LMFDB - Embedded newform 171.4.t.a.122.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,4,Mod(122,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("171.122");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	171.t (of order $6$, 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:	$10.0893266110$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			122.10
Character	$\chi$	$=$	171.122
Dual form			171.4.t.a.164.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.17093 q^{2} +(0.815694 - 5.13173i) q^{3} +9.39667 q^{4} +(4.61421 - 2.66402i) q^{5} +(-3.40220 + 21.4041i) q^{6} +(9.76769 + 16.9181i) q^{7} -5.82542 q^{8} +(-25.6693 - 8.37184i) q^{9} +O(q^{10})$	\(q-4.17093 q^{2} +(0.815694 - 5.13173i) q^{3} +9.39667 q^{4} +(4.61421 - 2.66402i) q^{5} +(-3.40220 + 21.4041i) q^{6} +(9.76769 + 16.9181i) q^{7} -5.82542 q^{8} +(-25.6693 - 8.37184i) q^{9} +(-19.2456 + 11.1114i) q^{10} +(-32.7948 + 18.9341i) q^{11} +(7.66481 - 48.2212i) q^{12} +25.8742i q^{13} +(-40.7404 - 70.5644i) q^{14} +(-9.90723 - 25.8519i) q^{15} -50.8759 q^{16} +(-23.1352 - 13.3571i) q^{17} +(107.065 + 34.9184i) q^{18} +(7.86200 + 82.4451i) q^{19} +(43.3582 - 25.0329i) q^{20} +(94.7867 - 36.3251i) q^{21} +(136.785 - 78.9729i) q^{22} -97.9419i q^{23} +(-4.75176 + 29.8945i) q^{24} +(-48.3060 + 83.6685i) q^{25} -107.920i q^{26} +(-63.9003 + 124.899i) q^{27} +(91.7837 + 158.974i) q^{28} +(-81.8134 + 141.705i) q^{29} +(41.3224 + 107.827i) q^{30} +(120.075 + 69.3255i) q^{31} +258.803 q^{32} +(70.4141 + 183.739i) q^{33} +(96.4952 + 55.7116i) q^{34} +(90.1404 + 52.0426i) q^{35} +(-241.206 - 78.6674i) q^{36} +417.111i q^{37} +(-32.7919 - 343.873i) q^{38} +(132.779 + 21.1054i) q^{39} +(-26.8797 + 15.5190i) q^{40} +(-30.1097 - 52.1515i) q^{41} +(-395.349 + 151.510i) q^{42} +133.789 q^{43} +(-308.162 + 177.918i) q^{44} +(-140.746 + 29.7540i) q^{45} +408.509i q^{46} +(294.925 + 170.275i) q^{47} +(-41.4992 + 261.082i) q^{48} +(-19.3154 + 33.4553i) q^{49} +(201.481 - 348.976i) q^{50} +(-87.4162 + 107.828i) q^{51} +243.131i q^{52} +(-144.275 - 249.891i) q^{53} +(266.524 - 520.945i) q^{54} +(-100.882 + 174.732i) q^{55} +(-56.9009 - 98.5553i) q^{56} +(429.499 + 26.9043i) q^{57} +(341.238 - 591.042i) q^{58} +(15.4984 + 26.8439i) q^{59} +(-93.0949 - 242.922i) q^{60} +(249.176 - 431.586i) q^{61} +(-500.826 - 289.152i) q^{62} +(-109.094 - 516.050i) q^{63} -672.444 q^{64} +(68.9293 + 119.389i) q^{65} +(-293.693 - 766.361i) q^{66} +357.851i q^{67} +(-217.394 - 125.512i) q^{68} +(-502.611 - 79.8906i) q^{69} +(-375.969 - 217.066i) q^{70} +(-183.267 + 317.427i) q^{71} +(149.534 + 48.7695i) q^{72} +(207.280 - 359.020i) q^{73} -1739.74i q^{74} +(389.961 + 316.141i) q^{75} +(73.8767 + 774.709i) q^{76} +(-640.659 - 369.885i) q^{77} +(-553.814 - 88.0293i) q^{78} -1173.81i q^{79} +(-234.752 + 135.534i) q^{80} +(588.825 + 429.798i) q^{81} +(125.586 + 217.521i) q^{82} +(-862.312 + 497.856i) q^{83} +(890.680 - 341.335i) q^{84} -142.334 q^{85} -558.024 q^{86} +(660.457 + 535.432i) q^{87} +(191.044 - 110.299i) q^{88} +(486.608 + 842.829i) q^{89} +(587.043 - 124.102i) q^{90} +(-437.743 + 252.731i) q^{91} -920.328i q^{92} +(453.705 - 559.646i) q^{93} +(-1230.11 - 710.206i) q^{94} +(255.912 + 359.474i) q^{95} +(211.104 - 1328.11i) q^{96} +1236.11i q^{97} +(80.5633 - 139.540i) q^{98} +(1000.33 - 211.472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 6 q^{2} - 3 q^{3} + 446 q^{4} - 3 q^{5} - 53 q^{6} - 8 q^{7} - 48 q^{8} - 31 q^{9}+O(q^{10}) $ 116 * q - 6 * q^2 - 3 * q^3 + 446 * q^4 - 3 * q^5 - 53 * q^6 - 8 * q^7 - 48 * q^8 - 31 * q^9	\( 116 q - 6 q^{2} - 3 q^{3} + 446 q^{4} - 3 q^{5} - 53 q^{6} - 8 q^{7} - 48 q^{8} - 31 q^{9} - 6 q^{10} - 81 q^{11} - 105 q^{12} - 3 q^{14} - 261 q^{15} + 1646 q^{16} + 270 q^{17} - 24 q^{18} + 11 q^{19} - 261 q^{20} + 78 q^{21} - 105 q^{22} - 893 q^{24} + 1251 q^{25} - 198 q^{27} - 50 q^{28} + 177 q^{29} - 419 q^{30} + 180 q^{31} - 390 q^{32} + 150 q^{33} + 591 q^{34} - 375 q^{35} - 999 q^{36} + 1161 q^{38} + 751 q^{39} - 426 q^{40} - 108 q^{41} + 1540 q^{42} - 518 q^{43} + 15 q^{44} + 905 q^{45} - 1341 q^{47} - 3135 q^{48} - 2376 q^{49} + 753 q^{50} + 1008 q^{51} - 528 q^{53} - 76 q^{54} - 127 q^{55} - 24 q^{56} - 1459 q^{57} - 18 q^{58} - 270 q^{59} - 1419 q^{60} - 419 q^{61} - 492 q^{62} - 1213 q^{63} + 6848 q^{64} - 2466 q^{65} + 1487 q^{66} + 1842 q^{68} - 1281 q^{69} - 1032 q^{70} - 1386 q^{71} + 1251 q^{72} + 787 q^{73} + 1251 q^{75} + 881 q^{76} + 3234 q^{77} - 540 q^{78} + 642 q^{80} + 2281 q^{81} - 540 q^{82} + 2160 q^{83} - 5520 q^{84} - 502 q^{85} - 8322 q^{86} - 703 q^{87} - 1056 q^{88} + 990 q^{89} + 213 q^{90} + 3003 q^{91} + 2345 q^{93} - 48 q^{94} - 5097 q^{95} - 4413 q^{96} + 2964 q^{98} - 3248 q^{99}+O(q^{100}) \) 116 * q - 6 * q^2 - 3 * q^3 + 446 * q^4 - 3 * q^5 - 53 * q^6 - 8 * q^7 - 48 * q^8 - 31 * q^9 - 6 * q^10 - 81 * q^11 - 105 * q^12 - 3 * q^14 - 261 * q^15 + 1646 * q^16 + 270 * q^17 - 24 * q^18 + 11 * q^19 - 261 * q^20 + 78 * q^21 - 105 * q^22 - 893 * q^24 + 1251 * q^25 - 198 * q^27 - 50 * q^28 + 177 * q^29 - 419 * q^30 + 180 * q^31 - 390 * q^32 + 150 * q^33 + 591 * q^34 - 375 * q^35 - 999 * q^36 + 1161 * q^38 + 751 * q^39 - 426 * q^40 - 108 * q^41 + 1540 * q^42 - 518 * q^43 + 15 * q^44 + 905 * q^45 - 1341 * q^47 - 3135 * q^48 - 2376 * q^49 + 753 * q^50 + 1008 * q^51 - 528 * q^53 - 76 * q^54 - 127 * q^55 - 24 * q^56 - 1459 * q^57 - 18 * q^58 - 270 * q^59 - 1419 * q^60 - 419 * q^61 - 492 * q^62 - 1213 * q^63 + 6848 * q^64 - 2466 * q^65 + 1487 * q^66 + 1842 * q^68 - 1281 * q^69 - 1032 * q^70 - 1386 * q^71 + 1251 * q^72 + 787 * q^73 + 1251 * q^75 + 881 * q^76 + 3234 * q^77 - 540 * q^78 + 642 * q^80 + 2281 * q^81 - 540 * q^82 + 2160 * q^83 - 5520 * q^84 - 502 * q^85 - 8322 * q^86 - 703 * q^87 - 1056 * q^88 + 990 * q^89 + 213 * q^90 + 3003 * q^91 + 2345 * q^93 - 48 * q^94 - 5097 * q^95 - 4413 * q^96 + 2964 * q^98 - 3248 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−4.17093			−1.47465			−0.737324	−	0.675540i	$-0.763911\pi$
$2$	−4.17093			−1.47465			−0.737324	+	0.675540i	$0.763911\pi$
$3$	0.815694	−	5.13173i	0.156980	−	0.987602i
$3$	0.815694	−	5.13173i	0.156980	−	0.987602i
$4$	9.39667			1.17458
$5$	4.61421	−	2.66402i	0.412708	−	0.238277i	−0.279245	−	0.960220i	$-0.590084\pi$
$5$	4.61421	−	2.66402i	0.412708	−	0.238277i	0.691952	+	0.721943i	$0.256751\pi$
$6$	−3.40220	+	21.4041i	−0.231491	+	1.45636i
$7$	9.76769	+	16.9181i	0.527406	+	0.913493i	0.999490	+	0.0319397i	$0.0101685\pi$
$7$	9.76769	+	16.9181i	0.527406	+	0.913493i	−0.472084	+	0.881553i	$0.656498\pi$
$8$	−5.82542			−0.257450
$9$	−25.6693	−	8.37184i	−0.950714	−	0.310068i
$10$	−19.2456	+	11.1114i	−0.608598	+	0.351374i
$11$	−32.7948	+	18.9341i	−0.898910	+	0.518986i	−0.876846	−	0.480770i	$-0.840357\pi$
$11$	−32.7948	+	18.9341i	−0.898910	+	0.518986i	−0.0220638	+	0.999757i	$0.507024\pi$
$12$	7.66481	−	48.2212i	0.184387	−	1.16002i
$13$			25.8742i			0.552016i	0.961155	+	0.276008i	$0.0890117\pi$
$13$			25.8742i			0.552016i	−0.961155	+	0.276008i	$0.910988\pi$
$14$	−40.7404	−	70.5644i	−0.777737	−	1.34708i
$15$	−9.90723	−	25.8519i	−0.170536	−	0.444996i
$16$	−50.8759			−0.794936
$17$	−23.1352	−	13.3571i	−0.330065	−	0.190563i	0.325805	−	0.945437i	$-0.394365\pi$
$17$	−23.1352	−	13.3571i	−0.330065	−	0.190563i	−0.655870	+	0.754874i	$0.727698\pi$
$18$	107.065	+	34.9184i	1.40197	+	0.457241i
$19$	7.86200	+	82.4451i	0.0949299	+	0.995484i
$19$	7.86200	+	82.4451i	0.0949299	+	0.995484i
$20$	43.3582	−	25.0329i	0.484760	−	0.279876i
$21$	94.7867	−	36.3251i	0.984960	−	0.377466i
$22$	136.785	−	78.9729i	1.32558	−	0.765321i
$23$		−	97.9419i		−	0.887926i	−0.896045	−	0.443963i	$-0.853572\pi$
$23$		−	97.9419i		−	0.887926i	0.896045	−	0.443963i	$-0.146428\pi$
$24$	−4.75176	+	29.8945i	−0.0404146	+	0.254258i
$25$	−48.3060	+	83.6685i	−0.386448	+	0.669348i
$26$		−	107.920i		−	0.814029i
$27$	−63.9003	+	124.899i	−0.455467	+	0.890252i
$28$	91.7837	+	158.974i	0.619482	+	1.07297i
$29$	−81.8134	+	141.705i	−0.523875	+	0.907378i	0.475739	+	0.879587i	$0.342181\pi$
$29$	−81.8134	+	141.705i	−0.523875	+	0.907378i	−0.999614	+	0.0277914i	$0.991153\pi$
$30$	41.3224	+	107.827i	0.251480	+	0.656211i
$31$	120.075	+	69.3255i	0.695683	+	0.401653i	0.805737	−	0.592273i	$-0.201769\pi$
$31$	120.075	+	69.3255i	0.695683	+	0.401653i	−0.110055	+	0.993926i	$0.535103\pi$
$32$	258.803			1.42970
$33$	70.4141	+	183.739i	0.371440	+	0.969236i
$34$	96.4952	+	55.7116i	0.486729	+	0.281013i
$35$	90.1404	+	52.0426i	0.435329	+	0.251337i
$36$	−241.206	−	78.6674i	−1.11669	−	0.364201i
$37$			417.111i			1.85331i	0.375910	+	0.926656i	$0.377330\pi$
$37$			417.111i			1.85331i	−0.375910	+	0.926656i	$0.622670\pi$
$38$	−32.7919	−	343.873i	−0.139988	−	1.46799i
$39$	132.779	+	21.1054i	0.545172	+	0.0866557i
$40$	−26.8797	+	15.5190i	−0.106251	+	0.0613443i
$41$	−30.1097	−	52.1515i	−0.114691	−	0.198651i	0.802965	−	0.596026i	$-0.203255\pi$
$41$	−30.1097	−	52.1515i	−0.114691	−	0.198651i	−0.917656	+	0.397375i	$0.869921\pi$
$42$	−395.349	+	151.510i	−1.45247	+	0.556629i
$43$	133.789			0.474479			0.237240	−	0.971451i	$-0.423757\pi$
$43$	133.789			0.474479			0.237240	+	0.971451i	$0.423757\pi$
$44$	−308.162	+	177.918i	−1.05585	+	0.609593i
$45$	−140.746	+	29.7540i	−0.466249	+	0.0985657i
$46$			408.509i			1.30938i
$47$	294.925	+	170.275i	0.915303	+	0.528451i	0.882134	−	0.470999i	$-0.156107\pi$
