LMFDB - Embedded newform 770.2.n.h.421.1

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:	$12$
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} + 7 x^{10} - 9 x^{9} + 55 x^{8} - 32 x^{7} + 287 x^{6} - 302 x^{5} + 1175 x^{4} + \cdots + 361 $ x^12 - 3x^11 + 7x^10 - 9x^9 + 55x^8 - 32x^7 + 287x^6 - 302x^5 + 1175x^4 - 1639x^3 + 1692x^2 - 988*x + 361
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			421.1
Root			$0.603111 - 1.85618i$ of defining polynomial
Character	$\chi$	$=$	770.421
Dual form			770.2.n.h.631.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.912128 - 2.80724i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(2.38798 + 1.73497i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-4.62157 + 3.35777i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.912128 - 2.80724i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(2.38798 + 1.73497i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-4.62157 + 3.35777i) q^{9} -1.00000 q^{10} +(0.355779 - 3.29749i) q^{11} -2.95171 q^{12} +(-4.69299 + 3.40966i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.912128 - 2.80724i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.380053 + 0.276124i) q^{17} +(1.76528 - 5.43299i) q^{18} +(-1.25005 - 3.84724i) q^{19} +(0.809017 - 0.587785i) q^{20} -2.95171 q^{21} +(1.65038 + 2.87684i) q^{22} -7.69830 q^{23} +(2.38798 - 1.73497i) q^{24} +(0.309017 + 0.951057i) q^{25} +(1.79256 - 5.51694i) q^{26} +(6.47759 + 4.70624i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(0.813681 - 2.50425i) q^{29} +(0.912128 + 2.80724i) q^{30} +(2.60621 - 1.89352i) q^{31} +1.00000 q^{32} +(-9.58136 + 2.00897i) q^{33} -0.469771 q^{34} +(0.809017 - 0.587785i) q^{35} +(1.76528 + 5.43299i) q^{36} +(-1.40934 + 4.33749i) q^{37} +(3.27266 + 2.37773i) q^{38} +(13.8523 + 10.0643i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(0.563872 + 1.73542i) q^{41} +(2.38798 - 1.73497i) q^{42} -0.790717 q^{43} +(-3.02615 - 1.35735i) q^{44} -5.71258 q^{45} +(6.22805 - 4.52495i) q^{46} +(-1.32435 - 4.07592i) q^{47} +(-0.912128 + 2.80724i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(0.428491 - 1.31876i) q^{51} +(1.79256 + 5.51694i) q^{52} +(-11.2778 + 8.19378i) q^{53} -8.00674 q^{54} +(2.22605 - 2.45860i) q^{55} +1.00000 q^{56} +(-9.65994 + 7.01836i) q^{57} +(0.813681 + 2.50425i) q^{58} +(-4.02897 + 12.3999i) q^{59} +(-2.38798 - 1.73497i) q^{60} +(5.41759 + 3.93611i) q^{61} +(-0.995482 + 3.06378i) q^{62} +(1.76528 + 5.43299i) q^{63} +(-0.809017 + 0.587785i) q^{64} -5.80086 q^{65} +(6.57064 - 7.25707i) q^{66} -6.73018 q^{67} +(0.380053 - 0.276124i) q^{68} +(7.02183 + 21.6110i) q^{69} +(-0.309017 + 0.951057i) q^{70} +(-9.29195 - 6.75100i) q^{71} +(-4.62157 - 3.35777i) q^{72} +(3.78691 - 11.6549i) q^{73} +(-1.40934 - 4.33749i) q^{74} +(2.38798 - 1.73497i) q^{75} -4.04523 q^{76} +(-3.02615 - 1.35735i) q^{77} -17.1224 q^{78} +(-3.19789 + 2.32340i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(2.00732 - 6.17789i) q^{81} +(-1.47624 - 1.07255i) q^{82} +(7.64360 + 5.55340i) q^{83} +(-0.912128 + 2.80724i) q^{84} +(0.145167 + 0.446779i) q^{85} +(0.639704 - 0.464772i) q^{86} -7.77222 q^{87} +(3.24604 - 0.680614i) q^{88} -11.2766 q^{89} +(4.62157 - 3.35777i) q^{90} +(1.79256 + 5.51694i) q^{91} +(-2.37891 + 7.32152i) q^{92} +(-7.69276 - 5.58912i) q^{93} +(3.46718 + 2.51906i) q^{94} +(1.25005 - 3.84724i) q^{95} +(-0.912128 - 2.80724i) q^{96} +(13.5518 - 9.84599i) q^{97} +1.00000 q^{98} +(9.42794 + 16.4342i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9	$ 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9} - 12 q^{10} - q^{11} - 10 q^{12} - 3 q^{14} - 3 q^{16} - 8 q^{18} - q^{19} + 3 q^{20} - 10 q^{21} - q^{22} - 4 q^{23} + 5 q^{24} - 3 q^{25} + 3 q^{27} - 3 q^{28} + 22 q^{29} + 6 q^{31} + 12 q^{32} - 29 q^{33} - 30 q^{34} + 3 q^{35} - 8 q^{36} - 10 q^{37} + 14 q^{38} + 20 q^{39} + 3 q^{40} + 16 q^{41} + 5 q^{42} + 30 q^{43} + 14 q^{44} - 22 q^{45} - 4 q^{46} + 34 q^{47} - 3 q^{49} - 3 q^{50} + 37 q^{51} - 26 q^{53} - 52 q^{54} + 11 q^{55} + 12 q^{56} - 19 q^{57} + 22 q^{58} + q^{59} - 5 q^{60} + 40 q^{61} - 4 q^{62} - 8 q^{63} - 3 q^{64} + 16 q^{66} - 58 q^{67} + 14 q^{69} + 3 q^{70} - 14 q^{71} - 3 q^{72} + 32 q^{73} - 10 q^{74} + 5 q^{75} - 26 q^{76} + 14 q^{77} - 60 q^{78} + 16 q^{79} + 3 q^{80} - 46 q^{81} + q^{82} + 35 q^{83} - 15 q^{85} + 5 q^{86} - q^{88} - 58 q^{89} + 3 q^{90} + 6 q^{92} + 46 q^{93} - 16 q^{94} + q^{95} + 57 q^{97} + 12 q^{98} + 69 q^{99}+O(q^{100}) $ 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9 - 12 * q^10 - q^11 - 10 * q^12 - 3 * q^14 - 3 * q^16 - 8 * q^18 - q^19 + 3 * q^20 - 10 * q^21 - q^22 - 4 * q^23 + 5 * q^24 - 3 * q^25 + 3 * q^27 - 3 * q^28 + 22 * q^29 + 6 * q^31 + 12 * q^32 - 29 * q^33 - 30 * q^34 + 3 * q^35 - 8 * q^36 - 10 * q^37 + 14 * q^38 + 20 * q^39 + 3 * q^40 + 16 * q^41 + 5 * q^42 + 30 * q^43 + 14 * q^44 - 22 * q^45 - 4 * q^46 + 34 * q^47 - 3 * q^49 - 3 * q^50 + 37 * q^51 - 26 * q^53 - 52 * q^54 + 11 * q^55 + 12 * q^56 - 19 * q^57 + 22 * q^58 + q^59 - 5 * q^60 + 40 * q^61 - 4 * q^62 - 8 * q^63 - 3 * q^64 + 16 * q^66 - 58 * q^67 + 14 * q^69 + 3 * q^70 - 14 * q^71 - 3 * q^72 + 32 * q^73 - 10 * q^74 + 5 * q^75 - 26 * q^76 + 14 * q^77 - 60 * q^78 + 16 * q^79 + 3 * q^80 - 46 * q^81 + q^82 + 35 * q^83 - 15 * q^85 + 5 * q^86 - q^88 - 58 * q^89 + 3 * q^90 + 6 * q^92 + 46 * q^93 - 16 * q^94 + q^95 + 57 * q^97 + 12 * q^98 + 69 * 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
$3$	−0.912128	−	2.80724i	−0.526617	−	1.62076i	−0.761095	−	0.648640i	$-0.775338\pi$
$3$	−0.912128	−	2.80724i	−0.526617	−	1.62076i	0.234478	−	0.972121i	$-0.424662\pi$
$4$	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
$6$	2.38798	+	1.73497i	0.974889	+	0.708299i
$7$	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
$9$	−4.62157	+	3.35777i	−1.54052	+	1.11926i
$10$	−1.00000			−0.316228
$11$	0.355779	−	3.29749i	0.107271	−	0.994230i
$11$	0.355779	−	3.29749i	0.107271	−	0.994230i
$12$	−2.95171			−0.852085
$13$	−4.69299	+	3.40966i	−1.30160	+	0.945669i	−0.999970	−	0.00775545i	$-0.997531\pi$
$13$	−4.69299	+	3.40966i	−1.30160	+	0.945669i	−0.301632	+	0.953424i	$0.597531\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$	0.912128	−	2.80724i	0.235510	−	0.724826i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.380053	+	0.276124i	0.0921763	+	0.0669700i	0.632919	−	0.774218i	$-0.281857\pi$
$17$	0.380053	+	0.276124i	0.0921763	+	0.0669700i	−0.540743	+	0.841188i	$0.681857\pi$
$18$	1.76528	−	5.43299i	0.416081	−	1.28057i
$19$	−1.25005	−	3.84724i	−0.286780	−	0.882618i	−0.985859	−	0.167574i	$-0.946407\pi$
$19$	−1.25005	−	3.84724i	−0.286780	−	0.882618i	0.699079	−	0.715044i	$-0.253593\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$	−2.95171			−0.644115
$22$	1.65038	+	2.87684i	0.351863	+	0.613345i
$23$	−7.69830			−1.60521			−0.802603	−	0.596513i	$-0.796552\pi$
$23$	−7.69830			−1.60521			−0.802603	+	0.596513i	$0.796552\pi$
$24$	2.38798	−	1.73497i	0.487445	−	0.354149i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	1.79256	−	5.51694i	0.351551	−	1.08196i
$27$	6.47759	+	4.70624i	1.24661	+	0.905717i
$28$	−0.809017	−	0.587785i	−0.152890	−	0.111081i
$29$	0.813681	−	2.50425i	0.151097	−	0.465028i	−0.846648	−	0.532154i	$-0.821383\pi$
$29$	0.813681	−	2.50425i	0.151097	−	0.465028i	0.997745	+	0.0671257i	$0.0213829\pi$
$30$	0.912128	+	2.80724i	0.166531	+	0.512530i
$31$	2.60621	−	1.89352i	0.468089	−	0.340086i	−0.328607	−	0.944467i	$-0.606579\pi$
$31$	2.60621	−	1.89352i	0.468089	−	0.340086i	0.796696	+	0.604380i	$0.206579\pi$
$32$	1.00000			0.176777
$33$	−9.58136	+	2.00897i	−1.66790	+	0.349717i
$34$	−0.469771			−0.0805650
$35$	0.809017	−	0.587785i	0.136749	−	0.0993538i
$36$	1.76528	+	5.43299i	0.294214	+	0.905498i
$37$	−1.40934	+	4.33749i	−0.231693	+	0.713079i	0.765849	+	0.643020i	$0.222319\pi$
$37$	−1.40934	+	4.33749i	−0.231693	+	0.713079i	−0.997543	+	0.0700590i	$0.977681\pi$
$38$	3.27266	+	2.37773i	0.530896	+	0.385718i
$39$	13.8523	+	10.0643i	2.21815	+	1.61158i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	0.563872	+	1.73542i	0.0880621	+	0.271027i	0.985384	−	0.170350i	$-0.0544900\pi$
$41$	0.563872	+	1.73542i	0.0880621	+	0.271027i	−0.897321	+	0.441378i	$0.854490\pi$
$42$	2.38798	−	1.73497i	0.368474	−	0.267712i
$43$	−0.790717			−0.120583			−0.0602916	−	0.998181i	$-0.519203\pi$
$43$	−0.790717			−0.120583			−0.0602916	+	0.998181i	$0.519203\pi$
$44$	−3.02615	−	1.35735i	−0.456210	−	0.204627i
$45$	−5.71258			−0.851581
$46$	6.22805	−	4.52495i	0.918276	−	0.667167i
$47$	−1.32435	−	4.07592i	−0.193176	−	0.594534i	−0.999993	−	0.00373276i	$-0.998812\pi$
$47$	−1.32435	−	4.07592i	−0.193176	−	0.594534i	0.806817	−	0.590801i	$-0.201188\pi$
$48$	−0.912128	+	2.80724i	−0.131654	+	0.405190i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$	0.428491	−	1.31876i	0.0600008	−	0.184663i
$52$	1.79256	+	5.51694i	0.248584	+	0.765062i
$53$	−11.2778	+	8.19378i	−1.54912	+	1.12550i	−0.604846	+	0.796343i	$0.706765\pi$
$53$	−11.2778	+	8.19378i	−1.54912	+	1.12550i	−0.944274	+	0.329159i	$0.893235\pi$
$54$	−8.00674			−1.08958
$55$	2.22605	−	2.45860i	0.300160	−	0.331518i
$56$	1.00000			0.133631
$57$	−9.65994	+	7.01836i	−1.27949	+	0.929604i
$58$	0.813681	+	2.50425i	0.106842	+	0.328824i
