LMFDB - Embedded newform 170.2.n.b.9.1

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			9.1
Root			$-2.32088 - 0.961341i$ of defining polynomial
Character	$\chi$	$=$	170.9
Dual form			170.2.n.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.961341 + 2.32088i) q^{3} +1.00000i q^{4} +(2.19336 - 0.434925i) q^{5} +(-2.32088 + 0.961341i) q^{6} +(0.124542 - 0.0515871i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.34100 - 2.34100i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.961341 + 2.32088i) q^{3} +1.00000i q^{4} +(2.19336 - 0.434925i) 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} +(1.85848 + 1.24340i) q^{10} +(-1.51559 + 0.627776i) q^{11} +(-2.32088 - 0.961341i) q^{12} -3.30730 q^{13} +(0.124542 + 0.0515871i) q^{14} +(-1.09916 + 5.50865i) q^{15} -1.00000 q^{16} +(2.59524 - 3.20386i) q^{17} -3.31068i q^{18} +(3.24252 - 3.24252i) q^{19} +(0.434925 + 2.19336i) q^{20} +0.338641i q^{21} +(-1.51559 - 0.627776i) q^{22} +(1.86243 + 4.49630i) q^{23} +(-0.961341 - 2.32088i) q^{24} +(4.62168 - 1.90790i) 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} +(-1.24340 + 1.85848i) 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} +(-6.15283 - 4.11651i) 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} +(-5.50865 - 1.09916i) q^{60} +(-1.57765 - 3.80879i) q^{61} +(2.89707 + 6.99415i) q^{62} +(-0.412320 - 0.170788i) q^{63} -1.00000i q^{64} +(-7.25412 + 1.43843i) q^{65} +(2.91399 - 2.91399i) q^{66} -11.9573i q^{67} +(3.20386 + 2.59524i) q^{68} -12.2258 q^{69} +(0.295603 + 0.0589828i) q^{70} +(-12.0949 - 5.00986i) q^{71} +3.31068 q^{72} +(14.0700 + 5.82799i) q^{73} +(2.92202 - 1.21034i) q^{74} +(-0.0150102 + 12.5605i) 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} +(-2.19336 + 0.434925i) q^{80} -7.97145i q^{81} +(-1.66641 + 4.02306i) q^{82} +(-0.434038 - 0.434038i) q^{83} -0.338641 q^{84} +(4.29886 - 8.15597i) q^{85} -2.20941 q^{86} +(12.7944 + 12.7944i) q^{87} +(0.627776 - 1.51559i) q^{88} +12.1784i q^{89} +(-1.43990 - 7.26152i) 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} +(5.70178 - 8.52228i) 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} + 8 q^{10} - 8 q^{11} + 24 q^{13} + 16 q^{15} - 20 q^{16} - 4 q^{20} - 8 q^{22} - 16 q^{23} + 8 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} - 32 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} + 8 q^{60} + 8 q^{61} + 8 q^{62} + 24 q^{63} - 28 q^{65} - 8 q^{66} - 20 q^{68} - 16 q^{69} + 8 q^{71} + 28 q^{72} + 60 q^{73} + 28 q^{74} - 8 q^{78} + 56 q^{79} + 4 q^{80} - 4 q^{82} + 16 q^{84} + 84 q^{85} + 48 q^{86} + 72 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} + 8 q^{92} - 72 q^{93} + 32 q^{94} + 88 q^{95} - 48 q^{97} + 36 q^{98} + 72 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 + 8 * q^10 - 8 * q^11 + 24 * q^13 + 16 * q^15 - 20 * q^16 - 4 * q^20 - 8 * q^22 - 16 * q^23 + 8 * 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 - 32 * 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 + 8 * q^60 + 8 * q^61 + 8 * q^62 + 24 * q^63 - 28 * q^65 - 8 * q^66 - 20 * q^68 - 16 * q^69 + 8 * q^71 + 28 * q^72 + 60 * q^73 + 28 * q^74 - 8 * q^78 + 56 * q^79 + 4 * q^80 - 4 * q^82 + 16 * q^84 + 84 * q^85 + 48 * q^86 + 72 * q^87 + 8 * q^88 - 12 * q^90 - 24 * q^91 + 8 * q^92 - 72 * q^93 + 32 * q^94 + 88 * 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 $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

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

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	0.358628	+	0.933481i	$0.383245\pi$
$3$	−0.961341	+	2.32088i	−0.555031	+	1.33996i	−0.913659	+	0.406482i	$0.866755\pi$
$4$			1.00000i			0.500000i
$5$	2.19336	−	0.434925i	0.980902	−	0.194504i
$5$	2.19336	−	0.434925i	0.980902	−	0.194504i
$6$	−2.32088	+	0.961341i	−0.947497	+	0.392466i
$7$	0.124542	−	0.0515871i	0.0470726	−	0.0194981i	−0.359023	−	0.933329i	$-0.616890\pi$
$7$	0.124542	−	0.0515871i	0.0470726	−	0.0194981i	0.406096	+	0.913831i	$0.366890\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.34100	−	2.34100i	−0.780334	−	0.780334i
$10$	1.85848	+	1.24340i	0.587703	+	0.393199i
$11$	−1.51559	+	0.627776i	−0.456966	+	0.189282i	−0.599279	−	0.800540i	$-0.704546\pi$
$11$	−1.51559	+	0.627776i	−0.456966	+	0.189282i	0.142313	+	0.989822i	$0.454546\pi$
$12$	−2.32088	−	0.961341i	−0.669981	−	0.277515i
$13$	−3.30730			−0.917281			−0.458640	−	0.888622i	$-0.651663\pi$
$13$	−3.30730			−0.917281			−0.458640	+	0.888622i	$0.651663\pi$
$14$	0.124542	+	0.0515871i	0.0332853	+	0.0137872i
$15$	−1.09916	+	5.50865i	−0.283802	+	1.42233i
$16$	−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	−0.229438	−	0.973323i	$-0.573689\pi$
$19$	3.24252	−	3.24252i	0.743886	−	0.743886i	0.973323	+	0.229438i	$0.0736887\pi$
$20$	0.434925	+	2.19336i	0.0972521	+	0.490451i
$21$			0.338641i			0.0738976i
$22$	−1.51559	−	0.627776i	−0.323124	−	0.133842i
$23$	1.86243	+	4.49630i	0.388343	+	0.937543i	0.990291	+	0.139008i	$0.0443914\pi$
$23$	1.86243	+	4.49630i	0.388343	+	0.937543i	−0.601948	+	0.798535i	$0.705609\pi$
$24$	−0.961341	−	2.32088i	−0.196233	−	0.473748i
$25$	4.62168	−	1.90790i	0.924336	−	0.381579i
$26$	−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	−0.430967	−	0.902368i	$-0.641827\pi$
$29$	2.75636	−	6.65444i	0.511843	−	1.23570i	0.942810	−	0.333331i	$-0.108173\pi$
$30$	−4.67243	+	3.11798i	−0.853065	+	0.569263i
$31$	6.99415	+	2.89707i	1.25619	+	0.520330i	0.908737	−	0.417369i	$-0.137048\pi$
$31$	6.99415	+	2.89707i	1.25619	+	0.520330i	0.347450	+	0.937699i	$0.387048\pi$
$32$	−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	$-0.791285\pi$
$37$	1.21034	−	2.92202i	0.198979	−	0.480377i	0.991601	+	0.129336i	$0.0412846\pi$
$38$	4.58562			0.743886
$39$	3.17945	−	7.67586i	0.509119	−	1.22912i
$40$	−1.24340	+	1.85848i	−0.196599	+	0.293851i
$41$	1.66641	+	4.02306i	0.260249	+	0.628297i	0.998954	−	0.0457323i	$-0.0145621\pi$
$41$	1.66641	+	4.02306i	0.260249	+	0.628297i	−0.738705	+	0.674029i	$0.764562\pi$
$42$	−0.239455	+	0.239455i	−0.0369488	+	0.0369488i
$43$	−1.56229	+	1.56229i	−0.238246	+	0.238246i	−0.816124	−	0.577877i	$-0.803881\pi$
$43$	−1.56229	+	1.56229i	−0.238246	+	0.238246i	0.577877	+	0.816124i	$0.303881\pi$
$44$	−0.627776	−	1.51559i	−0.0946408	−	0.228483i
$45$	−6.15283	−	4.11651i	−0.917209	−	0.613653i
$46$	−1.86243	+	4.49630i	−0.274600	+	0.662943i