$47$	294.925	+	170.275i	0.915303	+	0.528451i	0.0331696	+	0.999450i	$0.489440\pi$
$48$	−41.4992	+	261.082i	−0.124789	+	0.785081i
$49$	−19.3154	+	33.4553i	−0.0563132	+	0.0975372i
$50$	201.481	−	348.976i	0.569875	−	0.987052i
$51$	−87.4162	+	107.828i	−0.240014	+	0.296058i
$52$			243.131i			0.648389i
$53$	−144.275	−	249.891i	−0.373918	−	0.647645i	0.616246	−	0.787553i	$-0.288653\pi$
$53$	−144.275	−	249.891i	−0.373918	−	0.647645i	−0.990164	+	0.139908i	$0.955319\pi$
$54$	266.524	−	520.945i	0.671654	−	1.31281i
$55$	−100.882	+	174.732i	−0.247325	+	0.428379i
$56$	−56.9009	−	98.5553i	−0.135780	−	0.235179i
$57$	429.499	+	26.9043i	0.998044	+	0.0625185i
$58$	341.238	−	591.042i	0.772531	−	1.33806i
$59$	15.4984	+	26.8439i	0.0341986	+	0.0592336i	0.882618	−	0.470091i	$-0.155779\pi$
$59$	15.4984	+	26.8439i	0.0341986	+	0.0592336i	−0.848420	+	0.529324i	$0.822445\pi$
$60$	−93.0949	−	242.922i	−0.200308	−	0.522685i
$61$	249.176	−	431.586i	0.523012	−	0.905884i	−0.476629	−	0.879105i	$-0.658141\pi$
$61$	249.176	−	431.586i	0.523012	−	0.905884i	0.999641	−	0.0267796i	$-0.00852522\pi$
$62$	−500.826	−	289.152i	−1.02589	−	0.592296i
$63$	−109.094	−	516.050i	−0.218167	−	1.03200i
$64$	−672.444			−1.31337
$65$	68.9293	+	119.389i	0.131533	+	0.227821i
$66$	−293.693	−	766.361i	−0.547743	−	1.42928i
$67$			357.851i			0.652515i	0.945281	+	0.326258i	$0.105788\pi$
$67$			357.851i			0.652515i	−0.945281	+	0.326258i	$0.894212\pi$
$68$	−217.394	−	125.512i	−0.387689	−	0.223832i
$69$	−502.611	−	79.8906i	−0.876917	−	0.139387i
$70$	−375.969	−	217.066i	−0.641956	−	0.370633i
$71$	−183.267	+	317.427i	−0.306335	+	0.530587i	−0.977558	−	0.210668i	$-0.932436\pi$
$71$	−183.267	+	317.427i	−0.306335	+	0.530587i	0.671223	+	0.741256i	$0.265769\pi$
$72$	149.534	+	48.7695i	0.244761	+	0.0798270i
$73$	207.280	−	359.020i	0.332333	−	0.575618i	−0.650635	−	0.759390i	$-0.725497\pi$
$73$	207.280	−	359.020i	0.332333	−	0.575618i	0.982969	+	0.183772i	$0.0588307\pi$
$74$		−	1739.74i		−	2.73298i
$75$	389.961	+	316.141i	0.600384	+	0.486731i
$76$	73.8767	+	774.709i	0.111503	+	1.16928i
$77$	−640.659	−	369.885i	−0.948181	−	0.547432i
$78$	−553.814	−	88.0293i	−0.803936	−	0.127787i
$79$		−	1173.81i		−	1.67170i	−0.548959	−	0.835849i	$-0.684976\pi$
$79$		−	1173.81i		−	1.67170i	0.548959	−	0.835849i	$-0.315024\pi$
$80$	−234.752	+	135.534i	−0.328076	+	0.189415i
$81$	588.825	+	429.798i	0.807715	+	0.589573i
$82$	125.586	+	217.521i	0.169129	+	0.292940i
$83$	−862.312	+	497.856i	−1.14037	+	0.658395i	−0.946523	−	0.322636i	$-0.895431\pi$
$83$	−862.312	+	497.856i	−1.14037	+	0.658395i	−0.193851	+	0.981031i	$0.562098\pi$
$84$	890.680	−	341.335i	1.15692	−	0.443366i
$85$	−142.334			−0.181627
$86$	−558.024			−0.699689
$87$	660.457	+	535.432i	0.813890	+	0.659820i
$88$	191.044	−	110.299i	0.231424	−	0.133613i
$89$	486.608	+	842.829i	0.579554	+	1.00382i	0.995530	+	0.0944414i	$0.0301065\pi$
$89$	486.608	+	842.829i	0.579554	+	1.00382i	−0.415977	+	0.909375i	$0.636560\pi$
$90$	587.043	−	124.102i	0.687553	−	0.145350i
$91$	−437.743	+	252.731i	−0.504263	+	0.291136i
$92$		−	920.328i		−	1.04294i
$93$	453.705	−	559.646i	0.505881	−	0.624006i
$94$	−1230.11	−	710.206i	−1.34975	−	0.779278i
$95$	255.912	+	359.474i	0.276379	+	0.388224i
$96$	211.104	−	1328.11i	0.224435	−	1.41197i
$97$			1236.11i			1.29389i	0.762536	+	0.646946i	$0.223954\pi$
$97$			1236.11i			1.29389i	−0.762536	+	0.646946i	$0.776046\pi$
$98$	80.5633	−	139.540i	0.0830420	−	0.143833i
$99$	1000.33	−	211.472i	1.01553	−	0.214684i
$100$	−453.916	+	786.205i	−0.453916	+	0.786205i
$101$	504.105	+	291.045i	0.496636	+	0.286733i	0.727323	−	0.686295i	$-0.240764\pi$
$101$	504.105	+	291.045i	0.496636	+	0.286733i	−0.230687	+	0.973028i	$0.574097\pi$
$102$	364.607	−	449.744i	0.353936	−	0.436581i
$103$	−1534.42	−	885.895i	−1.46787	−	0.847474i	−0.468516	−	0.883455i	$-0.655211\pi$
$103$	−1534.42	−	885.895i	−1.46787	−	0.847474i	−0.999352	+	0.0359812i	$0.988544\pi$
$104$		−	150.728i		−	0.142116i
$105$	340.595	−	420.125i	0.316559	−	0.390476i
$106$	601.760	+	1042.28i	0.551397	+	0.955048i
$107$	195.280			0.176434			0.0882169	−	0.996101i	$-0.471883\pi$
$107$	195.280			0.176434			0.0882169	+	0.996101i	$0.471883\pi$
$108$	−600.450	+	1173.63i	−0.534985	+	1.04568i
$109$	915.564	+	528.601i	0.804542	+	0.464503i	0.845057	−	0.534676i	$-0.179566\pi$
$109$	915.564	+	528.601i	0.804542	+	0.464503i	−0.0405149	+	0.999179i	$0.512900\pi$
$110$	420.770	−	728.795i	0.364717	−	0.631708i
$111$	2140.50	+	340.235i	1.83033	+	0.290934i
$112$	−496.940	−	860.726i	−0.419254	−	0.726169i
$113$	−467.982	+	810.568i	−0.389593	+	0.674795i	−0.992395	−	0.123096i	$-0.960718\pi$
$113$	−467.982	+	810.568i	−0.389593	+	0.674795i	0.602802	+	0.797891i	$0.294051\pi$
$114$	−1791.41	−	112.216i	−1.47176	−	0.0921928i
$115$	−260.919	−	451.925i	−0.211572	−	0.366454i
$116$	−768.774	+	1331.56i	−0.615335	+	1.06579i
$117$	216.615	−	664.172i	0.171163	−	0.524810i
$118$	−64.6426	−	111.964i	−0.0504308	−	0.0873487i
$119$		−	521.872i		−	0.402016i
$120$	57.7138	+	150.598i	0.0439044	+	0.114564i
$121$	51.5006	−	89.2017i	0.0386932	−	0.0670186i
$122$	−1039.30	+	1800.12i	−0.771259	+	1.33586i
$123$	−292.188	+	111.975i	−0.214193	+	0.0820850i
$124$	1128.31	+	651.429i	0.817138	+	0.471775i
$125$			1180.76i			0.844880i
$126$	455.022	+	2152.41i	0.321719	+	1.52184i
$127$	−1140.22	+	658.306i	−0.796678	+	0.459962i	−0.842308	−	0.538996i	$-0.818804\pi$
$127$	−1140.22	+	658.306i	−0.796678	+	0.459962i	0.0456305	+	0.998958i	$0.485470\pi$
$128$	734.291			0.507053
$129$	109.131	−	686.568i	0.0744839	−	0.468596i
$130$	−287.499	−	497.963i	−0.193964	−	0.335956i
$131$	−1565.86	+	904.047i	−1.04435	+	0.602954i	−0.921061	−	0.389417i	$-0.872676\pi$
$131$	−1565.86	+	904.047i	−1.04435	+	0.602954i	−0.123286	+	0.992371i	$0.539343\pi$
$132$	661.659	+	1726.53i	0.436288	+	1.13845i
$133$	−1318.02	+	938.308i	−0.859301	+	0.611742i
$134$		−	1492.57i		−	0.962230i
$135$	37.8833	+	746.542i	0.0241517	+	0.475941i
$136$	134.772	+	77.8108i	0.0849751	+	0.0490604i
$137$	−440.787	−	254.489i	−0.274883	−	0.158704i	0.356222	−	0.934402i	$-0.384065\pi$
$137$	−440.787	−	254.489i	−0.274883	−	0.158704i	−0.631105	+	0.775698i	$0.717398\pi$
$138$	2096.36	+	333.218i	1.29314	+	0.205547i
$139$	−1157.89			−0.706555			−0.353278	−	0.935518i	$-0.614933\pi$
$139$	−1157.89			−0.706555			−0.353278	+	0.935518i	$0.614933\pi$
$140$	847.019	+	489.027i	0.511330	+	0.295217i
$141$	1114.37	−	1374.58i	0.665583	−	0.820999i
$142$	764.393	−	1323.97i	0.451736	−	0.782429i
$143$	−489.905	−	848.540i	−0.286489	−	0.496213i
$144$	1305.95	+	425.925i	0.755757	+	0.246485i
$145$			871.809i			0.499309i
$146$	−864.553	+	1497.45i	−0.490075	+	0.848834i
$147$	155.928	+	126.411i	0.0874879	+	0.0709264i
$148$			3919.45i			2.17687i
$149$	1933.59	−	1116.36i	1.06313	−	0.613796i	0.136830	−	0.990595i	$-0.456309\pi$
$149$	1933.59	−	1116.36i	1.06313	−	0.613796i	0.926295	+	0.376799i	$0.122975\pi$
$150$	−1626.50	−	1318.60i	−0.885355	−	0.717757i
$151$	1649.17	−	952.147i	0.888790	−	0.513143i	0.0152434	−	0.999884i	$-0.495148\pi$
$151$	1649.17	−	952.147i	0.888790	−	0.513143i	0.873546	+	0.486741i	$0.161814\pi$
$152$	−45.7995	−	480.277i	−0.0244397	−	0.256287i
$153$	482.040	+	536.551i	0.254710	+	0.283514i
$154$	2672.15	+	1542.76i	1.39823	+	0.807269i
$155$	738.737			0.382818
$156$	1247.68	+	198.321i	0.640350	+	0.101784i
$157$	−845.858	−	1465.07i	−0.429980	−	0.744747i	0.566891	−	0.823793i	$-0.308146\pi$
$157$	−845.858	−	1465.07i	−0.429980	−	0.744747i	−0.996871	+	0.0790457i	$0.974813\pi$
$158$			4895.89i			2.46517i
$159$	−1400.06	+	536.544i	−0.698313	+	0.267615i
$160$	1194.17	−	689.457i	0.590048	−	0.340665i
$161$	1656.99	−	956.666i	0.811114	−	0.468297i
$162$	−2455.95	−	1792.66i	−1.19110	−	0.869411i
$163$	−1948.31			−0.936217			−0.468108	−	0.883671i	$-0.655064\pi$
$163$	−1948.31			−0.936217			−0.468108	+	0.883671i	$0.655064\pi$
$164$	−282.931	−	490.051i	−0.134715	−	0.233333i
$165$	814.389	+	660.224i	0.384243	+	0.311505i
$166$	3596.64	−	2076.52i	1.68165	−	0.970901i
$167$	−3579.23			−1.65850			−0.829248	−	0.558880i	$-0.811231\pi$
$167$	−3579.23			−1.65850			−0.829248	+	0.558880i	$0.811231\pi$
$168$	−552.173	+	211.609i	−0.253578	+	0.0971786i
$169$	1527.53			0.695278
$170$	593.666			0.267836
$171$	488.405	−	2182.13i	0.218417	−	0.975856i
$172$	1257.17			0.557315
$173$	1338.82			0.588371			0.294186	−	0.955748i	$-0.404952\pi$
$173$	1338.82			0.588371			0.294186	+	0.955748i	$0.404952\pi$
$174$	−2754.72	−	2233.25i	−1.20020	−	0.973002i
$175$	−1887.35			−0.815260
$176$	1668.47	−	963.290i	0.714577	−	0.412561i
$177$	150.398	−	57.6369i	0.0638677	−	0.0244760i
$178$	−2029.61	−	3515.38i	−0.854637	−	1.48028i
$179$	2682.58			1.12014			0.560072	−	0.828444i	$-0.310774\pi$
$179$	2682.58			1.12014			0.560072	+	0.828444i	$0.310774\pi$
$180$	−1322.55	+	279.588i	−0.547649	+	0.115774i
$181$	−431.479	+	249.114i	−0.177191	+	0.102301i	−0.585972	−	0.810331i	$-0.699287\pi$
$181$	−431.479	+	249.114i	−0.177191	+	0.102301i	0.408781	+	0.912632i	$0.365954\pi$
$182$	1825.80	−	1054.12i	0.743610	−	0.429323i
$183$	−2011.53	−	1630.75i	−0.812550	−	0.658734i
$184$			570.553i			0.228596i
$185$	1111.19	+	1924.64i	0.441601	+	0.764876i
$186$	−1892.37	+	2334.24i	−0.745997	+	0.920189i
$187$	1011.62			0.395598
$188$	2771.31	+	1600.02i	1.07510	+	0.620710i
$189$	−2737.22	+	138.900i	−1.05346	+	0.0534577i
