LMFDB - Embedded newform 170.2.n.a.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(9,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("170.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.n (of order $8$, 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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 16 x^{15} + 52 x^{14} + 992 x^{13} + 6181 x^{12} + 8952 x^{11} + 6244 x^{10} - 11448 x^{9} + \cdots + 2048 $ x^20 - 16x^15 + 52x^14 + 992x^13 + 6181x^12 + 8952x^11 + 6244x^10 - 11448x^9 - 14520x^8 + 27936x^7 + 27880x^6 - 121104x^5 + 187460x^4 - 142208x^3 + 73856x^2 - 19456*x + 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			19.5
Root			$-2.32088 - 0.961341i$ of defining polynomial
Character	$\chi$	$=$	170.19
Dual form			170.2.n.a.9.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.961341 + 2.32088i) q^{3} -1.00000i q^{4} +(-1.24340 + 1.85848i) q^{5} +(-2.32088 - 0.961341i) q^{6} +(-0.124542 - 0.0515871i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.34100 + 2.34100i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.961341 + 2.32088i) q^{3} -1.00000i q^{4} +(-1.24340 + 1.85848i) q^{5} +(-2.32088 - 0.961341i) q^{6} +(-0.124542 - 0.0515871i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.34100 + 2.34100i) q^{9} +(-0.434925 - 2.19336i) q^{10} +(-1.51559 - 0.627776i) q^{11} +(2.32088 - 0.961341i) q^{12} +3.30730 q^{13} +(0.124542 - 0.0515871i) q^{14} +(-5.50865 - 1.09916i) q^{15} -1.00000 q^{16} +(-2.59524 - 3.20386i) q^{17} -3.31068i q^{18} +(3.24252 + 3.24252i) q^{19} +(1.85848 + 1.24340i) q^{20} -0.338641i q^{21} +(1.51559 - 0.627776i) q^{22} +(-1.86243 + 4.49630i) q^{23} +(-0.961341 + 2.32088i) q^{24} +(-1.90790 - 4.62168i) q^{25} +(-2.33862 + 2.33862i) q^{26} +(-0.721046 - 0.298667i) q^{27} +(-0.0515871 + 0.124542i) q^{28} +(2.75636 + 6.65444i) q^{29} +(4.67243 - 3.11798i) q^{30} +(6.99415 - 2.89707i) q^{31} +(0.707107 - 0.707107i) q^{32} -4.12100i q^{33} +(4.10058 + 0.430364i) q^{34} +(0.250730 - 0.167316i) q^{35} +(2.34100 + 2.34100i) q^{36} +(-1.21034 - 2.92202i) q^{37} -4.58562 q^{38} +(3.17945 + 7.67586i) q^{39} +(-2.19336 + 0.434925i) q^{40} +(1.66641 - 4.02306i) q^{41} +(0.239455 + 0.239455i) q^{42} +(1.56229 + 1.56229i) q^{43} +(-0.627776 + 1.51559i) q^{44} +(-1.43990 - 7.26152i) q^{45} +(-1.86243 - 4.49630i) q^{46} +12.8598 q^{47} +(-0.961341 - 2.32088i) q^{48} +(-4.93690 - 4.93690i) q^{49} +(4.61711 + 1.91894i) q^{50} +(4.94089 - 9.10325i) q^{51} -3.30730i q^{52} +(5.73483 - 5.73483i) q^{53} +(0.721046 - 0.298667i) q^{54} +(3.05119 - 2.03611i) q^{55} +(-0.0515871 - 0.124542i) q^{56} +(-4.40835 + 10.6427i) q^{57} +(-6.65444 - 2.75636i) q^{58} +(-0.746902 + 0.746902i) q^{59} +(-1.09916 + 5.50865i) q^{60} +(-1.57765 + 3.80879i) q^{61} +(-2.89707 + 6.99415i) q^{62} +(0.412320 - 0.170788i) q^{63} +1.00000i q^{64} +(-4.11231 + 6.14656i) q^{65} +(2.91399 + 2.91399i) q^{66} -11.9573i q^{67} +(-3.20386 + 2.59524i) q^{68} -12.2258 q^{69} +(-0.0589828 + 0.295603i) q^{70} +(-12.0949 + 5.00986i) q^{71} -3.31068 q^{72} +(-14.0700 + 5.82799i) q^{73} +(2.92202 + 1.21034i) q^{74} +(8.89224 - 8.87102i) q^{75} +(3.24252 - 3.24252i) q^{76} +(0.156369 + 0.156369i) q^{77} +(-7.67586 - 3.17945i) q^{78} +(6.14822 + 2.54668i) q^{79} +(1.24340 - 1.85848i) q^{80} +7.97145i q^{81} +(1.66641 + 4.02306i) q^{82} +(0.434038 - 0.434038i) q^{83} -0.338641 q^{84} +(9.18124 - 0.839501i) q^{85} -2.20941 q^{86} +(-12.7944 + 12.7944i) q^{87} +(-0.627776 - 1.51559i) q^{88} -12.1784i q^{89} +(6.15283 + 4.11651i) q^{90} +(-0.411899 - 0.170614i) q^{91} +(4.49630 + 1.86243i) q^{92} +(13.4475 + 13.4475i) q^{93} +(-9.09327 + 9.09327i) q^{94} +(-10.0579 + 1.99440i) q^{95} +(2.32088 + 0.961341i) q^{96} +(-0.683508 + 0.283118i) q^{97} +6.98183 q^{98} +(5.01761 - 2.07836i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5}+O(q^{10}) $ 20 * q - 4 * q^5	$ 20 q - 4 q^{5} + 4 q^{10} - 8 q^{11} - 24 q^{13} + 8 q^{15} - 20 q^{16} + 8 q^{20} + 8 q^{22} + 16 q^{23} - 12 q^{25} - 12 q^{26} + 24 q^{27} - 12 q^{29} - 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} - 8 q^{37} - 8 q^{38} + 4 q^{40} + 4 q^{41} + 8 q^{42} + 16 q^{43} - 8 q^{44} - 12 q^{45} + 16 q^{46} + 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} + 44 q^{53} - 24 q^{54} - 72 q^{57} + 16 q^{59} + 16 q^{60} + 8 q^{61} - 8 q^{62} - 24 q^{63} - 8 q^{65} - 8 q^{66} + 20 q^{68} - 16 q^{69} - 16 q^{70} + 8 q^{71} - 28 q^{72} - 60 q^{73} + 28 q^{74} + 64 q^{75} + 8 q^{78} + 56 q^{79} + 4 q^{80} + 4 q^{82} + 16 q^{84} - 16 q^{85} + 48 q^{86} - 72 q^{87} - 8 q^{88} + 32 q^{90} - 24 q^{91} - 8 q^{92} + 72 q^{93} + 32 q^{94} + 8 q^{95} + 48 q^{97} - 36 q^{98} + 72 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 + 4 * q^10 - 8 * q^11 - 24 * q^13 + 8 * q^15 - 20 * q^16 + 8 * q^20 + 8 * q^22 + 16 * q^23 - 12 * q^25 - 12 * q^26 + 24 * q^27 - 12 * q^29 - 8 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 - 8 * q^37 - 8 * q^38 + 4 * q^40 + 4 * q^41 + 8 * q^42 + 16 * q^43 - 8 * q^44 - 12 * q^45 + 16 * q^46 + 40 * q^47 - 56 * q^49 + 8 * q^50 - 8 * q^51 + 44 * q^53 - 24 * q^54 - 72 * q^57 + 16 * q^59 + 16 * q^60 + 8 * q^61 - 8 * q^62 - 24 * q^63 - 8 * q^65 - 8 * q^66 + 20 * q^68 - 16 * q^69 - 16 * q^70 + 8 * q^71 - 28 * q^72 - 60 * q^73 + 28 * q^74 + 64 * q^75 + 8 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^82 + 16 * q^84 - 16 * q^85 + 48 * q^86 - 72 * q^87 - 8 * q^88 + 32 * q^90 - 24 * q^91 - 8 * q^92 + 72 * q^93 + 32 * q^94 + 8 * q^95 + 48 * q^97 - 36 * q^98 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.961341	+	2.32088i	0.555031	+	1.33996i	0.913659	+	0.406482i	$0.133245\pi$
$3$	0.961341	+	2.32088i	0.555031	+	1.33996i	−0.358628	+	0.933481i	$0.616755\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−1.24340	+	1.85848i	−0.556067	+	0.831138i
$5$	−1.24340	+	1.85848i	−0.556067	+	0.831138i
$6$	−2.32088	−	0.961341i	−0.947497	−	0.392466i
$7$	−0.124542	−	0.0515871i	−0.0470726	−	0.0194981i	0.359023	−	0.933329i	$-0.383110\pi$
$7$	−0.124542	−	0.0515871i	−0.0470726	−	0.0194981i	−0.406096	+	0.913831i	$0.633110\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.34100	+	2.34100i	−0.780334	+	0.780334i
$10$	−0.434925	−	2.19336i	−0.137535	−	0.693602i
$11$	−1.51559	−	0.627776i	−0.456966	−	0.189282i	0.142313	−	0.989822i	$-0.454546\pi$
$11$	−1.51559	−	0.627776i	−0.456966	−	0.189282i	−0.599279	+	0.800540i	$0.704546\pi$
$12$	2.32088	−	0.961341i	0.669981	−	0.277515i
$13$	3.30730			0.917281			0.458640	−	0.888622i	$-0.348337\pi$
$13$	3.30730			0.917281			0.458640	+	0.888622i	$0.348337\pi$
$14$	0.124542	−	0.0515871i	0.0332853	−	0.0137872i
$15$	−5.50865	−	1.09916i	−1.42233	−	0.283802i
$16$	−1.00000			−0.250000
$17$	−2.59524	−	3.20386i	−0.629437	−	0.777051i
$17$	−2.59524	−	3.20386i	−0.629437	−	0.777051i
$18$		−	3.31068i		−	0.780334i
$19$	3.24252	+	3.24252i	0.743886	+	0.743886i	0.973323	−	0.229438i	$-0.0736887\pi$
$19$	3.24252	+	3.24252i	0.743886	+	0.743886i	−0.229438	+	0.973323i	$0.573689\pi$
$20$	1.85848	+	1.24340i	0.415569	+	0.278033i
$21$		−	0.338641i		−	0.0738976i
$22$	1.51559	−	0.627776i	0.323124	−	0.133842i
$23$	−1.86243	+	4.49630i	−0.388343	+	0.937543i	0.601948	+	0.798535i	$0.294391\pi$
$23$	−1.86243	+	4.49630i	−0.388343	+	0.937543i	−0.990291	+	0.139008i	$0.955609\pi$
$24$	−0.961341	+	2.32088i	−0.196233	+	0.473748i
$25$	−1.90790	−	4.62168i	−0.381579	−	0.924336i
$26$	−2.33862	+	2.33862i	−0.458640	+	0.458640i
$27$	−0.721046	−	0.298667i	−0.138765	−	0.0574785i
$28$	−0.0515871	+	0.124542i	−0.00974905	+	0.0235363i
$29$	2.75636	+	6.65444i	0.511843	+	1.23570i	0.942810	+	0.333331i	$0.108173\pi$
$29$	2.75636	+	6.65444i	0.511843	+	1.23570i	−0.430967	+	0.902368i	$0.641827\pi$
$30$	4.67243	−	3.11798i	0.853065	−	0.569263i
$31$	6.99415	−	2.89707i	1.25619	−	0.520330i	0.347450	−	0.937699i	$-0.387048\pi$
$31$	6.99415	−	2.89707i	1.25619	−	0.520330i	0.908737	+	0.417369i	$0.137048\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		−	4.12100i		−	0.717375i
$34$	4.10058	+	0.430364i	0.703244	+	0.0738068i
$35$	0.250730	−	0.167316i	0.0423811	−	0.0282815i
$36$	2.34100	+	2.34100i	0.390167	+	0.390167i
$37$	−1.21034	−	2.92202i	−0.198979	−	0.480377i	0.792622	−	0.609713i	$-0.208715\pi$
$37$	−1.21034	−	2.92202i	−0.198979	−	0.480377i	−0.991601	+	0.129336i	$0.958715\pi$
$38$	−4.58562			−0.743886
$39$	3.17945	+	7.67586i	0.509119	+	1.22912i
$40$	−2.19336	+	0.434925i	−0.346801	+	0.0687676i
$41$	1.66641	−	4.02306i	0.260249	−	0.628297i	−0.738705	−	0.674029i	$-0.764562\pi$
$41$	1.66641	−	4.02306i	0.260249	−	0.628297i	0.998954	+	0.0457323i	$0.0145621\pi$
$42$	0.239455	+	0.239455i	0.0369488	+	0.0369488i
$43$	1.56229	+	1.56229i	0.238246	+	0.238246i	0.816124	−	0.577877i	$-0.196119\pi$
$43$	1.56229	+	1.56229i	0.238246	+	0.238246i	−0.577877	+	0.816124i	$0.696119\pi$
$44$	−0.627776	+	1.51559i	−0.0946408	+	0.228483i
$45$	−1.43990	−	7.26152i	−0.214647	−	1.08248i
$46$	−1.86243	−	4.49630i	−0.274600	−	0.662943i
$47$	12.8598			1.87580			0.937900	−	0.346907i	$-0.112768\pi$
$47$	12.8598			1.87580			0.937900	+	0.346907i	$0.112768\pi$
$48$	−0.961341	−	2.32088i	−0.138758	−	0.334991i
$49$	−4.93690	−	4.93690i	−0.705271	−	0.705271i
$50$	4.61711	+	1.91894i	0.652958	+	0.271379i
$51$	4.94089	−	9.10325i	0.691862	−	1.27471i
$52$		−	3.30730i		−	0.458640i
$53$	5.73483	−	5.73483i	0.787740	−	0.787740i	−0.193383	−	0.981123i	$-0.561946\pi$
