LMFDB - Embedded newform 126.4.m.a.41.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,4,Mod(41,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("126.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	126.m (of order $6$, degree $2$, 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:	$7.43424066072$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.21
Character	$\chi$	$=$	126.41
Dual form			126.4.m.a.83.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 - 1.00000i) q^{2} +(2.86447 - 4.33530i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-4.49442 + 7.78456i) q^{5} +(0.626101 - 10.3734i) q^{6} +(-3.72666 - 18.1414i) q^{7} -8.00000i q^{8} +(-10.5897 - 24.8366i) q^{9} +O(q^{10})$	\(q+(1.73205 - 1.00000i) q^{2} +(2.86447 - 4.33530i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-4.49442 + 7.78456i) q^{5} +(0.626101 - 10.3734i) q^{6} +(-3.72666 - 18.1414i) q^{7} -8.00000i q^{8} +(-10.5897 - 24.8366i) q^{9} +17.9777i q^{10} +(57.4672 - 33.1787i) q^{11} +(-9.28899 - 18.5934i) q^{12} +(-42.3739 - 24.4646i) q^{13} +(-24.5962 - 27.6952i) q^{14} +(20.8743 + 41.7833i) q^{15} +(-8.00000 - 13.8564i) q^{16} +18.7313 q^{17} +(-43.1785 - 32.4287i) q^{18} +109.755i q^{19} +(17.9777 + 31.1383i) q^{20} +(-89.3235 - 35.8094i) q^{21} +(66.3574 - 114.934i) q^{22} +(-30.4552 - 17.5833i) q^{23} +(-34.6824 - 22.9157i) q^{24} +(22.1004 + 38.2790i) q^{25} -97.8583 q^{26} +(-138.008 - 25.2344i) q^{27} +(-70.2971 - 23.3734i) q^{28} +(-53.0095 + 30.6051i) q^{29} +(77.9387 + 51.4965i) q^{30} +(289.624 + 167.214i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(20.7732 - 344.177i) q^{33} +(32.4436 - 18.7313i) q^{34} +(157.972 + 52.5249i) q^{35} +(-107.216 - 12.9896i) q^{36} +251.926 q^{37} +(109.755 + 190.101i) q^{38} +(-227.440 + 113.626i) q^{39} +(62.2765 + 35.9554i) q^{40} +(134.377 - 232.749i) q^{41} +(-190.522 + 27.2998i) q^{42} +(69.7048 + 120.732i) q^{43} -265.430i q^{44} +(240.937 + 29.1904i) q^{45} -70.3332 q^{46} +(-57.9089 - 100.301i) q^{47} +(-82.9874 - 5.00881i) q^{48} +(-315.224 + 135.214i) q^{49} +(76.5579 + 44.2007i) q^{50} +(53.6553 - 81.2059i) q^{51} +(-169.495 + 97.8583i) q^{52} +438.701i q^{53} +(-264.271 + 94.3008i) q^{54} +596.476i q^{55} +(-145.132 + 29.8133i) q^{56} +(475.820 + 314.389i) q^{57} +(-61.2101 + 106.019i) q^{58} +(113.087 - 195.872i) q^{59} +(186.490 + 11.2558i) q^{60} +(-469.469 + 271.048i) q^{61} +668.858 q^{62} +(-411.109 + 284.669i) q^{63} -64.0000 q^{64} +(380.892 - 219.908i) q^{65} +(-308.197 - 616.905i) q^{66} +(307.015 - 531.766i) q^{67} +(37.4626 - 64.8872i) q^{68} +(-163.467 + 81.6655i) q^{69} +(326.141 - 66.9967i) q^{70} +116.615i q^{71} +(-198.693 + 84.7173i) q^{72} +352.359i q^{73} +(436.348 - 251.926i) q^{74} +(229.257 + 13.8371i) q^{75} +(380.202 + 219.510i) q^{76} +(-816.070 - 918.892i) q^{77} +(-280.312 + 424.245i) q^{78} +(390.954 + 677.153i) q^{79} +143.821 q^{80} +(-504.718 + 526.023i) q^{81} -537.510i q^{82} +(-122.693 - 212.511i) q^{83} +(-302.694 + 237.807i) q^{84} +(-84.1864 + 145.815i) q^{85} +(241.465 + 139.410i) q^{86} +(-19.1619 + 317.479i) q^{87} +(-265.430 - 459.738i) q^{88} +1642.23 q^{89} +(446.505 - 190.378i) q^{90} +(-285.910 + 859.894i) q^{91} +(-121.821 + 70.3332i) q^{92} +(1554.54 - 776.627i) q^{93} +(-200.602 - 115.818i) q^{94} +(-854.394 - 493.284i) q^{95} +(-148.747 + 74.3119i) q^{96} +(-969.077 + 559.497i) q^{97} +(-410.770 + 549.421i) q^{98} +(-1432.61 - 1075.94i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9}+O(q^{10}) $ 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9	$ 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9} + 24 q^{11} - 132 q^{14} - 120 q^{15} - 384 q^{16} + 120 q^{18} + 180 q^{21} + 348 q^{23} - 600 q^{25} - 96 q^{28} - 84 q^{29} + 192 q^{30} + 96 q^{36} - 672 q^{37} + 1368 q^{39} + 1128 q^{42} + 84 q^{43} - 1008 q^{46} - 42 q^{49} + 456 q^{50} + 2016 q^{51} - 528 q^{56} + 732 q^{57} + 504 q^{58} - 1008 q^{60} - 774 q^{63} - 3072 q^{64} - 6972 q^{65} + 1176 q^{67} + 216 q^{70} - 384 q^{72} + 2520 q^{74} + 1500 q^{77} + 2832 q^{78} + 348 q^{79} + 2268 q^{81} - 1080 q^{84} + 720 q^{85} + 1200 q^{86} + 180 q^{91} + 1392 q^{92} + 5232 q^{93} - 5892 q^{95} + 972 q^{99}+O(q^{100}) $ 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9 + 24 * q^11 - 132 * q^14 - 120 * q^15 - 384 * q^16 + 120 * q^18 + 180 * q^21 + 348 * q^23 - 600 * q^25 - 96 * q^28 - 84 * q^29 + 192 * q^30 + 96 * q^36 - 672 * q^37 + 1368 * q^39 + 1128 * q^42 + 84 * q^43 - 1008 * q^46 - 42 * q^49 + 456 * q^50 + 2016 * q^51 - 528 * q^56 + 732 * q^57 + 504 * q^58 - 1008 * q^60 - 774 * q^63 - 3072 * q^64 - 6972 * q^65 + 1176 * q^67 + 216 * q^70 - 384 * q^72 + 2520 * q^74 + 1500 * q^77 + 2832 * q^78 + 348 * q^79 + 2268 * q^81 - 1080 * q^84 + 720 * q^85 + 1200 * q^86 + 180 * q^91 + 1392 * q^92 + 5232 * q^93 - 5892 * q^95 + 972 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	2.86447	−	4.33530i	0.551267	−	0.834329i
$3$	2.86447	−	4.33530i	0.551267	−	0.834329i
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	−4.49442	+	7.78456i	−0.401993	+	0.696273i	−0.993966	−	0.109685i	$-0.965016\pi$
$5$	−4.49442	+	7.78456i	−0.401993	+	0.696273i	0.591973	+	0.805958i	$0.298349\pi$
$6$	0.626101	−	10.3734i	0.0426008	−	0.705822i
$7$	−3.72666	−	18.1414i	−0.201221	−	0.979546i
$7$	−3.72666	−	18.1414i	−0.201221	−	0.979546i
$8$		−	8.00000i		−	0.353553i
$9$	−10.5897	−	24.8366i	−0.392210	−	0.919876i
$10$			17.9777i			0.568504i
$11$	57.4672	−	33.1787i	1.57518	−	0.909432i	0.579665	−	0.814855i	$-0.303183\pi$
$11$	57.4672	−	33.1787i	1.57518	−	0.909432i	0.995517	−	0.0945776i	$-0.0301501\pi$
$12$	−9.28899	−	18.5934i	−0.223458	−	0.447288i
$13$	−42.3739	−	24.4646i	−0.904031	−	0.521942i	−0.0255249	−	0.999674i	$-0.508126\pi$
$13$	−42.3739	−	24.4646i	−0.904031	−	0.521942i	−0.878506	+	0.477732i	$0.841459\pi$
$14$	−24.5962	−	27.6952i	−0.469544	−	0.528705i
$15$	20.8743	+	41.7833i	0.359315	+	0.719227i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	18.7313			0.267236			0.133618	−	0.991033i	$-0.457340\pi$
$17$	18.7313			0.267236			0.133618	+	0.991033i	$0.457340\pi$
$18$	−43.1785	−	32.4287i	−0.565404	−	0.424640i
$19$			109.755i			1.32524i	0.748958	+	0.662618i	$0.230555\pi$
$19$			109.755i			1.32524i	−0.748958	+	0.662618i	$0.769445\pi$
$20$	17.9777	+	31.1383i	0.200997	+	0.348136i
$21$	−89.3235	−	35.8094i	−0.928190	−	0.372107i
$22$	66.3574	−	114.934i	0.643066	−	1.11382i
$23$	−30.4552	−	17.5833i	−0.276102	−	0.159407i	0.355556	−	0.934655i	$-0.384292\pi$
$23$	−30.4552	−	17.5833i	−0.276102	−	0.159407i	−0.631657	+	0.775248i	$0.717625\pi$
$24$	−34.6824	−	22.9157i	−0.294980	−	0.194902i
$25$	22.1004	+	38.2790i	0.176803	+	0.306232i
$26$	−97.8583			−0.738138
$27$	−138.008	−	25.2344i	−0.983691	−	0.179865i
$28$	−70.2971	−	23.3734i	−0.474461	−	0.157755i
$29$	−53.0095	+	30.6051i	−0.339435	+	0.195973i	−0.660022	−	0.751246i	$-0.729453\pi$
$29$	−53.0095	+	30.6051i	−0.339435	+	0.195973i	0.320587	+	0.947219i	$0.396120\pi$
$30$	77.9387	+	51.4965i	0.474320	+	0.313398i
$31$	289.624	+	167.214i	1.67800	+	0.968794i	0.962934	+	0.269736i	$0.0869365\pi$
$31$	289.624	+	167.214i	1.67800	+	0.968794i	0.715065	+	0.699057i	$0.246397\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	20.7732	−	344.177i	0.109580	−	1.81556i
$34$	32.4436	−	18.7313i	0.163648	−	0.0944822i
$35$	157.972	+	52.5249i	0.762920	+	0.253666i
$36$	−107.216	−	12.9896i	−0.496370	−	0.0601372i
$37$	251.926			1.11936			0.559680	−	0.828709i	$-0.310924\pi$
$37$	251.926			1.11936			0.559680	+	0.828709i	$0.310924\pi$
$38$	109.755	+	190.101i	0.468542	+	0.811538i
$39$	−227.440	+	113.626i	−0.933834	+	0.466529i
$40$	62.2765	+	35.9554i	0.246170	+	0.142126i
$41$	134.377	−	232.749i	0.511859	−	0.886567i	−0.488046	−	0.872818i	$-0.662290\pi$
$41$	134.377	−	232.749i	0.511859	−	0.886567i	0.999905	−	0.0137487i	$-0.00437648\pi$
$42$	−190.522	+	27.2998i	−0.699958	+	0.100297i
$43$	69.7048	+	120.732i	0.247207	+	0.428174i	0.962750	−	0.270394i	$-0.0871540\pi$
$43$	69.7048	+	120.732i	0.247207	+	0.428174i	−0.715543	+	0.698569i	$0.753821\pi$
$44$		−	265.430i		−	0.909432i
$45$	240.937	+	29.1904i	0.798150	+	0.0966989i
$46$	−70.3332			−0.225436
$47$	−57.9089	−	100.301i	−0.179721	−	0.311286i	0.762064	−	0.647502i	$-0.224186\pi$
$47$	−57.9089	−	100.301i	−0.179721	−	0.311286i	−0.941785	+	0.336216i	$0.890853\pi$
$48$	−82.9874	−	5.00881i	−0.249546	−	0.0150616i
$49$	−315.224	+	135.214i	−0.919021	+	0.394210i
$50$	76.5579	+	44.2007i	0.216538	+	0.125019i
$51$	53.6553	−	81.2059i	0.147318	−	0.222963i
$52$	−169.495	+	97.8583i	−0.452015	+	0.260971i
$53$			438.701i			1.13698i	0.822689	+	0.568492i	$0.192473\pi$
$53$			438.701i			1.13698i	−0.822689	+	0.568492i	$0.807527\pi$
$54$	−264.271	+	94.3008i	−0.665977	+	0.237643i
$55$			596.476i			1.46234i
$56$	−145.132	+	29.8133i	−0.346322	+	0.0711422i
$57$	475.820	+	314.389i	1.10568	+	0.730559i
$58$	−61.2101	+	106.019i	−0.138574	+	0.240017i
$59$	113.087	−	195.872i	0.249536	−	0.432209i	−0.713861	−	0.700287i	$-0.753055\pi$
$59$	113.087	−	195.872i	0.249536	−	0.432209i	0.963397	+	0.268078i	$0.0863886\pi$
$60$	186.490	+	11.2558i	0.401263	+	0.0242187i
$61$	−469.469	+	271.048i	−0.985399	+	0.568920i	−0.903896	−	0.427753i	$-0.859305\pi$
