LMFDB - Embedded newform 143.4.b.a.12.14

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			12.14
Character	$\chi$	$=$	143.12
Dual form			143.4.b.a.12.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18512i q^{2} -9.62593 q^{3} +3.22525 q^{4} -10.6961i q^{5} +21.0338i q^{6} -26.7047i q^{7} -24.5285i q^{8} +65.6585 q^{9} +O(q^{10})$	\(q-2.18512i q^{2} -9.62593 q^{3} +3.22525 q^{4} -10.6961i q^{5} +21.0338i q^{6} -26.7047i q^{7} -24.5285i q^{8} +65.6585 q^{9} -23.3723 q^{10} +11.0000i q^{11} -31.0460 q^{12} +(-34.6979 + 31.5128i) q^{13} -58.3529 q^{14} +102.960i q^{15} -27.7958 q^{16} -123.905 q^{17} -143.472i q^{18} -6.83875i q^{19} -34.4977i q^{20} +257.057i q^{21} +24.0363 q^{22} +164.747 q^{23} +236.110i q^{24} +10.5928 q^{25} +(68.8593 + 75.8191i) q^{26} -372.124 q^{27} -86.1292i q^{28} -184.074 q^{29} +224.980 q^{30} +90.4551i q^{31} -135.491i q^{32} -105.885i q^{33} +270.746i q^{34} -285.637 q^{35} +211.765 q^{36} +98.3280i q^{37} -14.9435 q^{38} +(333.999 - 303.340i) q^{39} -262.360 q^{40} +313.726i q^{41} +561.701 q^{42} +60.0728 q^{43} +35.4777i q^{44} -702.292i q^{45} -359.992i q^{46} -601.307i q^{47} +267.560 q^{48} -370.139 q^{49} -23.1465i q^{50} +1192.70 q^{51} +(-111.909 + 101.637i) q^{52} -106.651 q^{53} +813.136i q^{54} +117.657 q^{55} -655.026 q^{56} +65.8293i q^{57} +402.224i q^{58} -128.192i q^{59} +332.072i q^{60} -102.191 q^{61} +197.655 q^{62} -1753.39i q^{63} -518.430 q^{64} +(337.065 + 371.133i) q^{65} -231.372 q^{66} +186.555i q^{67} -399.623 q^{68} -1585.84 q^{69} +624.150i q^{70} -736.440i q^{71} -1610.51i q^{72} +814.458i q^{73} +214.858 q^{74} -101.965 q^{75} -22.0567i q^{76} +293.751 q^{77} +(-662.835 - 729.829i) q^{78} +171.066 q^{79} +297.307i q^{80} +1809.26 q^{81} +685.530 q^{82} +15.5435i q^{83} +829.074i q^{84} +1325.30i q^{85} -131.266i q^{86} +1771.88 q^{87} +269.814 q^{88} -878.761i q^{89} -1534.59 q^{90} +(841.539 + 926.596i) q^{91} +531.350 q^{92} -870.714i q^{93} -1313.93 q^{94} -73.1482 q^{95} +1304.23i q^{96} -750.148i q^{97} +808.799i q^{98} +722.244i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.18512i		−	0.772557i	−0.922382	−	0.386278i	$-0.873760\pi$
$2$		−	2.18512i		−	0.772557i	0.922382	−	0.386278i	$-0.126240\pi$
$3$	−9.62593			−1.85251			−0.926256	−	0.376896i	$-0.876991\pi$
$3$	−9.62593			−1.85251			−0.926256	+	0.376896i	$0.876991\pi$
$4$	3.22525			0.403156
$5$		−	10.6961i		−	0.956691i	−0.878172	−	0.478346i	$-0.841237\pi$
$5$		−	10.6961i		−	0.956691i	0.878172	−	0.478346i	$-0.158763\pi$
$6$			21.0338i			1.43117i
$7$		−	26.7047i		−	1.44192i	−0.692978	−	0.720958i	$-0.743702\pi$
$7$		−	26.7047i		−	1.44192i	0.692978	−	0.720958i	$-0.256298\pi$
$8$		−	24.5285i		−	1.08402i
$9$	65.6585			2.43180
$10$	−23.3723			−0.739098
$11$			11.0000i			0.301511i
$11$			11.0000i			0.301511i
$12$	−31.0460			−0.746851
$13$	−34.6979	+	31.5128i	−0.740266	+	0.672314i
$13$	−34.6979	+	31.5128i	−0.740266	+	0.672314i
$14$	−58.3529			−1.11396
$15$			102.960i			1.77228i
$16$	−27.7958			−0.434309
$17$	−123.905			−1.76772			−0.883861	−	0.467749i	$-0.845065\pi$
$17$	−123.905			−1.76772			−0.883861	+	0.467749i	$0.845065\pi$
$18$		−	143.472i		−	1.87870i
$19$		−	6.83875i		−	0.0825746i	−0.999147	−	0.0412873i	$-0.986854\pi$
$19$		−	6.83875i		−	0.0825746i	0.999147	−	0.0412873i	$-0.0131459\pi$
$20$		−	34.4977i		−	0.385696i
$21$			257.057i			2.67117i
$22$	24.0363			0.232935
$23$	164.747			1.49357			0.746785	−	0.665066i	$-0.231597\pi$
$23$	164.747			1.49357			0.746785	+	0.665066i	$0.231597\pi$
$24$			236.110i			2.00815i
$25$	10.5928			0.0847422
$26$	68.8593	+	75.8191i	0.519401	+	0.571898i
$27$	−372.124			−2.65242
$28$		−	86.1292i		−	0.581318i
$29$	−184.074			−1.17868			−0.589340	−	0.807885i	$-0.700612\pi$
$29$	−184.074			−1.17868			−0.589340	+	0.807885i	$0.700612\pi$
$30$	224.980			1.36919
$31$			90.4551i			0.524071i	0.965058	+	0.262036i	$0.0843938\pi$
$31$			90.4551i			0.524071i	−0.965058	+	0.262036i	$0.915606\pi$
$32$		−	135.491i		−	0.748489i
$33$		−	105.885i		−	0.558553i
$34$			270.746i			1.36567i
$35$	−285.637			−1.37947
$36$	211.765			0.980394
$37$			98.3280i			0.436892i	0.975849	+	0.218446i	$0.0700988\pi$
$37$			98.3280i			0.436892i	−0.975849	+	0.218446i	$0.929901\pi$
$38$	−14.9435			−0.0637936
$39$	333.999	−	303.340i	1.37135	−	1.24547i
$40$	−262.360			−1.03707
$41$			313.726i			1.19502i	0.801862	+	0.597510i	$0.203843\pi$
$41$			313.726i			1.19502i	−0.801862	+	0.597510i	$0.796157\pi$
$42$	561.701			2.06363
$43$	60.0728			0.213047			0.106523	−	0.994310i	$-0.466028\pi$
$43$	60.0728			0.213047			0.106523	+	0.994310i	$0.466028\pi$
$44$			35.4777i			0.121556i
$45$		−	702.292i		−	2.32648i
$46$		−	359.992i		−	1.15387i
$47$		−	601.307i		−	1.86616i	−0.359664	−	0.933082i	$-0.617109\pi$
$47$		−	601.307i		−	1.86616i	0.359664	−	0.933082i	$-0.382891\pi$
$48$	267.560			0.804562
$49$	−370.139			−1.07912
$50$		−	23.1465i		−	0.0654682i
$51$	1192.70			3.27473
$52$	−111.909	+	101.637i	−0.298443	+	0.271047i
$53$	−106.651			−0.276408			−0.138204	−	0.990404i	$-0.544133\pi$
$53$	−106.651			−0.276408			−0.138204	+	0.990404i	$0.544133\pi$
$54$			813.136i			2.04915i
$55$	117.657			0.288453
$56$	−655.026			−1.56306
$57$			65.8293i			0.152970i
$58$			402.224i			0.910597i
$59$		−	128.192i		−	0.282867i	−0.989948	−	0.141434i	$-0.954829\pi$
$59$		−	128.192i		−	0.282867i	0.989948	−	0.141434i	$-0.0451712\pi$
$60$			332.072i			0.714506i
$61$	−102.191			−0.214496			−0.107248	−	0.994232i	$-0.534204\pi$
$61$	−102.191			−0.214496			−0.107248	+	0.994232i	$0.534204\pi$
$62$	197.655			0.404875
$63$		−	1753.39i		−	3.50645i
$64$	−518.430			−1.01256
$65$	337.065	+	371.133i	0.643197	+	0.708206i
$66$	−231.372			−0.431514
$67$			186.555i			0.340169i	0.985430	+	0.170084i	$0.0544040\pi$
$67$			186.555i			0.340169i	−0.985430	+	0.170084i	$0.945596\pi$
$68$	−399.623			−0.712668
$69$	−1585.84			−2.76685
$70$			624.150i			1.06572i
$71$		−	736.440i		−	1.23098i	−0.788146	−	0.615489i	$-0.788959\pi$
$71$		−	736.440i		−	1.23098i	0.788146	−	0.615489i	$-0.211041\pi$
$72$		−	1610.51i		−	2.63611i
$73$			814.458i			1.30582i	0.757434	+	0.652911i	$0.226453\pi$
$73$			814.458i			1.30582i	−0.757434	+	0.652911i	$0.773547\pi$
$74$	214.858			0.337524
$75$	−101.965			−0.156986
$76$		−	22.0567i		−	0.0332905i
$77$	293.751			0.434754
$78$	−662.835	−	729.829i	−0.962195	−	1.05945i
$79$	171.066			0.243625			0.121813	−	0.992553i	$-0.461129\pi$
