LMFDB - Embedded newform 287.2.e.d.165.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(165,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("287.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.e (of order $3$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.14
Character	$\chi$	$=$	287.165
Dual form			287.2.e.d.247.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.889478 + 1.54062i) q^{2} +(-0.603897 + 1.04598i) q^{3} +(-0.582342 + 1.00865i) q^{4} +(1.26642 + 2.19350i) q^{5} -2.14861 q^{6} +(-0.862133 - 2.50135i) q^{7} +1.48599 q^{8} +(0.770616 + 1.33475i) q^{9} +O(q^{10})$	\(q+(0.889478 + 1.54062i) q^{2} +(-0.603897 + 1.04598i) q^{3} +(-0.582342 + 1.00865i) q^{4} +(1.26642 + 2.19350i) q^{5} -2.14861 q^{6} +(-0.862133 - 2.50135i) q^{7} +1.48599 q^{8} +(0.770616 + 1.33475i) q^{9} +(-2.25290 + 3.90213i) q^{10} +(-2.34721 + 4.06549i) q^{11} +(-0.703349 - 1.21824i) q^{12} -2.97799 q^{13} +(3.08678 - 3.55311i) q^{14} -3.05914 q^{15} +(2.48644 + 4.30664i) q^{16} +(3.50594 - 6.07246i) q^{17} +(-1.37089 + 2.37446i) q^{18} +(-1.39243 - 2.41176i) q^{19} -2.94995 q^{20} +(3.13700 + 0.608781i) q^{21} -8.35117 q^{22} +(-2.02178 - 3.50182i) q^{23} +(-0.897386 + 1.55432i) q^{24} +(-0.707620 + 1.22563i) q^{25} +(-2.64886 - 4.58795i) q^{26} -5.48488 q^{27} +(3.02503 + 0.587051i) q^{28} +7.66082 q^{29} +(-2.72104 - 4.71298i) q^{30} +(-0.621063 + 1.07571i) q^{31} +(-2.93728 + 5.08751i) q^{32} +(-2.83495 - 4.91028i) q^{33} +12.4738 q^{34} +(4.39487 - 5.05883i) q^{35} -1.79505 q^{36} +(2.74185 + 4.74902i) q^{37} +(2.47707 - 4.29042i) q^{38} +(1.79840 - 3.11492i) q^{39} +(1.88188 + 3.25952i) q^{40} +1.00000 q^{41} +(1.85239 + 5.37442i) q^{42} +9.18117 q^{43} +(-2.73376 - 4.73501i) q^{44} +(-1.95184 + 3.38069i) q^{45} +(3.59666 - 6.22959i) q^{46} +(3.88520 + 6.72936i) q^{47} -6.00622 q^{48} +(-5.51345 + 4.31298i) q^{49} -2.51765 q^{50} +(4.23445 + 7.33428i) q^{51} +(1.73421 - 3.00374i) q^{52} +(4.72129 - 8.17752i) q^{53} +(-4.87868 - 8.45011i) q^{54} -11.8902 q^{55} +(-1.28112 - 3.71697i) q^{56} +3.36354 q^{57} +(6.81413 + 11.8024i) q^{58} +(-0.816347 + 1.41395i) q^{59} +(1.78147 - 3.08559i) q^{60} +(-6.97655 - 12.0837i) q^{61} -2.20969 q^{62} +(2.67429 - 3.07831i) q^{63} -0.504809 q^{64} +(-3.77137 - 6.53221i) q^{65} +(5.04325 - 8.73517i) q^{66} +(1.87912 - 3.25473i) q^{67} +(4.08331 + 7.07250i) q^{68} +4.88379 q^{69} +(11.7029 + 2.27112i) q^{70} -6.77038 q^{71} +(1.14513 + 1.98342i) q^{72} +(-1.35286 + 2.34322i) q^{73} +(-4.87762 + 8.44829i) q^{74} +(-0.854660 - 1.48031i) q^{75} +3.24348 q^{76} +(12.1928 + 2.36619i) q^{77} +6.39855 q^{78} +(-6.23835 - 10.8051i) q^{79} +(-6.29774 + 10.9080i) q^{80} +(1.00045 - 1.73283i) q^{81} +(0.889478 + 1.54062i) q^{82} -0.292604 q^{83} +(-2.44085 + 2.80960i) q^{84} +17.7599 q^{85} +(8.16645 + 14.1447i) q^{86} +(-4.62635 + 8.01307i) q^{87} +(-3.48794 + 6.04128i) q^{88} +(-1.49749 - 2.59373i) q^{89} -6.94448 q^{90} +(2.56742 + 7.44898i) q^{91} +4.70947 q^{92} +(-0.750117 - 1.29924i) q^{93} +(-6.91159 + 11.9712i) q^{94} +(3.52679 - 6.10858i) q^{95} +(-3.54763 - 6.14467i) q^{96} +11.1466 q^{97} +(-11.5488 - 4.65784i) q^{98} -7.23520 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9}+O(q^{10}) $ 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9} + 2 q^{10} - 15 q^{11} - 4 q^{12} - 10 q^{13} + 21 q^{14} + 48 q^{15} - 33 q^{16} - 4 q^{17} - 10 q^{18} - 5 q^{19} - 52 q^{20} + 12 q^{21} + 32 q^{22} - 12 q^{23} - 16 q^{24} - 24 q^{25} - 31 q^{26} - 22 q^{27} + 60 q^{28} + 28 q^{29} + 33 q^{30} + 3 q^{31} - 16 q^{32} - 4 q^{33} - 48 q^{34} + 45 q^{35} + 114 q^{36} - 24 q^{37} - 45 q^{39} - 36 q^{40} + 34 q^{41} + 65 q^{42} + 28 q^{43} + 9 q^{44} + 21 q^{45} - 44 q^{46} - 19 q^{47} - 120 q^{48} - 10 q^{49} - 8 q^{50} - 2 q^{51} + 25 q^{52} - 4 q^{53} - 68 q^{54} + 18 q^{55} + 25 q^{56} - 24 q^{57} + q^{58} + 27 q^{59} - 66 q^{60} + q^{61} - 46 q^{62} + 37 q^{63} + 150 q^{64} - 22 q^{65} + 16 q^{66} - 49 q^{67} - 45 q^{68} + 24 q^{69} + 73 q^{70} + 80 q^{71} + 23 q^{72} + 14 q^{73} - 33 q^{74} - 27 q^{75} - 18 q^{76} - 20 q^{77} - 24 q^{78} - 61 q^{79} + 82 q^{80} - 53 q^{81} - 3 q^{82} - 36 q^{83} + 188 q^{84} - 26 q^{85} + 4 q^{86} + 17 q^{87} - 74 q^{88} - 18 q^{89} - 40 q^{90} + 7 q^{91} + 56 q^{92} + 36 q^{93} + 5 q^{94} - 20 q^{95} - 148 q^{96} + 52 q^{97} + 142 q^{98} + 76 q^{99}+O(q^{100}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9 + 2 * q^10 - 15 * q^11 - 4 * q^12 - 10 * q^13 + 21 * q^14 + 48 * q^15 - 33 * q^16 - 4 * q^17 - 10 * q^18 - 5 * q^19 - 52 * q^20 + 12 * q^21 + 32 * q^22 - 12 * q^23 - 16 * q^24 - 24 * q^25 - 31 * q^26 - 22 * q^27 + 60 * q^28 + 28 * q^29 + 33 * q^30 + 3 * q^31 - 16 * q^32 - 4 * q^33 - 48 * q^34 + 45 * q^35 + 114 * q^36 - 24 * q^37 - 45 * q^39 - 36 * q^40 + 34 * q^41 + 65 * q^42 + 28 * q^43 + 9 * q^44 + 21 * q^45 - 44 * q^46 - 19 * q^47 - 120 * q^48 - 10 * q^49 - 8 * q^50 - 2 * q^51 + 25 * q^52 - 4 * q^53 - 68 * q^54 + 18 * q^55 + 25 * q^56 - 24 * q^57 + q^58 + 27 * q^59 - 66 * q^60 + q^61 - 46 * q^62 + 37 * q^63 + 150 * q^64 - 22 * q^65 + 16 * q^66 - 49 * q^67 - 45 * q^68 + 24 * q^69 + 73 * q^70 + 80 * q^71 + 23 * q^72 + 14 * q^73 - 33 * q^74 - 27 * q^75 - 18 * q^76 - 20 * q^77 - 24 * q^78 - 61 * q^79 + 82 * q^80 - 53 * q^81 - 3 * q^82 - 36 * q^83 + 188 * q^84 - 26 * q^85 + 4 * q^86 + 17 * q^87 - 74 * q^88 - 18 * q^89 - 40 * q^90 + 7 * q^91 + 56 * q^92 + 36 * q^93 + 5 * q^94 - 20 * q^95 - 148 * q^96 + 52 * q^97 + 142 * q^98 + 76 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.889478	+	1.54062i	0.628956	+	1.08938i	0.987762	+	0.155971i	$0.0498507\pi$
$2$	0.889478	+	1.54062i	0.628956	+	1.08938i	−0.358806	+	0.933412i	$0.616816\pi$
$3$	−0.603897	+	1.04598i	−0.348660	+	0.603897i	−0.986012	−	0.166676i	$-0.946697\pi$
$3$	−0.603897	+	1.04598i	−0.348660	+	0.603897i	0.637352	+	0.770573i	$0.280030\pi$
$4$	−0.582342	+	1.00865i	−0.291171	+	0.504323i
$5$	1.26642	+	2.19350i	0.566359	+	0.980962i	0.996922	+	0.0784014i	$0.0249816\pi$
$5$	1.26642	+	2.19350i	0.566359	+	0.980962i	−0.430563	+	0.902560i	$0.641685\pi$
$6$	−2.14861			−0.877168
$7$	−0.862133	−	2.50135i	−0.325856	−	0.945420i
$7$	−0.862133	−	2.50135i	−0.325856	−	0.945420i
$8$	1.48599			0.525377
$9$	0.770616	+	1.33475i	0.256872	+	0.444916i
$10$	−2.25290	+	3.90213i	−0.712429	+	1.23396i
$11$	−2.34721	+	4.06549i	−0.707711	+	1.22579i	0.257993	+	0.966147i	$0.416939\pi$
$11$	−2.34721	+	4.06549i	−0.707711	+	1.22579i	−0.965704	+	0.259645i	$0.916395\pi$
$12$	−0.703349	−	1.21824i	−0.203039	−	0.351675i
$13$	−2.97799			−0.825946			−0.412973	−	0.910743i	$-0.635510\pi$
$13$	−2.97799			−0.825946			−0.412973	+	0.910743i	$0.635510\pi$
$14$	3.08678	−	3.55311i	0.824976	−	0.949609i
$15$	−3.05914			−0.789867
$16$	2.48644	+	4.30664i	0.621610	+	1.07666i
$17$	3.50594	−	6.07246i	0.850315	−	1.47279i	−0.0306101	−	0.999531i	$-0.509745\pi$
$17$	3.50594	−	6.07246i	0.850315	−	1.47279i	0.880925	−	0.473257i	$-0.156922\pi$
$18$	−1.37089	+	2.37446i	−0.323122	+	0.559664i
$19$	−1.39243	−	2.41176i	−0.319445	−	0.553296i	0.660927	−	0.750450i	$-0.270163\pi$
$19$	−1.39243	−	2.41176i	−0.319445	−	0.553296i	−0.980372	+	0.197154i	$0.936830\pi$
$20$	−2.94995			−0.659629
$21$	3.13700	+	0.608781i	0.684549	+	0.132847i
$22$	−8.35117			−1.78048
$23$	−2.02178	−	3.50182i	−0.421570	−	0.730181i	0.574523	−	0.818488i	$-0.305188\pi$
$23$	−2.02178	−	3.50182i	−0.421570	−	0.730181i	−0.996093	+	0.0883075i	$0.971854\pi$
$24$	−0.897386	+	1.55432i	−0.183178	+	0.317274i
$25$	−0.707620	+	1.22563i	−0.141524	+	0.245127i
$26$	−2.64886	−	4.58795i	−0.519483	−	0.899772i
$27$	−5.48488			−1.05556
$28$	3.02503	+	0.587051i	0.571676	+	0.110942i
$29$	7.66082			1.42258			0.711289	−	0.702900i	$-0.248112\pi$
$29$	7.66082			1.42258			0.711289	+	0.702900i	$0.248112\pi$
$30$	−2.72104	−	4.71298i	−0.496791	−	0.860468i
$31$	−0.621063	+	1.07571i	−0.111546	+	0.193204i	−0.916394	−	0.400278i	$-0.868914\pi$
$31$	−0.621063	+	1.07571i	−0.111546	+	0.193204i	0.804848	+	0.593482i	$0.202247\pi$
$32$	−2.93728	+	5.08751i	−0.519242	+	0.899353i
$33$	−2.83495	−	4.91028i	−0.493501	−	0.854770i
$34$	12.4738			2.13924
$35$	4.39487	−	5.05883i	0.742869	−	0.855098i
$36$	−1.79505			−0.299175
$37$	2.74185	+	4.74902i	0.450757	+	0.780734i	0.998433	−	0.0559566i	$-0.0178208\pi$
$37$	2.74185	+	4.74902i	0.450757	+	0.780734i	−0.547676	+	0.836690i	$0.684488\pi$
$38$	2.47707	−	4.29042i	0.401834	−	0.695997i
$39$	1.79840	−	3.11492i	0.287974	−	0.498786i
$40$	1.88188	+	3.25952i	0.297552	+	0.515375i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	1.85239	+	5.37442i	0.285830	+	0.829291i
$43$	9.18117			1.40012			0.700058	−	0.714086i	$-0.253157\pi$
$43$	9.18117			1.40012			0.700058	+	0.714086i	$0.253157\pi$
$44$	−2.73376	−	4.73501i	−0.412130	−	0.713830i
$45$	−1.95184	+	3.38069i	−0.290963	+	0.503963i
$46$	3.59666	−	6.22959i	0.530298	−	0.918503i
$47$	3.88520	+	6.72936i	0.566714	+	0.981578i	0.996888	+	0.0788315i	$0.0251189\pi$
$47$	3.88520	+	6.72936i	0.566714	+	0.981578i	−0.430174	+	0.902746i	$0.641548\pi$