$59$	−4.02897	+	12.3999i	−0.524528	+	1.61433i	0.240721	+	0.970594i	$0.422616\pi$
$59$	−4.02897	+	12.3999i	−0.524528	+	1.61433i	−0.765248	+	0.643735i	$0.777384\pi$
$60$	−2.38798	−	1.73497i	−0.308287	−	0.223984i
$61$	5.41759	+	3.93611i	0.693651	+	0.503967i	0.877858	−	0.478920i	$-0.158972\pi$
$61$	5.41759	+	3.93611i	0.693651	+	0.503967i	−0.184207	+	0.982887i	$0.558972\pi$
$62$	−0.995482	+	3.06378i	−0.126426	+	0.389100i
$63$	1.76528	+	5.43299i	0.222405	+	0.684492i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−5.80086			−0.719508
$66$	6.57064	−	7.25707i	0.808789	−	0.893284i
$67$	−6.73018			−0.822223			−0.411111	−	0.911585i	$-0.634859\pi$
$67$	−6.73018			−0.822223			−0.411111	+	0.911585i	$0.634859\pi$
$68$	0.380053	−	0.276124i	0.0460881	−	0.0334850i
$69$	7.02183	+	21.6110i	0.845329	+	2.60166i
$70$	−0.309017	+	0.951057i	−0.0369346	+	0.113673i
$71$	−9.29195	−	6.75100i	−1.10275	−	0.801196i	−0.121245	−	0.992623i	$-0.538689\pi$
$71$	−9.29195	−	6.75100i	−1.10275	−	0.801196i	−0.981507	+	0.191427i	$0.938689\pi$
$72$	−4.62157	−	3.35777i	−0.544658	−	0.395717i
$73$	3.78691	−	11.6549i	0.443225	−	1.36410i	−0.441195	−	0.897411i	$-0.645445\pi$
$73$	3.78691	−	11.6549i	0.443225	−	1.36410i	0.884419	−	0.466693i	$-0.154555\pi$
$74$	−1.40934	−	4.33749i	−0.163832	−	0.504223i
$75$	2.38798	−	1.73497i	0.275740	−	0.200337i
$76$	−4.04523			−0.464020
$77$	−3.02615	−	1.35735i	−0.344862	−	0.154684i
$78$	−17.1224			−1.93873
$79$	−3.19789	+	2.32340i	−0.359791	+	0.261403i	−0.752965	−	0.658061i	$-0.771377\pi$
$79$	−3.19789	+	2.32340i	−0.359791	+	0.261403i	0.393174	+	0.919464i	$0.371377\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$	2.00732	−	6.17789i	0.223035	−	0.686432i
$82$	−1.47624	−	1.07255i	−0.163023	−	0.118443i
$83$	7.64360	+	5.55340i	0.838994	+	0.609565i	0.922089	−	0.386977i	$-0.126481\pi$
$83$	7.64360	+	5.55340i	0.838994	+	0.609565i	−0.0830954	+	0.996542i	$0.526481\pi$
$84$	−0.912128	+	2.80724i	−0.0995213	+	0.306295i
$85$	0.145167	+	0.446779i	0.0157456	+	0.0484599i
$86$	0.639704	−	0.464772i	0.0689810	−	0.0501176i
$87$	−7.77222			−0.833269
$88$	3.24604	−	0.680614i	0.346029	−	0.0725537i
$89$	−11.2766			−1.19532			−0.597659	−	0.801751i	$-0.703902\pi$
$89$	−11.2766			−1.19532			−0.597659	+	0.801751i	$0.703902\pi$
$90$	4.62157	−	3.35777i	0.487157	−	0.353940i
$91$	1.79256	+	5.51694i	0.187912	+	0.578333i
$92$	−2.37891	+	7.32152i	−0.248018	+	0.763321i
$93$	−7.69276	−	5.58912i	−0.797702	−	0.579565i
$94$	3.46718	+	2.51906i	0.357613	+	0.259821i
$95$	1.25005	−	3.84724i	0.128252	−	0.394719i
$96$	−0.912128	−	2.80724i	−0.0930937	−	0.286513i
$97$	13.5518	−	9.84599i	1.37598	−	0.999709i	0.378739	−	0.925504i	$-0.376358\pi$
$97$	13.5518	−	9.84599i	1.37598	−	0.999709i	0.997243	−	0.0742056i	$-0.0236421\pi$
$98$	1.00000			0.101015
$99$	9.42794	+	16.4342i	0.947544	+	1.65170i
$100$	1.00000			0.100000
$101$	6.93358	−	5.03754i	0.689917	−	0.501254i	−0.186716	−	0.982414i	$-0.559784\pi$
$101$	6.93358	−	5.03754i	0.689917	−	0.501254i	0.876633	+	0.481160i	$0.159784\pi$
$102$	0.428491	+	1.31876i	0.0424269	+	0.130577i
$103$	0.742064	−	2.28384i	0.0731177	−	0.225033i	−0.907818	−	0.419363i	$-0.862253\pi$
$103$	0.742064	−	2.28384i	0.0731177	−	0.225033i	0.980936	+	0.194330i	$0.0622533\pi$
$104$	−4.69299	−	3.40966i	−0.460186	−	0.334344i
$105$	−2.38798	−	1.73497i	−0.233043	−	0.169316i
$106$	4.30772	−	13.2578i	0.418403	−	1.28771i
$107$	1.87315	+	5.76496i	0.181084	+	0.557320i	0.999859	−	0.0167951i	$-0.00534630\pi$
$107$	1.87315	+	5.76496i	0.181084	+	0.557320i	−0.818775	+	0.574115i	$0.805346\pi$
$108$	6.47759	−	4.70624i	0.623306	−	0.452859i
$109$	10.8776			1.04188			0.520942	−	0.853592i	$-0.325581\pi$
$109$	10.8776			1.04188			0.520942	+	0.853592i	$0.325581\pi$
$110$	−0.355779	+	3.29749i	−0.0339222	+	0.314403i
$111$	13.4619			1.27774
$112$	−0.809017	+	0.587785i	−0.0764449	+	0.0555405i
$113$	−2.01667	−	6.20668i	−0.189713	−	0.583875i	0.810285	−	0.586036i	$-0.199312\pi$
$113$	−2.01667	−	6.20668i	−0.189713	−	0.583875i	−0.999998	+	0.00216065i	$0.999312\pi$
$114$	3.68977	−	11.3559i	0.345578	−	1.06358i
$115$	−6.22805	−	4.52495i	−0.580769	−	0.421953i
$116$	−2.13024	−	1.54771i	−0.197788	−	0.143702i
$117$	10.2402	−	31.5160i	0.946703	−	2.91365i
$118$	−4.02897	−	12.3999i	−0.370897	−	1.14150i
$119$	0.380053	−	0.276124i	0.0348394	−	0.0253123i
$120$	2.95171			0.269453
$121$	−10.7468	−	2.34635i	−0.976986	−	0.213305i
$122$	−6.69651			−0.606274
$123$	4.35742	−	3.16585i	0.392895	−	0.285455i
$124$	−0.995482	−	3.06378i	−0.0893970	−	0.275136i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	−4.62157	−	3.35777i	−0.411722	−	0.299134i
$127$	3.27438	+	2.37898i	0.290554	+	0.211100i	0.723508	−	0.690316i	$-0.242529\pi$
$127$	3.27438	+	2.37898i	0.290554	+	0.211100i	−0.432954	+	0.901416i	$0.642529\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	0.721235	+	2.21973i	0.0635012	+	0.195437i
$130$	4.69299	−	3.40966i	0.411603	−	0.299047i
$131$	9.05921			0.791507			0.395753	−	0.918357i	$-0.370484\pi$
$131$	9.05921			0.791507			0.395753	+	0.918357i	$0.370484\pi$
$132$	−1.05015	+	9.73322i	−0.0914042	+	0.847168i
$133$	−4.04523			−0.350766
$134$	5.44483	−	3.95590i	0.470362	−	0.341738i
$135$	2.47422	+	7.61486i	0.212947	+	0.655383i
$136$	−0.145167	+	0.446779i	−0.0124480	+	0.0383110i
$137$	−14.2590	−	10.3597i	−1.21823	−	0.885093i	−0.222274	−	0.974984i	$-0.571348\pi$
$137$	−14.2590	−	10.3597i	−1.21823	−	0.885093i	−0.995952	+	0.0898917i	$0.971348\pi$
$138$	−18.3834	−	13.3563i	−1.56490	−	1.13697i
$139$	5.76834	−	17.7531i	0.489264	−	1.50580i	−0.336445	−	0.941703i	$-0.609225\pi$
$139$	5.76834	−	17.7531i	0.489264	−	1.50580i	0.825709	−	0.564097i	$-0.190775\pi$
$140$	−0.309017	−	0.951057i	−0.0261167	−	0.0803789i
$141$	−10.2341	+	7.43552i	−0.861868	+	0.626184i
$142$	11.4855			0.963840
$143$	9.57364	+	16.6882i	0.800588	+	1.39553i
$144$	5.71258			0.476048
$145$	2.13024	−	1.54771i	0.176907	−	0.128531i
$146$	3.78691	+	11.6549i	0.313407	+	0.964568i
$147$	−0.912128	+	2.80724i	−0.0752310	+	0.231537i
$148$	3.68969	+	2.68072i	0.303291	+	0.220354i
$149$	−10.5461	−	7.66218i	−0.863969	−	0.627710i	0.0649927	−	0.997886i	$-0.479298\pi$
$149$	−10.5461	−	7.66218i	−0.863969	−	0.627710i	−0.928962	+	0.370175i	$0.879298\pi$
$150$	−0.912128	+	2.80724i	−0.0744749	+	0.229210i
$151$	−2.83374	−	8.72136i	−0.230607	−	0.709734i	−0.997674	−	0.0681674i	$-0.978285\pi$
$151$	−2.83374	−	8.72136i	−0.230607	−	0.709734i	0.767067	−	0.641567i	$-0.221715\pi$
$152$	3.27266	−	2.37773i	0.265448	−	0.192859i
$153$	−2.68360			−0.216956
$154$	3.24604	−	0.680614i	0.261573	−	0.0548454i
$155$	3.22145			0.258753
$156$	13.8523	−	10.0643i	1.10907	−	0.805790i
$157$	2.80064	+	8.61948i	0.223515	+	0.687909i	0.998439	+	0.0558544i	$0.0177883\pi$
$157$	2.80064	+	8.61948i	0.223515	+	0.687909i	−0.774924	+	0.632055i	$0.782212\pi$
$158$	1.22149	−	3.75935i	0.0971762	−	0.299078i
$159$	33.2887	+	24.1856i	2.63996	+	1.91805i
$160$	0.809017	+	0.587785i	0.0639584	+	0.0464685i
$161$	−2.37891	+	7.32152i	−0.187484	+	0.577016i
$162$	2.00732	+	6.17789i	0.157710	+	0.485381i
$163$	1.37306	−	0.997585i	0.107546	−	0.0781369i	−0.532712	−	0.846296i	$-0.678827\pi$
$163$	1.37306	−	0.997585i	0.107546	−	0.0781369i	0.640259	+	0.768159i	$0.278827\pi$
$164$	1.82473			0.142487
$165$	−8.93233	−	4.00649i	−0.695381	−	0.311905i
$166$	−9.44801			−0.733308
$167$	−16.0624	+	11.6700i	−1.24295	+	0.903054i	−0.997791	−	0.0664300i	$-0.978839\pi$
$167$	−16.0624	+	11.6700i	−1.24295	+	0.903054i	−0.245156	+	0.969484i	$0.578839\pi$
$168$	−0.912128	−	2.80724i	−0.0703722	−	0.216583i
$169$	6.38118	−	19.6393i	0.490860	−	1.51071i
$170$	−0.380053	−	0.276124i	−0.0291487	−	0.0211778i
$171$	18.6953	+	13.5830i	1.42967	+	1.03871i
$172$	−0.244345	+	0.752017i	−0.0186311	+	0.0573407i
$173$	−3.86844	−	11.9058i	−0.294112	−	0.905185i	−0.983518	−	0.180809i	$-0.942128\pi$
$173$	−3.86844	−	11.9058i	−0.294112	−	0.905185i	0.689406	−	0.724375i	$-0.257872\pi$
$174$	6.28786	−	4.56840i	0.476681	−	0.346329i
$175$	1.00000			0.0755929
$176$	−2.22605	+	2.45860i	−0.167794	+	0.185324i
$177$	38.4845			2.89267
$178$	9.12296	−	6.62822i	0.683795	−	0.496806i
$179$	−5.03316	−	15.4905i	−0.376196	−	1.15781i	−0.942668	−	0.333732i	$-0.891692\pi$
$179$	−5.03316	−	15.4905i	−0.376196	−	1.15781i	0.566472	−	0.824081i	$-0.308308\pi$
$180$	−1.76528	+	5.43299i	−0.131576	+	0.404951i
$181$	9.57727	+	6.95829i	0.711873	+	0.517206i	0.883777	−	0.467908i	$-0.154992\pi$
$181$	9.57727	+	6.95829i	0.711873	+	0.517206i	−0.171904	+	0.985114i	$0.554992\pi$
$182$	−4.69299	−	3.40966i	−0.347868	−	0.252741i
$183$	6.10807	−	18.7987i	0.451522	−	1.38964i
$184$	−2.37891	−	7.32152i	−0.175375	−	0.539749i
$185$	−3.68969	+	2.68072i	−0.271271	+	0.197090i
$186$	9.50878			0.697217
$187$	1.04573	−	1.15498i	0.0764714	−	0.0844605i
$188$	−4.28567			−0.312565
$189$	6.47759	−	4.70624i	0.471175	−	0.342329i
$190$	1.25005	+	3.84724i	0.0906878	+	0.279108i
$191$	−8.44687	+	25.9968i	−0.611194	+	1.88106i	−0.164493	+	0.986378i	$0.552599\pi$
$191$	−8.44687	+	25.9968i	−0.611194	+	1.88106i	−0.446701	+	0.894683i	$0.647401\pi$
$192$	2.38798	+	1.73497i	0.172338	+	0.125211i
$193$	−13.6346	−	9.90612i	−0.981441	−	0.713058i	−0.0234104	−	0.999726i	$-0.507452\pi$
$193$	−13.6346	−	9.90612i	−0.981441	−	0.713058i	−0.958030	+	0.286668i	$0.907452\pi$
