LMFDB - Embedded newform 30.3.b.a.29.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,3,Mod(29,30)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(30, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("30.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	30.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:	$0.817440793081$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 16x^{2} + 81 $ x^4 + 16*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.3
Root			$-0.707107 + 2.91548i$ of defining polynomial
Character	$\chi$	$=$	30.29
Dual form			30.3.b.a.29.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(-0.707107 - 2.91548i) q^{3} +2.00000 q^{4} +(-2.82843 + 4.12311i) q^{5} +(-1.00000 - 4.12311i) q^{6} +5.83095i q^{7} +2.82843 q^{8} +(-8.00000 + 4.12311i) q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(-0.707107 - 2.91548i) q^{3} +2.00000 q^{4} +(-2.82843 + 4.12311i) q^{5} +(-1.00000 - 4.12311i) q^{6} +5.83095i q^{7} +2.82843 q^{8} +(-8.00000 + 4.12311i) q^{9} +(-4.00000 + 5.83095i) q^{10} -16.4924i q^{11} +(-1.41421 - 5.83095i) q^{12} +8.24621i q^{14} +(14.0208 + 5.33074i) q^{15} +4.00000 q^{16} -11.3137 q^{17} +(-11.3137 + 5.83095i) q^{18} +12.0000 q^{19} +(-5.65685 + 8.24621i) q^{20} +(17.0000 - 4.12311i) q^{21} -23.3238i q^{22} +24.0416 q^{23} +(-2.00000 - 8.24621i) q^{24} +(-9.00000 - 23.3238i) q^{25} +(17.6777 + 20.4083i) q^{27} +11.6619i q^{28} +(19.8284 + 7.53880i) q^{30} -32.0000 q^{31} +5.65685 q^{32} +(-48.0833 + 11.6619i) q^{33} -16.0000 q^{34} +(-24.0416 - 16.4924i) q^{35} +(-16.0000 + 8.24621i) q^{36} +23.3238i q^{37} +16.9706 q^{38} +(-8.00000 + 11.6619i) q^{40} +57.7235i q^{41} +(24.0416 - 5.83095i) q^{42} -40.8167i q^{43} -32.9848i q^{44} +(5.62742 - 44.6467i) q^{45} +34.0000 q^{46} -35.3553 q^{47} +(-2.82843 - 11.6619i) q^{48} +15.0000 q^{49} +(-12.7279 - 32.9848i) q^{50} +(8.00000 + 32.9848i) q^{51} +67.8823 q^{53} +(25.0000 + 28.8617i) q^{54} +(68.0000 + 46.6476i) q^{55} +16.4924i q^{56} +(-8.48528 - 34.9857i) q^{57} -16.4924i q^{59} +(28.0416 + 10.6615i) q^{60} -16.0000 q^{61} -45.2548 q^{62} +(-24.0416 - 46.6476i) q^{63} +8.00000 q^{64} +(-68.0000 + 16.4924i) q^{66} -5.83095i q^{67} -22.6274 q^{68} +(-17.0000 - 70.0928i) q^{69} +(-34.0000 - 23.3238i) q^{70} +(-22.6274 + 11.6619i) q^{72} +116.619i q^{73} +32.9848i q^{74} +(-61.6360 + 42.7317i) q^{75} +24.0000 q^{76} +96.1665 q^{77} -72.0000 q^{79} +(-11.3137 + 16.4924i) q^{80} +(47.0000 - 65.9697i) q^{81} +81.6333i q^{82} -43.8406 q^{83} +(34.0000 - 8.24621i) q^{84} +(32.0000 - 46.6476i) q^{85} -57.7235i q^{86} -46.6476i q^{88} +65.9697i q^{89} +(7.95837 - 63.1400i) q^{90} +48.0833 q^{92} +(22.6274 + 93.2952i) q^{93} -50.0000 q^{94} +(-33.9411 + 49.4773i) q^{95} +(-4.00000 - 16.4924i) q^{96} -163.267i q^{97} +21.2132 q^{98} +(68.0000 + 131.939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4} - 4 q^{6} - 32 q^{9}+O(q^{10}) $ 4 * q + 8 * q^4 - 4 * q^6 - 32 * q^9	$ 4 q + 8 q^{4} - 4 q^{6} - 32 q^{9} - 16 q^{10} + 8 q^{15} + 16 q^{16} + 48 q^{19} + 68 q^{21} - 8 q^{24} - 36 q^{25} + 68 q^{30} - 128 q^{31} - 64 q^{34} - 64 q^{36} - 32 q^{40} - 68 q^{45} + 136 q^{46} + 60 q^{49} + 32 q^{51} + 100 q^{54} + 272 q^{55} + 16 q^{60} - 64 q^{61} + 32 q^{64} - 272 q^{66} - 68 q^{69} - 136 q^{70} - 272 q^{75} + 96 q^{76} - 288 q^{79} + 188 q^{81} + 136 q^{84} + 128 q^{85} + 128 q^{90} - 200 q^{94} - 16 q^{96} + 272 q^{99}+O(q^{100}) $ 4 * q + 8 * q^4 - 4 * q^6 - 32 * q^9 - 16 * q^10 + 8 * q^15 + 16 * q^16 + 48 * q^19 + 68 * q^21 - 8 * q^24 - 36 * q^25 + 68 * q^30 - 128 * q^31 - 64 * q^34 - 64 * q^36 - 32 * q^40 - 68 * q^45 + 136 * q^46 + 60 * q^49 + 32 * q^51 + 100 * q^54 + 272 * q^55 + 16 * q^60 - 64 * q^61 + 32 * q^64 - 272 * q^66 - 68 * q^69 - 136 * q^70 - 272 * q^75 + 96 * q^76 - 288 * q^79 + 188 * q^81 + 136 * q^84 + 128 * q^85 + 128 * q^90 - 200 * q^94 - 16 * q^96 + 272 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$	−0.707107	−	2.91548i	−0.235702	−	0.971825i
$3$	−0.707107	−	2.91548i	−0.235702	−	0.971825i
$4$	2.00000			0.500000
$5$	−2.82843	+	4.12311i	−0.565685	+	0.824621i
$5$	−2.82843	+	4.12311i	−0.565685	+	0.824621i
$6$	−1.00000	−	4.12311i	−0.166667	−	0.687184i
$7$			5.83095i			0.832993i	0.909137	+	0.416497i	$0.136742\pi$
$7$			5.83095i			0.832993i	−0.909137	+	0.416497i	$0.863258\pi$
$8$	2.82843			0.353553
$9$	−8.00000	+	4.12311i	−0.888889	+	0.458123i
$10$	−4.00000	+	5.83095i	−0.400000	+	0.583095i
$11$		−	16.4924i		−	1.49931i	−0.661828	−	0.749656i	$-0.730219\pi$
$11$		−	16.4924i		−	1.49931i	0.661828	−	0.749656i	$-0.269781\pi$
$12$	−1.41421	−	5.83095i	−0.117851	−	0.485913i
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$			8.24621i			0.589015i
$15$	14.0208	+	5.33074i	0.934721	+	0.355382i
$16$	4.00000			0.250000
$17$	−11.3137			−0.665512			−0.332756	−	0.943013i	$-0.607979\pi$
$17$	−11.3137			−0.665512			−0.332756	+	0.943013i	$0.607979\pi$
$18$	−11.3137	+	5.83095i	−0.628539	+	0.323942i
$19$	12.0000			0.631579			0.315789	−	0.948829i	$-0.397731\pi$
$19$	12.0000			0.631579			0.315789	+	0.948829i	$0.397731\pi$
$20$	−5.65685	+	8.24621i	−0.282843	+	0.412311i
$21$	17.0000	−	4.12311i	0.809524	−	0.196338i
$22$		−	23.3238i		−	1.06017i
$23$	24.0416			1.04529			0.522644	−	0.852551i	$-0.324946\pi$
$23$	24.0416			1.04529			0.522644	+	0.852551i	$0.324946\pi$
$24$	−2.00000	−	8.24621i	−0.0833333	−	0.343592i
$25$	−9.00000	−	23.3238i	−0.360000	−	0.932952i
$26$		0			0
$27$	17.6777	+	20.4083i	0.654729	+	0.755864i
$28$			11.6619i			0.416497i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	19.8284	+	7.53880i	0.660948	+	0.251293i
$31$	−32.0000			−1.03226			−0.516129	−	0.856511i	$-0.672628\pi$
$31$	−32.0000			−1.03226			−0.516129	+	0.856511i	$0.672628\pi$
$32$	5.65685			0.176777
$33$	−48.0833	+	11.6619i	−1.45707	+	0.353391i
$34$	−16.0000			−0.470588
$35$	−24.0416	−	16.4924i	−0.686904	−	0.471212i
$36$	−16.0000	+	8.24621i	−0.444444	+	0.229061i
$37$			23.3238i			0.630373i	0.949030	+	0.315187i	$0.102067\pi$
$37$			23.3238i			0.630373i	−0.949030	+	0.315187i	$0.897933\pi$
$38$	16.9706			0.446594
$39$		0			0
$40$	−8.00000	+	11.6619i	−0.200000	+	0.291548i
$41$			57.7235i			1.40789i	0.710255	+	0.703945i	$0.248580\pi$
$41$			57.7235i			1.40789i	−0.710255	+	0.703945i	$0.751420\pi$
$42$	24.0416	−	5.83095i	0.572420	−	0.138832i
$43$		−	40.8167i		−	0.949225i	−0.880195	−	0.474612i	$-0.842588\pi$
$43$		−	40.8167i		−	0.949225i	0.880195	−	0.474612i	$-0.157412\pi$
$44$		−	32.9848i		−	0.749656i
$45$	5.62742	−	44.6467i	0.125054	−	0.992150i
$46$	34.0000			0.739130
$47$	−35.3553			−0.752241			−0.376121	−	0.926571i	$-0.622742\pi$
$47$	−35.3553			−0.752241			−0.376121	+	0.926571i	$0.622742\pi$
$48$	−2.82843	−	11.6619i	−0.0589256	−	0.242956i
$49$	15.0000			0.306122
$50$	−12.7279	−	32.9848i	−0.254558	−	0.659697i
$51$	8.00000	+	32.9848i	0.156863	+	0.646762i
$52$		0			0
$53$	67.8823			1.28080			0.640399	−	0.768043i	$-0.278769\pi$
$53$	67.8823			1.28080			0.640399	+	0.768043i	$0.278769\pi$
$54$	25.0000	+	28.8617i	0.462963	+	0.534477i
$55$	68.0000	+	46.6476i	1.23636	+	0.848138i
$56$			16.4924i			0.294508i
$57$	−8.48528	−	34.9857i	−0.148865	−	0.613784i
$58$		0			0
$59$		−	16.4924i		−	0.279533i	−0.990185	−	0.139766i	$-0.955365\pi$
$59$		−	16.4924i		−	0.279533i	0.990185	−	0.139766i	$-0.0446351\pi$
$60$	28.0416	+	10.6615i	0.467361	+	0.177691i
$61$	−16.0000			−0.262295			−0.131148	−	0.991363i	$-0.541866\pi$
$61$	−16.0000			−0.262295			−0.131148	+	0.991363i	$0.541866\pi$
$62$	−45.2548			−0.729917
$63$	−24.0416	−	46.6476i	−0.381613	−	0.740438i
$64$	8.00000			0.125000
$65$		0			0
