LMFDB - Embedded newform 560.2.bd.a.141.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(141,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))

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

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

chi := DirichletCharacter("560.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bd (of order $4$, degree $2$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			141.12
Character	$\chi$	$=$	560.141
Dual form			560.2.bd.a.421.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.381101 + 1.36190i) q^{2} +(-0.605289 - 0.605289i) q^{3} +(-1.70952 + 1.03804i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.593665 - 1.05502i) q^{6} -1.00000i q^{7} +(-2.06521 - 1.93260i) q^{8} -2.26725i q^{9} +O(q^{10})$	\(q+(0.381101 + 1.36190i) q^{2} +(-0.605289 - 0.605289i) q^{3} +(-1.70952 + 1.03804i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.593665 - 1.05502i) q^{6} -1.00000i q^{7} +(-2.06521 - 1.93260i) q^{8} -2.26725i q^{9} +(-1.23249 - 0.693527i) q^{10} +(-0.812056 + 0.812056i) q^{11} +(1.66307 + 0.406441i) q^{12} +(-2.79946 - 2.79946i) q^{13} +(1.36190 - 0.381101i) q^{14} +0.856008 q^{15} +(1.84494 - 3.54911i) q^{16} +4.69853 q^{17} +(3.08776 - 0.864052i) q^{18} +(-1.00378 - 1.00378i) q^{19} +(0.474810 - 1.94282i) q^{20} +(-0.605289 + 0.605289i) q^{21} +(-1.41541 - 0.796461i) q^{22} -8.15692i q^{23} +(0.0802678 + 2.41983i) q^{24} -1.00000i q^{25} +(2.74570 - 4.87946i) q^{26} +(-3.18821 + 3.18821i) q^{27} +(1.03804 + 1.70952i) q^{28} +(0.122932 + 0.122932i) q^{29} +(0.326226 + 1.16579i) q^{30} -2.46615 q^{31} +(5.53663 + 1.16005i) q^{32} +0.983058 q^{33} +(1.79062 + 6.39891i) q^{34} +(0.707107 + 0.707107i) q^{35} +(2.35350 + 3.87592i) q^{36} +(3.53721 - 3.53721i) q^{37} +(0.984504 - 1.74959i) q^{38} +3.38897i q^{39} +(2.82687 - 0.0937698i) q^{40} -4.84284i q^{41} +(-1.05502 - 0.593665i) q^{42} +(-2.21661 + 2.21661i) q^{43} +(0.545282 - 2.23118i) q^{44} +(1.60319 + 1.60319i) q^{45} +(11.1089 - 3.10861i) q^{46} -3.94282 q^{47} +(-3.26496 + 1.03152i) q^{48} -1.00000 q^{49} +(1.36190 - 0.381101i) q^{50} +(-2.84397 - 2.84397i) q^{51} +(7.69170 + 1.87979i) q^{52} +(7.19461 - 7.19461i) q^{53} +(-5.55704 - 3.12698i) q^{54} -1.14842i q^{55} +(-1.93260 + 2.06521i) q^{56} +1.21516i q^{57} +(-0.120571 + 0.214270i) q^{58} +(-6.54526 + 6.54526i) q^{59} +(-1.46337 + 0.888572i) q^{60} +(-1.81508 - 1.81508i) q^{61} +(-0.939855 - 3.35865i) q^{62} -2.26725 q^{63} +(0.530151 + 7.98241i) q^{64} +3.95904 q^{65} +(0.374645 + 1.33882i) q^{66} +(-0.162648 - 0.162648i) q^{67} +(-8.03225 + 4.87727i) q^{68} +(-4.93730 + 4.93730i) q^{69} +(-0.693527 + 1.23249i) q^{70} -6.00458i q^{71} +(-4.38168 + 4.68234i) q^{72} +7.09981i q^{73} +(6.16534 + 3.46928i) q^{74} +(-0.605289 + 0.605289i) q^{75} +(2.75795 + 0.674022i) q^{76} +(0.812056 + 0.812056i) q^{77} +(-4.61543 + 1.29154i) q^{78} -10.3006 q^{79} +(1.20503 + 3.81417i) q^{80} -2.94217 q^{81} +(6.59544 - 1.84561i) q^{82} +(-7.83163 - 7.83163i) q^{83} +(0.406441 - 1.66307i) q^{84} +(-3.32236 + 3.32236i) q^{85} +(-3.86355 - 2.17404i) q^{86} -0.148819i q^{87} +(3.24644 - 0.107687i) q^{88} +3.28176i q^{89} +(-1.57240 + 2.79435i) q^{90} +(-2.79946 + 2.79946i) q^{91} +(8.46722 + 13.9445i) q^{92} +(1.49274 + 1.49274i) q^{93} +(-1.50261 - 5.36971i) q^{94} +1.41956 q^{95} +(-2.64910 - 4.05343i) q^{96} +0.453882 q^{97} +(-0.381101 - 1.36190i) q^{98} +(1.84113 + 1.84113i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) $ 44 * q + 12 * q^4 + 12 * q^6	$ 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) $ 44 * q + 12 * q^4 + 12 * q^6 - 4 * q^10 + 12 * q^11 - 16 * q^12 + 4 * q^14 + 8 * q^15 - 8 * q^16 - 20 * q^18 + 8 * q^19 - 36 * q^22 + 12 * q^24 + 44 * q^26 - 24 * q^27 - 4 * q^28 + 12 * q^29 - 40 * q^32 - 16 * q^34 + 4 * q^36 + 28 * q^37 - 16 * q^38 + 4 * q^42 - 44 * q^43 - 32 * q^44 - 16 * q^46 - 32 * q^48 - 44 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 12 * q^53 - 80 * q^54 + 8 * q^56 + 4 * q^58 + 24 * q^59 - 16 * q^61 + 28 * q^63 + 72 * q^64 - 40 * q^65 - 20 * q^66 - 28 * q^67 + 56 * q^68 + 40 * q^69 + 12 * q^72 + 24 * q^74 - 12 * q^77 + 84 * q^78 - 16 * q^79 + 20 * q^81 + 48 * q^82 + 16 * q^85 - 64 * q^86 + 28 * q^88 - 36 * q^90 - 16 * q^92 + 88 * q^93 + 96 * q^94 - 32 * q^95 + 48 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.381101	+	1.36190i	0.269479	+	0.963006i
$2$	0.381101	+	1.36190i	0.269479	+	0.963006i
$3$	−0.605289	−	0.605289i	−0.349464	−	0.349464i	0.510446	−	0.859910i	$-0.329480\pi$
$3$	−0.605289	−	0.605289i	−0.349464	−	0.349464i	−0.859910	+	0.510446i	$0.829480\pi$
$4$	−1.70952	+	1.03804i	−0.854762	+	0.519020i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	0.593665	−	1.05502i	0.242363	−	0.430709i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.06521	−	1.93260i	−0.730161	−	0.683276i
$9$		−	2.26725i		−	0.755750i
$10$	−1.23249	−	0.693527i	−0.389746	−	0.219312i
$11$	−0.812056	+	0.812056i	−0.244844	+	0.244844i	−0.818851	−	0.574007i	$-0.805388\pi$
$11$	−0.812056	+	0.812056i	−0.244844	+	0.244844i	0.574007	+	0.818851i	$0.305388\pi$
$12$	1.66307	+	0.406441i	0.480087	+	0.117329i
$13$	−2.79946	−	2.79946i	−0.776431	−	0.776431i	0.202791	−	0.979222i	$-0.434999\pi$
$13$	−2.79946	−	2.79946i	−0.776431	−	0.776431i	−0.979222	+	0.202791i	$0.934999\pi$
$14$	1.36190	−	0.381101i	0.363982	−	0.101854i
$15$	0.856008			0.221020
$16$	1.84494	−	3.54911i	0.461235	−	0.887278i
$17$	4.69853			1.13956			0.569780	−	0.821797i	$-0.307028\pi$
$17$	4.69853			1.13956			0.569780	+	0.821797i	$0.307028\pi$
$18$	3.08776	−	0.864052i	0.727792	−	0.203659i
$19$	−1.00378	−	1.00378i	−0.230283	−	0.230283i	0.582528	−	0.812811i	$-0.302064\pi$
$19$	−1.00378	−	1.00378i	−0.230283	−	0.230283i	−0.812811	+	0.582528i	$0.802064\pi$
$20$	0.474810	−	1.94282i	0.106171	−	0.434428i
$21$	−0.605289	+	0.605289i	−0.132085	+	0.132085i
$22$	−1.41541	−	0.796461i	−0.301767	−	0.169806i
$23$		−	8.15692i		−	1.70084i	−0.526107	−	0.850418i	$-0.676349\pi$
$23$		−	8.15692i		−	1.70084i	0.526107	−	0.850418i	$-0.323651\pi$
$24$	0.0802678	+	2.41983i	0.0163846	+	0.493945i
$25$		−	1.00000i		−	0.200000i
$26$	2.74570	−	4.87946i	0.538476	−	0.956940i
$27$	−3.18821	+	3.18821i	−0.613571	+	0.613571i
$28$	1.03804	+	1.70952i	0.196171	+	0.323070i
$29$	0.122932	+	0.122932i	0.0228279	+	0.0228279i	0.718429	−	0.695601i	$-0.244862\pi$
$29$	0.122932	+	0.122932i	0.0228279	+	0.0228279i	−0.695601	+	0.718429i	$0.744862\pi$
$30$	0.326226	+	1.16579i	0.0595604	+	0.212844i
$31$	−2.46615			−0.442934			−0.221467	−	0.975168i	$-0.571085\pi$
$31$	−2.46615			−0.442934			−0.221467	+	0.975168i	$0.571085\pi$
$32$	5.53663	+	1.16005i	0.978747	+	0.205070i
$33$	0.983058			0.171128
$34$	1.79062	+	6.39891i	0.307088	+	1.09740i
$35$	0.707107	+	0.707107i	0.119523	+	0.119523i
$36$	2.35350	+	3.87592i	0.392250	+	0.645986i
$37$	3.53721	−	3.53721i	0.581513	−	0.581513i	−0.353806	−	0.935319i	$-0.615113\pi$
$37$	3.53721	−	3.53721i	0.581513	−	0.581513i	0.935319	+	0.353806i	$0.115113\pi$
$38$	0.984504	−	1.74959i	0.159708	−	0.283821i
$39$			3.38897i			0.542669i
$40$	2.82687	−	0.0937698i	0.446968	−	0.0148263i
$41$		−	4.84284i		−	0.756324i	−0.925739	−	0.378162i	$-0.876556\pi$
$41$		−	4.84284i		−	0.756324i	0.925739	−	0.378162i	$-0.123444\pi$
$42$	−1.05502	−	0.593665i	−0.162793	−	0.0916045i
$43$	−2.21661	+	2.21661i	−0.338030	+	0.338030i	−0.855625	−	0.517596i	$-0.826827\pi$
$43$	−2.21661	+	2.21661i	−0.338030	+	0.338030i	0.517596	+	0.855625i	$0.326827\pi$
$44$	0.545282	−	2.23118i	0.0822043	−	0.336363i
$45$	1.60319	+	1.60319i	0.238989	+	0.238989i
$46$	11.1089	−	3.10861i	1.63792	−	0.458340i
$47$	−3.94282			−0.575119			−0.287560	−	0.957763i	$-0.592844\pi$
$47$	−3.94282			−0.575119			−0.287560	+	0.957763i	$0.592844\pi$
$48$	−3.26496	+	1.03152i	−0.471257	+	0.148886i
$49$	−1.00000			−0.142857
$50$	1.36190	−	0.381101i	0.192601	−	0.0538959i
$51$	−2.84397	−	2.84397i	−0.398235	−	0.398235i
$52$	7.69170	+	1.87979i	1.06665	+	0.260680i
$53$	7.19461	−	7.19461i	0.988255	−	0.988255i	−0.0116763	−	0.999932i	$-0.503717\pi$
$53$	7.19461	−	7.19461i	0.988255	−	0.988255i	0.999932	+	0.0116763i	$0.00371678\pi$
$54$	−5.55704	−	3.12698i	−0.756218	−	0.425528i
$55$		−	1.14842i		−	0.154853i
$56$	−1.93260	+	2.06521i	−0.258254	+	0.275975i
$57$			1.21516i			0.160951i
$58$	−0.120571	+	0.214270i	−0.0158318	+	0.0281351i
$59$	−6.54526	+	6.54526i	−0.852120	+	0.852120i	−0.990394	−	0.138274i	$-0.955845\pi$
$59$	−6.54526	+	6.54526i	−0.852120	+	0.852120i	0.138274	+	0.990394i	$0.455845\pi$
$60$	−1.46337	+	0.888572i	−0.188920	+	0.114714i
$61$	−1.81508	−	1.81508i	−0.232398	−	0.232398i	0.581295	−	0.813693i	$-0.302546\pi$
$61$	−1.81508	−	1.81508i	−0.232398	−	0.232398i	−0.813693	+	0.581295i	$0.802546\pi$
$62$	−0.939855	−	3.35865i	−0.119362	−	0.426549i
$63$	−2.26725			−0.285647