$47$	−12.8598			−1.87580			−0.937900	−	0.346907i	$-0.887232\pi$
$47$	−12.8598			−1.87580			−0.937900	+	0.346907i	$0.887232\pi$
$48$	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	$-0.438054\pi$
$53$	−5.73483	−	5.73483i	−0.787740	−	0.787740i	−0.981123	+	0.193383i	$0.938054\pi$
$54$	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	0.656814	−	0.754052i	$-0.271904\pi$
$59$	−0.746902	−	0.746902i	−0.0972383	−	0.0972383i	−0.754052	+	0.656814i	$0.771904\pi$
$60$	−5.50865	−	1.09916i	−0.711164	−	0.141901i
$61$	−1.57765	−	3.80879i	−0.201998	−	0.487665i	0.790124	−	0.612948i	$-0.210016\pi$
$61$	−1.57765	−	3.80879i	−0.201998	−	0.487665i	−0.992121	+	0.125282i	$0.960016\pi$
$62$	2.89707	+	6.99415i	0.367929	+	0.888258i
$63$	−0.412320	−	0.170788i	−0.0519474	−	0.0215173i
$64$		−	1.00000i		−	0.125000i
$65$	−7.25412	+	1.43843i	−0.899762	+	0.178415i
$66$	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
$70$	0.295603	+	0.0589828i	0.0353313	+	0.00704979i
$71$	−12.0949	−	5.00986i	−1.43540	−	0.594561i	−0.476719	−	0.879056i	$-0.658174\pi$
$71$	−12.0949	−	5.00986i	−1.43540	−	0.594561i	−0.958677	+	0.284495i	$0.908174\pi$
$72$	3.31068			0.390167
$73$	14.0700	+	5.82799i	1.64677	+	0.682114i	0.996955	−	0.0779784i	$-0.0248465\pi$
$73$	14.0700	+	5.82799i	1.64677	+	0.682114i	0.649815	+	0.760093i	$0.274847\pi$
$74$	2.92202	−	1.21034i	0.339678	−	0.140699i
$75$	−0.0150102	+	12.5605i	−0.00173323	+	1.45036i
$76$	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	−0.00899120	−	0.999960i	$-0.502862\pi$
$79$	6.14822	−	2.54668i	0.691729	−	0.286524i	0.700720	+	0.713436i	$0.252862\pi$
$80$	−2.19336	+	0.434925i	−0.245225	+	0.0486261i
$81$		−	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	$-0.260725\pi$
$83$	−0.434038	−	0.434038i	−0.0476418	−	0.0476418i	−0.730526	+	0.682885i	$0.760725\pi$
$84$	−0.338641			−0.0369488
$85$	4.29886	−	8.15597i	0.466277	−	0.884639i
$86$	−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	$0.223332\pi$
$89$			12.1784i			1.29091i	−0.763799	+	0.645454i	$0.776668\pi$
$90$	−1.43990	−	7.26152i	−0.151778	−	0.765431i
$91$	−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
$95$	5.70178	−	8.52228i	0.584990	−	0.874368i
$96$	2.32088	−	0.961341i	0.236874	−	0.0981165i
$97$	0.683508	+	0.283118i	0.0693998	+	0.0287463i	0.417113	−	0.908854i	$-0.363042\pi$
$97$	0.683508	+	0.283118i	0.0693998	+	0.0287463i	−0.347714	+	0.937601i	$0.613042\pi$
$98$	−6.98183			−0.705271
$99$	5.01761	+	2.07836i	0.504289	+	0.208883i
$100$	1.90790	+	4.62168i	0.190790	+	0.462168i
$101$	−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
$105$	0.147283	+	0.742763i	0.0143734	+	0.0724862i
$106$		−	8.11028i		−	0.787740i
$107$	−3.70947	−	1.53651i	−0.358608	−	0.148540i	0.196103	−	0.980583i	$-0.437171\pi$
$107$	−3.70947	−	1.53651i	−0.358608	−	0.148540i	−0.554711	+	0.832043i	$0.687171\pi$
$108$	0.298667	+	0.721046i	0.0287393	+	0.0693827i
$109$	3.59335	+	8.67512i	0.344181	+	0.830926i	0.997284	+	0.0736565i	$0.0234668\pi$
$109$	3.59335	+	8.67512i	0.344181	+	0.830926i	−0.653103	+	0.757269i	$0.726533\pi$
$110$	−3.59726	−	0.717775i	−0.342986	−	0.0684372i
$111$	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	$-0.201898\pi$
$113$	−1.94643	−	4.69910i	−0.183105	−	0.442054i	−0.988603	+	0.150544i	$0.951898\pi$
$114$	−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
$125$	9.30723	−	6.19479i	0.832464	−	0.554079i
$126$	−0.170788	−	0.412320i	−0.0152150	−	0.0367323i
$127$	3.01322	−	3.01322i	0.267380	−	0.267380i	−0.560663	−	0.828044i	$-0.689454\pi$
$127$	3.01322	−	3.01322i	0.267380	−	0.267380i	0.828044	+	0.560663i	$0.189454\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−2.12399	−	5.12777i	−0.187007	−	0.451475i
$130$	−6.14656	−	4.11231i	−0.539089	−	0.360674i
$131$	−6.22666	+	15.0325i	−0.544026	+	1.31339i	0.377835	+	0.925873i	$0.376669\pi$
$131$	−6.22666	+	15.0325i	−0.544026	+	1.31339i	−0.921861	+	0.387521i	$0.873331\pi$
$132$	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	0.271143	−	0.962539i	$-0.412598\pi$
$139$	−2.56721	−	1.06337i	−0.217748	−	0.0901940i	−0.488891	+	0.872345i	$0.662598\pi$
$140$	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
$145$	3.15152	−	15.7944i	0.261719	−	1.31165i
$146$	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	$0.190603\pi$
$149$			13.7604i			1.12730i	−0.826015	+	0.563648i	$0.809397\pi$
$150$	−8.89224	+	8.87102i	−0.726049	+	0.724315i
$151$	13.5269	−	13.5269i	1.10080	−	1.10080i	0.106489	−	0.994314i	$-0.466039\pi$
$151$	13.5269	−	13.5269i	1.10080	−	1.10080i	0.994314	−	0.106489i	$-0.0339610\pi$
$152$			4.58562i			0.371943i
$153$	−13.5757	+	1.42480i	−1.09753	+	0.115188i
$154$	−0.221140			−0.0178200
$155$	16.6007	+	3.31240i	1.33340	+	0.266058i
$156$	7.67586	+	3.17945i	0.614561	+	0.254560i
$157$	6.59788			0.526568			0.263284	−	0.964718i	$-0.415194\pi$
$157$	6.59788			0.526568			0.263284	+	0.964718i	$0.415194\pi$
$158$	6.14822	+	2.54668i	0.489126	+	0.202603i
$159$	18.8230	−	7.79675i	1.49276	−	0.618322i
$160$	−1.85848	−	1.24340i	−0.146926	−	0.0982997i
$161$	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	−0.714786	+	0.699344i	$0.753476\pi$
$163$	−21.8922	+	9.06803i	−1.71473	+	0.710263i	−0.999940	+	0.0109192i	$0.996524\pi$
$164$	−4.02306	+	1.66641i	−0.314149	+	0.130125i
$165$	−1.79233	−	9.03886i	−0.139532	−	0.703674i
$166$		−	0.613822i		−	0.0476418i
$167$	−0.155358	+	0.375066i	−0.0120219	+	0.0290235i	−0.929777	−	0.368124i	$-0.880000\pi$
$167$	−0.155358	+	0.375066i	−0.0120219	+	0.0290235i	0.917755	+	0.397148i	$0.130000\pi$
$168$	−0.239455	−	0.239455i	−0.0184744	−	0.0184744i
$169$	−2.06175			−0.158596
$170$	8.80689	−	2.72739i	0.675458	−	0.209181i
$171$	−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	$-0.849059\pi$
$173$	0.819509	−	1.97847i	0.0623061	−	0.150420i	0.951966	+	0.306203i	$0.0990587\pi$
$174$			18.0940i			1.37170i
$175$	0.477172	−	0.476033i	0.0360708	−	0.0359847i
$176$	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	0.704058	−	0.710142i	$-0.251369\pi$
$179$	−0.0813980	−	0.0813980i	−0.00608397	−	0.00608397i	−0.710142	+	0.704058i	$0.751369\pi$
$180$	4.11651	−	6.15283i	0.306826	−	0.458605i
$181$	7.09374	−	2.93832i	0.527273	−	0.218404i	−0.103135	−	0.994667i	$-0.532887\pi$
$181$	7.09374	−	2.93832i	0.527273	−	0.218404i	0.630409	+	0.776264i	$0.282887\pi$
$182$	−0.411899	−	0.170614i	−0.0305320	−	0.0126468i