$66$	−68.0000	+	16.4924i	−1.03030	+	0.249885i
$67$		−	5.83095i		−	0.0870291i	−0.999053	−	0.0435146i	$-0.986145\pi$
$67$		−	5.83095i		−	0.0870291i	0.999053	−	0.0435146i	$-0.0138555\pi$
$68$	−22.6274			−0.332756
$69$	−17.0000	−	70.0928i	−0.246377	−	1.01584i
$70$	−34.0000	−	23.3238i	−0.485714	−	0.333197i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−22.6274	+	11.6619i	−0.314270	+	0.161971i
$73$			116.619i			1.59752i	0.601649	+	0.798761i	$0.294511\pi$
$73$			116.619i			1.59752i	−0.601649	+	0.798761i	$0.705489\pi$
$74$			32.9848i			0.445741i
$75$	−61.6360	+	42.7317i	−0.821814	+	0.569756i
$76$	24.0000			0.315789
$77$	96.1665			1.24892
$78$		0			0
$79$	−72.0000			−0.911392			−0.455696	−	0.890135i	$-0.650610\pi$
$79$	−72.0000			−0.911392			−0.455696	+	0.890135i	$0.650610\pi$
$80$	−11.3137	+	16.4924i	−0.141421	+	0.206155i
$81$	47.0000	−	65.9697i	0.580247	−	0.814441i
$82$			81.6333i			0.995528i
$83$	−43.8406			−0.528200			−0.264100	−	0.964495i	$-0.585075\pi$
$83$	−43.8406			−0.528200			−0.264100	+	0.964495i	$0.585075\pi$
$84$	34.0000	−	8.24621i	0.404762	−	0.0981692i
$85$	32.0000	−	46.6476i	0.376471	−	0.548795i
$86$		−	57.7235i		−	0.671203i
$87$		0			0
$88$		−	46.6476i		−	0.530087i
$89$			65.9697i			0.741232i	0.928786	+	0.370616i	$0.120853\pi$
$89$			65.9697i			0.741232i	−0.928786	+	0.370616i	$0.879147\pi$
$90$	7.95837	−	63.1400i	0.0884263	−	0.701556i
$91$		0			0
$92$	48.0833			0.522644
$93$	22.6274	+	93.2952i	0.243306	+	1.00317i
$94$	−50.0000			−0.531915
$95$	−33.9411	+	49.4773i	−0.357275	+	0.520813i
$96$	−4.00000	−	16.4924i	−0.0416667	−	0.171796i
$97$		−	163.267i		−	1.68316i	−0.540131	−	0.841581i	$-0.681625\pi$
$97$		−	163.267i		−	1.68316i	0.540131	−	0.841581i	$-0.318375\pi$
$98$	21.2132			0.216461
$99$	68.0000	+	131.939i	0.686869	+	1.33272i
$100$	−18.0000	−	46.6476i	−0.180000	−	0.466476i
$101$		−	131.939i		−	1.30633i	−0.757215	−	0.653165i	$-0.773441\pi$
$101$		−	131.939i		−	1.30633i	0.757215	−	0.653165i	$-0.226559\pi$
$102$	11.3137	+	46.6476i	0.110919	+	0.457330i
$103$		−	99.1262i		−	0.962390i	−0.876614	−	0.481195i	$-0.840203\pi$
$103$		−	99.1262i		−	0.962390i	0.876614	−	0.481195i	$-0.159797\pi$
$104$		0			0
$105$	−31.0833	+	81.7547i	−0.296031	+	0.778616i
$106$	96.0000			0.905660
$107$	−55.1543			−0.515461			−0.257731	−	0.966217i	$-0.582975\pi$
$107$	−55.1543			−0.515461			−0.257731	+	0.966217i	$0.582975\pi$
$108$	35.3553	+	40.8167i	0.327364	+	0.377932i
$109$	80.0000			0.733945			0.366972	−	0.930232i	$-0.380394\pi$
$109$	80.0000			0.733945			0.366972	+	0.930232i	$0.380394\pi$
$110$	96.1665	+	65.9697i	0.874241	+	0.599724i
$111$	68.0000	−	16.4924i	0.612613	−	0.148580i
$112$			23.3238i			0.208248i
$113$	−152.735			−1.35164			−0.675819	−	0.737068i	$-0.736210\pi$
$113$	−152.735			−1.35164			−0.675819	+	0.737068i	$0.736210\pi$
$114$	−12.0000	−	49.4773i	−0.105263	−	0.434011i
$115$	−68.0000	+	99.1262i	−0.591304	+	0.861967i
$116$		0			0
$117$		0			0
$118$		−	23.3238i		−	0.197659i
$119$		−	65.9697i		−	0.554367i
$120$	39.6569	+	15.0776i	0.330474	+	0.125647i
$121$	−151.000			−1.24793
$122$	−22.6274			−0.185471
$123$	168.291	−	40.8167i	1.36822	−	0.331843i
$124$	−64.0000			−0.516129
$125$	121.622	+	28.8617i	0.972979	+	0.230894i
$126$	−34.0000	−	65.9697i	−0.269841	−	0.523569i
$127$			40.8167i			0.321391i	0.987004	+	0.160696i	$0.0513737\pi$
$127$			40.8167i			0.321391i	−0.987004	+	0.160696i	$0.948626\pi$
$128$	11.3137			0.0883883
$129$	−119.000	+	28.8617i	−0.922481	+	0.223734i
$130$		0			0
$131$		−	49.4773i		−	0.377689i	−0.982007	−	0.188845i	$-0.939526\pi$
$131$		−	49.4773i		−	0.377689i	0.982007	−	0.188845i	$-0.0604742\pi$
$132$	−96.1665	+	23.3238i	−0.728534	+	0.176696i
$133$			69.9714i			0.526101i
$134$		−	8.24621i		−	0.0615389i
$135$	−134.146	+	15.1634i	−0.993672	+	0.112322i
$136$	−32.0000			−0.235294
$137$	−50.9117			−0.371618			−0.185809	−	0.982586i	$-0.559491\pi$
$137$	−50.9117			−0.371618			−0.185809	+	0.982586i	$0.559491\pi$
$138$	−24.0416	−	99.1262i	−0.174215	−	0.718306i
$139$	44.0000			0.316547			0.158273	−	0.987395i	$-0.449407\pi$
$139$	44.0000			0.316547			0.158273	+	0.987395i	$0.449407\pi$
$140$	−48.0833	−	32.9848i	−0.343452	−	0.235606i
$141$	25.0000	+	103.078i	0.177305	+	0.731047i
$142$		0			0
$143$		0			0
$144$	−32.0000	+	16.4924i	−0.222222	+	0.114531i
$145$		0			0
$146$			164.924i			1.12962i
$147$	−10.6066	−	43.7321i	−0.0721538	−	0.297498i
$148$			46.6476i			0.315187i
$149$			8.24621i			0.0553437i	0.999617	+	0.0276718i	$0.00880935\pi$
$149$			8.24621i			0.0553437i	−0.999617	+	0.0276718i	$0.991191\pi$
$150$	−87.1665	+	60.4318i	−0.581110	+	0.402878i
$151$	136.000			0.900662			0.450331	−	0.892862i	$-0.351306\pi$
$151$	136.000			0.900662			0.450331	+	0.892862i	$0.351306\pi$
$152$	33.9411			0.223297
$153$	90.5097	−	46.6476i	0.591566	−	0.304886i
$154$	136.000			0.883117
$155$	90.5097	−	131.939i	0.583933	−	0.851222i
$156$		0			0
$157$			116.619i			0.742796i	0.928474	+	0.371398i	$0.121122\pi$
$157$			116.619i			0.742796i	−0.928474	+	0.371398i	$0.878878\pi$
$158$	−101.823			−0.644452
$159$	−48.0000	−	197.909i	−0.301887	−	1.24471i
$160$	−16.0000	+	23.3238i	−0.100000	+	0.145774i
$161$			140.186i			0.870718i
$162$	66.4680	−	93.2952i	0.410297	−	0.575896i
$163$		−	99.1262i		−	0.608136i	−0.952650	−	0.304068i	$-0.901655\pi$
$163$		−	99.1262i		−	0.608136i	0.952650	−	0.304068i	$-0.0983450\pi$
$164$			115.447i			0.703945i
$165$	87.9167	−	231.237i	0.532829	−	1.40144i
$166$	−62.0000			−0.373494
$167$	292.742			1.75295			0.876474	−	0.481450i	$-0.159890\pi$
$167$	292.742			1.75295			0.876474	+	0.481450i	$0.159890\pi$
$168$	48.0833	−	11.6619i	0.286210	−	0.0694161i
$169$	169.000			1.00000
$170$	45.2548	−	65.9697i	0.266205	−	0.388057i
$171$	−96.0000	+	49.4773i	−0.561404	+	0.289341i
$172$		−	81.6333i		−	0.474612i
$173$	−164.049			−0.948259			−0.474129	−	0.880455i	$-0.657237\pi$
$173$	−164.049			−0.948259			−0.474129	+	0.880455i	$0.657237\pi$
$174$		0			0
$175$	136.000	−	52.4786i	0.777143	−	0.299878i
$176$		−	65.9697i		−	0.374828i
$177$	−48.0833	+	11.6619i	−0.271657	+	0.0658865i
$178$			93.2952i			0.524131i
$179$		−	16.4924i		−	0.0921364i	−0.998938	−	0.0460682i	$-0.985331\pi$
$179$		−	16.4924i		−	0.0921364i	0.998938	−	0.0460682i	$-0.0146692\pi$
$180$	11.2548	−	89.2935i	0.0625269	−	0.496075i
$181$	−82.0000			−0.453039			−0.226519	−	0.974007i	$-0.572735\pi$
$181$	−82.0000			−0.453039			−0.226519	+	0.974007i	$0.572735\pi$
$182$		0			0
$183$	11.3137	+	46.6476i	0.0618235	+	0.254905i
$184$	68.0000			0.369565
$185$	−96.1665	−	65.9697i	−0.519819	−	0.356593i
$186$	32.0000	+	131.939i	0.172043	+	0.709352i
$187$			186.590i			0.997810i
$188$	−70.7107			−0.376121
$189$	−119.000	+	103.078i	−0.629630	+	0.545384i
$190$	−48.0000	+	69.9714i	−0.252632	+	0.368271i
$191$			296.864i			1.55426i	0.629340	+	0.777130i	$0.283325\pi$
$191$			296.864i			1.55426i	−0.629340	+	0.777130i	$0.716675\pi$
$192$	−5.65685	−	23.3238i	−0.0294628	−	0.121478i
$193$			116.619i			0.604244i	0.953269	+	0.302122i	$0.0976950\pi$
$193$			116.619i			0.604244i	−0.953269	+	0.302122i	$0.902305\pi$
$194$		−	230.894i		−	1.19017i
$195$		0			0
$196$	30.0000			0.153061
$197$	−192.333			−0.976310			−0.488155	−	0.872757i	$-0.662330\pi$
$197$	−192.333			−0.976310			−0.488155	+	0.872757i	$0.662330\pi$
$198$	96.1665	+	186.590i	0.485690	+	0.942376i
$199$	−312.000			−1.56784			−0.783920	−	0.620862i	$-0.786783\pi$
$199$	−312.000			−1.56784			−0.783920	+	0.620862i	$0.786783\pi$
$200$	−25.4558	−	65.9697i	−0.127279	−	0.329848i
$201$	−17.0000	+	4.12311i	−0.0845771	+	0.0205130i
$202$		−	186.590i		−	0.923715i
$203$		0			0
$204$	16.0000	+	65.9697i	0.0784314	+	0.323381i
