LMFDB - Embedded newform 143.4.b.a.12.17

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			12.17
Character	$\chi$	$=$	143.12
Dual form			143.4.b.a.12.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.468651i q^{2} -6.65460 q^{3} +7.78037 q^{4} -3.45502i q^{5} +3.11869i q^{6} +11.5900i q^{7} -7.39549i q^{8} +17.2837 q^{9} +O(q^{10})$	\(q-0.468651i q^{2} -6.65460 q^{3} +7.78037 q^{4} -3.45502i q^{5} +3.11869i q^{6} +11.5900i q^{7} -7.39549i q^{8} +17.2837 q^{9} -1.61920 q^{10} +11.0000i q^{11} -51.7752 q^{12} +(30.5990 - 35.5064i) q^{13} +5.43166 q^{14} +22.9918i q^{15} +58.7770 q^{16} +69.5462 q^{17} -8.10003i q^{18} -136.796i q^{19} -26.8813i q^{20} -77.1267i q^{21} +5.15517 q^{22} +13.6317 q^{23} +49.2140i q^{24} +113.063 q^{25} +(-16.6401 - 14.3402i) q^{26} +64.6581 q^{27} +90.1743i q^{28} +119.298 q^{29} +10.7751 q^{30} -190.188i q^{31} -86.7099i q^{32} -73.2006i q^{33} -32.5930i q^{34} +40.0436 q^{35} +134.473 q^{36} -173.788i q^{37} -64.1097 q^{38} +(-203.624 + 236.281i) q^{39} -25.5516 q^{40} +390.436i q^{41} -36.1455 q^{42} -443.009 q^{43} +85.5840i q^{44} -59.7155i q^{45} -6.38853i q^{46} +470.604i q^{47} -391.138 q^{48} +208.672 q^{49} -52.9871i q^{50} -462.802 q^{51} +(238.071 - 276.253i) q^{52} -395.914 q^{53} -30.3021i q^{54} +38.0052 q^{55} +85.7136 q^{56} +910.323i q^{57} -55.9094i q^{58} -743.180i q^{59} +178.885i q^{60} +430.086 q^{61} -89.1320 q^{62} +200.318i q^{63} +429.579 q^{64} +(-122.675 - 105.720i) q^{65} -34.3056 q^{66} +967.071i q^{67} +541.095 q^{68} -90.7136 q^{69} -18.7665i q^{70} -52.6426i q^{71} -127.821i q^{72} -287.872i q^{73} -81.4460 q^{74} -752.388 q^{75} -1064.32i q^{76} -127.490 q^{77} +(110.733 + 95.4286i) q^{78} +564.168 q^{79} -203.076i q^{80} -896.934 q^{81} +182.978 q^{82} +1074.48i q^{83} -600.074i q^{84} -240.284i q^{85} +207.617i q^{86} -793.883 q^{87} +81.3504 q^{88} -628.445i q^{89} -27.9858 q^{90} +(411.518 + 354.641i) q^{91} +106.060 q^{92} +1265.63i q^{93} +220.549 q^{94} -472.634 q^{95} +577.019i q^{96} -629.130i q^{97} -97.7946i q^{98} +190.121i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	0.468651i		−	0.165693i	−0.996562	−	0.0828467i	$-0.973599\pi$
$2$		−	0.468651i		−	0.165693i	0.996562	−	0.0828467i	$-0.0264012\pi$
$3$	−6.65460			−1.28068			−0.640339	−	0.768092i	$-0.721206\pi$
$3$	−6.65460			−1.28068			−0.640339	+	0.768092i	$0.721206\pi$
$4$	7.78037			0.972546
$5$		−	3.45502i		−	0.309027i	−0.987991	−	0.154513i	$-0.950619\pi$
$5$		−	3.45502i		−	0.309027i	0.987991	−	0.154513i	$-0.0493809\pi$
$6$			3.11869i			0.212200i
$7$			11.5900i			0.625800i	0.949786	+	0.312900i	$0.101301\pi$
$7$			11.5900i			0.625800i	−0.949786	+	0.312900i	$0.898699\pi$
$8$		−	7.39549i		−	0.326838i
$9$	17.2837			0.640137
$10$	−1.61920			−0.0512036
$11$			11.0000i			0.301511i
$11$			11.0000i			0.301511i
$12$	−51.7752			−1.24552
$13$	30.5990	−	35.5064i	0.652817	−	0.757515i
$13$	30.5990	−	35.5064i	0.652817	−	0.757515i
$14$	5.43166			0.103691
$15$			22.9918i			0.395764i
$16$	58.7770			0.918391
$17$	69.5462			0.992202			0.496101	−	0.868265i	$-0.334764\pi$
$17$	69.5462			0.992202			0.496101	+	0.868265i	$0.334764\pi$
$18$		−	8.10003i		−	0.106066i
$19$		−	136.796i		−	1.65175i	−0.563856	−	0.825873i	$-0.690683\pi$
$19$		−	136.796i		−	1.65175i	0.563856	−	0.825873i	$-0.309317\pi$
$20$		−	26.8813i		−	0.300543i
$21$		−	77.1267i		−	0.801449i
$22$	5.15517			0.0499584
$23$	13.6317			0.123583			0.0617915	−	0.998089i	$-0.480319\pi$
$23$	13.6317			0.123583			0.0617915	+	0.998089i	$0.480319\pi$
$24$			49.2140i			0.418574i
$25$	113.063			0.904503
$26$	−16.6401	−	14.3402i	−0.125515	−	0.108167i
$27$	64.6581			0.460869
$28$			90.1743i			0.608619i
$29$	119.298			0.763902			0.381951	−	0.924183i	$-0.375252\pi$
$29$	119.298			0.763902			0.381951	+	0.924183i	$0.375252\pi$
$30$	10.7751			0.0655754
$31$		−	190.188i		−	1.10190i	−0.834539	−	0.550949i	$-0.814266\pi$
$31$		−	190.188i		−	1.10190i	0.834539	−	0.550949i	$-0.185734\pi$
$32$		−	86.7099i		−	0.479009i
$33$		−	73.2006i		−	0.386139i
$34$		−	32.5930i		−	0.164401i
$35$	40.0436			0.193389
$36$	134.473			0.622562
$37$		−	173.788i		−	0.772178i	−0.922462	−	0.386089i	$-0.873826\pi$
$37$		−	173.788i		−	0.772178i	0.922462	−	0.386089i	$-0.126174\pi$
$38$	−64.1097			−0.273683
$39$	−203.624	+	236.281i	−0.836049	+	0.970134i
$40$	−25.5516			−0.101002
$41$			390.436i			1.48722i	0.668616	+	0.743608i	$0.266887\pi$
$41$			390.436i			1.48722i	−0.668616	+	0.743608i	$0.733113\pi$
$42$	−36.1455			−0.132795
$43$	−443.009			−1.57112			−0.785561	−	0.618784i	$-0.787626\pi$
$43$	−443.009			−1.57112			−0.785561	+	0.618784i	$0.787626\pi$
$44$			85.5840i			0.293234i
$45$		−	59.7155i		−	0.197819i
$46$		−	6.38853i		−	0.0204769i
$47$			470.604i			1.46052i	0.683167	+	0.730262i	$0.260602\pi$
$47$			470.604i			1.46052i	−0.683167	+	0.730262i	$0.739398\pi$
$48$	−391.138			−1.17616
$49$	208.672			0.608374
$50$		−	52.9871i		−	0.149870i
$51$	−462.802			−1.27069
$52$	238.071	−	276.253i	0.634895	−	0.736718i
$53$	−395.914			−1.02609			−0.513047	−	0.858361i	$-0.671483\pi$
$53$	−395.914			−1.02609			−0.513047	+	0.858361i	$0.671483\pi$
$54$		−	30.3021i		−	0.0763629i
$55$	38.0052			0.0931750
$56$	85.7136			0.204535
$57$			910.323i			2.11536i
$58$		−	55.9094i		−	0.126573i
$59$		−	743.180i		−	1.63990i	−0.572438	−	0.819948i	$-0.694002\pi$
$59$		−	743.180i		−	1.63990i	0.572438	−	0.819948i	$-0.305998\pi$
$60$			178.885i			0.384898i
$61$	430.086			0.902735			0.451367	−	0.892338i	$-0.350936\pi$
$61$	430.086			0.902735			0.451367	+	0.892338i	$0.350936\pi$
$62$	−89.1320			−0.182577
$63$			200.318i			0.400598i
$64$	429.579			0.839022
$65$	−122.675	−	105.720i	−0.234092	−	0.201738i
$66$	−34.3056			−0.0639807
$67$			967.071i			1.76338i	0.471828	+	0.881691i	$0.343594\pi$
$67$			967.071i			1.76338i	−0.471828	+	0.881691i	$0.656406\pi$
$68$	541.095			0.964962
$69$	−90.7136			−0.158270
$70$		−	18.7665i		−	0.0320433i
$71$		−	52.6426i		−	0.0879934i	−0.999032	−	0.0439967i	$-0.985991\pi$
$71$		−	52.6426i		−	0.0879934i	0.999032	−	0.0439967i	$-0.0140091\pi$
$72$		−	127.821i		−	0.209221i
$73$		−	287.872i		−	0.461545i	−0.973008	−	0.230773i	$-0.925875\pi$
$73$		−	287.872i		−	0.461545i	0.973008	−	0.230773i	$-0.0741254\pi$
$74$	−81.4460			−0.127945
$75$	−752.388			−1.15838
$76$		−	1064.32i		−	1.60640i
$77$	−127.490			−0.188686
$78$	110.733	+	95.4286i	0.160745	+	0.138528i
$79$	564.168			0.803466			0.401733	−	0.915757i	$-0.368408\pi$
