
$218$	2.87648	−	2.08989i	0.194820	−	0.141545i
$219$	0.525151	+	0.909588i	0.0354864	+	0.0614643i
$220$	−1.71860	−	1.60806i	−0.115868	−	0.108415i
$221$	1.65644	−	2.86904i	0.111424	−	0.192992i
$222$	8.54627	+	3.80504i	0.573588	+	0.255378i
$223$	6.12081	+	18.8379i	0.409880	+	1.26148i	0.916751	+	0.399459i	$0.130802\pi$
$223$	6.12081	+	18.8379i	0.409880	+	1.26148i	−0.506871	+	0.862022i	$0.669198\pi$
$224$	9.08474	−	2.18678i	0.606999	−	0.146111i
$225$	3.09289	+	2.24712i	0.206193	+	0.149808i
$226$	0.973504	−	9.26227i	0.0647565	−	0.616117i
$227$	−0.663718	−	0.737134i	−0.0440525	−	0.0489253i	0.720716	−	0.693231i	$-0.243813\pi$
$227$	−0.663718	−	0.737134i	−0.0440525	−	0.0489253i	−0.764768	+	0.644305i	$0.777147\pi$
$228$	4.32668	+	0.919664i	0.286541	+	0.0609062i
$229$	−15.3507	−	6.83459i	−1.01441	−	0.451642i	−0.168914	−	0.985631i	$-0.554026\pi$
$229$	−15.3507	−	6.83459i	−1.01441	−	0.451642i	−0.845492	+	0.533989i	$0.820693\pi$
$230$	5.80230			0.382592
$231$	−6.47607	+	5.92119i	−0.426094	+	0.389586i
$232$	−23.7855			−1.56160
$233$	−13.6015	−	6.05579i	−0.891065	−	0.396728i	−0.0904461	−	0.995901i	$-0.528829\pi$
$233$	−13.6015	−	6.05579i	−0.891065	−	0.396728i	−0.800619	+	0.599173i	$0.795496\pi$
$234$	−4.92163	−	1.04613i	−0.321737	−	0.0683874i
$235$	7.60735	+	8.44882i	0.496249	+	0.551140i
$236$	−0.398810	+	3.79442i	−0.0259603	+	0.246996i
$237$	7.62814	+	5.54217i	0.495501	+	0.360003i
$238$	−1.61489	−	1.69971i	−0.104678	−	0.110176i
$239$	−3.05616	−	9.40588i	−0.197686	−	0.608416i	−0.999935	−	0.0114255i	$-0.996363\pi$
$239$	−3.05616	−	9.40588i	−0.197686	−	0.608416i	0.802248	−	0.596990i	$-0.203637\pi$
$240$	−2.24374	−	0.998978i	−0.144833	−	0.0644837i
$241$	−12.7514	+	22.0861i	−0.821391	+	1.42269i	0.0832555	+	0.996528i	$0.473468\pi$
$241$	−12.7514	+	22.0861i	−0.821391	+	1.42269i	−0.904647	+	0.426163i	$0.859865\pi$
$242$	12.7520	+	0.488518i	0.819730	+	0.0314031i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	6.05654	−	4.40033i	0.387730	−	0.281703i
$245$	−7.50210	−	1.17905i	−0.479292	−	0.0753265i
$246$	0.686825	−	2.11383i	0.0437904	−	0.134773i
$247$	3.06572	−	29.1684i	0.195067	−	1.85594i
$248$	−5.68545	+	2.53133i	−0.361027	+	0.160739i
$249$	5.81681	+	6.46022i	0.368625	+	0.409400i
$250$	7.43047	−	8.25237i	0.469944	−	0.521926i
$251$	8.20415	−	5.96066i	0.517841	−	0.376234i	−0.297949	−	0.954582i	$-0.596302\pi$
$251$	8.20415	−	5.96066i	0.517841	−	0.376234i	0.815790	+	0.578348i	$0.196302\pi$
$252$	0.824874	−	1.52139i	0.0519622	−	0.0958386i
$253$	11.5565	−	10.0116i	0.726551	−	0.629426i
$254$	−3.14747	−	5.45158i	−0.197490	−	0.342062i
$255$	−0.0866209	−	0.824143i	−0.00542441	−	0.0516099i
$256$	13.5341	+	2.87675i	0.845879	+	0.179797i
$257$	2.96933	−	0.631150i	0.185221	−	0.0393700i	−0.114367	−	0.993439i	$-0.536484\pi$
$257$	2.96933	−	0.631150i	0.185221	−	0.0393700i	0.299588	+	0.954069i	$0.403151\pi$
$258$	−8.50432	−	6.17875i	−0.529456	−	0.384672i
$259$	17.5899	+	12.0737i	1.09298	+	0.750226i
$260$	0.951085	−	2.92714i	0.0589838	−	0.181533i
$261$	−5.16892	+	5.74067i	−0.319948	+	0.355339i
$262$	2.31947	+	22.0683i	0.143297	+	1.36338i
$263$	−6.66249	+	11.5398i	−0.410827	+	0.711573i	−0.994980	−	0.100070i	$-0.968093\pi$
$263$	−6.66249	+	11.5398i	−0.410827	+	0.711573i	0.584154	+	0.811643i	$0.301427\pi$
$264$	−9.77103	+	2.96924i	−0.601365	+	0.182744i
$265$	0.137601			0.00845276
$266$	−19.1811	−	7.93167i	−1.17607	−	0.486322i
$267$	−0.0161947	−	0.0498422i	−0.000991100	−	0.00305029i
$268$	1.94442	−	0.413299i	0.118774	−	0.0252463i
$269$	17.1286	−	7.62614i	1.04435	−	0.464974i	0.188431	−	0.982086i	$-0.439660\pi$
$269$	17.1286	−	7.62614i	1.04435	−	0.464974i	0.855918	+	0.517112i	$0.172993\pi$
$270$	−1.14979	+	0.511919i	−0.0699739	+	0.0311544i
$271$	29.7205	−	6.31730i	1.80539	−	0.383748i	0.822625	−	0.568585i	$-0.192509\pi$
$271$	29.7205	−	6.31730i	1.80539	−	0.383748i	0.982769	+	0.184836i	$0.0591754\pi$
$272$	−0.534376	−	1.64464i	−0.0324013	−	0.0997209i
$273$	−10.6041	−	4.38494i	−0.641787	−	0.265389i
$274$	8.57540			0.518059
$275$	0.242738	−	12.6772i	0.0146376	−	0.764465i
$276$	−1.50777	+	2.61154i	−0.0907572	+	0.157196i
$277$	−1.09530	−	10.4211i	−0.0658103	−	0.626143i	−0.976865	−	0.213858i	$-0.931397\pi$
$277$	−1.09530	−	10.4211i	−0.0658103	−	0.626143i	0.911055	−	0.412286i	$-0.135270\pi$
$278$	−12.0765	+	13.4123i	−0.724300	+	0.804417i
$279$	−0.624588	+	1.92228i	−0.0373931	+	0.115084i
$280$	−7.28665	−	5.00158i	−0.435460	−	0.298901i
$281$	0.592927	+	0.430787i	0.0353711	+	0.0256986i	0.605330	−	0.795974i	$-0.293041\pi$
$281$	0.592927	+	0.430787i	0.0353711	+	0.0256986i	−0.569959	+	0.821673i	$0.693041\pi$
$282$	11.8918	−	2.52768i	0.708147	−	0.150521i
$283$	−5.04821	−	1.07303i	−0.300085	−	0.0637850i	0.0554087	−	0.998464i	$-0.482354\pi$
$283$	−5.04821	−	1.07303i	−0.300085	−	0.0637850i	−0.355493	+	0.934679i	$0.615687\pi$
$284$	−0.722246	−	6.87172i	−0.0428574	−	0.407761i
$285$	−3.66818	−	6.35348i	−0.217284	−	0.376347i
$286$	6.49448	+	15.3723i	0.384026	+	0.908982i
$287$	2.41598	−	4.45602i	0.142611	−	0.263031i
$288$	2.85727	−	2.07593i	0.168366	−	0.122325i
$289$	−10.9848	+	12.1999i	−0.646165	+	0.717639i
$290$	6.50561	+	7.22521i	0.382022	+	0.424279i
$291$	−8.77021	+	3.90475i	−0.514119	+	0.228901i
$292$	−0.0718127	+	0.683253i	−0.00420252	+	0.0399843i
$293$	2.77899	−	8.55285i	0.162350	−	0.499663i	−0.836481	−	0.547996i	$-0.815391\pi$
$293$	2.77899	−	8.55285i	0.162350	−	0.499663i	0.998831	+	0.0483330i	$0.0153909\pi$
$294$	−5.10310	+	6.31719i	−0.297619	+	0.368426i
$295$	5.11940	−	3.71947i	0.298063	−	0.216556i
$296$	12.4147	+	21.5029i	0.721589	+	1.24983i
$297$	−1.40675	+	3.00351i	−0.0816279	+	0.174281i
$298$	8.73686	−	15.1327i	0.506113	−	0.876613i
$299$	18.2660	+	8.13255i	1.05635	+	0.470317i
$300$	0.772756	+	2.37830i	0.0446151	+	0.137311i
$301$	−16.5125	−	17.3797i	−0.951762	−	1.00175i
$302$	20.0258	+	14.5496i	1.15236	+	0.837235i
$303$	−0.907129	+	8.63076i	−0.0521132	+	0.495824i
$304$	−10.2440	−	11.3771i	−0.587531	−	0.652519i
$305$	−12.1451	−	2.58153i	−0.695428	−	0.147818i
$306$	−0.809542	−	0.360431i	−0.0462784	−	0.0206045i
$307$	−7.68124			−0.438392			−0.219196	−	0.975681i	$-0.570343\pi$
$307$	−7.68124			−0.438392			−0.219196	+	0.975681i	$0.570343\pi$
$308$	−5.70363	+	0.643517i	−0.324995	+	0.0366678i
$309$	13.4221			0.763557
$310$	2.32396	+	1.03469i	0.131992	+	0.0587667i
$311$	−2.23024	−	0.474053i	−0.126465	−	0.0268811i	0.144244	−	0.989542i	$-0.453925\pi$
$311$	−2.23024	−	0.474053i	−0.126465	−	0.0268811i	−0.270710	+	0.962661i	$0.587258\pi$
$312$	−8.93584	−	9.92425i	−0.505892	−	0.561850i
$313$	1.45215	−	13.8163i	0.0820803	−	0.780942i	−0.873622	−	0.486606i	$-0.838235\pi$
$313$	1.45215	−	13.8163i	0.0820803	−	0.780942i	0.955702	−	0.294336i	$-0.0950985\pi$
$314$	−2.66475	−	1.93605i	−0.150380	−	0.109258i
$315$	−2.79063	+	0.671730i	−0.157234	+	0.0378477i
$316$	1.90588	+	5.86571i	0.107214	+	0.329972i
$317$	13.6172	+	6.06277i	0.764819	+	0.340519i	0.751796	−	0.659396i	$-0.229188\pi$
