LMFDB - Embedded newform 121.3.d.c.112.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,3,Mod(40,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("121.40");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	121.d (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:	$3.29701119876$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			112.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	121.112
Dual form			121.3.d.c.94.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.92705 + 0.951057i) q^{2} +(-2.92705 + 2.12663i) q^{3} +(4.42705 + 3.21644i) q^{4} +(1.23607 + 3.80423i) q^{5} +(-10.5902 + 3.44095i) q^{6} +(-0.527864 + 0.726543i) q^{7} +(2.66312 + 3.66547i) q^{8} +(1.26393 - 3.88998i) q^{9} +O(q^{10})$	\(q+(2.92705 + 0.951057i) q^{2} +(-2.92705 + 2.12663i) q^{3} +(4.42705 + 3.21644i) q^{4} +(1.23607 + 3.80423i) q^{5} +(-10.5902 + 3.44095i) q^{6} +(-0.527864 + 0.726543i) q^{7} +(2.66312 + 3.66547i) q^{8} +(1.26393 - 3.88998i) q^{9} +12.3107i q^{10} -19.7984 q^{12} +(8.09017 + 2.62866i) q^{13} +(-2.23607 + 1.62460i) q^{14} +(-11.7082 - 8.50651i) q^{15} +(-2.45492 - 7.55545i) q^{16} +(23.5172 - 7.64121i) q^{17} +(7.39919 - 10.1841i) q^{18} +(6.97214 + 9.59632i) q^{19} +(-6.76393 + 20.8172i) q^{20} -3.24920i q^{21} -7.23607 q^{23} +(-15.5902 - 5.06555i) q^{24} +(7.28115 - 5.29007i) q^{25} +(21.1803 + 15.3884i) q^{26} +(-5.48936 - 16.8945i) q^{27} +(-4.67376 + 1.51860i) q^{28} +(-2.03444 + 2.80017i) q^{29} +(-26.1803 - 36.0341i) q^{30} +(10.2361 - 31.5034i) q^{31} -42.5730i q^{32} +76.1033 q^{34} +(-3.41641 - 1.11006i) q^{35} +(18.1074 - 13.1558i) q^{36} +(-32.5623 - 23.6579i) q^{37} +(11.2812 + 34.7198i) q^{38} +(-29.2705 + 9.51057i) q^{39} +(-10.6525 + 14.6619i) q^{40} +(0.767997 + 1.05706i) q^{41} +(3.09017 - 9.51057i) q^{42} +33.0625i q^{43} +16.3607 q^{45} +(-21.1803 - 6.88191i) q^{46} +(-18.4164 + 13.3803i) q^{47} +(23.2533 + 16.8945i) q^{48} +(14.8926 + 45.8347i) q^{49} +(26.3435 - 8.55951i) q^{50} +(-52.5861 + 72.3786i) q^{51} +(27.3607 + 37.6587i) q^{52} +(-24.2705 + 74.6969i) q^{53} -54.6718i q^{54} -4.06888 q^{56} +(-40.8156 - 13.2618i) q^{57} +(-8.61803 + 6.26137i) q^{58} +(-25.2984 - 18.3803i) q^{59} +(-24.4721 - 75.3175i) q^{60} +(26.7082 - 8.67802i) q^{61} +(59.9230 - 82.4769i) q^{62} +(2.15905 + 2.97168i) q^{63} +(30.6697 - 94.3916i) q^{64} +34.0260i q^{65} -76.5066 q^{67} +(128.689 + 41.8137i) q^{68} +(21.1803 - 15.3884i) q^{69} +(-8.94427 - 6.49839i) q^{70} +(-19.2574 - 59.2680i) q^{71} +(17.6246 - 5.72658i) q^{72} +(55.3353 - 76.1625i) q^{73} +(-72.8115 - 100.216i) q^{74} +(-10.0623 + 30.9686i) q^{75} +64.9089i q^{76} -94.7214 q^{78} +(-62.6869 - 20.3682i) q^{79} +(25.7082 - 18.6781i) q^{80} +(81.7771 + 59.4145i) q^{81} +(1.24265 + 3.82447i) q^{82} +(-53.9296 + 17.5228i) q^{83} +(10.4508 - 14.3844i) q^{84} +(58.1378 + 80.0198i) q^{85} +(-31.4443 + 96.7755i) q^{86} -12.5227i q^{87} -62.2968 q^{89} +(47.8885 + 15.5599i) q^{90} +(-6.18034 + 4.49028i) q^{91} +(-32.0344 - 23.2744i) q^{92} +(37.0344 + 113.980i) q^{93} +(-66.6312 + 21.6498i) q^{94} +(-27.8885 + 38.3853i) q^{95} +(90.5370 + 124.613i) q^{96} +(22.3754 - 68.8644i) q^{97} +148.324i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} - 5 q^{3} + 11 q^{4} - 4 q^{5} - 20 q^{6} - 20 q^{7} - 5 q^{8} + 14 q^{9}+O(q^{10}) $ 4 * q + 5 * q^2 - 5 * q^3 + 11 * q^4 - 4 * q^5 - 20 * q^6 - 20 * q^7 - 5 * q^8 + 14 * q^9	$ 4 q + 5 q^{2} - 5 q^{3} + 11 q^{4} - 4 q^{5} - 20 q^{6} - 20 q^{7} - 5 q^{8} + 14 q^{9} - 30 q^{12} + 10 q^{13} - 20 q^{15} - 21 q^{16} + 65 q^{17} + 5 q^{18} + 10 q^{19} - 36 q^{20} - 20 q^{23} - 40 q^{24} + 9 q^{25} + 40 q^{26} + 25 q^{27} - 50 q^{28} + 50 q^{29} - 60 q^{30} + 32 q^{31} + 130 q^{34} + 40 q^{35} + 21 q^{36} - 90 q^{37} + 25 q^{38} - 50 q^{39} + 20 q^{40} + 135 q^{41} - 10 q^{42} - 24 q^{45} - 40 q^{46} - 20 q^{47} + 55 q^{48} + 111 q^{49} + 45 q^{50} - 65 q^{51} + 20 q^{52} - 30 q^{53} + 100 q^{56} - 85 q^{57} - 30 q^{58} - 52 q^{59} - 80 q^{60} + 80 q^{61} + 110 q^{62} - 130 q^{63} + 31 q^{64} - 230 q^{67} + 195 q^{68} + 40 q^{69} - 162 q^{71} - 10 q^{72} - 85 q^{73} - 90 q^{74} - 200 q^{78} - 130 q^{79} + 76 q^{80} + 184 q^{81} - 80 q^{82} - 10 q^{83} - 70 q^{84} - 90 q^{86} + 122 q^{89} + 120 q^{90} + 20 q^{91} - 70 q^{92} + 90 q^{93} - 110 q^{94} - 40 q^{95} + 105 q^{96} + 170 q^{97}+O(q^{100}) $ 4 * q + 5 * q^2 - 5 * q^3 + 11 * q^4 - 4 * q^5 - 20 * q^6 - 20 * q^7 - 5 * q^8 + 14 * q^9 - 30 * q^12 + 10 * q^13 - 20 * q^15 - 21 * q^16 + 65 * q^17 + 5 * q^18 + 10 * q^19 - 36 * q^20 - 20 * q^23 - 40 * q^24 + 9 * q^25 + 40 * q^26 + 25 * q^27 - 50 * q^28 + 50 * q^29 - 60 * q^30 + 32 * q^31 + 130 * q^34 + 40 * q^35 + 21 * q^36 - 90 * q^37 + 25 * q^38 - 50 * q^39 + 20 * q^40 + 135 * q^41 - 10 * q^42 - 24 * q^45 - 40 * q^46 - 20 * q^47 + 55 * q^48 + 111 * q^49 + 45 * q^50 - 65 * q^51 + 20 * q^52 - 30 * q^53 + 100 * q^56 - 85 * q^57 - 30 * q^58 - 52 * q^59 - 80 * q^60 + 80 * q^61 + 110 * q^62 - 130 * q^63 + 31 * q^64 - 230 * q^67 + 195 * q^68 + 40 * q^69 - 162 * q^71 - 10 * q^72 - 85 * q^73 - 90 * q^74 - 200 * q^78 - 130 * q^79 + 76 * q^80 + 184 * q^81 - 80 * q^82 - 10 * q^83 - 70 * q^84 - 90 * q^86 + 122 * q^89 + 120 * q^90 + 20 * q^91 - 70 * q^92 + 90 * q^93 - 110 * q^94 - 40 * q^95 + 105 * q^96 + 170 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	2.92705	+	0.951057i	1.46353	+	0.475528i	0.929145	−	0.369716i	$-0.120545\pi$
$2$	2.92705	+	0.951057i	1.46353	+	0.475528i	0.534381	+	0.845244i	$0.320545\pi$
$3$	−2.92705	+	2.12663i	−0.975684	+	0.708876i	−0.956740	−	0.290945i	$-0.906030\pi$
$3$	−2.92705	+	2.12663i	−0.975684	+	0.708876i	−0.0189438	+	0.999821i	$0.506030\pi$
$4$	4.42705	+	3.21644i	1.10676	+	0.804110i
$5$	1.23607	+	3.80423i	0.247214	+	0.760845i	0.995264	+	0.0972039i	$0.0309899\pi$
$5$	1.23607	+	3.80423i	0.247214	+	0.760845i	−0.748051	+	0.663641i	$0.769010\pi$
$6$	−10.5902	+	3.44095i	−1.76503	+	0.573492i
$7$	−0.527864	+	0.726543i	−0.0754091	+	0.103792i	−0.845055	−	0.534679i	$-0.820433\pi$
$7$	−0.527864	+	0.726543i	−0.0754091	+	0.103792i	0.769646	+	0.638471i	$0.220433\pi$
$8$	2.66312	+	3.66547i	0.332890	+	0.458184i
$9$	1.26393	−	3.88998i	0.140437	−	0.432220i
$10$			12.3107i			1.23107i
$11$		0			0
$11$		0			0
$12$	−19.7984			−1.64986
$13$	8.09017	+	2.62866i	0.622321	+	0.202204i	0.603170	−	0.797612i	$-0.293904\pi$
$13$	8.09017	+	2.62866i	0.622321	+	0.202204i	0.0191503	+	0.999817i	$0.493904\pi$
$14$	−2.23607	+	1.62460i	−0.159719	+	0.116043i
$15$	−11.7082	−	8.50651i	−0.780547	−	0.567101i
$16$	−2.45492	−	7.55545i	−0.153432	−	0.472216i
$17$	23.5172	−	7.64121i	1.38337	−	0.449483i	0.479591	−	0.877492i	$-0.340785\pi$
$17$	23.5172	−	7.64121i	1.38337	−	0.449483i	0.903774	+	0.428009i	$0.140785\pi$
$18$	7.39919	−	10.1841i	0.411066	−	0.565784i
$19$	6.97214	+	9.59632i	0.366955	+	0.505070i	0.952070	−	0.305880i	$-0.0989508\pi$
$19$	6.97214	+	9.59632i	0.366955	+	0.505070i	−0.585115	+	0.810950i	$0.698951\pi$
$20$	−6.76393	+	20.8172i	−0.338197	+	1.04086i
$21$		−	3.24920i		−	0.154724i
$22$		0			0
$23$	−7.23607			−0.314612			−0.157306	−	0.987550i	$-0.550281\pi$
$23$	−7.23607			−0.314612			−0.157306	+	0.987550i	$0.550281\pi$
$24$	−15.5902	−	5.06555i	−0.649590	−	0.211065i
$25$	7.28115	−	5.29007i	0.291246	−	0.211603i
$26$	21.1803	+	15.3884i	0.814628	+	0.591862i
$27$	−5.48936	−	16.8945i	−0.203310	−	0.625722i
$28$	−4.67376	+	1.51860i	−0.166920	+	0.0542356i
$29$	−2.03444	+	2.80017i	−0.0701532	+	0.0965576i	−0.842652	−	0.538459i	$-0.819007\pi$
$29$	−2.03444	+	2.80017i	−0.0701532	+	0.0965576i	0.772499	+	0.635016i	$0.219007\pi$
$30$	−26.1803	−	36.0341i	−0.872678	−	1.20114i
$31$	10.2361	−	31.5034i	0.330196	−	1.01624i	−0.638845	−	0.769336i	$-0.720587\pi$
$31$	10.2361	−	31.5034i	0.330196	−	1.01624i	0.969040	−	0.246902i	$-0.0794127\pi$
$32$		−	42.5730i		−	1.33041i
$33$		0			0
$34$	76.1033			2.23833
$35$	−3.41641	−	1.11006i	−0.0976117	−	0.0317159i
$36$	18.1074	−	13.1558i	0.502983	−	0.365439i
$37$	−32.5623	−	23.6579i	−0.880062	−	0.639403i	0.0532056	−	0.998584i	$-0.483056\pi$
$37$	−32.5623	−	23.6579i	−0.880062	−	0.639403i	−0.933268	+	0.359181i	$0.883056\pi$
$38$	11.2812	+	34.7198i	0.296872	+	0.913679i
$39$	−29.2705	+	9.51057i	−0.750526	+	0.243861i
$40$	−10.6525	+	14.6619i	−0.266312	+	0.366547i
$41$	0.767997	+	1.05706i	0.0187316	+	0.0257819i	0.818280	−	0.574820i	$-0.194928\pi$
$41$	0.767997	+	1.05706i	0.0187316	+	0.0257819i	−0.799548	+	0.600602i	$0.794928\pi$
$42$	3.09017	−	9.51057i	0.0735755	−	0.226442i
$43$			33.0625i			0.768895i	0.923147	+	0.384447i	$0.125608\pi$
$43$			33.0625i			0.768895i	−0.923147	+	0.384447i	$0.874392\pi$
$44$		0			0
$45$	16.3607			0.363571
$46$	−21.1803	−	6.88191i	−0.460442	−	0.149607i
$47$	−18.4164	+	13.3803i	−0.391838	+	0.284687i	−0.766208	−	0.642592i	$-0.777859\pi$
$47$	−18.4164	+	13.3803i	−0.391838	+	0.284687i	0.374370	+	0.927279i	$0.377859\pi$
$48$	23.2533	+	16.8945i	0.484444	+	0.351969i
$49$	14.8926	+	45.8347i	0.303931	+	0.935403i
$50$	26.3435	−	8.55951i	0.526869	−	0.171190i
$51$	−52.5861	+	72.3786i	−1.03110	+	1.41919i
$52$	27.3607	+	37.6587i	0.526167	+	0.724207i
