LMFDB - Embedded newform 170.2.d.a.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(169,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("170.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.d (of order $2$, degree $1$, 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:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			169.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	170.169
Dual form			170.2.d.a.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +1.00000i q^{6} -2.00000 q^{7} +1.00000i q^{8} -2.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +1.00000i q^{6} -2.00000 q^{7} +1.00000i q^{8} -2.00000 q^{9} +(-1.00000 + 2.00000i) q^{10} +1.00000 q^{12} -1.00000i q^{13} +2.00000i q^{14} +(2.00000 + 1.00000i) q^{15} +1.00000 q^{16} +(-1.00000 - 4.00000i) q^{17} +2.00000i q^{18} -5.00000 q^{19} +(2.00000 + 1.00000i) q^{20} +2.00000 q^{21} +4.00000 q^{23} -1.00000i q^{24} +(3.00000 + 4.00000i) q^{25} -1.00000 q^{26} +5.00000 q^{27} +2.00000 q^{28} -9.00000i q^{29} +(1.00000 - 2.00000i) q^{30} +5.00000i q^{31} -1.00000i q^{32} +(-4.00000 + 1.00000i) q^{34} +(4.00000 + 2.00000i) q^{35} +2.00000 q^{36} -2.00000 q^{37} +5.00000i q^{38} +1.00000i q^{39} +(1.00000 - 2.00000i) q^{40} -10.0000i q^{41} -2.00000i q^{42} -6.00000i q^{43} +(4.00000 + 2.00000i) q^{45} -4.00000i q^{46} +7.00000i q^{47} -1.00000 q^{48} -3.00000 q^{49} +(4.00000 - 3.00000i) q^{50} +(1.00000 + 4.00000i) q^{51} +1.00000i q^{52} -1.00000i q^{53} -5.00000i q^{54} -2.00000i q^{56} +5.00000 q^{57} -9.00000 q^{58} -5.00000 q^{59} +(-2.00000 - 1.00000i) q^{60} +5.00000i q^{61} +5.00000 q^{62} +4.00000 q^{63} -1.00000 q^{64} +(-1.00000 + 2.00000i) q^{65} +2.00000i q^{67} +(1.00000 + 4.00000i) q^{68} -4.00000 q^{69} +(2.00000 - 4.00000i) q^{70} +5.00000i q^{71} -2.00000i q^{72} -11.0000 q^{73} +2.00000i q^{74} +(-3.00000 - 4.00000i) q^{75} +5.00000 q^{76} +1.00000 q^{78} +16.0000i q^{79} +(-2.00000 - 1.00000i) q^{80} +1.00000 q^{81} -10.0000 q^{82} -6.00000i q^{83} -2.00000 q^{84} +(-2.00000 + 9.00000i) q^{85} -6.00000 q^{86} +9.00000i q^{87} +5.00000 q^{89} +(2.00000 - 4.00000i) q^{90} +2.00000i q^{91} -4.00000 q^{92} -5.00000i q^{93} +7.00000 q^{94} +(10.0000 + 5.00000i) q^{95} +1.00000i q^{96} -7.00000 q^{97} +3.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 2 q^{4} - 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 - 2 * q^4 - 4 * q^5 - 4 * q^7 - 4 * q^9	$ 2 q - 2 q^{3} - 2 q^{4} - 4 q^{5} - 4 q^{7} - 4 q^{9} - 2 q^{10} + 2 q^{12} + 4 q^{15} + 2 q^{16} - 2 q^{17} - 10 q^{19} + 4 q^{20} + 4 q^{21} + 8 q^{23} + 6 q^{25} - 2 q^{26} + 10 q^{27} + 4 q^{28} + 2 q^{30} - 8 q^{34} + 8 q^{35} + 4 q^{36} - 4 q^{37} + 2 q^{40} + 8 q^{45} - 2 q^{48} - 6 q^{49} + 8 q^{50} + 2 q^{51} + 10 q^{57} - 18 q^{58} - 10 q^{59} - 4 q^{60} + 10 q^{62} + 8 q^{63} - 2 q^{64} - 2 q^{65} + 2 q^{68} - 8 q^{69} + 4 q^{70} - 22 q^{73} - 6 q^{75} + 10 q^{76} + 2 q^{78} - 4 q^{80} + 2 q^{81} - 20 q^{82} - 4 q^{84} - 4 q^{85} - 12 q^{86} + 10 q^{89} + 4 q^{90} - 8 q^{92} + 14 q^{94} + 20 q^{95} - 14 q^{97}+O(q^{100}) $ 2 * q - 2 * q^3 - 2 * q^4 - 4 * q^5 - 4 * q^7 - 4 * q^9 - 2 * q^10 + 2 * q^12 + 4 * q^15 + 2 * q^16 - 2 * q^17 - 10 * q^19 + 4 * q^20 + 4 * q^21 + 8 * q^23 + 6 * q^25 - 2 * q^26 + 10 * q^27 + 4 * q^28 + 2 * q^30 - 8 * q^34 + 8 * q^35 + 4 * q^36 - 4 * q^37 + 2 * q^40 + 8 * q^45 - 2 * q^48 - 6 * q^49 + 8 * q^50 + 2 * q^51 + 10 * q^57 - 18 * q^58 - 10 * q^59 - 4 * q^60 + 10 * q^62 + 8 * q^63 - 2 * q^64 - 2 * q^65 + 2 * q^68 - 8 * q^69 + 4 * q^70 - 22 * q^73 - 6 * q^75 + 10 * q^76 + 2 * q^78 - 4 * q^80 + 2 * q^81 - 20 * q^82 - 4 * q^84 - 4 * q^85 - 12 * q^86 + 10 * q^89 + 4 * q^90 - 8 * q^92 + 14 * q^94 + 20 * q^95 - 14 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$71$	$137$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.00000			−0.577350			−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000			−0.577350			−0.288675	+	0.957427i	$0.593215\pi$
$4$	−1.00000			−0.500000
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$			1.00000i			0.408248i
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$			1.00000i			0.353553i
$9$	−2.00000			−0.666667
$10$	−1.00000	+	2.00000i	−0.316228	+	0.632456i
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$	1.00000			0.288675
$13$		−	1.00000i		−	0.277350i	−0.990338	−	0.138675i	$-0.955716\pi$
$13$		−	1.00000i		−	0.277350i	0.990338	−	0.138675i	$-0.0442844\pi$
$14$			2.00000i			0.534522i
$15$	2.00000	+	1.00000i	0.516398	+	0.258199i
$16$	1.00000			0.250000
$17$	−1.00000	−	4.00000i	−0.242536	−	0.970143i
$17$	−1.00000	−	4.00000i	−0.242536	−	0.970143i
$18$			2.00000i			0.471405i
$19$	−5.00000			−1.14708			−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000			−1.14708			−0.573539	+	0.819178i	$0.694430\pi$
$20$	2.00000	+	1.00000i	0.447214	+	0.223607i
$21$	2.00000			0.436436
$22$		0			0
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$		−	1.00000i		−	0.204124i
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	−1.00000			−0.196116
$27$	5.00000			0.962250
$28$	2.00000			0.377964
$29$		−	9.00000i		−	1.67126i	−0.549294	−	0.835629i	$-0.685103\pi$
$29$		−	9.00000i		−	1.67126i	0.549294	−	0.835629i	$-0.314897\pi$
$30$	1.00000	−	2.00000i	0.182574	−	0.365148i
$31$			5.00000i			0.898027i	0.893525	+	0.449013i	$0.148224\pi$
$31$			5.00000i			0.898027i	−0.893525	+	0.449013i	$0.851776\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−4.00000	+	1.00000i	−0.685994	+	0.171499i
$35$	4.00000	+	2.00000i	0.676123	+	0.338062i
$36$	2.00000			0.333333
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$			5.00000i			0.811107i
$39$			1.00000i			0.160128i
$40$	1.00000	−	2.00000i	0.158114	−	0.316228i
$41$		−	10.0000i		−	1.56174i	−0.624695	−	0.780869i	$-0.714777\pi$
$41$		−	10.0000i		−	1.56174i	0.624695	−	0.780869i	$-0.285223\pi$
$42$		−	2.00000i		−	0.308607i
$43$		−	6.00000i		−	0.914991i	−0.889212	−	0.457496i	$-0.848747\pi$
$43$		−	6.00000i		−	0.914991i	0.889212	−	0.457496i	$-0.151253\pi$
$44$		0			0
$45$	4.00000	+	2.00000i	0.596285	+	0.298142i
$46$		−	4.00000i		−	0.589768i
$47$			7.00000i			1.02105i	0.859861	+	0.510527i	$0.170550\pi$
$47$			7.00000i			1.02105i	−0.859861	+	0.510527i	$0.829450\pi$
$48$	−1.00000			−0.144338
$49$	−3.00000			−0.428571
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$	1.00000	+	4.00000i	0.140028	+	0.560112i
$52$			1.00000i			0.138675i
$53$		−	1.00000i		−	0.137361i	−0.997639	−	0.0686803i	$-0.978121\pi$
$53$		−	1.00000i		−	0.137361i	0.997639	−	0.0686803i	$-0.0218788\pi$
$54$		−	5.00000i		−	0.680414i
$55$		0			0
$56$		−	2.00000i		−	0.267261i
$57$	5.00000			0.662266
$58$	−9.00000			−1.18176
$59$	−5.00000			−0.650945			−0.325472	−	0.945552i	$-0.605523\pi$
$59$	−5.00000			−0.650945			−0.325472	+	0.945552i	$0.605523\pi$
$60$	−2.00000	−	1.00000i	−0.258199	−	0.129099i
$61$			5.00000i			0.640184i	0.947386	+	0.320092i	$0.103714\pi$
