LMFDB - Embedded newform 770.2.n.i.421.3

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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 11 x^{10} - 21 x^{9} + 61 x^{8} - 34 x^{7} + 141 x^{6} + 192 x^{5} + 289 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 11x^10 - 21x^9 + 61x^8 - 34x^7 + 141x^6 + 192x^5 + 289x^4 - 55x^3 + 222x^2 - 24*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.3
Root			$0.237961 + 0.732370i$ of defining polynomial
Character	$\chi$	$=$	770.421
Dual form			770.2.n.i.631.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(1.00585 + 3.09567i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-2.63334 - 1.91323i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-6.14442 + 4.46418i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(1.00585 + 3.09567i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-2.63334 - 1.91323i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-6.14442 + 4.46418i) q^{9} +1.00000 q^{10} +(2.49790 + 2.18185i) q^{11} +3.25498 q^{12} +(-2.89538 + 2.10361i) q^{13} +(0.309017 + 0.951057i) q^{14} +(1.00585 - 3.09567i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.44003 - 1.77278i) q^{17} +(2.34696 - 7.22320i) q^{18} +(0.885918 + 2.72658i) q^{19} +(-0.809017 + 0.587785i) q^{20} +3.25498 q^{21} +(-3.30331 - 0.296926i) q^{22} -9.00193 q^{23} +(-2.63334 + 1.91323i) q^{24} +(0.309017 + 0.951057i) q^{25} +(1.10594 - 3.40372i) q^{26} +(-12.1000 - 8.79115i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(0.483487 - 1.48802i) q^{29} +(1.00585 + 3.09567i) q^{30} +(0.382855 - 0.278160i) q^{31} +1.00000 q^{32} +(-4.24180 + 9.92730i) q^{33} +3.01604 q^{34} +(-0.809017 + 0.587785i) q^{35} +(2.34696 + 7.22320i) q^{36} +(-3.36628 + 10.3604i) q^{37} +(-2.31936 - 1.68512i) q^{38} +(-9.42440 - 6.84723i) q^{39} +(0.309017 - 0.951057i) q^{40} +(1.18737 + 3.65435i) q^{41} +(-2.63334 + 1.91323i) q^{42} +2.25195 q^{43} +(2.84696 - 1.70142i) q^{44} +7.59492 q^{45} +(7.28272 - 5.29120i) q^{46} +(-2.97076 - 9.14306i) q^{47} +(1.00585 - 3.09567i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(3.03367 - 9.33668i) q^{51} +(1.10594 + 3.40372i) q^{52} +(4.54794 - 3.30427i) q^{53} +14.9564 q^{54} +(-0.738384 - 3.23339i) q^{55} +1.00000 q^{56} +(-7.54949 + 5.48503i) q^{57} +(0.483487 + 1.48802i) q^{58} +(-0.845616 + 2.60254i) q^{59} +(-2.63334 - 1.91323i) q^{60} +(9.62595 + 6.99366i) q^{61} +(-0.146237 + 0.450073i) q^{62} +(2.34696 + 7.22320i) q^{63} +(-0.809017 + 0.587785i) q^{64} +3.57888 q^{65} +(-2.40343 - 10.5246i) q^{66} +0.752899 q^{67} +(-2.44003 + 1.77278i) q^{68} +(-9.05455 - 27.8670i) q^{69} +(0.309017 - 0.951057i) q^{70} +(1.54038 + 1.11915i) q^{71} +(-6.14442 - 4.46418i) q^{72} +(0.515256 - 1.58579i) q^{73} +(-3.36628 - 10.3604i) q^{74} +(-2.63334 + 1.91323i) q^{75} +2.86689 q^{76} +(2.84696 - 1.70142i) q^{77} +11.6492 q^{78} +(11.7628 - 8.54615i) q^{79} +(0.309017 + 0.951057i) q^{80} +(8.00295 - 24.6305i) q^{81} +(-3.10858 - 2.25851i) q^{82} +(4.30054 + 3.12453i) q^{83} +(1.00585 - 3.09567i) q^{84} +(0.932008 + 2.86842i) q^{85} +(-1.82187 + 1.32367i) q^{86} +5.09274 q^{87} +(-1.30317 + 3.04988i) q^{88} -11.1627 q^{89} +(-6.14442 + 4.46418i) q^{90} +(1.10594 + 3.40372i) q^{91} +(-2.78175 + 8.56135i) q^{92} +(1.24619 + 0.905407i) q^{93} +(7.77755 + 5.65072i) q^{94} +(0.885918 - 2.72658i) q^{95} +(1.00585 + 3.09567i) q^{96} +(0.854015 - 0.620478i) q^{97} +1.00000 q^{98} +(-25.0884 - 2.25513i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9	\( 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9} + 12 q^{10} + q^{11} + 2 q^{12} - 6 q^{13} - 3 q^{14} + 2 q^{15} - 3 q^{16} - 6 q^{17} - 13 q^{19} - 3 q^{20} + 2 q^{21} + q^{22} - 12 q^{23} - 3 q^{24} - 3 q^{25} + 4 q^{26} - 7 q^{27} - 3 q^{28} - 26 q^{29} + 2 q^{30} + 12 q^{32} - 15 q^{33} + 14 q^{34} - 3 q^{35} - 18 q^{37} + 2 q^{38} - 40 q^{39} - 3 q^{40} + 16 q^{41} - 3 q^{42} + 38 q^{43} + 6 q^{44} + 30 q^{45} + 8 q^{46} - 26 q^{47} + 2 q^{48} - 3 q^{49} - 3 q^{50} - 13 q^{51} + 4 q^{52} + 8 q^{54} + 11 q^{55} + 12 q^{56} - 41 q^{57} - 26 q^{58} + 21 q^{59} - 3 q^{60} + 4 q^{61} - 3 q^{64} + 4 q^{65} - 30 q^{66} + 10 q^{67} - 6 q^{68} + 18 q^{69} - 3 q^{70} - 4 q^{71} - 15 q^{72} - 14 q^{73} - 18 q^{74} - 3 q^{75} + 22 q^{76} + 6 q^{77} + 40 q^{78} - 2 q^{79} - 3 q^{80} + 26 q^{81} - 29 q^{82} + 35 q^{83} + 2 q^{84} - q^{85} - 37 q^{86} + 28 q^{87} - 19 q^{88} + 2 q^{89} - 15 q^{90} + 4 q^{91} - 2 q^{92} + 6 q^{93} + 4 q^{94} - 13 q^{95} + 2 q^{96} + 19 q^{97} + 12 q^{98} - 81 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9 + 12 * q^10 + q^11 + 2 * q^12 - 6 * q^13 - 3 * q^14 + 2 * q^15 - 3 * q^16 - 6 * q^17 - 13 * q^19 - 3 * q^20 + 2 * q^21 + q^22 - 12 * q^23 - 3 * q^24 - 3 * q^25 + 4 * q^26 - 7 * q^27 - 3 * q^28 - 26 * q^29 + 2 * q^30 + 12 * q^32 - 15 * q^33 + 14 * q^34 - 3 * q^35 - 18 * q^37 + 2 * q^38 - 40 * q^39 - 3 * q^40 + 16 * q^41 - 3 * q^42 + 38 * q^43 + 6 * q^44 + 30 * q^45 + 8 * q^46 - 26 * q^47 + 2 * q^48 - 3 * q^49 - 3 * q^50 - 13 * q^51 + 4 * q^52 + 8 * q^54 + 11 * q^55 + 12 * q^56 - 41 * q^57 - 26 * q^58 + 21 * q^59 - 3 * q^60 + 4 * q^61 - 3 * q^64 + 4 * q^65 - 30 * q^66 + 10 * q^67 - 6 * q^68 + 18 * q^69 - 3 * q^70 - 4 * q^71 - 15 * q^72 - 14 * q^73 - 18 * q^74 - 3 * q^75 + 22 * q^76 + 6 * q^77 + 40 * q^78 - 2 * q^79 - 3 * q^80 + 26 * q^81 - 29 * q^82 + 35 * q^83 + 2 * q^84 - q^85 - 37 * q^86 + 28 * q^87 - 19 * q^88 + 2 * q^89 - 15 * q^90 + 4 * q^91 - 2 * q^92 + 6 * q^93 + 4 * q^94 - 13 * q^95 + 2 * q^96 + 19 * q^97 + 12 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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
$3$	1.00585	+	3.09567i	0.580725	+	1.78729i	0.615799	+	0.787903i	$0.288833\pi$
$3$	1.00585	+	3.09567i	0.580725	+	1.78729i	−0.0350736	+	0.999385i	$0.511167\pi$
$4$	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
$6$	−2.63334	−	1.91323i	−1.07506	−	0.781074i
$7$	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
$9$	−6.14442	+	4.46418i	−2.04814	+	1.48806i
$10$	1.00000			0.316228
$11$	2.49790	+	2.18185i	0.753146	+	0.657854i
$11$	2.49790	+	2.18185i	0.753146	+	0.657854i
$12$	3.25498			0.939633
$13$	−2.89538	+	2.10361i	−0.803033	+	0.583438i	−0.911802	−	0.410629i	$-0.865309\pi$
$13$	−2.89538	+	2.10361i	−0.803033	+	0.583438i	0.108769	+	0.994067i	$0.465309\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$	1.00585	−	3.09567i	0.259708	−	0.799300i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−2.44003	−	1.77278i	−0.591794	−	0.429963i	0.251163	−	0.967945i	$-0.419187\pi$
$17$	−2.44003	−	1.77278i	−0.591794	−	0.429963i	−0.842957	+	0.537982i	$0.819187\pi$
$18$	2.34696	−	7.22320i	0.553184	−	1.70252i
$19$	0.885918	+	2.72658i	0.203244	+	0.625519i	0.999781	+	0.0209301i	$0.00666274\pi$
$19$	0.885918	+	2.72658i	0.203244	+	0.625519i	−0.796537	+	0.604589i	$0.793337\pi$
$20$	−0.809017	+	0.587785i	−0.180902	+	0.131433i
$21$	3.25498			0.710296
$22$	−3.30331	−	0.296926i	−0.704267	−	0.0633049i
$23$	−9.00193			−1.87703			−0.938516	−	0.345235i	$-0.887799\pi$
$23$	−9.00193			−1.87703			−0.938516	+	0.345235i	$0.887799\pi$
$24$	−2.63334	+	1.91323i	−0.537528	+	0.390537i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	1.10594	−	3.40372i	0.216892	−	0.667524i
$27$	−12.1000	−	8.79115i	−2.32864	−	1.69186i
$28$	−0.809017	−	0.587785i	−0.152890	−	0.111081i
$29$	0.483487	−	1.48802i	0.0897814	−	0.276319i	−0.896077	−	0.443898i	$-0.853595\pi$
$29$	0.483487	−	1.48802i	0.0897814	−	0.276319i	0.985859	+	0.167580i	$0.0535951\pi$
$30$	1.00585	+	3.09567i	0.183641	+	0.565190i
$31$	0.382855	−	0.278160i	0.0687627	−	0.0499590i	−0.552873	−	0.833266i	$-0.686468\pi$
$31$	0.382855	−	0.278160i	0.0687627	−	0.0499590i	0.621636	+	0.783307i	$0.286468\pi$
$32$	1.00000			0.176777
$33$	−4.24180	+	9.92730i	−0.738403	+	1.72812i
$34$	3.01604			0.517247
$35$	−0.809017	+	0.587785i	−0.136749	+	0.0993538i
$36$	2.34696	+	7.22320i	0.391160	+	1.20387i
$37$	−3.36628	+	10.3604i	−0.553414	+	1.70323i	0.146682	+	0.989184i	$0.453140\pi$
$37$	−3.36628	+	10.3604i	−0.553414	+	1.70323i	−0.700096	+	0.714049i	$0.746860\pi$
$38$	−2.31936	−	1.68512i	−0.376250	−	0.273362i
$39$	−9.42440	−	6.84723i	−1.50911	−	1.09643i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	1.18737	+	3.65435i	0.185436	+	0.570714i	0.999956	−	0.00942255i	$-0.00299934\pi$
$41$	1.18737	+	3.65435i	0.185436	+	0.570714i	−0.814520	+	0.580136i	$0.802999\pi$
$42$	−2.63334	+	1.91323i	−0.406333	+	0.295218i
$43$	2.25195			0.343420			0.171710	−	0.985148i	$-0.445071\pi$
$43$	2.25195			0.343420			0.171710	+	0.985148i	$0.445071\pi$
$44$	2.84696	−	1.70142i	0.429195	−	0.256498i
$45$	7.59492			1.13218
$46$	7.28272	−	5.29120i	1.07378	−	0.780145i
$47$	−2.97076	−	9.14306i	−0.433330	−	1.33365i	−0.894788	−	0.446491i	$-0.852674\pi$
$47$	−2.97076	−	9.14306i	−0.433330	−	1.33365i	0.461458	−	0.887162i	$-0.347326\pi$
$48$	1.00585	−	3.09567i	0.145181	−	0.446822i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$	3.03367	−	9.33668i	0.424799	−	1.30740i
$52$	1.10594	+	3.40372i	0.153366	+	0.472011i
$53$	4.54794	−	3.30427i	0.624708	−	0.453877i	−0.229855	−	0.973225i	$-0.573825\pi$
$53$	4.54794	−	3.30427i	0.624708	−	0.453877i	0.854563	+	0.519348i	$0.173825\pi$
$54$	14.9564			2.03531
$55$	−0.738384	−	3.23339i	−0.0995637	−	0.435990i
$56$	1.00000			0.133631
