LMFDB - Embedded newform 143.4.h.b.92.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [143,4,Mod(14,143)] 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("143.14"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(143, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			92.17
Character	$\chi$	$=$	143.92
Dual form			143.4.h.b.14.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.35922 + 2.44061i) q^{2} +(-2.65195 + 8.16188i) q^{3} +(2.85561 + 8.78865i) q^{4} +(-4.97791 + 3.61667i) q^{5} +(-28.8285 + 20.9451i) q^{6} +(-0.679316 - 2.09072i) q^{7} +(-1.59225 + 4.90045i) q^{8} +(-37.7399 - 27.4196i) q^{9} -25.5488 q^{10} +(19.1661 + 31.0429i) q^{11} -79.3048 q^{12} +(10.5172 + 7.64121i) q^{13} +(2.82067 - 8.68113i) q^{14} +(-16.3176 - 50.2204i) q^{15} +(42.4998 - 30.8779i) q^{16} +(-3.50470 + 2.54631i) q^{17} +(-59.8557 - 184.217i) q^{18} +(-8.21001 + 25.2678i) q^{19} +(-46.0006 - 33.4214i) q^{20} +18.8657 q^{21} +(-11.3807 + 151.057i) q^{22} +0.674151 q^{23} +(-35.7743 - 25.9916i) q^{24} +(-26.9278 + 82.8752i) q^{25} +(16.6804 + 51.3370i) q^{26} +(136.422 - 99.1162i) q^{27} +(16.4347 - 11.9405i) q^{28} +(24.9474 + 76.7802i) q^{29} +(67.7542 - 208.526i) q^{30} +(-235.385 - 171.017i) q^{31} +259.348 q^{32} +(-304.196 + 74.1069i) q^{33} -17.9876 q^{34} +(10.9430 + 7.95056i) q^{35} +(133.211 - 409.983i) q^{36} +(103.994 + 320.062i) q^{37} +(-89.2482 + 64.8426i) q^{38} +(-90.2578 + 65.5761i) q^{39} +(-9.79720 - 30.1527i) q^{40} +(-50.1702 + 154.408i) q^{41} +(63.3740 + 46.0439i) q^{42} +258.374 q^{43} +(-218.094 + 257.090i) q^{44} +287.034 q^{45} +(2.26462 + 1.64534i) q^{46} +(25.8516 - 79.5631i) q^{47} +(139.314 + 428.764i) q^{48} +(273.583 - 198.770i) q^{49} +(-292.722 + 212.675i) q^{50} +(-11.4884 - 35.3576i) q^{51} +(-37.1229 + 114.252i) q^{52} +(205.091 + 149.008i) q^{53} +700.175 q^{54} +(-207.679 - 85.2115i) q^{55} +11.3271 q^{56} +(-184.460 - 134.018i) q^{57} +(-103.587 + 318.808i) q^{58} +(-7.74232 - 23.8284i) q^{59} +(394.773 - 286.819i) q^{60} +(-350.827 + 254.891i) q^{61} +(-373.322 - 1148.97i) q^{62} +(-31.6895 + 97.5301i) q^{63} +(531.208 + 385.945i) q^{64} -79.9895 q^{65} +(-1202.73 - 493.484i) q^{66} +852.622 q^{67} +(-32.3867 - 23.5303i) q^{68} +(-1.78782 + 5.50234i) q^{69} +(17.3557 + 53.4153i) q^{70} +(365.175 - 265.315i) q^{71} +(194.460 - 141.284i) q^{72} +(-150.432 - 462.981i) q^{73} +(-431.808 + 1328.97i) q^{74} +(-605.006 - 439.562i) q^{75} -245.515 q^{76} +(51.8822 - 61.1588i) q^{77} -463.241 q^{78} +(-105.201 - 76.4327i) q^{79} +(-99.8851 + 307.415i) q^{80} +(57.9751 + 178.429i) q^{81} +(-545.383 + 396.244i) q^{82} +(447.485 - 325.117i) q^{83} +(53.8730 + 165.804i) q^{84} +(8.23692 - 25.3506i) q^{85} +(867.934 + 630.591i) q^{86} -692.830 q^{87} +(-182.642 + 44.4943i) q^{88} +1549.44 q^{89} +(964.208 + 700.538i) q^{90} +(8.83111 - 27.1794i) q^{91} +(1.92511 + 5.92488i) q^{92} +(2020.05 - 1467.65i) q^{93} +(281.024 - 204.176i) q^{94} +(-50.5165 - 155.474i) q^{95} +(-687.779 + 2116.77i) q^{96} +(-219.150 - 159.222i) q^{97} +1404.15 q^{98} +(127.859 - 1697.08i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 4 q^{2} - 12 q^{3} - 148 q^{4} - 16 q^{5} + 77 q^{6} + 56 q^{7} - 34 q^{8} - 241 q^{9} + 60 q^{10} - 47 q^{11} + 244 q^{12} + 247 q^{13} + 117 q^{14} - 2 q^{15} + 212 q^{16} - 344 q^{17} - 461 q^{18}+ \cdots - 11439 q^{99}+O(q^{100}) $ 76 * q + 4 * q^2 - 12 * q^3 - 148 * q^4 - 16 * q^5 + 77 * q^6 + 56 * q^7 - 34 * q^8 - 241 * q^9 + 60 * q^10 - 47 * q^11 + 244 * q^12 + 247 * q^13 + 117 * q^14 - 2 * q^15 + 212 * q^16 - 344 * q^17 - 461 * q^18 - 59 * q^19 + 55 * q^20 - 296 * q^21 - 76 * q^22 + 1680 * q^23 + 784 * q^24 - 89 * q^25 + 13 * q^26 - 309 * q^27 - 654 * q^28 - 306 * q^29 + 606 * q^30 + 344 * q^31 - 2408 * q^32 + 1265 * q^33 - 116 * q^34 + 934 * q^35 - 3571 * q^36 + 188 * q^37 - 9 * q^38 + 91 * q^39 - 1803 * q^40 + 1518 * q^41 + 1734 * q^42 - 966 * q^43 + 1513 * q^44 + 2272 * q^45 - 165 * q^46 - 2146 * q^47 + 2320 * q^48 - 2085 * q^49 - 71 * q^50 - 501 * q^51 + 1924 * q^52 + 814 * q^53 - 6546 * q^54 - 1924 * q^55 + 6538 * q^56 - 1099 * q^57 - 4169 * q^58 - 41 * q^59 - 2812 * q^60 + 1788 * q^61 - 3931 * q^62 + 4980 * q^63 + 4256 * q^64 - 1352 * q^65 - 1543 * q^66 + 9878 * q^67 + 648 * q^68 - 2994 * q^69 + 6094 * q^70 - 612 * q^71 + 2965 * q^72 + 3436 * q^73 + 2616 * q^74 + 5089 * q^75 - 6632 * q^76 - 2604 * q^77 + 2704 * q^78 - 7688 * q^79 - 11093 * q^80 - 3972 * q^81 + 1076 * q^82 + 2007 * q^83 - 5729 * q^84 - 2128 * q^85 + 2433 * q^86 + 1812 * q^87 - 9006 * q^88 + 7454 * q^89 - 2204 * q^90 - 728 * q^91 + 2143 * q^92 - 8158 * q^93 + 4055 * q^94 + 824 * q^95 + 811 * q^96 + 5711 * q^97 - 4086 * q^98 - 11439 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	3.35922	+	2.44061i	1.18766	+	0.862887i	0.993015	−	0.117986i	$-0.0376438\pi$
$2$	3.35922	+	2.44061i	1.18766	+	0.862887i	0.194647	+	0.980873i	$0.437644\pi$
$3$	−2.65195	+	8.16188i	−0.510369	+	1.57075i	0.281185	+	0.959654i	$0.409273\pi$
$3$	−2.65195	+	8.16188i	−0.510369	+	1.57075i	−0.791553	+	0.611100i	$0.790727\pi$
$4$	2.85561	+	8.78865i	0.356951	+	1.09858i
$5$	−4.97791	+	3.61667i	−0.445238	+	0.323484i	−0.787713	−	0.616043i	$-0.788735\pi$
$5$	−4.97791	+	3.61667i	−0.445238	+	0.323484i	0.342475	+	0.939527i	$0.388735\pi$
$6$	−28.8285	+	20.9451i	−1.96153	+	1.42513i
$7$	−0.679316	−	2.09072i	−0.0366796	−	0.112888i	0.931040	−	0.364916i	$-0.118902\pi$
$7$	−0.679316	−	2.09072i	−0.0366796	−	0.112888i	−0.967720	+	0.252028i	$0.918902\pi$
$8$	−1.59225	+	4.90045i	−0.0703683	+	0.216571i
$9$	−37.7399	−	27.4196i	−1.39777	−	1.01554i
$10$	−25.5488			−0.807923
$11$	19.1661	+	31.0429i	0.525345	+	0.850890i
$11$	19.1661	+	31.0429i	0.525345	+	0.850890i
$12$	−79.3048			−1.90778
$13$	10.5172	+	7.64121i	0.224381	+	0.163022i
$13$	10.5172	+	7.64121i	0.224381	+	0.163022i
$14$	2.82067	−	8.68113i	0.0538468	−	0.165724i
$15$	−16.3176	−	50.2204i	−0.280879	−	0.864456i
$16$	42.4998	−	30.8779i	0.664059	−	0.482467i
$17$	−3.50470	+	2.54631i	−0.0500008	+	0.0363277i	−0.612505	−	0.790467i	$-0.709838\pi$
$17$	−3.50470	+	2.54631i	−0.0500008	+	0.0363277i	0.562504	+	0.826794i	$0.309838\pi$
$18$	−59.8557	−	184.217i	−0.783785	−	2.41224i
$19$	−8.21001	+	25.2678i	−0.0991319	+	0.305096i	−0.988308	−	0.152468i	$-0.951278\pi$
$19$	−8.21001	+	25.2678i	−0.0991319	+	0.305096i	0.889177	+	0.457564i	$0.151278\pi$
$20$	−46.0006	−	33.4214i	−0.514302	−	0.373662i
$21$	18.8657			0.196040
$22$	−11.3807	+	151.057i	−0.110290	+	1.46388i
$23$	0.674151			0.00611175			0.00305587	−	0.999995i	$-0.499027\pi$
$23$	0.674151			0.00611175			0.00305587	+	0.999995i	$0.499027\pi$
$24$	−35.7743	−	25.9916i	−0.304267	−	0.221063i
$25$	−26.9278	+	82.8752i	−0.215422	+	0.663001i
$26$	16.6804	+	51.3370i	0.125819	+	0.387231i
$27$	136.422	−	99.1162i	0.972384	−	0.706478i
$28$	16.4347	−	11.9405i	0.110924	−	0.0805911i
$29$	24.9474	+	76.7802i	0.159745	+	0.491646i	0.998611	−	0.0526933i	$-0.0167806\pi$
$29$	24.9474	+	76.7802i	0.159745	+	0.491646i	−0.838865	+	0.544339i	$0.816781\pi$
$30$	67.7542	−	208.526i	0.412339	−	1.26905i
$31$	−235.385	−	171.017i	−1.36375	−	0.990824i	−0.998196	−	0.0600345i	$-0.980879\pi$
$31$	−235.385	−	171.017i	−1.36375	−	0.990824i	−0.365556	−	0.930789i	$-0.619121\pi$
$32$	259.348			1.43271
$33$	−304.196	+	74.1069i	−1.60466	+	0.390920i
$34$	−17.9876			−0.0907308
$35$	10.9430	+	7.95056i	0.0528488	+	0.0383969i
$36$	133.211	−	409.983i	0.616719	−	1.89807i
$37$	103.994	+	320.062i	0.462069	+	1.42210i	0.862631	+	0.505834i	$0.168815\pi$
$37$	103.994	+	320.062i	0.462069	+	1.42210i	−0.400561	+	0.916270i	$0.631185\pi$
$38$	−89.2482	+	64.8426i	−0.380999	+	0.276812i
$39$	−90.2578	+	65.5761i	−0.370585	+	0.269246i
$40$	−9.79720	−	30.1527i	−0.0387268	−	0.119189i
$41$	−50.1702	+	154.408i	−0.191104	+	0.588158i	0.808896	+	0.587952i	$0.200066\pi$
$41$	−50.1702	+	154.408i	−0.191104	+	0.588158i	−1.00000		0.000206071i	$0.999934\pi$
$42$	63.3740	+	46.0439i	0.232829	+	0.169160i
$43$	258.374			0.916317			0.458159	−	0.888870i	$-0.348509\pi$
$43$	258.374			0.916317			0.458159	+	0.888870i	$0.348509\pi$
$44$	−218.094	+	257.090i	−0.747249	+	0.880860i
$45$	287.034			0.950855
$46$	2.26462	+	1.64534i	0.00725869	+	0.00527375i
$47$	25.8516	−	79.5631i	0.0802308	−	0.246925i	−0.902893	−	0.429865i	$-0.858561\pi$
$47$	25.8516	−	79.5631i	0.0802308	−	0.246925i	0.983124	+	0.182940i	$0.0585613\pi$
$48$	139.314	+	428.764i	0.418922	+	1.28931i
$49$	273.583	−	198.770i	0.797619	−	0.579504i
$50$	−292.722	+	212.675i	−0.827944	+	0.601537i
$51$	−11.4884	−	35.3576i	−0.0315430	−	0.0970795i
$52$	−37.1229	+	114.252i	−0.0990003	+	0.304692i
$53$	205.091	+	149.008i	0.531537	+	0.386184i	0.820933	−	0.571025i	$-0.193454\pi$
$53$	205.091	+	149.008i	0.531537	+	0.386184i	−0.289395	+	0.957210i	$0.593454\pi$
$54$	700.175			1.76448
$55$	−207.679	−	85.2115i	−0.509153	−	0.208908i
$56$	11.3271			0.0270295
$57$	−184.460	−	134.018i	−0.428638	−	0.311423i
$58$	−103.587	+	318.808i	−0.234511	+	0.721751i
$59$	−7.74232	−	23.8284i	−0.0170841	−	0.0525796i	0.942151	−	0.335189i	$-0.108800\pi$
$59$	−7.74232	−	23.8284i	−0.0170841	−	0.0525796i	−0.959235	+	0.282609i	$0.908800\pi$
