LMFDB - Embedded newform 861.2.n.a.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(379,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("861.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.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:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			379.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	861.379
Dual form			861.2.n.a.652.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30902 + 0.951057i) q^{2} -1.00000 q^{3} +(0.190983 + 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-1.30902 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.690983 - 2.12663i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.30902 + 0.951057i) q^{2} -1.00000 q^{3} +(0.190983 + 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-1.30902 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.690983 - 2.12663i) q^{8} +1.00000 q^{9} +(0.500000 - 1.53884i) q^{10} +(-0.309017 + 0.951057i) q^{11} +(-0.190983 - 0.587785i) q^{12} +(-4.85410 - 3.52671i) q^{13} -1.61803 q^{14} +(0.309017 + 0.951057i) q^{15} +(3.92705 - 2.85317i) q^{16} +(1.61803 - 4.97980i) q^{17} +(1.30902 + 0.951057i) q^{18} +(-6.35410 + 4.61653i) q^{19} +(0.500000 - 0.363271i) q^{20} +(0.809017 - 0.587785i) q^{21} +(-1.30902 + 0.951057i) q^{22} +(-5.92705 - 4.30625i) q^{23} +(-0.690983 + 2.12663i) q^{24} +(3.23607 - 2.35114i) q^{25} +(-3.00000 - 9.23305i) q^{26} -1.00000 q^{27} +(-0.500000 - 0.363271i) q^{28} +(1.88197 + 5.79210i) q^{29} +(-0.500000 + 1.53884i) q^{30} +(1.64590 - 5.06555i) q^{31} +3.38197 q^{32} +(0.309017 - 0.951057i) q^{33} +(6.85410 - 4.97980i) q^{34} +(0.809017 + 0.587785i) q^{35} +(0.190983 + 0.587785i) q^{36} +(-3.16312 - 9.73508i) q^{37} -12.7082 q^{38} +(4.85410 + 3.52671i) q^{39} -2.23607 q^{40} +(3.30902 - 5.48183i) q^{41} +1.61803 q^{42} +(6.47214 + 4.70228i) q^{43} -0.618034 q^{44} +(-0.309017 - 0.951057i) q^{45} +(-3.66312 - 11.2739i) q^{46} +(3.42705 + 2.48990i) q^{47} +(-3.92705 + 2.85317i) q^{48} +(0.309017 - 0.951057i) q^{49} +6.47214 q^{50} +(-1.61803 + 4.97980i) q^{51} +(1.14590 - 3.52671i) q^{52} +(-0.836881 - 2.57565i) q^{53} +(-1.30902 - 0.951057i) q^{54} +1.00000 q^{55} +(0.690983 + 2.12663i) q^{56} +(6.35410 - 4.61653i) q^{57} +(-3.04508 + 9.37181i) q^{58} +(-2.42705 - 1.76336i) q^{59} +(-0.500000 + 0.363271i) q^{60} +(-3.30902 + 2.40414i) q^{61} +(6.97214 - 5.06555i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(-3.42705 - 2.48990i) q^{64} +(-1.85410 + 5.70634i) q^{65} +(1.30902 - 0.951057i) q^{66} +(-0.881966 - 2.71441i) q^{67} +3.23607 q^{68} +(5.92705 + 4.30625i) q^{69} +(0.500000 + 1.53884i) q^{70} +(-2.69098 + 8.28199i) q^{71} +(0.690983 - 2.12663i) q^{72} -3.85410 q^{73} +(5.11803 - 15.7517i) q^{74} +(-3.23607 + 2.35114i) q^{75} +(-3.92705 - 2.85317i) q^{76} +(-0.309017 - 0.951057i) q^{77} +(3.00000 + 9.23305i) q^{78} +15.0000 q^{79} +(-3.92705 - 2.85317i) q^{80} +1.00000 q^{81} +(9.54508 - 4.02874i) q^{82} -11.8541 q^{83} +(0.500000 + 0.363271i) q^{84} -5.23607 q^{85} +(4.00000 + 12.3107i) q^{86} +(-1.88197 - 5.79210i) q^{87} +(1.80902 + 1.31433i) q^{88} +(-0.381966 + 0.277515i) q^{89} +(0.500000 - 1.53884i) q^{90} +6.00000 q^{91} +(1.39919 - 4.30625i) q^{92} +(-1.64590 + 5.06555i) q^{93} +(2.11803 + 6.51864i) q^{94} +(6.35410 + 4.61653i) q^{95} -3.38197 q^{96} +(4.11803 + 12.6740i) q^{97} +(1.30902 - 0.951057i) q^{98} +(-0.309017 + 0.951057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 4 q^{3} + 3 q^{4} + q^{5} - 3 q^{6} - q^{7} + 5 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 + q^5 - 3 * q^6 - q^7 + 5 * q^8 + 4 * q^9	\( 4 q + 3 q^{2} - 4 q^{3} + 3 q^{4} + q^{5} - 3 q^{6} - q^{7} + 5 q^{8} + 4 q^{9} + 2 q^{10} + q^{11} - 3 q^{12} - 6 q^{13} - 2 q^{14} - q^{15} + 9 q^{16} + 2 q^{17} + 3 q^{18} - 12 q^{19} + 2 q^{20} + q^{21} - 3 q^{22} - 17 q^{23} - 5 q^{24} + 4 q^{25} - 12 q^{26} - 4 q^{27} - 2 q^{28} + 12 q^{29} - 2 q^{30} + 20 q^{31} + 18 q^{32} - q^{33} + 14 q^{34} + q^{35} + 3 q^{36} + 3 q^{37} - 24 q^{38} + 6 q^{39} + 11 q^{41} + 2 q^{42} + 8 q^{43} + 2 q^{44} + q^{45} + q^{46} + 7 q^{47} - 9 q^{48} - q^{49} + 8 q^{50} - 2 q^{51} + 18 q^{52} - 19 q^{53} - 3 q^{54} + 4 q^{55} + 5 q^{56} + 12 q^{57} - q^{58} - 3 q^{59} - 2 q^{60} - 11 q^{61} + 10 q^{62} - q^{63} - 7 q^{64} + 6 q^{65} + 3 q^{66} - 8 q^{67} + 4 q^{68} + 17 q^{69} + 2 q^{70} - 13 q^{71} + 5 q^{72} - 2 q^{73} + 16 q^{74} - 4 q^{75} - 9 q^{76} + q^{77} + 12 q^{78} + 60 q^{79} - 9 q^{80} + 4 q^{81} + 27 q^{82} - 34 q^{83} + 2 q^{84} - 12 q^{85} + 16 q^{86} - 12 q^{87} + 5 q^{88} - 6 q^{89} + 2 q^{90} + 24 q^{91} - 19 q^{92} - 20 q^{93} + 4 q^{94} + 12 q^{95} - 18 q^{96} + 12 q^{97} + 3 q^{98} + q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 + q^5 - 3 * q^6 - q^7 + 5 * q^8 + 4 * q^9 + 2 * q^10 + q^11 - 3 * q^12 - 6 * q^13 - 2 * q^14 - q^15 + 9 * q^16 + 2 * q^17 + 3 * q^18 - 12 * q^19 + 2 * q^20 + q^21 - 3 * q^22 - 17 * q^23 - 5 * q^24 + 4 * q^25 - 12 * q^26 - 4 * q^27 - 2 * q^28 + 12 * q^29 - 2 * q^30 + 20 * q^31 + 18 * q^32 - q^33 + 14 * q^34 + q^35 + 3 * q^36 + 3 * q^37 - 24 * q^38 + 6 * q^39 + 11 * q^41 + 2 * q^42 + 8 * q^43 + 2 * q^44 + q^45 + q^46 + 7 * q^47 - 9 * q^48 - q^49 + 8 * q^50 - 2 * q^51 + 18 * q^52 - 19 * q^53 - 3 * q^54 + 4 * q^55 + 5 * q^56 + 12 * q^57 - q^58 - 3 * q^59 - 2 * q^60 - 11 * q^61 + 10 * q^62 - q^63 - 7 * q^64 + 6 * q^65 + 3 * q^66 - 8 * q^67 + 4 * q^68 + 17 * q^69 + 2 * q^70 - 13 * q^71 + 5 * q^72 - 2 * q^73 + 16 * q^74 - 4 * q^75 - 9 * q^76 + q^77 + 12 * q^78 + 60 * q^79 - 9 * q^80 + 4 * q^81 + 27 * q^82 - 34 * q^83 + 2 * q^84 - 12 * q^85 + 16 * q^86 - 12 * q^87 + 5 * q^88 - 6 * q^89 + 2 * q^90 + 24 * q^91 - 19 * q^92 - 20 * q^93 + 4 * q^94 + 12 * q^95 - 18 * q^96 + 12 * q^97 + 3 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.30902	+	0.951057i	0.925615	+	0.672499i	0.944915	−	0.327315i	$-0.106144\pi$
$2$	1.30902	+	0.951057i	0.925615	+	0.672499i	−0.0193004	+	0.999814i	$0.506144\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.190983	+	0.587785i	0.0954915	+	0.293893i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i	0.857877	−	0.513855i	$-0.171783\pi$
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i	−0.996074	+	0.0885298i	$0.971783\pi$
$6$	−1.30902	−	0.951057i	−0.534404	−	0.388267i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$	0.690983	−	2.12663i	0.244299	−	0.751876i
$9$	1.00000			0.333333
$10$	0.500000	−	1.53884i	0.158114	−	0.486624i
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i	−0.986773	−	0.162108i	$-0.948171\pi$
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i	0.893601	+	0.448862i	$0.148171\pi$
$12$	−0.190983	−	0.587785i	−0.0551320	−	0.169679i
$13$	−4.85410	−	3.52671i	−1.34629	−	0.978134i	−0.999187	−	0.0403050i	$-0.987167\pi$
$13$	−4.85410	−	3.52671i	−1.34629	−	0.978134i	−0.347098	−	0.937829i	$-0.612833\pi$
$14$	−1.61803			−0.432438
$15$	0.309017	+	0.951057i	0.0797878	+	0.245562i
$16$	3.92705	−	2.85317i	0.981763	−	0.713292i
$17$	1.61803	−	4.97980i	0.392431	−	1.20778i	−0.538513	−	0.842617i	$-0.681014\pi$
$17$	1.61803	−	4.97980i	0.392431	−	1.20778i	0.930944	−	0.365161i	$-0.118986\pi$
$18$	1.30902	+	0.951057i	0.308538	+	0.224166i
$19$	−6.35410	+	4.61653i	−1.45773	+	1.05910i	−0.473784	+	0.880641i	$0.657112\pi$
$19$	−6.35410	+	4.61653i	−1.45773	+	1.05910i	−0.983947	+	0.178463i	$0.942888\pi$
$20$	0.500000	−	0.363271i	0.111803	−	0.0812299i
$21$	0.809017	−	0.587785i	0.176542	−	0.128265i
$22$	−1.30902	+	0.951057i	−0.279083	+	0.202766i
$23$	−5.92705	−	4.30625i	−1.23588	−	0.897916i	−0.238559	−	0.971128i	$-0.576675\pi$
$23$	−5.92705	−	4.30625i	−1.23588	−	0.897916i	−0.997316	+	0.0732118i	$0.976675\pi$
$24$	−0.690983	+	2.12663i	−0.141046	+	0.434096i
$25$	3.23607	−	2.35114i	0.647214	−	0.470228i
$26$	−3.00000	−	9.23305i	−0.588348	−	1.81075i
$27$	−1.00000			−0.192450
$28$	−0.500000	−	0.363271i	−0.0944911	−	0.0686518i
$29$	1.88197	+	5.79210i	0.349472	+	1.07557i	0.959146	+	0.282912i	$0.0913006\pi$
$29$	1.88197	+	5.79210i	0.349472	+	1.07557i	−0.609673	+	0.792653i	$0.708699\pi$
$30$	−0.500000	+	1.53884i	−0.0912871	+	0.280953i
$31$	1.64590	−	5.06555i	0.295612	−	0.909800i	−0.687403	−	0.726276i	$-0.741249\pi$
$31$	1.64590	−	5.06555i	0.295612	−	0.909800i	0.983015	−	0.183524i	$-0.0587506\pi$
$32$	3.38197			0.597853
$33$	0.309017	−	0.951057i	0.0537930	−	0.165558i
$34$	6.85410	−	4.97980i	1.17547	−	0.854028i
$35$	0.809017	+	0.587785i	0.136749	+	0.0993538i
$36$	0.190983	+	0.587785i	0.0318305	+	0.0979642i
$37$	−3.16312	−	9.73508i	−0.520014	−	1.60044i	−0.773971	−	0.633222i	$-0.781732\pi$
$37$	−3.16312	−	9.73508i	−0.520014	−	1.60044i	0.253957	−	0.967216i	$-0.418268\pi$
$38$	−12.7082			−2.06154
$39$	4.85410	+	3.52671i	0.777278	+	0.564726i
$40$	−2.23607			−0.353553
$41$	3.30902	−	5.48183i	0.516782	−	0.856117i
$41$	3.30902	−	5.48183i	0.516782	−	0.856117i
$42$	1.61803			0.249668
$43$	6.47214	+	4.70228i	0.986991	+	0.717091i	0.959260	−	0.282524i	$-0.0911717\pi$
$43$	6.47214	+	4.70228i	0.986991	+	0.717091i	0.0277313	+	0.999615i	$0.491172\pi$
$44$	−0.618034			−0.0931721
$45$	−0.309017	−	0.951057i	−0.0460655	−	0.141775i
$46$	−3.66312	−	11.2739i	−0.540097	−	1.66225i
$47$	3.42705	+	2.48990i	0.499887	+	0.363189i	0.808974	−	0.587845i	$-0.200023\pi$
$47$	3.42705	+	2.48990i	0.499887	+	0.363189i	−0.309087	+	0.951034i	$0.600023\pi$
