LMFDB - Embedded newform 175.4.x.a.103.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,4,Mod(3,175)] 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("175.3"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([21, 10])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$928$
Relative dimension:	$58$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			103.12
Character	$\chi$	$=$	175.103
Dual form			175.4.x.a.17.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.65654 - 0.191631i) q^{2} +(-3.56883 - 4.40714i) q^{3} +(5.37736 + 0.565184i) q^{4} +(-7.45211 - 8.33463i) q^{5} +(12.2050 + 16.7988i) q^{6} +(5.89045 + 17.5585i) q^{7} +(9.37758 + 1.48526i) q^{8} +(-1.07270 + 5.04663i) q^{9} +(25.6517 + 31.9039i) q^{10} +(45.0384 - 9.57321i) q^{11} +(-16.7000 - 25.7158i) q^{12} +(34.9937 + 17.8302i) q^{13} +(-18.1739 - 65.3323i) q^{14} +(-10.1366 + 62.5873i) q^{15} +(-76.3155 - 16.2214i) q^{16} +(19.9528 + 51.9788i) q^{17} +(4.88944 - 18.2476i) q^{18} +(-3.07560 - 29.2623i) q^{19} +(-35.3621 - 49.0301i) q^{20} +(56.3609 - 88.6234i) q^{21} +(-166.519 + 26.3740i) q^{22} +(1.05355 - 20.1029i) q^{23} +(-26.9212 - 46.6289i) q^{24} +(-13.9321 + 124.221i) q^{25} +(-124.539 - 71.9027i) q^{26} +(-110.357 + 56.2297i) q^{27} +(21.7513 + 97.7479i) q^{28} +(159.008 - 218.856i) q^{29} +(49.0583 - 226.910i) q^{30} +(50.0497 - 112.413i) q^{31} +(202.574 + 54.2796i) q^{32} +(-202.925 - 164.325i) q^{33} +(-62.9974 - 193.886i) q^{34} +(102.448 - 179.943i) q^{35} +(-8.62054 + 26.5313i) q^{36} +(12.2917 - 7.98236i) q^{37} +(5.63846 + 107.588i) q^{38} +(-46.3065 - 217.855i) q^{39} +(-57.5036 - 89.2270i) q^{40} +(8.43713 - 2.74139i) q^{41} +(-223.069 + 313.254i) q^{42} +(-140.993 - 140.993i) q^{43} +(247.598 - 26.0236i) q^{44} +(50.0557 - 28.6675i) q^{45} +(-7.70469 + 73.3052i) q^{46} +(28.8124 + 11.0601i) q^{47} +(200.867 + 394.224i) q^{48} +(-273.605 + 206.855i) q^{49} +(74.7480 - 451.549i) q^{50} +(157.870 - 273.438i) q^{51} +(178.097 + 115.657i) q^{52} +(376.650 - 305.005i) q^{53} +(414.300 - 184.458i) q^{54} +(-415.420 - 304.038i) q^{55} +(29.1591 + 173.406i) q^{56} +(-117.987 + 117.987i) q^{57} +(-623.358 + 769.784i) q^{58} +(-181.296 + 201.350i) q^{59} +(-89.8812 + 330.826i) q^{60} +(204.406 - 184.048i) q^{61} +(-204.550 + 401.453i) q^{62} +(-94.9302 + 10.8919i) q^{63} +(-136.704 - 44.4177i) q^{64} +(-112.169 - 424.533i) q^{65} +(710.512 + 639.748i) q^{66} +(332.139 - 127.496i) q^{67} +(77.9158 + 290.786i) q^{68} +(-92.3563 + 67.1008i) q^{69} +(-409.087 + 638.336i) q^{70} +(562.908 + 408.976i) q^{71} +(-17.5549 + 45.7320i) q^{72} +(-473.477 + 729.091i) q^{73} +(-46.4749 + 26.8323i) q^{74} +(597.181 - 381.923i) q^{75} -159.092i q^{76} +(433.388 + 734.418i) q^{77} +(127.574 + 805.469i) q^{78} +(-500.071 - 1123.18i) q^{79} +(433.512 + 756.945i) q^{80} +(768.917 + 342.344i) q^{81} +(-31.3760 + 8.40718i) q^{82} +(-110.810 + 699.629i) q^{83} +(353.162 - 444.706i) q^{84} +(284.534 - 553.651i) q^{85} +(488.529 + 542.567i) q^{86} +(-1532.00 + 