$60$	394.773	−	286.819i	0.849415	−	0.617136i
$61$	−350.827	+	254.891i	−0.736374	+	0.535007i	−0.891573	−	0.452876i	$-0.850398\pi$
$61$	−350.827	+	254.891i	−0.736374	+	0.535007i	0.155200	+	0.987883i	$0.450398\pi$
$62$	−373.322	−	1148.97i	−0.764708	−	2.35353i
$63$	−31.6895	+	97.5301i	−0.0633730	+	0.195042i
$64$	531.208	+	385.945i	1.03752	+	0.753800i
$65$	−79.9895			−0.152638
$66$	−1202.73	−	493.484i	−2.24311	−	0.920358i
$67$	852.622			1.55469			0.777346	−	0.629073i	$-0.216565\pi$
$67$	852.622			1.55469			0.777346	+	0.629073i	$0.216565\pi$
$68$	−32.3867	−	23.5303i	−0.0577568	−	0.0419628i
$69$	−1.78782	+	5.50234i	−0.00311925	+	0.00960005i
$70$	17.3557	+	53.4153i	0.0296343	+	0.0912051i
$71$	365.175	−	265.315i	0.610398	−	0.443480i	−0.239157	−	0.970981i	$-0.576871\pi$
$71$	365.175	−	265.315i	0.610398	−	0.443480i	0.849554	+	0.527501i	$0.176871\pi$
$72$	194.460	−	141.284i	0.318297	−	0.231256i
$73$	−150.432	−	462.981i	−0.241187	−	0.742299i	−0.996240	−	0.0866346i	$-0.972389\pi$
$73$	−150.432	−	462.981i	−0.241187	−	0.742299i	0.755053	−	0.655664i	$-0.227611\pi$
$74$	−431.808	+	1328.97i	−0.678333	+	2.08769i
$75$	−605.006	−	439.562i	−0.931467	−	0.676750i
$76$	−245.515			−0.370559
$77$	51.8822	−	61.1588i	0.0767860	−	0.0905155i
$78$	−463.241			−0.672459
$79$	−105.201	−	76.4327i	−0.149823	−	0.108853i	0.510349	−	0.859968i	$-0.329516\pi$
$79$	−105.201	−	76.4327i	−0.149823	−	0.108853i	−0.660171	+	0.751115i	$0.729516\pi$
$80$	−99.8851	+	307.415i	−0.139594	+	0.429625i
$81$	57.9751	+	178.429i	0.0795269	+	0.244759i
$82$	−545.383	+	396.244i	−0.734481	+	0.533632i
$83$	447.485	−	325.117i	0.591782	−	0.429954i	−0.251171	−	0.967943i	$-0.580816\pi$
$83$	447.485	−	325.117i	0.591782	−	0.429954i	0.842952	+	0.537988i	$0.180816\pi$
$84$	53.8730	+	165.804i	0.0699765	+	0.215366i
$85$	8.23692	−	25.3506i	0.0105108	−	0.0323490i
$86$	867.934	+	630.591i	1.08828	+	0.790679i
$87$	−692.830			−0.853783
$88$	−182.642	+	44.4943i	−0.221246	+	0.0538990i
$89$	1549.44			1.84540			0.922700	−	0.385519i	$-0.125978\pi$
$89$	1549.44			1.84540			0.922700	+	0.385519i	$0.125978\pi$
$90$	964.208	+	700.538i	1.12929	+	0.820480i
$91$	8.83111	−	27.1794i	0.0101731	−	0.0313096i
$92$	1.92511	+	5.92488i	0.00218159	+	0.00671425i
$93$	2020.05	−	1467.65i	2.25236	−	1.63643i
$94$	281.024	−	204.176i	0.308356	−	0.224033i
$95$	−50.5165	−	155.474i	−0.0545567	−	0.167908i
$96$	−687.779	+	2116.77i	−0.731210	+	2.25043i
$97$	−219.150	−	159.222i	−0.229395	−	0.166666i	0.467150	−	0.884178i	$-0.345281\pi$
$97$	−219.150	−	159.222i	−0.229395	−	0.166666i	−0.696546	+	0.717512i	$0.745281\pi$
$98$	1404.15			1.44735
$99$	127.859	−	1697.08i	0.129801	−	1.72286i
$100$	−805.256			−0.805256
$101$	876.046	+	636.485i	0.863068	+	0.627056i	0.928718	−	0.370787i	$-0.120912\pi$
$101$	876.046	+	636.485i	0.863068	+	0.627056i	−0.0656499	+	0.997843i	$0.520912\pi$
$102$	47.7023	−	146.813i	0.0463062	−	0.142516i
$103$	34.3374	+	105.680i	0.0328482	+	0.101096i	0.966136	−	0.258032i	$-0.0830740\pi$
$103$	34.3374	+	105.680i	0.0328482	+	0.101096i	−0.933288	+	0.359128i	$0.883074\pi$
$104$	−54.1915	+	39.3724i	−0.0510953	+	0.0371229i
$105$	−93.9119	+	68.2310i	−0.0872844	+	0.0634158i
$106$	325.277	+	1001.10i	0.298053	+	0.917314i
$107$	−126.214	+	388.448i	−0.114034	+	0.350960i	−0.991744	−	0.128231i	$-0.959070\pi$
$107$	−126.214	+	388.448i	−0.114034	+	0.350960i	0.877711	+	0.479191i	$0.159070\pi$
$108$	1260.66	+	915.926i	1.12322	+	0.816065i
$109$	−785.113			−0.689910			−0.344955	−	0.938619i	$-0.612106\pi$
$109$	−785.113			−0.689910			−0.344955	+	0.938619i	$0.612106\pi$
$110$	−489.670	−	793.108i	−0.424438	−	0.687454i
$111$	−2888.09			−2.46960
$112$	−93.4277	−	67.8792i	−0.0788222	−	0.0572677i
$113$	696.365	−	2143.19i	0.579722	−	1.78420i	−0.0397848	−	0.999208i	$-0.512667\pi$
$113$	696.365	−	2143.19i	0.579722	−	1.78420i	0.619506	−	0.784992i	$-0.287333\pi$
$114$	−292.555	−	900.392i	−0.240353	−	0.739732i
$115$	−3.35587	+	2.43818i	−0.00272118	+	0.00197706i
$116$	−603.554	+	438.508i	−0.483092	+	0.350987i
$117$	−187.400	−	576.757i	−0.148078	−	0.455737i
$118$	32.1478	−	98.9409i	0.0250801	−	0.0771885i
$119$	7.70442	+	5.59759i	0.00593498	+	0.00431202i
$120$	272.084			0.206981
$121$	−596.323	+	1189.94i	−0.448026	+	0.894021i
$122$	−1800.59			−1.33621
$123$	−1127.21	−	818.966i	−0.826318	−	0.600355i
$124$	830.842	−	2557.07i	0.601709	−	1.85187i
$125$	−403.362	−	1241.42i	−0.288622	−	0.888288i
$126$	−344.485	+	250.283i	−0.243565	+	0.176960i
$127$	395.677	−	287.476i	0.276462	−	0.200861i	−0.440911	−	0.897551i	$-0.645344\pi$
$127$	395.677	−	287.476i	0.276462	−	0.200861i	0.717373	+	0.696690i	$0.245344\pi$
$128$	201.357	+	619.712i	0.139044	+	0.427932i
$129$	−685.196	+	2108.82i	−0.467660	+	1.43931i
$130$	−268.702	−	195.224i	−0.181283	−	0.131710i
$131$	−2008.91			−1.33984			−0.669920	−	0.742433i	$-0.733672\pi$
$131$	−2008.91			−1.33984			−0.669920	+	0.742433i	$0.733672\pi$
$132$	−1519.96	−	2461.85i	−1.00224	−	1.62331i
$133$	58.4051			0.0380779
$134$	2864.14	+	2080.92i	1.84645	+	1.34152i
$135$	−320.625	+	986.784i	−0.204408	+	0.629102i
$136$	−6.89771	−	21.2290i	−0.00434907	−	0.0133851i
$137$	−738.250	+	536.370i	−0.460387	+	0.334491i	−0.793683	−	0.608332i	$-0.791839\pi$
$137$	−738.250	+	536.370i	−0.460387	+	0.334491i	0.333296	+	0.942822i	$0.391839\pi$
$138$	−19.4347	+	14.1202i	−0.0119884	+	0.00871006i
$139$	−756.214	−	2327.39i	−0.461447	−	1.42019i	−0.863396	−	0.504527i	$-0.831667\pi$
$139$	−756.214	−	2327.39i	−0.461447	−	1.42019i	0.401949	−	0.915662i	$-0.368333\pi$
$140$	−38.6258	+	118.878i	−0.0233177	+	0.0717645i
$141$	580.827	+	421.995i	0.346911	+	0.252046i
$142$	1874.23			1.10762
$143$	−35.6313	+	472.937i	−0.0208366	+	0.276566i
$144$	−2450.60			−1.41817
$145$	−401.874	−	291.979i	−0.230164	−	0.167224i
$146$	624.625	−	1922.40i	0.354071	−	1.08972i
$147$	896.805	+	2760.08i	0.503178	+	1.54862i
$148$	−2515.94	+	1827.94i	−1.39736	+	1.01524i
$149$	2170.52	−	1576.98i	1.19340	−	0.867053i	0.199777	−	0.979841i	$-0.435978\pi$
$149$	2170.52	−	1576.98i	1.19340	−	0.867053i	0.993619	+	0.112788i	$0.0359781\pi$
$150$	−959.543	−	2953.17i	−0.522309	−	1.60750i
$151$	−1056.53	+	3251.66i	−0.569398	+	1.75243i	0.0851104	+	0.996372i	$0.472876\pi$
$151$	−1056.53	+	3251.66i	−0.569398	+	1.75243i	−0.654508	+	0.756055i	$0.727124\pi$
$152$	−110.751	−	80.4655i	−0.0590995	−	0.0429383i
$153$	202.086			0.106782
$154$	323.549	−	78.8215i	0.169301	−	0.0412443i
$155$	1790.24			0.927711
$156$	−834.066	−	605.985i	−0.428069	−	0.311010i
$157$	−937.704	+	2885.96i	−0.476668	+	1.46703i	0.367027	+	0.930210i	$0.380376\pi$
$157$	−937.704	+	2885.96i	−0.476668	+	1.46703i	−0.843695	+	0.536823i	$0.819624\pi$
$158$	−166.849	−	513.508i	−0.0840113	−	0.258560i
$159$	−1760.08	+	1278.77i	−0.877881	+	0.637818i
$160$	−1291.01	+	937.975i	−0.637897	+	0.463459i
$161$	−0.457962	−	1.40946i	−0.000224177	−	0.000689945i
$162$	−240.726	+	740.877i	−0.116748	+	0.359314i
$163$	−2914.62	−	2117.60i	−1.40056	−	1.01756i	−0.994612	−	0.103667i	$-0.966942\pi$
$163$	−2914.62	−	2117.60i	−1.40056	−	1.01756i	−0.405945	−	0.913897i	$-0.633058\pi$
$164$	−1500.30			−0.714354
$165$	1246.24	−	1469.07i	0.587998	−	0.693134i
$166$	2296.68			1.07384
$167$	−2843.62	−	2066.01i	−1.31764	−	0.957321i	−0.999958	−	0.00912280i	$-0.997096\pi$
$167$	−2843.62	−	2066.01i	−1.31764	−	0.957321i	−0.317680	−	0.948198i	$-0.602904\pi$
$168$	−30.0390	+	92.4505i	−0.0137950	+	0.0424566i
$169$	52.2239	+	160.729i	0.0237705	+	0.0731582i
$170$	89.5407	−	65.0551i	0.0403968	−	0.0293500i
$171$	1002.68	−	728.489i	0.448402	−	0.325783i
$172$	737.814	+	2270.76i	0.327080	+	1.00665i
$173$	−228.385	+	702.896i	−0.100369	+	0.308903i	−0.988616	−	0.150463i	$-0.951923\pi$
$173$	−228.385	+	702.896i	−0.100369	+	0.308903i	0.888247	+	0.459366i	$0.151923\pi$
$174$	−2327.37	−	1690.93i	−1.01401	−	0.736719i
$175$	191.561			0.0827466
$176$	1773.09	+	727.507i	0.759386	+	0.311579i
$177$	215.017			0.0913088
$178$	5204.91	+	3781.59i	2.19171	+	1.59237i
$179$	313.984	−	966.344i	0.131108	−	0.403508i	−0.863857	−	0.503738i	$-0.831958\pi$
$179$	313.984	−	966.344i	0.131108	−	0.403508i	0.994964	+	0.100230i	$0.0319578\pi$
$180$	819.655	+	2522.64i	0.339408	+	1.04459i
$181$	536.075	−	389.481i	0.220144	−	0.159944i	−0.472247	−	0.881466i	$-0.656557\pi$
$181$	536.075	−	389.481i	0.220144	−	0.159944i	0.692392	+	0.721522i	$0.256557\pi$
$182$	95.9999	−	69.7480i	0.0390988	−	0.0284070i
$183$	−1150.01	−	3539.37i	−0.464542	−	1.42971i
$184$	−1.07342	+	3.30365i	−0.000430074	+	0.00132363i
$185$	−1675.23	−	1217.13i	−0.665759	−	0.483703i
$186$	10367.7			4.08710
$187$	−146.216	−	59.9931i	−0.0571785	−	0.0234606i
$188$	773.075			0.299906
$189$	−299.898	−	217.888i	−0.115420	−	0.0838574i
$190$	209.756	−	645.562i	0.0800909	−	0.246495i
$191$	−12.5619	−	38.6617i	−0.00475890	−	0.0146464i	0.948649	−	0.316331i	$-0.102451\pi$
$191$	−12.5619	−	38.6617i	−0.00475890	−	0.0146464i	−0.953408	+	0.301685i	$0.902451\pi$
$192$	−4558.78	+	3312.15i	−1.71355	+	1.24497i
$193$	1922.10	−	1396.48i	0.716868	−	0.520835i	−0.168514	−	0.985699i	$-0.553897\pi$
$193$	1922.10	−	1396.48i	0.716868	−	0.520835i	0.885382	+	0.464864i	$0.153897\pi$
$194$	−347.574	−	1069.72i	−0.128631	−	0.395885i
