LMFDB - Embedded newform 363.3.h.q.251.2

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			251.2
Character	$\chi$	$=$	363.251
Dual form			363.3.h.q.269.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.73676 - 0.889226i) q^{2} +(-2.95896 - 0.494538i) q^{3} +(3.46304 + 2.51605i) q^{4} +(4.70571 - 1.52898i) q^{5} +(7.65819 + 3.98461i) q^{6} +(9.04489 + 6.57149i) q^{7} +(-0.474528 - 0.653131i) q^{8} +(8.51086 + 2.92664i) q^{9} -14.2380 q^{10} +(-9.00271 - 9.15748i) q^{12} +(-5.22225 + 16.0724i) q^{13} +(-18.9101 - 26.0275i) q^{14} +(-14.6801 + 2.19703i) q^{15} +(-4.57317 - 14.0748i) q^{16} +(0.0595216 - 0.0193397i) q^{17} +(-20.6897 - 15.5776i) q^{18} +(-4.35333 + 3.16288i) q^{19} +(20.1430 + 6.54487i) q^{20} +(-23.5136 - 23.9178i) q^{21} -8.69537i q^{23} +(1.08111 + 2.16726i) q^{24} +(-0.419501 + 0.304785i) q^{25} +(28.5840 - 39.3425i) q^{26} +(-23.7360 - 12.8687i) q^{27} +(14.7886 + 45.5147i) q^{28} +(-29.3632 + 40.4149i) q^{29} +(42.1296 + 7.04122i) q^{30} +(-7.59453 + 23.3736i) q^{31} +45.8150i q^{32} -0.180094 q^{34} +(52.6103 + 17.0941i) q^{35} +(22.1099 + 31.5488i) q^{36} +(31.7618 + 23.0763i) q^{37} +(14.7265 - 4.78493i) q^{38} +(23.4008 - 44.9750i) q^{39} +(-3.23161 - 2.34790i) q^{40} +(-25.8089 - 35.5228i) q^{41} +(43.0826 + 86.3661i) q^{42} +0.201842 q^{43} +(44.5244 + 0.758975i) q^{45} +(-7.73215 + 23.7971i) q^{46} +(8.76165 + 12.0594i) q^{47} +(6.57130 + 43.9082i) q^{48} +(23.4836 + 72.2751i) q^{49} +(1.41909 - 0.461092i) q^{50} +(-0.185686 + 0.0277898i) q^{51} +(-58.5238 + 42.5200i) q^{52} +(-93.1486 - 30.2658i) q^{53} +(53.5163 + 56.3252i) q^{54} -9.02585i q^{56} +(14.4455 - 7.20594i) q^{57} +(116.298 - 84.4953i) q^{58} +(-8.51816 + 11.7242i) q^{59} +(-56.3657 - 29.3275i) q^{60} +(9.06134 + 27.8879i) q^{61} +(41.5687 - 57.2145i) q^{62} +(57.7474 + 82.4002i) q^{63} +(22.4472 - 69.0854i) q^{64} +83.6168i q^{65} +82.8515 q^{67} +(0.254785 + 0.0827848i) q^{68} +(-4.30019 + 25.7292i) q^{69} +(-128.781 - 93.5648i) q^{70} +(-25.3986 + 8.25251i) q^{71} +(-2.12716 - 6.94748i) q^{72} +(-11.3022 - 8.21153i) q^{73} +(-66.4042 - 91.3976i) q^{74} +(1.39201 - 0.694387i) q^{75} -23.0337 q^{76} +(-104.035 + 102.277i) q^{78} +(15.5088 - 47.7311i) q^{79} +(-43.0400 - 59.2395i) q^{80} +(63.8696 + 49.8164i) q^{81} +(39.0447 + 120.167i) q^{82} +(57.2933 - 18.6157i) q^{83} +(-21.2501 - 141.990i) q^{84} +(0.250521 - 0.182014i) q^{85} +(-0.552394 - 0.179484i) q^{86} +(106.871 - 105.065i) q^{87} +40.3489i q^{89} +(-121.178 - 41.6694i) q^{90} +(-152.854 + 111.055i) q^{91} +(21.8779 - 30.1124i) q^{92} +(34.0310 - 65.4056i) q^{93} +(-13.2550 - 40.7946i) q^{94} +(-15.6495 + 21.5397i) q^{95} +(22.6573 - 135.565i) q^{96} +(-9.52170 + 29.3048i) q^{97} -218.681i 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 $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−2.73676	−	0.889226i	−1.36838	−	0.444613i	−0.469546	−	0.882908i	$-0.655583\pi$
$2$	−2.73676	−	0.889226i	−1.36838	−	0.444613i	−0.898831	+	0.438295i	$0.855583\pi$
$3$	−2.95896	−	0.494538i	−0.986319	−	0.164846i
$3$	−2.95896	−	0.494538i	−0.986319	−	0.164846i
$4$	3.46304	+	2.51605i	0.865760	+	0.629011i
$5$	4.70571	−	1.52898i	0.941142	−	0.305796i	0.202031	−	0.979379i	$-0.435246\pi$
$5$	4.70571	−	1.52898i	0.941142	−	0.305796i	0.739111	+	0.673584i	$0.235246\pi$
$6$	7.65819	+	3.98461i	1.27636	+	0.664102i
$7$	9.04489	+	6.57149i	1.29213	+	0.938785i	0.999846	−	0.0175478i	$-0.00558591\pi$
$7$	9.04489	+	6.57149i	1.29213	+	0.938785i	0.292280	+	0.956333i	$0.405586\pi$
$8$	−0.474528	−	0.653131i	−0.0593159	−	0.0816414i
$9$	8.51086	+	2.92664i	0.945652	+	0.325182i
$10$	−14.2380			−1.42380
$11$		0			0
$11$		0			0
$12$	−9.00271	−	9.15748i	−0.750226	−	0.763123i
$13$	−5.22225	+	16.0724i	−0.401711	+	1.23634i	0.521899	+	0.853007i	$0.325224\pi$
$13$	−5.22225	+	16.0724i	−0.401711	+	1.23634i	−0.923610	+	0.383333i	$0.874776\pi$
$14$	−18.9101	−	26.0275i	−1.35072	−	1.85911i
$15$	−14.6801	+	2.19703i	−0.978675	+	0.146468i
$16$	−4.57317	−	14.0748i	−0.285823	−	0.879673i
$17$	0.0595216	−	0.0193397i	0.00350127	−	0.00113763i	−0.307266	−	0.951624i	$-0.599414\pi$
$17$	0.0595216	−	0.0193397i	0.00350127	−	0.00113763i	0.310767	+	0.950486i	$0.399414\pi$
$18$	−20.6897	−	15.5776i	−1.14943	−	0.865420i
$19$	−4.35333	+	3.16288i	−0.229123	+	0.166467i	−0.696424	−	0.717631i	$-0.745226\pi$
$19$	−4.35333	+	3.16288i	−0.229123	+	0.166467i	0.467301	+	0.884098i	$0.345226\pi$
$20$	20.1430	+	6.54487i	1.00715	+	0.327243i
$21$	−23.5136	−	23.9178i	−1.11969	−	1.13894i
$22$		0			0
$23$		−	8.69537i		−	0.378060i	−0.981971	−	0.189030i	$-0.939466\pi$
$23$		−	8.69537i		−	0.378060i	0.981971	−	0.189030i	$-0.0605343\pi$
$24$	1.08111	+	2.16726i	0.0450462	+	0.0903025i
$25$	−0.419501	+	0.304785i	−0.0167800	+	0.0121914i
$26$	28.5840	−	39.3425i	1.09939	−	1.51317i
$27$	−23.7360	−	12.8687i	−0.879109	−	0.476620i
$28$	14.7886	+	45.5147i	0.528165	+	1.62552i
$29$	−29.3632	+	40.4149i	−1.01252	+	1.39362i	−0.0952067	+	0.995458i	$0.530351\pi$
$29$	−29.3632	+	40.4149i	−1.01252	+	1.39362i	−0.917316	+	0.398160i	$0.869649\pi$
$30$	42.1296	+	7.04122i	1.40432	+	0.234707i
$31$	−7.59453	+	23.3736i	−0.244985	+	0.753986i	0.750654	+	0.660695i	$0.229739\pi$
$31$	−7.59453	+	23.3736i	−0.244985	+	0.753986i	−0.995639	+	0.0932904i	$0.970261\pi$
$32$			45.8150i			1.43172i
$33$		0			0
$34$	−0.180094			−0.00529687
$35$	52.6103	+	17.0941i	1.50315	+	0.488403i
$36$	22.1099	+	31.5488i	0.614164	+	0.876355i
$37$	31.7618	+	23.0763i	0.858427	+	0.623684i	0.927456	−	0.373931i	$-0.121990\pi$
$37$	31.7618	+	23.0763i	0.858427	+	0.623684i	−0.0690298	+	0.997615i	$0.521990\pi$
$38$	14.7265	−	4.78493i	0.387540	−	0.125919i
$39$	23.4008	−	44.9750i	0.600021	−	1.15321i
$40$	−3.23161	−	2.34790i	−0.0807903	−	0.0586976i
$41$	−25.8089	−	35.5228i	−0.629484	−	0.866411i	0.368516	−	0.929621i	$-0.379866\pi$
$41$	−25.8089	−	35.5228i	−0.629484	−	0.866411i	−0.998000	+	0.0632106i	$0.979866\pi$
$42$	43.0826	+	86.3661i	1.02578	+	2.05634i
$43$	0.201842			0.00469401			0.00234701	−	0.999997i	$-0.499253\pi$
$43$	0.201842			0.00469401			0.00234701	+	0.999997i	$0.499253\pi$
$44$		0			0
$45$	44.5244	+	0.758975i	0.989431	+	0.0168661i
$46$	−7.73215	+	23.7971i	−0.168090	+	0.517328i
$47$	8.76165	+	12.0594i	0.186418	+	0.256582i	0.891989	−	0.452057i	$-0.149309\pi$
$47$	8.76165	+	12.0594i	0.186418	+	0.256582i	−0.705571	+	0.708639i	$0.749309\pi$
$48$	6.57130	+	43.9082i	0.136902	+	0.914755i
$49$	23.4836	+	72.2751i	0.479257	+	1.47500i
$50$	1.41909	−	0.461092i	0.0283819	−	0.00922183i
$51$	−0.185686	+	0.0277898i	−0.00364091	+	0.000544898i
$52$	−58.5238	+	42.5200i	−1.12546	+	0.817693i
$53$	−93.1486	−	30.2658i	−1.75752	−	0.571053i	−0.760582	−	0.649242i	$-0.775086\pi$
$53$	−93.1486	−	30.2658i	−1.75752	−	0.571053i	−0.996939	+	0.0781891i	$0.975086\pi$
$54$	53.5163	+	56.3252i	0.991042	+	1.04306i
$55$		0			0
$56$		−	9.02585i		−	0.161176i
$57$	14.4455	−	7.20594i	0.253429	−	0.126420i
$58$	116.298	−	84.4953i	2.00513	−	1.45681i
$59$	−8.51816	+	11.7242i	−0.144376	+	0.198716i	−0.875080	−	0.483978i	$-0.839192\pi$
$59$	−8.51816	+	11.7242i	−0.144376	+	0.198716i	0.730705	+	0.682694i	$0.239192\pi$
$60$	−56.3657	−	29.3275i	−0.939428	−	0.488791i
$61$	9.06134	+	27.8879i	0.148547	+	0.457179i	0.997450	−	0.0713686i	$-0.0227366\pi$
$61$	9.06134	+	27.8879i	0.148547	+	0.457179i	−0.848903	+	0.528548i	$0.822737\pi$
$62$	41.5687	−	57.2145i	0.670464	−	0.922814i
$63$	57.7474	+	82.4002i	0.916626	+	1.30794i
$64$	22.4472	−	69.0854i	0.350738	−	1.07946i
$65$			83.6168i			1.28641i
$66$		0			0
$67$	82.8515			1.23659			0.618294	−	0.785947i	$-0.287824\pi$
$67$	82.8515			1.23659			0.618294	+	0.785947i	$0.287824\pi$
$68$	0.254785	+	0.0827848i	0.00374684	+	0.00121742i
$69$	−4.30019	+	25.7292i	−0.0623216	+	0.372887i
$70$	−128.781	−	93.5648i	−1.83973	−	1.33664i
$71$	−25.3986	+	8.25251i	−0.357727	+	0.116232i	−0.482366	−	0.875970i	$-0.660223\pi$
$71$	−25.3986	+	8.25251i	−0.357727	+	0.116232i	0.124640	+	0.992202i	$0.460223\pi$
$72$	−2.12716	−	6.94748i	−0.0295439	−	0.0964928i
$73$	−11.3022	−	8.21153i	−0.154825	−	0.112487i	0.507676	−	0.861548i	$-0.330505\pi$
$73$	−11.3022	−	8.21153i	−0.154825	−	0.112487i	−0.662501	+	0.749061i	$0.730505\pi$
$74$	−66.4042	−	91.3976i	−0.897354	−	1.23510i
$75$	1.39201	−	0.694387i	0.0185602	−	0.00925850i
$76$	−23.0337			−0.303075
$77$		0			0
$78$	−104.035	+	102.277i	−1.33379	+	1.31124i
$79$	15.5088	−	47.7311i	0.196314	−	0.604191i	−0.803645	−	0.595109i	$-0.797109\pi$
$79$	15.5088	−	47.7311i	0.196314	−	0.604191i	0.999959	−	0.00908239i	$-0.00289105\pi$
$80$	−43.0400	−	59.2395i	−0.538000	−	0.740493i
$81$	63.8696	+	49.8164i	0.788514	+	0.615017i
$82$	39.0447	+	120.167i	0.476155	+	1.46545i
