LMFDB - Embedded newform 170.2.n.b.19.1

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			19.1
Root			$-2.32088 + 0.961341i$ of defining polynomial
Character	$\chi$	$=$	170.19
Dual form			170.2.n.b.9.1

$q$-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 $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

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

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	$-0.866755\pi$
$3$	−0.961341	−	2.32088i	−0.555031	−	1.33996i	0.358628	−	0.933481i	$-0.383245\pi$
$4$		−	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	0.406096	−	0.913831i	$-0.366890\pi$
$7$	0.124542	+	0.0515871i	0.0470726	+	0.0194981i	−0.359023	+	0.933329i	$0.616890\pi$
$8$	−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	0.142313	−	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	$-0.651663\pi$
$13$	−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	0.973323	−	0.229438i	$-0.0736887\pi$
$19$	3.24252	+	3.24252i	0.743886	+	0.743886i	−0.229438	+	0.973323i	$0.573689\pi$
$20$	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	−0.601948	−	0.798535i	$-0.705609\pi$
$23$	1.86243	−	4.49630i	0.388343	−	0.937543i	0.990291	−	0.139008i	$-0.0443914\pi$
$24$	−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	0.942810	+	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	0.991601	−	0.129336i	$-0.0412846\pi$
$37$	1.21034	+	2.92202i	0.198979	+	0.480377i	−0.792622	+	0.609713i	$0.791285\pi$
$38$	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	−0.738705	−	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	0.577877	−	0.816124i	$-0.303881\pi$
$43$	−1.56229	−	1.56229i	−0.238246	−	0.238246i	−0.816124	+	0.577877i	$0.803881\pi$
$44$	−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	−0.981123	−	0.193383i	$-0.938054\pi$
$53$	−5.73483	+	5.73483i	−0.787740	+	0.787740i	0.193383	+	0.981123i	$0.438054\pi$
$54$	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	$0.271904\pi$
$60$	−5.50865	+	1.09916i	−0.711164	+	0.141901i
$61$	−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
$65$	−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	$0.260669\pi$
$67$			11.9573i			1.46081i	−0.683013	+	0.730406i	$0.739331\pi$
$68$	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	−0.958677	−	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	0.649815	−	0.760093i	$-0.274847\pi$
$73$	14.0700	−	5.82799i	1.64677	−	0.682114i	0.996955	+	0.0779784i	$0.0248465\pi$
$74$	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	0.700720	−	0.713436i	$-0.252862\pi$
$79$	6.14822	+	2.54668i	0.691729	+	0.286524i	−0.00899120	+	0.999960i	$0.502862\pi$
$80$	−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	−0.730526	−	0.682885i	$-0.760725\pi$
$83$	−0.434038	+	0.434038i	−0.0476418	+	0.0476418i	0.682885	+	0.730526i	$0.260725\pi$
$84$	−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	$-0.776668\pi$
$89$		−	12.1784i		−	1.29091i	0.763799	−	0.645454i	$-0.223332\pi$
$90$	−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	−0.347714	−	0.937601i	$-0.613042\pi$
$97$	0.683508	−	0.283118i	0.0693998	−	0.0287463i	0.417113	+	0.908854i	$0.363042\pi$
$98$	−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	$0.0267670\pi$
$103$			1.70485i			0.167984i	−0.996466	+	0.0839921i	$0.973233\pi$
$104$	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	−0.554711	−	0.832043i	$-0.687171\pi$
$107$	−3.70947	+	1.53651i	−0.358608	+	0.148540i	0.196103	+	0.980583i	$0.437171\pi$
$108$	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	$-0.0234668\pi$
$110$	−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	−0.988603	−	0.150544i	$-0.951898\pi$
$113$	−1.94643	+	4.69910i	−0.183105	+	0.442054i	0.805499	+	0.592598i	$0.201898\pi$
$114$	−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	0.828044	−	0.560663i	$-0.189454\pi$
$127$	3.01322	+	3.01322i	0.267380	+	0.267380i	−0.560663	+	0.828044i	$0.689454\pi$
$128$	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	−0.921861	−	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	$0.0478936\pi$
$137$			3.50896i			0.299790i	−0.988702	+	0.149895i	$0.952106\pi$
$138$	−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
$145$	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	$-0.809397\pi$
$149$		−	13.7604i		−	1.12730i	0.826015	−	0.563648i	$-0.190603\pi$
$150$	−8.89224	−	8.87102i	−0.726049	−	0.724315i
$151$	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
$155$	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	−0.999940	−	0.0109192i	$-0.996524\pi$