$64$	0.530151	+	7.98241i	0.0662688	+	0.997802i
$65$	3.95904			0.491058
$66$	0.374645	+	1.33882i	0.0461156	+	0.164798i
$67$	−0.162648	−	0.162648i	−0.0198706	−	0.0198706i	0.697102	−	0.716972i	$-0.254473\pi$
$67$	−0.162648	−	0.162648i	−0.0198706	−	0.0198706i	−0.716972	+	0.697102i	$0.754473\pi$
$68$	−8.03225	+	4.87727i	−0.974053	+	0.591455i
$69$	−4.93730	+	4.93730i	−0.594381	+	0.594381i
$70$	−0.693527	+	1.23249i	−0.0828923	+	0.147310i
$71$		−	6.00458i		−	0.712613i	−0.934369	−	0.356306i	$-0.884036\pi$
$71$		−	6.00458i		−	0.712613i	0.934369	−	0.356306i	$-0.115964\pi$
$72$	−4.38168	+	4.68234i	−0.516385	+	0.551819i
$73$			7.09981i			0.830970i	0.909600	+	0.415485i	$0.136388\pi$
$73$			7.09981i			0.830970i	−0.909600	+	0.415485i	$0.863612\pi$
$74$	6.16534	+	3.46928i	0.716707	+	0.403295i
$75$	−0.605289	+	0.605289i	−0.0698928	+	0.0698928i
$76$	2.75795	+	0.674022i	0.316359	+	0.0773156i
$77$	0.812056	+	0.812056i	0.0925424	+	0.0925424i
$78$	−4.61543	+	1.29154i	−0.522594	+	0.146238i
$79$	−10.3006			−1.15890			−0.579452	−	0.815006i	$-0.696733\pi$
$79$	−10.3006			−1.15890			−0.579452	+	0.815006i	$0.696733\pi$
$80$	1.20503	+	3.81417i	0.134726	+	0.426437i
$81$	−2.94217			−0.326908
$82$	6.59544	−	1.84561i	0.728345	−	0.203814i
$83$	−7.83163	−	7.83163i	−0.859633	−	0.859633i	0.131662	−	0.991295i	$-0.457969\pi$
$83$	−7.83163	−	7.83163i	−0.859633	−	0.859633i	−0.991295	+	0.131662i	$0.957969\pi$
$84$	0.406441	−	1.66307i	0.0443464	−	0.181456i
$85$	−3.32236	+	3.32236i	−0.360361	+	0.360361i
$86$	−3.86355	−	2.17404i	−0.416617	−	0.234433i
$87$		−	0.148819i		−	0.0159551i
$88$	3.24644	−	0.107687i	0.346072	−	0.0114795i
$89$			3.28176i			0.347866i	0.984757	+	0.173933i	$0.0556477\pi$
$89$			3.28176i			0.347866i	−0.984757	+	0.173933i	$0.944352\pi$
$90$	−1.57240	+	2.79435i	−0.165745	+	0.294551i
$91$	−2.79946	+	2.79946i	−0.293463	+	0.293463i
$92$	8.46722	+	13.9445i	0.882769	+	1.45381i
$93$	1.49274	+	1.49274i	0.154790	+	0.154790i
$94$	−1.50261	−	5.36971i	−0.154983	−	0.553843i
$95$	1.41956			0.145644
$96$	−2.64910	−	4.05343i	−0.270372	−	0.413701i
$97$	0.453882			0.0460847			0.0230424	−	0.999734i	$-0.492665\pi$
$97$	0.453882			0.0460847			0.0230424	+	0.999734i	$0.492665\pi$
$98$	−0.381101	−	1.36190i	−0.0384970	−	0.137572i
$99$	1.84113	+	1.84113i	0.185041	+	0.185041i
$100$	1.03804	+	1.70952i	0.103804	+	0.170952i
$101$	−13.1056	+	13.1056i	−1.30405	+	1.30405i	−0.378417	+	0.925635i	$0.623531\pi$
$101$	−13.1056	+	13.1056i	−1.30405	+	1.30405i	−0.925635	+	0.378417i	$0.876469\pi$
$102$	2.78935	−	4.95703i	0.276187	−	0.490819i
$103$		−	7.66619i		−	0.755373i	−0.925934	−	0.377686i	$-0.876720\pi$
$103$		−	7.66619i		−	0.755373i	0.925934	−	0.377686i	$-0.123280\pi$
$104$	0.371238	+	11.1917i	0.0364029	+	1.09744i
$105$		−	0.856008i		−	0.0835379i
$106$	12.5402	+	7.05644i	1.21801	+	0.685382i
$107$	−0.120113	+	0.120113i	−0.0116117	+	0.0116117i	−0.712889	−	0.701277i	$-0.752614\pi$
$107$	−0.120113	+	0.120113i	−0.0116117	+	0.0116117i	0.701277	+	0.712889i	$0.252614\pi$
$108$	2.14083	−	8.75981i	0.206001	−	0.842913i
$109$	3.37380	+	3.37380i	0.323152	+	0.323152i	0.849975	−	0.526823i	$-0.176617\pi$
$109$	3.37380	+	3.37380i	0.323152	+	0.323152i	−0.526823	+	0.849975i	$0.676617\pi$
$110$	1.56403	−	0.437665i	0.149124	−	0.0417297i
$111$	−4.28207			−0.406436
$112$	−3.54911	−	1.84494i	−0.335359	−	0.174331i
$113$	19.2238			1.80843			0.904213	−	0.427081i	$-0.140458\pi$
$113$	19.2238			1.80843			0.904213	+	0.427081i	$0.140458\pi$
$114$	−1.65492	+	0.463098i	−0.154997	+	0.0433731i
$115$	5.76782	+	5.76782i	0.537852	+	0.537852i
$116$	−0.337764	−	0.0825467i	−0.0313606	−	0.00766427i
$117$	−6.34708	+	6.34708i	−0.586788	+	0.586788i
$118$	−11.4084	−	6.41956i	−1.05023	−	0.590968i
$119$		−	4.69853i		−	0.430714i
$120$	−1.76783	−	1.65432i	−0.161380	−	0.151018i
$121$			9.68113i			0.880103i
$122$	1.78022	−	3.16368i	0.161174	−	0.286427i
$123$	−2.93132	+	2.93132i	−0.264308	+	0.264308i
$124$	4.21595	−	2.55997i	0.378603	−	0.229892i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−0.864052	−	3.08776i	−0.0769759	−	0.275079i
$127$	−4.68107			−0.415377			−0.207689	−	0.978195i	$-0.566594\pi$
$127$	−4.68107			−0.415377			−0.207689	+	0.978195i	$0.566594\pi$
$128$	−10.6692	+	3.76412i	−0.943031	+	0.332704i
$129$	2.68338			0.236259
$130$	1.50879	+	5.39180i	0.132330	+	0.472892i
$131$	3.72957	+	3.72957i	0.325854	+	0.325854i	0.851007	−	0.525154i	$-0.175992\pi$
$131$	3.72957	+	3.72957i	0.325854	+	0.325854i	−0.525154	+	0.851007i	$0.675992\pi$
$132$	−1.68056	+	1.02045i	−0.146274	+	0.0888191i
$133$	−1.00378	+	1.00378i	−0.0870389	+	0.0870389i
$134$	0.159524	−	0.283495i	0.0137808	−	0.0244902i
$135$		−	4.50881i		−	0.388057i
$136$	−9.70343	−	9.08036i	−0.832062	−	0.778634i
$137$		−	14.1902i		−	1.21235i	−0.795331	−	0.606175i	$-0.792703\pi$
$137$		−	14.1902i		−	1.21235i	0.795331	−	0.606175i	$-0.207297\pi$
$138$	−8.60570	−	4.84248i	−0.732566	−	0.412219i
$139$	−7.05584	+	7.05584i	−0.598468	+	0.598468i	−0.939905	−	0.341437i	$-0.889087\pi$
$139$	−7.05584	+	7.05584i	−0.598468	+	0.598468i	0.341437	+	0.939905i	$0.389087\pi$
$140$	−1.94282	−	0.474810i	−0.164198	−	0.0401288i
$141$	2.38655	+	2.38655i	0.200983	+	0.200983i
$142$	8.17762	−	2.28835i	0.686251	−	0.192034i
$143$	4.54664			0.380209
$144$	−8.04672	−	4.18294i	−0.670560	−	0.348579i
$145$	−0.173852			−0.0144376
$146$	−9.66921	+	2.70575i	−0.800229	+	0.223929i
$147$	0.605289	+	0.605289i	0.0499234	+	0.0499234i
$148$	−2.37517	+	9.71870i	−0.195238	+	0.798873i
$149$	14.9614	−	14.9614i	1.22569	−	1.22569i	0.260105	−	0.965580i	$-0.416243\pi$
$149$	14.9614	−	14.9614i	1.22569	−	1.22569i	0.965580	−	0.260105i	$-0.0837572\pi$
$150$	−1.05502	−	0.593665i	−0.0861418	−	0.0484725i
$151$			1.18322i			0.0962888i	0.998840	+	0.0481444i	$0.0153308\pi$
$151$			1.18322i			0.0962888i	−0.998840	+	0.0481444i	$0.984669\pi$
$152$	0.133112	+	4.01292i	0.0107968	+	0.325491i
$153$		−	10.6527i		−	0.861223i
$154$	−0.796461	+	1.41541i	−0.0641806	+	0.114057i
$155$	1.74383	−	1.74383i	0.140068	−	0.140068i
$156$	−3.51789	−	5.79352i	−0.281657	−	0.463853i
$157$	4.99207	+	4.99207i	0.398411	+	0.398411i	0.877672	−	0.479262i	$-0.159095\pi$
$157$	4.99207	+	4.99207i	0.398411	+	0.398411i	−0.479262	+	0.877672i	$0.659095\pi$
$158$	−3.92556	−	14.0283i	−0.312301	−	1.11603i
$159$	−8.70964			−0.690719
$160$	−4.73527	+	3.09471i	−0.374356	+	0.244658i
$161$	−8.15692			−0.642856
$162$	−1.12126	−	4.00693i	−0.0880949	−	0.314814i
$163$	5.00263	+	5.00263i	0.391836	+	0.391836i	0.875341	−	0.483505i	$-0.160637\pi$
$163$	5.00263	+	5.00263i	0.391836	+	0.391836i	−0.483505	+	0.875341i	$0.660637\pi$
$164$	5.02706	+	8.27894i	0.392548	+	0.646477i
$165$	−0.695127	+	0.695127i	−0.0541156	+	0.0541156i
$166$	7.68122	−	13.6505i	0.596178	−	1.05948i
$167$		−	24.8909i		−	1.92612i	−0.269293	−	0.963058i	$-0.586790\pi$
$167$		−	24.8909i		−	1.92612i	0.269293	−	0.963058i	$-0.413210\pi$
$168$	2.41983	−	0.0802678i	0.186694	−	0.00619279i
$169$			2.67398i			0.205691i
$170$	−5.79087	−	3.25856i	−0.444139	−	0.249920i
$171$	−2.27582	+	2.27582i	−0.174037	+	0.174037i
$172$	1.48842	−	6.09028i	0.113491	−	0.464379i
$173$	−10.3193	−	10.3193i	−0.784561	−	0.784561i	0.196036	−	0.980597i	$-0.437193\pi$
$173$	−10.3193	−	10.3193i	−0.784561	−	0.784561i	−0.980597	+	0.196036i	$0.937193\pi$
$174$	0.202676	−	0.0567150i	0.0153648	−	0.00429956i
$175$	−1.00000			−0.0755929
$176$	1.38388	+	4.38027i	0.104314	+	0.330176i
$177$	7.92355			0.595570
$178$	−4.46942	+	1.25068i	−0.334997	+	0.0937427i
$179$	16.6480	+	16.6480i	1.24433	+	1.24433i	0.958188	+	0.286141i	$0.0923725\pi$
$179$	16.6480	+	16.6480i	1.24433	+	1.24433i	0.286141	+	0.958188i	$0.407628\pi$
$180$	−4.40486	−	1.07651i	−0.328319	−	0.0802385i
$181$	−9.09342	+	9.09342i	−0.675909	+	0.675909i	−0.959072	−	0.283163i	$-0.908616\pi$
$181$	−9.09342	+	9.09342i	−0.675909	+	0.675909i	0.283163	+	0.959072i	$0.408616\pi$
$182$	−4.87946	−	2.74570i	−0.361689	−	0.203525i
$183$			2.19730i			0.162429i
$184$	−15.7640	+	16.8457i	−1.16214	+	1.24188i
$185$			5.00237i			0.367781i
$186$	−1.46407	+	2.60184i	−0.107351	+	0.190776i
$187$	−3.81547	+	3.81547i	−0.279015	+	0.279015i
$188$	6.74034	−	4.09281i	0.491590	−	0.298499i
$189$	3.18821	+	3.18821i	0.231908	+	0.231908i
$190$	0.540997	+	1.93330i	0.0392480	+	0.140256i
$191$	−4.53246			−0.327958			−0.163979	−	0.986464i	$-0.552433\pi$
$191$	−4.53246			−0.327958			−0.163979	+	0.986464i	$0.552433\pi$
$192$	4.51078	−	5.15256i	0.325537	−	0.371854i
$193$	21.9559			1.58042			0.790210	−	0.612836i	$-0.209971\pi$
$193$	21.9559			1.58042			0.790210	+	0.612836i	$0.209971\pi$
$194$	0.172975	+	0.618140i	0.0124189	+	0.0443799i
$195$	−2.39636	−	2.39636i	−0.171607	−	0.171607i
$196$	1.70952	−	1.03804i	0.122109	−	0.0741458i
$197$	−2.00733	+	2.00733i	−0.143016	+	0.143016i	−0.774990	−	0.631974i	$-0.782245\pi$
$197$	−2.00733	+	2.00733i	−0.143016	+	0.143016i	0.631974	+	0.774990i	$0.282245\pi$