$79$	564.168			0.803466			0.401733	+	0.915757i	$0.368408\pi$
$80$		−	203.076i		−	0.283807i
$81$	−896.934			−1.23036
$82$	182.978			0.246422
$83$			1074.48i			1.42095i	0.703720	+	0.710477i	$0.251521\pi$
$83$			1074.48i			1.42095i	−0.703720	+	0.710477i	$0.748479\pi$
$84$		−	600.074i		−	0.779446i
$85$		−	240.284i		−	0.306617i
$86$			207.617i			0.260325i
$87$	−793.883			−0.978313
$88$	81.3504			0.0985453
$89$		−	628.445i		−	0.748483i	−0.927331	−	0.374242i	$-0.877903\pi$
$89$		−	628.445i		−	0.748483i	0.927331	−	0.374242i	$-0.122097\pi$
$90$	−27.9858			−0.0327773
$91$	411.518	+	354.641i	0.474053	+	0.408533i
$92$	106.060			0.120190
$93$			1265.63i			1.41118i
$94$	220.549			0.241999
$95$	−472.634			−0.510434
$96$			577.019i			0.613456i
$97$		−	629.130i		−	0.658541i	−0.944236	−	0.329271i	$-0.893197\pi$
$97$		−	629.130i		−	0.658541i	0.944236	−	0.329271i	$-0.106803\pi$
$98$		−	97.7946i		−	0.100804i
$99$			190.121i			0.193008i
$100$	879.670			0.879670
$101$	94.2837			0.0928869			0.0464435	−	0.998921i	$-0.485211\pi$
$101$	94.2837			0.0928869			0.0464435	+	0.998921i	$0.485211\pi$
$102$			216.893i			0.210545i
$103$	−950.056			−0.908852			−0.454426	−	0.890784i	$-0.650156\pi$
$103$	−950.056			−0.908852			−0.454426	+	0.890784i	$0.650156\pi$
$104$	−262.587	−	226.294i	−0.247585	−	0.213365i
$105$	−266.474			−0.247669
$106$			185.546i			0.170017i
$107$	−1209.82			−1.09307			−0.546533	−	0.837438i	$-0.684053\pi$
$107$	−1209.82			−1.09307			−0.546533	+	0.837438i	$0.684053\pi$
$108$	503.064			0.448216
$109$		−	751.273i		−	0.660173i	−0.943951	−	0.330087i	$-0.892922\pi$
$109$		−	751.273i		−	0.660173i	0.943951	−	0.330087i	$-0.107078\pi$
$110$		−	17.8112i		−	0.0154385i
$111$			1156.49i			0.988912i
$112$			681.225i			0.574729i
$113$	261.719			0.217880			0.108940	−	0.994048i	$-0.465254\pi$
$113$	261.719			0.217880			0.108940	+	0.994048i	$0.465254\pi$
$114$	426.624			0.350500
$115$		−	47.0979i		−	0.0381905i
$116$	928.185			0.742930
$117$	528.863	−	613.682i	0.417892	−	0.484914i
$118$	−348.293			−0.271720
$119$			806.040i			0.620921i
$120$	170.036			0.129350
$121$	−121.000			−0.0909091
$122$		−	201.560i		−	0.149577i
$123$		−	2598.20i		−	1.90465i
$124$		−	1479.73i		−	1.07165i
$125$		−	822.512i		−	0.588542i
$126$	93.8792			0.0663764
$127$	−655.749			−0.458176			−0.229088	−	0.973406i	$-0.573574\pi$
$127$	−655.749			−0.458176			−0.229088	+	0.973406i	$0.573574\pi$
$128$		−	895.002i		−	0.618029i
$129$	2948.05			2.01210
$130$	−49.5459	+	57.4920i	−0.0334266	+	0.0387876i
$131$	924.346			0.616492			0.308246	−	0.951307i	$-0.400258\pi$
$131$	924.346			0.616492			0.308246	+	0.951307i	$0.400258\pi$
$132$		−	569.527i		−	0.375538i
$133$	1585.46			1.03366
$134$	453.219			0.292181
$135$		−	223.395i		−	0.142421i
$136$		−	514.329i		−	0.324289i
$137$			1358.80i			0.847376i	0.905808	+	0.423688i	$0.139265\pi$
$137$			1358.80i			0.847376i	−0.905808	+	0.423688i	$0.860735\pi$
$138$			42.5131i			0.0262243i
$139$	1932.17			1.17903			0.589513	−	0.807759i	$-0.299320\pi$
$139$	1932.17			1.17903			0.589513	+	0.807759i	$0.299320\pi$
$140$	311.554			0.188080
$141$		−	3131.68i		−	1.87046i
$142$	−24.6710			−0.0145799
$143$	390.570	+	336.589i	0.228400	+	0.196832i
$144$	1015.88			0.587896
$145$		−	412.179i		−	0.236066i
$146$	−134.911			−0.0764750
$147$	−1388.63			−0.779131
$148$		−	1352.13i		−	0.750978i
$149$		−	1649.22i		−	0.906775i	−0.891314	−	0.453387i	$-0.850215\pi$
$149$		−	1649.22i		−	0.906775i	0.891314	−	0.453387i	$-0.149785\pi$
$150$			352.608i			0.191935i
$151$			2892.17i			1.55868i	0.626599	+	0.779342i	$0.284447\pi$
$151$			2892.17i			1.55868i	−0.626599	+	0.779342i	$0.715553\pi$
$152$	−1011.67			−0.539853
$153$	1202.02			0.635145
$154$			59.7483i			0.0312640i
$155$	−657.105			−0.340516
$156$	−1584.27	+	1838.35i	−0.813096	+	0.943499i
$157$	−1487.86			−0.756331			−0.378165	−	0.925738i	$-0.623445\pi$
$157$	−1487.86			−0.756331			−0.378165	+	0.925738i	$0.623445\pi$
$158$		−	264.398i		−	0.133129i
$159$	2634.65			1.31410
$160$	−299.585			−0.148026
$161$			157.991i			0.0773383i
$162$			420.349i			0.203863i
$163$			109.419i			0.0525789i	0.999654	+	0.0262894i	$0.00836915\pi$
$163$			109.419i			0.0525789i	−0.999654	+	0.0262894i	$0.991631\pi$
$164$			3037.73i			1.44639i
$165$	−252.910			−0.119327
$166$	503.556			0.235443
$167$			813.879i			0.377125i	0.982061	+	0.188562i	$0.0603828\pi$
$167$			813.879i			0.377125i	−0.982061	+	0.188562i	$0.939617\pi$
$168$	−570.390			−0.261944
$169$	−324.408	−	2172.92i	−0.147659	−	0.989038i
$170$	−112.609			−0.0508044
$171$		−	2364.34i		−	1.05734i
$172$	−3446.77			−1.52799
$173$	2890.82			1.27043			0.635216	−	0.772334i	$-0.280911\pi$
$173$	2890.82			1.27043			0.635216	+	0.772334i	$0.280911\pi$
$174$			372.054i			0.162100i
$175$			1310.40i			0.566038i
$176$			646.547i			0.276905i
$177$			4945.57i			2.10018i
$178$	−294.521			−0.124019
$179$	−4254.68			−1.77659			−0.888295	−	0.459273i	$-0.848110\pi$
$179$	−4254.68			−1.77659			−0.888295	+	0.459273i	$0.848110\pi$
$180$		−	464.609i		−	0.192388i
$181$	−402.638			−0.165347			−0.0826735	−	0.996577i	$-0.526346\pi$
$181$	−402.638			−0.165347			−0.0826735	+	0.996577i	$0.526346\pi$
$182$	166.203	−	192.859i	0.0676912	−	0.0785475i
$183$	−2862.05			−1.15611
$184$		−	100.813i		−	0.0403916i
$185$	−600.442			−0.238624
$186$	593.138			0.233822
$187$			765.009i			0.299160i
$188$			3661.47i			1.42043i
$189$			749.387i			0.288412i
$190$			221.500i			0.0845754i
$191$	−3850.73			−1.45879			−0.729395	−	0.684093i	$-0.760198\pi$
$191$	−3850.73			−1.45879			−0.729395	+	0.684093i	$0.760198\pi$
$192$	−2858.68			−1.07452
$193$		−	377.229i		−	0.140692i	−0.997523	−	0.0703460i	$-0.977590\pi$
$193$		−	377.229i		−	0.140692i	0.997523	−	0.0703460i	$-0.0224103\pi$
$194$	−294.843			−0.109116
$195$	816.356	+	703.525i	0.299797	+	0.258361i
$196$	1623.55			0.591672
$197$			2482.71i			0.897898i	0.893557	+	0.448949i	$0.148202\pi$
$197$			2482.71i			0.897898i	−0.893557	+	0.448949i	$0.851798\pi$
$198$	89.1003			0.0319802
$199$	−1326.65			−0.472582			−0.236291	−	0.971682i	$-0.575932\pi$
$199$	−1326.65			−0.472582			−0.236291	+	0.971682i	$0.575932\pi$
$200$		−	836.155i		−	0.295625i
$201$		−	6435.47i		−	2.25832i
$202$		−	44.1862i		−	0.0153907i
$203$			1382.67i			0.478050i
$204$	−3600.77			−1.23581
$205$	1348.97			0.459589
$206$			445.245i			0.150591i
$207$	235.606			0.0791101
$208$	1798.52	−	2086.96i	0.599541	−	0.695695i
$209$	1504.76			0.498020
$210$			124.884i			0.0410371i
