LMFDB - Embedded newform 363.3.h.q.245.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(245,363)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			245.3
Character	$\chi$	$=$	363.245
Dual form			363.3.h.q.323.3

$q$-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} +(-2.18131 + 2.05958i) q^{3} +(1.09296 - 3.36379i) q^{4} +(3.81474 - 5.25053i) q^{5} +(2.00642 + 0.377094i) q^{6} +(2.89410 - 8.90713i) q^{7} +(-4.87795 + 1.58494i) q^{8} +(0.516261 - 8.98518i) q^{9} -4.41657 q^{10} +(4.54390 + 9.58852i) q^{12} +(3.37472 - 2.45188i) q^{13} +(-6.06145 + 1.96948i) q^{14} +(2.49276 + 19.3098i) q^{15} +(-8.62188 - 6.26416i) q^{16} +(-17.5904 + 24.2111i) q^{17} +(-5.15329 + 3.30982i) q^{18} +(3.18032 + 9.78800i) q^{19} +(-13.4923 - 18.5706i) q^{20} +(12.0320 + 25.3899i) q^{21} -27.8850i q^{23} +(7.37603 - 13.5038i) q^{24} +(-5.29047 - 16.2824i) q^{25} +(-2.69976 - 0.877206i) q^{26} +(17.3796 + 20.6628i) q^{27} +(-26.7986 - 19.4703i) q^{28} +(-15.3590 - 4.99043i) q^{29} +(9.63392 - 9.09627i) q^{30} +(14.2887 - 10.3813i) q^{31} +27.7684i q^{32} +20.3655 q^{34} +(-35.7270 - 49.1739i) q^{35} +(-29.6600 - 11.5570i) q^{36} +(4.49918 - 13.8470i) q^{37} +(4.11666 - 5.66610i) q^{38} +(-2.31149 + 12.2988i) q^{39} +(-10.2863 + 31.6580i) q^{40} +(33.2920 - 10.8172i) q^{41} +(9.16562 - 16.7801i) q^{42} -64.3417 q^{43} +(-45.2076 - 36.9867i) q^{45} +(-15.3521 + 11.1539i) q^{46} +(9.94471 - 3.23123i) q^{47} +(31.7086 - 4.09335i) q^{48} +(-31.3193 - 22.7548i) q^{49} +(-6.84809 + 9.42559i) q^{50} +(-11.4945 - 89.0408i) q^{51} +(-4.55916 - 14.0317i) q^{52} +(-35.5031 - 48.8658i) q^{53} +(4.42410 - 17.8334i) q^{54} +48.0356i q^{56} +(-27.0964 - 14.8006i) q^{57} +(3.39607 + 10.4520i) q^{58} +(38.6761 + 12.5666i) q^{59} +(67.6786 + 12.7198i) q^{60} +(-19.0197 - 13.8186i) q^{61} +(-11.4309 - 3.71411i) q^{62} +(-78.5381 - 30.6024i) q^{63} +(-19.1997 + 13.9494i) q^{64} -27.0724i q^{65} +30.8376 q^{67} +(62.2154 + 85.6321i) q^{68} +(57.4314 + 60.8259i) q^{69} +(-12.7820 + 39.3389i) q^{70} +(-0.585238 + 0.805511i) q^{71} +(11.7227 + 44.6475i) q^{72} +(-28.8838 + 88.8953i) q^{73} +(-9.42314 + 3.06176i) q^{74} +(45.0751 + 24.6209i) q^{75} +36.4007 q^{76} +(7.69570 - 3.64691i) q^{78} +(91.4806 - 66.4645i) q^{79} +(-65.7804 + 21.3733i) q^{80} +(-80.4669 - 9.27740i) q^{81} +(-19.2722 - 14.0020i) q^{82} +(61.1711 - 84.1948i) q^{83} +(98.5567 - 12.7230i) q^{84} +(60.0184 + 184.718i) q^{85} +(25.7365 + 35.4233i) q^{86} +(43.7809 - 20.7473i) q^{87} +20.3993i q^{89} +(-2.28010 + 39.6836i) q^{90} +(-12.0724 - 37.1551i) q^{91} +(-93.7992 - 30.4772i) q^{92} +(-9.78689 + 52.0735i) q^{93} +(-5.75681 - 4.18257i) q^{94} +(63.5243 + 20.6403i) q^{95} +(-57.1912 - 60.5715i) 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	0.697224	−	0.716854i	$-0.254418\pi$
$2$	−0.399998	−	0.550550i	−0.199999	−	0.275275i	−0.897222	+	0.441579i	$0.854418\pi$
$3$	−2.18131	+	2.05958i	−0.727105	+	0.686527i
$3$	−2.18131	+	2.05958i	−0.727105	+	0.686527i
$4$	1.09296	−	3.36379i	0.273240	−	0.840947i
$5$	3.81474	−	5.25053i	0.762947	−	1.05011i	−0.234016	−	0.972233i	$-0.575187\pi$
$5$	3.81474	−	5.25053i	0.762947	−	1.05011i	0.996963	−	0.0778742i	$-0.0248132\pi$
$6$	2.00642	+	0.377094i	0.334404	+	0.0628491i
$7$	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
$9$	0.516261	−	8.98518i	0.0573624	−	0.998353i
$10$	−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
$15$	2.49276	+	19.3098i	0.166184	+	1.28732i
$16$	−8.62188	−	6.26416i	−0.538867	−	0.391510i
$17$	−17.5904	+	24.2111i	−1.03473	+	1.42418i	−0.133391	+	0.991064i	$0.542587\pi$
$17$	−17.5904	+	24.2111i	−1.03473	+	1.42418i	−0.901337	+	0.433118i	$0.857413\pi$
$18$	−5.15329	+	3.30982i	−0.286294	+	0.183879i
$19$	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	$-0.792695\pi$
$23$		−	27.8850i		−	1.21239i	0.795316	−	0.606195i	$-0.207305\pi$
$24$	7.37603	−	13.5038i	0.307335	−	0.562658i
$25$	−5.29047	−	16.2824i	−0.211619	−	0.651296i
$26$	−2.69976	−	0.877206i	−0.103837	−	0.0337387i
$27$	17.3796	+	20.6628i	0.643688	+	0.765288i
$28$	−26.7986	−	19.4703i	−0.957092	−	0.695368i
$29$	−15.3590	−	4.99043i	−0.529619	−	0.172084i	0.0319872	−	0.999488i	$-0.489816\pi$
$29$	−15.3590	−	4.99043i	−0.529619	−	0.172084i	−0.561606	+	0.827405i	$0.689816\pi$
$30$	9.63392	−	9.09627i	0.321131	−	0.303209i
$31$	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
$36$	−29.6600	−	11.5570i	−0.823889	−	0.321029i
$37$	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
$39$	−2.31149	+	12.2988i	−0.0592689	+	0.315355i
$40$	−10.2863	+	31.6580i	−0.257158	+	0.791450i
$41$	33.2920	−	10.8172i	0.812001	−	0.263835i	0.126556	−	0.991959i	$-0.459608\pi$
$41$	33.2920	−	10.8172i	0.812001	−	0.263835i	0.685445	+	0.728125i	$0.259608\pi$
$42$	9.16562	−	16.7801i	0.218229	−	0.399526i
$43$	−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	−0.201304	−	0.979529i	$-0.564518\pi$
$47$	9.94471	−	3.23123i	0.211590	−	0.0687496i	0.412894	+	0.910779i	$0.364518\pi$
$48$	31.7086	−	4.09335i	0.660595	−	0.0852780i
$49$	−31.3193	−	22.7548i	−0.639170	−	0.464384i
$50$	−6.84809	+	9.42559i	−0.136962	+	0.188512i
$51$	−11.4945	−	89.0408i	−0.225383	−	1.74590i
$52$	−4.55916	−	14.0317i	−0.0876762	−	0.269840i
$53$	−35.5031	−	48.8658i	−0.669870	−	0.921997i	0.329888	−	0.944020i	$-0.392989\pi$
$53$	−35.5031	−	48.8658i	−0.669870	−	0.921997i	−0.999757	+	0.0220234i	$0.992989\pi$
$54$	4.42410	−	17.8334i	0.0819277	−	0.330248i
$55$		0			0
$56$			48.0356i			0.857778i
$57$	−27.0964	−	14.8006i	−0.475376	−	0.259660i
$58$	3.39607	+	10.4520i	0.0585529	+	0.180207i
$59$	38.6761	+	12.5666i	0.655528	+	0.212994i	0.617850	−	0.786296i	$-0.288004\pi$
$59$	38.6761	+	12.5666i	0.655528	+	0.212994i	0.0376779	+	0.999290i	$0.488004\pi$
$60$	67.6786	+	12.7198i	1.12798	+	0.211996i
$61$	−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
$63$	−78.5381	−	30.6024i	−1.24664	−	0.485753i
$64$	−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
$69$	57.4314	+	60.8259i	0.832339	+	0.881535i
$70$	−12.7820	+	39.3389i	−0.182600	+	0.561985i