$53$	5.73483	−	5.73483i	0.787740	−	0.787740i	0.981123	+	0.193383i	$0.0619461\pi$
$54$	0.721046	−	0.298667i	0.0981220	−	0.0406435i
$55$	3.05119	−	2.03611i	0.411423	−	0.274549i
$56$	−0.0515871	−	0.124542i	−0.00689362	−	0.0166427i
$57$	−4.40835	+	10.6427i	−0.583900	+	1.40966i
$58$	−6.65444	−	2.75636i	−0.873771	−	0.361928i
$59$	−0.746902	+	0.746902i	−0.0972383	+	0.0972383i	−0.754052	−	0.656814i	$-0.771904\pi$
$59$	−0.746902	+	0.746902i	−0.0972383	+	0.0972383i	0.656814	+	0.754052i	$0.271904\pi$
$60$	−1.09916	+	5.50865i	−0.141901	+	0.711164i
$61$	−1.57765	+	3.80879i	−0.201998	+	0.487665i	−0.992121	−	0.125282i	$-0.960016\pi$
$61$	−1.57765	+	3.80879i	−0.201998	+	0.487665i	0.790124	+	0.612948i	$0.210016\pi$
$62$	−2.89707	+	6.99415i	−0.367929	+	0.888258i
$63$	0.412320	−	0.170788i	0.0519474	−	0.0215173i
$64$			1.00000i			0.125000i
$65$	−4.11231	+	6.14656i	−0.510070	+	0.762386i
$66$	2.91399	+	2.91399i	0.358687	+	0.358687i
$67$		−	11.9573i		−	1.46081i	−0.683013	−	0.730406i	$-0.739331\pi$
$67$		−	11.9573i		−	1.46081i	0.683013	−	0.730406i	$-0.260669\pi$
$68$	−3.20386	+	2.59524i	−0.388526	+	0.314719i
$69$	−12.2258			−1.47182
$70$	−0.0589828	+	0.295603i	−0.00704979	+	0.0353313i
$71$	−12.0949	+	5.00986i	−1.43540	+	0.594561i	−0.958677	−	0.284495i	$-0.908174\pi$
$71$	−12.0949	+	5.00986i	−1.43540	+	0.594561i	−0.476719	+	0.879056i	$0.658174\pi$
$72$	−3.31068			−0.390167
$73$	−14.0700	+	5.82799i	−1.64677	+	0.682114i	−0.996955	−	0.0779784i	$-0.975153\pi$
$73$	−14.0700	+	5.82799i	−1.64677	+	0.682114i	−0.649815	+	0.760093i	$0.725153\pi$
$74$	2.92202	+	1.21034i	0.339678	+	0.140699i
$75$	8.89224	−	8.87102i	1.02679	−	1.02434i
$76$	3.24252	−	3.24252i	0.371943	−	0.371943i
$77$	0.156369	+	0.156369i	0.0178200	+	0.0178200i
$78$	−7.67586	−	3.17945i	−0.869121	−	0.360002i
$79$	6.14822	+	2.54668i	0.691729	+	0.286524i	0.700720	−	0.713436i	$-0.252862\pi$
$79$	6.14822	+	2.54668i	0.691729	+	0.286524i	−0.00899120	+	0.999960i	$0.502862\pi$
$80$	1.24340	−	1.85848i	0.139017	−	0.207784i
$81$			7.97145i			0.885716i
$82$	1.66641	+	4.02306i	0.184024	+	0.444273i
$83$	0.434038	−	0.434038i	0.0476418	−	0.0476418i	−0.682885	−	0.730526i	$-0.739275\pi$
$83$	0.434038	−	0.434038i	0.0476418	−	0.0476418i	0.730526	+	0.682885i	$0.239275\pi$
$84$	−0.338641			−0.0369488
$85$	9.18124	−	0.839501i	0.995846	−	0.0910566i
$86$	−2.20941			−0.238246
$87$	−12.7944	+	12.7944i	−1.37170	+	1.37170i
$88$	−0.627776	−	1.51559i	−0.0669212	−	0.161562i
$89$		−	12.1784i		−	1.29091i	−0.763799	−	0.645454i	$-0.776668\pi$
$89$		−	12.1784i		−	1.29091i	0.763799	−	0.645454i	$-0.223332\pi$
$90$	6.15283	+	4.11651i	0.648565	+	0.433918i
$91$	−0.411899	−	0.170614i	−0.0431788	−	0.0178852i
$92$	4.49630	+	1.86243i	0.468772	+	0.194172i
$93$	13.4475	+	13.4475i	1.39444	+	1.39444i
$94$	−9.09327	+	9.09327i	−0.937900	+	0.937900i
$95$	−10.0579	+	1.99440i	−1.03192	+	0.204621i
$96$	2.32088	+	0.961341i	0.236874	+	0.0981165i
$97$	−0.683508	+	0.283118i	−0.0693998	+	0.0287463i	−0.417113	−	0.908854i	$-0.636958\pi$
$97$	−0.683508	+	0.283118i	−0.0693998	+	0.0287463i	0.347714	+	0.937601i	$0.386958\pi$
$98$	6.98183			0.705271
$99$	5.01761	−	2.07836i	0.504289	−	0.208883i
$100$	−4.62168	+	1.90790i	−0.462168	+	0.190790i
$101$	−19.3513			−1.92553			−0.962766	−	0.270337i	$-0.912865\pi$
$101$	−19.3513			−1.92553			−0.962766	+	0.270337i	$0.912865\pi$
$102$	2.94324	+	9.93070i	0.291424	+	0.983286i
$103$		−	1.70485i		−	0.167984i	−0.996466	−	0.0839921i	$-0.973233\pi$
$103$		−	1.70485i		−	0.167984i	0.996466	−	0.0839921i	$-0.0267670\pi$
$104$	2.33862	+	2.33862i	0.229320	+	0.229320i
$105$	0.629358	+	0.421068i	0.0614190	+	0.0410920i
$106$			8.11028i			0.787740i
$107$	3.70947	−	1.53651i	0.358608	−	0.148540i	−0.196103	−	0.980583i	$-0.562829\pi$
$107$	3.70947	−	1.53651i	0.358608	−	0.148540i	0.554711	+	0.832043i	$0.312829\pi$
$108$	−0.298667	+	0.721046i	−0.0287393	+	0.0693827i
$109$	3.59335	−	8.67512i	0.344181	−	0.830926i	−0.653103	−	0.757269i	$-0.726533\pi$
$109$	3.59335	−	8.67512i	0.344181	−	0.830926i	0.997284	−	0.0736565i	$-0.0234668\pi$
$110$	−0.717775	+	3.59726i	−0.0684372	+	0.342986i
$111$	5.61812	−	5.61812i	0.533248	−	0.533248i
$112$	0.124542	+	0.0515871i	0.0117681	+	0.00487453i
$113$	1.94643	−	4.69910i	0.183105	−	0.442054i	−0.805499	−	0.592598i	$-0.798102\pi$
$113$	1.94643	−	4.69910i	0.183105	−	0.442054i	0.988603	+	0.150544i	$0.0481025\pi$
$114$	−4.40835	−	10.6427i	−0.412879	−	0.996779i
$115$	−6.04053	−	9.05200i	−0.563283	−	0.844103i
$116$	6.65444	−	2.75636i	0.617849	−	0.255922i
$117$	−7.74240	+	7.74240i	−0.715786	+	0.715786i
$118$		−	1.05628i		−	0.0972383i
$119$	0.157939	+	0.532898i	0.0144782	+	0.0488506i
$120$	−3.11798	−	4.67243i	−0.284631	−	0.426532i
$121$	−5.87528	−	5.87528i	−0.534116	−	0.534116i
$122$	−1.57765	−	3.80879i	−0.142834	−	0.344831i
$123$	10.9391			0.986341
$124$	−2.89707	−	6.99415i	−0.260165	−	0.628093i
$125$	10.9616	+	2.20083i	0.980434	+	0.196848i
$126$	−0.170788	+	0.412320i	−0.0152150	+	0.0367323i
$127$	−3.01322	−	3.01322i	−0.267380	−	0.267380i	0.560663	−	0.828044i	$-0.310546\pi$
$127$	−3.01322	−	3.01322i	−0.267380	−	0.267380i	−0.828044	+	0.560663i	$0.810546\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−2.12399	+	5.12777i	−0.187007	+	0.451475i
$130$	−1.43843	−	7.25412i	−0.126158	−	0.636228i
$131$	−6.22666	−	15.0325i	−0.544026	−	1.31339i	−0.921861	−	0.387521i	$-0.873331\pi$
$131$	−6.22666	−	15.0325i	−0.544026	−	1.31339i	0.377835	−	0.925873i	$-0.376669\pi$
$132$	−4.12100			−0.358687
$133$	−0.236559	−	0.571104i	−0.0205123	−	0.0495210i
$134$	8.45506	+	8.45506i	0.730406	+	0.730406i
$135$	1.45162	−	0.968686i	0.124935	−	0.0833712i
$136$	0.430364	−	4.10058i	0.0369034	−	0.351622i
$137$		−	3.50896i		−	0.299790i	−0.988702	−	0.149895i	$-0.952106\pi$
$137$		−	3.50896i		−	0.299790i	0.988702	−	0.149895i	$-0.0478936\pi$
$138$	8.64496	−	8.64496i	0.735908	−	0.735908i
$139$	−2.56721	+	1.06337i	−0.217748	+	0.0901940i	−0.488891	−	0.872345i	$-0.662598\pi$
$139$	−2.56721	+	1.06337i	−0.217748	+	0.0901940i	0.271143	+	0.962539i	$0.412598\pi$
$140$	−0.167316	−	0.250730i	−0.0141408	−	0.0211906i
$141$	12.3627	+	29.8462i	1.04113	+	2.51350i
$142$	5.00986	−	12.0949i	0.420418	−	1.01498i
$143$	−5.01250	−	2.07625i	−0.419166	−	0.173624i
$144$	2.34100	−	2.34100i	0.195084	−	0.195084i
$145$	−15.7944	−	3.15152i	−1.31165	−	0.261719i
$146$	5.82799	−	14.0700i	0.482328	−	1.16444i
$147$	6.71192	−	16.2040i	0.553590	−	1.33648i
$148$	−2.92202	+	1.21034i	−0.240189	+	0.0994894i
$149$		−	13.7604i		−	1.12730i	−0.826015	−	0.563648i	$-0.809397\pi$
$149$		−	13.7604i		−	1.12730i	0.826015	−	0.563648i	$-0.190603\pi$
$150$	−0.0150102	+	12.5605i	−0.00122558	+	1.02556i
$151$	13.5269	+	13.5269i	1.10080	+	1.10080i	0.994314	+	0.106489i	$0.0339610\pi$
$151$	13.5269	+	13.5269i	1.10080	+	1.10080i	0.106489	+	0.994314i	$0.466039\pi$
$152$			4.58562i			0.371943i
$153$	13.5757	+	1.42480i	1.09753	+	0.115188i
$154$	−0.221140			−0.0178200
$155$	−3.31240	+	16.6007i	−0.266058	+	1.33340i
$156$	7.67586	−	3.17945i	0.614561	−	0.254560i
$157$	−6.59788			−0.526568			−0.263284	−	0.964718i	$-0.584806\pi$
$157$	−6.59788			−0.526568			−0.263284	+	0.964718i	$0.584806\pi$
$158$	−6.14822	+	2.54668i	−0.489126	+	0.202603i
$159$	18.8230	+	7.79675i	1.49276	+	0.618322i
$160$	0.434925	+	2.19336i	0.0343838	+	0.173401i
$161$	0.463902	−	0.463902i	0.0365606	−	0.0365606i
$162$	−5.63666	−	5.63666i	−0.442858	−	0.442858i
$163$	21.8922	+	9.06803i	1.71473	+	0.710263i	0.999940	+	0.0109192i	$0.00347576\pi$
$163$	21.8922	+	9.06803i	1.71473	+	0.710263i	0.714786	+	0.699344i	$0.246524\pi$
$164$	−4.02306	−	1.66641i	−0.314149	−	0.130125i
$165$	7.65880	+	5.12407i	0.596237	+	0.398908i
$166$			0.613822i			0.0476418i
$167$	0.155358	+	0.375066i	0.0120219	+	0.0290235i	0.929777	−	0.368124i	$-0.120000\pi$
$167$	0.155358	+	0.375066i	0.0120219	+	0.0290235i	−0.917755	+	0.397148i	$0.870000\pi$
$168$	0.239455	−	0.239455i	0.0184744	−	0.0184744i
$169$	−2.06175			−0.158596
$170$	−5.89850	+	7.08574i	−0.452395	+	0.543451i
$171$	−15.1815			−1.16096
$172$	1.56229	−	1.56229i	0.119123	−	0.119123i
$173$	−0.819509	−	1.97847i	−0.0623061	−	0.150420i	0.889660	−	0.456623i	$-0.150941\pi$
$173$	−0.819509	−	1.97847i	−0.0623061	−	0.150420i	−0.951966	+	0.306203i	$0.900941\pi$
$174$		−	18.0940i		−	1.37170i
$175$	−0.000805471		0.674018i	−6.08879e−5		0.0509510i
$176$	1.51559	+	0.627776i	0.114242	+	0.0473204i
$177$	−2.45150	−	1.01544i	−0.184266	−	0.0763255i
$178$	8.61143	+	8.61143i	0.645454	+	0.645454i
$179$	−0.0813980	+	0.0813980i	−0.00608397	+	0.00608397i	−0.710142	−	0.704058i	$-0.751369\pi$
$179$	−0.0813980	+	0.0813980i	−0.00608397	+	0.00608397i	0.704058	+	0.710142i	$0.251369\pi$
$180$	−7.26152	+	1.43990i	−0.541242	+	0.107323i
$181$	7.09374	+	2.93832i	0.527273	+	0.218404i	0.630409	−	0.776264i	$-0.282887\pi$
$181$	7.09374	+	2.93832i	0.527273	+	0.218404i	−0.103135	+	0.994667i	$0.532887\pi$
$182$	0.411899	−	0.170614i	0.0305320	−	0.0126468i
$183$	−10.3564			−0.765568
$184$	−4.49630	+	1.86243i	−0.331472	+	0.137300i
$185$	6.93546	+	1.38386i	0.509905	+	0.101743i
$186$	−19.0177			−1.39444
$187$	1.92199	+	6.48496i	0.140550	+	0.474227i
$188$		−	12.8598i		−	0.937900i
$189$	0.0743934	+	0.0743934i	0.00541133	+	0.00541133i
$190$	5.70178	−	8.52228i	0.413650	−	0.618271i
$191$			22.9556i			1.66101i	0.557011	+	0.830505i	$0.311948\pi$
$191$			22.9556i			1.66101i	−0.557011	+	0.830505i	$0.688052\pi$
$192$	−2.32088	+	0.961341i	−0.167495	+	0.0693788i