$211$	3293.99			1.07473			0.537365	−	0.843350i	$-0.319420\pi$
$211$	3293.99			1.07473			0.537365	+	0.843350i	$0.319420\pi$
$212$	−3080.36			−0.997923
$213$			350.316i			0.112691i
$214$			566.985i			0.181114i
$215$			1530.61i			0.485519i
$216$		−	478.179i		−	0.150629i
$217$	2204.28			0.689568
$218$	−352.085			−0.109386
$219$			1915.67i			0.591091i
$220$	295.695			0.0906170
$221$	2128.04	−	2469.34i	0.647727	−	0.751609i
$222$	541.991			0.163856
$223$		−	3935.96i		−	1.18193i	−0.806696	−	0.590967i	$-0.798746\pi$
$223$		−	3935.96i		−	1.18193i	0.806696	−	0.590967i	$-0.201254\pi$
$224$	1004.97			0.299764
$225$	1954.14			0.579005
$226$		−	122.655i		−	0.0361013i
$227$			319.025i			0.0932795i	0.998912	+	0.0466397i	$0.0148513\pi$
$227$			319.025i			0.0932795i	−0.998912	+	0.0466397i	$0.985149\pi$
$228$			7082.65i			2.05728i
$229$		−	1181.26i		−	0.340872i	−0.985369	−	0.170436i	$-0.945482\pi$
$229$		−	1181.26i		−	0.340872i	0.985369	−	0.170436i	$-0.0545176\pi$
$230$	−22.0725			−0.00632790
$231$	848.394			0.241646
$232$		−	882.270i		−	0.249672i
$233$	−6259.22			−1.75989			−0.879946	−	0.475073i	$-0.842422\pi$
$233$	−6259.22			−1.75989			−0.879946	+	0.475073i	$0.842422\pi$
$234$	−287.603	−	247.852i	−0.0803469	−	0.0692420i
$235$	1625.95			0.451341
$236$		−	5782.21i		−	1.59487i
$237$	−3754.31			−1.02898
$238$	377.752			0.102882
$239$			2469.50i			0.668362i	0.942509	+	0.334181i	$0.108460\pi$
$239$			2469.50i			0.668362i	−0.942509	+	0.334181i	$0.891540\pi$
$240$			1351.39i			0.363466i
$241$			4082.66i			1.09123i	0.838035	+	0.545617i	$0.183704\pi$
$241$			4082.66i			1.09123i	−0.838035	+	0.545617i	$0.816296\pi$
$242$			56.7068i			0.0150630i
$243$	4222.96			1.11483
$244$	3346.22			0.877951
$245$		−	720.968i		−	0.188004i
$246$	−1217.65			−0.315587
$247$	−4857.14	−	4185.82i	−1.25122	−	1.07829i
$248$	−1406.54			−0.360142
$249$		−	7150.22i		−	1.81979i
$250$	−385.472			−0.0975175
$251$	−1800.08			−0.452669			−0.226335	−	0.974050i	$-0.572674\pi$
$251$	−1800.08			−0.452669			−0.226335	+	0.974050i	$0.572674\pi$
$252$			1558.54i			0.389600i
$253$			149.949i			0.0372617i
$254$			307.318i			0.0759167i
$255$			1598.99i			0.392678i
$256$	3017.19			0.736619
$257$	2982.53			0.723910			0.361955	−	0.932196i	$-0.382109\pi$
$257$	2982.53			0.723910			0.361955	+	0.932196i	$0.382109\pi$
$258$		−	1381.61i		−	0.333392i
$259$	2014.20			0.483229
$260$	−954.459	−	822.541i	−0.227666	−	0.196199i
$261$	2061.92			0.489002
$262$		−	433.196i		−	0.102149i
$263$	3021.93			0.708519			0.354259	−	0.935147i	$-0.384733\pi$
$263$	3021.93			0.708519			0.354259	+	0.935147i	$0.384733\pi$
$264$	−541.354			−0.126205
$265$			1367.89i			0.317090i
$266$		−	743.030i		−	0.171271i
$267$			4182.05i			0.958566i
$268$			7524.17i			1.71497i
$269$	−4105.73			−0.930598			−0.465299	−	0.885153i	$-0.654053\pi$
$269$	−4105.73			−0.930598			−0.465299	+	0.885153i	$0.654053\pi$
$270$	−104.695			−0.0235982
$271$			490.284i			0.109899i	0.998489	+	0.0549495i	$0.0174998\pi$
$271$			490.284i			0.109899i	−0.998489	+	0.0549495i	$0.982500\pi$
$272$	4087.72			0.911230
$273$	−2738.49	−	2360.00i	−0.607110	−	0.523200i
$274$	636.806			0.140405
$275$			1243.69i			0.272718i
$276$	−705.785			−0.153925
$277$	1772.57			0.384489			0.192245	−	0.981347i	$-0.438423\pi$
$277$	1772.57			0.384489			0.192245	+	0.981347i	$0.438423\pi$
$278$		−	905.515i		−	0.195357i
$279$		−	3287.16i		−	0.705365i
$280$		−	296.142i		−	0.0632068i
$281$			396.426i			0.0841595i	0.999114	+	0.0420797i	$0.0133984\pi$
$281$			396.426i			0.0841595i	−0.999114	+	0.0420797i	$0.986602\pi$
$282$	−1467.67			−0.309923
$283$	983.143			0.206508			0.103254	−	0.994655i	$-0.467075\pi$
$283$	983.143			0.206508			0.103254	+	0.994655i	$0.467075\pi$
$284$		−	409.579i		−	0.0855776i
$285$	3145.19			0.653701
$286$	157.743	−	183.041i	0.0326137	−	0.0378443i
$287$	−4525.15			−0.930700
$288$		−	1498.67i		−	0.306631i
$289$	−76.3197			−0.0155342
$290$	−193.168			−0.0391146
$291$			4186.61i			0.843380i
$292$		−	2239.75i		−	0.448874i
$293$			8194.68i			1.63392i	0.576695	+	0.816960i	$0.304342\pi$
$293$			8194.68i			1.63392i	−0.576695	+	0.816960i	$0.695658\pi$
$294$			650.784i			0.129097i
$295$	−2567.70			−0.506771
$296$	−1285.25			−0.252377
$297$			711.239i			0.138957i
$298$	−772.910			−0.150247
$299$	417.116	−	484.013i	0.0806771	−	0.0936161i
$300$	−5853.85			−1.12657
$301$		−	5134.47i		−	0.983209i
$302$	1355.42			0.258264
$303$	−627.420			−0.118958
$304$		−	8040.47i		−	1.51695i
$305$		−	1485.96i		−	0.278969i
$306$		−	563.327i		−	0.105239i
$307$		−	5224.91i		−	0.971341i	−0.874142	−	0.485670i	$-0.838576\pi$
$307$		−	5224.91i		−	0.971341i	0.874142	−	0.485670i	$-0.161424\pi$
$308$	−991.917			−0.183506
$309$	6322.24			1.16395
$310$			307.953i			0.0564212i
$311$	5812.89			1.05987			0.529934	−	0.848039i	$-0.322217\pi$
$311$	5812.89			1.05987			0.529934	+	0.848039i	$0.322217\pi$
$312$	1747.41	+	1505.90i	0.317076	+	0.273252i
$313$	8225.44			1.48540			0.742699	−	0.669626i	$-0.233546\pi$
$313$	8225.44			1.48540			0.742699	+	0.669626i	$0.233546\pi$
$314$			697.286i			0.125319i
$315$	692.102			0.123795
$316$	4389.43			0.781408
$317$		−	2807.87i		−	0.497495i	−0.968568	−	0.248747i	$-0.919981\pi$
$317$		−	2807.87i		−	0.497495i	0.968568	−	0.248747i	$-0.0800189\pi$
$318$		−	1234.73i		−	0.217737i
$319$			1312.28i			0.230325i
$320$		−	1484.21i		−	0.259280i
$321$	8050.89			1.39987
$322$	74.0429			0.0128144
$323$		−	9513.66i		−	1.63887i
$324$	−6978.47			−1.19658
$325$	3459.60	−	4014.45i	0.590475	−	0.685175i
$326$	51.2794			0.00871197
$327$			4999.42i			0.845469i
$328$	2887.47			0.486078
$329$	−5454.29			−0.913997
$330$			118.527i			0.0197717i
$331$		−	8649.46i		−	1.43631i	−0.695885	−	0.718153i	$-0.744988\pi$
$331$		−	8649.46i		−	1.43631i	0.695885	−	0.718153i	$-0.255012\pi$
$332$			8359.83i			1.38194i
$333$		−	3003.70i		−	0.494300i
$334$	381.425			0.0624870
$335$	3341.25			0.544932
$336$		−	4533.28i		−	0.736043i
$337$	−714.839			−0.115548			−0.0577741	−	0.998330i	$-0.518400\pi$
$337$	−714.839			−0.115548			−0.0577741	+	0.998330i	$0.518400\pi$
$338$	−1018.34	+	152.034i	−0.163877	+	0.0244662i
$339$	−1741.64			−0.279035
$340$		−	1869.50i		−	0.298199i
$341$	2092.07			0.332235
$342$	−1108.05			−0.175195
$343$			6393.87i			1.00652i
$344$			3276.27i			0.513502i
$345$			313.418i			0.0489097i
$346$		−	1354.79i		−	0.210502i
$347$	7193.68			1.11290			0.556451	−	0.830880i	$-0.312163\pi$
$347$	7193.68			1.11290			0.556451	+	0.830880i	$0.312163\pi$
