LMFDB - Embedded newform 731.2.e.a.681.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(307,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("731.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			681.6
Character	$\chi$	$=$	731.681
Dual form			731.2.e.a.307.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.94880 q^{2} +(-0.712581 - 1.23423i) q^{3} +1.79780 q^{4} +(2.11686 + 3.66650i) q^{5} +(1.38867 + 2.40525i) q^{6} +(-0.444390 + 0.769706i) q^{7} +0.394042 q^{8} +(0.484458 - 0.839105i) q^{9} +O(q^{10})$	\(q-1.94880 q^{2} +(-0.712581 - 1.23423i) q^{3} +1.79780 q^{4} +(2.11686 + 3.66650i) q^{5} +(1.38867 + 2.40525i) q^{6} +(-0.444390 + 0.769706i) q^{7} +0.394042 q^{8} +(0.484458 - 0.839105i) q^{9} +(-4.12532 - 7.14527i) q^{10} +0.221862 q^{11} +(-1.28108 - 2.21889i) q^{12} +(2.82311 - 4.88976i) q^{13} +(0.866025 - 1.50000i) q^{14} +(3.01686 - 5.22536i) q^{15} -4.36351 q^{16} +(0.500000 - 0.866025i) q^{17} +(-0.944108 + 1.63524i) q^{18} +(-0.611190 - 1.05861i) q^{19} +(3.80569 + 6.59165i) q^{20} +1.26666 q^{21} -0.432365 q^{22} +(3.95772 + 6.85498i) q^{23} +(-0.280786 - 0.486336i) q^{24} +(-6.46217 + 11.1928i) q^{25} +(-5.50166 + 9.52915i) q^{26} -5.65634 q^{27} +(-0.798926 + 1.38378i) q^{28} +(3.73607 - 6.47107i) q^{29} +(-5.87925 + 10.1832i) q^{30} +(3.84897 + 6.66661i) q^{31} +7.71551 q^{32} +(-0.158095 - 0.273828i) q^{33} +(-0.974398 + 1.68771i) q^{34} -3.76284 q^{35} +(0.870959 - 1.50855i) q^{36} +(-4.34553 - 7.52669i) q^{37} +(1.19108 + 2.06302i) q^{38} -8.04676 q^{39} +(0.834130 + 1.44476i) q^{40} +1.62069 q^{41} -2.46845 q^{42} +(5.99219 - 2.66338i) q^{43} +0.398865 q^{44} +4.10211 q^{45} +(-7.71279 - 13.3590i) q^{46} -1.62246 q^{47} +(3.10935 + 5.38556i) q^{48} +(3.10503 + 5.37808i) q^{49} +(12.5934 - 21.8125i) q^{50} -1.42516 q^{51} +(5.07539 - 8.79083i) q^{52} +(-0.771661 - 1.33656i) q^{53} +11.0231 q^{54} +(0.469651 + 0.813460i) q^{55} +(-0.175108 + 0.303296i) q^{56} +(-0.871044 + 1.50869i) q^{57} +(-7.28084 + 12.6108i) q^{58} +8.90841 q^{59} +(5.42372 - 9.39417i) q^{60} +(1.45489 - 2.51993i) q^{61} +(-7.50086 - 12.9919i) q^{62} +(0.430576 + 0.745780i) q^{63} -6.30892 q^{64} +23.9045 q^{65} +(0.308095 + 0.533636i) q^{66} +(1.47997 + 2.56338i) q^{67} +(0.898901 - 1.55694i) q^{68} +(5.64040 - 9.76945i) q^{69} +7.33301 q^{70} +(-1.96779 + 3.40832i) q^{71} +(0.190896 - 0.330642i) q^{72} +(4.30753 - 7.46087i) q^{73} +(8.46856 + 14.6680i) q^{74} +18.4193 q^{75} +(-1.09880 - 1.90318i) q^{76} +(-0.0985935 + 0.170769i) q^{77} +15.6815 q^{78} +(-8.35148 + 14.4652i) q^{79} +(-9.23693 - 15.9988i) q^{80} +(2.57723 + 4.46389i) q^{81} -3.15839 q^{82} +(-8.77140 - 15.1925i) q^{83} +2.27720 q^{84} +4.23371 q^{85} +(-11.6776 + 5.19039i) q^{86} -10.6490 q^{87} +0.0874230 q^{88} +(3.45530 + 5.98475i) q^{89} -7.99417 q^{90} +(2.50912 + 4.34592i) q^{91} +(7.11521 + 12.3239i) q^{92} +(5.48540 - 9.50100i) q^{93} +3.16184 q^{94} +(2.58760 - 4.48186i) q^{95} +(-5.49792 - 9.52268i) q^{96} +15.6672 q^{97} +(-6.05108 - 10.4808i) q^{98} +(0.107483 - 0.186166i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) $ 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.94880			−1.37801			−0.689003	−	0.724758i	$-0.741951\pi$
$2$	−1.94880			−1.37801			−0.689003	+	0.724758i	$0.741951\pi$
$3$	−0.712581	−	1.23423i	−0.411409	−	0.712581i	0.583635	−	0.812016i	$-0.301630\pi$
$3$	−0.712581	−	1.23423i	−0.411409	−	0.712581i	−0.995044	+	0.0994351i	$0.968296\pi$
$4$	1.79780			0.898901
$5$	2.11686	+	3.66650i	0.946687	+	1.63971i	0.752337	+	0.658778i	$0.228927\pi$
$5$	2.11686	+	3.66650i	0.946687	+	1.63971i	0.194350	+	0.980932i	$0.437740\pi$
$6$	1.38867	+	2.40525i	0.566924	+	0.981941i
$7$	−0.444390	+	0.769706i	−0.167964	+	0.290922i	−0.937704	−	0.347436i	$-0.887052\pi$
$7$	−0.444390	+	0.769706i	−0.167964	+	0.290922i	0.769740	+	0.638357i	$0.220386\pi$
$8$	0.394042			0.139315
$9$	0.484458	−	0.839105i	0.161486	−	0.279702i
$10$	−4.12532	−	7.14527i	−1.30454	−	2.25953i
$11$	0.221862			0.0668941			0.0334470	−	0.999440i	$-0.489351\pi$
$11$	0.221862			0.0668941			0.0334470	+	0.999440i	$0.489351\pi$
$12$	−1.28108	−	2.21889i	−0.369816	−	0.640540i
$13$	2.82311	−	4.88976i	0.782989	−	1.35618i	−0.147204	−	0.989106i	$-0.547028\pi$
$13$	2.82311	−	4.88976i	0.782989	−	1.35618i	0.930193	−	0.367070i	$-0.119639\pi$
$14$	0.866025	−	1.50000i	0.231455	−	0.400892i
$15$	3.01686	−	5.22536i	0.778951	−	1.34918i
$16$	−4.36351			−1.09088
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$18$	−0.944108	+	1.63524i	−0.222528	+	0.385431i
$19$	−0.611190	−	1.05861i	−0.140217	−	0.242862i	0.787362	−	0.616492i	$-0.211447\pi$
$19$	−0.611190	−	1.05861i	−0.140217	−	0.242862i	−0.927578	+	0.373629i	$0.878113\pi$
$20$	3.80569	+	6.59165i	0.850978	+	1.47394i
$21$	1.26666			0.276407
$22$	−0.432365			−0.0921804
$23$	3.95772	+	6.85498i	0.825243	+	1.42936i	0.901734	+	0.432292i	$0.142295\pi$
$23$	3.95772	+	6.85498i	0.825243	+	1.42936i	−0.0764910	+	0.997070i	$0.524372\pi$
$24$	−0.280786	−	0.486336i	−0.0573153	−	0.0992730i
$25$	−6.46217	+	11.1928i	−1.29243	+	2.23856i
$26$	−5.50166	+	9.52915i	−1.07896	+	1.86882i
$27$	−5.65634			−1.08856
$28$	−0.798926	+	1.38378i	−0.150983	+	0.261510i
$29$	3.73607	−	6.47107i	0.693771	−	1.20165i	−0.276822	−	0.960921i	$-0.589281\pi$
$29$	3.73607	−	6.47107i	0.693771	−	1.20165i	0.970593	−	0.240726i	$-0.0773855\pi$
$30$	−5.87925	+	10.1832i	−1.07340	+	1.85918i
$31$	3.84897	+	6.66661i	0.691296	+	1.19736i	0.971414	+	0.237393i	$0.0762931\pi$
$31$	3.84897	+	6.66661i	0.691296	+	1.19736i	−0.280118	+	0.959966i	$0.590374\pi$
$32$	7.71551			1.36392
$33$	−0.158095	−	0.273828i	−0.0275208	−	0.0476674i
$34$	−0.974398	+	1.68771i	−0.167108	+	0.289439i
$35$	−3.76284			−0.636036
$36$	0.870959	−	1.50855i	0.145160	−	0.251424i
$37$	−4.34553	−	7.52669i	−0.714401	−	1.23738i	−0.963190	−	0.268822i	$-0.913366\pi$
$37$	−4.34553	−	7.52669i	−0.714401	−	1.23738i	0.248788	−	0.968558i	$-0.419968\pi$
$38$	1.19108	+	2.06302i	0.193219	+	0.334666i
$39$	−8.04676			−1.28851
$40$	0.834130	+	1.44476i	0.131887	+	0.228436i
$41$	1.62069			0.253109			0.126555	−	0.991960i	$-0.459608\pi$
$41$	1.62069			0.253109			0.126555	+	0.991960i	$0.459608\pi$
$42$	−2.46845			−0.380890
$43$	5.99219	−	2.66338i	0.913801	−	0.406162i
$43$	5.99219	−	2.66338i	0.913801	−	0.406162i
$44$	0.398865			0.0601312
$45$	4.10211			0.611506
$46$	−7.71279	−	13.3590i	−1.13719	−	1.96967i
$47$	−1.62246			−0.236660			−0.118330	−	0.992974i	$-0.537754\pi$
$47$	−1.62246			−0.236660			−0.118330	+	0.992974i	$0.537754\pi$
$48$	3.10935	+	5.38556i	0.448797	+	0.777338i
$49$	3.10503	+	5.37808i	0.443576	+	0.768297i
$50$	12.5934	−	21.8125i	1.78098	−	3.08475i
$51$	−1.42516			−0.199563
$52$	5.07539	−	8.79083i	0.703830	−	1.21907i
$53$	−0.771661	−	1.33656i	−0.105996	−	0.183590i	0.808149	−	0.588978i	$-0.200470\pi$
$53$	−0.771661	−	1.33656i	−0.105996	−	0.183590i	−0.914145	+	0.405388i	$0.867136\pi$
$54$	11.0231			1.50005
$55$	0.469651	+	0.813460i	0.0633278	+	0.109687i
$56$	−0.175108	+	0.303296i	−0.0233998	+	0.0405297i
$57$	−0.871044	+	1.50869i	−0.115373	+	0.199831i
$58$	−7.28084	+	12.6108i	−0.956021	+	1.65588i
$59$	8.90841			1.15978			0.579888	−	0.814696i	$-0.303096\pi$
$59$	8.90841			1.15978			0.579888	+	0.814696i	$0.303096\pi$
$60$	5.42372	−	9.39417i	0.700200	−	1.21278i
$61$	1.45489	−	2.51993i	0.186279	−	0.322645i	−0.757728	−	0.652571i	$-0.773691\pi$
$61$	1.45489	−	2.51993i	0.186279	−	0.322645i	0.944007	+	0.329926i	$0.107024\pi$
$62$	−7.50086	−	12.9919i	−0.952610	−	1.64997i
$63$	0.430576	+	0.745780i	0.0542475	+	0.0939594i
$64$	−6.30892			−0.788615
$65$	23.9045			2.96498
$66$	0.308095	+	0.533636i	0.0379238	+	0.0656860i
$67$	1.47997	+	2.56338i	0.180807	+	0.313166i	0.942155	−	0.335176i	$-0.108796\pi$
$67$	1.47997	+	2.56338i	0.180807	+	0.313166i	−0.761349	+	0.648342i	$0.775463\pi$
$68$	0.898901	−	1.55694i	0.109008	−	0.188807i
$69$	5.64040	−	9.76945i	0.679024	−	1.17610i
$70$	7.33301			0.876462
$71$	−1.96779	+	3.40832i	−0.233534	+	0.404493i	−0.958846	−	0.283928i	$-0.908362\pi$
$71$	−1.96779	+	3.40832i	−0.233534	+	0.404493i	0.725312	+	0.688421i	$0.241696\pi$
$72$	0.190896	−	0.330642i	0.0224974	−	0.0389666i
$73$	4.30753	−	7.46087i	0.504159	−	0.873228i	−0.495830	−	0.868420i	$-0.665136\pi$
$73$	4.30753	−	7.46087i	0.504159	−	0.873228i	0.999988	−	0.00480863i	$-0.00153064\pi$