$48$	−6.00622			−0.866923
$49$	−5.51345	+	4.31298i	−0.787636	+	0.616141i
$50$	−2.51765			−0.356050
$51$	4.23445	+	7.33428i	0.592942	+	1.02701i
$52$	1.73421	−	3.00374i	0.240491	−	0.416543i
$53$	4.72129	−	8.17752i	0.648519	−	1.12327i	−0.334957	−	0.942233i	$-0.608722\pi$
$53$	4.72129	−	8.17752i	0.648519	−	1.12327i	0.983477	−	0.181035i	$-0.0579447\pi$
$54$	−4.87868	−	8.45011i	−0.663904	−	1.14991i
$55$	−11.8902			−1.60327
$56$	−1.28112	−	3.71697i	−0.171197	−	0.496702i
$57$	3.36354			0.445512
$58$	6.81413	+	11.8024i	0.894739	+	1.54973i
$59$	−0.816347	+	1.41395i	−0.106279	+	0.184081i	−0.914260	−	0.405128i	$-0.867227\pi$
$59$	−0.816347	+	1.41395i	−0.106279	+	0.184081i	0.807981	+	0.589209i	$0.200560\pi$
$60$	1.78147	−	3.08559i	0.229986	−	0.398348i
$61$	−6.97655	−	12.0837i	−0.893256	−	1.54717i	−0.835948	−	0.548809i	$-0.815082\pi$
$61$	−6.97655	−	12.0837i	−0.893256	−	1.54717i	−0.0573082	−	0.998357i	$-0.518252\pi$
$62$	−2.20969			−0.280631
$63$	2.67429	−	3.07831i	0.336929	−	0.387830i
$64$	−0.504809			−0.0631012
$65$	−3.77137	−	6.53221i	−0.467781	−	0.810221i
$66$	5.04325	−	8.73517i	0.620781	−	1.07522i
$67$	1.87912	−	3.25473i	0.229571	−	0.397629i	−0.728110	−	0.685460i	$-0.759601\pi$
$67$	1.87912	−	3.25473i	0.229571	−	0.397629i	0.957681	+	0.287832i	$0.0929344\pi$
$68$	4.08331	+	7.07250i	0.495174	+	0.857666i
$69$	4.88379			0.587939
$70$	11.7029	+	2.27112i	1.39876	+	0.271450i
$71$	−6.77038			−0.803497			−0.401748	−	0.915750i	$-0.631597\pi$
$71$	−6.77038			−0.803497			−0.401748	+	0.915750i	$0.631597\pi$
$72$	1.14513	+	1.98342i	0.134955	+	0.233748i
$73$	−1.35286	+	2.34322i	−0.158340	+	0.274254i	−0.934270	−	0.356565i	$-0.883948\pi$
$73$	−1.35286	+	2.34322i	−0.158340	+	0.274254i	0.775930	+	0.630819i	$0.217281\pi$
$74$	−4.87762	+	8.44829i	−0.567012	+	0.982094i
$75$	−0.854660	−	1.48031i	−0.0986876	−	0.170932i
$76$	3.24348			0.372053
$77$	12.1928	+	2.36619i	1.38950	+	0.269653i
$78$	6.39855			0.724493
$79$	−6.23835	−	10.8051i	−0.701870	−	1.21567i	−0.967809	−	0.251684i	$-0.919016\pi$
$79$	−6.23835	−	10.8051i	−0.701870	−	1.21567i	0.265940	−	0.963990i	$-0.414318\pi$
$80$	−6.29774	+	10.9080i	−0.704108	+	1.21955i
$81$	1.00045	−	1.73283i	0.111161	−	0.192537i
$82$	0.889478	+	1.54062i	0.0982264	+	0.170133i
$83$	−0.292604			−0.0321175			−0.0160587	−	0.999871i	$-0.505112\pi$
$83$	−0.292604			−0.0321175			−0.0160587	+	0.999871i	$0.505112\pi$
$84$	−2.44085	+	2.80960i	−0.266319	+	0.306553i
$85$	17.7599			1.92633
$86$	8.16645	+	14.1447i	0.880611	+	1.52526i
$87$	−4.62635	+	8.01307i	−0.495996	+	0.859091i
$88$	−3.48794	+	6.04128i	−0.371815	+	0.644003i
$89$	−1.49749	−	2.59373i	−0.158733	−	0.274934i	0.775679	−	0.631128i	$-0.217408\pi$
$89$	−1.49749	−	2.59373i	−0.158733	−	0.274934i	−0.934412	+	0.356194i	$0.884074\pi$
$90$	−6.94448			−0.732013
$91$	2.56742	+	7.44898i	0.269139	+	0.780865i
$92$	4.70947			0.490996
$93$	−0.750117	−	1.29924i	−0.0777835	−	0.134725i
$94$	−6.91159	+	11.9712i	−0.712876	+	1.23474i
$95$	3.52679	−	6.10858i	0.361841	−	0.626728i
$96$	−3.54763	−	6.14467i	−0.362078	−	0.627137i
$97$	11.1466			1.13176			0.565882	−	0.824486i	$-0.308536\pi$
$97$	11.1466			1.13176			0.565882	+	0.824486i	$0.308536\pi$
$98$	−11.5488	−	4.65784i	−1.16660	−	0.470513i
$99$	−7.23520			−0.727165
$100$	−0.824154	−	1.42748i	−0.0824154	−	0.142748i
$101$	0.860825	−	1.49099i	0.0856553	−	0.148359i	−0.820015	−	0.572342i	$-0.806035\pi$
$101$	0.860825	−	1.49099i	0.0856553	−	0.148359i	0.905670	+	0.423983i	$0.139368\pi$
$102$	−7.53290	+	13.0474i	−0.745868	+	1.29188i
$103$	−7.52163	−	13.0278i	−0.741128	−	1.28367i	−0.951982	−	0.306154i	$-0.900958\pi$
$103$	−7.52163	−	13.0278i	−0.741128	−	1.28367i	0.210854	−	0.977518i	$-0.432376\pi$
$104$	−4.42526			−0.433933
$105$	2.63739	+	7.65197i	0.257383	+	0.746756i
$106$	16.7979			1.63156
$107$	−0.868396	−	1.50411i	−0.0839510	−	0.145407i	0.820993	−	0.570939i	$-0.193421\pi$
$107$	−0.868396	−	1.50411i	−0.0839510	−	0.145407i	−0.904944	+	0.425531i	$0.860087\pi$
$108$	3.19407	−	5.53230i	0.307350	−	0.532346i
$109$	−9.05242	+	15.6792i	−0.867064	+	1.50180i	−0.00208157	+	0.999998i	$0.500663\pi$
$109$	−9.05242	+	15.6792i	−0.867064	+	1.50180i	−0.864983	+	0.501802i	$0.832671\pi$
$110$	−10.5761	−	18.3183i	−1.00839	−	1.74658i
$111$	−6.62317			−0.628644
$112$	8.62875	−	9.93234i	0.815340	−	0.938518i
$113$	−15.2644			−1.43595			−0.717976	−	0.696068i	$-0.754931\pi$
$113$	−15.2644			−1.43595			−0.717976	+	0.696068i	$0.754931\pi$
$114$	2.99179	+	5.18194i	0.280207	+	0.485333i
$115$	5.12083	−	8.86953i	0.477520	−	0.827088i
$116$	−4.46121	+	7.72705i	−0.414213	+	0.717439i
$117$	−2.29489	−	3.97486i	−0.212162	−	0.367476i
$118$	−2.90449			−0.267380
$119$	−18.2119	−	3.53429i	−1.66948	−	0.323988i
$120$	−4.54585			−0.414978
$121$	−5.51881	−	9.55886i	−0.501710	−	0.868987i
$122$	12.4110	−	21.4965i	1.12364	−	1.94620i
$123$	−0.603897	+	1.04598i	−0.0544516	+	0.0943129i
$124$	−0.723342	−	1.25287i	−0.0649581	−	0.112511i
$125$	9.07960			0.812104
$126$	7.12122	+	1.38198i	0.634409	+	0.123116i
$127$	5.98507			0.531090			0.265545	−	0.964099i	$-0.414448\pi$
$127$	5.98507			0.531090			0.265545	+	0.964099i	$0.414448\pi$
$128$	5.42553	+	9.39730i	0.479554	+	0.830612i
$129$	−5.54449	+	9.60333i	−0.488165	+	0.845526i
$130$	6.70911	−	11.6205i	0.588428	−	1.01919i
$131$	3.49696	+	6.05691i	0.305531	+	0.529195i	0.977379	−	0.211494i	$-0.0678328\pi$
$131$	3.49696	+	6.05691i	0.305531	+	0.529195i	−0.671849	+	0.740688i	$0.734499\pi$
$132$	6.60364			0.574773
$133$	−4.83218	+	5.56221i	−0.419004	+	0.482305i
$134$	6.68574			0.577560
$135$	−6.94614	−	12.0311i	−0.597828	−	1.03547i
$136$	5.20979	−	9.02362i	0.446736	−	0.773769i
$137$	−4.15488	+	7.19646i	−0.354975	+	0.614835i	−0.987114	−	0.160020i	$-0.948844\pi$
$137$	−4.15488	+	7.19646i	−0.354975	+	0.614835i	0.632138	+	0.774856i	$0.282177\pi$
$138$	4.34402	+	7.52406i	0.369788	+	0.640491i
$139$	−5.14052			−0.436013			−0.218007	−	0.975947i	$-0.569955\pi$
$139$	−5.14052			−0.436013			−0.218007	+	0.975947i	$0.569955\pi$
$140$	2.54325	+	7.37884i	0.214944	+	0.623626i
$141$	−9.38504			−0.790363
$142$	−6.02211	−	10.4306i	−0.505364	−	0.875316i
$143$	6.98997	−	12.1070i	0.584531	−	1.01244i
$144$	−3.83218	+	6.63753i	−0.319348	+	0.553128i
$145$	9.70178	+	16.8040i	0.805689	+	1.39549i
$146$	−4.81336			−0.398356
$147$	−1.18174	−	8.37156i	−0.0974681	−	0.690475i
$148$	−6.38677			−0.524989
$149$	−7.51583	−	13.0178i	−0.615721	−	1.06646i	−0.990258	−	0.139248i	$-0.955532\pi$
$149$	−7.51583	−	13.0178i	−0.615721	−	1.06646i	0.374537	−	0.927212i	$-0.377802\pi$
$150$	1.52040	−	2.63341i	0.124140	−	0.215017i
$151$	−2.73147	+	4.73104i	−0.222284	+	0.385006i	−0.955501	−	0.294988i	$-0.904684\pi$
$151$	−2.73147	+	4.73104i	−0.222284	+	0.385006i	0.733217	+	0.679994i	$0.238018\pi$
$152$	−2.06914	−	3.58385i	−0.167829	−	0.290689i
$153$	10.8069			0.873688
$154$	7.19982	+	20.8892i	0.580178	+	1.68330i
$155$	−3.14610			−0.252701
$156$	2.09457	+	3.62790i	0.167700	+	0.290464i
$157$	−10.9534	+	18.9719i	−0.874177	+	1.51412i	−0.0165404	+	0.999863i	$0.505265\pi$
$157$	−10.9534	+	18.9719i	−0.874177	+	1.51412i	−0.857637	+	0.514256i	$0.828068\pi$
$158$	11.0978	−	19.2219i	0.882890	−	1.52921i
$159$	5.70235	+	9.87676i	0.452226	+	0.783278i
$160$	−14.8793			−1.17631
$161$	−7.01623	+	8.07620i	−0.552956	+	0.636494i
$162$	3.55952			0.279662
$163$	−2.21627	−	3.83869i	−0.173592	−	0.300670i	0.766081	−	0.642744i	$-0.222204\pi$
$163$	−2.21627	−	3.83869i	−0.173592	−	0.300670i	−0.939673	+	0.342074i	$0.888871\pi$
$164$	−0.582342	+	1.00865i	−0.0454733	+	0.0787620i
$165$	7.18045	−	12.4369i	0.558998	−	0.968212i
$166$	−0.260265	−	0.450792i	−0.0202005	−	0.0349882i
$167$	−18.3642			−1.42107			−0.710534	−	0.703663i	$-0.751547\pi$
$167$	−18.3642			−1.42107			−0.710534	+	0.703663i	$0.751547\pi$
$168$	4.66155	+	0.904643i	0.359646	+	0.0697947i
$169$	−4.13158			−0.317814
$170$	15.7970	+	27.3613i	1.21158	+	2.09851i
$171$	2.14606	−	3.71708i	0.164113	−	0.284252i
$172$	−5.34658	+	9.26055i	−0.407673	+	0.706111i
$173$	−7.52914	−	13.0409i	−0.572430	−	0.991478i	−0.996316	−	0.0857620i	$-0.972668\pi$
$173$	−7.52914	−	13.0409i	−0.572430	−	0.991478i	0.423886	−	0.905716i	$-0.360666\pi$
$174$	−16.4601			−1.24784
$175$	3.67580	+	0.713343i	0.277864	+	0.0539236i
$176$	−23.3448			−1.75968
$177$	−0.985979	−	1.70777i	−0.0741107	−	0.128364i
$178$	2.66397	−	4.61412i	0.199673	−	0.345843i
$179$	−8.06462	+	13.9683i	−0.602778	+	1.04404i	0.389620	+	0.920976i	$0.372606\pi$
$179$	−8.06462	+	13.9683i	−0.602778	+	1.04404i	−0.992398	+	0.123067i	$0.960727\pi$
$180$	−2.27328	−	3.93743i	−0.169440	−	0.293479i
$181$	−2.53296			−0.188273			−0.0941366	−	0.995559i	$-0.530009\pi$
$181$	−2.53296			−0.188273			−0.0941366	+	0.995559i	$0.530009\pi$
$182$	−9.19239	+	10.5811i	−0.681385	+	0.784325i
$183$	16.8525			1.24577
$184$	−3.00434	−	5.20368i	−0.221483	−	0.383620i
$185$	−6.94464	+	12.0285i	−0.510580	+	0.884350i
$186$	1.33442	−	2.31129i	0.0978448	−	0.169472i
$187$	16.4584	+	28.5067i	1.20355	+	2.08462i