$83$	57.2933	−	18.6157i	0.690281	−	0.224286i	0.0571899	−	0.998363i	$-0.481786\pi$
$83$	57.2933	−	18.6157i	0.690281	−	0.224286i	0.633091	+	0.774078i	$0.281786\pi$
$84$	−21.2501	−	141.990i	−0.252978	−	1.69035i
$85$	0.250521	−	0.182014i	0.00294731	−	0.00214135i
$86$	−0.552394	−	0.179484i	−0.00642318	−	0.00208702i
$87$	106.871	−	105.065i	1.22840	−	1.20764i
$88$		0			0
$89$			40.3489i			0.453359i	0.973969	+	0.226679i	$0.0727869\pi$
$89$			40.3489i			0.453359i	−0.973969	+	0.226679i	$0.927213\pi$
$90$	−121.178	−	41.6694i	−1.34642	−	0.462993i
$91$	−152.854	+	111.055i	−1.67972	+	1.22039i
$92$	21.8779	−	30.1124i	0.237804	−	0.327309i
$93$	34.0310	−	65.4056i	0.365925	−	0.703286i
$94$	−13.2550	−	40.7946i	−0.141010	−	0.433986i
$95$	−15.6495	+	21.5397i	−0.164732	+	0.226734i
$96$	22.6573	−	135.565i	0.236013	−	1.41213i
$97$	−9.52170	+	29.3048i	−0.0981619	+	0.302111i	−0.988065	−	0.154039i	$-0.950772\pi$
$97$	−9.52170	+	29.3048i	−0.0981619	+	0.302111i	0.889903	+	0.456150i	$0.150772\pi$
$98$		−	218.681i		−	2.23144i
$99$		0			0
$100$	−2.21960			−0.0221960
$101$	−49.3806	−	16.0447i	−0.488917	−	0.158859i	0.0541757	−	0.998531i	$-0.482747\pi$
$101$	−49.3806	−	16.0447i	−0.488917	−	0.158859i	−0.543093	+	0.839673i	$0.682747\pi$
$102$	0.532889	+	0.0890631i	0.00522440	+	0.000873168i
$103$	41.3843	+	30.0674i	0.401789	+	0.291917i	0.770269	−	0.637719i	$-0.220122\pi$
$103$	41.3843	+	30.0674i	0.401789	+	0.291917i	−0.368480	+	0.929636i	$0.620122\pi$
$104$	12.9755	−	4.21599i	0.124764	−	0.0405384i
$105$	−147.218	−	76.5985i	−1.40207	−	0.729510i
$106$	228.012	+	165.660i	2.15105	+	1.56283i
$107$	40.2296	+	55.3713i	0.375978	+	0.517489i	0.954513	−	0.298168i	$-0.0963756\pi$
$107$	40.2296	+	55.3713i	0.375978	+	0.517489i	−0.578536	+	0.815657i	$0.696376\pi$
$108$	−49.8202	−	104.286i	−0.461298	−	0.965608i
$109$	−125.737			−1.15355			−0.576773	−	0.816904i	$-0.695688\pi$
$109$	−125.737			−1.15355			−0.576773	+	0.816904i	$0.695688\pi$
$110$		0			0
$111$	−82.5697	−	83.9892i	−0.743871	−	0.756659i
$112$	51.1284	−	157.357i	0.456504	−	1.40497i
$113$	58.0332	+	79.8758i	0.513568	+	0.706866i	0.984516	−	0.175295i	$-0.0560880\pi$
$113$	58.0332	+	79.8758i	0.513568	+	0.706866i	−0.470948	+	0.882161i	$0.656088\pi$
$114$	−45.9414	+	6.87559i	−0.402995	+	0.0603122i
$115$	−13.2950	−	40.9179i	−0.115609	−	0.355808i
$116$	−203.372	+	66.0794i	−1.75320	+	0.569650i
$117$	−91.4839	+	121.507i	−0.781914	+	1.03852i
$118$	33.7376	−	24.5118i	0.285912	−	0.207727i
$119$	0.665457	+	0.216220i	0.00559208	+	0.00181698i
$120$	8.40107	+	8.54550i	0.0700089	+	0.0712125i
$121$		0			0
$122$		−	84.3801i		−	0.691640i
$123$	58.7999	+	117.874i	0.478048	+	0.958326i
$124$	−85.1091	+	61.8354i	−0.686364	+	0.498672i
$125$	−74.2152	+	102.149i	−0.593722	+	0.817188i
$126$	−84.7682	−	276.860i	−0.672764	−	2.19730i
$127$	−6.44270	−	19.8286i	−0.0507299	−	0.156131i	0.922482	−	0.386040i	$-0.126157\pi$
$127$	−6.44270	−	19.8286i	−0.0507299	−	0.156131i	−0.973212	+	0.229909i	$0.926157\pi$
$128$	−15.1475	+	20.8488i	−0.118340	+	0.162881i
$129$	−0.597243	−	0.0998188i	−0.00462979	−	0.000773789i
$130$	74.3542	−	228.839i	0.571956	−	1.76030i
$131$		−	29.0290i		−	0.221595i	−0.993843	−	0.110798i	$-0.964659\pi$
$131$		−	29.0290i		−	0.221595i	0.993843	−	0.110798i	$-0.0353405\pi$
$132$		0			0
$133$	−60.1602			−0.452332
$134$	−226.744	−	73.6736i	−1.69212	−	0.549803i
$135$	−131.371	−	24.2648i	−0.973115	−	0.179739i
$136$	−0.0408760	−	0.0296982i	−0.000300559	−	0.000218369i
$137$	144.285	−	46.8811i	1.05318	−	0.342198i	0.269263	−	0.963067i	$-0.413220\pi$
$137$	144.285	−	46.8811i	1.05318	−	0.342198i	0.783915	+	0.620869i	$0.213220\pi$
$138$	34.6477	−	66.5908i	0.251070	−	0.482542i
$139$	15.5515	+	11.2988i	0.111881	+	0.0812863i	0.642319	−	0.766437i	$-0.277972\pi$
$139$	15.5515	+	11.2988i	0.111881	+	0.0812863i	−0.530438	+	0.847724i	$0.677972\pi$
$140$	139.182	+	191.567i	0.994156	+	1.36834i
$141$	−19.9615	−	40.0162i	−0.141571	−	0.283803i
$142$	76.8481			0.541184
$143$		0			0
$144$	2.27009	−	133.172i	0.0157645	−	0.924808i
$145$	−76.3810	+	235.076i	−0.526765	+	1.62122i
$146$	23.6295	+	32.5232i	0.161846	+	0.222761i
$147$	−33.7442	−	225.472i	−0.229552	−	1.53383i
$148$	51.9313	+	159.828i	0.350887	+	1.07992i
$149$	−172.775	+	56.1381i	−1.15957	+	0.376766i	−0.824739	−	0.565514i	$-0.808678\pi$
$149$	−172.775	+	56.1381i	−1.15957	+	0.376766i	−0.334827	+	0.942280i	$0.608678\pi$
$150$	−4.42707	+	0.662554i	−0.0295138	+	0.00441703i
$151$	−113.418	+	82.4026i	−0.751109	+	0.545713i	−0.896171	−	0.443710i	$-0.853662\pi$
$151$	−113.418	+	82.4026i	−0.751109	+	0.545713i	0.145061	+	0.989423i	$0.453662\pi$
$152$	4.13155	+	1.34242i	0.0271812	+	0.00883172i
$153$	0.563181	+	0.00960013i	0.00368092	+	6.27460e-5i
$154$		0			0
$155$			121.601i			0.784523i
$156$	194.197	−	96.8727i	1.24485	−	0.620979i
$157$	145.309	−	105.573i	0.925536	−	0.672441i	−0.0193599	−	0.999813i	$-0.506163\pi$
$157$	145.309	−	105.573i	0.925536	−	0.672441i	0.944896	+	0.327371i	$0.106163\pi$
$158$	−84.8875	+	116.838i	−0.537262	+	0.739478i
$159$	260.655	+	135.621i	1.63934	+	0.852961i
$160$	70.0501	+	215.592i	0.437813	+	1.34745i
$161$	57.1416	−	78.6486i	0.354917	−	0.488501i
$162$	−130.497	−	193.130i	−0.805540	−	1.19216i
$163$	68.3722	−	210.428i	0.419461	−	1.29097i	−0.488738	−	0.872431i	$-0.662543\pi$
$163$	68.3722	−	210.428i	0.419461	−	1.29097i	0.908199	−	0.418538i	$-0.137457\pi$
$164$		−	187.953i		−	1.14606i
$165$		0			0
$166$	−173.351			−1.04428
$167$	175.393	+	56.9886i	1.05026	+	0.341249i	0.782769	−	0.622312i	$-0.213806\pi$
$167$	175.393	+	56.9886i	1.05026	+	0.341249i	0.267488	+	0.963561i	$0.413806\pi$
$168$	−4.46363	+	26.7071i	−0.0265692	+	0.158971i
$169$	−94.3269	−	68.5325i	−0.558148	−	0.405518i
$170$	−0.847468	+	0.275359i	−0.00498510	+	0.00161976i
$171$	−46.3072	+	14.1782i	−0.270802	+	0.0829136i
$172$	0.698988	+	0.507845i	0.00406389	+	0.00295259i
$173$	143.153	+	197.033i	0.827472	+	1.13892i	0.988388	+	0.151950i	$0.0485552\pi$
$173$	143.153	+	197.033i	0.827472	+	1.13892i	−0.160916	+	0.986968i	$0.551445\pi$
$174$	−385.906	+	192.504i	−2.21785	+	1.10635i
$175$	−5.79723			−0.0331270
$176$		0			0
$177$	31.0030	−	30.4790i	0.175158	−	0.172198i
$178$	35.8793	−	110.425i	0.201569	−	0.620366i
$179$	186.107	+	256.154i	1.03970	+	1.43103i	0.897407	+	0.441203i	$0.145448\pi$
$179$	186.107	+	256.154i	1.03970	+	1.43103i	0.142295	+	0.989824i	$0.454552\pi$
$180$	152.280	+	114.654i	0.846001	+	0.636965i
$181$	−9.54820	−	29.3863i	−0.0527525	−	0.162355i	0.921209	−	0.389067i	$-0.127203\pi$
$181$	−9.54820	−	29.3863i	−0.0527525	−	0.162355i	−0.973962	+	0.226712i	$0.927203\pi$
$182$	517.078	−	168.009i	2.84109	−	0.923126i
$183$	−13.0205	−	87.0004i	−0.0711502	−	0.475412i
$184$	−5.67922	+	4.12619i	−0.0308653	+	0.0224250i
$185$	184.745	+	60.0272i	0.998621	+	0.324472i
$186$	−151.295	+	148.738i	−0.813413	+	0.799666i
$187$		0			0
$188$			63.8068i			0.339398i
$189$	−130.122	−	272.377i	−0.688477	−	1.44115i
$190$	61.9826	−	45.0330i	0.326224	−	0.237016i
$191$	173.938	−	239.405i	0.910669	−	1.25343i	−0.0562681	−	0.998416i	$-0.517920\pi$
$191$	173.938	−	239.405i	0.910669	−	1.25343i	0.966938	−	0.255013i	$-0.0820798\pi$
$192$	−100.586	+	193.320i	−0.523884	+	1.00687i
$193$	−24.5692	−	75.6161i	−0.127301	−	0.391793i	0.867012	−	0.498287i	$-0.166038\pi$
$193$	−24.5692	−	75.6161i	−0.127301	−	0.391793i	−0.994313	+	0.106494i	$0.966038\pi$
$194$	52.1171	−	71.7331i	0.268645	−	0.369758i
$195$	41.3517	−	247.419i	0.212060	−	1.26881i
$196$	−100.523	+	309.377i	−0.512871	+	1.57845i
$197$			360.331i			1.82909i	0.404485	+	0.914544i	$0.367451\pi$
$197$			360.331i			1.82909i	−0.404485	+	0.914544i	$0.632549\pi$
$198$		0			0
$199$	369.874			1.85866			0.929332	−	0.369245i	$-0.120384\pi$
$199$	369.874			1.85866			0.929332	+	0.369245i	$0.120384\pi$
$200$	0.398129	+	0.129360i	0.00199065	+	0.000646800i
$201$	−245.154	−	40.9732i	−1.21967	−	0.203847i
$202$	120.875	+	87.8211i	0.598393	+	0.434758i
$203$	−531.173	+	172.588i	−2.61661	+	0.850190i
$204$	−0.712959	−	0.370958i	−0.00349490	−	0.00181842i
$205$	−175.763	−	127.699i	−0.857379	−	0.622922i
$206$	−86.5219	−	119.087i	−0.420009	−	0.578093i
$207$	25.4482	−	74.0051i	0.122938	−	0.357513i
$208$	250.098			1.20239
$209$		0			0
$210$	334.786	+	340.541i	1.59422	+	1.62163i
$211$	−47.8204	+	147.176i	−0.226637	+	0.697517i	0.771484	+	0.636248i	$0.219515\pi$
$211$	−47.8204	+	147.176i	−0.226637	+	0.697517i	−0.998121	+	0.0612686i	$0.980485\pi$
$212$	−246.427	−	339.178i	−1.16239	−	1.59989i
$213$	79.2346	−	11.8582i	0.371993	−	0.0556725i
$214$	−60.8610	−	187.311i	−0.284397	−	0.875285i
$215$	0.949812	−	0.308613i	0.00441773	−	0.00143541i
$216$	2.85839	+	21.6093i	0.0132333	+	0.100043i