80.2887i) q^{87} +(436.570 - 22.8797i) q^{88} +(-368.430 - 409.183i) q^{89} +(-188.524 + 95.2317i) q^{90} +(-106.944 + 719.467i) q^{91} +(17.0272 - 107.505i) q^{92} +(-674.040 + 180.608i) q^{93} +(-103.234 - 45.9628i) q^{94} +(-220.971 + 243.700i) q^{95} +(-483.735 - 1086.49i) q^{96} +(-193.365 - 1220.86i) q^{97} +(1040.09 - 703.943i) q^{98} +237.561i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) $ 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−3.65654	−	0.191631i	−1.29278	−	0.0677518i	−0.606497	−	0.795086i	$-0.707426\pi$
$2$	−3.65654	−	0.191631i	−1.29278	−	0.0677518i	−0.686284	+	0.727334i	$0.740759\pi$
$3$	−3.56883	−	4.40714i	−0.686821	−	0.848154i	0.307830	−	0.951441i	$-0.400397\pi$
$3$	−3.56883	−	4.40714i	−0.686821	−	0.848154i	−0.994652	+	0.103288i	$0.967064\pi$
$4$	5.37736	+	0.565184i	0.672170	+	0.0706479i
$5$	−7.45211	−	8.33463i	−0.666537	−	0.745472i
$5$	−7.45211	−	8.33463i	−0.666537	−	0.745472i
$6$	12.2050	+	16.7988i	0.830446	+	1.14301i
$7$	5.89045	+	17.5585i	0.318054	+	0.948073i
$7$	5.89045	+	17.5585i	0.318054	+	0.948073i
$8$	9.37758	+	1.48526i	0.414435	+	0.0656400i
$9$	−1.07270	+	5.04663i	−0.0397294	+	0.186912i
$10$	25.6517	+	31.9039i	0.811179	+	1.00889i
$11$	45.0384	−	9.57321i	1.23451	−	0.262403i	0.455967	−	0.889997i	$-0.349293\pi$
$11$	45.0384	−	9.57321i	1.23451	−	0.262403i	0.778541	+	0.627594i	$0.215960\pi$
$12$	−16.7000	−	25.7158i	−0.401741	−	0.618626i
$13$	34.9937	+	17.8302i	0.746578	+	0.380401i	0.785516	−	0.618841i	$-0.212397\pi$
$13$	34.9937	+	17.8302i	0.746578	+	0.380401i	−0.0389379	+	0.999242i	$0.512397\pi$
$14$	−18.1739	−	65.3323i	−0.346941	−	1.24720i
$15$	−10.1366	+	62.5873i	−0.174483	+	1.07733i
$16$	−76.3155	−	16.2214i	−1.19243	−	0.253459i
$17$	19.9528	+	51.9788i	0.284663	+	0.741571i	0.999122	+	0.0418945i	$0.0133393\pi$
$17$	19.9528	+	51.9788i	0.284663	+	0.741571i	−0.714459	+	0.699677i	$0.753327\pi$
$18$	4.88944	−	18.2476i	0.0640251	−	0.238945i
$19$	−3.07560	−	29.2623i	−0.0371363	−	0.353328i	−0.997273	−	0.0737982i	$-0.976488\pi$
$19$	−3.07560	−	29.2623i	−0.0371363	−	0.353328i	0.960137	−	0.279530i	$-0.0901787\pi$
$20$	−35.3621	−	49.0301i	−0.395360	−	0.548174i
$21$	56.3609	−	88.6234i	0.585665	−	0.920915i
$22$	−166.519	+	26.3740i	−1.61373	+	0.255589i
$23$	1.05355	−	20.1029i	0.00955132	−	0.182250i	−0.989688	−	0.143243i	$-0.954247\pi$
$23$	1.05355	−	20.1029i	0.00955132	−	0.182250i	0.999239	−	0.0390074i	$-0.0124196\pi$
$24$	−26.9212	−	46.6289i	−0.228970	−	0.396587i
$25$	−13.9321	+	124.221i	−0.111457	+	0.993769i
$26$	−124.539	−	71.9027i	−0.939389	−	0.542357i
$27$	−110.357	+	56.2297i	−0.786600	+	0.400793i
$28$	21.7513	+	97.7479i	0.146807	+	0.659736i
$29$	159.008	−	218.856i	1.01817	−	1.40140i	0.104699	−	0.994504i	$-0.466612\pi$
$29$	159.008	−	218.856i	1.01817	−	1.40140i	0.913476	−	0.406893i	$-0.133388\pi$
$30$	49.0583	−	226.910i	0.298560	−	1.38093i
$31$	50.0497	−	112.413i	0.289974	−	0.651291i	−0.708547	−	0.705664i	$-0.750649\pi$
$31$	50.0497	−	112.413i	0.289974	−	0.651291i	0.998521	+	0.0543720i	$0.0173157\pi$
