LMFDB - Embedded newform 287.2.n.a.64.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(64,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("287.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.n (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.18
Character	$\chi$	$=$	287.64
Dual form			287.2.n.a.148.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.620352 + 1.90925i) q^{2} +1.77499i q^{3} +(-1.64235 + 1.19324i) q^{4} +(-2.14247 + 1.55660i) q^{5} +(-3.38889 + 1.10112i) q^{6} +(0.951057 + 0.309017i) q^{7} +(-0.0488123 - 0.0354642i) q^{8} -0.150586 q^{9} +O(q^{10})$	\(q+(0.620352 + 1.90925i) q^{2} +1.77499i q^{3} +(-1.64235 + 1.19324i) q^{4} +(-2.14247 + 1.55660i) q^{5} +(-3.38889 + 1.10112i) q^{6} +(0.951057 + 0.309017i) q^{7} +(-0.0488123 - 0.0354642i) q^{8} -0.150586 q^{9} +(-4.30101 - 3.12487i) q^{10} +(1.82737 - 2.51516i) q^{11} +(-2.11798 - 2.91515i) q^{12} +(-2.44685 + 0.795030i) q^{13} +2.00750i q^{14} +(-2.76294 - 3.80287i) q^{15} +(-1.21721 + 3.74620i) q^{16} +(4.16590 - 5.73387i) q^{17} +(-0.0934165 - 0.287506i) q^{18} +(-5.59889 - 1.81919i) q^{19} +(1.66130 - 5.11295i) q^{20} +(-0.548502 + 1.68811i) q^{21} +(5.93566 + 1.92861i) q^{22} +(0.192505 + 0.592470i) q^{23} +(0.0629486 - 0.0866413i) q^{24} +(0.622110 - 1.91466i) q^{25} +(-3.03582 - 4.17844i) q^{26} +5.05768i q^{27} +(-1.93070 + 0.627321i) q^{28} +(3.17721 + 4.37305i) q^{29} +(5.54661 - 7.63425i) q^{30} +(6.92942 + 5.03452i) q^{31} -8.02819 q^{32} +(4.46437 + 3.24356i) q^{33} +(13.5317 + 4.39671i) q^{34} +(-2.51863 + 0.818352i) q^{35} +(0.247315 - 0.179685i) q^{36} +(5.37814 - 3.90745i) q^{37} -11.8182i q^{38} +(-1.41117 - 4.34314i) q^{39} +0.159783 q^{40} +(-6.40013 - 0.195652i) q^{41} -3.56329 q^{42} +(1.35901 + 4.18262i) q^{43} +6.31124i q^{44} +(0.322627 - 0.234403i) q^{45} +(-1.01175 + 0.735080i) q^{46} +(4.01395 - 1.30421i) q^{47} +(-6.64946 - 2.16054i) q^{48} +(0.809017 + 0.587785i) q^{49} +4.04148 q^{50} +(10.1775 + 7.39442i) q^{51} +(3.06993 - 4.22539i) q^{52} +(-4.89382 - 6.73576i) q^{53} +(-9.65635 + 3.13754i) q^{54} +8.23313i q^{55} +(-0.0354642 - 0.0488123i) q^{56} +(3.22904 - 9.93797i) q^{57} +(-6.37824 + 8.77890i) q^{58} +(-1.70530 - 5.24839i) q^{59} +(9.07544 + 2.94879i) q^{60} +(-2.89181 + 8.90009i) q^{61} +(-5.31345 + 16.3531i) q^{62} +(-0.143216 - 0.0465338i) q^{63} +(-2.54587 - 7.83538i) q^{64} +(4.00477 - 5.51210i) q^{65} +(-3.42327 + 10.5357i) q^{66} +(-2.70283 - 3.72013i) q^{67} +14.3879i q^{68} +(-1.05163 + 0.341695i) q^{69} +(-3.12487 - 4.30101i) q^{70} +(4.49380 - 6.18519i) q^{71} +(0.00735047 + 0.00534043i) q^{72} +3.73091 q^{73} +(10.7966 + 7.84420i) q^{74} +(3.39850 + 1.10424i) q^{75} +(11.3661 - 3.69306i) q^{76} +(2.51516 - 1.82737i) q^{77} +(7.41669 - 5.38854i) q^{78} -5.47674i q^{79} +(-3.22348 - 9.92084i) q^{80} -9.42908 q^{81} +(-3.59679 - 12.3408i) q^{82} +10.7656 q^{83} +(-1.11349 - 3.42697i) q^{84} +18.7693i q^{85} +(-7.14257 + 5.18938i) q^{86} +(-7.76212 + 5.63951i) q^{87} +(-0.178396 + 0.0579643i) q^{88} +(14.2255 + 4.62216i) q^{89} +(0.647674 + 0.470563i) q^{90} -2.57277 q^{91} +(-1.02312 - 0.743338i) q^{92} +(-8.93621 + 12.2996i) q^{93} +(4.98012 + 6.85455i) q^{94} +(14.8272 - 4.81766i) q^{95} -14.2499i q^{96} +(-4.59850 - 6.32930i) q^{97} +(-0.620352 + 1.90925i) q^{98} +(-0.275177 + 0.378748i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9}+O(q^{10}) $ 88 * q - 24 * q^4 + 8 * q^5 + 10 * q^6 - 18 * q^8 - 116 * q^9	$ 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9} + 36 q^{10} - 10 q^{11} + 20 q^{15} - 12 q^{16} - 10 q^{17} + 20 q^{18} + 30 q^{19} - 30 q^{20} + 4 q^{21} - 20 q^{22} - 12 q^{23} + 60 q^{24} - 50 q^{25} - 30 q^{26} + 2 q^{31} + 24 q^{32} - 46 q^{33} + 50 q^{34} + 86 q^{36} - 48 q^{37} + 16 q^{39} - 60 q^{40} - 24 q^{41} - 4 q^{42} + 22 q^{43} - 16 q^{45} + 20 q^{46} + 20 q^{48} + 22 q^{49} - 16 q^{50} + 8 q^{51} + 70 q^{52} - 30 q^{54} + 8 q^{57} - 90 q^{58} - 4 q^{59} - 50 q^{60} - 64 q^{61} - 44 q^{62} + 14 q^{64} + 80 q^{65} - 26 q^{66} + 10 q^{67} + 40 q^{71} + 18 q^{72} + 124 q^{73} + 80 q^{74} + 70 q^{75} - 190 q^{76} + 8 q^{77} + 74 q^{78} + 26 q^{80} + 144 q^{81} - 58 q^{82} - 60 q^{83} + 26 q^{84} + 10 q^{86} + 8 q^{87} + 160 q^{88} - 164 q^{90} - 40 q^{91} - 156 q^{92} - 20 q^{93} + 10 q^{94} + 80 q^{95} - 90 q^{97} - 40 q^{99}+O(q^{100}) $ 88 * q - 24 * q^4 + 8 * q^5 + 10 * q^6 - 18 * q^8 - 116 * q^9 + 36 * q^10 - 10 * q^11 + 20 * q^15 - 12 * q^16 - 10 * q^17 + 20 * q^18 + 30 * q^19 - 30 * q^20 + 4 * q^21 - 20 * q^22 - 12 * q^23 + 60 * q^24 - 50 * q^25 - 30 * q^26 + 2 * q^31 + 24 * q^32 - 46 * q^33 + 50 * q^34 + 86 * q^36 - 48 * q^37 + 16 * q^39 - 60 * q^40 - 24 * q^41 - 4 * q^42 + 22 * q^43 - 16 * q^45 + 20 * q^46 + 20 * q^48 + 22 * q^49 - 16 * q^50 + 8 * q^51 + 70 * q^52 - 30 * q^54 + 8 * q^57 - 90 * q^58 - 4 * q^59 - 50 * q^60 - 64 * q^61 - 44 * q^62 + 14 * q^64 + 80 * q^65 - 26 * q^66 + 10 * q^67 + 40 * q^71 + 18 * q^72 + 124 * q^73 + 80 * q^74 + 70 * q^75 - 190 * q^76 + 8 * q^77 + 74 * q^78 + 26 * q^80 + 144 * q^81 - 58 * q^82 - 60 * q^83 + 26 * q^84 + 10 * q^86 + 8 * q^87 + 160 * q^88 - 164 * q^90 - 40 * q^91 - 156 * q^92 - 20 * q^93 + 10 * q^94 + 80 * q^95 - 90 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.620352	+	1.90925i	0.438655	+	1.35004i	0.889295	+	0.457335i	$0.151196\pi$
$2$	0.620352	+	1.90925i	0.438655	+	1.35004i	−0.450640	+	0.892706i	$0.648804\pi$
$3$			1.77499i			1.02479i	0.858750	+	0.512395i	$0.171242\pi$
$3$			1.77499i			1.02479i	−0.858750	+	0.512395i	$0.828758\pi$
$4$	−1.64235	+	1.19324i	−0.821174	+	0.596618i
$5$	−2.14247	+	1.55660i	−0.958143	+	0.696132i	−0.952719	−	0.303854i	$-0.901727\pi$
$5$	−2.14247	+	1.55660i	−0.958143	+	0.696132i	−0.00542444	+	0.999985i	$0.501727\pi$
$6$	−3.38889	+	1.10112i	−1.38351	+	0.449529i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$8$	−0.0488123	−	0.0354642i	−0.0172577	−	0.0125385i
$9$	−0.150586			−0.0501955
$10$	−4.30101	−	3.12487i	−1.36010	−	0.988171i
$11$	1.82737	−	2.51516i	0.550972	−	0.758348i	−0.439172	−	0.898403i	$-0.644728\pi$
$11$	1.82737	−	2.51516i	0.550972	−	0.758348i	0.990144	+	0.140055i	$0.0447280\pi$
$12$	−2.11798	−	2.91515i	−0.611409	−	0.841532i
$13$	−2.44685	+	0.795030i	−0.678635	+	0.220502i	−0.627998	−	0.778215i	$-0.716125\pi$
$13$	−2.44685	+	0.795030i	−0.678635	+	0.220502i	−0.0506371	+	0.998717i	$0.516125\pi$
$14$			2.00750i			0.536527i
$15$	−2.76294	−	3.80287i	−0.713389	−	0.981896i
$16$	−1.21721	+	3.74620i	−0.304303	+	0.936550i
$17$	4.16590	−	5.73387i	1.01038	−	1.39067i	0.0916435	−	0.995792i	$-0.470788\pi$
$17$	4.16590	−	5.73387i	1.01038	−	1.39067i	0.918735	−	0.394875i	$-0.129212\pi$
$18$	−0.0934165	−	0.287506i	−0.0220185	−	0.0677659i
$19$	−5.59889	−	1.81919i	−1.28447	−	0.417351i	−0.414320	−	0.910131i	$-0.635981\pi$
$19$	−5.59889	−	1.81919i	−1.28447	−	0.417351i	−0.870154	+	0.492780i	$0.835981\pi$
$20$	1.66130	−	5.11295i	0.371478	−	1.14329i
$21$	−0.548502	+	1.68811i	−0.119693	+	0.368377i
$22$	5.93566	+	1.92861i	1.26549	+	0.411182i
$23$	0.192505	+	0.592470i	0.0401401	+	0.123539i	0.969119	−	0.246595i	$-0.0793118\pi$
$23$	0.192505	+	0.592470i	0.0401401	+	0.123539i	−0.928978	+	0.370134i	$0.879312\pi$
$24$	0.0629486	−	0.0866413i	0.0128493	−	0.0176856i
$25$	0.622110	−	1.91466i	0.124422	−	0.382931i
$26$	−3.03582	−	4.17844i	−0.595373	−	0.819460i
$27$			5.05768i			0.973351i
$28$	−1.93070	+	0.627321i	−0.364867	+	0.118553i
$29$	3.17721	+	4.37305i	0.589993	+	0.812055i	0.994746	−	0.102370i	$-0.0326427\pi$
$29$	3.17721	+	4.37305i	0.589993	+	0.812055i	−0.404754	+	0.914426i	$0.632643\pi$
$30$	5.54661	−	7.63425i	1.01267	−	1.39382i
$31$	6.92942	+	5.03452i	1.24456	+	0.904226i	0.997893	−	0.0648745i	$-0.0206647\pi$
$31$	6.92942	+	5.03452i	1.24456	+	0.904226i	0.246667	+	0.969100i	$0.420665\pi$
$32$	−8.02819			−1.41920
$33$	4.46437	+	3.24356i	0.777148	+	0.564631i
$34$	13.5317	+	4.39671i	2.32066	+	0.754029i
$35$	−2.51863	+	0.818352i	−0.425726	+	0.138327i
$36$	0.247315	−	0.179685i	0.0412192	−	0.0299475i
$37$	5.37814	−	3.90745i	0.884160	−	0.642380i	−0.0501884	−	0.998740i	$-0.515982\pi$
$37$	5.37814	−	3.90745i	0.884160	−	0.642380i	0.934349	+	0.356360i	$0.115982\pi$
$38$		−	11.8182i		−	1.91716i
$39$	−1.41117	−	4.34314i	−0.225968	−	0.695458i
$40$	0.159783			0.0252638
$41$	−6.40013	−	0.195652i	−0.999533	−	0.0305557i
$41$	−6.40013	−	0.195652i	−0.999533	−	0.0305557i
$42$	−3.56329			−0.549828
$43$	1.35901	+	4.18262i	0.207248	+	0.637843i	0.999614	+	0.0277968i	$0.00884913\pi$
$43$	1.35901	+	4.18262i	0.207248	+	0.637843i	−0.792366	+	0.610046i	$0.791151\pi$
$44$			6.31124i			0.951456i
$45$	0.322627	−	0.234403i	0.0480945	−	0.0349427i
$46$	−1.01175	+	0.735080i	−0.149174	+	0.108382i
$47$	4.01395	−	1.30421i	0.585495	−	0.190239i	−0.00126580	−	0.999999i	$-0.500403\pi$
$47$	4.01395	−	1.30421i	0.585495	−	0.190239i	0.586761	+	0.809760i	$0.300403\pi$
$48$	−6.64946	−	2.16054i	−0.959767	−	0.311847i
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	4.04148			0.571551
$51$	10.1775	+	7.39442i	1.42514	+	1.03543i
$52$	3.06993	−	4.22539i	0.425722	−	0.585956i
$53$	−4.89382	−	6.73576i	−0.672218	−	0.925228i	0.327591	−	0.944820i	$-0.393763\pi$
$53$	−4.89382	−	6.73576i	−0.672218	−	0.925228i	−0.999808	+	0.0195917i	$0.993763\pi$
$54$	−9.65635	+	3.13754i	−1.31406	+	0.426965i