$71$	−0.585238	+	0.805511i	−0.00824279	+	0.0113452i	−0.813118	−	0.582098i	$-0.802232\pi$
$71$	−0.585238	+	0.805511i	−0.00824279	+	0.0113452i	0.804876	+	0.593443i	$0.202232\pi$
$72$	11.7227	+	44.6475i	0.162815	+	0.620105i
$73$	−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
$75$	45.0751	+	24.6209i	0.601001	+	0.328278i
$76$	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
$81$	−80.4669	−	9.27740i	−0.993419	−	0.114536i
$82$	−19.2722	−	14.0020i	−0.235026	−	0.170757i
$83$	61.1711	−	84.1948i	0.737001	−	1.01439i	−0.261784	−	0.965126i	$-0.584311\pi$
$83$	61.1711	−	84.1948i	0.737001	−	1.01439i	0.998786	−	0.0492686i	$-0.0156890\pi$
$84$	98.5567	−	12.7230i	1.17329	−	0.151464i
$85$	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	$0.0365595\pi$
$89$			20.3993i			0.229206i	−0.993411	+	0.114603i	$0.963440\pi$
$90$	−2.28010	+	39.6836i	−0.0253345	+	0.440929i
$91$	−12.0724	−	37.1551i	−0.132664	−	0.408298i
$92$	−93.7992	−	30.4772i	−1.01956	−	0.331274i
$93$	−9.78689	+	52.0735i	−0.105235	+	0.559930i
$94$	−5.75681	−	4.18257i	−0.0612427	−	0.0444954i
$95$	63.5243	+	20.6403i	0.668677	+	0.217266i
$96$	−57.1912	−	60.5715i	−0.595741	−	0.630953i
$97$	−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	0.924750	−	0.380575i	$-0.124274\pi$
$101$	27.9808	+	38.5123i	0.277038	+	0.381310i	−0.647712	+	0.761885i	$0.724274\pi$
$102$	−44.4236	+	41.9444i	−0.435525	+	0.411220i
$103$	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
$105$	179.209	+	33.6813i	1.70676	+	0.320774i
$106$	−12.7019	+	39.0924i	−0.119829	+	0.368797i
$107$	64.9745	−	21.1115i	0.607238	−	0.197304i	0.0107723	−	0.999942i	$-0.496571\pi$
$107$	64.9745	−	21.1115i	0.607238	−	0.197304i	0.596466	+	0.802638i	$0.296571\pi$
$108$	88.5004	−	35.8776i	0.819448	−	0.332200i
$109$	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	0.513399	−	0.858150i	$-0.328386\pi$
$113$	161.947	−	52.6196i	1.43316	−	0.465661i	0.919757	+	0.392489i	$0.128386\pi$
$114$	2.69005	+	20.8381i	0.0235970	+	0.182791i
$115$	−146.411	−	106.374i	−1.27314	−	0.924990i
$116$	−33.5735	+	46.2099i	−0.289427	+	0.398361i
$117$	−20.2883	−	31.5883i	−0.173405	−	0.269985i
$118$	−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
$123$	−50.3414	+	92.1634i	−0.409280	+	0.749296i
$124$	−19.3036	−	59.4104i	−0.155674	−	0.479116i
$125$	48.6363	+	15.8029i	0.389090	+	0.126423i
$126$	14.5669	+	55.4800i	0.115610	+	0.440317i
$127$	−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
$129$	140.349	−	132.517i	1.08798	−	1.02726i
$130$	−14.9047	+	10.8289i	−0.114651	+	0.0832991i
$131$		−	174.147i		−	1.32936i	−0.747126	−	0.664682i	$-0.768567\pi$
$131$		−	174.147i		−	1.32936i	0.747126	−	0.664682i	$-0.231433\pi$
$132$		0			0
$133$	96.3872			0.724716
$134$	−12.3350	−	16.9777i	−0.0920521	−	0.126699i
$135$	174.789	−	12.4290i	1.29473	−	0.0920664i
$136$	47.4319	−	145.980i	0.348764	−	1.07338i
$137$	−47.7841	+	65.7692i	−0.348789	+	0.480067i	−0.946983	−	0.321285i	$-0.895885\pi$
$137$	−47.7841	+	65.7692i	−0.348789	+	0.480067i	0.598194	+	0.801352i	$0.295885\pi$
$138$	10.5153	−	55.9490i	0.0761976	−	0.405428i
$139$	−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
$141$	−15.0376	+	27.5303i	−0.106649	+	0.195250i
$142$	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
$147$	115.183	−	14.8692i	0.783555	−	0.101151i
$148$	−41.6611	−	30.2686i	−0.281494	−	0.204517i
$149$	116.342	−	160.131i	0.780817	−	1.07470i	−0.214374	−	0.976752i	$-0.568771\pi$
$149$	116.342	−	160.131i	0.780817	−	1.07470i	0.995191	−	0.0979512i	$-0.0312289\pi$
$150$	−4.47492	−	34.6644i	−0.0298328	−	0.231096i
$151$	−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
$156$	38.8443	+	21.2175i	0.249002	+	0.136010i
$157$	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
$159$	178.087	+	33.4702i	1.12004	+	0.210505i
$160$	145.799	+	105.929i	0.911242	+	0.662056i
$161$	−248.375	−	80.7020i	−1.54270	−	0.501255i
$162$	27.0789	+	48.0120i	0.167154	+	0.296370i
$163$	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	0.495593	−	0.868555i	$-0.334951\pi$
$167$	−80.7610	−	111.158i	−0.483599	−	0.665617i	−0.979192	+	0.202938i	$0.934951\pi$
$168$	−98.9331	−	104.781i	−0.588887	−	0.623694i
$169$	−46.8468	+	144.180i	−0.277200	+	0.853135i
$170$	77.6891	−	106.930i	0.456994	−	0.628999i
$171$	89.5889	−	23.5225i	0.523911	−	0.137559i
$172$	−70.3230	+	216.432i	−0.408855	+	1.25833i
$173$	1.00649	−	0.327028i	0.00581785	−	0.00189034i	−0.306107	−	0.951997i	$-0.599026\pi$
$173$	1.00649	−	0.327028i	0.00581785	−	0.00189034i	0.311924	+	0.950107i	$0.399026\pi$
$174$	−28.9347	−	15.8047i	−0.166291	−	0.0908314i
$175$	−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	−0.530257	−	0.847837i	$-0.677904\pi$
$179$	−82.5005	+	26.8060i	−0.460897	+	0.149754i	0.0693597	+	0.997592i	$0.477904\pi$
$180$	−173.826	+	111.644i	−0.965699	+	0.620243i
$181$	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
$183$	69.9485	−	9.02984i	0.382232	−	0.0493434i
$184$	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
$189$	234.344	−	95.0019i	1.23992	−	0.502656i
$190$	−14.0461	−	43.2294i	−0.0739267	−	0.227523i
$191$	−27.2489	−	8.85370i	−0.142664	−	0.0463545i	0.236814	−	0.971555i	$-0.423897\pi$
$191$	−27.2489	−	8.85370i	−0.142664	−	0.0463545i	−0.379479	+	0.925200i	$0.623897\pi$
$192$	13.1506	−	69.9712i	0.0684929	−	0.364433i
$193$	−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
$195$	55.7577	+	59.0533i	0.285937	+	0.302838i
$196$	−110.773	+	80.4814i	−0.565169	+	0.410620i
$197$			336.692i			1.70910i	0.519370	+	0.854549i	$0.326166\pi$
$197$			336.692i			1.70910i	−0.519370	+	0.854549i	$0.673834\pi$
$198$		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
$201$	−67.2666	+	63.5126i	−0.334660	+	0.315983i
$202$	10.0107	−	30.8096i	0.0495577	−	0.152523i
$203$	−88.9007	+	122.361i	−0.437935	+	0.602765i
$204$	−312.077	−	58.6530i	−1.52979	−	0.287515i
$205$	70.2040	−	216.066i	0.342459	−	1.05398i
$206$	−34.0921	+	11.0772i	−0.165495	+	0.0537727i
$207$	−250.552	−	14.3959i	−1.21039	−	0.0695456i
$208$	−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
