LMFDB - Embedded newform 112.3.u.a.107.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [112,3,Mod(11,112)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("112.11"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(112, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	112.u (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.05177896084$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$30$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.20
Character	$\chi$	$=$	112.107
Dual form			112.3.u.a.67.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.841863 - 1.81419i) q^{2} +(-1.31900 + 4.92258i) q^{3} +(-2.58253 - 3.05459i) q^{4} +(-5.65734 + 1.51588i) q^{5} +(7.82005 + 6.53704i) q^{6} +(-5.37161 - 4.48841i) q^{7} +(-7.71573 + 2.11365i) q^{8} +(-14.6978 - 8.48576i) q^{9} +(-2.01262 + 11.5396i) q^{10} +(7.21466 + 1.93316i) q^{11} +(18.4428 - 8.68372i) q^{12} +(-13.5968 + 13.5968i) q^{13} +(-12.6650 + 5.96648i) q^{14} -29.8481i q^{15} +(-2.66103 + 15.7772i) q^{16} +(4.74908 + 8.22565i) q^{17} +(-27.7682 + 19.5206i) q^{18} +(21.8193 - 5.84646i) q^{19} +(19.2407 + 13.3660i) q^{20} +(29.1797 - 20.5220i) q^{21} +(9.58086 - 11.4613i) q^{22} +(-0.520600 + 0.901705i) q^{23} +(-0.227560 - 40.7692i) q^{24} +(8.05699 - 4.65170i) q^{25} +(13.2205 + 36.1137i) q^{26} +(28.7259 - 28.7259i) q^{27} +(0.162135 + 27.9995i) q^{28} +(-7.57831 + 7.57831i) q^{29} +(-54.1500 - 25.1280i) q^{30} +(-23.0044 + 13.2816i) q^{31} +(26.3825 + 18.1098i) q^{32} +(-19.0323 + 32.9649i) q^{33} +(18.9209 - 1.69084i) q^{34} +(37.1929 + 17.2497i) q^{35} +(12.0370 + 66.8104i) q^{36} +(-50.2858 + 13.4740i) q^{37} +(7.76228 - 44.5061i) q^{38} +(-48.9971 - 84.8654i) q^{39} +(40.4465 - 23.6538i) q^{40} -53.5245i q^{41} +(-12.6653 - 70.2140i) q^{42} +(13.7966 - 13.7966i) q^{43} +(-12.7271 - 27.0303i) q^{44} +(96.0136 + 25.7268i) q^{45} +(1.19759 + 1.70358i) q^{46} +(-33.2522 - 19.1982i) q^{47} +(-74.1544 - 33.9092i) q^{48} +(8.70842 + 48.2199i) q^{49} +(-1.65617 - 18.5330i) q^{50} +(-46.7554 + 12.5281i) q^{51} +(76.6468 + 6.41843i) q^{52} +(10.4867 - 39.1369i) q^{53} +(-27.9309 - 76.2975i) q^{54} -43.7462 q^{55} +(50.9328 + 23.2776i) q^{56} +115.118i q^{57} +(7.36856 + 20.1283i) q^{58} +(-79.1744 - 21.2147i) q^{59} +(-91.1738 + 77.0839i) q^{60} +(21.2183 + 79.1878i) q^{61} +(4.72873 + 52.9155i) q^{62} +(40.8631 + 111.552i) q^{63} +(55.0650 - 32.6167i) q^{64} +(56.3106 - 97.5328i) q^{65} +(43.7818 + 62.2799i) q^{66} +(-11.8774 + 44.3272i) q^{67} +(12.8613 - 35.7495i) q^{68} +(-3.75204 - 3.75204i) q^{69} +(62.6055 - 52.9529i) q^{70} +118.698 q^{71} +(131.340 + 34.4079i) q^{72} +(-105.794 + 61.0800i) q^{73} +(-17.8893 + 102.571i) q^{74} +(12.2712 + 45.7967i) q^{75} +(-74.2075 - 51.5502i) q^{76} +(-30.0775 - 42.7665i) q^{77} +(-195.210 + 17.4447i) q^{78} +(85.0760 + 49.1187i) q^{79} +(-8.86194 - 93.2906i) q^{80} +(27.1443 + 47.0153i) q^{81} +(-97.1033 - 45.0602i) q^{82} +(32.2600 + 32.2600i) q^{83} +(-138.044 - 36.1333i) q^{84} +(-39.3363 - 39.3363i) q^{85} +(-13.4147 - 36.6444i) q^{86} +(-27.3090 - 47.3006i) q^{87} +(-59.7524 + 0.333518i) q^{88} +(77.3095 + 44.6346i) q^{89} +(127.503 - 152.528i) q^{90} +(134.065 - 12.0088i) q^{91} +(4.09880 - 0.738466i) q^{92} +(-35.0369 - 130.759i) q^{93} +(-62.8228 + 44.1634i) q^{94} +(-114.577 + 66.1508i) q^{95} +(-123.945 + 105.983i) q^{96} -108.995 q^{97} +(94.8112 + 24.7959i) q^{98} +(-89.6350 - 89.6350i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{7} - 20 q^{8} + 16 q^{10} + 14 q^{11} - 2 q^{12} - 8 q^{13} + 20 q^{14} + 8 q^{16} - 4 q^{17} - 38 q^{18} - 2 q^{19} + 72 q^{20} + 14 q^{21}+ \cdots - 776 q^{99}+O(q^{100}) $ 120 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^7 - 20 * q^8 + 16 * q^10 + 14 * q^11 - 2 * q^12 - 8 * q^13 + 20 * q^14 + 8 * q^16 - 4 * q^17 - 38 * q^18 - 2 * q^19 + 72 * q^20 + 14 * q^21 + 52 * q^22 - 68 * q^23 - 142 * q^24 - 2 * q^26 - 44 * q^27 - 62 * q^28 - 40 * q^29 - 14 * q^30 + 88 * q^32 - 4 * q^33 + 168 * q^34 + 94 * q^35 - 272 * q^36 - 50 * q^37 + 138 * q^38 - 4 * q^39 - 206 * q^40 - 198 * q^42 - 104 * q^43 + 2 * q^44 - 84 * q^45 - 76 * q^46 - 856 * q^48 - 8 * q^49 - 320 * q^50 + 114 * q^51 + 76 * q^52 - 82 * q^53 + 350 * q^54 - 16 * q^55 + 8 * q^56 - 6 * q^58 + 62 * q^59 + 318 * q^60 - 2 * q^61 + 876 * q^62 + 112 * q^64 - 4 * q^65 + 162 * q^66 - 66 * q^67 + 192 * q^68 + 28 * q^69 + 112 * q^70 + 496 * q^71 + 248 * q^72 + 178 * q^74 + 12 * q^75 - 308 * q^76 + 94 * q^77 - 140 * q^78 + 204 * q^80 + 248 * q^81 + 266 * q^82 - 488 * q^83 + 620 * q^84 + 92 * q^85 - 408 * q^86 - 4 * q^87 - 370 * q^88 - 404 * q^90 - 488 * q^91 + 900 * q^92 - 38 * q^93 - 150 * q^94 + 768 * q^96 - 16 * q^97 + 432 * q^98 - 776 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.841863	−	1.81419i	0.420931	−	0.907093i
$2$	0.841863	−	1.81419i	0.420931	−	0.907093i
$3$	−1.31900	+	4.92258i	−0.439667	+	1.64086i	0.289979	+	0.957033i	$0.406352\pi$
$3$	−1.31900	+	4.92258i	−0.439667	+	1.64086i	−0.729646	+	0.683825i	$0.760315\pi$
$4$	−2.58253	−	3.05459i	−0.645634	−	0.763647i
$5$	−5.65734	+	1.51588i	−1.13147	+	0.303176i	−0.775516	−	0.631328i	$-0.782510\pi$
$5$	−5.65734	+	1.51588i	−1.13147	+	0.303176i	−0.355952	+	0.934504i	$0.615843\pi$
$6$	7.82005	+	6.53704i	1.30334	+	1.08951i
$7$	−5.37161	−	4.48841i	−0.767373	−	0.641201i
$7$	−5.37161	−	4.48841i	−0.767373	−	0.641201i
$8$	−7.71573	+	2.11365i	−0.964466	+	0.264206i
$9$	−14.6978	−	8.48576i	−1.63308	−	0.942862i
$10$	−2.01262	+	11.5396i	−0.201262	+	1.15396i
$11$	7.21466	+	1.93316i	0.655878	+	0.175742i	0.571385	−	0.820682i	$-0.306406\pi$
$11$	7.21466	+	1.93316i	0.655878	+	0.175742i	0.0844929	+	0.996424i	$0.473073\pi$
$12$	18.4428	−	8.68372i	1.53690	−	0.723643i
$13$	−13.5968	+	13.5968i	−1.04591	+	1.04591i	−0.0470131	+	0.998894i	$0.514970\pi$
$13$	−13.5968	+	13.5968i	−1.04591	+	1.04591i	−0.998894	+	0.0470131i	$0.985030\pi$
$14$	−12.6650	+	5.96648i	−0.904640	+	0.426177i
$15$		−	29.8481i		−	1.98988i
$16$	−2.66103	+	15.7772i	−0.166314	+	0.986073i
$17$	4.74908	+	8.22565i	0.279358	+	0.483862i	0.971225	−	0.238163i	$-0.0765452\pi$
$17$	4.74908	+	8.22565i	0.279358	+	0.483862i	−0.691868	+	0.722024i	$0.743212\pi$
$18$	−27.7682	+	19.5206i	−1.54268	+	1.08448i
$19$	21.8193	−	5.84646i	1.14838	−	0.307708i	0.366066	−	0.930589i	$-0.380704\pi$
$19$	21.8193	−	5.84646i	1.14838	−	0.307708i	0.782317	+	0.622881i	$0.214038\pi$
$20$	19.2407	+	13.3660i	0.962034	+	0.668302i
$21$	29.1797	−	20.5220i	1.38951	−	0.977236i
$22$	9.58086	−	11.4613i	0.435494	−	0.520967i
$23$	−0.520600	+	0.901705i	−0.0226348	+	0.0392046i	−0.877121	−	0.480270i	$-0.840539\pi$
$23$	−0.520600	+	0.901705i	−0.0226348	+	0.0392046i	0.854486	+	0.519474i	$0.173872\pi$
$24$	−0.227560	−	40.7692i	−0.00948166	−	1.69872i
$25$	8.05699	−	4.65170i	0.322280	−	0.186068i
$26$	13.2205	+	36.1137i	0.508480	+	1.38899i
$27$	28.7259	−	28.7259i	1.06392	−	1.06392i
$28$	0.162135	+	27.9995i	0.00579053	+	0.999983i
$29$	−7.57831	+	7.57831i	−0.261321	+	0.261321i	−0.825591	−	0.564270i	$-0.809158\pi$
$29$	−7.57831	+	7.57831i	−0.261321	+	0.261321i	0.564270	+	0.825591i	$0.309158\pi$
$30$	−54.1500	−	25.1280i	−1.80500	−	0.837601i
$31$	−23.0044	+	13.2816i	−0.742077	+	0.428439i	−0.822824	−	0.568296i	$-0.807603\pi$
$31$	−23.0044	+	13.2816i	−0.742077	+	0.428439i	0.0807468	+	0.996735i	$0.474269\pi$
$32$	26.3825	+	18.1098i	0.824452	+	0.565931i
$33$	−19.0323	+	32.9649i	−0.576735	+	0.998935i
$34$	18.9209	−	1.69084i	0.556498	−	0.0497307i
$35$	37.1929	+	17.2497i	1.06266	+	0.492849i
$36$	12.0370	+	66.8104i	0.334360	+	1.85584i
$37$	−50.2858	+	13.4740i	−1.35908	+	0.364163i	−0.863477	−	0.504389i	$-0.831718\pi$
$37$	−50.2858	+	13.4740i	−1.35908	+	0.364163i	−0.495598	+	0.868552i	$0.665051\pi$
$38$	7.76228	−	44.5061i	0.204270	−	1.17121i
$39$	−48.9971	−	84.8654i	−1.25634	−	2.17604i
$40$	40.4465	−	23.6538i	1.01116	−	0.591344i
$41$		−	53.5245i		−	1.30547i	−0.757584	−	0.652737i	$-0.773621\pi$
$41$		−	53.5245i		−	1.30547i	0.757584	−	0.652737i	$-0.226379\pi$
$42$	−12.6653	−	70.2140i	−0.301556	−	1.67176i
$43$	13.7966	−	13.7966i	0.320851	−	0.320851i	−0.528242	−	0.849094i	$-0.677149\pi$
$43$	13.7966	−	13.7966i	0.320851	−	0.320851i	0.849094	+	0.528242i	$0.177149\pi$
$44$	−12.7271	−	27.0303i	−0.289252	−	0.614324i
$45$	96.0136	+	25.7268i	2.13364	+	0.571706i
$46$	1.19759	+	1.70358i	0.0260345	+	0.0370342i
$47$	−33.2522	−	19.1982i	−0.707494	−	0.408472i	0.102638	−	0.994719i	$-0.467272\pi$
$47$	−33.2522	−	19.1982i	−0.707494	−	0.408472i	−0.810132	+	0.586247i	$0.800605\pi$
$48$	−74.1544	−	33.9092i	−1.54488	−	0.706442i
$49$	8.70842	+	48.2199i	0.177723	+	0.984081i
$50$	−1.65617	−	18.5330i	−0.0331235	−	0.370659i
$51$	−46.7554	+	12.5281i	−0.916773	+	0.245649i
$52$	76.6468	+	6.41843i	1.47398	+	0.123431i
$53$	10.4867	−	39.1369i	0.197862	−	0.738432i	−0.793645	−	0.608381i	$-0.791819\pi$
$53$	10.4867	−	39.1369i	0.197862	−	0.738432i	0.991507	−	0.130051i	$-0.0415142\pi$
$54$	−27.9309	−	76.2975i	−0.517239	−	1.41292i
$55$	−43.7462			−0.795386
$56$	50.9328	+	23.2776i	0.909515	+	0.415672i
$57$			115.118i			2.01962i
$58$	7.36856	+	20.1283i	0.127044	+	0.347041i
$59$	−79.1744	−	21.2147i	−1.34194	−	0.359572i	−0.484786	−	0.874633i	$-0.661103\pi$
$59$	−79.1744	−	21.2147i	−1.34194	−	0.359572i	−0.857154	+	0.515061i	$0.827769\pi$
$60$	−91.1738	+	77.0839i	−1.51956	+	1.28473i
$61$	21.2183	+	79.1878i	0.347841	+	1.29816i	0.889258	+	0.457406i	$0.151221\pi$
