LMFDB - Embedded newform 484.3.b.h.243.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [484,3,Mod(243,484)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(484, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("484.243");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	484.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:	$13.1880447950$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 7x^{8} + 4x^{7} - 7x^{6} + 82x^{5} - 28x^{4} + 64x^{3} + 448x^{2} - 512x + 1024 $ x^10 - 2x^9 + 7x^8 + 4x^7 - 7x^6 + 82x^5 - 28x^4 + 64x^3 + 448x^2 - 512*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			243.3
Root			$-0.231622 - 1.98654i$ of defining polynomial
Character	$\chi$	$=$	484.243
Dual form			484.3.b.h.243.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32980 - 1.49386i) q^{2} -5.74247i q^{3} +(-0.463244 + 3.97309i) q^{4} +2.62387 q^{5} +(-8.57845 + 7.63636i) q^{6} -5.65174i q^{7} +(6.55126 - 4.59140i) q^{8} -23.9759 q^{9} +(-3.48924 - 3.91971i) q^{10} +(22.8153 + 2.66016i) q^{12} -2.38854 q^{13} +(-8.44292 + 7.51571i) q^{14} -15.0675i q^{15} +(-15.5708 - 3.68102i) q^{16} -3.93033 q^{17} +(31.8833 + 35.8167i) q^{18} +12.6850i q^{19} +(-1.21549 + 10.4249i) q^{20} -32.4549 q^{21} +1.98248i q^{23} +(-26.3660 - 37.6204i) q^{24} -18.1153 q^{25} +(3.17628 + 3.56814i) q^{26} +85.9989i q^{27} +(22.4548 + 2.61814i) q^{28} -39.1748 q^{29} +(-22.5088 + 20.0368i) q^{30} -39.6375i q^{31} +(15.2072 + 28.1557i) q^{32} +(5.22657 + 5.87137i) q^{34} -14.8295i q^{35} +(11.1067 - 95.2585i) q^{36} -32.8407 q^{37} +(18.9496 - 16.8685i) q^{38} +13.7161i q^{39} +(17.1897 - 12.0473i) q^{40} -20.2535 q^{41} +(43.1587 + 48.4832i) q^{42} +11.7486i q^{43} -62.9099 q^{45} +(2.96155 - 2.63631i) q^{46} +13.1240i q^{47} +(-21.1381 + 89.4149i) q^{48} +17.0578 q^{49} +(24.0898 + 27.0617i) q^{50} +22.5698i q^{51} +(1.10648 - 9.48986i) q^{52} +51.4812 q^{53} +(128.470 - 114.362i) q^{54} +(-25.9494 - 37.0260i) q^{56} +72.8431 q^{57} +(52.0948 + 58.5218i) q^{58} -26.8316i q^{59} +(59.8645 + 6.97994i) q^{60} +95.2827 q^{61} +(-59.2129 + 52.7101i) q^{62} +135.506i q^{63} +(21.8381 - 60.1589i) q^{64} -6.26722 q^{65} +3.45987i q^{67} +(1.82070 - 15.6155i) q^{68} +11.3843 q^{69} +(-22.1532 + 19.7203i) q^{70} +18.0942i q^{71} +(-157.073 + 110.083i) q^{72} +54.0962 q^{73} +(43.6717 + 49.0595i) q^{74} +104.026i q^{75} +(-50.3985 - 5.87624i) q^{76} +(20.4899 - 18.2397i) q^{78} -97.1558i q^{79} +(-40.8559 - 9.65853i) q^{80} +278.063 q^{81} +(26.9332 + 30.2559i) q^{82} -118.858i q^{83} +(15.0346 - 128.946i) q^{84} -10.3127 q^{85} +(17.5509 - 15.6234i) q^{86} +224.960i q^{87} +21.4577 q^{89} +(83.6578 + 93.9787i) q^{90} +13.4994i q^{91} +(-7.87655 - 0.918371i) q^{92} -227.617 q^{93} +(19.6054 - 17.4523i) q^{94} +33.2838i q^{95} +(161.683 - 87.3268i) q^{96} +0.0566354 q^{97} +(-22.6836 - 25.4820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} - 4 q^{5} - 6 q^{6} + 12 q^{8} - 30 q^{9} + 2 q^{10} + 40 q^{12} + 4 q^{13} - 4 q^{14} - 40 q^{16} - 20 q^{17} + 22 q^{18} - 64 q^{20} - 32 q^{21} - 36 q^{24} - 10 q^{25} - 36 q^{26} - 40 q^{28}+ \cdots + 568 q^{98}+O(q^{100}) $ 10 * q + 4 * q^4 - 4 * q^5 - 6 * q^6 + 12 * q^8 - 30 * q^9 + 2 * q^10 + 40 * q^12 + 4 * q^13 - 4 * q^14 - 40 * q^16 - 20 * q^17 + 22 * q^18 - 64 * q^20 - 32 * q^21 - 36 * q^24 - 10 * q^25 - 36 * q^26 - 40 * q^28 - 28 * q^29 - 126 * q^30 - 80 * q^32 - 88 * q^34 - 4 * q^36 - 100 * q^37 + 40 * q^38 + 12 * q^40 - 100 * q^41 + 260 * q^42 - 44 * q^45 + 130 * q^46 + 24 * q^48 - 22 * q^49 + 198 * q^50 + 176 * q^52 + 100 * q^53 + 350 * q^54 + 136 * q^56 + 112 * q^57 + 116 * q^58 - 136 * q^60 + 52 * q^61 - 134 * q^62 - 368 * q^64 + 184 * q^65 - 176 * q^68 + 184 * q^69 - 36 * q^70 - 360 * q^72 - 84 * q^73 - 362 * q^74 - 504 * q^76 - 232 * q^78 - 120 * q^80 + 330 * q^81 + 220 * q^82 + 40 * q^84 + 216 * q^85 + 556 * q^86 + 28 * q^89 + 520 * q^90 + 152 * q^92 - 72 * q^93 + 272 * q^94 + 704 * q^96 - 180 * q^97 + 568 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$-1$	$1$

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 $

$2$	−1.32980	−	1.49386i	−0.664902	−	0.746931i
$2$	−1.32980	−	1.49386i	−0.664902	−	0.746931i
$3$		−	5.74247i		−	1.91416i	−0.289830	−	0.957078i	$-0.593599\pi$
$3$		−	5.74247i		−	1.91416i	0.289830	−	0.957078i	$-0.406401\pi$
$4$	−0.463244	+	3.97309i	−0.115811	+	0.993271i
$5$	2.62387			0.524775			0.262387	−	0.964963i	$-0.415490\pi$
$5$	2.62387			0.524775			0.262387	+	0.964963i	$0.415490\pi$
$6$	−8.57845	+	7.63636i	−1.42974	+	1.27273i
$7$		−	5.65174i		−	0.807391i	−0.914893	−	0.403696i	$-0.867725\pi$
$7$		−	5.65174i		−	0.807391i	0.914893	−	0.403696i	$-0.132275\pi$
$8$	6.55126	−	4.59140i	0.818908	−	0.573925i
$9$	−23.9759			−2.66399
$10$	−3.48924	−	3.91971i	−0.348924	−	0.391971i
$11$		0			0
$11$		0			0
$12$	22.8153	+	2.66016i	1.90128	+	0.221680i
$13$	−2.38854			−0.183734			−0.0918668	−	0.995771i	$-0.529283\pi$
$13$	−2.38854			−0.183734			−0.0918668	+	0.995771i	$0.529283\pi$
$14$	−8.44292	+	7.51571i	−0.603066	+	0.536836i
$15$		−	15.0675i		−	1.00450i
$16$	−15.5708	−	3.68102i	−0.973176	−	0.230064i
$17$	−3.93033			−0.231196			−0.115598	−	0.993296i	$-0.536878\pi$
$17$	−3.93033			−0.231196			−0.115598	+	0.993296i	$0.536878\pi$
$18$	31.8833	+	35.8167i	1.77129	+	1.98982i
$19$			12.6850i			0.667631i	0.942638	+	0.333815i	$0.108336\pi$
$19$			12.6850i			0.667631i	−0.942638	+	0.333815i	$0.891664\pi$
$20$	−1.21549	+	10.4249i	−0.0607747	+	0.521244i
$21$	−32.4549			−1.54547
$22$		0			0
$23$			1.98248i			0.0861946i	0.999071	+	0.0430973i	$0.0137226\pi$
$23$			1.98248i			0.0861946i	−0.999071	+	0.0430973i	$0.986277\pi$
$24$	−26.3660	−	37.6204i	−1.09858	−	1.56752i
$25$	−18.1153			−0.724611
$26$	3.17628	+	3.56814i	0.122165	+	0.137236i
$27$			85.9989i			3.18514i
$28$	22.4548	+	2.61814i	0.801959	+	0.0935048i
$29$	−39.1748			−1.35086			−0.675428	−	0.737426i	$-0.736041\pi$
$29$	−39.1748			−1.35086			−0.675428	+	0.737426i	$0.736041\pi$
$30$	−22.5088	+	20.0368i	−0.750293	+	0.667895i
$31$		−	39.6375i		−	1.27863i	−0.768945	−	0.639315i	$-0.779218\pi$
$31$		−	39.6375i		−	1.27863i	0.768945	−	0.639315i	$-0.220782\pi$
$32$	15.2072	+	28.1557i	0.475225	+	0.879864i
$33$		0			0
$34$	5.22657	+	5.87137i	0.153723	+	0.172687i
$35$		−	14.8295i		−	0.423699i
$36$	11.1067	−	95.2585i	0.308520	−	2.64607i
$37$	−32.8407			−0.887587			−0.443793	−	0.896129i	$-0.646368\pi$
$37$	−32.8407			−0.887587			−0.443793	+	0.896129i	$0.646368\pi$
$38$	18.9496	−	16.8685i	0.498674	−	0.443909i
$39$			13.7161i			0.351695i
$40$	17.1897	−	12.0473i	0.429742	−	0.301182i
$41$	−20.2535			−0.493988			−0.246994	−	0.969017i	$-0.579443\pi$
$41$	−20.2535			−0.493988			−0.246994	+	0.969017i	$0.579443\pi$
$42$	43.1587	+	48.4832i	1.02759	+	1.15436i
$43$			11.7486i			0.273224i	0.990625	+	0.136612i	$0.0436214\pi$
$43$			11.7486i			0.273224i	−0.990625	+	0.136612i	$0.956379\pi$
$44$		0			0
$45$	−62.9099			−1.39800
$46$	2.96155	−	2.63631i	0.0643814	−	0.0573110i
$47$			13.1240i			0.279233i	0.990206	+	0.139617i	$0.0445870\pi$
$47$			13.1240i			0.279233i	−0.990206	+	0.139617i	$0.955413\pi$
$48$	−21.1381	+	89.4149i	−0.440377	+	1.86281i
$49$	17.0578			0.348119
$50$	24.0898	+	27.0617i	0.481795	+	0.541234i
$51$			22.5698i			0.442545i
$52$	1.10648	−	9.48986i	0.0212784	−	0.182497i
$53$	51.4812			0.971344			0.485672	−	0.874141i	$-0.338575\pi$
$53$	51.4812			0.971344			0.485672	+	0.874141i	$0.338575\pi$
$54$	128.470	−	114.362i	2.37908	−	2.11781i
$55$		0			0
$56$	−25.9494	−	37.0260i	−0.463382	−	0.661179i
$57$	72.8431			1.27795
$58$	52.0948	+	58.5218i	0.898187	+	1.00900i
$59$		−	26.8316i		−	0.454773i	−0.973805	−	0.227386i	$-0.926982\pi$
