LMFDB - Embedded newform 690.2.d.b.139.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(139,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("690.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	690.139
Dual form			690.2.d.b.139.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(0.707107 - 2.12132i) q^{5} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(0.707107 - 2.12132i) q^{5} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(-2.12132 - 0.707107i) q^{10} +4.24264 q^{11} -1.00000i q^{12} +4.82843i q^{13} +2.00000 q^{14} +(2.12132 + 0.707107i) q^{15} +1.00000 q^{16} -1.17157i q^{17} +1.00000i q^{18} +2.24264 q^{19} +(-0.707107 + 2.12132i) q^{20} -2.00000 q^{21} -4.24264i q^{22} -1.00000i q^{23} -1.00000 q^{24} +(-4.00000 - 3.00000i) q^{25} +4.82843 q^{26} -1.00000i q^{27} -2.00000i q^{28} +7.65685 q^{29} +(0.707107 - 2.12132i) q^{30} +6.00000 q^{31} -1.00000i q^{32} +4.24264i q^{33} -1.17157 q^{34} +(4.24264 + 1.41421i) q^{35} +1.00000 q^{36} -3.41421i q^{37} -2.24264i q^{38} -4.82843 q^{39} +(2.12132 + 0.707107i) q^{40} -1.17157 q^{41} +2.00000i q^{42} +1.75736i q^{43} -4.24264 q^{44} +(-0.707107 + 2.12132i) q^{45} -1.00000 q^{46} -4.82843i q^{47} +1.00000i q^{48} +3.00000 q^{49} +(-3.00000 + 4.00000i) q^{50} +1.17157 q^{51} -4.82843i q^{52} +13.4142i q^{53} -1.00000 q^{54} +(3.00000 - 9.00000i) q^{55} -2.00000 q^{56} +2.24264i q^{57} -7.65685i q^{58} +8.48528 q^{59} +(-2.12132 - 0.707107i) q^{60} -3.41421 q^{61} -6.00000i q^{62} -2.00000i q^{63} -1.00000 q^{64} +(10.2426 + 3.41421i) q^{65} +4.24264 q^{66} +0.585786i q^{67} +1.17157i q^{68} +1.00000 q^{69} +(1.41421 - 4.24264i) q^{70} +5.65685 q^{71} -1.00000i q^{72} -3.65685i q^{73} -3.41421 q^{74} +(3.00000 - 4.00000i) q^{75} -2.24264 q^{76} +8.48528i q^{77} +4.82843i q^{78} -7.65685 q^{79} +(0.707107 - 2.12132i) q^{80} +1.00000 q^{81} +1.17157i q^{82} -1.41421i q^{83} +2.00000 q^{84} +(-2.48528 - 0.828427i) q^{85} +1.75736 q^{86} +7.65685i q^{87} +4.24264i q^{88} -14.8284 q^{89} +(2.12132 + 0.707107i) q^{90} -9.65685 q^{91} +1.00000i q^{92} +6.00000i q^{93} -4.82843 q^{94} +(1.58579 - 4.75736i) q^{95} +1.00000 q^{96} +6.00000i q^{97} -3.00000i q^{98} -4.24264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 8 q^{14} + 4 q^{16} - 8 q^{19} - 8 q^{21} - 4 q^{24} - 16 q^{25} + 8 q^{26} + 8 q^{29} + 24 q^{31} - 16 q^{34} + 4 q^{36} - 8 q^{39} - 16 q^{41} - 4 q^{46} + 12 q^{49} - 12 q^{50} + 16 q^{51} - 4 q^{54} + 12 q^{55} - 8 q^{56} - 8 q^{61} - 4 q^{64} + 24 q^{65} + 4 q^{69} - 8 q^{74} + 12 q^{75} + 8 q^{76} - 8 q^{79} + 4 q^{81} + 8 q^{84} + 24 q^{85} + 24 q^{86} - 48 q^{89} - 16 q^{91} - 8 q^{94} + 12 q^{95} + 4 q^{96}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 8 * q^14 + 4 * q^16 - 8 * q^19 - 8 * q^21 - 4 * q^24 - 16 * q^25 + 8 * q^26 + 8 * q^29 + 24 * q^31 - 16 * q^34 + 4 * q^36 - 8 * q^39 - 16 * q^41 - 4 * q^46 + 12 * q^49 - 12 * q^50 + 16 * q^51 - 4 * q^54 + 12 * q^55 - 8 * q^56 - 8 * q^61 - 4 * q^64 + 24 * q^65 + 4 * q^69 - 8 * q^74 + 12 * q^75 + 8 * q^76 - 8 * q^79 + 4 * q^81 + 8 * q^84 + 24 * q^85 + 24 * q^86 - 48 * q^89 - 16 * q^91 - 8 * q^94 + 12 * q^95 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$1$

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
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$	0.707107	−	2.12132i	0.316228	−	0.948683i
$5$	0.707107	−	2.12132i	0.316228	−	0.948683i
$6$	1.00000			0.408248
$7$			2.00000i			0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	−2.12132	−	0.707107i	−0.670820	−	0.223607i
$11$	4.24264			1.27920			0.639602	−	0.768706i	$-0.279099\pi$
$11$	4.24264			1.27920			0.639602	+	0.768706i	$0.279099\pi$
$12$		−	1.00000i		−	0.288675i
$13$			4.82843i			1.33916i	0.742738	+	0.669582i	$0.233527\pi$
$13$			4.82843i			1.33916i	−0.742738	+	0.669582i	$0.766473\pi$
$14$	2.00000			0.534522
$15$	2.12132	+	0.707107i	0.547723	+	0.182574i
$16$	1.00000			0.250000
$17$		−	1.17157i		−	0.284148i	−0.989856	−	0.142074i	$-0.954623\pi$
$17$		−	1.17157i		−	0.284148i	0.989856	−	0.142074i	$-0.0453771\pi$
$18$			1.00000i			0.235702i
$19$	2.24264			0.514497			0.257249	−	0.966345i	$-0.417184\pi$
$19$	2.24264			0.514497			0.257249	+	0.966345i	$0.417184\pi$
$20$	−0.707107	+	2.12132i	−0.158114	+	0.474342i
$21$	−2.00000			−0.436436
$22$		−	4.24264i		−	0.904534i
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	−1.00000			−0.204124
$25$	−4.00000	−	3.00000i	−0.800000	−	0.600000i
$26$	4.82843			0.946932
$27$		−	1.00000i		−	0.192450i
$28$		−	2.00000i		−	0.377964i
$29$	7.65685			1.42184			0.710921	−	0.703272i	$-0.248278\pi$
$29$	7.65685			1.42184			0.710921	+	0.703272i	$0.248278\pi$
$30$	0.707107	−	2.12132i	0.129099	−	0.387298i
$31$	6.00000			1.07763			0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000			1.07763			0.538816	+	0.842424i	$0.318872\pi$
$32$		−	1.00000i		−	0.176777i
$33$			4.24264i			0.738549i
$34$	−1.17157			−0.200923
$35$	4.24264	+	1.41421i	0.717137	+	0.239046i
$36$	1.00000			0.166667
$37$		−	3.41421i		−	0.561293i	−0.959811	−	0.280647i	$-0.909451\pi$
$37$		−	3.41421i		−	0.561293i	0.959811	−	0.280647i	$-0.0905489\pi$
$38$		−	2.24264i		−	0.363804i
$39$	−4.82843			−0.773167
$40$	2.12132	+	0.707107i	0.335410	+	0.111803i
$41$	−1.17157			−0.182969			−0.0914845	−	0.995807i	$-0.529161\pi$
$41$	−1.17157			−0.182969			−0.0914845	+	0.995807i	$0.529161\pi$
$42$			2.00000i			0.308607i
$43$			1.75736i			0.267995i	0.990982	+	0.133997i	$0.0427814\pi$
$43$			1.75736i			0.267995i	−0.990982	+	0.133997i	$0.957219\pi$
$44$	−4.24264			−0.639602
$45$	−0.707107	+	2.12132i	−0.105409	+	0.316228i
$46$	−1.00000			−0.147442
$47$		−	4.82843i		−	0.704298i	−0.935944	−	0.352149i	$-0.885451\pi$
$47$		−	4.82843i		−	0.704298i	0.935944	−	0.352149i	$-0.114549\pi$
$48$			1.00000i			0.144338i
$49$	3.00000			0.428571
$50$	−3.00000	+	4.00000i	−0.424264	+	0.565685i
$51$	1.17157			0.164053
$52$		−	4.82843i		−	0.669582i
$53$			13.4142i			1.84258i	0.388872	+	0.921292i	$0.372865\pi$
$53$			13.4142i			1.84258i	−0.388872	+	0.921292i	$0.627135\pi$
$54$	−1.00000			−0.136083
$55$	3.00000	−	9.00000i	0.404520	−	1.21356i
$56$	−2.00000			−0.267261
$57$			2.24264i			0.297045i
$58$		−	7.65685i		−	1.00539i
$59$	8.48528			1.10469			0.552345	−	0.833616i	$-0.313733\pi$
$59$	8.48528			1.10469			0.552345	+	0.833616i	$0.313733\pi$
$60$	−2.12132	−	0.707107i	−0.273861	−	0.0912871i
$61$	−3.41421			−0.437145			−0.218573	−	0.975821i	$-0.570140\pi$
$61$	−3.41421			−0.437145			−0.218573	+	0.975821i	$0.570140\pi$
$62$		−	6.00000i		−	0.762001i
$63$		−	2.00000i		−	0.251976i
$64$	−1.00000			−0.125000
$65$	10.2426	+	3.41421i	1.27044	+	0.423481i
$66$	4.24264			0.522233
$67$			0.585786i			0.0715652i	0.999360	+	0.0357826i	$0.0113924\pi$
$67$			0.585786i			0.0715652i	−0.999360	+	0.0357826i	$0.988608\pi$
$68$			1.17157i			0.142074i
$69$	1.00000			0.120386
$70$	1.41421	−	4.24264i	0.169031	−	0.507093i
$71$	5.65685			0.671345			0.335673	−	0.941979i	$-0.391036\pi$