$195$	212.129	−	652.865i	0.0779018	−	0.239757i
$196$	2528.16	+	1836.82i	0.921343	+	0.669395i
$197$	3903.38			1.41170			0.705849	−	0.708362i	$-0.250566\pi$
$197$	3903.38			1.41170			0.705849	+	0.708362i	$0.250566\pi$
$198$	4571.43	−	5388.81i	1.64079	−	1.93417i
$199$	3133.72			1.11630			0.558150	−	0.829740i	$-0.311511\pi$
$199$	3133.72			1.11630			0.558150	+	0.829740i	$0.311511\pi$
$200$	−363.250	−	263.917i	−0.128428	−	0.0933086i
$201$	−2261.11	+	6959.00i	−0.793466	+	2.44204i
$202$	1389.42	+	4276.18i	0.483955	+	1.48946i
$203$	143.579	−	104.316i	0.0496416	−	0.0360667i
$204$	277.939	−	201.935i	0.0953904	−	0.0693052i
$205$	−308.699	−	950.079i	−0.105173	−	0.323690i
$206$	−142.576	+	438.805i	−0.0482222	+	0.148413i
$207$	−25.4424	−	18.4850i	−0.00854284	−	0.00620674i
$208$	682.924			0.227655
$209$	−941.740	+	229.422i	−0.311682	+	0.0759306i
$210$	−481.996			−0.158385
$211$	360.470	+	261.897i	0.117610	+	0.0854488i	0.645036	−	0.764153i	$-0.276843\pi$
$211$	360.470	+	261.897i	0.117610	+	0.0854488i	−0.527425	+	0.849601i	$0.676843\pi$
$212$	−723.916	+	2227.98i	−0.234522	+	0.721786i
$213$	1197.04	+	3684.11i	0.385070	+	1.18512i
$214$	−1372.03	+	996.841i	−0.438272	+	0.318424i
$215$	−1286.16	+	934.452i	−0.407979	+	0.296414i
$216$	268.496	+	826.346i	0.0845780	+	0.260304i
$217$	−197.648	+	608.298i	−0.0618305	+	0.190295i
$218$	−2637.37	−	1916.16i	−0.819380	−	0.595315i
$219$	4177.73			1.28906
$220$	155.845	−	2068.55i	0.0477595	−	0.633916i
$221$	−56.3166			−0.0171415
$222$	−9701.73	−	7048.72i	−2.93305	−	2.13099i
$223$	−1288.72	+	3966.26i	−0.386990	+	1.19103i	0.548036	+	0.836455i	$0.315376\pi$
$223$	−1288.72	+	3966.26i	−0.386990	+	1.19103i	−0.935026	+	0.354579i	$0.884624\pi$
$224$	−176.179	−	542.224i	−0.0525512	−	0.161736i
$225$	3288.66	−	2389.35i	0.974417	−	0.707956i
$226$	7569.95	−	5499.89i	2.22808	−	1.61879i
$227$	290.488	+	894.032i	0.0849357	+	0.261405i	0.984500	−	0.175382i	$-0.0561162\pi$
$227$	290.488	+	894.032i	0.0849357	+	0.261405i	−0.899565	+	0.436787i	$0.856116\pi$
$228$	651.093	−	2003.86i	0.189122	−	0.582056i
$229$	4920.56	+	3575.00i	1.41991	+	1.03163i	0.991786	+	0.127907i	$0.0408258\pi$
$229$	4920.56	+	3575.00i	1.41991	+	1.03163i	0.428125	+	0.903719i	$0.359174\pi$
$230$	−17.2237			−0.00493782
$231$	361.582	+	585.646i	0.102988	+	0.166808i
$232$	−415.980			−0.117717
$233$	363.929	+	264.410i	0.102325	+	0.0743435i	0.637771	−	0.770226i	$-0.279857\pi$
$233$	363.929	+	264.410i	0.102325	+	0.0743435i	−0.535446	+	0.844569i	$0.679857\pi$
$234$	778.125	−	2394.82i	0.217383	−	0.669036i
$235$	159.066	+	489.555i	0.0441546	+	0.135894i
$236$	187.311	−	136.089i	0.0516648	−	0.0375367i
$237$	902.821	−	655.938i	0.247445	−	0.179780i
$238$	12.2193	+	37.6070i	0.00332797	+	0.0102424i
$239$	1761.46	−	5421.22i	0.476734	−	1.46724i	−0.366870	−	0.930272i	$-0.619571\pi$
$239$	1761.46	−	5421.22i	0.476734	−	1.46724i	0.843605	−	0.536965i	$-0.180429\pi$
$240$	−2244.19	−	1630.50i	−0.603591	−	0.438535i
$241$	2914.08			0.778889			0.389444	−	0.921050i	$-0.372667\pi$
$241$	2914.08			0.778889			0.389444	+	0.921050i	$0.372667\pi$
$242$	−4907.36	+	2541.88i	−1.30354	+	0.675199i
$243$	2942.85			0.776889
$244$	−3241.97	−	2355.43i	−0.850598	−	0.617996i
$245$	−642.990	+	1978.92i	−0.167670	+	0.516035i
$246$	−1787.76	−	5502.17i	−0.463348	−	1.42604i
$247$	−279.423	+	203.013i	−0.0719808	+	0.0522971i
$248$	1212.85	−	881.189i	0.310549	−	0.225627i
$249$	1466.85	+	4514.51i	0.373326	+	1.14898i
$250$	1674.85	−	5154.65i	0.423707	−	1.30404i
$251$	−3367.31	−	2446.49i	−0.846783	−	0.615224i	0.0774744	−	0.996994i	$-0.475314\pi$
$251$	−3367.31	−	2446.49i	−0.846783	−	0.615224i	−0.924257	+	0.381771i	$0.875314\pi$
$252$	−947.651			−0.236891
$253$	12.9208	+	20.9276i	0.00321077	+	0.00520042i
$254$	2030.78			0.501664
$255$	185.065	+	134.457i	0.0454479	+	0.0330198i
$256$	787.151	−	2422.60i	0.192176	−	0.591456i
$257$	−1301.34	−	4005.12i	−0.315858	−	0.972111i	−0.975400	−	0.220443i	$-0.929250\pi$
$257$	−1301.34	−	4005.12i	−0.315858	−	0.972111i	0.659542	−	0.751668i	$-0.270750\pi$
$258$	−7448.53	+	5411.67i	−1.79738	+	1.30588i
$259$	598.514	−	434.846i	0.143590	−	0.104324i
$260$	−228.419	−	703.000i	−0.0544843	−	0.167685i
$261$	1163.77	−	3581.72i	0.275999	−	0.849438i
$262$	−6748.36	−	4902.97i	−1.59128	−	1.15613i
$263$	−6038.85			−1.41586			−0.707931	−	0.706282i	$-0.750371\pi$
$263$	−6038.85			−1.41586			−0.707931	+	0.706282i	$0.750371\pi$
$264$	121.200	−	1608.69i	0.0282550	−	0.375031i
$265$	−1559.84			−0.361585
$266$	196.195	+	142.544i	0.0452237	+	0.0328570i
$267$	−4109.05	+	12646.4i	−0.941834	+	2.89867i
$268$	2434.75	+	7493.40i	0.554949	+	1.70796i
$269$	−2878.48	+	2091.34i	−0.652432	+	0.474020i	−0.864099	−	0.503322i	$-0.832111\pi$
$269$	−2878.48	+	2091.34i	−0.652432	+	0.474020i	0.211667	+	0.977342i	$0.432111\pi$
$270$	−3485.41	+	2532.30i	−0.785612	+	0.570780i
$271$	2402.09	+	7392.86i	0.538437	+	1.65714i	0.736104	+	0.676868i	$0.236663\pi$
$271$	2402.09	+	7392.86i	0.538437	+	1.65714i	−0.197668	+	0.980269i	$0.563337\pi$
$272$	−70.3240	+	216.435i	−0.0156766	+	0.0482475i
$273$	198.415	+	144.157i	0.0439876	+	0.0319589i
$274$	−3789.02			−0.835412
$275$	−3088.78	+	752.476i	−0.677312	+	0.165004i
$276$	−53.4634			−0.0116599
$277$	−2135.61	−	1551.61i	−0.463237	−	0.336561i	0.331563	−	0.943433i	$-0.392424\pi$
$277$	−2135.61	−	1551.61i	−0.463237	−	0.336561i	−0.794800	+	0.606872i	$0.792424\pi$
$278$	3139.97	−	9663.82i	0.677419	−	2.08488i
$279$	4194.17	+	12908.3i	0.899994	+	2.76990i
$280$	−56.3854	+	40.9664i	−0.0120345	+	0.00874361i
$281$	891.724	−	647.875i	0.189309	−	0.137541i	−0.489094	−	0.872231i	$-0.662672\pi$
$281$	891.724	−	647.875i	0.189309	−	0.137541i	0.678403	+	0.734690i	$0.262672\pi$
$282$	921.196	+	2835.15i	0.194526	+	0.598690i
$283$	1223.20	−	3764.63i	0.256932	−	0.790756i	−0.736511	−	0.676426i	$-0.763528\pi$
$283$	1223.20	−	3764.63i	0.256932	−	0.790756i	0.993443	−	0.114330i	$-0.0364721\pi$
$284$	3374.55	+	2451.76i	0.705081	+	0.512271i
$285$	1402.93			0.291587
$286$	−1273.95	+	1501.74i	−0.263392	+	0.310488i
$287$	356.905			0.0734057
$288$	−9787.77	−	7111.23i	−2.00260	−	1.45498i
$289$	−1512.40	+	4654.69i	−0.307837	+	0.947424i
$290$	−637.375	−	1961.64i	−0.129062	−	0.397212i
$291$	1880.73	−	1366.43i	0.378867	−	0.275263i
$292$	3639.40	−	2644.18i	0.729384	−	0.529928i
$293$	−664.366	−	2044.71i	−0.132466	−	0.407690i	0.862721	−	0.505680i	$-0.168758\pi$
$293$	−664.366	−	2044.71i	−0.132466	−	0.407690i	−0.995187	+	0.0979906i	$0.968758\pi$
$294$	−3723.73	+	11460.5i	−0.738681	+	2.27343i
$295$	124.720	+	90.6144i	0.0246152	+	0.0178840i
$296$	−1734.03			−0.340502
$297$	5691.52	+	2335.26i	1.11197	+	0.456247i
$298$	11140.0			2.16552
$299$	7.09020	+	5.15133i	0.00137136	+	0.000996351i
$300$	2135.50	−	6572.40i	0.410978	−	1.26486i
$301$	−175.517	−	540.187i	−0.0336102	−	0.103441i
$302$	−11485.2	+	8344.46i	−2.18840	+	1.58997i
$303$	−7518.15	+	5462.25i	−1.42543	+	1.03564i
$304$	431.293	+	1327.38i	0.0813696	+	0.250430i
$305$	824.532	−	2537.65i	0.154795	−	0.476411i
$306$	678.850	+	493.213i	0.126821	+	0.0921410i
$307$	−4334.13			−0.805738			−0.402869	−	0.915258i	$-0.631987\pi$
$307$	−4334.13			−0.805738			−0.402869	+	0.915258i	$0.631987\pi$
$308$	685.659	+	281.329i	0.126848	+	0.0520461i
$309$	−953.605			−0.175562
$310$	6013.79	+	4369.27i	1.10181	+	0.800510i
$311$	597.272	−	1838.22i	0.108901	−	0.335163i	−0.881725	−	0.471763i	$-0.843618\pi$
$311$	597.272	−	1838.22i	0.108901	−	0.335163i	0.990626	+	0.136600i	$0.0436177\pi$
$312$	−177.639	−	546.718i	−0.0322335	−	0.0992045i
$313$	3228.81	−	2345.87i	0.583077	−	0.423630i	−0.256755	−	0.966476i	$-0.582653\pi$
$313$	3228.81	−	2345.87i	0.583077	−	0.423630i	0.839832	+	0.542846i	$0.182653\pi$
$314$	−10193.5	+	7405.98i	−1.83201	+	1.33103i
$315$	−194.987	−	600.107i	−0.0348770	−	0.107340i
$316$	371.329	−	1142.83i	0.0661041	−	0.203447i
$317$	−5771.53	−	4193.26i	−1.02259	−	0.742956i	−0.0557790	−	0.998443i	$-0.517764\pi$
$317$	−5771.53	−	4193.26i	−1.02259	−	0.742956i	−0.966813	+	0.255487i	$0.917764\pi$
$318$	−9033.46			−1.59299
$319$	−1905.34	+	2246.01i	−0.334415	+	0.394209i
$320$	−4040.14			−0.705784
$321$	−2835.75	−	2060.29i	−0.493072	−	0.358238i
$322$	1.90156	−	5.85239i	0.000329098	−	0.00101286i
$323$	−35.5661	−	109.461i	−0.00612678	−	0.0188563i
$324$	−1402.60	+	1019.05i	−0.240500	+	0.174734i
$325$	−916.472	+	665.856i	−0.156421	+	0.113646i
$326$	−4622.61	−	14226.9i	−0.785346	−	2.41705i
$327$	2082.08	−	6408.00i	0.352109	−	1.08368i
$328$	−676.786	−	491.713i	−0.113931	−	0.0827754i
$329$	−183.906			−0.0308178
$330$	7771.83	−	1893.34i	1.29644	−	0.315833i
$331$	5833.01			0.968614			0.484307	−	0.874898i	$-0.339072\pi$
$331$	5833.01			0.968614			0.484307	+	0.874898i	$0.339072\pi$
$332$	4135.18	+	3004.38i	0.683577	+	0.496648i
$333$	4851.24	−	14930.6i	0.798338	−	2.45703i
$334$	−4510.00	−	13880.3i	−0.738850	−	2.27395i
$335$	−4244.28	+	3083.65i	−0.692208	+	0.502919i
$336$	801.788	−	582.533i	0.130182	−	0.0945827i
$337$	−2115.57	−	6511.05i	−0.341966	−	1.05246i	−0.963188	−	0.268828i	$-0.913364\pi$
$337$	−2115.57	−	6511.05i	−0.341966	−	1.05246i	0.621223	−	0.783634i	$-0.286636\pi$
$338$	−216.845	+	667.380i	−0.0348959	+	0.107399i
$339$	15645.7	+	11367.3i	2.50667	+	1.82120i
