LMFDB - Embedded newform 161.4.e.b.93.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [161,4,Mod(93,161)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("161.93"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(161, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [44,0,18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.9
Character	$\chi$	$=$	161.93
Dual form			161.4.e.b.116.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.904891 + 1.56732i) q^{2} +(4.25067 + 7.36238i) q^{3} +(2.36235 + 4.09170i) q^{4} +(10.8661 - 18.8206i) q^{5} -15.3856 q^{6} +(-11.8667 + 14.2190i) q^{7} -23.0289 q^{8} +(-22.6364 + 39.2075i) q^{9} +(19.6653 + 34.0613i) q^{10} +(14.7263 + 25.5066i) q^{11} +(-20.0831 + 34.7850i) q^{12} -17.0560 q^{13} +(-11.5477 - 31.4656i) q^{14} +184.753 q^{15} +(1.93988 - 3.35997i) q^{16} +(28.8033 + 49.8887i) q^{17} +(-40.9670 - 70.9570i) q^{18} +(-41.5109 + 71.8990i) q^{19} +102.678 q^{20} +(-155.128 - 26.9268i) q^{21} -53.3026 q^{22} +(-11.5000 + 19.9186i) q^{23} +(-97.8884 - 169.548i) q^{24} +(-173.645 - 300.761i) q^{25} +(15.4338 - 26.7321i) q^{26} -155.344 q^{27} +(-86.2134 - 14.9648i) q^{28} +257.310 q^{29} +(-167.181 + 289.567i) q^{30} +(73.4231 + 127.173i) q^{31} +(-88.6049 - 153.468i) q^{32} +(-125.193 + 216.841i) q^{33} -104.255 q^{34} +(138.666 + 377.845i) q^{35} -213.900 q^{36} +(141.917 - 245.808i) q^{37} +(-75.1256 - 130.121i) q^{38} +(-72.4994 - 125.573i) q^{39} +(-250.235 + 433.419i) q^{40} -88.2572 q^{41} +(182.576 - 218.768i) q^{42} +182.096 q^{43} +(-69.5770 + 120.511i) q^{44} +(491.940 + 852.065i) q^{45} +(-20.8125 - 36.0483i) q^{46} +(241.120 - 417.632i) q^{47} +32.9832 q^{48} +(-61.3620 - 337.467i) q^{49} +628.517 q^{50} +(-244.867 + 424.121i) q^{51} +(-40.2921 - 69.7880i) q^{52} +(-54.5878 - 94.5488i) q^{53} +(140.570 - 243.474i) q^{54} +640.068 q^{55} +(273.278 - 327.449i) q^{56} -705.797 q^{57} +(-232.838 + 403.287i) q^{58} +(-202.067 - 349.989i) q^{59} +(436.451 + 755.955i) q^{60} +(85.7124 - 148.458i) q^{61} -265.760 q^{62} +(-288.872 - 787.133i) q^{63} +351.749 q^{64} +(-185.332 + 321.005i) q^{65} +(-226.572 - 392.434i) q^{66} +(37.0345 + 64.1457i) q^{67} +(-136.087 + 235.709i) q^{68} -195.531 q^{69} +(-717.681 - 124.574i) q^{70} +396.453 q^{71} +(521.293 - 902.905i) q^{72} +(180.327 + 312.336i) q^{73} +(256.839 + 444.859i) q^{74} +(1476.21 - 2556.87i) q^{75} -392.252 q^{76} +(-537.432 - 93.2867i) q^{77} +262.416 q^{78} +(144.523 - 250.321i) q^{79} +(-42.1579 - 73.0197i) q^{80} +(-49.1335 - 85.1017i) q^{81} +(79.8631 - 138.327i) q^{82} +1009.86 q^{83} +(-256.288 - 698.346i) q^{84} +1251.92 q^{85} +(-164.777 + 285.403i) q^{86} +(1093.74 + 1894.42i) q^{87} +(-339.130 - 587.390i) q^{88} +(-743.744 + 1288.20i) q^{89} -1780.61 q^{90} +(202.398 - 242.520i) q^{91} -108.668 q^{92} +(-624.196 + 1081.14i) q^{93} +(436.375 + 755.823i) q^{94} +(902.124 + 1562.52i) q^{95} +(753.261 - 1304.69i) q^{96} +670.236 q^{97} +(584.443 + 209.197i) q^{98} -1333.40 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 18 q^{3} - 88 q^{4} + 20 q^{5} - 72 q^{6} - 44 q^{7} + 42 q^{8} - 126 q^{9} + 200 q^{10} - 20 q^{11} + 161 q^{12} - 392 q^{13} - 200 q^{14} + 40 q^{15} - 324 q^{16} + 242 q^{17} - 85 q^{18} + 128 q^{19}+ \cdots + 7140 q^{99}+O(q^{100}) $ 44 * q + 18 * q^3 - 88 * q^4 + 20 * q^5 - 72 * q^6 - 44 * q^7 + 42 * q^8 - 126 * q^9 + 200 * q^10 - 20 * q^11 + 161 * q^12 - 392 * q^13 - 200 * q^14 + 40 * q^15 - 324 * q^16 + 242 * q^17 - 85 * q^18 + 128 * q^19 - 92 * q^20 + 82 * q^21 + 28 * q^22 - 506 * q^23 + 66 * q^24 - 668 * q^25 + 340 * q^26 - 756 * q^27 + 760 * q^28 - 380 * q^29 - 493 * q^30 + 508 * q^31 + 487 * q^32 + 1240 * q^33 - 832 * q^34 + 1436 * q^35 - 940 * q^36 + 102 * q^37 + 423 * q^38 + 520 * q^39 + 2048 * q^40 - 1840 * q^41 + 441 * q^42 - 1456 * q^43 - 1132 * q^44 + 570 * q^45 + 1384 * q^47 - 2646 * q^48 + 638 * q^49 - 1950 * q^50 - 1688 * q^51 + 1892 * q^52 + 480 * q^53 + 1695 * q^54 - 2508 * q^55 + 2049 * q^56 - 604 * q^57 - 791 * q^58 + 650 * q^59 + 2490 * q^60 + 960 * q^61 - 5108 * q^62 + 1868 * q^63 + 7582 * q^64 - 800 * q^65 - 1221 * q^66 + 2136 * q^67 + 2290 * q^68 - 828 * q^69 - 1717 * q^70 - 272 * q^71 - 4114 * q^72 + 2562 * q^73 + 1928 * q^74 + 1820 * q^75 - 9290 * q^76 + 100 * q^77 + 5210 * q^78 - 790 * q^79 - 2248 * q^80 + 506 * q^81 + 3838 * q^82 - 4052 * q^83 - 2133 * q^84 + 2784 * q^85 - 3419 * q^86 + 3340 * q^87 + 5101 * q^88 + 2618 * q^89 - 13560 * q^90 - 2914 * q^91 + 4048 * q^92 - 206 * q^93 + 3516 * q^94 + 4410 * q^95 + 3818 * q^96 - 10316 * q^97 + 1437 * q^98 + 7140 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

$n$	$24$	$120$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.904891	+	1.56732i	−0.319927	+	0.554130i	−0.980473	−	0.196656i	$-0.936992\pi$
$2$	−0.904891	+	1.56732i	−0.319927	+	0.554130i	0.660545	+	0.750786i	$0.270325\pi$
$3$	4.25067	+	7.36238i	0.818042	+	1.41689i	0.907123	+	0.420867i	$0.138274\pi$
$3$	4.25067	+	7.36238i	0.818042	+	1.41689i	−0.0890800	+	0.996024i	$0.528393\pi$
$4$	2.36235	+	4.09170i	0.295293	+	0.511463i
$5$	10.8661	−	18.8206i	0.971894	−	1.68337i	0.282069	−	0.959394i	$-0.408979\pi$
$5$	10.8661	−	18.8206i	0.971894	−	1.68337i	0.689825	−	0.723976i	$-0.257687\pi$
$6$	−15.3856			−1.04686
$7$	−11.8667	+	14.2190i	−0.640743	+	0.767756i
$7$	−11.8667	+	14.2190i	−0.640743	+	0.767756i
$8$	−23.0289			−1.01774
$9$	−22.6364	+	39.2075i	−0.838387	+	1.45213i
$10$	19.6653	+	34.0613i	0.621871	+	1.07711i
$11$	14.7263	+	25.5066i	0.403648	+	0.699140i	0.994163	−	0.107887i	$-0.0344086\pi$
$11$	14.7263	+	25.5066i	0.403648	+	0.699140i	−0.590515	+	0.807027i	$0.701075\pi$
$12$	−20.0831	+	34.7850i	−0.483125	+	0.836797i
$13$	−17.0560			−0.363883			−0.181941	−	0.983309i	$-0.558238\pi$
$13$	−17.0560			−0.363883			−0.181941	+	0.983309i	$0.558238\pi$
$14$	−11.5477	−	31.4656i	−0.220446	−	0.600681i
$15$	184.753			3.18020
$16$	1.93988	−	3.35997i	0.0303107	−	0.0524996i
$17$	28.8033	+	49.8887i	0.410931	+	0.711753i	0.994992	−	0.0999569i	$-0.0318705\pi$
$17$	28.8033	+	49.8887i	0.410931	+	0.711753i	−0.584061	+	0.811710i	$0.698537\pi$
$18$	−40.9670	−	70.9570i	−0.536446	−	0.929151i
$19$	−41.5109	+	71.8990i	−0.501224	+	0.868145i	0.498775	+	0.866731i	$0.333783\pi$
$19$	−41.5109	+	71.8990i	−0.501224	+	0.868145i	−0.999999	+	0.00141372i	$0.999550\pi$
$20$	102.678			1.14797
$21$	−155.128	−	26.9268i	−1.61198	−	0.279806i
$22$	−53.3026			−0.516552
$23$	−11.5000	+	19.9186i	−0.104257	+	0.180579i
$23$	−11.5000	+	19.9186i	−0.104257	+	0.180579i
$24$	−97.8884	−	169.548i	−0.832558	−	1.44203i
$25$	−173.645	−	300.761i	−1.38916	−	2.40609i
$26$	15.4338	−	26.7321i	0.116416	−	0.201638i
$27$	−155.344			−1.10726
$28$	−86.2134	−	14.9648i	−0.581885	−	0.101003i
$29$	257.310			1.64763			0.823817	−	0.566857i	$-0.191841\pi$
$29$	257.310			1.64763			0.823817	+	0.566857i	$0.191841\pi$
$30$	−167.181	+	289.567i	−1.01743	+	1.76225i
$31$	73.4231	+	127.173i	0.425393	+	0.736802i	0.996457	−	0.0841032i	$-0.0268025\pi$
$31$	73.4231	+	127.173i	0.425393	+	0.736802i	−0.571064	+	0.820906i	$0.693469\pi$
$32$	−88.6049	−	153.468i	−0.489477	−	0.847800i
$33$	−125.193	+	216.841i	−0.660403	+	1.14385i
$34$	−104.255			−0.525872
$35$	138.666	+	377.845i	0.669683	+	1.82478i
$36$	−213.900			−0.990280
$37$	141.917	−	245.808i	0.630569	−	1.09218i	−0.356866	−	0.934156i	$-0.616155\pi$
$37$	141.917	−	245.808i	0.630569	−	1.09218i	0.987435	−	0.158023i	$-0.0505119\pi$
$38$	−75.1256	−	130.121i	−0.320710	−	0.555486i
$39$	−72.4994	−	125.573i	−0.297672	−	0.515582i
$40$	−250.235	+	433.419i	−0.989139	+	1.71324i
$41$	−88.2572			−0.336182			−0.168091	−	0.985771i	$-0.553760\pi$
$41$	−88.2572			−0.336182			−0.168091	+	0.985771i	$0.553760\pi$
$42$	182.576	−	218.768i	0.670765	−	0.803730i
$43$	182.096			0.645801			0.322901	−	0.946433i	$-0.395342\pi$
$43$	182.096			0.645801			0.322901	+	0.946433i	$0.395342\pi$
$44$	−69.5770	+	120.511i	−0.238389	+	0.412902i
$45$	491.940	+	852.065i	1.62965	+	2.82263i
$46$	−20.8125	−	36.0483i	−0.0667094	−	0.115544i
$47$	241.120	−	417.632i	0.748319	−	1.29613i	−0.200309	−	0.979733i	$-0.564195\pi$
$47$	241.120	−	417.632i	0.748319	−	1.29613i	0.948628	−	0.316394i	$-0.102472\pi$
$48$	32.9832			0.0991816
$49$	−61.3620	−	337.467i	−0.178898	−	0.983868i
$50$	628.517			1.77772
$51$	−244.867	+	424.121i	−0.672317	+	1.16449i
$52$	−40.2921	−	69.7880i	−0.107452	−	0.186113i
$53$	−54.5878	−	94.5488i	−0.141476	−	0.245043i	0.786577	−	0.617492i	$-0.211851\pi$
$53$	−54.5878	−	94.5488i	−0.141476	−	0.245043i	−0.928053	+	0.372449i	$0.878518\pi$
$54$	140.570	−	243.474i	0.354242	−	0.613566i
$55$	640.068			1.56921
$56$	273.278	−	327.449i	0.652112	−	0.781379i
$57$	−705.797			−1.64009
$58$	−232.838	+	403.287i	−0.527123	+	0.913003i