$348$	−6176.70			−0.951454
$349$			4972.78i			0.762713i	0.924428	+	0.381356i	$0.124543\pi$
$349$			4972.78i			0.762713i	−0.924428	+	0.381356i	$0.875457\pi$
$350$	614.119			0.0937887
$351$	1978.47	−	2295.78i	0.300863	−	0.349115i
$352$	953.809			0.144427
$353$			2431.78i			0.366659i	0.983051	+	0.183330i	$0.0586876\pi$
$353$			2431.78i			0.366659i	−0.983051	+	0.183330i	$0.941312\pi$
$354$	2317.75			0.347986
$355$	−181.881			−0.0271923
$356$		−	4889.53i		−	0.727934i
$357$		−	5363.87i		−	0.795199i
$358$			1993.96i			0.294369i
$359$			4539.72i			0.667402i	0.942679	+	0.333701i	$0.108298\pi$
$359$			4539.72i			0.667402i	−0.942679	+	0.333701i	$0.891702\pi$
$360$	−441.626			−0.0646548
$361$	−11854.2			−1.72827
$362$			188.697i			0.0273969i
$363$	805.207			0.116425
$364$	3201.76	+	2759.24i	0.461039	+	0.397317i
$365$	−994.603			−0.142630
$366$			1341.30i			0.191560i
$367$	−12893.9			−1.83393			−0.916967	−	0.398964i	$-0.869370\pi$
$367$	−12893.9			−1.83393			−0.916967	+	0.398964i	$0.869370\pi$
$368$	801.232			0.113498
$369$			6748.18i			0.952022i
$370$			281.398i			0.0395383i
$371$		−	4588.64i		−	0.642130i
$372$			9847.04i			1.37243i
$373$	4943.47			0.686229			0.343114	−	0.939294i	$-0.388518\pi$
$373$	4943.47			0.686229			0.343114	+	0.939294i	$0.388518\pi$
$374$	358.522			0.0495689
$375$			5473.49i			0.753733i
$376$	3480.35			0.477354
$377$	3650.41	−	4235.86i	0.498688	−	0.578668i
$378$	351.201			0.0477879
$379$			2212.86i			0.299913i	0.988693	+	0.149956i	$0.0479133\pi$
$379$			2212.86i			0.299913i	−0.988693	+	0.149956i	$0.952087\pi$
$380$	−3677.26			−0.496420
$381$	4363.75			0.586776
$382$			1804.65i			0.241712i
$383$		−	14067.2i		−	1.87677i	−0.345597	−	0.938383i	$-0.612324\pi$
$383$		−	14067.2i		−	1.87677i	0.345597	−	0.938383i	$-0.387676\pi$
$384$			5955.88i			0.791497i
$385$			440.480i			0.0583090i
$386$	−176.789			−0.0233117
$387$	−7656.84			−1.00573
$388$		−	4894.86i		−	0.640462i
$389$	−9822.69			−1.28028			−0.640141	−	0.768257i	$-0.721124\pi$
$389$	−9822.69			−1.28028			−0.640141	+	0.768257i	$0.721124\pi$
$390$	329.708	−	382.586i	0.0428087	−	0.0496744i
$391$	948.035			0.122619
$392$		−	1543.23i		−	0.198840i
$393$	−6151.15			−0.789529
$394$	1163.53			0.148776
$395$		−	1949.21i		−	0.248292i
$396$			1479.21i			0.187710i
$397$		−	1365.99i		−	0.172688i	−0.996265	−	0.0863441i	$-0.972482\pi$
$397$		−	1365.99i		−	0.172688i	0.996265	−	0.0863441i	$-0.0275184\pi$
$398$			621.738i			0.0783037i
$399$	−10550.6			−1.32379
$400$	6645.50			0.830687
$401$			13912.0i			1.73250i	0.499610	+	0.866250i	$0.333477\pi$
$401$			13912.0i			1.73250i	−0.499610	+	0.866250i	$0.666523\pi$
$402$	−3015.99			−0.374189
$403$	−6752.90	−	5819.56i	−0.834704	−	0.719338i
$404$	733.562			0.0903368
$405$			3098.93i			0.380215i
$406$	647.989			0.0792097
$407$	1911.67			0.232820
$408$			3422.65i			0.415310i
$409$			6892.66i			0.833301i	0.909067	+	0.416651i	$0.136796\pi$
$409$			6892.66i			0.833301i	−0.909067	+	0.416651i	$0.863204\pi$
$410$		−	632.194i		−	0.0761509i
$411$		−	9042.30i		−	1.08522i
$412$	−7391.78			−0.883900
$413$	8613.45			1.02625
$414$		−	110.417i		−	0.0131080i
$415$	3712.34			0.439113
$416$	−3078.75	−	2653.23i	−0.362857	−	0.312705i
$417$	−12857.8			−1.50995
$418$		−	705.207i		−	0.0825186i
$419$	−4253.11			−0.495890			−0.247945	−	0.968774i	$-0.579755\pi$
$419$	−4253.11			−0.495890			−0.247945	+	0.968774i	$0.579755\pi$
$420$	−2073.27			−0.240869
$421$			16604.7i			1.92224i	0.276133	+	0.961119i	$0.410947\pi$
$421$			16604.7i			1.92224i	−0.276133	+	0.961119i	$0.589053\pi$
$422$		−	1543.73i		−	0.178075i
$423$			8133.78i			0.934936i
$424$			2927.98i			0.335366i
$425$	7863.09			0.897450
$426$	164.176			0.0186722
$427$			4984.68i			0.564931i
$428$	−9412.87			−1.06306
$429$	−2599.09	−	2239.86i	−0.292506	−	0.252078i
$430$	717.321			0.0804472
$431$			12392.8i			1.38501i	0.721413	+	0.692505i	$0.243493\pi$
$431$			12392.8i			1.38501i	−0.721413	+	0.692505i	$0.756507\pi$
$432$	3800.41			0.423258
$433$	−2304.50			−0.255767			−0.127884	−	0.991789i	$-0.540818\pi$
$433$	−2304.50			−0.255767			−0.127884	+	0.991789i	$0.540818\pi$
$434$		−	1033.04i		−	0.114257i
$435$			2742.88i			0.302325i
$436$		−	5845.18i		−	0.642049i
$437$		−	1864.77i		−	0.204128i
$438$	897.781			0.0979398
$439$	−8562.55			−0.930907			−0.465453	−	0.885072i	$-0.654109\pi$
$439$	−8562.55			−0.930907			−0.465453	+	0.885072i	$0.654109\pi$
$440$		−	281.068i		−	0.0304531i
$441$	3606.63			0.389443
$442$	−1157.26	−	997.310i	−0.124537	−	0.107324i
$443$	8542.60			0.916187			0.458094	−	0.888904i	$-0.348532\pi$
$443$	8542.60			0.916187			0.458094	+	0.888904i	$0.348532\pi$
$444$			8997.92i			0.961762i
$445$	−2171.29			−0.231301
$446$	−1844.59			−0.195838
$447$			10974.9i			1.16129i
$448$			4978.82i			0.525060i
$449$		−	6995.03i		−	0.735225i	−0.929979	−	0.367612i	$-0.880175\pi$
$449$		−	6995.03i		−	0.735225i	0.929979	−	0.367612i	$-0.119825\pi$
$450$		−	915.812i		−	0.0959373i
$451$	−4294.80			−0.448412
$452$	2036.27			0.211899
$453$		−	19246.2i		−	1.99617i
$454$	149.512			0.0154558
$455$	1225.29	−	1421.81i	0.126248	−	0.146495i
$456$	6732.29			0.691378
$457$			5905.72i			0.604503i	0.953228	+	0.302252i	$0.0977383\pi$
$457$			5905.72i			0.604503i	−0.953228	+	0.302252i	$0.902262\pi$
$458$	−553.598			−0.0564802
$459$	4496.73			0.457275
$460$		−	366.439i		−	0.0371420i
$461$		−	16268.9i		−	1.64364i	−0.569747	−	0.821820i	$-0.692959\pi$
$461$		−	16268.9i		−	1.64364i	0.569747	−	0.821820i	$-0.307041\pi$
$462$		−	397.601i		−	0.0400391i
$463$			12086.2i			1.21316i	0.795021	+	0.606582i	$0.207460\pi$
$463$			12086.2i			1.21316i	−0.795021	+	0.606582i	$0.792540\pi$
$464$	7012.00			0.701561
$465$	4372.77			0.436091
$466$			2933.39i			0.291602i
$467$	11438.9			1.13347			0.566736	−	0.823900i	$-0.308206\pi$
$467$	11438.9			1.13347			0.566736	+	0.823900i	$0.308206\pi$
$468$	4114.75	−	4774.67i	0.406419	−	0.471601i
$469$	−11208.3			−1.10352
$470$		−	762.003i		−	0.0747842i
$471$	9901.09			0.968616
$472$	−5496.18			−0.535980
$473$		−	4873.10i		−	0.473711i
$474$			1759.46i			0.170495i
$475$		−	15466.6i		−	1.49401i
$476$			6271.28i			0.603874i
$477$	−6842.85			−0.656840
$478$	1157.33			0.110743
$479$			12569.7i			1.19901i	0.800373	+	0.599503i	$0.204635\pi$
$479$			12569.7i			1.19901i	−0.800373	+	0.599503i	$0.795365\pi$
$480$	1993.62			0.189574
$481$	−6170.59	−	5317.73i	−0.584937	−	0.504091i
$482$	1913.34			0.180810
$483$		−	1051.37i		−	0.0990455i
$484$	−941.424			−0.0884132