$61$	−469.469	+	271.048i	−0.985399	+	0.568920i	−0.0815032	+	0.996673i	$0.525972\pi$
$62$	668.858			1.37008
$63$	−411.109	+	284.669i	−0.822140	+	0.569285i
$64$	−64.0000			−0.125000
$65$	380.892	−	219.908i	0.726828	−	0.419635i
$66$	−308.197	−	616.905i	−0.574794	−	1.15054i
$67$	307.015	−	531.766i	0.559819	−	0.969635i	−0.437692	−	0.899125i	$-0.644204\pi$
$67$	307.015	−	531.766i	0.559819	−	0.969635i	0.997511	−	0.0705100i	$-0.0224627\pi$
$68$	37.4626	−	64.8872i	0.0668090	−	0.115717i
$69$	−163.467	+	81.6655i	−0.285204	+	0.142484i
$70$	326.141	−	66.9967i	0.556876	−	0.114395i
$71$			116.615i			0.194925i	0.995239	+	0.0974625i	$0.0310726\pi$
$71$			116.615i			0.194925i	−0.995239	+	0.0974625i	$0.968927\pi$
$72$	−198.693	+	84.7173i	−0.325225	+	0.138667i
$73$			352.359i			0.564938i	0.959276	+	0.282469i	$0.0911534\pi$
$73$			352.359i			0.564938i	−0.959276	+	0.282469i	$0.908847\pi$
$74$	436.348	−	251.926i	0.685465	−	0.395753i
$75$	229.257	+	13.8371i	0.352964	+	0.0213036i
$76$	380.202	+	219.510i	0.573844	+	0.331309i
$77$	−816.070	−	918.892i	−1.20779	−	1.35997i
$78$	−280.312	+	424.245i	−0.406911	+	0.615850i
$79$	390.954	+	677.153i	0.556782	+	0.964375i	0.997762	+	0.0668582i	$0.0212975\pi$
$79$	390.954	+	677.153i	0.556782	+	0.964375i	−0.440980	+	0.897517i	$0.645369\pi$
$80$	143.821			0.200997
$81$	−504.718	+	526.023i	−0.692343	+	0.721568i
$82$		−	537.510i		−	0.723879i
$83$	−122.693	−	212.511i	−0.162257	−	0.281038i	0.773421	−	0.633893i	$-0.218544\pi$
$83$	−122.693	−	212.511i	−0.162257	−	0.281038i	−0.935678	+	0.352855i	$0.885211\pi$
$84$	−302.694	+	237.807i	−0.393175	+	0.308891i
$85$	−84.1864	+	145.815i	−0.107427	+	0.186069i
$86$	241.465	+	139.410i	0.302765	+	0.174801i
$87$	−19.1619	+	317.479i	−0.0236134	+	0.391234i
$88$	−265.430	−	459.738i	−0.321533	−	0.556911i
$89$	1642.23			1.95592			0.977958	−	0.208803i	$-0.0669566\pi$
$89$	1642.23			1.95592			0.977958	+	0.208803i	$0.0669566\pi$
$90$	446.505	−	190.378i	0.522953	−	0.222973i
$91$	−285.910	+	859.894i	−0.329357	+	0.990565i
$92$	−121.821	+	70.3332i	−0.138051	+	0.0797037i
$93$	1554.54	−	776.627i	1.73332	−	0.865940i
$94$	−200.602	−	115.818i	−0.220112	−	0.127082i
$95$	−854.394	−	493.284i	−0.922726	−	0.532736i
$96$	−148.747	+	74.3119i	−0.158140	+	0.0790045i
$97$	−969.077	+	559.497i	−1.01438	+	0.585652i	−0.912471	−	0.409141i	$-0.865828\pi$
$97$	−969.077	+	559.497i	−1.01438	+	0.585652i	−0.101909	+	0.994794i	$0.532495\pi$
$98$	−410.770	+	549.421i	−0.423409	+	0.566326i
$99$	−1432.61	−	1075.94i	−1.45437	−	1.09228i
$100$	176.803			0.176803
$101$	−763.867	−	1323.06i	−0.752551	−	1.30346i	−0.946583	−	0.322461i	$-0.895490\pi$
$101$	−763.867	−	1323.06i	−0.752551	−	1.30346i	0.194032	−	0.980995i	$-0.437843\pi$
$102$	11.7277	−	194.308i	0.0113845	−	0.188621i
$103$	−1493.11	−	862.049i	−1.42836	−	0.824662i	−0.431366	−	0.902177i	$-0.641968\pi$
$103$	−1493.11	−	862.049i	−1.42836	−	0.824662i	−0.996991	+	0.0775146i	$0.975302\pi$
$104$	−195.717	+	338.991i	−0.184534	+	0.319623i
$105$	680.218	−	534.402i	0.632214	−	0.496689i
$106$	438.701	+	759.852i	0.401985	+	0.696258i
$107$		−	669.357i		−	0.604758i	−0.953188	−	0.302379i	$-0.902219\pi$
$107$		−	669.357i		−	0.604758i	0.953188	−	0.302379i	$-0.0977809\pi$
$108$	−363.431	+	427.605i	−0.323807	+	0.380985i
$109$	−316.634			−0.278239			−0.139120	−	0.990276i	$-0.544427\pi$
$109$	−316.634			−0.278239			−0.139120	+	0.990276i	$0.544427\pi$
$110$	596.476	+	1033.13i	0.517016	+	0.895498i
$111$	721.632	−	1092.17i	0.617066	−	0.933914i
$112$	−221.562	+	196.770i	−0.186925	+	0.166009i
$113$	580.400	+	335.094i	0.483181	+	0.278965i	0.721741	−	0.692163i	$-0.243342\pi$
$113$	580.400	+	335.094i	0.483181	+	0.278965i	−0.238560	+	0.971128i	$0.576675\pi$
$114$	1138.53	+	68.7176i	0.935381	+	0.0564561i
$115$	273.757	−	158.053i	0.221982	−	0.128161i
$116$			244.840i			0.195973i
$117$	−158.893	+	1311.50i	−0.125553	+	1.03631i
$118$		−	452.346i		−	0.352897i
$119$	−69.8052	−	339.813i	−0.0537734	−	0.261770i
$120$	334.266	−	166.994i	0.254285	−	0.127037i
$121$	1536.15	−	2660.69i	1.15413	−	1.99902i
$122$	−542.096	+	938.938i	−0.402287	+	0.696782i
$123$	−624.115	−	1249.27i	−0.457517	−	0.915794i
$124$	1158.50	−	668.858i	0.839000	−	0.484397i
$125$	−1520.92			−1.08828
$126$	−427.392	+	904.171i	−0.302183	+	0.639285i
$127$	−2290.65			−1.60049			−0.800246	−	0.599671i	$-0.795298\pi$
$127$	−2290.65			−1.60049			−0.800246	+	0.599671i	$0.795298\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	723.078	+	43.6423i	0.493515	+	0.0297867i
$130$	439.816	−	761.784i	0.296726	−	0.513945i
$131$	−697.263	+	1207.69i	−0.465039	+	0.805471i	−0.999203	−	0.0399094i	$-0.987293\pi$
$131$	−697.263	+	1207.69i	−0.465039	+	0.805471i	0.534164	+	0.845381i	$0.320626\pi$
$132$	−1150.72	−	760.314i	−0.758766	−	0.501340i
$133$	1991.11	−	409.019i	1.29813	−	0.266665i
$134$		−	1228.06i		−	0.791704i
$135$	816.705	−	960.919i	0.520672	−	0.612613i
$136$		−	149.851i		−	0.0944822i
$137$	1237.96	−	714.737i	0.772016	−	0.445724i	−0.0615774	−	0.998102i	$-0.519613\pi$
$137$	1237.96	−	714.737i	0.772016	−	0.445724i	0.833593	+	0.552379i	$0.186280\pi$
$138$	−201.467	+	304.915i	−0.124275	+	0.188088i
$139$	210.788	+	121.698i	0.128624	+	0.0742612i	0.562932	−	0.826504i	$-0.309673\pi$
$139$	210.788	+	121.698i	0.128624	+	0.0742612i	−0.434307	+	0.900765i	$0.643007\pi$
$140$	497.896	−	442.183i	0.300571	−	0.266938i
$141$	−600.714	−	36.2568i	−0.358789	−	0.0216551i
$142$	116.615	+	201.983i	0.0689164	+	0.119367i
$143$	−3246.81			−1.89868
$144$	−259.429	+	345.428i	−0.150133	+	0.199900i
$145$		−	550.208i		−	0.315119i
$146$	352.359	+	610.303i	0.199736	+	0.345953i
$147$	−316.756	+	1753.91i	−0.177725	+	0.984080i
$148$	503.851	−	872.696i	0.279840	−	0.484697i
$149$	1065.50	+	615.165i	0.585831	+	0.338230i	0.763447	−	0.645870i	$-0.223505\pi$
$149$	1065.50	+	615.165i	0.585831	+	0.338230i	−0.177616	+	0.984100i	$0.556839\pi$
$150$	410.921	−	205.290i	0.223677	−	0.111746i
$151$	837.344	+	1450.32i	0.451272	+	0.781626i	0.998465	−	0.0553802i	$-0.0176371\pi$
$151$	837.344	+	1450.32i	0.451272	+	0.781626i	−0.547193	+	0.837006i	$0.684304\pi$
$152$	878.039			0.468542
$153$	−198.358	−	465.223i	−0.104813	−	0.245824i
$154$	−2332.37	−	775.498i	−1.22044	−	0.405788i
$155$	−2603.38	+	1503.06i	−1.34909	+	0.778897i
$156$	−61.2692	+	1015.13i	−0.0314452	+	0.520994i
$157$	518.343	+	299.266i	0.263492	+	0.152127i	0.625927	−	0.779882i	$-0.284721\pi$
$157$	518.343	+	299.266i	0.263492	+	0.152127i	−0.362434	+	0.932009i	$0.618054\pi$
$158$	1354.31	+	781.908i	0.681916	+	0.393704i
$159$	1901.90	+	1256.64i	0.948619	+	0.626782i
$160$	249.106	−	143.821i	0.123085	−	0.0710630i
$161$	−205.490	+	618.028i	−0.100590	+	0.302530i
$162$	−348.174	+	1415.82i	−0.168859	+	0.686649i
$163$	−1800.96			−0.865414			−0.432707	−	0.901535i	$-0.642441\pi$
$163$	−1800.96			−0.865414			−0.432707	+	0.901535i	$0.642441\pi$
$164$	−537.510	−	930.995i	−0.255930	−	0.443283i
$165$	2585.90	+	1708.59i	1.22007	+	0.806141i
$166$	−425.023	−	245.387i	−0.198724	−	0.114733i
$167$	195.287	−	338.247i	0.0904895	−	0.156732i	−0.817228	−	0.576315i	$-0.804490\pi$
$167$	195.287	−	338.247i	0.0904895	−	0.156732i	0.907717	+	0.419583i	$0.137824\pi$
$168$	−286.475	+	714.588i	−0.131560	+	0.328165i
$169$	98.5300	+	170.659i	0.0448475	+	0.0776782i
$170$			336.746i			0.151925i
$171$	2725.94	−	1162.27i	1.21905	−	0.519770i
$172$	557.639			0.247207
$173$	−510.530	−	884.264i	−0.224364	−	0.388609i	0.731765	−	0.681557i	$-0.238697\pi$
$173$	−510.530	−	884.264i	−0.224364	−	0.388609i	−0.956128	+	0.292948i	$0.905364\pi$
$174$	284.290	+	569.052i	0.123862	+	0.247930i
$175$	612.075	−	543.585i	0.264392	−	0.234807i
$176$	−919.475	−	530.859i	−0.393796	−	0.227358i
$177$	−525.230	−	1051.33i	−0.223043	−	0.446457i
$178$	2844.43	−	1642.23i	1.19775	−	0.691521i
$179$			2447.76i			1.02209i	0.859554	+	0.511045i	$0.170741\pi$
$179$			2447.76i			1.02209i	−0.859554	+	0.511045i	$0.829259\pi$
$180$	582.992	−	776.249i	0.241409	−	0.321434i
$181$		−	676.711i		−	0.277898i	−0.990300	−	0.138949i	$-0.955628\pi$
$181$		−	676.711i		−	0.277898i	0.990300	−	0.138949i	$-0.0443724\pi$
$182$	364.684	+	1775.29i	0.148529	+	0.723040i
$183$	−169.703	+	2811.70i	−0.0685510	+	1.13577i
$184$	−140.666	+	243.641i	−0.0563590	+	0.0976167i
$185$	−1132.26	+	1961.13i	−0.449975	+	0.779379i
$186$	1915.92	−	2899.70i	0.755280	−	1.14310i
$187$	1076.44	−	621.481i	0.420946	−	0.243033i
$188$	−463.271			−0.179721
$189$	56.5208	+	2597.71i	0.0217528	+	0.999763i
$190$	−1973.14			−0.753402
$191$	1970.38	−	1137.60i	0.746450	−	0.430963i	−0.0779596	−	0.996957i	$-0.524841\pi$
$191$	1970.38	−	1137.60i	0.746450	−	0.430963i	0.824410	+	0.565993i	$0.191507\pi$
$192$	−183.326	+	277.459i	−0.0689084	+	0.104291i
$193$	−1135.76	+	1967.19i	−0.423593	+	0.733685i	−0.996288	−	0.0860835i	$-0.972565\pi$
$193$	−1135.76	+	1967.19i	−0.423593	+	0.733685i	0.572694	+	0.819769i	$0.305898\pi$
$194$	−1118.99	+	1938.15i	−0.414119	+	0.717275i
$195$	137.685	−	2281.20i	0.0505631	−	0.837745i
$196$	−162.053	+	1362.40i	−0.0590574	+	0.496500i
$197$			3485.27i			1.26048i	0.776400	+	0.630241i	$0.217044\pi$
$197$			3485.27i			1.26048i	−0.776400	+	0.630241i	$0.782956\pi$