$79$	171.066			0.243625			0.121813	+	0.992553i	$0.461129\pi$
$80$			297.307i			0.415500i
$81$	1809.26			2.48184
$82$	685.530			0.923220
$83$			15.5435i			0.0205557i	0.999947	+	0.0102779i	$0.00327160\pi$
$83$			15.5435i			0.0205557i	−0.999947	+	0.0102779i	$0.996728\pi$
$84$			829.074i			1.07690i
$85$			1325.30i			1.69116i
$86$		−	131.266i		−	0.164591i
$87$	1771.88			2.18352
$88$	269.814			0.326844
$89$		−	878.761i		−	1.04661i	−0.852145	−	0.523306i	$-0.824698\pi$
$89$		−	878.761i		−	1.04661i	0.852145	−	0.523306i	$-0.175302\pi$
$90$	−1534.59			−1.79734
$91$	841.539	+	926.596i	0.969420	+	1.06740i
$92$	531.350			0.602142
$93$		−	870.714i		−	0.970848i
$94$	−1313.93			−1.44172
$95$	−73.1482			−0.0789984
$96$			1304.23i			1.38658i
$97$		−	750.148i		−	0.785217i	−0.919706	−	0.392608i	$-0.871573\pi$
$97$		−	750.148i		−	0.785217i	0.919706	−	0.392608i	$-0.128427\pi$
$98$			808.799i			0.833684i
$99$			722.244i			0.733215i
$100$	34.1644			0.0341644
$101$	437.955			0.431467			0.215734	−	0.976452i	$-0.430786\pi$
$101$	437.955			0.431467			0.215734	+	0.976452i	$0.430786\pi$
$102$		−	2606.19i		−	2.52991i
$103$	574.072			0.549175			0.274587	−	0.961562i	$-0.411459\pi$
$103$	574.072			0.549175			0.274587	+	0.961562i	$0.411459\pi$
$104$	772.962	+	851.088i	0.728800	+	0.802462i
$105$	2749.52			2.55548
$106$			233.045i			0.213541i
$107$	−1434.37			−1.29594			−0.647969	−	0.761666i	$-0.724382\pi$
$107$	−1434.37			−1.29594			−0.647969	+	0.761666i	$0.724382\pi$
$108$	−1200.19			−1.06934
$109$		−	865.847i		−	0.760854i	−0.924811	−	0.380427i	$-0.875777\pi$
$109$		−	865.847i		−	0.760854i	0.924811	−	0.380427i	$-0.124223\pi$
$110$		−	257.096i		−	0.222846i
$111$		−	946.498i		−	0.809348i
$112$			742.277i			0.626237i
$113$	−1379.35			−1.14830			−0.574150	−	0.818750i	$-0.694668\pi$
$113$	−1379.35			−1.14830			−0.574150	+	0.818750i	$0.694668\pi$
$114$	143.845			0.118178
$115$		−	1762.15i		−	1.42888i
$116$	−593.685			−0.475192
$117$	−2278.21	+	2069.08i	−1.80018	+	1.63493i
$118$	−280.115			−0.218531
$119$			3308.83i			2.54891i
$120$	2525.46			1.92118
$121$	−121.000			−0.0909091
$122$			223.300i			0.165710i
$123$		−	3019.91i		−	2.21379i
$124$			291.740i			0.211283i
$125$		−	1450.32i		−	1.03776i
$126$	−3831.37			−2.70893
$127$	−1552.57			−1.08479			−0.542395	−	0.840124i	$-0.682482\pi$
$127$	−1552.57			−1.08479			−0.542395	+	0.840124i	$0.682482\pi$
$128$			48.9046i			0.0337703i
$129$	−578.257			−0.394672
$130$	810.971	−	736.528i	0.547129	−	0.496906i
$131$	862.203			0.575046			0.287523	−	0.957774i	$-0.407168\pi$
$131$	862.203			0.575046			0.287523	+	0.957774i	$0.407168\pi$
$132$		−	341.506i		−	0.225184i
$133$	−182.627			−0.119066
$134$	407.645			0.262799
$135$			3980.29i			2.53755i
$136$			3039.20i			1.91624i
$137$		−	2179.06i		−	1.35890i	−0.733722	−	0.679450i	$-0.762218\pi$
$137$		−	2179.06i		−	1.35890i	0.733722	−	0.679450i	$-0.237782\pi$
$138$			3465.25i			2.13755i
$139$	67.1707			0.0409881			0.0204941	−	0.999790i	$-0.493476\pi$
$139$	67.1707			0.0409881			0.0204941	+	0.999790i	$0.493476\pi$
$140$	−921.249			−0.556141
$141$			5788.14i			3.45709i
$142$	−1609.21			−0.951000
$143$	−346.641	−	381.677i	−0.202710	−	0.223199i
$144$	−1825.03			−1.05615
$145$			1968.88i			1.12763i
$146$	1779.69			1.00882
$147$	3562.94			1.99909
$148$			317.132i			0.176136i
$149$		−	1613.56i		−	0.887165i	−0.896233	−	0.443583i	$-0.853707\pi$
$149$		−	1613.56i		−	0.887165i	0.896233	−	0.443583i	$-0.146293\pi$
$150$			222.807i			0.121281i
$151$			186.568i			0.100548i	0.998735	+	0.0502738i	$0.0160094\pi$
$151$			186.568i			0.100548i	−0.998735	+	0.0502738i	$0.983991\pi$
$152$	−167.744			−0.0895123
$153$	−8135.39			−4.29874
$154$		−	641.882i		−	0.335872i
$155$	967.519			0.501374
$156$	1077.23	−	978.347i	0.552869	−	0.502118i
$157$	976.990			0.496639			0.248319	−	0.968678i	$-0.420122\pi$
$157$	976.990			0.496639			0.248319	+	0.968678i	$0.420122\pi$
$158$		−	373.799i		−	0.188214i
$159$	1026.61			0.512049
$160$	−1449.23			−0.716073
$161$		−	4399.51i		−	2.15360i
$162$		−	3953.46i		−	1.91736i
$163$		−	584.180i		−	0.280715i	−0.990101	−	0.140357i	$-0.955175\pi$
$163$		−	584.180i		−	0.280715i	0.990101	−	0.140357i	$-0.0448252\pi$
$164$			1011.85i			0.481779i
$165$	−1132.56			−0.534363
$166$	33.9645			0.0158804
$167$		−	1354.91i		−	0.627820i	−0.949453	−	0.313910i	$-0.898361\pi$
$167$		−	1354.91i		−	0.627820i	0.949453	−	0.313910i	$-0.101639\pi$
$168$	6305.24			2.89559
$169$	210.887	−	2186.86i	0.0959884	−	0.995382i
$170$	2895.94			1.30652
$171$		−	449.022i		−	0.200805i
$172$	193.750			0.0858912
$173$	−338.017			−0.148549			−0.0742745	−	0.997238i	$-0.523664\pi$
$173$	−338.017			−0.148549			−0.0742745	+	0.997238i	$0.523664\pi$
$174$		−	3871.78i		−	1.68689i
$175$		−	282.877i		−	0.122191i
$176$		−	305.754i		−	0.130949i
$177$			1233.97i			0.524015i
$178$	−1920.20			−0.808567
$179$	−1281.20			−0.534978			−0.267489	−	0.963561i	$-0.586194\pi$
$179$	−1281.20			−0.534978			−0.267489	+	0.963561i	$0.586194\pi$
$180$		−	2265.07i		−	0.937934i
$181$	−2700.95			−1.10917			−0.554587	−	0.832126i	$-0.687124\pi$
$181$	−2700.95			−1.10917			−0.554587	+	0.832126i	$0.687124\pi$
$182$	2024.72	−	1838.86i	0.824629	−	0.748932i
$183$	983.687			0.397356
$184$		−	4041.00i		−	1.61906i
$185$	1051.73			0.417971
$186$	−1902.62			−0.750035
$187$		−	1362.95i		−	0.532988i
$188$		−	1939.37i		−	0.752355i
$189$			9937.46i			3.82457i
$190$			159.838i			0.0610307i
$191$	3746.73			1.41939			0.709696	−	0.704508i	$-0.248832\pi$
$191$	3746.73			1.41939			0.709696	+	0.704508i	$0.248832\pi$
$192$	4990.38			1.87578
$193$			4399.82i			1.64096i	0.571672	+	0.820482i	$0.306295\pi$
$193$			4399.82i			1.64096i	−0.571672	+	0.820482i	$0.693705\pi$
$194$	−1639.16			−0.606624
$195$	−3244.56	−	3572.50i	−1.19153	−	1.31196i
$196$	−1193.79			−0.435055
$197$			1893.23i			0.684705i	0.939572	+	0.342352i	$0.111224\pi$
$197$			1893.23i			0.684705i	−0.939572	+	0.342352i	$0.888776\pi$
$198$	1578.19			0.566450
$199$	−1812.82			−0.645764			−0.322882	−	0.946439i	$-0.604652\pi$
$199$	−1812.82			−0.645764			−0.322882	+	0.946439i	$0.604652\pi$
$200$		−	259.825i		−	0.0918621i
$201$		−	1795.76i		−	0.630166i
$202$		−	956.985i		−	0.333333i
$203$			4915.64i			1.69956i
$204$	3846.74			1.32023
$205$	3355.66			1.14326
$206$		−	1254.42i		−	0.424269i
$207$	10817.0			3.63206
$208$	964.455	−	875.923i	0.321504	−	0.291992i
$209$	75.2263			0.0248972
$210$		−	6008.03i		−	1.97425i