$213$	−0.382426	−	2.96242i	−0.00179543	−	0.0139081i
$214$	−37.6126	−	27.3271i	−0.175760	−	0.127697i
$215$	−245.447	+	337.828i	−1.14161	+	1.57129i
$216$	−117.526	−	73.2465i	−0.544102	−	0.339104i
$217$	−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
$222$	14.2489	−	26.0864i	0.0641841	−	0.117506i
$223$	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
$225$	−149.032	+	39.1299i	−0.662363	+	0.173911i
$226$	−93.7480	−	68.1119i	−0.414814	−	0.301380i
$227$	8.58713	+	2.79013i	0.0378288	+	0.0122913i	0.327870	−	0.944723i	$-0.393669\pi$
$227$	8.58713	+	2.79013i	0.0378288	+	0.0122913i	−0.290041	+	0.957014i	$0.593669\pi$
$228$	−79.4015	+	74.9702i	−0.348252	+	0.328817i
$229$	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	0.762025	−	0.647548i	$-0.224206\pi$
$233$	−20.8090	−	28.6411i	−0.0893089	−	0.122923i	−0.851333	+	0.524625i	$0.824206\pi$
$234$	−9.27564	+	23.8050i	−0.0396395	+	0.101731i
$235$	20.9708	−	64.5413i	0.0892373	−	0.274644i
$236$	84.5431	−	116.364i	0.358233	−	0.493066i
$237$	−62.6588	+	333.392i	−0.264383	+	1.40672i
$238$	58.9399	−	181.398i	0.247647	−	0.762178i
$239$	124.397	−	40.4191i	0.520491	−	0.169118i	−0.0369772	−	0.999316i	$-0.511773\pi$
$239$	124.397	−	40.4191i	0.520491	−	0.169118i	0.557468	+	0.830198i	$0.311773\pi$
$240$	99.4676	−	182.102i	0.414448	−	0.758758i
$241$	−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
$246$	70.8770	−	9.14970i	0.288118	−	0.0371939i
$247$	34.7317	+	25.2340i	0.140614	+	0.102162i
$248$	−53.2456	+	73.2863i	−0.214700	+	0.295509i
$249$	39.9725	+	309.642i	0.160532	+	1.24354i
$250$	−10.7541	−	33.0978i	−0.0430165	−	0.132391i
$251$	−237.797	−	327.300i	−0.947399	−	1.30398i	−0.952673	−	0.303997i	$-0.901679\pi$
$251$	−237.797	−	327.300i	−0.947399	−	1.30398i	0.00527361	−	0.999986i	$-0.498321\pi$
$252$	−188.779	+	230.738i	−0.749124	+	0.915628i
$253$		0			0
$254$			98.8936i			0.389345i
$255$	−511.360	−	279.315i	−2.00533	−	1.09535i
$256$	2.58048	+	7.94189i	0.0100800	+	0.0310230i
$257$	130.624	+	42.4423i	0.508265	+	0.165145i	0.551913	−	0.833902i	$-0.313898\pi$
$257$	130.624	+	42.4423i	0.508265	+	0.165145i	−0.0436481	+	0.999047i	$0.513898\pi$
$258$	−129.097	−	24.2629i	−0.500374	−	0.0940422i
$259$	−110.316	−	80.1495i	−0.425932	−	0.309457i
$260$	−91.0657	−	29.5891i	−0.350253	−	0.113804i
$261$	−52.7691	+	135.427i	−0.202180	+	0.518876i
$262$	−95.8764	+	69.6583i	−0.365941	+	0.265871i
$263$			138.001i			0.524720i	0.964970	+	0.262360i	$0.0845008\pi$
$263$			138.001i			0.524720i	−0.964970	+	0.262360i	$0.915499\pi$
$264$		0			0
$265$	−392.007			−1.47927
$266$	−38.5547	−	53.0659i	−0.144942	−	0.199496i
$267$	−42.0140	−	44.4973i	−0.157356	−	0.166657i
$268$	33.7044	−	103.731i	0.125763	−	0.387057i
$269$	18.1588	−	24.9935i	0.0675049	−	0.0929125i	−0.773930	−	0.633272i	$-0.781712\pi$
$269$	18.1588	−	24.9935i	0.0675049	−	0.0929125i	0.841434	+	0.540359i	$0.181712\pi$
$270$	−76.7580	−	91.2585i	−0.284289	−	0.337995i
$271$	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
$273$	102.858	+	56.1828i	0.376768	+	0.205798i
$274$	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
$279$	−85.9013	−	133.746i	−0.307890	−	0.479375i
$280$	252.212	+	183.243i	0.900758	+	0.654439i
$281$	233.485	−	321.364i	0.830907	−	1.14365i	−0.156847	−	0.987623i	$-0.550133\pi$
$281$	233.485	−	321.364i	0.830907	−	1.14365i	0.987754	−	0.156022i	$-0.0498672\pi$
$282$	21.1718	−	2.73312i	0.0750772	−	0.00969191i
$283$	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
$288$	249.504	+	14.3357i	0.866332	+	0.0497768i
$289$	−187.449	−	576.909i	−0.648613	−	1.99622i
$290$	67.8338	+	22.0405i	0.233910	+	0.0760019i
$291$	105.329	−	560.427i	0.361954	−	1.92587i
$292$	267.456	+	194.318i	0.915945	+	0.665473i
$293$	−347.720	−	112.981i	−1.18676	−	0.385601i	−0.351885	−	0.936043i	$-0.614459\pi$
$293$	−347.720	−	112.981i	−1.18676	−	0.385601i	−0.834873	+	0.550442i	$0.814459\pi$
$294$	−54.2590	−	57.4661i	−0.184555	−	0.195463i
$295$	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
$300$	132.085	−	124.713i	0.440283	−	0.415711i
$301$	−186.211	+	573.100i	−0.618643	+	1.90399i
$302$	−35.5658	+	48.9521i	−0.117768	+	0.162093i
$303$	−140.354	−	26.3787i	−0.463215	−	0.0870583i
$304$	33.8933	−	104.313i	0.111491	−	0.343135i
$305$	−145.110	+	47.1492i	−0.475771	+	0.154588i
$306$	10.5139	−	182.988i	0.0343592	−	0.597999i
$307$	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	0.253985	−	0.967208i	$-0.418259\pi$
$311$	319.700	−	103.877i	1.02797	−	0.334009i	0.773989	+	0.633199i	$0.218259\pi$
$312$	−8.21762	−	63.6567i	−0.0263385	−	0.204028i
$313$	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
$315$	−460.281	+	295.627i	−1.46121	+	0.938497i
$316$	−123.588	−	380.364i	−0.391101	−	1.20368i
$317$	−91.8833	−	126.467i	−0.289853	−	0.398948i	0.639114	−	0.769112i	$-0.279301\pi$
$317$	−91.8833	−	126.467i	−0.289853	−	0.398948i	−0.928966	+	0.370164i	$0.879301\pi$
$318$	−52.8072	−	111.433i	−0.166060	−	0.350420i
$319$		0			0
$320$			154.022i			0.481318i
$321$	−98.2490	+	179.871i	−0.306072	+	0.560346i
$322$	54.9191	+	169.024i	0.170556	+	0.524918i
$323$	−292.921	−	95.1758i	−0.906877	−	0.294662i
$324$	−119.154	+	260.534i	−0.367761	+	0.804117i
$325$	−57.7764	−	41.9770i	−0.177773	−	0.129160i
$326$	−90.5082	−	29.4079i	−0.277633	−	0.0902083i
$327$	−82.2910	+	77.6986i	−0.251655	+	0.237610i
$328$	−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
$333$	−122.095	−	47.5746i	−0.366653	−	0.142867i
$334$	−28.8938	+	88.9259i	−0.0865083	+	0.266245i
$335$	117.638	−	161.914i	0.351157	−	0.483326i
$336$	55.3079	−	294.279i	0.164607	−	0.875830i
$337$	−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
$339$	−244.882	+	448.322i	−0.722366	+	1.32248i
$340$	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
$345$	538.454	−	69.5105i	1.56074	−	0.201480i
$346$	−0.582638	−	0.423311i	−0.00168393	−	0.00122344i
$347$	−353.427	+	486.450i	−1.01852	+	1.40187i	−0.105285	+	0.994442i	$0.533575\pi$
$347$	−353.427	+	486.450i	−1.01852	+	1.40187i	−0.913236	+	0.407431i	$0.866425\pi$