$198$	−1.80578	+	3.20909i	−0.128331	+	0.228060i
$199$			7.06629i			0.500916i	0.968127	+	0.250458i	$0.0805813\pi$
$199$			7.06629i			0.500916i	−0.968127	+	0.250458i	$0.919419\pi$
$200$	−1.93260	+	2.06521i	−0.136655	+	0.146032i
$201$			0.196898i			0.0138881i
$202$	−22.8430	−	12.8539i	−1.60723	−	0.904395i
$203$	0.122932	−	0.122932i	0.00862813	−	0.00862813i
$204$	7.81399	+	1.90968i	0.547089	+	0.133704i
$205$	3.42440	+	3.42440i	0.239171	+	0.239171i
$206$	10.4406	−	2.92160i	0.727428	−	0.203557i
$207$	−18.4938			−1.28541
$208$	−15.1004	+	4.77076i	−1.04703	+	0.330792i
$209$	1.63025			0.112767
$210$	1.16579	−	0.326226i	0.0804475	−	0.0225117i
$211$	−5.92777	−	5.92777i	−0.408084	−	0.408084i	0.472986	−	0.881070i	$-0.343176\pi$
$211$	−5.92777	−	5.92777i	−0.408084	−	0.408084i	−0.881070	+	0.472986i	$0.843176\pi$
$212$	−4.83105	+	19.7677i	−0.331798	+	1.35765i
$213$	−3.63451	+	3.63451i	−0.249033	+	0.249033i
$214$	−0.209356	−	0.117806i	−0.0143113	−	0.00805305i
$215$		−	3.13476i		−	0.213789i
$216$	12.7458	−	0.422790i	0.867244	−	0.0287672i
$217$			2.46615i			0.167413i
$218$	−3.30901	+	5.88053i	−0.224114	+	0.398280i
$219$	4.29744	−	4.29744i	0.290394	−	0.290394i
$220$	1.19211	+	1.96325i	0.0803719	+	0.132362i
$221$	−13.1534	−	13.1534i	−0.884791	−	0.884791i
$222$	−1.63190	−	5.83173i	−0.109526	−	0.391400i
$223$	26.1813			1.75323			0.876615	−	0.481192i	$-0.159796\pi$
$223$	26.1813			1.75323			0.876615	+	0.481192i	$0.159796\pi$
$224$	1.16005	−	5.53663i	0.0775090	−	0.369932i
$225$	−2.26725			−0.151150
$226$	7.32623	+	26.1809i	0.487334	+	1.74153i
$227$	2.25330	+	2.25330i	0.149557	+	0.149557i	0.777920	−	0.628363i	$-0.216275\pi$
$227$	2.25330	+	2.25330i	0.149557	+	0.149557i	−0.628363	+	0.777920i	$0.716275\pi$
$228$	−1.26138	−	2.07734i	−0.0835371	−	0.137575i
$229$	8.75526	−	8.75526i	0.578564	−	0.578564i	−0.355944	−	0.934507i	$-0.615841\pi$
$229$	8.75526	−	8.75526i	0.578564	−	0.578564i	0.934507	+	0.355944i	$0.115841\pi$
$230$	−5.65705	+	10.0533i	−0.373015	+	0.662894i
$231$		−	0.983058i		−	0.0646805i
$232$	−0.0163021	−	0.491458i	−0.00107028	−	0.0322658i
$233$		−	24.0934i		−	1.57841i	−0.614131	−	0.789204i	$-0.710493\pi$
$233$		−	24.0934i		−	1.57841i	0.614131	−	0.789204i	$-0.289507\pi$
$234$	−11.0629	−	6.22519i	−0.723207	−	0.406953i
$235$	2.78799	−	2.78799i	0.181869	−	0.181869i
$236$	4.39503	−	17.9835i	0.286092	−	1.17063i
$237$	6.23482	+	6.23482i	0.404995	+	0.404995i
$238$	6.39891	−	1.79062i	0.414780	−	0.116068i
$239$	21.4289			1.38612			0.693061	−	0.720879i	$-0.256262\pi$
$239$	21.4289			1.38612			0.693061	+	0.720879i	$0.256262\pi$
$240$	1.57929	−	3.03807i	0.101942	−	0.196106i
$241$	7.30564			0.470598			0.235299	−	0.971923i	$-0.424393\pi$
$241$	7.30564			0.470598			0.235299	+	0.971923i	$0.424393\pi$
$242$	−13.1847	+	3.68949i	−0.847544	+	0.237169i
$243$	11.3455	+	11.3455i	0.727814	+	0.727814i
$244$	4.98706	+	1.21880i	0.319264	+	0.0780254i
$245$	0.707107	−	0.707107i	0.0451754	−	0.0451754i
$246$	−5.10928	−	2.87502i	−0.325756	−	0.183305i
$247$			5.62010i			0.357598i
$248$	5.09312	+	4.76608i	0.323413	+	0.302646i
$249$			9.48080i			0.600821i
$250$	−0.693527	+	1.23249i	−0.0438625	+	0.0779492i
$251$	14.2655	−	14.2655i	0.900433	−	0.900433i	−0.0950406	−	0.995473i	$-0.530298\pi$
$251$	14.2655	−	14.2655i	0.900433	−	0.900433i	0.995473	+	0.0950406i	$0.0302981\pi$
$252$	3.87592	−	2.35350i	0.244160	−	0.148256i
$253$	6.62388	+	6.62388i	0.416440	+	0.416440i
$254$	−1.78396	−	6.37513i	−0.111936	−	0.400011i
$255$	4.02198			0.251866
$256$	−9.19238	−	13.0958i	−0.574524	−	0.818488i
$257$	16.1267			1.00596			0.502979	−	0.864299i	$-0.332237\pi$
$257$	16.1267			1.00596			0.502979	+	0.864299i	$0.332237\pi$
$258$	1.02264	+	3.65449i	0.0636668	+	0.227518i
$259$	−3.53721	−	3.53721i	−0.219791	−	0.219791i
$260$	−6.76807	+	4.10964i	−0.419738	+	0.254869i
$261$	0.278718	−	0.278718i	0.0172522	−	0.0172522i
$262$	−3.65794	+	6.50063i	−0.225988	+	0.401610i
$263$			16.7414i			1.03232i	0.856492	+	0.516160i	$0.172639\pi$
$263$			16.7414i			1.03232i	−0.856492	+	0.516160i	$0.827361\pi$
$264$	−2.03022	−	1.89985i	−0.124951	−	0.116928i
$265$			10.1747i			0.625028i
$266$	−1.74959	−	0.984504i	−0.107274	−	0.0603638i
$267$	1.98642	−	1.98642i	0.121567	−	0.121567i
$268$	0.446885	+	0.109215i	0.0272979	+	0.00667138i
$269$	−7.19225	−	7.19225i	−0.438519	−	0.438519i	0.452994	−	0.891513i	$-0.350356\pi$
$269$	−7.19225	−	7.19225i	−0.438519	−	0.438519i	−0.891513	+	0.452994i	$0.850356\pi$
$270$	6.14053	−	1.71831i	0.373701	−	0.104573i
$271$	18.4417			1.12025			0.560125	−	0.828408i	$-0.310753\pi$
$271$	18.4417			1.12025			0.560125	+	0.828408i	$0.310753\pi$
$272$	8.66851	−	16.6756i	0.525606	−	1.01111i
$273$	3.38897			0.205110
$274$	19.3256	−	5.40790i	1.16750	−	0.326703i
$275$	0.812056	+	0.812056i	0.0489688	+	0.0489688i
$276$	3.31531	−	13.5655i	0.199558	−	0.816550i
$277$	−16.8558	+	16.8558i	−1.01277	+	1.01277i	−0.0128486	+	0.999917i	$0.504090\pi$
$277$	−16.8558	+	16.8558i	−1.01277	+	1.01277i	−0.999917	+	0.0128486i	$0.995910\pi$
$278$	−12.2983	−	6.92033i	−0.737603	−	0.415054i
$279$			5.59139i			0.334748i
$280$	−0.0937698	−	2.82687i	−0.00560382	−	0.168938i
$281$			17.9304i			1.06964i	0.844967	+	0.534818i	$0.179620\pi$
$281$			17.9304i			1.06964i	−0.844967	+	0.534818i	$0.820380\pi$
$282$	−2.34071	+	4.15974i	−0.139387	+	0.247709i
$283$	19.6883	−	19.6883i	1.17035	−	1.17035i	0.188222	−	0.982127i	$-0.439728\pi$
$283$	19.6883	−	19.6883i	1.17035	−	1.17035i	0.982127	−	0.188222i	$-0.0602724\pi$
$284$	6.23300	+	10.2650i	0.369861	+	0.609114i
$285$	−0.859245	−	0.859245i	−0.0508973	−	0.0508973i
$286$	1.73273	+	6.19205i	0.102459	+	0.366144i
$287$	−4.84284			−0.285864
$288$	2.63012	−	12.5529i	0.154981	−	0.739688i
$289$	5.07618			0.298599
$290$	−0.0662553	−	0.236769i	−0.00389064	−	0.0139035i
$291$	−0.274730	−	0.274730i	−0.0161049	−	0.0161049i
$292$	−7.36989	−	12.1373i	−0.431290	−	0.710281i
$293$	18.2273	−	18.2273i	1.06485	−	1.06485i	0.0671045	−	0.997746i	$-0.478624\pi$
$293$	18.2273	−	18.2273i	1.06485	−	1.06485i	0.997746	−	0.0671045i	$-0.0213761\pi$
$294$	−0.593665	+	1.05502i	−0.0346232	+	0.0615299i
$295$		−	9.25639i		−	0.538928i
$296$	−14.1410	+	0.469071i	−0.821932	+	0.0272642i
$297$		−	5.17801i		−	0.300459i
$298$	26.0777	+	14.6741i	1.51064	+	0.850046i
$299$	−22.8350	+	22.8350i	−1.32058	+	1.32058i
$300$	0.406441	−	1.66307i	0.0234659	−	0.0960175i
$301$	2.21661	+	2.21661i	0.127763	+	0.127763i
$302$	−1.61142	+	0.450925i	−0.0927267	+	0.0259478i
$303$	15.8653			0.911438
$304$	−5.41445	+	1.71061i	−0.310540	+	0.0981104i
$305$	2.56691			0.146981
$306$	14.5079	−	4.05977i	0.829363	−	0.232082i
$307$	17.6406	+	17.6406i	1.00680	+	1.00680i	0.999977	+	0.00682294i	$0.00217183\pi$
$307$	17.6406	+	17.6406i	1.00680	+	1.00680i	0.00682294	+	0.999977i	$0.497828\pi$
$308$	−2.23118	−	0.545282i	−0.127133	−	0.0310703i
$309$	−4.64027	+	4.64027i	−0.263975	+	0.263975i
$310$	3.03950	+	1.71034i	0.172632	+	0.0971410i
$311$			18.4188i			1.04444i	0.852812	+	0.522218i	$0.174895\pi$
$311$			18.4188i			1.04444i	−0.852812	+	0.522218i	$0.825105\pi$
$312$	6.54951	−	6.99892i	0.370793	−	0.396236i
$313$			19.9601i			1.12821i	0.825703	+	0.564105i	$0.190779\pi$
$313$			19.9601i			1.12821i	−0.825703	+	0.564105i	$0.809221\pi$
$314$	−4.89620	+	8.70117i	−0.276308	+	0.491035i
$315$	1.60319	−	1.60319i	0.0903294	−	0.0903294i
$316$	17.6091	−	10.6924i	0.990587	−	0.601495i
$317$	−22.4232	−	22.4232i	−1.25941	−	1.25941i	−0.951375	−	0.308035i	$-0.900329\pi$
$317$	−22.4232	−	22.4232i	−1.25941	−	1.25941i	−0.308035	−	0.951375i	$-0.599671\pi$
$318$	−3.31925	−	11.8616i	−0.186135	−	0.665167i
$319$	−0.199655			−0.0111786
$320$	−6.01929	−	5.26955i	−0.336489	−	0.294577i
$321$	0.145406			0.00811576
$322$	−3.10861	−	11.1089i	−0.173236	−	0.619074i
$323$	−4.71630	−	4.71630i	−0.262422	−	0.262422i
$324$	5.02971	−	3.05409i	0.279428	−	0.169672i
$325$	−2.79946	+	2.79946i	−0.155286	+	0.155286i
$326$	−4.90656	+	8.71957i	−0.271749	+	0.482932i
$327$		−	4.08425i		−	0.225860i
$328$	−9.35924	+	10.0015i	−0.516778	+	0.552238i
$329$			3.94282i			0.217375i
$330$	−1.21160	−	0.681777i	−0.0666966	−	0.0375306i
$331$	3.88438	−	3.88438i	0.213505	−	0.213505i	−0.592250	−	0.805754i	$-0.701760\pi$
$331$	3.88438	−	3.88438i	0.213505	−	0.213505i	0.805754	+	0.592250i	$0.201760\pi$
$332$	21.5179	+	5.25880i	1.18095	+	0.288614i
$333$	−8.01973	−	8.01973i	−0.439479	−	0.439479i
$334$	33.8988	−	9.48596i	1.85486	−	0.519049i
$335$	0.230019			0.0125673
$336$	1.03152	+	3.26496i	0.0562738	+	0.178118i
$337$	14.4218			0.785604			0.392802	−	0.919623i	$-0.371506\pi$
$337$	14.4218			0.785604			0.392802	+	0.919623i	$0.371506\pi$
$338$	−3.64168	+	1.01906i	−0.198081	+	0.0554294i
$339$	−11.6360	−	11.6360i	−0.631980	−	0.631980i
$340$	2.23091	−	9.12840i	0.120988	−	0.495057i
$341$	2.00266	−	2.00266i	0.108450	−	0.108450i
$342$	−3.96676	−	2.23212i	−0.214498	−	0.120699i
