LMFDB - Embedded newform 363.3.b.n.122.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [363,3,Mod(122,363)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(363, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("363.122"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-4,-44,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 10 x^{10} - 12 x^{9} + 290 x^{8} + 580 x^{7} + 3656 x^{6} + 5424 x^{5} + \cdots + 48312 $ x^12 - 4x^11 + 10x^10 - 12x^9 + 290x^8 + 580x^7 + 3656x^6 + 5424x^5 + 6124x^4 + 6920x^3 - 32528x^2 - 23952*x + 48312
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			122.1
Root			$-0.156151 + 2.44140i$ of defining polynomial
Character	$\chi$	$=$	363.122
Dual form			363.3.b.n.122.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.83317i q^{2} +(1.74344 - 2.44140i) q^{3} -10.6932 q^{4} -0.620885i q^{5} +(-9.35829 - 6.68291i) q^{6} -1.92745 q^{7} +25.6562i q^{8} +(-2.92083 - 8.51286i) q^{9} -2.37996 q^{10} +(-18.6430 + 26.1064i) q^{12} -15.9458 q^{13} +7.38824i q^{14} +(-1.51582 - 1.08248i) q^{15} +55.5719 q^{16} +14.4412i q^{17} +(-32.6313 + 11.1960i) q^{18} -16.4986 q^{19} +6.63925i q^{20} +(-3.36039 + 4.70566i) q^{21} -10.6669i q^{23} +(62.6370 + 44.7301i) q^{24} +24.6145 q^{25} +61.1231i q^{26} +(-25.8755 - 7.71077i) q^{27} +20.6106 q^{28} -19.1659i q^{29} +(-4.14932 + 5.81042i) q^{30} +22.0054 q^{31} -110.392i q^{32} +55.3557 q^{34} +1.19672i q^{35} +(31.2330 + 91.0298i) q^{36} -20.6452 q^{37} +63.2420i q^{38} +(-27.8006 + 38.9301i) q^{39} +15.9296 q^{40} -27.0161i q^{41} +(18.0376 + 12.8810i) q^{42} -53.1596 q^{43} +(-5.28550 + 1.81350i) q^{45} -40.8879 q^{46} -45.7258i q^{47} +(96.8864 - 135.673i) q^{48} -45.2849 q^{49} -94.3516i q^{50} +(35.2567 + 25.1774i) q^{51} +170.512 q^{52} -60.4562i q^{53} +(-29.5567 + 99.1854i) q^{54} -49.4511i q^{56} +(-28.7643 + 40.2796i) q^{57} -73.4661 q^{58} -40.5384i q^{59} +(16.2090 + 11.5751i) q^{60} -64.1073 q^{61} -84.3505i q^{62} +(5.62974 + 16.4081i) q^{63} -200.863 q^{64} +9.90052i q^{65} -25.7214 q^{67} -154.423i q^{68} +(-26.0420 - 18.5970i) q^{69} +4.58724 q^{70} +114.125i q^{71} +(218.408 - 74.9374i) q^{72} +84.4359 q^{73} +79.1367i q^{74} +(42.9139 - 60.0937i) q^{75} +176.423 q^{76} +(149.226 + 106.565i) q^{78} +65.2788 q^{79} -34.5038i q^{80} +(-63.9375 + 49.7292i) q^{81} -103.558 q^{82} +89.6649i q^{83} +(35.9334 - 50.3187i) q^{84} +8.96633 q^{85} +203.770i q^{86} +(-46.7915 - 33.4145i) q^{87} -146.530i q^{89} +(6.95145 + 20.2602i) q^{90} +30.7348 q^{91} +114.063i q^{92} +(38.3651 - 53.7239i) q^{93} -175.275 q^{94} +10.2437i q^{95} +(-269.510 - 192.462i) q^{96} +62.3547 q^{97} +173.585i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} - 44 q^{4} - 12 q^{9} - 80 q^{12} + 68 q^{15} + 92 q^{16} - 88 q^{25} - 232 q^{27} - 8 q^{31} + 116 q^{34} + 164 q^{36} - 244 q^{37} + 404 q^{42} - 52 q^{45} + 540 q^{48} + 100 q^{49} - 460 q^{58}+ \cdots - 156 q^{97}+O(q^{100}) $ 12 * q - 4 * q^3 - 44 * q^4 - 12 * q^9 - 80 * q^12 + 68 * q^15 + 92 * q^16 - 88 * q^25 - 232 * q^27 - 8 * q^31 + 116 * q^34 + 164 * q^36 - 244 * q^37 + 404 * q^42 - 52 * q^45 + 540 * q^48 + 100 * q^49 - 460 * q^58 + 24 * q^60 - 1276 * q^64 - 128 * q^67 + 128 * q^69 - 784 * q^70 + 684 * q^75 + 528 * q^78 + 348 * q^81 - 380 * q^82 + 120 * q^91 + 196 * q^93 - 156 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	3.83317i		−	1.91659i	−0.285787	−	0.958293i	$-0.592255\pi$
$2$		−	3.83317i		−	1.91659i	0.285787	−	0.958293i	$-0.407745\pi$
$3$	1.74344	−	2.44140i	0.581147	−	0.813799i
$3$	1.74344	−	2.44140i	0.581147	−	0.813799i
$4$	−10.6932			−2.67330
$5$		−	0.620885i		−	0.124177i	−0.998071	−	0.0620885i	$-0.980224\pi$
$5$		−	0.620885i		−	0.124177i	0.998071	−	0.0620885i	$-0.0197761\pi$
$6$	−9.35829	−	6.68291i	−1.55972	−	1.11382i
$7$	−1.92745			−0.275350			−0.137675	−	0.990477i	$-0.543963\pi$
$7$	−1.92745			−0.275350			−0.137675	+	0.990477i	$0.543963\pi$
$8$			25.6562i			3.20703i
$9$	−2.92083	−	8.51286i	−0.324536	−	0.945873i
$10$	−2.37996			−0.237996
$11$		0			0
$11$		0			0
$12$	−18.6430	+	26.1064i	−1.55358	+	2.17553i
$13$	−15.9458			−1.22660			−0.613301	−	0.789849i	$-0.710159\pi$
$13$	−15.9458			−1.22660			−0.613301	+	0.789849i	$0.710159\pi$
$14$			7.38824i			0.527732i
$15$	−1.51582	−	1.08248i	−0.101055	−	0.0721650i
$16$	55.5719			3.47325
$17$			14.4412i			0.849484i	0.905315	+	0.424742i	$0.139635\pi$
$17$			14.4412i			0.849484i	−0.905315	+	0.424742i	$0.860365\pi$
$18$	−32.6313	+	11.1960i	−1.81285	+	0.622002i
$19$	−16.4986			−0.868348			−0.434174	−	0.900829i	$-0.642960\pi$
$19$	−16.4986			−0.868348			−0.434174	+	0.900829i	$0.642960\pi$
$20$			6.63925i			0.331962i
$21$	−3.36039	+	4.70566i	−0.160019	+	0.224079i
$22$		0			0
$23$		−	10.6669i		−	0.463776i	−0.972742	−	0.231888i	$-0.925510\pi$
$23$		−	10.6669i		−	0.463776i	0.972742	−	0.231888i	$-0.0744903\pi$
$24$	62.6370	+	44.7301i	2.60988	+	1.86376i
$25$	24.6145			0.984580
$26$			61.1231i			2.35089i
$27$	−25.8755	−	7.71077i	−0.958354	−	0.285584i
$28$	20.6106			0.736093
$29$		−	19.1659i		−	0.660892i	−0.943825	−	0.330446i	$-0.892801\pi$
$29$		−	19.1659i		−	0.660892i	0.943825	−	0.330446i	$-0.107199\pi$
$30$	−4.14932	+	5.81042i	−0.138311	+	0.193681i
$31$	22.0054			0.709852			0.354926	−	0.934894i	$-0.384506\pi$
$31$	22.0054			0.709852			0.354926	+	0.934894i	$0.384506\pi$
$32$		−	110.392i		−	3.44975i
$33$		0			0
$34$	55.3557			1.62811
$35$			1.19672i			0.0341921i
$36$	31.2330	+	91.0298i	0.867584	+	2.52861i
$37$	−20.6452			−0.557979			−0.278990	−	0.960294i	$-0.589999\pi$
$37$	−20.6452			−0.557979			−0.278990	+	0.960294i	$0.589999\pi$
$38$			63.2420i			1.66426i
$39$	−27.8006	+	38.9301i	−0.712836	+	0.998207i
$40$	15.9296			0.398239
$41$		−	27.0161i		−	0.658930i	−0.944168	−	0.329465i	$-0.893132\pi$
$41$		−	27.0161i		−	0.658930i	0.944168	−	0.329465i	$-0.106868\pi$
$42$	18.0376	+	12.8810i	0.429467	+	0.306690i
$43$	−53.1596			−1.23627			−0.618134	−	0.786072i	$-0.712111\pi$
$43$	−53.1596			−1.23627			−0.618134	+	0.786072i	$0.712111\pi$
$44$		0			0
$45$	−5.28550	+	1.81350i	−0.117456	+	0.0402999i
$46$	−40.8879			−0.888867
$47$		−	45.7258i		−	0.972888i	−0.873712	−	0.486444i	$-0.838294\pi$
$47$		−	45.7258i		−	0.972888i	0.873712	−	0.486444i	$-0.161706\pi$
$48$	96.8864	−	135.673i	2.01847	−	2.82652i
$49$	−45.2849			−0.924183
$50$		−	94.3516i		−	1.88703i
$51$	35.2567	+	25.1774i	0.691309	+	0.493675i
$52$	170.512			3.27908
$53$		−	60.4562i		−	1.14068i	−0.821408	−	0.570341i	$-0.806811\pi$
$53$		−	60.4562i		−	1.14068i	0.821408	−	0.570341i	$-0.193189\pi$
$54$	−29.5567	+	99.1854i	−0.547346	+	1.83677i
$55$		0			0
$56$		−	49.4511i		−	0.883055i
$57$	−28.7643	+	40.2796i	−0.504638	+	0.706660i
$58$	−73.4661			−1.26666
$59$		−	40.5384i		−	0.687092i	−0.939136	−	0.343546i	$-0.888372\pi$
$59$		−	40.5384i		−	0.687092i	0.939136	−	0.343546i	$-0.111628\pi$
$60$	16.2090	+	11.5751i	0.270151	+	0.192919i
$61$	−64.1073			−1.05094			−0.525469	−	0.850812i	$-0.676110\pi$
$61$	−64.1073			−1.05094			−0.525469	+	0.850812i	$0.676110\pi$
$62$		−	84.3505i		−	1.36049i
$63$	5.62974	+	16.4081i	0.0893610	+	0.260446i
$64$	−200.863			−3.13849
$65$			9.90052i			0.152316i
$66$		0			0