$163$	−21.8922	−	9.06803i	−1.71473	−	0.710263i	−0.714786	−	0.699344i	$-0.753476\pi$
$164$	−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	0.917755	−	0.397148i	$-0.130000\pi$
$167$	−0.155358	−	0.375066i	−0.0120219	−	0.0290235i	−0.929777	+	0.368124i	$0.880000\pi$
$168$	−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	0.951966	−	0.306203i	$-0.0990587\pi$
$173$	0.819509	+	1.97847i	0.0623061	+	0.150420i	−0.889660	+	0.456623i	$0.849059\pi$
$174$		−	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	−0.710142	−	0.704058i	$-0.751369\pi$
$179$	−0.0813980	+	0.0813980i	−0.00608397	+	0.00608397i	0.704058	+	0.710142i	$0.251369\pi$
$180$	4.11651	+	6.15283i	0.306826	+	0.458605i
$181$	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
$185$	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	$0.311948\pi$
$191$			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	−0.952844	−	0.303462i	$-0.901857\pi$
$193$	−0.896081	+	2.16333i	−0.0645013	+	0.155720i	0.888342	+	0.459182i	$0.151857\pi$
$194$	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	−0.188271	−	0.982117i	$-0.560288\pi$
$197$	−14.2583	−	5.90598i	−1.01586	−	0.420783i	−0.827590	+	0.561334i	$0.810288\pi$
$198$	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
$210$	−0.421068	−	0.629358i	−0.0290564	−	0.0434298i
$211$	−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
$215$	−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	−0.226738	−	0.973956i	$-0.572806\pi$
$223$	11.1583	−	11.1583i	0.747218	−	0.747218i	0.973956	+	0.226738i	$0.0728061\pi$
$224$	−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	$0.251114\pi$
$227$	−4.45014	+	10.7436i	−0.295366	+	0.713077i	−0.999994	+	0.00350001i	$0.998886\pi$
$228$	−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	$0.0923718\pi$
$230$	−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	0.242095	−	0.970253i	$-0.422166\pi$
$233$	16.7809	−	6.95088i	1.09935	−	0.455367i	0.857259	+	0.514885i	$0.172166\pi$
$234$		−	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	−0.103922	−	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
$245$	−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	$-0.918369\pi$
$251$		−	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
$255$	14.7964	−	17.8178i	0.926586	−	1.11579i
$256$	1.00000			0.0625000
$257$	9.70776	−	9.70776i	0.605553	−	0.605553i	−0.336228	−	0.941781i	$-0.609151\pi$
$257$	9.70776	−	9.70776i	0.605553	−	0.605553i	0.941781	+	0.336228i	$0.109151\pi$
$258$	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	0.559134	−	0.829078i	$-0.311134\pi$
$263$	−4.37776	−	4.37776i	−0.269944	−	0.269944i	−0.829078	+	0.559134i	$0.811134\pi$
$264$	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	0.189224	−	0.981934i	$-0.439403\pi$
$269$	16.6859	−	6.91153i	1.01736	−	0.421403i	0.828134	+	0.560530i	$0.189403\pi$
$270$	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	−0.0430590	−	0.999073i	$-0.513710\pi$
$277$	10.5343	−	4.36345i	0.632945	−	0.262174i	0.676004	+	0.736898i	$0.263710\pi$
$278$	−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	0.321559	−	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	$-0.572844\pi$
$283$	10.4675	−	25.2708i	0.622228	−	1.50219i	0.849081	−	0.528262i	$-0.177156\pi$
$284$	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	$0.0924658\pi$
$307$			10.0370i			0.572843i	−0.958104	+	0.286422i	$0.907534\pi$
$308$	−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	0.0540497	−	0.998538i	$-0.482787\pi$
$313$	−10.8593	−	4.49807i	−0.613804	−	0.254246i	−0.667854	+	0.744292i	$0.732787\pi$
$314$	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	0.526130	+	0.850404i	$0.323642\pi$
$317$	−7.96264	+	19.2235i	−0.447226	+	1.07970i	−0.973357	+	0.229296i	$0.926358\pi$
$318$	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	−0.819553	−	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
$335$	−5.20051	+	26.2266i	−0.284134	+	1.43291i
$336$			0.338641i			0.0184744i
$337$	−6.61231	−	15.9635i	−0.360196	−	0.869589i	−0.995271	−	0.0971388i	$-0.969031\pi$
$337$	−6.61231	−	15.9635i	−0.360196	−	0.869589i	0.635075	−	0.772450i	$-0.280969\pi$
$338$	−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	0.994122	−	0.108270i	$-0.0345310\pi$
$347$	30.1868	+	12.5038i	1.62051	+	0.671239i	0.626392	+	0.779508i	$0.284531\pi$
$348$	−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	$0.496616\pi$
$350$	0.674018		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	0.911597	−	0.411086i	$-0.134850\pi$