$198$	−3557.29	−	430.979i	−1.27679	−	0.154689i
$199$			1681.87i			0.599119i	0.954078	+	0.299559i	$0.0968397\pi$
$199$			1681.87i			0.599119i	−0.954078	+	0.299559i	$0.903160\pi$
$200$	306.232	−	176.803i	0.108269	−	0.0625093i
$201$	−1425.93	−	2854.23i	−0.500385	−	1.00160i
$202$	−2646.11	−	1527.73i	−0.921682	−	0.532134i
$203$	752.768	+	847.615i	0.260266	+	0.293059i
$204$	−173.995	−	348.279i	−0.0597161	−	0.119531i
$205$	1207.90	+	2092.14i	0.411528	+	0.712787i
$206$	−3448.20			−1.16625
$207$	−114.200	+	942.605i	−0.0383452	+	0.316500i
$208$			782.866i			0.260971i
$209$	3641.52	+	6307.30i	1.20521	+	2.08749i
$210$	643.770	−	1605.83i	0.211544	−	0.527680i
$211$	−524.934	+	909.213i	−0.171270	+	0.296648i	−0.938864	−	0.344288i	$-0.888120\pi$
$211$	−524.934	+	909.213i	−0.171270	+	0.296648i	0.767594	+	0.640936i	$0.221454\pi$
$212$	1519.70	+	877.401i	0.492329	+	0.284246i
$213$	505.562	+	334.040i	0.162632	+	0.107456i
$214$	−669.357	−	1159.36i	−0.213814	−	0.370337i
$215$	−1253.13			−0.397502
$216$	−201.875	+	1104.06i	−0.0635919	+	0.347787i
$217$	1954.18	−	5877.35i	0.611330	−	1.83862i
$218$	−548.427	+	316.634i	−0.170386	+	0.0983724i
$219$	1527.58	+	1009.32i	0.471344	+	0.311432i
$220$	2066.25	+	1192.95i	0.633213	+	0.365586i
$221$	−793.719	−	458.254i	−0.241590	−	0.139482i
$222$	157.731	−	2613.33i	0.0476856	−	0.790069i
$223$	−2044.58	+	1180.44i	−0.613969	+	0.354475i	−0.774517	−	0.632553i	$-0.782007\pi$
$223$	−2044.58	+	1180.44i	−0.613969	+	0.354475i	0.160548	+	0.987028i	$0.448674\pi$
$224$	−186.987	+	562.377i	−0.0557750	+	0.167747i
$225$	716.686	−	954.260i	0.212351	−	0.282744i
$226$	1340.38			0.394515
$227$	−2115.70	−	3664.51i	−0.618609	−	1.07146i	−0.989740	−	0.142881i	$-0.954363\pi$
$227$	−2115.70	−	3664.51i	−0.618609	−	1.07146i	0.371131	−	0.928580i	$-0.378970\pi$
$228$	2040.72	−	1019.51i	0.592762	−	0.296135i
$229$	−1566.76	−	904.568i	−0.452115	−	0.261029i	0.256608	−	0.966516i	$-0.417395\pi$
$229$	−1566.76	−	904.568i	−0.452115	−	0.261029i	−0.708723	+	0.705487i	$0.750728\pi$
$230$	316.107	−	547.513i	0.0906238	−	0.156965i
$231$	−6321.28	+	905.773i	−1.80047	+	0.257989i
$232$	244.840	+	424.076i	0.0692869	+	0.120008i
$233$		−	3054.99i		−	0.858965i	−0.903075	−	0.429483i	$-0.858696\pi$
$233$		−	3054.99i		−	0.858965i	0.903075	−	0.429483i	$-0.141304\pi$
$234$	1036.29	+	2430.47i	0.289505	+	0.678995i
$235$	1041.07			0.288986
$236$	−452.346	−	783.486i	−0.124768	−	0.216104i
$237$	4055.54	+	244.777i	1.11154	+	0.0670885i
$238$	−460.719	−	518.769i	−0.125479	−	0.141289i
$239$	−4054.15	−	2340.67i	−1.09724	−	0.633494i	−0.161748	−	0.986832i	$-0.551713\pi$
$239$	−4054.15	−	2340.67i	−1.09724	−	0.633494i	−0.935496	+	0.353338i	$0.885047\pi$
$240$	411.972	−	623.509i	0.110803	−	0.167697i
$241$	1242.85	−	717.561i	0.332196	−	0.191793i	−0.324620	−	0.945845i	$-0.605236\pi$
$241$	1242.85	−	717.561i	0.332196	−	0.191793i	0.656816	+	0.754051i	$0.271903\pi$
$242$		−	6144.61i		−	1.63219i
$243$	834.722	+	3694.88i	0.220360	+	0.975419i
$244$			2168.38i			0.568920i
$245$	364.168	−	3061.59i	0.0949626	−	0.798358i
$246$	−2330.27	−	1539.68i	−0.603953	−	0.399050i
$247$	2685.10	−	4650.74i	0.691697	−	1.19805i
$248$	1337.72	−	2316.99i	0.342520	−	0.593263i
$249$	−1272.75	−	76.8185i	−0.323925	−	0.0195509i
$250$	−2634.31	+	1520.92i	−0.666433	+	0.384765i
$251$	6180.07			1.55411			0.777057	−	0.629431i	$-0.216712\pi$
$251$	6180.07			1.55411			0.777057	+	0.629431i	$0.216712\pi$
$252$	163.907	+	1993.46i	0.0409728	+	0.498318i
$253$	−2333.56			−0.579881
$254$	−3967.53	+	2290.65i	−0.980098	+	0.565860i
$255$	391.003	+	782.656i	0.0960219	+	0.192203i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	2736.86	−	4740.38i	0.664283	−	1.15057i	−0.315196	−	0.949027i	$-0.602070\pi$
$257$	2736.86	−	4740.38i	0.664283	−	1.15057i	0.979479	−	0.201546i	$-0.0645964\pi$
$258$	1296.05	−	647.487i	0.312746	−	0.156243i
$259$	−938.840	−	4570.29i	−0.225238	−	1.09646i
$260$		−	1759.26i		−	0.419635i
$261$	1321.48	+	992.482i	0.313401	+	0.235376i
$262$			2789.05i			0.657665i
$263$	−3980.72	+	2298.27i	−0.933316	+	0.538850i	−0.887859	−	0.460116i	$-0.847808\pi$
$263$	−3980.72	+	2298.27i	−0.933316	+	0.538850i	−0.0454569	+	0.998966i	$0.514474\pi$
$264$	−2753.41	−	166.186i	−0.641898	−	0.0387425i
$265$	−3415.09	−	1971.70i	−0.791651	−	0.457060i
$266$	3039.69	−	2699.55i	0.700658	−	0.622256i
$267$	4704.13	−	7119.58i	1.07823	−	1.63188i
$268$	−1228.06	−	2127.06i	−0.279910	−	0.484817i
$269$	1598.04			0.362210			0.181105	−	0.983464i	$-0.442033\pi$
$269$	1598.04			0.362210			0.181105	+	0.983464i	$0.442033\pi$
$270$	453.656	−	2481.07i	0.102254	−	0.559233i
$271$		−	233.977i		−	0.0524469i	−0.999656	−	0.0262235i	$-0.991652\pi$
$271$		−	233.977i		−	0.0524469i	0.999656	−	0.0262235i	$-0.00834814\pi$
$272$	−149.851	−	259.549i	−0.0334045	−	0.0578583i
$273$	2908.92	+	3702.64i	0.644894	+	0.820858i
$274$	1429.47	−	2475.92i	0.315174	−	0.545898i
$275$	2540.09	+	1466.52i	0.556994	+	0.321581i
$276$	−44.0357	+	729.596i	−0.00960375	+	0.159118i
$277$	1072.11	+	1856.95i	0.232552	+	0.402791i	0.958558	−	0.284896i	$-0.0919592\pi$
$277$	1072.11	+	1856.95i	0.232552	+	0.402791i	−0.726007	+	0.687688i	$0.758626\pi$
$278$	486.793			0.105021
$279$	1086.03	−	8964.03i	0.233042	−	1.92352i
$280$	420.199	−	1263.78i	0.0896846	−	0.269733i
$281$	7133.55	−	4118.56i	1.51442	−	0.874351i	0.514563	−	0.857453i	$-0.327954\pi$
$281$	7133.55	−	4118.56i	1.51442	−	0.874351i	0.999857	−	0.0168983i	$-0.00537914\pi$
$282$	−1076.72	+	537.915i	−0.227369	+	0.113590i
$283$	5110.18	+	2950.36i	1.07339	+	0.619721i	0.929105	−	0.369816i	$-0.120579\pi$
$283$	5110.18	+	2950.36i	1.07339	+	0.619721i	0.144283	+	0.989537i	$0.453913\pi$
$284$	403.967	+	233.230i	0.0844050	+	0.0487312i
$285$	−4585.92	+	2291.06i	−0.953145	+	0.476177i
$286$	−5623.64	+	3246.81i	−1.16270	+	0.671286i
$287$	−4723.18	−	1570.43i	−0.971429	−	0.322994i
$288$	−103.917	+	857.728i	−0.0212617	+	0.175493i
$289$	−4562.14			−0.928585
$290$	−550.208	−	952.988i	−0.111411	−	0.192970i
$291$	−350.301	+	5803.90i	−0.0705671	+	1.16918i
$292$	1220.61	+	704.718i	0.244625	+	0.141235i
$293$	−938.848	+	1626.13i	−0.187195	+	0.324231i	−0.944314	−	0.329046i	$-0.893273\pi$
$293$	−938.848	+	1626.13i	−0.187195	+	0.324231i	0.757119	+	0.653277i	$0.226606\pi$
$294$	1205.27	+	3354.61i	0.239091	+	0.665459i
$295$	1016.52	+	1760.66i	0.200623	+	0.347490i
$296$		−	2015.40i		−	0.395753i
$297$	−8768.18	+	3128.78i	−1.71307	+	0.611280i
$298$	2460.66			0.478329
$299$	860.335	+	1490.14i	0.166403	+	0.288218i
$300$	506.446	−	766.494i	0.0974656	−	0.147512i
$301$	1930.49	−	1714.47i	0.369673	−	0.328308i
$302$	2900.64	+	1674.69i	0.552693	+	0.319098i
$303$	−7923.92	−	478.258i	−1.50237	−	0.0906772i
$304$	1520.81	−	878.039i	0.286922	−	0.165654i
$305$		−	4872.82i		−	0.914808i
$306$	−808.790	−	607.432i	−0.151096	−	0.113479i
$307$			9599.67i			1.78463i	0.451412	+	0.892316i	$0.350921\pi$
$307$			9599.67i			1.78463i	−0.451412	+	0.892316i	$0.649079\pi$
$308$	−4815.28	+	989.165i	−0.890831	+	0.182996i
$309$	−8014.21	+	4003.78i	−1.47545	+	0.737111i
$310$	−3006.13	+	5206.77i	−0.550763	+	0.953950i
$311$	−0.327604	+	0.567426i	−5.97322e−5	+	0.000103459i	−0.866055	−	0.499948i	$-0.833352\pi$
$311$	−0.327604	+	0.567426i	−5.97322e−5	+	0.000103459i	0.865996	+	0.500052i	$0.166686\pi$
$312$	909.004	+	1819.52i	0.164943	+	0.330160i
$313$	−3460.31	+	1997.81i	−0.624883	+	0.360776i	−0.778768	−	0.627313i	$-0.784155\pi$
$313$	−3460.31	+	1997.81i	−0.624883	+	0.360776i	0.153885	+	0.988089i	$0.450822\pi$
$314$	1197.06			0.215141
$315$	−368.333	−	4479.73i	−0.0658832	−	0.801282i
$316$	3127.63			0.556782
$317$	−3027.91	+	1748.17i	−0.536481	+	0.309738i	−0.743652	−	0.668567i	$-0.766908\pi$
$317$	−3027.91	+	1748.17i	−0.536481	+	0.309738i	0.207171	+	0.978305i	$0.433575\pi$
$318$	4550.83	+	274.671i	0.802509	+	0.0484364i
$319$	−2030.87	+	3517.57i	−0.356448	+	0.617387i
$320$	287.643	−	498.212i	0.0502491	−	0.0870341i
$321$	−2901.86	−	1917.35i	−0.504567	−	0.333383i
$322$	262.108	+	1275.95i	0.0453624	+	0.220825i
$323$			2055.85i			0.354151i
$324$	812.762	+	2800.44i	0.139363	+	0.480185i
$325$		−	2162.70i		−	0.369124i
$326$	−3119.36	+	1800.96i	−0.529956	+	0.305970i
$327$	−906.988	+	1372.70i	−0.153384	+	0.232143i
$328$	−1861.99	−	1075.02i	−0.313449	−	0.180970i
$329$	−1603.80	+	1424.34i	−0.268755	+	0.238682i
$330$	6187.50	+	373.454i	1.03215	+	0.0622969i
$331$	1167.71	+	2022.54i	0.193907	+	0.335857i	0.946542	−	0.322581i	$-0.104551\pi$
$331$	1167.71	+	2022.54i	0.193907	+	0.335857i	−0.752634	+	0.658439i	$0.771217\pi$
$332$	−981.548			−0.162257
$333$	−2667.81	−	6256.99i	−0.439024	−	1.02967i
$334$		−	781.147i		−	0.127971i
$335$	2759.71	+	4779.96i	0.450087	+	0.779573i
$336$	218.399	+	1524.18i	0.0354602	+	0.247472i
$337$	955.521	−	1655.01i	0.154453	−	0.267520i	−0.778407	−	0.627760i	$-0.783972\pi$
$337$	955.521	−	1655.01i	0.154453	−	0.267520i	0.932860	+	0.360240i	$0.117305\pi$
$338$	341.318	+	197.060i	0.0549268	+	0.0317120i
$339$	3115.27	−	1556.34i	0.499110	−	0.249348i
$340$	336.746	+	583.261i	0.0537135	+	0.0930346i
$341$	22191.8			3.52421
$342$	3559.20	−	4739.05i	0.562748	−	0.749293i
$343$	3627.71	+	5214.72i	0.571072	+	0.820900i
$344$	965.858	−	557.639i	0.151383	−	0.0874007i