$61$			5.00000i			0.640184i	−0.947386	+	0.320092i	$0.896286\pi$
$62$	5.00000			0.635001
$63$	4.00000			0.503953
$64$	−1.00000			−0.125000
$65$	−1.00000	+	2.00000i	−0.124035	+	0.248069i
$66$		0			0
$67$			2.00000i			0.244339i	0.992509	+	0.122169i	$0.0389851\pi$
$67$			2.00000i			0.244339i	−0.992509	+	0.122169i	$0.961015\pi$
$68$	1.00000	+	4.00000i	0.121268	+	0.485071i
$69$	−4.00000			−0.481543
$70$	2.00000	−	4.00000i	0.239046	−	0.478091i
$71$			5.00000i			0.593391i	0.954972	+	0.296695i	$0.0958846\pi$
$71$			5.00000i			0.593391i	−0.954972	+	0.296695i	$0.904115\pi$
$72$		−	2.00000i		−	0.235702i
$73$	−11.0000			−1.28745			−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000			−1.28745			−0.643726	+	0.765256i	$0.722612\pi$
$74$			2.00000i			0.232495i
$75$	−3.00000	−	4.00000i	−0.346410	−	0.461880i
$76$	5.00000			0.573539
$77$		0			0
$78$	1.00000			0.113228
$79$			16.0000i			1.80014i	0.435745	+	0.900070i	$0.356485\pi$
$79$			16.0000i			1.80014i	−0.435745	+	0.900070i	$0.643515\pi$
$80$	−2.00000	−	1.00000i	−0.223607	−	0.111803i
$81$	1.00000			0.111111
$82$	−10.0000			−1.10432
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$	−2.00000			−0.218218
$85$	−2.00000	+	9.00000i	−0.216930	+	0.976187i
$86$	−6.00000			−0.646997
$87$			9.00000i			0.964901i
$88$		0			0
$89$	5.00000			0.529999			0.264999	−	0.964249i	$-0.414628\pi$
$89$	5.00000			0.529999			0.264999	+	0.964249i	$0.414628\pi$
$90$	2.00000	−	4.00000i	0.210819	−	0.421637i
$91$			2.00000i			0.209657i
$92$	−4.00000			−0.417029
$93$		−	5.00000i		−	0.518476i
$94$	7.00000			0.721995
$95$	10.0000	+	5.00000i	1.02598	+	0.512989i
$96$			1.00000i			0.102062i
$97$	−7.00000			−0.710742			−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000			−0.710742			−0.355371	+	0.934725i	$0.615646\pi$
$98$			3.00000i			0.303046i
$99$		0			0
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$	−8.00000			−0.796030			−0.398015	−	0.917379i	$-0.630301\pi$
$101$	−8.00000			−0.796030			−0.398015	+	0.917379i	$0.630301\pi$
$102$	4.00000	−	1.00000i	0.396059	−	0.0990148i
$103$		−	16.0000i		−	1.57653i	−0.615338	−	0.788263i	$-0.710980\pi$
$103$		−	16.0000i		−	1.57653i	0.615338	−	0.788263i	$-0.289020\pi$
$104$	1.00000			0.0980581
$105$	−4.00000	−	2.00000i	−0.390360	−	0.195180i
$106$	−1.00000			−0.0971286
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$	−5.00000			−0.481125
$109$		−	9.00000i		−	0.862044i	−0.902342	−	0.431022i	$-0.858153\pi$
$109$		−	9.00000i		−	0.862044i	0.902342	−	0.431022i	$-0.141847\pi$
$110$		0			0
$111$	2.00000			0.189832
$112$	−2.00000			−0.188982
$113$	9.00000			0.846649			0.423324	−	0.905978i	$-0.360863\pi$
$113$	9.00000			0.846649			0.423324	+	0.905978i	$0.360863\pi$
$114$		−	5.00000i		−	0.468293i
$115$	−8.00000	−	4.00000i	−0.746004	−	0.373002i
$116$			9.00000i			0.835629i
$117$			2.00000i			0.184900i
$118$			5.00000i			0.460287i
$119$	2.00000	+	8.00000i	0.183340	+	0.733359i
$120$	−1.00000	+	2.00000i	−0.0912871	+	0.182574i
$121$	11.0000			1.00000
$122$	5.00000			0.452679
$123$			10.0000i			0.901670i
$124$		−	5.00000i		−	0.449013i
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		−	4.00000i		−	0.356348i
$127$			7.00000i			0.621150i	0.950549	+	0.310575i	$0.100522\pi$
$127$			7.00000i			0.621150i	−0.950549	+	0.310575i	$0.899478\pi$
$128$			1.00000i			0.0883883i
$129$			6.00000i			0.528271i
$130$	2.00000	+	1.00000i	0.175412	+	0.0877058i
$131$		−	20.0000i		−	1.74741i	−0.486458	−	0.873704i	$-0.661711\pi$
$131$		−	20.0000i		−	1.74741i	0.486458	−	0.873704i	$-0.338289\pi$
$132$		0			0
$133$	10.0000			0.867110
$134$	2.00000			0.172774
$135$	−10.0000	−	5.00000i	−0.860663	−	0.430331i
$136$	4.00000	−	1.00000i	0.342997	−	0.0857493i
$137$			2.00000i			0.170872i	0.996344	+	0.0854358i	$0.0272282\pi$
$137$			2.00000i			0.170872i	−0.996344	+	0.0854358i	$0.972772\pi$
$138$			4.00000i			0.340503i
$139$		−	14.0000i		−	1.18746i	−0.804663	−	0.593732i	$-0.797654\pi$
$139$		−	14.0000i		−	1.18746i	0.804663	−	0.593732i	$-0.202346\pi$
$140$	−4.00000	−	2.00000i	−0.338062	−	0.169031i
$141$		−	7.00000i		−	0.589506i
$142$	5.00000			0.419591
$143$		0			0
$144$	−2.00000			−0.166667
$145$	−9.00000	+	18.0000i	−0.747409	+	1.49482i
$146$			11.0000i			0.910366i
$147$	3.00000			0.247436
$148$	2.00000			0.164399
$149$	20.0000			1.63846			0.819232	−	0.573462i	$-0.194400\pi$
$149$	20.0000			1.63846			0.819232	+	0.573462i	$0.194400\pi$
$150$	−4.00000	+	3.00000i	−0.326599	+	0.244949i
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$		−	5.00000i		−	0.405554i
$153$	2.00000	+	8.00000i	0.161690	+	0.646762i
$154$		0			0
$155$	5.00000	−	10.0000i	0.401610	−	0.803219i
$156$		−	1.00000i		−	0.0800641i
$157$		−	18.0000i		−	1.43656i	−0.695756	−	0.718278i	$-0.744931\pi$
$157$		−	18.0000i		−	1.43656i	0.695756	−	0.718278i	$-0.255069\pi$
$158$	16.0000			1.27289
$159$			1.00000i			0.0793052i
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$	−8.00000			−0.630488
$162$		−	1.00000i		−	0.0785674i
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$			10.0000i			0.780869i
$165$		0			0
$166$	−6.00000			−0.465690
$167$	18.0000			1.39288			0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000			1.39288			0.696441	+	0.717614i	$0.254766\pi$
$168$			2.00000i			0.154303i
$169$	12.0000			0.923077
$170$	9.00000	+	2.00000i	0.690268	+	0.153393i
$171$	10.0000			0.764719
$172$			6.00000i			0.457496i
$173$	−16.0000			−1.21646			−0.608229	−	0.793762i	$-0.708120\pi$
$173$	−16.0000			−1.21646			−0.608229	+	0.793762i	$0.708120\pi$
$174$	9.00000			0.682288
$175$	−6.00000	−	8.00000i	−0.453557	−	0.604743i
$176$		0			0
$177$	5.00000			0.375823
$178$		−	5.00000i		−	0.374766i
$179$	20.0000			1.49487			0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000			1.49487			0.747435	+	0.664335i	$0.231285\pi$
$180$	−4.00000	−	2.00000i	−0.298142	−	0.149071i
$181$			10.0000i			0.743294i	0.928374	+	0.371647i	$0.121207\pi$
$181$			10.0000i			0.743294i	−0.928374	+	0.371647i	$0.878793\pi$
$182$	2.00000			0.148250
$183$		−	5.00000i		−	0.369611i
$184$			4.00000i			0.294884i
$185$	4.00000	+	2.00000i	0.294086	+	0.147043i
$186$	−5.00000			−0.366618
$187$		0			0
$188$		−	7.00000i		−	0.510527i
$189$	−10.0000			−0.727393
$190$	5.00000	−	10.0000i	0.362738	−	0.725476i
$191$	−18.0000			−1.30243			−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000			−1.30243			−0.651217	+	0.758891i	$0.725741\pi$
$192$	1.00000			0.0721688
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$			7.00000i			0.502571i
$195$	1.00000	−	2.00000i	0.0716115	−	0.143223i
$196$	3.00000			0.214286
$197$	8.00000			0.569976			0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000			0.569976			0.284988	+	0.958531i	$0.408010\pi$
$198$		0			0
$199$			1.00000i			0.0708881i	0.999372	+	0.0354441i	$0.0112846\pi$
$199$			1.00000i			0.0708881i	−0.999372	+	0.0354441i	$0.988715\pi$
$200$	−4.00000	+	3.00000i	−0.282843	+	0.212132i
$201$		−	2.00000i		−	0.141069i
