LMFDB - Embedded newform 363.3.h.q.245.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [363,3,Mod(245,363)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(363, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("363.245"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,-4,18,0,10,0] 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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			245.4
Character	$\chi$	$=$	363.245
Dual form			363.3.h.q.323.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.399998 + 0.550550i) q^{2} +(2.97531 + 0.384091i) q^{3} +(1.09296 - 3.36379i) q^{4} +(-3.81474 + 5.25053i) q^{5} +(0.978656 + 1.79169i) q^{6} +(2.89410 - 8.90713i) q^{7} +(4.87795 - 1.58494i) q^{8} +(8.70495 + 2.28558i) q^{9} -4.41657 q^{10} +(4.54390 - 9.58852i) q^{12} +(3.37472 - 2.45188i) q^{13} +(6.06145 - 1.96948i) q^{14} +(-13.3667 + 14.1568i) q^{15} +(-8.62188 - 6.26416i) q^{16} +(17.5904 - 24.2111i) q^{17} +(2.22363 + 5.70673i) q^{18} +(3.18032 + 9.78800i) q^{19} +(13.4923 + 18.5706i) q^{20} +(12.0320 - 25.3899i) q^{21} +27.8850i q^{23} +(15.1222 - 2.84212i) q^{24} +(-5.29047 - 16.2824i) q^{25} +(2.69976 + 0.877206i) q^{26} +(25.0221 + 10.1438i) q^{27} +(-26.7986 - 19.4703i) q^{28} +(15.3590 + 4.99043i) q^{29} +(-13.1407 - 1.69636i) q^{30} +(14.2887 - 10.3813i) q^{31} -27.7684i q^{32} +20.3655 q^{34} +(35.7270 + 49.1739i) q^{35} +(17.2024 - 26.7836i) q^{36} +(4.49918 - 13.8470i) q^{37} +(-4.11666 + 5.66610i) q^{38} +(10.9826 - 5.99890i) q^{39} +(-10.2863 + 31.6580i) q^{40} +(-33.2920 + 10.8172i) q^{41} +(18.7912 - 3.53168i) q^{42} -64.3417 q^{43} +(-45.2076 + 36.9867i) q^{45} +(-15.3521 + 11.1539i) q^{46} +(-9.94471 + 3.23123i) q^{47} +(-23.2468 - 21.9494i) q^{48} +(-31.3193 - 22.7548i) q^{49} +(6.84809 - 9.42559i) q^{50} +(61.6361 - 65.2792i) q^{51} +(-4.55916 - 14.0317i) q^{52} +(35.5031 + 48.8658i) q^{53} +(4.42410 + 17.8334i) q^{54} -48.0356i q^{56} +(5.70294 + 30.3439i) q^{57} +(3.39607 + 10.4520i) q^{58} +(-38.6761 - 12.5666i) q^{59} +(33.0111 + 60.4356i) q^{60} +(-19.0197 - 13.8186i) q^{61} +(11.4309 + 3.71411i) q^{62} +(45.5510 - 70.9214i) q^{63} +(-19.1997 + 13.9494i) q^{64} +27.0724i q^{65} +30.8376 q^{67} +(-62.2154 - 85.6321i) q^{68} +(-10.7104 + 82.9665i) q^{69} +(-12.7820 + 39.3389i) q^{70} +(0.585238 - 0.805511i) q^{71} +(46.0849 - 2.64790i) q^{72} +(-28.8838 + 88.8953i) q^{73} +(9.42314 - 3.06176i) q^{74} +(-9.48688 - 50.4772i) q^{75} +36.4007 q^{76} +(7.69570 + 3.64691i) q^{78} +(91.4806 - 66.4645i) q^{79} +(65.7804 - 21.3733i) q^{80} +(70.5522 + 39.7917i) q^{81} +(-19.2722 - 14.0020i) q^{82} +(-61.1711 + 84.1948i) q^{83} +(-72.2557 - 68.2233i) q^{84} +(60.0184 + 184.718i) q^{85} +(-25.7365 - 35.4233i) q^{86} +(43.7809 + 20.7473i) q^{87} -20.3993i q^{89} +(-38.4460 - 10.0944i) q^{90} +(-12.0724 - 37.1551i) q^{91} +(93.7992 + 30.4772i) q^{92} +(46.5005 - 25.3995i) q^{93} +(-5.75681 - 4.18257i) q^{94} +(-63.5243 - 20.6403i) q^{95} +(10.6656 - 82.6195i) q^{96} +(-153.778 + 111.726i) q^{97} -26.3447i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3} + 18 q^{4} + 10 q^{6} + 22 q^{9} + 72 q^{10} + 56 q^{12} + 42 q^{13} - 28 q^{15} - 30 q^{16} - 94 q^{18} - 84 q^{19} - 112 q^{21} - 48 q^{24} + 108 q^{25} + 38 q^{27} - 132 q^{28} + 148 q^{30}+ \cdots - 126 q^{97}+O(q^{100}) $ 24 * q - 4 * q^3 + 18 * q^4 + 10 * q^6 + 22 * q^9 + 72 * q^10 + 56 * q^12 + 42 * q^13 - 28 * q^15 - 30 * q^16 - 94 * q^18 - 84 * q^19 - 112 * q^21 - 48 * q^24 + 108 * q^25 + 38 * q^27 - 132 * q^28 + 148 * q^30 + 264 * q^34 - 46 * q^36 + 42 * q^37 + 82 * q^39 + 294 * q^40 + 206 * q^42 - 624 * q^43 - 472 * q^45 + 60 * q^46 + 88 * q^48 - 138 * q^49 - 182 * q^51 - 114 * q^52 + 560 * q^54 + 24 * q^57 + 54 * q^58 + 562 * q^60 - 264 * q^61 + 122 * q^63 - 294 * q^64 + 96 * q^67 - 152 * q^69 - 336 * q^70 + 306 * q^72 - 72 * q^73 - 62 * q^75 - 1632 * q^76 - 776 * q^78 + 250 * q^81 - 798 * q^82 - 328 * q^84 - 330 * q^85 + 1848 * q^87 + 230 * q^90 - 300 * q^91 + 266 * q^93 - 120 * q^94 + 386 * q^96 - 126 * q^97

Character values

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

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.399998	+	0.550550i	0.199999	+	0.275275i	0.897222	−	0.441579i	$-0.145582\pi$
$2$	0.399998	+	0.550550i	0.199999	+	0.275275i	−0.697224	+	0.716854i	$0.745582\pi$
$3$	2.97531	+	0.384091i	0.991770	+	0.128030i
$3$	2.97531	+	0.384091i	0.991770	+	0.128030i
$4$	1.09296	−	3.36379i	0.273240	−	0.840947i
$5$	−3.81474	+	5.25053i	−0.762947	+	1.05011i	0.234016	+	0.972233i	$0.424813\pi$
$5$	−3.81474	+	5.25053i	−0.762947	+	1.05011i	−0.996963	+	0.0778742i	$0.975187\pi$
$6$	0.978656	+	1.79169i	0.163109	+	0.298615i
$7$	2.89410	−	8.90713i	0.413443	−	1.27245i	−0.500193	−	0.865914i	$-0.666738\pi$
$7$	2.89410	−	8.90713i	0.413443	−	1.27245i	0.913636	−	0.406533i	$-0.133262\pi$
$8$	4.87795	−	1.58494i	0.609744	−	0.198118i
$9$	8.70495	+	2.28558i	0.967216	+	0.253953i
$10$	−4.41657			−0.441657
$11$		0			0
$11$		0			0
$12$	4.54390	−	9.58852i	0.378658	−	0.799043i
$13$	3.37472	−	2.45188i	0.259594	−	0.188606i	−0.450374	−	0.892840i	$-0.648709\pi$
$13$	3.37472	−	2.45188i	0.259594	−	0.188606i	0.709968	+	0.704234i	$0.248709\pi$
$14$	6.06145	−	1.96948i	0.432961	−	0.140677i
$15$	−13.3667	+	14.1568i	−0.891114	+	0.943784i
$16$	−8.62188	−	6.26416i	−0.538867	−	0.391510i
$17$	17.5904	−	24.2111i	1.03473	−	1.42418i	0.133391	−	0.991064i	$-0.457413\pi$
$17$	17.5904	−	24.2111i	1.03473	−	1.42418i	0.901337	−	0.433118i	$-0.142587\pi$
$18$	2.22363	+	5.70673i	0.123535	+	0.317041i
$19$	3.18032	+	9.78800i	0.167385	+	0.515158i	0.999204	−	0.0398887i	$-0.0127003\pi$
$19$	3.18032	+	9.78800i	0.167385	+	0.515158i	−0.831819	+	0.555047i	$0.812700\pi$
$20$	13.4923	+	18.5706i	0.674617	+	0.928530i
$21$	12.0320	−	25.3899i	0.572952	−	1.20904i
$22$		0			0
$23$			27.8850i			1.21239i	0.795316	+	0.606195i	$0.207305\pi$
$23$			27.8850i			1.21239i	−0.795316	+	0.606195i	$0.792695\pi$
$24$	15.1222	−	2.84212i	0.630091	−	0.118422i
$25$	−5.29047	−	16.2824i	−0.211619	−	0.651296i
$26$	2.69976	+	0.877206i	0.103837	+	0.0337387i
$27$	25.0221	+	10.1438i	0.926743	+	0.375696i
$28$	−26.7986	−	19.4703i	−0.957092	−	0.695368i
$29$	15.3590	+	4.99043i	0.529619	+	0.172084i	0.561606	−	0.827405i	$-0.310184\pi$
$29$	15.3590	+	4.99043i	0.529619	+	0.172084i	−0.0319872	+	0.999488i	$0.510184\pi$
$30$	−13.1407	−	1.69636i	−0.438022	−	0.0565454i
$31$	14.2887	−	10.3813i	0.460924	−	0.334881i	−0.332969	−	0.942938i	$-0.608051\pi$
$31$	14.2887	−	10.3813i	0.460924	−	0.334881i	0.793894	+	0.608057i	$0.208051\pi$
$32$		−	27.7684i		−	0.867761i
$33$		0			0
$34$	20.3655			0.598986
$35$	35.7270	+	49.1739i	1.02077	+	1.40497i
$36$	17.2024	−	26.7836i	0.477844	−	0.743988i
$37$	4.49918	−	13.8470i	0.121599	−	0.374244i	−0.871667	−	0.490099i	$-0.836961\pi$
$37$	4.49918	−	13.8470i	0.121599	−	0.374244i	0.993266	+	0.115855i	$0.0369607\pi$
$38$	−4.11666	+	5.66610i	−0.108333	+	0.149108i
$39$	10.9826	−	5.99890i	0.281605	−	0.153818i
$40$	−10.2863	+	31.6580i	−0.257158	+	0.791450i
$41$	−33.2920	+	10.8172i	−0.812001	+	0.263835i	−0.685445	−	0.728125i	$-0.740392\pi$
$41$	−33.2920	+	10.8172i	−0.812001	+	0.263835i	−0.126556	+	0.991959i	$0.540392\pi$
$42$	18.7912	−	3.53168i	0.447409	−	0.0840876i
$43$	−64.3417			−1.49632			−0.748159	−	0.663519i	$-0.769062\pi$
$43$	−64.3417			−1.49632			−0.748159	+	0.663519i	$0.769062\pi$
$44$		0			0
$45$	−45.2076	+	36.9867i	−1.00461	+	0.821928i
$46$	−15.3521	+	11.1539i	−0.333741	+	0.242477i
$47$	−9.94471	+	3.23123i	−0.211590	+	0.0687496i	−0.412894	−	0.910779i	$-0.635482\pi$
$47$	−9.94471	+	3.23123i	−0.211590	+	0.0687496i	0.201304	+	0.979529i	$0.435482\pi$
$48$	−23.2468	−	21.9494i	−0.484308	−	0.457279i
$49$	−31.3193	−	22.7548i	−0.639170	−	0.464384i
$50$	6.84809	−	9.42559i	0.136962	−	0.188512i
$51$	61.6361	−	65.2792i	1.20855	−	1.27998i
$52$	−4.55916	−	14.0317i	−0.0876762	−	0.269840i
$53$	35.5031	+	48.8658i	0.669870	+	0.921997i	0.999757	−	0.0220234i	$-0.00701083\pi$
$53$	35.5031	+	48.8658i	0.669870	+	0.921997i	−0.329888	+	0.944020i	$0.607011\pi$
$54$	4.42410	+	17.8334i	0.0819277	+	0.330248i
$55$		0			0
$56$		−	48.0356i		−	0.857778i
$57$	5.70294	+	30.3439i	0.100052	+	0.532349i
$58$	3.39607	+	10.4520i	0.0585529	+	0.180207i
$59$	−38.6761	−	12.5666i	−0.655528	−	0.212994i	−0.0376779	−	0.999290i	$-0.511996\pi$
$59$	−38.6761	−	12.5666i	−0.655528	−	0.212994i	−0.617850	+	0.786296i	$0.711996\pi$
$60$	33.0111	+	60.4356i	0.550185	+	1.00726i
$61$	−19.0197	−	13.8186i	−0.311798	−	0.226535i	0.420869	−	0.907121i	$-0.361725\pi$
$61$	−19.0197	−	13.8186i	−0.311798	−	0.226535i	−0.732668	+	0.680586i	$0.761725\pi$
$62$	11.4309	+	3.71411i	0.184369	+	0.0599050i
$63$	45.5510	−	70.9214i	0.723031	−	1.12574i
$64$	−19.1997	+	13.9494i	−0.299995	+	0.217959i
$65$			27.0724i			0.416498i
$66$		0			0
$67$	30.8376			0.460263			0.230132	−	0.973159i	$-0.426084\pi$
$67$	30.8376			0.460263			0.230132	+	0.973159i	$0.426084\pi$