$183$	10.3564			0.765568
$184$	−4.49630	−	1.86243i	−0.331472	−	0.137300i
$185$	1.38386	−	6.93546i	0.101743	−	0.509905i
$186$	−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
$190$	10.0579	−	1.99440i	0.729679	−	0.144689i
$191$		−	22.9556i		−	1.66101i	−0.557011	−	0.830505i	$-0.688052\pi$
$191$		−	22.9556i		−	1.66101i	0.557011	−	0.830505i	$-0.311948\pi$
$192$	2.32088	+	0.961341i	0.167495	+	0.0693788i
$193$	−0.896081	−	2.16333i	−0.0645013	−	0.155720i	0.888342	−	0.459182i	$-0.151857\pi$
$193$	−0.896081	−	2.16333i	−0.0645013	−	0.155720i	−0.952844	+	0.303462i	$0.901857\pi$
$194$	0.283118	+	0.683508i	0.0203267	+	0.0490730i
$195$	3.63526	−	18.2188i	0.260326	−	1.30467i
$196$	−4.93690	−	4.93690i	−0.352636	−	0.352636i
$197$	−14.2583	+	5.90598i	−1.01586	+	0.420783i	−0.827590	−	0.561334i	$-0.810288\pi$
$197$	−14.2583	+	5.90598i	−1.01586	+	0.420783i	−0.188271	+	0.982117i	$0.560288\pi$
$198$	2.07836	+	5.01761i	0.147703	+	0.356586i
$199$	−4.14908	+	10.0168i	−0.294121	+	0.710070i	0.705878	+	0.708333i	$0.250553\pi$
$199$	−4.14908	+	10.0168i	−0.294121	+	0.710070i	−0.999998	+	0.00173629i	$0.999447\pi$
$200$	−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
$210$	−0.421068	+	0.629358i	−0.0290564	+	0.0434298i
$211$	−5.18792	−	12.5247i	−0.357151	−	0.862239i	−0.995698	−	0.0926563i	$-0.970464\pi$
$211$	−5.18792	−	12.5247i	−0.357151	−	0.862239i	0.638547	−	0.769583i	$-0.279536\pi$
$212$	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
$215$	−2.74718	+	4.10614i	−0.187356	+	0.280036i
$216$	−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	$-0.0728061\pi$
$223$	11.1583	+	11.1583i	0.747218	+	0.747218i	−0.226738	+	0.973956i	$0.572806\pi$
$224$	−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	−0.999994	−	0.00350001i	$-0.998886\pi$
$227$	−4.45014	−	10.7436i	−0.295366	−	0.713077i	0.704628	−	0.709577i	$-0.251114\pi$
$228$	−10.6427	+	4.40835i	−0.704829	+	0.291950i
$229$	10.1700	+	10.1700i	0.672050	+	0.672050i	0.958188	−	0.286139i	$-0.0923718\pi$
$229$	10.1700	+	10.1700i	0.672050	+	0.672050i	−0.286139	+	0.958188i	$0.592372\pi$
$230$	−2.12943	+	10.6720i	−0.140410	+	0.703693i
$231$	−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	$-0.172166\pi$
$233$	16.7809	+	6.95088i	1.09935	+	0.455367i	0.242095	+	0.970253i	$0.422166\pi$
$234$			10.9494i			0.715786i
$235$	−28.2063	+	5.59306i	−1.83997	+	0.364851i
$236$	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	$0.609210\pi$
$240$	1.09916	−	5.50865i	0.0709505	−	0.355582i
$241$	8.16373	+	3.38153i	0.525872	+	0.217823i	0.629794	−	0.776762i	$-0.283139\pi$
$241$	8.16373	+	3.38153i	0.525872	+	0.217823i	−0.103922	+	0.994585i	$0.533139\pi$
$242$	−8.30890			−0.534116
$243$	20.6639	+	8.55928i	1.32559	+	0.549078i
$244$	3.80879	−	1.57765i	0.243833	−	0.100999i
$245$	−8.68123	+	12.9756i	−0.554623	+	0.828980i
$246$	−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
$250$	10.9616	+	2.20083i	0.693272	+	0.139193i
$251$			8.03716i			0.507301i	0.967296	+	0.253650i	$0.0816313\pi$
$251$			8.03716i			0.507301i	−0.967296	+	0.253650i	$0.918369\pi$
$252$	0.170788	−	0.412320i	0.0107587	−	0.0259737i
$253$	−5.64534	−	5.64534i	−0.354919	−	0.354919i
$254$	4.26134			0.267380
$255$	14.7964	+	17.8178i	0.926586	+	1.11579i
$256$	1.00000			0.0625000
$257$	9.70776	+	9.70776i	0.605553	+	0.605553i	0.941781	−	0.336228i	$-0.109151\pi$
$257$	9.70776	+	9.70776i	0.605553	+	0.605553i	−0.336228	+	0.941781i	$0.609151\pi$
$258$	2.12399	−	5.12777i	0.132234	−	0.319241i
$259$		−	0.426353i		−	0.0264923i
$260$	−1.43843	−	7.25412i	−0.0892075	−	0.449881i
$261$	−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	$-0.811134\pi$
$263$	−4.37776	+	4.37776i	−0.269944	+	0.269944i	0.559134	+	0.829078i	$0.311134\pi$
$264$	2.91399	+	2.91399i	0.179344	+	0.179344i
$265$	−15.0728	−	10.0843i	−0.925914	−	0.619477i
$266$	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	0.828134	−	0.560530i	$-0.189403\pi$
$269$	16.6859	+	6.91153i	1.01736	+	0.421403i	0.189224	+	0.981934i	$0.439403\pi$
$270$	1.71141	+	0.341485i	0.104153	+	0.0207821i
$271$	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
$275$	−5.80682	+	5.79296i	−0.350165	+	0.349329i
$276$		−	12.2258i		−	0.735908i
$277$	10.5343	+	4.36345i	0.632945	+	0.262174i	0.676004	−	0.736898i	$-0.263710\pi$
$277$	10.5343	+	4.36345i	0.632945	+	0.262174i	−0.0430590	+	0.999073i	$0.513710\pi$
$278$	−1.06337	−	2.56721i	−0.0637768	−	0.153971i
$279$	−9.59127	−	23.1554i	−0.574214	−	1.38628i
$280$	−0.0589828	+	0.295603i	−0.00352489	+	0.0176657i
$281$	21.2631	+	21.2631i	1.26845	+	1.26845i	0.946890	+	0.321559i	$0.104207\pi$
$281$	21.2631	+	21.2631i	1.26845	+	1.26845i	0.321559	+	0.946890i	$0.395793\pi$
$282$	29.8462	−	12.3627i	1.77731	−	0.736187i
$283$	10.4675	+	25.2708i	0.622228	+	1.50219i	0.849081	+	0.528262i	$0.177156\pi$
$283$	10.4675	+	25.2708i	0.622228	+	1.50219i	−0.226853	+	0.973929i	$0.572844\pi$
$284$	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	$-0.388483\pi$
$293$	11.7499			0.686436			0.343218	+	0.939256i	$0.388483\pi$
$294$	6.71192	−	16.2040i	0.391447	−	0.945037i
$295$	−1.96307	−	1.31338i	−0.114295	−	0.0764680i
$296$	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
$300$	−12.5605	−	0.0150102i	−0.725182	−	0.000866614i
$301$	−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	0.693580	+	0.720379i	$0.256032\pi$
$311$	−5.40060	+	13.0382i	−0.306240	+	0.739329i	−0.999820	+	0.0189496i	$0.993968\pi$
$312$	3.17945	+	7.67586i	0.180001	+	0.434560i
$313$	−10.8593	+	4.49807i	−0.613804	+	0.254246i	−0.667854	−	0.744292i	$-0.732787\pi$
$313$	−10.8593	+	4.49807i	−0.613804	+	0.254246i	0.0540497	+	0.998538i	$0.482787\pi$
$314$	4.66540	+	4.66540i	0.263284	+	0.263284i
$315$	−0.978647	−	0.195273i	−0.0551405	−	0.0110024i
$316$	2.54668	+	6.14822i	0.143262	+	0.345865i
$317$	−7.96264	−	19.2235i	−0.447226	−	1.07970i	−0.973357	−	0.229296i	$-0.926358\pi$
$317$	−7.96264	−	19.2235i	−0.447226	−	1.07970i	0.526130	−	0.850404i	$-0.323642\pi$
$318$	18.8230	+	7.79675i	1.05554	+	0.437220i
$319$			11.8157i			0.661555i
$320$	−0.434925	−	2.19336i	−0.0243130	−	0.122613i
$321$	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
$325$	−15.2853	+	6.30999i	−0.847876	+	0.350015i
$326$	−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
$330$	5.12407	−	7.65880i	0.282071	−	0.421603i
$331$	−4.48556	−	4.48556i	−0.246549	−	0.246549i	0.573004	−	0.819553i	$-0.305778\pi$