$485$	−2173.66			−0.203507
$486$		−	1979.10i		−	0.184720i
$487$			12546.0i			1.16737i	0.811978	+	0.583687i	$0.198391\pi$
$487$			12546.0i			1.16737i	−0.811978	+	0.583687i	$0.801609\pi$
$488$		−	3180.69i		−	0.295048i
$489$		−	728.140i		−	0.0673366i
$490$	−337.883			−0.0311510
$491$	4510.82			0.414604			0.207302	−	0.978277i	$-0.433532\pi$
$491$	4510.82			0.414604			0.207302	+	0.978277i	$0.433532\pi$
$492$		−	20214.9i		−	1.85235i
$493$	8296.76			0.757945
$494$	−1961.69	+	2276.30i	−0.178665	+	0.207319i
$495$	656.871			0.0596448
$496$		−	11178.7i		−	1.01197i
$497$	610.127			0.0550663
$498$	−3350.96			−0.301526
$499$			10387.6i			0.931889i	0.884814	+	0.465944i	$0.154285\pi$
$499$			10387.6i			0.931889i	−0.884814	+	0.465944i	$0.845715\pi$
$500$		−	6399.45i		−	0.572384i
$501$		−	5416.04i		−	0.482975i
$502$			843.609i			0.0750042i
$503$	−16193.4			−1.43544			−0.717720	−	0.696331i	$-0.754814\pi$
$503$	−16193.4			−1.43544			−0.717720	+	0.696331i	$0.754814\pi$
$504$	1481.45			0.130930
$505$		−	325.752i		−	0.0287045i
$506$	70.2738			0.00617401
$507$	2158.80	+	14459.9i	0.189104	+	1.26664i
$508$	−5101.97			−0.445597
$509$			1633.29i			0.142228i	0.997468	+	0.0711142i	$0.0226555\pi$
$509$			1633.29i			0.142228i	−0.997468	+	0.0711142i	$0.977345\pi$
$510$	749.370			0.0650641
$511$	3336.43			0.288835
$512$		−	8574.03i		−	0.740082i
$513$		−	8844.98i		−	0.761239i
$514$		−	1397.77i		−	0.119947i
$515$			3282.46i			0.280859i
$516$	22936.9			1.95686
$517$	−5176.65			−0.440365
$518$		−	943.958i		−	0.0800678i
$519$	−19237.2			−1.62702
$520$	−781.852	+	907.245i	−0.0659355	+	0.0765102i
$521$	5358.69			0.450611			0.225306	−	0.974288i	$-0.427662\pi$
$521$	5358.69			0.450611			0.225306	+	0.974288i	$0.427662\pi$
$522$		−	966.320i		−	0.0810243i
$523$	−2402.72			−0.200886			−0.100443	−	0.994943i	$-0.532026\pi$
$523$	−2402.72			−0.200886			−0.100443	+	0.994943i	$0.532026\pi$
$524$	7191.75			0.599567
$525$		−	8720.16i		−	0.724912i
$526$		−	1416.23i		−	0.117397i
$527$		−	13226.9i		−	1.09331i
$528$		−	4302.51i		−	0.354627i
$529$	−11981.2			−0.984727
$530$	641.064			0.0525397
$531$		−	12844.9i		−	1.04976i
$532$	12335.5			1.00528
$533$	13863.0	+	11946.9i	1.12659	+	0.970880i
$534$	1959.92			0.158828
$535$			4179.97i			0.337786i
$536$	7151.97			0.576339
$537$	28313.2			2.27524
$538$			1924.16i			0.154194i
$539$			2295.40i			0.183432i
$540$		−	1738.10i		−	0.138511i
$541$			6711.56i			0.533368i	0.963784	+	0.266684i	$0.0859281\pi$
$541$			6711.56i			0.533368i	−0.963784	+	0.266684i	$0.914072\pi$
$542$	229.772			0.0182095
$543$	2679.39			0.211756
$544$		−	6030.35i		−	0.475274i
$545$	−2595.66			−0.204011
$546$	−1106.02	+	1283.40i	−0.0866907	+	0.100594i
$547$	−11094.2			−0.867189			−0.433595	−	0.901108i	$-0.642755\pi$
$547$	−11094.2			−0.867189			−0.433595	+	0.901108i	$0.642755\pi$
$548$			10572.0i			0.824112i
$549$	7433.47			0.577874
$550$	582.858			0.0451875
$551$		−	16319.6i		−	1.26177i
$552$			670.872i			0.0517286i
$553$			6538.69i			0.502809i
$554$		−	830.719i		−	0.0637073i
$555$	3995.70			0.305600
$556$	15033.0			1.14666
$557$			7187.13i			0.546730i	0.961910	+	0.273365i	$0.0881366\pi$
$557$			7187.13i			0.546730i	−0.961910	+	0.273365i	$0.911863\pi$
$558$	−1540.53			−0.116874
$559$	−13555.6	+	15729.7i	−1.02566	+	1.19015i
$560$	2353.65			0.177607
$561$		−	5090.83i		−	0.383128i
$562$	185.786			0.0139447
$563$	1718.98			0.128679			0.0643395	−	0.997928i	$-0.479506\pi$
$563$	1718.98			0.128679			0.0643395	+	0.997928i	$0.479506\pi$
$564$		−	24365.6i		−	1.81911i
$565$		−	904.246i		−	0.0673308i
$566$		−	460.752i		−	0.0342170i
$567$		−	10395.4i		−	0.769961i
$568$	−389.318			−0.0287596
$569$	−7181.26			−0.529093			−0.264547	−	0.964373i	$-0.585222\pi$
$569$	−7181.26			−0.529093			−0.264547	+	0.964373i	$0.585222\pi$
$570$		−	1474.00i		−	0.108314i
$571$	−22731.5			−1.66599			−0.832997	−	0.553278i	$-0.813377\pi$
$571$	−22731.5			−1.66599			−0.832997	+	0.553278i	$0.813377\pi$
$572$	3038.78	+	2618.78i	0.222129	+	0.191428i
$573$	25625.0			1.86824
$574$			2120.72i			0.154211i
$575$	1541.24			0.111781
$576$	7424.72			0.537089
$577$			10364.7i			0.747811i	0.927467	+	0.373905i	$0.121982\pi$
$577$			10364.7i			0.747811i	−0.927467	+	0.373905i	$0.878018\pi$
$578$			35.7673i			0.00257392i
$579$			2510.31i			0.180181i
$580$		−	3206.90i		−	0.229585i
$581$	−12453.2			−0.889234
$582$	1962.06			0.139742
$583$		−	4355.05i		−	0.309379i
$584$	−2128.95			−0.150850
$585$	−2120.28	−	1827.23i	−0.149851	−	0.129140i
$586$	3840.45			0.270730
$587$			13510.7i			0.949991i	0.879988	+	0.474996i	$0.157550\pi$
$587$			13510.7i			0.949991i	−0.879988	+	0.474996i	$0.842450\pi$
$588$	−10804.1			−0.757741
$589$	−26017.0			−1.82006
$590$			1203.36i			0.0839686i
$591$		−	16521.5i		−	1.14992i
$592$		−	10214.7i		−	0.709161i
$593$			10472.2i			0.725198i	0.931945	+	0.362599i	$0.118111\pi$
$593$			10472.2i			0.725198i	−0.931945	+	0.362599i	$0.881889\pi$
$594$	333.323			0.0230243
$595$	2784.89			0.191881
$596$		−	12831.5i		−	0.881880i
$597$	8828.34			0.605226
$598$	−226.833	−	195.482i	−0.0155116	−	0.0133677i
$599$	−11954.7			−0.815451			−0.407726	−	0.913104i	$-0.633678\pi$
$599$	−11954.7			−0.815451			−0.407726	+	0.913104i	$0.633678\pi$
$600$			5564.28i			0.378601i
$601$	11581.5			0.786056			0.393028	−	0.919527i	$-0.371428\pi$
$601$	11581.5			0.786056			0.393028	+	0.919527i	$0.371428\pi$
$602$	−2406.28			−0.162911
$603$			16714.6i			1.12881i
$604$			22502.1i			1.51589i
$605$			418.058i			0.0280933i
$606$			294.041i			0.0197106i
$607$	19639.9			1.31328			0.656639	−	0.754205i	$-0.271978\pi$
$607$	19639.9			1.31328			0.656639	+	0.754205i	$0.271978\pi$
$608$	−11861.6			−0.791201
$609$		−	9201.09i		−	0.612228i
$610$	−696.395			−0.0462233
$611$	16709.5	+	14400.0i	1.10637	+	0.953456i
$612$	9352.12			0.617708
$613$			1278.58i			0.0842435i	0.999112	+	0.0421218i	$0.0134117\pi$
$613$			1278.58i			0.0842435i	−0.999112	+	0.0421218i	$0.986588\pi$
$614$	−2448.66			−0.160945
$615$	−8976.82			−0.588586
$616$			942.850i			0.0616696i
$617$		−	15522.9i		−	1.01285i	−0.862283	−	0.506426i	$-0.830966\pi$
$617$		−	15522.9i		−	1.01285i	0.862283	−	0.506426i	$-0.169034\pi$
$618$		−	2962.93i		−	0.192858i
$619$		−	144.033i		−	0.00935247i	−0.999989	−	0.00467624i	$-0.998512\pi$
$619$		−	144.033i		−	0.00935247i	0.999989	−	0.00467624i	$-0.00148850\pi$
$620$	−5112.52			−0.331167
$621$	881.402			0.0569556
$622$		−	2724.22i		−	0.175613i
$623$	7283.66			0.468401