$340$	246.319			0.0392898
$341$	797.459	−	10584.7i	0.126642	−	1.68093i
$342$	5146.18			0.813665
$343$	−1211.44	−	880.161i	−0.190704	−	0.138555i
$344$	−411.397	+	1266.15i	−0.0644797	+	0.198448i
$345$	−11.0005	−	33.8561i	−0.00171666	−	0.00528334i
$346$	−2482.69	+	1803.78i	−0.385752	+	0.280265i
$347$	−1326.25	+	963.574i	−0.205177	+	0.149070i	−0.685629	−	0.727951i	$-0.740473\pi$
$347$	−1326.25	+	963.574i	−0.205177	+	0.149070i	0.480452	+	0.877021i	$0.340473\pi$
$348$	−1978.45	−	6089.04i	−0.304759	−	0.937950i
$349$	1884.12	−	5798.71i	0.288981	−	0.889392i	−0.696196	−	0.717852i	$-0.745126\pi$
$349$	1884.12	−	5798.71i	0.288981	−	0.889392i	0.985177	−	0.171541i	$-0.0548745\pi$
$350$	643.496	+	467.527i	0.0982751	+	0.0714010i
$351$	2192.14			0.333356
$352$	4970.69	+	8050.91i	0.752666	+	1.21908i
$353$	1745.44			0.263174			0.131587	−	0.991305i	$-0.457993\pi$
$353$	1745.44			0.263174			0.131587	+	0.991305i	$0.457993\pi$
$354$	722.288	+	524.773i	0.108444	+	0.0787892i
$355$	−858.252	+	2641.43i	−0.128314	+	0.394908i
$356$	4424.60	+	13617.5i	0.658717	+	2.02732i
$357$	−66.1186	+	48.0380i	−0.00980215	+	0.00712168i
$358$	3413.21	−	2479.84i	0.503894	−	0.366100i
$359$	1356.63	+	4175.27i	0.199443	+	0.613823i	0.999896	+	0.0144273i	$0.00459250\pi$
$359$	1356.63	+	4175.27i	0.199443	+	0.613823i	−0.800453	+	0.599396i	$0.795407\pi$
$360$	−457.030	+	1406.60i	−0.0669101	+	0.205928i
$361$	4977.99	+	3616.72i	0.725760	+	0.527296i
$362$	2751.36			0.399471
$363$	−8130.73	−	8022.78i	−1.17563	−	1.16002i
$364$	264.088			0.0380274
$365$	2423.28	+	1760.62i	0.347508	+	0.252479i
$366$	4775.09	−	14696.2i	0.681962	−	2.09886i
$367$	2692.60	+	8286.96i	0.382977	+	1.17868i	0.937937	+	0.346804i	$0.112733\pi$
$367$	2692.60	+	8286.96i	0.382977	+	1.17868i	−0.554961	+	0.831877i	$0.687267\pi$
$368$	28.6513	−	20.8164i	0.00405856	−	0.00294872i
$369$	6127.23	−	4451.69i	0.864420	−	0.628038i
$370$	−2656.93	−	8177.19i	−0.373317	−	1.14895i
$371$	172.211	−	530.012i	0.0240991	−	0.0741694i
$372$	18667.1	+	13562.5i	2.60174	+	1.89027i
$373$	−10129.8			−1.40616			−0.703081	−	0.711109i	$-0.748193\pi$
$373$	−10129.8			−1.40616			−0.703081	+	0.711109i	$0.748193\pi$
$374$	−344.752	−	558.387i	−0.0476649	−	0.0772019i
$375$	11202.0			1.54259
$376$	348.733	+	253.369i	0.0478312	+	0.0347514i
$377$	−324.316	+	998.142i	−0.0443054	+	0.136358i
$378$	−475.640	−	1463.87i	−0.0647203	−	0.199189i
$379$	−6108.95	+	4438.41i	−0.827957	+	0.601546i	−0.918981	−	0.394303i	$-0.870986\pi$
$379$	−6108.95	+	4438.41i	−0.827957	+	0.601546i	0.0910237	+	0.995849i	$0.470986\pi$
$380$	1222.15	−	887.944i	0.164987	−	0.119870i
$381$	1297.03	+	3991.84i	0.174406	+	0.536767i
$382$	52.1599	−	160.532i	0.00698621	−	0.0215014i
$383$	−7318.51	−	5317.21i	−0.976393	−	0.709391i	−0.0194935	−	0.999810i	$-0.506205\pi$
$383$	−7318.51	−	5317.21i	−0.976393	−	0.709391i	−0.956900	+	0.290419i	$0.906205\pi$
$384$	−5592.00			−0.743139
$385$	−37.0738	+	492.084i	−0.00490768	+	0.0651400i
$386$	9865.02			1.30082
$387$	−9751.00	−	7084.52i	−1.28080	−	0.930559i
$388$	773.541	−	2380.71i	0.101213	−	0.311501i
$389$	−2617.42	−	8055.59i	−0.341153	−	1.04996i	−0.963611	−	0.267308i	$-0.913866\pi$
$389$	−2617.42	−	8055.59i	−0.341153	−	1.04996i	0.622458	−	0.782653i	$-0.286134\pi$
$390$	2305.98	−	1675.39i	0.299404	−	0.217530i
$391$	−2.36269	+	1.71660i	−0.000305592	+	0.000222026i
$392$	538.448	+	1657.17i	0.0693769	+	0.213520i
$393$	5327.53	−	16396.5i	0.683813	−	2.10456i
$394$	13112.3	+	9526.65i	1.67662	+	1.21814i
$395$	800.111			0.101919
$396$	15280.2	−	3722.49i	1.93904	−	0.472379i
$397$	−7496.00			−0.947641			−0.473820	−	0.880621i	$-0.657125\pi$
$397$	−7496.00			−0.947641			−0.473820	+	0.880621i	$0.657125\pi$
$398$	10526.9	+	7648.21i	1.32579	+	0.963242i
$399$	−154.888	+	476.695i	−0.0194338	+	0.0598110i
$400$	1414.59	+	4353.65i	0.176823	+	0.544206i
$401$	−8956.20	+	6507.06i	−1.11534	+	0.810342i	−0.983496	−	0.180929i	$-0.942090\pi$
$401$	−8956.20	+	6507.06i	−1.11534	+	0.810342i	−0.131843	+	0.991271i	$0.542090\pi$
$402$	−24579.8	+	17858.3i	−3.04957	+	2.21565i
$403$	−1168.82	−	3597.25i	−0.144474	−	0.444644i
$404$	−3092.20	+	9516.82i	−0.380799	+	1.17198i
$405$	−933.914	−	678.528i	−0.114584	−	0.0832502i
$406$	736.907			0.0900790
$407$	−7942.48	+	9362.62i	−0.967307	+	1.14026i
$408$	191.561			0.0232443
$409$	5786.51	+	4204.14i	0.699571	+	0.508268i	0.879792	−	0.475358i	$-0.157681\pi$
$409$	5786.51	+	4204.14i	0.699571	+	0.508268i	−0.180222	+	0.983626i	$0.557681\pi$
$410$	1281.79	−	3944.94i	0.154397	−	0.475187i
$411$	−2419.98	−	7447.94i	−0.290435	−	0.893868i
$412$	−830.727	+	603.559i	−0.0993374	+	0.0721728i
$413$	−44.5591	+	32.3741i	−0.00530898	+	0.00385720i
$414$	−40.3518	−	124.190i	−0.00479030	−	0.0147430i
$415$	−1051.70	+	3236.81i	−0.124400	+	0.382864i
$416$	2727.62	+	1981.73i	0.321473	+	0.233564i
$417$	21001.3			2.46628
$418$	−3723.44	−	1527.74i	−0.435692	−	0.178766i
$419$	−6604.83			−0.770088			−0.385044	−	0.922898i	$-0.625814\pi$
$419$	−6604.83			−0.770088			−0.385044	+	0.922898i	$0.625814\pi$
$420$	−867.834	−	630.518i	−0.100824	−	0.0732527i
$421$	−5141.54	+	15824.0i	−0.595210	+	1.83187i	−0.0415336	+	0.999137i	$0.513224\pi$
$421$	−5141.54	+	15824.0i	−0.595210	+	1.83187i	−0.553677	+	0.832732i	$0.686776\pi$
$422$	571.707	+	1759.53i	0.0659485	+	0.202969i
$423$	−3157.23	+	2293.86i	−0.362907	+	0.263668i
$424$	−1056.76	+	767.783i	−0.121040	+	0.0879407i
$425$	−116.652	−	359.019i	−0.0133140	−	0.0409764i
$426$	−4970.38	+	15297.2i	−0.565295	+	1.73980i
$427$	771.228	+	560.330i	0.0874059	+	0.0635041i
$428$	−3774.35			−0.426262
$429$	−3765.56	−	1545.03i	−0.423783	−	0.173880i
$430$	−6601.14			−0.740314
$431$	7598.38	+	5520.55i	0.849190	+	0.616973i	0.924923	−	0.380155i	$-0.124129\pi$
$431$	7598.38	+	5520.55i	0.849190	+	0.616973i	−0.0757322	+	0.997128i	$0.524129\pi$
$432$	2737.39	−	8424.83i	0.304868	−	0.938286i
$433$	−765.977	−	2357.44i	−0.0850128	−	0.261642i	0.899510	−	0.436901i	$-0.143924\pi$
$433$	−765.977	−	2357.44i	−0.0850128	−	0.261642i	−0.984522	+	0.175258i	$0.943924\pi$
$434$	−2148.56	+	1561.02i	−0.237637	+	0.172653i
$435$	3448.85	−	2505.73i	0.380137	−	0.276186i
$436$	−2241.97	−	6900.09i	−0.246264	−	0.757923i
$437$	−5.53479	+	17.0343i	−0.000605869	+	0.00186467i
$438$	14033.9	+	10196.2i	1.53097	+	1.11232i
$439$	−14103.0			−1.53326			−0.766630	−	0.642089i	$-0.778068\pi$
$439$	−14103.0			−1.53326			−0.766630	+	0.642089i	$0.778068\pi$
$440$	748.253	−	882.042i	0.0810717	−	0.0955675i
$441$	−15775.2			−1.70340
$442$	−189.180	−	137.447i	−0.0203583	−	0.0147911i
$443$	5007.09	−	15410.2i	0.537007	−	1.65274i	−0.202264	−	0.979331i	$-0.564830\pi$
$443$	5007.09	−	15410.2i	0.537007	−	1.65274i	0.739272	−	0.673407i	$-0.235170\pi$
$444$	−8247.26	−	25382.4i	−0.881526	−	2.71306i
$445$	−7712.99	+	5603.82i	−0.821642	+	0.596958i
$446$	−14009.2	+	10178.3i	−1.48734	+	1.08062i
$447$	7114.96	+	21897.6i	0.752855	+	2.31705i
$448$	446.045	−	1372.79i	0.0470394	−	0.144772i
$449$	8508.14	+	6181.53i	0.894263	+	0.649720i	0.936986	−	0.349367i	$-0.113603\pi$
$449$	8508.14	+	6181.53i	0.894263	+	0.649720i	−0.0427233	+	0.999087i	$0.513603\pi$
$450$	16878.8			1.76816
$451$	−5754.84	+	1401.97i	−0.600853	+	0.146377i
$452$	20824.3			2.16702
$453$	−23737.8	−	17246.5i	−2.46203	−	1.78877i
$454$	−1206.17	+	3712.22i	−0.124688	+	0.383751i
$455$	54.3382	+	167.236i	0.00559871	+	0.0172311i
$456$	950.457	−	690.547i	0.0976080	−	0.0709163i
$457$	−7717.74	+	5607.27i	−0.789979	+	0.573954i	−0.907957	−	0.419063i	$-0.862359\pi$
$457$	−7717.74	+	5607.27i	−0.789979	+	0.573954i	0.117978	+	0.993016i	$0.462359\pi$
$458$	7804.04	+	24018.4i	0.796199	+	2.45045i
$459$	−225.736	+	694.744i	−0.0229552	+	0.0706490i
$460$	−31.0113	−	22.5311i	−0.00314329	−	0.00228373i
$461$	10538.3			1.06468			0.532339	−	0.846531i	$-0.321313\pi$
$461$	10538.3			1.06468			0.532339	+	0.846531i	$0.321313\pi$
$462$	−214.705	+	2849.79i	−0.0216211	+	0.286979i
$463$	−2071.48			−0.207926			−0.103963	−	0.994581i	$-0.533152\pi$
$463$	−2071.48			−0.207926			−0.103963	+	0.994581i	$0.533152\pi$
$464$	3431.07	+	2492.82i	0.343283	+	0.249410i
$465$	−4747.62	+	14611.7i	−0.473475	+	1.45721i
$466$	577.193	+	1776.42i	0.0573776	+	0.176590i
$467$	10742.8	−	7805.10i	1.06449	−	0.773398i	0.0895772	−	0.995980i	$-0.471448\pi$
$467$	10742.8	−	7805.10i	1.06449	−	0.773398i	0.974914	+	0.222582i	$0.0714484\pi$
$468$	4533.78	−	3293.98i	0.447807	−	0.325351i
$469$	−579.200	−	1782.59i	−0.0570255	−	0.175506i
$470$	−660.477	+	2032.74i	−0.0648203	+	0.199496i
$471$	−21068.1	−	15306.8i	−2.06107	−	1.49746i
$472$	129.098			0.0125894
$473$	4952.01	+	8020.67i	0.481382	+	0.779685i
$474$	4633.66			0.449011
$475$	−1873.00	−	1360.81i	−0.180924	−	0.131449i
$476$	−27.1945	+	83.6960i	−0.00261861	+	0.00805924i
$477$	−3654.39	−	11247.1i	−0.350782	−	1.07960i
$478$	19148.2	−	13912.0i	1.83226	−	1.33121i
$479$	−1751.60	+	1272.61i	−0.167083	+	0.121393i	−0.668185	−	0.743996i	$-0.732928\pi$
$479$	−1751.60	+	1272.61i	−0.167083	+	0.121393i	0.501101	+	0.865389i	$0.332928\pi$
$480$	−4231.93	−	13024.5i	−0.402418	−	1.23851i
$481$	−1351.93	+	4160.80i	−0.128155	+	0.394421i
$482$	9789.01	+	7112.14i	0.925057	+	0.672093i
$483$	12.7183			0.00119815