$193$	0.896081	−	2.16333i	0.0645013	−	0.155720i	−0.888342	−	0.459182i	$-0.848143\pi$
$193$	0.896081	−	2.16333i	0.0645013	−	0.155720i	0.952844	+	0.303462i	$0.0981426\pi$
$194$	0.283118	−	0.683508i	0.0203267	−	0.0490730i
$195$	−18.2188	−	3.63526i	−1.30467	−	0.260326i
$196$	−4.93690	+	4.93690i	−0.352636	+	0.352636i
$197$	14.2583	+	5.90598i	1.01586	+	0.420783i	0.827590	−	0.561334i	$-0.189712\pi$
$197$	14.2583	+	5.90598i	1.01586	+	0.420783i	0.188271	+	0.982117i	$0.439712\pi$
$198$	−2.07836	+	5.01761i	−0.147703	+	0.356586i
$199$	−4.14908	−	10.0168i	−0.294121	−	0.710070i	−0.999998	−	0.00173629i	$-0.999447\pi$
$199$	−4.14908	−	10.0168i	−0.294121	−	0.710070i	0.705878	−	0.708333i	$-0.250553\pi$
$200$	1.91894	−	4.61711i	0.135689	−	0.326479i
$201$	27.7514	−	11.4950i	1.95743	−	0.810796i
$202$	13.6835	−	13.6835i	0.962766	−	0.962766i
$203$		−	0.970952i		−	0.0681475i
$204$	−9.10325	−	4.94089i	−0.637355	−	0.345931i
$205$	5.40477	+	8.09928i	0.377485	+	0.565678i
$206$	1.20551	+	1.20551i	0.0839921	+	0.0839921i
$207$	−6.16590	−	14.8858i	−0.428560	−	1.03463i
$208$	−3.30730			−0.229320
$209$	−2.87874	−	6.94990i	−0.199127	−	0.480735i
$210$	−0.742763	+	0.147283i	−0.0512555	+	0.0101635i
$211$	−5.18792	+	12.5247i	−0.357151	+	0.862239i	0.638547	+	0.769583i	$0.279536\pi$
$211$	−5.18792	+	12.5247i	−0.357151	+	0.862239i	−0.995698	+	0.0926563i	$0.970464\pi$
$212$	−5.73483	−	5.73483i	−0.393870	−	0.393870i
$213$	−23.2546	−	23.2546i	−1.59338	−	1.59338i
$214$	−1.53651	+	3.70947i	−0.105034	+	0.253574i
$215$	−4.84603	+	0.960925i	−0.330496	+	0.0655346i
$216$	−0.298667	−	0.721046i	−0.0203217	−	0.0490610i
$217$	−1.02052			−0.0692774
$218$	3.59335	+	8.67512i	0.243372	+	0.587553i
$219$	−27.0522	−	27.0522i	−1.82802	−	1.82802i
$220$	−2.03611	−	3.05119i	−0.137274	−	0.205711i
$221$	−8.58324	−	10.5961i	−0.577371	−	0.712774i
$222$			7.94522i			0.533248i
$223$	−11.1583	+	11.1583i	−0.747218	+	0.747218i	−0.973956	−	0.226738i	$-0.927194\pi$
$223$	−11.1583	+	11.1583i	−0.747218	+	0.747218i	0.226738	+	0.973956i	$0.427194\pi$
$224$	−0.124542	+	0.0515871i	−0.00832134	+	0.00344681i
$225$	15.2858	+	6.35298i	1.01905	+	0.423532i
$226$	1.94643	+	4.69910i	0.129475	+	0.312579i
$227$	4.45014	−	10.7436i	0.295366	−	0.713077i	−0.704628	−	0.709577i	$-0.748886\pi$
$227$	4.45014	−	10.7436i	0.295366	−	0.713077i	0.999994	−	0.00350001i	$-0.00111409\pi$
$228$	10.6427	+	4.40835i	0.704829	+	0.291950i
$229$	10.1700	−	10.1700i	0.672050	−	0.672050i	−0.286139	−	0.958188i	$-0.592372\pi$
$229$	10.1700	−	10.1700i	0.672050	−	0.672050i	0.958188	+	0.286139i	$0.0923718\pi$
$230$	10.6720	+	2.12943i	0.703693	+	0.140410i
$231$	−0.212591	+	0.513240i	−0.0139874	+	0.0337687i
$232$	−2.75636	+	6.65444i	−0.180964	+	0.436885i
$233$	−16.7809	+	6.95088i	−1.09935	+	0.455367i	−0.857259	−	0.514885i	$-0.827834\pi$
$233$	−16.7809	+	6.95088i	−1.09935	+	0.455367i	−0.242095	+	0.970253i	$0.577834\pi$
$234$		−	10.9494i		−	0.715786i
$235$	−15.9900	+	23.8997i	−1.04307	+	1.55905i
$236$	0.746902	+	0.746902i	0.0486192	+	0.0486192i
$237$			16.7175i			1.08592i
$238$	−0.488495	−	0.265136i	−0.0316644	−	0.0171862i
$239$	−10.4013			−0.672802			−0.336401	−	0.941719i	$-0.609210\pi$
$239$	−10.4013			−0.672802			−0.336401	+	0.941719i	$0.609210\pi$
$240$	5.50865	+	1.09916i	0.355582	+	0.0709505i
$241$	8.16373	−	3.38153i	0.525872	−	0.217823i	−0.103922	−	0.994585i	$-0.533139\pi$
$241$	8.16373	−	3.38153i	0.525872	−	0.217823i	0.629794	+	0.776762i	$0.283139\pi$
$242$	8.30890			0.534116
$243$	−20.6639	+	8.55928i	−1.32559	+	0.549078i
$244$	3.80879	+	1.57765i	0.243833	+	0.100999i
$245$	15.3137	−	3.03657i	0.978355	−	0.193999i
$246$	−7.73508	+	7.73508i	−0.493170	+	0.493170i
$247$	10.7240	+	10.7240i	0.682352	+	0.682352i
$248$	6.99415	+	2.89707i	0.444129	+	0.183964i
$249$	1.42461	+	0.590093i	0.0902810	+	0.0373956i
$250$	−9.30723	+	6.19479i	−0.588641	+	0.391793i
$251$		−	8.03716i		−	0.507301i	−0.967296	−	0.253650i	$-0.918369\pi$
$251$		−	8.03716i		−	0.507301i	0.967296	−	0.253650i	$-0.0816313\pi$
$252$	−0.170788	−	0.412320i	−0.0107587	−	0.0259737i
$253$	5.64534	−	5.64534i	0.354919	−	0.354919i
$254$	4.26134			0.267380
$255$	10.7747	+	20.5016i	0.674737	+	1.28386i
$256$	1.00000			0.0625000
$257$	−9.70776	+	9.70776i	−0.605553	+	0.605553i	−0.941781	−	0.336228i	$-0.890849\pi$
$257$	−9.70776	+	9.70776i	−0.605553	+	0.605553i	0.336228	+	0.941781i	$0.390849\pi$
$258$	−2.12399	−	5.12777i	−0.132234	−	0.319241i
$259$			0.426353i			0.0264923i
$260$	6.14656	+	4.11231i	0.381193	+	0.255035i
$261$	−22.0307	−	9.12542i	−1.36367	−	0.564849i
$262$	15.0325	+	6.22666i	0.928710	+	0.384684i
$263$	4.37776	+	4.37776i	0.269944	+	0.269944i	0.829078	−	0.559134i	$-0.188866\pi$
$263$	4.37776	+	4.37776i	0.269944	+	0.269944i	−0.559134	+	0.829078i	$0.688866\pi$
$264$	2.91399	−	2.91399i	0.179344	−	0.179344i
$265$	3.52736	+	17.7888i	0.216684	+	1.09276i
$266$	0.571104	+	0.236559i	0.0350166	+	0.0145044i
$267$	28.2646	−	11.7076i	1.72977	−	0.716493i
$268$	−11.9573			−0.730406
$269$	16.6859	−	6.91153i	1.01736	−	0.421403i	0.189224	−	0.981934i	$-0.439403\pi$
$269$	16.6859	−	6.91153i	1.01736	−	0.421403i	0.828134	+	0.560530i	$0.189403\pi$
$270$	−0.341485	+	1.71141i	−0.0207821	+	0.104153i
$271$	3.01906			0.183395			0.0916973	−	0.995787i	$-0.470771\pi$
$271$	3.01906			0.183395			0.0916973	+	0.995787i	$0.470771\pi$
$272$	2.59524	+	3.20386i	0.157359	+	0.194263i
$273$		−	1.11999i		−	0.0677848i
$274$	2.48121	+	2.48121i	0.149895	+	0.149895i
$275$	−0.00980197	+	8.20228i	−0.000591081	+	0.494616i
$276$			12.2258i			0.735908i
$277$	−10.5343	+	4.36345i	−0.632945	+	0.262174i	−0.676004	−	0.736898i	$-0.736290\pi$
$277$	−10.5343	+	4.36345i	−0.632945	+	0.262174i	0.0430590	+	0.999073i	$0.486290\pi$
$278$	1.06337	−	2.56721i	0.0637768	−	0.153971i
$279$	−9.59127	+	23.1554i	−0.574214	+	1.38628i
$280$	0.295603	+	0.0589828i	0.0176657	+	0.00352489i
$281$	21.2631	−	21.2631i	1.26845	−	1.26845i	0.321559	−	0.946890i	$-0.395793\pi$
$281$	21.2631	−	21.2631i	1.26845	−	1.26845i	0.946890	−	0.321559i	$-0.104207\pi$
$282$	−29.8462	−	12.3627i	−1.77731	−	0.736187i
$283$	−10.4675	+	25.2708i	−0.622228	+	1.50219i	0.226853	+	0.973929i	$0.427156\pi$
$283$	−10.4675	+	25.2708i	−0.622228	+	1.50219i	−0.849081	+	0.528262i	$0.822844\pi$
$284$	5.00986	+	12.0949i	0.297280	+	0.717698i
$285$	−14.2979	−	21.4260i	−0.846933	−	1.26917i
$286$	5.01250	−	2.07625i	0.296395	−	0.122771i
$287$	−0.415077	+	0.415077i	−0.0245012	+	0.0245012i
$288$			3.31068i			0.195084i
$289$	−3.52949	+	16.6296i	−0.207617	+	0.978210i
$290$	13.3968	−	8.93988i	0.786687	−	0.524968i
$291$	−1.31417	−	1.31417i	−0.0770380	−	0.0770380i
$292$	5.82799	+	14.0700i	0.341057	+	0.823385i
$293$	−11.7499			−0.686436			−0.343218	−	0.939256i	$-0.611517\pi$
$293$	−11.7499			−0.686436			−0.343218	+	0.939256i	$0.611517\pi$
$294$	6.71192	+	16.2040i	0.391447	+	0.945037i
$295$	−0.459402	−	2.31680i	−0.0267474	−	0.134889i
$296$	1.21034	−	2.92202i	0.0703496	−	0.169839i
$297$	0.905311	+	0.905311i	0.0525315	+	0.0525315i
$298$	9.73008	+	9.73008i	0.563648	+	0.563648i
$299$	−6.15961	+	14.8706i	−0.356220	+	0.859990i
$300$	−8.87102	−	8.89224i	−0.512168	−	0.513394i
$301$	−0.113977	−	0.275165i	−0.00656952	−	0.0158602i
$302$	−19.1299			−1.10080
$303$	−18.6033	−	44.9122i	−1.06873	−	2.58014i
$304$	−3.24252	−	3.24252i	−0.185971	−	0.185971i
$305$	−5.11690	−	7.66789i	−0.292993	−	0.439062i
$306$	−10.6070	+	8.59199i	−0.606360	+	0.491172i
$307$		−	10.0370i		−	0.572843i	−0.958104	−	0.286422i	$-0.907534\pi$
$307$		−	10.0370i		−	0.572843i	0.958104	−	0.286422i	$-0.0924658\pi$
$308$	0.156369	−	0.156369i	0.00890998	−	0.00890998i
$309$	3.95676	−	1.63895i	0.225092	−	0.0932364i
$310$	−9.39626	−	14.0807i	−0.533672	−	0.799730i
$311$	−5.40060	−	13.0382i	−0.306240	−	0.739329i	−0.999820	−	0.0189496i	$-0.993968\pi$
$311$	−5.40060	−	13.0382i	−0.306240	−	0.739329i	0.693580	−	0.720379i	$-0.256032\pi$
$312$	−3.17945	+	7.67586i	−0.180001	+	0.434560i
$313$	10.8593	+	4.49807i	0.613804	+	0.254246i	0.667854	−	0.744292i	$-0.267213\pi$
$313$	10.8593	+	4.49807i	0.613804	+	0.254246i	−0.0540497	+	0.998538i	$0.517213\pi$
$314$	4.66540	−	4.66540i	0.263284	−	0.263284i
$315$	−0.195273	+	0.978647i	−0.0110024	+	0.0551405i
$316$	2.54668	−	6.14822i	0.143262	−	0.345865i
$317$	7.96264	−	19.2235i	0.447226	−	1.07970i	−0.526130	−	0.850404i	$-0.676358\pi$
$317$	7.96264	−	19.2235i	0.447226	−	1.07970i	0.973357	−	0.229296i	$-0.0736424\pi$
$318$	−18.8230	+	7.79675i	−1.05554	+	0.437220i
$319$		−	11.8157i		−	0.661555i
$320$	−1.85848	−	1.24340i	−0.103892	−	0.0695084i
$321$	7.13213	+	7.13213i	0.398077	+	0.398077i
$322$			0.656057i			0.0365606i
$323$	1.97349	−	18.8037i	0.109808	−	1.04627i
$324$	7.97145			0.442858
$325$	−6.30999	−	15.2853i	−0.350015	−	0.847876i
$326$	−21.8922	+	9.06803i	−1.21249	+	0.502232i
$327$	23.5884			1.30444
$328$	4.02306	−	1.66641i	0.222137	−	0.0920120i
$329$	−1.60159	−	0.663402i	−0.0882987	−	0.0365745i
$330$	−9.03886	+	1.79233i	−0.497573	+	0.0986643i
$331$	−4.48556	+	4.48556i	−0.246549	+	0.246549i	−0.819553	−	0.573004i	$-0.805778\pi$
$331$	−4.48556	+	4.48556i	−0.246549	+	0.246549i	0.573004	+	0.819553i	$0.305778\pi$
$332$	−0.434038	−	0.434038i	−0.0238209	−	0.0238209i
$333$	9.67387	+	4.00705i	0.530125	+	0.219585i
$334$	−0.375066	−	0.155358i	−0.0205227	−	0.00850079i
$335$	22.2223	+	14.8677i	1.21414	+	0.812309i
$336$			0.338641i			0.0184744i
$337$	6.61231	+	15.9635i	0.360196	+	0.869589i	0.995271	+	0.0971388i	$0.0309691\pi$