$68$	−62.2154	−	85.6321i	−0.914932	−	1.25930i
$69$	−10.7104	+	82.9665i	−0.155223	+	1.20241i
$70$	−12.7820	+	39.3389i	−0.182600	+	0.561985i
$71$	0.585238	−	0.805511i	0.00824279	−	0.0113452i	−0.804876	−	0.593443i	$-0.797768\pi$
$71$	0.585238	−	0.805511i	0.00824279	−	0.0113452i	0.813118	+	0.582098i	$0.197768\pi$
$72$	46.0849	−	2.64790i	0.640067	−	0.0367763i
$73$	−28.8838	+	88.8953i	−0.395669	+	1.21774i	0.532771	+	0.846260i	$0.321151\pi$
$73$	−28.8838	+	88.8953i	−0.395669	+	1.21774i	−0.928439	+	0.371484i	$0.878849\pi$
$74$	9.42314	−	3.06176i	0.127340	−	0.0413752i
$75$	−9.48688	−	50.4772i	−0.126492	−	0.673030i
$76$	36.4007			0.478957
$77$		0			0
$78$	7.69570	+	3.64691i	0.0986629	+	0.0467553i
$79$	91.4806	−	66.4645i	1.15798	−	0.841323i	0.168460	−	0.985708i	$-0.446121\pi$
$79$	91.4806	−	66.4645i	1.15798	−	0.841323i	0.989522	+	0.144385i	$0.0461205\pi$
$80$	65.7804	−	21.3733i	0.822255	−	0.267167i
$81$	70.5522	+	39.7917i	0.871015	+	0.491256i
$82$	−19.2722	−	14.0020i	−0.235026	−	0.170757i
$83$	−61.1711	+	84.1948i	−0.737001	+	1.01439i	0.261784	+	0.965126i	$0.415689\pi$
$83$	−61.1711	+	84.1948i	−0.737001	+	1.01439i	−0.998786	+	0.0492686i	$0.984311\pi$
$84$	−72.2557	−	68.2233i	−0.860187	−	0.812182i
$85$	60.0184	+	184.718i	0.706099	+	2.17315i
$86$	−25.7365	−	35.4233i	−0.299262	−	0.411899i
$87$	43.7809	+	20.7473i	0.503228	+	0.238475i
$88$		0			0
$89$		−	20.3993i		−	0.229206i	−0.993411	−	0.114603i	$-0.963440\pi$
$89$		−	20.3993i		−	0.229206i	0.993411	−	0.114603i	$-0.0365595\pi$
$90$	−38.4460	−	10.0944i	−0.427178	−	0.112160i
$91$	−12.0724	−	37.1551i	−0.132664	−	0.408298i
$92$	93.7992	+	30.4772i	1.01956	+	0.331274i
$93$	46.5005	−	25.3995i	0.500006	−	0.273113i
$94$	−5.75681	−	4.18257i	−0.0612427	−	0.0444954i
$95$	−63.5243	−	20.6403i	−0.668677	−	0.217266i
$96$	10.6656	−	82.6195i	0.111100	−	0.860620i
$97$	−153.778	+	111.726i	−1.58534	+	1.15181i	−0.675100	+	0.737726i	$0.735900\pi$
$97$	−153.778	+	111.726i	−1.58534	+	1.15181i	−0.910237	+	0.414089i	$0.864100\pi$
$98$		−	26.3447i		−	0.268824i
$99$		0			0
$100$	−60.5528			−0.605528
$101$	−27.9808	−	38.5123i	−0.277038	−	0.381310i	0.647712	−	0.761885i	$-0.275726\pi$
$101$	−27.9808	−	38.5123i	−0.277038	−	0.381310i	−0.924750	+	0.380575i	$0.875726\pi$
$102$	60.5937	+	7.82221i	0.594056	+	0.0766883i
$103$	16.2776	−	50.0973i	0.158035	−	0.486382i	−0.840421	−	0.541935i	$-0.817692\pi$
$103$	16.2776	−	50.0973i	0.158035	−	0.486382i	0.998456	+	0.0555527i	$0.0176921\pi$
$104$	12.5756	−	17.3089i	0.120920	−	0.166432i
$105$	87.4115	+	160.030i	0.832491	+	1.52410i
$106$	−12.7019	+	39.0924i	−0.119829	+	0.368797i
$107$	−64.9745	+	21.1115i	−0.607238	+	0.197304i	−0.596466	−	0.802638i	$-0.703429\pi$
$107$	−64.9745	+	21.1115i	−0.607238	+	0.197304i	−0.0107723	+	0.999942i	$0.503429\pi$
$108$	61.4697	−	73.0821i	0.569164	−	0.676686i
$109$	37.7254			0.346105			0.173053	−	0.984913i	$-0.444637\pi$
$109$	37.7254			0.346105			0.173053	+	0.984913i	$0.444637\pi$
$110$		0			0
$111$	18.7050	−	39.4711i	0.168513	−	0.355596i
$112$	−80.7483	+	58.6671i	−0.720967	+	0.523813i
$113$	−161.947	+	52.6196i	−1.43316	+	0.465661i	−0.919757	−	0.392489i	$-0.871614\pi$
$113$	−161.947	+	52.6196i	−1.43316	+	0.465661i	−0.513399	+	0.858150i	$0.671614\pi$
$114$	−14.4247	+	15.2772i	−0.126532	+	0.134011i
$115$	−146.411	−	106.374i	−1.27314	−	0.924990i
$116$	33.5735	−	46.2099i	0.289427	−	0.398361i
$117$	34.9807	−	13.6303i	0.298981	−	0.116498i
$118$	−8.55181	−	26.3198i	−0.0724730	−	0.223049i
$119$	−164.743	−	226.749i	−1.38439	−	1.90545i
$120$	−42.7645	+	90.2415i	−0.356371	+	0.752013i
$121$		0			0
$122$		−	15.9987i		−	0.131137i
$123$	−103.209	+	19.3975i	−0.839097	+	0.157703i
$124$	−19.3036	−	59.4104i	−0.155674	−	0.479116i
$125$	−48.6363	−	15.8029i	−0.389090	−	0.126423i
$126$	57.2660	−	3.29033i	0.454492	−	0.0261138i
$127$	−117.567	−	85.4178i	−0.925728	−	0.672581i	0.0192151	−	0.999815i	$-0.493883\pi$
$127$	−117.567	−	85.4178i	−0.925728	−	0.672581i	−0.944943	+	0.327235i	$0.893883\pi$
$128$	−120.997	−	39.3142i	−0.945287	−	0.307142i
$129$	−191.437	−	24.7131i	−1.48400	−	0.191574i
$130$	−14.9047	+	10.8289i	−0.114651	+	0.0832991i
$131$			174.147i			1.32936i	0.747126	+	0.664682i	$0.231433\pi$
$131$			174.147i			1.32936i	−0.747126	+	0.664682i	$0.768567\pi$
$132$		0			0
$133$	96.3872			0.724716
$134$	12.3350	+	16.9777i	0.0920521	+	0.126699i
$135$	−148.713	+	92.6832i	−1.10158	+	0.686542i
$136$	47.4319	−	145.980i	0.348764	−	1.07338i
$137$	47.7841	−	65.7692i	0.348789	−	0.480067i	−0.598194	−	0.801352i	$-0.704115\pi$
$137$	47.7841	−	65.7692i	0.348789	−	0.480067i	0.946983	+	0.321285i	$0.104115\pi$
$138$	−49.9613	+	27.2898i	−0.362038	+	0.197752i
$139$	−0.210449	+	0.647694i	−0.00151402	+	0.00465967i	−0.951811	−	0.306686i	$-0.900780\pi$
$139$	−0.210449	+	0.647694i	−0.00151402	+	0.00465967i	0.950297	+	0.311346i	$0.100780\pi$
$140$	204.459	−	66.4327i	1.46042	−	0.474520i
$141$	−30.8297	+	5.79425i	−0.218650	+	0.0410939i
$142$	0.677567			0.00477160
$143$		0			0
$144$	−60.7358	−	74.2352i	−0.421776	−	0.515522i
$145$	−84.7928	+	61.6055i	−0.584778	+	0.424866i
$146$	−60.4947	+	19.6559i	−0.414347	+	0.134630i
$147$	−84.4448	−	79.7321i	−0.574454	−	0.542395i
$148$	−41.6611	−	30.2686i	−0.281494	−	0.204517i
$149$	−116.342	+	160.131i	−0.780817	+	1.07470i	0.214374	+	0.976752i	$0.431229\pi$
$149$	−116.342	+	160.131i	−0.780817	+	1.07470i	−0.995191	+	0.0979512i	$0.968771\pi$
$150$	23.9955	−	25.4138i	0.159970	−	0.169425i
$151$	−27.4763	−	84.5632i	−0.181962	−	0.560021i	0.817921	−	0.575331i	$-0.195127\pi$
$151$	−27.4763	−	84.5632i	−0.181962	−	0.560021i	−0.999883	+	0.0153094i	$0.995127\pi$
$152$	31.0269	+	42.7048i	0.204124	+	0.280953i
$153$	208.460	−	170.552i	1.36248	−	1.11472i
$154$		0			0
$155$			114.625i			0.739516i
$156$	−8.17549	−	43.4997i	−0.0524070	−	0.278844i
$157$	20.6228	+	63.4705i	0.131356	+	0.404271i	0.995005	−	0.0998213i	$-0.0318271\pi$
$157$	20.6228	+	63.4705i	0.131356	+	0.404271i	−0.863650	+	0.504092i	$0.831827\pi$
$158$	73.1840	+	23.7789i	0.463190	+	0.150500i
$159$	86.8638	+	159.027i	0.546314	+	1.00017i
$160$	145.799	+	105.929i	0.911242	+	0.662056i
$161$	248.375	+	80.7020i	1.54270	+	0.501255i
$162$	6.31343	+	54.7591i	0.0389718	+	0.338019i
$163$	113.136	−	82.1980i	0.694085	−	0.504282i	−0.183915	−	0.982942i	$-0.558877\pi$
$163$	113.136	−	82.1980i	0.694085	−	0.504282i	0.878001	+	0.478660i	$0.158877\pi$
$164$			123.810i			0.754940i
$165$		0			0
$166$	−70.8217			−0.426637
$167$	80.7610	+	111.158i	0.483599	+	0.665617i	0.979192	−	0.202938i	$-0.0650491\pi$
$167$	80.7610	+	111.158i	0.483599	+	0.665617i	−0.495593	+	0.868555i	$0.665049\pi$
$168$	18.4500	−	142.921i	0.109822	−	0.850719i
$169$	−46.8468	+	144.180i	−0.277200	+	0.853135i
$170$	−77.6891	+	106.930i	−0.456994	+	0.628999i
$171$	5.31321	+	92.4729i	0.0310714	+	0.540777i
$172$	−70.3230	+	216.432i	−0.408855	+	1.25833i
$173$	−1.00649	+	0.327028i	−0.00581785	+	0.00189034i	−0.311924	−	0.950107i	$-0.600974\pi$
$173$	−1.00649	+	0.327028i	−0.00581785	+	0.00189034i	0.306107	+	0.951997i	$0.400974\pi$
$174$	6.08983	+	32.4024i	0.0349990	+	0.186221i
$175$	−160.341			−0.916232
$176$		0			0
$177$	−110.247	−	52.2448i	−0.622863	−	0.295168i
$178$	11.2308	−	8.15968i	0.0630945	−	0.0458409i
$179$	82.5005	−	26.8060i	0.460897	−	0.149754i	−0.0693597	−	0.997592i	$-0.522096\pi$
$179$	82.5005	−	26.8060i	0.460897	−	0.149754i	0.530257	+	0.847837i	$0.322096\pi$
$180$	75.0055	+	192.494i	0.416697	+	1.06941i
$181$	87.5116	+	63.5809i	0.483490	+	0.351276i	0.802675	−	0.596416i	$-0.203409\pi$
$181$	87.5116	+	63.5809i	0.483490	+	0.351276i	−0.319185	+	0.947692i	$0.603409\pi$
$182$	15.6268	−	21.5084i	0.0858614	−	0.118178i
$183$	−51.2819	−	48.4200i	−0.280229	−	0.264590i
$184$	44.1961	+	136.022i	0.240196	+	0.739248i
$185$	55.5412	+	76.4459i	0.300223	+	0.413221i
$186$	32.5838	+	15.4411i	0.175182	+	0.0830168i
$187$		0			0
$188$			36.9835i			0.196721i
$189$	162.769	−	193.518i	0.861209	−	1.02390i
$190$	−14.0461	−	43.2294i	−0.0739267	−	0.227523i
$191$	27.2489	+	8.85370i	0.142664	+	0.0463545i	0.379479	−	0.925200i	$-0.376103\pi$
$191$	27.2489	+	8.85370i	0.142664	+	0.0463545i	−0.236814	+	0.971555i	$0.576103\pi$
$192$	−62.4828	+	34.1293i	−0.325431	+	0.177757i
$193$	−10.2703	−	7.46178i	−0.0532137	−	0.0386621i	0.560860	−	0.827910i	$-0.310470\pi$
$193$	−10.2703	−	7.46178i	−0.0532137	−	0.0386621i	−0.614074	+	0.789248i	$0.710470\pi$
$194$	−123.021	−	39.9721i	−0.634131	−	0.206042i
$195$	−10.3983	+	80.5487i	−0.0533244	+	0.413070i
$196$	−110.773	+	80.4814i	−0.565169	+	0.410620i
$197$		−	336.692i		−	1.70910i	−0.519370	−	0.854549i	$-0.673834\pi$
$197$		−	336.692i		−	1.70910i	0.519370	−	0.854549i	$-0.326166\pi$
$198$		0			0
$199$	183.863			0.923932			0.461966	−	0.886898i	$-0.347144\pi$
$199$	183.863			0.923932			0.461966	+	0.886898i	$0.347144\pi$
$200$	−51.6134	−	71.0397i	−0.258067	−	0.355199i
$201$	91.7516	+	11.8445i	0.456476	+	0.0589277i
$202$	10.0107	−	30.8096i	0.0495577	−	0.152523i