$74$	8.46856	+	14.6680i	0.984450	+	1.70512i
$75$	18.4193			2.12687
$76$	−1.09880	−	1.90318i	−0.126041	−	0.218309i
$77$	−0.0985935	+	0.170769i	−0.0112358	+	0.0194609i
$78$	15.6815			1.77558
$79$	−8.35148	+	14.4652i	−0.939615	+	1.62746i	−0.173426	+	0.984847i	$0.555484\pi$
$79$	−8.35148	+	14.4652i	−0.939615	+	1.62746i	−0.766190	+	0.642614i	$0.777850\pi$
$80$	−9.23693	−	15.9988i	−1.03272	−	1.78872i
$81$	2.57723	+	4.46389i	0.286359	+	0.495988i
$82$	−3.15839			−0.348786
$83$	−8.77140	−	15.1925i	−0.962787	−	1.66760i	−0.715448	−	0.698666i	$-0.753777\pi$
$83$	−8.77140	−	15.1925i	−0.962787	−	1.66760i	−0.247339	−	0.968929i	$-0.579556\pi$
$84$	2.27720			0.248462
$85$	4.23371			0.459211
$86$	−11.6776	+	5.19039i	−1.25922	+	0.559694i
$87$	−10.6490			−1.14169
$88$	0.0874230			0.00931933
$89$	3.45530	+	5.98475i	0.366261	+	0.634382i	0.988978	−	0.148065i	$-0.0473045\pi$
$89$	3.45530	+	5.98475i	0.366261	+	0.634382i	−0.622717	+	0.782447i	$0.713971\pi$
$90$	−7.99417			−0.842660
$91$	2.50912	+	4.34592i	0.263027	+	0.455577i
$92$	7.11521	+	12.3239i	0.741812	+	1.28486i
$93$	5.48540	−	9.50100i	0.568810	−	0.985208i
$94$	3.16184			0.326119
$95$	2.58760	−	4.48186i	0.265483	−	0.459829i
$96$	−5.49792	−	9.52268i	−0.561129	−	0.971904i
$97$	15.6672			1.59077			0.795383	−	0.606107i	$-0.207269\pi$
$97$	15.6672			1.59077			0.795383	+	0.606107i	$0.207269\pi$
$98$	−6.05108	−	10.4808i	−0.611251	−	1.05872i
$99$	0.107483	−	0.186166i	0.0108024	−	0.0187104i
$100$	−11.6177	+	20.1225i	−1.16177	+	2.01225i
$101$	−3.62521	+	6.27905i	−0.360722	+	0.624789i	−0.988080	−	0.153942i	$-0.950803\pi$
$101$	−3.62521	+	6.27905i	−0.360722	+	0.624789i	0.627358	+	0.778731i	$0.284136\pi$
$102$	2.77735			0.274998
$103$	−5.22444	+	9.04899i	−0.514779	+	0.891623i	0.485074	+	0.874473i	$0.338793\pi$
$103$	−5.22444	+	9.04899i	−0.514779	+	0.891623i	−0.999853	+	0.0171501i	$0.994541\pi$
$104$	1.11242	−	1.92677i	0.109082	−	0.188935i
$105$	2.68133	+	4.64420i	0.261671	+	0.453227i
$106$	1.50381	+	2.60468i	0.146063	+	0.252988i
$107$	12.5385			1.21214			0.606071	−	0.795411i	$-0.292745\pi$
$107$	12.5385			1.21214			0.606071	+	0.795411i	$0.292745\pi$
$108$	−10.1690			−0.978512
$109$	7.12181	+	12.3353i	0.682145	+	1.18151i	0.974325	+	0.225147i	$0.0722862\pi$
$109$	7.12181	+	12.3353i	0.682145	+	1.18151i	−0.292179	+	0.956364i	$0.594380\pi$
$110$	−0.915254	−	1.58527i	−0.0872660	−	0.151149i
$111$	−6.19309	+	10.7267i	−0.587822	+	1.01814i
$112$	1.93910	−	3.35862i	0.183228	−	0.317360i
$113$	17.9491			1.68851			0.844255	−	0.535941i	$-0.180043\pi$
$113$	17.9491			1.68851			0.844255	+	0.535941i	$0.180043\pi$
$114$	1.69749	−	2.94013i	0.158984	−	0.275369i
$115$	−16.7559	+	29.0220i	−1.56249	+	2.70632i
$116$	6.71672	−	11.6337i	0.623632	−	1.08016i
$117$	−2.73535	−	4.73777i	−0.252883	−	0.438007i
$118$	−17.3607			−1.59818
$119$	0.444390	+	0.769706i	0.0407372	+	0.0705588i
$120$	1.18877	−	2.05901i	0.108519	−	0.187961i
$121$	−10.9508			−0.995525
$122$	−2.83527	+	4.91084i	−0.256694	+	0.444606i
$123$	−1.15487	−	2.00030i	−0.104131	−	0.180361i
$124$	6.91969	+	11.9853i	0.621406	+	1.07631i
$125$	−33.5494			−3.00075
$126$	−0.839105	−	1.45337i	−0.0747534	−	0.129477i
$127$	4.55963			0.404602			0.202301	−	0.979323i	$-0.435158\pi$
$127$	4.55963			0.404602			0.202301	+	0.979323i	$0.435158\pi$
$128$	−3.13622			−0.277206
$129$	−7.55714	−	5.49785i	−0.665369	−	0.484058i
$130$	−46.5849			−4.08576
$131$	14.2904			1.24856			0.624279	−	0.781201i	$-0.285393\pi$
$131$	14.2904			1.24856			0.624279	+	0.781201i	$0.285393\pi$
$132$	−0.284223	−	0.492289i	−0.0247385	−	0.0428483i
$133$	1.08643			0.0942052
$134$	−2.88415	−	4.99549i	−0.249153	−	0.431545i
$135$	−11.9737	−	20.7390i	−1.03053	−	1.78493i
$136$	0.197021	−	0.341250i	0.0168944	−	0.0292619i
$137$	5.63189			0.481165			0.240582	−	0.970629i	$-0.422662\pi$
$137$	5.63189			0.481165			0.240582	+	0.970629i	$0.422662\pi$
$138$	−10.9920	+	19.0387i	−0.935699	+	1.62068i
$139$	5.23377	+	9.06515i	0.443922	+	0.768896i	0.997976	−	0.0635846i	$-0.0202533\pi$
$139$	5.23377	+	9.06515i	0.443922	+	0.768896i	−0.554054	+	0.832481i	$0.686920\pi$
$140$	−6.76485			−0.571734
$141$	1.15613	+	2.00248i	0.0973640	+	0.168639i
$142$	3.83482	−	6.64211i	0.321811	−	0.557393i
$143$	0.626341	−	1.08486i	0.0523773	−	0.0907201i
$144$	−2.11394	+	3.66144i	−0.176161	+	0.305120i
$145$	31.6349			2.62714
$146$	−8.39450	+	14.5397i	−0.694734	+	1.20331i
$147$	4.42518	−	7.66463i	0.364982	−	0.632168i
$148$	−7.81241	−	13.5315i	−0.642176	−	1.11228i
$149$	−0.956779	−	1.65719i	−0.0783824	−	0.135762i	0.824170	−	0.566343i	$-0.191642\pi$
$149$	−0.956779	−	1.65719i	−0.0783824	−	0.135762i	−0.902552	+	0.430581i	$0.858309\pi$
$150$	−35.8954			−2.93085
$151$	−11.2328			−0.914109			−0.457055	−	0.889439i	$-0.651096\pi$
$151$	−11.2328			−0.914109			−0.457055	+	0.889439i	$0.651096\pi$
$152$	−0.240834	−	0.417137i	−0.0195342	−	0.0338343i
$153$	−0.484458	−	0.839105i	−0.0391661	−	0.0678376i
$154$	0.192139	−	0.332794i	0.0154830	−	0.0268173i
$155$	−16.2954	+	28.2245i	−1.30888	+	2.26705i
$156$	−14.4665			−1.15825
$157$	1.21447	−	2.10352i	0.0969249	−	0.167879i	−0.813485	−	0.581585i	$-0.802433\pi$
$157$	1.21447	−	2.10352i	0.0969249	−	0.167879i	0.910410	+	0.413706i	$0.135766\pi$
$158$	16.2753	−	28.1897i	1.29480	−	2.24265i
$159$	−1.09974	+	1.90481i	−0.0872152	+	0.151061i
$160$	16.3326	+	28.2889i	1.29121	+	2.23644i
$161$	−7.03509			−0.554443
$162$	−5.02249	−	8.69921i	−0.394604	−	0.683475i
$163$	6.74265	−	11.6786i	0.528125	−	0.914739i	−0.471337	−	0.881953i	$-0.656229\pi$
$163$	6.74265	−	11.6786i	0.528125	−	0.914739i	0.999462	−	0.0327864i	$-0.0104381\pi$
$164$	2.91368			0.227520
$165$	0.669329	−	1.15931i	0.0521072	−	0.0902523i
$166$	17.0937	+	29.6071i	1.32673	+	2.29796i
$167$	−7.24570	−	12.5499i	−0.560689	−	0.971142i	−0.997436	−	0.0715576i	$-0.977203\pi$
$167$	−7.24570	−	12.5499i	−0.560689	−	0.971142i	0.436748	−	0.899584i	$-0.356130\pi$
$168$	0.499115			0.0385075
$169$	−9.43986	−	16.3503i	−0.726143	−	1.25772i
$170$	−8.25064			−0.632795
$171$	−1.18438			−0.0905720
$172$	10.7728	−	4.78824i	0.821417	−	0.365100i
$173$	17.7279			1.34782			0.673912	−	0.738811i	$-0.264613\pi$
$173$	17.7279			1.34782			0.673912	+	0.738811i	$0.264613\pi$
$174$	20.7527			1.57326
$175$	−5.74345	−	9.94794i	−0.434164	−	0.751994i
$176$	−0.968099			−0.0729732
$177$	−6.34796	−	10.9950i	−0.477142	−	0.826434i
$178$	−6.73367	−	11.6631i	−0.504710	−	0.874183i
$179$	−1.09798	+	1.90176i	−0.0820670	+	0.142144i	−0.904138	−	0.427241i	$-0.859485\pi$
$179$	−1.09798	+	1.90176i	−0.0820670	+	0.142144i	0.822071	+	0.569386i	$0.192819\pi$
$180$	7.37478			0.549684
$181$	−0.164604	+	0.285102i	−0.0122349	+	0.0211914i	−0.872078	−	0.489367i	$-0.837228\pi$
$181$	−0.164604	+	0.285102i	−0.0122349	+	0.0211914i	0.859843	+	0.510558i	$0.170561\pi$
$182$	−4.88976	−	8.46932i	−0.362453	−	0.627788i
$183$	−4.14689			−0.306547
$184$	1.55951	+	2.70115i	0.114968	+	0.199131i
$185$	18.3978	−	31.8658i	1.35263	−	2.34282i
$186$	−10.6899	+	18.5155i	−0.783824	+	1.35762i
$187$	0.110931	−	0.192139i	0.00811210	−	0.0140506i
$188$	−2.91686			−0.212734
$189$	2.51362	−	4.35372i	0.182839	−	0.316687i
$190$	−5.04271	+	8.73423i	−0.365837	+	0.633648i
$191$	−6.57361	−	11.3858i	−0.475649	−	0.823849i	0.523961	−	0.851742i	$-0.324454\pi$
$191$	−6.57361	−	11.3858i	−0.475649	−	0.823849i	−0.999611	+	0.0278929i	$0.991120\pi$
$192$	4.49561	+	7.78663i	0.324443	+	0.561952i
$193$	−19.6460			−1.41415			−0.707076	−	0.707137i	$-0.749986\pi$
$193$	−19.6460			−1.41415			−0.707076	+	0.707137i	$0.749986\pi$
$194$	−30.5322			−2.19209
$195$	−17.0339	−	29.5035i	−1.21982	−	2.11279i
$196$	5.58224	+	9.66872i	0.398731	+	0.690623i
$197$	−8.64661	+	14.9764i	−0.616046	+	1.06702i	0.374154	+	0.927366i	$0.377933\pi$
$197$	−8.64661	+	14.9764i	−0.616046	+	1.06702i	−0.990200	+	0.139656i	$0.955400\pi$
$198$	−0.209462	+	0.362799i	−0.0148858	+	0.0257830i
$199$	−24.9613			−1.76946			−0.884730	−	0.466103i	$-0.845658\pi$
$199$	−24.9613			−1.76946			−0.884730	+	0.466103i	$0.845658\pi$
$200$	−2.54636	+	4.41043i	−0.180055	+	0.311865i
$201$	2.10919	−	3.65322i	0.148771	−	0.257679i
$202$	7.06480	−	12.2366i	0.497077	−	0.860963i
$203$	3.32055	+	5.75136i	0.233057	+	0.403666i
$204$	−2.56216			−0.179387
$205$	3.43077	+	5.94227i	0.239615	+	0.415026i
