LMFDB - Embedded newform 143.4.b.a.12.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(12,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("143.12");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			12.9
Character	$\chi$	$=$	143.12
Dual form			143.4.b.a.12.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.37885i q^{2} +7.92479 q^{3} -3.41661 q^{4} +15.9579i q^{5} -26.7767i q^{6} +29.7230i q^{7} -15.4866i q^{8} +35.8023 q^{9} +O(q^{10})$	\(q-3.37885i q^{2} +7.92479 q^{3} -3.41661 q^{4} +15.9579i q^{5} -26.7767i q^{6} +29.7230i q^{7} -15.4866i q^{8} +35.8023 q^{9} +53.9193 q^{10} +11.0000i q^{11} -27.0759 q^{12} +(22.5386 - 41.0976i) q^{13} +100.430 q^{14} +126.463i q^{15} -79.6597 q^{16} +67.2115 q^{17} -120.970i q^{18} -45.1665i q^{19} -54.5220i q^{20} +235.549i q^{21} +37.1673 q^{22} -162.809 q^{23} -122.728i q^{24} -129.655 q^{25} +(-138.863 - 76.1544i) q^{26} +69.7561 q^{27} -101.552i q^{28} +155.706 q^{29} +427.299 q^{30} -235.170i q^{31} +145.265i q^{32} +87.1727i q^{33} -227.097i q^{34} -474.318 q^{35} -122.322 q^{36} -64.5862i q^{37} -152.611 q^{38} +(178.613 - 325.690i) q^{39} +247.133 q^{40} -303.508i q^{41} +795.883 q^{42} -154.693 q^{43} -37.5827i q^{44} +571.329i q^{45} +550.108i q^{46} +18.5539i q^{47} -631.286 q^{48} -540.459 q^{49} +438.084i q^{50} +532.637 q^{51} +(-77.0056 + 140.415i) q^{52} +289.937 q^{53} -235.695i q^{54} -175.537 q^{55} +460.308 q^{56} -357.935i q^{57} -526.106i q^{58} +345.435i q^{59} -432.075i q^{60} -428.842 q^{61} -794.603 q^{62} +1064.15i q^{63} -146.448 q^{64} +(655.832 + 359.669i) q^{65} +294.543 q^{66} -114.458i q^{67} -229.636 q^{68} -1290.23 q^{69} +1602.65i q^{70} +976.925i q^{71} -554.454i q^{72} +206.971i q^{73} -218.227 q^{74} -1027.49 q^{75} +154.316i q^{76} -326.953 q^{77} +(-1100.46 - 603.508i) q^{78} +998.746 q^{79} -1271.20i q^{80} -413.859 q^{81} -1025.51 q^{82} -895.839i q^{83} -804.779i q^{84} +1072.56i q^{85} +522.683i q^{86} +1233.94 q^{87} +170.352 q^{88} +611.865i q^{89} +1930.43 q^{90} +(1221.55 + 669.915i) q^{91} +556.256 q^{92} -1863.67i q^{93} +62.6909 q^{94} +720.762 q^{95} +1151.20i q^{96} -1170.49i q^{97} +1826.13i q^{98} +393.825i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 152 q^{4} + 360 q^{9}+O(q^{10}) $ 36 * q - 152 * q^4 + 360 * q^9	$ 36 q - 152 q^{4} + 360 q^{9} - 112 q^{10} - 108 q^{12} - 50 q^{13} + 8 q^{14} + 728 q^{16} + 276 q^{17} + 44 q^{22} - 472 q^{23} - 1172 q^{25} + 152 q^{26} - 12 q^{27} - 572 q^{29} + 712 q^{30} + 68 q^{35} - 430 q^{36} - 50 q^{38} + 640 q^{39} - 216 q^{40} + 1126 q^{42} + 920 q^{43} + 1674 q^{48} - 2164 q^{49} - 340 q^{51} - 800 q^{52} + 2432 q^{53} + 440 q^{55} - 2274 q^{56} - 1844 q^{61} + 2796 q^{62} - 2592 q^{64} + 2264 q^{65} + 1078 q^{66} - 4548 q^{68} - 3288 q^{69} - 4036 q^{74} + 820 q^{75} - 616 q^{77} + 2222 q^{78} + 360 q^{79} + 852 q^{81} + 1948 q^{82} - 2480 q^{87} + 264 q^{88} - 496 q^{90} + 4600 q^{91} + 454 q^{92} - 488 q^{94} + 952 q^{95}+O(q^{100}) $ 36 * q - 152 * q^4 + 360 * q^9 - 112 * q^10 - 108 * q^12 - 50 * q^13 + 8 * q^14 + 728 * q^16 + 276 * q^17 + 44 * q^22 - 472 * q^23 - 1172 * q^25 + 152 * q^26 - 12 * q^27 - 572 * q^29 + 712 * q^30 + 68 * q^35 - 430 * q^36 - 50 * q^38 + 640 * q^39 - 216 * q^40 + 1126 * q^42 + 920 * q^43 + 1674 * q^48 - 2164 * q^49 - 340 * q^51 - 800 * q^52 + 2432 * q^53 + 440 * q^55 - 2274 * q^56 - 1844 * q^61 + 2796 * q^62 - 2592 * q^64 + 2264 * q^65 + 1078 * q^66 - 4548 * q^68 - 3288 * q^69 - 4036 * q^74 + 820 * q^75 - 616 * q^77 + 2222 * q^78 + 360 * q^79 + 852 * q^81 + 1948 * q^82 - 2480 * q^87 + 264 * q^88 - 496 * q^90 + 4600 * q^91 + 454 * q^92 - 488 * q^94 + 952 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	3.37885i		−	1.19460i	−0.802017	−	0.597302i	$-0.796240\pi$
$2$		−	3.37885i		−	1.19460i	0.802017	−	0.597302i	$-0.203760\pi$
$3$	7.92479			1.52513			0.762563	−	0.646914i	$-0.223941\pi$
$3$	7.92479			1.52513			0.762563	+	0.646914i	$0.223941\pi$
$4$	−3.41661			−0.427077
$5$			15.9579i			1.42732i	0.700493	+	0.713659i	$0.252964\pi$
$5$			15.9579i			1.42732i	−0.700493	+	0.713659i	$0.747036\pi$
$6$		−	26.7767i		−	1.82192i
$7$			29.7230i			1.60489i	0.596724	+	0.802447i	$0.296469\pi$
$7$			29.7230i			1.60489i	−0.596724	+	0.802447i	$0.703531\pi$
$8$		−	15.4866i		−	0.684416i
$9$	35.8023			1.32601
$10$	53.9193			1.70508
$11$			11.0000i			0.301511i
$11$			11.0000i			0.301511i
$12$	−27.0759			−0.651346
$13$	22.5386	−	41.0976i	0.480852	−	0.876802i
$13$	22.5386	−	41.0976i	0.480852	−	0.876802i
$14$	100.430			1.91721
$15$			126.463i			2.17684i
$16$	−79.6597			−1.24468
$17$	67.2115			0.958893			0.479447	−	0.877571i	$-0.340837\pi$
$17$	67.2115			0.958893			0.479447	+	0.877571i	$0.340837\pi$
$18$		−	120.970i		−	1.58406i
$19$		−	45.1665i		−	0.545363i	−0.962104	−	0.272681i	$-0.912089\pi$
$19$		−	45.1665i		−	0.545363i	0.962104	−	0.272681i	$-0.0879105\pi$
$20$		−	54.5220i		−	0.609575i
$21$			235.549i			2.44766i
$22$	37.1673			0.360186
$23$	−162.809			−1.47600			−0.738002	−	0.674799i	$-0.764230\pi$
$23$	−162.809			−1.47600			−0.738002	+	0.674799i	$0.764230\pi$
$24$		−	122.728i		−	1.04382i
$25$	−129.655			−1.03724
$26$	−138.863	−	76.1544i	−1.04743	−	0.574427i
$27$	69.7561			0.497206
$28$		−	101.552i		−	0.685412i
$29$	155.706			0.997029			0.498514	−	0.866881i	$-0.333879\pi$
$29$	155.706			0.997029			0.498514	+	0.866881i	$0.333879\pi$
$30$	427.299			2.60046
$31$		−	235.170i		−	1.36251i	−0.732047	−	0.681254i	$-0.761435\pi$
$31$		−	235.170i		−	1.36251i	0.732047	−	0.681254i	$-0.238565\pi$
$32$			145.265i			0.802485i
$33$			87.1727i			0.459843i
$34$		−	227.097i		−	1.14550i
$35$	−474.318			−2.29069
$36$	−122.322			−0.566308
$37$		−	64.5862i		−	0.286970i	−0.989652	−	0.143485i	$-0.954169\pi$
$37$		−	64.5862i		−	0.286970i	0.989652	−	0.143485i	$-0.0458310\pi$
$38$	−152.611			−0.651492
$39$	178.613	−	325.690i	0.733360	−	1.33723i
$40$	247.133			0.976880
$41$		−	303.508i		−	1.15610i	−0.816002	−	0.578049i	$-0.803814\pi$
$41$		−	303.508i		−	1.15610i	0.816002	−	0.578049i	$-0.196186\pi$
$42$	795.883			2.92399
$43$	−154.693			−0.548614			−0.274307	−	0.961642i	$-0.588449\pi$
$43$	−154.693			−0.548614			−0.274307	+	0.961642i	$0.588449\pi$
$44$		−	37.5827i		−	0.128768i
$45$			571.329i			1.89264i
$46$			550.108i			1.76324i
$47$			18.5539i			0.0575823i	0.999585	+	0.0287912i	$0.00916578\pi$
$47$			18.5539i			0.0575823i	−0.999585	+	0.0287912i	$0.990834\pi$
$48$	−631.286			−1.89830
$49$	−540.459			−1.57568
$50$			438.084i			1.23909i
$51$	532.637			1.46243
$52$	−77.0056	+	140.415i	−0.205361	+	0.374462i
$53$	289.937			0.751433			0.375716	−	0.926735i	$-0.377397\pi$
$53$	289.937			0.751433			0.375716	+	0.926735i	$0.377397\pi$
$54$		−	235.695i		−	0.593964i
$55$	−175.537			−0.430353
$56$	460.308			1.09841
