LMFDB - Embedded newform 363.3.h.q.269.2

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			269.2
Character	$\chi$	$=$	363.269
Dual form			363.3.h.q.251.2

$q$-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 $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$

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	−0.898831	−	0.438295i	$-0.855583\pi$
$2$	−2.73676	+	0.889226i	−1.36838	+	0.444613i	−0.469546	+	0.882908i	$0.655583\pi$
$3$	−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	0.739111	−	0.673584i	$-0.235246\pi$
$5$	4.70571	+	1.52898i	0.941142	+	0.305796i	0.202031	+	0.979379i	$0.435246\pi$
$6$	7.65819	−	3.98461i	1.27636	−	0.664102i
$7$	9.04489	−	6.57149i	1.29213	−	0.938785i	0.292280	−	0.956333i	$-0.405586\pi$
$7$	9.04489	−	6.57149i	1.29213	−	0.938785i	0.999846	+	0.0175478i	$0.00558591\pi$
$8$	−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	−0.923610	−	0.383333i	$-0.874776\pi$
$13$	−5.22225	−	16.0724i	−0.401711	−	1.23634i	0.521899	−	0.853007i	$-0.325224\pi$
$14$	−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	0.310767	−	0.950486i	$-0.399414\pi$
$17$	0.0595216	+	0.0193397i	0.00350127	+	0.00113763i	−0.307266	+	0.951624i	$0.599414\pi$
$18$	−20.6897	+	15.5776i	−1.14943	+	0.865420i
$19$	−4.35333	−	3.16288i	−0.229123	−	0.166467i	0.467301	−	0.884098i	$-0.345226\pi$
$19$	−4.35333	−	3.16288i	−0.229123	−	0.166467i	−0.696424	+	0.717631i	$0.745226\pi$
$20$	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	$0.0605343\pi$
$23$			8.69537i			0.378060i	−0.981971	+	0.189030i	$0.939466\pi$
$24$	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	−0.917316	−	0.398160i	$-0.869649\pi$
$29$	−29.3632	−	40.4149i	−1.01252	−	1.39362i	−0.0952067	−	0.995458i	$-0.530351\pi$
$30$	42.1296	−	7.04122i	1.40432	−	0.234707i
$31$	−7.59453	−	23.3736i	−0.244985	−	0.753986i	−0.995639	−	0.0932904i	$-0.970261\pi$
$31$	−7.59453	−	23.3736i	−0.244985	−	0.753986i	0.750654	−	0.660695i	$-0.229739\pi$
$32$		−	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	−0.0690298	−	0.997615i	$-0.521990\pi$
$37$	31.7618	−	23.0763i	0.858427	−	0.623684i	0.927456	+	0.373931i	$0.121990\pi$
$38$	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	−0.998000	−	0.0632106i	$-0.979866\pi$
$41$	−25.8089	+	35.5228i	−0.629484	+	0.866411i	0.368516	+	0.929621i	$0.379866\pi$
$42$	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	−0.705571	−	0.708639i	$-0.749309\pi$
$47$	8.76165	−	12.0594i	0.186418	−	0.256582i	0.891989	+	0.452057i	$0.149309\pi$
$48$	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	−0.996939	−	0.0781891i	$-0.975086\pi$
$53$	−93.1486	+	30.2658i	−1.75752	+	0.571053i	−0.760582	+	0.649242i	$0.775086\pi$
$54$	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	0.730705	−	0.682694i	$-0.239192\pi$
$59$	−8.51816	−	11.7242i	−0.144376	−	0.198716i	−0.875080	+	0.483978i	$0.839192\pi$
$60$	−56.3657	+	29.3275i	−0.939428	+	0.488791i
$61$	9.06134	−	27.8879i	0.148547	−	0.457179i	−0.848903	−	0.528548i	$-0.822737\pi$
$61$	9.06134	−	27.8879i	0.148547	−	0.457179i	0.997450	+	0.0713686i	$0.0227366\pi$
$62$	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	0.124640	−	0.992202i	$-0.460223\pi$
$71$	−25.3986	−	8.25251i	−0.357727	−	0.116232i	−0.482366	+	0.875970i	$0.660223\pi$
$72$	−2.12716	+	6.94748i	−0.0295439	+	0.0964928i
$73$	−11.3022	+	8.21153i	−0.154825	+	0.112487i	−0.662501	−	0.749061i	$-0.730505\pi$
$73$	−11.3022	+	8.21153i	−0.154825	+	0.112487i	0.507676	+	0.861548i	$0.330505\pi$
$74$	−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	0.999959	+	0.00908239i	$0.00289105\pi$