$317$	13.6172	+	6.06277i	0.764819	+	0.340519i	0.0130231	+	0.999915i	$0.495855\pi$
$318$	0.0735719	−	0.127430i	0.00412571	−	0.00714594i
$319$	25.4241	+	3.16536i	1.42348	+	0.177226i
$320$	−4.67863	−	8.10363i	−0.261543	−	0.453006i
$321$	−12.7440	+	9.25903i	−0.711298	+	0.516789i
$322$	9.18347	−	10.7655i	0.511775	−	0.599936i
$323$	1.59619	−	4.91257i	0.0888144	−	0.273343i
$324$	0.0683734	−	0.650530i	0.00379852	−	0.0361405i
$325$	15.1474	−	6.74406i	0.840227	−	0.374093i
$326$	−3.16659	−	3.51685i	−0.175381	−	0.194780i
$327$	2.05074	−	2.27758i	0.113406	−	0.125950i
$328$	4.77244	−	3.46738i	0.263514	−	0.191454i
$329$	27.7161	−	0.742312i	1.52804	−	0.0409250i
$330$	3.57443	+	2.15598i	0.196766	+	0.118683i
$331$	2.86642	+	4.96478i	0.157553	+	0.272889i	0.933986	−	0.357311i	$-0.116306\pi$
$331$	2.86642	+	4.96478i	0.157553	+	0.272889i	−0.776433	+	0.630200i	$0.782973\pi$
$332$	0.594376	+	5.65511i	0.0326206	+	0.310364i
$333$	7.88763	+	1.67657i	0.432239	+	0.0918753i
$334$	5.61799	−	1.19414i	0.307403	−	0.0653405i
$335$	−2.66731	−	1.93791i	−0.145731	−	0.105880i
$336$	−5.40472	+	2.58187i	−0.294851	+	0.140853i
$337$	1.73218	−	5.33110i	0.0943579	−	0.290404i	−0.892728	−	0.450596i	$-0.851211\pi$
$337$	1.73218	−	5.33110i	0.0943579	−	0.290404i	0.987086	+	0.160192i	$0.0512115\pi$
$338$	−4.51057	+	5.00950i	−0.245343	+	0.272481i
$339$	−0.839138	−	7.98387i	−0.0455757	−	0.433624i
$340$	0.271026	−	0.469431i	0.0146985	−	0.0254585i
$341$	6.41398	−	1.94909i	0.347337	−	0.105549i
$342$	−7.84516			−0.424218
$343$	−14.0614	+	12.0531i	−0.759243	+	0.650807i
$344$	−8.62152	−	26.5343i	−0.464841	−	1.43063i
$345$	4.89216	−	1.03986i	0.263385	−	0.0559842i
$346$	1.41091	−	0.628176i	0.0758508	−	0.0337710i
$347$	−7.72920	+	3.44126i	−0.414925	+	0.184737i	−0.603572	−	0.797308i	$-0.706256\pi$
$347$	−7.72920	+	3.44126i	−0.414925	+	0.184737i	0.188647	+	0.982045i	$0.439590\pi$
$348$	−4.94250	+	1.05056i	−0.264946	+	0.0563159i
$349$	3.92658	+	12.0848i	0.210185	+	0.646882i	0.999461	+	0.0328433i	$0.0104562\pi$
$349$	3.92658	+	12.0848i	0.210185	+	0.646882i	−0.789276	+	0.614039i	$0.789544\pi$
$350$	−1.53858	−	11.6331i	−0.0822407	−	0.621815i
$351$	−4.33711			−0.231498
$352$	−11.0690	−	3.83231i	−0.589977	−	0.204263i
$353$	−9.59838	+	16.6249i	−0.510870	+	0.884853i	0.489050	+	0.872256i	$0.337343\pi$
$353$	−9.59838	+	16.6249i	−0.510870	+	0.884853i	−0.999921	+	0.0125979i	$0.995990\pi$
$354$	−0.707322	−	6.72972i	−0.0375938	−	0.357681i
$355$	−7.66818	+	8.51638i	−0.406985	+	0.452002i
$356$	0.0105932	−	0.0326024i	0.000561437	−	0.00172793i
$357$	−1.66619	−	1.14368i	−0.0881844	−	0.0605300i
$358$	−6.70500	−	4.87147i	−0.354370	−	0.257465i
$359$	−29.2124	+	6.20928i	−1.54177	+	0.327713i	−0.898862	−	0.438231i	$-0.855605\pi$
$359$	−29.2124	+	6.20928i	−1.54177	+	0.327713i	−0.642907	+	0.765944i	$0.722272\pi$
$360$	−3.26747	−	0.694522i	−0.172211	−	0.0366045i
$361$	−2.79398	−	26.5829i	−0.147051	−	1.39910i
$362$	1.85993	+	3.22150i	0.0977560	+	0.169318i
$363$	10.8393	−	1.87346i	0.568915	−	0.0983313i
$364$	−3.92563	−	6.39749i	−0.205759	−	0.335319i
$365$	0.921839	−	0.669755i	0.0482513	−	0.0350566i
$366$	−8.88443	+	9.86716i	−0.464396	+	0.515764i
$367$	23.5888	+	26.1980i	1.23132	+	1.36752i	0.906752	+	0.421663i	$0.138554\pi$
$367$	23.5888	+	26.1980i	1.23132	+	1.36752i	0.324572	+	0.945861i	$0.394780\pi$
$368$	9.53459	−	4.24507i	0.497025	−	0.221290i
$369$	0.200260	−	1.90535i	0.0104251	−	0.0991884i
$370$	3.13626	−	9.65241i	0.163046	−	0.501805i
$371$	0.217785	−	0.255302i	0.0113068	−	0.0132546i
$372$	−1.06960	+	0.777110i	−0.0554562	+	0.0402913i
$373$	3.22038	+	5.57787i	0.166745	+	0.288811i	0.937274	−	0.348594i	$-0.113341\pi$
$373$	3.22038	+	5.57787i	0.166745	+	0.288811i	−0.770528	+	0.637406i	$0.780008\pi$
$374$	0.555914	+	2.88599i	0.0287456	+	0.149231i
$375$	4.78598	−	8.28956i	0.247147	−	0.428071i
$376$	29.4777	+	13.1243i	1.52019	+	0.676834i
$377$	10.3531	+	31.8637i	0.533214	+	1.64106i
$378$	−0.870001	+	2.94352i	−0.0447480	+	0.151398i
$379$	4.48572	+	3.25906i	0.230416	+	0.167407i	0.697003	−	0.717069i	$-0.254517\pi$
$379$	4.48572	+	3.25906i	0.230416	+	0.167407i	−0.466587	+	0.884475i	$0.654517\pi$
$380$	0.501612	−	4.77252i	0.0257322	−	0.244825i
$381$	−3.63076	−	4.03237i	−0.186010	−	0.206585i
$382$	21.6778	+	4.60776i	1.10913	+	0.235754i
$383$	27.6312	+	12.3022i	1.41189	+	0.628612i	0.964103	−	0.265530i	$-0.0855469\pi$
$383$	27.6312	+	12.3022i	1.41189	+	0.628612i	0.447783	+	0.894142i	$0.352214\pi$
$384$	−2.94265			−0.150166
$385$	7.12301	+	6.31583i	0.363022	+	0.321885i
$386$	4.77271			0.242925
$387$	−8.27766	−	3.68545i	−0.420777	−	0.187342i
$388$	−6.14239	−	1.30560i	−0.311832	−	0.0662820i
$389$	−22.2783	−	24.7426i	−1.12955	−	1.25450i	−0.963304	−	0.268414i	$-0.913501\pi$
$389$	−22.2783	−	24.7426i	−1.12955	−	1.25450i	−0.166251	−	0.986083i	$-0.553166\pi$
$390$	−0.570588	+	5.42878i	−0.0288929	+	0.274897i
$391$	2.84889	+	2.06984i	0.144074	+	0.104676i
$392$	−20.8126	+	5.60333i	−1.05120	+	0.283011i
$393$	5.91061	+	18.1910i	0.298151	+	0.917614i
$394$	−24.1249	−	10.7411i	−1.21540	−	0.541129i
$395$	5.11463	−	8.85881i	0.257345	−	0.445735i
$396$	−1.89922	+	1.04856i	−0.0954393	+	0.0526920i
$397$	−5.70553	−	9.88228i	−0.286353	−	0.495977i	0.686584	−	0.727051i	$-0.259110\pi$
$397$	−5.70553	−	9.88228i	−0.286353	−	0.495977i	−0.972936	+	0.231074i	$0.925776\pi$
$398$	5.35084	−	3.88761i	0.268213	−	0.194869i
$399$	−17.5938	−	3.24997i	−0.880793	−	0.162702i
$400$	2.67454	−	8.23138i	0.133727	−	0.411569i
$401$	0.717644	−	6.82792i	0.0358374	−	0.340970i	−0.961882	−	0.273466i	$-0.911830\pi$
$401$	0.717644	−	6.82792i	0.0358374	−	0.340970i	0.997719	−	0.0675039i	$-0.0215035\pi$
$402$	−3.22082	+	1.43400i	−0.160640	+	0.0715216i
$403$	5.86574	+	6.51456i	0.292193	+	0.324514i
$404$	−3.79838	+	4.21853i	−0.188976	+	0.209880i
$405$	−0.877690	+	0.637679i	−0.0436127	+	0.0316865i
$406$	23.7021	−	0.634805i	1.17632	−	0.0315048i
$407$	−10.4083	−	24.6363i	−0.515922	−	1.22118i
$408$	−1.17598	−	2.03685i	−0.0582195	−	0.100839i
$409$	2.13540	+	20.3170i	0.105589	+	1.00461i	0.911144	+	0.412088i	$0.135200\pi$
$409$	2.13540	+	20.3170i	0.105589	+	1.00461i	−0.805555	+	0.592521i	$0.798133\pi$
$410$	−2.35859	−	0.501333i	−0.116482	−	0.0247591i
$411$	7.23027	−	1.53684i	0.356643	−	0.0758068i
$412$	7.10282	+	5.16050i	0.349931	+	0.254240i
$413$	1.20162	−	15.3853i	0.0591279	−	0.757063i
$414$	1.65272	−	5.08655i	0.0812268	−	0.249990i
$415$	6.31056	−	7.00859i	0.309773	−	0.344038i
$416$	−1.60114	−	15.2338i	−0.0785023	−	0.746900i
$417$	−7.77850	+	13.4728i	−0.380915	+	0.659764i
$418$	14.8881	+	21.3391i	0.728199	+	1.04373i
$419$	−11.0291			−0.538809			−0.269405	−	0.963027i	$-0.586827\pi$
$419$	−11.0291			−0.538809			−0.269405	+	0.963027i	$0.586827\pi$
$420$	−1.73503	−	0.717462i	−0.0846609	−	0.0350086i
$421$	−6.18452	−	19.0340i	−0.301415	−	0.927661i	−0.980991	−	0.194055i	$-0.937836\pi$
$421$	−6.18452	−	19.0340i	−0.301415	−	0.927661i	0.679575	−	0.733606i	$-0.262164\pi$
$422$	4.20597	−	0.894006i	0.204743	−	0.0435195i