$48$	−3.92705	+	2.85317i	−0.566821	+	0.411820i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	6.47214			0.915298
$51$	−1.61803	+	4.97980i	−0.226570	+	0.697311i
$52$	1.14590	−	3.52671i	0.158907	−	0.489067i
$53$	−0.836881	−	2.57565i	−0.114954	−	0.353793i	0.876983	−	0.480521i	$-0.159553\pi$
$53$	−0.836881	−	2.57565i	−0.114954	−	0.353793i	−0.991938	+	0.126728i	$0.959553\pi$
$54$	−1.30902	−	0.951057i	−0.178135	−	0.129422i
$55$	1.00000			0.134840
$56$	0.690983	+	2.12663i	0.0923365	+	0.284182i
$57$	6.35410	−	4.61653i	0.841621	−	0.611474i
$58$	−3.04508	+	9.37181i	−0.399839	+	1.23058i
$59$	−2.42705	−	1.76336i	−0.315975	−	0.229569i	0.418481	−	0.908226i	$-0.362563\pi$
$59$	−2.42705	−	1.76336i	−0.315975	−	0.229569i	−0.734456	+	0.678656i	$0.762563\pi$
$60$	−0.500000	+	0.363271i	−0.0645497	+	0.0468981i
$61$	−3.30902	+	2.40414i	−0.423676	+	0.307819i	−0.779115	−	0.626881i	$-0.784331\pi$
$61$	−3.30902	+	2.40414i	−0.423676	+	0.307819i	0.355439	+	0.934699i	$0.384331\pi$
$62$	6.97214	−	5.06555i	0.885462	−	0.643326i
$63$	−0.809017	+	0.587785i	−0.101927	+	0.0740540i
$64$	−3.42705	−	2.48990i	−0.428381	−	0.311237i
$65$	−1.85410	+	5.70634i	−0.229973	+	0.707784i
$66$	1.30902	−	0.951057i	0.161129	−	0.117067i
$67$	−0.881966	−	2.71441i	−0.107749	−	0.331618i	0.882617	−	0.470094i	$-0.155780\pi$
$67$	−0.881966	−	2.71441i	−0.107749	−	0.331618i	−0.990366	+	0.138475i	$0.955780\pi$
$68$	3.23607			0.392431
$69$	5.92705	+	4.30625i	0.713533	+	0.518412i
$70$	0.500000	+	1.53884i	0.0597614	+	0.183927i
$71$	−2.69098	+	8.28199i	−0.319361	+	0.982892i	0.654561	+	0.756009i	$0.272853\pi$
$71$	−2.69098	+	8.28199i	−0.319361	+	0.982892i	−0.973922	+	0.226883i	$0.927147\pi$
$72$	0.690983	−	2.12663i	0.0814331	−	0.250625i
$73$	−3.85410			−0.451089			−0.225544	−	0.974233i	$-0.572416\pi$
$73$	−3.85410			−0.451089			−0.225544	+	0.974233i	$0.572416\pi$
$74$	5.11803	−	15.7517i	0.594959	−	1.83110i
$75$	−3.23607	+	2.35114i	−0.373669	+	0.271486i
$76$	−3.92705	−	2.85317i	−0.450464	−	0.327281i
$77$	−0.309017	−	0.951057i	−0.0352158	−	0.108383i
$78$	3.00000	+	9.23305i	0.339683	+	1.04544i
$79$	15.0000			1.68763			0.843816	−	0.536633i	$-0.180304\pi$
$79$	15.0000			1.68763			0.843816	+	0.536633i	$0.180304\pi$
$80$	−3.92705	−	2.85317i	−0.439058	−	0.318994i
$81$	1.00000			0.111111
$82$	9.54508	−	4.02874i	1.05408	−	0.444900i
$83$	−11.8541			−1.30116			−0.650578	−	0.759439i	$-0.725473\pi$
$83$	−11.8541			−1.30116			−0.650578	+	0.759439i	$0.725473\pi$
$84$	0.500000	+	0.363271i	0.0545545	+	0.0396361i
$85$	−5.23607			−0.567931
$86$	4.00000	+	12.3107i	0.431331	+	1.32750i
$87$	−1.88197	−	5.79210i	−0.201768	−	0.620978i
$88$	1.80902	+	1.31433i	0.192842	+	0.140108i
$89$	−0.381966	+	0.277515i	−0.0404883	+	0.0294165i	−0.607845	−	0.794055i	$-0.707966\pi$
$89$	−0.381966	+	0.277515i	−0.0404883	+	0.0294165i	0.567357	+	0.823472i	$0.307966\pi$
$90$	0.500000	−	1.53884i	0.0527046	−	0.162208i
$91$	6.00000			0.628971
$92$	1.39919	−	4.30625i	0.145875	−	0.448958i
$93$	−1.64590	+	5.06555i	−0.170672	+	0.525273i
$94$	2.11803	+	6.51864i	0.218459	+	0.672346i
$95$	6.35410	+	4.61653i	0.651917	+	0.473646i
$96$	−3.38197			−0.345170
$97$	4.11803	+	12.6740i	0.418123	+	1.28685i	0.909428	+	0.415862i	$0.136520\pi$
$97$	4.11803	+	12.6740i	0.418123	+	1.28685i	−0.491305	+	0.870988i	$0.663480\pi$
$98$	1.30902	−	0.951057i	0.132231	−	0.0960712i
$99$	−0.309017	+	0.951057i	−0.0310574	+	0.0955848i
$100$	2.00000	+	1.45309i	0.200000	+	0.145309i
$101$	−3.23607	+	2.35114i	−0.322001	+	0.233947i	−0.737029	−	0.675861i	$-0.763772\pi$
$101$	−3.23607	+	2.35114i	−0.322001	+	0.233947i	0.415028	+	0.909809i	$0.363772\pi$
$102$	−6.85410	+	4.97980i	−0.678657	+	0.493073i
$103$	6.66312	−	4.84104i	0.656537	−	0.477002i	−0.208955	−	0.977925i	$-0.567006\pi$
$103$	6.66312	−	4.84104i	0.656537	−	0.477002i	0.865492	+	0.500923i	$0.167006\pi$
$104$	−10.8541	+	7.88597i	−1.06433	+	0.773283i
$105$	−0.809017	−	0.587785i	−0.0789520	−	0.0573620i
$106$	1.35410	−	4.16750i	0.131522	−	0.404783i
$107$	−11.7082	+	8.50651i	−1.13187	+	0.822355i	−0.985967	−	0.166943i	$-0.946610\pi$
$107$	−11.7082	+	8.50651i	−1.13187	+	0.822355i	−0.145908	+	0.989298i	$0.546610\pi$
$108$	−0.190983	−	0.587785i	−0.0183773	−	0.0565597i
$109$	13.7984			1.32164			0.660822	−	0.750542i	$-0.270208\pi$
$109$	13.7984			1.32164			0.660822	+	0.750542i	$0.270208\pi$
$110$	1.30902	+	0.951057i	0.124810	+	0.0906797i
$111$	3.16312	+	9.73508i	0.300230	+	0.924013i
$112$	−1.50000	+	4.61653i	−0.141737	+	0.436221i
$113$	−2.78115	+	8.55951i	−0.261629	+	0.805211i	0.730822	+	0.682568i	$0.239137\pi$
$113$	−2.78115	+	8.55951i	−0.261629	+	0.805211i	−0.992451	+	0.122643i	$0.960863\pi$
$114$	12.7082			1.19023
$115$	−2.26393	+	6.96767i	−0.211113	+	0.649738i
$116$	−3.04508	+	2.21238i	−0.282729	+	0.205415i
$117$	−4.85410	−	3.52671i	−0.448762	−	0.326045i
$118$	−1.50000	−	4.61653i	−0.138086	−	0.424986i
$119$	1.61803	+	4.97980i	0.148325	+	0.456497i
$120$	2.23607			0.204124
$121$	8.09017	+	5.87785i	0.735470	+	0.534350i
$122$	−6.61803			−0.599169
$123$	−3.30902	+	5.48183i	−0.298364	+	0.494280i
$124$	3.29180			0.295612
$125$	−7.28115	−	5.29007i	−0.651246	−	0.473158i
$126$	−1.61803			−0.144146
$127$	−1.54508	−	4.75528i	−0.137104	−	0.421963i	0.858807	−	0.512299i	$-0.171206\pi$
$127$	−1.54508	−	4.75528i	−0.137104	−	0.421963i	−0.995911	+	0.0903358i	$0.971206\pi$
$128$	−4.20820	−	12.9515i	−0.371956	−	1.14476i
$129$	−6.47214	−	4.70228i	−0.569840	−	0.414013i
$130$	−7.85410	+	5.70634i	−0.688850	+	0.500479i
$131$	−0.527864	+	1.62460i	−0.0461197	+	0.141942i	−0.971465	−	0.237184i	$-0.923775\pi$
$131$	−0.527864	+	1.62460i	−0.0461197	+	0.141942i	0.925345	+	0.379126i	$0.123775\pi$
$132$	0.618034			0.0537930
$133$	2.42705	−	7.46969i	0.210452	−	0.647705i
$134$	1.42705	−	4.39201i	0.123278	−	0.379412i
$135$	0.309017	+	0.951057i	0.0265959	+	0.0818539i
$136$	−9.47214	−	6.88191i	−0.812229	−	0.590119i
$137$	0.708204			0.0605059			0.0302530	−	0.999542i	$-0.490369\pi$
$137$	0.708204			0.0605059			0.0302530	+	0.999542i	$0.490369\pi$
$138$	3.66312	+	11.2739i	0.311825	+	0.959700i
$139$	9.66312	−	7.02067i	0.819615	−	0.595485i	−0.0969872	−	0.995286i	$-0.530921\pi$
$139$	9.66312	−	7.02067i	0.819615	−	0.595485i	0.916602	+	0.399800i	$0.130921\pi$
$140$	−0.190983	+	0.587785i	−0.0161410	+	0.0496769i
$141$	−3.42705	−	2.48990i	−0.288610	−	0.209687i
$142$	−11.3992	+	8.28199i	−0.956599	+	0.695010i
$143$	4.85410	−	3.52671i	0.405920	−	0.294918i
$144$	3.92705	−	2.85317i	0.327254	−	0.237764i
$145$	4.92705	−	3.57971i	0.409169	−	0.297279i
$146$	−5.04508	−	3.66547i	−0.417534	−	0.303356i
$147$	−0.309017	+	0.951057i	−0.0254873	+	0.0784418i
$148$	5.11803	−	3.71847i	0.420700	−	0.305656i
$149$	−0.336881	−	1.03681i	−0.0275984	−	0.0849390i	0.936309	−	0.351178i	$-0.114219\pi$
$149$	−0.336881	−	1.03681i	−0.0275984	−	0.0849390i	−0.963907	+	0.266239i	$0.914219\pi$
$150$	−6.47214			−0.528448
$151$	−18.4894	−	13.4333i	−1.50464	−	1.09319i	−0.968486	−	0.249068i	$-0.919876\pi$
$151$	−18.4894	−	13.4333i	−1.50464	−	1.09319i	−0.536157	−	0.844119i	$-0.680124\pi$
$152$	5.42705	+	16.7027i	0.440192	+	1.35477i
$153$	1.61803	−	4.97980i	0.130810	−	0.402593i
$154$	0.500000	−	1.53884i	0.0402911	−	0.124003i
$155$	−5.32624			−0.427814
$156$	−1.14590	+	3.52671i	−0.0917453	+	0.282363i
$157$	2.04508	−	1.48584i	0.163216	−	0.118583i	−0.503179	−	0.864182i	$-0.667837\pi$
$157$	2.04508	−	1.48584i	0.163216	−	0.118583i	0.666395	+	0.745599i	$0.267837\pi$
$158$	19.6353	+	14.2658i	1.56210	+	1.13493i
$159$	0.836881	+	2.57565i	0.0663690	+	0.204263i
$160$	−1.04508	−	3.21644i	−0.0826212	−	0.254282i
$161$	7.32624			0.577388
$162$	1.30902	+	0.951057i	0.102846	+	0.0747221i
$163$	8.41641			0.659224			0.329612	−	0.944116i	$-0.393082\pi$
$163$	8.41641			0.659224			0.329612	+	0.944116i	$0.393082\pi$
$164$	3.85410	+	0.898056i	0.300955	+	0.0701264i
$165$	−1.00000			−0.0778499
$166$	−15.5172	−	11.2739i	−1.20437	−	0.875026i
$167$	−1.81966			−0.140810			−0.0704048	−	0.997519i	$-0.522429\pi$
$167$	−1.81966			−0.140810			−0.0704048	+	0.997519i	$0.522429\pi$
$168$	−0.690983	−	2.12663i	−0.0533105	−	0.164073i
$169$	7.10739	+	21.8743i	0.546722	+	1.68264i
$170$	−6.85410	−	4.97980i	−0.525686	−	0.381933i
$171$	−6.35410	+	4.61653i	−0.485910	+	0.353035i
$172$	−1.52786	+	4.70228i	−0.116499	+	0.358546i
$173$	11.6525			0.885921			0.442961	−	0.896541i	$-0.353928\pi$
$173$	11.6525			0.885921			0.442961	+	0.896541i	$0.353928\pi$
$174$	3.04508	−	9.37181i	0.230847	−	0.710475i
$175$	−1.23607	+	3.80423i	−0.0934380	+	0.287572i
$176$	1.50000	+	4.61653i	0.113067	+	0.347984i
$177$	2.42705	+	1.76336i	0.182428	+	0.132542i
$178$	−0.763932			−0.0572591
$179$	4.40983	+	13.5721i	0.329606	+	1.01442i	0.969318	+	0.245809i	$0.0790536\pi$
$179$	4.40983	+	13.5721i	0.329606	+	1.01442i	−0.639712	+	0.768615i	$0.720946\pi$
$180$	0.500000	−	0.363271i	0.0372678	−	0.0270766i
$181$	2.42705	−	7.46969i	0.180401	−	0.555218i	−0.819438	−	0.573168i	$-0.805714\pi$
$181$	2.42705	−	7.46969i	0.180401	−	0.555218i	0.999839	+	0.0179504i	$0.00571408\pi$
$182$	7.85410	+	5.70634i	0.582185	+	0.422982i
$183$	3.30902	−	2.40414i	0.244610	−	0.177719i
$184$	−13.2533	+	9.62908i	−0.977045	+	0.709865i
$185$	−8.28115	+	6.01661i	−0.608842	+	0.442350i
$186$	−6.97214	+	5.06555i	−0.511222	+	0.371424i
$187$	4.23607	+	3.07768i	0.309772	+	0.225063i
$188$	−0.809017	+	2.48990i	−0.0590036	+	0.181594i
$189$	0.809017	−	0.587785i	0.0588473	−	0.0427551i