$331$	−4.48556	−	4.48556i	−0.246549	−	0.246549i	−0.819553	+	0.573004i	$0.805778\pi$
$332$	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
$335$	−5.20051	−	26.2266i	−0.284134	−	1.43291i
$336$		−	0.338641i		−	0.0184744i
$337$	−6.61231	+	15.9635i	−0.360196	+	0.869589i	0.635075	+	0.772450i	$0.280969\pi$
$337$	−6.61231	+	15.9635i	−0.360196	+	0.869589i	−0.995271	+	0.0971388i	$0.969031\pi$
$338$	−1.45788	−	1.45788i	−0.0792980	−	0.0792980i
$339$	12.7772			0.693964
$340$	8.15597	+	4.29886i	0.442320	+	0.233138i
$341$	−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
$345$	−26.8156	+	5.31731i	−1.44371	+	0.286274i
$346$	1.97847	−	0.819509i	0.106363	−	0.0440571i
$347$	30.1868	−	12.5038i	1.62051	−	0.671239i	0.626392	−	0.779508i	$-0.284531\pi$
$347$	30.1868	−	12.5038i	1.62051	−	0.671239i	0.994122	+	0.108270i	$0.0345310\pi$
$348$	−12.7944	+	12.7944i	−0.685851	+	0.685851i
$349$	−18.4819	−	18.4819i	−0.989311	−	0.989311i	0.0106320	−	0.999943i	$-0.496616\pi$
$349$	−18.4819	−	18.4819i	−0.989311	−	0.989311i	−0.999943	+	0.0106320i	$0.996616\pi$
$350$	0.674018		0.000805471i	0.0360278		4.30542e-5i
$351$	−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	$-0.727898\pi$
$353$	−24.6632			−1.31269			−0.656345	+	0.754461i	$0.727898\pi$
$354$	2.45150	+	1.01544i	0.130296	+	0.0539703i
$355$	−28.7073	−	5.72808i	−1.52363	−	0.304015i
$356$	−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	−0.411086	−	0.911597i	$-0.634850\pi$
$359$	9.48333	−	9.48333i	0.500511	−	0.500511i	0.911597	+	0.411086i	$0.134850\pi$
$360$	7.26152	−	1.43990i	0.382716	−	0.0758892i
$361$		−	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
$365$	33.3954	+	6.66350i	1.74799	+	0.348783i
$366$	7.32309	+	7.32309i	0.382784	+	0.382784i
$367$	10.4840	−	4.34261i	0.547259	−	0.226682i	−0.0918843	−	0.995770i	$-0.529289\pi$
$367$	10.4840	−	4.34261i	0.547259	−	0.226682i	0.639143	+	0.769088i	$0.279289\pi$
$368$	−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	0.247507	+	0.968886i	$0.420389\pi$
$379$	−11.9263	+	28.7926i	−0.612613	+	1.47898i	−0.860120	+	0.510092i	$0.829611\pi$
$380$	8.52228	+	5.70178i	0.437184	+	0.292495i
$381$	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	$-0.501055\pi$
$383$	19.5054	−	19.5054i	0.996681	−	0.996681i	0.999995	+	0.00331356i	$0.00105474\pi$
$384$	0.961341	+	2.32088i	0.0490582	+	0.118437i
$385$	−0.274966	+	0.410984i	−0.0140136	+	0.0209457i
$386$	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	0.191487	−	0.981495i	$-0.438669\pi$
$389$	23.1348	−	23.1348i	1.17298	−	1.17298i	0.981495	−	0.191487i	$-0.0613309\pi$
$390$	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	0.992822	+	0.119598i	$0.0381606\pi$
$397$	7.47899	+	18.0559i	0.375360	+	0.906198i	−0.617463	+	0.786600i	$0.711839\pi$
$398$	−10.0168	+	4.14908i	−0.502095	+	0.207975i
$399$	1.09805	+	1.09805i	0.0549713	+	0.0549713i
$400$	−4.62168	+	1.90790i	−0.231084	+	0.0953948i
$401$	−0.112991	−	0.272785i	−0.00564252	−	0.0136222i	0.921033	−	0.389484i	$-0.127347\pi$
$401$	−0.112991	−	0.272785i	−0.00564252	−	0.0136222i	−0.926676	+	0.375862i	$0.877347\pi$
$402$	11.4950	+	27.7514i	0.573319	+	1.38411i
$403$	−23.1318	−	9.58150i	−1.15228	−	0.477288i
$404$		−	19.3513i		−	0.962766i
$405$	−3.46698	−	17.4843i	−0.172276	−	0.868801i
$406$	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	$0.439600\pi$
$410$	−1.90531	+	9.54880i	−0.0940964	+	0.471582i
$411$	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
$415$	−1.14078	−	0.763228i	−0.0559985	−	0.0374654i
$416$	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	−0.139291	−	0.990252i	$-0.544482\pi$
$419$	9.46569	−	3.92082i	0.462429	−	0.191544i	0.601720	+	0.798707i	$0.294482\pi$
$420$	−0.742763	+	0.147283i	−0.0362431	+	0.00718670i
$421$		−	27.3819i		−	1.33451i	−0.744828	−	0.667257i	$-0.767468\pi$
$421$		−	27.3819i		−	1.33451i	0.744828	−	0.667257i	$-0.232532\pi$
$422$	5.18792	−	12.5247i	0.252544	−	0.609695i
$423$	30.1049	+	30.1049i	1.46375	+	1.46375i
$424$	8.11028			0.393870
$425$	5.88172	−	19.7587i	0.285305	−	0.958437i
$426$	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
$430$	−4.84603	+	0.960925i	−0.233696	+	0.0463399i
$431$	−7.07239	+	2.92948i	−0.340665	+	0.141108i	−0.546456	−	0.837488i	$-0.684023\pi$
$431$	−7.07239	+	2.92948i	−0.340665	+	0.141108i	0.205791	+	0.978596i	$0.434023\pi$
$432$	−0.721046	+	0.298667i	−0.0346914	+	0.0143696i
$433$	8.43456	−	8.43456i	0.405339	−	0.405339i	−0.474770	−	0.880110i	$-0.657469\pi$
$433$	8.43456	−	8.43456i	0.405339	−	0.405339i	0.880110	+	0.474770i	$0.157469\pi$
$434$	0.721617	+	0.721617i	0.0346387	+	0.0346387i
$435$	33.6273	+	22.4981i	1.61231	+	1.07870i
$436$	−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	−0.0589645	−	0.998260i	$-0.518780\pi$
$439$	−16.8988	−	6.99971i	−0.806535	−	0.334078i	−0.747571	+	0.664182i	$0.768780\pi$
$440$	0.717775	−	3.59726i	0.0342186	−	0.171493i
$441$	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
$445$	5.29669	+	26.7116i	0.251087	+	1.26625i
$446$			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	0.831294	−	0.555833i	$-0.187601\pi$
$449$	−3.16897	−	7.65057i	−0.149553	−	0.361053i	−0.980847	+	0.194780i	$0.937601\pi$
$450$	−6.31643	−	15.3009i	−0.297759	−	0.721291i
$451$	−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	0.999790	+	0.0204820i	$0.00652007\pi$
$457$	21.8109	+	21.8109i	1.02027	+	1.02027i	0.0204820	+	0.999790i	$0.493480\pi$
$458$			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	−0.990823	−	0.135167i	$-0.956843\pi$
$461$	−18.3717	+	18.3717i	−0.855656	+	0.855656i	0.135167	+	0.990823i	$0.456843\pi$
$462$	0.212591	−	0.513240i	0.00989062	−	0.0238781i
$463$	4.34471			0.201916			0.100958	−	0.994891i	$-0.467809\pi$
$463$	4.34471			0.201916			0.100958	+	0.994891i	$0.467809\pi$
$464$	−2.75636	+	6.65444i	−0.127961	+	0.308925i
$465$	−23.6467	+	35.3440i	−1.09659	+	1.63904i
$466$	6.95088	+	16.7809i	0.321993	+	0.777360i
$467$	−5.23030	+	5.23030i	−0.242029	+	0.242029i	−0.817689	−	0.575660i	$-0.804745\pi$
$467$	−5.23030	+	5.23030i	−0.242029	+	0.242029i	0.575660	+	0.817689i	$0.304745\pi$
$468$	−7.74240	+	7.74240i	−0.357893	+	0.357893i
$469$	−0.616841	−	1.48919i	−0.0284831	−	0.0687642i
$470$	−23.8997	−	15.9900i	−1.10241	−	0.737562i
$471$	−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	−0.0670024	−	0.997753i	$-0.521344\pi$