$79$	15.5088	+	47.7311i	0.196314	+	0.604191i	−0.803645	+	0.595109i	$0.797109\pi$
$80$	−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	0.633091	−	0.774078i	$-0.281786\pi$
$83$	57.2933	+	18.6157i	0.690281	+	0.224286i	0.0571899	+	0.998363i	$0.481786\pi$
$84$	−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	$-0.927213\pi$
$89$		−	40.3489i		−	0.453359i	0.973969	−	0.226679i	$-0.0727869\pi$
$90$	−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	0.889903	−	0.456150i	$-0.150772\pi$
$97$	−9.52170	−	29.3048i	−0.0981619	−	0.302111i	−0.988065	+	0.154039i	$0.950772\pi$
$98$			218.681i			2.23144i
$99$		0			0
$100$	−2.21960			−0.0221960
$101$	−49.3806	+	16.0447i	−0.488917	+	0.158859i	−0.543093	−	0.839673i	$-0.682747\pi$
$101$	−49.3806	+	16.0447i	−0.488917	+	0.158859i	0.0541757	+	0.998531i	$0.482747\pi$
$102$	0.532889	−	0.0890631i	0.00522440	−	0.000873168i
$103$	41.3843	−	30.0674i	0.401789	−	0.291917i	−0.368480	−	0.929636i	$-0.620122\pi$
$103$	41.3843	−	30.0674i	0.401789	−	0.291917i	0.770269	+	0.637719i	$0.220122\pi$
$104$	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	−0.578536	−	0.815657i	$-0.696376\pi$
$107$	40.2296	−	55.3713i	0.375978	−	0.517489i	0.954513	+	0.298168i	$0.0963756\pi$
$108$	−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	−0.470948	−	0.882161i	$-0.656088\pi$
$113$	58.0332	−	79.8758i	0.513568	−	0.706866i	0.984516	+	0.175295i	$0.0560880\pi$
$114$	−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	−0.973212	−	0.229909i	$-0.926157\pi$
$127$	−6.44270	+	19.8286i	−0.0507299	+	0.156131i	0.922482	+	0.386040i	$0.126157\pi$
$128$	−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	$0.0353405\pi$
$131$			29.0290i			0.221595i	−0.993843	+	0.110798i	$0.964659\pi$
$132$		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	0.783915	−	0.620869i	$-0.213220\pi$
$137$	144.285	+	46.8811i	1.05318	+	0.342198i	0.269263	+	0.963067i	$0.413220\pi$
$138$	34.6477	+	66.5908i	0.251070	+	0.482542i
$139$	15.5515	−	11.2988i	0.111881	−	0.0812863i	−0.530438	−	0.847724i	$-0.677972\pi$
$139$	15.5515	−	11.2988i	0.111881	−	0.0812863i	0.642319	+	0.766437i	$0.277972\pi$
$140$	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	−0.334827	−	0.942280i	$-0.608678\pi$
$149$	−172.775	−	56.1381i	−1.15957	−	0.376766i	−0.824739	+	0.565514i	$0.808678\pi$
$150$	−4.42707	−	0.662554i	−0.0295138	−	0.00441703i
$151$	−113.418	−	82.4026i	−0.751109	−	0.545713i	0.145061	−	0.989423i	$-0.453662\pi$
$151$	−113.418	−	82.4026i	−0.751109	−	0.545713i	−0.896171	+	0.443710i	$0.853662\pi$
$152$	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	0.944896	−	0.327371i	$-0.106163\pi$
$157$	145.309	+	105.573i	0.925536	+	0.672441i	−0.0193599	+	0.999813i	$0.506163\pi$
$158$	−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	0.908199	+	0.418538i	$0.137457\pi$
$163$	68.3722	+	210.428i	0.419461	+	1.29097i	−0.488738	+	0.872431i	$0.662543\pi$
$164$			187.953i			1.14606i
$165$		0			0
$166$	−173.351			−1.04428
$167$	175.393	−	56.9886i	1.05026	−	0.341249i	0.267488	−	0.963561i	$-0.413806\pi$
$167$	175.393	−	56.9886i	1.05026	−	0.341249i	0.782769	+	0.622312i	$0.213806\pi$
$168$	−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	−0.160916	−	0.986968i	$-0.551445\pi$
$173$	143.153	−	197.033i	0.827472	−	1.13892i	0.988388	−	0.151950i	$-0.0485552\pi$
$174$	−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	0.142295	−	0.989824i	$-0.454552\pi$
$179$	186.107	−	256.154i	1.03970	−	1.43103i	0.897407	−	0.441203i	$-0.145448\pi$
$180$	152.280	−	114.654i	0.846001	−	0.636965i