$59$		−	26.8316i		−	0.454773i	0.973805	−	0.227386i	$-0.0730180\pi$
$60$	59.8645	+	6.97994i	0.997742	+	0.116332i
$61$	95.2827			1.56201			0.781006	−	0.624524i	$-0.214707\pi$
$61$	95.2827			1.56201			0.781006	+	0.624524i	$0.214707\pi$
$62$	−59.2129	+	52.7101i	−0.955047	+	0.850163i
$63$			135.506i			2.15089i
$64$	21.8381	−	60.1589i	0.341220	−	0.939983i
$65$	−6.26722			−0.0964188
$66$		0			0
$67$			3.45987i			0.0516399i	0.999667	+	0.0258200i	$0.00821966\pi$
$67$			3.45987i			0.0516399i	−0.999667	+	0.0258200i	$0.991780\pi$
$68$	1.82070	−	15.6155i	0.0267751	−	0.229640i
$69$	11.3843			0.164990
$70$	−22.1532	+	19.7203i	−0.316474	+	0.281718i
$71$			18.0942i			0.254848i	0.991848	+	0.127424i	$0.0406710\pi$
$71$			18.0942i			0.254848i	−0.991848	+	0.127424i	$0.959329\pi$
$72$	−157.073	+	110.083i	−2.18157	+	1.52893i
$73$	54.0962			0.741043			0.370522	−	0.928824i	$-0.379179\pi$
$73$	54.0962			0.741043			0.370522	+	0.928824i	$0.379179\pi$
$74$	43.6717	+	49.0595i	0.590158	+	0.662966i
$75$			104.026i			1.38702i
$76$	−50.3985	−	5.87624i	−0.663138	−	0.0773190i
$77$		0			0
$78$	20.4899	−	18.2397i	0.262692	−	0.233842i
$79$		−	97.1558i		−	1.22982i	−0.788597	−	0.614910i	$-0.789192\pi$
$79$		−	97.1558i		−	1.22982i	0.788597	−	0.614910i	$-0.210808\pi$
$80$	−40.8559	−	9.65853i	−0.510698	−	0.120732i
$81$	278.063			3.43287
$82$	26.9332	+	30.2559i	0.328453	+	0.368975i
$83$		−	118.858i		−	1.43202i	−0.698090	−	0.716010i	$-0.745966\pi$
$83$		−	118.858i		−	1.43202i	0.698090	−	0.716010i	$-0.254034\pi$
$84$	15.0346	−	128.946i	0.178983	−	1.53507i
$85$	−10.3127			−0.121326
$86$	17.5509	−	15.6234i	0.204080	−	0.181667i
$87$			224.960i			2.58575i
$88$		0			0
$89$	21.4577			0.241098			0.120549	−	0.992707i	$-0.461535\pi$
$89$	21.4577			0.241098			0.120549	+	0.992707i	$0.461535\pi$
$90$	83.6578	+	93.9787i	0.929531	+	1.04421i
$91$			13.4994i			0.148345i
$92$	−7.87655	−	0.918371i	−0.0856147	−	0.00998229i
$93$	−227.617			−2.44750
$94$	19.6054	−	17.4523i	0.208568	−	0.185663i
$95$			33.2838i			0.350356i
$96$	161.683	−	87.3268i	1.68420	−	0.909655i
$97$	0.0566354			0.000583870			0.000291935	−	1.00000i	$-0.499907\pi$
$97$	0.0566354			0.000583870			0.000291935		1.00000i	$0.499907\pi$
$98$	−22.6836	−	25.4820i	−0.231465	−	0.260021i
$99$		0			0
$100$	8.39180	−	71.9736i	0.0839180	−	0.719736i
$101$	−151.041			−1.49546			−0.747728	−	0.664006i	$-0.768855\pi$
$101$	−151.041			−1.49546			−0.747728	+	0.664006i	$0.768855\pi$
$102$	33.7162	−	30.0134i	0.330551	−	0.294249i
$103$			8.63968i			0.0838804i	0.999120	+	0.0419402i	$0.0133539\pi$
$103$			8.63968i			0.0838804i	−0.999120	+	0.0419402i	$0.986646\pi$
$104$	−15.6479	+	10.9667i	−0.150461	+	0.105449i
$105$	−85.1577			−0.811026
$106$	−68.4599	−	76.9058i	−0.645848	−	0.725526i
$107$		−	135.015i		−	1.26183i	−0.775853	−	0.630913i	$-0.782680\pi$
$107$		−	135.015i		−	1.26183i	0.775853	−	0.630913i	$-0.217320\pi$
$108$	−341.681	−	39.8385i	−3.16371	−	0.368875i
$109$	−153.316			−1.40657			−0.703285	−	0.710908i	$-0.748284\pi$
$109$	−153.316			−1.40657			−0.703285	+	0.710908i	$0.748284\pi$
$110$		0			0
$111$			188.587i			1.69898i
$112$	−20.8041	+	88.0022i	−0.185751	+	0.785734i
$113$	−138.852			−1.22878			−0.614389	−	0.789003i	$-0.710598\pi$
$113$	−138.852			−1.22878			−0.614389	+	0.789003i	$0.710598\pi$
$114$	−96.8671	−	108.818i	−0.849711	−	0.954540i
$115$			5.20177i			0.0452328i
$116$	18.1475	−	155.645i	0.156444	−	1.34177i
$117$	57.2674			0.489465
$118$	−40.0827	+	35.6807i	−0.339684	+	0.302379i
$119$			22.2132i			0.186666i
$120$	−69.1810	−	98.7113i	−0.576509	−	0.822594i
$121$		0			0
$122$	−126.707	−	142.339i	−1.03858	−	1.16671i
$123$			116.305i			0.945569i
$124$	157.483	+	18.3618i	1.27003	+	0.148079i
$125$	−113.129			−0.905033
$126$	202.427	−	180.196i	1.60656	−	1.43013i
$127$			123.765i			0.974530i	0.873254	+	0.487265i	$0.162005\pi$
$127$			123.765i			0.974530i	−0.873254	+	0.487265i	$0.837995\pi$
$128$	−118.909	+	47.3765i	−0.928980	+	0.370129i
$129$	67.4662			0.522994
$130$	8.33417	+	9.36236i	0.0641090	+	0.0720181i
$131$		−	98.9561i		−	0.755390i	−0.925930	−	0.377695i	$-0.876717\pi$
$131$		−	98.9561i		−	0.755390i	0.925930	−	0.377695i	$-0.123283\pi$
$132$		0			0
$133$	71.6922			0.539039
$134$	5.16857	−	4.60095i	0.0385714	−	0.0343355i
$135$			225.650i			1.67148i
$136$	−25.7486	+	18.0457i	−0.189328	+	0.132689i
$137$	−125.665			−0.917265			−0.458632	−	0.888626i	$-0.651660\pi$
$137$	−125.665			−0.917265			−0.458632	+	0.888626i	$0.651660\pi$
$138$	−15.1389	−	17.0066i	−0.109702	−	0.123236i
$139$			201.867i			1.45228i	0.687548	+	0.726139i	$0.258687\pi$
$139$			201.867i			1.45228i	−0.687548	+	0.726139i	$0.741313\pi$
$140$	58.9187	+	6.86966i	0.420848	+	0.0490690i
$141$	75.3639			0.534496
$142$	27.0303	−	24.0618i	0.190354	−	0.169449i
$143$		0			0
$144$	373.325	+	88.2558i	2.59253	+	0.612888i
$145$	−102.790			−0.708895
$146$	−71.9373	−	80.8122i	−0.492721	−	0.553508i
$147$		−	97.9541i		−	0.666354i
$148$	15.2133	−	130.479i	0.102792	−	0.881614i
$149$	41.1801			0.276377			0.138188	−	0.990406i	$-0.455872\pi$
$149$	41.1801			0.276377			0.138188	+	0.990406i	$0.455872\pi$
$150$	155.401	−	138.335i	1.03601	−	0.922232i
$151$		−	119.450i		−	0.791059i	−0.918453	−	0.395530i	$-0.870561\pi$
$151$		−	119.450i		−	0.791059i	0.918453	−	0.395530i	$-0.129439\pi$
$152$	58.2418	+	83.1027i	0.383170	+	0.546728i
$153$	94.2335			0.615905
$154$		0			0
$155$		−	104.004i		−	0.670992i
$156$	−54.4952	−	6.35390i	−0.349328	−	0.0407301i
$157$	121.227			0.772146			0.386073	−	0.922468i	$-0.373831\pi$
$157$	121.227			0.772146			0.386073	+	0.922468i	$0.373831\pi$
$158$	−145.137	+	129.198i	−0.918591	+	0.817710i
$159$		−	295.629i		−	1.85930i
$160$	39.9018	+	73.8769i	0.249386	+	0.461731i
$161$	11.2044			0.0695928
$162$	−369.769	−	415.387i	−2.28252	−	2.56412i
$163$		−	122.252i		−	0.750012i	−0.927022	−	0.375006i	$-0.877641\pi$
$163$		−	122.252i		−	0.750012i	0.927022	−	0.375006i	$-0.122359\pi$
$164$	9.38231	−	80.4688i	0.0572092	−	0.490664i
$165$		0			0
$166$	−177.557	+	158.057i	−1.06962	+	0.952153i
$167$			143.333i			0.858280i	0.903238	+	0.429140i	$0.141183\pi$
$167$			143.333i			0.858280i	−0.903238	+	0.429140i	$0.858817\pi$
$168$	−212.621	+	149.014i	−1.26560	+	0.886986i
$169$	−163.295			−0.966242
$170$	13.7139	+	15.4057i	0.0806698	+	0.0906221i
$171$		−	304.135i		−	1.77856i
$172$	−46.6784	−	5.44249i	−0.271386	−	0.0316424i
$173$	−273.225			−1.57933			−0.789667	−	0.613535i	$-0.789747\pi$
$173$	−273.225			−1.57933			−0.789667	+	0.613535i	$0.789747\pi$
$174$	336.059	−	299.153i	1.93138	−	1.71927i
$175$			102.383i			0.585045i
$176$		0			0
$177$	−154.080			−0.870506
$178$	−28.5346	−	32.0549i	−0.160306	−	0.180083i
$179$		−	260.106i		−	1.45311i	−0.687110	−	0.726553i	$-0.741121\pi$
$179$		−	260.106i		−	1.45311i	0.687110	−	0.726553i	$-0.258879\pi$
$180$	29.1426	−	249.946i	0.161904	−	1.38859i
$181$	273.183			1.50930			0.754650	−	0.656127i	$-0.227807\pi$
$181$	273.183			1.50930			0.754650	+	0.656127i	$0.227807\pi$
$182$	20.1662	−	17.9515i	0.110803	−	0.0986348i
$183$		−	547.158i		−	2.98993i
$184$	9.10235	+	12.9877i	0.0494693	+	0.0705855i
$185$	−86.1699			−0.465783
$186$	302.686	+	340.028i	1.62734	+	1.82811i
$187$		0			0
$188$	−52.1426	−	6.07960i	−0.277354	−	0.0323383i
$189$	486.044			2.57166
$190$	49.7214	−	44.2609i	0.261692	−	0.232952i
$191$		−	259.932i		−	1.36090i	−0.732794	−	0.680450i	$-0.761784\pi$
$191$		−	259.932i		−	1.36090i	0.732794	−	0.680450i	$-0.238216\pi$
$192$	−345.461	−	125.404i	−1.79928	−	0.653148i
$193$	301.717			1.56330			0.781649	−	0.623719i	$-0.214379\pi$
$193$	301.717			1.56330			0.781649	+	0.623719i	$0.214379\pi$