$53$	−24.2705	+	74.6969i	−0.457934	+	1.40938i	0.409721	+	0.912211i	$0.365626\pi$
$53$	−24.2705	+	74.6969i	−0.457934	+	1.40938i	−0.867656	+	0.497166i	$0.834374\pi$
$54$		−	54.6718i		−	1.01244i
$55$		0			0
$56$	−4.06888			−0.0726586
$57$	−40.8156	−	13.2618i	−0.716063	−	0.232663i
$58$	−8.61803	+	6.26137i	−0.148587	+	0.107955i
$59$	−25.2984	−	18.3803i	−0.428786	−	0.311531i	0.352377	−	0.935858i	$-0.385373\pi$
$59$	−25.2984	−	18.3803i	−0.428786	−	0.311531i	−0.781163	+	0.624327i	$0.785373\pi$
$60$	−24.4721	−	75.3175i	−0.407869	−	1.25529i
$61$	26.7082	−	8.67802i	0.437839	−	0.142263i	−0.0817992	−	0.996649i	$-0.526067\pi$
$61$	26.7082	−	8.67802i	0.437839	−	0.142263i	0.519639	+	0.854386i	$0.326067\pi$
$62$	59.9230	−	82.4769i	0.966500	−	1.33027i
$63$	2.15905	+	2.97168i	0.0342707	+	0.0471696i
$64$	30.6697	−	94.3916i	0.479214	−	1.47487i
$65$			34.0260i			0.523477i
$66$		0			0
$67$	−76.5066			−1.14189			−0.570945	−	0.820989i	$-0.693423\pi$
$67$	−76.5066			−1.14189			−0.570945	+	0.820989i	$0.693423\pi$
$68$	128.689	+	41.8137i	1.89249	+	0.614908i
$69$	21.1803	−	15.3884i	0.306961	−	0.223021i
$70$	−8.94427	−	6.49839i	−0.127775	−	0.0928342i
$71$	−19.2574	−	59.2680i	−0.271230	−	0.834761i	−0.990192	−	0.139712i	$-0.955382\pi$
$71$	−19.2574	−	59.2680i	−0.271230	−	0.834761i	0.718962	−	0.695049i	$-0.244618\pi$
$72$	17.6246	−	5.72658i	0.244786	−	0.0795359i
$73$	55.3353	−	76.1625i	0.758018	−	1.04332i	−0.239358	−	0.970931i	$-0.576937\pi$
$73$	55.3353	−	76.1625i	0.758018	−	1.04332i	0.997376	−	0.0723912i	$-0.0230630\pi$
$74$	−72.8115	−	100.216i	−0.983940	−	1.35428i
$75$	−10.0623	+	30.9686i	−0.134164	+	0.412915i
$76$			64.9089i			0.854064i
$77$		0			0
$78$	−94.7214			−1.21438
$79$	−62.6869	−	20.3682i	−0.793505	−	0.257825i	−0.115909	−	0.993260i	$-0.536978\pi$
$79$	−62.6869	−	20.3682i	−0.793505	−	0.257825i	−0.677596	+	0.735434i	$0.736978\pi$
$80$	25.7082	−	18.6781i	0.321353	−	0.233476i
$81$	81.7771	+	59.4145i	1.00959	+	0.733513i
$82$	1.24265	+	3.82447i	0.0151542	+	0.0466399i
$83$	−53.9296	+	17.5228i	−0.649754	+	0.211118i	−0.615306	−	0.788289i	$-0.710967\pi$
$83$	−53.9296	+	17.5228i	−0.649754	+	0.211118i	−0.0344482	+	0.999406i	$0.510967\pi$
$84$	10.4508	−	14.3844i	0.124415	−	0.171242i
$85$	58.1378	+	80.0198i	0.683974	+	0.941409i
$86$	−31.4443	+	96.7755i	−0.365631	+	1.12530i
$87$		−	12.5227i		−	0.143939i
$88$		0			0
$89$	−62.2968			−0.699964			−0.349982	−	0.936756i	$-0.613812\pi$
$89$	−62.2968			−0.699964			−0.349982	+	0.936756i	$0.613812\pi$
$90$	47.8885	+	15.5599i	0.532095	+	0.172888i
$91$	−6.18034	+	4.49028i	−0.0679158	+	0.0493437i
$92$	−32.0344	−	23.2744i	−0.348200	−	0.252982i
$93$	37.0344	+	113.980i	0.398220	+	1.22559i
$94$	−66.6312	+	21.6498i	−0.708842	+	0.230317i
$95$	−27.8885	+	38.3853i	−0.293564	+	0.404056i
$96$	90.5370	+	124.613i	0.943093	+	1.29806i
$97$	22.3754	−	68.8644i	0.230674	−	0.709942i	−0.766992	−	0.641657i	$-0.778247\pi$
$97$	22.3754	−	68.8644i	0.230674	−	0.709942i	0.997666	−	0.0682849i	$-0.0217527\pi$
$98$			148.324i			1.51351i
$99$		0			0
$100$	49.2492			0.492492
$101$	61.2279	+	19.8942i	0.606217	+	0.196972i	0.596011	−	0.802976i	$-0.296751\pi$
$101$	61.2279	+	19.8942i	0.606217	+	0.196972i	0.0102059	+	0.999948i	$0.496751\pi$
$102$	−222.758	+	161.843i	−2.18391	+	1.58670i
$103$	26.3820	+	19.1676i	0.256136	+	0.186093i	0.708442	−	0.705769i	$-0.249399\pi$
$103$	26.3820	+	19.1676i	0.256136	+	0.186093i	−0.452306	+	0.891863i	$0.649399\pi$
$104$	11.9098	+	36.6547i	0.114518	+	0.352449i
$105$	12.3607	−	4.01623i	0.117721	−	0.0382498i
$106$	−142.082	+	195.559i	−1.34040	+	1.84490i
$107$	−3.17627	−	4.37177i	−0.0296848	−	0.0408576i	0.793917	−	0.608027i	$-0.208039\pi$
$107$	−3.17627	−	4.37177i	−0.0296848	−	0.0408576i	−0.823601	+	0.567169i	$0.808039\pi$
$108$	30.0385	−	92.4490i	0.278134	−	0.856009i
$109$		−	137.002i		−	1.25690i	−0.777850	−	0.628450i	$-0.783690\pi$
$109$		−	137.002i		−	1.25690i	0.777850	−	0.628450i	$-0.216310\pi$
$110$		0			0
$111$	145.623			1.31192
$112$	6.78522	+	2.20465i	0.0605823	+	0.0196844i
$113$	37.6246	−	27.3359i	0.332961	−	0.241910i	−0.408725	−	0.912658i	$-0.634026\pi$
$113$	37.6246	−	27.3359i	0.332961	−	0.241910i	0.741686	+	0.670747i	$0.234026\pi$
$114$	−106.857	−	77.6359i	−0.937339	−	0.681016i
$115$	−8.94427	−	27.5276i	−0.0777763	−	0.239371i
$116$	−18.0132	+	5.85283i	−0.155286	+	0.0504554i
$117$	20.4508	−	28.1482i	0.174794	−	0.240583i
$118$	−56.5689	−	77.8604i	−0.479397	−	0.659834i
$119$	−6.86223	+	21.1198i	−0.0576658	+	0.177477i
$120$		−	65.5699i		−	0.546416i
$121$		0			0
$122$	86.4296			0.708439
$123$	−4.49593	−	1.46082i	−0.0365523	−	0.0118766i
$124$	146.644	−	106.543i	1.18262	−	0.859221i
$125$	110.026	+	79.9388i	0.880210	+	0.639510i
$126$	3.49342	+	10.7516i	0.0277256	+	0.0853305i
$127$	−79.3475	+	25.7816i	−0.624784	+	0.203005i	−0.604263	−	0.796785i	$-0.706532\pi$
$127$	−79.3475	+	25.7816i	−0.624784	+	0.203005i	−0.0205206	+	0.999789i	$0.506532\pi$
$128$	79.4483	−	109.351i	0.620690	−	0.854307i
$129$	−70.3115	−	96.7755i	−0.545051	−	0.750198i
$130$	−32.3607	+	99.5959i	−0.248928	+	0.766123i
$131$			85.0901i			0.649543i	0.945793	+	0.324771i	$0.105287\pi$
$131$			85.0901i			0.649543i	−0.945793	+	0.324771i	$0.894713\pi$
$132$		0			0
$133$	−10.6525			−0.0800938
$134$	−223.939	−	72.7621i	−1.67118	−	0.543001i
$135$	57.4853	−	41.7655i	0.425817	−	0.309374i
$136$	90.6378	+	65.8522i	0.666454	+	0.484207i
$137$	18.1525	+	55.8676i	0.132500	+	0.407793i	0.995193	−	0.0979356i	$-0.0312239\pi$
$137$	18.1525	+	55.8676i	0.132500	+	0.407793i	−0.862693	+	0.505728i	$0.831224\pi$
$138$	76.6312	−	24.8990i	0.555298	−	0.180427i
$139$	94.6262	−	130.242i	0.680764	−	0.936991i	−0.319179	−	0.947694i	$-0.603407\pi$
$139$	94.6262	−	130.242i	0.680764	−	0.936991i	0.999943	+	0.0107035i	$0.00340710\pi$
$140$	−11.5542	−	15.9030i	−0.0825298	−	0.113593i
$141$	25.4508	−	78.3297i	0.180502	−	0.555530i
$142$		−	191.795i		−	1.35067i
$143$		0			0
$144$	−32.4934			−0.225649
$145$	−13.1672	−	4.27828i	−0.0908082	−	0.0295054i
$146$	234.404	−	170.305i	1.60551	−	1.16647i
$147$	−141.065	−	102.490i	−0.959625	−	0.697208i
$148$	−68.0608	−	209.469i	−0.459870	−	1.41533i
$149$	244.490	−	79.4397i	1.64087	−	0.533152i	0.664141	−	0.747608i	$-0.268798\pi$
$149$	244.490	−	79.4397i	1.64087	−	0.533152i	0.976734	+	0.214455i	$0.0687976\pi$
$150$	−58.9058	+	81.0768i	−0.392705	+	0.540512i
$151$	−169.395	−	233.152i	−1.12182	−	1.54406i	−0.802741	−	0.596328i	$-0.796626\pi$
$151$	−169.395	−	233.152i	−1.12182	−	1.54406i	−0.319081	−	0.947727i	$-0.603374\pi$
$152$	−16.6074	+	51.1123i	−0.109259	+	0.336265i
$153$		−	101.140i		−	0.661043i
$154$		0			0
$155$	132.498			0.854829
$156$	−160.172	−	52.0431i	−1.02674	−	0.333610i
$157$	−223.790	+	162.593i	−1.42542	+	1.03563i	−0.434568	+	0.900639i	$0.643099\pi$
$157$	−223.790	+	162.593i	−1.42542	+	1.03563i	−0.990848	+	0.134986i	$0.956901\pi$
$158$	−164.116	−	119.238i	−1.03871	−	0.754668i
$159$	−87.8115	−	270.256i	−0.552274	−	1.69972i
$160$	161.957	−	52.6232i	1.01223	−	0.328895i
$161$	3.81966	−	5.25731i	0.0237246	−	0.0326541i
$162$	182.859	+	251.684i	1.12876	+	1.55360i
$163$	−21.4352	+	65.9707i	−0.131504	+	0.404728i	−0.995030	−	0.0995765i	$-0.968251\pi$
$163$	−21.4352	+	65.9707i	−0.131504	+	0.404728i	0.863526	+	0.504305i	$0.168251\pi$
$164$			7.14987i			0.0435967i
$165$		0			0
$166$	−174.520			−1.05132
$167$	274.846	+	89.3029i	1.64578	+	0.534748i	0.977820	−	0.209446i	$-0.0671660\pi$
$167$	274.846	+	89.3029i	1.64578	+	0.534748i	0.667964	+	0.744194i	$0.267166\pi$
$168$	11.9098	−	8.65300i	0.0708918	−	0.0515059i
$169$	−78.1829	−	56.8032i	−0.462620	−	0.336113i
$170$	94.0689	+	289.514i	0.553346	+	1.70303i
$171$	46.1418	−	14.9924i	0.269835	−	0.0876748i
$172$	−106.343	+	146.369i	−0.618276	+	0.850984i
$173$	107.687	+	148.218i	0.622468	+	0.856753i	0.997530	−	0.0702464i	$-0.0223786\pi$
$173$	107.687	+	148.218i	0.622468	+	0.856753i	−0.375062	+	0.927000i	$0.622379\pi$
$174$	11.9098	−	36.6547i	0.0684473	−	0.210659i
$175$			8.08250i			0.0461857i
$176$		0			0
$177$	113.138			0.639196
$178$	−182.346	−	59.2478i	−1.02442	−	0.332853i
$179$	−1.65905	+	1.20537i	−0.00926846	+	0.00673393i	−0.592410	−	0.805637i	$-0.701823\pi$
$179$	−1.65905	+	1.20537i	−0.00926846	+	0.00673393i	0.583141	+	0.812371i	$0.301823\pi$
$180$	72.4296	+	52.6232i	0.402386	+	0.292351i
$181$	−22.5279	−	69.3336i	−0.124463	−	0.383059i	0.869340	−	0.494215i	$-0.164545\pi$
$181$	−22.5279	−	69.3336i	−0.124463	−	0.383059i	−0.993803	+	0.111156i	$0.964545\pi$
$182$	−22.3607	+	7.26543i	−0.122861	+	0.0399199i
$183$	−59.7214	+	82.1994i	−0.326346	+	0.449177i
$184$	−19.2705	−	26.5236i	−0.104731	−	0.144150i
$185$	49.7508	−	153.117i	0.268923	−	0.827660i
$186$			368.848i			1.98305i
$187$		0			0
$188$	−124.567			−0.662592
$189$	15.1722	+	4.92975i	0.0802762	+	0.0260833i
$190$	−118.138	+	85.8321i	−0.621778	+	0.451748i
$191$	83.9787	+	61.0141i	0.439679	+	0.319446i	0.785507	−	0.618852i	$-0.212402\pi$
$191$	83.9787	+	61.0141i	0.439679	+	0.319446i	−0.345828	+	0.938298i	$0.612402\pi$
$192$	110.964	+	341.512i	0.577938	+	1.77871i