$190$	−1067.39	−	1499.34i	−0.407562	−	0.572494i
$191$	−1915.61	+	1105.98i	−0.725702	+	0.418984i	−0.816848	−	0.576854i	$-0.804280\pi$
$191$	−1915.61	+	1105.98i	−0.725702	+	0.418984i	0.0911461	+	0.995838i	$0.470947\pi$
$192$	−548.509	+	3450.80i	−0.206173	+	1.29708i
$193$	1706.99	−	985.531i	0.636642	−	0.367565i	−0.146678	−	0.989184i	$-0.546858\pi$
$193$	1706.99	−	985.531i	0.636642	−	0.367565i	0.783320	+	0.621619i	$0.213525\pi$
$194$		−	5155.71i		−	1.90803i
$195$	668.897	−	256.341i	0.245645	−	0.0941384i
$196$	−181.501	+	314.368i	−0.0661445	+	0.114566i
$197$		−	930.308i		−	0.336455i	−0.985748	−	0.168228i	$-0.946196\pi$
$197$		−	930.308i		−	0.336455i	0.985748	−	0.168228i	$-0.0538044\pi$
$198$	−4172.32	+	882.035i	−1.49755	+	0.316583i
$199$	−2096.12	−	3630.59i	−0.746685	−	1.29330i	−0.949403	−	0.314059i	$-0.898311\pi$
$199$	−2096.12	−	3630.59i	−0.746685	−	1.29330i	0.202719	−	0.979237i	$-0.435022\pi$
$200$	281.403	−	487.404i	0.0994910	−	0.172323i
$201$	1836.40	+	291.897i	0.644425	+	0.102432i
$202$	−2102.59	−	1213.93i	−0.732363	−	0.422830i
$203$	−3196.51			−1.10518
$204$	−821.422	+	1013.23i	−0.281917	+	0.347745i
$205$	−277.865	−	160.425i	−0.0946680	−	0.0546566i
$206$	6399.94	+	3695.01i	2.16459	+	1.24973i
$207$	−819.954	+	2514.10i	−0.275318	+	0.844164i
$208$		−	1316.37i		−	0.438818i
$209$	−1818.86	−	2554.91i	−0.601976	−	0.845584i
$210$	−1420.60	+	1752.31i	−0.466813	+	0.575815i
$211$	4664.84	−	2693.25i	1.52199	−	0.878724i	0.522332	−	0.852742i	$-0.325062\pi$
$211$	4664.84	−	2693.25i	1.52199	−	0.878724i	0.999662	−	0.0259815i	$-0.00827111\pi$
$212$	−1355.70	−	2348.14i	−0.439198	−	0.760713i
$213$	1479.46	+	1199.40i	0.475920	+	0.385829i
$214$	−814.499			−0.260177
$215$	617.330	−	356.416i	0.195821	−	0.113057i
$216$	372.246	−	727.589i	0.117260	−	0.229195i
$217$			2708.60i			0.847335i
$218$	−3818.75	−	2204.76i	−1.18642	−	0.684977i
$219$	−1673.32	−	1356.56i	−0.516312	−	0.418574i
$220$	−947.951	+	1641.90i	−0.290504	+	0.503167i
$221$	345.604	−	598.604i	0.105194	−	0.182201i
$222$	−8927.87	−	1419.10i	−2.69910	−	0.429024i
$223$			2954.38i			0.887174i	0.896231	+	0.443587i	$0.146294\pi$
$223$			2954.38i			0.887174i	−0.896231	+	0.443587i	$0.853706\pi$
$224$	2527.91	+	4378.47i	0.754032	+	1.30602i
$225$	1940.44	−	1743.30i	0.574945	−	0.516533i
$226$	1951.92	−	3380.82i	0.574512	−	0.995084i
$227$	1522.99	+	2637.89i	0.445305	+	0.771290i	0.998073	−	0.0620444i	$-0.0197620\pi$
$227$	1522.99	+	2637.89i	0.445305	+	0.771290i	−0.552769	+	0.833335i	$0.686429\pi$
$228$	4035.86	+	252.811i	1.17229	+	0.0734333i
$229$	−538.587	+	932.860i	−0.155418	+	0.269193i	−0.933211	−	0.359328i	$-0.883006\pi$
$229$	−538.587	+	932.860i	−0.155418	+	0.269193i	0.777793	+	0.628521i	$0.216339\pi$
$230$	1088.27	+	1884.95i	0.311994	+	0.540390i
$231$	−2420.73	+	2985.98i	−0.689491	+	0.850489i
$232$	476.598	−	825.492i	0.134871	−	0.233604i
$233$	−3768.47	−	2175.73i	−1.05957	−	0.611746i	−0.134260	−	0.990946i	$-0.542866\pi$
$233$	−3768.47	−	2175.73i	−1.05957	−	0.611746i	−0.925315	+	0.379200i	$0.876199\pi$
$234$	−903.485	+	2770.22i	−0.252405	+	0.773909i
$235$	1814.46			0.503670
$236$	145.633	+	252.244i	0.0401691	+	0.0695749i
$237$	−6023.69	−	957.472i	−1.65097	−	0.262424i
$238$			2176.69i			0.592832i
$239$	−3324.55	−	1919.43i	−0.899779	−	0.519487i	−0.0226503	−	0.999743i	$-0.507210\pi$
$239$	−3324.55	−	1919.43i	−0.899779	−	0.519487i	−0.877128	+	0.480256i	$0.840544\pi$
$240$	504.039	+	1315.24i	0.135565	+	0.353743i
$241$	2646.81	+	1528.14i	0.707452	+	0.408448i	0.810117	−	0.586268i	$-0.199404\pi$
$241$	2646.81	+	1528.14i	0.707452	+	0.408448i	−0.102665	+	0.994716i	$0.532737\pi$
$242$	−214.806	+	372.054i	−0.0570588	+	0.0988287i
$243$	2685.91	−	2671.10i	0.709058	−	0.705150i
$244$	2341.43	−	4055.47i	0.614322	−	1.06404i
$245$			205.826i			0.0536725i
$246$	1218.70	−	467.041i	0.315859	−	0.121046i
$247$	−2133.20	+	203.423i	−0.549523	+	0.0524028i
$248$	−699.490	−	403.851i	−0.179103	−	0.103405i
$249$	1851.48	+	4831.25i	0.471216	+	1.22959i
$250$		−	4924.85i		−	1.24590i
$251$	3276.60	−	1891.75i	0.823973	−	0.475721i	−0.0278118	−	0.999613i	$-0.508854\pi$
$251$	3276.60	−	1891.75i	0.823973	−	0.475721i	0.851785	+	0.523892i	$0.175521\pi$
$252$	−1025.12	−	4849.15i	−0.256255	−	1.21217i
$253$	1854.44	+	3211.99i	0.460821	+	0.798166i
$254$	4755.77	−	2745.75i	1.17482	−	0.678282i
$255$	−116.101	+	730.420i	−0.0285119	+	0.179375i
$256$	2316.88			0.565644
$257$	−1994.12			−0.484006			−0.242003	−	0.970275i	$-0.577804\pi$
$257$	−1994.12			−0.484006			−0.242003	+	0.970275i	$0.577804\pi$
$258$	−455.177	+	2863.63i	−0.109837	+	0.691014i
$259$	−7056.73	+	4074.21i	−1.69299	+	0.977447i
$260$	647.706	+	1121.86i	0.154496	+	0.267595i
$261$	3286.42	−	2952.54i	0.779404	−	0.700220i
$262$	6531.08	−	3770.72i	1.54004	−	0.889144i
$263$		−	3698.46i		−	0.867136i	−0.901121	−	0.433568i	$-0.857254\pi$
$263$		−	3698.46i		−	0.867136i	0.901121	−	0.433568i	$-0.142746\pi$
$264$	−410.192	−	1070.36i	−0.0956272	−	0.249530i
$265$	−1331.43	−	768.700i	−0.308638	−	0.178192i
$266$	5497.38	−	3913.62i	1.26717	−	0.902103i
$267$	4722.09	−	1809.65i	1.08235	−	0.414789i
$268$			3362.61i			0.766434i
$269$	−2590.29	+	4486.52i	−0.587111	+	1.01691i	0.407498	+	0.913206i	$0.366401\pi$
$269$	−2590.29	+	4486.52i	−0.587111	+	1.01691i	−0.994609	+	0.103700i	$0.966932\pi$
$270$	−158.009	−	3113.77i	−0.0356152	−	0.701846i
$271$	−2397.47	+	4152.54i	−0.537402	+	0.930808i	0.461641	+	0.887067i	$0.347261\pi$
$271$	−2397.47	+	4152.54i	−0.537402	+	0.930808i	−0.999043	+	0.0437408i	$0.986072\pi$
$272$	1177.02	+	679.555i	0.262381	+	0.151486i
$273$	939.883	+	2452.53i	0.208367	+	0.543714i
$274$	1838.49	+	1061.45i	0.405356	+	0.234032i
$275$		−	3658.53i		−	0.802245i
$276$	−4722.87	−	750.706i	−1.03001	−	0.163722i
$277$	2229.47	+	3861.55i	0.483594	+	0.837610i	0.999822	−	0.0188411i	$-0.00599767\pi$
$277$	2229.47	+	3861.55i	0.483594	+	0.837610i	−0.516228	+	0.856451i	$0.672664\pi$
$278$	4829.49			1.04192
$279$	−2501.87	−	2784.79i	−0.536856	−	0.597566i
$280$	−525.106	−	303.170i	−0.112075	−	0.0647067i
$281$	−3630.85	+	6288.82i	−0.770813	+	1.33509i	0.166305	+	0.986074i	$0.446816\pi$
$281$	−3630.85	+	6288.82i	−0.770813	+	1.33509i	−0.937118	+	0.349013i	$0.886517\pi$
$282$	−4647.98	+	5733.29i	−0.981501	+	1.21068i
$283$	2399.43	+	4155.94i	0.503998	+	0.872950i	0.999989	+	0.00462263i	$0.00147143\pi$
$283$	2399.43	+	4155.94i	0.503998	+	0.872950i	−0.495991	+	0.868327i	$0.665195\pi$
$284$	−1722.10	+	2982.76i	−0.359816	+	0.623219i
$285$	2053.47	−	1020.05i	0.426797	−	0.212009i
$286$	2043.36	+	3539.20i	0.422470	+	0.731739i
$287$	588.204	−	1018.80i	0.120978	−	0.209540i
$288$	−6643.30	−	2166.66i	−1.35924	−	0.443305i
$289$	−2099.68	−	3636.75i	−0.427371	−	0.740229i
$290$		−	3636.26i		−	0.736305i
$291$	6343.36	+	1008.28i	1.27785	+	0.203116i
$292$	1947.75	−	3373.60i	0.390354	−	0.676112i
$293$	1938.59	−	3357.74i	0.386532	−	0.669492i	−0.605449	−	0.795884i	$-0.707006\pi$
$293$	1938.59	−	3357.74i	0.386532	−	0.669492i	0.991980	+	0.126392i	$0.0403397\pi$
$294$	−650.365	−	527.250i	−0.129014	−	0.104591i
$295$	143.025	+	82.5758i	0.0282280	+	0.0162975i
$296$		−	2429.85i		−	0.477135i
$297$	−269.250	−	5305.94i	−0.0526043	−	1.03664i
$298$	−8064.86	+	4656.25i	−1.56773	+	0.905132i
$299$	2534.17			0.490149
$300$	3664.34	+	2970.68i	0.705202	+	0.571707i
$301$	1306.81	+	2263.46i	0.250243	+	0.433433i
$302$	−6878.56	+	3971.34i	−1.31065	+	0.756705i
$303$	1904.76	−	2349.52i	0.361140	−	0.445468i
$304$	−399.987	−	4194.47i	−0.0754632	−	0.791346i
$305$		−	2655.24i		−	0.498487i
$306$	−2010.56	−	2237.92i	−0.375607	−	0.418083i
$307$	−5729.95	−	3308.19i	−1.06523	−	0.615010i	−0.138355	−	0.990383i	$-0.544182\pi$
$307$	−5729.95	−	3308.19i	−1.06523	−	0.615010i	−0.926874	+	0.375372i	$0.877515\pi$
$308$	−6020.06	−	3475.69i	−1.11372	−	0.643005i
$309$	−5797.79	+	7151.58i	−1.06739	+	1.31663i
$310$	−3081.22			−0.564522
$311$	−140.598	−	81.1740i	−0.0256352	−	0.0148005i	0.487128	−	0.873331i	$-0.338045\pi$
$311$	−140.598	−	81.1740i	−0.0256352	−	0.0148005i	−0.512763	+	0.858530i	$0.671378\pi$
$312$	−773.496	−	122.948i	−0.140354	−	0.0223095i
$313$	3904.65	−	6763.05i	0.705124	−	1.22131i	−0.261523	−	0.965197i	$-0.584225\pi$
$313$	3904.65	−	6763.05i	0.705124	−	1.22131i	0.966647	−	0.256113i	$-0.0824420\pi$
$314$	3528.02	+	6110.71i	0.634069	+	1.09824i
$315$	−1878.15	−	2090.54i	−0.335941	−	0.373931i
$316$		−	11029.9i		−	1.96355i
$317$	−1787.97	+	3096.85i	−0.316790	+	0.548696i	−0.979816	−	0.199900i	$-0.935938\pi$
$317$	−1787.97	+	3096.85i	−0.316790	+	0.548696i	0.663027	+	0.748596i	$0.269272\pi$
$318$	5839.54	−	2237.89i	1.02977	−	0.394637i
$319$		−	6196.26i		−	1.08754i
$320$	−3102.80	+	1791.40i	−0.542037	+	0.312945i
$321$	159.289	−	1002.12i	0.0276966	−	0.174246i
$322$	−6911.21	+	3990.19i	−1.19611	+	0.690573i
$323$	919.338	−	2012.39i	0.158369	−	0.346665i
$324$	5532.99	+	4038.67i	0.948730	+	0.692502i
$325$	−2164.86	−	1249.88i	−0.369491	−	0.213326i
$326$	8126.26			1.38059
$327$	3459.46	−	4267.25i	0.585041	−	0.721649i
$328$	175.402	+	303.805i	0.0295273	+	0.0511427i
$329$			6652.78i			1.11483i
$330$	−3396.76	−	2753.75i	−0.566622	−	0.459361i
$331$	8866.58	−	5119.12i	1.47236	−	0.850067i	0.472843	−	0.881147i	$-0.343228\pi$
$331$	8866.58	−	5119.12i	1.47236	−	0.850067i	0.999517	+	0.0310792i	$0.00989440\pi$
$332$	−8102.86	+	4678.19i	−1.33946	+	0.773340i