$71$	5.65685			0.671345			0.335673	+	0.941979i	$0.391036\pi$
$72$		−	1.00000i		−	0.117851i
$73$		−	3.65685i		−	0.428002i	−0.976833	−	0.214001i	$-0.931350\pi$
$73$		−	3.65685i		−	0.428002i	0.976833	−	0.214001i	$-0.0686496\pi$
$74$	−3.41421			−0.396894
$75$	3.00000	−	4.00000i	0.346410	−	0.461880i
$76$	−2.24264			−0.257249
$77$			8.48528i			0.966988i
$78$			4.82843i			0.546712i
$79$	−7.65685			−0.861463			−0.430732	−	0.902480i	$-0.641744\pi$
$79$	−7.65685			−0.861463			−0.430732	+	0.902480i	$0.641744\pi$
$80$	0.707107	−	2.12132i	0.0790569	−	0.237171i
$81$	1.00000			0.111111
$82$			1.17157i			0.129379i
$83$		−	1.41421i		−	0.155230i	−0.996983	−	0.0776151i	$-0.975269\pi$
$83$		−	1.41421i		−	0.155230i	0.996983	−	0.0776151i	$-0.0247305\pi$
$84$	2.00000			0.218218
$85$	−2.48528	−	0.828427i	−0.269567	−	0.0898555i
$86$	1.75736			0.189501
$87$			7.65685i			0.820901i
$88$			4.24264i			0.452267i
$89$	−14.8284			−1.57181			−0.785905	−	0.618347i	$-0.787803\pi$
$89$	−14.8284			−1.57181			−0.785905	+	0.618347i	$0.787803\pi$
$90$	2.12132	+	0.707107i	0.223607	+	0.0745356i
$91$	−9.65685			−1.01231
$92$			1.00000i			0.104257i
$93$			6.00000i			0.622171i
$94$	−4.82843			−0.498014
$95$	1.58579	−	4.75736i	0.162698	−	0.488095i
$96$	1.00000			0.102062
$97$			6.00000i			0.609208i	0.952479	+	0.304604i	$0.0985241\pi$
$97$			6.00000i			0.609208i	−0.952479	+	0.304604i	$0.901476\pi$
$98$		−	3.00000i		−	0.303046i
$99$	−4.24264			−0.426401
$100$	4.00000	+	3.00000i	0.400000	+	0.300000i
$101$	−9.31371			−0.926749			−0.463374	−	0.886163i	$-0.653361\pi$
$101$	−9.31371			−0.926749			−0.463374	+	0.886163i	$0.653361\pi$
$102$		−	1.17157i		−	0.116003i
$103$		−	12.1421i		−	1.19640i	−0.801347	−	0.598200i	$-0.795883\pi$
$103$		−	12.1421i		−	1.19640i	0.801347	−	0.598200i	$-0.204117\pi$
$104$	−4.82843			−0.473466
$105$	−1.41421	+	4.24264i	−0.138013	+	0.414039i
$106$	13.4142			1.30290
$107$		−	15.0711i		−	1.45698i	−0.685059	−	0.728488i	$-0.740224\pi$
$107$		−	15.0711i		−	1.45698i	0.685059	−	0.728488i	$-0.259776\pi$
$108$			1.00000i			0.0962250i
$109$	−15.4142			−1.47641			−0.738207	−	0.674574i	$-0.764327\pi$
$109$	−15.4142			−1.47641			−0.738207	+	0.674574i	$0.764327\pi$
$110$	−9.00000	−	3.00000i	−0.858116	−	0.286039i
$111$	3.41421			0.324063
$112$			2.00000i			0.188982i
$113$			16.9706i			1.59646i	0.602355	+	0.798228i	$0.294229\pi$
$113$			16.9706i			1.59646i	−0.602355	+	0.798228i	$0.705771\pi$
$114$	2.24264			0.210043
$115$	−2.12132	−	0.707107i	−0.197814	−	0.0659380i
$116$	−7.65685			−0.710921
$117$		−	4.82843i		−	0.446388i
$118$		−	8.48528i		−	0.781133i
$119$	2.34315			0.214796
$120$	−0.707107	+	2.12132i	−0.0645497	+	0.193649i
$121$	7.00000			0.636364
$122$			3.41421i			0.309108i
$123$		−	1.17157i		−	0.105637i
$124$	−6.00000			−0.538816
$125$	−9.19239	+	6.36396i	−0.822192	+	0.569210i
$126$	−2.00000			−0.178174
$127$			2.00000i			0.177471i	0.996055	+	0.0887357i	$0.0282826\pi$
$127$			2.00000i			0.177471i	−0.996055	+	0.0887357i	$0.971717\pi$
$128$			1.00000i			0.0883883i
$129$	−1.75736			−0.154727
$130$	3.41421	−	10.2426i	0.299446	−	0.898339i
$131$	−10.3431			−0.903685			−0.451842	−	0.892098i	$-0.649233\pi$
$131$	−10.3431			−0.903685			−0.451842	+	0.892098i	$0.649233\pi$
$132$		−	4.24264i		−	0.369274i
$133$			4.48528i			0.388923i
$134$	0.585786			0.0506042
$135$	−2.12132	−	0.707107i	−0.182574	−	0.0608581i
$136$	1.17157			0.100462
$137$		−	8.48528i		−	0.724947i	−0.931994	−	0.362473i	$-0.881932\pi$
$137$		−	8.48528i		−	0.724947i	0.931994	−	0.362473i	$-0.118068\pi$
$138$		−	1.00000i		−	0.0851257i
$139$	−16.9706			−1.43942			−0.719712	−	0.694273i	$-0.755726\pi$
$139$	−16.9706			−1.43942			−0.719712	+	0.694273i	$0.755726\pi$
$140$	−4.24264	−	1.41421i	−0.358569	−	0.119523i
$141$	4.82843			0.406627
$142$		−	5.65685i		−	0.474713i
$143$			20.4853i			1.71307i
$144$	−1.00000			−0.0833333
$145$	5.41421	−	16.2426i	0.449626	−	1.34888i
$146$	−3.65685			−0.302643
$147$			3.00000i			0.247436i
$148$			3.41421i			0.280647i
$149$	12.7279			1.04271			0.521356	−	0.853339i	$-0.325426\pi$
$149$	12.7279			1.04271			0.521356	+	0.853339i	$0.325426\pi$
$150$	−4.00000	−	3.00000i	−0.326599	−	0.244949i
$151$	−15.6569			−1.27414			−0.637068	−	0.770807i	$-0.719853\pi$
$151$	−15.6569			−1.27414			−0.637068	+	0.770807i	$0.719853\pi$
$152$			2.24264i			0.181902i
$153$			1.17157i			0.0947161i
$154$	8.48528			0.683763
$155$	4.24264	−	12.7279i	0.340777	−	1.02233i
$156$	4.82843			0.386584
$157$		−	6.92893i		−	0.552989i	−0.961016	−	0.276494i	$-0.910827\pi$
$157$		−	6.92893i		−	0.552989i	0.961016	−	0.276494i	$-0.0891728\pi$
$158$			7.65685i			0.609147i
$159$	−13.4142			−1.06382
$160$	−2.12132	−	0.707107i	−0.167705	−	0.0559017i
$161$	2.00000			0.157622
$162$		−	1.00000i		−	0.0785674i
$163$			1.17157i			0.0917647i	0.998947	+	0.0458823i	$0.0146099\pi$
$163$			1.17157i			0.0917647i	−0.998947	+	0.0458823i	$0.985390\pi$
$164$	1.17157			0.0914845
$165$	9.00000	+	3.00000i	0.700649	+	0.233550i
$166$	−1.41421			−0.109764
$167$			8.82843i			0.683164i	0.939852	+	0.341582i	$0.110963\pi$
$167$			8.82843i			0.683164i	−0.939852	+	0.341582i	$0.889037\pi$
$168$		−	2.00000i		−	0.154303i
$169$	−10.3137			−0.793362
$170$	−0.828427	+	2.48528i	−0.0635375	+	0.190612i
$171$	−2.24264			−0.171499
$172$		−	1.75736i		−	0.133997i
$173$			3.17157i			0.241130i	0.992705	+	0.120565i	$0.0384707\pi$
$173$			3.17157i			0.241130i	−0.992705	+	0.120565i	$0.961529\pi$
$174$	7.65685			0.580465
$175$	6.00000	−	8.00000i	0.453557	−	0.604743i
$176$	4.24264			0.319801
$177$			8.48528i			0.637793i
$178$			14.8284i			1.11144i
$179$	10.3431			0.773083			0.386542	−	0.922272i	$-0.373670\pi$
$179$	10.3431			0.773083			0.386542	+	0.922272i	$0.373670\pi$
$180$	0.707107	−	2.12132i	0.0527046	−	0.158114i
$181$	16.3848			1.21787			0.608935	−	0.793220i	$-0.291597\pi$
$181$	16.3848			1.21787			0.608935	+	0.793220i	$0.291597\pi$
$182$			9.65685i			0.715814i
$183$		−	3.41421i		−	0.252386i
$184$	1.00000			0.0737210
$185$	−7.24264	−	2.41421i	−0.532490	−	0.177497i
$186$	6.00000			0.439941
$187$		−	4.97056i		−	0.363484i
$188$			4.82843i			0.352149i
$189$	2.00000			0.145479
$190$	−4.75736	−	1.58579i	−0.345135	−	0.115045i
$191$	−5.17157			−0.374202			−0.187101	−	0.982341i	$-0.559909\pi$
$191$	−5.17157			−0.374202			−0.187101	+	0.982341i	$0.559909\pi$
$192$		−	1.00000i		−	0.0721688i
$193$			12.9706i			0.933642i	0.884352	+	0.466821i	$0.154601\pi$
$193$			12.9706i			0.933642i	−0.884352	+	0.466821i	$0.845399\pi$
$194$	6.00000			0.430775
$195$	−3.41421	+	10.2426i	−0.244497	+	0.733491i
$196$	−3.00000			−0.214286
$197$			24.6274i			1.75463i	0.479914	+	0.877315i	$0.340668\pi$
$197$			24.6274i			1.75463i	−0.479914	+	0.877315i	$0.659332\pi$
$198$			4.24264i			0.301511i
$199$	14.0000			0.992434			0.496217	−	0.868199i	$-0.334722\pi$
$199$	14.0000			0.992434			0.496217	+	0.868199i	$0.334722\pi$
$200$	3.00000	−	4.00000i	0.212132	−	0.282843i
$201$	−0.585786			−0.0413182
$202$			9.31371i			0.655310i
$203$			15.3137i			1.07481i