$55$			8.23313i			1.11015i
$56$	−0.0354642	−	0.0488123i	−0.00473910	−	0.00652282i
$57$	3.22904	−	9.93797i	0.427697	−	1.31632i
$58$	−6.37824	+	8.77890i	−0.837504	+	1.15273i
$59$	−1.70530	−	5.24839i	−0.222012	−	0.683282i	−0.998581	−	0.0532503i	$-0.983042\pi$
$59$	−1.70530	−	5.24839i	−0.222012	−	0.683282i	0.776569	−	0.630032i	$-0.216958\pi$
$60$	9.07544	+	2.94879i	1.17163	+	0.380687i
$61$	−2.89181	+	8.90009i	−0.370259	+	1.13954i	0.576363	+	0.817194i	$0.304471\pi$
$61$	−2.89181	+	8.90009i	−0.370259	+	1.13954i	−0.946622	+	0.322346i	$0.895529\pi$
$62$	−5.31345	+	16.3531i	−0.674809	+	2.07685i
$63$	−0.143216	−	0.0465338i	−0.0180435	−	0.00586270i
$64$	−2.54587	−	7.83538i	−0.318234	−	0.979422i
$65$	4.00477	−	5.51210i	0.496731	−	0.683691i
$66$	−3.42327	+	10.5357i	−0.421375	+	1.29686i
$67$	−2.70283	−	3.72013i	−0.330204	−	0.454486i	0.611345	−	0.791365i	$-0.290629\pi$
$67$	−2.70283	−	3.72013i	−0.330204	−	0.454486i	−0.941548	+	0.336878i	$0.890629\pi$
$68$			14.3879i			1.74479i
$69$	−1.05163	+	0.341695i	−0.126601	+	0.0411352i
$70$	−3.12487	−	4.30101i	−0.373493	−	0.514070i
$71$	4.49380	−	6.18519i	0.533316	−	0.734047i	−0.454315	−	0.890841i	$-0.650116\pi$
$71$	4.49380	−	6.18519i	0.533316	−	0.734047i	0.987631	+	0.156794i	$0.0501159\pi$
$72$	0.00735047	+	0.00534043i	0.000866261	+	0.000629375i
$73$	3.73091			0.436670			0.218335	−	0.975874i	$-0.429937\pi$
$73$	3.73091			0.436670			0.218335	+	0.975874i	$0.429937\pi$
$74$	10.7966	+	7.84420i	1.25508	+	0.911869i
$75$	3.39850	+	1.10424i	0.392424	+	0.127506i
$76$	11.3661	−	3.69306i	1.30378	−	0.423623i
$77$	2.51516	−	1.82737i	0.286629	−	0.208248i
$78$	7.41669	−	5.38854i	0.839775	−	0.610132i
$79$		−	5.47674i		−	0.616182i	−0.951357	−	0.308091i	$-0.900310\pi$
$79$		−	5.47674i		−	0.616182i	0.951357	−	0.308091i	$-0.0996901\pi$
$80$	−3.22348	−	9.92084i	−0.360396	−	1.10918i
$81$	−9.42908			−1.04768
$82$	−3.59679	−	12.3408i	−0.397199	−	1.36281i
$83$	10.7656			1.18167			0.590837	−	0.806791i	$-0.298798\pi$
$83$	10.7656			1.18167			0.590837	+	0.806791i	$0.298798\pi$
$84$	−1.11349	−	3.42697i	−0.121492	−	0.373913i
$85$			18.7693i			2.03581i
$86$	−7.14257	+	5.18938i	−0.770204	+	0.559586i
$87$	−7.76212	+	5.63951i	−0.832187	+	0.604619i
$88$	−0.178396	+	0.0579643i	−0.0190171	+	0.00617902i
$89$	14.2255	+	4.62216i	1.50790	+	0.489948i	0.942312	−	0.334737i	$-0.108648\pi$
$89$	14.2255	+	4.62216i	1.50790	+	0.489948i	0.565592	+	0.824685i	$0.308648\pi$
$90$	0.647674	+	0.470563i	0.0682709	+	0.0496017i
$91$	−2.57277			−0.269700
$92$	−1.02312	−	0.743338i	−0.106667	−	0.0774984i
$93$	−8.93621	+	12.2996i	−0.926642	+	1.27541i
$94$	4.98012	+	6.85455i	0.513660	+	0.706993i
$95$	14.8272	−	4.81766i	1.52124	−	0.494281i
$96$		−	14.2499i		−	1.45438i
$97$	−4.59850	−	6.32930i	−0.466907	−	0.642643i	0.509016	−	0.860757i	$-0.330009\pi$
$97$	−4.59850	−	6.32930i	−0.466907	−	0.642643i	−0.975923	+	0.218114i	$0.930009\pi$
$98$	−0.620352	+	1.90925i	−0.0626650	+	0.192863i
$99$	−0.275177	+	0.378748i	−0.0276563	+	0.0380656i
$100$	1.26292	+	3.88686i	0.126292	+	0.388686i
$101$	−14.0936	−	4.57929i	−1.40237	−	0.455656i	−0.492410	−	0.870363i	$-0.663884\pi$
$101$	−14.0936	−	4.57929i	−1.40237	−	0.455656i	−0.909955	+	0.414707i	$0.863884\pi$
$102$	−7.80411	+	24.0186i	−0.772722	+	2.37819i
$103$	1.47144	−	4.52864i	0.144986	−	0.446220i	−0.852023	−	0.523504i	$-0.824625\pi$
$103$	1.47144	−	4.52864i	0.144986	−	0.446220i	0.997009	+	0.0772835i	$0.0246247\pi$
$104$	0.147632	+	0.0479684i	0.0144765	+	0.00470369i
$105$	−1.45257	−	4.47054i	−0.141756	−	0.436280i
$106$	9.82434	−	13.5220i	0.954224	−	1.31338i
$107$	5.48381	−	16.8774i	0.530140	−	1.63160i	−0.223783	−	0.974639i	$-0.571841\pi$
$107$	5.48381	−	16.8774i	0.530140	−	1.63160i	0.753923	−	0.656963i	$-0.228159\pi$
$108$	−6.03501	−	8.30647i	−0.580719	−	0.799291i
$109$			11.5623i			1.10746i	0.832695	+	0.553732i	$0.186797\pi$
$109$			11.5623i			1.10746i	−0.832695	+	0.553732i	$0.813203\pi$
$110$	−15.7191	+	5.10743i	−1.49875	+	0.486975i
$111$	6.93567	+	9.54614i	0.658305	+	0.906079i
$112$	−2.31528	+	3.18671i	−0.218773	+	0.301116i
$113$	−6.14511	−	4.46469i	−0.578084	−	0.420002i	0.259949	−	0.965622i	$-0.416294\pi$
$113$	−6.14511	−	4.46469i	−0.578084	−	0.420002i	−0.838033	+	0.545620i	$0.816294\pi$
$114$	20.9772			1.96469
$115$	−1.33468	−	0.969698i	−0.124459	−	0.0904248i
$116$	−10.4362	−	3.39092i	−0.968974	−	0.314839i
$117$	0.368463	−	0.119721i	0.0340644	−	0.0110682i
$118$	8.96257	−	6.51169i	0.825072	−	0.599450i
$119$	5.73387	−	4.16590i	0.525623	−	0.381887i
$120$			0.283612i			0.0258901i
$121$	0.412452	+	1.26940i	0.0374957	+	0.115400i
$122$	−18.7864			−1.70084
$123$	0.347280	−	11.3602i	0.0313132	−	1.02431i
$124$	−17.3879			−1.56148
$125$	−2.44426	−	7.52267i	−0.218621	−	0.672848i
$126$		−	0.302302i		−	0.0269312i
$127$	−3.71264	+	2.69739i	−0.329444	+	0.239355i	−0.740195	−	0.672393i	$-0.765267\pi$
$127$	−3.71264	+	2.69739i	−0.329444	+	0.239355i	0.410751	+	0.911748i	$0.365267\pi$
$128$	0.390454	−	0.283682i	0.0345116	−	0.0250741i
$129$	−7.42410	+	2.41224i	−0.653655	+	0.212386i
$130$	13.0083	+	4.22666i	1.14090	+	0.370702i
$131$	4.04330	+	2.93763i	0.353265	+	0.256662i	0.750237	−	0.661169i	$-0.229939\pi$
$131$	4.04330	+	2.93763i	0.353265	+	0.256662i	−0.396973	+	0.917830i	$0.629939\pi$
$132$	−11.2024			−0.975043
$133$	−4.76270	−	3.46031i	−0.412979	−	0.300046i
$134$	5.42594	−	7.46816i	0.468730	−	0.645151i
$135$	−7.87277	−	10.8359i	−0.677580	−	0.932609i
$136$	−0.406694	+	0.132143i	−0.0348737	+	0.0113312i
$137$		−	12.2973i		−	1.05063i	−0.850908	−	0.525315i	$-0.823947\pi$
$137$		−	12.2973i		−	1.05063i	0.850908	−	0.525315i	$-0.176053\pi$
$138$	−1.30476	−	1.79585i	−0.111068	−	0.152873i
$139$	3.94928	−	12.1546i	0.334973	−	1.03094i	−0.631762	−	0.775162i	$-0.717668\pi$
$139$	3.94928	−	12.1546i	0.334973	−	1.03094i	0.966735	−	0.255779i	$-0.0823320\pi$
$140$	3.15998	−	4.34934i	0.267067	−	0.367586i
$141$	2.31496	+	7.12472i	0.194955	+	0.600010i
$142$	14.5968	+	4.74278i	1.22494	+	0.398006i
$143$	−2.47167	+	7.60703i	−0.206692	+	0.636131i
$144$	0.183296	−	0.564127i	0.0152747	−	0.0470106i
$145$	−13.6142	−	4.42351i	−1.13059	−	0.367353i
$146$	2.31448	+	7.12323i	0.191548	+	0.589523i
$147$	−1.04331	+	1.43600i	−0.0860510	+	0.118439i
$148$	−4.17027	+	12.8348i	−0.342794	+	1.05501i
$149$	12.7812	+	17.5919i	1.04708	+	1.44118i	0.891314	+	0.453387i	$0.149784\pi$
$149$	12.7812	+	17.5919i	1.04708	+	1.44118i	0.155765	+	0.987794i	$0.450216\pi$
$150$			7.17358i			0.585720i
$151$	6.80284	−	2.21038i	0.553607	−	0.179878i	−0.0188354	−	0.999823i	$-0.505996\pi$
$151$	6.80284	−	2.21038i	0.553607	−	0.179878i	0.572443	+	0.819945i	$0.305996\pi$
$152$	0.208779	+	0.287359i	0.0169342	+	0.0233079i
$153$	−0.627328	+	0.863442i	−0.0507164	+	0.0698052i
$154$	5.04917	+	3.66844i	0.406874	+	0.295611i
$155$	−22.6828			−1.82193
$156$	7.50002	+	5.44908i	0.600482	+	0.436276i
$157$	−7.00899	−	2.27736i	−0.559378	−	0.181753i	0.0156631	−	0.999877i	$-0.495014\pi$
$157$	−7.00899	−	2.27736i	−0.559378	−	0.181753i	−0.575041	+	0.818124i	$0.695014\pi$
$158$	10.4564	−	3.39751i	0.831870	−	0.270291i
$159$	11.9559	−	8.68647i	0.948165	−	0.688882i
$160$	17.2002	−	12.4967i	1.35979	−	0.987947i
$161$			0.622960i			0.0490961i
$162$	−5.84935	−	18.0024i	−0.459568	−	1.41440i
$163$	−3.28689			−0.257449			−0.128724	−	0.991680i	$-0.541088\pi$
$163$	−3.28689			−0.257449			−0.128724	+	0.991680i	$0.541088\pi$
$164$	10.7447	−	7.31554i	0.839021	−	0.571248i
$165$	−14.6137			−1.13768
$166$	6.67844	+	20.5541i	0.518347	+	1.59531i
$167$		−	12.8111i		−	0.991354i	−0.868507	−	0.495677i	$-0.834920\pi$
$167$		−	12.8111i		−	0.991354i	0.868507	−	0.495677i	$-0.165080\pi$
$168$	0.0866413	−	0.0629486i	0.00668452	−	0.00485659i
$169$	−5.16221	+	3.75056i	−0.397093	+	0.288505i
$170$	−35.8352	+	11.6436i	−2.74843	+	0.893020i
$171$	0.843117	+	0.273945i	0.0644748	+	0.0209491i
$172$	−7.22283	−	5.24769i	−0.550735	−	0.400133i
$173$	1.39406			0.105989			0.0529943	−	0.998595i	$-0.483123\pi$
$173$	1.39406			0.105989			0.0529943	+	0.998595i	$0.483123\pi$
$174$	−15.5825	−	11.3213i	−1.18130	−	0.858267i
$175$	1.18332	−	1.62870i	0.0894508	−	0.123118i
$176$	7.19798	+	9.90716i	0.542568	+	0.746781i
$177$	9.31583	−	3.02690i	0.700221	−	0.227516i
$178$			30.0274i			2.25065i
$179$	−8.59331	−	11.8277i	−0.642294	−	0.884042i	0.356442	−	0.934318i	$-0.383990\pi$
$179$	−8.59331	−	11.8277i	−0.642294	−	0.884042i	−0.998735	+	0.0502760i	$0.983990\pi$
$180$	−0.250169	+	0.769941i	−0.0186465	+	0.0573880i
$181$	−4.50910	+	6.20625i	−0.335159	+	0.461307i	−0.943020	−	0.332737i	$-0.892028\pi$
$181$	−4.50910	+	6.20625i	−0.335159	+	0.461307i	0.607861	+	0.794044i	$0.292028\pi$
$182$	−1.59602	−	4.91205i	−0.118305	−	0.364106i
$183$	−15.7976	−	5.13294i	−1.16779	−	0.379438i
$184$	0.0116149	−	0.0357469i	0.000856259	−	0.00263529i
$185$	−5.44019	+	16.7432i	−0.399971	+	1.23098i
$186$	−29.0266	−	9.43132i	−2.12834	−	0.691538i
$187$	−6.80894	−	20.9558i	−0.497919	−	1.53244i
$188$	−5.03608	+	6.93156i	−0.367294	+	0.505536i
$189$	−1.56291	+	4.81014i	−0.113685	+	0.349886i
$190$	18.3962	+	25.3202i	1.33460	+	1.83692i
$191$			6.88849i			0.498433i	0.968448	+	0.249217i	$0.0801731\pi$
$191$			6.88849i			0.498433i	−0.968448	+	0.249217i	$0.919827\pi$
$192$	13.9077	−	4.51889i	1.00370	−	0.326123i
$193$	−1.79438	−	2.46975i	−0.129162	−	0.177777i	0.739538	−	0.673115i	$-0.235044\pi$