$59$	−202.067	−	349.989i	−0.445878	−	0.772284i	0.552235	−	0.833689i	$-0.313775\pi$
$59$	−202.067	−	349.989i	−0.445878	−	0.772284i	−0.998113	+	0.0614049i	$0.980442\pi$
$60$	436.451	+	755.955i	0.939092	+	1.62656i
$61$	85.7124	−	148.458i	0.179907	−	0.311608i	−0.761941	−	0.647646i	$-0.775754\pi$
$61$	85.7124	−	148.458i	0.179907	−	0.311608i	0.941849	+	0.336038i	$0.109087\pi$
$62$	−265.760			−0.544379
$63$	−288.872	−	787.133i	−0.577690	−	1.57412i
$64$	351.749			0.687010
$65$	−185.332	+	321.005i	−0.353656	+	0.612549i
$66$	−226.572	−	392.434i	−0.422562	−	0.731899i
$67$	37.0345	+	64.1457i	0.0675296	+	0.116965i	0.897813	−	0.440376i	$-0.145155\pi$
$67$	37.0345	+	64.1457i	0.0675296	+	0.116965i	−0.830284	+	0.557341i	$0.811822\pi$
$68$	−136.087	+	235.709i	−0.242690	+	0.420352i
$69$	−195.531			−0.341147
$70$	−717.681	−	124.574i	−1.22542	−	0.212706i
$71$	396.453			0.662680			0.331340	−	0.943511i	$-0.392499\pi$
$71$	396.453			0.662680			0.331340	+	0.943511i	$0.392499\pi$
$72$	521.293	−	902.905i	0.853263	−	1.47789i
$73$	180.327	+	312.336i	0.289119	+	0.500769i	0.973600	−	0.228262i	$-0.0733043\pi$
$73$	180.327	+	312.336i	0.289119	+	0.500769i	−0.684481	+	0.729031i	$0.739971\pi$
$74$	256.839	+	444.859i	0.403473	+	0.698835i
$75$	1476.21	−	2556.87i	2.27278	−	3.93657i
$76$	−392.252			−0.592032
$77$	−537.432	−	93.2867i	−0.795403	−	0.138065i
$78$	262.416			0.380933
$79$	144.523	−	250.321i	0.205824	−	0.356498i	−0.744571	−	0.667544i	$-0.767346\pi$
$79$	144.523	−	250.321i	0.205824	−	0.356498i	0.950395	+	0.311045i	$0.100679\pi$
$80$	−42.1579	−	73.0197i	−0.0589175	−	0.102048i
$81$	−49.1335	−	85.1017i	−0.0673985	−	0.116738i
$82$	79.8631	−	138.327i	0.107554	−	0.186289i
$83$	1009.86			1.33550			0.667749	−	0.744386i	$-0.267258\pi$
$83$	1009.86			1.33550			0.667749	+	0.744386i	$0.267258\pi$
$84$	−256.288	−	698.346i	−0.332897	−	0.907093i
$85$	1251.92			1.59752
$86$	−164.777	+	285.403i	−0.206609	+	0.357858i
$87$	1093.74	+	1894.42i	1.34783	+	2.33452i
$88$	−339.130	−	587.390i	−0.410811	−	0.711545i
$89$	−743.744	+	1288.20i	−0.885806	+	1.53426i	−0.0410190	+	0.999158i	$0.513060\pi$
$89$	−743.744	+	1288.20i	−0.885806	+	1.53426i	−0.844787	+	0.535103i	$0.820273\pi$
$90$	−1780.61			−2.08547
$91$	202.398	−	242.520i	0.233155	−	0.279373i
$92$	−108.668			−0.123146
$93$	−624.196	+	1081.14i	−0.695979	+	1.20547i
$94$	436.375	+	755.823i	0.478815	+	0.829332i
$95$	902.124	+	1562.52i	0.974273	+	1.68749i
$96$	753.261	−	1304.69i	0.800827	−	1.38707i
$97$	670.236			0.701569			0.350784	−	0.936456i	$-0.385915\pi$
$97$	670.236			0.701569			0.350784	+	0.936456i	$0.385915\pi$
$98$	584.443	+	209.197i	0.602425	+	0.215633i
$99$	−1333.40			−1.35365
$100$	820.417	−	1421.00i	0.820417	−	1.42100i
$101$	−499.605	−	865.342i	−0.492204	−	0.852522i	0.507756	−	0.861501i	$-0.330475\pi$
$101$	−499.605	−	865.342i	−0.492204	−	0.852522i	−0.999960	+	0.00897893i	$0.997142\pi$
$102$	−443.155	−	767.567i	−0.430185	−	0.745103i
$103$	223.089	−	386.402i	0.213414	−	0.369643i	−0.739367	−	0.673303i	$-0.764875\pi$
$103$	223.089	−	386.402i	0.213414	−	0.369643i	0.952781	+	0.303659i	$0.0982084\pi$
$104$	392.781			0.370339
$105$	−2192.41	+	2627.01i	−2.03769	+	2.44162i
$106$	197.584			0.181048
$107$	383.391	−	664.052i	0.346390	−	0.599966i	−0.639215	−	0.769028i	$-0.720741\pi$
$107$	383.391	−	664.052i	0.346390	−	0.599966i	0.985605	+	0.169062i	$0.0540739\pi$
$108$	−366.977	−	635.622i	−0.326966	−	0.566322i
$109$	189.467	+	328.167i	0.166492	+	0.288373i	0.937184	−	0.348835i	$-0.113423\pi$
$109$	189.467	+	328.167i	0.166492	+	0.288373i	−0.770692	+	0.637208i	$0.780089\pi$
$110$	−579.192	+	1003.19i	−0.502034	+	0.869549i
$111$	2412.98			2.06333
$112$	24.7556	+	67.4551i	0.0208855	+	0.0569099i
$113$	−698.233			−0.581277			−0.290638	−	0.956833i	$-0.593868\pi$
$113$	−698.233			−0.581277			−0.290638	+	0.956833i	$0.593868\pi$
$114$	638.669	−	1106.21i	0.524709	−	0.908823i
$115$	249.920	+	432.875i	0.202654	+	0.351007i
$116$	607.856	+	1052.84i	0.486535	+	0.842703i
$117$	386.087	−	668.722i	0.305075	−	0.528405i
$118$	731.392			0.570594
$119$	−1051.17	−	182.461i	−0.809753	−	0.140556i
$120$	−4254.66			−3.23663
$121$	231.775	−	401.446i	0.174136	−	0.301612i
$122$	155.121	+	268.677i	0.115114	+	0.199384i
$123$	−375.153	−	649.783i	−0.275011	−	0.476333i
$124$	−346.902	+	600.851i	−0.251231	+	0.435145i
$125$	−4830.83			−3.45666
$126$	1495.08	+	259.515i	1.05708	+	0.183487i
$127$	−1001.38			−0.699671			−0.349835	−	0.936811i	$-0.613762\pi$
$127$	−1001.38			−0.699671			−0.349835	+	0.936811i	$0.613762\pi$
$128$	390.545	−	676.443i	0.269684	−	0.467107i
$129$	774.033	+	1340.66i	0.528293	+	0.915030i
$130$	−335.410	−	580.948i	−0.226288	−	0.391942i
$131$	−1286.60	+	2228.46i	−0.858098	+	1.48627i	0.0156425	+	0.999878i	$0.495021\pi$
$131$	−1286.60	+	2228.46i	−0.858098	+	1.48627i	−0.873741	+	0.486392i	$0.838313\pi$
$132$	−1183.00			−0.780050
$133$	−529.736	−	1443.45i	−0.345368	−	0.941075i
$134$	−134.049			−0.0864183
$135$	−1687.99	+	2923.68i	−1.07614	+	1.86393i
$136$	−663.308	−	1148.88i	−0.418222	−	0.724382i
$137$	264.845	+	458.726i	0.165163	+	0.286070i	0.936713	−	0.350098i	$-0.113852\pi$
$137$	264.845	+	458.726i	0.165163	+	0.286070i	−0.771550	+	0.636168i	$0.780518\pi$
$138$	176.934	−	306.459i	0.109142	−	0.189040i
$139$	−2158.93			−1.31740			−0.658698	−	0.752408i	$-0.728892\pi$
$139$	−2158.93			−1.31740			−0.658698	+	0.752408i	$0.728892\pi$
$140$	−1218.45	+	1459.98i	−0.735556	+	0.881364i
$141$	4099.69			2.44863
$142$	−358.746	+	621.367i	−0.212009	+	0.367211i
$143$	−251.171	−	435.040i	−0.146881	−	0.254405i
$144$	87.8241	+	152.116i	0.0508241	+	0.0880300i
$145$	2795.96	−	4842.75i	1.60132	−	2.77358i
$146$	−652.705			−0.369988
$147$	2223.73	−	1886.23i	1.24769	−	1.05832i
$148$	1341.03			0.744811
$149$	−1263.53	+	2188.50i	−0.694714	+	1.20328i	0.275563	+	0.961283i	$0.411136\pi$
$149$	−1263.53	+	2188.50i	−0.694714	+	1.20328i	−0.970277	+	0.241997i	$0.922198\pi$
$150$	2671.62	+	4627.38i	1.45425	+	2.51883i
$151$	1037.87	+	1797.65i	0.559343	+	0.968811i	0.997551	+	0.0699377i	$0.0222800\pi$
$151$	1037.87	+	1797.65i	0.559343	+	0.968811i	−0.438208	+	0.898874i	$0.644387\pi$
$152$	955.951	−	1655.76i	0.510117	−	0.883549i
$153$	−2608.02			−1.37808
$154$	632.527	−	757.912i	0.330977	−	0.396586i
$155$	3191.29			1.65375
$156$	342.537	−	593.292i	0.175801	−	0.304496i
$157$	−1489.59	−	2580.04i	−0.757211	−	1.31153i	−0.944268	−	0.329179i	$-0.893228\pi$
$157$	−1489.59	−	2580.04i	−0.757211	−	1.31153i	0.187057	−	0.982349i	$-0.440105\pi$
$158$	261.555	+	453.027i	0.131698	+	0.228107i
$159$	464.070	−	803.793i	0.231466	−	0.400911i
$160$	−3851.16			−1.90288
$161$	−146.756	−	399.887i	−0.0718384	−	0.195749i
$162$	177.842			0.0862504
$163$	804.510	−	1393.45i	0.386589	−	0.669593i	−0.605399	−	0.795922i	$-0.706986\pi$
$163$	804.510	−	1393.45i	0.386589	−	0.669593i	0.991988	+	0.126330i	$0.0403197\pi$
$164$	−208.494	−	361.122i	−0.0992723	−	0.171945i
$165$	2720.72	+	4712.43i	1.28368	+	2.22341i
$166$	−913.812	+	1582.77i	−0.427262	+	0.740040i
$167$	−297.589			−0.137893			−0.0689466	−	0.997620i	$-0.521964\pi$
$167$	−297.589			−0.137893			−0.0689466	+	0.997620i	$0.521964\pi$
$168$	3572.42	+	620.096i	1.64058	+	0.284770i
$169$	−1906.09			−0.867589
$170$	−1132.85	+	1962.15i	−0.511091	+	0.885236i
$171$	−1879.32	−	3255.08i	−0.840439	−	1.45568i
$172$	430.175	+	745.085i	0.190701	+	0.330303i
$173$	389.504	−	674.641i	0.171176	−	0.296485i	−0.767655	−	0.640863i	$-0.778577\pi$
$173$	389.504	−	674.641i	0.171176	−	0.296485i	0.938831	+	0.344378i	$0.111910\pi$
$174$	−3958.87			−1.72483
$175$	6337.12	+	1099.99i	2.73738	+	0.475151i
$176$	114.269			0.0489394
$177$	1717.84	−	2975.38i	0.729495	−	1.26352i
$178$	−1346.01	−	2331.37i	−0.566787	−	0.981704i
$179$	−1122.78	−	1944.70i	−0.468828	−	0.812033i	0.530537	−	0.847662i	$-0.321990\pi$
$179$	−1122.78	−	1944.70i	−0.468828	−	0.812033i	−0.999365	+	0.0356281i	$0.988657\pi$
$180$	−2324.27	+	4025.75i	−0.962447	+	1.66701i
$181$	−1341.48			−0.550890			−0.275445	−	0.961317i	$-0.588825\pi$
$181$	−1341.48			−0.550890			−0.275445	+	0.961317i	$0.588825\pi$
$182$	196.956	+	536.676i	0.0802164	+	0.218577i
$183$	1457.34			0.588687
$184$	264.832	−	458.703i	0.106107	−	0.183783i
$185$	−3084.18	−	5341.95i	−1.22569	−	2.12296i
$186$	−1129.66	−	1956.62i	−0.445325	−	0.771326i
$187$	−848.329	+	1469.35i	−0.331743	+	0.574596i
$188$	2278.44			0.883894
$189$	1843.43	−	2208.85i	0.709468	−	0.850105i
$190$	−3265.29			−1.24679
$191$	−1296.84	+	2246.19i	−0.491288	+	0.850937i	−0.999950	−	0.0100301i	$-0.996807\pi$
$191$	−1296.84	+	2246.19i	−0.491288	+	0.850937i	0.508661	+	0.860967i	$0.330141\pi$
$192$	1495.17	+	2589.71i	0.562003	+	0.973418i
$193$	240.478	+	416.520i	0.0896891	+	0.155346i	0.907380	−	0.420312i	$-0.138079\pi$