$181$	−9.54820	+	29.3863i	−0.0527525	+	0.162355i	−0.973962	−	0.226712i	$-0.927203\pi$
$181$	−9.54820	+	29.3863i	−0.0527525	+	0.162355i	0.921209	+	0.389067i	$0.127203\pi$
$182$	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	0.966938	+	0.255013i	$0.0820798\pi$
$191$	173.938	+	239.405i	0.910669	+	1.25343i	−0.0562681	+	0.998416i	$0.517920\pi$
$192$	−100.586	−	193.320i	−0.523884	−	1.00687i
$193$	−24.5692	+	75.6161i	−0.127301	+	0.391793i	−0.994313	−	0.106494i	$-0.966038\pi$
$193$	−24.5692	+	75.6161i	−0.127301	+	0.391793i	0.867012	+	0.498287i	$0.166038\pi$
$194$	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	$-0.632549\pi$
$197$		−	360.331i		−	1.82909i	0.404485	−	0.914544i	$-0.367451\pi$
$198$		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	−0.998121	−	0.0612686i	$-0.980485\pi$
$211$	−47.8204	−	147.176i	−0.226637	−	0.697517i	0.771484	−	0.636248i	$-0.219515\pi$
$212$	−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	0.999912	−	0.0132452i	$-0.00421621\pi$
$223$	289.076	+	210.026i	1.29631	+	0.941821i	0.296393	+	0.955066i	$0.404216\pi$
$224$	−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	0.920886	−	0.389832i	$-0.127467\pi$
$227$	60.2830	+	82.9725i	0.265564	+	0.365517i	−0.655322	+	0.755350i	$0.727467\pi$
$228$	68.1557	−	11.3910i	0.298929	−	0.0499607i
$229$	−114.140	−	351.286i	−0.498426	−	1.53400i	−0.811548	−	0.584285i	$-0.801375\pi$
$229$	−114.140	−	351.286i	−0.498426	−	1.53400i	0.313122	−	0.949713i	$-0.398625\pi$
$230$		−	123.804i		−	0.538280i
$231$		0			0
$232$	40.3299			0.173836
$233$	−16.4775	+	5.35387i	−0.0707190	+	0.0229780i	−0.344163	−	0.938910i	$-0.611837\pi$
$233$	−16.4775	+	5.35387i	−0.0707190	+	0.0229780i	0.273444	+	0.961888i	$0.411837\pi$
$234$	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	−0.988348	−	0.152209i	$-0.951361\pi$
$239$	−128.623	+	177.035i	−0.538172	+	0.740730i	0.450176	+	0.892940i	$0.351361\pi$
$240$	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	−0.596973	−	0.802262i	$-0.703630\pi$
$251$	−152.702	+	49.6160i	−0.608376	+	0.197673i	−0.0114036	+	0.999935i	$0.503630\pi$
$252$	−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	0.778026	−	0.628232i	$-0.216221\pi$
$257$	−15.3895	−	21.1818i	−0.0598811	−	0.0824193i	−0.837907	+	0.545813i	$0.816221\pi$
$258$	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	$0.138036\pi$
$263$			221.020i			0.840378i	−0.907437	+	0.420189i	$0.861964\pi$
$264$		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	0.522247	−	0.852794i	$-0.325094\pi$
$269$	119.300	+	38.7629i	0.443494	+	0.144100i	−0.0787531	+	0.996894i	$0.525094\pi$
$270$	337.952	−	183.225i	1.25167	−	0.678611i
$271$	−323.549	+	235.072i	−1.19391	+	0.867425i	−0.993672	−	0.112323i	$-0.964171\pi$
$271$	−323.549	+	235.072i	−1.19391	+	0.867425i	−0.200236	+	0.979748i	$0.564171\pi$
$272$	−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	0.983684	−	0.179903i	$-0.0575783\pi$
$277$	22.7480	+	70.0112i	0.0821228	+	0.252748i	−0.901562	+	0.432651i	$0.857578\pi$
$278$	−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	0.915415	−	0.402511i	$-0.131863\pi$
$281$	398.855	+	129.596i	1.41941	+	0.461195i	0.503996	+	0.863706i	$0.331863\pi$
$282$	19.0464	−	127.265i	0.0675405	−	0.451293i
$283$	214.669	+	155.966i	0.758548	+	0.551117i	0.898465	−	0.439046i	$-0.144683\pi$
$283$	214.669	+	155.966i	0.758548	+	0.551117i	−0.139917	+	0.990163i	$0.544683\pi$
$284$	−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	0.956168	−	0.292819i	$-0.0945932\pi$
$293$	111.987	+	154.137i	0.382209	+	0.526065i	−0.573959	+	0.818884i	$0.694593\pi$