$32$	202.574	+	54.2796i	1.11907	+	0.299855i
$33$	−202.925	−	164.325i	−1.07044	−	0.866829i
$34$	−62.9974	−	193.886i	−0.317764	−	0.977976i
$35$	102.448	−	179.943i	0.494767	−	0.869026i
$36$	−8.62054	+	26.5313i	−0.0399099	+	0.122830i
$37$	12.2917	−	7.98236i	0.0546149	−	0.0354673i	−0.517043	−	0.855960i	$-0.672967\pi$
$37$	12.2917	−	7.98236i	0.0546149	−	0.0354673i	0.571658	+	0.820492i	$0.306301\pi$
$38$	5.63846	+	107.588i	0.0240705	+	0.459292i
$39$	−46.3065	−	217.855i	−0.190128	−	0.894480i
$40$	−57.5036	−	89.2270i	−0.227303	−	0.352701i
$41$	8.43713	−	2.74139i	0.0321380	−	0.0104423i	−0.292904	−	0.956142i	$-0.594622\pi$
$41$	8.43713	−	2.74139i	0.0321380	−	0.0104423i	0.325042	+	0.945700i	$0.394622\pi$
$42$	−223.069	+	313.254i	−0.819530	+	1.15086i
$43$	−140.993	−	140.993i	−0.500030	−	0.500030i	0.411417	−	0.911447i	$-0.365034\pi$
$43$	−140.993	−	140.993i	−0.500030	−	0.500030i	−0.911447	+	0.411417i	$0.865034\pi$
$44$	247.598	−	26.0236i	0.848338	−	0.0891639i
$45$	50.0557	−	28.6675i	0.165819	−	0.0949668i
$46$	−7.70469	+	73.3052i	−0.0246955	+	0.234962i
$47$	28.8124	+	11.0601i	0.0894196	+	0.0343250i	0.402667	−	0.915347i	$-0.368083\pi$
$47$	28.8124	+	11.0601i	0.0894196	+	0.0343250i	−0.313247	+	0.949672i	$0.601417\pi$
$48$	200.867	+	394.224i	0.604014	+	1.18544i
$49$	−273.605	+	206.855i	−0.797683	+	0.603077i
$50$	74.7480	−	451.549i	0.211419	−	1.27717i
$51$	157.870	−	273.438i	0.433454	−	0.750765i
$52$	178.097	+	115.657i	0.474953	+	0.308438i
$53$	376.650	−	305.005i	0.976166	−	0.790484i	−0.00163927	−	0.999999i	$-0.500522\pi$
$53$	376.650	−	305.005i	0.976166	−	0.790484i	0.977805	+	0.209515i	$0.0671885\pi$
$54$	414.300	−	184.458i	1.04406	−	0.464844i
$55$	−415.420	−	304.038i	−1.01846	−	0.745390i
$56$	29.1591	+	173.406i	0.0695811	+	0.413791i
$57$	−117.987	+	117.987i	−0.274171	+	0.274171i
$58$	−623.358	+	769.784i	−1.41122	+	1.74272i
$59$	−181.296	+	201.350i	−0.400046	+	0.444296i	−0.909188	−	0.416387i	$-0.863296\pi$
$59$	−181.296	+	201.350i	−0.400046	+	0.444296i	0.509142	+	0.860683i	$0.329963\pi$
$60$	−89.8812	+	330.826i	−0.193394	+	0.711824i
$61$	204.406	−	184.048i	0.429042	−	0.386311i	−0.426125	−	0.904665i	$-0.640121\pi$
$61$	204.406	−	184.048i	0.429042	−	0.386311i	0.855167	+	0.518353i	$0.173455\pi$
$62$	−204.550	+	401.453i	−0.418999	+	0.822331i
$63$	−94.9302	+	10.8919i	−0.189843	+	0.0217818i
$64$	−136.704	−	44.4177i	−0.266999	−	0.0867533i
$65$	−112.169	−	424.533i	−0.214044	−	0.810104i
$66$	710.512	+	639.748i	1.32512	+	1.19314i
$67$	332.139	−	127.496i	0.605631	−	0.232480i	−0.0361768	−	0.999345i	$-0.511518\pi$
$67$	332.139	−	127.496i	0.605631	−	0.232480i	0.641808	+	0.766865i	$0.278185\pi$
$68$	77.9158	+	290.786i	0.138951	+	0.518573i
$69$	−92.3563	+	67.1008i	−0.161136	+	0.117072i
$70$	−409.087	+	638.336i	−0.698503	+	1.08994i
$71$	562.908	+	408.976i	0.940913	+	0.683613i	0.948640	−	0.316357i	$-0.102460\pi$
$71$	562.908	+	408.976i	0.940913	+	0.683613i	−0.00772718	+	0.999970i	$0.502460\pi$
$72$	−17.5549	+	45.7320i	−0.0287342	+	0.0748551i
$73$	−473.477	+	729.091i	−0.759127	+	1.16895i	0.221897	+	0.975070i	$0.428775\pi$