$57$		−	357.935i		−	0.831747i
$58$		−	526.106i		−	1.19105i
$59$			345.435i			0.762235i	0.924527	+	0.381117i	$0.124461\pi$
$59$			345.435i			0.762235i	−0.924527	+	0.381117i	$0.875539\pi$
$60$		−	432.075i		−	0.929678i
$61$	−428.842			−0.900125			−0.450063	−	0.892997i	$-0.648598\pi$
$61$	−428.842			−0.900125			−0.450063	+	0.892997i	$0.648598\pi$
$62$	−794.603			−1.62766
$63$			1064.15i			2.12810i
$64$	−146.448			−0.286031
$65$	655.832	+	359.669i	1.25148	+	0.686329i
$66$	294.543			0.549330
$67$		−	114.458i		−	0.208706i	−0.994540	−	0.104353i	$-0.966723\pi$
$67$		−	114.458i		−	0.208706i	0.994540	−	0.104353i	$-0.0332772\pi$
$68$	−229.636			−0.409521
$69$	−1290.23			−2.25109
$70$			1602.65i			2.73647i
$71$			976.925i			1.63295i	0.577378	+	0.816477i	$0.304076\pi$
$71$			976.925i			1.63295i	−0.577378	+	0.816477i	$0.695924\pi$
$72$		−	554.454i		−	0.907542i
$73$			206.971i			0.331837i	0.986139	+	0.165919i	$0.0530589\pi$
$73$			206.971i			0.331837i	−0.986139	+	0.165919i	$0.946941\pi$
$74$	−218.227			−0.342816
$75$	−1027.49			−1.58192
$76$			154.316i			0.232912i
$77$	−326.953			−0.483893
$78$	−1100.46	−	603.508i	−1.59746	−	0.876074i
$79$	998.746			1.42238			0.711188	−	0.703002i	$-0.248158\pi$
$79$	998.746			1.42238			0.711188	+	0.703002i	$0.248158\pi$
$80$		−	1271.20i		−	1.77656i
$81$	−413.859			−0.567708
$82$	−1025.51			−1.38108
$83$		−	895.839i		−	1.18471i	−0.805676	−	0.592356i	$-0.798198\pi$
$83$		−	895.839i		−	1.18471i	0.805676	−	0.592356i	$-0.201802\pi$
$84$		−	804.779i		−	1.04534i
$85$			1072.56i			1.36865i
$86$			522.683i			0.655377i
$87$	1233.94			1.52059
$88$	170.352			0.206359
$89$			611.865i			0.728737i	0.931255	+	0.364368i	$0.118715\pi$
$89$			611.865i			0.728737i	−0.931255	+	0.364368i	$0.881285\pi$
$90$	1930.43			2.26095
$91$	1221.55	+	669.915i	1.40717	+	0.771716i
$92$	556.256			0.630367
$93$		−	1863.67i		−	2.07800i
$94$	62.6909			0.0687880
$95$	720.762			0.778407
$96$			1151.20i			1.22389i
$97$		−	1170.49i		−	1.22521i	−0.790391	−	0.612603i	$-0.790122\pi$
$97$		−	1170.49i		−	1.22521i	0.790391	−	0.612603i	$-0.209878\pi$
$98$			1826.13i			1.88231i
$99$			393.825i			0.399807i
$100$	442.981			0.442981
$101$	1887.58			1.85962			0.929808	−	0.368045i	$-0.119973\pi$
$101$	1887.58			1.85962			0.929808	+	0.368045i	$0.119973\pi$
$102$		−	1799.70i		−	1.74703i
$103$	1125.62			1.07680			0.538400	−	0.842690i	$-0.319029\pi$
$103$	1125.62			1.07680			0.538400	+	0.842690i	$0.319029\pi$
$104$	−636.461	−	349.045i	−0.600097	−	0.329103i
$105$	−3758.87			−3.49360
$106$		−	979.654i		−	0.897664i
$107$	−763.339			−0.689671			−0.344836	−	0.938663i	$-0.612065\pi$
$107$	−763.339			−0.689671			−0.344836	+	0.938663i	$0.612065\pi$
$108$	−238.330			−0.212345
$109$		−	1113.53i		−	0.978504i	−0.872142	−	0.489252i	$-0.837270\pi$
$109$		−	1113.53i		−	0.978504i	0.872142	−	0.489252i	$-0.162730\pi$
$110$			593.113i			0.514101i
$111$		−	511.832i		−	0.437666i
$112$		−	2367.73i		−	1.99758i
$113$	−1241.84			−1.03383			−0.516915	−	0.856037i	$-0.672920\pi$
$113$	−1241.84			−1.03383			−0.516915	+	0.856037i	$0.672920\pi$
$114$	−1209.41			−0.993608
$115$		−	2598.10i		−	2.10673i
$116$	−531.986			−0.425808
$117$	806.932	−	1471.39i	0.637614	−	1.16265i
$118$	1167.17			0.910568
$119$			1997.73i			1.53892i
$120$	1958.48			1.48987
$121$	−121.000			−0.0909091
$122$			1448.99i			1.07529i
$123$		−	2405.24i		−	1.76319i
$124$			803.484i			0.581895i
$125$		−	74.2822i		−	0.0531520i
$126$	3595.61			2.54224
$127$	65.6987			0.0459041			0.0229520	−	0.999737i	$-0.492693\pi$
$127$	65.6987			0.0459041			0.0229520	+	0.999737i	$0.492693\pi$
$128$			1656.95i			1.14418i
$129$	−1225.91			−0.836706
$130$	1215.27	−	2215.96i	0.819891	−	1.49502i
$131$	−2275.86			−1.51788			−0.758941	−	0.651159i	$-0.774283\pi$
$131$	−2275.86			−1.51788			−0.758941	+	0.651159i	$0.774283\pi$
$132$		−	297.835i		−	0.196388i
$133$	1342.48			0.875249
$134$	−386.737			−0.249321
$135$			1113.16i			0.709672i
$136$		−	1040.88i		−	0.656282i
$137$			2527.29i			1.57607i	0.615633	+	0.788033i	$0.288901\pi$
$137$			2527.29i			1.57607i	−0.615633	+	0.788033i	$0.711099\pi$
$138$			4359.49i			2.68916i
$139$	−1851.37			−1.12972			−0.564859	−	0.825187i	$-0.691069\pi$
$139$	−1851.37			−1.12972			−0.564859	+	0.825187i	$0.691069\pi$
$140$	1620.56			0.978302
$141$			147.036i			0.0878203i
$142$	3300.88			1.95073
$143$	452.074	+	247.924i	0.264366	+	0.144982i
$144$	−2852.00			−1.65046
$145$			2484.74i			1.42308i
$146$	699.324			0.396414
$147$	−4283.02			−2.40311
$148$			220.666i			0.122558i
$149$			3458.33i			1.90146i	0.310018	+	0.950731i	$0.399665\pi$
$149$			3458.33i			1.90146i	−0.310018	+	0.950731i	$0.600335\pi$
$150$			3471.72i			1.88977i
$151$		−	1307.25i		−	0.704521i	−0.935902	−	0.352260i	$-0.885413\pi$
$151$		−	1307.25i		−	0.704521i	0.935902	−	0.352260i	$-0.114587\pi$
$152$	−699.473			−0.373255
$153$	2406.32			1.27150
$154$			1104.73i			0.578061i
$155$	3752.82			1.94473
$156$	−610.253	+	1112.76i	−0.313201	+	0.571101i
$157$	1318.24			0.670110			0.335055	−	0.942199i	$-0.391245\pi$
$157$	1318.24			0.670110			0.335055	+	0.942199i	$0.391245\pi$
$158$		−	3374.61i		−	1.69917i
$159$	2297.69			1.14603
$160$	−2318.13			−1.14540
$161$		−	4839.19i		−	2.36883i
$162$			1398.37i			0.678186i
$163$		−	774.231i		−	0.372039i	−0.982546	−	0.186020i	$-0.940441\pi$
$163$		−	774.231i		−	0.372039i	0.982546	−	0.186020i	$-0.0595588\pi$
$164$			1036.97i			0.493742i
$165$	−1391.09			−0.656342
$166$	−3026.90			−1.41526
$167$			1942.21i			0.899958i	0.893039	+	0.449979i	$0.148569\pi$
$167$			1942.21i			0.899958i	−0.893039	+	0.449979i	$0.851431\pi$
$168$	3647.84			1.67522
$169$	−1181.03	−	1852.56i	−0.537563	−	0.843224i
$170$	3624.00			1.63499
$171$		−	1617.06i		−	0.723157i
$172$	528.525			0.234300
$173$	−406.260			−0.178540			−0.0892699	−	0.996007i	$-0.528453\pi$
$173$	−406.260			−0.178540			−0.0892699	+	0.996007i	$0.528453\pi$
$174$		−	4169.28i		−	1.81651i
$175$		−	3853.74i		−	1.66466i
$176$		−	876.256i		−	0.375286i
$177$			2737.50i			1.16250i
$178$	2067.40			0.870551
$179$	−2995.36			−1.25075			−0.625373	−	0.780326i	$-0.715053\pi$
$179$	−2995.36			−1.25075			−0.625373	+	0.780326i	$0.715053\pi$
$180$		−	1952.01i		−	0.808302i
$181$	−4067.94			−1.67054			−0.835270	−	0.549840i	$-0.814689\pi$
$181$	−4067.94			−1.67054			−0.835270	+	0.549840i	$0.814689\pi$
$182$	2263.54	−	4127.42i	0.921894	−	1.68101i
$183$	−3398.49			−1.37280
$184$			2521.36i			1.01020i
$185$	1030.66			0.409598
$186$	−6297.06			−2.48238
$187$			739.327i			0.289117i
$188$		−	63.3916i		−	0.0245921i
$189$			2073.36i			0.797963i
$190$		−	2435.35i		−	0.929887i
$191$	63.3394			0.0239952			0.0119976	−	0.999928i	$-0.496181\pi$
$191$	63.3394			0.0239952			0.0119976	+	0.999928i	$0.496181\pi$
$192$	−1160.57			−0.436233
$193$		−	11.5033i		−	0.00429028i	−0.999998	−	0.00214514i	$-0.999317\pi$