$204$	−1.17157			−0.0820265
$205$	−0.828427	+	2.48528i	−0.0578599	+	0.173580i
$206$	−12.1421			−0.845983
$207$			1.00000i			0.0695048i
$208$			4.82843i			0.334791i
$209$	9.51472			0.658147
$210$	4.24264	+	1.41421i	0.292770	+	0.0975900i
$211$	−20.4853			−1.41026			−0.705132	−	0.709076i	$-0.749112\pi$
$211$	−20.4853			−1.41026			−0.705132	+	0.709076i	$0.749112\pi$
$212$		−	13.4142i		−	0.921292i
$213$			5.65685i			0.387601i
$214$	−15.0711			−1.03024
$215$	3.72792	+	1.24264i	0.254242	+	0.0847474i
$216$	1.00000			0.0680414
$217$			12.0000i			0.814613i
$218$			15.4142i			1.04398i
$219$	3.65685			0.247107
$220$	−3.00000	+	9.00000i	−0.202260	+	0.606780i
$221$	5.65685			0.380521
$222$		−	3.41421i		−	0.229147i
$223$			16.0000i			1.07144i	0.844396	+	0.535720i	$0.179960\pi$
$223$			16.0000i			1.07144i	−0.844396	+	0.535720i	$0.820040\pi$
$224$	2.00000			0.133631
$225$	4.00000	+	3.00000i	0.266667	+	0.200000i
$226$	16.9706			1.12887
$227$		−	14.3848i		−	0.954751i	−0.878699	−	0.477376i	$-0.841588\pi$
$227$		−	14.3848i		−	0.954751i	0.878699	−	0.477376i	$-0.158412\pi$
$228$		−	2.24264i		−	0.148523i
$229$	−1.75736			−0.116130			−0.0580648	−	0.998313i	$-0.518493\pi$
$229$	−1.75736			−0.116130			−0.0580648	+	0.998313i	$0.518493\pi$
$230$	−0.707107	+	2.12132i	−0.0466252	+	0.139876i
$231$	−8.48528			−0.558291
$232$			7.65685i			0.502697i
$233$		−	26.1421i		−	1.71263i	−0.516455	−	0.856314i	$-0.672749\pi$
$233$		−	26.1421i		−	1.71263i	0.516455	−	0.856314i	$-0.327251\pi$
$234$	−4.82843			−0.315644
$235$	−10.2426	−	3.41421i	−0.668156	−	0.222719i
$236$	−8.48528			−0.552345
$237$		−	7.65685i		−	0.497366i
$238$		−	2.34315i		−	0.151884i
$239$	11.1716			0.722629			0.361314	−	0.932444i	$-0.382328\pi$
$239$	11.1716			0.722629			0.361314	+	0.932444i	$0.382328\pi$
$240$	2.12132	+	0.707107i	0.136931	+	0.0456435i
$241$	−10.4853			−0.675416			−0.337708	−	0.941251i	$-0.609652\pi$
$241$	−10.4853			−0.675416			−0.337708	+	0.941251i	$0.609652\pi$
$242$		−	7.00000i		−	0.449977i
$243$			1.00000i			0.0641500i
$244$	3.41421			0.218573
$245$	2.12132	−	6.36396i	0.135526	−	0.406579i
$246$	−1.17157			−0.0746968
$247$			10.8284i			0.688996i
$248$			6.00000i			0.381000i
$249$	1.41421			0.0896221
$250$	6.36396	+	9.19239i	0.402492	+	0.581378i
$251$	−24.7279			−1.56081			−0.780406	−	0.625273i	$-0.784988\pi$
$251$	−24.7279			−1.56081			−0.780406	+	0.625273i	$0.784988\pi$
$252$			2.00000i			0.125988i
$253$		−	4.24264i		−	0.266733i
$254$	2.00000			0.125491
$255$	0.828427	−	2.48528i	0.0518781	−	0.155634i
$256$	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	$-0.189739\pi$
$258$			1.75736i			0.109408i
$259$	6.82843			0.424298
$260$	−10.2426	−	3.41421i	−0.635222	−	0.211741i
$261$	−7.65685			−0.473947
$262$			10.3431i			0.639002i
$263$		−	17.6569i		−	1.08877i	−0.838836	−	0.544384i	$-0.816763\pi$
$263$		−	17.6569i		−	1.08877i	0.838836	−	0.544384i	$-0.183237\pi$
$264$	−4.24264			−0.261116
$265$	28.4558	+	9.48528i	1.74803	+	0.582676i
$266$	4.48528			0.275010
$267$		−	14.8284i		−	0.907485i
$268$		−	0.585786i		−	0.0357826i
$269$	24.8284			1.51382			0.756908	−	0.653521i	$-0.226709\pi$
$269$	24.8284			1.51382			0.756908	+	0.653521i	$0.226709\pi$
$270$	−0.707107	+	2.12132i	−0.0430331	+	0.129099i
$271$	−1.65685			−0.100647			−0.0503234	−	0.998733i	$-0.516025\pi$
$271$	−1.65685			−0.100647			−0.0503234	+	0.998733i	$0.516025\pi$
$272$		−	1.17157i		−	0.0710370i
$273$		−	9.65685i		−	0.584459i
$274$	−8.48528			−0.512615
$275$	−16.9706	−	12.7279i	−1.02336	−	0.767523i
$276$	−1.00000			−0.0601929
$277$		−	30.4853i		−	1.83168i	−0.401540	−	0.915842i	$-0.631525\pi$
$277$		−	30.4853i		−	1.83168i	0.401540	−	0.915842i	$-0.368475\pi$
$278$			16.9706i			1.01783i
$279$	−6.00000			−0.359211
$280$	−1.41421	+	4.24264i	−0.0845154	+	0.253546i
$281$	−30.1421			−1.79813			−0.899065	−	0.437816i	$-0.855752\pi$
$281$	−30.1421			−1.79813			−0.899065	+	0.437816i	$0.855752\pi$
$282$		−	4.82843i		−	0.287529i
$283$		−	27.2132i		−	1.61766i	−0.588045	−	0.808829i	$-0.700102\pi$
$283$		−	27.2132i		−	1.61766i	0.588045	−	0.808829i	$-0.299898\pi$
$284$	−5.65685			−0.335673
$285$	4.75736	+	1.58579i	0.281802	+	0.0939339i
$286$	20.4853			1.21132
$287$		−	2.34315i		−	0.138312i
$288$			1.00000i			0.0589256i
$289$	15.6274			0.919260
$290$	−16.2426	−	5.41421i	−0.953801	−	0.317934i
$291$	−6.00000			−0.351726
$292$			3.65685i			0.214001i
$293$		−	28.0416i		−	1.63821i	−0.573644	−	0.819105i	$-0.694471\pi$
$293$		−	28.0416i		−	1.63821i	0.573644	−	0.819105i	$-0.305529\pi$
$294$	3.00000			0.174964
$295$	6.00000	−	18.0000i	0.349334	−	1.04800i
$296$	3.41421			0.198447
$297$		−	4.24264i		−	0.246183i
$298$		−	12.7279i		−	0.737309i
$299$	4.82843			0.279235
$300$	−3.00000	+	4.00000i	−0.173205	+	0.230940i
$301$	−3.51472			−0.202585
$302$			15.6569i			0.900951i
$303$		−	9.31371i		−	0.535059i
$304$	2.24264			0.128624
$305$	−2.41421	+	7.24264i	−0.138237	+	0.414712i
$306$	1.17157			0.0669744
$307$			25.4558i			1.45284i	0.687250	+	0.726421i	$0.258818\pi$
$307$			25.4558i			1.45284i	−0.687250	+	0.726421i	$0.741182\pi$
$308$		−	8.48528i		−	0.483494i
$309$	12.1421			0.690742
$310$	−12.7279	−	4.24264i	−0.722897	−	0.240966i
$311$	17.7990			1.00929			0.504644	−	0.863328i	$-0.331624\pi$
$311$	17.7990			1.00929			0.504644	+	0.863328i	$0.331624\pi$
$312$		−	4.82843i		−	0.273356i
$313$			18.0000i			1.01742i	0.860938	+	0.508710i	$0.169877\pi$
$313$			18.0000i			1.01742i	−0.860938	+	0.508710i	$0.830123\pi$
$314$	−6.92893			−0.391022
$315$	−4.24264	−	1.41421i	−0.239046	−	0.0796819i
$316$	7.65685			0.430732
$317$		−	2.48528i		−	0.139587i	−0.997561	−	0.0697937i	$-0.977766\pi$
$317$		−	2.48528i		−	0.139587i	0.997561	−	0.0697937i	$-0.0222341\pi$
$318$			13.4142i			0.752232i
$319$	32.4853			1.81883
$320$	−0.707107	+	2.12132i	−0.0395285	+	0.118585i
$321$	15.0711			0.841185
$322$		−	2.00000i		−	0.111456i
$323$		−	2.62742i		−	0.146193i
$324$	−1.00000			−0.0555556
$325$	14.4853	−	19.3137i	0.803499	−	1.07133i
$326$	1.17157			0.0648874
$327$		−	15.4142i		−	0.852408i
$328$		−	1.17157i		−	0.0646893i
$329$	9.65685			0.532400
$330$	3.00000	−	9.00000i	0.165145	−	0.495434i
$331$	−3.51472			−0.193186			−0.0965932	−	0.995324i	$-0.530795\pi$
$331$	−3.51472			−0.193186			−0.0965932	+	0.995324i	$0.530795\pi$
$332$			1.41421i			0.0776151i
$333$			3.41421i			0.187098i
$334$	8.82843			0.483070
$335$	1.24264	+	0.414214i	0.0678927	+	0.0226309i
$336$	−2.00000			−0.109109
$337$			9.51472i			0.518300i	0.965837	+	0.259150i	$0.0834424\pi$
$337$			9.51472i			0.518300i	−0.965837	+	0.259150i	$0.916558\pi$
$338$			10.3137i			0.560992i
$339$	−16.9706			−0.921714
$340$	2.48528	+	0.828427i	0.134783	+	0.0449278i
$341$	25.4558			1.37851
$342$			2.24264i			0.121268i
$343$			20.0000i			1.07990i
$344$	−1.75736			−0.0947505
$345$	0.707107	−	2.12132i	0.0380693	−	0.114208i
$346$	3.17157			0.170505
$347$		−	7.79899i		−	0.418672i	−0.977844	−	0.209336i	$-0.932870\pi$
$347$		−	7.79899i		−	0.418672i	0.977844	−	0.209336i	$-0.0671302\pi$