$206$	10.1814	−	17.6346i	0.709369	−	1.22866i
$207$	7.66940			0.533060
$208$	−12.3187	+	21.3365i	−0.854145	+	1.47942i
$209$	−0.135600	−	0.234866i	−0.00937966	−	0.0162460i
$210$	−5.22536	−	9.05059i	−0.360584	−	0.624550i
$211$	−8.64696			−0.595281			−0.297641	−	0.954678i	$-0.596200\pi$
$211$	−8.64696			−0.595281			−0.297641	+	0.954678i	$0.596200\pi$
$212$	−1.38729	−	2.40287i	−0.0952798	−	0.165029i
$213$	5.60884			0.384312
$214$	−24.4349			−1.67034
$215$	22.4499	+	16.3324i	1.53107	+	1.11386i
$216$	−2.22883			−0.151653
$217$	−6.84178			−0.464450
$218$	−13.8789	−	24.0390i	−0.940001	−	1.62813i
$219$	−12.2779			−0.829661
$220$	0.844340	+	1.46244i	0.0569254	+	0.0985977i
$221$	−2.82311	−	4.88976i	−0.189903	−	0.328921i
$222$	12.0691	−	20.9042i	0.810022	−	1.40300i
$223$	1.12416			0.0752796			0.0376398	−	0.999291i	$-0.488016\pi$
$223$	1.12416			0.0752796			0.0376398	+	0.999291i	$0.488016\pi$
$224$	−3.42869	+	5.93867i	−0.229089	+	0.396794i
$225$	6.26129	+	10.8449i	0.417420	+	0.722992i
$226$	−34.9791			−2.32678
$227$	5.72577	+	9.91732i	0.380032	+	0.658235i	0.991066	−	0.133369i	$-0.0425795\pi$
$227$	5.72577	+	9.91732i	0.380032	+	0.658235i	−0.611034	+	0.791604i	$0.709246\pi$
$228$	−1.56597	+	2.71233i	−0.103709	+	0.179629i
$229$	1.15901	−	2.00746i	0.0765892	−	0.132656i	−0.825187	−	0.564860i	$-0.808930\pi$
$229$	1.15901	−	2.00746i	0.0765892	−	0.132656i	0.901776	+	0.432203i	$0.142264\pi$
$230$	32.6538	−	56.5580i	2.15313	−	3.72932i
$231$	0.281023			0.0184900
$232$	1.47217	−	2.54987i	0.0966526	−	0.167407i
$233$	7.28549	−	12.6188i	0.477289	−	0.826688i	−0.522373	−	0.852717i	$-0.674953\pi$
$233$	7.28549	−	12.6188i	0.477289	−	0.826688i	0.999661	+	0.0260293i	$0.00828631\pi$
$234$	5.33064	+	9.23293i	0.348475	+	0.603576i
$235$	−3.43451	−	5.94875i	−0.224043	−	0.388054i
$236$	16.0156			1.04252
$237$	23.8044			1.54626
$238$	−0.866025	−	1.50000i	−0.0561361	−	0.0972305i
$239$	3.58093	+	6.20235i	0.231631	+	0.401197i	0.958288	−	0.285803i	$-0.0922604\pi$
$239$	3.58093	+	6.20235i	0.231631	+	0.401197i	−0.726657	+	0.687000i	$0.758927\pi$
$240$	−13.1641	+	22.8009i	−0.849740	+	1.47179i
$241$	−1.55519	+	2.69368i	−0.100179	+	0.173515i	−0.911758	−	0.410727i	$-0.865275\pi$
$241$	−1.55519	+	2.69368i	−0.100179	+	0.173515i	0.811579	+	0.584242i	$0.198608\pi$
$242$	21.3408			1.37184
$243$	−4.81155	+	8.33385i	−0.308661	+	0.534617i
$244$	2.61560	−	4.53034i	0.167446	−	0.290026i
$245$	−13.1458	+	22.7692i	−0.839856	+	1.45467i
$246$	2.25061	+	3.89817i	0.143494	+	0.248538i
$247$	−6.90182			−0.439152
$248$	1.51665	+	2.62692i	0.0963077	+	0.166810i
$249$	−12.5007	+	21.6518i	−0.792197	+	1.37213i
$250$	65.3809			4.13505
$251$	−0.133387	+	0.231033i	−0.00841931	+	0.0145827i	−0.870204	−	0.492691i	$-0.836013\pi$
$251$	−0.133387	+	0.231033i	−0.00841931	+	0.0145827i	0.861785	+	0.507274i	$0.169347\pi$
$252$	0.774091	+	1.34076i	0.0487631	+	0.0844602i
$253$	0.878071	+	1.52086i	0.0552038	+	0.0956158i
$254$	−8.88579			−0.557544
$255$	−3.01686	−	5.22536i	−0.188923	−	0.327225i
$256$	18.7297			1.17061
$257$	−7.24510			−0.451937			−0.225968	−	0.974135i	$-0.572555\pi$
$257$	−7.24510			−0.451937			−0.225968	+	0.974135i	$0.572555\pi$
$258$	14.7273	+	10.7142i	0.916883	+	0.667035i
$259$	7.72445			0.479974
$260$	42.9755			2.66523
$261$	−3.61994	−	6.26992i	−0.224069	−	0.388098i
$262$	−27.8491			−1.72052
$263$	2.30196	+	3.98711i	0.141945	+	0.245856i	0.928229	−	0.372009i	$-0.121331\pi$
$263$	2.30196	+	3.98711i	0.141945	+	0.245856i	−0.786284	+	0.617865i	$0.787998\pi$
$264$	−0.0622960	−	0.107900i	−0.00383405	−	0.00664077i
$265$	3.26699	−	5.65860i	0.200690	−	0.347605i
$266$	−2.11722			−0.129815
$267$	4.92436	−	8.52924i	0.301366	−	0.521981i
$268$	2.66069	+	4.60844i	0.162527	+	0.281505i
$269$	11.7498			0.716399			0.358199	−	0.933645i	$-0.383391\pi$
$269$	11.7498			0.716399			0.358199	+	0.933645i	$0.383391\pi$
$270$	23.3342	+	40.4161i	1.42008	+	2.45964i
$271$	−5.73715	+	9.93704i	−0.348507	+	0.603632i	−0.985984	−	0.166837i	$-0.946645\pi$
$271$	−5.73715	+	9.93704i	−0.348507	+	0.603632i	0.637477	+	0.770469i	$0.279978\pi$
$272$	−2.18176	+	3.77891i	−0.132288	+	0.229130i
$273$	3.57590	−	6.19364i	0.216423	−	0.374856i
$274$	−10.9754			−0.663048
$275$	−1.43371	+	2.48326i	−0.0864562	+	0.149746i
$276$	10.1403	−	17.5635i	0.610375	−	1.05720i
$277$	−7.51319	−	13.0132i	−0.451424	−	0.781889i	0.547051	−	0.837099i	$-0.315750\pi$
$277$	−7.51319	−	13.0132i	−0.451424	−	0.781889i	−0.998475	+	0.0552102i	$0.982417\pi$
$278$	−10.1995	−	17.6661i	−0.611728	−	1.05954i
$279$	7.45865			0.446538
$280$	−1.48272			−0.0886092
$281$	−3.85532	−	6.67761i	−0.229989	−	0.398353i	0.727815	−	0.685773i	$-0.240536\pi$
$281$	−3.85532	−	6.67761i	−0.229989	−	0.398353i	−0.957805	+	0.287420i	$0.907202\pi$
$282$	−2.25307	−	3.90243i	−0.134168	−	0.232386i
$283$	−10.1947	+	17.6577i	−0.606009	+	1.04964i	0.385882	+	0.922548i	$0.373897\pi$
$283$	−10.1947	+	17.6577i	−0.606009	+	1.04964i	−0.991891	+	0.127091i	$0.959436\pi$
$284$	−3.53770	+	6.12748i	−0.209924	+	0.363599i
$285$	−7.37551			−0.436887
$286$	−1.22061	+	2.11416i	−0.0721762	+	0.125013i
$287$	−0.720219	+	1.24746i	−0.0425132	+	0.0736349i
$288$	3.73783	−	6.47412i	0.220254	−	0.381491i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	−61.6500			−3.62021
$291$	−11.1642	−	19.3369i	−0.654455	−	1.13355i
$292$	7.74409	−	13.4132i	0.453189	−	0.784946i
$293$	−11.3504			−0.663095			−0.331547	−	0.943439i	$-0.607571\pi$
$293$	−11.3504			−0.663095			−0.331547	+	0.943439i	$0.607571\pi$
$294$	−8.62376	+	14.9368i	−0.502948	+	0.871131i
$295$	18.8578	+	32.6627i	1.09795	+	1.90170i
$296$	−1.71232	−	2.96583i	−0.0995267	−	0.172385i
$297$	−1.25493			−0.0728185
$298$	1.86457	+	3.22952i	0.108011	+	0.187081i
$299$	44.6923			2.58462
$300$	33.1142			1.91185
$301$	−0.612849	+	5.79581i	−0.0353240	+	0.334065i
$302$	21.8904			1.25965
$303$	10.3330			0.593617
$304$	2.66693	+	4.61927i	0.152959	+	0.264933i
$305$	12.3191			0.705392
$306$	0.944108	+	1.63524i	0.0539711	+	0.0934807i
$307$	−5.81376	−	10.0697i	−0.331809	−	0.574710i	0.651058	−	0.759028i	$-0.274326\pi$
$307$	−5.81376	−	10.0697i	−0.331809	−	0.574710i	−0.982867	+	0.184318i	$0.940992\pi$
$308$	−0.177252	+	0.307009i	−0.0100998	+	0.0174934i
$309$	14.8913			0.847138
$310$	31.7565	−	55.0038i	1.80365	−	3.12401i
$311$	−1.28734	−	2.22974i	−0.0729985	−	0.126437i	0.827216	−	0.561885i	$-0.189923\pi$
$311$	−1.28734	−	2.22974i	−0.0729985	−	0.126437i	−0.900214	+	0.435447i	$0.856590\pi$
$312$	−3.17076			−0.179509
$313$	−8.40064	−	14.5503i	−0.474832	−	0.822434i	0.524752	−	0.851255i	$-0.324158\pi$
$313$	−8.40064	−	14.5503i	−0.474832	−	0.822434i	−0.999585	+	0.0288214i	$0.990825\pi$
$314$	−2.36674	+	4.09932i	−0.133563	+	0.231338i
$315$	−1.82294	+	3.15742i	−0.102711	+	0.177900i
$316$	−15.0143	+	26.0056i	−0.844621	+	1.46293i
$317$	−24.8706			−1.39687			−0.698437	−	0.715671i	$-0.746121\pi$
$317$	−24.8706			−1.39687			−0.698437	+	0.715671i	$0.746121\pi$
$318$	2.14317	−	3.71208i	0.120183	−	0.208163i
$319$	0.828895	−	1.43569i	0.0464092	−	0.0803831i
$320$	−13.3551	−	23.1317i	−0.746572	−	1.29310i
$321$	−8.93469	−	15.4753i	−0.498685	−	0.863749i
$322$	13.7100			0.764026
$323$	−1.22238			−0.0680150
$324$	4.63335	+	8.02520i	0.257408	+	0.445844i
$325$	36.4868	+	63.1970i	2.02392	+	3.50554i
$326$	−13.1400	+	22.7592i	−0.727760	+	1.26052i
$327$	10.1497	−	17.5798i	0.561281	−	0.972167i
$328$	0.638619			0.0352618
$329$	0.721005	−	1.24882i	0.0397503	−	0.0688495i
$330$	−1.30438	+	2.25926i	−0.0718040	+	0.124368i
$331$	−4.85266	+	8.40505i	−0.266726	+	0.461983i	−0.968014	−	0.250895i	$-0.919275\pi$
$331$	−4.85266	+	8.40505i	−0.266726	+	0.461983i	0.701288	+	0.712878i	$0.252609\pi$
$332$	−15.7692	−	27.3131i	−0.865450	−	1.49900i
$333$	−8.42091			−0.461463
$334$	14.1204	+	24.4572i	0.772633	+	1.33824i
$335$	−6.26575	+	10.8526i	−0.342335	+	0.592941i
$336$	−5.52706			−0.301526
$337$	5.67386	−	9.82742i	0.309075	−	0.535334i	−0.669085	−	0.743186i	$-0.733314\pi$
$337$	5.67386	−	9.82742i	0.309075	−	0.535334i	0.978160	+	0.207852i	$0.0666472\pi$
$338$	18.3964	+	31.8634i	1.00063	+	1.73314i
$339$	−12.7902	−	22.1533i	−0.694668	−	1.20320i
$340$	7.61138			0.412785
$341$	0.853942	+	1.47907i	0.0462436	+	0.0800962i
$342$	2.30812			0.124809
$343$	−11.7408			−0.633946
$344$	2.36117	−	1.04948i	0.127306	−	0.0565844i
$345$	47.7597			2.57129