$188$	−9.05005			−0.660043
$189$	4.72869	+	13.7196i	0.343962	+	0.997952i
$190$	12.5480			0.910329
$191$	−10.0288	−	17.3704i	−0.725660	−	1.25688i	−0.958702	−	0.284414i	$-0.908201\pi$
$191$	−10.0288	−	17.3704i	−0.725660	−	1.25688i	0.233041	−	0.972467i	$-0.425132\pi$
$192$	0.304853	−	0.528021i	0.0220009	−	0.0381066i
$193$	−4.98077	+	8.62695i	−0.358524	+	0.620981i	−0.987714	−	0.156270i	$-0.950053\pi$
$193$	−4.98077	+	8.62695i	−0.358524	+	0.620981i	0.629191	+	0.777251i	$0.283386\pi$
$194$	9.91464	+	17.1727i	0.711830	+	1.23293i
$195$	9.11009			0.652387
$196$	−1.13956	−	8.07275i	−0.0813970	−	0.576625i
$197$	22.6858			1.61630			0.808150	−	0.588977i	$-0.200469\pi$
$197$	22.6858			1.61630			0.808150	+	0.588977i	$0.200469\pi$
$198$	−6.43555	−	11.1467i	−0.457355	−	0.792162i
$199$	1.60371	−	2.77770i	0.113684	−	0.196906i	−0.803569	−	0.595211i	$-0.797068\pi$
$199$	1.60371	−	2.77770i	0.113684	−	0.196906i	0.917253	+	0.398306i	$0.130402\pi$
$200$	−1.05152	+	1.82128i	−0.0743535	+	0.128784i
$201$	2.26959	+	3.93104i	0.160085	+	0.277275i
$202$	3.06274			0.215493
$203$	−6.60464	−	19.1623i	−0.463555	−	1.34493i
$204$	−9.86359			−0.690590
$205$	1.26642	+	2.19350i	0.0884503	+	0.153200i
$206$	13.3806	−	23.1760i	0.932274	−	1.61475i
$207$	3.11603	−	5.39713i	0.216579	−	0.375126i
$208$	−7.40459	−	12.8251i	−0.513416	−	0.889263i
$209$	13.0733			0.904300
$210$	−9.44288	+	10.8695i	−0.651621	+	0.750065i
$211$	9.40518			0.647479			0.323740	−	0.946146i	$-0.395060\pi$
$211$	9.40518			0.647479			0.323740	+	0.946146i	$0.395060\pi$
$212$	5.49881	+	9.52422i	0.377660	+	0.654126i
$213$	4.08861	−	7.08169i	0.280147	−	0.485229i
$214$	1.54484	−	2.67574i	0.105603	−	0.182910i
$215$	11.6272	+	20.1389i	0.792968	+	1.37346i
$216$	−8.15047			−0.554569
$217$	3.22617	+	0.626086i	0.219007	+	0.0425015i
$218$	−32.2077			−2.18138
$219$	−1.63398	−	2.83013i	−0.110414	−	0.191243i
$220$	6.92416	−	11.9930i	0.466827	−	0.808567i
$221$	−10.4406	+	18.0837i	−0.702314	+	1.21644i
$222$	−5.89117	−	10.2038i	−0.395389	−	0.684834i
$223$	3.72574			0.249494			0.124747	−	0.992189i	$-0.460188\pi$
$223$	3.72574			0.249494			0.124747	+	0.992189i	$0.460188\pi$
$224$	15.2579	+	2.96103i	1.01946	+	0.197842i
$225$	−2.18121			−0.145414
$226$	−13.5773	−	23.5166i	−0.903151	−	1.56430i
$227$	0.416353	−	0.721145i	0.0276343	−	0.0478641i	−0.851878	−	0.523741i	$-0.824536\pi$
$227$	0.416353	−	0.721145i	0.0276343	−	0.0478641i	0.879512	+	0.475877i	$0.157869\pi$
$228$	−1.95873	+	3.39262i	−0.129720	+	0.224682i
$229$	10.1667	+	17.6092i	0.671831	+	1.16365i	0.977384	+	0.211471i	$0.0678254\pi$
$229$	10.1667	+	17.6092i	0.671831	+	1.16365i	−0.305553	+	0.952175i	$0.598841\pi$
$230$	18.2195			1.20136
$231$	−9.83819	+	11.3245i	−0.647306	+	0.745097i
$232$	11.3839			0.747390
$233$	1.79796	+	3.11416i	0.117788	+	0.204015i	0.918891	−	0.394512i	$-0.129086\pi$
$233$	1.79796	+	3.11416i	0.117788	+	0.204015i	−0.801103	+	0.598527i	$0.795753\pi$
$234$	4.08250	−	7.07110i	0.266882	−	0.462252i
$235$	−9.84055	+	17.0443i	−0.641927	+	1.11185i
$236$	−0.950786	−	1.64681i	−0.0618909	−	0.107198i
$237$	15.0693			0.978856
$238$	−10.7541	−	31.2013i	−0.697084	−	2.02248i
$239$	7.82576			0.506206			0.253103	−	0.967439i	$-0.418549\pi$
$239$	7.82576			0.506206			0.253103	+	0.967439i	$0.418549\pi$
$240$	−7.60637	−	13.1746i	−0.490989	−	0.850418i
$241$	6.52499	−	11.3016i	0.420311	−	0.728001i	−0.575658	−	0.817690i	$-0.695254\pi$
$241$	6.52499	−	11.3016i	0.420311	−	0.728001i	0.995970	+	0.0896897i	$0.0285875\pi$
$242$	9.81772	−	17.0048i	0.631107	−	1.09311i
$243$	−7.01897	−	12.1572i	−0.450267	−	0.779886i
$244$	16.2510			1.04036
$245$	−16.4428	−	6.63171i	−1.05049	−	0.423685i
$246$	−2.14861			−0.136991
$247$	4.14664	+	7.18220i	0.263845	+	0.456992i
$248$	−0.922894	+	1.59850i	−0.0586038	+	0.101505i
$249$	0.176703	−	0.306058i	0.0111981	−	0.0193956i
$250$	8.07610	+	13.9882i	0.510777	+	0.884692i
$251$	−2.49236			−0.157316			−0.0786582	−	0.996902i	$-0.525064\pi$
$251$	−2.49236			−0.157316			−0.0786582	+	0.996902i	$0.525064\pi$
$252$	1.54757	+	4.49004i	0.0974878	+	0.282846i
$253$	18.9822			1.19340
$254$	5.32359	+	9.22073i	0.334032	+	0.578560i
$255$	−10.7252	+	18.5765i	−0.671635	+	1.16331i
$256$	−10.1566	+	17.5917i	−0.634787	+	1.09948i
$257$	10.1665	+	17.6089i	0.634171	+	1.09842i	0.986690	+	0.162611i	$0.0519917\pi$
$257$	10.1665	+	17.6089i	0.634171	+	1.09842i	−0.352520	+	0.935804i	$0.614675\pi$
$258$	−19.7268			−1.22814
$259$	9.51509	−	10.9526i	0.591239	−	0.680561i
$260$	8.78492			0.544817
$261$	5.90355	+	10.2252i	0.365421	+	0.632927i
$262$	−6.22094	+	10.7750i	−0.384331	+	0.665680i
$263$	11.8247	−	20.4810i	0.729144	−	1.26291i	−0.228102	−	0.973637i	$-0.573252\pi$
$263$	11.8247	−	20.4810i	0.729144	−	1.26291i	0.957245	−	0.289277i	$-0.0934148\pi$
$264$	−4.21271	−	7.29663i	−0.259274	−	0.449076i
$265$	23.9165			1.46918
$266$	−12.8674	−	2.49710i	−0.788949	−	0.153107i
$267$	3.61732			0.221376
$268$	2.18858	+	3.79073i	0.133689	+	0.231556i
$269$	−2.01639	+	3.49249i	−0.122941	+	0.212941i	−0.920926	−	0.389737i	$-0.872566\pi$
$269$	−2.01639	+	3.49249i	−0.122941	+	0.212941i	0.797985	+	0.602677i	$0.205899\pi$
$270$	12.3569	−	21.4027i	0.752015	−	1.30253i
$271$	−8.85417	−	15.3359i	−0.537852	−	0.931588i	−0.999019	−	0.0442742i	$-0.985902\pi$
$271$	−8.85417	−	15.3359i	−0.537852	−	0.931588i	0.461167	−	0.887313i	$-0.347431\pi$
$272$	34.8692			2.11426
$273$	−9.34195	−	1.81294i	−0.565400	−	0.109724i
$274$	−14.7827			−0.893055
$275$	−3.32187	−	5.75365i	−0.200316	−	0.346958i
$276$	−2.84403	+	4.92601i	−0.171191	+	0.296511i
$277$	−8.77982	+	15.2071i	−0.527528	+	0.913705i	0.471957	+	0.881622i	$0.343548\pi$
$277$	−8.77982	+	15.2071i	−0.527528	+	0.913705i	−0.999485	+	0.0320839i	$0.989786\pi$
$278$	−4.57238	−	7.91960i	−0.274233	−	0.474986i
$279$	−1.91441			−0.114612
$280$	6.53074	−	7.51737i	0.390286	−	0.449249i
$281$	−13.2569			−0.790843			−0.395421	−	0.918500i	$-0.629401\pi$
$281$	−13.2569			−0.790843			−0.395421	+	0.918500i	$0.629401\pi$
$282$	−8.34778	−	14.4588i	−0.497103	−	0.861008i
$283$	−4.79165	+	8.29938i	−0.284834	+	0.493347i	−0.972569	−	0.232615i	$-0.925272\pi$
$283$	−4.79165	+	8.29938i	−0.284834	+	0.493347i	0.687735	+	0.725962i	$0.258605\pi$
$284$	3.94268	−	6.82892i	0.233955	−	0.405222i
$285$	4.25964	+	7.37791i	0.252319	+	0.437030i
$286$	24.8697			1.47058
$287$	−0.862133	−	2.50135i	−0.0508901	−	0.147650i
$288$	−9.05405			−0.533515
$289$	−16.0832	−	27.8569i	−0.946070	−	1.63864i
$290$	−17.2590	+	29.8935i	−1.01349	+	1.75541i
$291$	−6.73139	+	11.6591i	−0.394601	+	0.683469i
$292$	−1.57566	−	2.72912i	−0.0922083	−	0.159709i
$293$	19.5179			1.14025			0.570125	−	0.821558i	$-0.306895\pi$
$293$	19.5179			1.14025			0.570125	+	0.821558i	$0.306895\pi$
$294$	11.8463	−	9.26693i	0.690889	−	0.540458i
$295$	−4.13534			−0.240769
$296$	4.07436	+	7.05699i	0.236817	+	0.410179i
$297$	12.8742	−	22.2987i	0.747035	−	1.29390i
$298$	13.3703	−	23.1581i	0.774522	−	1.34151i
$299$	6.02084	+	10.4284i	0.348194	+	0.603090i
$300$	1.99082			0.114940
$301$	−7.91539	−	22.9653i	−0.456236	−	1.32370i
$302$	−9.71831			−0.559226
$303$	1.03970	+	1.80081i	0.0597292	+	0.103454i
$304$	6.92439	−	11.9934i	0.397141	−	0.687868i
$305$	17.6704	−	30.6061i	1.01181	−	1.75250i
$306$	9.61252	+	16.6494i	0.549511	+	0.951782i
$307$	11.4155			0.651519			0.325759	−	0.945453i	$-0.394380\pi$
$307$	11.4155			0.651519			0.325759	+	0.945453i	$0.394380\pi$
$308$	−9.48703	+	10.9203i	−0.540574	+	0.622241i
$309$	18.1692			1.03361
$310$	−2.79838	−	4.84694i	−0.158938	−	0.275288i
$311$	−12.2738	+	21.2589i	−0.695985	+	1.20548i	0.273863	+	0.961769i	$0.411699\pi$
$311$	−12.2738	+	21.2589i	−0.695985	+	1.20548i	−0.969848	+	0.243712i	$0.921635\pi$
$312$	2.67240	−	4.62874i	0.151295	−	0.262051i
$313$	−6.35070	−	10.9997i	−0.358963	−	0.621742i	0.628825	−	0.777547i	$-0.283536\pi$
$313$	−6.35070	−	10.9997i	−0.358963	−	0.621742i	−0.987788	+	0.155805i	$0.950203\pi$
$314$	−38.9713			−2.19928
$315$	10.1390	+	1.96763i	0.571269	+	0.110863i
$316$	14.5314			0.817456
$317$	−13.3042	−	23.0435i	−0.747237	−	1.29425i	−0.949142	−	0.314847i	$-0.898047\pi$
$317$	−13.3042	−	23.0435i	−0.747237	−	1.29425i	0.201906	−	0.979405i	$-0.435287\pi$
$318$	−10.1442	+	17.5703i	−0.568860	+	0.985295i
$319$	−17.9816	+	31.1450i	−1.00677	+	1.74378i
$320$	−0.639299	−	1.10730i	−0.0357379	−	0.0618998i
$321$	2.09769			0.117082
$322$	−18.6831	−	3.62574i	−1.04117	−	0.202055i
$323$	−19.5271			−1.08652
$324$	1.16521	+	2.01820i	0.0647339	+	0.112122i
$325$	2.10729	−	3.64993i	0.116891	−	0.202461i
$326$	3.94265	−	6.82887i	0.218363	−	0.378216i
$327$	−10.9335	−	18.9373i	−0.604622	−	1.04724i
$328$	1.48599			0.0820501
$329$	13.4829	−	15.5198i	0.743336	−	0.855635i
$330$	25.5474			1.40634
$331$	6.65530	+	11.5273i	0.365809	+	0.633599i	0.988906	−	0.148546i	$-0.0474592\pi$
$331$	6.65530	+	11.5273i	0.365809	+	0.633599i	−0.623097	+	0.782145i	$0.714126\pi$
$332$	0.170396	−	0.295134i	0.00935167	−	0.0161976i
$333$	−4.22582	+	7.31934i	−0.231574	+	0.401097i
$334$	−16.3346	−	28.2923i	−0.893789	−	1.54809i