$423$	9.57347	−	4.26238i	0.465478	−	0.207244i
$424$	0.356773	−	0.158846i	0.0173264	−	0.00771422i
$425$	2.85639	−	0.607143i	0.138555	−	0.0294508i
$426$	3.78691	+	11.6549i	0.183476	+	0.564682i
$427$	−24.0122	+	18.4479i	−1.16203	+	0.892758i
$428$	−10.3038			−0.498055
$429$	8.23070	+	11.7971i	0.397382	+	0.569569i
$430$	−5.70211	+	9.87634i	−0.274980	+	0.476279i
$431$	−1.89139	−	17.9954i	−0.0911049	−	0.866806i	−0.940670	−	0.339322i	$-0.889802\pi$
$431$	−1.89139	−	17.9954i	−0.0911049	−	0.866806i	0.849565	−	0.527484i	$-0.176864\pi$
$432$	−1.51485	+	1.68241i	−0.0728833	+	0.0809451i
$433$	4.29438	−	13.2168i	0.206375	−	0.635156i	−0.793279	−	0.608858i	$-0.791628\pi$
$433$	4.29438	−	13.2168i	0.206375	−	0.635156i	0.999654	−	0.0262985i	$-0.00837205\pi$
$434$	5.59795	−	2.67418i	0.268710	−	0.128365i
$435$	6.78001	+	4.92596i	0.325076	+	0.236182i
$436$	1.96091	−	0.416803i	0.0939103	−	0.0199613i
$437$	30.4940	+	6.48170i	1.45873	+	0.310062i
$438$	−0.127366	−	1.21181i	−0.00608578	−	0.0579023i
$439$	−14.2244	−	24.6375i	−0.678895	−	1.17588i	−0.975314	−	0.220823i	$-0.929126\pi$
$439$	−14.2244	−	24.6375i	−0.678895	−	1.17588i	0.296418	−	0.955058i	$-0.404208\pi$
$440$	4.31168	+	10.2056i	0.205551	+	0.486535i
$441$	−3.17049	+	6.24083i	−0.150976	+	0.297182i
$442$	−3.10934	+	2.25906i	−0.147896	+	0.107453i
$443$	−10.3937	+	11.5434i	−0.493819	+	0.548441i	−0.937610	−	0.347689i	$-0.886967\pi$
$443$	−10.3937	+	11.5434i	−0.493819	+	0.548441i	0.443791	+	0.896130i	$0.353633\pi$
$444$	3.52944	+	3.91984i	0.167500	+	0.186027i
$445$	−0.0519403	+	0.0231253i	−0.00246221	+	0.00109624i
$446$	2.40196	−	22.8531i	0.113736	−	1.08213i
$447$	4.65440	−	14.3248i	0.220146	−	0.677538i
$448$	−22.4403	−	4.14522i	−1.06020	−	0.195843i
$449$	−23.2757	+	16.9108i	−1.09845	+	0.798069i	−0.980806	−	0.194987i	$-0.937533\pi$
$449$	−23.2757	+	16.9108i	−1.09845	+	0.798069i	−0.117642	+	0.993056i	$0.537533\pi$
$450$	−2.21759	−	3.84098i	−0.104538	−	0.181066i
$451$	−5.56265	+	3.07113i	−0.261935	+	0.144614i
$452$	2.62556	−	4.54760i	0.123496	−	0.213901i
$453$	19.4921	+	8.67843i	0.915818	+	0.407748i
$454$	0.355598	+	1.09442i	0.0166891	+	0.0513636i
$455$	−3.52858	+	11.9384i	−0.165422	+	0.559681i
$456$	−16.8453	−	12.2388i	−0.788854	−	0.573136i
$457$	2.10334	−	20.0120i	0.0983903	−	0.936121i	−0.828297	−	0.560289i	$-0.810690\pi$
$457$	2.10334	−	20.0120i	0.0983903	−	0.936121i	0.926688	−	0.375832i	$-0.122643\pi$
$458$	13.0441	+	14.4869i	0.609511	+	0.676930i
$459$	−0.747153	−	0.158812i	−0.0348741	−	0.00741272i
$460$	2.98868	+	1.33064i	0.139348	+	0.0620416i
$461$	−34.4580			−1.60487			−0.802435	−	0.596739i	$-0.796463\pi$
$461$	−34.4580			−1.60487			−0.802435	+	0.596739i	$0.796463\pi$
$462$	9.65751	−	3.21960i	0.449308	−	0.149789i
$463$	−15.6018			−0.725075			−0.362538	−	0.931969i	$-0.618090\pi$
$463$	−15.6018			−0.725075			−0.362538	+	0.931969i	$0.618090\pi$
$464$	15.9764	+	7.11315i	0.741685	+	0.330220i
$465$	2.14486	+	0.455904i	0.0994655	+	0.0211420i
$466$	11.5577	+	12.8362i	0.535402	+	0.594624i
$467$	−1.01349	+	9.64276i	−0.0468989	+	0.446213i	0.945724	+	0.324971i	$0.105355\pi$
$467$	−1.01349	+	9.64276i	−0.0468989	+	0.446213i	−0.992623	+	0.121243i	$0.961312\pi$
$468$	−2.29515	−	1.66752i	−0.106093	−	0.0770813i
$469$	−7.81719	+	1.88167i	−0.360964	+	0.0868876i
$470$	−4.07577	−	12.5439i	−0.188001	−	0.578608i
$471$	−2.59373	−	1.15480i	−0.119513	−	0.0532104i
$472$	8.97991	−	15.5537i	0.413334	−	0.715916i
$473$	5.68428	+	29.5096i	0.261364	+	1.35685i
$474$	−5.46935	−	9.47319i	−0.251215	−	0.435118i
$475$	20.9152	−	15.1958i	0.959656	−	0.697231i
$476$	−0.442011	−	1.24584i	−0.0202595	−	0.0571029i
$477$	0.0391941	−	0.120627i	0.00179457	−	0.00552313i
$478$	−1.19931	+	11.4107i	−0.0548552	+	0.521913i
$479$	8.31778	−	3.70332i	0.380049	−	0.169209i	−0.207816	−	0.978168i	$-0.566635\pi$
$479$	8.31778	−	3.70332i	0.380049	−	0.169209i	0.587865	+	0.808959i	$0.299969\pi$
$480$	−2.56382	−	2.84742i	−0.117022	−	0.129966i
$481$	23.4020	−	25.9906i	1.06704	−	1.18507i
$482$	23.9359	−	17.3905i	1.09025	−	0.792114i
$483$	5.81363	−	10.7226i	0.264529	−	0.487896i
$484$	6.45633	+	3.17605i	0.293470	+	0.144366i
$485$	5.20755	+	9.01974i	0.236463	+	0.409565i
$486$	0.121266	+	1.15377i	0.00550074	+	0.0523360i
$487$	−34.7344	−	7.38302i	−1.57397	−	0.334557i	−0.663511	−	0.748166i	$-0.730934\pi$
$487$	−34.7344	−	7.38302i	−1.57397	−	0.334557i	−0.910454	+	0.413610i	$0.864268\pi$
$488$	−34.4701	+	7.32684i	−1.56039	+	0.331671i
$489$	−3.30015	−	2.39770i	−0.149238	−	0.108428i
$490$	7.39457	+	4.78956i	0.334053	+	0.216370i
$491$	−1.02032	+	3.14023i	−0.0460465	+	0.141717i	−0.971436	−	0.237300i	$-0.923738\pi$
$491$	−1.02032	+	3.14023i	−0.0460465	+	0.141717i	0.925390	+	0.379016i	$0.123738\pi$
$492$	0.838539	−	0.931292i	0.0378043	−	0.0419859i
$493$	0.616778	+	5.86825i	0.0277783	+	0.264293i
$494$	−17.0127	+	29.4668i	−0.765436	+	1.32577i
$495$	3.40013	+	1.17720i	0.152825	+	0.0529111i
$496$	4.57584			0.205461
$497$	3.66444	+	27.7065i	0.164372	+	1.24281i
$498$	−3.11645	−	9.59145i	−0.139652	−	0.429803i
$499$	7.72034	−	1.64101i	0.345610	−	0.0734616i	−0.0318366	−	0.999493i	$-0.510136\pi$
$499$	7.72034	−	1.64101i	0.345610	−	0.0734616i	0.377446	+	0.926031i	$0.376802\pi$
$500$	5.71984	−	2.54664i	0.255799	−	0.113889i
$501$	4.52275	−	2.01366i	0.202062	−	0.0899636i
$502$	−11.5076	+	2.44601i	−0.513609	+	0.109171i
$503$	−2.94011	−	9.04873i	−0.131093	−	0.403463i	0.863869	−	0.503717i	$-0.168034\pi$
$503$	−2.94011	−	9.04873i	−0.131093	−	0.403463i	−0.994962	+	0.100254i	$0.968034\pi$
$504$	−6.46012	+	4.96315i	−0.287757	+	0.221076i
$505$	9.41495			0.418960
$506$	−16.9720	+	5.15749i	−0.754498	+	0.229278i
$507$	−2.90527	+	5.03208i	−0.129028	+	0.223482i
$508$	−0.371000	−	3.52983i	−0.0164605	−	0.156611i
$509$	−17.0874	+	18.9775i	−0.757387	+	0.841164i	−0.991372	−	0.131076i	$-0.958157\pi$
$509$	−17.0874	+	18.9775i	−0.757387	+	0.841164i	0.233985	+	0.972240i	$0.424823\pi$
$510$	−0.297081	+	0.914322i	−0.0131550	+	0.0404868i
$511$	0.216373	−	2.77040i	0.00957178	−	0.122555i
$512$	−17.7476	−	12.8944i	−0.784341	−	0.569857i
$513$	−6.61457	+	1.40597i	−0.292041	+	0.0620751i
$514$	−3.44478	−	0.732212i	−0.151943	−	0.0322965i
$515$	−1.52208	−	14.4817i	−0.0670710	−	0.638138i
$516$	−2.96347	−	5.13288i	−0.130459	−	0.225962i
$517$	−29.7618	−	17.9513i	−1.30892	−	0.789497i
$518$	−12.9450	−	21.0961i	−0.568771	−	0.926910i
$519$	1.07701	−	0.782497i	0.0472757	−	0.0343478i
$520$	−9.69435	+	10.7667i	−0.425125	+	0.472149i
$521$	5.55728	+	6.17198i	0.243469	+	0.270400i	0.852477	−	0.522764i	$-0.175099\pi$
$521$	5.55728	+	6.17198i	0.243469	+	0.270400i	−0.609009	+	0.793164i	$0.708432\pi$
$522$	8.18698	−	3.64508i	0.358334	−	0.159541i
$523$	−3.02841	+	28.8134i	−0.132423	+	1.25992i	0.703348	+	0.710845i	$0.251687\pi$
$523$	−3.02841	+	28.8134i	−0.132423	+	1.25992i	−0.835772	+	0.549077i	$0.814979\pi$
$524$	−3.86621	+	11.8990i	−0.168896	+	0.519809i
$525$	−3.38207	−	9.53259i	−0.147606	−	0.416037i
$526$	12.5063	−	9.08635i	0.545300	−	0.396184i