$345$	98.9574	−	1639.56i	0.0154426	−	0.255857i
$346$	−1768.53	−	1021.06i	−0.274788	−	0.158649i
$347$	297.253	+	171.619i	0.0459866	+	0.0265504i	0.522817	−	0.852445i	$-0.324881\pi$
$347$	297.253	+	171.619i	0.0459866	+	0.0265504i	−0.476830	+	0.878995i	$0.658214\pi$
$348$	1061.46	+	701.337i	0.163506	+	0.108033i
$349$	−3767.94	+	2175.42i	−0.577918	+	0.333661i	−0.760306	−	0.649566i	$-0.774951\pi$
$349$	−3767.94	+	2175.42i	−0.577918	+	0.333661i	0.182388	+	0.983227i	$0.441617\pi$
$350$	516.560	−	1553.59i	0.0788894	−	0.237266i
$351$	5230.59	+	4445.59i	0.795408	+	0.676034i
$352$	−2123.44			−0.321533
$353$	−1617.00	−	2800.73i	−0.243808	−	0.422288i	0.717988	−	0.696056i	$-0.245063\pi$
$353$	−1617.00	−	2800.73i	−0.243808	−	0.422288i	−0.961796	+	0.273768i	$0.911730\pi$
$354$	−1961.06	−	1295.73i	−0.294432	−	0.194540i
$355$	−907.798	−	524.118i	−0.135721	−	0.0783585i
$356$	3284.47	−	5688.87i	0.488979	−	0.846936i
$357$	−1673.15	−	670.757i	−0.248046	−	0.0994404i
$358$	2447.76	+	4239.64i	0.361363	+	0.625899i
$359$			6058.56i			0.890692i	0.895358	+	0.445346i	$0.146919\pi$
$359$			6058.56i			0.890692i	−0.895358	+	0.445346i	$0.853081\pi$
$360$	233.523	−	1927.50i	0.0341882	−	0.282189i
$361$	−5187.12			−0.756250
$362$	−676.711	−	1172.10i	−0.0982518	−	0.170177i
$363$	−7134.65	−	14281.2i	−1.03160	−	2.06492i
$364$	2406.94	+	2710.21i	0.346588	+	0.390257i
$365$	−2742.96	−	1583.65i	−0.393351	−	0.227101i
$366$	2517.76	+	5039.71i	0.359578	+	0.719753i
$367$	7201.91	−	4158.03i	1.02435	−	0.591409i	0.108990	−	0.994043i	$-0.465238\pi$
$367$	7201.91	−	4158.03i	1.02435	−	0.591409i	0.915361	+	0.402634i	$0.131905\pi$
$368$			562.665i			0.0797037i
$369$	−7203.71	−	872.757i	−1.01629	−	0.123127i
$370$			4529.04i			0.636361i
$371$	7958.66	−	1634.89i	1.11373	−	0.228785i
$372$	418.773	−	6938.35i	0.0583665	−	0.967034i
$373$	−431.018	+	746.545i	−0.0598318	+	0.103632i	−0.894390	−	0.447288i	$-0.852390\pi$
$373$	−431.018	+	746.545i	−0.0598318	+	0.103632i	0.834558	+	0.550920i	$0.185723\pi$
$374$	1242.96	−	2152.87i	0.171850	−	0.297654i
$375$	−4356.62	+	6593.64i	−0.599933	+	0.907984i
$376$	−802.409	+	463.271i	−0.110056	+	0.0635409i
$377$	2994.96			0.409146
$378$	2695.60	+	4442.84i	0.366791	+	0.604537i
$379$	9815.25			1.33028			0.665139	−	0.746719i	$-0.268372\pi$
$379$	9815.25			1.33028			0.665139	+	0.746719i	$0.268372\pi$
$380$	−3417.57	+	1973.14i	−0.461363	+	0.266368i
$381$	−6561.50	+	9930.67i	−0.882299	+	1.33534i
$382$	2275.20	−	3940.77i	0.304737	−	0.527820i
$383$	−1352.71	+	2342.96i	−0.180470	+	0.312584i	−0.942041	−	0.335498i	$-0.891095\pi$
$383$	−1352.71	+	2342.96i	−0.180470	+	0.312584i	0.761570	+	0.648082i	$0.224429\pi$
$384$	−40.0705	+	663.899i	−0.00532510	+	0.0882278i
$385$	10820.9	−	2222.86i	1.43243	−	0.294253i
$386$			4543.03i			0.599052i
$387$	2260.43	−	3009.75i	0.296910	−	0.395334i
$388$			4475.97i			0.585652i
$389$	−6056.01	+	3496.44i	−0.789336	+	0.455723i	−0.839729	−	0.543006i	$-0.817286\pi$
$389$	−6056.01	+	3496.44i	−0.789336	+	0.455723i	0.0503926	+	0.998729i	$0.483953\pi$
$390$	−2042.72	−	4088.84i	−0.265224	−	0.530888i
$391$	−570.465	−	329.358i	−0.0737843	−	0.0425994i
$392$	1081.71	+	2521.79i	0.139374	+	0.324923i
$393$	3238.43	+	6482.24i	0.415667	+	0.832025i
$394$	3485.27	+	6036.66i	0.445648	+	0.771884i
$395$	−7028.45			−0.895291
$396$	−6592.38	+	2810.81i	−0.836565	+	0.356688i
$397$		−	22.8921i		−	0.00289400i	−0.999999	−	0.00144700i	$-0.999539\pi$
$397$		−	22.8921i		−	0.00289400i	0.999999	−	0.00144700i	$-0.000460595\pi$
$398$	1681.87	+	2913.09i	0.211821	+	0.366884i
$399$	3930.25	−	9803.68i	0.493130	−	1.23007i
$400$	353.606	−	612.463i	0.0442007	−	0.0765579i
$401$	−10278.3	−	5934.17i	−1.27998	−	0.738998i	−0.303137	−	0.952947i	$-0.598034\pi$
$401$	−10278.3	−	5934.17i	−1.27998	−	0.738998i	−0.976845	+	0.213949i	$0.931367\pi$
$402$	−5324.01	−	3517.74i	−0.660541	−	0.436440i
$403$	−8181.66	−	14171.0i	−1.01131	−	1.75164i
$404$	−6110.94			−0.752551
$405$	−1826.45	−	6293.18i	−0.224091	−	0.772125i
$406$	2151.45	+	715.343i	0.262992	+	0.0874431i
$407$	14477.5	−	8358.56i	1.76320	−	1.01798i
$408$	−649.647	−	429.242i	−0.0788293	−	0.0520849i
$409$	3271.46	+	1888.78i	0.395510	+	0.228348i	0.684545	−	0.728971i	$-0.260001\pi$
$409$	3271.46	+	1888.78i	0.395510	+	0.228348i	−0.289035	+	0.957319i	$0.593334\pi$
$410$	4184.28	+	2415.80i	0.504017	+	0.290994i
$411$	447.498	−	7414.28i	0.0537067	−	0.889828i
$412$	−5972.45	+	3448.20i	−0.714179	+	0.412331i
$413$	−3974.83	−	1321.61i	−0.473580	−	0.157462i
$414$	744.805	+	1746.84i	0.0884182	+	0.207373i
$415$	2205.74			0.260905
$416$	782.866	+	1355.96i	0.0922672	+	0.159812i
$417$	1131.39	−	565.227i	0.132865	−	0.0663772i
$418$	12614.6	+	7283.04i	1.47608	+	0.852214i
$419$	−5522.32	+	9564.93i	−0.643873	+	1.11522i	0.340688	+	0.940177i	$0.389340\pi$
$419$	−5522.32	+	9564.93i	−0.643873	+	1.11522i	−0.984561	+	0.175044i	$0.943993\pi$
$420$	−490.788	−	3425.15i	−0.0570190	−	0.397929i
$421$	−1394.24	−	2414.90i	−0.161404	−	0.279561i	0.773968	−	0.633224i	$-0.218269\pi$
$421$	−1394.24	−	2414.90i	−0.161404	−	0.279561i	−0.935373	+	0.353664i	$0.884936\pi$
$422$			2099.74i			0.242212i
$423$	−1877.91	+	2500.42i	−0.215856	+	0.287410i
$424$	3509.60			0.401985
$425$	413.969	+	717.016i	0.0472481	+	0.0818362i
$426$	1209.70	+	73.0129i	0.137582	+	0.00830396i
$427$	6666.75	+	7506.74i	0.755566	+	0.850765i
$428$	−2318.72	−	1338.71i	−0.261868	−	0.151190i
$429$	−9300.38	+	14075.9i	−1.04668	+	1.58413i
$430$	−2170.49	+	1253.13i	−0.243419	+	0.140538i
$431$			10345.4i			1.15620i	0.815966	+	0.578100i	$0.196206\pi$
$431$			10345.4i			1.15620i	−0.815966	+	0.578100i	$0.803794\pi$
$432$	754.407	+	2114.17i	0.0840195	+	0.235459i
$433$		−	5236.75i		−	0.581206i	−0.956844	−	0.290603i	$-0.906144\pi$
$433$		−	5236.75i		−	0.581206i	0.956844	−	0.290603i	$-0.0938559\pi$
$434$	−2492.60	−	12134.0i	−0.275689	−	1.34206i
$435$	−2385.32	−	1576.05i	−0.262913	−	0.173715i
$436$	−633.268	+	1096.85i	−0.0695598	+	0.120481i
$437$	1929.85	−	3342.60i	0.211252	−	0.365900i
$438$	3655.17	+	220.612i	0.398746	+	0.0240668i
$439$	−5187.63	+	2995.08i	−0.563991	+	0.325621i	−0.754746	−	0.656017i	$-0.772240\pi$
$439$	−5187.63	+	2995.08i	−0.563991	+	0.325621i	0.190755	+	0.981638i	$0.438907\pi$
$440$	4771.81			0.517016
$441$	6696.38	+	6397.24i	0.723073	+	0.690772i
$442$	−1833.01			−0.197257
$443$	−3479.08	+	2008.65i	−0.373129	+	0.215426i	−0.674824	−	0.737978i	$-0.735781\pi$
$443$	−3479.08	+	2008.65i	−0.373129	+	0.215426i	0.301696	+	0.953404i	$0.402447\pi$
$444$	−2340.13	−	4684.15i	−0.250130	−	0.500676i
$445$	−7380.89	+	12784.1i	−0.786265	+	1.36185i
$446$	−2360.88	+	4089.16i	−0.250652	+	0.434142i
$447$	5719.00	−	2857.13i	0.605144	−	0.302321i
$448$	238.506	+	1161.05i	0.0251526	+	0.122443i
$449$			1948.54i			0.204805i	0.994743	+	0.102402i	$0.0326529\pi$
$449$			1948.54i			0.204805i	−0.994743	+	0.102402i	$0.967347\pi$
$450$	287.076	−	2369.51i	0.0300730	−	0.248222i
$451$		−	17833.9i		−	1.86201i
$452$	2321.60	−	1340.38i	0.241590	−	0.139482i
$453$	8686.13	+	524.262i	0.900905	+	0.0543752i
$454$	−7329.01	−	4231.41i	−0.757638	−	0.437422i
$455$	−5408.90	−	6090.41i	−0.557304	−	0.627523i
$456$	2515.11	−	3806.56i	0.258291	−	0.390918i
$457$	−6701.72	−	11607.7i	−0.685980	−	1.18815i	−0.973128	−	0.230266i	$-0.926040\pi$
$457$	−6701.72	−	11607.7i	−0.685980	−	1.18815i	0.287147	−	0.957886i	$-0.407293\pi$
$458$	−3618.27			−0.369150
$459$	−2585.07	−	472.673i	−0.262878	−	0.0480664i
$460$		−	1264.43i		−	0.128161i
$461$	8561.65	+	14829.2i	0.864980	+	1.49819i	0.867067	+	0.498191i	$0.166002\pi$
$461$	8561.65	+	14829.2i	0.864980	+	1.49819i	−0.00208770	+	0.999998i	$0.500665\pi$
$462$	−10043.0	+	7890.12i	−1.01135	+	0.794549i
$463$	6153.89	−	10658.9i	0.617701	−	1.06989i	−0.372203	−	0.928151i	$-0.621397\pi$
$463$	6153.89	−	10658.9i	0.617701	−	1.06989i	0.989904	−	0.141739i	$-0.0452693\pi$
$464$	848.152	+	489.681i	0.0848588	+	0.0489933i
$465$	−941.070	+	15591.9i	−0.0938518	+	1.55496i
$466$	−3054.99	−	5291.39i	−0.303690	−	0.526007i
$467$	−15514.3			−1.53730			−0.768648	−	0.639672i	$-0.779070\pi$
$467$	−15514.3			−1.53730			−0.768648	+	0.639672i	$0.779070\pi$
$468$	4225.37	+	3173.41i	0.417346	+	0.313443i
$469$	−10791.1	−	3587.99i	−1.06245	−	0.353258i
$470$	1803.18	−	1041.07i	0.176967	−	0.102172i
$471$	2782.18	−	1389.94i	0.272179	−	0.135977i
$472$	−1566.97	−	904.692i	−0.152809	−	0.0882242i
$473$	8011.48	+	4625.43i	0.778791	+	0.449635i
$474$	7269.17	−	3631.57i	0.704397	−	0.351906i
$475$	−4201.30	+	2425.62i	−0.405829	+	0.234306i
$476$	−1316.76	−	437.814i	−0.126793	−	0.0421579i
$477$	10895.9	−	4645.69i	1.04588	−	0.445936i
$478$	−9362.66			−0.895896
$479$	−9726.27	−	16846.4i	−0.927776	−	1.60695i	−0.787035	−	0.616908i	$-0.788385\pi$
$479$	−9726.27	−	16846.4i	−0.927776	−	1.60695i	−0.140741	−	0.990047i	$-0.544948\pi$
$480$	90.0468	−	1491.92i	0.00856261	−	0.141868i
$481$	−10675.1	−	6163.25i	−1.01194	−	0.584241i
$482$	1435.12	−	2485.71i	0.135618	−	0.234898i
$483$	2090.71	+	2661.18i	0.196958	+	0.250700i
$484$	−6144.61	−	10642.8i	−0.577067	−	0.999509i
$485$		−	10058.5i		−	0.941713i
$486$	5140.66	+	5565.00i	0.479805	+	0.519411i
$487$	20747.4			1.93050			0.965250	−	0.261329i	$-0.0841607\pi$
$487$	20747.4			1.93050			0.965250	+	0.261329i	$0.0841607\pi$