$193$	−327.177	+	106.306i	−1.69522	+	0.550810i	−0.987765	−	0.155950i	$-0.950156\pi$
$193$	−327.177	+	106.306i	−1.69522	+	0.550810i	−0.707454	+	0.706760i	$0.750156\pi$
$194$	130.988	−	180.289i	0.675195	−	0.929326i
$195$	−72.3607	−	99.5959i	−0.371080	−	0.510748i
$196$	−81.4944	+	250.814i	−0.415788	+	1.27966i
$197$		−	99.0718i		−	0.502903i	−0.967870	−	0.251451i	$-0.919092\pi$
$197$		−	99.0718i		−	0.502903i	0.967870	−	0.251451i	$-0.0809078\pi$
$198$		0			0
$199$	−153.469			−0.771201			−0.385601	−	0.922666i	$-0.626006\pi$
$199$	−153.469			−0.771201			−0.385601	+	0.922666i	$0.626006\pi$
$200$	38.7812	+	12.6008i	0.193906	+	0.0630038i
$201$	223.939	−	162.701i	1.11412	−	0.809457i
$202$	160.297	+	116.462i	0.793549	+	0.576547i
$203$	−0.960533	−	2.95622i	−0.00473169	−	0.0145626i
$204$	−465.603	+	151.283i	−2.28237	+	0.741586i
$205$	−3.07199	+	4.22823i	−0.0149853	+	0.0206255i
$206$	58.9919	+	81.1953i	0.286368	+	0.394152i
$207$	−9.14590	+	28.1482i	−0.0441831	+	0.135982i
$208$		−	67.5780i		−	0.324894i
$209$		0			0
$210$	40.0000			0.190476
$211$	317.192	+	103.062i	1.50328	+	0.488445i	0.940972	−	0.338483i	$-0.109914\pi$
$211$	317.192	+	103.062i	1.50328	+	0.488445i	0.562307	+	0.826929i	$0.309914\pi$
$212$	−347.705	+	252.623i	−1.64012	+	1.19162i
$213$	182.408	+	132.527i	0.856377	+	0.622194i
$214$	−5.13932	−	15.8172i	−0.0240155	−	0.0739122i
$215$	−125.777	+	40.8675i	−0.585010	+	0.190081i
$216$	47.3075	−	65.1131i	0.219016	−	0.301450i
$217$	17.4853	+	24.0664i	0.0805774	+	0.110905i
$218$	130.297	−	401.012i	0.597692	−	1.83951i
$219$			340.609i			1.55529i
$220$		0			0
$221$	210.344			0.951785
$222$	426.246	+	138.496i	1.92003	+	0.623855i
$223$	−92.2067	+	66.9921i	−0.413483	+	0.300413i	−0.775010	−	0.631949i	$-0.782255\pi$
$223$	−92.2067	+	66.9921i	−0.413483	+	0.300413i	0.361528	+	0.932361i	$0.382255\pi$
$224$	30.9311	+	22.4728i	0.138085	+	0.100325i
$225$	−11.3754	−	35.0098i	−0.0505573	−	0.155599i
$226$	136.127	−	44.2304i	0.602332	−	0.195710i
$227$	−22.9327	+	31.5641i	−0.101025	+	0.139049i	−0.856537	−	0.516086i	$-0.827388\pi$
$227$	−22.9327	+	31.5641i	−0.101025	+	0.139049i	0.755512	+	0.655135i	$0.227388\pi$
$228$	−138.037	−	189.992i	−0.605425	−	0.833296i
$229$	41.4721	−	127.638i	0.181101	−	0.557372i	−0.818758	−	0.574138i	$-0.805337\pi$
$229$	41.4721	−	127.638i	0.181101	−	0.557372i	0.999859	+	0.0167665i	$0.00533721\pi$
$230$		−	89.0813i		−	0.387310i
$231$		0			0
$232$	−15.6819			−0.0675944
$233$	−254.256	−	82.6127i	−1.09123	−	0.354561i	−0.292506	−	0.956264i	$-0.594489\pi$
$233$	−254.256	−	82.6127i	−1.09123	−	0.354561i	−0.798720	+	0.601703i	$0.794489\pi$
$234$	86.6312	−	62.9412i	0.370219	−	0.268980i
$235$	−73.6656	−	53.5212i	−0.313471	−	0.227750i
$236$	−52.8779	−	162.741i	−0.224059	−	0.689582i
$237$	226.803	−	73.6929i	0.956976	−	0.310940i
$238$	−40.1722	+	55.2923i	−0.168791	+	0.232321i
$239$	64.7395	+	89.1063i	0.270877	+	0.372830i	0.922685	−	0.385554i	$-0.125990\pi$
$239$	64.7395	+	89.1063i	0.270877	+	0.372830i	−0.651809	+	0.758383i	$0.725990\pi$
$240$	−35.5279	+	109.344i	−0.148033	+	0.455598i
$241$		−	191.103i		−	0.792960i	−0.918043	−	0.396480i	$-0.870232\pi$
$241$		−	191.103i		−	0.792960i	0.918043	−	0.396480i	$-0.129768\pi$
$242$		0			0
$243$	−205.843			−0.847090
$244$	146.151	+	47.4873i	0.598979	+	0.194620i
$245$	−155.957	+	113.310i	−0.636561	+	0.462489i
$246$	−11.7705	−	8.55178i	−0.0478476	−	0.0347633i
$247$	31.1803	+	95.9632i	0.126236	+	0.388515i
$248$	142.735	−	46.3773i	0.575542	−	0.187005i
$249$	120.590	−	165.978i	0.484298	−	0.666579i
$250$	246.026	+	338.626i	0.984105	+	1.35450i
$251$	−131.992	+	406.229i	−0.525864	+	1.61844i	0.236737	+	0.971574i	$0.423922\pi$
$251$	−131.992	+	406.229i	−0.525864	+	1.61844i	−0.762601	+	0.646869i	$0.776078\pi$
$252$			20.1003i			0.0797629i
$253$		0			0
$254$	−256.774			−1.01092
$255$	−340.344	−	110.585i	−1.33468	−	0.433665i
$256$	15.3713	−	11.1679i	0.0600442	−	0.0436247i
$257$	−22.8795	−	16.6229i	−0.0890251	−	0.0646805i	0.542382	−	0.840132i	$-0.317522\pi$
$257$	−22.8795	−	16.6229i	−0.0890251	−	0.0646805i	−0.631407	+	0.775451i	$0.717522\pi$
$258$	−113.766	−	350.137i	−0.440955	−	1.35712i
$259$	34.3769	−	11.1697i	0.132730	−	0.0431264i
$260$	−109.443	+	150.635i	−0.420934	+	0.579365i
$261$	8.32121	+	11.4532i	0.0318820	+	0.0438819i
$262$	−80.9255	+	249.063i	−0.308876	+	0.950622i
$263$			94.5506i			0.359508i	0.983712	+	0.179754i	$0.0575302\pi$
$263$			94.5506i			0.359508i	−0.983712	+	0.179754i	$0.942470\pi$
$264$		0			0
$265$	−314.164			−1.18552
$266$	−31.1803	−	10.1311i	−0.117219	−	0.0380869i
$267$	182.346	−	132.482i	0.682944	−	0.496188i
$268$	−338.699	−	246.079i	−1.26380	−	0.918205i
$269$	72.3081	+	222.541i	0.268803	+	0.827291i	0.990793	+	0.135387i	$0.0432278\pi$
$269$	72.3081	+	222.541i	0.268803	+	0.827291i	−0.721990	+	0.691904i	$0.756772\pi$
$270$	207.984	−	67.5780i	0.770310	−	0.250289i
$271$	84.2999	−	116.029i	0.311070	−	0.428151i	−0.624645	−	0.780909i	$-0.714756\pi$
$271$	84.2999	−	116.029i	0.311070	−	0.428151i	0.935715	+	0.352758i	$0.114756\pi$
$272$	−115.466	−	158.925i	−0.424506	−	0.584282i
$273$	8.54102	−	26.2866i	0.0312858	−	0.0962877i
$274$			180.791i			0.659822i
$275$		0			0
$276$	143.262			0.519067
$277$	−370.036	−	120.232i	−1.33587	−	0.434051i	−0.447955	−	0.894056i	$-0.647848\pi$
$277$	−370.036	−	120.232i	−1.33587	−	0.434051i	−0.887916	+	0.460005i	$0.847848\pi$
$278$	400.843	−	291.229i	1.44188	−	1.04759i
$279$	−109.610	−	79.6363i	−0.392867	−	0.285435i
$280$	−5.02942	−	15.4790i	−0.0179622	−	0.0552820i
$281$	96.0886	−	31.2211i	0.341952	−	0.111107i	−0.133006	−	0.991115i	$-0.542463\pi$
$281$	96.0886	−	31.2211i	0.341952	−	0.111107i	0.474959	+	0.880008i	$0.342463\pi$
$282$	148.992	−	205.070i	0.528340	−	0.727198i
$283$	−1.24612	−	1.71513i	−0.00440324	−	0.00606055i	0.806810	−	0.590811i	$-0.201192\pi$
$283$	−1.24612	−	1.71513i	−0.00440324	−	0.00606055i	−0.811213	+	0.584751i	$0.801192\pi$
$284$	105.379	−	324.323i	0.371052	−	1.14198i
$285$		−	171.664i		−	0.602331i
$286$		0			0
$287$	−1.17340			−0.00408849
$288$	−165.608	−	53.8094i	−0.575029	−	0.186838i
$289$	260.866	−	189.530i	0.902649	−	0.655813i
$290$	−34.4721	−	25.0455i	−0.118869	−	0.0863637i
$291$	80.9549	+	249.154i	0.278196	+	0.856198i
$292$	489.945	−	159.193i	1.67789	−	0.545180i
$293$	−276.323	+	380.326i	−0.943082	+	1.29804i	0.0114501	+	0.999934i	$0.496355\pi$
$293$	−276.323	+	380.326i	−0.943082	+	1.29804i	−0.954532	+	0.298107i	$0.903645\pi$
$294$	−315.431	−	434.153i	−1.07289	−	1.47671i
$295$	38.6525	−	118.960i	0.131025	−	0.403255i
$296$		−	182.360i		−	0.616081i
$297$		0			0
$298$	791.187			2.65499
$299$	−58.5410	−	19.0211i	−0.195789	−	0.0636158i
$300$	−144.155	+	104.735i	−0.480517	+	0.349116i
$301$	−24.0213	−	17.4525i	−0.0798049	−	0.0579817i
$302$	−274.087	−	843.553i	−0.907573	−	2.79322i
$303$	−221.525	+	71.9778i	−0.731105	+	0.237550i
$304$	55.3885	−	76.2358i	0.182199	−	0.250776i
$305$	66.0263	+	90.8774i	0.216480	+	0.297959i
$306$	96.1894	−	296.041i	0.314345	−	0.967453i
$307$			99.4185i			0.323839i	0.986804	+	0.161919i	$0.0517685\pi$
$307$			99.4185i			0.323839i	−0.986804	+	0.161919i	$0.948232\pi$
$308$		0			0
$309$	−117.984			−0.381824
$310$	387.830	+	126.014i	1.25106	+	0.406495i
$311$	−274.430	+	199.385i	−0.882410	+	0.641109i	−0.933888	−	0.357566i	$-0.883607\pi$
$311$	−274.430	+	199.385i	−0.882410	+	0.641109i	0.0514778	+	0.998674i	$0.483607\pi$
$312$	−112.812	−	81.9624i	−0.361575	−	0.262700i
$313$	119.401	+	367.478i	0.381472	+	1.17405i	0.939007	+	0.343897i	$0.111747\pi$
$313$	119.401	+	367.478i	0.381472	+	1.17405i	−0.557535	+	0.830153i	$0.688253\pi$
$314$	−809.681	+	263.081i	−2.57860	+	0.837838i
$315$	−8.63621	+	11.8867i	−0.0274166	+	0.0377356i
$316$	−212.005	−	291.800i	−0.670902	−	0.923417i
$317$	−78.2035	+	240.686i	−0.246699	+	0.759261i	0.748654	+	0.662961i	$0.230701\pi$
$317$	−78.2035	+	240.686i	−0.246699	+	0.759261i	−0.995352	+	0.0962996i	$0.969299\pi$
$318$		−	874.567i		−	2.75021i
$319$		0			0
$320$	396.997			1.24062
$321$	18.5942	+	6.04163i	0.0579260	+	0.0188213i
$322$	16.1803	−	11.7557i	0.0502495	−	0.0365084i
$323$	237.293	+	172.403i	0.734652	+	0.533756i
$324$	170.928	+	526.062i	0.527556	+	1.62365i
$325$	72.8115	−	23.6579i	0.224035	−	0.0727935i
$326$	−125.484	+	172.714i	−0.384919	+	0.529796i
$327$	291.353	+	401.012i	0.890986	+	1.22634i
$328$	−1.82934	+	5.63014i	−0.00557727	+	0.0171651i
$329$		−	20.4433i		−	0.0621376i
$330$		0			0
$331$	372.116			1.12422			0.562109	−	0.827063i	$-0.309990\pi$
$331$	372.116			1.12422			0.562109	+	0.827063i	$0.309990\pi$
$332$	−295.110	−	95.8870i	−0.888885	−	0.288816i
$333$	−133.185	+	96.7648i	−0.399956	+	0.290585i
$334$	719.556	+	522.788i	2.15436	+	1.56523i
$335$	−94.5673	−	291.048i	−0.282291	−	0.868801i
$336$	−24.5492	+	7.97650i	−0.0730629	+	0.0237396i
$337$	−48.3247	+	66.5132i	−0.143397	+	0.197369i	−0.874674	−	0.484712i	$-0.838925\pi$
$337$	−48.3247	+	66.5132i	−0.143397	+	0.197369i	0.731277	+	0.682080i	$0.238925\pi$
$338$	−174.822	−	240.622i	−0.517225	−	0.711900i
$339$	−51.9959	+	160.027i	−0.153380	+	0.472056i
$340$			541.248i			1.59191i
$341$		0			0
$342$	149.318			0.436603