$190$	3.92705	+	12.0862i	0.284898	+	0.876827i
$191$	19.6180			1.41951			0.709756	−	0.704448i	$-0.248805\pi$
$191$	19.6180			1.41951			0.709756	+	0.704448i	$0.248805\pi$
$192$	3.42705	+	2.48990i	0.247326	+	0.179693i
$193$	−1.43769	−	4.42477i	−0.103487	−	0.318502i	0.885885	−	0.463905i	$-0.153552\pi$
$193$	−1.43769	−	4.42477i	−0.103487	−	0.318502i	−0.989372	+	0.145403i	$0.953552\pi$
$194$	−6.66312	+	20.5070i	−0.478384	+	1.47231i
$195$	1.85410	−	5.70634i	0.132775	−	0.408639i
$196$	0.618034			0.0441453
$197$	−1.83688	+	5.65334i	−0.130872	+	0.402784i	−0.994925	−	0.100617i	$-0.967918\pi$
$197$	−1.83688	+	5.65334i	−0.130872	+	0.402784i	0.864053	+	0.503401i	$0.167918\pi$
$198$	−1.30902	+	0.951057i	−0.0930278	+	0.0675886i
$199$	−19.3713	−	14.0741i	−1.37320	−	0.997686i	−0.997480	−	0.0709513i	$-0.977397\pi$
$199$	−19.3713	−	14.0741i	−1.37320	−	0.997686i	−0.375717	−	0.926734i	$-0.622603\pi$
$200$	−2.76393	−	8.50651i	−0.195440	−	0.601501i
$201$	0.881966	+	2.71441i	0.0622091	+	0.191460i
$202$	−6.47214			−0.455378
$203$	−4.92705	−	3.57971i	−0.345811	−	0.251247i
$204$	−3.23607			−0.226570
$205$	−6.23607	−	1.45309i	−0.435546	−	0.101488i
$206$	13.3262			0.928483
$207$	−5.92705	−	4.30625i	−0.411959	−	0.299305i
$208$	−29.1246			−2.01943
$209$	−2.42705	−	7.46969i	−0.167883	−	0.516690i
$210$	−0.500000	−	1.53884i	−0.0345033	−	0.106190i
$211$	9.85410	+	7.15942i	0.678384	+	0.492875i	0.872821	−	0.488040i	$-0.162288\pi$
$211$	9.85410	+	7.15942i	0.678384	+	0.492875i	−0.194437	+	0.980915i	$0.562288\pi$
$212$	1.35410	−	0.983813i	0.0930001	−	0.0675685i
$213$	2.69098	−	8.28199i	0.184383	−	0.567473i
$214$	−23.4164			−1.60071
$215$	2.47214	−	7.60845i	0.168598	−	0.518892i
$216$	−0.690983	+	2.12663i	−0.0470154	+	0.144699i
$217$	1.64590	+	5.06555i	0.111731	+	0.343872i
$218$	18.0623	+	13.1230i	1.22333	+	0.888804i
$219$	3.85410			0.260436
$220$	0.190983	+	0.587785i	0.0128761	+	0.0396285i
$221$	−25.4164	+	18.4661i	−1.70969	+	1.24216i
$222$	−5.11803	+	15.7517i	−0.343500	+	1.05718i
$223$	13.1353	+	9.54332i	0.879602	+	0.639068i	0.933146	−	0.359497i	$-0.117052\pi$
$223$	13.1353	+	9.54332i	0.879602	+	0.639068i	−0.0535444	+	0.998565i	$0.517052\pi$
$224$	−2.73607	+	1.98787i	−0.182811	+	0.132820i
$225$	3.23607	−	2.35114i	0.215738	−	0.156743i
$226$	−11.7812	+	8.55951i	−0.783671	+	0.569370i
$227$	5.78115	−	4.20025i	0.383709	−	0.278781i	−0.379164	−	0.925330i	$-0.623788\pi$
$227$	5.78115	−	4.20025i	0.383709	−	0.278781i	0.762873	+	0.646549i	$0.223788\pi$
$228$	3.92705	+	2.85317i	0.260075	+	0.188956i
$229$	5.63525	−	17.3435i	0.372388	−	1.14609i	−0.572836	−	0.819670i	$-0.694157\pi$
$229$	5.63525	−	17.3435i	0.372388	−	1.14609i	0.945224	−	0.326423i	$-0.105843\pi$
$230$	−9.59017	+	6.96767i	−0.632357	+	0.459434i
$231$	0.309017	+	0.951057i	0.0203318	+	0.0625749i
$232$	13.6180			0.894068
$233$	−21.1353	−	15.3557i	−1.38462	−	1.00598i	−0.996432	−	0.0844013i	$-0.973102\pi$
$233$	−21.1353	−	15.3557i	−1.38462	−	1.00598i	−0.388185	−	0.921582i	$-0.626898\pi$
$234$	−3.00000	−	9.23305i	−0.196116	−	0.603583i
$235$	1.30902	−	4.02874i	0.0853909	−	0.262806i
$236$	0.572949	−	1.76336i	0.0372958	−	0.114785i
$237$	−15.0000			−0.974355
$238$	−2.61803	+	8.05748i	−0.169702	+	0.522289i
$239$	10.6631	−	7.74721i	0.689740	−	0.501125i	−0.186835	−	0.982391i	$-0.559823\pi$
$239$	10.6631	−	7.74721i	0.689740	−	0.501125i	0.876575	+	0.481266i	$0.159823\pi$
$240$	3.92705	+	2.85317i	0.253490	+	0.184171i
$241$	−8.50000	−	26.1603i	−0.547533	−	1.68513i	−0.714890	−	0.699237i	$-0.753523\pi$
$241$	−8.50000	−	26.1603i	−0.547533	−	1.68513i	0.167357	−	0.985896i	$-0.446477\pi$
$242$	5.00000	+	15.3884i	0.321412	+	0.989205i
$243$	−1.00000			−0.0641500
$244$	−2.04508	−	1.48584i	−0.130923	−	0.0951212i
$245$	−1.00000			−0.0638877
$246$	−9.54508	+	4.02874i	−0.608572	+	0.256863i
$247$	47.1246			2.99847
$248$	−9.63525	−	7.00042i	−0.611839	−	0.444527i
$249$	11.8541			0.751223
$250$	−4.50000	−	13.8496i	−0.284605	−	0.875924i
$251$	7.41641	+	22.8254i	0.468120	+	1.44072i	0.855017	+	0.518601i	$0.173547\pi$
$251$	7.41641	+	22.8254i	0.468120	+	1.44072i	−0.386897	+	0.922123i	$0.626453\pi$
$252$	−0.500000	−	0.363271i	−0.0314970	−	0.0228839i
$253$	5.92705	−	4.30625i	0.372631	−	0.270732i
$254$	2.50000	−	7.69421i	0.156864	−	0.482778i
$255$	5.23607			0.327895
$256$	4.19098	−	12.8985i	0.261936	−	0.806157i
$257$	1.78115	−	5.48183i	0.111105	−	0.341947i	−0.880010	−	0.474956i	$-0.842464\pi$
$257$	1.78115	−	5.48183i	0.111105	−	0.341947i	0.991115	+	0.133009i	$0.0424640\pi$
$258$	−4.00000	−	12.3107i	−0.249029	−	0.766433i
$259$	8.28115	+	6.01661i	0.514566	+	0.373854i
$260$	−3.70820			−0.229973
$261$	1.88197	+	5.79210i	0.116491	+	0.358522i
$262$	−2.23607	+	1.62460i	−0.138145	+	0.100368i
$263$	9.75329	−	30.0175i	0.601414	−	1.85096i	0.0816298	−	0.996663i	$-0.473987\pi$
$263$	9.75329	−	30.0175i	0.601414	−	1.85096i	0.519784	−	0.854298i	$-0.326013\pi$
$264$	−1.80902	−	1.31433i	−0.111337	−	0.0808913i
$265$	−2.19098	+	1.59184i	−0.134591	+	0.0977861i
$266$	10.2812	−	7.46969i	0.630378	−	0.457996i
$267$	0.381966	−	0.277515i	0.0233759	−	0.0169836i
$268$	1.42705	−	1.03681i	0.0871710	−	0.0633334i
$269$	17.9443	+	13.0373i	1.09408	+	0.794897i	0.980084	−	0.198584i	$-0.0636343\pi$
$269$	17.9443	+	13.0373i	1.09408	+	0.794897i	0.113998	+	0.993481i	$0.463634\pi$
$270$	−0.500000	+	1.53884i	−0.0304290	+	0.0936509i
$271$	−10.8992	+	7.91872i	−0.662078	+	0.481028i	−0.867364	−	0.497674i	$-0.834188\pi$
$271$	−10.8992	+	7.91872i	−0.662078	+	0.481028i	0.205286	+	0.978702i	$0.434188\pi$
$272$	−7.85410	−	24.1724i	−0.476225	−	1.46567i
$273$	−6.00000			−0.363137
$274$	0.927051	+	0.673542i	0.0560052	+	0.0406902i
$275$	1.23607	+	3.80423i	0.0745377	+	0.229403i
$276$	−1.39919	+	4.30625i	−0.0842212	+	0.259206i
$277$	4.67376	−	14.3844i	0.280819	−	0.864272i	−0.706802	−	0.707412i	$-0.749863\pi$
$277$	4.67376	−	14.3844i	0.280819	−	0.864272i	0.987621	−	0.156861i	$-0.0501373\pi$
$278$	19.3262			1.15911
$279$	1.64590	−	5.06555i	0.0985373	−	0.303267i
$280$	1.80902	−	1.31433i	0.108109	−	0.0785461i
$281$	−14.2984	−	10.3884i	−0.852969	−	0.619719i	0.0729937	−	0.997332i	$-0.476745\pi$
$281$	−14.2984	−	10.3884i	−0.852969	−	0.619719i	−0.925963	+	0.377614i	$0.876745\pi$
$282$	−2.11803	−	6.51864i	−0.126127	−	0.388179i
$283$	−7.41641	−	22.8254i	−0.440860	−	1.35683i	−0.886961	−	0.461844i	$-0.847188\pi$
$283$	−7.41641	−	22.8254i	−0.440860	−	1.35683i	0.446101	−	0.894982i	$-0.352812\pi$
$284$	−5.38197			−0.319361
$285$	−6.35410	−	4.61653i	−0.376385	−	0.273459i
$286$	9.70820			0.574058
$287$	0.545085	+	6.37988i	0.0321753	+	0.376592i
$288$	3.38197			0.199284
$289$	−8.42705	−	6.12261i	−0.495709	−	0.360154i
$290$	9.85410			0.578653
$291$	−4.11803	−	12.6740i	−0.241403	−	0.742963i
$292$	−0.736068	−	2.26538i	−0.0430751	−	0.132572i
$293$	−14.1803	−	10.3026i	−0.828424	−	0.601885i	0.0906888	−	0.995879i	$-0.471093\pi$
$293$	−14.1803	−	10.3026i	−0.828424	−	0.601885i	−0.919113	+	0.393994i	$0.871093\pi$
$294$	−1.30902	+	0.951057i	−0.0763434	+	0.0554667i
$295$	−0.927051	+	2.85317i	−0.0539750	+	0.166118i
$296$	−22.8885			−1.33037
$297$	0.309017	−	0.951057i	0.0179310	−	0.0551859i
$298$	0.545085	−	1.67760i	0.0315759	−	0.0971807i
$299$	13.5836	+	41.8060i	0.785559	+	2.41770i
$300$	−2.00000	−	1.45309i	−0.115470	−	0.0838939i
$301$	−8.00000			−0.461112
$302$	−11.4271	−	35.1688i	−0.657553	−	2.02374i
$303$	3.23607	−	2.35114i	0.185907	−	0.135070i
$304$	−11.7812	+	36.2587i	−0.675695	+	2.07958i
$305$	3.30902	+	2.40414i	0.189474	+	0.137661i
$306$	6.85410	−	4.97980i	0.391823	−	0.284676i
$307$	16.1074	−	11.7027i	0.919297	−	0.667909i	−0.0240517	−	0.999711i	$-0.507657\pi$
$307$	16.1074	−	11.7027i	0.919297	−	0.667909i	0.943349	+	0.331802i	$0.107657\pi$
$308$	0.500000	−	0.363271i	0.0284901	−	0.0206993i
$309$	−6.66312	+	4.84104i	−0.379052	+	0.275397i
$310$	−6.97214	−	5.06555i	−0.395991	−	0.287704i
$311$	−10.5451	+	32.4544i	−0.597957	+	1.84032i	−0.0585370	+	0.998285i	$0.518644\pi$
$311$	−10.5451	+	32.4544i	−0.597957	+	1.84032i	−0.539420	+	0.842037i	$0.681356\pi$
$312$	10.8541	−	7.88597i	0.614493	−	0.446455i
$313$	0.437694	+	1.34708i	0.0247399	+	0.0761417i	0.962664	−	0.270698i	$-0.0872546\pi$
$313$	0.437694	+	1.34708i	0.0247399	+	0.0761417i	−0.937924	+	0.346840i	$0.887255\pi$
$314$	4.09017			0.230822
$315$	0.809017	+	0.587785i	0.0455829	+	0.0331179i
$316$	2.86475	+	8.81678i	0.161155	+	0.495983i
$317$	−4.56231	+	14.0413i	−0.256245	+	0.788640i	0.737337	+	0.675525i	$0.236083\pi$
$317$	−4.56231	+	14.0413i	−0.256245	+	0.788640i	−0.993582	+	0.113115i	$0.963917\pi$
$318$	−1.35410	+	4.16750i	−0.0759343	+	0.233702i
$319$	−6.09017			−0.340984
$320$	−1.30902	+	4.02874i	−0.0731763	+	0.225213i
$321$	11.7082	−	8.50651i	0.653488	−	0.474787i
$322$	9.59017	+	6.96767i	0.534439	+	0.388293i
$323$	12.7082	+	39.1118i	0.707103	+	2.17624i
$324$	0.190983	+	0.587785i	0.0106102	+	0.0326547i
$325$	−24.0000			−1.33128
$326$	11.0172	+	8.00448i	0.610187	+	0.443327i
$327$	−13.7984			−0.763052
$328$	−9.37132	−	10.8249i	−0.517445	−	0.597705i
$329$	−4.23607			−0.233542
$330$	−1.30902	−	0.951057i	−0.0720590	−	0.0523539i
$331$	4.23607			0.232835			0.116418	−	0.993200i	$-0.462859\pi$
$331$	4.23607			0.232835			0.116418	+	0.993200i	$0.462859\pi$
$332$	−2.26393	−	6.96767i	−0.124249	−	0.382400i
$333$	−3.16312	−	9.73508i	−0.173338	−	0.533479i
$334$	−2.38197	−	1.73060i	−0.130335	−	0.0946942i
$335$	−2.30902	+	1.67760i	−0.126155	+	0.0916570i