$73$	−473.477	+	729.091i	−0.759127	+	1.16895i	−0.981025	+	0.193884i	$0.937892\pi$
$74$	−46.4749	+	26.8323i	−0.0730081	+	0.0421512i
$75$	597.181	−	381.923i	0.919420	−	0.588009i
$76$		−	159.092i		−	0.240121i
$77$	433.388	+	734.418i	0.641417	+	1.08694i
$78$	127.574	+	805.469i	0.185191	+	1.16925i
$79$	−500.071	−	1123.18i	−0.712182	−	1.59959i	−0.797561	−	0.603238i	$-0.793877\pi$
$79$	−500.071	−	1123.18i	−0.712182	−	1.59959i	0.0853790	−	0.996349i	$-0.472790\pi$
$80$	433.512	+	756.945i	0.605852	+	1.05786i
$81$	768.917	+	342.344i	1.05476	+	0.469607i
$82$	−31.3760	+	8.40718i	−0.0422549	+	0.0113222i
$83$	−110.810	+	699.629i	−0.146542	+	0.925232i	0.799377	+	0.600830i	$0.205163\pi$
$83$	−110.810	+	699.629i	−0.146542	+	0.925232i	−0.945919	+	0.324402i	$0.894837\pi$
$84$	353.162	−	444.706i	0.458727	−	0.577636i
$85$	284.534	−	553.651i	0.363083	−	0.706493i
$86$	488.529	+	542.567i	0.612552	+	0.680308i
$87$	−1532.00	+	80.2887i	−1.88790	+	0.0989408i
$88$	436.570	−	22.8797i	0.528847	−	0.0277157i
$89$	−368.430	−	409.183i	−0.438804	−	0.487341i	0.482659	−	0.875808i	$-0.339671\pi$
$89$	−368.430	−	409.183i	−0.438804	−	0.487341i	−0.921462	+	0.388468i	$0.873004\pi$
$90$	−188.524	+	95.2317i	−0.220802	+	0.111537i
$91$	−106.944	+	719.467i	−0.123195	+	0.828798i
$92$	17.0272	−	107.505i	0.0192957	−	0.121828i
$93$	−674.040	+	180.608i	−0.751555	+	0.201379i
$94$	−103.234	−	45.9628i	−0.113274	−	0.0504330i
$95$	−220.971	+	243.700i	−0.238644	+	0.263191i
$96$	−483.735	−	1086.49i	−0.514281	−	1.15509i
$97$	−193.365	−	1220.86i	−0.202405	−	1.27793i	−0.854362	−	0.519678i	$-0.826052\pi$
$97$	−193.365	−	1220.86i	−0.202405	−	1.27793i	0.651958	−	0.758255i	$-0.273948\pi$
$98$	1040.09	−	703.943i	1.07209	−	0.725602i
$99$			237.561i			0.241170i
$100$	−145.126	+	660.108i	−0.145126	+	0.660108i
$101$	409.809	−	236.603i	0.403738	−	0.233098i	−0.284358	−	0.958718i	$-0.591780\pi$
$101$	409.809	−	236.603i	0.403738	−	0.233098i	0.688096	+	0.725620i	$0.258447\pi$
$102$	−629.655	+	969.584i	−0.611227	+	0.941207i
$103$	23.3888	−	60.9298i	0.0223744	−	0.0582873i	−0.921938	−	0.387337i	$-0.873395\pi$
$103$	23.3888	−	60.9298i	0.0223744	−	0.0582873i	0.944313	+	0.329050i	$0.106728\pi$
$104$	301.674	+	219.179i	0.284438	+	0.206657i
$105$	−1158.65	+	190.684i	−1.07688	+	0.177227i
$106$	−1435.68	+	1043.08i	−1.31553	+	0.955785i
$107$	−341.515	−	1274.55i	−0.308556	−	1.15155i	−0.929841	−	0.367962i	$-0.880056\pi$
$107$	−341.515	−	1274.55i	−0.308556	−	1.15155i	0.621285	−	0.783585i	$-0.286611\pi$
$108$	−625.209	+	239.995i	−0.557044	+	0.213829i
$109$	−719.382	−	647.735i	−0.632150	−	0.569190i	0.289517	−	0.957173i	$-0.406505\pi$
$109$	−719.382	−	647.735i	−0.632150	−	0.569190i	−0.921667	+	0.387983i	$0.873172\pi$
$110$	1460.74	+	1191.33i	1.26614	+	1.03263i
$111$	−79.0465	−	25.6838i	−0.0675924	−	0.0219621i
$112$	−164.709	−	1435.54i	−0.138960	−	1.21112i
$113$	980.457	−	1924.25i	0.816227	−	1.60193i	0.0178008	−	0.999842i	$-0.494334\pi$
$113$	980.457	−	1924.25i	0.816227	−	1.60193i	0.798426	−	0.602093i	$-0.205666\pi$