$343$	−83.0132	−	26.9726i	−0.242021	−	0.0786373i
$344$	−121.189	+	88.0493i	−0.352295	+	0.255957i
$345$	84.7214	+	61.5537i	0.245569	+	0.178416i
$346$	174.241	+	536.259i	0.503587	+	1.54988i
$347$	218.209	−	70.9005i	0.628845	−	0.204324i	0.0227815	−	0.999740i	$-0.492748\pi$
$347$	218.209	−	70.9005i	0.628845	−	0.204324i	0.606063	+	0.795416i	$0.292748\pi$
$348$	40.2786	−	55.4388i	0.115743	−	0.159307i
$349$	136.584	+	187.991i	0.391357	+	0.538657i	0.958549	−	0.284929i	$-0.0919701\pi$
$349$	136.584	+	187.991i	0.391357	+	0.538657i	−0.567192	+	0.823586i	$0.691970\pi$
$350$	−7.68692	+	23.6579i	−0.0219626	+	0.0675940i
$351$		−	151.109i		−	0.430510i
$352$		0			0
$353$	34.6443			0.0981426			0.0490713	−	0.998795i	$-0.484374\pi$
$353$	34.6443			0.0981426			0.0490713	+	0.998795i	$0.484374\pi$
$354$	331.160	+	107.600i	0.935480	+	0.303956i
$355$	201.666	−	146.519i	0.568072	−	0.412729i
$356$	−275.791	−	200.374i	−0.774694	−	0.562848i
$357$	−24.8278	−	76.4121i	−0.0695456	−	0.214039i
$358$	−6.00251	+	1.95033i	−0.0167668	+	0.00544786i
$359$	−265.557	+	365.508i	−0.739714	+	1.01813i	0.258921	+	0.965898i	$0.416633\pi$
$359$	−265.557	+	365.508i	−0.739714	+	1.01813i	−0.998635	+	0.0522304i	$0.983367\pi$
$360$	43.5704	+	59.9696i	0.121029	+	0.166582i
$361$	68.0764	−	209.518i	0.188577	−	0.580381i
$362$		−	224.368i		−	0.619802i
$363$		0			0
$364$	−41.8034			−0.114845
$365$	358.138	+	116.366i	0.981199	+	0.318811i
$366$	−252.984	+	183.803i	−0.691212	+	0.502195i
$367$	−298.387	−	216.791i	−0.813044	−	0.590711i	0.101668	−	0.994818i	$-0.467582\pi$
$367$	−298.387	−	216.791i	−0.813044	−	0.590711i	−0.914711	+	0.404108i	$0.867582\pi$
$368$	17.7639	+	54.6718i	0.0482716	+	0.148565i
$369$	5.08263	−	1.65145i	0.0137741	−	0.00447547i
$370$	291.246	−	400.866i	0.787152	−	1.08342i
$371$	−41.4590	−	57.0634i	−0.111749	−	0.153810i
$372$	−202.658	+	623.716i	−0.544778	+	1.67665i
$373$			593.166i			1.59026i	0.606440	+	0.795129i	$0.292597\pi$
$373$			593.166i			1.59026i	−0.606440	+	0.795129i	$0.707403\pi$
$374$		0			0
$375$	−492.053			−1.31214
$376$	−98.0902	−	31.8714i	−0.260878	−	0.0847644i
$377$	−23.8197	+	17.3060i	−0.0631821	+	0.0459045i
$378$	39.7214	+	28.8593i	0.105083	+	0.0763472i
$379$	−86.9114	−	267.486i	−0.229318	−	0.705767i	−0.997825	−	0.0659256i	$-0.979000\pi$
$379$	−86.9114	−	267.486i	−0.229318	−	0.705767i	0.768507	−	0.639841i	$-0.221000\pi$
$380$	−246.928	+	80.2318i	−0.649811	+	0.211136i
$381$	177.426	−	244.207i	0.465686	−	0.640962i
$382$	187.782	+	258.460i	0.491576	+	0.676597i
$383$	197.016	−	606.354i	0.514403	−	1.58317i	−0.269963	−	0.962871i	$-0.587012\pi$
$383$	197.016	−	606.354i	0.514403	−	1.58317i	0.784366	−	0.620298i	$-0.212988\pi$
$384$			489.034i			1.27353i
$385$		0			0
$386$	−1058.77			−2.74292
$387$	128.612	+	41.7887i	0.332332	+	0.107981i
$388$	320.555	−	232.897i	0.826173	−	0.600250i
$389$	−539.994	−	392.328i	−1.38816	−	1.00856i	−0.996064	−	0.0886314i	$-0.971751\pi$
$389$	−539.994	−	392.328i	−1.38816	−	1.00856i	−0.392094	−	0.919925i	$-0.628249\pi$
$390$	−117.082	−	360.341i	−0.300210	−	0.923952i
$391$	−170.172	+	55.2923i	−0.435223	+	0.141413i
$392$	−128.345	+	176.652i	−0.327411	+	0.450642i
$393$	−180.955	−	249.063i	−0.460445	−	0.633748i
$394$	94.2229	−	289.988i	0.239144	−	0.736011i
$395$		−	263.652i		−	0.667473i
$396$		0			0
$397$	−5.37384			−0.0135361			−0.00676805	−	0.999977i	$-0.502154\pi$
$397$	−5.37384			−0.0135361			−0.00676805	+	0.999977i	$0.502154\pi$
$398$	−449.212	−	145.958i	−1.12867	−	0.366728i
$399$	31.1803	−	22.6538i	0.0781462	−	0.0567765i
$400$	−57.8435	−	42.0257i	−0.144609	−	0.105064i
$401$	−87.3885	−	268.954i	−0.217927	−	0.670709i	−0.998933	−	0.0461858i	$-0.985293\pi$
$401$	−87.3885	−	268.954i	−0.217927	−	0.670709i	0.781006	−	0.624523i	$-0.214707\pi$
$402$	810.218	−	263.256i	2.01547	−	0.654865i
$403$	165.623	−	227.961i	0.410975	−	0.565659i
$404$	207.071	+	285.009i	0.512551	+	0.705467i
$405$	−124.944	+	384.539i	−0.308504	+	0.949479i
$406$		−	9.56652i		−	0.0235629i
$407$		0			0
$408$	−405.344			−0.993491
$409$	29.5379	+	9.59745i	0.0722198	+	0.0234656i	0.344904	−	0.938638i	$-0.387911\pi$
$409$	29.5379	+	9.59745i	0.0722198	+	0.0234656i	−0.272684	+	0.962104i	$0.587911\pi$
$410$	−13.0132	+	9.45461i	−0.0317394	+	0.0230600i
$411$	−171.943	−	124.924i	−0.418352	−	0.303951i
$412$	55.1428	+	169.712i	0.133842	+	0.411922i
$413$	26.7082	−	8.67802i	0.0646688	−	0.0210122i
$414$	−53.5410	+	73.6929i	−0.129326	+	0.178002i
$415$	−133.321	−	183.501i	−0.321256	−	0.442171i
$416$	111.910	−	344.423i	0.269014	−	0.827940i
$417$			582.459i			1.39678i
$418$		0			0
$419$	−245.156			−0.585098			−0.292549	−	0.956251i	$-0.594503\pi$
$419$	−245.156			−0.585098			−0.292549	+	0.956251i	$0.594503\pi$
$420$	67.6393	+	21.9773i	0.161046	+	0.0523270i
$421$	62.6262	−	45.5006i	0.148756	−	0.108077i	−0.510918	−	0.859629i	$-0.670694\pi$
$421$	62.6262	−	45.5006i	0.148756	−	0.108077i	0.659674	+	0.751552i	$0.270694\pi$
$422$	830.419	+	603.335i	1.96782	+	1.42970i
$423$	28.7721	+	88.5513i	0.0680191	+	0.209341i
$424$	−338.435	+	109.964i	−0.798195	+	0.259349i
$425$	130.810	−	180.044i	0.307788	−	0.423634i
$426$	407.877	+	561.395i	0.957458	+	1.31783i
$427$	−7.79335	+	23.9855i	−0.0182514	+	0.0561720i
$428$		−	29.5703i		−	0.0690896i
$429$		0			0
$430$	−407.023			−0.946566
$431$	−427.474	−	138.895i	−0.991819	−	0.322262i	−0.232227	−	0.972662i	$-0.574601\pi$
$431$	−427.474	−	138.895i	−0.991819	−	0.322262i	−0.759592	+	0.650400i	$0.774601\pi$
$432$	−114.170	+	82.9491i	−0.264282	+	0.192012i
$433$	−116.789	−	84.8520i	−0.269720	−	0.195963i	0.444701	−	0.895679i	$-0.353310\pi$
$433$	−116.789	−	84.8520i	−0.269720	−	0.195963i	−0.714421	+	0.699716i	$0.753310\pi$
$434$	28.2918	+	87.0732i	0.0651885	+	0.200629i
$435$	47.6393	−	15.4790i	0.109516	−	0.0355838i
$436$	440.659	−	606.516i	1.01069	−	1.39109i
$437$	−50.4508	−	69.4396i	−0.115448	−	0.158901i
$438$	−323.939	+	996.981i	−0.739586	+	2.27621i
$439$		−	155.406i		−	0.354001i	−0.984211	−	0.177000i	$-0.943361\pi$
$439$		−	155.406i		−	0.354001i	0.984211	−	0.177000i	$-0.0566394\pi$
$440$		0			0
$441$	197.120			0.446983
$442$	615.689	+	200.049i	1.39296	+	0.452601i
$443$	−262.370	+	190.623i	−0.592257	+	0.430300i	−0.843122	−	0.537722i	$-0.819285\pi$
$443$	−262.370	+	190.623i	−0.592257	+	0.430300i	0.250865	+	0.968022i	$0.419285\pi$
$444$	644.681	+	468.388i	1.45198	+	1.05493i
$445$	−77.0031	−	236.991i	−0.173041	−	0.532564i
$446$	−333.607	+	108.395i	−0.747997	+	0.243039i
$447$	−546.697	+	752.464i	−1.22304	+	1.68336i
$448$	52.3901	+	72.1088i	0.116942	+	0.160957i
$449$	−120.950	+	372.245i	−0.269376	+	0.829055i	0.721277	+	0.692647i	$0.243556\pi$
$449$	−120.950	+	372.245i	−0.269376	+	0.829055i	−0.990653	+	0.136407i	$0.956444\pi$
$450$		−	113.294i		−	0.251765i
$451$		0			0
$452$	254.490			0.563032
$453$	991.656	+	322.209i	2.18909	+	0.711277i
$454$	−97.1443	+	70.5795i	−0.213974	+	0.155461i
$455$	−24.7214	−	17.9611i	−0.0543327	−	0.0394750i
$456$	−60.0861	−	184.926i	−0.131768	−	0.405540i
$457$	49.6885	−	16.1448i	0.108728	−	0.0353277i	−0.254148	−	0.967165i	$-0.581795\pi$
$457$	49.6885	−	16.1448i	0.108728	−	0.0353277i	0.362875	+	0.931838i	$0.381795\pi$
$458$	242.782	−	334.161i	0.530092	−	0.729609i
$459$	−258.189	−	355.366i	−0.562503	−	0.774219i
$460$	48.9443	−	150.635i	0.106401	−	0.327467i
$461$		−	339.293i		−	0.735994i	−0.929827	−	0.367997i	$-0.880044\pi$
$461$		−	339.293i		−	0.735994i	0.929827	−	0.367997i	$-0.119956\pi$
$462$		0			0
$463$	676.869			1.46192			0.730960	−	0.682420i	$-0.239072\pi$
$463$	676.869			1.46192			0.730960	+	0.682420i	$0.239072\pi$
$464$	26.1509	+	8.49695i	0.0563597	+	0.0183124i
$465$	−387.830	+	281.775i	−0.834042	+	0.605967i
$466$	−665.650	−	483.623i	−1.42843	−	1.03782i
$467$	113.992	+	350.831i	0.244094	+	0.751244i	0.995784	+	0.0917275i	$0.0292389\pi$
$467$	113.992	+	350.831i	0.244094	+	0.751244i	−0.751690	+	0.659516i	$0.770761\pi$
$468$	181.074	−	58.8345i	0.386910	−	0.125715i
$469$	40.3851	−	55.5853i	0.0861089	−	0.118519i
$470$	−164.721	−	226.720i	−0.350471	−	0.482382i
$471$	309.271	−	951.837i	0.656625	−	2.02088i
$472$		−	141.679i		−	0.300168i
$473$		0			0
$474$	733.951			1.54842
$475$	101.530	+	32.9892i	0.213748	+	0.0694510i
$476$	−98.3100	+	71.4264i	−0.206534	+	0.150055i
$477$	259.894	+	188.824i	0.544850	+	0.395857i
$478$	104.751	+	322.390i	0.219144	+	0.674456i
$479$	452.166	−	146.918i	0.943979	−	0.306717i	0.203712	−	0.979031i	$-0.434699\pi$
$479$	452.166	−	146.918i	0.943979	−	0.306717i	0.740267	+	0.672313i	$0.234699\pi$
$480$	−362.148	+	498.454i	−0.754475	+	1.03845i
$481$	−201.246	−	276.992i	−0.418391	−	0.575866i
$482$	181.750	−	559.370i	0.377075	−	1.16052i
$483$			23.5114i			0.0486779i
$484$		0			0
$485$	289.633			0.597182
$486$	−602.513	−	195.768i	−1.23974	−	0.402815i
$487$	144.941	−	105.306i	0.297620	−	0.216234i	−0.428946	−	0.903330i	$-0.641115\pi$
$487$	144.941	−	105.306i	0.297620	−	0.216234i	0.726566	+	0.687096i	$0.241115\pi$
$488$	102.936	+	74.7875i	0.210935	+	0.153253i
$489$	−77.5532	−	238.684i	−0.158596	−	0.488107i
$490$	−564.259	+	183.339i	−1.15155	+	0.374161i
