LMFDB - Embedded newform 770.2.n.e.631.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			631.1
Root			$-0.390899 + 1.20306i$ of defining polynomial
Character	$\chi$	$=$	770.631
Dual form			770.2.n.e.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.632489 + 1.94660i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-1.65588 + 1.20306i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.962157 - 0.699048i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.632489 + 1.94660i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-1.65588 + 1.20306i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.962157 - 0.699048i) q^{9} +1.00000 q^{10} +(-2.40640 + 2.28238i) q^{11} -2.04678 q^{12} +(2.83240 + 2.05786i) q^{13} +(0.309017 - 0.951057i) q^{14} +(0.632489 + 1.94660i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.46489 + 2.51739i) q^{17} +(-0.367511 - 1.13108i) q^{18} +(-1.37408 + 4.22898i) q^{19} +(0.809017 + 0.587785i) q^{20} +2.04678 q^{21} +(-3.28837 + 0.432036i) q^{22} -2.00000 q^{23} +(-1.65588 - 1.20306i) q^{24} +(0.309017 - 0.951057i) q^{25} +(1.08188 + 3.32969i) q^{26} +(-2.99831 + 2.17840i) q^{27} +(0.809017 - 0.587785i) q^{28} +(-0.403663 - 1.24235i) q^{29} +(-0.632489 + 1.94660i) q^{30} +(4.61803 + 3.35520i) q^{31} -1.00000 q^{32} +(-2.92085 - 6.12787i) q^{33} -4.28284 q^{34} +(-0.809017 - 0.587785i) q^{35} +(0.367511 - 1.13108i) q^{36} +(-0.101212 - 0.311499i) q^{37} +(-3.59738 + 2.61365i) q^{38} +(-5.79730 + 4.21198i) q^{39} +(0.309017 + 0.951057i) q^{40} +(1.19755 - 3.68568i) q^{41} +(1.65588 + 1.20306i) q^{42} +2.63928 q^{43} +(-2.91429 - 1.58333i) q^{44} -1.18929 q^{45} +(-1.61803 - 1.17557i) q^{46} +(3.77797 - 11.6274i) q^{47} +(-0.632489 - 1.94660i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(0.809017 - 0.587785i) q^{50} +(-2.70885 - 8.33698i) q^{51} +(-1.08188 + 3.32969i) q^{52} +(-0.883011 - 0.641545i) q^{53} -3.70611 q^{54} +(-0.605270 + 3.26093i) q^{55} +1.00000 q^{56} +(-7.36304 - 5.34956i) q^{57} +(0.403663 - 1.24235i) q^{58} +(3.10910 + 9.56883i) q^{59} +(-1.65588 + 1.20306i) q^{60} +(10.5189 - 7.64244i) q^{61} +(1.76393 + 5.42882i) q^{62} +(-0.367511 + 1.13108i) q^{63} +(-0.809017 - 0.587785i) q^{64} +3.50105 q^{65} +(1.23885 - 6.67439i) q^{66} -8.44661 q^{67} +(-3.46489 - 2.51739i) q^{68} +(1.26498 - 3.89320i) q^{69} +(-0.309017 - 0.951057i) q^{70} +(4.75672 - 3.45596i) q^{71} +(0.962157 - 0.699048i) q^{72} +(2.29967 + 7.07764i) q^{73} +(0.101212 - 0.311499i) q^{74} +(1.65588 + 1.20306i) q^{75} -4.44661 q^{76} +(2.91429 + 1.58333i) q^{77} -7.16586 q^{78} +(0.403663 + 0.293278i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(-3.44661 - 10.6076i) q^{81} +(3.13522 - 2.27787i) q^{82} +(-10.2037 + 7.41342i) q^{83} +(0.632489 + 1.94660i) q^{84} +(-1.32347 + 4.07323i) q^{85} +(2.13522 + 1.55133i) q^{86} +2.67366 q^{87} +(-1.42705 - 2.99391i) q^{88} +1.39645 q^{89} +(-0.962157 - 0.699048i) q^{90} +(1.08188 - 3.32969i) q^{91} +(-0.618034 - 1.90211i) q^{92} +(-9.45208 + 6.86734i) q^{93} +(9.89085 - 7.18612i) q^{94} +(1.37408 + 4.22898i) q^{95} +(0.632489 - 1.94660i) q^{96} +(7.92705 + 5.75934i) q^{97} -1.00000 q^{98} +(3.91083 - 0.513816i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 13 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 13 * q^9	\( 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 13 q^{9} + 8 q^{10} + 8 q^{11} + 4 q^{12} + 8 q^{13} - 2 q^{14} + q^{15} - 2 q^{16} - 9 q^{17} - 7 q^{18} - 9 q^{19} + 2 q^{20} - 4 q^{21} - 8 q^{22} - 16 q^{23} + q^{24} - 2 q^{25} + 7 q^{26} - 22 q^{27} + 2 q^{28} - q^{30} + 28 q^{31} - 8 q^{32} - q^{33} + 4 q^{34} - 2 q^{35} + 7 q^{36} + 4 q^{37} - 6 q^{38} - 13 q^{39} - 2 q^{40} + 8 q^{41} - q^{42} - 14 q^{43} - 7 q^{44} - 12 q^{45} - 4 q^{46} - q^{48} - 2 q^{49} + 2 q^{50} + 4 q^{51} - 7 q^{52} + 10 q^{53} - 28 q^{54} + 7 q^{55} + 8 q^{56} - 17 q^{57} + 31 q^{59} + q^{60} + 28 q^{61} + 32 q^{62} - 7 q^{63} - 2 q^{64} + 2 q^{65} + 36 q^{66} - 26 q^{67} - 9 q^{68} + 2 q^{69} + 2 q^{70} + 34 q^{71} + 13 q^{72} - 24 q^{73} - 4 q^{74} - q^{75} + 6 q^{76} + 7 q^{77} - 2 q^{78} + 2 q^{80} + 14 q^{81} - 3 q^{82} - 21 q^{83} + q^{84} - 11 q^{85} - 11 q^{86} - 52 q^{87} + 2 q^{88} - 14 q^{89} - 13 q^{90} + 7 q^{91} + 4 q^{92} + 14 q^{93} + 5 q^{94} + 9 q^{95} + q^{96} + 50 q^{97} - 8 q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 13 * q^9 + 8 * q^10 + 8 * q^11 + 4 * q^12 + 8 * q^13 - 2 * q^14 + q^15 - 2 * q^16 - 9 * q^17 - 7 * q^18 - 9 * q^19 + 2 * q^20 - 4 * q^21 - 8 * q^22 - 16 * q^23 + q^24 - 2 * q^25 + 7 * q^26 - 22 * q^27 + 2 * q^28 - q^30 + 28 * q^31 - 8 * q^32 - q^33 + 4 * q^34 - 2 * q^35 + 7 * q^36 + 4 * q^37 - 6 * q^38 - 13 * q^39 - 2 * q^40 + 8 * q^41 - q^42 - 14 * q^43 - 7 * q^44 - 12 * q^45 - 4 * q^46 - q^48 - 2 * q^49 + 2 * q^50 + 4 * q^51 - 7 * q^52 + 10 * q^53 - 28 * q^54 + 7 * q^55 + 8 * q^56 - 17 * q^57 + 31 * q^59 + q^60 + 28 * q^61 + 32 * q^62 - 7 * q^63 - 2 * q^64 + 2 * q^65 + 36 * q^66 - 26 * q^67 - 9 * q^68 + 2 * q^69 + 2 * q^70 + 34 * q^71 + 13 * q^72 - 24 * q^73 - 4 * q^74 - q^75 + 6 * q^76 + 7 * q^77 - 2 * q^78 + 2 * q^80 + 14 * q^81 - 3 * q^82 - 21 * q^83 + q^84 - 11 * q^85 - 11 * q^86 - 52 * q^87 + 2 * q^88 - 14 * q^89 - 13 * q^90 + 7 * q^91 + 4 * q^92 + 14 * q^93 + 5 * q^94 + 9 * q^95 + q^96 + 50 * q^97 - 8 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.632489	+	1.94660i	−0.365167	+	1.12387i	0.584709	+	0.811243i	$0.301209\pi$
$3$	−0.632489	+	1.94660i	−0.365167	+	1.12387i	−0.949876	+	0.312626i	$0.898791\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$	−1.65588	+	1.20306i	−0.676009	+	0.491149i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−0.962157	−	0.699048i	−0.320719	−	0.233016i
$10$	1.00000			0.316228
$11$	−2.40640	+	2.28238i	−0.725557	+	0.688162i
$11$	−2.40640	+	2.28238i	−0.725557	+	0.688162i
$12$	−2.04678			−0.590853
$13$	2.83240	+	2.05786i	0.785568	+	0.570748i	0.906645	−	0.421895i	$-0.138635\pi$
$13$	2.83240	+	2.05786i	0.785568	+	0.570748i	−0.121077	+	0.992643i	$0.538635\pi$
$14$	0.309017	−	0.951057i	0.0825883	−	0.254181i
$15$	0.632489	+	1.94660i	0.163308	+	0.502610i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−3.46489	+	2.51739i	−0.840360	+	0.610557i	−0.922471	−	0.386066i	$-0.873834\pi$
$17$	−3.46489	+	2.51739i	−0.840360	+	0.610557i	0.0821111	+	0.996623i	$0.473834\pi$
$18$	−0.367511	−	1.13108i	−0.0866233	−	0.266599i
$19$	−1.37408	+	4.22898i	−0.315235	+	0.970194i	0.660423	+	0.750894i	$0.270377\pi$
$19$	−1.37408	+	4.22898i	−0.315235	+	0.970194i	−0.975658	+	0.219300i	$0.929623\pi$
$20$	0.809017	+	0.587785i	0.180902	+	0.131433i
$21$	2.04678			0.446643
$22$	−3.28837	+	0.432036i	−0.701082	+	0.0921103i
$23$	−2.00000			−0.417029			−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000			−0.417029			−0.208514	+	0.978019i	$0.566863\pi$
$24$	−1.65588	−	1.20306i	−0.338004	−	0.245575i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	1.08188	+	3.32969i	0.212175	+	0.653006i
$27$	−2.99831	+	2.17840i	−0.577025	+	0.419233i
$28$	0.809017	−	0.587785i	0.152890	−	0.111081i
$29$	−0.403663	−	1.24235i	−0.0749583	−	0.230698i	0.906556	−	0.422085i	$-0.138702\pi$
$29$	−0.403663	−	1.24235i	−0.0749583	−	0.230698i	−0.981515	+	0.191387i	$0.938702\pi$
$30$	−0.632489	+	1.94660i	−0.115476	+	0.355399i
$31$	4.61803	+	3.35520i	0.829423	+	0.602611i	0.919396	−	0.393333i	$-0.128678\pi$
$31$	4.61803	+	3.35520i	0.829423	+	0.602611i	−0.0899727	+	0.995944i	$0.528678\pi$
$32$	−1.00000			−0.176777
$33$	−2.92085	−	6.12787i	−0.508455	−	1.06673i
$34$	−4.28284			−0.734502
$35$	−0.809017	−	0.587785i	−0.136749	−	0.0993538i
$36$	0.367511	−	1.13108i	0.0612519	−	0.188514i
$37$	−0.101212	−	0.311499i	−0.0166392	−	0.0512102i	0.942392	−	0.334510i	$-0.108571\pi$
$37$	−0.101212	−	0.311499i	−0.0166392	−	0.0512102i	−0.959031	+	0.283300i	$0.908571\pi$
$38$	−3.59738	+	2.61365i	−0.583572	+	0.423990i
$39$	−5.79730	+	4.21198i	−0.928311	+	0.674457i
$40$	0.309017	+	0.951057i	0.0488599	+	0.150375i
$41$	1.19755	−	3.68568i	0.187026	−	0.575606i	−0.812952	−	0.582331i	$-0.802141\pi$
$41$	1.19755	−	3.68568i	0.187026	−	0.575606i	0.999977	+	0.00672509i	$0.00214068\pi$
$42$	1.65588	+	1.20306i	0.255507	+	0.185637i
$43$	2.63928			0.402487			0.201243	−	0.979541i	$-0.435502\pi$
$43$	2.63928			0.402487			0.201243	+	0.979541i	$0.435502\pi$
$44$	−2.91429	−	1.58333i	−0.439345	−	0.238696i
$45$	−1.18929			−0.177289
$46$	−1.61803	−	1.17557i	−0.238566	−	0.173328i
$47$	3.77797	−	11.6274i	0.551073	−	1.69603i	−0.155021	−	0.987911i	$-0.549544\pi$
$47$	3.77797	−	11.6274i	0.551073	−	1.69603i	0.706094	−	0.708118i	$-0.250456\pi$
$48$	−0.632489	−	1.94660i	−0.0912919	−	0.280967i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	0.809017	−	0.587785i	0.114412	−	0.0831254i
$51$	−2.70885	−	8.33698i	−0.379315	−	1.16741i
$52$	−1.08188	+	3.32969i	−0.150030	+	0.461745i
$53$	−0.883011	−	0.641545i	−0.121291	−	0.0881230i	0.525486	−	0.850802i	$-0.323884\pi$
$53$	−0.883011	−	0.641545i	−0.121291	−	0.0881230i	−0.646777	+	0.762679i	$0.723884\pi$
$54$	−3.70611			−0.504338
$55$	−0.605270	+	3.26093i	−0.0816146	+	0.439703i
$56$	1.00000			0.133631
$57$	−7.36304	−	5.34956i	−0.975258	−	0.708566i
$58$	0.403663	−	1.24235i	0.0530035	−	0.163128i
$59$	3.10910	+	9.56883i	0.404770	+	1.24576i	0.921087	+	0.389357i	$0.127303\pi$