$348$		−	7.65685i		−	0.410450i
$349$	−25.3137			−1.35501			−0.677506	−	0.735517i	$-0.736939\pi$
$349$	−25.3137			−1.35501			−0.677506	+	0.735517i	$0.736939\pi$
$350$	−8.00000	−	6.00000i	−0.427618	−	0.320713i
$351$	4.82843			0.257722
$352$		−	4.24264i		−	0.226134i
$353$		−	26.1421i		−	1.39141i	−0.718330	−	0.695703i	$-0.755093\pi$
$353$		−	26.1421i		−	1.39141i	0.718330	−	0.695703i	$-0.244907\pi$
$354$	8.48528			0.450988
$355$	4.00000	−	12.0000i	0.212298	−	0.636894i
$356$	14.8284			0.785905
$357$			2.34315i			0.124012i
$358$		−	10.3431i		−	0.546652i
$359$	19.7990			1.04495			0.522475	−	0.852654i	$-0.325009\pi$
$359$	19.7990			1.04495			0.522475	+	0.852654i	$0.325009\pi$
$360$	−2.12132	−	0.707107i	−0.111803	−	0.0372678i
$361$	−13.9706			−0.735293
$362$		−	16.3848i		−	0.861165i
$363$			7.00000i			0.367405i
$364$	9.65685			0.506157
$365$	−7.75736	−	2.58579i	−0.406039	−	0.135346i
$366$	−3.41421			−0.178464
$367$		−	34.9706i		−	1.82545i	−0.408576	−	0.912724i	$-0.633975\pi$
$367$		−	34.9706i		−	1.82545i	0.408576	−	0.912724i	$-0.366025\pi$
$368$		−	1.00000i		−	0.0521286i
$369$	1.17157			0.0609896
$370$	−2.41421	+	7.24264i	−0.125509	+	0.376527i
$371$	−26.8284			−1.39286
$372$		−	6.00000i		−	0.311086i
$373$			19.2132i			0.994822i	0.867515	+	0.497411i	$0.165716\pi$
$373$			19.2132i			0.994822i	−0.867515	+	0.497411i	$0.834284\pi$
$374$	−4.97056			−0.257022
$375$	−6.36396	−	9.19239i	−0.328634	−	0.474693i
$376$	4.82843			0.249007
$377$			36.9706i			1.90408i
$378$		−	2.00000i		−	0.102869i
$379$	19.2132			0.986916			0.493458	−	0.869770i	$-0.335733\pi$
$379$	19.2132			0.986916			0.493458	+	0.869770i	$0.335733\pi$
$380$	−1.58579	+	4.75736i	−0.0813491	+	0.244047i
$381$	−2.00000			−0.102463
$382$			5.17157i			0.264601i
$383$		−	18.6274i		−	0.951817i	−0.879495	−	0.475908i	$-0.842119\pi$
$383$		−	18.6274i		−	0.951817i	0.879495	−	0.475908i	$-0.157881\pi$
$384$	−1.00000			−0.0510310
$385$	18.0000	+	6.00000i	0.917365	+	0.305788i
$386$	12.9706			0.660184
$387$		−	1.75736i		−	0.0893316i
$388$		−	6.00000i		−	0.304604i
$389$	−6.38478			−0.323721			−0.161861	−	0.986814i	$-0.551749\pi$
$389$	−6.38478			−0.323721			−0.161861	+	0.986814i	$0.551749\pi$
$390$	10.2426	+	3.41421i	0.518656	+	0.172885i
$391$	−1.17157			−0.0592490
$392$			3.00000i			0.151523i
$393$		−	10.3431i		−	0.521743i
$394$	24.6274			1.24071
$395$	−5.41421	+	16.2426i	−0.272419	+	0.817256i
$396$	4.24264			0.213201
$397$			8.34315i			0.418730i	0.977838	+	0.209365i	$0.0671398\pi$
$397$			8.34315i			0.418730i	−0.977838	+	0.209365i	$0.932860\pi$
$398$		−	14.0000i		−	0.701757i
$399$	−4.48528			−0.224545
$400$	−4.00000	−	3.00000i	−0.200000	−	0.150000i
$401$	−28.9706			−1.44672			−0.723360	−	0.690471i	$-0.757403\pi$
$401$	−28.9706			−1.44672			−0.723360	+	0.690471i	$0.757403\pi$
$402$			0.585786i			0.0292164i
$403$			28.9706i			1.44313i
$404$	9.31371			0.463374
$405$	0.707107	−	2.12132i	0.0351364	−	0.105409i
$406$	15.3137			0.760007
$407$		−	14.4853i		−	0.718009i
$408$			1.17157i			0.0580015i
$409$	−18.0000			−0.890043			−0.445021	−	0.895520i	$-0.646804\pi$
$409$	−18.0000			−0.890043			−0.445021	+	0.895520i	$0.646804\pi$
$410$	2.48528	+	0.828427i	0.122739	+	0.0409131i
$411$	8.48528			0.418548
$412$			12.1421i			0.598200i
$413$			16.9706i			0.835067i
$414$	1.00000			0.0491473
$415$	−3.00000	−	1.00000i	−0.147264	−	0.0490881i
$416$	4.82843			0.236733
$417$		−	16.9706i		−	0.831052i
$418$		−	9.51472i		−	0.465380i
$419$	24.9289			1.21786			0.608929	−	0.793225i	$-0.291599\pi$
$419$	24.9289			1.21786			0.608929	+	0.793225i	$0.291599\pi$
$420$	1.41421	−	4.24264i	0.0690066	−	0.207020i
$421$	10.2426			0.499196			0.249598	−	0.968350i	$-0.419702\pi$
$421$	10.2426			0.499196			0.249598	+	0.968350i	$0.419702\pi$
$422$			20.4853i			0.997208i
$423$			4.82843i			0.234766i
$424$	−13.4142			−0.651452
$425$	−3.51472	+	4.68629i	−0.170489	+	0.227319i
$426$	5.65685			0.274075
$427$		−	6.82843i		−	0.330451i
$428$			15.0711i			0.728488i
$429$	−20.4853			−0.989039
$430$	1.24264	−	3.72792i	0.0599255	−	0.179776i
$431$	8.48528			0.408722			0.204361	−	0.978896i	$-0.434488\pi$
$431$	8.48528			0.408722			0.204361	+	0.978896i	$0.434488\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			26.9706i			1.29612i	0.761588	+	0.648061i	$0.224420\pi$
$433$			26.9706i			1.29612i	−0.761588	+	0.648061i	$0.775580\pi$
$434$	12.0000			0.576018
$435$	16.2426	+	5.41421i	0.778775	+	0.259592i
$436$	15.4142			0.738207
$437$		−	2.24264i		−	0.107280i
$438$		−	3.65685i		−	0.174731i
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$	9.00000	+	3.00000i	0.429058	+	0.143019i
$441$	−3.00000			−0.142857
$442$		−	5.65685i		−	0.269069i
$443$		−	23.3137i		−	1.10767i	−0.832627	−	0.553834i	$-0.813164\pi$
$443$		−	23.3137i		−	1.10767i	0.832627	−	0.553834i	$-0.186836\pi$
$444$	−3.41421			−0.162031
$445$	−10.4853	+	31.4558i	−0.497050	+	1.49115i
$446$	16.0000			0.757622
$447$			12.7279i			0.602010i
$448$		−	2.00000i		−	0.0944911i
$449$	22.8284			1.07734			0.538670	−	0.842517i	$-0.318927\pi$
$449$	22.8284			1.07734			0.538670	+	0.842517i	$0.318927\pi$
$450$	3.00000	−	4.00000i	0.141421	−	0.188562i
$451$	−4.97056			−0.234055
$452$		−	16.9706i		−	0.798228i
$453$		−	15.6569i		−	0.735623i
$454$	−14.3848			−0.675111
$455$	−6.82843	+	20.4853i	−0.320122	+	0.960365i
$456$	−2.24264			−0.105021
$457$		−	1.02944i		−	0.0481550i	−0.999710	−	0.0240775i	$-0.992335\pi$
$457$		−	1.02944i		−	0.0481550i	0.999710	−	0.0240775i	$-0.00766485\pi$
$458$			1.75736i			0.0821160i
$459$	−1.17157			−0.0546843
$460$	2.12132	+	0.707107i	0.0989071	+	0.0329690i
$461$	−12.8284			−0.597479			−0.298740	−	0.954335i	$-0.596566\pi$
$461$	−12.8284			−0.597479			−0.298740	+	0.954335i	$0.596566\pi$
$462$			8.48528i			0.394771i
$463$			2.97056i			0.138054i	0.997615	+	0.0690269i	$0.0219894\pi$
$463$			2.97056i			0.138054i	−0.997615	+	0.0690269i	$0.978011\pi$
$464$	7.65685			0.355461
$465$	12.7279	+	4.24264i	0.590243	+	0.196748i
$466$	−26.1421			−1.21101
$467$		−	39.3553i		−	1.82115i	−0.413346	−	0.910574i	$-0.635640\pi$
$467$		−	39.3553i		−	1.82115i	0.413346	−	0.910574i	$-0.364360\pi$
$468$			4.82843i			0.223194i
$469$	−1.17157			−0.0540982
$470$	−3.41421	+	10.2426i	−0.157486	+	0.472458i
$471$	6.92893			0.319268
$472$			8.48528i			0.390567i
$473$			7.45584i			0.342820i
$474$	−7.65685			−0.351691
$475$	−8.97056	−	6.72792i	−0.411598	−	0.308698i
$476$	−2.34315			−0.107398
$477$		−	13.4142i		−	0.614195i
$478$		−	11.1716i		−	0.510976i
$479$	−4.68629			−0.214122			−0.107061	−	0.994252i	$-0.534144\pi$
$479$	−4.68629			−0.214122			−0.107061	+	0.994252i	$0.534144\pi$
$480$	0.707107	−	2.12132i	0.0322749	−	0.0968246i
$481$	16.4853			0.751664
$482$			10.4853i			0.477591i
$483$			2.00000i			0.0910032i
$484$	−7.00000			−0.318182
$485$	12.7279	+	4.24264i	0.577945	+	0.192648i
$486$	1.00000			0.0453609
$487$			27.9411i			1.26613i	0.774097	+	0.633067i	$0.218204\pi$
$487$			27.9411i			1.26613i	−0.774097	+	0.633067i	$0.781796\pi$