$205$	−238.000	−	163.267i	−1.16098	−	0.796423i
$206$		−	140.186i		−	0.680513i
$207$	−192.333	+	99.1262i	−0.929145	+	0.478870i
$208$		0			0
$209$		−	197.909i		−	0.946933i
$210$	−43.9584	+	115.619i	−0.209326	+	0.550565i
$211$	−12.0000			−0.0568720			−0.0284360	−	0.999596i	$-0.509053\pi$
$211$	−12.0000			−0.0568720			−0.0284360	+	0.999596i	$0.509053\pi$
$212$	135.765			0.640399
$213$		0			0
$214$	−78.0000			−0.364486
$215$	168.291	+	115.447i	0.782751	+	0.536963i
$216$	50.0000	+	57.7235i	0.231481	+	0.267238i
$217$		−	186.590i		−	0.859864i
$218$	113.137			0.518977
$219$	340.000	−	82.4621i	1.55251	−	0.376539i
$220$	136.000	+	93.2952i	0.618182	+	0.424069i
$221$		0			0
$222$	96.1665	−	23.3238i	0.433183	−	0.105062i
$223$		−	40.8167i		−	0.183034i	−0.995803	−	0.0915172i	$-0.970828\pi$
$223$		−	40.8167i		−	0.183034i	0.995803	−	0.0915172i	$-0.0291716\pi$
$224$			32.9848i			0.147254i
$225$	168.167	+	149.483i	0.747407	+	0.664367i
$226$	−216.000			−0.955752
$227$	−159.806			−0.703992			−0.351996	−	0.936002i	$-0.614497\pi$
$227$	−159.806			−0.703992			−0.351996	+	0.936002i	$0.614497\pi$
$228$	−16.9706	−	69.9714i	−0.0744323	−	0.306892i
$229$	82.0000			0.358079			0.179039	−	0.983842i	$-0.442701\pi$
$229$	82.0000			0.358079			0.179039	+	0.983842i	$0.442701\pi$
$230$	−96.1665	+	140.186i	−0.418115	+	0.609503i
$231$	−68.0000	−	280.371i	−0.294372	−	1.21373i
$232$		0			0
$233$	192.333			0.825464			0.412732	−	0.910853i	$-0.364575\pi$
$233$	192.333			0.825464			0.412732	+	0.910853i	$0.364575\pi$
$234$		0			0
$235$	100.000	−	145.774i	0.425532	−	0.620314i
$236$		−	32.9848i		−	0.139766i
$237$	50.9117	+	209.914i	0.214817	+	0.885714i
$238$		−	93.2952i		−	0.391997i
$239$			461.788i			1.93217i	0.258231	+	0.966083i	$0.416861\pi$
$239$			461.788i			1.93217i	−0.258231	+	0.966083i	$0.583139\pi$
$240$	56.0833	+	21.3229i	0.233680	+	0.0888456i
$241$	304.000			1.26141			0.630705	−	0.776022i	$-0.282766\pi$
$241$	304.000			1.26141			0.630705	+	0.776022i	$0.282766\pi$
$242$	−213.546			−0.882423
$243$	−225.567	−	90.3798i	−0.928260	−	0.371933i
$244$	−32.0000			−0.131148
$245$	−42.4264	+	61.8466i	−0.173169	+	0.252435i
$246$	238.000	−	57.7235i	0.967480	−	0.234648i
$247$		0			0
$248$	−90.5097			−0.364958
$249$	31.0000	+	127.816i	0.124498	+	0.513318i
$250$	172.000	+	40.8167i	0.688000	+	0.163267i
$251$		−	346.341i		−	1.37984i	−0.723884	−	0.689922i	$-0.757645\pi$
$251$		−	346.341i		−	1.37984i	0.723884	−	0.689922i	$-0.242355\pi$
$252$	−48.0833	−	93.2952i	−0.190807	−	0.370219i
$253$		−	396.505i		−	1.56721i
$254$			57.7235i			0.227258i
$255$	−158.627	−	60.3104i	−0.622068	−	0.236511i
$256$	16.0000			0.0625000
$257$	390.323			1.51877			0.759383	−	0.650644i	$-0.225501\pi$
$257$	390.323			1.51877			0.759383	+	0.650644i	$0.225501\pi$
$258$	−168.291	+	40.8167i	−0.652292	+	0.158204i
$259$	−136.000			−0.525097
$260$		0			0
$261$		0			0
$262$		−	69.9714i		−	0.267066i
$263$	295.571			1.12384			0.561921	−	0.827191i	$-0.310062\pi$
$263$	295.571			1.12384			0.561921	+	0.827191i	$0.310062\pi$
$264$	−136.000	+	32.9848i	−0.515152	+	0.124943i
$265$	−192.000	+	279.886i	−0.724528	+	1.05617i
$266$			98.9545i			0.372010i
$267$	192.333	−	46.6476i	0.720348	−	0.174710i
$268$		−	11.6619i		−	0.0435146i
$269$		−	74.2159i		−	0.275896i	−0.990440	−	0.137948i	$-0.955949\pi$
$269$		−	74.2159i		−	0.275896i	0.990440	−	0.137948i	$-0.0440506\pi$
$270$	−189.711	+	21.4443i	−0.702632	+	0.0794234i
$271$	40.0000			0.147601			0.0738007	−	0.997273i	$-0.476487\pi$
$271$	40.0000			0.147601			0.0738007	+	0.997273i	$0.476487\pi$
$272$	−45.2548			−0.166378
$273$		0			0
$274$	−72.0000			−0.262774
$275$	−384.666	+	148.432i	−1.39879	+	0.539752i
$276$	−34.0000	−	140.186i	−0.123188	−	0.507919i
$277$			443.152i			1.59983i	0.600115	+	0.799914i	$0.295122\pi$
$277$			443.152i			1.59983i	−0.600115	+	0.799914i	$0.704878\pi$
$278$	62.2254			0.223832
$279$	256.000	−	131.939i	0.917563	−	0.472901i
$280$	−68.0000	−	46.6476i	−0.242857	−	0.166599i
$281$		−	519.511i		−	1.84879i	−0.381431	−	0.924397i	$-0.624569\pi$
$281$		−	519.511i		−	1.84879i	0.381431	−	0.924397i	$-0.375431\pi$
$282$	35.3553	+	145.774i	0.125374	+	0.516928i
$283$			320.702i			1.13322i	0.823985	+	0.566612i	$0.191746\pi$
$283$			320.702i			1.13322i	−0.823985	+	0.566612i	$0.808254\pi$
$284$		0			0
$285$	168.250	+	63.9688i	0.590350	+	0.224452i
$286$		0			0
$287$	−336.583			−1.17276
$288$	−45.2548	+	23.3238i	−0.157135	+	0.0809854i
$289$	−161.000			−0.557093
$290$		0			0
$291$	−476.000	+	115.447i	−1.63574	+	0.396725i
$292$			233.238i			0.798761i
$293$	84.8528			0.289600			0.144800	−	0.989461i	$-0.453746\pi$
$293$	84.8528			0.289600			0.144800	+	0.989461i	$0.453746\pi$
$294$	−15.0000	−	61.8466i	−0.0510204	−	0.210363i
$295$	68.0000	+	46.6476i	0.230508	+	0.158128i
$296$			65.9697i			0.222871i
$297$	336.583	−	291.548i	1.13328	−	0.981642i
$298$			11.6619i			0.0391339i
$299$		0			0
$300$	−123.272	+	85.4634i	−0.410907	+	0.284878i
$301$	238.000			0.790698
$302$	192.333			0.636864
$303$	−384.666	+	93.2952i	−1.26953	+	0.307905i
$304$	48.0000			0.157895
$305$	45.2548	−	65.9697i	0.148377	−	0.216294i
$306$	128.000	−	65.9697i	0.418301	−	0.215587i
$307$		−	367.350i		−	1.19658i	−0.801280	−	0.598290i	$-0.795847\pi$
$307$		−	367.350i		−	1.19658i	0.801280	−	0.598290i	$-0.204153\pi$
$308$	192.333			0.624458
$309$	−289.000	+	70.0928i	−0.935275	+	0.226838i
$310$	128.000	−	186.590i	0.412903	−	0.601905i
$311$			98.9545i			0.318182i	0.987264	+	0.159091i	$0.0508563\pi$
$311$			98.9545i			0.318182i	−0.987264	+	0.159091i	$0.949144\pi$
$312$		0			0
$313$			186.590i			0.596136i	0.954545	+	0.298068i	$0.0963422\pi$
$313$			186.590i			0.596136i	−0.954545	+	0.298068i	$0.903658\pi$
$314$			164.924i			0.525236i
$315$	260.333	+	32.8132i	0.826454	+	0.104169i
$316$	−144.000			−0.455696
$317$	−520.431			−1.64174			−0.820868	−	0.571117i	$-0.806510\pi$
$317$	−520.431			−1.64174			−0.820868	+	0.571117i	$0.806510\pi$
$318$	−67.8823	−	279.886i	−0.213466	−	0.880144i
$319$		0			0
$320$	−22.6274	+	32.9848i	−0.0707107	+	0.103078i
$321$	39.0000	+	160.801i	0.121495	+	0.500938i
$322$			198.252i			0.615691i
$323$	−135.765			−0.420324
$324$	94.0000	−	131.939i	0.290123	−	0.407220i
$325$		0			0
$326$		−	140.186i		−	0.430017i
$327$	−56.5685	−	233.238i	−0.172992	−	0.713266i
$328$			163.267i			0.497764i
$329$		−	206.155i		−	0.626612i
$330$	124.333	−	327.019i	0.376767	−	0.990966i
$331$	292.000			0.882175			0.441088	−	0.897464i	$-0.354593\pi$
$331$	292.000			0.882175			0.441088	+	0.897464i	$0.354593\pi$
$332$	−87.6812			−0.264100
$333$	−96.1665	−	186.590i	−0.288788	−	0.560332i
$334$	414.000			1.23952
$335$	24.0416	+	16.4924i	0.0717661	+	0.0492311i
$336$	68.0000	−	16.4924i	0.202381	−	0.0490846i
$337$		−	326.533i		−	0.968942i	−0.874807	−	0.484471i	$-0.839012\pi$
$337$		−	326.533i		−	0.968942i	0.874807	−	0.484471i	$-0.160988\pi$
$338$	239.002			0.707107
$339$	108.000	+	445.295i	0.318584	+	1.31356i
$340$	64.0000	−	93.2952i	0.188235	−	0.274398i
$341$			527.758i			1.54768i
$342$	−135.765	+	69.9714i	−0.396972	+	0.204595i
$343$			373.181i			1.08799i
$344$		−	115.447i		−	0.335602i
$345$	337.083	+	128.160i	0.977053	+	0.371477i
$346$	−232.000			−0.670520
$347$	394.566			1.13708			0.568538	−	0.822657i	$-0.307509\pi$
$347$	394.566			1.13708			0.568538	+	0.822657i	$0.307509\pi$
$348$		0			0
$349$	254.000			0.727794			0.363897	−	0.931439i	$-0.381446\pi$
$349$	254.000			0.727794			0.363897	+	0.931439i	$0.381446\pi$
$350$	192.333	−	74.2159i	0.549523	−	0.212045i
$351$		0			0
$352$		−	93.2952i		−	0.265043i
$353$	345.068			0.977530			0.488765	−	0.872415i	$-0.337448\pi$