$194$	−0.0753140	−	0.0846055i	−0.000388217	−	0.000436111i
$195$			35.9893i			0.184561i
$196$	−7.90194	+	67.7722i	−0.0403160	+	0.345777i
$197$	27.4087			0.139130			0.0695652	−	0.997577i	$-0.477839\pi$
$197$	27.4087			0.139130			0.0695652	+	0.997577i	$0.477839\pi$
$198$		0			0
$199$			258.899i			1.30100i	0.759507	+	0.650499i	$0.225440\pi$
$199$			258.899i			1.30100i	−0.759507	+	0.650499i	$0.774560\pi$
$200$	−118.678	+	83.1745i	−0.593390	+	0.415873i
$201$	19.8682			0.0988469
$202$	200.855	+	225.634i	0.994331	+	1.11700i
$203$			221.406i			1.09067i
$204$	−89.6718	−	10.4553i	−0.439568	−	0.0512516i
$205$	−53.1426			−0.259232
$206$	12.9065	−	11.4891i	0.0626528	−	0.0557722i
$207$		−	47.5318i		−	0.229622i
$208$	37.1914	+	8.79224i	0.178805	+	0.0422704i
$209$		0			0
$210$	113.243	+	127.214i	0.539253	+	0.605780i
$211$		−	27.8516i		−	0.131998i	−0.997820	−	0.0659990i	$-0.978977\pi$
$211$		−	27.8516i		−	0.131998i	0.997820	−	0.0659990i	$-0.0210234\pi$
$212$	−23.8484	+	204.539i	−0.112492	+	0.964808i
$213$	103.906			0.487820
$214$	−201.694	+	179.544i	−0.942497	+	0.838991i
$215$			30.8270i			0.143381i
$216$	394.855	+	563.401i	1.82803	+	2.60834i
$217$	−224.021			−1.03235
$218$	203.880	+	229.033i	0.935231	+	1.05061i
$219$		−	310.645i		−	1.41847i
$220$		0			0
$221$	9.38774			0.0424785
$222$	281.722	−	250.783i	1.26902	−	1.12965i
$223$			212.433i			0.952615i	0.879279	+	0.476308i	$0.158025\pi$
$223$			212.433i			0.952615i	−0.879279	+	0.476308i	$0.841975\pi$
$224$	159.128	−	85.9471i	0.710395	−	0.383692i
$225$	434.331			1.93036
$226$	184.646	+	207.426i	0.817017	+	0.917813i
$227$			132.026i			0.581612i	0.956782	+	0.290806i	$0.0939235\pi$
$227$			132.026i			0.581612i	−0.956782	+	0.290806i	$0.906077\pi$
$228$	−33.7441	+	289.412i	−0.148001	+	1.26935i
$229$	−274.044			−1.19670			−0.598349	−	0.801236i	$-0.704176\pi$
$229$	−274.044			−1.19670			−0.598349	+	0.801236i	$0.704176\pi$
$230$	7.77073	−	6.91733i	0.0337858	−	0.0300754i
$231$		0			0
$232$	−256.645	+	179.867i	−1.10623	+	0.775290i
$233$	−175.327			−0.752474			−0.376237	−	0.926523i	$-0.622782\pi$
$233$	−175.327			−0.752474			−0.376237	+	0.926523i	$0.622782\pi$
$234$	−76.1544	−	85.5496i	−0.325446	−	0.365597i
$235$			34.4356i			0.146535i
$236$	106.604	+	12.4296i	0.451712	+	0.0526677i
$237$	−557.914			−2.35407
$238$	33.1835	−	29.5392i	0.139426	−	0.124114i
$239$		−	47.1871i		−	0.197436i	−0.995115	−	0.0987179i	$-0.968526\pi$
$239$		−	47.1871i		−	0.197436i	0.995115	−	0.0987179i	$-0.0314741\pi$
$240$	−55.4638	+	234.613i	−0.231099	+	0.977556i
$241$	9.89020			0.0410382			0.0205191	−	0.999789i	$-0.493468\pi$
$241$	9.89020			0.0410382			0.0205191	+	0.999789i	$0.493468\pi$
$242$		0			0
$243$		−	822.775i		−	3.38591i
$244$	−44.1391	+	378.566i	−0.180898	+	1.55150i
$245$	44.7576			0.182684
$246$	173.744	−	154.663i	0.706275	−	0.628711i
$247$		−	30.2985i		−	0.122666i
$248$	−181.992	−	259.676i	−0.733837	−	1.04708i
$249$	−682.536			−2.74111
$250$	150.439	+	168.999i	0.601758	+	0.675997i
$251$		−	228.136i		−	0.908907i	−0.890770	−	0.454454i	$-0.849835\pi$
$251$		−	228.136i		−	0.908907i	0.890770	−	0.454454i	$-0.150165\pi$
$252$	−538.376	−	62.7723i	−2.13641	−	0.249096i
$253$		0			0
$254$	184.888	−	164.584i	0.727906	−	0.647967i
$255$			59.2204i			0.232237i
$256$	228.900	+	114.633i	0.894142	+	0.447784i
$257$	−392.820			−1.52848			−0.764241	−	0.644931i	$-0.776886\pi$
$257$	−392.820			−1.52848			−0.764241	+	0.644931i	$0.776886\pi$
$258$	−89.7169	−	100.785i	−0.347740	−	0.390640i
$259$			185.607i			0.716630i
$260$	2.90325	−	24.9002i	0.0111664	−	0.0957700i
$261$	939.254			3.59867
$262$	−147.827	+	131.592i	−0.564224	+	0.502260i
$263$		−	249.116i		−	0.947208i	−0.880738	−	0.473604i	$-0.842953\pi$
$263$		−	249.116i		−	0.947208i	0.880738	−	0.473604i	$-0.157047\pi$
$264$		0			0
$265$	135.080			0.509737
$266$	−95.3366	−	107.098i	−0.358408	−	0.402625i
$267$		−	123.220i		−	0.461499i
$268$	−13.7464	−	1.60277i	−0.0512924	−	0.00598047i
$269$	−71.2955			−0.265039			−0.132520	−	0.991180i	$-0.542307\pi$
$269$	−71.2955			−0.265039			−0.132520	+	0.991180i	$0.542307\pi$
$270$	337.090	−	300.071i	1.24848	−	1.11137i
$271$		−	275.651i		−	1.01716i	−0.861014	−	0.508581i	$-0.830170\pi$
$271$		−	275.651i		−	1.01716i	0.861014	−	0.508581i	$-0.169830\pi$
$272$	61.1985	+	14.4676i	0.224994	+	0.0531898i
$273$	77.5198			0.283955
$274$	167.110	+	187.726i	0.609891	+	0.685133i
$275$		0			0
$276$	−5.27371	+	45.2308i	−0.0191077	+	0.163880i
$277$	162.557			0.586848			0.293424	−	0.955982i	$-0.405205\pi$
$277$	162.557			0.586848			0.293424	+	0.955982i	$0.405205\pi$
$278$	301.561	−	268.443i	1.08475	−	0.965622i
$279$			950.347i			3.40626i
$280$	−68.0880	−	97.1517i	−0.243171	−	0.346970i
$281$	−168.953			−0.601255			−0.300627	−	0.953742i	$-0.597196\pi$
$281$	−168.953			−0.601255			−0.300627	+	0.953742i	$0.597196\pi$
$282$	−100.219	−	112.583i	−0.355387	−	0.399231i
$283$		−	202.567i		−	0.715785i	−0.933763	−	0.357892i	$-0.883495\pi$
$283$		−	202.567i		−	0.715785i	0.933763	−	0.357892i	$-0.116505\pi$
$284$	−71.8899	−	8.38205i	−0.253134	−	0.0295143i
$285$	191.131			0.670636
$286$		0			0
$287$			114.467i			0.398841i
$288$	−364.607	−	675.059i	−1.26600	−	2.34395i
$289$	−273.552			−0.946548
$290$	136.690	+	153.554i	0.471346	+	0.529496i
$291$		−	0.325227i		−	0.00111762i
$292$	−25.0597	+	214.929i	−0.0858210	+	0.736057i
$293$	506.376			1.72825			0.864123	−	0.503281i	$-0.167874\pi$
$293$	506.376			1.72825			0.864123	+	0.503281i	$0.167874\pi$
$294$	−146.330	+	130.260i	−0.497720	+	0.443060i
$295$		−	70.4027i		−	0.238653i
$296$	−215.148	+	150.785i	−0.726852	+	0.509408i
$297$		0			0
$298$	−54.7615	−	61.5174i	−0.183763	−	0.206434i
$299$		−	4.73522i		−	0.0158368i
$300$	−413.306	−	48.1896i	−1.37769	−	0.160632i
$301$	66.4003			0.220599
$302$	−178.442	+	158.845i	−0.590866	+	0.525977i
$303$			867.348i			2.86253i
$304$	46.6936	−	197.515i	0.153597	−	0.649722i
$305$	250.010			0.819704
$306$	−125.312	−	140.772i	−0.409516	−	0.460038i
$307$			41.0747i			0.133794i	0.997760	+	0.0668969i	$0.0213099\pi$
$307$			41.0747i			0.133794i	−0.997760	+	0.0668969i	$0.978690\pi$
$308$		0			0
$309$	49.6131			0.160560
$310$	−155.367	+	138.305i	−0.501185	+	0.446144i
$311$		−	469.894i		−	1.51091i	−0.655198	−	0.755457i	$-0.727415\pi$
$311$		−	469.894i		−	1.51091i	0.655198	−	0.755457i	$-0.272585\pi$
$312$	62.9761	+	89.8577i	0.201846	+	0.288006i
$313$	−204.777			−0.654238			−0.327119	−	0.944983i	$-0.606078\pi$
$313$	−204.777			−0.654238			−0.327119	+	0.944983i	$0.606078\pi$
$314$	−161.208	−	181.096i	−0.513401	−	0.576739i
$315$			355.550i			1.12873i
$316$	386.008	+	45.0068i	1.22155	+	0.142427i
$317$	−11.6988			−0.0369049			−0.0184524	−	0.999830i	$-0.505874\pi$
$317$	−11.6988			−0.0369049			−0.0184524	+	0.999830i	$0.505874\pi$
$318$	−441.629	+	393.129i	−1.38877	+	1.23625i
$319$		0			0
$320$	57.3004	−	157.850i	0.179064	−	0.493280i
$321$	−775.322			−2.41533
$322$	−14.8997	−	16.7379i	−0.0462724	−	0.0519810i
$323$		−	49.8562i		−	0.154354i
$324$	−128.811	+	1104.77i	−0.397564	+	3.40977i
$325$	43.2690			0.133135
$326$	−182.628	+	162.571i	−0.560207	+	0.498684i
$327$			880.413i			2.69239i
$328$	−132.686	+	92.9919i	−0.404530	+	0.283512i
$329$	74.1732			0.225450
$330$		0			0
$331$		−	53.1038i		−	0.160434i	−0.996777	−	0.0802172i	$-0.974439\pi$
$331$		−	53.1038i		−	0.160434i	0.996777	−	0.0802172i	$-0.0255614\pi$
$332$	472.232	+	55.0601i	1.42238	+	0.165844i
$333$	787.387			2.36453
$334$	214.119	−	190.604i	0.641076	−	0.570672i
$335$			9.07828i			0.0270993i
$336$	505.350	+	119.467i	1.50402	+	0.355557i
$337$	177.750			0.527448			0.263724	−	0.964598i	$-0.415049\pi$
$337$	177.750			0.527448			0.263724	+	0.964598i	$0.415049\pi$