$194$	−5.17635	+	15.9312i	−0.371640	+	1.14379i
$195$	5.29112	+	16.2844i	0.378905	+	1.16615i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	−4.65860			−0.331911			−0.165956	−	0.986133i	$-0.553071\pi$
$197$	−4.65860			−0.331911			−0.165956	+	0.986133i	$0.553071\pi$
$198$	−17.2871	−	7.75394i	−1.22854	−	0.551049i
$199$	−12.2080			−0.865404			−0.432702	−	0.901537i	$-0.642440\pi$
$199$	−12.2080			−0.865404			−0.432702	+	0.901537i	$0.642440\pi$
$200$	−0.809017	+	0.587785i	−0.0572061	+	0.0415627i
$201$	6.13879	+	18.8932i	0.432997	+	1.33263i
$202$	−2.64839	+	8.15091i	−0.186340	+	0.573496i
$203$	−2.13024	−	1.54771i	−0.149514	−	0.108628i
$204$	−1.12180	−	0.815038i	−0.0785420	−	0.0570641i
$205$	−0.563872	+	1.73542i	−0.0393825	+	0.121207i
$206$	0.742064	+	2.28384i	0.0517020	+	0.159122i
$207$	35.5783	−	25.8491i	2.47286	−	1.79664i
$208$	5.80086			0.402217
$209$	−13.1310	+	2.75324i	−0.908289	+	0.190446i
$210$	2.95171			0.203687
$211$	6.36608	−	4.62522i	0.438259	−	0.318414i	−0.346684	−	0.937982i	$-0.612692\pi$
$211$	6.36608	−	4.62522i	0.438259	−	0.318414i	0.784943	+	0.619568i	$0.212692\pi$
$212$	4.30772	+	13.2578i	0.295856	+	0.910550i
$213$	−10.4762	+	32.2425i	−0.717819	+	2.20922i
$214$	−4.90397	−	3.56294i	−0.335228	−	0.243558i
$215$	−0.639704	−	0.464772i	−0.0436274	−	0.0316972i
$216$	−2.47422	+	7.61486i	−0.168349	+	0.518126i
$217$	−0.995482	−	3.06378i	−0.0675778	−	0.207983i
$218$	−8.80015	+	6.39369i	−0.596022	+	0.433035i
$219$	−36.1723			−2.44430
$220$	−1.65038	−	2.87684i	−0.111269	−	0.193957i
$221$	−2.72507			−0.183308
$222$	−10.8909	+	7.91269i	−0.730948	+	0.531065i
$223$	−7.37480	−	22.6973i	−0.493853	−	1.51992i	−0.818736	−	0.574170i	$-0.805325\pi$
$223$	−7.37480	−	22.6973i	−0.493853	−	1.51992i	0.324883	−	0.945754i	$-0.394675\pi$
$224$	0.309017	−	0.951057i	0.0206471	−	0.0635451i
$225$	−4.62157	−	3.35777i	−0.308105	−	0.223851i
$226$	5.27972	+	3.83594i	0.351202	+	0.255163i
$227$	7.01614	−	21.5935i	0.465677	−	1.43321i	−0.392451	−	0.919773i	$-0.628373\pi$
$227$	7.01614	−	21.5935i	0.465677	−	1.43321i	0.858128	−	0.513435i	$-0.171627\pi$
$228$	3.68977	+	11.3559i	0.244361	+	0.752065i
$229$	12.8394	−	9.32835i	0.848450	−	0.616435i	−0.0762684	−	0.997087i	$-0.524301\pi$
$229$	12.8394	−	9.32835i	0.848450	−	0.616435i	0.924718	+	0.380653i	$0.124301\pi$
$230$	7.69830			0.507611
$231$	−1.05015	+	9.73322i	−0.0690951	+	0.640399i
$232$	2.63313			0.172873
$233$	23.6579	−	17.1885i	1.54988	−	1.12605i	0.606146	−	0.795353i	$-0.292715\pi$
$233$	23.6579	−	17.1885i	1.54988	−	1.12605i	0.943735	−	0.330701i	$-0.107285\pi$
$234$	10.2402	+	31.5160i	0.669420	+	2.06026i
$235$	1.32435	−	4.07592i	0.0863908	−	0.265884i
$236$	10.5480	+	7.66356i	0.686615	+	0.498855i
$237$	9.43924	+	6.85801i	0.613145	+	0.445476i
$238$	−0.145167	+	0.446779i	−0.00940979	+	0.0289604i
$239$	−2.69700	−	8.30051i	−0.174454	−	0.536915i	0.825154	−	0.564908i	$-0.191088\pi$
$239$	−2.69700	−	8.30051i	−0.174454	−	0.536915i	−0.999608	+	0.0279929i	$0.991088\pi$
$240$	−2.38798	+	1.73497i	−0.154144	+	0.111992i
$241$	−9.58858			−0.617655			−0.308828	−	0.951118i	$-0.599937\pi$
$241$	−9.58858			−0.617655			−0.308828	+	0.951118i	$0.599937\pi$
$242$	10.0735	−	4.41860i	0.647551	−	0.284038i
$243$	4.84646			0.310900
$244$	5.41759	−	3.93611i	0.346826	−	0.251984i
$245$	−0.309017	−	0.951057i	−0.0197424	−	0.0607608i
$246$	−1.66439	+	5.12245i	−0.106117	+	0.326596i
$247$	18.9842	+	13.7929i	1.20794	+	0.877618i
$248$	2.60621	+	1.89352i	0.165494	+	0.120239i
$249$	8.61779	−	26.5228i	0.546130	−	1.68082i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	−2.18486	+	1.58740i	−0.137907	+	0.100196i	−0.654600	−	0.755975i	$-0.727163\pi$
$251$	−2.18486	+	1.58740i	−0.137907	+	0.100196i	0.516693	+	0.856171i	$0.327163\pi$
$252$	5.71258			0.359859
$253$	−2.73889	+	25.3850i	−0.172193	+	1.59594i
$254$	−4.04736			−0.253954
$255$	1.12180	−	0.815038i	0.0702501	−	0.0510397i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	2.75904	−	8.49146i	0.172104	−	0.529682i	−0.827385	−	0.561635i	$-0.810173\pi$
$257$	2.75904	−	8.49146i	0.172104	−	0.529682i	0.999489	+	0.0319525i	$0.0101725\pi$
$258$	−1.88822	−	1.37187i	−0.117555	−	0.0854090i
$259$	3.68969	+	2.68072i	0.229266	+	0.166572i
$260$	−1.79256	+	5.51694i	−0.111170	+	0.342146i
$261$	4.64822	+	14.3057i	0.287717	+	0.885503i
$262$	−7.32905	+	5.32487i	−0.452790	+	0.328971i
$263$	0.182846			0.0112748			0.00563739	−	0.999984i	$-0.498206\pi$
$263$	0.182846			0.0112748			0.00563739	+	0.999984i	$0.498206\pi$
$264$	−4.87145	−	8.49160i	−0.299817	−	0.522622i
$265$	−13.9401			−0.856333
$266$	3.27266	−	2.37773i	0.200660	−	0.145788i
$267$	10.2857	+	31.6561i	0.629475	+	1.93732i
$268$	−2.07974	+	6.40079i	−0.127040	+	0.390990i
$269$	4.62385	+	3.35942i	0.281921	+	0.204828i	0.719755	−	0.694228i	$-0.244254\pi$
$269$	4.62385	+	3.35942i	0.281921	+	0.204828i	−0.437834	+	0.899056i	$0.644254\pi$
$270$	−6.47759	−	4.70624i	−0.394213	−	0.286413i
$271$	−0.958200	+	2.94904i	−0.0582065	+	0.179141i	−0.975932	−	0.218073i	$-0.930023\pi$
$271$	−0.958200	+	2.94904i	−0.0582065	+	0.179141i	0.917726	+	0.397214i	$0.130023\pi$
$272$	−0.145167	−	0.446779i	−0.00880205	−	0.0270899i
$273$	13.8523	−	10.0643i	0.838382	−	0.609120i
$274$	17.6250			1.06477
$275$	3.24604	−	0.680614i	0.195743	−	0.0410426i
$276$	22.7231			1.36777
$277$	−17.3882	+	12.6332i	−1.04475	+	0.759058i	−0.971208	−	0.238234i	$-0.923432\pi$
$277$	−17.3882	+	12.6332i	−1.04475	+	0.759058i	−0.0735459	+	0.997292i	$0.523432\pi$
$278$	5.76834	+	17.7531i	0.345962	+	1.06476i
$279$	−5.68677	+	17.5021i	−0.340458	+	1.04782i
$280$	0.809017	+	0.587785i	0.0483480	+	0.0351269i
$281$	9.51149	+	6.91050i	0.567408	+	0.412246i	0.834163	−	0.551518i	$-0.185951\pi$
$281$	9.51149	+	6.91050i	0.567408	+	0.412246i	−0.266755	+	0.963764i	$0.585951\pi$
$282$	3.90908	−	12.0309i	0.232782	−	0.716431i
$283$	1.19879	+	3.68948i	0.0712604	+	0.219317i	0.980344	−	0.197297i	$-0.0632165\pi$
$283$	1.19879	+	3.68948i	0.0712604	+	0.219317i	−0.909083	+	0.416615i	$0.863216\pi$
$284$	−9.29195	+	6.75100i	−0.551376	+	0.400598i
$285$	−11.9403			−0.707285
$286$	−17.5543	−	7.87377i	−1.03801	−	0.465586i
$287$	1.82473			0.107710
$288$	−4.62157	+	3.35777i	−0.272329	+	0.197858i
$289$	−5.18509	−	15.9581i	−0.305006	−	0.938710i
$290$	−0.813681	+	2.50425i	−0.0477810	+	0.147055i
$291$	−40.0011	−	29.0625i	−2.34491	−	1.70367i
$292$	−9.91426	−	7.20313i	−0.580188	−	0.421532i
$293$	−9.45846	+	29.1101i	−0.552569	+	1.70063i	0.149709	+	0.988730i	$0.452166\pi$
$293$	−9.45846	+	29.1101i	−0.552569	+	1.70063i	−0.702278	+	0.711903i	$0.747834\pi$
$294$	−0.912128	−	2.80724i	−0.0531964	−	0.163722i
$295$	−10.5480	+	7.66356i	−0.614128	+	0.446190i
$296$	−4.56071			−0.265086
$297$	17.8234	−	19.6854i	1.03422	−	1.14226i
$298$	13.0357			0.755137
$299$	36.1281	−	26.2486i	2.08934	−	1.51799i
$300$	−0.912128	−	2.80724i	−0.0526617	−	0.162076i
$301$	−0.244345	+	0.752017i	−0.0140838	+	0.0433455i
$302$	7.41883	+	5.39010i	0.426906	+	0.310165i
$303$	−20.4659	−	14.8693i	−1.17573	−	0.854221i
$304$	−1.25005	+	3.84724i	−0.0716950	+	0.220655i
$305$	2.06934	+	6.36876i	0.118490	+	0.364674i
$306$	2.17108	−	1.57738i	0.124112	−	0.0901729i
$307$	−2.56751			−0.146536			−0.0732678	−	0.997312i	$-0.523343\pi$
$307$	−2.56751			−0.146536			−0.0732678	+	0.997312i	$0.523343\pi$
$308$	−2.22605	+	2.45860i	−0.126841	+	0.140092i
$309$	−7.08814			−0.403230
$310$	−2.60621	+	1.89352i	−0.148023	+	0.107545i
$311$	−10.0518	−	30.9364i	−0.569987	−	1.75424i	−0.652646	−	0.757663i	$-0.726341\pi$
$311$	−10.0518	−	30.9364i	−0.569987	−	1.75424i	0.0826588	−	0.996578i	$-0.473659\pi$
$312$	−5.29112	+	16.2844i	−0.299551	+	0.921923i
$313$	6.30013	+	4.57731i	0.356104	+	0.258725i	0.751425	−	0.659818i	$-0.229367\pi$
$313$	6.30013	+	4.57731i	0.356104	+	0.258725i	−0.395321	+	0.918543i	$0.629367\pi$
$314$	−7.33217	−	5.32713i	−0.413778	−	0.300627i
$315$	−1.76528	+	5.43299i	−0.0994625	+	0.306114i
$316$	1.22149	+	3.75935i	0.0687140	+	0.211480i
$317$	14.1321	−	10.2675i	0.793736	−	0.576683i	−0.115334	−	0.993327i	$-0.536794\pi$
$317$	14.1321	−	10.2675i	0.793736	−	0.576683i	0.909070	+	0.416644i	$0.136794\pi$
$318$	−41.1471			−2.30741
$319$	−7.96825	−	3.57406i	−0.446136	−	0.200109i
$320$	−1.00000			−0.0559017
$321$	14.4751	−	10.5168i	0.807920	−	0.586988i
$322$	−2.37891	−	7.32152i	−0.132571	−	0.408012i
$323$	0.587235	−	1.80732i	0.0326746	−	0.100562i
$324$	−5.25523	−	3.81815i	−0.291957	−	0.212119i
$325$	−4.69299	−	3.40966i	−0.260320	−	0.189134i
$326$	−0.524462	+	1.61413i	−0.0290472	+	0.0893982i
$327$	−9.92175	−	30.5360i	−0.548674	−	1.68865i
$328$	−1.47624	+	1.07255i	−0.0815115	+	0.0592216i
$329$	−4.28567			−0.236277
$330$	9.58136	−	2.00897i	0.527436	−	0.110590i
$331$	−2.01742			−0.110887			−0.0554437	−	0.998462i	$-0.517657\pi$
$331$	−2.01742			−0.110887			−0.0554437	+	0.998462i	$0.517657\pi$
$332$	7.64360	−	5.55340i	0.419497	−	0.304782i
$333$	−8.05094	−	24.7783i	−0.441189	−	1.35784i
$334$	6.13530	−	18.8825i	0.335708	−	1.03320i
$335$	−5.44483	−	3.95590i	−0.297483	−	0.216134i
$336$	2.38798	+	1.73497i	0.130275	+	0.0946504i
$337$	7.21021	−	22.1908i	0.392765	−	1.20881i	−0.537923	−	0.842994i	$-0.680791\pi$
$337$	7.21021	−	22.1908i	0.392765	−	1.20881i	0.930688	−	0.365813i	$-0.119209\pi$
$338$	6.38118	+	19.6393i	0.347091	+	1.06823i