$67$	−25.7214			−0.383901			−0.191951	−	0.981405i	$-0.561481\pi$
$67$	−25.7214			−0.383901			−0.191951	+	0.981405i	$0.561481\pi$
$68$		−	154.423i		−	2.27093i
$69$	−26.0420	−	18.5970i	−0.377420	−	0.269522i
$70$	4.58724			0.0655321
$71$			114.125i			1.60740i	0.595036	+	0.803699i	$0.297138\pi$
$71$			114.125i			1.60740i	−0.595036	+	0.803699i	$0.702862\pi$
$72$	218.408	−	74.9374i	3.03344	−	1.04080i
$73$	84.4359			1.15666			0.578328	−	0.815804i	$-0.303705\pi$
$73$	84.4359			1.15666			0.578328	+	0.815804i	$0.303705\pi$
$74$			79.1367i			1.06942i
$75$	42.9139	−	60.0937i	0.572186	−	0.801250i
$76$	176.423			2.32136
$77$		0			0
$78$	149.226	+	106.565i	1.91315	+	1.36621i
$79$	65.2788			0.826314			0.413157	−	0.910660i	$-0.364426\pi$
$79$	65.2788			0.826314			0.413157	+	0.910660i	$0.364426\pi$
$80$		−	34.5038i		−	0.431297i
$81$	−63.9375	+	49.7292i	−0.789352	+	0.613941i
$82$	−103.558			−1.26290
$83$			89.6649i			1.08030i	0.841569	+	0.540150i	$0.181633\pi$
$83$			89.6649i			1.08030i	−0.841569	+	0.540150i	$0.818367\pi$
$84$	35.9334	−	50.3187i	0.427778	−	0.599032i
$85$	8.96633			0.105486
$86$			203.770i			2.36942i
$87$	−46.7915	−	33.4145i	−0.537833	−	0.384075i
$88$		0			0
$89$		−	146.530i		−	1.64640i	−0.567750	−	0.823201i	$-0.692186\pi$
$89$		−	146.530i		−	1.64640i	0.567750	−	0.823201i	$-0.307814\pi$
$90$	6.95145	+	20.2602i	0.0772383	+	0.225114i
$91$	30.7348			0.337745
$92$			114.063i			1.23981i
$93$	38.3651	−	53.7239i	0.412528	−	0.577677i
$94$	−175.275			−1.86462
$95$			10.2437i			0.107829i
$96$	−269.510	−	192.462i	−2.80740	−	2.00481i
$97$	62.3547			0.642832			0.321416	−	0.946938i	$-0.395841\pi$
$97$	62.3547			0.642832			0.321416	+	0.946938i	$0.395841\pi$
$98$			173.585i			1.77128i
$99$		0			0
$100$	−263.208			−2.63208
$101$			88.2635i			0.873896i	0.899487	+	0.436948i	$0.143941\pi$
$101$			88.2635i			0.873896i	−0.899487	+	0.436948i	$0.856059\pi$
$102$	96.5094	−	135.145i	0.946170	−	1.32495i
$103$	−30.0534			−0.291781			−0.145890	−	0.989301i	$-0.546605\pi$
$103$	−30.0534			−0.291781			−0.145890	+	0.989301i	$0.546605\pi$
$104$		−	409.110i		−	3.93375i
$105$	2.92167	+	2.08642i	0.0278255	+	0.0198706i
$106$	−231.739			−2.18622
$107$		−	120.202i		−	1.12338i	−0.827348	−	0.561689i	$-0.810152\pi$
$107$		−	120.202i		−	1.12338i	0.827348	−	0.561689i	$-0.189848\pi$
$108$	276.693	+	82.4529i	2.56197	+	0.763453i
$109$	−152.110			−1.39551			−0.697753	−	0.716338i	$-0.745817\pi$
$109$	−152.110			−1.39551			−0.697753	+	0.716338i	$0.745817\pi$
$110$		0			0
$111$	−35.9937	+	50.4032i	−0.324268	+	0.454083i
$112$	−107.112			−0.956357
$113$			129.552i			1.14648i	0.819387	+	0.573241i	$0.194314\pi$
$113$			129.552i			1.14648i	−0.819387	+	0.573241i	$0.805686\pi$
$114$	154.399	+	110.259i	1.35437	+	0.967181i
$115$	−6.62288			−0.0575903
$116$			204.945i			1.76676i
$117$	46.5750	+	135.745i	0.398077	+	1.16021i
$118$	−155.391			−1.31687
$119$		−	27.8347i		−	0.233905i
$120$	27.7722	−	38.8904i	0.231435	−	0.324086i
$121$		0			0
$122$			245.734i			2.01422i
$123$	−65.9571	−	47.1011i	−0.536237	−	0.382935i
$124$	−235.309			−1.89765
$125$		−	30.8049i		−	0.246439i
$126$	62.8951	−	21.5798i	0.499167	−	0.171268i
$127$	63.1439			0.497196			0.248598	−	0.968607i	$-0.420030\pi$
$127$	63.1439			0.497196			0.248598	+	0.968607i	$0.420030\pi$
$128$			328.376i			2.56544i
$129$	−92.6805	+	129.784i	−0.718454	+	1.00607i
$130$	37.9504			0.291926
$131$		−	79.8306i		−	0.609394i	−0.952449	−	0.304697i	$-0.901445\pi$
$131$		−	79.8306i		−	0.609394i	0.952449	−	0.304697i	$-0.0985552\pi$
$132$		0			0
$133$	31.8002			0.239099
$134$			98.5945i			0.735780i
$135$	−4.78750	+	16.0657i	−0.0354629	+	0.119005i
$136$	−370.507			−2.72432
$137$			83.5542i			0.609885i	0.952371	+	0.304942i	$0.0986372\pi$
$137$			83.5542i			0.609885i	−0.952371	+	0.304942i	$0.901363\pi$
$138$	−71.2856	+	99.8235i	−0.516562	+	0.723359i
$139$	−80.8218			−0.581452			−0.290726	−	0.956806i	$-0.593897\pi$
$139$	−80.8218			−0.581452			−0.290726	+	0.956806i	$0.593897\pi$
$140$		−	12.7968i		−	0.0914058i
$141$	−111.635	−	79.7202i	−0.791735	−	0.565391i
$142$	437.462			3.08072
$143$		0			0
$144$	−162.316	−	473.076i	−1.12719	−	3.28525i
$145$	−11.8998			−0.0820675
$146$		−	323.657i		−	2.21683i
$147$	−78.9516	+	110.558i	−0.537086	+	0.752098i
$148$	220.764			1.49165
$149$		−	273.816i		−	1.83769i	−0.394613	−	0.918847i	$-0.629121\pi$
$149$		−	273.816i		−	1.83769i	0.394613	−	0.918847i	$-0.370879\pi$
$150$	−230.350	−	164.496i	−1.53566	−	1.09664i
$151$	−4.36383			−0.0288995			−0.0144498	−	0.999896i	$-0.504600\pi$
$151$	−4.36383			−0.0288995			−0.0144498	+	0.999896i	$0.504600\pi$
$152$		−	423.292i		−	2.78482i
$153$	122.936	−	42.1803i	0.803504	−	0.275688i
$154$		0			0
$155$		−	13.6628i		−	0.0881472i
$156$	297.278	−	416.288i	1.90563	−	2.66851i
$157$	137.724			0.877222			0.438611	−	0.898677i	$-0.355471\pi$
$157$	137.724			0.877222			0.438611	+	0.898677i	$0.355471\pi$
$158$		−	250.225i		−	1.58370i
$159$	−147.597	−	105.402i	−0.928286	−	0.662904i
$160$	−68.5406			−0.428379
$161$			20.5598i			0.127701i
$162$	190.621	+	245.084i	1.17667	+	1.51286i
$163$	−301.797			−1.85152			−0.925759	−	0.378115i	$-0.876573\pi$
$163$	−301.797			−1.85152			−0.925759	+	0.378115i	$0.876573\pi$
$164$			288.889i			1.76152i
$165$		0			0
$166$	343.701			2.07049
$167$		−	140.149i		−	0.839213i	−0.907706	−	0.419606i	$-0.862168\pi$
$167$		−	140.149i		−	0.839213i	0.907706	−	0.419606i	$-0.137832\pi$
$168$	−120.730	−	86.2150i	−0.718629	−	0.513185i
$169$	85.2695			0.504553
$170$		−	34.3695i		−	0.202174i
$171$	48.1896	+	140.450i	0.281810	+	0.821347i
$172$	568.446			3.30492
$173$		−	187.690i		−	1.08492i	−0.840083	−	0.542458i	$-0.817494\pi$
$173$		−	187.690i		−	1.08492i	0.840083	−	0.542458i	$-0.182506\pi$
$174$	−128.084	+	179.360i	−0.736113	+	1.03080i
$175$	−47.4432			−0.271104
$176$		0			0
$177$	−98.9703	−	70.6763i	−0.559154	−	0.399301i
$178$	−561.674			−3.15547
$179$			118.994i			0.664771i	0.943144	+	0.332386i	$0.107854\pi$
$179$			118.994i			0.664771i	−0.943144	+	0.332386i	$0.892146\pi$
$180$	56.5190	−	19.3921i	0.313994	−	0.107734i
$181$	207.591			1.14691			0.573456	−	0.819236i	$-0.305602\pi$
$181$	207.591			1.14691			0.573456	+	0.819236i	$0.305602\pi$
$182$		−	117.812i		−	0.647317i
$183$	−111.767	+	156.511i	−0.610750	+	0.855253i
$184$	273.671			1.48734
$185$			12.8183i			0.0692881i
$186$	−205.933	−	147.060i	−1.10717	−	0.790646i
$187$		0			0
$188$			488.955i			2.60083i
$189$	49.8738	+	14.8621i	0.263882	+	0.0786355i
$190$	39.2660			0.206663
$191$		−	368.710i		−	1.93042i	−0.261480	−	0.965209i	$-0.584210\pi$
$191$		−	368.710i		−	1.93042i	0.261480	−	0.965209i	$-0.415790\pi$
$192$	−350.193	+	490.387i	−1.82392	+	2.55410i
$193$	204.400			1.05907			0.529533	−	0.848289i	$-0.322367\pi$
$193$	204.400			1.05907			0.529533	+	0.848289i	$0.322367\pi$
$194$		−	239.016i		−	1.23204i
$195$	24.1711	+	17.2610i	0.123954	+	0.0885178i
$196$	484.241			2.47062
$197$			61.4657i			0.312009i	0.987756	+	0.156004i	$0.0498614\pi$
$197$			61.4657i			0.312009i	−0.987756	+	0.156004i	$0.950139\pi$
$198$		0			0
$199$	−53.9505			−0.271108			−0.135554	−	0.990770i	$-0.543281\pi$
$199$	−53.9505			−0.271108			−0.135554	+	0.990770i	$0.543281\pi$