$359$	9.48333	+	9.48333i	0.500511	+	0.500511i	−0.411086	+	0.911597i	$0.634850\pi$
$360$	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	0.639143	−	0.769088i	$-0.279289\pi$
$367$	10.4840	+	4.34261i	0.547259	+	0.226682i	−0.0918843	+	0.995770i	$0.529289\pi$
$368$	−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	$-0.915479\pi$
$373$		−	10.1364i		−	0.524842i	0.964953	−	0.262421i	$-0.0845210\pi$
$374$	−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	$-0.420389\pi$
$380$	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	0.999995	−	0.00331356i	$-0.00105474\pi$
$383$	19.5054	+	19.5054i	0.996681	+	0.996681i	−0.00331356	+	0.999995i	$0.501055\pi$
$384$	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	0.981495	+	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	$-0.711839\pi$
$397$	7.47899	−	18.0559i	0.375360	−	0.906198i	0.992822	−	0.119598i	$-0.0381606\pi$
$398$	−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	−0.926676	−	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
$405$	−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	0.601720	−	0.798707i	$-0.294482\pi$
$419$	9.46569	+	3.92082i	0.462429	+	0.191544i	−0.139291	+	0.990252i	$0.544482\pi$
$420$	−0.742763	−	0.147283i	−0.0362431	−	0.00718670i
$421$			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
$425$	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	0.205791	−	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	0.880110	−	0.474770i	$-0.157469\pi$
$433$	8.43456	+	8.43456i	0.405339	+	0.405339i	−0.474770	+	0.880110i	$0.657469\pi$
$434$	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	−0.747571	−	0.664182i	$-0.768780\pi$
$439$	−16.8988	+	6.99971i	−0.806535	+	0.334078i	−0.0589645	+	0.998260i	$0.518780\pi$
$440$	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	$-0.885532\pi$
$443$		−	14.8138i		−	0.703824i	0.936033	−	0.351912i	$-0.114468\pi$
$444$	−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	−0.980847	−	0.194780i	$-0.937601\pi$
$449$	−3.16897	+	7.65057i	−0.149553	+	0.361053i	0.831294	+	0.555833i	$0.187601\pi$
$450$	−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	0.0204820	−	0.999790i	$-0.493480\pi$
$457$	21.8109	−	21.8109i	1.02027	−	1.02027i	0.999790	−	0.0204820i	$-0.00652007\pi$
$458$		−	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	$-0.467809\pi$
$463$	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	0.575660	−	0.817689i	$-0.304745\pi$
$467$	−5.23030	−	5.23030i	−0.242029	−	0.242029i	−0.817689	+	0.575660i	$0.804745\pi$
$468$	−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	−0.752896	−	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
$485$	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	−0.997801	−	0.0662754i	$-0.978888\pi$
$487$	−5.41519	+	13.0734i	−0.245385	+	0.592413i	0.752416	+	0.658688i	$0.228888\pi$
$488$	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	0.923572	−	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
$495$	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	0.436588	−	0.899662i	$-0.356187\pi$
$499$	2.43813	+	1.00991i	0.109146	+	0.0452096i	−0.327442	+	0.944871i	$0.606187\pi$
$500$	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	0.421931	−	0.906628i	$-0.361352\pi$
$503$	1.77624	+	0.735741i	0.0791984	+	0.0328051i	−0.342733	+	0.939433i	$0.611352\pi$
$504$	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	−0.658724	−	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	$-0.560277\pi$
$523$	−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	−0.878606	−	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	$-0.975748\pi$
$547$	−8.08911	−	19.5288i	−0.345865	−	0.834993i	0.651234	−	0.758877i	$-0.274252\pi$
$548$	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	−0.503120	−	0.864217i	$-0.667815\pi$
$563$	8.56797	−	8.56797i	0.361097	−	0.361097i	0.864217	+	0.503120i	$0.167815\pi$
$564$	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	$0.242701\pi$
$570$	−5.04033	−	25.2606i	−0.211116	−	1.05805i
$571$	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
$575$	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	$0.192554\pi$
$577$			27.3213i			1.13740i	−0.822545	+	0.568701i	$0.807446\pi$
$578$	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	−0.938324	−	0.345757i	$-0.887622\pi$
$587$	−31.1108	−	31.1108i	−1.28408	−	1.28408i	−0.345757	−	0.938324i	$-0.612378\pi$
$588$	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	−0.735677	−	0.677332i	$-0.763136\pi$