$343$			1.00000i			0.0539949i
$344$	8.86157	−	0.293946i	0.477784	−	0.0158485i
$345$		−	6.98240i		−	0.375920i
$346$	10.1211	−	17.9865i	0.544114	−	0.966960i
$347$	−23.2708	+	23.2708i	−1.24924	+	1.24924i	−0.293185	+	0.956056i	$0.594715\pi$
$347$	−23.2708	+	23.2708i	−1.24924	+	1.24924i	−0.956056	+	0.293185i	$0.905285\pi$
$348$	0.154480	+	0.254409i	0.00828100	+	0.0136378i
$349$	3.49358	+	3.49358i	0.187007	+	0.187007i	0.794401	−	0.607394i	$-0.207785\pi$
$349$	3.49358	+	3.49358i	0.187007	+	0.187007i	−0.607394	+	0.794401i	$0.707785\pi$
$350$	−0.381101	−	1.36190i	−0.0203707	−	0.0727964i
$351$	17.8505			0.952792
$352$	−5.43808	+	3.55403i	−0.289851	+	0.189430i
$353$	8.24329			0.438746			0.219373	−	0.975641i	$-0.429599\pi$
$353$	8.24329			0.438746			0.219373	+	0.975641i	$0.429599\pi$
$354$	3.01967	+	10.7911i	0.160494	+	0.573538i
$355$	4.24588	+	4.24588i	0.225348	+	0.225348i
$356$	−3.40660	−	5.61025i	−0.180550	−	0.297343i
$357$	−2.84397	+	2.84397i	−0.150519	+	0.150519i
$358$	−16.3283	+	29.0174i	−0.862975	+	1.53362i
$359$		−	20.9198i		−	1.10410i	−0.833810	−	0.552051i	$-0.813845\pi$
$359$		−	20.9198i		−	1.10410i	0.833810	−	0.552051i	$-0.186155\pi$
$360$	−0.212600	−	6.40923i	−0.0112050	−	0.337796i
$361$		−	16.9848i		−	0.893939i
$362$	−15.8498	−	8.91878i	−0.833047	−	0.468761i
$363$	5.85988	−	5.85988i	0.307564	−	0.307564i
$364$	1.87979	−	7.69170i	0.0985278	−	0.403155i
$365$	−5.02032	−	5.02032i	−0.262776	−	0.262776i
$366$	−2.99250	+	0.837394i	−0.156420	+	0.0437713i
$367$	−33.3855			−1.74271			−0.871355	−	0.490654i	$-0.836758\pi$
$367$	−33.3855			−1.74271			−0.871355	+	0.490654i	$0.836758\pi$
$368$	−28.9498	−	15.0491i	−1.50911	−	0.784486i
$369$	−10.9799			−0.571592
$370$	−6.81270	+	1.90641i	−0.354176	+	0.0991094i
$371$	−7.19461	−	7.19461i	−0.373525	−	0.373525i
$372$	−4.10139	−	1.00235i	−0.212647	−	0.0519693i
$373$	−13.0059	+	13.0059i	−0.673421	+	0.673421i	−0.958503	−	0.285082i	$-0.907979\pi$
$373$	−13.0059	+	13.0059i	−0.673421	+	0.673421i	0.285082	+	0.958503i	$0.407979\pi$
$374$	−6.65036	−	3.74219i	−0.343882	−	0.193504i
$375$		−	0.856008i		−	0.0442041i
$376$	8.14273	+	7.61987i	0.419929	+	0.392965i
$377$		−	0.688287i		−	0.0354486i
$378$	−3.12698	+	5.55704i	−0.160835	+	0.285823i
$379$	11.6155	−	11.6155i	0.596649	−	0.596649i	−0.342770	−	0.939419i	$-0.611365\pi$
$379$	11.6155	−	11.6155i	0.596649	−	0.596649i	0.939419	+	0.342770i	$0.111365\pi$
$380$	−2.42677	+	1.47356i	−0.124491	+	0.0755922i
$381$	2.83340	+	2.83340i	0.145159	+	0.145159i
$382$	−1.72733	−	6.17275i	−0.0883778	−	0.315825i
$383$	−29.1530			−1.48965			−0.744824	−	0.667261i	$-0.767467\pi$
$383$	−29.1530			−1.48965			−0.744824	+	0.667261i	$0.767467\pi$
$384$	8.73632	+	4.17956i	0.445824	+	0.213287i
$385$	−1.14842			−0.0585289
$386$	8.36742	+	29.9017i	0.425891	+	1.52196i
$387$	5.02561	+	5.02561i	0.255466	+	0.255466i
$388$	−0.775922	+	0.471148i	−0.0393915	+	0.0239189i
$389$	15.9257	−	15.9257i	0.807466	−	0.807466i	−0.176784	−	0.984250i	$-0.556569\pi$
$389$	15.9257	−	15.9257i	0.807466	−	0.807466i	0.984250	+	0.176784i	$0.0565693\pi$
$390$	2.35034	−	4.17686i	0.119014	−	0.211503i
$391$		−	38.3255i		−	1.93821i
$392$	2.06521	+	1.93260i	0.104309	+	0.0976108i
$393$		−	4.51494i		−	0.227748i
$394$	−3.49877	−	1.96878i	−0.176266	−	0.0991857i
$395$	7.28360	−	7.28360i	0.366478	−	0.366478i
$396$	−5.05863	−	1.23629i	−0.254206	−	0.0621259i
$397$	3.04529	+	3.04529i	0.152839	+	0.152839i	0.779385	−	0.626546i	$-0.215532\pi$
$397$	3.04529	+	3.04529i	0.152839	+	0.152839i	−0.626546	+	0.779385i	$0.715532\pi$
$398$	−9.62356	+	2.69297i	−0.482386	+	0.134987i
$399$	1.21516			0.0608339
$400$	−3.54911	−	1.84494i	−0.177456	−	0.0922471i
$401$	−23.7861			−1.18782			−0.593909	−	0.804532i	$-0.702416\pi$
$401$	−23.7861			−1.18782			−0.593909	+	0.804532i	$0.702416\pi$
$402$	−0.268155	+	0.0750381i	−0.0133743	+	0.00374256i
$403$	6.90391	+	6.90391i	0.343908	+	0.343908i
$404$	8.80016	−	36.0084i	0.437824	−	1.79148i
$405$	2.08043	−	2.08043i	0.103377	−	0.103377i
$406$	0.214270	+	0.120571i	0.0106340	+	0.00598384i
$407$			5.74482i			0.284760i
$408$	0.377140	+	11.3696i	0.0186712	+	0.562880i
$409$			14.7195i			0.727831i	0.931432	+	0.363916i	$0.118560\pi$
$409$			14.7195i			0.727831i	−0.931432	+	0.363916i	$0.881440\pi$
$410$	−3.35864	+	5.96873i	−0.165871	+	0.294774i
$411$	−8.58917	+	8.58917i	−0.423673	+	0.423673i
$412$	7.95782	+	13.1055i	0.392054	+	0.645664i
$413$	6.54526	+	6.54526i	0.322071	+	0.322071i
$414$	−7.04800	−	25.1866i	−0.346391	−	1.23785i
$415$	11.0756			0.543679
$416$	−12.2521	−	18.7471i	−0.600708	−	0.919152i
$417$	8.54164			0.418286
$418$	0.621292	+	2.22024i	0.0303884	+	0.108595i
$419$	3.77105	+	3.77105i	0.184228	+	0.184228i	0.793195	−	0.608968i	$-0.208416\pi$
$419$	3.77105	+	3.77105i	0.184228	+	0.184228i	−0.608968	+	0.793195i	$0.708416\pi$
$420$	0.888572	+	1.46337i	0.0433579	+	0.0714050i
$421$	−14.6768	+	14.6768i	−0.715305	+	0.715305i	−0.967640	−	0.252335i	$-0.918801\pi$
$421$	−14.6768	+	14.6768i	−0.715305	+	0.715305i	0.252335	+	0.967640i	$0.418801\pi$
$422$	5.81392	−	10.3321i	0.283017	−	0.502958i
$423$			8.93936i			0.434646i
$424$	−28.7626	+	0.954081i	−1.39684	+	0.0463343i
$425$		−	4.69853i		−	0.227912i
$426$	−6.33494	−	3.56471i	−0.306929	−	0.172711i
$427$	−1.81508	+	1.81508i	−0.0878380	+	0.0878380i
$428$	0.0806536	−	0.330017i	0.00389854	−	0.0159520i
$429$	−2.75203	−	2.75203i	−0.132869	−	0.132869i
$430$	4.26922	−	1.19466i	0.205880	−	0.0576117i
$431$	−1.85417			−0.0893123			−0.0446561	−	0.999002i	$-0.514219\pi$
$431$	−1.85417			−0.0893123			−0.0446561	+	0.999002i	$0.514219\pi$
$432$	5.43325	+	17.1974i	0.261407	+	0.827409i
$433$	−31.1008			−1.49461			−0.747304	−	0.664482i	$-0.768652\pi$
$433$	−31.1008			−1.49461			−0.747304	+	0.664482i	$0.768652\pi$
$434$	−3.35865	+	0.939855i	−0.161220	+	0.0451145i
$435$	0.105231	+	0.105231i	0.00504543	+	0.00504543i
$436$	−9.26974	−	2.26545i	−0.443940	−	0.108495i
$437$	−8.18777	+	8.18777i	−0.391674	+	0.391674i
$438$	7.49043	+	4.21491i	0.357906	+	0.201396i
$439$		−	8.31669i		−	0.396934i	−0.980108	−	0.198467i	$-0.936404\pi$
$439$		−	8.31669i		−	0.396934i	0.980108	−	0.198467i	$-0.0635963\pi$
$440$	−2.21943	+	2.37173i	−0.105807	+	0.113068i
$441$			2.26725i			0.107964i
$442$	12.9007	−	22.9263i	0.613626	−	1.09049i
$443$	13.1234	−	13.1234i	0.623512	−	0.623512i	−0.322916	−	0.946428i	$-0.604663\pi$
$443$	13.1234	−	13.1234i	0.623512	−	0.623512i	0.946428	+	0.322916i	$0.104663\pi$
$444$	7.32029	−	4.44496i	0.347406	−	0.210949i
$445$	−2.32056	−	2.32056i	−0.110005	−	0.110005i
$446$	9.97773	+	35.6562i	0.472459	+	1.68837i
$447$	−18.1119			−0.856666
$448$	7.98241	−	0.530151i	0.377134	−	0.0250473i
$449$	23.1718			1.09355			0.546773	−	0.837281i	$-0.315856\pi$
$449$	23.1718			1.09355			0.546773	+	0.837281i	$0.315856\pi$
$450$	−0.864052	−	3.08776i	−0.0407318	−	0.145558i
$451$	3.93265	+	3.93265i	0.185181	+	0.185181i
$452$	−32.8636	+	19.9551i	−1.54577	+	0.938611i
$453$	0.716188	−	0.716188i	0.0336495	−	0.0336495i
$454$	−2.21003	+	3.92750i	−0.103722	+	0.184327i
$455$		−	3.95904i		−	0.185603i
$456$	2.34841	−	2.50955i	0.109974	−	0.117520i
$457$		−	22.2382i		−	1.04026i	−0.854088	−	0.520128i	$-0.825884\pi$
$457$		−	22.2382i		−	1.04026i	0.854088	−	0.520128i	$-0.174116\pi$
$458$	15.2604	+	8.58711i	0.713071	+	0.401249i
$459$	−14.9799	+	14.9799i	−0.699202	+	0.699202i
$460$	−15.8474	−	3.87299i	−0.738891	−	0.180579i
$461$	−24.2390	−	24.2390i	−1.12892	−	1.12892i	−0.990353	−	0.138567i	$-0.955750\pi$
$461$	−24.2390	−	24.2390i	−1.12892	−	1.12892i	−0.138567	−	0.990353i	$-0.544250\pi$
$462$	1.33882	−	0.374645i	0.0622877	−	0.0174300i
$463$	−2.31569			−0.107619			−0.0538097	−	0.998551i	$-0.517136\pi$
$463$	−2.31569			−0.107619			−0.0538097	+	0.998551i	$0.517136\pi$
$464$	0.663102	−	0.209497i	0.0307837	−	0.00972565i
$465$	−2.11105			−0.0978975
$466$	32.8127	−	9.18201i	1.52002	−	0.425349i
$467$	15.2836	+	15.2836i	0.707242	+	0.707242i	0.965954	−	0.258713i	$-0.0832983\pi$
$467$	15.2836	+	15.2836i	0.707242	+	0.707242i	−0.258713	+	0.965954i	$0.583298\pi$
$468$	4.26195	−	17.4390i	0.197009	−	0.806119i
$469$	−0.162648	+	0.162648i	−0.00751038	+	0.00751038i
$470$	4.85947	+	2.73445i	0.224151	+	0.126131i
$471$		−	6.04329i		−	0.278460i
$472$	26.1666	−	0.867970i	1.20442	−	0.0399516i
$473$		−	3.60002i		−	0.165529i
$474$	−6.11508	+	10.8673i	−0.280875	+	0.499151i
$475$	−1.00378	+	1.00378i	−0.0460567	+	0.0460567i
$476$	4.87727	+	8.03225i	0.223549	+	0.368157i
$477$	−16.3120	−	16.3120i	−0.746874	−	0.746874i
$478$	8.16659	+	29.1840i	0.373531	+	1.33484i
$479$	27.7338			1.26719			0.633594	−	0.773665i	$-0.281579\pi$
$479$	27.7338			1.26719			0.633594	+	0.773665i	$0.281579\pi$
$480$	4.73940	+	0.993012i	0.216323	+	0.0453246i
$481$	−19.8046			−0.903010
$482$	2.78419	+	9.94953i	0.126816	+	0.453189i
$483$	4.93730	+	4.93730i	0.224655	+	0.224655i