$203$	88.9007	−	122.361i	0.437935	−	0.602765i
$204$	−152.220	−	278.678i	−0.746174	−	1.36607i
$205$	70.2040	−	216.066i	0.342459	−	1.05398i
$206$	34.0921	−	11.0772i	0.165495	−	0.0537727i
$207$	−63.7334	+	242.737i	−0.307891	+	1.17264i
$208$	−44.4554			−0.213728
$209$		0			0
$210$	−53.1401	+	112.136i	−0.253048	+	0.533981i
$211$	145.630	−	105.806i	0.690187	−	0.501450i	−0.186534	−	0.982448i	$-0.559726\pi$
$211$	145.630	−	105.806i	0.690187	−	0.501450i	0.876722	+	0.480998i	$0.159726\pi$
$212$	203.178	−	66.0165i	0.958386	−	0.311399i
$213$	2.05065	−	2.17186i	0.00962748	−	0.0101965i
$214$	−37.6126	−	27.3271i	−0.175760	−	0.127697i
$215$	245.447	−	337.828i	1.14161	−	1.57129i
$216$	138.134	+	9.82246i	0.639508	+	0.0454744i
$217$	−51.1149	−	157.315i	−0.235553	−	0.724956i
$218$	15.0901	+	20.7697i	0.0692206	+	0.0952740i
$219$	−120.082	+	253.397i	−0.548321	+	1.15706i
$220$		0			0
$221$		−	124.835i		−	0.564865i
$222$	29.2128	−	5.49036i	0.131589	−	0.0247313i
$223$	81.2895	+	250.183i	0.364527	+	1.12190i	0.950277	+	0.311407i	$0.100800\pi$
$223$	81.2895	+	250.183i	0.364527	+	1.12190i	−0.585750	+	0.810492i	$0.699200\pi$
$224$	−247.336	−	80.3645i	−1.10418	−	0.358770i
$225$	−8.83856	−	153.829i	−0.0392825	−	0.683686i
$226$	−93.7480	−	68.1119i	−0.414814	−	0.301380i
$227$	−8.58713	−	2.79013i	−0.0378288	−	0.0122913i	0.290041	−	0.957014i	$-0.406331\pi$
$227$	−8.58713	−	2.79013i	−0.0378288	−	0.0122913i	−0.327870	+	0.944723i	$0.606331\pi$
$228$	108.304	+	13.9812i	0.475015	+	0.0613210i
$229$	285.121	−	207.153i	1.24507	−	0.904597i	0.247145	−	0.968979i	$-0.420508\pi$
$229$	285.121	−	207.153i	1.24507	−	0.904597i	0.997925	+	0.0643820i	$0.0205076\pi$
$230$		−	123.156i		−	0.535460i
$231$		0			0
$232$	82.8298			0.357025
$233$	20.8090	+	28.6411i	0.0893089	+	0.122923i	0.851333	−	0.524625i	$-0.175794\pi$
$233$	20.8090	+	28.6411i	0.0893089	+	0.122923i	−0.762025	+	0.647548i	$0.775794\pi$
$234$	21.4964	+	13.8066i	0.0918648	+	0.0590024i
$235$	20.9708	−	64.5413i	0.0892373	−	0.274644i
$236$	−84.5431	+	116.364i	−0.358233	+	0.493066i
$237$	297.712	−	162.616i	1.25617	−	0.686142i
$238$	58.9399	−	181.398i	0.247647	−	0.762178i
$239$	−124.397	+	40.4191i	−0.520491	+	0.169118i	−0.557468	−	0.830198i	$-0.688227\pi$
$239$	−124.397	+	40.4191i	−0.520491	+	0.169118i	0.0369772	+	0.999316i	$0.488227\pi$
$240$	203.926	−	38.3267i	0.849693	−	0.159695i
$241$	−134.526			−0.558198			−0.279099	−	0.960262i	$-0.590036\pi$
$241$	−134.526			−0.558198			−0.279099	+	0.960262i	$0.590036\pi$
$242$		0			0
$243$	194.631	+	145.491i	0.800952	+	0.598729i
$244$	−67.2707	+	48.8750i	−0.275700	+	0.200308i
$245$	238.950	−	77.6395i	0.975306	−	0.316896i
$246$	−51.9626	−	49.0627i	−0.211230	−	0.199442i
$247$	34.7317	+	25.2340i	0.140614	+	0.102162i
$248$	53.2456	−	73.2863i	0.214700	−	0.295509i
$249$	−214.341	+	227.010i	−0.860809	+	0.911688i
$250$	−10.7541	−	33.0978i	−0.0430165	−	0.132391i
$251$	237.797	+	327.300i	0.947399	+	1.30398i	0.952673	+	0.303997i	$0.0983213\pi$
$251$	237.797	+	327.300i	0.947399	+	1.30398i	−0.00527361	+	0.999986i	$0.501679\pi$
$252$	−188.779	−	230.738i	−0.749124	−	0.915628i
$253$		0			0
$254$		−	98.8936i		−	0.389345i
$255$	107.625	+	572.645i	0.422059	+	2.24567i
$256$	2.58048	+	7.94189i	0.0100800	+	0.0310230i
$257$	−130.624	−	42.4423i	−0.508265	−	0.165145i	0.0436481	−	0.999047i	$-0.486102\pi$
$257$	−130.624	−	42.4423i	−0.508265	−	0.165145i	−0.551913	+	0.833902i	$0.686102\pi$
$258$	−62.9684	−	115.281i	−0.244064	−	0.446824i
$259$	−110.316	−	80.1495i	−0.425932	−	0.309457i
$260$	91.0657	+	29.5891i	0.350253	+	0.113804i
$261$	122.293	+	78.5455i	0.468555	+	0.300941i
$262$	−95.8764	+	69.6583i	−0.365941	+	0.265871i
$263$		−	138.001i		−	0.524720i	−0.964970	−	0.262360i	$-0.915499\pi$
$263$		−	138.001i		−	0.524720i	0.964970	−	0.262360i	$-0.0845008\pi$
$264$		0			0
$265$	−392.007			−1.47927
$266$	38.5547	+	53.0659i	0.144942	+	0.199496i
$267$	7.83519	−	60.6943i	0.0293453	−	0.227319i
$268$	33.7044	−	103.731i	0.125763	−	0.387057i
$269$	−18.1588	+	24.9935i	−0.0675049	+	0.0929125i	−0.841434	−	0.540359i	$-0.818288\pi$
$269$	−18.1588	+	24.9935i	−0.0675049	+	0.0929125i	0.773930	+	0.633272i	$0.218288\pi$
$270$	−110.512	−	44.8008i	−0.409302	−	0.165929i
$271$	61.9531	−	190.672i	0.228609	−	0.703587i	−0.769296	−	0.638893i	$-0.779393\pi$
$271$	61.9531	−	190.672i	0.228609	−	0.703587i	0.997905	−	0.0646943i	$-0.0206072\pi$
$272$	−303.324	+	98.5560i	−1.11516	+	0.362338i
$273$	−21.6483	−	115.185i	−0.0792977	−	0.421922i
$274$	55.3227			0.201908
$275$		0			0
$276$	267.376	+	126.707i	0.968753	+	0.459082i
$277$	129.127	−	93.8163i	0.466162	−	0.338687i	−0.329781	−	0.944057i	$-0.606975\pi$
$277$	129.127	−	93.8163i	0.466162	−	0.338687i	0.795944	+	0.605370i	$0.206975\pi$
$278$	−0.440767	+	0.143214i	−0.00158549	+	0.000515158i
$279$	148.109	−	57.7109i	0.530858	−	0.206849i
$280$	252.212	+	183.243i	0.900758	+	0.654439i
$281$	−233.485	+	321.364i	−0.830907	+	1.14365i	0.156847	+	0.987623i	$0.449867\pi$
$281$	−233.485	+	321.364i	−0.830907	+	1.14365i	−0.987754	+	0.156022i	$0.950133\pi$
$282$	−15.5218	−	14.6556i	−0.0550419	−	0.0519702i
$283$	20.8866	+	64.2824i	0.0738043	+	0.227146i	0.981153	−	0.193233i	$-0.0618972\pi$
$283$	20.8866	+	64.2824i	0.0738043	+	0.227146i	−0.907349	+	0.420379i	$0.861897\pi$
$284$	−2.06993	−	2.84901i	−0.00728847	−	0.0100317i
$285$	−181.077	−	85.8104i	−0.635357	−	0.301089i
$286$		0			0
$287$			327.843i			1.14231i
$288$	63.4668	−	241.722i	0.220371	−	0.839313i
$289$	−187.449	−	576.909i	−0.648613	−	1.99622i
$290$	−67.8338	−	22.0405i	−0.233910	−	0.0760019i
$291$	−500.449	+	273.355i	−1.71976	+	0.939364i
$292$	267.456	+	194.318i	0.915945	+	0.665473i
$293$	347.720	+	112.981i	1.18676	+	0.385601i	0.834873	−	0.550442i	$-0.185541\pi$
$293$	347.720	+	112.981i	1.18676	+	0.385601i	0.351885	+	0.936043i	$0.385541\pi$
$294$	10.1188	−	78.3837i	0.0344176	−	0.266611i
$295$	213.521	−	155.132i	0.723800	−	0.525871i
$296$		−	74.6761i		−	0.252284i
$297$		0			0
$298$	−134.696			−0.452001
$299$	68.3706	+	94.1041i	0.228664	+	0.314729i
$300$	−180.164	−	23.2578i	−0.600545	−	0.0775260i
$301$	−186.211	+	573.100i	−0.618643	+	1.90399i
$302$	35.5658	−	48.9521i	0.117768	−	0.162093i
$303$	−68.4594	−	125.333i	−0.225938	−	0.413641i
$304$	33.8933	−	104.313i	0.111491	−	0.343135i
$305$	145.110	−	47.1492i	0.475771	−	0.154588i
$306$	177.281	+	46.5470i	0.579349	+	0.152114i
$307$	484.160			1.57707			0.788534	−	0.614992i	$-0.210841\pi$
$307$	484.160			1.57707			0.788534	+	0.614992i	$0.210841\pi$
$308$		0			0
$309$	67.6729	−	142.803i	0.219006	−	0.462146i
$310$	−63.1068	+	45.8498i	−0.203570	+	0.147902i
$311$	−319.700	+	103.877i	−1.02797	+	0.334009i	−0.773989	−	0.633199i	$-0.781741\pi$
$311$	−319.700	+	103.877i	−1.02797	+	0.334009i	−0.253985	+	0.967208i	$0.581741\pi$
$312$	44.0647	−	46.6692i	0.141233	−	0.149581i
$313$	395.686	+	287.483i	1.26417	+	0.918475i	0.998955	−	0.0457136i	$-0.0145562\pi$
$313$	395.686	+	287.483i	1.26417	+	0.918475i	0.265218	+	0.964189i	$0.414556\pi$
$314$	−26.6946	+	36.7420i	−0.0850146	+	0.117013i
$315$	198.610	+	509.713i	0.630509	+	1.61814i
$316$	−123.588	−	380.364i	−0.391101	−	1.20368i
$317$	91.8833	+	126.467i	0.289853	+	0.398948i	0.928966	−	0.370164i	$-0.120699\pi$
$317$	91.8833	+	126.467i	0.289853	+	0.398948i	−0.639114	+	0.769112i	$0.720699\pi$
$318$	−52.8072	+	111.433i	−0.166060	+	0.350420i
$319$		0			0
$320$		−	154.022i		−	0.481318i
$321$	−201.428	+	37.8571i	−0.627502	+	0.117935i
$322$	54.9191	+	169.024i	0.170556	+	0.524918i
$323$	292.921	+	95.1758i	0.906877	+	0.294662i
$324$	210.962	−	193.832i	0.651117	−	0.598247i
$325$	−57.7764	−	41.9770i	−0.177773	−	0.129160i
$326$	90.5082	+	29.4079i	0.277633	+	0.0902083i
$327$	112.245	+	14.4900i	0.343257	+	0.0443119i
$328$	−145.252	+	105.532i	−0.442842	+	0.321744i
$329$			97.9303i			0.297661i
$330$		0			0
$331$	40.2792			0.121689			0.0608447	−	0.998147i	$-0.480621\pi$
$331$	40.2792			0.121689			0.0608447	+	0.998147i	$0.480621\pi$
$332$	216.356	+	297.788i	0.651674	+	0.896953i
$333$	70.8136	−	110.255i	0.212653	−	0.331095i
$334$	−28.8938	+	88.9259i	−0.0865083	+	0.266245i
$335$	−117.638	+	161.914i	−0.351157	+	0.483326i
$336$	−262.785	+	143.538i	−0.782098	+	0.427197i
$337$	−3.68219	+	11.3326i	−0.0109264	+	0.0336279i	−0.956371	−	0.292155i	$-0.905628\pi$
$337$	−3.68219	+	11.3326i	−0.0109264	+	0.0336279i	0.945445	+	0.325783i	$0.105628\pi$
$338$	−98.1167	+	31.8801i	−0.290286	+	0.0943197i
$339$	−502.052	+	94.3576i	−1.48098	+	0.278341i
$340$	686.950			2.02044
$341$		0			0
$342$	−48.7857	+	39.9142i	−0.142648	+	0.116708i
$343$	77.9447	−	56.6301i	0.227244	−	0.165102i
$344$	−313.856	+	101.978i	−0.912372	+	0.296448i
$345$	−394.761	−	372.731i	−1.14424	−	1.08038i
$346$	−0.582638	−	0.423311i	−0.00168393	−	0.00122344i
$347$	353.427	−	486.450i	1.01852	−	1.40187i	0.105285	−	0.994442i	$-0.466425\pi$
$347$	353.427	−	486.450i	1.01852	−	1.40187i	0.913236	−	0.407431i	$-0.133575\pi$
$348$	117.640	−	124.594i	0.338047	−	0.358028i