$484$	−12160.8	−	1842.87i	−1.14208	−	0.173072i
$485$	1666.77			0.156049
$486$	9885.68	+	7182.37i	0.922682	+	0.670368i
$487$	2772.09	−	8531.61i	0.257937	−	0.793849i	−0.735300	−	0.677742i	$-0.762959\pi$
$487$	2772.09	−	8531.61i	0.257937	−	0.793849i	0.993237	−	0.116106i	$-0.0370414\pi$
$488$	−690.475	−	2125.06i	−0.0640498	−	0.197125i
$489$	25013.0	−	18173.0i	2.31314	−	1.68060i
$490$	−6989.72	+	5078.33i	−0.644415	+	0.468195i
$491$	−4752.62	−	14627.1i	−0.436828	−	1.34442i	−0.891201	−	0.453608i	$-0.850137\pi$
$491$	−4752.62	−	14627.1i	−0.436828	−	1.34442i	0.454373	−	0.890812i	$-0.349863\pi$
$492$	3978.74	−	12245.3i	0.364584	−	1.12207i
$493$	−282.939	−	205.567i	−0.0258478	−	0.0187795i
$494$	−1434.12			−0.130615
$495$	5501.31	+	8910.36i	0.499526	+	0.809072i
$496$	−15284.4			−1.38365
$497$	−802.768	−	583.245i	−0.0724528	−	0.0526401i
$498$	−6090.70	+	18745.3i	−0.548054	+	1.68674i
$499$	1861.37	+	5728.71i	0.166987	+	0.513932i	0.999177	−	0.0405576i	$-0.0129134\pi$
$499$	1861.37	+	5728.71i	0.166987	+	0.513932i	−0.832191	+	0.554490i	$0.812913\pi$
$500$	9758.57	−	7090.02i	0.872833	−	0.634150i
$501$	24403.6	−	17730.3i	2.17620	−	1.58110i
$502$	−5340.57	−	16436.6i	−0.474823	−	1.46136i
$503$	5386.14	−	16576.8i	0.477448	−	1.46943i	−0.365181	−	0.930937i	$-0.618993\pi$
$503$	5386.14	−	16576.8i	0.477448	−	1.46943i	0.842628	−	0.538496i	$-0.181007\pi$
$504$	−427.484	−	310.585i	−0.0377811	−	0.0274496i
$505$	−6662.84			−0.587114
$506$	−7.67231	+	101.835i	−0.000674062	+	0.00894688i
$507$	−1450.34			−0.127045
$508$	3656.43	+	2656.55i	0.319346	+	0.232018i
$509$	−3226.37	+	9929.74i	−0.280955	+	0.864691i	0.706627	+	0.707587i	$0.250216\pi$
$509$	−3226.37	+	9929.74i	−0.280955	+	0.864691i	−0.987582	+	0.157105i	$0.949784\pi$
$510$	293.514	+	903.343i	0.0254844	+	0.0784328i
$511$	−865.772	+	629.021i	−0.0749501	+	0.0544545i
$512$	12774.1	−	9280.94i	1.10262	−	0.801100i
$513$	1384.43	+	4260.82i	0.119150	+	0.366706i
$514$	5403.46	−	16630.1i	0.463689	−	1.42709i
$515$	−553.137	−	401.877i	−0.0473284	−	0.0343861i
$516$	−20490.3			−1.74813
$517$	2965.34	−	722.404i	0.252255	−	0.0614532i
$518$	3071.83			0.260557
$519$	−5131.28	−	3728.09i	−0.433985	−	0.315309i
$520$	127.364	−	391.985i	0.0107409	−	0.0330571i
$521$	−720.385	−	2217.12i	−0.0605771	−	0.186437i	0.916189	−	0.400748i	$-0.131250\pi$
$521$	−720.385	−	2217.12i	−0.0605771	−	0.186437i	−0.976766	+	0.214310i	$0.931250\pi$
$522$	12651.0	−	9191.47i	1.06076	−	0.770689i
$523$	14320.2	−	10404.2i	1.19728	−	0.869876i	0.203268	−	0.979123i	$-0.434844\pi$
$523$	14320.2	−	10404.2i	1.19728	−	0.869876i	0.994015	+	0.109247i	$0.0348439\pi$
$524$	−5736.65	−	17655.6i	−0.478257	−	1.47192i
$525$	−508.011	+	1563.50i	−0.0422313	+	0.129975i
$526$	−20285.8	−	14738.5i	−1.68157	−	1.22173i
$527$	1260.41			0.104183
$528$	−10640.0	+	12542.4i	−0.876981	+	1.03379i
$529$	−12166.5			−0.999963
$530$	−5239.84	−	3806.96i	−0.429441	−	0.312008i
$531$	−361.172	+	1111.57i	−0.0295170	+	0.0908441i
$532$	166.782	+	513.302i	0.0135919	+	0.0418317i
$533$	−1707.51	+	1240.58i	−0.138763	+	0.100817i
$534$	−44668.1	+	32453.3i	−3.61981	+	2.62994i
$535$	−776.603	−	2390.14i	−0.0627579	−	0.193149i
$536$	−1357.59	+	4178.23i	−0.109401	+	0.336702i
$537$	7054.51	+	5125.40i	0.566898	+	0.411876i
$538$	−14773.6			−1.18389
$539$	11413.9	+	4683.18i	0.912118	+	0.374246i
$540$	−9588.08			−0.764084
$541$	−10715.9	−	7785.53i	−0.851591	−	0.618717i	0.0739931	−	0.997259i	$-0.476426\pi$
$541$	−10715.9	−	7785.53i	−0.851591	−	0.618717i	−0.925584	+	0.378541i	$0.876426\pi$
$542$	−9973.99	+	30696.8i	−0.790442	+	2.43273i
$543$	1757.25	+	5408.26i	0.138878	+	0.427423i
$544$	−908.936	+	660.381i	−0.0716366	+	0.0520470i
$545$	3908.23	−	2839.49i	0.307174	−	0.223175i
$546$	314.687	+	968.508i	0.0246655	+	0.0759127i
$547$	2877.43	−	8855.82i	0.224918	−	0.692226i	−0.773382	−	0.633940i	$-0.781437\pi$
$547$	2877.43	−	8855.82i	0.224918	−	0.692226i	0.998300	−	0.0582859i	$-0.0185635\pi$
$548$	−6822.12	−	4956.56i	−0.531801	−	0.386376i
$549$	20229.2			1.57261
$550$	−12212.4	−	5010.80i	−0.946797	−	0.388475i
$551$	−2144.89			−0.165835
$552$	−24.1173	−	17.5222i	−0.00185960	−	0.00135108i
$553$	−88.3349	+	271.867i	−0.00679273	+	0.0209059i
$554$	−3387.10	−	10424.4i	−0.259755	−	0.799443i
$555$	14376.7	−	10445.3i	1.09956	−	0.798877i
$556$	18295.1	−	13292.2i	1.39548	−	1.01388i
$557$	2680.45	+	8249.59i	0.203904	+	0.627551i	0.999757	+	0.0220613i	$0.00702289\pi$
$557$	2680.45	+	8249.59i	0.203904	+	0.627551i	−0.795853	+	0.605490i	$0.792977\pi$
$558$	−17415.1	+	53598.2i	−1.32122	+	4.06629i
$559$	2717.37	+	1974.29i	0.205604	+	0.149380i
$560$	710.572			0.0536199
$561$	877.415	−	1034.30i	0.0660329	−	0.0778398i
$562$	4576.71			0.343517
$563$	−3013.56	−	2189.48i	−0.225589	−	0.163900i	0.469250	−	0.883065i	$-0.344524\pi$
$563$	−3013.56	−	2189.48i	−0.225589	−	0.163900i	−0.694839	+	0.719166i	$0.744524\pi$
$564$	−2050.16	+	6309.74i	−0.153062	+	0.471078i
$565$	4284.76	+	13187.1i	0.319047	+	0.981925i
$566$	13297.0	−	9660.84i	0.987482	−	0.717447i
$567$	333.662	−	242.420i	0.0247134	−	0.0179553i
$568$	718.712	+	2211.97i	0.0530924	+	0.163402i
$569$	3975.67	−	12235.8i	0.292915	−	0.901500i	−0.690999	−	0.722856i	$-0.742829\pi$
$569$	3975.67	−	12235.8i	0.292915	−	0.901500i	0.983914	−	0.178644i	$-0.0571710\pi$
$570$	4712.73	+	3424.00i	0.346306	+	0.251606i
$571$	23526.9			1.72429			0.862146	−	0.506661i	$-0.169120\pi$
$571$	23526.9			1.72429			0.862146	+	0.506661i	$0.169120\pi$
$572$	−4258.23	+	1037.37i	−0.311268	+	0.0758298i
$573$	348.865			0.0254347
$574$	1198.92	+	871.068i	0.0871813	+	0.0633409i
$575$	−18.1534	+	55.8704i	−0.00131661	+	0.00405210i
$576$	−9465.26	−	29131.1i	−0.684698	−	2.10728i
$577$	−6944.76	+	5045.66i	−0.501064	+	0.364044i	−0.809423	−	0.587226i	$-0.800220\pi$
$577$	−6944.76	+	5045.66i	−0.501064	+	0.364044i	0.308359	+	0.951270i	$0.400220\pi$
$578$	−16440.8	+	11944.9i	−1.18313	+	0.859591i
$579$	6300.62	+	19391.3i	0.452237	+	1.39184i
$580$	1418.51	−	4365.71i	0.101552	−	0.312545i
$581$	−983.712	−	714.709i	−0.0702431	−	0.0510346i
$582$	9652.70			0.687487
$583$	−694.829	+	9222.53i	−0.0493600	+	0.655160i
$584$	2508.34			0.177733
$585$	3018.80	+	2193.28i	0.213354	+	0.155010i
$586$	2758.59	−	8490.08i	0.194465	−	0.598502i
$587$	−517.660	−	1593.19i	−0.0363988	−	0.112024i	0.931206	−	0.364493i	$-0.118758\pi$
$587$	−517.660	−	1593.19i	−0.0363988	−	0.112024i	−0.967605	+	0.252469i	$0.918758\pi$
$588$	−21696.5	+	15763.4i	−1.52168	+	1.10556i
$589$	6253.73	−	4543.60i	0.437488	−	0.317854i
$590$	197.807	+	608.787i	0.0138027	+	0.0424803i
$591$	−10351.6	+	31858.9i	−0.720487	+	2.21743i
$592$	14302.6	+	10391.4i	0.992959	+	0.721427i
$593$	27794.4			1.92476			0.962378	−	0.271716i	$-0.0875911\pi$
$593$	27794.4			1.92476			0.962378	+	0.271716i	$0.0875911\pi$
$594$	13419.6	+	21735.4i	0.926958	+	1.50137i
$595$	−58.5965			−0.00403735
$596$	20057.7	+	14572.7i	1.37851	+	1.00155i
$597$	−8310.49	+	25577.1i	−0.569725	+	1.75343i
$598$	11.2451	+	34.6089i	0.000768974	+	0.00236666i
$599$	4240.90	−	3081.19i	0.289279	−	0.210174i	−0.433675	−	0.901069i	$-0.642783\pi$
$599$	4240.90	−	3081.19i	0.289279	−	0.210174i	0.722955	+	0.690895i	$0.242783\pi$
$600$	3117.38	−	2264.91i	0.212111	−	0.154107i
$601$	5874.62	+	18080.2i	0.398720	+	1.22713i	0.926026	+	0.377459i	$0.123202\pi$
$601$	5874.62	+	18080.2i	0.398720	+	1.22713i	−0.527306	+	0.849675i	$0.676798\pi$
$602$	728.787	−	2242.98i	0.0493408	−	0.151855i
$603$	−32177.9	−	23378.6i	−2.17311	−	1.57886i
$604$	−31594.7			−2.12843
$605$	−1335.18	−	8080.13i	−0.0897235	−	0.542982i
$606$	−38586.3			−2.58657
$607$	−21956.2	−	15952.1i	−1.46816	−	1.06668i	−0.981141	−	0.193293i	$-0.938083\pi$
$607$	−21956.2	−	15952.1i	−1.46816	−	1.06668i	−0.487022	−	0.873390i	$-0.661917\pi$
$608$	−2129.25	+	6553.16i	−0.142027	+	0.437114i
$609$	470.650	+	1448.51i	0.0313164	+	0.0963821i
$610$	8963.20	−	6512.15i	0.594934	−	0.432245i
$611$	879.846	−	639.245i	0.0582565	−	0.0423258i
$612$	577.078	+	1776.06i	0.0381160	+	0.117309i
$613$	4571.10	−	14068.4i	0.301183	−	0.926945i	−0.679891	−	0.733313i	$-0.737973\pi$
$613$	4571.10	−	14068.4i	0.301183	−	0.926945i	0.981074	−	0.193632i	$-0.0620269\pi$
$614$	−14559.3	−	10577.9i	−0.956945	−	0.695261i
$615$	8573.08			0.562114
$616$	217.096	+	351.626i	0.0141998	+	0.0229991i
$617$	−603.355			−0.0393682			−0.0196841	−	0.999806i	$-0.506266\pi$
$617$	−603.355			−0.0393682			−0.0196841	+	0.999806i	$0.506266\pi$
$618$	−3203.37	−	2327.38i	−0.208509	−	0.151490i
$619$	3905.72	−	12020.6i	0.253609	−	0.780529i	−0.740491	−	0.672066i	$-0.765407\pi$
$619$	3905.72	−	12020.6i	0.253609	−	0.780529i	0.994100	−	0.108463i	$-0.0345929\pi$
$620$	5112.21	+	15733.8i	0.331147	+	1.01917i
$621$	91.9688	−	66.8193i	0.00594297	−	0.00431782i
$622$	6492.74	−	4717.25i	0.418545	−	0.304091i
$623$	−1052.56	−	3239.45i	−0.0676885	−	0.208324i
$624$	−1811.08	+	5573.94i	−0.116188	+	0.357590i
$625$	−2314.52	−	1681.60i	−0.148129	−	0.107622i
$626$	16571.6			1.05804
$627$	624.933	−	8294.78i	0.0398045	−	0.528328i
$628$	−28041.4			−1.78180
$629$	−1179.45	−	856.917i	−0.0747656	−	0.0543204i
$630$	809.627	−	2491.78i	0.0512005	−	0.157579i