$200$			631.515i			3.15758i
$201$	−44.8437	+	62.7961i	−0.223103	+	0.312418i
$202$	338.329			1.67490
$203$			36.9412i			0.181976i
$204$	−377.008	−	269.227i	−1.84808	−	1.31974i
$205$	−16.7739			−0.0818239
$206$			115.200i			0.559223i
$207$	−90.8054	+	31.1560i	−0.438674	+	0.150512i
$208$	−886.141			−4.26029
$209$		0			0
$210$	7.99759	−	11.1993i	0.0380838	−	0.0533299i
$211$	153.970			0.729714			0.364857	−	0.931064i	$-0.381118\pi$
$211$	153.970			0.729714			0.364857	+	0.931064i	$0.381118\pi$
$212$			646.470i			3.04939i
$213$	278.625	+	198.971i	1.30810	+	0.934135i
$214$	−460.753			−2.15305
$215$			33.0059i			0.153516i
$216$	197.829	−	663.869i	0.915876	−	3.07347i
$217$	−42.4143			−0.195458
$218$			583.064i			2.67461i
$219$	147.209	−	206.141i	0.672187	−	0.941285i
$220$		0			0
$221$		−	230.277i		−	1.04198i
$222$	193.204	+	137.970i	0.870289	+	0.621487i
$223$	−155.734			−0.698357			−0.349178	−	0.937056i	$-0.613539\pi$
$223$	−155.734			−0.698357			−0.349178	+	0.937056i	$0.613539\pi$
$224$			212.775i			0.949886i
$225$	−71.8947	−	209.540i	−0.319532	−	0.931288i
$226$	496.597			2.19733
$227$		−	76.7844i		−	0.338257i	−0.985594	−	0.169129i	$-0.945905\pi$
$227$		−	76.7844i		−	0.338257i	0.985594	−	0.169129i	$-0.0540953\pi$
$228$	307.583	−	430.719i	1.34905	−	1.88912i
$229$	−42.1829			−0.184205			−0.0921023	−	0.995750i	$-0.529359\pi$
$229$	−42.1829			−0.184205			−0.0921023	+	0.995750i	$0.529359\pi$
$230$			25.3867i			0.110377i
$231$		0			0
$232$	491.724			2.11950
$233$		−	46.7608i		−	0.200690i	−0.994953	−	0.100345i	$-0.968005\pi$
$233$		−	46.7608i		−	0.200690i	0.994953	−	0.100345i	$-0.0319946\pi$
$234$	520.333	−	178.530i	2.22364	−	0.762949i
$235$	−28.3904			−0.120810
$236$			433.486i			1.83680i
$237$	113.810	−	159.371i	0.480210	−	0.672453i
$238$	−106.695			−0.448299
$239$		−	157.528i		−	0.659114i	−0.944136	−	0.329557i	$-0.893101\pi$
$239$		−	157.528i		−	0.659114i	0.944136	−	0.329557i	$-0.106899\pi$
$240$	−84.2373	−	60.1553i	−0.350989	−	0.250647i
$241$	267.401			1.10955			0.554773	−	0.832002i	$-0.312805\pi$
$241$	267.401			1.10955			0.554773	+	0.832002i	$0.312805\pi$
$242$		0			0
$243$	9.93733	+	242.797i	0.0408944	+	0.999163i
$244$	685.513			2.80948
$245$			28.1167i			0.114762i
$246$	−180.546	+	252.825i	−0.733929	+	1.02774i
$247$	263.084			1.06512
$248$			564.576i			2.27652i
$249$	218.908	+	156.326i	0.879147	+	0.627813i
$250$	−118.080			−0.472322
$251$			327.642i			1.30535i	0.757639	+	0.652673i	$0.226353\pi$
$251$			327.642i			1.30535i	−0.757639	+	0.652673i	$0.773647\pi$
$252$	−60.2000	−	175.455i	−0.238889	−	0.696251i
$253$		0			0
$254$		−	242.042i		−	0.952919i
$255$	15.6323	−	21.8904i	0.0613030	−	0.0858446i
$256$	455.270			1.77840
$257$		−	6.13018i		−	0.0238528i	−0.999929	−	0.0119264i	$-0.996204\pi$
$257$		−	6.13018i		−	0.0238528i	0.999929	−	0.0119264i	$-0.00379639\pi$
$258$	497.483	+	355.261i	1.92823	+	1.37698i
$259$	39.7926			0.153639
$260$		−	105.868i		−	0.407186i
$261$	−163.156	+	55.9802i	−0.625120	+	0.214483i
$262$	−306.004			−1.16796
$263$		−	171.833i		−	0.653356i	−0.945136	−	0.326678i	$-0.894071\pi$
$263$		−	171.833i		−	0.653356i	0.945136	−	0.326678i	$-0.105929\pi$
$264$		0			0
$265$	−37.5363			−0.141646
$266$		−	121.896i		−	0.458254i
$267$	−357.737	−	255.466i	−1.33984	−	0.956802i
$268$	275.044			1.02628
$269$		−	96.2444i		−	0.357786i	−0.983869	−	0.178893i	$-0.942748\pi$
$269$		−	96.2444i		−	0.357786i	0.983869	−	0.178893i	$-0.0572516\pi$
$270$	61.5827	+	18.3513i	0.228084	+	0.0679678i
$271$	81.6129			0.301155			0.150577	−	0.988598i	$-0.451887\pi$
$271$	81.6129			0.301155			0.150577	+	0.988598i	$0.451887\pi$
$272$			802.527i			2.95047i
$273$	53.5842	−	75.0357i	0.196279	−	0.274856i
$274$	320.278			1.16890
$275$		0			0
$276$	278.473	+	198.862i	1.00896	+	0.720514i
$277$	160.351			0.578886			0.289443	−	0.957195i	$-0.406530\pi$
$277$	160.351			0.578886			0.289443	+	0.957195i	$0.406530\pi$
$278$			309.804i			1.11440i
$279$	−64.2740	−	187.329i	−0.230373	−	0.671430i
$280$	−30.7034			−0.109655
$281$		−	342.068i		−	1.21732i	−0.793430	−	0.608662i	$-0.791707\pi$
$281$		−	342.068i		−	1.21732i	0.793430	−	0.608662i	$-0.208293\pi$
$282$	−305.581	+	427.915i	−1.08362	+	1.51743i
$283$	291.087			1.02858			0.514288	−	0.857618i	$-0.328056\pi$
$283$	291.087			1.02858			0.514288	+	0.857618i	$0.328056\pi$
$284$		−	1220.37i		−	4.29706i
$285$	25.0090	+	17.8593i	0.0877509	+	0.0626643i
$286$		0			0
$287$			52.0722i			0.181436i
$288$	−939.750	+	322.436i	−3.26302	+	1.11957i
$289$	80.4511			0.278377
$290$			45.6139i			0.157289i
$291$	108.712	−	152.232i	0.373580	−	0.523136i
$292$	−902.890			−3.09209
$293$		−	120.198i		−	0.410233i	−0.978738	−	0.205117i	$-0.934243\pi$
$293$		−	120.198i		−	0.410233i	0.978738	−	0.205117i	$-0.0657574\pi$
$294$	423.790	+	302.635i	1.44146	+	1.02937i
$295$	−25.1697			−0.0853209
$296$		−	529.679i		−	1.78946i
$297$		0			0
$298$	−1049.59			−3.52210
$299$			170.092i			0.568869i
$300$	−458.888	+	642.595i	−1.52963	+	2.14198i
$301$	102.462			0.340406
$302$			16.7273i			0.0553884i
$303$	215.486	+	153.882i	0.711176	+	0.507862i
$304$	−916.859			−3.01598
$305$			39.8032i			0.130502i
$306$	−161.684	−	471.235i	−0.528381	−	1.53998i
$307$	−140.853			−0.458806			−0.229403	−	0.973332i	$-0.573677\pi$
$307$	−140.853			−0.458806			−0.229403	+	0.973332i	$0.573677\pi$
$308$		0			0
$309$	−52.3963	+	73.3722i	−0.169567	+	0.237451i
$310$	−52.3719			−0.168942
$311$		−	409.326i		−	1.31616i	−0.752947	−	0.658081i	$-0.771368\pi$
$311$		−	409.326i		−	1.31616i	0.752947	−	0.658081i	$-0.228632\pi$
$312$	−998.799	−	713.259i	−3.20128	−	2.28609i
$313$	373.913			1.19461			0.597305	−	0.802014i	$-0.296238\pi$
$313$	373.913			1.19461			0.597305	+	0.802014i	$0.296238\pi$
$314$		−	527.919i		−	1.68127i
$315$	10.1875	−	3.49542i	0.0323414	−	0.0110966i
$316$	−698.040			−2.20899
$317$			176.622i			0.557168i	0.960412	+	0.278584i	$0.0898651\pi$
$317$			176.622i			0.557168i	−0.960412	+	0.278584i	$0.910135\pi$
$318$	−404.023	+	565.766i	−1.27051	+	1.77914i
$319$		0			0
$320$			124.713i			0.389728i
$321$	−293.460	−	209.564i	−0.914204	−	0.652848i
$322$	78.8093			0.244749
$323$		−	238.260i		−	0.737647i
$324$	683.698	−	531.765i	2.11018	−	1.64125i
$325$	−392.499			−1.20769
$326$			1156.84i			3.54859i
$327$	−265.195	+	371.361i	−0.810994	+	1.13566i
$328$	693.133			2.11321
$329$			88.1340i			0.267885i
$330$		0			0
$331$	97.5763			0.294793			0.147396	−	0.989078i	$-0.452911\pi$
$331$	97.5763			0.294793			0.147396	+	0.989078i	$0.452911\pi$
$332$		−	958.806i		−	2.88797i
$333$	60.3011	+	175.750i	0.181085	+	0.527777i
$334$	−537.214			−1.60842
$335$			15.9700i			0.0476717i
$336$	−186.743	+	261.503i	−0.555784	+	0.778282i
$337$	−170.086			−0.504707			−0.252353	−	0.967635i	$-0.581205\pi$
$337$	−170.086			−0.504707			−0.252353	+	0.967635i	$0.581205\pi$
$338$		−	326.853i		−	0.967020i
$339$	316.289	+	225.867i	0.933005	+	0.666275i
$340$	−95.8789			−0.281997
$341$		0			0
$342$	538.370	−	184.719i	1.57418	−	0.540114i
$343$	181.729			0.529823
$344$		−	1363.87i		−	3.96475i
$345$	−11.5466	+	16.1691i	−0.0334684	+	0.0468669i
$346$	−719.450			−2.07934
$347$			433.131i			1.24822i	0.781338	+	0.624108i	$0.214537\pi$