$338$	217.150	+	243.940i	0.642456	+	0.721716i
$339$			797.353i			2.35207i
$340$	4.77730	−	40.9732i	0.0140509	−	0.120510i
$341$		0			0
$342$	−454.335	+	404.439i	−1.32846	+	1.18257i
$343$		−	373.342i		−	1.08846i
$344$	53.9428	+	76.9685i	0.156810	+	0.223746i
$345$	29.8710			0.0865826
$346$	363.336	+	408.160i	1.05010	+	1.17965i
$347$		−	561.580i		−	1.61838i	−0.587544	−	0.809192i	$-0.699905\pi$
$347$		−	561.580i		−	1.61838i	0.587544	−	0.809192i	$-0.300095\pi$
$348$	−893.786	−	104.211i	−2.56835	−	0.299458i
$349$	−410.932			−1.17746			−0.588728	−	0.808331i	$-0.700371\pi$
$349$	−410.932			−1.17746			−0.588728	+	0.808331i	$0.700371\pi$
$350$	152.946	−	136.149i	0.436988	−	0.388997i
$351$		−	205.412i		−	0.585218i
$352$		0			0
$353$	−5.48150			−0.0155283			−0.00776416	−	0.999970i	$-0.502471\pi$
$353$	−5.48150			−0.0155283			−0.00776416	+	0.999970i	$0.502471\pi$
$354$	204.896	+	230.173i	0.578801	+	0.650207i
$355$			47.4770i			0.133738i
$356$	−9.94016	+	85.2533i	−0.0279218	+	0.239476i
$357$	127.559			0.357307
$358$	−388.562	+	345.890i	−1.08537	+	0.966173i
$359$			602.633i			1.67864i	0.543636	+	0.839321i	$0.317047\pi$
$359$			602.633i			1.67864i	−0.543636	+	0.839321i	$0.682953\pi$
$360$	−412.139	+	288.845i	−1.14483	+	0.802346i
$361$	200.091			0.554269
$362$	−363.280	−	408.098i	−1.00354	−	1.12734i
$363$		0			0
$364$	−53.6342	−	6.25351i	−0.147347	−	0.0171800i
$365$	141.942			0.388881
$366$	−817.378	+	727.613i	−2.23327	+	1.98801i
$367$		−	215.805i		−	0.588024i	−0.955802	−	0.294012i	$-0.905009\pi$
$367$		−	215.805i		−	0.588024i	0.955802	−	0.294012i	$-0.0949905\pi$
$368$	7.29753	−	30.8688i	0.0198302	−	0.0838825i
$369$	485.597			1.31598
$370$	114.589	+	128.726i	0.309700	+	0.347908i
$371$		−	290.958i		−	0.784255i
$372$	105.442	−	904.342i	0.283447	−	2.43103i
$373$	147.198			0.394632			0.197316	−	0.980340i	$-0.436777\pi$
$373$	147.198			0.394632			0.197316	+	0.980340i	$0.436777\pi$
$374$		0			0
$375$			649.640i			1.73237i
$376$	60.2574	+	85.9785i	0.160259	+	0.228666i
$377$	93.5705			0.248198
$378$	−646.342	−	726.082i	−1.70990	−	1.92085i
$379$		−	418.824i		−	1.10508i	−0.833487	−	0.552538i	$-0.813659\pi$
$379$		−	418.824i		−	1.10508i	0.833487	−	0.552538i	$-0.186341\pi$
$380$	−132.239	−	15.4185i	−0.347998	−	0.0405751i
$381$	710.718			1.86540
$382$	−388.302	+	345.658i	−1.01650	+	0.904865i
$383$			508.317i			1.32720i	0.748088	+	0.663599i	$0.230972\pi$
$383$			508.317i			1.32720i	−0.748088	+	0.663599i	$0.769028\pi$
$384$	272.058	+	682.834i	0.708485	+	1.77821i
$385$		0			0
$386$	−401.224	−	450.723i	−1.03944	−	1.16768i
$387$		−	281.685i		−	0.727868i
$388$	−0.0262360	+	0.225017i	−6.76186e−5	+	0.000579942i
$389$	136.791			0.351647			0.175823	−	0.984422i	$-0.443741\pi$
$389$	136.791			0.351647			0.175823	+	0.984422i	$0.443741\pi$
$390$	53.7631	−	47.8587i	0.137854	−	0.122715i
$391$		−	7.79180i		−	0.0199279i
$392$	111.750	−	78.3193i	0.285077	−	0.199794i
$393$	−568.252			−1.44593
$394$	−36.4482	−	40.9448i	−0.0925080	−	0.103921i
$395$		−	254.925i		−	0.645379i
$396$		0			0
$397$	748.561			1.88554			0.942772	−	0.333438i	$-0.108209\pi$
$397$	748.561			1.88554			0.942772	+	0.333438i	$0.108209\pi$
$398$	386.759	−	344.284i	0.971755	−	0.865036i
$399$		−	411.690i		−	1.03181i
$400$	282.070	+	66.6826i	0.705174	+	0.166707i
$401$	233.282			0.581750			0.290875	−	0.956761i	$-0.406054\pi$
$401$	233.282			0.581750			0.290875	+	0.956761i	$0.406054\pi$
$402$	−26.4208	−	29.6804i	−0.0657235	−	0.0738318i
$403$			94.6756i			0.234927i
$404$	69.9688	−	600.099i	0.173190	−	1.48539i
$405$	729.601			1.80148
$406$	330.750	−	294.426i	0.814655	−	0.725188i
$407$		0			0
$408$	103.627	+	147.861i	0.253988	+	0.362404i
$409$	536.046			1.31063			0.655313	−	0.755358i	$-0.272537\pi$
$409$	536.046			1.31063			0.655313	+	0.755358i	$0.272537\pi$
$410$	70.6693	+	79.3877i	0.172364	+	0.193629i
$411$			721.629i			1.75579i
$412$	−34.3262	−	4.00228i	−0.0833159	−	0.00971427i
$413$	−151.645			−0.367179
$414$	−71.0059	+	63.2079i	−0.171512	+	0.152676i
$415$		−	311.868i		−	0.751488i
$416$	−36.3229	−	67.2508i	−0.0873147	−	0.161661i
$417$	1159.21			2.77989
$418$		0			0
$419$		−	408.745i		−	0.975524i	−0.872977	−	0.487762i	$-0.837813\pi$
$419$		−	408.745i		−	0.975524i	0.872977	−	0.487762i	$-0.162187\pi$
$420$	39.4488	−	338.339i	0.0939257	−	0.805569i
$421$	−386.634			−0.918370			−0.459185	−	0.888341i	$-0.651859\pi$
$421$	−386.634			−0.918370			−0.459185	+	0.888341i	$0.651859\pi$
$422$	−41.6064	+	37.0371i	−0.0985933	+	0.0877657i
$423$		−	314.659i		−	0.743876i
$424$	337.267	−	236.371i	0.795441	−	0.557479i
$425$	71.1991			0.167527
$426$	−138.174	−	155.221i	−0.324352	−	0.364368i
$427$		−	538.513i		−	1.26115i
$428$	536.428	+	62.5451i	1.25334	+	0.146133i
$429$		0			0
$430$	46.0512	−	40.9938i	0.107096	−	0.0953345i
$431$		−	150.143i		−	0.348359i	−0.984714	−	0.174179i	$-0.944273\pi$
$431$		−	150.143i		−	0.348359i	0.984714	−	0.174179i	$-0.0557273\pi$
$432$	316.563	−	1339.07i	0.732786	−	3.09971i
$433$	249.278			0.575700			0.287850	−	0.957676i	$-0.407060\pi$
$433$	249.278			0.575700			0.287850	+	0.957676i	$0.407060\pi$
$434$	297.904	+	334.656i	0.686414	+	0.771097i
$435$			590.267i			1.35694i
$436$	71.0228	−	609.138i	0.162896	−	1.39711i
$437$	−25.1477			−0.0575462
$438$	−464.061	+	413.098i	−1.05950	+	0.943145i
$439$			308.839i			0.703505i	0.936093	+	0.351753i	$0.114414\pi$
$439$			308.839i			0.703505i	−0.936093	+	0.351753i	$0.885586\pi$
$440$		0			0
$441$	−408.978			−0.927387
$442$	−12.4839	−	14.0240i	−0.0282440	−	0.0317285i
$443$		−	187.453i		−	0.423145i	−0.977362	−	0.211572i	$-0.932142\pi$
$443$		−	187.453i		−	0.423145i	0.977362	−	0.211572i	$-0.0678584\pi$
$444$	−749.271	−	87.3617i	−1.68755	−	0.196761i
$445$	56.3024			0.126522
$446$	317.346	−	282.494i	0.711538	−	0.633396i
$447$		−	236.476i		−	0.529028i
$448$	−340.003	−	123.423i	−0.758935	−	0.275498i
$449$	−144.028			−0.320775			−0.160388	−	0.987054i	$-0.551274\pi$
$449$	−144.028			−0.320775			−0.160388	+	0.987054i	$0.551274\pi$
$450$	−577.575	−	648.830i	−1.28350	−	1.44185i
$451$		0			0
$452$	64.3224	−	551.671i	0.142306	−	1.22051i
$453$	−685.937			−1.51421
$454$	197.229	−	175.569i	0.434424	−	0.386715i
$455$			35.4207i			0.0778477i
$456$	477.214	−	334.452i	1.04652	−	0.733447i
$457$	−718.168			−1.57148			−0.785742	−	0.618554i	$-0.787719\pi$
$457$	−718.168			−1.57148			−0.785742	+	0.618554i	$0.787719\pi$
$458$	364.425	+	409.384i	0.795687	+	0.893851i
$459$		−	338.004i		−	0.736393i
$460$	−20.6671	−	2.40969i	−0.0449284	−	0.00523846i
$461$	−283.840			−0.615705			−0.307852	−	0.951434i	$-0.599610\pi$
$461$	−283.840			−0.615705			−0.307852	+	0.951434i	$0.599610\pi$
$462$		0			0
$463$		−	428.178i		−	0.924790i	−0.886674	−	0.462395i	$-0.846990\pi$
$463$		−	428.178i		−	0.924790i	0.886674	−	0.462395i	$-0.153010\pi$
$464$	609.984	+	144.203i	1.31462	+	0.310783i
$465$	−597.239			−1.28438
$466$	233.150	+	261.914i	0.500322	+	0.562046i
$467$			415.333i			0.889363i	0.895689	+	0.444681i	$0.146683\pi$
$467$			415.333i			0.889363i	−0.895689	+	0.444681i	$0.853317\pi$
$468$	−26.5288	+	227.528i	−0.0566855	+	0.486172i
$469$	19.5543			0.0416936
$470$	51.4421	−	45.7926i	0.109451	−	0.0974311i
$471$		−	696.141i		−	1.47801i
$472$	−123.195	−	175.781i	−0.261005	−	0.372417i
$473$		0			0
$474$	741.916	+	833.446i	1.56522	+	1.75833i
$475$		−	229.792i		−	0.483773i
$476$	−88.2550	−	10.2901i	−0.185410	−	0.0216179i
$477$	−1234.31			−2.58765
$478$	−70.4911	+	62.7496i	−0.147471	+	0.131275i
$479$			176.184i			0.367816i	0.982943	+	0.183908i	$0.0588748\pi$
$479$			176.184i			0.367816i	−0.982943	+	0.183908i	$0.941125\pi$
$480$	424.236	−	229.135i	0.883825	−	0.477364i