$333$	3491.98	−	10706.9i	0.574653	−	1.76197i
$334$	14928.7			2.44570
$335$	953.322	+	1651.20i	0.155479	+	0.269298i
$336$	−4822.36	+	1848.07i	−0.782980	+	0.300062i
$337$	−2694.10	+	1555.44i	−0.435481	+	0.251425i	−0.701679	−	0.712493i	$-0.747566\pi$
$337$	−2694.10	+	1555.44i	−0.435481	+	0.251425i	0.266198	+	0.963918i	$0.414233\pi$
$338$	−6371.21			−1.02529
$339$	3777.89	+	3062.73i	0.605270	+	0.490692i
$340$	−1337.47			−0.213336
$341$	−5250.47			−0.833809
$342$	−2037.10	+	9101.50i	−0.322088	+	1.43904i
$343$	5945.97			0.936012
$344$	−779.376			−0.122155
$345$	−2531.98	+	970.332i	−0.395123	+	0.151423i
$346$	−5584.11			−0.867640
$347$	1103.25	−	636.963i	0.170679	−	0.0985416i	−0.412227	−	0.911081i	$-0.635249\pi$
$347$	1103.25	−	636.963i	0.170679	−	0.0985416i	0.582906	+	0.812540i	$0.301916\pi$
$348$	6206.10	+	5031.28i	0.955982	+	0.775014i
$349$	−706.211	−	1223.19i	−0.108317	−	0.187611i	0.806772	−	0.590863i	$-0.201213\pi$
$349$	−706.211	−	1223.19i	−0.108317	−	0.187611i	−0.915089	+	0.403253i	$0.867879\pi$
$350$	7872.02			1.20222
$351$	−3231.66	−	1653.37i	−0.491434	−	0.251425i
$352$	−8487.41	+	4900.21i	−1.28517	+	0.741995i
$353$	3181.18	−	1836.66i	0.479652	−	0.276927i	−0.240619	−	0.970620i	$-0.577351\pi$
$353$	3181.18	−	1836.66i	0.479652	−	0.276927i	0.720271	+	0.693692i	$0.244017\pi$
$354$	−627.299	+	240.400i	−0.0941824	+	0.0360935i
$355$			1952.90i			0.291970i
$356$	4572.49	+	7919.79i	0.680735	+	1.17907i
$357$	−2678.11	−	425.688i	−0.397032	−	0.0631086i
$358$	−11188.9			−1.65182
$359$	−2702.20	−	1560.12i	−0.397261	−	0.229359i	0.288040	−	0.957618i	$-0.406996\pi$
$359$	−2702.20	−	1560.12i	−0.397261	−	0.229359i	−0.685301	+	0.728259i	$0.740330\pi$
$360$	819.906	−	173.329i	0.120036	−	0.0253757i
$361$	−6735.38	+	1296.37i	−0.981977	+	0.189002i
$362$	1799.67	−	1039.04i	0.261294	−	0.150858i
$363$	−415.750	−	337.049i	−0.0601136	−	0.0487341i
$364$	−4113.33	+	2374.83i	−0.592299	+	0.341964i
$365$		−	2208.79i		−	0.316750i
$366$	8389.96	+	6801.74i	1.19822	+	0.971400i
$367$	−4845.29	+	8392.28i	−0.689160	+	1.19366i	0.282949	+	0.959135i	$0.408687\pi$
$367$	−4845.29	+	8392.28i	−0.689160	+	1.19366i	−0.972110	+	0.234526i	$0.924646\pi$
$368$			4982.88i			0.705845i
$369$	336.290	+	1590.77i	0.0474433	+	0.224423i
$370$	−4634.69	−	8027.53i	−0.651206	−	1.12792i
$371$	2818.46	−	4881.72i	0.394413	−	0.683143i
$372$	4263.31	−	5258.81i	0.594200	−	0.732947i
$373$	4983.50	+	2877.22i	0.691784	+	0.399402i	0.804280	−	0.594250i	$-0.202551\pi$
$373$	4983.50	+	2877.22i	0.691784	+	0.399402i	−0.112496	+	0.993652i	$0.535884\pi$
$374$	−4219.39			−0.583368
$375$	6059.32	+	963.136i	0.834405	+	0.132630i
$376$	−1718.06	−	991.925i	−0.235645	−	0.136049i
$377$	−3666.50	−	2116.86i	−0.500887	−	0.289187i
$378$	11416.7	−	579.344i	1.55348	−	0.0788313i
$379$		−	10303.4i		−	1.39644i	−0.715883	−	0.698220i	$-0.753976\pi$
$379$		−	10303.4i		−	1.39644i	0.715883	−	0.698220i	$-0.246024\pi$
$380$	2404.72	+	3377.86i	0.324630	+	0.456002i
$381$	2448.18	+	6388.27i	0.329197	+	0.859005i
$382$	7989.90	−	4612.97i	1.07015	−	0.617853i
$383$	7438.37	+	12883.6i	0.992384	+	1.71886i	0.602873	+	0.797837i	$0.294022\pi$
$383$	7438.37	+	12883.6i	0.992384	+	1.71886i	0.389510	+	0.921022i	$0.372644\pi$
$384$	598.956	−	3768.18i	0.0795973	−	0.500766i
$385$	−3941.52			−0.521762
$386$	−7119.74	+	4110.58i	−0.938822	+	0.542029i
$387$	−3434.26	−	1120.06i	−0.451094	−	0.147121i
$388$			11615.3i			1.51978i
$389$	11350.4	+	6553.18i	1.47941	+	0.854138i	0.999728	−	0.0233049i	$-0.00741884\pi$
$389$	11350.4	+	6553.18i	1.47941	+	0.854138i	0.479682	+	0.877443i	$0.340752\pi$
$390$	−2789.92	+	1069.18i	−0.362239	+	0.138821i
$391$	−1308.22	+	2265.90i	−0.169206	+	0.293073i
$392$	112.520	−	194.891i	0.0144978	−	0.0251109i
$393$	3362.07	+	8772.97i	0.431536	+	1.12605i
$394$			3880.25i			0.496153i
$395$	−3127.06	−	5416.22i	−0.398327	−	0.689923i
$396$	9399.80	−	1987.13i	1.19282	−	0.252164i
$397$	4993.96	−	8649.79i	0.631334	−	1.09350i	−0.355946	−	0.934507i	$-0.615841\pi$
$397$	4993.96	−	8649.79i	0.631334	−	1.09350i	0.987279	−	0.158995i	$-0.0508255\pi$
$398$	8742.79	+	15143.0i	1.10110	+	1.90716i
$399$	3740.04	+	7529.11i	0.469264	+	0.944679i
$400$	2457.61	−	4256.71i	0.307202	−	0.532089i
$401$	1406.33	+	2435.83i	0.175134	+	0.303341i	0.940208	−	0.340602i	$-0.110631\pi$
$401$	1406.33	+	2435.83i	0.175134	+	0.303341i	−0.765074	+	0.643943i	$0.777298\pi$
$402$	−7659.49	−	1217.48i	−0.950300	−	0.151051i
$403$	−1793.74	+	3106.85i	−0.221719	+	0.384028i
$404$	4736.91	+	2734.85i	0.583341	+	0.336792i
$405$	3861.95	+	414.543i	0.473832	+	0.0508612i
$406$	13332.4			1.62975
$407$	−7897.61	−	13679.1i	−0.961843	−	1.66596i
$408$	509.237	−	628.145i	0.0617916	−	0.0762201i
$409$			10562.4i			1.27696i	0.769640	+	0.638479i	$0.220436\pi$
$409$			10562.4i			1.27696i	−0.769640	+	0.638479i	$0.779564\pi$
$410$	1158.96	+	669.124i	0.139602	+	0.0805992i
$411$	−1665.51	+	2054.42i	−0.199887	+	0.246562i
$412$	−14418.4	−	8324.46i	−1.72413	−	0.995429i
$413$	−302.766	+	524.407i	−0.0360730	+	0.0624803i
$414$	3419.97	−	10486.1i	0.405996	−	1.24484i
$415$	−2652.59	+	4594.43i	−0.313761	+	0.543449i
$416$			6696.33i			0.789218i
$417$	−944.486	+	5941.99i	−0.110915	+	0.697795i
$418$	7586.33	+	10656.4i	0.887702	+	1.24694i
$419$	−9443.88	−	5452.43i	−1.10111	−	0.635724i	−0.164595	−	0.986361i	$-0.552632\pi$
$419$	−9443.88	−	5452.43i	−1.10111	−	0.635724i	−0.936512	+	0.350637i	$0.885965\pi$
$420$	3200.46	−	3947.78i	0.371825	−	0.458647i
$421$			2521.15i			0.291861i	0.989295	+	0.145930i	$0.0466176\pi$
$421$			2521.15i			0.291861i	−0.989295	+	0.145930i	$0.953382\pi$
$422$	−19456.7	+	11233.3i	−2.24440	+	1.29581i
$423$	−6145.00	−	6839.91i	−0.706336	−	0.786212i
$424$	840.461	+	1455.72i	0.0962651	+	0.166736i
$425$	2235.14	−	1290.46i	0.255106	−	0.147286i
$426$	−6170.73	−	5002.61i	−0.701815	−	0.568961i
$427$	9735.51			1.10336
$428$	1834.98			0.207236
$429$	−4754.09	+	1821.91i	−0.535034	+	0.205041i
$430$	−2574.84	+	1486.58i	−0.288767	+	0.166720i
$431$	−5386.36	−	9329.45i	−0.601976	−	1.04265i	−0.992522	−	0.122070i	$-0.961047\pi$
$431$	−5386.36	−	9329.45i	−0.601976	−	1.04265i	0.390545	−	0.920584i	$-0.372287\pi$
$432$	3250.99	−	6354.35i	0.362068	−	0.707694i
$433$	−3959.09	+	2285.78i	−0.439404	+	0.253690i	−0.703345	−	0.710849i	$-0.748311\pi$
$433$	−3959.09	+	2285.78i	−0.439404	+	0.253690i	0.263941	+	0.964539i	$0.414978\pi$
$434$		−	11297.4i		−	1.24952i
$435$	4473.89	+	711.130i	0.493119	+	0.0783817i
$436$	8603.25	+	4967.09i	0.945002	+	0.545597i
$437$	8074.82	−	770.019i	0.883916	−	0.0842907i
$438$	6979.29	+	5658.11i	0.761378	+	0.617249i
$439$			800.047i			0.0869799i	0.999054	+	0.0434900i	$0.0138477\pi$
$439$			800.047i			0.0869799i	−0.999054	+	0.0434900i	$0.986152\pi$
$440$	587.678	−	1017.89i	0.0636737	−	0.110286i
$441$	775.895	−	697.067i	0.0837809	−	0.0752691i
$442$	−1441.49	+	2496.74i	−0.155124	+	0.268682i
$443$	−5462.19	−	3153.59i	−0.585816	−	0.338221i	0.177626	−	0.984098i	$-0.443158\pi$
$443$	−5462.19	−	3153.59i	−0.585816	−	0.338221i	−0.763441	+	0.645877i	$0.776492\pi$
$444$	20113.6	+	3197.07i	2.14988	+	0.341726i
$445$	4490.62	+	2592.66i	0.478373	+	0.276189i
$446$		−	12322.5i		−	1.30827i
$447$	−4151.63	−	10833.3i	−0.439296	−	1.14630i
$448$	−6568.22	−	11376.5i	−0.692677	−	1.19975i
$449$	−5106.61			−0.536739			−0.268370	−	0.963316i	$-0.586485\pi$
$449$	−5106.61			−0.536739			−0.268370	+	0.963316i	$0.586485\pi$
$450$	−8093.45	+	7271.19i	−0.847842	+	0.761705i
$451$	1974.89	+	1140.20i	0.206194	+	0.119046i
$452$	−4397.47	+	7616.64i	−0.457610	+	0.792603i
$453$	−3540.94	−	9239.74i	−0.367258	−	0.958324i
$454$	−6352.27	−	11002.5i	−0.656667	−	1.13738i
$455$	−1346.56	+	2332.31i	−0.138742	+	0.240308i
$456$	−2502.01	−	156.729i	−0.256946	−	0.0160954i
$457$	5112.07	+	8854.37i	0.523266	+	0.906324i	0.999633	+	0.0270775i	$0.00862008\pi$
$457$	5112.07	+	8854.37i	0.523266	+	0.906324i	−0.476367	+	0.879247i	$0.658047\pi$
$458$	2246.41	−	3890.89i	0.229187	−	0.396964i
$459$	3146.63	−	2036.04i	0.319983	−	0.207046i
$460$	−2451.77	−	4246.59i	−0.248509	−	0.430431i
$461$		−	14167.6i		−	1.43135i	−0.698435	−	0.715673i	$-0.746120\pi$
$461$		−	14167.6i		−	1.43135i	0.698435	−	0.715673i	$-0.253880\pi$
$462$	10096.7	−	12454.3i	1.01676	−	1.25417i
$463$	−3506.09	+	6072.73i	−0.351926	+	0.609555i	−0.986587	−	0.163237i	$-0.947807\pi$
$463$	−3506.09	+	6072.73i	−0.351926	+	0.609555i	0.634660	+	0.772791i	$0.281140\pi$
$464$	4162.33	−	7209.37i	0.416447	−	0.721308i
$465$	602.584	−	3791.00i	0.0600949	−	0.378072i
$466$	15718.0	+	9074.82i	1.56250	+	0.902109i
$467$		−	10079.7i		−	0.998783i	−0.866377	−	0.499391i	$-0.833557\pi$
$467$		−	10079.7i		−	0.998783i	0.866377	−	0.499391i	$-0.166443\pi$
$468$	2035.46	−	6241.01i	0.201045	−	0.616433i
$469$	−6054.18	+	3495.38i	−0.596068	+	0.344140i
$470$	−7568.00			−0.742736
$471$	−8208.30	+	3145.67i	−0.803012	+	0.307738i
$472$	−90.2845	−	156.377i	−0.00880441	−	0.0152497i
$473$	−4387.58	+	2533.17i	−0.426514	+	0.246248i
$474$	25124.4	+	3993.55i	2.43460	+	0.386983i
$475$	−7277.84	−	3324.79i	−0.703011	−	0.321162i
$476$		−	4903.86i		−	0.472202i
$477$	1611.38	+	7622.37i	0.154675	+	0.731665i
$478$	13866.5	+	8005.81i	1.32686	+	0.766061i
$479$	−17003.8	−	9817.16i	−1.62197	−	0.936446i	−0.986392	−	0.164410i	$-0.947428\pi$
$479$	−17003.8	−	9817.16i	−1.62197	−	0.936446i	−0.635579	−	0.772036i	$-0.719239\pi$
$480$	−2564.02	−	6690.56i	−0.243815	−	0.636210i