$193$		−	11.5033i		−	0.00429028i	0.999998	−	0.00214514i	$-0.000682820\pi$
$194$	−3954.90			−1.46364
$195$	5197.33	+	2850.30i	1.90866	+	1.04674i
$196$	1846.54			0.672937
$197$		−	3754.82i		−	1.35797i	−0.734153	−	0.678984i	$-0.762420\pi$
$197$		−	3754.82i		−	1.35797i	0.734153	−	0.678984i	$-0.237580\pi$
$198$	1330.67			0.477611
$199$	1430.28			0.509496			0.254748	−	0.967008i	$-0.418008\pi$
$199$	1430.28			0.509496			0.254748	+	0.967008i	$0.418008\pi$
$200$			2007.91i			0.709903i
$201$		−	907.057i		−	0.318303i
$202$		−	6377.85i		−	2.22150i
$203$			4628.05i			1.60012i
$204$	−1819.81			−0.624571
$205$	4843.35			1.65012
$206$		−	3803.29i		−	1.28635i
$207$	−5828.94			−1.95720
$208$	−1795.42	+	3273.82i	−0.598508	+	1.09134i
$209$	496.831			0.164433
$210$			12700.6i			4.17346i
$211$	646.479			0.210926			0.105463	−	0.994423i	$-0.466367\pi$
$211$	646.479			0.210926			0.105463	+	0.994423i	$0.466367\pi$
$212$	−990.603			−0.320919
$213$			7741.93i			2.49046i
$214$			2579.21i			0.823883i
$215$		−	2468.57i		−	0.783048i
$216$		−	1080.28i		−	0.340296i
$217$	6989.96			2.18668
$218$	−3762.45			−1.16892
$219$			1640.20i			0.506094i
$220$	599.742			0.183794
$221$	1514.85	−	2762.23i	0.461086	−	0.840759i
$222$	−1729.40			−0.522837
$223$			2569.76i			0.771676i	0.922567	+	0.385838i	$0.126088\pi$
$223$			2569.76i			0.771676i	−0.922567	+	0.385838i	$0.873912\pi$
$224$	−4317.73			−1.28790
$225$	−4641.94			−1.37539
$226$			4196.00i			1.23502i
$227$		−	2035.96i		−	0.595292i	−0.954676	−	0.297646i	$-0.903798\pi$
$227$		−	2035.96i		−	0.595292i	0.954676	−	0.297646i	$-0.0962015\pi$
$228$			1222.92i			0.355220i
$229$			1538.12i			0.443850i	0.975064	+	0.221925i	$0.0712340\pi$
$229$			1538.12i			0.443850i	−0.975064	+	0.221925i	$0.928766\pi$
$230$	−8778.57			−2.51670
$231$	−2591.04			−0.737999
$232$		−	2411.35i		−	0.682382i
$233$	−3217.04			−0.904528			−0.452264	−	0.891884i	$-0.649384\pi$
$233$	−3217.04			−0.904528			−0.452264	+	0.891884i	$0.649384\pi$
$234$	−4971.59	−	2726.50i	−1.38890	−	0.761696i
$235$	−296.082			−0.0821884
$236$		−	1180.22i		−	0.325533i
$237$	7914.85			2.16930
$238$	6750.03			1.83840
$239$			2456.46i			0.664833i	0.943133	+	0.332416i	$0.107864\pi$
$239$			2456.46i			0.664833i	−0.943133	+	0.332416i	$0.892136\pi$
$240$		−	10074.0i		−	2.70948i
$241$		−	2999.95i		−	0.801840i	−0.916113	−	0.400920i	$-0.868690\pi$
$241$		−	2999.95i		−	0.801840i	0.916113	−	0.400920i	$-0.131310\pi$
$242$			408.841i			0.108600i
$243$	−5163.16			−1.36303
$244$	1465.19			0.384423
$245$		−	8624.59i		−	2.24900i
$246$	−8126.93			−2.10632
$247$	−1856.23	−	1017.99i	−0.478175	−	0.262239i
$248$	−3641.97			−0.932522
$249$		−	7099.33i		−	1.80684i
$250$	−250.988			−0.0634956
$251$	6719.50			1.68976			0.844882	−	0.534953i	$-0.179671\pi$
$251$	6719.50			1.68976			0.844882	+	0.534953i	$0.179671\pi$
$252$		−	3635.80i		−	0.908863i
$253$		−	1790.90i		−	0.445032i
$254$		−	221.986i		−	0.0548372i
$255$			8499.77i			2.08736i
$256$	4426.99			1.08081
$257$	3162.46			0.767582			0.383791	−	0.923420i	$-0.374618\pi$
$257$	3162.46			0.767582			0.383791	+	0.923420i	$0.374618\pi$
$258$			4142.15i			0.999532i
$259$	1919.70			0.460557
$260$	−2240.72	−	1228.85i	−0.534476	−	0.293115i
$261$	5574.62			1.32207
$262$			7689.78i			1.81327i
$263$	−3986.13			−0.934584			−0.467292	−	0.884103i	$-0.654770\pi$
$263$	−3986.13			−0.934584			−0.467292	+	0.884103i	$0.654770\pi$
$264$	1350.01			0.314724
$265$			4626.79i			1.07253i
$266$		−	4536.05i		−	1.04558i
$267$			4848.90i			1.11142i
$268$			391.060i			0.0891335i
$269$	392.072			0.0888664			0.0444332	−	0.999012i	$-0.485852\pi$
$269$	392.072			0.0888664			0.0444332	+	0.999012i	$0.485852\pi$
$270$	3761.20			0.847776
$271$		−	2008.72i		−	0.450263i	−0.974328	−	0.225132i	$-0.927719\pi$
$271$		−	2008.72i		−	0.450263i	0.974328	−	0.225132i	$-0.0722812\pi$
$272$	−5354.05			−1.19352
$273$	9680.49	+	5308.93i	2.14612	+	1.17696i
$274$	8539.33			1.88277
$275$		−	1426.20i		−	0.312739i
$276$	4408.21			0.961389
$277$	2346.94			0.509075			0.254538	−	0.967063i	$-0.418077\pi$
$277$	2346.94			0.509075			0.254538	+	0.967063i	$0.418077\pi$
$278$			6255.48i			1.34956i
$279$		−	8419.61i		−	1.80670i
$280$			7345.55i			1.56779i
$281$			1820.28i			0.386438i	0.981156	+	0.193219i	$0.0618927\pi$
$281$			1820.28i			0.386438i	−0.981156	+	0.193219i	$0.938107\pi$
$282$	496.812			0.104910
$283$	−8633.48			−1.81345			−0.906726	−	0.421720i	$-0.861427\pi$
$283$	−8633.48			−1.81345			−0.906726	+	0.421720i	$0.861427\pi$
$284$		−	3337.78i		−	0.697396i
$285$	5711.89			1.18717
$286$	837.699	−	1527.49i	0.173196	−	0.315812i
$287$	9021.18			1.85541
$288$			5200.83i			1.06410i
$289$	−395.613			−0.0805236
$290$	8395.55			1.70001
$291$		−	9275.87i		−	1.86859i
$292$		−	707.140i		−	0.141720i
$293$			3869.65i			0.771560i	0.922591	+	0.385780i	$0.126068\pi$
$293$			3869.65i			0.771560i	−0.922591	+	0.385780i	$0.873932\pi$
$294$			14471.7i			2.87077i
$295$	−5512.43			−1.08795
$296$	−1000.22			−0.196407
$297$			767.317i			0.149913i
$298$	11685.2			2.27149
$299$	−3669.49	+	6691.07i	−0.709739	+	1.29416i
$300$	3510.53			0.675601
$301$		−	4597.94i		−	0.880467i
$302$	−4417.00			−0.841623
$303$	14958.7			2.83615
$304$			3597.94i			0.678804i
$305$		−	6843.43i		−	1.28477i
$306$		−	8130.60i		−	1.51894i
$307$			3689.01i			0.685808i	0.939370	+	0.342904i	$0.111411\pi$
$307$			3689.01i			0.685808i	−0.939370	+	0.342904i	$0.888589\pi$
$308$	1117.07			0.206660
$309$	8920.27			1.64225
$310$		−	12680.2i		−	2.32318i
$311$	4423.63			0.806563			0.403282	−	0.915076i	$-0.367870\pi$
$311$	4423.63			0.806563			0.403282	+	0.915076i	$0.367870\pi$
$312$	−5043.82	−	2766.11i	−0.915224	−	0.501923i
$313$	5343.66			0.964989			0.482494	−	0.875899i	$-0.339731\pi$
$313$	5343.66			0.964989			0.482494	+	0.875899i	$0.339731\pi$
$314$		−	4454.14i		−	0.800515i
$315$	−16981.6			−3.03748
$316$	−3412.33			−0.607463
$317$			5110.04i			0.905389i	0.891666	+	0.452695i	$0.149537\pi$
$317$			5110.04i			0.905389i	−0.891666	+	0.452695i	$0.850463\pi$
$318$		−	7763.55i		−	1.36905i
$319$			1712.76i			0.300615i
$320$		−	2337.00i		−	0.408257i
$321$	−6049.30			−1.05184
$322$	−16350.9			−2.82981
$323$		−	3035.71i		−	0.522945i
$324$	1414.00			0.242455
$325$	−2922.24	+	5328.50i	−0.498758	+	0.909453i
$326$	−2616.01			−0.444439
$327$		−	8824.50i		−	1.49234i
$328$	−4700.30			−0.791252
$329$	−551.479			−0.0924135
$330$			4700.29i			0.784069i
$331$			822.481i			0.136579i	0.997666	+	0.0682895i	$0.0217541\pi$
$331$			822.481i			0.136579i	−0.997666	+	0.0682895i	$0.978246\pi$
$332$			3060.73i			0.505963i
$333$		−	2312.33i		−	0.380526i
$334$	6562.44			1.07509
$335$	1826.51			0.297890
$336$		−	18763.7i		−	3.04656i
$337$	9504.92			1.53640			0.768198	−	0.640212i	$-0.221153\pi$
$337$	9504.92			1.53640			0.768198	+	0.640212i	$0.221153\pi$