$114$	454.033	−	408.813i	0.373018	−	0.335867i
$115$	−175.402	+	141.028i	−0.142229	+	0.114356i
$116$	978.738	−	1087.00i	0.783392	−	0.870045i
$117$	−127.520	+	157.474i	−0.100763	+	0.124432i
$118$	701.500	−	701.500i	0.547274	−	0.547274i
$119$	−795.142	+	656.520i	−0.612525	+	0.505741i
$120$	−188.015	+	571.862i	−0.143028	+	0.435030i
$121$	720.882	−	320.957i	0.541609	−	0.241140i
$122$	−782.689	+	633.809i	−0.580831	+	0.470347i
$123$	−42.1924	−	27.4000i	−0.0309297	−	0.0200860i
$124$	332.669	−	576.200i	0.240924	−	0.417293i
$125$	1139.16	−	809.590i	0.815117	−	0.579296i
$126$	349.203	−	21.6352i	0.246901	−	0.0152970i
$127$	1131.71	+	2221.10i	0.790729	+	1.55189i	0.833314	+	0.552800i	$0.186441\pi$
$127$	1131.71	+	2221.10i	0.790729	+	1.55189i	−0.0425847	+	0.999093i	$0.513559\pi$
$128$	−1074.98	−	412.644i	−0.742307	−	0.284945i
$129$	−118.196	+	1124.56i	−0.0806711	+	0.767534i
$130$	328.797	+	1573.81i	0.221826	+	1.06179i
$131$	2855.69	−	300.145i	1.90460	−	0.200182i	0.922166	−	0.386794i	$-0.126417\pi$
$131$	2855.69	−	300.145i	1.90460	−	0.200182i	0.982434	+	0.186612i	$0.0597508\pi$
$132$	−998.326	−	998.326i	−0.658281	−	0.658281i
$133$	495.688	−	226.371i	0.323170	−	0.147585i
$134$	−1238.91	+	402.547i	−0.798699	+	0.259513i
$135$	1291.05	+	500.755i	0.823078	+	0.319245i
$136$	109.907	+	517.071i	0.0692973	+	0.326018i
$137$	−119.831	−	2286.51i	−0.0747289	−	1.42591i	−0.736618	−	0.676309i	$-0.763578\pi$
$137$	−119.831	−	2286.51i	−0.0747289	−	1.42591i	0.661889	−	0.749602i	$-0.269755\pi$
$138$	350.563	−	227.658i	0.216245	−	0.140431i
$139$	425.263	−	1308.83i	0.259499	−	0.798655i	−0.733411	−	0.679785i	$-0.762073\pi$
$139$	425.263	−	1308.83i	0.259499	−	0.798655i	0.992910	−	0.118870i	$-0.0379271\pi$
$140$	652.600	−	909.716i	0.393962	−	0.549179i
$141$	−54.0834	−	166.452i	−0.0323025	−	0.0994167i
$142$	−1979.92	−	1603.31i	−1.17008	−	0.947511i
$143$	1746.75	+	468.041i	1.02148	+	0.273703i
$144$	163.726	−	367.736i	0.0947491	−	0.212810i
$145$	−3009.03	+	305.664i	−1.72335	+	0.175062i
$146$	1871.00	−	2575.21i	1.06058	−	1.45977i
$147$	1888.09	+	467.585i	1.05937	+	0.262352i
$148$	70.6087	−	35.9769i	0.0392162	−	0.0199817i
$149$	−693.724	−	400.522i	−0.381423	−	0.220215i	0.297014	−	0.954873i	$-0.404009\pi$
$149$	−693.724	−	400.522i	−0.381423	−	0.220215i	−0.678437	+	0.734658i	$0.737342\pi$
$150$	−2256.80	+	1282.08i	−1.22845	+	0.697875i
$151$	41.3152	+	71.5601i	0.0222661	+	0.0385661i	0.876944	−	0.480593i	$-0.159579\pi$
$151$	41.3152	+	71.5601i	0.0222661	+	0.0385661i	−0.854678	+	0.519159i	$0.826245\pi$
$152$	14.6206	−	278.978i	0.00780190	−	0.148869i
$153$	−283.721	+	44.9370i	−0.149918	+	0.0237447i
$154$	−1443.96	−	2768.48i	−0.755569	−	1.44864i
$155$	−1309.90	+	420.571i	−0.678798	+	0.217943i
$156$	−125.879	−	1197.66i	−0.0646050	−	0.614675i
$157$	245.248	−	915.279i	0.124668	−	0.465269i	−0.875159	−	0.483835i	$-0.839243\pi$
$157$	245.248	−	915.279i	0.124668	−	0.465269i	0.999828	+	0.0185662i	$0.00591014\pi$
$158$	1613.29	+	4202.77i	0.812320	+	2.11617i
$159$	−2688.40	−	571.436i	−1.34090	−	0.285018i