$479$	−17.9443	−	7.43279i	−0.819898	−	0.339613i	−0.752896	+	0.658140i	$0.771344\pi$
$480$	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
$485$	1.62232	+	0.323707i	0.0736656	+	0.0146988i
$486$	8.55928	+	20.6639i	0.388257	+	0.937335i
$487$	−5.41519	−	13.0734i	−0.245385	−	0.592413i	0.752416	−	0.658688i	$-0.228888\pi$
$487$	−5.41519	−	13.0734i	−0.245385	−	0.592413i	−0.997801	+	0.0662754i	$0.978888\pi$
$488$	3.80879	+	1.57765i	0.172416	+	0.0714169i
$489$		−	59.5266i		−	2.69189i
$490$	−15.3137	+	3.03657i	−0.691802	+	0.137178i
$491$	11.9689	−	11.9689i	0.540148	−	0.540148i	−0.383425	−	0.923572i	$-0.625255\pi$
$491$	11.9689	−	11.9689i	0.540148	−	0.540148i	0.923572	+	0.383425i	$0.125255\pi$
$492$		−	10.9391i		−	0.493170i
$493$	−14.1665	−	26.1008i	−0.638028	−	1.17552i
$494$	−15.1660			−0.682352
$495$	11.9094	+	2.37632i	0.535287	+	0.106808i
$496$	−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	−0.327442	−	0.944871i	$-0.606187\pi$
$499$	2.43813	−	1.00991i	0.109146	−	0.0452096i	0.436588	+	0.899662i	$0.356187\pi$
$500$	6.19479	+	9.30723i	0.277039	+	0.416232i
$501$	−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	$-0.611352\pi$
$503$	1.77624	−	0.735741i	0.0791984	−	0.0328051i	0.421931	+	0.906628i	$0.361352\pi$
$504$	0.412320	−	0.170788i	0.0183662	−	0.00760752i
$505$	−42.4445	+	8.41638i	−1.88876	+	0.374524i
$506$		−	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	$0.401644\pi$
$510$	−2.13648	+	23.0617i	−0.0946047	+	1.02119i
$511$	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
$515$	−0.741483	−	3.73936i	−0.0326736	−	0.164776i
$516$	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
$520$	4.11231	−	6.14656i	0.180337	−	0.269544i
$521$	−37.8110	+	15.6618i	−1.65653	+	0.686156i	−0.997804	−	0.0662286i	$-0.978903\pi$
$521$	−37.8110	+	15.6618i	−1.65653	+	0.686156i	−0.658724	+	0.752385i	$0.728903\pi$
$522$	−22.0307	−	9.12542i	−0.964258	−	0.399409i
$523$	−8.60955			−0.376469			−0.188235	−	0.982124i	$-0.560277\pi$
$523$	−8.60955			−0.376469			−0.188235	+	0.982124i	$0.560277\pi$
$524$	−15.0325	−	6.22666i	−0.656697	−	0.272013i
$525$	0.646092	+	1.56509i	0.0281978	+	0.0683062i
$526$	−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
$530$	−3.52736	−	17.7888i	−0.153219	−	0.772695i
$531$			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
$535$	−8.80447	−	1.75679i	−0.380651	−	0.0759526i
$536$	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	−0.283591	−	0.958945i	$-0.591526\pi$
$541$	−27.0320	−	11.1970i	−1.16220	−	0.481398i	−0.878606	+	0.477548i	$0.841526\pi$
$542$	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	0.651234	+	0.758877i	$0.274252\pi$
$547$	−8.08911	+	19.5288i	−0.345865	+	0.834993i	−0.997099	+	0.0761155i	$0.975748\pi$
$548$	3.50896			0.149895
$549$	−5.22310	+	12.6097i	−0.222916	+	0.538168i
$550$	−8.20228	−	0.00980197i	−0.349747	−	0.000417957i
$551$	−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
$555$	14.7660	+	9.87911i	0.626783	+	0.419345i
$556$	1.06337	−	2.56721i	0.0450970	−	0.108874i
$557$	−11.6189			−0.492310			−0.246155	−	0.969231i	$-0.579167\pi$
$557$	−11.6189			−0.492310			−0.246155	+	0.969231i	$0.579167\pi$
$558$	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	$-0.167815\pi$
$563$	8.56797	+	8.56797i	0.361097	+	0.361097i	−0.503120	+	0.864217i	$0.667815\pi$
$564$	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	0.723134	−	0.690708i	$-0.242701\pi$
$569$	0.773484	+	0.773484i	0.0324262	+	0.0324262i	−0.690708	+	0.723134i	$0.742701\pi$
$570$	−5.04033	+	25.2606i	−0.211116	+	1.05805i
$571$	0.284151	+	0.686000i	0.0118913	+	0.0287082i	0.929714	−	0.368283i	$-0.120054\pi$
$571$	0.284151	+	0.686000i	0.0118913	+	0.0287082i	−0.917822	+	0.396991i	$0.870054\pi$
$572$	2.07625	+	5.01250i	0.0868122	+	0.209583i
$573$	53.2773	+	22.0682i	2.22569	+	0.921912i
$574$			0.587007i			0.0245012i
$575$	17.1860	+	17.2271i	0.716706	+	0.718421i
$576$	−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
$580$	15.7944	+	3.15152i	0.655827	+	0.130860i
$581$	−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
$585$	20.3493	+	13.6145i	0.841339	+	0.562892i
$586$	8.30843	+	8.30843i	0.343218	+	0.343218i
$587$	−31.1108	+	31.1108i	−1.28408	+	1.28408i	−0.345757	+	0.938324i	$0.612378\pi$
$587$	−31.1108	+	31.1108i	−1.28408	+	1.28408i	−0.938324	+	0.345757i	$0.887622\pi$
$588$	16.2040	−	6.71192i	0.668242	−	0.276795i
$589$	32.0725	−	13.2849i	1.32153	−	0.547394i
$590$	−0.459402	−	2.31680i	−0.0189133	−	0.0953813i
$591$		−	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	$-0.263136\pi$
$593$	−1.42079	−	1.42079i	−0.0583449	−	0.0583449i	−0.735677	+	0.677332i	$0.763136\pi$
$594$	−1.28030			−0.0525315
$595$	0.114647	−	1.23753i	0.00470006	−	0.0507338i
$596$	−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	$-0.944662\pi$
$599$		−	8.46693i		−	0.345949i	0.984926	−	0.172975i	$-0.0553379\pi$
$600$	−8.87102	−	8.89224i	−0.362158	−	0.363024i
$601$	14.3426	−	5.94092i	0.585049	−	0.242335i	−0.0704703	−	0.997514i	$-0.522450\pi$
$601$	14.3426	−	5.94092i	0.585049	−	0.242335i	0.655519	+	0.755179i	$0.272450\pi$
$602$	−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
$605$	−10.3313	+	15.4419i	−0.420028	+	0.627803i
$606$	44.9122	−	18.6033i	1.82443	−	0.755706i
$607$	7.91404	+	3.27810i	0.321221	+	0.133054i	0.537467	−	0.843285i	$-0.319381\pi$
$607$	7.91404	+	3.27810i	0.321221	+	0.133054i	−0.216246	+	0.976339i	$0.569381\pi$
$608$	−4.58562			−0.185971
$609$	2.25347	+	0.933417i	0.0913151	+	0.0378240i
$610$	1.80383	−	9.04021i	0.0730348	−	0.366028i
$611$	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
$615$	−23.9933	+	4.75766i	−0.967503	+	0.191848i
$616$		−	0.221140i		−	0.00890998i
$617$	−40.1488	−	16.6302i	−1.61633	−	0.669505i	−0.622726	−	0.782440i	$-0.713975\pi$
$617$	−40.1488	−	16.6302i	−1.61633	−	0.669505i	−0.993602	+	0.112935i	$0.963975\pi$
$618$	1.63895	+	3.95676i	0.0659281	+	0.159164i
$619$	8.86032	+	21.3907i	0.356126	+	0.859765i	0.995837	+	0.0911494i	$0.0290541\pi$
$619$	8.86032	+	21.3907i	0.356126	+	0.859765i	−0.639711	+	0.768616i	$0.720946\pi$
$620$	−3.31240	+	16.6007i	−0.133029	+	0.666701i
$621$	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	−0.998371	−	0.0570526i	$-0.981830\pi$
$631$	−23.6457	+	23.6457i	−0.941319	+	0.941319i	0.0570526	+	0.998371i	$0.481830\pi$
$632$	−2.54668	+	6.14822i	−0.101301	+	0.244563i