$193$	240.478	+	416.520i	0.0896891	+	0.155346i	−0.817691	+	0.575658i	$0.804746\pi$
$194$	−606.491	+	1050.47i	−0.224451	+	0.388760i
$195$	−3151.14			−1.15722
$196$	1235.85	−	1048.29i	0.450384	−	0.382029i
$197$	4397.32			1.59033			0.795167	−	0.606391i	$-0.207383\pi$
$197$	4397.32			1.59033			0.795167	+	0.606391i	$0.207383\pi$
$198$	1206.58	−	2089.86i	0.433071	−	0.750101i
$199$	−591.674	−	1024.81i	−0.210767	−	0.365060i	0.741188	−	0.671298i	$-0.234263\pi$
$199$	−591.674	−	1024.81i	−0.210767	−	0.365060i	−0.951955	+	0.306238i	$0.900930\pi$
$200$	3998.84	+	6926.20i	1.41380	+	2.44878i
$201$	−314.843	+	545.325i	−0.110484	+	0.191364i
$202$	1808.35			0.629878
$203$	−3053.43	+	3658.71i	−1.05571	+	1.26498i
$204$	−2313.84			−0.794123
$205$	−959.012	+	1661.06i	−0.326733	+	0.565919i
$206$	403.742	+	699.302i	0.136554	+	0.236518i
$207$	−520.638	−	901.772i	−0.174816	−	0.302790i
$208$	−33.0866	+	57.3076i	−0.0110295	+	0.0191037i
$209$	−2445.20			−0.809273
$210$	−2133.46	−	5813.36i	−0.701062	−	1.91029i
$211$	−1195.95			−0.390203			−0.195102	−	0.980783i	$-0.562504\pi$
$211$	−1195.95			−0.390203			−0.195102	+	0.980783i	$0.562504\pi$
$212$	257.911	−	446.714i	0.0835536	−	0.144719i
$213$	1685.19	+	2918.84i	0.542100	+	0.938945i
$214$	693.853	+	1201.79i	0.221639	+	0.383891i
$215$	1978.68	−	3427.17i	0.627650	−	1.08712i
$216$	3577.41			1.12691
$217$	−2679.56	−	465.115i	−0.838252	−	0.145503i
$218$	−685.789			−0.213062
$219$	−1533.02	+	2655.27i	−0.473023	+	0.819301i
$220$	1512.06	+	2618.97i	0.463378	+	0.802595i
$221$	−491.268	−	850.901i	−0.149531	−	0.258995i
$222$	−2183.48	+	3781.90i	−0.660115	+	1.14335i
$223$	6021.32			1.80815			0.904075	−	0.427375i	$-0.140561\pi$
$223$	6021.32			1.80815			0.904075	+	0.427375i	$0.140561\pi$
$224$	3233.62	+	561.287i	0.964532	+	0.167422i
$225$	15722.8			4.65860
$226$	631.825	−	1094.35i	0.185966	−	0.322103i
$227$	−958.967	−	1660.98i	−0.280392	−	0.485653i	0.691090	−	0.722769i	$-0.257131\pi$
$227$	−958.967	−	1660.98i	−0.280392	−	0.485653i	−0.971481	+	0.237117i	$0.923798\pi$
$228$	−1667.34	−	2887.91i	−0.484307	−	0.838845i
$229$	−1428.21	+	2473.74i	−0.412135	+	0.713839i	−0.995123	−	0.0986420i	$-0.968550\pi$
$229$	−1428.21	+	2473.74i	−0.412135	+	0.713839i	0.582988	+	0.812481i	$0.301883\pi$
$230$	−904.603			−0.259338
$231$	−1597.63	−	4353.31i	−0.455050	−	1.23994i
$232$	−5925.58			−1.67687
$233$	1738.48	−	3011.13i	0.488805	−	0.846635i	−0.511112	−	0.859514i	$-0.670766\pi$
$233$	1738.48	−	3011.13i	0.488805	−	0.846635i	0.999917	+	0.0128793i	$0.00409972\pi$
$234$	698.733	+	1210.24i	0.195203	+	0.338102i
$235$	−5240.07	−	9076.08i	−1.45457	−	2.51940i
$236$	954.702	−	1653.59i	0.263330	−	0.456100i
$237$	2457.28			0.673492
$238$	1237.17	−	1482.41i	0.336948	−	0.403741i
$239$	1464.40			0.396335			0.198167	−	0.980168i	$-0.436501\pi$
$239$	1464.40			0.396335			0.198167	+	0.980168i	$0.436501\pi$
$240$	358.399	−	620.766i	0.0963940	−	0.166959i
$241$	135.626	+	234.911i	0.0362508	+	0.0627882i	0.883582	−	0.468277i	$-0.155125\pi$
$241$	135.626	+	234.911i	0.0362508	+	0.0627882i	−0.847331	+	0.531065i	$0.821792\pi$
$242$	419.462	+	726.529i	0.111422	+	0.192988i
$243$	−1679.45	+	2908.89i	−0.443360	+	0.767922i
$244$	809.929			0.212502
$245$	−7018.11	−	2512.08i	−1.83008	−	0.655064i
$246$	1357.89			0.351934
$247$	708.009	−	1226.31i	0.182387	−	0.315903i
$248$	−1690.85	−	2928.65i	−0.432941	−	0.749876i
$249$	4292.58	+	7434.97i	1.09249	+	1.89226i
$250$	4371.38	−	7571.45i	1.10588	−	1.91544i
$251$	−365.791			−0.0919861			−0.0459931	−	0.998942i	$-0.514645\pi$
$251$	−365.791			−0.0919861			−0.0459931	+	0.998942i	$0.514645\pi$
$252$	2538.30	−	3041.46i	0.634514	−	0.760293i
$253$	−677.408			−0.168333
$254$	906.140	−	1569.48i	0.223844	−	0.387709i
$255$	5321.49	+	9217.10i	1.30684	+	2.26352i
$256$	2113.80	+	3661.20i	0.516064	+	0.893848i
$257$	2606.27	−	4514.18i	0.632585	−	1.09567i	−0.354436	−	0.935080i	$-0.615327\pi$
$257$	2606.27	−	4514.18i	0.632585	−	1.09567i	0.987021	−	0.160589i	$-0.0513395\pi$
$258$	−2801.66			−0.676061
$259$	1811.06	+	4934.86i	0.434494	+	1.18393i
$260$	−1751.27			−0.417728
$261$	−5824.60	+	10088.5i	−1.38135	+	2.39258i
$262$	−2328.47	−	4033.02i	−0.549058	−	0.950996i
$263$	342.741	+	593.645i	0.0803587	+	0.139185i	0.903404	−	0.428790i	$-0.141060\pi$
$263$	342.741	+	593.645i	0.0803587	+	0.139185i	−0.823045	+	0.567976i	$0.807727\pi$
$264$	2883.06	−	4993.60i	0.672121	−	1.16415i
$265$	−2372.63			−0.549998
$266$	2741.70	+	475.900i	0.631971	+	0.109697i
$267$	−12645.7			−2.89851
$268$	−174.977	+	303.068i	−0.0398821	+	0.0690778i
$269$	−2888.30	−	5002.69i	−0.654658	−	1.13390i	−0.981979	−	0.188988i	$-0.939479\pi$
$269$	−2888.30	−	5002.69i	−0.654658	−	1.13390i	0.327322	−	0.944913i	$-0.393854\pi$
$270$	−3054.89	−	5291.22i	−0.688572	−	1.19264i
$271$	−205.387	+	355.741i	−0.0460382	+	0.0797406i	−0.888126	−	0.459600i	$-0.847993\pi$
$271$	−205.387	+	355.741i	−0.0460382	+	0.0797406i	0.842088	+	0.539340i	$0.181326\pi$
$272$	223.500			0.0498223
$273$	2645.85	+	459.263i	0.586572	+	0.101816i
$274$	−958.625			−0.211360
$275$	5114.27	−	8858.17i	1.12146	−	1.94243i
$276$	−461.912	−	800.055i	−0.100738	−	0.174484i
$277$	−3271.85	−	5667.00i	−0.709698	−	1.22923i	−0.964969	−	0.262363i	$-0.915498\pi$
$277$	−3271.85	−	5667.00i	−0.709698	−	1.22923i	0.255272	−	0.966869i	$-0.417835\pi$
$278$	1953.59	−	3383.73i	0.421471	−	0.730008i
$279$	−6648.16			−1.42658
$280$	−3193.34	−	8701.36i	−0.681566	−	1.85716i
$281$	9067.27			1.92494			0.962469	−	0.271391i	$-0.0874836\pi$
$281$	9067.27			1.92494			0.962469	+	0.271391i	$0.0874836\pi$
$282$	−3709.77	+	6425.52i	−0.783382	+	1.35686i
$283$	−377.566	−	653.964i	−0.0793074	−	0.137364i	0.823644	−	0.567107i	$-0.191938\pi$
$283$	−377.566	−	653.964i	−0.0793074	−	0.137364i	−0.902951	+	0.429743i	$0.858604\pi$
$284$	936.558	+	1622.17i	0.195685	+	0.338936i
$285$	−7669.27	+	13283.6i	−1.59399	+	2.76088i
$286$	909.128			0.187965
$287$	1047.32	−	1254.93i	0.215406	−	0.258106i
$288$	8022.80			1.64149
$289$	797.242	−	1380.86i	0.162272	−	0.281063i
$290$	5060.08	+	8764.32i	1.02461	+	1.77468i
$291$	2848.96	+	4934.54i	0.573913	+	0.994047i
$292$	−851.990	+	1475.69i	−0.170750	+	0.295747i
$293$	1834.91			0.365858			0.182929	−	0.983126i	$-0.441442\pi$
$293$	1834.91			0.365858			0.182929	+	0.983126i	$0.441442\pi$
$294$	944.090	+	5192.12i	0.187280	+	1.02997i
$295$	−8782.71			−1.73339
$296$	−3268.20	+	5660.69i	−0.641758	+	1.11156i
$297$	−2287.64	−	3962.31i	−0.446944	−	0.774129i
$298$	−2286.71	−	3960.70i	−0.444516	−	0.769924i
$299$	196.144	−	339.731i	0.0379374	−	0.0657095i
$300$	13949.3			2.68454
$301$	−2160.89	+	2589.24i	−0.413792	+	0.495818i
$302$	−3756.64			−0.715797
$303$	4247.32	−	7356.57i	0.805287	−	1.39480i
$304$	161.052	+	278.951i	0.0303848	+	0.0526281i
$305$	−1862.72	−	3226.32i	−0.349702	−	0.605701i
$306$	2359.97	−	4087.59i	0.440884	−	0.763633i
$307$	−8449.11			−1.57074			−0.785368	−	0.619029i	$-0.787526\pi$
$307$	−8449.11			−1.57074			−0.785368	+	0.619029i	$0.787526\pi$
$308$	−887.898	−	2419.39i	−0.164262	−	0.447589i
$309$	3793.11			0.698326
$310$	−2887.77	+	5001.77i	−0.529079	+	0.916392i
$311$	−923.412	−	1599.40i	−0.168366	−	0.291619i	0.769479	−	0.638672i	$-0.220516\pi$
$311$	−923.412	−	1599.40i	−0.168366	−	0.291619i	−0.937846	+	0.347053i	$0.887182\pi$
$312$	1669.58	+	2891.80i	0.302953	+	0.524731i
$313$	687.747	−	1191.21i	0.124197	−	0.215116i	−0.797222	−	0.603687i	$-0.793698\pi$
$313$	687.747	−	1191.21i	0.124197	−	0.215116i	0.921419	+	0.388571i	$0.127031\pi$
$314$	5391.66			0.969009
$315$	−17953.3	−	3116.30i	−3.21128	−	0.557409i
$316$	1365.65			0.243114
$317$	−5523.84	+	9567.57i	−0.978705	+	1.69517i	−0.311583	+	0.950219i	$0.600859\pi$
$317$	−5523.84	+	9567.57i	−0.978705	+	1.69517i	−0.667122	+	0.744948i	$0.732474\pi$
$318$	839.865	+	1454.69i	0.148105	+	0.256525i
$319$	3789.22	+	6563.12i	0.665065	+	1.15193i
$320$	3822.14	−	6620.14i	0.667701	−	1.15649i
$321$	6518.67			1.13345
$322$	759.548	+	131.841i	0.131453	+	0.0228175i
$323$	−4782.60			−0.823873
$324$	232.141	−	402.079i	0.0398046	−	0.0689436i
$325$	2961.68	+	5129.77i	0.505490	+	0.875534i
$326$	1455.99	+	2521.84i	0.247361	+	0.428442i
$327$	−1610.73	+	2789.86i	−0.272396	+	0.471803i
$328$	2032.47			0.342147
$329$	3077.03	+	8384.42i	0.515629	+	1.40501i
$330$	−9847.82			−1.64274
$331$	2541.83	−	4402.57i	0.422089	−	0.731079i	−0.574055	−	0.818817i	$-0.694630\pi$
$331$	2541.83	−	4402.57i	0.422089	−	0.731079i	0.996144	+	0.0877377i	$0.0279637\pi$
$332$	2385.64	+	4132.04i	0.394364	+	0.683058i
$333$	6425.01	+	11128.4i	1.05732	+	1.83134i
$334$	269.286	−	466.417i	0.0441158	−	0.0764107i
$335$	1609.68			0.262527
$336$	−391.403	+	468.990i	−0.0635499	+	0.0761473i
$337$	−2550.67			−0.412296			−0.206148	−	0.978521i	$-0.566093\pi$
$337$	−2550.67			−0.412296			−0.206148	+	0.978521i	$0.566093\pi$