$484$	−10.0494	−	16.5501i	−0.456791	−	0.752278i
$485$	−0.320943	+	0.320943i	−0.0145733	+	0.0145733i
$486$	−11.1276	+	19.7752i	−0.504758	+	0.897020i
$487$			37.6955i			1.70815i	0.520152	+	0.854074i	$0.325875\pi$
$487$			37.6955i			1.70815i	−0.520152	+	0.854074i	$0.674125\pi$
$488$	0.240699	+	7.25634i	0.0108959	+	0.328479i
$489$		−	6.05608i		−	0.273865i
$490$	1.23249	+	0.693527i	0.0556780	+	0.0313304i
$491$	13.0302	−	13.0302i	0.588045	−	0.588045i	−0.349056	−	0.937102i	$-0.613498\pi$
$491$	13.0302	−	13.0302i	0.588045	−	0.588045i	0.937102	+	0.349056i	$0.113498\pi$
$492$	1.96833	−	8.05398i	0.0887391	−	0.363102i
$493$	0.577600	+	0.577600i	0.0260138	+	0.0260138i
$494$	−7.65399	+	2.14183i	−0.344369	+	0.0963653i
$495$	−2.60376			−0.117030
$496$	−4.54991	+	8.75265i	−0.204297	+	0.393006i
$497$	−6.00458			−0.269342
$498$	−12.9119	+	3.61314i	−0.578595	+	0.161909i
$499$	−20.9927	−	20.9927i	−0.939762	−	0.939762i	0.0585244	−	0.998286i	$-0.481360\pi$
$499$	−20.9927	−	20.9927i	−0.939762	−	0.939762i	−0.998286	+	0.0585244i	$0.981360\pi$
$500$	−1.94282	−	0.474810i	−0.0868856	−	0.0212341i
$501$	−15.0662	+	15.0662i	−0.673108	+	0.673108i
$502$	24.8648	+	13.9916i	1.10977	+	0.624474i
$503$		−	7.53500i		−	0.335969i	−0.985790	−	0.167984i	$-0.946274\pi$
$503$		−	7.53500i		−	0.335969i	0.985790	−	0.167984i	$-0.0537258\pi$
$504$	4.68234	+	4.38168i	0.208568	+	0.195175i
$505$		−	18.5341i		−	0.824755i
$506$	−6.49667	+	11.5454i	−0.288812	+	0.513256i
$507$	1.61853	−	1.61853i	0.0718815	−	0.0718815i
$508$	8.00239	−	4.85914i	0.355049	−	0.215589i
$509$	−12.2119	−	12.2119i	−0.541281	−	0.541281i	0.382623	−	0.923905i	$-0.375021\pi$
$509$	−12.2119	−	12.2119i	−0.541281	−	0.541281i	−0.923905	+	0.382623i	$0.875021\pi$
$510$	1.53278	+	5.47752i	0.0678727	+	0.242549i
$511$	7.09981			0.314077
$512$	14.3319	−	17.5099i	0.633387	−	0.773835i
$513$	6.40053			0.282590
$514$	6.14591	+	21.9629i	0.271085	+	0.968743i
$515$	5.42082	+	5.42082i	0.238870	+	0.238870i
$516$	−4.58730	+	2.78546i	−0.201945	+	0.122623i
$517$	3.20179	−	3.20179i	0.140815	−	0.140815i
$518$	3.46928	−	6.16534i	0.152431	−	0.270890i
$519$			12.4923i			0.548352i
$520$	−8.17623	−	7.65122i	−0.358551	−	0.335528i
$521$			20.0636i			0.879003i	0.898242	+	0.439502i	$0.144845\pi$
$521$			20.0636i			0.879003i	−0.898242	+	0.439502i	$0.855155\pi$
$522$	0.485804	+	0.273365i	0.0212631	+	0.0119649i
$523$	−25.1733	+	25.1733i	−1.10075	+	1.10075i	−0.106433	+	0.994320i	$0.533943\pi$
$523$	−25.1733	+	25.1733i	−1.10075	+	1.10075i	−0.994320	+	0.106433i	$0.966057\pi$
$524$	−10.2472	−	2.50434i	−0.447652	−	0.109403i
$525$	0.605289	+	0.605289i	0.0264170	+	0.0264170i
$526$	−22.8001	+	6.38018i	−0.994131	+	0.278189i
$527$	−11.5873			−0.504751
$528$	1.81368	−	3.48898i	0.0789305	−	0.151838i
$529$	−43.5354			−1.89284
$530$	−13.8569	+	3.87760i	−0.601905	+	0.168432i
$531$	14.8397	+	14.8397i	0.643990	+	0.643990i
$532$	0.674022	−	2.75795i	0.0292226	−	0.119573i
$533$	−13.5573	+	13.5573i	−0.587233	+	0.587233i
$534$	3.46232	+	1.94827i	0.149829	+	0.0843098i
$535$		−	0.169865i		−	0.00734391i
$536$	0.0215688	+	0.650234i	0.000931631	+	0.0280858i
$537$		−	20.1537i		−	0.869696i
$538$	7.05413	−	12.5361i	0.304125	−	0.540469i
$539$	0.812056	−	0.812056i	0.0349777	−	0.0349777i
$540$	4.68033	+	7.70792i	0.201409	+	0.331696i
$541$	−2.43357	−	2.43357i	−0.104627	−	0.104627i	0.652855	−	0.757483i	$-0.273571\pi$
$541$	−2.43357	−	2.43357i	−0.104627	−	0.104627i	−0.757483	+	0.652855i	$0.773571\pi$
$542$	7.02814	+	25.1156i	0.301884	+	1.07881i
$543$	11.0083			0.472411
$544$	26.0140	+	5.45052i	1.11534	+	0.233689i
$545$	−4.77128			−0.204379
$546$	1.29154	+	4.61543i	0.0552728	+	0.197522i
$547$	2.34767	+	2.34767i	0.100379	+	0.100379i	0.755513	−	0.655134i	$-0.227388\pi$
$547$	2.34767	+	2.34767i	0.100379	+	0.100379i	−0.655134	+	0.755513i	$0.727388\pi$
$548$	14.7300	+	24.2585i	0.629235	+	1.03627i
$549$	−4.11525	+	4.11525i	−0.175634	+	0.175634i
$550$	−0.796461	+	1.41541i	−0.0339612	+	0.0603534i
$551$		−	0.246794i		−	0.0105138i
$552$	19.7383	−	0.654738i	0.840120	−	0.0278675i
$553$			10.3006i			0.438025i
$554$	−29.3796	−	16.5321i	−1.24822	−	0.702380i
$555$	3.02788	−	3.02788i	0.128526	−	0.128526i
$556$	4.73787	−	19.3864i	0.200930	−	0.822165i
$557$	14.3487	+	14.3487i	0.607973	+	0.607973i	0.942416	−	0.334443i	$-0.108548\pi$
$557$	14.3487	+	14.3487i	0.607973	+	0.607973i	−0.334443	+	0.942416i	$0.608548\pi$
$558$	−7.61489	+	2.13088i	−0.322364	+	0.0902076i
$559$	12.4106			0.524914
$560$	3.81417	−	1.20503i	0.161178	−	0.0509218i
$561$	4.61893			0.195011
$562$	−24.4193	+	6.83328i	−1.03007	+	0.288245i
$563$	−18.2878	−	18.2878i	−0.770739	−	0.770739i	0.207497	−	0.978236i	$-0.433468\pi$
$563$	−18.2878	−	18.2878i	−0.770739	−	0.770739i	−0.978236	+	0.207497i	$0.933468\pi$
$564$	−6.55719	−	1.60252i	−0.276107	−	0.0674784i
$565$	−13.5933	+	13.5933i	−0.571875	+	0.571875i
$566$	34.3167	+	19.3102i	1.44244	+	0.811668i
$567$			2.94217i			0.123560i
$568$	−11.6044	+	12.4007i	−0.486911	+	0.520322i
$569$		−	1.39010i		−	0.0582762i	−0.999575	−	0.0291381i	$-0.990724\pi$
$569$		−	1.39010i		−	0.0582762i	0.999575	−	0.0291381i	$-0.00927626\pi$
$570$	0.842744	−	1.49766i	0.0352987	−	0.0627302i
$571$	10.6954	−	10.6954i	0.447587	−	0.447587i	−0.446965	−	0.894552i	$-0.647495\pi$
$571$	10.6954	−	10.6954i	0.447587	−	0.447587i	0.894552	+	0.446965i	$0.147495\pi$
$572$	−7.77259	+	4.71960i	−0.324988	+	0.197336i
$573$	2.74345	+	2.74345i	0.114609	+	0.114609i
$574$	−1.84561	−	6.59544i	−0.0770343	−	0.275288i
$575$	−8.15692			−0.340167
$576$	18.0981	−	1.20198i	0.754089	−	0.0500827i
$577$	3.44573			0.143448			0.0717239	−	0.997425i	$-0.477150\pi$
$577$	3.44573			0.143448			0.0717239	+	0.997425i	$0.477150\pi$
$578$	1.93454	+	6.91323i	0.0804662	+	0.287553i
$579$	−13.2897	−	13.2897i	−0.552300	−	0.552300i
$580$	0.297204	−	0.180466i	0.0123407	−	0.00749343i
$581$	−7.83163	+	7.83163i	−0.324911	+	0.324911i
$582$	0.269454	−	0.478853i	0.0111692	−	0.0198491i
$583$			11.6849i			0.483937i
$584$	13.7211	−	14.6626i	0.567781	−	0.606741i
$585$		−	8.97613i		−	0.371117i
$586$	31.7701	+	17.8773i	1.31241	+	0.738502i
$587$	2.25967	−	2.25967i	0.0932666	−	0.0932666i	−0.658934	−	0.752201i	$-0.728992\pi$
$587$	2.25967	−	2.25967i	0.0932666	−	0.0932666i	0.752201	+	0.658934i	$0.228992\pi$
$588$	−1.66307	−	0.406441i	−0.0685839	−	0.0167614i
$589$	2.47548	+	2.47548i	0.102000	+	0.102000i
$590$	12.6062	−	3.52762i	0.518991	−	0.145230i
$591$	2.43003			0.0999581
$592$	−6.02800	−	19.0799i	−0.247749	−	0.784178i
$593$	−26.4329			−1.08547			−0.542735	−	0.839904i	$-0.682611\pi$
$593$	−26.4329			−1.08547			−0.542735	+	0.839904i	$0.682611\pi$
$594$	7.05191	−	1.97335i	0.289344	−	0.0809674i
$595$	3.32236	+	3.32236i	0.136204	+	0.136204i
$596$	−10.0463	+	41.1074i	−0.411513	+	1.68382i
$597$	4.27715	−	4.27715i	0.175052	−	0.175052i
$598$	−39.8014	−	22.3965i	−1.62760	−	0.915859i
$599$			41.6771i			1.70288i	0.524453	+	0.851439i	$0.324270\pi$
$599$			41.6771i			1.70288i	−0.524453	+	0.851439i	$0.675730\pi$
$600$	2.41983	−	0.0802678i	0.0987890	−	0.00327692i
$601$			37.0190i			1.51004i	0.655704	+	0.755018i	$0.272372\pi$
$601$			37.0190i			1.51004i	−0.655704	+	0.755018i	$0.727628\pi$
$602$	−2.17404	+	3.86355i	−0.0886073	+	0.157466i
$603$	−0.368763	+	0.368763i	−0.0150172	+	0.0150172i
$604$	−1.22823	−	2.02274i	−0.0499759	−	0.0823040i
$605$	−6.84559	−	6.84559i	−0.278313	−	0.278313i
$606$	6.04629	+	21.6069i	0.245614	+	0.877721i
$607$	13.3712			0.542720			0.271360	−	0.962478i	$-0.412527\pi$
$607$	13.3712			0.542720			0.271360	+	0.962478i	$0.412527\pi$
$608$	−4.39313	−	6.72200i	−0.178165	−	0.272613i
$609$	−0.148819			−0.00603044
$610$	0.978254	+	3.49587i	0.0396084	+	0.141544i
$611$	11.0378	+	11.0378i	0.446541	+	0.446541i
$612$	11.0580	+	18.2111i	0.446992	+	0.736141i
$613$	22.7096	−	22.7096i	0.917233	−	0.917233i	−0.0795940	−	0.996827i	$-0.525362\pi$
$613$	22.7096	−	22.7096i	0.917233	−	0.917233i	0.996827	+	0.0795940i	$0.0253624\pi$
$614$	−17.3018	+	30.7474i	−0.698243	+	1.24087i
$615$		−	4.14551i		−	0.167163i
$616$	−0.107687	−	3.24644i	−0.00433884	−	0.130803i
$617$		−	1.42378i		−	0.0573194i	−0.999589	−	0.0286597i	$-0.990876\pi$
$617$		−	1.42378i		−	0.0573194i	0.999589	−	0.0286597i	$-0.00912391\pi$
$618$	−8.08797	−	4.55115i	−0.325346	−	0.183074i
$619$	19.8935	−	19.8935i	0.799588	−	0.799588i	−0.183442	−	0.983030i	$-0.558724\pi$
$619$	19.8935	−	19.8935i	0.799588	−	0.799588i	0.983030	+	0.183442i	$0.0587241\pi$
$620$	−1.17095	+	4.79130i	−0.0470267	+	0.192423i
$621$	26.0060	+	26.0060i	1.04358	+	1.04358i
$622$	−25.0846	+	7.01944i	−1.00580	+	0.281454i
$623$	3.28176			0.131481
$624$	12.0278	+	6.25245i	0.481498	+	0.250298i
$625$	−1.00000			−0.0400000
$626$	−27.1835	+	7.60680i	−1.08647	+	0.304029i
$627$	−0.986775	−	0.986775i	−0.0394080	−	0.0394080i
$628$	−13.7160	−	3.35209i	−0.547329	−	0.133763i
$629$	16.6197	−	16.6197i	0.662670	−	0.662670i