$481$	−10792.4			−1.02306
$482$	−11039.7	−	6373.75i	−1.04324	−	0.602316i
$483$	−3557.75	−	9283.59i	−0.335162	−	0.874571i
$484$	483.934	−	838.199i	0.0454484	−	0.0787189i
$485$	3293.01	+	5703.65i	0.308305	+	0.533999i
$486$	−11202.7	+	11141.0i	−1.04561	+	1.03985i
$487$			3968.11i			0.369224i	0.982811	+	0.184612i	$0.0591029\pi$
$487$			3968.11i			0.369224i	−0.982811	+	0.184612i	$0.940897\pi$
$488$	−1451.56	+	2514.17i	−0.134649	+	0.233220i
$489$	−1589.22	+	9998.19i	−0.146968	+	0.924609i
$490$		−	858.487i		−	0.0791480i
$491$	−5612.01	+	3240.09i	−0.515817	+	0.297807i	−0.735222	−	0.677827i	$-0.762922\pi$
$491$	−5612.01	+	3240.09i	−0.515817	+	0.297807i	0.219404	+	0.975634i	$0.429589\pi$
$492$	−2745.59	+	1052.19i	−0.251587	+	0.0964158i
$493$	3785.54	−	2185.58i	0.345825	−	0.199662i
$494$	8897.43	−	848.464i	0.810353	−	0.0772757i
$495$	4052.39	−	3640.68i	0.367962	−	0.330579i
$496$	−6108.94	−	3527.00i	−0.553024	−	0.319288i
$497$	−7160.37			−0.646251
$498$	−7722.40	−	20150.8i	−0.694877	−	1.81321i
$499$	−2040.88	−	3534.90i	−0.183091	−	0.317122i	0.759841	−	0.650109i	$-0.225277\pi$
$499$	−2040.88	−	3534.90i	−0.183091	−	0.317122i	−0.942931	+	0.332987i	$0.891943\pi$
$500$			11095.2i			0.992383i
$501$	−2919.55	+	18367.6i	−0.260351	+	1.63793i
$502$	−13666.5	+	7890.34i	−1.21507	+	0.701520i
$503$	13892.2	−	8020.69i	1.23146	−	0.710984i	0.264126	−	0.964488i	$-0.414917\pi$
$503$	13892.2	−	8020.69i	1.23146	−	0.710984i	0.967334	+	0.253505i	$0.0815833\pi$
$504$	635.517	+	3006.21i	0.0561670	+	0.265689i
$505$	3101.39			0.273288
$506$	−7734.75	−	13397.0i	−0.679549	−	1.17701i
$507$	1245.99	−	7838.85i	0.109145	−	0.686658i
$508$	−10714.3	+	6185.88i	−0.935765	+	0.540264i
$509$	12246.6			1.06644			0.533222	−	0.845975i	$-0.320981\pi$
$509$	12246.6			1.06644			0.533222	+	0.845975i	$0.320981\pi$
$510$	484.250	−	3046.53i	0.0420450	−	0.264515i
$511$	8098.60			0.701098
$512$	−15537.9			−1.34118
$513$	−10799.7	−	4286.31i	−0.929470	−	0.368899i
$514$	8317.33			0.713739
$515$	−9440.15			−0.807734
$516$	1025.47	−	6451.45i	0.0874876	−	0.550406i
$517$	−12896.0			−1.09703
$518$	29433.1	−	16993.2i	2.49656	−	1.44139i
$519$	1092.06	−	6870.44i	0.0923628	−	0.581077i
$520$	−401.542	−	695.492i	−0.0338631	−	0.0586525i
$521$	3229.45			0.271564			0.135782	−	0.990739i	$-0.456645\pi$
$521$	3229.45			0.271564			0.135782	+	0.990739i	$0.456645\pi$
$522$	−13707.5	+	12314.8i	−1.14935	+	1.03258i
$523$	−13508.0	+	7798.86i	−1.12938	+	0.652047i	−0.943778	−	0.330579i	$-0.892756\pi$
$523$	−13508.0	+	7798.86i	−1.12938	+	0.652047i	−0.185600	+	0.982625i	$0.559423\pi$
$524$	−14713.8	+	8495.04i	−1.22667	+	0.708220i
$525$	−1539.50	+	9685.38i	−0.127980	+	0.805152i
$526$			15426.0i			1.27872i
$527$	−1851.98	−	3207.72i	−0.153080	−	0.265143i
$528$	−3582.39	−	9347.87i	−0.295271	−	0.770481i
$529$	2574.39			0.211588
$530$	5553.30	+	3206.20i	0.455132	+	0.262770i
$531$	−173.099	−	818.815i	−0.0141466	−	0.0669182i
$532$	−12385.0	+	8816.97i	−1.00932	+	0.718542i
$533$	1349.38	−	779.064i	0.109659	−	0.0633115i
$534$	−19695.5	+	7547.92i	−1.59608	+	0.611667i
$535$	901.062	−	520.228i	0.0728155	−	0.0420401i
$536$		−	2084.64i		−	0.167990i
$537$	2188.17	−	13766.3i	0.175841	−	1.10626i
$538$	10803.9	−	18712.9i	0.865781	−	1.49958i
$539$		−	1462.88i		−	0.116903i
$540$	355.977	+	7015.01i	0.0283682	+	0.559033i
$541$	7593.71	+	13152.7i	0.603473	+	1.04525i	0.992291	+	0.123931i	$0.0395502\pi$
$541$	7593.71	+	13152.7i	0.603473	+	1.04525i	−0.388818	+	0.921315i	$0.627116\pi$
$542$	9999.69	−	17320.0i	0.792478	−	1.37261i
$543$	926.433	+	2417.43i	0.0732174	+	0.191053i
$544$	−5987.46	−	3456.86i	−0.471894	−	0.272448i
$545$	5632.81			0.442721
$546$	−3920.19	−	10229.3i	−0.307268	−	0.801786i
$547$	13924.5	+	8039.33i	1.08843	+	0.628404i	0.933157	−	0.359469i	$-0.117042\pi$
$547$	13924.5	+	8039.33i	1.08843	+	0.628404i	0.155270	+	0.987872i	$0.450375\pi$
$548$	−4141.93	−	2391.35i	−0.322873	−	0.186411i
$549$	−10009.3	+	8992.44i	−0.778121	+	0.699067i
$550$			15259.5i			1.18303i
$551$	−12326.1	−	5631.03i	−0.953012	−	0.435372i
$552$	2927.92	+	465.397i	0.225762	+	0.0358851i
$553$	19858.7	−	11465.4i	1.52709	−	0.881663i
$554$	−9298.95	−	16106.3i	−0.713131	−	1.23518i
$555$	10783.1	−	4132.41i	0.824716	−	0.316056i
$556$	−10880.3			−0.829909
$557$	12024.0	−	6942.05i	0.914672	−	0.528086i	0.0327405	−	0.999464i	$-0.489577\pi$
$557$	12024.0	−	6942.05i	0.914672	−	0.528086i	0.881931	+	0.471378i	$0.156243\pi$
$558$	10435.1	+	11615.2i	0.791673	+	0.881199i
$559$			3461.68i			0.261920i
$560$	−4585.97	−	2647.71i	−0.346059	−	0.199797i
$561$	825.171	−	5191.35i	0.0621012	−	0.390694i
$562$	15144.0	−	26230.2i	1.13668	−	1.96878i
$563$	12061.7	−	20891.5i	0.902912	−	1.56389i	0.0792169	−	0.996857i	$-0.474758\pi$
$563$	12061.7	−	20891.5i	0.902912	−	1.56389i	0.823695	−	0.567033i	$-0.191909\pi$
$564$	10471.4	−	12916.5i	0.781784	−	0.964332i
$565$			4986.84i			0.371324i
$566$	−10007.9	−	17334.1i	−0.743219	−	1.28729i
$567$	−1519.93	+	14159.9i	−0.112577	+	1.04879i
$568$	1067.61	−	1849.15i	0.0788658	−	0.136600i
$569$	5557.22	+	9625.40i	0.409439	+	0.709170i	0.994827	−	0.101584i	$-0.0323910\pi$
$569$	5557.22	+	9625.40i	0.409439	+	0.709170i	−0.585388	+	0.810754i	$0.699058\pi$
$570$	−8564.89	+	4254.56i	−0.629375	+	0.312638i
$571$	12974.4	−	22472.2i	0.950893	−	1.64699i	0.207393	−	0.978258i	$-0.433502\pi$
$571$	12974.4	−	22472.2i	0.950893	−	1.64699i	0.743499	−	0.668737i	$-0.233165\pi$
$572$	−4603.47	−	7973.45i	−0.336505	−	0.582844i
$573$	4113.04	+	10732.6i	0.299868	+	0.782476i
$574$	−2453.36	+	4249.34i	−0.178399	+	0.308997i
$575$	8194.65	+	4731.18i	0.594331	+	0.343137i
$576$	17261.2	+	5629.59i	1.24864	+	0.407233i
$577$	−9811.07			−0.707869			−0.353934	−	0.935270i	$-0.615156\pi$
$577$	−9811.07			−0.707869			−0.353934	+	0.935270i	$0.615156\pi$
$578$	8757.60	+	15168.6i	0.630222	+	1.09158i
$579$	−3665.10	−	9563.70i	−0.263068	−	0.686449i
$580$			8192.11i			0.586480i
$581$	−16845.6	−	9725.80i	−1.20288	−	0.694483i
$582$	−26457.7	−	4205.48i	−1.88438	−	0.299524i
$583$	9462.93	+	5463.42i	0.672238	+	0.388117i
$584$	−1207.50	+	2091.45i	−0.0855592	+	0.148193i
$585$	−769.860	−	3641.70i	−0.0544099	−	0.257377i
$586$	−8085.74	+	14004.9i	−0.569998	+	0.987265i
$587$			13628.8i			0.958301i	0.877733	+	0.479150i	$0.159055\pi$
$587$			13628.8i			0.958301i	−0.877733	+	0.479150i	$0.840945\pi$
$588$	1465.20	+	1187.84i	0.102762	+	0.0833090i
$589$	−4771.51	+	10444.7i	−0.333798	+	0.730670i
$590$	−596.549	−	344.418i	−0.0416264	−	0.0240330i
$591$	−4774.09	−	758.847i	−0.332284	−	0.0528169i
$592$		−	21220.9i		−	1.47327i
$593$	−4220.73	+	2436.84i	−0.292284	+	0.168750i	−0.638972	−	0.769230i	$-0.720640\pi$
$593$	−4220.73	+	2436.84i	−0.292284	+	0.168750i	0.346687	+	0.937981i	$0.387307\pi$
$594$	1123.02	+	22130.7i	0.0775728	+	1.52868i
$595$	−1390.28	−	2408.03i	−0.0957911	−	0.165915i
$596$	18169.3	−	10490.0i	1.24873	−	0.720954i
$597$	−20341.0	+	7795.29i	−1.39448	+	0.534405i
$598$	−10569.8			−0.722797
$599$	23872.9			1.62841			0.814207	−	0.580575i	$-0.197172\pi$
$599$	23872.9			1.62841			0.814207	+	0.580575i	$0.197172\pi$
$600$	−2271.69	−	1841.66i	−0.154569	−	0.125309i
$601$	24992.4	−	14429.4i	1.69628	−	0.979347i	0.747045	−	0.664773i	$-0.231472\pi$
$601$	24992.4	−	14429.4i	1.69628	−	0.979347i	0.949233	−	0.314573i	$-0.101861\pi$
$602$	−5450.60	−	9440.72i	−0.369020	−	0.639161i
$603$	2995.88	−	9185.79i	0.202324	−	0.620355i
$604$	15496.7	−	8947.01i	1.04396	−	0.602730i
$605$		−	548.794i		−	0.0368788i
$606$	−7944.62	+	9799.71i	−0.532555	+	0.656907i
$607$	12688.7	+	7325.83i	0.848466	+	0.489862i	0.860133	−	0.510070i	$-0.170380\pi$
$607$	12688.7	+	7325.83i	0.848466	+	0.489862i	−0.0116670	+	0.999932i	$0.503714\pi$
$608$	2034.71	+	21337.1i	0.135721	+	1.42324i
$609$	−2607.38	+	16403.6i	−0.173491	+	1.09148i
$610$			11074.8i			0.735093i
$611$	−4405.73	+	7630.95i	−0.291713	+	0.505262i
$612$	4529.57	+	5041.80i	0.299178	+	0.333011i
$613$	1148.95	−	1990.05i	0.0757028	−	0.131121i	−0.825689	−	0.564126i	$-0.809213\pi$
$613$	1148.95	−	1990.05i	0.0757028	−	0.131121i	0.901392	+	0.433005i	$0.142547\pi$
$614$	23899.2	+	13798.2i	1.57084	+	0.906923i
$615$	−1049.91	+	1295.07i	−0.0688400	+	0.0849143i
$616$	3732.11	+	2154.74i	0.244109	+	0.140936i
$617$			23700.4i			1.54642i	0.634147	+	0.773212i	$0.281351\pi$
$617$			23700.4i			1.54642i	−0.634147	+	0.773212i	$0.718649\pi$
$618$	24182.2	−	29828.8i	1.57403	−	1.94157i
$619$	814.069	+	1410.01i	0.0528598	+	0.0915558i	0.891245	−	0.453523i	$-0.149833\pi$
$619$	814.069	+	1410.01i	0.0528598	+	0.0915558i	−0.838385	+	0.545079i	$0.816500\pi$
$620$	6941.67			0.449652
$621$	12232.8	+	6258.52i	0.790478	+	0.404421i
$622$	586.423	+	338.571i	0.0378029	+	0.0218255i
$623$	−9506.06	+	16465.0i	−0.611320	+	1.05884i
$624$	−6755.27	−	1073.76i	−0.433377	−	0.0688858i
$625$	−2892.70	−	5010.30i	−0.185133	−	0.320659i
$626$	−16286.0	+	28208.2i	−1.03981	+	1.80100i
$627$	−14594.7	+	7249.85i	−0.929598	+	0.461772i
$628$	−7948.25	−	13766.8i	−0.505048	−	0.874768i
$629$	5571.39	−	9649.93i	0.353173	−	0.611713i
$630$	7833.62	+	8719.48i	0.495395	+	0.551417i
$631$	6394.92	+	11076.3i	0.403451	+	0.698798i	0.994140	−	0.108102i	$-0.0344772\pi$
$631$	6394.92	+	11076.3i	0.403451	+	0.698798i	−0.590689	+	0.806899i	$0.701144\pi$
$632$			6837.95i			0.430378i
$633$	−10015.9	−	26135.6i	−0.628906	−	1.64107i