$338$	1724.81	−	2987.45i	0.277565	−	0.480757i
$339$	−2967.96	−	5140.66i	−0.475509	−	0.823606i
$340$	2957.46	+	5122.48i	0.471738	+	0.817074i
$341$	−2162.50	+	3745.55i	−0.343418	+	0.594818i
$342$	6802.31			1.07552
$343$	5526.62	+	3132.11i	0.869998	+	0.493056i
$344$	−4193.48			−0.657260
$345$	−2124.66	+	3680.02i	−0.331559	+	0.574277i
$346$	704.917	+	1220.95i	0.109528	+	0.189707i
$347$	−58.3605	−	101.083i	−0.00902870	−	0.0156382i	0.861476	−	0.507799i	$-0.169541\pi$
$347$	−58.3605	−	101.083i	−0.00902870	−	0.0156382i	−0.870504	+	0.492161i	$0.836207\pi$
$348$	−5167.60	+	8950.54i	−0.796012	+	1.37873i
$349$	1643.58			0.252089			0.126044	−	0.992025i	$-0.459772\pi$
$349$	1643.58			0.252089			0.126044	+	0.992025i	$0.459772\pi$
$350$	−7458.44	+	8936.91i	−1.13906	+	1.36485i
$351$	2649.55			0.402913
$352$	2609.64	−	4520.02i	0.395154	−	0.684426i
$353$	4795.18	+	8305.49i	0.723007	+	1.25229i	0.959789	+	0.280722i	$0.0905740\pi$
$353$	4795.18	+	8305.49i	0.723007	+	1.25229i	−0.236782	+	0.971563i	$0.576093\pi$
$354$	3108.91	+	5384.79i	0.466770	+	0.808470i
$355$	4307.90	−	7461.50i	0.644055	−	1.11554i
$356$	−7027.92			−1.04629
$357$	−3124.84	−	8514.70i	−0.463260	−	1.26231i
$358$	4063.96			0.599963
$359$	−5109.14	+	8849.28i	−0.751114	+	1.30097i	0.196169	+	0.980570i	$0.437150\pi$
$359$	−5109.14	+	8849.28i	−0.751114	+	1.30097i	−0.947283	+	0.320398i	$0.896184\pi$
$360$	−11328.8	−	19622.1i	−1.65856	−	2.87271i
$361$	−16.8089	−	29.1138i	−0.00245063	−	0.00424462i
$362$	1213.89	−	2102.52i	0.176245	−	0.305265i
$363$	3940.80			0.569802
$364$	1470.45	+	255.239i	0.211738	+	0.0367532i
$365$	7837.82			1.12397
$366$	−1318.73	+	2284.11i	−0.188337	+	0.326209i
$367$	−2634.44	−	4562.99i	−0.374705	−	0.649008i	0.615578	−	0.788076i	$-0.288923\pi$
$367$	−2634.44	−	4562.99i	−0.374705	−	0.649008i	−0.990283	+	0.139068i	$0.955589\pi$
$368$	44.6173	+	77.2794i	0.00632021	+	0.0109469i
$369$	1997.83	−	3460.34i	0.281851	−	0.488180i
$370$	11163.4			1.56853
$371$	1992.17	+	345.799i	0.278783	+	0.0483907i
$372$	−5898.26			−0.822072
$373$	−3088.65	+	5349.69i	−0.428751	+	0.742618i	−0.996763	−	0.0804022i	$-0.974380\pi$
$373$	−3088.65	+	5349.69i	−0.428751	+	0.742618i	0.568012	+	0.823021i	$0.307713\pi$
$374$	−1535.29	−	2659.20i	−0.212267	−	0.367658i
$375$	−20534.3	−	35566.4i	−2.82770	−	4.89771i
$376$	−5552.73	+	9617.62i	−0.761597	+	1.31912i
$377$	−4388.68			−0.599545
$378$	1793.86	+	4888.00i	0.244091	+	0.665110i
$379$	−6856.50			−0.929274			−0.464637	−	0.885501i	$-0.653815\pi$
$379$	−6856.50			−0.929274			−0.464637	+	0.885501i	$0.653815\pi$
$380$	−4262.26	+	7382.44i	−0.575392	+	0.996609i
$381$	−4256.54	−	7372.55i	−0.572360	−	0.991357i
$382$	−2347.00	−	4065.12i	−0.314353	−	0.544476i
$383$	−2952.57	+	5114.00i	−0.393914	+	0.682280i	−0.992962	−	0.118434i	$-0.962213\pi$
$383$	−2952.57	+	5114.00i	−0.393914	+	0.682280i	0.599048	+	0.800713i	$0.295546\pi$
$384$	6640.31			0.882453
$385$	−7595.51	+	9101.15i	−1.00546	+	1.20477i
$386$	−870.426			−0.114776
$387$	−4122.02	+	7139.54i	−0.541431	+	0.937787i
$388$	1583.33	+	2742.41i	0.207169	+	0.358826i
$389$	1301.71	+	2254.62i	0.169663	+	0.293866i	0.938302	−	0.345818i	$-0.112399\pi$
$389$	1301.71	+	2254.62i	0.169663	+	0.293866i	−0.768638	+	0.639684i	$0.779065\pi$
$390$	2851.44	−	4938.84i	0.370226	−	0.641251i
$391$	−1324.95			−0.171370
$392$	1413.10	+	7771.49i	0.182072	+	1.00133i
$393$	−21875.7			−2.80784
$394$	−3979.09	+	6891.99i	−0.508791	+	0.881252i
$395$	−3140.81	−	5440.04i	−0.400079	−	0.692957i
$396$	−3149.95	−	5455.88i	−0.399725	−	0.692344i
$397$	6170.18	−	10687.1i	0.780031	−	1.35105i	−0.151892	−	0.988397i	$-0.548536\pi$
$397$	6170.18	−	10687.1i	0.780031	−	1.35105i	0.931923	−	0.362657i	$-0.118130\pi$
$398$	2141.60			0.269721
$399$	8375.49	−	10035.8i	1.05088	−	1.25919i
$400$	−1347.40			−0.168425
$401$	−358.650	+	621.200i	−0.0446637	+	0.0773598i	−0.887493	−	0.460821i	$-0.847555\pi$
$401$	−358.650	+	621.200i	−0.0446637	+	0.0773598i	0.842829	+	0.538181i	$0.180888\pi$
$402$	−569.798	−	986.918i	−0.0706938	−	0.122445i
$403$	−1252.30	−	2169.05i	−0.154793	−	0.268110i
$404$	2360.48	−	4088.47i	0.290689	−	0.503488i
$405$	−2135.56			−0.262017
$406$	−2971.33	−	8096.42i	−0.363214	−	0.989701i
$407$	8359.64			1.01811
$408$	5639.01	−	9767.06i	0.684247	−	1.18515i
$409$	−1958.42	−	3392.09i	−0.236767	−	0.410093i	0.723018	−	0.690830i	$-0.242755\pi$
$409$	−1958.42	−	3392.09i	−0.236767	−	0.410093i	−0.959785	+	0.280737i	$0.909421\pi$
$410$	−1735.60	−	3006.15i	−0.209062	−	0.362106i
$411$	−2251.54	+	3899.79i	−0.270220	+	0.468035i
$412$	2108.05			0.252079
$413$	7374.38	+	1280.04i	0.878619	+	0.152509i
$414$	1884.48			0.223713
$415$	10973.2	−	19006.2i	1.29796	−	2.24814i
$416$	1511.24	+	2617.55i	0.178112	+	0.308500i
$417$	−9176.90	−	15894.9i	−1.07769	−	1.86661i
$418$	2212.64	−	3832.40i	0.258908	−	0.448442i
$419$	13598.9			1.58555			0.792777	−	0.609511i	$-0.208634\pi$
$419$	13598.9			1.58555			0.792777	+	0.609511i	$0.208634\pi$
$420$	−15928.2	−	2764.79i	−1.85051	−	0.321210i
$421$	−6068.09			−0.702472			−0.351236	−	0.936287i	$-0.614239\pi$
$421$	−6068.09			−0.702472			−0.351236	+	0.936287i	$0.614239\pi$
$422$	1082.21	−	1874.44i	0.124837	−	0.216223i
$423$	10916.2	+	18907.4i	1.25476	+	2.17331i
$424$	1257.10	+	2177.36i	0.143986	+	0.249391i
$425$	10003.1	−	17325.8i	1.14169	−	1.97747i
$426$	−6099.65			−0.693730
$427$	1093.81	+	2980.46i	0.123965	+	0.337786i
$428$	3622.80			0.409147
$429$	2135.29	−	3698.43i	0.240309	−	0.416228i
$430$	3580.98	+	6202.44i	0.401605	+	0.695600i
$431$	982.411	+	1701.58i	0.109794	+	0.190168i	0.915687	−	0.401893i	$-0.131648\pi$
$431$	982.411	+	1701.58i	0.109794	+	0.190168i	−0.805893	+	0.592061i	$0.798314\pi$
$432$	−301.349	+	521.953i	−0.0335618	+	0.0581307i
$433$	−9228.91			−1.02428			−0.512140	−	0.858902i	$-0.671147\pi$
$433$	−9228.91			−1.02428			−0.512140	+	0.858902i	$0.671147\pi$
$434$	3153.69	−	3778.85i	0.348807	−	0.417950i
$435$	47538.9			5.23981
$436$	−895.174	+	1550.49i	−0.0983281	+	0.170309i
$437$	−954.751	−	1653.68i	−0.104512	−	0.181021i
$438$	−2774.44	−	4805.47i	−0.302666	−	0.524233i
$439$	1179.30	−	2042.61i	0.128212	−	0.222069i	−0.794772	−	0.606908i	$-0.792410\pi$
$439$	1179.30	−	2042.61i	0.128212	−	0.222069i	0.922984	+	0.384839i	$0.125743\pi$
$440$	−14740.1			−1.59706
$441$	14620.2	+	5233.20i	1.57869	+	0.565079i
$442$	1778.18			0.191356
$443$	5953.88	−	10312.4i	0.638550	−	1.10600i	−0.347202	−	0.937790i	$-0.612868\pi$
$443$	5953.88	−	10312.4i	0.638550	−	1.10600i	0.985751	−	0.168210i	$-0.0537986\pi$
$444$	5700.29	+	9873.18i	0.609287	+	1.05532i
$445$	16163.2	+	27995.5i	1.72182	+	2.98228i
$446$	−5448.63	+	9437.31i	−0.578476	+	1.00195i
$447$	−21483.4			−2.27322
$448$	−4174.11	+	5001.53i	−0.440196	+	0.527456i
$449$	−4204.65			−0.441937			−0.220969	−	0.975281i	$-0.570922\pi$
$449$	−4204.65			−0.441937			−0.220969	+	0.975281i	$0.570922\pi$
$450$	−14227.4	+	24642.6i	−1.49041	+	2.58147i
$451$	−1299.70	−	2251.14i	−0.135699	−	0.235038i
$452$	−1649.47	−	2856.96i	−0.171647	−	0.297301i
$453$	−8823.31	+	15282.4i	−0.915133	+	1.58506i
$454$	3471.04			0.358820
$455$	−2365.09	−	6444.51i	−0.243686	−	0.664008i
$456$	16253.7			1.66919
$457$	2046.02	−	3543.81i	0.209428	−	0.362740i	−0.742106	−	0.670282i	$-0.766173\pi$
$457$	2046.02	−	3543.81i	0.209428	−	0.362740i	0.951535	+	0.307542i	$0.0995064\pi$
$458$	−2584.75	−	4476.92i	−0.263706	−	0.456753i
$459$	−4474.42	−	7749.93i	−0.455007	−	0.788095i
$460$	−1180.80	+	2045.20i	−0.119685	+	0.207300i
$461$	−12113.9			−1.22386			−0.611931	−	0.790911i	$-0.709607\pi$
$461$	−12113.9			−1.22386			−0.611931	+	0.790911i	$0.709607\pi$
$462$	8268.70	+	1435.27i	0.832673	+	0.144534i
$463$	−2527.84			−0.253734			−0.126867	−	0.991920i	$-0.540492\pi$
$463$	−2527.84			−0.253734			−0.126867	+	0.991920i	$0.540492\pi$
$464$	499.152	−	864.557i	0.0499408	−	0.0865001i
$465$	13565.2	+	23495.5i	1.35284	+	2.34318i
$466$	3146.27	+	5449.49i	0.312764	+	0.541723i
$467$	−6603.57	+	11437.7i	−0.654340	+	1.13335i	0.327719	+	0.944775i	$0.393720\pi$
$467$	−6603.57	+	11437.7i	−0.654340	+	1.13335i	−0.982059	+	0.188575i	$0.939613\pi$
$468$	3648.28			0.360346
$469$	−1351.57	−	234.603i	−0.133070	−	0.0230980i
$470$	18966.8			1.86143
$471$	12663.5	−	21933.8i	1.23886	−	2.14577i
$472$	4653.37	+	8059.88i	0.453790	+	0.785987i
$473$	2681.60	+	4644.67i	0.260677	+	0.451505i
$474$	−2223.57	+	3851.34i	−0.215469	+	0.373202i
$475$	28832.6			2.78511
$476$	−1736.65	−	4732.11i	−0.167225	−	0.455664i
$477$	4942.70			0.474445
$478$	−1325.12	+	2295.17i	−0.126798	+	0.219621i
$479$	1509.74	+	2614.95i	0.144012	+	0.249437i	0.929004	−	0.370070i	$-0.120666\pi$
$479$	1509.74	+	2614.95i	0.144012	+	0.249437i	−0.784992	+	0.619506i	$0.787333\pi$
$480$	−16370.0	−	28353.7i	−1.55664	−	2.69617i