$217$	−222.291	+	161.504i	−1.02438	+	0.744257i
$218$	344.110	+	111.808i	1.57849	+	0.512882i
$219$	29.3818	+	29.8870i	0.134164	+	0.136470i
$220$		0			0
$221$			1.05765i			0.00478576i
$222$	151.288	+	303.281i	0.681476	+	1.36613i
$223$	289.076	−	210.026i	1.29631	−	0.941821i	0.296393	−	0.955066i	$-0.404216\pi$
$223$	289.076	−	210.026i	1.29631	−	0.941821i	0.999912	+	0.0132452i	$0.00421621\pi$
$224$	−301.073	+	414.392i	−1.34408	+	1.84996i
$225$	−4.46231	+	1.36626i	−0.0198325	+	0.00607226i
$226$	−87.7950	−	270.205i	−0.388473	−	1.19560i
$227$	60.2830	−	82.9725i	0.265564	−	0.365517i	−0.655322	−	0.755350i	$-0.727467\pi$
$227$	60.2830	−	82.9725i	0.265564	−	0.365517i	0.920886	+	0.389832i	$0.127467\pi$
$228$	68.1557	+	11.3910i	0.298929	+	0.0499607i
$229$	−114.140	+	351.286i	−0.498426	+	1.53400i	0.313122	+	0.949713i	$0.398625\pi$
$229$	−114.140	+	351.286i	−0.498426	+	1.53400i	−0.811548	+	0.584285i	$0.801375\pi$
$230$			123.804i			0.538280i
$231$		0			0
$232$	40.3299			0.173836
$233$	−16.4775	−	5.35387i	−0.0707190	−	0.0229780i	0.273444	−	0.961888i	$-0.411837\pi$
$233$	−16.4775	−	5.35387i	−0.0707190	−	0.0229780i	−0.344163	+	0.938910i	$0.611837\pi$
$234$	358.416	−	251.184i	1.53169	−	1.07344i
$235$	59.6683	+	43.3516i	0.253908	+	0.184475i
$236$	−58.9975	+	19.1694i	−0.249989	+	0.0812264i
$237$	−69.4947	+	133.565i	−0.293226	+	0.563564i
$238$	−1.62893	−	1.18348i	−0.00684422	−	0.00497262i
$239$	−128.623	−	177.035i	−0.538172	−	0.740730i	0.450176	−	0.892940i	$-0.351361\pi$
$239$	−128.623	−	177.035i	−0.538172	−	0.740730i	−0.988348	+	0.152209i	$0.951361\pi$
$240$	98.0574	+	196.572i	0.408572	+	0.819050i
$241$	118.033			0.489765			0.244883	−	0.969553i	$-0.421251\pi$
$241$	118.033			0.489765			0.244883	+	0.969553i	$0.421251\pi$
$242$		0			0
$243$	−164.351	−	178.991i	−0.676343	−	0.736587i
$244$	−38.7876	+	119.376i	−0.158965	+	0.489245i
$245$	221.014	+	304.199i	0.902097	+	1.24163i
$246$	−56.1043	−	374.879i	−0.228066	−	1.52390i
$247$	−28.1010	−	86.4859i	−0.113769	−	0.350145i
$248$	18.8698	−	6.13117i	0.0760880	−	0.0247225i
$249$	−178.735	+	26.7494i	−0.717810	+	0.107427i
$250$	293.942	−	213.561i	1.17577	−	0.854246i
$251$	−152.702	−	49.6160i	−0.608376	−	0.197673i	−0.0114036	−	0.999935i	$-0.503630\pi$
$251$	−152.702	−	49.6160i	−0.608376	−	0.197673i	−0.596973	+	0.802262i	$0.703630\pi$
$252$	−7.34098	+	430.650i	−0.0291309	+	1.70893i
$253$		0			0
$254$			59.9950i			0.236201i
$255$	−0.831295	+	0.414681i	−0.00325998	+	0.00162620i
$256$	−175.076	+	127.200i	−0.683891	+	0.496876i
$257$	−15.3895	+	21.1818i	−0.0598811	+	0.0824193i	−0.837907	−	0.545813i	$-0.816221\pi$
$257$	−15.3895	+	21.1818i	−0.0598811	+	0.0824193i	0.778026	+	0.628232i	$0.216221\pi$
$258$	1.54575	+	0.804264i	0.00599127	+	0.00311730i
$259$	135.636	+	417.445i	0.523691	+	1.61176i
$260$	−210.384	+	289.568i	−0.809168	+	1.11372i
$261$	−368.186	+	258.031i	−1.41067	+	0.988623i
$262$	−25.8133	+	79.4451i	−0.0985240	+	0.303226i
$263$		−	221.020i		−	0.840378i	−0.907437	−	0.420189i	$-0.861964\pi$
$263$		−	221.020i		−	0.840378i	0.907437	−	0.420189i	$-0.138036\pi$
$264$		0			0
$265$	−484.606			−1.82870
$266$	164.644	+	53.4960i	0.618961	+	0.201113i
$267$	19.9541	−	119.391i	0.0747344	−	0.447156i
$268$	286.918	+	208.458i	1.07059	+	0.777828i
$269$	119.300	−	38.7629i	0.443494	−	0.144100i	−0.0787531	−	0.996894i	$-0.525094\pi$
$269$	119.300	−	38.7629i	0.443494	−	0.144100i	0.522247	+	0.852794i	$0.325094\pi$
$270$	337.952	+	183.225i	1.25167	+	0.678611i
$271$	−323.549	−	235.072i	−1.19391	−	0.867425i	−0.200236	−	0.979748i	$-0.564171\pi$
$271$	−323.549	−	235.072i	−1.19391	−	0.867425i	−0.993672	+	0.112323i	$0.964171\pi$
$272$	−0.544405	−	0.749309i	−0.00200149	−	0.00275481i
$273$	507.211	−	253.015i	1.85792	−	0.926796i
$274$	−436.561			−1.59329
$275$		0			0
$276$	−79.6276	+	78.2819i	−0.288506	+	0.283630i
$277$	22.7480	−	70.0112i	0.0821228	−	0.252748i	−0.901562	−	0.432651i	$-0.857578\pi$
$277$	22.7480	−	70.0112i	0.0821228	−	0.252748i	0.983684	+	0.179903i	$0.0575783\pi$
$278$	−32.5134	−	44.7508i	−0.116955	−	0.160974i
$279$	−133.042	+	176.703i	−0.476853	+	0.633343i
$280$	−13.8003	−	42.4730i	−0.0492869	−	0.151689i
$281$	398.855	−	129.596i	1.41941	−	0.461195i	0.503996	−	0.863706i	$-0.331863\pi$
$281$	398.855	−	129.596i	1.41941	−	0.461195i	0.915415	+	0.402511i	$0.131863\pi$
$282$	19.0464	+	127.265i	0.0675405	+	0.451293i
$283$	214.669	−	155.966i	0.758548	−	0.551117i	−0.139917	−	0.990163i	$-0.544683\pi$
$283$	214.669	−	155.966i	0.758548	−	0.551117i	0.898465	+	0.439046i	$0.144683\pi$
$284$	−108.720	−	35.3253i	−0.382817	−	0.124385i
$285$	56.9585	−	55.9959i	0.199854	−	0.196477i
$286$		0			0
$287$		−	490.903i		−	1.71046i
$288$	−134.084	+	389.925i	−0.465569	+	1.35391i
$289$	−233.803	+	169.868i	−0.809006	+	0.587777i
$290$	418.072	−	575.427i	1.44163	−	1.98423i
$291$	42.6667	−	82.0028i	0.146621	−	0.281797i
$292$	−18.4794	−	56.8737i	−0.0632856	−	0.194773i
$293$	111.987	−	154.137i	0.382209	−	0.526065i	−0.573959	−	0.818884i	$-0.694593\pi$
$293$	111.987	−	154.137i	0.382209	−	0.526065i	0.956168	+	0.292819i	$0.0945932\pi$
$294$	−108.146	+	647.069i	−0.367844	+	2.20091i
$295$	−22.1579	+	68.1950i	−0.0751115	+	0.231169i
$296$		−	31.6949i		−	0.107078i
$297$		0			0
$298$	522.763			1.75424
$299$	139.756	+	45.4094i	0.467410	+	0.151871i
$300$	6.56771	+	1.09768i	0.0218924	+	0.00365893i
$301$	1.82564	+	1.32641i	0.00606526	+	0.00440667i
$302$	383.671	−	124.662i	1.27043	−	0.412788i
$303$	138.180	+	71.8963i	0.456041	+	0.237282i
$304$	64.4253	+	46.8077i	0.211925	+	0.153973i
$305$	85.2801	+	117.378i	0.279607	+	0.384846i
$306$	−1.53275	−	0.527068i	−0.00500899	−	0.00172244i
$307$	−285.254			−0.929166			−0.464583	−	0.885530i	$-0.653796\pi$
$307$	−285.254			−0.929166			−0.464583	+	0.885530i	$0.653796\pi$
$308$		0			0
$309$	−107.585	−	109.434i	−0.348171	−	0.354156i
$310$	108.131	−	332.792i	0.348809	−	1.07352i
$311$	−296.766	−	408.463i	−0.954230	−	1.31339i	−0.949623	−	0.313396i	$-0.898533\pi$
$311$	−296.766	−	408.463i	−0.954230	−	1.31339i	−0.00460774	−	0.999989i	$-0.501467\pi$
$312$	−40.4789	+	6.05807i	−0.129740	+	0.0194169i
$313$	24.7740	+	76.2465i	0.0791501	+	0.243599i	0.982800	−	0.184673i	$-0.0591225\pi$
$313$	24.7740	+	76.2465i	0.0791501	+	0.243599i	−0.903650	+	0.428272i	$0.859123\pi$
$314$	−491.554	+	159.716i	−1.56546	+	0.508648i
$315$	397.731	+	299.457i	1.26264	+	0.950656i
$316$	173.801	−	126.274i	0.550004	−	0.399601i
$317$	8.23294	+	2.67505i	0.0259714	+	0.00843863i	0.321974	−	0.946749i	$-0.395654\pi$
$317$	8.23294	+	2.67505i	0.0259714	+	0.00843863i	−0.296002	+	0.955187i	$0.595654\pi$
$318$	−592.752	−	602.942i	−1.86400	−	1.89604i
$319$		0			0
$320$		−	359.417i		−	1.12318i
$321$	−91.6545	−	183.736i	−0.285528	−	0.572388i
$322$	−226.319	+	164.430i	−0.702854	+	0.510653i
$323$	−0.197948	+	0.272452i	−0.000612842	+	0.000843504i
$324$	95.8427	+	333.215i	0.295811	+	1.02844i
$325$	−2.70790	−	8.33406i	−0.00833200	−	0.0256433i
$326$	−374.236	+	515.091i	−1.14796	+	1.58003i
$327$	372.049	+	62.1816i	1.13777	+	0.190158i
$328$	−10.9541	+	33.7131i	−0.0333965	+	0.102784i
$329$			166.653i			0.506544i
$330$		0			0
$331$	28.2554			0.0853638			0.0426819	−	0.999089i	$-0.486410\pi$
$331$	28.2554			0.0853638			0.0426819	+	0.999089i	$0.486410\pi$
$332$	245.247	+	79.6856i	0.738696	+	0.240017i
$333$	202.784	+	289.354i	0.608962	+	0.868932i
$334$	−429.332	−	311.928i	−1.28542	−	0.933916i
$335$	389.875	−	126.678i	1.16381	−	0.378143i
$336$	−229.106	+	440.328i	−0.681863	+	1.31050i
$337$	233.420	+	169.589i	0.692640	+	0.503232i	0.877527	−	0.479527i	$-0.159192\pi$
$337$	233.420	+	169.589i	0.692640	+	0.503232i	−0.184887	+	0.982760i	$0.559192\pi$
$338$	197.209	+	271.435i	0.583458	+	0.803061i
$339$	−132.216	−	265.049i	−0.390018	−	0.781855i
$340$	1.32552			0.00389859
$341$		0			0
$342$	139.339	+	2.37521i	0.407424	+	0.00694506i
$343$	−93.2616	+	287.030i	−0.271900	+	0.836821i
$344$	−0.0957798	−	0.131830i	−0.000278430	−	0.000383226i
$345$	19.1040	+	127.649i	0.0553738	+	0.369998i
$346$	−216.567	−	666.526i	−0.625917	−	1.92637i
$347$	−250.710	+	81.4606i	−0.722507	+	0.234757i	−0.647110	−	0.762397i	$-0.724023\pi$
$347$	−250.710	+	81.4606i	−0.722507	+	0.234757i	−0.0753975	+	0.997154i	$0.524023\pi$
$348$	634.447	−	94.9512i	1.82312	−	0.272848i
$349$	394.738	−	286.794i	1.13106	−	0.821760i	0.145207	−	0.989401i	$-0.453615\pi$
$349$	394.738	−	286.794i	1.13106	−	0.821760i	0.985848	+	0.167641i	$0.0536150\pi$
$350$	15.8656	+	5.15505i	0.0453303	+	0.0147287i
$351$	330.787	−	314.291i	0.942412	−	0.895415i
$352$		0			0
$353$			437.345i			1.23894i	0.785021	+	0.619469i	$0.212652\pi$
$353$			437.345i			1.23894i	−0.785021	+	0.619469i	$0.787348\pi$