$631$	−675.948	−	2080.35i	−0.0426451	−	0.131248i	0.927467	−	0.373905i	$-0.121981\pi$
$631$	−675.948	−	2080.35i	−0.0426451	−	0.131248i	−0.970112	+	0.242656i	$0.921981\pi$
$632$	542.061	−	393.830i	0.0341171	−	0.0247875i
$633$	−3093.52	+	2247.57i	−0.194244	+	0.141126i
$634$	−9153.69	−	28172.2i	−0.573406	−	1.76476i
$635$	−929.941	+	2862.06i	−0.0581159	+	0.178862i
$636$	−16264.7	−	11817.0i	−1.01406	−	0.736754i
$637$	4396.18			0.273442
$638$	−11882.1	+	2894.66i	−0.737330	+	0.179625i
$639$	−21056.5			−1.30357
$640$	−3243.63	−	2356.63i	−0.200337	−	0.145553i
$641$	9224.40	−	28389.8i	0.568396	−	1.74934i	−0.0892427	−	0.996010i	$-0.528445\pi$
$641$	9224.40	−	28389.8i	0.568396	−	1.74934i	0.657639	−	0.753333i	$-0.271555\pi$
$642$	−4497.52	−	13841.9i	−0.276484	−	0.850932i
$643$	−17318.3	+	12582.5i	−1.06216	+	0.771701i	−0.974486	−	0.224449i	$-0.927942\pi$
$643$	−17318.3	+	12582.5i	−1.06216	+	0.771701i	−0.0876692	+	0.996150i	$0.527942\pi$
$644$	11.0795	−	8.04973i	0.000677940	−	0.000492552i
$645$	−4216.04	−	12975.6i	−0.257374	−	0.792116i
$646$	147.678	−	454.507i	0.00899431	−	0.0276816i
$647$	−9071.40	−	6590.76i	−0.551211	−	0.400478i	0.277021	−	0.960864i	$-0.410653\pi$
$647$	−9071.40	−	6590.76i	−0.551211	−	0.400478i	−0.828232	+	0.560386i	$0.810653\pi$
$648$	−966.695			−0.0586039
$649$	591.313	−	697.042i	0.0357644	−	0.0421591i
$650$	−4703.72			−0.283839
$651$	−4440.70	−	3226.35i	−0.267350	−	0.194241i
$652$	10287.8	−	31662.6i	0.617948	−	1.90185i
$653$	7957.00	+	24489.1i	0.476847	+	1.46759i	0.843450	+	0.537208i	$0.180521\pi$
$653$	7957.00	+	24489.1i	0.476847	+	1.46759i	−0.366602	+	0.930378i	$0.619479\pi$
$654$	22633.6	−	16444.3i	1.35328	−	0.983215i
$655$	10000.2	−	7265.55i	0.596548	−	0.433418i
$656$	2635.57	+	8111.45i	0.156862	+	0.482773i
$657$	−7017.50	+	21597.6i	−0.416710	+	1.28250i
$658$	−617.779	−	448.843i	−0.0366011	−	0.0265923i
$659$	8761.33			0.517895			0.258948	−	0.965891i	$-0.416624\pi$
$659$	8761.33			0.517895			0.258948	+	0.965891i	$0.416624\pi$
$660$	16469.9	+	6757.69i	0.971351	+	0.398549i
$661$	5810.78			0.341926			0.170963	−	0.985277i	$-0.445312\pi$
$661$	5810.78			0.341926			0.170963	+	0.985277i	$0.445312\pi$
$662$	19594.3	+	14236.1i	1.15039	+	0.835804i
$663$	149.349	−	459.649i	0.00874846	−	0.0269250i
$664$	880.710	+	2710.55i	0.0514732	+	0.158418i
$665$	−290.736	+	211.232i	−0.0169537	+	0.0123176i
$666$	52736.2	−	38315.1i	3.06830	−	2.22925i
$667$	16.8183	+	51.7614i	0.000976323	+	0.00300481i
$668$	10037.2	−	30891.3i	0.581363	−	1.78925i
$669$	−28954.5	−	21036.7i	−1.67331	−	1.21573i
$670$	−21783.5			−1.25607
$671$	−14636.5	−	6005.43i	−0.842082	−	0.345510i
$672$	4892.78			0.280868
$673$	25780.9	+	18730.9i	1.47664	+	1.07284i	0.978619	+	0.205682i	$0.0659413\pi$
$673$	25780.9	+	18730.9i	1.47664	+	1.07284i	0.498025	+	0.867163i	$0.334059\pi$
$674$	8784.31	−	27035.3i	0.502016	−	1.54505i
$675$	4540.74	+	13974.9i	0.258923	+	0.796883i
$676$	−1263.46	+	917.955i	−0.0718853	+	0.0522278i
$677$	−11724.0	+	8518.00i	−0.665570	+	0.483565i	−0.868539	−	0.495620i	$-0.834941\pi$
$677$	−11724.0	+	8518.00i	−0.665570	+	0.483565i	0.202970	+	0.979185i	$0.434941\pi$
$678$	24814.3	+	76370.4i	1.40558	+	4.32594i
$679$	−184.016	+	566.344i	−0.0104004	+	0.0320093i
$680$	111.114	+	80.7293i	0.00626624	+	0.00455269i
$681$	−8067.34			−0.453952
$682$	28512.1	−	33610.2i	1.60086	−	1.88710i
$683$	17072.9			0.956478			0.478239	−	0.878230i	$-0.341275\pi$
$683$	17072.9			0.956478			0.478239	+	0.878230i	$0.341275\pi$
$684$	9265.69	+	6731.92i	0.517957	+	0.376318i
$685$	1735.07	−	5340.01i	0.0967793	−	0.297856i
$686$	−1921.35	−	5913.30i	−0.106935	−	0.329112i
$687$	−42227.8	+	30680.3i	−2.34511	+	1.70382i
$688$	10980.8	−	7978.04i	0.608488	−	0.442093i
$689$	1018.39	+	3134.29i	0.0563102	+	0.173305i
$690$	45.6766	−	140.578i	0.00252011	−	0.00775611i
$691$	7999.48	+	5811.96i	0.440397	+	0.319967i	0.785793	−	0.618490i	$-0.212255\pi$
$691$	7999.48	+	5811.96i	0.440397	+	0.319967i	−0.345395	+	0.938457i	$0.612255\pi$
$692$	−6829.68			−0.375182
$693$	−3634.98	+	885.538i	−0.199252	+	0.0485408i
$694$	−6806.86			−0.372312
$695$	12181.7	+	8850.56i	0.664863	+	0.483051i
$696$	1103.16	−	3395.18i	0.0600793	−	0.184905i
$697$	−217.339	−	668.902i	−0.0118111	−	0.0363507i
$698$	20481.6	−	14880.7i	1.11066	−	0.806940i
$699$	−3123.20	+	2269.14i	−0.168999	+	0.122785i
$700$	547.023	+	1683.56i	0.0295365	+	0.0909039i
$701$	−944.085	+	2905.59i	−0.0508667	+	0.156552i	−0.973263	−	0.229693i	$-0.926228\pi$
$701$	−944.085	+	2905.59i	−0.0508667	+	0.156552i	0.922396	+	0.386244i	$0.126228\pi$
$702$	7363.89	+	5350.18i	0.395915	+	0.287649i
$703$	−8941.06			−0.479685
$704$	−1799.68	+	23887.3i	−0.0963466	+	1.27882i
$705$	−4417.52			−0.235991
$706$	5863.31	+	4259.94i	0.312562	+	0.227089i
$707$	735.599	−	2263.94i	0.0391302	−	0.120430i
$708$	614.004	+	1889.71i	0.0325928	+	0.100310i
$709$	8619.44	−	6262.39i	0.456572	−	0.331719i	−0.335613	−	0.942000i	$-0.608943\pi$
$709$	8619.44	−	6262.39i	0.456572	−	0.331719i	0.792185	+	0.610281i	$0.208943\pi$
$710$	−9329.77	+	6778.47i	−0.493155	+	0.358298i
$711$	1874.50	+	5769.12i	0.0988739	+	0.304302i
$712$	−2467.11	+	7592.97i	−0.129858	+	0.399661i
$713$	−158.685	−	115.291i	−0.00833491	−	0.00605567i
$714$	−339.349			−0.0177868
$715$	−1533.09	−	2483.11i	−0.0801876	−	0.129878i
$716$	9389.47			0.490085
$717$	39576.0	+	28753.7i	2.06136	+	1.49766i
$718$	−5633.02	+	17336.7i	−0.292789	+	0.901112i
$719$	−889.804	−	2738.53i	−0.0461531	−	0.142045i	0.925324	−	0.379176i	$-0.123793\pi$
$719$	−889.804	−	2738.53i	−0.0461531	−	0.142045i	−0.971477	+	0.237132i	$0.923793\pi$
$720$	12198.9	−	8862.99i	0.631423	−	0.458756i
$721$	197.621	−	143.580i	0.0102077	−	0.00741635i
$722$	7895.13	+	24298.7i	0.406962	+	1.25250i
$723$	−7728.00	+	23784.3i	−0.397520	+	1.22344i
$724$	4953.83	+	3599.17i	0.254292	+	0.184754i
$725$	−7034.95			−0.360374
$726$	−7732.39	−	46794.2i	−0.395283	−	2.39215i
$727$	13697.2			0.698761			0.349381	−	0.936981i	$-0.386392\pi$
$727$	13697.2			0.698761			0.349381	+	0.936981i	$0.386392\pi$
$728$	119.130	+	86.5529i	0.00606489	+	0.00440640i
$729$	−9369.64	+	28836.8i	−0.476027	+	1.46506i
$730$	3843.34	+	11828.6i	0.194861	+	0.599721i
$731$	−905.522	+	657.900i	−0.0458166	+	0.0332877i
$732$	27822.3	−	20214.1i	1.40484	−	1.02067i
$733$	4862.90	+	14966.5i	0.245041	+	0.754160i	0.995630	+	0.0933897i	$0.0297702\pi$
$733$	4862.90	+	14966.5i	0.245041	+	0.754160i	−0.750588	+	0.660770i	$0.770230\pi$
$734$	−11180.3	+	34409.3i	−0.562222	+	1.73034i
$735$	−14446.5	−	10496.0i	−0.724990	−	0.526736i
$736$	174.840			0.00875636
$737$	16341.4	+	26467.9i	0.816749	+	1.32287i
$738$	31447.6			1.56856
$739$	−6876.58	−	4996.13i	−0.342299	−	0.248695i	0.403332	−	0.915054i	$-0.367852\pi$
$739$	−6876.58	−	4996.13i	−0.342299	−	0.248695i	−0.745631	+	0.666359i	$0.767852\pi$
$740$	5913.11	−	18198.7i	0.293743	−	0.904049i
$741$	−915.948	−	2819.00i	−0.0454091	−	0.139755i
$742$	1872.05	−	1360.12i	0.0926215	−	0.0672934i
$743$	1369.59	−	995.065i	0.0676250	−	0.0491324i	−0.553459	−	0.832876i	$-0.686693\pi$
$743$	1369.59	−	995.065i	0.0676250	−	0.0491324i	0.621084	+	0.783744i	$0.286693\pi$
$744$	3975.72	+	12236.0i	0.195910	+	0.602949i
$745$	−5101.27	+	15700.1i	−0.250867	+	0.772090i
$746$	−34028.0	−	24722.8i	−1.67005	−	1.21336i
$747$	−25802.6			−1.26381
$748$	109.723	−	1456.36i	0.00536345	−	0.0711895i
$749$	897.876			0.0438020
$750$	37630.0	+	27339.8i	1.83207	+	1.33108i
$751$	−1315.97	+	4050.13i	−0.0639418	+	0.196793i	−0.977924	−	0.208962i	$-0.932991\pi$
$751$	−1315.97	+	4050.13i	−0.0639418	+	0.196793i	0.913982	+	0.405755i	$0.132991\pi$
$752$	−1358.05	−	4179.66i	−0.0658552	−	0.202681i
$753$	28897.9	−	20995.6i	1.39854	−	1.01610i
$754$	−3525.53	+	2561.45i	−0.170281	+	0.123717i
$755$	−6500.86	−	20007.6i	−0.313365	−	0.964439i
$756$	1058.56	−	3257.90i	0.0509250	−	0.156731i
$757$	−5648.23	−	4103.68i	−0.271187	−	0.197029i	0.443878	−	0.896087i	$-0.353603\pi$
$757$	−5648.23	−	4103.68i	−0.271187	−	0.197029i	−0.715064	+	0.699059i	$0.753603\pi$
$758$	−31353.7			−1.50240
$759$	−205.074	+	49.9592i	−0.00980726	+	0.00238920i
$760$	842.327			0.0402032
$761$	27421.8	+	19923.1i	1.30623	+	0.949030i	0.999996	−	0.00292657i	$-0.000931557\pi$
$761$	27421.8	+	19923.1i	1.30623	+	0.949030i	0.306232	+	0.951957i	$0.400932\pi$
$762$	−5385.55	+	16575.0i	−0.256034	+	0.787991i
$763$	533.340	+	1641.45i	0.0253056	+	0.0778827i
$764$	303.912	−	220.805i	0.0143916	−	0.0104561i
$765$	−1005.97	+	730.877i	−0.0475435	+	0.0345424i
$766$	−11607.2	−	35723.3i	−0.547501	−	1.68503i
$767$	100.650	−	309.769i	0.00473829	−	0.0145830i
$768$	17685.5	+	12849.3i	0.830951	+	0.603721i
$769$	−33303.6			−1.56172			−0.780858	−	0.624709i	$-0.785218\pi$
$769$	−33303.6			−1.56172			−0.780858	+	0.624709i	$0.785218\pi$
$770$	−1325.53	+	1562.53i	−0.0620372	+	0.0731296i
$771$	36140.4			1.68815
$772$	17762.0	+	12904.8i	0.828067	+	0.601626i
$773$	−746.130	+	2296.35i	−0.0347172	+	0.106849i	−0.966913	−	0.255105i	$-0.917890\pi$
$773$	−746.130	+	2296.35i	−0.0347172	+	0.106849i	0.932196	+	0.361953i	$0.117890\pi$
$774$	−15465.2	−	47596.9i	−0.718196	−	2.21038i
$775$	20511.4	−	14902.4i	0.950700	−	0.690724i
$776$	1129.20	−	820.415i	0.0522372	−	0.0379525i
$777$	1961.93	+	6038.19i	0.0905840	+	0.278789i