$481$	−2420.54	+	4192.50i	−0.229453	+	0.397425i
$482$	−490.907			−0.0463905
$483$	2320.31	−	2780.26i	0.218588	−	0.261918i
$484$	2190.13			0.205685
$485$	7282.86	−	12614.3i	0.681851	−	1.18100i
$486$	−3039.43	−	5264.45i	−0.283686	−	0.491359i
$487$	1281.86	+	2220.25i	0.119275	+	0.206590i	0.919480	−	0.393136i	$-0.128610\pi$
$487$	1281.86	+	2220.25i	0.119275	+	0.206590i	−0.800206	+	0.599726i	$0.795276\pi$
$488$	−1973.86	+	3418.83i	−0.183099	+	0.317138i
$489$	13678.8			1.26499
$490$	10287.8	−	8726.44i	0.948484	−	0.804532i
$491$	−7124.37			−0.654823			−0.327412	−	0.944882i	$-0.606176\pi$
$491$	−7124.37			−0.654823			−0.327412	+	0.944882i	$0.606176\pi$
$492$	1772.48	−	3070.03i	0.162418	−	0.281316i
$493$	7411.39	+	12836.9i	0.677063	+	1.17271i
$494$	1281.34	+	2219.35i	0.116701	+	0.202132i
$495$	−14488.9	+	25095.5i	−1.31561	+	2.27870i
$496$	569.729			0.0515758
$497$	−4704.59	+	5637.17i	−0.424607	+	0.508776i
$498$	−15537.3			−1.39808
$499$	3157.75	−	5469.38i	0.283287	−	0.490667i	−0.688905	−	0.724851i	$-0.741908\pi$
$499$	3157.75	−	5469.38i	0.283287	−	0.490667i	0.972192	+	0.234184i	$0.0752418\pi$
$500$	−11412.1	−	19766.3i	−1.02073	−	1.76795i
$501$	−1264.96	−	2190.97i	−0.112802	−	0.195380i
$502$	331.001	−	573.310i	0.0294289	−	0.0509723i
$503$	−19637.6			−1.74075			−0.870377	−	0.492386i	$-0.836125\pi$
$503$	−19637.6			−1.74075			−0.870377	+	0.492386i	$0.836125\pi$
$504$	6652.41	+	18126.8i	0.587940	+	1.60205i
$505$	−21715.1			−1.91348
$506$	612.980	−	1061.71i	0.0538543	−	0.0932784i
$507$	−8102.18	−	14033.4i	−0.709725	−	1.22928i
$508$	−2365.61	−	4097.35i	−0.206608	−	0.357856i
$509$	8991.72	−	15574.1i	0.783008	−	1.35621i	−0.147174	−	0.989111i	$-0.547018\pi$
$509$	8991.72	−	15574.1i	0.783008	−	1.35621i	0.930182	−	0.367099i	$-0.119649\pi$
$510$	−19261.5			−1.67238
$511$	−6581.00	−	1142.32i	−0.569719	−	0.0988911i
$512$	−1402.31			−0.121042
$513$	6448.48	−	11169.1i	0.554985	−	0.961262i
$514$	4716.77	+	8169.69i	0.404762	+	0.701069i
$515$	−4848.22	−	8397.36i	−0.414831	−	0.718509i
$516$	−3657.07	+	6334.22i	−0.312003	+	0.540404i
$517$	14203.2			1.20823
$518$	−9373.30	−	1627.01i	−0.795057	−	0.138005i
$519$	6622.62			0.560117
$520$	4267.99	−	7392.38i	0.359931	−	0.623418i
$521$	6736.46	+	11667.9i	0.566468	+	0.981152i	0.996911	+	0.0785339i	$0.0250239\pi$
$521$	6736.46	+	11667.9i	0.566468	+	0.981152i	−0.430443	+	0.902618i	$0.641643\pi$
$522$	−10541.2	−	18258.0i	−0.883865	−	1.53090i
$523$	−2955.08	+	5118.35i	−0.247068	+	0.427935i	−0.962711	−	0.270532i	$-0.912800\pi$
$523$	−2955.08	+	5118.35i	−0.247068	+	0.427935i	0.715643	+	0.698466i	$0.246134\pi$
$524$	−12157.6			−1.01356
$525$	18838.5	+	51332.0i	1.56606	+	4.26726i
$526$	−1240.57			−0.102836
$527$	−4229.65	+	7325.98i	−0.349614	+	0.605549i
$528$	485.719	+	841.290i	0.0400345	+	0.0693418i
$529$	−264.500	−	458.127i	−0.0217391	−	0.0376533i
$530$	2146.97	−	3718.66i	0.175959	−	0.304770i
$531$	18296.3			1.49527
$532$	4654.75	−	5577.45i	0.379340	−	0.454536i
$533$	1505.31			0.122331
$534$	11442.9	−	19819.7i	0.927311	−	1.60615i
$535$	−8331.93	−	14431.3i	−0.673310	−	1.16621i
$536$	−852.865	−	1477.20i	−0.0687279	−	0.119040i
$537$	9545.10	−	16532.6i	0.767042	−	1.32856i
$538$	10454.4			0.837771
$539$	7704.00	−	6534.76i	0.615649	−	0.522211i
$540$	−15950.4			−1.27111
$541$	3763.90	−	6519.27i	0.299118	−	0.518087i	−0.676817	−	0.736152i	$-0.736641\pi$
$541$	3763.90	−	6519.27i	0.299118	−	0.518087i	0.975934	+	0.218064i	$0.0699743\pi$
$542$	−371.705	−	643.813i	−0.0294578	−	0.0510224i
$543$	−5702.17	−	9876.45i	−0.450651	−	0.780551i
$544$	5104.22	−	8840.77i	0.402283	−	0.696774i
$545$	8235.08			0.647252
$546$	−3114.02	+	3731.30i	−0.244080	+	0.292463i
$547$	−24554.3			−1.91932			−0.959659	−	0.281167i	$-0.909279\pi$
$547$	−24554.3			−1.91932			−0.959659	+	0.281167i	$0.909279\pi$
$548$	−1251.31	+	2167.34i	−0.0975428	+	0.168949i
$549$	3880.45	+	6721.13i	0.301664	+	0.522497i
$550$	9255.71	+	16031.4i	0.717572	+	1.24287i
$551$	−10681.2	+	18500.4i	−0.825833	+	1.43038i
$552$	4502.87			0.347200
$553$	1844.31	+	5025.47i	0.141823	+	0.386447i
$554$	11842.7			0.908206
$555$	26219.7	−	45413.8i	2.00534	−	3.47335i
$556$	−5100.14	−	8833.69i	−0.389018	−	0.673799i
$557$	4469.49	+	7741.39i	0.339997	+	0.588892i	0.984432	−	0.175767i	$-0.0562405\pi$
$557$	4469.49	+	7741.39i	0.339997	+	0.588892i	−0.644435	+	0.764659i	$0.722907\pi$
$558$	6015.85	−	10419.8i	0.456400	−	0.790509i
$559$	−3105.83			−0.234996
$560$	1538.55	+	267.059i	0.116099	+	0.0201523i
$561$	−14423.9			−1.08552
$562$	−8204.88	+	14211.3i	−0.615840	+	1.06667i
$563$	711.078	+	1231.62i	0.0532298	+	0.0921967i	0.891413	−	0.453193i	$-0.149715\pi$
$563$	711.078	+	1231.62i	0.0532298	+	0.0921967i	−0.838183	+	0.545390i	$0.816382\pi$
$564$	9684.89	+	16774.7i	0.723063	+	1.25238i
$565$	−7587.08	+	13141.2i	−0.564939	+	0.978504i
$566$	1366.62			0.101490
$567$	1793.12	+	311.247i	0.132811	+	0.0230532i
$568$	−9129.87			−0.674438
$569$	12973.1	−	22470.1i	0.955819	−	1.65553i	0.223337	−	0.974741i	$-0.428305\pi$
$569$	12973.1	−	22470.1i	0.955819	−	1.65553i	0.732482	−	0.680786i	$-0.238362\pi$
$570$	−13879.7	−	24040.3i	−1.01992	−	1.76656i
$571$	−823.236	−	1425.89i	−0.0603351	−	0.104503i	0.834280	−	0.551341i	$-0.185884\pi$
$571$	−823.236	−	1425.89i	−0.0603351	−	0.104503i	−0.894615	+	0.446837i	$0.852550\pi$
$572$	1186.70	−	2055.43i	0.0867458	−	0.150248i
$573$	−22049.8			−1.60758
$574$	1019.16	+	2777.06i	0.0741099	+	0.201938i
$575$	7987.65			0.579318
$576$	−7962.35	+	13791.2i	−0.575980	+	0.997627i
$577$	−9273.97	−	16063.0i	−0.669117	−	1.15894i	−0.978152	−	0.207893i	$-0.933339\pi$
$577$	−9273.97	−	16063.0i	−0.669117	−	1.15894i	0.309035	−	0.951051i	$-0.399994\pi$
$578$	1442.83	+	2499.06i	0.103830	+	0.179840i
$579$	−2044.39	+	3540.98i	−0.146739	+	0.254159i
$580$	26420.1			1.89144
$581$	−11983.7	+	14359.2i	−0.855711	+	1.02534i
$582$	−10312.0			−0.734442
$583$	1607.75	−	2784.70i	0.114213	−	0.197823i
$584$	−4152.74	−	7192.75i	−0.294249	−	0.509654i
$585$	−8390.52	−	14532.8i	−0.593000	−	1.02711i
$586$	−1660.39	+	2875.88i	−0.117048	+	0.202733i
$587$	−4693.77			−0.330039			−0.165019	−	0.986290i	$-0.552769\pi$
$587$	−4693.77			−0.330039			−0.165019	+	0.986290i	$0.552769\pi$
$588$	12971.1	+	4642.91i	0.909727	+	0.325630i
$589$	−12191.4			−0.852869
$590$	7947.39	−	13765.3i	0.554557	−	0.960521i
$591$	18691.6	+	32374.7i	1.30096	+	2.25333i
$592$	−550.606	−	953.677i	−0.0382259	−	0.0662093i
$593$	3466.46	−	6004.09i	0.240051	−	0.415781i	−0.720677	−	0.693271i	$-0.756169\pi$
$593$	3466.46	−	6004.09i	0.240051	−	0.415781i	0.960729	+	0.277489i	$0.0895024\pi$
$594$	8280.25			0.571958
$595$	−14856.2	+	17801.1i	−1.02360	+	1.22651i
$596$	−11939.6			−0.820577
$597$	5030.03	−	8712.26i	0.344833	−	0.597268i
$598$	354.977	+	614.839i	0.0242744	+	0.0420445i
$599$	2552.88	+	4421.71i	0.174136	+	0.301613i	0.939862	−	0.341554i	$-0.110953\pi$
$599$	2552.88	+	4421.71i	0.174136	+	0.301613i	−0.765726	+	0.643167i	$0.777620\pi$
$600$	−33995.6	+	58882.0i	−2.31311	+	4.00642i
$601$	−11976.1			−0.812838			−0.406419	−	0.913687i	$-0.633223\pi$
$601$	−11976.1			−0.812838			−0.406419	+	0.913687i	$0.633223\pi$
$602$	−2102.79	−	5729.77i	−0.142364	−	0.387920i
$603$	−3353.32			−0.226464
$604$	−4903.63	+	8493.33i	−0.330341	+	0.572167i
$605$	−5036.98	−	8724.31i	−0.338483	−	0.586270i
$606$	7686.72	+	13313.8i	0.515267	+	0.892468i
$607$	−11288.9	+	19553.0i	−0.754866	+	1.30747i	0.190575	+	0.981673i	$0.438965\pi$
$607$	−11288.9	+	19553.0i	−0.754866	+	1.30747i	−0.945441	+	0.325794i	$0.894369\pi$
$608$	14712.3			0.981351
$609$	−39915.9	−	6928.56i	−2.65595	−	0.461017i
$610$	6742.23			0.447516
$611$	−4112.54	+	7123.13i	−0.272300	+	0.471638i
$612$	−6161.03	−	10671.2i	−0.406936	−	0.704834i
$613$	−753.840	−	1305.69i	−0.0496693	−	0.0860298i	0.840122	−	0.542398i	$-0.182483\pi$
$613$	−753.840	−	1305.69i	−0.0496693	−	0.0860298i	−0.889791	+	0.456368i	$0.849150\pi$
$614$	7645.52	−	13242.4i	0.502521	−	0.870392i
$615$	−16305.8			−1.06913
$616$	12376.5	+	2148.29i	0.809517	+	0.140515i
$617$	2494.59			0.162769			0.0813844	−	0.996683i	$-0.474066\pi$
$617$	2494.59			0.162769			0.0813844	+	0.996683i	$0.474066\pi$
$618$	−3432.35	+	5945.01i	−0.223413	+	0.386964i
$619$	−1847.09	−	3199.25i	−0.119937	−	0.207736i	0.799806	−	0.600259i	$-0.204936\pi$
$619$	−1847.09	−	3199.25i	−0.119937	−	0.207736i	−0.919742	+	0.392523i	$0.871603\pi$
$620$	7538.94	+	13057.8i	0.488341	+	0.845831i
$621$	1786.46	−	3094.24i	0.115440	−	0.199948i
$622$	3342.35			0.215460
$623$	−9491.20	−	25862.1i	−0.610364	−	1.66315i
$624$	−562.561			−0.0360905
$625$	−30786.8	+	53324.3i	−1.97035	+	3.41275i
$626$	1244.67	+	2155.84i	0.0794682	+	0.137643i
$627$	−10393.7	−	18002.5i	−0.662020	−	1.14665i
$628$	7037.85	−	12189.9i	0.447198	−	0.774570i
$629$	16350.7			1.03648