$336$	1.50000	−	4.61653i	0.0818317	−	0.251852i
$337$	−4.70820			−0.256472			−0.128236	−	0.991744i	$-0.540932\pi$
$337$	−4.70820			−0.256472			−0.128236	+	0.991744i	$0.540932\pi$
$338$	−11.5000	+	35.3934i	−0.625518	+	1.92515i
$339$	2.78115	−	8.55951i	0.151051	−	0.464889i
$340$	−1.00000	−	3.07768i	−0.0542326	−	0.166911i
$341$	4.30902	+	3.13068i	0.233346	+	0.169536i
$342$	−12.7082			−0.687181
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	14.4721	−	10.5146i	0.780285	−	0.566910i
$345$	2.26393	−	6.96767i	0.121886	−	0.375127i
$346$	15.2533	+	11.0822i	0.820022	+	0.595781i
$347$	10.8262	−	7.86572i	0.581183	−	0.422254i	−0.257967	−	0.966154i	$-0.583053\pi$
$347$	10.8262	−	7.86572i	0.581183	−	0.422254i	0.839150	+	0.543900i	$0.183053\pi$
$348$	3.04508	−	2.21238i	0.163234	−	0.118596i
$349$	9.78115	−	7.10642i	0.523573	−	0.380398i	−0.294375	−	0.955690i	$-0.595112\pi$
$349$	9.78115	−	7.10642i	0.523573	−	0.380398i	0.817948	+	0.575292i	$0.195112\pi$
$350$	−5.23607	+	3.80423i	−0.279880	+	0.203344i
$351$	4.85410	+	3.52671i	0.259093	+	0.188242i
$352$	−1.04508	+	3.21644i	−0.0557032	+	0.171437i
$353$	6.78115	−	4.92680i	0.360924	−	0.262227i	−0.392513	−	0.919746i	$-0.628394\pi$
$353$	6.78115	−	4.92680i	0.360924	−	0.262227i	0.753438	+	0.657519i	$0.228394\pi$
$354$	1.50000	+	4.61653i	0.0797241	+	0.245366i
$355$	8.70820			0.462183
$356$	−0.236068	−	0.171513i	−0.0125116	−	0.00909019i
$357$	−1.61803	−	4.97980i	−0.0856354	−	0.263559i
$358$	−7.13525	+	21.9601i	−0.377110	+	1.16063i
$359$	8.84346	−	27.2174i	0.466740	−	1.43648i	−0.390041	−	0.920797i	$-0.627539\pi$
$359$	8.84346	−	27.2174i	0.466740	−	1.43648i	0.856781	−	0.515680i	$-0.172461\pi$
$360$	−2.23607			−0.117851
$361$	13.1910	−	40.5977i	0.694262	−	2.13672i
$362$	10.2812	−	7.46969i	0.540365	−	0.392598i
$363$	−8.09017	−	5.87785i	−0.424624	−	0.308507i
$364$	1.14590	+	3.52671i	0.0600614	+	0.184850i
$365$	1.19098	+	3.66547i	0.0623389	+	0.191859i
$366$	6.61803			0.345930
$367$	13.1353	+	9.54332i	0.685655	+	0.498157i	0.875229	−	0.483709i	$-0.160711\pi$
$367$	13.1353	+	9.54332i	0.685655	+	0.498157i	−0.189574	+	0.981866i	$0.560711\pi$
$368$	−35.5623			−1.85381
$369$	3.30902	−	5.48183i	0.172261	−	0.285372i
$370$	−16.5623			−0.861033
$371$	2.19098	+	1.59184i	0.113750	+	0.0826443i
$372$	−3.29180			−0.170672
$373$	−5.95492	−	18.3273i	−0.308334	−	0.948954i	−0.978412	−	0.206663i	$-0.933739\pi$
$373$	−5.95492	−	18.3273i	−0.308334	−	0.948954i	0.670078	−	0.742290i	$-0.266261\pi$
$374$	2.61803	+	8.05748i	0.135375	+	0.416642i
$375$	7.28115	+	5.29007i	0.375997	+	0.273178i
$376$	7.66312	−	5.56758i	0.395195	−	0.287126i
$377$	11.2918	−	34.7526i	0.581557	−	1.78985i
$378$	1.61803			0.0832227
$379$	−6.10081	+	18.7764i	−0.313378	+	0.964477i	0.663039	+	0.748585i	$0.269266\pi$
$379$	−6.10081	+	18.7764i	−0.313378	+	0.964477i	−0.976417	+	0.215893i	$0.930734\pi$
$380$	−1.50000	+	4.61653i	−0.0769484	+	0.236823i
$381$	1.54508	+	4.75528i	0.0791571	+	0.243621i
$382$	25.6803	+	18.6579i	1.31392	+	0.954619i
$383$	23.0902			1.17985			0.589926	−	0.807457i	$-0.299157\pi$
$383$	23.0902			1.17985			0.589926	+	0.807457i	$0.299157\pi$
$384$	4.20820	+	12.9515i	0.214749	+	0.660929i
$385$	−0.809017	+	0.587785i	−0.0412313	+	0.0299563i
$386$	2.32624	−	7.15942i	0.118402	−	0.364405i
$387$	6.47214	+	4.70228i	0.328997	+	0.239030i
$388$	−6.66312	+	4.84104i	−0.338269	+	0.245767i
$389$	−19.2533	+	13.9883i	−0.976180	+	0.709237i	−0.956852	−	0.290577i	$-0.906153\pi$
$389$	−19.2533	+	13.9883i	−0.976180	+	0.709237i	−0.0193287	+	0.999813i	$0.506153\pi$
$390$	7.85410	−	5.70634i	0.397708	−	0.288952i
$391$	−31.0344	+	22.5478i	−1.56948	+	1.14029i
$392$	−1.80902	−	1.31433i	−0.0913692	−	0.0663836i
$393$	0.527864	−	1.62460i	0.0266272	−	0.0819502i
$394$	−7.78115	+	5.65334i	−0.392009	+	0.284811i
$395$	−4.63525	−	14.2658i	−0.233225	−	0.717793i
$396$	−0.618034			−0.0310574
$397$	27.4443	+	19.9394i	1.37739	+	1.00073i	0.997119	+	0.0758557i	$0.0241688\pi$
$397$	27.4443	+	19.9394i	1.37739	+	1.00073i	0.380270	+	0.924876i	$0.375831\pi$
$398$	−11.9721	−	36.8464i	−0.600109	−	1.84695i
$399$	−2.42705	+	7.46969i	−0.121505	+	0.373952i
$400$	6.00000	−	18.4661i	0.300000	−	0.923305i
$401$	−23.4164			−1.16936			−0.584680	−	0.811264i	$-0.698780\pi$
$401$	−23.4164			−1.16936			−0.584680	+	0.811264i	$0.698780\pi$
$402$	−1.42705	+	4.39201i	−0.0711748	+	0.219054i
$403$	−25.8541	+	18.7841i	−1.28788	+	0.935703i
$404$	−2.00000	−	1.45309i	−0.0995037	−	0.0722937i
$405$	−0.309017	−	0.951057i	−0.0153552	−	0.0472584i
$406$	−3.04508	−	9.37181i	−0.151125	−	0.465115i
$407$	10.2361			0.507383
$408$	9.47214	+	6.88191i	0.468941	+	0.340705i
$409$	12.6525			0.625625			0.312812	−	0.949815i	$-0.398729\pi$
$409$	12.6525			0.625625			0.312812	+	0.949815i	$0.398729\pi$
$410$	−6.78115	−	7.83297i	−0.334897	−	0.386843i
$411$	−0.708204			−0.0349331
$412$	4.11803	+	2.99193i	0.202881	+	0.147402i
$413$	3.00000			0.147620
$414$	−3.66312	−	11.2739i	−0.180032	−	0.554083i
$415$	3.66312	+	11.2739i	0.179815	+	0.553415i
$416$	−16.4164	−	11.9272i	−0.804881	−	0.584780i
$417$	−9.66312	+	7.02067i	−0.473205	+	0.343804i
$418$	3.92705	−	12.0862i	0.192078	−	0.591156i
$419$	7.85410			0.383698			0.191849	−	0.981424i	$-0.438552\pi$
$419$	7.85410			0.383698			0.191849	+	0.981424i	$0.438552\pi$
$420$	0.190983	−	0.587785i	0.00931902	−	0.0286810i
$421$	−2.76393	+	8.50651i	−0.134706	+	0.414582i	−0.995544	−	0.0942967i	$-0.969940\pi$
$421$	−2.76393	+	8.50651i	−0.134706	+	0.414582i	0.860838	+	0.508879i	$0.169940\pi$
$422$	6.09017	+	18.7436i	0.296465	+	0.912425i
$423$	3.42705	+	2.48990i	0.166629	+	0.121063i
$424$	−6.05573			−0.294092
$425$	−6.47214	−	19.9192i	−0.313945	−	0.966222i
$426$	11.3992	−	8.28199i	0.552292	−	0.401264i
$427$	1.26393	−	3.88998i	0.0611660	−	0.188249i
$428$	−7.23607	−	5.25731i	−0.349769	−	0.254122i
$429$	−4.85410	+	3.52671i	−0.234358	+	0.170271i
$430$	10.4721	−	7.60845i	0.505011	−	0.366912i
$431$	−1.78115	+	1.29408i	−0.0857951	+	0.0623338i	−0.629856	−	0.776712i	$-0.716886\pi$
$431$	−1.78115	+	1.29408i	−0.0857951	+	0.0623338i	0.544061	+	0.839046i	$0.316886\pi$
$432$	−3.92705	+	2.85317i	−0.188940	+	0.137273i
$433$	22.2254	+	16.1477i	1.06809	+	0.776010i	0.975567	−	0.219701i	$-0.0705083\pi$
$433$	22.2254	+	16.1477i	1.06809	+	0.776010i	0.0925186	+	0.995711i	$0.470508\pi$
$434$	−2.66312	+	8.19624i	−0.127834	+	0.393432i
$435$	−4.92705	+	3.57971i	−0.236234	+	0.171634i
$436$	2.63525	+	8.11048i	0.126206	+	0.388422i
$437$	57.5410			2.75256
$438$	5.04508	+	3.66547i	0.241063	+	0.175143i
$439$	−1.29180	−	3.97574i	−0.0616541	−	0.189752i	0.915485	−	0.402351i	$-0.131807\pi$
$439$	−1.29180	−	3.97574i	−0.0616541	−	0.189752i	−0.977139	+	0.212600i	$0.931807\pi$
$440$	0.690983	−	2.12663i	0.0329413	−	0.101383i
$441$	0.309017	−	0.951057i	0.0147151	−	0.0452884i
$442$	−50.8328			−2.41787
$443$	−0.0623059	+	0.191758i	−0.00296024	+	0.00911069i	−0.952526	−	0.304458i	$-0.901525\pi$
$443$	−0.0623059	+	0.191758i	−0.00296024	+	0.00911069i	0.949565	+	0.313569i	$0.101525\pi$
$444$	−5.11803	+	3.71847i	−0.242891	+	0.176471i
$445$	0.381966	+	0.277515i	0.0181069	+	0.0131555i
$446$	8.11803	+	24.9847i	0.384400	+	1.18306i
$447$	0.336881	+	1.03681i	0.0159339	+	0.0490396i
$448$	4.23607			0.200135
$449$	−5.00000	−	3.63271i	−0.235965	−	0.171438i	0.463519	−	0.886087i	$-0.346587\pi$
$449$	−5.00000	−	3.63271i	−0.235965	−	0.171438i	−0.699484	+	0.714649i	$0.746587\pi$
$450$	6.47214			0.305099
$451$	4.19098	+	4.84104i	0.197346	+	0.227956i
$452$	−5.56231			−0.261629
$453$	18.4894	+	13.4333i	0.868706	+	0.631152i
$454$	11.5623			0.542646
$455$	−1.85410	−	5.70634i	−0.0869216	−	0.267517i
$456$	−5.42705	−	16.7027i	−0.254145	−	0.782178i
$457$	1.04508	+	0.759299i	0.0488870	+	0.0355185i	0.611960	−	0.790888i	$-0.290381\pi$
$457$	1.04508	+	0.759299i	0.0488870	+	0.0355185i	−0.563073	+	0.826407i	$0.690381\pi$
$458$	23.8713	−	17.3435i	1.11543	−	0.810410i
$459$	−1.61803	+	4.97980i	−0.0755234	+	0.232437i
$460$	−4.52786			−0.211113
$461$	3.30902	−	10.1841i	0.154116	−	0.474321i	−0.843954	−	0.536416i	$-0.819778\pi$
$461$	3.30902	−	10.1841i	0.154116	−	0.474321i	0.998070	+	0.0620944i	$0.0197780\pi$
$462$	−0.500000	+	1.53884i	−0.0232621	+	0.0715934i
$463$	−10.0172	−	30.8298i	−0.465540	−	1.43278i	−0.858302	−	0.513144i	$-0.828481\pi$
$463$	−10.0172	−	30.8298i	−0.465540	−	1.43278i	0.392763	−	0.919640i	$-0.371519\pi$
$464$	23.9164	+	17.3763i	1.11029	+	0.806674i
$465$	5.32624			0.246998
$466$	−13.0623	−	40.2016i	−0.605100	−	1.86231i
$467$	−20.1525	+	14.6416i	−0.932545	+	0.677534i	−0.946615	−	0.322367i	$-0.895521\pi$
$467$	−20.1525	+	14.6416i	−0.932545	+	0.677534i	0.0140693	+	0.999901i	$0.495521\pi$
$468$	1.14590	−	3.52671i	0.0529692	−	0.163022i
$469$	2.30902	+	1.67760i	0.106620	+	0.0774643i
$470$	5.54508	−	4.02874i	0.255776	−	0.185832i
$471$	−2.04508	+	1.48584i	−0.0942325	+	0.0684639i
$472$	−5.42705	+	3.94298i	−0.249800	+	0.181491i
$473$	−6.47214	+	4.70228i	−0.297589	+	0.216211i
$474$	−19.6353	−	14.2658i	−0.901877	−	0.655252i
$475$	−9.70820	+	29.8788i	−0.445443	+	1.37093i
$476$	−2.61803	+	1.90211i	−0.119997	+	0.0871832i
$477$	−0.836881	−	2.57565i	−0.0383182	−	0.117931i
$478$	21.3262			0.975439
$479$	−0.527864	−	0.383516i	−0.0241187	−	0.0175233i	0.575661	−	0.817689i	$-0.304745\pi$
$479$	−0.527864	−	0.383516i	−0.0241187	−	0.0175233i	−0.599779	+	0.800165i	$0.704745\pi$
$480$	1.04508	+	3.21644i	0.0477014	+	0.146810i