$202$			8.00000i			0.562878i
$203$			18.0000i			1.26335i
$204$	−1.00000	−	4.00000i	−0.0700140	−	0.280056i
$205$	−10.0000	+	20.0000i	−0.698430	+	1.39686i
$206$	−16.0000			−1.11477
$207$	−8.00000			−0.556038
$208$		−	1.00000i		−	0.0693375i
$209$		0			0
$210$	−2.00000	+	4.00000i	−0.138013	+	0.276026i
$211$		−	20.0000i		−	1.37686i	−0.725304	−	0.688428i	$-0.758301\pi$
$211$		−	20.0000i		−	1.37686i	0.725304	−	0.688428i	$-0.241699\pi$
$212$			1.00000i			0.0686803i
$213$		−	5.00000i		−	0.342594i
$214$			12.0000i			0.820303i
$215$	−6.00000	+	12.0000i	−0.409197	+	0.818393i
$216$			5.00000i			0.340207i
$217$		−	10.0000i		−	0.678844i
$218$	−9.00000			−0.609557
$219$	11.0000			0.743311
$220$		0			0
$221$	−4.00000	+	1.00000i	−0.269069	+	0.0672673i
$222$		−	2.00000i		−	0.134231i
$223$			9.00000i			0.602685i	0.953516	+	0.301342i	$0.0974347\pi$
$223$			9.00000i			0.602685i	−0.953516	+	0.301342i	$0.902565\pi$
$224$			2.00000i			0.133631i
$225$	−6.00000	−	8.00000i	−0.400000	−	0.533333i
$226$		−	9.00000i		−	0.598671i
$227$	−27.0000			−1.79205			−0.896026	−	0.444001i	$-0.853559\pi$
$227$	−27.0000			−1.79205			−0.896026	+	0.444001i	$0.853559\pi$
$228$	−5.00000			−0.331133
$229$		0			0			−	1.00000i	$-0.5\pi$
$229$		0			0				1.00000i	$0.5\pi$
$230$	−4.00000	+	8.00000i	−0.263752	+	0.527504i
$231$		0			0
$232$	9.00000			0.590879
$233$	−21.0000			−1.37576			−0.687878	−	0.725826i	$-0.741458\pi$
$233$	−21.0000			−1.37576			−0.687878	+	0.725826i	$0.741458\pi$
$234$	2.00000			0.130744
$235$	7.00000	−	14.0000i	0.456630	−	0.913259i
$236$	5.00000			0.325472
$237$		−	16.0000i		−	1.03931i
$238$	8.00000	−	2.00000i	0.518563	−	0.129641i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	2.00000	+	1.00000i	0.129099	+	0.0645497i
$241$			10.0000i			0.644157i	0.946713	+	0.322078i	$0.104381\pi$
$241$			10.0000i			0.644157i	−0.946713	+	0.322078i	$0.895619\pi$
$242$		−	11.0000i		−	0.707107i
$243$	−16.0000			−1.02640
$244$		−	5.00000i		−	0.320092i
$245$	6.00000	+	3.00000i	0.383326	+	0.191663i
$246$	10.0000			0.637577
$247$			5.00000i			0.318142i
$248$	−5.00000			−0.317500
$249$			6.00000i			0.380235i
$250$	−11.0000	+	2.00000i	−0.695701	+	0.126491i
$251$	−8.00000			−0.504956			−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000			−0.504956			−0.252478	+	0.967603i	$0.581245\pi$
$252$	−4.00000			−0.251976
$253$		0			0
$254$	7.00000			0.439219
$255$	2.00000	−	9.00000i	0.125245	−	0.563602i
$256$	1.00000			0.0625000
$257$		−	18.0000i		−	1.12281i	−0.827541	−	0.561405i	$-0.810261\pi$
$257$		−	18.0000i		−	1.12281i	0.827541	−	0.561405i	$-0.189739\pi$
$258$	6.00000			0.373544
$259$	4.00000			0.248548
$260$	1.00000	−	2.00000i	0.0620174	−	0.124035i
$261$			18.0000i			1.11417i
$262$	−20.0000			−1.23560
$263$		−	21.0000i		−	1.29492i	−0.762101	−	0.647458i	$-0.775832\pi$
$263$		−	21.0000i		−	1.29492i	0.762101	−	0.647458i	$-0.224168\pi$
$264$		0			0
$265$	−1.00000	+	2.00000i	−0.0614295	+	0.122859i
$266$		−	10.0000i		−	0.613139i
$267$	−5.00000			−0.305995
$268$		−	2.00000i		−	0.122169i
$269$			1.00000i			0.0609711i	0.999535	+	0.0304855i	$0.00970535\pi$
$269$			1.00000i			0.0609711i	−0.999535	+	0.0304855i	$0.990295\pi$
$270$	−5.00000	+	10.0000i	−0.304290	+	0.608581i
$271$	22.0000			1.33640			0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000			1.33640			0.668202	+	0.743980i	$0.267064\pi$
$272$	−1.00000	−	4.00000i	−0.0606339	−	0.242536i
$273$		−	2.00000i		−	0.121046i
$274$	2.00000			0.120824
$275$		0			0
$276$	4.00000			0.240772
$277$	18.0000			1.08152			0.540758	−	0.841178i	$-0.318138\pi$
$277$	18.0000			1.08152			0.540758	+	0.841178i	$0.318138\pi$
$278$	−14.0000			−0.839664
$279$		−	10.0000i		−	0.598684i
$280$	−2.00000	+	4.00000i	−0.119523	+	0.239046i
$281$	−23.0000			−1.37206			−0.686032	−	0.727571i	$-0.740649\pi$
$281$	−23.0000			−1.37206			−0.686032	+	0.727571i	$0.740649\pi$
$282$	−7.00000			−0.416844
$283$	−21.0000			−1.24832			−0.624160	−	0.781296i	$-0.714559\pi$
$283$	−21.0000			−1.24832			−0.624160	+	0.781296i	$0.714559\pi$
$284$		−	5.00000i		−	0.296695i
$285$	−10.0000	−	5.00000i	−0.592349	−	0.296174i
$286$		0			0
$287$			20.0000i			1.18056i
$288$			2.00000i			0.117851i
$289$	−15.0000	+	8.00000i	−0.882353	+	0.470588i
$290$	18.0000	+	9.00000i	1.05700	+	0.528498i
$291$	7.00000			0.410347
$292$	11.0000			0.643726
$293$			29.0000i			1.69420i	0.531435	+	0.847099i	$0.321653\pi$
$293$			29.0000i			1.69420i	−0.531435	+	0.847099i	$0.678347\pi$
$294$		−	3.00000i		−	0.174964i
$295$	10.0000	+	5.00000i	0.582223	+	0.291111i
$296$		−	2.00000i		−	0.116248i
$297$		0			0
$298$		−	20.0000i		−	1.15857i
$299$		−	4.00000i		−	0.231326i
$300$	3.00000	+	4.00000i	0.173205	+	0.230940i
$301$			12.0000i			0.691669i
$302$			8.00000i			0.460348i
$303$	8.00000			0.459588
$304$	−5.00000			−0.286770
$305$	5.00000	−	10.0000i	0.286299	−	0.572598i
$306$	8.00000	−	2.00000i	0.457330	−	0.114332i
$307$			2.00000i			0.114146i	0.998370	+	0.0570730i	$0.0181768\pi$
$307$			2.00000i			0.114146i	−0.998370	+	0.0570730i	$0.981823\pi$
$308$		0			0
$309$			16.0000i			0.910208i
$310$	−10.0000	−	5.00000i	−0.567962	−	0.283981i
$311$			20.0000i			1.13410i	0.823685	+	0.567048i	$0.191915\pi$
$311$			20.0000i			1.13410i	−0.823685	+	0.567048i	$0.808085\pi$
$312$	−1.00000			−0.0566139
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$	−18.0000			−1.01580
$315$	−8.00000	−	4.00000i	−0.450749	−	0.225374i
$316$		−	16.0000i		−	0.900070i
$317$	−12.0000			−0.673987			−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000			−0.673987			−0.336994	+	0.941507i	$0.609410\pi$
$318$	1.00000			0.0560772
$319$		0			0
$320$	2.00000	+	1.00000i	0.111803	+	0.0559017i
$321$	12.0000			0.669775
$322$			8.00000i			0.445823i
$323$	5.00000	+	20.0000i	0.278207	+	1.11283i
$324$	−1.00000			−0.0555556
$325$	4.00000	−	3.00000i	0.221880	−	0.166410i
$326$		−	4.00000i		−	0.221540i
$327$			9.00000i			0.497701i
$328$	10.0000			0.552158
$329$		−	14.0000i		−	0.771845i
$330$		0			0
$331$	7.00000			0.384755			0.192377	−	0.981321i	$-0.438380\pi$
$331$	7.00000			0.384755			0.192377	+	0.981321i	$0.438380\pi$
$332$			6.00000i			0.329293i
$333$	4.00000			0.219199
$334$		−	18.0000i		−	0.984916i
$335$	2.00000	−	4.00000i	0.109272	−	0.218543i
$336$	2.00000			0.109109
$337$	23.0000			1.25289			0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000			1.25289			0.626445	+	0.779466i	$0.284509\pi$
$338$		−	12.0000i		−	0.652714i
$339$	−9.00000			−0.488813
$340$	2.00000	−	9.00000i	0.108465	−	0.488094i
$341$		0			0
$342$		−	10.0000i		−	0.540738i
$343$	20.0000			1.07990
$344$	6.00000			0.323498
$345$	8.00000	+	4.00000i	0.430706	+	0.215353i
$346$			16.0000i			0.860165i
$347$	23.0000			1.23470			0.617352	−	0.786687i	$-0.288205\pi$
$347$	23.0000			1.23470			0.617352	+	0.786687i	$0.288205\pi$
$348$		−	9.00000i		−	0.482451i
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$	−8.00000	+	6.00000i	−0.427618	+	0.320713i