$346$	−34.5480			−1.85731
$347$	2.75693	+	4.77514i	0.148000	+	0.256343i	0.930488	−	0.366322i	$-0.119383\pi$
$347$	2.75693	+	4.77514i	0.148000	+	0.256343i	−0.782488	+	0.622665i	$0.786050\pi$
$348$	−19.1448			−1.02627
$349$	−4.87093	−	8.43669i	−0.260735	−	0.451606i	0.705703	−	0.708508i	$-0.250631\pi$
$349$	−4.87093	−	8.43669i	−0.260735	−	0.451606i	−0.966437	+	0.256902i	$0.917298\pi$
$350$	11.1928	+	19.3865i	0.598280	+	1.03625i
$351$	−15.9685	+	27.6582i	−0.852333	+	1.47628i
$352$	1.71178			0.0912383
$353$	−0.904159	+	1.56605i	−0.0481235	+	0.0833524i	−0.889084	−	0.457744i	$-0.848657\pi$
$353$	−0.904159	+	1.56605i	−0.0481235	+	0.0833524i	0.840960	+	0.541097i	$0.181991\pi$
$354$	12.3709	+	21.4270i	0.657505	+	1.13883i
$355$	−16.6621			−0.884335
$356$	6.21194	+	10.7594i	0.329232	+	0.570247i
$357$	0.633328	−	1.09696i	0.0335192	−	0.0580570i
$358$	2.13974	−	3.70614i	0.113089	−	0.195876i
$359$	7.56234	−	13.0984i	0.399125	−	0.691305i	−0.594493	−	0.804101i	$-0.702647\pi$
$359$	7.56234	−	13.0984i	0.399125	−	0.691305i	0.993618	+	0.112796i	$0.0359806\pi$
$360$	1.61640			0.0851918
$361$	8.75289	−	15.1605i	0.460679	−	0.797919i
$362$	0.320779	−	0.555605i	0.0168597	−	0.0292019i
$363$	7.80331	+	13.5157i	0.409568	+	0.709392i
$364$	4.51090	+	7.81311i	0.236436	+	0.409518i
$365$	36.4737			1.90912
$366$	8.08144			0.422424
$367$	−8.34441	−	14.4529i	−0.435575	−	0.754437i	0.561768	−	0.827295i	$-0.310121\pi$
$367$	−8.34441	−	14.4529i	−0.435575	−	0.754437i	−0.997342	+	0.0728577i	$0.976788\pi$
$368$	−17.2696	−	29.9118i	−0.900239	−	1.55926i
$369$	0.785155	−	1.35993i	0.0408736	−	0.0707951i
$370$	−35.8535	+	62.1000i	−1.86393	+	3.22843i
$371$	1.37167			0.0712138
$372$	9.86167	−	17.0809i	0.511304	−	0.885604i
$373$	2.85428	−	4.94376i	0.147789	−	0.255978i	−0.782621	−	0.622498i	$-0.786118\pi$
$373$	2.85428	−	4.94376i	0.147789	−	0.255978i	0.930410	+	0.366520i	$0.119451\pi$
$374$	−0.216182	+	0.374439i	−0.0111785	+	0.0193618i
$375$	23.9066	+	41.4075i	1.23453	+	2.13828i
$376$	−0.639316			−0.0329702
$377$	−21.0947	−	36.5370i	−1.08643	−	1.88175i
$378$	−4.89854	+	8.48451i	−0.251954	+	0.436396i
$379$	−9.10399			−0.467641			−0.233820	−	0.972280i	$-0.575123\pi$
$379$	−9.10399			−0.467641			−0.233820	+	0.972280i	$0.575123\pi$
$380$	4.65200	−	8.05750i	0.238643	−	0.413341i
$381$	−3.24911	−	5.62762i	−0.166457	−	0.288312i
$382$	12.8106	+	22.1886i	0.655448	+	1.13527i
$383$	−17.3057			−0.884281			−0.442141	−	0.896946i	$-0.645781\pi$
$383$	−17.3057			−0.884281			−0.442141	+	0.896946i	$0.645781\pi$
$384$	2.23481	+	3.87081i	0.114045	+	0.197531i
$385$	−0.834833			−0.0425470
$386$	38.2861			1.94871
$387$	0.668105	−	6.31838i	0.0339617	−	0.321181i
$388$	28.1666			1.42994
$389$	−6.72163			−0.340800			−0.170400	−	0.985375i	$-0.554506\pi$
$389$	−6.72163			−0.340800			−0.170400	+	0.985375i	$0.554506\pi$
$390$	33.1955	+	57.4963i	1.68092	+	2.91144i
$391$	7.91545			0.400301
$392$	1.22351	+	2.11919i	0.0617967	+	0.107035i
$393$	−10.1831	−	17.6376i	−0.513668	−	0.889699i
$394$	16.8505	−	29.1859i	0.848915	−	1.47036i
$395$	−70.7156			−3.55809
$396$	0.193233	−	0.334690i	0.00971033	−	0.0168188i
$397$	−5.08295	−	8.80392i	−0.255106	−	0.441856i	0.709818	−	0.704385i	$-0.248777\pi$
$397$	−5.08295	−	8.80392i	−0.255106	−	0.441856i	−0.964924	+	0.262528i	$0.915444\pi$
$398$	48.6445			2.43833
$399$	−0.774167	−	1.34090i	−0.0387568	−	0.0671288i
$400$	28.1977	−	48.8399i	1.40989	−	2.44200i
$401$	−13.1123	+	22.7111i	−0.654795	+	1.13414i	0.327150	+	0.944973i	$0.393912\pi$
$401$	−13.1123	+	22.7111i	−0.654795	+	1.13414i	−0.981945	+	0.189166i	$0.939421\pi$
$402$	−4.11038	+	7.11938i	−0.205007	+	0.355083i
$403$	43.4642			2.16511
$404$	−6.51742	+	11.2885i	−0.324254	+	0.561624i
$405$	−10.9113	+	18.8988i	−0.542185	+	0.939091i
$406$	−6.47107	−	11.2082i	−0.321154	−	0.556254i
$407$	−0.964111	−	1.66989i	−0.0477892	−	0.0827733i
$408$	−0.561573			−0.0278020
$409$	−14.6313			−0.723471			−0.361736	−	0.932281i	$-0.617816\pi$
$409$	−14.6313			−0.723471			−0.361736	+	0.932281i	$0.617816\pi$
$410$	−6.68587	−	11.5803i	−0.330191	−	0.571908i
$411$	−4.01318	−	6.95103i	−0.197955	−	0.342869i
$412$	−9.39250	+	16.2683i	−0.462735	+	0.801481i
$413$	−3.95881	+	6.85686i	−0.194800	+	0.337404i
$414$	−14.9461			−0.734560
$415$	37.1356	−	64.3208i	1.82292	−	3.15738i
$416$	21.7817	−	37.7270i	1.06794	−	1.84972i
$417$	7.45896	−	12.9193i	0.365267	−	0.632661i
$418$	0.264257	+	0.457706i	0.0129252	+	0.0223872i
$419$	−13.5209			−0.660539			−0.330269	−	0.943887i	$-0.607140\pi$
$419$	−13.5209			−0.660539			−0.330269	+	0.943887i	$0.607140\pi$
$420$	4.82050	+	8.34935i	0.235216	+	0.407406i
$421$	2.48434	−	4.30301i	0.121079	−	0.209716i	−0.799114	−	0.601179i	$-0.794698\pi$
$421$	2.48434	−	4.30301i	0.121079	−	0.209716i	0.920194	+	0.391464i	$0.128031\pi$
$422$	16.8512			0.820301
$423$	−0.786013	+	1.36141i	−0.0382172	+	0.0661942i
$424$	−0.304067	−	0.526659i	−0.0147668	−	0.0255768i
$425$	6.46217	+	11.1928i	0.313461	+	0.542931i
$426$	−10.9305			−0.529584
$427$	1.29307	+	2.23967i	0.0625762	+	0.108385i
$428$	22.5417			1.08960
$429$	−1.78528			−0.0861939
$430$	−43.7503	−	31.8285i	−2.10983	−	1.53491i
$431$	10.6684			0.513879			0.256939	−	0.966428i	$-0.417286\pi$
$431$	10.6684			0.513879			0.256939	+	0.966428i	$0.417286\pi$
$432$	24.6815			1.18749
$433$	−10.6850	−	18.5069i	−0.513487	−	0.889386i	−0.999878	−	0.0156445i	$-0.995020\pi$
$433$	−10.6850	−	18.5069i	−0.513487	−	0.889386i	0.486390	−	0.873742i	$-0.338313\pi$
$434$	13.3332			0.640015
$435$	−22.5424	−	39.0447i	−1.08083	−	1.87205i
$436$	12.8036	+	22.1765i	0.613181	+	1.06206i
$437$	4.83784	−	8.37939i	0.231425	−	0.400841i
$438$	23.9270			1.14328
$439$	6.75973	−	11.7082i	0.322624	−	0.558802i	−0.658404	−	0.752665i	$-0.728768\pi$
$439$	6.75973	−	11.7082i	0.322624	−	0.558802i	0.981029	+	0.193863i	$0.0621016\pi$
$440$	0.185062	+	0.320537i	0.00882249	+	0.0152810i
$441$	6.01703			0.286525
$442$	5.50166	+	9.52915i	0.261687	+	0.453255i
$443$	−7.01635	+	12.1527i	−0.333357	+	0.577391i	−0.983168	−	0.182705i	$-0.941515\pi$
$443$	−7.01635	+	12.1527i	−0.333357	+	0.577391i	0.649811	+	0.760096i	$0.274848\pi$
$444$	−11.1339	+	19.2846i	−0.528394	+	0.915205i
$445$	−14.6287	+	25.3377i	−0.693469	+	1.20112i
$446$	−2.19077			−0.103736
$447$	−1.36357	+	2.36176i	−0.0644944	+	0.111708i
$448$	2.80362	−	4.85601i	0.132459	−	0.229425i
$449$	−10.7643	−	18.6444i	−0.508000	−	0.879883i	−0.999957	−	0.00926289i	$-0.997051\pi$
$449$	−10.7643	−	18.6444i	−0.508000	−	0.879883i	0.491957	−	0.870620i	$-0.336282\pi$
$450$	−12.2020	−	21.1344i	−0.575207	−	0.996287i
$451$	0.359570			0.0169315
$452$	32.2690			1.51780
$453$	8.00425	+	13.8638i	0.376072	+	0.651377i
$454$	−11.1583	−	19.3268i	−0.523687	−	0.907052i
$455$	−10.6229	+	18.3994i	−0.498009	+	0.862577i
$456$	−0.343228	+	0.594488i	−0.0160731	+	0.0278394i
$457$	16.2500			0.760141			0.380070	−	0.924958i	$-0.375900\pi$
$457$	16.2500			0.760141			0.380070	+	0.924958i	$0.375900\pi$
$458$	−2.25866	+	3.91212i	−0.105540	+	0.182801i
$459$	−2.82817	+	4.89854i	−0.132008	+	0.228644i
$460$	−30.1238	+	52.1759i	−1.40453	+	2.43271i
$461$	19.4012	+	33.6038i	0.903602	+	1.56508i	0.822783	+	0.568355i	$0.192420\pi$
$461$	19.4012	+	33.6038i	0.903602	+	1.56508i	0.0808186	+	0.996729i	$0.474247\pi$
$462$	−0.547657			−0.0254793
$463$	0.00203399	+	0.00352297i	9.45273e−5	+	0.000163726i	0.866073	−	0.499918i	$-0.166637\pi$
$463$	0.00203399	+	0.00352297i	9.45273e−5	+	0.000163726i	−0.865978	+	0.500082i	$0.833303\pi$
$464$	−16.3024	+	28.2366i	−0.756820	+	1.31085i
$465$	46.4473			2.15394
$466$	−14.1979	+	24.5915i	−0.657707	+	1.13918i
$467$	−3.00474	−	5.20436i	−0.139043	−	0.240829i	0.788092	−	0.615558i	$-0.211069\pi$
$467$	−3.00474	−	5.20436i	−0.139043	−	0.240829i	−0.927135	+	0.374729i	$0.877736\pi$
$468$	−4.91762	−	8.51757i	−0.227317	−	0.393725i
$469$	−2.63073			−0.121476
$470$	6.69317	+	11.5929i	0.308733	+	0.534741i
$471$	−3.46162			−0.159503
$472$	3.51028			0.161574
$473$	1.32944	−	0.590905i	0.0611279	−	0.0271698i
$474$	−46.3899			−2.13076
$475$	15.7985			0.724883
$476$	0.798926	+	1.38378i	0.0366187	+	0.0634254i
$477$	−1.49535			−0.0684673
$478$	−6.97850	−	12.0871i	−0.319189	−	0.552852i
$479$	−17.6591	−	30.5865i	−0.806865	−	1.39753i	−0.915024	−	0.403398i	$-0.867829\pi$
$479$	−17.6591	−	30.5865i	−0.806865	−	1.39753i	0.108159	−	0.994134i	$-0.465504\pi$