$527$	0.771945	+	1.33705i	0.0336264	+	0.0582427i
$528$	7.45101	+	0.927669i	0.324264	+	0.0403716i
$529$	0.873373	−	1.51273i	0.0379727	−	0.0657707i
$530$	−0.145833	−	0.0649290i	−0.00633458	−	0.00282034i
$531$	−1.80244	−	5.54734i	−0.0782192	−	0.240734i
$532$	−8.06091	−	8.48429i	−0.349485	−	0.367841i
$533$	−6.72230	−	4.88404i	−0.291175	−	0.211551i
$534$	−0.00635521	+	0.0604658i	−0.000275017	+	0.00261661i
$535$	11.4351	+	12.7000i	0.494384	+	0.549069i
$536$	−9.15294	−	1.94552i	−0.395347	−	0.0840336i
$537$	−6.52630	−	2.90570i	−0.281631	−	0.125390i
$538$	−21.7518			−0.937788
$539$	22.9920	−	3.21962i	0.990337	−	0.138679i
$540$	−0.709637			−0.0305379
$541$	12.0897	+	5.38267i	0.519776	+	0.231419i	0.649819	−	0.760089i	$-0.274845\pi$
$541$	12.0897	+	5.38267i	0.519776	+	0.231419i	−0.130043	+	0.991508i	$0.541511\pi$
$542$	−34.4795	−	7.32884i	−1.48102	−	0.314801i
$543$	2.14553	+	2.38285i	0.0920734	+	0.102258i
$544$	0.281990	−	2.68296i	0.0120902	−	0.115031i
$545$	−2.68993	−	1.95435i	−0.115224	−	0.0837150i
$546$	9.16936	+	9.65095i	0.392412	+	0.413023i
$547$	3.95118	+	12.1605i	0.168940	+	0.519945i	0.999305	−	0.0372753i	$-0.0118678\pi$
$547$	3.95118	+	12.1605i	0.168940	+	0.519945i	−0.830365	+	0.557220i	$0.811868\pi$
$548$	4.41706	+	1.96660i	0.188687	+	0.0840091i
$549$	−5.72248	+	9.91162i	−0.244229	+	0.423018i
$550$	−6.23919	+	13.3211i	−0.266040	+	0.568014i
$551$	26.1190	+	45.2394i	1.11271	+	1.92727i
$552$	11.4840	−	8.34363i	0.488792	−	0.355129i
$553$	−8.34135	−	23.5107i	−0.354710	−	0.999775i
$554$	−3.75652	+	11.5614i	−0.159599	+	0.491196i
$555$	0.914450	−	8.70041i	0.0388162	−	0.369312i
$556$	−9.29627	+	4.13897i	−0.394250	+	0.175531i
$557$	1.12775	+	1.25250i	0.0477845	+	0.0530700i	0.766563	−	0.642169i	$-0.221965\pi$
$557$	1.12775	+	1.25250i	0.0477845	+	0.0530700i	−0.718779	+	0.695239i	$0.755299\pi$
$558$	1.56901	−	1.74256i	0.0664216	−	0.0737687i
$559$	−31.7933	+	23.0992i	−1.34471	+	0.976992i
$560$	3.39859	+	5.53858i	0.143617	+	0.234048i
$561$	0.985926	+	2.33367i	0.0416258	+	0.0985274i
$562$	−0.425127	−	0.736341i	−0.0179329	−	0.0310607i
$563$	0.672221	+	6.39576i	0.0283307	+	0.269549i	0.999513	+	0.0312103i	$0.00993616\pi$
$563$	0.672221	+	6.39576i	0.0283307	+	0.269549i	−0.971182	+	0.238339i	$0.923397\pi$
$564$	6.70496	+	1.42518i	0.282330	+	0.0600111i
$565$	−8.51896	+	1.81076i	−0.358395	+	0.0761793i
$566$	4.84389	+	3.51929i	0.203604	+	0.147927i
$567$	−0.206010	+	2.63772i	−0.00865162	+	0.110774i
$568$	−10.0509	+	30.9334i	−0.421726	+	1.29794i
$569$	19.9237	−	22.1275i	0.835246	−	0.927635i	−0.163012	−	0.986624i	$-0.552121\pi$
$569$	19.9237	−	22.1275i	0.835246	−	0.927635i	0.998259	+	0.0589891i	$0.0187877\pi$
$570$	0.889651	+	8.46446i	0.0372634	+	0.354537i
$571$	−14.1607	+	24.5271i	−0.592607	+	1.02643i	0.401273	+	0.915959i	$0.368568\pi$
$571$	−14.1607	+	24.5271i	−0.592607	+	1.02643i	−0.993880	+	0.110467i	$0.964765\pi$
$572$	−0.180129	+	9.40741i	−0.00753156	+	0.393344i
$573$	19.1032			0.798049
$574$	−4.66316	+	3.58259i	−0.194637	+	0.149534i
$575$	5.44631	+	16.7620i	0.227127	+	0.699025i
$576$	−8.43665	+	1.79326i	−0.351527	+	0.0747194i
$577$	13.1857	−	5.87065i	0.548928	−	0.244399i	−0.113482	−	0.993540i	$-0.536200\pi$
$577$	13.1857	−	5.87065i	0.548928	−	0.244399i	0.662410	+	0.749142i	$0.269534\pi$
$578$	17.3987	−	7.74639i	0.723689	−	0.322207i
$579$	4.02407	−	0.855342i	0.167234	−	0.0355468i
$580$	1.69398	+	5.21353i	0.0703386	+	0.216480i
$581$	−3.01566	−	22.8012i	−0.125111	−	0.945952i
$582$	11.1374			0.461661
$583$	−0.402489	+	0.122309i	−0.0166694	+	0.00506553i
$584$	1.61699	−	2.80071i	0.0669116	−	0.115894i
$585$	0.491834	+	4.67949i	0.0203348	+	0.193473i
$586$	−6.98104	+	7.75323i	−0.288384	+	0.320283i
$587$	−14.5271	+	44.7098i	−0.599597	+	1.84537i	−0.0692299	+	0.997601i	$0.522054\pi$
$587$	−14.5271	+	44.7098i	−0.599597	+	1.84537i	−0.530367	+	0.847768i	$0.677946\pi$
$588$	−4.07725	+	2.08359i	−0.168143	+	0.0859259i
$589$	11.0577	+	8.03392i	0.455626	+	0.331032i
$590$	−7.18076	+	1.52632i	−0.295627	+	0.0628375i
$591$	−22.2657	−	4.73272i	−0.915888	−	0.194678i
$592$	−1.90825	−	18.1558i	−0.0784287	−	0.746199i
$593$	−6.81701	−	11.8074i	−0.279941	−	0.484872i	0.691429	−	0.722445i	$-0.256982\pi$
$593$	−6.81701	−	11.8074i	−0.279941	−	0.484872i	−0.971370	+	0.237572i	$0.923648\pi$
$594$	2.90816	−	2.51940i	0.119323	−	0.103372i
$595$	−1.04502	+	1.92742i	−0.0428415	+	0.0790165i
$596$	7.97061	−	5.79099i	0.326489	−	0.237208i
$597$	3.81479	−	4.23676i	0.156129	−	0.173399i
$598$	−15.5213	−	17.2382i	−0.634714	−	0.704921i
$599$	−8.99043	+	4.00280i	−0.367339	+	0.163550i	−0.582101	−	0.813117i	$-0.697769\pi$
$599$	−8.99043	+	4.00280i	−0.367339	+	0.163550i	0.214762	+	0.976666i	$0.431102\pi$
$600$	1.23045	−	11.7070i	0.0502331	−	0.477936i
$601$	3.62671	−	11.1619i	0.147936	−	0.455301i	−0.849440	−	0.527684i	$-0.823060\pi$
$601$	3.62671	−	11.1619i	0.147936	−	0.455301i	0.997377	+	0.0723829i	$0.0230604\pi$
$602$	9.29944	+	26.2111i	0.379017	+	1.06829i
$603$	−2.45861	+	1.78629i	−0.100122	+	0.0727432i
$604$	6.97832	+	12.0868i	0.283944	+	0.491805i
$605$	−3.25054	−	11.4825i	−0.132153	−	0.466830i
$606$	5.03395	−	8.71906i	0.204490	−	0.354187i
$607$	−17.6482	−	7.85749i	−0.716319	−	0.318926i	0.0160149	−	0.999872i	$-0.494902\pi$
$607$	−17.6482	−	7.85749i	−0.716319	−	0.318926i	−0.732333	+	0.680946i	$0.761569\pi$
$608$	−7.38030	−	22.7142i	−0.299311	−	0.921183i
$609$	19.8704	−	4.78300i	0.805191	−	0.193817i
$610$	11.6536	+	8.46682i	0.471840	+	0.342812i
$611$	4.75089	−	45.2017i	0.192200	−	1.82866i
$612$	−0.334325	−	0.371305i	−0.0135143	−	0.0150091i
$613$	−33.1389	−	7.04389i	−1.33847	−	0.284500i	−0.517602	−	0.855621i	$-0.673175\pi$
$613$	−33.1389	−	7.04389i	−1.33847	−	0.284500i	−0.820866	+	0.571121i	$0.806509\pi$
$614$	8.14078	+	3.62451i	0.328535	+	0.146273i
$615$	−2.07847			−0.0838118
$616$	25.7595	+	8.15299i	1.03788	+	0.328493i
$617$	8.05159			0.324145			0.162072	−	0.986779i	$-0.448182\pi$
$617$	8.05159			0.324145			0.162072	+	0.986779i	$0.448182\pi$
$618$	−14.2251	−	6.33342i	−0.572217	−	0.254767i
$619$	−31.9632	−	6.79398i	−1.28471	−	0.273073i	−0.485558	−	0.874204i	$-0.661384\pi$
$619$	−31.9632	−	6.79398i	−1.28471	−	0.273073i	−0.799150	+	0.601131i	$0.794717\pi$
$620$	0.959750	+	1.06591i	0.0385445	+	0.0428080i
$621$	0.481889	−	4.58487i	0.0193376	−	0.183985i
$622$	2.13998	+	1.55479i	0.0858054	+	0.0623412i
$623$	−0.0393013	+	0.132970i	−0.00157457	+	0.00532733i
$624$	3.03419	+	9.33826i	0.121465	+	0.373830i
$625$	7.97586	+	3.55108i	0.319034	+	0.142043i
$626$	−8.05844	+	13.9576i	−0.322080	+	0.557859i
$627$	16.3770	+	15.3237i	0.654035	+	0.611970i
$628$	−0.928575	−	1.60834i	−0.0370542	−	0.0641797i
$629$	4.98316	−	3.62048i	0.198692	−	0.144358i
$630$	3.27454	+	0.604881i	0.130461	+	0.0240990i
$631$	1.15136	−	3.54352i	0.0458349	−	0.141065i	−0.925520	−	0.378699i	$-0.876372\pi$
$631$	1.15136	−	3.54352i	0.0458349	−	0.141065i	0.971355	+	0.237633i	$0.0763716\pi$
$632$	3.03473	−	28.8735i	0.120715	−	1.14853i