$57$	−7.54949	+	5.48503i	−0.999955	+	0.726510i
$58$	0.483487	+	1.48802i	0.0634850	+	0.195387i
$59$	−0.845616	+	2.60254i	−0.110090	+	0.338822i	−0.990891	−	0.134664i	$-0.957004\pi$
$59$	−0.845616	+	2.60254i	−0.110090	+	0.338822i	0.880801	+	0.473486i	$0.157004\pi$
$60$	−2.63334	−	1.91323i	−0.339962	−	0.246997i
$61$	9.62595	+	6.99366i	1.23248	+	0.895447i	0.997073	−	0.0764508i	$-0.0243588\pi$
$61$	9.62595	+	6.99366i	1.23248	+	0.895447i	0.235404	+	0.971898i	$0.424359\pi$
$62$	−0.146237	+	0.450073i	−0.0185722	+	0.0571593i
$63$	2.34696	+	7.22320i	0.295689	+	0.910038i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	3.57888			0.443906
$66$	−2.40343	−	10.5246i	−0.295842	−	1.29549i
$67$	0.752899			0.0919813			0.0459907	−	0.998942i	$-0.485356\pi$
$67$	0.752899			0.0919813			0.0459907	+	0.998942i	$0.485356\pi$
$68$	−2.44003	+	1.77278i	−0.295897	+	0.214982i
$69$	−9.05455	−	27.8670i	−1.09004	−	3.35480i
$70$	0.309017	−	0.951057i	0.0369346	−	0.113673i
$71$	1.54038	+	1.11915i	0.182809	+	0.132819i	0.675426	−	0.737427i	$-0.263960\pi$
$71$	1.54038	+	1.11915i	0.182809	+	0.132819i	−0.492617	+	0.870246i	$0.663960\pi$
$72$	−6.14442	−	4.46418i	−0.724127	−	0.526109i
$73$	0.515256	−	1.58579i	0.0603061	−	0.185603i	−0.916365	−	0.400344i	$-0.868891\pi$
$73$	0.515256	−	1.58579i	0.0603061	−	0.185603i	0.976671	+	0.214741i	$0.0688907\pi$
$74$	−3.36628	−	10.3604i	−0.391323	−	1.20437i
$75$	−2.63334	+	1.91323i	−0.304072	+	0.220921i
$76$	2.86689			0.328855
$77$	2.84696	−	1.70142i	0.324441	−	0.193894i
$78$	11.6492			1.31901
$79$	11.7628	−	8.54615i	1.32341	−	0.961517i	0.323531	−	0.946218i	$-0.395130\pi$
$79$	11.7628	−	8.54615i	1.32341	−	0.961517i	0.999883	−	0.0152990i	$-0.00487003\pi$
$80$	0.309017	+	0.951057i	0.0345492	+	0.106331i
$81$	8.00295	−	24.6305i	0.889216	−	2.73673i
$82$	−3.10858	−	2.25851i	−0.343285	−	0.249411i
$83$	4.30054	+	3.12453i	0.472046	+	0.342961i	0.798238	−	0.602342i	$-0.205766\pi$
$83$	4.30054	+	3.12453i	0.472046	+	0.342961i	−0.326192	+	0.945303i	$0.605766\pi$
$84$	1.00585	−	3.09567i	0.109747	−	0.337766i
$85$	0.932008	+	2.86842i	0.101090	+	0.311124i
$86$	−1.82187	+	1.32367i	−0.196457	+	0.142735i
$87$	5.09274			0.545999
$88$	−1.30317	+	3.04988i	−0.138919	+	0.325118i
$89$	−11.1627			−1.18324			−0.591621	−	0.806216i	$-0.701512\pi$
$89$	−11.1627			−1.18324			−0.591621	+	0.806216i	$0.701512\pi$
$90$	−6.14442	+	4.46418i	−0.647679	+	0.470566i
$91$	1.10594	+	3.40372i	0.115934	+	0.356807i
$92$	−2.78175	+	8.56135i	−0.290017	+	0.892582i
$93$	1.24619	+	0.905407i	0.129223	+	0.0938863i
$94$	7.77755	+	5.65072i	0.802193	+	0.582828i
$95$	0.885918	−	2.72658i	0.0908933	−	0.279741i
$96$	1.00585	+	3.09567i	0.102659	+	0.315951i
$97$	0.854015	−	0.620478i	0.0867120	−	0.0630000i	−0.543585	−	0.839354i	$-0.682933\pi$
$97$	0.854015	−	0.620478i	0.0867120	−	0.0630000i	0.630297	+	0.776354i	$0.282933\pi$
$98$	1.00000			0.101015
$99$	−25.0884	−	2.25513i	−2.52147	−	0.226649i
$100$	1.00000			0.100000
$101$	−4.55928	+	3.31251i	−0.453665	+	0.329607i	−0.791041	−	0.611763i	$-0.790461\pi$
$101$	−4.55928	+	3.31251i	−0.453665	+	0.329607i	0.337376	+	0.941370i	$0.390461\pi$
$102$	3.03367	+	9.33668i	0.300378	+	0.924469i
$103$	−2.37411	+	7.30676i	−0.233928	+	0.719956i	0.763334	+	0.646004i	$0.223561\pi$
$103$	−2.37411	+	7.30676i	−0.233928	+	0.719956i	−0.997262	+	0.0739522i	$0.976439\pi$
$104$	−2.89538	−	2.10361i	−0.283915	−	0.206276i
$105$	−2.63334	−	1.91323i	−0.256987	−	0.186712i
$106$	−1.73716	+	5.34643i	−0.168728	+	0.519291i
$107$	5.42034	+	16.6821i	0.524004	+	1.61272i	0.766278	+	0.642510i	$0.222107\pi$
$107$	5.42034	+	16.6821i	0.524004	+	1.61272i	−0.242274	+	0.970208i	$0.577893\pi$
$108$	−12.1000	+	8.79115i	−1.16432	+	0.845929i
$109$	10.2643			0.983138			0.491569	−	0.870839i	$-0.336424\pi$
$109$	10.2643			0.983138			0.491569	+	0.870839i	$0.336424\pi$
$110$	2.49790	+	2.18185i	0.238166	+	0.208032i
$111$	−35.4582			−3.36555
$112$	−0.809017	+	0.587785i	−0.0764449	+	0.0555405i
$113$	3.31848	+	10.2132i	0.312177	+	0.960781i	0.976901	+	0.213692i	$0.0685490\pi$
$113$	3.31848	+	10.2132i	0.312177	+	0.960781i	−0.664724	+	0.747089i	$0.731451\pi$
$114$	2.88365	−	8.87496i	0.270079	−	0.831216i
$115$	7.28272	+	5.29120i	0.679117	+	0.493407i
$116$	−1.26579	−	0.919648i	−0.117525	−	0.0853871i
$117$	8.39949	−	25.8510i	0.776533	−	2.38992i
$118$	−0.845616	−	2.60254i	−0.0778453	−	0.239583i
$119$	−2.44003	+	1.77278i	−0.223677	+	0.162511i
$120$	3.25498			0.297138
$121$	1.47903	+	10.9001i	0.134457	+	0.990919i
$122$	−11.8983			−1.07722
$123$	−10.1184	+	7.35142i	−0.912342	+	0.662855i
$124$	−0.146237	−	0.450073i	−0.0131325	−	0.0404177i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	−6.14442	−	4.46418i	−0.547389	−	0.397701i
$127$	−0.223724	−	0.162545i	−0.0198523	−	0.0144235i	0.577815	−	0.816168i	$-0.303906\pi$
$127$	−0.223724	−	0.162545i	−0.0198523	−	0.0144235i	−0.597667	+	0.801744i	$0.703906\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	2.26512	+	6.97132i	0.199433	+	0.613790i
$130$	−2.89538	+	2.10361i	−0.253941	+	0.184499i
$131$	−16.8708			−1.47400			−0.737002	−	0.675890i	$-0.763759\pi$
$131$	−16.8708			−1.47400			−0.737002	+	0.675890i	$0.763759\pi$
$132$	8.13063	+	7.10190i	0.707681	+	0.618141i
$133$	2.86689			0.248591
$134$	−0.609108	+	0.442543i	−0.0526190	+	0.0382299i
$135$	4.62178	+	14.2244i	0.397780	+	1.22424i
$136$	0.932008	−	2.86842i	0.0799190	−	0.245965i
$137$	−10.9125	−	7.92841i	−0.932319	−	0.677370i	0.0142402	−	0.999899i	$-0.495467\pi$
$137$	−10.9125	−	7.92841i	−0.932319	−	0.677370i	−0.946560	+	0.322529i	$0.895467\pi$
$138$	23.7051	+	17.2228i	2.01791	+	1.46610i
$139$	−0.456056	+	1.40360i	−0.0386821	+	0.119051i	−0.968533	−	0.248885i	$-0.919936\pi$
$139$	−0.456056	+	1.40360i	−0.0386821	+	0.119051i	0.929851	+	0.367937i	$0.119936\pi$
$140$	0.309017	+	0.951057i	0.0261167	+	0.0803789i
$141$	25.3158	−	18.3930i	2.13198	−	1.54897i
$142$	−1.90401			−0.159781
$143$	−11.8221	−	1.06266i	−0.988617	−	0.0888644i
$144$	7.59492			0.632910
$145$	−1.26579	+	0.919648i	−0.105118	+	0.0763726i
$146$	0.515256	+	1.58579i	0.0426429	+	0.131241i
$147$	1.00585	−	3.09567i	0.0829607	−	0.255327i
$148$	8.81305	+	6.40305i	0.724428	+	0.526328i
$149$	13.3049	+	9.66656i	1.08998	+	0.791916i	0.979396	−	0.201951i	$-0.0647282\pi$
$149$	13.3049	+	9.66656i	1.08998	+	0.791916i	0.110583	+	0.993867i	$0.464728\pi$
$150$	1.00585	−	3.09567i	0.0821269	−	0.252761i
$151$	2.43349	+	7.48952i	0.198035	+	0.609489i	0.999928	+	0.0120208i	$0.00382644\pi$
$151$	2.43349	+	7.48952i	0.198035	+	0.609489i	−0.801893	+	0.597468i	$0.796174\pi$
$152$	−2.31936	+	1.68512i	−0.188125	+	0.136681i
$153$	22.9066			1.85189
$154$	−1.30317	+	3.04988i	−0.105013	+	0.245766i
$155$	−0.473234			−0.0380111
$156$	−9.42440	+	6.84723i	−0.754556	+	0.548217i
$157$	−3.64188	−	11.2086i	−0.290654	−	0.894540i	−0.984647	−	0.174559i	$-0.944150\pi$
$157$	−3.64188	−	11.2086i	−0.290654	−	0.894540i	0.693993	−	0.719982i	$-0.255850\pi$
$158$	−4.49298	+	13.8280i	−0.357442	+	1.10009i
$159$	14.8035	+	10.7554i	1.17399	+	0.852956i
$160$	−0.809017	−	0.587785i	−0.0639584	−	0.0464685i
$161$	−2.78175	+	8.56135i	−0.219233	+	0.674729i
$162$	8.00295	+	24.6305i	0.628771	+	1.93516i
$163$	6.64146	−	4.82530i	0.520199	−	0.377947i	−0.296480	−	0.955039i	$-0.595813\pi$
$163$	6.64146	−	4.82530i	0.520199	−	0.377947i	0.816679	+	0.577092i	$0.195813\pi$
$164$	3.84241			0.300042
$165$	9.26681	−	5.53808i	0.721420	−	0.431139i
$166$	−5.31576			−0.412583
$167$	−16.3421	+	11.8732i	−1.26459	+	0.918777i	−0.998973	−	0.0453026i	$-0.985575\pi$
$167$	−16.3421	+	11.8732i	−1.26459	+	0.918777i	−0.265614	+	0.964079i	$0.585575\pi$
$168$	1.00585	+	3.09567i	0.0776027	+	0.238836i
$169$	−0.0592090	+	0.182227i	−0.00455454	+	0.0140174i
$170$	−2.44003	−	1.77278i	−0.187142	−	0.135966i
$171$	−17.6154	−	12.7983i	−1.34708	−	0.978713i
$172$	0.695892	−	2.14174i	0.0530613	−	0.163306i
$173$	−7.64124	−	23.5173i	−0.580953	−	1.78799i	−0.614950	−	0.788566i	$-0.710824\pi$
$173$	−7.64124	−	23.5173i	−0.580953	−	1.78799i	0.0339973	−	0.999422i	$-0.489176\pi$
$174$	−4.12012	+	2.99344i	−0.312345	+	0.226932i
$175$	1.00000			0.0755929
$176$	−0.738384	−	3.23339i	−0.0556578	−	0.243726i
$177$	−8.90717			−0.669504
$178$	9.03079	−	6.56126i	0.676887	−	0.491787i
$179$	7.90992	+	24.3442i	0.591215	+	1.81957i	0.572730	+	0.819744i	$0.305884\pi$
$179$	7.90992	+	24.3442i	0.591215	+	1.81957i	0.0184852	+	0.999829i	$0.494116\pi$
$180$	2.34696	−	7.22320i	0.174932	−	0.538386i
$181$	1.81983	+	1.32218i	0.135267	+	0.0982771i	0.653361	−	0.757046i	$-0.273358\pi$
$181$	1.81983	+	1.32218i	0.135267	+	0.0982771i	−0.518094	+	0.855324i	$0.673358\pi$
$182$	−2.89538	−	2.10361i	−0.214620	−	0.155930i
$183$	−11.9679	+	36.8334i	−0.884691	+	2.72280i
$184$	−2.78175	−	8.56135i	−0.205073	−	0.631151i
$185$	8.81305	−	6.40305i	0.647948	−	0.470762i
$186$	−1.54037			−0.112945
$187$	−2.22700	−	9.75202i	−0.162854	−	0.713139i
$188$	−9.61359			−0.701143
$189$	−12.1000	+	8.79115i	−0.880144	+	0.639462i
$190$	0.885918	+	2.72658i	0.0642713	+	0.197807i
$191$	8.05663	−	24.7957i	0.582957	−	1.79416i	−0.0243667	−	0.999703i	$-0.507757\pi$
$191$	8.05663	−	24.7957i	0.582957	−	1.79416i	0.607324	−	0.794454i	$-0.292243\pi$
$192$	−2.63334	−	1.91323i	−0.190045	−	0.138076i
$193$	19.2116	+	13.9580i	1.38288	+	1.00472i	0.996604	+	0.0823394i	$0.0262391\pi$