$193$	−1.79438	−	2.46975i	−0.129162	−	0.177777i	−0.868700	+	0.495338i	$0.835044\pi$
$194$	9.23150	−	12.7061i	0.662783	−	0.912242i
$195$	9.78391	+	7.10843i	0.700640	+	0.509045i
$196$	−2.03005			−0.145004
$197$	3.54445	+	2.57519i	0.252531	+	0.183475i	0.706848	−	0.707366i	$-0.250117\pi$
$197$	3.54445	+	2.57519i	0.252531	+	0.183475i	−0.454317	+	0.890840i	$0.650117\pi$
$198$	−0.893830	−	0.290423i	−0.0635217	−	0.0206395i
$199$	9.60992	−	3.12245i	0.681229	−	0.221345i	0.0520956	−	0.998642i	$-0.483410\pi$
$199$	9.60992	−	3.12245i	0.681229	−	0.221345i	0.629133	+	0.777297i	$0.283410\pi$
$200$	−0.0982684	+	0.0713961i	−0.00694862	+	0.00504847i
$201$	6.60319	−	4.79750i	0.465753	−	0.338390i
$202$		−	29.7489i		−	2.09313i
$203$	1.67036	+	5.14083i	0.117236	+	0.360816i
$204$	−25.5384			−1.78804
$205$	14.0167	−	9.54326i	0.978967	−	0.666530i
$206$	9.55910			0.666014
$207$	−0.0289887	−	0.0892180i	−0.00201485	−	0.00620108i
$208$		−	10.1341i		−	0.702675i
$209$	−14.8068	+	10.7578i	−1.02421	+	0.744129i
$210$	7.63425	−	5.54661i	0.526814	−	0.382752i
$211$	−10.6987	+	3.47622i	−0.736529	+	0.239313i	−0.653175	−	0.757207i	$-0.726563\pi$
$211$	−10.6987	+	3.47622i	−0.736529	+	0.239313i	−0.0833540	+	0.996520i	$0.526563\pi$
$212$	16.0747	+	5.22299i	1.10402	+	0.358716i
$213$	10.9786	+	7.97645i	0.752244	+	0.546538i
$214$	35.6250			2.43528
$215$	−9.42230	−	6.84570i	−0.642596	−	0.466873i
$216$	0.179366	−	0.246877i	0.0122043	−	0.0167978i
$217$	5.03452	+	6.92942i	0.341765	+	0.470399i
$218$	−22.0752	+	7.17267i	−1.49512	+	0.485795i
$219$			6.62233i			0.447496i
$220$	−9.82407	−	13.5217i	−0.662339	−	0.911631i
$221$	−5.63474	+	17.3419i	−0.379033	+	1.16654i
$222$	−13.9234	+	19.1639i	−0.934475	+	1.28619i
$223$	5.57133	+	17.1468i	0.373084	+	1.14823i	0.944762	+	0.327757i	$0.106293\pi$
$223$	5.57133	+	17.1468i	0.373084	+	1.14823i	−0.571678	+	0.820478i	$0.693707\pi$
$224$	−7.63526	−	2.48085i	−0.510152	−	0.165758i
$225$	−0.0936813	+	0.288321i	−0.00624542	+	0.0192214i
$226$	4.71205	−	14.5022i	0.313441	−	0.964672i
$227$	8.70191	+	2.82742i	0.577566	+	0.187663i	0.583210	−	0.812321i	$-0.301796\pi$
$227$	8.70191	+	2.82742i	0.577566	+	0.187663i	−0.00564370	+	0.999984i	$0.501796\pi$
$228$	6.55513	+	20.1746i	0.434124	+	1.33610i
$229$	11.7511	−	16.1739i	0.776532	−	1.06880i	−0.219124	−	0.975697i	$-0.570320\pi$
$229$	11.7511	−	16.1739i	0.776532	−	1.06880i	0.995656	−	0.0931072i	$-0.0296799\pi$
$230$	1.02342	−	3.14978i	0.0674826	−	0.207690i
$231$	3.24356	+	4.46437i	0.213410	+	0.293734i
$232$		−	0.326136i		−	0.0214119i
$233$	−28.4666	+	9.24935i	−1.86491	+	0.605945i	−0.871634	+	0.490158i	$0.836939\pi$
$233$	−28.4666	+	9.24935i	−1.86491	+	0.605945i	−0.993274	+	0.115788i	$0.963061\pi$
$234$	0.457153	+	0.629217i	0.0298850	+	0.0411332i
$235$	−6.56965	+	9.04235i	−0.428557	+	0.589858i
$236$	9.06327	+	6.58485i	0.589969	+	0.428637i
$237$	9.72116			0.631457
$238$	11.5107	+	8.36304i	0.746130	+	0.542095i
$239$	11.3555	+	3.68961i	0.734523	+	0.238661i	0.652308	−	0.757954i	$-0.273801\pi$
$239$	11.3555	+	3.68961i	0.734523	+	0.238661i	0.0822147	+	0.996615i	$0.473801\pi$
$240$	17.6094	−	5.72164i	1.13668	−	0.369330i
$241$	−7.41168	+	5.38490i	−0.477428	+	0.346872i	−0.800329	−	0.599561i	$-0.795342\pi$
$241$	−7.41168	+	5.38490i	−0.477428	+	0.346872i	0.322901	+	0.946433i	$0.395342\pi$
$242$	−2.16773	+	1.57495i	−0.139347	+	0.101241i
$243$		−	1.56349i		−	0.100298i
$244$	−5.87054	−	18.0677i	−0.375823	−	1.15666i
$245$	−2.64824			−0.169190
$246$	21.9048	−	6.38426i	1.39660	−	0.407045i
$247$	15.1460			0.963715
$248$	−0.159696	−	0.491492i	−0.0101407	−	0.0312098i
$249$			19.1088i			1.21097i
$250$	12.8463	−	9.33340i	0.812472	−	0.590296i
$251$	−2.00918	+	1.45975i	−0.126818	+	0.0921388i	−0.649386	−	0.760459i	$-0.724974\pi$
$251$	−2.00918	+	1.45975i	−0.126818	+	0.0921388i	0.522568	+	0.852598i	$0.324974\pi$
$252$	0.290737	−	0.0944661i	0.0183147	−	0.00595080i
$253$	1.84193	+	0.598480i	0.115801	+	0.0376261i
$254$	−7.45313	−	5.41502i	−0.467651	−	0.339768i
$255$	−33.3153			−2.08628
$256$	−12.5465	−	9.11557i	−0.784157	−	0.569723i
$257$	7.09916	−	9.77116i	0.442834	−	0.609508i	−0.528005	−	0.849241i	$-0.677060\pi$
$257$	7.09916	−	9.77116i	0.442834	−	0.609508i	0.970839	+	0.239733i	$0.0770599\pi$
$258$	−9.21110	−	12.6780i	−0.573458	−	0.789297i
$259$	6.32238	−	2.05427i	0.392854	−	0.127646i
$260$			13.8314i			0.857789i
$261$	−0.478444	−	0.658522i	−0.0296150	−	0.0407615i
$262$	−3.10039	+	9.54201i	−0.191543	+	0.589507i
$263$	12.0657	−	16.6070i	0.744004	−	1.02403i	−0.254374	−	0.967106i	$-0.581869\pi$
$263$	12.0657	−	16.6070i	0.744004	−	1.02403i	0.998378	−	0.0569279i	$-0.0181305\pi$
$264$	−0.102886	−	0.316651i	−0.00633220	−	0.0194885i
$265$	20.9697	+	6.81348i	1.28816	+	0.418549i
$266$	3.65202	−	11.2398i	0.223920	−	0.689155i
$267$	−8.20428	+	25.2502i	−0.502094	+	1.54529i
$268$	8.87799	+	2.88464i	0.542310	+	0.176207i
$269$	−2.45819	−	7.56553i	−0.149878	−	0.461278i	0.847728	−	0.530432i	$-0.177970\pi$
$269$	−2.45819	−	7.56553i	−0.149878	−	0.461278i	−0.997606	+	0.0691535i	$0.977970\pi$
$270$	15.8046	−	21.7531i	0.961837	−	1.32385i
$271$	−5.21819	+	16.0599i	−0.316982	+	0.975572i	0.657948	+	0.753063i	$0.271425\pi$
$271$	−5.21819	+	16.0599i	−0.316982	+	0.975572i	−0.974931	+	0.222509i	$0.928575\pi$
$272$	16.4094	+	22.5856i	0.994967	+	1.36945i
$273$		−	4.56664i		−	0.276386i
$274$	23.4786	−	7.62865i	1.41839	−	0.460864i
$275$	−3.67884	−	5.06348i	−0.221842	−	0.305340i
$276$	1.31942	−	1.81602i	0.0794196	−	0.109312i
$277$	−21.9342	−	15.9361i	−1.31790	−	0.957509i	−0.999956	−	0.00939912i	$-0.997008\pi$
$277$	−21.9342	−	15.9361i	−1.31790	−	0.957509i	−0.317942	−	0.948110i	$-0.602992\pi$
$278$	25.6561			1.53875
$279$	−1.04348	−	0.758130i	−0.0624713	−	0.0453880i
$280$	0.151962	+	0.0493755i	0.00908148	+	0.00295075i
$281$	−13.7995	+	4.48372i	−0.823207	+	0.267476i	−0.690181	−	0.723637i	$-0.742469\pi$
$281$	−13.7995	+	4.48372i	−0.823207	+	0.267476i	−0.133025	+	0.991113i	$0.542469\pi$
$282$	−12.1667	+	8.83966i	−0.724519	+	0.526394i
$283$	−15.0032	+	10.9005i	−0.891847	+	0.647965i	−0.936359	−	0.351044i	$-0.885827\pi$
$283$	−15.0032	+	10.9005i	−0.891847	+	0.647965i	0.0445118	+	0.999009i	$0.485827\pi$
$284$			15.5204i			0.920967i
$285$	8.55129	+	26.3182i	0.506535	+	1.55895i
$286$	−16.0570			−0.949469
$287$	−6.02643	−	2.16383i	−0.355729	−	0.127727i
$288$	1.20894			0.0712372
$289$	−10.2692	−	31.6054i	−0.604072	−	1.85914i
$290$		−	28.7369i		−	1.68749i
$291$	11.2344	−	8.16230i	0.658574	−	0.478482i
$292$	−6.12746	+	4.45186i	−0.358583	+	0.260525i
$293$	18.3683	−	5.96823i	1.07309	−	0.348668i	0.281399	−	0.959591i	$-0.409201\pi$
$293$	18.3683	−	5.96823i	1.07309	−	0.348668i	0.791690	+	0.610923i	$0.209201\pi$
$294$	−3.38889	−	1.10112i	−0.197644	−	0.0642185i
$295$	11.8232	+	8.59006i	0.688373	+	0.500132i
$296$	−0.401094			−0.0233131
$297$	12.7208	+	9.24224i	0.738138	+	0.536289i
$298$	−25.6583	+	35.3156i	−1.48635	+	2.04578i
$299$	−0.942064	−	1.29664i	−0.0544809	−	0.0749866i
$300$	−6.89913	+	2.24166i	−0.398322	+	0.129423i
$301$			4.39786i			0.253489i
$302$	8.44031	+	11.6171i	0.485685	+	0.668488i
$303$	8.12818	−	25.0160i	0.466952	−	1.43713i
$304$	13.6301	−	18.7602i	0.781740	−	1.07597i
$305$	−7.65823	−	23.5696i	−0.438509	−	1.34959i
$306$	−2.03769	−	0.662085i	−0.116487	−	0.0378489i
$307$	−0.0316250	+	0.0973318i	−0.00180494	+	0.00555502i	−0.951955	−	0.306238i	$-0.900930\pi$
$307$	−0.0316250	+	0.0973318i	−0.00180494	+	0.00555502i	0.950150	+	0.311793i	$0.100930\pi$
$308$	−1.95028	+	6.00235i	−0.111128	+	0.342016i
$309$	8.03829	+	2.61180i	0.457282	+	0.148580i
$310$	−14.0713	−	43.3071i	−0.799197	−	2.45968i
$311$	16.0862	−	22.1408i	0.912167	−	1.25549i	−0.0542547	−	0.998527i	$-0.517278\pi$
$311$	16.0862	−	22.1408i	0.912167	−	1.25549i	0.966421	−	0.256963i	$-0.0827217\pi$
$312$	−0.0851434	+	0.262044i	−0.00482029	+	0.0148353i
$313$	−1.14940	−	1.58201i	−0.0649679	−	0.0894207i	0.775297	−	0.631597i	$-0.217600\pi$
$313$	−1.14940	−	1.58201i	−0.0649679	−	0.0894207i	−0.840265	+	0.542177i	$0.817600\pi$
$314$		−	14.7946i		−	0.834910i
$315$	0.379271	−	0.123233i	0.0213695	−	0.00694338i
$316$	6.53505	+	8.99472i	0.367625	+	0.505993i
$317$	−19.5632	+	26.9264i	−1.09878	+	1.51234i	−0.261784	+	0.965126i	$0.584311\pi$
$317$	−19.5632	+	26.9264i	−1.09878	+	1.51234i	−0.836994	+	0.547212i	$0.815689\pi$
$318$	24.0015	+	17.4381i	1.34594	+	0.977880i
$319$	16.8048			0.940890
$320$	17.6510	+	12.8242i	0.986721	+	0.716894i
$321$	29.9572	+	9.73370i	1.67205	+	0.543282i
$322$	−1.18938	+	0.386454i	−0.0662818	+	0.0215362i
$323$	−33.7554	+	24.5247i	−1.87820	+	1.36459i
$324$	15.4858	−	11.2511i	0.860325	−	0.625062i
$325$			5.17948i			0.287306i
$326$	−2.03902	−	6.27547i	−0.112931	−	0.347566i
$327$	−20.5229			−1.13492
$328$	0.305467	+	0.236526i	0.0168666	+	0.0130600i
$329$	4.22052			0.232685
$330$	−9.06564	−	27.9012i	−0.499047	−	1.53591i
$331$		−	12.7410i		−	0.700307i	−0.936692	−	0.350153i	$-0.886129\pi$
$331$		−	12.7410i		−	0.700307i	0.936692	−	0.350153i	$-0.113871\pi$
$332$	−17.6808	+	12.8459i	−0.970361	+	0.705009i
$333$	−0.809875	+	0.588408i	−0.0443809	+	0.0322446i
$334$	24.4596	−	7.94740i	1.33837	−	0.434862i
$335$	11.5815	+	3.76306i	0.632765	+	0.205598i
$336$	−5.65637	−	4.10959i	−0.308580	−	0.224197i
$337$	4.38217			0.238712			0.119356	−	0.992852i	$-0.461917\pi$