$294$	−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	−0.00460774	+	0.999989i	$0.501467\pi$
$311$	−296.766	+	408.463i	−0.954230	+	1.31339i	−0.949623	+	0.313396i	$0.898533\pi$
$312$	−40.4789	−	6.05807i	−0.129740	−	0.0194169i
$313$	24.7740	−	76.2465i	0.0791501	−	0.243599i	−0.903650	−	0.428272i	$-0.859123\pi$
$313$	24.7740	−	76.2465i	0.0791501	−	0.243599i	0.982800	+	0.184673i	$0.0591225\pi$
$314$	−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	−0.296002	−	0.955187i	$-0.595654\pi$
$317$	8.23294	−	2.67505i	0.0259714	−	0.00843863i	0.321974	+	0.946749i	$0.395654\pi$
$318$	−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	−0.184887	−	0.982760i	$-0.559192\pi$
$337$	233.420	−	169.589i	0.692640	−	0.503232i	0.877527	+	0.479527i	$0.159192\pi$
$338$	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	−0.0753975	−	0.997154i	$-0.524023\pi$
$347$	−250.710	−	81.4606i	−0.722507	−	0.234757i	−0.647110	+	0.762397i	$0.724023\pi$
$348$	634.447	+	94.9512i	1.82312	+	0.272848i
$349$	394.738	+	286.794i	1.13106	+	0.821760i	0.985848	−	0.167641i	$-0.0536150\pi$
$349$	394.738	+	286.794i	1.13106	+	0.821760i	0.145207	+	0.989401i	$0.453615\pi$
$350$	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	$-0.787348\pi$
$353$		−	437.345i		−	1.23894i	0.785021	−	0.619469i	$-0.212652\pi$
$354$	−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	0.961028	−	0.276452i	$-0.0891587\pi$
$359$	144.007	+	198.208i	0.401132	+	0.552111i	−0.559895	+	0.828563i	$0.689159\pi$
$360$	−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	−0.807570	−	0.589772i	$-0.799217\pi$
$367$	−182.111	+	132.311i	−0.496216	+	0.360522i	0.311354	+	0.950294i	$0.399217\pi$
$368$	−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	0.573024	+	0.819538i	$0.305770\pi$
$379$	−141.092	+	434.237i	−0.372275	+	1.14574i	−0.945299	+	0.326205i	$0.894230\pi$
$380$	−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	−0.679403	−	0.733765i	$-0.737761\pi$
$383$	−305.540	+	99.2761i	−0.797755	+	0.259206i	−0.118352	+	0.992972i	$0.537761\pi$
$384$	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	0.977852	−	0.209299i	$-0.0671181\pi$
$389$	185.407	+	255.190i	0.476624	+	0.656017i	−0.501228	+	0.865315i	$0.667118\pi$
$390$	−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	−0.152084	−	0.988368i	$-0.548598\pi$
$401$	−343.284	−	111.540i	−0.856070	−	0.278154i	−0.703986	+	0.710214i	$0.748598\pi$
$402$	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	0.967553	+	0.252670i	$0.0813087\pi$
$409$	136.320	+	419.551i	0.333302	+	1.02580i	−0.634251	+	0.773127i	$0.718691\pi$
$410$	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	$-0.844547\pi$
$419$		−	393.180i		−	0.938377i	0.883098	−	0.469188i	$-0.155453\pi$
$420$	−317.096	+	635.671i	−0.754990	+	1.51350i
$421$	569.050	+	413.439i	1.35166	+	0.982041i	0.998927	+	0.0463181i	$0.0147488\pi$
$421$	569.050	+	413.439i	1.35166	+	0.982041i	0.352737	+	0.935723i	$0.385251\pi$
$422$	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	−0.471103	−	0.882078i	$-0.656144\pi$
$431$	−143.851	+	46.7401i	−0.333762	+	0.108446i	0.137342	+	0.990524i	$0.456144\pi$
$432$	−72.5759	−	392.929i	−0.168000	−	0.909558i
$433$	381.538	−	277.204i	0.881150	−	0.640193i	−0.0524055	−	0.998626i	$-0.516689\pi$
$433$	381.538	−	277.204i	0.881150	−	0.640193i	0.933555	+	0.358433i	$0.116689\pi$
$434$	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	−0.137230	−	0.990539i	$-0.543820\pi$
$443$	375.325	−	516.591i	0.847235	−	1.16612i	0.984465	−	0.175580i	$-0.0561801\pi$
$444$	−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	−0.638252	−	0.769827i	$-0.720342\pi$
