LMFDB - Embedded newform 143.4.b.a.12.12

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			12.12
Character	$\chi$	$=$	143.12
Dual form			143.4.b.a.12.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32803i q^{2} -4.42417 q^{3} +2.58028 q^{4} -12.1881i q^{5} +10.2996i q^{6} +11.2388i q^{7} -24.6312i q^{8} -7.42671 q^{9} +O(q^{10})$	\(q-2.32803i q^{2} -4.42417 q^{3} +2.58028 q^{4} -12.1881i q^{5} +10.2996i q^{6} +11.2388i q^{7} -24.6312i q^{8} -7.42671 q^{9} -28.3743 q^{10} -11.0000i q^{11} -11.4156 q^{12} +(15.1779 - 44.3467i) q^{13} +26.1642 q^{14} +53.9224i q^{15} -36.6999 q^{16} -96.5636 q^{17} +17.2896i q^{18} +125.475i q^{19} -31.4488i q^{20} -49.7223i q^{21} -25.6083 q^{22} -211.521 q^{23} +108.973i q^{24} -23.5508 q^{25} +(-103.240 - 35.3346i) q^{26} +152.310 q^{27} +28.9992i q^{28} -168.479 q^{29} +125.533 q^{30} -13.2819i q^{31} -111.611i q^{32} +48.6659i q^{33} +224.803i q^{34} +136.980 q^{35} -19.1630 q^{36} -63.5699i q^{37} +292.109 q^{38} +(-67.1496 + 196.197i) q^{39} -300.209 q^{40} -249.705i q^{41} -115.755 q^{42} +229.842 q^{43} -28.3831i q^{44} +90.5177i q^{45} +492.427i q^{46} -197.005i q^{47} +162.367 q^{48} +216.690 q^{49} +54.8269i q^{50} +427.214 q^{51} +(39.1632 - 114.427i) q^{52} +443.046 q^{53} -354.581i q^{54} -134.070 q^{55} +276.825 q^{56} -555.121i q^{57} +392.224i q^{58} -769.428i q^{59} +139.135i q^{60} -566.158 q^{61} -30.9206 q^{62} -83.4672i q^{63} -553.433 q^{64} +(-540.504 - 184.990i) q^{65} +113.296 q^{66} -525.648i q^{67} -249.161 q^{68} +935.805 q^{69} -318.893i q^{70} +234.648i q^{71} +182.929i q^{72} -742.562i q^{73} -147.992 q^{74} +104.193 q^{75} +323.760i q^{76} +123.627 q^{77} +(456.753 + 156.326i) q^{78} +1022.54 q^{79} +447.304i q^{80} -473.323 q^{81} -581.321 q^{82} +631.264i q^{83} -128.298i q^{84} +1176.93i q^{85} -535.078i q^{86} +745.381 q^{87} -270.943 q^{88} +1309.02i q^{89} +210.728 q^{90} +(498.403 + 170.581i) q^{91} -545.783 q^{92} +58.7612i q^{93} -458.633 q^{94} +1529.30 q^{95} +493.787i q^{96} -567.936i q^{97} -504.460i q^{98} +81.6938i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.32803i		−	0.823083i	−0.911391	−	0.411541i	$-0.864991\pi$
$2$		−	2.32803i		−	0.823083i	0.911391	−	0.411541i	$-0.135009\pi$
$3$	−4.42417			−0.851432			−0.425716	−	0.904857i	$-0.639978\pi$
$3$	−4.42417			−0.851432			−0.425716	+	0.904857i	$0.639978\pi$
$4$	2.58028			0.322535
$5$		−	12.1881i		−	1.09014i	−0.838390	−	0.545070i	$-0.816503\pi$
$5$		−	12.1881i		−	1.09014i	0.838390	−	0.545070i	$-0.183497\pi$
$6$			10.2996i			0.700799i
$7$			11.2388i			0.606838i	0.952857	+	0.303419i	$0.0981281\pi$
$7$			11.2388i			0.606838i	−0.952857	+	0.303419i	$0.901872\pi$
$8$		−	24.6312i		−	1.08856i
$9$	−7.42671			−0.275063
$10$	−28.3743			−0.897276
$11$		−	11.0000i		−	0.301511i
$11$		−	11.0000i		−	0.301511i
$12$	−11.4156			−0.274617
$13$	15.1779	−	44.3467i	0.323815	−	0.946121i
$13$	15.1779	−	44.3467i	0.323815	−	0.946121i
$14$	26.1642			0.499477
$15$			53.9224i			0.928181i
$16$	−36.6999			−0.573436
$17$	−96.5636			−1.37765			−0.688827	−	0.724926i	$-0.741874\pi$
$17$	−96.5636			−1.37765			−0.688827	+	0.724926i	$0.741874\pi$
$18$			17.2896i			0.226400i
$19$			125.475i			1.51504i	0.652809	+	0.757522i	$0.273590\pi$
$19$			125.475i			1.51504i	−0.652809	+	0.757522i	$0.726410\pi$
$20$		−	31.4488i		−	0.351609i
$21$		−	49.7223i		−	0.516681i
$22$	−25.6083			−0.248169
$23$	−211.521			−1.91762			−0.958808	−	0.284056i	$-0.908320\pi$
$23$	−211.521			−1.91762			−0.958808	+	0.284056i	$0.908320\pi$
$24$			108.973i			0.926831i
$25$	−23.5508			−0.188406
$26$	−103.240	−	35.3346i	−0.778735	−	0.266526i
$27$	152.310			1.08563
$28$			28.9992i			0.195726i
$29$	−168.479			−1.07882			−0.539410	−	0.842043i	$-0.681353\pi$
$29$	−168.479			−1.07882			−0.539410	+	0.842043i	$0.681353\pi$
$30$	125.533			0.763969
$31$		−	13.2819i		−	0.0769514i	−0.999260	−	0.0384757i	$-0.987750\pi$
$31$		−	13.2819i		−	0.0769514i	0.999260	−	0.0384757i	$-0.0122502\pi$
$32$		−	111.611i		−	0.616570i
$33$			48.6659i			0.256716i
$34$			224.803i			1.13392i
$35$	136.980			0.661538
$36$	−19.1630			−0.0887175
$37$		−	63.5699i		−	0.282455i	−0.989977	−	0.141227i	$-0.954895\pi$
$37$		−	63.5699i		−	0.282455i	0.989977	−	0.141227i	$-0.0451048\pi$
$38$	292.109			1.24701
$39$	−67.1496	+	196.197i	−0.275706	+	0.805558i
$40$	−300.209			−1.18668
$41$		−	249.705i		−	0.951157i	−0.879673	−	0.475578i	$-0.842239\pi$
$41$		−	249.705i		−	0.951157i	0.879673	−	0.475578i	$-0.157761\pi$
$42$	−115.755			−0.425271
$43$	229.842			0.815129			0.407565	−	0.913176i	$-0.366378\pi$
$43$	229.842			0.815129			0.407565	+	0.913176i	$0.366378\pi$
$44$		−	28.3831i		−	0.0972480i
$45$			90.5177i			0.299858i
$46$			492.427i			1.57836i
$47$		−	197.005i		−	0.611407i	−0.952127	−	0.305703i	$-0.901108\pi$
$47$		−	197.005i		−	0.611407i	0.952127	−	0.305703i	$-0.0988916\pi$
$48$	162.367			0.488242
$49$	216.690			0.631748
$50$			54.8269i			0.155074i
$51$	427.214			1.17298
$52$	39.1632	−	114.427i	0.104442	−	0.305157i
$53$	443.046			1.14825			0.574123	−	0.818769i	$-0.305343\pi$
$53$	443.046			1.14825			0.574123	+	0.818769i	$0.305343\pi$
$54$		−	354.581i		−	0.893563i
$55$	−134.070			−0.328690
$56$	276.825			0.660576
$57$		−	555.121i		−	1.28996i
$58$			392.224i			0.887959i
$59$		−	769.428i		−	1.69781i	−0.528543	−	0.848907i	$-0.677261\pi$
$59$		−	769.428i		−	1.69781i	0.528543	−	0.848907i	$-0.322739\pi$
$60$			139.135i			0.299371i
$61$	−566.158			−1.18835			−0.594173	−	0.804337i	$-0.702521\pi$
$61$	−566.158			−1.18835			−0.594173	+	0.804337i	$0.702521\pi$
$62$	−30.9206			−0.0633373
$63$		−	83.4672i		−	0.166919i
$64$	−553.433			−1.08092
$65$	−540.504	−	184.990i	−1.03140	−	0.353003i
$66$	113.296			0.211299
$67$		−	525.648i		−	0.958480i	−0.877684	−	0.479240i	$-0.840912\pi$
$67$		−	525.648i		−	0.958480i	0.877684	−	0.479240i	$-0.159088\pi$
$68$	−249.161			−0.444342
$69$	935.805			1.63272
$70$		−	318.893i		−	0.544501i
$71$			234.648i			0.392220i	0.980582	+	0.196110i	$0.0628309\pi$
$71$			234.648i			0.392220i	−0.980582	+	0.196110i	$0.937169\pi$
$72$			182.929i			0.299422i
$73$		−	742.562i		−	1.19055i	−0.803521	−	0.595276i	$-0.797043\pi$
$73$		−	742.562i		−	1.19055i	0.803521	−	0.595276i	$-0.202957\pi$
$74$	−147.992			−0.232483
$75$	104.193			0.160415
$76$			323.760i			0.488655i
$77$	123.627			0.182968
$78$	456.753	+	156.326i	0.663040	+	0.226929i
$79$	1022.54			1.45626			0.728131	−	0.685438i	$-0.240389\pi$