$488$	2168.38	+	3755.75i	0.201144	+	0.348391i
$489$	−5158.80	+	7807.72i	−0.477074	+	0.722040i
$490$	−2430.83	−	5667.00i	−0.224110	−	0.522467i
$491$	342.738	+	197.880i	0.0315022	+	0.0181878i	0.515668	−	0.856788i	$-0.327544\pi$
$491$	342.738	+	197.880i	0.0315022	+	0.0181878i	−0.484166	+	0.874976i	$0.660877\pi$
$492$	−5575.82	−	336.536i	−0.510930	−	0.0308378i
$493$	−992.939	+	573.273i	−0.0907093	+	0.0523711i
$494$		−	10740.4i		−	0.978207i
$495$	14814.5	−	6316.48i	1.34517	−	0.573545i
$496$		−	5350.86i		−	0.484397i
$497$	2115.57	−	434.585i	0.190938	−	0.0392229i
$498$	−2281.29	+	1139.70i	−0.205275	+	0.102552i
$499$	−10146.7	+	17574.6i	−0.910278	+	1.57665i	−0.0966055	+	0.995323i	$0.530799\pi$
$499$	−10146.7	+	17574.6i	−0.910278	+	1.57665i	−0.813672	+	0.581324i	$0.802535\pi$
$500$	−3041.84	+	5268.62i	−0.272070	+	0.471239i
$501$	−907.008	−	1815.52i	−0.0808825	−	0.161899i
$502$	10704.2	−	6180.07i	0.951696	−	0.549462i
$503$	9434.59			0.836318			0.418159	−	0.908374i	$-0.362676\pi$
$503$	9434.59			0.836318			0.418159	+	0.908374i	$0.362676\pi$
$504$	2277.36	+	3288.87i	0.201273	+	0.290670i
$505$	13732.6			1.21008
$506$	−4041.85	+	2333.56i	−0.355103	+	0.205019i
$507$	1022.09	+	61.6897i	0.0895321	+	0.00540382i
$508$	−4581.31	+	7935.05i	−0.400123	+	0.693034i
$509$	−1055.39	+	1828.00i	−0.0919048	+	0.159184i	−0.908313	−	0.418292i	$-0.862629\pi$
$509$	−1055.39	+	1828.00i	−0.0919048	+	0.159184i	0.816408	+	0.577476i	$0.195962\pi$
$510$	1459.89	+	964.597i	0.126755	+	0.0837511i
$511$	6392.30	−	1313.12i	0.553383	−	0.113677i
$512$			512.000i			0.0441942i
$513$	2769.59	−	15147.1i	0.238364	−	1.30362i
$514$		−	10947.4i		−	0.939438i
$515$	13421.4	−	7748.82i	1.14838	−	0.663017i
$516$	1597.34	−	2417.53i	0.136277	−	0.206252i
$517$	−6655.72	−	3842.68i	−0.566186	−	0.326888i
$518$	−6196.41	−	6977.14i	−0.525588	−	0.591811i
$519$	−5295.95	−	319.643i	−0.447912	−	0.0270343i
$520$	−1759.26	−	3047.14i	−0.148363	−	0.256973i
$521$	−2781.94			−0.233933			−0.116967	−	0.993136i	$-0.537317\pi$
$521$	−2781.94			−0.233933			−0.116967	+	0.993136i	$0.537317\pi$
$522$	3281.35	+	397.548i	0.275136	+	0.0333338i
$523$			16345.8i			1.36664i	0.730119	+	0.683320i	$0.239464\pi$
$523$			16345.8i			1.36664i	−0.730119	+	0.683320i	$0.760536\pi$
$524$	2789.05	+	4830.78i	0.232520	+	0.402736i
$525$	−603.336	−	4210.61i	−0.0501557	−	0.350031i
$526$	−4596.54	+	7961.45i	−0.381024	+	0.659954i
$527$	5425.04	+	3132.15i	0.448422	+	0.258897i
$528$	−4935.24	+	2465.57i	−0.406778	+	0.203220i
$529$	−5465.16	−	9465.93i	−0.449179	−	0.778000i
$530$	−7886.82			−0.646380
$531$	−6062.34	−	734.476i	−0.495449	−	0.0600255i
$532$	2565.34	−	7715.45i	0.209063	−	0.628773i
$533$	−11388.2	+	6574.97i	−0.925473	+	0.534322i
$534$	1028.20	−	17035.6i	0.0833235	−	1.38053i
$535$	5210.65	+	3008.37i	0.421077	+	0.243109i
$536$	−4254.13	−	2456.12i	−0.342818	−	0.197926i
$537$	10611.8	+	7011.52i	0.852759	+	0.563444i
$538$	2767.89	−	1598.04i	0.221807	−	0.128060i
$539$	−13628.8	+	18229.1i	−1.08912	+	1.45674i
$540$	−1695.31	−	4750.99i	−0.135101	−	0.378611i
$541$	−4367.39			−0.347077			−0.173539	−	0.984827i	$-0.555520\pi$
$541$	−4367.39			−0.347077			−0.173539	+	0.984827i	$0.555520\pi$
$542$	−233.977	−	405.261i	−0.0185428	−	0.0321170i
$543$	−2933.75	−	1938.42i	−0.231858	−	0.153196i
$544$	−519.098	−	299.701i	−0.0409120	−	0.0236206i
$545$	1423.09	−	2464.86i	0.111850	−	0.193730i
$546$	8741.04	+	3504.24i	0.685132	+	0.274666i
$547$	−1279.61	−	2216.36i	−0.100023	−	0.173244i	0.811671	−	0.584115i	$-0.198558\pi$
$547$	−1279.61	−	2216.36i	−0.100023	−	0.173244i	−0.911694	+	0.410870i	$0.865225\pi$
$548$		−	5717.90i		−	0.445724i
$549$	11703.4	+	8789.73i	0.909819	+	0.683309i
$550$	5866.09			0.454784
$551$	−3359.05	−	5818.05i	−0.259710	−	0.449832i
$552$	653.324	+	1307.73i	0.0503756	+	0.100835i
$553$	10827.6	−	9615.99i	0.832614	−	0.739446i
$554$	3713.90	+	2144.22i	0.284816	+	0.164439i
$555$	5258.77	+	10526.3i	0.402203	+	0.805073i
$556$	843.150	−	486.793i	0.0643121	−	0.0371306i
$557$			11605.3i			0.882823i	0.897305	+	0.441411i	$0.145522\pi$
$557$			11605.3i			0.882823i	−0.897305	+	0.441411i	$0.854478\pi$
$558$	−7082.98	−	16612.2i	−0.537359	−	1.26030i
$559$		−	6821.19i		−	0.516110i
$560$	−535.973	−	2609.13i	−0.0404447	−	0.196885i
$561$	389.110	−	6446.89i	0.0292838	−	0.485183i
$562$	8237.12	−	14267.1i	0.618259	−	1.07086i
$563$	147.052	−	254.701i	0.0110080	−	0.0190664i	−0.860469	−	0.509503i	$-0.829829\pi$
$563$	147.052	−	254.701i	0.0110080	−	0.0190664i	0.871477	+	0.490437i	$0.163163\pi$
$564$	−1327.02	+	2008.42i	−0.0990741	+	0.149946i
$565$	−5217.12	+	3012.11i	−0.388471	+	0.224284i
$566$	11801.5			0.876418
$567$	11423.7	+	7196.01i	0.846123	+	0.532987i
$568$	932.921			0.0689164
$569$	−6601.43	+	3811.34i	−0.486373	+	0.280808i	−0.723069	−	0.690776i	$-0.757269\pi$
$569$	−6601.43	+	3811.34i	−0.486373	+	0.280808i	0.236695	+	0.971584i	$0.423936\pi$
$570$	−5651.99	+	8554.14i	−0.415326	+	0.628585i
$571$	−2212.29	+	3831.80i	−0.162139	+	0.280834i	−0.935636	−	0.352967i	$-0.885173\pi$
$571$	−2212.29	+	3831.80i	−0.162139	+	0.280834i	0.773496	+	0.633801i	$0.218506\pi$
$572$	−6493.62	+	11247.3i	−0.474671	+	0.822155i
$573$	712.254	−	11800.8i	0.0519281	−	0.860361i
$574$	−9751.21	+	2003.12i	−0.709072	+	0.145659i
$575$		−	1554.39i		−	0.112735i
$576$	677.738	+	1589.55i	0.0490262	+	0.114984i
$577$		−	21320.1i		−	1.53825i	−0.639099	−	0.769124i	$-0.720693\pi$
$577$		−	21320.1i		−	1.53825i	0.639099	−	0.769124i	$-0.279307\pi$
$578$	−7901.85	+	4562.14i	−0.568640	+	0.328304i
$579$	5275.01	+	10558.8i	0.378622	+	0.757873i
$580$	−1905.98	−	1100.42i	−0.136451	−	0.0787798i
$581$	−3398.03	+	3017.79i	−0.242640	+	0.215489i
$582$	5197.16	+	10402.9i	0.370153	+	0.740921i
$583$	14555.5	+	25210.9i	1.03401	+	1.79096i
$584$	2818.87			0.199736
$585$	−9495.30	−	7131.33i	−0.671081	−	0.504007i
$586$			3755.39i			0.264734i
$587$	−7958.62	−	13784.7i	−0.559604	−	0.969262i	−0.997529	−	0.0702508i	$-0.977620\pi$
$587$	−7958.62	−	13784.7i	−0.559604	−	0.969262i	0.437926	−	0.899011i	$-0.355713\pi$
$588$	5442.20	+	4605.09i	0.381688	+	0.322977i
$589$	−18352.6	+	31787.6i	−1.28388	+	2.22375i
$590$	3521.32	+	2033.03i	0.245712	+	0.141862i
$591$	15109.7	+	9983.43i	1.05166	+	0.694862i
$592$	−2015.40	−	3490.78i	−0.139920	−	0.242348i
$593$	−10320.7			−0.714702			−0.357351	−	0.933970i	$-0.616320\pi$
$593$	−10320.7			−0.714702			−0.357351	+	0.933970i	$0.616320\pi$
$594$	−12058.2	+	14187.4i	−0.832916	+	0.979992i
$595$	2959.03	+	983.861i	0.203880	+	0.0677888i
$596$	4261.99	−	2460.66i	0.292916	−	0.169115i
$597$	7291.42	+	4817.66i	0.499862	+	0.330274i
$598$	2980.29	+	1720.67i	0.203801	+	0.117665i
$599$	−14115.3	−	8149.48i	−0.962832	−	0.555891i	−0.0657884	−	0.997834i	$-0.520956\pi$
$599$	−14115.3	−	8149.48i	−0.962832	−	0.555891i	−0.897043	+	0.441942i	$0.854290\pi$
$600$	110.696	−	1834.05i	0.00753194	−	0.124791i
$601$	−10634.4	+	6139.76i	−0.721772	+	0.416715i	−0.815405	−	0.578891i	$-0.803485\pi$
$601$	−10634.4	+	6139.76i	−0.721772	+	0.416715i	0.0936324	+	0.995607i	$0.470152\pi$
$602$	1629.24	−	4900.05i	0.110304	−	0.331746i
$603$	−16458.5	−	1994.01i	−1.11151	−	0.134664i
$604$	6698.75			0.451272
$605$	13808.2	+	23916.6i	0.927908	+	1.60718i
$606$	−14202.9	+	7095.55i	−0.952067	+	0.475639i
$607$	−16715.3	−	9650.56i	−1.11771	−	0.645312i	−0.176896	−	0.984229i	$-0.556606\pi$
$607$	−16715.3	−	9650.56i	−1.11771	−	0.645312i	−0.940816	+	0.338918i	$0.889939\pi$
$608$	1756.08	−	3041.61i	0.117135	−	0.202884i
$609$	5830.94	−	835.513i	0.387983	−	0.0555939i
$610$	−4872.82	−	8439.96i	−0.323434	−	0.560203i
$611$			5666.86i			0.375216i
$612$	−2008.30	−	243.313i	−0.132648	−	0.0160708i
$613$	6168.41			0.406427			0.203214	−	0.979134i	$-0.434861\pi$
$613$	6168.41			0.406427			0.203214	+	0.979134i	$0.434861\pi$
$614$	9599.67	+	16627.1i	0.630963	+	1.09286i
$615$	12530.0	+	756.266i	0.821561	+	0.0495863i
$616$	−7351.14	+	6528.56i	−0.480821	+	0.427018i
$617$	1923.21	+	1110.37i	0.125487	+	0.0724500i	0.561430	−	0.827525i	$-0.310252\pi$
$617$	1923.21	+	1110.37i	0.125487	+	0.0724500i	−0.435942	+	0.899975i	$0.643585\pi$
$618$	−9877.24	+	14949.0i	−0.642914	+	0.973035i
$619$	−4974.55	+	2872.06i	−0.323011	+	0.186491i	−0.652734	−	0.757587i	$-0.726378\pi$
$619$	−4974.55	+	2872.06i	−0.323011	+	0.186491i	0.329723	+	0.944078i	$0.393045\pi$
$620$			12024.5i			0.778897i
$621$	3759.35	+	3195.15i	0.242927	+	0.206469i
$622$			1.31041i			8.44740e-5i
$623$	−6120.04	−	29792.5i	−0.393570	−	1.91591i
$624$	3393.96	+	2242.49i	0.217736	+	0.143865i
$625$	4073.10	−	7054.82i	0.260679	−	0.451508i
$626$	−3995.62	+	6920.62i	−0.255107	+	0.441859i
$627$	37775.1	+	2279.96i	2.40605	+	0.145220i
$628$	2073.37	−	1197.06i	0.131746	−	0.0760637i
$629$	4718.90			0.299133
$630$	−5117.70	−	7390.78i	−0.323641	−	0.467390i
$631$	−24057.5			−1.51777			−0.758885	−	0.651225i	$-0.774256\pi$
$631$	−24057.5			−1.51777			−0.758885	+	0.651225i	$0.774256\pi$
$632$	5417.22	−	3127.63i	0.340958	−	0.196852i
$633$	2438.05	+	4880.16i	0.153087	+	0.306428i
$634$	−3496.33	+	6055.82i	−0.219017	+	0.379349i
$635$	10295.2	−	17831.7i	0.643387	−	1.11438i
$636$	8156.94	−	4075.08i	0.508559	−	0.254069i
$637$	16665.2	+	1982.28i	1.03658	+	0.123298i