$59$	3.10910	+	9.56883i	0.404770	+	1.24576i	−0.516316	+	0.856398i	$0.672697\pi$
$60$	−1.65588	+	1.20306i	−0.213773	+	0.155315i
$61$	10.5189	−	7.64244i	1.34681	−	0.978514i	0.347645	−	0.937626i	$-0.386981\pi$
$61$	10.5189	−	7.64244i	1.34681	−	0.978514i	0.999164	−	0.0408875i	$-0.0130185\pi$
$62$	1.76393	+	5.42882i	0.224020	+	0.689461i
$63$	−0.367511	+	1.13108i	−0.0463021	+	0.142503i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	3.50105			0.434251
$66$	1.23885	−	6.67439i	0.152492	−	0.821560i
$67$	−8.44661			−1.03192			−0.515959	−	0.856613i	$-0.672564\pi$
$67$	−8.44661			−1.03192			−0.515959	+	0.856613i	$0.672564\pi$
$68$	−3.46489	−	2.51739i	−0.420180	−	0.305279i
$69$	1.26498	−	3.89320i	0.152285	−	0.468686i
$70$	−0.309017	−	0.951057i	−0.0369346	−	0.113673i
$71$	4.75672	−	3.45596i	0.564519	−	0.410147i	−0.268591	−	0.963254i	$-0.586558\pi$
$71$	4.75672	−	3.45596i	0.564519	−	0.410147i	0.833110	+	0.553107i	$0.186558\pi$
$72$	0.962157	−	0.699048i	0.113391	−	0.0823836i
$73$	2.29967	+	7.07764i	0.269156	+	0.828375i	0.990707	+	0.136015i	$0.0434294\pi$
$73$	2.29967	+	7.07764i	0.269156	+	0.828375i	−0.721551	+	0.692361i	$0.756571\pi$
$74$	0.101212	−	0.311499i	0.0117657	−	0.0362111i
$75$	1.65588	+	1.20306i	0.191204	+	0.138918i
$76$	−4.44661			−0.510061
$77$	2.91429	+	1.58333i	0.332114	+	0.180437i
$78$	−7.16586			−0.811373
$79$	0.403663	+	0.293278i	0.0454156	+	0.0329964i	0.610261	−	0.792200i	$-0.291064\pi$
$79$	0.403663	+	0.293278i	0.0454156	+	0.0329964i	−0.564846	+	0.825196i	$0.691064\pi$
$80$	−0.309017	+	0.951057i	−0.0345492	+	0.106331i
$81$	−3.44661	−	10.6076i	−0.382957	−	1.17862i
$82$	3.13522	−	2.27787i	0.346228	−	0.251549i
$83$	−10.2037	+	7.41342i	−1.12000	+	0.813729i	−0.984209	−	0.177009i	$-0.943358\pi$
$83$	−10.2037	+	7.41342i	−1.12000	+	0.813729i	−0.135792	+	0.990737i	$0.543358\pi$
$84$	0.632489	+	1.94660i	0.0690102	+	0.212391i
$85$	−1.32347	+	4.07323i	−0.143551	+	0.441803i
$86$	2.13522	+	1.55133i	0.230247	+	0.167284i
$87$	2.67366			0.286647
$88$	−1.42705	−	2.99391i	−0.152124	−	0.319152i
$89$	1.39645			0.148023			0.0740117	−	0.997257i	$-0.476420\pi$
$89$	1.39645			0.148023			0.0740117	+	0.997257i	$0.476420\pi$
$90$	−0.962157	−	0.699048i	−0.101420	−	0.0736862i
$91$	1.08188	−	3.32969i	0.113412	−	0.349047i
$92$	−0.618034	−	1.90211i	−0.0644345	−	0.198309i
$93$	−9.45208	+	6.86734i	−0.980135	+	0.712110i
$94$	9.89085	−	7.18612i	1.02016	−	0.741192i
$95$	1.37408	+	4.22898i	0.140977	+	0.433884i
$96$	0.632489	−	1.94660i	0.0645531	−	0.198674i
$97$	7.92705	+	5.75934i	0.804870	+	0.584772i	0.912339	−	0.409436i	$-0.134275\pi$
$97$	7.92705	+	5.75934i	0.804870	+	0.584772i	−0.107469	+	0.994208i	$0.534275\pi$
$98$	−1.00000			−0.101015
$99$	3.91083	−	0.513816i	0.393053	−	0.0516405i
$100$	1.00000			0.100000
$101$	14.0667	+	10.2201i	1.39969	+	1.01694i	0.994722	+	0.102606i	$0.0327181\pi$
$101$	14.0667	+	10.2201i	1.39969	+	1.01694i	0.404970	+	0.914330i	$0.367282\pi$
$102$	2.70885	−	8.33698i	0.268216	−	0.825484i
$103$	2.12291	+	6.53364i	0.209176	+	0.643779i	0.999516	+	0.0311098i	$0.00990416\pi$
$103$	2.12291	+	6.53364i	0.209176	+	0.643779i	−0.790340	+	0.612669i	$0.790096\pi$
$104$	−2.83240	+	2.05786i	−0.277740	+	0.201790i
$105$	1.65588	−	1.20306i	0.161597	−	0.117407i
$106$	−0.337280	−	1.03804i	−0.0327596	−	0.100824i
$107$	−0.540856	+	1.66458i	−0.0522865	+	0.160921i	−0.973790	−	0.227448i	$-0.926962\pi$
$107$	−0.540856	+	1.66458i	−0.0522865	+	0.160921i	0.921504	+	0.388370i	$0.126962\pi$
$108$	−2.99831	−	2.17840i	−0.288512	−	0.209617i
$109$	5.88436			0.563620			0.281810	−	0.959470i	$-0.409065\pi$
$109$	5.88436			0.563620			0.281810	+	0.959470i	$0.409065\pi$
$110$	−2.40640	+	2.28238i	−0.229441	+	0.217616i
$111$	0.670380			0.0636297
$112$	0.809017	+	0.587785i	0.0764449	+	0.0555405i
$113$	5.29282	−	16.2896i	0.497907	−	1.53240i	−0.314470	−	0.949267i	$-0.601827\pi$
$113$	5.29282	−	16.2896i	0.497907	−	1.53240i	0.812377	−	0.583132i	$-0.198173\pi$
$114$	−2.81243	−	8.65577i	−0.263408	−	0.810687i
$115$	−1.61803	+	1.17557i	−0.150882	+	0.109623i
$116$	1.05680	−	0.767813i	0.0981217	−	0.0712896i
$117$	−1.28667	−	3.95998i	−0.118953	−	0.366100i
$118$	−3.10910	+	9.56883i	−0.286216	+	0.880882i
$119$	3.46489	+	2.51739i	0.317626	+	0.230769i
$120$	−2.04678			−0.186844
$121$	0.581513	−	10.9846i	0.0528649	−	0.998602i
$122$	13.0021			1.17715
$123$	6.41710	+	4.66230i	0.578611	+	0.420385i
$124$	−1.76393	+	5.42882i	−0.158406	+	0.487523i
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$	−0.962157	+	0.699048i	−0.0857158	+	0.0622762i
$127$	−8.04339	+	5.84387i	−0.713736	+	0.518559i	−0.884377	−	0.466774i	$-0.845416\pi$
$127$	−8.04339	+	5.84387i	−0.713736	+	0.518559i	0.170641	+	0.985333i	$0.445416\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−1.66932	+	5.13763i	−0.146975	+	0.452343i
$130$	2.83240	+	2.05786i	0.248418	+	0.180486i
$131$	7.65112			0.668482			0.334241	−	0.942488i	$-0.391520\pi$
$131$	7.65112			0.668482			0.334241	+	0.942488i	$0.391520\pi$
$132$	4.92536	−	4.67151i	0.428698	−	0.406603i
$133$	4.44661			0.385570
$134$	−6.83345	−	4.96479i	−0.590320	−	0.428893i
$135$	−1.14525	+	3.52472i	−0.0985676	+	0.303360i
$136$	−1.32347	−	4.07323i	−0.113487	−	0.349276i
$137$	−1.74779	+	1.26984i	−0.149323	+	0.108490i	−0.659939	−	0.751320i	$-0.729418\pi$
$137$	−1.74779	+	1.26984i	−0.149323	+	0.108490i	0.510615	+	0.859809i	$0.329418\pi$
$138$	3.31175	−	2.40613i	0.281915	−	0.204823i
$139$	6.52995	+	20.0971i	0.553863	+	1.70462i	0.698926	+	0.715194i	$0.253662\pi$
$139$	6.52995	+	20.0971i	0.553863	+	1.70462i	−0.145062	+	0.989423i	$0.546338\pi$
$140$	0.309017	−	0.951057i	0.0261167	−	0.0803789i
$141$	20.2444	+	14.7084i	1.70488	+	1.23867i
$142$	5.87963			0.493408
$143$	−11.5127	+	1.51258i	−0.962742	+	0.126488i
$144$	1.18929			0.0991077
$145$	−1.05680	−	0.767813i	−0.0877627	−	0.0637634i
$146$	−2.29967	+	7.07764i	−0.190322	+	0.585750i
$147$	−0.632489	−	1.94660i	−0.0521668	−	0.160553i
$148$	0.264977	−	0.192517i	0.0217810	−	0.0158248i
$149$	12.9515	−	9.40980i	1.06103	−	0.770881i	0.0867488	−	0.996230i	$-0.472352\pi$
$149$	12.9515	−	9.40980i	1.06103	−	0.770881i	0.974278	+	0.225349i	$0.0723522\pi$
$150$	0.632489	+	1.94660i	0.0516425	+	0.158939i
$151$	3.99826	−	12.3054i	0.325374	−	1.00140i	−0.645898	−	0.763424i	$-0.723517\pi$
$151$	3.99826	−	12.3054i	0.325374	−	1.00140i	0.971272	−	0.237974i	$-0.0764832\pi$
$152$	−3.59738	−	2.61365i	−0.291786	−	0.211995i
$153$	5.09355			0.411789
$154$	1.42705	+	2.99391i	0.114995	+	0.241257i
$155$	5.70820			0.458494
$156$	−5.79730	−	4.21198i	−0.464155	−	0.337229i
$157$	5.71542	−	17.5902i	0.456140	−	1.40385i	−0.413652	−	0.910435i	$-0.635747\pi$
$157$	5.71542	−	17.5902i	0.456140	−	1.40385i	0.869792	−	0.493419i	$-0.164253\pi$
$158$	0.154186	+	0.474534i	0.0122663	+	0.0377519i
$159$	1.80733	−	1.31310i	0.143330	−	0.104136i
$160$	−0.809017	+	0.587785i	−0.0639584	+	0.0464685i
$161$	0.618034	+	1.90211i	0.0487079	+	0.149908i
$162$	3.44661	−	10.6076i	0.270791	−	0.833410i
$163$	−5.28225	−	3.83778i	−0.413738	−	0.300598i	0.361376	−	0.932420i	$-0.382307\pi$
$163$	−5.28225	−	3.83778i	−0.413738	−	0.300598i	−0.775113	+	0.631822i	$0.782307\pi$
$164$	3.87535			0.302614
$165$	−5.96489	−	3.24072i	−0.464366	−	0.252290i
$166$	−12.6125			−0.978917
$167$	9.70820	+	7.05342i	0.751243	+	0.545810i	0.896212	−	0.443626i	$-0.146308\pi$
$167$	9.70820	+	7.05342i	0.751243	+	0.545810i	−0.144969	+	0.989436i	$0.546308\pi$
$168$	−0.632489	+	1.94660i	−0.0487976	+	0.150183i
$169$	−0.229502	−	0.706334i	−0.0176540	−	0.0543334i
$170$	−3.46489	+	2.51739i	−0.265745	+	0.193075i
$171$	4.27834	−	3.10839i	0.327173	−	0.237705i
$172$	0.815583	+	2.51011i	0.0621876	+	0.191394i
$173$	−2.33108	+	7.17434i	−0.177229	+	0.545455i	−0.999728	−	0.0233115i	$-0.992579\pi$
$173$	−2.33108	+	7.17434i	−0.177229	+	0.545455i	0.822499	+	0.568766i	$0.192579\pi$
$174$	2.16304	+	1.57154i	0.163980	+	0.119138i
$175$	−1.00000			−0.0755929
$176$	0.605270	−	3.26093i	0.0456240	−	0.245802i
$177$	−20.5931			−1.54788
$178$	1.12975	+	0.820813i	0.0846785	+	0.0615225i
$179$	2.06058	−	6.34183i	0.154015	−	0.474010i	−0.844044	−	0.536273i	$-0.819832\pi$
$179$	2.06058	−	6.34183i	0.154015	−	0.474010i	0.998060	+	0.0622628i	$0.0198317\pi$
$180$	−0.367511	−	1.13108i	−0.0273927	−	0.0843060i
$181$	2.63928	−	1.91755i	0.196176	−	0.142530i	−0.485361	−	0.874314i	$-0.661312\pi$
$181$	2.63928	−	1.91755i	0.196176	−	0.142530i	0.681537	+	0.731783i	$0.261312\pi$
$182$	2.83240	−	2.05786i	0.209952	−	0.152539i
$183$	8.22367	+	25.3099i	0.607911	+	1.87096i
$184$	0.618034	−	1.90211i	0.0455621	−	0.140226i
$185$	−0.264977	−	0.192517i	−0.0194815	−	0.0141541i
$186$	−11.6834			−0.856670
$187$	2.59228	−	13.9660i	0.189566	−	1.02130i
$188$	12.2258			0.891655
$189$	2.99831	+	2.17840i	0.218095	+	0.158455i
$190$	−1.37408	+	4.22898i	−0.0996861	+	0.306802i
$191$	−4.23460	−	13.0328i	−0.306405	−	0.943018i	−0.979149	−	0.203143i	$-0.934884\pi$
$191$	−4.23460	−	13.0328i	−0.306405	−	0.943018i	0.672744	−	0.739875i	$-0.265116\pi$
$192$	1.65588	−	1.20306i	0.119503	−	0.0868237i
$193$	−9.01787	+	6.55186i	−0.649120	+	0.471613i	−0.862971	−	0.505253i	$-0.831399\pi$
$193$	−9.01787	+	6.55186i	−0.649120	+	0.471613i	0.213851	+	0.976866i	$0.431399\pi$
$194$	3.02786	+	9.31881i	0.217388	+	0.669051i
$195$	−2.21437	+	6.81513i	−0.158574	+	0.488042i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	−3.51254			−0.250258			−0.125129	−	0.992140i	$-0.539935\pi$