$481$	−18.9787	+	58.4105i	−0.865355	+	2.66329i
$482$	13.7533	−	42.3283i	0.626445	−	1.92800i
$483$	−7.32624			−0.333355
$484$	−1.90983	+	5.87785i	−0.0868105	+	0.267175i
$485$	10.7812	−	7.83297i	0.489547	−	0.355677i
$486$	−1.30902	−	0.951057i	−0.0593782	−	0.0431408i
$487$	−9.16312	−	28.2012i	−0.415221	−	1.27792i	−0.912053	−	0.410071i	$-0.865504\pi$
$487$	−9.16312	−	28.2012i	−0.415221	−	1.27792i	0.496833	−	0.867846i	$-0.334496\pi$
$488$	2.82624	+	8.69827i	0.127938	+	0.393752i
$489$	−8.41641			−0.380603
$490$	−1.30902	−	0.951057i	−0.0591354	−	0.0429644i
$491$	−4.67376			−0.210924			−0.105462	−	0.994423i	$-0.533632\pi$
$491$	−4.67376			−0.210924			−0.105462	+	0.994423i	$0.533632\pi$
$492$	−3.85410	−	0.898056i	−0.173756	−	0.0404875i
$493$	31.8885			1.43619
$494$	61.6869	+	44.8182i	2.77543	+	2.01646i
$495$	1.00000			0.0449467
$496$	−7.98936	−	24.5887i	−0.358733	−	1.10407i
$497$	−2.69098	−	8.28199i	−0.120707	−	0.371498i
$498$	15.5172	+	11.2739i	0.695343	+	0.505196i
$499$	−14.8262	+	10.7719i	−0.663714	+	0.482216i	−0.867915	−	0.496713i	$-0.834540\pi$
$499$	−14.8262	+	10.7719i	−0.663714	+	0.482216i	0.204201	+	0.978929i	$0.434540\pi$
$500$	1.71885	−	5.29007i	0.0768692	−	0.236579i
$501$	1.81966			0.0812964
$502$	−12.0000	+	36.9322i	−0.535586	+	1.64836i
$503$	−6.38854	+	19.6619i	−0.284851	+	0.876682i	0.701592	+	0.712579i	$0.252473\pi$
$503$	−6.38854	+	19.6619i	−0.284851	+	0.876682i	−0.986443	+	0.164103i	$0.947527\pi$
$504$	0.690983	+	2.12663i	0.0307788	+	0.0947275i
$505$	3.23607	+	2.35114i	0.144003	+	0.104624i
$506$	11.8541			0.526979
$507$	−7.10739	−	21.8743i	−0.315650	−	0.971472i
$508$	2.50000	−	1.81636i	0.110920	−	0.0805878i
$509$	5.02786	−	15.4742i	0.222856	−	0.685881i	−0.775646	−	0.631168i	$-0.782576\pi$
$509$	5.02786	−	15.4742i	0.222856	−	0.685881i	0.998502	−	0.0547125i	$-0.0174242\pi$
$510$	6.85410	+	4.97980i	0.303505	+	0.220509i
$511$	3.11803	−	2.26538i	0.137934	−	0.100215i
$512$	−4.28115	+	3.11044i	−0.189202	+	0.137463i
$513$	6.35410	−	4.61653i	0.280540	−	0.203825i
$514$	7.54508	−	5.48183i	0.332799	−	0.241793i
$515$	−6.66312	−	4.84104i	−0.293612	−	0.213322i
$516$	1.52786	−	4.70228i	0.0672605	−	0.207006i
$517$	−3.42705	+	2.48990i	−0.150722	+	0.109506i
$518$	5.11803	+	15.7517i	0.224874	+	0.692089i
$519$	−11.6525			−0.511487
$520$	10.8541	+	7.88597i	0.475984	+	0.345823i
$521$	−5.82624	−	17.9313i	−0.255252	−	0.785585i	−0.993780	−	0.111362i	$-0.964479\pi$
$521$	−5.82624	−	17.9313i	−0.255252	−	0.785585i	0.738528	−	0.674223i	$-0.235521\pi$
$522$	−3.04508	+	9.37181i	−0.133280	+	0.410193i
$523$	2.82624	−	8.69827i	0.123583	−	0.380349i	−0.870057	−	0.492950i	$-0.835918\pi$
$523$	2.82624	−	8.69827i	0.123583	−	0.380349i	0.993640	+	0.112602i	$0.0359184\pi$
$524$	−1.05573			−0.0461197
$525$	1.23607	−	3.80423i	0.0539464	−	0.166030i
$526$	41.3156	−	30.0175i	1.80145	−	1.30883i
$527$	−22.5623	−	16.3925i	−0.982829	−	0.714067i
$528$	−1.50000	−	4.61653i	−0.0652791	−	0.200908i
$529$	9.47871	+	29.1725i	0.412118	+	1.26837i
$530$	−4.38197			−0.190340
$531$	−2.42705	−	1.76336i	−0.105325	−	0.0765231i
$532$	4.85410			0.210452
$533$	−35.3951	+	14.9394i	−1.53313	+	0.647097i
$534$	0.763932			0.0330586
$535$	11.7082	+	8.50651i	0.506190	+	0.367768i
$536$	−6.38197			−0.275659
$537$	−4.40983	−	13.5721i	−0.190298	−	0.585678i
$538$	11.0902	+	34.1320i	0.478131	+	1.47154i
$539$	0.809017	+	0.587785i	0.0348468	+	0.0253177i
$540$	−0.500000	+	0.363271i	−0.0215166	+	0.0156327i
$541$	12.1459	−	37.3812i	0.522193	−	1.60714i	−0.247608	−	0.968860i	$-0.579644\pi$
$541$	12.1459	−	37.3812i	0.522193	−	1.60714i	0.769801	−	0.638284i	$-0.220356\pi$
$542$	−21.7984			−0.936320
$543$	−2.42705	+	7.46969i	−0.104155	+	0.320555i
$544$	5.47214	−	16.8415i	0.234616	−	0.722073i
$545$	−4.26393	−	13.1230i	−0.182647	−	0.562129i
$546$	−7.85410	−	5.70634i	−0.336125	−	0.244209i
$547$	41.3050			1.76607			0.883036	−	0.469305i	$-0.155496\pi$
$547$	41.3050			1.76607			0.883036	+	0.469305i	$0.155496\pi$
$548$	0.135255	+	0.416272i	0.00577780	+	0.0177823i
$549$	−3.30902	+	2.40414i	−0.141225	+	0.102606i
$550$	−2.00000	+	6.15537i	−0.0852803	+	0.262466i
$551$	−38.6976	−	28.1154i	−1.64857	−	1.19776i
$552$	13.2533	−	9.62908i	0.564097	−	0.409841i
$553$	−12.1353	+	8.81678i	−0.516044	+	0.374928i
$554$	19.7984	−	14.3844i	0.841152	−	0.611133i
$555$	8.28115	−	6.01661i	0.351515	−	0.255391i
$556$	5.97214	+	4.33901i	0.253275	+	0.184015i
$557$	10.0902	−	31.0543i	0.427534	−	1.31582i	−0.473012	−	0.881056i	$-0.656833\pi$
$557$	10.0902	−	31.0543i	0.427534	−	1.31582i	0.900547	−	0.434759i	$-0.143167\pi$
$558$	6.97214	−	5.06555i	0.295154	−	0.214442i
$559$	−14.8328	−	45.6507i	−0.627361	−	1.93082i
$560$	4.85410			0.205123
$561$	−4.23607	−	3.07768i	−0.178847	−	0.129940i
$562$	−8.83688	−	27.1971i	−0.372761	−	1.14724i
$563$	−0.555728	+	1.71036i	−0.0234211	+	0.0720829i	−0.962084	−	0.272754i	$-0.912066\pi$
$563$	−0.555728	+	1.71036i	−0.0234211	+	0.0720829i	0.938663	+	0.344836i	$0.112066\pi$
$564$	0.809017	−	2.48990i	0.0340658	−	0.104844i
$565$	9.00000			0.378633
$566$	12.0000	−	36.9322i	0.504398	−	1.55238i
$567$	−0.809017	+	0.587785i	−0.0339755	+	0.0246847i
$568$	15.7533	+	11.4454i	0.660993	+	0.480240i
$569$	−5.98936	−	18.4333i	−0.251087	−	0.772766i	−0.994575	−	0.104017i	$-0.966830\pi$
$569$	−5.98936	−	18.4333i	−0.251087	−	0.772766i	0.743489	−	0.668749i	$-0.233170\pi$
$570$	−3.92705	−	12.0862i	−0.164486	−	0.506236i
$571$	−31.0344			−1.29875			−0.649375	−	0.760468i	$-0.724970\pi$
$571$	−31.0344			−1.29875			−0.649375	+	0.760468i	$0.724970\pi$
$572$	3.00000	+	2.17963i	0.125436	+	0.0911348i
$573$	−19.6180			−0.819555
$574$	−5.35410	+	8.86978i	−0.223476	+	0.370217i
$575$	−29.3050			−1.22210
$576$	−3.42705	−	2.48990i	−0.142794	−	0.103746i
$577$	−3.23607			−0.134719			−0.0673596	−	0.997729i	$-0.521457\pi$
$577$	−3.23607			−0.134719			−0.0673596	+	0.997729i	$0.521457\pi$
$578$	−5.20820	−	16.0292i	−0.216633	−	0.666727i
$579$	1.43769	+	4.42477i	0.0597485	+	0.183887i
$580$	3.04508	+	2.21238i	0.126440	+	0.0918642i
$581$	9.59017	−	6.96767i	0.397867	−	0.289068i
$582$	6.66312	−	20.5070i	0.276195	−	0.850041i
$583$	2.70820			0.112162
$584$	−2.66312	+	8.19624i	−0.110201	+	0.339163i
$585$	−1.85410	+	5.70634i	−0.0766577	+	0.235928i
$586$	−8.76393	−	26.9726i	−0.362035	−	1.11423i
$587$	−14.2254	−	10.3354i	−0.587146	−	0.426587i	0.254147	−	0.967166i	$-0.418205\pi$
$587$	−14.2254	−	10.3354i	−0.587146	−	0.426587i	−0.841293	+	0.540579i	$0.818205\pi$
$588$	−0.618034			−0.0254873
$589$	12.9271	+	39.7854i	0.532650	+	1.63933i
$590$	−3.92705	+	2.85317i	−0.161674	+	0.117463i
$591$	1.83688	−	5.65334i	0.0755592	−	0.232547i
$592$	−40.1976	−	29.2052i	−1.65211	−	1.20033i
$593$	11.6631	−	8.47375i	0.478947	−	0.347975i	−0.321971	−	0.946750i	$-0.604345\pi$
$593$	11.6631	−	8.47375i	0.478947	−	0.347975i	0.800918	+	0.598774i	$0.204345\pi$
$594$	1.30902	−	0.951057i	0.0537096	−	0.0390223i
$595$	4.23607	−	3.07768i	0.173662	−	0.126173i
$596$	0.545085	−	0.396027i	0.0223276	−	0.0162219i
$597$	19.3713	+	14.0741i	0.792815	+	0.576014i
$598$	−21.9787	+	67.6435i	−0.898776	+	2.76615i
$599$	13.9271	−	10.1186i	0.569044	−	0.413435i	−0.265714	−	0.964052i	$-0.585608\pi$
$599$	13.9271	−	10.1186i	0.569044	−	0.413435i	0.834758	+	0.550617i	$0.185608\pi$
$600$	2.76393	+	8.50651i	0.112837	+	0.347277i
$601$	1.59675			0.0651327			0.0325663	−	0.999470i	$-0.489632\pi$
$601$	1.59675			0.0651327			0.0325663	+	0.999470i	$0.489632\pi$
$602$	−10.4721	−	7.60845i	−0.426812	−	0.310097i
$603$	−0.881966	−	2.71441i	−0.0359164	−	0.110539i
$604$	4.36475	−	13.4333i	0.177599	−	0.546593i
$605$	3.09017	−	9.51057i	0.125633	−	0.386659i
$606$	6.47214			0.262913
$607$	0.225425	−	0.693786i	0.00914971	−	0.0281599i	−0.946377	−	0.323063i	$-0.895287\pi$
$607$	0.225425	−	0.693786i	0.00914971	−	0.0281599i	0.955527	+	0.294903i	$0.0952874\pi$
$608$	−21.4894	+	15.6129i	−0.871509	+	0.633188i
$609$	4.92705	+	3.57971i	0.199654	+	0.145057i
$610$	2.04508	+	6.29412i	0.0828031	+	0.254842i
$611$	−7.85410	−	24.1724i	−0.317743	−	0.977912i
$612$	3.23607			0.130810
$613$	1.85410	+	1.34708i	0.0748865	+	0.0544082i	0.624599	−	0.780946i	$-0.285263\pi$
$613$	1.85410	+	1.34708i	0.0748865	+	0.0544082i	−0.549712	+	0.835354i	$0.685263\pi$
$614$	32.2148			1.30008
$615$	6.23607	+	1.45309i	0.251463	+	0.0585940i
$616$	−2.23607			−0.0900937
$617$	−24.5795	−	17.8581i	−0.989534	−	0.718939i	−0.0297154	−	0.999558i	$-0.509460\pi$
$617$	−24.5795	−	17.8581i	−0.989534	−	0.718939i	−0.959819	+	0.280620i	$0.909460\pi$
$618$	−13.3262			−0.536060
$619$	12.7467	+	39.2303i	0.512334	+	1.57680i	0.788082	+	0.615571i	$0.211074\pi$
$619$	12.7467	+	39.2303i	0.512334	+	1.57680i	−0.275748	+	0.961230i	$0.588926\pi$
$620$	−1.01722	−	3.13068i	−0.0408526	−	0.125731i
$621$	5.92705	+	4.30625i	0.237844	+	0.172804i
$622$	−44.6697	+	32.4544i	−1.79109	+	1.30130i
$623$	0.145898	−	0.449028i	0.00584528	−	0.0179899i
$624$	29.1246			1.16592
$625$	3.39919	−	10.4616i	0.135967	−	0.418465i
$626$	−0.708204	+	2.17963i	−0.0283055	+	0.0871154i
$627$	2.42705	+	7.46969i	0.0969271	+	0.298311i
$628$	1.26393	+	0.918300i	0.0504364	+	0.0366442i
$629$	−53.5967			−2.13704
$630$	0.500000	+	1.53884i	0.0199205	+	0.0613089i
$631$	−21.3262	+	15.4944i	−0.848984	+	0.616823i	−0.924866	−	0.380294i	$-0.875823\pi$
$631$	−21.3262	+	15.4944i	−0.848984	+	0.616823i	0.0758816	+	0.997117i	$0.475823\pi$
$632$	10.3647	−	31.8994i	0.412287	−	1.26889i