$335$	9.51899			0.520078
$336$	5.17816	+	15.0236i	0.282492	+	0.819606i
$337$	−6.90555			−0.376169			−0.188085	−	0.982153i	$-0.560228\pi$
$337$	−6.90555			−0.376169			−0.188085	+	0.982153i	$0.560228\pi$
$338$	−3.67495	−	6.36520i	−0.199891	−	0.346221i
$339$	9.21812	−	15.9662i	0.500659	−	0.867167i
$340$	−10.3423	+	17.9134i	−0.560892	+	0.971493i
$341$	−2.91553	−	5.04985i	−0.157885	−	0.273465i
$342$	7.63549			0.412880
$343$	15.5416	+	10.0727i	0.839167	+	0.543874i
$344$	13.6431			0.735589
$345$	6.18491	+	10.7126i	0.332984	+	0.576746i
$346$	13.3940	−	23.1991i	0.720066	−	1.24719i
$347$	−0.0280907	+	0.0486546i	−0.00150799	+	0.00261192i	−0.866778	−	0.498693i	$-0.833813\pi$
$347$	−0.0280907	+	0.0486546i	−0.00150799	+	0.00261192i	0.865270	+	0.501305i	$0.167147\pi$
$348$	−5.38823	−	9.33269i	−0.288839	−	0.500285i
$349$	−6.22816			−0.333386			−0.166693	−	0.986009i	$-0.553309\pi$
$349$	−6.22816			−0.333386			−0.166693	+	0.986009i	$0.553309\pi$
$350$	2.17055	+	6.29751i	0.116021	+	0.336616i
$351$	16.3339			0.871839
$352$	−13.7888	−	23.8829i	−0.734947	−	1.27296i
$353$	0.907346	−	1.57157i	0.0482932	−	0.0836462i	−0.840868	−	0.541240i	$-0.817955\pi$
$353$	0.907346	−	1.57157i	0.0482932	−	0.0836462i	0.889162	+	0.457593i	$0.151288\pi$
$354$	1.75401	−	3.03804i	0.0932248	−	0.161470i
$355$	−8.57412	−	14.8508i	−0.455067	−	0.788199i
$356$	3.48820			0.184874
$357$	14.6949	−	16.9149i	0.777737	−	0.895234i
$358$	−28.6932			−1.51648
$359$	11.1760	+	19.3573i	0.589845	+	1.02164i	0.994252	+	0.107062i	$0.0341443\pi$
$359$	11.1760	+	19.3573i	0.589845	+	1.02164i	−0.404408	+	0.914579i	$0.632522\pi$
$360$	−2.90042	+	5.02367i	−0.152865	+	0.264771i
$361$	5.62227	−	9.73807i	0.295909	−	0.512530i
$362$	−2.25301	−	3.90233i	−0.118416	−	0.205102i
$363$	13.3312			0.699705
$364$	−9.00850	−	1.74823i	−0.472174	−	0.0916323i
$365$	−6.85314			−0.358710
$366$	14.9899	+	25.9633i	0.783535	+	1.35712i
$367$	−1.14125	+	1.97670i	−0.0595727	+	0.103183i	−0.894274	−	0.447521i	$-0.852307\pi$
$367$	−1.14125	+	1.97670i	−0.0595727	+	0.103183i	0.834701	+	0.550703i	$0.185640\pi$
$368$	10.0541	−	17.4141i	0.524104	−	0.907775i
$369$	0.770616	+	1.33475i	0.0401167	+	0.0694841i
$370$	−24.7084			−1.28453
$371$	−24.5252	−	4.75947i	−1.27328	−	0.247099i
$372$	1.74730			0.0905932
$373$	1.76165	+	3.05126i	0.0912147	+	0.157988i	0.908023	−	0.418921i	$-0.137592\pi$
$373$	1.76165	+	3.05126i	0.0912147	+	0.157988i	−0.816808	+	0.576910i	$0.804258\pi$
$374$	−29.2787	+	50.7122i	−1.51396	+	2.62226i
$375$	−5.48314	+	9.49708i	−0.283148	+	0.490427i
$376$	5.77336	+	9.99976i	0.297739	+	0.515698i
$377$	−22.8138			−1.17497
$378$	−16.9306	+	19.4884i	−0.870815	+	1.00237i
$379$	−15.2688			−0.784306			−0.392153	−	0.919900i	$-0.628270\pi$
$379$	−15.2688			−0.784306			−0.392153	+	0.919900i	$0.628270\pi$
$380$	4.10760	+	7.11457i	0.210715	+	0.364970i
$381$	−3.61437	+	6.26027i	−0.185170	+	0.320723i
$382$	17.8408	−	30.9012i	0.912817	−	1.58104i
$383$	5.55136	+	9.61525i	0.283661	+	0.491316i	0.972284	−	0.233804i	$-0.0751175\pi$
$383$	5.55136	+	9.61525i	0.283661	+	0.491316i	−0.688622	+	0.725120i	$0.741784\pi$
$384$	−13.1059			−0.668806
$385$	10.2509	+	29.7415i	0.522436	+	1.51577i
$386$	−17.7211			−0.901982
$387$	7.07516	+	12.2545i	0.359651	+	0.622933i
$388$	−6.49112	+	11.2430i	−0.329537	+	0.570775i
$389$	8.23333	−	14.2605i	0.417446	−	0.723038i	−0.578236	−	0.815870i	$-0.696259\pi$
$389$	8.23333	−	14.2605i	0.417446	−	0.723038i	0.995682	+	0.0928318i	$0.0295919\pi$
$390$	8.10322	+	14.0352i	0.410323	+	0.710700i
$391$	−28.3529			−1.43387
$392$	−8.19294	+	6.40905i	−0.413806	+	0.323706i
$393$	−8.44722			−0.426106
$394$	20.1786	+	34.9503i	1.01658	+	1.76077i
$395$	15.8007	−	27.3676i	0.795020	−	1.37701i
$396$	4.21336	−	7.29775i	0.211729	−	0.366726i
$397$	10.0828	+	17.4640i	0.506043	+	0.876491i	0.999976	+	0.00699145i	$0.00222547\pi$
$397$	10.0828	+	17.4640i	0.506043	+	0.876491i	−0.493933	+	0.869500i	$0.664441\pi$
$398$	5.70584			0.286008
$399$	−2.89982	−	8.41337i	−0.145172	−	0.421195i
$400$	−7.03782			−0.351891
$401$	9.35452	+	16.2025i	0.467143	+	0.809115i	0.999295	−	0.0375336i	$-0.0119501\pi$
$401$	9.35452	+	16.2025i	0.467143	+	0.809115i	−0.532153	+	0.846648i	$0.678617\pi$
$402$	−4.03750	+	6.99316i	−0.201372	+	0.348787i
$403$	1.84952	−	3.20346i	0.0921311	−	0.159576i
$404$	1.00259	+	1.73653i	0.0498806	+	0.0863958i
$405$	5.06796			0.251829
$406$	23.6472	−	27.2197i	1.17359	−	1.35089i
$407$	−25.7428			−1.27602
$408$	6.29235	+	10.8987i	0.311518	+	0.539565i
$409$	−2.68157	+	4.64462i	−0.132595	+	0.229662i	−0.924676	−	0.380754i	$-0.875664\pi$
$409$	−2.68157	+	4.64462i	−0.132595	+	0.229662i	0.792081	+	0.610416i	$0.208998\pi$
$410$	−2.25290	+	3.90213i	−0.111263	+	0.192713i
$411$	−5.01824	−	8.69185i	−0.247532	−	0.428737i
$412$	17.5206			0.863180
$413$	4.24059	+	0.822949i	0.208666	+	0.0404947i
$414$	11.0866			0.544875
$415$	−0.370559	−	0.641826i	−0.0181900	−	0.0315060i
$416$	8.74718	−	15.1506i	0.428866	−	0.742817i
$417$	3.10435	−	5.37689i	0.152021	−	0.263307i
$418$	11.6284	+	20.1410i	0.568765	+	0.985130i
$419$	2.79177			0.136387			0.0681934	−	0.997672i	$-0.478277\pi$
$419$	2.79177			0.136387			0.0681934	+	0.997672i	$0.478277\pi$
$420$	−9.25399	−	1.79587i	−0.451548	−	0.0876296i
$421$	−21.6956			−1.05738			−0.528689	−	0.848815i	$-0.677316\pi$
$421$	−21.6956			−1.05738			−0.528689	+	0.848815i	$0.677316\pi$
$422$	8.36570	+	14.4898i	0.407236	+	0.705353i
$423$	−5.98799	+	10.3715i	−0.291146	+	0.504280i
$424$	7.01579	−	12.1517i	0.340717	−	0.590139i
$425$	4.96174	+	8.59399i	0.240680	+	0.416870i
$426$	14.5469			0.704801
$427$	−24.2109	+	27.8686i	−1.17165	+	1.34865i
$428$	2.02281			0.0977764
$429$	8.44245	+	14.6228i	0.407605	+	0.705993i
$430$	−20.6843	+	35.8262i	−0.997483	+	1.72769i
$431$	−2.30849	+	3.99843i	−0.111196	+	0.192597i	−0.916253	−	0.400601i	$-0.868802\pi$
$431$	−2.30849	+	3.99843i	−0.111196	+	0.192597i	0.805057	+	0.593198i	$0.202135\pi$
$432$	−13.6378	−	23.6214i	−0.656150	−	1.13648i
$433$	−5.83701			−0.280509			−0.140254	−	0.990115i	$-0.544792\pi$
$433$	−5.83701			−0.280509			−0.140254	+	0.990115i	$0.544792\pi$
$434$	1.90504	+	5.52719i	0.0914451	+	0.265314i
$435$	−23.4355			−1.12365
$436$	−10.5432	−	18.2614i	−0.504928	−	0.874561i
$437$	−5.63037	+	9.75209i	−0.269337	+	0.466506i
$438$	2.90677	−	5.03468i	0.138891	−	0.240566i
$439$	10.0719	+	17.4450i	0.480703	+	0.832603i	0.999755	−	0.0221404i	$-0.00704807\pi$
$439$	10.0719	+	17.4450i	0.480703	+	0.832603i	−0.519052	+	0.854743i	$0.673715\pi$
$440$	−17.6687			−0.842323
$441$	−10.0055	−	4.03541i	−0.476452	−	0.192162i
$442$	−37.1469			−1.76690
$443$	−2.57205	−	4.45491i	−0.122202	−	0.211659i	0.798434	−	0.602082i	$-0.205662\pi$
$443$	−2.57205	−	4.45491i	−0.122202	−	0.211659i	−0.920636	+	0.390423i	$0.872329\pi$
$444$	3.85695	−	6.68044i	0.183043	−	0.317039i
$445$	3.79289	−	6.56947i	0.179800	−	0.311423i
$446$	3.31396	+	5.73995i	0.156921	+	0.271794i
$447$	18.1552			0.858709
$448$	0.435213	+	1.26270i	0.0205619	+	0.0596571i
$449$	6.86081			0.323782			0.161891	−	0.986809i	$-0.448241\pi$
$449$	6.86081			0.323782			0.161891	+	0.986809i	$0.448241\pi$
$450$	−1.94014	−	3.36043i	−0.0914592	−	0.158412i
$451$	−2.34721	+	4.06549i	−0.110526	+	0.191436i
$452$	8.88909	−	15.3964i	0.418108	−	0.724184i
$453$	−3.29905	−	5.71412i	−0.155003	−	0.268473i
$454$	1.48135			0.0695231
$455$	−13.0879	+	15.0651i	−0.613570	+	0.706265i
$456$	4.99819			0.234062
$457$	−3.61273	−	6.25744i	−0.168997	−	0.292711i	0.769071	−	0.639164i	$-0.220719\pi$
$457$	−3.61273	−	6.25744i	−0.168997	−	0.292711i	−0.938067	+	0.346453i	$0.887386\pi$
$458$	−18.0860	+	31.3259i	−0.845105	+	1.46376i
$459$	−19.2296	+	33.3067i	−0.897562	+	1.55462i
$460$	5.96415	+	10.3302i	0.278080	+	0.481648i
$461$	8.14091			0.379160			0.189580	−	0.981865i	$-0.439287\pi$
$461$	8.14091			0.379160			0.189580	+	0.981865i	$0.439287\pi$
$462$	−26.1976	−	5.08404i	−1.21882	−	0.236531i
$463$	18.0745			0.839993			0.419996	−	0.907526i	$-0.362031\pi$
$463$	18.0745			0.839993			0.419996	+	0.907526i	$0.362031\pi$
$464$	19.0482	+	32.9924i	0.884289	+	1.53163i
$465$	1.89992	−	3.29076i	0.0881067	−	0.152605i
$466$	−3.19849	+	5.53994i	−0.148167	+	0.256633i
$467$	17.2081	+	29.8053i	0.796296	+	1.37923i	0.922013	+	0.387159i	$0.126544\pi$
$467$	17.2081	+	29.8053i	0.796296	+	1.37923i	−0.125717	+	0.992066i	$0.540123\pi$
$468$	5.34564			0.247102
$469$	−9.76125	−	1.89432i	−0.450733	−	0.0874714i
$470$	−35.0118			−1.61497
$471$	−13.2295	−	22.9141i	−0.609582	−	1.05583i
$472$	−1.21308	+	2.10112i	−0.0558367	+	0.0967120i
$473$	−21.5502	+	37.3260i	−0.990878	+	1.71625i
$474$	13.4038	+	23.2161i	0.615657	+	1.06635i
$475$	3.94125			0.180837
$476$	14.1704	−	16.3112i	0.649499	−	0.747622i
$477$	14.5532			0.666346
$478$	6.96084	+	12.0565i	0.318381	+	0.551453i
$479$	10.6171	−	18.3893i	0.485105	−	0.840227i	−0.514748	−	0.857341i	$-0.672115\pi$
$479$	10.6171	−	18.3893i	0.485105	−	0.840227i	0.999854	+	0.0171142i	$0.00544789\pi$
$480$	8.98554	−	15.5634i	0.410132	−	0.710369i
$481$	−8.16519	−	14.1425i	−0.372301	−	0.644844i