$480$	23.2766	−	40.3163i	1.06243	−	1.84018i
$481$	−49.0716			−2.23747
$482$	3.03076	−	5.24942i	0.138047	−	0.239105i
$483$	5.01307	+	8.68290i	0.228103	+	0.395085i
$484$	−19.6873			−0.894879
$485$	33.1653	+	57.4440i	1.50596	+	2.60840i
$486$	9.37672	−	16.2410i	0.425337	−	0.736705i
$487$	18.0870	−	31.3275i	0.819598	−	1.41959i	−0.0863807	−	0.996262i	$-0.527530\pi$
$487$	18.0870	−	31.3275i	0.819598	−	1.41959i	0.905979	−	0.423323i	$-0.139137\pi$
$488$	0.573285	−	0.992959i	0.0259514	−	0.0449491i
$489$	−19.2187			−0.869101
$490$	25.6185	−	44.3726i	1.15733	−	2.00455i
$491$	6.16598	−	10.6798i	0.278267	−	0.481972i	−0.692687	−	0.721238i	$-0.743573\pi$
$491$	6.16598	−	10.6798i	0.278267	−	0.481972i	0.970954	+	0.239266i	$0.0769068\pi$
$492$	−2.07623	−	3.59614i	−0.0936038	−	0.162127i
$493$	−3.73607	−	6.47107i	−0.168264	−	0.291442i
$494$	13.4502			0.605154
$495$	0.910104			0.0409061
$496$	−16.7950	−	29.0898i	−0.754119	−	1.30617i
$497$	−1.74893	−	3.02924i	−0.0784504	−	0.135880i
$498$	24.3612	−	42.1949i	1.09165	−	1.89080i
$499$	18.7265	−	32.4352i	0.838312	−	1.45200i	−0.0529937	−	0.998595i	$-0.516876\pi$
$499$	18.7265	−	32.4352i	0.838312	−	1.45200i	0.891305	−	0.453404i	$-0.149790\pi$
$500$	−60.3152			−2.69738
$501$	−10.3263	+	17.8857i	−0.461345	+	0.799072i
$502$	0.259944	−	0.450236i	0.0116019	−	0.0200950i
$503$	−4.61599	+	7.99512i	−0.205817	+	0.356485i	−0.950393	−	0.311053i	$-0.899318\pi$
$503$	−4.61599	+	7.99512i	−0.205817	+	0.356485i	0.744576	+	0.667538i	$0.232652\pi$
$504$	0.169665	+	0.293868i	0.00755748	+	0.0130899i
$505$	−30.6962			−1.36596
$506$	−1.71118	−	2.96385i	−0.0760712	−	0.131759i
$507$	−13.4533	+	23.3018i	−0.597483	+	1.03487i
$508$	8.19732			0.363697
$509$	15.8510	−	27.4547i	0.702582	−	1.21691i	−0.264974	−	0.964255i	$-0.585364\pi$
$509$	15.8510	−	27.4547i	0.702582	−	1.21691i	0.967557	−	0.252653i	$-0.0813031\pi$
$510$	5.87925	+	10.1832i	0.260337	+	0.450918i
$511$	3.82845	+	6.63107i	0.169361	+	0.293341i
$512$	−30.2279			−1.33590
$513$	3.45710	+	5.98788i	0.152635	+	0.264371i
$514$	14.1192			0.622772
$515$	−44.2375			−1.94934
$516$	−13.5862	−	9.88404i	−0.598101	−	0.435121i
$517$	−0.359963			−0.0158311
$518$	−15.0534			−0.661407
$519$	−12.6325	−	21.8802i	−0.554507	−	0.960434i
$520$	9.41935			0.413066
$521$	21.4765	+	37.1984i	0.940902	+	1.62969i	0.763755	+	0.645506i	$0.223353\pi$
$521$	21.4765	+	37.1984i	0.940902	+	1.62969i	0.177147	+	0.984184i	$0.443313\pi$
$522$	7.05452	+	12.2188i	0.308768	+	0.534802i
$523$	8.11627	−	14.0578i	0.354900	−	0.614704i	−0.632201	−	0.774804i	$-0.717848\pi$
$523$	8.11627	−	14.0578i	0.354900	−	0.614704i	0.987101	+	0.160100i	$0.0511817\pi$
$524$	25.6913			1.12233
$525$	−8.18534	+	14.1774i	−0.357238	+	0.618754i
$526$	−4.48605	−	7.77006i	−0.195601	−	0.338791i
$527$	7.69794			0.335328
$528$	0.689849	+	1.19485i	0.0300218	+	0.0519993i
$529$	−19.8272	+	34.3417i	−0.862051	+	1.49312i
$530$	−6.36670	+	11.0275i	−0.276552	+	0.479002i
$531$	4.31575	−	7.47509i	0.187287	−	0.324391i
$532$	1.95318			0.0846812
$533$	4.57538	−	7.92479i	0.198182	−	0.343261i
$534$	−9.59656	+	16.6217i	−0.415284	+	0.719293i
$535$	26.5422	+	45.9724i	1.14752	+	1.98756i
$536$	0.583168	+	1.01008i	0.0251890	+	0.0436287i
$537$	3.12960			0.135052
$538$	−22.8980			−0.987202
$539$	0.688891	+	1.19319i	0.0296726	+	0.0513945i
$540$	−21.5263	−	37.2846i	−0.926344	−	1.60448i
$541$	−8.72975	+	15.1204i	−0.375321	+	0.650075i	−0.990375	−	0.138410i	$-0.955801\pi$
$541$	−8.72975	+	15.1204i	−0.375321	+	0.650075i	0.615054	+	0.788485i	$0.289134\pi$
$542$	11.1805	−	19.3652i	0.480245	−	0.831809i
$543$	0.469173			0.0201342
$544$	3.85775	−	6.68182i	0.165400	−	0.286481i
$545$	−30.1517	+	52.2243i	−1.29156	+	2.23704i
$546$	−6.96870	+	12.0701i	−0.298233	+	0.516554i
$547$	−7.34043	−	12.7140i	−0.313854	−	0.543611i	0.665339	−	0.746541i	$-0.268287\pi$
$547$	−7.34043	−	12.7140i	−0.313854	−	0.543611i	−0.979193	+	0.202930i	$0.934954\pi$
$548$	10.1250			0.432520
$549$	−1.40966	−	2.44160i	−0.0601628	−	0.104205i
$550$	2.79401	−	4.83937i	0.119137	−	0.206352i
$551$	−9.13380			−0.389113
$552$	2.22255	−	3.84957i	0.0945980	−	0.163849i
$553$	−7.42263	−	12.8564i	−0.315642	−	0.546709i
$554$	14.6417	+	25.3601i	0.622065	+	1.07745i
$555$	−52.4395			−2.22593
$556$	9.40928	+	16.2974i	0.399042	+	0.691162i
$557$	−29.5345			−1.25142			−0.625708	−	0.780058i	$-0.715190\pi$
$557$	−29.5345			−1.25142			−0.625708	+	0.780058i	$0.715190\pi$
$558$	−14.5354			−0.615332
$559$	3.89329	−	36.8194i	0.164668	−	1.55730i
$560$	16.4192			0.693838
$561$	−0.316190			−0.0133495
$562$	7.51323	+	13.0133i	0.316927	+	0.548933i
$563$	5.74524			0.242133			0.121066	−	0.992644i	$-0.461369\pi$
$563$	5.74524			0.242133			0.121066	+	0.992644i	$0.461369\pi$
$564$	2.07850	+	3.60007i	0.0875206	+	0.151590i
$565$	37.9957	+	65.8105i	1.59849	+	2.76867i
$566$	19.8673	−	34.4112i	0.835085	−	1.44641i
$567$	−4.58118			−0.192391
$568$	−0.775392	+	1.34302i	−0.0325347	+	0.0563518i
$569$	4.69661	+	8.13476i	0.196892	+	0.341027i	0.947519	−	0.319699i	$-0.103582\pi$
$569$	4.69661	+	8.13476i	0.196892	+	0.341027i	−0.750627	+	0.660726i	$0.770249\pi$
$570$	14.3734			0.602034
$571$	−5.17269	−	8.95936i	−0.216470	−	0.374938i	0.737256	−	0.675613i	$-0.236121\pi$
$571$	−5.17269	−	8.95936i	−0.216470	−	0.374938i	−0.953726	+	0.300676i	$0.902788\pi$
$572$	1.12604	−	1.95036i	0.0470820	−	0.0815484i
$573$	−9.36845	+	16.2266i	−0.391373	+	0.677877i
$574$	1.40356	−	2.43103i	0.0585834	−	0.101469i
$575$	−102.302			−4.26629
$576$	−3.05640	+	5.29385i	−0.127350	+	0.220577i
$577$	−11.4201	+	19.7802i	−0.475426	+	0.823462i	−0.999604	−	0.0281467i	$-0.991039\pi$
$577$	−11.4201	+	19.7802i	−0.475426	+	0.823462i	0.524178	+	0.851609i	$0.324373\pi$
$578$	0.974398	+	1.68771i	0.0405296	+	0.0701993i
$579$	13.9994	+	24.2477i	0.581795	+	1.00770i
$580$	56.8734			2.36154
$581$	15.5917			0.646853
$582$	21.7567	+	37.6837i	0.901843	+	1.56204i
$583$	−0.171203	−	0.296532i	−0.00709049	−	0.0122811i
$584$	1.69735	−	2.93989i	0.0702367	−	0.121654i
$585$	11.5807	−	20.0583i	0.478803	−	0.829311i
$586$	22.1195			0.913749
$587$	−7.67742	+	13.2977i	−0.316881	+	0.548854i	−0.979836	−	0.199806i	$-0.935969\pi$
$587$	−7.67742	+	13.2977i	−0.316881	+	0.548854i	0.662955	+	0.748660i	$0.269302\pi$
$588$	7.95559	−	13.7795i	0.328083	−	0.568257i
$589$	4.70491	−	8.14913i	0.193862	−	0.335779i
$590$	−36.7501	−	63.6530i	−1.51298	−	2.62055i
$591$	24.6456			1.01379
$592$	18.9618	+	32.8428i	0.779325	+	1.34983i
$593$	−9.19090	+	15.9191i	−0.377425	+	0.653719i	−0.990687	−	0.136160i	$-0.956524\pi$
$593$	−9.19090	+	15.9191i	−0.377425	+	0.653719i	0.613262	+	0.789880i	$0.289857\pi$
$594$	2.44560			0.100344
$595$	−1.88142	+	3.25872i	−0.0771307	+	0.133594i
$596$	−1.72010	−	2.97930i	−0.0704581	−	0.122037i
$597$	17.7870	+	30.8079i	0.727971	+	1.26088i
$598$	−87.0962			−3.56163
$599$	−16.0198	−	27.7472i	−0.654553	−	1.13372i	−0.982006	−	0.188852i	$-0.939523\pi$
$599$	−16.0198	−	27.7472i	−0.654553	−	1.13372i	0.327453	−	0.944868i	$-0.393810\pi$
$600$	7.25796			0.296305
$601$	−19.8551			−0.809906			−0.404953	−	0.914337i	$-0.632712\pi$
$601$	−19.8551			−0.809906			−0.404953	+	0.914337i	$0.632712\pi$
$602$	1.19432	−	11.2948i	0.0486767	−	0.460344i
$603$	2.86792			0.116791
$604$	−20.1943			−0.821694
$605$	−23.1812	−	40.1511i	−0.942451	−	1.63237i
$606$	−20.1369			−0.818008
$607$	−9.64815	−	16.7111i	−0.391606	−	0.678282i	0.601055	−	0.799208i	$-0.294747\pi$
$607$	−9.64815	−	16.7111i	−0.391606	−	0.678282i	−0.992662	+	0.120925i	$0.961414\pi$
$608$	−4.71564	−	8.16773i	−0.191244	−	0.331245i
$609$	4.73232	−	8.19661i	0.191763	−	0.332144i
$610$	−24.0075			−0.972034
$611$	−4.58038	+	7.93344i	−0.185302	+	0.320953i
$612$	−0.870959	−	1.50855i	−0.0352064	−	0.0609793i
$613$	4.18296			0.168948			0.0844741	−	0.996426i	$-0.473079\pi$
$613$	4.18296			0.168948			0.0844741	+	0.996426i	$0.473079\pi$
$614$	11.3298	+	19.6239i	0.457235	+	0.791954i
$615$	4.88940	−	8.46869i	0.197160	−	0.341491i
$616$	−0.0388499	+	0.0672901i	−0.00156531	+	0.00271119i
$617$	1.09940	−	1.90422i	0.0442603	−	0.0766610i	−0.843047	−	0.537841i	$-0.819240\pi$
$617$	1.09940	−	1.90422i	0.0442603	−	0.0766610i	0.887307	+	0.461180i	$0.152574\pi$
$618$	−29.0201			−1.16736
$619$	10.7808	−	18.6729i	0.433317	−	0.750527i	−0.563839	−	0.825884i	$-0.690676\pi$