$633$	34.0558			1.35360
$634$	7.96264	−	19.2235i	0.316237	−	0.763463i
$635$	5.29857	−	7.91962i	0.210267	−	0.314281i
$636$	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
$640$	1.24340	−	1.85848i	0.0491498	−	0.0734629i
$641$	3.28884	−	7.93995i	0.129901	−	0.313609i	−0.845525	−	0.533936i	$-0.820712\pi$
$641$	3.28884	−	7.93995i	0.129901	−	0.313609i	0.975426	+	0.220327i	$0.0707124\pi$
$642$	10.0864			0.398077
$643$	6.04126	−	14.5849i	0.238244	−	0.575172i	−0.758857	−	0.651257i	$-0.774242\pi$
$643$	6.04126	−	14.5849i	0.238244	−	0.575172i	0.997101	+	0.0760849i	$0.0242420\pi$
$644$	−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	$-0.621314\pi$
$653$	0.546789	−	0.226487i	0.0213975	−	0.00886313i	0.393357	+	0.919386i	$0.371314\pi$
$654$	−16.6795	−	16.6795i	−0.652220	−	0.652220i
$655$	−7.11932	+	35.6798i	−0.278175	+	1.39413i
$656$	−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	$0.127457\pi$
$659$			20.0132i			0.779606i	−0.920898	+	0.389803i	$0.872543\pi$
$660$	9.03886	−	1.79233i	0.351837	−	0.0697662i
$661$	−17.9228	+	17.9228i	−0.697117	+	0.697117i	−0.963788	−	0.266671i	$-0.914076\pi$
$661$	−17.9228	+	17.9228i	−0.697117	+	0.697117i	0.266671	+	0.963788i	$0.414076\pi$
$662$		−	6.34354i		−	0.246549i
$663$	−16.3410	−	30.1072i	−0.634632	−	1.16927i
$664$	0.613822			0.0238209
$665$	0.270472	−	1.35552i	0.0104885	−	0.0525649i
$666$	−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
$670$	14.8677	−	22.2223i	0.574389	−	0.858524i
$671$	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	$-0.552980\pi$
$673$	10.7534	−	4.45421i	0.414514	−	0.171697i	0.580187	+	0.814484i	$0.302980\pi$
$674$	−15.9635	+	6.61231i	−0.614892	+	0.254697i
$675$	2.76262	−	2.75603i	0.106333	−	0.106079i
$676$		−	2.06175i		−	0.0792980i
$677$	−6.52935	+	15.7632i	−0.250943	+	0.605831i	−0.998281	−	0.0586141i	$-0.981332\pi$
$677$	−6.52935	+	15.7632i	−0.250943	+	0.605831i	0.747337	+	0.664445i	$0.231332\pi$
$678$	9.03487	+	9.03487i	0.346982	+	0.346982i
$679$	0.0997310			0.00382733
$680$	2.72739	+	8.80689i	0.104591	+	0.337729i
$681$	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	$-0.930964\pi$
$683$	−3.49863	+	8.44645i	−0.133871	+	0.323194i	0.842701	+	0.538381i	$0.180964\pi$
$684$		−	15.1815i		−	0.580479i
$685$	−1.52613	−	7.69641i	−0.0583105	−	0.294065i
$686$	−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
$690$	−22.7214	−	15.2016i	−0.864990	−	0.578716i
$691$	10.3497	−	4.28697i	0.393719	−	0.163084i	−0.177035	−	0.984204i	$-0.556651\pi$
$691$	10.3497	−	4.28697i	0.393719	−	0.163084i	0.570755	+	0.821121i	$0.306651\pi$
$692$	1.97847	+	0.819509i	0.0752102	+	0.0311531i
$693$	0.732122			0.0278110
$694$	30.1868	+	12.5038i	1.14588	+	0.474637i
$695$	−6.09330	−	1.21582i	−0.231132	−	0.0461186i
$696$	−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
$700$	0.476033	+	0.477172i	0.0179924	+	0.0180354i
$701$			9.32304i			0.352127i	0.984379	+	0.176063i	$0.0563363\pi$
$701$			9.32304i			0.352127i	−0.984379	+	0.176063i	$0.943664\pi$
$702$	−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
$705$	14.1350	−	70.8403i	0.532356	−	2.66800i
$706$	−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	−0.832325	−	0.554288i	$-0.812991\pi$
$709$	3.94502	−	9.52413i	0.148158	−	0.357686i	0.980483	+	0.196602i	$0.0629906\pi$
$710$	−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	0.450734	+	0.892658i	$0.351162\pi$
$719$	−13.3853	+	32.3150i	−0.499188	+	1.20515i	−0.949922	+	0.312488i	$0.898838\pi$
$720$	6.15283	+	4.11651i	0.229302	+	0.153413i
$721$	−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
$725$	0.0430372	−	36.0135i	0.00159836	−	1.33751i
$726$	7.98769	−	19.2840i	0.296451	−	0.715696i
$727$	5.76858			0.213945			0.106972	−	0.994262i	$-0.465884\pi$
$727$	5.76858			0.213945			0.106972	+	0.994262i	$0.465884\pi$
$728$	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	−0.977271	−	0.211994i	$-0.932004\pi$
$733$	−32.1981	−	32.1981i	−1.18926	−	1.18926i	−0.211994	−	0.977271i	$-0.567996\pi$
$734$	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	0.0493987	−	0.998779i	$-0.484269\pi$
$739$	−25.8085	−	25.8085i	−0.949380	−	0.949380i	−0.998779	+	0.0493987i	$0.984269\pi$
$740$	6.93546	+	1.38386i	0.254953	+	0.0508716i
$741$	−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	$-0.256754\pi$
$743$	18.2827	+	7.57295i	0.670728	+	0.277824i	−0.0212172	+	0.999775i	$0.506754\pi$
$744$		−	19.0177i		−	0.697222i
$745$	5.98474	+	30.1816i	0.219264	+	1.10577i
$746$	−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
$750$	−15.6457	+	23.3248i	−0.571300	+	0.851702i
$751$	46.5640	+	19.2875i	1.69915	+	0.703809i	0.999938	−	0.0111097i	$-0.00353640\pi$
$751$	46.5640	+	19.2875i	1.69915	+	0.703809i	0.699207	+	0.714919i	$0.253536\pi$
$752$	12.8598			0.468950
$753$	−18.6533	−	7.72645i	−0.679764	−	0.281568i
$754$	−22.0082	+	9.11611i	−0.801493	+	0.331989i
$755$	23.7862	−	35.5526i	0.865669	−	1.29389i
$756$	0.0743934	+	0.0743934i	0.00270566	+	0.00270566i
$757$	13.4117	−	13.4117i	0.487458	−	0.487458i	−0.420045	−	0.907503i	$-0.637986\pi$
$757$	13.4117	−	13.4117i	0.487458	−	0.487458i	0.907503	+	0.420045i	$0.137986\pi$
$758$	−28.7926	+	11.9263i	−1.04580	+	0.433183i
$759$	18.5293	−	7.67507i	0.672570	−	0.278588i
$760$	1.99440	+	10.0579i	0.0723445	+	0.364839i
$761$			43.6160i			1.58108i	0.612411	+	0.790540i	$0.290200\pi$
$761$			43.6160i			1.58108i	−0.612411	+	0.790540i	$0.709800\pi$
$762$	−4.09661	+	9.89008i	−0.148404	+	0.358280i
$763$	0.895049	+	0.895049i	0.0324029	+	0.0324029i
$764$	22.9556			0.830505
$765$	−29.1568	+	9.02951i	−1.05417	+	0.326463i
$766$	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	$0.0926777\pi$
$769$			15.9208i			0.574118i	−0.957913	+	0.287059i	$0.907322\pi$
$770$	−0.485040	+	0.0961792i	−0.0174796	+	0.00346606i
$771$	−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	$-0.997252\pi$
$773$	−27.5618	+	27.5618i	−0.991329	+	0.991329i	0.00863410	+	0.999963i	$0.497252\pi$
$774$	5.17223	+	5.17223i	0.185912	+	0.185912i
$775$	37.8520	+	0.0452343i	1.35969	+	0.00162486i
$776$	−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
$780$	18.2188	+	3.63526i	0.652337	+	0.130163i
$781$	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
$785$	14.4715	−	2.86958i	0.516511	−	0.102420i
$786$		−	40.8746i		−	1.45795i
$787$	33.5579	+	13.9001i	1.19621	+	0.495486i	0.889772	−	0.456404i	$-0.150863\pi$