$630$	2.79435	+	1.57240i	0.111330	+	0.0626459i
$631$		−	9.15758i		−	0.364558i	−0.983247	−	0.182279i	$-0.941653\pi$
$631$		−	9.15758i		−	0.364558i	0.983247	−	0.182279i	$-0.0583473\pi$
$632$	21.2728	+	19.9068i	0.846186	+	0.791851i
$633$			7.17603i			0.285221i
$634$	21.9925	−	39.0835i	0.873435	−	1.55220i
$635$	3.31001	−	3.31001i	0.131354	−	0.131354i
$636$	14.8893	−	9.04096i	0.590401	−	0.358497i
$637$	2.79946	+	2.79946i	0.110919	+	0.110919i
$638$	−0.0760889	−	0.271910i	−0.00301239	−	0.0107650i
$639$	−13.6139			−0.538557
$640$	4.88262	−	10.2059i	0.193002	−	0.403423i
$641$	−22.5024			−0.888793			−0.444396	−	0.895830i	$-0.646582\pi$
$641$	−22.5024			−0.888793			−0.444396	+	0.895830i	$0.646582\pi$
$642$	0.0554144	+	0.198028i	0.00218703	+	0.00781553i
$643$	−5.57036	−	5.57036i	−0.219673	−	0.219673i	0.588687	−	0.808361i	$-0.299645\pi$
$643$	−5.57036	−	5.57036i	−0.219673	−	0.219673i	−0.808361	+	0.588687i	$0.799645\pi$
$644$	13.9445	−	8.46722i	0.549488	−	0.333655i
$645$	−1.89744	+	1.89744i	−0.0747115	+	0.0747115i
$646$	4.62572	−	8.22050i	0.181997	−	0.323431i
$647$		−	34.4395i		−	1.35396i	−0.736003	−	0.676979i	$-0.763289\pi$
$647$		−	34.4395i		−	1.35396i	0.736003	−	0.676979i	$-0.236711\pi$
$648$	6.07619	+	5.68602i	0.238695	+	0.223368i
$649$		−	10.6302i		−	0.417273i
$650$	−4.87946	−	2.74570i	−0.191388	−	0.107695i
$651$	1.49274	−	1.49274i	0.0585050	−	0.0585050i
$652$	−13.7450	−	3.35918i	−0.538298	−	0.131556i
$653$	21.9881	+	21.9881i	0.860459	+	0.860459i	0.991391	−	0.130932i	$-0.0417970\pi$
$653$	21.9881	+	21.9881i	0.860459	+	0.860459i	−0.130932	+	0.991391i	$0.541797\pi$
$654$	5.56233	−	1.55651i	0.217504	−	0.0608645i
$655$	−5.27441			−0.206088
$656$	−17.1878	−	8.93475i	−0.671069	−	0.348843i
$657$	16.0970			0.628005
$658$	−5.36971	+	1.50261i	−0.209333	+	0.0585780i
$659$	−32.2167	−	32.2167i	−1.25498	−	1.25498i	−0.953458	−	0.301527i	$-0.902504\pi$
$659$	−32.2167	−	32.2167i	−1.25498	−	1.25498i	−0.301527	−	0.953458i	$-0.597496\pi$
$660$	0.466766	−	1.90991i	0.0181688	−	0.0743430i
$661$	−19.7402	+	19.7402i	−0.767803	+	0.767803i	−0.977719	−	0.209916i	$-0.932681\pi$
$661$	−19.7402	+	19.7402i	−0.767803	+	0.767803i	0.209916	+	0.977719i	$0.432681\pi$
$662$	6.77046	+	3.80978i	0.263142	+	0.148071i
$663$			15.9232i			0.618405i
$664$	1.03856	+	31.3093i	0.0403038	+	1.21504i
$665$		−	1.41956i		−	0.0550482i
$666$	7.86571	−	13.9784i	0.304790	−	0.541651i
$667$	1.00275	−	1.00275i	0.0388265	−	0.0388265i
$668$	25.8378	+	42.5516i	0.999694	+	1.64637i
$669$	−15.8473	−	15.8473i	−0.612691	−	0.612691i
$670$	0.0876604	+	0.313262i	0.00338662	+	0.0121024i
$671$	2.94790			0.113802
$672$	−4.05343	+	2.64910i	−0.156364	+	0.102191i
$673$	−14.0802			−0.542752			−0.271376	−	0.962473i	$-0.587479\pi$
$673$	−14.0802			−0.542752			−0.271376	+	0.962473i	$0.587479\pi$
$674$	5.49616	+	19.6410i	0.211704	+	0.756541i
$675$	3.18821	+	3.18821i	0.122714	+	0.122714i
$676$	−2.77570	−	4.57123i	−0.106758	−	0.175817i
$677$	22.3722	−	22.3722i	0.859834	−	0.859834i	−0.131485	−	0.991318i	$-0.541974\pi$
$677$	22.3722	−	22.3722i	0.859834	−	0.859834i	0.991318	+	0.131485i	$0.0419744\pi$
$678$	11.4125	−	20.2815i	0.438295	−	0.778906i
$679$		−	0.453882i		−	0.0174184i
$680$	13.2821	−	0.440580i	0.509347	−	0.0168955i
$681$		−	2.72780i		−	0.104529i
$682$	3.49062	+	1.96419i	0.133663	+	0.0752129i
$683$	0.229997	−	0.229997i	0.00880059	−	0.00880059i	−0.702693	−	0.711493i	$-0.748019\pi$
$683$	0.229997	−	0.229997i	0.00880059	−	0.00880059i	0.711493	+	0.702693i	$0.248019\pi$
$684$	1.52818	−	6.25297i	0.0584313	−	0.239088i
$685$	10.0340	+	10.0340i	0.383379	+	0.383379i
$686$	−1.36190	+	0.381101i	−0.0519974	+	0.0145505i
$687$	−10.5989			−0.404374
$688$	3.77748	+	11.9565i	0.144015	+	0.455838i
$689$	−40.2821			−1.53462
$690$	9.50930	−	2.66100i	0.362013	−	0.101303i
$691$	14.0479	+	14.0479i	0.534407	+	0.534407i	0.921881	−	0.387474i	$-0.126652\pi$
$691$	14.0479	+	14.0479i	0.534407	+	0.534407i	−0.387474	+	0.921881i	$0.626652\pi$
$692$	28.3529	+	6.92922i	1.07782	+	0.263410i
$693$	1.84113	−	1.84113i	0.0699389	−	0.0699389i
$694$	−40.5609	−	22.8239i	−1.53967	−	0.866382i
$695$		−	9.97846i		−	0.378504i
$696$	−0.287607	+	0.307342i	−0.0109017	+	0.0116498i
$697$		−	22.7542i		−	0.861877i
$698$	−3.42649	+	6.08931i	−0.129694	+	0.230484i
$699$	−14.5835	+	14.5835i	−0.551597	+	0.551597i
$700$	1.70952	−	1.03804i	0.0646139	−	0.0392343i
$701$	−28.2923	−	28.2923i	−1.06859	−	1.06859i	−0.997468	−	0.0711175i	$-0.977343\pi$
$701$	−28.2923	−	28.2923i	−1.06859	−	1.06859i	−0.0711175	−	0.997468i	$-0.522657\pi$
$702$	6.80287	+	24.3106i	0.256758	+	0.917544i
$703$	−7.10117			−0.267826
$704$	−6.91268	−	6.05166i	−0.260531	−	0.228080i
$705$	−3.37509			−0.127113
$706$	3.14153	+	11.2265i	0.118233	+	0.422515i
$707$	13.1056	+	13.1056i	0.492885	+	0.492885i
$708$	−13.5455	+	8.22497i	−0.509071	+	0.309113i
$709$	24.0847	−	24.0847i	0.904521	−	0.904521i	−0.0913019	−	0.995823i	$-0.529103\pi$
$709$	24.0847	−	24.0847i	0.904521	−	0.904521i	0.995823	+	0.0913019i	$0.0291028\pi$
$710$	−4.16434	+	7.40056i	−0.156285	+	0.277738i
$711$			23.3539i			0.875842i
$712$	6.34232	−	6.77752i	0.237689	−	0.253998i
$713$			20.1162i			0.753359i
$714$	−4.95703	−	2.78935i	−0.185512	−	0.104389i
$715$	−3.21496	+	3.21496i	−0.120233	+	0.120233i
$716$	−45.7414	−	11.1788i	−1.70944	−	0.417772i
$717$	−12.9707	−	12.9707i	−0.484399	−	0.484399i
$718$	28.4905	−	7.97254i	1.06326	−	0.297533i
$719$	41.4094			1.54431			0.772154	−	0.635435i	$-0.219179\pi$
$719$	41.4094			1.54431			0.772154	+	0.635435i	$0.219179\pi$
$720$	8.64768	−	2.73210i	0.322280	−	0.101819i
$721$	−7.66619			−0.285504
$722$	23.1316	−	6.47295i	0.860869	−	0.240898i
$723$	−4.42203	−	4.42203i	−0.164457	−	0.164457i
$724$	6.10607	−	24.9848i	0.226930	−	0.928551i
$725$	0.122932	−	0.122932i	0.00456558	−	0.00456558i
$726$	10.2138	+	5.74735i	0.379068	+	0.213304i
$727$		−	35.4737i		−	1.31565i	−0.753172	−	0.657824i	$-0.771477\pi$
$727$		−	35.4737i		−	1.31565i	0.753172	−	0.657824i	$-0.228523\pi$
$728$	11.1917	−	0.371238i	0.414792	−	0.0137590i
$729$		−	4.90810i		−	0.181782i
$730$	4.92391	−	8.75041i	0.182242	−	0.323867i
$731$	−10.4148	+	10.4148i	−0.385206	+	0.385206i
$732$	−2.28089	−	3.75634i	−0.0843040	−	0.138838i
$733$	−3.87401	−	3.87401i	−0.143090	−	0.143090i	0.631933	−	0.775023i	$-0.282262\pi$
$733$	−3.87401	−	3.87401i	−0.143090	−	0.143090i	−0.775023	+	0.631933i	$0.782262\pi$
$734$	−12.7233	−	45.4676i	−0.469624	−	1.67824i
$735$	−0.856008			−0.0315743
$736$	9.46243	−	45.1619i	0.348790	−	1.66469i
$737$	0.264158			0.00973039
$738$	−4.18446	−	14.9535i	−0.154032	−	0.550446i
$739$	−6.10697	−	6.10697i	−0.224649	−	0.224649i	0.585804	−	0.810453i	$-0.300779\pi$
$739$	−6.10697	−	6.10697i	−0.224649	−	0.224649i	−0.810453	+	0.585804i	$0.800779\pi$
$740$	−5.19266	−	8.55166i	−0.190886	−	0.314365i
$741$	3.40179	−	3.40179i	0.124968	−	0.124968i
$742$	7.05644	−	12.5402i	0.259050	−	0.460365i
$743$			30.6238i			1.12348i	0.827314	+	0.561739i	$0.189868\pi$
$743$			30.6238i			1.12348i	−0.827314	+	0.561739i	$0.810132\pi$
$744$	−0.197953	−	5.96766i	−0.00725730	−	0.218785i
$745$			21.1586i			0.775191i
$746$	−22.6693	−	12.7561i	−0.829981	−	0.467035i
$747$	−17.7562	+	17.7562i	−0.649667	+	0.649667i
$748$	2.56202	−	10.4832i	0.0936768	−	0.383306i
$749$	0.120113	+	0.120113i	0.00438882	+	0.00438882i
$750$	1.16579	−	0.326226i	0.0425688	−	0.0119121i
$751$	8.12562			0.296508			0.148254	−	0.988949i	$-0.452635\pi$
$751$	8.12562			0.296508			0.148254	+	0.988949i	$0.452635\pi$
$752$	−7.27427	+	13.9935i	−0.265265	+	0.510291i
$753$	−17.2696			−0.629338
$754$	0.937375	−	0.262307i	0.0341372	−	0.00955266i
$755$	−0.836660	−	0.836660i	−0.0304492	−	0.0304492i
$756$	−8.75981	−	2.14083i	−0.318591	−	0.0778612i
$757$	−25.0324	+	25.0324i	−0.909816	+	0.909816i	−0.996257	−	0.0864406i	$-0.972451\pi$
$757$	−25.0324	+	25.0324i	−0.909816	+	0.909816i	0.0864406	+	0.996257i	$0.472451\pi$
$758$	20.2458	+	11.3925i	0.735362	+	0.413792i
$759$		−	8.01873i		−	0.291061i
$760$	−2.93169	−	2.74344i	−0.106343	−	0.0995150i
$761$			25.7347i			0.932884i	0.884552	+	0.466442i	$0.154464\pi$
$761$			25.7347i			0.932884i	−0.884552	+	0.466442i	$0.845536\pi$
$762$	−2.77898	+	4.93861i	−0.100672	+	0.178907i
$763$	3.37380	−	3.37380i	0.122140	−	0.122140i
$764$	7.74836	−	4.70488i	0.280326	−	0.170217i
$765$	7.53262	+	7.53262i	0.272343	+	0.272343i
$766$	−11.1102	−	39.7033i	−0.401429	−	1.43454i
$767$	36.6464			1.32322
$768$	−2.36270	+	13.4908i	−0.0852567	+	0.486807i
$769$	−36.8962			−1.33051			−0.665256	−	0.746616i	$-0.731677\pi$
$769$	−36.8962			−1.33051			−0.665256	+	0.746616i	$0.731677\pi$
$770$	−0.437665	−	1.56403i	−0.0157723	−	0.0563637i
$771$	−9.76133	−	9.76133i	−0.351546	−	0.351546i
$772$	−37.5341	+	22.7911i	−1.35088	+	0.820271i
$773$	8.52408	−	8.52408i	0.306590	−	0.306590i	−0.536995	−	0.843585i	$-0.680441\pi$