$630$	21130.0	−	25318.5i	1.33625	−	1.60113i
$631$	20618.4			1.30080			0.650401	−	0.759591i	$-0.274601\pi$
$631$	20618.4			1.30080			0.650401	+	0.759591i	$0.274601\pi$
$632$	−3328.21	+	5764.63i	−0.209476	+	0.362824i
$633$	−5083.61	−	8805.07i	−0.319203	−	0.552876i
$634$	−9996.94	−	17315.2i	−0.626229	−	1.08466i
$635$	−10881.1	+	18846.6i	−0.680006	+	1.17780i
$636$	4385.17			0.273402
$637$	1046.59	+	5755.82i	0.0650979	+	0.358013i
$638$	−13715.3			−0.851089
$639$	−8974.28	+	15543.9i	−0.555582	+	0.962297i
$640$	−8487.40	−	14700.6i	−0.524209	−	0.907957i
$641$	9995.76	+	17313.2i	0.615926	+	1.06682i	0.990221	+	0.139506i	$0.0445513\pi$
$641$	9995.76	+	17313.2i	0.615926	+	1.06682i	−0.374295	+	0.927310i	$0.622115\pi$
$642$	−5898.69	+	10216.8i	−0.362621	+	0.628078i
$643$	511.913			0.0313964			0.0156982	−	0.999877i	$-0.495003\pi$
$643$	511.913			0.0313964			0.0156982	+	0.999877i	$0.495003\pi$
$644$	1289.53	−	1545.15i	0.0789047	−	0.0945459i
$645$	33642.9			2.05378
$646$	4327.73	−	7495.85i	0.263579	−	0.456533i
$647$	2427.91	+	4205.26i	0.147528	+	0.255527i	0.930313	−	0.366766i	$-0.119535\pi$
$647$	2427.91	+	4205.26i	0.147528	+	0.255527i	−0.782785	+	0.622292i	$0.786202\pi$
$648$	1131.49	+	1959.80i	0.0685944	+	0.118809i
$649$	5951.37	−	10308.1i	0.359956	−	0.623462i
$650$	−10720.0			−0.646880
$651$	−7965.59	−	21705.0i	−0.479564	−	1.30674i
$652$	7602.12			0.456629
$653$	5841.87	−	10118.4i	0.350092	−	0.606378i	−0.636173	−	0.771546i	$-0.719484\pi$
$653$	5841.87	−	10118.4i	0.350092	−	0.606378i	0.986265	+	0.165169i	$0.0528169\pi$
$654$	−2915.06	−	5049.04i	−0.174294	−	0.301885i
$655$	27960.7	+	48429.3i	1.66796	+	2.88899i
$656$	−171.209	+	296.542i	−0.0101899	+	0.0176494i
$657$	−16327.9			−0.969575
$658$	−15925.4	−	2764.31i	−0.943522	−	0.163775i
$659$	−635.988			−0.0375942			−0.0187971	−	0.999823i	$-0.505984\pi$
$659$	−635.988			−0.0375942			−0.0187971	+	0.999823i	$0.505984\pi$
$660$	−12854.6	+	22264.8i	−0.758126	+	1.31311i
$661$	−10168.0	−	17611.5i	−0.598321	−	1.03632i	−0.993069	−	0.117533i	$-0.962501\pi$
$661$	−10168.0	−	17611.5i	−0.598321	−	1.03632i	0.394748	−	0.918789i	$-0.370832\pi$
$662$	4600.15	+	7967.69i	0.270075	+	0.467784i
$663$	4176.44	−	7233.81i	0.244645	−	0.423737i
$664$	−23255.9			−1.35920
$665$	−32922.8	−	5714.70i	−1.91984	−	0.333243i
$666$	−23255.7			−1.35306
$667$	−2959.07	+	5125.26i	−0.171778	+	0.297528i
$668$	−703.009	−	1217.65i	−0.0407189	−	0.0705272i
$669$	25594.7	+	44331.2i	1.47914	+	2.56195i
$670$	−1456.59	+	2522.88i	−0.0839894	+	0.145474i
$671$	5048.89			0.290477
$672$	9612.64	+	26193.0i	0.551809	+	1.50360i
$673$	31087.1			1.78056			0.890281	−	0.455412i	$-0.150508\pi$
$673$	31087.1			1.78056			0.890281	+	0.455412i	$0.150508\pi$
$674$	2308.08	−	3997.71i	0.131905	−	0.228466i
$675$	26974.7	+	46721.5i	1.53816	+	2.66417i
$676$	−4502.85	−	7799.17i	−0.256193	−	0.443740i
$677$	11413.4	−	19768.6i	0.647936	−	1.12226i	−0.335680	−	0.941976i	$-0.608966\pi$
$677$	11413.4	−	19768.6i	0.647936	−	1.12226i	0.983615	−	0.180281i	$-0.0577007\pi$
$678$	10742.7			0.608513
$679$	−7953.51	+	9530.11i	−0.449525	+	0.538634i
$680$	−28830.3			−1.62587
$681$	8152.52	−	14120.6i	0.458745	−	0.794569i
$682$	−3913.64	−	6778.63i	−0.219738	−	0.380597i
$683$	2600.36	+	4503.96i	0.145681	+	0.252327i	0.929627	−	0.368502i	$-0.120129\pi$
$683$	2600.36	+	4503.96i	0.145681	+	0.252327i	−0.783946	+	0.620829i	$0.786796\pi$
$684$	8879.20	−	15379.2i	0.496352	−	0.859707i
$685$	11511.4			0.642082
$686$	−9910.00	+	5827.74i	−0.551553	+	0.324350i
$687$	−24283.5			−1.34858
$688$	353.246	−	611.839i	0.0195747	−	0.0339043i
$689$	931.048	+	1612.62i	0.0514806	+	0.0891670i
$690$	−3845.17	−	6660.03i	−0.212149	−	0.367454i
$691$	−5580.27	+	9665.31i	−0.307212	+	0.532107i	−0.977751	−	0.209767i	$-0.932729\pi$
$691$	−5580.27	+	9665.31i	−0.307212	+	0.532107i	0.670539	+	0.741874i	$0.266063\pi$
$692$	3680.57			0.202188
$693$	15823.1	−	18959.7i	0.867344	−	1.03928i
$694$	211.240			0.0115541
$695$	−23459.2	+	40632.4i	−1.28037	+	2.21766i
$696$	−25187.7	−	43626.4i	−1.37175	−	2.37594i
$697$	−2542.10	−	4403.04i	−0.138147	−	0.239278i
$698$	−1487.26	+	2576.02i	−0.0806501	+	0.139690i
$699$	29558.8			1.59945
$700$	10469.6	+	28528.2i	0.565308	+	1.54038i
$701$	16057.2			0.865152			0.432576	−	0.901598i	$-0.357605\pi$
$701$	16057.2			0.865152			0.432576	+	0.901598i	$0.357605\pi$
$702$	−2397.55	+	4152.68i	−0.128903	+	0.223266i
$703$	11782.2	+	20407.4i	0.632113	+	1.09485i
$704$	5179.95	+	8971.93i	0.277310	+	0.480316i
$705$	44547.7	−	77158.9i	2.37981	−	4.12194i
$706$	−17356.4			−0.925239
$707$	18233.0	+	3164.86i	0.969905	+	0.168355i
$708$	16232.5			0.861659
$709$	14071.5	−	24372.6i	0.745370	−	1.29102i	−0.204652	−	0.978835i	$-0.565606\pi$
$709$	14071.5	−	24372.6i	0.745370	−	1.29102i	0.950022	−	0.312184i	$-0.101060\pi$
$710$	7796.35	+	13503.7i	0.412101	+	0.713780i
$711$	6542.98	+	11332.8i	0.345121	+	0.597767i
$712$	17127.6	−	29665.9i	0.901523	−	1.56148i
$713$	−3377.46			−0.177401
$714$	16172.9	+	2807.26i	0.847695	+	0.147142i
$715$	−10917.0			−0.571010
$716$	5304.77	−	9188.13i	0.276883	−	0.479576i
$717$	6224.67	+	10781.5i	0.324219	+	0.561563i
$718$	−9246.42	−	16015.3i	−0.480604	−	0.832430i
$719$	7748.24	−	13420.4i	0.401892	−	0.696098i	−0.592062	−	0.805893i	$-0.701686\pi$
$719$	7748.24	−	13420.4i	0.401892	−	0.696098i	0.993954	+	0.109794i	$0.0350192\pi$
$720$	3817.22			0.197583
$721$	2846.92	+	7757.43i	0.147053	+	0.400696i
$722$	60.8408			0.00313609
$723$	−1153.00	+	1997.06i	−0.0593094	+	0.102727i
$724$	−3169.03	−	5488.92i	−0.162674	−	0.281760i
$725$	−44680.6	−	77389.0i	−2.28882	−	3.96435i
$726$	−3565.99	+	6176.48i	−0.182295	+	0.315745i
$727$	3682.29			0.187852			0.0939260	−	0.995579i	$-0.470058\pi$
$727$	3682.29			0.187852			0.0939260	+	0.995579i	$0.470058\pi$
$728$	−4661.02	+	5584.96i	−0.237292	+	0.284330i
$729$	−31208.3			−1.58555
$730$	−7092.37	+	12284.3i	−0.359589	+	0.622827i
$731$	5244.98	+	9084.56i	0.265380	+	0.459651i
$732$	3442.74	+	5963.01i	0.173835	+	0.301092i
$733$	−4258.90	+	7376.62i	−0.214606	+	0.371708i	−0.953151	−	0.302496i	$-0.902180\pi$
$733$	−4258.90	+	7376.62i	−0.214606	+	0.371708i	0.738545	+	0.674204i	$0.235513\pi$
$734$	9535.53			0.479513
$735$	−11336.8	−	62348.0i	−0.568932	−	3.12890i
$736$	4075.82			0.204126
$737$	−1090.76	+	1889.25i	−0.0545165	+	0.0944253i
$738$	3615.64	+	6262.46i	0.180343	+	0.312364i
$739$	−5576.08	−	9658.06i	−0.277564	−	0.480754i	0.693215	−	0.720731i	$-0.256194\pi$
$739$	−5576.08	−	9658.06i	−0.277564	−	0.480754i	−0.970779	+	0.239976i	$0.922860\pi$
$740$	14571.8	−	25239.1i	0.723878	−	1.25379i
$741$	12038.1			0.596800
$742$	−2344.67	+	2809.45i	−0.116005	+	0.139000i
$743$	−11717.7			−0.578573			−0.289286	−	0.957243i	$-0.593418\pi$
$743$	−11717.7			−0.578573			−0.289286	+	0.957243i	$0.593418\pi$
$744$	14374.5	−	24897.4i	0.708328	−	1.22686i
$745$	27459.3	+	47560.9i	1.35038	+	2.33892i
$746$	−5589.78	−	9681.78i	−0.274338	−	0.475168i
$747$	−22859.6	+	39594.0i	−1.11966	+	1.93932i
$748$	−8016.18			−0.391846
$749$	4892.59	+	13331.6i	0.238680	+	0.650367i
$750$	74325.2			3.61863
$751$	−8226.75	+	14249.2i	−0.399732	+	0.692356i	−0.993693	−	0.112138i	$-0.964230\pi$
$751$	−8226.75	+	14249.2i	−0.399732	+	0.692356i	0.593961	+	0.804494i	$0.297563\pi$
$752$	−935.489	−	1620.32i	−0.0453641	−	0.0785729i
$753$	−1554.86	−	2693.09i	−0.0752486	−	0.130334i
$754$	3971.28	−	6878.45i	0.191811	−	0.332226i
$755$	45110.5			2.17449
$756$	13392.7	+	2324.70i	0.644298	+	0.111836i
$757$	818.042			0.0392764			0.0196382	−	0.999807i	$-0.493749\pi$
$757$	818.042			0.0392764			0.0196382	+	0.999807i	$0.493749\pi$
$758$	6204.38	−	10746.3i	0.297300	−	0.514939i
$759$	−2879.44	−	4987.33i	−0.137704	−	0.238510i
$760$	−20774.9	−	35983.2i	−0.991560	−	1.71743i
$761$	−929.612	+	1610.13i	−0.0442817	+	0.0766982i	−0.887317	−	0.461160i	$-0.847433\pi$
$761$	−929.612	+	1610.13i	−0.0442817	+	0.0766982i	0.843035	+	0.537859i	$0.180767\pi$
$762$	15406.8			0.732455
$763$	−6914.57	−	1200.22i	−0.328079	−	0.0569475i
$764$	−12254.3			−0.580297
$765$	−28339.0	+	49084.5i	−1.33934	+	2.31981i
$766$	−5343.50	−	9255.22i	−0.252048	−	0.436560i
$767$	3446.44	+	5969.41i	0.162247	+	0.281021i
$768$	−17970.1	+	31125.2i	−0.844324	+	1.46241i
$769$	−10110.2			−0.474100			−0.237050	−	0.971497i	$-0.576180\pi$
$769$	−10110.2			−0.474100			−0.237050	+	0.971497i	$0.576180\pi$
$770$	−7391.28	−	20140.1i	−0.345926	−	0.942597i
$771$	44313.5			2.06993
$772$	−1136.18	+	1967.93i	−0.0529692	+	0.0917453i
$773$	2899.34	+	5021.80i	0.134905	+	0.233663i	0.925561	−	0.378598i	$-0.123594\pi$
$773$	2899.34	+	5021.80i	0.134905	+	0.233663i	−0.790656	+	0.612261i	$0.790260\pi$
$774$	−7459.95	−	12921.0i	−0.346437	−	0.600047i
$775$	25499.1	−	44165.7i	1.18187	−	2.04707i
$776$	−15434.8			−0.714017