$197$	−3.51254			−0.250258			−0.125129	+	0.992140i	$0.539935\pi$
$198$	3.46594	+	1.88304i	0.246314	+	0.133822i
$199$	19.5167			1.38350			0.691752	−	0.722135i	$-0.256839\pi$
$199$	19.5167			1.38350			0.691752	+	0.722135i	$0.256839\pi$
$200$	0.809017	+	0.587785i	0.0572061	+	0.0415627i
$201$	5.34238	−	16.4422i	0.376823	−	1.15974i
$202$	5.37301	+	16.5364i	0.378044	+	1.16350i
$203$	−1.05680	+	0.767813i	−0.0741731	+	0.0538899i
$204$	7.09186	−	5.15254i	0.496530	−	0.360750i
$205$	−1.19755	−	3.68568i	−0.0836405	−	0.257419i
$206$	−2.12291	+	6.53364i	−0.147910	+	0.455220i
$207$	1.92431	+	1.39810i	0.133749	+	0.0971744i
$208$	−3.50105			−0.242754
$209$	−6.34554	−	13.3128i	−0.438930	−	0.920863i
$210$	2.04678			0.141241
$211$	11.6090	+	8.43443i	0.799197	+	0.580650i	0.910678	−	0.413116i	$-0.135560\pi$
$211$	11.6090	+	8.43443i	0.799197	+	0.580650i	−0.111482	+	0.993766i	$0.535560\pi$
$212$	0.337280	−	1.03804i	0.0231645	−	0.0712930i
$213$	3.71880	+	11.4453i	0.254808	+	0.784218i
$214$	−1.41598	+	1.02877i	−0.0967943	+	0.0703252i
$215$	2.13522	−	1.55133i	0.145621	−	0.105800i
$216$	−1.14525	−	3.52472i	−0.0779245	−	0.239827i
$217$	1.76393	−	5.42882i	0.119744	−	0.368533i
$218$	4.76055	+	3.45874i	0.322425	+	0.234256i
$219$	−15.2319			−1.02927
$220$	−3.28837	+	0.432036i	−0.221702	+	0.0291278i
$221$	−14.9944			−1.00863
$222$	0.542349	+	0.394039i	0.0364001	+	0.0264462i
$223$	4.10933	−	12.6472i	0.275181	−	0.846920i	−0.713990	−	0.700155i	$-0.753114\pi$
$223$	4.10933	−	12.6472i	0.275181	−	0.846920i	0.989171	−	0.146765i	$-0.0468860\pi$
$224$	0.309017	+	0.951057i	0.0206471	+	0.0635451i
$225$	−0.962157	+	0.699048i	−0.0641438	+	0.0466032i
$226$	13.8568	−	10.0675i	0.921740	−	0.669683i
$227$	−5.84475	−	17.9883i	−0.387930	−	1.19392i	−0.934333	−	0.356402i	$-0.884003\pi$
$227$	−5.84475	−	17.9883i	−0.387930	−	1.19392i	0.546403	−	0.837523i	$-0.315997\pi$
$228$	2.81243	−	8.65577i	0.186258	−	0.573242i
$229$	−3.14799	−	2.28715i	−0.208025	−	0.151139i	0.478895	−	0.877872i	$-0.341038\pi$
$229$	−3.14799	−	2.28715i	−0.208025	−	0.151139i	−0.686920	+	0.726733i	$0.741038\pi$
$230$	−2.00000			−0.131876
$231$	−4.92536	+	4.67151i	−0.324065	+	0.307363i
$232$	1.30628			0.0857615
$233$	−5.60189	−	4.07001i	−0.366992	−	0.266635i	0.388971	−	0.921250i	$-0.372831\pi$
$233$	−5.60189	−	4.07001i	−0.366992	−	0.266635i	−0.755962	+	0.654615i	$0.772831\pi$
$234$	1.28667	−	3.95998i	0.0841125	−	0.258872i
$235$	−3.77797	−	11.6274i	−0.246448	−	0.758487i
$236$	−8.13973	+	5.91386i	−0.529851	+	0.384960i
$237$	−0.826208	+	0.600275i	−0.0536680	+	0.0389921i
$238$	1.32347	+	4.07323i	0.0857879	+	0.264028i
$239$	−8.23460	+	25.3435i	−0.532652	+	1.63934i	0.216015	+	0.976390i	$0.430694\pi$
$239$	−8.23460	+	25.3435i	−0.532652	+	1.63934i	−0.748668	+	0.662945i	$0.769306\pi$
$240$	−1.65588	−	1.20306i	−0.106886	−	0.0776575i
$241$	−0.0928140			−0.00597868			−0.00298934	−	0.999996i	$-0.500952\pi$
$241$	−0.0928140			−0.00597868			−0.00298934	+	0.999996i	$0.500952\pi$
$242$	6.92705	−	8.54494i	0.445288	−	0.549289i
$243$	11.7103			0.751216
$244$	10.5189	+	7.64244i	0.673404	+	0.489257i
$245$	−0.309017	+	0.951057i	−0.0197424	+	0.0607608i
$246$	2.45112	+	7.54376i	0.156277	+	0.480972i
$247$	−12.5946	+	9.15051i	−0.801375	+	0.582233i
$248$	−4.61803	+	3.35520i	−0.293245	+	0.213055i
$249$	−7.97724	−	24.5514i	−0.505537	−	1.55588i
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	−16.9944	−	12.3472i	−1.07268	−	0.779347i	−0.0962870	−	0.995354i	$-0.530697\pi$
$251$	−16.9944	−	12.3472i	−1.07268	−	0.779347i	−0.976392	+	0.216007i	$0.930697\pi$
$252$	−1.18929			−0.0749184
$253$	4.81280	−	4.56475i	0.302578	−	0.286984i
$254$	−9.94218			−0.623828
$255$	−7.09186	−	5.15254i	−0.444110	−	0.322664i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−1.30733	−	4.02354i	−0.0815488	−	0.250981i	0.901967	−	0.431806i	$-0.142123\pi$
$257$	−1.30733	−	4.02354i	−0.0815488	−	0.250981i	−0.983515	+	0.180824i	$0.942123\pi$
$258$	−4.37033	+	3.17523i	−0.272085	+	0.197681i
$259$	−0.264977	+	0.192517i	−0.0164649	+	0.0119624i
$260$	1.08188	+	3.32969i	0.0670955	+	0.206499i
$261$	−0.480073	+	1.47751i	−0.0297158	+	0.0914558i
$262$	6.18989	+	4.49722i	0.382413	+	0.277839i
$263$	−16.4789			−1.01613			−0.508066	−	0.861318i	$-0.669639\pi$
$263$	−16.4789			−1.01613			−0.508066	+	0.861318i	$0.669639\pi$
$264$	6.73055	−	0.884280i	0.414237	−	0.0544237i
$265$	−1.09146			−0.0670480
$266$	3.59738	+	2.61365i	0.220570	+	0.160253i
$267$	−0.883239	+	2.71833i	−0.0540534	+	0.166359i
$268$	−2.61015	−	8.03320i	−0.159440	−	0.490706i
$269$	−16.4108	+	11.9231i	−1.00058	+	0.726966i	−0.962213	−	0.272298i	$-0.912216\pi$
$269$	−16.4108	+	11.9231i	−1.00058	+	0.726966i	−0.0383697	+	0.999264i	$0.512216\pi$
$270$	−2.99831	+	2.17840i	−0.182471	+	0.132573i
$271$	−4.27811	−	13.1667i	−0.259877	−	0.799818i	−0.992830	−	0.119539i	$-0.961858\pi$
$271$	−4.27811	−	13.1667i	−0.259877	−	0.799818i	0.732953	−	0.680279i	$-0.238142\pi$
$272$	1.32347	−	4.07323i	0.0802473	−	0.246976i
$273$	5.79730	+	4.21198i	0.350868	+	0.254921i
$274$	−2.16038			−0.130513
$275$	1.42705	+	2.99391i	0.0860544	+	0.180540i
$276$	4.09355			0.246403
$277$	−6.87963	−	4.99834i	−0.413357	−	0.300321i	0.361603	−	0.932332i	$-0.382230\pi$
$277$	−6.87963	−	4.99834i	−0.413357	−	0.300321i	−0.774959	+	0.632011i	$0.782230\pi$
$278$	−6.52995	+	20.0971i	−0.391641	+	1.20535i
$279$	−2.09783	−	6.45646i	−0.125594	−	0.386538i
$280$	0.809017	−	0.587785i	0.0483480	−	0.0351269i
$281$	1.66856	−	1.21228i	0.0995380	−	0.0723186i	−0.536903	−	0.843644i	$-0.680406\pi$
$281$	1.66856	−	1.21228i	0.0995380	−	0.0723186i	0.636441	+	0.771325i	$0.280406\pi$
$282$	7.73266	+	23.7987i	0.460473	+	1.41719i
$283$	−8.44278	+	25.9842i	−0.501871	+	1.54460i	0.304097	+	0.952641i	$0.401645\pi$
$283$	−8.44278	+	25.9842i	−0.501871	+	1.54460i	−0.805968	+	0.591959i	$0.798355\pi$
$284$	4.75672	+	3.45596i	0.282259	+	0.205073i
$285$	−9.10121			−0.539109
$286$	−10.2031	−	5.54330i	−0.603319	−	0.327782i
$287$	−3.87535			−0.228755
$288$	0.962157	+	0.699048i	0.0566957	+	0.0411918i
$289$	0.414933	−	1.27703i	0.0244078	−	0.0751196i
$290$	−0.403663	−	1.24235i	−0.0237039	−	0.0729531i
$291$	−16.2249	+	11.7881i	−0.951120	+	0.691029i
$292$	−6.02060	+	4.37422i	−0.352329	+	0.255982i
$293$	−5.88984	−	18.1271i	−0.344088	−	1.05899i	−0.962070	−	0.272802i	$-0.912050\pi$
$293$	−5.88984	−	18.1271i	−0.344088	−	1.05899i	0.617982	−	0.786192i	$-0.287950\pi$
$294$	0.632489	−	1.94660i	0.0368875	−	0.113528i
$295$	8.13973	+	5.91386i	0.473913	+	0.344318i
$296$	0.327530			0.0190373
$297$	2.24320	−	12.0854i	0.130164	−	0.701264i
$298$	16.0089			0.927372
$299$	−5.66481	−	4.11573i	−0.327604	−	0.238019i
$300$	−0.632489	+	1.94660i	−0.0365167	+	0.112387i
$301$	−0.815583	−	2.51011i	−0.0470094	−	0.144680i
$302$	10.4676	−	7.60514i	0.602342	−	0.437627i
$303$	−28.7915	+	20.9182i	−1.65403	+	1.20172i
$304$	−1.37408	−	4.22898i	−0.0788088	−	0.242548i
$305$	4.01787	−	12.3657i	0.230062	−	0.708059i
$306$	4.12077	+	2.99391i	0.235569	+	0.171151i
$307$	27.8834			1.59139			0.795694	−	0.605699i	$-0.207106\pi$
$307$	27.8834			1.59139			0.795694	+	0.605699i	$0.207106\pi$
$308$	−0.605270	+	3.26093i	−0.0344885	+	0.185809i
$309$	−14.0611			−0.799908
$310$	4.61803	+	3.35520i	0.262287	+	0.190562i
$311$	6.49975	−	20.0042i	0.368567	−	1.13433i	−0.579150	−	0.815221i	$-0.696615\pi$
$311$	6.49975	−	20.0042i	0.368567	−	1.13433i	0.947717	−	0.319112i	$-0.103385\pi$
$312$	−2.21437	−	6.81513i	−0.125364	−	0.385831i
$313$	−3.19417	+	2.32070i	−0.180545	+	0.131174i	−0.674387	−	0.738378i	$-0.735592\pi$
$313$	−3.19417	+	2.32070i	−0.180545	+	0.131174i	0.493842	+	0.869552i	$0.335592\pi$
$314$	14.9632	−	10.8714i	0.844420	−	0.613507i
$315$	0.367511	+	1.13108i	0.0207069	+	0.0637294i
$316$	−0.154186	+	0.474534i	−0.00867361	+	0.0266946i
$317$	22.7516	+	16.5300i	1.27786	+	0.928417i	0.999486	−	0.0320561i	$-0.0102055\pi$
$317$	22.7516	+	16.5300i	1.27786	+	0.928417i	0.278371	+	0.960474i	$0.410206\pi$
$318$	2.23398			0.125275
$319$	3.80688	+	2.06827i	0.213144	+	0.115801i
$320$	−1.00000			−0.0559017
$321$	−2.89819	−	2.10566i	−0.161761	−	0.117526i
$322$	−0.618034	+	1.90211i	−0.0344417	+	0.106001i
$323$	−5.88496	−	18.1120i	−0.327448	−	1.00778i
$324$	9.02334	−	6.55584i	0.501297	−	0.364213i
$325$	2.83240	−	2.05786i	0.157114	−	0.114150i
$326$	−2.01764	−	6.20965i	−0.111747	−	0.343921i
$327$	−3.72179	+	11.4545i	−0.205816	+	0.633435i
$328$	3.13522	+	2.27787i	0.173114	+	0.125775i
$329$	−12.2258			−0.674028
$330$	−2.92085	−	6.12787i	−0.160788	−	0.337328i
$331$	30.2738			1.66400			0.831999	−	0.554777i	$-0.187196\pi$
$331$	30.2738			1.66400			0.831999	+	0.554777i	$0.187196\pi$
$332$	−10.2037	−	7.41342i	−0.560001	−	0.406864i
$333$	−0.120371	+	0.370464i	−0.00659629	+	0.0203013i
$334$	3.70820	+	11.4127i	0.202904	+	0.624474i
$335$	−6.83345	+	4.96479i	−0.373351	+	0.271256i
$336$	−1.65588	+	1.20306i	−0.0903355	+	0.0656326i
$337$	9.91215	+	30.5065i	0.539949	+	1.66179i	0.732705	+	0.680546i	$0.238257\pi$
$337$	9.91215	+	30.5065i	0.539949	+	1.66179i	−0.192756	+	0.981247i	$0.561743\pi$
$338$	0.229502	−	0.706334i	0.0124832	−	0.0384195i
$339$	28.3617	+	20.6060i	1.54040	+	1.11916i
$340$	−4.28284			−0.232270
$341$	−18.7707	+	2.46615i	−1.01649	+	0.133549i
$342$	5.28832			0.285959