$773$	8.52408	−	8.52408i	0.306590	−	0.306590i	0.843585	+	0.536995i	$0.180441\pi$
$774$	−4.92909	+	8.75962i	−0.177173	+	0.314858i
$775$			2.46615i			0.0885869i
$776$	−0.937359	−	0.877170i	−0.0336492	−	0.0314886i
$777$			4.28207i			0.153618i
$778$	27.7585	+	15.6199i	0.995190	+	0.559999i
$779$	−4.86115	+	4.86115i	−0.174169	+	0.174169i
$780$	6.58416	+	1.60912i	0.235751	+	0.0576156i
$781$	4.87606	+	4.87606i	0.174479	+	0.174479i
$782$	52.1954	−	14.6059i	1.86650	−	0.522306i
$783$	−0.783866			−0.0280131
$784$	−1.84494	+	3.54911i	−0.0658908	+	0.126754i
$785$	−7.05985			−0.251977
$786$	6.14888	−	1.72065i	0.219323	−	0.0613735i
$787$	−27.9778	−	27.9778i	−0.997302	−	0.997302i	0.00269473	−	0.999996i	$-0.499142\pi$
$787$	−27.9778	−	27.9778i	−0.997302	−	0.997302i	−0.999996	+	0.00269473i	$0.999142\pi$
$788$	1.34789	−	5.51527i	0.0480165	−	0.196473i
$789$	10.1334	−	10.1334i	0.360759	−	0.360759i
$790$	12.6953	+	7.14372i	0.451678	+	0.254162i
$791$		−	19.2238i		−	0.683521i
$792$	−0.244154	−	7.36049i	−0.00867563	−	0.261544i
$793$			10.1625i			0.360881i
$794$	−2.98680	+	5.30793i	−0.105998	+	0.188371i
$795$	6.15865	−	6.15865i	0.218425	−	0.218425i
$796$	−7.33510	−	12.0800i	−0.259986	−	0.428164i
$797$	38.7907	+	38.7907i	1.37404	+	1.37404i	0.854364	+	0.519675i	$0.173947\pi$
$797$	38.7907	+	38.7907i	1.37404	+	1.37404i	0.519675	+	0.854364i	$0.326053\pi$
$798$	0.463098	+	1.65492i	0.0163935	+	0.0585834i
$799$	−18.5255			−0.655383
$800$	1.16005	−	5.53663i	0.0410139	−	0.195749i
$801$	7.44058			0.262900
$802$	−9.06490	−	32.3941i	−0.320093	−	1.14388i
$803$	−5.76544	−	5.76544i	−0.203458	−	0.203458i
$804$	−0.204388	−	0.336602i	−0.00720821	−	0.0118710i
$805$	5.76782	−	5.76782i	0.203289	−	0.203289i
$806$	−6.77132	+	12.0335i	−0.238509	+	0.423862i
$807$			8.70679i			0.306493i
$808$	52.3934	−	1.73794i	1.84319	−	0.0611404i
$809$		−	17.4239i		−	0.612592i	−0.951936	−	0.306296i	$-0.900910\pi$
$809$		−	17.4239i		−	0.612592i	0.951936	−	0.306296i	$-0.0990898\pi$
$810$	3.62618	+	2.04047i	0.127411	+	0.0716950i
$811$	28.3952	−	28.3952i	0.997089	−	0.997089i	−0.00290663	−	0.999996i	$-0.500925\pi$
$811$	28.3952	−	28.3952i	0.997089	−	0.997089i	0.999996	+	0.00290663i	$0.000925210\pi$
$812$	−0.0825467	+	0.337764i	−0.00289682	+	0.0118532i
$813$	−11.1625	−	11.1625i	−0.391487	−	0.391487i
$814$	−7.82385	+	2.18936i	−0.274226	+	0.0767370i
$815$	−7.07479			−0.247819
$816$	−15.3405	+	4.84661i	−0.537026	+	0.169665i
$817$	4.44999			0.155685
$818$	−20.0464	+	5.60961i	−0.700906	+	0.196135i
$819$	6.34708	+	6.34708i	0.221785	+	0.221785i
$820$	−9.40877	−	2.29943i	−0.328568	−	0.0802995i
$821$	15.5070	−	15.5070i	0.541198	−	0.541198i	−0.382682	−	0.923880i	$-0.624999\pi$
$821$	15.5070	−	15.5070i	0.541198	−	0.541198i	0.923880	+	0.382682i	$0.124999\pi$
$822$	−14.9709	−	8.42422i	−0.522171	−	0.293828i
$823$		−	4.43237i		−	0.154503i	−0.997012	−	0.0772513i	$-0.975386\pi$
$823$		−	4.43237i		−	0.154503i	0.997012	−	0.0772513i	$-0.0246144\pi$
$824$	−14.8157	+	15.8323i	−0.516128	+	0.551543i
$825$		−	0.983058i		−	0.0342257i
$826$	−6.41956	+	11.4084i	−0.223365	+	0.396948i
$827$	12.0984	−	12.0984i	0.420704	−	0.420704i	−0.464742	−	0.885446i	$-0.653853\pi$
$827$	12.0984	−	12.0984i	0.420704	−	0.420704i	0.885446	+	0.464742i	$0.153853\pi$
$828$	31.6156	−	19.1973i	1.09872	−	0.667152i
$829$	−7.49482	−	7.49482i	−0.260306	−	0.260306i	0.564873	−	0.825178i	$-0.308925\pi$
$829$	−7.49482	−	7.49482i	−0.260306	−	0.260306i	−0.825178	+	0.564873i	$0.808925\pi$
$830$	4.22092	+	15.0838i	0.146510	+	0.523567i
$831$	20.4053			0.707850
$832$	20.8623	−	23.8306i	0.723271	−	0.826178i
$833$	−4.69853			−0.162794
$834$	3.25523	+	11.6328i	0.112719	+	0.402812i
$835$	17.6005	+	17.6005i	0.609092	+	0.609092i
$836$	−2.78696	+	1.69227i	−0.0963890	+	0.0585284i
$837$	7.86262	−	7.86262i	0.271772	−	0.271772i
$838$	−3.69862	+	6.57292i	−0.127767	+	0.227058i
$839$		−	6.63304i		−	0.228998i	−0.993423	−	0.114499i	$-0.963474\pi$
$839$		−	6.63304i		−	0.228998i	0.993423	−	0.114499i	$-0.0365263\pi$
$840$	−1.65432	+	1.76783i	−0.0570794	+	0.0609961i
$841$		−	28.9698i		−	0.998958i
$842$	−25.5817	−	14.3950i	−0.881602	−	0.496083i
$843$	10.8531	−	10.8531i	0.373799	−	0.373799i
$844$	16.2869	+	3.98039i	0.560619	+	0.137011i
$845$	−1.89079	−	1.89079i	−0.0650451	−	0.0650451i
$846$	−12.1745	+	3.40680i	−0.418567	+	0.117128i
$847$	9.68113			0.332648
$848$	−12.2608	−	38.8081i	−0.421039	−	1.33268i
$849$	−23.8342			−0.817989
$850$	6.39891	−	1.79062i	0.219481	−	0.0614176i
$851$	−28.8527	−	28.8527i	−0.989059	−	0.989059i
$852$	2.44051	−	9.98605i	0.0836105	−	0.342116i
$853$	−14.2806	+	14.2806i	−0.488958	+	0.488958i	−0.907977	−	0.419019i	$-0.862374\pi$
$853$	−14.2806	+	14.2806i	−0.488958	+	0.488958i	0.419019	+	0.907977i	$0.362374\pi$
$854$	−3.16368	−	1.78022i	−0.108259	−	0.0609180i
$855$		−	3.21850i		−	0.110070i
$856$	0.480187	−	0.0159282i	0.0164124	−	0.000544415i
$857$		−	49.1654i		−	1.67946i	−0.543005	−	0.839729i	$-0.682714\pi$
$857$		−	49.1654i		−	1.67946i	0.543005	−	0.839729i	$-0.317286\pi$
$858$	2.69918	−	4.79679i	0.0921485	−	0.163760i
$859$	26.6661	−	26.6661i	0.909836	−	0.909836i	−0.0864230	−	0.996259i	$-0.527544\pi$
$859$	26.6661	−	26.6661i	0.909836	−	0.909836i	0.996259	+	0.0864230i	$0.0275437\pi$
$860$	3.25401	+	5.35895i	0.110961	+	0.182739i
$861$	2.93132	+	2.93132i	0.0998990	+	0.0998990i
$862$	−0.706627	−	2.52519i	−0.0240678	−	0.0860083i
$863$	42.6788			1.45280			0.726402	−	0.687270i	$-0.241191\pi$
$863$	42.6788			1.45280			0.726402	+	0.687270i	$0.241191\pi$
$864$	−21.3504	+	13.9535i	−0.726356	+	0.474706i
$865$	14.5937			0.496200
$866$	−11.8526	−	42.3561i	−0.402766	−	1.43932i
$867$	−3.07256	−	3.07256i	−0.104350	−	0.104350i
$868$	−2.55997	−	4.21595i	−0.0868910	−	0.143099i
$869$	8.36464	−	8.36464i	0.283751	−	0.283751i
$870$	−0.103210	+	0.183417i	−0.00349914	+	0.00621842i
$871$			0.910653i			0.0308563i
$872$	−0.447402	−	13.4878i	−0.0151509	−	0.456754i
$873$		−	1.02906i		−	0.0348285i
$874$	−14.2713	−	8.03053i	−0.482733	−	0.271637i
$875$	0.707107	−	0.707107i	0.0239046	−	0.0239046i
$876$	−2.88566	+	11.8075i	−0.0974973	+	0.398938i
$877$	17.9270	+	17.9270i	0.605350	+	0.605350i	0.941727	−	0.336377i	$-0.109202\pi$
$877$	17.9270	+	17.9270i	0.605350	+	0.605350i	−0.336377	+	0.941727i	$0.609202\pi$
$878$	11.3265	−	3.16950i	0.382250	−	0.106966i
$879$	−22.0656			−0.744254
$880$	−4.07587	−	2.11877i	−0.137398	−	0.0714237i
$881$	−6.43903			−0.216937			−0.108468	−	0.994100i	$-0.534595\pi$
$881$	−6.43903			−0.216937			−0.108468	+	0.994100i	$0.534595\pi$
$882$	−3.08776	+	0.864052i	−0.103970	+	0.0290941i
$883$	−39.6889	−	39.6889i	−1.33564	−	1.33564i	−0.900236	−	0.435401i	$-0.856606\pi$
$883$	−39.6889	−	39.6889i	−1.33564	−	1.33564i	−0.435401	−	0.900236i	$-0.643394\pi$
$884$	36.1397	+	8.83225i	1.21551	+	0.297061i
$885$	−5.60279	+	5.60279i	−0.188336	+	0.188336i
$886$	22.8741	+	12.8714i	0.768470	+	0.432422i
$887$			26.0147i			0.873490i	0.899585	+	0.436745i	$0.143869\pi$
$887$			26.0147i			0.873490i	−0.899585	+	0.436745i	$0.856131\pi$
$888$	8.84335	+	8.27550i	0.296763	+	0.277708i
$889$			4.68107i			0.156998i
$890$	2.27599	−	4.04473i	0.0762914	−	0.135580i
$891$	2.38921	−	2.38921i	0.0800415	−	0.0800415i
$892$	−44.7576	+	27.1773i	−1.49859	+	0.909962i
$893$	3.95773	+	3.95773i	0.132440	+	0.132440i
$894$	−6.90249	−	24.6666i	−0.230854	−	0.824974i
$895$	−23.5438			−0.786982
$896$	3.76412	+	10.6692i	0.125750	+	0.356432i
$897$	27.6436			0.922992
$898$	8.83081	+	31.5576i	0.294688	+	1.05309i
$899$	−0.303169	−	0.303169i	−0.0101113	−	0.0101113i
$900$	3.87592	−	2.35350i	0.129197	−	0.0784499i
$901$	33.8041	−	33.8041i	1.12618	−	1.12618i
$902$	−3.85713	+	6.85461i	−0.128428	+	0.228233i
$903$		−	2.68338i		−	0.0892973i
$904$	−39.7012	−	37.1519i	−1.32044	−	1.23565i
$905$		−	12.8600i		−	0.427482i
$906$	1.24831	+	0.702434i	0.0414725	+	0.0233368i
$907$	8.98598	−	8.98598i	0.298375	−	0.298375i	−0.542002	−	0.840377i	$-0.682334\pi$
$907$	8.98598	−	8.98598i	0.298375	−	0.298375i	0.840377	+	0.542002i	$0.182334\pi$
$908$	−6.19109	−	1.51305i	−0.205459	−	0.0502124i
$909$	29.7136	+	29.7136i	0.985537	+	0.985537i
$910$	5.39180	−	1.50879i	0.178736	−	0.0500160i
$911$	10.7782			0.357096			0.178548	−	0.983931i	$-0.442860\pi$
$911$	10.7782			0.357096			0.178548	+	0.983931i	$0.442860\pi$
$912$	4.31273	+	2.24189i	0.142809	+	0.0742365i
$913$	12.7194			0.420952
$914$	30.2861	−	8.47499i	1.00177	−	0.280328i
$915$	−1.55373	−	1.55373i	−0.0513646	−	0.0513646i
$916$	−5.87900	+	24.0556i	−0.194248	+	0.794820i
$917$	3.72957	−	3.72957i	0.123161	−	0.123161i
$918$	−26.1099	−	14.6922i	−0.861756	−	0.484915i
$919$		−	9.09715i		−	0.300087i	−0.988679	−	0.150044i	$-0.952059\pi$
$919$		−	9.09715i		−	0.300087i	0.988679	−	0.150044i	$-0.0479414\pi$
$920$	−0.764873	−	23.0586i	−0.0252171	−	0.760219i
$921$		−	21.3553i		−	0.703680i
$922$	23.7734	−	42.2484i	0.782937	−	1.39138i