$354$	−111.950	+	55.8449i	−0.316244	+	0.157754i
$355$	−106.901	+	77.6678i	−0.301128	+	0.218782i
$356$	−101.520	+	139.730i	−0.285168	+	0.392500i
$357$	−1.86213	−	0.968881i	−0.00521605	−	0.00271395i
$358$	−281.550	−	866.521i	−0.786452	−	2.42045i
$359$	144.007	−	198.208i	0.401132	−	0.552111i	−0.559895	−	0.828563i	$-0.689159\pi$
$359$	144.007	−	198.208i	0.401132	−	0.552111i	0.961028	+	0.276452i	$0.0891587\pi$
$360$	−20.6323	−	29.4404i	−0.0573121	−	0.0817790i
$361$	−102.607	+	315.793i	−0.284231	+	0.874774i
$362$			88.9137i			0.245618i
$363$		0			0
$364$	−808.761			−2.22187
$365$	−65.7402	−	21.3603i	−0.180110	−	0.0585213i
$366$	−41.7292	+	249.677i	−0.114014	+	0.682178i
$367$	−182.111	−	132.311i	−0.496216	−	0.360522i	0.311354	−	0.950294i	$-0.399217\pi$
$367$	−182.111	−	132.311i	−0.496216	−	0.360522i	−0.807570	+	0.589772i	$0.799217\pi$
$368$	−122.385	+	39.7654i	−0.332569	+	0.108058i
$369$	−115.693	−	377.863i	−0.313532	−	1.02402i
$370$	−452.224	−	328.560i	−1.22223	−	0.887999i
$371$	−643.627	−	885.876i	−1.73484	−	2.38781i
$372$	282.414	−	140.879i	0.759178	−	0.378706i
$373$	−283.156			−0.759131			−0.379566	−	0.925165i	$-0.623927\pi$
$373$	−283.156			−0.759131			−0.379566	+	0.925165i	$0.623927\pi$
$374$		0			0
$375$	270.116	−	265.551i	0.720310	−	0.708136i
$376$	3.71871	−	11.4450i	0.00989019	−	0.0304389i
$377$	−496.224	−	682.994i	−1.31624	−	1.81165i
$378$	113.908	+	861.137i	0.301344	+	2.27814i
$379$	−141.092	−	434.237i	−0.372275	−	1.14574i	−0.945299	−	0.326205i	$-0.894230\pi$
$379$	−141.092	−	434.237i	−0.372275	−	1.14574i	0.573024	−	0.819538i	$-0.305770\pi$
$380$	−108.390	+	35.2180i	−0.285236	+	0.0926789i
$381$	9.25768	+	61.8581i	0.0242984	+	0.162357i
$382$	−688.910	+	500.523i	−1.80343	+	1.31027i
$383$	−305.540	−	99.2761i	−0.797755	−	0.259206i	−0.118352	−	0.992972i	$-0.537761\pi$
$383$	−305.540	−	99.2761i	−0.797755	−	0.259206i	−0.679403	+	0.733765i	$0.737761\pi$
$384$	55.1314	−	54.1997i	0.143571	−	0.141145i
$385$		0			0
$386$			228.790i			0.592721i
$387$	1.71785	+	0.590719i	0.00443890	+	0.00152641i
$388$	−106.706	+	77.5266i	−0.275016	+	0.199811i
$389$	185.407	−	255.190i	0.476624	−	0.656017i	−0.501228	−	0.865315i	$-0.667118\pi$
$389$	185.407	−	255.190i	0.476624	−	0.656017i	0.977852	+	0.209299i	$0.0671181\pi$
$390$	−333.181	+	640.353i	−0.854309	+	1.64193i
$391$	−0.168166	−	0.517562i	−0.000430093	−	0.00132369i
$392$	36.0615	−	49.6344i	0.0919936	−	0.126618i
$393$	−14.3559	+	85.8954i	−0.0365291	+	0.218563i
$394$	320.415	−	986.136i	0.813236	−	2.50288i
$395$		−	248.321i		−	0.628661i
$396$		0			0
$397$	−338.199			−0.851885			−0.425943	−	0.904750i	$-0.640057\pi$
$397$	−338.199			−0.851885			−0.425943	+	0.904750i	$0.640057\pi$
$398$	−1012.25	−	328.902i	−2.54335	−	0.826386i
$399$	178.011	+	29.7515i	0.446144	+	0.0745652i
$400$	6.20823	+	4.51054i	0.0155206	+	0.0112764i
$401$	−343.284	+	111.540i	−0.856070	+	0.278154i	−0.703986	−	0.710214i	$-0.748598\pi$
$401$	−343.284	+	111.540i	−0.856070	+	0.278154i	−0.152084	+	0.988368i	$0.548598\pi$
$402$	634.492	+	330.131i	1.57834	+	0.821221i
$403$	−336.009	−	244.125i	−0.833770	−	0.605769i
$404$	−130.638	−	179.807i	−0.323361	−	0.445068i
$405$	376.720	+	136.766i	0.930173	+	0.337694i
$406$	1607.16			3.95852
$407$		0			0
$408$	0.106264	+	0.108090i	0.000260450	+	0.000264928i
$409$	136.320	−	419.551i	0.333302	−	1.02580i	−0.634251	−	0.773127i	$-0.718691\pi$
$409$	136.320	−	419.551i	0.333302	−	1.02580i	0.967553	−	0.252670i	$-0.0813087\pi$
$410$	367.466	+	505.774i	0.896259	+	1.23359i
$411$	−450.119	+	67.3647i	−1.09518	+	0.163904i
$412$	67.6643	+	208.249i	0.164234	+	0.505460i
$413$	−154.092	+	50.0674i	−0.373103	+	0.121229i
$414$	−135.453	+	179.905i	−0.327180	+	0.434552i
$415$	241.143	−	175.200i	0.581066	−	0.422169i
$416$	−736.358	−	239.257i	−1.77009	−	0.575138i
$417$	−40.4284	−	41.1235i	−0.0969507	−	0.0986174i
$418$		0			0
$419$			393.180i			0.938377i	0.883098	+	0.469188i	$0.155453\pi$
$419$			393.180i			0.938377i	−0.883098	+	0.469188i	$0.844547\pi$
$420$	−317.096	−	635.671i	−0.754990	−	1.51350i
$421$	569.050	−	413.439i	1.35166	−	0.982041i	0.352737	−	0.935723i	$-0.385251\pi$
$421$	569.050	−	413.439i	1.35166	−	0.982041i	0.998927	−	0.0463181i	$-0.0147488\pi$
$422$	261.745	−	360.262i	0.620250	−	0.853701i
$423$	39.2758	+	128.278i	0.0928506	+	0.303257i
$424$	24.4340	+	75.2002i	0.0576274	+	0.177359i
$425$	−0.0190749	+	0.0262544i	−4.48821e−5	+	6.17749e-5i
$426$	−227.390	−	38.0043i	−0.533780	−	0.0892120i
$427$	−101.307	+	311.790i	−0.237252	+	0.730187i
$428$			292.973i			0.684515i
$429$		0			0
$430$	−2.87383			−0.00668332
$431$	−143.851	−	46.7401i	−0.333762	−	0.108446i	0.137342	−	0.990524i	$-0.456144\pi$
$431$	−143.851	−	46.7401i	−0.333762	−	0.108446i	−0.471103	+	0.882078i	$0.656144\pi$
$432$	−72.5759	+	392.929i	−0.168000	+	0.909558i
$433$	381.538	+	277.204i	0.881150	+	0.640193i	0.933555	−	0.358433i	$-0.116689\pi$
$433$	381.538	+	277.204i	0.881150	+	0.640193i	−0.0524055	+	0.998626i	$0.516689\pi$
$434$	751.969	−	244.330i	1.73265	−	0.562971i
$435$	342.262	−	657.808i	0.786810	−	1.51220i
$436$	−435.431	−	316.359i	−0.998695	−	0.725594i
$437$	27.5024	+	37.8538i	0.0629345	+	0.0866220i
$438$	−53.8347	−	107.920i	−0.122910	−	0.246394i
$439$	506.417			1.15357			0.576784	−	0.816897i	$-0.304307\pi$
$439$	506.417			1.15357			0.576784	+	0.816897i	$0.304307\pi$
$440$		0			0
$441$	−11.6571	+	683.851i	−0.0264334	+	1.55068i
$442$	0.940493	−	2.89454i	0.00212781	−	0.00654873i
$443$	375.325	+	516.591i	0.847235	+	1.16612i	0.984465	+	0.175580i	$0.0561801\pi$
$443$	375.325	+	516.591i	0.847235	+	1.16612i	−0.137230	+	0.990539i	$0.543820\pi$
$444$	−74.6215	−	498.607i	−0.168066	−	1.12299i
$445$	61.6926	+	189.870i	0.138635	+	0.426675i
$446$	−977.891	+	317.736i	−2.19258	+	0.712413i
$447$	538.997	−	80.6663i	1.20581	−	0.180461i
$448$	657.027	−	477.358i	1.46658	−	1.06553i
$449$	−315.250	−	102.431i	−0.702116	−	0.228131i	−0.0638637	−	0.997959i	$-0.520342\pi$
$449$	−315.250	−	102.431i	−0.702116	−	0.228131i	−0.638252	+	0.769827i	$0.720342\pi$
$450$	13.4272	+	0.228883i	0.0298381	+	0.000508629i
$451$		0			0
$452$			422.627i			0.935016i
$453$	376.349	−	187.737i	0.830792	−	0.414430i
$454$	−238.761	+	173.470i	−0.525906	+	0.382093i
$455$	−549.487	+	756.305i	−1.20766	+	1.66221i
$456$	−11.5612	−	6.01538i	−0.0253535	−	0.0131916i
$457$	−26.5560	−	81.7309i	−0.0581094	−	0.178842i	0.917789	−	0.397069i	$-0.129973\pi$
$457$	−26.5560	−	81.7309i	−0.0581094	−	0.178842i	−0.975898	+	0.218227i	$0.929973\pi$
$458$	624.744	−	859.887i	1.36407	−	1.87748i
$459$	−1.66168	−	0.306921i	−0.00362022	−	0.000668673i
$460$	56.9100	−	175.151i	0.123717	−	0.380763i
$461$			65.3245i			0.141702i	0.997487	+	0.0708508i	$0.0225714\pi$
$461$			65.3245i			0.141702i	−0.997487	+	0.0708508i	$0.977429\pi$
$462$		0			0
$463$	535.374			1.15632			0.578158	−	0.815925i	$-0.303772\pi$
$463$	535.374			1.15632			0.578158	+	0.815925i	$0.303772\pi$
$464$	703.113	+	228.455i	1.51533	+	0.492361i
$465$	60.1364	−	359.812i	0.129326	−	0.773790i
$466$	40.3341	+	29.3045i	0.0865539	+	0.0628851i
$467$	−473.636	+	153.894i	−1.01421	+	0.329537i	−0.768530	−	0.639814i	$-0.779011\pi$
$467$	−473.636	+	153.894i	−1.01421	+	0.329537i	−0.245681	+	0.969351i	$0.579011\pi$
$468$	−622.528	+	190.604i	−1.33019	+	0.407274i
$469$	749.382	+	544.458i	1.59783	+	1.16089i
$470$	−124.748	−	171.701i	−0.265422	−	0.365322i
$471$	−482.174	+	240.526i	−1.02372	+	0.510671i
$472$	11.6996			0.0247872
$473$		0			0
$474$	308.959	−	303.737i	0.651812	−	0.640796i
$475$	0.862227	−	2.65366i	0.00181521	−	0.00558665i
$476$	1.76048	+	2.42310i	0.00369850	+	0.00509055i
$477$	−704.198	−	530.200i	−1.47631	−	1.11153i
$478$	194.586	+	598.875i	0.407084	+	1.25288i
$479$	826.166	−	268.438i	1.72477	−	0.560412i	0.732094	−	0.681204i	$-0.238543\pi$
$479$	826.166	−	268.438i	1.72477	−	0.560412i	0.992678	+	0.120791i	$0.0385432\pi$
$480$	−100.657	−	672.571i	−0.209702	−	1.40119i
$481$	−536.760	+	389.979i	−1.11592	+	0.810767i
$482$	−323.029	−	104.958i	−0.670184	−	0.217756i
$483$	−207.974	+	204.459i	−0.430588	+	0.423311i
$484$		0			0
$485$			152.458i			0.314347i
$486$	290.626	+	635.999i	0.597997	+	1.30864i
$487$	−195.067	+	141.725i	−0.400549	+	0.291016i	−0.769764	−	0.638328i	$-0.779626\pi$
$487$	−195.067	+	141.725i	−0.400549	+	0.291016i	0.369216	+	0.929344i	$0.379626\pi$
$488$	13.9146	−	19.1518i	0.0285136	−	0.0392456i
$489$	−306.375	+	588.835i	−0.626534	+	1.20416i
$490$	−334.359	−	1029.05i	−0.682365	−	2.10010i
$491$	−293.922	+	404.549i	−0.598619	+	0.823928i	−0.995581	−	0.0939071i	$-0.970064\pi$
$491$	−293.922	+	404.549i	−0.598619	+	0.823928i	0.396962	+	0.917835i	$0.370064\pi$
$492$	−92.9501	+	556.146i	−0.188923	+	1.13038i