$449$	−315.250	+	102.431i	−0.702116	+	0.228131i	−0.0638637	+	0.997959i	$0.520342\pi$
$450$	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	−0.975898	−	0.218227i	$-0.929973\pi$
$457$	−26.5560	+	81.7309i	−0.0581094	+	0.178842i	0.917789	+	0.397069i	$0.129973\pi$
$458$	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	$-0.977429\pi$
$461$		−	65.3245i		−	0.141702i	0.997487	−	0.0708508i	$-0.0225714\pi$
$462$		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	−0.245681	−	0.969351i	$-0.579011\pi$
$467$	−473.636	−	153.894i	−1.01421	−	0.329537i	−0.768530	+	0.639814i	$0.779011\pi$
$468$	−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	0.992678	−	0.120791i	$-0.0385432\pi$
$479$	826.166	+	268.438i	1.72477	+	0.560412i	0.732094	+	0.681204i	$0.238543\pi$
$480$	−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	0.369216	−	0.929344i	$-0.379626\pi$
$487$	−195.067	−	141.725i	−0.400549	−	0.291016i	−0.769764	+	0.638328i	$0.779626\pi$
$488$	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	0.396962	−	0.917835i	$-0.370064\pi$
$491$	−293.922	−	404.549i	−0.598619	−	0.823928i	−0.995581	+	0.0939071i	$0.970064\pi$
$492$	−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	−0.0388311	−	0.999246i	$-0.512363\pi$
$499$	448.855	−	326.112i	0.899509	−	0.653531i	0.938340	+	0.345715i	$0.112363\pi$
$500$	−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	−0.208776	−	0.977964i	$-0.566948\pi$
$503$	395.277	−	544.051i	0.785838	−	1.08161i	0.994614	−	0.103650i	$-0.0330521\pi$
$504$	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	0.255154	+	0.966900i	$0.417874\pi$
$509$	−378.324	+	520.719i	−0.743270	+	1.02302i	−0.998424	+	0.0561224i	$0.982126\pi$
$510$	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	0.995931	−	0.0901206i	$-0.0287252\pi$
$521$	313.882	+	432.022i	0.602462	+	0.829217i	−0.393469	+	0.919338i	$0.628725\pi$
$522$	1237.08	+	378.767i	2.36989	+	0.725606i
$523$	307.507	−	946.409i	0.587967	−	1.80958i	0.000954046	−	1.00000i	$-0.499696\pi$
$523$	307.507	−	946.409i	0.587967	−	1.80958i	0.587013	−	0.809577i	$-0.300304\pi$
$524$	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	0.929329	+	0.369254i	$0.120387\pi$
$541$	213.440	+	656.899i	0.394528	+	1.21423i	−0.534801	+	0.844978i	$0.679613\pi$
$542$	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	0.521620	−	0.853178i	$-0.325328\pi$
$547$	−70.3505	−	51.1127i	−0.128612	−	0.0934418i	−0.650231	+	0.759736i	$0.725328\pi$
$548$	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	−0.995700	−	0.0926409i	$-0.970469\pi$
$557$	−432.298	−	595.007i	−0.776118	−	1.06824i	0.219581	−	0.975594i	$-0.429531\pi$
$558$	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	−0.747918	−	0.663792i	$-0.768946\pi$
$563$	−542.073	+	176.130i	−0.962829	+	0.312842i	−0.214911	+	0.976634i	$0.568946\pi$
$564$	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	−0.407805	−	0.913069i	$-0.633706\pi$
$569$	333.772	−	459.398i	0.586594	−	0.807378i	0.994399	+	0.105691i	$0.0337055\pi$
$570$	−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	0.551331	+	0.834287i	$0.314120\pi$
$577$	−222.195	+	683.846i	−0.385087	+	1.18518i	−0.936417	+	0.350888i	$0.885880\pi$
$578$	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	0.471980	−	0.881609i	$-0.343540\pi$
$587$	−300.738	−	413.930i	−0.512331	−	0.705162i	−0.984310	+	0.176447i	$0.943540\pi$
$588$	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	$0.0653480\pi$
$593$			241.775i			0.407715i	−0.979001	+	0.203858i	$0.934652\pi$
$594$		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	0.667118	−	0.744952i	$-0.267528\pi$