$349$	41.0865	+	126.451i	0.117726	+	0.362324i	0.992506	−	0.122197i	$-0.0389939\pi$
$349$	41.0865	+	126.451i	0.117726	+	0.362324i	−0.874780	+	0.484521i	$0.838994\pi$
$350$	−64.1359	−	88.2755i	−0.183245	−	0.252216i
$351$	109.314	−	27.1185i	0.311435	−	0.0772608i
$352$		0			0
$353$		−	172.864i		−	0.489699i	−0.969561	−	0.244850i	$-0.921261\pi$
$353$		−	172.864i		−	0.489699i	0.969561	−	0.244850i	$-0.0787386\pi$
$354$	−15.3351	−	81.5942i	−0.0433195	−	0.230492i
$355$	1.99683	+	6.14562i	0.00562488	+	0.0173116i
$356$	−68.6190	−	22.2957i	−0.192750	−	0.0626282i
$357$	−403.069	−	737.925i	−1.12904	−	2.06702i
$358$	47.7581	+	34.6983i	0.133402	+	0.0969226i
$359$	−573.248	−	186.259i	−1.59679	−	0.518829i	−0.630479	−	0.776206i	$-0.717142\pi$
$359$	−573.248	−	186.259i	−1.59679	−	0.518829i	−0.966311	+	0.257377i	$0.917142\pi$
$360$	−161.899	+	252.071i	−0.449719	+	0.700198i
$361$	206.365	−	149.933i	0.571647	−	0.415326i
$362$			73.6117i			0.203347i
$363$		0			0
$364$	−138.177			−0.379606
$365$	−356.564	−	490.768i	−0.976886	−	1.34457i
$366$	6.14496	−	47.6011i	0.0167895	−	0.130058i
$367$	76.9025	−	236.681i	0.209543	−	0.644909i	−0.789953	−	0.613168i	$-0.789895\pi$
$367$	76.9025	−	236.681i	0.209543	−	0.644909i	0.999496	−	0.0317407i	$-0.0101051\pi$
$368$	174.676	−	240.421i	0.474663	−	0.653318i
$369$	−314.529	+	18.0719i	−0.852382	+	0.0489753i
$370$	−19.8709	+	61.1563i	−0.0537051	+	0.165287i
$371$	538.004	−	174.808i	1.45015	−	0.471181i
$372$	−34.6152	−	184.179i	−0.0930517	−	0.495104i
$373$	−677.639			−1.81673			−0.908364	−	0.418181i	$-0.862668\pi$
$373$	−677.639			−1.81673			−0.908364	+	0.418181i	$0.862668\pi$
$374$		0			0
$375$	−138.638	−	65.6992i	−0.369702	−	0.175198i
$376$	−43.3885	+	31.5236i	−0.115395	+	0.0838394i
$377$	64.0681	−	20.8170i	0.169942	−	0.0552175i
$378$	171.648	+	12.2056i	0.454095	+	0.0322900i
$379$	92.0872	+	66.9053i	0.242974	+	0.176531i	0.702607	−	0.711578i	$-0.252019\pi$
$379$	92.0872	+	66.9053i	0.242974	+	0.176531i	−0.459633	+	0.888109i	$0.652019\pi$
$380$	−138.859	+	191.123i	−0.365419	+	0.502956i
$381$	−316.992	−	299.301i	−0.831999	−	0.785567i
$382$	6.02509	+	18.5433i	0.0157725	+	0.0485428i
$383$	−354.229	−	487.554i	−0.924880	−	1.27299i	−0.961824	−	0.273670i	$-0.911762\pi$
$383$	−354.229	−	487.554i	−0.924880	−	1.27299i	0.0369437	−	0.999317i	$-0.488238\pi$
$384$	−344.903	−	163.446i	−0.898184	−	0.425640i
$385$		0			0
$386$		−	8.63898i		−	0.0223808i
$387$	−560.091	−	147.058i	−1.44726	−	0.379995i
$388$	207.750	+	639.388i	0.535437	+	1.64791i
$389$	432.894	+	140.656i	1.11284	+	0.361583i	0.807030	−	0.590510i	$-0.201073\pi$
$389$	432.894	+	140.656i	1.11284	+	0.361583i	0.305808	+	0.952093i	$0.401073\pi$
$390$	−48.5053	+	26.4945i	−0.124373	+	0.0679347i
$391$	675.126	+	490.508i	1.72666	+	1.25450i
$392$	−188.839	−	61.3576i	−0.481733	−	0.156524i
$393$	−66.8882	+	518.141i	−0.170199	+	1.31842i
$394$	185.366	−	134.676i	0.470472	−	0.341818i
$395$			733.867i			1.85789i
$396$		0			0
$397$	327.783			0.825649			0.412824	−	0.910811i	$-0.364542\pi$
$397$	327.783			0.825649			0.412824	+	0.910811i	$0.364542\pi$
$398$	73.5446	+	101.225i	0.184785	+	0.254335i
$399$	286.782	+	37.0214i	0.718752	+	0.0927856i
$400$	−56.3818	+	173.525i	−0.140954	+	0.433813i
$401$	−148.146	+	203.906i	−0.369442	+	0.508494i	−0.952749	−	0.303758i	$-0.901759\pi$
$401$	−148.146	+	203.906i	−0.369442	+	0.508494i	0.583307	+	0.812252i	$0.301759\pi$
$402$	30.1795	+	55.2516i	0.0750733	+	0.137442i
$403$	22.7665	−	70.0681i	0.0564926	−	0.173866i
$404$	−160.129	+	52.0291i	−0.396359	+	0.128785i
$405$	−478.066	+	218.642i	−1.18041	+	0.539857i
$406$	102.926			0.253513
$407$		0			0
$408$	197.194	−	416.119i	0.483319	−	1.01990i
$409$	−367.117	+	266.726i	−0.897595	+	0.652141i	−0.937847	−	0.347048i	$-0.887184\pi$
$409$	−367.117	+	266.726i	−0.897595	+	0.652141i	0.0402518	+	0.999190i	$0.487184\pi$
$410$	147.036	−	47.7750i	0.358625	−	0.116524i
$411$	167.434	−	177.330i	0.407382	−	0.431461i
$412$	−150.726	−	109.509i	−0.365840	−	0.265798i
$413$	−223.865	+	308.124i	−0.542047	+	0.746064i
$414$	−159.132	+	62.0060i	−0.384377	+	0.149773i
$415$	−208.716	−	642.362i	−0.502930	−	1.54786i
$416$	−68.0847	−	93.7105i	−0.163665	−	0.225266i
$417$	−0.874924	+	1.84626i	−0.00209814	+	0.00442748i
$418$		0			0
$419$			295.753i			0.705855i	0.935651	+	0.352927i	$0.114814\pi$
$419$			295.753i			0.705855i	−0.935651	+	0.352927i	$0.885186\pi$
$420$	633.845	−	119.127i	1.50916	−	0.283636i
$421$	70.7602	+	217.778i	0.168077	+	0.517286i	0.999250	−	0.0387271i	$-0.0123303\pi$
$421$	70.7602	+	217.778i	0.168077	+	0.517286i	−0.831173	+	0.556013i	$0.812330\pi$
$422$	116.503	+	37.8541i	0.276073	+	0.0897017i
$423$	−93.9534	+	5.39828i	−0.222112	+	0.0127619i
$424$	250.632	+	182.095i	0.591113	+	0.429469i
$425$	−487.276	−	158.326i	−1.14653	−	0.372531i
$426$	2.01597	+	0.260248i	0.00473233	+	0.000610910i
$427$	−178.129	+	129.418i	−0.417164	+	0.303088i
$428$			241.635i			0.564567i
$429$		0			0
$430$	284.169			0.660859
$431$	−328.552	−	452.213i	−0.762301	−	1.04922i	−0.997019	−	0.0771542i	$-0.975417\pi$
$431$	−328.552	−	452.213i	−0.762301	−	1.04922i	0.234718	−	0.972064i	$-0.424583\pi$
$432$	−152.195	−	244.201i	−0.352303	−	0.565280i
$433$	89.0813	−	274.164i	0.205730	−	0.633173i	−0.793952	−	0.607980i	$-0.791980\pi$
$433$	89.0813	−	274.164i	0.205730	−	0.633173i	0.999683	−	0.0251929i	$-0.00802000\pi$
$434$	66.1641	−	91.0671i	0.152452	−	0.209832i
$435$	−275.947	+	150.728i	−0.634361	+	0.346500i
$436$	41.2325	−	126.900i	0.0945698	−	0.291056i
$437$	−272.938	+	88.6831i	−0.624573	+	0.202936i
$438$	−187.540	+	35.2470i	−0.428174	+	0.0804726i
$439$	179.800			0.409567			0.204784	−	0.978807i	$-0.434351\pi$
$439$	179.800			0.409567			0.204784	+	0.978807i	$0.434351\pi$
$440$		0			0
$441$	−220.625	−	269.662i	−0.500284	−	0.611479i
$442$	68.7279	−	49.9338i	0.155493	−	0.112972i
$443$	267.511	−	86.9195i	0.603862	−	0.196207i	0.00889983	−	0.999960i	$-0.497167\pi$
$443$	267.511	−	86.9195i	0.603862	−	0.196207i	0.594962	+	0.803754i	$0.297167\pi$
$444$	−112.329	−	106.060i	−0.252993	−	0.238874i
$445$	107.107	+	77.8180i	0.240690	+	0.174872i
$446$	−105.223	+	144.827i	−0.235925	+	0.324724i
$447$	−407.658	+	431.753i	−0.911986	+	0.965890i
$448$	68.6831	+	211.385i	0.153310	+	0.471841i
$449$	−163.228	−	224.664i	−0.363536	−	0.500365i	0.587593	−	0.809156i	$-0.300075\pi$
$449$	−163.228	−	224.664i	−0.363536	−	0.500365i	−0.951130	+	0.308791i	$0.900075\pi$
$450$	81.1552	−	66.3974i	0.180345	−	0.147550i
$451$		0			0
$452$			602.265i			1.33245i
$453$	−49.2704	−	262.155i	−0.108765	−	0.578709i
$454$	−1.89873	−	5.84368i	−0.00418222	−	0.0128716i
$455$	241.137	+	78.3502i	0.529972	+	0.172198i
$456$	75.9120	+	138.977i	0.166474	+	0.304775i
$457$	−280.102	−	203.506i	−0.612915	−	0.445309i	0.237525	−	0.971381i	$-0.423664\pi$
$457$	−280.102	−	203.506i	−0.612915	−	0.445309i	−0.850439	+	0.526073i	$0.823664\pi$
$458$	228.096	+	74.1127i	0.498025	+	0.161818i
$459$	685.740	−	427.378i	1.49399	−	0.931106i
$460$	−517.841	+	376.234i	−1.12574	+	0.817899i
$461$			67.1487i			0.145659i	0.997344	+	0.0728294i	$0.0232029\pi$
$461$			67.1487i			0.145659i	−0.997344	+	0.0728294i	$0.976797\pi$
$462$		0			0
$463$	−754.683			−1.62999			−0.814993	−	0.579471i	$-0.803259\pi$
$463$	−754.683			−1.62999			−0.814993	+	0.579471i	$0.803259\pi$
$464$	−101.162	−	139.238i	−0.218022	−	0.300081i
$465$	−44.0264	+	341.045i	−0.0946805	+	0.733430i
$466$	−7.44480	+	22.9127i	−0.0159760	+	0.0491690i
$467$	170.090	−	234.109i	0.364218	−	0.501303i	−0.587100	−	0.809515i	$-0.699730\pi$
$467$	170.090	−	234.109i	0.364218	−	0.501303i	0.951318	+	0.308211i	$0.0997304\pi$
$468$	−7.61680	−	132.565i	−0.0162752	−	0.283259i
$469$	89.2473	−	274.675i	0.190293	−	0.585661i
$470$	43.9215	−	14.2709i	0.0934499	−	0.0303637i
$471$	36.9809	+	196.766i	0.0785156	+	0.417761i
$472$	−208.578			−0.441902
$473$		0			0
$474$	208.612	+	98.8590i	0.440110	+	0.208563i
$475$	142.547	−	103.566i	0.300099	−	0.218034i
$476$	−942.794	+	306.332i	−1.98066	+	0.643555i
$477$	197.366	+	506.520i	0.413765	+	1.06189i
$478$	−72.0114	−	52.3193i	−0.150651	−	0.109455i
$479$	97.6527	−	134.407i	0.203868	−	0.280600i	−0.694825	−	0.719179i	$-0.744518\pi$
$479$	97.6527	−	134.407i	0.203868	−	0.280600i	0.898693	+	0.438579i	$0.144518\pi$
$480$	393.110	+	371.172i	0.818980	+	0.773274i
$481$	−18.7678	−	57.7613i	−0.0390183	−	0.120086i
$482$	−53.8100	−	74.0631i	−0.111639	−	0.153658i
$483$	707.997	+	335.512i	1.46583	+	0.694642i
$484$		0			0
$485$		−	1233.62i		−	2.54355i
$486$	−2.24807	+	165.350i	−0.00462566	+	0.340227i
$487$	−6.35332	−	19.5535i	−0.0130458	−	0.0401510i	0.944322	−	0.329024i	$-0.106720\pi$
$487$	−6.35332	−	19.5535i	−0.0130458	−	0.0401510i	−0.957368	+	0.288873i	$0.906720\pi$
$488$	−114.679	−	37.2614i	−0.234998	−	0.0763554i
$489$	368.186	−	201.110i	0.752937	−	0.411268i
$490$	138.324	+	100.498i	0.282293	+	0.205098i
$491$	455.169	+	147.893i	0.927024	+	0.301209i	0.733345	−	0.679856i	$-0.237958\pi$