$339$	−15.5842	+	11.3226i	−0.846416	+	0.614958i
$340$	0.469771			0.0254769
$341$	−5.31663	−	9.26761i	−0.287911	−	0.501869i
$342$	−23.1087			−1.24958
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	−0.244345	−	0.752017i	−0.0131742	−	0.0405460i
$345$	−7.02183	+	21.6110i	−0.378043	+	1.16350i
$346$	10.1277	+	7.35822i	0.544469	+	0.395580i
$347$	−6.64391	−	4.82708i	−0.356664	−	0.259131i	0.394996	−	0.918683i	$-0.370746\pi$
$347$	−6.64391	−	4.82708i	−0.356664	−	0.259131i	−0.751659	+	0.659552i	$0.770746\pi$
$348$	−2.40175	+	7.39182i	−0.128747	+	0.396243i
$349$	−5.43962	−	16.7414i	−0.291176	−	0.896148i	−0.984479	−	0.175502i	$-0.943845\pi$
$349$	−5.43962	−	16.7414i	−0.291176	−	0.896148i	0.693303	−	0.720646i	$-0.256155\pi$
$350$	−0.809017	+	0.587785i	−0.0432438	+	0.0314184i
$351$	−46.4460			−2.47910
$352$	0.355779	−	3.29749i	0.0189631	−	0.175757i
$353$	−34.5532			−1.83908			−0.919541	−	0.392994i	$-0.871439\pi$
$353$	−34.5532			−1.83908			−0.919541	+	0.392994i	$0.871439\pi$
$354$	−31.1346	+	22.6206i	−1.65478	+	1.20227i
$355$	−3.54921	−	10.9233i	−0.188372	−	0.579751i
$356$	−3.48466	+	10.7247i	−0.184687	+	0.568407i
$357$	−1.12180	−	0.815038i	−0.0593722	−	0.0431364i
$358$	13.1770	+	9.57364i	0.696425	+	0.505983i
$359$	−2.58431	+	7.95370i	−0.136395	+	0.419780i	−0.995804	−	0.0915076i	$-0.970831\pi$
$359$	−2.58431	+	7.95370i	−0.136395	+	0.419780i	0.859409	+	0.511288i	$0.170831\pi$
$360$	−1.76528	−	5.43299i	−0.0930386	−	0.286343i
$361$	2.13265	−	1.54946i	0.112245	−	0.0815507i
$362$	−11.8382			−0.622200
$363$	3.21572	+	32.3092i	0.168782	+	1.69579i
$364$	5.80086			0.304048
$365$	9.91426	−	7.20313i	0.518936	−	0.377029i
$366$	6.10807	+	18.7987i	0.319274	+	0.982625i
$367$	5.33662	−	16.4244i	0.278569	−	0.857349i	−0.709683	−	0.704521i	$-0.751162\pi$
$367$	5.33662	−	16.4244i	0.278569	−	0.857349i	0.988253	−	0.152828i	$-0.0488380\pi$
$368$	6.22805	+	4.52495i	0.324660	+	0.235879i
$369$	−8.43312	−	6.12702i	−0.439011	−	0.318960i
$370$	1.40934	−	4.33749i	0.0732679	−	0.225495i
$371$	4.30772	+	13.2578i	0.223646	+	0.688311i
$372$	−7.69276	+	5.58912i	−0.398851	+	0.289782i
$373$	−22.9242			−1.18697			−0.593486	−	0.804844i	$-0.702249\pi$
$373$	−22.9242			−1.18697			−0.593486	+	0.804844i	$0.702249\pi$
$374$	−0.167134	+	1.54906i	−0.00864232	+	0.0801002i
$375$	2.95171			0.152426
$376$	3.46718	−	2.51906i	0.178806	−	0.129910i
$377$	4.72005	+	14.5268i	0.243095	+	0.748169i
$378$	−2.47422	+	7.61486i	−0.127260	+	0.391666i
$379$	−3.08947	−	2.24463i	−0.158696	−	0.115299i	0.505603	−	0.862766i	$-0.331270\pi$
$379$	−3.08947	−	2.24463i	−0.158696	−	0.115299i	−0.664299	+	0.747467i	$0.731270\pi$
$380$	−3.27266	−	2.37773i	−0.167884	−	0.121975i
$381$	3.69171	−	11.3619i	0.189132	−	0.582088i
$382$	−8.44687	−	25.9968i	−0.432179	−	1.33011i
$383$	9.49579	−	6.89910i	0.485212	−	0.352527i	−0.318128	−	0.948048i	$-0.603054\pi$
$383$	9.49579	−	6.89910i	0.485212	−	0.352527i	0.803340	+	0.595520i	$0.203054\pi$
$384$	−2.95171			−0.150629
$385$	−1.65038	−	2.87684i	−0.0841113	−	0.146618i
$386$	16.8533			0.857810
$387$	3.65436	−	2.65505i	0.185761	−	0.134964i
$388$	−5.17635	−	15.9312i	−0.262789	−	0.808782i
$389$	−2.46329	+	7.58123i	−0.124894	+	0.384384i	−0.993882	−	0.110450i	$-0.964771\pi$
$389$	−2.46329	+	7.58123i	−0.124894	+	0.384384i	0.868988	+	0.494833i	$0.164771\pi$
$390$	−13.8523	−	10.0643i	−0.701441	−	0.509626i
$391$	−2.92576	−	2.12569i	−0.147962	−	0.107501i
$392$	0.309017	−	0.951057i	0.0156077	−	0.0480356i
$393$	−8.26316	−	25.4314i	−0.416821	−	1.28284i
$394$	3.76888	−	2.73826i	0.189874	−	0.137951i
$395$	−3.95281			−0.198888
$396$	18.5432	−	3.88806i	0.931833	−	0.195382i
$397$	0.554176			0.0278133			0.0139066	−	0.999903i	$-0.495573\pi$
$397$	0.554176			0.0278133			0.0139066	+	0.999903i	$0.495573\pi$
$398$	9.87650	−	7.17570i	0.495064	−	0.359685i
$399$	3.68977	+	11.3559i	0.184719	+	0.568508i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	9.58036	+	6.96054i	0.478420	+	0.347593i	0.800714	−	0.599047i	$-0.204454\pi$
$401$	9.58036	+	6.96054i	0.478420	+	0.347593i	−0.322293	+	0.946640i	$0.604454\pi$
$402$	−16.0716	−	11.6767i	−0.801576	−	0.582379i
$403$	−5.77465	+	17.7725i	−0.287656	+	0.885314i
$404$	−2.64839	−	8.15091i	−0.131762	−	0.405523i
$405$	5.25523	−	3.81815i	0.261134	−	0.189725i
$406$	2.63313			0.130680
$407$	13.8014	+	6.19045i	0.684110	+	0.306849i
$408$	1.38663			0.0686482
$409$	6.77783	−	4.92438i	0.335142	−	0.243495i	−0.407467	−	0.913220i	$-0.633588\pi$
$409$	6.77783	−	4.92438i	0.335142	−	0.243495i	0.742609	+	0.669725i	$0.233588\pi$
$410$	−0.563872	−	1.73542i	−0.0278477	−	0.0857063i
$411$	−16.0763	+	49.4778i	−0.792985	+	2.44056i
$412$	−1.94275	−	1.41149i	−0.0957123	−	0.0695391i
$413$	10.5480	+	7.66356i	0.519033	+	0.377099i
$414$	−13.5897	+	41.8247i	−0.667896	+	2.05557i
$415$	2.91960	+	8.98559i	0.143317	+	0.441085i
$416$	−4.69299	+	3.40966i	−0.230093	+	0.167172i
$417$	−55.0987			−2.69820
$418$	9.00487	−	9.94561i	0.440442	−	0.486456i
$419$	−25.1963			−1.23092			−0.615461	−	0.788167i	$-0.711030\pi$
$419$	−25.1963			−1.23092			−0.615461	+	0.788167i	$0.711030\pi$
$420$	−2.38798	+	1.73497i	−0.116522	+	0.0846579i
$421$	8.35379	+	25.7103i	0.407139	+	1.25304i	0.919096	+	0.394033i	$0.128921\pi$
$421$	8.35379	+	25.7103i	0.407139	+	1.25304i	−0.511957	+	0.859011i	$0.671079\pi$
$422$	−2.43162	+	7.48377i	−0.118370	+	0.364304i
$423$	19.8066	+	14.3903i	0.963028	+	0.699681i
$424$	−11.2778	−	8.19378i	−0.547697	−	0.397925i
$425$	−0.145167	+	0.446779i	−0.00704164	+	0.0216719i
$426$	−10.4762	−	32.2425i	−0.507575	−	1.56215i
$427$	5.41759	−	3.93611i	0.262176	−	0.190482i
$428$	6.06164			0.293000
$429$	38.1153	−	42.0972i	1.84022	−	2.03247i
$430$	0.790717			0.0381318
$431$	−13.2906	+	9.65615i	−0.640183	+	0.465120i	−0.859913	−	0.510440i	$-0.829482\pi$
$431$	−13.2906	+	9.65615i	−0.640183	+	0.465120i	0.219730	+	0.975561i	$0.429482\pi$
$432$	−2.47422	−	7.61486i	−0.119041	−	0.366370i
$433$	−3.55065	+	10.9278i	−0.170633	+	0.525155i	−0.999407	−	0.0344284i	$-0.989039\pi$
$433$	−3.55065	+	10.9278i	−0.170633	+	0.525155i	0.828774	+	0.559584i	$0.189039\pi$
$434$	2.60621	+	1.89352i	0.125102	+	0.0908919i
$435$	−6.28786	−	4.56840i	−0.301480	−	0.219038i
$436$	3.36136	−	10.3452i	0.160980	−	0.495445i
$437$	9.62322	+	29.6172i	0.460341	+	1.41678i
$438$	29.2640	−	21.2615i	1.39829	−	1.01592i
$439$	36.6689			1.75011			0.875056	−	0.484022i	$-0.160824\pi$
$439$	36.6689			1.75011			0.875056	+	0.484022i	$0.160824\pi$
$440$	3.02615	+	1.35735i	0.144266	+	0.0647089i
$441$	5.71258			0.272028
$442$	2.20463	−	1.60176i	0.104864	−	0.0761879i
$443$	−3.55007	−	10.9260i	−0.168669	−	0.519110i	0.830619	−	0.556841i	$-0.187987\pi$
$443$	−3.55007	−	10.9260i	−0.168669	−	0.519110i	−0.999288	+	0.0377316i	$0.987987\pi$
$444$	4.15995	−	12.8030i	0.197422	−	0.607604i
$445$	−9.12296	−	6.62822i	−0.432470	−	0.314208i
$446$	19.3075	+	14.0277i	0.914236	+	0.664231i
$447$	−11.8902	+	36.5943i	−0.562388	+	1.73085i
$448$	0.309017	+	0.951057i	0.0145997	+	0.0449332i
$449$	0.955625	−	0.694302i	0.0450987	−	0.0327661i	−0.565008	−	0.825086i	$-0.691127\pi$
$449$	0.955625	−	0.694302i	0.0450987	−	0.0327661i	0.610106	+	0.792320i	$0.291127\pi$
$450$	5.71258			0.269294
$451$	5.92314	−	1.24194i	0.278910	−	0.0584805i
$452$	−6.52609			−0.306961
$453$	−21.8982	+	15.9100i	−1.02887	+	0.747516i
$454$	7.01614	+	21.5935i	0.329284	+	1.01343i
$455$	−1.79256	+	5.51694i	−0.0840367	+	0.258638i
$456$	−9.65994	−	7.01836i	−0.452368	−	0.328665i
$457$	9.05398	+	6.57810i	0.423527	+	0.307711i	0.779056	−	0.626955i	$-0.215699\pi$
$457$	9.05398	+	6.57810i	0.423527	+	0.307711i	−0.355528	+	0.934666i	$0.615699\pi$
$458$	−4.90420	+	15.0936i	−0.229158	+	0.705277i
$459$	1.16232	+	3.57724i	0.0542523	+	0.166971i
$460$	−6.22805	+	4.52495i	−0.290385	+	0.210977i
$461$	0.438159			0.0204071			0.0102036	−	0.999948i	$-0.496752\pi$
$461$	0.438159			0.0204071			0.0102036	+	0.999948i	$0.496752\pi$
$462$	−4.87145	−	8.49160i	−0.226640	−	0.395065i
$463$	20.1741			0.937570			0.468785	−	0.883312i	$-0.344692\pi$
$463$	20.1741			0.937570			0.468785	+	0.883312i	$0.344692\pi$
$464$	−2.13024	+	1.54771i	−0.0988941	+	0.0718508i
$465$	−2.93837	−	9.04338i	−0.136264	−	0.419377i
$466$	−9.03652	+	27.8115i	−0.418609	+	1.28834i
$467$	−2.64912	−	1.92470i	−0.122587	−	0.0890643i	0.524803	−	0.851224i	$-0.324139\pi$
$467$	−2.64912	−	1.92470i	−0.122587	−	0.0890643i	−0.647389	+	0.762160i	$0.724139\pi$
$468$	−26.8091	−	19.4779i	−1.23925	−	0.900368i
$469$	−2.07974	+	6.40079i	−0.0960335	+	0.295561i
$470$	1.32435	+	4.07592i	0.0610875	+	0.188008i
$471$	21.6424	−	15.7241i	0.997230	−	0.724530i
$472$	−13.0380			−0.600124
$473$	−0.281320	+	2.60738i	−0.0129351	+	0.119887i
$474$	−11.6675			−0.535908
$475$	3.27266	−	2.37773i	0.150160	−	0.109098i
$476$	−0.145167	−	0.446779i	−0.00665373	−	0.0204781i
$477$	24.6082	−	75.7363i	1.12673	−	3.46773i
$478$	7.06083	+	5.13000i	0.322955	+	0.234641i
$479$	21.8915	+	15.9051i	1.00025	+	0.726724i	0.962142	−	0.272550i	$-0.0878670\pi$
$479$	21.8915	+	15.9051i	1.00025	+	0.726724i	0.0381076	+	0.999274i	$0.487867\pi$
$480$	0.912128	−	2.80724i	0.0416328	−	0.128132i
$481$	−8.17536	−	25.1612i	−0.372764	−	1.14725i
$482$	7.75733	−	5.63603i	0.353337	−	0.256714i
$483$	22.7231			1.03394
$484$	−5.55247	+	9.49579i	−0.252385	+	0.431627i