$338$	−6259.53	+	3990.50i	−1.00732	+	0.642174i
$339$	−9841.34			−1.57672
$340$		−	3664.51i		−	0.584517i
$341$	2586.87			0.410811
$342$	−5463.80			−0.863885
$343$		−	5869.07i		−	0.923907i
$344$			2395.66i			0.375481i
$345$		−	20589.4i		−	3.21303i
$346$			1372.69i			0.213284i
$347$	6061.47			0.937743			0.468871	−	0.883266i	$-0.344661\pi$
$347$	6061.47			0.937743			0.468871	+	0.883266i	$0.344661\pi$
$348$	−4215.88			−0.649410
$349$			6923.75i			1.06195i	0.847388	+	0.530974i	$0.178174\pi$
$349$			6923.75i			1.06195i	−0.847388	+	0.530974i	$0.821826\pi$
$350$	−13021.2			−1.98861
$351$	1572.20	−	2866.81i	0.239083	−	0.435951i
$352$	−1597.92			−0.241958
$353$			6061.58i			0.913953i	0.889479	+	0.456977i	$0.151068\pi$
$353$			6061.58i			0.913953i	−0.889479	+	0.456977i	$0.848932\pi$
$354$	9249.60			1.38873
$355$	−15589.7			−2.33075
$356$		−	2090.51i		−	0.311226i
$357$			15831.6i			2.34705i
$358$			10120.9i			1.49415i
$359$		−	9291.31i		−	1.36595i	−0.730441	−	0.682976i	$-0.760685\pi$
$359$		−	9291.31i		−	1.36595i	0.730441	−	0.682976i	$-0.239315\pi$
$360$	8847.93			1.29535
$361$	4818.99			0.702579
$362$			13745.0i			1.99563i
$363$	−958.899			−0.138648
$364$	−4173.55	−	2288.84i	−0.600971	−	0.329582i
$365$	−3302.83			−0.473638
$366$			11483.0i			1.63996i
$367$	−5809.94			−0.826366			−0.413183	−	0.910648i	$-0.635583\pi$
$367$	−5809.94			−0.826366			−0.413183	+	0.910648i	$0.635583\pi$
$368$	12969.3			1.83716
$369$		−	10866.3i		−	1.53300i
$370$		−	3482.45i		−	0.489308i
$371$			8617.82i			1.20597i
$372$			6367.44i			0.887463i
$373$	−4683.59			−0.650153			−0.325077	−	0.945688i	$-0.605390\pi$
$373$	−4683.59			−0.650153			−0.325077	+	0.945688i	$0.605390\pi$
$374$	2498.07			0.345380
$375$		−	588.671i		−	0.0810636i
$376$	287.337			0.0394103
$377$	3509.39	−	6399.13i	0.479423	−	0.874197i
$378$	7005.58			0.953249
$379$			5717.97i			0.774967i	0.921877	+	0.387484i	$0.126656\pi$
$379$			5717.97i			0.774967i	−0.921877	+	0.387484i	$0.873344\pi$
$380$	−2462.57			−0.332439
$381$	520.649			0.0700095
$382$		−	214.014i		−	0.0286647i
$383$			6841.79i			0.912791i	0.889777	+	0.456395i	$0.150860\pi$
$383$			6841.79i			0.912791i	−0.889777	+	0.456395i	$0.849140\pi$
$384$			13131.0i			1.74502i
$385$		−	5217.49i		−	0.690670i
$386$	−38.8678			−0.00512518
$387$	−5538.35			−0.727468
$388$			3999.10i			0.523257i
$389$	11360.3			1.48069			0.740346	−	0.672226i	$-0.234662\pi$
$389$	11360.3			1.48069			0.740346	+	0.672226i	$0.234662\pi$
$390$	9630.72	−	17561.0i	1.25044	−	2.28009i
$391$	−10942.7			−1.41533
$392$			8369.85i			1.07842i
$393$	−18035.7			−2.31496
$394$	−12687.0			−1.62223
$395$			15937.9i			2.03018i
$396$		−	1345.55i		−	0.170748i
$397$			3443.34i			0.435306i	0.976026	+	0.217653i	$0.0698401\pi$
$397$			3443.34i			0.435306i	−0.976026	+	0.217653i	$0.930160\pi$
$398$		−	4832.69i		−	0.608645i
$399$	10638.9			1.33487
$400$	10328.3			1.29103
$401$		−	13238.2i		−	1.64859i	−0.566160	−	0.824296i	$-0.691571\pi$
$401$		−	13238.2i		−	1.64859i	0.566160	−	0.824296i	$-0.308429\pi$
$402$	−3064.81			−0.380246
$403$	−9664.91	−	5300.39i	−1.19465	−	0.655164i
$404$	−6449.13			−0.794199
$405$		−	6604.32i		−	0.810300i
$406$	15637.5			1.91151
$407$	710.448			0.0865249
$408$		−	8248.72i		−	1.00091i
$409$			3353.80i			0.405464i	0.979234	+	0.202732i	$0.0649820\pi$
$409$			3353.80i			0.405464i	−0.979234	+	0.202732i	$0.935018\pi$
$410$		−	16365.0i		−	1.97124i
$411$			20028.3i			2.40370i
$412$	−3845.80			−0.459876
$413$	−10267.4			−1.22331
$414$			19695.1i			2.33807i
$415$	14295.7			1.69096
$416$	5970.06	+	3274.07i	0.703620	+	0.385877i
$417$	−14671.7			−1.72296
$418$		−	1678.72i		−	0.196432i
$419$	−10111.2			−1.17891			−0.589455	−	0.807802i	$-0.700657\pi$
$419$	−10111.2			−1.17891			−0.589455	+	0.807802i	$0.700657\pi$
$420$	12842.6			1.49203
$421$		−	15045.5i		−	1.74174i	−0.491517	−	0.870868i	$-0.663557\pi$
$421$		−	15045.5i		−	1.74174i	0.491517	−	0.870868i	$-0.336443\pi$
$422$		−	2184.35i		−	0.251973i
$423$			664.273i			0.0763547i
$424$		−	4490.13i		−	0.514293i
$425$	−8714.30			−0.994602
$426$	26158.8			2.97511
$427$		−	12746.5i		−	1.44460i
$428$	2608.04			0.294542
$429$	3582.59	+	1964.75i	0.403191	+	0.221116i
$430$	−8340.93			−0.935431
$431$			11739.2i			1.31197i	0.754775	+	0.655984i	$0.227746\pi$
$431$			11739.2i			1.31197i	−0.754775	+	0.655984i	$0.772254\pi$
$432$	−5556.75			−0.618864
$433$	8328.98			0.924400			0.462200	−	0.886776i	$-0.347060\pi$
$433$	8328.98			0.924400			0.462200	+	0.886776i	$0.347060\pi$
$434$		−	23618.0i		−	2.61221i
$435$			19691.0i			2.17037i
$436$			3804.51i			0.417896i
$437$			7353.52i			0.804958i
$438$	5541.99			0.604581
$439$	−6986.54			−0.759566			−0.379783	−	0.925076i	$-0.624001\pi$
$439$	−6986.54			−0.759566			−0.379783	+	0.925076i	$0.624001\pi$
$440$			2718.47i			0.294540i
$441$	−19349.6			−2.08937
$442$	−9333.16	−	5118.45i	−1.00437	−	0.550814i
$443$	1295.06			0.138894			0.0694471	−	0.997586i	$-0.477877\pi$
$443$	1295.06			0.138894			0.0694471	+	0.997586i	$0.477877\pi$
$444$			1748.73i			0.186917i
$445$	−9764.09			−1.04014
$446$	8682.82			0.921847
$447$			27406.6i			2.89997i
$448$		−	4352.87i		−	0.459049i
$449$		−	6597.74i		−	0.693467i	−0.937964	−	0.346733i	$-0.887291\pi$
$449$		−	6597.74i		−	0.693467i	0.937964	−	0.346733i	$-0.112709\pi$
$450$			15684.4i			1.64304i
$451$	3338.59			0.348576
$452$	4242.89			0.441524
$453$		−	10359.7i		−	1.07448i
$454$	−6879.19			−0.711138
$455$	−10690.4	+	19493.3i	−1.10148	+	2.00848i
$456$	−5543.18			−0.569261
$457$		−	13502.7i		−	1.38212i	−0.722795	−	0.691062i	$-0.757143\pi$
$457$		−	13502.7i		−	1.38212i	0.722795	−	0.691062i	$-0.242857\pi$
$458$	5197.06			0.530224
$459$	4688.41			0.476768
$460$			8876.69i			0.899734i
$461$		−	5634.11i		−	0.569211i	−0.958645	−	0.284606i	$-0.908137\pi$
$461$		−	5634.11i		−	0.569211i	0.958645	−	0.284606i	$-0.0918627\pi$
$462$			8754.72i			0.881615i
$463$			9772.64i			0.980936i	0.871459	+	0.490468i	$0.163174\pi$
$463$			9772.64i			0.980936i	−0.871459	+	0.490468i	$0.836826\pi$
$464$	−12403.5			−1.24098
$465$	29740.3			2.96596
$466$			10869.9i			1.08055i
$467$	−6449.11			−0.639035			−0.319517	−	0.947580i	$-0.603521\pi$
$467$	−6449.11			−0.639035			−0.319517	+	0.947580i	$0.603521\pi$
$468$	−2756.97	+	5027.16i	−0.272310	+	0.496540i
$469$	3402.05			0.334951
$470$			1000.42i			0.0981825i
$471$	10446.8			1.02200
$472$	5349.61			0.521686
$473$		−	1701.62i		−	0.165413i
$474$		−	26743.1i		−	2.59146i
$475$			5856.05i			0.565672i
$476$		−	6825.47i		−	0.657237i
$477$	10380.4			0.996407
$478$	8300.00			0.794211
$479$		−	10705.6i		−	1.02119i	−0.859821	−	0.510596i	$-0.829425\pi$
$479$		−	10705.6i		−	1.02119i	0.859821	−	0.510596i	$-0.170575\pi$
$480$	−18370.7			−1.74688
$481$	−2654.34	−	1455.68i	−0.251616	−	0.137990i