$633$	3.38600	−	1.50755i	0.134582	−	0.0599196i
$634$	−11.5711	−	12.8510i	−0.459546	−	0.510377i
$635$	−3.93896	+	4.37466i	−0.156313	+	0.173603i
$636$	0.0671194	−	0.0487651i	0.00266146	−	0.00193366i
$637$	16.5655	+	25.4421i	0.656348	+	1.00805i
$638$	−25.4515	−	15.3515i	−1.00763	−	0.607770i
$639$	5.28163	+	9.14805i	0.208938	+	0.361891i
$640$	0.333700	+	3.17494i	0.0131906	+	0.125501i
$641$	40.3409	+	8.57472i	1.59337	+	0.338681i	0.917312	−	0.398169i	$-0.130354\pi$
$641$	40.3409	+	8.57472i	1.59337	+	0.338681i	0.676056	+	0.736850i	$0.263688\pi$
$642$	17.8754	−	3.79953i	0.705485	−	0.149955i
$643$	21.8174	+	15.8513i	0.860394	+	0.625113i	0.927992	−	0.372600i	$-0.121534\pi$
$643$	21.8174	+	15.8513i	0.860394	+	0.625113i	−0.0675979	+	0.997713i	$0.521534\pi$
$644$	7.19912	−	3.43907i	0.283685	−	0.135518i
$645$	−3.03769	+	9.34905i	−0.119609	+	0.368118i
$646$	−4.00975	+	4.45328i	−0.157762	+	0.175212i
$647$	−4.40283	−	41.8902i	−0.173093	−	1.64687i	−0.644244	−	0.764820i	$-0.722828\pi$
$647$	−4.40283	−	41.8902i	−0.173093	−	1.64687i	0.471151	−	0.882053i	$-0.343839\pi$
$648$	−1.53955	+	2.66658i	−0.0604792	+	0.104753i
$649$	−11.6684	+	15.4301i	−0.458025	+	0.605684i
$650$	−19.2359			−0.754494
$651$	4.24061	−	3.25795i	0.166202	−	0.127689i
$652$	−0.824539	−	2.53767i	−0.0322914	−	0.0993828i
$653$	32.8213	−	6.97639i	1.28440	−	0.273007i	0.485374	−	0.874307i	$-0.338683\pi$
$653$	32.8213	−	6.97639i	1.28440	−	0.273007i	0.799024	+	0.601299i	$0.205350\pi$
$654$	−3.24813	+	1.44616i	−0.127012	+	0.0565494i
$655$	18.9567	−	8.44008i	0.740701	−	0.329781i
$656$	−4.24251	+	0.901774i	−0.165642	+	0.0352084i
$657$	−0.324561	−	0.998896i	−0.0126623	−	0.0389707i
$658$	−29.7245	−	12.2915i	−1.15878	−	0.479174i
$659$	42.6300			1.66063			0.830314	−	0.557296i	$-0.188161\pi$
$659$	42.6300			1.66063			0.830314	+	0.557296i	$0.188161\pi$
$660$	1.34671	+	1.93024i	0.0524204	+	0.0751344i
$661$	18.3700	−	31.8178i	0.714510	−	1.23757i	−0.248638	−	0.968597i	$-0.579983\pi$
$661$	18.3700	−	31.8178i	0.714510	−	1.23757i	0.963148	−	0.268972i	$-0.0866838\pi$
$662$	−0.695198	−	6.61436i	−0.0270196	−	0.257075i
$663$	−2.21675	+	2.46195i	−0.0860914	+	0.0956142i
$664$	8.27141	−	25.4568i	0.320993	−	0.987915i
$665$	−1.51137	+	19.3513i	−0.0586083	+	0.750410i
$666$	−7.56840	−	5.49876i	−0.293269	−	0.213073i
$667$	−34.8342	+	7.40425i	−1.34879	+	0.286694i
$668$	3.16759	+	0.673293i	0.122558	+	0.0260505i
$669$	−2.07043	−	19.6989i	−0.0800476	−	0.761602i
$670$	1.91245	+	3.31246i	0.0738844	+	0.127972i
$671$	37.8197	−	3.24433i	1.46001	−	0.125246i
$672$	−9.34087	+	0.250173i	−0.360332	+	0.00965064i
$673$	−14.6805	+	10.6660i	−0.565893	+	0.411145i	−0.833611	−	0.552352i	$-0.813730\pi$
$673$	−14.6805	+	10.6660i	−0.565893	+	0.411145i	0.267718	+	0.963497i	$0.413730\pi$
$674$	−4.35137	+	4.83269i	−0.167608	+	0.186148i
$675$	−2.55810	−	2.84106i	−0.0984615	−	0.109353i
$676$	−3.47216	+	1.54590i	−0.133545	+	0.0594579i
$677$	2.18655	−	20.8037i	0.0840361	−	0.799550i	−0.868616	−	0.495486i	$-0.834990\pi$
$677$	2.18655	−	20.8037i	0.0840361	−	0.799550i	0.952652	−	0.304063i	$-0.0983435\pi$
$678$	−2.87797	+	8.85747i	−0.110528	+	0.340169i
$679$	24.9772	+	4.61384i	0.958535	+	0.177063i
$680$	−2.06429	+	1.49979i	−0.0791617	+	0.0575144i
$681$	0.495956	+	0.859021i	0.0190051	+	0.0329177i
$682$	−7.71741	−	0.960836i	−0.295515	−	0.0367923i
$683$	13.8552	−	23.9979i	0.530154	−	0.918254i	−0.469227	−	0.883078i	$-0.655467\pi$
$683$	13.8552	−	23.9979i	0.530154	−	0.918254i	0.999381	−	0.0351767i	$-0.0111994\pi$
$684$	−4.04092	−	1.79913i	−0.154508	−	0.0687916i
$685$	−2.47808	−	7.62676i	−0.0946827	−	0.291403i
$686$	20.5901	−	6.13914i	0.786132	−	0.234393i
$687$	13.5943	+	9.87683i	0.518655	+	0.376825i
$688$	−2.14423	+	20.4010i	−0.0817480	+	0.777780i
$689$	−0.368086	−	0.408801i	−0.0140230	−	0.0155741i
$690$	−5.67551	−	1.20637i	−0.216063	−	0.0459256i
$691$	−9.31863	−	4.14892i	−0.354497	−	0.157832i	0.221759	−	0.975102i	$-0.428820\pi$
$691$	−9.31863	−	4.14892i	−0.354497	−	0.157832i	−0.576256	+	0.817269i	$0.695487\pi$
$692$	0.870796			0.0331027
$693$	7.56564	−	4.44534i	0.287395	−	0.168865i
$694$	9.81542			0.372588
$695$	15.4184	+	6.86471i	0.584853	+	0.260393i
$696$	23.2658	+	4.94529i	0.881887	+	0.187451i
$697$	−0.979209	−	1.08752i	−0.0370902	−	0.0411928i
$698$	1.54089	−	14.6606i	0.0583234	−	0.554910i
$699$	12.0452	+	8.75137i	0.455592	+	0.331007i
$700$	1.87532	−	6.34487i	0.0708805	−	0.239814i
$701$	−9.70382	−	29.8653i	−0.366508	−	1.12800i	−0.949031	−	0.315182i	$-0.897934\pi$
$701$	−9.70382	−	29.8653i	−0.366508	−	1.12800i	0.582523	−	0.812814i	$-0.302066\pi$
$702$	4.59658	+	2.04653i	0.173487	+	0.0772413i
$703$	27.2652	−	47.2248i	1.02833	−	1.78112i
$704$	20.8883	+	19.5448i	0.787257	+	0.736623i
$705$	−5.68450	−	9.84585i	−0.214091	−	0.370816i
$706$	18.0173	−	13.0903i	0.678091	−	0.492662i
$707$	14.9013	−	17.4683i	0.560422	−	0.656962i
$708$	1.17900	−	3.62859i	0.0443095	−	0.136371i
$709$	1.81963	−	17.3127i	0.0683378	−	0.650191i	−0.905718	−	0.423882i	$-0.860667\pi$
$709$	1.81963	−	17.3127i	0.0683378	−	0.650191i	0.974055	−	0.226309i	$-0.0726660\pi$
$710$	12.1455	−	5.40753i	0.455813	−	0.202941i
$711$	−6.30917	−	7.00704i	−0.236612	−	0.262785i
$712$	−0.107976	+	0.119919i	−0.00404656	+	0.00449416i
$713$	−7.53844	+	5.47700i	−0.282317	+	0.205115i
$714$	1.22621	+	1.99832i	0.0458899	+	0.0747853i
$715$	11.7950	−	10.2182i	0.441108	−	0.382141i
$716$	−2.33647	−	4.04688i	−0.0873179	−	0.151239i
$717$	1.03378	+	9.83575i	0.0386072	+	0.367323i
$718$	33.8900	+	7.20353i	1.26476	+	0.268833i
$719$	4.71424	−	1.00204i	0.175812	−	0.0373699i	−0.119165	−	0.992875i	$-0.538022\pi$
$719$	4.71424	−	1.00204i	0.175812	−	0.0373699i	0.294976	+	0.955505i	$0.404688\pi$
$720$	1.98701	+	1.44365i	0.0740515	+	0.0538016i
$721$	−29.2780	−	20.0965i	−1.09037	−	0.748433i
$722$	−9.58241	+	29.4916i	−0.356620	+	1.09756i
$723$	17.0647	−	18.9523i	0.634644	−	0.704844i
$724$	0.219235	+	2.08589i	0.00814782	+	0.0775213i
$725$	−14.7661	+	25.5757i	−0.548400	+	0.949857i
$726$	−12.3718	−	3.12913i	−0.459160	−	0.116133i
$727$	34.0541			1.26300			0.631498	−	0.775378i	$-0.282441\pi$
$727$	34.0541			1.26300			0.631498	+	0.775378i	$0.282441\pi$
$728$	4.63269	+	35.0274i	0.171699	+	1.29820i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−1.29302	+	0.274840i	−0.0478569	+	0.0101723i
$731$	−6.32285	+	2.81511i	−0.233859	+	0.104121i
$732$	−6.83907	+	3.04495i	−0.252779	+	0.112545i
$733$	−11.5424	+	2.45341i	−0.426327	+	0.0906187i	−0.416078	−	0.909329i	$-0.636596\pi$
$733$	−11.5424	+	2.45341i	−0.426327	+	0.0906187i	−0.0102491	+	0.999947i	$0.503262\pi$
$734$	−12.6381	−	38.8960i	−0.466480	−	1.43568i
$735$	7.09303	+	2.71306i	0.261630	+	0.100073i
$736$	16.2820			0.600161
$737$	9.52457	+	3.29761i	0.350842	+	0.121469i
$738$	−1.11131	+	1.92484i	−0.0409078	+	0.0708543i
$739$	4.60981	+	43.8594i	0.169574	+	1.61339i	0.666435	+	0.745563i	$0.267819\pi$
$739$	4.60981	+	43.8594i	0.169574	+	1.61339i	−0.496860	+	0.867830i	$0.665514\pi$
$740$	3.82903	−	4.25257i	0.140758	−	0.156328i