$778$	10868.1	−	33448.6i	0.500823	−	1.54138i
$779$	−3489.65	−	2535.38i	−0.160500	−	0.116610i
$780$	6343.56			0.291200
$781$	15235.1	+	6251.03i	0.698022	+	0.286401i
$782$	−12.1264			−0.000554524
$783$	11013.5	+	8001.79i	0.502671	+	0.365212i
$784$	5489.63	−	16895.3i	0.250074	−	0.769649i
$785$	−5769.73	−	17757.4i	−0.262332	−	0.807374i
$786$	57913.8	−	42076.8i	2.62814	−	1.90945i
$787$	−4907.03	+	3565.16i	−0.222257	+	0.161479i	−0.693342	−	0.720608i	$-0.743863\pi$
$787$	−4907.03	+	3565.16i	−0.222257	+	0.161479i	0.471085	+	0.882088i	$0.343863\pi$
$788$	11146.5	+	34305.5i	0.503907	+	1.55087i
$789$	16014.8	−	49288.4i	0.722612	−	2.22397i
$790$	2687.75	+	1952.76i	0.121045	+	0.0879445i
$791$	−4953.87			−0.222679
$792$	8112.89	+	3328.75i	0.363989	+	0.149346i
$793$	−5637.40			−0.252446
$794$	−25180.7	−	18294.8i	−1.12548	−	0.817707i
$795$	4136.62	−	12731.2i	0.184542	−	0.567962i
$796$	8948.68	+	27541.2i	0.398464	+	1.22635i
$797$	−14950.8	+	10862.4i	−0.664471	+	0.482766i	−0.868170	−	0.496267i	$-0.834704\pi$
$797$	−14950.8	+	10862.4i	−0.664471	+	0.482766i	0.203699	+	0.979034i	$0.434704\pi$
$798$	−1683.73	+	1223.30i	−0.0746910	+	0.0542662i
$799$	111.990	+	344.671i	0.00495861	+	0.0152610i
$800$	−6983.66	+	21493.5i	−0.308637	+	0.949888i
$801$	−58475.8	−	42485.2i	−2.57945	−	1.87408i
$802$	−45967.0			−2.02388
$803$	11489.1	−	13543.4i	0.504908	−	0.595187i
$804$	−67617.0			−2.96601
$805$	7.37724	+	5.35988i	0.000322998	+	0.000234672i
$806$	4853.18	−	14936.6i	0.212092	−	0.652752i
$807$	−9435.66	−	29040.0i	−0.411587	−	1.26674i
$808$	−4513.95	+	3279.58i	−0.196535	+	0.142791i
$809$	−21558.6	+	15663.3i	−0.936911	+	0.680706i	−0.947675	−	0.319237i	$-0.896574\pi$
$809$	−21558.6	+	15663.3i	−0.936911	+	0.680706i	0.0107643	+	0.999942i	$0.496574\pi$
$810$	−1481.19	−	4558.65i	−0.0642517	−	0.197746i
$811$	−5307.75	+	16335.6i	−0.229815	+	0.707299i	0.767951	+	0.640508i	$0.221276\pi$
$811$	−5307.75	+	16335.6i	−0.229815	+	0.707299i	−0.997767	+	0.0667913i	$0.978724\pi$
$812$	1326.80	+	963.977i	0.0573419	+	0.0416613i
$813$	−66709.8			−2.87776
$814$	−49531.0	+	12066.5i	−2.13275	+	0.519572i
$815$	22167.4			0.952748
$816$	−1580.02	−	1147.95i	−0.0677841	−	0.0492480i
$817$	−2121.25	+	6528.54i	−0.0908362	+	0.279565i
$818$	9177.44	+	28245.3i	0.392276	+	1.20730i
$819$	−1078.53	+	783.600i	−0.0460159	+	0.0334325i
$820$	7468.39	−	5426.10i	0.318058	−	0.231083i
$821$	10718.5	+	32988.2i	0.455638	+	1.40231i	0.870384	+	0.492373i	$0.163870\pi$
$821$	10718.5	+	32988.2i	0.455638	+	1.40231i	−0.414746	+	0.909937i	$0.636130\pi$
$822$	10048.3	−	30925.5i	0.426368	−	1.31223i
$823$	−5883.89	−	4274.89i	−0.249209	−	0.181061i	0.456167	−	0.889894i	$-0.349222\pi$
$823$	−5883.89	−	4274.89i	−0.249209	−	0.181061i	−0.705376	+	0.708833i	$0.749222\pi$
$824$	−572.552			−0.0242061
$825$	2049.70	−	27205.8i	0.0864986	−	1.14810i
$826$	−228.696			−0.00963360
$827$	−22014.7	−	15994.6i	−0.925668	−	0.672537i	0.0192601	−	0.999815i	$-0.493869\pi$
$827$	−22014.7	−	15994.6i	−0.925668	−	0.672537i	−0.944928	+	0.327277i	$0.893869\pi$
$828$	89.8046	−	276.390i	0.00376923	−	0.0116005i
$829$	9563.22	+	29432.6i	0.400656	+	1.23309i	0.924468	+	0.381260i	$0.124510\pi$
$829$	9563.22	+	29432.6i	0.400656	+	1.23309i	−0.523812	+	0.851834i	$0.675490\pi$
$830$	−11432.7	+	8306.34i	−0.478114	+	0.347370i
$831$	18327.6	−	13315.8i	0.765077	−	0.555861i
$832$	2637.75	+	8118.15i	0.109913	+	0.338277i
$833$	−452.696	+	1393.26i	−0.0188295	+	0.0579513i
$834$	70547.9	+	51256.0i	2.92910	+	2.12812i
$835$	21627.3			0.896341
$836$	−4705.55	−	7621.48i	−0.194671	−	0.315304i
$837$	−49062.1			−2.02609
$838$	−22187.1	−	16119.8i	−0.914605	−	0.664499i
$839$	2651.88	−	8161.66i	0.109122	−	0.335842i	−0.881554	−	0.472083i	$-0.843502\pi$
$839$	2651.88	−	8161.66i	0.109122	−	0.335842i	0.990676	+	0.136241i	$0.0435021\pi$
$840$	−184.831	−	568.852i	−0.00759200	−	0.0233658i
$841$	14458.3	−	10504.6i	0.592820	−	0.430709i
$842$	−55892.0	+	40607.9i	−2.28761	+	1.66204i
$843$	2923.07	+	8996.27i	0.119426	+	0.367554i
$844$	−1272.36	+	3915.92i	−0.0518914	+	0.159705i
$845$	−841.268	−	611.217i	−0.0342491	−	0.0248834i
$846$	−16204.3			−0.658527
$847$	2892.92	+	438.397i	0.117358	+	0.0177845i
$848$	13317.4			0.539293
$849$	27482.5	+	19967.2i	1.11095	+	0.807154i
$850$	484.366	−	1490.72i	0.0195454	−	0.0601546i
$851$	70.1079	+	215.770i	0.00282405	+	0.00869154i
$852$	−28960.1	+	21040.7i	−1.16450	+	0.846061i
$853$	11101.5	−	8065.71i	0.445613	−	0.323757i	−0.342248	−	0.939610i	$-0.611188\pi$
$853$	11101.5	−	8065.71i	0.445613	−	0.323757i	0.787861	+	0.615853i	$0.211188\pi$
$854$	1223.17	+	3764.54i	0.0490118	+	0.150843i
$855$	−2356.55	+	7252.71i	−0.0942600	+	0.290102i
$856$	−1702.61	−	1237.02i	−0.0679835	−	0.0493929i
$857$	−14377.6			−0.573080			−0.286540	−	0.958068i	$-0.592505\pi$
$857$	−14377.6			−0.573080			−0.286540	+	0.958068i	$0.592505\pi$
$858$	−8878.52	−	14380.4i	−0.353273	−	0.572188i
$859$	−2556.76			−0.101555			−0.0507773	−	0.998710i	$-0.516170\pi$
$859$	−2556.76			−0.101555			−0.0507773	+	0.998710i	$0.516170\pi$
$860$	−11885.3	−	8635.21i	−0.471264	−	0.342393i
$861$	−946.496	+	2913.02i	−0.0374640	+	0.115302i
$862$	12051.1	+	37089.4i	0.476174	+	1.46551i
$863$	7980.86	−	5798.44i	0.314799	−	0.228715i	−0.419154	−	0.907915i	$-0.637673\pi$
$863$	7980.86	−	5798.44i	0.314799	−	0.228715i	0.733953	+	0.679200i	$0.237673\pi$
$864$	35380.7	−	25705.6i	1.39314	−	1.01218i
$865$	−1405.26	−	4324.95i	−0.0552373	−	0.170003i
$866$	3180.51	−	9788.59i	0.124801	−	0.384099i
$867$	−33980.2	−	24688.1i	−1.33106	−	0.967071i
$868$	−5910.52			−0.231125
$869$	356.409	−	4730.64i	0.0139129	−	0.184668i
$870$	17701.0			0.689791
$871$	8967.21	+	6515.06i	0.348843	+	0.253449i
$872$	1250.10	−	3847.41i	0.0485478	−	0.149415i
$873$	3904.90	+	12018.1i	0.151387	+	0.465922i
$874$	−60.1668	+	43.7137i	−0.00232857	+	0.00169181i
$875$	−2321.45	+	1686.63i	−0.0896907	+	0.0651641i
$876$	11930.0	+	36716.6i	0.460132	+	1.41614i
$877$	2994.50	−	9216.12i	0.115299	−	0.354853i	−0.876710	−	0.481018i	$-0.840267\pi$
$877$	2994.50	−	9216.12i	0.115299	−	0.354853i	0.992009	+	0.126165i	$0.0402670\pi$
$878$	−47375.2	−	34420.1i	−1.82100	−	1.32303i
$879$	18450.5			0.707987
$880$	−11457.5	+	2791.21i	−0.438899	+	0.106923i
$881$	−8946.66			−0.342135			−0.171067	−	0.985259i	$-0.554722\pi$
$881$	−8946.66			−0.342135			−0.171067	+	0.985259i	$0.554722\pi$
$882$	−52992.3	−	38501.2i	−2.02307	−	1.46984i
$883$	2273.56	−	6997.29i	0.0866492	−	0.266679i	−0.898338	−	0.439304i	$-0.855225\pi$
$883$	2273.56	−	6997.29i	0.0866492	−	0.266679i	0.984988	+	0.172625i	$0.0552250\pi$
$884$	−160.818	−	494.947i	−0.00611866	−	0.0188313i
$885$	−1070.34	+	777.644i	−0.0406542	+	0.0295370i
$886$	54430.4	−	39546.0i	2.06391	−	1.49952i
$887$	−2175.26	−	6694.76i	−0.0823428	−	0.253425i	0.901406	−	0.432975i	$-0.142536\pi$
$887$	−2175.26	−	6694.76i	−0.0823428	−	0.253425i	−0.983749	+	0.179549i	$0.942536\pi$
$888$	4598.58	−	14153.0i	0.173782	−	0.534845i
$889$	−869.822	−	631.963i	−0.0328154	−	0.0238418i
$890$	−39586.4			−1.49094
$891$	−4427.80	+	5219.50i	−0.166484	+	0.196251i
$892$	−38538.2			−1.44658
$893$	1798.14	+	1306.43i	0.0673825	+	0.0489563i
$894$	−29542.9	+	90923.7i	−1.10521	+	3.40150i
$895$	1931.96	+	5945.95i	0.0721544	+	0.222068i
$896$	1158.86	−	841.960i	0.0432084	−	0.0313928i
$897$	−60.8474	+	44.2082i	−0.00226492	+	0.00164556i
$898$	13494.0	+	41530.2i	0.501447	+	1.54330i
$899$	7258.48	−	22339.3i	0.269281	−	0.828762i
$900$	30390.3	+	22079.8i	1.12557	+	0.817772i
$901$	−1098.20			−0.0406065
$902$	−22753.4	−	9335.82i	−0.839918	−	0.344622i
$903$	4874.41			0.179635
$904$	9393.82	+	6825.01i	0.345613	+	0.251102i
$905$	−1259.91	+	3877.61i	−0.0462772	+	0.142426i
$906$	−37648.3	−	115870.i	−1.38055	−	4.24890i
$907$	−27897.4	+	20268.7i	−1.02130	+	0.742018i	−0.966549	−	0.256482i	$-0.917437\pi$
$907$	−27897.4	+	20268.7i	−1.02130	+	0.742018i	−0.0547512	+	0.998500i	$0.517437\pi$
$908$	−7027.81	+	5106.00i	−0.256857	+	0.186618i
$909$	−15609.7	−	48041.7i	−0.569573	−	1.75296i
$910$	−225.624	+	694.399i	−0.00821908	+	0.0252957i
$911$	8217.63	+	5970.45i	0.298861	+	0.217135i	0.727102	−	0.686529i	$-0.240867\pi$
$911$	8217.63	+	5970.45i	0.298861	+	0.217135i	−0.428241	+	0.903664i	$0.640867\pi$
$912$	−11977.7			−0.434892
$913$	18669.1	+	7660.01i	0.676733	+	0.277666i
$914$	−39610.7			−1.43349
$915$	18525.4	+	13459.5i	0.669322	+	0.486291i
$916$	−17368.2	+	53453.9i	−0.626487	+	1.92813i
$917$	1364.68	+	4200.06i	0.0491448	+	0.151252i
$918$	−2453.90	+	1782.86i	−0.0882252	+	0.0640994i
$919$	−22453.3	+	16313.3i	−0.805949	+	0.585556i	−0.912653	−	0.408735i	$-0.865970\pi$
$919$	−22453.3	+	16313.3i	−0.805949	+	0.585556i	0.106704	+	0.994291i	$0.465970\pi$
$920$	−6.60479	−	20.3275i	−0.000236689	−	0.000728453i
$921$	11493.9	−	35374.6i	0.411224	−	1.26562i
$922$	35400.4	+	25719.9i	1.26448	+	0.918698i
$923$	5867.95			0.209259
$924$	−4114.51	+	4850.19i	−0.146491	+	0.172684i
$925$	−29325.5			−1.04240
$926$	−6958.56	−	5055.69i	−0.246946	−	0.179417i
$927$	1601.81	−	4929.86i	0.0567533	−	0.174669i
$928$	6470.06	+	19912.8i	0.228869	+	0.704385i
$929$	−14388.2	+	10453.7i	−0.508141	+	0.369186i	−0.812118	−	0.583493i	$-0.801685\pi$