$481$	78.4412			0.163079
$482$	−13.1520	−	14.7746i	−0.0272864	−	0.0306527i
$483$		−	64.3412i		−	0.133212i
$484$		0			0
$485$	0.148604			0.000306401
$486$	−1229.11	+	1094.13i	−2.52904	+	2.25130i
$487$			768.354i			1.57773i	0.614567	+	0.788865i	$0.289331\pi$
$487$			768.354i			1.57773i	−0.614567	+	0.788865i	$0.710669\pi$
$488$	624.222	−	437.481i	1.27914	−	0.896477i
$489$	−702.028			−1.43564
$490$	−59.5188	−	66.8617i	−0.121467	−	0.136452i
$491$			187.589i			0.382055i	0.981585	+	0.191028i	$0.0611820\pi$
$491$			187.589i			0.382055i	−0.981585	+	0.191028i	$0.938818\pi$
$492$	−462.090	−	53.8776i	−0.939207	−	0.109507i
$493$	153.970			0.312313
$494$	−45.2618	+	40.2911i	−0.0916231	+	0.0815610i
$495$		0			0
$496$	−145.906	+	617.188i	−0.294166	+	1.24433i
$497$	102.264			0.205762
$498$	907.640	+	1019.61i	1.82257	+	2.04742i
$499$		−	463.814i		−	0.929487i	−0.885445	−	0.464744i	$-0.846146\pi$
$499$		−	463.814i		−	0.929487i	0.885445	−	0.464744i	$-0.153854\pi$
$500$	52.4064	−	449.472i	0.104813	−	0.898943i
$501$	823.084			1.64288
$502$	−340.803	+	303.376i	−0.678891	+	0.604334i
$503$		−	516.384i		−	1.02661i	−0.858207	−	0.513304i	$-0.828421\pi$
$503$		−	516.384i		−	1.02661i	0.858207	−	0.513304i	$-0.171579\pi$
$504$	622.162	+	887.734i	1.23445	+	1.76138i
$505$	−396.313			−0.784777
$506$		0			0
$507$			937.716i			1.84954i
$508$	−491.730	−	57.3335i	−0.967972	−	0.112861i
$509$	163.127			0.320486			0.160243	−	0.987078i	$-0.448772\pi$
$509$	163.127			0.320486			0.160243	+	0.987078i	$0.448772\pi$
$510$	88.4670	−	78.7515i	0.173465	−	0.154415i
$511$		−	305.737i		−	0.598312i
$512$	−133.147	−	494.384i	−0.260052	−	0.965594i
$513$	−1090.89			−2.12650
$514$	522.373	+	586.818i	1.01629	+	1.14167i
$515$			22.6694i			0.0440183i
$516$	−31.2533	+	268.049i	−0.0605685	+	0.519475i
$517$		0			0
$518$	277.271	−	246.821i	0.535273	−	0.476489i
$519$			1568.99i			3.02309i
$520$	−41.0582	+	28.7753i	−0.0789581	+	0.0553372i
$521$	794.025			1.52404			0.762020	−	0.647553i	$-0.224208\pi$
$521$	794.025			1.52404			0.762020	+	0.647553i	$0.224208\pi$
$522$	−1249.02	−	1403.11i	−2.39276	−	2.68796i
$523$		−	582.806i		−	1.11435i	−0.830394	−	0.557176i	$-0.811885\pi$
$523$		−	582.806i		−	1.11435i	0.830394	−	0.557176i	$-0.188115\pi$
$524$	393.161	+	45.8408i	0.750307	+	0.0874825i
$525$	587.930			1.11987
$526$	−372.144	+	331.275i	−0.707499	+	0.629800i
$527$			155.789i			0.295614i
$528$		0			0
$529$	525.070			0.992570
$530$	−179.630	−	201.791i	−0.338925	−	0.380738i
$531$			643.313i			1.21151i
$532$	−33.2110	+	284.839i	−0.0624267	+	0.535412i
$533$	48.3762			0.0907621
$534$	−184.074	+	163.859i	−0.344708	+	0.306852i
$535$		−	354.264i		−	0.662175i
$536$	15.8857	+	22.6665i	0.0296374	+	0.0422883i
$537$	−1493.65			−2.78147
$538$	94.8091	+	106.506i	0.176225	+	0.197966i
$539$		0			0
$540$	−896.528	−	104.531i	−1.66024	−	0.193576i
$541$	444.970			0.822496			0.411248	−	0.911524i	$-0.365093\pi$
$541$	444.970			0.822496			0.411248	+	0.911524i	$0.365093\pi$
$542$	−411.784	+	366.562i	−0.759750	+	0.676313i
$543$		−	1568.75i		−	2.88904i
$544$	−59.7693	−	110.661i	−0.109870	−	0.203421i
$545$	−402.282			−0.738133
$546$	−103.086	−	115.804i	−0.188802	−	0.212095i
$547$			831.549i			1.52020i	0.649806	+	0.760100i	$0.274850\pi$
$547$			831.549i			1.52020i	−0.649806	+	0.760100i	$0.725150\pi$
$548$	58.2137	−	499.279i	0.106229	−	0.911093i
$549$	−2284.49			−4.16119
$550$		0			0
$551$		−	496.932i		−	0.901873i
$552$	74.5816	−	52.2699i	0.135112	−	0.0946919i
$553$	−549.099			−0.992946
$554$	−216.169	−	242.838i	−0.390197	−	0.438335i
$555$			494.828i			0.891582i
$556$	−802.033	−	93.5135i	−1.44251	−	0.168190i
$557$	−404.131			−0.725550			−0.362775	−	0.931877i	$-0.618171\pi$
$557$	−404.131			−0.725550			−0.362775	+	0.931877i	$0.618171\pi$
$558$	1419.69	−	1263.77i	2.54424	−	2.26483i
$559$		−	28.0621i		−	0.0502005i
$560$	−54.5875	+	230.907i	−0.0974776	+	0.412333i
$561$		0			0
$562$	224.674	+	252.392i	0.399775	+	0.449096i
$563$			11.9750i			0.0212699i	0.999943	+	0.0106350i	$0.00338528\pi$
$563$			11.9750i			0.0212699i	−0.999943	+	0.0106350i	$0.996615\pi$
$564$	−34.9119	+	299.427i	−0.0619005	+	0.530899i
$565$	−364.330			−0.644832
$566$	−302.607	+	269.375i	−0.534642	+	0.475927i
$567$		−	1571.54i		−	2.77167i
$568$	83.0779	+	118.540i	0.146264	+	0.208697i
$569$	−390.548			−0.686376			−0.343188	−	0.939267i	$-0.611507\pi$
$569$	−390.548			−0.686376			−0.343188	+	0.939267i	$0.611507\pi$
$570$	−254.167	−	285.524i	−0.445907	−	0.500919i
$571$			799.779i			1.40066i	0.713817	+	0.700332i	$0.246965\pi$
$571$			799.779i			1.40066i	−0.713817	+	0.700332i	$0.753035\pi$
$572$		0			0
$573$	−1492.65			−2.60498
$574$	170.999	−	152.219i	0.297907	−	0.265190i
$575$		−	35.9131i		−	0.0624576i
$576$	−523.589	+	1442.37i	−0.909008	+	2.50411i
$577$	560.791			0.971907			0.485954	−	0.873985i	$-0.338472\pi$
$577$	560.791			0.971907			0.485954	+	0.873985i	$0.338472\pi$
$578$	363.771	+	408.650i	0.629362	+	0.707006i
$579$		−	1732.60i		−	2.99240i
$580$	47.6168	−	408.393i	0.0820979	−	0.704125i
$581$	−671.753			−1.15620
$582$	−0.485844	+	0.432488i	−0.000834784	+	0.000743107i
$583$		0			0
$584$	354.398	−	248.377i	0.606846	−	0.425303i
$585$	150.263			0.256859
$586$	−673.380	−	756.455i	−1.14911	−	1.29088i
$587$			120.056i			0.204525i	0.994757	+	0.102262i	$0.0326081\pi$
$587$			120.056i			0.204525i	−0.994757	+	0.102262i	$0.967392\pi$
$588$	389.180	+	45.3766i	0.661870	+	0.0771711i
$589$	502.801			0.853652
$590$	−105.172	+	93.6218i	−0.178257	+	0.158681i
$591$		−	157.393i		−	0.266317i
$592$	511.356	+	120.887i	0.863778	+	0.204201i
$593$	231.649			0.390639			0.195320	−	0.980740i	$-0.437426\pi$
$593$	231.649			0.390639			0.195320	+	0.980740i	$0.437426\pi$
$594$		0			0
$595$			58.2847i			0.0979575i
$596$	−19.0764	+	163.612i	−0.0320075	+	0.274517i
$597$	1486.72			2.49031
$598$	−7.07376	+	6.29691i	−0.0118290	+	0.0105300i
$599$			475.122i			0.793192i	0.917993	+	0.396596i	$0.129809\pi$
$599$			475.122i			0.793192i	−0.917993	+	0.396596i	$0.870191\pi$
$600$	477.627	+	681.504i	0.796045	+	1.13584i
$601$	−318.831			−0.530500			−0.265250	−	0.964180i	$-0.585454\pi$
$601$	−318.831			−0.530500			−0.265250	+	0.964180i	$0.585454\pi$
$602$	−88.2994	−	99.1929i	−0.146677	−	0.164772i
$603$		−	82.9538i		−	0.137568i
$604$	474.585	+	55.3345i	0.785736	+	0.0916134i
$605$		0			0
$606$	1295.70	−	1153.40i	2.13812	−	1.90330i
$607$		−	499.680i		−	0.823196i	−0.911366	−	0.411598i	$-0.864971\pi$
$607$		−	499.680i		−	0.823196i	0.911366	−	0.411598i	$-0.135029\pi$
$608$	−357.154	+	192.903i	−0.587425	+	0.317275i
$609$	1271.42			2.08771
$610$	−332.464	−	373.480i	−0.545023	−	0.612262i
$611$		−	31.3471i		−	0.0513045i
$612$	−43.6531	+	374.398i	−0.0713286	+	0.611761i
$613$	1055.33			1.72158			0.860788	−	0.508963i	$-0.169971\pi$
$613$	1055.33			1.72158			0.860788	+	0.508963i	$0.169971\pi$
$614$	61.3599	−	54.6213i	0.0999347	−	0.0889598i
$615$			305.170i			0.496211i
$616$		0			0
$617$	−188.341			−0.305253			−0.152627	−	0.988284i	$-0.548773\pi$
$617$	−188.341			−0.305253			−0.152627	+	0.988284i	$0.548773\pi$
$618$	−65.9756	−	74.1151i	−0.106757	−	0.119927i
$619$			164.992i			0.266546i	0.991079	+	0.133273i	$0.0425486\pi$
$619$			164.992i			0.266546i	−0.991079	+	0.133273i	$0.957451\pi$
$620$	413.216	+	48.1792i	0.666478	+	0.0777083i
$621$	−170.491			−0.274542
$622$	−701.957	+	624.867i	−1.12855	+	1.00461i
$623$		−	121.273i		−	0.194660i
$624$	50.4892	−	213.571i	0.0809121	−	0.342261i
$625$	156.045			0.249673
$626$	272.313	+	305.908i	0.435004	+	0.488671i
$627$		0			0
$628$	−56.1576	+	481.645i	−0.0894230	+	0.766950i
$629$	129.075			0.205207
$630$	531.143	−	472.812i	0.843084	−	0.750496i