$491$	377.802	−	520.000i	0.769455	−	1.05906i	−0.226913	−	0.973915i	$-0.572863\pi$
$491$	377.802	−	520.000i	0.769455	−	1.05906i	0.996368	−	0.0851491i	$-0.0271366\pi$
$492$	−15.2051	−	20.9280i	−0.0309047	−	0.0425366i
$493$	−26.4477	+	81.3978i	−0.0536465	+	0.165107i
$494$			310.543i			0.628631i
$495$		0			0
$496$	−263.151			−0.530546
$497$	53.2260	+	17.2942i	0.107095	+	0.0347971i
$498$	510.828	−	371.138i	1.02576	−	0.745258i
$499$	425.290	+	308.991i	0.852284	+	0.619220i	0.925775	−	0.378075i	$-0.123414\pi$
$499$	425.290	+	308.991i	0.852284	+	0.619220i	−0.0734909	+	0.997296i	$0.523414\pi$
$500$	229.974	+	707.786i	0.459947	+	1.41557i
$501$	−994.402	+	323.101i	−1.98483	+	0.644912i
$502$	−772.694	+	1063.52i	−1.53923	+	2.11857i
$503$	376.964	+	518.847i	0.749432	+	1.03150i	0.998020	+	0.0628955i	$0.0200335\pi$
$503$	376.964	+	518.847i	0.749432	+	1.03150i	−0.248588	+	0.968609i	$0.579967\pi$
$504$	−5.14279	+	15.8279i	−0.0102040	+	0.0314045i
$505$			257.515i			0.509932i
$506$		0			0
$507$	349.644			0.689634
$508$	−434.200	−	141.080i	−0.854725	−	0.277717i
$509$	368.371	−	267.637i	0.723715	−	0.525809i	−0.163854	−	0.986485i	$-0.552393\pi$
$509$	368.371	−	267.637i	0.723715	−	0.525809i	0.887569	+	0.460675i	$0.152393\pi$
$510$	−891.033	−	647.374i	−1.74712	−	1.26936i
$511$	26.1258	+	80.4069i	0.0511268	+	0.157352i
$512$	−458.586	+	149.004i	−0.895677	+	0.291023i
$513$	123.853	−	170.468i	0.241428	−	0.332297i
$514$	−51.1600	−	70.4157i	−0.0995331	−	0.136996i
$515$	−40.3081	+	124.055i	−0.0782681	+	0.240884i
$516$		−	654.583i		−	1.26857i
$517$		0			0
$518$	111.246			0.214761
$519$	−630.410	−	204.833i	−1.21466	−	0.394668i
$520$	−124.721	+	90.6154i	−0.239849	+	0.174260i
$521$	146.622	+	106.527i	0.281423	+	0.204466i	0.719538	−	0.694453i	$-0.244354\pi$
$521$	146.622	+	106.527i	0.281423	+	0.204466i	−0.438115	+	0.898919i	$0.644354\pi$
$522$	13.4640	+	41.4379i	0.0257931	+	0.0793830i
$523$	325.991	−	105.921i	0.623310	−	0.202526i	0.0197008	−	0.999806i	$-0.493729\pi$
$523$	325.991	−	105.921i	0.623310	−	0.202526i	0.603609	+	0.797280i	$0.293729\pi$
$524$	−273.687	+	376.698i	−0.522304	+	0.718890i
$525$	−17.1885	−	23.6579i	−0.0327399	−	0.0450627i
$526$	−89.9230	+	276.754i	−0.170956	+	0.526149i
$527$		−	819.088i		−	1.55425i
$528$		0			0
$529$	−476.639			−0.901020
$530$	−919.574	−	298.788i	−1.73505	−	0.563751i
$531$	−103.475	+	75.1787i	−0.194868	+	0.141580i
$532$	−47.1591	−	34.2631i	−0.0886448	−	0.0644042i
$533$	3.43459	+	10.5706i	0.00644388	+	0.0198322i
$534$	659.734	−	214.361i	1.23546	−	0.401424i
$535$	12.7051	−	17.4871i	0.0237478	−	0.0326861i
$536$	−203.746	−	280.432i	−0.380123	−	0.523195i
$537$	2.29276	−	7.05638i	0.00426956	−	0.0131404i
$538$			720.159i			1.33859i
$539$		0			0
$540$	388.827			0.720049
$541$	−290.220	−	94.2981i	−0.536451	−	0.174303i	0.0282474	−	0.999601i	$-0.491007\pi$
$541$	−290.220	−	94.2981i	−0.536451	−	0.174303i	−0.564698	+	0.825298i	$0.691007\pi$
$542$	357.100	−	259.448i	0.658856	−	0.478687i
$543$	213.387	+	155.035i	0.392978	+	0.285515i
$544$	−325.309	−	1001.20i	−0.597995	−	1.84044i
$545$	521.187	−	169.344i	0.956307	−	0.310723i
$546$	50.0000	−	68.8191i	0.0915751	−	0.126042i
$547$	88.9226	+	122.391i	0.162564	+	0.223750i	0.882526	−	0.470263i	$-0.155841\pi$
$547$	88.9226	+	122.391i	0.162564	+	0.223750i	−0.719962	+	0.694013i	$0.755841\pi$
$548$	−99.3328	+	305.715i	−0.181264	+	0.557874i
$549$		−	114.863i		−	0.209222i
$550$		0			0
$551$	−41.0557			−0.0745113
$552$	112.812	+	36.6547i	0.204369	+	0.0664034i
$553$	47.8885	−	34.7931i	0.0865977	−	0.0629169i
$554$	−968.768	−	703.851i	−1.74868	−	1.27049i
$555$	180.000	+	553.983i	0.324324	+	0.998168i
$556$	837.830	−	272.227i	1.50689	−	0.489618i
$557$	−64.0758	+	88.1928i	−0.115037	+	0.158335i	−0.862653	−	0.505796i	$-0.831199\pi$
$557$	−64.0758	+	88.1928i	−0.115037	+	0.158335i	0.747615	+	0.664132i	$0.231199\pi$
$558$	−245.095	−	337.345i	−0.439239	−	0.604560i
$559$	−86.9098	+	267.481i	−0.155474	+	0.478499i
$560$			28.5376i			0.0509600i
$561$		0			0
$562$	310.949			0.553291
$563$	947.888	+	307.987i	1.68364	+	0.547047i	0.985612	−	0.169026i	$-0.0540622\pi$
$563$	947.888	+	307.987i	1.68364	+	0.547047i	0.698026	+	0.716073i	$0.254062\pi$
$564$	364.615	−	264.908i	0.646480	−	0.469695i
$565$	150.498	+	109.344i	0.266369	+	0.193528i
$566$	−2.01626	−	6.20541i	−0.00356230	−	0.0109636i
$567$	−86.3344	+	28.0517i	−0.152265	+	0.0494740i
$568$	165.961	−	228.425i	0.292184	−	0.402157i
$569$	58.3835	+	80.3580i	0.102607	+	0.141227i	0.857233	−	0.514929i	$-0.172182\pi$
$569$	58.3835	+	80.3580i	0.102607	+	0.141227i	−0.754626	+	0.656155i	$0.772182\pi$
$570$	163.262	−	502.470i	0.286425	−	0.881526i
$571$		−	930.127i		−	1.62894i	−0.580202	−	0.814472i	$-0.697027\pi$
$571$		−	930.127i		−	1.62894i	0.580202	−	0.814472i	$-0.302973\pi$
$572$		0			0
$573$	−375.564			−0.655435
$574$	−3.43459	−	1.11597i	−0.00598360	−	0.00194419i
$575$	−52.6869	+	38.2793i	−0.0916294	+	0.0665727i
$576$	−328.417	−	238.609i	−0.570169	−	0.414252i
$577$	−107.337	−	330.349i	−0.186026	−	0.572529i	0.813939	−	0.580951i	$-0.197319\pi$
$577$	−107.337	−	330.349i	−0.186026	−	0.572529i	−0.999965	+	0.00842219i	$0.997319\pi$
$578$	943.821	−	306.666i	1.63291	−	0.530564i
$579$	731.591	−	1006.95i	1.26354	−	1.73912i
$580$	−44.5310	−	61.2916i	−0.0767775	−	0.105675i
$581$	15.7364	−	48.4318i	0.0270851	−	0.0833593i
$582$			806.278i			1.38536i
$583$		0			0
$584$	426.536			0.730370
$585$	132.361	+	43.0066i	0.226258	+	0.0735155i
$586$	−1170.52	+	850.435i	−1.99748	+	1.45125i
$587$	514.043	+	373.474i	0.875712	+	0.636242i	0.932114	−	0.362166i	$-0.117963\pi$
$587$	514.043	+	373.474i	0.875712	+	0.636242i	−0.0564016	+	0.998408i	$0.517963\pi$
$588$	−294.849	−	907.453i	−0.501445	−	1.54329i
$589$	373.684	−	121.417i	0.634438	−	0.206141i
$590$	226.276	−	311.442i	0.383518	−	0.527867i
$591$	210.689	+	289.988i	0.356495	+	0.490674i
$592$	−98.8084	+	304.101i	−0.166906	+	0.513684i
$593$			341.152i			0.575299i	0.957736	+	0.287650i	$0.0928739\pi$
$593$			341.152i			0.575299i	−0.957736	+	0.287650i	$0.907126\pi$
$594$		0			0
$595$	−88.8266			−0.149288
$596$	1337.88	+	434.705i	2.24477	+	0.729371i
$597$	449.212	−	326.371i	0.752448	−	0.546686i
$598$	−153.262	−	111.352i	−0.256292	−	0.186207i
$599$	−138.334	−	425.749i	−0.230942	−	0.710767i	−0.997634	−	0.0687514i	$-0.978098\pi$
$599$	−138.334	−	425.749i	−0.230942	−	0.710767i	0.766692	−	0.642016i	$-0.221902\pi$
$600$	−140.312	+	45.5900i	−0.233853	+	0.0759833i
$601$	−471.303	+	648.693i	−0.784198	+	1.07936i	0.210609	+	0.977570i	$0.432455\pi$
$601$	−471.303	+	648.693i	−0.784198	+	1.07936i	−0.994806	+	0.101785i	$0.967545\pi$
$602$	−53.7132	−	73.9299i	−0.0892246	−	0.122807i
$603$	−96.6991	+	297.609i	−0.160363	+	0.493548i
$604$		−	1577.03i		−	2.61097i
$605$		0			0
$606$	−716.869			−1.18295
$607$	−969.586	−	315.037i	−1.59734	−	0.519007i	−0.630892	−	0.775870i	$-0.717311\pi$
$607$	−969.586	−	315.037i	−1.59734	−	0.519007i	−0.966448	+	0.256863i	$0.917311\pi$
$608$	408.544	−	296.825i	0.671948	−	0.488199i
$609$	9.09830	+	6.61030i	0.0149397	+	0.0108544i
$610$	106.833	+	328.798i	0.175136	+	0.539012i
$611$	−184.164	+	59.8385i	−0.301414	+	0.0979354i
$612$	325.309	−	447.750i	0.531551	−	0.731618i
$613$	−439.791	−	605.321i	−0.717441	−	0.987473i	−0.999605	−	0.0281068i	$-0.991052\pi$
$613$	−439.791	−	605.321i	−0.717441	−	0.987473i	0.282164	−	0.959366i	$-0.408948\pi$
$614$	−94.5526	+	291.003i	−0.153994	+	0.473946i
$615$		−	18.9092i		−	0.0307467i
$616$		0			0
$617$	517.100			0.838088			0.419044	−	0.907966i	$-0.362365\pi$
$617$	517.100			0.838088			0.419044	+	0.907966i	$0.362365\pi$
$618$	−345.344	−	112.209i	−0.558810	−	0.181568i
$619$	560.833	−	407.469i	0.906031	−	0.658270i	−0.0339769	−	0.999423i	$-0.510817\pi$
$619$	560.833	−	407.469i	0.906031	−	0.658270i	0.940008	+	0.341153i	$0.110817\pi$
$620$	586.577	+	426.173i	0.946093	+	0.687376i
$621$	39.7214	+	122.250i	0.0639635	+	0.196860i
$622$	−992.895	+	322.611i	−1.59629	+	0.518668i
$623$	32.8843	−	45.2613i	0.0527837	−	0.0726505i
$624$	143.713	+	197.804i	0.230310	+	0.316994i
$625$	−98.5764	+	303.387i	−0.157722	+	0.485419i
$626$			1189.18i			1.89965i
$627$		0			0
$628$	−1513.70			−2.41035
$629$	−946.550	−	307.553i	−1.50485	−	0.488955i
$630$	−36.5836	+	26.5795i	−0.0580692	+	0.0421897i
$631$	725.530	+	527.128i	1.14981	+	0.835385i	0.988456	−	0.151511i	$-0.0484139\pi$
$631$	725.530	+	527.128i	1.14981	+	0.835385i	0.161354	+	0.986897i	$0.448414\pi$
$632$	−92.2837	−	284.020i	−0.146018	−	0.449399i
$633$	−1147.61	+	372.881i	−1.81297	+	0.589070i
$634$	−457.812	+	630.124i	−0.722100	+	0.993886i
$635$	−196.158	−	269.988i	−0.308910	−	0.425178i
$636$	480.517	−	1478.88i	0.755529	−	2.32528i
$637$			409.958i			0.643577i
$638$		0			0
$639$	−254.892			−0.398891
$640$	514.200	+	167.074i	0.803438	+	0.261053i
$641$	−460.136	+	334.308i	−0.717840	+	0.521541i	−0.885693	−	0.464271i	$-0.846317\pi$
$641$	−460.136	+	334.308i	−0.717840	+	0.521541i	0.167853	+	0.985812i	$0.446317\pi$
$642$	48.6803	+	35.3683i	0.0758261	+	0.0550909i
$643$	204.109	+	628.182i	0.317432	+	0.976955i	0.974742	+	0.223335i	$0.0716943\pi$