$160$	−1057.20	−	2092.88i	−0.522371	−	1.03410i
$161$	359.184	−	99.9164i	0.175824	−	0.0489100i
$162$	−2745.97	−	1399.14i	−1.33175	−	0.678561i
$163$	403.678	+	621.610i	0.193979	+	0.298701i	0.922255	−	0.386583i	$-0.126345\pi$
$163$	403.678	+	621.610i	0.193979	+	0.298701i	−0.728276	+	0.685284i	$0.759678\pi$
$164$	46.9189	−	9.97292i	0.0223399	−	0.00474850i
$165$	142.627	+	2915.87i	0.0672941	+	1.37576i
$166$	539.253	−	2536.98i	0.252133	−	1.18619i
$167$	−2423.98	−	383.921i	−1.12319	−	0.177896i	−0.432911	−	0.901437i	$-0.642514\pi$
$167$	−2423.98	−	383.921i	−1.12319	−	0.177896i	−0.690282	+	0.723540i	$0.742514\pi$
$168$	660.158	−	747.363i	0.303169	−	0.343216i
$169$	−384.718	−	529.519i	−0.175111	−	0.241019i
$170$	−1146.50	+	1969.92i	−0.517252	+	0.888741i
$171$	150.975	+	15.8682i	0.0675169	+	0.00709631i
$172$	−678.486	−	837.860i	−0.300779	−	0.371432i
$173$	−3618.13	−	189.618i	−1.59007	−	0.0833318i	−0.763363	−	0.645970i	$-0.776453\pi$
$173$	−3618.13	−	189.618i	−1.59007	−	0.0833318i	−0.826703	+	0.562638i	$0.809786\pi$
$174$	5617.20			2.44735
$175$	−2263.21	+	487.090i	−0.977615	+	0.210403i
$176$	−3592.42			−1.53857
$177$	1534.39	+	80.4139i	0.651592	+	0.0341485i
$178$	1268.77	+	1566.80i	0.534259	+	0.659754i
$179$	3326.03	+	349.580i	1.38882	+	0.145971i	0.769240	−	0.638960i	$-0.220635\pi$
$179$	3326.03	+	349.580i	1.38882	+	0.145971i	0.619583	+	0.784931i	$0.287302\pi$
$180$	285.370	−	125.865i	0.118168	−	0.0521191i
$181$	−25.4301	−	35.0016i	−0.0104431	−	0.0143737i	0.803764	−	0.594949i	$-0.202828\pi$
$181$	−25.4301	−	35.0016i	−0.0104431	−	0.0143737i	−0.814207	+	0.580575i	$0.802828\pi$
$182$	528.916	−	2610.26i	0.215417	−	1.06311i
$183$	−1540.62	−	244.010i	−0.622326	−	0.0985668i
$184$	39.7379	−	186.952i	0.0159213	−	0.0749037i
$185$	−158.129	−	42.9618i	−0.0628427	−	0.0170736i
$186$	2499.26	−	531.234i	0.985240	−	0.209419i
$187$	1396.25	+	2150.03i	0.546009	+	0.840779i
$188$	148.684	+	75.7582i	0.0576802	+	0.0293896i
$189$	−1637.36	−	1606.49i	−0.630162	−	0.618280i
$190$	854.689	−	848.753i	0.326346	−	0.324079i
$191$	−2133.24	−	453.435i	−0.808147	−	0.171777i	−0.214731	−	0.976673i	$-0.568888\pi$
$191$	−2133.24	−	453.435i	−0.808147	−	0.171777i	−0.593416	+	0.804896i	$0.702221\pi$
$192$	292.117	+	760.990i	0.109801	+	0.286040i
$193$	134.013	−	500.142i	0.0499816	−	0.186534i	−0.936422	−	0.350877i	$-0.885884\pi$
$193$	134.013	−	500.142i	0.0499816	−	0.186534i	0.986403	+	0.164343i	$0.0525503\pi$
$194$	473.092	+	4501.17i	0.175083	+	1.66580i
$195$	−1470.66	+	2009.43i	−0.540083	+	0.737939i
$196$	−1588.19	+	957.699i	−0.578785	+	0.349016i
$197$	3707.49	−	587.209i	1.34085	−	0.212370i	0.555550	−	0.831483i	$-0.312508\pi$
$197$	3707.49	−	587.209i	1.34085	−	0.212370i	0.785302	+	0.619113i	$0.212508\pi$
$198$	45.5241	−	868.652i	0.0163397	−	0.311780i
$199$	1644.01	+	2847.51i	0.585633	+	1.01435i	0.994796	+	0.101884i	$0.0324872\pi$
$199$	1644.01	+	2847.51i	0.585633	+	1.01435i	−0.409164	+	0.912461i	$0.634179\pi$
$200$	−315.151	+	1144.20i	−0.111423	+	0.404536i