$624$	−11968.4	+	13887.9i	−0.767820	+	0.890962i
$625$	11291.1			0.722627
$626$		−	3854.86i		−	0.246120i
$627$	−10013.6			−0.637804
$628$	−11576.1			−0.735566
$629$		−	12086.3i		−	0.766157i
$630$		−	324.355i		−	0.0205121i
$631$		−	2470.98i		−	0.155892i	−0.996958	−	0.0779461i	$-0.975164\pi$
$631$		−	2470.98i		−	0.155892i	0.996958	−	0.0779461i	$-0.0248362\pi$
$632$		−	4172.30i		−	0.262603i
$633$	−21920.2			−1.37638
$634$	−1315.91			−0.0824315
$635$			2265.63i			0.141589i
$636$	20498.5			1.27802
$637$	6385.16	−	7409.20i	0.397157	−	0.460853i
$638$	615.003			0.0381633
$639$		−	909.859i		−	0.0563278i
$640$	−3092.25			−0.190987
$641$	10419.0			0.642004			0.321002	−	0.947079i	$-0.395980\pi$
$641$	10419.0			0.642004			0.321002	+	0.947079i	$0.395980\pi$
$642$		−	3773.06i		−	0.231948i
$643$			9261.78i			0.568039i	0.958819	+	0.284019i	$0.0916680\pi$
$643$			9261.78i			0.568039i	−0.958819	+	0.284019i	$0.908332\pi$
$644$			1229.23i			0.0752150i
$645$		−	10185.6i		−	0.621793i
$646$	−4458.59			−0.271549
$647$	−25679.8			−1.56040			−0.780200	−	0.625530i	$-0.784883\pi$
$647$	−25679.8			−1.56040			−0.780200	+	0.625530i	$0.784883\pi$
$648$			6633.27i			0.402129i
$649$	8174.98			0.494447
$650$	−1881.38	−	1621.35i	−0.113529	−	0.0978377i
$651$	−14668.6			−0.883114
$652$			851.320i			0.0511354i
$653$	5017.38			0.300682			0.150341	−	0.988634i	$-0.451963\pi$
$653$	5017.38			0.300682			0.150341	+	0.988634i	$0.451963\pi$
$654$	2342.99			0.140089
$655$		−	3193.64i		−	0.190513i
$656$			22948.7i			1.36585i
$657$		−	4975.48i		−	0.295452i
$658$			2556.16i			0.151443i
$659$	31041.0			1.83488			0.917439	−	0.397876i	$-0.130253\pi$
$659$	31041.0			1.83488			0.917439	+	0.397876i	$0.130253\pi$
$660$	−1967.73			−0.116051
$661$			11389.0i			0.670167i	0.942189	+	0.335083i	$0.108764\pi$
$661$			11389.0i			0.670167i	−0.942189	+	0.335083i	$0.891236\pi$
$662$	−4053.58			−0.237986
$663$	−14161.3	+	16432.4i	−0.829530	+	0.962569i
$664$	7946.29			0.464422
$665$		−	5477.82i		−	0.319429i
$666$	−1407.69			−0.0819021
$667$	1626.24			0.0944053
$668$			6332.27i			0.366771i
$669$			26192.2i			1.51368i
$670$		−	1565.88i		−	0.0902916i
$671$			4730.94i			0.272185i
$672$	−6687.64			−0.383901
$673$	−15036.7			−0.861250			−0.430625	−	0.902531i	$-0.641707\pi$
$673$	−15036.7			−0.861250			−0.430625	+	0.902531i	$0.641707\pi$
$674$			335.010i			0.0191456i
$675$	7310.43			0.416857
$676$	−2524.01	−	16906.1i	−0.143606	−	0.961885i
$677$	4944.67			0.280708			0.140354	−	0.990101i	$-0.455176\pi$
$677$	4944.67			0.280708			0.140354	+	0.990101i	$0.455176\pi$
$678$			816.221i			0.0462342i
$679$	7291.61			0.412115
$680$	−1777.02			−0.100214
$681$		−	2122.98i		−	0.119461i
$682$		−	980.452i		−	0.0550491i
$683$		−	22667.8i		−	1.26993i	−0.772543	−	0.634963i	$-0.781015\pi$
$683$		−	22667.8i		−	1.26993i	0.772543	−	0.634963i	$-0.218985\pi$
$684$		−	18395.4i		−	1.02832i
$685$	4694.70			0.261862
$686$	2996.50			0.166774
$687$			7860.80i			0.436547i
$688$	−26038.8			−1.44290
$689$	−12114.6	+	14057.5i	−0.669852	+	0.777282i
$690$	146.884			0.00810401
$691$		−	22832.2i		−	1.25699i	−0.777815	−	0.628493i	$-0.783672\pi$
$691$		−	22832.2i		−	1.25699i	0.777815	−	0.628493i	$-0.216328\pi$
$692$	22491.6			1.23555
$693$	−2203.49			−0.120785
$694$		−	3371.33i		−	0.184400i
$695$		−	6675.70i		−	0.364351i
$696$			5871.16i			0.319749i
$697$			27153.4i			1.47562i
$698$	2330.50			0.126376
$699$	41652.6			2.25386
$700$			10195.4i			0.550498i
$701$	11640.8			0.627200			0.313600	−	0.949555i	$-0.398465\pi$
$701$	11640.8			0.627200			0.313600	+	0.949555i	$0.398465\pi$
$702$	−1075.92	−	927.214i	−0.0578461	−	0.0498510i
$703$	−23773.5			−1.27544
$704$			4725.37i			0.252975i
$705$	−10820.0			−0.578023
$706$	1139.66			0.0607530
$707$			1092.75i			0.0581286i
$708$			38478.3i			2.04252i
$709$		−	17442.6i		−	0.923936i	−0.886897	−	0.461968i	$-0.847144\pi$
$709$		−	17442.6i		−	0.923936i	0.886897	−	0.461968i	$-0.152856\pi$
$710$			85.2390i			0.00450558i
$711$	9750.90			0.514328
$712$	−4647.66			−0.244632
$713$		−	2592.59i		−	0.136176i
$714$	−2513.79			−0.131759
$715$	1162.92	−	1349.43i	0.0608263	−	0.0705815i
$716$	−33103.0			−1.72781
$717$		−	16433.5i		−	0.855957i
$718$	2127.55			0.110584
$719$	−9631.17			−0.499558			−0.249779	−	0.968303i	$-0.580358\pi$
$719$	−9631.17			−0.499558			−0.249779	+	0.968303i	$0.580358\pi$
$720$		−	3509.90i		−	0.181675i
$721$		−	11011.1i		−	0.568760i
$722$			5555.48i			0.286362i
$723$		−	27168.5i		−	1.39752i
$724$	−3132.67			−0.160808
$725$	13488.2			0.690951
$726$		−	377.361i		−	0.0192909i
$727$	−36098.8			−1.84158			−0.920792	−	0.390053i	$-0.872457\pi$
$727$	−36098.8			−1.84158			−0.920792	+	0.390053i	$0.872457\pi$
$728$	2622.75	−	3043.38i	0.133524	−	0.154938i
$729$	−3884.93			−0.197375
$730$			466.122i			0.0236328i
$731$	−30809.6			−1.55887
$732$	−22267.8			−1.12437
$733$		−	12551.0i		−	0.632442i	−0.948686	−	0.316221i	$-0.897586\pi$
$733$		−	12551.0i		−	0.632442i	0.948686	−	0.316221i	$-0.102414\pi$
$734$			6042.72i			0.303870i
$735$			4797.75i			0.240772i
$736$		−	1182.00i		−	0.0591974i
$737$	−10637.8			−0.531680
$738$	3162.54			0.157744
$739$			38489.6i			1.91592i	0.286904	+	0.957959i	$0.407374\pi$
$739$			38489.6i			1.91592i	−0.286904	+	0.957959i	$0.592626\pi$
$740$	−4671.66			−0.232072
$741$	32322.3	+	27854.9i	1.60241	+	1.38094i
$742$	−2150.47			−0.106397
$743$			1045.18i			0.0516068i	0.999667	+	0.0258034i	$0.00821439\pi$
$743$			1045.18i			0.0516068i	−0.999667	+	0.0258034i	$0.991786\pi$
$744$	9359.93			0.461225
$745$	−5698.10			−0.280218
$746$		−	2316.77i		−	0.113704i
$747$			18570.9i			0.909605i
$748$			5952.05i			0.290947i
$749$		−	14021.8i		−	0.684041i
$750$	2565.16			0.124889
$751$	21408.8			1.04024			0.520119	−	0.854094i	$-0.325888\pi$
$751$	21408.8			1.04024			0.520119	+	0.854094i	$0.325888\pi$
$752$			27660.7i			1.34133i
$753$	11978.8			0.579724
$754$	−1985.14	−	1710.77i	−0.0958813	−	0.0826293i
$755$	9992.51			0.481675
$756$			5830.50i			0.280494i
$757$	−18766.9			−0.901050			−0.450525	−	0.892764i	$-0.648763\pi$
$757$	−18766.9			−0.901050			−0.450525	+	0.892764i	$0.648763\pi$
$758$	1037.06			0.0496935
$759$		−	997.850i		−	0.0477202i
$760$			3495.36i			0.166829i
$761$			6430.44i			0.306312i	0.988202	+	0.153156i	$0.0489437\pi$
$761$			6430.44i			0.306312i	−0.988202	+	0.153156i	$0.951056\pi$
$762$		−	2045.08i		−	0.0972248i
$763$	8707.24			0.413137
$764$	−29960.1			−1.41874
$765$		−	4152.99i		−	0.196277i
$766$	−6592.62			−0.310968