$193$	19.2116	+	13.9580i	1.38288	+	1.00472i	0.386277	+	0.922383i	$0.373761\pi$
$194$	−0.326205	+	1.00395i	−0.0234201	+	0.0720797i
$195$	3.59980	+	11.0791i	0.257787	+	0.793387i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	8.36713			0.596133			0.298067	−	0.954545i	$-0.403658\pi$
$197$	8.36713			0.596133			0.298067	+	0.954545i	$0.403658\pi$
$198$	21.6224	−	12.9221i	1.53664	−	0.918336i
$199$	6.83066			0.484213			0.242106	−	0.970250i	$-0.422162\pi$
$199$	6.83066			0.484213			0.242106	+	0.970250i	$0.422162\pi$
$200$	−0.809017	+	0.587785i	−0.0572061	+	0.0415627i
$201$	0.757300	+	2.33073i	0.0534159	+	0.164397i
$202$	1.74149	−	5.35976i	0.122531	−	0.377111i
$203$	−1.26579	−	0.919648i	−0.0888408	−	0.0645466i
$204$	−7.94225	−	5.77038i	−0.556069	−	0.404008i
$205$	1.18737	−	3.65435i	0.0829295	−	0.255231i
$206$	−2.37411	−	7.30676i	−0.165412	−	0.509086i
$207$	55.3117	−	40.1863i	3.84443	−	2.79314i
$208$	3.57888			0.248151
$209$	−3.73605	+	8.74366i	−0.258428	+	0.604812i
$210$	3.25498			0.224615
$211$	−2.29958	+	1.67075i	−0.158310	+	0.115019i	−0.664120	−	0.747626i	$-0.731194\pi$
$211$	−2.29958	+	1.67075i	−0.158310	+	0.115019i	0.505810	+	0.862645i	$0.331194\pi$
$212$	−1.73716	−	5.34643i	−0.119309	−	0.367194i
$213$	−1.91514	+	5.89421i	−0.131223	+	0.403864i
$214$	−14.1906	−	10.3101i	−0.970051	−	0.704783i
$215$	−1.82187	−	1.32367i	−0.124250	−	0.0902732i
$216$	4.62178	−	14.2244i	0.314472	−	0.967847i
$217$	−0.146237	−	0.450073i	−0.00992725	−	0.0305529i
$218$	−8.30396	+	6.03318i	−0.562415	+	0.408618i
$219$	5.42737			0.366748
$220$	−3.30331	−	0.296926i	−0.222709	−	0.0200188i
$221$	10.7941			0.726087
$222$	28.6863	−	20.8418i	1.92530	−	1.39881i
$223$	6.18417	+	19.0329i	0.414122	+	1.27454i	0.913033	+	0.407885i	$0.133733\pi$
$223$	6.18417	+	19.0329i	0.414122	+	1.27454i	−0.498911	+	0.866653i	$0.666267\pi$
$224$	0.309017	−	0.951057i	0.0206471	−	0.0635451i
$225$	−6.14442	−	4.46418i	−0.409628	−	0.297612i
$226$	−8.68791	−	6.31213i	−0.577911	−	0.419877i
$227$	−3.81124	+	11.7298i	−0.252961	+	0.778534i	0.741263	+	0.671214i	$0.234227\pi$
$227$	−3.81124	+	11.7298i	−0.252961	+	0.778534i	−0.994225	+	0.107320i	$0.965773\pi$
$228$	2.88365	+	8.87496i	0.190974	+	0.587759i
$229$	−4.48450	+	3.25818i	−0.296344	+	0.215307i	−0.726015	−	0.687679i	$-0.758630\pi$
$229$	−4.48450	+	3.25818i	−0.296344	+	0.215307i	0.429671	+	0.902986i	$0.358630\pi$
$230$	−9.00193			−0.593570
$231$	8.13063	+	7.10190i	0.534956	+	0.467271i
$232$	1.56460			0.102721
$233$	−10.4865	+	7.61891i	−0.686995	+	0.499131i	−0.875671	−	0.482908i	$-0.839581\pi$
$233$	−10.4865	+	7.61891i	−0.686995	+	0.499131i	0.188676	+	0.982039i	$0.439581\pi$
$234$	8.39949	+	25.8510i	0.549092	+	1.68993i
$235$	−2.97076	+	9.14306i	−0.193791	+	0.596428i
$236$	2.21385	+	1.60846i	0.144109	+	0.104702i
$237$	38.2876	+	27.8176i	2.48705	+	1.80695i
$238$	0.932008	−	2.86842i	0.0604131	−	0.185932i
$239$	−6.58543	−	20.2679i	−0.425976	−	1.31102i	−0.902056	−	0.431618i	$-0.857943\pi$
$239$	−6.58543	−	20.2679i	−0.425976	−	1.31102i	0.476080	−	0.879402i	$-0.342057\pi$
$240$	−2.63334	+	1.91323i	−0.169981	+	0.123499i
$241$	7.67156			0.494169			0.247084	−	0.968994i	$-0.420528\pi$
$241$	7.67156			0.494169			0.247084	+	0.968994i	$0.420528\pi$
$242$	−7.60349	−	7.94902i	−0.488771	−	0.510983i
$243$	39.4286			2.52935
$244$	9.62595	−	6.99366i	0.616238	−	0.447723i
$245$	0.309017	+	0.951057i	0.0197424	+	0.0607608i
$246$	3.86487	−	11.8949i	0.246415	−	0.758388i
$247$	−8.30073	−	6.03083i	−0.528163	−	0.383733i
$248$	0.382855	+	0.278160i	0.0243113	+	0.0176632i
$249$	−5.34683	+	16.4559i	−0.338842	+	1.04285i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−21.9391	+	15.9397i	−1.38478	+	1.00610i	−0.388368	+	0.921504i	$0.626961\pi$
$251$	−21.9391	+	15.9397i	−1.38478	+	1.00610i	−0.996415	+	0.0845997i	$0.973039\pi$
$252$	7.59492			0.478435
$253$	−22.4859	−	19.6409i	−1.41368	−	1.23481i
$254$	0.276538			0.0173515
$255$	−7.94225	+	5.77038i	−0.497363	+	0.361355i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	2.08190	−	6.40742i	0.129865	−	0.399684i	−0.864891	−	0.501960i	$-0.832613\pi$
$257$	2.08190	−	6.40742i	0.129865	−	0.399684i	0.994756	+	0.102276i	$0.0326125\pi$
$258$	−5.93016	−	4.30851i	−0.369195	−	0.268236i
$259$	8.81305	+	6.40305i	0.547616	+	0.397866i
$260$	1.10594	−	3.40372i	0.0685872	−	0.211090i
$261$	3.67205	+	11.3014i	0.227294	+	0.699539i
$262$	13.6487	−	9.91638i	0.843221	−	0.612636i
$263$	32.1781			1.98419			0.992094	−	0.125496i	$-0.0400521\pi$
$263$	32.1781			1.98419			0.992094	+	0.125496i	$0.0400521\pi$
$264$	−10.7522	−	0.966490i	−0.661753	−	0.0594834i
$265$	−5.62157			−0.345330
$266$	−2.31936	+	1.68512i	−0.142209	+	0.103321i
$267$	−11.2279	−	34.5560i	−0.687138	−	2.11479i
$268$	0.232659	−	0.716050i	0.0142119	−	0.0437397i
$269$	24.3128	+	17.6643i	1.48238	+	1.07701i	0.976781	+	0.214242i	$0.0687280\pi$
$269$	24.3128	+	17.6643i	1.48238	+	1.07701i	0.505598	+	0.862769i	$0.331272\pi$
$270$	−12.1000	−	8.79115i	−0.736381	−	0.535012i
$271$	−2.75899	+	8.49130i	−0.167597	+	0.515810i	−0.999218	−	0.0395331i	$-0.987413\pi$
$271$	−2.75899	+	8.49130i	−0.167597	+	0.515810i	0.831622	+	0.555343i	$0.187413\pi$
$272$	0.932008	+	2.86842i	0.0565113	+	0.173924i
$273$	−9.42440	+	6.84723i	−0.570391	+	0.414413i
$274$	13.4886			0.814877
$275$	−1.30317	+	3.04988i	−0.0785842	+	0.183914i
$276$	−29.3011			−1.76372
$277$	−1.35972	+	0.987894i	−0.0816977	+	0.0593568i	−0.627884	−	0.778307i	$-0.716079\pi$
$277$	−1.35972	+	0.987894i	−0.0816977	+	0.0593568i	0.546187	+	0.837663i	$0.316079\pi$
$278$	−0.456056	−	1.40360i	−0.0273524	−	0.0841820i
$279$	−1.11066	+	3.41827i	−0.0664936	+	0.204646i
$280$	−0.809017	−	0.587785i	−0.0483480	−	0.0351269i
$281$	−6.39205	−	4.64409i	−0.381317	−	0.277043i	0.380571	−	0.924752i	$-0.375728\pi$
$281$	−6.39205	−	4.64409i	−0.381317	−	0.277043i	−0.761888	+	0.647708i	$0.775728\pi$
$282$	−9.66978	+	29.7605i	−0.575827	+	1.77221i
$283$	8.35701	+	25.7202i	0.496773	+	1.52891i	0.814176	+	0.580619i	$0.197189\pi$
$283$	8.35701	+	25.7202i	0.496773	+	1.52891i	−0.317403	+	0.948291i	$0.602811\pi$
$284$	1.54038	−	1.11915i	0.0914047	−	0.0664094i
$285$	9.33169			0.552761
$286$	10.1889	−	6.08917i	0.602484	−	0.360060i
$287$	3.84241			0.226810
$288$	−6.14442	+	4.46418i	−0.362063	+	0.263055i
$289$	−2.44232	−	7.51667i	−0.143666	−	0.442157i
$290$	0.483487	−	1.48802i	0.0283914	−	0.0873796i
$291$	2.77980	+	2.01965i	0.162955	+	0.118394i
$292$	−1.34896	−	0.980075i	−0.0789418	−	0.0573545i
$293$	3.15220	−	9.70148i	0.184154	−	0.566767i	−0.815779	−	0.578364i	$-0.803692\pi$
$293$	3.15220	−	9.70148i	0.184154	−	0.566767i	0.999933	+	0.0115969i	$0.00369150\pi$
$294$	1.00585	+	3.09567i	0.0586621	+	0.180543i
$295$	2.21385	−	1.60846i	0.128895	−	0.0936480i
$296$	−10.8935			−0.633173
$297$	−11.0436	−	48.3598i	−0.640813	−	2.80612i
$298$	−16.4457			−0.952676
$299$	26.0640	−	18.9366i	1.50732	−	1.09513i
$300$	1.00585	+	3.09567i	0.0580725	+	0.178729i
$301$	0.695892	−	2.14174i	0.0401106	−	0.123448i
$302$	−6.37097	−	4.62878i	−0.366608	−	0.266356i
$303$	−14.8404	−	10.7822i	−0.852558	−	0.619420i
$304$	0.885918	−	2.72658i	0.0508109	−	0.156380i
$305$	−3.67679	−	11.3160i	−0.210532	−	0.647951i
$306$	−18.5318	+	13.4642i	−1.05939	+	0.769695i
$307$	15.3552			0.876370			0.438185	−	0.898885i	$-0.355621\pi$
$307$	15.3552			0.876370			0.438185	+	0.898885i	$0.355621\pi$
$308$	−0.738384	−	3.23339i	−0.0420733	−	0.184239i
$309$	−25.0073			−1.42262
$310$	0.382855	−	0.278160i	0.0217447	−	0.0157984i
$311$	−8.14507	−	25.0679i	−0.461865	−	1.42147i	−0.862883	−	0.505403i	$-0.831344\pi$
$311$	−8.14507	−	25.0679i	−0.461865	−	1.42147i	0.401019	−	0.916070i	$-0.368656\pi$
$312$	3.59980	−	11.0791i	0.203799	−	0.627228i
$313$	−6.96136	−	5.05773i	−0.393480	−	0.285880i	0.373400	−	0.927670i	$-0.378192\pi$
$313$	−6.96136	−	5.05773i	−0.393480	−	0.285880i	−0.766880	+	0.641791i	$0.778192\pi$
$314$	9.53457	+	6.92727i	0.538067	+	0.390928i
$315$	2.34696	−	7.22320i	0.132236	−	0.406981i
$316$	−4.49298	−	13.8280i	−0.252750	−	0.777883i
$317$	−2.32785	+	1.69128i	−0.130745	+	0.0949919i	−0.651236	−	0.758876i	$-0.725749\pi$
$317$	−2.32785	+	1.69128i	−0.130745	+	0.0949919i	0.520491	+	0.853867i	$0.325749\pi$
$318$	−18.2981			−1.02611
$319$	4.45435	−	2.66203i	0.249396	−	0.149045i
$320$	1.00000			0.0559017
$321$	−46.1903	+	33.5592i	−2.57809	+	1.87309i
$322$	−2.78175	−	8.56135i	−0.155021	−	0.477105i
$323$	2.67196	−	8.22346i	0.148672	−	0.457566i
$324$	−20.9520	−	15.2225i	−1.16400	−	0.845695i
$325$	−2.89538	−	2.10361i	−0.160607	−	0.116688i
$326$	−2.53681	+	7.80751i	−0.140501	+	0.432418i
$327$	10.3243	+	31.7748i	0.570933	+	1.75715i
$328$	−3.10858	+	2.25851i	−0.171642	+	0.124705i
$329$	−9.61359			−0.530014
$330$	−4.24180	+	9.92730i	−0.233504	+	0.546480i
$331$	−19.4901			−1.07128			−0.535638	−	0.844448i	$-0.679929\pi$
$331$	−19.4901			−1.07128			−0.535638	+	0.844448i	$0.679929\pi$
$332$	4.30054	−	3.12453i	0.236023	−	0.171481i
$333$	−25.5667	−	78.6861i	−1.40104	−	4.31197i
$334$	6.24212	−	19.2113i	0.341553	−	1.05119i
$335$	−0.609108	−	0.442543i	−0.0332792	−	0.0241787i
$336$	−2.63334	−	1.91323i	−0.143660	−	0.104375i
$337$	−8.69469	+	26.7595i	−0.473630	+	1.45768i	0.374167	+	0.927362i	$0.377929\pi$
$337$	−8.69469	+	26.7595i	−0.473630	+	1.45768i	−0.847796	+	0.530322i	$0.822071\pi$
$338$	−0.0592090	−	0.182227i	−0.00322055	−	0.00991183i