$347$			433.131i			1.24822i	−0.781338	+	0.624108i	$0.785463\pi$
$348$	500.351	+	357.309i	1.43779	+	1.02675i
$349$	412.379			1.18160			0.590800	−	0.806818i	$-0.298812\pi$
$349$	412.379			1.18160			0.590800	+	0.806818i	$0.298812\pi$
$350$			181.858i			0.519594i
$351$	412.607	+	122.955i	1.17552	+	0.350298i
$352$		0			0
$353$			116.450i			0.329888i	0.986303	+	0.164944i	$0.0527443\pi$
$353$			116.450i			0.329888i	−0.986303	+	0.164944i	$0.947256\pi$
$354$	−270.915	+	379.370i	−0.765295	+	1.07167i
$355$	70.8586			0.199602
$356$			1566.87i			4.40133i
$357$	−67.9555	−	48.5282i	−0.190352	−	0.135933i
$358$	456.125			1.27409
$359$		−	579.340i		−	1.61376i	−0.590716	−	0.806880i	$-0.701154\pi$
$359$		−	579.340i		−	1.61376i	0.590716	−	0.806880i	$-0.298846\pi$
$360$	−46.5275	−	135.606i	−0.129243	−	0.376684i
$361$	−88.7961			−0.245973
$362$		−	795.733i		−	2.19816i
$363$		0			0
$364$	−328.653			−0.902894
$365$		−	52.4249i		−	0.143630i
$366$	599.935	+	428.423i	1.63917	+	1.17056i
$367$	−135.045			−0.367970			−0.183985	−	0.982929i	$-0.558900\pi$
$367$	−135.045			−0.367970			−0.183985	+	0.982929i	$0.558900\pi$
$368$		−	592.778i		−	1.61081i
$369$	−229.985	+	78.9095i	−0.623265	+	0.213847i
$370$	49.1348			0.132797
$371$			116.526i			0.314087i
$372$	−410.247	+	574.481i	−1.10281	+	1.54430i
$373$	125.984			0.337760			0.168880	−	0.985637i	$-0.445985\pi$
$373$	125.984			0.337760			0.168880	+	0.985637i	$0.445985\pi$
$374$		0			0
$375$	−75.2069	−	53.7065i	−0.200552	−	0.143217i
$376$	1173.15			3.12008
$377$			305.616i			0.810651i
$378$	56.9690	−	191.175i	0.150712	−	0.505753i
$379$	−402.169			−1.06113			−0.530565	−	0.847644i	$-0.678020\pi$
$379$	−402.169			−1.06113			−0.530565	+	0.847644i	$0.678020\pi$
$380$		−	109.538i		−	0.288259i
$381$	110.088	−	154.159i	0.288944	−	0.404618i
$382$	−1413.33			−3.69981
$383$		−	417.205i		−	1.08931i	−0.838661	−	0.544653i	$-0.816661\pi$
$383$		−	417.205i		−	1.08931i	0.838661	−	0.544653i	$-0.183339\pi$
$384$	801.697	+	572.505i	2.08775	+	1.49090i
$385$		0			0
$386$		−	783.499i		−	2.02979i
$387$	155.270	+	452.540i	0.401214	+	1.16935i
$388$	−666.772			−1.71848
$389$			423.279i			1.08812i	0.839046	+	0.544061i	$0.183114\pi$
$389$			423.279i			1.08812i	−0.839046	+	0.544061i	$0.816886\pi$
$390$	66.1643	−	92.6520i	0.169652	−	0.237569i
$391$	154.042			0.393970
$392$		−	1161.84i		−	2.96388i
$393$	−194.898	−	139.180i	−0.495924	−	0.354147i
$394$	235.609			0.597992
$395$		−	40.5306i		−	0.102609i
$396$		0			0
$397$	230.173			0.579781			0.289891	−	0.957060i	$-0.406381\pi$
$397$	230.173			0.579781			0.289891	+	0.957060i	$0.406381\pi$
$398$			206.802i			0.519602i
$399$	55.4418	−	77.6369i	0.138952	−	0.194579i
$400$	1367.88			3.41969
$401$			420.358i			1.04827i	0.851634	+	0.524137i	$0.175612\pi$
$401$			420.358i			1.04827i	−0.851634	+	0.524137i	$0.824388\pi$
$402$	240.708	+	171.894i	0.598777	+	0.427596i
$403$	−350.895			−0.870706
$404$		−	943.821i		−	2.33619i
$405$	30.8761	+	39.6978i	0.0762372	+	0.0980193i
$406$	141.602			0.348773
$407$		0			0
$408$	−645.958	+	904.555i	−1.58323	+	2.21705i
$409$	−432.898			−1.05843			−0.529215	−	0.848488i	$-0.677514\pi$
$409$	−432.898			−1.05843			−0.529215	+	0.848488i	$0.677514\pi$
$410$			64.2973i			0.156823i
$411$	203.989	+	145.672i	0.496323	+	0.354433i
$412$	321.367			0.780018
$413$			78.1357i			0.189190i
$414$	119.426	+	348.073i	0.288470	+	0.840756i
$415$	55.6716			0.134148
$416$			1760.29i			4.23147i
$417$	−140.908	+	197.318i	−0.337909	+	0.473185i
$418$		0			0
$419$			258.662i			0.617331i	0.951171	+	0.308665i	$0.0998823\pi$
$419$			258.662i			0.617331i	−0.951171	+	0.308665i	$0.900118\pi$
$420$	−31.2421	−	22.3105i	−0.0743859	−	0.0531202i
$421$	559.980			1.33012			0.665060	−	0.746790i	$-0.268406\pi$
$421$	559.980			1.33012			0.665060	+	0.746790i	$0.268406\pi$
$422$		−	590.192i		−	1.39856i
$423$	−389.257	+	133.557i	−0.920229	+	0.315738i
$424$	1551.08			3.65820
$425$			355.464i			0.836385i
$426$	762.689	−	1068.02i	1.79035	−	2.50708i
$427$	123.563			0.289376
$428$			1285.34i			3.00313i
$429$		0			0
$430$	126.517			0.294227
$431$		−	137.319i		−	0.318606i	−0.987230	−	0.159303i	$-0.949075\pi$
$431$		−	137.319i		−	0.318606i	0.987230	−	0.159303i	$-0.0509247\pi$
$432$	−1437.95	−	428.502i	−3.32860	−	0.991904i
$433$	443.788			1.02491			0.512457	−	0.858713i	$-0.328735\pi$
$433$	443.788			1.02491			0.512457	+	0.858713i	$0.328735\pi$
$434$			162.581i			0.374611i
$435$	−20.7466	+	29.0521i	−0.0476933	+	0.0667864i
$436$	1626.55			3.73061
$437$			175.988i			0.402719i
$438$	−790.175	−	564.277i	−1.80405	−	1.28830i
$439$	−850.056			−1.93635			−0.968173	−	0.250281i	$-0.919477\pi$
$439$	−850.056			−1.93635			−0.968173	+	0.250281i	$0.919477\pi$
$440$		0			0
$441$	132.270	+	385.504i	0.299931	+	0.874159i
$442$	−882.693			−1.99704
$443$		−	300.820i		−	0.679052i	−0.940597	−	0.339526i	$-0.889733\pi$
$443$		−	300.820i		−	0.679052i	0.940597	−	0.339526i	$-0.110267\pi$
$444$	384.889	−	538.972i	0.866866	−	1.21390i
$445$	−90.9781			−0.204445
$446$			596.954i			1.33846i
$447$	−668.494	−	477.383i	−1.49551	−	1.06797i
$448$	387.154			0.864182
$449$			242.612i			0.540339i	0.962813	+	0.270170i	$0.0870798\pi$
$449$			242.612i			0.540339i	−0.962813	+	0.270170i	$0.912920\pi$
$450$	−803.202	+	275.585i	−1.78489	+	0.612411i
$451$		0			0
$452$		−	1385.33i		−	3.06489i
$453$	−7.60808	+	10.6538i	−0.0167949	+	0.0235184i
$454$	−294.328			−0.648299
$455$		−	19.0827i		−	0.0419401i
$456$	−1033.42	−	737.985i	−2.26628	−	1.61839i
$457$	−643.634			−1.40839			−0.704194	−	0.710007i	$-0.748692\pi$
$457$	−643.634			−1.40839			−0.704194	+	0.710007i	$0.748692\pi$
$458$			161.694i			0.353044i
$459$	111.353	−	373.675i	0.242599	−	0.814106i
$460$	70.8199			0.153956
$461$			526.878i			1.14290i	0.820636	+	0.571451i	$0.193619\pi$
$461$			526.878i			1.14290i	−0.820636	+	0.571451i	$0.806381\pi$
$462$		0			0
$463$	487.010			1.05186			0.525928	−	0.850529i	$-0.323718\pi$
$463$	487.010			1.05186			0.525928	+	0.850529i	$0.323718\pi$
$464$		−	1065.08i		−	2.29544i
$465$	−33.3564	−	23.8203i	−0.0717341	−	0.0512265i
$466$	−179.242			−0.384640
$467$		−	395.720i		−	0.847367i	−0.905810	−	0.423683i	$-0.860737\pi$
$467$		−	395.720i		−	0.847367i	0.905810	−	0.423683i	$-0.139263\pi$
$468$	−498.037	−	1451.55i	−1.06418	−	3.10159i
$469$	49.5767			0.105707
$470$			108.825i			0.231543i
$471$	240.113	−	336.238i	0.509795	−	0.713882i
$472$	1040.06			2.20352
$473$		0			0
$474$	−610.898	−	436.252i	−1.28881	−	0.920363i
$475$	−406.105			−0.854958
$476$			297.642i			0.625299i
$477$	−514.655	+	176.582i	−1.07894	+	0.370193i
$478$	−603.833			−1.26325
$479$		−	283.860i		−	0.592610i	−0.955093	−	0.296305i	$-0.904246\pi$
$479$		−	283.860i		−	0.592610i	0.955093	−	0.296305i	$-0.0957545\pi$
$480$	−119.496	+	167.335i	−0.248951	+	0.348614i
$481$	329.205			0.684418
$482$		−	1024.99i		−	2.12654i
$483$	50.1946	+	35.8448i	0.103923	+	0.0742129i
$484$		0			0
$485$		−	38.7151i		−	0.0798249i
$486$	930.682	−	38.0915i	1.91498	−	0.0783776i
$487$	185.942			0.381811			0.190906	−	0.981608i	$-0.438858\pi$
$487$	185.942			0.381811			0.190906	+	0.981608i	$0.438858\pi$
$488$		−	1644.75i		−	3.37039i