$79$	1022.54			1.45626			0.728131	+	0.685438i	$0.240389\pi$
$80$			447.304i			0.625126i
$81$	−473.323			−0.649277
$82$	−581.321			−0.782881
$83$			631.264i			0.834823i	0.908718	+	0.417411i	$0.137063\pi$
$83$			631.264i			0.834823i	−0.908718	+	0.417411i	$0.862937\pi$
$84$		−	128.298i		−	0.166648i
$85$			1176.93i			1.50184i
$86$		−	535.078i		−	0.670919i
$87$	745.381			0.918543
$88$	−270.943			−0.328212
$89$			1309.02i			1.55906i	0.626367	+	0.779528i	$0.284541\pi$
$89$			1309.02i			1.55906i	−0.626367	+	0.779528i	$0.715459\pi$
$90$	210.728			0.246807
$91$	498.403	+	170.581i	0.574142	+	0.196503i
$92$	−545.783			−0.618498
$93$			58.7612i			0.0655189i
$94$	−458.633			−0.503238
$95$	1529.30			1.65161
$96$			493.787i			0.524968i
$97$		−	567.936i		−	0.594486i	−0.954802	−	0.297243i	$-0.903933\pi$
$97$		−	567.936i		−	0.594486i	0.954802	−	0.297243i	$-0.0960672\pi$
$98$		−	504.460i		−	0.519981i
$99$			81.6938i			0.0829347i
$100$	−60.7676			−0.0607676
$101$	1214.71			1.19672			0.598359	−	0.801228i	$-0.295820\pi$
$101$	1214.71			1.19672			0.598359	+	0.801228i	$0.295820\pi$
$102$		−	994.566i		−	0.965458i
$103$	−1481.35			−1.41710			−0.708551	−	0.705659i	$-0.750651\pi$
$103$	−1481.35			−1.41710			−0.708551	+	0.705659i	$0.750651\pi$
$104$	−1092.31	−	373.850i	−1.02990	−	0.352490i
$105$	−606.023			−0.563255
$106$		−	1031.42i		−	0.945101i
$107$	1589.09			1.43573			0.717864	−	0.696184i	$-0.245120\pi$
$107$	1589.09			1.43573			0.717864	+	0.696184i	$0.245120\pi$
$108$	393.002			0.350154
$109$		−	544.286i		−	0.478286i	−0.970984	−	0.239143i	$-0.923134\pi$
$109$		−	544.286i		−	0.478286i	0.970984	−	0.239143i	$-0.0768664\pi$
$110$			312.118i			0.270539i
$111$			281.244i			0.240491i
$112$		−	412.463i		−	0.347983i
$113$	−1460.89			−1.21618			−0.608092	−	0.793867i	$-0.708065\pi$
$113$	−1460.89			−1.21618			−0.608092	+	0.793867i	$0.708065\pi$
$114$	−1292.34			−1.06174
$115$			2578.05i			2.09047i
$116$	−434.724			−0.347958
$117$	−112.722	+	329.350i	−0.0890695	+	0.260243i
$118$	−1791.25			−1.39744
$119$		−	1085.26i		−	0.836012i
$120$	1328.17			1.01038
$121$	−121.000			−0.0909091
$122$			1318.03i			0.978108i
$123$			1104.74i			0.809846i
$124$		−	34.2709i		−	0.0248195i
$125$		−	1236.48i		−	0.884751i
$126$	−194.314			−0.137388
$127$	2662.64			1.86040			0.930199	−	0.367054i	$-0.119634\pi$
$127$	2662.64			1.86040			0.930199	+	0.367054i	$0.119634\pi$
$128$			395.520i			0.273120i
$129$	−1016.86			−0.694027
$130$	−430.663	+	1258.31i	−0.290551	+	0.848931i
$131$	−1872.80			−1.24907			−0.624533	−	0.780998i	$-0.714711\pi$
$131$	−1872.80			−1.24907			−0.624533	+	0.780998i	$0.714711\pi$
$132$			125.572i			0.0828001i
$133$	−1410.18			−0.919386
$134$	−1223.72			−0.788908
$135$		−	1856.37i		−	1.18349i
$136$			2378.48i			1.49965i
$137$		−	755.499i		−	0.471144i	−0.971857	−	0.235572i	$-0.924304\pi$
$137$		−	755.499i		−	0.471144i	0.971857	−	0.235572i	$-0.0756963\pi$
$138$		−	2178.58i		−	1.34386i
$139$	−766.845			−0.467935			−0.233967	−	0.972244i	$-0.575171\pi$
$139$	−766.845			−0.467935			−0.233967	+	0.972244i	$0.575171\pi$
$140$	353.447			0.213369
$141$			871.584i			0.520572i
$142$	546.268			0.322829
$143$	−487.814	−	166.957i	−0.285266	−	0.0976338i
$144$	272.559			0.157731
$145$			2053.45i			1.17607i
$146$	−1728.71			−0.979923
$147$	−958.672			−0.537891
$148$		−	164.028i		−	0.0911015i
$149$			2016.90i			1.10893i	0.832207	+	0.554465i	$0.187077\pi$
$149$			2016.90i			1.10893i	−0.832207	+	0.554465i	$0.812923\pi$
$150$		−	242.564i		−	0.132035i
$151$			419.616i			0.226145i	0.993587	+	0.113072i	$0.0360692\pi$
$151$			419.616i			0.226145i	−0.993587	+	0.113072i	$0.963931\pi$
$152$	3090.59			1.64921
$153$	717.149			0.378942
$154$		−	287.807i		−	0.150598i
$155$	−161.881			−0.0838878
$156$	−173.265	+	506.245i	−0.0889249	+	0.259821i
$157$	−2017.55			−1.02559			−0.512795	−	0.858511i	$-0.671390\pi$
$157$	−2017.55			−1.02559			−0.512795	+	0.858511i	$0.671390\pi$
$158$		−	2380.50i		−	1.19862i
$159$	−1960.11			−0.977653
$160$	−1360.33			−0.672148
$161$		−	2377.24i		−	1.16368i
$162$			1101.91i			0.534409i
$163$		−	3040.73i		−	1.46116i	−0.682829	−	0.730578i	$-0.739251\pi$
$163$		−	3040.73i		−	1.46116i	0.682829	−	0.730578i	$-0.260749\pi$
$164$		−	644.310i		−	0.306781i
$165$	593.147			0.279857
$166$	1469.60			0.687128
$167$		−	3471.08i		−	1.60838i	−0.594370	−	0.804192i	$-0.702598\pi$
$167$		−	3471.08i		−	1.60838i	0.594370	−	0.804192i	$-0.297402\pi$
$168$	−1224.72			−0.562436
$169$	−1736.26	−	1346.18i	−0.790288	−	0.612735i
$170$	2739.93			1.23613
$171$		−	931.863i		−	0.416733i
$172$	593.056			0.262908
$173$	3435.65			1.50987			0.754935	−	0.655800i	$-0.227668\pi$
$173$	3435.65			1.50987			0.754935	+	0.655800i	$0.227668\pi$
$174$		−	1735.27i		−	0.756037i
$175$		−	264.682i		−	0.114332i
$176$			403.699i			0.172897i
$177$			3404.08i			1.44557i
$178$	3047.44			1.28323
$179$	2660.00			1.11072			0.555358	−	0.831612i	$-0.312581\pi$
$179$	2660.00			1.11072			0.555358	+	0.831612i	$0.312581\pi$
$180$			233.561i			0.0967146i
$181$	−1753.10			−0.719926			−0.359963	−	0.932967i	$-0.617211\pi$
$181$	−1753.10			−0.719926			−0.359963	+	0.932967i	$0.617211\pi$
$182$	397.118	−	1160.30i	0.161738	−	0.472566i
$183$	2504.78			1.01180
$184$			5210.01i			2.08743i
$185$	−774.798			−0.307915
$186$	136.798			0.0539275
$187$			1062.20i			0.415378i
$188$		−	508.328i		−	0.197200i
$189$			1711.78i			0.658801i
$190$		−	3560.26i		−	1.35941i
$191$	983.755			0.372681			0.186340	−	0.982485i	$-0.440337\pi$
$191$	983.755			0.372681			0.186340	+	0.982485i	$0.440337\pi$
$192$	2448.48			0.920334
$193$		−	1276.21i		−	0.475977i	−0.971268	−	0.237988i	$-0.923512\pi$
$193$		−	1276.21i		−	0.475977i	0.971268	−	0.237988i	$-0.0764880\pi$
$194$	−1322.17			−0.489311
$195$	2391.28	+	818.429i	0.878171	+	0.300559i
$196$	559.120			0.203761
$197$			4254.59i			1.53872i	0.638817	+	0.769358i	$0.279424\pi$
$197$			4254.59i			1.53872i	−0.638817	+	0.769358i	$0.720576\pi$
$198$	190.185			0.0682621
$199$	556.569			0.198262			0.0991309	−	0.995074i	$-0.468394\pi$
$199$	556.569			0.198262			0.0991309	+	0.995074i	$0.468394\pi$
$200$			580.084i			0.205091i
$201$			2325.56i			0.816081i
$202$		−	2827.89i		−	0.984997i
$203$		−	1893.50i		−	0.654669i
$204$	1102.33			0.378327
$205$	−3043.44			−1.03689
$206$			3448.62i			1.16639i
$207$	1570.90			0.527465
$208$	−557.027	+	1627.52i	−0.185687	+	0.542540i
$209$	1380.22			0.456803
$210$			1410.84i			0.463605i