$339$	−28.2790	+	20.5459i	−1.53590	+	1.11590i
$340$	3.01604			0.163568
$341$	1.56324	+	0.140516i	0.0846541	+	0.00760935i
$342$	21.7738			1.17739
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	0.695892	+	2.14174i	0.0375200	+	0.115475i
$345$	−9.05455	+	27.8670i	−0.487481	+	1.50031i
$346$	20.0050	+	14.5345i	1.07548	+	0.781379i
$347$	0.187446	+	0.136187i	0.0100626	+	0.00731092i	0.592805	−	0.805346i	$-0.298020\pi$
$347$	0.187446	+	0.136187i	0.0100626	+	0.00731092i	−0.582743	+	0.812657i	$0.698020\pi$
$348$	1.57374	−	4.84349i	0.0843615	−	0.259638i
$349$	−7.32620	−	22.5477i	−0.392162	−	1.20695i	−0.931149	−	0.364638i	$-0.881193\pi$
$349$	−7.32620	−	22.5477i	−0.392162	−	1.20695i	0.538987	−	0.842314i	$-0.318807\pi$
$350$	−0.809017	+	0.587785i	−0.0432438	+	0.0314184i
$351$	53.5272			2.85707
$352$	2.49790	+	2.18185i	0.133139	+	0.116293i
$353$	20.1884			1.07452			0.537259	−	0.843417i	$-0.319460\pi$
$353$	20.1884			1.07452			0.537259	+	0.843417i	$0.319460\pi$
$354$	7.20605	−	5.23550i	0.382997	−	0.278264i
$355$	−0.588373	−	1.81082i	−0.0312276	−	0.0961086i
$356$	−3.44946	+	10.6163i	−0.182821	+	0.562665i
$357$	−7.94225	−	5.77038i	−0.420349	−	0.305401i
$358$	−20.7084	−	15.0456i	−1.09448	−	0.795183i
$359$	7.95503	−	24.4831i	0.419850	−	1.29217i	−0.487989	−	0.872850i	$-0.662269\pi$
$359$	7.95503	−	24.4831i	0.419850	−	1.29217i	0.907840	−	0.419317i	$-0.137731\pi$
$360$	2.34696	+	7.22320i	0.123696	+	0.380696i
$361$	8.72196	−	6.33687i	0.459050	−	0.333520i
$362$	−2.24943			−0.118228
$363$	−32.2555	+	15.5424i	−1.69298	+	0.815766i
$364$	3.57888			0.187584
$365$	−1.34896	+	0.980075i	−0.0706077	+	0.0512995i
$366$	−11.9679	−	36.8334i	−0.625571	−	1.92531i
$367$	−5.82638	+	17.9317i	−0.304134	+	0.936030i	0.675864	+	0.737026i	$0.263771\pi$
$367$	−5.82638	+	17.9317i	−0.304134	+	0.936030i	−0.979999	+	0.199003i	$0.936229\pi$
$368$	7.28272	+	5.29120i	0.379638	+	0.275823i
$369$	−23.6094	−	17.1532i	−1.22906	−	0.892961i
$370$	−3.36628	+	10.3604i	−0.175005	+	0.538609i
$371$	−1.73716	−	5.34643i	−0.0901889	−	0.277573i
$372$	1.24619	−	0.905407i	0.0646117	−	0.0469432i
$373$	8.46477			0.438289			0.219145	−	0.975692i	$-0.429673\pi$
$373$	8.46477			0.438289			0.219145	+	0.975692i	$0.429673\pi$
$374$	7.53377	+	6.58056i	0.389562	+	0.340273i
$375$	3.25498			0.168087
$376$	7.77755	−	5.65072i	0.401097	−	0.291414i
$377$	1.73034	+	5.32545i	0.0891173	+	0.274275i
$378$	4.62178	−	14.2244i	0.237719	−	0.731623i
$379$	−13.1386	−	9.54579i	−0.674887	−	0.490334i	0.196771	−	0.980450i	$-0.436955\pi$
$379$	−13.1386	−	9.54579i	−0.674887	−	0.490334i	−0.871657	+	0.490116i	$0.836955\pi$
$380$	−2.31936	−	1.68512i	−0.118981	−	0.0864446i
$381$	0.278154	−	0.856071i	0.0142503	−	0.0438578i
$382$	8.05663	+	24.7957i	0.412213	+	1.26866i
$383$	−27.7802	+	20.1835i	−1.41950	+	1.03133i	−0.427650	+	0.903944i	$0.640658\pi$
$383$	−27.7802	+	20.1835i	−1.41950	+	1.03133i	−0.991853	+	0.127385i	$0.959342\pi$
$384$	3.25498			0.166105
$385$	−3.30331	−	0.296926i	−0.168352	−	0.0151328i
$386$	−23.7468			−1.20868
$387$	−13.8370	+	10.0531i	−0.703372	+	0.511030i
$388$	−0.326205	−	1.00395i	−0.0165605	−	0.0509681i
$389$	−0.551571	+	1.69756i	−0.0279658	+	0.0860698i	−0.964065	−	0.265666i	$-0.914408\pi$
$389$	−0.551571	+	1.69756i	−0.0279658	+	0.0860698i	0.936099	+	0.351735i	$0.114408\pi$
$390$	−9.42440	−	6.84723i	−0.477223	−	0.346723i
$391$	21.9650	+	15.9585i	1.11082	+	0.807055i
$392$	0.309017	−	0.951057i	0.0156077	−	0.0480356i
$393$	−16.9694	−	52.2264i	−0.855992	−	2.63447i
$394$	−6.76915	+	4.91807i	−0.341025	+	0.247769i
$395$	−14.5396			−0.731565
$396$	−9.89749	+	23.1636i	−0.497367	+	1.16401i
$397$	1.25072			0.0627718			0.0313859	−	0.999507i	$-0.490008\pi$
$397$	1.25072			0.0627718			0.0313859	+	0.999507i	$0.490008\pi$
$398$	−5.52612	+	4.01496i	−0.276999	+	0.201252i
$399$	2.88365	+	8.87496i	0.144363	+	0.444304i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	15.7174	+	11.4193i	0.784889	+	0.570255i	0.906442	−	0.422330i	$-0.138788\pi$
$401$	15.7174	+	11.4193i	0.784889	+	0.570255i	−0.121554	+	0.992585i	$0.538788\pi$
$402$	−1.98264	−	1.44047i	−0.0988850	−	0.0718442i
$403$	−0.523367	+	1.61076i	−0.0260707	+	0.0802375i
$404$	1.74149	+	5.35976i	0.0866424	+	0.266658i
$405$	−20.9520	+	15.2225i	−1.04111	+	0.756413i
$406$	1.56460			0.0776497
$407$	−31.0134	+	18.5344i	−1.53728	+	0.918717i
$408$	9.81716			0.486022
$409$	5.48134	−	3.98243i	0.271035	−	0.196918i	−0.443963	−	0.896045i	$-0.646428\pi$
$409$	5.48134	−	3.98243i	0.271035	−	0.196918i	0.714998	+	0.699127i	$0.246428\pi$
$410$	1.18737	+	3.65435i	0.0586400	+	0.180475i
$411$	13.5675	−	41.7564i	0.669234	−	2.05969i
$412$	6.21550	+	4.51583i	0.306216	+	0.222479i
$413$	2.21385	+	1.60846i	0.108937	+	0.0791470i
$414$	−21.1272	+	65.0228i	−1.03834	+	3.19569i
$415$	−1.64266	−	5.05559i	−0.0806350	−	0.248169i
$416$	−2.89538	+	2.10361i	−0.141958	+	0.103138i
$417$	−4.80379			−0.235243
$418$	−2.11687	−	9.26977i	−0.103539	−	0.453399i
$419$	26.3741			1.28846			0.644228	−	0.764833i	$-0.277179\pi$
$419$	26.3741			1.28846			0.644228	+	0.764833i	$0.277179\pi$
$420$	−2.63334	+	1.91323i	−0.128494	+	0.0933561i
$421$	5.92724	+	18.2422i	0.288876	+	0.889069i	0.985210	+	0.171351i	$0.0548132\pi$
$421$	5.92724	+	18.2422i	0.288876	+	0.889069i	−0.696334	+	0.717718i	$0.745187\pi$
$422$	0.878363	−	2.70332i	0.0427580	−	0.131596i
$423$	59.0699	+	42.9168i	2.87208	+	2.08669i
$424$	4.54794	+	3.30427i	0.220868	+	0.160470i
$425$	0.932008	−	2.86842i	0.0452090	−	0.139139i
$426$	−1.91514	−	5.89421i	−0.0927890	−	0.285575i
$427$	9.62595	−	6.99366i	0.465832	−	0.338447i
$428$	17.5406			0.847856
$429$	−8.60159	−	37.6664i	−0.415289	−	1.81855i
$430$	2.25195			0.108599
$431$	−22.2339	+	16.1538i	−1.07097	+	0.778103i	−0.976086	−	0.217385i	$-0.930247\pi$
$431$	−22.2339	+	16.1538i	−1.07097	+	0.778103i	−0.0948813	+	0.995489i	$0.530247\pi$
$432$	4.62178	+	14.2244i	0.222366	+	0.684371i
$433$	2.14129	−	6.59020i	0.102904	−	0.316705i	−0.886329	−	0.463056i	$-0.846753\pi$
$433$	2.14129	−	6.59020i	0.102904	−	0.316705i	0.989233	+	0.146351i	$0.0467529\pi$
$434$	0.382855	+	0.278160i	0.0183776	+	0.0133521i
$435$	−4.12012	−	2.99344i	−0.197544	−	0.143524i
$436$	3.17183	−	9.76189i	0.151903	−	0.467510i
$437$	−7.97497	−	24.5444i	−0.381495	−	1.17412i
$438$	−4.39084	+	3.19013i	−0.209802	+	0.152430i
$439$	−9.07635			−0.433191			−0.216595	−	0.976261i	$-0.569495\pi$
$439$	−9.07635			−0.433191			−0.216595	+	0.976261i	$0.569495\pi$
$440$	2.84696	−	1.70142i	0.135723	−	0.0811119i
$441$	7.59492			0.361663
$442$	−8.73257	+	6.34459i	−0.415366	+	0.301781i
$443$	−7.29251	−	22.4440i	−0.346478	−	1.06635i	−0.960788	−	0.277284i	$-0.910566\pi$
$443$	−7.29251	−	22.4440i	−0.346478	−	1.06635i	0.614311	−	0.789064i	$-0.289434\pi$
$444$	−10.9572	+	33.7228i	−0.520006	+	1.60041i
$445$	9.03079	+	6.56126i	0.428101	+	0.311033i
$446$	−16.1904	−	11.7630i	−0.766636	−	0.556993i
$447$	−16.5419	+	50.9106i	−0.782404	+	2.40799i
$448$	0.309017	+	0.951057i	0.0145997	+	0.0449332i
$449$	24.2871	−	17.6456i	1.14618	−	0.832747i	0.158210	−	0.987405i	$-0.449428\pi$
$449$	24.2871	−	17.6456i	1.14618	−	0.832747i	0.987968	+	0.154658i	$0.0494276\pi$
$450$	7.59492			0.358028
$451$	−5.00732	+	11.7189i	−0.235786	+	0.551820i
$452$	10.7388			0.505113
$453$	−20.7374	+	15.0666i	−0.974328	+	0.707891i
$454$	−3.81124	−	11.7298i	−0.178871	−	0.550507i
$455$	1.10594	−	3.40372i	0.0518470	−	0.159569i
$456$	−7.54949	−	5.48503i	−0.353537	−	0.256860i
$457$	1.69973	+	1.23493i	0.0795101	+	0.0577674i	0.626830	−	0.779156i	$-0.284352\pi$
$457$	1.69973	+	1.23493i	0.0795101	+	0.0577674i	−0.547320	+	0.836923i	$0.684352\pi$
$458$	1.71293	−	5.27185i	0.0800398	−	0.246337i
$459$	13.9395	+	42.9013i	0.650639	+	2.00246i
$460$	7.28272	−	5.29120i	0.339558	−	0.246704i
$461$	33.6599			1.56770			0.783848	−	0.620953i	$-0.213254\pi$
$461$	33.6599			1.56770			0.783848	+	0.620953i	$0.213254\pi$
$462$	−10.7522	−	0.966490i	−0.500238	−	0.0449652i
$463$	31.2506			1.45234			0.726168	−	0.687517i	$-0.241299\pi$
$463$	31.2506			1.45234			0.726168	+	0.687517i	$0.241299\pi$
$464$	−1.26579	+	0.919648i	−0.0587627	+	0.0426936i
$465$	−0.476001	−	1.46498i	−0.0220740	−	0.0679368i
$466$	4.00550	−	12.3277i	0.185551	−	0.571068i
$467$	−21.7836	−	15.8267i	−1.00803	−	0.732373i	−0.0442314	−	0.999021i	$-0.514084\pi$
$467$	−21.7836	−	15.8267i	−1.00803	−	0.732373i	−0.963794	+	0.266648i	$0.914084\pi$
$468$	−21.9902	−	15.9768i	−1.01650	−	0.738527i
$469$	0.232659	−	0.716050i	0.0107432	−	0.0330641i
$470$	−2.97076	−	9.14306i	−0.137031	−	0.421738i
$471$	31.0349	−	22.5482i	1.43001	−	1.03896i
$472$	−2.73647			−0.125956
$473$	5.62516	+	4.91343i	0.258645	+	0.225920i
$474$	−47.3261			−2.17376
$475$	−2.31936	+	1.68512i	−0.106420	+	0.0773184i
$476$	0.932008	+	2.86842i	0.0427185	+	0.131474i
$477$	−13.1936	+	40.6057i	−0.604093	+	1.85921i
$478$	17.2409	+	12.5262i	0.788580	+	0.572937i
$479$	−28.9917	−	21.0637i	−1.32467	−	0.962426i	−0.999861	−	0.0166441i	$-0.994702\pi$
$479$	−28.9917	−	21.0637i	−1.32467	−	0.962426i	−0.324804	−	0.945781i	$-0.605298\pi$
$480$	1.00585	−	3.09567i	0.0459104	−	0.141298i
$481$	−12.0475	−	37.0785i	−0.549320	−	1.69063i
$482$	−6.20642	+	4.50923i	−0.282695	+	0.205390i
$483$	−29.3011			−1.33325
$484$	10.8237	+	1.96168i	0.491985	+	0.0891671i
$485$	−1.05562			−0.0479332
$486$	−31.8984	+	23.1756i	−1.44694	+	1.05127i