$351$		−	5.00000i		−	0.266880i
$352$		0			0
$353$			4.00000i			0.212899i	0.994318	+	0.106449i	$0.0339482\pi$
$353$			4.00000i			0.212899i	−0.994318	+	0.106449i	$0.966052\pi$
$354$		−	5.00000i		−	0.265747i
$355$	5.00000	−	10.0000i	0.265372	−	0.530745i
$356$	−5.00000			−0.264999
$357$	−2.00000	−	8.00000i	−0.105851	−	0.423405i
$358$		−	20.0000i		−	1.05703i
$359$	−30.0000			−1.58334			−0.791670	−	0.610949i	$-0.790788\pi$
$359$	−30.0000			−1.58334			−0.791670	+	0.610949i	$0.790788\pi$
$360$	−2.00000	+	4.00000i	−0.105409	+	0.210819i
$361$	6.00000			0.315789
$362$	10.0000			0.525588
$363$	−11.0000			−0.577350
$364$		−	2.00000i		−	0.104828i
$365$	22.0000	+	11.0000i	1.15153	+	0.575766i
$366$	−5.00000			−0.261354
$367$	−2.00000			−0.104399			−0.0521996	−	0.998637i	$-0.516623\pi$
$367$	−2.00000			−0.104399			−0.0521996	+	0.998637i	$0.516623\pi$
$368$	4.00000			0.208514
$369$			20.0000i			1.04116i
$370$	2.00000	−	4.00000i	0.103975	−	0.207950i
$371$			2.00000i			0.103835i
$372$			5.00000i			0.259238i
$373$			34.0000i			1.76045i	0.474554	+	0.880227i	$0.342610\pi$
$373$			34.0000i			1.76045i	−0.474554	+	0.880227i	$0.657390\pi$
$374$		0			0
$375$	2.00000	+	11.0000i	0.103280	+	0.568038i
$376$	−7.00000			−0.360997
$377$	−9.00000			−0.463524
$378$			10.0000i			0.514344i
$379$		−	4.00000i		−	0.205466i	−0.994709	−	0.102733i	$-0.967241\pi$
$379$		−	4.00000i		−	0.205466i	0.994709	−	0.102733i	$-0.0327588\pi$
$380$	−10.0000	−	5.00000i	−0.512989	−	0.256495i
$381$		−	7.00000i		−	0.358621i
$382$			18.0000i			0.920960i
$383$		−	31.0000i		−	1.58403i	−0.610504	−	0.792013i	$-0.709033\pi$
$383$		−	31.0000i		−	1.58403i	0.610504	−	0.792013i	$-0.290967\pi$
$384$		−	1.00000i		−	0.0510310i
$385$		0			0
$386$		−	14.0000i		−	0.712581i
$387$			12.0000i			0.609994i
$388$	7.00000			0.355371
$389$	−10.0000			−0.507020			−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000			−0.507020			−0.253510	+	0.967333i	$0.581585\pi$
$390$	−2.00000	−	1.00000i	−0.101274	−	0.0506370i
$391$	−4.00000	−	16.0000i	−0.202289	−	0.809155i
$392$		−	3.00000i		−	0.151523i
$393$			20.0000i			1.00887i
$394$		−	8.00000i		−	0.403034i
$395$	16.0000	−	32.0000i	0.805047	−	1.61009i
$396$		0			0
$397$	18.0000			0.903394			0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000			0.903394			0.451697	+	0.892171i	$0.350819\pi$
$398$	1.00000			0.0501255
$399$	−10.0000			−0.500626
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$		−	10.0000i		−	0.499376i	−0.968326	−	0.249688i	$-0.919672\pi$
$401$		−	10.0000i		−	0.499376i	0.968326	−	0.249688i	$-0.0803281\pi$
$402$	−2.00000			−0.0997509
$403$	5.00000			0.249068
$404$	8.00000			0.398015
$405$	−2.00000	−	1.00000i	−0.0993808	−	0.0496904i
$406$	18.0000			0.893325
$407$		0			0
$408$	−4.00000	+	1.00000i	−0.198030	+	0.0495074i
$409$	−25.0000			−1.23617			−0.618085	−	0.786111i	$-0.712091\pi$
$409$	−25.0000			−1.23617			−0.618085	+	0.786111i	$0.712091\pi$
$410$	20.0000	+	10.0000i	0.987730	+	0.493865i
$411$		−	2.00000i		−	0.0986527i
$412$			16.0000i			0.788263i
$413$	10.0000			0.492068
$414$			8.00000i			0.393179i
$415$	−6.00000	+	12.0000i	−0.294528	+	0.589057i
$416$	−1.00000			−0.0490290
$417$			14.0000i			0.685583i
$418$		0			0
$419$		−	24.0000i		−	1.17248i	−0.810139	−	0.586238i	$-0.800608\pi$
$419$		−	24.0000i		−	1.17248i	0.810139	−	0.586238i	$-0.199392\pi$
$420$	4.00000	+	2.00000i	0.195180	+	0.0975900i
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$	−20.0000			−0.973585
$423$		−	14.0000i		−	0.680703i
$424$	1.00000			0.0485643
$425$	13.0000	−	16.0000i	0.630593	−	0.776114i
$426$	−5.00000			−0.242251
$427$		−	10.0000i		−	0.483934i
$428$	12.0000			0.580042
$429$		0			0
$430$	12.0000	+	6.00000i	0.578691	+	0.289346i
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$	5.00000			0.240563
$433$		−	6.00000i		−	0.288342i	−0.989553	−	0.144171i	$-0.953949\pi$
$433$		−	6.00000i		−	0.288342i	0.989553	−	0.144171i	$-0.0460515\pi$
$434$	−10.0000			−0.480015
$435$	9.00000	−	18.0000i	0.431517	−	0.863034i
$436$			9.00000i			0.431022i
$437$	−20.0000			−0.956730
$438$		−	11.0000i		−	0.525600i
$439$		−	24.0000i		−	1.14546i	−0.819745	−	0.572729i	$-0.805885\pi$
$439$		−	24.0000i		−	1.14546i	0.819745	−	0.572729i	$-0.194115\pi$
$440$		0			0
$441$	6.00000			0.285714
$442$	1.00000	+	4.00000i	0.0475651	+	0.190261i
$443$		−	26.0000i		−	1.23530i	−0.786454	−	0.617649i	$-0.788085\pi$
$443$		−	26.0000i		−	1.23530i	0.786454	−	0.617649i	$-0.211915\pi$
$444$	−2.00000			−0.0949158
$445$	−10.0000	−	5.00000i	−0.474045	−	0.237023i
$446$	9.00000			0.426162
$447$	−20.0000			−0.945968
$448$	2.00000			0.0944911
$449$			16.0000i			0.755087i	0.925992	+	0.377543i	$0.123231\pi$
$449$			16.0000i			0.755087i	−0.925992	+	0.377543i	$0.876769\pi$
$450$	−8.00000	+	6.00000i	−0.377124	+	0.282843i
$451$		0			0
$452$	−9.00000			−0.423324
$453$	8.00000			0.375873
$454$			27.0000i			1.26717i
$455$	2.00000	−	4.00000i	0.0937614	−	0.187523i
$456$			5.00000i			0.234146i
$457$		−	18.0000i		−	0.842004i	−0.907060	−	0.421002i	$-0.861678\pi$
$457$		−	18.0000i		−	0.842004i	0.907060	−	0.421002i	$-0.138322\pi$
$458$		0			0
$459$	−5.00000	−	20.0000i	−0.233380	−	0.933520i
$460$	8.00000	+	4.00000i	0.373002	+	0.186501i
$461$	32.0000			1.49039			0.745194	−	0.666847i	$-0.232357\pi$
$461$	32.0000			1.49039			0.745194	+	0.666847i	$0.232357\pi$
$462$		0			0
$463$			29.0000i			1.34774i	0.738848	+	0.673872i	$0.235370\pi$
$463$			29.0000i			1.34774i	−0.738848	+	0.673872i	$0.764630\pi$
$464$		−	9.00000i		−	0.417815i
$465$	−5.00000	+	10.0000i	−0.231869	+	0.463739i
$466$			21.0000i			0.972806i
$467$			12.0000i			0.555294i	0.960683	+	0.277647i	$0.0895545\pi$
$467$			12.0000i			0.555294i	−0.960683	+	0.277647i	$0.910445\pi$
$468$		−	2.00000i		−	0.0924500i
$469$		−	4.00000i		−	0.184703i
$470$	−14.0000	−	7.00000i	−0.645772	−	0.322886i
$471$			18.0000i			0.829396i
$472$		−	5.00000i		−	0.230144i
$473$		0			0
$474$	−16.0000			−0.734904
$475$	−15.0000	−	20.0000i	−0.688247	−	0.917663i
$476$	−2.00000	−	8.00000i	−0.0916698	−	0.366679i
$477$			2.00000i			0.0915737i
$478$		0			0
$479$			21.0000i			0.959514i	0.877401	+	0.479757i	$0.159275\pi$
$479$			21.0000i			0.959514i	−0.877401	+	0.479757i	$0.840725\pi$
$480$	1.00000	−	2.00000i	0.0456435	−	0.0912871i
$481$			2.00000i			0.0911922i
$482$	10.0000			0.455488
$483$	8.00000			0.364013
$484$	−11.0000			−0.500000
$485$	14.0000	+	7.00000i	0.635707	+	0.317854i
$486$			16.0000i			0.725775i
$487$	−32.0000			−1.45006			−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000			−1.45006			−0.725029	+	0.688718i	$0.758174\pi$
$488$	−5.00000			−0.226339
$489$	−4.00000			−0.180886
$490$	3.00000	−	6.00000i	0.135526	−	0.271052i
$491$	−33.0000			−1.48927			−0.744635	−	0.667472i	$-0.767376\pi$
$491$	−33.0000			−1.48927			−0.744635	+	0.667472i	$0.767376\pi$
$492$		−	10.0000i		−	0.450835i
$493$	−36.0000	+	9.00000i	−1.62136	+	0.405340i
$494$	5.00000			0.224961