$489$	−526.166	+	736.807i	−1.07600	+	1.50676i
$490$	107.776			0.219952
$491$		−	603.898i		−	1.22993i	−0.788553	−	0.614967i	$-0.789169\pi$
$491$		−	603.898i		−	1.22993i	0.788553	−	0.614967i	$-0.210831\pi$
$492$	705.293	+	503.662i	1.43352	+	1.02370i
$493$	276.778			0.561417
$494$		−	1008.45i		−	2.04139i
$495$		0			0
$496$	1222.88			2.46549
$497$		−	219.971i		−	0.442597i
$498$	599.223	−	839.111i	1.20326	−	1.68496i
$499$	−831.869			−1.66707			−0.833536	−	0.552465i	$-0.813687\pi$
$499$	−831.869			−1.66707			−0.833536	+	0.552465i	$0.813687\pi$
$500$			329.403i			0.658806i
$501$	−342.158	−	244.341i	−0.682950	−	0.487706i
$502$	1255.91			2.50181
$503$			865.650i			1.72097i	0.509472	+	0.860487i	$0.329841\pi$
$503$			865.650i			1.72097i	−0.509472	+	0.860487i	$0.670159\pi$
$504$	−420.970	+	144.438i	−0.835258	+	0.286583i
$505$	54.8015			0.108518
$506$		0			0
$507$	148.662	−	208.177i	0.293220	−	0.410605i
$508$	−675.211			−1.32916
$509$			224.906i			0.441859i	0.975290	+	0.220930i	$0.0709091\pi$
$509$			224.906i			0.441859i	−0.975290	+	0.220930i	$0.929091\pi$
$510$	−83.9095	−	59.9212i	−0.164529	−	0.117493i
$511$	−162.746			−0.318485
$512$		−	431.622i		−	0.843012i
$513$	426.910	+	127.217i	0.832184	+	0.247986i
$514$	−23.4980			−0.0457160
$515$			18.6597i			0.0362324i
$516$	991.053	−	1387.80i	1.92064	−	2.68954i
$517$		0			0
$518$		−	152.532i		−	0.294463i
$519$	−458.227	−	327.227i	−0.882903	−	0.630496i
$520$	−254.010			−0.488481
$521$			685.513i			1.31576i	0.753121	+	0.657882i	$0.228547\pi$
$521$			685.513i			1.31576i	−0.753121	+	0.657882i	$0.771453\pi$
$522$	214.582	+	625.406i	0.411076	+	1.19810i
$523$	144.428			0.276153			0.138076	−	0.990422i	$-0.455908\pi$
$523$	144.428			0.276153			0.138076	+	0.990422i	$0.455908\pi$
$524$			853.645i			1.62909i
$525$	−82.7144	+	115.828i	−0.157551	+	0.220624i
$526$	−658.664			−1.25221
$527$			317.785i			0.603008i
$528$		0			0
$529$	415.218			0.784912
$530$			143.883i			0.271478i
$531$	−345.098	+	118.406i	−0.649902	+	0.222986i
$532$	−340.046			−0.639185
$533$			430.795i			0.808246i
$534$	−979.246	+	1371.27i	−1.83379	+	2.56792i
$535$	−74.6313			−0.139498
$536$		−	659.914i		−	1.23118i
$537$	290.512	+	207.459i	0.540990	+	0.386330i
$538$	−368.921			−0.685727
$539$		0			0
$540$	51.1937	−	171.794i	0.0948032	−	0.318137i
$541$	175.837			0.325023			0.162511	−	0.986707i	$-0.448041\pi$
$541$	175.837			0.325023			0.162511	+	0.986707i	$0.448041\pi$
$542$		−	312.836i		−	0.577189i
$543$	361.923	−	506.812i	0.666525	−	0.933356i
$544$	1594.19			2.93050
$545$			94.4428i			0.173290i
$546$	−287.625	−	205.398i	−0.526785	−	0.376186i
$547$	−257.468			−0.470691			−0.235345	−	0.971912i	$-0.575622\pi$
$547$	−257.468			−0.470691			−0.235345	+	0.971912i	$0.575622\pi$
$548$		−	893.463i		−	1.63041i
$549$	187.246	+	545.736i	0.341068	+	0.994055i
$550$		0			0
$551$			316.210i			0.573884i
$552$	477.130	−	668.140i	0.864366	−	1.21040i
$553$	−125.821			−0.227525
$554$		−	614.655i		−	1.10949i
$555$	31.2945	+	22.3480i	0.0563866	+	0.0402666i
$556$	864.245			1.55440
$557$			702.773i			1.26171i	0.775901	+	0.630855i	$0.217296\pi$
$557$			702.773i			1.26171i	−0.775901	+	0.630855i	$0.782704\pi$
$558$	−718.064	+	246.373i	−1.28685	+	0.441529i
$559$	847.673			1.51641
$560$			66.5042i			0.118757i
$561$		0			0
$562$	−1311.21			−2.33311
$563$			791.940i			1.40664i	0.710872	+	0.703322i	$0.248301\pi$
$563$			791.940i			1.40664i	−0.710872	+	0.703322i	$0.751699\pi$
$564$	1193.73	+	852.464i	2.11655	+	1.51146i
$565$	80.4371			0.142367
$566$		−	1115.79i		−	1.97135i
$567$	123.236	−	95.8504i	0.217348	−	0.169048i
$568$	−2928.03			−5.15497
$569$		−	422.423i		−	0.742395i	−0.928554	−	0.371197i	$-0.878947\pi$
$569$		−	422.423i		−	0.742395i	0.928554	−	0.371197i	$-0.121053\pi$
$570$	68.4579	−	95.8638i	0.120102	−	0.168182i
$571$	−637.530			−1.11652			−0.558258	−	0.829668i	$-0.688530\pi$
$571$	−637.530			−1.11652			−0.558258	+	0.829668i	$0.688530\pi$
$572$		0			0
$573$	−900.167	−	642.824i	−1.57097	−	1.12186i
$574$	199.602			0.347738
$575$		−	262.559i		−	0.456625i
$576$	586.687	+	1709.92i	1.01855	+	2.96861i
$577$	606.711			1.05149			0.525746	−	0.850641i	$-0.323786\pi$
$577$	606.711			1.05149			0.525746	+	0.850641i	$0.323786\pi$
$578$		−	308.383i		−	0.533534i
$579$	356.359	−	499.021i	0.615473	−	0.861866i
$580$	127.247			0.219391
$581$		−	172.825i		−	0.297460i
$582$	−583.533	−	416.711i	−1.00263	−	0.715998i
$583$		0			0
$584$			2166.31i			3.70943i
$585$	84.2817	−	28.9177i	0.144071	−	0.0494320i
$586$	−460.741			−0.786248
$587$			950.811i			1.61978i	0.586582	+	0.809890i	$0.300473\pi$
$587$			950.811i			1.61978i	−0.586582	+	0.809890i	$0.699527\pi$
$588$	844.246	−	1182.23i	1.43579	−	2.01059i
$589$	−363.059			−0.616398
$590$			96.4797i			0.163525i
$591$	150.062	+	107.162i	0.253912	+	0.181323i
$592$	−1147.30			−1.93800
$593$			590.217i			0.995307i	0.867376	+	0.497654i	$0.165805\pi$
$593$			590.217i			0.995307i	−0.867376	+	0.497654i	$0.834195\pi$
$594$		0			0
$595$	−17.2821			−0.0290456
$596$			2927.98i			4.91271i
$597$	−94.0595	+	131.715i	−0.157554	+	0.220627i
$598$	651.991			1.09029
$599$		−	567.280i		−	0.947045i	−0.880782	−	0.473522i	$-0.842982\pi$
$599$		−	567.280i		−	0.947045i	0.880782	−	0.473522i	$-0.157018\pi$
$600$	1541.78	+	1101.01i	2.56963	+	1.83502i
$601$	−13.6571			−0.0227239			−0.0113620	−	0.999935i	$-0.503617\pi$
$601$	−13.6571			−0.0227239			−0.0113620	+	0.999935i	$0.503617\pi$
$602$		−	392.756i		−	0.652418i
$603$	75.1278	+	218.963i	0.124590	+	0.363122i
$604$	46.6633			0.0772572
$605$		0			0
$606$	589.857	−	825.996i	0.973362	−	1.36303i
$607$	683.261			1.12564			0.562818	−	0.826581i	$-0.309717\pi$
$607$	683.261			1.12564			0.562818	+	0.826581i	$0.309717\pi$
$608$			1821.31i			2.99558i
$609$	90.1881	+	64.4048i	0.148092	+	0.105755i
$610$	152.573			0.250119
$611$			729.135i			1.19335i
$612$	−1314.58	+	451.043i	−2.14801	+	0.736999i
$613$	284.867			0.464710			0.232355	−	0.972631i	$-0.425357\pi$
$613$	284.867			0.464710			0.232355	+	0.972631i	$0.425357\pi$
$614$			539.916i			0.879341i
$615$	−29.2443	+	40.9517i	−0.0475517	+	0.0665882i
$616$		0			0
$617$			1136.28i			1.84162i	0.390010	+	0.920811i	$0.372472\pi$
$617$			1136.28i			1.84162i	−0.390010	+	0.920811i	$0.627528\pi$
$618$	281.248	+	200.844i	0.455095	+	0.324991i
$619$	−318.917			−0.515213			−0.257606	−	0.966250i	$-0.582934\pi$
$619$	−318.917			−0.515213			−0.257606	+	0.966250i	$0.582934\pi$
$620$			146.099i			0.235644i
$621$	−82.2497	+	276.011i	−0.132447	+	0.444462i
$622$	−1569.02			−2.52254
$623$			282.429i			0.453337i
$624$	−1544.93	+	2163.42i	−2.47586	+	3.46702i
$625$	596.236			0.953978
$626$		−	1433.27i		−	2.28957i
$627$		0			0
$628$	−1472.71			−2.34508
$629$		−	298.142i		−	0.473994i
$630$	−13.3986	−	39.0506i	−0.0212675	−	0.0619850i
$631$	−204.174			−0.323572			−0.161786	−	0.986826i	$-0.551725\pi$
$631$	−204.174			−0.323572			−0.161786	+	0.986826i	$0.551725\pi$
$632$			1674.81i			2.65001i
$633$	268.437	−	375.901i	0.424071	−	0.593840i
$634$	677.024			1.06786
$635$		−	39.2051i		−	0.0617403i
$636$	1578.29	+	1127.08i	2.48159	+	1.77214i
$637$	722.106			1.13360
$638$		0			0
$639$	971.533	−	333.340i	1.52040	−	0.521659i