$211$	−1325.41			−0.432441			−0.216221	−	0.976345i	$-0.569373\pi$
$211$	−1325.41			−0.432441			−0.216221	+	0.976345i	$0.569373\pi$
$212$	−343.975			−0.111436
$213$			7088.92i			2.28040i
$214$			3134.26i			1.00119i
$215$		−	642.547i		−	0.203820i
$216$			9127.66i			2.87527i
$217$	2415.57			0.755667
$218$	−1891.98			−0.587803
$219$		−	7839.91i		−	2.41905i
$220$	379.475			0.116292
$221$	4299.23	−	3904.58i	1.30859	−	1.18846i
$222$	−2068.21			−0.625267
$223$		−	4204.82i		−	1.26267i	−0.775510	−	0.631335i	$-0.782507\pi$
$223$		−	4204.82i		−	1.26267i	0.775510	−	0.631335i	$-0.217493\pi$
$224$	−3618.24			−1.07926
$225$	695.506			0.206076
$226$			3014.04i			0.887128i
$227$		−	1904.70i		−	0.556915i	−0.960449	−	0.278457i	$-0.910177\pi$
$227$		−	1904.70i		−	0.556915i	0.960449	−	0.278457i	$-0.0898231\pi$
$228$			212.316i			0.0616709i
$229$			1435.67i			0.414287i	0.978311	+	0.207144i	$0.0664168\pi$
$229$			1435.67i			0.414287i	−0.978311	+	0.207144i	$0.933583\pi$
$230$	−3850.52			−1.10389
$231$	−2827.63			−0.805387
$232$			4515.07i			1.27771i
$233$	−3393.91			−0.954258			−0.477129	−	0.878833i	$-0.658323\pi$
$233$	−3393.91			−0.954258			−0.477129	+	0.878833i	$0.658323\pi$
$234$	4521.20	+	4978.17i	1.26308	+	1.39074i
$235$	−6431.66			−1.78534
$236$		−	413.451i		−	0.114040i
$237$	−1646.67			−0.451319
$238$	7230.20			1.96918
$239$		−	2424.86i		−	0.656281i	−0.944629	−	0.328141i	$-0.893578\pi$
$239$		−	2424.86i		−	0.656281i	0.944629	−	0.328141i	$-0.106422\pi$
$240$		−	2861.86i		−	0.769718i
$241$			490.657i			0.131145i	0.997848	+	0.0655726i	$0.0208874\pi$
$241$			490.657i			0.131145i	−0.997848	+	0.0655726i	$0.979113\pi$
$242$			264.400i			0.0702324i
$243$	−7368.48			−1.94522
$244$	−329.593			−0.0864754
$245$			3959.06i			1.03239i
$246$	−6598.86			−1.71028
$247$	215.508	+	237.290i	0.0555160	+	0.0611272i
$248$	2218.73			0.568103
$249$		−	149.621i		−	0.0380797i
$250$	−3169.12			−0.801731
$251$	−3053.17			−0.767786			−0.383893	−	0.923378i	$-0.625417\pi$
$251$	−3053.17			−0.767786			−0.383893	+	0.923378i	$0.625417\pi$
$252$		−	5655.12i		−	1.41365i
$253$			1812.22i			0.450328i
$254$			3392.55i			0.838061i
$255$		−	12757.2i		−	3.13290i
$256$	−4040.58			−0.986470
$257$	5974.51			1.45012			0.725058	−	0.688688i	$-0.241813\pi$
$257$	5974.51			1.45012			0.725058	+	0.688688i	$0.241813\pi$
$258$			1263.56i			0.304906i
$259$	2625.82			0.629963
$260$	1087.12	+	1197.00i	0.259309	+	0.285518i
$261$	−12086.0			−2.86631
$262$		−	1884.02i		−	0.444256i
$263$	4968.60			1.16493			0.582466	−	0.812855i	$-0.302088\pi$
$263$	4968.60			1.16493			0.582466	+	0.812855i	$0.302088\pi$
$264$	−2597.21			−0.605481
$265$			1140.75i			0.264437i
$266$			399.061i			0.0919850i
$267$			8458.89i			1.93886i
$268$			601.686i			0.137141i
$269$	332.151			0.0752848			0.0376424	−	0.999291i	$-0.488015\pi$
$269$	332.151			0.0752848			0.0376424	+	0.999291i	$0.488015\pi$
$270$	8697.41			1.96040
$271$		−	2607.83i		−	0.584554i	−0.956334	−	0.292277i	$-0.905587\pi$
$271$		−	2607.83i		−	0.584554i	0.956334	−	0.292277i	$-0.0944130\pi$
$272$	3444.02			0.767738
$273$	−8100.60	−	8919.34i	−1.79586	−	1.97737i
$274$	−4761.50			−1.04983
$275$			116.521i			0.0255507i
$276$	−5114.73			−1.11547
$277$	2509.89			0.544420			0.272210	−	0.962238i	$-0.412245\pi$
$277$	2509.89			0.544420			0.272210	+	0.962238i	$0.412245\pi$
$278$		−	146.776i		−	0.0316656i
$279$			5939.15i			1.27444i
$280$			7006.24i			1.49537i
$281$		−	4952.03i		−	1.05129i	−0.850703	−	0.525647i	$-0.823823\pi$
$281$		−	4952.03i		−	1.05129i	0.850703	−	0.525647i	$-0.176177\pi$
$282$	12647.8			2.67080
$283$	1053.35			0.221255			0.110627	−	0.993862i	$-0.464714\pi$
$283$	1053.35			0.221255			0.110627	+	0.993862i	$0.464714\pi$
$284$		−	2375.20i		−	0.496276i
$285$	704.119			0.146345
$286$	−834.010	+	757.452i	−0.172434	+	0.156605i
$287$	8377.96			1.72312
$288$		−	8896.14i		−	1.82017i
$289$	10439.3			2.12484
$290$	4302.24			0.871160
$291$			7220.88i			1.45462i
$292$			2626.83i			0.526450i
$293$		−	637.936i		−	0.127197i	−0.997976	−	0.0635984i	$-0.979742\pi$
$293$		−	637.936i		−	0.127197i	0.997976	−	0.0635984i	$-0.0202577\pi$
$294$		−	7785.44i		−	1.54441i
$295$	−1371.16			−0.270617
$296$	2411.84			0.473599
$297$		−	4093.37i		−	0.799735i
$298$	−3525.81			−0.685385
$299$	−5716.37	+	5191.63i	−1.10564	+	1.00415i
$300$	−328.864			−0.0632898
$301$		−	1604.22i		−	0.307196i
$302$	407.674			0.0776788
$303$	−4215.73			−0.799298
$304$			190.088i			0.0358629i
$305$			1093.05i			0.205206i
$306$			17776.8i			3.32102i
$307$			2338.28i			0.434699i	0.976094	+	0.217349i	$0.0697411\pi$
$307$			2338.28i			0.434699i	−0.976094	+	0.217349i	$0.930259\pi$
$308$	947.421			0.175274
$309$	−5525.98			−1.01735
$310$		−	2114.15i		−	0.387340i
$311$	2462.13			0.448921			0.224461	−	0.974483i	$-0.427938\pi$
$311$	2462.13			0.448921			0.224461	+	0.974483i	$0.427938\pi$
$312$	−7440.48	−	8192.51i	−1.35011	−	1.48657i
$313$	−3968.69			−0.716688			−0.358344	−	0.933590i	$-0.616659\pi$
$313$	−3968.69			−0.716688			−0.358344	+	0.933590i	$0.616659\pi$
$314$		−	2134.84i		−	0.383682i
$315$	−18754.5			−3.35459
$316$	551.730			0.0982190
$317$			7200.69i			1.27581i	0.770116	+	0.637904i	$0.220198\pi$
$317$			7200.69i			1.27581i	−0.770116	+	0.637904i	$0.779802\pi$
$318$		−	2243.27i		−	0.395587i
$319$		−	2024.82i		−	0.355385i
$320$			5545.20i			0.968707i
$321$	13807.1			2.40074
$322$	−9613.46			−1.66378
$323$			847.353i			0.145969i
$324$	5835.32			1.00057
$325$	−367.547	+	333.808i	−0.0627318	+	0.0569734i
$326$	−1276.50			−0.216868
$327$			8334.58i			1.40949i
$328$	7695.24			1.29542
$329$	−16057.7			−2.69085
$330$			2474.79i			0.412826i
$331$		−	829.201i		−	0.137695i	−0.997627	−	0.0688475i	$-0.978068\pi$
$331$		−	829.201i		−	0.137695i	0.997627	−	0.0688475i	$-0.0219322\pi$
$332$			50.1317i			0.00828716i
$333$			6456.07i			1.06243i
$334$	−2960.64			−0.485026
$335$	1995.41			0.325436
$336$		−	7145.11i		−	1.16011i
$337$	−10481.0			−1.69417			−0.847086	−	0.531455i	$-0.821645\pi$
$337$	−10481.0			−1.69417			−0.847086	+	0.531455i	$0.821645\pi$
$338$	−4778.54	−	460.812i	−0.768989	−	0.0741565i
$339$	13277.5			2.12724
$340$			4274.42i			0.681803i
$341$	−995.006			−0.158013
$342$	−981.168			−0.155133
$343$			724.750i			0.114090i
$344$		−	1473.50i		−	0.230947i
$345$			16962.4i			2.64702i
$346$			738.608i			0.114763i
$347$	−2485.40			−0.384505			−0.192253	−	0.981345i	$-0.561579\pi$
$347$	−2485.40			−0.384505			−0.192253	+	0.981345i	$0.561579\pi$