$741$	−9.06318	+	27.8936i	−0.332944	+	1.02470i
$742$	−0.351282	+	0.167810i	−0.0128960	+	0.00616050i
$743$	13.6490	+	9.91657i	0.500733	+	0.363804i	0.809297	−	0.587400i	$-0.199848\pi$
$743$	13.6490	+	9.91657i	0.500733	+	0.363804i	−0.308564	+	0.951204i	$0.599848\pi$
$744$	6.08750	−	1.29394i	0.223179	−	0.0474381i
$745$	−15.9834	−	3.39738i	−0.585586	−	0.124470i
$746$	−0.781046	−	7.43115i	−0.0285961	−	0.272074i
$747$	−4.34654	−	7.52843i	−0.159032	−	0.275451i
$748$	−0.375502	+	1.61402i	−0.0137297	+	0.0590143i
$749$	41.6620	−	1.11582i	1.52230	−	0.0407711i
$750$	−8.98386	+	6.52715i	−0.328044	+	0.238338i
$751$	2.51057	−	2.78827i	0.0916118	−	0.101745i	−0.695596	−	0.718434i	$-0.744859\pi$
$751$	2.51057	−	2.78827i	0.0916118	−	0.101745i	0.787207	+	0.616688i	$0.211526\pi$
$752$	−15.8748	−	17.6308i	−0.578896	−	0.642929i
$753$	−9.26416	+	4.12467i	−0.337605	+	0.150311i
$754$	4.06283	−	38.6553i	0.147960	−	1.40774i
$755$	7.15309	−	22.0149i	0.260328	−	0.801206i
$756$	−1.12316	+	1.31664i	−0.0408490	+	0.0478859i
$757$	−18.9243	+	13.7493i	−0.687816	+	0.499727i	−0.875941	−	0.482418i	$-0.839759\pi$
$757$	−18.9243	+	13.7493i	−0.687816	+	0.499727i	0.188126	+	0.982145i	$0.439759\pi$
$758$	−3.21624	−	5.57069i	−0.116819	−	0.202337i
$759$	−13.3855	+	7.39013i	−0.485863	+	0.268245i
$760$	−11.2947	+	19.5630i	−0.409702	+	0.709624i
$761$	−18.7311	−	8.33964i	−0.679004	−	0.302312i	0.0381046	−	0.999274i	$-0.487868\pi$
$761$	−18.7311	−	8.33964i	−0.679004	−	0.302312i	−0.717108	+	0.696962i	$0.754535\pi$
$762$	1.94524	+	5.98684i	0.0704687	+	0.216880i
$763$	−7.88348	+	1.89763i	−0.285401	+	0.0686987i
$764$	10.1092	+	7.34477i	0.365738	+	0.265724i
$765$	−0.0866209	+	0.824143i	−0.00313179	+	0.0297970i
$766$	−23.4792	−	26.0763i	−0.848340	−	0.942177i
$767$	−24.7448	−	5.25966i	−0.893482	−	0.189915i
$768$	−12.6402	−	5.62778i	−0.456114	−	0.203075i
$769$	−39.4686			−1.42327			−0.711637	−	0.702547i	$-0.752046\pi$
$769$	−39.4686			−1.42327			−0.711637	+	0.702547i	$0.752046\pi$
$770$	−4.56893	−	10.0548i	−0.164653	−	0.362349i
$771$	−3.03566			−0.109327
$772$	2.45835	+	1.09453i	0.0884779	+	0.0393929i
$773$	1.00807	+	0.214272i	0.0362578	+	0.00770683i	0.226005	−	0.974126i	$-0.427433\pi$
$773$	1.00807	+	0.214272i	0.0362578	+	0.00770683i	−0.189747	+	0.981833i	$0.560767\pi$
$774$	7.03385	+	7.81188i	0.252826	+	0.280792i
$775$	−0.807706	+	7.68481i	−0.0290136	+	0.276046i
$776$	23.9145	+	17.3749i	0.858481	+	0.623723i
$777$	−14.6952	−	15.4670i	−0.527188	−	0.554877i
$778$	11.9360	+	36.7351i	0.427925	+	1.31702i
$779$	−11.8355	−	5.26951i	−0.424051	−	0.188800i
$780$	−1.53889	+	2.66543i	−0.0551010	+	0.0954377i
$781$	14.8599	−	31.7268i	0.531728	−	1.13528i
$782$	−2.04264	−	3.53796i	−0.0730447	−	0.126517i
$783$	6.24952	−	4.54054i	0.223340	−	0.162266i
$784$	15.6552	+	2.46041i	0.559115	+	0.0878716i
$785$	−0.951831	+	2.92943i	−0.0339723	+	0.104556i
$786$	2.31947	−	22.0683i	0.0827328	−	0.787150i
$787$	−11.6112	+	5.16962i	−0.413893	+	0.184277i	−0.603110	−	0.797658i	$-0.706072\pi$
$787$	−11.6112	+	5.16962i	−0.413893	+	0.184277i	0.189217	+	0.981935i	$0.439405\pi$
$788$	−9.96312	−	11.0652i	−0.354921	−	0.394180i
$789$	8.91615	−	9.90239i	0.317423	−	0.352534i
$790$	−9.60078	+	6.97538i	−0.341580	+	0.248173i
$791$	−10.1236	+	18.6718i	−0.359953	+	0.663894i
$792$	10.1748	−	0.872840i	0.361547	−	0.0310150i
$793$	24.8190	+	42.9878i	0.881350	+	1.52654i
$794$	1.38377	+	13.1657i	0.0491083	+	0.467234i
$795$	−0.134594	−	0.0286088i	−0.00477356	−	0.00101465i
$796$	3.64769	−	0.775340i	0.129289	−	0.0274812i
$797$	18.4216	+	13.3840i	0.652525	+	0.474087i	0.864130	−	0.503268i	$-0.167869\pi$
$797$	18.4216	+	13.3840i	0.652525	+	0.474087i	−0.211605	+	0.977355i	$0.567869\pi$
$798$	17.1129	+	11.7463i	0.605788	+	0.415815i
$799$	2.47358	−	7.61291i	0.0875091	−	0.269325i
$800$	9.03467	−	10.0340i	0.319424	−	0.354756i
$801$	0.00547804	+	0.0521201i	0.000193557	+	0.00184157i
$802$	−3.98243	+	6.89778i	−0.140625	+	0.243569i
$803$	−2.10110	+	2.77846i	−0.0741462	+	0.0980498i
$804$	−1.98786			−0.0701064
$805$	−12.2283	−	5.05660i	−0.430992	−	0.178222i
$806$	−3.14267	−	9.67214i	−0.110696	−	0.340687i
$807$	−18.3399	+	3.89826i	−0.645594	+	0.137225i
$808$	24.4112	−	10.8685i	0.858782	−	0.382354i
$809$	−17.9285	+	7.98227i	−0.630331	+	0.280641i	−0.696931	−	0.717138i	$-0.745452\pi$
$809$	−17.9285	+	7.98227i	−0.630331	+	0.280641i	0.0665998	+	0.997780i	$0.478785\pi$
$810$	1.23110	−	0.261678i	0.0432563	−	0.00919441i
$811$	6.99036	+	21.5141i	0.245465	+	0.755463i	0.995560	+	0.0941327i	$0.0300078\pi$
$811$	6.99036	+	21.5141i	0.245465	+	0.755463i	−0.750095	+	0.661330i	$0.769992\pi$
$812$	12.3542	+	5.10864i	0.433546	+	0.179278i
$813$	−30.3845			−1.06563
$814$	−0.593985	+	31.0215i	−0.0208192	+	1.08730i
$815$	−2.21273	+	3.83257i	−0.0775087	+	0.134249i
$816$	0.180759	+	1.71980i	0.00632781	+	0.0602051i
$817$	−41.0002	+	45.5353i	−1.43442	+	1.59308i
$818$	7.32371	−	22.5401i	0.256067	−	0.788095i
$819$	9.46066	+	6.49383i	0.330582	+	0.226913i
$820$	−1.09990	−	0.799124i	−0.0384102	−	0.0279066i
$821$	−26.9088	+	5.71964i	−0.939123	+	0.199617i	−0.651950	−	0.758262i	$-0.726049\pi$
$821$	−26.9088	+	5.71964i	−0.939123	+	0.199617i	−0.287173	+	0.957879i	$0.592716\pi$
$822$	−8.38801	−	1.78293i	−0.292565	−	0.0621867i
$823$	0.843323	+	8.02369i	0.0293964	+	0.279688i	0.999339	+	0.0363541i	$0.0115744\pi$
$823$	0.843323	+	8.02369i	0.0293964	+	0.279688i	−0.969943	+	0.243334i	$0.921759\pi$
$824$	−20.6640	−	35.7911i	−0.719864	−	1.24684i
$825$	−2.87318	+	12.3497i	−0.100031	+	0.429962i
$826$	−8.53331	+	15.7388i	−0.296912	+	0.547622i
$827$	−16.8449	+	12.2385i	−0.585753	+	0.425574i	−0.840794	−	0.541356i	$-0.817911\pi$
$827$	−16.8449	+	12.2385i	−0.585753	+	0.425574i	0.255041	+	0.966930i	$0.417911\pi$
$828$	2.01779	−	2.24099i	0.0701231	−	0.0778796i
$829$	−29.3942	−	32.6456i	−1.02090	−	1.13383i	−0.990944	−	0.134276i	$-0.957129\pi$
$829$	−29.3942	−	32.6456i	−1.02090	−	1.13383i	−0.0299583	−	0.999551i	$-0.509537\pi$
$830$	−9.99520	+	4.45015i	−0.346938	+	0.154467i
$831$	−1.09530	+	10.4211i	−0.0379956	+	0.361504i
$832$	−11.5597	+	35.5773i	−0.400762	+	1.23342i
$833$	1.92211	+	4.98948i	0.0665973	+	0.172875i
$834$	14.6012	−	10.6084i	0.505597	−	0.367338i
$835$	−2.68550	−	4.65143i	−0.0929357	−	0.160969i
$836$	2.77490	+	14.4057i	0.0959721	+	0.498233i
$837$	1.01060	−	1.75042i	0.0349316	−	0.0605033i
$838$	11.6890	+	5.20427i	0.403789	+	0.179778i
$839$	1.27255	+	3.91651i	0.0439334	+	0.135213i	0.970617	−	0.240629i	$-0.0773536\pi$
$839$	1.27255	+	3.91651i	0.0439334	+	0.135213i	−0.926684	+	0.375842i	$0.877354\pi$
$840$	6.08753	+	6.40726i	0.210040	+	0.221071i
$841$	−24.8150	−	18.0292i	−0.855691	−	0.621696i
$842$	−2.42696	+	23.0910i	−0.0836386	+	0.795768i
$843$	−0.490405	−	0.544650i	−0.0168904	−	0.0187587i
$844$	2.37145	+	0.504068i	0.0816288	+	0.0173507i
$845$	5.75877	+	2.56397i	0.198108	+	0.0882033i
$846$	−12.1575			−0.417983
$847$	−26.4491	−	12.1427i	−0.908802	−	0.417228i
$848$	−0.287142			−0.00986051