$485$	16.7510			0.760624
$486$	−3.92087	+	2.84868i	−0.177854	+	0.129219i
$487$	7.94440	+	24.4503i	0.359995	+	1.10795i	0.953056	+	0.302794i	$0.0979192\pi$
$487$	7.94440	+	24.4503i	0.359995	+	1.10795i	−0.593061	+	0.805157i	$0.702081\pi$
$488$	−2.06934	+	6.36876i	−0.0936744	+	0.288300i
$489$	−4.05287	−	2.94458i	−0.183277	−	0.133159i
$490$	0.809017	+	0.587785i	0.0365477	+	0.0265534i
$491$	−8.96397	+	27.5883i	−0.404538	+	1.24504i	0.516742	+	0.856141i	$0.327145\pi$
$491$	−8.96397	+	27.5883i	−0.404538	+	1.24504i	−0.921280	+	0.388900i	$0.872855\pi$
$492$	−1.66439	−	5.12245i	−0.0750363	−	0.230938i
$493$	1.00073	−	0.727070i	0.0450705	−	0.0327456i
$494$	−23.4658			−1.05578
$495$	−2.03241	+	18.8372i	−0.0913502	+	0.846667i
$496$	−3.22145			−0.144647
$497$	−9.29195	+	6.75100i	−0.416801	+	0.302824i
$498$	8.61779	+	26.5228i	0.386172	+	1.18852i
$499$	7.04866	−	21.6935i	0.315541	−	0.971137i	−0.659990	−	0.751275i	$-0.729439\pi$
$499$	7.04866	−	21.6935i	0.315541	−	0.971137i	0.975531	−	0.219862i	$-0.0705607\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	47.4115	+	34.4465i	2.11819	+	1.53896i
$502$	0.834544	−	2.56846i	0.0372475	−	0.114636i
$503$	−8.69956	−	26.7745i	−0.387894	−	1.19382i	−0.934359	−	0.356333i	$-0.884027\pi$
$503$	−8.69956	−	26.7745i	−0.387894	−	1.19382i	0.546465	−	0.837482i	$-0.315973\pi$
$504$	−4.62157	+	3.35777i	−0.205861	+	0.149567i
$505$	8.57037			0.381377
$506$	−12.7051	−	22.1468i	−0.564812	−	0.984546i
$507$	−60.9526			−2.70700
$508$	3.27438	−	2.37898i	0.145277	−	0.105550i
$509$	11.0610	+	34.0422i	0.490270	+	1.50890i	0.824201	+	0.566298i	$0.191625\pi$
$509$	11.0610	+	34.0422i	0.490270	+	1.50890i	−0.333931	+	0.942598i	$0.608375\pi$
$510$	−0.428491	+	1.31876i	−0.0189739	+	0.0583957i
$511$	−9.91426	−	7.20313i	−0.438581	−	0.318648i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	10.0088	−	30.8039i	0.441899	−	1.36002i
$514$	2.75904	+	8.49146i	0.121696	+	0.374542i
$515$	1.94275	−	1.41149i	0.0856077	−	0.0621976i
$516$	2.33397			0.102747
$517$	−13.9115	+	2.91689i	−0.611825	+	0.128285i
$518$	−4.56071			−0.200386
$519$	−29.8941	+	21.7193i	−1.31220	+	0.953372i
$520$	−1.79256	−	5.51694i	−0.0786091	−	0.241934i
$521$	−6.02051	+	18.5292i	−0.263763	+	0.811780i	0.728213	+	0.685351i	$0.240351\pi$
$521$	−6.02051	+	18.5292i	−0.263763	+	0.811780i	−0.991976	+	0.126428i	$0.959649\pi$
$522$	−12.1692	−	8.84143i	−0.532631	−	0.386979i
$523$	20.8358	+	15.1381i	0.911086	+	0.661942i	0.941289	−	0.337601i	$-0.109616\pi$
$523$	20.8358	+	15.1381i	0.911086	+	0.661942i	−0.0302035	+	0.999544i	$0.509616\pi$
$524$	2.79945	−	8.61582i	0.122295	−	0.376384i
$525$	−0.912128	−	2.80724i	−0.0398085	−	0.122518i
$526$	−0.147926	+	0.107474i	−0.00644987	+	0.00468611i
$527$	1.51334			0.0659222
$528$	8.93233	+	4.00649i	0.388730	+	0.174360i
$529$	36.2638			1.57669
$530$	11.2778	−	8.19378i	0.489875	−	0.355915i
$531$	−23.0158	−	70.8354i	−0.998802	−	3.07400i
$532$	−1.25005	+	3.84724i	−0.0541963	+	0.166799i
$533$	−8.56344	−	6.22170i	−0.370924	−	0.269492i
$534$	−26.9283	−	19.5646i	−1.16530	−	0.846642i
$535$	−1.87315	+	5.76496i	−0.0809833	+	0.249241i
$536$	−2.07974	−	6.40079i	−0.0898311	−	0.276472i
$537$	−38.8946	+	28.2586i	−1.67843	+	1.21945i
$538$	−5.71539			−0.246408
$539$	−2.22605	+	2.45860i	−0.0958826	+	0.105899i
$540$	8.00674			0.344555
$541$	10.6738	−	7.75495i	0.458902	−	0.333412i	−0.334199	−	0.942503i	$-0.608466\pi$
$541$	10.6738	−	7.75495i	0.458902	−	0.333412i	0.793100	+	0.609091i	$0.208466\pi$
$542$	−0.958200	−	2.94904i	−0.0411582	−	0.126672i
$543$	10.7979	−	33.2326i	0.463383	−	1.42615i
$544$	0.380053	+	0.276124i	0.0162946	+	0.0118387i
$545$	8.80015	+	6.39369i	0.376957	+	0.273875i
$546$	−5.29112	+	16.2844i	−0.226439	+	0.696908i
$547$	10.4389	+	32.1275i	0.446334	+	1.37367i	0.881014	+	0.473090i	$0.156861\pi$
$547$	10.4389	+	32.1275i	0.446334	+	1.37367i	−0.434680	+	0.900585i	$0.643139\pi$
$548$	−14.2590	+	10.3597i	−0.609113	+	0.442546i
$549$	−38.2543			−1.63266
$550$	−2.22605	+	2.45860i	−0.0949189	+	0.104835i
$551$	−10.6516			−0.453774
$552$	−18.3834	+	13.3563i	−0.782449	+	0.568483i
$553$	1.22149	+	3.75935i	0.0519429	+	0.159864i
$554$	6.64169	−	20.4410i	0.282178	−	0.868456i
$555$	10.8909	+	7.91269i	0.462292	+	0.335875i
$556$	−15.1017	−	10.9720i	−0.640455	−	0.465318i
$557$	−7.78665	+	23.9648i	−0.329931	+	1.01542i	0.639235	+	0.769012i	$0.279251\pi$
$557$	−7.78665	+	23.9648i	−0.329931	+	1.01542i	−0.969165	+	0.246411i	$0.920749\pi$
$558$	−5.68677	−	17.5021i	−0.240740	−	0.740922i
$559$	3.71083	−	2.69608i	0.156951	−	0.114032i
$560$	−1.00000			−0.0422577
$561$	−4.19615	−	1.88213i	−0.177161	−	0.0794636i
$562$	−11.7569			−0.495933
$563$	−33.1275	+	24.0685i	−1.39616	+	1.01437i	−0.400998	+	0.916079i	$0.631337\pi$
$563$	−33.1275	+	24.0685i	−1.39616	+	1.01437i	−0.995158	+	0.0982878i	$0.968663\pi$
$564$	3.90908	+	12.0309i	0.164602	+	0.506593i
$565$	2.01667	−	6.20668i	0.0848420	−	0.261117i
$566$	−3.13846	−	2.28023i	−0.131919	−	0.0958451i
$567$	−5.25523	−	3.81815i	−0.220699	−	0.160347i
$568$	3.54921	−	10.9233i	0.148921	−	0.458333i
$569$	−11.1035	−	34.1730i	−0.465483	−	1.43261i	−0.858375	−	0.513023i	$-0.828525\pi$
$569$	−11.1035	−	34.1730i	−0.465483	−	1.43261i	0.392892	−	0.919585i	$-0.371475\pi$
$570$	9.65994	−	7.01836i	0.404610	−	0.293967i
$571$	8.88506			0.371828			0.185914	−	0.982566i	$-0.440475\pi$
$571$	8.88506			0.371828			0.185914	+	0.982566i	$0.440475\pi$
$572$	18.8298	−	3.94814i	0.787314	−	0.165080i
$573$	80.6839			3.37062
$574$	−1.47624	+	1.07255i	−0.0616169	+	0.0447673i
$575$	−2.37891	−	7.32152i	−0.0992072	−	0.305328i
$576$	1.76528	−	5.43299i	0.0735535	−	0.226374i
$577$	20.3647	+	14.7958i	0.847793	+	0.615958i	0.924537	−	0.381093i	$-0.124452\pi$
$577$	20.3647	+	14.7958i	0.847793	+	0.615958i	−0.0767436	+	0.997051i	$0.524452\pi$
$578$	13.5748	+	9.86263i	0.564635	+	0.410231i
$579$	−15.3724	+	47.3113i	−0.638854	+	1.96619i
$580$	−0.813681	−	2.50425i	−0.0337863	−	0.103983i
$581$	7.64360	−	5.55340i	0.317110	−	0.230394i
$582$	49.4441			2.04952
$583$	23.0065	+	40.1035i	0.952831	+	1.66092i
$584$	12.2547			0.507103
$585$	26.8091	−	19.4779i	1.10842	−	0.805314i
$586$	−9.45846	−	29.1101i	−0.390725	−	1.20253i
$587$	11.5283	−	35.4804i	0.475823	−	1.46443i	−0.369022	−	0.929420i	$-0.620307\pi$
$587$	11.5283	−	35.4804i	0.475823	−	1.46443i	0.844845	−	0.535011i	$-0.179693\pi$
$588$	2.38798	+	1.73497i	0.0984787	+	0.0715490i
$589$	−10.5427	−	7.65973i	−0.434405	−	0.315614i
$590$	4.02897	−	12.3999i	0.165870	−	0.510496i
$591$	4.24924	+	13.0778i	0.174790	+	0.537949i
$592$	3.68969	−	2.68072i	0.151645	−	0.110177i
$593$	−12.7375			−0.523065			−0.261533	−	0.965195i	$-0.584228\pi$
$593$	−12.7375			−0.523065			−0.261533	+	0.965195i	$0.584228\pi$
$594$	−2.84863	+	26.4021i	−0.116881	+	1.08329i
$595$	0.469771			0.0192587
$596$	−10.5461	+	7.66218i	−0.431985	+	0.313855i
$597$	11.1353	+	34.2709i	0.455737	+	1.40261i
$598$	−13.7997	+	42.4711i	−0.564311	+	1.73677i
$599$	5.35480	+	3.89049i	0.218791	+	0.158961i	0.691782	−	0.722106i	$-0.256826\pi$
$599$	5.35480	+	3.89049i	0.218791	+	0.158961i	−0.472991	+	0.881067i	$0.656826\pi$
$600$	2.38798	+	1.73497i	0.0974889	+	0.0708299i
$601$	−10.6912	+	32.9042i	−0.436105	+	1.34219i	0.455846	+	0.890059i	$0.349337\pi$
$601$	−10.6912	+	32.9042i	−0.436105	+	1.34219i	−0.891950	+	0.452133i	$0.850663\pi$
$602$	−0.244345	−	0.752017i	−0.00995876	−	0.0306499i
$603$	31.1040	−	22.5984i	1.26665	−	0.920278i
$604$	−9.17018			−0.373129
$605$	−7.31523	−	8.21507i	−0.297406	−	0.333990i
$606$	25.2972			1.02763
$607$	20.2601	−	14.7199i	0.822334	−	0.597461i	−0.0950461	−	0.995473i	$-0.530300\pi$
$607$	20.2601	−	14.7199i	0.822334	−	0.597461i	0.917380	+	0.398012i	$0.130300\pi$
$608$	−1.25005	−	3.84724i	−0.0506960	−	0.156026i
$609$	−2.40175	+	7.39182i	−0.0973237	+	0.299532i
$610$	−5.41759	−	3.93611i	−0.219352	−	0.159368i
$611$	20.1126	+	14.6127i	0.813670	+	0.591166i
$612$	−0.829279	+	2.55226i	−0.0335216	+	0.103169i
$613$	5.49429	+	16.9097i	0.221912	+	0.682976i	0.998590	+	0.0530780i	$0.0169032\pi$
$613$	5.49429	+	16.9097i	0.221912	+	0.682976i	−0.776678	+	0.629898i	$0.783097\pi$
$614$	2.07716	−	1.50915i	0.0838274	−	0.0609041i
$615$	5.38607			0.217187
$616$	0.355779	−	3.29749i	0.0143347	−	0.132860i
$617$	30.5946			1.23169			0.615847	−	0.787866i	$-0.288814\pi$
$617$	30.5946			1.23169			0.615847	+	0.787866i	$0.288814\pi$
$618$	5.73442	−	4.16630i	0.230672	−	0.167593i
$619$	−4.42759	−	13.6267i	−0.177960	−	0.547704i	0.821796	−	0.569781i	$-0.192972\pi$
$619$	−4.42759	−	13.6267i	−0.177960	−	0.547704i	−0.999756	+	0.0220771i	$0.992972\pi$
$620$	0.995482	−	3.06378i	0.0399795	−	0.123044i
$621$	−49.8664	−	36.2301i	−2.00107	−	1.45386i
$622$	26.3160	+	19.1197i	1.05518	+	0.766631i
$623$	−3.48466	+	10.7247i	−0.139610	+	0.429675i
$624$	−5.29112	−	16.2844i	−0.211814	−	0.651898i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−7.78739			−0.311247
$627$	19.7061	+	34.3505i	0.786987	+	1.37183i
$628$	9.06306			0.361655
$629$	−1.73331	+	1.25932i	−0.0691115	+	0.0502125i
$630$	−1.76528	−	5.43299i	−0.0703306	−	0.216455i
$631$	4.02709	−	12.3941i	0.160316	−	0.493402i	−0.838345	−	0.545141i	$-0.816476\pi$
$631$	4.02709	−	12.3941i	0.160316	−	0.493402i	0.998661	+	0.0517387i	$0.0164763\pi$
$632$	−3.19789	−	2.32340i	−0.127205	−	0.0924201i