$491$	455.169	+	147.893i	0.927024	+	0.301209i	0.193679	+	0.981065i	$0.437958\pi$
$492$	−47.5544	+	368.374i	−0.0966552	+	0.748727i
$493$	390.993	−	284.073i	0.793090	−	0.576214i
$494$			29.2151i			0.0591398i
$495$		0			0
$496$	−188.225			−0.379486
$497$	−5.48105	−	7.54402i	−0.0110283	−	0.0151791i
$498$	−210.717	−	27.2020i	−0.423126	−	0.0546224i
$499$	−78.7852	+	242.476i	−0.157886	+	0.485924i	−0.998442	−	0.0558013i	$-0.982229\pi$
$499$	−78.7852	+	242.476i	−0.157886	+	0.485924i	0.840556	+	0.541725i	$0.182229\pi$
$500$	−106.315	+	146.330i	−0.212630	+	0.292660i
$501$	197.594	+	361.749i	0.394400	+	0.722054i
$502$	−85.0764	+	261.838i	−0.169475	+	0.521590i
$503$	243.035	−	78.9669i	0.483171	−	0.156992i	−0.0572955	−	0.998357i	$-0.518248\pi$
$503$	243.035	−	78.9669i	0.483171	−	0.156992i	0.540467	+	0.841365i	$0.318248\pi$
$504$	109.789	−	418.147i	0.217836	−	0.829657i
$505$	308.949			0.611781
$506$		0			0
$507$	−194.762	+	410.986i	−0.384146	+	0.810623i
$508$	−415.824	+	302.114i	−0.818551	+	0.594712i
$509$	50.3488	−	16.3593i	0.0989171	−	0.0321401i	−0.259140	−	0.965840i	$-0.583439\pi$
$509$	50.3488	−	16.3593i	0.0989171	−	0.0321401i	0.358057	+	0.933700i	$0.383439\pi$
$510$	−272.220	+	288.310i	−0.533764	+	0.565313i
$511$	708.209	+	514.544i	1.38593	+	1.00694i
$512$	−302.461	+	416.301i	−0.590743	+	0.813089i
$513$	−19.7096	+	277.176i	−0.0384202	+	0.540305i
$514$	−28.8827	−	88.8919i	−0.0561921	−	0.172941i
$515$	200.943	+	276.574i	0.390181	+	0.537037i
$516$	−292.362	+	616.942i	−0.566594	+	1.19562i
$517$		0			0
$518$		−	92.7942i		−	0.179139i
$519$	−3.12023	+	0.586427i	−0.00601199	+	0.00112992i
$520$	42.9082	+	132.058i	0.0825157	+	0.253957i
$521$	−829.134	−	269.402i	−1.59143	−	0.517086i	−0.626460	−	0.779454i	$-0.715497\pi$
$521$	−829.134	−	269.402i	−1.59143	−	0.517086i	−0.964968	+	0.262367i	$0.915497\pi$
$522$	5.67366	+	98.7463i	0.0108691	+	0.189169i
$523$	−573.820	−	416.904i	−1.09717	−	0.797140i	−0.116574	−	0.993182i	$-0.537191\pi$
$523$	−573.820	−	416.904i	−1.09717	−	0.797140i	−0.980596	+	0.196042i	$0.937191\pi$
$524$	585.793	+	190.336i	1.11793	+	0.363236i
$525$	−477.063	−	61.5854i	−0.908692	−	0.117306i
$526$	75.9766	−	55.2002i	0.144442	−	0.104943i
$527$		−	528.555i		−	1.00295i
$528$		0			0
$529$	−248.573			−0.469892
$530$	−156.802	−	215.819i	−0.295852	−	0.407206i
$531$	−307.952	−	197.789i	−0.579947	−	0.372485i
$532$	105.347	−	324.226i	0.198022	−	0.609448i
$533$	−85.8288	+	118.133i	−0.161030	+	0.221638i
$534$	36.5493	−	19.9639i	0.0684443	−	0.0373856i
$535$	137.014	−	421.686i	0.256101	−	0.788198i
$536$	150.425	−	48.8759i	0.280643	−	0.0911864i
$537$	255.761	−	48.0686i	0.476277	−	0.0895133i
$538$	−21.0236			−0.0390774
$539$		0			0
$540$	149.229	+	601.538i	0.276351	+	1.11396i
$541$	138.021	−	100.278i	0.255122	−	0.185357i	−0.452872	−	0.891576i	$-0.649600\pi$
$541$	138.021	−	100.278i	0.255122	−	0.185357i	0.707994	+	0.706219i	$0.249600\pi$
$542$	129.756	−	42.1601i	0.239401	−	0.0777862i
$543$	235.953	+	222.785i	0.434537	+	0.410286i
$544$	−672.302	−	488.456i	−1.23585	−	0.897897i
$545$	−143.913	+	198.079i	−0.264060	+	0.363447i
$546$	54.7557	−	57.9921i	0.100285	−	0.106213i
$547$	−32.7797	−	100.886i	−0.0599264	−	0.184434i	0.916612	−	0.399778i	$-0.130913\pi$
$547$	−32.7797	−	100.886i	−0.0599264	−	0.184434i	−0.976538	+	0.215344i	$0.930913\pi$
$548$	−169.008	−	232.619i	−0.308408	−	0.424487i
$549$	−133.982	−	163.761i	−0.244047	−	0.298290i
$550$		0			0
$551$			166.205i			0.301642i
$552$	79.2525	+	421.682i	0.143573	+	0.763917i
$553$	−327.254	−	1007.18i	−0.591779	−	1.82131i
$554$	103.301	+	33.5645i	0.186464	+	0.0605858i
$555$	135.890	+	248.783i	0.244847	+	0.448258i
$556$	1.94870	+	1.41581i	0.00350485	+	0.00254642i
$557$	−697.965	−	226.782i	−1.25308	−	0.407150i	−0.394055	−	0.919087i	$-0.628928\pi$
$557$	−697.965	−	226.782i	−1.25308	−	0.407150i	−0.859023	+	0.511937i	$0.828928\pi$
$558$	91.0161	+	58.4573i	0.163111	+	0.104762i
$559$	−217.135	+	157.758i	−0.388435	+	0.282215i
$560$		−	647.771i		−	1.15673i
$561$		0			0
$562$	−270.320			−0.480997
$563$	583.990	+	803.794i	1.03728	+	1.42770i	0.899336	+	0.437258i	$0.144050\pi$
$563$	583.990	+	803.794i	1.03728	+	1.42770i	0.137947	+	0.990440i	$0.455950\pi$
$564$	−14.2050	+	110.037i	−0.0251862	+	0.195102i
$565$	341.502	−	1051.04i	0.604429	−	1.86024i
$566$	−27.0360	+	37.2119i	−0.0477669	+	0.0657455i
$567$	558.615	−	513.257i	0.985212	−	0.905215i
$568$	1.57807	−	4.85681i	0.00277830	−	0.00855073i
$569$	−1014.04	+	329.482i	−1.78215	+	0.579055i	−0.999080	−	0.0428814i	$-0.986346\pi$
$569$	−1014.04	+	329.482i	−1.78215	+	0.579055i	−0.783068	+	0.621936i	$0.786346\pi$
$570$	−25.1874	−	134.016i	−0.0441885	−	0.235115i
$571$	−409.079			−0.716425			−0.358213	−	0.933640i	$-0.616614\pi$
$571$	−409.079			−0.716425			−0.358213	+	0.933640i	$0.616614\pi$
$572$		0			0
$573$	77.6733	+	36.8086i	0.135556	+	0.0642384i
$574$	−180.494	+	131.136i	−0.314449	+	0.228460i
$575$	454.035	−	147.525i	0.789625	−	0.256565i
$576$	−199.014	+	77.5462i	−0.345511	+	0.134629i
$577$	−371.961	−	270.246i	−0.644647	−	0.468363i	0.216797	−	0.976217i	$-0.430439\pi$
$577$	−371.961	−	270.246i	−0.644647	−	0.468363i	−0.861444	+	0.507853i	$0.830439\pi$
$578$	242.638	−	333.962i	0.419788	−	0.577789i
$579$	−27.6912	−	26.1458i	−0.0478259	−	0.0451568i
$580$	114.553	+	352.557i	0.197505	+	0.607858i
$581$	572.899	+	788.527i	0.986056	+	1.35719i
$582$	−350.674	−	166.181i	−0.602533	−	0.285534i
$583$		0			0
$584$			479.406i			0.820901i
$585$	−61.8761	+	235.664i	−0.105771	+	0.402844i
$586$	76.8856	+	236.629i	0.131204	+	0.403804i
$587$	−55.9862	−	18.1910i	−0.0953768	−	0.0309898i	0.260940	−	0.965355i	$-0.415968\pi$
$587$	−55.9862	−	18.1910i	−0.0953768	−	0.0309898i	−0.356317	+	0.934365i	$0.615968\pi$
$588$	−360.497	+	196.910i	−0.613090	+	0.334881i
$589$	147.055	+	106.842i	0.249669	+	0.181395i
$590$	170.816	+	55.5014i	0.289518	+	0.0940702i
$591$	129.321	−	1001.76i	0.218816	−	1.69503i
$592$	−125.531	+	91.2039i	−0.212046	+	0.154061i
$593$		−	149.728i		−	0.252493i	−0.991999	−	0.126247i	$-0.959707\pi$
$593$		−	149.728i		−	0.252493i	0.991999	−	0.126247i	$-0.0402931\pi$
$594$		0			0
$595$	1819.01			3.05715
$596$	411.489	+	566.366i	0.690418	+	0.950278i
$597$	547.048	+	70.6199i	0.916328	+	0.118291i
$598$	−24.4609	+	75.2828i	−0.0409045	+	0.125891i
$599$	260.728	−	358.862i	0.435273	−	0.599102i	−0.533881	−	0.845560i	$-0.679267\pi$
$599$	260.728	−	358.862i	0.435273	−	0.599102i	0.969153	+	0.246458i	$0.0792668\pi$
$600$	−126.280	−	231.189i	−0.210467	−	0.385316i
$601$	−127.932	+	393.733i	−0.212864	+	0.655129i	0.786434	+	0.617674i	$0.211925\pi$
$601$	−127.932	+	393.733i	−0.212864	+	0.655129i	−0.999298	+	0.0374549i	$0.988075\pi$
$602$	−390.004	+	126.720i	−0.647847	+	0.210498i
$603$	268.440	+	70.4819i	0.445174	+	0.116885i
$604$	−314.483			−0.520668
$605$		0			0
$606$	41.6185	−	87.8232i	0.0686774	−	0.144923i
$607$	308.111	−	223.856i	0.507597	−	0.368791i	−0.304314	−	0.952572i	$-0.598427\pi$
$607$	308.111	−	223.856i	0.507597	−	0.368791i	0.811911	+	0.583781i	$0.198427\pi$
$608$	271.797	−	88.3121i	0.447034	−	0.145250i
$609$	311.505	−	329.917i	0.511503	−	0.541736i
$610$	84.0017	+	61.0308i	0.137708	+	0.100051i
$611$	−25.6380	+	35.2877i	−0.0419608	+	0.0577541i
$612$	−345.862	−	887.621i	−0.565135	−	1.45036i
$613$	34.9041	+	107.424i	0.0569399	+	0.175243i	0.975482	−	0.220081i	$-0.0706323\pi$
$613$	34.9041	+	107.424i	0.0569399	+	0.175243i	−0.918542	+	0.395324i	$0.870632\pi$
$614$	193.663	+	266.554i	0.315412	+	0.434127i
$615$	291.868	−	615.898i	0.474582	−	1.00146i
$616$		0			0
$617$		−	378.251i		−	0.613049i	−0.951863	−	0.306524i	$-0.900834\pi$
$617$		−	378.251i		−	0.613049i	0.951863	−	0.306524i	$-0.0991661\pi$
$618$	105.689	−	19.8636i	0.171018	−	0.0321418i
$619$	−9.05390	−	27.8651i	−0.0146267	−	0.0450162i	0.943477	−	0.331439i	$-0.107534\pi$
$619$	−9.05390	−	27.8651i	−0.0146267	−	0.0450162i	−0.958103	+	0.286422i	$0.907534\pi$
$620$	385.574	+	125.281i	0.621894	+	0.202066i
$621$	−282.860	+	697.740i	−0.455491	+	1.12357i
$622$	−185.069	−	134.460i	−0.297538	−	0.216174i
$623$	−181.699	−	59.0377i	−0.291652	−	0.0947635i
$624$	−132.269	−	17.0749i	−0.211969	−	0.0273637i
$625$	614.774	−	446.660i	0.983639	−	0.714655i
$626$			332.837i			0.531689i
$627$		0			0
$628$	236.041			0.375862
$629$	−256.110	−	352.505i	−0.407169	−	0.560421i
$630$	−201.179	+	313.229i	−0.319331	+	0.497189i
$631$	−300.638	+	925.267i	−0.476446	+	1.46635i	0.367551	+	0.930003i	$0.380196\pi$
$631$	−300.638	+	925.267i	−0.476446	+	1.46635i	−0.843997	+	0.536347i	$0.819804\pi$
$632$	340.895	−	469.202i	0.539392	−	0.742409i
$633$	473.932	−	258.871i	0.748708	−	0.408959i
$634$	−32.8730	+	101.173i	−0.0518501	+	0.159578i
$635$	896.978	−	291.446i	1.41256	−	0.458970i
$636$	629.874	−	118.381i	0.990367	−	0.186133i
$637$	−161.486			−0.253510
$638$		0			0
$639$	6.93552	−	5.67432i	0.0108537	−	0.00888000i
$640$	667.991	−	485.324i	1.04374	−	0.758319i