$353$	345.068			0.977530			0.488765	+	0.872415i	$0.337448\pi$
$354$	−68.0000	+	16.4924i	−0.192090	+	0.0465888i
$355$		0			0
$356$			131.939i			0.370616i
$357$	−192.333	+	46.6476i	−0.538748	+	0.130666i
$358$		−	23.3238i		−	0.0651503i
$359$		−	395.818i		−	1.10256i	−0.834321	−	0.551279i	$-0.814140\pi$
$359$		−	395.818i		−	1.10256i	0.834321	−	0.551279i	$-0.185860\pi$
$360$	15.9167	−	126.280i	0.0442132	−	0.350778i
$361$	−217.000			−0.601108
$362$	−115.966			−0.320347
$363$	106.773	+	440.237i	0.294141	+	1.21277i
$364$		0			0
$365$	−480.833	−	329.848i	−1.31735	−	0.903694i
$366$	16.0000	+	65.9697i	0.0437158	+	0.180245i
$367$		−	413.998i		−	1.12806i	−0.825755	−	0.564029i	$-0.809250\pi$
$367$		−	413.998i		−	1.12806i	0.825755	−	0.564029i	$-0.190750\pi$
$368$	96.1665			0.261322
$369$	−238.000	−	461.788i	−0.644986	−	1.25146i
$370$	−136.000	−	93.2952i	−0.367568	−	0.252149i
$371$			395.818i			1.06690i
$372$	45.2548	+	186.590i	0.121653	+	0.501587i
$373$		−	629.743i		−	1.68832i	−0.536092	−	0.844159i	$-0.680100\pi$
$373$		−	629.743i		−	1.68832i	0.536092	−	0.844159i	$-0.319900\pi$
$374$			263.879i			0.705558i
$375$	−1.85429	−	374.995i	−0.00494478	−	0.999988i
$376$	−100.000			−0.265957
$377$		0			0
$378$	−168.291	+	145.774i	−0.445215	+	0.385645i
$379$	−572.000			−1.50923			−0.754617	−	0.656165i	$-0.772178\pi$
$379$	−572.000			−1.50923			−0.754617	+	0.656165i	$0.772178\pi$
$380$	−67.8823	+	98.9545i	−0.178638	+	0.260407i
$381$	119.000	−	28.8617i	0.312336	−	0.0757526i
$382$			419.829i			1.09903i
$383$	−193.747			−0.505868			−0.252934	−	0.967484i	$-0.581395\pi$
$383$	−193.747			−0.505868			−0.252934	+	0.967484i	$0.581395\pi$
$384$	−8.00000	−	32.9848i	−0.0208333	−	0.0858980i
$385$	−272.000	+	396.505i	−0.706494	+	1.02988i
$386$			164.924i			0.427265i
$387$	168.291	+	326.533i	0.434862	+	0.843755i
$388$		−	326.533i		−	0.841581i
$389$			387.572i			0.996329i	0.867083	+	0.498164i	$0.165992\pi$
$389$			387.572i			0.996329i	−0.867083	+	0.498164i	$0.834008\pi$
$390$		0			0
$391$	−272.000			−0.695652
$392$	42.4264			0.108231
$393$	−144.250	+	34.9857i	−0.367048	+	0.0890222i
$394$	−272.000			−0.690355
$395$	203.647	−	296.864i	0.515561	−	0.751553i
$396$	136.000	+	263.879i	0.343434	+	0.666361i
$397$			513.124i			1.29250i	0.763124	+	0.646252i	$0.223664\pi$
$397$			513.124i			1.29250i	−0.763124	+	0.646252i	$0.776336\pi$
$398$	−441.235			−1.10863
$399$	204.000	−	49.4773i	0.511278	−	0.124003i
$400$	−36.0000	−	93.2952i	−0.0900000	−	0.233238i
$401$			65.9697i			0.164513i	0.996611	+	0.0822565i	$0.0262127\pi$
$401$			65.9697i			0.164513i	−0.996611	+	0.0822565i	$0.973787\pi$
$402$	−24.0416	+	5.83095i	−0.0598051	+	0.0145049i
$403$		0			0
$404$		−	263.879i		−	0.653165i
$405$	139.064	+	380.376i	0.343368	+	0.939201i
$406$		0			0
$407$	384.666			0.945126
$408$	22.6274	+	93.2952i	0.0554594	+	0.228665i
$409$	640.000			1.56479			0.782396	−	0.622781i	$-0.213997\pi$
$409$	640.000			1.56479			0.782396	+	0.622781i	$0.213997\pi$
$410$	−336.583	−	230.894i	−0.820934	−	0.563156i
$411$	36.0000	+	148.432i	0.0875912	+	0.361148i
$412$		−	198.252i		−	0.481195i
$413$	96.1665			0.232849
$414$	−272.000	+	140.186i	−0.657005	+	0.338613i
$415$	124.000	−	180.760i	0.298795	−	0.435565i
$416$		0			0
$417$	−31.1127	−	128.281i	−0.0746108	−	0.307628i
$418$		−	279.886i		−	0.669583i
$419$		−	577.235i		−	1.37765i	−0.724928	−	0.688824i	$-0.758127\pi$
$419$		−	577.235i		−	1.37765i	0.724928	−	0.688824i	$-0.241873\pi$
$420$	−62.1665	+	163.509i	−0.148016	+	0.389308i
$421$	−656.000			−1.55819			−0.779097	−	0.626903i	$-0.784322\pi$
$421$	−656.000			−1.55819			−0.779097	+	0.626903i	$0.784322\pi$
$422$	−16.9706			−0.0402146
$423$	282.843	−	145.774i	0.668659	−	0.344619i
$424$	192.000			0.452830
$425$	101.823	+	263.879i	0.239584	+	0.620891i
$426$		0			0
$427$		−	93.2952i		−	0.218490i
$428$	−110.309			−0.257731
$429$		0			0
$430$	238.000	+	163.267i	0.553488	+	0.379690i
$431$		−	362.833i		−	0.841841i	−0.907098	−	0.420920i	$-0.861707\pi$
$431$		−	362.833i		−	0.841841i	0.907098	−	0.420920i	$-0.138293\pi$
$432$	70.7107	+	81.6333i	0.163682	+	0.188966i
$433$		−	163.267i		−	0.377059i	−0.982068	−	0.188530i	$-0.939628\pi$
$433$		−	163.267i		−	0.377059i	0.982068	−	0.188530i	$-0.0603722\pi$
$434$		−	263.879i		−	0.608016i
$435$		0			0
$436$	160.000			0.366972
$437$	288.500			0.660182
$438$	480.833	−	116.619i	1.09779	−	0.266254i
$439$	432.000			0.984055			0.492027	−	0.870580i	$-0.336256\pi$
$439$	432.000			0.984055			0.492027	+	0.870580i	$0.336256\pi$
$440$	192.333	+	131.939i	0.437121	+	0.299862i
$441$	−120.000	+	61.8466i	−0.272109	+	0.140242i
$442$		0			0
$443$	123.037			0.277735			0.138867	−	0.990311i	$-0.455654\pi$
$443$	123.037			0.277735			0.138867	+	0.990311i	$0.455654\pi$
$444$	136.000	−	32.9848i	0.306306	−	0.0742902i
$445$	−272.000	−	186.590i	−0.611236	−	0.419304i
$446$		−	57.7235i		−	0.129425i
$447$	24.0416	−	5.83095i	0.0537844	−	0.0130446i
$448$			46.6476i			0.104124i
$449$			865.852i			1.92840i	0.265174	+	0.964201i	$0.414571\pi$
$449$			865.852i			1.92840i	−0.265174	+	0.964201i	$0.585429\pi$
$450$	237.823	+	211.400i	0.528496	+	0.469778i
$451$	952.000			2.11086
$452$	−305.470			−0.675819
$453$	−96.1665	−	396.505i	−0.212288	−	0.875286i
$454$	−226.000			−0.497797
$455$		0			0
$456$	−24.0000	−	98.9545i	−0.0526316	−	0.217006i
$457$		−	466.476i		−	1.02074i	−0.859956	−	0.510368i	$-0.829509\pi$
$457$		−	466.476i		−	1.02074i	0.859956	−	0.510368i	$-0.170491\pi$
$458$	115.966			0.253200
$459$	−200.000	−	230.894i	−0.435730	−	0.503037i
$460$	−136.000	+	198.252i	−0.295652	+	0.430983i
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$	−96.1665	−	396.505i	−0.208153	−	0.858235i
$463$			612.250i			1.32235i	0.750230	+	0.661177i	$0.229943\pi$
$463$			612.250i			1.32235i	−0.750230	+	0.661177i	$0.770057\pi$
$464$		0			0
$465$	−448.666	−	170.584i	−0.964873	−	0.366846i
$466$	272.000			0.583691
$467$	−767.918			−1.64436			−0.822182	−	0.569225i	$-0.807243\pi$
$467$	−767.918			−1.64436			−0.822182	+	0.569225i	$0.807243\pi$
$468$		0			0
$469$	34.0000			0.0724947
$470$	141.421	−	206.155i	0.300897	−	0.438628i
$471$	340.000	−	82.4621i	0.721868	−	0.175079i
$472$		−	46.6476i		−	0.0988297i
$473$	−673.166			−1.42318
$474$	72.0000	+	296.864i	0.151899	+	0.626295i
$475$	−108.000	−	279.886i	−0.227368	−	0.589233i
$476$		−	131.939i		−	0.277184i
$477$	−543.058	+	279.886i	−1.13849	+	0.586762i
$478$			653.067i			1.36625i
$479$			560.742i			1.17065i	0.810798	+	0.585326i	$0.199033\pi$
$479$			560.742i			1.17065i	−0.810798	+	0.585326i	$0.800967\pi$
$480$	79.3137	+	30.1552i	0.165237	+	0.0628233i
$481$		0			0
$482$	429.921			0.891952
$483$	408.708	−	99.1262i	0.846186	−	0.205230i
$484$	−302.000			−0.623967
$485$	673.166	+	461.788i	1.38797	+	0.952140i
$486$	−319.000	−	127.816i	−0.656379	−	0.262996i
$487$			647.236i			1.32903i	0.747277	+	0.664513i	$0.231361\pi$
$487$			647.236i			1.32903i	−0.747277	+	0.664513i	$0.768639\pi$
$488$	−45.2548			−0.0927353
$489$	−289.000	+	70.0928i	−0.591002	+	0.143339i
$490$	−60.0000	+	87.4643i	−0.122449	+	0.178499i
$491$		−	346.341i		−	0.705379i	−0.935740	−	0.352689i	$-0.885267\pi$
$491$		−	346.341i		−	0.705379i	0.935740	−	0.352689i	$-0.114733\pi$
$492$	336.583	−	81.6333i	0.684111	−	0.165921i
$493$		0			0
$494$		0			0
$495$	−736.333	−	92.8097i	−1.48754	−	0.187494i
$496$	−128.000			−0.258065
$497$		0			0
$498$	43.8406	+	180.760i	0.0880334	+	0.362971i
$499$	−660.000			−1.32265			−0.661323	−	0.750102i	$-0.730005\pi$
$499$	−660.000			−1.32265			−0.661323	+	0.750102i	$0.730005\pi$
$500$	243.245	+	57.7235i	0.486489	+	0.115447i
$501$	−207.000	−	853.483i	−0.413174	−	1.70356i
$502$		−	489.800i		−	0.975697i