$634$	7457.50	−	12916.8i	0.467153	−	0.809133i
$635$	−3507.47	+	6075.12i	−0.219197	+	0.379660i
$636$	−13155.9	+	5041.73i	−0.820227	+	0.314336i
$637$	−865.628	−	499.771i	−0.0538421	−	0.0310858i
$638$			25844.2i			1.60373i
$639$	7361.78	−	6613.85i	0.455755	−	0.409452i
$640$	3388.17	−	1956.16i	0.209264	−	0.120819i
$641$	24618.2			1.51695			0.758473	−	0.651705i	$-0.225946\pi$
$641$	24618.2			1.51695			0.758473	+	0.651705i	$0.225946\pi$
$642$	−664.382	+	4179.79i	−0.0408428	+	0.256952i
$643$	3516.27	+	6090.37i	0.215658	+	0.373531i	0.953476	−	0.301469i	$-0.0974769\pi$
$643$	3516.27	+	6090.37i	0.215658	+	0.373531i	−0.737818	+	0.675000i	$0.764144\pi$
$644$	15570.2	−	8989.47i	0.952722	−	0.550054i
$645$	−1325.48	−	3458.70i	−0.0809156	−	0.211141i
$646$	−3834.50	+	8393.56i	−0.233539	+	0.511208i
$647$		−	7142.46i		−	0.434002i	−0.976171	−	0.217001i	$-0.930373\pi$
$647$		−	7142.46i		−	0.434002i	0.976171	−	0.217001i	$-0.0696275\pi$
$648$	−3430.15	−	2503.76i	−0.207946	−	0.151785i
$649$	−1016.53	−	586.895i	−0.0614829	−	0.0354972i
$650$	9029.46	+	5213.16i	0.544869	+	0.314580i
$651$	13899.8	+	2209.39i	0.836830	+	0.133015i
$652$	−18307.6			−1.09967
$653$	26447.0	+	15269.2i	1.58492	+	0.915052i	0.994126	+	0.108226i	$0.0345169\pi$
$653$	26447.0	+	15269.2i	1.58492	+	0.915052i	0.590789	+	0.806826i	$0.298816\pi$
$654$	−14429.2	+	17798.4i	−0.862729	+	1.06418i
$655$	−4816.79	+	8342.93i	−0.287340	+	0.497687i
$656$	1531.86	+	2653.26i	0.0911723	+	0.157915i
$657$	−8326.40	+	7480.48i	−0.494435	+	0.444203i
$658$		−	27748.3i		−	1.64398i
$659$	−11068.1	+	19170.5i	−0.654252	+	1.13320i	0.327829	+	0.944737i	$0.393683\pi$
$659$	−11068.1	+	19170.5i	−0.654252	+	1.13320i	−0.982081	+	0.188460i	$0.939650\pi$
$660$	7652.54	+	6203.91i	0.451325	+	0.365889i
$661$		−	8852.67i		−	0.520921i	−0.965484	−	0.260461i	$-0.916126\pi$
$661$		−	8852.67i		−	0.520921i	0.965484	−	0.260461i	$-0.0838744\pi$
$662$	−36981.9	+	21351.5i	−2.17121	+	1.25355i
$663$	−2789.97	−	2261.82i	−0.163429	−	0.132492i
$664$	5023.33	−	2900.22i	0.293589	−	0.169504i
$665$	−3581.97	+	7840.79i	−0.208876	+	0.457222i
$666$	−14564.8	+	44657.9i	−0.847411	+	2.59828i
$667$	13878.9	+	8012.96i	0.805684	+	0.465162i
$668$	−33632.8			−1.94804
$669$	15161.1	+	2409.87i	0.876175	+	0.139269i
$670$	−3976.24	−	6887.05i	−0.229277	−	0.397119i
$671$			18871.7i			1.08574i
$672$	24531.1	−	9401.06i	1.40820	−	0.539663i
$673$	−9635.77	+	5563.21i	−0.551904	+	0.318642i	−0.749890	−	0.661563i	$-0.769893\pi$
$673$	−9635.77	+	5563.21i	−0.551904	+	0.318642i	0.197986	+	0.980205i	$0.436560\pi$
$674$	11236.9	−	6487.64i	0.642181	−	0.370763i
$675$	−7363.34	−	11379.8i	−0.419874	−	0.648903i
$676$	14353.7			0.816663
$677$	11214.4	+	19423.9i	0.636638	+	1.10269i	0.986166	+	0.165763i	$0.0530086\pi$
$677$	11214.4	+	19423.9i	0.636638	+	1.10269i	−0.349528	+	0.936926i	$0.613658\pi$
$678$	−15757.3	−	12774.4i	−0.892560	−	0.723598i
$679$	−20912.6	+	12073.9i	−1.18196	+	0.682406i
$680$	829.157			0.0467599
$681$	14779.2	−	5663.84i	0.831632	−	0.318706i
$682$	21899.3			1.22957
$683$	−16602.9			−0.930148			−0.465074	−	0.885272i	$-0.653972\pi$
$683$	−16602.9			−0.930148			−0.465074	+	0.885272i	$0.653972\pi$
$684$	4589.38	−	20504.7i	0.256549	−	1.14622i
$685$	−2711.85			−0.151262
$686$	−24800.2			−1.38029
$687$	4347.86	+	3524.81i	0.241457	+	0.195749i
$688$	−6806.63			−0.377181
$689$	6465.73	−	3732.99i	0.357511	−	0.206409i
$690$	10560.7	−	4047.19i	0.582667	−	0.223295i
$691$	−1465.59	−	2538.48i	−0.0806856	−	0.139752i	0.822859	−	0.568246i	$-0.192378\pi$
$691$	−1465.59	−	2538.48i	−0.0806856	−	0.139752i	−0.903545	+	0.428494i	$0.859044\pi$
$692$	12580.4			0.691092
$693$	13348.6	+	14858.2i	0.731707	+	0.814452i
$694$	−4601.59	+	2656.73i	−0.251691	+	0.145314i
$695$	−5342.76	+	3084.65i	−0.291601	+	0.168356i
$696$	−3847.44	−	3119.12i	−0.209536	−	0.169871i
$697$			1608.71i			0.0874238i
$698$	2945.56	+	5101.86i	0.159729	+	0.276659i
$699$	−14239.2	+	17564.1i	−0.770494	+	0.950406i
$700$	−17734.8			−0.957591
$701$	−11698.5	−	6754.14i	−0.630309	−	0.363909i	0.150563	−	0.988600i	$-0.451891\pi$
$701$	−11698.5	−	6754.14i	−0.630309	−	0.363909i	−0.780872	+	0.624691i	$0.785225\pi$
$702$	13479.0	+	6896.09i	0.724691	+	0.370764i
$703$	−34388.7	+	3279.33i	−1.84494	+	0.175935i
$704$	22052.7	−	12732.1i	1.18060	−	0.681619i
$705$	1480.05	−	9311.33i	0.0790663	−	0.497426i
$706$	−13268.5	+	7660.57i	−0.707318	+	0.408370i
$707$			11371.3i			0.604899i
$708$	1413.24	−	541.595i	0.0750180	−	0.0287492i
$709$	2119.02	−	3670.25i	0.112245	−	0.194413i	−0.804430	−	0.594047i	$-0.797529\pi$
$709$	2119.02	−	3670.25i	0.112245	−	0.194413i	0.916675	+	0.399634i	$0.130863\pi$
$710$		−	8145.43i		−	0.430553i
$711$	−9826.97	+	30130.9i	−0.518341	+	1.58931i
$712$	−2834.69	−	4909.84i	−0.149206	−	0.258432i
$713$	6789.87	−	11760.4i	0.356638	−	0.617715i
$714$	11170.2	+	1775.51i	0.585482	+	0.0930630i
$715$	−4521.05	−	2610.23i	−0.236472	−	0.136527i
$716$	25207.3			1.31570
$717$	−12561.8	+	15495.0i	−0.654294	+	0.807074i
$718$	11270.7	+	6507.14i	0.585820	+	0.338223i
$719$	19547.7	+	11285.8i	1.01391	+	0.585384i	0.912335	−	0.409443i	$-0.134277\pi$
$719$	19547.7	+	11285.8i	1.01391	+	0.585384i	0.101579	+	0.994827i	$0.467610\pi$
$720$	7160.60	−	1513.76i	0.370638	−	0.0783535i
$721$		−	34612.6i		−	1.78785i
$722$	28092.8	−	5407.06i	1.44807	−	0.278712i
$723$	10001.0	−	12336.2i	0.514440	−	0.634563i
$724$	−4054.47	+	2340.85i	−0.208126	+	0.120161i
$725$	−7904.16	−	13690.4i	−0.404901	−	0.701309i
$726$	1734.07	+	1405.81i	0.0886463	+	0.0718655i
$727$	22025.3			1.12362			0.561812	−	0.827265i	$-0.310105\pi$
$727$	22025.3			1.12362			0.561812	+	0.827265i	$0.310105\pi$
$728$	2550.04	−	1472.27i	0.129822	−	0.0749530i
$729$	−11516.5	−	15962.2i	−0.585099	−	0.810962i
$730$			9212.73i			0.467094i
$731$	−3095.23	−	1787.03i	−0.156609	−	0.0904182i
$732$	−18901.7	−	15323.6i	−0.954408	−	0.773738i
$733$	14001.3	−	24251.0i	0.705527	−	1.22201i	−0.260973	−	0.965346i	$-0.584043\pi$
$733$	14001.3	−	24251.0i	0.705527	−	1.22201i	0.966501	−	0.256663i	$-0.0826232\pi$
$734$	20209.4	−	35003.6i	1.01627	−	1.76023i
$735$	1056.24	+	167.891i	0.0530070	+	0.00842553i
$736$		−	25347.7i		−	1.26947i
$737$	−6775.60	−	11735.7i	−0.338646	−	0.586553i
$738$	−1402.64	−	6634.98i	−0.0699621	−	0.330944i
$739$	2586.48	−	4479.91i	0.128748	−	0.222999i	−0.794444	−	0.607338i	$-0.792237\pi$
$739$	2586.48	−	4479.91i	0.128748	−	0.222999i	0.923192	+	0.384339i	$0.125571\pi$
$740$	10441.5	+	18085.2i	0.518698	+	0.898411i
$741$	−696.126	+	11112.9i	−0.0345113	+	0.550936i
$742$	−11755.6	+	20361.3i	−0.581620	+	1.00739i
$743$	−16790.7	−	29082.4i	−0.829060	−	1.43597i	−0.898776	−	0.438407i	$-0.855543\pi$
$743$	−16790.7	−	29082.4i	−0.829060	−	1.43597i	0.0697162	−	0.997567i	$-0.477791\pi$
$744$	−2643.02	+	3260.17i	−0.130239	+	0.160650i
$745$	5947.99	−	10302.2i	0.292507	−	0.506636i
$746$	−20785.8	−	12000.7i	−1.02014	−	0.588977i
$747$	26302.9	−	5560.47i	1.28832	−	0.272352i
$748$	9505.85			0.464664
$749$	1907.43	+	3303.77i	0.0930521	+	0.161171i
$750$	−25273.0	−	4017.17i	−1.23045	−	0.195582i
$751$		−	20270.0i		−	0.984906i	−0.870339	−	0.492453i	$-0.836100\pi$
$751$		−	20270.0i		−	0.984906i	0.870339	−	0.492453i	$-0.163900\pi$
$752$	−15004.6	−	8662.90i	−0.727608	−	0.420085i
$753$	−7035.22	−	18357.7i	−0.340475	−	0.888436i
$754$	15292.7	+	8829.26i	0.738632	+	0.426449i
$755$	5073.07	−	8786.81i	0.244540	−	0.423556i
$756$	−25720.7	+	1305.20i	−1.23737	+	0.0627906i
$757$	−3228.05	+	5591.15i	−0.154988	+	0.268446i	−0.933055	−	0.359735i	$-0.882867\pi$
$757$	−3228.05	+	5591.15i	−0.154988	+	0.268446i	0.778067	+	0.628181i	$0.216200\pi$
$758$			42974.8i			2.05926i
$759$	17995.7	−	6896.49i	0.860610	−	0.329811i
$760$	−1490.80	−	2094.09i	−0.0711537	−	0.0999482i
$761$	−19996.1	−	11544.8i	−0.952507	−	0.549930i	−0.0586482	−	0.998279i	$-0.518679\pi$
$761$	−19996.1	−	11544.8i	−0.952507	−	0.549930i	−0.893859	+	0.448349i	$0.852012\pi$
$762$	−10211.2	−	26645.0i	−0.485449	−	1.26673i
$763$			20652.8i			0.979925i
$764$	−18000.4	+	10392.5i	−0.852397	+	0.492132i
$765$	3653.62	+	1191.60i	0.172675	+	0.0563168i
$766$	−31024.9	−	53736.8i	−1.46342	−	2.53471i
$767$	−694.566	+	401.008i	−0.0326979	+	0.0188782i
$768$	1889.86	−	11889.6i	0.0887949	−	0.558631i
$769$	−6922.25			−0.324607			−0.162304	−	0.986741i	$-0.551892\pi$
$769$	−6922.25			−0.324607			−0.162304	+	0.986741i	$0.551892\pi$
$770$	16439.8			0.769415
$771$	−1626.59	+	10233.3i	−0.0759795	+	0.478006i
$772$	16040.0	−	9260.71i	0.747789	−	0.431736i
$773$	19977.0	+	34601.2i	0.929527	+	1.60999i	0.784114	+	0.620616i	$0.213118\pi$
$773$	19977.0	+	34601.2i	0.929527	+	1.60999i	0.145412	+	0.989371i	$0.453549\pi$
$774$	14324.1	+	4671.69i	0.665204	+	0.216951i
$775$	−11600.7	+	6697.68i	−0.537691	+	0.310436i
$776$		−	7200.84i		−	0.333112i
$777$	15151.6	+	39536.5i	0.699562	+	1.82544i
$778$	−47341.9	−	27332.9i	−2.18161	−	1.25955i
$779$	4062.91	−	2892.41i	0.186867	−	0.133031i
$780$	6285.41	−	2408.76i	0.288530	−	0.110573i
$781$		−	13880.0i		−	0.635934i
$782$	5456.49	−	9450.92i	0.249519	−	0.432179i
$783$	−12470.9	−	19273.4i	−0.569188	−	0.879662i
$784$	982.690	−	1702.07i	0.0447654	−	0.0775359i
$785$	−7805.94	−	4506.76i	−0.354912	−	0.204909i
$786$	−14022.9	−	36591.5i	−0.636364	−	1.66053i
$787$	−27698.2	−	15991.6i	−1.25456	−	0.724319i	−0.282545	−	0.959254i	$-0.591179\pi$
$787$	−27698.2	−	15991.6i	−1.25456	−	0.724319i	−0.972011	+	0.234935i	$0.924512\pi$