$493$	−0.966128	+	2.97344i	−0.00195969	+	0.00603131i
$494$			261.679i			0.529714i
$495$		0			0
$496$	363.708			0.733283
$497$	−283.959	−	92.2638i	−0.571346	−	0.185641i
$498$	512.939	+	85.7288i	1.03000	+	0.172146i
$499$	448.855	+	326.112i	0.899509	+	0.653531i	0.938340	−	0.345715i	$-0.112363\pi$
$499$	448.855	+	326.112i	0.899509	+	0.653531i	−0.0388311	+	0.999246i	$0.512363\pi$
$500$	−514.021	+	167.015i	−1.02804	+	0.334031i
$501$	−490.797	−	255.365i	−0.979635	−	0.509712i
$502$	373.789	+	271.574i	0.744600	+	0.540984i
$503$	395.277	+	544.051i	0.785838	+	1.08161i	0.994614	+	0.103650i	$0.0330521\pi$
$503$	395.277	+	544.051i	0.785838	+	1.08161i	−0.208776	+	0.977964i	$0.566948\pi$
$504$	26.4154	−	76.8178i	0.0524115	−	0.152416i
$505$	−256.903			−0.508719
$506$		0			0
$507$	245.217	+	249.433i	0.483664	+	0.491979i
$508$	27.5783	−	84.8773i	0.0542880	−	0.167081i
$509$	−378.324	−	520.719i	−0.743270	−	1.02302i	−0.998424	−	0.0561224i	$-0.982126\pi$
$509$	−378.324	−	520.719i	−0.743270	−	1.02302i	0.255154	−	0.966900i	$-0.417874\pi$
$510$	2.64380	−	0.395670i	0.00518392	−	0.000775824i
$511$	−48.2651	−	148.545i	−0.0944523	−	0.290694i
$512$	690.287	−	224.288i	1.34822	−	0.438062i
$513$	144.033	−	19.0521i	0.280765	−	0.0371386i
$514$	60.9525	−	44.2846i	0.118585	−	0.0861568i
$515$	240.715	+	78.2130i	0.467407	+	0.151870i
$516$	−1.81713	−	1.84837i	−0.00352157	−	0.00358211i
$517$		0			0
$518$		−	1263.06i		−	2.43833i
$519$	−326.143	−	653.806i	−0.628406	−	1.25974i
$520$	54.6127	−	39.6785i	0.105025	−	0.0763048i
$521$	313.882	−	432.022i	0.602462	−	0.829217i	−0.393469	−	0.919338i	$-0.628725\pi$
$521$	313.882	−	432.022i	0.602462	−	0.829217i	0.995931	+	0.0901206i	$0.0287252\pi$
$522$	1237.08	−	378.767i	2.36989	−	0.725606i
$523$	307.507	+	946.409i	0.587967	+	1.80958i	0.587013	+	0.809577i	$0.300304\pi$
$523$	307.507	+	946.409i	0.587967	+	1.80958i	0.000954046		1.00000i	$0.499696\pi$
$524$	73.0382	−	100.528i	0.139386	−	0.191848i
$525$	17.1538	+	2.86695i	0.0326738	+	0.00546086i
$526$	−196.536	+	604.876i	−0.373643	+	1.14996i
$527$			1.53811i			0.00291861i
$528$		0			0
$529$	453.391			0.857071
$530$	1326.25	+	430.924i	2.50235	+	0.813064i
$531$	−106.810	+	74.8539i	−0.201148	+	0.140968i
$532$	−208.337	−	151.366i	−0.391611	−	0.284522i
$533$	705.718	−	229.302i	1.32405	−	0.430210i
$534$	−160.775	+	309.000i	−0.301076	+	0.578651i
$535$	273.970	+	199.051i	0.512094	+	0.372058i
$536$	−39.3153	−	54.1129i	−0.0733494	−	0.100957i
$537$	−424.004	−	849.985i	−0.789579	−	1.58284i
$538$	−360.964			−0.670936
$539$		0			0
$540$	−393.890	−	414.564i	−0.729426	−	0.767711i
$541$	213.440	−	656.899i	0.394528	−	1.21423i	−0.534801	−	0.844978i	$-0.679613\pi$
$541$	213.440	−	656.899i	0.394528	−	1.21423i	0.929329	−	0.369254i	$-0.120387\pi$
$542$	676.442	+	931.043i	1.24805	+	1.71779i
$543$	13.7201	+	91.6749i	0.0252671	+	0.168830i
$544$	0.886051	+	2.72698i	0.00162877	+	0.00501284i
$545$	−591.680	+	192.248i	−1.08565	+	0.352749i
$546$	−1613.10	+	241.416i	−2.95440	+	0.442155i
$547$	−70.3505	+	51.1127i	−0.128612	+	0.0934418i	−0.650231	−	0.759736i	$-0.725328\pi$
$547$	−70.3505	+	51.1127i	−0.128612	+	0.0934418i	0.521620	+	0.853178i	$0.325328\pi$
$548$	617.621	+	200.677i	1.12705	+	0.366199i
$549$	−4.49800	+	263.870i	−0.00819307	+	0.480637i
$550$		0			0
$551$		−	268.812i		−	0.487861i
$552$	18.8451	−	9.40064i	0.0341397	−	0.0170301i
$553$	453.940	−	329.807i	0.820868	−	0.596395i
$554$	−124.511	+	171.375i	−0.224750	+	0.309342i
$555$	−516.966	−	268.981i	−0.931471	−	0.484651i
$556$	25.4270	+	78.2564i	0.0457321	+	0.140749i
$557$	−432.298	+	595.007i	−0.776118	+	1.06824i	0.219581	+	0.975594i	$0.429531\pi$
$557$	−432.298	+	595.007i	−0.776118	+	1.06824i	−0.995700	+	0.0926409i	$0.970469\pi$
$558$	521.232	−	365.288i	0.934107	−	0.654638i
$559$	−1.05407	+	3.24410i	−0.00188564	+	0.00580339i
$560$		−	818.651i		−	1.46188i
$561$		0			0
$562$	−1206.81			−2.14734
$563$	−542.073	−	176.130i	−0.962829	−	0.312842i	−0.214911	−	0.976634i	$-0.568946\pi$
$563$	−542.073	−	176.130i	−0.962829	−	0.312842i	−0.747918	+	0.663792i	$0.768946\pi$
$564$	31.5549	−	188.802i	0.0559484	−	0.334755i
$565$	395.216	+	287.141i	0.699497	+	0.508214i
$566$	−726.186	+	235.952i	−1.28301	+	0.416876i
$567$	250.325	+	870.302i	0.441491	+	1.53492i
$568$	17.4423	+	12.6726i	0.0307083	+	0.0223109i
$569$	333.772	+	459.398i	0.586594	+	0.807378i	0.994399	−	0.105691i	$-0.0337055\pi$
$569$	333.772	+	459.398i	0.586594	+	0.807378i	−0.407805	+	0.913069i	$0.633706\pi$
$570$	−205.674	+	102.598i	−0.360832	+	0.179996i
$571$	229.442			0.401825			0.200912	−	0.979609i	$-0.435609\pi$
$571$	229.442			0.401825			0.200912	+	0.979609i	$0.435609\pi$
$572$		0			0
$573$	−633.070	+	622.370i	−1.10483	+	1.08616i
$574$	−436.523	+	1343.48i	−0.760494	+	2.34056i
$575$	2.65022	+	3.64771i	0.00460908	+	0.00634385i
$576$	393.233	−	522.282i	0.682696	−	0.906740i
$577$	−222.195	−	683.846i	−0.385087	−	1.18518i	−0.936417	−	0.350888i	$-0.885880\pi$
$577$	−222.195	−	683.846i	−0.385087	−	1.18518i	0.551331	−	0.834287i	$-0.314120\pi$
$578$	790.912	−	256.983i	1.36836	−	0.444607i
$579$	35.3041	+	235.895i	0.0609742	+	0.407419i
$580$	−855.973	+	621.901i	−1.47582	+	1.07224i
$581$	640.544	+	208.125i	1.10249	+	0.358219i
$582$	−189.687	+	186.481i	−0.325923	+	0.320415i
$583$		0			0
$584$			11.2784i			0.0193124i
$585$	−244.716	+	711.651i	−0.418318	+	1.21650i
$586$	−443.544	+	322.254i	−0.756902	+	0.549921i
$587$	−300.738	+	413.930i	−0.512331	+	0.705162i	−0.984310	−	0.176447i	$-0.943540\pi$
$587$	−300.738	+	413.930i	−0.512331	+	0.705162i	0.471980	+	0.881609i	$0.343540\pi$
$588$	450.441	−	865.722i	0.766057	−	1.47232i
$589$	−40.8662	−	125.773i	−0.0693824	−	0.213537i
$590$	121.281	−	166.930i	0.205562	−	0.282931i
$591$	178.197	−	1066.20i	0.301518	−	1.80407i
$592$	179.541	−	552.571i	0.303279	−	0.933398i
$593$		−	241.775i		−	0.407715i	−0.979001	−	0.203858i	$-0.934652\pi$
$593$		−	241.775i		−	0.407715i	0.979001	−	0.203858i	$-0.0653480\pi$
$594$		0			0
$595$	3.46204			0.00581856
$596$	−739.573	−	240.302i	−1.24089	−	0.403191i
$597$	−1094.44	−	182.917i	−1.83324	−	0.306393i
$598$	−342.098	−	248.549i	−0.572070	−	0.415633i
$599$	460.604	−	149.659i	0.768955	−	0.249849i	0.101837	−	0.994801i	$-0.467528\pi$
$599$	460.604	−	149.659i	0.768955	−	0.249849i	0.667118	+	0.744952i	$0.267528\pi$
$600$	−1.11407	−	0.579661i	−0.00185679	−	0.000966102i
$601$	−391.082	−	284.138i	−0.650719	−	0.472775i	0.212797	−	0.977096i	$-0.431743\pi$
$601$	−391.082	−	284.138i	−0.650719	−	0.472775i	−0.863516	+	0.504321i	$0.831743\pi$
$602$	−3.81686	−	5.25346i	−0.00634030	−	0.00872668i
$603$	705.138	+	242.476i	1.16938	+	0.402116i
$604$	−600.098			−0.993540
$605$		0			0
$606$	−314.234	−	319.636i	−0.518538	−	0.527453i
$607$	−153.768	+	473.248i	−0.253324	+	0.779651i	0.740831	+	0.671691i	$0.234432\pi$
$607$	−153.768	+	473.248i	−0.253324	+	0.779651i	−0.994155	+	0.107960i	$0.965568\pi$
$608$	−144.907	−	199.448i	−0.238334	−	0.328039i
$609$	1657.07	−	247.997i	2.72097	−	0.407220i
$610$	−129.015	−	397.068i	−0.211500	−	0.650931i
$611$	−239.579	+	77.8439i	−0.392109	+	0.127404i
$612$	1.92616	+	1.45023i	0.00314733	+	0.00236966i
$613$	847.792	−	615.957i	1.38302	−	1.00482i	0.386431	−	0.922318i	$-0.373708\pi$
$613$	847.792	−	615.957i	1.38302	−	1.00482i	0.996591	−	0.0825060i	$-0.0262924\pi$
$614$	780.670	+	253.655i	1.27145	+	0.413119i
$615$	456.922	+	464.777i	0.742963	+	0.755735i
$616$		0			0
$617$			322.739i			0.523078i	0.965193	+	0.261539i	$0.0842301\pi$
$617$			322.739i			0.523078i	−0.965193	+	0.261539i	$0.915770\pi$
$618$	197.121	+	395.162i	0.318967	+	0.639421i
$619$	−435.469	+	316.387i	−0.703504	+	0.511126i	−0.881072	−	0.472983i	$-0.843177\pi$
$619$	−435.469	+	316.387i	−0.703504	+	0.511126i	0.177567	+	0.984109i	$0.443177\pi$
$620$	−305.954	+	421.109i	−0.493474	+	0.679208i
$621$	−111.898	+	206.393i	−0.180191	+	0.332356i
$622$	448.959	+	1381.75i	0.721799	+	2.22147i
$623$	−265.153	+	364.951i	−0.425606	+	0.585797i
$624$	−740.029	−	123.683i	−1.18594	−	0.198210i
$625$	−189.047	+	581.826i	−0.302475	+	0.930921i
$626$		−	230.698i		−	0.368527i
$627$		0			0
$628$	768.838			1.22426
$629$	2.33680	+	0.759273i	0.00371511	+	0.00120711i
$630$	−822.207	−	1173.21i	−1.30509	−	1.86224i
$631$	−714.632	−	519.211i	−1.13254	−	0.822838i	−0.146477	−	0.989214i	$-0.546793\pi$
$631$	−714.632	−	519.211i	−1.13254	−	0.822838i	−0.986062	+	0.166376i	$0.946793\pi$
$632$	−38.5340	+	12.5205i	−0.0609715	+	0.0198109i
$633$	214.283	−	411.839i	0.338519	−	0.650614i
$634$	−20.1528	−	14.6419i	−0.0317868	−	0.0230945i
$635$	−60.6349	−	83.4568i	−0.0954881	−	0.131428i
$636$	561.431	+	1125.48i	0.882753	+	1.76962i
$637$	−1284.27			−2.01613