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	−0.815583	+	2.51011i	−0.0439733	+	0.135336i
$345$	−1.26498	−	3.89320i	−0.0681041	−	0.209603i
$346$	−6.10285	+	4.43398i	−0.328091	+	0.238372i
$347$	13.4770	−	9.79162i	0.723484	−	0.525642i	−0.164012	−	0.986458i	$-0.552443\pi$
$347$	13.4770	−	9.79162i	0.723484	−	0.525642i	0.887495	+	0.460817i	$0.152443\pi$
$348$	0.826208	+	2.54281i	0.0442894	+	0.136309i
$349$	1.68397	−	5.18272i	0.0901408	−	0.277425i	−0.895816	−	0.444425i	$-0.853408\pi$
$349$	1.68397	−	5.18272i	0.0901408	−	0.277425i	0.985957	+	0.167000i	$0.0534080\pi$
$350$	−0.809017	−	0.587785i	−0.0432438	−	0.0314184i
$351$	−12.9753			−0.692569
$352$	2.40640	−	2.28238i	0.128262	−	0.121651i
$353$	12.9302			0.688207			0.344104	−	0.938932i	$-0.388183\pi$
$353$	12.9302			0.688207			0.344104	+	0.938932i	$0.388183\pi$
$354$	−16.6602	−	12.1043i	−0.885480	−	0.643339i
$355$	1.81691	−	5.59186i	0.0964313	−	0.296785i
$356$	0.431527	+	1.32810i	0.0228709	+	0.0703894i
$357$	−7.09186	+	5.15254i	−0.375341	+	0.272701i
$358$	5.39468	−	3.91946i	0.285118	−	0.207150i
$359$	−9.43574	−	29.0402i	−0.497999	−	1.53268i	−0.812230	−	0.583337i	$-0.801747\pi$
$359$	−9.43574	−	29.0402i	−0.497999	−	1.53268i	0.314231	−	0.949347i	$-0.398253\pi$
$360$	0.367511	−	1.13108i	0.0193696	−	0.0596134i
$361$	−0.624828	−	0.453964i	−0.0328857	−	0.0238929i
$362$	3.26233			0.171464
$363$	21.0149	+	8.07962i	1.10299	+	0.424070i
$364$	3.50105			0.183505
$365$	6.02060	+	4.37422i	0.315133	+	0.228957i
$366$	−8.22367	+	25.3099i	−0.429858	+	1.32297i
$367$	8.60418	+	26.4809i	0.449134	+	1.38229i	0.877885	+	0.478871i	$0.158954\pi$
$367$	8.60418	+	26.4809i	0.449134	+	1.38229i	−0.428751	+	0.903423i	$0.641046\pi$
$368$	1.61803	−	1.17557i	0.0843459	−	0.0612808i
$369$	−3.72870	+	2.70906i	−0.194108	+	0.141028i
$370$	−0.101212	−	0.311499i	−0.00526177	−	0.0161941i
$371$	−0.337280	+	1.03804i	−0.0175107	+	0.0538924i
$372$	−9.45208	−	6.86734i	−0.490068	−	0.356055i
$373$	14.5146			0.751539			0.375770	−	0.926713i	$-0.377378\pi$
$373$	14.5146			0.751539			0.375770	+	0.926713i	$0.377378\pi$
$374$	10.3062	−	9.77506i	0.532923	−	0.505456i
$375$	2.04678			0.105695
$376$	9.89085	+	7.18612i	0.510082	+	0.370596i
$377$	1.41324	−	4.34951i	0.0727857	−	0.224011i
$378$	1.14525	+	3.52472i	0.0589054	+	0.181292i
$379$	9.64411	−	7.00686i	0.495385	−	0.359918i	−0.311867	−	0.950126i	$-0.600954\pi$
$379$	9.64411	−	7.00686i	0.495385	−	0.359918i	0.807251	+	0.590208i	$0.200954\pi$
$380$	−3.59738	+	2.61365i	−0.184542	+	0.134077i
$381$	−6.28832	−	19.3534i	−0.322160	−	0.991507i
$382$	4.23460	−	13.0328i	0.216661	−	0.666815i
$383$	−25.7208	−	18.6872i	−1.31427	−	0.954874i	−0.999985	−	0.00554556i	$-0.998235\pi$
$383$	−25.7208	−	18.6872i	−1.31427	−	0.954874i	−0.314286	−	0.949328i	$-0.601765\pi$
$384$	2.04678			0.104449
$385$	3.28837	−	0.432036i	0.167591	−	0.0220186i
$386$	−11.1467			−0.567352
$387$	−2.53941	−	1.84499i	−0.129085	−	0.0937859i
$388$	−3.02786	+	9.31881i	−0.153717	+	0.473091i
$389$	0.937276	+	2.88464i	0.0475218	+	0.146257i	0.972002	−	0.234974i	$-0.0755004\pi$
$389$	0.937276	+	2.88464i	0.0475218	+	0.146257i	−0.924480	+	0.381231i	$0.875500\pi$
$390$	−5.79730	+	4.21198i	−0.293558	+	0.213282i
$391$	6.92979	−	5.03479i	0.350454	−	0.254620i
$392$	−0.309017	−	0.951057i	−0.0156077	−	0.0480356i
$393$	−4.83925	+	14.8937i	−0.244108	+	0.751286i
$394$	−2.84171	−	2.06462i	−0.143163	−	0.104014i
$395$	0.498955			0.0251051
$396$	1.69718	+	3.56064i	0.0852865	+	0.178929i
$397$	−28.8927			−1.45008			−0.725041	−	0.688706i	$-0.758179\pi$
$397$	−28.8927			−1.45008			−0.725041	+	0.688706i	$0.758179\pi$
$398$	15.7894	+	11.4716i	0.791449	+	0.575021i
$399$	−2.81243	+	8.65577i	−0.140798	+	0.433330i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	−29.3557	+	21.3282i	−1.46595	+	1.06508i	−0.484192	+	0.874962i	$0.660886\pi$
$401$	−29.3557	+	21.3282i	−1.46595	+	1.06508i	−0.981762	+	0.190116i	$0.939114\pi$
$402$	13.9865	−	10.1618i	0.697585	−	0.506825i
$403$	6.17561	+	19.0066i	0.307629	+	0.946784i
$404$	−5.37301	+	16.5364i	−0.267317	+	0.822718i
$405$	−9.02334	−	6.55584i	−0.448373	−	0.325762i
$406$	−1.30628			−0.0648296
$407$	0.954516	+	0.518587i	0.0473136	+	0.0257054i
$408$	8.76602			0.433983
$409$	−4.81071	−	3.49518i	−0.237874	−	0.172826i	0.462461	−	0.886639i	$-0.346966\pi$
$409$	−4.81071	−	3.49518i	−0.237874	−	0.172826i	−0.700336	+	0.713814i	$0.746966\pi$
$410$	1.19755	−	3.68568i	0.0591427	−	0.182023i
$411$	−1.36642	−	4.20540i	−0.0674004	−	0.207437i
$412$	−5.55785	+	4.03801i	−0.273816	+	0.198939i
$413$	8.13973	−	5.91386i	0.400530	−	0.291002i
$414$	0.735023	+	2.26217i	0.0361244	+	0.111179i
$415$	−3.89747	+	11.9952i	−0.191319	+	0.588820i
$416$	−2.83240	−	2.05786i	−0.138870	−	0.100895i
$417$	−43.2512			−2.11802
$418$	2.69140	−	14.5001i	0.131641	−	0.709222i
$419$	7.10047			0.346881			0.173440	−	0.984844i	$-0.444512\pi$
$419$	7.10047			0.346881			0.173440	+	0.984844i	$0.444512\pi$
$420$	1.65588	+	1.20306i	0.0807985	+	0.0587035i
$421$	−6.71987	+	20.6816i	−0.327507	+	1.00796i	0.642790	+	0.766043i	$0.277777\pi$
$421$	−6.71987	+	20.6816i	−0.327507	+	1.00796i	−0.970296	+	0.241919i	$0.922223\pi$
$422$	4.43424	+	13.6472i	0.215856	+	0.664335i
$423$	−11.7631	+	8.54640i	−0.571942	+	0.415540i
$424$	0.883011	−	0.641545i	0.0428828	−	0.0311562i
$425$	1.32347	+	4.07323i	0.0641978	+	0.197581i
$426$	−3.71880	+	11.4453i	−0.180176	+	0.554526i
$427$	−10.5189	−	7.64244i	−0.509046	−	0.369843i
$428$	−1.75025			−0.0846013
$429$	4.33728	−	23.3673i	0.209406	−	1.12819i
$430$	2.63928			0.127278
$431$	15.2047	+	11.0469i	0.732384	+	0.532108i	0.890317	−	0.455342i	$-0.150483\pi$
$431$	15.2047	+	11.0469i	0.732384	+	0.532108i	−0.157933	+	0.987450i	$0.550483\pi$
$432$	1.14525	−	3.52472i	0.0551010	−	0.169583i
$433$	−10.0272	−	30.8606i	−0.481877	−	1.48307i	−0.836453	−	0.548039i	$-0.815375\pi$
$433$	−10.0272	−	30.8606i	−0.481877	−	1.48307i	0.354576	−	0.935027i	$-0.384625\pi$
$434$	4.61803	−	3.35520i	0.221673	−	0.161055i
$435$	2.16304	−	1.57154i	0.103710	−	0.0753496i
$436$	1.81837	+	5.59636i	0.0870840	+	0.268017i
$437$	2.74816	−	8.45795i	0.131462	−	0.404599i
$438$	−12.3228	−	8.95306i	−0.588807	−	0.427794i
$439$	−17.1535			−0.818690			−0.409345	−	0.912380i	$-0.634243\pi$
$439$	−17.1535			−0.818690			−0.409345	+	0.912380i	$0.634243\pi$
$440$	−2.91429	−	1.58333i	−0.138933	−	0.0754822i
$441$	1.18929			0.0566330
$442$	−12.1307	−	8.81350i	−0.577001	−	0.419216i
$443$	1.30980	−	4.03116i	0.0622307	−	0.191526i	−0.915108	−	0.403210i	$-0.867895\pi$
$443$	1.30980	−	4.03116i	0.0622307	−	0.191526i	0.977338	+	0.211683i	$0.0678945\pi$
$444$	0.207159	+	0.637569i	0.00983132	+	0.0302577i
$445$	1.12975	−	0.820813i	0.0535554	−	0.0389103i
$446$	10.7584	−	7.81641i	0.509423	−	0.370118i
$447$	10.1255	+	31.1629i	0.478918	+	1.47396i
$448$	−0.309017	+	0.951057i	−0.0145997	+	0.0449332i
$449$	−10.6458	−	7.73463i	−0.502406	−	0.365020i	0.307529	−	0.951539i	$-0.400498\pi$
$449$	−10.6458	−	7.73463i	−0.502406	−	0.365020i	−0.809935	+	0.586519i	$0.800498\pi$
$450$	−1.18929			−0.0560638
$451$	5.53032	+	11.6025i	0.260413	+	0.546339i
$452$	17.1279			0.805630
$453$	21.4248	+	15.5660i	1.00662	+	0.731356i
$454$	5.84475	−	17.9883i	0.274308	−	0.844232i
$455$	−1.08188	−	3.32969i	−0.0507194	−	0.156098i
$456$	7.36304	−	5.34956i	0.344806	−	0.250516i
$457$	0.549640	−	0.399337i	0.0257111	−	0.0186802i	−0.574855	−	0.818255i	$-0.694942\pi$
$457$	0.549640	−	0.399337i	0.0257111	−	0.0186802i	0.600567	+	0.799575i	$0.294942\pi$
$458$	−1.20242	−	3.70068i	−0.0561856	−	0.172922i
$459$	4.90494	−	15.0958i	0.228943	−	0.704614i
$460$	−1.61803	−	1.17557i	−0.0754412	−	0.0548113i
$461$	−33.9310			−1.58033			−0.790163	−	0.612897i	$-0.790004\pi$
$461$	−33.9310			−1.58033			−0.790163	+	0.612897i	$0.790004\pi$
$462$	−6.73055	+	0.884280i	−0.313133	+	0.0411404i
$463$	−8.67985			−0.403387			−0.201693	−	0.979449i	$-0.564644\pi$
$463$	−8.67985			−0.403387			−0.201693	+	0.979449i	$0.564644\pi$
$464$	1.05680	+	0.767813i	0.0490609	+	0.0356448i
$465$	−3.61037	+	11.1116i	−0.167427	+	0.515288i
$466$	−2.13973	−	6.58541i	−0.0991211	−	0.305063i
$467$	−3.70656	+	2.69297i	−0.171519	+	0.124616i	−0.670233	−	0.742151i	$-0.733806\pi$
$467$	−3.70656	+	2.69297i	−0.171519	+	0.124616i	0.498714	+	0.866767i	$0.333806\pi$
$468$	3.36856	−	2.44740i	0.155712	−	0.113131i
$469$	2.61015	+	8.03320i	0.120525	+	0.370939i
$470$	3.77797	−	11.6274i	0.174265	−	0.536332i
$471$	30.6262	+	22.2513i	1.41118	+	1.02528i
$472$	−10.0613			−0.463107
$473$	−6.35117	+	6.02384i	−0.292027	+	0.276976i
$474$	−1.02125			−0.0469075
$475$	3.59738	+	2.61365i	0.165059	+	0.119923i
$476$	−1.32347	+	4.07323i	−0.0606612	+	0.186696i
$477$	0.401125	+	1.23453i	0.0183662	+	0.0565255i
$478$	−21.5585	+	15.6631i	−0.986062	+	0.716416i
$479$	−31.4651	+	22.8607i	−1.43768	+	1.04453i	−0.449156	+	0.893453i	$0.648275\pi$
$479$	−31.4651	+	22.8607i	−1.43768	+	1.04453i	−0.988521	+	0.151081i	$0.951725\pi$
$480$	−0.632489	−	1.94660i	−0.0288690	−	0.0888497i
$481$	0.354349	−	1.09057i	0.0161569	−	0.0497259i
$482$	−0.0750881	−	0.0545547i	−0.00342017	−	0.00248490i
$483$	−4.09355			−0.186263
$484$	10.6267	−	2.84138i	0.483031	−	0.129154i
$485$	9.79837			0.444921
$486$	9.47383	+	6.88314i	0.429742	+	0.312225i
$487$	6.10595	−	18.7922i	0.276687	−	0.851555i	−0.712081	−	0.702097i	$-0.752247\pi$
$487$	6.10595	−	18.7922i	0.276687	−	0.851555i	0.988768	−	0.149458i	$-0.0477527\pi$