$348$	−21.9387	−	169.946i	−0.0630424	−	0.488350i
$349$	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	$0.0787386\pi$
$353$			172.864i			0.489699i	−0.969561	+	0.244850i	$0.921261\pi$
$354$	72.8618	+	39.7985i	0.205824	+	0.112425i
$355$	1.99683	+	6.14562i	0.00562488	+	0.0173116i
$356$	68.6190	+	22.2957i	0.192750	+	0.0626282i
$357$	−826.364	−	155.310i	−2.31474	−	0.435042i
$358$	47.7581	+	34.6983i	0.133402	+	0.0969226i
$359$	573.248	+	186.259i	1.59679	+	0.518829i	0.966311	−	0.257377i	$-0.0828583\pi$
$359$	573.248	+	186.259i	1.59679	+	0.518829i	0.630479	+	0.776206i	$0.282858\pi$
$360$	279.143	+	108.768i	0.775396	+	0.302134i
$361$	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
$366$	−32.9506	−	34.8982i	−0.0900290	−	0.0953503i
$367$	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
$369$	−80.0074	−	304.719i	−0.216822	−	0.825798i
$370$	−19.8709	+	61.1563i	−0.0537051	+	0.165287i
$371$	−538.004	+	174.808i	−1.45015	+	0.471181i
$372$	164.468	+	89.8354i	0.442117	+	0.241493i
$373$	−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
$378$	−146.040	−	91.0176i	−0.386350	−	0.240787i
$379$	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
$381$	432.376	−	55.8166i	1.13485	−	0.146500i
$382$	6.02509	+	18.5433i	0.0157725	+	0.0485428i
$383$	354.229	+	487.554i	0.924880	+	1.27299i	0.961824	+	0.273670i	$0.0882378\pi$
$383$	354.229	+	487.554i	0.924880	+	1.27299i	−0.0369437	+	0.999317i	$0.511762\pi$
$384$	−344.903	+	163.446i	−0.898184	+	0.425640i
$385$		0			0
$386$			8.63898i			0.0223808i
$387$	−33.2171	+	578.122i	−0.0858324	+	1.49386i
$388$	207.750	+	639.388i	0.535437	+	1.64791i
$389$	−432.894	−	140.656i	−1.11284	−	0.361583i	−0.305808	−	0.952093i	$-0.598927\pi$
$389$	−432.894	−	140.656i	−1.11284	−	0.361583i	−0.807030	+	0.590510i	$0.798927\pi$
$390$	10.2088	−	54.3186i	0.0261765	−	0.139278i
$391$	675.126	+	490.508i	1.72666	+	1.25450i
$392$	188.839	+	61.3576i	0.481733	+	0.156524i
$393$	358.669	+	379.869i	0.912644	+	0.966587i
$394$	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
$399$	−210.251	+	198.517i	−0.526944	+	0.497537i
$400$	−56.3818	+	173.525i	−0.140954	+	0.433813i
$401$	148.146	−	203.906i	0.369442	−	0.508494i	−0.583307	−	0.812252i	$-0.698241\pi$
$401$	148.146	−	203.906i	0.369442	−	0.508494i	0.952749	+	0.303758i	$0.0982414\pi$
$402$	61.8733	+	11.6287i	0.153914	+	0.0289271i
$403$	22.7665	−	70.0681i	0.0564926	−	0.173866i
$404$	160.129	−	52.0291i	0.396359	−	0.128785i
$405$	−355.672	+	387.104i	−0.878201	+	0.955812i
$406$	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
$411$	−31.2248	−	241.878i	−0.0759726	−	0.588512i
$412$	−150.726	−	109.509i	−0.365840	−	0.265798i
$413$	223.865	−	308.124i	0.542047	−	0.746064i
$414$	92.2944	+	143.699i	0.222933	+	0.347100i
$415$	−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	$-0.885186\pi$
$419$		−	295.753i		−	0.705855i	0.935651	−	0.352927i	$-0.114814\pi$
$420$	309.166	−	566.010i	0.736109	−	1.34764i
$421$	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
$423$	−23.8991	−	91.0232i	−0.0564991	−	0.215185i
$424$	250.632	+	182.095i	0.591113	+	0.429469i
$425$	487.276	+	158.326i	1.14653	+	0.372531i
$426$	−1.47799	+	1.39550i	−0.00346945	+	0.00327583i
$427$	−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	$0.0245834\pi$
$431$	328.552	+	452.213i	0.762301	+	1.04922i	−0.234718	+	0.972064i	$0.575417\pi$
$432$	−20.4095	−	287.020i	−0.0472443	−	0.664399i
$433$	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
$435$	58.0781	−	309.019i	0.133513	−	0.710387i
$436$	41.2325	−	126.900i	0.0945698	−	0.291056i
$437$	272.938	−	88.6831i	0.624573	−	0.202936i
$438$	−91.4750	+	167.469i	−0.208847	+	0.382350i
$439$	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	−0.594962	−	0.803754i	$-0.702833\pi$
$443$	−267.511	+	86.9195i	−0.603862	+	0.196207i	−0.00889983	+	0.999960i	$0.502833\pi$
$444$	153.216	−	19.7791i	0.345082	−	0.0445476i
$445$	107.107	+	77.8180i	0.240690	+	0.174872i
$446$	105.223	−	144.827i	0.235925	−	0.324724i
$447$	76.0241	+	588.911i	0.170076	+	1.31747i
$448$	68.6831	+	211.385i	0.153310	+	0.471841i
$449$	163.228	+	224.664i	0.363536	+	0.500365i	0.951130	−	0.308791i	$-0.0999245\pi$
$449$	163.228	+	224.664i	0.363536	+	0.500365i	−0.587593	+	0.809156i	$0.699925\pi$
$450$	81.1552	+	66.3974i	0.180345	+	0.147550i
$451$		0			0
$452$		−	602.265i		−	1.33245i
$453$	234.099	+	127.869i	0.516775	+	0.282272i
$454$	−1.89873	−	5.84368i	−0.00418222	−	0.0128716i
$455$	−241.137	−	78.3502i	−0.529972	−	0.172198i
$456$	155.633	+	29.2503i	0.341301	+	0.0641454i
$457$	−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
$459$	−805.981	+	57.3120i	−1.75595	+	0.124863i
$460$	−517.841	+	376.234i	−1.12574	+	0.817899i
$461$		−	67.1487i		−	0.145659i	−0.997344	−	0.0728294i	$-0.976797\pi$
$461$		−	67.1487i		−	0.145659i	0.997344	−	0.0728294i	$-0.0232029\pi$
$462$		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
$465$	236.079	+	250.033i	0.507698	+	0.537706i
$466$	−7.44480	+	22.9127i	−0.0159760	+	0.0491690i
$467$	−170.090	+	234.109i	−0.364218	+	0.501303i	−0.951318	−	0.308211i	$-0.900270\pi$
$467$	−170.090	+	234.109i	−0.364218	+	0.501303i	0.587100	+	0.809515i	$0.300270\pi$
$468$	−128.431	+	33.7209i	−0.274425	+	0.0720532i
$469$	89.2473	−	274.675i	0.190293	−	0.585661i
$470$	−43.9215	+	14.2709i	−0.0934499	+	0.0303637i
$471$	−175.708	−	95.9748i	−0.373052	−	0.203768i
$472$	−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
$477$	−457.397	+	293.774i	−0.958904	+	0.615879i
$478$	−72.0114	−	52.3193i	−0.150651	−	0.109455i
$479$	−97.6527	+	134.407i	−0.203868	+	0.280600i	−0.898693	−	0.438579i	$-0.855482\pi$
$479$	−97.6527	+	134.407i	−0.203868	+	0.280600i	0.694825	+	0.719179i	$0.255482\pi$
$480$	−536.202	+	69.2198i	−1.11709	+	0.144208i
$481$	−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
$486$	−157.952	−	48.9580i	−0.325004	−	0.100737i
$487$	−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
$489$	−77.4915	+	412.312i	−0.158469	+	0.843174i
$490$	138.324	+	100.498i	0.282293	+	0.205098i