$777$	−28634.1	+	34310.2i	−1.32206	+	1.58413i
$778$	−4711.60			−0.217120
$779$	3663.64	−	6345.60i	0.168502	−	0.291855i
$780$	−7444.09	−	12893.5i	−0.341720	−	0.591876i
$781$	5838.26	+	10112.2i	0.267490	+	0.463306i
$782$	1198.94	−	2076.62i	0.0548259	−	0.0949612i
$783$	−39971.7			−1.82436
$784$	−1252.91	−	448.471i	−0.0570752	−	0.0204296i
$785$	−64744.1			−2.94372
$786$	19795.1	−	34286.1i	0.898305	−	1.55591i
$787$	−15269.5	−	26447.5i	−0.691611	−	1.19791i	−0.971310	−	0.237818i	$-0.923568\pi$
$787$	−15269.5	−	26447.5i	−0.691611	−	1.19791i	0.279699	−	0.960088i	$-0.409765\pi$
$788$	10388.0	+	17992.5i	0.469615	+	0.813397i
$789$	−2913.76	+	5046.78i	−0.131474	+	0.227719i
$790$	11368.4			0.511985
$791$	8285.74	−	9928.20i	0.372449	−	0.446279i
$792$	30706.8			1.37767
$793$	−1461.91	+	2532.10i	−0.0654652	+	0.113389i
$794$	11166.7	+	19341.2i	0.499106	+	0.864478i
$795$	−10085.3	−	17468.2i	−0.449921	−	0.779287i
$796$	2795.48	−	4841.91i	0.124476	−	0.215599i
$797$	−38360.4			−1.70489			−0.852444	−	0.522818i	$-0.824881\pi$
$797$	−38360.4			−1.70489			−0.852444	+	0.522818i	$0.824881\pi$
$798$	8150.30	+	22208.3i	0.361551	+	0.985170i
$799$	27780.2			1.23003
$800$	−30771.5	+	53297.8i	−1.35992	+	2.35545i
$801$	−33671.5	−	58320.7i	−1.48530	−	2.57261i
$802$	−649.078	−	1124.24i	−0.0285783	−	0.0494990i
$803$	−5311.09	+	9199.07i	−0.233405	+	0.404269i
$804$	−2975.07			−0.130501
$805$	−9120.80	−	1583.18i	−0.399337	−	0.0693163i
$806$	4532.79			0.198090
$807$	24554.5	−	42529.6i	1.07108	−	1.85516i
$808$	11505.4	+	19927.9i	0.500937	+	0.867649i
$809$	−3232.59	−	5599.02i	−0.140484	−	0.243326i	0.787195	−	0.616705i	$-0.211533\pi$
$809$	−3232.59	−	5599.02i	−0.140484	−	0.243326i	−0.927679	+	0.373378i	$0.878199\pi$
$810$	1932.45	−	3347.10i	0.0838263	−	0.145191i
$811$	22923.4			0.992540			0.496270	−	0.868168i	$-0.334703\pi$
$811$	22923.4			0.992540			0.496270	+	0.868168i	$0.334703\pi$
$812$	−22183.6	−	3850.60i	−0.958734	−	0.166416i
$813$	−3492.13			−0.150645
$814$	−7564.56	+	13102.2i	−0.325722	+	0.564167i
$815$	−17483.8	−	30282.8i	−0.751448	−	1.30155i
$816$	950.025	+	1645.49i	0.0407568	+	0.0705928i
$817$	−7558.99	+	13092.6i	−0.323691	+	0.560649i
$818$	7088.63			0.302993
$819$	4927.00	+	13425.3i	0.210212	+	0.572794i
$820$	−9062.07			−0.385928
$821$	−3557.22	+	6161.29i	−0.151215	+	0.261913i	−0.931675	−	0.363294i	$-0.881652\pi$
$821$	−3557.22	+	6161.29i	−0.151215	+	0.261913i	0.780459	+	0.625207i	$0.214985\pi$
$822$	−4074.80	−	7057.76i	−0.172901	−	0.299474i
$823$	−14248.9	−	24679.9i	−0.603507	−	1.04530i	−0.992286	−	0.123974i	$-0.960436\pi$
$823$	−14248.9	−	24679.9i	−0.603507	−	1.04530i	0.388779	−	0.921331i	$-0.372897\pi$
$824$	−5137.50	+	8898.41i	−0.217200	+	0.376202i
$825$	86956.3			3.66961
$826$	−8679.23	+	10399.7i	−0.365604	+	0.438077i
$827$	5663.26			0.238127			0.119063	−	0.992887i	$-0.462011\pi$
$827$	5663.26			0.238127			0.119063	+	0.992887i	$0.462011\pi$
$828$	2459.86	−	4260.59i	0.103244	−	0.178824i
$829$	7366.66	+	12759.4i	0.308630	+	0.534563i	0.978063	−	0.208309i	$-0.0667961\pi$
$829$	7366.66	+	12759.4i	0.308630	+	0.534563i	−0.669433	+	0.742873i	$0.733463\pi$
$830$	19859.2	+	34397.1i	0.830508	+	1.43848i
$831$	27815.1	−	48177.2i	1.16113	−	2.01113i
$832$	−5999.42			−0.249991
$833$	15068.4	−	12781.4i	0.626756	−	0.531632i
$834$	33216.4			1.37912
$835$	−3233.64	+	5600.82i	−0.134018	+	0.232125i
$836$	−5776.41	−	10005.0i	−0.238973	−	0.413913i
$837$	−11405.9	−	19755.5i	−0.471021	−	0.815832i
$838$	−12305.5	+	21313.7i	−0.507262	+	0.878604i
$839$	6042.63			0.248647			0.124323	−	0.992242i	$-0.460324\pi$
$839$	6042.63			0.248647			0.124323	+	0.992242i	$0.460324\pi$
$840$	50488.9	−	60497.2i	2.07385	−	2.48494i
$841$	41819.7			1.71469
$842$	5490.96	−	9510.62i	0.224740	−	0.389261i
$843$	38542.0	+	66756.7i	1.57468	+	2.72743i
$844$	−2825.26	−	4893.49i	−0.115224	−	0.199574i
$845$	−20711.8	+	35873.9i	−0.843205	+	1.46047i
$846$	−39511.9			−1.60573
$847$	2957.77	+	8059.46i	0.119988	+	0.326950i
$848$	−423.576			−0.0171529
$849$	3209.82	−	5559.57i	0.129754	−	0.224740i
$850$	18103.4	+	31355.9i	0.730518	+	1.26529i
$851$	3264.10	+	5653.58i	0.131483	+	0.227735i
$852$	−7962.01	+	13790.6i	−0.320157	+	0.554528i
$853$	−2550.44			−0.102375			−0.0511873	−	0.998689i	$-0.516301\pi$
$853$	−2550.44			−0.102375			−0.0511873	+	0.998689i	$0.516301\pi$
$854$	−5661.10	−	982.646i	−0.226837	−	0.0393741i
$855$	−81683.5			−3.26727
$856$	−8829.07	+	15292.4i	−0.352537	+	0.610611i
$857$	−6612.95	−	11454.0i	−0.263587	−	0.456546i	0.703605	−	0.710591i	$-0.251572\pi$
$857$	−6612.95	−	11454.0i	−0.263587	−	0.456546i	−0.967192	+	0.254045i	$0.918239\pi$
$858$	3864.41	+	6693.35i	0.153763	+	0.266325i
$859$	−15924.7	+	27582.5i	−0.632532	+	1.09558i	0.354500	+	0.935056i	$0.384651\pi$
$859$	−15924.7	+	27582.5i	−0.632532	+	1.09558i	−0.987032	+	0.160522i	$0.948682\pi$
$860$	18697.3			0.741364
$861$	13691.1	+	2376.49i	0.541919	+	0.0940656i
$862$	−3555.90			−0.140504
$863$	−4772.78	+	8266.69i	−0.188259	+	0.326073i	−0.944670	−	0.328023i	$-0.893618\pi$
$863$	−4772.78	+	8266.69i	−0.188259	+	0.326073i	0.756411	+	0.654096i	$0.226951\pi$
$864$	13764.3	+	23840.4i	0.541979	+	0.938734i
$865$	−8464.78	−	14661.4i	−0.332730	−	0.576305i
$866$	8351.16	−	14464.6i	0.327695	−	0.567585i
$867$	13555.3			0.530982
$868$	−4426.94	−	12062.7i	−0.173111	−	0.471701i
$869$	8513.14			0.332323
$870$	−43017.5	+	74508.5i	−1.67636	+	2.90353i
$871$	−631.660	−	1094.07i	−0.0245729	−	0.0425615i
$872$	−4363.22	−	7557.33i	−0.169447	−	0.293490i
$873$	−15171.8	+	26278.3i	−0.588186	+	1.01877i
$874$	3455.78			0.133745
$875$	57326.1	−	68689.8i	2.21483	−	2.65387i
$876$	−14486.1			−0.558722
$877$	−14090.2	+	24404.9i	−0.542522	+	0.939676i	0.456236	+	0.889859i	$0.349197\pi$
$877$	−14090.2	+	24404.9i	−0.542522	+	0.939676i	−0.998758	+	0.0498171i	$0.984136\pi$
$878$	2134.27	+	3696.67i	0.0820368	+	0.142092i
$879$	7799.59	+	13509.3i	0.299287	+	0.518381i
$880$	1241.66	−	2150.61i	0.0475639	−	0.0823831i
$881$	20667.4			0.790354			0.395177	−	0.918605i	$-0.370683\pi$
$881$	20667.4			0.790354			0.395177	+	0.918605i	$0.370683\pi$
$882$	−21431.8	+	18179.1i	−0.818193	+	0.694015i
$883$	10477.9			0.399329			0.199665	−	0.979864i	$-0.436015\pi$
$883$	10477.9			0.399329			0.199665	+	0.979864i	$0.436015\pi$
$884$	2321.09	−	4020.25i	0.0883107	−	0.152959i
$885$	−37332.4	−	64661.6i	−1.41798	−	2.45602i
$886$	10775.2	+	18663.2i	0.408579	+	0.707679i
$887$	8030.09	−	13908.5i	0.303973	−	0.526496i	−0.673059	−	0.739589i	$-0.735020\pi$
$887$	8030.09	−	13908.5i	0.303973	−	0.526496i	0.977032	+	0.213092i	$0.0683534\pi$
$888$	−55568.2			−2.09994
$889$	11883.1	−	14238.7i	0.448309	−	0.537176i
$890$	−58503.8			−2.20343
$891$	1447.10	−	2506.46i	0.0544106	−	0.0942419i
$892$	14224.4	+	24637.4i	0.533934	+	0.924801i
$893$	20018.2	+	34672.6i	0.750151	+	1.29930i
$894$	19440.1	−	33671.3i	0.727266	−	1.25966i
$895$	−48800.8			−1.82260
$896$	4983.89	+	13580.3i	0.185826	+	0.506347i
$897$	3334.97			0.124138
$898$	3804.75	−	6590.02i	0.141388	−	0.244891i
$899$	18892.5	+	32722.8i	0.700892	+	1.21398i
$900$	37142.6	+	64332.9i	1.37565	+	2.38270i
$901$	3144.62	−	5446.63i	0.116273	−	0.201391i
$902$	4704.34			0.173656
$903$	−28248.2	−	4903.28i	−1.04102	−	0.180699i
$904$	16079.6			0.591591
$905$	−14576.6	+	25247.4i	−0.535407	+	0.927351i
$906$	−15968.3	−	27657.9i	−0.585552	−	1.01421i
$907$	−16671.1	−	28875.2i	−0.610313	−	1.05709i	−0.991187	−	0.132467i	$-0.957710\pi$
$907$	−16671.1	−	28875.2i	−0.610313	−	1.05709i	0.380874	−	0.924627i	$-0.375623\pi$
$908$	4530.83	−	7847.62i	0.165596	−	0.286820i
$909$	45237.2			1.65063
$910$	12240.7	+	2124.73i	0.445908	+	0.0774002i
$911$	35651.8			1.29659			0.648296	−	0.761388i	$-0.275482\pi$
$911$	35651.8			1.29659			0.648296	+	0.761388i	$0.275482\pi$
$912$	−1369.16	+	2371.46i	−0.0497122	+	0.0861040i
$913$	14871.4	+	25758.1i	0.539072	+	0.933700i
$914$	3702.85	+	6413.52i	0.134004	+	0.232101i
$915$	15835.6	−	27428.1i	0.572142	−	0.990978i
$916$	−13495.7			−0.486803
$917$	−16418.8	−	44738.7i	−0.591272	−	1.61113i
$918$	16195.5			0.582276
$919$	4075.06	−	7058.21i	0.146272	−	0.253350i	−0.783575	−	0.621297i	$-0.786606\pi$
$919$	4075.06	−	7058.21i	0.146272	−	0.253350i	0.929847	+	0.367947i	$0.119939\pi$
$920$	−5755.40	−	9968.64i	−0.206250	−	0.357235i
$921$	−35914.4	−	62205.6i	−1.28493	−	2.22556i
$922$	10961.7	−	18986.3i	0.391546	−	0.678178i
$923$	−6761.89			−0.241138
$924$	14038.3	−	16821.1i	0.499811	−	0.598888i
$925$	−98572.7			−3.50384
$926$	2287.42	−	3961.93i	0.0811764	−	0.140602i
$927$	10099.9	+	17493.5i	0.357847	+	0.619809i
$928$	−22799.0	−	39489.0i	−0.806479	−	1.39686i
$929$	−17043.4	+	29520.1i	−0.601913	+	1.04254i	0.390618	+	0.920553i	$0.372261\pi$
$929$	−17043.4	+	29520.1i	−0.601913	+	1.04254i	−0.992531	+	0.121991i	$0.961072\pi$