$487$	−3.18378	−	9.79866i	−0.144271	−	0.444020i	0.852646	−	0.522489i	$-0.174997\pi$
$487$	−3.18378	−	9.79866i	−0.144271	−	0.444020i	−0.996916	+	0.0784698i	$0.974997\pi$
$488$	−3.67679	+	11.3160i	−0.166440	+	0.512251i
$489$	21.6179	+	15.7063i	0.977593	+	0.710263i
$490$	−0.809017	−	0.587785i	−0.0365477	−	0.0265534i
$491$	6.20903	−	19.1094i	0.280210	−	0.862397i	−0.707584	−	0.706629i	$-0.750215\pi$
$491$	6.20903	−	19.1094i	0.280210	−	0.862397i	0.987794	−	0.155768i	$-0.0497851\pi$
$492$	3.86487	+	11.8949i	0.174242	+	0.536261i
$493$	−3.81766	+	2.77369i	−0.171939	+	0.124921i
$494$	10.2603			0.461631
$495$	18.9714	+	16.5710i	0.852700	+	0.744811i
$496$	−0.473234			−0.0212489
$497$	1.54038	−	1.11915i	0.0690955	−	0.0502008i
$498$	−5.34683	−	16.4559i	−0.239597	−	0.737405i
$499$	8.08581	−	24.8856i	0.361970	−	1.11403i	−0.589886	−	0.807486i	$-0.700827\pi$
$499$	8.08581	−	24.8856i	0.361970	−	1.11403i	0.951857	−	0.306544i	$-0.0991726\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	−53.1932	−	38.6471i	−2.37650	−	1.72663i
$502$	8.37999	−	25.7910i	0.374017	−	1.15111i
$503$	−0.550400	−	1.69396i	−0.0245411	−	0.0755298i	0.938036	−	0.346538i	$-0.112643\pi$
$503$	−0.550400	−	1.69396i	−0.0245411	−	0.0755298i	−0.962577	+	0.271008i	$0.912643\pi$
$504$	−6.14442	+	4.46418i	−0.273694	+	0.198851i
$505$	5.63558			0.250780
$506$	29.7361	+	2.67291i	1.32193	+	0.118825i
$507$	−0.623670			−0.0276981
$508$	−0.223724	+	0.162545i	−0.00992614	+	0.00721176i
$509$	−2.46231	−	7.57822i	−0.109140	−	0.335899i	0.881540	−	0.472110i	$-0.156507\pi$
$509$	−2.46231	−	7.57822i	−0.109140	−	0.335899i	−0.990680	+	0.136211i	$0.956507\pi$
$510$	3.03367	−	9.33668i	0.134333	−	0.413435i
$511$	−1.34896	−	0.980075i	−0.0596744	−	0.0433560i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	13.2501	−	40.7798i	0.585008	−	1.80047i
$514$	2.08190	+	6.40742i	0.0918285	+	0.282619i
$515$	6.21550	−	4.51583i	0.273888	−	0.198991i
$516$	7.33008			0.322689
$517$	12.5282	−	29.3202i	0.550987	−	1.28950i
$518$	−10.8935			−0.478634
$519$	65.1160	−	47.3096i	2.85828	−	2.07666i
$520$	1.10594	+	3.40372i	0.0484985	+	0.149263i
$521$	−11.7814	+	36.2594i	−0.516153	+	1.58855i	0.265023	+	0.964242i	$0.414621\pi$
$521$	−11.7814	+	36.2594i	−0.516153	+	1.58855i	−0.781175	+	0.624312i	$0.785379\pi$
$522$	−9.61355	−	6.98465i	−0.420774	−	0.305710i
$523$	6.29448	+	4.57321i	0.275238	+	0.199972i	0.716838	−	0.697240i	$-0.245589\pi$
$523$	6.29448	+	4.57321i	0.275238	+	0.199972i	−0.441600	+	0.897212i	$0.645589\pi$
$524$	−5.21335	+	16.0450i	−0.227746	+	0.700931i
$525$	1.00585	+	3.09567i	0.0438987	+	0.135106i
$526$	−26.0327	+	18.9138i	−1.13508	+	0.824682i
$527$	−1.42729			−0.0621739
$528$	9.26681	−	5.53808i	0.403286	−	0.241014i
$529$	58.0348			2.52325
$530$	4.54794	−	3.30427i	0.197550	−	0.143529i
$531$	−6.42239	−	19.7661i	−0.278708	−	0.857775i
$532$	0.885918	−	2.72658i	0.0384094	−	0.118212i
$533$	−11.1252	−	8.08295i	−0.481887	−	0.350111i
$534$	29.3951	+	21.3568i	1.27205	+	0.924199i
$535$	5.42034	−	16.6821i	0.234342	−	0.721229i
$536$	0.232659	+	0.716050i	0.0100493	+	0.0309286i
$537$	−67.4056	+	48.9731i	−2.90877	+	2.11334i
$538$	−30.0523			−1.29565
$539$	−0.738384	−	3.23339i	−0.0318045	−	0.139272i
$540$	14.9564			0.643621
$541$	7.82435	−	5.68472i	0.336395	−	0.244405i	−0.406744	−	0.913542i	$-0.633336\pi$
$541$	7.82435	−	5.68472i	0.336395	−	0.244405i	0.743139	+	0.669137i	$0.233336\pi$
$542$	−2.75899	−	8.49130i	−0.118509	−	0.364733i
$543$	−2.26258	+	6.96351i	−0.0970967	+	0.298833i
$544$	−2.44003	−	1.77278i	−0.104615	−	0.0760075i
$545$	−8.30396	−	6.03318i	−0.355702	−	0.258433i
$546$	3.59980	−	11.0791i	0.154057	−	0.474140i
$547$	−11.9457	−	36.7652i	−0.510763	−	1.57197i	−0.790861	−	0.611996i	$-0.790367\pi$
$547$	−11.9457	−	36.7652i	−0.510763	−	1.57197i	0.280098	−	0.959972i	$-0.409633\pi$
$548$	−10.9125	+	7.92841i	−0.466160	+	0.338685i
$549$	−90.3669			−3.85677
$550$	−0.738384	−	3.23339i	−0.0314848	−	0.137872i
$551$	4.48553			0.191090
$552$	23.7051	−	17.2228i	1.00896	−	0.733050i
$553$	−4.49298	−	13.8280i	−0.191061	−	0.588024i
$554$	0.519367	−	1.59845i	0.0220658	−	0.0679115i
$555$	28.6863	+	20.8418i	1.21767	+	0.884687i
$556$	1.19397	+	0.867469i	0.0506356	+	0.0367889i
$557$	0.398464	−	1.22635i	0.0168835	−	0.0519619i	−0.942260	−	0.334883i	$-0.891303\pi$
$557$	0.398464	−	1.22635i	0.0168835	−	0.0519619i	0.959143	+	0.282921i	$0.0913033\pi$
$558$	−1.11066	−	3.41827i	−0.0470181	−	0.144707i
$559$	−6.52025	+	4.73724i	−0.275777	+	0.200364i
$560$	1.00000			0.0422577
$561$	27.9491	−	16.7031i	1.18001	−	0.705205i
$562$	7.90100			0.333284
$563$	18.5105	−	13.4487i	0.780126	−	0.566795i	−0.124891	−	0.992170i	$-0.539858\pi$
$563$	18.5105	−	13.4487i	0.780126	−	0.566795i	0.905017	+	0.425376i	$0.139858\pi$
$564$	−9.66978	−	29.7605i	−0.407171	−	1.25314i
$565$	3.31848	−	10.2132i	0.139610	−	0.429674i
$566$	−21.8789	−	15.8960i	−0.919641	−	0.668158i
$567$	−20.9520	−	15.2225i	−0.879901	−	0.639285i
$568$	−0.588373	+	1.81082i	−0.0246876	+	0.0759805i
$569$	−1.02122	−	3.14298i	−0.0428116	−	0.131761i	0.927366	−	0.374155i	$-0.122067\pi$
$569$	−1.02122	−	3.14298i	−0.0428116	−	0.131761i	−0.970178	+	0.242394i	$0.922067\pi$
$570$	−7.54949	+	5.48503i	−0.316213	+	0.229743i
$571$	−1.86937			−0.0782307			−0.0391153	−	0.999235i	$-0.512454\pi$
$571$	−1.86937			−0.0782307			−0.0391153	+	0.999235i	$0.512454\pi$
$572$	−4.66390	+	10.9151i	−0.195007	+	0.456385i
$573$	84.8633			3.54521
$574$	−3.10858	+	2.25851i	−0.129749	+	0.0942685i
$575$	−2.78175	−	8.56135i	−0.116007	−	0.357033i
$576$	2.34696	−	7.22320i	0.0977900	−	0.300967i
$577$	12.4137	+	9.01909i	0.516790	+	0.375470i	0.815393	−	0.578908i	$-0.196521\pi$
$577$	12.4137	+	9.01909i	0.516790	+	0.375470i	−0.298603	+	0.954377i	$0.596521\pi$
$578$	6.39407	+	4.64556i	0.265958	+	0.193230i
$579$	−23.8857	+	73.5125i	−0.992654	+	3.05508i
$580$	0.483487	+	1.48802i	0.0200757	+	0.0617867i
$581$	4.30054	−	3.12453i	0.178417	−	0.129627i
$582$	−3.43603			−0.142428
$583$	18.5698	+	1.66919i	0.769081	+	0.0691308i
$584$	1.66740			0.0689976
$585$	−21.9902	+	15.9768i	−0.909181	+	0.660559i
$586$	3.15220	+	9.70148i	0.130216	+	0.400765i
$587$	2.85687	−	8.79254i	0.117916	−	0.362907i	−0.874628	−	0.484794i	$-0.838895\pi$
$587$	2.85687	−	8.79254i	0.117916	−	0.362907i	0.992544	+	0.121887i	$0.0388945\pi$
$588$	−2.63334	−	1.91323i	−0.108597	−	0.0789003i
$589$	1.09760	+	0.797455i	0.0452259	+	0.0328586i
$590$	−0.845616	+	2.60254i	−0.0348135	+	0.107145i
$591$	8.41604	+	25.9019i	0.346189	+	1.06546i
$592$	8.81305	−	6.40305i	0.362214	−	0.263164i
$593$	15.5998			0.640606			0.320303	−	0.947315i	$-0.396215\pi$
$593$	15.5998			0.640606			0.320303	+	0.947315i	$0.396215\pi$
$594$	37.3596	+	32.6327i	1.53288	+	1.33893i
$595$	3.01604			0.123646
$596$	13.3049	−	9.66656i	0.544989	−	0.395958i
$597$	6.87059	+	21.1455i	0.281195	+	0.865428i
$598$	−9.95555	+	30.6400i	−0.407113	+	1.25296i
$599$	18.8259	+	13.6778i	0.769206	+	0.558861i	0.901720	−	0.432320i	$-0.142305\pi$
$599$	18.8259	+	13.6778i	0.769206	+	0.558861i	−0.132514	+	0.991181i	$0.542305\pi$
$600$	−2.63334	−	1.91323i	−0.107506	−	0.0781074i
$601$	2.54357	−	7.82830i	0.103754	−	0.319323i	−0.885682	−	0.464293i	$-0.846309\pi$
$601$	2.54357	−	7.82830i	0.103754	−	0.319323i	0.989436	+	0.144970i	$0.0463085\pi$
$602$	0.695892	+	2.14174i	0.0283624	+	0.0872906i
$603$	−4.62613	+	3.36108i	−0.188391	+	0.136874i
$604$	7.87495			0.320427
$605$	5.21036	−	9.68773i	0.211831	−	0.393862i
$606$	18.3437			0.745163
$607$	30.0437	−	21.8280i	1.21943	−	0.885971i	0.223381	−	0.974731i	$-0.428291\pi$
$607$	30.0437	−	21.8280i	1.21943	−	0.885971i	0.996053	+	0.0887604i	$0.0282905\pi$
$608$	0.885918	+	2.72658i	0.0359287	+	0.110577i
$609$	1.57374	−	4.84349i	0.0637713	−	0.196268i
$610$	9.62595	+	6.99366i	0.389743	+	0.283165i
$611$	27.8349	+	20.2233i	1.12608	+	0.818146i
$612$	7.07853	−	21.7855i	0.286132	−	0.880625i
$613$	−5.43589	−	16.7299i	−0.219553	−	0.675716i	−0.998799	−	0.0489972i	$-0.984397\pi$
$613$	−5.43589	−	16.7299i	−0.219553	−	0.675716i	0.779245	−	0.626719i	$-0.215603\pi$
$614$	−12.4227	+	9.02559i	−0.501338	+	0.364243i
$615$	12.5070			0.504330
$616$	2.49790	+	2.18185i	0.100643	+	0.0879094i
$617$	5.16685			0.208010			0.104005	−	0.994577i	$-0.466834\pi$
$617$	5.16685			0.208010			0.104005	+	0.994577i	$0.466834\pi$
$618$	20.2314	−	14.6989i	0.813825	−	0.591278i
$619$	−5.40352	−	16.6303i	−0.217186	−	0.668429i	−0.998991	−	0.0449066i	$-0.985701\pi$
$619$	−5.40352	−	16.6303i	−0.217186	−	0.668429i	0.781805	−	0.623522i	$-0.214299\pi$
$620$	−0.146237	+	0.450073i	−0.00587304	+	0.0180754i
$621$	108.923	+	79.1373i	4.37094	+	3.17567i
$622$	21.3241	+	15.4928i	0.855017	+	0.621206i
$623$	−3.44946	+	10.6163i	−0.138200	+	0.425335i
$624$	3.59980	+	11.0791i	0.144107	+	0.443517i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	8.60472			0.343914
$627$	−30.8254	−	2.77082i	−1.23105	−	0.110656i
$628$	−11.7854			−0.470288
$629$	26.5805	−	19.3119i	1.05983	−	0.770015i
$630$	2.34696	+	7.22320i	0.0935051	+	0.287779i
$631$	−5.75587	+	17.7147i	−0.229138	+	0.705213i	0.768708	+	0.639600i	$0.220900\pi$
$631$	−5.75587	+	17.7147i	−0.229138	+	0.705213i	−0.997845	+	0.0656126i	$0.979100\pi$
$632$	11.7628	+	8.54615i	0.467898	+	0.339947i
$633$	−7.48511	−	5.43825i	−0.297506	−	0.216151i
$634$	0.889160	−	2.73655i	0.0353130	−	0.108682i
$635$	0.0854549	+	0.263003i	0.00339117	+	0.0104370i