$61$	21.2183	+	79.1878i	0.347841	+	1.29816i	−0.541417	+	0.840754i	$0.682112\pi$
$62$	4.72873	+	52.9155i	0.0762698	+	0.853476i
$63$	40.8631	+	111.552i	0.648621	+	1.77066i
$64$	55.0650	−	32.6167i	0.860390	−	0.509636i
$65$	56.3106	−	97.5328i	0.866317	−	1.50051i
$66$	43.7818	+	62.2799i	0.663361	+	0.943635i
$67$	−11.8774	+	44.3272i	−0.177275	+	0.661600i	0.818878	+	0.573968i	$0.194597\pi$
$67$	−11.8774	+	44.3272i	−0.177275	+	0.661600i	−0.996153	+	0.0876319i	$0.972070\pi$
$68$	12.8613	−	35.7495i	0.189137	−	0.525728i
$69$	−3.75204	−	3.75204i	−0.0543774	−	0.0543774i
$70$	62.6055	−	52.9529i	0.894365	−	0.756471i
$71$	118.698			1.67181			0.835905	−	0.548875i	$-0.184944\pi$
$71$	118.698			1.67181			0.835905	+	0.548875i	$0.184944\pi$
$72$	131.340	+	34.4079i	1.82416	+	0.477887i
$73$	−105.794	+	61.0800i	−1.44923	+	0.836713i	−0.998436	−	0.0559151i	$-0.982192\pi$
$73$	−105.794	+	61.0800i	−1.44923	+	0.836713i	−0.450794	+	0.892628i	$0.648859\pi$
$74$	−17.8893	+	102.571i	−0.241748	+	1.38609i
$75$	12.2712	+	45.7967i	0.163616	+	0.610623i
$76$	−74.2075	−	51.5502i	−0.976415	−	0.678293i
$77$	−30.0775	−	42.7665i	−0.390617	−	0.555409i
$78$	−195.210	+	17.4447i	−2.50270	+	0.223650i
$79$	85.0760	+	49.1187i	1.07691	+	0.621755i	0.930062	−	0.367404i	$-0.119753\pi$
$79$	85.0760	+	49.1187i	1.07691	+	0.621755i	0.146850	+	0.989159i	$0.453087\pi$
$80$	−8.86194	−	93.2906i	−0.110774	−	1.16613i
$81$	27.1443	+	47.0153i	0.335115	+	0.580436i
$82$	−97.1033	−	45.0602i	−1.18419	−	0.549515i
$83$	32.2600	+	32.2600i	0.388675	+	0.388675i	0.874215	−	0.485540i	$-0.161377\pi$
$83$	32.2600	+	32.2600i	0.388675	+	0.388675i	−0.485540	+	0.874215i	$0.661377\pi$
$84$	−138.044	−	36.1333i	−1.64338	−	0.430158i
$85$	−39.3363	−	39.3363i	−0.462780	−	0.462780i
$86$	−13.4147	−	36.6444i	−0.155985	−	0.426098i
$87$	−27.3090	−	47.3006i	−0.313897	−	0.543685i
$88$	−59.7524	+	0.333518i	−0.679004	+	0.00378997i
$89$	77.3095	+	44.6346i	0.868646	+	0.501513i	0.866898	−	0.498486i	$-0.166110\pi$
$89$	77.3095	+	44.6346i	0.868646	+	0.501513i	0.00174766	+	0.999998i	$0.499444\pi$
$90$	127.503	−	152.528i	1.41670	−	1.69476i
$91$	134.065	−	12.0088i	1.47324	−	0.131964i
$92$	4.09880	−	0.738466i	0.0445522	−	0.00802681i
$93$	−35.0369	−	130.759i	−0.376740	−	1.40601i
$94$	−62.8228	+	44.1634i	−0.668328	+	0.469824i
$95$	−114.577	+	66.1508i	−1.20607	+	0.696324i
$96$	−123.945	+	105.983i	−1.29110	+	1.10399i
$97$	−108.995			−1.12366			−0.561832	−	0.827251i	$-0.689903\pi$
$97$	−108.995			−1.12366			−0.561832	+	0.827251i	$0.689903\pi$
$98$	94.8112	+	24.7959i	0.967461	+	0.253019i
$99$	−89.6350	−	89.6350i	−0.905404	−	0.905404i
$100$	−35.0165	−	12.5976i	−0.350165	−	0.125976i
$101$	8.00902	−	29.8901i	0.0792973	−	0.295941i	−0.914876	−	0.403735i	$-0.867712\pi$
$101$	8.00902	−	29.8901i	0.0792973	−	0.295941i	0.994173	+	0.107793i	$0.0343785\pi$
$102$	−16.6334	+	95.3699i	−0.163072	+	0.934999i
$103$	20.8349	−	36.0871i	0.202281	−	0.350361i	−0.746982	−	0.664844i	$-0.768498\pi$
$103$	20.8349	−	36.0871i	0.202281	−	0.350361i	0.949263	+	0.314483i	$0.101831\pi$
$104$	76.1703	−	133.648i	0.732407	−	1.28508i
$105$	−133.971	+	160.333i	−1.27591	+	1.52698i
$106$	−62.1733	−	51.9727i	−0.586540	−	0.490309i
$107$	29.9168	+	111.651i	0.279596	+	1.04347i	0.952699	+	0.303917i	$0.0982945\pi$
$107$	29.9168	+	111.651i	0.279596	+	1.04347i	−0.673103	+	0.739549i	$0.735039\pi$
$108$	−161.932	−	13.5602i	−1.49937	−	0.125558i
$109$	−30.5360	−	8.18210i	−0.280147	−	0.0750651i	0.116010	−	0.993248i	$-0.462990\pi$
$109$	−30.5360	−	8.18210i	−0.280147	−	0.0750651i	−0.396157	+	0.918183i	$0.629656\pi$
$110$	−36.8283	+	79.3637i	−0.334803	+	0.721489i
$111$		−	265.308i		−	2.39016i
$112$	85.1083	−	72.8050i	0.759896	−	0.650045i
$113$	−85.4462			−0.756161			−0.378081	−	0.925773i	$-0.623416\pi$
$113$	−85.4462			−0.756161			−0.378081	+	0.925773i	$0.623416\pi$
$114$	208.846	+	96.9139i	1.83198	+	0.850122i
$115$	1.57833	−	5.89042i	0.0137246	−	0.0512210i
$116$	42.7199	+	3.57737i	0.368275	+	0.0308394i
$117$	315.222	−	84.4634i	2.69420	−	0.721909i
$118$	−105.141	+	125.777i	−0.891029	+	1.06591i
$119$	11.4098	−	65.5008i	0.0958810	−	0.550427i
$120$	63.0886	+	230.300i	0.525738	+	1.91917i
$121$	−56.4749	−	32.6058i	−0.466735	−	0.269469i
$122$	161.524	+	28.1713i	1.32397	+	0.230912i
$123$	263.478	+	70.5988i	2.14210	+	0.573974i
$124$	99.9795	+	35.9688i	0.806286	+	0.290071i
$125$	65.0068	−	65.0068i	0.520055	−	0.520055i
$126$	236.777	+	19.7779i	1.87918	+	0.156968i
$127$		−	3.40293i		−	0.0267947i	−0.999910	−	0.0133974i	$-0.995735\pi$
$127$		−	3.40293i		−	0.0267947i	0.999910	−	0.0133974i	$-0.00426464\pi$
$128$	−12.8156	−	127.357i	−0.100122	−	0.994975i
$129$	49.7171	+	86.1125i	0.385404	+	0.667539i
$130$	−129.537	−	184.267i	−0.996437	−	1.41744i
$131$	47.3910	−	12.6984i	0.361764	−	0.0969343i	−0.0733586	−	0.997306i	$-0.523372\pi$
$131$	47.3910	−	12.6984i	0.361764	−	0.0969343i	0.435122	+	0.900371i	$0.356705\pi$
$132$	149.846	−	26.9971i	1.13519	−	0.204524i
$133$	−143.446	−	66.5289i	−1.07854	−	0.500217i
$134$	70.4186	+	58.8653i	0.525512	+	0.439293i
$135$	−118.967	+	206.058i	−0.881240	+	1.52635i
$136$	−54.0288	−	53.4290i	−0.397270	−	0.392860i
$137$	2.58046	−	1.48983i	0.0188355	−	0.0108747i	−0.490553	−	0.871412i	$-0.663205\pi$
$137$	2.58046	−	1.48983i	0.0188355	−	0.0108747i	0.509388	+	0.860537i	$0.329872\pi$
$138$	−9.96560	+	3.64819i	−0.0722145	+	0.0264362i
$139$	−141.609	+	141.609i	−1.01877	+	1.01877i	−0.0189511	+	0.999820i	$0.506033\pi$
$139$	−141.609	+	141.609i	−1.01877	+	1.01877i	−0.999820	+	0.0189511i	$0.993967\pi$
$140$	−43.3612	−	158.157i	−0.309723	−	1.12969i
$141$	138.364	−	138.364i	0.981306	−	0.981306i
$142$	99.9278	−	215.341i	0.703717	−	1.51649i
$143$	−124.381	+	71.8114i	−0.869797	+	0.502178i
$144$	172.992	−	209.308i	1.20134	−	1.45353i
$145$	31.3853	−	54.3609i	0.216450	−	0.374903i
$146$	21.7467	+	243.350i	0.148950	+	1.66678i
$147$	−248.853	−	20.7343i	−1.69288	−	0.141050i
$148$	171.022	+	118.805i	1.15556	+	0.802738i
$149$	−175.104	+	46.9191i	−1.17520	+	0.314893i	−0.793020	−	0.609196i	$-0.791492\pi$
$149$	−175.104	+	46.9191i	−1.17520	+	0.314893i	−0.382178	+	0.924089i	$0.624826\pi$
$150$	93.4144	+	16.2923i	0.622763	+	0.108616i
$151$	22.5856	+	39.1194i	0.149574	+	0.259069i	0.931070	−	0.364841i	$-0.118877\pi$
$151$	22.5856	+	39.1194i	0.149574	+	0.259069i	−0.781496	+	0.623910i	$0.785543\pi$
$152$	−155.994	+	91.2280i	−1.02628	+	0.600184i
$153$		−	161.198i		−	1.05358i
$154$	−102.908	+	18.5627i	−0.668231	+	0.120537i
$155$	110.010	−	110.010i	0.709745	−	0.709745i
$156$	−132.692	+	368.834i	−0.850592	+	2.36432i
$157$	60.2447	+	16.1425i	0.383725	+	0.102819i	0.445524	−	0.895270i	$-0.353017\pi$
$157$	60.2447	+	16.1425i	0.383725	+	0.102819i	−0.0617997	+	0.998089i	$0.519684\pi$
$158$	160.733	−	112.992i	1.01730	−	0.715142i
$159$	178.822	+	103.243i	1.12467	+	0.649328i
$160$	−176.707	−	62.4607i	−1.10442	−	0.390379i
$161$	6.84368	−	2.50695i	0.0425073	−	0.0155711i
$162$	108.146	−	9.66436i	0.667570	−	0.0596565i
$163$	−28.2062	+	7.55783i	−0.173044	+	0.0463671i	−0.344301	−	0.938859i	$-0.611884\pi$
$163$	−28.2062	+	7.55783i	−0.173044	+	0.0463671i	0.171257	+	0.985226i	$0.445217\pi$
$164$	−163.495	+	138.229i	−0.996922	+	0.842858i
$165$	57.7013	−	215.344i	0.349705	−	1.30512i
$166$	85.6841	−	31.3671i	0.516169	−	0.188959i
$167$	137.063			0.820737			0.410368	−	0.911920i	$-0.365400\pi$
$167$	137.063			0.820737			0.410368	+	0.911920i	$0.365400\pi$
$168$	−181.766	+	220.018i	−1.08194	+	1.30963i
$169$		−	200.746i		−	1.18784i
$170$	−104.479	+	38.2475i	−0.614582	+	0.224985i
$171$	−370.306	−	99.2232i	−2.16553	−	0.580253i
$172$	−77.7731	−	6.51275i	−0.452169	−	0.0378648i
$173$	10.1842	+	38.0081i	0.0588685	+	0.219700i	0.989093	−	0.147290i	$-0.0470550\pi$
$173$	10.1842	+	38.0081i	0.0588685	+	0.219700i	−0.930225	+	0.366990i	$0.880388\pi$
$174$	−108.802	+	9.72300i	−0.625301	+	0.0558793i
$175$	−64.1577	−	11.1759i	−0.366616	−	0.0638622i
$176$	−49.6982	+	108.683i	−0.282376	+	0.617515i
$177$	208.862	−	361.760i	1.18001	−	2.04384i
$178$	146.059	−	102.677i	0.820559	−	0.576839i
$179$	8.73072	−	32.5835i	0.0487750	−	0.182031i	−0.937241	−	0.348683i	$-0.886629\pi$
$179$	8.73072	−	32.5835i	0.0487750	−	0.182031i	0.986016	+	0.166652i	$0.0532957\pi$
$180$	−169.374	−	359.723i	−0.940966	−	1.99846i
$181$	81.6173	+	81.6173i	0.450924	+	0.450924i	0.895661	−	0.444737i	$-0.146703\pi$
$181$	81.6173	+	81.6173i	0.450924	+	0.450924i	−0.444737	+	0.895661i	$0.646703\pi$
$182$	91.0779	−	253.328i	0.500428	−	1.39191i
$183$	−417.795			−2.28303
$184$	2.11092	−	8.05768i	0.0114724	−	0.0437917i
$185$	264.059	−	152.454i	1.42734	−	0.824078i
$186$	−266.718	−	46.5180i	−1.43397	−	0.250097i
$187$	18.3615	+	68.5260i	0.0981897	+	0.366449i
$188$	27.2325	+	151.152i	0.144854	+	0.803999i
$189$	−283.238	+	25.3709i	−1.49862	+	0.134238i
$190$	23.5521	+	263.553i	0.123958	+	1.38712i
$191$	30.6407	+	17.6904i	0.160423	+	0.0926200i	0.578062	−	0.815993i	$-0.303809\pi$
$191$	30.6407	+	17.6904i	0.160423	+	0.0926200i	−0.417639	+	0.908613i	$0.637142\pi$
$192$	87.9276	+	314.083i	0.457956	+	1.63585i
$193$	38.9119	+	67.3973i	0.201616	+	0.349209i	0.949049	−	0.315128i	$-0.102047\pi$
$193$	38.9119	+	67.3973i	0.201616	+	0.349209i	−0.747433	+	0.664337i	$0.768714\pi$
$194$	−91.7592	+	197.738i	−0.472986	+	1.01927i
$195$	405.839	+	405.839i	2.08123	+	2.08123i
$196$	124.802	−	151.130i	0.636747	−	0.771073i
$197$	125.415	+	125.415i	0.636622	+	0.636622i	0.949721	−	0.313099i	$-0.101367\pi$