$482$	23.2153			1.05743
$483$	−4.21047	−	12.2160i	−0.191583	−	0.555849i
$484$	12.8553			0.584334
$485$	14.1162	+	24.4500i	0.640984	+	1.11022i
$486$	12.4864	−	21.6272i	0.566397	−	0.981028i
$487$	12.4026	−	21.4819i	0.562014	−	0.973437i	−0.435307	−	0.900282i	$-0.643360\pi$
$487$	12.4026	−	21.4819i	0.562014	−	0.973437i	0.997321	−	0.0731546i	$-0.0233066\pi$
$488$	−10.3671	−	17.9563i	−0.469296	−	0.812845i
$489$	5.35360			0.242098
$490$	−4.40859	−	31.2310i	−0.199160	−	1.41087i
$491$	37.9360			1.71203			0.856014	−	0.516953i	$-0.172934\pi$
$491$	37.9360			1.71203			0.856014	+	0.516953i	$0.172934\pi$
$492$	−0.703349	−	1.21824i	−0.0317094	−	0.0549224i
$493$	26.8583	−	46.5200i	1.20964	−	2.09516i
$494$	−7.37669	+	12.7768i	−0.331893	+	0.574856i
$495$	−9.16278	−	15.8704i	−0.411836	−	0.713321i
$496$	−6.17694			−0.277353
$497$	5.83697	+	16.9351i	0.261824	+	0.759641i
$498$	0.628693			0.0281724
$499$	−12.0350	−	20.8453i	−0.538762	−	0.933164i	−0.998971	−	0.0453530i	$-0.985559\pi$
$499$	−12.0350	−	20.8453i	−0.538762	−	0.933164i	0.460209	−	0.887811i	$-0.347775\pi$
$500$	−5.28743	+	9.15810i	−0.236461	+	0.409562i
$501$	11.0901	−	19.2086i	0.495470	−	0.858179i
$502$	−2.21690	−	3.83978i	−0.0989451	−	0.171378i
$503$	3.13580			0.139819			0.0699093	−	0.997553i	$-0.477729\pi$
$503$	3.13580			0.139819			0.0699093	+	0.997553i	$0.477729\pi$
$504$	3.97397	−	4.57433i	0.177015	−	0.203757i
$505$	4.36065			0.194046
$506$	16.8842	+	29.2443i	0.750595	+	1.30007i
$507$	2.49505	−	4.32155i	0.110809	−	0.191927i
$508$	−3.48536	+	6.03682i	−0.154638	+	0.267841i
$509$	−10.3017	−	17.8431i	−0.456616	−	0.790881i	0.542164	−	0.840273i	$-0.317605\pi$
$509$	−10.3017	−	17.8431i	−0.456616	−	0.790881i	−0.998780	+	0.0493914i	$0.984272\pi$
$510$	−38.1592			−1.68972
$511$	7.02756	+	1.36380i	0.310881	+	0.0603310i
$512$	−14.4341			−0.637905
$513$	7.63731	+	13.2282i	0.337195	+	0.584040i
$514$	−18.0858	+	31.3255i	−0.797731	+	1.38171i
$515$	19.0510	−	32.9973i	0.839489	−	1.45404i
$516$	−6.45757	−	11.1848i	−0.284279	−	0.492385i
$517$	−36.4775			−1.60428
$518$	25.3373	+	4.91707i	1.11325	+	0.216044i
$519$	18.1873			0.798334
$520$	−5.60423	−	9.70680i	−0.245762	−	0.425672i
$521$	0.888626	−	1.53915i	0.0389314	−	0.0674312i	−0.845903	−	0.533337i	$-0.820938\pi$
$521$	0.888626	−	1.53915i	0.0389314	−	0.0674312i	0.884835	+	0.465905i	$0.154271\pi$
$522$	−10.5022	+	18.1903i	−0.459667	+	0.796166i
$523$	11.6965	+	20.2589i	0.511452	+	0.885861i	0.999912	+	0.0132745i	$0.00422553\pi$
$523$	11.6965	+	20.2589i	0.511452	+	0.885861i	−0.488460	+	0.872586i	$0.662441\pi$
$524$	−8.14570			−0.355847
$525$	−2.96595	+	3.41403i	−0.129445	+	0.149000i
$526$	42.0713			1.83440
$527$	4.35482	+	7.54276i	0.189699	+	0.328568i
$528$	14.0979	−	24.4182i	0.613531	−	1.06267i
$529$	3.32482	−	5.75876i	0.144557	−	0.250381i
$530$	21.2732	+	36.8462i	0.924048	+	1.60050i
$531$	−2.51636			−0.109201
$532$	−2.79631	−	8.11307i	−0.121236	−	0.351746i
$533$	−2.97799			−0.128991
$534$	3.21752	+	5.57291i	0.139236	+	0.241163i
$535$	2.19950	−	3.80965i	0.0950927	−	0.164705i
$536$	2.79235	−	4.83650i	0.120611	−	0.208905i
$537$	−9.74040	−	16.8709i	−0.420329	−	0.728032i
$538$	−7.17414			−0.309299
$539$	−4.59315	−	32.5384i	−0.197841	−	1.40153i
$540$	16.1801			0.696281
$541$	−13.4619	−	23.3167i	−0.578772	−	1.00246i	−0.995621	−	0.0934868i	$-0.970199\pi$
$541$	−13.4619	−	23.3167i	−0.578772	−	1.00246i	0.416848	−	0.908976i	$-0.363135\pi$
$542$	15.7512	−	27.2818i	0.676571	−	1.17185i
$543$	1.52965	−	2.64942i	0.0656434	−	0.113698i
$544$	20.5958	+	35.6730i	0.883038	+	1.52947i
$545$	−45.8565			−1.96428
$546$	−5.51640	−	16.0050i	−0.236080	−	0.684950i
$547$	−24.3464			−1.04098			−0.520489	−	0.853869i	$-0.674250\pi$
$547$	−24.3464			−1.04098			−0.520489	+	0.853869i	$0.674250\pi$
$548$	−4.83912	−	8.38160i	−0.206717	−	0.358044i
$549$	10.7525	−	18.6239i	0.458905	−	0.794847i
$550$	5.90946	−	10.2355i	0.251980	−	0.436443i
$551$	−10.6672	−	18.4761i	−0.454436	−	0.787106i
$552$	7.25726			0.308890
$553$	−21.6491	+	24.9197i	−0.920614	+	1.05970i
$554$	−31.2378			−1.32717
$555$	−8.38769	−	14.5279i	−0.356038	−	0.616676i
$556$	2.99354	−	5.18497i	0.126954	−	0.219892i
$557$	19.7214	−	34.1586i	0.835625	−	1.44734i	−0.0578963	−	0.998323i	$-0.518439\pi$
$557$	19.7214	−	34.1586i	0.835625	−	1.44734i	0.893521	−	0.449022i	$-0.148227\pi$
$558$	−1.70282	−	2.94937i	−0.0720862	−	0.124857i
$559$	−27.3414			−1.15642
$560$	32.7141	+	6.34866i	1.38243	+	0.268280i
$561$	−39.7566			−1.67853
$562$	−11.7918	−	20.4239i	−0.497405	−	0.861531i
$563$	2.26124	−	3.91658i	0.0952998	−	0.165064i	−0.814434	−	0.580256i	$-0.802952\pi$
$563$	2.26124	−	3.91658i	0.0952998	−	0.165064i	0.909734	+	0.415192i	$0.136286\pi$
$564$	5.46530	−	9.46618i	0.230131	−	0.398598i
$565$	−19.3311	−	33.4824i	−0.813264	−	1.40861i
$566$	−17.0483			−0.716592
$567$	−5.19694	−	1.00854i	−0.218251	−	0.0423548i
$568$	−10.0607			−0.422139
$569$	4.89698	+	8.48182i	0.205292	+	0.355577i	0.950226	−	0.311562i	$-0.100852\pi$
$569$	4.89698	+	8.48182i	0.205292	+	0.355577i	−0.744934	+	0.667139i	$0.767519\pi$
$570$	−7.57771	+	13.1250i	−0.317395	+	0.549745i
$571$	−14.5378	+	25.1803i	−0.608390	+	1.05376i	0.383116	+	0.923700i	$0.374851\pi$
$571$	−14.5378	+	25.1803i	−0.608390	+	1.05376i	−0.991506	+	0.130062i	$0.958483\pi$
$572$	8.14111	+	14.1008i	0.340397	+	0.589585i
$573$	24.2255			1.01204
$574$	3.08678	−	3.55311i	0.128840	−	0.148304i
$575$	5.72261			0.238649
$576$	−0.389014	−	0.673793i	−0.0162089	−	0.0280747i
$577$	−21.7675	+	37.7024i	−0.906193	+	1.56957i	−0.0868846	+	0.996218i	$0.527691\pi$
$577$	−21.7675	+	37.7024i	−0.906193	+	1.56957i	−0.819308	+	0.573353i	$0.805642\pi$
$578$	28.6113	−	49.5562i	1.19007	−	2.06127i
$579$	−6.01575	−	10.4196i	−0.250006	−	0.433023i
$580$	−22.5990			−0.938373
$581$	0.252264	+	0.731904i	0.0104657	+	0.0303645i
$582$	−23.9497			−0.992747
$583$	22.1637	+	38.3887i	0.917929	+	1.58990i
$584$	−2.01034	+	3.48201i	−0.0831884	+	0.144087i
$585$	5.81256	−	10.0677i	0.240320	−	0.416246i
$586$	17.3608	+	30.0697i	0.717167	+	1.24217i
$587$	22.0541			0.910271			0.455135	−	0.890422i	$-0.349591\pi$
$587$	22.0541			0.910271			0.455135	+	0.890422i	$0.349591\pi$
$588$	9.13212	+	3.68316i	0.376602	+	0.151891i
$589$	3.45915			0.142532
$590$	−3.67829	−	6.37099i	−0.151433	−	0.262290i
$591$	−13.6999	+	23.7290i	−0.563539	+	0.976079i
$592$	−13.6349	+	23.6163i	−0.560390	+	0.970623i
$593$	−17.3875	−	30.1160i	−0.714019	−	1.23672i	−0.963337	−	0.268296i	$-0.913539\pi$
$593$	−17.3875	−	30.1160i	−0.714019	−	1.23672i	0.249317	−	0.968422i	$-0.419794\pi$
$594$	45.8051			1.87941
$595$	−15.3114	−	44.4236i	−0.627706	−	1.82119i
$596$	17.5071			0.717120
$597$	1.93695	+	3.35489i	0.0792739	+	0.137306i
$598$	−10.7108	+	18.5517i	−0.437997	+	0.758633i
$599$	13.9229	−	24.1151i	0.568873	−	0.985317i	−0.427805	−	0.903871i	$-0.640713\pi$
$599$	13.9229	−	24.1151i	0.568873	−	0.985317i	0.996678	−	0.0814460i	$-0.0259538\pi$
$600$	−1.27002	−	2.19973i	−0.0518482	−	0.0898037i
$601$	−6.64710			−0.271141			−0.135570	−	0.990768i	$-0.543287\pi$
$601$	−6.64710			−0.271141			−0.135570	+	0.990768i	$0.543287\pi$
$602$	28.3402	−	32.6217i	1.15506	−	1.32956i
$603$	5.79232			0.235881
$604$	−3.18129	−	5.51016i	−0.129445	−	0.224205i
$605$	13.9782	−	24.2110i	0.568296	−	0.984317i
$606$	−1.84958	+	3.20356i	−0.0751340	+	0.130136i
$607$	5.97161	+	10.3431i	0.242380	+	0.419815i	0.961392	−	0.275183i	$-0.0887385\pi$
$607$	5.97161	+	10.3431i	0.242380	+	0.419815i	−0.719012	+	0.694998i	$0.755405\pi$
$608$	16.3598			0.663478
$609$	24.0320	+	4.66376i	0.973824	+	0.188985i
$610$	62.8699			2.54553
$611$	−11.5701	−	20.0400i	−0.468075	−	0.810730i
$612$	−6.29333	+	10.9004i	−0.254393	+	0.440621i
$613$	5.08967	−	8.81556i	0.205570	−	0.356057i	−0.744744	−	0.667350i	$-0.767429\pi$
$613$	5.08967	−	8.81556i	0.205570	−	0.356057i	0.950314	+	0.311293i	$0.100762\pi$
$614$	10.1539	+	17.5870i	0.409777	+	0.709754i
$615$	−3.05914			−0.123356
$616$	18.1184	+	3.51614i	0.730011	+	0.141669i
$617$	−28.4430			−1.14507			−0.572536	−	0.819880i	$-0.694040\pi$
$617$	−28.4430			−1.14507			−0.572536	+	0.819880i	$0.694040\pi$
$618$	16.1611	+	27.9918i	0.650094	+	1.12600i
$619$	−20.0144	+	34.6660i	−0.804448	+	1.39334i	0.112215	+	0.993684i	$0.464205\pi$
$619$	−20.0144	+	34.6660i	−0.804448	+	1.39334i	−0.916663	+	0.399661i	$0.869128\pi$
$620$	1.83210	−	3.17330i	0.0735791	−	0.127443i
$621$	11.0892	+	19.2071i	0.444994	+	0.770753i
$622$	−43.6692			−1.75098
$623$	−5.19677	+	5.98187i	−0.208204	+	0.239659i
$624$	17.8864			0.716031
$625$	15.0366	+	26.0442i	0.601466	+	1.04177i
$626$	11.2976	−	19.5680i	0.451544	−	0.782097i
$627$	−7.89494	+	13.6744i	−0.315294	+	0.546104i
$628$	−12.7573	−	22.0962i	−0.509070	−	0.881735i
$629$	38.4510			1.53314
$630$	5.98707	+	17.3705i	0.238530	+	0.692059i
$631$	−13.5759			−0.540446			−0.270223	−	0.962798i	$-0.587097\pi$
$631$	−13.5759			−0.540446			−0.270223	+	0.962798i	$0.587097\pi$
$632$	−9.27013	−	16.0563i	−0.368746	−	0.638687i
$633$	−5.67976	+	9.83764i	−0.225750	+	0.391011i