$503$	−182.434			−0.362691			−0.181345	−	0.983419i	$-0.558045\pi$
$503$	−182.434			−0.362691			−0.181345	+	0.983419i	$0.558045\pi$
$504$	−68.0000	−	131.939i	−0.134921	−	0.261784i
$505$	544.000	+	373.181i	1.07723	+	0.738972i
$506$		−	560.742i		−	1.10819i
$507$	−119.501	−	492.715i	−0.235702	−	0.971825i
$508$			81.6333i			0.160696i
$509$		−	395.818i		−	0.777639i	−0.921314	−	0.388819i	$-0.872883\pi$
$509$		−	395.818i		−	0.777639i	0.921314	−	0.388819i	$-0.127117\pi$
$510$	−224.333	−	85.2918i	−0.439869	−	0.167239i
$511$	−680.000			−1.33072
$512$	22.6274			0.0441942
$513$	212.132	+	244.900i	0.413513	+	0.477388i
$514$	552.000			1.07393
$515$	408.708	+	280.371i	0.793607	+	0.544410i
$516$	−238.000	+	57.7235i	−0.461240	+	0.111867i
$517$			583.095i			1.12784i
$518$	−192.333			−0.371299
$519$	116.000	+	478.280i	0.223507	+	0.921542i
$520$		0			0
$521$		−	131.939i		−	0.253243i	−0.991951	−	0.126621i	$-0.959587\pi$
$521$		−	131.939i		−	0.253243i	0.991951	−	0.126621i	$-0.0404133\pi$
$522$		0			0
$523$			145.774i			0.278726i	0.990241	+	0.139363i	$0.0445055\pi$
$523$			145.774i			0.278726i	−0.990241	+	0.139363i	$0.955494\pi$
$524$		−	98.9545i		−	0.188845i
$525$	−249.167	−	359.397i	−0.474603	−	0.684565i
$526$	418.000			0.794677
$527$	362.039			0.686980
$528$	−192.333	+	46.6476i	−0.364267	+	0.0883478i
$529$	49.0000			0.0926276
$530$	−271.529	+	395.818i	−0.512319	+	0.746827i
$531$	68.0000	+	131.939i	0.128060	+	0.248473i
$532$			139.943i			0.263050i
$533$		0			0
$534$	272.000	−	65.9697i	0.509363	−	0.123539i
$535$	156.000	−	227.407i	0.291589	−	0.425060i
$536$		−	16.4924i		−	0.0307694i
$537$	−48.0833	+	11.6619i	−0.0895405	+	0.0217168i
$538$		−	104.957i		−	0.195088i
$539$		−	247.386i		−	0.458973i
$540$	−268.291	+	30.3268i	−0.496836	+	0.0561608i
$541$	418.000			0.772643			0.386322	−	0.922364i	$-0.373745\pi$
$541$	418.000			0.772643			0.386322	+	0.922364i	$0.373745\pi$
$542$	56.5685			0.104370
$543$	57.9828	+	239.069i	0.106782	+	0.440274i
$544$	−64.0000			−0.117647
$545$	−226.274	+	329.848i	−0.415182	+	0.605227i
$546$		0			0
$547$			285.717i			0.522334i	0.965294	+	0.261167i	$0.0841073\pi$
$547$			285.717i			0.522334i	−0.965294	+	0.261167i	$0.915893\pi$
$548$	−101.823			−0.185809
$549$	128.000	−	65.9697i	0.233151	−	0.120163i
$550$	−544.000	+	209.914i	−0.989091	+	0.381662i
$551$		0			0
$552$	−48.0833	−	198.252i	−0.0871074	−	0.359153i
$553$		−	419.829i		−	0.759184i
$554$			626.712i			1.13125i
$555$	−124.333	+	327.019i	−0.224024	+	0.589223i
$556$	88.0000			0.158273
$557$	424.264			0.761695			0.380847	−	0.924638i	$-0.375632\pi$
$557$	424.264			0.761695			0.380847	+	0.924638i	$0.375632\pi$
$558$	362.039	−	186.590i	0.648815	−	0.334392i
$559$		0			0
$560$	−96.1665	−	65.9697i	−0.171726	−	0.117803i
$561$	544.000	−	131.939i	0.969697	−	0.235186i
$562$		−	734.700i		−	1.30730i
$563$	−813.173			−1.44436			−0.722178	−	0.691707i	$-0.756859\pi$
$563$	−813.173			−1.44436			−0.722178	+	0.691707i	$0.756859\pi$
$564$	50.0000	+	206.155i	0.0886525	+	0.365524i
$565$	432.000	−	629.743i	0.764602	−	1.11459i
$566$			453.542i			0.801310i
$567$	384.666	+	274.055i	0.678423	+	0.483342i
$568$		0			0
$569$		−	453.542i		−	0.797085i	−0.917150	−	0.398543i	$-0.869516\pi$
$569$		−	453.542i		−	0.797085i	0.917150	−	0.398543i	$-0.130484\pi$
$570$	237.941	+	90.4656i	0.417441	+	0.158712i
$571$	220.000			0.385289			0.192644	−	0.981269i	$-0.438294\pi$
$571$	220.000			0.385289			0.192644	+	0.981269i	$0.438294\pi$
$572$		0			0
$573$	865.499	−	209.914i	1.51047	−	0.366343i
$574$	−476.000			−0.829268
$575$	−216.375	−	560.742i	−0.376304	−	0.975204i
$576$	−64.0000	+	32.9848i	−0.111111	+	0.0572654i
$577$		−	46.6476i		−	0.0808451i	−0.999183	−	0.0404225i	$-0.987130\pi$
$577$		−	46.6476i		−	0.0808451i	0.999183	−	0.0404225i	$-0.0128704\pi$
$578$	−227.688			−0.393925
$579$	340.000	−	82.4621i	0.587219	−	0.142422i
$580$		0			0
$581$		−	255.633i		−	0.439987i
$582$	−673.166	+	163.267i	−1.15664	+	0.280527i
$583$		−	1119.54i		−	1.92031i
$584$			329.848i			0.564809i
$585$		0			0
$586$	120.000			0.204778
$587$	55.1543			0.0939597			0.0469798	−	0.998896i	$-0.485040\pi$
$587$	55.1543			0.0939597			0.0469798	+	0.998896i	$0.485040\pi$
$588$	−21.2132	−	87.4643i	−0.0360769	−	0.148749i
$589$	−384.000			−0.651952
$590$	96.1665	+	65.9697i	0.162994	+	0.111813i
$591$	136.000	+	560.742i	0.230118	+	0.948803i
$592$			93.2952i			0.157593i
$593$	390.323			0.658217			0.329109	−	0.944292i	$-0.393252\pi$
$593$	390.323			0.658217			0.329109	+	0.944292i	$0.393252\pi$
$594$	476.000	−	412.311i	0.801347	−	0.694126i
$595$	272.000	+	186.590i	0.457143	+	0.313597i
$596$			16.4924i			0.0276718i
$597$	220.617	+	909.628i	0.369543	+	1.52367i
$598$		0			0
$599$			98.9545i			0.165200i	0.996583	+	0.0825998i	$0.0263223\pi$
$599$			98.9545i			0.165200i	−0.996583	+	0.0825998i	$0.973678\pi$
$600$	−174.333	+	120.864i	−0.290555	+	0.201439i
$601$	−880.000			−1.46423			−0.732113	−	0.681183i	$-0.761466\pi$
$601$	−880.000			−1.46423			−0.732113	+	0.681183i	$0.761466\pi$
$602$	336.583			0.559108
$603$	24.0416	+	46.6476i	0.0398700	+	0.0773592i
$604$	272.000			0.450331
$605$	427.092	−	622.589i	0.705938	−	1.02907i
$606$	−544.000	+	131.939i	−0.897690	+	0.217722i
$607$		−	425.659i		−	0.701251i	−0.936516	−	0.350626i	$-0.885969\pi$
$607$		−	425.659i		−	0.701251i	0.936516	−	0.350626i	$-0.114031\pi$
$608$	67.8823			0.111648
$609$		0			0
$610$	64.0000	−	93.2952i	0.104918	−	0.152943i
$611$		0			0
$612$	181.019	−	93.2952i	0.295783	−	0.152443i
$613$			606.419i			0.989264i	0.869102	+	0.494632i	$0.164697\pi$
$613$			606.419i			0.989264i	−0.869102	+	0.494632i	$0.835303\pi$
$614$		−	519.511i		−	0.846110i
$615$	−307.709	+	809.330i	−0.500339	+	1.31598i
$616$	272.000			0.441558
$617$	−113.137			−0.183366			−0.0916832	−	0.995788i	$-0.529225\pi$
$617$	−113.137			−0.183366			−0.0916832	+	0.995788i	$0.529225\pi$
$618$	−408.708	+	99.1262i	−0.661339	+	0.160398i
$619$	52.0000			0.0840065			0.0420032	−	0.999117i	$-0.486626\pi$
$619$	52.0000			0.0840065			0.0420032	+	0.999117i	$0.486626\pi$
$620$	181.019	−	263.879i	0.291967	−	0.425611i
$621$	425.000	+	490.650i	0.684380	+	0.790096i
$622$			139.943i			0.224988i
$623$	−384.666			−0.617442
$624$		0			0
$625$	−463.000	+	419.829i	−0.740800	+	0.671726i
$626$			263.879i			0.421532i
$627$	−576.999	+	139.943i	−0.920254	+	0.223194i
$628$			233.238i			0.371398i
$629$		−	263.879i		−	0.419521i
$630$	368.167	+	46.4049i	0.584391	+	0.0736585i
$631$	−544.000			−0.862124			−0.431062	−	0.902322i	$-0.641861\pi$
$631$	−544.000			−0.862124			−0.431062	+	0.902322i	$0.641861\pi$
$632$	−203.647			−0.322226
$633$	8.48528	+	34.9857i	0.0134049	+	0.0552697i
$634$	−736.000			−1.16088
$635$	−168.291	−	115.447i	−0.265026	−	0.181806i
$636$	−96.0000	−	395.818i	−0.150943	−	0.622356i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−32.0000	+	46.6476i	−0.0500000	+	0.0728869i
$641$			849.360i			1.32505i	0.749038	+	0.662527i	$0.230516\pi$
$641$			849.360i			1.32505i	−0.749038	+	0.662527i	$0.769484\pi$
$642$	55.1543	+	227.407i	0.0859102	+	0.354217i
$643$		−	367.350i		−	0.571306i	−0.958333	−	0.285653i	$-0.907789\pi$
$643$		−	367.350i		−	0.571306i	0.958333	−	0.285653i	$-0.0922105\pi$
$644$			280.371i			0.435359i
$645$	217.583	−	572.283i	0.337338	−	0.887260i
$646$	−192.000			−0.297214
$647$	−971.565			−1.50165			−0.750823	−	0.660504i	$-0.770343\pi$
$647$	−971.565			−1.50165			−0.750823	+	0.660504i	$0.770343\pi$
$648$	132.936	−	186.590i	0.205148	−	0.287948i
$649$	−272.000			−0.419106
$650$		0			0
$651$	−544.000	+	131.939i	−0.835637	+	0.202672i
$652$		−	198.252i		−	0.304068i