$197$	125.415	+	125.415i	0.636622	+	0.636622i	−0.313099	+	0.949721i	$0.601367\pi$
$198$	−238.075	+	87.1541i	−1.20240	+	0.440172i
$199$	−35.6242	−	61.7029i	−0.179016	−	0.310065i	0.762528	−	0.646955i	$-0.223958\pi$
$199$	−35.6242	−	61.7029i	−0.179016	−	0.310065i	−0.941544	+	0.336891i	$0.890625\pi$
$200$	−52.3335	+	52.9210i	−0.261667	+	0.264605i
$201$	−202.538	−	116.935i	−1.00765	−	0.581767i
$202$	−47.4836	−	39.6932i	−0.235068	−	0.196501i
$203$	74.7223	−	6.69320i	0.368090	−	0.0329714i
$204$	159.016	+	110.464i	0.779488	+	0.541492i
$205$	81.1367	+	302.806i	0.395789	+	1.47710i
$206$	−47.9286	−	68.1788i	−0.232663	−	0.330965i
$207$	15.3033	−	8.83536i	0.0739290	−	0.0426829i
$208$	−178.337	−	250.700i	−0.857391	−	1.20529i
$209$	168.721			0.807276
$210$	178.088	+	378.025i	0.848039	+	1.80012i
$211$	−135.886	−	135.886i	−0.644012	−	0.644012i	0.307528	−	0.951539i	$-0.400498\pi$
$211$	−135.886	−	135.886i	−0.644012	−	0.644012i	−0.951539	+	0.307528i	$0.900498\pi$
$212$	−146.629	+	69.0399i	−0.691649	+	0.325660i
$213$	−156.563	+	584.302i	−0.735039	+	2.74320i
$214$	227.741	+	39.7201i	1.06421	+	0.185608i
$215$	−57.1381	+	98.9661i	−0.265759	+	0.460307i
$216$	−160.925	+	282.358i	−0.745023	+	1.30721i
$217$	183.184	+	31.9095i	0.844165	+	0.147048i
$218$	−40.5510	+	48.5098i	−0.186014	+	0.222522i
$219$	−161.129	−	601.342i	−0.735750	−	2.74586i
$220$	112.976	+	133.627i	0.513528	+	0.607394i
$221$	−176.415	−	47.2702i	−0.798257	−	0.213892i
$222$	−481.317	−	223.353i	−2.16810	−	1.00609i
$223$		−	102.577i		−	0.459987i	−0.973192	−	0.229993i	$-0.926130\pi$
$223$		−	102.577i		−	0.459987i	0.973192	−	0.229993i	$-0.0738705\pi$
$224$	−60.4322	−	215.694i	−0.269787	−	0.962920i
$225$	−157.893			−0.701746
$226$	−71.9340	+	155.015i	−0.318292	+	0.685908i
$227$	−1.27542	+	4.75992i	−0.00561857	+	0.0209688i	−0.968678	−	0.248319i	$-0.920122\pi$
$227$	−1.27542	+	4.75992i	−0.00561857	+	0.0209688i	0.963060	+	0.269288i	$0.0867884\pi$
$228$	351.640	−	297.297i	1.54228	−	1.30394i
$229$	−54.3988	+	14.5761i	−0.237549	+	0.0636511i	−0.375629	−	0.926770i	$-0.622573\pi$
$229$	−54.3988	+	14.5761i	−0.237549	+	0.0636511i	0.138080	+	0.990421i	$0.455907\pi$
$230$	−9.35757	−	7.82231i	−0.0406851	−	0.0340100i
$231$	250.194	−	91.6498i	1.08309	−	0.396753i
$232$	42.4543	−	74.4901i	0.182993	−	0.321078i
$233$	199.339	+	115.088i	0.855530	+	0.493941i	0.862513	−	0.506035i	$-0.168889\pi$
$233$	199.339	+	115.088i	0.855530	+	0.493941i	−0.00698268	+	0.999976i	$0.502223\pi$
$234$	112.141	−	642.977i	0.479235	−	2.74776i
$235$	217.221	+	58.2043i	0.924346	+	0.247678i
$236$	139.668	+	296.633i	0.591816	+	1.25692i
$237$	−354.006	+	354.006i	−1.49369	+	1.49369i
$238$	−109.225	−	75.8422i	−0.458929	−	0.318665i
$239$		−	264.818i		−	1.10802i	−0.832509	−	0.554012i	$-0.813096\pi$
$239$		−	264.818i		−	1.10802i	0.832509	−	0.554012i	$-0.186904\pi$
$240$	470.919	+	79.4268i	1.96216	+	0.330945i
$241$	−54.6458	−	94.6493i	−0.226746	−	0.392736i	0.730096	−	0.683345i	$-0.239475\pi$
$241$	−54.6458	−	94.6493i	−0.226746	−	0.392736i	−0.956842	+	0.290609i	$0.906142\pi$
$242$	−106.697	+	75.0063i	−0.440897	+	0.309943i
$243$	85.9235	−	23.0231i	0.353595	−	0.0947454i
$244$	187.089	−	269.318i	0.766759	−	1.10376i
$245$	−122.362	−	259.596i	−0.499437	−	1.05957i
$246$	349.892	−	418.564i	1.42232	−	1.70148i
$247$	−217.179	+	376.165i	−0.879268	+	1.52294i
$248$	149.423	−	151.100i	0.602512	−	0.609276i
$249$	−201.353	+	116.251i	−0.808648	+	0.466873i
$250$	−63.2076	−	172.661i	−0.252830	−	0.690645i
$251$	−259.432	+	259.432i	−1.03359	+	1.03359i	−0.0341785	+	0.999416i	$0.510881\pi$
$251$	−259.432	+	259.432i	−1.03359	+	1.03359i	−0.999416	+	0.0341785i	$0.989119\pi$
$252$	235.214	−	412.906i	0.933390	−	1.63852i
$253$	−5.49909	+	5.49909i	−0.0217355	+	0.0217355i
$254$	−6.17355	−	2.86480i	−0.0243053	−	0.0112787i
$255$	245.520	−	141.751i	0.962825	−	0.555887i
$256$	−241.838	−	83.9670i	−0.944679	−	0.327996i
$257$	−68.6823	+	118.961i	−0.267246	+	0.462884i	−0.968150	−	0.250372i	$-0.919447\pi$
$257$	−68.6823	+	118.961i	−0.267246	+	0.462884i	0.700903	+	0.713256i	$0.252780\pi$
$258$	198.079	−	17.7011i	0.767748	−	0.0686088i
$259$	330.593	+	153.326i	1.27642	+	0.591991i
$260$	−443.347	+	79.8761i	−1.70518	+	0.307216i
$261$	175.692	−	47.0765i	0.673149	−	0.180370i
$262$	16.8595	−	96.6664i	0.0643493	−	0.368956i
$263$	108.466	+	187.868i	0.412417	+	0.714328i	0.995154	−	0.0983336i	$-0.0313512\pi$
$263$	108.466	+	187.868i	0.412417	+	0.714328i	−0.582736	+	0.812661i	$0.698018\pi$
$264$	77.1716	−	294.575i	0.292317	−	1.11582i
$265$			237.308i			0.895500i
$266$	−241.457	+	204.229i	−0.907735	+	0.767779i
$267$	−321.689	+	321.689i	−1.20483	+	1.20483i
$268$	166.075	−	78.1958i	0.619684	−	0.291775i
$269$	110.514	+	29.6120i	0.410831	+	0.110082i	0.458314	−	0.888790i	$-0.348453\pi$
$269$	110.514	+	29.6120i	0.410831	+	0.110082i	−0.0474831	+	0.998872i	$0.515120\pi$
$270$	273.672	+	389.301i	1.01360	+	1.44186i
$271$	58.8834	+	33.9963i	0.217282	+	0.125448i	0.604691	−	0.796460i	$-0.293297\pi$
$271$	58.8834	+	33.9963i	0.217282	+	0.125448i	−0.387409	+	0.921908i	$0.626630\pi$
$272$	−142.415	+	53.0383i	−0.523584	+	0.194994i
$273$	−117.717	+	675.783i	−0.431199	+	2.47540i
$274$	−0.530434	−	5.93567i	−0.00193589	−	0.0216630i
$275$	67.1209	−	17.9850i	0.244076	−	0.0654000i
$276$	−1.77117	+	21.1507i	−0.00641727	+	0.0766330i
$277$	−82.5737	+	308.169i	−0.298100	+	1.11252i	0.640624	+	0.767855i	$0.278676\pi$
$277$	−82.5737	+	308.169i	−0.298100	+	1.11252i	−0.938724	+	0.344670i	$0.887991\pi$
$278$	137.690	+	376.121i	0.495287	+	1.35295i
$279$	450.818			1.61583
$280$	−323.430	−	54.4814i	−1.15511	−	0.194576i
$281$		−	390.428i		−	1.38942i	−0.719288	−	0.694712i	$-0.755532\pi$
$281$		−	390.428i		−	1.38942i	0.719288	−	0.694712i	$-0.244468\pi$
$282$	−134.535	−	367.502i	−0.477073	−	1.30320i
$283$	341.072	+	91.3899i	1.20520	+	0.322933i	0.804877	−	0.593441i	$-0.202231\pi$
$283$	341.072	+	91.3899i	1.20520	+	0.322933i	0.400323	+	0.916374i	$0.368898\pi$
$284$	−306.543	−	362.575i	−1.07938	−	1.27667i
$285$	−174.506	−	651.265i	−0.612301	−	2.28514i
$286$	25.5675	+	286.106i	0.0893967	+	1.00037i
$287$	−240.240	+	287.513i	−0.837071	+	1.00179i
$288$	−234.088	−	490.049i	−0.812805	−	1.70156i
$289$	99.3925	−	172.153i	0.343919	−	0.595685i
$290$	−72.1986	−	102.703i	−0.248961	−	0.354149i
$291$	143.765	−	536.538i	0.494038	−	1.84377i
$292$	459.790	+	165.415i	1.57462	+	0.566490i
$293$	−38.1713	−	38.1713i	−0.130278	−	0.130278i	0.638961	−	0.769239i	$-0.279364\pi$
$293$	−38.1713	−	38.1713i	−0.130278	−	0.130278i	−0.769239	+	0.638961i	$0.779364\pi$
$294$	−247.116	+	434.010i	−0.840529	+	1.47622i
$295$	480.076			1.62738
$296$	359.512	−	210.249i	1.21457	−	0.710299i
$297$	262.780	−	151.716i	0.884780	−	0.510828i
$298$	−62.2940	+	357.171i	−0.209040	+	1.19856i
$299$	−5.18181	−	19.3388i	−0.0173305	−	0.0646782i
$300$	108.199	−	155.755i	0.360665	−	0.519184i
$301$	−136.035	+	12.1852i	−0.451943	+	0.0404825i
$302$	89.9838	−	8.04129i	0.297960	−	0.0266268i
$303$	136.572	+	78.8500i	0.450734	+	0.260231i
$304$	34.1788	+	359.804i	0.112430	+	1.18357i
$305$	−240.078	−	415.828i	−0.787142	−	1.36337i
$306$	−292.443	−	135.707i	−0.955697	−	0.443486i
$307$	−414.769	−	414.769i	−1.35104	−	1.35104i	−0.884500	−	0.466540i	$-0.845500\pi$
$307$	−414.769	−	414.769i	−1.35104	−	1.35104i	−0.466540	−	0.884500i	$-0.654500\pi$
$308$	−52.9579	+	202.320i	−0.171941	+	0.656885i
$309$	150.160	+	150.160i	0.485956	+	0.485956i
$310$	−106.966	−	292.193i	−0.345050	−	0.942558i
$311$	−146.921	−	254.474i	−0.472414	−	0.818246i	0.527087	−	0.849811i	$-0.323284\pi$
$311$	−146.921	−	254.474i	−0.472414	−	0.818246i	−0.999502	+	0.0315655i	$0.989951\pi$
$312$	557.424	+	551.236i	1.78662	+	1.76678i
$313$	225.880	+	130.412i	0.721660	+	0.416651i	0.815363	−	0.578949i	$-0.196537\pi$
$313$	225.880	+	130.412i	0.721660	+	0.416651i	−0.0937033	+	0.995600i	$0.529870\pi$
$314$	80.0033	−	95.7053i	0.254788	−	0.304794i
$315$	−400.276	−	569.143i	−1.27072	−	1.80680i
$316$	−69.6744	−	386.723i	−0.220489	−	1.22381i
$317$	43.0429	+	160.638i	0.135782	+	0.506746i	0.999993	+	0.00361672i	$0.00115124\pi$
$317$	43.0429	+	160.638i	0.135782	+	0.506746i	−0.864211	+	0.503129i	$0.832182\pi$
$318$	337.846	−	237.500i	1.06241	−	0.746857i
$319$	−69.3250	+	40.0248i	−0.217320	+	0.125470i
$320$	−262.078	+	267.996i	−0.818994	+	0.837487i
$321$	−589.070			−1.83511
$322$	1.21337	−	14.5262i	0.00376824	−	0.0451124i
$323$	151.712	+	151.712i	0.469698	+	0.469698i
$324$	73.5114	−	204.333i	0.226887	−	0.630659i
$325$	−46.3009	+	172.797i	−0.142464	+	0.531685i
$326$	−10.0344	+	57.5339i	−0.0307805	+	0.176484i
$327$	80.5540	−	139.524i	0.246343	−	0.426678i
$328$	113.132	+	412.980i	0.344915	+	1.25909i
$329$	92.4488	+	252.375i	0.280999	+	0.767096i
$330$	−342.098	−	285.971i	−1.03666	−	0.866579i
$331$	42.4320	+	158.358i	0.128193	+	0.478424i	0.999933	−	0.0115447i	$-0.00367486\pi$
$331$	42.4320	+	158.358i	0.128193	+	0.478424i	−0.871740	+	0.489969i	$0.837008\pi$
$332$	15.2285	−	181.854i	0.0458689	−	0.547752i
$333$	853.426	+	228.675i	2.56284	+	0.686711i
$334$	115.388	−	248.658i	0.345474	−	0.744484i
$335$		−	268.779i		−	0.802325i
$336$	246.130	+	514.982i	0.732531	+	1.53268i
$337$	551.846			1.63753			0.818763	−	0.574132i	$-0.194660\pi$
$337$	551.846			1.63753			0.818763	+	0.574132i	$0.194660\pi$
$338$	−364.190	−	169.000i	−1.07748	−	0.500001i
$339$	112.704	−	420.616i	0.332459	−	1.24075i
$340$	−18.5689	+	221.743i	−0.0546143	+	0.652186i