$636$	14.8035	−	10.7554i	0.586996	−	0.426478i
$637$	3.57888			0.141800
$638$	−2.03894	+	4.77183i	−0.0807224	+	0.188919i
$639$	−14.4608			−0.572062
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	−4.45657	−	13.7159i	−0.176024	−	0.541746i	0.823655	−	0.567091i	$-0.191931\pi$
$641$	−4.45657	−	13.7159i	−0.176024	−	0.541746i	−0.999679	+	0.0253455i	$0.991931\pi$
$642$	17.6431	−	54.2999i	0.696318	−	2.14305i
$643$	−18.6342	−	13.5385i	−0.734861	−	0.533908i	0.156236	−	0.987720i	$-0.450064\pi$
$643$	−18.6342	−	13.5385i	−0.734861	−	0.533908i	−0.891098	+	0.453812i	$0.850064\pi$
$644$	7.28272	+	5.29120i	0.286979	+	0.208503i
$645$	2.26512	−	6.97132i	0.0891889	−	0.274495i
$646$	2.67196	+	8.22346i	0.105127	+	0.323548i
$647$	−10.4297	+	7.57763i	−0.410034	+	0.297907i	−0.773616	−	0.633655i	$-0.781554\pi$
$647$	−10.4297	+	7.57763i	−0.410034	+	0.297907i	0.363581	+	0.931562i	$0.381554\pi$
$648$	25.8981			1.01737
$649$	−7.79062	+	4.65588i	−0.305809	+	0.182759i
$650$	3.57888			0.140375
$651$	1.24619	−	0.905407i	0.0488419	−	0.0354857i
$652$	−2.53681	−	7.80751i	−0.0993493	−	0.305766i
$653$	−7.36088	+	22.6545i	−0.288054	+	0.886538i	0.697413	+	0.716669i	$0.254334\pi$
$653$	−7.36088	+	22.6545i	−0.288054	+	0.886538i	−0.985467	+	0.169869i	$0.945666\pi$
$654$	−27.0293	−	19.6379i	−1.05693	−	0.767903i
$655$	13.6487	+	9.91638i	0.533300	+	0.387465i
$656$	1.18737	−	3.65435i	0.0463590	−	0.142678i
$657$	3.91333	+	12.0440i	0.152673	+	0.469881i
$658$	7.77755	−	5.65072i	0.303201	−	0.220288i
$659$	19.4714			0.758498			0.379249	−	0.925295i	$-0.376182\pi$
$659$	19.4714			0.758498			0.379249	+	0.925295i	$0.376182\pi$
$660$	−2.40343	−	10.5246i	−0.0935533	−	0.409670i
$661$	−28.6251			−1.11339			−0.556694	−	0.830718i	$-0.687930\pi$
$661$	−28.6251			−1.11339			−0.556694	+	0.830718i	$0.687930\pi$
$662$	15.7679	−	11.4560i	0.612835	−	0.445251i
$663$	10.8571	+	33.4149i	0.421657	+	1.29773i
$664$	−1.64266	+	5.05559i	−0.0637476	+	0.196195i
$665$	−2.31936	−	1.68512i	−0.0899411	−	0.0653460i
$666$	66.9344	+	48.6307i	2.59366	+	1.88440i
$667$	−4.35232	+	13.3951i	−0.168523	+	0.518659i
$668$	6.24212	+	19.2113i	0.241515	+	0.743306i
$669$	−52.6994	+	38.2883i	−2.03748	+	1.48031i
$670$	0.752899			0.0290870
$671$	8.78554	+	38.4719i	0.339162	+	1.48519i
$672$	3.25498			0.125564
$673$	4.66232	−	3.38737i	0.179719	−	0.130574i	−0.494289	−	0.869298i	$-0.664571\pi$
$673$	4.66232	−	3.38737i	0.179719	−	0.130574i	0.674008	+	0.738724i	$0.264571\pi$
$674$	−8.69469	−	26.7595i	−0.334907	−	1.03074i
$675$	4.62178	−	14.2244i	0.177892	−	0.547497i
$676$	0.155011	+	0.112622i	0.00596197	+	0.00433163i
$677$	−16.3342	−	11.8675i	−0.627776	−	0.456106i	0.227853	−	0.973695i	$-0.426829\pi$
$677$	−16.3342	−	11.8675i	−0.627776	−	0.456106i	−0.855629	+	0.517590i	$0.826829\pi$
$678$	10.8016	−	33.2440i	0.414834	−	1.27673i
$679$	−0.326205	−	1.00395i	−0.0125186	−	0.0385282i
$680$	−2.44003	+	1.77278i	−0.0935708	+	0.0679832i
$681$	−40.1452			−1.53837
$682$	−1.34728	+	0.805169i	−0.0515900	+	0.0308315i
$683$	−19.0998			−0.730833			−0.365417	−	0.930844i	$-0.619073\pi$
$683$	−19.0998			−0.730833			−0.365417	+	0.930844i	$0.619073\pi$
$684$	−17.6154	+	12.7983i	−0.673541	+	0.489356i
$685$	4.16821	+	12.8284i	0.159259	+	0.490149i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	−14.5970	−	10.6053i	−0.556910	−	0.404619i
$688$	−1.82187	−	1.32367i	−0.0694581	−	0.0504643i
$689$	−6.21709	+	19.1342i	−0.236852	+	0.728956i
$690$	−9.05455	−	27.8670i	−0.344701	−	1.06088i
$691$	1.43601	−	1.04333i	0.0546285	−	0.0396900i	−0.560136	−	0.828401i	$-0.689251\pi$
$691$	1.43601	−	1.04333i	0.0546285	−	0.0396900i	0.614764	+	0.788711i	$0.289251\pi$
$692$	−24.7276			−0.940001
$693$	−9.89749	+	23.1636i	−0.375974	+	0.879911i
$694$	−0.231696			−0.00879505
$695$	1.19397	−	0.867469i	0.0452898	−	0.0329050i
$696$	1.57374	+	4.84349i	0.0596526	+	0.183592i
$697$	3.58116	−	11.0217i	0.135646	−	0.417475i
$698$	19.1802	+	13.9353i	0.725983	+	0.527457i
$699$	−34.1335	−	24.7994i	−1.29105	−	0.938001i
$700$	0.309017	−	0.951057i	0.0116797	−	0.0359466i
$701$	2.62859	+	8.08997i	0.0992806	+	0.305554i	0.988346	−	0.152227i	$-0.0486444\pi$
$701$	2.62859	+	8.08997i	0.0992806	+	0.305554i	−0.889065	+	0.457781i	$0.848644\pi$
$702$	−43.3044	+	31.4625i	−1.63442	+	1.18748i
$703$	−31.2305			−1.17788
$704$	−3.30331	−	0.296926i	−0.124498	−	0.0111908i
$705$	−31.2921			−1.17853
$706$	−16.3327	+	11.8664i	−0.614690	+	0.446599i
$707$	1.74149	+	5.35976i	0.0654955	+	0.201574i
$708$	−2.75247	+	8.47122i	−0.103444	+	0.318368i
$709$	−17.8817	−	12.9918i	−0.671562	−	0.487918i	0.198986	−	0.980002i	$-0.436235\pi$
$709$	−17.8817	−	12.9918i	−0.671562	−	0.487918i	−0.870548	+	0.492084i	$0.836235\pi$
$710$	1.54038	+	1.11915i	0.0578094	+	0.0420010i
$711$	−34.1238	+	105.022i	−1.27974	+	3.93864i
$712$	−3.44946	−	10.6163i	−0.129274	−	0.397864i
$713$	−3.44643	+	2.50398i	−0.129070	+	0.0937748i
$714$	9.81716			0.367398
$715$	8.93970	+	7.80860i	0.334326	+	0.292025i
$716$	25.5970			0.956606
$717$	56.1188	−	40.7727i	2.09580	−	1.52268i
$718$	7.95503	+	24.4831i	0.296879	+	0.913700i
$719$	6.22460	−	19.1574i	0.232139	−	0.714449i	−0.765350	−	0.643615i	$-0.777434\pi$
$719$	6.22460	−	19.1574i	0.232139	−	0.714449i	0.997488	−	0.0708341i	$-0.0225661\pi$
$720$	−6.14442	−	4.46418i	−0.228989	−	0.166370i
$721$	6.21550	+	4.51583i	0.231477	+	0.168178i
$722$	−3.33149	+	10.2533i	−0.123985	+	0.381587i
$723$	7.71640	+	23.7486i	0.286976	+	0.883222i
$724$	1.81983	−	1.32218i	0.0676334	−	0.0491386i
$725$	1.56460			0.0581077
$726$	16.9597	−	31.5334i	0.629432	−	1.17031i
$727$	−41.7541			−1.54857			−0.774287	−	0.632835i	$-0.781891\pi$
$727$	−41.7541			−1.54857			−0.774287	+	0.632835i	$0.781891\pi$
$728$	−2.89538	+	2.10361i	−0.107310	+	0.0779651i
$729$	15.6503	+	48.1666i	0.579640	+	1.78395i
$730$	0.515256	−	1.58579i	0.0190705	−	0.0586929i
$731$	−5.49483	−	3.99223i	−0.203234	−	0.147658i
$732$	31.3323	+	22.7643i	1.15808	+	0.841391i
$733$	14.8512	−	45.7074i	0.548542	−	1.68824i	−0.163873	−	0.986481i	$-0.552399\pi$
$733$	14.8512	−	45.7074i	0.548542	−	1.68824i	0.712415	−	0.701758i	$-0.247601\pi$
$734$	−5.82638	−	17.9317i	−0.215056	−	0.661873i
$735$	−2.63334	+	1.91323i	−0.0971321	+	0.0705706i
$736$	−9.00193			−0.331816
$737$	1.88067	+	1.64272i	0.0692753	+	0.0605102i
$738$	29.1828			1.07423
$739$	−32.3355	+	23.4931i	−1.18948	+	0.864208i	−0.993209	−	0.116341i	$-0.962883\pi$
$739$	−32.3355	+	23.4931i	−1.18948	+	0.864208i	−0.196272	+	0.980550i	$0.562883\pi$
$740$	−3.36628	−	10.3604i	−0.123747	−	0.380854i
$741$	10.3202	−	31.7624i	0.379124	−	1.16682i
$742$	4.54794	+	3.30427i	0.166960	+	0.121304i
$743$	−14.1077	−	10.2499i	−0.517562	−	0.376031i	0.298123	−	0.954528i	$-0.403640\pi$
$743$	−14.1077	−	10.2499i	−0.517562	−	0.376031i	−0.815685	+	0.578497i	$0.803640\pi$
$744$	−0.476001	+	1.46498i	−0.0174510	+	0.0537088i
$745$	−5.08201	−	15.6408i	−0.186191	−	0.573036i
$746$	−6.84815	+	4.97547i	−0.250728	+	0.182165i
$747$	−40.3728			−1.47716
$748$	−9.96291	−	0.895542i	−0.364280	−	0.0327442i
$749$	17.5406			0.640919
$750$	−2.63334	+	1.91323i	−0.0961559	+	0.0698613i
$751$	8.78605	+	27.0407i	0.320608	+	0.986729i	0.973384	+	0.229179i	$0.0736040\pi$
$751$	8.78605	+	27.0407i	0.320608	+	0.986729i	−0.652777	+	0.757550i	$0.726396\pi$
$752$	−2.97076	+	9.14306i	−0.108333	+	0.333413i
$753$	−71.4114	−	51.8834i	−2.60238	−	1.89074i
$754$	−4.53010	−	3.29131i	−0.164977	−	0.119862i
$755$	2.43349	−	7.48952i	0.0885639	−	0.272572i
$756$	4.62178	+	14.2244i	0.168093	+	0.517336i
$757$	−16.1477	+	11.7320i	−0.586897	+	0.426406i	−0.841204	−	0.540718i	$-0.818153\pi$
$757$	−16.1477	+	11.7320i	−0.586897	+	0.426406i	0.254307	+	0.967124i	$0.418153\pi$
$758$	16.2403			0.589873
$759$	38.1844	−	89.3649i	1.38601	−	3.24374i
$760$	2.86689			0.103993
$761$	−17.7783	+	12.9167i	−0.644463	+	0.468230i	−0.861381	−	0.507960i	$-0.830400\pi$
$761$	−17.7783	+	12.9167i	−0.644463	+	0.468230i	0.216917	+	0.976190i	$0.430400\pi$
$762$	0.278154	+	0.856071i	0.0100765	+	0.0310122i
$763$	3.17183	−	9.76189i	0.114828	−	0.353404i
$764$	−21.0925	−	15.3246i	−0.763101	−	0.554425i
$765$	−18.5318	−	13.4642i	−0.670019	−	0.486798i
$766$	10.6111	−	32.6576i	0.383395	−	1.17997i
$767$	−3.02636	−	9.31418i	−0.109276	−	0.336315i
$768$	−2.63334	+	1.91323i	−0.0950224	+	0.0690378i
$769$	23.8878			0.861417			0.430708	−	0.902491i	$-0.358264\pi$
$769$	23.8878			0.861417			0.430708	+	0.902491i	$0.358264\pi$
$770$	2.84696	−	1.70142i	0.102597	−	0.0613148i
$771$	21.9293			0.789766
$772$	19.2116	−	13.9580i	0.691441	−	0.502361i
$773$	1.18085	+	3.63429i	0.0424723	+	0.130716i	0.970044	−	0.242928i	$-0.0781080\pi$
$773$	1.18085	+	3.63429i	0.0424723	+	0.130716i	−0.927572	+	0.373645i	$0.878108\pi$
$774$	5.28525	−	16.2663i	0.189974	−	0.584681i
$775$	0.382855	+	0.278160i	0.0137525	+	0.00999181i
$776$	0.854015	+	0.620478i	0.0306573	+	0.0222739i
$777$	−10.9572	+	33.7228i	−0.393087	+	1.20980i
$778$	−0.551571	−	1.69756i	−0.0197748	−	0.0608605i
$779$	−8.91195	+	6.47491i	−0.319304	+	0.231988i
$780$	11.6492			0.417108
$781$	1.40589	+	6.15641i	0.0503068	+	0.220294i
$782$	−27.1502			−0.970889
$783$	−18.9316	+	13.7546i	−0.676561	+	0.491550i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	−3.64188	+	11.2086i	−0.129984	+	0.400051i
$786$	44.4264	+	32.2777i	1.58464	+	1.15131i