$653$	350.725			0.537098			0.268549	−	0.963266i	$-0.413456\pi$
$653$	350.725			0.537098			0.268549	+	0.963266i	$0.413456\pi$
$654$	−80.0000	−	329.848i	−0.122324	−	0.504355i
$655$	204.000	+	139.943i	0.311450	+	0.213653i
$656$			230.894i			0.351972i
$657$	−480.833	−	932.952i	−0.731861	−	1.42002i
$658$		−	291.548i		−	0.443081i
$659$			577.235i			0.875925i	0.898993	+	0.437963i	$0.144300\pi$
$659$			577.235i			0.875925i	−0.898993	+	0.437963i	$0.855700\pi$
$660$	175.833	−	462.474i	0.266414	−	0.700719i
$661$	80.0000			0.121029			0.0605144	−	0.998167i	$-0.480726\pi$
$661$	80.0000			0.121029			0.0605144	+	0.998167i	$0.480726\pi$
$662$	412.950			0.623792
$663$		0			0
$664$	−124.000			−0.186747
$665$	−288.500	−	197.909i	−0.433834	−	0.297608i
$666$	−136.000	−	263.879i	−0.204204	−	0.396214i
$667$		0			0
$668$	585.484			0.876474
$669$	−119.000	+	28.8617i	−0.177877	+	0.0431416i
$670$	34.0000	+	23.3238i	0.0507463	+	0.0348117i
$671$			263.879i			0.393262i
$672$	96.1665	−	23.3238i	0.143105	−	0.0347080i
$673$			489.800i			0.727786i	0.931441	+	0.363893i	$0.118553\pi$
$673$			489.800i			0.727786i	−0.931441	+	0.363893i	$0.881447\pi$
$674$		−	461.788i		−	0.685145i
$675$	316.901	−	595.986i	0.469483	−	0.882942i
$676$	338.000			0.500000
$677$	192.333			0.284096			0.142048	−	0.989860i	$-0.454631\pi$
$677$	192.333			0.284096			0.142048	+	0.989860i	$0.454631\pi$
$678$	152.735	+	629.743i	0.225273	+	0.928824i
$679$	952.000			1.40206
$680$	90.5097	−	131.939i	0.133102	−	0.194029i
$681$	113.000	+	465.911i	0.165932	+	0.684157i
$682$			746.362i			1.09437i
$683$	236.174			0.345789			0.172894	−	0.984940i	$-0.444688\pi$
$683$	236.174			0.345789			0.172894	+	0.984940i	$0.444688\pi$
$684$	−192.000	+	98.9545i	−0.280702	+	0.144670i
$685$	144.000	−	209.914i	0.210219	−	0.306444i
$686$			527.758i			0.769326i
$687$	−57.9828	−	239.069i	−0.0843999	−	0.347990i
$688$		−	163.267i		−	0.237306i
$689$		0			0
$690$	476.708	+	181.245i	0.690881	+	0.262674i
$691$	−548.000			−0.793054			−0.396527	−	0.918023i	$-0.629785\pi$
$691$	−548.000			−0.793054			−0.396527	+	0.918023i	$0.629785\pi$
$692$	−328.098			−0.474129
$693$	−769.332	+	396.505i	−1.11015	+	0.572157i
$694$	558.000			0.804035
$695$	−124.451	+	181.417i	−0.179066	+	0.261031i
$696$		0			0
$697$		−	653.067i		−	0.936968i
$698$	359.210			0.514628
$699$	−136.000	−	560.742i	−0.194564	−	0.802207i
$700$	272.000	−	104.957i	0.388571	−	0.149939i
$701$			57.7235i			0.0823445i	0.999152	+	0.0411722i	$0.0131092\pi$
$701$			57.7235i			0.0823445i	−0.999152	+	0.0411722i	$0.986891\pi$
$702$		0			0
$703$			279.886i			0.398130i
$704$		−	131.939i		−	0.187414i
$705$	−495.711	−	188.470i	−0.703136	−	0.267333i
$706$	488.000			0.691218
$707$	769.332			1.08816
$708$	−96.1665	+	23.3238i	−0.135828	+	0.0329432i
$709$	1230.00			1.73484			0.867419	−	0.497579i	$-0.165777\pi$
$709$	1230.00			1.73484			0.867419	+	0.497579i	$0.165777\pi$
$710$		0			0
$711$	576.000	−	296.864i	0.810127	−	0.417530i
$712$			186.590i			0.262065i
$713$	−769.332			−1.07901
$714$	−272.000	+	65.9697i	−0.380952	+	0.0923945i
$715$		0			0
$716$		−	32.9848i		−	0.0460682i
$717$	1346.33	−	326.533i	1.87773	−	0.455416i
$718$		−	559.771i		−	0.779626i
$719$		−	626.712i		−	0.871644i	−0.900033	−	0.435822i	$-0.856458\pi$
$719$		−	626.712i		−	0.871644i	0.900033	−	0.435822i	$-0.143542\pi$
$720$	22.5097	−	178.587i	0.0312634	−	0.248037i
$721$	578.000			0.801664
$722$	−306.884			−0.425048
$723$	−214.960	−	886.305i	−0.297317	−	1.22587i
$724$	−164.000			−0.226519
$725$		0			0
$726$	151.000	+	622.589i	0.207989	+	0.857561i
$727$			367.350i			0.505296i	0.967558	+	0.252648i	$0.0813014\pi$
$727$			367.350i			0.505296i	−0.967558	+	0.252648i	$0.918699\pi$
$728$		0			0
$729$	−104.000	+	721.543i	−0.142661	+	0.989772i
$730$	−680.000	−	466.476i	−0.931507	−	0.639008i
$731$			461.788i			0.631721i
$732$	22.6274	+	93.2952i	0.0309118	+	0.127453i
$733$			1002.92i			1.36825i	0.729367	+	0.684123i	$0.239815\pi$
$733$			1002.92i			1.36825i	−0.729367	+	0.684123i	$0.760185\pi$
$734$		−	585.481i		−	0.797658i
$735$	210.312	+	79.9610i	0.286139	+	0.108791i
$736$	136.000			0.184783
$737$	−96.1665			−0.130484
$738$	−336.583	−	653.067i	−0.456074	−	0.884914i
$739$	−340.000			−0.460081			−0.230041	−	0.973181i	$-0.573886\pi$
$739$	−340.000			−0.460081			−0.230041	+	0.973181i	$0.573886\pi$
$740$	−192.333	−	131.939i	−0.259910	−	0.178296i
$741$		0			0
$742$			559.771i			0.754409i
$743$	1243.09			1.67307			0.836537	−	0.547911i	$-0.184577\pi$
$743$	1243.09			1.67307			0.836537	+	0.547911i	$0.184577\pi$
$744$	64.0000	+	263.879i	0.0860215	+	0.354676i
$745$	−34.0000	−	23.3238i	−0.0456376	−	0.0313071i
$746$		−	890.591i		−	1.19382i
$747$	350.725	−	180.760i	0.469511	−	0.241981i
$748$			373.181i			0.498905i
$749$		−	321.602i		−	0.429375i
$750$	−2.62237	−	530.324i	−0.00349649	−	0.707098i
$751$	−520.000			−0.692410			−0.346205	−	0.938159i	$-0.612530\pi$
$751$	−520.000			−0.692410			−0.346205	+	0.938159i	$0.612530\pi$
$752$	−141.421			−0.188060
$753$	−1009.75	+	244.900i	−1.34097	+	0.325232i
$754$		0			0
$755$	−384.666	+	560.742i	−0.509492	+	0.742705i
$756$	−238.000	+	206.155i	−0.314815	+	0.272692i
$757$		−	816.333i		−	1.07838i	−0.842184	−	0.539190i	$-0.818731\pi$
$757$		−	816.333i		−	1.07838i	0.842184	−	0.539190i	$-0.181269\pi$
$758$	−808.930			−1.06719
$759$	−1156.00	+	280.371i	−1.52306	+	0.369395i
$760$	−96.0000	+	139.943i	−0.126316	+	0.184135i
$761$		−	395.818i		−	0.520129i	−0.965591	−	0.260064i	$-0.916256\pi$
$761$		−	395.818i		−	0.520129i	0.965591	−	0.260064i	$-0.0837438\pi$
$762$	168.291	−	40.8167i	0.220855	−	0.0535652i
$763$			466.476i			0.611371i
$764$			593.727i			0.777130i
$765$	−63.6670	+	505.120i	−0.0832248	+	0.660288i
$766$	−274.000			−0.357702
$767$		0			0
$768$	−11.3137	−	46.6476i	−0.0147314	−	0.0607391i
$769$	−306.000			−0.397919			−0.198960	−	0.980008i	$-0.563756\pi$
$769$	−306.000			−0.397919			−0.198960	+	0.980008i	$0.563756\pi$
$770$	−384.666	+	560.742i	−0.499566	+	0.728237i
$771$	−276.000	−	1137.98i	−0.357977	−	1.47598i
$772$			233.238i			0.302122i
$773$	305.470			0.395175			0.197587	−	0.980285i	$-0.436689\pi$
$773$	305.470			0.395175			0.197587	+	0.980285i	$0.436689\pi$
$774$	238.000	+	461.788i	0.307494	+	0.596625i
$775$	288.000	+	746.362i	0.371613	+	0.963048i
$776$		−	461.788i		−	0.595087i
$777$	96.1665	+	396.505i	0.123766	+	0.510302i
$778$			548.109i			0.704511i
$779$			692.682i			0.889194i
$780$		0			0
$781$		0			0
$782$	−384.666			−0.491900
$783$		0			0
$784$	60.0000			0.0765306
$785$	−480.833	−	329.848i	−0.612526	−	0.420189i
$786$	−204.000	+	49.4773i	−0.259542	+	0.0629482i
$787$			565.602i			0.718681i	0.933206	+	0.359341i	$0.116998\pi$
$787$			565.602i			0.718681i	−0.933206	+	0.359341i	$0.883002\pi$
$788$	−384.666			−0.488155
$789$	−209.000	−	861.729i	−0.264892	−	1.09218i
$790$	288.000	−	419.829i	0.364557	−	0.531429i
$791$		−	890.591i		−	1.12590i
$792$	192.333	+	373.181i	0.242845	+	0.471188i
$793$		0			0
$794$			725.667i			0.913938i
$795$	951.765	+	361.862i	1.19719	+	0.455173i
$796$	−624.000			−0.783920
$797$	−1063.49			−1.33436			−0.667182	−	0.744894i	$-0.732500\pi$
$797$	−1063.49			−1.33436			−0.667182	+	0.744894i	$0.732500\pi$
$798$	288.500	−	69.9714i	0.361528	−	0.0876835i
$799$	400.000			0.500626
$800$	−50.9117	−	131.939i	−0.0636396	−	0.164924i
$801$	−272.000	−	527.758i	−0.339576	−	0.658873i
$802$			93.2952i			0.116328i
$803$	1923.33			2.39518
$804$	−34.0000	+	8.24621i	−0.0422886	+	0.0102565i
$805$	−578.000	−	396.505i	−0.718012	−	0.492552i
$806$		0			0
$807$	−216.375	+	52.4786i	−0.268122	+	0.0650292i
$808$		−	373.181i		−	0.461858i
$809$			791.636i			0.978537i	0.872133	+	0.489268i	$0.162736\pi$