$633$	−9.85410	−	7.15942i	−0.391665	−	0.284562i
$634$	−19.3262	+	14.0413i	−0.767543	+	0.557653i
$635$	−4.04508	+	2.93893i	−0.160524	+	0.116628i
$636$	−1.35410	+	0.983813i	−0.0536936	+	0.0390107i
$637$	−4.85410	+	3.52671i	−0.192327	+	0.139733i
$638$	−7.97214	−	5.79210i	−0.315620	−	0.229311i
$639$	−2.69098	+	8.28199i	−0.106454	+	0.327631i
$640$	−11.0172	+	8.00448i	−0.435494	+	0.316405i
$641$	2.36475	+	7.27794i	0.0934018	+	0.287461i	0.986834	−	0.161737i	$-0.0517097\pi$
$641$	2.36475	+	7.27794i	0.0934018	+	0.287461i	−0.893432	+	0.449198i	$0.851710\pi$
$642$	23.4164			0.924172
$643$	9.25329	+	6.72291i	0.364914	+	0.265126i	0.755099	−	0.655611i	$-0.227589\pi$
$643$	9.25329	+	6.72291i	0.364914	+	0.265126i	−0.390185	+	0.920737i	$0.627589\pi$
$644$	1.39919	+	4.30625i	0.0551357	+	0.169690i
$645$	−2.47214	+	7.60845i	−0.0973403	+	0.299583i
$646$	−20.5623	+	63.2843i	−0.809013	+	2.48989i
$647$	36.4164			1.43168			0.715838	−	0.698266i	$-0.246045\pi$
$647$	36.4164			1.43168			0.715838	+	0.698266i	$0.246045\pi$
$648$	0.690983	−	2.12663i	0.0271444	−	0.0835418i
$649$	2.42705	−	1.76336i	0.0952701	−	0.0692178i
$650$	−31.4164	−	22.8254i	−1.23225	−	0.895284i
$651$	−1.64590	−	5.06555i	−0.0645078	−	0.198535i
$652$	1.60739	+	4.94704i	0.0629503	+	0.193741i
$653$	−31.6525			−1.23866			−0.619329	−	0.785132i	$-0.712595\pi$
$653$	−31.6525			−1.23866			−0.619329	+	0.785132i	$0.712595\pi$
$654$	−18.0623	−	13.1230i	−0.706292	−	0.513151i
$655$	1.70820			0.0667451
$656$	−2.64590	−	30.9686i	−0.103305	−	1.20912i
$657$	−3.85410			−0.150363
$658$	−5.54508	−	4.02874i	−0.216170	−	0.157057i
$659$	−33.6312			−1.31009			−0.655043	−	0.755592i	$-0.727349\pi$
$659$	−33.6312			−1.31009			−0.655043	+	0.755592i	$0.727349\pi$
$660$	−0.190983	−	0.587785i	−0.00743400	−	0.0228795i
$661$	−6.07953	−	18.7109i	−0.236466	−	0.727768i	−0.996924	−	0.0783802i	$-0.975025\pi$
$661$	−6.07953	−	18.7109i	−0.236466	−	0.727768i	0.760457	−	0.649388i	$-0.224975\pi$
$662$	5.54508	+	4.02874i	0.215516	+	0.156581i
$663$	25.4164	−	18.4661i	0.987091	−	0.717164i
$664$	−8.19098	+	25.2093i	−0.317872	+	0.978309i
$665$	−7.85410			−0.304569
$666$	5.11803	−	15.7517i	0.198320	−	0.610366i
$667$	13.7877	−	42.4343i	0.533863	−	1.64306i
$668$	−0.347524	−	1.06957i	−0.0134461	−	0.0413829i
$669$	−13.1353	−	9.54332i	−0.507838	−	0.368966i
$670$	−4.61803			−0.178410
$671$	−1.26393	−	3.88998i	−0.0487936	−	0.150171i
$672$	2.73607	−	1.98787i	0.105546	−	0.0766837i
$673$	−2.96149	+	9.11454i	−0.114157	+	0.351340i	−0.991770	−	0.128030i	$-0.959135\pi$
$673$	−2.96149	+	9.11454i	−0.114157	+	0.351340i	0.877613	+	0.479370i	$0.159135\pi$
$674$	−6.16312	−	4.47777i	−0.237394	−	0.172477i
$675$	−3.23607	+	2.35114i	−0.124556	+	0.0904955i
$676$	−11.5000	+	8.35524i	−0.442308	+	0.321355i
$677$	−37.2705	+	27.0786i	−1.43242	+	1.04072i	−0.442863	+	0.896589i	$0.646037\pi$
$677$	−37.2705	+	27.0786i	−1.43242	+	1.04072i	−0.989559	+	0.144126i	$0.953963\pi$
$678$	11.7812	−	8.55951i	0.452452	−	0.328726i
$679$	−10.7812	−	7.83297i	−0.413743	−	0.300602i
$680$	−3.61803	+	11.1352i	−0.138745	+	0.427014i
$681$	−5.78115	+	4.20025i	−0.221534	+	0.160954i
$682$	2.66312	+	8.19624i	0.101976	+	0.313850i
$683$	40.4164			1.54649			0.773245	−	0.634107i	$-0.218632\pi$
$683$	40.4164			1.54649			0.773245	+	0.634107i	$0.218632\pi$
$684$	−3.92705	−	2.85317i	−0.150155	−	0.109094i
$685$	−0.218847	−	0.673542i	−0.00836172	−	0.0257347i
$686$	−0.500000	+	1.53884i	−0.0190901	+	0.0587533i
$687$	−5.63525	+	17.3435i	−0.214998	+	0.661697i
$688$	38.8328			1.48049
$689$	−5.02129	+	15.4539i	−0.191296	+	0.588748i
$690$	9.59017	−	6.96767i	0.365092	−	0.265255i
$691$	−21.4615	−	15.5927i	−0.816434	−	0.593174i	0.0992551	−	0.995062i	$-0.468354\pi$
$691$	−21.4615	−	15.5927i	−0.816434	−	0.593174i	−0.915689	+	0.401888i	$0.868354\pi$
$692$	2.22542	+	6.84915i	0.0845980	+	0.260366i
$693$	−0.309017	−	0.951057i	−0.0117386	−	0.0361276i
$694$	21.6525			0.821917
$695$	−9.66312	−	7.02067i	−0.366543	−	0.266309i
$696$	−13.6180			−0.516190
$697$	−21.9443	−	25.3480i	−0.831199	−	0.960124i
$698$	19.5623			0.740444
$699$	21.1353	+	15.3557i	0.799409	+	0.580804i
$700$	−2.47214			−0.0934380
$701$	0.489357	+	1.50609i	0.0184828	+	0.0568841i	0.959873	−	0.280437i	$-0.0904793\pi$
$701$	0.489357	+	1.50609i	0.0184828	+	0.0568841i	−0.941390	+	0.337321i	$0.890479\pi$
$702$	3.00000	+	9.23305i	0.113228	+	0.348479i
$703$	65.0410	+	47.2551i	2.45307	+	1.78226i
$704$	3.42705	−	2.48990i	0.129162	−	0.0938416i
$705$	−1.30902	+	4.02874i	−0.0493004	+	0.151731i
$706$	13.5623			0.510424
$707$	1.23607	−	3.80423i	0.0464871	−	0.143073i
$708$	−0.572949	+	1.76336i	−0.0215327	+	0.0662710i
$709$	4.76393	+	14.6619i	0.178913	+	0.550638i	0.999791	−	0.0204663i	$-0.00651508\pi$
$709$	4.76393	+	14.6619i	0.178913	+	0.550638i	−0.820877	+	0.571105i	$0.806515\pi$
$710$	11.3992	+	8.28199i	0.427804	+	0.310818i
$711$	15.0000			0.562544
$712$	0.326238	+	1.00406i	0.0122263	+	0.0376286i
$713$	−31.5689	+	22.9361i	−1.18226	+	0.858965i
$714$	2.61803	−	8.05748i	0.0979775	−	0.301544i
$715$	−4.85410	−	3.52671i	−0.181533	−	0.131892i
$716$	−7.13525	+	5.18407i	−0.266657	+	0.193738i
$717$	−10.6631	+	7.74721i	−0.398221	+	0.289325i
$718$	37.4615	−	27.2174i	1.39805	−	1.01574i
$719$	−2.47214	+	1.79611i	−0.0921951	+	0.0669837i	−0.632928	−	0.774211i	$-0.718147\pi$
$719$	−2.47214	+	1.79611i	−0.0921951	+	0.0669837i	0.540733	+	0.841194i	$0.318147\pi$
$720$	−3.92705	−	2.85317i	−0.146353	−	0.106331i
$721$	−2.54508	+	7.83297i	−0.0947839	+	0.291715i
$722$	55.8779	−	40.5977i	2.07956	−	1.51089i
$723$	8.50000	+	26.1603i	0.316118	+	0.972912i
$724$	4.85410			0.180401
$725$	19.7082	+	14.3188i	0.731944	+	0.531789i
$726$	−5.00000	−	15.3884i	−0.185567	−	0.571118i
$727$	−0.0663712	+	0.204270i	−0.00246157	+	0.00757594i	−0.952280	−	0.305227i	$-0.901268\pi$
$727$	−0.0663712	+	0.204270i	−0.00246157	+	0.00757594i	0.949818	+	0.312803i	$0.101268\pi$
$728$	4.14590	−	12.7598i	0.153657	−	0.472908i
$729$	1.00000			0.0370370
$730$	−1.92705	+	5.93085i	−0.0713234	+	0.219511i
$731$	33.8885	−	24.6215i	1.25341	−	0.910658i
$732$	2.04508	+	1.48584i	0.0755885	+	0.0549183i
$733$	5.51722	+	16.9803i	0.203783	+	0.627180i	0.999761	+	0.0218546i	$0.00695709\pi$
$733$	5.51722	+	16.9803i	0.203783	+	0.627180i	−0.795978	+	0.605326i	$0.793043\pi$
$734$	8.11803	+	24.9847i	0.299642	+	0.922204i
$735$	1.00000			0.0368856
$736$	−20.0451	−	14.5636i	−0.738872	−	0.536822i
$737$	2.85410			0.105132
$738$	9.54508	−	4.02874i	0.351359	−	0.148300i
$739$	−14.5967			−0.536950			−0.268475	−	0.963287i	$-0.586520\pi$
$739$	−14.5967			−0.536950			−0.268475	+	0.963287i	$0.586520\pi$
$740$	−5.11803	−	3.71847i	−0.188143	−	0.136694i
$741$	−47.1246			−1.73117
$742$	1.35410	+	4.16750i	0.0497106	+	0.152994i
$743$	−8.58359	−	26.4176i	−0.314901	−	0.969167i	−0.975795	−	0.218687i	$-0.929823\pi$
$743$	−8.58359	−	26.4176i	−0.314901	−	0.969167i	0.660894	−	0.750480i	$-0.270177\pi$
$744$	9.63525	+	7.00042i	0.353246	+	0.256648i
$745$	−0.881966	+	0.640786i	−0.0323127	+	0.0234766i
$746$	9.63525	−	29.6543i	0.352772	−	1.08572i
$747$	−11.8541			−0.433719
$748$	−1.00000	+	3.07768i	−0.0365636	+	0.112531i
$749$	4.47214	−	13.7638i	0.163408	−	0.502919i
$750$	4.50000	+	13.8496i	0.164317	+	0.505715i
$751$	7.59017	+	5.51458i	0.276969	+	0.201230i	0.717594	−	0.696461i	$-0.245243\pi$
$751$	7.59017	+	5.51458i	0.276969	+	0.201230i	−0.440625	+	0.897691i	$0.645243\pi$
$752$	20.5623			0.749830
$753$	−7.41641	−	22.8254i	−0.270269	−	0.831802i
$754$	47.8328	−	34.7526i	1.74197	−	1.26561i
$755$	−7.06231	+	21.7355i	−0.257024	+	0.791037i
$756$	0.500000	+	0.363271i	0.0181848	+	0.0132120i
$757$	−29.6246	+	21.5235i	−1.07672	+	0.782286i	−0.977109	−	0.212740i	$-0.931761\pi$
$757$	−29.6246	+	21.5235i	−1.07672	+	0.782286i	−0.0996159	+	0.995026i	$0.531761\pi$
$758$	−25.8435	+	18.7764i	−0.938677	+	0.681989i
$759$	−5.92705	+	4.30625i	−0.215138	+	0.156307i
$760$	14.2082	−	10.3229i	0.515386	−	0.374450i
$761$	30.0517	+	21.8338i	1.08937	+	0.791475i	0.979293	−	0.202448i	$-0.0648897\pi$
$761$	30.0517	+	21.8338i	1.08937	+	0.791475i	0.110079	+	0.993923i	$0.464890\pi$
$762$	−2.50000	+	7.69421i	−0.0905654	+	0.278732i
$763$	−11.1631	+	8.11048i	−0.404132	+	0.293619i
$764$	3.74671	+	11.5312i	0.135551	+	0.417184i
$765$	−5.23607			−0.189310
$766$	30.2254	+	21.9601i	1.09209	+	0.793449i
$767$	5.56231	+	17.1190i	0.200843	+	0.618132i
$768$	−4.19098	+	12.8985i	−0.151229	+	0.465435i
$769$	−6.30902	+	19.4172i	−0.227509	+	0.700201i	0.770518	+	0.637418i	$0.219997\pi$
$769$	−6.30902	+	19.4172i	−0.227509	+	0.700201i	−0.998027	+	0.0627827i	$0.980003\pi$
$770$	−1.61803			−0.0583099
$771$	−1.78115	+	5.48183i	−0.0641467	+	0.197423i
$772$	2.32624	−	1.69011i	0.0837231	−	0.0608284i
$773$	−38.3885	−	27.8909i	−1.38074	−	1.00317i	−0.996811	−	0.0798038i	$-0.974571\pi$
$773$	−38.3885	−	27.8909i	−1.38074	−	1.00317i	−0.383929	−	0.923362i	$-0.625429\pi$
$774$	4.00000	+	12.3107i	0.143777	+	0.442500i
$775$	−6.58359	−	20.2622i	−0.236490	−	0.727840i
$776$	29.7984			1.06970
$777$	−8.28115	−	6.01661i	−0.297085	−	0.215845i
$778$	−38.5066			−1.38053
$779$	4.28115	+	50.1082i	0.153388	+	1.79531i
$780$	3.70820			0.132775
$781$	−7.04508	−	5.11855i	−0.252093	−	0.183156i
$782$	−62.0689			−2.21958
$783$	−1.88197	−	5.79210i	−0.0672560	−	0.206993i
$784$	−1.50000	−	4.61653i	−0.0535714	−	0.164876i
$785$	−2.04508	−	1.48584i	−0.0729922	−	0.0530319i