$491$	−455.169	−	147.893i	−0.927024	−	0.301209i	−0.193679	−	0.981065i	$-0.562042\pi$
$491$	−455.169	−	147.893i	−0.927024	−	0.301209i	−0.733345	+	0.679856i	$0.762042\pi$
$492$	254.997	+	270.069i	0.518286	+	0.548920i
$493$	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
$498$	154.484	−	145.863i	0.310210	−	0.292897i
$499$	−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
$501$	405.104	+	76.1368i	0.808591	+	0.151970i
$502$	−85.0764	+	261.838i	−0.169475	+	0.521590i
$503$	−243.035	+	78.9669i	−0.483171	+	0.156992i	−0.540467	−	0.841365i	$-0.681752\pi$
$503$	−243.035	+	78.9669i	−0.483171	+	0.156992i	0.0572955	+	0.998357i	$0.481752\pi$
$504$	431.608	+	24.7989i	0.856365	+	0.0492042i
$505$	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	−0.358057	−	0.933700i	$-0.616561\pi$
$509$	−50.3488	+	16.3593i	−0.0989171	+	0.0321401i	0.259140	+	0.965840i	$0.416561\pi$
$510$	50.7663	+	393.254i	0.0995417	+	0.771087i
$511$	708.209	+	514.544i	1.38593	+	1.00694i
$512$	302.461	−	416.301i	0.590743	−	0.813089i
$513$	−146.975	+	235.825i	−0.286501	+	0.459699i
$514$	−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
$519$	−1.52193	+	2.78629i	−0.00293242	+	0.00536858i
$520$	42.9082	+	132.058i	0.0825157	+	0.253957i
$521$	829.134	+	269.402i	1.59143	+	0.517086i	0.964968	−	0.262367i	$-0.0845032\pi$
$521$	829.134	+	269.402i	1.59143	+	0.517086i	0.626460	+	0.779454i	$0.284503\pi$
$522$	95.6666	−	25.1183i	0.183269	−	0.0481194i
$523$	−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
$525$	349.753	−	330.234i	0.666197	−	0.629018i
$526$	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
$531$	132.881	−	341.025i	0.250246	−	0.642231i
$532$	105.347	−	324.226i	0.198022	−	0.609448i
$533$	85.8288	−	118.133i	0.161030	−	0.221638i
$534$	−7.69246	+	40.9296i	−0.0144054	+	0.0766472i
$535$	137.014	−	421.686i	0.256101	−	0.788198i
$536$	−150.425	+	48.8759i	−0.280643	+	0.0911864i
$537$	124.750	−	228.389i	0.232310	−	0.425305i
$538$	−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
$543$	−321.840	+	41.5472i	−0.592708	+	0.0765143i
$544$	−672.302	−	488.456i	−1.23585	−	0.897897i
$545$	143.913	−	198.079i	0.264060	−	0.363447i
$546$	−10.2114	−	79.1012i	−0.0187022	−	0.144874i
$547$	−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
$552$	−376.553	−	205.681i	−0.682162	−	0.372610i
$553$	−327.254	−	1007.18i	−0.591779	−	1.82131i
$554$	−103.301	−	33.5645i	−0.186464	−	0.0605858i
$555$	278.599	+	52.3610i	0.501980	+	0.0943441i
$556$	1.94870	+	1.41581i	0.00350485	+	0.00254642i
$557$	697.965	+	226.782i	1.25308	+	0.407150i	0.859023	−	0.511937i	$-0.171072\pi$
$557$	697.965	+	226.782i	1.25308	+	0.407150i	0.394055	+	0.919087i	$0.371072\pi$
$558$	−39.2733	+	100.791i	−0.0703822	+	0.180629i
$559$	−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	$-0.855950\pi$
$563$	−583.990	−	803.794i	−1.03728	−	1.42770i	−0.137947	−	0.990440i	$-0.544050\pi$
$564$	76.1705	+	80.6727i	0.135054	+	0.143037i
$565$	341.502	−	1051.04i	0.604429	−	1.86024i
$566$	27.0360	−	37.2119i	0.0477669	−	0.0657455i
$567$	−315.515	+	689.880i	−0.556463	+	1.21672i
$568$	1.57807	−	4.85681i	0.00277830	−	0.00855073i
$569$	1014.04	−	329.482i	1.78215	−	0.579055i	0.783068	−	0.621936i	$-0.213654\pi$
$569$	1014.04	−	329.482i	1.78215	−	0.579055i	0.999080	+	0.0428814i	$0.0136537\pi$
$570$	119.673	+	65.3678i	0.209953	+	0.114680i
$571$	−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
$576$	115.426	+	179.714i	0.200392	+	0.312003i
$577$	−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
$579$	37.7708	−	4.87593i	0.0652345	−	0.00842130i
$580$	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
$585$	−243.250	−	13.9764i	−0.415812	−	0.0238913i
$586$	76.8856	+	236.629i	0.131204	+	0.403804i
$587$	55.9862	+	18.1910i	0.0953768	+	0.0309898i	0.356317	−	0.934365i	$-0.384032\pi$
$587$	55.9862	+	18.1910i	0.0953768	+	0.0309898i	−0.260940	+	0.965355i	$0.584032\pi$
$588$	75.8732	−	403.701i	0.129036	−	0.686567i
$589$	147.055	+	106.842i	0.249669	+	0.181395i
$590$	−170.816	−	55.5014i	−0.289518	−	0.0940702i
$591$	−693.445	−	734.432i	−1.17334	−	1.24269i
$592$	−125.531	+	91.2039i	−0.212046	+	0.154061i
$593$			149.728i			0.252493i	0.991999	+	0.126247i	$0.0402931\pi$
$593$			149.728i			0.252493i	−0.991999	+	0.126247i	$0.959707\pi$
$594$		0			0
$595$	1819.01			3.05715
$596$	−411.489	−	566.366i	−0.690418	−	0.950278i
$597$	−401.062	+	378.680i	−0.671795	+	0.634304i
$598$	−24.4609	+	75.2828i	−0.0409045	+	0.125891i
$599$	−260.728	+	358.862i	−0.435273	+	0.599102i	−0.969153	−	0.246458i	$-0.920733\pi$
$599$	−260.728	+	358.862i	−0.435273	+	0.599102i	0.533881	+	0.845560i	$0.320733\pi$
$600$	−258.897	−	48.6581i	−0.431495	−	0.0810968i
$601$	−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
$603$	15.9203	−	277.082i	0.0264018	−	0.459506i
$604$	−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
$609$	−58.0926	−	450.007i	−0.0953901	−	0.738927i
$610$	84.0017	+	61.0308i	0.137708	+	0.100051i
$611$	25.6380	−	35.2877i	0.0419608	−	0.0577541i
$612$	801.539	−	514.808i	1.30970	−	0.841189i
$613$	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	$0.0991661\pi$
$617$			378.251i			0.613049i	−0.951863	+	0.306524i	$0.900834\pi$
$618$	51.5512	−	94.3782i	0.0834161	−	0.152715i
$619$	−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
$621$	576.181	−	484.629i	0.927828	−	0.780401i
$622$	−185.069	−	134.460i	−0.297538	−	0.216174i
$623$	181.699	+	59.0377i	0.291652	+	0.0947635i
$624$	96.9712	−	91.5595i	0.155403	−	0.146730i
$625$	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
$630$	346.869	+	135.158i	0.550585	+	0.214536i
$631$	−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
$633$	−99.7477	+	530.732i	−0.157579	+	0.838439i
$634$	−32.8730	+	101.173i	−0.0518501	+	0.159578i
$635$	−896.978	+	291.446i	−1.41256	+	0.458970i
$636$	307.228	−	562.464i	0.483064	−	0.884377i
$637$	−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	−0.874648	−	0.484758i	$-0.838908\pi$
$641$	−831.582	+	270.198i	−1.29732	+	0.421525i	−0.422672	+	0.906283i	$0.638908\pi$