$930$	−49099.9			−1.73124
$931$	26810.7	+	9596.68i	0.943808	+	0.337828i
$932$	16427.5			0.577363
$933$	7850.25	−	13597.0i	0.275461	−	0.477113i
$934$	−11951.0	−	20699.8i	−0.418682	−	0.725179i
$935$	18436.1	+	31932.2i	0.644838	+	1.11689i
$936$	−8891.16	+	15399.9i	−0.310488	+	0.537781i
$937$	−40324.6			−1.40592			−0.702959	−	0.711230i	$-0.748138\pi$
$937$	−40324.6			−1.40592			−0.702959	+	0.711230i	$0.748138\pi$
$938$	1590.72	−	1906.04i	0.0553719	−	0.0663481i
$939$	11693.6			0.406395
$940$	24757.7	−	42881.7i	0.859051	−	1.48792i
$941$	−5595.75	−	9692.12i	−0.193853	−	0.335764i	0.752671	−	0.658397i	$-0.228765\pi$
$941$	−5595.75	−	9692.12i	−0.193853	−	0.335764i	−0.946524	+	0.322633i	$0.895432\pi$
$942$	22918.2	+	39695.5i	0.792691	+	1.37298i
$943$	1014.96	−	1757.96i	0.0350494	−	0.0607073i
$944$	−1567.94			−0.0540595
$945$	−21541.0	−	58696.0i	−0.741513	−	2.02051i
$946$	−9706.22			−0.333590
$947$	15188.2	−	26306.8i	0.521173	−	0.902698i	−0.478524	−	0.878075i	$-0.658828\pi$
$947$	15188.2	−	26306.8i	0.521173	−	0.902698i	0.999697	−	0.0246237i	$-0.00783877\pi$
$948$	5804.95	+	10054.5i	0.198878	+	0.344466i
$949$	−3075.66	−	5327.19i	−0.105205	−	0.182221i
$950$	−26090.3	+	45189.8i	−0.891033	+	1.54331i
$951$	−93920.1			−3.20249
$952$	24207.3	+	4201.87i	0.824121	+	0.143050i
$953$	18316.4			0.622588			0.311294	−	0.950314i	$-0.399238\pi$
$953$	18316.4			0.622588			0.311294	+	0.950314i	$0.399238\pi$
$954$	−4472.60	+	7746.77i	−0.151788	+	0.262905i
$955$	28183.2	+	48814.8i	0.954961	+	1.65404i
$956$	3459.41	+	5991.88i	0.117035	+	0.202710i
$957$	−32213.5	+	55795.4i	−1.08810	+	1.88465i
$958$	−5464.61			−0.184294
$959$	−9665.49	−	1677.72i	−0.325459	−	0.0564927i
$960$	64986.7			2.18483
$961$	4113.59	−	7124.94i	0.138081	−	0.239164i
$962$	−4380.65	−	7587.50i	−0.146817	−	0.254294i
$963$	17357.2	+	30063.6i	0.580818	+	1.00601i
$964$	−640.791	+	1109.88i	−0.0214092	+	0.0370819i
$965$	10452.2			0.348673
$966$	2257.92	+	6152.50i	0.0752044	+	0.204921i
$967$	8602.55			0.286080			0.143040	−	0.989717i	$-0.454312\pi$
$967$	8602.55			0.286080			0.143040	+	0.989717i	$0.454312\pi$
$968$	−5337.52	+	9244.86i	−0.177226	+	0.306964i
$969$	−20329.3	−	35211.3i	−0.673963	−	1.16734i
$970$	13180.4	+	22829.1i	0.436285	+	0.755668i
$971$	26695.5	−	46238.0i	0.882286	−	1.52816i	0.0334932	−	0.999439i	$-0.489337\pi$
$971$	26695.5	−	46238.0i	0.882286	−	1.52816i	0.848793	−	0.528725i	$-0.177330\pi$
$972$	−15869.7			−0.523685
$973$	25619.4	−	30697.9i	0.844111	−	1.01144i
$974$	−4639.79			−0.152637
$975$	−25178.2	+	43610.0i	−0.827025	+	1.43245i
$976$	−332.544	−	575.983i	−0.0109062	−	0.0188901i
$977$	−3692.85	−	6396.20i	−0.120926	−	0.209450i	0.799207	−	0.601056i	$-0.205253\pi$
$977$	−3692.85	−	6396.20i	−0.120926	−	0.209450i	−0.920133	+	0.391606i	$0.871920\pi$
$978$	−12377.9	+	21439.1i	−0.404704	+	0.700967i
$979$	−43810.3			−1.43022
$980$	−6300.53	−	34650.4i	−0.205370	−	1.12946i
$981$	−17155.5			−0.558340
$982$	6446.77	−	11166.1i	0.209496	−	0.362857i
$983$	−8712.51	−	15090.5i	−0.282692	−	0.489636i	0.689355	−	0.724423i	$-0.257894\pi$
$983$	−8712.51	−	15090.5i	−0.282692	−	0.489636i	−0.972047	+	0.234787i	$0.924561\pi$
$984$	8639.36	+	14963.8i	0.279891	+	0.484785i
$985$	47781.7	−	82760.3i	1.54564	−	2.67712i
$986$	−26826.0			−0.866443
$987$	−48649.9	+	58293.7i	−1.56894	+	1.87995i
$988$	6690.25			0.215430
$989$	−2094.11	+	3627.10i	−0.0673294	+	0.116618i
$990$	−26221.7	−	45417.3i	−0.841798	−	1.45804i
$991$	−21263.7	−	36829.9i	−0.681600	−	1.18057i	−0.974493	−	0.224420i	$-0.927951\pi$
$991$	−21263.7	−	36829.9i	−0.681600	−	1.18057i	0.292893	−	0.956145i	$-0.405382\pi$
$992$	13011.3	−	22536.2i	0.416441	−	0.721296i
$993$	43217.9			1.38115
$994$	−4578.10	−	12474.6i	−0.146085	−	0.398059i
$995$	−25716.8			−0.819374
$996$	−20281.1	+	35127.9i	−0.645213	+	1.11754i
$997$	−3308.74	−	5730.91i	−0.105104	−	0.182046i	0.808677	−	0.588254i	$-0.200184\pi$
$997$	−3308.74	−	5730.91i	−0.105104	−	0.182046i	−0.913781	+	0.406208i	$0.866851\pi$
$998$	5714.83	+	9898.38i	0.181262	+	0.313956i
$999$	−22046.0	+	38184.9i	−0.698204	+	1.20932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.e.b.93.9	✓	44
7.2	even	3		1127.4.a.j.1.14		22
7.4	even	3	inner	161.4.e.b.116.9	yes	44
7.5	odd	6		1127.4.a.m.1.14		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.e.b.93.9	✓	44	1.1	even	1	trivial
161.4.e.b.116.9	yes	44	7.4	even	3	inner
1127.4.a.j.1.14		22	7.2	even	3
1127.4.a.m.1.14		22	7.5	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.904891 + 1.56732i) q^{2} +(4.25067 + 7.36238i) q^{3} +(2.36235 + 4.09170i) q^{4} +(10.8661 - 18.8206i) q^{5} -15.3856 q^{6} +(-11.8667 + 14.2190i) q^{7} -23.0289 q^{8} +(-22.6364 + 39.2075i) q^{9} +(19.6653 + 34.0613i) q^{10} +(14.7263 + 25.5066i) q^{11} +(-20.0831 + 34.7850i) q^{12} -17.0560 q^{13} +(-11.5477 - 31.4656i) q^{14} +184.753 q^{15} +(1.93988 - 3.35997i) q^{16} +(28.8033 + 49.8887i) q^{17} +(-40.9670 - 70.9570i) q^{18} +(-41.5109 + 71.8990i) q^{19} +102.678 q^{20} +(-155.128 - 26.9268i) q^{21} -53.3026 q^{22} +(-11.5000 + 19.9186i) q^{23} +(-97.8884 - 169.548i) q^{24} +(-173.645 - 300.761i) q^{25} +(15.4338 - 26.7321i) q^{26} -155.344 q^{27} +(-86.2134 - 14.9648i) q^{28} +257.310 q^{29} +(-167.181 + 289.567i) q^{30} +(73.4231 + 127.173i) q^{31} +(-88.6049 - 153.468i) q^{32} +(-125.193 + 216.841i) q^{33} -104.255 q^{34} +(138.666 + 377.845i) q^{35} -213.900 q^{36} +(141.917 - 245.808i) q^{37} +(-75.1256 - 130.121i) q^{38} +(-72.4994 - 125.573i) q^{39} +(-250.235 + 433.419i) q^{40} -88.2572 q^{41} +(182.576 - 218.768i) q^{42} +182.096 q^{43} +(-69.5770 + 120.511i) q^{44} +(491.940 + 852.065i) q^{45} +(-20.8125 - 36.0483i) q^{46} +(241.120 - 417.632i) q^{47} +32.9832 q^{48} +(-61.3620 - 337.467i) q^{49} +628.517 q^{50} +(-244.867 + 424.121i) q^{51} +(-40.2921 - 69.7880i) q^{52} +(-54.5878 - 94.5488i) q^{53} +(140.570 - 243.474i) q^{54} +640.068 q^{55} +(273.278 - 327.449i) q^{56} -705.797 q^{57} +(-232.838 + 403.287i) q^{58} +(-202.067 - 349.989i) q^{59} +(436.451 + 755.955i) q^{60} +(85.7124 - 148.458i) q^{61} -265.760 q^{62} +(-288.872 - 787.133i) q^{63} +351.749 q^{64} +(-185.332 + 321.005i) q^{65} +(-226.572 - 392.434i) q^{66} +(37.0345 + 64.1457i) q^{67} +(-136.087 + 235.709i) q^{68} -195.531 q^{69} +(-717.681 - 124.574i) q^{70} +396.453 q^{71} +(521.293 - 902.905i) q^{72} +(180.327 + 312.336i) q^{73} +(256.839 + 444.859i) q^{74} +(1476.21 - 2556.87i) q^{75} -392.252 q^{76} +(-537.432 - 93.2867i) q^{77} +262.416 q^{78} +(144.523 - 250.321i) q^{79} +(-42.1579 - 73.0197i) q^{80} +(-49.1335 - 85.1017i) q^{81} +(79.8631 - 138.327i) q^{82} +1009.86 q^{83} +(-256.288 - 698.346i) q^{84} +1251.92 q^{85} +(-164.777 + 285.403i) q^{86} +(1093.74 + 1894.42i) q^{87} +(-339.130 - 587.390i) q^{88} +(-743.744 + 1288.20i) q^{89} -1780.61 q^{90} +(202.398 - 242.520i) q^{91} -108.668 q^{92} +(-624.196 + 1081.14i) q^{93} +(436.375 + 755.823i) q^{94} +(902.124 + 1562.52i) q^{95} +(753.261 - 1304.69i) q^{96} +670.236 q^{97} +(584.443 + 209.197i) q^{98} -1333.40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 18 q^{3} - 88 q^{4} + 20 q^{5} - 72 q^{6} - 44 q^{7} + 42 q^{8} - 126 q^{9} + 200 q^{10} - 20 q^{11} + 161 q^{12} - 392 q^{13} - 200 q^{14} + 40 q^{15} - 324 q^{16} + 242 q^{17} - 85 q^{18} + 128 q^{19}+ \cdots + 7140 q^{99}+O(q^{100}) \) 44 * q + 18 * q^3 - 88 * q^4 + 20 * q^5 - 72 * q^6 - 44 * q^7 + 42 * q^8 - 126 * q^9 + 200 * q^10 - 20 * q^11 + 161 * q^12 - 392 * q^13 - 200 * q^14 + 40 * q^15 - 324 * q^16 + 242 * q^17 - 85 * q^18 + 128 * q^19 - 92 * q^20 + 82 * q^21 + 28 * q^22 - 506 * q^23 + 66 * q^24 - 668 * q^25 + 340 * q^26 - 756 * q^27 + 760 * q^28 - 380 * q^29 - 493 * q^30 + 508 * q^31 + 487 * q^32 + 1240 * q^33 - 832 * q^34 + 1436 * q^35 - 940 * q^36 + 102 * q^37 + 423 * q^38 + 520 * q^39 + 2048 * q^40 - 1840 * q^41 + 441 * q^42 - 1456 * q^43 - 1132 * q^44 + 570 * q^45 + 1384 * q^47 - 2646 * q^48 + 638 * q^49 - 1950 * q^50 - 1688 * q^51 + 1892 * q^52 + 480 * q^53 + 1695 * q^54 - 2508 * q^55 + 2049 * q^56 - 604 * q^57 - 791 * q^58 + 650 * q^59 + 2490 * q^60 + 960 * q^61 - 5108 * q^62 + 1868 * q^63 + 7582 * q^64 - 800 * q^65 - 1221 * q^66 + 2136 * q^67 + 2290 * q^68 - 828 * q^69 - 1717 * q^70 - 272 * q^71 - 4114 * q^72 + 2562 * q^73 + 1928 * q^74 + 1820 * q^75 - 9290 * q^76 + 100 * q^77 + 5210 * q^78 - 790 * q^79 - 2248 * q^80 + 506 * q^81 + 3838 * q^82 - 4052 * q^83 - 2133 * q^84 + 2784 * q^85 - 3419 * q^86 + 3340 * q^87 + 5101 * q^88 + 2618 * q^89 - 13560 * q^90 - 2914 * q^91 + 4048 * q^92 - 206 * q^93 + 3516 * q^94 + 4410 * q^95 + 3818 * q^96 - 10316 * q^97 + 1437 * q^98 + 7140 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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