$348$	5714.77			0.880298
$349$			2987.37i			0.458196i	0.973403	+	0.229098i	$0.0735777\pi$
$349$			2987.37i			0.458196i	−0.973403	+	0.229098i	$0.926422\pi$
$350$	−618.120			−0.0943997
$351$	12911.9	−	11726.7i	1.96350	−	1.78326i
$352$	1490.40			0.225678
$353$		−	7919.41i		−	1.19407i	−0.802214	−	0.597036i	$-0.796345\pi$
$353$		−	7919.41i		−	1.19407i	0.802214	−	0.597036i	$-0.203655\pi$
$354$	2696.37			0.404831
$355$	−7877.06			−1.17766
$356$		−	2834.22i		−	0.421948i
$357$		−	31850.6i		−	4.72188i
$358$			2799.57i			0.413301i
$359$			2486.95i			0.365616i	0.983149	+	0.182808i	$0.0585187\pi$
$359$			2486.95i			0.365616i	−0.983149	+	0.182808i	$0.941481\pi$
$360$	−17226.2			−2.52194
$361$	6812.23			0.993181
$362$			5901.91i			0.856899i
$363$	1164.74			0.168410
$364$	2714.17	+	2988.50i	0.390828	+	0.430330i
$365$	8711.55			1.24927
$366$		−	2149.47i		−	0.306980i
$367$	63.9563			0.00909671			0.00454835	−	0.999990i	$-0.498552\pi$
$367$	63.9563			0.00909671			0.00454835	+	0.999990i	$0.498552\pi$
$368$	−4579.27			−0.648671
$369$			20598.8i			2.90605i
$370$		−	2298.15i		−	0.322906i
$371$			2848.07i			0.398557i
$372$		−	2808.27i		−	0.391403i
$373$	13587.6			1.88617			0.943083	−	0.332558i	$-0.107912\pi$
$373$	13587.6			1.88617			0.943083	+	0.332558i	$0.107912\pi$
$374$	−2978.21			−0.411764
$375$			13960.7i			1.92247i
$376$	−14749.2			−2.02295
$377$	6386.98	−	5800.69i	0.872537	−	0.792443i
$378$	21714.5			2.95470
$379$			4873.24i			0.660479i	0.943897	+	0.330240i	$0.107130\pi$
$379$			4873.24i			0.660479i	−0.943897	+	0.330240i	$0.892870\pi$
$380$	−235.921			−0.0318487
$381$	14944.9			2.00958
$382$		−	8187.05i		−	1.09656i
$383$			9976.19i			1.33096i	0.746414	+	0.665482i	$0.231774\pi$
$383$			9976.19i			1.33096i	−0.746414	+	0.665482i	$0.768226\pi$
$384$		−	470.753i		−	0.0625599i
$385$		−	3142.00i		−	0.415925i
$386$	9614.14			1.26774
$387$	3944.29			0.518087
$388$		−	2419.41i		−	0.316565i
$389$	−446.870			−0.0582447			−0.0291223	−	0.999576i	$-0.509271\pi$
$389$	−446.870			−0.0582447			−0.0291223	+	0.999576i	$0.509271\pi$
$390$	−7806.35	+	7089.76i	−1.01356	+	0.920524i
$391$	−20412.9			−2.64022
$392$			9078.97i			1.16979i
$393$	−8299.51			−1.06528
$394$	4136.93			0.528973
$395$		−	1829.74i		−	0.233074i
$396$			2329.42i			0.295600i
$397$		−	7164.73i		−	0.905762i	−0.891571	−	0.452881i	$-0.850396\pi$
$397$		−	7164.73i		−	0.905762i	0.891571	−	0.452881i	$-0.149604\pi$
$398$			3961.22i			0.498889i
$399$	1757.95			0.220571
$400$	−294.435			−0.0368043
$401$			13550.4i			1.68746i	0.536765	+	0.843732i	$0.319646\pi$
$401$			13550.4i			1.68746i	−0.536765	+	0.843732i	$0.680354\pi$
$402$	−3923.96			−0.486839
$403$	−2850.49	−	3138.60i	−0.352340	−	0.387952i
$404$	1412.51			0.173949
$405$		−	19352.1i		−	2.37436i
$406$	10741.3			1.31300
$407$	−1081.61			−0.131728
$408$		−	29255.1i		−	3.54986i
$409$		−	11178.3i		−	1.35142i	−0.737169	−	0.675708i	$-0.763838\pi$
$409$		−	11178.3i		−	1.35142i	0.737169	−	0.675708i	$-0.236162\pi$
$410$		−	7332.51i		−	0.883237i
$411$			20975.4i			2.51738i
$412$	1851.53			0.221403
$413$	−3423.32			−0.407871
$414$		−	23636.5i		−	2.80597i
$415$	166.256			0.0196655
$416$	4269.70	+	4701.25i	0.503220	+	0.554081i
$417$	−646.581			−0.0759309
$418$		−	164.378i		−	0.0192345i
$419$	5466.19			0.637329			0.318664	−	0.947868i	$-0.396766\pi$
$419$	5466.19			0.637329			0.318664	+	0.947868i	$0.396766\pi$
$420$	8867.88			1.03026
$421$		−	155.233i		−	0.0179705i	−0.999960	−	0.00898526i	$-0.997140\pi$
$421$		−	155.233i		−	0.0179705i	0.999960	−	0.00898526i	$-0.00286014\pi$
$422$			2896.18i			0.334085i
$423$		−	39481.0i		−	4.53813i
$424$			2615.99i			0.299631i
$425$	−1312.49			−0.149801
$426$	15490.2			1.76174
$427$			2728.99i			0.309286i
$428$	−4626.19			−0.522466
$429$	3336.74	+	3673.99i	0.375523	+	0.413478i
$430$	−1404.04			−0.157463
$431$		−	7469.64i		−	0.834802i	−0.908722	−	0.417401i	$-0.862941\pi$
$431$		−	7469.64i		−	0.834802i	0.908722	−	0.417401i	$-0.137059\pi$
$432$	10343.5			1.15197
$433$	14418.1			1.60021			0.800104	−	0.599861i	$-0.204778\pi$
$433$	14418.1			1.60021			0.800104	+	0.599861i	$0.204778\pi$
$434$		−	5278.32i		−	0.583796i
$435$		−	18952.3i		−	2.08895i
$436$		−	2792.57i		−	0.306743i
$437$		−	1126.66i		−	0.123331i
$438$	−17131.2			−1.86885
$439$	8328.65			0.905478			0.452739	−	0.891643i	$-0.350447\pi$
$439$	8328.65			0.905478			0.452739	+	0.891643i	$0.350447\pi$
$440$		−	2885.96i		−	0.312688i
$441$	−24302.8			−2.62421
$442$	−8531.98	−	9394.33i	−0.918156	−	1.01096i
$443$	−11095.7			−1.19000			−0.595001	−	0.803725i	$-0.702848\pi$
$443$	−11095.7			−1.19000			−0.595001	+	0.803725i	$0.702848\pi$
$444$		−	3052.69i		−	0.326294i
$445$	−9399.34			−1.00128
$446$	−9188.03			−0.975484
$447$			15532.0i			1.64348i
$448$			13844.5i			1.46003i
$449$		−	2976.06i		−	0.312804i	−0.987693	−	0.156402i	$-0.950010\pi$
$449$		−	2976.06i		−	0.312804i	0.987693	−	0.156402i	$-0.0499896\pi$
$450$		−	1519.77i		−	0.159205i
$451$	−3450.99			−0.360312
$452$	−4448.74			−0.462945
$453$		−	1795.89i		−	0.186266i
$454$	−4162.01			−0.430248
$455$	9910.99	−	9001.21i	1.02117	−	0.927436i
$456$	1614.70			0.165823
$457$			6420.09i			0.657153i	0.944477	+	0.328577i	$0.106569\pi$
$457$			6420.09i			0.657153i	−0.944477	+	0.328577i	$0.893431\pi$
$458$	3137.11			0.320060
$459$	46107.9			4.68874
$460$		−	5683.38i		−	0.576063i
$461$			17531.6i			1.77121i	0.464435	+	0.885607i	$0.346257\pi$
$461$			17531.6i			1.77121i	−0.464435	+	0.885607i	$0.653743\pi$
$462$			6178.71i			0.622207i
$463$			3416.02i			0.342885i	0.985194	+	0.171443i	$0.0548428\pi$
$463$			3416.02i			0.342885i	−0.985194	+	0.171443i	$0.945157\pi$
$464$	5116.48			0.511911
$465$	−9313.27			−0.928802
$466$			7416.09i			0.737219i
$467$	−4849.17			−0.480498			−0.240249	−	0.970711i	$-0.577229\pi$
$467$	−4849.17			−0.480498			−0.240249	+	0.970711i	$0.577229\pi$
$468$	−7347.80	+	6673.31i	−0.725753	+	0.659132i
$469$	4981.88			0.490495
$470$			14054.0i			1.37928i
$471$	−9404.44			−0.920029
$472$	−3144.36			−0.306633
$473$			660.801i			0.0642361i
$474$			3598.17i			0.348669i
$475$		−	72.4414i		−	0.00699756i
$476$			10671.8i			1.02761i
$477$	−7002.54			−0.672168
$478$	−5298.61			−0.507014
$479$		−	5650.57i		−	0.539000i	−0.963000	−	0.269500i	$-0.913141\pi$
$479$		−	5650.57i		−	0.539000i	0.963000	−	0.269500i	$-0.0868585\pi$
$480$	13950.2			1.32653
$481$	−3098.59	−	3411.77i	−0.293729	−	0.323417i
$482$	1072.14			0.101317
$483$			42349.4i			3.98957i