$211$	−33.9176			−0.0110663			−0.00553314	−	0.999985i	$-0.501761\pi$
$211$	−33.9176			−0.0110663			−0.00553314	+	0.999985i	$0.501761\pi$
$212$	1143.18			0.370349
$213$		−	1038.12i		−	0.333949i
$214$		−	3699.44i		−	1.18172i
$215$		−	2801.34i		−	0.888605i
$216$		−	3751.57i		−	1.18177i
$217$	149.272			0.0466970
$218$	−1267.11			−0.393668
$219$			3285.22i			1.01368i
$220$	−345.937			−0.106014
$221$	−1465.63	+	4282.28i	−0.446104	+	1.30343i
$222$	654.744			0.197944
$223$		−	2947.33i		−	0.885058i	−0.896754	−	0.442529i	$-0.854081\pi$
$223$		−	2947.33i		−	0.885058i	0.896754	−	0.442529i	$-0.145919\pi$
$224$	1254.37			0.374158
$225$	174.905			0.0518236
$226$			3400.99i			1.00102i
$227$			2176.60i			0.636415i	0.948021	+	0.318207i	$0.103081\pi$
$227$			2176.60i			0.636415i	−0.948021	+	0.318207i	$0.896919\pi$
$228$		−	1432.37i		−	0.416057i
$229$		−	970.516i		−	0.280059i	−0.990147	−	0.140029i	$-0.955280\pi$
$229$		−	970.516i		−	0.280059i	0.990147	−	0.140029i	$-0.0447197\pi$
$230$	6001.77			1.72063
$231$	−546.946			−0.155785
$232$			4149.84i			1.17436i
$233$	816.690			0.229627			0.114814	−	0.993387i	$-0.463373\pi$
$233$	816.690			0.229627			0.114814	+	0.993387i	$0.463373\pi$
$234$	766.736	+	262.420i	0.214201	+	0.0733115i
$235$	−2401.12			−0.666519
$236$		−	1985.34i		−	0.547604i
$237$	−4523.89			−1.23991
$238$	−2526.51			−0.688107
$239$			1646.41i			0.445597i	0.974865	+	0.222799i	$0.0715192\pi$
$239$			1646.41i			0.445597i	−0.974865	+	0.222799i	$0.928481\pi$
$240$		−	1978.95i		−	0.532252i
$241$			1039.36i			0.277804i	0.990306	+	0.138902i	$0.0443573\pi$
$241$			1039.36i			0.277804i	−0.990306	+	0.138902i	$0.955643\pi$
$242$			281.692i			0.0748257i
$243$	−2018.30			−0.532814
$244$	−1460.85			−0.383283
$245$		−	2641.04i		−	0.688694i
$246$	2571.87			0.666570
$247$	5564.39	+	1904.44i	1.43341	+	0.490594i
$248$	−327.148			−0.0837659
$249$		−	2792.82i		−	0.710795i
$250$	−2878.56			−0.728223
$251$	−2973.47			−0.747745			−0.373872	−	0.927480i	$-0.621970\pi$
$251$	−2973.47			−0.747745			−0.373872	+	0.927480i	$0.621970\pi$
$252$		−	215.369i		−	0.0538371i
$253$			2326.73i			0.578183i
$254$		−	6198.69i		−	1.53126i
$255$		−	5206.94i		−	1.27871i
$256$	−3506.69			−0.856124
$257$	619.988			0.150482			0.0752408	−	0.997165i	$-0.476027\pi$
$257$	619.988			0.150482			0.0752408	+	0.997165i	$0.476027\pi$
$258$			2367.28i			0.571242i
$259$	714.448			0.171404
$260$	−1394.65	−	477.327i	−0.332664	−	0.113856i
$261$	1251.25			0.296744
$262$			4359.94i			1.02808i
$263$	345.797			0.0810751			0.0405376	−	0.999178i	$-0.487093\pi$
$263$	345.797			0.0810751			0.0405376	+	0.999178i	$0.487093\pi$
$264$	1198.70			0.279450
$265$		−	5399.90i		−	1.25175i
$266$			3282.95i			0.756731i
$267$		−	5791.34i		−	1.32743i
$268$		−	1356.32i		−	0.309143i
$269$	−4280.95			−0.970312			−0.485156	−	0.874428i	$-0.661237\pi$
$269$	−4280.95			−0.970312			−0.485156	+	0.874428i	$0.661237\pi$
$270$	−4321.69			−0.974109
$271$			1874.34i			0.420140i	0.977686	+	0.210070i	$0.0673692\pi$
$271$			1874.34i			0.420140i	−0.977686	+	0.210070i	$0.932631\pi$
$272$	3543.87			0.789996
$273$	−2205.02	−	754.680i	−0.488843	−	0.167309i
$274$	−1758.82			−0.387790
$275$			259.059i			0.0568066i
$276$	2414.64			0.526609
$277$	1419.94			0.307999			0.153999	−	0.988071i	$-0.450785\pi$
$277$	1419.94			0.307999			0.153999	+	0.988071i	$0.450785\pi$
$278$			1785.24i			0.385149i
$279$			98.6405i			0.0211665i
$280$		−	3373.98i		−	0.720121i
$281$		−	2777.12i		−	0.589569i	−0.955564	−	0.294785i	$-0.904752\pi$
$281$		−	2777.12i		−	0.589569i	0.955564	−	0.294785i	$-0.0952479\pi$
$282$	2029.07			0.428473
$283$	−2440.65			−0.512655			−0.256328	−	0.966590i	$-0.582513\pi$
$283$	−2440.65			−0.512655			−0.256328	+	0.966590i	$0.582513\pi$
$284$			605.458i			0.126505i
$285$	−6765.89			−1.40624
$286$	−388.680	+	1135.64i	−0.0803607	+	0.234798i
$287$	2806.39			0.577198
$288$			828.903i			0.169596i
$289$	4411.53			0.897929
$290$	4780.49			0.968000
$291$			2512.65i			0.506165i
$292$		−	1916.02i		−	0.383995i
$293$			317.086i			0.0632230i	0.999500	+	0.0316115i	$0.0100639\pi$
$293$			317.086i			0.0632230i	−0.999500	+	0.0316115i	$0.989936\pi$
$294$			2231.82i			0.442728i
$295$	−9377.90			−1.85086
$296$	−1565.80			−0.307468
$297$		−	1675.41i		−	0.327330i
$298$	4695.39			0.912741
$299$	−3210.44	+	9380.26i	−0.620952	+	1.81430i
$300$	268.846			0.0517395
$301$			2583.14i			0.494651i
$302$	976.878			0.186136
$303$	−5374.10			−1.01892
$304$		−	4604.91i		−	0.868781i
$305$			6900.42i			1.29546i
$306$		−	1669.54i		−	0.311900i
$307$		−	3816.32i		−	0.709475i	−0.934966	−	0.354738i	$-0.884570\pi$
$307$		−	3816.32i		−	0.709475i	0.934966	−	0.354738i	$-0.115430\pi$
$308$	318.992			0.0590137
$309$	6553.74			1.20657
$310$			376.864i			0.0690466i
$311$	230.529			0.0420324			0.0210162	−	0.999779i	$-0.493310\pi$
$311$	230.529			0.0420324			0.0210162	+	0.999779i	$0.493310\pi$
$312$	4832.58	+	1653.98i	0.876894	+	0.300122i
$313$	−2534.47			−0.457689			−0.228845	−	0.973463i	$-0.573495\pi$
$313$	−2534.47			−0.457689			−0.228845	+	0.973463i	$0.573495\pi$
$314$			4696.90i			0.844145i
$315$	−1017.31			−0.181965
$316$	2638.44			0.469696
$317$		−	5707.60i		−	1.01126i	−0.862749	−	0.505632i	$-0.831259\pi$
$317$		−	5707.60i		−	1.01126i	0.862749	−	0.505632i	$-0.168741\pi$
$318$			4563.19i			0.804689i
$319$			1853.27i			0.325277i
$320$			6745.32i			1.17836i
$321$	−7030.39			−1.22242
$322$	−5534.28			−0.957806
$323$		−	12116.3i		−	2.08721i
$324$	−1221.31			−0.209415
$325$	−357.451	+	1044.40i	−0.0610087	+	0.178255i
$326$	−7078.91			−1.20265
$327$			2408.01i			0.407228i
$328$	−6150.54			−1.03539
$329$	2214.10			0.371025
$330$		−	1380.86i		−	0.230345i
$331$			6344.75i			1.05359i	0.849992	+	0.526796i	$0.176607\pi$
$331$			6344.75i			1.05359i	−0.849992	+	0.526796i	$0.823393\pi$
$332$			1628.84i			0.269260i
$333$			472.115i			0.0776929i
$334$	−8080.77			−1.32383
$335$	−6406.68			−1.04488
$336$			1824.81i			0.296284i
$337$	4487.00			0.725290			0.362645	−	0.931927i	$-0.381874\pi$
$337$	4487.00			0.725290			0.362645	+	0.931927i	$0.381874\pi$
$338$	−3133.95	+	4042.07i	−0.504332	+	0.650472i
$339$	6463.22			1.03550
$340$			3036.81i			0.484395i
$341$	−146.100			−0.0232017
$342$	−2169.40			−0.343006
$343$			6290.23i			0.990206i
$344$		−	5661.28i		−	0.887313i
$345$		−	11405.7i		−	1.77989i
$346$		−	7998.29i		−	1.24275i
$347$	10263.9			1.58789			0.793944	−	0.607990i	$-0.208024\pi$
$347$	10263.9			1.58789			0.793944	+	0.607990i	$0.208024\pi$