$337$	6.61231	+	15.9635i	0.360196	+	0.869589i	−0.635075	+	0.772450i	$0.719031\pi$
$338$	1.45788	−	1.45788i	0.0792980	−	0.0792980i
$339$	12.7772			0.693964
$340$	−0.839501	−	9.18124i	−0.0455283	−	0.497923i
$341$	−12.4189			−0.672524
$342$	10.7349	−	10.7349i	0.580479	−	0.580479i
$343$	0.721282	+	1.74133i	0.0389456	+	0.0940230i
$344$			2.20941i			0.119123i
$345$	15.2016	−	22.7214i	0.818428	−	1.22328i
$346$	1.97847	+	0.819509i	0.106363	+	0.0440571i
$347$	−30.1868	−	12.5038i	−1.62051	−	0.671239i	−0.626392	−	0.779508i	$-0.715469\pi$
$347$	−30.1868	−	12.5038i	−1.62051	−	0.671239i	−0.994122	+	0.108270i	$0.965469\pi$
$348$	12.7944	+	12.7944i	0.685851	+	0.685851i
$349$	−18.4819	+	18.4819i	−0.989311	+	0.989311i	−0.999943	−	0.0106320i	$-0.996616\pi$
$349$	−18.4819	+	18.4819i	−0.989311	+	0.989311i	0.0106320	+	0.999943i	$0.496616\pi$
$350$	−0.476033	−	0.477172i	−0.0254450	−	0.0255059i
$351$	−2.38472	−	0.987783i	−0.127287	−	0.0527239i
$352$	−1.51559	+	0.627776i	−0.0807810	+	0.0334606i
$353$	24.6632			1.31269			0.656345	−	0.754461i	$-0.272102\pi$
$353$	24.6632			1.31269			0.656345	+	0.754461i	$0.272102\pi$
$354$	2.45150	−	1.01544i	0.130296	−	0.0539703i
$355$	5.72808	−	28.7073i	0.304015	−	1.52363i
$356$	−12.1784			−0.645454
$357$	−1.08496	+	0.878854i	−0.0574222	+	0.0465139i
$358$		−	0.115114i		−	0.00608397i
$359$	9.48333	+	9.48333i	0.500511	+	0.500511i	0.911597	−	0.411086i	$-0.134850\pi$
$359$	9.48333	+	9.48333i	0.500511	+	0.500511i	−0.411086	+	0.911597i	$0.634850\pi$
$360$	4.11651	−	6.15283i	0.216959	−	0.324282i
$361$			2.02790i			0.106732i
$362$	−7.09374	+	2.93832i	−0.372839	+	0.154435i
$363$	7.98769	−	19.2840i	0.419245	−	1.01215i
$364$	−0.170614	+	0.411899i	−0.00894262	+	0.0215894i
$365$	6.66350	−	33.3954i	0.348783	−	1.74799i
$366$	7.32309	−	7.32309i	0.382784	−	0.382784i
$367$	−10.4840	−	4.34261i	−0.547259	−	0.226682i	0.0918843	−	0.995770i	$-0.470711\pi$
$367$	−10.4840	−	4.34261i	−0.547259	−	0.226682i	−0.639143	+	0.769088i	$0.720711\pi$
$368$	1.86243	−	4.49630i	0.0970858	−	0.234386i
$369$	5.51694	+	13.3191i	0.287200	+	0.693363i
$370$	−5.88264	+	3.92557i	−0.305824	+	0.204081i
$371$	−1.01007	+	0.418386i	−0.0524404	+	0.0217215i
$372$	13.4475	−	13.4475i	0.697222	−	0.697222i
$373$			10.1364i			0.524842i	0.964953	+	0.262421i	$0.0845210\pi$
$373$			10.1364i			0.524842i	−0.964953	+	0.262421i	$0.915479\pi$
$374$	−5.94461	−	3.22650i	−0.307389	−	0.166838i
$375$	5.42996	+	27.5563i	0.280402	+	1.42300i
$376$	9.09327	+	9.09327i	0.468950	+	0.468950i
$377$	9.11611	+	22.0082i	0.469504	+	1.13348i
$378$	−0.105208			−0.00541133
$379$	−11.9263	−	28.7926i	−0.612613	−	1.47898i	−0.860120	−	0.510092i	$-0.829611\pi$
$379$	−11.9263	−	28.7926i	−0.612613	−	1.47898i	0.247507	−	0.968886i	$-0.420389\pi$
$380$	1.99440	+	10.0579i	0.102311	+	0.515961i
$381$	4.09661	−	9.89008i	0.209875	−	0.506684i
$382$	−16.2321	−	16.2321i	−0.830505	−	0.830505i
$383$	−19.5054	−	19.5054i	−0.996681	−	0.996681i	0.00331356	−	0.999995i	$-0.498945\pi$
$383$	−19.5054	−	19.5054i	−0.996681	−	0.996681i	−0.999995	+	0.00331356i	$0.998945\pi$
$384$	0.961341	−	2.32088i	0.0490582	−	0.118437i
$385$	−0.485040	+	0.0961792i	−0.0247199	+	0.00490174i
$386$	0.896081	+	2.16333i	0.0456093	+	0.110111i
$387$	−7.31463			−0.371824
$388$	0.283118	+	0.683508i	0.0143732	+	0.0346999i
$389$	23.1348	+	23.1348i	1.17298	+	1.17298i	0.981495	+	0.191487i	$0.0613309\pi$
$389$	23.1348	+	23.1348i	1.17298	+	1.17298i	0.191487	+	0.981495i	$0.438669\pi$
$390$	15.4531	−	10.3121i	0.782500	−	0.522174i
$391$	19.2390	−	5.70200i	0.972957	−	0.288362i
$392$		−	6.98183i		−	0.352636i
$393$	28.9027	−	28.9027i	1.45795	−	1.45795i
$394$	−14.2583	+	5.90598i	−0.718322	+	0.297539i
$395$	−12.3777	+	8.25980i	−0.622788	+	0.415596i
$396$	−2.07836	−	5.01761i	−0.104442	−	0.252145i
$397$	−7.47899	+	18.0559i	−0.375360	+	0.906198i	0.617463	+	0.786600i	$0.288161\pi$
$397$	−7.47899	+	18.0559i	−0.375360	+	0.906198i	−0.992822	+	0.119598i	$0.961839\pi$
$398$	10.0168	+	4.14908i	0.502095	+	0.207975i
$399$	1.09805	−	1.09805i	0.0549713	−	0.0549713i
$400$	1.90790	+	4.62168i	0.0953948	+	0.231084i
$401$	−0.112991	+	0.272785i	−0.00564252	+	0.0136222i	−0.926676	−	0.375862i	$-0.877347\pi$
$401$	−0.112991	+	0.272785i	−0.00564252	+	0.0136222i	0.921033	+	0.389484i	$0.127347\pi$
$402$	−11.4950	+	27.7514i	−0.573319	+	1.38411i
$403$	23.1318	−	9.58150i	1.15228	−	0.477288i
$404$			19.3513i			0.962766i
$405$	−14.8148	−	9.91173i	−0.736152	−	0.492518i
$406$	0.686567	+	0.686567i	0.0340737	+	0.0340737i
$407$			5.18839i			0.257179i
$408$	9.93070	−	2.94324i	0.491643	−	0.145712i
$409$	7.62908			0.377234			0.188617	−	0.982051i	$-0.439600\pi$
$409$	7.62908			0.377234			0.188617	+	0.982051i	$0.439600\pi$
$410$	−9.54880	−	1.90531i	−0.471582	−	0.0940964i
$411$	8.14388	−	3.37330i	0.401708	−	0.166393i
$412$	−1.70485			−0.0839921
$413$	0.131551	−	0.0544904i	0.00647322	−	0.00268130i
$414$	14.8858	+	6.16590i	0.731597	+	0.303037i
$415$	0.266966	+	1.34633i	0.0131049	+	0.0660890i
$416$	2.33862	−	2.33862i	0.114660	−	0.114660i
$417$	−4.93592	−	4.93592i	−0.241713	−	0.241713i
$418$	6.94990	+	2.87874i	0.339931	+	0.140804i
$419$	9.46569	+	3.92082i	0.462429	+	0.191544i	0.601720	−	0.798707i	$-0.294482\pi$
$419$	9.46569	+	3.92082i	0.462429	+	0.191544i	−0.139291	+	0.990252i	$0.544482\pi$
$420$	0.421068	−	0.629358i	0.0205460	−	0.0307095i
$421$			27.3819i			1.33451i	0.744828	+	0.667257i	$0.232532\pi$
$421$			27.3819i			1.33451i	−0.744828	+	0.667257i	$0.767468\pi$
$422$	−5.18792	−	12.5247i	−0.252544	−	0.609695i
$423$	−30.1049	+	30.1049i	−1.46375	+	1.46375i
$424$	8.11028			0.393870
$425$	−9.85580	+	18.1070i	−0.478076	+	0.878318i
$426$	32.8870			1.59338
$427$	0.392969	−	0.392969i	0.0190171	−	0.0190171i
$428$	−1.53651	−	3.70947i	−0.0742701	−	0.179304i
$429$		−	13.6294i		−	0.658034i
$430$	2.74718	−	4.10614i	0.132481	−	0.198016i
$431$	−7.07239	−	2.92948i	−0.340665	−	0.141108i	0.205791	−	0.978596i	$-0.434023\pi$
$431$	−7.07239	−	2.92948i	−0.340665	−	0.141108i	−0.546456	+	0.837488i	$0.684023\pi$
$432$	0.721046	+	0.298667i	0.0346914	+	0.0143696i
$433$	−8.43456	−	8.43456i	−0.405339	−	0.405339i	0.474770	−	0.880110i	$-0.342531\pi$
$433$	−8.43456	−	8.43456i	−0.405339	−	0.405339i	−0.880110	+	0.474770i	$0.842531\pi$
$434$	0.721617	−	0.721617i	0.0346387	−	0.0346387i
$435$	−7.86952	−	39.6867i	−0.377315	−	1.90283i
$436$	−8.67512	−	3.59335i	−0.415463	−	0.172090i
$437$	−20.6183	+	8.54039i	−0.986308	+	0.408542i
$438$	38.2575			1.82802
$439$	−16.8988	+	6.99971i	−0.806535	+	0.334078i	−0.747571	−	0.664182i	$-0.768780\pi$
$439$	−16.8988	+	6.99971i	−0.806535	+	0.334078i	−0.0589645	+	0.998260i	$0.518780\pi$
$440$	3.59726	+	0.717775i	0.171493	+	0.0342186i
$441$	23.1146			1.10069
$442$	13.5619	+	1.42334i	0.645073	+	0.0677016i
$443$			14.8138i			0.703824i	0.936033	+	0.351912i	$0.114468\pi$
$443$			14.8138i			0.703824i	−0.936033	+	0.351912i	$0.885532\pi$
$444$	−5.61812	−	5.61812i	−0.266624	−	0.266624i
$445$	22.6333	+	15.1427i	1.07292	+	0.717831i
$446$		−	15.7803i		−	0.747218i
$447$	31.9363	−	13.2284i	1.51054	−	0.625684i
$448$	0.0515871	−	0.124542i	0.00243726	−	0.00588407i
$449$	−3.16897	+	7.65057i	−0.149553	+	0.361053i	−0.980847	−	0.194780i	$-0.937601\pi$
$449$	−3.16897	+	7.65057i	−0.149553	+	0.361053i	0.831294	+	0.555833i	$0.187601\pi$
$450$	−15.3009	+	6.31643i	−0.721291	+	0.297759i
$451$	−5.05117	+	5.05117i	−0.237850	+	0.237850i
$452$	−4.69910	−	1.94643i	−0.221027	−	0.0915523i
$453$	−18.3904	+	44.3983i	−0.864056	+	2.08601i
$454$	4.45014	+	10.7436i	0.208856	+	0.504222i
$455$	0.829240	−	0.553364i	0.0388754	−	0.0259421i
$456$	−10.6427	+	4.40835i	−0.498390	+	0.206440i
$457$	−21.8109	+	21.8109i	−1.02027	+	1.02027i	−0.0204820	+	0.999790i	$0.506520\pi$
$457$	−21.8109	+	21.8109i	−1.02027	+	1.02027i	−0.999790	+	0.0204820i	$0.993480\pi$
$458$			14.3825i			0.672050i
$459$	0.914397	+	3.08525i	0.0426804	+	0.144007i
$460$	−9.05200	+	6.04053i	−0.422052	+	0.281641i
$461$	−18.3717	−	18.3717i	−0.855656	−	0.855656i	0.135167	−	0.990823i	$-0.456843\pi$
$461$	−18.3717	−	18.3717i	−0.855656	−	0.855656i	−0.990823	+	0.135167i	$0.956843\pi$
$462$	−0.212591	−	0.513240i	−0.00989062	−	0.0238781i
$463$	−4.34471			−0.201916			−0.100958	−	0.994891i	$-0.532191\pi$
$463$	−4.34471			−0.201916			−0.100958	+	0.994891i	$0.532191\pi$
$464$	−2.75636	−	6.65444i	−0.127961	−	0.308925i
$465$	−41.7127	+	8.27126i	−1.93438	+	0.383571i
$466$	6.95088	−	16.7809i	0.321993	−	0.777360i
$467$	5.23030	+	5.23030i	0.242029	+	0.242029i	0.817689	−	0.575660i	$-0.195255\pi$
$467$	5.23030	+	5.23030i	0.242029	+	0.242029i	−0.575660	+	0.817689i	$0.695255\pi$
$468$	7.74240	+	7.74240i	0.357893	+	0.357893i
$469$	−0.616841	+	1.48919i	−0.0284831	+	0.0687642i
$470$	−5.59306	−	28.2063i	−0.257989	−	1.30106i
$471$	−6.34281	−	15.3129i	−0.292261	−	0.705581i
$472$	−1.05628			−0.0486192
$473$	−1.38701	−	3.34854i	−0.0637749	−	0.153966i
$474$	−11.8211	−	11.8211i	−0.542960	−	0.542960i
$475$	8.79951	−	21.1723i	0.403749	−	0.971452i
$476$	0.532898	−	0.157939i	0.0244253	−	0.00723911i
$477$			26.8505i			1.22940i
$478$	7.35480	−	7.35480i	0.336401	−	0.336401i
$479$	−17.9443	+	7.43279i	−0.819898	+	0.339613i	−0.752896	−	0.658140i	$-0.771344\pi$
$479$	−17.9443	+	7.43279i	−0.819898	+	0.339613i	−0.0670024	+	0.997753i	$0.521344\pi$
$480$	−4.67243	+	3.11798i	−0.213266	+	0.142316i
$481$	−4.00296	−	9.66401i	−0.182519	−	0.440641i
$482$	−3.38153	+	8.16373i	−0.154024	+	0.371848i