$638$			8123.49i			0.504094i
$639$	2896.33	−	1234.92i	0.179307	−	0.0764515i
$640$		−	1150.57i		−	0.0710630i
$641$	11837.8	−	6834.54i	0.729429	−	0.421136i	−0.0887844	−	0.996051i	$-0.528298\pi$
$641$	11837.8	−	6834.54i	0.729429	−	0.421136i	0.818213	+	0.574915i	$0.194965\pi$
$642$	−6943.52	−	419.085i	−0.426852	−	0.0257632i
$643$	20421.6	+	11790.4i	1.25249	+	0.723124i	0.971603	−	0.236617i	$-0.0760388\pi$
$643$	20421.6	+	11790.4i	1.25249	+	0.723124i	0.280885	+	0.959741i	$0.409372\pi$
$644$	1729.93	+	1947.89i	0.105852	+	0.119189i
$645$	−3589.55	+	5432.70i	−0.219129	+	0.331647i
$646$	2055.85	+	3560.84i	0.125211	+	0.216872i
$647$	25891.5			1.57326			0.786629	−	0.617425i	$-0.211824\pi$
$647$	25891.5			1.57326			0.786629	+	0.617425i	$0.211824\pi$
$648$	4208.19	+	4037.74i	0.255113	+	0.244780i
$649$		−	15008.3i		−	0.907744i
$650$	−2162.70	−	3745.91i	−0.130505	−	0.226041i
$651$	−19882.4	−	25307.4i	−1.19701	−	1.52362i
$652$	−3601.93	+	6238.72i	−0.216353	+	0.374735i
$653$	15330.2	+	8850.89i	0.918708	+	0.530416i	0.883223	−	0.468954i	$-0.155369\pi$
$653$	15330.2	+	8850.89i	0.918708	+	0.530416i	0.0354854	+	0.999370i	$0.488702\pi$
$654$	−198.245	+	3284.58i	−0.0118532	+	0.196387i
$655$	−6267.58	−	10855.8i	−0.373885	−	0.647588i
$656$	−4300.08			−0.255930
$657$	8751.41	−	3731.36i	0.519673	−	0.221574i
$658$	−1353.53	+	4070.83i	−0.0801914	+	0.241181i
$659$	−16234.0	+	9372.72i	−0.959618	+	0.554036i	−0.896055	−	0.443942i	$-0.853580\pi$
$659$	−16234.0	+	9372.72i	−0.959618	+	0.554036i	−0.0635624	+	0.997978i	$0.520246\pi$
$660$	11090.5	−	5540.66i	0.654088	−	0.326773i
$661$	−10069.2	−	5813.43i	−0.592504	−	0.342082i	0.173583	−	0.984819i	$-0.444465\pi$
$661$	−10069.2	−	5813.43i	−0.592504	−	0.342082i	−0.766087	+	0.642737i	$0.777799\pi$
$662$	4045.08	+	2335.43i	0.237487	+	0.137113i
$663$	−4260.25	+	2128.36i	−0.249554	+	0.124673i
$664$	−1700.09	+	981.548i	−0.0993619	+	0.0573666i
$665$	−5764.86	+	17338.2i	−0.336168	+	1.01105i
$666$	−10877.8	−	8169.61i	−0.632890	−	0.475324i
$667$	2152.55			0.124958
$668$	−781.147	−	1352.99i	−0.0452447	−	0.0783662i
$669$	−739.074	+	12245.2i	−0.0427119	+	0.707663i
$670$	9559.92	+	5519.42i	0.551242	+	0.318259i
$671$	−17986.0	+	31152.7i	−1.03479	+	1.79231i
$672$	1902.46	+	2421.55i	0.109210	+	0.139008i
$673$	−2240.43	−	3880.53i	−0.128324	−	0.222264i	0.794703	−	0.606998i	$-0.207626\pi$
$673$	−2240.43	−	3880.53i	−0.128324	−	0.222264i	−0.923027	+	0.384734i	$0.874293\pi$
$674$		−	3822.08i		−	0.218429i
$675$	−2084.08	−	5840.49i	−0.118839	−	0.333038i
$676$	788.240			0.0448475
$677$	−6548.02	−	11341.5i	−0.371730	−	0.643855i	0.618102	−	0.786098i	$-0.287902\pi$
$677$	−6548.02	−	11341.5i	−0.371730	−	0.643855i	−0.989832	+	0.142243i	$0.954568\pi$
$678$	3839.46	−	5810.93i	0.217483	−	0.329156i
$679$	13761.5	+	15495.4i	0.777788	+	0.875786i
$680$	1166.52	+	673.492i	0.0657854	+	0.0379812i
$681$	−21947.1	−	1324.64i	−1.23497	−	0.0745381i
$682$	38437.4	−	22191.8i	2.15813	−	1.24600i
$683$		−	12353.9i		−	0.692109i	−0.938214	−	0.346054i	$-0.887521\pi$
$683$		−	12353.9i		−	0.692109i	0.938214	−	0.346054i	$-0.112479\pi$
$684$	1425.67	−	11767.5i	0.0796959	−	0.657808i
$685$			12849.3i			0.716711i
$686$	11498.1	+	5404.46i	0.639941	+	0.300792i
$687$	−8409.50	+	4201.26i	−0.467019	+	0.233316i
$688$	1115.28	−	1931.72i	0.0618017	−	0.107044i
$689$	10732.6	−	18589.4i	0.593440	−	1.02787i
$690$	−1468.16	−	2938.75i	−0.0810026	−	0.162140i
$691$	−10460.0	+	6039.10i	−0.575858	+	0.332472i	−0.759486	−	0.650524i	$-0.774549\pi$
$691$	−10460.0	+	6039.10i	−0.575858	+	0.332472i	0.183627	+	0.982996i	$0.441216\pi$
$692$	−4084.24			−0.224364
$693$	−14180.3	+	29999.2i	−0.777294	+	1.64441i
$694$	686.476			0.0375479
$695$	−1894.74	+	1093.93i	−0.103412	+	0.0597050i
$696$	2539.84	+	153.295i	0.138322	+	0.00834860i
$697$	2517.07	−	4359.69i	0.136787	−	0.236923i
$698$	−4350.85	+	7535.89i	−0.235934	+	0.408650i
$699$	−13244.3	−	8750.91i	−0.716659	−	0.473519i
$700$	−658.884	−	3207.46i	−0.0355764	−	0.173187i
$701$		−	14395.9i		−	0.775645i	−0.921734	−	0.387822i	$-0.873227\pi$
$701$		−	14395.9i		−	0.775645i	0.921734	−	0.387822i	$-0.126773\pi$
$702$	13505.2	+	2469.39i	0.726100	+	0.132765i
$703$			27650.0i			1.48342i
$704$	−3677.90	+	2123.44i	−0.196898	+	0.113679i
$705$	2982.10	−	4513.34i	0.159309	−	0.241110i
$706$	−5601.45	−	3234.00i	−0.298603	−	0.172398i
$707$	−21155.5	+	18788.2i	−1.12537	+	0.999440i
$708$	−4692.38	−	283.214i	−0.249083	−	0.0150337i
$709$	−14380.2	−	24907.2i	−0.761719	−	1.31934i	−0.941964	−	0.335715i	$-0.891022\pi$
$709$	−14380.2	−	24907.2i	−0.761719	−	1.31934i	0.180244	−	0.983622i	$-0.442311\pi$
$710$	−2096.47			−0.110816
$711$	12678.1	−	16880.8i	0.668730	−	0.890408i
$712$		−	13137.9i		−	0.691521i
$713$	−5880.36	−	10185.1i	−0.308866	−	0.534971i
$714$	−3568.73	+	511.362i	−0.187054	+	0.0268029i
$715$	14592.5	−	25275.0i	0.763258	−	1.32200i
$716$	8479.28	+	4895.51i	0.442578	+	0.255522i
$717$	−21760.5	+	10871.2i	−1.13342	+	0.566238i
$718$	6058.56	+	10493.7i	0.314907	+	0.545435i
$719$	12676.1			0.657493			0.328746	−	0.944418i	$-0.393374\pi$
$719$	12676.1			0.657493			0.328746	+	0.944418i	$0.393374\pi$
$720$	−1523.02	−	3572.04i	−0.0788328	−	0.184892i
$721$	−10074.5	+	30299.8i	−0.520380	+	1.56508i
$722$	−8984.36	+	5187.12i	−0.463107	+	0.267375i
$723$	449.266	−	7443.57i	0.0231098	−	0.382890i
$724$	−2344.20	−	1353.42i	−0.120333	−	0.0694745i
$725$	−2343.06	−	1352.77i	−0.120026	−	0.0692972i
$726$	−26638.7	−	17601.0i	−1.36179	−	0.899773i
$727$	−12063.6	+	6964.93i	−0.615426	+	0.355316i	−0.775086	−	0.631856i	$-0.782294\pi$
$727$	−12063.6	+	6964.93i	−0.615426	+	0.355316i	0.159660	+	0.987172i	$0.448960\pi$
$728$	6879.15	+	2287.28i	0.350218	+	0.116445i
$729$	18409.5	+	6965.09i	0.935297	+	0.353863i
$730$	−6334.59			−0.321170
$731$	1305.66	+	2261.48i	0.0660625	+	0.114424i
$732$	9400.60	+	6211.26i	0.474667	+	0.313627i
$733$	−868.392	−	501.367i	−0.0437583	−	0.0252638i	0.477961	−	0.878381i	$-0.341376\pi$
$733$	−868.392	−	501.367i	−0.0437583	−	0.0252638i	−0.521720	+	0.853117i	$0.674709\pi$
$734$	8316.05	−	14403.8i	0.418190	−	0.724325i
$735$	−12229.8	−	10348.6i	−0.613744	−	0.519339i
$736$	562.665	+	974.565i	0.0281795	+	0.0488084i
$737$		−	40745.5i		−	2.03647i
$738$	−13349.9	+	5692.05i	−0.665878	+	0.283912i
$739$	25136.6			1.25124			0.625619	−	0.780129i	$-0.284847\pi$
$739$	25136.6			1.25124			0.625619	+	0.780129i	$0.284847\pi$
$740$	4529.04	+	7844.52i	0.224987	+	0.389690i
$741$	−12471.0	−	24962.6i	−0.618262	−	1.23755i
$742$	12149.9	−	10790.4i	0.601129	−	0.533864i
$743$	−20262.2	−	11698.4i	−1.00047	−	0.577620i	−0.0920810	−	0.995752i	$-0.529352\pi$
$743$	−20262.2	−	11698.4i	−1.00047	−	0.577620i	−0.908387	+	0.418131i	$0.862685\pi$
$744$	−6213.01	−	12436.3i	−0.306156	−	0.612821i
$745$	−9577.58	+	5529.62i	−0.471000	+	0.271932i
$746$			1724.07i			0.0846150i
$747$	−3978.79	+	5297.72i	−0.194881	+	0.259482i
$748$		−	4971.85i		−	0.243033i
$749$	−12143.1	+	2494.46i	−0.592389	+	0.121690i
$750$	−952.249	+	15777.1i	−0.0463616	+	0.768133i
$751$	13579.4	−	23520.2i	0.659811	−	1.14283i	−0.320853	−	0.947129i	$-0.603970\pi$
$751$	13579.4	−	23520.2i	0.659811	−	1.14283i	0.980664	−	0.195697i	$-0.0626971\pi$
$752$	−926.542	+	1604.82i	−0.0449302	+	0.0778214i
$753$	17702.6	−	26792.5i	0.856731	−	1.29664i
$754$	5187.42	−	2994.96i	0.250550	−	0.144655i
$755$	−15053.5			−0.725633
$756$	9111.76	+	4999.62i	0.438348	+	0.240522i
$757$	20937.2			1.00525			0.502626	−	0.864504i	$-0.332367\pi$
$757$	20937.2			1.00525			0.502626	+	0.864504i	$0.332367\pi$
$758$	17000.5	−	9815.25i	0.814626	−	0.470325i
$759$	−6684.41	+	10116.7i	−0.319669	+	0.483811i
$760$	−3946.27	+	6835.15i	−0.188351	+	0.326233i
$761$	11543.8	−	19994.5i	0.549885	−	0.952429i	−0.448397	−	0.893835i	$-0.648005\pi$
$761$	11543.8	−	19994.5i	0.549885	−	0.952429i	0.998282	−	0.0585944i	$-0.0186619\pi$
$762$	−1434.18	+	23761.9i	−0.0681822	+	1.12966i
$763$	1179.99	+	5744.20i	0.0559874	+	0.272548i
$764$		−	9100.81i		−	0.430963i
$765$	4513.07	+	546.775i	0.213294	+	0.0258414i
$766$			5410.83i			0.255224i
$767$	−9583.83	+	5533.23i	−0.451176	+	0.260487i
$768$	594.495	+	1189.98i	0.0279323	+	0.0559110i
$769$	18738.6	+	10818.8i	0.878716	+	0.507327i	0.870235	−	0.492637i	$-0.163967\pi$
$769$	18738.6	+	10818.8i	0.878716	+	0.507327i	0.00848126	+	0.999964i	$0.497300\pi$
$770$	16519.6	−	14671.0i	0.773147	−	0.686634i
$771$	−12711.3	−	25443.8i	−0.593759	−	1.18850i
$772$	4543.03	+	7868.75i	0.211797	+	0.366843i
$773$	−13555.7			−0.630742			−0.315371	−	0.948968i	$-0.602129\pi$
$773$	−13555.7			−0.630742			−0.315371	+	0.948968i	$0.602129\pi$
$774$	905.440	−	7473.47i	0.0420483	−	0.347065i
$775$			14782.0i			0.685142i
$776$	4475.97	+	7752.61i	0.207059	+	0.358637i
$777$	−22502.9	−	9021.30i	−1.03898	−	0.416522i
$778$	−6992.88	+	12112.0i	−0.322245	+	0.558145i
$779$	25545.3	+	14748.6i	1.17491	+	0.678335i
$780$	−7626.94	−	5039.36i	−0.350113	−	0.231331i
$781$	3869.14	+	6701.55i	0.177271	+	0.307042i
$782$	−1317.43			−0.0602447
$783$	8088.04	−	2886.08i	0.369148	−	0.131724i
$784$	4395.37	+	3286.16i	0.200226	+	0.149698i
$785$	−4659.31	+	2690.05i	−0.211844	+	0.122308i
$786$	12091.4	+	7989.14i	0.548709	+	0.362549i
$787$	−19060.3	−	11004.5i	−0.863311	−	0.498433i	0.00180871	−	0.999998i	$-0.499424\pi$