$599$	460.604	+	149.659i	0.768955	+	0.249849i	0.101837	+	0.994801i	$0.467528\pi$
$600$	−1.11407	+	0.579661i	−0.00185679	+	0.000966102i
$601$	−391.082	+	284.138i	−0.650719	+	0.472775i	−0.863516	−	0.504321i	$-0.831743\pi$
$601$	−391.082	+	284.138i	−0.650719	+	0.472775i	0.212797	+	0.977096i	$0.431743\pi$
$602$	−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	−0.994155	−	0.107960i	$-0.965568\pi$
$607$	−153.768	−	473.248i	−0.253324	−	0.779651i	0.740831	−	0.671691i	$-0.234432\pi$
$608$	−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	0.996591	+	0.0825060i	$0.0262924\pi$
$613$	847.792	+	615.957i	1.38302	+	1.00482i	0.386431	+	0.922318i	$0.373708\pi$
$614$	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	$-0.915770\pi$
$617$		−	322.739i		−	0.523078i	0.965193	−	0.261539i	$-0.0842301\pi$
$618$	197.121	−	395.162i	0.318967	−	0.639421i
$619$	−435.469	−	316.387i	−0.703504	−	0.511126i	0.177567	−	0.984109i	$-0.443177\pi$
$619$	−435.469	−	316.387i	−0.703504	−	0.511126i	−0.881072	+	0.472983i	$0.843177\pi$
$620$	−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	−0.986062	−	0.166376i	$-0.946793\pi$
$631$	−714.632	+	519.211i	−1.13254	+	0.822838i	−0.146477	+	0.989214i	$0.546793\pi$
$632$	−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	−0.922561	−	0.385850i	$-0.873908\pi$
$641$	−173.396	+	238.659i	−0.270509	+	0.372323i	0.652053	+	0.758174i	$0.273908\pi$
$642$	87.4528	−	584.343i	0.136219	−	0.910192i
$643$	258.185	−	794.613i	0.401532	−	1.23579i	−0.522224	−	0.852809i	$-0.674897\pi$
$643$	258.185	−	794.613i	0.401532	−	1.23579i	0.923756	−	0.382981i	$-0.125103\pi$
$644$	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	0.361448	−	0.932392i	$-0.382282\pi$
$647$	777.637	−	252.670i	1.20191	−	0.390525i	0.840464	+	0.541867i	$0.182282\pi$
$648$	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	0.666312	−	0.745673i	$-0.267872\pi$
$653$	−162.445	−	223.586i	−0.248767	−	0.342399i	−0.915079	+	0.403275i	$0.867872\pi$
$654$	−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	$0.233157\pi$
$659$			881.372i			1.33744i	−0.743515	+	0.668719i	$0.766843\pi$
$660$		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	0.950029	−	0.312163i	$-0.101054\pi$
$673$	−1.37662	−	4.23681i	−0.00204550	−	0.00629541i	−0.952074	+	0.305868i	$0.901054\pi$
$674$	−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	0.296854	−	0.954923i	$-0.404062\pi$
$677$	−16.4345	−	5.33989i	−0.0242755	−	0.00788758i	−0.321130	+	0.947035i	$0.604062\pi$
$678$	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	$0.292420\pi$
$683$			1085.69i			1.58958i	−0.606882	+	0.794792i	$0.707580\pi$
$684$	−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	0.895817	−	0.444423i	$-0.146591\pi$
$691$	−62.2864	−	191.698i	−0.0901395	−	0.277421i	−0.985957	+	0.167002i	$0.946591\pi$
$692$		−	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	−0.589930	−	0.807455i	$-0.700845\pi$
$701$	252.573	−	347.637i	0.360304	−	0.495916i	0.950233	+	0.311539i	$0.100845\pi$
$702$	−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	−0.643985	−	0.765038i	$-0.722720\pi$
$709$	231.622	−	712.859i	0.326688	−	1.00544i	0.970673	−	0.240404i	$-0.0772801\pi$
$710$	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	0.583734	−	0.811945i	$-0.301591\pi$
$719$	−265.207	−	365.026i	−0.368855	−	0.507685i	−0.952589	+	0.304260i	$0.901591\pi$
$720$	−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	−0.491526	+	0.870863i	$0.663561\pi$
$733$	−1078.72	+	783.739i	−1.47166	+	1.06922i	−0.980130	+	0.198357i	$0.936439\pi$