$484$	−390.255			−0.0366506
$485$	−8023.68			−0.751210
$486$			16101.0i			1.50279i
$487$		−	17894.1i		−	1.66500i	−0.554022	−	0.832502i	$-0.686908\pi$
$487$		−	17894.1i		−	1.66500i	0.554022	−	0.832502i	$-0.313092\pi$
$488$			2506.60i			0.232518i
$489$			5623.28i			0.520028i
$490$	8651.02			0.797578
$491$	216.780			0.0199250			0.00996248	−	0.999950i	$-0.496829\pi$
$491$	216.780			0.0199250			0.00996248	+	0.999950i	$0.496829\pi$
$492$		−	9739.95i		−	0.892502i
$493$	22807.6			2.08358
$494$	518.508	−	470.911i	0.0472242	−	0.0428893i
$495$	7725.22			0.701460
$496$		−	2514.27i		−	0.227609i
$497$	−19666.4			−1.77497
$498$	−326.940			−0.0294187
$499$		−	19511.8i		−	1.75043i	−0.483731	−	0.875217i	$-0.660719\pi$
$499$		−	19511.8i		−	1.75043i	0.483731	−	0.875217i	$-0.339281\pi$
$500$		−	4677.64i		−	0.418381i
$501$			13042.2i			1.16304i
$502$			6671.54i			0.593158i
$503$	−3662.99			−0.324701			−0.162351	−	0.986733i	$-0.551908\pi$
$503$	−3662.99			−0.324701			−0.162351	+	0.986733i	$0.551908\pi$
$504$	−43008.1			−3.80105
$505$		−	4684.43i		−	0.412781i
$506$	3959.91			0.347904
$507$	−2029.98	+	21050.5i	−0.177820	+	1.84396i
$508$	−5007.42			−0.437339
$509$		−	16263.0i		−	1.41620i	−0.706113	−	0.708099i	$-0.749553\pi$
$509$		−	16263.0i		−	1.41620i	0.706113	−	0.708099i	$-0.250447\pi$
$510$	−27876.1			−2.42034
$511$	21749.8			1.88289
$512$			9220.39i			0.795874i
$513$			2544.87i			0.219023i
$514$		−	13055.0i		−	1.12030i
$515$		−	6140.35i		−	0.525391i
$516$	−1865.02			−0.159114
$517$	6614.38			0.562669
$518$		−	5737.73i		−	0.486682i
$519$	3253.73			0.275189
$520$	9103.35	−	8267.71i	0.767708	−	0.697236i
$521$	−16503.1			−1.38774			−0.693870	−	0.720100i	$-0.744096\pi$
$521$	−16503.1			−1.38774			−0.693870	+	0.720100i	$0.744096\pi$
$522$			26409.4i			2.21439i
$523$	−1750.65			−0.146369			−0.0731843	−	0.997318i	$-0.523316\pi$
$523$	−1750.65			−0.146369			−0.0731843	+	0.997318i	$0.523316\pi$
$524$	2780.82			0.231833
$525$			2722.95i			0.226361i
$526$		−	10857.0i		−	0.899976i
$527$		−	11207.8i		−	0.926413i
$528$			2943.16i			0.242585i
$529$	14974.5			1.23075
$530$	2492.68			0.204292
$531$		−	8416.90i		−	0.687876i
$532$	−589.016			−0.0480021
$533$	−9886.39	−	10885.6i	−0.803428	−	0.884633i
$534$	18483.7			1.49788
$535$			15342.2i			1.23981i
$536$	4575.91			0.368749
$537$	12332.7			0.991053
$538$		−	725.791i		−	0.0581618i
$539$		−	4071.53i		−	0.325368i
$540$			12837.4i			1.02303i
$541$			5779.53i			0.459301i	0.973273	+	0.229650i	$0.0737582\pi$
$541$			5779.53i			0.459301i	−0.973273	+	0.229650i	$0.926242\pi$
$542$	−5698.42			−0.451601
$543$	25999.2			2.05476
$544$			16788.0i			1.32312i
$545$	−9261.21			−0.727902
$546$	−19489.8	+	17700.8i	−1.52763	+	1.38741i
$547$	11474.9			0.896950			0.448475	−	0.893795i	$-0.351967\pi$
$547$	11474.9			0.896950			0.448475	+	0.893795i	$0.351967\pi$
$548$		−	7028.00i		−	0.547849i
$549$	−6709.73			−0.521611
$550$	254.611			0.0197394
$551$			1258.84i			0.0973290i
$552$			38898.3i			2.99932i
$553$		−	4568.25i		−	0.351287i
$554$		−	5484.40i		−	0.420596i
$555$	−10123.9			−0.774296
$556$	216.642			0.0165246
$557$		−	5282.92i		−	0.401875i	−0.979604	−	0.200937i	$-0.935601\pi$
$557$		−	5282.92i		−	0.401875i	0.979604	−	0.200937i	$-0.0643988\pi$
$558$	12977.8			0.984574
$559$	−2084.40	+	1893.06i	−0.157711	+	0.143234i
$560$	7939.49			0.599116
$561$			13119.7i			0.987367i
$562$	−10820.8			−0.812184
$563$	−16115.4			−1.20637			−0.603183	−	0.797603i	$-0.706101\pi$
$563$	−16115.4			−1.20637			−0.603183	+	0.797603i	$0.706101\pi$
$564$			18668.2i			1.39375i
$565$			14753.7i			1.09857i
$566$		−	2301.69i		−	0.170932i
$567$		−	48315.8i		−	3.57861i
$568$	−18063.8			−1.33440
$569$	−15726.6			−1.15869			−0.579343	−	0.815084i	$-0.696691\pi$
$569$	−15726.6			−1.15869			−0.579343	+	0.815084i	$0.696691\pi$
$570$		−	1538.59i		−	0.113060i
$571$	12318.4			0.902814			0.451407	−	0.892318i	$-0.350922\pi$
$571$	12318.4			0.902814			0.451407	+	0.892318i	$0.350922\pi$
$572$	−1118.00	−	1231.00i	−0.0817239	−	0.0899839i
$573$	−36065.7			−2.62944
$574$		−	18306.8i		−	1.33121i
$575$	1745.13			0.126568
$576$	−34039.4			−2.46234
$577$			11049.6i			0.797227i	0.917119	+	0.398613i	$0.130508\pi$
$577$			11049.6i			0.797227i	−0.917119	+	0.398613i	$0.869492\pi$
$578$		−	22811.2i		−	1.64156i
$579$		−	42352.4i		−	3.03991i
$580$			6350.13i			0.454612i
$581$	415.085			0.0296396
$582$	15778.5			1.12378
$583$		−	1173.16i		−	0.0833401i
$584$	19977.4			1.41553
$585$	22131.2	+	24368.1i	1.56412	+	1.72221i
$586$	−1393.97			−0.0982667
$587$			20768.3i			1.46031i	0.683282	+	0.730154i	$0.260552\pi$
$587$			20768.3i			1.46031i	−0.683282	+	0.730154i	$0.739448\pi$
$588$	11491.4			0.805945
$589$	618.600			0.0432750
$590$			2996.15i			0.209067i
$591$		−	18224.1i		−	1.26842i
$592$		−	2733.10i		−	0.189746i
$593$		−	2504.18i		−	0.173413i	−0.996234	−	0.0867067i	$-0.972366\pi$
$593$		−	2504.18i		−	0.173413i	0.996234	−	0.0867067i	$-0.0276343\pi$
$594$	−8944.50			−0.617841
$595$	35391.7			2.43852
$596$		−	5204.12i		−	0.357666i
$597$	17450.0			1.19629
$598$	11344.3	+	12491.0i	0.775761	+	0.854169i
$599$	16077.2			1.09666			0.548329	−	0.836263i	$-0.315264\pi$
$599$	16077.2			1.09666			0.548329	+	0.836263i	$0.315264\pi$
$600$			2501.06i			0.170176i
$601$	24338.6			1.65190			0.825951	−	0.563741i	$-0.190639\pi$
$601$	24338.6			1.65190			0.825951	+	0.563741i	$0.190639\pi$
$602$	−3505.42			−0.237326
$603$			12248.9i			0.827221i
$604$			601.729i			0.0405364i
$605$			1294.23i			0.0869719i
$606$			9211.87i			0.617503i
$607$	13267.3			0.887154			0.443577	−	0.896236i	$-0.353709\pi$
$607$	13267.3			0.887154			0.443577	+	0.896236i	$0.353709\pi$
$608$	−926.590			−0.0618062
$609$		−	47317.6i		−	3.14845i
$610$	2388.45			0.158534
$611$	18948.9	+	20864.1i	1.25465	+	1.38146i
$612$	−26238.7			−1.73306
$613$			1989.59i			0.131091i	0.997850	+	0.0655456i	$0.0208788\pi$
$613$			1989.59i			0.131091i	−0.997850	+	0.0655456i	$0.979121\pi$
$614$	5109.42			0.335829
$615$	−32301.3			−2.11791
$616$		−	7205.29i		−	0.471281i
$617$		−	14924.0i		−	0.973772i	−0.873465	−	0.486886i	$-0.838133\pi$
$617$		−	14924.0i		−	0.973772i	0.873465	−	0.486886i	$-0.161867\pi$
$618$			12074.9i			0.785963i
$619$		−	9795.82i		−	0.636070i	−0.948079	−	0.318035i	$-0.896977\pi$
$619$		−	9795.82i		−	0.636070i	0.948079	−	0.318035i	$-0.103023\pi$
$620$	3120.49			0.202132
$621$	−61306.3			−3.96157
$622$		−	5380.05i		−	0.346817i
$623$	−23467.0			−1.50913