$787$	−19060.3	−	11004.5i	−0.863311	−	0.498433i	−0.865120	+	0.501566i	$0.832758\pi$
$788$	12073.3	+	6970.53i	0.545805	+	0.315120i
$789$	−1438.95	+	23841.0i	−0.0649278	+	1.07574i
$790$	−12173.6	+	7028.45i	−0.548251	+	0.316533i
$791$	3916.14	−	11778.1i	0.176033	−	0.529431i
$792$	−8607.53	+	11460.8i	−0.386181	+	0.514196i
$793$	26524.3			1.18777
$794$	−22.8921	−	39.6502i	−0.00102318	−	0.00177221i
$795$	−18330.4	+	9157.57i	−0.817749	+	0.408535i
$796$	5826.17	+	3363.74i	0.259426	+	0.149780i
$797$	14681.9	−	25429.8i	0.652520	−	1.13020i	−0.329989	−	0.943985i	$-0.607045\pi$
$797$	14681.9	−	25429.8i	0.652520	−	1.13020i	0.982509	−	0.186214i	$-0.0596217\pi$
$798$	−2996.29	−	20910.7i	−0.132917	−	0.927609i
$799$	−1084.71	−	1878.77i	−0.0480279	−	0.0831867i
$800$		−	1414.42i		−	0.0625093i
$801$	−17390.7	−	40787.6i	−0.767129	−	1.79920i
$802$	−23736.7			−1.04510
$803$	11690.8	+	20249.1i	0.513773	+	0.889881i
$804$	−12739.2	−	768.890i	−0.558802	−	0.0337272i
$805$	−3887.51	−	4377.33i	−0.170207	−	0.191653i
$806$	−28342.1	−	16363.3i	−1.23860	−	0.715103i
$807$	4577.54	−	6928.00i	0.199674	−	0.302202i
$808$	−10584.5	+	6110.94i	−0.460841	+	0.266067i
$809$		−	41755.6i		−	1.81465i	−0.420432	−	0.907324i	$-0.638122\pi$
$809$		−	41755.6i		−	1.81465i	0.420432	−	0.907324i	$-0.361878\pi$
$810$	−9456.68	−	9073.66i	−0.410215	−	0.393600i
$811$			505.959i			0.0219070i	0.999940	+	0.0109535i	$0.00348668\pi$
$811$			505.959i			0.0219070i	−0.999940	+	0.0109535i	$0.996513\pi$
$812$	4441.76	−	912.437i	0.191965	−	0.0394338i
$813$	−1014.36	−	670.220i	−0.0437580	−	0.0289122i
$814$	16717.1	−	28954.9i	0.719822	−	1.24677i
$815$	8094.29	−	14019.7i	0.347890	−	0.602564i
$816$	−1554.46	−	93.8216i	−0.0666877	−	0.00402502i
$817$	−13251.0	+	7650.44i	−0.567432	+	0.327607i
$818$	7555.12			0.322932
$819$	24384.6	−	2004.95i	1.04037	−	0.0855418i
$820$	9663.18			0.411528
$821$	−22334.9	+	12895.0i	−0.949442	+	0.548161i	−0.892908	−	0.450240i	$-0.851338\pi$
$821$	−22334.9	+	12895.0i	−0.949442	+	0.548161i	−0.0565347	+	0.998401i	$0.518005\pi$
$822$	−6639.19	−	13289.4i	−0.281713	−	0.563894i
$823$	−7652.99	+	13255.4i	−0.324139	+	0.561425i	−0.981338	−	0.192292i	$-0.938408\pi$
$823$	−7652.99	+	13255.4i	−0.324139	+	0.561425i	0.657199	+	0.753717i	$0.271741\pi$
$824$	−6896.39	+	11944.9i	−0.291562	+	0.505001i
$825$	13633.8	−	6811.26i	0.575356	−	0.287439i
$826$	−8206.21	+	1685.74i	−0.345679	+	0.0710101i
$827$			8921.04i			0.375109i	0.982254	+	0.187554i	$0.0600561\pi$
$827$			8921.04i			0.375109i	−0.982254	+	0.187554i	$0.939944\pi$
$828$	3036.88	+	2280.81i	0.127462	+	0.0957291i
$829$			1174.38i			0.0492011i	0.999697	+	0.0246006i	$0.00783139\pi$
$829$			1174.38i			0.0492011i	−0.999697	+	0.0246006i	$0.992169\pi$
$830$	3820.46	−	2205.74i	0.159771	−	0.0922440i
$831$	11121.4	+	671.249i	0.464258	+	0.0280209i
$832$	2711.93	+	1565.73i	0.113004	+	0.0652428i
$833$	−5904.56	+	2532.74i	−0.245595	+	0.105347i
$834$	1394.40	−	2110.39i	0.0578947	−	0.0876223i
$835$	1755.40	+	3040.45i	0.0727523	+	0.126011i
$836$	29132.2			1.20521
$837$	−35750.9	−	30385.4i	−1.47638	−	1.25481i
$838$			22089.3i			0.910574i
$839$	13404.5	+	23217.3i	0.551579	+	0.955363i	0.998161	+	0.0606203i	$0.0193079\pi$
$839$	13404.5	+	23217.3i	0.551579	+	0.955363i	−0.446582	+	0.894743i	$0.647359\pi$
$840$	−4275.22	−	5441.74i	−0.175606	−	0.223521i
$841$	−10321.2	+	17876.8i	−0.423189	+	0.732985i
$842$	−4829.80	−	2788.49i	−0.197679	−	0.114130i
$843$	2578.63	−	42723.6i	0.105353	−	1.74553i
$844$	2099.74	+	3636.85i	0.0856350	+	0.148324i
$845$	−1771.34			−0.0721136
$846$	−752.215	+	6208.76i	−0.0305694	+	0.252319i
$847$	−53993.5	−	17952.5i	−2.19037	−	0.728284i
$848$	6078.81	−	3509.60i	0.246164	−	0.142123i
$849$	27428.7	−	13703.0i	1.10877	−	0.553927i
$850$	1434.03	+	827.938i	0.0578669	+	0.0334095i
$851$	−7672.43	−	4429.68i	−0.309057	−	0.178434i
$852$	2168.27	−	1083.24i	0.0871876	−	0.0435576i
$853$	34918.2	−	20160.0i	1.40161	−	0.809222i	0.407056	−	0.913403i	$-0.366555\pi$
$853$	34918.2	−	20160.0i	1.40161	−	0.809222i	0.994558	+	0.104181i	$0.0332221\pi$
$854$	19053.9	+	6335.31i	0.763479	+	0.253852i
$855$	−3203.79	+	26444.0i	−0.128149	+	1.05774i
$856$	−5354.85			−0.213814
$857$	3860.50	+	6686.58i	0.153876	+	0.266522i	0.932649	−	0.360784i	$-0.117491\pi$
$857$	3860.50	+	6686.58i	0.153876	+	0.266522i	−0.778773	+	0.627306i	$0.784158\pi$
$858$	−2032.83	+	33680.5i	−0.0808854	+	1.34013i
$859$	37480.7	+	21639.5i	1.48874	+	0.859523i	0.999917	−	0.0128616i	$-0.00409408\pi$
$859$	37480.7	+	21639.5i	1.48874	+	0.859523i	0.488820	+	0.872385i	$0.337427\pi$
$860$	−2506.26	+	4340.97i	−0.0993754	+	0.172123i
$861$	−20337.7	+	15977.9i	−0.805000	+	0.632436i
$862$	10345.4	+	17918.8i	0.408779	+	0.708025i
$863$			21165.5i			0.834856i	0.908710	+	0.417428i	$0.137068\pi$
$863$			21165.5i			0.834856i	−0.908710	+	0.417428i	$0.862932\pi$
$864$	3420.84	+	2907.44i	0.134698	+	0.114483i
$865$	9178.15			0.360770
$866$	−5236.75	−	9070.32i	−0.205487	−	0.355915i
$867$	−13068.1	+	19778.2i	−0.511898	+	0.774745i
$868$	−16451.4	−	18524.2i	−0.643313	−	0.724368i
$869$	44934.1	+	25942.7i	1.75407	+	1.01271i
$870$	−5707.54	−	344.486i	−0.222418	−	0.0134243i
$871$	−26018.8	+	15022.0i	−1.01219	+	0.584386i
$872$			2533.07i			0.0983724i
$873$	24158.2	+	18143.7i	0.936577	+	0.703405i
$874$		−	7719.41i		−	0.298756i
$875$	5667.94	+	27591.7i	0.218984	+	1.06602i
$876$	6551.55	−	3273.06i	0.252690	−	0.126240i
$877$	7087.12	−	12275.2i	0.272879	−	0.472640i	−0.696719	−	0.717344i	$-0.745357\pi$
$877$	7087.12	−	12275.2i	0.272879	−	0.472640i	0.969598	+	0.244704i	$0.0786908\pi$
$878$	−5990.16	+	10375.3i	−0.230249	+	0.398802i
$879$	4360.48	+	8728.19i	0.167321	+	0.334920i
$880$	8265.02	−	4771.81i	0.316606	−	0.182793i
$881$	16308.0			0.623645			0.311823	−	0.950140i	$-0.399061\pi$
$881$	16308.0			0.623645			0.311823	+	0.950140i	$0.399061\pi$
$882$	17995.7	+	4383.97i	0.687015	+	0.167365i
$883$	−28226.0			−1.07574			−0.537871	−	0.843027i	$-0.680771\pi$
$883$	−28226.0			−1.07574			−0.537871	+	0.843027i	$0.680771\pi$
$884$	−3174.87	+	1833.01i	−0.120795	+	0.0697409i
$885$	10544.8	+	636.442i	0.400518	+	0.0241738i
$886$	−4017.29	+	6958.16i	−0.152329	+	0.263842i
$887$	25871.3	−	44810.5i	0.979340	−	1.69627i	0.314540	−	0.949244i	$-0.398150\pi$
$887$	25871.3	−	44810.5i	0.979340	−	1.69627i	0.664800	−	0.747022i	$-0.268517\pi$
$888$	−8737.38	−	5773.06i	−0.330189	−	0.218166i
$889$	8536.48	+	41555.8i	0.322052	+	1.56776i
$890$			29523.6i			1.11195i
$891$	−11552.0	+	46975.0i	−0.434349	+	1.76624i
$892$			9443.51i			0.354475i
$893$	11008.5	−	6355.78i	0.412527	−	0.238172i
$894$	7048.47	−	10667.7i	0.263687	−	0.399084i
$895$	−19054.7	−	11001.3i	−0.711653	−	0.410873i
$896$	1574.16	+	1772.50i	0.0586930	+	0.0660881i
$897$	8924.63	+	538.657i	0.332201	+	0.0200504i
$898$	1948.54	+	3374.97i	0.0724094	+	0.125417i
$899$	−20470.4			−0.759430
$900$	−1872.28	−	4391.19i	−0.0693438	−	0.162637i
$901$			8217.44i			0.303843i
$902$	−17833.9	−	30889.2i	−0.658319	−	1.14024i
$903$	−1902.93	−	13280.3i	−0.0701279	−	0.489414i
$904$	2680.75	−	4643.20i	0.0986289	−	0.170830i
$905$	5267.90	+	3041.42i	0.193493	+	0.111713i
$906$	15569.1	−	7778.08i	0.570914	−	0.285220i
$907$	3027.85	+	5244.40i	0.110847	+	0.191993i	0.916112	−	0.400922i	$-0.131310\pi$
$907$	3027.85	+	5244.40i	0.110847	+	0.191993i	−0.805265	+	0.592915i	$0.797977\pi$
$908$	−16925.6			−0.618609
$909$	−24771.2	+	32982.6i	−0.903860	+	1.20348i
$910$	−15458.9	−	5139.99i	−0.563140	−	0.187241i
$911$	10003.4	−	5775.46i	0.363806	−	0.210043i	−0.306943	−	0.951728i	$-0.599306\pi$
$911$	10003.4	−	5775.46i	0.363806	−	0.210043i	0.670749	+	0.741685i	$0.265973\pi$
$912$	549.741	−	9108.27i	0.0199602	−	0.330707i
$913$	−14101.7	−	8141.62i	−0.511170	−	0.295124i
$914$	−23215.4	−	13403.4i	−0.840151	−	0.485061i
$915$	−21125.1	−	13958.0i	−0.763251	−	0.504304i
$916$	−6267.03	+	3618.27i	−0.226057	+	0.130514i
$917$	24507.8	+	8148.69i	0.882572	+	0.293450i
$918$	−4950.15	+	1766.38i	−0.177973	+	0.0635068i
$919$	−36885.9			−1.32400			−0.661999	−	0.749505i	$-0.730292\pi$
$919$	−36885.9			−1.32400			−0.661999	+	0.749505i	$0.730292\pi$
$920$	−1264.43	−	2190.05i	−0.0453119	−	0.0784825i
$921$	41617.4	+	27497.9i	1.48897	+	0.983808i
$922$	29658.4	+	17123.3i	1.05938	+	0.611633i
$923$	2852.94	−	4941.44i	0.101740	−	0.176218i
$924$	−9504.87	+	23709.1i	−0.338406	+	0.844126i
$925$	5567.65	+	9643.45i	0.197906	+	0.342783i
$926$		−	24615.6i		−	0.873562i
$927$	−5598.85	+	46212.7i	−0.198371	+	1.63735i
$928$	1958.72			0.0692869
$929$	−11193.6	−	19388.0i	−0.395319	−	0.684713i	0.597823	−	0.801628i	$-0.296033\pi$
$929$	−11193.6	−	19388.0i	−0.395319	−	0.684713i	−0.993142	+	0.116915i	$0.962699\pi$
$930$	13961.9	+	27947.1i	0.492291	+	0.985399i
$931$	−14840.4	−	34597.4i	−0.522421	−	1.21792i
$932$	−10582.8	−	6109.97i	−0.371943	−	0.214741i
$933$	1.52155	+	3.04563i	5.33906e−5	+	0.000106870i
$934$	−26871.6	+	15514.3i	−0.941398	+	0.543516i
$935$			11172.8i			0.390791i
$936$	10492.0	+	1271.14i	0.366390	+	0.0443895i
$937$			18336.5i			0.639304i	0.947535	+	0.319652i	$0.103566\pi$
$937$			18336.5i			0.639304i	−0.947535	+	0.319652i	$0.896434\pi$
$938$	−22278.8	+	4576.56i	−0.775510	+	0.159307i