$787$	25.7425	+	18.7031i	0.917623	+	0.666692i	0.942931	−	0.332988i	$-0.108057\pi$
$787$	25.7425	+	18.7031i	0.917623	+	0.666692i	−0.0253085	+	0.999680i	$0.508057\pi$
$788$	2.58558	−	7.95761i	0.0921076	−	0.283478i
$789$	32.3662	+	99.6130i	1.15227	+	3.54632i
$790$	11.7628	−	8.54615i	0.418500	−	0.304058i
$791$	10.7388			0.381829
$792$	−5.60797	−	24.5573i	−0.199271	−	0.872606i
$793$	−42.5827			−1.51216
$794$	−1.01185	+	0.735154i	−0.0359093	+	0.0260897i
$795$	−5.65443	−	17.4025i	−0.200542	−	0.617205i
$796$	2.11079	−	6.49634i	0.0748150	−	0.230257i
$797$	30.1766	+	21.9245i	1.06891	+	0.776607i	0.975716	−	0.219041i	$-0.0702928\pi$
$797$	30.1766	+	21.9245i	1.06891	+	0.776607i	0.0931926	+	0.995648i	$0.470293\pi$
$798$	−7.54949	−	5.48503i	−0.267249	−	0.194168i
$799$	−8.95994	+	27.5759i	−0.316980	+	0.975563i
$800$	0.309017	+	0.951057i	0.0109254	+	0.0336249i
$801$	68.5882	−	49.8322i	2.42344	−	1.76074i
$802$	−19.4278			−0.686018
$803$	4.74703	−	2.83695i	0.167519	−	0.100114i
$804$	2.45068			0.0864287
$805$	7.28272	−	5.29120i	0.256682	−	0.186490i
$806$	−0.523367	−	1.61076i	−0.0184348	−	0.0567365i
$807$	−30.2280	+	93.0321i	−1.06407	+	3.27488i
$808$	−4.55928	−	3.31251i	−0.160395	−	0.116534i
$809$	27.8586	+	20.2405i	0.979456	+	0.711617i	0.957587	−	0.288144i	$-0.0930382\pi$
$809$	27.8586	+	20.2405i	0.979456	+	0.711617i	0.0218694	+	0.999761i	$0.493038\pi$
$810$	8.00295	−	24.6305i	0.281195	−	0.865429i
$811$	−8.98867	−	27.6643i	−0.315635	−	0.971424i	−0.975492	−	0.220033i	$-0.929383\pi$
$811$	−8.98867	−	27.6643i	−0.315635	−	0.971424i	0.659858	−	0.751391i	$-0.270617\pi$
$812$	−1.26579	+	0.919648i	−0.0444204	+	0.0322733i
$813$	−29.0614			−1.01923
$814$	14.1961	−	33.2239i	0.497574	−	1.16450i
$815$	−8.20930			−0.287559
$816$	−7.94225	+	5.77038i	−0.278034	+	0.202004i
$817$	1.99505	+	6.14012i	0.0697979	+	0.214816i
$818$	−2.09368	+	6.44370i	−0.0732040	+	0.225299i
$819$	−21.9902	−	15.9768i	−0.768398	−	0.558274i
$820$	−3.10858	−	2.25851i	−0.108556	−	0.0788707i
$821$	2.30184	−	7.08435i	0.0803349	−	0.247245i	−0.902820	−	0.430018i	$-0.858507\pi$
$821$	2.30184	−	7.08435i	0.0803349	−	0.247245i	0.983155	+	0.182773i	$0.0585072\pi$
$822$	13.5675	+	41.7564i	0.473220	+	1.45642i
$823$	−35.1068	+	25.5066i	−1.22375	+	0.889104i	−0.996405	−	0.0847118i	$-0.973003\pi$
$823$	−35.1068	+	25.5066i	−1.22375	+	0.889104i	−0.227341	+	0.973815i	$0.573003\pi$
$824$	−7.68278			−0.267642
$825$	−10.7522	−	0.966490i	−0.374344	−	0.0336489i
$826$	−2.73647			−0.0952140
$827$	−5.82282	+	4.23053i	−0.202479	+	0.147110i	−0.684404	−	0.729103i	$-0.739938\pi$
$827$	−5.82282	+	4.23053i	−0.202479	+	0.147110i	0.481925	+	0.876212i	$0.339938\pi$
$828$	−21.1272	−	65.0228i	−0.734220	−	2.25970i
$829$	−2.85066	+	8.77343i	−0.0990075	+	0.304714i	−0.988277	−	0.152669i	$-0.951213\pi$
$829$	−2.85066	+	8.77343i	−0.0990075	+	0.304714i	0.889270	+	0.457383i	$0.151213\pi$
$830$	4.30054	+	3.12453i	0.149274	+	0.108454i
$831$	−4.42587	−	3.21558i	−0.153532	−	0.111547i
$832$	1.10594	−	3.40372i	0.0383414	−	0.118003i
$833$	0.932008	+	2.86842i	0.0322922	+	0.0993850i
$834$	3.88635	−	2.82360i	0.134573	−	0.0977733i
$835$	20.1999			0.699047
$836$	7.16121	+	6.25514i	0.247676	+	0.216338i
$837$	−7.07788			−0.244647
$838$	−21.3371	+	15.5023i	−0.737076	+	0.535517i
$839$	−0.940146	−	2.89347i	−0.0324574	−	0.0998937i	0.933515	−	0.358537i	$-0.116724\pi$
$839$	−0.940146	−	2.89347i	−0.0324574	−	0.0998937i	−0.965973	+	0.258644i	$0.916724\pi$
$840$	1.00585	−	3.09567i	0.0347050	−	0.106811i
$841$	21.4810	+	15.6069i	0.740726	+	0.538169i
$842$	−15.5177	−	11.2743i	−0.534776	−	0.388537i
$843$	7.94719	−	24.4589i	0.273716	−	0.842410i
$844$	0.878363	+	2.70332i	0.0302345	+	0.0930522i
$845$	0.155011	−	0.112622i	0.00533255	−	0.00387432i
$846$	−73.0144			−2.51029
$847$	10.8237	+	1.96168i	0.371906	+	0.0674040i
$848$	−5.62157			−0.193045
$849$	−71.2156	+	51.7412i	−2.44411	+	1.77575i
$850$	0.932008	+	2.86842i	0.0319676	+	0.0983862i
$851$	30.3031	−	93.2632i	1.03878	−	3.19702i
$852$	5.01391	+	3.64282i	0.171774	+	0.124801i
$853$	−24.2591	−	17.6253i	−0.830616	−	0.603478i	0.0891173	−	0.996021i	$-0.471595\pi$
$853$	−24.2591	−	17.6253i	−0.830616	−	0.603478i	−0.919734	+	0.392543i	$0.871595\pi$
$854$	−3.67679	+	11.3160i	−0.125817	+	0.387225i
$855$	6.72848	+	20.7081i	0.230109	+	0.708203i
$856$	−14.1906	+	10.3101i	−0.485026	+	0.352392i
$857$	−7.77150			−0.265469			−0.132735	−	0.991152i	$-0.542376\pi$
$857$	−7.77150			−0.265469			−0.132735	+	0.991152i	$0.542376\pi$
$858$	29.0986	+	25.4169i	0.993409	+	0.867717i
$859$	−50.9695			−1.73906			−0.869529	−	0.493883i	$-0.835577\pi$
$859$	−50.9695			−1.73906			−0.869529	+	0.493883i	$0.835577\pi$
$860$	−1.82187	+	1.32367i	−0.0621252	+	0.0451366i
$861$	3.86487	+	11.8949i	0.131714	+	0.405375i
$862$	8.49258	−	26.1375i	0.289258	−	0.890246i
$863$	20.4245	+	14.8393i	0.695258	+	0.505135i	0.878384	−	0.477955i	$-0.158622\pi$
$863$	20.4245	+	14.8393i	0.695258	+	0.505135i	−0.183126	+	0.983089i	$0.558622\pi$
$864$	−12.1000	−	8.79115i	−0.411650	−	0.299081i
$865$	−7.64124	+	23.5173i	−0.259810	+	0.799613i
$866$	2.14129	+	6.59020i	0.0727638	+	0.223944i
$867$	20.8126	−	15.1212i	0.706832	−	0.513544i
$868$	−0.473234			−0.0160626
$869$	48.0287	+	4.31718i	1.62926	+	0.146450i
$870$	5.09274			0.172660
$871$	−2.17993	+	1.58381i	−0.0738640	+	0.0536653i
$872$	3.17183	+	9.76189i	0.107412	+	0.330579i
$873$	−2.47750	+	7.62496i	−0.0838506	+	0.258066i
$874$	20.8788	+	15.1693i	0.706234	+	0.513109i
$875$	−0.809017	−	0.587785i	−0.0273498	−	0.0198708i
$876$	1.67715	−	5.16174i	0.0566656	−	0.174399i
$877$	−0.386708	−	1.19016i	−0.0130582	−	0.0401890i	0.944315	−	0.329042i	$-0.106726\pi$
$877$	−0.386708	−	1.19016i	−0.0130582	−	0.0401890i	−0.957373	+	0.288854i	$0.906726\pi$
$878$	7.34292	−	5.33495i	0.247812	−	0.180046i
$879$	33.2033			1.11992
$880$	−1.30317	+	3.04988i	−0.0439299	+	0.102811i
$881$	−16.6655			−0.561476			−0.280738	−	0.959784i	$-0.590579\pi$
$881$	−16.6655			−0.561476			−0.280738	+	0.959784i	$0.590579\pi$
$882$	−6.14442	+	4.46418i	−0.206893	+	0.150317i
$883$	−0.383077	−	1.17899i	−0.0128916	−	0.0396762i	0.944404	−	0.328788i	$-0.106640\pi$
$883$	−0.383077	−	1.17899i	−0.0128916	−	0.0396762i	−0.957295	+	0.289112i	$0.906640\pi$
$884$	3.33555	−	10.2658i	0.112187	−	0.345275i
$885$	7.20605	+	5.23550i	0.242229	+	0.175990i
$886$	19.0920	+	13.8712i	0.641409	+	0.466011i
$887$	−12.4476	+	38.3099i	−0.417951	+	1.28632i	0.491634	+	0.870802i	$0.336400\pi$
$887$	−12.4476	+	38.3099i	−0.417951	+	1.28632i	−0.909585	+	0.415519i	$0.863600\pi$
$888$	−10.9572	−	33.7228i	−0.367700	−	1.13166i
$889$	−0.223724	+	0.162545i	−0.00750346	+	0.00545158i
$890$	−11.1627			−0.374174
$891$	73.7308	−	44.0634i	2.47007	−	1.47618i
$892$	20.0124			0.670064
$893$	22.2974	−	16.2000i	0.746154	−	0.542113i
$894$	−16.5419	−	50.9106i	−0.553243	−	1.70271i
$895$	7.90992	−	24.3442i	0.264399	−	0.813738i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	84.8378	+	61.6383i	2.83265	+	2.05804i
$898$	−9.27684	+	28.5512i	−0.309572	+	0.952765i
$899$	−0.228803	−	0.704183i	−0.00763100	−	0.0234858i
$900$	−6.14442	+	4.46418i	−0.204814	+	0.148806i
$901$	−16.9549			−0.564849
$902$	−2.83718	−	12.4240i	−0.0944676	−	0.413674i
$903$	7.33008			0.243930
$904$	−8.68791	+	6.31213i	−0.288955	+	0.209938i
$905$	−0.695113	−	2.13934i	−0.0231063	−	0.0711140i
$906$	7.92098	−	24.3783i	0.263157	−	0.809914i
$907$	6.96678	+	5.06166i	0.231328	+	0.168070i	0.697411	−	0.716671i	$-0.254335\pi$
$907$	6.96678	+	5.06166i	0.231328	+	0.168070i	−0.466083	+	0.884741i	$0.654335\pi$
$908$	9.97797	+	7.24942i	0.331130	+	0.240580i
$909$	13.2265	−	40.7069i	0.438695	−	1.35016i
$910$	1.10594	+	3.40372i	0.0366614	+	0.112832i
$911$	−4.16217	+	3.02400i	−0.137899	+	0.100189i	−0.654596	−	0.755979i	$-0.727161\pi$
$911$	−4.16217	+	3.02400i	−0.137899	+	0.100189i	0.516697	+	0.856168i	$0.327161\pi$
$912$	9.33169			0.309003
$913$	3.92507	+	17.1879i	0.129901	+	0.568837i
$914$	−2.10098			−0.0694943
$915$	31.3323	−	22.7643i	1.03581	−	0.752563i
$916$	1.71293	+	5.27185i	0.0565967	+	0.174187i
$917$	−5.21335	+	16.0450i	−0.172160	+	0.529854i
$918$	−36.4940	−	26.5145i	−1.20448	−	0.875108i
$919$	−17.5975	−	12.7853i	−0.580486	−	0.421748i	0.258413	−	0.966035i	$-0.416800\pi$
$919$	−17.5975	−	12.7853i	−0.580486	−	0.421748i	−0.838899	+	0.544286i	$0.816800\pi$
$920$	−2.78175	+	8.56135i	−0.0917116	+	0.282259i
$921$	15.4450	+	47.5348i	0.508930	+	1.56633i
$922$	−27.2314	+	19.7848i	−0.896818	+	0.651577i
$923$	−6.81424			−0.224293
$924$	9.26681	−	5.53808i	0.304856	−	0.182190i
$925$	−10.8935			−0.358177
$926$	−25.2822	+	18.3686i	−0.830826	+	0.603630i
$927$	−18.0312	−	55.4943i	−0.592222	−	1.82267i
$928$	0.483487	−	1.48802i	0.0158713	−	0.0488467i
$929$	37.3113	+	27.1082i	1.22414	+	0.889392i	0.996437	−	0.0843381i	$-0.0268776\pi$
$929$	37.3113	+	27.1082i	1.22414	+	0.889392i	0.227706	+	0.973730i	$0.426878\pi$
$930$	1.24619	+	0.905407i	0.0408640	+	0.0296895i
$931$	0.885918	−	2.72658i	0.0290348	−	0.0893599i
$932$	4.00550	+	12.3277i	0.131204	+	0.403806i
$933$	69.4095	−	50.4290i	2.27237	−	1.65097i
$934$	26.9260			0.881047
$935$	−3.93042	+	9.19855i	−0.128538	+	0.300825i
$936$	27.1813			0.888450
$937$	−9.13294	+	6.63547i	−0.298360	+	0.216771i	−0.726886	−	0.686758i	$-0.759033\pi$
$937$	−9.13294	+	6.63547i	−0.298360	+	0.216771i	0.428526	+	0.903530i	$0.359033\pi$