$634$	23.6675	−	40.9934i	0.939958	−	1.62805i
$635$	7.57960	+	13.1282i	0.300787	+	0.520979i
$636$	−13.2829			−0.526700
$637$	16.4190	−	12.8440i	0.650545	−	0.508899i
$638$	−63.9768			−2.53287
$639$	−5.21737	−	9.03674i	−0.206396	−	0.357488i
$640$	−13.7420	+	23.8018i	−0.543199	+	0.940848i
$641$	2.55742	−	4.42957i	0.101012	−	0.174958i	−0.811090	−	0.584921i	$-0.801125\pi$
$641$	2.55742	−	4.42957i	0.101012	−	0.174958i	0.912102	+	0.409964i	$0.134459\pi$
$642$	1.86585	+	3.23174i	0.0736391	+	0.127547i
$643$	−24.0339			−0.947804			−0.473902	−	0.880578i	$-0.657155\pi$
$643$	−24.0339			−0.947804			−0.473902	+	0.880578i	$0.657155\pi$
$644$	−4.06019	−	11.7800i	−0.159994	−	0.464197i
$645$	−28.0865			−1.10591
$646$	−17.3689	−	30.0838i	−0.683371	−	1.18363i
$647$	14.0436	−	24.3242i	0.552111	−	0.956284i	−0.446011	−	0.895027i	$-0.647156\pi$
$647$	14.0436	−	24.3242i	0.552111	−	0.956284i	0.998122	−	0.0612568i	$-0.0195109\pi$
$648$	1.48666	−	2.57497i	0.0584016	−	0.101155i
$649$	−3.83228	−	6.63770i	−0.150430	−	0.260553i
$650$	7.49754			0.294078
$651$	−2.60315	+	2.99642i	−0.102025	+	0.117439i
$652$	5.16251			0.202179
$653$	−14.9366	−	25.8709i	−0.584513	−	1.01241i	−0.994936	−	0.100510i	$-0.967952\pi$
$653$	−14.9366	−	25.8709i	−0.584513	−	1.01241i	0.410423	−	0.911895i	$-0.365381\pi$
$654$	19.4501	−	33.6886i	0.760561	−	1.31733i
$655$	−8.85721	+	15.3411i	−0.346080	+	0.599428i
$656$	2.48644	+	4.30664i	0.0970792	+	0.168146i
$657$	−4.17015			−0.162693
$658$	35.9029	+	6.96749i	1.39964	+	0.271621i
$659$	25.6367			0.998664			0.499332	−	0.866411i	$-0.333579\pi$
$659$	25.6367			0.998664			0.499332	+	0.866411i	$0.333579\pi$
$660$	8.36296	+	14.4851i	0.325528	+	0.563831i
$661$	−7.51672	+	13.0193i	−0.292367	+	0.506394i	−0.974369	−	0.224956i	$-0.927776\pi$
$661$	−7.51672	+	13.0193i	−0.292367	+	0.506394i	0.682002	+	0.731350i	$0.261109\pi$
$662$	−11.8395	+	20.5066i	−0.460155	+	0.797012i
$663$	−12.6101	−	21.8414i	−0.489738	−	0.848250i
$664$	−0.434807			−0.0168738
$665$	−18.3202	−	3.55531i	−0.710429	−	0.137869i
$666$	−15.0351			−0.582598
$667$	−15.4885	−	26.8268i	−0.599716	−	1.03874i
$668$	10.6943	−	18.5230i	0.413774	−	0.716677i
$669$	−2.24996	+	3.89705i	−0.0869885	+	0.150669i
$670$	8.46693	+	14.6652i	0.327106	+	0.566564i
$671$	65.5018			2.52867
$672$	−12.3114	+	14.1714i	−0.474923	+	0.546672i
$673$	−18.1067			−0.697961			−0.348981	−	0.937130i	$-0.613472\pi$
$673$	−18.1067			−0.697961			−0.348981	+	0.937130i	$0.613472\pi$
$674$	−6.14233	−	10.6388i	−0.236594	−	0.409792i
$675$	3.88121	−	6.72245i	0.149388	−	0.258747i
$676$	2.40599	−	4.16730i	0.0925382	−	0.160281i
$677$	15.5784	+	26.9825i	0.598725	+	1.03702i	0.993010	+	0.118034i	$0.0376592\pi$
$677$	15.5784	+	26.9825i	0.598725	+	1.03702i	−0.394284	+	0.918989i	$0.629007\pi$
$678$	32.7972			1.25957
$679$	−9.60984	−	27.8815i	−0.368792	−	1.06999i
$680$	26.3910			1.01205
$681$	0.502869	+	0.870995i	0.0192700	+	0.0333766i
$682$	5.18661	−	8.98347i	0.198605	−	0.343995i
$683$	16.1961	−	28.0525i	0.619728	−	1.07340i	−0.369807	−	0.929109i	$-0.620576\pi$
$683$	16.1961	−	28.0525i	0.619728	−	1.07340i	0.989535	−	0.144292i	$-0.0460905\pi$
$684$	2.49948	+	4.32923i	0.0955700	+	0.165532i
$685$	−21.0472			−0.804173
$686$	−1.69429	+	32.9031i	−0.0646882	+	1.25625i
$687$	−24.5585			−0.936964
$688$	22.8284	+	39.5400i	0.870326	+	1.50745i
$689$	−14.0600	+	24.3526i	−0.535642	+	0.927759i
$690$	−11.0027	+	19.0572i	−0.418865	+	0.725495i
$691$	19.6860	+	34.0972i	0.748892	+	1.29712i	0.948354	+	0.317214i	$0.102747\pi$
$691$	19.6860	+	34.0972i	0.748892	+	1.29712i	−0.199462	+	0.979906i	$0.563919\pi$
$692$	17.5381			0.666700
$693$	6.23770	+	18.0977i	0.236951	+	0.687476i
$694$	−0.0999444			−0.00379384
$695$	−6.51004	−	11.2757i	−0.246940	−	0.427713i
$696$	−6.87471	+	11.9073i	−0.260585	+	0.451347i
$697$	3.50594	−	6.07246i	0.132797	−	0.230011i
$698$	−5.53981	−	9.59523i	−0.209685	−	0.363185i
$699$	−4.34313			−0.164272
$700$	−2.86008	+	3.29217i	−0.108101	+	0.124432i
$701$	−25.4429			−0.960966			−0.480483	−	0.877004i	$-0.659539\pi$
$701$	−25.4429			−0.960966			−0.480483	+	0.877004i	$0.659539\pi$
$702$	14.5286	+	25.1643i	0.548348	+	0.949767i
$703$	7.63566	−	13.2254i	0.287984	−	0.498804i
$704$	1.18489	−	2.05230i	0.0446574	−	0.0773489i
$705$	−11.8854	−	20.5861i	−0.447629	−	0.775316i
$706$	3.22826			0.121497
$707$	−4.47163	−	0.867786i	−0.168173	−	0.0326365i
$708$	2.29671			0.0863156
$709$	11.9825	+	20.7543i	0.450011	+	0.779442i	0.998386	−	0.0567903i	$-0.0180866\pi$
$709$	11.9825	+	20.7543i	0.450011	+	0.779442i	−0.548375	+	0.836233i	$0.684753\pi$
$710$	15.2530	−	26.4189i	0.572434	−	0.991485i
$711$	9.61475	−	16.6532i	0.360581	−	0.624545i
$712$	−2.22525	−	3.85425i	−0.0833949	−	0.144444i
$713$	5.02261			0.188098
$714$	39.1303	+	7.59382i	1.46442	+	0.284192i
$715$	35.4089			1.32422
$716$	−9.39273	−	16.2687i	−0.351023	−	0.607990i
$717$	−4.72595	+	8.18559i	−0.176494	+	0.305697i
$718$	−19.8815	+	34.4358i	−0.741972	+	1.28513i
$719$	14.1152	+	24.4483i	0.526409	+	0.911767i	0.999527	+	0.0307675i	$0.00979516\pi$
$719$	14.1152	+	24.4483i	0.526409	+	0.911767i	−0.473118	+	0.880999i	$0.656872\pi$
$720$	−19.4125			−0.723463
$721$	−26.1025	+	30.0459i	−0.972107	+	1.11897i
$722$	20.0036			0.744455
$723$	7.88084	+	13.6500i	0.293092	+	0.507650i
$724$	1.47505	−	2.55486i	0.0548197	−	0.0949505i
$725$	−5.42095	+	9.38936i	−0.201329	+	0.348712i
$726$	11.8578	+	20.5383i	0.440084	+	0.762247i
$727$	17.4611			0.647595			0.323798	−	0.946126i	$-0.395040\pi$
$727$	17.4611			0.647595			0.323798	+	0.946126i	$0.395040\pi$
$728$	3.81517	+	11.0691i	0.141399	+	0.410249i
$729$	22.9577			0.850284
$730$	−6.09572	−	10.5581i	−0.225613	−	0.390773i
$731$	32.1886	−	55.7523i	1.19054	−	2.06207i
$732$	−9.81391	+	16.9982i	−0.362733	+	0.628271i
$733$	−7.14287	−	12.3718i	−0.263828	−	0.456963i	0.703428	−	0.710767i	$-0.251652\pi$
$733$	−7.14287	−	12.3718i	−0.263828	−	0.456963i	−0.967256	+	0.253803i	$0.918318\pi$
$734$	−4.06046			−0.149874
$735$	16.8664	−	13.1940i	0.622128	−	0.486669i
$736$	23.7541			0.875587
$737$	8.82138	+	15.2791i	0.324940	+	0.562812i
$738$	−1.37089	+	2.37446i	−0.0504632	+	0.0874049i
$739$	−6.04718	+	10.4740i	−0.222449	+	0.385293i	−0.955551	−	0.294826i	$-0.904738\pi$
$739$	−6.04718	+	10.4740i	−0.222449	+	0.385293i	0.733102	+	0.680119i	$0.238072\pi$
$740$	−8.08831	−	14.0094i	−0.297332	−	0.514994i
$741$	−10.0166			−0.367968
$742$	−14.4821	−	42.0174i	−0.531653	−	1.54251i
$743$	9.11337			0.334337			0.167168	−	0.985928i	$-0.446538\pi$
$743$	9.11337			0.334337			0.167168	+	0.985928i	$0.446538\pi$
$744$	−1.11467	−	1.93066i	−0.0408656	−	0.0707814i
$745$	19.0363	−	32.9719i	0.697437	−	1.20800i
$746$	−3.13389	+	5.42806i	−0.114740	+	0.198736i
$747$	−0.225485	−	0.390552i	−0.00825008	−	0.0142896i
$748$	−38.3376			−1.40176
$749$	−3.01362	+	3.46890i	−0.110115	+	0.126751i
$750$	−19.5085			−0.712351
$751$	4.32709	+	7.49474i	0.157898	+	0.273487i	0.934110	−	0.356984i	$-0.116195\pi$
$751$	4.32709	+	7.49474i	0.157898	+	0.273487i	−0.776213	+	0.630471i	$0.782862\pi$
$752$	−19.3206	+	33.4643i	−0.704550	+	1.22032i
$753$	1.50513	−	2.60696i	0.0548500	−	0.0950030i
$754$	−20.2924	−	35.1475i	−0.739006	−	1.28000i
$755$	−13.8367			−0.503569
$756$	−16.5919	−	3.21990i	−0.603442	−	0.117107i
$757$	23.7596			0.863556			0.431778	−	0.901980i	$-0.357886\pi$
$757$	23.7596			0.863556			0.431778	+	0.901980i	$0.357886\pi$
$758$	−13.5813	−	23.5235i	−0.493294	−	0.854410i
$759$	−11.4633	+	19.8550i	−0.416091	+	0.720690i
$760$	5.24078	−	9.07730i	0.190103	−	0.329268i
$761$	23.9353	+	41.4572i	0.867655	+	1.50282i	0.864387	+	0.502827i	$0.167707\pi$
$761$	23.9353	+	41.4572i	0.867655	+	1.50282i	0.00326770	+	0.999995i	$0.498960\pi$
$762$	−12.8596			−0.465854
$763$	47.0236	+	9.12562i	1.70237	+	0.330370i
$764$	23.3608			0.845165
$765$	13.6861	+	23.7050i	0.494821	+	0.857055i
$766$	−9.87563	+	17.1051i	−0.356821	+	0.618032i
$767$	2.43107	−	4.21074i	0.0877809	−	0.152041i
$768$	−12.2671	−	21.2472i	−0.442650	−	0.766693i
$769$	−37.0906			−1.33752			−0.668761	−	0.743478i	$-0.733175\pi$
$769$	−37.0906			−1.33752			−0.668761	+	0.743478i	$0.733175\pi$
$770$	−36.7024	+	42.2472i	−1.32266	+	1.52248i
$771$	−24.5582			−0.884440
$772$	−5.80102	−	10.0477i	−0.208783	−	0.361623i
$773$	7.53779	−	13.0558i	0.271115	−	0.469586i	−0.698032	−	0.716066i	$-0.745941\pi$
$773$	7.53779	−	13.0558i	0.271115	−	0.469586i	0.969148	+	0.246481i	$0.0792742\pi$
$774$	−12.5864	+	21.8003i	−0.452409	+	0.783595i
$775$	−0.878954	−	1.52239i	−0.0315730	−	0.0546860i
$776$	16.5637			0.594603
$777$	5.71006	+	16.5668i	0.204847	+	0.594332i
$778$	29.2934			1.05022
$779$	−1.39243	−	2.41176i	−0.0498890	−	0.0864103i
$780$	−5.30519	+	9.18885i	−0.189956	+	0.329014i
$781$	15.8915	−	27.5249i	0.568643	−	0.984919i
$782$	−25.2193	−	43.6811i	−0.901840	−	1.56203i
$783$	−42.0186			−1.50162
$784$	−32.2833	−	13.0205i	−1.15298	−	0.465017i
$785$	−55.4863			−1.98039
$786$	−7.51361	−	13.0140i	−0.268002	−	0.464192i
$787$	−22.0136	+	38.1287i	−0.784702	+	1.35914i	0.144476	+	0.989508i	$0.453850\pi$