$488$		−	3.41421i		−	0.154554i
$489$	−1.17157			−0.0529804
$490$	−6.36396	−	2.12132i	−0.287494	−	0.0958315i
$491$	26.6274			1.20168			0.600839	−	0.799370i	$-0.294833\pi$
$491$	26.6274			1.20168			0.600839	+	0.799370i	$0.294833\pi$
$492$			1.17157i			0.0528186i
$493$		−	8.97056i		−	0.404014i
$494$	10.8284			0.487194
$495$	−3.00000	+	9.00000i	−0.134840	+	0.404520i
$496$	6.00000			0.269408
$497$			11.3137i			0.507489i
$498$		−	1.41421i		−	0.0633724i
$499$	−13.4558			−0.602366			−0.301183	−	0.953566i	$-0.597382\pi$
$499$	−13.4558			−0.602366			−0.301183	+	0.953566i	$0.597382\pi$
$500$	9.19239	−	6.36396i	0.411096	−	0.284605i
$501$	−8.82843			−0.394425
$502$			24.7279i			1.10366i
$503$			22.1421i			0.987269i	0.869669	+	0.493635i	$0.164332\pi$
$503$			22.1421i			0.987269i	−0.869669	+	0.493635i	$0.835668\pi$
$504$	2.00000			0.0890871
$505$	−6.58579	+	19.7574i	−0.293064	+	0.879191i
$506$	−4.24264			−0.188608
$507$		−	10.3137i		−	0.458048i
$508$		−	2.00000i		−	0.0887357i
$509$	−22.9706			−1.01815			−0.509076	−	0.860721i	$-0.670013\pi$
$509$	−22.9706			−1.01815			−0.509076	+	0.860721i	$0.670013\pi$
$510$	−2.48528	−	0.828427i	−0.110050	−	0.0366834i
$511$	7.31371			0.323539
$512$		−	1.00000i		−	0.0441942i
$513$		−	2.24264i		−	0.0990150i
$514$	−18.0000			−0.793946
$515$	−25.7574	−	8.58579i	−1.13500	−	0.378335i
$516$	1.75736			0.0773634
$517$		−	20.4853i		−	0.900942i
$518$		−	6.82843i		−	0.300024i
$519$	−3.17157			−0.139217
$520$	−3.41421	+	10.2426i	−0.149723	+	0.449170i
$521$	−16.2843			−0.713427			−0.356713	−	0.934214i	$-0.616103\pi$
$521$	−16.2843			−0.713427			−0.356713	+	0.934214i	$0.616103\pi$
$522$			7.65685i			0.335131i
$523$		−	2.92893i		−	0.128073i	−0.997948	−	0.0640366i	$-0.979603\pi$
$523$		−	2.92893i		−	0.128073i	0.997948	−	0.0640366i	$-0.0203974\pi$
$524$	10.3431			0.451842
$525$	8.00000	+	6.00000i	0.349149	+	0.261861i
$526$	−17.6569			−0.769875
$527$		−	7.02944i		−	0.306207i
$528$			4.24264i			0.184637i
$529$	−1.00000			−0.0434783
$530$	9.48528	−	28.4558i	0.412014	−	1.23604i
$531$	−8.48528			−0.368230
$532$		−	4.48528i		−	0.194462i
$533$		−	5.65685i		−	0.245026i
$534$	−14.8284			−0.641689
$535$	−31.9706	−	10.6569i	−1.38221	−	0.460736i
$536$	−0.585786			−0.0253021
$537$			10.3431i			0.446340i
$538$		−	24.8284i		−	1.07043i
$539$	12.7279			0.548230
$540$	2.12132	+	0.707107i	0.0912871	+	0.0304290i
$541$	35.9411			1.54523			0.772615	−	0.634875i	$-0.218948\pi$
$541$	35.9411			1.54523			0.772615	+	0.634875i	$0.218948\pi$
$542$			1.65685i			0.0711680i
$543$			16.3848i			0.703138i
$544$	−1.17157			−0.0502308
$545$	−10.8995	+	32.6985i	−0.466883	+	1.40065i
$546$	−9.65685			−0.413275
$547$			4.48528i			0.191777i	0.995392	+	0.0958884i	$0.0305692\pi$
$547$			4.48528i			0.191777i	−0.995392	+	0.0958884i	$0.969431\pi$
$548$			8.48528i			0.362473i
$549$	3.41421			0.145715
$550$	−12.7279	+	16.9706i	−0.542720	+	0.723627i
$551$	17.1716			0.731534
$552$			1.00000i			0.0425628i
$553$		−	15.3137i		−	0.651205i
$554$	−30.4853			−1.29520
$555$	2.41421	−	7.24264i	0.102478	−	0.307433i
$556$	16.9706			0.719712
$557$			14.8701i			0.630065i	0.949081	+	0.315032i	$0.102015\pi$
$557$			14.8701i			0.630065i	−0.949081	+	0.315032i	$0.897985\pi$
$558$			6.00000i			0.254000i
$559$	−8.48528			−0.358889
$560$	4.24264	+	1.41421i	0.179284	+	0.0597614i
$561$	4.97056			0.209857
$562$			30.1421i			1.27147i
$563$		−	21.8995i		−	0.922954i	−0.887152	−	0.461477i	$-0.847320\pi$
$563$		−	21.8995i		−	0.922954i	0.887152	−	0.461477i	$-0.152680\pi$
$564$	−4.82843			−0.203313
$565$	36.0000	+	12.0000i	1.51453	+	0.504844i
$566$	−27.2132			−1.14386
$567$			2.00000i			0.0839921i
$568$			5.65685i			0.237356i
$569$	−25.6569			−1.07559			−0.537796	−	0.843075i	$-0.680743\pi$
$569$	−25.6569			−1.07559			−0.537796	+	0.843075i	$0.680743\pi$
$570$	1.58579	−	4.75736i	0.0664213	−	0.199264i
$571$	−42.7279			−1.78811			−0.894054	−	0.447959i	$-0.852151\pi$
$571$	−42.7279			−1.78811			−0.894054	+	0.447959i	$0.852151\pi$
$572$		−	20.4853i		−	0.856533i
$573$		−	5.17157i		−	0.216046i
$574$	−2.34315			−0.0978010
$575$	−3.00000	+	4.00000i	−0.125109	+	0.166812i
$576$	1.00000			0.0416667
$577$			20.6274i			0.858731i	0.903131	+	0.429365i	$0.141263\pi$
$577$			20.6274i			0.858731i	−0.903131	+	0.429365i	$0.858737\pi$
$578$		−	15.6274i		−	0.650015i
$579$	−12.9706			−0.539038
$580$	−5.41421	+	16.2426i	−0.224813	+	0.674439i
$581$	2.82843			0.117343
$582$			6.00000i			0.248708i
$583$			56.9117i			2.35704i
$584$	3.65685			0.151322
$585$	−10.2426	−	3.41421i	−0.423481	−	0.141160i
$586$	−28.0416			−1.15839
$587$		−	26.8284i		−	1.10733i	−0.832740	−	0.553664i	$-0.813229\pi$
$587$		−	26.8284i		−	1.10733i	0.832740	−	0.553664i	$-0.186771\pi$
$588$		−	3.00000i		−	0.123718i
$589$	13.4558			0.554438
$590$	−18.0000	−	6.00000i	−0.741048	−	0.247016i
$591$	−24.6274			−1.01304
$592$		−	3.41421i		−	0.140323i
$593$		−	12.3431i		−	0.506872i	−0.967352	−	0.253436i	$-0.918439\pi$
$593$		−	12.3431i		−	0.506872i	0.967352	−	0.253436i	$-0.0815608\pi$
$594$	−4.24264			−0.174078
$595$	1.65685	−	4.97056i	0.0679244	−	0.203773i
$596$	−12.7279			−0.521356
$597$			14.0000i			0.572982i
$598$		−	4.82843i		−	0.197449i
$599$	40.1421			1.64016			0.820082	−	0.572247i	$-0.193928\pi$
$599$	40.1421			1.64016			0.820082	+	0.572247i	$0.193928\pi$
$600$	4.00000	+	3.00000i	0.163299	+	0.122474i
$601$	−20.9706			−0.855407			−0.427704	−	0.903919i	$-0.640677\pi$
$601$	−20.9706			−0.855407			−0.427704	+	0.903919i	$0.640677\pi$
$602$			3.51472i			0.143249i
$603$		−	0.585786i		−	0.0238551i
$604$	15.6569			0.637068
$605$	4.94975	−	14.8492i	0.201236	−	0.603708i
$606$	−9.31371			−0.378344
$607$			16.9706i			0.688814i	0.938820	+	0.344407i	$0.111920\pi$
$607$			16.9706i			0.688814i	−0.938820	+	0.344407i	$0.888080\pi$
$608$		−	2.24264i		−	0.0909511i
$609$	−15.3137			−0.620543
$610$	7.24264	+	2.41421i	0.293246	+	0.0977486i
$611$	23.3137			0.943172
$612$		−	1.17157i		−	0.0473580i
$613$		−	14.2426i		−	0.575255i	−0.957742	−	0.287627i	$-0.907134\pi$
$613$		−	14.2426i		−	0.575255i	0.957742	−	0.287627i	$-0.0928665\pi$
$614$	25.4558			1.02731
$615$	−2.48528	−	0.828427i	−0.100216	−	0.0334054i
$616$	−8.48528			−0.341882
$617$			31.3137i			1.26064i	0.776334	+	0.630321i	$0.217077\pi$
$617$			31.3137i			1.26064i	−0.776334	+	0.630321i	$0.782923\pi$
$618$		−	12.1421i		−	0.488428i
$619$	19.2132			0.772244			0.386122	−	0.922448i	$-0.373814\pi$
$619$	19.2132			0.772244			0.386122	+	0.922448i	$0.373814\pi$
$620$	−4.24264	+	12.7279i	−0.170389	+	0.511166i
$621$	−1.00000			−0.0401286
$622$		−	17.7990i		−	0.713674i
$623$		−	29.6569i		−	1.18818i
$624$	−4.82843			−0.193292
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$	18.0000			0.719425
$627$			9.51472i			0.379981i
$628$			6.92893i			0.276494i
$629$	−4.00000			−0.159490
$630$	−1.41421	+	4.24264i	−0.0563436	+	0.169031i
$631$	35.1716			1.40016			0.700079	−	0.714065i	$-0.253148\pi$
$631$	35.1716			1.40016			0.700079	+	0.714065i	$0.253148\pi$