$624$	−9283.77	+	8431.57i	−0.595590	+	0.540918i
$625$	−14188.7			−0.908077
$626$			8672.06i			0.553682i
$627$	−724.123			−0.0461223
$628$	3151.04			0.200223
$629$		−	12183.3i		−	0.772305i
$630$			40980.8i			2.59161i
$631$		−	8845.70i		−	0.558069i	−0.960281	−	0.279035i	$-0.909986\pi$
$631$		−	8845.70i		−	0.558069i	0.960281	−	0.279035i	$-0.0900144\pi$
$632$		−	4195.99i		−	0.264094i
$633$	12758.3			0.801102
$634$	15734.4			0.985634
$635$			16606.5i			1.03781i
$636$	3311.08			0.206436
$637$	12843.1	−	11664.1i	0.798839	−	0.725510i
$638$	−4424.47			−0.274555
$639$		−	48353.6i		−	2.99349i
$640$	523.090			0.0323078
$641$	−13803.0			−0.850522			−0.425261	−	0.905071i	$-0.639818\pi$
$641$	−13803.0			−0.850522			−0.425261	+	0.905071i	$0.639818\pi$
$642$		−	30170.2i		−	1.85471i
$643$		−	12431.0i		−	0.762413i	−0.924490	−	0.381206i	$-0.875509\pi$
$643$		−	12431.0i		−	0.762413i	0.924490	−	0.381206i	$-0.124491\pi$
$644$		−	14189.5i		−	0.868238i
$645$			6185.11i			0.377579i
$646$	1851.57			0.112769
$647$	−21054.0			−1.27932			−0.639659	−	0.768659i	$-0.720925\pi$
$647$	−21054.0			−1.27932			−0.639659	+	0.768659i	$0.720925\pi$
$648$		−	44378.5i		−	2.69036i
$649$	1410.11			0.0852877
$650$	729.411	+	803.135i	0.0440152	+	0.0484639i
$651$	−23252.1			−1.39988
$652$		−	1884.13i		−	0.113172i
$653$	3926.83			0.235327			0.117664	−	0.993054i	$-0.462460\pi$
$653$	3926.83			0.235327			0.117664	+	0.993054i	$0.462460\pi$
$654$	18212.1			1.08891
$655$		−	9222.24i		−	0.550142i
$656$		−	8720.26i		−	0.519008i
$657$			53476.1i			3.17550i
$658$			35088.0i			2.07884i
$659$	−1220.65			−0.0721543			−0.0360772	−	0.999349i	$-0.511486\pi$
$659$	−1220.65			−0.0721543			−0.0360772	+	0.999349i	$0.511486\pi$
$660$	−3652.80			−0.215432
$661$			23883.6i			1.40539i	0.711490	+	0.702696i	$0.248020\pi$
$661$			23883.6i			1.40539i	−0.711490	+	0.702696i	$0.751980\pi$
$662$	−1811.90			−0.106377
$663$	−41384.1	+	37585.2i	−2.42417	+	2.20164i
$664$	381.260			0.0222827
$665$			1953.40i			0.113909i
$666$	14107.3			0.820791
$667$	−30325.6			−1.76044
$668$		−	4369.91i		−	0.253109i
$669$			40475.3i			2.33911i
$670$		−	4360.22i		−	0.251418i
$671$		−	1124.10i		−	0.0646730i
$672$	34829.0			1.99934
$673$	28377.4			1.62536			0.812681	−	0.582709i	$-0.198007\pi$
$673$	28377.4			1.62536			0.812681	+	0.582709i	$0.198007\pi$
$674$			22902.2i			1.30884i
$675$	−3941.83			−0.224772
$676$	680.162	−	7053.15i	0.0386983	−	0.401295i
$677$	518.536			0.0294372			0.0147186	−	0.999892i	$-0.495315\pi$
$677$	518.536			0.0294372			0.0147186	+	0.999892i	$0.495315\pi$
$678$		−	29012.9i		−	1.64341i
$679$	−20032.5			−1.13222
$680$	32507.6			1.83325
$681$			18334.6i			1.03169i
$682$			2174.21i			0.122074i
$683$			28142.4i			1.57663i	0.615270	+	0.788317i	$0.289047\pi$
$683$			28142.4i			1.57663i	−0.615270	+	0.788317i	$0.710953\pi$
$684$		−	1448.21i		−	0.0809556i
$685$	−23307.5			−1.30005
$686$	1583.67			0.0881408
$687$		−	13819.7i		−	0.767472i
$688$	−1669.77			−0.0925282
$689$	3700.56	−	3360.87i	0.204615	−	0.185833i
$690$	37064.8			2.04498
$691$		−	6982.37i		−	0.384402i	−0.981356	−	0.192201i	$-0.938437\pi$
$691$		−	6982.37i		−	0.384402i	0.981356	−	0.192201i	$-0.0615626\pi$
$692$	−1090.19			−0.0598884
$693$	19287.3			1.05723
$694$			5430.90i			0.297052i
$695$		−	718.467i		−	0.0392130i
$696$		−	43461.7i		−	2.36697i
$697$		−	38872.1i		−	2.11246i
$698$	6527.77			0.353983
$699$	32669.5			1.76777
$700$		−	912.348i		−	0.0492621i
$701$	34491.6			1.85839			0.929193	−	0.369595i	$-0.120504\pi$
$701$	34491.6			1.85839			0.929193	+	0.369595i	$0.120504\pi$
$702$	−25624.2	−	28214.1i	−1.37767	−	1.51691i
$703$	672.441			0.0360762
$704$		−	5702.74i		−	0.305298i
$705$	61910.7			3.30737
$706$	−17304.9			−0.922489
$707$		−	11695.5i		−	0.622140i
$708$			3979.85i			0.211260i
$709$			1575.58i			0.0834586i	0.999129	+	0.0417293i	$0.0132867\pi$
$709$			1575.58i			0.0834586i	−0.999129	+	0.0417293i	$0.986713\pi$
$710$			17212.3i			0.909813i
$711$	11231.9			0.592447
$712$	−21554.7			−1.13455
$713$			14902.2i			0.782737i
$714$	−69597.4			−3.64792
$715$	−4082.46	+	3707.72i	−0.213532	+	0.193931i
$716$	−4132.18			−0.215680
$717$			23341.5i			1.21577i
$718$	5434.29			0.282459
$719$	−6687.94			−0.346896			−0.173448	−	0.984843i	$-0.555491\pi$
$719$	−6687.94			−0.346896			−0.173448	+	0.984843i	$0.555491\pi$
$720$			19520.8i			1.01041i
$721$		−	15330.4i		−	0.791865i
$722$		−	14885.5i		−	0.767289i
$723$		−	4723.03i		−	0.242948i
$724$	−8711.25			−0.447170
$725$	−1949.86			−0.0998840
$726$		−	2545.09i		−	0.130106i
$727$	14153.6			0.722047			0.361024	−	0.932557i	$-0.382427\pi$
$727$	14153.6			0.722047			0.361024	+	0.932557i	$0.382427\pi$
$728$	22728.0	−	20641.7i	1.15708	−	1.05087i
$729$	22078.4			1.12170
$730$		−	19035.8i		−	0.965131i
$731$	−7443.30			−0.376608
$732$	3172.63			0.160197
$733$		−	13551.3i		−	0.682849i	−0.939909	−	0.341424i	$-0.889091\pi$
$733$		−	13551.3i		−	0.682849i	0.939909	−	0.341424i	$-0.110909\pi$
$734$		−	139.752i		−	0.00702772i
$735$		−	38109.6i		−	1.91251i
$736$		−	22321.7i		−	1.11792i
$737$	−2052.10			−0.102565
$738$	45010.9			2.24509
$739$			8728.80i			0.434498i	0.976116	+	0.217249i	$0.0697084\pi$
$739$			8728.80i			0.434498i	−0.976116	+	0.217249i	$0.930292\pi$
$740$	3392.09			0.168508
$741$	−2074.47	−	2284.14i	−0.102844	−	0.113239i
$742$	6223.39			0.307908
$743$			8496.99i			0.419548i	0.977750	+	0.209774i	$0.0672729\pi$
$743$			8496.99i			0.419548i	−0.977750	+	0.209774i	$0.932727\pi$
$744$	−21357.3			−1.05242
$745$	−17258.8			−0.848743
$746$		−	29690.6i		−	1.45717i
$747$			1020.56i			0.0499873i
$748$		−	4395.85i		−	0.214878i
$749$			38304.3i			1.86864i
$750$	30505.7			1.48522
$751$	19269.1			0.936269			0.468135	−	0.883657i	$-0.344926\pi$
$751$	19269.1			0.936269			0.468135	+	0.883657i	$0.344926\pi$
$752$			16713.8i			0.810492i
$753$	29389.6			1.42233
$754$	−12675.2	−	13956.3i	−0.612207	−	0.674084i
$755$	1995.56			0.0961931
$756$			32050.8i			1.54190i
$757$	−18894.3			−0.907167			−0.453584	−	0.891214i	$-0.649855\pi$
$757$	−18894.3			−0.907167			−0.453584	+	0.891214i	$0.649855\pi$
$758$	10648.6			0.510258
$759$		−	17444.3i		−	0.834238i
$760$			1794.22i			0.0856356i
$761$		−	15205.4i		−	0.724302i	−0.932119	−	0.362151i	$-0.882042\pi$
$761$		−	15205.4i		−	0.724302i	0.932119	−	0.362151i	$-0.117958\pi$
$762$		−	32656.4i		−	1.55252i
$763$	−23122.2			−1.09709
$764$	12084.1			0.572236
$765$			87017.2i			4.11257i
$766$	21799.2			1.02825