$619$	10.7808	−	18.6729i	0.433317	−	0.750527i	0.997157	+	0.0753571i	$0.0240097\pi$
$620$	−29.2960	+	50.7421i	−1.17656	+	2.03785i
$621$	−22.3863	−	38.7741i	−0.898329	−	1.55595i
$622$	2.50877	+	4.34531i	0.100592	+	0.174231i
$623$	−6.14200			−0.246074
$624$	35.1121			1.40561
$625$	−38.7084	−	67.0450i	−1.54834	−	2.68180i
$626$	16.3711	+	28.3556i	0.654322	+	1.13332i
$627$	−0.193252	+	0.334722i	−0.00771775	+	0.0133675i
$628$	2.18337	−	3.78171i	0.0871259	−	0.150906i
$629$	−8.69107			−0.346536
$630$	3.55253	−	6.15316i	0.141536	−	0.245148i
$631$	−15.3758	+	26.6317i	−0.612101	+	1.06019i	0.378785	+	0.925485i	$0.376342\pi$
$631$	−15.3758	+	26.6317i	−0.612101	+	1.06019i	−0.990886	+	0.134705i	$0.956991\pi$
$632$	−3.29083	+	5.69989i	−0.130902	+	0.226729i
$633$	6.16166	+	10.6723i	0.244904	+	0.424186i
$634$	48.4678			1.92490
$635$	9.65210	+	16.7179i	0.383032	+	0.663430i
$636$	−1.97712	+	3.42447i	−0.0783979	+	0.135789i
$637$	35.0634			1.38926
$638$	−1.61535	+	2.79786i	−0.0639522	+	0.110768i
$639$	1.90662	+	3.30237i	0.0754249	+	0.130640i
$640$	−6.63894	−	11.4990i	−0.262427	−	0.454537i
$641$	49.2992			1.94720			0.973601	−	0.228258i	$-0.0733029\pi$
$641$	49.2992			1.94720			0.973601	+	0.228258i	$0.0733029\pi$
$642$	17.4119	+	30.1582i	0.687192	+	1.19025i
$643$	−19.2722			−0.760023			−0.380011	−	0.924982i	$-0.624080\pi$
$643$	−19.2722			−0.760023			−0.380011	+	0.924982i	$0.624080\pi$
$644$	−12.6477			−0.498390
$645$	4.16049	−	39.3464i	0.163819	−	1.54926i
$646$	2.38217			0.0937252
$647$	−12.7590			−0.501609			−0.250805	−	0.968038i	$-0.580695\pi$
$647$	−12.7590			−0.501609			−0.250805	+	0.968038i	$0.580695\pi$
$648$	1.01554	+	1.75896i	0.0398940	+	0.0690984i
$649$	1.97644			0.0775821
$650$	−71.1053	−	123.158i	−2.78898	−	4.83065i
$651$	4.87532	+	8.44430i	0.191079	+	0.330958i
$652$	12.1220	−	20.9958i	0.474732	−	0.822260i
$653$	−38.8026			−1.51846			−0.759232	−	0.650820i	$-0.774425\pi$
$653$	−38.8026			−1.51846			−0.759232	+	0.650820i	$0.774425\pi$
$654$	−19.7797	+	34.2595i	−0.773449	+	1.33965i
$655$	30.2508	+	52.3958i	1.18199	+	2.04727i
$656$	−7.07190			−0.276111
$657$	−4.17363	−	7.22895i	−0.162829	−	0.282028i
$658$	−1.40509	+	2.43369i	−0.0547761	+	0.0948751i
$659$	16.7907	−	29.0824i	0.654073	−	1.13289i	−0.328052	−	0.944660i	$-0.606392\pi$
$659$	16.7907	−	29.0824i	0.654073	−	1.13289i	0.982125	−	0.188229i	$-0.0602746\pi$
$660$	1.20332	−	2.08421i	0.0468392	−	0.0811279i
$661$	−33.7051			−1.31098			−0.655488	−	0.755205i	$-0.727537\pi$
$661$	−33.7051			−1.31098			−0.655488	+	0.755205i	$0.727537\pi$
$662$	9.45684	−	16.3797i	0.367550	−	0.636616i
$663$	−4.02338	+	6.96870i	−0.156255	+	0.270642i
$664$	−3.45630	−	5.98648i	−0.134130	−	0.232321i
$665$	2.29981	+	3.98339i	0.0891829	+	0.154469i
$666$	16.4106			0.635899
$667$	59.1454			2.29012
$668$	−13.0263	−	22.5623i	−0.504004	−	0.872960i
$669$	−0.801057	−	1.38747i	−0.0309707	−	0.0536428i
$670$	12.2107	−	21.1495i	0.471739	−	0.817076i
$671$	0.322784	−	0.559079i	0.0124610	−	0.0215830i
$672$	9.77289			0.376997
$673$	3.67455	−	6.36450i	0.141643	−	0.245334i	−0.786472	−	0.617626i	$-0.788095\pi$
$673$	3.67455	−	6.36450i	0.141643	−	0.245334i	0.928116	+	0.372292i	$0.121428\pi$
$674$	−11.0572	+	19.1516i	−0.425907	+	0.737693i
$675$	36.5523	−	63.3104i	1.40690	−	2.43682i
$676$	−16.9710	−	29.3946i	−0.652731	−	1.13056i
$677$	26.4021			1.01471			0.507357	−	0.861736i	$-0.330623\pi$
$677$	26.4021			1.01471			0.507357	+	0.861736i	$0.330623\pi$
$678$	24.9255	+	43.1722i	0.957257	+	1.65802i
$679$	−6.96236	+	12.0592i	−0.267191	+	0.462788i
$680$	1.66826			0.0639748
$681$	8.16014	−	14.1338i	0.312697	−	0.541607i
$682$	−1.66416	−	2.88241i	−0.0637239	−	0.110373i
$683$	−7.84981	−	13.5963i	−0.300365	−	0.520247i	0.675854	−	0.737036i	$-0.263775\pi$
$683$	−7.84981	−	13.5963i	−0.300365	−	0.520247i	−0.976219	+	0.216789i	$0.930442\pi$
$684$	−2.12929			−0.0814153
$685$	11.9219	+	20.6494i	0.455513	+	0.788971i
$686$	22.8805			0.873582
$687$	−3.30354			−0.126038
$688$	−26.1470	+	11.6217i	−0.996845	+	0.443073i
$689$	−8.71393			−0.331974
$690$	−93.0738			−3.54326
$691$	−0.598797	−	1.03715i	−0.0227793	−	0.0394549i	0.854411	−	0.519598i	$-0.173918\pi$
$691$	−0.598797	−	1.03715i	−0.0227793	−	0.0394549i	−0.877190	+	0.480143i	$0.840585\pi$
$692$	31.8712			1.21156
$693$	0.0955287	+	0.165461i	0.00362884	+	0.00628533i
$694$	−5.37269	−	9.30578i	−0.203945	−	0.353242i
$695$	−22.1583	+	38.3793i	−0.840511	+	1.45581i
$696$	−4.19615			−0.159055
$697$	0.810345	−	1.40356i	0.0306940	−	0.0531636i
$698$	9.49244	+	16.4414i	0.359294	+	0.622315i
$699$	−20.7660			−0.785443
$700$	−10.3256	−	17.8844i	−0.390270	−	0.675968i
$701$	−18.8268	+	32.6089i	−0.711078	+	1.23162i	0.253375	+	0.967368i	$0.418459\pi$
$701$	−18.8268	+	32.6089i	−0.711078	+	1.23162i	−0.964453	+	0.264255i	$0.914874\pi$
$702$	31.1193	−	53.9001i	1.17452	−	2.03433i
$703$	−5.31190	+	9.20047i	−0.200342	+	0.347002i
$704$	−1.39971			−0.0527536
$705$	−4.89474	+	8.47794i	−0.184347	+	0.319298i
$706$	1.76202	−	3.05191i	0.0663145	−	0.114860i
$707$	−3.22202	−	5.58070i	−0.121176	−	0.209884i
$708$	−11.4124	−	19.7668i	−0.428903	−	0.742883i
$709$	−46.6831			−1.75322			−0.876610	−	0.481201i	$-0.840201\pi$
$709$	−46.6831			−1.75322			−0.876610	+	0.481201i	$0.840201\pi$
$710$	32.4711			1.21862
$711$	8.09188	+	14.0155i	0.303469	+	0.525624i
$712$	1.36153	+	2.35824i	0.0510255	+	0.0883788i
$713$	−30.4663	+	52.7692i	−1.14097	+	1.97622i
$714$	−1.23423	+	2.13774i	−0.0461897	+	0.0800030i
$715$	5.30350			0.198340
$716$	−1.97395	+	3.41899i	−0.0737701	+	0.127774i
$717$	5.10340	−	8.83936i	0.190590	−	0.330112i
$718$	−14.7374	+	25.5260i	−0.549997	+	0.952622i
$719$	3.38775	+	5.86776i	0.126342	+	0.218831i	0.922257	−	0.386578i	$-0.126343\pi$
$719$	3.38775	+	5.86776i	0.126342	+	0.218831i	−0.795915	+	0.605409i	$0.793010\pi$
$720$	−17.8996			−0.667079
$721$	−4.64337	−	8.04256i	−0.172928	−	0.299521i
$722$	−17.0576	+	29.5446i	−0.634818	+	1.09954i
$723$	4.43281			0.164858
$724$	−0.295925	+	0.512557i	−0.0109980	+	0.0190490i
$725$	48.2863	+	83.6343i	1.79331	+	3.10610i
$726$	−15.2071	−	26.3394i	−0.564387	−	0.977547i
$727$	17.3106			0.642015			0.321008	−	0.947077i	$-0.395978\pi$
$727$	17.3106			0.642015			0.321008	+	0.947077i	$0.395978\pi$
$728$	0.988698	+	1.71247i	0.0366436	+	0.0634685i
$729$	29.1778			1.08066
$730$	−71.0798			−2.63078
$731$	0.689540	−	6.52108i	0.0255035	−	0.241191i
$732$	−7.45529			−0.275556
$733$	−15.2017			−0.561487			−0.280743	−	0.959783i	$-0.590581\pi$
$733$	−15.2017			−0.561487			−0.280743	+	0.959783i	$0.590581\pi$
$734$	16.2615	+	28.1658i	0.600224	+	1.03962i
$735$	37.4699			1.38210
$736$	30.5359	+	52.8896i	1.12557	+	1.94954i
$737$	0.328349	+	0.568717i	0.0120949	+	0.0209490i
$738$	−1.53011	+	2.65022i	−0.0563240	+	0.0975561i
$739$	24.3880			0.897128			0.448564	−	0.893751i	$-0.351936\pi$
$739$	24.3880			0.897128			0.448564	+	0.893751i	$0.351936\pi$
$740$	33.0755	−	57.2885i	1.21588	−	2.10597i
$741$	4.91810	+	8.51840i	0.180671	+	0.312931i
$742$	−2.67311			−0.0981331
$743$	13.7332	+	23.7866i	0.503823	+	0.872647i	0.999990	+	0.00442035i	$0.00140705\pi$
$743$	13.7332	+	23.7866i	0.503823	+	0.872647i	−0.496167	+	0.868227i	$0.665260\pi$
$744$	2.16148	−	3.74379i	0.0792436	−	0.137254i
$745$	4.05073	−	7.01607i	0.148407	−	0.257049i
$746$	−5.56241	+	9.63437i	−0.203654	+	0.352739i
$747$	−16.9975			−0.621906
$748$	0.199432	−	0.345427i	0.00729197	−	0.0126301i
$749$	−5.57198	+	9.65095i	−0.203596	+	0.352638i
$750$	−46.5892	−	80.6948i	−1.70120	−	2.94656i
$751$	5.44792	+	9.43607i	0.198797	+	0.344327i	0.948139	−	0.317857i	$-0.102963\pi$
$751$	5.44792	+	9.43607i	0.198797	+	0.344327i	−0.749341	+	0.662184i	$0.769630\pi$
$752$	7.07962			0.258167
$753$	0.380196			0.0138551
$754$	41.1092	+	71.2032i	1.49711	+	2.59307i
$755$	−23.7782	−	41.1850i	−0.865376	−	1.49887i
$756$	4.51900	−	7.82713i	0.164354	−	0.284670i
$757$	−2.92627	+	5.06844i	−0.106357	+	0.184216i	−0.914292	−	0.405056i	$-0.867252\pi$
$757$	−2.92627	+	5.06844i	−0.106357	+	0.184216i	0.807935	+	0.589272i	$0.200585\pi$
$758$	17.7418			0.644412
$759$	1.25139	−	2.16748i	0.0454227	−	0.0786744i
$760$	1.01962	−	1.76604i	0.0369856	−	0.0640610i
$761$	−11.7394	+	20.3332i	−0.425553	+	0.737079i	−0.996472	−	0.0839270i	$-0.973254\pi$
$761$	−11.7394	+	20.3332i	−0.425553	+	0.737079i	0.570919	+	0.821006i	$0.306587\pi$