$938$	0.232659	+	0.716050i	0.00759658	+	0.0233799i
$939$	8.65502	−	26.6374i	0.282446	−	0.869279i
$940$	7.77755	+	5.65072i	0.253676	+	0.184306i
$941$	10.3201	+	7.49799i	0.336426	+	0.244428i	0.743152	−	0.669122i	$-0.233330\pi$
$941$	10.3201	+	7.49799i	0.336426	+	0.244428i	−0.406727	+	0.913550i	$0.633330\pi$
$942$	−11.8543	+	36.4837i	−0.386233	+	1.18870i
$943$	−10.6886	−	32.8962i	−0.348070	−	1.07125i
$944$	2.21385	−	1.60846i	0.0720547	−	0.0523508i
$945$	14.9564			0.486532
$946$	−7.43890	−	0.668664i	−0.241859	−	0.0217402i
$947$	−47.3261			−1.53789			−0.768945	−	0.639315i	$-0.779218\pi$
$947$	−47.3261			−1.53789			−0.768945	+	0.639315i	$0.779218\pi$
$948$	38.2876	−	27.8176i	1.24352	−	0.903473i
$949$	1.84404	+	5.67537i	0.0598601	+	0.184230i
$950$	0.885918	−	2.72658i	0.0287430	−	0.0884618i
$951$	−7.57712	−	5.50510i	−0.245705	−	0.178515i
$952$	−2.44003	−	1.77278i	−0.0790818	−	0.0574563i
$953$	−1.60050	+	4.92582i	−0.0518452	+	0.159563i	−0.973627	−	0.228146i	$-0.926734\pi$
$953$	−1.60050	+	4.92582i	−0.0518452	+	0.159563i	0.921782	+	0.387709i	$0.126734\pi$
$954$	−13.1936	−	40.6057i	−0.427158	−	1.31466i
$955$	−21.0925	+	15.3246i	−0.682538	+	0.495893i
$956$	−21.3109			−0.689244
$957$	12.7212	+	11.1116i	0.411217	+	0.359188i
$958$	35.8357			1.15780
$959$	−10.9125	+	7.92841i	−0.352384	+	0.256022i
$960$	1.00585	+	3.09567i	0.0324635	+	0.0999124i
$961$	−9.51032	+	29.2698i	−0.306785	+	0.944186i
$962$	31.5409	+	22.9158i	1.01692	+	0.738834i
$963$	−107.777	−	78.3043i	−3.47306	−	2.52332i
$964$	2.37064	−	7.29609i	0.0763532	−	0.234991i
$965$	−7.33818	−	22.5846i	−0.236224	−	0.727024i
$966$	23.7051	−	17.2228i	0.762700	−	0.554134i
$967$	39.6832			1.27612			0.638062	−	0.769985i	$-0.279736\pi$
$967$	39.6832			1.27612			0.638062	+	0.769985i	$0.279736\pi$
$968$	−9.90958	+	4.77496i	−0.318506	+	0.153473i
$969$	28.1447			0.904139
$970$	0.854015	−	0.620478i	0.0274208	−	0.0199223i
$971$	0.443026	+	1.36350i	0.0142174	+	0.0437566i	0.957914	−	0.287057i	$-0.0926769\pi$
$971$	0.443026	+	1.36350i	0.0142174	+	0.0437566i	−0.943696	+	0.330814i	$0.892677\pi$
$972$	12.1841	−	37.4989i	0.390806	−	1.20278i
$973$	1.19397	+	0.867469i	0.0382769	+	0.0278098i
$974$	8.33524	+	6.05590i	0.267078	+	0.194044i
$975$	3.59980	−	11.0791i	0.115286	−	0.354814i
$976$	−3.67679	−	11.3160i	−0.117691	−	0.362216i
$977$	26.9204	−	19.5588i	0.861259	−	0.625742i	−0.0669679	−	0.997755i	$-0.521333\pi$
$977$	26.9204	−	19.5588i	0.861259	−	0.625742i	0.928227	+	0.372014i	$0.121333\pi$
$978$	−26.7211			−0.854448
$979$	−27.8833	−	24.3553i	−0.891153	−	0.778399i
$980$	1.00000			0.0319438
$981$	−63.0679	+	45.8215i	−2.01360	+	1.46297i
$982$	6.20903	+	19.1094i	0.198138	+	0.609807i
$983$	12.7949	−	39.3785i	0.408093	−	1.25598i	−0.510193	−	0.860060i	$-0.670426\pi$
$983$	12.7949	−	39.3785i	0.408093	−	1.25598i	0.918285	−	0.395919i	$-0.129574\pi$
$984$	−10.1184	−	7.35142i	−0.322562	−	0.234355i
$985$	−6.76915	−	4.91807i	−0.215683	−	0.156703i
$986$	1.45822	−	4.48793i	0.0464391	−	0.142925i
$987$	−9.66978	−	29.7605i	−0.307793	−	0.947288i
$988$	−8.30073	+	6.03083i	−0.264081	+	0.191866i
$989$	−20.2719			−0.644610
$990$	−25.0884	−	2.25513i	−0.797360	−	0.0716728i
$991$	−37.2508			−1.18331			−0.591655	−	0.806191i	$-0.701525\pi$
$991$	−37.2508			−1.18331			−0.591655	+	0.806191i	$0.701525\pi$
$992$	0.382855	−	0.278160i	0.0121556	−	0.00883160i
$993$	−19.6041	−	60.3351i	−0.622117	−	1.91468i
$994$	−0.588373	+	1.81082i	−0.0186620	+	0.0574359i
$995$	−5.52612	−	4.01496i	−0.175190	−	0.127283i
$996$	13.9982	+	10.1703i	0.443550	+	0.322258i
$997$	6.19562	−	19.0681i	0.196217	−	0.603894i	−0.803743	−	0.594977i	$-0.797161\pi$
$997$	6.19562	−	19.0681i	0.196217	−	0.603894i	0.999960	−	0.00891779i	$-0.00283866\pi$
$998$	8.08581	+	24.8856i	0.255952	+	0.787738i
$999$	131.811	−	95.7666i	4.17033	−	3.02992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.i.421.3	✓	12
11.2	odd	10		8470.2.a.cy.1.6		6
11.4	even	5	inner	770.2.n.i.631.3	yes	12
11.9	even	5		8470.2.a.de.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.i.421.3	✓	12	1.1	even	1	trivial
770.2.n.i.631.3	yes	12	11.4	even	5	inner
8470.2.a.cy.1.6		6	11.2	odd	10
8470.2.a.de.1.6		6	11.9	even	5

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)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(1.00585 + 3.09567i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-2.63334 - 1.91323i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-6.14442 + 4.46418i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(1.00585 + 3.09567i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-2.63334 - 1.91323i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-6.14442 + 4.46418i) q^{9} +1.00000 q^{10} +(2.49790 + 2.18185i) q^{11} +3.25498 q^{12} +(-2.89538 + 2.10361i) q^{13} +(0.309017 + 0.951057i) q^{14} +(1.00585 - 3.09567i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.44003 - 1.77278i) q^{17} +(2.34696 - 7.22320i) q^{18} +(0.885918 + 2.72658i) q^{19} +(-0.809017 + 0.587785i) q^{20} +3.25498 q^{21} +(-3.30331 - 0.296926i) q^{22} -9.00193 q^{23} +(-2.63334 + 1.91323i) q^{24} +(0.309017 + 0.951057i) q^{25} +(1.10594 - 3.40372i) q^{26} +(-12.1000 - 8.79115i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(0.483487 - 1.48802i) q^{29} +(1.00585 + 3.09567i) q^{30} +(0.382855 - 0.278160i) q^{31} +1.00000 q^{32} +(-4.24180 + 9.92730i) q^{33} +3.01604 q^{34} +(-0.809017 + 0.587785i) q^{35} +(2.34696 + 7.22320i) q^{36} +(-3.36628 + 10.3604i) q^{37} +(-2.31936 - 1.68512i) q^{38} +(-9.42440 - 6.84723i) q^{39} +(0.309017 - 0.951057i) q^{40} +(1.18737 + 3.65435i) q^{41} +(-2.63334 + 1.91323i) q^{42} +2.25195 q^{43} +(2.84696 - 1.70142i) q^{44} +7.59492 q^{45} +(7.28272 - 5.29120i) q^{46} +(-2.97076 - 9.14306i) q^{47} +(1.00585 - 3.09567i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(3.03367 - 9.33668i) q^{51} +(1.10594 + 3.40372i) q^{52} +(4.54794 - 3.30427i) q^{53} +14.9564 q^{54} +(-0.738384 - 3.23339i) q^{55} +1.00000 q^{56} +(-7.54949 + 5.48503i) q^{57} +(0.483487 + 1.48802i) q^{58} +(-0.845616 + 2.60254i) q^{59} +(-2.63334 - 1.91323i) q^{60} +(9.62595 + 6.99366i) q^{61} +(-0.146237 + 0.450073i) q^{62} +(2.34696 + 7.22320i) q^{63} +(-0.809017 + 0.587785i) q^{64} +3.57888 q^{65} +(-2.40343 - 10.5246i) q^{66} +0.752899 q^{67} +(-2.44003 + 1.77278i) q^{68} +(-9.05455 - 27.8670i) q^{69} +(0.309017 - 0.951057i) q^{70} +(1.54038 + 1.11915i) q^{71} +(-6.14442 - 4.46418i) q^{72} +(0.515256 - 1.58579i) q^{73} +(-3.36628 - 10.3604i) q^{74} +(-2.63334 + 1.91323i) q^{75} +2.86689 q^{76} +(2.84696 - 1.70142i) q^{77} +11.6492 q^{78} +(11.7628 - 8.54615i) q^{79} +(0.309017 + 0.951057i) q^{80} +(8.00295 - 24.6305i) q^{81} +(-3.10858 - 2.25851i) q^{82} +(4.30054 + 3.12453i) q^{83} +(1.00585 - 3.09567i) q^{84} +(0.932008 + 2.86842i) q^{85} +(-1.82187 + 1.32367i) q^{86} +5.09274 q^{87} +(-1.30317 + 3.04988i) q^{88} -11.1627 q^{89} +(-6.14442 + 4.46418i) q^{90} +(1.10594 + 3.40372i) q^{91} +(-2.78175 + 8.56135i) q^{92} +(1.24619 + 0.905407i) q^{93} +(7.77755 + 5.65072i) q^{94} +(0.885918 - 2.72658i) q^{95} +(1.00585 + 3.09567i) q^{96} +(0.854015 - 0.620478i) q^{97} +1.00000 q^{98} +(-25.0884 - 2.25513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9	\( 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9} + 12 q^{10} + q^{11} + 2 q^{12} - 6 q^{13} - 3 q^{14} + 2 q^{15} - 3 q^{16} - 6 q^{17} - 13 q^{19} - 3 q^{20} + 2 q^{21} + q^{22} - 12 q^{23} - 3 q^{24} - 3 q^{25} + 4 q^{26} - 7 q^{27} - 3 q^{28} - 26 q^{29} + 2 q^{30} + 12 q^{32} - 15 q^{33} + 14 q^{34} - 3 q^{35} - 18 q^{37} + 2 q^{38} - 40 q^{39} - 3 q^{40} + 16 q^{41} - 3 q^{42} + 38 q^{43} + 6 q^{44} + 30 q^{45} + 8 q^{46} - 26 q^{47} + 2 q^{48} - 3 q^{49} - 3 q^{50} - 13 q^{51} + 4 q^{52} + 8 q^{54} + 11 q^{55} + 12 q^{56} - 41 q^{57} - 26 q^{58} + 21 q^{59} - 3 q^{60} + 4 q^{61} - 3 q^{64} + 4 q^{65} - 30 q^{66} + 10 q^{67} - 6 q^{68} + 18 q^{69} - 3 q^{70} - 4 q^{71} - 15 q^{72} - 14 q^{73} - 18 q^{74} - 3 q^{75} + 22 q^{76} + 6 q^{77} + 40 q^{78} - 2 q^{79} - 3 q^{80} + 26 q^{81} - 29 q^{82} + 35 q^{83} + 2 q^{84} - q^{85} - 37 q^{86} + 28 q^{87} - 19 q^{88} + 2 q^{89} - 15 q^{90} + 4 q^{91} - 2 q^{92} + 6 q^{93} + 4 q^{94} - 13 q^{95} + 2 q^{96} + 19 q^{97} + 12 q^{98} - 81 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9 + 12 * q^10 + q^11 + 2 * q^12 - 6 * q^13 - 3 * q^14 + 2 * q^15 - 3 * q^16 - 6 * q^17 - 13 * q^19 - 3 * q^20 + 2 * q^21 + q^22 - 12 * q^23 - 3 * q^24 - 3 * q^25 + 4 * q^26 - 7 * q^27 - 3 * q^28 - 26 * q^29 + 2 * q^30 + 12 * q^32 - 15 * q^33 + 14 * q^34 - 3 * q^35 - 18 * q^37 + 2 * q^38 - 40 * q^39 - 3 * q^40 + 16 * q^41 - 3 * q^42 + 38 * q^43 + 6 * q^44 + 30 * q^45 + 8 * q^46 - 26 * q^47 + 2 * q^48 - 3 * q^49 - 3 * q^50 - 13 * q^51 + 4 * q^52 + 8 * q^54 + 11 * q^55 + 12 * q^56 - 41 * q^57 - 26 * q^58 + 21 * q^59 - 3 * q^60 + 4 * q^61 - 3 * q^64 + 4 * q^65 - 30 * q^66 + 10 * q^67 - 6 * q^68 + 18 * q^69 - 3 * q^70 - 4 * q^71 - 15 * q^72 - 14 * q^73 - 18 * q^74 - 3 * q^75 + 22 * q^76 + 6 * q^77 + 40 * q^78 - 2 * q^79 - 3 * q^80 + 26 * q^81 - 29 * q^82 + 35 * q^83 + 2 * q^84 - q^85 - 37 * q^86 + 28 * q^87 - 19 * q^88 + 2 * q^89 - 15 * q^90 + 4 * q^91 - 2 * q^92 + 6 * q^93 + 4 * q^94 - 13 * q^95 + 2 * q^96 + 19 * q^97 + 12 * q^98 - 81 * q^99

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