$640$	203.884			0.318568
$641$		−	167.647i		−	0.261540i	−0.991413	−	0.130770i	$-0.958255\pi$
$641$		−	167.647i		−	0.261540i	0.991413	−	0.130770i	$-0.0417450\pi$
$642$	−803.296	+	1124.88i	−1.25124	+	1.75215i
$643$	194.763			0.302897			0.151449	−	0.988465i	$-0.451606\pi$
$643$	194.763			0.302897			0.151449	+	0.988465i	$0.451606\pi$
$644$		−	219.850i		−	0.341383i
$645$	80.5806	+	57.5439i	0.124931	+	0.0892154i
$646$	−913.292			−1.41376
$647$		−	133.888i		−	0.206937i	−0.994633	−	0.103469i	$-0.967006\pi$
$647$		−	133.888i		−	0.206937i	0.994633	−	0.103469i	$-0.0329941\pi$
$648$	−1275.86	−	1640.40i	−1.96893	−	2.53148i
$649$		0			0
$650$			1504.52i			2.31464i
$651$	−73.9468	+	103.550i	−0.113590	+	0.159063i
$652$	3227.18			4.94967
$653$			360.838i			0.552585i	0.961074	+	0.276293i	$0.0891059\pi$
$653$			360.838i			0.552585i	−0.961074	+	0.276293i	$0.910894\pi$
$654$	1423.49	+	1016.54i	2.17659	+	1.55434i
$655$	−49.5656			−0.0756726
$656$		−	1501.34i		−	2.28863i
$657$	−246.623	−	718.791i	−0.375377	−	1.09405i
$658$	337.833			0.513424
$659$		−	281.019i		−	0.426433i	−0.977005	−	0.213216i	$-0.931606\pi$
$659$		−	281.019i		−	0.426433i	0.977005	−	0.213216i	$-0.0683939\pi$
$660$		0			0
$661$	−301.249			−0.455748			−0.227874	−	0.973691i	$-0.573177\pi$
$661$	−301.249			−0.455748			−0.227874	+	0.973691i	$0.573177\pi$
$662$		−	374.027i		−	0.564995i
$663$	−562.198	−	401.475i	−0.847961	−	0.605543i
$664$	−2300.46			−3.46456
$665$		−	19.7443i		−	0.0296906i
$666$	673.680	−	231.145i	1.01153	−	0.347064i
$667$	−204.439			−0.306506
$668$			1498.64i			2.24347i
$669$	−271.512	+	380.207i	−0.405848	+	0.568322i
$670$	61.2158			0.0913669
$671$		0			0
$672$	519.467	+	370.960i	0.773016	+	0.552024i
$673$	469.517			0.697648			0.348824	−	0.937188i	$-0.386581\pi$
$673$	469.517			0.697648			0.348824	+	0.937188i	$0.386581\pi$
$674$			651.970i			0.967314i
$675$	−636.914	−	189.797i	−0.943576	−	0.281180i
$676$	−911.805			−1.34882
$677$		−	437.913i		−	0.646843i	−0.946255	−	0.323421i	$-0.895167\pi$
$677$		−	437.913i		−	0.646843i	0.946255	−	0.323421i	$-0.104833\pi$
$678$	865.787	−	1212.39i	1.27697	−	1.78819i
$679$	−120.185			−0.177004
$680$			230.042i			0.338298i
$681$	−187.461	−	133.869i	−0.275273	−	0.196577i
$682$		0			0
$683$		−	848.684i		−	1.24258i	−0.783580	−	0.621291i	$-0.786608\pi$
$683$		−	848.684i		−	1.24258i	0.783580	−	0.621291i	$-0.213392\pi$
$684$	−515.301	−	1501.86i	−0.753365	−	2.19571i
$685$	51.8775			0.0757336
$686$		−	696.600i		−	1.01545i
$687$	−73.5433	+	102.985i	−0.107050	+	0.149906i
$688$	−2954.18			−4.29387
$689$			964.024i			1.39916i
$690$	61.9789	+	44.2601i	0.0898245	+	0.0641451i
$691$	−1104.18			−1.59794			−0.798970	−	0.601370i	$-0.794622\pi$
$691$	−1104.18			−1.59794			−0.798970	+	0.601370i	$0.794622\pi$
$692$			2007.01i			2.90031i
$693$		0			0
$694$	1660.27			2.39231
$695$			50.1810i			0.0722029i
$696$	857.292	−	1200.49i	1.23174	−	1.72485i
$697$	390.146			0.559751
$698$		−	1580.72i		−	2.26464i
$699$	−114.162	−	81.5246i	−0.163321	−	0.116630i
$700$	507.320			0.724743
$701$			950.887i			1.35647i	0.734844	+	0.678236i	$0.237255\pi$
$701$			950.887i			1.35647i	−0.734844	+	0.678236i	$0.762745\pi$
$702$	471.306	−	1581.59i	0.671376	−	2.25298i
$703$	340.617			0.484520
$704$		0			0
$705$	−49.4970	+	69.3122i	−0.0702085	+	0.0983152i
$706$	446.374			0.632258
$707$		−	170.123i		−	0.240627i
$708$	1058.31	+	755.757i	1.49479	+	1.06745i
$709$	−995.240			−1.40372			−0.701862	−	0.712313i	$-0.747648\pi$
$709$	−995.240			−1.40372			−0.701862	+	0.712313i	$0.747648\pi$
$710$		−	271.613i		−	0.382554i
$711$	−190.668	−	555.709i	−0.268169	−	0.781588i
$712$	3759.40			5.28006
$713$		−	234.729i		−	0.329213i
$714$	−186.017	+	260.485i	−0.260528	+	0.364825i
$715$		0			0
$716$		−	1272.43i		−	1.77714i
$717$	−384.589	−	274.641i	−0.536386	−	0.383042i
$718$	−2220.71			−3.09291
$719$		−	1099.64i		−	1.52940i	−0.644386	−	0.764701i	$-0.722887\pi$
$719$		−	1099.64i		−	1.52940i	0.644386	−	0.764701i	$-0.277113\pi$
$720$	−293.726	+	100.780i	−0.407952	+	0.139972i
$721$	57.9264			0.0803417
$722$			340.371i			0.471428i
$723$	466.197	−	652.831i	0.644809	−	0.902947i
$724$	−2219.82			−3.06604
$725$		−	471.758i		−	0.650701i
$726$		0			0
$727$	−1427.40			−1.96342			−0.981708	−	0.190395i	$-0.939023\pi$
$727$	−1427.40			−1.96342			−0.981708	+	0.190395i	$0.939023\pi$
$728$			788.538i			1.08316i
$729$	610.088	+	399.041i	0.836883	+	0.547381i
$730$	−200.954			−0.275279
$731$		−	767.689i		−	1.05019i
$732$	1195.15	−	1673.61i	1.63272	−	2.28635i
$733$	−324.830			−0.443151			−0.221576	−	0.975143i	$-0.571120\pi$
$733$	−324.830			−0.443151			−0.221576	+	0.975143i	$0.571120\pi$
$734$			517.651i			0.705247i
$735$	68.6440	+	49.0198i	0.0933933	+	0.0666937i
$736$	−1177.53			−1.59991
$737$		0			0
$738$	302.474	+	881.571i	0.409856	+	1.19454i
$739$	−344.719			−0.466467			−0.233233	−	0.972421i	$-0.574931\pi$
$739$	−344.719			−0.466467			−0.233233	+	0.972421i	$0.574931\pi$
$740$		−	137.069i		−	0.185228i
$741$	458.671	−	642.292i	0.618990	−	0.866791i
$742$	446.665			0.601974
$743$		−	236.630i		−	0.318479i	−0.987240	−	0.159239i	$-0.949096\pi$
$743$		−	236.630i		−	0.318479i	0.987240	−	0.159239i	$-0.0509041\pi$
$744$	1378.35	+	984.305i	1.85263	+	1.32299i
$745$	−170.008			−0.228199
$746$		−	482.920i		−	0.647346i
$747$	763.305	−	261.896i	1.02183	−	0.350597i
$748$		0			0
$749$			231.682i			0.309322i
$750$	−205.866	+	288.281i	−0.274488	+	0.384375i
$751$	−251.272			−0.334583			−0.167292	−	0.985907i	$-0.553502\pi$
$751$	−251.272			−0.334583			−0.167292	+	0.985907i	$0.553502\pi$
$752$		−	2541.07i		−	3.37908i
$753$	799.904	+	571.225i	1.06229	+	0.758598i
$754$	1171.48			1.55368
$755$			2.70943i			0.00358865i
$756$	−533.311	−	158.924i	−0.705438	−	0.210216i
$757$	−33.2746			−0.0439559			−0.0219779	−	0.999758i	$-0.506996\pi$
$757$	−33.2746			−0.0439559			−0.0219779	+	0.999758i	$0.506996\pi$
$758$			1541.58i			2.03375i
$759$		0			0
$760$	−262.815			−0.345810
$761$		−	1143.98i		−	1.50326i	−0.659586	−	0.751629i	$-0.729268\pi$
$761$		−	1143.98i		−	1.50326i	0.659586	−	0.751629i	$-0.270732\pi$
$762$	−590.919	−	421.985i	−0.775485	−	0.553786i
$763$	293.184			0.384252
$764$			3942.69i			5.16059i
$765$	−26.1891	−	76.3291i	−0.0342341	−	0.0997766i
$766$	−1599.22			−2.08775
$767$			646.419i			0.842788i
$768$	793.736	−	1111.49i	1.03351	−	1.44726i
$769$	−344.520			−0.448010			−0.224005	−	0.974588i	$-0.571913\pi$
$769$	−344.520			−0.448010			−0.224005	+	0.974588i	$0.571913\pi$
$770$		0			0
$771$	−14.9662	−	10.6876i	−0.0194114	−	0.0138620i
$772$	−2185.69			−2.83120
$773$			1184.63i			1.53250i	0.642541	+	0.766252i	$0.277880\pi$
$773$			1184.63i			1.53250i	−0.642541	+	0.766252i	$0.722120\pi$
$774$	1734.66	−	595.176i	2.24117	−	0.768962i
$775$	541.652			0.698906
$776$			1599.79i			2.06158i
$777$	69.3761	−	97.1495i	0.0892871	−	0.125032i
$778$	1622.50			2.08548
$779$			445.729i			0.572181i
$780$	−258.467	−	184.575i	−0.331367	−	0.236635i
$781$		0			0
$782$		−	590.471i		−	0.755078i
$783$	−147.784	+	495.927i	−0.188740	+	0.633368i
$784$	−2516.57			−3.20991
$785$		−	85.5106i		−	0.108931i
$786$	−533.501	+	747.078i	−0.678754	+	0.950481i