$786$	2.23607	−	1.62460i	0.0797579	−	0.0579475i
$787$	5.04508	−	15.5272i	0.179838	−	0.553484i	−0.819983	−	0.572387i	$-0.806017\pi$
$787$	5.04508	−	15.5272i	0.179838	−	0.553484i	0.999821	+	0.0189032i	$0.00601743\pi$
$788$	−3.67376			−0.130872
$789$	−9.75329	+	30.0175i	−0.347226	+	1.06865i
$790$	7.50000	−	23.0826i	0.266838	−	0.821243i
$791$	−2.78115	−	8.55951i	−0.0988864	−	0.304341i
$792$	1.80902	+	1.31433i	0.0642806	+	0.0467026i
$793$	24.5410			0.871477
$794$	16.9615	+	52.2021i	0.601941	+	1.85258i
$795$	2.19098	−	1.59184i	0.0777062	−	0.0564568i
$796$	4.57295	−	14.0741i	0.162084	−	0.498843i
$797$	13.5902	+	9.87384i	0.481389	+	0.349749i	0.801863	−	0.597508i	$-0.203842\pi$
$797$	13.5902	+	9.87384i	0.481389	+	0.349749i	−0.320474	+	0.947257i	$0.603842\pi$
$798$	−10.2812	+	7.46969i	−0.363949	+	0.264424i
$799$	17.9443	−	13.0373i	0.634823	−	0.461226i
$800$	10.9443	−	7.95148i	0.386938	−	0.281127i
$801$	−0.381966	+	0.277515i	−0.0134961	+	0.00980549i
$802$	−30.6525	−	22.2703i	−1.08238	−	0.786393i
$803$	1.19098	−	3.66547i	0.0420289	−	0.129352i
$804$	−1.42705	+	1.03681i	−0.0503282	+	0.0365656i
$805$	−2.26393	−	6.96767i	−0.0797931	−	0.245578i
$806$	−51.7082			−1.82134
$807$	−17.9443	−	13.0373i	−0.631668	−	0.458934i
$808$	2.76393	+	8.50651i	0.0972348	+	0.299258i
$809$	−6.43363	+	19.8007i	−0.226194	+	0.696155i	0.771974	+	0.635654i	$0.219270\pi$
$809$	−6.43363	+	19.8007i	−0.226194	+	0.696155i	−0.998168	+	0.0605003i	$0.980730\pi$
$810$	0.500000	−	1.53884i	0.0175682	−	0.0540694i
$811$	−29.3607			−1.03099			−0.515496	−	0.856892i	$-0.672392\pi$
$811$	−29.3607			−1.03099			−0.515496	+	0.856892i	$0.672392\pi$
$812$	1.16312	−	3.57971i	0.0408175	−	0.125623i
$813$	10.8992	−	7.91872i	0.382251	−	0.277722i
$814$	13.3992	+	9.73508i	0.469641	+	0.341214i
$815$	−2.60081	−	8.00448i	−0.0911025	−	0.280385i
$816$	7.85410	+	24.1724i	0.274949	+	0.846205i
$817$	−62.8328			−2.19824
$818$	16.5623	+	12.0332i	0.579087	+	0.420732i
$819$	6.00000			0.209657
$820$	−0.336881	−	3.94298i	−0.0117644	−	0.137695i
$821$	50.1246			1.74936			0.874681	−	0.484700i	$-0.161071\pi$
$821$	50.1246			1.74936			0.874681	+	0.484700i	$0.161071\pi$
$822$	−0.927051	−	0.673542i	−0.0323346	−	0.0234925i
$823$	−5.34752			−0.186403			−0.0932015	−	0.995647i	$-0.529710\pi$
$823$	−5.34752			−0.186403			−0.0932015	+	0.995647i	$0.529710\pi$
$824$	−5.69098	−	17.5150i	−0.198255	−	0.610165i
$825$	−1.23607	−	3.80423i	−0.0430344	−	0.132446i
$826$	3.92705	+	2.85317i	0.136640	+	0.0992745i
$827$	−26.8992	+	19.5434i	−0.935376	+	0.679591i	−0.947303	−	0.320338i	$-0.896203\pi$
$827$	−26.8992	+	19.5434i	−0.935376	+	0.679591i	0.0119269	+	0.999929i	$0.496203\pi$
$828$	1.39919	−	4.30625i	0.0486251	−	0.149653i
$829$	13.7984			0.479237			0.239619	−	0.970867i	$-0.422978\pi$
$829$	13.7984			0.479237			0.239619	+	0.970867i	$0.422978\pi$
$830$	−5.92705	+	18.2416i	−0.205731	+	0.633175i
$831$	−4.67376	+	14.3844i	−0.162131	+	0.498988i
$832$	7.85410	+	24.1724i	0.272292	+	0.838029i
$833$	−4.23607	−	3.07768i	−0.146771	−	0.106635i
$834$	−19.3262			−0.669213
$835$	0.562306	+	1.73060i	0.0194594	+	0.0598899i
$836$	3.92705	−	2.85317i	0.135820	−	0.0986789i
$837$	−1.64590	+	5.06555i	−0.0568906	+	0.175091i
$838$	10.2812	+	7.46969i	0.355157	+	0.258036i
$839$	−40.2148	+	29.2177i	−1.38837	+	1.00871i	−0.392326	+	0.919826i	$0.628330\pi$
$839$	−40.2148	+	29.2177i	−1.38837	+	1.00871i	−0.996042	+	0.0888826i	$0.971670\pi$
$840$	−1.80902	+	1.31433i	−0.0624170	+	0.0453486i
$841$	−6.54508	+	4.75528i	−0.225693	+	0.163975i
$842$	−11.7082	+	8.50651i	−0.403491	+	0.293154i
$843$	14.2984	+	10.3884i	0.492462	+	0.357795i
$844$	−2.32624	+	7.15942i	−0.0800724	+	0.246438i
$845$	18.6074	−	13.5191i	0.640114	−	0.465070i
$846$	2.11803	+	6.51864i	0.0728195	+	0.224115i
$847$	−10.0000			−0.343604
$848$	−10.6353	−	7.72696i	−0.365216	−	0.265345i
$849$	7.41641	+	22.8254i	0.254530	+	0.783364i
$850$	10.4721	−	32.2299i	0.359191	−	1.10548i
$851$	−23.1738	+	71.3215i	−0.794386	+	2.44487i
$852$	5.38197			0.184383
$853$	4.58359	−	14.1068i	0.156939	−	0.483009i	−0.841413	−	0.540393i	$-0.818276\pi$
$853$	4.58359	−	14.1068i	0.156939	−	0.483009i	0.998352	+	0.0573834i	$0.0182757\pi$
$854$	5.35410	−	3.88998i	0.183214	−	0.133112i
$855$	6.35410	+	4.61653i	0.217306	+	0.157882i
$856$	10.0000	+	30.7768i	0.341793	+	1.05193i
$857$	4.64590	+	14.2986i	0.158701	+	0.488431i	0.998517	−	0.0544398i	$-0.0173373\pi$
$857$	4.64590	+	14.2986i	0.158701	+	0.488431i	−0.839816	+	0.542871i	$0.817337\pi$
$858$	−9.70820			−0.331433
$859$	26.5344	+	19.2784i	0.905343	+	0.657771i	0.939833	−	0.341635i	$-0.110980\pi$
$859$	26.5344	+	19.2784i	0.905343	+	0.657771i	−0.0344894	+	0.999405i	$0.510980\pi$
$860$	4.94427			0.168598
$861$	−0.545085	−	6.37988i	−0.0185764	−	0.217426i
$862$	−3.56231			−0.121333
$863$	15.0451	+	10.9309i	0.512141	+	0.372092i	0.813635	−	0.581376i	$-0.197485\pi$
$863$	15.0451	+	10.9309i	0.512141	+	0.372092i	−0.301494	+	0.953468i	$0.597485\pi$
$864$	−3.38197			−0.115057
$865$	−3.60081	−	11.0822i	−0.122431	−	0.376805i
$866$	13.7361	+	42.2753i	0.466771	+	1.43657i
$867$	8.42705	+	6.12261i	0.286198	+	0.207935i
$868$	−2.66312	+	1.93487i	−0.0903921	+	0.0656737i
$869$	−4.63525	+	14.2658i	−0.157240	+	0.483936i
$870$	−9.85410			−0.334085
$871$	−5.29180	+	16.2865i	−0.179306	+	0.551846i
$872$	9.53444	−	29.3440i	0.322877	−	0.993713i
$873$	4.11803	+	12.6740i	0.139374	+	0.428950i
$874$	75.3222	+	54.7248i	2.54781	+	1.85109i
$875$	9.00000			0.304256
$876$	0.736068	+	2.26538i	0.0248694	+	0.0765402i
$877$	−33.2877	+	24.1850i	−1.12405	+	0.816668i	−0.984818	−	0.173592i	$-0.944462\pi$
$877$	−33.2877	+	24.1850i	−1.12405	+	0.816668i	−0.139229	+	0.990260i	$0.544462\pi$
$878$	2.09017	−	6.43288i	0.0705398	−	0.217099i
$879$	14.1803	+	10.3026i	0.478291	+	0.347499i
$880$	3.92705	−	2.85317i	0.132381	−	0.0961803i
$881$	16.3713	−	11.8945i	0.551564	−	0.400735i	−0.276798	−	0.960928i	$-0.589273\pi$
$881$	16.3713	−	11.8945i	0.551564	−	0.400735i	0.828362	+	0.560194i	$0.189273\pi$
$882$	1.30902	−	0.951057i	0.0440769	−	0.0320237i
$883$	9.69098	−	7.04091i	0.326128	−	0.236946i	−0.412658	−	0.910886i	$-0.635400\pi$
$883$	9.69098	−	7.04091i	0.326128	−	0.236946i	0.738786	+	0.673940i	$0.235400\pi$
$884$	−15.7082	−	11.4127i	−0.528324	−	0.383850i
$885$	0.927051	−	2.85317i	0.0311625	−	0.0959082i
$886$	−0.263932	+	0.191758i	−0.00886697	+	0.00644223i
$887$	15.9058	+	48.9529i	0.534063	+	1.64368i	0.745664	+	0.666322i	$0.232132\pi$
$887$	15.9058	+	48.9529i	0.534063	+	1.64368i	−0.211601	+	0.977356i	$0.567868\pi$
$888$	22.8885			0.768089
$889$	4.04508	+	2.93893i	0.135668	+	0.0985684i
$890$	0.236068	+	0.726543i	0.00791302	+	0.0243538i
$891$	−0.309017	+	0.951057i	−0.0103525	+	0.0318616i
$892$	−3.10081	+	9.54332i	−0.103823	+	0.319534i
$893$	−33.2705			−1.11336
$894$	−0.545085	+	1.67760i	−0.0182304	+	0.0561073i
$895$	11.5451	−	8.38800i	0.385910	−	0.280380i
$896$	11.0172	+	8.00448i	0.368060	+	0.267411i
$897$	−13.5836	−	41.8060i	−0.453543	−	1.39586i
$898$	−3.09017	−	9.51057i	−0.103120	−	0.317372i
$899$	32.4377			1.08186
$900$	2.00000	+	1.45309i	0.0666667	+	0.0484362i
$901$	−14.1803			−0.472416
$902$	0.881966	+	10.3229i	0.0293663	+	0.343714i
$903$	8.00000			0.266223
$904$	16.2812	+	11.8290i	0.541503	+	0.393425i
$905$	−7.85410			−0.261079
$906$	11.4271	+	35.1688i	0.379638	+	1.16841i
$907$	3.71885	+	11.4454i	0.123482	+	0.380039i	0.993622	−	0.112767i	$-0.0359712\pi$
$907$	3.71885	+	11.4454i	0.123482	+	0.380039i	−0.870139	+	0.492806i	$0.835971\pi$
$908$	3.57295	+	2.59590i	0.118572	+	0.0861479i
$909$	−3.23607	+	2.35114i	−0.107334	+	0.0779824i
$910$	3.00000	−	9.23305i	0.0994490	−	0.306073i
$911$	29.2705			0.969775			0.484888	−	0.874576i	$-0.338860\pi$
$911$	29.2705			0.969775			0.484888	+	0.874576i	$0.338860\pi$
$912$	11.7812	−	36.2587i	0.390113	−	1.20064i
$913$	3.66312	−	11.2739i	0.121232	−	0.373112i
$914$	0.645898	+	1.98787i	0.0213644	+	0.0657529i
$915$	−3.30902	−	2.40414i	−0.109393	−	0.0794785i
$916$	11.2705			0.372388
$917$	−0.527864	−	1.62460i	−0.0174316	−	0.0536490i
$918$	−6.85410	+	4.97980i	−0.226219	+	0.164358i
$919$	−12.9443	+	39.8384i	−0.426992	+	1.31415i	0.474082	+	0.880481i	$0.342780\pi$
$919$	−12.9443	+	39.8384i	−0.426992	+	1.31415i	−0.901074	+	0.433666i	$0.857220\pi$
$920$	13.2533	+	9.62908i	0.436948	+	0.317461i
$921$	−16.1074	+	11.7027i	−0.530757	+	0.385617i
$922$	14.0172	−	10.1841i	0.461633	−	0.335396i
$923$	42.2705	−	30.7113i	1.39135	−	1.01088i
$924$	−0.500000	+	0.363271i	−0.0164488	+	0.0119507i
$925$	−33.1246	−	24.0664i	−1.08913	−	0.791300i
$926$	16.2082	−	49.8837i	0.532635	−	1.63928i
$927$	6.66312	−	4.84104i	0.218846	−	0.159001i
$928$	6.36475	+	19.5887i	0.208933	+	0.643030i
$929$	50.6869			1.66298			0.831492	−	0.555537i	$-0.187487\pi$
$929$	50.6869			1.66298			0.831492	+	0.555537i	$0.187487\pi$
$930$	6.97214	+	5.06555i	0.228625	+	0.166106i
$931$	2.42705	+	7.46969i	0.0795434	+	0.244809i
$932$	4.98936	−	15.3557i	0.163432	−	0.502991i
$933$	10.5451	−	32.4544i	0.345231	−	1.06251i
$934$	−40.3050			−1.31882
$935$	1.61803	−	4.97980i	0.0529154	−	0.162857i
$936$	−10.8541	+	7.88597i	−0.354777	+	0.257761i
$937$	38.5795	+	28.0297i	1.26034	+	0.915689i	0.998774	−	0.0494968i	$-0.0157618\pi$
$937$	38.5795	+	28.0297i	1.26034	+	0.915689i	0.261564	+	0.965186i	$0.415762\pi$
$938$	1.42705	+	4.39201i	0.0465949	+	0.143404i
$939$	−0.437694	−	1.34708i	−0.0142836	−	0.0439604i
$940$	2.61803			0.0853909