$337$	4.38217			0.238712			0.119356	+	0.992852i	$0.461917\pi$
$338$	−10.3631	−	7.52926i	−0.563680	−	0.409538i
$339$	7.92477	−	10.9075i	0.430414	−	0.592415i
$340$	−22.3962	−	30.8257i	−1.21460	−	1.67176i
$341$	25.3252	−	8.22865i	1.37144	−	0.445606i
$342$			1.77966i			0.0962330i
$343$	0.587785	+	0.809017i	0.0317374	+	0.0436828i
$344$	0.0819965	−	0.252359i	0.00442096	−	0.0136063i
$345$	1.72120	−	2.36903i	0.0926665	−	0.127544i
$346$	0.864809	+	2.66161i	0.0464924	+	0.143089i
$347$	28.5996	+	9.29258i	1.53531	+	0.498852i	0.950077	−	0.312015i	$-0.101004\pi$
$347$	28.5996	+	9.29258i	1.53531	+	0.498852i	0.585231	+	0.810867i	$0.301004\pi$
$348$	6.01884	−	18.5241i	0.322644	−	0.992995i
$349$	−4.22853	+	13.0141i	−0.226348	+	0.696627i	0.771804	+	0.635860i	$0.219355\pi$
$349$	−4.22853	+	13.0141i	−0.226348	+	0.696627i	−0.998152	+	0.0607668i	$0.980645\pi$
$350$	3.84367	+	1.24889i	0.205453	+	0.0667557i
$351$	−4.02101	−	12.3754i	−0.214626	−	0.660549i
$352$	−14.6704	+	20.1921i	−0.781937	+	1.07624i
$353$	−10.4093	+	32.0367i	−0.554034	+	1.70514i	0.144448	+	0.989512i	$0.453859\pi$
$353$	−10.4093	+	32.0367i	−0.554034	+	1.70514i	−0.698482	+	0.715628i	$0.746141\pi$
$354$	11.5582	+	15.9085i	0.614310	+	0.845526i
$355$			20.2467i			1.07458i
$356$	−28.8786	+	9.38323i	−1.53056	+	0.497310i
$357$	7.39442	+	10.1775i	0.391354	+	0.538653i
$358$	17.2511	−	23.7440i	0.911747	−	1.25491i
$359$	−1.52434	−	1.10750i	−0.0804518	−	0.0584516i	0.546832	−	0.837242i	$-0.315834\pi$
$359$	−1.52434	−	1.10750i	−0.0804518	−	0.0584516i	−0.627284	+	0.778791i	$0.715834\pi$
$360$	−0.0240611			−0.00126813
$361$	12.6668	+	9.20297i	0.666674	+	0.484367i
$362$	−14.6465	−	4.75893i	−0.769802	−	0.250124i
$363$	−2.25317	+	0.732098i	−0.118261	+	0.0384252i
$364$	4.22539	−	3.06993i	0.221471	−	0.160908i
$365$	−7.99338	+	5.80753i	−0.418393	+	0.303980i
$366$		−	33.3457i		−	1.74301i
$367$	−5.61433	−	17.2791i	−0.293066	−	0.901964i	−0.983864	−	0.178917i	$-0.942741\pi$
$367$	−5.61433	−	17.2791i	−0.293066	−	0.901964i	0.690798	−	0.723047i	$-0.257259\pi$
$368$	−2.45383			−0.127915
$369$	0.963773	+	0.0294625i	0.0501720	+	0.00153376i
$370$	−35.3417			−1.83733
$371$	−2.57283	−	7.91836i	−0.133575	−	0.411101i
$372$		−	30.8633i		−	1.60019i
$373$	−20.9665	+	15.2331i	−1.08561	+	0.788738i	−0.978652	−	0.205526i	$-0.934110\pi$
$373$	−20.9665	+	15.2331i	−1.08561	+	0.788738i	−0.106954	+	0.994264i	$0.534110\pi$
$374$	35.7857	−	25.9999i	1.85044	−	1.34442i
$375$	13.3527	−	4.33854i	0.689528	−	0.224041i
$376$	−0.242183	−	0.0786900i	−0.0124896	−	0.00405813i
$377$	−11.2509	−	8.17423i	−0.579449	−	0.420994i
$378$	−10.1533			−0.522229
$379$	−27.7420	−	20.1558i	−1.42501	−	1.03533i	−0.990919	−	0.134464i	$-0.957069\pi$
$379$	−27.7420	−	20.1558i	−1.42501	−	1.03533i	−0.434093	−	0.900868i	$-0.642931\pi$
$380$	−18.6029	+	25.6047i	−0.954307	+	1.31349i
$381$	−4.78784	−	6.58990i	−0.245289	−	0.337611i
$382$	−13.1518	+	4.27328i	−0.672905	+	0.218640i
$383$			10.3857i			0.530682i	0.964155	+	0.265341i	$0.0854846\pi$
$383$			10.3857i			0.530682i	−0.964155	+	0.265341i	$0.914515\pi$
$384$	0.503532	+	0.693052i	0.0256957	+	0.0353672i
$385$	−2.54418	+	7.83017i	−0.129663	+	0.399062i
$386$	3.60221	−	4.95802i	0.183348	−	0.252357i
$387$	−0.204649	−	0.629845i	−0.0104029	−	0.0320168i
$388$	15.1047	+	4.90781i	0.766825	+	0.249157i
$389$	−3.95134	+	12.1610i	−0.200341	+	0.616587i	0.799531	+	0.600624i	$0.205081\pi$
$389$	−3.95134	+	12.1610i	−0.200341	+	0.616587i	−0.999873	+	0.0159624i	$0.994919\pi$
$390$	−7.50227	+	23.0896i	−0.379892	+	1.16919i
$391$	4.19910	+	1.36437i	0.212358	+	0.0689992i
$392$	−0.0186446	−	0.0573823i	−0.000941696	−	0.00289824i
$393$	−5.21426	+	7.17681i	−0.263024	+	0.362022i
$394$	−2.71787	+	8.36474i	−0.136924	+	0.421409i
$395$	8.52509	+	11.7338i	0.428944	+	0.590390i
$396$		−	0.950388i		−	0.0477588i
$397$	−16.1636	+	5.25187i	−0.811227	+	0.263584i	−0.685118	−	0.728433i	$-0.740249\pi$
$397$	−16.1636	+	5.25187i	−0.811227	+	0.263584i	−0.126110	+	0.992016i	$0.540249\pi$
$398$	11.9231	+	16.4107i	0.597649	+	0.822593i
$399$	6.14200	−	8.45374i	0.307485	−	0.423217i
$400$	6.41544	+	4.66109i	0.320772	+	0.233055i
$401$	−19.1028			−0.953949			−0.476975	−	0.878917i	$-0.658267\pi$
$401$	−19.1028			−0.953949			−0.476975	+	0.878917i	$0.658267\pi$
$402$	13.2559	+	9.63098i	0.661145	+	0.480350i
$403$	−20.9579	−	6.80962i	−1.04398	−	0.339211i
$404$	28.6108	−	9.29620i	1.42344	−	0.462503i
$405$	20.2016	−	14.6773i	1.00382	−	0.729320i
$406$	−8.77890	+	6.37824i	−0.435689	+	0.316547i
$407$		−	20.6672i		−	1.02443i
$408$	−0.234552	−	0.721877i	−0.0116121	−	0.0357382i
$409$	−3.87872			−0.191790			−0.0958952	−	0.995391i	$-0.530571\pi$
$409$	−3.87872			−0.191790			−0.0958952	+	0.995391i	$0.530571\pi$
$410$	26.9157	+	20.8411i	1.32927	+	1.02927i
$411$	21.8276			1.07668
$412$	2.98711	+	9.19339i	0.147164	+	0.452926i
$413$		−	5.51848i		−	0.271547i
$414$	0.152356	−	0.110693i	0.00748788	−	0.00544026i
$415$	−23.0649	+	16.7577i	−1.13221	+	0.822601i
$416$	19.6438	−	6.38265i	0.963116	−	0.312935i
$417$	21.5743	+	7.00992i	1.05650	+	0.343277i
$418$	−29.7246	−	21.5962i	−1.45388	−	1.05630i
$419$	−33.4698			−1.63511			−0.817554	−	0.575853i	$-0.804670\pi$
$419$	−33.4698			−1.63511			−0.817554	+	0.575853i	$0.804670\pi$
$420$	7.72003	+	5.60893i	0.376699	+	0.273688i
$421$	−13.8034	+	18.9987i	−0.672734	+	0.925939i	−0.999818	−	0.0190560i	$-0.993934\pi$
$421$	−13.8034	+	18.9987i	−0.672734	+	0.925939i	0.327084	+	0.944995i	$0.393934\pi$
$422$	−13.2739	−	18.2700i	−0.646164	−	0.889368i
$423$	−0.604447	+	0.196397i	−0.0293892	+	0.00954913i
$424$			0.502343i			0.0243959i
$425$	−8.38674	−	11.5434i	−0.406817	−	0.559935i
$426$	−8.41839	+	25.9091i	−0.407872	+	1.25530i
$427$	−5.50056	+	7.57087i	−0.266191	+	0.366380i
$428$	11.1324	+	34.2621i	0.538106	+	1.65612i
$429$	−13.5024	−	4.38719i	−0.651901	−	0.211816i
$430$	7.22499	−	22.2362i	0.348420	−	1.07233i
$431$	−5.67205	+	17.4568i	−0.273213	+	0.840863i	0.716474	+	0.697614i	$0.245755\pi$
$431$	−5.67205	+	17.4568i	−0.273213	+	0.840863i	−0.989687	+	0.143249i	$0.954245\pi$
$432$	−18.9471	−	6.15628i	−0.911591	−	0.296194i
$433$	−4.90768	−	15.1043i	−0.235848	−	0.725865i	−0.997008	−	0.0773010i	$-0.975370\pi$
$433$	−4.90768	−	15.1043i	−0.235848	−	0.725865i	0.761160	−	0.648564i	$-0.224630\pi$
$434$	−10.1068	+	13.9108i	−0.485141	+	0.667740i
$435$	7.85168	−	24.1650i	0.376459	−	1.15862i
$436$	−13.7965	−	18.9893i	−0.660734	−	0.909422i
$437$		−	3.66738i		−	0.175435i
$438$	−12.6437	+	4.10817i	−0.604137	+	0.196296i
$439$	0.321933	+	0.443102i	0.0153650	+	0.0211481i	0.816630	−	0.577161i	$-0.195839\pi$
$439$	0.321933	+	0.443102i	0.0153650	+	0.0211481i	−0.801265	+	0.598309i	$0.795839\pi$
$440$	0.291981	−	0.401878i	0.0139197	−	0.0191588i
$441$	−0.121827	−	0.0885125i	−0.00580128	−	0.00421488i
$442$	−36.6055			−1.74115
$443$	−1.60456	−	1.16578i	−0.0762349	−	0.0553879i	0.549015	−	0.835812i	$-0.315003\pi$
$443$	−1.60456	−	1.16578i	−0.0762349	−	0.0553879i	−0.625250	+	0.780425i	$0.715003\pi$
$444$	−22.7816	−	7.40219i	−1.08117	−	0.351292i
$445$	−37.6727	+	12.2406i	−1.78586	+	0.580260i
$446$	−29.2813	+	21.2741i	−1.38651	+	1.00736i
$447$	−31.2253	+	22.6865i	−1.47691	+	1.07304i
$448$		−	8.23861i		−	0.389238i
$449$	−5.25167	−	16.1630i	−0.247842	−	0.762778i	−0.995156	−	0.0983075i	$-0.968657\pi$
$449$	−5.25167	−	16.1630i	−0.247842	−	0.762778i	0.747314	−	0.664470i	$-0.231343\pi$
$450$	−0.608592			−0.0286893
$451$	−12.1875	+	15.7398i	−0.573887	+	0.741158i
$452$	15.4198			0.725289
$453$	3.92340	+	12.0750i	0.184337	+	0.567332i
$454$			18.3681i			0.862057i
$455$	5.51210	−	4.00477i	0.258411	−	0.187747i
$456$	−0.510059	+	0.370580i	−0.0238857	+	0.0173540i
$457$	29.5751	−	9.60954i	1.38347	−	0.449515i	0.479658	−	0.877455i	$-0.340761\pi$
$457$	29.5751	−	9.60954i	1.38347	−	0.449515i	0.903807	+	0.427940i	$0.140761\pi$
$458$	38.1698	+	12.4021i	1.78356	+	0.579513i
$459$	29.0000	+	21.0698i	1.35361	+	0.983452i
$460$	3.34908			0.156152
$461$	−0.941139	−	0.683778i	−0.0438332	−	0.0318467i	0.565653	−	0.824643i	$-0.308624\pi$
$461$	−0.941139	−	0.683778i	−0.0438332	−	0.0318467i	−0.609486	+	0.792797i	$0.708624\pi$
$462$	−6.51144	+	8.96223i	−0.302940	+	0.416961i
$463$	−0.0727993	−	0.100200i	−0.00338327	−	0.00465668i	0.807322	−	0.590111i	$-0.200916\pi$
$463$	−0.0727993	−	0.100200i	−0.00338327	−	0.00465668i	−0.810705	+	0.585454i	$0.800916\pi$
$464$	−20.2497	+	6.57951i	−0.940067	+	0.305446i
$465$		−	40.2617i		−	1.86709i
$466$	−35.3186	−	48.6118i	−1.63610	−	2.25190i
$467$	3.08705	−	9.50096i	0.142852	−	0.439652i	−0.853877	−	0.520475i	$-0.825755\pi$
$467$	3.08705	−	9.50096i	0.142852	−	0.439652i	0.996728	+	0.0808231i	$0.0257549\pi$
$468$	−0.462289	+	0.636286i	−0.0213693	+	0.0294123i
$469$	−1.42096	−	4.37328i	−0.0656140	−	0.201939i
$470$	−21.3396	−	6.93364i	−0.984320	−	0.319825i
$471$	4.04229	−	12.4409i	0.186259	−	0.573245i
$472$	−0.102890	+	0.316663i	−0.00473590	+	0.0145756i
$473$	13.0033	+	4.22504i	0.597895	+	0.194268i
$474$	6.03054	+	18.5601i	0.276992	+	0.852493i
$475$	−6.96625	+	9.58822i	−0.319633	+	0.439938i
$476$	−4.44611	+	13.6837i	−0.203787	+	0.627192i
$477$	0.736942	+	1.01431i	0.0337423	+	0.0464423i
$478$			23.9692i			1.09633i
$479$	−14.6716	+	4.76710i	−0.670364	+	0.217814i	−0.624372	−	0.781127i	$-0.714645\pi$
$479$	−14.6716	+	4.76710i	−0.670364	+	0.217814i	−0.0459922	+	0.998942i	$0.514645\pi$