$483$	1.52263	+	0.630695i	0.0692822	+	0.0286976i
$484$	−5.87528	+	5.87528i	−0.267058	+	0.267058i
$485$	0.323707	−	1.62232i	0.0146988	−	0.0736656i
$486$	8.55928	−	20.6639i	0.388257	−	0.937335i
$487$	5.41519	−	13.0734i	0.245385	−	0.592413i	−0.752416	−	0.658688i	$-0.771112\pi$
$487$	5.41519	−	13.0734i	0.245385	−	0.592413i	0.997801	+	0.0662754i	$0.0211116\pi$
$488$	−3.80879	+	1.57765i	−0.172416	+	0.0714169i
$489$			59.5266i			2.69189i
$490$	−8.68123	+	12.9756i	−0.392178	+	0.586177i
$491$	11.9689	+	11.9689i	0.540148	+	0.540148i	0.923572	−	0.383425i	$-0.125255\pi$
$491$	11.9689	+	11.9689i	0.540148	+	0.540148i	−0.383425	+	0.923572i	$0.625255\pi$
$492$		−	10.9391i		−	0.493170i
$493$	14.1665	−	26.1008i	0.638028	−	1.17552i
$494$	−15.1660			−0.682352
$495$	−2.37632	+	11.9094i	−0.106808	+	0.535287i
$496$	−6.99415	+	2.89707i	−0.314047	+	0.130082i
$497$	1.76477			0.0791606
$498$	−1.42461	+	0.590093i	−0.0638383	+	0.0264427i
$499$	2.43813	+	1.00991i	0.109146	+	0.0452096i	0.436588	−	0.899662i	$-0.356187\pi$
$499$	2.43813	+	1.00991i	0.109146	+	0.0452096i	−0.327442	+	0.944871i	$0.606187\pi$
$500$	2.20083	−	10.9616i	0.0984241	−	0.490217i
$501$	−0.721133	+	0.721133i	−0.0322179	+	0.0322179i
$502$	5.68313	+	5.68313i	0.253650	+	0.253650i
$503$	−1.77624	−	0.735741i	−0.0791984	−	0.0328051i	0.342733	−	0.939433i	$-0.388648\pi$
$503$	−1.77624	−	0.735741i	−0.0791984	−	0.0328051i	−0.421931	+	0.906628i	$0.638648\pi$
$504$	0.412320	+	0.170788i	0.0183662	+	0.00760752i
$505$	24.0615	−	35.9641i	1.07072	−	1.60038i
$506$			7.98371i			0.354919i
$507$	−1.98204	−	4.78507i	−0.0880256	−	0.212513i
$508$	−3.01322	+	3.01322i	−0.133690	+	0.133690i
$509$	13.7217			0.608202			0.304101	−	0.952640i	$-0.401644\pi$
$509$	13.7217			0.608202			0.304101	+	0.952640i	$0.401644\pi$
$510$	−22.1156	−	6.87793i	−0.979297	−	0.304560i
$511$	2.05296			0.0908176
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−1.36957	−	3.30644i	−0.0604682	−	0.145983i
$514$		−	13.7288i		−	0.605553i
$515$	3.16843	+	2.11982i	0.139618	+	0.0934104i
$516$	5.12777	+	2.12399i	0.225738	+	0.0935036i
$517$	−19.4902	−	8.07309i	−0.857177	−	0.355054i
$518$	−0.301477	−	0.301477i	−0.0132462	−	0.0132462i
$519$	3.80397	−	3.80397i	0.166976	−	0.166976i
$520$	−7.25412	+	1.43843i	−0.318114	+	0.0630792i
$521$	−37.8110	−	15.6618i	−1.65653	−	0.686156i	−0.658724	−	0.752385i	$-0.728903\pi$
$521$	−37.8110	−	15.6618i	−1.65653	−	0.686156i	−0.997804	+	0.0662286i	$0.978903\pi$
$522$	22.0307	−	9.12542i	0.964258	−	0.399409i
$523$	8.60955			0.376469			0.188235	−	0.982124i	$-0.439723\pi$
$523$	8.60955			0.376469			0.188235	+	0.982124i	$0.439723\pi$
$524$	−15.0325	+	6.22666i	−0.656697	+	0.272013i
$525$	−1.56509	+	0.646092i	−0.0683062	+	0.0281978i
$526$	−6.19108			−0.269944
$527$	−27.4333	−	14.8897i	−1.19501	−	0.648606i
$528$			4.12100i			0.179344i
$529$	−0.484610	−	0.484610i	−0.0210700	−	0.0210700i
$530$	−15.0728	−	10.0843i	−0.654720	−	0.438036i
$531$		−	3.49700i		−	0.151757i
$532$	−0.571104	+	0.236559i	−0.0247605	+	0.0102561i
$533$	5.51132	−	13.3055i	0.238722	−	0.576325i
$534$	−11.7076	+	28.2646i	−0.506637	+	1.22313i
$535$	−1.75679	+	8.80447i	−0.0759526	+	0.380651i
$536$	8.45506	−	8.45506i	0.365203	−	0.365203i
$537$	−0.267167	−	0.110664i	−0.0115291	−	0.00477551i
$538$	−6.91153	+	16.6859i	−0.297977	+	0.719381i
$539$	4.38302	+	10.5816i	0.188790	+	0.455780i
$540$	−0.968686	−	1.45162i	−0.0416856	−	0.0624677i
$541$	−27.0320	+	11.1970i	−1.16220	+	0.481398i	−0.878606	−	0.477548i	$-0.841526\pi$
$541$	−27.0320	+	11.1970i	−1.16220	+	0.481398i	−0.283591	+	0.958945i	$0.591526\pi$
$542$	−2.13480	+	2.13480i	−0.0916973	+	0.0916973i
$543$			19.2885i			0.827748i
$544$	−4.10058	−	0.430364i	−0.175811	−	0.0184517i
$545$	11.6545	+	17.4648i	0.499226	+	0.748112i
$546$	0.791952	+	0.791952i	0.0338924	+	0.0338924i
$547$	8.08911	+	19.5288i	0.345865	+	0.834993i	0.997099	+	0.0761155i	$0.0242518\pi$
$547$	8.08911	+	19.5288i	0.345865	+	0.834993i	−0.651234	+	0.758877i	$0.725748\pi$
$548$	−3.50896			−0.149895
$549$	−5.22310	−	12.6097i	−0.222916	−	0.538168i
$550$	−5.79296	−	5.80682i	−0.247013	−	0.247604i
$551$	−12.6396	+	30.5147i	−0.538466	+	1.29997i
$552$	−8.64496	−	8.64496i	−0.367954	−	0.367954i
$553$	−0.634339	−	0.634339i	−0.0269748	−	0.0269748i
$554$	4.36345	−	10.5343i	0.185385	−	0.447559i
$555$	3.45557	+	17.4267i	0.146681	+	0.739724i
$556$	1.06337	+	2.56721i	0.0450970	+	0.108874i
$557$	11.6189			0.492310			0.246155	−	0.969231i	$-0.420833\pi$
$557$	11.6189			0.492310			0.246155	+	0.969231i	$0.420833\pi$
$558$	−9.59127	−	23.1554i	−0.406031	−	0.980245i
$559$	5.16695	+	5.16695i	0.218539	+	0.218539i
$560$	−0.250730	+	0.167316i	−0.0105953	+	0.00707039i
$561$	−13.2031	+	10.6950i	−0.557437	+	0.451543i
$562$			30.0705i			1.26845i
$563$	−8.56797	+	8.56797i	−0.361097	+	0.361097i	−0.864217	−	0.503120i	$-0.832185\pi$
$563$	−8.56797	+	8.56797i	−0.361097	+	0.361097i	0.503120	+	0.864217i	$0.332185\pi$
$564$	29.8462	−	12.3627i	1.25675	−	0.520563i
$565$	6.31298	+	9.46027i	0.265589	+	0.397997i
$566$	−10.4675	−	25.2708i	−0.439982	−	1.06221i
$567$	0.411224	−	0.992783i	0.0172698	−	0.0416930i
$568$	−12.0949	−	5.00986i	−0.507489	−	0.210209i
$569$	0.773484	−	0.773484i	0.0324262	−	0.0324262i	−0.690708	−	0.723134i	$-0.742701\pi$
$569$	0.773484	−	0.773484i	0.0324262	−	0.0324262i	0.723134	+	0.690708i	$0.242701\pi$
$570$	25.2606	+	5.04033i	1.05805	+	0.211116i
$571$	0.284151	−	0.686000i	0.0118913	−	0.0287082i	−0.917822	−	0.396991i	$-0.870054\pi$
$571$	0.284151	−	0.686000i	0.0118913	−	0.0287082i	0.929714	+	0.368283i	$0.120054\pi$
$572$	−2.07625	+	5.01250i	−0.0868122	+	0.209583i
$573$	−53.2773	+	22.0682i	−2.22569	+	0.921912i
$574$		−	0.587007i		−	0.0245012i
$575$	24.3338	+	0.0290796i	1.01479	+	0.00121270i
$576$	−2.34100	−	2.34100i	−0.0975418	−	0.0975418i
$577$		−	27.3213i		−	1.13740i	−0.822545	−	0.568701i	$-0.807446\pi$
$577$		−	27.3213i		−	1.13740i	0.822545	−	0.568701i	$-0.192554\pi$
$578$	−9.26316	−	14.2546i	−0.385297	−	0.592914i
$579$	5.88228			0.244459
$580$	−3.15152	+	15.7944i	−0.130860	+	0.655827i
$581$	−0.0764468	+	0.0316653i	−0.00317155	+	0.00131370i
$582$	1.85852			0.0770380
$583$	−12.2918	+	5.09144i	−0.509075	+	0.210866i
$584$	−14.0700	−	5.82799i	−0.582221	−	0.241164i
$585$	−4.76217	−	24.0160i	−0.196892	−	0.992941i
$586$	8.30843	−	8.30843i	0.343218	−	0.343218i
$587$	31.1108	+	31.1108i	1.28408	+	1.28408i	0.938324	+	0.345757i	$0.112378\pi$
$587$	31.1108	+	31.1108i	1.28408	+	1.28408i	0.345757	+	0.938324i	$0.387622\pi$
$588$	−16.2040	−	6.71192i	−0.668242	−	0.276795i
$589$	32.0725	+	13.2849i	1.32153	+	0.547394i
$590$	1.96307	+	1.31338i	0.0808184	+	0.0540710i
$591$			38.7695i			1.59476i
$592$	1.21034	+	2.92202i	0.0497447	+	0.120094i
$593$	1.42079	−	1.42079i	0.0583449	−	0.0583449i	−0.677332	−	0.735677i	$-0.736864\pi$
$593$	1.42079	−	1.42079i	0.0583449	−	0.0583449i	0.735677	+	0.677332i	$0.236864\pi$
$594$	−1.28030			−0.0525315
$595$	−1.18676	−	0.369081i	−0.0486525	−	0.0151308i
$596$	−13.7604			−0.563648
$597$	19.2591	−	19.2591i	0.788221	−	0.788221i
$598$	−6.15961	−	14.8706i	−0.251885	−	0.608105i
$599$			8.46693i			0.345949i	0.984926	+	0.172975i	$0.0553379\pi$
$599$			8.46693i			0.345949i	−0.984926	+	0.172975i	$0.944662\pi$
$600$	12.5605	+	0.0150102i	0.512781	+	0.000612788i
$601$	14.3426	+	5.94092i	0.585049	+	0.242335i	0.655519	−	0.755179i	$-0.272450\pi$
$601$	14.3426	+	5.94092i	0.585049	+	0.242335i	−0.0704703	+	0.997514i	$0.522450\pi$
$602$	0.275165	+	0.113977i	0.0112149	+	0.00464535i
$603$	27.9920	+	27.9920i	1.13992	+	1.13992i
$604$	13.5269	−	13.5269i	0.550402	−	0.550402i
$605$	18.2244	−	3.61375i	0.740928	−	0.146920i
$606$	44.9122	+	18.6033i	1.82443	+	0.755706i
$607$	−7.91404	+	3.27810i	−0.321221	+	0.133054i	−0.537467	−	0.843285i	$-0.680619\pi$
$607$	−7.91404	+	3.27810i	−0.321221	+	0.133054i	0.216246	+	0.976339i	$0.430619\pi$
$608$	4.58562			0.185971
$609$	2.25347	−	0.933417i	0.0913151	−	0.0378240i
$610$	9.04021	+	1.80383i	0.366028	+	0.0730348i
$611$	42.5314			1.72063
$612$	1.42480	−	13.5757i	0.0575940	−	0.548766i
$613$		−	42.5536i		−	1.71873i	−0.511367	−	0.859363i	$-0.670861\pi$
$613$		−	42.5536i		−	1.71873i	0.511367	−	0.859363i	$-0.329139\pi$
$614$	7.09725	+	7.09725i	0.286422	+	0.286422i
$615$	−13.6017	+	20.3300i	−0.548472	+	0.819785i
$616$			0.221140i			0.00890998i
$617$	40.1488	−	16.6302i	1.61633	−	0.669505i	0.622726	−	0.782440i	$-0.286025\pi$
$617$	40.1488	−	16.6302i	1.61633	−	0.669505i	0.993602	+	0.112935i	$0.0360251\pi$
$618$	−1.63895	+	3.95676i	−0.0659281	+	0.159164i
$619$	8.86032	−	21.3907i	0.356126	−	0.859765i	−0.639711	−	0.768616i	$-0.720946\pi$
$619$	8.86032	−	21.3907i	0.356126	−	0.859765i	0.995837	−	0.0911494i	$-0.0290541\pi$
$620$	16.6007	+	3.31240i	0.666701	+	0.133029i
$621$	2.68579	−	2.68579i	0.107777	−	0.107777i
$622$	13.0382	+	5.40060i	0.522784	+	0.216544i
$623$	−0.628249	+	1.51673i	−0.0251702	+	0.0607663i
$624$	−3.17945	−	7.67586i	−0.127280	−	0.307281i
$625$	−17.7199	+	17.6354i	−0.708795	+	0.705415i
$626$	−10.8593	+	4.49807i	−0.434025	+	0.179779i
$627$	13.3625	−	13.3625i	0.533645	−	0.533645i
$628$			6.59788i			0.263284i
$629$	−6.22064	+	11.4611i	−0.248033	+	0.456984i
$630$	−0.553929	−	0.830086i	−0.0220691	−	0.0330714i
$631$	−23.6457	−	23.6457i	−0.941319	−	0.941319i	0.0570526	−	0.998371i	$-0.481830\pi$
$631$	−23.6457	−	23.6457i	−0.941319	−	0.941319i	−0.998371	+	0.0570526i	$0.981830\pi$
$632$	2.54668	+	6.14822i	0.101301	+	0.244563i