$767$	−26387.7	−	22740.5i	−1.24225	−	1.07055i
$768$	−20078.2			−0.943372
$769$		−	7845.05i		−	0.367880i	−0.982937	−	0.183940i	$-0.941115\pi$
$769$		−	7845.05i		−	0.367880i	0.982937	−	0.183940i	$-0.0588852\pi$
$770$	206.432			0.00966140
$771$	−19847.5			−0.927096
$772$		−	2934.98i		−	0.136829i
$773$			9384.02i			0.436636i	0.975878	+	0.218318i	$0.0700570\pi$
$773$			9384.02i			0.436636i	−0.975878	+	0.218318i	$0.929943\pi$
$774$			3588.39i			0.166643i
$775$		−	21503.2i		−	0.996669i
$776$	−4652.73			−0.215236
$777$	−13403.7			−0.618861
$778$			4603.42i			0.212134i
$779$	53410.1			2.45650
$780$	6351.54	+	5473.68i	0.291566	+	0.251268i
$781$	579.069			0.0265310
$782$		−	444.298i		−	0.0203172i
$783$	7713.61			0.352059
$784$	12265.1			0.558725
$785$			5140.58i			0.233726i
$786$			2882.75i			0.130820i
$787$			9065.31i			0.410602i	0.978699	+	0.205301i	$0.0658173\pi$
$787$			9065.31i			0.410602i	−0.978699	+	0.205301i	$0.934183\pi$
$788$			19316.4i			0.873247i
$789$	−20109.8			−0.907384
$790$	−913.501			−0.0411404
$791$			3033.32i			0.136350i
$792$	1406.04			0.0630824
$793$	13160.2	−	15270.8i	0.589321	−	0.683835i
$794$	−640.174			−0.0286133
$795$		−	9102.77i		−	0.406091i
$796$	−10321.8			−0.459608
$797$	5468.59			0.243046			0.121523	−	0.992589i	$-0.461222\pi$
$797$	5468.59			0.243046			0.121523	+	0.992589i	$0.461222\pi$
$798$			4944.57i			0.219343i
$799$			32728.7i			1.44914i
$800$		−	9803.66i		−	0.433265i
$801$		−	10861.8i		−	0.479132i
$802$	6519.89			0.287064
$803$	3166.59			0.139161
$804$		−	50070.3i		−	2.19632i
$805$	545.864			0.0238996
$806$	−2727.35	+	3164.76i	−0.119189	+	0.138305i
$807$	27322.0			1.19180
$808$		−	697.274i		−	0.0303589i
$809$	4431.29			0.192578			0.0962892	−	0.995353i	$-0.469303\pi$
$809$	4431.29			0.192578			0.0962892	+	0.995353i	$0.469303\pi$
$810$	1452.32			0.0629990
$811$		−	24745.9i		−	1.07145i	−0.844393	−	0.535725i	$-0.820039\pi$
$811$		−	24745.9i		−	1.07145i	0.844393	−	0.535725i	$-0.179961\pi$
$812$			10757.6i			0.464925i
$813$		−	3262.64i		−	0.140745i
$814$		−	895.906i		−	0.0385768i
$815$	378.045			0.0162483
$816$	−27202.1			−1.16699
$817$			60602.0i			2.59510i
$818$	3230.26			0.138072
$819$	7112.56	+	6129.51i	0.303459	+	0.261517i
$820$	10495.4			0.446972
$821$		−	38903.8i		−	1.65378i	−0.562366	−	0.826888i	$-0.690109\pi$
$821$		−	38903.8i		−	1.65378i	0.562366	−	0.826888i	$-0.309891\pi$
$822$	−4237.69			−0.179813
$823$	42785.6			1.81216			0.906082	−	0.423102i	$-0.139059\pi$
$823$	42785.6			1.81216			0.906082	+	0.423102i	$0.139059\pi$
$824$			7026.13i			0.297047i
$825$		−	8276.27i		−	0.349264i
$826$		−	4036.70i		−	0.170042i
$827$		−	15938.6i		−	0.670179i	−0.942186	−	0.335090i	$-0.891233\pi$
$827$		−	15938.6i		−	0.670179i	0.942186	−	0.335090i	$-0.108767\pi$
$828$	1833.10			0.0769381
$829$	20256.8			0.848670			0.424335	−	0.905505i	$-0.360508\pi$
$829$	20256.8			0.848670			0.424335	+	0.905505i	$0.360508\pi$
$830$		−	1739.80i		−	0.0727581i
$831$	−11795.8			−0.492407
$832$	13144.7	−	15252.8i	0.547728	−	0.635572i
$833$	14512.4			0.603630
$834$			6025.84i			0.250189i
$835$	2811.97			0.116542
$836$	11707.6			0.484348
$837$		−	12297.2i		−	0.507830i
$838$			1993.23i			0.0821657i
$839$		−	37780.0i		−	1.55460i	−0.629130	−	0.777300i	$-0.716589\pi$
$839$		−	37780.0i		−	1.55460i	0.629130	−	0.777300i	$-0.283411\pi$
$840$			1970.71i			0.0809475i
$841$	−10156.9			−0.416454
$842$	7781.81			0.318502
$843$		−	2638.06i		−	0.107781i
$844$	25628.5			1.04522
$845$	−7507.48	+	1120.84i	−0.305639	+	0.0456307i
$846$	3811.91			0.154913
$847$		−	1402.39i		−	0.0568909i
$848$	−23270.6			−0.942355
$849$	−6542.43			−0.264471
$850$		−	3685.05i		−	0.148701i
$851$		−	2369.03i		−	0.0954281i
$852$			2725.58i			0.109597i
$853$		−	8226.02i		−	0.330192i	−0.986278	−	0.165096i	$-0.947207\pi$
$853$		−	8226.02i		−	0.330192i	0.986278	−	0.165096i	$-0.0527933\pi$
$854$	2336.08			0.0936054
$855$	−8168.86			−0.326747
$856$			8947.24i			0.357255i
$857$	−48849.7			−1.94711			−0.973556	−	0.228447i	$-0.926635\pi$
$857$	−48849.7			−1.94711			−0.973556	+	0.228447i	$0.926635\pi$
$858$	−1049.71	+	1218.07i	−0.0417677	+	0.0484663i
$859$	−5923.09			−0.235266			−0.117633	−	0.993057i	$-0.537531\pi$
$859$	−5923.09			−0.235266			−0.117633	+	0.993057i	$0.537531\pi$
$860$			11908.7i			0.472189i
$861$	30113.0			1.19193
$862$	5807.90			0.229487
$863$		−	41950.8i		−	1.65472i	−0.561672	−	0.827360i	$-0.689842\pi$
$863$		−	41950.8i		−	1.65472i	0.561672	−	0.827360i	$-0.310158\pi$
$864$		−	5606.50i		−	0.220760i
$865$		−	9987.84i		−	0.392598i
$866$			1080.01i			0.0423789i
$867$	507.877			0.0198944
$868$	17150.1			0.670636
$869$			6205.85i			0.242254i
$870$	1285.46			0.0500932
$871$	34337.2	+	29591.4i	1.33579	+	1.15117i
$872$	−5556.03			−0.215769
$873$		−	10873.7i		−	0.421557i
$874$	−873.926			−0.0338226
$875$	9532.90			0.368310
$876$			14904.6i			0.574863i
$877$		−	8624.62i		−	0.332078i	−0.986119	−	0.166039i	$-0.946902\pi$
$877$		−	8624.62i		−	0.332078i	0.986119	−	0.166039i	$-0.0530978\pi$
$878$			4012.85i			0.154245i
$879$		−	54532.3i		−	2.09253i
$880$	2233.84			0.0855711
$881$	14593.9			0.558095			0.279047	−	0.960277i	$-0.409981\pi$
$881$	14593.9			0.558095			0.279047	+	0.960277i	$0.409981\pi$
$882$		−	1690.25i		−	0.0645280i
$883$	5844.68			0.222751			0.111376	−	0.993778i	$-0.464474\pi$
$883$	5844.68			0.222751			0.111376	+	0.993778i	$0.464474\pi$
$884$	16556.9	−	19212.3i	0.629944	−	0.730974i
$885$	17087.0			0.649011
$886$		−	4003.50i		−	0.151806i
$887$	49965.1			1.89139			0.945696	−	0.325052i	$-0.105382\pi$
$887$	49965.1			1.89139			0.945696	+	0.325052i	$0.105382\pi$
$888$	8552.81			0.323214
$889$		−	7600.12i		−	0.286727i
$890$			1017.58i			0.0383251i
$891$		−	9866.27i		−	0.370968i
$892$		−	30623.2i		−	1.14948i
$893$	64376.8			2.41242
$894$	5143.41			0.192417
$895$			14700.0i			0.549014i
$896$	10373.1			0.386763
$897$	−2775.74	+	3220.91i	−0.103321	+	0.119892i
$898$	−3278.23			−0.121822
$899$		−	22689.2i		−	0.841742i
$900$	15203.9			0.563109
$901$	−27534.3			−1.01809
$902$			2012.76i			0.0742990i
$903$			34167.8i			1.25917i
$904$		−	1935.54i		−	0.0712115i
$905$			1391.12i			0.0510966i
$906$	−9019.77			−0.330753
$907$	−36442.4			−1.33412			−0.667062	−	0.745002i	$-0.732449\pi$
$907$	−36442.4			−1.33412			−0.667062	+	0.745002i	$0.732449\pi$
$908$			2482.13i			0.0907185i
$909$	1629.57			0.0594603
$910$	−666.331	−	574.236i	−0.0242733	−	0.0209184i
$911$	27482.6			0.999492			0.499746	−	0.866172i	$-0.333427\pi$