$480$	22.1814	+	30.5301i	1.01244	+	1.39350i
$481$	−10.0530	+	13.8367i	−0.458376	+	0.630900i
$482$	−14.8789	−	10.8102i	−0.677717	−	0.492390i
$483$	−1.10575			−0.0503132
$484$	−2.19208	−	1.59264i	−0.0996401	−	0.0723927i
$485$	19.7043	+	6.40233i	0.894728	+	0.290715i
$486$	2.98508	−	0.969911i	0.135406	−	0.0439960i
$487$	−10.4269	+	7.57556i	−0.472486	+	0.343282i	−0.798410	−	0.602115i	$-0.794325\pi$
$487$	−10.4269	+	7.57556i	−0.472486	+	0.343282i	0.325923	+	0.945396i	$0.394325\pi$
$488$	0.456791	−	0.331878i	0.0206779	−	0.0150234i
$489$		−	5.83419i		−	0.263831i
$490$	−1.64284	−	5.05615i	−0.0742160	−	0.228413i
$491$	21.5239			0.971362			0.485681	−	0.874136i	$-0.338572\pi$
$491$	21.5239			0.971362			0.485681	+	0.874136i	$0.338572\pi$
$492$	12.9850	+	19.0717i	0.585410	+	0.859821i
$493$	38.3104			1.72541
$494$	9.39583	+	28.9174i	0.422738	+	1.30105i
$495$		−	1.23980i		−	0.0557248i
$496$	−27.2949	+	19.8309i	−1.22558	+	0.890433i
$497$	6.18519	−	4.49380i	0.277444	−	0.201575i
$498$	−36.4833	+	11.8542i	−1.63486	+	0.531197i
$499$	12.7845	+	4.15392i	0.572311	+	0.185955i	0.580853	−	0.814008i	$-0.302719\pi$
$499$	12.7845	+	4.15392i	0.572311	+	0.185955i	−0.00854215	+	0.999964i	$0.502719\pi$
$500$	12.9907	+	9.43826i	0.580960	+	0.422092i
$501$	22.7396			1.01593
$502$	−4.03342	−	2.93045i	−0.180020	−	0.130793i
$503$	12.9923	−	17.8824i	0.579300	−	0.797338i	−0.414318	−	0.910132i	$-0.635980\pi$
$503$	12.9923	−	17.8824i	0.579300	−	0.797338i	0.993618	+	0.112794i	$0.0359799\pi$
$504$	0.00534043	+	0.00735047i	0.000237882	+	0.000327416i
$505$	37.3233	−	12.1271i	1.66086	−	0.539647i
$506$			3.88797i			0.172841i
$507$	−6.65721	−	9.16287i	−0.295657	−	0.406937i
$508$	2.87883	−	8.86012i	0.127727	−	0.393104i
$509$	−5.63393	+	7.75444i	−0.249720	+	0.343709i	−0.915413	−	0.402516i	$-0.868136\pi$
$509$	−5.63393	+	7.75444i	−0.249720	+	0.343709i	0.665694	+	0.746225i	$0.268136\pi$
$510$	−20.6672	−	63.6070i	−0.915158	−	2.81657i
$511$	3.54831	+	1.15292i	0.156968	+	0.0510020i
$512$	9.91890	−	30.5272i	0.438358	−	1.34913i
$513$	9.20088	−	28.3174i	0.406229	−	1.25024i
$514$	23.0595	+	7.49249i	1.01711	+	0.330480i
$515$	3.89674	+	11.9929i	0.171711	+	0.528472i
$516$	9.31459	−	12.8204i	0.410052	−	0.564388i
$517$	4.05467	−	12.4790i	0.178324	−	0.548825i
$518$	7.84420	+	10.7966i	0.344654	+	0.474376i
$519$			2.47445i			0.108616i
$520$	−0.390964	+	0.127032i	−0.0171449	+	0.00557072i
$521$	−20.2573	−	27.8818i	−0.887489	−	1.22152i	−0.974290	−	0.225298i	$-0.927664\pi$
$521$	−20.2573	−	27.8818i	−0.887489	−	1.22152i	0.0868009	−	0.996226i	$-0.472336\pi$
$522$	0.960477	−	1.32198i	0.0420389	−	0.0578616i
$523$	−27.0432	−	19.6480i	−1.18252	−	0.859149i	−0.190063	−	0.981772i	$-0.560869\pi$
$523$	−27.0432	−	19.6480i	−1.18252	−	0.859149i	−0.992453	+	0.122623i	$0.960869\pi$
$524$	−10.1458			−0.443221
$525$	2.89093	+	2.10039i	0.126171	+	0.0916683i
$526$	39.1919	+	12.7342i	1.70885	+	0.555238i
$527$	57.7345	−	18.7591i	2.51495	−	0.817158i
$528$	−17.5851	+	12.7763i	−0.765294	+	0.556018i
$529$	18.2934	−	13.2910i	0.795366	−	0.577868i
$530$			44.2632i			1.92267i
$531$	0.256796	+	0.790336i	0.0111440	+	0.0342977i
$532$	11.9510			0.518141
$533$	15.8157	−	4.60957i	0.685055	−	0.199663i
$534$	−53.2983			−2.30644
$535$	14.5225	+	44.6955i	0.627860	+	1.93236i
$536$			0.277442i			0.0119837i
$537$	20.9940	−	15.2530i	0.905957	−	0.658217i
$538$	12.9195	−	9.38657i	0.557000	−	0.404684i
$539$	2.95674	−	0.960704i	0.127356	−	0.0413804i
$540$	25.8597	+	8.40232i	1.11282	+	0.361578i
$541$	31.4567	+	22.8546i	1.35243	+	0.982596i	0.998887	+	0.0471772i	$0.0150225\pi$
$541$	31.4567	+	22.8546i	1.35243	+	0.982596i	0.353541	+	0.935419i	$0.384977\pi$
$542$	−33.8995			−1.45611
$543$	−11.0160	−	8.00361i	−0.472743	−	0.343468i
$544$	−33.4446	+	46.0325i	−1.43393	+	1.97363i
$545$	−17.9978	−	24.7719i	−0.770941	−	1.06111i
$546$	8.71884	−	2.83292i	0.373132	−	0.121238i
$547$		−	34.3643i		−	1.46931i	−0.678440	−	0.734655i	$-0.737344\pi$
$547$		−	34.3643i		−	1.46931i	0.678440	−	0.734655i	$-0.262656\pi$
$548$	14.6736	+	20.1965i	0.626825	+	0.862751i
$549$	0.435468	−	1.34023i	0.0185853	−	0.0571997i
$550$	7.38526	−	10.1649i	0.314909	−	0.433435i
$551$	−9.83343	−	30.2642i	−0.418918	−	1.28930i
$552$	0.0634503	+	0.0206162i	0.00270062	+	0.000877486i
$553$	1.69241	−	5.20869i	0.0719685	−	0.221496i
$554$	16.8191	−	51.7638i	0.714574	−	2.19923i
$555$	−29.7190	−	9.65629i	−1.26150	−	0.409887i
$556$	8.01725	+	24.6746i	0.340007	+	1.04643i
$557$	−7.80986	+	10.7494i	−0.330914	+	0.455465i	−0.941760	−	0.336285i	$-0.890829\pi$
$557$	−7.80986	+	10.7494i	−0.330914	+	0.455465i	0.610846	+	0.791750i	$0.290829\pi$
$558$	0.800134	−	2.46256i	0.0338724	−	0.104248i
$559$	−6.65061	−	9.15378i	−0.281291	−	0.387164i
$560$		−	10.4314i		−	0.440807i
$561$	37.1962	−	12.0858i	1.57043	−	0.510262i
$562$	−17.1210	−	23.5651i	−0.722207	−	0.994033i
$563$	27.1314	−	37.3432i	1.14345	−	1.57383i	0.383914	−	0.923369i	$-0.374576\pi$
$563$	27.1314	−	37.3432i	1.14345	−	1.57383i	0.759540	−	0.650461i	$-0.225424\pi$
$564$	−12.3034	−	8.93898i	−0.518069	−	0.376399i
$565$	20.1155			0.846264
$566$	−30.1189	−	21.8827i	−1.26599	−	0.919797i
$567$	−8.96759	−	2.91375i	−0.376603	−	0.122366i
$568$	−0.438706	+	0.142544i	−0.0184077	+	0.00598102i
$569$	−37.9427	+	27.5670i	−1.59064	+	1.15567i	−0.687623	+	0.726068i	$0.741346\pi$
$569$	−37.9427	+	27.5670i	−1.59064	+	1.15567i	−0.903019	+	0.429601i	$0.858654\pi$
$570$	−44.9430	+	32.6530i	−1.88246	+	1.36768i
$571$			27.9629i			1.17021i	0.810957	+	0.585106i	$0.198947\pi$
$571$			27.9629i			1.17021i	−0.810957	+	0.585106i	$0.801053\pi$
$572$	−5.01763	−	15.4427i	−0.209798	−	0.645691i
$573$	−12.2270			−0.510790
$574$	0.392771	−	12.8483i	0.0163940	−	0.536276i
$575$	1.25414			0.0523011
$576$	0.383373	+	1.17990i	0.0159739	+	0.0491626i
$577$		−	7.91718i		−	0.329596i	−0.986327	−	0.164798i	$-0.947303\pi$
$577$		−	7.91718i		−	0.329596i	0.986327	−	0.164798i	$-0.0526973\pi$
$578$	53.9720	−	39.2129i	2.24494	−	1.63104i
$579$	4.38378	−	3.18500i	0.182184	−	0.132364i
$580$	27.6375	−	8.97997i	1.14758	−	0.372873i
$581$	10.2387	+	3.32674i	0.424771	+	0.138017i
$582$	22.5531	+	16.3858i	0.934857	+	0.679214i
$583$	−25.8843			−1.07202
$584$	−0.182114	−	0.132314i	−0.00753595	−	0.00547519i
$585$	−0.603064	+	0.830047i	−0.0249336	+	0.0343182i
$586$	22.7896	+	31.3673i	0.941432	+	1.29577i
$587$	−23.6526	+	7.68520i	−0.976247	+	0.317202i	−0.753335	−	0.657637i	$-0.771556\pi$
$587$	−23.6526	+	7.68520i	−0.976247	+	0.317202i	−0.222912	+	0.974839i	$0.571556\pi$
$588$		−	3.60333i		−	0.148599i
$589$	−29.6383	−	40.7936i	−1.22123	−	1.68087i
$590$	−9.06599	+	27.9022i	−0.373241	+	1.14872i
$591$	−4.57093	+	6.29135i	−0.188023	+	0.258792i
$592$	8.09173	+	24.9038i	0.332568	+	1.02354i
$593$	25.0700	+	8.14573i	1.02950	+	0.334505i	0.774593	−	0.632461i	$-0.217955\pi$
$593$	25.0700	+	8.14573i	1.02950	+	0.334505i	0.254908	+	0.966965i	$0.417955\pi$
$594$	−9.75430	+	30.0207i	−0.400224	+	1.23176i
$595$	−5.80003	+	17.8506i	−0.237778	+	0.731805i
$596$	−41.9825	−	13.6409i	−1.71967	−	0.558754i
$597$	5.54232	+	17.0575i	0.226832	+	0.698117i
$598$	1.89119	−	2.60300i	0.0773366	−	0.106445i
$599$	11.4468	−	35.2297i	0.467705	−	1.43945i	−0.387843	−	0.921725i	$-0.626780\pi$
$599$	11.4468	−	35.2297i	0.467705	−	1.43945i	0.855548	−	0.517723i	$-0.173220\pi$
$600$	−0.126727	−	0.174425i	−0.00517362	−	0.00712088i
$601$		−	36.4277i		−	1.48592i	−0.669337	−	0.742959i	$-0.733422\pi$
$601$		−	36.4277i		−	1.48592i	0.669337	−	0.742959i	$-0.266578\pi$
$602$	−8.39660	+	2.72822i	−0.342220	+	0.111194i
$603$	0.407010	+	0.560201i	0.0165747	+	0.0228132i
$604$	−8.53514	+	11.7476i	−0.347290	+	0.478003i
$605$	−2.85961	−	2.07763i	−0.116260	−	0.0844676i
$606$	52.8040			2.14501
$607$	31.8909	+	23.1701i	1.29441	+	0.940445i	0.999885	−	0.0151982i	$-0.00483791\pi$
$607$	31.8909	+	23.1701i	1.29441	+	0.940445i	0.294527	+	0.955643i	$0.404838\pi$
$608$	44.9489	+	14.6048i	1.82292	+	0.592303i
$609$	−9.12492	+	2.96487i	−0.369760	+	0.120142i
$610$	40.2494	−	29.2429i	1.62965	−	1.18401i
$611$	−8.78466	+	6.38243i	−0.355389	+	0.258205i
$612$		−	2.16662i		−	0.0875806i
$613$	−6.44112	−	19.8237i	−0.260154	−	0.800673i	−0.992770	−	0.120031i	$-0.961701\pi$
$613$	−6.44112	−	19.8237i	−0.260154	−	0.800673i	0.732616	−	0.680643i	$-0.238299\pi$
$614$	−0.205449			−0.00829125
$615$	16.9392	+	24.8794i	0.683054	+	1.00324i
$616$	−0.187577			−0.00755768
$617$	−2.75396	−	8.47583i	−0.110870	−	0.341224i	0.880193	−	0.474616i	$-0.157413\pi$
$617$	−2.75396	−	8.47583i	−0.110870	−	0.341224i	−0.991063	+	0.133392i	$0.957413\pi$
$618$			16.9673i			0.682525i
$619$	−17.2291	+	12.5177i	−0.692497	+	0.503129i	−0.877480	−	0.479613i	$-0.840777\pi$
$619$	−17.2291	+	12.5177i	−0.692497	+	0.503129i	0.184983	+	0.982742i	$0.440777\pi$
$620$	37.2531	−	27.0660i	1.49612	−	1.08699i
$621$	−2.99652	+	0.973629i	−0.120246	+	0.0390704i
$622$	52.2513	+	16.9775i	2.09509	+	0.680735i
$623$	12.1010	+	8.79187i	0.484815	+	0.352239i
$624$	17.9879			0.720094
$625$	25.0901	+	18.2290i	1.00360	+	0.729160i
$626$	2.30742	−	3.17589i	0.0922231	−	0.126934i
$627$	−19.0949	−	26.2819i	−0.762577	−	1.04960i
$628$	14.2286	−	4.62316i	0.567784	−	0.184484i
$629$		−	47.1155i		−	1.87862i
$630$	0.470563	+	0.647674i	0.0187477	+	0.0258040i
$631$	−0.377846	+	1.16289i	−0.0150418	+	0.0462939i	−0.958296	−	0.285779i	$-0.907748\pi$