$348$	1923.29			0.296262
$349$			387.767i			0.0594748i	0.999558	+	0.0297374i	$0.00946710\pi$
$349$			387.767i			0.0594748i	−0.999558	+	0.0297374i	$0.990533\pi$
$350$	−616.188			−0.0941047
$351$	2311.74	−	6754.43i	0.351543	−	1.02714i
$352$	−1227.72			−0.185903
$353$		−	4347.27i		−	0.655473i	−0.944769	−	0.327736i	$-0.893714\pi$
$353$		−	4347.27i		−	0.655473i	0.944769	−	0.327736i	$-0.106286\pi$
$354$	7924.80			1.18983
$355$	2859.92			0.427575
$356$			3377.64i			0.502850i
$357$			4801.37i			0.711808i
$358$		−	6192.57i		−	0.914210i
$359$			7416.44i			1.09032i	0.838332	+	0.545160i	$0.183531\pi$
$359$			7416.44i			1.09032i	−0.838332	+	0.545160i	$0.816469\pi$
$360$	2229.56			0.326412
$361$	−8884.87			−1.29536
$362$			4081.26i			0.592559i
$363$	535.325			0.0774029
$364$	1286.02	+	440.147i	0.185181	+	0.0633791i
$365$	−9050.46			−1.29787
$366$		−	5831.20i		−	0.832792i
$367$	8198.92			1.16616			0.583079	−	0.812415i	$-0.301848\pi$
$367$	8198.92			1.16616			0.583079	+	0.812415i	$0.301848\pi$
$368$	7762.80			1.09963
$369$			1854.49i			0.261628i
$370$			1803.75i			0.253440i
$371$			4979.30i			0.696799i
$372$			151.620i			0.0211321i
$373$	−6464.32			−0.897345			−0.448672	−	0.893696i	$-0.648103\pi$
$373$	−6464.32			−0.897345			−0.448672	+	0.893696i	$0.648103\pi$
$374$	2472.83			0.341891
$375$			5470.39i			0.753306i
$376$	−4852.47			−0.665550
$377$	−2557.16	+	7471.50i	−0.349338	+	1.02069i
$378$	3985.07			0.542248
$379$			3028.79i			0.410498i	0.978710	+	0.205249i	$0.0658004\pi$
$379$			3028.79i			0.410498i	−0.978710	+	0.205249i	$0.934200\pi$
$380$	3946.03			0.532703
$381$	−11780.0			−1.58400
$382$		−	2290.21i		−	0.306747i
$383$			4881.16i			0.651216i	0.945505	+	0.325608i	$0.105569\pi$
$383$			4881.16i			0.651216i	−0.945505	+	0.325608i	$0.894431\pi$
$384$		−	1749.85i		−	0.232543i
$385$		−	1506.78i		−	0.199461i
$386$	−2971.05			−0.391768
$387$	−1706.97			−0.224212
$388$		−	1465.43i		−	0.191743i
$389$	−1720.74			−0.224280			−0.112140	−	0.993692i	$-0.535770\pi$
$389$	−1720.74			−0.224280			−0.112140	+	0.993692i	$0.535770\pi$
$390$	1905.33	−	5566.98i	0.247384	−	0.722807i
$391$	20425.2			2.64181
$392$		−	5337.32i		−	0.687693i
$393$	8285.61			1.06350
$394$	9904.82			1.26649
$395$		−	12462.9i		−	1.58753i
$396$			210.793i			0.0267493i
$397$			2534.62i			0.320426i	0.987082	+	0.160213i	$0.0512181\pi$
$397$			2534.62i			0.320426i	−0.987082	+	0.160213i	$0.948782\pi$
$398$		−	1295.71i		−	0.163186i
$399$	6238.89			0.782795
$400$	864.312			0.108039
$401$			10810.1i			1.34621i	0.739547	+	0.673105i	$0.235040\pi$
$401$			10810.1i			1.34621i	−0.739547	+	0.673105i	$0.764960\pi$
$402$	5413.97			0.671702
$403$	−589.007	−	201.591i	−0.0728053	−	0.0249180i
$404$	3134.30			0.385983
$405$			5768.93i			0.707803i
$406$	−4408.13			−0.538847
$407$	−699.268			−0.0851633
$408$		−	10522.8i		−	1.27685i
$409$		−	1829.76i		−	0.221212i	−0.993864	−	0.110606i	$-0.964721\pi$
$409$		−	1829.76i		−	0.221212i	0.993864	−	0.110606i	$-0.0352792\pi$
$410$			7085.23i			0.853450i
$411$			3342.46i			0.401147i
$412$	−3822.29			−0.457065
$413$	8647.44			1.03030
$414$		−	3657.11i		−	0.434148i
$415$	7693.94			0.910074
$416$	−4949.59	−	1694.02i	−0.583350	−	0.199654i
$417$	3392.65			0.398415
$418$		−	3213.19i		−	0.375987i
$419$	2610.45			0.304365			0.152182	−	0.988352i	$-0.451370\pi$
$419$	2610.45			0.304365			0.152182	+	0.988352i	$0.451370\pi$
$420$	−1563.71			−0.181669
$421$			11782.8i			1.36403i	0.731336	+	0.682017i	$0.238897\pi$
$421$			11782.8i			1.36403i	−0.731336	+	0.682017i	$0.761103\pi$
$422$			78.9612i			0.00910846i
$423$			1463.10i			0.168176i
$424$		−	10912.7i		−	1.24993i
$425$	2274.15			0.259559
$426$	−2416.78			−0.274867
$427$		−	6362.94i		−	0.721134i
$428$	4100.29			0.463072
$429$	2158.17	+	738.646i	0.242885	+	0.0831286i
$430$	−6521.61			−0.731395
$431$		−	3641.98i		−	0.407025i	−0.979072	−	0.203513i	$-0.934764\pi$
$431$		−	3641.98i		−	0.407025i	0.979072	−	0.203513i	$-0.0652358\pi$
$432$	−5589.75			−0.622539
$433$	−6381.22			−0.708226			−0.354113	−	0.935203i	$-0.615217\pi$
$433$	−6381.22			−0.708226			−0.354113	+	0.935203i	$0.615217\pi$
$434$		−	347.510i		−	0.0384355i
$435$		−	9084.81i		−	1.00134i
$436$		−	1404.41i		−	0.154264i
$437$		−	26540.5i		−	2.90527i
$438$	7648.10			0.834338
$439$	6036.50			0.656279			0.328140	−	0.944629i	$-0.393578\pi$
$439$	6036.50			0.656279			0.328140	+	0.944629i	$0.393578\pi$
$440$			3302.29i			0.357797i
$441$	−1609.29			−0.173771
$442$	9969.27	+	3412.03i	1.07283	+	0.367181i
$443$	−9038.97			−0.969423			−0.484712	−	0.874674i	$-0.661075\pi$
$443$	−9038.97			−0.969423			−0.484712	+	0.874674i	$0.661075\pi$
$444$			725.688i			0.0775668i
$445$	15954.5			1.69959
$446$	−6861.48			−0.728476
$447$		−	8923.09i		−	0.944178i
$448$		−	6219.92i		−	0.655946i
$449$		−	14919.0i		−	1.56809i	−0.620707	−	0.784043i	$-0.713154\pi$
$449$		−	14919.0i		−	1.56809i	0.620707	−	0.784043i	$-0.286846\pi$
$450$		−	407.183i		−	0.0426551i
$451$	−2746.76			−0.286785
$452$	−3769.50			−0.392262
$453$		−	1856.45i		−	0.192547i
$454$	5067.19			0.523822
$455$	2079.07	−	6074.61i	0.214216	−	0.625895i
$456$	−13673.3			−1.40419
$457$		−	1598.53i		−	0.163624i	−0.996648	−	0.0818120i	$-0.973929\pi$
$457$		−	1598.53i		−	0.163624i	0.996648	−	0.0818120i	$-0.0260707\pi$
$458$	−2259.39			−0.230512
$459$	−14707.6			−1.49562
$460$			6652.08i			0.674250i
$461$			8908.16i			0.899988i	0.893032	+	0.449994i	$0.148574\pi$
$461$			8908.16i			0.899988i	−0.893032	+	0.449994i	$0.851426\pi$
$462$			1273.31i			0.128224i
$463$			1540.67i			0.154646i	0.997006	+	0.0773228i	$0.0246372\pi$
$463$			1540.67i			0.154646i	−0.997006	+	0.0773228i	$0.975363\pi$
$464$	6183.17			0.618635
$465$	716.190			0.0714248
$466$		−	1901.28i		−	0.189002i
$467$	−3724.08			−0.369015			−0.184507	−	0.982831i	$-0.559069\pi$
$467$	−3724.08			−0.369015			−0.184507	+	0.982831i	$0.559069\pi$
$468$	−290.854	+	849.815i	−0.0287280	+	0.0839375i
$469$	5907.65			0.581642
$470$			5589.89i			0.548601i
$471$	8925.97			0.873220
$472$	−18951.9			−1.84816
$473$		−	2528.26i		−	0.245771i
$474$			10531.8i			1.02055i
$475$		−	2955.03i		−	0.285444i
$476$		−	2800.27i		−	0.269643i
$477$	−3290.37			−0.315840
$478$	3832.90			0.366763
$479$			17212.6i			1.64189i	0.571011	+	0.820943i	$0.306551\pi$
$479$			17212.6i			1.64189i	−0.571011	+	0.820943i	$0.693449\pi$
$480$	6018.34			0.572289
$481$	−2819.11	−	964.857i	−0.267236	−	0.0914629i
$482$	2419.65			0.228656
$483$			10517.3i			0.990796i