$633$	−18.7908	−	13.6523i	−0.746867	−	0.542631i
$634$	−5.39797	+	16.6132i	−0.214381	+	0.659796i
$635$	1.25070	+	3.84927i	0.0496326	+	0.152753i
$636$	33.2887	−	24.1856i	1.31998	−	0.959023i
$637$	5.80086			0.229838
$638$	8.54723	−	1.79214i	0.338388	−	0.0709516i
$639$	65.6117			2.59556
$640$	0.809017	−	0.587785i	0.0319792	−	0.0232343i
$641$	−8.26420	−	25.4346i	−0.326416	−	1.00461i	−0.970797	−	0.239901i	$-0.922885\pi$
$641$	−8.26420	−	25.4346i	−0.326416	−	1.00461i	0.644381	−	0.764704i	$-0.277115\pi$
$642$	−5.52899	+	17.0165i	−0.218212	+	0.671587i
$643$	−5.97210	−	4.33899i	−0.235517	−	0.171113i	0.463767	−	0.885957i	$-0.346498\pi$
$643$	−5.97210	−	4.33899i	−0.235517	−	0.171113i	−0.699284	+	0.714844i	$0.746498\pi$
$644$	6.22805	+	4.52495i	0.245420	+	0.178308i
$645$	−0.721235	+	2.21973i	−0.0283986	+	0.0874019i
$646$	0.587235	+	1.80732i	0.0231044	+	0.0711082i
$647$	−7.36488	+	5.35090i	−0.289543	+	0.210366i	−0.723069	−	0.690776i	$-0.757269\pi$
$647$	−7.36488	+	5.35090i	−0.289543	+	0.210366i	0.433526	+	0.901141i	$0.357269\pi$
$648$	6.49582			0.255180
$649$	39.4551	+	17.6971i	1.54875	+	0.694672i
$650$	5.80086			0.227528
$651$	−7.69276	+	5.58912i	−0.301503	+	0.219055i
$652$	−0.524462	−	1.61413i	−0.0205395	−	0.0632141i
$653$	11.4223	−	35.1543i	0.446990	−	1.37569i	−0.433297	−	0.901251i	$-0.642650\pi$
$653$	11.4223	−	35.1543i	0.446990	−	1.37569i	0.880287	−	0.474442i	$-0.157350\pi$
$654$	25.9755	+	18.8723i	1.01572	+	0.737965i
$655$	7.32905	+	5.32487i	0.286370	+	0.208060i
$656$	0.563872	−	1.73542i	0.0220155	−	0.0677568i
$657$	21.6330	+	66.5796i	0.843985	+	2.59752i
$658$	3.46718	−	2.51906i	0.135165	−	0.0982030i
$659$	−47.4959			−1.85018			−0.925089	−	0.379750i	$-0.876010\pi$
$659$	−47.4959			−1.85018			−0.925089	+	0.379750i	$0.876010\pi$
$660$	−6.57064	+	7.25707i	−0.255762	+	0.282481i
$661$	23.6252			0.918915			0.459457	−	0.888200i	$-0.348044\pi$
$661$	23.6252			0.918915			0.459457	+	0.888200i	$0.348044\pi$
$662$	1.63213	−	1.18581i	0.0634343	−	0.0460877i
$663$	2.48562	+	7.64994i	0.0965333	+	0.297099i
$664$	−2.91960	+	8.98559i	−0.113302	+	0.348709i
$665$	−3.27266	−	2.37773i	−0.126908	−	0.0922043i
$666$	21.0776	+	15.3138i	0.816742	+	0.593398i
$667$	−6.26396	+	19.2785i	−0.242541	+	0.746466i
$668$	6.13530	+	18.8825i	0.237382	+	0.730586i
$669$	−56.9900	+	41.4057i	−2.20336	+	1.60084i
$670$	6.73018			0.260010
$671$	14.9067	−	16.4641i	0.575468	−	0.635588i
$672$	−2.95171			−0.113865
$673$	11.3560	−	8.25065i	0.437743	−	0.318039i	−0.346994	−	0.937867i	$-0.612798\pi$
$673$	11.3560	−	8.25065i	0.437743	−	0.318039i	0.784738	+	0.619828i	$0.212798\pi$
$674$	7.21021	+	22.1908i	0.277727	+	0.854756i
$675$	−2.47422	+	7.61486i	−0.0952327	+	0.293096i
$676$	−16.7062	−	12.1377i	−0.642544	−	0.466836i
$677$	34.2682	+	24.8973i	1.31703	+	0.956882i	0.999964	+	0.00847962i	$0.00269918\pi$
$677$	34.2682	+	24.8973i	1.31703	+	0.956882i	0.317070	+	0.948402i	$0.397301\pi$
$678$	5.95263	−	18.3203i	0.228609	−	0.703587i
$679$	−5.17635	−	15.9312i	−0.198650	−	0.611382i
$680$	−0.380053	+	0.276124i	−0.0145744	+	0.0105889i
$681$	−67.0176			−2.56812
$682$	9.74860	+	4.37262i	0.373293	+	0.167436i
$683$	25.5960			0.979402			0.489701	−	0.871890i	$-0.337106\pi$
$683$	25.5960			0.979402			0.489701	+	0.871890i	$0.337106\pi$
$684$	18.6953	−	13.5830i	0.714834	−	0.519357i
$685$	−5.44644	−	16.7624i	−0.208098	−	0.640459i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	−37.8981	−	27.5346i	−1.44590	−	1.05051i
$688$	0.639704	+	0.464772i	0.0243885	+	0.0177193i
$689$	24.9885	−	76.9067i	0.951985	−	2.92991i
$690$	−7.02183	−	21.6110i	−0.267317	−	0.822716i
$691$	−36.9816	+	26.8687i	−1.40685	+	1.02213i	−0.413074	+	0.910697i	$0.635545\pi$
$691$	−36.9816	+	26.8687i	−1.40685	+	1.02213i	−0.993772	+	0.111436i	$0.964455\pi$
$692$	−12.5185			−0.475884
$693$	18.5432	−	3.88806i	0.704400	−	0.147695i
$694$	8.21232			0.311735
$695$	15.1017	−	10.9720i	0.572840	−	0.416193i
$696$	−2.40175	−	7.39182i	−0.0910380	−	0.280186i
$697$	−0.264891	+	0.815250i	−0.0100335	+	0.0308798i
$698$	14.2411	+	10.3468i	0.539034	+	0.391631i
$699$	−69.8312	−	50.7354i	−2.64126	−	1.91899i
$700$	0.309017	−	0.951057i	0.0116797	−	0.0359466i
$701$	−11.7219	−	36.0762i	−0.442729	−	1.36258i	−0.884955	−	0.465676i	$-0.845811\pi$
$701$	−11.7219	−	36.0762i	−0.442729	−	1.36258i	0.442226	−	0.896904i	$-0.354189\pi$
$702$	37.5756	−	27.3002i	1.41820	−	1.03038i
$703$	18.4491			0.695821
$704$	1.65038	+	2.87684i	0.0622012	+	0.108425i
$705$	−12.6501			−0.476429
$706$	27.9541	−	20.3099i	1.05207	−	0.764372i
$707$	−2.64839	−	8.15091i	−0.0996030	−	0.306546i
$708$	11.8924	−	36.6009i	0.446942	−	1.37555i
$709$	−35.4970	−	25.7901i	−1.33312	−	0.968566i	−0.999667	−	0.0257981i	$-0.991787\pi$
$709$	−35.4970	−	25.7901i	−1.33312	−	0.968566i	−0.333450	−	0.942768i	$-0.608213\pi$
$710$	9.29195	+	6.75100i	0.348721	+	0.253360i
$711$	6.97784	−	21.4756i	0.261689	−	0.805397i
$712$	−3.48466	−	10.7247i	−0.130593	−	0.401925i
$713$	−20.0634	+	14.5769i	−0.751379	+	0.545909i
$714$	1.38663			0.0518932
$715$	−2.06382	+	19.1283i	−0.0771825	+	0.715356i
$716$	−16.2877			−0.608698
$717$	−20.8415	+	15.1423i	−0.778341	+	0.565498i
$718$	−2.58431	−	7.95370i	−0.0964458	−	0.296830i
$719$	−11.2402	+	34.5937i	−0.419187	+	1.29013i	0.489264	+	0.872136i	$0.337265\pi$
$719$	−11.2402	+	34.5937i	−0.419187	+	1.29013i	−0.908452	+	0.417990i	$0.862735\pi$
$720$	4.62157	+	3.35777i	0.172236	+	0.125137i
$721$	−1.94275	−	1.41149i	−0.0723517	−	0.0525666i
$722$	−0.814601	+	2.50708i	−0.0303163	+	0.0933040i
$723$	8.74602	+	26.9175i	0.325268	+	1.00107i
$724$	9.57727	−	6.95829i	0.355936	−	0.258603i
$725$	2.63313			0.0977919
$726$	−21.5924	−	24.2485i	−0.801370	−	0.899946i
$727$	0.665574			0.0246848			0.0123424	−	0.999924i	$-0.496071\pi$
$727$	0.665574			0.0246848			0.0123424	+	0.999924i	$0.496071\pi$
$728$	−4.69299	+	3.40966i	−0.173934	+	0.126370i
$729$	−10.4425	−	32.1388i	−0.386761	−	1.19033i
$730$	−3.78691	+	11.6549i	−0.140160	+	0.431368i
$731$	−0.300514	−	0.218336i	−0.0111149	−	0.00807546i
$732$	−15.9911	−	11.6182i	−0.591050	−	0.429423i
$733$	5.61323	−	17.2757i	0.207329	−	0.638094i	−0.792280	−	0.610157i	$-0.791106\pi$
$733$	5.61323	−	17.2757i	0.207329	−	0.638094i	0.999610	−	0.0279369i	$-0.00889374\pi$
$734$	5.33662	+	16.4244i	0.196978	+	0.606237i
$735$	−2.38798	+	1.73497i	−0.0880820	+	0.0639953i
$736$	−7.69830			−0.283763
$737$	−2.39446	+	22.1927i	−0.0882009	+	0.817478i
$738$	10.4239			0.383709
$739$	−18.7936	+	13.6543i	−0.691332	+	0.502282i	−0.877098	−	0.480312i	$-0.840523\pi$
$739$	−18.7936	+	13.6543i	−0.691332	+	0.502282i	0.185766	+	0.982594i	$0.440523\pi$
$740$	1.40934	+	4.33749i	0.0518082	+	0.159449i
$741$	21.4038	−	65.8742i	0.786289	−	2.41995i
$742$	−11.2778	−	8.19378i	−0.414020	−	0.300803i
$743$	11.4731	+	8.33569i	0.420907	+	0.305807i	0.778003	−	0.628261i	$-0.216233\pi$
$743$	11.4731	+	8.33569i	0.420907	+	0.305807i	−0.357096	+	0.934068i	$0.616233\pi$
$744$	2.93837	−	9.04338i	0.107726	−	0.331547i
$745$	−4.02825	−	12.3977i	−0.147584	−	0.454215i
$746$	18.5461	−	13.4745i	0.679021	−	0.493338i
$747$	−53.9725			−1.97475
$748$	−0.775302	−	1.35146i	−0.0283478	−	0.0494142i
$749$	6.06164			0.221487
$750$	−2.38798	+	1.73497i	−0.0871968	+	0.0633522i
$751$	−8.78893	−	27.0496i	−0.320713	−	0.987052i	−0.973339	−	0.229372i	$-0.926333\pi$
$751$	−8.78893	−	27.0496i	−0.320713	−	0.987052i	0.652626	−	0.757680i	$-0.273667\pi$
$752$	−1.32435	+	4.07592i	−0.0482939	+	0.148633i
$753$	6.44908	+	4.68553i	0.235018	+	0.170750i
$754$	−12.3572	−	8.97806i	−0.450024	−	0.326962i
$755$	2.83374	−	8.72136i	0.103130	−	0.317403i
$756$	−2.47422	−	7.61486i	−0.0899865	−	0.276950i
$757$	−31.6800	+	23.0169i	−1.15143	+	0.836563i	−0.988670	−	0.150103i	$-0.952040\pi$
$757$	−31.6800	+	23.0169i	−1.15143	+	0.836563i	−0.162760	+	0.986666i	$0.552040\pi$
$758$	3.81880			0.138705
$759$	73.7601	−	15.4657i	2.67732	−	0.561368i
$760$	4.04523			0.146736
$761$	10.6635	−	7.74749i	0.386552	−	0.280846i	−0.377489	−	0.926014i	$-0.623213\pi$
$761$	10.6635	−	7.74749i	0.386552	−	0.280846i	0.764041	+	0.645168i	$0.223213\pi$
$762$	3.69171	+	11.3619i	0.133736	+	0.411598i
$763$	3.36136	−	10.3452i	0.121689	−	0.374521i
$764$	22.1142	+	16.0669i	0.800063	+	0.581280i
$765$	−2.17108	−	1.57738i	−0.0784956	−	0.0570304i
$766$	−3.62707	+	11.1630i	−0.131051	+	0.403335i
$767$	−23.3715	−	71.9301i	−0.843896	−	2.59724i
$768$	2.38798	−	1.73497i	0.0861689	−	0.0626053i
$769$	8.58896			0.309726			0.154863	−	0.987936i	$-0.450506\pi$
$769$	8.58896			0.309726			0.154863	+	0.987936i	$0.450506\pi$
$770$	3.02615	+	1.35735i	0.109055	+	0.0489153i
$771$	−26.3542			−0.949122
$772$	−13.6346	+	9.90612i	−0.490720	+	0.356529i
$773$	1.02453	+	3.15319i	0.0368499	+	0.113412i	0.967789	−	0.251761i	$-0.0810097\pi$
$773$	1.02453	+	3.15319i	0.0368499	+	0.113412i	−0.930940	+	0.365173i	$0.881010\pi$
$774$	−1.39584	+	4.29596i	−0.0501725	+	0.154415i
$775$	2.60621	+	1.89352i	0.0936177	+	0.0680172i
$776$	13.5518	+	9.84599i	0.486483	+	0.353451i
$777$	4.15995	−	12.8030i	0.149237	−	0.459305i
$778$	−2.46329	−	7.58123i	−0.0883133	−	0.271800i
$779$	5.97172	−	4.33871i	0.213959	−	0.155450i
$780$	17.1224			0.613082
$781$	−25.5672	+	28.2382i	−0.914866	+	1.01044i
$782$	3.61644			0.129323
$783$	17.0563	−	12.3921i	0.609543	−	0.442859i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	−2.80064	+	8.61948i	−0.0999591	+	0.307642i