$488$	4.01787	+	12.3657i	0.181880	+	0.559770i
$489$	10.8116	−	7.85507i	0.488916	−	0.355219i
$490$	−0.809017	+	0.587785i	−0.0365477	+	0.0265534i
$491$	−9.48935	−	29.2052i	−0.428248	−	1.31801i	−0.899850	−	0.436200i	$-0.856324\pi$
$491$	−9.48935	−	29.2052i	−0.428248	−	1.31801i	0.471601	−	0.881812i	$-0.343676\pi$
$492$	−2.45112	+	7.54376i	−0.110505	+	0.340099i
$493$	4.52612	+	3.28842i	0.203846	+	0.148103i
$494$	−15.5678			−0.700427
$495$	2.86191	−	2.71441i	0.128633	−	0.122004i
$496$	−5.70820			−0.256306
$497$	−4.75672	−	3.45596i	−0.213368	−	0.155021i
$498$	7.97724	−	24.5514i	0.357469	−	1.10018i
$499$	−5.74711	−	17.6878i	−0.257276	−	0.791814i	−0.993373	−	0.114938i	$-0.963333\pi$
$499$	−5.74711	−	17.6878i	−0.257276	−	0.791814i	0.736097	−	0.676876i	$-0.236667\pi$
$500$	0.809017	−	0.587785i	0.0361803	−	0.0262866i
$501$	−19.8705	+	14.4368i	−0.887749	+	0.644988i
$502$	−6.49129	−	19.9782i	−0.289721	−	0.891668i
$503$	−0.474891	+	1.46156i	−0.0211743	+	0.0651679i	−0.961085	−	0.276252i	$-0.910908\pi$
$503$	−0.474891	+	1.46156i	−0.0211743	+	0.0651679i	0.939911	+	0.341420i	$0.110908\pi$
$504$	−0.962157	−	0.699048i	−0.0428579	−	0.0311381i
$505$	17.3874			0.773731
$506$	6.57673	−	0.864071i	0.292371	−	0.0384127i
$507$	1.52011			0.0675103
$508$	−8.04339	−	5.84387i	−0.356868	−	0.259280i
$509$	−5.88639	+	18.1165i	−0.260910	+	0.802998i	0.731698	+	0.681629i	$0.238728\pi$
$509$	−5.88639	+	18.1165i	−0.260910	+	0.802998i	−0.992608	+	0.121369i	$0.961272\pi$
$510$	−2.70885	−	8.33698i	−0.119950	−	0.369168i
$511$	6.02060	−	4.37422i	0.266336	−	0.193504i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−5.09249	−	15.6731i	−0.224839	−	0.691983i
$514$	1.30733	−	4.02354i	0.0576637	−	0.177471i
$515$	5.55785	+	4.03801i	0.244908	+	0.177936i
$516$	−5.40202			−0.237811
$517$	17.4468	+	36.6029i	0.767309	+	1.60979i
$518$	−0.327530			−0.0143908
$519$	−12.4912	−	9.07537i	−0.548302	−	0.398365i
$520$	−1.08188	+	3.32969i	−0.0474437	+	0.146017i
$521$	5.61697	+	17.2873i	0.246084	+	0.757368i	0.995456	+	0.0952196i	$0.0303553\pi$
$521$	5.61697	+	17.2873i	0.246084	+	0.757368i	−0.749372	+	0.662149i	$0.769645\pi$
$522$	−1.25685	+	0.913153i	−0.0550107	+	0.0399676i
$523$	−13.9907	+	10.1649i	−0.611772	+	0.444478i	−0.850038	−	0.526722i	$-0.823421\pi$
$523$	−13.9907	+	10.1649i	−0.611772	+	0.444478i	0.238266	+	0.971200i	$0.423421\pi$
$524$	2.36433	+	7.27665i	0.103286	+	0.317882i
$525$	0.632489	−	1.94660i	0.0276041	−	0.0849566i
$526$	−13.3317	−	9.68605i	−0.581290	−	0.422332i
$527$	−24.4473			−1.06494
$528$	5.96489	+	3.24072i	0.259589	+	0.141034i
$529$	−19.0000			−0.826087
$530$	−0.883011	−	0.641545i	−0.0383556	−	0.0278669i
$531$	3.69763	−	11.3801i	0.160463	−	0.493856i
$532$	1.37408	+	4.22898i	0.0595738	+	0.183349i
$533$	10.9766	−	7.97494i	0.475448	−	0.345433i
$534$	−2.31235	+	1.68002i	−0.100065	+	0.0727016i
$535$	0.540856	+	1.66458i	0.0233832	+	0.0719662i
$536$	2.61015	−	8.03320i	0.112741	−	0.346981i
$537$	11.0417	+	8.02227i	0.476485	+	0.346186i
$538$	−20.2848			−0.874541
$539$	0.605270	−	3.26093i	0.0260708	−	0.140458i
$540$	−3.70611			−0.159486
$541$	19.8034	+	14.3880i	0.851415	+	0.618589i	0.925536	−	0.378660i	$-0.123615\pi$
$541$	19.8034	+	14.3880i	0.851415	+	0.618589i	−0.0741211	+	0.997249i	$0.523615\pi$
$542$	4.27811	−	13.1667i	0.183761	−	0.565557i
$543$	2.06339	+	6.35046i	0.0885485	+	0.272524i
$544$	3.46489	−	2.51739i	0.148556	−	0.107932i
$545$	4.76055	−	3.45874i	0.203920	−	0.148156i
$546$	2.21437	+	6.81513i	0.0947663	+	0.291661i
$547$	−12.3052	+	37.8714i	−0.526131	+	1.61926i	0.235939	+	0.971768i	$0.424183\pi$
$547$	−12.3052	+	37.8714i	−0.526131	+	1.61926i	−0.762069	+	0.647495i	$0.775817\pi$
$548$	−1.74779	−	1.26984i	−0.0746617	−	0.0542449i
$549$	−15.4633			−0.659957
$550$	−0.605270	+	3.26093i	−0.0258088	+	0.139046i
$551$	5.80852			0.247451
$552$	3.31175	+	2.40613i	0.140958	+	0.102412i
$553$	0.154186	−	0.474534i	0.00655664	−	0.0201793i
$554$	−2.62778	−	8.08749i	−0.111644	−	0.343604i
$555$	0.542349	−	0.394039i	0.0230214	−	0.0167260i
$556$	−17.0956	+	12.4207i	−0.725017	+	0.526755i
$557$	−7.09355	−	21.8317i	−0.300563	−	0.925039i	−0.981296	−	0.192507i	$-0.938338\pi$
$557$	−7.09355	−	21.8317i	−0.300563	−	0.925039i	0.680732	−	0.732532i	$-0.261662\pi$
$558$	2.09783	−	6.45646i	0.0888082	−	0.273324i
$559$	7.47552	+	5.43128i	0.316181	+	0.229719i
$560$	1.00000			0.0422577
$561$	25.5467	+	13.8795i	1.07858	+	0.585993i
$562$	2.06245			0.0869994
$563$	−12.8747	−	9.35402i	−0.542604	−	0.394225i	0.282447	−	0.959283i	$-0.408854\pi$
$563$	−12.8747	−	9.35402i	−0.542604	−	0.394225i	−0.825051	+	0.565058i	$0.808854\pi$
$564$	−7.73266	+	23.7987i	−0.325604	+	1.00210i
$565$	−5.29282	−	16.2896i	−0.222671	−	0.685310i
$566$	−22.1035	+	16.0591i	−0.929079	+	0.675015i
$567$	−9.02334	+	6.55584i	−0.378945	+	0.275319i
$568$	1.81691	+	5.59186i	0.0762357	+	0.234629i
$569$	−5.48037	+	16.8669i	−0.229749	+	0.707095i	0.768025	+	0.640419i	$0.221239\pi$
$569$	−5.48037	+	16.8669i	−0.229749	+	0.707095i	−0.997775	+	0.0666761i	$0.978761\pi$
$570$	−7.36304	−	5.34956i	−0.308404	−	0.224068i
$571$	−1.05280			−0.0440584			−0.0220292	−	0.999757i	$-0.507013\pi$
$571$	−1.05280			−0.0440584			−0.0220292	+	0.999757i	$0.507013\pi$
$572$	−4.99617	−	10.4818i	−0.208900	−	0.438267i
$573$	28.0479			1.17172
$574$	−3.13522	−	2.27787i	−0.130862	−	0.0950766i
$575$	−0.618034	+	1.90211i	−0.0257738	+	0.0793236i
$576$	0.367511	+	1.13108i	0.0153130	+	0.0471285i
$577$	10.3734	−	7.53674i	0.431852	−	0.313759i	−0.350537	−	0.936549i	$-0.614001\pi$
$577$	10.3734	−	7.53674i	0.431852	−	0.313759i	0.782389	+	0.622790i	$0.214001\pi$
$578$	1.08631	−	0.789250i	0.0451845	−	0.0328285i
$579$	−7.05016	−	21.6982i	−0.292995	−	0.901745i
$580$	0.403663	−	1.24235i	0.0167612	−	0.0515856i
$581$	10.2037	+	7.41342i	0.423321	+	0.307560i
$582$	−20.0551			−0.831310
$583$	3.58912	−	0.471550i	0.148646	−	0.0195296i
$584$	−7.44187			−0.307947
$585$	−3.36856	−	2.44740i	−0.139273	−	0.101188i
$586$	5.88984	−	18.1271i	0.243307	−	0.748822i
$587$	−3.01612	−	9.28265i	−0.124488	−	0.383136i	0.869319	−	0.494251i	$-0.164558\pi$
$587$	−3.01612	−	9.28265i	−0.124488	−	0.383136i	−0.993808	+	0.111115i	$0.964558\pi$
$588$	1.65588	−	1.20306i	0.0682872	−	0.0496136i
$589$	−20.5346	+	14.9193i	−0.846113	+	0.614737i
$590$	3.10910	+	9.56883i	0.128000	+	0.393942i
$591$	2.22164	−	6.83752i	0.0913862	−	0.281258i
$592$	0.264977	+	0.192517i	0.0108905	+	0.00791241i
$593$	−25.4142			−1.04364			−0.521818	−	0.853057i	$-0.674746\pi$
$593$	−25.4142			−1.04364			−0.521818	+	0.853057i	$0.674746\pi$
$594$	8.91839	−	8.45875i	0.365926	−	0.347067i
$595$	4.28284			0.175579
$596$	12.9515	+	9.40980i	0.530513	+	0.385441i
$597$	−12.3441	+	37.9912i	−0.505211	+	1.55488i
$598$	−2.16376	−	6.65938i	−0.0884829	−	0.272322i
$599$	33.4386	−	24.2945i	1.36626	−	0.992648i	0.368244	−	0.929729i	$-0.379959\pi$
$599$	33.4386	−	24.2945i	1.36626	−	0.992648i	0.998019	−	0.0629192i	$-0.0200411\pi$
$600$	−1.65588	+	1.20306i	−0.0676009	+	0.0491149i
$601$	−12.1265	−	37.3215i	−0.494650	−	1.52238i	−0.817501	−	0.575927i	$-0.804641\pi$
$601$	−12.1265	−	37.3215i	−0.494650	−	1.52238i	0.322851	−	0.946450i	$-0.395359\pi$
$602$	0.815583	−	2.51011i	0.0332407	−	0.102304i
$603$	8.12697	+	5.90459i	0.330956	+	0.240453i
$604$	12.9386			0.526466
$605$	−5.98614	−	9.22855i	−0.243371	−	0.375194i
$606$	−35.5882			−1.44567
$607$	6.32725	+	4.59702i	0.256815	+	0.186587i	0.708742	−	0.705468i	$-0.249263\pi$
$607$	6.32725	+	4.59702i	0.256815	+	0.186587i	−0.451927	+	0.892055i	$0.649263\pi$
$608$	1.37408	−	4.22898i	0.0557262	−	0.171508i
$609$	−0.826208	−	2.54281i	−0.0334796	−	0.103040i
$610$	10.5189	−	7.64244i	0.425898	−	0.309433i
$611$	34.6283	−	25.1589i	1.40091	−	1.01782i
$612$	1.57399	+	4.84426i	0.0636249	+	0.195817i
$613$	−0.379876	+	1.16914i	−0.0153430	+	0.0472210i	−0.958435	−	0.285311i	$-0.907903\pi$
$613$	−0.379876	+	1.16914i	−0.0153430	+	0.0472210i	0.943092	+	0.332532i	$0.107903\pi$
$614$	22.5581	+	16.3894i	0.910372	+	0.661424i
$615$	7.93198			0.319848
$616$	−2.40640	+	2.28238i	−0.0969566	+	0.0919596i
$617$	−8.43129			−0.339431			−0.169715	−	0.985493i	$-0.554285\pi$
$617$	−8.43129			−0.339431			−0.169715	+	0.985493i	$0.554285\pi$
$618$	−11.3757	−	8.26491i	−0.457597	−	0.332463i
$619$	2.22345	−	6.84306i	0.0893678	−	0.275046i	−0.896377	−	0.443292i	$-0.853810\pi$
$619$	2.22345	−	6.84306i	0.0893678	−	0.275046i	0.985745	+	0.168246i	$0.0538104\pi$
$620$	1.76393	+	5.42882i	0.0708412	+	0.218027i
$621$	5.99662	−	4.35680i	0.240636	−	0.174832i
$622$	17.0166	−	12.3633i	0.682302	−	0.495722i
$623$	−0.431527	−	1.32810i	−0.0172888	−	0.0532093i
$624$	2.21437	−	6.81513i	0.0886458	−	0.272824i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−3.94821			−0.157802
$627$	29.9281	−	3.93205i	1.19521	−	0.157031i
$628$	18.4955			0.738050
$629$	1.13486	+	0.824521i	0.0452497	+	0.0328758i
$630$	−0.367511	+	1.13108i	−0.0146420	+	0.0450635i
$631$	2.83111	+	8.71327i	0.112705	+	0.346870i	0.991461	−	0.130400i	$-0.0416263\pi$
$631$	2.83111	+	8.71327i	0.112705	+	0.346870i	−0.878757	+	0.477270i	$0.841626\pi$
$632$	−0.403663	+	0.293278i	−0.0160569	+	0.0116660i
$633$	−23.7610	+	17.2634i	−0.944416	+	0.686158i
$634$	8.69034	+	26.7461i	0.345137	+	1.06222i
$635$	−3.07230	+	9.45558i	−0.121921	+	0.375233i
$636$	1.80733	+	1.31310i	0.0716651	+	0.0520678i