$762$	6.33185	+	10.9671i	0.229379	+	0.397295i
$763$	−12.6594			−0.458303
$764$	−11.8180	−	20.4695i	−0.427562	−	0.740559i
$765$	2.05105	−	3.55253i	0.0741560	−	0.128442i
$766$	33.7253			1.21855
$767$	25.1494	−	43.5600i	0.908092	−	1.57286i
$768$	−13.3464	−	23.1167i	−0.481597	−	0.834151i
$769$	−14.4519	−	25.0314i	−0.521148	−	0.902654i	−0.999698	−	0.0245937i	$-0.992171\pi$
$769$	−14.4519	−	25.0314i	−0.521148	−	0.902654i	0.478550	−	0.878060i	$-0.341163\pi$
$770$	1.62692			0.0586301
$771$	5.16272	+	8.94209i	0.185931	+	0.322042i
$772$	−35.3197			−1.27118
$773$	11.2809			0.405746			0.202873	−	0.979205i	$-0.434972\pi$
$773$	11.2809			0.405746			0.202873	+	0.979205i	$0.434972\pi$
$774$	−1.30200	+	12.3132i	−0.0467994	+	0.442590i
$775$	−99.4908			−3.57382
$776$	6.17354			0.221617
$777$	−5.50429	−	9.53372i	−0.197465	−	0.342020i
$778$	13.0991			0.469625
$779$	−0.990550	−	1.71568i	−0.0354901	−	0.0614707i
$780$	−30.6235	−	53.0415i	−1.09650	−	1.89919i
$781$	−0.436579	+	0.756178i	−0.0156220	+	0.0270582i
$782$	−15.4256			−0.551618
$783$	−21.1325	+	36.6026i	−0.755215	+	1.30807i
$784$	−13.5489	−	23.4673i	−0.483888	−	0.838118i
$785$	10.2834			0.367030
$786$	19.8447	+	34.3721i	0.707837	+	1.22601i
$787$	−9.35742	+	16.2075i	−0.333556	+	0.577736i	−0.983206	−	0.182497i	$-0.941582\pi$
$787$	−9.35742	+	16.2075i	−0.333556	+	0.577736i	0.649650	+	0.760233i	$0.274915\pi$
$788$	−15.5449	+	26.9246i	−0.553764	+	0.959148i
$789$	3.28066	−	5.68227i	0.116795	−	0.202294i
$790$	137.810			4.90307
$791$	−7.97641	+	13.8155i	−0.283608	+	0.491224i
$792$	0.0423527	−	0.0733571i	0.00150494	−	0.00260663i
$793$	−8.21459	−	14.2281i	−0.291709	−	0.505254i
$794$	9.90562	+	17.1570i	0.351537	+	0.608881i
$795$	−9.31199			−0.330262
$796$	−44.8755			−1.59057
$797$	−17.5890	−	30.4650i	−0.623033	−	1.07912i	−0.988918	−	0.148465i	$-0.952567\pi$
$797$	−17.5890	−	30.4650i	−0.623033	−	1.07912i	0.365885	−	0.930660i	$-0.380766\pi$
$798$	1.50869	+	2.61313i	0.0534071	+	0.0925039i
$799$	−0.811230	+	1.40509i	−0.0286992	+	0.0497085i
$800$	−49.8589	+	86.3582i	−1.76278	+	3.05322i
$801$	6.69578			0.236584
$802$	25.5531	−	44.2593i	0.902312	−	1.56285i
$803$	0.955680	−	1.65529i	0.0337252	−	0.0584138i
$804$	3.79191	−	6.56777i	0.133730	−	0.231628i
$805$	−14.8923	−	25.7942i	−0.524884	−	0.909126i
$806$	−84.7028			−2.98353
$807$	−8.37269	−	14.5019i	−0.294733	−	0.510492i
$808$	−1.42848	+	2.47421i	−0.0502539	+	0.0870423i
$809$	53.2008			1.87044			0.935220	−	0.354066i	$-0.115201\pi$
$809$	53.2008			1.87044			0.935220	+	0.354066i	$0.115201\pi$
$810$	21.2638	−	36.8300i	0.747134	−	1.29407i
$811$	−2.72967	−	4.72793i	−0.0958517	−	0.166020i	0.814112	−	0.580708i	$-0.197224\pi$
$811$	−2.72967	−	4.72793i	−0.0958517	−	0.166020i	−0.909964	+	0.414688i	$0.863891\pi$
$812$	5.96969	+	10.3398i	0.209495	+	0.362856i
$813$	16.3527			0.573515
$814$	1.87886	+	3.25427i	0.0658538	+	0.114062i
$815$	57.0929			1.99988
$816$	6.21871			0.217698
$817$	−6.48186	−	4.71558i	−0.226772	−	0.164977i
$818$	28.5134			0.996948
$819$	4.86225			0.169901
$820$	6.16785	+	10.6830i	0.215391	+	0.373067i
$821$	22.1526			0.773132			0.386566	−	0.922262i	$-0.373661\pi$
$821$	22.1526			0.773132			0.386566	+	0.922262i	$0.373661\pi$
$822$	7.82086	+	13.5461i	0.272784	+	0.472475i
$823$	−12.3616	−	21.4110i	−0.430899	−	0.746339i	0.566052	−	0.824370i	$-0.308470\pi$
$823$	−12.3616	−	21.4110i	−0.430899	−	0.746339i	−0.996951	+	0.0780306i	$0.975137\pi$
$824$	−2.05864	+	3.56568i	−0.0717163	+	0.124216i
$825$	4.08655			0.142275
$826$	7.71491	−	13.3626i	0.268436	−	0.464945i
$827$	8.77478	+	15.1984i	0.305129	+	0.528499i	0.977290	−	0.211906i	$-0.0679671\pi$
$827$	8.77478	+	15.1984i	0.305129	+	0.528499i	−0.672161	+	0.740405i	$0.734634\pi$
$828$	13.7881			0.479168
$829$	20.3073	+	35.1732i	0.705300	+	1.22162i	0.966583	+	0.256353i	$0.0825211\pi$
$829$	20.3073	+	35.1732i	0.705300	+	1.22162i	−0.261283	+	0.965262i	$0.584146\pi$
$830$	−72.3697	+	125.348i	−2.51199	+	4.35089i
$831$	−10.7075	+	18.5460i	−0.371439	+	0.643352i
$832$	−17.8107	+	30.8491i	−0.617477	+	1.06950i
$833$	6.21007			0.215166
$834$	−14.5360	+	25.1771i	−0.503340	+	0.871811i
$835$	30.6762	−	53.1328i	1.06159	−	1.83874i
$836$	−0.243782	−	0.422243i	−0.00843139	−	0.0146036i
$837$	−21.7711	−	37.7087i	−0.752519	−	1.30340i
$838$	26.3494			0.910226
$839$	0.558126			0.0192686			0.00963432	−	0.999954i	$-0.496933\pi$
$839$	0.558126			0.0192686			0.00963432	+	0.999954i	$0.496933\pi$
$840$	1.05655	+	1.83001i	0.0364546	+	0.0631412i
$841$	−13.4165	−	23.2380i	−0.462638	−	0.801312i
$842$	−4.84147	+	8.38568i	−0.166848	+	0.288990i
$843$	−5.49446	+	9.51668i	−0.189239	+	0.327772i
$844$	−15.5455			−0.535099
$845$	39.9657	−	69.2226i	1.37486	−	2.38133i
$846$	1.53178	−	2.65312i	0.0526636	−	0.0912160i
$847$	4.86642	−	8.42888i	0.167212	−	0.289620i
$848$	3.36715	+	5.83208i	0.115629	+	0.200274i
$849$	29.0581			0.997270
$850$	−12.5934	−	21.8125i	−0.431952	−	0.748162i
$851$	34.3969	−	59.5771i	1.17911	−	2.04228i
$852$	10.0836			0.345458
$853$	−4.71564	+	8.16773i	−0.161460	+	0.279658i	−0.935393	−	0.353611i	$-0.884954\pi$
$853$	−4.71564	+	8.16773i	−0.161460	+	0.279658i	0.773932	+	0.633268i	$0.218287\pi$
$854$	−2.51993	−	4.36465i	−0.0862304	−	0.149355i
$855$	−2.50717	−	4.34254i	−0.0857434	−	0.148512i
$856$	4.94069			0.168869
$857$	10.6627	+	18.4684i	0.364232	+	0.630868i	0.988653	−	0.150220i	$-0.0479983\pi$
$857$	10.6627	+	18.4684i	0.364232	+	0.630868i	−0.624421	+	0.781088i	$0.714665\pi$
$858$	3.47914			0.118776
$859$	−21.6340			−0.738142			−0.369071	−	0.929401i	$-0.620324\pi$
$859$	−21.6340			−0.738142			−0.369071	+	0.929401i	$0.620324\pi$
$860$	40.3605	+	29.3624i	1.37628	+	1.00125i
$861$	2.05286			0.0699611
$862$	−20.7905			−0.708128
$863$	−10.9626	−	18.9878i	−0.373171	−	0.646351i	0.616880	−	0.787057i	$-0.288396\pi$
$863$	−10.9626	−	18.9878i	−0.373171	−	0.646351i	−0.990051	+	0.140706i	$0.955063\pi$
$864$	−43.6416			−1.48472
$865$	37.5274	+	64.9993i	1.27597	+	2.21004i
$866$	20.8228	+	36.0662i	0.707589	+	1.22558i
$867$	−0.712581	+	1.23423i	−0.0242005	+	0.0419165i
$868$	−12.3002			−0.417495
$869$	−1.85288	+	3.20928i	−0.0628547	+	0.108867i
$870$	43.9306	+	76.0900i	1.48939	+	2.57969i
$871$	16.7124			0.566278
$872$	2.80629	+	4.86063i	0.0950329	+	0.164602i
$873$	7.59011	−	13.1465i	0.256886	−	0.444940i
$874$	−9.42797	+	16.3297i	−0.318906	+	0.552361i
$875$	14.9090	−	25.8232i	0.504017	−	0.872983i
$876$	−22.0732			−0.745783
$877$	−4.80304	+	8.31912i	−0.162187	+	0.280917i	−0.935653	−	0.352922i	$-0.885188\pi$
$877$	−4.80304	+	8.31912i	−0.162187	+	0.280917i	0.773466	+	0.633838i	$0.218522\pi$
$878$	−13.1733	+	22.8169i	−0.444579	+	0.770033i
$879$	8.08804	+	14.0089i	0.272803	+	0.472509i
$880$	−2.04933	−	3.54954i	−0.0690828	−	0.119655i
$881$	57.2442			1.92861			0.964303	−	0.264800i	$-0.0853058\pi$
$881$	57.2442			1.92861			0.964303	+	0.264800i	$0.0853058\pi$
$882$	−11.7260			−0.394834
$883$	3.20886	+	5.55790i	0.107987	+	0.187038i	0.914955	−	0.403557i	$-0.132226\pi$
$883$	3.20886	+	5.55790i	0.107987	+	0.187038i	−0.806968	+	0.590595i	$0.798893\pi$
$884$	−5.07539	−	8.79083i	−0.170704	−	0.295668i
$885$	26.8755	−	46.5497i	0.903408	−	1.56475i
$886$	13.6734	−	23.6831i	0.459368	−	0.795648i
$887$	−1.86466			−0.0626091			−0.0313046	−	0.999510i	$-0.509966\pi$
$887$	−1.86466			−0.0626091			−0.0313046	+	0.999510i	$0.509966\pi$
$888$	−2.44033	+	4.22678i	−0.0818923	+	0.141842i
$889$	−2.02626	+	3.50958i	−0.0679585	+	0.117708i
$890$	28.5084	−	49.3780i	0.955605	−	1.65516i
$891$	0.571791	+	0.990370i	0.0191557	+	0.0331787i
$892$	2.02102			0.0676689
$893$	0.991631	+	1.71756i	0.0331837	+	0.0574758i
$894$	2.65731	−	4.60259i	0.0888737	−	0.153934i
$895$	−9.29708			−0.310767
$896$	1.39371	−	2.41397i	0.0465605	−	0.0806451i
$897$	−31.8469	−	55.1604i	−1.06334	−	1.84175i
$898$	20.9775	+	36.3341i	0.700028	+	1.21248i
$899$	57.5202			1.91840
$900$	11.2566	+	19.4969i	0.375219	+	0.649898i
$901$	−1.54332			−0.0514155
$902$	−0.700729			−0.0233317
$903$	7.59004	−	3.37359i	0.252581	−	0.112266i
$904$	7.07270			0.235234
$905$	−1.39377			−0.0463304
$906$	−15.5986	−	27.0176i	−0.518230	−	0.897601i
$907$	19.5543			0.649291			0.324645	−	0.945836i	$-0.394755\pi$
$907$	19.5543			0.649291			0.324645	+	0.945836i	$0.394755\pi$
$908$	10.2938	+	17.8294i	0.341612	+	0.591689i
$909$	3.51252	+	6.08387i	0.116503	+	0.201789i