$642$	138.327	−	17.8570i	0.215463	−	0.0278147i
$643$	−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
$645$	−160.388	−	1242.43i	−0.248664	−	1.92624i
$646$	64.7688	+	199.338i	0.100261	+	0.308572i
$647$	436.536	+	600.841i	0.674708	+	0.928656i	0.999855	−	0.0170072i	$-0.00541382\pi$
$647$	436.536	+	600.841i	0.674708	+	0.928656i	−0.325147	+	0.945663i	$0.605414\pi$
$648$	407.218	−	82.2808i	0.628423	−	0.126977i
$649$		0			0
$650$			48.5994i			0.0747684i
$651$	435.501	+	237.879i	0.668973	+	0.365406i
$652$	−152.844	−	470.405i	−0.234423	−	0.721479i
$653$	1057.97	+	343.757i	1.62018	+	0.526427i	0.971983	−	0.235050i	$-0.0755254\pi$
$653$	1057.97	+	343.757i	1.62018	+	0.526427i	0.648192	+	0.761477i	$0.275525\pi$
$654$	75.6931	+	14.2261i	0.115739	+	0.0217524i
$655$	−914.364	−	664.324i	−1.39598	−	1.01424i
$656$	−354.801	−	115.282i	−0.540855	−	0.175734i
$657$	783.828	+	305.420i	1.19304	+	0.464870i
$658$	−53.9155	+	39.1719i	−0.0819385	+	0.0595318i
$659$			829.020i			1.25800i	0.777407	+	0.628998i	$0.216535\pi$
$659$			829.020i			1.25800i	−0.777407	+	0.628998i	$0.783465\pi$
$660$		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
$663$	−257.108	−	272.305i	−0.387795	−	0.410716i
$664$	−164.946	+	507.651i	−0.248412	+	0.764535i
$665$	367.692	−	506.084i	0.552920	−	0.761029i
$666$	22.6457	+	86.2493i	0.0340026	+	0.129503i
$667$	−139.158	+	428.284i	−0.208633	+	0.642105i
$668$	−462.181	+	150.172i	−0.691887	+	0.224808i
$669$	−692.591	−	378.306i	−1.03526	−	0.565480i
$670$	−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
$675$	244.494	−	392.297i	0.362213	−	0.581181i
$676$	433.788	+	315.166i	0.641699	+	0.466221i
$677$	−595.961	+	820.270i	−0.880297	+	1.21163i	0.0960413	+	0.995377i	$0.469382\pi$
$677$	−595.961	+	820.270i	−0.880297	+	1.21163i	−0.976339	+	0.216248i	$0.930618\pi$
$678$	344.776	−	44.5080i	0.508519	−	0.0656461i
$679$	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	$-0.865235\pi$
$683$		−	561.211i		−	0.821685i	0.911706	−	0.410842i	$-0.134765\pi$
$684$	18.7923	−	327.067i	0.0274741	−	0.478169i
$685$	163.040	+	501.784i	0.238014	+	0.732532i
$686$	−62.3554	−	20.2605i	−0.0908970	−	0.0295342i
$687$	−195.291	+	1039.09i	−0.284267	+	1.51251i
$688$	554.746	+	403.047i	0.806318	+	0.585824i
$689$	−239.626	−	77.8593i	−0.347788	−	0.113003i
$690$	−253.649	−	268.642i	−0.367608	−	0.389336i
$691$	−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
$696$	−180.678	+	170.595i	−0.259595	+	0.245107i
$697$	−323.722	+	996.315i	−0.464451	+	1.42943i
$698$	53.1831	−	73.2003i	0.0761936	−	0.104871i
$699$	104.380	+	19.6175i	0.149327	+	0.0280651i
$700$	−175.246	+	539.352i	−0.250352	+	0.770503i
$701$	−672.521	+	218.515i	−0.959373	+	0.311719i	−0.746519	−	0.665365i	$-0.768276\pi$
$701$	−672.521	+	218.515i	−0.959373	+	0.311719i	−0.212855	+	0.977084i	$0.568276\pi$
$702$	−28.7952	−	71.0301i	−0.0410188	−	0.101182i
$703$	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
$708$	55.2451	+	427.949i	0.0780297	+	0.604447i
$709$	−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
$711$	−549.968	−	856.282i	−0.773513	−	1.20434i
$712$	−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
$717$	−188.103	+	344.373i	−0.262348	+	0.480297i
$718$	−126.753	−	390.105i	−0.176536	−	0.543321i
$719$	−801.511	−	260.427i	−1.11476	−	0.362207i	−0.306993	−	0.951712i	$-0.599323\pi$
$719$	−801.511	−	260.427i	−1.11476	−	0.362207i	−0.807765	+	0.589505i	$0.799323\pi$
$720$	158.084	+	602.083i	0.219560	+	0.836226i
$721$	−399.114	−	289.974i	−0.553557	−	0.402183i
$722$	−165.091	−	53.6412i	−0.228657	−	0.0742953i
$723$	293.443	−	277.067i	0.405868	−	0.383218i
$724$	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
$729$	−124.901	+	718.221i	−0.171332	+	0.985213i
$730$	127.567	−	392.612i	0.174750	−	0.537824i
$731$	1131.80	−	1557.78i	1.54828	−	2.13103i
$732$	46.0765	−	245.161i	0.0629461	−	0.334920i
$733$	−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
$735$	361.320	−	661.493i	0.491592	−	0.899990i
$736$	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
$741$	−127.732	+	16.4893i	−0.172378	+	0.0222528i
$742$	311.441	+	226.275i	0.419732	+	0.304953i
$743$	7.44321	−	10.2447i	0.0100178	−	0.0137883i	−0.803979	−	0.594658i	$-0.797287\pi$
$743$	7.44321	−	10.2447i	0.0100178	−	0.0137883i	0.813997	+	0.580870i	$0.197287\pi$
$744$	−34.7936	−	269.524i	−0.0467656	−	0.362263i
$745$	−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
$750$	91.6257	+	50.0477i	0.122168	+	0.0667303i
$751$	−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
$753$	1192.81	+	224.181i	1.58408	+	0.297717i
$754$	37.0879	+	26.9459i	0.0491882	+	0.0357373i
$755$	−548.817	−	178.321i	−0.726910	−	0.236187i
$756$	−63.4370	−	892.118i	−0.0839114	−	1.18005i
$757$	−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	$-0.963476\pi$
$761$	−605.245	−	833.048i	−0.795328	−	1.09468i	0.198096	−	0.980183i	$-0.436524\pi$
$762$	−203.679	−	215.718i	−0.267296	−	0.283095i
$763$	109.181	−	336.025i	0.143095	−	0.440400i
$764$	−59.5640	+	81.9828i	−0.0779633	+	0.107307i
$765$	1690.71	−	443.914i	2.21008	−	0.580280i
$766$	126.732	−	390.041i	0.165447	−	0.509192i
$767$	161.333	−	52.4203i	0.210343	−	0.0683446i
$768$	−21.9858	−	12.0091i	−0.0286273	−	0.0156368i
$769$	−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	0.0262141	−	0.999656i	$-0.491655\pi$
$773$	490.859	−	159.490i	0.635005	−	0.206326i	0.608791	+	0.793331i	$0.291655\pi$
$774$	331.572	−	212.960i	0.428387	−	0.275142i
$775$	−244.626	−	177.732i	−0.315647	−	0.229331i
$776$	573.041	−	788.723i	0.738455	−	1.01640i
$777$	405.709	−	52.3740i	0.522148	−	0.0674055i
$778$	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
$783$	−163.816	−	404.090i	−0.209216	−	0.516079i
$784$	127.491	+	392.378i	0.162617	+	0.500483i
$785$	411.925	+	133.843i	0.524745	+	0.170500i
$786$	65.6698	−	349.412i	0.0835493	−	0.444544i
$787$	−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
$789$	−284.225	−	301.024i	−0.360234	−	0.381526i
$790$	−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
$795$	855.090	−	807.369i	1.07558	−	1.01556i