$482$	−10136.4			−0.957881
$483$		−	38349.5i		−	3.61276i
$484$	413.410			0.0388251
$485$	18678.5			1.74876
$486$			17445.5i			1.62828i
$487$		−	1658.91i		−	0.154358i	−0.997017	−	0.0771788i	$-0.975409\pi$
$487$		−	1658.91i		−	0.154358i	0.997017	−	0.0771788i	$-0.0245912\pi$
$488$			6641.30i			0.616060i
$489$		−	6135.61i		−	0.567407i
$490$	−29141.2			−2.68666
$491$	13135.8			1.20735			0.603674	−	0.797231i	$-0.293703\pi$
$491$	13135.8			1.20735			0.603674	+	0.797231i	$0.293703\pi$
$492$			8217.76i			0.753019i
$493$	10465.2			0.956044
$494$	−3439.63	+	6271.93i	−0.313271	+	0.571230i
$495$	−6284.62			−0.570652
$496$			18733.5i			1.69589i
$497$	−29037.2			−2.62072
$498$	−23987.6			−2.15845
$499$			2072.35i			0.185914i	0.995670	+	0.0929572i	$0.0296320\pi$
$499$			2072.35i			0.185914i	−0.995670	+	0.0929572i	$0.970368\pi$
$500$			253.794i			0.0227000i
$501$			15391.6i			1.37255i
$502$		−	22704.2i		−	2.01860i
$503$	17297.3			1.53330			0.766648	−	0.642067i	$-0.221923\pi$
$503$	17297.3			1.53330			0.766648	+	0.642067i	$0.221923\pi$
$504$	16480.1			1.45651
$505$			30121.8i			2.65427i
$506$	−6051.19			−0.531636
$507$	−9359.37	−	14681.2i	−0.819851	−	1.28602i
$508$	−224.467			−0.0196046
$509$		−	7812.38i		−	0.680309i	−0.940369	−	0.340155i	$-0.889521\pi$
$509$		−	7812.38i		−	0.680309i	0.940369	−	0.340155i	$-0.110479\pi$
$510$	28719.4			2.49357
$511$	−6151.81			−0.532564
$512$		−	1702.55i		−	0.146959i
$513$		−	3150.64i		−	0.271158i
$514$		−	10685.5i		−	0.916956i
$515$			17962.5i			1.53694i
$516$	4188.45			0.357338
$517$	−204.093			−0.0173617
$518$		−	6486.37i		−	0.550183i
$519$	−3219.53			−0.272296
$520$	5570.03	−	10156.6i	0.469735	−	0.856530i
$521$	−5499.03			−0.462412			−0.231206	−	0.972905i	$-0.574267\pi$
$521$	−5499.03			−0.462412			−0.231206	+	0.972905i	$0.574267\pi$
$522$		−	18835.8i		−	1.57935i
$523$	−2481.04			−0.207435			−0.103718	−	0.994607i	$-0.533074\pi$
$523$	−2481.04			−0.207435			−0.103718	+	0.994607i	$0.533074\pi$
$524$	7775.72			0.648252
$525$		−	30540.0i		−	2.53881i
$526$			13468.5i			1.11646i
$527$		−	15806.1i		−	1.30650i
$528$		−	6944.15i		−	0.572358i
$529$	14339.9			1.17859
$530$	15633.2			1.28125
$531$			12367.4i			1.01073i
$532$	−4586.75			−0.373798
$533$	−12473.5	−	6840.64i	−1.01367	−	0.555912i
$534$	16383.7			1.32770
$535$		−	12181.3i		−	0.984381i
$536$	−1772.57			−0.142842
$537$	−23737.6			−1.90755
$538$		−	1324.75i		−	0.106160i
$539$		−	5945.05i		−	0.475086i
$540$		−	3803.24i		−	0.303084i
$541$			244.713i			0.0194474i	0.999953	+	0.00972370i	$0.00309520\pi$
$541$			244.713i			0.0194474i	−0.999953	+	0.00972370i	$0.996905\pi$
$542$	−6787.17			−0.537886
$543$	−32237.6			−2.54778
$544$			9763.50i			0.769498i
$545$	17769.6			1.39664
$546$	17938.1	−	32708.9i	1.40601	−	2.56376i
$547$	10392.5			0.812344			0.406172	−	0.913797i	$-0.366863\pi$
$547$	10392.5			0.812344			0.406172	+	0.913797i	$0.366863\pi$
$548$		−	8634.78i		−	0.673101i
$549$	−15353.5			−1.19358
$550$	−4818.93			−0.373599
$551$		−	7032.68i		−	0.543743i
$552$			19981.2i			1.54068i
$553$			29685.8i			2.28276i
$554$		−	7929.95i		−	0.608143i
$555$	8167.77			0.624689
$556$	6325.40			0.482476
$557$			11050.2i			0.840593i	0.907387	+	0.420297i	$0.138074\pi$
$557$			11050.2i			0.840593i	−0.907387	+	0.420297i	$0.861926\pi$
$558$	−28448.6			−2.15829
$559$	−3486.55	+	6357.50i	−0.263802	+	0.481026i
$560$	37784.0			2.85119
$561$			5859.01i			0.440940i
$562$	6150.46			0.461640
$563$	11527.9			0.862957			0.431478	−	0.902123i	$-0.357992\pi$
$563$	11527.9			0.862957			0.431478	+	0.902123i	$0.357992\pi$
$564$		−	502.365i		−	0.0375060i
$565$		−	19817.2i		−	1.47560i
$566$			29171.2i			2.16636i
$567$		−	12301.1i		−	0.911110i
$568$	15129.2			1.11762
$569$	7375.91			0.543435			0.271717	−	0.962377i	$-0.412408\pi$
$569$	7375.91			0.543435			0.271717	+	0.962377i	$0.412408\pi$
$570$		−	19299.6i		−	1.41820i
$571$	−810.966			−0.0594359			−0.0297179	−	0.999558i	$-0.509461\pi$
$571$	−810.966			−0.0594359			−0.0297179	+	0.999558i	$0.509461\pi$
$572$	−1544.56	−	847.061i	−0.112904	−	0.0619186i
$573$	501.952			0.0365957
$574$		−	30481.2i		−	2.21648i
$575$	21109.0			1.53097
$576$	−5243.16			−0.379280
$577$			22294.8i			1.60857i	0.594243	+	0.804286i	$0.297452\pi$
$577$			22294.8i			1.60857i	−0.594243	+	0.804286i	$0.702548\pi$
$578$			1336.71i			0.0961938i
$579$		−	91.1611i		−	0.00654322i
$580$		−	8489.39i		−	0.607763i
$581$	26627.1			1.90134
$582$	−31341.7			−2.23223
$583$			3189.31i			0.226566i
$584$	3205.27			0.227115
$585$	23480.3	+	12876.9i	1.65947	+	0.910079i
$586$	13074.9			0.921708
$587$			2536.43i			0.178347i	0.996016	+	0.0891734i	$0.0284225\pi$
$587$			2536.43i			0.178347i	−0.996016	+	0.0891734i	$0.971577\pi$
$588$	14633.4			1.02631
$589$	−10621.8			−0.743061
$590$			18625.7i			1.29967i
$591$		−	29756.1i		−	2.07107i
$592$			5144.92i			0.357187i
$593$		−	5466.02i		−	0.378520i	−0.981927	−	0.189260i	$-0.939391\pi$
$593$		−	5466.02i		−	0.378520i	0.981927	−	0.189260i	$-0.0606089\pi$
$594$	2592.65			0.179087
$595$	−31879.6			−2.19653
$596$		−	11815.8i		−	0.812070i
$597$	11334.6			0.777045
$598$	22608.1	+	12398.6i	1.54601	+	0.847857i
$599$	−13642.0			−0.930543			−0.465271	−	0.885168i	$-0.654043\pi$
$599$	−13642.0			−0.930543			−0.465271	+	0.885168i	$0.654043\pi$
$600$			15912.3i			1.08269i
$601$	26522.3			1.80011			0.900056	−	0.435775i	$-0.143526\pi$
$601$	26522.3			1.80011			0.900056	+	0.435775i	$0.143526\pi$
$602$	−15535.7			−1.05181
$603$		−	4097.87i		−	0.276746i
$604$			4466.37i			0.300884i
$605$		−	1930.91i		−	0.129756i
$606$		−	50543.1i		−	3.38807i
$607$	−13170.8			−0.880700			−0.440350	−	0.897826i	$-0.645146\pi$
$607$	−13170.8			−0.880700			−0.440350	+	0.897826i	$0.645146\pi$
$608$	6561.12			0.437646
$609$			36676.3i			2.44039i
$610$	−23122.9			−1.53479
$611$	762.522	+	418.179i	0.0504883	+	0.0276886i
$612$	−8221.48			−0.543029
$613$		−	3904.27i		−	0.257247i	−0.991694	−	0.128623i	$-0.958944\pi$
$613$		−	3904.27i		−	0.257247i	0.991694	−	0.128623i	$-0.0410558\pi$
$614$	12464.6			0.819268
$615$	38382.6			2.51664
$616$			5063.39i			0.331184i
$617$			12856.7i			0.838881i	0.907783	+	0.419440i	$0.137774\pi$
$617$			12856.7i			0.838881i	−0.907783	+	0.419440i	$0.862226\pi$
$618$		−	30140.2i		−	1.96184i
$619$			13579.4i			0.881749i	0.897569	+	0.440875i	$0.145332\pi$
$619$			13579.4i			0.881749i	−0.897569	+	0.440875i	$0.854668\pi$
$620$	−12821.9			−0.830550
$621$	−11356.9			−0.733878
$622$		−	14946.8i		−	0.963523i
$623$	−18186.5			−1.16954
$624$	−14228.3	+	25944.3i	−0.912800	+	1.66443i
$625$	−15021.5			−0.961374
$626$		−	18055.4i		−	1.15278i
$627$	3937.28			0.250781
$628$	−4503.92			−0.286188
$629$		−	4340.94i		−	0.275174i
$630$			57378.4i			3.62859i
$631$			3727.24i			0.235149i	0.993064	+	0.117575i	$0.0375119\pi$