$641$	831.582	−	270.198i	1.29732	−	0.421525i	0.422672	−	0.906283i	$-0.361092\pi$
$641$	831.582	−	270.198i	1.29732	−	0.421525i	0.874648	+	0.484758i	$0.161092\pi$
$642$	−101.413	−	95.7534i	−0.157964	−	0.149149i
$643$	−590.727	−	429.188i	−0.918704	−	0.667477i	0.0244973	−	0.999700i	$-0.492202\pi$
$643$	−590.727	−	429.188i	−0.918704	−	0.667477i	−0.943201	+	0.332223i	$0.892202\pi$
$644$	542.929	−	747.278i	0.843058	−	1.16037i
$645$	860.037	−	910.871i	1.33339	−	1.41220i
$646$	64.7688	+	199.338i	0.100261	+	0.308572i
$647$	−436.536	−	600.841i	−0.674708	−	0.928656i	0.325147	−	0.945663i	$-0.394586\pi$
$647$	−436.536	−	600.841i	−0.674708	−	0.928656i	−0.999855	+	0.0170072i	$0.994586\pi$
$648$	407.218	+	82.2808i	0.628423	+	0.126977i
$649$		0			0
$650$		−	48.5994i		−	0.0747684i
$651$	−91.6592	−	487.695i	−0.140798	−	0.749148i
$652$	−152.844	−	470.405i	−0.234423	−	0.721479i
$653$	−1057.97	−	343.757i	−1.62018	−	0.526427i	−0.648192	−	0.761477i	$-0.724475\pi$
$653$	−1057.97	−	343.757i	−1.62018	−	0.526427i	−0.971983	+	0.235050i	$0.924475\pi$
$654$	36.9202	+	67.5924i	0.0564530	+	0.103352i
$655$	−914.364	−	664.324i	−1.39598	−	1.01424i
$656$	354.801	+	115.282i	0.540855	+	0.175734i
$657$	−454.609	+	707.812i	−0.691947	+	1.07734i
$658$	−53.9155	+	39.1719i	−0.0819385	+	0.0595318i
$659$		−	829.020i		−	1.25800i	−0.777407	−	0.628998i	$-0.783465\pi$
$659$		−	829.020i		−	1.25800i	0.777407	−	0.628998i	$-0.216535\pi$
$660$		0			0
$661$	−1040.95			−1.57480			−0.787402	−	0.616439i	$-0.788575\pi$
$661$	−1040.95			−1.57480			−0.787402	+	0.616439i	$0.788575\pi$
$662$	16.1116	+	22.1757i	0.0243378	+	0.0334981i
$663$	47.9481	−	371.423i	0.0723198	−	0.560216i
$664$	−164.946	+	507.651i	−0.248412	+	0.764535i
$665$	−367.692	+	506.084i	−0.552920	+	0.761029i
$666$	89.0259	−	5.11516i	0.133672	−	0.00768041i
$667$	−139.158	+	428.284i	−0.208633	+	0.642105i
$668$	462.181	−	150.172i	0.691887	−	0.224808i
$669$	145.768	+	775.596i	0.217890	+	1.15934i
$670$	−136.196			−0.203278
$671$		0			0
$672$	−705.035	−	334.109i	−1.04916	−	0.497186i
$673$	−205.745	+	149.482i	−0.305713	+	0.222113i	−0.730055	−	0.683389i	$-0.760505\pi$
$673$	−205.745	+	149.482i	−0.305713	+	0.222113i	0.424342	+	0.905502i	$0.360505\pi$
$674$	−7.71203	+	2.50579i	−0.0114422	+	0.00371779i
$675$	32.7870	−	461.085i	0.0485733	−	0.683088i
$676$	433.788	+	315.166i	0.641699	+	0.466221i
$677$	595.961	−	820.270i	0.880297	−	1.21163i	−0.0960413	−	0.995377i	$-0.530618\pi$
$677$	595.961	−	820.270i	0.880297	−	1.21163i	0.976339	−	0.216248i	$-0.0693819\pi$
$678$	−252.768	−	238.662i	−0.372815	−	0.352009i
$679$	550.110	+	1693.06i	0.810177	+	2.49347i
$680$	585.534	+	805.919i	0.861080	+	1.18518i
$681$	−24.4777	−	11.5997i	−0.0359438	−	0.0170334i
$682$		0			0
$683$			561.211i			0.821685i	0.911706	+	0.410842i	$0.134765\pi$
$683$			561.211i			0.821685i	−0.911706	+	0.410842i	$0.865235\pi$
$684$	316.867	+	83.1968i	0.463255	+	0.121633i
$685$	163.040	+	501.784i	0.238014	+	0.732532i
$686$	62.3554	+	20.2605i	0.0908970	+	0.0295342i
$687$	927.889	−	506.831i	1.35064	−	0.737745i
$688$	554.746	+	403.047i	0.806318	+	0.585824i
$689$	239.626	+	77.8593i	0.347788	+	0.113003i
$690$	47.3031	−	366.427i	0.0685552	−	0.531054i
$691$	−462.234	+	335.833i	−0.668935	+	0.486010i	−0.869668	−	0.493636i	$-0.835667\pi$
$691$	−462.234	+	335.833i	−0.668935	+	0.486010i	0.200734	+	0.979646i	$0.435667\pi$
$692$			3.74304i			0.00540902i
$693$		0			0
$694$	409.185			0.589603
$695$	−2.59794	−	3.57575i	−0.00373804	−	0.00514497i
$696$	246.444	+	31.8142i	0.354087	+	0.0457100i
$697$	−323.722	+	996.315i	−0.464451	+	1.42943i
$698$	−53.1831	+	73.2003i	−0.0761936	+	0.104871i
$699$	50.9124	+	93.2087i	0.0728360	+	0.133346i
$700$	−175.246	+	539.352i	−0.250352	+	0.770503i
$701$	672.521	−	218.515i	0.959373	−	0.311719i	0.212855	−	0.977084i	$-0.431724\pi$
$701$	672.521	−	218.515i	0.959373	−	0.311719i	0.746519	+	0.665365i	$0.231724\pi$
$702$	58.6554	+	49.3353i	0.0835547	+	0.0702783i
$703$	149.844			0.213149
$704$		0			0
$705$	87.1843	−	183.976i	0.123666	−	0.260959i
$706$	95.1701	−	69.1451i	0.134802	−	0.0979393i
$707$	−424.013	+	137.770i	−0.599736	+	0.194866i
$708$	−296.236	+	313.745i	−0.418413	+	0.443143i
$709$	−739.545	−	537.311i	−1.04308	−	0.757843i	−0.0721966	−	0.997390i	$-0.523001\pi$
$709$	−739.545	−	537.311i	−1.04308	−	0.757843i	−0.970885	+	0.239548i	$0.923001\pi$
$710$	−2.58474	+	3.55759i	−0.00364048	+	0.00501069i
$711$	948.244	−	369.484i	1.33368	−	0.519668i
$712$	−32.3317	−	99.5069i	−0.0454098	−	0.139757i
$713$	289.483	+	398.439i	0.406007	+	0.558820i
$714$	245.038	−	517.078i	0.343190	−	0.724199i
$715$		0			0
$716$		−	306.812i		−	0.428509i
$717$	−385.645	+	72.4796i	−0.537860	+	0.101087i
$718$	−126.753	−	390.105i	−0.176536	−	0.543321i
$719$	801.511	+	260.427i	1.11476	+	0.362207i	0.807765	−	0.589505i	$-0.200677\pi$
$719$	801.511	+	260.427i	1.11476	+	0.362207i	0.306993	+	0.951712i	$0.400677\pi$
$720$	621.465	−	35.7075i	0.863146	−	0.0495938i
$721$	−399.114	−	289.974i	−0.553557	−	0.402183i
$722$	165.091	+	53.6412i	0.228657	+	0.0742953i
$723$	−400.256	−	51.6701i	−0.553604	−	0.0714663i
$724$	309.520	−	224.879i	0.427513	−	0.310607i
$725$		−	276.482i		−	0.381355i
$726$		0			0
$727$	958.596			1.31856			0.659282	−	0.751895i	$-0.270860\pi$
$727$	958.596			1.31856			0.659282	+	0.751895i	$0.270860\pi$
$728$	−117.777	−	162.107i	−0.161782	−	0.222674i
$729$	523.207	+	507.638i	0.717704	+	0.696348i
$730$	127.567	−	392.612i	0.174750	−	0.537824i
$731$	−1131.80	+	1557.78i	−1.54828	+	2.13103i
$732$	−218.924	+	119.580i	−0.299076	+	0.163361i
$733$	−311.526	+	958.778i	−0.425001	+	1.30802i	0.477992	+	0.878364i	$0.341365\pi$
$733$	−311.526	+	958.778i	−0.425001	+	1.30802i	−0.902993	+	0.429655i	$0.858635\pi$
$734$	161.066	−	52.3334i	0.219436	−	0.0712989i
$735$	740.771	−	139.223i	1.00785	−	0.189419i
$736$	774.320			1.05207
$737$		0			0
$738$	−135.760	−	165.935i	−0.183957	−	0.224844i
$739$	916.677	−	666.005i	1.24043	−	0.901224i	0.242802	−	0.970076i	$-0.421933\pi$
$739$	916.677	−	666.005i	1.24043	−	0.901224i	0.997627	+	0.0688515i	$0.0219335\pi$
$740$	317.852	−	103.276i	0.429530	−	0.139563i
$741$	93.6454	+	88.4193i	0.126377	+	0.119324i
$742$	311.441	+	226.275i	0.419732	+	0.304953i
$743$	−7.44321	+	10.2447i	−0.0100178	+	0.0137883i	−0.813997	−	0.580870i	$-0.802713\pi$
$743$	−7.44321	+	10.2447i	−0.0100178	+	0.0137883i	0.803979	+	0.594658i	$0.202713\pi$
$744$	186.571	−	197.598i	0.250767	−	0.265589i
$745$	−396.959	−	1221.71i	−0.532830	−	1.63988i
$746$	−271.054	−	373.074i	−0.363343	−	0.500099i
$747$	−724.925	+	593.100i	−0.970449	+	0.793976i
$748$		0			0
$749$			639.835i			0.854253i
$750$	−19.2843	−	102.607i	−0.0257124	−	0.136809i
$751$	−59.2741	−	182.427i	−0.0789270	−	0.242912i	0.903806	−	0.427943i	$-0.140762\pi$
$751$	−59.2741	−	182.427i	−0.0789270	−	0.242912i	−0.982733	+	0.185031i	$0.940762\pi$
$752$	105.983	+	34.4360i	0.140935	+	0.0457925i
$753$	581.808	+	1065.15i	0.772653	+	1.41455i
$754$	37.0879	+	26.9459i	0.0491882	+	0.0357373i
$755$	548.817	+	178.321i	0.726910	+	0.236187i
$756$	−473.052	−	759.026i	−0.625731	−	1.00400i
$757$	−417.065	+	303.015i	−0.550944	+	0.400284i	−0.828133	−	0.560531i	$-0.810597\pi$
$757$	−417.065	+	303.015i	−0.550944	+	0.400284i	0.277189	+	0.960815i	$0.410597\pi$
$758$			77.4605i			0.102191i
$759$		0			0
$760$	−342.582			−0.450766
$761$	605.245	+	833.048i	0.795328	+	1.09468i	0.993424	+	0.114493i	$0.0365242\pi$
$761$	605.245	+	833.048i	0.795328	+	1.09468i	−0.198096	+	0.980183i	$0.563476\pi$
$762$	37.9841	−	294.239i	0.0498480	−	0.386141i
$763$	109.181	−	336.025i	0.143095	−	0.440400i
$764$	59.5640	−	81.9828i	0.0779633	−	0.107307i
$765$	100.270	+	1745.14i	0.131072	+	2.28122i
$766$	126.732	−	390.041i	0.165447	−	0.509192i
$767$	−161.333	+	52.4203i	−0.210343	+	0.0683446i
$768$	4.62731	+	24.6207i	0.00602514	+	0.0320582i
$769$	−1094.35			−1.42308			−0.711539	−	0.702647i	$-0.752001\pi$
$769$	−1094.35			−1.42308			−0.711539	+	0.702647i	$0.752001\pi$
$770$		0			0
$771$	−372.346	−	176.451i	−0.482938	−	0.228860i
$772$	−36.3248	+	26.3915i	−0.0470529	+	0.0341859i
$773$	−490.859	+	159.490i	−0.635005	+	0.206326i	−0.608791	−	0.793331i	$-0.708345\pi$
$773$	−490.859	+	159.490i	−0.635005	+	0.206326i	−0.0262141	+	0.999656i	$0.508345\pi$
$774$	−143.072	−	367.181i	−0.184848	−	0.474394i
$775$	−244.626	−	177.732i	−0.315647	−	0.229331i
$776$	−573.041	+	788.723i	−0.738455	+	1.01640i
$777$	−297.441	−	280.841i	−0.382806	−	0.361443i
$778$	95.7186	+	294.592i	0.123032	+	0.378653i
$779$	−211.758	−	291.460i	−0.271833	−	0.374147i
$780$	259.584	+	123.014i	0.332800	+	0.157710i
$781$		0			0
$782$			567.892i			0.726205i
$783$	333.691	+	280.669i	0.426169	+	0.358453i
$784$	127.491	+	392.378i	0.162617	+	0.500483i
$785$	−411.925	−	133.843i	−0.524745	−	0.170500i
$786$	−312.017	+	170.430i	−0.396969	+	0.216832i
$787$	−587.721	−	427.004i	−0.746786	−	0.542572i	0.148043	−	0.988981i	$-0.452703\pi$
$787$	−587.721	−	427.004i	−0.746786	−	0.542572i	−0.894829	+	0.446409i	$0.852703\pi$