$631$			486.689i			0.771298i	0.922646	+	0.385649i	$0.126022\pi$
$631$			486.689i			0.771298i	−0.922646	+	0.385649i	$0.873978\pi$
$632$	−446.081	−	636.493i	−0.705825	−	1.00711i
$633$	−159.937			−0.252665
$634$	15.5572	+	17.4764i	0.0245381	+	0.0275654i
$635$			324.745i			0.511409i
$636$	1174.56	+	136.949i	1.84679	+	0.215328i
$637$	−40.7432			−0.0639611
$638$		0			0
$639$		−	433.826i		−	0.678915i
$640$	−312.004	+	124.310i	−0.487506	+	0.194235i
$641$	143.117			0.223271			0.111636	−	0.993749i	$-0.464391\pi$
$641$	143.117			0.223271			0.111636	+	0.993749i	$0.464391\pi$
$642$	1031.03	+	1158.22i	1.60596	+	1.80409i
$643$		−	1037.72i		−	1.61387i	−0.590638	−	0.806937i	$-0.701124\pi$
$643$		−	1037.72i		−	1.61387i	0.590638	−	0.806937i	$-0.298876\pi$
$644$	−5.19039	+	44.5162i	−0.00805962	+	0.0691246i
$645$	177.023			0.274454
$646$	−74.4783	+	66.2990i	−0.115291	+	0.102630i
$647$			383.185i			0.592248i	0.955149	+	0.296124i	$0.0956942\pi$
$647$			383.185i			0.592248i	−0.955149	+	0.296124i	$0.904306\pi$
$648$	1821.66	−	1276.70i	2.81120	−	1.97021i
$649$		0			0
$650$	−57.5393	−	64.6379i	−0.0885220	−	0.0994429i
$651$			1286.43i			1.97609i
$652$	485.717	+	56.6325i	0.744965	+	0.0868597i
$653$	−39.5749			−0.0606048			−0.0303024	−	0.999541i	$-0.509647\pi$
$653$	−39.5749			−0.0606048			−0.0303024	+	0.999541i	$0.509647\pi$
$654$	1315.21	−	1170.78i	2.01103	−	1.79018i
$655$		−	259.648i		−	0.396410i
$656$	315.363	+	74.5534i	0.480737	+	0.113649i
$657$	−1297.01			−1.97413
$658$	−98.6358	−	110.805i	−0.149902	−	0.168396i
$659$		−	1076.03i		−	1.63282i	−0.577470	−	0.816412i	$-0.695960\pi$
$659$		−	1076.03i		−	1.63282i	0.577470	−	0.816412i	$-0.304040\pi$
$660$		0			0
$661$	−341.729			−0.516989			−0.258494	−	0.966013i	$-0.583226\pi$
$661$	−341.729			−0.516989			−0.258494	+	0.966013i	$0.583226\pi$
$662$	−79.3297	+	70.6176i	−0.119833	+	0.106673i
$663$		−	53.9088i		−	0.0813104i
$664$	−545.723	−	778.668i	−0.821872	−	1.17269i
$665$	188.111			0.282874
$666$	−1047.07	−	1176.25i	−1.57218	−	1.76614i
$667$		−	77.6632i		−	0.116437i
$668$	−569.473	−	66.3980i	−0.852505	−	0.0993983i
$669$	1219.89			1.82345
$670$	13.5617	−	12.0723i	0.0202413	−	0.0180184i
$671$		0			0
$672$	−493.549	−	913.790i	−0.734447	−	1.35981i
$673$	1090.45			1.62028			0.810138	−	0.586239i	$-0.199392\pi$
$673$	1090.45			1.62028			0.810138	+	0.586239i	$0.199392\pi$
$674$	−236.373	−	265.534i	−0.350701	−	0.393967i
$675$		−	1557.89i		−	2.30799i
$676$	75.6454	−	648.785i	0.111901	−	0.959740i
$677$	68.0346			0.100494			0.0502471	−	0.998737i	$-0.483999\pi$
$677$	68.0346			0.100494			0.0502471	+	0.998737i	$0.483999\pi$
$678$	1191.14	−	1060.32i	1.75684	−	1.56390i
$679$		−	0.320089i		−	0.000471412i
$680$	−67.5612	+	47.3498i	−0.0993547	+	0.0696320i
$681$	758.155			1.11330
$682$		0			0
$683$			1090.21i			1.59621i	0.602518	+	0.798106i	$0.294164\pi$
$683$			1090.21i			1.59621i	−0.602518	+	0.798106i	$0.705836\pi$
$684$	1208.35	+	140.889i	1.76660	+	0.205977i
$685$	−329.730			−0.481358
$686$	−557.721	+	496.471i	−0.813004	+	0.723719i
$687$			1573.69i			2.29067i
$688$	43.2470	−	182.936i	0.0628590	−	0.265895i
$689$	−122.965			−0.178468
$690$	−39.7226	−	44.6231i	−0.0575690	−	0.0646712i
$691$		−	359.357i		−	0.520053i	−0.965601	−	0.260027i	$-0.916269\pi$
$691$		−	359.357i		−	0.520053i	0.965601	−	0.260027i	$-0.0837313\pi$
$692$	126.570	−	1085.55i	0.182904	−	1.56871i
$693$		0			0
$694$	−838.922	+	746.791i	−1.20882	+	1.07607i
$695$			529.673i			0.762119i
$696$	1032.88	+	1473.77i	1.48403	+	2.11749i
$697$	79.6030			0.114208
$698$	546.459	+	613.876i	0.782893	+	0.879478i
$699$			1006.81i			1.44035i
$700$	−406.776	−	47.4283i	−0.581108	−	0.0677546i
$701$	−180.147			−0.256986			−0.128493	−	0.991710i	$-0.541014\pi$
$701$	−180.147			−0.256986			−0.128493	+	0.991710i	$0.541014\pi$
$702$	−306.856	+	273.157i	−0.437117	+	0.389113i
$703$		−	416.584i		−	0.592580i
$704$		0			0
$705$	197.746			0.280490
$706$	7.28932	+	8.18860i	0.0103248	+	0.0115986i
$707$			853.644i			1.20742i
$708$	71.3764	−	612.171i	0.100814	−	0.864648i
$709$	−1015.72			−1.43261			−0.716306	−	0.697786i	$-0.754169\pi$
$709$	−1015.72			−1.43261			−0.716306	+	0.697786i	$0.754169\pi$
$710$	70.9241	−	63.1351i	0.0998931	−	0.0889227i
$711$			2329.40i			3.27623i
$712$	140.575	−	98.5210i	0.197437	−	0.138372i
$713$	78.5804			0.110211
$714$	−169.628	−	190.555i	−0.237574	−	0.266884i
$715$		0			0
$716$	1033.42	+	120.493i	1.44333	+	0.168286i
$717$	−270.971			−0.377923
$718$	900.250	−	801.383i	1.25383	−	1.11613i
$719$			335.376i			0.466448i	0.972423	+	0.233224i	$0.0749275\pi$
$719$			335.376i			0.466448i	−0.972423	+	0.233224i	$0.925073\pi$
$720$	979.558	+	231.572i	1.36050	+	0.321628i
$721$	48.8292			0.0677243
$722$	−266.082	−	298.908i	−0.368535	−	0.414001i
$723$		−	56.7942i		−	0.0785535i
$724$	−126.551	+	1085.38i	−0.174794	+	1.49914i
$725$	709.663			0.978845
$726$		0			0
$727$		−	818.836i		−	1.12632i	−0.826347	−	0.563161i	$-0.809585\pi$
$727$		−	818.836i		−	1.12632i	0.826347	−	0.563161i	$-0.190415\pi$
$728$	61.9811	+	88.4380i	0.0851389	+	0.121481i
$729$	−2222.20			−3.04828
$730$	−188.754	−	212.041i	−0.258568	−	0.290467i
$731$		−	46.1761i		−	0.0631684i
$732$	2173.90	+	253.468i	2.96982	+	0.346267i
$733$	248.050			0.338404			0.169202	−	0.985581i	$-0.445881\pi$
$733$	248.050			0.338404			0.169202	+	0.985581i	$0.445881\pi$
$734$	−322.382	+	286.978i	−0.439213	+	0.390978i
$735$		−	257.019i		−	0.349686i
$736$	−55.8179	+	30.1479i	−0.0758396	+	0.0409618i
$737$		0			0
$738$	−645.748	−	725.414i	−0.874998	−	0.982946i
$739$		−	1074.21i		−	1.45360i	−0.686850	−	0.726799i	$-0.741007\pi$
$739$		−	1074.21i		−	1.45360i	0.686850	−	0.726799i	$-0.258993\pi$
$740$	39.9177	−	342.360i	0.0539428	−	0.462649i
$741$	−173.988			−0.234802
$742$	−434.652	+	386.918i	−0.585784	+	0.521452i
$743$		−	12.5429i		−	0.0168814i	−0.999964	−	0.00844070i	$-0.997313\pi$
$743$		−	12.5429i		−	0.0168814i	0.999964	−	0.00844070i	$-0.00268679\pi$
$744$	−1491.18	+	1045.08i	−2.00427	+	1.40468i
$745$	108.051			0.145036
$746$	−195.744	−	219.893i	−0.262392	−	0.294763i
$747$			2849.73i			3.81489i
$748$		0			0
$749$	−763.072			−1.01879
$750$	970.473	−	863.894i	1.29396	−	1.15186i
$751$		−	1.16551i		−	0.00155195i	−1.00000		0.000775974i	$-0.999753\pi$
$751$		−	1.16551i		−	0.00155195i	1.00000		0.000775974i	$-0.000247000\pi$
$752$	48.3095	−	204.351i	0.0642414	−	0.271743i
$753$	−1310.06			−1.73979
$754$	−124.430	−	139.781i	−0.165027	−	0.185386i
$755$		−	313.422i		−	0.415128i
$756$	−225.157	+	1931.09i	−0.297826	+	2.55435i
$757$	1447.87			1.91265			0.956323	−	0.292311i	$-0.0944241\pi$
$757$	1447.87			1.91265			0.956323	+	0.292311i	$0.0944241\pi$
$758$	−625.665	+	556.954i	−0.825416	+	0.734768i
$759$		0			0
$760$	152.819	+	218.051i	0.201078	+	0.286909i
$761$	−1208.38			−1.58789			−0.793943	−	0.607992i	$-0.791975\pi$
$761$	−1208.38			−1.58789			−0.793943	+	0.607992i	$0.791975\pi$
$762$	−945.116	−	1061.71i	−1.24031	−	1.39333i
$763$			866.503i			1.13565i
$764$	1032.73	+	120.412i	1.35174	+	0.157607i
$765$	247.257			0.323212
$766$	759.355	−	675.962i	0.991326	−	0.882457i
$767$			64.0882i			0.0835570i
$768$	658.275	−	1314.45i	0.857129	−	1.71153i
$769$	−292.708			−0.380635			−0.190317	−	0.981723i	$-0.560952\pi$
$769$	−292.708			−0.380635			−0.190317	+	0.981723i	$0.560952\pi$
$770$		0			0
$771$			2255.75i			2.92575i
$772$	−139.768	+	1198.75i	−0.181047	+	1.55278i
$773$	434.924			0.562644			0.281322	−	0.959613i	$-0.409227\pi$
$773$	434.924			0.562644			0.281322	+	0.959613i	$0.409227\pi$
$774$	−420.798	+	374.586i	−0.543667	+	0.483961i
$775$			718.044i			0.926509i
$776$	0.371034	−	0.260036i	0.000478136	−	0.000335098i