$788$		−	8741.80i		−	0.395195i
$789$	−18979.5	−	3016.81i	−0.856385	−	0.136123i
$790$	13042.7	+	22590.7i	0.587392	+	1.01739i
$791$	−18284.4			−0.821894
$792$	−5827.36	+	1231.91i	−0.261447	+	0.0552704i
$793$	11166.9	+	6447.24i	0.500063	+	0.288711i
$794$	−20829.5	+	36077.7i	−0.930994	+	1.61253i
$795$	−5030.80	+	6205.50i	−0.224433	+	0.276838i
$796$	−19696.6	−	34115.5i	−0.877044	−	1.51908i
$797$	−1390.86	+	2409.04i	−0.0618154	+	0.107067i	−0.895277	−	0.445510i	$-0.853022\pi$
$797$	−1390.86	+	2409.04i	−0.0618154	+	0.107067i	0.833462	+	0.552578i	$0.186356\pi$
$798$	−15599.4	−	31403.4i	−0.691998	−	1.39307i
$799$	−4548.76	−	7878.69i	−0.201406	−	0.348846i
$800$	−12501.8	+	21653.7i	−0.552505	+	0.956967i
$801$	−5434.84	−	25708.6i	−0.239739	−	1.13404i
$802$	−5865.70	−	10159.7i	−0.258261	−	0.447321i
$803$			15698.7i			0.689906i
$804$	17256.0	+	2742.86i	0.756931	+	0.120315i
$805$	5097.15	−	8828.51i	0.223169	−	0.386539i
$806$	7481.58	−	12958.5i	0.326957	−	0.566306i
$807$	20910.7	+	16952.3i	0.912133	+	0.739466i
$808$	−2936.62	−	1695.46i	−0.127859	−	0.0738194i
$809$			1863.50i			0.0809856i	0.999180	+	0.0404928i	$0.0128928\pi$
$809$			1863.50i			0.0809856i	−0.999180	+	0.0404928i	$0.987107\pi$
$810$	−16107.9	−	1729.03i	−0.698735	−	0.0750023i
$811$	10767.5	−	6216.62i	0.466212	−	0.269168i	−0.248441	−	0.968647i	$-0.579918\pi$
$811$	10767.5	−	6216.62i	0.466212	−	0.269168i	0.714653	+	0.699479i	$0.246585\pi$
$812$	−30036.6			−1.29812
$813$	19354.1	+	15690.4i	0.834906	+	0.676858i
$814$	32940.4	+	57054.5i	1.41838	+	2.45671i
$815$	−8989.91	+	5190.33i	−0.386384	+	0.223079i
$816$	4447.38	−	5485.86i	0.190796	−	0.235347i
$817$	1051.85	+	11030.2i	0.0450422	+	0.472336i
$818$		−	44054.9i		−	1.88306i
$819$	13352.4	−	2822.71i	0.569682	−	0.120432i
$820$	−2611.01	−	1507.47i	−0.111196	−	0.0641988i
$821$	34277.0	+	19789.8i	1.45710	+	0.841255i	0.998867	−	0.0475790i	$-0.0151506\pi$
$821$	34277.0	+	19789.8i	1.45710	+	0.841255i	0.458229	+	0.888834i	$0.348484\pi$
$822$	6946.75	−	8568.83i	0.294763	−	0.363591i
$823$	−33744.0			−1.42921			−0.714606	−	0.699527i	$-0.753394\pi$
$823$	−33744.0			−1.42921			−0.714606	+	0.699527i	$0.753394\pi$
$824$	8938.62	+	5160.71i	0.377902	+	0.218182i
$825$	−18774.6	−	2984.24i	−0.792299	−	0.125937i
$826$	1262.82	−	2187.26i	0.0531950	−	0.0921364i
$827$	15620.9	+	27056.1i	0.656821	+	1.13765i	0.981434	+	0.191801i	$0.0614327\pi$
$827$	15620.9	+	27056.1i	0.656821	+	1.13765i	−0.324613	+	0.945847i	$0.605234\pi$
$828$	−7704.84	+	23624.2i	−0.323384	+	0.991541i
$829$		−	20332.0i		−	0.851820i	−0.904765	−	0.425910i	$-0.859954\pi$
$829$		−	20332.0i		−	0.851820i	0.904765	−	0.425910i	$-0.140046\pi$
$830$	11063.8	−	19163.0i	0.462686	−	0.801396i
$831$	21635.0	−	8291.17i	0.903140	−	0.346110i
$832$		−	17398.9i		−	0.725000i
$833$	893.731	−	515.996i	0.0371740	−	0.0214624i
$834$	3939.39	−	24783.6i	0.163561	−	1.02900i
$835$	−16515.3	+	9535.12i	−0.684474	+	0.395181i
$836$	−17091.2	−	24007.7i	−0.707071	−	0.993209i
$837$	−16331.5	+	10567.4i	−0.674433	+	0.436394i
$838$	39389.8	+	22741.7i	1.62374	+	0.937469i
$839$	25114.4			1.03343			0.516714	−	0.856158i	$-0.327155\pi$
$839$	25114.4			1.03343			0.516714	+	0.856158i	$0.327155\pi$
$840$	−1984.11	+	2447.41i	−0.0814980	+	0.100528i
$841$	−1192.37	−	2065.25i	−0.0488898	−	0.0846796i
$842$		−	10515.6i		−	0.430392i
$843$	29310.9	+	23762.3i	1.19753	+	0.970839i
$844$	43834.0	−	25307.6i	1.78771	−	1.03213i
$845$	7048.33	−	4069.35i	0.286947	−	0.165669i
$846$	25630.4	+	28528.8i	1.04160	+	1.15939i
$847$	2012.17			0.0816280
$848$	7340.11	+	12713.4i	0.297241	+	0.514837i
$849$	23284.4	−	8923.26i	0.941245	−	0.360713i
$850$	−9322.60	+	5382.41i	−0.376191	+	0.217194i
$851$	40852.6			1.64560
$852$	13902.0	+	11270.4i	0.559009	+	0.453188i
$853$	−31326.3			−1.25744			−0.628718	−	0.777633i	$-0.716420\pi$
$853$	−31326.3			−1.25744			−0.628718	+	0.777633i	$0.716420\pi$
$854$	−40606.1			−1.62706
$855$	−3559.61	−	11369.9i	−0.142382	−	0.454787i
$856$	−1137.59			−0.0454228
$857$	−24564.7			−0.979131			−0.489565	−	0.871967i	$-0.662845\pi$
$857$	−24564.7			−0.979131			−0.489565	+	0.871967i	$0.662845\pi$
$858$	19829.0	−	7599.06i	0.788986	−	0.302363i
$859$	4073.56			0.161802			0.0809010	−	0.996722i	$-0.474220\pi$
$859$	4073.56			0.161802			0.0809010	+	0.996722i	$0.474220\pi$
$860$	5800.85	−	3349.12i	0.230008	−	0.132795i
$861$	−4748.41	−	3849.53i	−0.187950	−	0.152371i
$862$	22466.1	+	38912.5i	0.887703	+	1.53755i
$863$	1936.20			0.0763718			0.0381859	−	0.999271i	$-0.487842\pi$
$863$	1936.20			0.0763718			0.0381859	+	0.999271i	$0.487842\pi$
$864$	−16537.6	+	32324.3i	−0.651182	+	1.27279i
$865$	6177.58	−	3566.63i	0.242825	−	0.140195i
$866$	16513.1	−	9533.85i	0.647966	−	0.374103i
$867$	−20375.5	+	7808.50i	−0.798140	+	0.305871i
$868$			25451.8i			0.995267i
$869$	22225.1	+	38495.0i	0.867588	+	1.50271i
$870$	−18660.3	−	2966.07i	−0.727176	−	0.115585i
$871$	−9259.12			−0.360199
$872$	−5333.54	−	3079.32i	−0.207129	−	0.119586i
$873$	10348.5	−	31730.0i	0.401195	−	1.23012i
$874$	−33679.5	+	3211.70i	−1.30346	+	0.124299i
$875$	−19976.2	+	11533.3i	−0.771793	+	0.445595i
$876$	−15723.6	−	12747.1i	−0.606452	−	0.491650i
$877$	17373.9	−	10030.9i	0.668958	−	0.386223i	−0.126723	−	0.991938i	$-0.540446\pi$
$877$	17373.9	−	10030.9i	0.668958	−	0.386223i	0.795682	+	0.605715i	$0.207113\pi$
$878$		−	3336.94i		−	0.128265i
$879$	−15649.7	−	12687.2i	−0.600514	−	0.486836i
$880$	5132.44	−	8889.65i	0.196607	−	0.340534i
$881$			11172.1i			0.427240i	0.976917	+	0.213620i	$0.0685254\pi$
$881$			11172.1i			0.427240i	−0.976917	+	0.213620i	$0.931475\pi$
$882$	−3236.21	+	2907.42i	−0.123547	+	0.110995i
$883$	16303.1	+	28237.8i	0.621340	+	1.07619i	0.989237	+	0.146325i	$0.0467446\pi$
$883$	16303.1	+	28237.8i	0.621340	+	1.07619i	−0.367897	+	0.929867i	$0.619922\pi$
$884$	3247.53	−	5624.89i	0.123559	−	0.214011i
$885$	540.422	−	666.611i	0.0205266	−	0.0253197i
$886$	22782.4	+	13153.4i	0.863871	+	0.498756i
$887$	4010.28			0.151806			0.0759031	−	0.997115i	$-0.475816\pi$
$887$	4010.28			0.151806			0.0759031	+	0.997115i	$0.475816\pi$
$888$	−12469.3	−	1982.01i	−0.471219	−	0.0749008i
$889$	−22274.6	−	12860.2i	−0.840344	−	0.485173i
$890$	−18730.1	−	10813.8i	−0.705431	−	0.407281i
$891$	−27448.2	−	2946.30i	−1.03204	−	0.110780i
$892$			27761.3i			1.04206i
$893$	−11719.6	+	25653.8i	−0.439174	+	0.961335i
$894$	17316.2	+	45184.7i	0.647806	+	1.69038i
$895$	12378.0	−	7146.44i	0.462292	−	0.266904i
$896$	7172.32	+	12422.8i	0.267422	+	0.463189i
$897$	2067.10	−	13004.7i	0.0769438	−	0.484072i
$898$	21299.3			0.791501
$899$	−19647.6	+	11343.5i	−0.728902	+	0.420832i
$900$	18233.7	−	16381.2i	0.675322	−	0.606712i
$901$			7708.37i			0.285020i
$902$	−8237.11	−	4755.70i	−0.304064	−	0.175551i
$903$	12681.4	−	4859.89i	0.467343	−	0.179100i
$904$	2726.19	−	4721.90i	0.100301	−	0.173726i
$905$	−1327.29	+	2298.93i	−0.0487521	+	0.0844410i
$906$	14769.0	+	38538.3i	0.541577	+	1.41319i
$907$		−	49584.1i		−	1.81523i	−0.419803	−	0.907615i	$-0.637901\pi$
$907$		−	49584.1i		−	1.81523i	0.419803	−	0.907615i	$-0.362099\pi$
$908$	14311.0	+	24787.4i	0.523048	+	0.905945i
$909$	−10503.4	−	11691.2i	−0.383253	−	0.426593i
$910$	5616.41	−	9727.90i	0.204596	−	0.354370i
$911$	−13641.3	−	23627.4i	−0.496109	−	0.859286i	0.503881	−	0.863773i	$-0.331905\pi$
$911$	−13641.3	−	23627.4i	−0.496109	−	0.859286i	−0.999990	+	0.00448728i	$0.998572\pi$
$912$	−21851.1	−	1368.78i	−0.793381	−	0.0496983i
$913$	18852.9	−	32654.2i	0.683396	−	1.18368i
$914$	−21322.1	−	36931.0i	−0.771633	−	1.33651i
$915$	−13626.0	−	2165.86i	−0.492307	−	0.0782527i
$916$	−5060.92	+	8765.77i	−0.182552	+	0.316189i
$917$	−30589.6	−	17660.9i	−1.10159	−	0.636003i
$918$	−13124.4	+	8492.17i	−0.471862	+	0.305320i
$919$	−732.911			−0.0263074			−0.0131537	−	0.999913i	$-0.504187\pi$
$919$	−732.911			−0.0263074			−0.0131537	+	0.999913i	$0.504187\pi$
$920$	1519.96	+	2632.65i	0.0544692	+	0.0943434i
$921$	−21650.6	+	26706.1i	−0.774605	+	0.955478i
$922$			59092.1i			2.11073i
$923$	−8213.18	−	4741.88i	−0.292893	−	0.169102i
$924$	−22746.8	+	28058.2i	−0.809865	+	0.998970i
$925$	−34899.0	−	20149.0i	−1.24051	−	0.716209i
$926$	14623.7	−	25328.9i	0.518967	−	0.898878i
$927$	31970.8	+	35586.2i	1.13275	+	1.26084i
$928$	−21173.6	+	36673.7i	−0.748984	+	1.29728i
$929$			27728.9i			0.979284i	0.871924	+	0.489642i	$0.162872\pi$
$929$			27728.9i			0.979284i	−0.871924	+	0.489642i	$0.837128\pi$
$930$	−2513.34	+	15812.0i	−0.0886188	+	0.557523i
$931$	−2910.08	−	1329.43i	−0.102443	−	0.0467996i
$932$	−35411.1	−	20444.6i	−1.24456	−	0.718547i
$933$	−531.248	+	655.295i	−0.0186412	+	0.0229940i
$934$			42041.6i			1.47285i
$935$	4667.82	−	2694.97i	0.163266	−	0.0942620i
$936$	−1261.87	+	3869.08i	−0.0440658	+	0.135112i
$937$	−19288.2	−	33408.1i	−0.672483	−	1.16478i	−0.977198	−	0.212331i	$-0.931894\pi$
$937$	−19288.2	−	33408.1i	−0.672483	−	1.16478i	0.304714	−	0.952444i	$-0.401439\pi$
$938$	25251.6	−	14579.0i	0.878990	−	0.507485i
$939$	−31521.1	−	25554.2i	−1.09548	−	0.888103i
$940$	17049.9			0.591603
$941$	35754.0			1.23862			0.619312	−	0.785145i	$-0.287411\pi$
$941$	35754.0			1.23862			0.619312	+	0.785145i	$0.287411\pi$
$942$	34236.3	−	13120.4i	1.18416	−	0.453805i
$943$	−5107.82	+	2949.00i	−0.176388	+	0.101837i
$944$	−788.494	−	1365.71i	−0.0271857	−	0.0470870i
$945$	−12260.1	+	7932.90i	−0.422031	+	0.273077i