$788$	−1132.56	−	367.992i	−1.43726	−	0.466995i
$789$	53.0051	−	410.597i	0.0671800	−	0.520401i
$790$	−404.030	+	293.545i	−0.511430	+	0.371576i
$791$			1594.77i			2.01614i
$792$		0			0
$793$	−98.0678			−0.123667
$794$	131.112	+	180.461i	0.165129	+	0.227280i
$795$	−1166.34	−	150.566i	−1.46710	−	0.189392i
$796$	200.955	−	618.475i	0.252456	−	0.776978i
$797$	862.522	−	1187.16i	1.08221	−	1.48954i	0.225147	−	0.974325i	$-0.427714\pi$
$797$	862.522	−	1187.16i	1.08221	−	1.48954i	0.857064	−	0.515211i	$-0.172286\pi$
$798$	94.3299	+	172.696i	0.118208	+	0.216411i
$799$	−96.6996	+	297.611i	−0.121026	+	0.372479i
$800$	−452.136	+	146.908i	−0.565170	+	0.183635i
$801$	46.6242	−	177.575i	0.0582075	−	0.221692i
$802$	−171.519			−0.213864
$803$		0			0
$804$	140.123	−	295.687i	0.174283	−	0.367770i
$805$	−1371.21	+	996.246i	−1.70337	+	1.23757i
$806$	47.6825	−	15.4930i	0.0591594	−	0.0192221i
$807$	−63.6279	+	67.3887i	−0.0788449	+	0.0835052i
$808$	−197.529	−	143.513i	−0.244466	−	0.177615i
$809$	15.0886	−	20.7677i	0.0186510	−	0.0256709i	−0.799590	−	0.600547i	$-0.794950\pi$
$809$	15.0886	−	20.7677i	0.0186510	−	0.0256709i	0.818241	+	0.574876i	$0.194950\pi$
$810$	−311.599	−	175.743i	−0.384690	−	0.216966i
$811$	203.045	+	624.909i	0.250364	+	0.770541i	0.994708	+	0.102744i	$0.0327624\pi$
$811$	203.045	+	624.909i	0.250364	+	0.770541i	−0.744344	+	0.667797i	$0.767238\pi$
$812$	−314.433	−	432.780i	−0.387233	−	0.532980i
$813$	257.565	−	543.513i	0.316808	−	0.668528i
$814$		0			0
$815$			907.588i			1.11360i
$816$	−940.338	+	176.731i	−1.15238	+	0.216582i
$817$	−204.627	−	629.777i	−0.250461	−	0.770841i
$818$	−293.692	−	95.4262i	−0.359036	−	0.116658i
$819$	−20.1689	−	351.026i	−0.0246262	−	0.428603i
$820$	−650.070	−	472.303i	−0.792768	−	0.575979i
$821$	895.899	+	291.095i	1.09123	+	0.354562i	0.798721	−	0.601701i	$-0.205510\pi$
$821$	895.899	+	291.095i	1.09123	+	0.354562i	0.292508	+	0.956263i	$0.405510\pi$
$822$	164.602	+	21.2490i	0.200246	+	0.0258503i
$823$	165.283	−	120.085i	0.200830	−	0.145912i	−0.482825	−	0.875717i	$-0.660389\pi$
$823$	165.283	−	120.085i	0.200830	−	0.145912i	0.683655	+	0.729805i	$0.260389\pi$
$824$		−	270.172i		−	0.327878i
$825$		0			0
$826$	−259.183			−0.313781
$827$	−68.2953	−	94.0004i	−0.0825820	−	0.113664i	0.765727	−	0.643165i	$-0.222379\pi$
$827$	−68.2953	−	94.0004i	−0.0825820	−	0.113664i	−0.848309	+	0.529501i	$0.822379\pi$
$828$	746.859	+	479.688i	0.902004	+	0.579334i
$829$	468.065	−	1440.56i	0.564614	−	1.73770i	−0.104482	−	0.994527i	$-0.533319\pi$
$829$	468.065	−	1440.56i	0.564614	−	1.73770i	0.669096	−	0.743176i	$-0.266681\pi$
$830$	270.166	−	371.852i	0.325501	−	0.448014i
$831$	420.227	−	229.536i	0.505688	−	0.276217i
$832$	−30.5913	+	94.1505i	−0.0367684	+	0.113162i
$833$	−1101.84	+	358.009i	−1.32273	+	0.429782i
$834$	−1.36643	+	0.256811i	−0.00163840	+	0.000307927i
$835$	−891.721			−1.06793
$836$		0			0
$837$	462.837	−	114.821i	0.552972	−	0.137181i
$838$	−162.827	+	118.301i	−0.194304	+	0.141170i
$839$	−800.614	+	260.135i	−0.954248	+	0.310054i	−0.744441	−	0.667689i	$-0.767284\pi$
$839$	−800.614	+	260.135i	−0.954248	+	0.310054i	−0.209807	+	0.977743i	$0.567284\pi$
$840$	680.028	+	642.077i	0.809557	+	0.764378i
$841$	−469.390	−	341.032i	−0.558133	−	0.405508i
$842$	−91.5934	+	126.068i	−0.108781	+	0.149724i
$843$	−818.123	+	866.479i	−0.970490	+	1.02785i
$844$	−196.742	−	605.509i	−0.233106	−	0.717428i
$845$	−578.312	−	795.979i	−0.684393	−	0.941987i
$846$	−40.5532	−	49.5667i	−0.0479352	−	0.0585895i
$847$		0			0
$848$		−	643.713i		−	0.759095i
$849$	37.4539	+	199.282i	0.0441153	+	0.234726i
$850$	−107.743	−	331.599i	−0.126757	−	0.390117i
$851$	386.125	+	125.459i	0.453730	+	0.147426i
$852$	−5.06439	−	9.27173i	−0.00594412	−	0.0108823i
$853$	292.677	+	212.642i	0.343115	+	0.249287i	0.745975	−	0.665974i	$-0.231984\pi$
$853$	292.677	+	212.642i	0.343115	+	0.249287i	−0.402860	+	0.915262i	$0.631984\pi$
$854$	−142.503	−	46.3019i	−0.166865	−	0.0542177i
$855$	−505.801	−	324.863i	−0.591580	−	0.379956i
$856$	−283.482	+	205.962i	−0.331171	+	0.240610i
$857$			519.778i			0.606509i	0.952910	+	0.303254i	$0.0980732\pi$
$857$			519.778i			0.606509i	−0.952910	+	0.303254i	$0.901927\pi$
$858$		0			0
$859$	−1258.77			−1.46538			−0.732692	−	0.680560i	$-0.761737\pi$
$859$	−1258.77			−1.46538			−0.732692	+	0.680560i	$0.761737\pi$
$860$	−868.120	−	1194.86i	−1.00944	−	1.38938i
$861$	−125.921	+	975.434i	−0.146250	+	1.13291i
$862$	117.546	−	361.768i	0.136364	−	0.419685i
$863$	667.030	−	918.087i	0.772920	−	1.06383i	−0.223109	−	0.974794i	$-0.571620\pi$
$863$	667.030	−	918.087i	0.772920	−	1.06383i	0.996028	−	0.0890389i	$-0.0283796\pi$
$864$	281.677	−	694.821i	0.326015	−	0.804191i
$865$	2.12242	−	6.53213i	0.00245366	−	0.00755159i
$866$	186.573	−	60.6213i	0.215442	−	0.0700015i
$867$	−336.134	−	1788.48i	−0.387697	−	2.06284i
$868$	−585.043			−0.674012
$869$		0			0
$870$	−193.361	−	91.6318i	−0.222254	−	0.105324i
$871$	104.068	−	75.6102i	0.119482	−	0.0868085i
$872$	184.023	−	59.7927i	0.211036	−	0.0685696i
$873$	−1593.99	+	621.098i	−1.82587	+	0.711453i
$874$	−157.999	−	114.793i	−0.180777	−	0.131342i
$875$	−281.517	+	387.474i	−0.321733	+	0.442828i
$876$	721.129	+	680.884i	0.823207	+	0.777265i
$877$	451.922	+	1390.87i	0.515304	+	1.58594i	0.782728	+	0.622364i	$0.213828\pi$
$877$	451.922	+	1390.87i	0.515304	+	1.58594i	−0.267423	+	0.963579i	$0.586172\pi$
$878$	71.9196	+	98.9888i	0.0819130	+	0.112744i
$879$	991.181	+	469.710i	1.12762	+	0.534369i
$880$		0			0
$881$		−	1493.59i		−	1.69534i	−0.530526	−	0.847668i	$-0.678006\pi$
$881$		−	1493.59i		−	1.69534i	0.530526	−	0.847668i	$-0.321994\pi$
$882$	60.2129	−	229.329i	0.0682686	−	0.260011i
$883$	410.383	+	1263.03i	0.464760	+	1.43038i	0.859285	+	0.511498i	$0.170909\pi$
$883$	410.383	+	1263.03i	0.464760	+	1.43038i	−0.394525	+	0.918885i	$0.629091\pi$
$884$	−419.919	−	136.440i	−0.475022	−	0.154344i
$885$	694.876	−	379.555i	0.785170	−	0.428875i
$886$	154.857	+	112.510i	0.174782	+	0.126987i
$887$	−792.059	−	257.356i	−0.892964	−	0.290142i	−0.173634	−	0.984810i	$-0.555551\pi$
$887$	−792.059	−	257.356i	−0.892964	−	0.290142i	−0.719330	+	0.694668i	$0.755551\pi$
$888$	28.6824	−	222.185i	0.0323000	−	0.250208i
$889$	−1101.08	+	799.981i	−1.23856	+	0.899866i
$890$			90.0949i			0.101230i
$891$		0			0
$892$	930.411			1.04306
$893$	−63.2546	−	87.0625i	−0.0708339	−	0.0974944i
$894$	−400.764	−	51.7357i	−0.448281	−	0.0578699i
$895$	−173.972	+	535.430i	−0.194382	+	0.598246i
$896$	−700.354	+	963.954i	−0.781645	+	1.07584i
$897$	167.279	+	306.249i	0.186488	+	0.341415i
$898$	58.3978	−	179.730i	0.0650310	−	0.200145i
$899$	271.266	−	88.1396i	0.301742	−	0.0980419i
$900$	−527.109	−	138.398i	−0.585677	−	0.153776i
$901$	1807.61			2.00622
$902$		0			0
$903$	−774.160	+	1633.63i	−0.857320	+	1.80911i
$904$	−706.569	+	513.352i	−0.781603	+	0.567868i
$905$	−667.668	+	216.938i	−0.737754	+	0.239711i
$906$	124.621	−	131.987i	0.137551	−	0.145681i
$907$	−442.323	−	321.366i	−0.487677	−	0.354318i	0.316614	−	0.948555i	$-0.397454\pi$
$907$	−442.323	−	321.366i	−0.487677	−	0.354318i	−0.804290	+	0.594237i	$0.797454\pi$
$908$	−18.7708	+	25.8358i	−0.0206727	+	0.0284535i
$909$	−155.549	−	399.200i	−0.171121	−	0.439164i
$910$	53.3186	+	164.098i	0.0585919	+	0.180327i
$911$	32.7594	+	45.0894i	0.0359598	+	0.0494944i	0.826618	−	0.562763i	$-0.190262\pi$
$911$	32.7594	+	45.0894i	0.0359598	+	0.0494944i	−0.790658	+	0.612257i	$0.790262\pi$
$912$	140.909	−	297.345i	0.154505	−	0.326037i
$913$		0			0
$914$		−	235.612i		−	0.257781i
$915$	449.858	−	84.5479i	0.491648	−	0.0924021i
$916$	−385.191	−	1185.50i	−0.420515	−	1.29421i
$917$	1551.15	+	503.999i	1.69155	+	0.549617i
$918$	509.587	+	206.584i	0.555106	+	0.225037i
$919$	864.120	+	627.820i	0.940283	+	0.683155i	0.948489	−	0.316811i	$-0.102612\pi$
$919$	864.120	+	627.820i	0.940283	+	0.683155i	−0.00820611	+	0.999966i	$0.502612\pi$
$920$	−882.783	−	286.834i	−0.959547	−	0.311776i
$921$	1440.53	+	185.961i	1.56409	+	0.201912i
$922$	−36.9687	+	26.8593i	−0.0400962	+	0.0291316i
$923$		−	4.15331i		−	0.00449979i
$924$		0			0
$925$	−249.266			−0.269477
$926$	−301.872	−	415.491i	−0.325995	−	0.448694i
$927$	256.197	−	398.891i	0.276372	−	0.430303i
$928$	138.576	−	426.493i	0.149328	−	0.459583i
$929$	494.520	−	680.648i	0.532314	−	0.732667i	−0.455167	−	0.890406i	$-0.650420\pi$
$929$	494.520	−	680.648i	0.532314	−	0.732667i	0.987481	+	0.157739i	$0.0504204\pi$
$930$	−205.373	+	112.179i	−0.220831	+	0.120622i
$931$	123.119	−	378.921i	0.132244	−	0.407004i
$932$	119.086	−	38.6934i	0.127775	−	0.0415165i
$933$	−991.104	+	186.272i	−1.06228	+	0.199648i
$934$	196.924			0.210839
$935$		0			0
$936$	149.031	−	121.930i	0.159221	−	0.130268i
$937$	1014.10	−	736.790i	1.08229	−	0.786329i	0.104208	−	0.994556i	$-0.466769\pi$
$937$	1014.10	−	736.790i	1.08229	−	0.786329i	0.978081	+	0.208227i	$0.0667693\pi$
$938$	186.921	−	60.7343i	0.199276	−	0.0647487i