$341$	−191.644	+	51.3509i	−0.562007	+	0.150589i
$342$	−491.756	+	588.271i	−1.43788	+	1.72009i
$343$	169.652	−	298.106i	0.494614	−	0.869113i
$344$	−77.2896	+	135.612i	−0.224679	+	0.394221i
$345$	26.9142	+	15.5389i	0.0780122	+	0.0450404i
$346$	77.5275	+	13.5215i	0.224068	+	0.0390795i
$347$	−366.106	−	98.0978i	−1.05506	−	0.282703i	−0.310719	−	0.950502i	$-0.600570\pi$
$347$	−366.106	−	98.0978i	−1.05506	−	0.282703i	−0.744342	+	0.667799i	$0.767237\pi$
$348$	−73.9574	+	205.573i	−0.212521	+	0.590728i
$349$	−261.972	+	261.972i	−0.750636	+	0.750636i	−0.974598	−	0.223962i	$-0.928101\pi$
$349$	−261.972	+	261.972i	−0.750636	+	0.750636i	0.223962	+	0.974598i	$0.428101\pi$
$350$	−74.2871	+	106.985i	−0.212249	+	0.305673i
$351$			781.162i			2.22553i
$352$	155.331	+	181.658i	0.441282	+	0.516073i
$353$	−92.5812	−	160.355i	−0.262270	−	0.454264i	0.704575	−	0.709630i	$-0.251138\pi$
$353$	−92.5812	−	160.355i	−0.262270	−	0.454264i	−0.966845	+	0.255365i	$0.917804\pi$
$354$	−480.466	−	683.467i	−1.35725	−	1.93070i
$355$	−671.518	+	179.933i	−1.89160	+	0.506852i
$356$	−63.3139	−	351.419i	−0.177848	−	0.987132i
$357$	307.383	+	142.561i	0.861017	+	0.399331i
$358$	−51.7624	−	43.2699i	−0.144588	−	0.120866i
$359$	196.827	−	340.914i	0.548265	−	0.949622i	−0.450129	−	0.892963i	$-0.648622\pi$
$359$	196.827	−	340.914i	0.548265	−	0.949622i	0.998394	−	0.0566585i	$-0.0180446\pi$
$360$	−795.193	+	4.43850i	−2.20887	+	0.0123292i
$361$	129.264	−	74.6308i	0.358073	−	0.206734i
$362$	216.779	−	79.3583i	0.598838	−	0.219222i
$363$	234.995	−	234.995i	0.647369	−	0.647369i
$364$	−382.908	−	378.499i	−1.05195	−	1.03983i
$365$	505.921	−	505.921i	1.38609	−	1.38609i
$366$	−351.726	+	757.957i	−0.960999	+	2.07092i
$367$	−132.795	+	76.6692i	−0.361839	+	0.208908i	−0.669887	−	0.742463i	$-0.733658\pi$
$367$	−132.795	+	76.6692i	−0.361839	+	0.208908i	0.308048	+	0.951371i	$0.400324\pi$
$368$	−12.8410	−	10.6130i	−0.0348941	−	0.0288398i
$369$	−454.195	+	786.690i	−1.23088	+	2.13195i
$370$	−54.2793	−	607.397i	−0.146701	−	1.64161i
$371$	−231.993	+	163.160i	−0.625318	+	0.439784i
$372$	−308.932	+	444.714i	−0.830463	+	1.19547i
$373$	−518.550	+	138.945i	−1.39021	+	0.372507i	−0.874821	−	0.484446i	$-0.839021\pi$
$373$	−518.550	+	138.945i	−1.39021	+	0.372507i	−0.515394	+	0.856953i	$0.672354\pi$
$374$	139.777	+	24.3783i	0.373734	+	0.0651827i
$375$	234.257	+	405.745i	0.624685	+	1.08199i
$376$	297.143	+	77.8443i	0.790275	+	0.207033i
$377$		−	206.081i		−	0.546635i
$378$	−192.420	+	535.206i	−0.509048	+	1.41589i
$379$	−285.309	+	285.309i	−0.752793	+	0.752793i	−0.975000	−	0.222207i	$-0.928674\pi$
$379$	−285.309	+	285.309i	−0.752793	+	0.752793i	0.222207	+	0.975000i	$0.428674\pi$
$380$	497.961	+	179.148i	1.31042	+	0.471441i
$381$	16.7512	+	4.48847i	0.0439664	+	0.0117808i
$382$	57.8890	−	40.6950i	0.151542	−	0.106531i
$383$	−234.274	−	135.258i	−0.611681	−	0.353154i	0.161942	−	0.986800i	$-0.448224\pi$
$383$	−234.274	−	135.258i	−0.611681	−	0.353154i	−0.773623	+	0.633646i	$0.781558\pi$
$384$	643.827	+	104.898i	1.67663	+	0.273171i
$385$	234.988	+	196.351i	0.610358	+	0.510002i
$386$	155.030	−	13.8540i	0.401631	−	0.0358913i
$387$	−319.854	+	85.7045i	−0.826495	+	0.221459i
$388$	281.485	+	332.936i	0.725476	+	0.858083i
$389$	97.0998	−	362.381i	0.249614	−	0.931571i	−0.721394	−	0.692525i	$-0.756498\pi$
$389$	97.0998	−	362.381i	0.249614	−	0.931571i	0.971008	−	0.239047i	$-0.0768349\pi$
$390$	1077.93	−	394.606i	2.76392	−	1.01181i
$391$	−9.88947			−0.0252928
$392$	−169.112	−	353.646i	−0.431408	−	0.902157i
$393$			250.035i			0.636222i
$394$	333.107	−	121.943i	0.845449	−	0.309501i
$395$	−555.762	−	148.916i	−1.40699	−	0.377003i
$396$	−42.3126	+	505.283i	−0.106850	+	1.27597i
$397$	−83.6957	−	312.357i	−0.210820	−	0.786792i	−0.987596	−	0.157015i	$-0.949813\pi$
$397$	−83.6957	−	312.357i	−0.210820	−	0.786792i	0.776776	−	0.629777i	$-0.216854\pi$
$398$	−141.931	+	12.6835i	−0.356611	+	0.0318681i
$399$	516.699	−	618.372i	1.29498	−	1.54980i
$400$	51.9508	+	139.495i	0.129877	+	0.348737i
$401$	−146.006	+	252.890i	−0.364105	+	0.630648i	−0.988632	−	0.150355i	$-0.951958\pi$
$401$	−146.006	+	252.890i	−0.364105	+	0.630648i	0.624527	+	0.781003i	$0.285292\pi$
$402$	−382.651	+	268.997i	−0.951868	+	0.669148i
$403$	132.199	−	493.373i	0.328037	−	1.22425i
$404$	−111.985	+	52.7279i	−0.277192	+	0.130515i
$405$	−224.834	−	224.834i	−0.555146	−	0.555146i
$406$	50.7632	−	141.195i	0.125032	−	0.347770i
$407$	−388.842			−0.955386
$408$	334.272	−	195.488i	0.819294	−	0.479137i
$409$	−442.624	+	255.549i	−1.08221	+	0.624814i	−0.931492	−	0.363763i	$-0.881492\pi$
$409$	−442.624	+	255.549i	−1.08221	+	0.624814i	−0.150718	+	0.988577i	$0.548159\pi$
$410$	617.652	+	107.724i	1.50647	+	0.262742i
$411$	3.93018	+	14.6676i	0.00956248	+	0.0356876i
$412$	−164.038	+	29.5542i	−0.398151	+	0.0717334i
$413$	330.074	+	469.324i	0.799211	+	1.13638i
$414$	−3.14571	−	35.2012i	−0.00759833	−	0.0850270i
$415$	−231.408	−	133.604i	−0.557610	−	0.321936i
$416$	−604.952	+	112.482i	−1.45421	+	0.270389i
$417$	−510.300	−	883.865i	−1.22374	−	2.11958i
$418$	142.040	−	306.091i	0.339808	−	0.732274i
$419$	446.096	+	446.096i	1.06467	+	1.06467i	0.997759	+	0.0669099i	$0.0213140\pi$
$419$	446.096	+	446.096i	1.06467	+	1.06467i	0.0669099	+	0.997759i	$0.478686\pi$
$420$	835.734	−	4.83943i	1.98984	−	0.0115224i
$421$	−223.519	−	223.519i	−0.530923	−	0.530923i	0.389924	−	0.920847i	$-0.372501\pi$
$421$	−223.519	−	223.519i	−0.530923	−	0.530923i	−0.920847	+	0.389924i	$0.872501\pi$
$422$	−360.921	+	132.125i	−0.855263	+	0.313093i
$423$	325.822	+	564.340i	0.770265	+	1.33414i
$424$	1.80921	+	324.135i	0.00426701	+	0.764470i
$425$	76.5266	+	44.1826i	0.180062	+	0.103959i
$426$	928.227	+	775.937i	2.17894	+	1.82145i
$427$	241.450	−	520.602i	0.565458	−	1.21921i
$428$	263.786	−	379.726i	0.616323	−	0.887209i
$429$	−189.439	−	706.994i	−0.441582	−	1.64801i
$430$	131.440	+	186.975i	0.305675	+	0.434825i
$431$	−652.201	+	376.548i	−1.51323	+	0.873662i	−0.513347	+	0.858181i	$0.671595\pi$
$431$	−652.201	+	376.548i	−1.51323	+	0.873662i	−0.999880	+	0.0154807i	$0.995072\pi$
$432$	376.773	+	529.655i	0.872161	+	1.22605i
$433$	757.347			1.74907			0.874535	−	0.484962i	$-0.161167\pi$
$433$	757.347			1.74907			0.874535	+	0.484962i	$0.161167\pi$
$434$	212.105	−	305.466i	0.488722	−	0.703839i
$435$	226.198	+	226.198i	0.519996	+	0.519996i
$436$	53.8674	+	114.406i	0.123549	+	0.262398i
$437$	−6.08732	+	22.7182i	−0.0139298	+	0.0519867i
$438$	−1226.59	−	213.929i	−2.80044	−	0.488423i
$439$	35.2461	−	61.0481i	0.0802873	−	0.139062i	−0.823086	−	0.567917i	$-0.807750\pi$
$439$	35.2461	−	61.0481i	0.0802873	−	0.139062i	0.903373	+	0.428855i	$0.141083\pi$
$440$	337.534	−	92.4643i	0.767123	−	0.210146i
$441$	281.188	−	782.623i	0.637616	−	1.77465i
$442$	−234.274	+	280.254i	−0.530031	+	0.634059i
$443$	198.394	+	740.417i	0.447843	+	1.67137i	0.708320	+	0.705891i	$0.249453\pi$
$443$	198.394	+	740.417i	0.447843	+	1.67137i	−0.260478	+	0.965480i	$0.583880\pi$
$444$	−810.406	+	685.167i	−1.82524	+	1.54317i
$445$	−505.027	−	135.322i	−1.13489	−	0.304093i
$446$	−186.094	−	86.3558i	−0.417251	−	0.193623i
$447$		−	923.851i		−	2.06678i
$448$	−442.185	−	71.9496i	−0.987019	−	0.160602i
$449$	130.409			0.290442			0.145221	−	0.989399i	$-0.453611\pi$
$449$	130.409			0.290442			0.145221	+	0.989399i	$0.453611\pi$
$450$	−132.924	+	286.447i	−0.295387	+	0.636549i
$451$	103.471	−	386.161i	0.229427	−	0.856232i
$452$	220.668	+	261.003i	0.488203	+	0.577441i
$453$	−222.359	+	59.5808i	−0.490858	+	0.131525i
$454$	7.56164	+	6.32103i	0.0166556	+	0.0139230i
$455$	−740.246	+	271.164i	−1.62691	+	0.595964i
$456$	−243.320	−	888.223i	−0.533597	−	1.94786i
$457$	−24.6672	−	14.2416i	−0.0539763	−	0.0311633i	0.472769	−	0.881186i	$-0.343255\pi$
$457$	−24.6672	−	14.2416i	−0.0539763	−	0.0311633i	−0.526745	+	0.850023i	$0.676588\pi$
$458$	−19.3525	+	110.960i	−0.0422544	+	0.242272i
$459$	372.711	+	99.8677i	0.812007	+	0.217577i
$460$	−22.0689	+	10.3911i	−0.0479759	+	0.0225892i
$461$	−257.019	+	257.019i	−0.557525	+	0.557525i	−0.928602	−	0.371077i	$-0.878989\pi$
$461$	−257.019	+	257.019i	−0.557525	+	0.557525i	0.371077	+	0.928602i	$0.378989\pi$
$462$	44.3589	−	531.054i	0.0960149	−	1.14947i
$463$			404.292i			0.873200i	0.899656	+	0.436600i	$0.143817\pi$
$463$			404.292i			0.873200i	−0.899656	+	0.436600i	$0.856183\pi$
$464$	−99.3981	−	139.730i	−0.214220	−	0.301143i
$465$	396.431	+	686.638i	0.852540	+	1.47664i
$466$	376.607	−	264.749i	0.808169	−	0.568130i
$467$	−564.902	+	151.365i	−1.20964	+	0.324122i	−0.806621	−	0.591069i	$-0.798706\pi$
$467$	−564.902	+	151.365i	−1.20964	+	0.324122i	−0.403020	+	0.915191i	$0.632039\pi$
$468$	−1072.07	−	744.743i	−2.29075	−	1.59133i
$469$	262.759	−	184.798i	0.560255	−	0.394025i
$470$	288.464	−	345.080i	0.613753	−	0.734212i
$471$	−158.926	+	275.267i	−0.337422	+	0.584432i
$472$	655.729	−	3.66006i	1.38926	−	0.00775436i
$473$	126.209	−	72.8667i	0.266826	−	0.154052i
$474$	344.208	+	940.256i	0.726176	+	1.98366i
$475$	148.602	−	148.602i	0.312845	−	0.312845i
$476$	−229.544	+	134.306i	−0.482236	+	0.282155i
$477$	−486.237	+	486.237i	−1.01937	+	1.01937i
$478$	−480.428	−	222.940i	−1.00508	−	0.466402i
$479$	618.650	−	357.178i	1.29154	−	0.745674i	0.312617	−	0.949879i	$-0.398794\pi$
$479$	618.650	−	357.178i	1.29154	−	0.745674i	0.978928	+	0.204206i	$0.0654611\pi$
$480$	540.544	−	787.468i	1.12613	−	1.64056i
$481$	500.522	−	866.929i	1.04059	−	1.80235i