$787$	1199.85			1.52458			0.762292	−	0.647233i	$-0.224074\pi$
$787$	1199.85			1.52458			0.762292	+	0.647233i	$0.224074\pi$
$788$		−	657.266i		−	0.834094i
$789$	−419.511	−	299.580i	−0.531700	−	0.379696i
$790$	−155.361			−0.196659
$791$		−	249.706i		−	0.315684i
$792$		0			0
$793$	1022.24			1.28908
$794$		−	882.294i		−	1.11120i
$795$	−65.4423	+	91.6409i	−0.0823174	+	0.115272i
$796$	576.904			0.724754
$797$		−	1221.08i		−	1.53210i	−0.642783	−	0.766048i	$-0.722220\pi$
$797$		−	1221.08i		−	1.53210i	0.642783	−	0.766048i	$-0.277780\pi$
$798$	−297.596	−	212.518i	−0.372927	−	0.266313i
$799$	660.336			0.826453
$800$		−	2717.24i		−	3.39655i
$801$	−1247.39	+	427.988i	−1.55729	+	0.534318i
$802$	1611.30			2.00911
$803$		0			0
$804$	479.524	−	671.492i	0.596422	−	0.835189i
$805$	12.7653			0.0158575
$806$			1345.04i			1.66878i
$807$	−234.971	−	167.796i	−0.291166	−	0.207926i
$808$	−2264.51			−2.80261
$809$			985.567i			1.21825i	0.793073	+	0.609127i	$0.208480\pi$
$809$			985.567i			1.21825i	−0.793073	+	0.609127i	$0.791520\pi$
$810$	152.169	−	118.353i	0.187862	−	0.146115i
$811$	312.547			0.385385			0.192692	−	0.981259i	$-0.438278\pi$
$811$	312.547			0.385385			0.192692	+	0.981259i	$0.438278\pi$
$812$		−	395.020i		−	0.486478i
$813$	142.287	−	199.249i	0.175015	−	0.245079i
$814$		0			0
$815$			187.381i			0.229916i
$816$	1959.29	+	1399.16i	2.40108	+	1.71465i
$817$	877.058			1.07351
$818$			1659.37i			2.02857i
$819$	−89.7709	−	261.641i	−0.109610	−	0.319464i
$820$	179.367			0.218740
$821$		−	376.986i		−	0.459178i	−0.973288	−	0.229589i	$-0.926262\pi$
$821$		−	376.986i		−	0.459178i	0.973288	−	0.229589i	$-0.0737383\pi$
$822$	558.385	−	781.925i	0.679301	−	0.951246i
$823$	−1435.09			−1.74373			−0.871864	−	0.489748i	$-0.837089\pi$
$823$	−1435.09			−1.74373			−0.871864	+	0.489748i	$0.837089\pi$
$824$		−	771.057i		−	0.935749i
$825$		0			0
$826$	299.508			0.362600
$827$			711.817i			0.860722i	0.902657	+	0.430361i	$0.141614\pi$
$827$			711.817i			0.860722i	−0.902657	+	0.430361i	$0.858386\pi$
$828$	971.002	−	333.158i	1.17271	−	0.402365i
$829$	1313.36			1.58428			0.792138	−	0.610342i	$-0.208968\pi$
$829$	1313.36			1.58428			0.792138	+	0.610342i	$0.208968\pi$
$830$		−	213.399i		−	0.257107i
$831$	279.563	−	391.481i	0.336418	−	0.471097i
$832$	3202.93			3.84968
$833$		−	653.970i		−	0.785078i
$834$	756.354	+	540.125i	0.906899	+	0.647632i
$835$	−87.0161			−0.104211
$836$		0			0
$837$	−569.402	−	169.679i	−0.680289	−	0.202722i
$838$	991.495			1.18317
$839$		−	1195.33i		−	1.42470i	−0.701823	−	0.712351i	$-0.747630\pi$
$839$		−	1195.33i		−	1.42470i	0.701823	−	0.712351i	$-0.252370\pi$
$840$	−53.5296	+	74.9592i	−0.0637257	+	0.0892371i
$841$	473.670			0.563222
$842$		−	2146.50i		−	2.54929i
$843$	−835.124	−	596.376i	−0.990657	−	0.707444i
$844$	−1646.43			−1.95075
$845$		−	52.9425i		−	0.0626539i
$846$	511.947	+	1492.09i	0.605139	+	1.76370i
$847$		0			0
$848$		−	3359.67i		−	3.96187i
$849$	507.493	−	710.659i	0.597754	−	0.837054i
$850$	1362.55			1.60300
$851$			220.220i			0.258777i
$852$	−2979.40	−	2127.64i	−3.49694	−	2.49723i
$853$	280.038			0.328298			0.164149	−	0.986436i	$-0.447512\pi$
$853$	280.038			0.328298			0.164149	+	0.986436i	$0.447512\pi$
$854$		−	473.640i		−	0.554614i
$855$	87.2034	−	29.9202i	0.101992	−	0.0349943i
$856$	3083.92			3.60271
$857$		−	1450.04i		−	1.69200i	−0.533184	−	0.845999i	$-0.679005\pi$
$857$		−	1450.04i		−	1.69200i	0.533184	−	0.845999i	$-0.320995\pi$
$858$		0			0
$859$	451.309			0.525389			0.262694	−	0.964879i	$-0.415389\pi$
$859$	451.309			0.525389			0.262694	+	0.964879i	$0.415389\pi$
$860$		−	352.940i		−	0.410395i
$861$	127.129	+	90.7848i	0.147653	+	0.105441i
$862$	−526.368			−0.610636
$863$		−	443.496i		−	0.513900i	−0.966425	−	0.256950i	$-0.917282\pi$
$863$		−	443.496i		−	0.513900i	0.966425	−	0.256950i	$-0.0827176\pi$
$864$	−851.206	+	2856.45i	−0.985192	+	3.30608i
$865$	−116.534			−0.134722
$866$		−	1701.12i		−	1.96434i
$867$	140.262	−	196.413i	0.161778	−	0.226543i
$868$	453.545			0.522517
$869$		0			0
$870$	111.362	+	79.5252i	0.128002	+	0.0914083i
$871$	410.149			0.470894
$872$		−	3902.57i		−	4.47543i
$873$	−182.127	−	530.817i	−0.208622	−	0.608037i
$874$	674.593			0.771846
$875$			59.3748i			0.0678569i
$876$	−1574.14	+	2204.31i	−1.79696	+	2.51634i
$877$	−1013.08			−1.15516			−0.577582	−	0.816332i	$-0.696004\pi$
$877$	−1013.08			−1.15516			−0.577582	+	0.816332i	$0.696004\pi$
$878$			3258.41i			3.71118i
$879$	−293.452	−	209.559i	−0.333847	−	0.238406i
$880$		0			0
$881$		−	213.844i		−	0.242729i	−0.992608	−	0.121364i	$-0.961273\pi$
$881$		−	213.844i		−	0.242729i	0.992608	−	0.121364i	$-0.0387269\pi$
$882$	1477.70	−	507.012i	1.67540	−	0.574843i
$883$	405.012			0.458678			0.229339	−	0.973347i	$-0.426344\pi$
$883$	405.012			0.458678			0.229339	+	0.973347i	$0.426344\pi$
$884$			2462.40i			2.78552i
$885$	−43.8818	+	61.4491i	−0.0495840	+	0.0694340i
$886$	−1153.09			−1.30146
$887$			703.939i			0.793617i	0.917901	+	0.396809i	$0.129882\pi$
$887$			703.939i			0.793617i	−0.917901	+	0.396809i	$0.870118\pi$
$888$	−1293.16	−	923.464i	−1.45626	−	1.03994i
$889$	−121.707			−0.136903
$890$			348.735i			0.391837i
$891$		0			0
$892$	1665.29			1.86692
$893$			754.411i			0.844805i
$894$	−1829.89	+	2562.45i	−2.04686	+	2.86628i
$895$	73.8816			0.0825492
$896$		−	632.928i		−	0.706393i
$897$	415.262	+	296.545i	0.462945	+	0.330597i
$898$	929.975			1.03561
$899$		−	421.753i		−	0.469135i
$900$	768.785	+	2240.65i	0.854206	+	2.48961i
$901$	873.061			0.968991
$902$		0			0
$903$	178.637	−	250.151i	0.197826	−	0.277022i
$904$	−3323.83			−3.67680
$905$		−	128.890i		−	0.142420i
$906$	40.8380	+	29.1631i	0.0450750	+	0.0321888i
$907$	884.283			0.974953			0.487477	−	0.873136i	$-0.337917\pi$
$907$	884.283			0.974953			0.487477	+	0.873136i	$0.337917\pi$
$908$			821.072i			0.904264i
$909$	751.375	−	257.803i	0.826595	−	0.283611i
$910$	−73.1474			−0.0803818
$911$		−	849.732i		−	0.932747i	−0.884588	−	0.466373i	$-0.845560\pi$
$911$		−	849.732i		−	0.932747i	0.884588	−	0.466373i	$-0.154440\pi$
$912$	−1598.49	+	2238.42i	−1.75273	+	2.45440i
$913$		0			0
$914$			2467.16i			2.69930i
$915$	97.1754	+	69.3946i	0.106203	+	0.0758410i
$916$	451.070			0.492435
$917$			153.869i			0.167796i
$918$	−1432.36	−	426.835i	−1.56030	−	0.464962i
$919$	1026.78			1.11728			0.558640	−	0.829410i	$-0.311323\pi$
$919$	1026.78			1.11728			0.558640	+	0.829410i	$0.311323\pi$
$920$		−	169.918i		−	0.184694i
$921$	−245.570	+	343.879i	−0.266634	+	0.373376i
$922$	2019.61			2.19047
$923$		−	1819.82i		−	1.97164i
$924$		0			0
$925$	−508.172			−0.549375
$926$		−	1866.79i		−	2.01597i
$927$	87.7808	+	255.840i	0.0946934	+	0.275987i
$928$	−2115.76			−2.27991
$929$			322.042i			0.346654i	0.984864	+	0.173327i	$0.0554518\pi$
$929$			322.042i			0.346654i	−0.984864	+	0.173327i	$0.944548\pi$
$930$	−91.3074	+	127.861i	−0.0981800	+	0.137485i
$931$	747.138			0.802512
$932$			500.023i			0.536505i
$933$	−999.327	−	713.636i	−1.07109	−	0.764883i
$934$	−1516.86			−1.62405
$935$		0			0
$936$	−3482.70	+	1194.94i	−3.72083	+	1.27665i
$937$	−952.845			−1.01691			−0.508455	−	0.861088i	$-0.669783\pi$
$937$	−952.845			−1.01691			−0.508455	+	0.861088i	$0.669783\pi$