$643$	204.109	+	628.182i	0.317432	+	0.976955i	−0.657310	+	0.753620i	$0.728306\pi$
$644$	33.8197	−	10.9887i	0.0525150	−	0.0170632i
$645$	281.246	−	387.102i	0.436040	−	0.600158i
$646$	530.603	+	730.312i	0.821366	+	1.13051i
$647$	10.9242	−	33.6211i	0.0168843	−	0.0519647i	−0.942259	−	0.334884i	$-0.891303\pi$
$647$	10.9242	−	33.6211i	0.0168843	−	0.0519647i	0.959144	+	0.282919i	$0.0913029\pi$
$648$			457.979i			0.706758i
$649$		0			0
$650$	235.623			0.362497
$651$	−102.361	−	33.2590i	−0.157236	−	0.0510891i
$652$	−307.086	+	223.111i	−0.470990	+	0.342194i
$653$	−339.336	−	246.542i	−0.519657	−	0.377553i	0.296817	−	0.954934i	$-0.404075\pi$
$653$	−339.336	−	246.542i	−0.519657	−	0.377553i	−0.816475	+	0.577381i	$0.804075\pi$
$654$	471.418	+	1450.88i	0.720823	+	2.21847i
$655$	−323.702	+	105.177i	−0.494202	+	0.160576i
$656$	6.10118	−	8.39755i	0.00930058	−	0.0128011i
$657$	−226.331	−	311.518i	−0.344491	−	0.474152i
$658$	19.4427	−	59.8385i	0.0295482	−	0.0909400i
$659$			1281.39i			1.94445i	0.234058	+	0.972223i	$0.424800\pi$
$659$			1281.39i			1.94445i	−0.234058	+	0.972223i	$0.575200\pi$
$660$		0			0
$661$	70.6950			0.106952			0.0534758	−	0.998569i	$-0.482970\pi$
$661$	70.6950			0.106952			0.0534758	+	0.998569i	$0.482970\pi$
$662$	1089.20	+	353.904i	1.64532	+	0.534598i
$663$	−615.689	+	447.324i	−0.928641	+	0.674697i
$664$	−207.850	−	151.012i	−0.313027	−	0.227428i
$665$	−13.1672	−	40.5244i	−0.0198003	−	0.0609390i
$666$	−481.869	+	156.569i	−0.723527	+	0.235088i
$667$	14.7214	−	20.2622i	0.0220710	−	0.0303781i
$668$	929.520	+	1279.37i	1.39150	+	1.91523i
$669$	127.426	−	392.178i	0.190473	−	0.586216i
$670$		−	941.852i		−	1.40575i
$671$		0			0
$672$	−138.328			−0.205845
$673$	760.848	+	247.215i	1.13053	+	0.367332i	0.813778	−	0.581175i	$-0.197407\pi$
$673$	760.848	+	247.215i	1.13053	+	0.367332i	0.316754	+	0.948508i	$0.397407\pi$
$674$	−204.707	+	148.728i	−0.303719	+	0.220665i
$675$	−129.342	−	93.9724i	−0.191618	−	0.139218i
$676$	−163.415	−	502.941i	−0.241739	−	0.743996i
$677$	−890.245	+	289.258i	−1.31499	+	0.427265i	−0.880770	−	0.473545i	$-0.842974\pi$
$677$	−890.245	+	289.258i	−1.31499	+	0.427265i	−0.434215	+	0.900809i	$0.642974\pi$
$678$	−304.390	+	418.956i	−0.448952	+	0.617930i
$679$	38.2217	+	52.6077i	0.0562912	+	0.0774782i
$680$	−138.482	+	426.204i	−0.203650	+	0.626771i
$681$		−	141.159i		−	0.207282i
$682$		0			0
$683$	−241.319			−0.353322			−0.176661	−	0.984272i	$-0.556530\pi$
$683$	−241.319			−0.353322			−0.176661	+	0.984272i	$0.556530\pi$
$684$	252.494	+	82.0404i	0.369144	+	0.119942i
$685$	−190.095	+	138.112i	−0.277511	+	0.201624i
$686$	−217.331	−	157.900i	−0.316809	−	0.230176i
$687$	150.048	+	461.799i	0.218410	+	0.672197i
$688$	249.802	−	81.1655i	0.363084	−	0.117973i
$689$	−392.705	+	540.512i	−0.569964	+	0.784488i
$690$	189.443	+	260.746i	0.274555	+	0.377892i
$691$	−281.477	+	866.296i	−0.407347	+	1.25368i	0.511573	+	0.859240i	$0.329063\pi$
$691$	−281.477	+	866.296i	−0.407347	+	1.25368i	−0.918920	+	0.394444i	$0.870937\pi$
$692$			1002.54i			1.44876i
$693$		0			0
$694$	706.140			1.01749
$695$	612.433	+	198.992i	0.881199	+	0.286319i
$696$	45.9017	−	33.3495i	0.0659507	−	0.0479160i
$697$	26.1384	+	18.9906i	0.0375012	+	0.0272462i
$698$	220.997	+	680.159i	0.316614	+	0.974439i
$699$	919.906	−	298.896i	1.31603	−	0.427605i
$700$	−25.9969	+	35.7817i	−0.0371384	+	0.0511167i
$701$	−253.951	−	349.534i	−0.362270	−	0.498622i	0.588509	−	0.808490i	$-0.299715\pi$
$701$	−253.951	−	349.534i	−0.362270	−	0.498622i	−0.950779	+	0.309869i	$0.899715\pi$
$702$	143.713	−	442.304i	0.204720	−	0.630062i
$703$		−	477.424i		−	0.679124i
$704$		0			0
$705$	329.443			0.467295
$706$	101.406	+	32.9487i	0.143634	+	0.0466696i
$707$	−46.7740	+	33.9833i	−0.0661584	+	0.0480669i
$708$	500.867	+	363.901i	0.707439	+	0.513984i
$709$	−270.797	−	833.428i	−0.381942	−	1.17550i	−0.938674	−	0.344806i	$-0.887945\pi$
$709$	−270.797	−	833.428i	−0.381942	−	1.17550i	0.556732	−	0.830692i	$-0.312055\pi$
$710$	729.633	−	237.072i	1.02765	−	0.333904i
$711$	−158.464	+	218.107i	−0.222875	+	0.306761i
$712$	−165.904	−	228.347i	−0.233011	−	0.320712i
$713$	−74.0689	+	227.961i	−0.103883	+	0.319720i
$714$		−	247.275i		−	0.346323i
$715$		0			0
$716$	−11.2217			−0.0156728
$717$	−378.992	−	123.142i	−0.528580	−	0.171746i
$718$	−1124.92	+	817.301i	−1.56674	+	1.13830i
$719$	−406.366	−	295.242i	−0.565182	−	0.410629i	0.268170	−	0.963372i	$-0.413581\pi$
$719$	−406.366	−	295.242i	−0.565182	−	0.410629i	−0.833352	+	0.552743i	$0.813581\pi$
$720$	−40.1641	−	123.612i	−0.0557834	−	0.171684i
$721$	−27.8522	+	9.04972i	−0.0386299	+	0.0125516i
$722$	398.526	−	548.524i	0.551976	−	0.759729i
$723$	406.406	+	559.370i	0.562110	+	0.773678i
$724$	123.276	−	379.403i	0.170270	−	0.524037i
$725$			31.1508i			0.0429666i
$726$		0			0
$727$	−393.878			−0.541786			−0.270893	−	0.962609i	$-0.587319\pi$
$727$	−393.878			−0.541786			−0.270893	+	0.962609i	$0.587319\pi$
$728$	−32.9180	−	10.6957i	−0.0452170	−	0.0146919i
$729$	−133.481	+	96.9798i	−0.183102	+	0.133031i
$730$	937.617	+	681.219i	1.28441	+	0.933176i
$731$	252.637	+	777.537i	0.345605	+	1.06366i
$732$	−528.779	+	171.811i	−0.722376	+	0.234714i
$733$	−364.875	+	502.208i	−0.497784	+	0.685140i	−0.981800	−	0.189919i	$-0.939178\pi$
$733$	−364.875	+	502.208i	−0.497784	+	0.685140i	0.484016	+	0.875059i	$0.339178\pi$
$734$	−667.214	−	918.341i	−0.909010	−	1.25115i
$735$	215.528	−	663.327i	0.293235	−	0.902485i
$736$			308.061i			0.418562i
$737$		0			0
$738$	16.4477			0.0222869
$739$	808.400	+	262.665i	1.09391	+	0.355433i	0.799756	−	0.600325i	$-0.204962\pi$
$739$	808.400	+	262.665i	1.09391	+	0.355433i	0.294154	+	0.955758i	$0.404962\pi$
$740$	712.741	−	517.837i	0.963164	−	0.699780i
$741$	−295.344	−	214.580i	−0.398575	−	0.289582i
$742$	−67.0820	−	206.457i	−0.0904071	−	0.278244i
$743$	−385.766	+	125.343i	−0.519200	+	0.168698i	−0.556882	−	0.830591i	$-0.688003\pi$
$743$	−385.766	+	125.343i	−0.519200	+	0.168698i	0.0376820	+	0.999290i	$0.488003\pi$
$744$	−319.164	+	439.292i	−0.428984	+	0.590446i
$745$	604.413	+	831.904i	0.811293	+	1.11665i
$746$	−564.135	+	1736.23i	−0.756213	+	2.32738i
$747$			231.933i			0.310486i
$748$		0			0
$749$	4.85292			0.00647919
$750$	−1440.26	−	467.970i	−1.92035	−	0.623960i
$751$	687.197	−	499.278i	0.915043	−	0.664818i	−0.0272422	−	0.999629i	$-0.508673\pi$
$751$	687.197	−	499.278i	0.915043	−	0.664818i	0.942285	+	0.334811i	$0.108673\pi$
$752$	146.305	+	106.297i	0.194554	+	0.141352i
$753$	−477.551	−	1469.75i	−0.634198	−	1.95186i
$754$	−86.1803	+	28.0017i	−0.114298	+	0.0371375i
$755$	677.580	−	932.610i	0.897458	−	1.23524i
$756$	51.3119	+	70.6248i	0.0678729	+	0.0934190i
$757$	185.571	−	571.129i	0.245140	−	0.754464i	−0.750473	−	0.660901i	$-0.770174\pi$
$757$	185.571	−	571.129i	0.245140	−	0.754464i	0.995613	−	0.0935631i	$-0.0298257\pi$
$758$		−	865.602i		−	1.14196i
$759$		0			0
$760$	−214.971			−0.282856
$761$	−332.142	−	107.920i	−0.436455	−	0.141813i	0.0825445	−	0.996587i	$-0.473695\pi$
$761$	−332.142	−	107.920i	−0.436455	−	0.141813i	−0.518999	+	0.854775i	$0.673695\pi$
$762$	751.591	−	546.062i	0.986339	−	0.716617i
$763$	99.5379	+	72.3185i	0.130456	+	0.0947818i
$764$	175.530	+	540.225i	0.229751	+	0.707101i
$765$	384.758	−	125.015i	0.502951	−	0.163419i
$766$	1153.35	−	1587.45i	1.50568	−	2.07240i
$767$	−156.353	−	215.201i	−0.203849	−	0.280575i
$768$	−21.2426	+	65.3781i	−0.0276597	+	0.0851278i
$769$		−	768.616i		−	0.999500i	−0.866170	−	0.499750i	$-0.833425\pi$
$769$		−	768.616i		−	0.999500i	0.866170	−	0.499750i	$-0.166575\pi$
$770$		0			0
$771$	102.320			0.132711
$772$	−1790.36	−	581.723i	−2.31912	−	0.753527i
$773$	−5.65248	+	4.10676i	−0.00731239	+	0.00531276i	−0.591435	−	0.806352i	$-0.701439\pi$
$773$	−5.65248	+	4.10676i	−0.00731239	+	0.00531276i	0.584123	+	0.811665i	$0.301439\pi$
$774$	336.712	+	244.635i	0.435028	+	0.316066i
$775$	−92.1246	−	283.530i	−0.118870	−	0.365846i
$776$	312.008	−	101.378i	0.402073	−	0.130641i
$777$	−76.8692	+	105.801i	−0.0989307	+	0.136166i
$778$	−1207.46	−	1661.93i	−1.55201	−	2.13616i
$779$	−4.78928	+	14.7399i	−0.00614799	+	0.0189216i
$780$		−	673.660i		−	0.863667i
$781$		0			0
$782$	−550.689			−0.704206
$783$	58.4752	+	18.9998i	0.0746810	+	0.0242653i
$784$	309.742	−	225.041i	0.395079	−	0.287042i
$785$	−895.161	−	650.373i	−1.14033	−	0.828500i
$786$	−292.791	−	901.119i	−0.372508	−	1.14646i
$787$	1048.74	−	340.758i	1.33258	−	0.432983i	0.445786	−	0.895140i	$-0.352924\pi$
$787$	1048.74	−	340.758i	1.33258	−	0.432983i	0.886798	+	0.462157i	$0.152924\pi$
$788$	318.659	−	438.596i	0.404389	−	0.556594i
$789$	−201.074	−	276.754i	−0.254847	−	0.350766i
$790$	250.748	−	771.722i	0.317402	−	0.976863i
$791$			41.7655i			0.0528009i
$792$		0			0
$793$	238.885			0.301243
$794$	−15.7295	−	5.11082i	−0.0198104	−	0.00643680i
$795$	919.574	−	668.110i	1.15670	−	0.840390i
$796$	−679.415	−	493.624i	−0.853537	−	0.620131i
$797$	−222.914	−	686.058i	−0.279691	−	0.860800i	−0.987940	−	0.154837i	$-0.950515\pi$
$797$	−222.914	−	686.058i	−0.279691	−	0.860800i	0.708249	−	0.705963i	$-0.249485\pi$
$798$	112.812	−	36.6547i	0.141368	−	0.0459332i
$799$	−330.861	+	455.391i	−0.414094	+	0.569951i