$482$	−217.716	+	19.4559i	−0.451692	+	0.0403649i
$483$	3.31382	+	36.9952i	0.00686091	+	0.0765946i
$484$	46.2511	+	256.713i	0.0955601	+	0.530399i
$485$	616.624	−	165.224i	1.27139	−	0.340668i
$486$	30.5676	−	175.264i	0.0628962	−	0.360624i
$487$	−127.023	−	220.010i	−0.260827	−	0.451765i	0.705635	−	0.708575i	$-0.250662\pi$
$487$	−127.023	−	220.010i	−0.260827	−	0.451765i	−0.966462	+	0.256810i	$0.917328\pi$
$488$	−331.090	−	566.143i	−0.678463	−	1.16013i
$489$		−	148.816i		−	0.304327i
$490$	−573.967	+	3.44357i	−1.17136	+	0.00702770i
$491$	114.061	−	114.061i	0.232304	−	0.232304i	−0.581350	−	0.813654i	$-0.697475\pi$
$491$	114.061	−	114.061i	0.232304	−	0.232304i	0.813654	+	0.581350i	$0.197475\pi$
$492$	−464.791	−	987.141i	−0.944698	−	2.00638i
$493$	−98.3265	−	26.3465i	−0.199445	−	0.0534412i
$494$	499.598	+	710.683i	1.01133	+	1.43863i
$495$	642.972	+	371.220i	1.29893	+	0.749939i
$496$	−148.331	−	398.287i	−0.299053	−	0.802998i
$497$	−637.602	−	532.767i	−1.28290	−	1.07197i
$498$	41.3897	+	463.160i	0.0831118	+	0.930040i
$499$	382.109	−	102.386i	0.765750	−	0.205182i	0.145257	−	0.989394i	$-0.453599\pi$
$499$	382.109	−	102.386i	0.765750	−	0.205182i	0.620493	+	0.784212i	$0.286933\pi$
$500$	−366.452	−	30.6868i	−0.732903	−	0.0613735i
$501$	−180.786	+	674.703i	−0.360851	+	1.34671i
$502$	252.252	+	689.064i	0.502493	+	1.37264i
$503$	−385.707			−0.766812			−0.383406	−	0.923580i	$-0.625249\pi$
$503$	−385.707			−0.766812			−0.383406	+	0.923580i	$0.625249\pi$
$504$	−551.070	−	774.332i	−1.09339	−	1.53637i
$505$			181.239i			0.358889i
$506$	5.34689	+	14.6058i	0.0105670	+	0.0288653i
$507$	988.186	+	264.784i	1.94908	+	0.522256i
$508$	−10.3946	+	8.78819i	−0.0204617	+	0.0172996i
$509$	−64.0703	−	239.114i	−0.125875	−	0.469771i	0.873994	−	0.485936i	$-0.161521\pi$
$509$	−64.0703	−	239.114i	−0.125875	−	0.469771i	−0.999869	+	0.0161645i	$0.994854\pi$
$510$	−50.4686	−	564.754i	−0.0989579	−	1.10736i
$511$	842.435	+	146.747i	1.64860	+	0.287176i
$512$	−355.926	+	368.050i	−0.695168	+	0.718847i
$513$	458.834	−	794.724i	0.894414	−	1.54917i
$514$	157.997	+	224.752i	0.307387	+	0.437260i
$515$	−63.1665	+	235.741i	−0.122653	+	0.457749i
$516$	134.642	−	374.254i	0.260935	−	0.725298i
$517$	−202.790	−	202.790i	−0.392244	−	0.392244i
$518$	556.475	−	470.677i	1.07428	−	0.908643i
$519$	−200.531			−0.386379
$520$	−228.327	+	871.558i	−0.439090	+	1.67607i
$521$	−788.594	+	455.295i	−1.51362	+	0.873886i	−0.513743	+	0.857944i	$0.671741\pi$
$521$	−788.594	+	455.295i	−1.51362	+	0.873886i	−0.999873	+	0.0159422i	$0.994925\pi$
$522$	62.5029	−	358.369i	0.119737	−	0.686532i
$523$	−150.016	−	559.868i	−0.286838	−	1.07049i	−0.947486	−	0.319798i	$-0.896385\pi$
$523$	−150.016	−	559.868i	−0.286838	−	1.07049i	0.660648	−	0.750696i	$-0.270282\pi$
$524$	−161.177	−	111.966i	−0.307590	−	0.213676i
$525$	139.638	−	301.080i	0.265978	−	0.573486i
$526$	432.141	−	38.6177i	0.821561	−	0.0734178i
$527$	−218.499	−	126.151i	−0.414610	−	0.239375i
$528$	−469.447	−	387.996i	−0.889103	−	0.734840i
$529$	263.958	+	457.189i	0.498975	+	0.864251i
$530$	430.520	+	199.780i	0.812301	+	0.376944i
$531$	983.664	+	983.664i	1.85247	+	1.85247i
$532$	167.236	+	609.981i	0.314353	+	1.14658i
$533$	727.761	+	727.761i	1.36541	+	1.36541i
$534$	312.785	+	854.420i	0.585740	+	1.60004i
$535$	−338.499	−	586.297i	−0.632708	−	1.09588i
$536$	−2.04915	−	367.121i	−0.00382304	−	0.684928i
$537$	148.879	+	85.9552i	0.277242	+	0.160066i
$538$	146.759	−	175.563i	0.272786	−	0.326325i
$539$	−30.3887	+	364.725i	−0.0563798	+	0.676670i
$540$	936.659	−	168.754i	1.73455	−	0.312508i
$541$	147.579	+	550.773i	0.272790	+	1.01806i	0.957308	+	0.289069i	$0.0933458\pi$
$541$	147.579	+	550.773i	0.272790	+	1.01806i	−0.684519	+	0.728995i	$0.739988\pi$
$542$	111.247	−	78.2051i	0.205253	−	0.144290i
$543$	−509.420	+	294.114i	−0.938159	+	0.541646i
$544$	−23.6724	+	303.018i	−0.0435154	+	0.557018i
$545$	185.156			0.339735
$546$	1126.89	+	782.477i	2.06391	+	1.43311i
$547$	−462.494	−	462.494i	−0.845509	−	0.845509i	0.144060	−	0.989569i	$-0.453984\pi$
$547$	−462.494	−	462.494i	−0.845509	−	0.845509i	−0.989569	+	0.144060i	$0.953984\pi$
$548$	−11.2150	−	4.03472i	−0.0204653	−	0.00736262i
$549$	360.107	−	1343.94i	0.655932	−	2.44797i
$550$	23.8785	−	136.911i	0.0434154	−	0.248928i
$551$	−121.047	+	209.659i	−0.219686	+	0.380507i
$552$	36.8802	+	21.0192i	0.0668120	+	0.0380783i
$553$	−236.531	−	645.702i	−0.427723	−	1.16763i
$554$	489.561	+	409.240i	0.883683	+	0.738701i
$555$	402.175	+	1500.94i	0.724639	+	2.70439i
$556$	798.269	+	66.8473i	1.43574	+	0.120229i
$557$	624.019	+	167.205i	1.12032	+	0.300189i	0.771013	−	0.636819i	$-0.219750\pi$
$557$	624.019	+	167.205i	1.12032	+	0.300189i	0.349308	+	0.937008i	$0.386417\pi$
$558$	379.526	−	817.866i	0.680155	−	1.46571i
$559$			375.179i			0.671161i
$560$	−371.123	+	540.897i	−0.662720	+	0.965887i
$561$	−361.543			−0.644462
$562$	−708.309	−	328.687i	−1.26034	−	0.584852i
$563$	−187.317	+	699.075i	−0.332712	+	1.24170i	0.573617	+	0.819124i	$0.305540\pi$
$563$	−187.317	+	699.075i	−0.332712	+	1.24170i	−0.906329	+	0.422573i	$0.861127\pi$
$564$	−779.976	−	65.3154i	−1.38294	−	0.115807i
$565$	483.399	−	129.526i	0.855573	−	0.229250i
$566$	452.934	−	541.830i	0.800236	−	0.957296i
$567$	65.2152	−	374.383i	0.115018	−	0.660287i
$568$	−915.845	+	250.887i	−1.61240	+	0.441703i
$569$	−309.266	−	178.555i	−0.543525	−	0.313804i	0.202981	−	0.979183i	$-0.434937\pi$
$569$	−309.266	−	178.555i	−0.543525	−	0.313804i	−0.746506	+	0.665378i	$0.768270\pi$
$570$	−1328.42	−	231.689i	−2.33057	−	0.406473i
$571$	−144.033	−	38.5936i	−0.252248	−	0.0675896i	0.130479	−	0.991451i	$-0.458348\pi$
$571$	−144.033	−	38.5936i	−0.252248	−	0.0675896i	−0.382727	+	0.923861i	$0.625015\pi$
$572$	540.573	+	194.477i	0.945057	+	0.339996i
$573$	−127.498	+	127.498i	−0.222509	+	0.222509i
$574$	319.352	+	677.885i	0.556363	+	1.18098i
$575$			9.68670i			0.0168464i
$576$	−1086.11	+	12.1250i	−1.88561	+	0.0210503i
$577$	−157.935	−	273.551i	−0.273717	−	0.474092i	0.696094	−	0.717951i	$-0.254920\pi$
$577$	−157.935	−	273.551i	−0.273717	−	0.474092i	−0.969811	+	0.243859i	$0.921587\pi$
$578$	−228.642	−	325.245i	−0.395575	−	0.562708i
$579$	−383.093	+	102.649i	−0.661646	+	0.177288i
$580$	−247.104	+	44.5198i	−0.426041	+	0.0767582i
$581$	−28.4922	−	318.084i	−0.0490399	−	0.547477i
$582$	−852.349	−	712.508i	−1.46452	−	1.22424i
$583$	151.316	−	262.087i	0.259547	−	0.449549i
$584$	687.174	−	694.888i	1.17667	−	1.18988i
$585$	−1655.28	+	955.676i	−2.82954	+	1.63363i
$586$	−101.385	+	37.1148i	−0.173012	+	0.0633359i
$587$	478.624	−	478.624i	0.815373	−	0.815373i	−0.170061	−	0.985434i	$-0.554396\pi$
$587$	478.624	−	478.624i	0.815373	−	0.815373i	0.985434	+	0.170061i	$0.0543965\pi$
$588$	579.336	+	813.690i	0.985266	+	1.38383i
$589$	−424.289	+	424.289i	−0.720355	+	0.720355i
$590$	404.158	−	870.946i	0.685013	−	1.47618i
$591$	−782.784	+	451.941i	−1.32451	+	0.764705i
$592$	−78.7701	−	829.222i	−0.133058	−	1.40071i
$593$	−128.062	+	221.810i	−0.215956	+	0.374047i	−0.953568	−	0.301178i	$-0.902620\pi$
$593$	−128.062	+	221.810i	−0.215956	+	0.374047i	0.737612	+	0.675225i	$0.235954\pi$
$594$	−54.0164	−	604.455i	−0.0909367	−	1.01760i
$595$	34.7420	+	387.856i	0.0583899	+	0.651859i
$596$	595.532	+	413.702i	0.999214	+	0.694131i
$597$	350.725	−	93.9765i	0.587479	−	0.157415i
$598$	−39.4465	−	6.87983i	−0.0659640	−	0.0115047i
$599$	471.523	+	816.703i	0.787184	+	1.36344i	0.927685	+	0.373363i	$0.121795\pi$
$599$	471.523	+	816.703i	0.787184	+	1.36344i	−0.140501	+	0.990081i	$0.544871\pi$
$600$	−191.480	−	327.418i	−0.319133	−	0.545697i
$601$			349.582i			0.581666i	0.956774	+	0.290833i	$0.0939325\pi$
$601$			349.582i			0.581666i	−0.956774	+	0.290833i	$0.906068\pi$
$602$	−92.4163	+	257.050i	−0.153515	+	0.426994i
$603$	550.721	−	550.721i	0.913302	−	0.913302i
$604$	61.1656	−	170.017i	0.101268	−	0.281485i
$605$	368.924	+	98.8530i	0.609792	+	0.163393i
$606$	258.024	−	181.386i	0.425782	−	0.299318i
$607$	490.840	+	283.387i	0.808633	+	0.466865i	0.846481	−	0.532419i	$-0.178717\pi$
$607$	490.840	+	283.387i	0.808633	+	0.466865i	−0.0378477	+	0.999284i	$0.512050\pi$
$608$	681.525	+	240.899i	1.12093	+	0.396215i
$609$	−65.6109	+	376.654i	−0.107735	+	0.618480i
$610$	−956.502	+	85.4766i	−1.56804	+	0.140126i
$611$	713.157	−	191.090i	1.16720	−	0.312749i
$612$	−492.394	+	416.300i	−0.804565	+	0.680228i
$613$	−207.219	+	773.352i	−0.338041	+	1.26159i	0.562494	+	0.826801i	$0.309842\pi$
$613$	−207.219	+	773.352i	−0.338041	+	1.26159i	−0.900535	+	0.434784i	$0.856825\pi$
$614$	−1101.65	+	403.290i	−1.79421	+	0.656823i
$615$	−1597.61			−2.59773
$616$	322.464	+	266.401i	0.523480	+	0.432470i
$617$			635.134i			1.02939i	0.857373	+	0.514695i	$0.172095\pi$
$617$			635.134i			1.02939i	−0.857373	+	0.514695i	$0.827905\pi$
$618$	398.833	−	146.004i	0.645361	−	0.236253i
$619$	−497.833	−	133.394i	−0.804254	−	0.215499i	−0.166803	−	0.985990i	$-0.553345\pi$
$619$	−497.833	−	133.394i	−0.804254	−	0.215499i	−0.637451	+	0.770491i	$0.720011\pi$
$620$	−620.142	−	51.9309i	−1.00023	−	0.0837596i
$621$	10.9476	+	40.8570i	0.0176290	+	0.0657923i
$622$	−585.351	+	52.3091i	−0.941078	+	0.0840983i
$623$	−214.938	−	586.756i	−0.345005	−	0.941824i
$624$	1469.32	−	547.206i	2.35468	−	0.876932i
$625$	−385.516	+	667.733i	−0.616825	+	1.06837i
$626$	426.751	−	299.999i	0.681710	−	0.479231i
$627$	−222.543	+	830.540i	−0.354932	+	1.32463i
$628$	−106.275	−	225.712i	−0.169228	−	0.359413i
$629$	−349.644	−	349.644i	−0.555873	−	0.555873i