$796$	200.955	−	618.475i	0.252456	−	0.776978i
$797$	−862.522	+	1187.16i	−1.08221	+	1.48954i	−0.225147	+	0.974325i	$0.572286\pi$
$797$	−862.522	+	1187.16i	−1.08221	+	1.48954i	−0.857064	+	0.515211i	$0.827714\pi$
$798$	193.393	+	36.3471i	0.242348	+	0.0455477i
$799$	−96.6996	+	297.611i	−0.121026	+	0.372479i
$800$	452.136	−	146.908i	0.565170	−	0.183635i
$801$	183.291	+	10.5314i	0.228828	+	0.0131478i
$802$	−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
$807$	11.8660	+	91.9181i	0.0147038	+	0.113901i
$808$	−197.529	−	143.513i	−0.244466	−	0.177615i
$809$	−15.0886	+	20.7677i	−0.0186510	+	0.0256709i	−0.818241	−	0.574876i	$-0.805050\pi$
$809$	−15.0886	+	20.7677i	−0.0186510	+	0.0256709i	0.799590	+	0.600547i	$0.205050\pi$
$810$	355.388	+	40.9743i	0.438750	+	0.0505855i
$811$	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
$816$	−458.661	+	839.702i	−0.562085	+	1.02905i
$817$	−204.627	−	629.777i	−0.250461	−	0.770841i
$818$	293.692	+	95.4262i	0.359036	+	0.116658i
$819$	−340.078	+	89.2911i	−0.415235	+	0.109025i
$820$	−650.070	−	472.303i	−0.792768	−	0.575979i
$821$	−895.899	−	291.095i	−1.09123	−	0.354562i	−0.292508	−	0.956263i	$-0.594490\pi$
$821$	−895.899	−	291.095i	−1.09123	−	0.354562i	−0.798721	+	0.601701i	$0.794490\pi$
$822$	−120.676	+	113.942i	−0.146808	+	0.138615i
$823$	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	0.848309	−	0.529501i	$-0.177621\pi$
$827$	68.2953	+	94.0004i	0.0825820	+	0.113664i	−0.765727	+	0.643165i	$0.777621\pi$
$828$	−322.268	+	827.069i	−0.389213	+	0.998875i
$829$	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
$831$	−88.4445	+	470.590i	−0.106431	+	0.566294i
$832$	−30.5913	+	94.1505i	−0.0367684	+	0.113162i
$833$	1101.84	−	358.009i	1.32273	−	0.429782i
$834$	−0.666491	+	1.22019i	−0.000799149	+	0.00146306i
$835$	−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	0.209807	−	0.977743i	$-0.432716\pi$
$839$	800.614	−	260.135i	0.954248	−	0.310054i	0.744441	+	0.667689i	$0.232716\pi$
$840$	−927.558	+	119.741i	−1.10424	+	0.142549i
$841$	−469.390	−	341.032i	−0.558133	−	0.405508i
$842$	91.5934	−	126.068i	0.108781	−	0.149724i
$843$	152.572	+	1181.88i	0.180987	+	1.40199i
$844$	−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
$849$	−177.955	−	97.2024i	−0.209605	−	0.114490i
$850$	−107.743	−	331.599i	−0.126757	−	0.390117i
$851$	−386.125	−	125.459i	−0.453730	−	0.147426i
$852$	−10.3829	−	1.95140i	−0.0121865	−	0.00229038i
$853$	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
$855$	218.252	−	560.122i	0.255266	−	0.655113i
$856$	−283.482	+	205.962i	−0.331171	+	0.240610i
$857$		−	519.778i		−	0.606509i	−0.952910	−	0.303254i	$-0.901927\pi$
$857$		−	519.778i		−	0.606509i	0.952910	−	0.303254i	$-0.0980732\pi$
$858$		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
$861$	675.218	+	715.128i	0.784225	+	0.830578i
$862$	117.546	−	361.768i	0.136364	−	0.419685i
$863$	−667.030	+	918.087i	−0.772920	+	1.06383i	0.223109	+	0.974794i	$0.428380\pi$
$863$	−667.030	+	918.087i	−0.772920	+	1.06383i	−0.996028	+	0.0890389i	$0.971620\pi$
$864$	−573.772	+	482.602i	−0.664087	+	0.558567i
$865$	2.12242	−	6.53213i	0.00245366	−	0.00755159i
$866$	−186.573	+	60.6213i	−0.215442	+	0.0700015i
$867$	1597.08	+	872.353i	1.84207	+	1.00617i
$868$	−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
$873$	924.489	+	1439.40i	1.05898	+	1.64880i
$874$	−157.999	−	114.793i	−0.180777	−	0.131342i
$875$	281.517	−	387.474i	0.321733	−	0.442828i
$876$	−983.619	+	126.978i	−1.12285	+	0.144952i
$877$	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	$0.321994\pi$
$881$			1493.59i			1.69534i	−0.530526	+	0.847668i	$0.678006\pi$
$882$	236.712	+	13.6008i	0.268381	+	0.0154204i
$883$	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
$885$	−146.249	+	778.155i	−0.165254	+	0.879271i
$886$	154.857	+	112.510i	0.174782	+	0.126987i
$887$	792.059	+	257.356i	0.892964	+	0.290142i	0.719330	−	0.694668i	$-0.244449\pi$
$887$	792.059	+	257.356i	0.892964	+	0.290142i	0.173634	+	0.984810i	$0.444449\pi$
$888$	−153.801	−	162.892i	−0.173200	−	0.183437i
$889$	−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
$894$	293.815	−	277.418i	0.328652	−	0.310311i
$895$	−173.972	+	535.430i	−0.194382	+	0.598246i
$896$	700.354	−	963.954i	0.781645	−	1.07584i
$897$	342.953	+	64.4558i	0.382333	+	0.0718571i
$898$	58.3978	−	179.730i	0.0650310	−	0.200145i
$899$	−271.266	+	88.1396i	−0.301742	+	0.0980419i
$900$	−31.2611	+	544.078i	−0.0347345	+	0.604531i
$901$	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
$906$	−23.2406	−	180.031i	−0.0256519	−	0.198709i
$907$	−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
$909$	360.485	−	231.530i	0.396573	−	0.254709i
$910$	53.3186	+	164.098i	0.0585919	+	0.180327i
$911$	−32.7594	−	45.0894i	−0.0359598	−	0.0494944i	0.790658	−	0.612257i	$-0.209738\pi$
$911$	−32.7594	−	45.0894i	−0.0359598	−	0.0494944i	−0.826618	+	0.562763i	$0.809738\pi$
$912$	140.909	+	297.345i	0.154505	+	0.326037i
$913$		0			0
$914$			235.612i			0.257781i
$915$	219.424	−	401.713i	0.239807	−	0.439031i
$916$	−385.191	−	1185.50i	−0.420515	−	1.29421i
$917$	−1551.15	−	503.999i	−1.69155	−	0.549617i
$918$	353.944	+	420.808i	0.385560	+	0.458397i
$919$	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
$921$	−1056.10	+	997.165i	−1.14669	+	1.08270i
$922$	−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
$927$	−441.730	−	172.121i	−0.476516	−	0.185675i
$928$	138.576	−	426.493i	0.149328	−	0.459583i
$929$	−494.520	+	680.648i	−0.532314	+	0.732667i	−0.987481	−	0.157739i	$-0.949580\pi$
$929$	−494.520	+	680.648i	−0.532314	+	0.732667i	0.455167	+	0.890406i	$0.349580\pi$
$930$	43.2245	−	229.986i	0.0464779	−	0.247297i
$931$	123.119	−	378.921i	0.132244	−	0.407004i
$932$	−119.086	+	38.6934i	−0.127775	+	0.0415165i
$933$	−483.423	+	885.035i	−0.518138	+	0.948591i
$934$	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
$939$	−1455.21	+	187.857i	−1.54974	+	0.200061i
$940$	−194.183	−	141.082i	−0.206578	−	0.150088i
$941$	802.302	−	1104.27i	0.852605	−	1.17351i	−0.130677	−	0.991425i	$-0.541715\pi$