$593$	−1.42079	+	1.42079i	−0.0583449	+	0.0583449i	0.677332	+	0.735677i	$0.263136\pi$
$594$	−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	$0.0553379\pi$
$599$			8.46693i			0.345949i	−0.984926	+	0.172975i	$0.944662\pi$
$600$	−8.87102	+	8.89224i	−0.362158	+	0.363024i
$601$	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
$605$	−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	−0.216246	−	0.976339i	$-0.569381\pi$
$607$	7.91404	−	3.27810i	0.321221	−	0.133054i	0.537467	+	0.843285i	$0.319381\pi$
$608$	−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	$0.329139\pi$
$613$			42.5536i			1.71873i	−0.511367	+	0.859363i	$0.670861\pi$
$614$	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	−0.993602	−	0.112935i	$-0.963975\pi$
$617$	−40.1488	+	16.6302i	−1.61633	+	0.669505i	−0.622726	+	0.782440i	$0.713975\pi$
$618$	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	$-0.0290541\pi$
$620$	−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	0.0570526	−	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
$635$	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	0.975426	−	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	0.997101	−	0.0760849i	$-0.0242420\pi$
$643$	6.04126	+	14.5849i	0.238244	+	0.575172i	−0.758857	+	0.651257i	$0.774242\pi$
$644$	−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	$0.0342714\pi$
$647$			5.46670i			0.214918i	−0.994210	+	0.107459i	$0.965729\pi$
$648$	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	0.393357	−	0.919386i	$-0.371314\pi$
$653$	0.546789	+	0.226487i	0.0213975	+	0.00886313i	−0.371959	+	0.928249i	$0.621314\pi$
$654$	−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	$-0.872543\pi$
$659$		−	20.0132i		−	0.779606i	0.920898	−	0.389803i	$-0.127457\pi$
$660$	9.03886	+	1.79233i	0.351837	+	0.0697662i
$661$	−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
$665$	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	0.580187	−	0.814484i	$-0.302980\pi$
$673$	10.7534	+	4.45421i	0.414514	+	0.171697i	−0.165673	+	0.986181i	$0.552980\pi$
$674$	−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	0.747337	−	0.664445i	$-0.231332\pi$
$677$	−6.52935	−	15.7632i	−0.250943	−	0.605831i	−0.998281	+	0.0586141i	$0.981332\pi$
$678$	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	0.842701	−	0.538381i	$-0.180964\pi$
$683$	−3.49863	−	8.44645i	−0.133871	−	0.323194i	−0.976573	+	0.215187i	$0.930964\pi$
$684$			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	0.570755	−	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
$695$	−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	$-0.943664\pi$
$701$		−	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
$705$	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	0.980483	−	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	$-0.351162\pi$
$720$	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	−0.211994	+	0.977271i	$0.567996\pi$
$733$	−32.1981	+	32.1981i	−1.18926	+	1.18926i	−0.977271	+	0.211994i	$0.932004\pi$
$734$	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	$0.484269\pi$
$740$	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	−0.0212172	−	0.999775i	$-0.506754\pi$
$743$	18.2827	−	7.57295i	0.670728	−	0.277824i	0.691945	+	0.721950i	$0.256754\pi$
$744$			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	0.699207	−	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
$755$	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	0.907503	−	0.420045i	$-0.137986\pi$
$757$	13.4117	+	13.4117i	0.487458	+	0.487458i	−0.420045	+	0.907503i	$0.637986\pi$
$758$	−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	$-0.709800\pi$
$761$		−	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
$765$	−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	$-0.907322\pi$
$769$		−	15.9208i		−	0.574118i	0.957913	−	0.287059i	$-0.0926777\pi$
$770$	−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	0.00863410	−	0.999963i	$-0.497252\pi$
$773$	−27.5618	−	27.5618i	−0.991329	−	0.991329i	−0.999963	+	0.00863410i	$0.997252\pi$
$774$	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	0.306438	−	0.951891i	$-0.400863\pi$
$787$	33.5579	−	13.9001i	1.19621	−	0.495486i	0.889772	+	0.456404i	$0.150863\pi$
$788$	−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	−0.615559	−	0.788091i	$-0.711070\pi$
$797$	4.87076	−	4.87076i	0.172531	−	0.172531i	0.788091	+	0.615559i	$0.211070\pi$