$786$	21.6332	+	15.7175i	0.771632	+	0.560623i
$787$	−16.2486	−	11.8053i	−0.579202	−	0.420815i	0.259235	−	0.965814i	$-0.416530\pi$
$787$	−16.2486	−	11.8053i	−0.579202	−	0.420815i	−0.838436	+	0.545000i	$0.816530\pi$
$788$	−1.43959	+	4.43059i	−0.0512831	+	0.157833i
$789$	−0.166779	−	0.513294i	−0.00593750	−	0.0182737i
$790$	3.19789	−	2.32340i	0.113776	−	0.0826630i
$791$	−6.52609			−0.232041
$792$	−12.7165	+	14.0450i	−0.451860	+	0.499066i
$793$	−38.8455			−1.37944
$794$	−0.448338	+	0.325736i	−0.0159109	+	0.0115600i
$795$	12.7151	+	39.1332i	0.450960	+	1.38791i
$796$	−3.77249	+	11.6105i	−0.133712	+	0.411524i
$797$	17.2113	+	12.5047i	0.609655	+	0.442940i	0.849293	−	0.527922i	$-0.177029\pi$
$797$	17.2113	+	12.5047i	0.609655	+	0.442940i	−0.239638	+	0.970862i	$0.577029\pi$
$798$	−9.65994	−	7.01836i	−0.341958	−	0.248447i
$799$	0.622139	−	1.91475i	0.0220097	−	0.0677389i
$800$	0.309017	+	0.951057i	0.0109254	+	0.0336249i
$801$	52.1156	−	37.8642i	1.84142	−	1.33787i
$802$	−11.8420			−0.418155
$803$	−37.0846	−	16.6339i	−1.30869	−	0.586996i
$804$	19.8655			0.700603
$805$	−6.22805	+	4.52495i	−0.219510	+	0.159483i
$806$	−5.77465	−	17.7725i	−0.203403	−	0.626011i
$807$	5.21317	−	16.0445i	0.183512	−	0.564793i
$808$	6.93358	+	5.03754i	0.243922	+	0.177220i
$809$	−4.05771	−	2.94810i	−0.142662	−	0.103650i	0.514165	−	0.857691i	$-0.328102\pi$
$809$	−4.05771	−	2.94810i	−0.142662	−	0.103650i	−0.656827	+	0.754041i	$0.728102\pi$
$810$	−2.00732	+	6.17789i	−0.0705300	+	0.217069i
$811$	8.67176	+	26.6889i	0.304507	+	0.937175i	0.979861	+	0.199682i	$0.0639908\pi$
$811$	8.67176	+	26.6889i	0.304507	+	0.937175i	−0.675354	+	0.737494i	$0.736009\pi$
$812$	−2.13024	+	1.54771i	−0.0747569	+	0.0543141i
$813$	9.15266			0.320998
$814$	−14.8042	+	3.10408i	−0.518888	+	0.108798i
$815$	1.69719			0.0594501
$816$	−1.12180	+	0.815038i	−0.0392710	+	0.0285321i
$817$	0.988432	+	3.04208i	0.0345809	+	0.106429i
$818$	−2.58890	+	7.96782i	−0.0905188	+	0.278588i
$819$	−26.8091	−	19.4779i	−0.936785	−	0.680614i
$820$	1.47624	+	1.07255i	0.0515524	+	0.0374550i
$821$	−14.0463	+	43.2301i	−0.490220	+	1.50874i	0.334056	+	0.942553i	$0.391582\pi$
$821$	−14.0463	+	43.2301i	−0.490220	+	1.50874i	−0.824276	+	0.566188i	$0.808418\pi$
$822$	−16.0763	−	49.4778i	−0.560725	−	1.72573i
$823$	24.6684	−	17.9226i	0.859885	−	0.624743i	−0.0679686	−	0.997687i	$-0.521652\pi$
$823$	24.6684	−	17.9226i	0.859885	−	0.624743i	0.927854	+	0.372944i	$0.121652\pi$
$824$	2.40137			0.0836556
$825$	−4.87145	−	8.49160i	−0.169602	−	0.295640i
$826$	−13.0380			−0.453651
$827$	28.2628	−	20.5341i	0.982793	−	0.714041i	0.0244616	−	0.999701i	$-0.492213\pi$
$827$	28.2628	−	20.5341i	0.982793	−	0.714041i	0.958331	+	0.285660i	$0.0922129\pi$
$828$	−13.5897	−	41.8247i	−0.472274	−	1.45351i
$829$	−11.3832	+	35.0338i	−0.395354	+	1.21678i	0.533331	+	0.845907i	$0.320940\pi$
$829$	−11.3832	+	35.0338i	−0.395354	+	1.21678i	−0.928685	+	0.370869i	$0.879060\pi$
$830$	−7.64360	−	5.55340i	−0.265313	−	0.192761i
$831$	51.3248	+	37.2896i	1.78044	+	1.29356i
$832$	1.79256	−	5.51694i	0.0621460	−	0.191266i
$833$	−0.145167	−	0.446779i	−0.00502974	−	0.0154800i
$834$	44.5758	−	32.3862i	1.54353	−	1.12144i
$835$	−19.8542			−0.687084
$836$	−1.43921	+	13.3391i	−0.0497760	+	0.461342i
$837$	25.7933			0.891547
$838$	20.3843	−	14.8100i	0.704163	−	0.511604i
$839$	−3.71637	−	11.4378i	−0.128303	−	0.394877i	0.866185	−	0.499723i	$-0.166565\pi$
$839$	−3.71637	−	11.4378i	−0.128303	−	0.394877i	−0.994488	+	0.104846i	$0.966565\pi$
$840$	0.912128	−	2.80724i	0.0314714	−	0.0968590i
$841$	17.8523	+	12.9704i	0.615596	+	0.447257i
$842$	−21.8705	−	15.8899i	−0.753707	−	0.547600i
$843$	10.7238	−	33.0043i	0.369346	−	1.13673i
$844$	−2.43162	−	7.48377i	−0.0837000	−	0.257602i
$845$	16.7062	−	12.1377i	0.574709	−	0.417551i
$846$	−24.4823			−0.841717
$847$	−5.55247	+	9.49579i	−0.190785	+	0.326279i
$848$	13.9401			0.478704
$849$	9.26382	−	6.73056i	0.317934	−	0.230992i
$850$	−0.145167	−	0.446779i	−0.00497919	−	0.0153244i
$851$	10.8495	−	33.3913i	0.371916	−	1.14464i
$852$	27.4271	+	19.9270i	0.939638	+	0.682687i
$853$	11.1080	+	8.07046i	0.380332	+	0.276327i	0.761482	−	0.648186i	$-0.224472\pi$
$853$	11.1080	+	8.07046i	0.380332	+	0.276327i	−0.381150	+	0.924513i	$0.624472\pi$
$854$	−2.06934	+	6.36876i	−0.0708112	+	0.217935i
$855$	7.14098	+	21.9777i	0.244216	+	0.751621i
$856$	−4.90397	+	3.56294i	−0.167614	+	0.121779i
$857$	25.3293			0.865233			0.432616	−	0.901578i	$-0.357591\pi$
$857$	25.3293			0.865233			0.432616	+	0.901578i	$0.357591\pi$
$858$	−6.09180	+	56.4610i	−0.207971	+	1.92755i
$859$	−43.9737			−1.50036			−0.750181	−	0.661232i	$-0.770034\pi$
$859$	−43.9737			−1.50036			−0.750181	+	0.661232i	$0.770034\pi$
$860$	−0.639704	+	0.464772i	−0.0218137	+	0.0158486i
$861$	−1.66439	−	5.12245i	−0.0567221	−	0.174573i
$862$	5.07654	−	15.6240i	0.172908	−	0.532155i
$863$	12.2806	+	8.92240i	0.418038	+	0.303722i	0.776848	−	0.629688i	$-0.216817\pi$
$863$	12.2806	+	8.92240i	0.418038	+	0.303722i	−0.358810	+	0.933411i	$0.616817\pi$
$864$	6.47759	+	4.70624i	0.220372	+	0.160110i
$865$	3.86844	−	11.9058i	0.131531	−	0.404811i
$866$	−3.55065	−	10.9278i	−0.120656	−	0.371341i
$867$	−40.0687	+	29.1116i	−1.36080	+	0.988682i
$868$	−3.22145			−0.109343
$869$	6.52366	+	11.3716i	0.221300	+	0.385756i
$870$	7.77222			0.263503
$871$	31.5847	−	22.9476i	1.07021	−	0.777551i
$872$	3.36136	+	10.3452i	0.113830	+	0.350333i
$873$	−29.5703	+	91.0080i	−1.00080	+	3.08015i
$874$	−25.1939	−	18.3045i	−0.852197	−	0.619157i
$875$	0.809017	+	0.587785i	0.0273498	+	0.0198708i
$876$	−11.1779	+	34.4019i	−0.377665	+	1.16233i
$877$	−13.1293	−	40.4078i	−0.443344	−	1.36447i	−0.884289	−	0.466940i	$-0.845356\pi$
$877$	−13.1293	−	40.4078i	−0.443344	−	1.36447i	0.440945	−	0.897534i	$-0.354644\pi$
$878$	−29.6658	+	21.5534i	−1.00117	+	0.727394i
$879$	90.3465			3.04731
$880$	−3.24604	+	0.680614i	−0.109424	+	0.0229435i
$881$	51.3494			1.73000			0.865002	−	0.501768i	$-0.167317\pi$
$881$	51.3494			1.73000			0.865002	+	0.501768i	$0.167317\pi$
$882$	−4.62157	+	3.35777i	−0.155616	+	0.113062i
$883$	−1.51253	−	4.65510i	−0.0509008	−	0.156656i	0.922375	−	0.386295i	$-0.126245\pi$
$883$	−1.51253	−	4.65510i	−0.0509008	−	0.156656i	−0.973276	+	0.229639i	$0.926245\pi$
$884$	−0.842094	+	2.59170i	−0.0283227	+	0.0871683i
$885$	31.1346	+	22.6206i	1.04658	+	0.760383i
$886$	9.29420	+	6.75263i	0.312245	+	0.226859i
$887$	16.2062	−	49.8775i	0.544151	−	1.67472i	−0.178850	−	0.983876i	$-0.557238\pi$
$887$	16.2062	−	49.8775i	0.544151	−	1.67472i	0.723001	−	0.690847i	$-0.242762\pi$
$888$	4.15995	+	12.8030i	0.139599	+	0.429641i
$889$	3.27438	−	2.37898i	0.109819	−	0.0797883i
$890$	11.2766			0.377993
$891$	−19.6574	−	8.81707i	−0.658546	−	0.295383i
$892$	−23.8654			−0.799071
$893$	−14.0256	+	10.1902i	−0.469347	+	0.341001i
$894$	−11.8902	−	36.5943i	−0.397668	−	1.22390i
$895$	5.03316	−	15.4905i	0.168240	−	0.517790i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	−106.639	−	77.4781i	−3.56059	−	2.58692i
$898$	−0.365016	+	1.12340i	−0.0121808	+	0.0374885i
$899$	−2.62123	−	8.06732i	−0.0874230	−	0.269060i
$900$	−4.62157	+	3.35777i	−0.154052	+	0.111926i
$901$	−6.54865			−0.218167
$902$	−4.06193	+	4.48628i	−0.135247	+	0.149377i
$903$	2.33397			0.0776695
$904$	5.27972	−	3.83594i	0.175601	−	0.127581i
$905$	3.65819	+	11.2588i	0.121602	+	0.374254i
$906$	8.36438	−	25.7429i	0.277888	−	0.855251i
$907$	36.8202	+	26.7514i	1.22259	+	0.888266i	0.996313	−	0.0857959i	$-0.0273433\pi$
$907$	36.8202	+	26.7514i	1.22259	+	0.888266i	0.226281	+	0.974062i	$0.427343\pi$
$908$	−18.3685	−	13.3455i	−0.609580	−	0.442886i
$909$	−15.1291	+	46.5627i	−0.501802	+	1.54439i
$910$	−1.79256	−	5.51694i	−0.0594229	−	0.182885i
$911$	−23.5625	+	17.1192i	−0.780662	+	0.567184i	−0.905178	−	0.425033i	$-0.860262\pi$
$911$	−23.5625	+	17.1192i	−0.780662	+	0.567184i	0.124516	+	0.992218i	$0.460262\pi$
$912$	11.9403			0.395384
$913$	21.0317	−	23.2289i	0.696048	−	0.768764i
$914$	−11.1913			−0.370176
$915$	15.9911	−	11.6182i	0.528651	−	0.384087i
$916$	−4.90420	−	15.0936i	−0.162039	−	0.498706i
$917$	2.79945	−	8.61582i	0.0924460	−	0.284519i
$918$	−3.04298	−	2.21086i	−0.100433	−	0.0729691i
$919$	6.58668	+	4.78550i	0.217275	+	0.157859i	0.691099	−	0.722760i	$-0.257127\pi$
$919$	6.58668	+	4.78550i	0.217275	+	0.157859i	−0.473824	+	0.880619i	$0.657127\pi$
$920$	2.37891	−	7.32152i	0.0784302	−	0.241383i
$921$	2.34190	+	7.20762i	0.0771682	+	0.237499i
$922$	−0.354478	+	0.257543i	−0.0116741	+	0.00848174i
$923$	66.6256			2.19301
$924$	8.93233	+	4.00649i	0.293852	+	0.131804i
$925$	−4.56071			−0.149955
$926$	−16.3212	+	11.8580i	−0.536348	+	0.389679i
$927$	4.23910	+	13.0466i	0.139230	+	0.428507i
$928$	0.813681	−	2.50425i	0.0267104	−	0.0822061i
$929$	−18.9082	−	13.7376i	−0.620358	−	0.450716i	0.232689	−	0.972551i	$-0.425248\pi$
$929$	−18.9082	−	13.7376i	−0.620358	−	0.450716i	−0.853046	+	0.521835i	$0.825248\pi$
$930$	7.69276	+	5.58912i	0.252256	+	0.183274i
$931$	−1.25005	+	3.84724i	−0.0409686	+	0.126088i
$932$	−9.03652	−	27.8115i	−0.296001	−	0.910997i
$933$	−77.6773	+	56.4359i	−2.54304	+	1.84763i
$934$	3.27449			0.107145
$935$	1.52489	−	0.319733i	0.0498694	−	0.0104564i
$936$	33.1379			1.08314
$937$	−41.1613	+	29.9054i	−1.34468	+	0.976968i	−0.345424	+	0.938447i	$0.612265\pi$