$939$	1066.87	+	1007.33i	1.13618	+	1.07277i
$940$	−194.183	−	141.082i	−0.206578	−	0.150088i
$941$	−802.302	+	1104.27i	−0.852605	+	1.17351i	0.130677	+	0.991425i	$0.458285\pi$
$941$	−802.302	+	1104.27i	−0.852605	+	1.17351i	−0.983283	+	0.182086i	$0.941715\pi$
$942$	−93.5370	+	99.0656i	−0.0992962	+	0.105165i
$943$	−301.638	−	928.348i	−0.319871	−	0.984462i
$944$	254.742	+	350.622i	0.269853	+	0.371421i
$945$	395.151	+	1592.84i	0.418149	+	1.68555i
$946$		0			0
$947$		−	1289.80i		−	1.36199i	−0.732289	−	0.680994i	$-0.761548\pi$
$947$		−	1289.80i		−	1.36199i	0.732289	−	0.680994i	$-0.238452\pi$
$948$	−221.618	−	1179.17i	−0.233774	−	1.24385i
$949$	120.486	+	370.816i	0.126961	+	0.390744i
$950$	114.037	+	37.0528i	0.120039	+	0.0390030i
$951$	224.807	+	411.569i	0.236390	+	0.432775i
$952$	−1162.99	−	844.964i	−1.22163	−	0.887567i
$953$	−630.883	−	204.986i	−0.661997	−	0.215096i	−0.0413004	−	0.999147i	$-0.513150\pi$
$953$	−630.883	−	204.986i	−0.661997	−	0.215096i	−0.620696	+	0.784051i	$0.713150\pi$
$954$	−199.918	+	311.266i	−0.209558	+	0.326275i
$955$	−150.434	+	109.297i	−0.157523	+	0.114447i
$956$			462.623i			0.483915i
$957$		0			0
$958$	113.059			0.118015
$959$	−447.523	−	615.962i	−0.466656	−	0.642296i
$960$	59.1583	−	458.262i	0.0616232	−	0.477356i
$961$	−200.571	+	617.295i	−0.208711	+	0.642347i
$962$	24.2934	−	33.4370i	0.0252530	−	0.0347578i
$963$	−613.852	+	35.2701i	−0.637437	+	0.0366252i
$964$	−147.031	+	452.516i	−0.152522	+	0.469415i
$965$	78.3566	−	25.4596i	0.0811986	−	0.0263830i
$966$	98.4809	+	523.991i	0.101947	+	0.542434i
$967$	101.038			0.104486			0.0522428	−	0.998634i	$-0.483363\pi$
$967$	101.038			0.104486			0.0522428	+	0.998634i	$0.483363\pi$
$968$		0			0
$969$	834.975	+	395.686i	0.861687	+	0.408345i
$970$	679.169	−	493.445i	0.700174	−	0.508706i
$971$	−611.753	+	198.771i	−0.630024	+	0.204707i	−0.606586	−	0.795018i	$-0.707461\pi$
$971$	−611.753	+	198.771i	−0.630024	+	0.204707i	−0.0234383	+	0.999725i	$0.507461\pi$
$972$	702.126	−	495.682i	0.722352	−	0.509961i
$973$	5.16004	+	3.74899i	0.00530323	+	0.00385302i
$974$	8.22387	−	11.3192i	0.00844340	−	0.0116213i
$975$	−155.780	−	147.086i	−0.159774	−	0.150857i
$976$	77.4235	+	238.285i	0.0793273	+	0.244144i
$977$	−882.805	−	1215.08i	−0.903588	−	1.24368i	−0.969309	−	0.245844i	$-0.920935\pi$
$977$	−882.805	−	1215.08i	−0.903588	−	1.24368i	0.0657216	−	0.997838i	$-0.479065\pi$
$978$	257.995	+	122.261i	0.263798	+	0.125011i
$979$		0			0
$980$		−	888.634i		−	0.906769i
$981$	328.398	+	86.2245i	0.334758	+	0.0878945i
$982$	100.644	+	309.750i	0.102489	+	0.315428i
$983$	693.417	+	225.305i	0.705409	+	0.229201i	0.639686	−	0.768637i	$-0.279065\pi$
$983$	693.417	+	225.305i	0.705409	+	0.229201i	0.0657234	+	0.997838i	$0.479065\pi$
$984$	−472.704	+	258.200i	−0.480391	+	0.262399i
$985$	1767.82	+	1284.39i	1.79474	+	1.30395i
$986$	312.793	+	101.633i	0.317234	+	0.103076i
$987$	−37.6142	+	291.373i	−0.0381096	+	0.295211i
$988$	122.842	−	89.2502i	0.124334	−	0.0903342i
$989$		−	1794.17i		−	1.81412i
$990$		0			0
$991$	1823.31			1.83987			0.919936	−	0.392069i	$-0.128241\pi$
$991$	1823.31			1.83987			0.919936	+	0.392069i	$0.128241\pi$
$992$	−288.272	−	396.772i	−0.290597	−	0.399972i
$993$	119.843	+	15.4709i	0.120688	+	0.0155799i
$994$	1.96095	−	6.03518i	0.00197279	−	0.00607161i
$995$	−701.387	+	965.376i	−0.704912	+	0.970228i
$996$	529.348	+	969.113i	0.531474	+	0.973005i
$997$	3.39072	−	10.4356i	0.00340093	−	0.0104670i	−0.949342	−	0.314246i	$-0.898248\pi$
$997$	3.39072	−	10.4356i	0.00340093	−	0.0104670i	0.952743	+	0.303779i	$0.0982484\pi$
$998$	−165.009	+	53.6147i	−0.165340	+	0.0537221i
$999$	253.040	−	300.843i	0.253294	−	0.301144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.q.245.4		24
3.2	odd	2	inner	363.3.h.q.245.3		24
11.2	odd	10		363.3.b.k.122.4	yes	6
11.3	even	5	inner	363.3.h.q.269.4		24
11.4	even	5	inner	363.3.h.q.323.3		24
11.5	even	5	inner	363.3.h.q.251.3		24
11.6	odd	10		363.3.h.p.251.4		24
11.7	odd	10		363.3.h.p.323.4		24
11.8	odd	10		363.3.h.p.269.3		24
11.9	even	5		363.3.b.j.122.3	✓	6
11.10	odd	2		363.3.h.p.245.3		24
33.2	even	10		363.3.b.k.122.3	yes	6
33.5	odd	10	inner	363.3.h.q.251.4		24
33.8	even	10		363.3.h.p.269.4		24
33.14	odd	10	inner	363.3.h.q.269.3		24
33.17	even	10		363.3.h.p.251.3		24
33.20	odd	10		363.3.b.j.122.4	yes	6
33.26	odd	10	inner	363.3.h.q.323.4		24
33.29	even	10		363.3.h.p.323.3		24
33.32	even	2		363.3.h.p.245.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.3.b.j.122.3	✓	6	11.9	even	5
363.3.b.j.122.4	yes	6	33.20	odd	10
363.3.b.k.122.3	yes	6	33.2	even	10
363.3.b.k.122.4	yes	6	11.2	odd	10
363.3.h.p.245.3		24	11.10	odd	2
363.3.h.p.245.4		24	33.32	even	2
363.3.h.p.251.3		24	33.17	even	10
363.3.h.p.251.4		24	11.6	odd	10
363.3.h.p.269.3		24	11.8	odd	10
363.3.h.p.269.4		24	33.8	even	10
363.3.h.p.323.3		24	33.29	even	10
363.3.h.p.323.4		24	11.7	odd	10
363.3.h.q.245.3		24	3.2	odd	2	inner
363.3.h.q.245.4		24	1.1	even	1	trivial
363.3.h.q.251.3		24	11.5	even	5	inner
363.3.h.q.251.4		24	33.5	odd	10	inner
363.3.h.q.269.3		24	33.14	odd	10	inner
363.3.h.q.269.4		24	11.3	even	5	inner
363.3.h.q.323.3		24	11.4	even	5	inner
363.3.h.q.323.4		24	33.26	odd	10	inner

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.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.399998 + 0.550550i) q^{2} +(2.97531 + 0.384091i) q^{3} +(1.09296 - 3.36379i) q^{4} +(-3.81474 + 5.25053i) q^{5} +(0.978656 + 1.79169i) q^{6} +(2.89410 - 8.90713i) q^{7} +(4.87795 - 1.58494i) q^{8} +(8.70495 + 2.28558i) q^{9} -4.41657 q^{10} +(4.54390 - 9.58852i) q^{12} +(3.37472 - 2.45188i) q^{13} +(6.06145 - 1.96948i) q^{14} +(-13.3667 + 14.1568i) q^{15} +(-8.62188 - 6.26416i) q^{16} +(17.5904 - 24.2111i) q^{17} +(2.22363 + 5.70673i) q^{18} +(3.18032 + 9.78800i) q^{19} +(13.4923 + 18.5706i) q^{20} +(12.0320 - 25.3899i) q^{21} +27.8850i q^{23} +(15.1222 - 2.84212i) q^{24} +(-5.29047 - 16.2824i) q^{25} +(2.69976 + 0.877206i) q^{26} +(25.0221 + 10.1438i) q^{27} +(-26.7986 - 19.4703i) q^{28} +(15.3590 + 4.99043i) q^{29} +(-13.1407 - 1.69636i) q^{30} +(14.2887 - 10.3813i) q^{31} -27.7684i q^{32} +20.3655 q^{34} +(35.7270 + 49.1739i) q^{35} +(17.2024 - 26.7836i) q^{36} +(4.49918 - 13.8470i) q^{37} +(-4.11666 + 5.66610i) q^{38} +(10.9826 - 5.99890i) q^{39} +(-10.2863 + 31.6580i) q^{40} +(-33.2920 + 10.8172i) q^{41} +(18.7912 - 3.53168i) q^{42} -64.3417 q^{43} +(-45.2076 + 36.9867i) q^{45} +(-15.3521 + 11.1539i) q^{46} +(-9.94471 + 3.23123i) q^{47} +(-23.2468 - 21.9494i) q^{48} +(-31.3193 - 22.7548i) q^{49} +(6.84809 - 9.42559i) q^{50} +(61.6361 - 65.2792i) q^{51} +(-4.55916 - 14.0317i) q^{52} +(35.5031 + 48.8658i) q^{53} +(4.42410 + 17.8334i) q^{54} -48.0356i q^{56} +(5.70294 + 30.3439i) q^{57} +(3.39607 + 10.4520i) q^{58} +(-38.6761 - 12.5666i) q^{59} +(33.0111 + 60.4356i) q^{60} +(-19.0197 - 13.8186i) q^{61} +(11.4309 + 3.71411i) q^{62} +(45.5510 - 70.9214i) q^{63} +(-19.1997 + 13.9494i) q^{64} +27.0724i q^{65} +30.8376 q^{67} +(-62.2154 - 85.6321i) q^{68} +(-10.7104 + 82.9665i) q^{69} +(-12.7820 + 39.3389i) q^{70} +(0.585238 - 0.805511i) q^{71} +(46.0849 - 2.64790i) q^{72} +(-28.8838 + 88.8953i) q^{73} +(9.42314 - 3.06176i) q^{74} +(-9.48688 - 50.4772i) q^{75} +36.4007 q^{76} +(7.69570 + 3.64691i) q^{78} +(91.4806 - 66.4645i) q^{79} +(65.7804 - 21.3733i) q^{80} +(70.5522 + 39.7917i) q^{81} +(-19.2722 - 14.0020i) q^{82} +(-61.1711 + 84.1948i) q^{83} +(-72.2557 - 68.2233i) q^{84} +(60.0184 + 184.718i) q^{85} +(-25.7365 - 35.4233i) q^{86} +(43.7809 + 20.7473i) q^{87} -20.3993i q^{89} +(-38.4460 - 10.0944i) q^{90} +(-12.0724 - 37.1551i) q^{91} +(93.7992 + 30.4772i) q^{92} +(46.5005 - 25.3995i) q^{93} +(-5.75681 - 4.18257i) q^{94} +(-63.5243 - 20.6403i) q^{95} +(10.6656 - 82.6195i) q^{96} +(-153.778 + 111.726i) q^{97} -26.3447i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3} + 18 q^{4} + 10 q^{6} + 22 q^{9} + 72 q^{10} + 56 q^{12} + 42 q^{13} - 28 q^{15} - 30 q^{16} - 94 q^{18} - 84 q^{19} - 112 q^{21} - 48 q^{24} + 108 q^{25} + 38 q^{27} - 132 q^{28} + 148 q^{30}+ \cdots - 126 q^{97}+O(q^{100}) \) 24 * q - 4 * q^3 + 18 * q^4 + 10 * q^6 + 22 * q^9 + 72 * q^10 + 56 * q^12 + 42 * q^13 - 28 * q^15 - 30 * q^16 - 94 * q^18 - 84 * q^19 - 112 * q^21 - 48 * q^24 + 108 * q^25 + 38 * q^27 - 132 * q^28 + 148 * q^30 + 264 * q^34 - 46 * q^36 + 42 * q^37 + 82 * q^39 + 294 * q^40 + 206 * q^42 - 624 * q^43 - 472 * q^45 + 60 * q^46 + 88 * q^48 - 138 * q^49 - 182 * q^51 - 114 * q^52 + 560 * q^54 + 24 * q^57 + 54 * q^58 + 562 * q^60 - 264 * q^61 + 122 * q^63 - 294 * q^64 + 96 * q^67 - 152 * q^69 - 336 * q^70 + 306 * q^72 - 72 * q^73 - 62 * q^75 - 1632 * q^76 - 776 * q^78 + 250 * q^81 - 798 * q^82 - 328 * q^84 - 330 * q^85 + 1848 * q^87 + 230 * q^90 - 300 * q^91 + 266 * q^93 - 120 * q^94 + 386 * q^96 - 126 * q^97

Introduction

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Modular forms

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