$484$	−312.214			−0.0293214
$485$	−6922.09			−0.648074
$486$			4698.66i			0.438550i
$487$			5524.03i			0.514000i	0.966411	+	0.257000i	$0.0827340\pi$
$487$			5524.03i			0.514000i	−0.966411	+	0.257000i	$0.917266\pi$
$488$			13945.2i			1.29358i
$489$			13452.7i			1.24408i
$490$	−6148.43			−0.566852
$491$	4866.63			0.447307			0.223654	−	0.974669i	$-0.428202\pi$
$491$	4866.63			0.447307			0.223654	+	0.974669i	$0.428202\pi$
$492$			2850.54i			0.261204i
$493$	16269.0			1.48624
$494$	4433.59	−	12954.1i	0.403799	−	1.17982i
$495$	995.695			0.0904104
$496$			487.443i			0.0441267i
$497$	−2637.16			−0.238014
$498$	−6501.77			−0.585043
$499$		−	15161.8i		−	1.36019i	−0.733123	−	0.680096i	$-0.761938\pi$
$499$		−	15161.8i		−	1.36019i	0.733123	−	0.680096i	$-0.238062\pi$
$500$		−	3190.46i		−	0.285363i
$501$			15356.6i			1.36943i
$502$			6922.33i			0.615456i
$503$	−13119.4			−1.16295			−0.581476	−	0.813564i	$-0.697525\pi$
$503$	−13119.4			−1.16295			−0.581476	+	0.813564i	$0.697525\pi$
$504$	−2055.90			−0.181700
$505$		−	14805.1i		−	1.30459i
$506$	5416.69			0.475892
$507$	7681.53	+	5955.73i	0.672877	+	0.521703i
$508$	6870.35			0.600044
$509$		−	19667.6i		−	1.71268i	−0.516415	−	0.856338i	$-0.672734\pi$
$509$		−	19667.6i		−	1.71268i	0.516415	−	0.856338i	$-0.327266\pi$
$510$	−12121.9			−1.05249
$511$	8345.50			0.722472
$512$			11327.8i			0.977781i
$513$			19111.0i			1.64478i
$514$		−	1443.35i		−	0.123859i
$515$			18054.9i			1.54484i
$516$	−2623.78			−0.223848
$517$	−2167.05			−0.184346
$518$		−	1663.26i		−	0.141080i
$519$	−15199.9			−1.28555
$520$	−4556.53	+	13313.3i	−0.384264	+	1.12274i
$521$	−2762.52			−0.232299			−0.116150	−	0.993232i	$-0.537055\pi$
$521$	−2762.52			−0.232299			−0.116150	+	0.993232i	$0.537055\pi$
$522$		−	2912.94i		−	0.244245i
$523$	−1400.01			−0.117052			−0.0585260	−	0.998286i	$-0.518640\pi$
$523$	−1400.01			−0.117052			−0.0585260	+	0.998286i	$0.518640\pi$
$524$	−4832.36			−0.402868
$525$			1171.00i			0.0973460i
$526$		−	805.026i		−	0.0667315i
$527$			1282.54i			0.106012i
$528$		−	1786.03i		−	0.147210i
$529$	32574.1			2.67725
$530$	−12571.1			−1.03029
$531$			5714.31i			0.467006i
$532$	−3638.67			−0.296534
$533$	−11073.6	−	3790.00i	−0.899909	−	0.307999i
$534$	−13482.4			−1.09259
$535$		−	19368.0i		−	1.56514i
$536$	−12947.3			−1.04336
$537$	−11768.3			−0.945699
$538$			9966.17i			0.798647i
$539$		−	2383.59i		−	0.190479i
$540$		−	4789.96i		−	0.381717i
$541$			108.617i			0.00863184i	0.999991	+	0.00431592i	$0.00137380\pi$
$541$			108.617i			0.00863184i	−0.999991	+	0.00431592i	$0.998626\pi$
$542$	4363.51			0.345810
$543$	7756.00			0.612968
$544$			10777.6i			0.849420i
$545$	−6633.83			−0.521398
$546$	−1756.92	+	5133.36i	−0.137709	+	0.402358i
$547$	8622.88			0.674018			0.337009	−	0.941501i	$-0.390585\pi$
$547$	8622.88			0.674018			0.337009	+	0.941501i	$0.390585\pi$
$548$		−	1949.40i		−	0.151960i
$549$	4204.69			0.326870
$550$	603.096			0.0467566
$551$		−	21139.9i		−	1.63446i
$552$		−	23050.0i		−	1.77731i
$553$			11492.1i			0.883715i
$554$		−	3305.65i		−	0.253508i
$555$	3427.84			0.262169
$556$	−1978.67			−0.150925
$557$			1883.31i			0.143264i	0.997431	+	0.0716322i	$0.0228208\pi$
$557$			1883.31i			0.143264i	−0.997431	+	0.0716322i	$0.977179\pi$
$558$	229.638			0.0174218
$559$	3488.51	−	10192.7i	0.263951	−	0.771210i
$560$	−5027.15			−0.379350
$561$		−	4699.35i		−	0.353666i
$562$	−6465.21			−0.485264
$563$	509.273			0.0381231			0.0190615	−	0.999818i	$-0.493932\pi$
$563$	509.273			0.0381231			0.0190615	+	0.999818i	$0.493932\pi$
$564$			2248.93i			0.167903i
$565$			17805.5i			1.32581i
$566$			5681.90i			0.421958i
$567$		−	5319.58i		−	0.394006i
$568$	5779.66			0.426953
$569$	−3575.98			−0.263468			−0.131734	−	0.991285i	$-0.542054\pi$
$569$	−3575.98			−0.263468			−0.131734	+	0.991285i	$0.542054\pi$
$570$			15751.2i			1.15745i
$571$	−16937.7			−1.24137			−0.620683	−	0.784062i	$-0.713145\pi$
$571$	−16937.7			−1.24137			−0.620683	+	0.784062i	$0.713145\pi$
$572$	−1258.70	−	430.795i	−0.0920083	−	0.0314903i
$573$	−4352.30			−0.317312
$574$		−	6533.35i		−	0.475081i
$575$	4981.48			0.361291
$576$	4110.19			0.297322
$577$			256.818i			0.0185294i	0.999957	+	0.00926471i	$0.00294909\pi$
$577$			256.818i			0.0185294i	−0.999957	+	0.00926471i	$0.997051\pi$
$578$		−	10270.2i		−	0.739070i
$579$			5646.16i			0.405262i
$580$			5298.47i			0.379323i
$581$	−7094.65			−0.506602
$582$	5849.52			0.416616
$583$		−	4873.50i		−	0.346209i
$584$	−18290.2			−1.29598
$585$	4014.16	+	1373.87i	0.283701	+	0.0970983i
$586$	738.185			0.0520378
$587$			4743.77i			0.333554i	0.985995	+	0.166777i	$0.0533361\pi$
$587$			4743.77i			0.333554i	−0.985995	+	0.166777i	$0.946664\pi$
$588$	−2473.64			−0.173489
$589$	1666.54			0.116585
$590$			21832.0i			1.52341i
$591$		−	18823.1i		−	1.31011i
$592$			2333.01i			0.161970i
$593$		−	20217.1i		−	1.40003i	−0.714128	−	0.700016i	$-0.753176\pi$
$593$		−	20217.1i		−	1.40003i	0.714128	−	0.700016i	$-0.246824\pi$
$594$	−3900.39			−0.269419
$595$	−13227.3			−0.911371
$596$			5204.15i			0.357669i
$597$	−2462.35			−0.168806
$598$	21837.5	+	7474.00i	1.49331	+	0.511095i
$599$	18748.6			1.27888			0.639439	−	0.768842i	$-0.279167\pi$
$599$	18748.6			1.27888			0.639439	+	0.768842i	$0.279167\pi$
$600$		−	2566.39i		−	0.174621i
$601$	12380.1			0.840256			0.420128	−	0.907465i	$-0.361985\pi$
$601$	12380.1			0.840256			0.420128	+	0.907465i	$0.361985\pi$
$602$	6013.63			0.407139
$603$			3903.84i			0.263643i
$604$			1082.73i			0.0729396i
$605$			1474.77i			0.0991037i
$606$			12511.1i			0.838658i
$607$	18810.9			1.25784			0.628921	−	0.777470i	$-0.283497\pi$
$607$	18810.9			1.25784			0.628921	+	0.777470i	$0.283497\pi$
$608$	14004.4			0.934132
$609$			8377.18i			0.557406i
$610$	16064.4			1.06627
$611$	−8736.52	−	2990.12i	−0.578465	−	0.197983i
$612$	1850.45			0.122222
$613$			9515.18i			0.626941i	0.949598	+	0.313470i	$0.101492\pi$
$613$			9515.18i			0.626941i	−0.949598	+	0.313470i	$0.898508\pi$
$614$	−8884.51			−0.583957
$615$	13464.7			0.882845
$616$		−	3045.07i		−	0.199171i
$617$		−	22793.7i		−	1.48726i	−0.668591	−	0.743630i	$-0.733102\pi$
$617$		−	22793.7i		−	1.48726i	0.668591	−	0.743630i	$-0.266898\pi$
$618$		−	15257.3i		−	0.993104i
$619$			7594.02i			0.493101i	0.969130	+	0.246550i	$0.0792971\pi$
$619$			7594.02i			0.493101i	−0.969130	+	0.246550i	$0.920703\pi$
$620$	−417.699			−0.0270568
$621$	−32216.7			−2.08182
$622$		−	536.678i		−	0.0345962i
$623$	−14711.8			−0.946094