$495$		0			0
$496$			5.00000i			0.224507i
$497$		−	10.0000i		−	0.448561i
$498$	6.00000			0.268866
$499$			6.00000i			0.268597i	0.990941	+	0.134298i	$0.0428781\pi$
$499$			6.00000i			0.268597i	−0.990941	+	0.134298i	$0.957122\pi$
$500$	2.00000	+	11.0000i	0.0894427	+	0.491935i
$501$	−18.0000			−0.804181
$502$			8.00000i			0.357057i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$			4.00000i			0.178174i
$505$	16.0000	+	8.00000i	0.711991	+	0.355995i
$506$		0			0
$507$	−12.0000			−0.532939
$508$		−	7.00000i		−	0.310575i
$509$	−20.0000			−0.886484			−0.443242	−	0.896402i	$-0.646172\pi$
$509$	−20.0000			−0.886484			−0.443242	+	0.896402i	$0.646172\pi$
$510$	−9.00000	−	2.00000i	−0.398527	−	0.0885615i
$511$	22.0000			0.973223
$512$		−	1.00000i		−	0.0441942i
$513$	−25.0000			−1.10378
$514$	−18.0000			−0.793946
$515$	−16.0000	+	32.0000i	−0.705044	+	1.41009i
$516$		−	6.00000i		−	0.264135i
$517$		0			0
$518$		−	4.00000i		−	0.175750i
$519$	16.0000			0.702322
$520$	−2.00000	−	1.00000i	−0.0877058	−	0.0438529i
$521$		−	40.0000i		−	1.75243i	−0.481919	−	0.876216i	$-0.660060\pi$
$521$		−	40.0000i		−	1.75243i	0.481919	−	0.876216i	$-0.339940\pi$
$522$	18.0000			0.787839
$523$			34.0000i			1.48672i	0.668894	+	0.743358i	$0.266768\pi$
$523$			34.0000i			1.48672i	−0.668894	+	0.743358i	$0.733232\pi$
$524$			20.0000i			0.873704i
$525$	6.00000	+	8.00000i	0.261861	+	0.349149i
$526$	−21.0000			−0.915644
$527$	20.0000	−	5.00000i	0.871214	−	0.217803i
$528$		0			0
$529$	−7.00000			−0.304348
$530$	2.00000	+	1.00000i	0.0868744	+	0.0434372i
$531$	10.0000			0.433963
$532$	−10.0000			−0.433555
$533$	−10.0000			−0.433148
$534$			5.00000i			0.216371i
$535$	24.0000	+	12.0000i	1.03761	+	0.518805i
$536$	−2.00000			−0.0863868
$537$	−20.0000			−0.863064
$538$	1.00000			0.0431131
$539$		0			0
$540$	10.0000	+	5.00000i	0.430331	+	0.215166i
$541$		−	10.0000i		−	0.429934i	−0.976621	−	0.214967i	$-0.931036\pi$
$541$		−	10.0000i		−	0.429934i	0.976621	−	0.214967i	$-0.0689643\pi$
$542$		−	22.0000i		−	0.944981i
$543$		−	10.0000i		−	0.429141i
$544$	−4.00000	+	1.00000i	−0.171499	+	0.0428746i
$545$	−9.00000	+	18.0000i	−0.385518	+	0.771035i
$546$	−2.00000			−0.0855921
$547$	13.0000			0.555840			0.277920	−	0.960604i	$-0.410355\pi$
$547$	13.0000			0.555840			0.277920	+	0.960604i	$0.410355\pi$
$548$		−	2.00000i		−	0.0854358i
$549$		−	10.0000i		−	0.426790i
$550$		0			0
$551$			45.0000i			1.91706i
$552$		−	4.00000i		−	0.170251i
$553$		−	32.0000i		−	1.36078i
$554$		−	18.0000i		−	0.764747i
$555$	−4.00000	−	2.00000i	−0.169791	−	0.0848953i
$556$			14.0000i			0.593732i
$557$		−	3.00000i		−	0.127114i	−0.997978	−	0.0635570i	$-0.979756\pi$
$557$		−	3.00000i		−	0.127114i	0.997978	−	0.0635570i	$-0.0202445\pi$
$558$	−10.0000			−0.423334
$559$	−6.00000			−0.253773
$560$	4.00000	+	2.00000i	0.169031	+	0.0845154i
$561$		0			0
$562$			23.0000i			0.970196i
$563$			24.0000i			1.01148i	0.862686	+	0.505740i	$0.168780\pi$
$563$			24.0000i			1.01148i	−0.862686	+	0.505740i	$0.831220\pi$
$564$			7.00000i			0.294753i
$565$	−18.0000	−	9.00000i	−0.757266	−	0.378633i
$566$			21.0000i			0.882696i
$567$	−2.00000			−0.0839921
$568$	−5.00000			−0.209795
$569$	15.0000			0.628833			0.314416	−	0.949285i	$-0.398191\pi$
$569$	15.0000			0.628833			0.314416	+	0.949285i	$0.398191\pi$
$570$	−5.00000	+	10.0000i	−0.209427	+	0.418854i
$571$		−	20.0000i		−	0.836974i	−0.908223	−	0.418487i	$-0.862561\pi$
$571$		−	20.0000i		−	0.836974i	0.908223	−	0.418487i	$-0.137439\pi$
$572$		0			0
$573$	18.0000			0.751961
$574$	20.0000			0.834784
$575$	12.0000	+	16.0000i	0.500435	+	0.667246i
$576$	2.00000			0.0833333
$577$		−	28.0000i		−	1.16566i	−0.812596	−	0.582828i	$-0.801946\pi$
$577$		−	28.0000i		−	1.16566i	0.812596	−	0.582828i	$-0.198054\pi$
$578$	8.00000	+	15.0000i	0.332756	+	0.623918i
$579$	−14.0000			−0.581820
$580$	9.00000	−	18.0000i	0.373705	−	0.747409i
$581$			12.0000i			0.497844i
$582$		−	7.00000i		−	0.290159i
$583$		0			0
$584$		−	11.0000i		−	0.455183i
$585$	2.00000	−	4.00000i	0.0826898	−	0.165380i
$586$	29.0000			1.19798
$587$			12.0000i			0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$	−3.00000			−0.123718
$589$		−	25.0000i		−	1.03011i
$590$	5.00000	−	10.0000i	0.205847	−	0.411693i
$591$	−8.00000			−0.329076
$592$	−2.00000			−0.0821995
$593$		−	6.00000i		−	0.246390i	−0.992382	−	0.123195i	$-0.960686\pi$
$593$		−	6.00000i		−	0.246390i	0.992382	−	0.123195i	$-0.0393141\pi$
$594$		0			0
$595$	4.00000	−	18.0000i	0.163984	−	0.737928i
$596$	−20.0000			−0.819232
$597$		−	1.00000i		−	0.0409273i
$598$	−4.00000			−0.163572
$599$	20.0000			0.817178			0.408589	−	0.912719i	$-0.366021\pi$
$599$	20.0000			0.817178			0.408589	+	0.912719i	$0.366021\pi$
$600$	4.00000	−	3.00000i	0.163299	−	0.122474i
$601$		−	30.0000i		−	1.22373i	−0.790964	−	0.611863i	$-0.790420\pi$
$601$		−	30.0000i		−	1.22373i	0.790964	−	0.611863i	$-0.209580\pi$
$602$	12.0000			0.489083
$603$		−	4.00000i		−	0.162893i
$604$	8.00000			0.325515
$605$	−22.0000	−	11.0000i	−0.894427	−	0.447214i
$606$		−	8.00000i		−	0.324978i
$607$	38.0000			1.54237			0.771186	−	0.636610i	$-0.219664\pi$
$607$	38.0000			1.54237			0.771186	+	0.636610i	$0.219664\pi$
$608$			5.00000i			0.202777i
$609$		−	18.0000i		−	0.729397i
$610$	−10.0000	−	5.00000i	−0.404888	−	0.202444i
$611$	7.00000			0.283190
$612$	−2.00000	−	8.00000i	−0.0808452	−	0.323381i
$613$		−	41.0000i		−	1.65597i	−0.560747	−	0.827987i	$-0.689486\pi$
$613$		−	41.0000i		−	1.65597i	0.560747	−	0.827987i	$-0.310514\pi$
$614$	2.00000			0.0807134
$615$	10.0000	−	20.0000i	0.403239	−	0.806478i
$616$		0			0
$617$	33.0000			1.32853			0.664265	−	0.747497i	$-0.268745\pi$
$617$	33.0000			1.32853			0.664265	+	0.747497i	$0.268745\pi$
$618$	16.0000			0.643614
$619$			26.0000i			1.04503i	0.852631	+	0.522514i	$0.175006\pi$
$619$			26.0000i			1.04503i	−0.852631	+	0.522514i	$0.824994\pi$
$620$	−5.00000	+	10.0000i	−0.200805	+	0.401610i
$621$	20.0000			0.802572
$622$	20.0000			0.801927
$623$	−10.0000			−0.400642
$624$			1.00000i			0.0400320i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		−	14.0000i		−	0.559553i
$627$		0			0
$628$			18.0000i			0.718278i
$629$	2.00000	+	8.00000i	0.0797452	+	0.318981i
$630$	−4.00000	+	8.00000i	−0.159364	+	0.318728i
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$	−16.0000			−0.636446
$633$			20.0000i			0.794929i
$634$			12.0000i			0.476581i
$635$	7.00000	−	14.0000i	0.277787	−	0.555573i
$636$		−	1.00000i		−	0.0396526i
$637$			3.00000i			0.118864i
$638$		0			0
$639$		−	10.0000i		−	0.395594i
$640$	1.00000	−	2.00000i	0.0395285	−	0.0790569i
$641$		−	10.0000i		−	0.394976i	−0.980305	−	0.197488i	$-0.936722\pi$
$641$		−	10.0000i		−	0.394976i	0.980305	−	0.197488i	$-0.0632784\pi$
$642$		−	12.0000i		−	0.473602i
$643$	−36.0000			−1.41970			−0.709851	−	0.704352i	$-0.751238\pi$
$643$	−36.0000			−1.41970			−0.709851	+	0.704352i	$0.751238\pi$
$644$	8.00000			0.315244
$645$	6.00000	−	12.0000i	0.236250	−	0.472500i