$637$	−3.50105			−0.138716
$638$	1.86413	+	3.91089i	0.0738016	+	0.154834i
$639$	−6.99260			−0.276623
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	−2.41847	+	7.44328i	−0.0955237	+	0.293992i	−0.987390	−	0.158308i	$-0.949396\pi$
$641$	−2.41847	+	7.44328i	−0.0955237	+	0.293992i	0.891866	+	0.452300i	$0.149396\pi$
$642$	−1.10701	−	3.40703i	−0.0436902	−	0.134465i
$643$	34.0742	−	24.7564i	1.34376	−	0.976296i	0.344459	−	0.938801i	$-0.388062\pi$
$643$	34.0742	−	24.7564i	1.34376	−	0.976296i	0.999297	−	0.0374945i	$-0.0119377\pi$
$644$	−1.61803	+	1.17557i	−0.0637595	+	0.0463240i
$645$	1.66932	+	5.13763i	0.0657293	+	0.202294i
$646$	5.88496	−	18.1120i	0.231541	−	0.712609i
$647$	16.6237	+	12.0778i	0.653545	+	0.474828i	0.864477	−	0.502673i	$-0.167650\pi$
$647$	16.6237	+	12.0778i	0.653545	+	0.474828i	−0.210932	+	0.977501i	$0.567650\pi$
$648$	11.1535			0.438149
$649$	−29.3214	−	15.9303i	−1.15097	−	0.625318i
$650$	3.50105			0.137322
$651$	9.45208	+	6.86734i	0.370456	+	0.269152i
$652$	2.01764	−	6.20965i	0.0790168	−	0.243189i
$653$	−8.98293	−	27.6466i	−0.351529	−	1.08190i	−0.957995	−	0.286786i	$-0.907413\pi$
$653$	−8.98293	−	27.6466i	−0.351529	−	1.08190i	0.606465	−	0.795110i	$-0.292587\pi$
$654$	−9.74378	+	7.07927i	−0.381012	+	0.276821i
$655$	6.18989	−	4.49722i	0.241859	−	0.175721i
$656$	1.19755	+	3.68568i	0.0467564	+	0.143902i
$657$	2.73497	−	8.41738i	0.106701	−	0.328393i
$658$	−9.89085	−	7.18612i	−0.385585	−	0.280144i
$659$	−16.3882			−0.638395			−0.319198	−	0.947688i	$-0.603413\pi$
$659$	−16.3882			−0.638395			−0.319198	+	0.947688i	$0.603413\pi$
$660$	1.23885	−	6.67439i	0.0482223	−	0.259800i
$661$	37.7386			1.46786			0.733932	−	0.679223i	$-0.237683\pi$
$661$	37.7386			1.46786			0.733932	+	0.679223i	$0.237683\pi$
$662$	24.4920	+	17.7945i	0.951909	+	0.691602i
$663$	9.48381	−	29.1882i	0.368320	−	1.13357i
$664$	−3.89747	−	11.9952i	−0.151251	−	0.465503i
$665$	3.59738	−	2.61365i	0.139500	−	0.101353i
$666$	−0.315135	+	0.228959i	−0.0122112	+	0.00887199i
$667$	0.807326	+	2.48469i	0.0312598	+	0.0962077i
$668$	−3.70820	+	11.4127i	−0.143475	+	0.441570i
$669$	22.0200	+	15.9984i	0.851341	+	0.618535i
$670$	−8.44661			−0.326321
$671$	−7.86978	+	42.3989i	−0.303810	+	1.63679i
$672$	−2.04678			−0.0789561
$673$	17.0102	+	12.3587i	0.655697	+	0.476392i	0.865207	−	0.501415i	$-0.167187\pi$
$673$	17.0102	+	12.3587i	0.655697	+	0.476392i	−0.209510	+	0.977806i	$0.567187\pi$
$674$	−9.91215	+	30.5065i	−0.381802	+	1.17506i
$675$	1.14525	+	3.52472i	0.0440808	+	0.135667i
$676$	0.600843	−	0.436538i	0.0231094	−	0.0167899i
$677$	−5.57572	+	4.05099i	−0.214292	+	0.155692i	−0.689754	−	0.724044i	$-0.742281\pi$
$677$	−5.57572	+	4.05099i	−0.214292	+	0.155692i	0.475461	+	0.879737i	$0.342281\pi$
$678$	10.8332	+	33.3412i	0.416047	+	1.28046i
$679$	3.02786	−	9.31881i	0.116199	−	0.357623i
$680$	−3.46489	−	2.51739i	−0.132873	−	0.0965376i
$681$	38.7127			1.48348
$682$	−16.6353	−	9.03796i	−0.637000	−	0.346081i
$683$	−1.37212			−0.0525026			−0.0262513	−	0.999655i	$-0.508357\pi$
$683$	−1.37212			−0.0525026			−0.0262513	+	0.999655i	$0.508357\pi$
$684$	4.27834	+	3.10839i	0.163586	+	0.118852i
$685$	−0.667595	+	2.05465i	−0.0255075	+	0.0785040i
$686$	0.309017	+	0.951057i	0.0117983	+	0.0363115i
$687$	6.44323	−	4.68128i	0.245824	−	0.178602i
$688$	−2.13522	+	1.55133i	−0.0814047	+	0.0591440i
$689$	−1.18083	−	3.63423i	−0.0449862	−	0.138453i
$690$	1.26498	−	3.89320i	0.0481569	−	0.148212i
$691$	7.60212	+	5.52326i	0.289198	+	0.210115i	0.722919	−	0.690932i	$-0.242800\pi$
$691$	7.60212	+	5.52326i	0.289198	+	0.210115i	−0.433721	+	0.901047i	$0.642800\pi$
$692$	−7.54354			−0.286762
$693$	−1.69718	−	3.56064i	−0.0644705	−	0.135257i
$694$	16.6585			0.632348
$695$	17.0956	+	12.4207i	0.648475	+	0.471144i
$696$	−0.826208	+	2.54281i	−0.0313173	+	0.0963848i
$697$	5.12892	+	15.7852i	0.194272	+	0.597906i
$698$	4.40869	−	3.20310i	0.166871	−	0.121239i
$699$	11.4658	−	8.33040i	0.433677	−	0.315085i
$700$	−0.309017	−	0.951057i	−0.0116797	−	0.0359466i
$701$	−4.18191	+	12.8706i	−0.157949	+	0.486116i	−0.998448	−	0.0556970i	$-0.982262\pi$
$701$	−4.18191	+	12.8706i	−0.157949	+	0.486116i	0.840499	+	0.541813i	$0.182262\pi$
$702$	−10.4972	−	7.62667i	−0.396192	−	0.287850i
$703$	1.45640			0.0549290
$704$	3.28837	−	0.432036i	0.123935	−	0.0162830i
$705$	25.0234			0.942436
$706$	10.4608	+	7.60021i	0.393697	+	0.286038i
$707$	5.37301	−	16.5364i	0.202073	−	0.621917i
$708$	−6.36363	−	19.5852i	−0.239160	−	0.736059i
$709$	32.5027	−	23.6146i	1.22067	−	0.886866i	0.224511	−	0.974472i	$-0.427922\pi$
$709$	32.5027	−	23.6146i	1.22067	−	0.886866i	0.996155	+	0.0876056i	$0.0279215\pi$
$710$	4.75672	−	3.45596i	0.178517	−	0.129700i
$711$	−0.183372	−	0.564360i	−0.00687697	−	0.0211651i
$712$	−0.431527	+	1.32810i	−0.0161722	+	0.0497728i
$713$	−9.23607	−	6.71040i	−0.345893	−	0.251306i
$714$	−8.76602			−0.328060
$715$	−8.42491	+	7.99070i	−0.315074	+	0.298835i
$716$	6.66819			0.249202
$717$	−44.1254	−	32.0590i	−1.64789	−	1.19726i
$718$	9.43574	−	29.0402i	0.352139	−	1.08377i
$719$	4.07405	+	12.5386i	0.151936	+	0.467612i	0.997838	−	0.0657273i	$-0.0209368\pi$
$719$	4.07405	+	12.5386i	0.151936	+	0.467612i	−0.845901	+	0.533340i	$0.820937\pi$
$720$	0.962157	−	0.699048i	0.0358575	−	0.0260520i
$721$	5.55785	−	4.03801i	0.206985	−	0.150383i
$722$	−0.238663	−	0.734530i	−0.00888212	−	0.0273364i
$723$	0.0587038	−	0.180672i	0.00218322	−	0.00671925i
$724$	2.63928	+	1.91755i	0.0980882	+	0.0712652i
$725$	−1.30628			−0.0485141
$726$	12.2523	+	18.8888i	0.454725	+	0.701028i
$727$	−40.5403			−1.50356			−0.751779	−	0.659415i	$-0.770804\pi$
$727$	−40.5403			−1.50356			−0.751779	+	0.659415i	$0.770804\pi$
$728$	2.83240	+	2.05786i	0.104976	+	0.0762695i
$729$	2.93320	−	9.02746i	0.108637	−	0.334350i
$730$	2.29967	+	7.07764i	0.0851144	+	0.261955i
$731$	−9.14483	+	6.64411i	−0.338234	+	0.245741i
$732$	−21.5299	+	15.6424i	−0.795766	+	0.578158i
$733$	−7.07029	−	21.7601i	−0.261147	−	0.803728i	−0.992556	−	0.121789i	$-0.961137\pi$
$733$	−7.07029	−	21.7601i	−0.261147	−	0.803728i	0.731409	−	0.681939i	$-0.238863\pi$
$734$	−8.60418	+	26.4809i	−0.317586	+	0.977429i
$735$	−1.65588	−	1.20306i	−0.0610779	−	0.0443757i
$736$	2.00000			0.0737210
$737$	20.3259	−	19.2783i	0.748715	−	0.710127i
$738$	−4.60892			−0.169657
$739$	24.3545	+	17.6945i	0.895893	+	0.650904i	0.937408	−	0.348234i	$-0.113218\pi$
$739$	24.3545	+	17.6945i	0.895893	+	0.650904i	−0.0415148	+	0.999138i	$0.513218\pi$
$740$	0.101212	−	0.311499i	0.00372064	−	0.0114509i
$741$	−9.84644	−	30.3042i	−0.361718	−	1.11325i
$742$	−0.883011	+	0.641545i	−0.0324164	+	0.0235519i
$743$	−23.9999	+	17.4369i	−0.880471	+	0.639700i	−0.933376	−	0.358900i	$-0.883152\pi$
$743$	−23.9999	+	17.4369i	−0.880471	+	0.639700i	0.0529050	+	0.998600i	$0.483152\pi$
$744$	−3.61037	−	11.1116i	−0.132363	−	0.407371i
$745$	4.94703	−	15.2254i	0.181245	−	0.557815i
$746$	11.7426	+	8.53149i	0.429927	+	0.312360i
$747$	14.9999			0.548818
$748$	14.0836	−	1.85034i	0.514946	−	0.0676552i
$749$	1.75025			0.0639526
$750$	1.65588	+	1.20306i	0.0604641	+	0.0439297i
$751$	14.6575	−	45.1113i	0.534861	−	1.64613i	−0.209088	−	0.977897i	$-0.567049\pi$
$751$	14.6575	−	45.1113i	0.534861	−	1.64613i	0.743949	−	0.668236i	$-0.232951\pi$
$752$	3.77797	+	11.6274i	0.137768	+	0.424007i
$753$	34.7838	−	25.2719i	1.26759	−	0.920959i
$754$	3.69992	−	2.68815i	0.134743	−	0.0978965i
$755$	−3.99826	−	12.3054i	−0.145512	−	0.447839i
$756$	−1.14525	+	3.52472i	−0.0416524	+	0.128193i
$757$	21.4809	+	15.6068i	0.780736	+	0.567238i	0.905200	−	0.424986i	$-0.139721\pi$
$757$	21.4809	+	15.6068i	0.780736	+	0.567238i	−0.124464	+	0.992224i	$0.539721\pi$
$758$	11.9208			0.432982
$759$	5.84171	+	12.2557i	0.212041	+	0.444855i
$760$	−4.44661			−0.161295
$761$	39.4370	+	28.6526i	1.42959	+	1.03866i	0.990093	+	0.140412i	$0.0448428\pi$
$761$	39.4370	+	28.6526i	1.42959	+	1.03866i	0.439496	+	0.898245i	$0.355157\pi$
$762$	6.28832	−	19.3534i	0.227802	−	0.701101i
$763$	−1.81837	−	5.59636i	−0.0658294	−	0.202602i
$764$	11.0863	−	8.05470i	0.401090	−	0.291409i
$765$	4.12077	−	2.99391i	0.148987	−	0.108245i
$766$	−9.82447	−	30.2366i	−0.354972	−	1.09249i
$767$	−10.8851	+	33.5009i	−0.393038	+	1.20965i
$768$	1.65588	+	1.20306i	0.0597513	+	0.0434119i
$769$	−25.8289			−0.931415			−0.465708	−	0.884939i	$-0.654200\pi$
$769$	−25.8289			−0.931415			−0.465708	+	0.884939i	$0.654200\pi$
$770$	2.91429	+	1.58333i	0.105024	+	0.0570592i
$771$	8.65908			0.311849
$772$	−9.01787	−	6.55186i	−0.324560	−	0.235807i
$773$	11.9360	−	36.7352i	0.429308	−	1.32127i	−0.469501	−	0.882932i	$-0.655566\pi$
$773$	11.9360	−	36.7352i	0.429308	−	1.32127i	0.898809	−	0.438341i	$-0.144434\pi$
$774$	−0.969967	−	2.98525i	−0.0348647	−	0.107303i
$775$	4.61803	−	3.35520i	0.165885	−	0.120522i
$776$	−7.92705	+	5.75934i	−0.284565	+	0.206748i
$777$	−0.207159	−	0.637569i	−0.00743178	−	0.0228727i
$778$	−0.937276	+	2.88464i	−0.0336030	+	0.103419i
$779$	13.9411	+	10.1288i	0.499492	+	0.362902i
$780$	−7.16586			−0.256579
$781$	−3.55877	+	19.1730i	−0.127343	+	0.686065i
$782$	8.56569			0.306308
$783$	3.91663	+	2.84560i	0.139969	+	0.101693i
$784$	0.309017	−	0.951057i	0.0110363	−	0.0339663i
$785$	−5.71542	−	17.5902i	−0.203992	−	0.627823i
$786$	−12.6693	+	9.20480i	−0.451900	+	0.328324i
$787$	−8.55225	+	6.21357i	−0.304855	+	0.221490i	−0.729686	−	0.683783i	$-0.760334\pi$