$631$	−0.377846	+	1.16289i	−0.0150418	+	0.0462939i	0.943254	+	0.332072i	$0.107748\pi$
$632$	−0.194228	+	0.267332i	−0.00772599	+	0.0106339i
$633$	−6.17025	−	18.9901i	−0.245245	−	0.754787i
$634$	−63.5452	−	20.6471i	−2.52370	−	0.820001i
$635$	3.75548	−	11.5582i	0.149032	−	0.458673i
$636$	−9.27075	+	28.5324i	−0.367609	+	1.13138i
$637$	−2.44685	−	0.795030i	−0.0969478	−	0.0315003i
$638$	10.4249	+	32.0845i	0.412726	+	1.27024i
$639$	−0.676706	+	0.931406i	−0.0267701	+	0.0368458i
$640$	−0.394959	+	1.21556i	−0.0156121	+	0.0480492i
$641$	−12.0445	−	16.5779i	−0.475730	−	0.654786i	0.501948	−	0.864898i	$-0.332617\pi$
$641$	−12.0445	−	16.5779i	−0.475730	−	0.654786i	−0.977677	+	0.210112i	$0.932617\pi$
$642$			63.2341i			2.49565i
$643$	34.0175	−	11.0530i	1.34152	−	0.435886i	0.451689	−	0.892176i	$-0.350822\pi$
$643$	34.0175	−	11.0530i	1.34152	−	0.435886i	0.889831	+	0.456289i	$0.150822\pi$
$644$	−0.743338	−	1.02312i	−0.0292916	−	0.0403165i
$645$	12.1511	−	16.7245i	0.478447	−	0.658526i
$646$	−67.7639	−	49.2334i	−2.66614	−	1.93706i
$647$	35.0352			1.37738			0.688688	−	0.725057i	$-0.258187\pi$
$647$	35.0352			1.37738			0.688688	+	0.725057i	$0.258187\pi$
$648$	0.460255	+	0.334395i	0.0180805	+	0.0131363i
$649$	−16.3167	−	5.30163i	−0.640488	−	0.208107i
$650$	−9.88890	+	3.21310i	−0.387874	+	0.126028i
$651$	−12.2996	+	8.93621i	−0.482061	+	0.350238i
$652$	5.39821	−	3.92203i	0.211410	−	0.153599i
$653$		−	6.87376i		−	0.268991i	−0.990914	−	0.134496i	$-0.957059\pi$
$653$		−	6.87376i		−	0.268991i	0.990914	−	0.134496i	$-0.0429414\pi$
$654$	−12.7314	−	39.1833i	−0.497838	−	1.53219i
$655$	−13.2354			−0.517148
$656$	8.52328	−	23.7380i	0.332778	−	0.926814i
$657$	−0.561825			−0.0219189
$658$	2.61820	+	8.05801i	0.102068	+	0.314134i
$659$			22.6095i			0.880743i	0.897816	+	0.440371i	$0.145153\pi$
$659$			22.6095i			0.880743i	−0.897816	+	0.440371i	$0.854847\pi$
$660$	24.0008	−	17.4376i	0.934231	−	0.678758i
$661$	11.6633	−	8.47387i	0.453649	−	0.329595i	−0.337386	−	0.941366i	$-0.609543\pi$
$661$	11.6633	−	8.47387i	0.453649	−	0.329595i	0.791035	+	0.611771i	$0.209543\pi$
$662$	24.3256	−	7.90387i	0.945442	−	0.307193i
$663$	−30.7817	−	10.0016i	−1.19546	−	0.388430i
$664$	−0.525492	−	0.381792i	−0.0203930	−	0.0148164i
$665$	15.5903			0.604565
$666$	−1.62582	−	1.18123i	−0.0629994	−	0.0457717i
$667$	−1.97927	+	2.72424i	−0.0766378	+	0.105483i
$668$	15.2867	+	21.0403i	0.591460	+	0.814075i
$669$	−30.4354	+	9.88905i	−1.17670	+	0.382333i
$670$			24.4463i			0.944445i
$671$	17.1007	+	23.5371i	0.660165	+	0.908639i
$672$	4.40347	−	13.5525i	0.169868	−	0.522799i
$673$	−28.7976	+	39.6366i	−1.11007	+	1.52788i	−0.288751	+	0.957404i	$0.593240\pi$
$673$	−28.7976	+	39.6366i	−1.11007	+	1.52788i	−0.821316	+	0.570473i	$0.806760\pi$
$674$	2.71848	+	8.36663i	0.104712	+	0.322271i
$675$	9.68372	+	3.14643i	0.372726	+	0.121106i
$676$	4.00284	−	12.3195i	0.153955	−	0.473826i
$677$	1.20686	−	3.71434i	0.0463835	−	0.142754i	−0.925183	−	0.379522i	$-0.876088\pi$
$677$	1.20686	−	3.71434i	0.0463835	−	0.142754i	0.971566	+	0.236769i	$0.0760883\pi$
$678$	25.7413	+	8.36384i	0.988587	+	0.321211i
$679$	−2.41758	−	7.44054i	−0.0927781	−	0.285542i
$680$	0.665637	−	0.916171i	0.0255260	−	0.0351336i
$681$	−5.01865	+	15.4458i	−0.192315	+	0.591884i
$682$	31.4210	+	43.2473i	1.20317	+	1.65603i
$683$			0.613666i			0.0234813i	0.999931	+	0.0117406i	$0.00373725\pi$
$683$			0.613666i			0.0234813i	−0.999931	+	0.0117406i	$0.996263\pi$
$684$	−1.71157	+	0.556124i	−0.0654437	+	0.0212639i
$685$	19.1420	+	26.3467i	0.731377	+	1.00665i
$686$	−1.17998	+	1.62410i	−0.0450518	+	0.0620085i
$687$	28.7086	+	20.8580i	1.09530	+	0.795782i
$688$	−17.3231			−0.660438
$689$	17.3296	+	12.5907i	0.660205	+	0.479667i
$690$	5.59082	+	1.81657i	0.212839	+	0.0691555i
$691$	−17.7306	+	5.76104i	−0.674505	+	0.219160i	−0.626188	−	0.779672i	$-0.715386\pi$
$691$	−17.7306	+	5.76104i	−0.674505	+	0.219160i	−0.0483172	+	0.998832i	$0.515386\pi$
$692$	−2.28954	+	1.66345i	−0.0870352	+	0.0632348i
$693$	−0.378748	+	0.275177i	−0.0143875	+	0.0104531i
$694$			60.3684i			2.29155i
$695$	10.4586	+	32.1884i	0.396719	+	1.22098i
$696$	0.578887			0.0219427
$697$	−27.7841	+	35.8824i	−1.05240	+	1.35914i
$698$	−27.4702			−1.03976
$699$	−16.4175	−	50.5279i	−0.620967	−	1.91114i
$700$			4.08688i			0.154470i
$701$	2.75962	−	2.00498i	0.104229	−	0.0757271i	−0.534450	−	0.845200i	$-0.679481\pi$
$701$	2.75962	−	2.00498i	0.104229	−	0.0757271i	0.638679	+	0.769473i	$0.279481\pi$
$702$	21.1332	−	15.3542i	0.797622	−	0.579506i
$703$	−37.2200	+	12.0935i	−1.40378	+	0.456115i
$704$	−24.3594	−	7.91486i	−0.918081	−	0.298303i
$705$	−16.0501	−	11.6611i	−0.604481	−	0.439181i
$706$	−67.6233			−2.54504
$707$	−11.9887	−	8.71032i	−0.450882	−	0.327585i
$708$	−11.6880	+	16.0872i	−0.439264	+	0.604594i
$709$	14.4095	+	19.8330i	0.541161	+	0.744844i	0.988780	−	0.149381i	$-0.0477279\pi$
$709$	14.4095	+	19.8330i	0.541161	+	0.744844i	−0.447619	+	0.894224i	$0.647728\pi$
$710$	−38.6558	+	12.5600i	−1.45073	+	0.471370i
$711$			0.824723i			0.0309295i
$712$	−0.530460	−	0.730115i	−0.0198798	−	0.0273622i
$713$	−1.64885	+	5.07464i	−0.0617500	+	0.190047i
$714$	−14.8443	+	20.4314i	−0.555534	+	0.764627i
$715$	−6.54559	−	20.1452i	−0.244791	−	0.753390i
$716$	28.2264	+	9.17132i	1.05487	+	0.342748i
$717$	−6.54902	+	20.1558i	−0.244578	+	0.752732i
$718$	1.16886	−	3.59739i	0.0436215	−	0.134253i
$719$	32.0239	+	10.4052i	1.19429	+	0.388048i	0.837657	−	0.546197i	$-0.183925\pi$
$719$	32.0239	+	10.4052i	1.19429	+	0.388048i	0.356632	+	0.934245i	$0.383925\pi$
$720$	0.485412	+	1.49394i	0.0180902	+	0.0556760i
$721$	2.79885	−	3.85229i	0.104235	−	0.143467i
$722$	−9.71286	+	29.8931i	−0.361475	+	1.11251i
$723$	−9.55814	−	13.1557i	−0.355471	−	0.489264i
$724$		−	15.5732i		−	0.578775i
$725$	10.3495	−	3.36274i	0.384369	−	0.124889i
$726$	−2.79551	−	3.84769i	−0.103751	−	0.142801i
$727$	−22.4771	+	30.9370i	−0.833628	+	1.14739i	0.153609	+	0.988132i	$0.450910\pi$
$727$	−22.4771	+	30.9370i	−0.833628	+	1.14739i	−0.987237	+	0.159259i	$0.949090\pi$
$728$	0.125583	+	0.0912413i	0.00465441	+	0.00338163i
$729$	−25.5121			−0.944892
$730$	−16.0467	−	11.6586i	−0.593915	−	0.431505i
$731$	29.6441	+	9.63194i	1.09643	+	0.356250i
$732$	32.0699	−	10.4201i	1.18534	−	0.385140i
$733$	−14.3302	+	10.4115i	−0.529299	+	0.384558i	−0.820095	−	0.572227i	$-0.806080\pi$
$733$	−14.3302	+	10.4115i	−0.529299	+	0.384558i	0.290797	+	0.956785i	$0.406080\pi$
$734$	29.5073	−	21.4383i	1.08913	−	0.791302i
$735$		−	4.70060i		−	0.173384i
$736$	−1.54547	−	4.75646i	−0.0569667	−	0.175325i
$737$	−14.2958			−0.526592
$738$	0.541627	+	1.85836i	0.0199376	+	0.0684071i
$739$	15.2904			0.562467			0.281233	−	0.959639i	$-0.409256\pi$
$739$	15.2904			0.562467			0.281233	+	0.959639i	$0.409256\pi$
$740$	−11.0439	−	33.9896i	−0.405982	−	1.24948i
$741$			26.8839i			0.987606i
$742$	13.5220	−	9.82434i	0.496410	−	0.360663i
$743$	−31.5468	+	22.9201i	−1.15734	+	0.840856i	−0.989439	−	0.144949i	$-0.953698\pi$
$743$	−31.5468	+	22.9201i	−1.15734	+	0.840856i	−0.167899	+	0.985804i	$0.553698\pi$
$744$	0.872394	−	0.283458i	0.0319835	−	0.0103921i
$745$	−54.7669	−	17.7948i	−2.00650	−	0.651952i
$746$	−42.0903	−	30.5804i	−1.54103	−	1.11963i
$747$	−1.62115			−0.0593147
$748$	36.1878	+	26.2920i	1.32316	+	0.961330i
$749$	10.4308	−	14.3568i	0.381134	−	0.524586i
$750$	16.5667	+	22.8021i	0.604929	+	0.832614i
$751$	7.73488	−	2.51322i	0.282250	−	0.0917086i	−0.164471	−	0.986382i	$-0.552592\pi$
$751$	7.73488	−	2.51322i	0.282250	−	0.0917086i	0.446721	+	0.894673i	$0.352592\pi$
$752$			16.6246i			0.606235i
$753$	−2.59105	−	3.56627i	−0.0944229	−	0.129962i
$754$	8.62713	−	26.5516i	0.314181	−	0.966951i
$755$	−11.1342	+	15.3250i	−0.405216	+	0.557733i
$756$	−3.17279	−	9.76484i	−0.115393	−	0.355144i
$757$	13.3351	+	4.33285i	0.484674	+	0.157480i	0.541154	−	0.840924i	$-0.317988\pi$
$757$	13.3351	+	4.33285i	0.484674	+	0.157480i	−0.0564799	+	0.998404i	$0.517988\pi$
$758$	21.2725	−	65.4700i	0.772652	−	2.37798i
$759$	−1.06230	+	3.26941i	−0.0385589	+	0.118672i
$760$	−0.894605	−	0.290675i	−0.0324507	−	0.0105439i
$761$	7.12697	+	21.9345i	0.258352	+	0.795127i	0.993151	+	0.116841i	$0.0372768\pi$
$761$	7.12697	+	21.9345i	0.258352	+	0.795127i	−0.734798	+	0.678286i	$0.762723\pi$
$762$	9.61159	−	13.2292i	0.348191	−	0.479244i
$763$	−3.57294	+	10.9964i	−0.129349	+	0.398095i
$764$	−8.21959	−	11.3133i	−0.297374	−	0.409301i
$765$		−	2.82640i		−	0.102189i
$766$	−19.8288	+	6.44276i	−0.716443	+	0.232786i
$767$	8.34526	+	11.4863i	0.301330	+	0.414745i
$768$	16.1800	−	22.2699i	0.583847	−	0.803596i
$769$	0.109378	+	0.0794677i	0.00394427	+	0.00286568i	0.589756	−	0.807582i	$-0.299224\pi$
$769$	0.109378	+	0.0794677i	0.00394427	+	0.00286568i	−0.585811	+	0.810447i	$0.699224\pi$
$770$	−16.5280			−0.595628
$771$	17.3437	+	12.6009i	0.624618	+	0.453812i
$772$	5.89399	+	1.91507i	0.212129	+	0.0689250i
$773$	12.9658	−	4.21283i	0.466346	−	0.151525i	−0.0664126	−	0.997792i	$-0.521155\pi$
$773$	12.9658	−	4.21283i	0.466346	−	0.151525i	0.532759	+	0.846267i	$0.321155\pi$
$774$	1.07557	−	0.781451i	0.0386607	−	0.0280887i
$775$	13.9502	−	10.1354i	0.501107	−	0.364076i
$776$			0.472030i			0.0169449i
$777$	3.64630	+	11.2222i	0.130810	+	0.402593i
$778$	−25.6695			−0.920298
$779$	35.4777	+	12.7385i	1.27112	+	0.456404i
$780$	−24.5506			−0.879054