$946$	18300.3	−	10565.7i	0.628958	−	0.363129i
$947$		−	38967.3i		−	1.33714i	−0.743651	−	0.668568i	$-0.766908\pi$
$947$		−	38967.3i		−	1.33714i	0.743651	−	0.668568i	$-0.233092\pi$
$948$	−56602.6	−	8997.05i	−1.93921	−	0.308239i
$949$	9289.36	+	5363.22i	0.317751	+	0.183453i
$950$	30355.4	+	13867.5i	1.03669	+	0.473600i
$951$	14433.8	+	11701.5i	0.492163	+	0.398997i
$952$			3040.12i			0.103499i
$953$	−13266.8	+	22978.8i	−0.450948	+	0.781065i	−0.998445	−	0.0557423i	$-0.982247\pi$
$953$	−13266.8	+	22978.8i	−0.450948	+	0.781065i	0.547497	+	0.836808i	$0.315581\pi$
$954$	−6720.96	−	31792.4i	−0.228091	−	1.07895i
$955$	−5892.70	+	10206.5i	−0.199668	+	0.345836i
$956$	−31239.7	−	18036.2i	−1.05687	−	0.610182i
$957$	−31797.5	−	5054.25i	−1.07405	−	0.170722i
$958$	70921.8	+	40946.7i	2.39184	+	1.38093i
$959$		−	9943.06i		−	0.334805i
$960$	6662.05	+	17384.0i	0.223976	+	0.584443i
$961$	−5283.44	−	9151.19i	−0.177350	−	0.307180i
$962$	45014.4			1.50865
$963$	−5012.69	−	1634.85i	−0.167738	−	0.0547065i
$964$	24871.2	+	14359.4i	0.830962	+	0.479756i
$965$	5250.94	−	9094.90i	0.175165	−	0.303394i
$966$	14839.1	+	38721.2i	0.494245	+	1.28968i
$967$	−12525.4	−	21694.6i	−0.416534	−	0.721458i	0.579054	−	0.815289i	$-0.303422\pi$
$967$	−12525.4	−	21694.6i	−0.416534	−	0.721458i	−0.995588	+	0.0938312i	$0.970089\pi$
$968$	−300.013	+	519.638i	−0.00996155	+	0.0172539i
$969$	−9577.17	−	6359.29i	−0.317506	−	0.210825i
$970$	−13734.9	−	23789.6i	−0.454640	−	0.787460i
$971$	16599.9	−	28751.9i	0.548627	−	0.950250i	−0.449742	−	0.893159i	$-0.648484\pi$
$971$	16599.9	−	28751.9i	0.548627	−	0.950250i	0.998369	−	0.0570913i	$-0.0181826\pi$
$972$	25238.6	−	25099.5i	0.832849	−	0.828258i
$973$	−11309.9	−	19589.4i	−0.372641	−	0.645434i
$974$		−	16550.7i		−	0.544476i
$975$	−8179.90	+	10089.9i	−0.268684	+	0.331422i
$976$	−12677.1	+	21957.3i	−0.415762	+	0.720120i
$977$	7483.67	−	12962.1i	0.245060	−	0.424457i	−0.717088	−	0.696982i	$-0.754526\pi$
$977$	7483.67	−	12962.1i	0.245060	−	0.424457i	0.962149	+	0.272526i	$0.0878589\pi$
$978$	6628.54	−	41701.8i	0.216725	−	1.36347i
$979$	−31916.4	−	18427.0i	−1.04193	−	0.601561i
$980$			1934.08i			0.0630428i
$981$	−19076.5	−	21233.8i	−0.620862	−	0.691072i
$982$	23407.3	−	13514.2i	0.760649	−	0.439161i
$983$	−32409.0			−1.05156			−0.525782	−	0.850620i	$-0.676227\pi$
$983$	−32409.0			−1.05156			−0.525782	+	0.850620i	$0.676227\pi$
$984$	1702.12	−	652.303i	0.0551438	−	0.0211328i
$985$	−2478.36	−	4292.64i	−0.0801695	−	0.138858i
$986$	−15789.2	+	9115.91i	−0.509971	+	0.294432i
$987$	34140.2	+	5426.63i	1.10101	+	0.175007i
$988$	−20045.0	+	1911.50i	−0.645461	+	0.0615515i
$989$		−	13103.5i		−	0.421302i
$990$	−16902.2	+	15185.0i	−0.542614	+	0.487487i
$991$	47088.5	+	27186.5i	1.50940	+	0.871452i	0.999940	+	0.0109573i	$0.00348788\pi$
$991$	47088.5	+	27186.5i	1.50940	+	0.871452i	0.509459	+	0.860495i	$0.329845\pi$
$992$	31075.9	+	17941.7i	0.994618	+	0.574243i
$993$	−19037.5	−	49676.5i	−0.608396	−	1.58755i
$994$	29865.4			0.952991
$995$	−19343.9	−	11168.2i	−0.616325	−	0.355835i
$996$	17397.7	+	45397.7i	0.553483	+	1.44426i
$997$	8563.09	−	14831.7i	0.272012	−	0.471138i	−0.697365	−	0.716716i	$-0.745644\pi$
$997$	8563.09	−	14831.7i	0.272012	−	0.471138i	0.969377	+	0.245578i	$0.0789777\pi$
$998$	8512.36	+	14743.8i	0.269994	+	0.467643i
$999$	−52096.7	−	26653.5i	−1.64992	−	0.844123i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.4.t.a.122.10	yes	116
9.2	odd	6		171.4.k.a.65.10	yes	116
19.12	odd	6		171.4.k.a.50.10	✓	116
171.164	even	6	inner	171.4.t.a.164.10	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.4.k.a.50.10	✓	116	19.12	odd	6
171.4.k.a.65.10	yes	116	9.2	odd	6
171.4.t.a.122.10	yes	116	1.1	even	1	trivial
171.4.t.a.164.10	yes	116	171.164	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	171.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-4.17093 q^{2} +(0.815694 - 5.13173i) q^{3} +9.39667 q^{4} +(4.61421 - 2.66402i) q^{5} +(-3.40220 + 21.4041i) q^{6} +(9.76769 + 16.9181i) q^{7} -5.82542 q^{8} +(-25.6693 - 8.37184i) q^{9} +O(q^{10})\)	\(q-4.17093 q^{2} +(0.815694 - 5.13173i) q^{3} +9.39667 q^{4} +(4.61421 - 2.66402i) q^{5} +(-3.40220 + 21.4041i) q^{6} +(9.76769 + 16.9181i) q^{7} -5.82542 q^{8} +(-25.6693 - 8.37184i) q^{9} +(-19.2456 + 11.1114i) q^{10} +(-32.7948 + 18.9341i) q^{11} +(7.66481 - 48.2212i) q^{12} +25.8742i q^{13} +(-40.7404 - 70.5644i) q^{14} +(-9.90723 - 25.8519i) q^{15} -50.8759 q^{16} +(-23.1352 - 13.3571i) q^{17} +(107.065 + 34.9184i) q^{18} +(7.86200 + 82.4451i) q^{19} +(43.3582 - 25.0329i) q^{20} +(94.7867 - 36.3251i) q^{21} +(136.785 - 78.9729i) q^{22} -97.9419i q^{23} +(-4.75176 + 29.8945i) q^{24} +(-48.3060 + 83.6685i) q^{25} -107.920i q^{26} +(-63.9003 + 124.899i) q^{27} +(91.7837 + 158.974i) q^{28} +(-81.8134 + 141.705i) q^{29} +(41.3224 + 107.827i) q^{30} +(120.075 + 69.3255i) q^{31} +258.803 q^{32} +(70.4141 + 183.739i) q^{33} +(96.4952 + 55.7116i) q^{34} +(90.1404 + 52.0426i) q^{35} +(-241.206 - 78.6674i) q^{36} +417.111i q^{37} +(-32.7919 - 343.873i) q^{38} +(132.779 + 21.1054i) q^{39} +(-26.8797 + 15.5190i) q^{40} +(-30.1097 - 52.1515i) q^{41} +(-395.349 + 151.510i) q^{42} +133.789 q^{43} +(-308.162 + 177.918i) q^{44} +(-140.746 + 29.7540i) q^{45} +408.509i q^{46} +(294.925 + 170.275i) q^{47} +(-41.4992 + 261.082i) q^{48} +(-19.3154 + 33.4553i) q^{49} +(201.481 - 348.976i) q^{50} +(-87.4162 + 107.828i) q^{51} +243.131i q^{52} +(-144.275 - 249.891i) q^{53} +(266.524 - 520.945i) q^{54} +(-100.882 + 174.732i) q^{55} +(-56.9009 - 98.5553i) q^{56} +(429.499 + 26.9043i) q^{57} +(341.238 - 591.042i) q^{58} +(15.4984 + 26.8439i) q^{59} +(-93.0949 - 242.922i) q^{60} +(249.176 - 431.586i) q^{61} +(-500.826 - 289.152i) q^{62} +(-109.094 - 516.050i) q^{63} -672.444 q^{64} +(68.9293 + 119.389i) q^{65} +(-293.693 - 766.361i) q^{66} +357.851i q^{67} +(-217.394 - 125.512i) q^{68} +(-502.611 - 79.8906i) q^{69} +(-375.969 - 217.066i) q^{70} +(-183.267 + 317.427i) q^{71} +(149.534 + 48.7695i) q^{72} +(207.280 - 359.020i) q^{73} -1739.74i q^{74} +(389.961 + 316.141i) q^{75} +(73.8767 + 774.709i) q^{76} +(-640.659 - 369.885i) q^{77} +(-553.814 - 88.0293i) q^{78} -1173.81i q^{79} +(-234.752 + 135.534i) q^{80} +(588.825 + 429.798i) q^{81} +(125.586 + 217.521i) q^{82} +(-862.312 + 497.856i) q^{83} +(890.680 - 341.335i) q^{84} -142.334 q^{85} -558.024 q^{86} +(660.457 + 535.432i) q^{87} +(191.044 - 110.299i) q^{88} +(486.608 + 842.829i) q^{89} +(587.043 - 124.102i) q^{90} +(-437.743 + 252.731i) q^{91} -920.328i q^{92} +(453.705 - 559.646i) q^{93} +(-1230.11 - 710.206i) q^{94} +(255.912 + 359.474i) q^{95} +(211.104 - 1328.11i) q^{96} +1236.11i q^{97} +(80.5633 - 139.540i) q^{98} +(1000.33 - 211.472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 6 q^{2} - 3 q^{3} + 446 q^{4} - 3 q^{5} - 53 q^{6} - 8 q^{7} - 48 q^{8} - 31 q^{9}+O(q^{10}) \) 116 * q - 6 * q^2 - 3 * q^3 + 446 * q^4 - 3 * q^5 - 53 * q^6 - 8 * q^7 - 48 * q^8 - 31 * q^9	\( 116 q - 6 q^{2} - 3 q^{3} + 446 q^{4} - 3 q^{5} - 53 q^{6} - 8 q^{7} - 48 q^{8} - 31 q^{9} - 6 q^{10} - 81 q^{11} - 105 q^{12} - 3 q^{14} - 261 q^{15} + 1646 q^{16} + 270 q^{17} - 24 q^{18} + 11 q^{19} - 261 q^{20} + 78 q^{21} - 105 q^{22} - 893 q^{24} + 1251 q^{25} - 198 q^{27} - 50 q^{28} + 177 q^{29} - 419 q^{30} + 180 q^{31} - 390 q^{32} + 150 q^{33} + 591 q^{34} - 375 q^{35} - 999 q^{36} + 1161 q^{38} + 751 q^{39} - 426 q^{40} - 108 q^{41} + 1540 q^{42} - 518 q^{43} + 15 q^{44} + 905 q^{45} - 1341 q^{47} - 3135 q^{48} - 2376 q^{49} + 753 q^{50} + 1008 q^{51} - 528 q^{53} - 76 q^{54} - 127 q^{55} - 24 q^{56} - 1459 q^{57} - 18 q^{58} - 270 q^{59} - 1419 q^{60} - 419 q^{61} - 492 q^{62} - 1213 q^{63} + 6848 q^{64} - 2466 q^{65} + 1487 q^{66} + 1842 q^{68} - 1281 q^{69} - 1032 q^{70} - 1386 q^{71} + 1251 q^{72} + 787 q^{73} + 1251 q^{75} + 881 q^{76} + 3234 q^{77} - 540 q^{78} + 642 q^{80} + 2281 q^{81} - 540 q^{82} + 2160 q^{83} - 5520 q^{84} - 502 q^{85} - 8322 q^{86} - 703 q^{87} - 1056 q^{88} + 990 q^{89} + 213 q^{90} + 3003 q^{91} + 2345 q^{93} - 48 q^{94} - 5097 q^{95} - 4413 q^{96} + 2964 q^{98} - 3248 q^{99}+O(q^{100}) \) 116 * q - 6 * q^2 - 3 * q^3 + 446 * q^4 - 3 * q^5 - 53 * q^6 - 8 * q^7 - 48 * q^8 - 31 * q^9 - 6 * q^10 - 81 * q^11 - 105 * q^12 - 3 * q^14 - 261 * q^15 + 1646 * q^16 + 270 * q^17 - 24 * q^18 + 11 * q^19 - 261 * q^20 + 78 * q^21 - 105 * q^22 - 893 * q^24 + 1251 * q^25 - 198 * q^27 - 50 * q^28 + 177 * q^29 - 419 * q^30 + 180 * q^31 - 390 * q^32 + 150 * q^33 + 591 * q^34 - 375 * q^35 - 999 * q^36 + 1161 * q^38 + 751 * q^39 - 426 * q^40 - 108 * q^41 + 1540 * q^42 - 518 * q^43 + 15 * q^44 + 905 * q^45 - 1341 * q^47 - 3135 * q^48 - 2376 * q^49 + 753 * q^50 + 1008 * q^51 - 528 * q^53 - 76 * q^54 - 127 * q^55 - 24 * q^56 - 1459 * q^57 - 18 * q^58 - 270 * q^59 - 1419 * q^60 - 419 * q^61 - 492 * q^62 - 1213 * q^63 + 6848 * q^64 - 2466 * q^65 + 1487 * q^66 + 1842 * q^68 - 1281 * q^69 - 1032 * q^70 - 1386 * q^71 + 1251 * q^72 + 787 * q^73 + 1251 * q^75 + 881 * q^76 + 3234 * q^77 - 540 * q^78 + 642 * q^80 + 2281 * q^81 - 540 * q^82 + 2160 * q^83 - 5520 * q^84 - 502 * q^85 - 8322 * q^86 - 703 * q^87 - 1056 * q^88 + 990 * q^89 + 213 * q^90 + 3003 * q^91 + 2345 * q^93 - 48 * q^94 - 5097 * q^95 - 4413 * q^96 + 2964 * q^98 - 3248 * q^99

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