$630$	−1369.51	+	247.034i	−2.17382	+	0.392118i
$631$	−195.784			−0.310275			−0.155138	−	0.987893i	$-0.549582\pi$
$631$	−195.784			−0.310275			−0.155138	+	0.987893i	$0.549582\pi$
$632$	−760.243	−	199.165i	−1.20292	−	0.315135i
$633$	848.146	−	489.677i	1.33988	−	0.773581i
$634$	327.664	+	57.1476i	0.516820	+	0.0901382i
$635$	5.15843	+	19.2515i	0.00812352	+	0.0303174i
$636$	−146.450	−	812.858i	−0.230267	−	1.27808i
$637$	−774.043	−	537.230i	−1.21514	−	0.843376i
$638$	14.2503	+	159.464i	0.0223359	+	0.249943i
$639$	−1744.60	−	1007.25i	−2.73021	−	1.57628i
$640$	265.560	+	701.074i	0.414938	+	1.09543i
$641$	55.7606	+	96.5802i	0.0869901	+	0.150671i	0.906237	−	0.422769i	$-0.138942\pi$
$641$	55.7606	+	96.5802i	0.0869901	+	0.150671i	−0.819247	+	0.573440i	$0.805608\pi$
$642$	−495.916	+	1068.68i	−0.772455	+	1.66461i
$643$	−755.061	−	755.061i	−1.17428	−	1.17428i	−0.981179	−	0.193100i	$-0.938146\pi$
$643$	−755.061	−	755.061i	−1.17428	−	1.17428i	−0.193100	−	0.981179i	$-0.561854\pi$
$644$	−25.3317	−	14.4303i	−0.0393350	−	0.0224074i
$645$	−411.803	−	411.803i	−0.638454	−	0.638454i
$646$	402.955	−	147.513i	0.623770	−	0.228349i
$647$	−130.351	−	225.775i	−0.201470	−	0.348957i	0.747532	−	0.664226i	$-0.231239\pi$
$647$	−130.351	−	225.775i	−0.201470	−	0.348957i	−0.949002	+	0.315269i	$0.897905\pi$
$648$	−308.812	−	305.384i	−0.476562	−	0.471271i
$649$	−530.205	−	306.114i	−0.816957	−	0.471670i
$650$	274.508	+	229.470i	0.422319	+	0.353031i
$651$	−398.697	+	859.648i	−0.612437	+	1.32050i
$652$	95.9296	+	66.6400i	0.147131	+	0.102209i
$653$	−147.919	−	552.041i	−0.226522	−	0.845393i	−0.981789	−	0.189975i	$-0.939159\pi$
$653$	−147.919	−	552.041i	−0.226522	−	0.845393i	0.755267	−	0.655418i	$-0.227507\pi$
$654$	−185.306	−	263.600i	−0.283343	−	0.403058i
$655$	−248.858	+	143.678i	−0.379936	+	0.219356i
$656$	844.464	+	142.430i	1.28729	+	0.217119i
$657$	2073.24			3.15562
$658$	535.683	+	44.7456i	0.814109	+	0.0680024i
$659$	137.173	+	137.173i	0.208154	+	0.208154i	0.803482	−	0.595329i	$-0.202978\pi$
$659$	137.173	+	137.173i	0.208154	+	0.208154i	−0.595329	+	0.803482i	$0.702978\pi$
$660$	−806.803	+	379.880i	−1.22243	+	0.575576i
$661$	174.098	−	649.744i	0.263386	−	0.982971i	−0.699845	−	0.714295i	$-0.746747\pi$
$661$	174.098	−	649.744i	0.263386	−	0.982971i	0.963231	−	0.268675i	$-0.0865859\pi$
$662$	323.013	+	56.3365i	0.487935	+	0.0851004i
$663$	465.382	−	806.065i	0.701934	−	1.21578i
$664$	−317.096	−	180.723i	−0.477554	−	0.272173i
$665$	912.372	+	158.930i	1.37199	+	0.238992i
$666$	1133.33	−	1355.76i	1.70169	−	2.03567i
$667$	−2.88813	−	10.7787i	−0.00433004	−	0.0161599i
$668$	−353.970	−	418.671i	−0.529895	−	0.626753i
$669$	504.943	+	135.299i	0.754773	+	0.202241i
$670$	−487.615	−	226.275i	−0.727783	−	0.337724i
$671$			612.331i			0.912565i
$672$	1141.48	−	12.9817i	1.69863	−	0.0193180i
$673$	−1004.84			−1.49307			−0.746535	−	0.665346i	$-0.768284\pi$
$673$	−1004.84			−1.49307			−0.746535	+	0.665346i	$0.768284\pi$
$674$	464.579	−	1001.15i	0.689286	−	1.48539i
$675$	97.8200	−	365.069i	0.144919	−	0.540843i
$676$	−613.196	+	518.433i	−0.907094	+	0.766912i
$677$	327.816	−	87.8380i	0.484219	−	0.129746i	−0.00844762	−	0.999964i	$-0.502689\pi$
$677$	327.816	−	87.8380i	0.484219	−	0.129746i	0.492666	+	0.870218i	$0.336022\pi$
$678$	−668.193	−	558.566i	−0.985536	−	0.823843i
$679$	585.481	+	489.216i	0.862270	+	0.720495i
$680$	386.651	+	220.365i	0.568605	+	0.324066i
$681$	−21.7488	−	12.5567i	−0.0319365	−	0.0184386i
$682$	−68.1781	+	390.909i	−0.0999679	+	0.573180i
$683$	401.145	+	107.487i	0.587328	+	0.157374i	0.540232	−	0.841516i	$-0.318337\pi$
$683$	401.145	+	107.487i	0.587328	+	0.157374i	0.0470965	+	0.998890i	$0.485003\pi$
$684$	653.242	+	1387.38i	0.955032	+	2.02833i
$685$	−12.3402	+	12.3402i	−0.0180148	+	0.0180148i
$686$	−397.995	−	558.745i	−0.580167	−	0.814497i
$687$		−	287.008i		−	0.417770i
$688$	180.958	+	254.384i	0.263020	+	0.369745i
$689$	389.551	+	674.722i	0.565386	+	0.979278i
$690$	50.8486	−	35.7457i	0.0736936	−	0.0518054i
$691$	482.480	−	129.280i	0.698234	−	0.187091i	0.107795	−	0.994173i	$-0.465621\pi$
$691$	482.480	−	129.280i	0.698234	−	0.187091i	0.590440	+	0.807082i	$0.298954\pi$
$692$	89.7980	−	129.266i	0.129766	−	0.186801i
$693$	79.1661	+	883.802i	0.114237	+	1.27533i
$694$	−486.179	+	581.599i	−0.700546	+	0.838039i
$695$	586.469	−	1015.79i	0.843841	−	1.46157i
$696$	310.686	+	307.237i	0.446388	+	0.441432i
$697$	440.273	−	254.192i	0.631669	−	0.364694i
$698$	254.721	+	695.810i	0.364930	+	0.996862i
$699$	−829.458	+	829.458i	−1.18663	+	1.18663i
$700$	131.552	+	224.838i	0.187931	+	0.321197i
$701$	815.801	−	815.801i	1.16377	−	1.16377i	0.180123	−	0.983644i	$-0.442350\pi$
$701$	815.801	−	815.801i	1.16377	−	1.16377i	0.983644	−	0.180123i	$-0.0576496\pi$
$702$	1417.17	+	657.631i	2.01876	+	0.936796i
$703$	−1018.42	+	587.987i	−1.44868	+	0.836397i
$704$	460.328	−	128.869i	0.653875	−	0.183053i
$705$	−573.030	+	992.517i	−0.812808	+	1.40783i
$706$	−368.855	+	32.9623i	−0.522457	+	0.0466887i
$707$	−177.180	+	124.610i	−0.250608	+	0.176252i
$708$	−1644.42	+	296.269i	−2.32263	+	0.418460i
$709$	816.282	−	218.722i	1.15131	−	0.308494i	0.367822	−	0.929896i	$-0.380103\pi$
$709$	816.282	−	218.722i	1.15131	−	0.308494i	0.783492	+	0.621402i	$0.213437\pi$
$710$	−238.895	+	1369.74i	−0.336471	+	1.92921i
$711$	−833.618	−	1443.87i	−1.17246	−	2.03076i
$712$	−690.841	−	180.984i	−0.970282	−	0.254190i
$713$		−	27.6576i		−	0.0387904i
$714$	517.407	−	437.633i	0.724659	−	0.612931i
$715$	594.809	−	594.809i	0.831900	−	0.831900i
$716$	−122.077	+	57.4792i	−0.170498	+	0.0802782i
$717$	1303.59	+	349.295i	1.81811	+	0.487161i
$718$	−452.780	−	644.084i	−0.630613	−	0.897052i
$719$	353.727	+	204.224i	0.491970	+	0.284039i	0.725392	−	0.688336i	$-0.241659\pi$
$719$	353.727	+	204.224i	0.491970	+	0.284039i	−0.233421	+	0.972376i	$0.574992\pi$
$720$	−661.391	+	1446.36i	−0.918598	+	2.00884i
$721$	−273.891	+	100.331i	−0.379876	+	0.139155i
$722$	−26.5713	−	297.338i	−0.0368023	−	0.411826i
$723$	537.996	−	144.156i	0.744117	−	0.199385i
$724$	38.5278	−	460.087i	0.0532152	−	0.635479i
$725$	−25.8063	+	96.3104i	−0.0355949	+	0.132842i
$726$	−228.491	−	624.158i	−0.314726	−	0.859721i
$727$	758.052			1.04271			0.521357	−	0.853339i	$-0.325426\pi$
$727$	758.052			1.04271			0.521357	+	0.853339i	$0.325426\pi$
$728$	−1009.02	+	376.022i	−1.38602	+	0.516514i
$729$			941.930i			1.29209i
$730$	−491.919	−	1343.75i	−0.673861	−	1.84076i
$731$	179.007	+	47.9648i	0.244880	+	0.0656153i
$732$	1078.97	+	1276.19i	1.47400	+	1.74343i
$733$	−18.2582	−	68.1405i	−0.0249089	−	0.0929611i	0.952352	−	0.305000i	$-0.0986564\pi$
$733$	−18.2582	−	68.1405i	−0.0249089	−	0.0929611i	−0.977261	+	0.212039i	$0.931990\pi$
$734$	27.2970	+	305.460i	0.0371894	+	0.416157i
$735$	1439.28	−	259.930i	1.95820	−	0.353646i
$736$	−30.0644	+	14.3612i	−0.0408484	+	0.0195126i
$737$	−171.383	+	296.844i	−0.232542	+	0.402774i
$738$	1044.83	+	1486.28i	1.41576	+	2.01393i
$739$	84.3525	−	314.808i	0.114144	−	0.425992i	−0.885077	−	0.465444i	$-0.845895\pi$
$739$	84.3525	−	314.808i	0.114144	−	0.425992i	0.999221	+	0.0394523i	$0.0125613\pi$
$740$	−1147.63	−	412.872i	−1.55085	−	0.557936i
$741$	−1565.24	−	1565.24i	−2.11234	−	2.11234i
$742$	100.696	+	558.236i	0.135709	+	0.752340i
$743$	235.260			0.316635			0.158318	−	0.987388i	$-0.449393\pi$
$743$	235.260			0.316635			0.158318	+	0.987388i	$0.449393\pi$
$744$	546.714	+	934.848i	0.734831	+	1.25652i
$745$	919.502	−	530.875i	1.23423	−	0.712583i
$746$	−184.476	+	1057.72i	−0.247287	+	1.41785i
$747$	−200.399	−	747.900i	−0.268272	−	1.00121i
$748$	161.900	−	233.057i	0.216443	−	0.311574i
$749$	340.433	−	734.023i	0.454517	−	0.980005i
$750$	933.309	−	83.4040i	1.24441	−	0.111205i
$751$	1085.97	+	626.985i	1.44603	+	0.834866i	0.998242	−	0.0592730i	$-0.0188782\pi$
$751$	1085.97	+	626.985i	1.44603	+	0.834866i	0.447789	+	0.894139i	$0.352212\pi$
$752$	391.378	−	473.539i	0.520449	−	0.629706i
$753$	−934.883	−	1619.27i	−1.24154	−	2.15042i
$754$	−373.870	−	173.492i	−0.495849	−	0.230096i
$755$	−187.075	−	187.075i	−0.247781	−	0.247781i
$756$	808.970	+	799.656i	1.07007	+	1.05775i
$757$	−749.884	−	749.884i	−0.990600	−	0.990600i	0.00935611	−	0.999956i	$-0.497022\pi$
$757$	−749.884	−	749.884i	−0.990600	−	0.990600i	−0.999956	+	0.00935611i	$0.997022\pi$
$758$	277.412	+	757.793i	0.365979	+	0.999727i
$759$	−19.8164	−	34.3230i	−0.0261085	−	0.0452213i
$760$	744.222	−	752.576i	0.979239	−	0.990232i
$761$	−150.685	−	86.9981i	−0.198009	−	0.114321i	0.397717	−	0.917508i	$-0.369802\pi$
$761$	−150.685	−	86.9981i	−0.198009	−	0.114321i	−0.595727	+	0.803187i	$0.703136\pi$
$762$	22.2451	−	26.6111i	0.0291930	−	0.0349227i
$763$	127.303	+	181.009i	0.166845	+	0.237233i
$764$	−25.0937	−	139.281i	−0.0328452	−	0.182305i
$765$	244.357	+	911.953i	0.319421	+	1.19210i
$766$	−442.610	+	311.148i	−0.577820	+	0.406198i
$767$	1364.97	−	788.066i	1.77962	−	1.02747i
$768$	732.318	−	1079.71i	0.953539	−	1.40588i
$769$	1395.34			1.81449			0.907245	−	0.420602i	$-0.138181\pi$
$769$	1395.34			1.81449			0.907245	+	0.420602i	$0.138181\pi$
$770$	554.044	−	261.011i	0.719538	−	0.338975i
$771$	−495.004	−	495.004i	−0.642029	−	0.642029i
$772$	105.380	−	292.916i	0.136502	−	0.379424i
$773$	72.1216	−	269.162i	0.0933009	−	0.348204i	−0.903455	−	0.428682i	$-0.858978\pi$
$773$	72.1216	−	269.162i	0.0933009	−	0.348204i	0.996756	+	0.0804782i	$0.0256447\pi$
$774$	−113.789	+	652.425i	−0.147014	+	0.842927i