$734$	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	−0.886207	−	0.463289i	$-0.846669\pi$
$739$	−326.316	−	1004.30i	−0.441565	−	1.35900i	0.444643	−	0.895708i	$-0.353331\pi$
$740$	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	0.872633	−	0.488377i	$-0.162411\pi$
$743$	959.620	+	311.799i	1.29155	+	0.419649i	0.418914	+	0.908026i	$0.362411\pi$
$744$	−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	0.614542	−	0.788884i	$-0.289341\pi$
$751$	40.6835	+	29.5583i	0.0541725	+	0.0393586i	−0.560369	+	0.828243i	$0.689341\pi$
$752$	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	0.994661	−	0.103197i	$-0.0329072\pi$
$757$	97.8844	+	301.257i	0.129306	+	0.397962i	−0.865355	+	0.501159i	$0.832907\pi$
$758$		−	1313.86i		−	1.73333i
$759$		0			0
$760$	21.4944			0.0282821
$761$	67.8819	−	22.0562i	0.0892009	−	0.0289831i	−0.264077	−	0.964502i	$-0.585067\pi$
$761$	67.8819	−	22.0562i	0.0892009	−	0.0289831i	0.353277	+	0.935519i	$0.385067\pi$
$762$	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	−0.342657	−	0.939461i	$-0.611327\pi$
$773$	507.637	−	698.702i	0.656710	−	0.903884i	0.999367	+	0.0355767i	$0.0113268\pi$
$774$	−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	0.376546	+	0.926398i	$0.377112\pi$
$787$	−371.943	+	1144.72i	−0.472609	+	1.45454i	−0.849155	+	0.528143i	$0.822888\pi$
$788$	−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	0.658021	−	0.752999i	$-0.271394\pi$
$797$	595.973	+	193.643i	0.747770	+	0.242965i	0.0897487	+	0.995964i	$0.471394\pi$
$798$	−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	0.0629493	−	0.998017i	$-0.479949\pi$
$809$	−382.449	−	124.265i	−0.472743	−	0.153604i	−0.535692	+	0.844413i	$0.679949\pi$
$810$	−909.374	+	709.285i	−1.12268	+	0.875660i
$811$	448.052	+	325.529i	0.552469	+	0.401392i	0.828695	−	0.559701i	$-0.189084\pi$
$811$	448.052	+	325.529i	0.552469	+	0.401392i	−0.276226	+	0.961093i	$0.589084\pi$
$812$	−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	0.722544	−	0.691325i	$-0.242973\pi$
$821$	−129.901	−	178.794i	−0.158223	−	0.217776i	−0.880767	+	0.473549i	$0.842973\pi$
$822$	1291.77	−	215.896i	1.57149	−	0.262648i
$823$	222.107	+	683.574i	0.269875	+	0.830589i	0.990530	+	0.137295i	$0.0438409\pi$
$823$	222.107	+	683.574i	0.269875	+	0.830589i	−0.720656	+	0.693293i	$0.756159\pi$
$824$			41.2972i			0.0501179i
$825$		0			0
$826$	466.232			0.564446
$827$	−610.949	+	198.509i	−0.738753	+	0.240035i	−0.654135	−	0.756378i	$-0.726967\pi$
$827$	−610.949	+	198.509i	−0.738753	+	0.240035i	−0.0846182	+	0.996413i	$0.526967\pi$
$828$	274.328	+	192.254i	0.331314	+	0.232191i
$829$	−664.227	+	482.589i	−0.801239	+	0.582134i	−0.911277	−	0.411793i	$-0.864903\pi$
$829$	−664.227	+	482.589i	−0.801239	+	0.582134i	0.110038	+	0.993927i	$0.464903\pi$
$830$	−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	−0.671402	−	0.741093i	$-0.734308\pi$
$839$	202.110	−	278.180i	0.240894	−	0.331562i	0.912296	+	0.409531i	$0.134308\pi$
$840$	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	−0.993700	−	0.112077i	$-0.964250\pi$
$853$	−105.689	+	325.277i	−0.123903	+	0.381333i	0.869797	+	0.493410i	$0.164250\pi$
$854$	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	$0.305804\pi$
$857$			1404.79i			1.63920i	−0.572937	+	0.819600i	$0.694196\pi$
$858$		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	0.0828067	−	0.996566i	$-0.473612\pi$
$863$	−376.240	−	122.248i	−0.435968	−	0.141655i	−0.518775	+	0.854911i	$0.673612\pi$
$864$	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	−0.0743391	−	0.997233i	$-0.523685\pi$