$624$	2464.38	−	7200.43i	0.158100	−	0.461936i
$625$	−18014.2			−1.15291
$626$			5900.32i			0.376716i
$627$	−6106.33			−0.388937
$628$	−5205.83			−0.330789
$629$			6138.53i			0.389125i
$630$			2368.33i			0.149772i
$631$			5644.80i			0.356127i	0.984019	+	0.178063i	$0.0569832\pi$
$631$			5644.80i			0.356127i	−0.984019	+	0.178063i	$0.943017\pi$
$632$		−	25186.4i		−	1.58522i
$633$	150.057			0.00942218
$634$	−13287.5			−0.832354
$635$		−	32452.6i		−	2.02810i
$636$	−5057.63			−0.315327
$637$	3288.89	−	9609.47i	0.204569	−	0.597710i
$638$	4314.47			0.267730
$639$		−	1742.66i		−	0.107885i
$640$	4820.65			0.297739
$641$	9926.91			0.611684			0.305842	−	0.952082i	$-0.401062\pi$
$641$	9926.91			0.611684			0.305842	+	0.952082i	$0.401062\pi$
$642$			16367.0i			1.00616i
$643$		−	19451.9i		−	1.19301i	−0.802608	−	0.596507i	$-0.796555\pi$
$643$		−	19451.9i		−	1.19301i	0.802608	−	0.596507i	$-0.203445\pi$
$644$		−	6133.94i		−	0.375328i
$645$			12393.6i			0.756587i
$646$	−28207.0			−1.71794
$647$	15799.7			0.960048			0.480024	−	0.877255i	$-0.340628\pi$
$647$	15799.7			0.960048			0.480024	+	0.877255i	$0.340628\pi$
$648$			11658.5i			0.706774i
$649$	−8463.71			−0.511910
$650$	2431.39	+	832.157i	0.146719	+	0.0502152i
$651$	−660.405			−0.0397593
$652$		−	7845.94i		−	0.471274i
$653$	−23363.9			−1.40015			−0.700076	−	0.714069i	$-0.746850\pi$
$653$	−23363.9			−1.40015			−0.700076	+	0.714069i	$0.746850\pi$
$654$	5605.93			0.335182
$655$			22826.0i			1.36166i
$656$			9164.17i			0.545428i
$657$			5514.79i			0.327477i
$658$		−	5154.48i		−	0.305384i
$659$	13875.7			0.820214			0.410107	−	0.912037i	$-0.365491\pi$
$659$	13875.7			0.820214			0.410107	+	0.912037i	$0.365491\pi$
$660$	1530.48			0.0902637
$661$		−	29373.5i		−	1.72844i	−0.503116	−	0.864219i	$-0.667813\pi$
$661$		−	29373.5i		−	1.72844i	0.503116	−	0.864219i	$-0.332187\pi$
$662$	14770.8			0.867194
$663$	6484.21	−	18945.5i	0.379828	−	1.10978i
$664$	15548.8			0.908751
$665$			17187.5i			1.00226i
$666$	1099.10			0.0639476
$667$	35636.9			2.06876
$668$		−	8956.35i		−	0.518760i
$669$			13039.5i			0.753567i
$670$			14914.9i			0.860021i
$671$			6227.74i			0.358300i
$672$	−5549.57			−0.318570
$673$	15149.8			0.867731			0.433865	−	0.900978i	$-0.357149\pi$
$673$	15149.8			0.867731			0.433865	+	0.900978i	$0.357149\pi$
$674$		−	10445.9i		−	0.596973i
$675$	−3587.01			−0.204540
$676$	−4480.05	−	3473.52i	−0.254896	−	0.197629i
$677$	−30766.1			−1.74658			−0.873292	−	0.487198i	$-0.838019\pi$
$677$	−30766.1			−1.74658			−0.873292	+	0.487198i	$0.838019\pi$
$678$		−	15046.6i		−	0.852301i
$679$	6382.92			0.360757
$680$	28989.2			1.63483
$681$		−	9629.66i		−	0.541864i
$682$			340.126i			0.0190969i
$683$			26618.7i			1.49127i	0.666356	+	0.745633i	$0.267853\pi$
$683$			26618.7i			1.49127i	−0.666356	+	0.745633i	$0.732147\pi$
$684$		−	2404.47i		−	0.134411i
$685$	−9208.13			−0.513613
$686$	14643.8			0.815021
$687$			4293.73i			0.238451i
$688$	−8435.17			−0.467424
$689$	6724.50	−	19647.6i	0.371819	−	1.08638i
$690$	−26552.8			−1.46500
$691$			10279.6i			0.565925i	0.959131	+	0.282963i	$0.0913172\pi$
$691$			10279.6i			0.565925i	−0.959131	+	0.282963i	$0.908683\pi$
$692$	8864.94			0.486986
$693$	−918.139			−0.0503279
$694$		−	23894.8i		−	1.30696i
$695$			9346.41i			0.510115i
$696$		−	18359.6i		−	0.999885i
$697$			24112.4i			1.31036i
$698$	902.733			0.0489527
$699$	−3613.18			−0.195512
$700$		−	682.955i		−	0.0368761i
$701$	31431.4			1.69351			0.846754	−	0.531984i	$-0.178553\pi$
$701$	31431.4			1.69351			0.846754	+	0.531984i	$0.178553\pi$
$702$	−15724.5	−	5381.80i	−0.845418	−	0.289349i
$703$	7976.40			0.427931
$704$			6087.77i			0.325911i
$705$	10623.0			0.567496
$706$	−10120.6			−0.539508
$707$			13651.9i			0.726213i
$708$			8783.48i			0.466248i
$709$			2196.16i			0.116331i	0.998307	+	0.0581653i	$0.0185250\pi$
$709$			2196.16i			0.116331i	−0.998307	+	0.0581653i	$0.981475\pi$
$710$		−	6657.99i		−	0.351929i
$711$	−7594.10			−0.400564
$712$	32242.8			1.69712
$713$			2809.39i			0.147563i
$714$	11177.7			0.585876
$715$	−2034.89	+	5945.54i	−0.106435	+	0.310980i
$716$	6863.56			0.358245
$717$		−	7284.02i		−	0.379396i
$718$	17265.7			0.897424
$719$	−16398.1			−0.850548			−0.425274	−	0.905065i	$-0.639822\pi$
$719$	−16398.1			−0.850548			−0.425274	+	0.905065i	$0.639822\pi$
$720$		−	3321.99i		−	0.171949i
$721$		−	16648.6i		−	0.859951i
$722$			20684.2i			1.06619i
$723$		−	4598.29i		−	0.236531i
$724$	−4523.48			−0.232201
$725$	3967.82			0.203257
$726$		−	1246.25i		−	0.0637090i
$727$	−25808.4			−1.31662			−0.658308	−	0.752749i	$-0.728727\pi$
$727$	−25808.4			−1.31662			−0.658308	+	0.752749i	$0.728727\pi$
$728$	4201.62	−	12276.3i	0.213904	−	0.624985i
$729$	21709.0			1.10293
$730$			21069.7i			1.06825i
$731$	−22194.4			−1.12297
$732$	6463.04			0.326340
$733$		−	15295.7i		−	0.770748i	−0.922761	−	0.385374i	$-0.874072\pi$
$733$		−	15295.7i		−	0.770748i	0.922761	−	0.385374i	$-0.125928\pi$
$734$		−	19087.3i		−	0.959845i
$735$			11684.4i			0.586376i
$736$			23608.1i			1.18234i
$737$	−5782.13			−0.288993
$738$	4317.30			0.215342
$739$		−	32090.9i		−	1.59741i	−0.601724	−	0.798704i	$-0.705519\pi$
$739$		−	32090.9i		−	1.59741i	0.601724	−	0.798704i	$-0.294481\pi$
$740$	−1999.20			−0.0993134
$741$	−24617.8	−	8425.57i	−1.22046	−	0.417707i
$742$	11591.9			0.573523
$743$			31245.1i			1.54276i	0.636374	+	0.771381i	$0.280434\pi$
$743$			31245.1i			1.54276i	−0.636374	+	0.771381i	$0.719566\pi$
$744$	1447.36			0.0713209
$745$	24582.2			1.20889
$746$			15049.1i			0.738589i
$747$		−	4688.22i		−	0.229629i
$748$			2740.77i			0.133974i
$749$			17859.4i			0.871253i
$750$	12735.2			0.620033
$751$	−3862.48			−0.187675			−0.0938375	−	0.995588i	$-0.529913\pi$
$751$	−3862.48			−0.187675			−0.0938375	+	0.995588i	$0.529913\pi$
$752$			7230.06i			0.350603i
$753$	13155.1			0.636654
$754$	17393.9	+	5953.14i	0.840116	+	0.287534i
$755$	5114.34			0.246530
$756$			4416.86i			0.212486i
$757$	28021.2			1.34537			0.672687	−	0.739927i	$-0.265140\pi$
$757$	28021.2			1.34537			0.672687	+	0.739927i	$0.265140\pi$
$758$	7051.12			0.337874
$759$		−	10293.9i		−	0.492283i
$760$		−	37668.5i		−	1.79787i
$761$			10279.6i			0.489666i	0.969565	+	0.244833i	$0.0787332\pi$
$761$			10279.6i			0.489666i	−0.969565	+	0.244833i	$0.921267\pi$
$762$			27424.1i			1.30377i
$763$	6117.11			0.290242
$764$	2538.36			0.120203
$765$		−	8740.72i		−	0.413100i
$766$	11363.5			0.536005
$767$	−34121.6	−	11678.3i	−1.60634	−	0.549777i