$809$			791.636i			0.978537i	−0.872133	+	0.489268i	$0.837264\pi$
$810$	196.666	+	537.933i	0.242798	+	0.664115i
$811$	436.000			0.537608			0.268804	−	0.963195i	$-0.413372\pi$
$811$	436.000			0.537608			0.268804	+	0.963195i	$0.413372\pi$
$812$		0			0
$813$	−28.2843	−	116.619i	−0.0347900	−	0.143443i
$814$	544.000			0.668305
$815$	408.708	+	280.371i	0.501482	+	0.344014i
$816$	32.0000	+	131.939i	0.0392157	+	0.161690i
$817$		−	489.800i		−	0.599510i
$818$	905.097			1.10648
$819$		0			0
$820$	−476.000	−	326.533i	−0.580488	−	0.398211i
$821$		−	799.882i		−	0.974278i	−0.873324	−	0.487139i	$-0.838040\pi$
$821$		−	799.882i		−	0.974278i	0.873324	−	0.487139i	$-0.161960\pi$
$822$	50.9117	+	209.914i	0.0619364	+	0.255370i
$823$		−	1311.96i		−	1.59412i	−0.603897	−	0.797062i	$-0.706386\pi$
$823$		−	1311.96i		−	1.59412i	0.603897	−	0.797062i	$-0.293614\pi$
$824$		−	280.371i		−	0.340256i
$825$	704.749	+	1016.53i	0.854242	+	1.23215i
$826$	136.000			0.164649
$827$	985.707			1.19191			0.595953	−	0.803019i	$-0.296774\pi$
$827$	985.707			1.19191			0.595953	+	0.803019i	$0.296774\pi$
$828$	−384.666	+	198.252i	−0.464573	+	0.239435i
$829$	−1488.00			−1.79493			−0.897467	−	0.441082i	$-0.854595\pi$
$829$	−1488.00			−1.79493			−0.897467	+	0.441082i	$0.854595\pi$
$830$	175.362	−	255.633i	0.211280	−	0.307991i
$831$	1292.00	−	313.356i	1.55475	−	0.377083i
$832$		0			0
$833$	−169.706			−0.203728
$834$	−44.0000	−	181.417i	−0.0527578	−	0.217526i
$835$	−828.000	+	1207.01i	−0.991617	+	1.44552i
$836$		−	395.818i		−	0.473467i
$837$	−565.685	−	653.067i	−0.675849	−	0.780247i
$838$		−	816.333i		−	0.974145i
$839$		−	461.788i		−	0.550403i	−0.961387	−	0.275201i	$-0.911255\pi$
$839$		−	461.788i		−	0.550403i	0.961387	−	0.275201i	$-0.0887445\pi$
$840$	−87.9167	+	231.237i	−0.104663	+	0.275282i
$841$	841.000			1.00000
$842$	−927.724			−1.10181
$843$	−1514.62	+	367.350i	−1.79671	+	0.435765i
$844$	−24.0000			−0.0284360
$845$	−478.004	+	696.805i	−0.565685	+	0.824621i
$846$	400.000	−	206.155i	0.472813	−	0.243682i
$847$		−	880.474i		−	1.03952i
$848$	271.529			0.320199
$849$	935.000	−	226.771i	1.10130	−	0.267103i
$850$	144.000	+	373.181i	0.169412	+	0.439036i
$851$			560.742i			0.658922i
$852$		0			0
$853$		−	326.533i		−	0.382806i	−0.981512	−	0.191403i	$-0.938696\pi$
$853$		−	326.533i		−	0.382806i	0.981512	−	0.191403i	$-0.0613037\pi$
$854$		−	131.939i		−	0.154496i
$855$	67.5290	−	535.761i	0.0789813	−	0.626621i
$856$	−156.000			−0.182243
$857$	−288.500			−0.336639			−0.168319	−	0.985732i	$-0.553834\pi$
$857$	−288.500			−0.336639			−0.168319	+	0.985732i	$0.553834\pi$
$858$		0			0
$859$	796.000			0.926659			0.463329	−	0.886186i	$-0.346655\pi$
$859$	796.000			0.926659			0.463329	+	0.886186i	$0.346655\pi$
$860$	336.583	+	230.894i	0.391375	+	0.268481i
$861$	238.000	+	981.299i	0.276423	+	1.13972i
$862$		−	513.124i		−	0.595271i
$863$	−352.139			−0.408041			−0.204020	−	0.978967i	$-0.565401\pi$
$863$	−352.139			−0.408041			−0.204020	+	0.978967i	$0.565401\pi$
$864$	100.000	+	115.447i	0.115741	+	0.133619i
$865$	464.000	−	676.390i	0.536416	−	0.781954i
$866$		−	230.894i		−	0.266621i
$867$	113.844	+	469.392i	0.131308	+	0.541397i
$868$		−	373.181i		−	0.429932i
$869$			1187.45i			1.36646i
$870$		0			0
$871$		0			0
$872$	226.274			0.259489
$873$	673.166	+	1306.13i	0.771095	+	1.49614i
$874$	408.000			0.466819
$875$	−168.291	+	709.174i	−0.192333	+	0.810485i
$876$	680.000	−	164.924i	0.776256	−	0.188270i
$877$			676.390i			0.771255i	0.922655	+	0.385627i	$0.126015\pi$
$877$			676.390i			0.771255i	−0.922655	+	0.385627i	$0.873985\pi$
$878$	610.940			0.695832
$879$	−60.0000	−	247.386i	−0.0682594	−	0.281441i
$880$	272.000	+	186.590i	0.309091	+	0.212035i
$881$			519.511i			0.589684i	0.955546	+	0.294842i	$0.0952670\pi$
$881$			519.511i			0.589684i	−0.955546	+	0.294842i	$0.904733\pi$
$882$	−169.706	+	87.4643i	−0.192410	+	0.0991658i
$883$		−	1591.85i		−	1.80277i	−0.433014	−	0.901387i	$-0.642550\pi$
$883$		−	1591.85i		−	1.80277i	0.433014	−	0.901387i	$-0.357450\pi$
$884$		0			0
$885$	87.9167	−	231.237i	0.0993409	−	0.261285i
$886$	174.000			0.196388
$887$	−767.918			−0.865747			−0.432874	−	0.901455i	$-0.642500\pi$
$887$	−767.918			−0.865747			−0.432874	+	0.901455i	$0.642500\pi$
$888$	192.333	−	46.6476i	0.216591	−	0.0525311i
$889$	−238.000			−0.267717
$890$	−384.666	−	263.879i	−0.432209	−	0.296493i
$891$	−1088.00	−	775.144i	−1.22110	−	0.869971i
$892$		−	81.6333i		−	0.0915172i
$893$	−424.264			−0.475100
$894$	34.0000	−	8.24621i	0.0380313	−	0.00922395i
$895$	68.0000	+	46.6476i	0.0759777	+	0.0521202i
$896$			65.9697i			0.0736269i
$897$		0			0
$898$			1224.50i			1.36359i
$899$		0			0
$900$	336.333	+	298.965i	0.373703	+	0.332183i
$901$	−768.000			−0.852386
$902$	1346.33			1.49261
$903$	−168.291	−	693.883i	−0.186369	−	0.768420i
$904$	−432.000			−0.477876
$905$	231.931	−	338.095i	0.256277	−	0.373585i
$906$	−136.000	−	560.742i	−0.150110	−	0.618921i
$907$		−	332.364i		−	0.366444i	−0.983072	−	0.183222i	$-0.941347\pi$
$907$		−	332.364i		−	0.366444i	0.983072	−	0.183222i	$-0.0586526\pi$
$908$	−319.612			−0.351996
$909$	544.000	+	1055.52i	0.598460	+	1.16118i
$910$		0			0
$911$		−	692.682i		−	0.760353i	−0.924914	−	0.380177i	$-0.875863\pi$
$911$		−	692.682i		−	0.760353i	0.924914	−	0.380177i	$-0.124137\pi$
$912$	−33.9411	−	139.943i	−0.0372161	−	0.153446i
$913$			723.038i			0.791937i
$914$		−	659.697i		−	0.721769i
$915$	−224.333	−	85.2918i	−0.245173	−	0.0932150i
$916$	164.000			0.179039
$917$	288.500			0.314612
$918$	−282.843	−	326.533i	−0.308108	−	0.355701i
$919$	−912.000			−0.992383			−0.496192	−	0.868213i	$-0.665269\pi$
$919$	−912.000			−0.992383			−0.496192	+	0.868213i	$0.665269\pi$
$920$	−192.333	+	280.371i	−0.209058	+	0.304751i
$921$	−1071.00	+	259.756i	−1.16287	+	0.282037i
$922$		0			0
$923$		0			0
$924$	−136.000	−	560.742i	−0.147186	−	0.606864i
$925$	544.000	−	209.914i	0.588108	−	0.226934i
$926$			865.852i			0.935046i
$927$	408.708	+	793.009i	0.440893	+	0.855458i
$928$		0			0
$929$		−	1261.67i		−	1.35810i	−0.734094	−	0.679048i	$-0.762393\pi$
$929$		−	1261.67i		−	1.35810i	0.734094	−	0.679048i	$-0.237607\pi$
$930$	−634.510	−	241.242i	−0.682268	−	0.259400i
$931$	180.000			0.193340
$932$	384.666			0.412732
$933$	288.500	−	69.9714i	0.309217	−	0.0749962i
$934$	−1086.00			−1.16274
$935$	−769.332	−	527.758i	−0.822815	−	0.564447i
$936$		0			0
$937$			816.333i			0.871220i	0.900135	+	0.435610i	$0.143467\pi$
$937$			816.333i			0.871220i	−0.900135	+	0.435610i	$0.856533\pi$
$938$	48.0833			0.0512615
$939$	544.000	−	131.939i	0.579340	−	0.140511i
$940$	200.000	−	291.548i	0.212766	−	0.310157i
$941$		−	1055.52i		−	1.12170i	−0.827919	−	0.560848i	$-0.810475\pi$
$941$		−	1055.52i		−	1.12170i	0.827919	−	0.560848i	$-0.189525\pi$
$942$	480.833	−	116.619i	0.510438	−	0.123799i
$943$			1387.77i			1.47165i
$944$		−	65.9697i		−	0.0698831i
$945$	−88.4172	−	782.197i	−0.0935631	−	0.827722i
$946$	−952.000			−1.00634
$947$	−114.551			−0.120962			−0.0604812	−	0.998169i	$-0.519264\pi$
$947$	−114.551			−0.120962			−0.0604812	+	0.998169i	$0.519264\pi$
$948$	101.823	+	419.829i	0.107409	+	0.442857i
$949$		0			0
$950$	−152.735	−	395.818i	−0.160774	−	0.416651i
$951$	368.000	+	1517.30i	0.386961	+	1.59548i
$952$		−	186.590i		−	0.195998i
$953$	243.245			0.255241			0.127621	−	0.991823i	$-0.459266\pi$
$953$	243.245			0.255241			0.127621	+	0.991823i	$0.459266\pi$
$954$	−768.000	+	395.818i	−0.805031	+	0.414904i
$955$	−1224.00	−	839.657i	−1.28168	−	0.879222i
$956$			923.576i			0.966083i
$957$		0			0
$958$			793.009i			0.827776i
$959$		−	296.864i		−	0.309555i
$960$	112.167	+	42.6459i	0.116840	+	0.0444228i