$787$	−8.55225	+	6.21357i	−0.304855	+	0.221490i	0.424831	+	0.905273i	$0.360334\pi$
$788$	−1.08544	−	3.34063i	−0.0386670	−	0.119005i
$789$	10.4227	−	32.0778i	0.371059	−	1.14200i
$790$	0.403663	+	0.293278i	0.0143617	+	0.0104344i
$791$	−17.1279			−0.608999
$792$	−0.719843	+	3.87819i	−0.0255785	+	0.137806i
$793$	45.5209			1.61649
$794$	−23.3747	−	16.9827i	−0.829536	−	0.602693i
$795$	0.690337	−	2.12464i	0.0244837	−	0.0753532i
$796$	6.03100	+	18.5615i	0.213763	+	0.657895i
$797$	32.6059	−	23.6896i	1.15496	−	0.839128i	0.165828	−	0.986155i	$-0.446971\pi$
$797$	32.6059	−	23.6896i	1.15496	−	0.839128i	0.989132	+	0.147027i	$0.0469705\pi$
$798$	−7.36304	+	5.34956i	−0.260649	+	0.189372i
$799$	16.1805	+	49.7983i	0.572423	+	1.76174i
$800$	−0.309017	+	0.951057i	−0.0109254	+	0.0336249i
$801$	−1.34361	−	0.976187i	−0.0474740	−	0.0344919i
$802$	−36.2856			−1.28129
$803$	−21.6878	−	11.7829i	−0.765344	−	0.415811i
$804$	17.2883			0.609712
$805$	1.61803	+	1.17557i	0.0570282	+	0.0414334i
$806$	−6.17561	+	19.0066i	−0.217526	+	0.669478i
$807$	−12.8299	−	39.4865i	−0.451635	−	1.38999i
$808$	−14.0667	+	10.2201i	−0.494866	+	0.359541i
$809$	−11.9721	+	8.69827i	−0.420918	+	0.305815i	−0.778007	−	0.628256i	$-0.783769\pi$
$809$	−11.9721	+	8.69827i	−0.420918	+	0.305815i	0.357089	+	0.934070i	$0.383769\pi$
$810$	−3.44661	−	10.6076i	−0.121101	−	0.372712i
$811$	−9.51905	+	29.2966i	−0.334259	+	1.02874i	0.632827	+	0.774293i	$0.281895\pi$
$811$	−9.51905	+	29.2966i	−0.334259	+	1.02874i	−0.967086	+	0.254450i	$0.918105\pi$
$812$	−1.05680	−	0.767813i	−0.0370865	−	0.0269449i
$813$	28.3361			0.993790
$814$	0.467402	+	0.980596i	0.0163824	+	0.0343699i
$815$	−6.52922			−0.228708
$816$	7.09186	+	5.15254i	0.248265	+	0.180375i
$817$	−3.62658	+	11.1615i	−0.126878	+	0.390490i
$818$	−1.83753	−	5.65533i	−0.0642476	−	0.197734i
$819$	−3.36856	+	2.44740i	−0.117707	+	0.0855191i
$820$	3.13522	−	2.27787i	0.109487	−	0.0795468i
$821$	8.20169	+	25.2422i	0.286241	+	0.880960i	0.986024	+	0.166604i	$0.0532801\pi$
$821$	8.20169	+	25.2422i	0.286241	+	0.880960i	−0.699783	+	0.714356i	$0.746720\pi$
$822$	1.36642	−	4.20540i	0.0476593	−	0.146680i
$823$	−32.2338	−	23.4192i	−1.12360	−	0.816342i	−0.138848	−	0.990314i	$-0.544340\pi$
$823$	−32.2338	−	23.4192i	−1.12360	−	0.816342i	−0.984751	+	0.173971i	$0.944340\pi$
$824$	−6.86988			−0.239324
$825$	−6.73055	+	0.884280i	−0.234328	+	0.0307867i
$826$	10.0613			0.350076
$827$	−29.6818	−	21.5651i	−1.03214	−	0.749892i	−0.0634026	−	0.997988i	$-0.520195\pi$
$827$	−29.6818	−	21.5651i	−1.03214	−	0.749892i	−0.968736	+	0.248096i	$0.920195\pi$
$828$	−0.735023	+	2.26217i	−0.0255438	+	0.0786158i
$829$	5.21685	+	16.0558i	0.181189	+	0.557641i	0.999862	−	0.0166183i	$-0.00529001\pi$
$829$	5.21685	+	16.0558i	0.181189	+	0.557641i	−0.818673	+	0.574260i	$0.805290\pi$
$830$	−10.2037	+	7.41342i	−0.354176	+	0.257324i
$831$	14.0811	−	10.2305i	0.488467	−	0.354892i
$832$	−1.08188	−	3.32969i	−0.0375075	−	0.115436i
$833$	1.32347	−	4.07323i	0.0458556	−	0.141129i
$834$	−34.9910	−	25.4224i	−1.21164	−	0.880306i
$835$	12.0000			0.415277
$836$	10.7003	−	10.1488i	0.370078	−	0.351005i
$837$	−21.1553			−0.731233
$838$	5.74440	+	4.17355i	0.198437	+	0.144173i
$839$	−12.6107	+	38.8118i	−0.435370	+	1.33993i	0.457336	+	0.889294i	$0.348804\pi$
$839$	−12.6107	+	38.8118i	−0.435370	+	1.33993i	−0.892707	+	0.450638i	$0.851196\pi$
$840$	0.632489	+	1.94660i	0.0218229	+	0.0671641i
$841$	22.0810	−	16.0428i	0.761414	−	0.553200i
$842$	−17.5929	+	12.7820i	−0.606290	+	0.440495i
$843$	1.30448	+	4.01477i	0.0449286	+	0.138276i
$844$	−4.43424	+	13.6472i	−0.152633	+	0.469756i
$845$	−0.600843	−	0.436538i	−0.0206696	−	0.0150174i
$846$	−14.5400			−0.499896
$847$	−10.6267	+	2.84138i	−0.365137	+	0.0976310i
$848$	1.09146			0.0374810
$849$	−45.2409	−	32.8694i	−1.55266	−	1.12808i
$850$	−1.32347	+	4.07323i	−0.0453947	+	0.139711i
$851$	0.202425	+	0.622999i	0.00693902	+	0.0213561i
$852$	−9.73594	+	7.07357i	−0.333548	+	0.242337i
$853$	0.0773273	−	0.0561816i	0.00264764	−	0.00192362i	−0.586461	−	0.809978i	$-0.699479\pi$
$853$	0.0773273	−	0.0561816i	0.00264764	−	0.00192362i	0.589108	+	0.808054i	$0.299479\pi$
$854$	−4.01787	−	12.3657i	−0.137489	−	0.423146i
$855$	1.63418	−	5.02949i	0.0558878	−	0.172005i
$856$	−1.41598	−	1.02877i	−0.0483971	−	0.0351626i
$857$	51.9594			1.77490			0.887449	−	0.460906i	$-0.152475\pi$
$857$	51.9594			1.77490			0.887449	+	0.460906i	$0.152475\pi$
$858$	17.2439	−	16.3552i	0.588697	−	0.558357i
$859$	35.1186			1.19823			0.599115	−	0.800663i	$-0.295519\pi$
$859$	35.1186			1.19823			0.599115	+	0.800663i	$0.295519\pi$
$860$	2.13522	+	1.55133i	0.0728106	+	0.0529000i
$861$	2.45112	−	7.54376i	0.0835338	−	0.257091i
$862$	5.80768	+	17.8742i	0.197810	+	0.608797i
$863$	18.6337	−	13.5382i	0.634299	−	0.460845i	−0.223588	−	0.974684i	$-0.571777\pi$
$863$	18.6337	−	13.5382i	0.634299	−	0.460845i	0.857887	+	0.513839i	$0.171777\pi$
$864$	2.99831	−	2.17840i	0.102005	−	0.0741106i
$865$	2.33108	+	7.17434i	0.0792592	+	0.243935i
$866$	10.0272	−	30.8606i	0.340739	−	1.04869i
$867$	2.22343	+	1.61542i	0.0755117	+	0.0548625i
$868$	5.70820			0.193749
$869$	−1.64075	+	0.215566i	−0.0556585	+	0.00731259i
$870$	2.67366			0.0906457
$871$	−23.9242	−	17.3820i	−0.810641	−	0.588965i
$872$	−1.81837	+	5.59636i	−0.0615777	+	0.189517i
$873$	−3.60101	−	11.0828i	−0.121876	−	0.375095i
$874$	7.19476	−	5.22730i	0.243367	−	0.176816i
$875$	−0.809017	+	0.587785i	−0.0273498	+	0.0198708i
$876$	−4.70690	−	14.4864i	−0.159031	−	0.489448i
$877$	−9.49468	+	29.2216i	−0.320612	+	0.986744i	0.652770	+	0.757556i	$0.273607\pi$
$877$	−9.49468	+	29.2216i	−0.320612	+	0.986744i	−0.973382	+	0.229187i	$0.926393\pi$
$878$	−13.8774	−	10.0826i	−0.468341	−	0.340270i
$879$	39.0114			1.31582
$880$	−1.42705	−	2.99391i	−0.0481059	−	0.100925i
$881$	−42.3788			−1.42778			−0.713890	−	0.700258i	$-0.753068\pi$
$881$	−42.3788			−1.42778			−0.713890	+	0.700258i	$0.753068\pi$
$882$	0.962157	+	0.699048i	0.0323975	+	0.0235382i
$883$	11.8437	−	36.4510i	0.398571	−	1.22667i	−0.527575	−	0.849509i	$-0.676899\pi$
$883$	11.8437	−	36.4510i	0.398571	−	1.22667i	0.926146	−	0.377166i	$-0.123101\pi$
$884$	−4.63353	−	14.2606i	−0.155843	−	0.479634i
$885$	−16.6602	+	12.1043i	−0.560027	+	0.406883i
$886$	3.42911	−	2.49139i	0.115203	−	0.0837001i
$887$	−7.90516	−	24.3296i	−0.265429	−	0.816908i	−0.991594	−	0.129387i	$-0.958699\pi$
$887$	−7.90516	−	24.3296i	−0.265429	−	0.816908i	0.726165	−	0.687521i	$-0.241301\pi$
$888$	−0.207159	+	0.637569i	−0.00695179	+	0.0213954i
$889$	8.04339	+	5.84387i	0.269767	+	0.195997i
$890$	1.39645			0.0468091
$891$	32.5044	+	17.6596i	1.08894	+	0.591619i
$892$	13.2981			0.445252
$893$	43.9807	+	31.9539i	1.47176	+	1.06930i
$894$	−10.1255	+	31.1629i	−0.338646	+	1.04224i
$895$	−2.06058	−	6.34183i	−0.0688777	−	0.211984i
$896$	−0.809017	+	0.587785i	−0.0270274	+	0.0196365i
$897$	11.5946	−	8.42397i	0.387132	−	0.281268i
$898$	−4.06633	−	12.5149i	−0.135695	−	0.417627i
$899$	2.30419	−	7.09157i	0.0768491	−	0.236517i
$900$	−0.962157	−	0.699048i	−0.0320719	−	0.0233016i
$901$	4.67456			0.155732
$902$	−2.34564	+	12.6372i	−0.0781011	+	0.420774i
$903$	5.40202			0.179768
$904$	13.8568	+	10.0675i	0.460870	+	0.334842i
$905$	1.00812	−	3.10266i	0.0335109	−	0.103136i
$906$	8.18354	+	25.1864i	0.271880	+	0.836761i
$907$	40.2697	−	29.2576i	1.33713	−	0.971483i	0.337588	−	0.941294i	$-0.390389\pi$
$907$	40.2697	−	29.2576i	1.33713	−	0.971483i	0.999544	−	0.0301892i	$-0.00961099\pi$
$908$	15.3018	−	11.1174i	0.507807	−	0.368943i
$909$	−6.39008	−	19.6667i	−0.211946	−	0.652302i
$910$	1.08188	−	3.32969i	0.0358641	−	0.110378i
$911$	−18.0622	−	13.1229i	−0.598427	−	0.434782i	0.246893	−	0.969043i	$-0.420590\pi$
$911$	−18.0622	−	13.1229i	−0.598427	−	0.434782i	−0.845320	+	0.534260i	$0.820590\pi$
$912$	9.10121			0.301371
$913$	7.63395	−	41.1283i	0.252647	−	1.36115i
$914$	0.679393			0.0224723
$915$	21.5299	+	15.6424i	0.711755	+	0.517120i
$916$	1.20242	−	3.70068i	0.0397292	−	0.122274i
$917$	−2.36433	−	7.27665i	−0.0780770	−	0.240296i
$918$	12.8413	−	9.32974i	0.423826	−	0.307927i
$919$	14.5356	−	10.5607i	0.479485	−	0.348367i	−0.321641	−	0.946862i	$-0.604234\pi$
$919$	14.5356	−	10.5607i	0.479485	−	0.348367i	0.801126	+	0.598495i	$0.204234\pi$
$920$	−0.618034	−	1.90211i	−0.0203760	−	0.0627108i
$921$	−17.6359	+	54.2778i	−0.581123	+	1.78851i
$922$	−27.4508	−	19.9442i	−0.904044	−	0.656826i
$923$	20.5848			0.677558
$924$	−5.96489	−	3.24072i	−0.196231	−	0.106612i
$925$	−0.327530			−0.0107691
$926$	−7.02215	−	5.10189i	−0.230762	−	0.167658i
$927$	2.52476	−	7.77041i	0.0829240	−	0.255214i
$928$	0.403663	+	1.24235i	0.0132509	+	0.0407820i
$929$	−11.1232	+	8.08149i	−0.364941	+	0.265145i	−0.755110	−	0.655598i	$-0.772417\pi$
$929$	−11.1232	+	8.08149i	−0.364941	+	0.265145i	0.390169	+	0.920743i	$0.372417\pi$
$930$	−9.45208	+	6.86734i	−0.309946	+	0.225189i
$931$	−1.37408	−	4.22898i	−0.0450336	−	0.138599i
$932$	2.13973	−	6.58541i	0.0700892	−	0.215712i
$933$	34.8291	+	25.3048i	1.14025	+	0.828443i
$934$	−4.58156			−0.149913
$935$	−6.11184	−	12.8225i	−0.199878	−	0.419340i
$936$	4.16376			0.136097
$937$	6.78623	+	4.93048i	0.221696	+	0.161072i	0.693090	−	0.720851i	$-0.256249\pi$
$937$	6.78623	+	4.93048i	0.221696	+	0.161072i	−0.471394	+	0.881923i	$0.656249\pi$
$938$	−2.61015	+	8.03320i	−0.0852243	+	0.262293i
$939$	−2.49720	−	7.68558i	−0.0814929	−	0.250809i