$781$	−7.34488	−	22.6052i	−0.262821	−	0.808879i
$782$			8.86350i			0.316958i
$783$	−22.1175	+	16.0693i	−0.790415	+	0.574270i
$784$	−3.18671	+	2.31528i	−0.113811	+	0.0826885i
$785$	18.5615	−	6.03100i	0.662489	−	0.215256i
$786$	−16.9370	−	5.50315i	−0.604121	−	0.196291i
$787$	19.4636	+	14.1411i	0.693801	+	0.504076i	0.877907	−	0.478830i	$-0.158939\pi$
$787$	19.4636	+	14.1411i	0.693801	+	0.504076i	−0.184107	+	0.982906i	$0.558939\pi$
$788$	−8.89403			−0.316837
$789$	29.4773	+	21.4165i	1.04942	+	0.762448i
$790$	−17.1141	+	23.5556i	−0.608893	+	0.838069i
$791$	−4.46469	−	6.14511i	−0.158746	−	0.218495i
$792$	0.0268640	−	0.00872864i	0.000954571	−	0.000310159i
$793$		−	24.0763i		−	0.854974i
$794$	−20.0542	−	27.6023i	−0.711698	−	0.979568i
$795$	−12.0939	+	37.2211i	−0.428925	+	1.32010i
$796$	−12.0570	+	16.5951i	−0.427350	+	0.588196i
$797$	−2.99359	−	9.21332i	−0.106038	−	0.326353i	0.883934	−	0.467611i	$-0.154885\pi$
$797$	−2.99359	−	9.21332i	−0.106038	−	0.326353i	−0.989973	+	0.141258i	$0.954885\pi$
$798$	19.9505	+	6.48230i	0.706239	+	0.229471i
$799$	9.24353	−	28.4487i	0.327013	−	1.00644i
$800$	−4.99441	+	15.3712i	−0.176579	+	0.543455i
$801$	−2.14217	−	0.696034i	−0.0756900	−	0.0245932i
$802$	−11.8505	−	36.4720i	−0.418454	−	1.28787i
$803$	6.81775	−	9.38383i	0.240593	−	0.331148i
$804$	−5.12020	+	15.7583i	−0.180575	+	0.555754i
$805$	−0.969698	−	1.33468i	−0.0341774	−	0.0470411i
$806$		−	44.2380i		−	1.55822i
$807$	13.4287	−	4.36326i	0.472714	−	0.153594i
$808$	0.525540	+	0.723343i	0.0184884	+	0.0254471i
$809$	−32.0679	+	44.1377i	−1.12745	+	1.55180i	−0.334618	+	0.942354i	$0.608607\pi$
$809$	−32.0679	+	44.1377i	−1.12745	+	1.55180i	−0.792829	+	0.609444i	$0.791393\pi$
$810$	40.5546	+	29.4647i	1.42494	+	1.03528i
$811$	35.9494			1.26236			0.631178	−	0.775638i	$-0.282572\pi$
$811$	35.9494			1.26236			0.631178	+	0.775638i	$0.282572\pi$
$812$	−8.87753	−	6.44991i	−0.311540	−	0.226347i
$813$	−28.5062	−	9.26223i	−0.999757	−	0.324841i
$814$	39.4587	−	12.8209i	1.38303	−	0.449373i
$815$	7.04206	−	5.11636i	0.246673	−	0.179218i
$816$	−40.0892	+	29.1265i	−1.40340	+	1.01963i
$817$		−	25.8903i		−	0.905788i
$818$	−2.40617	−	7.40543i	−0.0841298	−	0.258925i
$819$	0.387425			0.0135377
$820$	−11.6329	+	32.3986i	−0.406238	+	1.13141i
$821$	9.65029			0.336797			0.168399	−	0.985719i	$-0.446140\pi$
$821$	9.65029			0.336797			0.168399	+	0.985719i	$0.446140\pi$
$822$	13.5408	+	41.6742i	0.472289	+	1.45356i
$823$		−	9.57842i		−	0.333883i	−0.985967	−	0.166941i	$-0.946611\pi$
$823$		−	9.57842i		−	0.333883i	0.985967	−	0.166941i	$-0.0533891\pi$
$824$	−0.232429	+	0.168870i	−0.00809705	+	0.00588285i
$825$	8.98763	−	6.52989i	0.312909	−	0.227342i
$826$	10.5361	−	3.42340i	0.366599	−	0.119115i
$827$	17.5544	+	5.70378i	0.610428	+	0.198340i	0.597886	−	0.801581i	$-0.296008\pi$
$827$	17.5544	+	5.70378i	0.610428	+	0.198340i	0.0125420	+	0.999921i	$0.496008\pi$
$828$	0.154068	+	0.111937i	0.00535422	+	0.00389007i
$829$	21.1690			0.735229			0.367614	−	0.929978i	$-0.380175\pi$
$829$	21.1690			0.735229			0.367614	+	0.929978i	$0.380175\pi$
$830$	−46.3029	−	33.6410i	−1.60720	−	1.16770i
$831$	28.2865	−	38.9330i	0.981246	−	1.35057i
$832$	12.4587	+	17.1480i	0.431929	+	0.594499i
$833$	6.74056	−	2.19014i	0.233547	−	0.0758839i
$834$			45.5393i			1.57690i
$835$	19.9418	+	27.4475i	0.690113	+	0.949859i
$836$	11.4814	−	35.3360i	0.397091	−	1.22212i
$837$	−25.4630	+	35.0468i	−0.880129	+	1.21139i
$838$	−20.7630	−	63.9021i	−0.717247	−	2.20746i
$839$	−47.4217	−	15.4082i	−1.63718	−	0.531951i	−0.661272	−	0.750146i	$-0.729983\pi$
$839$	−47.4217	−	15.4082i	−1.63718	−	0.531951i	−0.975905	+	0.218195i	$0.929983\pi$
$840$	−0.0876410	+	0.269731i	−0.00302390	+	0.00930661i
$841$	−0.0674367	+	0.207549i	−0.00232540	+	0.00715686i
$842$	−44.8361	−	14.5681i	−1.54515	−	0.502051i
$843$	−7.95855	−	24.4939i	−0.274107	−	0.843614i
$844$	13.4230	−	18.4752i	0.462040	−	0.635944i
$845$	5.22177	−	16.0710i	0.179635	−	0.552858i
$846$	−0.749939	−	1.03220i	−0.0257834	−	0.0354878i
$847$			1.33472i			0.0458616i
$848$	31.1903	−	10.1344i	1.07108	−	0.348015i
$849$	−19.3482	−	26.6305i	−0.664028	−	0.913957i
$850$	16.8364	−	23.1733i	0.577483	−	0.794837i
$851$	3.35036	+	2.43418i	0.114849	+	0.0834427i
$852$	−27.5486			−0.943798
$853$	−22.9708	−	16.6893i	−0.786506	−	0.571430i	0.120418	−	0.992723i	$-0.461576\pi$
$853$	−22.9708	−	16.6893i	−0.786506	−	0.571430i	−0.906925	+	0.421293i	$0.861576\pi$
$854$	−17.8669	−	5.80532i	−0.611394	−	0.198654i
$855$	−2.23278	+	0.725474i	−0.0763594	+	0.0248107i
$856$	−0.866222	+	0.629347i	−0.0296068	+	0.0215106i
$857$	−22.9231	+	16.6546i	−0.783039	+	0.568911i	−0.905890	−	0.423514i	$-0.860796\pi$
$857$	−22.9231	+	16.6546i	−0.783039	+	0.568911i	0.122851	+	0.992425i	$0.460796\pi$
$858$		−	28.5010i		−	0.973007i
$859$	13.0547	+	40.1781i	0.445419	+	1.37086i	0.882023	+	0.471206i	$0.156181\pi$
$859$	13.0547	+	40.1781i	0.445419	+	1.37086i	−0.436604	+	0.899654i	$0.643819\pi$
$860$	23.6433			0.806228
$861$	3.84077	−	10.6968i	0.130893	−	0.364548i
$862$	−36.8479			−1.25505
$863$	4.20990	+	12.9567i	0.143307	+	0.441052i	0.996789	−	0.0800688i	$-0.0255140\pi$
$863$	4.20990	+	12.9567i	0.143307	+	0.441052i	−0.853483	+	0.521121i	$0.825514\pi$
$864$		−	40.6040i		−	1.38138i
$865$	−2.98674	+	2.17000i	−0.101552	+	0.0737821i
$866$	25.7933	−	18.7399i	0.876492	−	0.636809i
$867$	56.0993	−	18.2278i	1.90523	−	0.619047i
$868$	−16.5369	−	5.37315i	−0.561298	−	0.182377i
$869$	−13.7749	−	10.0080i	−0.467280	−	0.339499i
$870$	51.0077			1.72932
$871$	9.57105	+	6.95378i	0.324303	+	0.235620i
$872$	0.410047	−	0.564381i	0.0138859	−	0.0191123i
$873$	0.692472	+	0.953107i	0.0234366	+	0.0322578i
$874$	7.00193	−	2.27506i	0.236844	−	0.0769552i
$875$		−	7.90980i		−	0.267400i
$876$	−7.90201	−	10.8762i	−0.266984	−	0.367472i
$877$	8.76329	−	26.9706i	0.295915	−	0.910734i	−0.686997	−	0.726660i	$-0.741071\pi$
$877$	8.76329	−	26.9706i	0.295915	−	0.910734i	0.982912	−	0.184074i	$-0.0589285\pi$
$878$	−0.646280	+	0.889527i	−0.0218109	+	0.0300201i
$879$	10.5936	+	32.6036i	0.357312	+	1.09969i
$880$	−30.8429	−	10.0215i	−1.03972	−	0.337824i
$881$	9.70741	−	29.8763i	0.327051	−	1.00656i	−0.643455	−	0.765484i	$-0.722500\pi$
$881$	9.70741	−	29.8763i	0.327051	−	1.00656i	0.970506	−	0.241076i	$-0.0775002\pi$
$882$	0.0934165	−	0.287506i	0.00314550	−	0.00968085i
$883$	−36.1919	−	11.7595i	−1.21796	−	0.395738i	−0.371618	−	0.928386i	$-0.621197\pi$
$883$	−36.1919	−	11.7595i	−1.21796	−	0.395738i	−0.846337	+	0.532648i	$0.821197\pi$
$884$	−11.4388	−	35.2051i	−0.384729	−	1.18407i
$885$	−15.2473	+	20.9861i	−0.512531	+	0.705438i
$886$	1.23037	−	3.78669i	0.0413351	−	0.127216i
$887$	−22.4189	−	30.8570i	−0.752754	−	1.03608i	−0.997782	−	0.0665608i	$-0.978797\pi$
$887$	−22.4189	−	30.8570i	−0.752754	−	1.03608i	0.245029	−	0.969516i	$-0.421203\pi$
$888$		−	0.711937i		−	0.0238910i
$889$	−4.36447	+	1.41810i	−0.146380	+	0.0475617i
$890$	−46.7406	−	64.3329i	−1.56675	−	2.15644i
$891$	−17.2304	+	23.7156i	−0.577240	+	0.794503i
$892$	−29.6103	−	21.5131i	−0.991425	−	0.720312i
$893$	−24.8463			−0.831449
$894$	−62.6849	−	45.5432i	−2.09650	−	1.52319i
$895$	36.8219	+	11.9641i	1.23082	+	0.399917i
$896$	0.459006	−	0.149140i	0.0153343	−	0.00498242i
$897$	2.30152	−	1.67215i	0.0768455	−	0.0558315i
$898$	27.6012	−	20.0535i	0.921064	−	0.669192i
$899$			46.2984i			1.54414i
$900$	−0.190178	−	0.585308i	−0.00633927	−	0.0195103i
$901$	−59.0091			−1.96588
$902$	−37.6117	−	13.5047i	−1.25233	−	0.449657i
$903$	−7.80616			−0.259773
$904$	0.141620	+	0.435863i	0.00471023	+	0.0144966i
$905$		−	20.3156i		−	0.675312i
$906$	−20.6202	+	14.9815i	−0.685060	+	0.497725i
$907$	35.0328	−	25.4529i	1.16325	−	0.845148i	0.173061	−	0.984911i	$-0.444634\pi$
$907$	35.0328	−	25.4529i	1.16325	−	0.845148i	0.990185	+	0.139763i	$0.0446341\pi$
$908$	−17.6654	+	5.73982i	−0.586246	+	0.190483i
$909$	2.12230	+	0.689578i	0.0703924	+	0.0228719i
$910$	11.0655	+	8.03958i	0.366819	+	0.266509i
$911$	−22.8849			−0.758211			−0.379106	−	0.925353i	$-0.623768\pi$
$911$	−22.8849			−0.758211			−0.379106	+	0.925353i	$0.623768\pi$
$912$	33.2992	+	24.1933i	1.10265	+	0.801119i
$913$	19.6726	−	27.0771i	0.651070	−	0.896120i
$914$	36.6939	+	50.5049i	1.21373	+	1.67055i
$915$	41.8358	−	13.5933i	1.38305	−	0.449380i
$916$			40.5850i			1.34097i
$917$	2.93763	+	4.04330i	0.0970090	+	0.133521i
$918$	−22.2371	+	68.4389i	−0.733935	+	2.25882i
$919$	−21.3960	+	29.4490i	−0.705788	+	0.971434i	0.294089	+	0.955778i	$0.404984\pi$
$919$	−21.3960	+	29.4490i	−0.705788	+	0.971434i	−0.999877	+	0.0156561i	$0.995016\pi$
$920$	0.0307590	+	0.0946664i	0.00101409	+	0.00312106i
$921$	−0.172763	−	0.0561341i	−0.00569273	−	0.00184968i
$922$	0.721662	−	2.22105i	0.0237667	−	0.0731463i
$923$	−6.07826	+	18.7070i	−0.200068	+	0.615747i
$924$	−10.6541	−	3.46173i	−0.350494	−	0.113883i
$925$	−4.13563	−	12.7281i	−0.135979	−	0.418499i
$926$	0.146145	−	0.201151i	0.00480261	−	0.00661023i
$927$	−0.221580	+	0.681952i	−0.00727763	+	0.0223982i
$928$	−25.5072	−	35.1077i	−0.837315	−	1.15247i
$929$			3.23933i			0.106279i	0.998587	+	0.0531394i	$0.0169228\pi$
$929$			3.23933i			0.106279i	−0.998587	+	0.0531394i	$0.983077\pi$
$930$	76.8696	−	24.9764i	2.52065	−	0.819009i
$931$	−3.46031	−	4.76270i	−0.113407	−	0.156091i
$932$	35.7154	−	49.1580i	1.16990	−	1.61022i
$933$	39.2997	+	28.5529i	1.28661	+	0.934780i