$646$	20.0000	−	5.00000i	0.786889	−	0.196722i
$647$			37.0000i			1.45462i	0.686309	+	0.727310i	$0.259230\pi$
$647$			37.0000i			1.45462i	−0.686309	+	0.727310i	$0.740770\pi$
$648$			1.00000i			0.0392837i
$649$		0			0
$650$	−3.00000	−	4.00000i	−0.117670	−	0.156893i
$651$			10.0000i			0.391931i
$652$	−4.00000			−0.156652
$653$	24.0000			0.939193			0.469596	−	0.882881i	$-0.344399\pi$
$653$	24.0000			0.939193			0.469596	+	0.882881i	$0.344399\pi$
$654$	9.00000			0.351928
$655$	−20.0000	+	40.0000i	−0.781465	+	1.56293i
$656$		−	10.0000i		−	0.390434i
$657$	22.0000			0.858302
$658$	−14.0000			−0.545777
$659$	−5.00000			−0.194772			−0.0973862	−	0.995247i	$-0.531048\pi$
$659$	−5.00000			−0.194772			−0.0973862	+	0.995247i	$0.531048\pi$
$660$		0			0
$661$	−8.00000			−0.311164			−0.155582	−	0.987823i	$-0.549725\pi$
$661$	−8.00000			−0.311164			−0.155582	+	0.987823i	$0.549725\pi$
$662$		−	7.00000i		−	0.272063i
$663$	4.00000	−	1.00000i	0.155347	−	0.0388368i
$664$	6.00000			0.232845
$665$	−20.0000	−	10.0000i	−0.775567	−	0.387783i
$666$		−	4.00000i		−	0.154997i
$667$		−	36.0000i		−	1.39393i
$668$	−18.0000			−0.696441
$669$		−	9.00000i		−	0.347960i
$670$	−4.00000	−	2.00000i	−0.154533	−	0.0772667i
$671$		0			0
$672$		−	2.00000i		−	0.0771517i
$673$	−1.00000			−0.0385472			−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000			−0.0385472			−0.0192736	+	0.999814i	$0.506135\pi$
$674$		−	23.0000i		−	0.885927i
$675$	15.0000	+	20.0000i	0.577350	+	0.769800i
$676$	−12.0000			−0.461538
$677$	−2.00000			−0.0768662			−0.0384331	−	0.999261i	$-0.512237\pi$
$677$	−2.00000			−0.0768662			−0.0384331	+	0.999261i	$0.512237\pi$
$678$			9.00000i			0.345643i
$679$	14.0000			0.537271
$680$	−9.00000	−	2.00000i	−0.345134	−	0.0766965i
$681$	27.0000			1.03464
$682$		0			0
$683$	39.0000			1.49229			0.746147	−	0.665782i	$-0.231902\pi$
$683$	39.0000			1.49229			0.746147	+	0.665782i	$0.231902\pi$
$684$	−10.0000			−0.382360
$685$	2.00000	−	4.00000i	0.0764161	−	0.152832i
$686$		−	20.0000i		−	0.763604i
$687$		0			0
$688$		−	6.00000i		−	0.228748i
$689$	−1.00000			−0.0380970
$690$	4.00000	−	8.00000i	0.152277	−	0.304555i
$691$			30.0000i			1.14125i	0.821209	+	0.570627i	$0.193300\pi$
$691$			30.0000i			1.14125i	−0.821209	+	0.570627i	$0.806700\pi$
$692$	16.0000			0.608229
$693$		0			0
$694$		−	23.0000i		−	0.873068i
$695$	−14.0000	+	28.0000i	−0.531050	+	1.06210i
$696$	−9.00000			−0.341144
$697$	−40.0000	+	10.0000i	−1.51511	+	0.378777i
$698$		−	10.0000i		−	0.378506i
$699$	21.0000			0.794293
$700$	6.00000	+	8.00000i	0.226779	+	0.302372i
$701$	−48.0000			−1.81293			−0.906467	−	0.422276i	$-0.861231\pi$
$701$	−48.0000			−1.81293			−0.906467	+	0.422276i	$0.861231\pi$
$702$	−5.00000			−0.188713
$703$	10.0000			0.377157
$704$		0			0
$705$	−7.00000	+	14.0000i	−0.263635	+	0.527271i
$706$	4.00000			0.150542
$707$	16.0000			0.601742
$708$	−5.00000			−0.187912
$709$			31.0000i			1.16423i	0.813107	+	0.582115i	$0.197775\pi$
$709$			31.0000i			1.16423i	−0.813107	+	0.582115i	$0.802225\pi$
$710$	−10.0000	−	5.00000i	−0.375293	−	0.187647i
$711$		−	32.0000i		−	1.20009i
$712$			5.00000i			0.187383i
$713$			20.0000i			0.749006i
$714$	−8.00000	+	2.00000i	−0.299392	+	0.0748481i
$715$		0			0
$716$	−20.0000			−0.747435
$717$		0			0
$718$			30.0000i			1.11959i
$719$			51.0000i			1.90198i	0.309223	+	0.950990i	$0.399931\pi$
$719$			51.0000i			1.90198i	−0.309223	+	0.950990i	$0.600069\pi$
$720$	4.00000	+	2.00000i	0.149071	+	0.0745356i
$721$			32.0000i			1.19174i
$722$		−	6.00000i		−	0.223297i
$723$		−	10.0000i		−	0.371904i
$724$		−	10.0000i		−	0.371647i
$725$	36.0000	−	27.0000i	1.33701	−	1.00275i
$726$			11.0000i			0.408248i
$727$		−	33.0000i		−	1.22390i	−0.790896	−	0.611951i	$-0.790385\pi$
$727$		−	33.0000i		−	1.22390i	0.790896	−	0.611951i	$-0.209615\pi$
$728$	−2.00000			−0.0741249
$729$	13.0000			0.481481
$730$	11.0000	−	22.0000i	0.407128	−	0.814257i
$731$	−24.0000	+	6.00000i	−0.887672	+	0.221918i
$732$			5.00000i			0.184805i
$733$		−	6.00000i		−	0.221615i	−0.993842	−	0.110808i	$-0.964656\pi$
$733$		−	6.00000i		−	0.221615i	0.993842	−	0.110808i	$-0.0353437\pi$
$734$			2.00000i			0.0738213i
$735$	−6.00000	−	3.00000i	−0.221313	−	0.110657i
$736$		−	4.00000i		−	0.147442i
$737$		0			0
$738$	20.0000			0.736210
$739$	−15.0000			−0.551784			−0.275892	−	0.961189i	$-0.588973\pi$
$739$	−15.0000			−0.551784			−0.275892	+	0.961189i	$0.588973\pi$
$740$	−4.00000	−	2.00000i	−0.147043	−	0.0735215i
$741$		−	5.00000i		−	0.183680i
$742$	2.00000			0.0734223
$743$	34.0000			1.24734			0.623670	−	0.781688i	$-0.285641\pi$
$743$	34.0000			1.24734			0.623670	+	0.781688i	$0.285641\pi$
$744$	5.00000			0.183309
$745$	−40.0000	−	20.0000i	−1.46549	−	0.732743i
$746$	34.0000			1.24483
$747$			12.0000i			0.439057i
$748$		0			0
$749$	24.0000			0.876941
$750$	11.0000	−	2.00000i	0.401663	−	0.0730297i
$751$		−	25.0000i		−	0.912263i	−0.889912	−	0.456131i	$-0.849235\pi$
$751$		−	25.0000i		−	0.912263i	0.889912	−	0.456131i	$-0.150765\pi$
$752$			7.00000i			0.255264i
$753$	8.00000			0.291536
$754$			9.00000i			0.327761i
$755$	16.0000	+	8.00000i	0.582300	+	0.291150i
$756$	10.0000			0.363696
$757$		−	13.0000i		−	0.472493i	−0.971693	−	0.236247i	$-0.924083\pi$
$757$		−	13.0000i		−	0.472493i	0.971693	−	0.236247i	$-0.0759173\pi$
$758$	−4.00000			−0.145287
$759$		0			0
$760$	−5.00000	+	10.0000i	−0.181369	+	0.362738i
$761$	22.0000			0.797499			0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000			0.797499			0.398750	+	0.917060i	$0.369444\pi$
$762$	−7.00000			−0.253583
$763$			18.0000i			0.651644i
$764$	18.0000			0.651217
$765$	4.00000	−	18.0000i	0.144620	−	0.650791i
$766$	−31.0000			−1.12008
$767$			5.00000i			0.180540i
$768$	−1.00000			−0.0360844
$769$	35.0000			1.26213			0.631066	−	0.775729i	$-0.282618\pi$
$769$	35.0000			1.26213			0.631066	+	0.775729i	$0.282618\pi$
$770$		0			0
$771$			18.0000i			0.648254i
$772$	−14.0000			−0.503871
$773$		−	26.0000i		−	0.935155i	−0.883952	−	0.467578i	$-0.845127\pi$
$773$		−	26.0000i		−	0.935155i	0.883952	−	0.467578i	$-0.154873\pi$
$774$	12.0000			0.431331
$775$	−20.0000	+	15.0000i	−0.718421	+	0.538816i
$776$		−	7.00000i		−	0.251285i
$777$	−4.00000			−0.143499
$778$			10.0000i			0.358517i
$779$			50.0000i			1.79144i
$780$	−1.00000	+	2.00000i	−0.0358057	+	0.0716115i
$781$		0			0
$782$	−16.0000	+	4.00000i	−0.572159	+	0.143040i
$783$		−	45.0000i		−	1.60817i
$784$	−3.00000			−0.107143
$785$	−18.0000	+	36.0000i	−0.642448	+	1.28490i
$786$	20.0000			0.713376
$787$	−7.00000			−0.249523			−0.124762	−	0.992187i	$-0.539817\pi$
$787$	−7.00000			−0.249523			−0.124762	+	0.992187i	$0.539817\pi$
$788$	−8.00000			−0.284988
$789$			21.0000i			0.747620i
$790$	−32.0000	−	16.0000i	−1.13851	−	0.569254i
$791$	−18.0000			−0.640006
$792$		0			0
$793$	5.00000			0.177555
$794$		−	18.0000i		−	0.638796i
$795$	1.00000	−	2.00000i	0.0354663	−	0.0709327i
$796$		−	1.00000i		−	0.0354441i