$787$	33.5579	+	13.9001i	1.19621	+	0.495486i	0.306438	+	0.951891i	$0.400863\pi$
$788$	−5.90598	−	14.2583i	−0.210392	−	0.507930i
$789$	−5.95175	−	14.3688i	−0.211888	−	0.511542i
$790$	14.5929	+	2.91177i	0.519192	+	0.103596i
$791$	−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	$-0.211070\pi$
$797$	4.87076	+	4.87076i	0.172531	+	0.172531i	−0.615559	+	0.788091i	$0.711070\pi$
$798$			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
$805$	1.21927	+	0.815744i	0.0429736	+	0.0287512i
$806$	−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	0.908614	−	0.417638i	$-0.137142\pi$
$809$	−0.830184	−	2.00424i	−0.0291877	−	0.0704653i	−0.937801	+	0.347172i	$0.887142\pi$
$810$	9.91173	−	14.8148i	0.348263	−	0.520538i
$811$	13.0269	−	31.4497i	0.457436	−	1.10435i	−0.511997	−	0.858987i	$-0.671094\pi$
$811$	13.0269	−	31.4497i	0.457436	−	1.10435i	0.969432	−	0.245360i	$-0.0789060\pi$
$812$	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	−0.710751	−	0.703443i	$-0.751645\pi$
$821$	8.28749	−	20.0078i	0.289235	−	0.698276i	0.999987	+	0.00516757i	$0.00164489\pi$
$822$	3.37330	+	8.14388i	0.117658	+	0.284050i
$823$	−18.0278	+	7.46737i	−0.628411	+	0.260296i	−0.674078	−	0.738660i	$-0.735459\pi$
$823$	−18.0278	+	7.46737i	−0.628411	+	0.260296i	0.0456669	+	0.998957i	$0.485459\pi$
$824$	1.20551	+	1.20551i	0.0419960	+	0.0419960i
$825$	−7.86245	−	19.0460i	−0.273735	−	0.663096i
$826$	−0.0544904	−	0.131551i	−0.00189596	−	0.00457726i
$827$	0.232580	+	0.561498i	0.00808760	+	0.0195252i	0.927872	−	0.372899i	$-0.121636\pi$
$827$	0.232580	+	0.561498i	0.00808760	+	0.0195252i	−0.919784	+	0.392425i	$0.871636\pi$
$828$	14.8858	+	6.16590i	0.517317	+	0.214280i
$829$		−	10.3168i		−	0.358317i	−0.983820	−	0.179159i	$-0.942662\pi$
$829$		−	10.3168i		−	0.358317i	0.983820	−	0.179159i	$-0.0573375\pi$
$830$	−0.266966	−	1.34633i	−0.00926654	−	0.0467319i
$831$	−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
$835$	−0.177630	+	0.890225i	−0.00614713	+	0.0308075i
$836$	−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	0.191575	−	0.981478i	$-0.438640\pi$
$839$	29.5752	−	12.2504i	1.02105	−	0.422932i	0.829474	+	0.558546i	$0.188640\pi$
$840$	−0.629358	−	0.421068i	−0.0217149	−	0.0145282i
$841$	−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
$845$	−4.52216	+	0.896705i	−0.155567	+	0.0308476i
$846$			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
$850$	18.1305	−	9.81249i	0.621871	−	0.336566i
$851$	15.3924			0.527646
$852$	23.2546	+	23.2546i	0.796689	+	0.796689i
$853$	11.5155	−	27.8008i	0.394282	−	0.951881i	−0.594714	−	0.803938i	$-0.702735\pi$
$853$	11.5155	−	27.8008i	0.394282	−	0.951881i	0.988996	−	0.147944i	$-0.0472654\pi$
$854$		−	0.555742i		−	0.0190171i
$855$	−33.2986	+	6.60281i	−1.13879	+	0.225811i
$856$	3.70947	−	1.53651i	0.126787	−	0.0525169i
$857$	1.33250	−	0.551941i	0.0455175	−	0.0188539i	−0.359809	−	0.933026i	$-0.617158\pi$
$857$	1.33250	−	0.551941i	0.0455175	−	0.0188539i	0.405326	+	0.914172i	$0.367158\pi$
$858$	−9.63745	+	9.63745i	−0.329017	+	0.329017i
$859$	6.47684	+	6.47684i	0.220987	+	0.220987i	0.808914	−	0.587927i	$-0.200056\pi$
$859$	6.47684	+	6.47684i	0.220987	+	0.220987i	−0.587927	+	0.808914i	$0.700056\pi$
$860$	−4.10614	−	2.74718i	−0.140018	−	0.0936782i
$861$	−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	$-0.614378\pi$
$863$	−20.6606			−0.703293			−0.351647	+	0.936133i	$0.614378\pi$
$864$	−0.721046	−	0.298667i	−0.0245305	−	0.0101609i
$865$	0.936995	−	4.69593i	0.0318588	−	0.159666i
$866$	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
$870$	7.86952	+	39.6867i	0.266802	+	1.34550i
$871$			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
$875$	0.839573	−	1.25165i	0.0283828	−	0.0423134i
$876$	−27.0522	−	27.0522i	−0.914008	−	0.914008i
$877$	−38.8470	+	16.0910i	−1.31177	+	0.543353i	−0.925400	−	0.378991i	$-0.876271\pi$
$877$	−38.8470	+	16.0910i	−1.31177	+	0.543353i	−0.386370	+	0.922344i	$0.626271\pi$
$878$	−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	−0.423062	−	0.906101i	$-0.639045\pi$
$881$	−40.4538	−	16.7565i	−1.36292	−	0.564541i	−0.939860	+	0.341560i	$0.889045\pi$
$882$	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	−0.558238	−	0.829681i	$-0.688522\pi$
$887$	12.6030	−	30.4264i	0.423169	−	1.02162i	0.981407	−	0.191939i	$-0.0614776\pi$
$888$	−7.94522			−0.266624
$889$	0.219830	−	0.530718i	0.00737288	−	0.0177997i
$890$	−15.1427	+	22.6333i	−0.507583	+	0.758670i
$891$	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
$895$	−0.213937	−	0.143133i	−0.00715114	−	0.00478442i
$896$	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	−0.940521	−	0.339735i	$-0.889663\pi$
$907$	−15.5311	−	37.4954i	−0.515701	−	1.24501i	0.424820	−	0.905278i	$-0.360337\pi$
$908$	10.7436	−	4.45014i	0.356539	−	0.147683i
$909$	45.3016	+	45.3016i	1.50256	+	1.50256i
$910$	−0.977649	−	0.195074i	−0.0324088	−	0.00646663i
$911$	−3.54723	−	8.56377i	−0.117525	−	0.283731i	0.854160	−	0.520010i	$-0.174072\pi$
$911$	−3.54723	−	8.56377i	−0.117525	−	0.283731i	−0.971685	+	0.236280i	$0.924072\pi$
$912$	−4.40835	−	10.6427i	−0.145975	−	0.352415i
$913$	0.930300	+	0.385343i	0.0307884	+	0.0127530i
$914$			30.8453i			1.02027i
$915$	22.7154	−	4.50426i	0.750947	−	0.148906i
$916$	−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	$0.232472\pi$
$920$	−10.6720	−	2.12943i	−0.351846	−	0.0702052i
$921$	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
$925$	0.0188980	−	15.8138i	0.000621363	−	0.519956i
$926$	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	−0.894391	−	0.447285i	$-0.852391\pi$
$929$	−36.8967	+	15.2831i	−1.21054	+	0.501423i	−0.316152	+	0.948709i	$0.602391\pi$
$930$	−41.7127	+	8.27126i	−1.36781	+	0.271225i
$931$			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
$935$	−1.39516	+	15.0598i	−0.0456267	+	0.492508i
$936$	−10.9494			−0.357893
$937$	20.4587	+	20.4587i	0.668357	+	0.668357i	0.957335	−	0.288979i	$-0.0933157\pi$
$937$	20.4587	+	20.4587i	0.668357	+	0.668357i	−0.288979	+	0.957335i	$0.593316\pi$
$938$	0.616841	−	1.48919i	0.0201406	−	0.0486236i
$939$		−	29.5274i		−	0.963590i
$940$	−5.59306	−	28.2063i	−0.182425	−	0.919987i
$941$	33.8328	−	14.0140i	1.10292	−	0.456843i	0.244424	−	0.969668i	$-0.421401\pi$
$941$	33.8328	−	14.0140i	1.10292	−	0.456843i	0.858493	+	0.512825i	$0.171401\pi$
$942$	−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