$631$			3727.24i			0.235149i	−0.993064	+	0.117575i	$0.962488\pi$
$632$		−	15467.1i		−	0.973497i
$633$	5123.21			0.321689
$634$	17266.0			1.08158
$635$			1048.41i			0.0655198i
$636$	−7850.32			−0.489443
$637$	−12181.2	+	22211.6i	−0.757670	+	1.38156i
$638$	5787.17			0.359116
$639$			34976.1i			2.16531i
$640$	−26441.4			−1.63311
$641$	19163.6			1.18084			0.590418	−	0.807097i	$-0.298963\pi$
$641$	19163.6			1.18084			0.590418	+	0.807097i	$0.298963\pi$
$642$			20439.7i			1.25653i
$643$			11698.2i			0.717466i	0.933440	+	0.358733i	$0.116791\pi$
$643$			11698.2i			0.717466i	−0.933440	+	0.358733i	$0.883209\pi$
$644$			16533.6i			1.01167i
$645$		−	19562.9i		−	1.19425i
$646$	−10257.2			−0.624712
$647$	6645.17			0.403785			0.201892	−	0.979408i	$-0.435291\pi$
$647$	6645.17			0.403785			0.201892	+	0.979408i	$0.435291\pi$
$648$			6409.26i			0.388548i
$649$	−3799.79			−0.229822
$650$	18004.2	+	9873.79i	1.08644	+	0.595818i
$651$	55393.9			3.33496
$652$			2645.25i			0.158889i
$653$	−21447.0			−1.28528			−0.642640	−	0.766168i	$-0.722161\pi$
$653$	−21447.0			−1.28528			−0.642640	+	0.766168i	$0.722161\pi$
$654$	−29816.6			−1.78276
$655$		−	36317.9i		−	2.16650i
$656$			24177.3i			1.43897i
$657$			7410.03i			0.440020i
$658$			1863.36i			0.110397i
$659$	−14305.8			−0.845639			−0.422820	−	0.906214i	$-0.638960\pi$
$659$	−14305.8			−0.845639			−0.422820	+	0.906214i	$0.638960\pi$
$660$	4752.83			0.280308
$661$		−	2818.21i		−	0.165833i	−0.996556	−	0.0829165i	$-0.973577\pi$
$661$		−	2818.21i		−	0.165833i	0.996556	−	0.0829165i	$-0.0264235\pi$
$662$	2779.04			0.163158
$663$	12004.9	−	21890.1i	0.703214	−	1.28226i
$664$	−13873.5			−0.810836
$665$			21423.2i			1.24926i
$666$	−7813.02			−0.454577
$667$	−25350.3			−1.47162
$668$		−	6635.79i		−	0.384351i
$669$			20364.8i			1.17690i
$670$		−	6171.52i		−	0.355860i
$671$		−	4717.27i		−	0.271398i
$672$	−34217.1			−1.96421
$673$	−15981.1			−0.915343			−0.457671	−	0.889121i	$-0.651316\pi$
$673$	−15981.1			−0.915343			−0.457671	+	0.889121i	$0.651316\pi$
$674$		−	32115.7i		−	1.83538i
$675$	−9044.22			−0.515722
$676$	4035.11	+	6329.49i	0.229580	+	0.360121i
$677$	29651.7			1.68332			0.841660	−	0.540008i	$-0.181579\pi$
$677$	29651.7			1.68332			0.841660	+	0.540008i	$0.181579\pi$
$678$			33252.4i			1.88355i
$679$	34790.4			1.96632
$680$	16610.2			0.936724
$681$		−	16134.5i		−	0.907895i
$682$		−	8740.63i		−	0.490757i
$683$		−	1400.31i		−	0.0784502i	−0.999230	−	0.0392251i	$-0.987511\pi$
$683$		−	1400.31i		−	0.0784502i	0.999230	−	0.0392251i	$-0.0124889\pi$
$684$			5524.87i			0.308843i
$685$	−40330.3			−2.24955
$686$	−19830.7			−1.10370
$687$			12189.2i			0.676927i
$688$	12322.8			0.682851
$689$	6534.77	−	11915.7i	0.361328	−	0.658858i
$690$	−69568.3			−3.83829
$691$		−	21259.1i		−	1.17038i	−0.810895	−	0.585192i	$-0.801019\pi$
$691$		−	21259.1i		−	1.17038i	0.810895	−	0.585192i	$-0.198981\pi$
$692$	1388.03			0.0762502
$693$	−11705.7			−0.641647
$694$		−	20480.8i		−	1.12023i
$695$		−	29543.9i		−	1.61247i
$696$		−	19109.4i		−	1.04072i
$697$		−	20399.2i		−	1.10857i
$698$	23394.3			1.26861
$699$	−25494.3			−1.37952
$700$			13166.7i			0.710936i
$701$	−16254.8			−0.875800			−0.437900	−	0.899024i	$-0.644278\pi$
$701$	−16254.8			−0.875800			−0.437900	+	0.899024i	$0.644278\pi$
$702$	−9686.51	−	5312.23i	−0.520789	−	0.285609i
$703$	−2917.13			−0.156503
$704$		−	1610.93i		−	0.0862416i
$705$	−2346.39			−0.125348
$706$	20481.2			1.09181
$707$			56104.6i			2.98449i
$708$		−	9352.99i		−	0.496478i
$709$		−	852.848i		−	0.0451754i	−0.999745	−	0.0225877i	$-0.992809\pi$
$709$		−	852.848i		−	0.0451754i	0.999745	−	0.0225877i	$-0.00719050\pi$
$710$			52675.2i			2.78432i
$711$	35757.4			1.88608
$712$	9475.69			0.498759
$713$			38287.8i			2.01107i
$714$	53492.5			2.80379
$715$	−3956.35	+	7214.15i	−0.206936	+	0.377334i
$716$	10234.0			0.534164
$717$			19466.9i			1.01395i
$718$	−31393.9			−1.63177
$719$	−6482.88			−0.336260			−0.168130	−	0.985765i	$-0.553773\pi$
$719$	−6482.88			−0.336260			−0.168130	+	0.985765i	$0.553773\pi$
$720$		−	45511.9i		−	2.35573i
$721$			33456.7i			1.72815i
$722$		−	16282.6i		−	0.839303i
$723$		−	23773.9i		−	1.22291i
$724$	13898.6			0.713449
$725$	−20188.0			−1.03416
$726$			3239.98i			0.165629i
$727$	−6186.81			−0.315620			−0.157810	−	0.987469i	$-0.550443\pi$
$727$	−6186.81			−0.315620			−0.157810	+	0.987469i	$0.550443\pi$
$728$	10374.7	−	18917.5i	0.528175	−	0.963092i
$729$	−29742.7			−1.51109
$730$			11159.7i			0.565809i
$731$	−10397.1			−0.526063
$732$	11611.3			0.586293
$733$			23421.7i			1.18022i	0.807324	+	0.590108i	$0.200915\pi$
$733$			23421.7i			1.18022i	−0.807324	+	0.590108i	$0.799085\pi$
$734$			19630.9i			0.987180i
$735$		−	68348.1i		−	3.43001i
$736$		−	23650.5i		−	1.18447i
$737$	1259.04			0.0629272
$738$	−36715.5			−1.83132
$739$		−	11120.5i		−	0.553550i	−0.960935	−	0.276775i	$-0.910734\pi$
$739$		−	11120.5i		−	0.553550i	0.960935	−	0.276775i	$-0.0892657\pi$
$740$	−3521.37			−0.174930
$741$	−14710.3	−	8067.34i	−0.729278	−	0.399947i
$742$	29118.3			1.44065
$743$			2989.71i			0.147620i	0.997272	+	0.0738102i	$0.0235159\pi$
$743$			2989.71i			0.147620i	−0.997272	+	0.0738102i	$0.976484\pi$
$744$	−28861.9			−1.42221
$745$	−55187.8			−2.71399
$746$			15825.1i			0.776675i
$747$		−	32073.1i		−	1.57094i
$748$		−	2525.99i		−	0.123475i
$749$		−	22688.8i		−	1.10685i
$750$	−1989.03			−0.0968388
$751$	−26272.3			−1.27655			−0.638276	−	0.769808i	$-0.720352\pi$
$751$	−26272.3			−1.27655			−0.638276	+	0.769808i	$0.720352\pi$
$752$		−	1478.00i		−	0.0716717i
$753$	53250.6			2.57710
$754$	−21621.7	−	11857.7i	−1.04432	−	0.572720i
$755$	20861.0			1.00558
$756$		−	7083.88i		−	0.340791i
$757$	−5797.16			−0.278338			−0.139169	−	0.990269i	$-0.544443\pi$
$757$	−5797.16			−0.278338			−0.139169	+	0.990269i	$0.544443\pi$
$758$	19320.2			0.925778
$759$		−	14192.5i		−	0.678730i
$760$		−	11162.1i		−	0.532754i
$761$		−	31515.5i		−	1.50123i	−0.660739	−	0.750616i	$-0.729757\pi$
$761$		−	31515.5i		−	1.50123i	0.660739	−	0.750616i	$-0.270243\pi$
$762$		−	1759.19i		−	0.0836336i
$763$	33097.5			1.57039
$764$	−216.406			−0.0102478
$765$			38399.9i			1.81484i
$766$	23117.4			1.09042
$767$	14196.6	+	7785.62i	0.668329	+	0.366522i
$768$	35083.0			1.64837
$769$		−	15877.3i		−	0.744540i	−0.928124	−	0.372270i	$-0.878580\pi$
$769$		−	15877.3i		−	0.744540i	0.928124	−	0.372270i	$-0.121420\pi$
$770$	−17629.1			−0.825077
$771$	25061.8			1.17066
$772$			39.3023i			0.00183228i
$773$		−	23317.7i		−	1.08497i	−0.840066	−	0.542485i	$-0.817484\pi$
$773$		−	23317.7i		−	1.08497i	0.840066	−	0.542485i	$-0.182516\pi$
$774$			18713.2i			0.869036i
$775$			30490.9i			1.41325i
$776$	−18126.8			−0.838551
$777$	15213.2			0.702407
$778$		−	38384.7i		−	1.76884i
$779$	−13708.4			−0.630493
$780$	−17757.3	−	9738.36i	−0.815143	−	0.447038i
$781$	−10746.2			−0.492354