$939$	−1250.83	+	20724.2i	−0.0434711	+	0.720242i
$940$	2082.13	−	3606.36i	0.0722465	−	0.125135i
$941$	5273.49	−	9133.95i	0.182689	−	0.316427i	−0.760106	−	0.649799i	$-0.774853\pi$
$941$	5273.49	−	9133.95i	0.182689	−	0.316427i	0.942796	+	0.333372i	$0.108186\pi$
$942$	3428.95	−	5189.63i	0.118600	−	0.179498i
$943$	−8184.98	+	4725.60i	−0.282651	+	0.163188i
$944$	−3618.77			−0.124768
$945$	−20476.0	−	11235.2i	−0.704852	−	0.386752i
$946$	18501.7			0.635880
$947$	9941.78	−	5739.89i	0.341145	−	0.196960i	−0.319633	−	0.947541i	$-0.603560\pi$
$947$	9941.78	−	5739.89i	0.341145	−	0.196960i	0.660778	+	0.750581i	$0.270226\pi$
$948$	8959.00	−	13559.2i	0.306936	−	0.464539i
$949$	8620.31	−	14930.8i	0.294865	−	0.510721i
$950$	−4851.24	+	8402.60i	−0.165679	+	0.286965i
$951$	−1094.53	+	18134.5i	−0.0373213	+	0.618350i
$952$	−2718.51	+	558.442i	−0.0925497	+	0.0190118i
$953$		−	3274.36i		−	0.111298i	−0.998450	−	0.0556489i	$-0.982277\pi$
$953$		−	3274.36i		−	0.111298i	0.998450	−	0.0556489i	$-0.0177228\pi$
$954$	14226.5	−	18942.4i	0.482808	−	0.642855i
$955$			20451.4i			0.692977i
$956$	−16216.6	+	9362.66i	−0.548622	+	0.316747i
$957$	9432.38	+	18880.4i	0.318605	+	0.637740i
$958$	−33692.8	−	19452.5i	−1.13629	−	0.656037i
$959$	−17579.8	−	19794.8i	−0.591952	−	0.666536i
$960$	−1335.96	−	2674.13i	−0.0449144	−	0.0899033i
$961$	41025.8	+	71058.8i	1.37712	+	2.38525i
$962$	−24653.0			−0.826242
$963$	−16624.6	+	7088.26i	−0.556303	+	0.237192i
$964$		−	5740.49i		−	0.191793i
$965$	−10209.1	−	17682.7i	−0.340563	−	0.589873i
$966$	6282.41	+	2518.59i	0.209248	+	0.0838864i
$967$	−8316.55	+	14404.7i	−0.276569	+	0.479031i	−0.970530	−	0.240981i	$-0.922531\pi$
$967$	−8316.55	+	14404.7i	−0.276569	+	0.479031i	0.693961	+	0.720013i	$0.255864\pi$
$968$	−21285.6	−	12289.2i	−0.706760	−	0.408048i
$969$	8912.74	+	5888.92i	0.295478	+	0.195232i
$970$	−10058.5	−	17421.8i	−0.332946	−	0.576679i
$971$	23196.9			0.766658			0.383329	−	0.923612i	$-0.374777\pi$
$971$	23196.9			0.766658			0.383329	+	0.923612i	$0.374777\pi$
$972$	14468.9	+	4498.20i	0.477459	+	0.148436i
$973$	1422.25	−	4277.52i	0.0468605	−	0.140936i
$974$	35935.5	−	20747.4i	1.18218	−	0.682535i
$975$	−9375.97	−	6194.99i	−0.307971	−	0.203486i
$976$	7511.50	+	4336.77i	0.246350	+	0.142230i
$977$	40553.6	+	23413.6i	1.32797	+	0.766703i	0.984985	−	0.172639i	$-0.0552294\pi$
$977$	40553.6	+	23413.6i	1.32797	+	0.766703i	0.342983	+	0.939342i	$0.388563\pi$
$978$	−1127.59	+	18682.2i	−0.0368673	+	0.610828i
$979$	94374.6	−	54487.2i	3.08092	−	1.77877i
$980$	−9877.32	−	7384.70i	−0.321959	−	0.240710i
$981$	3353.05	+	7864.13i	0.109128	+	0.255945i
$982$	791.521			0.0257214
$983$	−7117.50	−	12327.9i	−0.230939	−	0.399998i	0.727146	−	0.686483i	$-0.240846\pi$
$983$	−7117.50	−	12327.9i	−0.230939	−	0.399998i	−0.958085	+	0.286485i	$0.907513\pi$
$984$	−9994.14	+	4992.92i	−0.323782	+	0.161757i
$985$	−27131.3	−	15664.3i	−0.877639	−	0.506705i
$986$	−1146.55	+	1985.88i	−0.0370319	+	0.0641412i
$987$	1580.90	+	11032.9i	0.0509835	+	0.355808i
$988$	−10740.4	−	18602.9i	−0.345848	−	0.599027i
$989$		−	4902.56i		−	0.157626i
$990$	19342.9	−	25754.9i	0.620968	−	0.826814i
$991$	16183.4			0.518752			0.259376	−	0.965776i	$-0.416483\pi$
$991$	16183.4			0.518752			0.259376	+	0.965776i	$0.416483\pi$
$992$	−5350.86	−	9267.97i	−0.171260	−	0.296631i
$993$	12113.2	+	731.106i	0.387110	+	0.0233645i
$994$	3229.69	−	2868.29i	0.103058	−	0.0915258i
$995$	−13092.6	−	7559.04i	−0.417150	−	0.240842i
$996$	−2811.61	+	4255.30i	−0.0894471	+	0.135376i
$997$	40829.3	−	23572.8i	1.29697	−	0.748805i	0.317089	−	0.948396i	$-0.397295\pi$
$997$	40829.3	−	23572.8i	1.29697	−	0.748805i	0.979879	+	0.199591i	$0.0639612\pi$
$998$			40586.8i			1.28733i
$999$	−34767.8	−	6357.18i	−1.10110	−	0.201334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.4.m.a.41.21	yes	48
3.2	odd	2		378.4.m.a.125.6		48
7.6	odd	2	inner	126.4.m.a.41.16	✓	48
9.2	odd	6	inner	126.4.m.a.83.16	yes	48
9.4	even	3		1134.4.d.b.1133.46		48
9.5	odd	6		1134.4.d.b.1133.3		48
9.7	even	3		378.4.m.a.251.5		48
21.20	even	2		378.4.m.a.125.5		48
63.13	odd	6		1134.4.d.b.1133.4		48
63.20	even	6	inner	126.4.m.a.83.21	yes	48
63.34	odd	6		378.4.m.a.251.6		48
63.41	even	6		1134.4.d.b.1133.45		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.m.a.41.16	✓	48	7.6	odd	2	inner
126.4.m.a.41.21	yes	48	1.1	even	1	trivial
126.4.m.a.83.16	yes	48	9.2	odd	6	inner
126.4.m.a.83.21	yes	48	63.20	even	6	inner
378.4.m.a.125.5		48	21.20	even	2
378.4.m.a.125.6		48	3.2	odd	2
378.4.m.a.251.5		48	9.7	even	3
378.4.m.a.251.6		48	63.34	odd	6
1134.4.d.b.1133.3		48	9.5	odd	6
1134.4.d.b.1133.4		48	63.13	odd	6
1134.4.d.b.1133.45		48	63.41	even	6
1134.4.d.b.1133.46		48	9.4	even	3

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(2.86447 - 4.33530i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-4.49442 + 7.78456i) q^{5} +(0.626101 - 10.3734i) q^{6} +(-3.72666 - 18.1414i) q^{7} -8.00000i q^{8} +(-10.5897 - 24.8366i) q^{9} +O(q^{10})\)	\(q+(1.73205 - 1.00000i) q^{2} +(2.86447 - 4.33530i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-4.49442 + 7.78456i) q^{5} +(0.626101 - 10.3734i) q^{6} +(-3.72666 - 18.1414i) q^{7} -8.00000i q^{8} +(-10.5897 - 24.8366i) q^{9} +17.9777i q^{10} +(57.4672 - 33.1787i) q^{11} +(-9.28899 - 18.5934i) q^{12} +(-42.3739 - 24.4646i) q^{13} +(-24.5962 - 27.6952i) q^{14} +(20.8743 + 41.7833i) q^{15} +(-8.00000 - 13.8564i) q^{16} +18.7313 q^{17} +(-43.1785 - 32.4287i) q^{18} +109.755i q^{19} +(17.9777 + 31.1383i) q^{20} +(-89.3235 - 35.8094i) q^{21} +(66.3574 - 114.934i) q^{22} +(-30.4552 - 17.5833i) q^{23} +(-34.6824 - 22.9157i) q^{24} +(22.1004 + 38.2790i) q^{25} -97.8583 q^{26} +(-138.008 - 25.2344i) q^{27} +(-70.2971 - 23.3734i) q^{28} +(-53.0095 + 30.6051i) q^{29} +(77.9387 + 51.4965i) q^{30} +(289.624 + 167.214i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(20.7732 - 344.177i) q^{33} +(32.4436 - 18.7313i) q^{34} +(157.972 + 52.5249i) q^{35} +(-107.216 - 12.9896i) q^{36} +251.926 q^{37} +(109.755 + 190.101i) q^{38} +(-227.440 + 113.626i) q^{39} +(62.2765 + 35.9554i) q^{40} +(134.377 - 232.749i) q^{41} +(-190.522 + 27.2998i) q^{42} +(69.7048 + 120.732i) q^{43} -265.430i q^{44} +(240.937 + 29.1904i) q^{45} -70.3332 q^{46} +(-57.9089 - 100.301i) q^{47} +(-82.9874 - 5.00881i) q^{48} +(-315.224 + 135.214i) q^{49} +(76.5579 + 44.2007i) q^{50} +(53.6553 - 81.2059i) q^{51} +(-169.495 + 97.8583i) q^{52} +438.701i q^{53} +(-264.271 + 94.3008i) q^{54} +596.476i q^{55} +(-145.132 + 29.8133i) q^{56} +(475.820 + 314.389i) q^{57} +(-61.2101 + 106.019i) q^{58} +(113.087 - 195.872i) q^{59} +(186.490 + 11.2558i) q^{60} +(-469.469 + 271.048i) q^{61} +668.858 q^{62} +(-411.109 + 284.669i) q^{63} -64.0000 q^{64} +(380.892 - 219.908i) q^{65} +(-308.197 - 616.905i) q^{66} +(307.015 - 531.766i) q^{67} +(37.4626 - 64.8872i) q^{68} +(-163.467 + 81.6655i) q^{69} +(326.141 - 66.9967i) q^{70} +116.615i q^{71} +(-198.693 + 84.7173i) q^{72} +352.359i q^{73} +(436.348 - 251.926i) q^{74} +(229.257 + 13.8371i) q^{75} +(380.202 + 219.510i) q^{76} +(-816.070 - 918.892i) q^{77} +(-280.312 + 424.245i) q^{78} +(390.954 + 677.153i) q^{79} +143.821 q^{80} +(-504.718 + 526.023i) q^{81} -537.510i q^{82} +(-122.693 - 212.511i) q^{83} +(-302.694 + 237.807i) q^{84} +(-84.1864 + 145.815i) q^{85} +(241.465 + 139.410i) q^{86} +(-19.1619 + 317.479i) q^{87} +(-265.430 - 459.738i) q^{88} +1642.23 q^{89} +(446.505 - 190.378i) q^{90} +(-285.910 + 859.894i) q^{91} +(-121.821 + 70.3332i) q^{92} +(1554.54 - 776.627i) q^{93} +(-200.602 - 115.818i) q^{94} +(-854.394 - 493.284i) q^{95} +(-148.747 + 74.3119i) q^{96} +(-969.077 + 559.497i) q^{97} +(-410.770 + 549.421i) q^{98} +(-1432.61 - 1075.94i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9}+O(q^{10}) \) 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9	\( 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9} + 24 q^{11} - 132 q^{14} - 120 q^{15} - 384 q^{16} + 120 q^{18} + 180 q^{21} + 348 q^{23} - 600 q^{25} - 96 q^{28} - 84 q^{29} + 192 q^{30} + 96 q^{36} - 672 q^{37} + 1368 q^{39} + 1128 q^{42} + 84 q^{43} - 1008 q^{46} - 42 q^{49} + 456 q^{50} + 2016 q^{51} - 528 q^{56} + 732 q^{57} + 504 q^{58} - 1008 q^{60} - 774 q^{63} - 3072 q^{64} - 6972 q^{65} + 1176 q^{67} + 216 q^{70} - 384 q^{72} + 2520 q^{74} + 1500 q^{77} + 2832 q^{78} + 348 q^{79} + 2268 q^{81} - 1080 q^{84} + 720 q^{85} + 1200 q^{86} + 180 q^{91} + 1392 q^{92} + 5232 q^{93} - 5892 q^{95} + 972 q^{99}+O(q^{100}) \) 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9 + 24 * q^11 - 132 * q^14 - 120 * q^15 - 384 * q^16 + 120 * q^18 + 180 * q^21 + 348 * q^23 - 600 * q^25 - 96 * q^28 - 84 * q^29 + 192 * q^30 + 96 * q^36 - 672 * q^37 + 1368 * q^39 + 1128 * q^42 + 84 * q^43 - 1008 * q^46 - 42 * q^49 + 456 * q^50 + 2016 * q^51 - 528 * q^56 + 732 * q^57 + 504 * q^58 - 1008 * q^60 - 774 * q^63 - 3072 * q^64 - 6972 * q^65 + 1176 * q^67 + 216 * q^70 - 384 * q^72 + 2520 * q^74 + 1500 * q^77 + 2832 * q^78 + 348 * q^79 + 2268 * q^81 - 1080 * q^84 + 720 * q^85 + 1200 * q^86 + 180 * q^91 + 1392 * q^92 + 5232 * q^93 - 5892 * q^95 + 972 * q^99

Introduction

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