$911$	27482.6			0.999492			0.499746	+	0.866172i	$0.333427\pi$
$912$			53506.1i			1.94272i
$913$	−11819.3			−0.428434
$914$	2767.73			0.100162
$915$			9888.44i			0.357270i
$916$		−	9190.62i		−	0.331514i
$917$			10713.2i			0.385801i
$918$		−	2107.40i		−	0.0757675i
$919$	21715.6			0.779468			0.389734	−	0.920928i	$-0.372567\pi$
$919$	21715.6			0.779468			0.389734	+	0.920928i	$0.372567\pi$
$920$	−348.312			−0.0124821
$921$			34769.7i			1.24398i
$922$	−7624.45			−0.272340
$923$	−1869.15	−	1610.81i	−0.0666564	−	0.0574436i
$924$	6600.81			0.235012
$925$		−	19649.0i		−	0.698437i
$926$	5664.23			0.201013
$927$	−16420.5			−0.581790
$928$		−	10344.3i		−	0.365916i
$929$		−	12050.4i		−	0.425578i	−0.977098	−	0.212789i	$-0.931745\pi$
$929$		−	12050.4i		−	0.425578i	0.977098	−	0.212789i	$-0.0682547\pi$
$930$		−	2049.30i		−	0.0722574i
$931$		−	28545.6i		−	1.00488i
$932$	−48699.0			−1.71158
$933$	−38682.4			−1.35735
$934$		−	5360.88i		−	0.187809i
$935$	2643.12			0.0924485
$936$	−4538.48	−	3911.20i	−0.158488	−	0.136583i
$937$	−30209.9			−1.05327			−0.526636	−	0.850091i	$-0.676547\pi$
$937$	−30209.9			−1.05327			−0.526636	+	0.850091i	$0.676547\pi$
$938$			5252.80i			0.182847i
$939$	−54737.0			−1.90232
$940$	12650.5			0.438950
$941$			34124.9i			1.18219i	0.806602	+	0.591095i	$0.201304\pi$
$941$			34124.9i			1.18219i	−0.806602	+	0.591095i	$0.798696\pi$
$942$		−	4640.16i		−	0.160493i
$943$			5322.31i			0.183795i
$944$		−	43681.9i		−	1.50607i
$945$	2589.15			0.0891270
$946$	−2283.79			−0.0784908
$947$			17470.4i			0.599484i	0.954020	+	0.299742i	$0.0969005\pi$
$947$			17470.4i			0.599484i	−0.954020	+	0.299742i	$0.903099\pi$
$948$	−29209.9			−1.00073
$949$	−10221.3	−	8808.57i	−0.349628	−	0.301305i
$950$	−7248.42			−0.247547
$951$			18685.3i			0.637130i
$952$	5961.06			0.202940
$953$	−27848.2			−0.946582			−0.473291	−	0.880906i	$-0.656934\pi$
$953$	−27848.2			−0.946582			−0.473291	+	0.880906i	$0.656934\pi$
$954$			3206.91i			0.108834i
$955$			13304.3i			0.450805i
$956$			19213.6i			0.650013i
$957$		−	8732.71i		−	0.294972i
$958$	5890.80			0.198667
$959$	−15748.5			−0.530288
$960$			9876.80i			0.332055i
$961$	−6380.58			−0.214178
$962$	−2492.16	+	2891.86i	−0.0835245	+	0.0969201i
$963$	−20910.2			−0.699712
$964$			31764.6i			1.06127i
$965$	−1303.33			−0.0434775
$966$	−492.726			−0.0164112
$967$		−	11251.9i		−	0.374184i	−0.982342	−	0.187092i	$-0.940094\pi$
$967$		−	11251.9i		−	0.374184i	0.982342	−	0.187092i	$-0.0599062\pi$
$968$			894.854i			0.0297125i
$969$			63309.6i			2.09886i
$970$			1018.69i			0.0337197i
$971$	−8036.31			−0.265600			−0.132800	−	0.991143i	$-0.542397\pi$
$971$	−8036.31			−0.265600			−0.132800	+	0.991143i	$0.542397\pi$
$972$	32856.2			1.08422
$973$			22393.8i			0.737835i
$974$	5879.68			0.193426
$975$	−23022.3	+	26714.6i	−0.756208	+	0.877488i
$976$	25279.1			0.829063
$977$			52519.0i			1.71979i	0.510474	+	0.859893i	$0.329470\pi$
$977$			52519.0i			1.71979i	−0.510474	+	0.859893i	$0.670530\pi$
$978$	−341.244			−0.0111572
$979$	6912.89			0.225676
$980$		−	5609.39i		−	0.182842i
$981$		−	12984.8i		−	0.422601i
$982$		−	2114.00i		−	0.0686972i
$983$		−	58820.9i		−	1.90854i	−0.298943	−	0.954271i	$-0.596634\pi$
$983$		−	58820.9i		−	1.90854i	0.298943	−	0.954271i	$-0.403366\pi$
$984$	−19214.9			−0.622510
$985$	8577.83			0.277474
$986$		−	3888.29i		−	0.125586i
$987$	36296.1			1.17054
$988$	−37790.3	−	32567.2i	−1.21687	−	1.04868i
$989$	−6038.98			−0.194164
$990$		−	307.844i		−	0.00988274i
$991$	45745.1			1.46634			0.733170	−	0.680046i	$-0.238040\pi$
$991$	45745.1			1.46634			0.733170	+	0.680046i	$0.238040\pi$
$992$	−16491.2			−0.527819
$993$			57558.7i			1.83945i
$994$		−	285.937i		−	0.00912412i
$995$			4583.61i			0.146041i
$996$		−	55631.3i		−	1.76983i
$997$	−15148.3			−0.481194			−0.240597	−	0.970625i	$-0.577343\pi$
$997$	−15148.3			−0.481194			−0.240597	+	0.970625i	$0.577343\pi$
$998$	4868.16			0.154408
$999$		−	11236.8i		−	0.355873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.b.a.12.17	✓	36
13.5	odd	4		1859.4.a.j.1.9		18
13.8	odd	4		1859.4.a.k.1.10		18
13.12	even	2	inner	143.4.b.a.12.20	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.b.a.12.17	✓	36	1.1	even	1	trivial
143.4.b.a.12.20	yes	36	13.12	even	2	inner
1859.4.a.j.1.9		18	13.5	odd	4
1859.4.a.k.1.10		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)

\(f(q)\)	\(=\)	\(q-0.468651i q^{2} -6.65460 q^{3} +7.78037 q^{4} -3.45502i q^{5} +3.11869i q^{6} +11.5900i q^{7} -7.39549i q^{8} +17.2837 q^{9} +O(q^{10})\)	\(q-0.468651i q^{2} -6.65460 q^{3} +7.78037 q^{4} -3.45502i q^{5} +3.11869i q^{6} +11.5900i q^{7} -7.39549i q^{8} +17.2837 q^{9} -1.61920 q^{10} +11.0000i q^{11} -51.7752 q^{12} +(30.5990 - 35.5064i) q^{13} +5.43166 q^{14} +22.9918i q^{15} +58.7770 q^{16} +69.5462 q^{17} -8.10003i q^{18} -136.796i q^{19} -26.8813i q^{20} -77.1267i q^{21} +5.15517 q^{22} +13.6317 q^{23} +49.2140i q^{24} +113.063 q^{25} +(-16.6401 - 14.3402i) q^{26} +64.6581 q^{27} +90.1743i q^{28} +119.298 q^{29} +10.7751 q^{30} -190.188i q^{31} -86.7099i q^{32} -73.2006i q^{33} -32.5930i q^{34} +40.0436 q^{35} +134.473 q^{36} -173.788i q^{37} -64.1097 q^{38} +(-203.624 + 236.281i) q^{39} -25.5516 q^{40} +390.436i q^{41} -36.1455 q^{42} -443.009 q^{43} +85.5840i q^{44} -59.7155i q^{45} -6.38853i q^{46} +470.604i q^{47} -391.138 q^{48} +208.672 q^{49} -52.9871i q^{50} -462.802 q^{51} +(238.071 - 276.253i) q^{52} -395.914 q^{53} -30.3021i q^{54} +38.0052 q^{55} +85.7136 q^{56} +910.323i q^{57} -55.9094i q^{58} -743.180i q^{59} +178.885i q^{60} +430.086 q^{61} -89.1320 q^{62} +200.318i q^{63} +429.579 q^{64} +(-122.675 - 105.720i) q^{65} -34.3056 q^{66} +967.071i q^{67} +541.095 q^{68} -90.7136 q^{69} -18.7665i q^{70} -52.6426i q^{71} -127.821i q^{72} -287.872i q^{73} -81.4460 q^{74} -752.388 q^{75} -1064.32i q^{76} -127.490 q^{77} +(110.733 + 95.4286i) q^{78} +564.168 q^{79} -203.076i q^{80} -896.934 q^{81} +182.978 q^{82} +1074.48i q^{83} -600.074i q^{84} -240.284i q^{85} +207.617i q^{86} -793.883 q^{87} +81.3504 q^{88} -628.445i q^{89} -27.9858 q^{90} +(411.518 + 354.641i) q^{91} +106.060 q^{92} +1265.63i q^{93} +220.549 q^{94} -472.634 q^{95} +577.019i q^{96} -629.130i q^{97} -97.7946i q^{98} +190.121i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 152 q^{4} + 360 q^{9}+O(q^{10}) \) 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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