$797$			2.00000i			0.0708436i	0.999372	+	0.0354218i	$0.0112775\pi$
$797$			2.00000i			0.0708436i	−0.999372	+	0.0354218i	$0.988723\pi$
$798$			10.0000i			0.353996i
$799$	28.0000	−	7.00000i	0.990569	−	0.247642i
$800$	4.00000	−	3.00000i	0.141421	−	0.106066i
$801$	−10.0000			−0.353333
$802$	−10.0000			−0.353112
$803$		0			0
$804$			2.00000i			0.0705346i
$805$	16.0000	+	8.00000i	0.563926	+	0.281963i
$806$		−	5.00000i		−	0.176117i
$807$		−	1.00000i		−	0.0352017i
$808$		−	8.00000i		−	0.281439i
$809$		−	24.0000i		−	0.843795i	−0.906644	−	0.421898i	$-0.861364\pi$
$809$		−	24.0000i		−	0.843795i	0.906644	−	0.421898i	$-0.138636\pi$
$810$	−1.00000	+	2.00000i	−0.0351364	+	0.0702728i
$811$			30.0000i			1.05344i	0.850038	+	0.526721i	$0.176579\pi$
$811$			30.0000i			1.05344i	−0.850038	+	0.526721i	$0.823421\pi$
$812$		−	18.0000i		−	0.631676i
$813$	−22.0000			−0.771574
$814$		0			0
$815$	−8.00000	−	4.00000i	−0.280228	−	0.140114i
$816$	1.00000	+	4.00000i	0.0350070	+	0.140028i
$817$			30.0000i			1.04957i
$818$			25.0000i			0.874105i
$819$		−	4.00000i		−	0.139771i
$820$	10.0000	−	20.0000i	0.349215	−	0.698430i
$821$			15.0000i			0.523504i	0.965135	+	0.261752i	$0.0843002\pi$
$821$			15.0000i			0.523504i	−0.965135	+	0.261752i	$0.915700\pi$
$822$	−2.00000			−0.0697580
$823$	−46.0000			−1.60346			−0.801730	−	0.597687i	$-0.796087\pi$
$823$	−46.0000			−1.60346			−0.801730	+	0.597687i	$0.796087\pi$
$824$	16.0000			0.557386
$825$		0			0
$826$		−	10.0000i		−	0.347945i
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	8.00000			0.278019
$829$	10.0000			0.347314			0.173657	−	0.984806i	$-0.444442\pi$
$829$	10.0000			0.347314			0.173657	+	0.984806i	$0.444442\pi$
$830$	12.0000	+	6.00000i	0.416526	+	0.208263i
$831$	−18.0000			−0.624413
$832$			1.00000i			0.0346688i
$833$	3.00000	+	12.0000i	0.103944	+	0.415775i
$834$	14.0000			0.484780
$835$	−36.0000	−	18.0000i	−1.24583	−	0.622916i
$836$		0			0
$837$			25.0000i			0.864126i
$838$	−24.0000			−0.829066
$839$		−	9.00000i		−	0.310715i	−0.987858	−	0.155357i	$-0.950347\pi$
$839$		−	9.00000i		−	0.310715i	0.987858	−	0.155357i	$-0.0496529\pi$
$840$	2.00000	−	4.00000i	0.0690066	−	0.138013i
$841$	−52.0000			−1.79310
$842$		−	2.00000i		−	0.0689246i
$843$	23.0000			0.792162
$844$			20.0000i			0.688428i
$845$	−24.0000	−	12.0000i	−0.825625	−	0.412813i
$846$	−14.0000			−0.481330
$847$	−22.0000			−0.755929
$848$		−	1.00000i		−	0.0343401i
$849$	21.0000			0.720718
$850$	−16.0000	−	13.0000i	−0.548795	−	0.445896i
$851$	−8.00000			−0.274236
$852$			5.00000i			0.171297i
$853$	−16.0000			−0.547830			−0.273915	−	0.961754i	$-0.588319\pi$
$853$	−16.0000			−0.547830			−0.273915	+	0.961754i	$0.588319\pi$
$854$	−10.0000			−0.342193
$855$	−20.0000	−	10.0000i	−0.683986	−	0.341993i
$856$		−	12.0000i		−	0.410152i
$857$	−17.0000			−0.580709			−0.290354	−	0.956919i	$-0.593773\pi$
$857$	−17.0000			−0.580709			−0.290354	+	0.956919i	$0.593773\pi$
$858$		0			0
$859$	−25.0000			−0.852989			−0.426494	−	0.904490i	$-0.640252\pi$
$859$	−25.0000			−0.852989			−0.426494	+	0.904490i	$0.640252\pi$
$860$	6.00000	−	12.0000i	0.204598	−	0.409197i
$861$		−	20.0000i		−	0.681598i
$862$		0			0
$863$		−	36.0000i		−	1.22545i	−0.790295	−	0.612727i	$-0.790072\pi$
$863$		−	36.0000i		−	1.22545i	0.790295	−	0.612727i	$-0.209928\pi$
$864$		−	5.00000i		−	0.170103i
$865$	32.0000	+	16.0000i	1.08803	+	0.544016i
$866$	−6.00000			−0.203888
$867$	15.0000	−	8.00000i	0.509427	−	0.271694i
$868$			10.0000i			0.339422i
$869$		0			0
$870$	−18.0000	−	9.00000i	−0.610257	−	0.305129i
$871$	2.00000			0.0677674
$872$	9.00000			0.304778
$873$	14.0000			0.473828
$874$			20.0000i			0.676510i
$875$	4.00000	+	22.0000i	0.135225	+	0.743736i
$876$	−11.0000			−0.371656
$877$	−32.0000			−1.08056			−0.540282	−	0.841484i	$-0.681682\pi$
$877$	−32.0000			−1.08056			−0.540282	+	0.841484i	$0.681682\pi$
$878$	−24.0000			−0.809961
$879$		−	29.0000i		−	0.978146i
$880$		0			0
$881$			30.0000i			1.01073i	0.862907	+	0.505363i	$0.168641\pi$
$881$			30.0000i			1.01073i	−0.862907	+	0.505363i	$0.831359\pi$
$882$		−	6.00000i		−	0.202031i
$883$			44.0000i			1.48072i	0.672212	+	0.740359i	$0.265344\pi$
$883$			44.0000i			1.48072i	−0.672212	+	0.740359i	$0.734656\pi$
$884$	4.00000	−	1.00000i	0.134535	−	0.0336336i
$885$	−10.0000	−	5.00000i	−0.336146	−	0.168073i
$886$	−26.0000			−0.873487
$887$	8.00000			0.268614			0.134307	−	0.990940i	$-0.457119\pi$
$887$	8.00000			0.268614			0.134307	+	0.990940i	$0.457119\pi$
$888$			2.00000i			0.0671156i
$889$		−	14.0000i		−	0.469545i
$890$	−5.00000	+	10.0000i	−0.167600	+	0.335201i
$891$		0			0
$892$		−	9.00000i		−	0.301342i
$893$		−	35.0000i		−	1.17123i
$894$			20.0000i			0.668900i
$895$	−40.0000	−	20.0000i	−1.33705	−	0.668526i
$896$		−	2.00000i		−	0.0668153i
$897$			4.00000i			0.133556i
$898$	16.0000			0.533927
$899$	45.0000			1.50083
$900$	6.00000	+	8.00000i	0.200000	+	0.266667i
$901$	−4.00000	+	1.00000i	−0.133259	+	0.0333148i
$902$		0			0
$903$		−	12.0000i		−	0.399335i
$904$			9.00000i			0.299336i
$905$	10.0000	−	20.0000i	0.332411	−	0.664822i
$906$		−	8.00000i		−	0.265782i
$907$	−7.00000			−0.232431			−0.116216	−	0.993224i	$-0.537076\pi$
$907$	−7.00000			−0.232431			−0.116216	+	0.993224i	$0.537076\pi$
$908$	27.0000			0.896026
$909$	16.0000			0.530687
$910$	−4.00000	−	2.00000i	−0.132599	−	0.0662994i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$	5.00000			0.165567
$913$		0			0
$914$	−18.0000			−0.595387
$915$	−5.00000	+	10.0000i	−0.165295	+	0.330590i
$916$		0			0
$917$			40.0000i			1.32092i
$918$	−20.0000	+	5.00000i	−0.660098	+	0.165025i
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	4.00000	−	8.00000i	0.131876	−	0.263752i
$921$		−	2.00000i		−	0.0659022i
$922$		−	32.0000i		−	1.05386i
$923$	5.00000			0.164577
$924$		0			0
$925$	−6.00000	−	8.00000i	−0.197279	−	0.263038i
$926$	29.0000			0.952999
$927$			32.0000i			1.05102i
$928$	−9.00000			−0.295439
$929$		−	24.0000i		−	0.787414i	−0.919236	−	0.393707i	$-0.871192\pi$
$929$		−	24.0000i		−	0.787414i	0.919236	−	0.393707i	$-0.128808\pi$
$930$	10.0000	+	5.00000i	0.327913	+	0.163956i
$931$	15.0000			0.491605
$932$	21.0000			0.687878
$933$		−	20.0000i		−	0.654771i
$934$	12.0000			0.392652
$935$		0			0
$936$	−2.00000			−0.0653720
$937$			22.0000i			0.718709i	0.933201	+	0.359354i	$0.117003\pi$
$937$			22.0000i			0.718709i	−0.933201	+	0.359354i	$0.882997\pi$
$938$	−4.00000			−0.130605
$939$	−14.0000			−0.456873
$940$	−7.00000	+	14.0000i	−0.228315	+	0.456630i
$941$		−	45.0000i		−	1.46696i	−0.679712	−	0.733479i	$-0.737895\pi$
$941$		−	45.0000i		−	1.46696i	0.679712	−	0.733479i	$-0.262105\pi$
$942$	18.0000			0.586472
$943$		−	40.0000i		−	1.30258i
$944$	−5.00000			−0.162736
$945$	20.0000	+	10.0000i	0.650600	+	0.325300i
$946$		0			0
$947$	3.00000			0.0974869			0.0487435	−	0.998811i	$-0.484478\pi$
$947$	3.00000			0.0974869			0.0487435	+	0.998811i	$0.484478\pi$
$948$			16.0000i			0.519656i