$941$	802.302	−	1104.27i	0.852605	−	1.17351i	0.983283	−	0.182086i	$-0.0582848\pi$
$942$	17.4437	+	135.125i	0.0185177	+	0.143445i
$943$	−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	$0.238452\pi$
$947$			1289.80i			1.36199i	−0.732289	+	0.680994i	$0.761548\pi$
$948$	1052.97	+	575.155i	1.11073	+	0.606704i
$949$	120.486	+	370.816i	0.126961	+	0.390744i
$950$	−114.037	−	37.0528i	−0.120039	−	0.0390030i
$951$	460.894	+	86.6222i	0.484642	+	0.0910854i
$952$	−1162.99	−	844.964i	−1.22163	−	0.887567i
$953$	630.883	+	204.986i	0.661997	+	0.215096i	0.620696	−	0.784051i	$-0.286850\pi$
$953$	630.883	+	204.986i	0.661997	+	0.215096i	0.0413004	+	0.999147i	$0.486850\pi$
$954$	344.695	+	134.311i	0.361316	+	0.140787i
$955$	−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
$960$	−317.220	−	335.970i	−0.330437	−	0.349968i
$961$	−200.571	+	617.295i	−0.208711	+	0.642347i
$962$	−24.2934	+	33.4370i	−0.0252530	+	0.0347578i
$963$	−156.147	−	594.707i	−0.162146	−	0.617556i
$964$	−147.031	+	452.516i	−0.152522	+	0.469415i
$965$	−78.3566	+	25.4596i	−0.0811986	+	0.0263830i
$966$	−467.913	−	255.583i	−0.484382	−	0.264579i
$967$	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	0.0234383	−	0.999725i	$-0.492539\pi$
$971$	611.753	−	198.771i	0.630024	−	0.204707i	0.606586	+	0.795018i	$0.292539\pi$
$972$	−276.677	−	813.715i	−0.284647	−	0.837155i
$973$	5.16004	+	3.74899i	0.00530323	+	0.00385302i
$974$	−8.22387	+	11.3192i	−0.00844340	+	0.0116213i
$975$	212.483	−	27.4301i	0.217932	−	0.0281334i
$976$	77.4235	+	238.285i	0.0793273	+	0.244144i
$977$	882.805	+	1215.08i	0.903588	+	1.24368i	0.969309	+	0.245844i	$0.0790651\pi$
$977$	882.805	+	1215.08i	0.903588	+	1.24368i	−0.0657216	+	0.997838i	$0.520935\pi$
$978$	257.995	−	122.261i	0.263798	−	0.125011i
$979$		0			0
$980$			888.634i			0.906769i
$981$	19.4762	−	338.970i	0.0198534	−	0.345535i
$982$	100.644	+	309.750i	0.102489	+	0.315428i
$983$	−693.417	−	225.305i	−0.705409	−	0.229201i	−0.0657234	−	0.997838i	$-0.520935\pi$
$983$	−693.417	−	225.305i	−0.705409	−	0.229201i	−0.639686	+	0.768637i	$0.720935\pi$
$984$	99.4893	−	529.357i	0.101107	−	0.537964i
$985$	1767.82	+	1284.39i	1.79474	+	1.30395i
$986$	−312.793	−	101.633i	−0.317234	−	0.103076i
$987$	201.695	+	213.617i	0.204352	+	0.216430i
$988$	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
$993$	−87.8616	+	82.9583i	−0.0884810	+	0.0835431i
$994$	1.96095	−	6.03518i	0.00197279	−	0.00607161i
$995$	701.387	−	965.376i	0.704912	−	0.970228i
$996$	1085.26	+	203.968i	1.08962	+	0.204787i
$997$	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
$999$	364.312	−	147.690i	0.364677	−	0.147838i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.3.b.j.122.3	✓	6	33.20	odd	10
363.3.b.j.122.4	yes	6	11.9	even	5
363.3.b.k.122.3	yes	6	11.2	odd	10
363.3.b.k.122.4	yes	6	33.2	even	10
363.3.h.p.245.3		24	33.32	even	2
363.3.h.p.245.4		24	11.10	odd	2
363.3.h.p.251.3		24	11.6	odd	10
363.3.h.p.251.4		24	33.17	even	10
363.3.h.p.269.3		24	33.8	even	10
363.3.h.p.269.4		24	11.8	odd	10
363.3.h.p.323.3		24	11.7	odd	10
363.3.h.p.323.4		24	33.29	even	10
363.3.h.q.245.3		24	1.1	even	1	trivial
363.3.h.q.245.4		24	3.2	odd	2	inner
363.3.h.q.251.3		24	33.5	odd	10	inner
363.3.h.q.251.4		24	11.5	even	5	inner
363.3.h.q.269.3		24	11.3	even	5	inner
363.3.h.q.269.4		24	33.14	odd	10	inner
363.3.h.q.323.3		24	33.26	odd	10	inner
363.3.h.q.323.4		24	11.4	even	5	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} +(-2.18131 + 2.05958i) q^{3} +(1.09296 - 3.36379i) q^{4} +(3.81474 - 5.25053i) q^{5} +(2.00642 + 0.377094i) q^{6} +(2.89410 - 8.90713i) q^{7} +(-4.87795 + 1.58494i) q^{8} +(0.516261 - 8.98518i) q^{9} -4.41657 q^{10} +(4.54390 + 9.58852i) q^{12} +(3.37472 - 2.45188i) q^{13} +(-6.06145 + 1.96948i) q^{14} +(2.49276 + 19.3098i) q^{15} +(-8.62188 - 6.26416i) q^{16} +(-17.5904 + 24.2111i) q^{17} +(-5.15329 + 3.30982i) q^{18} +(3.18032 + 9.78800i) q^{19} +(-13.4923 - 18.5706i) q^{20} +(12.0320 + 25.3899i) q^{21} -27.8850i q^{23} +(7.37603 - 13.5038i) q^{24} +(-5.29047 - 16.2824i) q^{25} +(-2.69976 - 0.877206i) q^{26} +(17.3796 + 20.6628i) q^{27} +(-26.7986 - 19.4703i) q^{28} +(-15.3590 - 4.99043i) q^{29} +(9.63392 - 9.09627i) q^{30} +(14.2887 - 10.3813i) q^{31} +27.7684i q^{32} +20.3655 q^{34} +(-35.7270 - 49.1739i) q^{35} +(-29.6600 - 11.5570i) q^{36} +(4.49918 - 13.8470i) q^{37} +(4.11666 - 5.66610i) q^{38} +(-2.31149 + 12.2988i) q^{39} +(-10.2863 + 31.6580i) q^{40} +(33.2920 - 10.8172i) q^{41} +(9.16562 - 16.7801i) q^{42} -64.3417 q^{43} +(-45.2076 - 36.9867i) q^{45} +(-15.3521 + 11.1539i) q^{46} +(9.94471 - 3.23123i) q^{47} +(31.7086 - 4.09335i) q^{48} +(-31.3193 - 22.7548i) q^{49} +(-6.84809 + 9.42559i) q^{50} +(-11.4945 - 89.0408i) q^{51} +(-4.55916 - 14.0317i) q^{52} +(-35.5031 - 48.8658i) q^{53} +(4.42410 - 17.8334i) q^{54} +48.0356i q^{56} +(-27.0964 - 14.8006i) q^{57} +(3.39607 + 10.4520i) q^{58} +(38.6761 + 12.5666i) q^{59} +(67.6786 + 12.7198i) q^{60} +(-19.0197 - 13.8186i) q^{61} +(-11.4309 - 3.71411i) q^{62} +(-78.5381 - 30.6024i) q^{63} +(-19.1997 + 13.9494i) q^{64} -27.0724i q^{65} +30.8376 q^{67} +(62.2154 + 85.6321i) q^{68} +(57.4314 + 60.8259i) q^{69} +(-12.7820 + 39.3389i) q^{70} +(-0.585238 + 0.805511i) q^{71} +(11.7227 + 44.6475i) q^{72} +(-28.8838 + 88.8953i) q^{73} +(-9.42314 + 3.06176i) q^{74} +(45.0751 + 24.6209i) q^{75} +36.4007 q^{76} +(7.69570 - 3.64691i) q^{78} +(91.4806 - 66.4645i) q^{79} +(-65.7804 + 21.3733i) q^{80} +(-80.4669 - 9.27740i) q^{81} +(-19.2722 - 14.0020i) q^{82} +(61.1711 - 84.1948i) q^{83} +(98.5567 - 12.7230i) q^{84} +(60.0184 + 184.718i) q^{85} +(25.7365 + 35.4233i) q^{86} +(43.7809 - 20.7473i) q^{87} +20.3993i q^{89} +(-2.28010 + 39.6836i) q^{90} +(-12.0724 - 37.1551i) q^{91} +(-93.7992 - 30.4772i) q^{92} +(-9.78689 + 52.0735i) q^{93} +(-5.75681 - 4.18257i) q^{94} +(63.5243 + 20.6403i) q^{95} +(-57.1912 - 60.5715i) 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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