$945$	0.130816	−	0.195527i	0.00425545	−	0.00636050i
$946$	3.34854	−	1.38701i	0.108871	−	0.0450957i
$947$	48.7002	+	20.1723i	1.58254	+	0.655512i	0.988814	−	0.149152i	$-0.0476545\pi$
$947$	48.7002	+	20.1723i	1.58254	+	0.655512i	0.593731	+	0.804664i	$0.297654\pi$
$948$	−16.7175			−0.542960
$949$	−46.5338	−	19.2749i	−1.51055	−	0.625690i
$950$	21.1933	−	8.74888i	0.687600	−	0.283851i
$951$	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
$955$	−9.98397	−	50.3500i	−0.323074	−	1.62929i
$956$		−	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
$960$	5.50865	+	1.09916i	0.177791	+	0.0354753i
$961$	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	$-0.116181\pi$
$967$	17.9484	+	17.9484i	0.577183	+	0.577183i	−0.356943	+	0.934126i	$0.616181\pi$
$968$		−	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	−0.0130809	−	0.999914i	$-0.504164\pi$
$971$	30.7506	−	30.7506i	0.986834	−	0.986834i	0.999914	+	0.0130809i	$0.00416390\pi$
$972$	−8.55928	+	20.6639i	−0.274539	+	0.662796i
$973$	−0.374582			−0.0120086
$974$	5.41519	−	13.0734i	0.173514	−	0.418899i
$975$	0.0496432	−	41.5415i	0.00158986	−	1.33039i
$976$	1.57765	+	3.80879i	0.0504994	+	0.121916i
$977$	24.6535	−	24.6535i	0.788735	−	0.788735i	−0.192552	−	0.981287i	$-0.561676\pi$
$977$	24.6535	−	24.6535i	0.788735	−	0.788735i	0.981287	+	0.192552i	$0.0616765\pi$
$978$	42.0917	−	42.0917i	1.34594	−	1.34594i
$979$	−7.64530	−	18.4574i	−0.244345	−	0.589901i
$980$	−12.9756	−	8.68123i	−0.414490	−	0.277312i
$981$	11.8964	−	28.7205i	0.379824	−	0.916976i
$982$	16.9265			0.540148
$983$	21.2758	−	51.3642i	0.678591	−	1.63826i	−0.0879937	−	0.996121i	$-0.528046\pi$
$983$	21.2758	−	51.3642i	0.678591	−	1.63826i	0.766585	−	0.642143i	$-0.221954\pi$
$984$	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	−0.763487	−	0.645823i	$-0.776514\pi$
$991$	7.33631	−	17.7114i	0.233046	−	0.562622i	0.996533	+	0.0832011i	$0.0265144\pi$
$992$	−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
$995$	−4.74390	+	23.7749i	−0.150392	+	0.753716i
$996$	0.590093	+	1.42461i	0.0186978	+	0.0451405i
$997$	2.47887	+	5.98452i	0.0785066	+	0.189532i	0.958260	−	0.285899i	$-0.0922922\pi$
$997$	2.47887	+	5.98452i	0.0785066	+	0.189532i	−0.879753	+	0.475431i	$0.842292\pi$
$998$	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.b.9.1	yes	20
5.2	odd	4		850.2.l.h.451.5		20
5.3	odd	4		850.2.l.i.451.1		20
5.4	even	2		170.2.n.a.9.5	✓	20
17.2	even	8		170.2.n.a.19.5	yes	20
85.2	odd	8		850.2.l.h.801.5		20
85.19	even	8	inner	170.2.n.b.19.1	yes	20
85.53	odd	8		850.2.l.i.801.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.n.a.9.5	✓	20	5.4	even	2
170.2.n.a.19.5	yes	20	17.2	even	8
170.2.n.b.9.1	yes	20	1.1	even	1	trivial
170.2.n.b.19.1	yes	20	85.19	even	8	inner
850.2.l.h.451.5		20	5.2	odd	4
850.2.l.h.801.5		20	85.2	odd	8
850.2.l.i.451.1		20	5.3	odd	4
850.2.l.i.801.1		20	85.53	odd	8

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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.961341 + 2.32088i) q^{3} +1.00000i q^{4} +(2.19336 - 0.434925i) q^{5} +(-2.32088 + 0.961341i) q^{6} +(0.124542 - 0.0515871i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.34100 - 2.34100i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.961341 + 2.32088i) q^{3} +1.00000i q^{4} +(2.19336 - 0.434925i) 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} +(1.85848 + 1.24340i) q^{10} +(-1.51559 + 0.627776i) q^{11} +(-2.32088 - 0.961341i) q^{12} -3.30730 q^{13} +(0.124542 + 0.0515871i) q^{14} +(-1.09916 + 5.50865i) q^{15} -1.00000 q^{16} +(2.59524 - 3.20386i) q^{17} -3.31068i q^{18} +(3.24252 - 3.24252i) q^{19} +(0.434925 + 2.19336i) q^{20} +0.338641i q^{21} +(-1.51559 - 0.627776i) q^{22} +(1.86243 + 4.49630i) q^{23} +(-0.961341 - 2.32088i) q^{24} +(4.62168 - 1.90790i) 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} +(-1.24340 + 1.85848i) 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} +(-6.15283 - 4.11651i) 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} +(-5.50865 - 1.09916i) q^{60} +(-1.57765 - 3.80879i) q^{61} +(2.89707 + 6.99415i) q^{62} +(-0.412320 - 0.170788i) q^{63} -1.00000i q^{64} +(-7.25412 + 1.43843i) q^{65} +(2.91399 - 2.91399i) q^{66} -11.9573i q^{67} +(3.20386 + 2.59524i) q^{68} -12.2258 q^{69} +(0.295603 + 0.0589828i) q^{70} +(-12.0949 - 5.00986i) q^{71} +3.31068 q^{72} +(14.0700 + 5.82799i) q^{73} +(2.92202 - 1.21034i) q^{74} +(-0.0150102 + 12.5605i) 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} +(-2.19336 + 0.434925i) q^{80} -7.97145i q^{81} +(-1.66641 + 4.02306i) q^{82} +(-0.434038 - 0.434038i) q^{83} -0.338641 q^{84} +(4.29886 - 8.15597i) q^{85} -2.20941 q^{86} +(12.7944 + 12.7944i) q^{87} +(0.627776 - 1.51559i) q^{88} +12.1784i q^{89} +(-1.43990 - 7.26152i) 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} +(5.70178 - 8.52228i) 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	\( 20 q - 4 q^{5} + 8 q^{10} - 8 q^{11} + 24 q^{13} + 16 q^{15} - 20 q^{16} - 4 q^{20} - 8 q^{22} - 16 q^{23} + 8 q^{25} - 12 q^{26} - 24 q^{27} - 12 q^{29} + 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} + 8 q^{37} + 8 q^{38} - 4 q^{40} + 4 q^{41} - 8 q^{42} - 16 q^{43} - 8 q^{44} - 32 q^{45} + 16 q^{46} - 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} - 44 q^{53} - 24 q^{54} + 72 q^{57} + 16 q^{59} + 8 q^{60} + 8 q^{61} + 8 q^{62} + 24 q^{63} - 28 q^{65} - 8 q^{66} - 20 q^{68} - 16 q^{69} + 8 q^{71} + 28 q^{72} + 60 q^{73} + 28 q^{74} - 8 q^{78} + 56 q^{79} + 4 q^{80} - 4 q^{82} + 16 q^{84} + 84 q^{85} + 48 q^{86} + 72 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} + 8 q^{92} - 72 q^{93} + 32 q^{94} + 88 q^{95} - 48 q^{97} + 36 q^{98} + 72 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 + 8 * q^10 - 8 * q^11 + 24 * q^13 + 16 * q^15 - 20 * q^16 - 4 * q^20 - 8 * q^22 - 16 * q^23 + 8 * 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 - 32 * 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 + 8 * q^60 + 8 * q^61 + 8 * q^62 + 24 * q^63 - 28 * q^65 - 8 * q^66 - 20 * q^68 - 16 * q^69 + 8 * q^71 + 28 * q^72 + 60 * q^73 + 28 * q^74 - 8 * q^78 + 56 * q^79 + 4 * q^80 - 4 * q^82 + 16 * q^84 + 84 * q^85 + 48 * q^86 + 72 * q^87 + 8 * q^88 - 12 * q^90 - 24 * q^91 + 8 * q^92 - 72 * q^93 + 32 * q^94 + 88 * q^95 - 48 * q^97 + 36 * q^98 + 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more