$949$			11.0000i			0.357075i
$950$	−20.0000	+	15.0000i	−0.648886	+	0.486664i
$951$	12.0000			0.389127
$952$	−8.00000	+	2.00000i	−0.259281	+	0.0648204i
$953$		−	46.0000i		−	1.49009i	−0.667016	−	0.745043i	$-0.732429\pi$
$953$		−	46.0000i		−	1.49009i	0.667016	−	0.745043i	$-0.267571\pi$
$954$	2.00000			0.0647524
$955$	36.0000	+	18.0000i	1.16493	+	0.582466i
$956$		0			0
$957$		0			0
$958$	21.0000			0.678479
$959$		−	4.00000i		−	0.129167i
$960$	−2.00000	−	1.00000i	−0.0645497	−	0.0322749i
$961$	6.00000			0.193548
$962$	2.00000			0.0644826
$963$	24.0000			0.773389
$964$		−	10.0000i		−	0.322078i
$965$	−28.0000	−	14.0000i	−0.901352	−	0.450676i
$966$		−	8.00000i		−	0.257396i
$967$		−	8.00000i		−	0.257263i	−0.991692	−	0.128631i	$-0.958942\pi$
$967$		−	8.00000i		−	0.257263i	0.991692	−	0.128631i	$-0.0410584\pi$
$968$			11.0000i			0.353553i
$969$	−5.00000	−	20.0000i	−0.160623	−	0.642493i
$970$	7.00000	−	14.0000i	0.224756	−	0.449513i
$971$	57.0000			1.82922			0.914609	−	0.404341i	$-0.132499\pi$
$971$	57.0000			1.82922			0.914609	+	0.404341i	$0.132499\pi$
$972$	16.0000			0.513200
$973$			28.0000i			0.897639i
$974$			32.0000i			1.02535i
$975$	−4.00000	+	3.00000i	−0.128103	+	0.0960769i
$976$			5.00000i			0.160046i
$977$		−	8.00000i		−	0.255943i	−0.991778	−	0.127971i	$-0.959153\pi$
$977$		−	8.00000i		−	0.255943i	0.991778	−	0.127971i	$-0.0408466\pi$
$978$			4.00000i			0.127906i
$979$		0			0
$980$	−6.00000	−	3.00000i	−0.191663	−	0.0958315i
$981$			18.0000i			0.574696i
$982$			33.0000i			1.05307i
$983$	24.0000			0.765481			0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000			0.765481			0.382741	+	0.923856i	$0.374980\pi$
$984$	−10.0000			−0.318788
$985$	−16.0000	−	8.00000i	−0.509802	−	0.254901i
$986$	9.00000	+	36.0000i	0.286618	+	1.14647i
$987$			14.0000i			0.445625i
$988$		−	5.00000i		−	0.159071i
$989$		−	24.0000i		−	0.763156i
$990$		0			0
$991$		−	35.0000i		−	1.11181i	−0.831245	−	0.555906i	$-0.812372\pi$
$991$		−	35.0000i		−	1.11181i	0.831245	−	0.555906i	$-0.187628\pi$
$992$	5.00000			0.158750
$993$	−7.00000			−0.222138
$994$	−10.0000			−0.317181
$995$	1.00000	−	2.00000i	0.0317021	−	0.0634043i
$996$		−	6.00000i		−	0.190117i
$997$	18.0000			0.570066			0.285033	−	0.958518i	$-0.407995\pi$
$997$	18.0000			0.570066			0.285033	+	0.958518i	$0.407995\pi$
$998$	6.00000			0.189927
$999$	−10.0000			−0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.d.a.169.1	✓	2
3.2	odd	2		1530.2.f.e.1189.2		2
4.3	odd	2		1360.2.o.b.849.1		2
5.2	odd	4		850.2.b.i.101.2		2
5.3	odd	4		850.2.b.c.101.1		2
5.4	even	2		170.2.d.b.169.2	yes	2
15.14	odd	2		1530.2.f.b.1189.1		2
17.16	even	2		170.2.d.b.169.1	yes	2
20.19	odd	2		1360.2.o.a.849.1		2
51.50	odd	2		1530.2.f.b.1189.2		2
68.67	odd	2		1360.2.o.a.849.2		2
85.33	odd	4		850.2.b.c.101.2		2
85.67	odd	4		850.2.b.i.101.1		2
85.84	even	2	inner	170.2.d.a.169.2	yes	2
255.254	odd	2		1530.2.f.e.1189.1		2
340.339	odd	2		1360.2.o.b.849.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.d.a.169.1	✓	2	1.1	even	1	trivial
170.2.d.a.169.2	yes	2	85.84	even	2	inner
170.2.d.b.169.1	yes	2	17.16	even	2
170.2.d.b.169.2	yes	2	5.4	even	2
850.2.b.c.101.1		2	5.3	odd	4
850.2.b.c.101.2		2	85.33	odd	4
850.2.b.i.101.1		2	85.67	odd	4
850.2.b.i.101.2		2	5.2	odd	4
1360.2.o.a.849.1		2	20.19	odd	2
1360.2.o.a.849.2		2	68.67	odd	2
1360.2.o.b.849.1		2	4.3	odd	2
1360.2.o.b.849.2		2	340.339	odd	2
1530.2.f.b.1189.1		2	15.14	odd	2
1530.2.f.b.1189.2		2	51.50	odd	2
1530.2.f.e.1189.1		2	255.254	odd	2
1530.2.f.e.1189.2		2	3.2	odd	2

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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +1.00000i q^{6} -2.00000 q^{7} +1.00000i q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +1.00000i q^{6} -2.00000 q^{7} +1.00000i q^{8} -2.00000 q^{9} +(-1.00000 + 2.00000i) q^{10} +1.00000 q^{12} -1.00000i q^{13} +2.00000i q^{14} +(2.00000 + 1.00000i) q^{15} +1.00000 q^{16} +(-1.00000 - 4.00000i) q^{17} +2.00000i q^{18} -5.00000 q^{19} +(2.00000 + 1.00000i) q^{20} +2.00000 q^{21} +4.00000 q^{23} -1.00000i q^{24} +(3.00000 + 4.00000i) q^{25} -1.00000 q^{26} +5.00000 q^{27} +2.00000 q^{28} -9.00000i q^{29} +(1.00000 - 2.00000i) q^{30} +5.00000i q^{31} -1.00000i q^{32} +(-4.00000 + 1.00000i) q^{34} +(4.00000 + 2.00000i) q^{35} +2.00000 q^{36} -2.00000 q^{37} +5.00000i q^{38} +1.00000i q^{39} +(1.00000 - 2.00000i) q^{40} -10.0000i q^{41} -2.00000i q^{42} -6.00000i q^{43} +(4.00000 + 2.00000i) q^{45} -4.00000i q^{46} +7.00000i q^{47} -1.00000 q^{48} -3.00000 q^{49} +(4.00000 - 3.00000i) q^{50} +(1.00000 + 4.00000i) q^{51} +1.00000i q^{52} -1.00000i q^{53} -5.00000i q^{54} -2.00000i q^{56} +5.00000 q^{57} -9.00000 q^{58} -5.00000 q^{59} +(-2.00000 - 1.00000i) q^{60} +5.00000i q^{61} +5.00000 q^{62} +4.00000 q^{63} -1.00000 q^{64} +(-1.00000 + 2.00000i) q^{65} +2.00000i q^{67} +(1.00000 + 4.00000i) q^{68} -4.00000 q^{69} +(2.00000 - 4.00000i) q^{70} +5.00000i q^{71} -2.00000i q^{72} -11.0000 q^{73} +2.00000i q^{74} +(-3.00000 - 4.00000i) q^{75} +5.00000 q^{76} +1.00000 q^{78} +16.0000i q^{79} +(-2.00000 - 1.00000i) q^{80} +1.00000 q^{81} -10.0000 q^{82} -6.00000i q^{83} -2.00000 q^{84} +(-2.00000 + 9.00000i) q^{85} -6.00000 q^{86} +9.00000i q^{87} +5.00000 q^{89} +(2.00000 - 4.00000i) q^{90} +2.00000i q^{91} -4.00000 q^{92} -5.00000i q^{93} +7.00000 q^{94} +(10.0000 + 5.00000i) q^{95} +1.00000i q^{96} -7.00000 q^{97} +3.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 2 q^{4} - 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 - 2 * q^4 - 4 * q^5 - 4 * q^7 - 4 * q^9	\( 2 q - 2 q^{3} - 2 q^{4} - 4 q^{5} - 4 q^{7} - 4 q^{9} - 2 q^{10} + 2 q^{12} + 4 q^{15} + 2 q^{16} - 2 q^{17} - 10 q^{19} + 4 q^{20} + 4 q^{21} + 8 q^{23} + 6 q^{25} - 2 q^{26} + 10 q^{27} + 4 q^{28} + 2 q^{30} - 8 q^{34} + 8 q^{35} + 4 q^{36} - 4 q^{37} + 2 q^{40} + 8 q^{45} - 2 q^{48} - 6 q^{49} + 8 q^{50} + 2 q^{51} + 10 q^{57} - 18 q^{58} - 10 q^{59} - 4 q^{60} + 10 q^{62} + 8 q^{63} - 2 q^{64} - 2 q^{65} + 2 q^{68} - 8 q^{69} + 4 q^{70} - 22 q^{73} - 6 q^{75} + 10 q^{76} + 2 q^{78} - 4 q^{80} + 2 q^{81} - 20 q^{82} - 4 q^{84} - 4 q^{85} - 12 q^{86} + 10 q^{89} + 4 q^{90} - 8 q^{92} + 14 q^{94} + 20 q^{95} - 14 q^{97}+O(q^{100}) \) 2 * q - 2 * q^3 - 2 * q^4 - 4 * q^5 - 4 * q^7 - 4 * q^9 - 2 * q^10 + 2 * q^12 + 4 * q^15 + 2 * q^16 - 2 * q^17 - 10 * q^19 + 4 * q^20 + 4 * q^21 + 8 * q^23 + 6 * q^25 - 2 * q^26 + 10 * q^27 + 4 * q^28 + 2 * q^30 - 8 * q^34 + 8 * q^35 + 4 * q^36 - 4 * q^37 + 2 * q^40 + 8 * q^45 - 2 * q^48 - 6 * q^49 + 8 * q^50 + 2 * q^51 + 10 * q^57 - 18 * q^58 - 10 * q^59 - 4 * q^60 + 10 * q^62 + 8 * q^63 - 2 * q^64 - 2 * q^65 + 2 * q^68 - 8 * q^69 + 4 * q^70 - 22 * q^73 - 6 * q^75 + 10 * q^76 + 2 * q^78 - 4 * q^80 + 2 * q^81 - 20 * q^82 - 4 * q^84 - 4 * q^85 - 12 * q^86 + 10 * q^89 + 4 * q^90 - 8 * q^92 + 14 * q^94 + 20 * q^95 - 14 * q^97

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