$632$		−	7.65685i		−	0.304573i
$633$		−	20.4853i		−	0.814217i
$634$	−2.48528			−0.0987031
$635$	4.24264	+	1.41421i	0.168364	+	0.0561214i
$636$	13.4142			0.531908
$637$			14.4853i			0.573928i
$638$		−	32.4853i		−	1.28610i
$639$	−5.65685			−0.223782
$640$	2.12132	+	0.707107i	0.0838525	+	0.0279508i
$641$	−8.28427			−0.327209			−0.163605	−	0.986526i	$-0.552312\pi$
$641$	−8.28427			−0.327209			−0.163605	+	0.986526i	$0.552312\pi$
$642$		−	15.0711i		−	0.594808i
$643$		−	32.3848i		−	1.27713i	−0.769568	−	0.638565i	$-0.779528\pi$
$643$		−	32.3848i		−	1.27713i	0.769568	−	0.638565i	$-0.220472\pi$
$644$	−2.00000			−0.0788110
$645$	−1.24264	+	3.72792i	−0.0489289	+	0.146787i
$646$	−2.62742			−0.103374
$647$			29.6569i			1.16593i	0.812497	+	0.582966i	$0.198108\pi$
$647$			29.6569i			1.16593i	−0.812497	+	0.582966i	$0.801892\pi$
$648$			1.00000i			0.0392837i
$649$	36.0000			1.41312
$650$	−19.3137	−	14.4853i	−0.757546	−	0.568159i
$651$	−12.0000			−0.470317
$652$		−	1.17157i		−	0.0458823i
$653$			43.4558i			1.70056i	0.526332	+	0.850279i	$0.323567\pi$
$653$			43.4558i			1.70056i	−0.526332	+	0.850279i	$0.676433\pi$
$654$	−15.4142			−0.602743
$655$	−7.31371	+	21.9411i	−0.285770	+	0.857311i
$656$	−1.17157			−0.0457422
$657$			3.65685i			0.142667i
$658$		−	9.65685i		−	0.376463i
$659$	26.1005			1.01673			0.508366	−	0.861141i	$-0.330250\pi$
$659$	26.1005			1.01673			0.508366	+	0.861141i	$0.330250\pi$
$660$	−9.00000	−	3.00000i	−0.350325	−	0.116775i
$661$	9.27208			0.360642			0.180321	−	0.983608i	$-0.442286\pi$
$661$	9.27208			0.360642			0.180321	+	0.983608i	$0.442286\pi$
$662$			3.51472i			0.136603i
$663$			5.65685i			0.219694i
$664$	1.41421			0.0548821
$665$	9.51472	+	3.17157i	0.368965	+	0.122988i
$666$	3.41421			0.132298
$667$		−	7.65685i		−	0.296475i
$668$		−	8.82843i		−	0.341582i
$669$	−16.0000			−0.618596
$670$	0.414214	−	1.24264i	0.0160025	−	0.0480074i
$671$	−14.4853			−0.559198
$672$			2.00000i			0.0771517i
$673$		−	39.9411i		−	1.53962i	−0.638275	−	0.769809i	$-0.720352\pi$
$673$		−	39.9411i		−	1.53962i	0.638275	−	0.769809i	$-0.279648\pi$
$674$	9.51472			0.366493
$675$	−3.00000	+	4.00000i	−0.115470	+	0.153960i
$676$	10.3137			0.396681
$677$		−	24.5269i		−	0.942646i	−0.881961	−	0.471323i	$-0.843777\pi$
$677$		−	24.5269i		−	0.942646i	0.881961	−	0.471323i	$-0.156223\pi$
$678$			16.9706i			0.651751i
$679$	−12.0000			−0.460518
$680$	0.828427	−	2.48528i	0.0317687	−	0.0953062i
$681$	14.3848			0.551226
$682$		−	25.4558i		−	0.974755i
$683$			8.48528i			0.324680i	0.986735	+	0.162340i	$0.0519042\pi$
$683$			8.48528i			0.324680i	−0.986735	+	0.162340i	$0.948096\pi$
$684$	2.24264			0.0857495
$685$	−18.0000	−	6.00000i	−0.687745	−	0.229248i
$686$	20.0000			0.763604
$687$		−	1.75736i		−	0.0670474i
$688$			1.75736i			0.0669987i
$689$	−64.7696			−2.46752
$690$	−2.12132	−	0.707107i	−0.0807573	−	0.0269191i
$691$	−18.8284			−0.716267			−0.358134	−	0.933670i	$-0.616587\pi$
$691$	−18.8284			−0.716267			−0.358134	+	0.933670i	$0.616587\pi$
$692$		−	3.17157i		−	0.120565i
$693$		−	8.48528i		−	0.322329i
$694$	−7.79899			−0.296046
$695$	−12.0000	+	36.0000i	−0.455186	+	1.36556i
$696$	−7.65685			−0.290232
$697$			1.37258i			0.0519903i
$698$			25.3137i			0.958138i
$699$	26.1421			0.988786
$700$	−6.00000	+	8.00000i	−0.226779	+	0.302372i
$701$	38.1838			1.44218			0.721090	−	0.692841i	$-0.243641\pi$
$701$	38.1838			1.44218			0.721090	+	0.692841i	$0.243641\pi$
$702$		−	4.82843i		−	0.182237i
$703$		−	7.65685i		−	0.288784i
$704$	−4.24264			−0.159901
$705$	3.41421	−	10.2426i	0.128587	−	0.385760i
$706$	−26.1421			−0.983872
$707$		−	18.6274i		−	0.700556i
$708$		−	8.48528i		−	0.318896i
$709$	−35.4142			−1.33001			−0.665004	−	0.746839i	$-0.731570\pi$
$709$	−35.4142			−1.33001			−0.665004	+	0.746839i	$0.731570\pi$
$710$	−12.0000	−	4.00000i	−0.450352	−	0.150117i
$711$	7.65685			0.287154
$712$		−	14.8284i		−	0.555719i
$713$		−	6.00000i		−	0.224702i
$714$	2.34315			0.0876900
$715$	43.4558	+	14.4853i	1.62516	+	0.541719i
$716$	−10.3431			−0.386542
$717$			11.1716i			0.417210i
$718$		−	19.7990i		−	0.738892i
$719$	−28.1421			−1.04952			−0.524762	−	0.851249i	$-0.675846\pi$
$719$	−28.1421			−1.04952			−0.524762	+	0.851249i	$0.675846\pi$
$720$	−0.707107	+	2.12132i	−0.0263523	+	0.0790569i
$721$	24.2843			0.904394
$722$			13.9706i			0.519931i
$723$		−	10.4853i		−	0.389952i
$724$	−16.3848			−0.608935
$725$	−30.6274	−	22.9706i	−1.13747	−	0.853105i
$726$	7.00000			0.259794
$727$			31.6569i			1.17409i	0.809555	+	0.587044i	$0.199708\pi$
$727$			31.6569i			1.17409i	−0.809555	+	0.587044i	$0.800292\pi$
$728$		−	9.65685i		−	0.357907i
$729$	−1.00000			−0.0370370
$730$	−2.58579	+	7.75736i	−0.0957042	+	0.287113i
$731$	2.05887			0.0761502
$732$			3.41421i			0.126193i
$733$			8.58579i			0.317123i	0.987349	+	0.158562i	$0.0506857\pi$
$733$			8.58579i			0.317123i	−0.987349	+	0.158562i	$0.949314\pi$
$734$	−34.9706			−1.29079
$735$	6.36396	+	2.12132i	0.234738	+	0.0782461i
$736$	−1.00000			−0.0368605
$737$			2.48528i			0.0915465i
$738$		−	1.17157i		−	0.0431262i
$739$	−42.6274			−1.56807			−0.784037	−	0.620714i	$-0.786843\pi$
$739$	−42.6274			−1.56807			−0.784037	+	0.620714i	$0.786843\pi$
$740$	7.24264	+	2.41421i	0.266245	+	0.0887483i
$741$	−10.8284			−0.397792
$742$			26.8284i			0.984903i
$743$			2.34315i			0.0859617i	0.999076	+	0.0429808i	$0.0136854\pi$
$743$			2.34315i			0.0859617i	−0.999076	+	0.0429808i	$0.986315\pi$
$744$	−6.00000			−0.219971
$745$	9.00000	−	27.0000i	0.329734	−	0.989203i
$746$	19.2132			0.703445
$747$			1.41421i			0.0517434i
$748$			4.97056i			0.181742i
$749$	30.1421			1.10137
$750$	−9.19239	+	6.36396i	−0.335659	+	0.232379i
$751$	−48.8284			−1.78177			−0.890887	−	0.454224i	$-0.849916\pi$
$751$	−48.8284			−1.78177			−0.890887	+	0.454224i	$0.849916\pi$
$752$		−	4.82843i		−	0.176075i
$753$		−	24.7279i		−	0.901136i
$754$	36.9706			1.34639
$755$	−11.0711	+	33.2132i	−0.402917	+	1.20875i
$756$	−2.00000			−0.0727393
$757$		−	42.2426i		−	1.53533i	−0.640848	−	0.767667i	$-0.721417\pi$
$757$		−	42.2426i		−	1.53533i	0.640848	−	0.767667i	$-0.278583\pi$
$758$		−	19.2132i		−	0.697855i
$759$	4.24264			0.153998
$760$	4.75736	+	1.58579i	0.172568	+	0.0575225i
$761$	−24.3431			−0.882438			−0.441219	−	0.897399i	$-0.645454\pi$
$761$	−24.3431			−0.882438			−0.441219	+	0.897399i	$0.645454\pi$
$762$			2.00000i			0.0724524i
$763$		−	30.8284i		−	1.11606i
$764$	5.17157			0.187101
$765$	2.48528	+	0.828427i	0.0898555	+	0.0299518i
$766$	−18.6274			−0.673036
$767$			40.9706i			1.47936i
$768$			1.00000i			0.0360844i
$769$	−45.7990			−1.65155			−0.825777	−	0.563997i	$-0.809263\pi$
$769$	−45.7990			−1.65155			−0.825777	+	0.563997i	$0.809263\pi$
$770$	6.00000	−	18.0000i	0.216225	−	0.648675i
$771$	18.0000			0.648254
$772$		−	12.9706i		−	0.466821i
$773$		−	16.9289i		−	0.608891i	−0.952530	−	0.304446i	$-0.901529\pi$
$773$		−	16.9289i		−	0.608891i	0.952530	−	0.304446i	$-0.0984712\pi$
$774$	−1.75736			−0.0631670
$775$	−24.0000	−	18.0000i	−0.862105	−	0.646579i