$767$	4039.69	+	4447.99i	0.190176	+	0.209397i
$768$	38894.4			1.82745
$769$		−	20635.8i		−	0.967679i	−0.875157	−	0.483840i	$-0.839242\pi$
$769$		−	20635.8i		−	0.967679i	0.875157	−	0.483840i	$-0.160758\pi$
$770$	−6865.66			−0.321326
$771$	−57510.2			−2.68636
$772$			14190.5i			0.661565i
$773$		−	20528.2i		−	0.955171i	−0.878585	−	0.477586i	$-0.841512\pi$
$773$		−	20528.2i		−	0.955171i	0.878585	−	0.477586i	$-0.158488\pi$
$774$		−	8618.76i		−	0.400252i
$775$			958.171i			0.0444110i
$776$	−18400.0			−0.851189
$777$	−25275.9			−1.16701
$778$			976.464i			0.0449973i
$779$	2145.50			0.0986783
$780$	−10464.5	−	11522.2i	−0.480372	−	0.528925i
$781$	8100.84			0.371154
$782$			44604.6i			2.03972i
$783$	68498.5			3.12635
$784$	10288.3			0.468673
$785$		−	10450.0i		−	0.475130i
$786$			18135.4i			0.822989i
$787$		−	44153.3i		−	1.99987i	−0.0115529	−	0.999933i	$-0.503677\pi$
$787$		−	44153.3i		−	1.99987i	0.0115529	−	0.999933i	$-0.496323\pi$
$788$			6106.13i			0.276043i
$789$	−47827.4			−2.15805
$790$	−3998.21			−0.180063
$791$			36835.0i			1.65575i
$792$	17715.6			0.794818
$793$	3545.82	−	3220.34i	0.158784	−	0.144209i
$794$	−15655.8			−0.699753
$795$		−	10980.8i		−	0.489872i
$796$	−5846.78			−0.260344
$797$	39096.0			1.73758			0.868791	−	0.495179i	$-0.164898\pi$
$797$	39096.0			1.73758			0.868791	+	0.495179i	$0.164898\pi$
$798$		−	3841.33i		−	0.170403i
$799$			74504.7i			3.29886i
$800$		−	1435.23i		−	0.0634287i
$801$		−	57698.2i		−	2.54515i
$802$	29609.2			1.30366
$803$	−8959.03			−0.393720
$804$		−	5791.78i		−	0.254055i
$805$	−47057.7			−2.06033
$806$	−6858.22	+	6228.67i	−0.299715	+	0.272203i
$807$	−3197.26			−0.139466
$808$		−	10742.4i		−	0.467718i
$809$	−19382.3			−0.842331			−0.421166	−	0.906984i	$-0.638379\pi$
$809$	−19382.3			−0.842331			−0.421166	+	0.906984i	$0.638379\pi$
$810$	−42286.7			−1.83432
$811$		−	5800.42i		−	0.251147i	−0.992084	−	0.125574i	$-0.959923\pi$
$811$		−	5800.42i		−	0.251147i	0.992084	−	0.125574i	$-0.0400771\pi$
$812$			15854.2i			0.685187i
$813$			25102.8i			1.08289i
$814$			2363.44i			0.101767i
$815$	−6248.47			−0.268557
$816$	−33151.9			−1.42224
$817$		−	410.823i		−	0.0175923i
$818$	−24425.8			−1.04405
$819$	55254.2	+	60838.9i	2.35743	+	2.59571i
$820$	10822.8			0.460914
$821$		−	25555.9i		−	1.08637i	−0.839615	−	0.543183i	$-0.817219\pi$
$821$		−	25555.9i		−	1.08637i	0.839615	−	0.543183i	$-0.182781\pi$
$822$	45833.9			1.94482
$823$	12267.7			0.519594			0.259797	−	0.965663i	$-0.416344\pi$
$823$	12267.7			0.519594			0.259797	+	0.965663i	$0.416344\pi$
$824$		−	14081.1i		−	0.595315i
$825$		−	1121.62i		−	0.0473330i
$826$			7480.38i			0.315104i
$827$		−	10215.4i		−	0.429534i	−0.976665	−	0.214767i	$-0.931101\pi$
$827$		−	10215.4i		−	0.429534i	0.976665	−	0.214767i	$-0.0688992\pi$
$828$	34887.6			1.46429
$829$	−37057.6			−1.55255			−0.776274	−	0.630396i	$-0.782893\pi$
$829$	−37057.6			−1.55255			−0.776274	+	0.630396i	$0.782893\pi$
$830$		−	363.288i		−	0.0151927i
$831$	−24160.0			−1.00854
$832$	17988.4	−	16337.2i	0.749564	−	0.680758i
$833$	45862.0			1.90759
$834$			1412.86i			0.0586609i
$835$	−14492.3			−0.600630
$836$	242.623			0.0100374
$837$		−	33660.5i		−	1.39006i
$838$		−	11944.3i		−	0.492373i
$839$			41772.6i			1.71889i	0.511225	+	0.859447i	$0.329192\pi$
$839$			41772.6i			1.71889i	−0.511225	+	0.859447i	$0.670808\pi$
$840$		−	67441.6i		−	2.77019i
$841$	9494.29			0.389286
$842$	−339.203			−0.0138832
$843$			47667.9i			1.94753i
$844$	−4274.78			−0.174341
$845$	−23390.9	−	2255.67i	−0.952273	−	0.0918313i
$846$	−86270.6			−3.50596
$847$			3231.27i			0.131083i
$848$	2964.44			0.120046
$849$	−10139.5			−0.409877
$850$			2867.96i			0.115730i
$851$			16199.2i			0.652529i
$852$			22863.5i			0.919357i
$853$			24787.7i			0.994974i	0.867471	+	0.497487i	$0.165744\pi$
$853$			24787.7i			0.994974i	−0.867471	+	0.497487i	$0.834256\pi$
$854$	5963.16			0.238941
$855$	−4802.80			−0.192108
$856$			35182.9i			1.40482i
$857$	−14467.2			−0.576652			−0.288326	−	0.957532i	$-0.593099\pi$
$857$	−14467.2			−0.576652			−0.288326	+	0.957532i	$0.593099\pi$
$858$	8028.12	−	7291.18i	0.319435	−	0.290113i
$859$	27435.5			1.08974			0.544871	−	0.838520i	$-0.316579\pi$
$859$	27435.5			1.08974			0.544871	+	0.838520i	$0.316579\pi$
$860$		−	2072.37i		−	0.0821713i
$861$	−80645.6			−3.19210
$862$	−16322.1			−0.644932
$863$			22053.6i			0.869889i	0.900457	+	0.434945i	$0.143232\pi$
$863$			22053.6i			0.869889i	−0.900457	+	0.434945i	$0.856768\pi$
$864$			50419.5i			1.98531i
$865$			3615.48i			0.142116i
$866$		−	31505.3i		−	1.23625i
$867$	−100488.			−3.93629
$868$	7790.82			0.304652
$869$			1881.72i			0.0734558i
$870$	−41413.1			−1.61383
$871$	−5878.86	−	6473.06i	−0.228700	−	0.251815i
$872$	−21237.9			−0.824779
$873$		−	49253.6i		−	1.90949i
$874$	−2461.89			−0.0952801
$875$	−38730.3			−1.49637
$876$		−	25285.7i		−	0.975255i
$877$		−	2228.36i		−	0.0857998i	−0.999079	−	0.0428999i	$-0.986340\pi$
$877$		−	2228.36i		−	0.0857998i	0.999079	−	0.0428999i	$-0.0136597\pi$
$878$		−	18199.1i		−	0.699533i
$879$			6140.73i			0.235633i
$880$	−3270.38			−0.125278
$881$	−4639.34			−0.177416			−0.0887079	−	0.996058i	$-0.528274\pi$
$881$	−4639.34			−0.177416			−0.0887079	+	0.996058i	$0.528274\pi$
$882$			53104.6i			2.02735i
$883$	−35460.0			−1.35144			−0.675721	−	0.737158i	$-0.736168\pi$
$883$	−35460.0			−1.35144			−0.675721	+	0.737158i	$0.736168\pi$
$884$	13866.1	−	12593.2i	0.527564	−	0.479137i
$885$	13198.7			0.501320
$886$			24245.4i			0.919344i
$887$	43408.8			1.64321			0.821603	−	0.570060i	$-0.193080\pi$
$887$	43408.8			1.64321			0.821603	+	0.570060i	$0.193080\pi$
$888$	−23216.2			−0.877348
$889$			41460.8i			1.56418i
$890$			20538.7i			0.773549i
$891$			19901.9i			0.748303i
$892$		−	13561.6i		−	0.509053i
$893$	−4112.19			−0.154098
$894$	33939.2			1.26968
$895$			13703.8i			0.511809i
$896$	1305.98			0.0486940
$897$	55025.4	−	49974.3i	2.04821	−	1.86019i
$898$	−6503.06			−0.241659
$899$		−	16650.4i		−	0.617712i
$900$	2243.18			0.0830808
$901$	13214.5			0.488612
$902$			7540.83i			0.278361i
$903$			15442.2i			0.569084i
$904$			33833.3i			1.24478i
$905$			28889.8i			1.06114i
$906$	−3924.24			−0.143901
$907$	−18890.2			−0.691554			−0.345777	−	0.938317i	$-0.612385\pi$
$907$	−18890.2			−0.691554			−0.345777	+	0.938317i	$0.612385\pi$
$908$		−	6143.15i		−	0.224524i
$909$	28755.5			1.04924
$910$	−19668.7	−	21656.7i	−0.716497	−	0.788915i