$633$	−34.0558			−1.35360
$634$	7.96264	+	19.2235i	0.316237	+	0.763463i
$635$	9.34667	−	1.85336i	0.370911	−	0.0735485i
$636$	7.79675	−	18.8230i	0.309161	−	0.746381i
$637$	−16.3278	−	16.3278i	−0.646932	−	0.646932i
$638$	8.35500	+	8.35500i	0.330777	+	0.330777i
$639$	16.5860	−	40.0422i	0.656133	−	1.58404i
$640$	2.19336	−	0.434925i	0.0867003	−	0.0171919i
$641$	3.28884	+	7.93995i	0.129901	+	0.313609i	0.975426	−	0.220327i	$-0.0707124\pi$
$641$	3.28884	+	7.93995i	0.129901	+	0.313609i	−0.845525	+	0.533936i	$0.820712\pi$
$642$	−10.0864			−0.398077
$643$	−6.04126	−	14.5849i	−0.238244	−	0.575172i	0.758857	−	0.651257i	$-0.225758\pi$
$643$	−6.04126	−	14.5849i	−0.238244	−	0.575172i	−0.997101	+	0.0760849i	$0.975758\pi$
$644$	−0.463902	−	0.463902i	−0.0182803	−	0.0182803i
$645$	−6.88888	−	10.3233i	−0.271250	−	0.406479i
$646$	11.9008	+	14.6917i	0.468230	+	0.578037i
$647$		−	5.46670i		−	0.214918i	−0.994210	−	0.107459i	$-0.965729\pi$
$647$		−	5.46670i		−	0.214918i	0.994210	−	0.107459i	$-0.0342714\pi$
$648$	−5.63666	+	5.63666i	−0.221429	+	0.221429i
$649$	1.60088	−	0.663107i	0.0628401	−	0.0260292i
$650$	15.2702	+	6.34650i	0.598946	+	0.248930i
$651$	−0.981068	−	2.36851i	−0.0384511	−	0.0928291i
$652$	9.06803	−	21.8922i	0.355131	−	0.857363i
$653$	−0.546789	−	0.226487i	−0.0213975	−	0.00886313i	0.371959	−	0.928249i	$-0.378686\pi$
$653$	−0.546789	−	0.226487i	−0.0213975	−	0.00886313i	−0.393357	+	0.919386i	$0.628686\pi$
$654$	−16.6795	+	16.6795i	−0.652220	+	0.652220i
$655$	35.6798	+	7.11932i	1.39413	+	0.278175i
$656$	−1.66641	+	4.02306i	−0.0650623	+	0.157074i
$657$	19.2946	−	46.5813i	0.752754	−	1.81731i
$658$	1.60159	−	0.663402i	0.0624366	−	0.0258621i
$659$		−	20.0132i		−	0.779606i	−0.920898	−	0.389803i	$-0.872543\pi$
$659$		−	20.0132i		−	0.779606i	0.920898	−	0.389803i	$-0.127457\pi$
$660$	5.12407	−	7.65880i	0.199454	−	0.298119i
$661$	−17.9228	−	17.9228i	−0.697117	−	0.697117i	0.266671	−	0.963788i	$-0.414076\pi$
$661$	−17.9228	−	17.9228i	−0.697117	−	0.697117i	−0.963788	+	0.266671i	$0.914076\pi$
$662$		−	6.34354i		−	0.246549i
$663$	16.3410	−	30.1072i	0.634632	−	1.16927i
$664$	0.613822			0.0238209
$665$	1.35552	+	0.270472i	0.0525649	+	0.0104885i
$666$	−9.67387	+	4.00705i	−0.374855	+	0.155270i
$667$	−35.0539			−1.35729
$668$	0.375066	−	0.155358i	0.0145117	−	0.00601096i
$669$	−36.6242	−	15.1702i	−1.41597	−	0.586515i
$670$	−26.2266	+	5.20051i	−1.01322	+	0.200913i
$671$	4.78213	−	4.78213i	0.184612	−	0.184612i
$672$	−0.239455	−	0.239455i	−0.00923720	−	0.00923720i
$673$	−10.7534	−	4.45421i	−0.414514	−	0.171697i	0.165673	−	0.986181i	$-0.447020\pi$
$673$	−10.7534	−	4.45421i	−0.414514	−	0.171697i	−0.580187	+	0.814484i	$0.697020\pi$
$674$	−15.9635	−	6.61231i	−0.614892	−	0.254697i
$675$	−0.00466333	+	3.90227i	−0.000179492	+	0.150198i
$676$			2.06175i			0.0792980i
$677$	6.52935	+	15.7632i	0.250943	+	0.605831i	0.998281	−	0.0586141i	$-0.0186682\pi$
$677$	6.52935	+	15.7632i	0.250943	+	0.605831i	−0.747337	+	0.664445i	$0.768668\pi$
$678$	−9.03487	+	9.03487i	−0.346982	+	0.346982i
$679$	0.0997310			0.00382733
$680$	7.08574	+	5.89850i	0.271726	+	0.226197i
$681$	29.2127			1.11943
$682$	8.78152	−	8.78152i	0.336262	−	0.336262i
$683$	3.49863	+	8.44645i	0.133871	+	0.323194i	0.976573	−	0.215187i	$-0.0690361\pi$
$683$	3.49863	+	8.44645i	0.133871	+	0.323194i	−0.842701	+	0.538381i	$0.819036\pi$
$684$			15.1815i			0.580479i
$685$	6.52132	+	4.36305i	0.249167	+	0.166704i
$686$	−1.74133	−	0.721282i	−0.0664843	−	0.0275387i
$687$	33.3801	+	13.8265i	1.27353	+	0.527513i
$688$	−1.56229	−	1.56229i	−0.0595616	−	0.0595616i
$689$	18.9668	−	18.9668i	0.722579	−	0.722579i
$690$	5.31731	+	26.8156i	0.202427	+	1.02085i
$691$	10.3497	+	4.28697i	0.393719	+	0.163084i	0.570755	−	0.821121i	$-0.306651\pi$
$691$	10.3497	+	4.28697i	0.393719	+	0.163084i	−0.177035	+	0.984204i	$0.556651\pi$
$692$	−1.97847	+	0.819509i	−0.0752102	+	0.0311531i
$693$	−0.732122			−0.0278110
$694$	30.1868	−	12.5038i	1.14588	−	0.474637i
$695$	1.21582	−	6.09330i	0.0461186	−	0.231132i
$696$	−18.0940			−0.685851
$697$	−17.2141	+	5.10186i	−0.652030	+	0.193247i
$698$		−	26.1373i		−	0.989311i
$699$	−32.2644	−	32.2644i	−1.22035	−	1.22035i
$700$	0.674018		0.000805471i	0.0254755		3.04439e-5i
$701$		−	9.32304i		−	0.352127i	−0.984379	−	0.176063i	$-0.943664\pi$
$701$		−	9.32304i		−	0.352127i	0.984379	−	0.176063i	$-0.0563363\pi$
$702$	2.38472	−	0.987783i	0.0900054	−	0.0372815i
$703$	5.55016	−	13.3993i	0.209328	−	0.505363i
$704$	0.627776	−	1.51559i	0.0236602	−	0.0571208i
$705$	−70.8403	−	14.1350i	−2.66800	−	0.532356i
$706$	−17.4395	+	17.4395i	−0.656345	+	0.656345i
$707$	2.41006	+	0.998281i	0.0906397	+	0.0375442i
$708$	−1.01544	+	2.45150i	−0.0381627	+	0.0921330i
$709$	3.94502	+	9.52413i	0.148158	+	0.357686i	0.980483	−	0.196602i	$-0.0629906\pi$
$709$	3.94502	+	9.52413i	0.148158	+	0.357686i	−0.832325	+	0.554288i	$0.812991\pi$
$710$	16.2488	+	24.3495i	0.609806	+	0.913821i
$711$	−20.3548	+	8.43123i	−0.763364	+	0.316196i
$712$	8.61143	−	8.61143i	0.322727	−	0.322727i
$713$			36.8434i			1.37980i
$714$	0.145739	−	1.38863i	0.00545415	−	0.0519680i
$715$	10.0912	−	6.73402i	0.377390	−	0.251838i
$716$	0.0813980	+	0.0813980i	0.00304199	+	0.00304199i
$717$	−9.99916	−	24.1401i	−0.373426	−	0.901529i
$718$	−13.4115			−0.500511
$719$	−13.3853	−	32.3150i	−0.499188	−	1.20515i	−0.949922	−	0.312488i	$-0.898838\pi$
$719$	−13.3853	−	32.3150i	−0.499188	−	1.20515i	0.450734	−	0.892658i	$-0.351162\pi$
$720$	1.43990	+	7.26152i	0.0536617	+	0.270621i
$721$	−0.0879485	+	0.212326i	−0.00327537	+	0.00790745i
$722$	−1.43395	−	1.43395i	−0.0533659	−	0.0533659i
$723$	15.6963	+	15.6963i	0.583751	+	0.583751i
$724$	2.93832	−	7.09374i	0.109202	−	0.263637i
$725$	25.4959	−	25.4350i	0.946892	−	0.944632i
$726$	7.98769	+	19.2840i	0.296451	+	0.715696i
$727$	−5.76858			−0.213945			−0.106972	−	0.994262i	$-0.534116\pi$
$727$	−5.76858			−0.213945			−0.106972	+	0.994262i	$0.534116\pi$
$728$	−0.170614	−	0.411899i	−0.00632339	−	0.0152660i
$729$	−22.8202	−	22.8202i	−0.845193	−	0.845193i
$730$	18.9023	+	28.3259i	0.699605	+	1.04839i
$731$	0.950849	−	9.05985i	0.0351684	−	0.335091i
$732$			10.3564i			0.382784i
$733$	32.1981	−	32.1981i	1.18926	−	1.18926i	0.211994	−	0.977271i	$-0.432004\pi$
$733$	32.1981	−	32.1981i	1.18926	−	1.18926i	0.977271	−	0.211994i	$-0.0679956\pi$
$734$	10.4840	−	4.34261i	0.386971	−	0.160288i
$735$	21.7692	+	32.6221i	0.802969	+	1.20328i
$736$	1.86243	+	4.49630i	0.0686500	+	0.165736i
$737$	−7.50648	+	18.1223i	−0.276505	+	0.667542i
$738$	−13.3191	−	5.51694i	−0.490282	−	0.203081i
$739$	−25.8085	+	25.8085i	−0.949380	+	0.949380i	−0.998779	−	0.0493987i	$-0.984269\pi$
$739$	−25.8085	+	25.8085i	−0.949380	+	0.949380i	0.0493987	+	0.998779i	$0.484269\pi$
$740$	1.38386	−	6.93546i	0.0508716	−	0.254953i
$741$	−14.5797	+	35.1986i	−0.535600	+	1.29305i
$742$	0.418386	−	1.01007i	0.0153594	−	0.0370810i
$743$	−18.2827	+	7.57295i	−0.670728	+	0.277824i	−0.691945	−	0.721950i	$-0.743246\pi$
$743$	−18.2827	+	7.57295i	−0.670728	+	0.277824i	0.0212172	+	0.999775i	$0.493246\pi$
$744$			19.0177i			0.697222i
$745$	25.5734	+	17.1097i	0.936938	+	0.626852i
$746$	−7.16751	−	7.16751i	−0.262421	−	0.262421i
$747$			2.03217i			0.0743531i
$748$	6.48496	−	1.92199i	0.237114	−	0.0702751i
$749$	−0.541250			−0.0197768
$750$	−23.3248	−	15.6457i	−0.851702	−	0.571300i
$751$	46.5640	−	19.2875i	1.69915	−	0.703809i	0.699207	−	0.714919i	$-0.253536\pi$
$751$	46.5640	−	19.2875i	1.69915	−	0.703809i	0.999938	+	0.0111097i	$0.00353640\pi$
$752$	−12.8598			−0.468950
$753$	18.6533	−	7.72645i	0.679764	−	0.281568i
$754$	−22.0082	−	9.11611i	−0.801493	−	0.331989i
$755$	−41.9589	+	8.32007i	−1.52704	+	0.302799i
$756$	0.0743934	−	0.0743934i	0.00270566	−	0.00270566i
$757$	−13.4117	−	13.4117i	−0.487458	−	0.487458i	0.420045	−	0.907503i	$-0.362014\pi$
$757$	−13.4117	−	13.4117i	−0.487458	−	0.487458i	−0.907503	+	0.420045i	$0.862014\pi$
$758$	28.7926	+	11.9263i	1.04580	+	0.433183i
$759$	18.5293	+	7.67507i	0.672570	+	0.278588i
$760$	−8.52228	−	5.70178i	−0.309136	−	0.206825i
$761$		−	43.6160i		−	1.58108i	−0.612411	−	0.790540i	$-0.709800\pi$
$761$		−	43.6160i		−	1.58108i	0.612411	−	0.790540i	$-0.290200\pi$
$762$	4.09661	+	9.89008i	0.148404	+	0.358280i
$763$	−0.895049	+	0.895049i	−0.0324029	+	0.0324029i
$764$	22.9556			0.830505
$765$	−19.5280	+	23.4586i	−0.706038	+	0.848147i
$766$	27.5848			0.996681
$767$	−2.47023	+	2.47023i	−0.0891949	+	0.0891949i
$768$	0.961341	+	2.32088i	0.0346894	+	0.0837477i
$769$		−	15.9208i		−	0.574118i	−0.957913	−	0.287059i	$-0.907322\pi$
$769$		−	15.9208i		−	0.574118i	0.957913	−	0.287059i	$-0.0926777\pi$
$770$	0.274966	−	0.410984i	0.00990909	−	0.0148108i
$771$	−31.8630	−	13.1981i	−1.14752	−	0.475318i
$772$	−2.16333	−	0.896081i	−0.0778600	−	0.0322507i
$773$	27.5618	+	27.5618i	0.991329	+	0.991329i	0.999963	−	0.00863410i	$-0.00274835\pi$
$773$	27.5618	+	27.5618i	0.991329	+	0.991329i	−0.00863410	+	0.999963i	$0.502748\pi$
$774$	5.17223	−	5.17223i	0.185912	−	0.185912i
$775$	−26.7335	−	26.7974i	−0.960294	−	0.962592i
$776$	−0.683508	−	0.283118i	−0.0245365	−	0.0101634i
$777$	−0.989516	+	0.409871i	−0.0354987	+	0.0147040i
$778$	−32.7176			−1.17298
$779$	18.4482	−	7.64151i	0.660977	−	0.273786i
$780$	−3.63526	+	18.2188i	−0.130163	+	0.652337i
$781$	21.4759			0.768467
$782$	−9.57209	+	17.6359i	−0.342297	+	0.630659i
$783$		−	5.62139i		−	0.200892i
$784$	4.93690	+	4.93690i	0.176318	+	0.176318i