$798$		−	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	−0.937801	−	0.347172i	$-0.887142\pi$
$809$	−0.830184	+	2.00424i	−0.0291877	+	0.0704653i	0.908614	+	0.417638i	$0.137142\pi$
$810$	9.91173	+	14.8148i	0.348263	+	0.520538i
$811$	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	0.0456669	−	0.998957i	$-0.485459\pi$
$823$	−18.0278	−	7.46737i	−0.628411	−	0.260296i	−0.674078	+	0.738660i	$0.735459\pi$
$824$	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	−0.919784	−	0.392425i	$-0.871636\pi$
$827$	0.232580	−	0.561498i	0.00808760	−	0.0195252i	0.927872	+	0.372899i	$0.121636\pi$
$828$	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	$0.942662\pi$
$830$	−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	0.829474	−	0.558546i	$-0.188640\pi$
$839$	29.5752	+	12.2504i	1.02105	+	0.422932i	0.191575	+	0.981478i	$0.438640\pi$
$840$	−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	0.988996	+	0.147944i	$0.0472654\pi$
$853$	11.5155	+	27.8008i	0.394282	+	0.951881i	−0.594714	+	0.803938i	$0.702735\pi$
$854$			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	0.405326	−	0.914172i	$-0.367158\pi$
$857$	1.33250	+	0.551941i	0.0455175	+	0.0188539i	−0.359809	+	0.933026i	$0.617158\pi$
$858$	−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	$0.200056\pi$
$860$	−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	−0.386370	−	0.922344i	$-0.626271\pi$
$877$	−38.8470	−	16.0910i	−1.31177	−	0.543353i	−0.925400	+	0.378991i	$0.876271\pi$
$878$	−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	$-0.971137\pi$
$883$		−	5.38161i		−	0.181106i	0.995892	−	0.0905528i	$-0.0288634\pi$
$884$	−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	$0.0614776\pi$
$887$	12.6030	+	30.4264i	0.423169	+	1.02162i	−0.558238	+	0.829681i	$0.688522\pi$
$888$	−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	0.424820	+	0.905278i	$0.360337\pi$
$907$	−15.5311	+	37.4954i	−0.515701	+	1.24501i	−0.940521	+	0.339735i	$0.889663\pi$
$908$	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	−0.971685	−	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
$915$	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	−0.316152	−	0.948709i	$-0.602391\pi$
$929$	−36.8967	−	15.2831i	−1.21054	−	0.501423i	−0.894391	+	0.447285i	$0.852391\pi$
$930$	−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	−0.288979	−	0.957335i	$-0.593316\pi$
$937$	20.4587	−	20.4587i	0.668357	−	0.668357i	0.957335	+	0.288979i	$0.0933157\pi$
$938$	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	0.858493	−	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
$945$	0.130816	+	0.195527i	0.00425545	+	0.00636050i
$946$	3.34854	+	1.38701i	0.108871	+	0.0450957i
$947$	48.7002	−	20.1723i	1.58254	−	0.655512i	0.593731	−	0.804664i	$-0.297654\pi$
$947$	48.7002	−	20.1723i	1.58254	−	0.655512i	0.988814	+	0.149152i	$0.0476545\pi$
$948$	−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	$-0.947074\pi$
$953$		−	10.2185i		−	0.331011i	0.986209	−	0.165506i	$-0.0529256\pi$
$954$	−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	−0.356943	−	0.934126i	$-0.616181\pi$
$967$	17.9484	−	17.9484i	0.577183	−	0.577183i	0.934126	+	0.356943i	$0.116181\pi$
$968$			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
$975$	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	0.981287	−	0.192552i	$-0.0616765\pi$
$977$	24.6535	+	24.6535i	0.788735	+	0.788735i	−0.192552	+	0.981287i	$0.561676\pi$
$978$	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	0.766585	+	0.642143i	$0.221954\pi$
$983$	21.2758	+	51.3642i	0.678591	+	1.63826i	−0.0879937	+	0.996121i	$0.528046\pi$
$984$	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
$995$	−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	−0.879753	−	0.475431i	$-0.842292\pi$
$997$	2.47887	−	5.98452i	0.0785066	−	0.189532i	0.958260	+	0.285899i	$0.0922922\pi$
$998$	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.19.1	yes	20
5.2	odd	4		850.2.l.i.801.1		20
5.3	odd	4		850.2.l.h.801.5		20
5.4	even	2		170.2.n.a.19.5	yes	20
17.9	even	8		170.2.n.a.9.5	✓	20
85.9	even	8	inner	170.2.n.b.9.1	yes	20
85.43	odd	8		850.2.l.h.451.5		20
85.77	odd	8		850.2.l.i.451.1		20

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.961341 - 2.32088i) q^{3} -1.00000i q^{4} +(2.19336 + 0.434925i) q^{5} +(-2.32088 - 0.961341i) q^{6} +(0.124542 + 0.0515871i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.34100 + 2.34100i) q^{9} +O(q^{10})\)	\(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

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