$937$	−41.1613	+	29.9054i	−1.34468	+	0.976968i	−0.999258	+	0.0385216i	$0.987735\pi$
$938$	−2.07974	−	6.40079i	−0.0679060	−	0.208993i
$939$	7.10309	−	21.8611i	0.231801	−	0.713409i
$940$	−3.46718	−	2.51906i	−0.113087	−	0.0821625i
$941$	10.6827	+	7.76143i	0.348246	+	0.253015i	0.748133	−	0.663549i	$-0.230951\pi$
$941$	10.6827	+	7.76143i	0.348246	+	0.253015i	−0.399887	+	0.916564i	$0.630951\pi$
$942$	−8.26667	+	25.4422i	−0.269343	+	0.828951i
$943$	−4.34086	−	13.3598i	−0.141358	−	0.435054i
$944$	10.5480	−	7.66356i	0.343308	−	0.249428i
$945$	8.00674			0.260459
$946$	−1.30499	−	2.27477i	−0.0424288	−	0.0739592i
$947$	0.766130			0.0248959			0.0124479	−	0.999923i	$-0.496038\pi$
$947$	0.766130			0.0248959			0.0124479	+	0.999923i	$0.496038\pi$
$948$	9.43924	−	6.85801i	0.306572	−	0.222738i
$949$	21.9673	+	67.6085i	0.713090	+	2.19466i
$950$	−1.25005	+	3.84724i	−0.0405568	+	0.124821i
$951$	−41.7137	−	30.3068i	−1.35266	−	0.982765i
$952$	0.380053	+	0.276124i	0.0123176	+	0.00894924i
$953$	−2.29418	+	7.06076i	−0.0743157	+	0.228720i	−0.981314	−	0.192415i	$-0.938368\pi$
$953$	−2.29418	+	7.06076i	−0.0743157	+	0.228720i	0.906998	+	0.421135i	$0.138368\pi$
$954$	24.6082	+	75.7363i	0.796720	+	2.45205i
$955$	−22.1142	+	16.0669i	−0.715598	+	0.519913i
$956$	−8.72767			−0.282273
$957$	−2.76519	+	25.6288i	−0.0893859	+	0.828461i
$958$	−27.0594			−0.874250
$959$	−14.2590	+	10.3597i	−0.460446	+	0.334534i
$960$	0.912128	+	2.80724i	0.0294388	+	0.0906033i
$961$	−6.37263	+	19.6129i	−0.205569	+	0.632676i
$962$	21.4034	+	15.5505i	0.690072	+	0.501367i
$963$	−28.0143	−	20.3536i	−0.902748	−	0.655885i
$964$	−2.96304	+	9.11929i	−0.0954330	+	0.293712i
$965$	−5.20796	−	16.0284i	−0.167650	−	0.515974i
$966$	−18.3834	+	13.3563i	−0.591476	+	0.429733i
$967$	33.2841			1.07035			0.535173	−	0.844743i	$-0.320247\pi$
$967$	33.2841			1.07035			0.535173	+	0.844743i	$0.320247\pi$
$968$	−1.08944	−	10.9459i	−0.0350161	−	0.351815i
$969$	−5.60922			−0.180194
$970$	−13.5518	+	9.84599i	−0.435124	+	0.316136i
$971$	−5.86258	−	18.0432i	−0.188139	−	0.579033i	0.811849	−	0.583867i	$-0.198461\pi$
$971$	−5.86258	−	18.0432i	−0.188139	−	0.579033i	−0.999988	+	0.00483423i	$0.998461\pi$
$972$	1.49764	−	4.60925i	0.0480367	−	0.147842i
$973$	−15.1017	−	10.9720i	−0.484138	−	0.351747i
$974$	−20.7987	−	15.1111i	−0.666434	−	0.484192i
$975$	−5.29112	+	16.2844i	−0.169452	+	0.521518i
$976$	−2.06934	−	6.36876i	−0.0662378	−	0.203859i
$977$	−36.2008	+	26.3015i	−1.15817	+	0.841458i	−0.989545	−	0.144223i	$-0.953932\pi$
$977$	−36.2008	+	26.3015i	−1.15817	+	0.841458i	−0.168622	+	0.985681i	$0.553932\pi$
$978$	5.00962			0.160190
$979$	−4.01198	+	37.1845i	−0.128223	+	1.18842i
$980$	−1.00000			−0.0319438
$981$	−50.2716	+	36.5244i	−1.60505	+	1.16614i
$982$	−8.96397	−	27.5883i	−0.286052	−	0.880377i
$983$	0.304287	−	0.936499i	0.00970525	−	0.0298697i	−0.946087	−	0.323914i	$-0.895001\pi$
$983$	0.304287	−	0.936499i	0.00970525	−	0.0298697i	0.955792	+	0.294044i	$0.0950012\pi$
$984$	4.35742	+	3.16585i	0.138909	+	0.100924i
$985$	−3.76888	−	2.73826i	−0.120087	−	0.0872481i
$986$	−0.382244	+	1.17642i	−0.0121731	+	0.0374650i
$987$	3.90908	+	12.0309i	0.124427	+	0.382948i
$988$	18.9842	−	13.7929i	0.603969	−	0.438809i
$989$	6.08718			0.193561
$990$	−9.42794	−	16.4342i	−0.299640	−	0.522313i
$991$	−58.3261			−1.85279			−0.926395	−	0.376554i	$-0.877109\pi$
$991$	−58.3261			−1.85279			−0.926395	+	0.376554i	$0.877109\pi$
$992$	2.60621	−	1.89352i	0.0827471	−	0.0601193i
$993$	1.84014	+	5.66338i	0.0583952	+	0.179722i
$994$	3.54921	−	10.9233i	0.112574	−	0.346467i
$995$	−9.87650	−	7.17570i	−0.313106	−	0.227485i
$996$	−22.5617	−	16.3920i	−0.714894	−	0.519401i
$997$	10.1890	−	31.3586i	0.322690	−	0.993136i	−0.649783	−	0.760120i	$-0.725140\pi$
$997$	10.1890	−	31.3586i	0.322690	−	0.993136i	0.972473	−	0.233017i	$-0.0748597\pi$
$998$	7.04866	+	21.6935i	0.223121	+	0.686697i
$999$	−29.5424	+	21.4638i	−0.934680	+	0.679084i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.h.421.1	✓	12
11.2	odd	10		8470.2.a.cu.1.2		6
11.4	even	5	inner	770.2.n.h.631.1	yes	12
11.9	even	5		8470.2.a.da.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.h.421.1	✓	12	1.1	even	1	trivial
770.2.n.h.631.1	yes	12	11.4	even	5	inner
8470.2.a.cu.1.2		6	11.2	odd	10
8470.2.a.da.1.2		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)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.912128 - 2.80724i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(2.38798 + 1.73497i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-4.62157 + 3.35777i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.912128 - 2.80724i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(2.38798 + 1.73497i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-4.62157 + 3.35777i) q^{9} -1.00000 q^{10} +(0.355779 - 3.29749i) q^{11} -2.95171 q^{12} +(-4.69299 + 3.40966i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.912128 - 2.80724i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.380053 + 0.276124i) q^{17} +(1.76528 - 5.43299i) q^{18} +(-1.25005 - 3.84724i) q^{19} +(0.809017 - 0.587785i) q^{20} -2.95171 q^{21} +(1.65038 + 2.87684i) q^{22} -7.69830 q^{23} +(2.38798 - 1.73497i) q^{24} +(0.309017 + 0.951057i) q^{25} +(1.79256 - 5.51694i) q^{26} +(6.47759 + 4.70624i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(0.813681 - 2.50425i) q^{29} +(0.912128 + 2.80724i) q^{30} +(2.60621 - 1.89352i) q^{31} +1.00000 q^{32} +(-9.58136 + 2.00897i) q^{33} -0.469771 q^{34} +(0.809017 - 0.587785i) q^{35} +(1.76528 + 5.43299i) q^{36} +(-1.40934 + 4.33749i) q^{37} +(3.27266 + 2.37773i) q^{38} +(13.8523 + 10.0643i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(0.563872 + 1.73542i) q^{41} +(2.38798 - 1.73497i) q^{42} -0.790717 q^{43} +(-3.02615 - 1.35735i) q^{44} -5.71258 q^{45} +(6.22805 - 4.52495i) q^{46} +(-1.32435 - 4.07592i) q^{47} +(-0.912128 + 2.80724i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(0.428491 - 1.31876i) q^{51} +(1.79256 + 5.51694i) q^{52} +(-11.2778 + 8.19378i) q^{53} -8.00674 q^{54} +(2.22605 - 2.45860i) q^{55} +1.00000 q^{56} +(-9.65994 + 7.01836i) q^{57} +(0.813681 + 2.50425i) q^{58} +(-4.02897 + 12.3999i) q^{59} +(-2.38798 - 1.73497i) q^{60} +(5.41759 + 3.93611i) q^{61} +(-0.995482 + 3.06378i) q^{62} +(1.76528 + 5.43299i) q^{63} +(-0.809017 + 0.587785i) q^{64} -5.80086 q^{65} +(6.57064 - 7.25707i) q^{66} -6.73018 q^{67} +(0.380053 - 0.276124i) q^{68} +(7.02183 + 21.6110i) q^{69} +(-0.309017 + 0.951057i) q^{70} +(-9.29195 - 6.75100i) q^{71} +(-4.62157 - 3.35777i) q^{72} +(3.78691 - 11.6549i) q^{73} +(-1.40934 - 4.33749i) q^{74} +(2.38798 - 1.73497i) q^{75} -4.04523 q^{76} +(-3.02615 - 1.35735i) q^{77} -17.1224 q^{78} +(-3.19789 + 2.32340i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(2.00732 - 6.17789i) q^{81} +(-1.47624 - 1.07255i) q^{82} +(7.64360 + 5.55340i) q^{83} +(-0.912128 + 2.80724i) q^{84} +(0.145167 + 0.446779i) q^{85} +(0.639704 - 0.464772i) q^{86} -7.77222 q^{87} +(3.24604 - 0.680614i) q^{88} -11.2766 q^{89} +(4.62157 - 3.35777i) q^{90} +(1.79256 + 5.51694i) q^{91} +(-2.37891 + 7.32152i) q^{92} +(-7.69276 - 5.58912i) q^{93} +(3.46718 + 2.51906i) q^{94} +(1.25005 - 3.84724i) q^{95} +(-0.912128 - 2.80724i) q^{96} +(13.5518 - 9.84599i) q^{97} +1.00000 q^{98} +(9.42794 + 16.4342i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9} - 12 q^{10} - q^{11} - 10 q^{12} - 3 q^{14} - 3 q^{16} - 8 q^{18} - q^{19} + 3 q^{20} - 10 q^{21} - q^{22} - 4 q^{23} + 5 q^{24} - 3 q^{25} + 3 q^{27} - 3 q^{28} + 22 q^{29} + 6 q^{31} + 12 q^{32} - 29 q^{33} - 30 q^{34} + 3 q^{35} - 8 q^{36} - 10 q^{37} + 14 q^{38} + 20 q^{39} + 3 q^{40} + 16 q^{41} + 5 q^{42} + 30 q^{43} + 14 q^{44} - 22 q^{45} - 4 q^{46} + 34 q^{47} - 3 q^{49} - 3 q^{50} + 37 q^{51} - 26 q^{53} - 52 q^{54} + 11 q^{55} + 12 q^{56} - 19 q^{57} + 22 q^{58} + q^{59} - 5 q^{60} + 40 q^{61} - 4 q^{62} - 8 q^{63} - 3 q^{64} + 16 q^{66} - 58 q^{67} + 14 q^{69} + 3 q^{70} - 14 q^{71} - 3 q^{72} + 32 q^{73} - 10 q^{74} + 5 q^{75} - 26 q^{76} + 14 q^{77} - 60 q^{78} + 16 q^{79} + 3 q^{80} - 46 q^{81} + q^{82} + 35 q^{83} - 15 q^{85} + 5 q^{86} - q^{88} - 58 q^{89} + 3 q^{90} + 6 q^{92} + 46 q^{93} - 16 q^{94} + q^{95} + 57 q^{97} + 12 q^{98} + 69 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9 - 12 * q^10 - q^11 - 10 * q^12 - 3 * q^14 - 3 * q^16 - 8 * q^18 - q^19 + 3 * q^20 - 10 * q^21 - q^22 - 4 * q^23 + 5 * q^24 - 3 * q^25 + 3 * q^27 - 3 * q^28 + 22 * q^29 + 6 * q^31 + 12 * q^32 - 29 * q^33 - 30 * q^34 + 3 * q^35 - 8 * q^36 - 10 * q^37 + 14 * q^38 + 20 * q^39 + 3 * q^40 + 16 * q^41 + 5 * q^42 + 30 * q^43 + 14 * q^44 - 22 * q^45 - 4 * q^46 + 34 * q^47 - 3 * q^49 - 3 * q^50 + 37 * q^51 - 26 * q^53 - 52 * q^54 + 11 * q^55 + 12 * q^56 - 19 * q^57 + 22 * q^58 + q^59 - 5 * q^60 + 40 * q^61 - 4 * q^62 - 8 * q^63 - 3 * q^64 + 16 * q^66 - 58 * q^67 + 14 * q^69 + 3 * q^70 - 14 * q^71 - 3 * q^72 + 32 * q^73 - 10 * q^74 + 5 * q^75 - 26 * q^76 + 14 * q^77 - 60 * q^78 + 16 * q^79 + 3 * q^80 - 46 * q^81 + q^82 + 35 * q^83 - 15 * q^85 + 5 * q^86 - q^88 - 58 * q^89 + 3 * q^90 + 6 * q^92 + 46 * q^93 - 16 * q^94 + q^95 + 57 * q^97 + 12 * q^98 + 69 * q^99

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