$785$	8.20382	−	12.2620i	0.292807	−	0.437650i
$786$			40.8746i			1.45795i
$787$	−33.5579	+	13.9001i	−1.19621	+	0.495486i	−0.889772	−	0.456404i	$-0.849137\pi$
$787$	−33.5579	+	13.9001i	−1.19621	+	0.495486i	−0.306438	+	0.951891i	$0.599137\pi$
$788$	5.90598	−	14.2583i	0.210392	−	0.507930i
$789$	−5.95175	+	14.3688i	−0.211888	+	0.511542i
$790$	2.91177	−	14.5929i	0.103596	−	0.519192i
$791$	−0.484826	+	0.484826i	−0.0172384	+	0.0172384i
$792$	5.01761	+	2.07836i	0.178293	+	0.0738515i
$793$	−5.21777	+	12.5968i	−0.185289	+	0.447326i
$794$	−7.47899	−	18.0559i	−0.265419	−	0.640779i
$795$	−37.8947	+	25.2877i	−1.34399	+	0.896862i
$796$	−10.0168	+	4.14908i	−0.355035	+	0.147060i
$797$	−4.87076	+	4.87076i	−0.172531	+	0.172531i	−0.788091	−	0.615559i	$-0.788930\pi$
$797$	−4.87076	+	4.87076i	−0.172531	+	0.172531i	0.615559	+	0.788091i	$0.288930\pi$
$798$			1.55288i			0.0549713i
$799$	−33.3743	−	41.2011i	−1.18070	−	1.45759i
$800$	−4.61711	−	1.91894i	−0.163239	−	0.0678446i
$801$	28.5097	+	28.5097i	1.00734	+	1.00734i
$802$	−0.112991	−	0.272785i	−0.00398986	−	0.00963238i
$803$	24.9830			0.881630
$804$	−11.4950	−	27.7514i	−0.405398	−	0.978717i
$805$	0.285335	+	1.43897i	0.0100568	+	0.0507171i
$806$	−9.58150	+	23.1318i	−0.337494	+	0.814782i
$807$	32.0817	+	32.0817i	1.12933	+	1.12933i
$808$	−13.6835	−	13.6835i	−0.481383	−	0.481383i
$809$	−0.830184	+	2.00424i	−0.0291877	+	0.0704653i	−0.937801	−	0.347172i	$-0.887142\pi$
$809$	−0.830184	+	2.00424i	−0.0291877	+	0.0704653i	0.908614	+	0.417638i	$0.137142\pi$
$810$	17.4843	−	3.46698i	0.614335	−	0.121817i
$811$	13.0269	+	31.4497i	0.457436	+	1.10435i	0.969432	+	0.245360i	$0.0789060\pi$
$811$	13.0269	+	31.4497i	0.457436	+	1.10435i	−0.511997	+	0.858987i	$0.671094\pi$
$812$	−0.970952			−0.0340737
$813$	2.90234	+	7.00688i	0.101790	+	0.245742i
$814$	−3.66875	−	3.66875i	−0.128590	−	0.128590i
$815$	−44.0735	+	29.4109i	−1.54383	+	1.03022i
$816$	−4.94089	+	9.10325i	−0.172966	+	0.318677i
$817$			10.1315i			0.354456i
$818$	−5.39457	+	5.39457i	−0.188617	+	0.188617i
$819$	1.36367	−	0.564849i	0.0476503	−	0.0197374i
$820$	8.09928	−	5.40477i	0.282839	−	0.188743i
$821$	8.28749	+	20.0078i	0.289235	+	0.698276i	0.999987	−	0.00516757i	$-0.00164489\pi$
$821$	8.28749	+	20.0078i	0.289235	+	0.698276i	−0.710751	+	0.703443i	$0.751645\pi$
$822$	−3.37330	+	8.14388i	−0.117658	+	0.284050i
$823$	18.0278	+	7.46737i	0.628411	+	0.260296i	0.674078	−	0.738660i	$-0.264541\pi$
$823$	18.0278	+	7.46737i	0.628411	+	0.260296i	−0.0456669	+	0.998957i	$0.514541\pi$
$824$	1.20551	−	1.20551i	0.0419960	−	0.0419960i
$825$	−19.0460	+	7.86245i	−0.663096	+	0.273735i
$826$	−0.0544904	+	0.131551i	−0.00189596	+	0.00457726i
$827$	−0.232580	+	0.561498i	−0.00808760	+	0.0195252i	−0.927872	−	0.372899i	$-0.878364\pi$
$827$	−0.232580	+	0.561498i	−0.00808760	+	0.0195252i	0.919784	+	0.392425i	$0.128364\pi$
$828$	−14.8858	+	6.16590i	−0.517317	+	0.214280i
$829$			10.3168i			0.358317i	0.983820	+	0.179159i	$0.0573375\pi$
$829$			10.3168i			0.358317i	−0.983820	+	0.179159i	$0.942662\pi$
$830$	−1.14078	−	0.763228i	−0.0395969	−	0.0264920i
$831$	−20.2541	−	20.2541i	−0.702607	−	0.702607i
$832$			3.30730i			0.114660i
$833$	−3.00473	+	28.6296i	−0.104108	+	0.991956i
$834$	6.98045			0.241713
$835$	−0.890225	−	0.177630i	−0.0308075	−	0.00614713i
$836$	−6.94990	+	2.87874i	−0.240367	+	0.0995634i
$837$	−5.90837			−0.204223
$838$	−9.46569	+	3.92082i	−0.326987	+	0.135442i
$839$	29.5752	+	12.2504i	1.02105	+	0.422932i	0.829474	−	0.558546i	$-0.188640\pi$
$839$	29.5752	+	12.2504i	1.02105	+	0.422932i	0.191575	+	0.981478i	$0.438640\pi$
$840$	0.147283	+	0.742763i	0.00508176	+	0.0256278i
$841$	−16.1780	+	16.1780i	−0.557861	+	0.557861i
$842$	−19.3619	−	19.3619i	−0.667257	−	0.667257i
$843$	69.7902	+	28.9080i	2.40370	+	0.995646i
$844$	12.5247	+	5.18792i	0.431120	+	0.178576i
$845$	2.56358	−	3.83172i	0.0881900	−	0.131815i
$846$		−	42.5748i		−	1.46375i
$847$	0.428632	+	1.03481i	0.0147280	+	0.0355565i
$848$	−5.73483	+	5.73483i	−0.196935	+	0.196935i
$849$	−68.7133			−2.35824
$850$	−5.83448	−	19.7727i	−0.200121	−	0.678197i
$851$	15.3924			0.527646
$852$	−23.2546	+	23.2546i	−0.796689	+	0.796689i
$853$	−11.5155	−	27.8008i	−0.394282	−	0.951881i	−0.988996	−	0.147944i	$-0.952735\pi$
$853$	−11.5155	−	27.8008i	−0.394282	−	0.951881i	0.594714	−	0.803938i	$-0.297265\pi$
$854$			0.555742i			0.0190171i
$855$	18.8767	−	28.2145i	0.645571	−	0.964916i
$856$	3.70947	+	1.53651i	0.126787	+	0.0525169i
$857$	−1.33250	−	0.551941i	−0.0455175	−	0.0188539i	0.359809	−	0.933026i	$-0.382842\pi$
$857$	−1.33250	−	0.551941i	−0.0455175	−	0.0188539i	−0.405326	+	0.914172i	$0.632842\pi$
$858$	9.63745	+	9.63745i	0.329017	+	0.329017i
$859$	6.47684	−	6.47684i	0.220987	−	0.220987i	−0.587927	−	0.808914i	$-0.700056\pi$
$859$	6.47684	−	6.47684i	0.220987	−	0.220987i	0.808914	+	0.587927i	$0.200056\pi$
$860$	0.960925	+	4.84603i	0.0327673	+	0.165248i
$861$	−1.36238	−	0.564314i	−0.0464296	−	0.0192318i
$862$	7.07239	−	2.92948i	0.240887	−	0.0997785i
$863$	20.6606			0.703293			0.351647	−	0.936133i	$-0.385622\pi$
$863$	20.6606			0.703293			0.351647	+	0.936133i	$0.385622\pi$
$864$	−0.721046	+	0.298667i	−0.0245305	+	0.0101609i
$865$	4.69593	+	0.936995i	0.159666	+	0.0318588i
$866$	11.9283			0.405339
$867$	−41.9883	+	7.79517i	−1.42600	+	0.264738i
$868$			1.02052i			0.0346387i
$869$	−7.71942	−	7.71942i	−0.261863	−	0.261863i
$870$	33.6273	+	22.4981i	1.14007	+	0.762758i
$871$		−	39.5463i		−	1.33998i
$872$	8.67512	−	3.59335i	0.293777	−	0.121686i
$873$	0.937314	−	2.26288i	0.0317233	−	0.0765867i
$874$	8.54039	−	20.6183i	0.288883	−	0.697425i
$875$	−1.25165	−	0.839573i	−0.0423134	−	0.0283828i
$876$	−27.0522	+	27.0522i	−0.914008	+	0.914008i
$877$	38.8470	+	16.0910i	1.31177	+	0.543353i	0.925400	−	0.378991i	$-0.123729\pi$
$877$	38.8470	+	16.0910i	1.31177	+	0.543353i	0.386370	+	0.922344i	$0.373729\pi$
$878$	6.99971	−	16.8988i	0.236229	−	0.570306i
$879$	−11.2957	−	27.2701i	−0.380993	−	0.919799i
$880$	−3.05119	+	2.03611i	−0.102856	+	0.0686371i
$881$	−40.4538	+	16.7565i	−1.36292	+	0.564541i	−0.939860	−	0.341560i	$-0.889045\pi$
$881$	−40.4538	+	16.7565i	−1.36292	+	0.564541i	−0.423062	+	0.906101i	$0.639045\pi$
$882$	−16.3445	+	16.3445i	−0.550347	+	0.550347i
$883$			5.38161i			0.181106i	0.995892	+	0.0905528i	$0.0288634\pi$
$883$			5.38161i			0.181106i	−0.995892	+	0.0905528i	$0.971137\pi$
$884$	−10.5961	+	8.58324i	−0.356387	+	0.288685i
$885$	4.93539	−	3.29346i	0.165901	−	0.110708i
$886$	−10.4749	−	10.4749i	−0.351912	−	0.351912i
$887$	−12.6030	−	30.4264i	−0.423169	−	1.02162i	−0.981407	−	0.191939i	$-0.938522\pi$
$887$	−12.6030	−	30.4264i	−0.423169	−	1.02162i	0.558238	−	0.829681i	$-0.311478\pi$
$888$	7.94522			0.266624
$889$	0.219830	+	0.530718i	0.00737288	+	0.0177997i
$890$	−26.7116	+	5.29669i	−0.895376	+	0.177545i
$891$	5.00428	−	12.0814i	0.167650	−	0.404742i
$892$	11.1583	+	11.1583i	0.373609	+	0.373609i
$893$	41.6983	+	41.6983i	1.39538	+	1.39538i
$894$	−13.2284	+	31.9363i	−0.442426	+	1.06811i
$895$	−0.0500660	−	0.252487i	−0.00167352	−	0.00843972i
$896$	0.0515871	+	0.124542i	0.00172341	+	0.00416067i
$897$	−40.4345			−1.35007
$898$	−3.16897	−	7.65057i	−0.105750	−	0.255303i
$899$	38.5568	+	38.5568i	1.28594	+	1.28594i
$900$	6.35298	−	15.2858i	0.211766	−	0.509525i
$901$	−33.2569	−	3.49037i	−1.10795	−	0.116281i
$902$		−	7.14343i		−	0.237850i
$903$	0.529054	−	0.529054i	0.0176058	−	0.0176058i
$904$	4.69910	−	1.94643i	0.156290	−	0.0647373i
$905$	−14.2812	+	9.53005i	−0.474723	+	0.316790i
$906$	−18.3904	−	44.3983i	−0.610980	−	1.47504i
$907$	15.5311	−	37.4954i	0.515701	−	1.24501i	−0.424820	−	0.905278i	$-0.639663\pi$
$907$	15.5311	−	37.4954i	0.515701	−	1.24501i	0.940521	−	0.339735i	$-0.110337\pi$
$908$	−10.7436	−	4.45014i	−0.356539	−	0.147683i
$909$	45.3016	−	45.3016i	1.50256	−	1.50256i
$910$	−0.195074	+	0.977649i	−0.00646663	+	0.0324088i
$911$	−3.54723	+	8.56377i	−0.117525	+	0.283731i	−0.971685	−	0.236280i	$-0.924072\pi$
$911$	−3.54723	+	8.56377i	−0.117525	+	0.283731i	0.854160	+	0.520010i	$0.174072\pi$
$912$	4.40835	−	10.6427i	0.145975	−	0.352415i
$913$	−0.930300	+	0.385343i	−0.0307884	+	0.0127530i
$914$		−	30.8453i		−	1.02027i
$915$	12.8772	−	19.2472i	0.425707	−	0.636292i
$916$	−10.1700	−	10.1700i	−0.336025	−	0.336025i
$917$			2.19340i			0.0724323i
$918$	−2.82817	−	1.53502i	−0.0933437	−	0.0506633i
$919$	45.1666			1.48991			0.744954	−	0.667116i	$-0.232472\pi$
$919$	45.1666			1.48991			0.744954	+	0.667116i	$0.232472\pi$
$920$	2.12943	−	10.6720i	0.0702052	−	0.351846i
$921$	23.2948	−	9.64900i	0.767588	−	0.317945i
$922$	25.9815			0.855656
$923$	−40.0014	+	16.5691i	−1.31666	+	0.545379i
$924$	0.513240	+	0.212591i	0.0168843	+	0.00699372i
$925$	−11.1954	+	11.1687i	−0.368104	+	0.367225i
$926$	3.07218	−	3.07218i	0.100958	−	0.100958i
$927$	3.99106	+	3.99106i	0.131084	+	0.131084i
$928$	6.65444	+	2.75636i	0.218443	+	0.0904819i
$929$	−36.8967	−	15.2831i	−1.21054	−	0.501423i	−0.316152	−	0.948709i	$-0.602391\pi$
$929$	−36.8967	−	15.2831i	−1.21054	−	0.501423i	−0.894391	+	0.447285i	$0.852391\pi$
$930$	23.6467	−	35.3440i	0.775404	−	1.15898i
$931$		−	32.0160i		−	1.04928i
$932$	6.95088	+	16.7809i	0.227684	+	0.549677i
$933$	25.0683	−	25.0683i	0.820700	−	0.820700i
$934$	−7.39676			−0.242029
$935$	−14.4420	−	4.49143i	−0.472303	−	0.146885i
$936$	−10.9494			−0.357893
$937$	−20.4587	+	20.4587i	−0.668357	+	0.668357i	−0.957335	−	0.288979i	$-0.906684\pi$