$768$	15514.2			0.728932
$769$		−	1724.61i		−	0.0808726i	−0.999182	−	0.0404363i	$-0.987125\pi$
$769$		−	1724.61i		−	0.0808726i	0.999182	−	0.0404363i	$-0.0128748\pi$
$770$	−3507.83			−0.164173
$771$	−2742.93			−0.128125
$772$		−	3292.98i		−	0.153519i
$773$			17423.4i			0.810708i	0.914160	+	0.405354i	$0.132852\pi$
$773$			17423.4i			0.810708i	−0.914160	+	0.405354i	$0.867148\pi$
$774$			3973.87i			0.184545i
$775$			312.798i			0.0144981i
$776$	−13989.0			−0.647132
$777$	−3160.84			−0.145939
$778$			4005.93i			0.184601i
$779$	31331.7			1.44105
$780$	6170.18	+	2111.78i	0.283241	+	0.0969407i
$781$	2581.13			0.118259
$782$		−	47550.5i		−	2.17443i
$783$	−25661.0			−1.17120
$784$	−7952.49			−0.362267
$785$			24590.1i			1.11804i
$786$		−	19289.1i		−	0.875345i
$787$			4925.61i			0.223099i	0.993759	+	0.111549i	$0.0355814\pi$
$787$			4925.61i			0.223099i	−0.993759	+	0.111549i	$0.964419\pi$
$788$			10978.0i			0.496290i
$789$	−1529.87			−0.0690300
$790$	−29013.9			−1.30667
$791$		−	16418.6i		−	0.738026i
$792$	2012.22			0.0902790
$793$	−8593.09	+	25107.3i	−0.384804	+	1.12432i
$794$	5900.68			0.263737
$795$			23890.1i			1.06578i
$796$	1436.10			0.0639464
$797$	−18499.1			−0.822172			−0.411086	−	0.911597i	$-0.634850\pi$
$797$	−18499.1			−0.822172			−0.411086	+	0.911597i	$0.634850\pi$
$798$		−	14524.3i		−	0.644305i
$799$			19023.5i			0.842307i
$800$			2628.53i			0.116166i
$801$		−	9721.72i		−	0.428839i
$802$	25166.2			1.10804
$803$	−8168.19			−0.358965
$804$			6000.59i			0.263215i
$805$	−28974.1			−1.26858
$806$	−469.309	+	1371.23i	−0.0205096	+	0.0599248i
$807$	18939.6			0.826155
$808$		−	29919.8i		−	1.30269i
$809$	13137.7			0.570947			0.285474	−	0.958387i	$-0.407849\pi$
$809$	13137.7			0.570947			0.285474	+	0.958387i	$0.407849\pi$
$810$	13430.2			0.582581
$811$		−	38369.7i		−	1.66134i	−0.556769	−	0.830668i	$-0.687959\pi$
$811$		−	38369.7i		−	1.66134i	0.556769	−	0.830668i	$-0.312041\pi$
$812$		−	4885.77i		−	0.211154i
$813$		−	8292.39i		−	0.357721i
$814$			1627.92i			0.0700964i
$815$	−37060.9			−1.59287
$816$	−15678.7			−0.672628
$817$			28839.3i			1.23496i
$818$	−4259.73			−0.182076
$819$	−3701.50	−	1266.86i	−0.157925	−	0.0540507i
$820$	−7852.94			−0.334435
$821$			9292.86i			0.395034i	0.980299	+	0.197517i	$0.0632878\pi$
$821$			9292.86i			0.395034i	−0.980299	+	0.197517i	$0.936712\pi$
$822$	7781.34			0.330177
$823$	18581.4			0.787007			0.393503	−	0.919323i	$-0.371263\pi$
$823$	18581.4			0.787007			0.393503	+	0.919323i	$0.371263\pi$
$824$			36487.4i			1.54260i
$825$		−	1146.12i		−	0.0483670i
$826$		−	20131.5i		−	0.848020i
$827$			13331.2i			0.560546i	0.959920	+	0.280273i	$0.0904250\pi$
$827$			13331.2i			0.560546i	−0.959920	+	0.280273i	$0.909575\pi$
$828$	4053.37			0.170126
$829$	−12646.3			−0.529823			−0.264911	−	0.964273i	$-0.585343\pi$
$829$	−12646.3			−0.529823			−0.264911	+	0.964273i	$0.585343\pi$
$830$		−	17911.7i		−	0.749066i
$831$	−6282.04			−0.262240
$832$	−8399.95	+	24543.0i	−0.350019	+	1.02268i
$833$	−20924.3			−0.870330
$834$		−	7898.19i		−	0.327928i
$835$	−42306.0			−1.75336
$836$	3561.36			0.147335
$837$		−	2022.96i		−	0.0835407i
$838$		−	6077.21i		−	0.250517i
$839$		−	12168.4i		−	0.500714i	−0.968154	−	0.250357i	$-0.919452\pi$
$839$		−	12168.4i		−	0.500714i	0.968154	−	0.250357i	$-0.0805480\pi$
$840$			14927.1i			0.613134i
$841$	3996.24			0.163854
$842$	27430.7			1.12271
$843$			12286.4i			0.501978i
$844$	−87.5169			−0.00356926
$845$	−16407.4	+	21161.8i	−0.667968	+	0.861525i
$846$	3406.13			0.138422
$847$		−	1359.89i		−	0.0551671i
$848$	−16259.7			−0.658445
$849$	10797.8			0.436491
$850$		−	5294.28i		−	0.213638i
$851$			13446.4i			0.541639i
$852$		−	2678.65i		−	0.107710i
$853$			11577.8i			0.464730i	0.972629	+	0.232365i	$0.0746464\pi$
$853$			11577.8i			0.464730i	−0.972629	+	0.232365i	$0.925354\pi$
$854$	−14813.1			−0.593552
$855$	−11357.7			−0.454297
$856$		−	39141.1i		−	1.56287i
$857$	−26946.4			−1.07406			−0.537031	−	0.843562i	$-0.680454\pi$
$857$	−26946.4			−1.07406			−0.537031	+	0.843562i	$0.680454\pi$
$858$	1719.59	−	5024.29i	0.0684217	−	0.199914i
$859$	−25176.5			−1.00001			−0.500007	−	0.866021i	$-0.666669\pi$
$859$	−25176.5			−1.00001			−0.500007	+	0.866021i	$0.666669\pi$
$860$		−	7228.25i		−	0.286606i
$861$	−12415.9			−0.491445
$862$	−8478.63			−0.335016
$863$			40684.8i			1.60478i	0.596800	+	0.802390i	$0.296439\pi$
$863$			40684.8i			1.60478i	−0.596800	+	0.802390i	$0.703561\pi$
$864$		−	16999.5i		−	0.669367i
$865$		−	41874.2i		−	1.64597i
$866$			14855.7i			0.582929i
$867$	−19517.3			−0.764526
$868$	385.164			0.0150614
$869$		−	11247.9i		−	0.439080i
$870$	−21149.7			−0.824186
$871$	−23310.8	−	7978.23i	−0.906838	−	0.310370i
$872$	−13406.4			−0.520640
$873$			4217.90i			0.163521i
$874$	−61787.1			−2.39128
$875$	13896.5			0.536900
$876$			8476.80i			0.326946i
$877$		−	34068.3i		−	1.31175i	−0.754870	−	0.655875i	$-0.772300\pi$
$877$		−	34068.3i		−	1.31175i	0.754870	−	0.655875i	$-0.227700\pi$
$878$		−	14053.2i		−	0.540172i
$879$		−	1402.84i		−	0.0538301i
$880$	4920.34			0.188483
$881$	49161.2			1.88000			0.940001	−	0.341172i	$-0.110824\pi$
$881$	49161.2			1.88000			0.940001	+	0.341172i	$0.110824\pi$
$882$			3746.47i			0.143028i
$883$	4359.88			0.166163			0.0830813	−	0.996543i	$-0.473524\pi$
$883$	4359.88			0.166163			0.0830813	+	0.996543i	$0.473524\pi$
$884$	−3781.74	+	11049.5i	−0.143884	+	0.420401i
$885$	41489.4			1.57588
$886$			21043.0i			0.797915i
$887$	7881.70			0.298356			0.149178	−	0.988810i	$-0.452337\pi$
$887$	7881.70			0.298356			0.149178	+	0.988810i	$0.452337\pi$
$888$	6927.38			0.261788
$889$			29924.8i			1.12896i
$890$		−	37142.6i		−	1.39890i
$891$			5206.55i			0.195764i
$892$		−	7604.94i		−	0.285462i
$893$	24719.1			0.926309
$894$	−20773.2			−0.777137
$895$		−	32420.5i		−	1.21084i
$896$	−4445.16			−0.165739
$897$	14203.5	−	41499.9i	0.528699	−	1.54475i
$898$	−34731.8			−1.29066
$899$			2237.72i			0.0830167i
$900$	451.303			0.0167149
$901$	−42782.1			−1.58188
$902$			6394.54i			0.236047i
$903$		−	11428.3i		−	0.421162i
$904$			35983.4i			1.32388i
$905$			21367.0i			0.784820i
$906$	−4321.88			−0.158482
$907$	−3704.35			−0.135613			−0.0678064	−	0.997698i	$-0.521600\pi$
$907$	−3704.35			−0.135613			−0.0678064	+	0.997698i	$0.521600\pi$
$908$			5616.24i			0.205266i
$909$	−9021.31			−0.329173
$910$	−14141.9	−	4840.13i	−0.515163	−	0.176317i
$911$	193.701			0.00704458			0.00352229	−	0.999994i	$-0.498879\pi$