$201$	−1747.24	−	1008.77i	−0.613139	−	0.353996i
$202$	−1543.82	+	786.617i	−0.537737	+	0.273991i
$203$	4779.42	+	1502.79i	1.65246	+	0.519583i
$204$	1003.46	−	1381.15i	0.344395	−	0.474019i
$205$	−85.7229	−	49.8912i	−0.0292056	−	0.0169978i
$206$	−97.1979	+	218.310i	−0.0328743	+	0.0738368i
$207$	100.322	+	26.8812i	0.0336853	+	0.00902595i
$208$	−2381.33	−	1928.37i	−0.793826	−	0.642828i
$209$	−418.654	−	1288.49i	−0.138559	−	0.426442i
$210$	4273.19	−	475.210i	1.40418	−	0.156155i
$211$	−1271.60	+	3913.60i	−0.414885	+	1.27689i	0.497468	+	0.867482i	$0.334263\pi$
$211$	−1271.60	+	3913.60i	−0.414885	+	1.27689i	−0.912353	+	0.409404i	$0.865737\pi$
$212$	2197.77	−	1427.25i	0.711996	−	0.462376i
$213$	−206.506	−	3940.38i	−0.0664300	−	1.26756i
$214$	1004.52	+	4725.89i	0.320876	+	1.50960i
$215$	−124.430	+	2225.83i	−0.0394700	+	0.706047i
$216$	−1118.40	+	363.389i	−0.352302	+	0.114470i
$217$	2268.63	+	216.635i	0.709699	+	0.0677701i
$218$	2506.32	+	2506.32i	0.778667	+	0.778667i
$219$	4902.96	−	515.322i	1.51284	−	0.159006i
$220$	−2062.03	−	1869.71i	−0.631918	−	0.572981i
$221$	−228.570	+	2174.70i	−0.0695713	+	0.661927i
$222$	284.114	+	109.061i	0.0858942	+	0.0329717i
$223$	1878.13	+	3686.03i	0.563985	+	1.10688i	0.980273	+	0.197650i	$0.0633309\pi$
$223$	1878.13	+	3686.03i	0.563985	+	1.10688i	−0.416288	+	0.909233i	$0.636669\pi$
$224$	240.181	+	3876.64i	0.0716419	+	1.15633i
$225$	−611.954	−	203.562i	−0.181320	−	0.0603146i
$226$	−3953.82	+	6848.22i	−1.16374	+	2.01565i
$227$	−1338.03	−	868.925i	−0.391225	−	0.254064i	0.334005	−	0.942571i	$-0.391600\pi$
$227$	−1338.03	−	868.925i	−0.391225	−	0.254064i	−0.725230	+	0.688507i	$0.758266\pi$
$228$	−701.142	+	567.774i	−0.203659	+	0.164920i
$229$	−3915.24	+	1743.18i	−1.12981	+	0.503023i	−0.884555	−	0.466436i	$-0.845538\pi$
$229$	−3915.24	+	1743.18i	−1.12981	+	0.503023i	−0.245254	+	0.969459i	$0.578871\pi$
$230$	668.388	−	482.063i	0.191618	−	0.138201i
$231$	1690.00	−	4531.01i	0.481357	−	1.29056i
$232$	1816.17	−	1816.17i	0.513954	−	0.513954i
$233$	−1541.30	+	1903.35i	−0.433365	+	0.535162i	−0.946310	−	0.323260i	$-0.895221\pi$
$233$	−1541.30	+	1903.35i	−0.433365	+	0.535162i	0.512945	+	0.858422i	$0.328555\pi$
$234$	496.459	−	551.374i	0.138695	−	0.154036i
$235$	−122.532	−	322.562i	−0.0340132	−	0.0895387i
$236$	−1088.69	+	980.264i	−0.300288	+	0.270380i
$237$	−3165.33	+	6212.31i	−0.867554	+	1.70267i
$238$	3033.27	−	2248.22i	0.826126	−	0.612312i
$239$	6163.04	+	2002.49i	1.66801	+	0.541968i	0.982526	−	0.186123i	$-0.0595922\pi$
$239$	6163.04	+	2002.49i	1.66801	+	0.541968i	0.685480	+	0.728091i	$0.259592\pi$
$240$	1788.83	−	4611.95i	0.481118	−	1.24042i
$241$	−2804.65	−	2525.32i	−0.749641	−	0.674980i	0.202965	−	0.979186i	$-0.434942\pi$
$241$	−2804.65	−	2525.32i	−0.749641	−	0.674980i	−0.952606	+	0.304206i	$0.901609\pi$
$242$	−2697.44	+	1035.45i	−0.716519	+	0.275046i
$243$	−369.853	−	1380.31i	−0.0976381	−	0.364390i
$244$	1203.19	−	874.168i	0.315681	−	0.229356i
$245$	3763.00	+	738.891i	0.981262	+	0.192678i
$246$	149.027	+	108.275i	0.0386245	+	0.0280623i