$776$	−6.00000			−0.215387
$777$			6.82843i			0.244968i
$778$			6.38478i			0.228905i
$779$	−2.62742			−0.0941370
$780$	3.41421	−	10.2426i	0.122248	−	0.366745i
$781$	24.0000			0.858788
$782$			1.17157i			0.0418954i
$783$		−	7.65685i		−	0.273634i
$784$	3.00000			0.107143
$785$	−14.6985	−	4.89949i	−0.524611	−	0.174870i
$786$	−10.3431			−0.368928
$787$		−	2.72792i		−	0.0972399i	−0.998817	−	0.0486200i	$-0.984518\pi$
$787$		−	2.72792i		−	0.0972399i	0.998817	−	0.0486200i	$-0.0154823\pi$
$788$		−	24.6274i		−	0.877315i
$789$	17.6569			0.628601
$790$	16.2426	+	5.41421i	0.577887	+	0.192629i
$791$	−33.9411			−1.20681
$792$		−	4.24264i		−	0.150756i
$793$		−	16.4853i		−	0.585410i
$794$	8.34315			0.296087
$795$	−9.48528	+	28.4558i	−0.336408	+	1.00922i
$796$	−14.0000			−0.496217
$797$			21.4142i			0.758530i	0.925288	+	0.379265i	$0.123823\pi$
$797$			21.4142i			0.758530i	−0.925288	+	0.379265i	$0.876177\pi$
$798$			4.48528i			0.158777i
$799$	−5.65685			−0.200125
$800$	−3.00000	+	4.00000i	−0.106066	+	0.141421i
$801$	14.8284			0.523937
$802$			28.9706i			1.02299i
$803$		−	15.5147i		−	0.547503i
$804$	0.585786			0.0206591
$805$	1.41421	−	4.24264i	0.0498445	−	0.149533i
$806$	28.9706			1.02044
$807$			24.8284i			0.874002i
$808$		−	9.31371i		−	0.327655i
$809$	−13.3137			−0.468085			−0.234043	−	0.972226i	$-0.575196\pi$
$809$	−13.3137			−0.468085			−0.234043	+	0.972226i	$0.575196\pi$
$810$	−2.12132	−	0.707107i	−0.0745356	−	0.0248452i
$811$	6.82843			0.239779			0.119889	−	0.992787i	$-0.461746\pi$
$811$	6.82843			0.239779			0.119889	+	0.992787i	$0.461746\pi$
$812$		−	15.3137i		−	0.537406i
$813$		−	1.65685i		−	0.0581084i
$814$	−14.4853			−0.507709
$815$	2.48528	+	0.828427i	0.0870556	+	0.0290185i
$816$	1.17157			0.0410133
$817$			3.94113i			0.137883i
$818$			18.0000i			0.629355i
$819$	9.65685			0.337438
$820$	0.828427	−	2.48528i	0.0289299	−	0.0867898i
$821$	−6.68629			−0.233353			−0.116677	−	0.993170i	$-0.537224\pi$
$821$	−6.68629			−0.233353			−0.116677	+	0.993170i	$0.537224\pi$
$822$		−	8.48528i		−	0.295958i
$823$			32.2843i			1.12536i	0.826675	+	0.562679i	$0.190229\pi$
$823$			32.2843i			1.12536i	−0.826675	+	0.562679i	$0.809771\pi$
$824$	12.1421			0.422991
$825$	12.7279	−	16.9706i	0.443129	−	0.590839i
$826$	16.9706			0.590481
$827$		−	18.1005i		−	0.629416i	−0.949188	−	0.314708i	$-0.898093\pi$
$827$		−	18.1005i		−	0.629416i	0.949188	−	0.314708i	$-0.101907\pi$
$828$		−	1.00000i		−	0.0347524i
$829$	−50.2843			−1.74644			−0.873222	−	0.487322i	$-0.837974\pi$
$829$	−50.2843			−1.74644			−0.873222	+	0.487322i	$0.837974\pi$
$830$	−1.00000	+	3.00000i	−0.0347105	+	0.104132i
$831$	30.4853			1.05752
$832$		−	4.82843i		−	0.167396i
$833$		−	3.51472i		−	0.121778i
$834$	−16.9706			−0.587643
$835$	18.7279	+	6.24264i	0.648106	+	0.216035i
$836$	−9.51472			−0.329073
$837$		−	6.00000i		−	0.207390i
$838$		−	24.9289i		−	0.861156i
$839$	33.9411			1.17178			0.585889	−	0.810391i	$-0.300745\pi$
$839$	33.9411			1.17178			0.585889	+	0.810391i	$0.300745\pi$
$840$	−4.24264	−	1.41421i	−0.146385	−	0.0487950i
$841$	29.6274			1.02164
$842$		−	10.2426i		−	0.352985i
$843$		−	30.1421i		−	1.03815i
$844$	20.4853			0.705132
$845$	−7.29289	+	21.8787i	−0.250883	+	0.752649i
$846$	4.82843			0.166005
$847$			14.0000i			0.481046i
$848$			13.4142i			0.460646i
$849$	27.2132			0.933955
$850$	4.68629	+	3.51472i	0.160738	+	0.120554i
$851$	−3.41421			−0.117038
$852$		−	5.65685i		−	0.193801i
$853$			1.31371i			0.0449805i	0.999747	+	0.0224903i	$0.00715948\pi$
$853$			1.31371i			0.0449805i	−0.999747	+	0.0224903i	$0.992841\pi$
$854$	−6.82843			−0.233664
$855$	−1.58579	+	4.75736i	−0.0542328	+	0.162698i
$856$	15.0711			0.515118
$857$			45.1716i			1.54303i	0.636210	+	0.771516i	$0.280501\pi$
$857$			45.1716i			1.54303i	−0.636210	+	0.771516i	$0.719499\pi$
$858$			20.4853i			0.699356i
$859$	32.2843			1.10153			0.550763	−	0.834662i	$-0.314337\pi$
$859$	32.2843			1.10153			0.550763	+	0.834662i	$0.314337\pi$
$860$	−3.72792	−	1.24264i	−0.127121	−	0.0423737i
$861$	2.34315			0.0798542
$862$		−	8.48528i		−	0.289010i
$863$			22.6274i			0.770246i	0.922865	+	0.385123i	$0.125841\pi$
$863$			22.6274i			0.770246i	−0.922865	+	0.385123i	$0.874159\pi$
$864$	−1.00000			−0.0340207
$865$	6.72792	+	2.24264i	0.228756	+	0.0762521i
$866$	26.9706			0.916497
$867$			15.6274i			0.530735i
$868$		−	12.0000i		−	0.407307i
$869$	−32.4853			−1.10199
$870$	5.41421	−	16.2426i	0.183559	−	0.550677i
$871$	−2.82843			−0.0958376
$872$		−	15.4142i		−	0.521991i
$873$		−	6.00000i		−	0.203069i
$874$	−2.24264			−0.0758585
$875$	−12.7279	−	18.3848i	−0.430282	−	0.621519i
$876$	−3.65685			−0.123554
$877$			11.1716i			0.377237i	0.982050	+	0.188619i	$0.0604010\pi$
$877$			11.1716i			0.377237i	−0.982050	+	0.188619i	$0.939599\pi$
$878$		0			0
$879$	28.0416			0.945821
$880$	3.00000	−	9.00000i	0.101130	−	0.303390i
$881$	−2.14214			−0.0721704			−0.0360852	−	0.999349i	$-0.511489\pi$
$881$	−2.14214			−0.0721704			−0.0360852	+	0.999349i	$0.511489\pi$
$882$			3.00000i			0.101015i
$883$			13.1716i			0.443259i	0.975131	+	0.221629i	$0.0711375\pi$
$883$			13.1716i			0.443259i	−0.975131	+	0.221629i	$0.928862\pi$
$884$	−5.65685			−0.190261
$885$	18.0000	+	6.00000i	0.605063	+	0.201688i
$886$	−23.3137			−0.783239
$887$			48.4264i			1.62600i	0.582264	+	0.813000i	$0.302167\pi$
$887$			48.4264i			1.62600i	−0.582264	+	0.813000i	$0.697833\pi$
$888$			3.41421i			0.114574i
$889$	−4.00000			−0.134156
$890$	31.4558	+	10.4853i	1.05440	+	0.351467i
$891$	4.24264			0.142134
$892$		−	16.0000i		−	0.535720i
$893$		−	10.8284i		−	0.362359i
$894$	12.7279			0.425685
$895$	7.31371	−	21.9411i	0.244470	−	0.733411i
$896$	−2.00000			−0.0668153
$897$			4.82843i			0.161216i
$898$		−	22.8284i		−	0.761794i
$899$	45.9411			1.53222
$900$	−4.00000	−	3.00000i	−0.133333	−	0.100000i
$901$	15.7157			0.523567
$902$			4.97056i			0.165502i
$903$		−	3.51472i		−	0.116963i
$904$	−16.9706			−0.564433
$905$	11.5858	−	34.7574i	0.385125	−	1.15537i
$906$	−15.6569			−0.520164
$907$		−	27.2132i		−	0.903600i	−0.892119	−	0.451800i	$-0.850782\pi$
$907$		−	27.2132i		−	0.903600i	0.892119	−	0.451800i	$-0.149218\pi$
$908$			14.3848i			0.477376i
$909$	9.31371			0.308916
$910$	20.4853	+	6.82843i	0.679080	+	0.226360i
$911$	−0.201010			−0.00665976			−0.00332988	−	0.999994i	$-0.501060\pi$
$911$	−0.201010			−0.00665976			−0.00332988	+	0.999994i	$0.501060\pi$
$912$			2.24264i			0.0742613i
$913$		−	6.00000i		−	0.198571i
$914$	−1.02944			−0.0340508
$915$	−7.24264	−	2.41421i	−0.239434	−	0.0798114i
$916$	1.75736			0.0580648
$917$		−	20.6863i		−	0.683122i
$918$			1.17157i			0.0386677i
$919$	−5.02944			−0.165906			−0.0829529	−	0.996553i	$-0.526435\pi$
$919$	−5.02944			−0.165906			−0.0829529	+	0.996553i	$0.526435\pi$
$920$	0.707107	−	2.12132i	0.0233126	−	0.0699379i
$921$	−25.4558			−0.838799
$922$			12.8284i			0.422482i
$923$			27.3137i			0.899042i
$924$	8.48528			0.279145
$925$	−10.2426	+	13.6569i	−0.336776	+	0.449035i
$926$	2.97056			0.0976187