$923$	−16.8096	+	16.8096i	−0.553295	+	0.553295i
$924$	1.02045	+	1.68056i	0.0335705	+	0.0552864i
$925$	−3.53721	−	3.53721i	−0.116303	−	0.116303i
$926$	−0.882514	−	3.15373i	−0.0290012	−	0.103638i
$927$	−17.3812			−0.570873
$928$	0.538022	+	0.823236i	0.0176614	+	0.0270241i
$929$	22.8390			0.749323			0.374662	−	0.927162i	$-0.377759\pi$
$929$	22.8390			0.749323			0.374662	+	0.927162i	$0.377759\pi$
$930$	−0.804523	−	2.87503i	−0.0263814	−	0.0942759i
$931$	1.00378	+	1.00378i	0.0328976	+	0.0328976i
$932$	25.0099	+	41.1882i	0.819227	+	1.34916i
$933$	11.1487	−	11.1487i	0.364993	−	0.364993i
$934$	−14.9901	+	26.6393i	−0.490491	+	0.871665i
$935$		−	5.39589i		−	0.176464i
$936$	25.3744	−	0.841690i	0.829387	−	0.0275115i
$937$			33.3961i			1.09100i	0.838110	+	0.545501i	$0.183661\pi$
$937$			33.3961i			1.09100i	−0.838110	+	0.545501i	$0.816339\pi$
$938$	−0.283495	−	0.159524i	−0.00925643	−	0.00520865i
$939$	12.0816	−	12.0816i	0.394268	−	0.394268i
$940$	−1.87209	+	7.66019i	−0.0610608	+	0.249848i
$941$	29.0501	+	29.0501i	0.947005	+	0.947005i	0.998665	−	0.0516599i	$-0.0164512\pi$
$941$	29.0501	+	29.0501i	0.947005	+	0.947005i	−0.0516599	+	0.998665i	$0.516451\pi$
$942$	8.23034	−	2.30311i	0.268159	−	0.0750393i
$943$	−39.5026			−1.28638
$944$	11.1542	+	35.3055i	0.363039	+	1.14910i
$945$	−4.50881			−0.146672
$946$	4.90286	−	1.37197i	0.159406	−	0.0446067i
$947$	25.7211	+	25.7211i	0.835822	+	0.835822i	0.988306	−	0.152484i	$-0.0487272\pi$
$947$	25.7211	+	25.7211i	0.835822	+	0.835822i	−0.152484	+	0.988306i	$0.548727\pi$
$948$	−17.1306	−	4.18657i	−0.556375	−	0.135974i
$949$	19.8757	−	19.8757i	0.645191	−	0.645191i
$950$	−1.74959	−	0.984504i	−0.0567642	−	0.0319415i
$951$			27.1450i			0.880237i
$952$	−9.08036	+	9.70343i	−0.294296	+	0.314490i
$953$			54.2832i			1.75841i	0.476447	+	0.879203i	$0.341924\pi$
$953$			54.2832i			1.75841i	−0.476447	+	0.879203i	$0.658076\pi$
$954$	15.9987	−	28.4317i	0.517977	−	0.920511i
$955$	3.20494	−	3.20494i	0.103709	−	0.103709i
$956$	−36.6332	+	22.2441i	−1.18480	+	0.719425i
$957$	0.120849	+	0.120849i	0.00390650	+	0.00390650i
$958$	10.5694	+	37.7705i	0.341481	+	1.22031i
$959$	−14.1902			−0.458225
$960$	0.453813	+	6.83301i	0.0146468	+	0.220535i
$961$	−24.9181			−0.803809
$962$	−7.54754	−	26.9718i	−0.243342	−	0.869604i
$963$	0.272326	+	0.272326i	0.00877557	+	0.00877557i
$964$	−12.4892	+	7.58355i	−0.402249	+	0.244250i
$965$	−15.5252	+	15.5252i	−0.499773	+	0.499773i
$966$	−4.84248	+	8.60570i	−0.155804	+	0.276884i
$967$			45.1018i			1.45038i	0.688550	+	0.725188i	$0.258247\pi$
$967$			45.1018i			1.45038i	−0.688550	+	0.725188i	$0.741753\pi$
$968$	18.7097	−	19.9935i	0.601353	−	0.642616i
$969$			5.70945i			0.183414i
$970$	−0.559403	−	0.314779i	−0.0179613	−	0.0101070i
$971$	−5.81628	+	5.81628i	−0.186653	+	0.186653i	−0.794248	−	0.607594i	$-0.792135\pi$
$971$	−5.81628	+	5.81628i	−0.186653	+	0.186653i	0.607594	+	0.794248i	$0.292135\pi$
$972$	−31.1725	−	7.61830i	−0.999858	−	0.244357i
$973$	7.05584	+	7.05584i	0.226200	+	0.226200i
$974$	−51.3374	+	14.3658i	−1.64496	+	0.460310i
$975$	3.38897			0.108534
$976$	−9.79065	+	3.09321i	−0.313391	+	0.0990112i
$977$	34.1397			1.09223			0.546113	−	0.837712i	$-0.316107\pi$
$977$	34.1397			1.09223			0.546113	+	0.837712i	$0.316107\pi$
$978$	8.24775	−	2.30798i	0.263734	−	0.0738010i
$979$	−2.66498	−	2.66498i	−0.0851730	−	0.0851730i
$980$	−0.474810	+	1.94282i	−0.0151672	+	0.0620612i
$981$	7.64925	−	7.64925i	0.244222	−	0.244222i
$982$	22.7116	+	12.7800i	0.724757	+	0.407825i
$983$			36.7941i			1.17355i	0.809750	+	0.586775i	$0.199603\pi$
$983$			36.7941i			1.17355i	−0.809750	+	0.586775i	$0.800397\pi$
$984$	11.7188	−	0.388724i	0.373582	−	0.0123921i
$985$		−	2.83879i		−	0.0904515i
$986$	−0.566507	+	1.00675i	−0.0180413	+	0.0320616i
$987$	2.38655	−	2.38655i	0.0759646	−	0.0759646i
$988$	−5.83389	−	9.60769i	−0.185601	−	0.305661i
$989$	18.0807	+	18.0807i	0.574933	+	0.574933i
$990$	−0.992295	−	3.54605i	−0.0315372	−	0.112701i
$991$	−10.4310			−0.331350			−0.165675	−	0.986180i	$-0.552980\pi$
$991$	−10.4310			−0.331350			−0.165675	+	0.986180i	$0.552980\pi$
$992$	−13.6542	−	2.86086i	−0.433521	−	0.0908324i
$993$	−4.70235			−0.149224
$994$	−2.28835	−	8.17762i	−0.0725822	−	0.259378i
$995$	−4.99663	−	4.99663i	−0.158404	−	0.158404i
$996$	−9.84146	−	16.2076i	−0.311838	−	0.513559i
$997$	−6.70639	+	6.70639i	−0.212393	+	0.212393i	−0.805283	−	0.592890i	$-0.797987\pi$
$997$	−6.70639	+	6.70639i	−0.212393	+	0.212393i	0.592890	+	0.805283i	$0.297987\pi$
$998$	20.5895	−	36.5902i	0.651750	−	1.15824i
$999$			22.5547i			0.713600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bd.a.141.12	✓	44
4.3	odd	2		2240.2.bd.a.1681.14		44
16.5	even	4	inner	560.2.bd.a.421.12	yes	44
16.11	odd	4		2240.2.bd.a.561.14		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.12	✓	44	1.1	even	1	trivial
560.2.bd.a.421.12	yes	44	16.5	even	4	inner
2240.2.bd.a.561.14		44	16.11	odd	4
2240.2.bd.a.1681.14		44	4.3	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.381101 + 1.36190i) q^{2} +(-0.605289 - 0.605289i) q^{3} +(-1.70952 + 1.03804i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.593665 - 1.05502i) q^{6} -1.00000i q^{7} +(-2.06521 - 1.93260i) q^{8} -2.26725i q^{9} +O(q^{10})\)	\(q+(0.381101 + 1.36190i) q^{2} +(-0.605289 - 0.605289i) q^{3} +(-1.70952 + 1.03804i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.593665 - 1.05502i) q^{6} -1.00000i q^{7} +(-2.06521 - 1.93260i) q^{8} -2.26725i q^{9} +(-1.23249 - 0.693527i) q^{10} +(-0.812056 + 0.812056i) q^{11} +(1.66307 + 0.406441i) q^{12} +(-2.79946 - 2.79946i) q^{13} +(1.36190 - 0.381101i) q^{14} +0.856008 q^{15} +(1.84494 - 3.54911i) q^{16} +4.69853 q^{17} +(3.08776 - 0.864052i) q^{18} +(-1.00378 - 1.00378i) q^{19} +(0.474810 - 1.94282i) q^{20} +(-0.605289 + 0.605289i) q^{21} +(-1.41541 - 0.796461i) q^{22} -8.15692i q^{23} +(0.0802678 + 2.41983i) q^{24} -1.00000i q^{25} +(2.74570 - 4.87946i) q^{26} +(-3.18821 + 3.18821i) q^{27} +(1.03804 + 1.70952i) q^{28} +(0.122932 + 0.122932i) q^{29} +(0.326226 + 1.16579i) q^{30} -2.46615 q^{31} +(5.53663 + 1.16005i) q^{32} +0.983058 q^{33} +(1.79062 + 6.39891i) q^{34} +(0.707107 + 0.707107i) q^{35} +(2.35350 + 3.87592i) q^{36} +(3.53721 - 3.53721i) q^{37} +(0.984504 - 1.74959i) q^{38} +3.38897i q^{39} +(2.82687 - 0.0937698i) q^{40} -4.84284i q^{41} +(-1.05502 - 0.593665i) q^{42} +(-2.21661 + 2.21661i) q^{43} +(0.545282 - 2.23118i) q^{44} +(1.60319 + 1.60319i) q^{45} +(11.1089 - 3.10861i) q^{46} -3.94282 q^{47} +(-3.26496 + 1.03152i) q^{48} -1.00000 q^{49} +(1.36190 - 0.381101i) q^{50} +(-2.84397 - 2.84397i) q^{51} +(7.69170 + 1.87979i) q^{52} +(7.19461 - 7.19461i) q^{53} +(-5.55704 - 3.12698i) q^{54} -1.14842i q^{55} +(-1.93260 + 2.06521i) q^{56} +1.21516i q^{57} +(-0.120571 + 0.214270i) q^{58} +(-6.54526 + 6.54526i) q^{59} +(-1.46337 + 0.888572i) q^{60} +(-1.81508 - 1.81508i) q^{61} +(-0.939855 - 3.35865i) q^{62} -2.26725 q^{63} +(0.530151 + 7.98241i) q^{64} +3.95904 q^{65} +(0.374645 + 1.33882i) q^{66} +(-0.162648 - 0.162648i) q^{67} +(-8.03225 + 4.87727i) q^{68} +(-4.93730 + 4.93730i) q^{69} +(-0.693527 + 1.23249i) q^{70} -6.00458i q^{71} +(-4.38168 + 4.68234i) q^{72} +7.09981i q^{73} +(6.16534 + 3.46928i) q^{74} +(-0.605289 + 0.605289i) q^{75} +(2.75795 + 0.674022i) q^{76} +(0.812056 + 0.812056i) q^{77} +(-4.61543 + 1.29154i) q^{78} -10.3006 q^{79} +(1.20503 + 3.81417i) q^{80} -2.94217 q^{81} +(6.59544 - 1.84561i) q^{82} +(-7.83163 - 7.83163i) q^{83} +(0.406441 - 1.66307i) q^{84} +(-3.32236 + 3.32236i) q^{85} +(-3.86355 - 2.17404i) q^{86} -0.148819i q^{87} +(3.24644 - 0.107687i) q^{88} +3.28176i q^{89} +(-1.57240 + 2.79435i) q^{90} +(-2.79946 + 2.79946i) q^{91} +(8.46722 + 13.9445i) q^{92} +(1.49274 + 1.49274i) q^{93} +(-1.50261 - 5.36971i) q^{94} +1.41956 q^{95} +(-2.64910 - 4.05343i) q^{96} +0.453882 q^{97} +(-0.381101 - 1.36190i) q^{98} +(1.84113 + 1.84113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) \) 44 * q + 12 * q^4 + 12 * q^6	\( 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) \) 44 * q + 12 * q^4 + 12 * q^6 - 4 * q^10 + 12 * q^11 - 16 * q^12 + 4 * q^14 + 8 * q^15 - 8 * q^16 - 20 * q^18 + 8 * q^19 - 36 * q^22 + 12 * q^24 + 44 * q^26 - 24 * q^27 - 4 * q^28 + 12 * q^29 - 40 * q^32 - 16 * q^34 + 4 * q^36 + 28 * q^37 - 16 * q^38 + 4 * q^42 - 44 * q^43 - 32 * q^44 - 16 * q^46 - 32 * q^48 - 44 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 12 * q^53 - 80 * q^54 + 8 * q^56 + 4 * q^58 + 24 * q^59 - 16 * q^61 + 28 * q^63 + 72 * q^64 - 40 * q^65 - 20 * q^66 - 28 * q^67 + 56 * q^68 + 40 * q^69 + 12 * q^72 + 24 * q^74 - 12 * q^77 + 84 * q^78 - 16 * q^79 + 20 * q^81 + 48 * q^82 + 16 * q^85 - 64 * q^86 + 28 * q^88 - 36 * q^90 - 16 * q^92 + 88 * q^93 + 96 * q^94 - 32 * q^95 + 48 * q^96 + 28 * q^99

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