$787$	−22.0136	+	38.1287i	−0.784702	+	1.35914i	−0.929177	+	0.369635i	$0.879483\pi$
$788$	−13.2109	+	22.8820i	−0.470620	+	0.815137i
$789$	14.2818	+	24.7369i	0.508447	+	0.880656i
$790$	56.2175			2.00013
$791$	13.1599	+	38.1815i	0.467913	+	1.35758i
$792$	−10.7514			−0.382036
$793$	20.7761	+	35.9853i	0.737781	+	1.27787i
$794$	−17.9369	+	31.0676i	−0.636557	+	1.10255i
$795$	−14.4431	+	25.0162i	−0.512244	+	0.887232i
$796$	1.86781	+	3.23514i	0.0662028	+	0.114667i
$797$	12.7891			0.453015			0.226507	−	0.974009i	$-0.427269\pi$
$797$	12.7891			0.453015			0.226507	+	0.974009i	$0.427269\pi$
$798$	10.3825	−	11.9510i	0.367536	−	0.423062i
$799$	54.4850			1.92754
$800$	−4.15695	−	7.20005i	−0.146970	−	0.254560i
$801$	2.30798	−	3.99753i	0.0815484	−	0.141246i
$802$	−16.6413	+	28.8235i	−0.587624	+	1.01779i
$803$	−6.35090	−	11.0001i	−0.224119	−	0.388185i
$804$	−5.28671			−0.186448
$805$	−26.6006	−	5.16224i	−0.937548	−	0.181945i
$806$	6.58043			0.231786
$807$	−2.43538	−	4.21821i	−0.0857296	−	0.148488i
$808$	1.27918	−	2.21560i	0.0450013	−	0.0779445i
$809$	−14.3459	+	24.8478i	−0.504375	+	0.873604i	0.495612	+	0.868544i	$0.334944\pi$
$809$	−14.3459	+	24.8478i	−0.504375	+	0.873604i	−0.999987	+	0.00505951i	$0.998389\pi$
$810$	4.50783	+	7.80780i	0.158389	+	0.274338i
$811$	−19.8602			−0.697385			−0.348693	−	0.937237i	$-0.613374\pi$
$811$	−19.8602			−0.697385			−0.348693	+	0.937237i	$0.613374\pi$
$812$	23.1742	+	4.49729i	0.813254	+	0.157824i
$813$	21.3880			0.750111
$814$	−22.8976	−	39.6599i	−0.802562	−	1.39008i
$815$	5.61344	−	9.72277i	0.196630	−	0.340574i
$816$	−21.0574	+	36.4725i	−0.737157	+	1.27679i
$817$	−12.7841	−	22.1428i	−0.447261	−	0.774678i
$818$	−9.54080			−0.333586
$819$	−7.96400	+	9.16716i	−0.278285	+	0.320327i
$820$	−2.94995			−0.103017
$821$	0.148048	+	0.256426i	0.00516690	+	0.00894934i	0.868597	−	0.495519i	$-0.165022\pi$
$821$	0.148048	+	0.256426i	0.00516690	+	0.00894934i	−0.863430	+	0.504468i	$0.831689\pi$
$822$	8.92723	−	15.4624i	0.311373	−	0.539314i
$823$	−1.83486	+	3.17806i	−0.0639590	+	0.110780i	−0.896232	−	0.443586i	$-0.853706\pi$
$823$	−1.83486	+	3.17806i	−0.0639590	+	0.110780i	0.832273	+	0.554366i	$0.187039\pi$
$824$	−11.1771	−	19.3593i	−0.389372	−	0.674412i
$825$	8.02427			0.279369
$826$	2.50406	+	7.26513i	0.0871273	+	0.252786i
$827$	−3.96494			−0.137875			−0.0689373	−	0.997621i	$-0.521961\pi$
$827$	−3.96494			−0.137875			−0.0689373	+	0.997621i	$0.521961\pi$
$828$	3.62919	+	6.28594i	0.126123	+	0.218452i
$829$	−2.47733	+	4.29087i	−0.0860413	+	0.149028i	−0.905834	−	0.423632i	$-0.860755\pi$
$829$	−2.47733	+	4.29087i	−0.0860413	+	0.149028i	0.819793	+	0.572660i	$0.194088\pi$
$830$	0.659207	−	1.14178i	0.0228814	−	0.0396318i
$831$	−10.6042	−	18.3670i	−0.367856	−	0.637145i
$832$	1.50332			0.0521181
$833$	6.86060	+	48.6013i	0.237706	+	1.68393i
$834$	11.0450			0.382457
$835$	−23.2568	−	40.2819i	−0.804834	−	1.39401i
$836$	−7.61314	+	13.1863i	−0.263306	+	0.456059i
$837$	3.40645	−	5.90015i	0.117744	−	0.203939i
$838$	2.48322	+	4.30106i	0.0857813	+	0.148577i
$839$	45.6338			1.57545			0.787726	−	0.616025i	$-0.211258\pi$
$839$	45.6338			1.57545			0.787726	+	0.616025i	$0.211258\pi$
$840$	3.91913	+	11.3708i	0.135223	+	0.392328i
$841$	29.6881			1.02373
$842$	−19.2978	−	33.4247i	−0.665045	−	1.15189i
$843$	8.00583	−	13.8665i	0.275735	−	0.477588i
$844$	−5.47703	+	9.48650i	−0.188527	+	0.326539i
$845$	−5.23230	−	9.06261i	−0.179997	−	0.311763i
$846$	−21.3047			−0.732472
$847$	−19.1521	+	22.0455i	−0.658073	+	0.757491i
$848$	46.9568			1.61250
$849$	−5.78733	−	10.0239i	−0.198621	−	0.344021i
$850$	−8.82672	+	15.2883i	−0.302754	+	0.524385i
$851$	11.0868	−	19.2029i	0.380051	−	0.658268i
$852$	4.76194	+	8.24793i	0.163142	+	0.282569i
$853$	13.8659			0.474759			0.237379	−	0.971417i	$-0.423712\pi$
$853$	13.8659			0.474759			0.237379	+	0.971417i	$0.423712\pi$
$854$	−64.4700	−	12.5113i	−2.20612	−	0.428130i
$855$	10.8712			0.371788
$856$	−1.29043	−	2.23509i	−0.0441059	−	0.0763937i
$857$	−13.7287	+	23.7788i	−0.468963	+	0.812268i	−0.999371	−	0.0354750i	$-0.988706\pi$
$857$	−13.7287	+	23.7788i	−0.468963	+	0.812268i	0.530408	+	0.847743i	$0.322039\pi$
$858$	−15.0187	+	26.0132i	−0.512732	+	0.888077i
$859$	−6.32803	−	10.9605i	−0.215910	−	0.373967i	0.737644	−	0.675190i	$-0.235938\pi$
$859$	−6.32803	−	10.9605i	−0.215910	−	0.373967i	−0.953554	+	0.301223i	$0.902605\pi$
$860$	−27.0840			−0.923557
$861$	3.13700	+	0.608781i	0.106909	+	0.0207472i
$862$	−8.21341			−0.279750
$863$	−21.6459	−	37.4918i	−0.736834	−	1.27623i	−0.953914	−	0.300081i	$-0.902986\pi$
$863$	−21.6459	−	37.4918i	−0.736834	−	1.27623i	0.217079	−	0.976154i	$-0.430347\pi$
$864$	16.1106	−	27.9044i	0.548093	−	0.949326i
$865$	19.0701	−	33.0303i	0.648401	−	1.12306i
$866$	−5.19189	−	8.99262i	−0.176428	−	0.305582i
$867$	38.8504			1.31943
$868$	−2.51023	+	2.88947i	−0.0852028	+	0.0980748i
$869$	58.5710			1.98688
$870$	−20.8454	−	36.1053i	−0.706724	−	1.22408i
$871$	−5.59600	+	9.69255i	−0.189613	+	0.328420i
$872$	−13.4518	+	23.2992i	−0.455536	+	0.789011i
$873$	8.58974	+	14.8779i	0.290719	+	0.503539i
$874$	−20.0324			−0.677605
$875$	−7.82782	−	22.7112i	−0.264629	−	0.767779i
$876$	3.80614			0.128597
$877$	−25.1933	−	43.6361i	−0.850718	−	1.47349i	−0.880561	−	0.473933i	$-0.842834\pi$
$877$	−25.1933	−	43.6361i	−0.850718	−	1.47349i	0.0298425	−	0.999555i	$-0.490499\pi$
$878$	−17.9174	+	31.0338i	−0.604682	+	1.04734i
$879$	−11.7868	+	20.4154i	−0.397560	+	0.688593i
$880$	−29.5642	−	51.2068i	−0.996610	−	1.72618i
$881$	−4.56171			−0.153688			−0.0768440	−	0.997043i	$-0.524484\pi$
$881$	−4.56171			−0.153688			−0.0768440	+	0.997043i	$0.524484\pi$
$882$	−2.68264	−	19.0041i	−0.0903290	−	0.639901i
$883$	9.01017			0.303216			0.151608	−	0.988441i	$-0.451555\pi$
$883$	9.01017			0.303216			0.151608	+	0.988441i	$0.451555\pi$
$884$	−12.1600	−	21.0618i	−0.408987	−	0.708386i
$885$	2.49732	−	4.32549i	0.0839465	−	0.145400i
$886$	4.57555	−	7.92509i	0.153719	−	0.266249i
$887$	−7.13716	−	12.3619i	−0.239642	−	0.415073i	0.720969	−	0.692967i	$-0.243697\pi$
$887$	−7.13716	−	12.3619i	−0.239642	−	0.415073i	−0.960612	+	0.277894i	$0.910364\pi$
$888$	−9.84197			−0.330275
$889$	−5.15993	−	14.9707i	−0.173059	−	0.502102i
$890$	13.4948			0.452345
$891$	4.69655	+	8.13466i	0.157340	+	0.272521i
$892$	−2.16965	+	3.75795i	−0.0726453	+	0.125825i
$893$	10.8197	−	18.7403i	0.362068	−	0.627121i
$894$	16.1486	+	27.9702i	0.540090	+	0.935464i
$895$	−40.8527			−1.36555
$896$	18.8284	−	21.6729i	0.629011	−	0.724039i
$897$	−14.5439			−0.485606
$898$	6.10254	+	10.5699i	0.203644	+	0.352723i
$899$	−4.75785	+	8.24084i	−0.158683	+	0.274847i
$900$	1.27021	−	2.20007i	0.0423404	−	0.0733358i
$901$	−33.1051	−	57.3397i	−1.10289	−	1.91026i
$902$	−8.35117			−0.278064
$903$	28.8013	+	5.58932i	0.958448	+	0.186001i
$904$	−22.6827			−0.754416
$905$	−3.20778	−	5.55603i	−0.106630	−	0.184689i
$906$	5.86886	−	10.1652i	0.194980	−	0.337715i
$907$	20.1276	−	34.8621i	0.668327	−	1.15758i	−0.310044	−	0.950722i	$-0.600344\pi$
$907$	20.1276	−	34.8621i	0.668327	−	1.15758i	0.978372	−	0.206855i	$-0.0663228\pi$
$908$	0.484920	+	0.839906i	0.0160926	+	0.0278733i
$909$	2.65346			0.0880098
$910$	−34.8511	−	6.76336i	−1.15530	−	0.224203i
$911$	−7.43178			−0.246226			−0.123113	−	0.992393i	$-0.539288\pi$
$911$	−7.43178			−0.246226			−0.123113	+	0.992393i	$0.539288\pi$
$912$	8.36324	+	14.4856i	0.276934	+	0.479665i
$913$	0.686804	−	1.18958i	0.0227299	−	0.0393693i
$914$	6.42689	−	11.1317i	0.212583	−	0.368204i
$915$	21.3423	+	36.9659i	0.705553	+	1.22205i
$916$	−23.6819			−0.782471
$917$	12.1356	−	13.9690i	0.400752	−	0.461296i
$918$	−68.4173			−2.25811
$919$	−1.38629	−	2.40112i	−0.0457294	−	0.0792057i	0.842255	−	0.539080i	$-0.181228\pi$
$919$	−1.38629	−	2.40112i	−0.0457294	−	0.0792057i	−0.887984	+	0.459874i	$0.847895\pi$
$920$	7.60950	−	13.1800i	0.250878	−	0.434533i
$921$	−6.89381	+	11.9404i	−0.227159	+	0.393450i
$922$	7.24116	+	12.5421i	0.238475	+	0.413051i
$923$	20.1621			0.663644
$924$	−5.69322	−	16.5180i	−0.187293	−	0.543402i
$925$	−7.76074			−0.255172
$926$	16.0769	+	27.8459i	0.528318	+	0.915074i
$927$	11.5926	−	20.0789i	0.380750	−	0.659479i
$928$	−22.5019	+	38.9745i	−0.738662	+	1.27940i
$929$	8.56551	+	14.8359i	0.281025	+	0.486750i	0.971638	−	0.236475i	$-0.0759922\pi$
$929$	8.56551	+	14.8359i	0.281025	+	0.486750i	−0.690612	+	0.723225i	$0.742659\pi$
$930$	6.75975			0.221661
$931$	18.0790	+	7.29160i	0.592515	+	0.238972i
$932$	−4.18811			−0.137186
$933$	−14.8243	−	25.6764i	−0.485325	−	0.840607i
$934$	−30.6125	+	53.0223i	−1.00167	+	1.73494i
$935$	−41.6863	+	72.2027i	−1.36329	+	2.36128i
$936$	−3.41018	−	5.90661i	−0.111465	−	0.193063i
$937$	20.2782			0.662461			0.331231	−	0.943550i	$-0.392536\pi$
$937$	20.2782			0.662461			0.331231	+	0.943550i	$0.392536\pi$
$938$	−5.76400	−	16.7233i	−0.188201	−	0.546037i
$939$	15.3407			0.500624
$940$	−11.4611	−	19.8513i	−0.373821	−	0.647477i
$941$	4.81614	−	8.34180i	0.157002	−	0.271935i	−0.776784	−	0.629767i	$-0.783151\pi$