$777$	1065.84			1.37174
$778$	−181.905	−	204.346i	−0.233811	−	0.262656i
$779$		−	256.915i		−	0.329801i
$780$	−142.989	−	16.6718i	−0.183319	−	0.0213741i
$781$		0			0
$782$	−11.6399	+	10.3616i	−0.0148847	+	0.0132501i
$783$		−	3368.99i		−	4.30267i
$784$	−265.604	−	62.7901i	−0.338781	−	0.0800895i
$785$	318.084			0.405203
$786$	755.664	+	848.890i	0.961405	+	1.08001i
$787$			449.202i			0.570777i	0.958412	+	0.285389i	$0.0921227\pi$
$787$			449.202i			0.570777i	−0.958412	+	0.285389i	$0.907877\pi$
$788$	−12.6969	+	108.897i	−0.0161128	+	0.138194i
$789$	−1430.54			−1.81310
$790$	−380.822	+	339.000i	−0.482053	+	0.429114i
$791$			784.756i			0.992106i
$792$		0			0
$793$	−227.586			−0.286994
$794$	−995.439	−	1118.25i	−1.25370	−	1.40837i
$795$		−	775.694i		−	0.975716i
$796$	−1028.63	−	119.933i	−1.29224	−	0.150670i
$797$	165.810			0.208043			0.104022	−	0.994575i	$-0.466829\pi$
$797$	165.810			0.208043			0.104022	+	0.994575i	$0.466829\pi$
$798$	−615.008	+	547.467i	−0.770687	+	0.686049i
$799$		−	51.5815i		−	0.0645576i
$800$	−275.483	−	510.048i	−0.344353	−	0.637560i
$801$	−514.469			−0.642284
$802$	−310.219	−	348.490i	−0.386806	−	0.434527i
$803$		0			0
$804$	−9.20383	+	78.9381i	−0.0114476	+	0.0981818i
$805$	29.3991			0.0365206
$806$	141.432	−	125.900i	0.175474	−	0.156203i
$807$			409.412i			0.507326i
$808$	−989.509	+	693.490i	−1.22464	+	0.858279i
$809$	1221.43			1.50980			0.754901	−	0.655839i	$-0.227685\pi$
$809$	1221.43			1.50980			0.754901	+	0.655839i	$0.227685\pi$
$810$	−970.227	−	1089.92i	−1.19781	−	1.34558i
$811$			712.821i			0.878940i	0.898257	+	0.439470i	$0.144834\pi$
$811$			712.821i			0.878940i	−0.898257	+	0.439470i	$0.855166\pi$
$812$	−879.665	−	102.565i	−1.08333	−	0.126312i
$813$	−1582.92			−1.94701
$814$		0			0
$815$		−	320.774i		−	0.393588i
$816$	83.0799	−	351.430i	0.101814	−	0.430674i
$817$	−149.031			−0.182413
$818$	−712.836	−	800.778i	−0.871437	−	0.978946i
$819$		−	323.661i		−	0.395190i
$820$	24.6180	−	211.140i	0.0300220	−	0.257488i
$821$	101.692			0.123864			0.0619318	−	0.998080i	$-0.480274\pi$
$821$	101.692			0.123864			0.0619318	+	0.998080i	$0.480274\pi$
$822$	1078.01	−	959.625i	1.31145	−	1.16743i
$823$			936.441i			1.13784i	0.822393	+	0.568919i	$0.192638\pi$
$823$			936.441i			1.13784i	−0.822393	+	0.568919i	$0.807362\pi$
$824$	39.6682	+	56.6008i	0.0481410	+	0.0686903i
$825$		0			0
$826$	201.658	+	226.537i	0.244138	+	0.274258i
$827$			1304.16i			1.57698i	0.615049	+	0.788489i	$0.289136\pi$
$827$			1304.16i			1.57698i	−0.615049	+	0.788489i	$0.710864\pi$
$828$	188.848	+	22.0188i	0.228077	+	0.0265928i
$829$	793.199			0.956814			0.478407	−	0.878138i	$-0.341214\pi$
$829$	793.199			0.956814			0.478407	+	0.878138i	$0.341214\pi$
$830$	−465.887	+	414.723i	−0.561310	+	0.499666i
$831$		−	933.479i		−	1.12332i
$832$	−52.1610	+	143.692i	−0.0626935	+	0.172707i
$833$	−67.0430			−0.0804837
$834$	−1541.53	−	1731.70i	−1.84835	−	2.07638i
$835$			376.087i			0.450404i
$836$		0			0
$837$	3408.78			4.07262
$838$	−610.608	+	543.550i	−0.728649	+	0.648628i
$839$		−	827.557i		−	0.986362i	−0.869927	−	0.493181i	$-0.835834\pi$
$839$		−	827.557i		−	0.986362i	0.869927	−	0.493181i	$-0.164166\pi$
$840$	−557.890	+	390.993i	−0.664155	+	0.465468i
$841$	693.667			0.824812
$842$	514.147	+	577.577i	0.610626	+	0.685959i
$843$			970.205i			1.15090i
$844$	110.657	+	12.9021i	0.131110	+	0.0152868i
$845$	−428.465			−0.507060
$846$	−470.057	+	418.435i	−0.555624	+	0.494604i
$847$		0			0
$848$	−801.604	−	189.503i	−0.945288	−	0.223471i
$849$	−1163.24			−1.37012
$850$	−94.6808	−	106.362i	−0.111389	−	0.125131i
$851$		−	65.1059i		−	0.0765052i
$852$	−48.1336	+	412.826i	−0.0564949	+	0.484537i
$853$	−123.265			−0.144508			−0.0722538	−	0.997386i	$-0.523019\pi$
$853$	−123.265			−0.144508			−0.0722538	+	0.997386i	$0.523019\pi$
$854$	−804.464	+	716.117i	−0.941995	+	0.838544i
$855$		−	798.011i		−	0.933346i
$856$	−619.910	−	884.521i	−0.724194	−	1.03332i
$857$	119.223			0.139116			0.0695581	−	0.997578i	$-0.477841\pi$
$857$	119.223			0.139116			0.0695581	+	0.997578i	$0.477841\pi$
$858$		0			0
$859$		−	399.433i		−	0.464997i	−0.972597	−	0.232499i	$-0.925310\pi$
$859$		−	399.433i		−	0.464997i	0.972597	−	0.232499i	$-0.0746901\pi$
$860$	−122.478	−	14.2804i	−0.142417	−	0.0166051i
$861$	657.326			0.763445
$862$	−224.292	+	199.660i	−0.260200	+	0.231624i
$863$		−	723.815i		−	0.838719i	−0.907820	−	0.419360i	$-0.862255\pi$
$863$		−	723.815i		−	0.838719i	0.907820	−	0.419360i	$-0.137745\pi$
$864$	−2421.36	+	1307.80i	−2.80250	+	1.51366i
$865$	−716.908			−0.828795
$866$	−331.491	−	372.387i	−0.382784	−	0.430008i
$867$			1570.87i			1.81184i
$868$	103.776	−	890.054i	0.119558	−	1.02541i
$869$		0			0
$870$	881.778	−	784.940i	1.01354	−	0.902230i
$871$		−	8.26404i		−	0.00948799i
$872$	−1004.41	+	703.936i	−1.15185	+	0.807266i
$873$	−1.35789			−0.00155543
$874$	33.4415	+	37.5672i	0.0382626	+	0.0429830i
$875$			639.376i			0.730716i
$876$	1234.22	+	143.905i	1.40893	+	0.164275i
$877$	1331.26			1.51797			0.758984	−	0.651110i	$-0.225696\pi$
$877$	1331.26			1.51797			0.758984	+	0.651110i	$0.225696\pi$
$878$	461.362	−	410.695i	0.525470	−	0.467762i
$879$		−	2907.85i		−	3.30813i
$880$		0			0
$881$	−600.014			−0.681060			−0.340530	−	0.940234i	$-0.610606\pi$
$881$	−600.014			−0.681060			−0.340530	+	0.940234i	$0.610606\pi$
$882$	543.860	+	610.956i	0.616621	+	0.692694i
$883$		−	174.915i		−	0.198092i	−0.995083	−	0.0990458i	$-0.968421\pi$
$883$		−	174.915i		−	0.198092i	0.995083	−	0.0990458i	$-0.0315790\pi$
$884$	−4.34882	+	37.2983i	−0.00491948	+	0.0421927i
$885$	−404.285			−0.456820
$886$	−280.029	+	249.276i	−0.316060	+	0.281350i
$887$			1077.58i			1.21486i	0.794374	+	0.607429i	$0.207799\pi$
$887$			1077.58i			1.21486i	−0.794374	+	0.607429i	$0.792201\pi$
$888$	865.877	+	1235.48i	0.975087	+	1.39131i
$889$	699.489			0.786827
$890$	−74.8711	−	84.1079i	−0.0841248	−	0.0945033i
$891$		0			0
$892$	−844.015	−	98.4084i	−0.946205	−	0.110323i
$893$	−166.477			−0.186425
$894$	−353.262	+	314.466i	−0.395147	+	0.351752i
$895$		−	682.486i		−	0.762554i
$896$	267.760	+	672.046i	0.298839	+	0.750051i
$897$	−27.1918			−0.0303142
$898$	191.529	+	215.158i	0.213284	+	0.239597i
$899$			1552.79i			1.72724i
$900$	−201.201	+	1725.63i	−0.223557	+	1.91737i
$901$	−202.338			−0.224571
$902$		0			0
$903$		−	381.302i		−	0.422261i
$904$	−909.656	+	637.525i	−1.00626	+	0.705227i
$905$	716.799			0.792043
$906$	912.162	+	1024.70i	1.00680	+	1.13101i
$907$			144.563i			0.159386i	0.996819	+	0.0796932i	$0.0253941\pi$
$907$			144.563i			0.159386i	−0.996819	+	0.0796932i	$0.974606\pi$
$908$	−524.551	−	61.1603i	−0.577699	−	0.0673571i
$909$	3621.35			3.98388
$910$	52.9136	−	47.1026i	0.0581468	−	0.0517611i
$911$			918.460i			1.00819i	0.863648	+	0.504095i	$0.168174\pi$
$911$			918.460i			1.00819i	−0.863648	+	0.504095i	$0.831826\pi$
$912$	−1134.23	−	268.137i	−1.24367	−	0.294010i
$913$		0			0
$914$	955.023	+	1072.84i	1.04488	+	1.17379i
$915$		−	1435.67i		−	1.56904i
$916$	126.949	−	1088.80i	0.138591	−	1.18865i
$917$	−559.274			−0.609895
$918$	−504.932	+	449.480i	−0.550035	+	0.489629i
$919$		−	1564.99i		−	1.70293i	−0.524414	−	0.851463i	$-0.675716\pi$
$919$		−	1564.99i		−	1.70293i	0.524414	−	0.851463i	$-0.324284\pi$
$920$	23.8834	+	34.0782i	0.0259602	+	0.0370415i
$921$	235.870			0.256102
$922$	377.451	+	424.018i	0.409383	+	0.459889i
$923$		−	43.2187i		−	0.0468242i
$924$		0			0
$925$	594.919			0.643155
$926$	−639.638	+	569.392i	−0.690754	+	0.614894i
$927$		−	207.144i		−	0.223457i
$928$	−595.739	−	1102.99i	−0.641960	−	1.18857i
$929$	−1264.32			−1.36095			−0.680476	−	0.732770i	$-0.738227\pi$
$929$	−1264.32			−1.36095			−0.680476	+	0.732770i	$0.738227\pi$