$961$	63.0000			0.0655567
$962$		0			0
$963$	441.235	−	227.407i	0.458188	−	0.236144i
$964$	608.000			0.630705
$965$	−480.833	−	329.848i	−0.498272	−	0.341812i
$966$	578.000	−	140.186i	0.598344	−	0.145120i
$967$			938.783i			0.970820i	0.874287	+	0.485410i	$0.161330\pi$
$967$			938.783i			0.970820i	−0.874287	+	0.485410i	$0.838670\pi$
$968$	−427.092			−0.441211
$969$	96.0000	+	395.818i	0.0990712	+	0.408481i
$970$	952.000	+	653.067i	0.981443	+	0.673265i
$971$			1335.89i			1.37578i	0.725813	+	0.687892i	$0.241464\pi$
$971$			1335.89i			1.37578i	−0.725813	+	0.687892i	$0.758536\pi$
$972$	−451.134	−	180.760i	−0.464130	−	0.185967i
$973$			256.562i			0.263681i
$974$			915.329i			0.939763i
$975$		0			0
$976$	−64.0000			−0.0655738
$977$	305.470			0.312661			0.156331	−	0.987705i	$-0.450033\pi$
$977$	305.470			0.312661			0.156331	+	0.987705i	$0.450033\pi$
$978$	−408.708	+	99.1262i	−0.417902	+	0.101356i
$979$	1088.00			1.11134
$980$	−84.8528	+	123.693i	−0.0865845	+	0.126218i
$981$	−640.000	+	329.848i	−0.652396	+	0.336237i
$982$		−	489.800i		−	0.498778i
$983$	−1110.16			−1.12936			−0.564678	−	0.825311i	$-0.691000\pi$
$983$	−1110.16			−1.12936			−0.564678	+	0.825311i	$0.691000\pi$
$984$	476.000	−	115.447i	0.483740	−	0.117324i
$985$	544.000	−	793.009i	0.552284	−	0.805086i
$986$		0			0
$987$	−601.041	+	145.774i	−0.608957	+	0.147694i
$988$		0			0
$989$		−	981.299i		−	0.992213i
$990$	−1041.33	−	131.253i	−1.05185	−	0.132579i
$991$	640.000			0.645812			0.322906	−	0.946431i	$-0.395340\pi$
$991$	640.000			0.645812			0.322906	+	0.946431i	$0.395340\pi$
$992$	−181.019			−0.182479
$993$	−206.475	−	851.319i	−0.207931	−	0.857320i
$994$		0			0
$995$	882.469	−	1286.41i	0.886904	−	1.29287i
$996$	62.0000	+	255.633i	0.0622490	+	0.256659i
$997$			279.886i			0.280728i	0.990100	+	0.140364i	$0.0448273\pi$
$997$			279.886i			0.280728i	−0.990100	+	0.140364i	$0.955173\pi$
$998$	−933.381			−0.935251
$999$	−476.000	+	412.311i	−0.476476	+	0.412723i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.3.b.a.29.3	yes	4
3.2	odd	2	inner	30.3.b.a.29.1	✓	4
4.3	odd	2		240.3.c.c.209.4		4
5.2	odd	4		150.3.d.d.101.3		4
5.3	odd	4		150.3.d.d.101.2		4
5.4	even	2	inner	30.3.b.a.29.2	yes	4
8.3	odd	2		960.3.c.e.449.1		4
8.5	even	2		960.3.c.f.449.4		4
9.2	odd	6		810.3.j.c.539.4		8
9.4	even	3		810.3.j.c.269.2		8
9.5	odd	6		810.3.j.c.269.3		8
9.7	even	3		810.3.j.c.539.1		8
12.11	even	2		240.3.c.c.209.2		4
15.2	even	4		150.3.d.d.101.1		4
15.8	even	4		150.3.d.d.101.4		4
15.14	odd	2	inner	30.3.b.a.29.4	yes	4
20.3	even	4		1200.3.l.t.401.2		4
20.7	even	4		1200.3.l.t.401.3		4
20.19	odd	2		240.3.c.c.209.1		4
24.5	odd	2		960.3.c.f.449.2		4
24.11	even	2		960.3.c.e.449.3		4
40.19	odd	2		960.3.c.e.449.4		4
40.29	even	2		960.3.c.f.449.1		4
45.4	even	6		810.3.j.c.269.4		8
45.14	odd	6		810.3.j.c.269.1		8
45.29	odd	6		810.3.j.c.539.2		8
45.34	even	6		810.3.j.c.539.3		8
60.23	odd	4		1200.3.l.t.401.1		4
60.47	odd	4		1200.3.l.t.401.4		4
60.59	even	2		240.3.c.c.209.3		4
120.29	odd	2		960.3.c.f.449.3		4
120.59	even	2		960.3.c.e.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.b.a.29.1	✓	4	3.2	odd	2	inner
30.3.b.a.29.2	yes	4	5.4	even	2	inner
30.3.b.a.29.3	yes	4	1.1	even	1	trivial
30.3.b.a.29.4	yes	4	15.14	odd	2	inner
150.3.d.d.101.1		4	15.2	even	4
150.3.d.d.101.2		4	5.3	odd	4
150.3.d.d.101.3		4	5.2	odd	4
150.3.d.d.101.4		4	15.8	even	4
240.3.c.c.209.1		4	20.19	odd	2
240.3.c.c.209.2		4	12.11	even	2
240.3.c.c.209.3		4	60.59	even	2
240.3.c.c.209.4		4	4.3	odd	2
810.3.j.c.269.1		8	45.14	odd	6
810.3.j.c.269.2		8	9.4	even	3
810.3.j.c.269.3		8	9.5	odd	6
810.3.j.c.269.4		8	45.4	even	6
810.3.j.c.539.1		8	9.7	even	3
810.3.j.c.539.2		8	45.29	odd	6
810.3.j.c.539.3		8	45.34	even	6
810.3.j.c.539.4		8	9.2	odd	6
960.3.c.e.449.1		4	8.3	odd	2
960.3.c.e.449.2		4	120.59	even	2
960.3.c.e.449.3		4	24.11	even	2
960.3.c.e.449.4		4	40.19	odd	2
960.3.c.f.449.1		4	40.29	even	2
960.3.c.f.449.2		4	24.5	odd	2
960.3.c.f.449.3		4	120.29	odd	2
960.3.c.f.449.4		4	8.5	even	2
1200.3.l.t.401.1		4	60.23	odd	4
1200.3.l.t.401.2		4	20.3	even	4
1200.3.l.t.401.3		4	20.7	even	4
1200.3.l.t.401.4		4	60.47	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:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	30.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(-0.707107 - 2.91548i) q^{3} +2.00000 q^{4} +(-2.82843 + 4.12311i) q^{5} +(-1.00000 - 4.12311i) q^{6} +5.83095i q^{7} +2.82843 q^{8} +(-8.00000 + 4.12311i) q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(-0.707107 - 2.91548i) q^{3} +2.00000 q^{4} +(-2.82843 + 4.12311i) q^{5} +(-1.00000 - 4.12311i) q^{6} +5.83095i q^{7} +2.82843 q^{8} +(-8.00000 + 4.12311i) q^{9} +(-4.00000 + 5.83095i) q^{10} -16.4924i q^{11} +(-1.41421 - 5.83095i) q^{12} +8.24621i q^{14} +(14.0208 + 5.33074i) q^{15} +4.00000 q^{16} -11.3137 q^{17} +(-11.3137 + 5.83095i) q^{18} +12.0000 q^{19} +(-5.65685 + 8.24621i) q^{20} +(17.0000 - 4.12311i) q^{21} -23.3238i q^{22} +24.0416 q^{23} +(-2.00000 - 8.24621i) q^{24} +(-9.00000 - 23.3238i) q^{25} +(17.6777 + 20.4083i) q^{27} +11.6619i q^{28} +(19.8284 + 7.53880i) q^{30} -32.0000 q^{31} +5.65685 q^{32} +(-48.0833 + 11.6619i) q^{33} -16.0000 q^{34} +(-24.0416 - 16.4924i) q^{35} +(-16.0000 + 8.24621i) q^{36} +23.3238i q^{37} +16.9706 q^{38} +(-8.00000 + 11.6619i) q^{40} +57.7235i q^{41} +(24.0416 - 5.83095i) q^{42} -40.8167i q^{43} -32.9848i q^{44} +(5.62742 - 44.6467i) q^{45} +34.0000 q^{46} -35.3553 q^{47} +(-2.82843 - 11.6619i) q^{48} +15.0000 q^{49} +(-12.7279 - 32.9848i) q^{50} +(8.00000 + 32.9848i) q^{51} +67.8823 q^{53} +(25.0000 + 28.8617i) q^{54} +(68.0000 + 46.6476i) q^{55} +16.4924i q^{56} +(-8.48528 - 34.9857i) q^{57} -16.4924i q^{59} +(28.0416 + 10.6615i) q^{60} -16.0000 q^{61} -45.2548 q^{62} +(-24.0416 - 46.6476i) q^{63} +8.00000 q^{64} +(-68.0000 + 16.4924i) q^{66} -5.83095i q^{67} -22.6274 q^{68} +(-17.0000 - 70.0928i) q^{69} +(-34.0000 - 23.3238i) q^{70} +(-22.6274 + 11.6619i) q^{72} +116.619i q^{73} +32.9848i q^{74} +(-61.6360 + 42.7317i) q^{75} +24.0000 q^{76} +96.1665 q^{77} -72.0000 q^{79} +(-11.3137 + 16.4924i) q^{80} +(47.0000 - 65.9697i) q^{81} +81.6333i q^{82} -43.8406 q^{83} +(34.0000 - 8.24621i) q^{84} +(32.0000 - 46.6476i) q^{85} -57.7235i q^{86} -46.6476i q^{88} +65.9697i q^{89} +(7.95837 - 63.1400i) q^{90} +48.0833 q^{92} +(22.6274 + 93.2952i) q^{93} -50.0000 q^{94} +(-33.9411 + 49.4773i) q^{95} +(-4.00000 - 16.4924i) q^{96} -163.267i q^{97} +21.2132 q^{98} +(68.0000 + 131.939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} - 4 q^{6} - 32 q^{9}+O(q^{10}) \) 4 * q + 8 * q^4 - 4 * q^6 - 32 * q^9	\( 4 q + 8 q^{4} - 4 q^{6} - 32 q^{9} - 16 q^{10} + 8 q^{15} + 16 q^{16} + 48 q^{19} + 68 q^{21} - 8 q^{24} - 36 q^{25} + 68 q^{30} - 128 q^{31} - 64 q^{34} - 64 q^{36} - 32 q^{40} - 68 q^{45} + 136 q^{46} + 60 q^{49} + 32 q^{51} + 100 q^{54} + 272 q^{55} + 16 q^{60} - 64 q^{61} + 32 q^{64} - 272 q^{66} - 68 q^{69} - 136 q^{70} - 272 q^{75} + 96 q^{76} - 288 q^{79} + 188 q^{81} + 136 q^{84} + 128 q^{85} + 128 q^{90} - 200 q^{94} - 16 q^{96} + 272 q^{99}+O(q^{100}) \) 4 * q + 8 * q^4 - 4 * q^6 - 32 * q^9 - 16 * q^10 + 8 * q^15 + 16 * q^16 + 48 * q^19 + 68 * q^21 - 8 * q^24 - 36 * q^25 + 68 * q^30 - 128 * q^31 - 64 * q^34 - 64 * q^36 - 32 * q^40 - 68 * q^45 + 136 * q^46 + 60 * q^49 + 32 * q^51 + 100 * q^54 + 272 * q^55 + 16 * q^60 - 64 * q^61 + 32 * q^64 - 272 * q^66 - 68 * q^69 - 136 * q^70 - 272 * q^75 + 96 * q^76 - 288 * q^79 + 188 * q^81 + 136 * q^84 + 128 * q^85 + 128 * q^90 - 200 * q^94 - 16 * q^96 + 272 * q^99

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