$782$			36973.6i			1.69076i
$783$	10861.4			0.495729
$784$	43052.8			1.96122
$785$			21036.4i			0.956460i
$786$			60939.8i			2.76546i
$787$			8598.39i			0.389453i	0.980858	+	0.194726i	$0.0623819\pi$
$787$			8598.39i			0.389453i	−0.980858	+	0.194726i	$0.937618\pi$
$788$			12828.8i			0.579957i
$789$	−31589.3			−1.42536
$790$	53851.7			2.42526
$791$		−	36911.3i		−	1.65919i
$792$	6099.00			0.273634
$793$	−9665.50	+	17624.4i	−0.432827	+	0.789232i
$794$	11634.5			0.520018
$795$			36666.4i			1.63575i
$796$	−4886.70			−0.217594
$797$	12910.7			0.573803			0.286901	−	0.957960i	$-0.407375\pi$
$797$	12910.7			0.573803			0.286901	+	0.957960i	$0.407375\pi$
$798$		−	35947.2i		−	1.59463i
$799$			1247.04i			0.0552153i
$800$		−	18834.4i		−	0.832369i
$801$			21906.2i			0.966312i
$802$	−44729.9			−1.96941
$803$	−2276.68			−0.100053
$804$			3099.06i			0.135940i
$805$	77223.3			3.38107
$806$	−17909.2	+	32656.3i	−0.782661	+	1.42713i
$807$	3107.09			0.135532
$808$		−	29232.1i		−	1.27275i
$809$	888.680			0.0386209			0.0193105	−	0.999814i	$-0.493853\pi$
$809$	888.680			0.0386209			0.0193105	+	0.999814i	$0.493853\pi$
$810$	−22315.0			−0.967987
$811$		−	29388.7i		−	1.27247i	−0.771494	−	0.636237i	$-0.780490\pi$
$811$		−	29388.7i		−	1.27247i	0.771494	−	0.636237i	$-0.219510\pi$
$812$		−	15812.2i		−	0.683376i
$813$		−	15918.7i		−	0.686708i
$814$		−	2400.50i		−	0.103363i
$815$	12355.1			0.531019
$816$	−42429.7			−1.82026
$817$			6986.92i			0.299194i
$818$	11332.0			0.484368
$819$	43734.1	+	23984.5i	1.86593	+	1.02330i
$820$	−16547.9			−0.704727
$821$		−	30806.6i		−	1.30957i	−0.755815	−	0.654785i	$-0.772759\pi$
$821$		−	30806.6i		−	1.30957i	0.755815	−	0.654785i	$-0.227241\pi$
$822$	67672.4			2.87147
$823$	−40760.0			−1.72637			−0.863185	−	0.504887i	$-0.831534\pi$
$823$	−40760.0			−1.72637			−0.863185	+	0.504887i	$0.831534\pi$
$824$		−	17431.9i		−	0.736979i
$825$		−	11302.4i		−	0.476967i
$826$			34691.9i			1.46136i
$827$		−	15516.7i		−	0.652442i	−0.945294	−	0.326221i	$-0.894225\pi$
$827$		−	15516.7i		−	0.652442i	0.945294	−	0.326221i	$-0.105775\pi$
$828$	19915.2			0.835872
$829$	3549.00			0.148687			0.0743437	−	0.997233i	$-0.476314\pi$
$829$	3549.00			0.148687			0.0743437	+	0.997233i	$0.476314\pi$
$830$		−	48303.1i		−	2.02003i
$831$	18599.0			0.776404
$832$	−3300.73	+	6018.65i	−0.137539	+	0.250792i
$833$	−36325.1			−1.51091
$834$			49573.4i			2.05826i
$835$	−30993.7			−1.28453
$836$	−1697.48			−0.0702255
$837$		−	16404.5i		−	0.677447i
$838$			34164.1i			1.40833i
$839$		−	16466.9i		−	0.677595i	−0.940859	−	0.338798i	$-0.889980\pi$
$839$		−	16466.9i		−	0.677595i	0.940859	−	0.338798i	$-0.110020\pi$
$840$			58211.9i			2.39107i
$841$	−144.719			−0.00593379
$842$	−50836.3			−2.08068
$843$			14425.4i			0.589366i
$844$	−2208.77			−0.0900817
$845$	29563.0	−	18846.7i	1.20355	−	0.767273i
$846$	2244.48			0.0912136
$847$		−	3596.49i		−	0.145899i
$848$	−23096.3			−0.935295
$849$	−68418.5			−2.76574
$850$			29444.3i			1.18815i
$851$			10515.2i			0.423569i
$852$		−	26451.2i		−	1.06362i
$853$			1501.22i			0.0602590i	0.999546	+	0.0301295i	$0.00959197\pi$
$853$			1501.22i			0.0602590i	−0.999546	+	0.0301295i	$0.990408\pi$
$854$	−43068.5			−1.72573
$855$	25804.9			1.03218
$856$			11821.5i			0.472022i
$857$	−2386.20			−0.0951122			−0.0475561	−	0.998869i	$-0.515143\pi$
$857$	−2386.20			−0.0951122			−0.0475561	+	0.998869i	$0.515143\pi$
$858$	6638.58	−	12105.0i	0.264146	−	0.481653i
$859$	−6774.66			−0.269090			−0.134545	−	0.990907i	$-0.542957\pi$
$859$	−6774.66			−0.269090			−0.134545	+	0.990907i	$0.542957\pi$
$860$			8434.16i			0.334421i
$861$	71490.9			2.82974
$862$	39665.0			1.56728
$863$			24769.2i			0.977002i	0.872563	+	0.488501i	$0.162456\pi$
$863$			24769.2i			0.977002i	−0.872563	+	0.488501i	$0.837544\pi$
$864$			10133.1i			0.399001i
$865$		−	6483.06i		−	0.254833i
$866$		−	28142.4i		−	1.10429i
$867$	−3135.15			−0.122809
$868$	−23882.0			−0.933879
$869$			10986.2i			0.428862i
$870$	66533.0			2.59273
$871$	−4703.96	−	2579.73i	−0.182994	−	0.100357i
$872$	−17244.8			−0.669704
$873$		−	41906.1i		−	1.62464i
$874$	24846.4			0.961605
$875$	2207.89			0.0853033
$876$		−	5603.94i		−	0.216141i
$877$		−	17757.2i		−	0.683714i	−0.939752	−	0.341857i	$-0.888944\pi$
$877$		−	17757.2i		−	0.683714i	0.939752	−	0.341857i	$-0.111056\pi$
$878$			23606.5i			0.907380i
$879$			30666.1i			1.17673i
$880$	13983.2			0.535652
$881$	−10756.3			−0.411340			−0.205670	−	0.978621i	$-0.565937\pi$
$881$	−10756.3			−0.411340			−0.205670	+	0.978621i	$0.565937\pi$
$882$			65379.5i			2.49597i
$883$	−31636.9			−1.20574			−0.602869	−	0.797840i	$-0.705976\pi$
$883$	−31636.9			−1.20574			−0.602869	+	0.797840i	$0.705976\pi$
$884$	−5175.66	+	9437.48i	−0.196919	+	0.359069i
$885$	−43684.8			−1.65926
$886$		−	4375.81i		−	0.165923i
$887$	22566.4			0.854234			0.427117	−	0.904196i	$-0.359529\pi$
$887$	22566.4			0.854234			0.427117	+	0.904196i	$0.359529\pi$
$888$	−7926.52			−0.299546
$889$			1952.77i			0.0736712i
$890$			32991.4i			1.24255i
$891$		−	4552.45i		−	0.171170i
$892$		−	8779.87i		−	0.329565i
$893$	838.016			0.0314033
$894$	92602.6			3.46431
$895$		−	47799.7i		−	1.78521i
$896$	−49249.5			−1.83628
$897$	−29079.9	+	53025.3i	−1.08244	+	1.97376i
$898$	−22292.8			−0.828417
$899$		−	36617.3i		−	1.35846i
$900$	15859.7			0.587397
$901$	19487.1			0.720544
$902$		−	11280.6i		−	0.416411i
$903$		−	36437.7i		−	1.34282i
$904$			19231.9i			0.707569i
$905$		−	64915.9i		−	2.38439i
$906$	−35003.8			−1.28358
$907$	46118.8			1.68837			0.844183	−	0.536055i	$-0.180086\pi$
$907$	46118.8			1.68837			0.844183	+	0.536055i	$0.180086\pi$
$908$			6956.08i			0.254235i
$909$	67579.6			2.46587
$910$	65864.9	+	36121.4i	2.39934	+	1.31584i
$911$	11983.2			0.435809			0.217905	−	0.975970i	$-0.430078\pi$
$911$	11983.2			0.435809			0.217905	+	0.975970i	$0.430078\pi$
$912$			28512.9i			1.03526i
$913$	9854.23			0.357204
$914$	−45623.6			−1.65109
$915$		−	54232.7i		−	1.95943i
$916$		−	5255.15i		−	0.189558i
$917$		−	67645.4i		−	2.43604i
$918$		−	15841.4i		−	0.569548i
$919$	32509.5			1.16691			0.583455	−	0.812146i	$-0.301701\pi$
$919$	32509.5			1.16691			0.583455	+	0.812146i	$0.301701\pi$
$920$	−40235.6			−1.44188
$921$			29234.6i			1.04594i
$922$	−19036.8			−0.679982
$923$	40149.3	+	22018.5i	1.43178	+	0.785209i
$924$	8852.57			0.315182
$925$			8373.92i			0.297657i
$926$	33020.3			1.17183
$927$	40299.6			1.42785
$928$			22618.6i			0.800101i
$929$		−	14801.8i		−	0.522746i	−0.965238	−	0.261373i	$-0.915825\pi$
$929$		−	14801.8i		−	0.522746i	0.965238	−	0.261373i	$-0.0841753\pi$
$930$		−	100488.i		−	3.54315i
$931$			24410.6i			0.859318i
$932$	10991.4			0.386303
$933$	35056.3			1.23011
$934$			21790.6i			0.763393i
$935$	−11798.1			−0.412662
$936$	−22786.7	−	12496.6i	−0.795735	−	0.436394i