$934$	20.0547			0.656210
$935$	47.2077	+	34.2984i	1.54386	+	1.12168i
$936$	−0.0222313	−	0.00722339i	−0.000726653	−	0.000236104i
$937$	−12.0830	+	3.92599i	−0.394733	+	0.128256i	−0.499656	−	0.866224i	$-0.666540\pi$
$937$	−12.0830	+	3.92599i	−0.394733	+	0.128256i	0.104923	+	0.994480i	$0.466540\pi$
$938$	7.46816	−	5.42594i	0.243844	−	0.177163i
$939$	2.80806	−	2.04017i	0.0916375	−	0.0665785i
$940$		−	22.6898i		−	0.740061i
$941$	13.1390	+	40.4376i	0.428319	+	1.31823i	0.899780	+	0.436343i	$0.143727\pi$
$941$	13.1390	+	40.4376i	0.428319	+	1.31823i	−0.471462	+	0.881887i	$0.656273\pi$
$942$	26.2603			0.855608
$943$	−1.11614	−	3.82955i	−0.0363466	−	0.124707i
$944$	21.7372			0.707486
$945$	−4.13896	−	12.7384i	−0.134640	−	0.414381i
$946$			27.4476i			0.892398i
$947$	29.3843	−	21.3489i	0.954861	−	0.693747i	0.00290916	−	0.999996i	$-0.499074\pi$
$947$	29.3843	−	21.3489i	0.954861	−	0.693747i	0.951951	+	0.306249i	$0.0990740\pi$
$948$	−15.9655	+	11.5996i	−0.518537	+	0.376739i
$949$	−9.12899	+	2.96619i	−0.296340	+	0.0962866i
$950$	−22.6278	−	7.35221i	−0.734142	−	0.238537i
$951$	−47.7941	−	34.7245i	−1.54983	−	1.12602i
$952$	−0.427623			−0.0138593
$953$	28.6038	+	20.7819i	0.926570	+	0.673192i	0.945150	−	0.326635i	$-0.105915\pi$
$953$	28.6038	+	20.7819i	0.926570	+	0.673192i	−0.0185810	+	0.999827i	$0.505915\pi$
$954$	−1.47941	+	2.03624i	−0.0478977	+	0.0659256i
$955$	−10.7226	−	14.7584i	−0.346975	−	0.477570i
$956$	−23.0522	+	7.49011i	−0.745561	+	0.242248i
$957$			29.8284i			0.964215i
$958$	−18.2031	−	25.0545i	−0.588117	−	0.809473i
$959$	3.80008	−	11.6954i	0.122711	−	0.377665i
$960$	−22.7628	+	31.3303i	−0.734667	+	1.01118i
$961$	13.0909	+	40.2898i	0.422288	+	1.29967i
$962$	−32.6541	−	10.6100i	−1.05281	−	0.342079i
$963$	−0.825787	+	2.54151i	−0.0266106	+	0.0818991i
$964$	5.74710	−	17.6878i	0.185102	−	0.569685i
$965$	7.68882	+	2.49825i	0.247512	+	0.0804215i
$966$	−0.685952	−	2.11114i	−0.0220701	−	0.0679249i
$967$	−20.9920	+	28.8931i	−0.675059	+	0.929138i	−0.999861	−	0.0166434i	$-0.994702\pi$
$967$	−20.9920	+	28.8931i	−0.675059	+	0.929138i	0.324803	+	0.945782i	$0.394702\pi$
$968$	0.0248854	−	0.0765895i	0.000799848	−	0.00246168i
$969$	−43.5311	−	59.9155i	−1.39842	−	1.92476i
$970$			41.5921i			1.33544i
$971$	−8.46316	+	2.74985i	−0.271596	+	0.0882468i	−0.441649	−	0.897188i	$-0.645606\pi$
$971$	−8.46316	+	2.74985i	−0.271596	+	0.0882468i	0.170053	+	0.985435i	$0.445606\pi$
$972$	1.86561	+	2.56779i	0.0598394	+	0.0823619i
$973$	7.51197	−	10.3393i	0.240823	−	0.331464i
$974$	−20.9319	−	15.2079i	−0.670702	−	0.487294i
$975$	−9.19352			−0.294428
$976$	−29.8215	−	21.6666i	−0.954564	−	0.693532i
$977$	39.2554	+	12.7548i	1.25589	+	0.408063i	0.860028	−	0.510247i	$-0.170446\pi$
$977$	39.2554	+	12.7548i	1.25589	+	0.408063i	0.395862	+	0.918310i	$0.370446\pi$
$978$	11.1389	−	3.61925i	0.356183	−	0.115731i
$979$	37.6207	−	27.3331i	1.20236	−	0.873568i
$980$	4.34934	−	3.15998i	0.138935	−	0.100942i
$981$		−	1.74112i		−	0.0555897i
$982$	13.3524	+	41.0945i	0.426093	+	1.31138i
$983$	−45.2096			−1.44196			−0.720982	−	0.692954i	$-0.756309\pi$
$983$	−45.2096			−1.44196			−0.720982	+	0.692954i	$0.756309\pi$
$984$	−0.419831	+	0.542200i	−0.0133837	+	0.0172847i
$985$	−11.6024			−0.369684
$986$	23.7659	+	73.1440i	0.756861	+	2.32938i
$987$			7.49137i			0.238453i
$988$	−24.8750	+	18.0727i	−0.791378	+	0.574970i
$989$	−2.21646	+	1.61035i	−0.0704793	+	0.0512062i
$990$	2.36708	−	0.769110i	0.0752307	−	0.0244439i
$991$	−35.0231	−	11.3797i	−1.11254	−	0.361487i	−0.305626	−	0.952152i	$-0.598866\pi$
$991$	−35.0231	−	11.3797i	−1.11254	−	0.361487i	−0.806918	+	0.590664i	$0.798866\pi$
$992$	−55.6306	−	40.4180i	−1.76627	−	1.28327i
$993$	22.6151			0.717667
$994$	12.4168	+	9.02131i	0.393836	+	0.286139i
$995$	−15.7286	+	21.6485i	−0.498630	+	0.686305i
$996$	−22.8013	−	31.3833i	−0.722486	−	0.994417i
$997$	37.1503	−	12.0709i	1.17656	−	0.382288i	0.345473	−	0.938429i	$-0.387718\pi$
$997$	37.1503	−	12.0709i	1.17656	−	0.382288i	0.831088	+	0.556141i	$0.187718\pi$
$998$			26.9856i			0.854213i
$999$	19.7626	+	27.2009i	0.625261	+	0.860598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.n.a.64.18	✓	88
41.25	even	10	inner	287.2.n.a.148.18	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.n.a.64.18	✓	88	1.1	even	1	trivial
287.2.n.a.148.18	yes	88	41.25	even	10	inner

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.620352 + 1.90925i) q^{2} +1.77499i q^{3} +(-1.64235 + 1.19324i) q^{4} +(-2.14247 + 1.55660i) q^{5} +(-3.38889 + 1.10112i) q^{6} +(0.951057 + 0.309017i) q^{7} +(-0.0488123 - 0.0354642i) q^{8} -0.150586 q^{9} +O(q^{10})\)	\(q+(0.620352 + 1.90925i) q^{2} +1.77499i q^{3} +(-1.64235 + 1.19324i) q^{4} +(-2.14247 + 1.55660i) q^{5} +(-3.38889 + 1.10112i) q^{6} +(0.951057 + 0.309017i) q^{7} +(-0.0488123 - 0.0354642i) q^{8} -0.150586 q^{9} +(-4.30101 - 3.12487i) q^{10} +(1.82737 - 2.51516i) q^{11} +(-2.11798 - 2.91515i) q^{12} +(-2.44685 + 0.795030i) q^{13} +2.00750i q^{14} +(-2.76294 - 3.80287i) q^{15} +(-1.21721 + 3.74620i) q^{16} +(4.16590 - 5.73387i) q^{17} +(-0.0934165 - 0.287506i) q^{18} +(-5.59889 - 1.81919i) q^{19} +(1.66130 - 5.11295i) q^{20} +(-0.548502 + 1.68811i) q^{21} +(5.93566 + 1.92861i) q^{22} +(0.192505 + 0.592470i) q^{23} +(0.0629486 - 0.0866413i) q^{24} +(0.622110 - 1.91466i) q^{25} +(-3.03582 - 4.17844i) q^{26} +5.05768i q^{27} +(-1.93070 + 0.627321i) q^{28} +(3.17721 + 4.37305i) q^{29} +(5.54661 - 7.63425i) q^{30} +(6.92942 + 5.03452i) q^{31} -8.02819 q^{32} +(4.46437 + 3.24356i) q^{33} +(13.5317 + 4.39671i) q^{34} +(-2.51863 + 0.818352i) q^{35} +(0.247315 - 0.179685i) q^{36} +(5.37814 - 3.90745i) q^{37} -11.8182i q^{38} +(-1.41117 - 4.34314i) q^{39} +0.159783 q^{40} +(-6.40013 - 0.195652i) q^{41} -3.56329 q^{42} +(1.35901 + 4.18262i) q^{43} +6.31124i q^{44} +(0.322627 - 0.234403i) q^{45} +(-1.01175 + 0.735080i) q^{46} +(4.01395 - 1.30421i) q^{47} +(-6.64946 - 2.16054i) q^{48} +(0.809017 + 0.587785i) q^{49} +4.04148 q^{50} +(10.1775 + 7.39442i) q^{51} +(3.06993 - 4.22539i) q^{52} +(-4.89382 - 6.73576i) q^{53} +(-9.65635 + 3.13754i) q^{54} +8.23313i q^{55} +(-0.0354642 - 0.0488123i) q^{56} +(3.22904 - 9.93797i) q^{57} +(-6.37824 + 8.77890i) q^{58} +(-1.70530 - 5.24839i) q^{59} +(9.07544 + 2.94879i) q^{60} +(-2.89181 + 8.90009i) q^{61} +(-5.31345 + 16.3531i) q^{62} +(-0.143216 - 0.0465338i) q^{63} +(-2.54587 - 7.83538i) q^{64} +(4.00477 - 5.51210i) q^{65} +(-3.42327 + 10.5357i) q^{66} +(-2.70283 - 3.72013i) q^{67} +14.3879i q^{68} +(-1.05163 + 0.341695i) q^{69} +(-3.12487 - 4.30101i) q^{70} +(4.49380 - 6.18519i) q^{71} +(0.00735047 + 0.00534043i) q^{72} +3.73091 q^{73} +(10.7966 + 7.84420i) q^{74} +(3.39850 + 1.10424i) q^{75} +(11.3661 - 3.69306i) q^{76} +(2.51516 - 1.82737i) q^{77} +(7.41669 - 5.38854i) q^{78} -5.47674i q^{79} +(-3.22348 - 9.92084i) q^{80} -9.42908 q^{81} +(-3.59679 - 12.3408i) q^{82} +10.7656 q^{83} +(-1.11349 - 3.42697i) q^{84} +18.7693i q^{85} +(-7.14257 + 5.18938i) q^{86} +(-7.76212 + 5.63951i) q^{87} +(-0.178396 + 0.0579643i) q^{88} +(14.2255 + 4.62216i) q^{89} +(0.647674 + 0.470563i) q^{90} -2.57277 q^{91} +(-1.02312 - 0.743338i) q^{92} +(-8.93621 + 12.2996i) q^{93} +(4.98012 + 6.85455i) q^{94} +(14.8272 - 4.81766i) q^{95} -14.2499i q^{96} +(-4.59850 - 6.32930i) q^{97} +(-0.620352 + 1.90925i) q^{98} +(-0.275177 + 0.378748i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9}+O(q^{10}) \) 88 * q - 24 * q^4 + 8 * q^5 + 10 * q^6 - 18 * q^8 - 116 * q^9	\( 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9} + 36 q^{10} - 10 q^{11} + 20 q^{15} - 12 q^{16} - 10 q^{17} + 20 q^{18} + 30 q^{19} - 30 q^{20} + 4 q^{21} - 20 q^{22} - 12 q^{23} + 60 q^{24} - 50 q^{25} - 30 q^{26} + 2 q^{31} + 24 q^{32} - 46 q^{33} + 50 q^{34} + 86 q^{36} - 48 q^{37} + 16 q^{39} - 60 q^{40} - 24 q^{41} - 4 q^{42} + 22 q^{43} - 16 q^{45} + 20 q^{46} + 20 q^{48} + 22 q^{49} - 16 q^{50} + 8 q^{51} + 70 q^{52} - 30 q^{54} + 8 q^{57} - 90 q^{58} - 4 q^{59} - 50 q^{60} - 64 q^{61} - 44 q^{62} + 14 q^{64} + 80 q^{65} - 26 q^{66} + 10 q^{67} + 40 q^{71} + 18 q^{72} + 124 q^{73} + 80 q^{74} + 70 q^{75} - 190 q^{76} + 8 q^{77} + 74 q^{78} + 26 q^{80} + 144 q^{81} - 58 q^{82} - 60 q^{83} + 26 q^{84} + 10 q^{86} + 8 q^{87} + 160 q^{88} - 164 q^{90} - 40 q^{91} - 156 q^{92} - 20 q^{93} + 10 q^{94} + 80 q^{95} - 90 q^{97} - 40 q^{99}+O(q^{100}) \) 88 * q - 24 * q^4 + 8 * q^5 + 10 * q^6 - 18 * q^8 - 116 * q^9 + 36 * q^10 - 10 * q^11 + 20 * q^15 - 12 * q^16 - 10 * q^17 + 20 * q^18 + 30 * q^19 - 30 * q^20 + 4 * q^21 - 20 * q^22 - 12 * q^23 + 60 * q^24 - 50 * q^25 - 30 * q^26 + 2 * q^31 + 24 * q^32 - 46 * q^33 + 50 * q^34 + 86 * q^36 - 48 * q^37 + 16 * q^39 - 60 * q^40 - 24 * q^41 - 4 * q^42 + 22 * q^43 - 16 * q^45 + 20 * q^46 + 20 * q^48 + 22 * q^49 - 16 * q^50 + 8 * q^51 + 70 * q^52 - 30 * q^54 + 8 * q^57 - 90 * q^58 - 4 * q^59 - 50 * q^60 - 64 * q^61 - 44 * q^62 + 14 * q^64 + 80 * q^65 - 26 * q^66 + 10 * q^67 + 40 * q^71 + 18 * q^72 + 124 * q^73 + 80 * q^74 + 70 * q^75 - 190 * q^76 + 8 * q^77 + 74 * q^78 + 26 * q^80 + 144 * q^81 - 58 * q^82 - 60 * q^83 + 26 * q^84 + 10 * q^86 + 8 * q^87 + 160 * q^88 - 164 * q^90 - 40 * q^91 - 156 * q^92 - 20 * q^93 + 10 * q^94 + 80 * q^95 - 90 * q^97 - 40 * q^99

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