$775$	−123.564	+	214.019i	−0.159438	+	0.276154i
$776$	840.979	−	230.378i	1.08374	−	0.296879i
$777$	−1190.81	+	1425.13i	−1.53257	+	1.83414i
$778$	−575.682	−	481.232i	−0.739951	−	0.618550i
$779$	−312.928	−	1167.86i	−0.401705	−	1.49918i
$780$	191.578	−	2287.76i	0.245613	−	2.93303i
$781$	856.369	+	229.463i	1.09650	+	0.293807i
$782$	−8.32558	+	17.9413i	−0.0106465	+	0.0229429i
$783$			435.388i			0.556051i
$784$	−783.947	+	9.07940i	−0.999933	+	0.0115809i
$785$	−365.295			−0.465344
$786$	453.610	+	210.495i	0.577112	+	0.267806i
$787$	105.020	−	391.942i	0.133444	−	0.498020i	−0.866555	−	0.499081i	$-0.833671\pi$
$787$	105.020	−	391.942i	0.133444	−	0.498020i	0.999999	+	0.00106099i	$0.000337723\pi$
$788$	59.2025	−	706.977i	0.0751301	−	0.897179i
$789$	−1067.86	+	286.133i	−1.35344	+	0.362652i
$790$	−738.037	+	882.888i	−0.934223	+	1.11758i
$791$	458.984	+	383.517i	0.580258	+	0.484851i
$792$	881.056	+	502.142i	1.11244	+	0.634018i
$793$	−1365.20	−	788.199i	−1.72156	−	0.993946i
$794$	−637.133	−	111.122i	−0.802434	−	0.139952i
$795$	−1168.16	−	313.009i	−1.46939	−	0.393722i
$796$	−96.4762	+	268.167i	−0.121201	+	0.336893i
$797$	−51.2787	+	51.2787i	−0.0643396	+	0.0643396i	−0.738544	−	0.674205i	$-0.764487\pi$
$797$	−51.2787	+	51.2787i	−0.0643396	+	0.0643396i	0.674205	+	0.738544i	$0.264487\pi$
$798$	−686.852	−	1457.97i	−0.860716	−	1.82703i
$799$		−	364.695i		−	0.456439i
$800$	296.805	+	23.1870i	0.371006	+	0.0289838i
$801$	−757.517	−	1312.06i	−0.945714	−	1.63803i
$802$	335.872	+	477.781i	0.418793	+	0.595737i
$803$	−881.343	+	236.155i	−1.09756	+	0.294091i
$804$	165.872	+	920.658i	0.206308	+	1.14510i
$805$	−34.9168	+	24.5568i	−0.0433749	+	0.0305054i
$806$	−783.777	−	655.186i	−0.972428	−	0.812886i
$807$	−291.535	+	504.954i	−0.361258	+	0.625717i
$808$	1.38175	+	247.552i	0.00171009	+	0.306376i
$809$	451.634	−	260.751i	0.558262	−	0.322313i	−0.194186	−	0.980965i	$-0.562206\pi$
$809$	451.634	−	260.751i	0.558262	−	0.322313i	0.752448	+	0.658652i	$0.228873\pi$
$810$	−597.170	+	218.611i	−0.737247	+	0.269891i
$811$	649.211	−	649.211i	0.800507	−	0.800507i	−0.182667	−	0.983175i	$-0.558473\pi$
$811$	649.211	−	649.211i	0.800507	−	0.800507i	0.983175	+	0.182667i	$0.0584732\pi$
$812$	−213.418	−	210.960i	−0.262830	−	0.259803i
$813$	−245.017	+	245.017i	−0.301373	+	0.301373i
$814$	−327.352	+	705.432i	−0.402152	+	0.866624i
$815$	148.115	−	85.5145i	0.181737	−	0.104926i
$816$	−73.2400	−	771.005i	−0.0897548	−	0.944860i
$817$	220.371	−	381.693i	0.269731	−	0.467188i
$818$	90.9847	+	1018.14i	0.111228	+	1.24467i
$819$	−2072.35	−	961.138i	−2.53035	−	1.17355i
$820$	715.410	−	1029.85i	0.872451	−	1.25591i
$821$	−1042.70	+	279.392i	−1.27004	+	0.340307i	−0.830047	−	0.557693i	$-0.811687\pi$
$821$	−1042.70	+	279.392i	−1.27004	+	0.340307i	−0.439995	+	0.898000i	$0.645020\pi$
$822$	29.9184	+	5.21805i	0.0363971	+	0.00634800i
$823$	582.053	+	1008.15i	0.707233	+	1.22496i	0.965879	+	0.258992i	$0.0833903\pi$
$823$	582.053	+	1008.15i	0.707233	+	1.22496i	−0.258646	+	0.965972i	$0.583276\pi$
$824$	−84.4810	+	322.476i	−0.102525	+	0.391355i
$825$			354.130i			0.429248i
$826$	1129.32	−	203.709i	1.36721	−	0.246621i
$827$	755.728	−	755.728i	0.913818	−	0.913818i	−0.0827518	−	0.996570i	$-0.526371\pi$
$827$	755.728	−	755.728i	0.913818	−	0.913818i	0.996570	+	0.0827518i	$0.0263709\pi$
$828$	−66.5097	−	23.9277i	−0.0803257	−	0.0288981i
$829$	−889.368	−	238.305i	−1.07282	−	0.287461i	−0.321169	−	0.947022i	$-0.604076\pi$
$829$	−889.368	−	238.305i	−1.07282	−	0.287461i	−0.751651	+	0.659561i	$0.770742\pi$
$830$	−437.195	+	307.341i	−0.526742	+	0.370291i
$831$	−1408.07	−	812.951i	−1.69443	−	0.978280i
$832$	−305.224	+	1192.19i	−0.366856	+	1.43292i
$833$	−355.283	+	300.633i	−0.426511	+	0.360904i
$834$	−2033.10	+	181.685i	−2.43777	+	0.217848i
$835$	−775.412	+	207.771i	−0.928637	+	0.248828i
$836$	−435.727	−	515.372i	−0.521205	−	0.616474i
$837$	−279.297	+	1042.35i	−0.333688	+	1.24534i
$838$	1184.85	−	433.749i	1.41391	−	0.517601i
$839$	−352.385			−0.420006			−0.210003	−	0.977701i	$-0.567347\pi$
$839$	−352.385			−0.420006			−0.210003	+	0.977701i	$0.567347\pi$
$840$	694.793	−	1520.25i	0.827135	−	1.80982i
$841$			726.138i			0.863423i
$842$	−593.676	+	217.332i	−0.705078	+	0.258114i
$843$	1921.91	+	514.975i	2.27985	+	0.610884i
$844$	−64.1458	+	766.009i	−0.0760021	+	0.907593i
$845$	304.306	+	1135.69i	0.360126	+	1.34401i
$846$	1298.12	−	116.004i	1.53442	−	0.137121i
$847$	157.013	+	428.628i	0.185376	+	0.506054i
$848$	589.564	+	269.595i	0.695241	+	0.317919i
$849$	−899.748	+	1558.41i	−1.05977	+	1.83558i
$850$	144.580	−	101.638i	0.170094	−	0.119574i
$851$	14.0292	−	52.3575i	0.0164855	−	0.0615247i
$852$	2189.13	−	1030.74i	2.56940	−	1.20979i
$853$	1066.71	+	1066.71i	1.25054	+	1.25054i	0.955477	+	0.295067i	$0.0953418\pi$
$853$	1066.71	+	1066.71i	1.25054	+	1.25054i	0.295067	+	0.955477i	$0.404658\pi$
$854$	−741.201	−	876.311i	−0.867916	−	1.02613i
$855$	2245.36			2.62615
$856$	−466.820	−	798.234i	−0.545351	−	0.932516i
$857$	−633.873	+	365.967i	−0.739642	+	0.427032i	−0.821939	−	0.569576i	$-0.807108\pi$
$857$	−633.873	+	365.967i	−0.739642	+	0.427032i	0.0822974	+	0.996608i	$0.473774\pi$
$858$	−1442.10	−	251.516i	−1.68077	−	0.293142i
$859$	−184.333	−	687.941i	−0.214591	−	0.800863i	−0.986310	−	0.164900i	$-0.947270\pi$
$859$	−184.333	−	687.941i	−0.214591	−	0.800863i	0.771720	−	0.635963i	$-0.219397\pi$
$860$	449.862	−	81.0499i	0.523095	−	0.0942441i
$861$	−1098.43	−	1561.83i	−1.27576	−	1.81397i
$862$	134.065	+	1500.21i	0.155528	+	1.74039i
$863$	−480.367	−	277.340i	−0.556625	−	0.321367i	0.195165	−	0.980770i	$-0.437476\pi$
$863$	−480.367	−	277.340i	−0.556625	−	0.321367i	−0.751790	+	0.659403i	$0.770809\pi$
$864$	1278.08	−	237.640i	1.47926	−	0.275047i
$865$	−115.232	−	199.587i	−0.133216	−	0.230736i
$866$	637.582	−	1373.97i	0.736238	−	1.58657i
$867$	716.337	+	716.337i	0.826224	+	0.826224i
$868$	−375.608	−	641.959i	−0.432728	−	0.739584i
$869$	518.840	+	518.840i	0.597054	+	0.597054i
$870$	600.794	−	219.938i	0.690568	−	0.252802i
$871$	−441.213	−	764.203i	−0.506559	−	0.877385i
$872$	252.902	−	1.41161i	0.290025	−	0.00161882i
$873$	1601.99	+	924.909i	1.83504	+	1.05946i
$874$	36.0903	+	30.1691i	0.0412933	+	0.0345185i
$875$	−640.969	+	57.4144i	−0.732535	+	0.0656164i
$876$	−1420.73	+	2045.17i	−1.62184	+	2.33467i
$877$	264.868	+	988.502i	0.302016	+	1.12714i	0.935483	+	0.353371i	$0.114965\pi$
$877$	264.868	+	988.502i	0.302016	+	1.12714i	−0.633467	+	0.773770i	$0.718369\pi$
$878$	−81.0802	−	115.337i	−0.0923464	−	0.131363i
$879$	238.249	−	137.553i	0.271046	−	0.156488i
$880$	116.410	−	690.191i	0.132284	−	0.784308i
$881$	−308.332			−0.349980			−0.174990	−	0.984570i	$-0.555989\pi$
$881$	−308.332			−0.349980			−0.174990	+	0.984570i	$0.555989\pi$
$882$	−1183.10	−	1168.99i	−1.34138	−	1.32538i
$883$	385.418	+	385.418i	0.436487	+	0.436487i	0.890828	−	0.454341i	$-0.150125\pi$
$883$	385.418	+	385.418i	0.436487	+	0.436487i	−0.454341	+	0.890828i	$0.650125\pi$
$884$	311.206	+	660.951i	0.352043	+	0.747683i
$885$	−633.220	+	2363.21i	−0.715503	+	2.67029i
$886$	1510.27	+	263.406i	1.70460	+	0.297298i
$887$	56.3871	−	97.6653i	0.0635706	−	0.110107i	−0.832488	−	0.554042i	$-0.813085\pi$
$887$	56.3871	−	97.6653i	0.0635706	−	0.110107i	0.896059	+	0.443935i	$0.146418\pi$
$888$	560.768	+	2047.04i	0.631496	+	2.30523i
$889$	−15.2737	+	18.2792i	−0.0171808	+	0.0205616i
$890$	−670.661	+	802.290i	−0.753552	+	0.901449i
$891$	104.949	+	391.674i	0.117788	+	0.439589i
$892$	−313.331	+	264.909i	−0.351268	+	0.296983i
$893$	−837.780	−	224.483i	−0.938164	−	0.251380i
$894$	−1676.04	−	777.756i	−1.87476	−	0.869973i
$895$			197.571i			0.220749i
$896$	−502.789	+	741.633i	−0.561148	+	0.827716i
$897$	102.031			0.113747
$898$	109.786	−	236.585i	0.122256	−	0.263458i
$899$	73.6824	−	274.986i	0.0819604	−	0.305880i
$900$	407.764	+	482.298i	0.453071	+	0.535887i
$901$	371.729	−	99.6044i	0.412574	−	0.110549i
$902$	−613.458	−	512.811i	−0.680109	−	0.568526i
$903$	119.447	−	685.714i	0.132278	−	0.759373i
$904$	659.280	−	180.604i	0.729292	−	0.199783i
$905$	−585.459	−	338.015i	−0.646916	−	0.373497i
$906$	−79.1048	+	453.559i	−0.0873121	+	0.500617i
$907$	−503.413	−	134.889i	−0.555030	−	0.148720i	−0.0296081	−	0.999562i	$-0.509426\pi$
$907$	−503.413	−	134.889i	−0.555030	−	0.148720i	−0.525422	+	0.850842i	$0.676093\pi$
$908$	17.8334	−	8.39678i	0.0196403	−	0.00924755i
$909$	−371.355	+	371.355i	−0.408531	+	0.408531i
$910$	−131.244	+	1571.23i	−0.144224	+	1.72662i
$911$			968.776i			1.06342i	0.846926	+	0.531710i	$0.178450\pi$
$911$			968.776i			1.06342i	−0.846926	+	0.531710i	$0.821550\pi$
$912$	−1816.24	−	306.334i	−1.99149	−	0.335892i
$913$	170.381	+	295.109i	0.186617	+	0.323230i
$914$	−46.6033	+	32.7614i	−0.0509883	+	0.0358440i
$915$	2363.61	−	633.327i	2.58318	−	0.692160i
$916$	185.011	+	128.523i	0.201977	+	0.140308i
$917$	−311.562	−	144.499i	−0.339762	−	0.157578i
$918$	494.950	−	592.092i	0.539161	−	0.644981i
$919$	−174.458	+	302.170i	−0.189834	+	0.328803i	−0.945195	−	0.326507i	$-0.894128\pi$
$919$	−174.458	+	302.170i	−0.189834	+	0.328803i	0.755360	+	0.655309i	$0.227462\pi$
$920$	0.272301	+	48.7849i	0.000295979	+	0.0530271i
$921$	2588.81	−	1494.65i	2.81087	−	1.62286i
$922$	249.906	+	682.655i	0.271047	+	0.740407i
$923$	−1613.92	+	1613.92i	−1.74856	+	1.74856i
$924$	−926.086	−	527.550i	−1.00226	−	0.570941i
$925$	−342.475	+	342.475i	−0.370243	+	0.370243i
$926$	733.460	+	340.358i	0.792073	+	0.367557i