$910$	20.7019	−	35.8567i	0.686260	−	1.18864i
$911$	11.8434			0.392388			0.196194	−	0.980565i	$-0.437142\pi$
$911$	11.8434			0.392388			0.196194	+	0.980565i	$0.437142\pi$
$912$	3.80081	−	6.58320i	0.125857	−	0.217992i
$913$	−1.94605	−	3.37065i	−0.0644047	−	0.111552i
$914$	−31.6678			−1.04748
$915$	−8.77838	−	15.2046i	−0.290204	−	0.502648i
$916$	2.08366	−	3.60901i	0.0688461	−	0.119245i
$917$	−6.35051	+	10.9994i	−0.209712	+	0.363233i
$918$	5.51153	−	9.54625i	0.181908	−	0.315073i
$919$	−30.5431			−1.00752			−0.503762	−	0.863843i	$-0.668051\pi$
$919$	−30.5431			−1.00752			−0.503762	+	0.863843i	$0.668051\pi$
$920$	−6.60251	+	11.4359i	−0.217678	+	0.377030i
$921$	−8.28555	+	14.3510i	−0.273018	+	0.472881i
$922$	−37.8089	−	65.4869i	−1.24517	−	2.15670i
$923$	11.1106	+	19.2441i	0.365709	+	0.633427i
$924$	0.505224			0.0166207
$925$	112.326			3.69327
$926$	−0.00396382	−	0.00686554i	−0.000130259	−	0.000225616i
$927$	5.06203	+	8.76770i	0.166259	+	0.287969i
$928$	28.8257	−	49.9276i	0.946250	−	1.63895i
$929$	−18.6125	+	32.2378i	−0.610656	+	1.05769i	0.380474	+	0.924792i	$0.375761\pi$
$929$	−18.6125	+	32.2378i	−0.610656	+	1.05769i	−0.991130	+	0.132896i	$0.957572\pi$
$930$	−90.5162			−2.96814
$931$	3.79553	−	6.57406i	0.124394	−	0.215456i
$932$	13.0979	−	22.6862i	0.429035	−	0.743111i
$933$	−1.83467	+	3.17774i	−0.0600644	+	0.104035i
$934$	5.85562	+	10.1422i	0.191602	+	0.331864i
$935$	0.939302			0.0307185
$936$	−1.07784	−	1.86688i	−0.0352304	−	0.0610208i
$937$	−8.38755	+	14.5277i	−0.274009	+	0.474598i	−0.969885	−	0.243564i	$-0.921683\pi$
$937$	−8.38755	+	14.5277i	−0.274009	+	0.474598i	0.695875	+	0.718163i	$0.255017\pi$
$938$	5.12675			0.167394
$939$	−11.9723	+	20.7366i	−0.390700	+	0.676713i
$940$	−6.17458	−	10.6947i	−0.201393	−	0.348822i
$941$	−28.8686	−	50.0019i	−0.941090	−	1.63002i	−0.763397	−	0.645930i	$-0.776470\pi$
$941$	−28.8686	−	50.0019i	−0.941090	−	1.63002i	−0.177693	−	0.984086i	$-0.556863\pi$
$942$	6.74598			0.219796
$943$	6.41425	+	11.1098i	0.208877	+	0.361785i
$944$	−38.8719			−1.26517
$945$	21.2839			0.692366
$946$	−2.59081	+	1.15155i	−0.0842346	+	0.0374402i
$947$	8.91721			0.289770			0.144885	−	0.989448i	$-0.453719\pi$
$947$	8.91721			0.289770			0.144885	+	0.989448i	$0.453719\pi$
$948$	42.7956			1.38994
$949$	−24.3212	−	42.1256i	−0.789501	−	1.36746i
$950$	−30.7880			−0.998893
$951$	17.7223	+	30.6960i	0.574686	+	0.995386i
$952$	0.175108	+	0.303296i	0.00567529	+	0.00982989i
$953$	18.9099	−	32.7530i	0.612553	−	1.06097i	−0.378255	−	0.925701i	$-0.623476\pi$
$953$	18.9099	−	32.7530i	0.612553	−	1.06097i	0.990809	−	0.135272i	$-0.0431908\pi$
$954$	2.91413			0.0943484
$955$	27.8308	−	48.2043i	0.900583	−	1.55985i
$956$	6.43781	+	11.1506i	0.208214	+	0.360636i
$957$	−2.36262			−0.0763726
$958$	34.4140	+	59.6068i	1.11187	+	1.92581i
$959$	−2.50276	+	4.33490i	−0.0808182	+	0.139981i
$960$	−19.0331	+	32.9664i	−0.614292	+	1.06399i
$961$	−14.1292	+	24.4724i	−0.455779	+	0.789432i
$962$	95.6305			3.08325
$963$	6.07436	−	10.5211i	0.195744	−	0.339038i
$964$	−2.79593	+	4.84270i	−0.0900510	+	0.155973i
$965$	−41.5879	−	72.0323i	−1.33876	−	2.31880i
$966$	−9.76945	−	16.9212i	−0.314327	−	0.544430i
$967$	−39.5229			−1.27097			−0.635485	−	0.772113i	$-0.719200\pi$
$967$	−39.5229			−1.27097			−0.635485	+	0.772113i	$0.719200\pi$
$968$	−4.31506			−0.138691
$969$	0.871044	+	1.50869i	0.0279820	+	0.0484662i
$970$	−64.6324	−	111.947i	−2.07522	−	3.59439i
$971$	−13.7033	+	23.7347i	−0.439758	+	0.761684i	−0.997671	−	0.0682161i	$-0.978269\pi$
$971$	−13.7033	+	23.7347i	−0.439758	+	0.761684i	0.557912	+	0.829900i	$0.311603\pi$
$972$	−8.65021	+	14.9826i	−0.277456	+	0.480567i
$973$	−9.30334			−0.298251
$974$	−35.2478	+	61.0509i	−1.12941	+	1.95620i
$975$	51.9996	−	90.0659i	1.66532	−	2.88442i
$976$	−6.34841	+	10.9958i	−0.203208	+	0.351966i
$977$	24.1818	+	41.8841i	0.773645	+	1.33999i	0.935553	+	0.353187i	$0.114902\pi$
$977$	24.1818	+	41.8841i	0.773645	+	1.33999i	−0.161908	+	0.986806i	$0.551765\pi$
$978$	37.4534			1.19763
$979$	0.766601	+	1.32779i	0.0245007	+	0.0424364i
$980$	−23.6336	+	40.9346i	−0.754948	+	1.30761i
$981$	13.8009			0.440627
$982$	−12.0162	+	20.8127i	−0.383453	+	0.664160i
$983$	15.8429	+	27.4407i	0.505310	+	0.875222i	0.999981	+	0.00614182i	$0.00195501\pi$
$983$	15.8429	+	27.4407i	0.505310	+	0.875222i	−0.494672	+	0.869080i	$0.664712\pi$
$984$	−0.455068	−	0.788200i	−0.0145070	−	0.0251269i
$985$	−73.2146			−2.33281
$986$	7.28084	+	12.6108i	0.231869	+	0.401609i
$987$	−2.05510			−0.0654144
$988$	−12.4081			−0.394754
$989$	41.9729	+	30.5354i	1.33466	+	0.970970i
$990$	−1.77361			−0.0563689
$991$	11.9045			0.378160			0.189080	−	0.981962i	$-0.439449\pi$
$991$	11.9045			0.378160			0.189080	+	0.981962i	$0.439449\pi$
$992$	29.6968	+	51.4363i	0.942873	+	1.63310i
$993$	13.8316			0.438934
$994$	3.40832	+	5.90338i	0.108105	+	0.187244i
$995$	−52.8395	−	91.5208i	−1.67513	−	2.90140i
$996$	−22.4737	+	38.9256i	−0.712107	+	1.23341i
$997$	−16.1049			−0.510049			−0.255024	−	0.966935i	$-0.582083\pi$
$997$	−16.1049			−0.510049			−0.255024	+	0.966935i	$0.582083\pi$
$998$	−36.4940	+	63.2095i	−1.15520	+	2.00086i
$999$	24.5798	+	42.5735i	0.777672	+	1.34697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.a.681.6	yes	58
43.6	even	3	inner	731.2.e.a.307.6	✓	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.a.307.6	✓	58	43.6	even	3	inner
731.2.e.a.681.6	yes	58	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.94880 q^{2} +(-0.712581 - 1.23423i) q^{3} +1.79780 q^{4} +(2.11686 + 3.66650i) q^{5} +(1.38867 + 2.40525i) q^{6} +(-0.444390 + 0.769706i) q^{7} +0.394042 q^{8} +(0.484458 - 0.839105i) q^{9} +O(q^{10})\)	\(q-1.94880 q^{2} +(-0.712581 - 1.23423i) q^{3} +1.79780 q^{4} +(2.11686 + 3.66650i) q^{5} +(1.38867 + 2.40525i) q^{6} +(-0.444390 + 0.769706i) q^{7} +0.394042 q^{8} +(0.484458 - 0.839105i) q^{9} +(-4.12532 - 7.14527i) q^{10} +0.221862 q^{11} +(-1.28108 - 2.21889i) q^{12} +(2.82311 - 4.88976i) q^{13} +(0.866025 - 1.50000i) q^{14} +(3.01686 - 5.22536i) q^{15} -4.36351 q^{16} +(0.500000 - 0.866025i) q^{17} +(-0.944108 + 1.63524i) q^{18} +(-0.611190 - 1.05861i) q^{19} +(3.80569 + 6.59165i) q^{20} +1.26666 q^{21} -0.432365 q^{22} +(3.95772 + 6.85498i) q^{23} +(-0.280786 - 0.486336i) q^{24} +(-6.46217 + 11.1928i) q^{25} +(-5.50166 + 9.52915i) q^{26} -5.65634 q^{27} +(-0.798926 + 1.38378i) q^{28} +(3.73607 - 6.47107i) q^{29} +(-5.87925 + 10.1832i) q^{30} +(3.84897 + 6.66661i) q^{31} +7.71551 q^{32} +(-0.158095 - 0.273828i) q^{33} +(-0.974398 + 1.68771i) q^{34} -3.76284 q^{35} +(0.870959 - 1.50855i) q^{36} +(-4.34553 - 7.52669i) q^{37} +(1.19108 + 2.06302i) q^{38} -8.04676 q^{39} +(0.834130 + 1.44476i) q^{40} +1.62069 q^{41} -2.46845 q^{42} +(5.99219 - 2.66338i) q^{43} +0.398865 q^{44} +4.10211 q^{45} +(-7.71279 - 13.3590i) q^{46} -1.62246 q^{47} +(3.10935 + 5.38556i) q^{48} +(3.10503 + 5.37808i) q^{49} +(12.5934 - 21.8125i) q^{50} -1.42516 q^{51} +(5.07539 - 8.79083i) q^{52} +(-0.771661 - 1.33656i) q^{53} +11.0231 q^{54} +(0.469651 + 0.813460i) q^{55} +(-0.175108 + 0.303296i) q^{56} +(-0.871044 + 1.50869i) q^{57} +(-7.28084 + 12.6108i) q^{58} +8.90841 q^{59} +(5.42372 - 9.39417i) q^{60} +(1.45489 - 2.51993i) q^{61} +(-7.50086 - 12.9919i) q^{62} +(0.430576 + 0.745780i) q^{63} -6.30892 q^{64} +23.9045 q^{65} +(0.308095 + 0.533636i) q^{66} +(1.47997 + 2.56338i) q^{67} +(0.898901 - 1.55694i) q^{68} +(5.64040 - 9.76945i) q^{69} +7.33301 q^{70} +(-1.96779 + 3.40832i) q^{71} +(0.190896 - 0.330642i) q^{72} +(4.30753 - 7.46087i) q^{73} +(8.46856 + 14.6680i) q^{74} +18.4193 q^{75} +(-1.09880 - 1.90318i) q^{76} +(-0.0985935 + 0.170769i) q^{77} +15.6815 q^{78} +(-8.35148 + 14.4652i) q^{79} +(-9.23693 - 15.9988i) q^{80} +(2.57723 + 4.46389i) q^{81} -3.15839 q^{82} +(-8.77140 - 15.1925i) q^{83} +2.27720 q^{84} +4.23371 q^{85} +(-11.6776 + 5.19039i) q^{86} -10.6490 q^{87} +0.0874230 q^{88} +(3.45530 + 5.98475i) q^{89} -7.99417 q^{90} +(2.50912 + 4.34592i) q^{91} +(7.11521 + 12.3239i) q^{92} +(5.48540 - 9.50100i) q^{93} +3.16184 q^{94} +(2.58760 - 4.48186i) q^{95} +(-5.49792 - 9.52268i) q^{96} +15.6672 q^{97} +(-6.05108 - 10.4808i) q^{98} +(0.107483 - 0.186166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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