$877$	−917.111	−	666.320i	−1.04574	−	0.759772i	−0.971397	+	0.237461i	$0.923685\pi$
$878$	−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	$0.169517\pi$
$881$			894.628i			1.01547i	−0.861514	+	0.507735i	$0.830483\pi$
$882$	640.001	+	1861.17i	0.725624	+	2.11017i
$883$	−25.6769	−	18.6553i	−0.0290791	−	0.0211272i	0.573151	−	0.819450i	$-0.305721\pi$
$883$	−25.6769	−	18.6553i	−0.0290791	−	0.0211272i	−0.602230	+	0.798323i	$0.705721\pi$
$884$	−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	0.971019	+	0.239002i	$0.0768202\pi$
$887$	796.758	+	1096.64i	0.898262	+	1.23635i	−0.0727570	+	0.997350i	$0.523180\pi$
$888$	−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	−0.672462	−	0.740132i	$-0.734763\pi$
$907$	278.095	−	855.889i	0.306610	−	0.943648i	0.979072	−	0.203516i	$-0.0652370\pi$
$908$	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	−0.471193	−	0.882030i	$-0.656177\pi$
$911$	−304.231	+	98.8506i	−0.333953	+	0.108508i	0.137241	+	0.990538i	$0.456177\pi$
$912$	−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	−0.997706	−	0.0676988i	$-0.978434\pi$
$919$	−138.542	+	426.387i	−0.150752	+	0.463968i	0.846953	+	0.531667i	$0.178434\pi$
$920$	−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	0.455067	−	0.890457i	$-0.349615\pi$
$929$	278.538	+	90.5026i	0.299826	+	0.0974193i	−0.155241	+	0.987877i	$0.549615\pi$
$930$	−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	0.972444	−	0.233136i	$-0.0748987\pi$
$937$	45.6193	+	140.402i	0.0486865	+	0.149842i	−0.923758	+	0.382978i	$0.874899\pi$
$938$	−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	0.291327	−	0.956623i	$-0.405903\pi$
$941$	−33.1918	−	10.7847i	−0.0352729	−	0.0114609i	−0.326600	+	0.945163i	$0.605903\pi$
$942$	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	$0.151446\pi$
$947$			867.513i			0.916064i	−0.888936	+	0.458032i	$0.848554\pi$
$948$	−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	−0.992501	−	0.122237i	$-0.960993\pi$
$953$	−764.359	−	1052.05i	−0.802056	−	1.10394i	0.190445	−	0.981698i	$-0.439007\pi$
$954$	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	−0.901087	−	0.433638i	$-0.857230\pi$
$971$	−204.126	+	280.955i	−0.210222	+	0.289346i	0.690865	+	0.722984i	$0.257230\pi$
$972$	−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	−0.527180	−	0.849754i	$-0.676750\pi$
$977$	−443.757	+	144.185i	−0.454204	+	0.147580i	0.0729757	+	0.997334i	$0.476750\pi$
$978$	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	0.996241	−	0.0866277i	$-0.0276091\pi$
$983$	595.696	+	819.905i	0.605998	+	0.834084i	−0.390243	+	0.920712i	$0.627609\pi$
$984$	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	−0.644819	−	0.764335i	$-0.723067\pi$
$997$	−116.802	+	84.8616i	−0.117153	+	0.0851170i	0.527666	+	0.849452i	$0.323067\pi$
$998$	−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.269.2		24
3.2	odd	2	inner	363.3.h.q.269.5		24
11.2	odd	10		363.3.h.p.251.2		24
11.3	even	5		363.3.b.j.122.5	yes	6
11.4	even	5	inner	363.3.h.q.245.2		24
11.5	even	5	inner	363.3.h.q.323.5		24
11.6	odd	10		363.3.h.p.323.2		24
11.7	odd	10		363.3.h.p.245.5		24
11.8	odd	10		363.3.b.k.122.2	yes	6
11.9	even	5	inner	363.3.h.q.251.5		24
11.10	odd	2		363.3.h.p.269.5		24
33.2	even	10		363.3.h.p.251.5		24
33.5	odd	10	inner	363.3.h.q.323.2		24
33.8	even	10		363.3.b.k.122.5	yes	6
33.14	odd	10		363.3.b.j.122.2	✓	6
33.17	even	10		363.3.h.p.323.5		24
33.20	odd	10	inner	363.3.h.q.251.2		24
33.26	odd	10	inner	363.3.h.q.245.5		24
33.29	even	10		363.3.h.p.245.2		24
33.32	even	2		363.3.h.p.269.2		24

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