$911$	193.701			0.00704458			0.00352229	+	0.999994i	$0.498879\pi$
$912$			20372.9i			0.739708i
$913$	6943.91			0.251708
$914$	−3721.43			−0.134676
$915$		−	30528.6i		−	1.10300i
$916$		−	2504.20i		−	0.0903288i
$917$		−	21048.1i		−	0.757981i
$918$			34239.6i			1.23102i
$919$	−13466.4			−0.483370			−0.241685	−	0.970355i	$-0.577700\pi$
$919$	−13466.4			−0.483370			−0.241685	+	0.970355i	$0.577700\pi$
$920$	63500.4			2.27559
$921$			16884.1i			0.604070i
$922$	20738.5			0.740764
$923$	10405.9	+	3561.46i	0.371087	+	0.127007i
$924$	−1411.27			−0.0502462
$925$			1497.12i			0.0532162i
$926$	3586.72			0.127286
$927$	11001.5			0.389793
$928$			18804.2i			0.665169i
$929$		−	18200.2i		−	0.642766i	−0.946949	−	0.321383i	$-0.895852\pi$
$929$		−	18200.2i		−	0.642766i	0.946949	−	0.321383i	$-0.104148\pi$
$930$		−	1667.31i		−	0.0587885i
$931$			27189.0i			0.957126i
$932$	2107.29			0.0740628
$933$	−1019.90			−0.0357878
$934$			8669.77i			0.303730i
$935$	12946.2			0.452821
$936$	8112.29	+	2776.47i	0.283289	+	0.0969571i
$937$	30705.7			1.07055			0.535277	−	0.844676i	$-0.320207\pi$
$937$	30705.7			1.07055			0.535277	+	0.844676i	$0.320207\pi$
$938$		−	13753.2i		−	0.478739i
$939$	11212.9			0.389691
$940$	−6195.57			−0.214976
$941$			4039.04i			0.139924i	0.997550	+	0.0699622i	$0.0222879\pi$
$941$			4039.04i			0.139924i	−0.997550	+	0.0699622i	$0.977712\pi$
$942$		−	20779.9i		−	0.718733i
$943$			52817.9i			1.82395i
$944$			28237.9i			0.973587i
$945$	20863.4			0.718186
$946$	−5885.86			−0.202290
$947$		−	13877.7i		−	0.476203i	−0.971240	−	0.238101i	$-0.923475\pi$
$947$		−	13877.7i		−	0.476203i	0.971240	−	0.238101i	$-0.0765251\pi$
$948$	−11672.9			−0.399914
$949$	−32930.2	−	11270.5i	−1.12641	−	0.385518i
$950$	−6879.39			−0.234944
$951$			25251.4i			0.861023i
$952$	−26731.2			−0.910046
$953$	−18961.1			−0.644500			−0.322250	−	0.946655i	$-0.604439\pi$
$953$	−18961.1			−0.644500			−0.322250	+	0.946655i	$0.604439\pi$
$954$			7660.08i			0.259962i
$955$		−	11990.1i		−	0.406274i
$956$			4248.21i			0.143721i
$957$		−	8199.19i		−	0.276951i
$958$	40071.4			1.35141
$959$	8490.90			0.285908
$960$		−	29842.5i		−	1.00329i
$961$	29614.6			0.994078
$962$	−2246.21	+	6562.98i	−0.0752816	+	0.219957i
$963$	−11801.7			−0.394916
$964$			2681.83i			0.0896016i
$965$	−15554.6			−0.518881
$966$	24484.6			0.815507
$967$		−	5726.54i		−	0.190438i	−0.995456	−	0.0952189i	$-0.969645\pi$
$967$		−	5726.54i		−	0.190438i	0.995456	−	0.0952189i	$-0.0303551\pi$
$968$			2980.38i			0.0989596i
$969$			53604.5i			1.77711i
$970$			16114.8i			0.533418i
$971$	−2318.63			−0.0766306			−0.0383153	−	0.999266i	$-0.512199\pi$
$971$	−2318.63			−0.0766306			−0.0383153	+	0.999266i	$0.512199\pi$
$972$	−5207.78			−0.171851
$973$		−	8618.41i		−	0.283960i
$974$	12860.1			0.423064
$975$	1581.43	−	4620.61i	0.0519448	−	0.151772i
$976$	20778.0			0.681441
$977$		−	23844.8i		−	0.780823i	−0.920641	−	0.390411i	$-0.872333\pi$
$977$		−	23844.8i		−	0.780823i	0.920641	−	0.390411i	$-0.127667\pi$
$978$	31318.3			1.02398
$979$	14399.2			0.470073
$980$		−	6814.63i		−	0.222128i
$981$			4042.25i			0.131559i
$982$		−	11329.6i		−	0.368171i
$983$			17681.1i			0.573691i	0.957977	+	0.286845i	$0.0926066\pi$
$983$			17681.1i			0.573691i	−0.957977	+	0.286845i	$0.907393\pi$
$984$	27211.1			0.881562
$985$	51855.6			1.67742
$986$		−	37874.6i		−	1.22330i
$987$	−9795.55			−0.315902
$988$	14357.7	+	4913.99i	0.462327	+	0.158234i
$989$	−48616.3			−1.56310
$990$		−	2318.01i		−	0.0744153i
$991$	−12887.9			−0.413117			−0.206558	−	0.978434i	$-0.566226\pi$
$991$	−12887.9			−0.413117			−0.206558	+	0.978434i	$0.566226\pi$
$992$	−1482.40			−0.0474459
$993$		−	28070.3i		−	0.897062i
$994$			6139.39i			0.195905i
$995$		−	6783.54i		−	0.216133i
$996$		−	7206.26i		−	0.229256i
$997$	34860.6			1.10737			0.553684	−	0.832727i	$-0.313222\pi$
$997$	34860.6			1.10737			0.553684	+	0.832727i	$0.313222\pi$
$998$	−35297.2			−1.11955
$999$		−	9682.30i		−	0.306641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.b.a.12.12	✓	36
13.5	odd	4		1859.4.a.k.1.7		18
13.8	odd	4		1859.4.a.j.1.12		18
13.12	even	2	inner	143.4.b.a.12.25	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.b.a.12.12	✓	36	1.1	even	1	trivial
143.4.b.a.12.25	yes	36	13.12	even	2	inner
1859.4.a.j.1.12		18	13.8	odd	4
1859.4.a.k.1.7		18	13.5	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)

\(f(q)\)	\(=\)	\(q-2.32803i q^{2} -4.42417 q^{3} +2.58028 q^{4} -12.1881i q^{5} +10.2996i q^{6} +11.2388i q^{7} -24.6312i q^{8} -7.42671 q^{9} +O(q^{10})\)	\(q-2.32803i q^{2} -4.42417 q^{3} +2.58028 q^{4} -12.1881i q^{5} +10.2996i q^{6} +11.2388i q^{7} -24.6312i q^{8} -7.42671 q^{9} -28.3743 q^{10} -11.0000i q^{11} -11.4156 q^{12} +(15.1779 - 44.3467i) q^{13} +26.1642 q^{14} +53.9224i q^{15} -36.6999 q^{16} -96.5636 q^{17} +17.2896i q^{18} +125.475i q^{19} -31.4488i q^{20} -49.7223i q^{21} -25.6083 q^{22} -211.521 q^{23} +108.973i q^{24} -23.5508 q^{25} +(-103.240 - 35.3346i) q^{26} +152.310 q^{27} +28.9992i q^{28} -168.479 q^{29} +125.533 q^{30} -13.2819i q^{31} -111.611i q^{32} +48.6659i q^{33} +224.803i q^{34} +136.980 q^{35} -19.1630 q^{36} -63.5699i q^{37} +292.109 q^{38} +(-67.1496 + 196.197i) q^{39} -300.209 q^{40} -249.705i q^{41} -115.755 q^{42} +229.842 q^{43} -28.3831i q^{44} +90.5177i q^{45} +492.427i q^{46} -197.005i q^{47} +162.367 q^{48} +216.690 q^{49} +54.8269i q^{50} +427.214 q^{51} +(39.1632 - 114.427i) q^{52} +443.046 q^{53} -354.581i q^{54} -134.070 q^{55} +276.825 q^{56} -555.121i q^{57} +392.224i q^{58} -769.428i q^{59} +139.135i q^{60} -566.158 q^{61} -30.9206 q^{62} -83.4672i q^{63} -553.433 q^{64} +(-540.504 - 184.990i) q^{65} +113.296 q^{66} -525.648i q^{67} -249.161 q^{68} +935.805 q^{69} -318.893i q^{70} +234.648i q^{71} +182.929i q^{72} -742.562i q^{73} -147.992 q^{74} +104.193 q^{75} +323.760i q^{76} +123.627 q^{77} +(456.753 + 156.326i) q^{78} +1022.54 q^{79} +447.304i q^{80} -473.323 q^{81} -581.321 q^{82} +631.264i q^{83} -128.298i q^{84} +1176.93i q^{85} -535.078i q^{86} +745.381 q^{87} -270.943 q^{88} +1309.02i q^{89} +210.728 q^{90} +(498.403 + 170.581i) q^{91} -545.783 q^{92} +58.7612i q^{93} -458.633 q^{94} +1529.30 q^{95} +493.787i q^{96} -567.936i q^{97} -504.460i q^{98} +81.6938i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 152 q^{4} + 360 q^{9}+O(q^{10}) \) 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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