$800$	−225.214	−	309.981i	−0.281518	−	0.387476i
$801$	−78.7389	+	242.334i	−0.0983008	+	0.302539i
$802$		−	870.354i		−	1.08523i
$803$		0			0
$804$	1514.71			1.88396
$805$	24.7214	+	8.03246i	0.0307098	+	0.00997821i
$806$	701.591	−	509.735i	0.870460	−	0.632426i
$807$	−684.912	−	497.618i	−0.848713	−	0.616626i
$808$	90.1358	+	277.410i	0.111554	+	0.343329i
$809$	763.198	−	247.978i	0.943384	−	0.306524i	0.203360	−	0.979104i	$-0.434814\pi$
$809$	763.198	−	247.978i	0.943384	−	0.306524i	0.740024	+	0.672580i	$0.234814\pi$
$810$	−731.437	+	1006.74i	−0.903008	+	1.24288i
$811$	−291.464	−	401.165i	−0.359388	−	0.494655i	0.590590	−	0.806972i	$-0.298895\pi$
$811$	−291.464	−	401.165i	−0.359388	−	0.494655i	−0.949978	+	0.312316i	$0.898895\pi$
$812$	5.25617	−	16.1768i	0.00647311	−	0.0199222i
$813$			518.897i			0.638250i
$814$		0			0
$815$	−277.463			−0.340445
$816$	675.947	+	219.629i	0.828367	+	0.269153i
$817$	−317.278	+	230.516i	−0.388345	+	0.282149i
$818$	77.3313	+	56.1845i	0.0945370	+	0.0686851i
$819$	9.65558	+	29.7168i	0.0117895	+	0.0362843i
$820$	−27.1997	+	8.83772i	−0.0331704	+	0.0107777i
$821$	−171.147	+	235.563i	−0.208461	+	0.286922i	−0.900426	−	0.435009i	$-0.856745\pi$
$821$	−171.147	+	235.563i	−0.208461	+	0.286922i	0.691965	+	0.721931i	$0.256745\pi$
$822$	−384.476	−	529.185i	−0.467732	−	0.643778i
$823$	332.188	−	1022.37i	0.403631	−	1.24225i	−0.518402	−	0.855137i	$-0.673473\pi$
$823$	332.188	−	1022.37i	0.403631	−	1.24225i	0.922033	−	0.387112i	$-0.126527\pi$
$824$			147.748i			0.179306i
$825$		0			0
$826$	86.4296			0.104636
$827$	434.437	+	141.157i	0.525317	+	0.170686i	0.559657	−	0.828724i	$-0.310933\pi$
$827$	434.437	+	141.157i	0.525317	+	0.170686i	−0.0343400	+	0.999410i	$0.510933\pi$
$828$	−131.026	+	95.1962i	−0.158244	+	0.114971i
$829$	−1.78019	−	1.29339i	−0.00214740	−	0.00156018i	0.586711	−	0.809796i	$-0.300422\pi$
$829$	−1.78019	−	1.29339i	−0.00214740	−	0.00156018i	−0.588858	+	0.808236i	$0.700422\pi$
$830$	−215.718	−	663.913i	−0.259902	−	0.799895i
$831$	1338.80	−	435.004i	1.61108	−	0.523470i
$832$	496.246	−	683.024i	0.596450	−	0.820943i
$833$	700.466	+	964.108i	0.840895	+	1.15739i
$834$	−553.951	+	1704.89i	−0.664210	+	2.04423i
$835$			1155.96i			1.38438i
$836$		0			0
$837$	−588.423			−0.703015
$838$	−717.584	−	233.157i	−0.856305	−	0.278231i
$839$	−1175.03	+	853.709i	−1.40051	+	1.01753i	−0.405895	+	0.913920i	$0.633040\pi$
$839$	−1175.03	+	853.709i	−1.40051	+	1.01753i	−0.994618	+	0.103612i	$0.966960\pi$
$840$	47.6393	+	34.6120i	0.0567135	+	0.0412048i
$841$	256.181	+	788.445i	0.304615	+	0.937509i
$842$	226.584	−	73.6215i	0.269102	−	0.0874364i
$843$	−214.861	+	295.730i	−0.254876	+	0.350807i
$844$	1072.73	+	1476.49i	1.27101	+	1.74940i
$845$	119.453	−	367.638i	0.141364	−	0.435074i
$846$			286.558i			0.338721i
$847$		0			0
$848$	623.951			0.735792
$849$	7.29490	+	2.37026i	0.00859235	+	0.00279182i
$850$	554.120	−	402.592i	0.651906	−	0.473637i
$851$	235.623	+	171.190i	0.276878	+	0.201164i
$852$	381.264	+	1173.41i	0.447493	+	1.37724i
$853$	−1007.64	+	327.403i	−1.18129	+	0.383825i	−0.832846	−	0.553504i	$-0.813290\pi$
$853$	−1007.64	+	327.403i	−1.18129	+	0.383825i	−0.348445	+	0.937329i	$0.613290\pi$
$854$	−45.6231	+	62.7948i	−0.0534228	+	0.0735302i
$855$	114.069	+	157.002i	0.133414	+	0.183628i
$856$	7.56578	−	23.2851i	0.00883853	−	0.0272022i
$857$		−	951.067i		−	1.10976i	−0.831929	−	0.554882i	$-0.812763\pi$
$857$		−	951.067i		−	1.10976i	0.831929	−	0.554882i	$-0.187237\pi$
$858$		0			0
$859$	1146.23			1.33438			0.667188	−	0.744890i	$-0.267498\pi$
$859$	1146.23			1.33438			0.667188	+	0.744890i	$0.267498\pi$
$860$	−688.269	−	223.632i	−0.800313	−	0.260038i
$861$	3.43459	−	2.49537i	0.00398907	−	0.00289823i
$862$	−1119.14	−	813.104i	−1.29831	−	0.943276i
$863$	292.111	+	899.027i	0.338484	+	1.04175i	0.964980	+	0.262322i	$0.0844882\pi$
$863$	292.111	+	899.027i	0.338484	+	1.04175i	−0.626497	+	0.779424i	$0.715512\pi$
$864$	−719.250	+	233.699i	−0.832465	+	0.270484i
$865$	−430.748	+	592.873i	−0.497974	+	0.685403i
$866$	−261.147	−	359.439i	−0.301556	−	0.415056i
$867$	−360.508	+	1109.53i	−0.415810	+	1.27973i
$868$			162.784i			0.187539i
$869$		0			0
$870$	154.164			0.177200
$871$	−618.951	−	201.109i	−0.710621	−	0.230895i
$872$	502.177	−	364.853i	0.575891	−	0.418410i
$873$	−239.600	−	174.080i	−0.274456	−	0.199404i
$874$	−81.6312	−	251.235i	−0.0933995	−	0.287454i
$875$	−116.158	+	37.7420i	−0.132752	+	0.0431337i
$876$	−1095.55	+	1507.89i	−1.25063	+	1.72134i
$877$	93.2806	+	128.390i	0.106363	+	0.146396i	0.858880	−	0.512176i	$-0.171161\pi$
$877$	93.2806	+	128.390i	0.106363	+	0.146396i	−0.752517	+	0.658573i	$0.771161\pi$
$878$	147.800	−	454.883i	0.168337	−	0.518089i
$879$		−	1700.87i		−	1.93501i
$880$		0			0
$881$	402.370			0.456719			0.228360	−	0.973577i	$-0.426664\pi$
$881$	402.370			0.456719			0.228360	+	0.973577i	$0.426664\pi$
$882$	576.979	+	187.472i	0.654171	+	0.212553i
$883$	−640.141	+	465.089i	−0.724961	+	0.526715i	−0.887965	−	0.459910i	$-0.847882\pi$
$883$	−640.141	+	465.089i	−0.724961	+	0.526715i	0.163004	+	0.986625i	$0.447882\pi$
$884$	931.205	+	676.560i	1.05340	+	0.765340i
$885$	139.846	+	430.402i	0.158018	+	0.486330i
$886$	−949.263	+	308.434i	−1.07140	+	0.348120i
$887$	497.925	−	685.335i	0.561358	−	0.772644i	−0.430140	−	0.902762i	$-0.641536\pi$
$887$	497.925	−	685.335i	0.561358	−	0.772644i	0.991498	+	0.130119i	$0.0415358\pi$
$888$	387.812	+	533.777i	0.436725	+	0.601100i
$889$	23.1533	−	71.2585i	0.0260442	−	0.0801558i
$890$		−	766.920i		−	0.861707i
$891$		0			0
$892$	−623.680			−0.699192
$893$	−256.803	−	83.4405i	−0.287574	−	0.0934384i
$894$	−2315.85	+	1682.56i	−2.59043	+	1.88206i
$895$	−6.63621	−	4.82149i	−0.00741476	−	0.00538714i
$896$	37.5104	+	115.445i	0.0418643	+	0.128845i
$897$	211.803	−	68.8191i	0.236124	−	0.0767214i
$898$	−708.053	+	974.551i	−0.788478	+	1.08525i
$899$	67.3901	+	92.7545i	0.0749612	+	0.103175i
$900$	62.2477	−	191.579i	0.0691641	−	0.212865i
$901$			1942.12i			2.15552i
$902$		0			0
$903$	107.426			0.118966
$904$	200.398	+	65.1131i	0.221679	+	0.0720278i
$905$	235.915	−	171.402i	0.260679	−	0.189395i
$906$	2596.19	+	1886.24i	2.86555	+	2.08195i
$907$	131.861	+	405.826i	0.145381	+	0.447438i	0.997060	−	0.0766268i	$-0.0244150\pi$
$907$	131.861	+	405.826i	0.145381	+	0.447438i	−0.851678	+	0.524065i	$0.824415\pi$
$908$	−203.048	+	65.9744i	−0.223621	+	0.0726590i
$909$	154.776	−	213.031i	0.170271	−	0.234357i
$910$	−55.2786	−	76.0845i	−0.0607458	−	0.0836094i
$911$	43.2968	−	133.254i	0.0475267	−	0.146272i	−0.924477	−	0.381238i	$-0.875498\pi$
$911$	43.2968	−	133.254i	0.0475267	−	0.146272i	0.972004	+	0.234966i	$0.0754978\pi$
$912$			340.937i			0.373834i
$913$		0			0
$914$	160.795			0.175925
$915$	−386.525	−	125.590i	−0.422431	−	0.137256i
$916$	594.140	−	431.668i	0.648624	−	0.471253i
$917$	−61.8216	−	44.9160i	−0.0674172	−	0.0489815i
$918$	−417.758	−	1285.73i	−0.455074	−	1.40058i
$919$	−988.820	+	321.287i	−1.07597	+	0.349605i	−0.792811	−	0.609467i	$-0.791383\pi$
$919$	−988.820	+	321.287i	−1.07597	+	0.349605i	−0.283162	+	0.959072i	$0.591383\pi$
$920$	77.0820	−	106.094i	0.0837848	−	0.115320i
$921$	−211.426	−	291.003i	−0.229561	−	0.315964i
$922$	322.687	−	993.128i	0.349986	−	1.07715i
$923$		−	530.109i		−	0.574333i
$924$		0			0
$925$	−362.243			−0.391614
$926$	1981.23	+	643.741i	2.13956	+	0.695184i
$927$	107.907	−	78.3988i	0.116404	−	0.0845726i
$928$	119.212	+	86.6124i	0.128461	+	0.0933323i
$929$	507.998	+	1563.46i	0.546823	+	1.68295i	0.716617	+	0.697467i	$0.245690\pi$
$929$	507.998	+	1563.46i	0.546823	+	1.68295i	−0.169794	+	0.985480i	$0.554310\pi$
$930$	−1403.18	+	455.921i	−1.50880	+	0.490238i
$931$	−336.012	+	462.480i	−0.360915	+	0.496756i
$932$	−859.884	−	1183.53i	−0.922623	−	1.26988i
$933$	379.252	−	1167.22i	0.406487	−	1.25104i
$934$			1135.31i			1.21554i
$935$		0			0
$936$	157.639			0.168418
$937$	690.020	+	224.201i	0.736414	+	0.239275i	0.653125	−	0.757250i	$-0.273458\pi$
$937$	690.020	+	224.201i	0.736414	+	0.239275i	0.0832887	+	0.996525i	$0.473458\pi$
$938$	171.074	−	124.292i	0.182382	−	0.132508i
$939$	−1130.98	−	821.705i	−1.20445	−	0.875085i
$940$	−153.974	−	473.882i	−0.163802	−	0.504130i
$941$	174.425	−	56.6740i	0.185361	−	0.0602274i	−0.214866	−	0.976644i	$-0.568931\pi$
$941$	174.425	−	56.6740i	0.185361	−	0.0602274i	0.400227	+	0.916416i	$0.368931\pi$
$942$	1810.50	−	2491.94i	1.92198	−	2.64537i
$943$	−5.55728	−	7.64894i	−0.00589319	−	0.00811128i
$944$	−76.7664	+	236.263i	−0.0813204	+	0.250278i
$945$			63.8120i			0.0675259i
$946$		0			0
$947$	−926.439			−0.978288			−0.489144	−	0.872203i	$-0.662691\pi$
$947$	−926.439			−0.978288			−0.489144	+	0.872203i	$0.662691\pi$
$948$	1241.10	+	403.258i	1.30918	+	0.425377i
$949$	647.877	−	470.710i	0.682695	−	0.496007i
$950$	265.810	+	193.122i	0.279800	+	0.203287i
$951$	−282.943	−	870.809i	−0.297522	−	0.915677i
$952$	−95.6888	+	31.0912i	−0.100513	+	0.0326588i
$953$	146.849	−	202.120i	0.154091	−	0.212088i	−0.724991	−	0.688758i	$-0.758156\pi$
$953$	146.849	−	202.120i	0.154091	−	0.212088i	0.879082	+	0.476670i	$0.158156\pi$