$911$	11529.8			0.419317			0.209659	−	0.977775i	$-0.432765\pi$
$911$	11529.8			0.419317			0.209659	+	0.977775i	$0.432765\pi$
$912$		−	1829.78i		−	0.0664364i
$913$	−170.979			−0.00619778
$914$	14028.7			0.507688
$915$		−	10521.6i		−	0.380147i
$916$			4630.40i			0.167022i
$917$		−	23024.9i		−	0.829169i
$918$		−	100751.i		−	3.62232i
$919$	22570.6			0.810159			0.405079	−	0.914282i	$-0.367244\pi$
$919$	22570.6			0.810159			0.405079	+	0.914282i	$0.367244\pi$
$920$	−43223.0			−1.54894
$921$		−	22508.1i		−	0.805284i
$922$	38308.7			1.36836
$923$	23207.3	+	25552.9i	0.827603	+	0.911251i
$924$	−9119.81			−0.324697
$925$			1041.57i			0.0370232i
$926$	7464.41			0.264898
$927$	37692.7			1.33548
$928$			24940.4i			0.882229i
$929$			2774.81i			0.0979961i	0.998799	+	0.0489981i	$0.0156028\pi$
$929$			2774.81i			0.0979961i	−0.998799	+	0.0489981i	$0.984397\pi$
$930$			20350.6i			0.717552i
$931$			2531.29i			0.0891082i
$932$	−10946.2			−0.384715
$933$	−23700.3			−0.831632
$934$			10596.0i			0.371212i
$935$	−14578.3			−0.509905
$936$	50751.6	+	55881.2i	1.77229	+	1.95142i
$937$	−22882.5			−0.797799			−0.398900	−	0.916995i	$-0.630608\pi$
$937$	−22882.5			−0.797799			−0.398900	+	0.916995i	$0.630608\pi$
$938$		−	10886.0i		−	0.378935i
$939$	38202.3			1.32767
$940$	−20743.7			−0.719772
$941$		−	54684.3i		−	1.89443i	−0.320602	−	0.947214i	$-0.603885\pi$
$941$		−	54684.3i		−	1.89443i	0.320602	−	0.947214i	$-0.396115\pi$
$942$			20549.8i			0.710775i
$943$			51685.4i			1.78484i
$944$			3563.20i			0.122852i
$945$	106292.			3.65893
$946$	1443.93			0.0496260
$947$		−	14358.6i		−	0.492706i	−0.969180	−	0.246353i	$-0.920768\pi$
$947$		−	14358.6i		−	0.492706i	0.969180	−	0.246353i	$-0.0792323\pi$
$948$	−5310.91			−0.181952
$949$	−25665.8	−	28260.0i	−0.877923	−	0.966657i
$950$	−158.293			−0.00540601
$951$		−	69313.4i		−	2.36345i
$952$	81160.7			2.76306
$953$	27785.4			0.944448			0.472224	−	0.881479i	$-0.343451\pi$
$953$	27785.4			0.944448			0.472224	+	0.881479i	$0.343451\pi$
$954$			15301.4i			0.519288i
$955$		−	40075.5i		−	1.35792i
$956$		−	7820.78i		−	0.264584i
$957$			19490.7i			0.658355i
$958$	−12347.2			−0.416408
$959$	−58191.0			−1.95942
$960$		−	53377.7i		−	1.79454i
$961$	21608.9			0.725349
$962$	−7455.14	+	6770.79i	−0.249858	+	0.226922i
$963$	−94178.4			−3.15146
$964$			1582.49i			0.0528720i
$965$	47061.1			1.56990
$966$	92538.5			3.08217
$967$		−	27673.4i		−	0.920286i	−0.887845	−	0.460143i	$-0.847798\pi$
$967$		−	27673.4i		−	0.920286i	0.887845	−	0.460143i	$-0.152202\pi$
$968$			2967.95i			0.0985471i
$969$		−	8156.56i		−	0.270409i
$970$			17532.7i			0.580352i
$971$	36510.1			1.20666			0.603329	−	0.797492i	$-0.293840\pi$
$971$	36510.1			1.20666			0.603329	+	0.797492i	$0.293840\pi$
$972$	−23765.2			−0.784227
$973$		−	1793.77i		−	0.0591014i
$974$	−39100.7			−1.28631
$975$	3537.98	−	3213.21i	0.116211	−	0.105544i
$976$	2840.49			0.0931576
$977$			42977.4i			1.40734i	0.710528	+	0.703669i	$0.248456\pi$
$977$			42977.4i			1.40734i	−0.710528	+	0.703669i	$0.751544\pi$
$978$	12287.5			0.401751
$979$	9666.37			0.315565
$980$			12769.0i			0.416214i
$981$		−	56850.2i		−	1.85024i
$982$		−	473.691i		−	0.0153932i
$983$			47138.7i			1.52949i	0.644331	+	0.764746i	$0.277136\pi$
$983$			47138.7i			1.52949i	−0.644331	+	0.764746i	$0.722864\pi$
$984$	−74073.8			−2.39978
$985$	20250.2			0.655051
$986$		−	49837.4i		−	1.60968i
$987$	154570.			4.98483
$988$	695.068	+	765.320i	0.0223816	+	0.0246438i
$989$	9896.81			0.318200
$990$		−	16880.5i		−	0.541917i
$991$	−62194.4			−1.99361			−0.996806	−	0.0798556i	$-0.974554\pi$
$991$	−62194.4			−1.99361			−0.996806	+	0.0798556i	$0.974554\pi$
$992$	12255.9			0.392262
$993$			7981.83i			0.255081i
$994$			42973.4i			1.37126i
$995$			19390.1i			0.617797i
$996$		−	482.565i		−	0.0153521i
$997$	−42591.3			−1.35294			−0.676469	−	0.736471i	$-0.736491\pi$
$997$	−42591.3			−1.35294			−0.676469	+	0.736471i	$0.736491\pi$
$998$	−42635.6			−1.35231
$999$		−	36590.2i		−	1.15882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.b.a.12.14	✓	36
13.5	odd	4		1859.4.a.j.1.7		18
13.8	odd	4		1859.4.a.k.1.12		18
13.12	even	2	inner	143.4.b.a.12.23	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.b.a.12.14	✓	36	1.1	even	1	trivial
143.4.b.a.12.23	yes	36	13.12	even	2	inner
1859.4.a.j.1.7		18	13.5	odd	4
1859.4.a.k.1.12		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)

\(f(q)\)	\(=\)	\(q-2.18512i q^{2} -9.62593 q^{3} +3.22525 q^{4} -10.6961i q^{5} +21.0338i q^{6} -26.7047i q^{7} -24.5285i q^{8} +65.6585 q^{9} +O(q^{10})\)	\(q-2.18512i q^{2} -9.62593 q^{3} +3.22525 q^{4} -10.6961i q^{5} +21.0338i q^{6} -26.7047i q^{7} -24.5285i q^{8} +65.6585 q^{9} -23.3723 q^{10} +11.0000i q^{11} -31.0460 q^{12} +(-34.6979 + 31.5128i) q^{13} -58.3529 q^{14} +102.960i q^{15} -27.7958 q^{16} -123.905 q^{17} -143.472i q^{18} -6.83875i q^{19} -34.4977i q^{20} +257.057i q^{21} +24.0363 q^{22} +164.747 q^{23} +236.110i q^{24} +10.5928 q^{25} +(68.8593 + 75.8191i) q^{26} -372.124 q^{27} -86.1292i q^{28} -184.074 q^{29} +224.980 q^{30} +90.4551i q^{31} -135.491i q^{32} -105.885i q^{33} +270.746i q^{34} -285.637 q^{35} +211.765 q^{36} +98.3280i q^{37} -14.9435 q^{38} +(333.999 - 303.340i) q^{39} -262.360 q^{40} +313.726i q^{41} +561.701 q^{42} +60.0728 q^{43} +35.4777i q^{44} -702.292i q^{45} -359.992i q^{46} -601.307i q^{47} +267.560 q^{48} -370.139 q^{49} -23.1465i q^{50} +1192.70 q^{51} +(-111.909 + 101.637i) q^{52} -106.651 q^{53} +813.136i q^{54} +117.657 q^{55} -655.026 q^{56} +65.8293i q^{57} +402.224i q^{58} -128.192i q^{59} +332.072i q^{60} -102.191 q^{61} +197.655 q^{62} -1753.39i q^{63} -518.430 q^{64} +(337.065 + 371.133i) q^{65} -231.372 q^{66} +186.555i q^{67} -399.623 q^{68} -1585.84 q^{69} +624.150i q^{70} -736.440i q^{71} -1610.51i q^{72} +814.458i q^{73} +214.858 q^{74} -101.965 q^{75} -22.0567i q^{76} +293.751 q^{77} +(-662.835 - 729.829i) q^{78} +171.066 q^{79} +297.307i q^{80} +1809.26 q^{81} +685.530 q^{82} +15.5435i q^{83} +829.074i q^{84} +1325.30i q^{85} -131.266i q^{86} +1771.88 q^{87} +269.814 q^{88} -878.761i q^{89} -1534.59 q^{90} +(841.539 + 926.596i) q^{91} +531.350 q^{92} -870.714i q^{93} -1313.93 q^{94} -73.1482 q^{95} +1304.23i q^{96} -750.148i q^{97} +808.799i q^{98} +722.244i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 152 q^{4} + 360 q^{9}+O(q^{10}) \) 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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