$638$		0			0
$639$	−240.316	−	4.09649i	−0.376082	−	0.00641079i
$640$	−39.4025	+	121.269i	−0.0615665	+	0.189482i
$641$	−173.396	−	238.659i	−0.270509	−	0.372323i	0.652053	−	0.758174i	$-0.273908\pi$
$641$	−173.396	−	238.659i	−0.270509	−	0.372323i	−0.922561	+	0.385850i	$0.873908\pi$
$642$	87.4528	+	584.343i	0.136219	+	0.910192i
$643$	258.185	+	794.613i	0.401532	+	1.23579i	0.923756	+	0.382981i	$0.125103\pi$
$643$	258.185	+	794.613i	0.401532	+	1.23579i	−0.522224	+	0.852809i	$0.674897\pi$
$644$	395.767	−	128.592i	0.614545	−	0.199678i
$645$	−2.96307	+	0.443453i	−0.00459391	+	0.000687525i
$646$	0.784006	−	0.569614i	0.00121363	−	0.000881755i
$647$	777.637	+	252.670i	1.20191	+	0.390525i	0.840464	−	0.541867i	$-0.182282\pi$
$647$	777.637	+	252.670i	1.20191	+	0.390525i	0.361448	+	0.932392i	$0.382282\pi$
$648$	2.22875	−	65.3545i	0.00343943	−	0.100856i
$649$		0			0
$650$			25.2162i			0.0387942i
$651$	737.619	−	367.952i	1.13306	−	0.565210i
$652$	766.222	−	556.693i	1.17519	−	0.853823i
$653$	−162.445	+	223.586i	−0.248767	+	0.342399i	−0.915079	−	0.403275i	$-0.867872\pi$
$653$	−162.445	+	223.586i	−0.248767	+	0.342399i	0.666312	+	0.745673i	$0.267872\pi$
$654$	−962.915	−	501.012i	−1.47235	−	0.766073i
$655$	−44.3846	−	136.602i	−0.0677628	−	0.208552i
$656$	−381.947	+	525.706i	−0.582237	+	0.801380i
$657$	−72.1594	−	102.965i	−0.109832	−	0.156719i
$658$	148.192	−	456.088i	0.225216	−	0.693143i
$659$		−	881.372i		−	1.33744i	−0.743515	−	0.668719i	$-0.766843\pi$
$659$		−	881.372i		−	1.33744i	0.743515	−	0.668719i	$-0.233157\pi$
$660$		0			0
$661$	−501.036			−0.757997			−0.378999	−	0.925397i	$-0.623731\pi$
$661$	−501.036			−0.757997			−0.378999	+	0.925397i	$0.623731\pi$
$662$	−77.3282	−	25.1255i	−0.116810	−	0.0379539i
$663$	0.523050	−	3.12955i	0.000788914	−	0.00472029i
$664$	−39.3458	−	28.5864i	−0.0592557	−	0.0430518i
$665$	−283.096	+	91.9836i	−0.425709	+	0.138321i
$666$	−297.670	−	972.213i	−0.446952	−	1.45978i
$667$	351.423	+	255.323i	0.526870	+	0.382794i
$668$	464.007	+	638.650i	0.694621	+	0.956064i
$669$	−959.230	+	478.499i	−1.43383	+	0.715245i
$670$	−1179.64			−1.76065
$671$		0			0
$672$	1095.80	−	1077.28i	1.63065	−	1.60309i
$673$	−1.37662	+	4.23681i	−0.00204550	+	0.00629541i	−0.952074	−	0.305868i	$-0.901054\pi$
$673$	−1.37662	+	4.23681i	−0.00204550	+	0.00629541i	0.950029	+	0.312163i	$0.101054\pi$
$674$	−488.009	−	671.687i	−0.724049	−	0.996568i
$675$	13.8795	−	1.83592i	0.0205622	−	0.00271988i
$676$	−154.227	−	474.662i	−0.228146	−	0.702162i
$677$	−16.4345	+	5.33989i	−0.0242755	+	0.00788758i	−0.321130	−	0.947035i	$-0.604062\pi$
$677$	−16.4345	+	5.33989i	−0.0242755	+	0.00788758i	0.296854	+	0.954923i	$0.404062\pi$
$678$	126.155	+	842.944i	0.186069	+	1.24328i
$679$	−278.699	+	202.487i	−0.410455	+	0.298213i
$680$	−0.237759	−	0.0772525i	−0.000349645	−	0.000113607i
$681$	−219.408	+	215.700i	−0.322185	+	0.316740i
$682$		0			0
$683$		−	1085.69i		−	1.58958i	−0.606882	−	0.794792i	$-0.707580\pi$
$683$		−	1085.69i		−	1.58958i	0.606882	−	0.794792i	$-0.292420\pi$
$684$	−196.037	−	67.4112i	−0.286603	−	0.0985544i
$685$	607.284	−	441.218i	0.886547	−	0.644114i
$686$	510.468	−	702.600i	0.744123	−	1.02420i
$687$	511.458	−	982.993i	0.744481	−	1.43085i
$688$	−0.923060	−	2.84089i	−0.00134166	−	0.00412919i
$689$	972.890	−	1339.07i	1.41203	−	1.94349i
$690$	61.2260	−	366.332i	0.0887334	−	0.530916i
$691$	−62.2864	+	191.698i	−0.0901395	+	0.277421i	−0.985957	−	0.167002i	$-0.946591\pi$
$691$	−62.2864	+	191.698i	−0.0901395	+	0.277421i	0.895817	+	0.444423i	$0.146591\pi$
$692$			1042.51i			1.50652i
$693$		0			0
$694$	758.569			1.09304
$695$	90.4563	+	29.3910i	0.130153	+	0.0422892i
$696$	−119.334	−	19.9447i	−0.171457	−	0.0286561i
$697$	−2.22319	−	1.61524i	−0.00318965	−	0.00231742i
$698$	−1335.33	+	433.874i	−1.91308	+	0.621596i
$699$	46.1086	+	23.9906i	0.0659637	+	0.0343214i
$700$	−20.0760	−	14.5861i	−0.0286801	−	0.0208373i
$701$	252.573	+	347.637i	0.360304	+	0.495916i	0.950233	−	0.311539i	$-0.100845\pi$
$701$	252.573	+	347.637i	0.360304	+	0.495916i	−0.589930	+	0.807455i	$0.700845\pi$
$702$	−1184.76	+	565.992i	−1.68769	+	0.806257i
$703$	−211.257			−0.300508
$704$		0			0
$705$	−155.117	−	157.784i	−0.220024	−	0.223807i
$706$	388.899	−	1196.91i	0.550848	−	1.69534i
$707$	−341.204	−	469.627i	−0.482609	−	0.664254i
$708$	184.051	−	27.5451i	0.259959	−	0.0389054i
$709$	231.622	+	712.859i	0.326688	+	1.00544i	0.970673	+	0.240404i	$0.0772801\pi$
$709$	231.622	+	712.859i	0.326688	+	1.00544i	−0.643985	+	0.765038i	$0.722720\pi$
$710$	361.625	−	117.499i	0.509331	−	0.165492i
$711$	271.685	−	360.844i	0.382116	−	0.507517i
$712$	26.3531	−	19.1467i	0.0370128	−	0.0268914i
$713$	203.242	+	66.0372i	0.285052	+	0.0926189i
$714$	4.23464	+	4.30744i	0.00593087	+	0.00603283i
$715$		0			0
$716$			1355.32i			1.89291i
$717$	293.040	+	587.447i	0.408703	+	0.819312i
$718$	−570.362	+	414.392i	−0.794376	+	0.577148i
$719$	−265.207	+	365.026i	−0.368855	+	0.507685i	−0.952589	−	0.304260i	$-0.901591\pi$
$719$	−265.207	+	365.026i	−0.368855	+	0.507685i	0.583734	+	0.811945i	$0.301591\pi$
$720$	−192.935	−	630.141i	−0.267966	−	0.875197i
$721$	176.728	+	543.913i	0.245115	+	0.754387i
$722$	561.623	−	773.008i	0.777871	−	1.07065i
$723$	−349.256	−	58.3720i	−0.483065	−	0.0807359i
$724$	40.8716	−	125.790i	0.0564524	−	0.173743i
$725$		−	25.9035i		−	0.0357290i
$726$		0			0
$727$	300.631			0.413523			0.206761	−	0.978391i	$-0.433708\pi$
$727$	300.631			0.413523			0.206761	+	0.978391i	$0.433708\pi$
$728$	145.067	+	47.1352i	0.199268	+	0.0647462i
$729$	397.791	+	610.904i	0.545667	+	0.838002i
$730$	160.921	+	116.916i	0.220439	+	0.160158i
$731$	0.0120140	−	0.00390358i	1.64350e−5	−	5.34006e-6i
$732$	173.807	−	334.046i	0.237441	−	0.456347i
$733$	−1078.72	−	783.739i	−1.47166	−	1.06922i	−0.980130	−	0.198357i	$-0.936439\pi$
$733$	−1078.72	−	783.739i	−1.47166	−	1.06922i	−0.491526	−	0.870863i	$-0.663561\pi$
$734$	380.739	+	524.042i	0.518718	+	0.713954i
$735$	−503.532	−	1009.41i	−0.685078	−	1.37335i
$736$	398.379			0.541275
$737$		0			0
$738$	−19.3815	+	1137.00i	−0.0262623	+	1.54065i
$739$	−326.316	+	1004.30i	−0.441565	+	1.35900i	0.444643	+	0.895708i	$0.353331\pi$
$739$	−326.316	+	1004.30i	−0.441565	+	1.35900i	−0.886207	+	0.463289i	$0.846669\pi$
$740$	488.747	+	672.703i	0.660469	+	0.909058i
$741$	40.3790	+	269.805i	0.0544926	+	0.364109i
$742$	973.705	+	2996.76i	1.31227	+	4.03875i
$743$	959.620	−	311.799i	1.29155	−	0.419649i	0.418914	−	0.908026i	$-0.362411\pi$
$743$	959.620	−	311.799i	1.29155	−	0.419649i	0.872633	+	0.488377i	$0.162411\pi$
$744$	−58.8671	+	8.81004i	−0.0791224	+	0.0118415i
$745$	−727.196	+	528.339i	−0.976102	+	0.709180i
$746$	774.928	+	251.789i	1.03878	+	0.337519i
$747$	542.097	+	9.24073i	0.725699	+	0.0123705i
$748$		0			0
$749$			765.196i			1.02162i
$750$	−975.376	+	486.554i	−1.30050	+	0.648738i
$751$	40.6835	−	29.5583i	0.0541725	−	0.0393586i	−0.560369	−	0.828243i	$-0.689341\pi$
$751$	40.6835	−	29.5583i	0.0541725	−	0.0393586i	0.614542	+	0.788884i	$0.289341\pi$
$752$	129.664	−	178.468i	0.172426	−	0.237324i
$753$	427.303	+	222.329i	0.567468	+	0.295258i
$754$	750.708	+	2310.44i	0.995634	+	3.06425i
$755$	−407.718	+	561.176i	−0.540024	+	0.743279i
$756$	234.695	−	1270.65i	0.310443	−	1.68075i
$757$	97.8844	−	301.257i	0.129306	−	0.397962i	−0.865355	−	0.501159i	$-0.832907\pi$
$757$	97.8844	−	301.257i	0.129306	−	0.397962i	0.994661	+	0.103197i	$0.0329072\pi$
$758$			1313.86i			1.73333i
$759$		0			0
$760$	21.4944			0.0282821
$761$	67.8819	+	22.0562i	0.0892009	+	0.0289831i	0.353277	−	0.935519i	$-0.385067\pi$
$761$	67.8819	+	22.0562i	0.0892009	+	0.0289831i	−0.264077	+	0.964502i	$0.585067\pi$
$762$	29.6698	−	177.523i	0.0389368	−	0.232969i
$763$	−1137.27	−	826.277i	−1.49053	−	1.08293i
$764$	1204.71	−	391.433i	1.57684	−	0.512347i
$765$	2.66484	−	0.815915i	0.00348346	−	0.00106656i
$766$	747.910	+	543.389i	0.976384	+	0.709384i
$767$	−143.953	−	198.134i	−0.187683	−	0.258324i
$768$	580.948	−	289.798i	0.756443	−	0.377341i
$769$	634.282			0.824814			0.412407	−	0.911000i	$-0.364688\pi$
$769$	634.282			0.824814			0.412407	+	0.911000i	$0.364688\pi$
$770$		0			0
$771$	56.0119	−	55.0653i	0.0726484	−	0.0714206i
$772$	105.170	−	323.679i	0.136230	−	0.419273i
$773$	507.637	+	698.702i	0.656710	+	0.903884i	0.999367	−	0.0355767i	$-0.0113268\pi$
$773$	507.637	+	698.702i	0.656710	+	0.903884i	−0.342657	+	0.939461i	$0.611327\pi$
$774$	−4.17606	−	3.14421i	−0.00539543	−	0.00406229i
$775$	−3.93800	−	12.1199i	−0.00508130	−	0.0156386i
$776$	23.6582	−	7.68701i	0.0304873	−	0.00990594i
$777$	−194.899	−	1302.28i	−0.250835	−	1.67603i
$778$	−734.335	+	533.525i	−0.943875	+	0.685765i