$941$	−17.3992	−	12.6412i	−0.567197	−	0.412093i	0.266889	−	0.963727i	$-0.414004\pi$
$941$	−17.3992	−	12.6412i	−0.567197	−	0.412093i	−0.834086	+	0.551634i	$0.814004\pi$
$942$	−4.09017			−0.133265
$943$	−43.2188	+	18.2416i	−1.40740	+	0.594028i
$944$	−14.5623			−0.473963
$945$	−0.809017	−	0.587785i	−0.0263173	−	0.0191207i
$946$	−12.9443			−0.420855
$947$	5.21885	+	16.0620i	0.169590	+	0.521944i	0.999345	−	0.0361836i	$-0.0115201\pi$
$947$	5.21885	+	16.0620i	0.169590	+	0.521944i	−0.829755	+	0.558127i	$0.811520\pi$
$948$	−2.86475	−	8.81678i	−0.0930426	−	0.286356i
$949$	18.7082	+	13.5923i	0.607294	+	0.441225i
$950$	−41.1246	+	29.8788i	−1.33426	+	0.969396i
$951$	4.56231	−	14.0413i	0.147943	−	0.455321i
$952$	11.7082			0.379465
$953$	10.9787	−	33.7890i	0.355635	−	1.09453i	−0.600005	−	0.799996i	$-0.704835\pi$
$953$	10.9787	−	33.7890i	0.355635	−	1.09453i	0.955640	−	0.294537i	$-0.0951654\pi$
$954$	1.35410	−	4.16750i	0.0438407	−	0.134928i
$955$	−6.06231	−	18.6579i	−0.196172	−	0.603754i
$956$	6.59017	+	4.78804i	0.213141	+	0.154856i
$957$	6.09017			0.196867
$958$	−0.326238	−	1.00406i	−0.0105403	−	0.0324396i
$959$	−0.572949	+	0.416272i	−0.0185015	+	0.0134421i
$960$	1.30902	−	4.02874i	0.0422483	−	0.130027i
$961$	2.12868	+	1.54657i	0.0686670	+	0.0498895i
$962$	−80.3951	+	58.4105i	−2.59204	+	1.88323i
$963$	−11.7082	+	8.50651i	−0.377292	+	0.274118i
$964$	13.7533	−	9.99235i	0.442964	−	0.321832i
$965$	−3.76393	+	2.73466i	−0.121165	+	0.0880317i
$966$	−9.59017	−	6.96767i	−0.308559	−	0.224181i
$967$	−1.12868	+	3.47371i	−0.0362958	+	0.111707i	−0.967563	−	0.252630i	$-0.918704\pi$
$967$	−1.12868	+	3.47371i	−0.0362958	+	0.111707i	0.931267	+	0.364337i	$0.118704\pi$
$968$	18.0902	−	13.1433i	0.581440	−	0.422441i
$969$	−12.7082	−	39.1118i	−0.408246	−	1.25645i
$970$	21.5623			0.692324
$971$	3.70820	+	2.69417i	0.119002	+	0.0864600i	0.645694	−	0.763596i	$-0.276568\pi$
$971$	3.70820	+	2.69417i	0.119002	+	0.0864600i	−0.526692	+	0.850056i	$0.676568\pi$
$972$	−0.190983	−	0.587785i	−0.00612578	−	0.0188532i
$973$	−3.69098	+	11.3597i	−0.118327	+	0.364175i
$974$	14.8262	−	45.6305i	0.475063	−	1.46209i
$975$	24.0000			0.768615
$976$	−6.13525	+	18.8824i	−0.196385	+	0.604410i
$977$	−15.2533	+	11.0822i	−0.487996	+	0.354550i	−0.804413	−	0.594070i	$-0.797520\pi$
$977$	−15.2533	+	11.0822i	−0.487996	+	0.354550i	0.316417	+	0.948620i	$0.397520\pi$
$978$	−11.0172	−	8.00448i	−0.352292	−	0.255955i
$979$	−0.145898	−	0.449028i	−0.00466292	−	0.0143510i
$980$	−0.190983	−	0.587785i	−0.00610073	−	0.0187761i
$981$	13.7984			0.440548
$982$	−6.11803	−	4.44501i	−0.195234	−	0.141846i
$983$	−39.3607			−1.25541			−0.627705	−	0.778451i	$-0.716006\pi$
$983$	−39.3607			−1.25541			−0.627705	+	0.778451i	$0.716006\pi$
$984$	9.37132	+	10.8249i	0.298747	+	0.345085i
$985$	5.94427			0.189400
$986$	41.7426	+	30.3278i	1.32936	+	0.965834i
$987$	4.23607			0.134836
$988$	9.00000	+	27.6992i	0.286328	+	0.881227i
$989$	−18.1115	−	55.7413i	−0.575911	−	1.77247i
$990$	1.30902	+	0.951057i	0.0416033	+	0.0302266i
$991$	−25.8992	+	18.8169i	−0.822715	+	0.597737i	−0.917489	−	0.397762i	$-0.869787\pi$
$991$	−25.8992	+	18.8169i	−0.822715	+	0.597737i	0.0947741	+	0.995499i	$0.469787\pi$
$992$	5.56637	−	17.1315i	0.176732	−	0.543927i
$993$	−4.23607			−0.134428
$994$	4.35410	−	13.4005i	0.138104	−	0.425040i
$995$	−7.39919	+	22.7724i	−0.234570	+	0.721932i
$996$	2.26393	+	6.96767i	0.0717354	+	0.220779i
$997$	24.6074	+	17.8783i	0.779324	+	0.566212i	0.904776	−	0.425888i	$-0.140038\pi$
$997$	24.6074	+	17.8783i	0.779324	+	0.566212i	−0.125452	+	0.992100i	$0.540038\pi$
$998$	−29.6525			−0.938633
$999$	3.16312	+	9.73508i	0.100077	+	0.308004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.n.a.379.1	✓	4
41.37	even	5	inner	861.2.n.a.652.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.n.a.379.1	✓	4	1.1	even	1	trivial
861.2.n.a.652.1	yes	4	41.37	even	5	inner

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:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30902 + 0.951057i) q^{2} -1.00000 q^{3} +(0.190983 + 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-1.30902 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.690983 - 2.12663i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.30902 + 0.951057i) q^{2} -1.00000 q^{3} +(0.190983 + 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-1.30902 - 0.951057i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.690983 - 2.12663i) q^{8} +1.00000 q^{9} +(0.500000 - 1.53884i) q^{10} +(-0.309017 + 0.951057i) q^{11} +(-0.190983 - 0.587785i) q^{12} +(-4.85410 - 3.52671i) q^{13} -1.61803 q^{14} +(0.309017 + 0.951057i) q^{15} +(3.92705 - 2.85317i) q^{16} +(1.61803 - 4.97980i) q^{17} +(1.30902 + 0.951057i) q^{18} +(-6.35410 + 4.61653i) q^{19} +(0.500000 - 0.363271i) q^{20} +(0.809017 - 0.587785i) q^{21} +(-1.30902 + 0.951057i) q^{22} +(-5.92705 - 4.30625i) q^{23} +(-0.690983 + 2.12663i) q^{24} +(3.23607 - 2.35114i) q^{25} +(-3.00000 - 9.23305i) q^{26} -1.00000 q^{27} +(-0.500000 - 0.363271i) q^{28} +(1.88197 + 5.79210i) q^{29} +(-0.500000 + 1.53884i) q^{30} +(1.64590 - 5.06555i) q^{31} +3.38197 q^{32} +(0.309017 - 0.951057i) q^{33} +(6.85410 - 4.97980i) q^{34} +(0.809017 + 0.587785i) q^{35} +(0.190983 + 0.587785i) q^{36} +(-3.16312 - 9.73508i) q^{37} -12.7082 q^{38} +(4.85410 + 3.52671i) q^{39} -2.23607 q^{40} +(3.30902 - 5.48183i) q^{41} +1.61803 q^{42} +(6.47214 + 4.70228i) q^{43} -0.618034 q^{44} +(-0.309017 - 0.951057i) q^{45} +(-3.66312 - 11.2739i) q^{46} +(3.42705 + 2.48990i) q^{47} +(-3.92705 + 2.85317i) q^{48} +(0.309017 - 0.951057i) q^{49} +6.47214 q^{50} +(-1.61803 + 4.97980i) q^{51} +(1.14590 - 3.52671i) q^{52} +(-0.836881 - 2.57565i) q^{53} +(-1.30902 - 0.951057i) q^{54} +1.00000 q^{55} +(0.690983 + 2.12663i) q^{56} +(6.35410 - 4.61653i) q^{57} +(-3.04508 + 9.37181i) q^{58} +(-2.42705 - 1.76336i) q^{59} +(-0.500000 + 0.363271i) q^{60} +(-3.30902 + 2.40414i) q^{61} +(6.97214 - 5.06555i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(-3.42705 - 2.48990i) q^{64} +(-1.85410 + 5.70634i) q^{65} +(1.30902 - 0.951057i) q^{66} +(-0.881966 - 2.71441i) q^{67} +3.23607 q^{68} +(5.92705 + 4.30625i) q^{69} +(0.500000 + 1.53884i) q^{70} +(-2.69098 + 8.28199i) q^{71} +(0.690983 - 2.12663i) q^{72} -3.85410 q^{73} +(5.11803 - 15.7517i) q^{74} +(-3.23607 + 2.35114i) q^{75} +(-3.92705 - 2.85317i) q^{76} +(-0.309017 - 0.951057i) q^{77} +(3.00000 + 9.23305i) q^{78} +15.0000 q^{79} +(-3.92705 - 2.85317i) q^{80} +1.00000 q^{81} +(9.54508 - 4.02874i) q^{82} -11.8541 q^{83} +(0.500000 + 0.363271i) q^{84} -5.23607 q^{85} +(4.00000 + 12.3107i) q^{86} +(-1.88197 - 5.79210i) q^{87} +(1.80902 + 1.31433i) q^{88} +(-0.381966 + 0.277515i) q^{89} +(0.500000 - 1.53884i) q^{90} +6.00000 q^{91} +(1.39919 - 4.30625i) q^{92} +(-1.64590 + 5.06555i) q^{93} +(2.11803 + 6.51864i) q^{94} +(6.35410 + 4.61653i) q^{95} -3.38197 q^{96} +(4.11803 + 12.6740i) q^{97} +(1.30902 - 0.951057i) q^{98} +(-0.309017 + 0.951057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 4 q^{3} + 3 q^{4} + q^{5} - 3 q^{6} - q^{7} + 5 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 + q^5 - 3 * q^6 - q^7 + 5 * q^8 + 4 * q^9	\( 4 q + 3 q^{2} - 4 q^{3} + 3 q^{4} + q^{5} - 3 q^{6} - q^{7} + 5 q^{8} + 4 q^{9} + 2 q^{10} + q^{11} - 3 q^{12} - 6 q^{13} - 2 q^{14} - q^{15} + 9 q^{16} + 2 q^{17} + 3 q^{18} - 12 q^{19} + 2 q^{20} + q^{21} - 3 q^{22} - 17 q^{23} - 5 q^{24} + 4 q^{25} - 12 q^{26} - 4 q^{27} - 2 q^{28} + 12 q^{29} - 2 q^{30} + 20 q^{31} + 18 q^{32} - q^{33} + 14 q^{34} + q^{35} + 3 q^{36} + 3 q^{37} - 24 q^{38} + 6 q^{39} + 11 q^{41} + 2 q^{42} + 8 q^{43} + 2 q^{44} + q^{45} + q^{46} + 7 q^{47} - 9 q^{48} - q^{49} + 8 q^{50} - 2 q^{51} + 18 q^{52} - 19 q^{53} - 3 q^{54} + 4 q^{55} + 5 q^{56} + 12 q^{57} - q^{58} - 3 q^{59} - 2 q^{60} - 11 q^{61} + 10 q^{62} - q^{63} - 7 q^{64} + 6 q^{65} + 3 q^{66} - 8 q^{67} + 4 q^{68} + 17 q^{69} + 2 q^{70} - 13 q^{71} + 5 q^{72} - 2 q^{73} + 16 q^{74} - 4 q^{75} - 9 q^{76} + q^{77} + 12 q^{78} + 60 q^{79} - 9 q^{80} + 4 q^{81} + 27 q^{82} - 34 q^{83} + 2 q^{84} - 12 q^{85} + 16 q^{86} - 12 q^{87} + 5 q^{88} - 6 q^{89} + 2 q^{90} + 24 q^{91} - 19 q^{92} - 20 q^{93} + 4 q^{94} + 12 q^{95} - 18 q^{96} + 12 q^{97} + 3 q^{98} + q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 + q^5 - 3 * q^6 - q^7 + 5 * q^8 + 4 * q^9 + 2 * q^10 + q^11 - 3 * q^12 - 6 * q^13 - 2 * q^14 - q^15 + 9 * q^16 + 2 * q^17 + 3 * q^18 - 12 * q^19 + 2 * q^20 + q^21 - 3 * q^22 - 17 * q^23 - 5 * q^24 + 4 * q^25 - 12 * q^26 - 4 * q^27 - 2 * q^28 + 12 * q^29 - 2 * q^30 + 20 * q^31 + 18 * q^32 - q^33 + 14 * q^34 + q^35 + 3 * q^36 + 3 * q^37 - 24 * q^38 + 6 * q^39 + 11 * q^41 + 2 * q^42 + 8 * q^43 + 2 * q^44 + q^45 + q^46 + 7 * q^47 - 9 * q^48 - q^49 + 8 * q^50 - 2 * q^51 + 18 * q^52 - 19 * q^53 - 3 * q^54 + 4 * q^55 + 5 * q^56 + 12 * q^57 - q^58 - 3 * q^59 - 2 * q^60 - 11 * q^61 + 10 * q^62 - q^63 - 7 * q^64 + 6 * q^65 + 3 * q^66 - 8 * q^67 + 4 * q^68 + 17 * q^69 + 2 * q^70 - 13 * q^71 + 5 * q^72 - 2 * q^73 + 16 * q^74 - 4 * q^75 - 9 * q^76 + q^77 + 12 * q^78 + 60 * q^79 - 9 * q^80 + 4 * q^81 + 27 * q^82 - 34 * q^83 + 2 * q^84 - 12 * q^85 + 16 * q^86 - 12 * q^87 + 5 * q^88 - 6 * q^89 + 2 * q^90 + 24 * q^91 - 19 * q^92 - 20 * q^93 + 4 * q^94 + 12 * q^95 - 18 * q^96 + 12 * q^97 + 3 * q^98 + q^99

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