$954$	581.140	+	799.870i	0.609161	+	0.838438i
$955$	−128.308	+	394.892i	−0.134354	+	0.413499i
$956$			602.709i			0.630449i
$957$		0			0
$958$	1463.24			1.52739
$959$	−50.1722	−	16.3019i	−0.0523172	−	0.0169989i
$960$	−1162.03	+	844.264i	−1.21045	+	0.879442i
$961$	−110.220	−	80.0798i	−0.114693	−	0.0833297i
$962$	−325.623	−	1002.16i	−0.338486	−	1.04175i
$963$	−21.0207	+	6.83004i	−0.0218283	+	0.00709246i
$964$	614.673	−	846.025i	0.637628	−	0.877619i
$965$	−808.827	−	1113.25i	−0.838162	−	1.15363i
$966$	−22.3607	+	68.8191i	−0.0231477	+	0.0712413i
$967$			554.026i			0.572933i	0.958090	+	0.286466i	$0.0924806\pi$
$967$			554.026i			0.572933i	−0.958090	+	0.286466i	$0.907519\pi$
$968$		0			0
$969$	−1061.21			−1.09516
$970$	847.771	+	275.457i	0.873991	+	0.283977i
$971$	923.209	−	670.750i	0.950781	−	0.690783i	−0.000210287	−	1.00000i	$-0.500067\pi$
$971$	923.209	−	670.750i	0.950781	−	0.690783i	0.950992	+	0.309217i	$0.100067\pi$
$972$	−911.277	−	662.081i	−0.937528	−	0.681154i
$973$	44.6764	+	137.500i	0.0459162	+	0.141315i
$974$	524.402	−	170.389i	0.538400	−	0.174937i
$975$	−162.812	+	224.091i	−0.166986	+	0.229837i
$976$	−131.133	−	180.489i	−0.134357	−	0.184927i
$977$	39.7690	−	122.396i	0.0407052	−	0.125278i	−0.928639	−	0.370985i	$-0.879020\pi$
$977$	39.7690	−	122.396i	0.0407052	−	0.125278i	0.969344	+	0.245707i	$0.0790202\pi$
$978$		−	772.398i		−	0.789773i
$979$		0			0
$980$	−1054.89			−1.07641
$981$	−532.936	−	173.161i	−0.543258	−	0.176515i
$982$	1600.40	−	1162.76i	1.62973	−	1.18407i
$983$	1079.93	+	784.615i	1.09861	+	0.798184i	0.980832	−	0.194856i	$-0.0624240\pi$
$983$	1079.93	+	784.615i	1.09861	+	0.798184i	0.117774	+	0.993040i	$0.462424\pi$
$984$	−6.61863	−	20.3700i	−0.00672625	−	0.0207013i
$985$	376.892	−	122.460i	0.382631	−	0.124324i
$986$	−154.828	+	213.102i	−0.157026	+	0.216128i
$987$	43.4752	+	59.8385i	0.0440479	+	0.0606267i
$988$	−170.623	+	525.124i	−0.172695	+	0.531502i
$989$		−	239.242i		−	0.241903i
$990$		0			0
$991$	762.024			0.768944			0.384472	−	0.923137i	$-0.374383\pi$
$991$	762.024			0.768944			0.384472	+	0.923137i	$0.374383\pi$
$992$	−1341.19	−	435.780i	−1.35201	−	0.439295i
$993$	−1089.20	+	791.353i	−1.09688	+	0.796931i
$994$	139.348	+	101.242i	0.140189	+	0.101853i
$995$	−189.698	−	583.831i	−0.190651	−	0.586765i
$996$	1067.72	−	346.922i	1.07201	−	0.348316i
$997$	708.614	−	975.323i	0.710746	−	0.978258i	−0.289035	−	0.957319i	$-0.593334\pi$
$997$	708.614	−	975.323i	0.710746	−	0.978258i	0.999781	−	0.0209393i	$-0.00666568\pi$
$998$	950.977	+	1308.91i	0.952882	+	1.31153i
$999$	−220.942	+	679.991i	−0.221164	+	0.680671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.3.d.c.112.1		4
11.2	odd	10		121.3.d.d.118.1		4
11.3	even	5		121.3.d.d.40.1		4
11.4	even	5		121.3.b.b.120.4		4
11.5	even	5		121.3.d.a.94.1		4
11.6	odd	10	inner	121.3.d.c.94.1		4
11.7	odd	10		121.3.b.b.120.1		4
11.8	odd	10		11.3.d.a.7.1	✓	4
11.9	even	5		11.3.d.a.8.1	yes	4
11.10	odd	2		121.3.d.a.112.1		4
33.8	even	10		99.3.k.a.73.1		4
33.20	odd	10		99.3.k.a.19.1		4
33.26	odd	10		1089.3.c.e.604.1		4
33.29	even	10		1089.3.c.e.604.4		4
44.19	even	10		176.3.n.a.161.1		4
44.31	odd	10		176.3.n.a.129.1		4
55.8	even	20		275.3.q.d.249.2		8
55.9	even	10		275.3.x.e.151.1		4
55.19	odd	10		275.3.x.e.51.1		4
55.42	odd	20		275.3.q.d.74.2		8
55.52	even	20		275.3.q.d.249.1		8
55.53	odd	20		275.3.q.d.74.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.3.d.a.7.1	✓	4	11.8	odd	10
11.3.d.a.8.1	yes	4	11.9	even	5
99.3.k.a.19.1		4	33.20	odd	10
99.3.k.a.73.1		4	33.8	even	10
121.3.b.b.120.1		4	11.7	odd	10
121.3.b.b.120.4		4	11.4	even	5
121.3.d.a.94.1		4	11.5	even	5
121.3.d.a.112.1		4	11.10	odd	2
121.3.d.c.94.1		4	11.6	odd	10	inner
121.3.d.c.112.1		4	1.1	even	1	trivial
121.3.d.d.40.1		4	11.3	even	5
121.3.d.d.118.1		4	11.2	odd	10
176.3.n.a.129.1		4	44.31	odd	10
176.3.n.a.161.1		4	44.19	even	10
275.3.q.d.74.1		8	55.53	odd	20
275.3.q.d.74.2		8	55.42	odd	20
275.3.q.d.249.1		8	55.52	even	20
275.3.q.d.249.2		8	55.8	even	20
275.3.x.e.51.1		4	55.19	odd	10
275.3.x.e.151.1		4	55.9	even	10
1089.3.c.e.604.1		4	33.26	odd	10
1089.3.c.e.604.4		4	33.29	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	121.d (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.92705 + 0.951057i) q^{2} +(-2.92705 + 2.12663i) q^{3} +(4.42705 + 3.21644i) q^{4} +(1.23607 + 3.80423i) q^{5} +(-10.5902 + 3.44095i) q^{6} +(-0.527864 + 0.726543i) q^{7} +(2.66312 + 3.66547i) q^{8} +(1.26393 - 3.88998i) q^{9} +O(q^{10})\)	\(q+(2.92705 + 0.951057i) q^{2} +(-2.92705 + 2.12663i) q^{3} +(4.42705 + 3.21644i) q^{4} +(1.23607 + 3.80423i) q^{5} +(-10.5902 + 3.44095i) q^{6} +(-0.527864 + 0.726543i) q^{7} +(2.66312 + 3.66547i) q^{8} +(1.26393 - 3.88998i) q^{9} +12.3107i q^{10} -19.7984 q^{12} +(8.09017 + 2.62866i) q^{13} +(-2.23607 + 1.62460i) q^{14} +(-11.7082 - 8.50651i) q^{15} +(-2.45492 - 7.55545i) q^{16} +(23.5172 - 7.64121i) q^{17} +(7.39919 - 10.1841i) q^{18} +(6.97214 + 9.59632i) q^{19} +(-6.76393 + 20.8172i) q^{20} -3.24920i q^{21} -7.23607 q^{23} +(-15.5902 - 5.06555i) q^{24} +(7.28115 - 5.29007i) q^{25} +(21.1803 + 15.3884i) q^{26} +(-5.48936 - 16.8945i) q^{27} +(-4.67376 + 1.51860i) q^{28} +(-2.03444 + 2.80017i) q^{29} +(-26.1803 - 36.0341i) q^{30} +(10.2361 - 31.5034i) q^{31} -42.5730i q^{32} +76.1033 q^{34} +(-3.41641 - 1.11006i) q^{35} +(18.1074 - 13.1558i) q^{36} +(-32.5623 - 23.6579i) q^{37} +(11.2812 + 34.7198i) q^{38} +(-29.2705 + 9.51057i) q^{39} +(-10.6525 + 14.6619i) q^{40} +(0.767997 + 1.05706i) q^{41} +(3.09017 - 9.51057i) q^{42} +33.0625i q^{43} +16.3607 q^{45} +(-21.1803 - 6.88191i) q^{46} +(-18.4164 + 13.3803i) q^{47} +(23.2533 + 16.8945i) q^{48} +(14.8926 + 45.8347i) q^{49} +(26.3435 - 8.55951i) q^{50} +(-52.5861 + 72.3786i) q^{51} +(27.3607 + 37.6587i) q^{52} +(-24.2705 + 74.6969i) q^{53} -54.6718i q^{54} -4.06888 q^{56} +(-40.8156 - 13.2618i) q^{57} +(-8.61803 + 6.26137i) q^{58} +(-25.2984 - 18.3803i) q^{59} +(-24.4721 - 75.3175i) q^{60} +(26.7082 - 8.67802i) q^{61} +(59.9230 - 82.4769i) q^{62} +(2.15905 + 2.97168i) q^{63} +(30.6697 - 94.3916i) q^{64} +34.0260i q^{65} -76.5066 q^{67} +(128.689 + 41.8137i) q^{68} +(21.1803 - 15.3884i) q^{69} +(-8.94427 - 6.49839i) q^{70} +(-19.2574 - 59.2680i) q^{71} +(17.6246 - 5.72658i) q^{72} +(55.3353 - 76.1625i) q^{73} +(-72.8115 - 100.216i) q^{74} +(-10.0623 + 30.9686i) q^{75} +64.9089i q^{76} -94.7214 q^{78} +(-62.6869 - 20.3682i) q^{79} +(25.7082 - 18.6781i) q^{80} +(81.7771 + 59.4145i) q^{81} +(1.24265 + 3.82447i) q^{82} +(-53.9296 + 17.5228i) q^{83} +(10.4508 - 14.3844i) q^{84} +(58.1378 + 80.0198i) q^{85} +(-31.4443 + 96.7755i) q^{86} -12.5227i q^{87} -62.2968 q^{89} +(47.8885 + 15.5599i) q^{90} +(-6.18034 + 4.49028i) q^{91} +(-32.0344 - 23.2744i) q^{92} +(37.0344 + 113.980i) q^{93} +(-66.6312 + 21.6498i) q^{94} +(-27.8885 + 38.3853i) q^{95} +(90.5370 + 124.613i) q^{96} +(22.3754 - 68.8644i) q^{97} +148.324i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} - 5 q^{3} + 11 q^{4} - 4 q^{5} - 20 q^{6} - 20 q^{7} - 5 q^{8} + 14 q^{9}+O(q^{10}) \) 4 * q + 5 * q^2 - 5 * q^3 + 11 * q^4 - 4 * q^5 - 20 * q^6 - 20 * q^7 - 5 * q^8 + 14 * q^9	\( 4 q + 5 q^{2} - 5 q^{3} + 11 q^{4} - 4 q^{5} - 20 q^{6} - 20 q^{7} - 5 q^{8} + 14 q^{9} - 30 q^{12} + 10 q^{13} - 20 q^{15} - 21 q^{16} + 65 q^{17} + 5 q^{18} + 10 q^{19} - 36 q^{20} - 20 q^{23} - 40 q^{24} + 9 q^{25} + 40 q^{26} + 25 q^{27} - 50 q^{28} + 50 q^{29} - 60 q^{30} + 32 q^{31} + 130 q^{34} + 40 q^{35} + 21 q^{36} - 90 q^{37} + 25 q^{38} - 50 q^{39} + 20 q^{40} + 135 q^{41} - 10 q^{42} - 24 q^{45} - 40 q^{46} - 20 q^{47} + 55 q^{48} + 111 q^{49} + 45 q^{50} - 65 q^{51} + 20 q^{52} - 30 q^{53} + 100 q^{56} - 85 q^{57} - 30 q^{58} - 52 q^{59} - 80 q^{60} + 80 q^{61} + 110 q^{62} - 130 q^{63} + 31 q^{64} - 230 q^{67} + 195 q^{68} + 40 q^{69} - 162 q^{71} - 10 q^{72} - 85 q^{73} - 90 q^{74} - 200 q^{78} - 130 q^{79} + 76 q^{80} + 184 q^{81} - 80 q^{82} - 10 q^{83} - 70 q^{84} - 90 q^{86} + 122 q^{89} + 120 q^{90} + 20 q^{91} - 70 q^{92} + 90 q^{93} - 110 q^{94} - 40 q^{95} + 105 q^{96} + 170 q^{97}+O(q^{100}) \) 4 * q + 5 * q^2 - 5 * q^3 + 11 * q^4 - 4 * q^5 - 20 * q^6 - 20 * q^7 - 5 * q^8 + 14 * q^9 - 30 * q^12 + 10 * q^13 - 20 * q^15 - 21 * q^16 + 65 * q^17 + 5 * q^18 + 10 * q^19 - 36 * q^20 - 20 * q^23 - 40 * q^24 + 9 * q^25 + 40 * q^26 + 25 * q^27 - 50 * q^28 + 50 * q^29 - 60 * q^30 + 32 * q^31 + 130 * q^34 + 40 * q^35 + 21 * q^36 - 90 * q^37 + 25 * q^38 - 50 * q^39 + 20 * q^40 + 135 * q^41 - 10 * q^42 - 24 * q^45 - 40 * q^46 - 20 * q^47 + 55 * q^48 + 111 * q^49 + 45 * q^50 - 65 * q^51 + 20 * q^52 - 30 * q^53 + 100 * q^56 - 85 * q^57 - 30 * q^58 - 52 * q^59 - 80 * q^60 + 80 * q^61 + 110 * q^62 - 130 * q^63 + 31 * q^64 - 230 * q^67 + 195 * q^68 + 40 * q^69 - 162 * q^71 - 10 * q^72 - 85 * q^73 - 90 * q^74 - 200 * q^78 - 130 * q^79 + 76 * q^80 + 184 * q^81 - 80 * q^82 - 10 * q^83 - 70 * q^84 - 90 * q^86 + 122 * q^89 + 120 * q^90 + 20 * q^91 - 70 * q^92 + 90 * q^93 - 110 * q^94 - 40 * q^95 + 105 * q^96 + 170 * q^97

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