$927$			12.1421i			0.398800i
$928$		−	7.65685i		−	0.251349i
$929$	−42.1421			−1.38264			−0.691319	−	0.722549i	$-0.742970\pi$
$929$	−42.1421			−1.38264			−0.691319	+	0.722549i	$0.742970\pi$
$930$	4.24264	−	12.7279i	0.139122	−	0.417365i
$931$	6.72792			0.220499
$932$			26.1421i			0.856314i
$933$			17.7990i			0.582713i
$934$	−39.3553			−1.28775
$935$	−10.5442	−	3.51472i	−0.344831	−	0.114944i
$936$	4.82843			0.157822
$937$		−	44.4264i		−	1.45135i	−0.688039	−	0.725674i	$-0.741528\pi$
$937$		−	44.4264i		−	1.45135i	0.688039	−	0.725674i	$-0.258472\pi$
$938$			1.17157i			0.0382532i
$939$	−18.0000			−0.587408
$940$	10.2426	+	3.41421i	0.334078	+	0.111359i
$941$	−31.5563			−1.02871			−0.514354	−	0.857578i	$-0.671968\pi$
$941$	−31.5563			−1.02871			−0.514354	+	0.857578i	$0.671968\pi$
$942$		−	6.92893i		−	0.225757i
$943$			1.17157i			0.0381517i
$944$	8.48528			0.276172
$945$	1.41421	−	4.24264i	0.0460044	−	0.138013i
$946$	7.45584			0.242410
$947$		−	1.45584i		−	0.0473086i	−0.999720	−	0.0236543i	$-0.992470\pi$
$947$		−	1.45584i		−	0.0473086i	0.999720	−	0.0236543i	$-0.00753010\pi$
$948$			7.65685i			0.248683i
$949$	17.6569			0.573166
$950$	−6.72792	+	8.97056i	−0.218283	+	0.291043i
$951$	2.48528			0.0805908
$952$			2.34315i			0.0759418i
$953$			40.0833i			1.29842i	0.760607	+	0.649212i	$0.224901\pi$
$953$			40.0833i			1.29842i	−0.760607	+	0.649212i	$0.775099\pi$
$954$	−13.4142			−0.434301
$955$	−3.65685	+	10.9706i	−0.118333	+	0.354999i
$956$	−11.1716			−0.361314
$957$			32.4853i			1.05010i
$958$			4.68629i			0.151407i
$959$	16.9706			0.548008
$960$	−2.12132	−	0.707107i	−0.0684653	−	0.0228218i
$961$	5.00000			0.161290
$962$		−	16.4853i		−	0.531507i
$963$			15.0711i			0.485658i
$964$	10.4853			0.337708
$965$	27.5147	+	9.17157i	0.885730	+	0.295243i
$966$	2.00000			0.0643489
$967$		−	4.97056i		−	0.159843i	−0.996801	−	0.0799213i	$-0.974533\pi$
$967$		−	4.97056i		−	0.159843i	0.996801	−	0.0799213i	$-0.0254669\pi$
$968$			7.00000i			0.224989i
$969$	2.62742			0.0844048
$970$	4.24264	−	12.7279i	0.136223	−	0.408669i
$971$	−17.6152			−0.565299			−0.282650	−	0.959223i	$-0.591213\pi$
$971$	−17.6152			−0.565299			−0.282650	+	0.959223i	$0.591213\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	33.9411i		−	1.08810i
$974$	27.9411			0.895291
$975$	19.3137	+	14.4853i	0.618534	+	0.463900i
$976$	−3.41421			−0.109286
$977$		−	19.7990i		−	0.633426i	−0.948521	−	0.316713i	$-0.897421\pi$
$977$		−	19.7990i		−	0.633426i	0.948521	−	0.316713i	$-0.102579\pi$
$978$			1.17157i			0.0374628i
$979$	−62.9117			−2.01067
$980$	−2.12132	+	6.36396i	−0.0677631	+	0.203289i
$981$	15.4142			0.492138
$982$		−	26.6274i		−	0.849715i
$983$		−	20.4853i		−	0.653379i	−0.945132	−	0.326690i	$-0.894067\pi$
$983$		−	20.4853i		−	0.653379i	0.945132	−	0.326690i	$-0.105933\pi$
$984$	1.17157			0.0373484
$985$	52.2426	+	17.4142i	1.66459	+	0.554863i
$986$	−8.97056			−0.285681
$987$			9.65685i			0.307381i
$988$		−	10.8284i		−	0.344498i
$989$	1.75736			0.0558808
$990$	9.00000	+	3.00000i	0.286039	+	0.0953463i
$991$	51.9411			1.64996			0.824982	−	0.565159i	$-0.191185\pi$
$991$	51.9411			1.64996			0.824982	+	0.565159i	$0.191185\pi$
$992$		−	6.00000i		−	0.190500i
$993$		−	3.51472i		−	0.111536i
$994$	11.3137			0.358849
$995$	9.89949	−	29.6985i	0.313835	−	0.941505i
$996$	−1.41421			−0.0448111
$997$			46.9706i			1.48757i	0.668417	+	0.743786i	$0.266972\pi$
$997$			46.9706i			1.48757i	−0.668417	+	0.743786i	$0.733028\pi$
$998$			13.4558i			0.425937i
$999$	−3.41421			−0.108021

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.d.b.139.2	✓	4
3.2	odd	2		2070.2.d.a.829.3		4
5.2	odd	4		3450.2.a.bk.1.2		2
5.3	odd	4		3450.2.a.bg.1.2		2
5.4	even	2	inner	690.2.d.b.139.4	yes	4
15.14	odd	2		2070.2.d.a.829.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.d.b.139.2	✓	4	1.1	even	1	trivial
690.2.d.b.139.4	yes	4	5.4	even	2	inner
2070.2.d.a.829.1		4	15.14	odd	2
2070.2.d.a.829.3		4	3.2	odd	2
3450.2.a.bg.1.2		2	5.3	odd	4
3450.2.a.bk.1.2		2	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(0.707107 - 2.12132i) q^{5} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(0.707107 - 2.12132i) q^{5} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(-2.12132 - 0.707107i) q^{10} +4.24264 q^{11} -1.00000i q^{12} +4.82843i q^{13} +2.00000 q^{14} +(2.12132 + 0.707107i) q^{15} +1.00000 q^{16} -1.17157i q^{17} +1.00000i q^{18} +2.24264 q^{19} +(-0.707107 + 2.12132i) q^{20} -2.00000 q^{21} -4.24264i q^{22} -1.00000i q^{23} -1.00000 q^{24} +(-4.00000 - 3.00000i) q^{25} +4.82843 q^{26} -1.00000i q^{27} -2.00000i q^{28} +7.65685 q^{29} +(0.707107 - 2.12132i) q^{30} +6.00000 q^{31} -1.00000i q^{32} +4.24264i q^{33} -1.17157 q^{34} +(4.24264 + 1.41421i) q^{35} +1.00000 q^{36} -3.41421i q^{37} -2.24264i q^{38} -4.82843 q^{39} +(2.12132 + 0.707107i) q^{40} -1.17157 q^{41} +2.00000i q^{42} +1.75736i q^{43} -4.24264 q^{44} +(-0.707107 + 2.12132i) q^{45} -1.00000 q^{46} -4.82843i q^{47} +1.00000i q^{48} +3.00000 q^{49} +(-3.00000 + 4.00000i) q^{50} +1.17157 q^{51} -4.82843i q^{52} +13.4142i q^{53} -1.00000 q^{54} +(3.00000 - 9.00000i) q^{55} -2.00000 q^{56} +2.24264i q^{57} -7.65685i q^{58} +8.48528 q^{59} +(-2.12132 - 0.707107i) q^{60} -3.41421 q^{61} -6.00000i q^{62} -2.00000i q^{63} -1.00000 q^{64} +(10.2426 + 3.41421i) q^{65} +4.24264 q^{66} +0.585786i q^{67} +1.17157i q^{68} +1.00000 q^{69} +(1.41421 - 4.24264i) q^{70} +5.65685 q^{71} -1.00000i q^{72} -3.65685i q^{73} -3.41421 q^{74} +(3.00000 - 4.00000i) q^{75} -2.24264 q^{76} +8.48528i q^{77} +4.82843i q^{78} -7.65685 q^{79} +(0.707107 - 2.12132i) q^{80} +1.00000 q^{81} +1.17157i q^{82} -1.41421i q^{83} +2.00000 q^{84} +(-2.48528 - 0.828427i) q^{85} +1.75736 q^{86} +7.65685i q^{87} +4.24264i q^{88} -14.8284 q^{89} +(2.12132 + 0.707107i) q^{90} -9.65685 q^{91} +1.00000i q^{92} +6.00000i q^{93} -4.82843 q^{94} +(1.58579 - 4.75736i) q^{95} +1.00000 q^{96} +6.00000i q^{97} -3.00000i q^{98} -4.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 8 q^{14} + 4 q^{16} - 8 q^{19} - 8 q^{21} - 4 q^{24} - 16 q^{25} + 8 q^{26} + 8 q^{29} + 24 q^{31} - 16 q^{34} + 4 q^{36} - 8 q^{39} - 16 q^{41} - 4 q^{46} + 12 q^{49} - 12 q^{50} + 16 q^{51} - 4 q^{54} + 12 q^{55} - 8 q^{56} - 8 q^{61} - 4 q^{64} + 24 q^{65} + 4 q^{69} - 8 q^{74} + 12 q^{75} + 8 q^{76} - 8 q^{79} + 4 q^{81} + 8 q^{84} + 24 q^{85} + 24 q^{86} - 48 q^{89} - 16 q^{91} - 8 q^{94} + 12 q^{95} + 4 q^{96}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 8 * q^14 + 4 * q^16 - 8 * q^19 - 8 * q^21 - 4 * q^24 - 16 * q^25 + 8 * q^26 + 8 * q^29 + 24 * q^31 - 16 * q^34 + 4 * q^36 - 8 * q^39 - 16 * q^41 - 4 * q^46 + 12 * q^49 - 12 * q^50 + 16 * q^51 - 4 * q^54 + 12 * q^55 - 8 * q^56 - 8 * q^61 - 4 * q^64 + 24 * q^65 + 4 * q^69 - 8 * q^74 + 12 * q^75 + 8 * q^76 - 8 * q^79 + 4 * q^81 + 8 * q^84 + 24 * q^85 + 24 * q^86 - 48 * q^89 - 16 * q^91 - 8 * q^94 + 12 * q^95 + 4 * q^96

Introduction

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