$940$	9.89085	−	7.18612i	0.322604	−	0.234386i
$941$	22.7860	−	16.5550i	0.742802	−	0.539677i	−0.150786	−	0.988566i	$-0.548180\pi$
$941$	22.7860	−	16.5550i	0.742802	−	0.539677i	0.893587	+	0.448889i	$0.148180\pi$
$942$	11.6982	+	36.0033i	0.381147	+	1.17305i
$943$	−2.39510	+	7.37136i	−0.0779951	+	0.240044i
$944$	−8.13973	−	5.91386i	−0.264926	−	0.192480i
$945$	3.70611			0.120560
$946$	−8.67893	+	1.14026i	−0.282176	+	0.0370732i
$947$	−0.901036			−0.0292797			−0.0146399	−	0.999893i	$-0.504660\pi$
$947$	−0.901036			−0.0292797			−0.0146399	+	0.999893i	$0.504660\pi$
$948$	−0.826208	−	0.600275i	−0.0268340	−	0.0194960i
$949$	−8.05123	+	24.7791i	−0.261354	+	0.804365i
$950$	1.37408	+	4.22898i	0.0445810	+	0.137206i
$951$	−46.5674	+	33.8332i	−1.51005	+	1.09712i
$952$	−3.46489	+	2.51739i	−0.112298	+	0.0815892i
$953$	−1.68675	−	5.19129i	−0.0546393	−	0.168163i	0.920013	−	0.391888i	$-0.128178\pi$
$953$	−1.68675	−	5.19129i	−0.0546393	−	0.168163i	−0.974652	+	0.223726i	$0.928178\pi$
$954$	−0.401125	+	1.23453i	−0.0129869	+	0.0399695i
$955$	−11.0863	−	8.05470i	−0.358746	−	0.260644i
$956$	−26.6477			−0.861850
$957$	−6.43390	+	6.10231i	−0.207979	+	0.197260i
$958$	−38.8930			−1.25658
$959$	1.74779	+	1.26984i	0.0564390	+	0.0410053i
$960$	0.632489	−	1.94660i	0.0204135	−	0.0628262i
$961$	0.489357	+	1.50609i	0.0157857	+	0.0485834i
$962$	0.927697	−	0.674011i	0.0299101	−	0.0217310i
$963$	1.68401	−	1.22351i	0.0542665	−	0.0394269i
$964$	−0.0286811	−	0.0882714i	−0.000923756	−	0.00284303i
$965$	−3.44452	+	10.6011i	−0.110883	+	0.341263i
$966$	−3.31175	−	2.40613i	−0.106554	−	0.0774159i
$967$	−36.7612			−1.18216			−0.591079	−	0.806613i	$-0.701298\pi$
$967$	−36.7612			−1.18216			−0.591079	+	0.806613i	$0.701298\pi$
$968$	10.2673	+	3.94749i	0.330003	+	0.126877i
$969$	38.9791			1.25219
$970$	7.92705	+	5.75934i	0.254522	+	0.184921i
$971$	−14.6120	+	44.9711i	−0.468922	+	1.44319i	0.385061	+	0.922891i	$0.374180\pi$
$971$	−14.6120	+	44.9711i	−0.468922	+	1.44319i	−0.853983	+	0.520301i	$0.825820\pi$
$972$	3.61868	+	11.1372i	0.116069	+	0.357224i
$973$	17.0956	−	12.4207i	0.548061	−	0.398190i
$974$	15.9856	−	11.6142i	0.512211	−	0.372143i
$975$	2.21437	+	6.81513i	0.0709166	+	0.218259i
$976$	−4.01787	+	12.3657i	−0.128609	+	0.395817i
$977$	35.8403	+	26.0395i	1.14663	+	0.833078i	0.988030	−	0.154264i	$-0.0493008\pi$
$977$	35.8403	+	26.0395i	1.14663	+	0.833078i	0.158604	+	0.987342i	$0.449301\pi$
$978$	13.3638			0.427329
$979$	−3.36042	+	3.18723i	−0.107399	+	0.101864i
$980$	−1.00000			−0.0319438
$981$	−5.66168	−	4.11345i	−0.180764	−	0.131332i
$982$	9.48935	−	29.2052i	0.302817	−	0.931975i
$983$	−0.922119	−	2.83799i	−0.0294110	−	0.0905178i	0.935274	−	0.353926i	$-0.115153\pi$
$983$	−0.922119	−	2.83799i	−0.0294110	−	0.0905178i	−0.964685	+	0.263408i	$0.915153\pi$
$984$	−6.41710	+	4.66230i	−0.204570	+	0.148629i
$985$	−2.84171	+	2.06462i	−0.0905443	+	0.0657843i
$986$	1.72883	+	5.32078i	0.0550570	+	0.169448i
$987$	7.73266	−	23.7987i	0.246133	−	0.757520i
$988$	−12.5946	−	9.15051i	−0.400688	−	0.291117i
$989$	−5.27857			−0.167849
$990$	3.91083	−	0.513816i	0.124294	−	0.0163302i
$991$	−47.4047			−1.50586			−0.752930	−	0.658100i	$-0.771360\pi$
$991$	−47.4047			−1.50586			−0.752930	+	0.658100i	$0.771360\pi$
$992$	−4.61803	−	3.35520i	−0.146623	−	0.106528i
$993$	−19.1478	+	58.9310i	−0.607638	+	1.87012i
$994$	−1.81691	−	5.59186i	−0.0576287	−	0.177363i
$995$	15.7894	−	11.4716i	0.500556	−	0.363676i
$996$	20.8847	−	15.1736i	0.661757	−	0.480794i
$997$	5.17522	+	15.9277i	0.163901	+	0.504435i	0.998954	−	0.0457350i	$-0.0145630\pi$
$997$	5.17522	+	15.9277i	0.163901	+	0.504435i	−0.835053	+	0.550170i	$0.814563\pi$
$998$	5.74711	−	17.6878i	0.181922	−	0.559897i
$999$	0.982035	+	0.713490i	0.0310702	+	0.0225738i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.e.631.1	yes	8
11.3	even	5	inner	770.2.n.e.421.1	✓	8
11.5	even	5		8470.2.a.cq.1.1		4
11.6	odd	10		8470.2.a.ct.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.e.421.1	✓	8	11.3	even	5	inner
770.2.n.e.631.1	yes	8	1.1	even	1	trivial
8470.2.a.cq.1.1		4	11.5	even	5
8470.2.a.ct.1.1		4	11.6	odd	10

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.632489 + 1.94660i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-1.65588 + 1.20306i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.962157 - 0.699048i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.632489 + 1.94660i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-1.65588 + 1.20306i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.962157 - 0.699048i) q^{9} +1.00000 q^{10} +(-2.40640 + 2.28238i) q^{11} -2.04678 q^{12} +(2.83240 + 2.05786i) q^{13} +(0.309017 - 0.951057i) q^{14} +(0.632489 + 1.94660i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.46489 + 2.51739i) q^{17} +(-0.367511 - 1.13108i) q^{18} +(-1.37408 + 4.22898i) q^{19} +(0.809017 + 0.587785i) q^{20} +2.04678 q^{21} +(-3.28837 + 0.432036i) q^{22} -2.00000 q^{23} +(-1.65588 - 1.20306i) q^{24} +(0.309017 - 0.951057i) q^{25} +(1.08188 + 3.32969i) q^{26} +(-2.99831 + 2.17840i) q^{27} +(0.809017 - 0.587785i) q^{28} +(-0.403663 - 1.24235i) q^{29} +(-0.632489 + 1.94660i) q^{30} +(4.61803 + 3.35520i) q^{31} -1.00000 q^{32} +(-2.92085 - 6.12787i) q^{33} -4.28284 q^{34} +(-0.809017 - 0.587785i) q^{35} +(0.367511 - 1.13108i) q^{36} +(-0.101212 - 0.311499i) q^{37} +(-3.59738 + 2.61365i) q^{38} +(-5.79730 + 4.21198i) q^{39} +(0.309017 + 0.951057i) q^{40} +(1.19755 - 3.68568i) q^{41} +(1.65588 + 1.20306i) q^{42} +2.63928 q^{43} +(-2.91429 - 1.58333i) q^{44} -1.18929 q^{45} +(-1.61803 - 1.17557i) q^{46} +(3.77797 - 11.6274i) q^{47} +(-0.632489 - 1.94660i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(0.809017 - 0.587785i) q^{50} +(-2.70885 - 8.33698i) q^{51} +(-1.08188 + 3.32969i) q^{52} +(-0.883011 - 0.641545i) q^{53} -3.70611 q^{54} +(-0.605270 + 3.26093i) q^{55} +1.00000 q^{56} +(-7.36304 - 5.34956i) q^{57} +(0.403663 - 1.24235i) q^{58} +(3.10910 + 9.56883i) q^{59} +(-1.65588 + 1.20306i) q^{60} +(10.5189 - 7.64244i) q^{61} +(1.76393 + 5.42882i) q^{62} +(-0.367511 + 1.13108i) q^{63} +(-0.809017 - 0.587785i) q^{64} +3.50105 q^{65} +(1.23885 - 6.67439i) q^{66} -8.44661 q^{67} +(-3.46489 - 2.51739i) q^{68} +(1.26498 - 3.89320i) q^{69} +(-0.309017 - 0.951057i) q^{70} +(4.75672 - 3.45596i) q^{71} +(0.962157 - 0.699048i) q^{72} +(2.29967 + 7.07764i) q^{73} +(0.101212 - 0.311499i) q^{74} +(1.65588 + 1.20306i) q^{75} -4.44661 q^{76} +(2.91429 + 1.58333i) q^{77} -7.16586 q^{78} +(0.403663 + 0.293278i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(-3.44661 - 10.6076i) q^{81} +(3.13522 - 2.27787i) q^{82} +(-10.2037 + 7.41342i) q^{83} +(0.632489 + 1.94660i) q^{84} +(-1.32347 + 4.07323i) q^{85} +(2.13522 + 1.55133i) q^{86} +2.67366 q^{87} +(-1.42705 - 2.99391i) q^{88} +1.39645 q^{89} +(-0.962157 - 0.699048i) q^{90} +(1.08188 - 3.32969i) q^{91} +(-0.618034 - 1.90211i) q^{92} +(-9.45208 + 6.86734i) q^{93} +(9.89085 - 7.18612i) q^{94} +(1.37408 + 4.22898i) q^{95} +(0.632489 - 1.94660i) q^{96} +(7.92705 + 5.75934i) q^{97} -1.00000 q^{98} +(3.91083 - 0.513816i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 13 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 13 * q^9	\( 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 13 q^{9} + 8 q^{10} + 8 q^{11} + 4 q^{12} + 8 q^{13} - 2 q^{14} + q^{15} - 2 q^{16} - 9 q^{17} - 7 q^{18} - 9 q^{19} + 2 q^{20} - 4 q^{21} - 8 q^{22} - 16 q^{23} + q^{24} - 2 q^{25} + 7 q^{26} - 22 q^{27} + 2 q^{28} - q^{30} + 28 q^{31} - 8 q^{32} - q^{33} + 4 q^{34} - 2 q^{35} + 7 q^{36} + 4 q^{37} - 6 q^{38} - 13 q^{39} - 2 q^{40} + 8 q^{41} - q^{42} - 14 q^{43} - 7 q^{44} - 12 q^{45} - 4 q^{46} - q^{48} - 2 q^{49} + 2 q^{50} + 4 q^{51} - 7 q^{52} + 10 q^{53} - 28 q^{54} + 7 q^{55} + 8 q^{56} - 17 q^{57} + 31 q^{59} + q^{60} + 28 q^{61} + 32 q^{62} - 7 q^{63} - 2 q^{64} + 2 q^{65} + 36 q^{66} - 26 q^{67} - 9 q^{68} + 2 q^{69} + 2 q^{70} + 34 q^{71} + 13 q^{72} - 24 q^{73} - 4 q^{74} - q^{75} + 6 q^{76} + 7 q^{77} - 2 q^{78} + 2 q^{80} + 14 q^{81} - 3 q^{82} - 21 q^{83} + q^{84} - 11 q^{85} - 11 q^{86} - 52 q^{87} + 2 q^{88} - 14 q^{89} - 13 q^{90} + 7 q^{91} + 4 q^{92} + 14 q^{93} + 5 q^{94} + 9 q^{95} + q^{96} + 50 q^{97} - 8 q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 13 * q^9 + 8 * q^10 + 8 * q^11 + 4 * q^12 + 8 * q^13 - 2 * q^14 + q^15 - 2 * q^16 - 9 * q^17 - 7 * q^18 - 9 * q^19 + 2 * q^20 - 4 * q^21 - 8 * q^22 - 16 * q^23 + q^24 - 2 * q^25 + 7 * q^26 - 22 * q^27 + 2 * q^28 - q^30 + 28 * q^31 - 8 * q^32 - q^33 + 4 * q^34 - 2 * q^35 + 7 * q^36 + 4 * q^37 - 6 * q^38 - 13 * q^39 - 2 * q^40 + 8 * q^41 - q^42 - 14 * q^43 - 7 * q^44 - 12 * q^45 - 4 * q^46 - q^48 - 2 * q^49 + 2 * q^50 + 4 * q^51 - 7 * q^52 + 10 * q^53 - 28 * q^54 + 7 * q^55 + 8 * q^56 - 17 * q^57 + 31 * q^59 + q^60 + 28 * q^61 + 32 * q^62 - 7 * q^63 - 2 * q^64 + 2 * q^65 + 36 * q^66 - 26 * q^67 - 9 * q^68 + 2 * q^69 + 2 * q^70 + 34 * q^71 + 13 * q^72 - 24 * q^73 - 4 * q^74 - q^75 + 6 * q^76 + 7 * q^77 - 2 * q^78 + 2 * q^80 + 14 * q^81 - 3 * q^82 - 21 * q^83 + q^84 - 11 * q^85 - 11 * q^86 - 52 * q^87 + 2 * q^88 - 14 * q^89 - 13 * q^90 + 7 * q^91 + 4 * q^92 + 14 * q^93 + 5 * q^94 + 9 * q^95 + q^96 + 50 * q^97 - 8 * q^98 - 18 * q^99

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