$927$	−612.453	+	353.600i	−0.660683	+	0.381446i
$928$	−337.176	+	62.6928i	−0.363336	+	0.0675569i
$929$	−455.370	+	788.724i	−0.490172	+	0.849003i	−0.999936	−	0.0113110i	$-0.996400\pi$
$929$	−455.370	+	788.724i	−0.490172	+	0.849003i	0.509764	+	0.860314i	$0.329733\pi$
$930$	1579.43	−	141.144i	1.69831	−	0.151767i
$931$	471.927	+	1001.21i	0.506903	+	1.07541i
$932$	−163.252	−	906.117i	−0.175163	−	0.972228i
$933$	1446.46	−	387.577i	1.55033	−	0.415410i
$934$	−200.966	+	1152.27i	−0.215167	+	1.23369i
$935$	−207.754	−	359.841i	−0.222197	−	0.384857i
$936$	−2253.64	+	1317.96i	−2.40773	+	1.40808i
$937$		−	1479.64i		−	1.57913i	−0.613670	−	0.789563i	$-0.710307\pi$
$937$		−	1479.64i		−	1.57913i	0.613670	−	0.789563i	$-0.289693\pi$
$938$	−114.050	−	632.268i	−0.121588	−	0.674060i
$939$	−939.897	+	939.897i	−1.00095	+	1.00095i
$940$	−383.191	−	813.836i	−0.407650	−	0.865783i
$941$	−1303.04	−	349.147i	−1.38474	−	0.371039i	−0.511896	−	0.859047i	$-0.671057\pi$
$941$	−1303.04	−	349.147i	−1.38474	−	0.371039i	−0.872839	+	0.488008i	$0.837724\pi$
$942$	365.592	+	520.058i	0.388102	+	0.552078i
$943$	48.2633	+	27.8648i	0.0511806	+	0.0295491i
$944$	545.394	−	1192.70i	0.577748	−	1.26345i
$945$	1563.92	−	572.887i	1.65494	−	0.606230i
$946$	−25.9432	−	290.310i	−0.0274241	−	0.306881i
$947$	1765.37	−	473.030i	1.86417	−	0.499504i	0.864181	−	0.503180i	$-0.167837\pi$
$947$	1765.37	−	473.030i	1.86417	−	0.499504i	0.999993	+	0.00367631i	$0.00117021\pi$
$948$	1995.57	+	167.110i	2.10504	+	0.176276i
$949$	607.963	−	2268.95i	0.640635	−	2.39088i
$950$	−144.489	−	394.693i	−0.152093	−	0.415466i
$951$	−847.528			−0.891197
$952$	50.4106	+	529.503i	0.0529523	+	0.556200i
$953$		−	1022.54i		−	1.07297i	−0.843909	−	0.536487i	$-0.819751\pi$
$953$		−	1022.54i		−	1.07297i	0.843909	−	0.536487i	$-0.180249\pi$
$954$	472.780	+	1291.47i	0.495576	+	1.35374i
$955$	−200.162	−	53.6331i	−0.209593	−	0.0561603i
$956$	−808.909	+	683.901i	−0.846139	+	0.715377i
$957$	−105.585	−	394.050i	−0.110330	−	0.411756i
$958$	−127.168	−	1423.04i	−0.132743	−	1.48543i
$959$	−20.5482	−	3.57938i	−0.0214267	−	0.00373240i
$960$	−973.548	−	1643.59i	−1.01411	−	1.71207i
$961$	−127.698	+	221.180i	−0.132881	+	0.230156i
$962$	−1151.40	−	1637.87i	−1.19688	−	1.70257i
$963$	507.732	−	1894.88i	0.527240	−	1.96769i
$964$	−147.990	+	411.356i	−0.153517	+	0.426718i
$965$	−322.304	−	322.304i	−0.333994	−	0.333994i
$966$	69.9059	+	25.1330i	0.0723663	+	0.0260176i
$967$	−434.861			−0.449701			−0.224851	−	0.974393i	$-0.572189\pi$
$967$	−434.861			−0.449701			−0.224851	+	0.974393i	$0.572189\pi$
$968$	504.662	+	132.209i	0.521345	+	0.136580i
$969$	−946.924	+	546.707i	−0.977218	+	0.564197i
$970$	219.366	−	1257.77i	0.226151	−	1.29667i
$971$	−48.7552	−	181.957i	−0.0502113	−	0.187391i	0.936265	−	0.351294i	$-0.114258\pi$
$971$	−48.7552	−	181.957i	−0.0502113	−	0.187391i	−0.986476	+	0.163903i	$0.947592\pi$
$972$	−292.227	−	203.003i	−0.300645	−	0.208851i
$973$	1396.27	−	125.070i	1.43501	−	0.128541i
$974$	−506.074	+	45.2247i	−0.519583	+	0.0464319i
$975$	−789.538	−	455.840i	−0.809782	−	0.467528i
$976$	−1305.82	+	124.044i	−1.33793	+	0.127094i
$977$	535.246	+	927.073i	0.547846	+	0.948897i	0.998422	+	0.0561590i	$0.0178854\pi$
$977$	535.246	+	927.073i	0.547846	+	0.948897i	−0.450576	+	0.892738i	$0.648781\pi$
$978$	−269.980	−	125.283i	−0.276053	−	0.128101i
$979$	471.475	+	471.475i	0.481589	+	0.481589i
$980$	−476.954	+	1044.18i	−0.486688	+	1.06549i
$981$	379.380	+	379.380i	0.386728	+	0.386728i
$982$	−110.904	−	302.953i	−0.112937	−	0.308506i
$983$	728.499	+	1261.80i	0.741098	+	1.28362i	0.951996	+	0.306111i	$0.0990278\pi$
$983$	728.499	+	1261.80i	0.741098	+	1.28362i	−0.210898	+	0.977508i	$0.567639\pi$
$984$	−2182.15	+	12.1800i	−2.21763	+	0.0123781i
$985$	−899.626	−	519.399i	−0.913326	−	0.527309i
$986$	−130.575	+	156.202i	−0.132429	+	0.158420i
$987$	−1364.27	+	122.204i	−1.38224	+	0.123813i
$988$	1709.90	−	308.067i	1.73067	−	0.311809i
$989$	5.25796	+	19.6230i	0.00531644	+	0.0198412i
$990$	1214.76	−	853.953i	1.22703	−	0.862579i
$991$	−405.595	+	234.170i	−0.409278	+	0.236297i	−0.690480	−	0.723352i	$-0.742601\pi$
$991$	−405.595	+	234.170i	−0.409278	+	0.236297i	0.281201	+	0.959649i	$0.409267\pi$
$992$	−847.440	−	66.2038i	−0.854274	−	0.0667377i
$993$	−835.499			−0.841389
$994$	−1503.31	+	708.211i	−1.51239	+	0.712486i
$995$	295.072	+	295.072i	0.296555	+	0.296555i
$996$	875.102	+	314.828i	0.878616	+	0.316093i
$997$	−16.1417	+	60.2416i	−0.0161903	+	0.0604229i	−0.973548	−	0.228481i	$-0.926624\pi$
$997$	−16.1417	+	60.2416i	−0.0161903	+	0.0604229i	0.957358	+	0.288904i	$0.0932908\pi$
$998$	135.937	−	779.411i	0.136209	−	0.780973i
$999$	−1057.45	+	1831.56i	−1.05851	+	1.83339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.3.u.a.107.20	yes	120
7.4	even	3	inner	112.3.u.a.11.22	✓	120
16.3	odd	4	inner	112.3.u.a.51.22	yes	120
112.67	odd	12	inner	112.3.u.a.67.20	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.3.u.a.11.22	✓	120	7.4	even	3	inner
112.3.u.a.51.22	yes	120	16.3	odd	4	inner
112.3.u.a.67.20	yes	120	112.67	odd	12	inner
112.3.u.a.107.20	yes	120	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	112.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841863 - 1.81419i) q^{2} +(-1.31900 + 4.92258i) q^{3} +(-2.58253 - 3.05459i) q^{4} +(-5.65734 + 1.51588i) q^{5} +(7.82005 + 6.53704i) q^{6} +(-5.37161 - 4.48841i) q^{7} +(-7.71573 + 2.11365i) q^{8} +(-14.6978 - 8.48576i) q^{9} +(-2.01262 + 11.5396i) q^{10} +(7.21466 + 1.93316i) q^{11} +(18.4428 - 8.68372i) q^{12} +(-13.5968 + 13.5968i) q^{13} +(-12.6650 + 5.96648i) q^{14} -29.8481i q^{15} +(-2.66103 + 15.7772i) q^{16} +(4.74908 + 8.22565i) q^{17} +(-27.7682 + 19.5206i) q^{18} +(21.8193 - 5.84646i) q^{19} +(19.2407 + 13.3660i) q^{20} +(29.1797 - 20.5220i) q^{21} +(9.58086 - 11.4613i) q^{22} +(-0.520600 + 0.901705i) q^{23} +(-0.227560 - 40.7692i) q^{24} +(8.05699 - 4.65170i) q^{25} +(13.2205 + 36.1137i) q^{26} +(28.7259 - 28.7259i) q^{27} +(0.162135 + 27.9995i) q^{28} +(-7.57831 + 7.57831i) q^{29} +(-54.1500 - 25.1280i) q^{30} +(-23.0044 + 13.2816i) q^{31} +(26.3825 + 18.1098i) q^{32} +(-19.0323 + 32.9649i) q^{33} +(18.9209 - 1.69084i) q^{34} +(37.1929 + 17.2497i) q^{35} +(12.0370 + 66.8104i) q^{36} +(-50.2858 + 13.4740i) q^{37} +(7.76228 - 44.5061i) q^{38} +(-48.9971 - 84.8654i) q^{39} +(40.4465 - 23.6538i) q^{40} -53.5245i q^{41} +(-12.6653 - 70.2140i) q^{42} +(13.7966 - 13.7966i) q^{43} +(-12.7271 - 27.0303i) q^{44} +(96.0136 + 25.7268i) q^{45} +(1.19759 + 1.70358i) q^{46} +(-33.2522 - 19.1982i) q^{47} +(-74.1544 - 33.9092i) q^{48} +(8.70842 + 48.2199i) q^{49} +(-1.65617 - 18.5330i) q^{50} +(-46.7554 + 12.5281i) q^{51} +(76.6468 + 6.41843i) q^{52} +(10.4867 - 39.1369i) q^{53} +(-27.9309 - 76.2975i) q^{54} -43.7462 q^{55} +(50.9328 + 23.2776i) q^{56} +115.118i q^{57} +(7.36856 + 20.1283i) q^{58} +(-79.1744 - 21.2147i) q^{59} +(-91.1738 + 77.0839i) q^{60} +(21.2183 + 79.1878i) q^{61} +(4.72873 + 52.9155i) q^{62} +(40.8631 + 111.552i) q^{63} +(55.0650 - 32.6167i) q^{64} +(56.3106 - 97.5328i) q^{65} +(43.7818 + 62.2799i) q^{66} +(-11.8774 + 44.3272i) q^{67} +(12.8613 - 35.7495i) q^{68} +(-3.75204 - 3.75204i) q^{69} +(62.6055 - 52.9529i) q^{70} +118.698 q^{71} +(131.340 + 34.4079i) q^{72} +(-105.794 + 61.0800i) q^{73} +(-17.8893 + 102.571i) q^{74} +(12.2712 + 45.7967i) q^{75} +(-74.2075 - 51.5502i) q^{76} +(-30.0775 - 42.7665i) q^{77} +(-195.210 + 17.4447i) q^{78} +(85.0760 + 49.1187i) q^{79} +(-8.86194 - 93.2906i) q^{80} +(27.1443 + 47.0153i) q^{81} +(-97.1033 - 45.0602i) q^{82} +(32.2600 + 32.2600i) q^{83} +(-138.044 - 36.1333i) q^{84} +(-39.3363 - 39.3363i) q^{85} +(-13.4147 - 36.6444i) q^{86} +(-27.3090 - 47.3006i) q^{87} +(-59.7524 + 0.333518i) q^{88} +(77.3095 + 44.6346i) q^{89} +(127.503 - 152.528i) q^{90} +(134.065 - 12.0088i) q^{91} +(4.09880 - 0.738466i) q^{92} +(-35.0369 - 130.759i) q^{93} +(-62.8228 + 44.1634i) q^{94} +(-114.577 + 66.1508i) q^{95} +(-123.945 + 105.983i) q^{96} -108.995 q^{97} +(94.8112 + 24.7959i) q^{98} +(-89.6350 - 89.6350i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{7} - 20 q^{8} + 16 q^{10} + 14 q^{11} - 2 q^{12} - 8 q^{13} + 20 q^{14} + 8 q^{16} - 4 q^{17} - 38 q^{18} - 2 q^{19} + 72 q^{20} + 14 q^{21}+ \cdots - 776 q^{99}+O(q^{100}) \) 120 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^7 - 20 * q^8 + 16 * q^10 + 14 * q^11 - 2 * q^12 - 8 * q^13 + 20 * q^14 + 8 * q^16 - 4 * q^17 - 38 * q^18 - 2 * q^19 + 72 * q^20 + 14 * q^21 + 52 * q^22 - 68 * q^23 - 142 * q^24 - 2 * q^26 - 44 * q^27 - 62 * q^28 - 40 * q^29 - 14 * q^30 + 88 * q^32 - 4 * q^33 + 168 * q^34 + 94 * q^35 - 272 * q^36 - 50 * q^37 + 138 * q^38 - 4 * q^39 - 206 * q^40 - 198 * q^42 - 104 * q^43 + 2 * q^44 - 84 * q^45 - 76 * q^46 - 856 * q^48 - 8 * q^49 - 320 * q^50 + 114 * q^51 + 76 * q^52 - 82 * q^53 + 350 * q^54 - 16 * q^55 + 8 * q^56 - 6 * q^58 + 62 * q^59 + 318 * q^60 - 2 * q^61 + 876 * q^62 + 112 * q^64 - 4 * q^65 + 162 * q^66 - 66 * q^67 + 192 * q^68 + 28 * q^69 + 112 * q^70 + 496 * q^71 + 248 * q^72 + 178 * q^74 + 12 * q^75 - 308 * q^76 + 94 * q^77 - 140 * q^78 + 204 * q^80 + 248 * q^81 + 266 * q^82 - 488 * q^83 + 620 * q^84 + 92 * q^85 - 408 * q^86 - 4 * q^87 - 370 * q^88 - 404 * q^90 - 488 * q^91 + 900 * q^92 - 38 * q^93 - 150 * q^94 + 768 * q^96 - 16 * q^97 + 432 * q^98 - 776 * q^99

Introduction

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