$849$	4.71480	+	2.09916i	0.161811	+	0.0720431i
$850$	−3.31376	−	0.704361i	−0.113661	−	0.0241594i
$851$	24.8751	+	27.6266i	0.852709	+	0.947029i
$852$	−0.722246	+	6.87172i	−0.0247438	+	0.235421i
$853$	−40.2709	−	29.2585i	−1.37885	−	1.00179i	−0.996987	−	0.0775744i	$-0.975282\pi$
$853$	−40.2709	−	29.2585i	−1.37885	−	1.00179i	−0.381863	−	0.924219i	$-0.624718\pi$
$854$	34.1536	−	8.22110i	1.16871	−	0.281320i
$855$	2.26706	+	6.97729i	0.0775318	+	0.238618i
$856$	44.3099	+	19.7280i	1.51448	+	0.674290i
$857$	5.15518	−	8.92903i	0.176097	−	0.305010i	−0.764443	−	0.644691i	$-0.776986\pi$
$857$	5.15518	−	8.92903i	0.176097	−	0.305010i	0.940541	+	0.339681i	$0.110319\pi$
$858$	−3.15648	−	16.3866i	−0.107760	−	0.559431i
$859$	−22.8390	−	39.5583i	−0.779257	−	1.34971i	−0.932370	−	0.361505i	$-0.882263\pi$
$859$	−22.8390	−	39.5583i	−0.779257	−	1.34971i	0.153113	−	0.988209i	$-0.451070\pi$
$860$	−5.20201	+	3.77948i	−0.177387	+	0.128879i
$861$	−3.28965	+	3.85634i	−0.112111	+	0.131424i
$862$	−6.48683	+	19.9644i	−0.220942	+	0.679991i
$863$	−4.37750	+	41.6491i	−0.149012	+	1.41775i	0.623039	+	0.782191i	$0.285898\pi$
$863$	−4.37750	+	41.6491i	−0.149012	+	1.41775i	−0.772050	+	0.635561i	$0.780769\pi$
$864$	−3.22644	+	1.43651i	−0.109766	+	0.0488709i
$865$	−0.966403	−	1.07330i	−0.0328587	−	0.0364933i
$866$	−10.7878	+	11.9811i	−0.366585	+	0.407134i
$867$	13.2813	−	9.64940i	0.451055	−	0.327711i
$868$	3.49669	−	0.0936507i	0.118685	−	0.00317871i
$869$	−7.08624	+	30.4587i	−0.240384	+	1.03324i
$870$	−4.86124	−	8.41991i	−0.164811	−	0.285462i
$871$	1.37774	+	13.1083i	0.0466830	+	0.444159i
$872$	−9.23055	−	1.96201i	−0.312586	−	0.0664422i
$873$	9.39041	−	1.99599i	0.317817	−	0.0675541i
$874$	−29.2599	−	21.2585i	−0.989729	−	0.719080i
$875$	−22.8515	+	10.9163i	−0.772521	+	0.369039i
$876$	0.212300	−	0.653391i	0.00717294	−	0.0220760i
$877$	15.2702	−	16.9593i	0.515639	−	0.572675i	−0.427947	−	0.903804i	$-0.640763\pi$
$877$	15.2702	−	16.9593i	0.515639	−	0.572675i	0.943585	+	0.331129i	$0.107430\pi$
$878$	3.44988	+	32.8234i	0.116428	+	1.10774i
$879$	−4.49650	+	7.78817i	−0.151663	+	0.262688i
$880$	0.155945	−	8.14440i	0.00525691	−	0.274548i
$881$	−33.1692			−1.11750			−0.558750	−	0.829336i	$-0.688719\pi$
$881$	−33.1692			−1.11750			−0.558750	+	0.829336i	$0.688719\pi$
$882$	6.30500	−	5.11815i	0.212300	−	0.172337i
$883$	−8.05135	−	24.7795i	−0.270949	−	0.833896i	−0.990263	−	0.139211i	$-0.955543\pi$
$883$	−8.05135	−	24.7795i	−0.270949	−	0.833896i	0.719313	−	0.694686i	$-0.244457\pi$
$884$	−2.11964	+	0.450544i	−0.0712913	+	0.0151534i
$885$	−5.78085	+	2.57380i	−0.194321	+	0.0865174i
$886$	16.4624	−	7.32953i	0.553065	−	0.246240i
$887$	5.28912	−	1.12424i	0.177591	−	0.0377482i	−0.118258	−	0.992983i	$-0.537731\pi$
$887$	5.28912	−	1.12424i	0.177591	−	0.0377482i	0.295849	+	0.955235i	$0.404398\pi$
$888$	−7.67270	−	23.6141i	−0.257479	−	0.792438i
$889$	1.88233	+	14.2322i	0.0631314	+	0.477331i
$890$	0.0659597			0.00221097
$891$	2.00047	−	2.64539i	0.0670184	−	0.0886240i
$892$	6.47813	−	11.2204i	0.216904	−	0.375688i
$893$	−7.40749	−	70.4776i	−0.247882	−	2.35844i
$894$	−11.6922	+	12.9855i	−0.391046	+	0.434300i
$895$	−2.39498	+	7.37101i	−0.0800555	+	0.246386i
$896$	6.41887	+	4.40593i	0.214439	+	0.147192i
$897$	−16.1760	−	11.7525i	−0.540101	−	0.392406i
$898$	32.6478	−	6.93950i	1.08947	−	0.231574i
$899$	−15.2723	−	3.24623i	−0.509360	−	0.108268i
$900$	−0.261393	−	2.48699i	−0.00871311	−	0.0828997i
$901$	−0.0484410	−	0.0839022i	−0.00161380	−	0.00279519i
$902$	7.34460	−	0.630050i	0.244548	−	0.0209784i
$903$	12.5382	+	20.4331i	0.417244	+	0.679970i
$904$	−19.9977	+	14.5292i	−0.665114	+	0.483234i
$905$	2.32765	−	2.58512i	0.0773737	−	0.0859322i
$906$	−16.5632	−	18.3952i	−0.550274	−	0.611141i
$907$	−35.1130	+	15.6333i	−1.16591	+	0.519096i	−0.896115	−	0.443822i	$-0.853622\pi$
$907$	−35.1130	+	15.6333i	−1.16591	+	0.519096i	−0.269794	+	0.962918i	$0.586956\pi$
$908$	−0.0678204	+	0.645268i	−0.00225070	+	0.0214140i
$909$	2.68174	−	8.25355i	0.0889477	−	0.273753i
$910$	9.37299	−	10.9876i	0.310712	−	0.364236i
$911$	−34.9848	+	25.4179i	−1.15910	+	0.842134i	−0.989664	−	0.143407i	$-0.954194\pi$
$911$	−34.9848	+	25.4179i	−1.15910	+	0.842134i	−0.169435	+	0.985541i	$0.554194\pi$
$912$	7.65467	+	13.2583i	0.253472	+	0.439026i
$913$	−12.2290	+	26.1097i	−0.404721	+	0.864106i
$914$	−11.6721	+	20.2167i	−0.386080	+	0.668710i
$915$	11.3430	+	5.05023i	0.374988	+	0.166955i
$916$	3.39652	+	10.4534i	0.112224	+	0.345391i
$917$	14.3438	−	48.5303i	0.473676	−	1.60261i
$918$	0.716914	+	0.520868i	0.0236617	+	0.0171912i
$919$	−0.456306	+	4.34146i	−0.0150522	+	0.143212i	−0.999467	−	0.0326513i	$-0.989605\pi$
$919$	−0.456306	+	4.34146i	−0.0150522	+	0.143212i	0.984415	+	0.175863i	$0.0562716\pi$
$920$	−10.3046	−	11.4444i	−0.339732	−	0.377311i
$921$	7.51339	+	1.59702i	0.247575	+	0.0526236i
$922$	36.5195	+	16.2595i	1.20271	+	0.535479i
$923$	45.8141			1.50799
$924$	5.71279	+	0.556396i	0.187937	+	0.0183041i
$925$	30.8283			1.01363
$926$	16.5351	+	7.36192i	0.543379	+	0.241928i
$927$	−13.1288	−	2.79061i	−0.431206	−	0.0916557i
$928$	18.2555	+	20.2748i	0.599267	+	0.665553i
$929$	5.04615	−	48.0109i	0.165559	−	1.57519i	−0.524486	−	0.851419i	$-0.675743\pi$
$929$	5.04615	−	48.0109i	0.165559	−	1.57519i	0.690045	−	0.723767i	$-0.257591\pi$
$930$	−2.05805	−	1.49526i	−0.0674862	−	0.0490316i
$931$	33.5118	+	33.4320i	1.09831	+	1.09569i
$932$	3.00949	+	9.26225i	0.0985790	+	0.303395i
$933$	2.08294	+	0.927387i	0.0681926	+	0.0303613i
$934$	5.62420	−	9.74141i	0.184030	−	0.318749i
$935$	2.40608	−	1.32840i	0.0786873	−	0.0434432i
$936$	6.67720	+	11.5652i	0.218251	+	0.378022i
$937$	−26.1309	+	18.9852i	−0.853658	+	0.620219i	−0.926152	−	0.377150i	$-0.876904\pi$
$937$	−26.1309	+	18.9852i	−0.853658	+	0.620219i	0.0724940	+	0.997369i	$0.476904\pi$
$938$	9.17276	+	1.69441i	0.299501	+	0.0553246i
$939$	−4.29298	+	13.2124i	−0.140096	+	0.431172i
$940$	0.777338	−	7.39588i	0.0253540	−	0.241227i
$941$	−39.2585	+	17.4790i	−1.27979	+	0.569799i	−0.930182	−	0.367098i	$-0.880351\pi$
$941$	−39.2585	+	17.4790i	−1.27979	+	0.569799i	−0.349607	+	0.936897i	$0.613685\pi$
$942$	2.20399	+	2.44778i	0.0718098	+	0.0797529i
$943$	5.90994	−	6.56365i	0.192454	−	0.213742i
$944$	−10.6831	+	7.76169i	−0.347704	+	0.252622i
$945$	2.86930	−	0.0768476i	0.0933385	−	0.00249985i
$946$	7.90018	−	33.9572i	0.256857	−	1.10404i
$947$	−15.9156	−	27.5666i	−0.517187	−	0.895795i	−0.999801	−	0.0199611i	$-0.993646\pi$
$947$	−15.9156	−	27.5666i	−0.517187	−	0.895795i	0.482614	−	0.875833i	$-0.339688\pi$
$948$	−0.644687	−	6.13378i	−0.0209384	−	0.199216i
$949$	−4.45573	−	0.947095i	−0.144639	−	0.0307440i
$950$	−29.3368	+	6.23574i	−0.951813	+	0.202314i
$951$	−12.0591	−	8.76147i	−0.391044	−	0.284110i
$952$	−0.484527	+	6.20379i	−0.0157036	+	0.201066i
$953$	3.73927	−	11.5083i	0.121127	−	0.372790i	−0.872049	−	0.489419i	$-0.837209\pi$
$953$	3.73927	−	11.5083i	0.121127	−	0.372790i	0.993176	+	0.116629i	$0.0372088\pi$
$954$	−0.0984585	+	0.109349i	−0.00318771	+	0.00354031i