$929$	−14388.2	+	10453.7i	−0.508141	+	0.369186i	0.303977	+	0.952679i	$0.401685\pi$
$930$	−51609.8	+	37496.7i	−1.81973	+	1.32211i
$931$	2776.36	+	8544.75i	0.0977352	+	0.300798i
$932$	−1284.57	+	3953.49i	−0.0451474	+	0.138949i
$933$	13419.3	+	9749.73i	0.470879	+	0.342113i
$934$	55136.6			1.93161
$935$	944.827	−	230.174i	0.0330472	−	0.00805081i
$936$	3124.76			0.109120
$937$	−30700.2	−	22305.0i	−1.07036	−	0.777666i	−0.0943870	−	0.995536i	$-0.530089\pi$
$937$	−30700.2	−	22305.0i	−1.07036	−	0.777666i	−0.975978	+	0.217870i	$0.930089\pi$
$938$	2404.96	−	7401.72i	0.0837152	−	0.257649i
$939$	10584.0	+	32574.3i	0.367834	+	1.13208i
$940$	−3848.30	+	2795.95i	−0.133529	+	0.0970148i
$941$	−6906.28	+	5017.71i	−0.239254	+	0.173828i	−0.700951	−	0.713209i	$-0.747241\pi$
$941$	−6906.28	+	5017.71i	−0.239254	+	0.173828i	0.461697	+	0.887038i	$0.347241\pi$
$942$	−33414.1	−	102838.i	−1.15572	−	3.55695i
$943$	−33.8223	+	104.094i	−0.00116798	+	0.00359467i
$944$	−1064.82	−	773.635i	−0.0367128	−	0.0266734i
$945$	2280.89			0.0785159
$946$	−2940.47	+	39029.1i	−0.101060	+	1.34138i
$947$	39690.2			1.36194			0.680970	−	0.732311i	$-0.261558\pi$
$947$	39690.2			1.36194			0.680970	+	0.732311i	$0.261558\pi$
$948$	8342.91	+	6061.48i	0.285828	+	0.207666i
$949$	1955.61	−	6018.75i	0.0668934	−	0.205877i
$950$	−2970.59	−	9142.52i	−0.101451	−	0.312234i
$951$	49530.7	−	35986.2i	1.68890	−	1.22706i
$952$	−39.6981	+	28.8424i	−0.00135149	+	0.000981918i
$953$	−8958.18	−	27570.4i	−0.304495	−	0.937140i	−0.979865	−	0.199661i	$-0.936016\pi$
$953$	−8958.18	−	27570.4i	−0.304495	−	0.937140i	0.675370	−	0.737479i	$-0.263984\pi$
$954$	15173.9	−	46700.3i	0.514960	−	1.58488i
$955$	202.359	+	147.022i	0.00685672	+	0.00498170i
$956$	52675.3			1.78205
$957$	−13278.8	−	21507.4i	−0.448530	−	0.726475i
$958$	−8989.98			−0.303187
$959$	1622.90	+	1179.11i	0.0546469	+	0.0397033i
$960$	10714.3	−	32975.2i	0.360210	−	1.10861i
$961$	16953.2	+	52176.6i	0.569071	+	1.75142i
$962$	−14696.3	+	10677.5i	−0.492545	+	0.357855i
$963$	15414.4	−	11199.2i	0.515808	−	0.374756i
$964$	8321.45	+	25610.8i	0.278025	+	0.855673i
$965$	−4517.41	+	13903.2i	−0.150695	+	0.463791i
$966$	42.7237	+	31.0406i	0.00142299	+	0.00103386i
$967$	7443.57			0.247538			0.123769	−	0.992311i	$-0.460502\pi$
$967$	7443.57			0.247538			0.123769	+	0.992311i	$0.460502\pi$
$968$	−4881.76	−	4816.94i	−0.162093	−	0.159940i
$969$	987.729			0.0327455
$970$	5599.03	+	4067.93i	0.185334	+	0.134653i
$971$	1457.29	−	4485.08i	0.0481634	−	0.148232i	−0.924082	−	0.382193i	$-0.875169\pi$
$971$	1457.29	−	4485.08i	0.0481634	−	0.148232i	0.972246	+	0.233961i	$0.0751689\pi$
$972$	8403.63	+	25863.7i	0.277311	+	0.853476i
$973$	−4352.20	+	3162.06i	−0.143397	+	0.104184i
$974$	30134.4	−	21893.9i	0.991344	−	0.720254i
$975$	−3004.19	−	9245.95i	−0.0986780	−	0.303700i
$976$	−7039.58	+	21665.6i	−0.230872	+	0.710552i
$977$	31916.2	+	23188.5i	1.04513	+	0.759330i	0.971280	−	0.237939i	$-0.0764720\pi$
$977$	31916.2	+	23188.5i	1.04513	+	0.759330i	0.0738482	+	0.997269i	$0.476472\pi$
$978$	128377.			4.19740
$979$	29696.7	+	48099.2i	0.969471	+	1.57023i
$980$	−19228.2			−0.626756
$981$	29630.1	+	21527.5i	0.964338	+	0.700633i
$982$	19733.9	−	60734.8i	0.641278	−	1.97365i
$983$	4218.72	+	12983.9i	0.136883	+	0.421283i	0.995878	−	0.0907009i	$-0.0289107\pi$
$983$	4218.72	+	12983.9i	0.136883	+	0.421283i	−0.858995	+	0.511984i	$0.828911\pi$
$984$	5808.11	−	4219.84i	0.188166	−	0.136711i
$985$	−19430.7	+	14117.2i	−0.628542	+	0.456662i
$986$	−448.744	−	1381.09i	−0.0144938	−	0.0446074i
$987$	487.709	−	1501.01i	0.0157284	−	0.0484071i
$988$	−2582.13	−	1876.03i	−0.0831463	−	0.0604093i
$989$	174.183			0.00560030
$990$	−3266.64	+	43358.4i	−0.104869	+	1.39194i
$991$	−37372.6			−1.19796			−0.598981	−	0.800763i	$-0.704428\pi$
$991$	−37372.6			−1.19796			−0.598981	+	0.800763i	$0.704428\pi$
$992$	−61046.5	−	44352.9i	−1.95386	−	1.41956i
$993$	−15468.9	+	47608.3i	−0.494350	+	1.52145i
$994$	−1273.20	−	3918.49i	−0.0406271	−	0.125037i
$995$	−15599.4	+	11333.6i	−0.497020	+	0.361106i
$996$	−35487.7	+	25783.3i	−1.12899	+	0.820257i
$997$	−3172.40	−	9763.63i	−0.100773	−	0.310148i	0.887942	−	0.459955i	$-0.152135\pi$
$997$	−3172.40	−	9763.63i	−0.100773	−	0.310148i	−0.988715	+	0.149808i	$0.952135\pi$
$998$	−7728.82	+	23786.9i	−0.245142	+	0.754469i
$999$	45910.4	+	33355.9i	1.45399	+	1.05639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.b.92.17	yes	76
11.3	even	5	inner	143.4.h.b.14.17	✓	76
11.5	even	5		1573.4.a.q.1.7		38
11.6	odd	10		1573.4.a.r.1.32		38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.b.14.17	✓	76	11.3	even	5	inner
143.4.h.b.92.17	yes	76	1.1	even	1	trivial
1573.4.a.q.1.7		38	11.5	even	5
1573.4.a.r.1.32		38	11.6	odd	10

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.35922 + 2.44061i) q^{2} +(-2.65195 + 8.16188i) q^{3} +(2.85561 + 8.78865i) q^{4} +(-4.97791 + 3.61667i) q^{5} +(-28.8285 + 20.9451i) q^{6} +(-0.679316 - 2.09072i) q^{7} +(-1.59225 + 4.90045i) q^{8} +(-37.7399 - 27.4196i) q^{9} -25.5488 q^{10} +(19.1661 + 31.0429i) q^{11} -79.3048 q^{12} +(10.5172 + 7.64121i) q^{13} +(2.82067 - 8.68113i) q^{14} +(-16.3176 - 50.2204i) q^{15} +(42.4998 - 30.8779i) q^{16} +(-3.50470 + 2.54631i) q^{17} +(-59.8557 - 184.217i) q^{18} +(-8.21001 + 25.2678i) q^{19} +(-46.0006 - 33.4214i) q^{20} +18.8657 q^{21} +(-11.3807 + 151.057i) q^{22} +0.674151 q^{23} +(-35.7743 - 25.9916i) q^{24} +(-26.9278 + 82.8752i) q^{25} +(16.6804 + 51.3370i) q^{26} +(136.422 - 99.1162i) q^{27} +(16.4347 - 11.9405i) q^{28} +(24.9474 + 76.7802i) q^{29} +(67.7542 - 208.526i) q^{30} +(-235.385 - 171.017i) q^{31} +259.348 q^{32} +(-304.196 + 74.1069i) q^{33} -17.9876 q^{34} +(10.9430 + 7.95056i) q^{35} +(133.211 - 409.983i) q^{36} +(103.994 + 320.062i) q^{37} +(-89.2482 + 64.8426i) q^{38} +(-90.2578 + 65.5761i) q^{39} +(-9.79720 - 30.1527i) q^{40} +(-50.1702 + 154.408i) q^{41} +(63.3740 + 46.0439i) q^{42} +258.374 q^{43} +(-218.094 + 257.090i) q^{44} +287.034 q^{45} +(2.26462 + 1.64534i) q^{46} +(25.8516 - 79.5631i) q^{47} +(139.314 + 428.764i) q^{48} +(273.583 - 198.770i) q^{49} +(-292.722 + 212.675i) q^{50} +(-11.4884 - 35.3576i) q^{51} +(-37.1229 + 114.252i) q^{52} +(205.091 + 149.008i) q^{53} +700.175 q^{54} +(-207.679 - 85.2115i) q^{55} +11.3271 q^{56} +(-184.460 - 134.018i) q^{57} +(-103.587 + 318.808i) q^{58} +(-7.74232 - 23.8284i) q^{59} +(394.773 - 286.819i) q^{60} +(-350.827 + 254.891i) q^{61} +(-373.322 - 1148.97i) q^{62} +(-31.6895 + 97.5301i) q^{63} +(531.208 + 385.945i) q^{64} -79.9895 q^{65} +(-1202.73 - 493.484i) q^{66} +852.622 q^{67} +(-32.3867 - 23.5303i) q^{68} +(-1.78782 + 5.50234i) q^{69} +(17.3557 + 53.4153i) q^{70} +(365.175 - 265.315i) q^{71} +(194.460 - 141.284i) q^{72} +(-150.432 - 462.981i) q^{73} +(-431.808 + 1328.97i) q^{74} +(-605.006 - 439.562i) q^{75} -245.515 q^{76} +(51.8822 - 61.1588i) q^{77} -463.241 q^{78} +(-105.201 - 76.4327i) q^{79} +(-99.8851 + 307.415i) q^{80} +(57.9751 + 178.429i) q^{81} +(-545.383 + 396.244i) q^{82} +(447.485 - 325.117i) q^{83} +(53.8730 + 165.804i) q^{84} +(8.23692 - 25.3506i) q^{85} +(867.934 + 630.591i) q^{86} -692.830 q^{87} +(-182.642 + 44.4943i) q^{88} +1549.44 q^{89} +(964.208 + 700.538i) q^{90} +(8.83111 - 27.1794i) q^{91} +(1.92511 + 5.92488i) q^{92} +(2020.05 - 1467.65i) q^{93} +(281.024 - 204.176i) q^{94} +(-50.5165 - 155.474i) q^{95} +(-687.779 + 2116.77i) q^{96} +(-219.150 - 159.222i) q^{97} +1404.15 q^{98} +(127.859 - 1697.08i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{2} - 12 q^{3} - 148 q^{4} - 16 q^{5} + 77 q^{6} + 56 q^{7} - 34 q^{8} - 241 q^{9} + 60 q^{10} - 47 q^{11} + 244 q^{12} + 247 q^{13} + 117 q^{14} - 2 q^{15} + 212 q^{16} - 344 q^{17} - 461 q^{18}+ \cdots - 11439 q^{99}+O(q^{100}) \) 76 * q + 4 * q^2 - 12 * q^3 - 148 * q^4 - 16 * q^5 + 77 * q^6 + 56 * q^7 - 34 * q^8 - 241 * q^9 + 60 * q^10 - 47 * q^11 + 244 * q^12 + 247 * q^13 + 117 * q^14 - 2 * q^15 + 212 * q^16 - 344 * q^17 - 461 * q^18 - 59 * q^19 + 55 * q^20 - 296 * q^21 - 76 * q^22 + 1680 * q^23 + 784 * q^24 - 89 * q^25 + 13 * q^26 - 309 * q^27 - 654 * q^28 - 306 * q^29 + 606 * q^30 + 344 * q^31 - 2408 * q^32 + 1265 * q^33 - 116 * q^34 + 934 * q^35 - 3571 * q^36 + 188 * q^37 - 9 * q^38 + 91 * q^39 - 1803 * q^40 + 1518 * q^41 + 1734 * q^42 - 966 * q^43 + 1513 * q^44 + 2272 * q^45 - 165 * q^46 - 2146 * q^47 + 2320 * q^48 - 2085 * q^49 - 71 * q^50 - 501 * q^51 + 1924 * q^52 + 814 * q^53 - 6546 * q^54 - 1924 * q^55 + 6538 * q^56 - 1099 * q^57 - 4169 * q^58 - 41 * q^59 - 2812 * q^60 + 1788 * q^61 - 3931 * q^62 + 4980 * q^63 + 4256 * q^64 - 1352 * q^65 - 1543 * q^66 + 9878 * q^67 + 648 * q^68 - 2994 * q^69 + 6094 * q^70 - 612 * q^71 + 2965 * q^72 + 3436 * q^73 + 2616 * q^74 + 5089 * q^75 - 6632 * q^76 - 2604 * q^77 + 2704 * q^78 - 7688 * q^79 - 11093 * q^80 - 3972 * q^81 + 1076 * q^82 + 2007 * q^83 - 5729 * q^84 - 2128 * q^85 + 2433 * q^86 + 1812 * q^87 - 9006 * q^88 + 7454 * q^89 - 2204 * q^90 - 728 * q^91 + 2143 * q^92 - 8158 * q^93 + 4055 * q^94 + 824 * q^95 + 811 * q^96 + 5711 * q^97 - 4086 * q^98 - 11439 * q^99

Introduction

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