$779$	224.709	+	73.0123i	0.288458	+	0.0937257i
$780$	765.719	−	752.778i	0.981691	−	0.965100i
$781$		0			0
$782$			1.56598i			0.00200253i
$783$	1217.05	−	581.420i	1.55434	−	0.742554i
$784$	909.860	−	661.052i	1.16054	−	0.843179i
$785$	522.363	−	718.971i	0.665431	−	0.915887i
$786$	115.669	−	222.309i	0.147162	−	0.282836i
$787$	−371.943	−	1144.72i	−0.472609	−	1.45454i	−0.849155	−	0.528143i	$-0.822888\pi$
$787$	−371.943	−	1144.72i	−0.472609	−	1.45454i	0.376546	−	0.926398i	$-0.377112\pi$
$788$	−906.608	+	1247.84i	−1.15052	+	1.58355i
$789$	−109.303	+	653.987i	−0.138533	+	0.828881i
$790$	−220.814	+	679.595i	−0.279511	+	0.860246i
$791$			1103.83i			1.39549i
$792$		0			0
$793$	−495.547			−0.624902
$794$	925.567	+	300.735i	1.16570	+	0.378759i
$795$	1433.93	+	239.656i	1.80368	+	0.301454i
$796$	1280.89	+	930.620i	1.60916	+	1.16912i
$797$	595.973	−	193.643i	0.747770	−	0.242965i	0.0897487	−	0.995964i	$-0.471394\pi$
$797$	595.973	−	193.643i	0.747770	−	0.242965i	0.658021	+	0.752999i	$0.271394\pi$
$798$	−460.718	−	239.715i	−0.577341	−	0.300395i
$799$	0.754733	+	0.548346i	0.000944597	+	0.000686290i
$800$	−13.9637	−	19.2194i	−0.0174547	−	0.0240243i
$801$	−118.087	+	343.404i	−0.147424	+	0.428719i
$802$	1038.67			1.29510
$803$		0			0
$804$	−745.887	−	758.710i	−0.927721	−	0.943670i
$805$	148.640	−	457.466i	0.184645	−	0.568280i
$806$	702.493	+	966.898i	0.871579	+	1.19963i
$807$	−372.173	+	55.6994i	−0.461181	+	0.0690203i
$808$	12.9532	+	39.8657i	0.0160311	+	0.0493387i
$809$	−382.449	+	124.265i	−0.472743	+	0.153604i	−0.535692	−	0.844413i	$-0.679949\pi$
$809$	−382.449	+	124.265i	−0.472743	+	0.153604i	0.0629493	+	0.998017i	$0.479949\pi$
$810$	−909.374	−	709.285i	−1.12268	−	0.875660i
$811$	448.052	−	325.529i	0.552469	−	0.401392i	−0.276226	−	0.961093i	$-0.589084\pi$
$811$	448.052	−	325.529i	0.552469	−	0.401392i	0.828695	+	0.559701i	$0.189084\pi$
$812$	−2273.71	−	738.774i	−2.80014	−	0.909820i
$813$	841.116	+	855.576i	1.03458	+	1.05237i
$814$		0			0
$815$		−	1094.75i		−	1.34325i
$816$	1.24031	+	2.48640i	0.00151999	+	0.00304706i
$817$	−0.878687	+	0.638403i	−0.00107550	+	0.000781399i
$818$	−746.151	+	1026.99i	−0.912165	+	1.25549i
$819$	−1625.94	+	497.827i	−1.98528	+	0.607847i
$820$	−287.376	−	884.453i	−0.350459	−	1.07860i
$821$	−129.901	+	178.794i	−0.158223	+	0.217776i	−0.880767	−	0.473549i	$-0.842973\pi$
$821$	−129.901	+	178.794i	−0.158223	+	0.217776i	0.722544	+	0.691325i	$0.242973\pi$
$822$	1291.77	+	215.896i	1.57149	+	0.262648i
$823$	222.107	−	683.574i	0.269875	−	0.830589i	−0.720656	−	0.693293i	$-0.756159\pi$
$823$	222.107	−	683.574i	0.269875	−	0.830589i	0.990530	−	0.137295i	$-0.0438409\pi$
$824$		−	41.2972i		−	0.0501179i
$825$		0			0
$826$	466.232			0.564446
$827$	−610.949	−	198.509i	−0.738753	−	0.240035i	−0.0846182	−	0.996413i	$-0.526967\pi$
$827$	−610.949	−	198.509i	−0.738753	−	0.240035i	−0.654135	+	0.756378i	$0.726967\pi$
$828$	274.328	−	192.254i	0.331314	−	0.232191i
$829$	−664.227	−	482.589i	−0.801239	−	0.582134i	0.110038	−	0.993927i	$-0.464903\pi$
$829$	−664.227	−	482.589i	−0.801239	−	0.582134i	−0.911277	+	0.411793i	$0.864903\pi$
$830$	−815.741	+	265.050i	−0.982820	+	0.319338i
$831$	−101.934	+	195.910i	−0.122664	+	0.235753i
$832$	993.145	+	721.562i	1.19368	+	0.867262i
$833$	2.79556	+	3.84776i	0.00335602	+	0.00461916i
$834$	74.0747	+	148.495i	0.0888186	+	0.178051i
$835$	912.483			1.09279
$836$		0			0
$837$	481.052	−	457.062i	0.574733	−	0.546071i
$838$	349.626	−	1076.04i	0.417214	−	1.28405i
$839$	202.110	+	278.180i	0.240894	+	0.331562i	0.912296	−	0.409531i	$-0.134308\pi$
$839$	202.110	+	278.180i	0.240894	+	0.331562i	−0.671402	+	0.741093i	$0.734308\pi$
$840$	19.8300	+	132.501i	0.0236072	+	0.157739i
$841$	−511.287	−	1573.58i	−0.607952	−	1.87108i
$842$	−1924.99	+	625.468i	−2.28621	+	0.742836i
$843$	−1244.28	+	186.219i	−1.47602	+	0.220901i
$844$	−535.906	+	389.358i	−0.634959	+	0.461325i
$845$	−548.660	−	178.270i	−0.649302	−	0.210971i
$846$	6.57969	−	385.990i	0.00777741	−	0.456253i
$847$		0			0
$848$			1449.45i			1.70926i
$849$	−712.328	+	355.335i	−0.839020	+	0.418534i
$850$	0.0755494	−	0.0548898i	8.88816e−5	−	6.45763e-5i
$851$	200.657	−	276.180i	0.235789	−	0.324536i
$852$	304.228	+	158.292i	0.357075	+	0.185789i
$853$	−105.689	−	325.277i	−0.123903	−	0.381333i	0.869797	−	0.493410i	$-0.164250\pi$
$853$	−105.689	−	325.277i	−0.123903	−	0.381333i	−0.993700	+	0.112077i	$0.964250\pi$
$854$	554.503	−	763.208i	0.649301	−	0.893686i
$855$	−196.230	+	137.521i	−0.229509	+	0.160844i
$856$	17.0747	−	52.5504i	0.0199470	−	0.0613907i
$857$		−	1404.79i		−	1.63920i	−0.572937	−	0.819600i	$-0.694196\pi$
$857$		−	1404.79i		−	1.63920i	0.572937	−	0.819600i	$-0.305804\pi$
$858$		0			0
$859$	759.128			0.883735			0.441867	−	0.897080i	$-0.354316\pi$
$859$	759.128			0.883735			0.441867	+	0.897080i	$0.354316\pi$
$860$	4.06572	+	1.32103i	0.00472758	+	0.00153608i
$861$	−242.770	+	1452.56i	−0.281963	+	1.68706i
$862$	352.123	+	255.832i	0.408496	+	0.296789i
$863$	−376.240	+	122.248i	−0.435968	+	0.141655i	−0.518775	−	0.854911i	$-0.673612\pi$
$863$	−376.240	+	122.248i	−0.435968	+	0.141655i	0.0828067	+	0.996566i	$0.473612\pi$
$864$	589.582	−	1087.46i	0.682386	−	1.25864i
$865$	974.894	+	708.302i	1.12704	+	0.818846i
$866$	−797.679	−	1097.91i	−0.921108	−	1.26780i
$867$	775.819	−	387.007i	0.894831	−	0.446375i
$868$	−1176.15			−1.35501
$869$		0			0
$870$	−1521.63	+	1495.91i	−1.74900	+	1.71944i
$871$	−432.671	+	1331.62i	−0.496752	+	1.52884i
$872$	59.6655	+	82.1225i	0.0684237	+	0.0941772i
$873$	−166.802	+	221.543i	−0.191068	+	0.253772i
$874$	−41.6068	−	128.052i	−0.0476050	−	0.146513i
$875$	−1342.54	+	436.217i	−1.53433	+	0.498533i
$876$	26.5535	+	177.426i	0.0303122	+	0.202541i
$877$	−917.111	+	666.320i	−1.04574	+	0.759772i	−0.971397	−	0.237461i	$-0.923685\pi$
$877$	−917.111	+	666.320i	−1.04574	+	0.759772i	−0.0743391	+	0.997233i	$0.523685\pi$
$878$	−1385.94	−	450.319i	−1.57852	−	0.512891i
$879$	−407.592	+	400.703i	−0.463700	+	0.455863i
$880$		0			0
$881$		−	894.628i		−	1.01547i	−0.861514	−	0.507735i	$-0.830483\pi$
$881$		−	894.628i		−	1.01547i	0.861514	−	0.507735i	$-0.169517\pi$
$882$	640.001	−	1861.17i	0.725624	−	2.11017i
$883$	−25.6769	+	18.6553i	−0.0290791	+	0.0211272i	−0.602230	−	0.798323i	$-0.705721\pi$
$883$	−25.6769	+	18.6553i	−0.0290791	+	0.0211272i	0.573151	+	0.819450i	$0.305721\pi$
$884$	−2.66110	+	3.66270i	−0.00301030	+	0.00414332i
$885$	99.2893	−	190.828i	0.112191	−	0.215625i
$886$	−567.807	−	1747.53i	−0.640866	−	1.97238i
$887$	796.758	−	1096.64i	0.898262	−	1.23635i	−0.0727570	−	0.997350i	$-0.523180\pi$
$887$	796.758	−	1096.64i	0.898262	−	1.23635i	0.971019	−	0.239002i	$-0.0768202\pi$
$888$	−15.6744	+	93.7840i	−0.0176513	+	0.105613i
$889$	72.0300	−	221.686i	0.0810236	−	0.249365i
$890$		−	574.487i		−	0.645491i
$891$		0			0
$892$	1529.52			1.71470
$893$	−76.2847	−	24.7864i	−0.0854252	−	0.0277563i
$894$	−1546.83	−	258.526i	−1.73024	−	0.289179i
$895$	1267.42	+	920.833i	1.41611	+	1.02886i
$896$	−274.015	+	89.0330i	−0.305821	+	0.0993672i
$897$	−391.074	−	203.479i	−0.435980	−	0.226844i
$898$	771.678	+	560.657i	0.859330	+	0.624339i
$899$	−721.641	−	993.254i	−0.802715	−	1.10484i
$900$	−18.8907	−	6.49596i	−0.0209897	−	0.00721774i
$901$	−6.12969			−0.00680321
$902$		0			0
$903$	−4.74604	−	4.82763i	−0.00525586	−	0.00534621i
$904$	24.6310	−	75.8066i	0.0272467	−	0.0838568i
$905$	−89.8621	−	123.685i	−0.0992951	−	0.136668i
$906$	−1196.92	+	179.130i	−1.32110	+	0.197715i
$907$	278.095	+	855.889i	0.306610	+	0.943648i	0.979072	+	0.203516i	$0.0652370\pi$
$907$	278.095	+	855.889i	0.306610	+	0.943648i	−0.672462	+	0.740132i	$0.734763\pi$
$908$	417.525	−	135.662i	0.459829	−	0.149408i
$909$	−373.315	−	281.074i	−0.410687	−	0.309212i
$910$	2176.34	−	1581.20i	2.39158	−	1.73758i
$911$	−304.231	−	98.8506i	−0.333953	−	0.108508i	0.137241	−	0.990538i	$-0.456177\pi$
$911$	−304.231	−	98.8506i	−0.333953	−	0.108508i	−0.471193	+	0.882030i	$0.656177\pi$
$912$	−167.483	−	170.363i	−0.183644	−	0.186801i
$913$		0			0
$914$			247.292i			0.270560i
$915$	−194.292	−	389.491i	−0.212341	−	0.425673i
$916$	−1279.12	+	929.335i	−1.39642	+	1.01456i
$917$	190.764	−	262.564i	0.208030	−	0.286329i
$918$	4.27469	+	2.31758i	0.00465653	+	0.00252459i
$919$	−138.542	−	426.387i	−0.150752	−	0.463968i	0.846953	−	0.531667i	$-0.178434\pi$
$919$	−138.542	−	426.387i	−0.150752	−	0.463968i	−0.997706	+	0.0676988i	$0.978434\pi$
$920$	−20.4159	+	28.1001i	−0.0221912	+	0.0305435i
$921$	844.054	+	141.069i	0.916454	+	0.153169i
$922$	58.0882	−	178.777i	0.0630024	−	0.193901i
$923$		−	451.314i		−	0.488964i
$924$		0			0
$925$	−20.3574			−0.0220080
$926$	−1465.19	−	476.069i	−1.58228	−	0.514113i