$930$	794.210	+	892.192i	0.853990	+	0.959346i
$931$			216.378i			0.232415i
$932$	81.2190	−	696.587i	0.0871448	−	0.747411i
$933$	−2698.35			−2.89212
$934$	620.449	−	552.311i	0.664293	−	0.591339i
$935$		0			0
$936$	375.174	−	262.938i	0.400827	−	0.280916i
$937$	−1551.26			−1.65556			−0.827782	−	0.561049i	$-0.810398\pi$
$937$	−1551.26			−1.65556			−0.827782	+	0.561049i	$0.810398\pi$
$938$	−26.0034	−	29.2114i	−0.0277222	−	0.0311423i
$939$			1175.92i			1.25231i
$940$	−136.816	−	15.9521i	−0.145549	−	0.0169703i
$941$	−1357.23			−1.44233			−0.721164	−	0.692764i	$-0.756393\pi$
$941$	−1357.23			−1.44233			−0.721164	+	0.692764i	$0.756393\pi$
$942$	−1039.94	+	925.731i	−1.10397	+	0.982730i
$943$		−	40.1521i		−	0.0425791i
$944$	−98.7675	+	417.789i	−0.104627	+	0.442574i
$945$	1275.32			1.34954
$946$		0			0
$947$			17.9609i			0.0189661i	0.999955	+	0.00948304i	$0.00301859\pi$
$947$			17.9609i			0.0189661i	−0.999955	+	0.00948304i	$0.996981\pi$
$948$	258.450	−	2216.64i	0.272627	−	2.33823i
$949$	−129.211			−0.136155
$950$	−343.277	+	305.578i	−0.361345	+	0.321661i
$951$			67.1802i			0.0706417i
$952$	101.990	+	145.525i	0.107132	+	0.152862i
$953$	−909.911			−0.954786			−0.477393	−	0.878690i	$-0.658418\pi$
$953$	−909.911			−0.954786			−0.477393	+	0.878690i	$0.658418\pi$
$954$	1641.39	+	1843.89i	1.72054	+	1.93280i
$955$		−	682.029i		−	0.714166i
$956$	187.479	+	21.8592i	0.196107	+	0.0228652i
$957$		0			0
$958$	263.194	−	234.290i	0.274733	−	0.244561i
$959$			710.227i			0.740592i
$960$	−906.446	−	329.046i	−0.944215	−	0.342756i
$961$	−610.131			−0.634892
$962$	−104.311	−	117.180i	−0.108432	−	0.121809i
$963$			3237.12i			3.36150i
$964$	−4.58158	+	39.2946i	−0.00475267	+	0.0407620i
$965$	791.666			0.820380
$966$	−96.1168	+	85.5611i	−0.0994998	+	0.0885726i
$967$			840.940i			0.869638i	0.900518	+	0.434819i	$0.143188\pi$
$967$			840.940i			0.869638i	−0.900518	+	0.434819i	$0.856812\pi$
$968$		0			0
$969$	−286.298			−0.295457
$970$	−0.197615	−	0.221994i	−0.000203726	−	0.000228860i
$971$		−	330.453i		−	0.340323i	−0.985416	−	0.170161i	$-0.945571\pi$
$971$		−	330.453i		−	0.340323i	0.985416	−	0.170161i	$-0.0544289\pi$
$972$	3268.96	+	381.146i	3.36312	+	0.392125i
$973$	1140.90			1.17256
$974$	1147.81	−	1021.76i	1.17845	−	1.04904i
$975$		−	248.471i		−	0.254842i
$976$	−1483.63	−	350.737i	−1.52011	−	0.359362i
$977$	532.551			0.545088			0.272544	−	0.962143i	$-0.412135\pi$
$977$	532.551			0.545088			0.272544	+	0.962143i	$0.412135\pi$
$978$	933.560	+	1048.73i	0.954560	+	1.07232i
$979$		0			0
$980$	−20.7337	+	177.826i	−0.0211568	+	0.181455i
$981$	3675.90			3.74709
$982$	280.232	−	249.457i	0.285369	−	0.254029i
$983$			498.333i			0.506951i	0.967342	+	0.253476i	$0.0815737\pi$
$983$			498.333i			0.506951i	−0.967342	+	0.253476i	$0.918426\pi$
$984$	534.003	+	761.945i	0.542686	+	0.774334i
$985$	71.9169			0.0730121
$986$	−204.750	−	230.010i	−0.207657	−	0.233276i
$987$		−	425.937i		−	0.431547i
$988$	120.379	+	14.0356i	0.121841	+	0.0142061i
$989$	−23.2914			−0.0235505
$990$		0			0
$991$		−	1422.23i		−	1.43514i	−0.696484	−	0.717572i	$-0.745253\pi$
$991$		−	1422.23i		−	1.43514i	0.696484	−	0.717572i	$-0.254747\pi$
$992$	1116.02	−	602.775i	1.12502	−	0.607636i
$993$	−304.947			−0.307096
$994$	−135.991	−	152.768i	−0.136812	−	0.153690i
$995$			679.318i			0.682731i
$996$	316.181	−	2711.78i	0.317451	−	2.72267i
$997$	−971.406			−0.974329			−0.487165	−	0.873310i	$-0.661969\pi$
$997$	−971.406			−0.974329			−0.487165	+	0.873310i	$0.661969\pi$
$998$	−692.874	+	616.782i	−0.694263	+	0.618018i
$999$		−	2824.27i		−	2.82709i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.3.b.h.243.3		10
4.3	odd	2	inner	484.3.b.h.243.4		10
11.10	odd	2		44.3.b.a.23.8	yes	10
33.32	even	2		396.3.g.c.199.3		10
44.43	even	2		44.3.b.a.23.7	✓	10
88.21	odd	2		704.3.d.d.639.10		10
88.43	even	2		704.3.d.d.639.1		10
132.131	odd	2		396.3.g.c.199.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.3.b.a.23.7	✓	10	44.43	even	2
44.3.b.a.23.8	yes	10	11.10	odd	2
396.3.g.c.199.3		10	33.32	even	2
396.3.g.c.199.4		10	132.131	odd	2
484.3.b.h.243.3		10	1.1	even	1	trivial
484.3.b.h.243.4		10	4.3	odd	2	inner
704.3.d.d.639.1		10	88.43	even	2
704.3.d.d.639.10		10	88.21	odd	2

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:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	484.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32980 - 1.49386i) q^{2} -5.74247i q^{3} +(-0.463244 + 3.97309i) q^{4} +2.62387 q^{5} +(-8.57845 + 7.63636i) q^{6} -5.65174i q^{7} +(6.55126 - 4.59140i) q^{8} -23.9759 q^{9} +(-3.48924 - 3.91971i) q^{10} +(22.8153 + 2.66016i) q^{12} -2.38854 q^{13} +(-8.44292 + 7.51571i) q^{14} -15.0675i q^{15} +(-15.5708 - 3.68102i) q^{16} -3.93033 q^{17} +(31.8833 + 35.8167i) q^{18} +12.6850i q^{19} +(-1.21549 + 10.4249i) q^{20} -32.4549 q^{21} +1.98248i q^{23} +(-26.3660 - 37.6204i) q^{24} -18.1153 q^{25} +(3.17628 + 3.56814i) q^{26} +85.9989i q^{27} +(22.4548 + 2.61814i) q^{28} -39.1748 q^{29} +(-22.5088 + 20.0368i) q^{30} -39.6375i q^{31} +(15.2072 + 28.1557i) q^{32} +(5.22657 + 5.87137i) q^{34} -14.8295i q^{35} +(11.1067 - 95.2585i) q^{36} -32.8407 q^{37} +(18.9496 - 16.8685i) q^{38} +13.7161i q^{39} +(17.1897 - 12.0473i) q^{40} -20.2535 q^{41} +(43.1587 + 48.4832i) q^{42} +11.7486i q^{43} -62.9099 q^{45} +(2.96155 - 2.63631i) q^{46} +13.1240i q^{47} +(-21.1381 + 89.4149i) q^{48} +17.0578 q^{49} +(24.0898 + 27.0617i) q^{50} +22.5698i q^{51} +(1.10648 - 9.48986i) q^{52} +51.4812 q^{53} +(128.470 - 114.362i) q^{54} +(-25.9494 - 37.0260i) q^{56} +72.8431 q^{57} +(52.0948 + 58.5218i) q^{58} -26.8316i q^{59} +(59.8645 + 6.97994i) q^{60} +95.2827 q^{61} +(-59.2129 + 52.7101i) q^{62} +135.506i q^{63} +(21.8381 - 60.1589i) q^{64} -6.26722 q^{65} +3.45987i q^{67} +(1.82070 - 15.6155i) q^{68} +11.3843 q^{69} +(-22.1532 + 19.7203i) q^{70} +18.0942i q^{71} +(-157.073 + 110.083i) q^{72} +54.0962 q^{73} +(43.6717 + 49.0595i) q^{74} +104.026i q^{75} +(-50.3985 - 5.87624i) q^{76} +(20.4899 - 18.2397i) q^{78} -97.1558i q^{79} +(-40.8559 - 9.65853i) q^{80} +278.063 q^{81} +(26.9332 + 30.2559i) q^{82} -118.858i q^{83} +(15.0346 - 128.946i) q^{84} -10.3127 q^{85} +(17.5509 - 15.6234i) q^{86} +224.960i q^{87} +21.4577 q^{89} +(83.6578 + 93.9787i) q^{90} +13.4994i q^{91} +(-7.87655 - 0.918371i) q^{92} -227.617 q^{93} +(19.6054 - 17.4523i) q^{94} +33.2838i q^{95} +(161.683 - 87.3268i) q^{96} +0.0566354 q^{97} +(-22.6836 - 25.4820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} - 4 q^{5} - 6 q^{6} + 12 q^{8} - 30 q^{9} + 2 q^{10} + 40 q^{12} + 4 q^{13} - 4 q^{14} - 40 q^{16} - 20 q^{17} + 22 q^{18} - 64 q^{20} - 32 q^{21} - 36 q^{24} - 10 q^{25} - 36 q^{26} - 40 q^{28}+ \cdots + 568 q^{98}+O(q^{100}) \) 10 * q + 4 * q^4 - 4 * q^5 - 6 * q^6 + 12 * q^8 - 30 * q^9 + 2 * q^10 + 40 * q^12 + 4 * q^13 - 4 * q^14 - 40 * q^16 - 20 * q^17 + 22 * q^18 - 64 * q^20 - 32 * q^21 - 36 * q^24 - 10 * q^25 - 36 * q^26 - 40 * q^28 - 28 * q^29 - 126 * q^30 - 80 * q^32 - 88 * q^34 - 4 * q^36 - 100 * q^37 + 40 * q^38 + 12 * q^40 - 100 * q^41 + 260 * q^42 - 44 * q^45 + 130 * q^46 + 24 * q^48 - 22 * q^49 + 198 * q^50 + 176 * q^52 + 100 * q^53 + 350 * q^54 + 136 * q^56 + 112 * q^57 + 116 * q^58 - 136 * q^60 + 52 * q^61 - 134 * q^62 - 368 * q^64 + 184 * q^65 - 176 * q^68 + 184 * q^69 - 36 * q^70 - 360 * q^72 - 84 * q^73 - 362 * q^74 - 504 * q^76 - 232 * q^78 - 120 * q^80 + 330 * q^81 + 220 * q^82 + 40 * q^84 + 216 * q^85 + 556 * q^86 + 28 * q^89 + 520 * q^90 + 152 * q^92 - 72 * q^93 + 272 * q^94 + 704 * q^96 - 180 * q^97 + 568 * q^98

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