$938$		−	190.036i		−	0.202597i
$939$	651.895	−	912.869i	0.694244	−	0.972172i
$940$	303.585			0.322962
$941$		−	1291.41i		−	1.37238i	−0.727422	−	0.686190i	$-0.759282\pi$
$941$		−	1291.41i		−	1.37238i	0.727422	−	0.686190i	$-0.240718\pi$
$942$	−1288.86	−	920.396i	−1.36822	−	0.977066i
$943$	−288.177			−0.305596
$944$		−	2252.80i		−	2.38644i
$945$	9.22765	−	30.9659i	0.00976471	−	0.0327681i
$946$		0			0
$947$			1080.15i			1.14060i	0.821435	+	0.570302i	$0.193174\pi$
$947$			1080.15i			1.14060i	−0.821435	+	0.570302i	$0.806826\pi$
$948$	−1216.99	+	1704.19i	−1.28375	+	1.79767i
$949$	−1346.40			−1.41876
$950$			1556.67i			1.63860i
$951$	431.205	+	307.931i	0.453423	+	0.323797i
$952$	714.134			0.750141
$953$			647.480i			0.679412i	0.940532	+	0.339706i	$0.110328\pi$
$953$			647.480i			0.679412i	−0.940532	+	0.339706i	$0.889672\pi$
$954$	676.869	+	1972.76i	0.709507	+	2.06788i
$955$	−228.926			−0.239713
$956$			1684.48i			1.76201i
$957$		0			0
$958$	−1088.09			−1.13579
$959$		−	161.046i		−	0.167932i
$960$	304.474	+	217.430i	0.317160	+	0.226489i
$961$	−476.762			−0.496110
$962$		−	1261.90i		−	1.31175i
$963$	−1023.26	+	351.088i	−1.06257	+	0.364577i
$964$	−2859.37			−2.96615
$965$		−	126.909i		−	0.131512i
$966$	137.399	−	192.405i	0.142235	−	0.199177i
$967$	−4.41092			−0.00456145			−0.00228072	−	0.999997i	$-0.500726\pi$
$967$	−4.41092			−0.00456145			−0.00228072	+	0.999997i	$0.500726\pi$
$968$		0			0
$969$	−581.687	−	415.392i	−0.600296	−	0.428681i
$970$	−148.401			−0.152991
$971$			1112.88i			1.14612i	0.819515	+	0.573058i	$0.194243\pi$
$971$			1112.88i			1.14612i	−0.819515	+	0.573058i	$0.805757\pi$
$972$	−106.262	−	2596.28i	−0.109323	−	2.67107i
$973$	155.780			0.160103
$974$		−	712.748i		−	0.731775i
$975$	−684.298	+	958.245i	−0.701844	+	0.982815i
$976$	−3562.57			−3.65017
$977$			205.544i			0.210383i	0.994452	+	0.105191i	$0.0335456\pi$
$977$			205.544i			0.210383i	−0.994452	+	0.105191i	$0.966454\pi$
$978$	2824.31	+	2016.88i	2.88784	+	2.06225i
$979$		0			0
$980$		−	300.658i		−	0.306794i
$981$	444.288	+	1294.89i	0.452892	+	1.31997i
$982$	−2314.84			−2.35728
$983$		−	578.012i		−	0.588009i	−0.955804	−	0.294004i	$-0.905012\pi$
$983$		−	578.012i		−	0.588009i	0.955804	−	0.294004i	$-0.0949880\pi$
$984$	1208.44	−	1692.21i	1.22809	−	1.71973i
$985$	38.1631			0.0387443
$986$		−	1060.94i		−	1.07600i
$987$	215.170	+	153.656i	0.218004	+	0.155680i
$988$	−2813.21			−2.84738
$989$			567.045i			0.573352i
$990$		0			0
$991$	−576.755			−0.581993			−0.290997	−	0.956724i	$-0.593987\pi$
$991$	−576.755			−0.581993			−0.290997	+	0.956724i	$0.593987\pi$
$992$		−	2429.22i		−	2.44881i
$993$	170.119	−	238.222i	0.171318	−	0.239902i
$994$	−843.185			−0.848275
$995$			33.4970i			0.0336654i
$996$	−2340.83	−	1671.62i	−2.35023	−	1.67834i
$997$	−576.276			−0.578010			−0.289005	−	0.957328i	$-0.593324\pi$
$997$	−576.276			−0.578010			−0.289005	+	0.957328i	$0.593324\pi$
$998$			3188.70i			3.19509i
$999$	534.207	+	159.191i	0.534741	+	0.159350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.b.n.122.1	✓	12
3.2	odd	2	inner	363.3.b.n.122.12	yes	12
11.2	odd	10		363.3.h.r.323.11		48
11.3	even	5		363.3.h.r.251.2		48
11.4	even	5		363.3.h.r.269.11		48
11.5	even	5		363.3.h.r.245.12		48
11.6	odd	10		363.3.h.r.245.2		48
11.7	odd	10		363.3.h.r.269.1		48
11.8	odd	10		363.3.h.r.251.12		48
11.9	even	5		363.3.h.r.323.1		48
11.10	odd	2	inner	363.3.b.n.122.11	yes	12
33.2	even	10		363.3.h.r.323.2		48
33.5	odd	10		363.3.h.r.245.1		48
33.8	even	10		363.3.h.r.251.1		48
33.14	odd	10		363.3.h.r.251.11		48
33.17	even	10		363.3.h.r.245.11		48
33.20	odd	10		363.3.h.r.323.12		48
33.26	odd	10		363.3.h.r.269.2		48
33.29	even	10		363.3.h.r.269.12		48
33.32	even	2	inner	363.3.b.n.122.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.3.b.n.122.1	✓	12	1.1	even	1	trivial
363.3.b.n.122.2	yes	12	33.32	even	2	inner
363.3.b.n.122.11	yes	12	11.10	odd	2	inner
363.3.b.n.122.12	yes	12	3.2	odd	2	inner
363.3.h.r.245.1		48	33.5	odd	10
363.3.h.r.245.2		48	11.6	odd	10
363.3.h.r.245.11		48	33.17	even	10
363.3.h.r.245.12		48	11.5	even	5
363.3.h.r.251.1		48	33.8	even	10
363.3.h.r.251.2		48	11.3	even	5
363.3.h.r.251.11		48	33.14	odd	10
363.3.h.r.251.12		48	11.8	odd	10
363.3.h.r.269.1		48	11.7	odd	10
363.3.h.r.269.2		48	33.26	odd	10
363.3.h.r.269.11		48	11.4	even	5
363.3.h.r.269.12		48	33.29	even	10
363.3.h.r.323.1		48	11.9	even	5
363.3.h.r.323.2		48	33.2	even	10
363.3.h.r.323.11		48	11.2	odd	10
363.3.h.r.323.12		48	33.20	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.83317i q^{2} +(1.74344 - 2.44140i) q^{3} -10.6932 q^{4} -0.620885i q^{5} +(-9.35829 - 6.68291i) q^{6} -1.92745 q^{7} +25.6562i q^{8} +(-2.92083 - 8.51286i) q^{9} -2.37996 q^{10} +(-18.6430 + 26.1064i) q^{12} -15.9458 q^{13} +7.38824i q^{14} +(-1.51582 - 1.08248i) q^{15} +55.5719 q^{16} +14.4412i q^{17} +(-32.6313 + 11.1960i) q^{18} -16.4986 q^{19} +6.63925i q^{20} +(-3.36039 + 4.70566i) q^{21} -10.6669i q^{23} +(62.6370 + 44.7301i) q^{24} +24.6145 q^{25} +61.1231i q^{26} +(-25.8755 - 7.71077i) q^{27} +20.6106 q^{28} -19.1659i q^{29} +(-4.14932 + 5.81042i) q^{30} +22.0054 q^{31} -110.392i q^{32} +55.3557 q^{34} +1.19672i q^{35} +(31.2330 + 91.0298i) q^{36} -20.6452 q^{37} +63.2420i q^{38} +(-27.8006 + 38.9301i) q^{39} +15.9296 q^{40} -27.0161i q^{41} +(18.0376 + 12.8810i) q^{42} -53.1596 q^{43} +(-5.28550 + 1.81350i) q^{45} -40.8879 q^{46} -45.7258i q^{47} +(96.8864 - 135.673i) q^{48} -45.2849 q^{49} -94.3516i q^{50} +(35.2567 + 25.1774i) q^{51} +170.512 q^{52} -60.4562i q^{53} +(-29.5567 + 99.1854i) q^{54} -49.4511i q^{56} +(-28.7643 + 40.2796i) q^{57} -73.4661 q^{58} -40.5384i q^{59} +(16.2090 + 11.5751i) q^{60} -64.1073 q^{61} -84.3505i q^{62} +(5.62974 + 16.4081i) q^{63} -200.863 q^{64} +9.90052i q^{65} -25.7214 q^{67} -154.423i q^{68} +(-26.0420 - 18.5970i) q^{69} +4.58724 q^{70} +114.125i q^{71} +(218.408 - 74.9374i) q^{72} +84.4359 q^{73} +79.1367i q^{74} +(42.9139 - 60.0937i) q^{75} +176.423 q^{76} +(149.226 + 106.565i) q^{78} +65.2788 q^{79} -34.5038i q^{80} +(-63.9375 + 49.7292i) q^{81} -103.558 q^{82} +89.6649i q^{83} +(35.9334 - 50.3187i) q^{84} +8.96633 q^{85} +203.770i q^{86} +(-46.7915 - 33.4145i) q^{87} -146.530i q^{89} +(6.95145 + 20.2602i) q^{90} +30.7348 q^{91} +114.063i q^{92} +(38.3651 - 53.7239i) q^{93} -175.275 q^{94} +10.2437i q^{95} +(-269.510 - 192.462i) q^{96} +62.3547 q^{97} +173.585i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} - 44 q^{4} - 12 q^{9} - 80 q^{12} + 68 q^{15} + 92 q^{16} - 88 q^{25} - 232 q^{27} - 8 q^{31} + 116 q^{34} + 164 q^{36} - 244 q^{37} + 404 q^{42} - 52 q^{45} + 540 q^{48} + 100 q^{49} - 460 q^{58}+ \cdots - 156 q^{97}+O(q^{100}) \) 12 * q - 4 * q^3 - 44 * q^4 - 12 * q^9 - 80 * q^12 + 68 * q^15 + 92 * q^16 - 88 * q^25 - 232 * q^27 - 8 * q^31 + 116 * q^34 + 164 * q^36 - 244 * q^37 + 404 * q^42 - 52 * q^45 + 540 * q^48 + 100 * q^49 - 460 * q^58 + 24 * q^60 - 1276 * q^64 - 128 * q^67 + 128 * q^69 - 784 * q^70 + 684 * q^75 + 528 * q^78 + 348 * q^81 - 380 * q^82 + 120 * q^91 + 196 * q^93 - 156 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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