$941$	4.81614	−	8.34180i	0.157002	−	0.271935i	0.933786	+	0.357832i	$0.116484\pi$
$942$	23.5346	−	40.7632i	0.766800	−	1.32814i
$943$	−2.02178	−	3.50182i	−0.0658382	−	0.114035i
$944$	−8.11919			−0.264257
$945$	−24.1053	+	27.7471i	−0.784147	+	0.902612i
$946$	−76.6736			−2.49287
$947$	17.6923	+	30.6439i	0.574922	+	0.995794i	0.996050	+	0.0887930i	$0.0283009\pi$
$947$	17.6923	+	30.6439i	0.574922	+	0.995794i	−0.421128	+	0.907001i	$0.638366\pi$
$948$	−8.77548	+	15.1996i	−0.285014	+	0.493659i
$949$	4.02881	−	6.97810i	0.130781	−	0.226519i
$950$	3.50565	+	6.07197i	0.113738	+	0.197001i
$951$	32.1374			1.04213
$952$	−27.0627	−	5.25192i	−0.877108	−	0.170216i
$953$	−24.5962			−0.796749			−0.398374	−	0.917223i	$-0.630426\pi$
$953$	−24.5962			−0.796749			−0.398374	+	0.917223i	$0.630426\pi$
$954$	12.9448	+	22.4210i	0.419102	+	0.725906i
$955$	25.4013	−	43.9964i	0.821968	−	1.42369i
$956$	−4.55727	+	7.89342i	−0.147393	+	0.255291i
$957$	−21.7180	−	37.6167i	−0.702044	−	1.21598i
$958$	37.7745			1.22044
$959$	21.5829	+	4.18848i	0.696948	+	0.135253i
$960$	1.54428			0.0498415
$961$	14.7286	+	25.5106i	0.475115	+	0.822923i
$962$	14.5255	−	25.1589i	0.468321	−	0.811156i
$963$	1.33840	−	2.31818i	0.0431293	−	0.0747022i
$964$	7.59955	+	13.1628i	0.244765	+	0.423945i
$965$	−25.2309			−0.812212
$966$	15.0752	−	17.3526i	0.485035	−	0.558312i
$967$	32.7607			1.05351			0.526757	−	0.850016i	$-0.323408\pi$
$967$	32.7607			1.05351			0.526757	+	0.850016i	$0.323408\pi$
$968$	−8.20090	−	14.2044i	−0.263587	−	0.456546i
$969$	11.7924	−	20.4250i	0.378825	−	0.656144i
$970$	−25.1121	+	43.4955i	−0.806302	+	1.39656i
$971$	23.0553	+	39.9330i	0.739881	+	1.28151i	0.952549	+	0.304387i	$0.0984515\pi$
$971$	23.0553	+	39.9330i	0.739881	+	1.28151i	−0.212668	+	0.977125i	$0.568215\pi$
$972$	16.3498			0.524419
$973$	4.43181	+	12.8582i	0.142077	+	0.412216i
$974$	44.1272			1.41393
$975$	2.54517	+	4.40836i	0.0815106	+	0.141181i
$976$	34.6936	−	60.0910i	1.11051	−	1.92347i
$977$	−29.3700	+	50.8703i	−0.939629	+	1.62749i	−0.173466	+	0.984840i	$0.555497\pi$
$977$	−29.3700	+	50.8703i	−0.939629	+	1.62749i	−0.766163	+	0.642646i	$0.777837\pi$
$978$	4.76191	+	8.24787i	0.152269	+	0.263738i
$979$	14.0597			0.449350
$980$	16.2644	−	12.7231i	0.519547	−	0.406424i
$981$	−27.9038			−0.890899
$982$	33.7432	+	58.4450i	1.07679	+	1.86505i
$983$	−12.7337	+	22.0555i	−0.406143	+	0.703460i	−0.994454	−	0.105175i	$-0.966460\pi$
$983$	−12.7337	+	22.0555i	−0.406143	+	0.703460i	0.588311	+	0.808635i	$0.299793\pi$
$984$	−0.897386	+	1.55432i	−0.0286076	+	0.0495498i
$985$	28.7297	+	49.7613i	0.915405	+	1.58553i
$986$	95.5596			3.04324
$987$	8.09115	+	23.4752i	0.257544	+	0.747224i
$988$	−9.65906			−0.307296
$989$	−18.5623	−	32.1509i	−0.590247	−	1.02234i
$990$	16.3002	−	28.2327i	0.518053	−	0.897295i
$991$	−8.25706	+	14.3016i	−0.262294	+	0.454307i	−0.966851	−	0.255341i	$-0.917812\pi$
$991$	−8.25706	+	14.3016i	−0.262294	+	0.454307i	0.704557	+	0.709647i	$0.251146\pi$
$992$	−3.64847	−	6.31933i	−0.115839	−	0.200639i
$993$	−16.0765			−0.510171
$994$	−20.8987	+	24.0559i	−0.662865	+	0.763007i
$995$	8.12383			0.257543
$996$	0.205803	+	0.356461i	0.00652111	+	0.0112949i
$997$	3.06133	−	5.30237i	0.0969532	−	0.167928i	−0.813469	−	0.581608i	$-0.802424\pi$
$997$	3.06133	−	5.30237i	0.0969532	−	0.167928i	0.910422	+	0.413681i	$0.135757\pi$
$998$	21.4098	−	37.0829i	0.677716	−	1.17384i
$999$	−15.0387	−	26.0478i	−0.475803	−	0.824115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.e.d.165.14	✓	34
7.2	even	3	inner	287.2.e.d.247.14	yes	34
7.3	odd	6		2009.2.a.r.1.4		17
7.4	even	3		2009.2.a.s.1.4		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.14	✓	34	1.1	even	1	trivial
287.2.e.d.247.14	yes	34	7.2	even	3	inner
2009.2.a.r.1.4		17	7.3	odd	6
2009.2.a.s.1.4		17	7.4	even	3

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.889478 + 1.54062i) q^{2} +(-0.603897 + 1.04598i) q^{3} +(-0.582342 + 1.00865i) q^{4} +(1.26642 + 2.19350i) q^{5} -2.14861 q^{6} +(-0.862133 - 2.50135i) q^{7} +1.48599 q^{8} +(0.770616 + 1.33475i) q^{9} +O(q^{10})\)	\(q+(0.889478 + 1.54062i) q^{2} +(-0.603897 + 1.04598i) q^{3} +(-0.582342 + 1.00865i) q^{4} +(1.26642 + 2.19350i) q^{5} -2.14861 q^{6} +(-0.862133 - 2.50135i) q^{7} +1.48599 q^{8} +(0.770616 + 1.33475i) q^{9} +(-2.25290 + 3.90213i) q^{10} +(-2.34721 + 4.06549i) q^{11} +(-0.703349 - 1.21824i) q^{12} -2.97799 q^{13} +(3.08678 - 3.55311i) q^{14} -3.05914 q^{15} +(2.48644 + 4.30664i) q^{16} +(3.50594 - 6.07246i) q^{17} +(-1.37089 + 2.37446i) q^{18} +(-1.39243 - 2.41176i) q^{19} -2.94995 q^{20} +(3.13700 + 0.608781i) q^{21} -8.35117 q^{22} +(-2.02178 - 3.50182i) q^{23} +(-0.897386 + 1.55432i) q^{24} +(-0.707620 + 1.22563i) q^{25} +(-2.64886 - 4.58795i) q^{26} -5.48488 q^{27} +(3.02503 + 0.587051i) q^{28} +7.66082 q^{29} +(-2.72104 - 4.71298i) q^{30} +(-0.621063 + 1.07571i) q^{31} +(-2.93728 + 5.08751i) q^{32} +(-2.83495 - 4.91028i) q^{33} +12.4738 q^{34} +(4.39487 - 5.05883i) q^{35} -1.79505 q^{36} +(2.74185 + 4.74902i) q^{37} +(2.47707 - 4.29042i) q^{38} +(1.79840 - 3.11492i) q^{39} +(1.88188 + 3.25952i) q^{40} +1.00000 q^{41} +(1.85239 + 5.37442i) q^{42} +9.18117 q^{43} +(-2.73376 - 4.73501i) q^{44} +(-1.95184 + 3.38069i) q^{45} +(3.59666 - 6.22959i) q^{46} +(3.88520 + 6.72936i) q^{47} -6.00622 q^{48} +(-5.51345 + 4.31298i) q^{49} -2.51765 q^{50} +(4.23445 + 7.33428i) q^{51} +(1.73421 - 3.00374i) q^{52} +(4.72129 - 8.17752i) q^{53} +(-4.87868 - 8.45011i) q^{54} -11.8902 q^{55} +(-1.28112 - 3.71697i) q^{56} +3.36354 q^{57} +(6.81413 + 11.8024i) q^{58} +(-0.816347 + 1.41395i) q^{59} +(1.78147 - 3.08559i) q^{60} +(-6.97655 - 12.0837i) q^{61} -2.20969 q^{62} +(2.67429 - 3.07831i) q^{63} -0.504809 q^{64} +(-3.77137 - 6.53221i) q^{65} +(5.04325 - 8.73517i) q^{66} +(1.87912 - 3.25473i) q^{67} +(4.08331 + 7.07250i) q^{68} +4.88379 q^{69} +(11.7029 + 2.27112i) q^{70} -6.77038 q^{71} +(1.14513 + 1.98342i) q^{72} +(-1.35286 + 2.34322i) q^{73} +(-4.87762 + 8.44829i) q^{74} +(-0.854660 - 1.48031i) q^{75} +3.24348 q^{76} +(12.1928 + 2.36619i) q^{77} +6.39855 q^{78} +(-6.23835 - 10.8051i) q^{79} +(-6.29774 + 10.9080i) q^{80} +(1.00045 - 1.73283i) q^{81} +(0.889478 + 1.54062i) q^{82} -0.292604 q^{83} +(-2.44085 + 2.80960i) q^{84} +17.7599 q^{85} +(8.16645 + 14.1447i) q^{86} +(-4.62635 + 8.01307i) q^{87} +(-3.48794 + 6.04128i) q^{88} +(-1.49749 - 2.59373i) q^{89} -6.94448 q^{90} +(2.56742 + 7.44898i) q^{91} +4.70947 q^{92} +(-0.750117 - 1.29924i) q^{93} +(-6.91159 + 11.9712i) q^{94} +(3.52679 - 6.10858i) q^{95} +(-3.54763 - 6.14467i) q^{96} +11.1466 q^{97} +(-11.5488 - 4.65784i) q^{98} -7.23520 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9}+O(q^{10}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9} + 2 q^{10} - 15 q^{11} - 4 q^{12} - 10 q^{13} + 21 q^{14} + 48 q^{15} - 33 q^{16} - 4 q^{17} - 10 q^{18} - 5 q^{19} - 52 q^{20} + 12 q^{21} + 32 q^{22} - 12 q^{23} - 16 q^{24} - 24 q^{25} - 31 q^{26} - 22 q^{27} + 60 q^{28} + 28 q^{29} + 33 q^{30} + 3 q^{31} - 16 q^{32} - 4 q^{33} - 48 q^{34} + 45 q^{35} + 114 q^{36} - 24 q^{37} - 45 q^{39} - 36 q^{40} + 34 q^{41} + 65 q^{42} + 28 q^{43} + 9 q^{44} + 21 q^{45} - 44 q^{46} - 19 q^{47} - 120 q^{48} - 10 q^{49} - 8 q^{50} - 2 q^{51} + 25 q^{52} - 4 q^{53} - 68 q^{54} + 18 q^{55} + 25 q^{56} - 24 q^{57} + q^{58} + 27 q^{59} - 66 q^{60} + q^{61} - 46 q^{62} + 37 q^{63} + 150 q^{64} - 22 q^{65} + 16 q^{66} - 49 q^{67} - 45 q^{68} + 24 q^{69} + 73 q^{70} + 80 q^{71} + 23 q^{72} + 14 q^{73} - 33 q^{74} - 27 q^{75} - 18 q^{76} - 20 q^{77} - 24 q^{78} - 61 q^{79} + 82 q^{80} - 53 q^{81} - 3 q^{82} - 36 q^{83} + 188 q^{84} - 26 q^{85} + 4 q^{86} + 17 q^{87} - 74 q^{88} - 18 q^{89} - 40 q^{90} + 7 q^{91} + 56 q^{92} + 36 q^{93} + 5 q^{94} - 20 q^{95} - 148 q^{96} + 52 q^{97} + 142 q^{98} + 76 q^{99}+O(q^{100}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9 + 2 * q^10 - 15 * q^11 - 4 * q^12 - 10 * q^13 + 21 * q^14 + 48 * q^15 - 33 * q^16 - 4 * q^17 - 10 * q^18 - 5 * q^19 - 52 * q^20 + 12 * q^21 + 32 * q^22 - 12 * q^23 - 16 * q^24 - 24 * q^25 - 31 * q^26 - 22 * q^27 + 60 * q^28 + 28 * q^29 + 33 * q^30 + 3 * q^31 - 16 * q^32 - 4 * q^33 - 48 * q^34 + 45 * q^35 + 114 * q^36 - 24 * q^37 - 45 * q^39 - 36 * q^40 + 34 * q^41 + 65 * q^42 + 28 * q^43 + 9 * q^44 + 21 * q^45 - 44 * q^46 - 19 * q^47 - 120 * q^48 - 10 * q^49 - 8 * q^50 - 2 * q^51 + 25 * q^52 - 4 * q^53 - 68 * q^54 + 18 * q^55 + 25 * q^56 - 24 * q^57 + q^58 + 27 * q^59 - 66 * q^60 + q^61 - 46 * q^62 + 37 * q^63 + 150 * q^64 - 22 * q^65 + 16 * q^66 - 49 * q^67 - 45 * q^68 + 24 * q^69 + 73 * q^70 + 80 * q^71 + 23 * q^72 + 14 * q^73 - 33 * q^74 - 27 * q^75 - 18 * q^76 - 20 * q^77 - 24 * q^78 - 61 * q^79 + 82 * q^80 - 53 * q^81 - 3 * q^82 - 36 * q^83 + 188 * q^84 - 26 * q^85 + 4 * q^86 + 17 * q^87 - 74 * q^88 - 18 * q^89 - 40 * q^90 + 7 * q^91 + 56 * q^92 + 36 * q^93 + 5 * q^94 - 20 * q^95 - 148 * q^96 + 52 * q^97 + 142 * q^98 + 76 * q^99

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