$937$	−20.4587	+	20.4587i	−0.668357	+	0.668357i	0.288979	+	0.957335i	$0.406684\pi$
$938$	−0.616841	−	1.48919i	−0.0201406	−	0.0486236i
$939$			29.5274i			0.963590i
$940$	23.8997	+	15.9900i	0.779523	+	0.521535i
$941$	33.8328	+	14.0140i	1.10292	+	0.456843i	0.858493	−	0.512825i	$-0.171401\pi$
$941$	33.8328	+	14.0140i	1.10292	+	0.456843i	0.244424	+	0.969668i	$0.421401\pi$
$942$	15.3129	+	6.34281i	0.498921	+	0.206660i
$943$	14.9853	+	14.9853i	0.487990	+	0.487990i
$944$	0.746902	−	0.746902i	0.0243096	−	0.0243096i
$945$	−0.230760	+	0.0457576i	−0.00750661	+	0.00148850i
$946$	3.34854	+	1.38701i	0.108871	+	0.0450957i
$947$	−48.7002	+	20.1723i	−1.58254	+	0.655512i	−0.988814	−	0.149152i	$-0.952346\pi$
$947$	−48.7002	+	20.1723i	−1.58254	+	0.655512i	−0.593731	+	0.804664i	$0.702346\pi$
$948$	16.7175			0.542960
$949$	−46.5338	+	19.2749i	−1.51055	+	0.625690i
$950$	8.74888	+	21.1933i	0.283851	+	0.687600i
$951$	52.2704			1.69498
$952$	−0.265136	+	0.488495i	−0.00859311	+	0.0158322i
$953$			10.2185i			0.331011i	0.986209	+	0.165506i	$0.0529256\pi$
$953$			10.2185i			0.331011i	−0.986209	+	0.165506i	$0.947074\pi$
$954$	−18.9862	−	18.9862i	−0.614700	−	0.614700i
$955$	−42.6626	−	28.5431i	−1.38053	−	0.923633i
$956$			10.4013i			0.336401i
$957$	27.4230	−	11.3590i	0.886459	−	0.367183i
$958$	7.43279	−	17.9443i	0.240143	−	0.579755i
$959$	−0.181017	+	0.437014i	−0.00584534	+	0.0141119i
$960$	1.09916	−	5.50865i	0.0354753	−	0.177791i
$961$	18.6048	−	18.6048i	0.600155	−	0.600155i
$962$	9.66401	+	4.00296i	0.311580	+	0.129061i
$963$	−5.08689	+	12.2808i	−0.163923	+	0.395745i
$964$	−3.38153	−	8.16373i	−0.108912	−	0.262936i
$965$	2.90632	+	4.35524i	0.0935576	+	0.140200i
$966$	−1.52263	+	0.630695i	−0.0489899	+	0.0202923i
$967$	−17.9484	+	17.9484i	−0.577183	+	0.577183i	−0.934126	−	0.356943i	$-0.883819\pi$
$967$	−17.9484	+	17.9484i	−0.577183	+	0.577183i	0.356943	+	0.934126i	$0.383819\pi$
$968$		−	8.30890i		−	0.267058i
$969$	45.5384	−	13.4966i	1.46291	−	0.433572i
$970$	0.918256	+	1.37605i	0.0294834	+	0.0441822i
$971$	30.7506	+	30.7506i	0.986834	+	0.986834i	0.999914	−	0.0130809i	$-0.00416390\pi$
$971$	30.7506	+	30.7506i	0.986834	+	0.986834i	−0.0130809	+	0.999914i	$0.504164\pi$
$972$	8.55928	+	20.6639i	0.274539	+	0.662796i
$973$	0.374582			0.0120086
$974$	5.41519	+	13.0734i	0.173514	+	0.418899i
$975$	29.4093	−	29.3391i	0.941853	−	0.939604i
$976$	1.57765	−	3.80879i	0.0504994	−	0.121916i
$977$	−24.6535	−	24.6535i	−0.788735	−	0.788735i	0.192552	−	0.981287i	$-0.438324\pi$
$977$	−24.6535	−	24.6535i	−0.788735	−	0.788735i	−0.981287	+	0.192552i	$0.938324\pi$
$978$	−42.0917	−	42.0917i	−1.34594	−	1.34594i
$979$	−7.64530	+	18.4574i	−0.244345	+	0.589901i
$980$	−3.03657	−	15.3137i	−0.0969997	−	0.489178i
$981$	11.8964	+	28.7205i	0.379824	+	0.916976i
$982$	−16.9265			−0.540148
$983$	−21.2758	−	51.3642i	−0.678591	−	1.63826i	−0.766585	−	0.642143i	$-0.778046\pi$
$983$	−21.2758	−	51.3642i	−0.678591	−	1.63826i	0.0879937	−	0.996121i	$-0.471954\pi$
$984$	7.73508	+	7.73508i	0.246585	+	0.246585i
$985$	−28.7049	+	19.1552i	−0.914615	+	0.610336i
$986$	8.43885	+	28.4733i	0.268748	+	0.906775i
$987$		−	4.35487i		−	0.138617i
$988$	10.7240	−	10.7240i	0.341176	−	0.341176i
$989$	−9.93415	+	4.11486i	−0.315888	+	0.130845i
$990$	−6.74089	−	10.1015i	−0.214240	−	0.321047i
$991$	7.33631	+	17.7114i	0.233046	+	0.562622i	0.996533	−	0.0832011i	$-0.0265144\pi$
$991$	7.33631	+	17.7114i	0.233046	+	0.562622i	−0.763487	+	0.645823i	$0.776514\pi$
$992$	2.89707	−	6.99415i	0.0919821	−	0.222065i
$993$	−14.7226	−	6.09831i	−0.467208	−	0.193524i
$994$	−1.24788	+	1.24788i	−0.0395803	+	0.0395803i
$995$	23.7749	+	4.74390i	0.753716	+	0.150392i
$996$	0.590093	−	1.42461i	0.0186978	−	0.0451405i
$997$	−2.47887	+	5.98452i	−0.0785066	+	0.189532i	−0.958260	−	0.285899i	$-0.907708\pi$
$997$	−2.47887	+	5.98452i	−0.0785066	+	0.189532i	0.879753	+	0.475431i	$0.157708\pi$
$998$	−2.43813	+	1.00991i	−0.0771777	+	0.0319680i
$999$			2.46840i			0.0780967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.n.a.19.5	yes	20
5.2	odd	4		850.2.l.h.801.5		20
5.3	odd	4		850.2.l.i.801.1		20
5.4	even	2		170.2.n.b.19.1	yes	20
17.9	even	8		170.2.n.b.9.1	yes	20
85.9	even	8	inner	170.2.n.a.9.5	✓	20
85.43	odd	8		850.2.l.i.451.1		20
85.77	odd	8		850.2.l.h.451.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.n.a.9.5	✓	20	85.9	even	8	inner
170.2.n.a.19.5	yes	20	1.1	even	1	trivial
170.2.n.b.9.1	yes	20	17.9	even	8
170.2.n.b.19.1	yes	20	5.4	even	2
850.2.l.h.451.5		20	85.77	odd	8
850.2.l.h.801.5		20	5.2	odd	4
850.2.l.i.451.1		20	85.43	odd	8
850.2.l.i.801.1		20	5.3	odd	4

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.961341 + 2.32088i) q^{3} -1.00000i q^{4} +(-1.24340 + 1.85848i) q^{5} +(-2.32088 - 0.961341i) q^{6} +(-0.124542 - 0.0515871i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.34100 + 2.34100i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.961341 + 2.32088i) q^{3} -1.00000i q^{4} +(-1.24340 + 1.85848i) q^{5} +(-2.32088 - 0.961341i) q^{6} +(-0.124542 - 0.0515871i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.34100 + 2.34100i) q^{9} +(-0.434925 - 2.19336i) q^{10} +(-1.51559 - 0.627776i) q^{11} +(2.32088 - 0.961341i) q^{12} +3.30730 q^{13} +(0.124542 - 0.0515871i) q^{14} +(-5.50865 - 1.09916i) q^{15} -1.00000 q^{16} +(-2.59524 - 3.20386i) q^{17} -3.31068i q^{18} +(3.24252 + 3.24252i) q^{19} +(1.85848 + 1.24340i) q^{20} -0.338641i q^{21} +(1.51559 - 0.627776i) q^{22} +(-1.86243 + 4.49630i) q^{23} +(-0.961341 + 2.32088i) q^{24} +(-1.90790 - 4.62168i) q^{25} +(-2.33862 + 2.33862i) q^{26} +(-0.721046 - 0.298667i) q^{27} +(-0.0515871 + 0.124542i) q^{28} +(2.75636 + 6.65444i) q^{29} +(4.67243 - 3.11798i) q^{30} +(6.99415 - 2.89707i) q^{31} +(0.707107 - 0.707107i) q^{32} -4.12100i q^{33} +(4.10058 + 0.430364i) q^{34} +(0.250730 - 0.167316i) q^{35} +(2.34100 + 2.34100i) q^{36} +(-1.21034 - 2.92202i) q^{37} -4.58562 q^{38} +(3.17945 + 7.67586i) q^{39} +(-2.19336 + 0.434925i) q^{40} +(1.66641 - 4.02306i) q^{41} +(0.239455 + 0.239455i) q^{42} +(1.56229 + 1.56229i) q^{43} +(-0.627776 + 1.51559i) q^{44} +(-1.43990 - 7.26152i) q^{45} +(-1.86243 - 4.49630i) q^{46} +12.8598 q^{47} +(-0.961341 - 2.32088i) q^{48} +(-4.93690 - 4.93690i) q^{49} +(4.61711 + 1.91894i) q^{50} +(4.94089 - 9.10325i) q^{51} -3.30730i q^{52} +(5.73483 - 5.73483i) q^{53} +(0.721046 - 0.298667i) q^{54} +(3.05119 - 2.03611i) q^{55} +(-0.0515871 - 0.124542i) q^{56} +(-4.40835 + 10.6427i) q^{57} +(-6.65444 - 2.75636i) q^{58} +(-0.746902 + 0.746902i) q^{59} +(-1.09916 + 5.50865i) q^{60} +(-1.57765 + 3.80879i) q^{61} +(-2.89707 + 6.99415i) q^{62} +(0.412320 - 0.170788i) q^{63} +1.00000i q^{64} +(-4.11231 + 6.14656i) q^{65} +(2.91399 + 2.91399i) q^{66} -11.9573i q^{67} +(-3.20386 + 2.59524i) q^{68} -12.2258 q^{69} +(-0.0589828 + 0.295603i) q^{70} +(-12.0949 + 5.00986i) q^{71} -3.31068 q^{72} +(-14.0700 + 5.82799i) q^{73} +(2.92202 + 1.21034i) q^{74} +(8.89224 - 8.87102i) q^{75} +(3.24252 - 3.24252i) q^{76} +(0.156369 + 0.156369i) q^{77} +(-7.67586 - 3.17945i) q^{78} +(6.14822 + 2.54668i) q^{79} +(1.24340 - 1.85848i) q^{80} +7.97145i q^{81} +(1.66641 + 4.02306i) q^{82} +(0.434038 - 0.434038i) q^{83} -0.338641 q^{84} +(9.18124 - 0.839501i) q^{85} -2.20941 q^{86} +(-12.7944 + 12.7944i) q^{87} +(-0.627776 - 1.51559i) q^{88} -12.1784i q^{89} +(6.15283 + 4.11651i) q^{90} +(-0.411899 - 0.170614i) q^{91} +(4.49630 + 1.86243i) q^{92} +(13.4475 + 13.4475i) q^{93} +(-9.09327 + 9.09327i) q^{94} +(-10.0579 + 1.99440i) q^{95} +(2.32088 + 0.961341i) q^{96} +(-0.683508 + 0.283118i) q^{97} +6.98183 q^{98} +(5.01761 - 2.07836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5}+O(q^{10}) \) 20 * q - 4 * q^5	\( 20 q - 4 q^{5} + 4 q^{10} - 8 q^{11} - 24 q^{13} + 8 q^{15} - 20 q^{16} + 8 q^{20} + 8 q^{22} + 16 q^{23} - 12 q^{25} - 12 q^{26} + 24 q^{27} - 12 q^{29} - 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} - 8 q^{37} - 8 q^{38} + 4 q^{40} + 4 q^{41} + 8 q^{42} + 16 q^{43} - 8 q^{44} - 12 q^{45} + 16 q^{46} + 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} + 44 q^{53} - 24 q^{54} - 72 q^{57} + 16 q^{59} + 16 q^{60} + 8 q^{61} - 8 q^{62} - 24 q^{63} - 8 q^{65} - 8 q^{66} + 20 q^{68} - 16 q^{69} - 16 q^{70} + 8 q^{71} - 28 q^{72} - 60 q^{73} + 28 q^{74} + 64 q^{75} + 8 q^{78} + 56 q^{79} + 4 q^{80} + 4 q^{82} + 16 q^{84} - 16 q^{85} + 48 q^{86} - 72 q^{87} - 8 q^{88} + 32 q^{90} - 24 q^{91} - 8 q^{92} + 72 q^{93} + 32 q^{94} + 8 q^{95} + 48 q^{97} - 36 q^{98} + 72 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 + 4 * q^10 - 8 * q^11 - 24 * q^13 + 8 * q^15 - 20 * q^16 + 8 * q^20 + 8 * q^22 + 16 * q^23 - 12 * q^25 - 12 * q^26 + 24 * q^27 - 12 * q^29 - 8 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 - 8 * q^37 - 8 * q^38 + 4 * q^40 + 4 * q^41 + 8 * q^42 + 16 * q^43 - 8 * q^44 - 12 * q^45 + 16 * q^46 + 40 * q^47 - 56 * q^49 + 8 * q^50 - 8 * q^51 + 44 * q^53 - 24 * q^54 - 72 * q^57 + 16 * q^59 + 16 * q^60 + 8 * q^61 - 8 * q^62 - 24 * q^63 - 8 * q^65 - 8 * q^66 + 20 * q^68 - 16 * q^69 - 16 * q^70 + 8 * q^71 - 28 * q^72 - 60 * q^73 + 28 * q^74 + 64 * q^75 + 8 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^82 + 16 * q^84 - 16 * q^85 + 48 * q^86 - 72 * q^87 - 8 * q^88 + 32 * q^90 - 24 * q^91 - 8 * q^92 + 72 * q^93 + 32 * q^94 + 8 * q^95 + 48 * q^97 - 36 * q^98 + 72 * q^99

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