$927$	264.219	+	377.016i	0.285026	+	0.406706i
$928$	−1851.61	−	1345.27i	−1.99527	−	1.44965i
$929$	278.538	−	90.5026i	0.299826	−	0.0974193i	−0.155241	−	0.987877i	$-0.549615\pi$
$929$	278.538	−	90.5026i	0.299826	−	0.0974193i	0.455067	+	0.890457i	$0.349615\pi$
$930$	−484.533	+	931.244i	−0.521003	+	1.00134i
$931$	−330.829	−	240.361i	−0.355348	−	0.258175i
$932$	−43.5917	−	59.9988i	−0.0467722	−	0.0643764i
$933$	676.117	+	1355.39i	0.724669	+	1.45272i
$934$	1433.07			1.53434
$935$		0			0
$936$	122.771	+	2.09279i	0.131166	+	0.00223589i
$937$	45.6193	−	140.402i	0.0486865	−	0.149842i	−0.923758	−	0.382978i	$-0.874899\pi$
$937$	45.6193	−	140.402i	0.0486865	−	0.149842i	0.972444	+	0.233136i	$0.0748987\pi$
$938$	−1566.73	−	2156.42i	−1.67029	−	2.29895i
$939$	−35.5984	−	237.862i	−0.0379110	−	0.253314i
$940$	97.5592	+	300.256i	0.103786	+	0.319422i
$941$	−33.1918	+	10.7847i	−0.0352729	+	0.0114609i	−0.326600	−	0.945163i	$-0.605903\pi$
$941$	−33.1918	+	10.7847i	−0.0352729	+	0.0114609i	0.291327	+	0.956623i	$0.405903\pi$
$942$	1533.47	−	229.499i	1.62789	−	0.243630i
$943$	−308.884	+	224.418i	−0.327555	+	0.237983i
$944$	203.971	+	66.2742i	0.216071	+	0.0702057i
$945$	−1028.78	−	1082.77i	−1.08865	−	1.14579i
$946$		0			0
$947$		−	867.513i		−	0.916064i	−0.888936	−	0.458032i	$-0.848554\pi$
$947$		−	867.513i		−	0.916064i	0.888936	−	0.458032i	$-0.151446\pi$
$948$	−576.717	+	287.688i	−0.608352	+	0.303468i
$949$	191.002	−	138.771i	0.201267	−	0.146229i
$950$	−4.71941	+	6.49571i	−0.00496780	+	0.00683758i
$951$	−23.0380	−	11.9869i	−0.0242251	−	0.0126045i
$952$	−0.174558	−	0.537233i	−0.000183359	−	0.000564321i
$953$	−764.359	+	1052.05i	−0.802056	+	1.10394i	0.190445	+	0.981698i	$0.439007\pi$
$953$	−764.359	+	1052.05i	−0.802056	+	1.10394i	−0.992501	+	0.122237i	$0.960993\pi$
$954$	1455.75	+	2077.22i	1.52594	+	2.17738i
$955$	452.456	−	1392.52i	0.473776	−	1.45813i
$956$		−	936.699i		−	0.979811i
$957$		0			0
$958$	−2499.72			−2.60931
$959$	1613.12	+	524.135i	1.68209	+	0.546544i
$960$	−177.746	+	1063.50i	−0.185152	+	1.10781i
$961$	288.819	+	209.839i	0.300540	+	0.218355i
$962$	1815.76	−	589.976i	1.88748	−	0.613280i
$963$	180.337	+	588.995i	0.187266	+	0.611625i
$964$	408.754	+	296.977i	0.424019	+	0.308068i
$965$	−231.231	−	318.262i	−0.239617	−	0.329805i
$966$	750.985	−	374.619i	0.777417	−	0.387804i
$967$	−1422.62			−1.47117			−0.735585	−	0.677433i	$-0.763093\pi$
$967$	−1422.62			−1.47117			−0.735585	+	0.677433i	$0.763093\pi$
$968$		0			0
$969$	0.720457	−	0.708281i	0.000743506	−	0.000730940i
$970$	135.570	−	417.241i	0.139763	−	0.430145i
$971$	−204.126	−	280.955i	−0.210222	−	0.289346i	0.690865	−	0.722984i	$-0.257230\pi$
$971$	−204.126	−	280.955i	−0.210222	−	0.289346i	−0.901087	+	0.433638i	$0.857230\pi$
$972$	−118.807	−	1033.37i	−0.122229	−	1.06313i
$973$	66.4112	+	204.393i	0.0682541	+	0.210064i
$974$	659.877	−	214.407i	0.677491	−	0.220130i
$975$	3.89105	+	25.9993i	0.00399082	+	0.0266659i
$976$	351.077	−	255.073i	0.359710	−	0.261345i
$977$	−443.757	−	144.185i	−0.454204	−	0.147580i	0.0729757	−	0.997334i	$-0.476750\pi$
$977$	−443.757	−	144.185i	−0.454204	−	0.147580i	−0.527180	+	0.849754i	$0.676750\pi$
$978$	1362.08	−	1339.06i	1.39272	−	1.36918i
$979$		0			0
$980$			1609.54i			1.64238i
$981$	−1070.13	−	367.985i	−1.09085	−	0.375112i
$982$	1164.13	−	845.788i	1.18547	−	0.861291i
$983$	595.696	−	819.905i	0.605998	−	0.834084i	−0.390243	−	0.920712i	$-0.627609\pi$
$983$	595.696	−	819.905i	0.605998	−	0.834084i	0.996241	+	0.0866277i	$0.0276091\pi$
$984$	49.0850	−	94.3385i	0.0498832	−	0.0958725i
$985$	550.937	+	1695.61i	0.559327	+	1.72143i
$986$	5.28811	−	7.27846i	0.00536320	−	0.00738181i
$987$	82.4162	−	493.119i	0.0835017	−	0.499614i
$988$	120.288	−	370.207i	0.121749	−	0.374704i
$989$		−	1.75510i		−	0.00177462i
$990$		0			0
$991$	−1208.63			−1.21960			−0.609802	−	0.792554i	$-0.708751\pi$
$991$	−1208.63			−1.21960			−0.609802	+	0.792554i	$0.708751\pi$
$992$	−1070.86	−	347.944i	−1.07950	−	0.350750i
$993$	−83.6066	−	13.9734i	−0.0841960	−	0.0140719i
$994$	695.082	+	505.007i	0.699278	+	0.508055i
$995$	1740.52	−	565.529i	1.74927	−	0.568371i
$996$	−686.268	−	357.070i	−0.689024	−	0.358504i
$997$	−116.802	−	84.8616i	−0.117153	−	0.0851170i	0.527666	−	0.849452i	$-0.323067\pi$
$997$	−116.802	−	84.8616i	−0.117153	−	0.0851170i	−0.644819	+	0.764335i	$0.723067\pi$
$998$	−938.418	−	1291.62i	−0.940299	−	1.29421i
$999$	−456.934	−	956.472i	−0.457391	−	0.957429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.q.251.2		24
3.2	odd	2	inner	363.3.h.q.251.5		24
11.2	odd	10		363.3.h.p.245.2		24
11.3	even	5	inner	363.3.h.q.323.2		24
11.4	even	5		363.3.b.j.122.2	✓	6
11.5	even	5	inner	363.3.h.q.269.5		24
11.6	odd	10		363.3.h.p.269.2		24
11.7	odd	10		363.3.b.k.122.5	yes	6
11.8	odd	10		363.3.h.p.323.5		24
11.9	even	5	inner	363.3.h.q.245.5		24
11.10	odd	2		363.3.h.p.251.5		24
33.2	even	10		363.3.h.p.245.5		24
33.5	odd	10	inner	363.3.h.q.269.2		24
33.8	even	10		363.3.h.p.323.2		24
33.14	odd	10	inner	363.3.h.q.323.5		24
33.17	even	10		363.3.h.p.269.5		24
33.20	odd	10	inner	363.3.h.q.245.2		24
33.26	odd	10		363.3.b.j.122.5	yes	6
33.29	even	10		363.3.b.k.122.2	yes	6
33.32	even	2		363.3.h.p.251.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.3.b.j.122.2	✓	6	11.4	even	5
363.3.b.j.122.5	yes	6	33.26	odd	10
363.3.b.k.122.2	yes	6	33.29	even	10
363.3.b.k.122.5	yes	6	11.7	odd	10
363.3.h.p.245.2		24	11.2	odd	10
363.3.h.p.245.5		24	33.2	even	10
363.3.h.p.251.2		24	33.32	even	2
363.3.h.p.251.5		24	11.10	odd	2
363.3.h.p.269.2		24	11.6	odd	10
363.3.h.p.269.5		24	33.17	even	10
363.3.h.p.323.2		24	33.8	even	10
363.3.h.p.323.5		24	11.8	odd	10
363.3.h.q.245.2		24	33.20	odd	10	inner
363.3.h.q.245.5		24	11.9	even	5	inner
363.3.h.q.251.2		24	1.1	even	1	trivial
363.3.h.q.251.5		24	3.2	odd	2	inner
363.3.h.q.269.2		24	33.5	odd	10	inner
363.3.h.q.269.5		24	11.5	even	5	inner
363.3.h.q.323.2		24	11.3	even	5	inner
363.3.h.q.323.5		24	33.14	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+(-2.73676 - 0.889226i) q^{2} +(-2.95896 - 0.494538i) q^{3} +(3.46304 + 2.51605i) q^{4} +(4.70571 - 1.52898i) q^{5} +(7.65819 + 3.98461i) q^{6} +(9.04489 + 6.57149i) q^{7} +(-0.474528 - 0.653131i) q^{8} +(8.51086 + 2.92664i) q^{9} -14.2380 q^{10} +(-9.00271 - 9.15748i) q^{12} +(-5.22225 + 16.0724i) q^{13} +(-18.9101 - 26.0275i) q^{14} +(-14.6801 + 2.19703i) q^{15} +(-4.57317 - 14.0748i) q^{16} +(0.0595216 - 0.0193397i) q^{17} +(-20.6897 - 15.5776i) q^{18} +(-4.35333 + 3.16288i) q^{19} +(20.1430 + 6.54487i) q^{20} +(-23.5136 - 23.9178i) q^{21} -8.69537i q^{23} +(1.08111 + 2.16726i) q^{24} +(-0.419501 + 0.304785i) q^{25} +(28.5840 - 39.3425i) q^{26} +(-23.7360 - 12.8687i) q^{27} +(14.7886 + 45.5147i) q^{28} +(-29.3632 + 40.4149i) q^{29} +(42.1296 + 7.04122i) q^{30} +(-7.59453 + 23.3736i) q^{31} +45.8150i q^{32} -0.180094 q^{34} +(52.6103 + 17.0941i) q^{35} +(22.1099 + 31.5488i) q^{36} +(31.7618 + 23.0763i) q^{37} +(14.7265 - 4.78493i) q^{38} +(23.4008 - 44.9750i) q^{39} +(-3.23161 - 2.34790i) q^{40} +(-25.8089 - 35.5228i) q^{41} +(43.0826 + 86.3661i) q^{42} +0.201842 q^{43} +(44.5244 + 0.758975i) q^{45} +(-7.73215 + 23.7971i) q^{46} +(8.76165 + 12.0594i) q^{47} +(6.57130 + 43.9082i) q^{48} +(23.4836 + 72.2751i) q^{49} +(1.41909 - 0.461092i) q^{50} +(-0.185686 + 0.0277898i) q^{51} +(-58.5238 + 42.5200i) q^{52} +(-93.1486 - 30.2658i) q^{53} +(53.5163 + 56.3252i) q^{54} -9.02585i q^{56} +(14.4455 - 7.20594i) q^{57} +(116.298 - 84.4953i) q^{58} +(-8.51816 + 11.7242i) q^{59} +(-56.3657 - 29.3275i) q^{60} +(9.06134 + 27.8879i) q^{61} +(41.5687 - 57.2145i) q^{62} +(57.7474 + 82.4002i) q^{63} +(22.4472 - 69.0854i) q^{64} +83.6168i q^{65} +82.8515 q^{67} +(0.254785 + 0.0827848i) q^{68} +(-4.30019 + 25.7292i) q^{69} +(-128.781 - 93.5648i) q^{70} +(-25.3986 + 8.25251i) q^{71} +(-2.12716 - 6.94748i) q^{72} +(-11.3022 - 8.21153i) q^{73} +(-66.4042 - 91.3976i) q^{74} +(1.39201 - 0.694387i) q^{75} -23.0337 q^{76} +(-104.035 + 102.277i) q^{78} +(15.5088 - 47.7311i) q^{79} +(-43.0400 - 59.2395i) q^{80} +(63.8696 + 49.8164i) q^{81} +(39.0447 + 120.167i) q^{82} +(57.2933 - 18.6157i) q^{83} +(-21.2501 - 141.990i) q^{84} +(0.250521 - 0.182014i) q^{85} +(-0.552394 - 0.179484i) q^{86} +(106.871 - 105.065i) q^{87} +40.3489i q^{89} +(-121.178 - 41.6694i) q^{90} +(-152.854 + 111.055i) q^{91} +(21.8779 - 30.1124i) q^{92} +(34.0310 - 65.4056i) q^{93} +(-13.2550 - 40.7946i) q^{94} +(-15.6495 + 21.5397i) q^{95} +(22.6573 - 135.565i) q^{96} +(-9.52170 + 29.3048i) q^{97} -218.681i 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

L-functions

Modular forms

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