$937$	−17918.8			−0.624740			−0.312370	−	0.949960i	$-0.601123\pi$
$937$	−17918.8			−0.624740			−0.312370	+	0.949960i	$0.601123\pi$
$938$		−	11495.0i		−	0.400133i
$939$	42347.4			1.47173
$940$	1011.60			0.0351007
$941$			22238.5i			0.770408i	0.922832	+	0.385204i	$0.125869\pi$
$941$			22238.5i			0.770408i	−0.922832	+	0.385204i	$0.874131\pi$
$942$		−	35298.1i		−	1.22089i
$943$			49413.9i			1.70640i
$944$		−	27517.3i		−	0.948740i
$945$	−33086.5			−1.13895
$946$	−5749.52			−0.197603
$947$			32991.2i			1.13207i	0.824382	+	0.566035i	$0.191523\pi$
$947$			32991.2i			1.13207i	−0.824382	+	0.566035i	$0.808477\pi$
$948$	−27042.0			−0.926458
$949$	8506.01	+	4664.83i	0.290956	+	0.159565i
$950$	19786.7			0.675753
$951$			40496.0i			1.38083i
$952$	30938.0			1.05326
$953$	−20073.1			−0.682299			−0.341149	−	0.940009i	$-0.610816\pi$
$953$	−20073.1			−0.682299			−0.341149	+	0.940009i	$0.610816\pi$
$954$		−	35073.8i		−	1.19031i
$955$			1010.76i			0.0342488i
$956$		−	8392.76i		−	0.283935i
$957$			13573.3i			0.458477i
$958$	−36172.6			−1.21992
$959$	−75118.8			−2.52942
$960$		−	18520.2i		−	0.622644i
$961$	−25513.8			−0.856426
$962$	−4918.53	+	8968.61i	−0.164844	+	0.300582i
$963$	−27329.3			−0.914511
$964$			10249.7i			0.342447i
$965$	183.568			0.00612360
$966$	−129577.			−4.31582
$967$			51619.5i			1.71662i	0.513133	+	0.858309i	$0.328485\pi$
$967$			51619.5i			1.71662i	−0.513133	+	0.858309i	$0.671515\pi$
$968$			1873.87i			0.0622196i
$969$		−	24057.3i		−	0.797557i
$970$		−	63111.9i		−	2.08907i
$971$	33087.3			1.09353			0.546767	−	0.837285i	$-0.315858\pi$
$971$	33087.3			1.09353			0.546767	+	0.837285i	$0.315858\pi$
$972$	17640.5			0.582119
$973$		−	55028.2i		−	1.81308i
$974$	−5605.19			−0.184396
$975$	−23158.1	+	42227.3i	−0.760670	+	1.38703i
$976$	34161.4			1.12037
$977$			33361.3i			1.09245i	0.837639	+	0.546225i	$0.183936\pi$
$977$			33361.3i			1.09245i	−0.837639	+	0.546225i	$0.816064\pi$
$978$	−20731.3			−0.677826
$979$	−6730.52			−0.219722
$980$			29466.9i			0.960495i
$981$		−	39866.9i		−	1.29751i
$982$		−	44383.7i		−	1.44230i
$983$		−	33358.7i		−	1.08238i	−0.840901	−	0.541190i	$-0.817974\pi$
$983$		−	33358.7i		−	1.08238i	0.840901	−	0.541190i	$-0.182026\pi$
$984$	−37248.9			−1.20676
$985$	59919.1			1.93825
$986$		−	35360.4i		−	1.14209i
$987$	−4370.36			−0.140942
$988$	6342.03	+	3478.07i	0.204217	+	0.111996i
$989$	25185.4			0.809757
$990$			21234.8i			0.681703i
$991$	44625.1			1.43044			0.715219	−	0.698901i	$-0.246327\pi$
$991$	44625.1			1.43044			0.715219	+	0.698901i	$0.246327\pi$
$992$	34162.0			1.09339
$993$			6517.99i			0.208300i
$994$			98112.2i			3.13072i
$995$			22824.2i			0.727213i
$996$			24255.7i			0.771657i
$997$	−53638.1			−1.70385			−0.851923	−	0.523667i	$-0.824564\pi$
$997$	−53638.1			−1.70385			−0.851923	+	0.523667i	$0.824564\pi$
$998$	7002.17			0.222094
$999$		−	4505.28i		−	0.142683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.b.a.12.9	✓	36
13.5	odd	4		1859.4.a.j.1.5		18
13.8	odd	4		1859.4.a.k.1.14		18
13.12	even	2	inner	143.4.b.a.12.28	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.b.a.12.9	✓	36	1.1	even	1	trivial
143.4.b.a.12.28	yes	36	13.12	even	2	inner
1859.4.a.j.1.5		18	13.5	odd	4
1859.4.a.k.1.14		18	13.8	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.37885i q^{2} +7.92479 q^{3} -3.41661 q^{4} +15.9579i q^{5} -26.7767i q^{6} +29.7230i q^{7} -15.4866i q^{8} +35.8023 q^{9} +O(q^{10})\)	\(q-3.37885i q^{2} +7.92479 q^{3} -3.41661 q^{4} +15.9579i q^{5} -26.7767i q^{6} +29.7230i q^{7} -15.4866i q^{8} +35.8023 q^{9} +53.9193 q^{10} +11.0000i q^{11} -27.0759 q^{12} +(22.5386 - 41.0976i) q^{13} +100.430 q^{14} +126.463i q^{15} -79.6597 q^{16} +67.2115 q^{17} -120.970i q^{18} -45.1665i q^{19} -54.5220i q^{20} +235.549i q^{21} +37.1673 q^{22} -162.809 q^{23} -122.728i q^{24} -129.655 q^{25} +(-138.863 - 76.1544i) q^{26} +69.7561 q^{27} -101.552i q^{28} +155.706 q^{29} +427.299 q^{30} -235.170i q^{31} +145.265i q^{32} +87.1727i q^{33} -227.097i q^{34} -474.318 q^{35} -122.322 q^{36} -64.5862i q^{37} -152.611 q^{38} +(178.613 - 325.690i) q^{39} +247.133 q^{40} -303.508i q^{41} +795.883 q^{42} -154.693 q^{43} -37.5827i q^{44} +571.329i q^{45} +550.108i q^{46} +18.5539i q^{47} -631.286 q^{48} -540.459 q^{49} +438.084i q^{50} +532.637 q^{51} +(-77.0056 + 140.415i) q^{52} +289.937 q^{53} -235.695i q^{54} -175.537 q^{55} +460.308 q^{56} -357.935i q^{57} -526.106i q^{58} +345.435i q^{59} -432.075i q^{60} -428.842 q^{61} -794.603 q^{62} +1064.15i q^{63} -146.448 q^{64} +(655.832 + 359.669i) q^{65} +294.543 q^{66} -114.458i q^{67} -229.636 q^{68} -1290.23 q^{69} +1602.65i q^{70} +976.925i q^{71} -554.454i q^{72} +206.971i q^{73} -218.227 q^{74} -1027.49 q^{75} +154.316i q^{76} -326.953 q^{77} +(-1100.46 - 603.508i) q^{78} +998.746 q^{79} -1271.20i q^{80} -413.859 q^{81} -1025.51 q^{82} -895.839i q^{83} -804.779i q^{84} +1072.56i q^{85} +522.683i q^{86} +1233.94 q^{87} +170.352 q^{88} +611.865i q^{89} +1930.43 q^{90} +(1221.55 + 669.915i) q^{91} +556.256 q^{92} -1863.67i q^{93} +62.6909 q^{94} +720.762 q^{95} +1151.20i q^{96} -1170.49i q^{97} +1826.13i q^{98} +393.825i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 152 q^{4} + 360 q^{9}+O(q^{10}) \) 36 * q - 152 * q^4 + 360 * q^9	\( 36 q - 152 q^{4} + 360 q^{9} - 112 q^{10} - 108 q^{12} - 50 q^{13} + 8 q^{14} + 728 q^{16} + 276 q^{17} + 44 q^{22} - 472 q^{23} - 1172 q^{25} + 152 q^{26} - 12 q^{27} - 572 q^{29} + 712 q^{30} + 68 q^{35} - 430 q^{36} - 50 q^{38} + 640 q^{39} - 216 q^{40} + 1126 q^{42} + 920 q^{43} + 1674 q^{48} - 2164 q^{49} - 340 q^{51} - 800 q^{52} + 2432 q^{53} + 440 q^{55} - 2274 q^{56} - 1844 q^{61} + 2796 q^{62} - 2592 q^{64} + 2264 q^{65} + 1078 q^{66} - 4548 q^{68} - 3288 q^{69} - 4036 q^{74} + 820 q^{75} - 616 q^{77} + 2222 q^{78} + 360 q^{79} + 852 q^{81} + 1948 q^{82} - 2480 q^{87} + 264 q^{88} - 496 q^{90} + 4600 q^{91} + 454 q^{92} - 488 q^{94} + 952 q^{95}+O(q^{100}) \) 36 * q - 152 * q^4 + 360 * q^9 - 112 * q^10 - 108 * q^12 - 50 * q^13 + 8 * q^14 + 728 * q^16 + 276 * q^17 + 44 * q^22 - 472 * q^23 - 1172 * q^25 + 152 * q^26 - 12 * q^27 - 572 * q^29 + 712 * q^30 + 68 * q^35 - 430 * q^36 - 50 * q^38 + 640 * q^39 - 216 * q^40 + 1126 * q^42 + 920 * q^43 + 1674 * q^48 - 2164 * q^49 - 340 * q^51 - 800 * q^52 + 2432 * q^53 + 440 * q^55 - 2274 * q^56 - 1844 * q^61 + 2796 * q^62 - 2592 * q^64 + 2264 * q^65 + 1078 * q^66 - 4548 * q^68 - 3288 * q^69 - 4036 * q^74 + 820 * q^75 - 616 * q^77 + 2222 * q^78 + 360 * q^79 + 852 * q^81 + 1948 * q^82 - 2480 * q^87 + 264 * q^88 - 496 * q^90 + 4600 * q^91 + 454 * q^92 - 488 * q^94 + 952 * q^95

Introduction

L-functions

Modular forms

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Database

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