$955$	−2.16633	−	20.6113i	−0.0701008	−	0.666964i
$956$	−3.23457	+	5.60243i	−0.104613	+	0.181196i
$957$	−24.2104	−	8.38215i	−0.782611	−	0.270957i
$958$	−10.5629			−0.341271
$959$	−18.0727	−	7.47331i	−0.583596	−	0.241326i
$960$	2.89155	+	8.89928i	0.0933245	+	0.287223i
$961$	26.3266	−	5.59588i	0.849244	−	0.180512i
$962$	−37.0661	+	16.5029i	−1.19506	+	0.532075i
$963$	14.3905	−	6.40708i	0.463728	−	0.206465i
$964$	16.3172	−	3.46833i	0.525542	−	0.111707i
$965$	−1.37920	−	4.24473i	−0.0443979	−	0.136643i
$966$	−11.2211	+	8.62086i	−0.361032	+	0.277372i
$967$	33.0443			1.06263			0.531316	−	0.847174i	$-0.321698\pi$
$967$	33.0443			1.06263			0.531316	+	0.847174i	$0.321698\pi$
$968$	−21.6834	−	26.0195i	−0.696929	−	0.836299i
$969$	−2.58269	+	4.47335i	−0.0829680	+	0.143705i
$970$	−1.26300	−	12.0166i	−0.0405524	−	0.385830i
$971$	−22.7181	+	25.2310i	−0.729059	+	0.809702i	−0.987715	−	0.156267i	$-0.950054\pi$
$971$	−22.7181	+	25.2310i	−0.729059	+	0.809702i	0.258656	+	0.965970i	$0.416721\pi$
$972$	−0.202132	+	0.622098i	−0.00648339	+	0.0199538i
$973$	37.1398	−	17.7420i	1.19065	−	0.568781i
$974$	33.3286	+	24.2147i	1.06792	+	0.775888i
$975$	−16.2186	+	3.44736i	−0.519410	+	0.110404i
$976$	25.3442	+	5.38707i	0.811247	+	0.172436i
$977$	2.70886	+	25.7731i	0.0866641	+	0.824554i	0.948374	+	0.317153i	$0.102727\pi$
$977$	2.70886	+	25.7731i	0.0866641	+	0.824554i	−0.861710	+	0.507401i	$0.830606\pi$
$978$	2.36619	+	4.09837i	0.0756625	+	0.131051i
$979$	0.131373	−	0.113811i	0.00419869	−	0.00363741i
$980$	2.71044	+	4.16283i	0.0865818	+	0.132977i
$981$	−2.47946	+	1.80143i	−0.0791631	+	0.0575153i
$982$	2.56313	−	2.84664i	0.0817928	−	0.0908401i
$983$	19.2407	+	21.3689i	0.613682	+	0.681562i	0.967244	−	0.253849i	$-0.0816965\pi$
$983$	19.2407	+	21.3689i	0.613682	+	0.681562i	−0.353562	+	0.935411i	$0.615030\pi$
$984$	−5.38907	+	2.39937i	−0.171797	+	0.0764890i
$985$	−2.58137	+	24.5600i	−0.0822491	+	0.782548i
$986$	2.11534	−	6.51036i	0.0673663	−	0.207332i
$987$	−27.2648	−	5.03642i	−0.867848	−	0.160311i
$988$	−15.5206	+	11.2764i	−0.493776	+	0.358749i
$989$	−20.8862	−	36.1760i	−0.664144	−	1.15033i
$990$	−3.04807	−	2.85203i	−0.0968741	−	0.0906434i
$991$	−4.72392	+	8.18206i	−0.150060	+	0.259912i	−0.931249	−	0.364383i	$-0.881280\pi$
$991$	−4.72392	+	8.18206i	−0.150060	+	0.259912i	0.781189	+	0.624294i	$0.214613\pi$
$992$	6.52132	+	2.90348i	0.207052	+	0.0921855i
$993$	−1.77154	−	5.45225i	−0.0562182	−	0.173022i
$994$	9.19005	−	31.0932i	0.291491	−	0.986215i
$995$	−5.00381	−	3.63548i	−0.158632	−	0.115253i
$996$	0.594376	−	5.65511i	0.0188335	−	0.179189i
$997$	13.6149	+	15.1208i	0.431187	+	0.478881i	0.919108	−	0.394006i	$-0.128911\pi$
$997$	13.6149	+	15.1208i	0.431187	+	0.478881i	−0.487921	+	0.872888i	$0.662245\pi$
$998$	−8.95654	−	1.90377i	−0.283514	−	0.0602629i
$999$	−7.36668	−	3.27986i	−0.233072	−	0.103770i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.b.25.3	yes	64
3.2	odd	2		693.2.by.c.487.6		64
7.2	even	3	inner	231.2.y.b.58.6	yes	64
11.4	even	5	inner	231.2.y.b.4.6	✓	64
21.2	odd	6		693.2.by.c.289.3		64
33.26	odd	10		693.2.by.c.235.3		64
77.37	even	15	inner	231.2.y.b.37.3	yes	64
231.191	odd	30		693.2.by.c.37.6		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.b.4.6	✓	64	11.4	even	5	inner
231.2.y.b.25.3	yes	64	1.1	even	1	trivial
231.2.y.b.37.3	yes	64	77.37	even	15	inner
231.2.y.b.58.6	yes	64	7.2	even	3	inner
693.2.by.c.37.6		64	231.191	odd	30
693.2.by.c.235.3		64	33.26	odd	10
693.2.by.c.289.3		64	21.2	odd	6
693.2.by.c.487.6		64	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05983 - 0.471865i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.437687 - 0.486101i) q^{4} +(-0.113401 + 1.07894i) q^{5} +(0.938560 + 0.681904i) q^{6} +(1.82236 + 1.91807i) q^{7} +(0.951494 + 2.92840i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(-1.05983 - 0.471865i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.437687 - 0.486101i) q^{4} +(-0.113401 + 1.07894i) q^{5} +(0.938560 + 0.681904i) q^{6} +(1.82236 + 1.91807i) q^{7} +(0.951494 + 2.92840i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.629300 - 1.08998i) q^{10} +(-0.627333 - 3.25676i) q^{11} +(0.327057 + 0.566478i) q^{12} +(3.50880 - 2.54929i) q^{13} +(-1.02631 - 2.89273i) q^{14} +(0.335248 - 1.03179i) q^{15} +(0.236643 - 2.25151i) q^{16} +(0.697807 - 0.310684i) q^{17} +(-0.776274 - 0.862140i) q^{18} +(4.52489 - 5.02540i) q^{19} +(0.574108 - 0.417114i) q^{20} +(-1.38375 - 2.25505i) q^{21} +(-0.871885 + 3.74761i) q^{22} +(2.30506 + 3.99249i) q^{23} +(-0.321854 - 3.06223i) q^{24} +(3.73948 + 0.794852i) q^{25} +(-4.92163 + 1.04613i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.134754 - 1.72537i) q^{28} +(-2.38711 + 7.34675i) q^{29} +(-0.842168 + 0.935322i) q^{30} +(0.211274 + 2.01014i) q^{31} +(1.76589 - 3.05861i) q^{32} +(-0.0634935 + 3.31602i) q^{33} -0.886154 q^{34} +(-2.27615 + 1.74871i) q^{35} +(-0.202132 - 0.622098i) q^{36} +(7.88763 - 1.67657i) q^{37} +(-7.16691 + 3.19091i) q^{38} +(-3.96215 + 1.76406i) q^{39} +(-3.26747 + 0.694522i) q^{40} +(-0.592028 - 1.82207i) q^{41} +(0.402452 + 3.04290i) q^{42} -9.06103 q^{43} +(-1.30854 + 1.73039i) q^{44} +(-0.542442 + 0.939537i) q^{45} +(-0.559051 - 5.31902i) q^{46} +(7.01213 - 7.78776i) q^{47} +(-0.699587 + 2.15311i) q^{48} +(-0.358015 + 6.99084i) q^{49} +(-3.58814 - 2.60694i) q^{50} +(-0.747153 + 0.158812i) q^{51} +(-2.77497 - 0.589837i) q^{52} +(-0.0132578 - 0.126140i) q^{53} +(0.580062 + 1.00470i) q^{54} +(3.58499 - 0.307535i) q^{55} +(-3.88292 + 7.16163i) q^{56} +(-5.47085 + 3.97481i) q^{57} +(5.99659 - 6.65989i) q^{58} +(-3.90292 - 4.33463i) q^{59} +(-0.648285 + 0.288635i) q^{60} +(-1.19632 + 11.3823i) q^{61} +(0.724599 - 2.23009i) q^{62} +(0.884657 + 2.49347i) q^{63} +(-6.97787 + 5.06972i) q^{64} +(2.35263 + 4.07488i) q^{65} +(1.63200 - 3.48444i) q^{66} +(-1.51951 + 2.63186i) q^{67} +(-0.456445 - 0.203222i) q^{68} +(-1.42461 - 4.38449i) q^{69} +(3.23747 - 0.779290i) q^{70} +(8.54586 + 6.20893i) q^{71} +(-0.321854 + 3.06223i) q^{72} +(-0.702789 - 0.780526i) q^{73} +(-9.15062 - 1.94502i) q^{74} +(-3.49251 - 1.55497i) q^{75} -4.42334 q^{76} +(5.10347 - 7.13825i) q^{77} +5.03159 q^{78} +(-8.61373 - 3.83508i) q^{79} +(2.40241 + 0.510648i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.232326 + 2.21044i) q^{82} +(-7.03285 - 5.10966i) q^{83} +(-0.490533 + 1.65965i) q^{84} +(0.256077 + 0.788124i) q^{85} +(9.60311 + 4.27558i) q^{86} +(3.86242 - 6.68990i) q^{87} +(8.94017 - 4.93586i) q^{88} +(0.0262036 + 0.0453860i) q^{89} +(1.01823 - 0.739786i) q^{90} +(11.2840 + 2.08441i) q^{91} +(0.931854 - 2.86795i) q^{92} +(0.211274 - 2.01014i) q^{93} +(-11.1064 + 4.94489i) q^{94} +(4.90898 + 5.45198i) q^{95} +(-2.36322 + 2.62463i) q^{96} +(7.76672 - 5.64285i) q^{97} +(3.67816 - 7.24014i) q^{98} +(0.751545 - 3.23035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Introduction

L-functions

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