$247$	414.127	−	1078.84i	0.106681	−	0.277914i
$248$	636.308	−	979.829i	0.162926	−	0.250884i
$249$	3478.82	−	2008.50i	0.885387	−	0.511179i
$250$	−4320.53	+	2742.00i	−1.09302	+	0.693677i
$251$		−	5850.69i		−	1.47128i	−0.677370	−	0.735642i	$-0.736881\pi$
$251$		−	5850.69i		−	1.47128i	0.677370	−	0.735642i	$-0.263119\pi$
$252$	−516.630	+	4.91695i	−0.129145	+	0.00122912i
$253$	−144.999	−	915.489i	−0.0360317	−	0.227495i
$254$	−3712.49	−	8338.39i	−0.917096	−	2.05983i
$255$	−3455.47	+	721.906i	−0.848587	+	0.177284i
$256$	4902.11	+	2182.56i	1.19680	+	0.532851i
$257$	5779.28	−	1548.55i	1.40273	−	0.375860i	0.523405	−	0.852084i	$-0.324661\pi$
$257$	5779.28	−	1548.55i	1.40273	−	0.375860i	0.879324	+	0.476224i	$0.157995\pi$
$258$	647.688	−	4089.34i	0.156292	−	0.986788i
$259$	212.562	+	168.806i	0.0509961	+	0.0404984i
$260$	−363.235	−	2346.26i	−0.0866418	−	0.559650i
$261$	933.918	+	1037.22i	0.221487	+	0.245986i
$262$	−10499.4	+	550.253i	−2.47579	+	0.129751i
$263$	−4050.19	+	212.261i	−0.949601	+	0.0497665i	−0.520843	−	0.853653i	$-0.674382\pi$
$263$	−4050.19	+	212.261i	−0.949601	+	0.0497665i	−0.428759	+	0.903419i	$0.641049\pi$
$264$	−1658.88	−	1842.37i	−0.386730	−	0.429508i
$265$	−5348.94	−	866.306i	−1.23993	−	0.200818i
$266$	−1855.88	+	732.745i	−0.427787	+	0.168900i
$267$	−488.462	+	3084.03i	−0.111960	+	0.706889i
$268$	1858.09	−	497.875i	0.423512	−	0.113480i
$269$	−7610.41	−	3388.37i	−1.72496	−	0.768003i	−0.996562	−	0.0828508i	$-0.973598\pi$
$269$	−7610.41	−	3388.37i	−1.72496	−	0.768003i	−0.728400	−	0.685152i	$-0.759736\pi$
$270$	−4624.80	−	2078.43i	−1.04243	−	0.468479i
$271$	654.364	+	1469.73i	0.146678	+	0.329445i	0.971911	−	0.235348i	$-0.0756229\pi$
$271$	654.364	+	1469.73i	0.146678	+	0.329445i	−0.825233	+	0.564792i	$0.808956\pi$
$272$	−679.540	−	4290.45i	−0.151482	−	0.956422i
$273$	3552.45	−	2096.34i	0.787561	−	0.464748i
$274$			8383.68i			1.84845i
$275$	561.714	+	5728.10i	0.123173	+	1.25606i
$276$	−534.557	+	308.627i	−0.116582	+	0.0673085i
$277$	2774.90	−	4272.97i	0.601904	−	0.926851i	−0.398051	−	0.917363i	$-0.630313\pi$
$277$	2774.90	−	4272.97i	0.601904	−	0.926851i	0.999955	−	0.00948734i	$-0.00301996\pi$
$278$	−1805.80	+	4704.27i	−0.389585	+	1.01490i
$279$	513.621	+	373.168i	0.110214	+	0.0800751i
$280$	1227.98	−	1535.27i	0.262091	−	0.327678i
$281$	3813.85	−	2770.92i	0.809662	−	0.588254i	−0.104070	−	0.994570i	$-0.533187\pi$
$281$	3813.85	−	2770.92i	0.809662	−	0.588254i	0.913733	+	0.406316i	$0.133187\pi$
$282$	165.861	+	619.001i	0.0350243	+	0.130713i
$283$	1386.50	−	532.229i	0.291234	−	0.111794i	−0.208365	−	0.978051i	$-0.566814\pi$
$283$	1386.50	−	532.229i	0.291234	−	0.111794i	0.499599	+	0.866257i	$0.333481\pi$
$284$	2795.81	+	2517.36i	0.584158	+	0.525978i
$285$	1862.63	+	104.126i	0.387132	+	0.0216417i
$286$	−6297.38	−	2046.14i	−1.30200	−	0.423045i
$287$	97.8333	+	131.996i	0.0201217	+	0.0271480i
$288$	−491.229	+	964.092i	−0.100507	+	0.197256i
$289$	1347.39	−	1213.19i	0.274250	−	0.246935i
$290$	11061.2	−	541.049i	2.23978	−	0.109557i
$291$	−4690.41	+	5209.22i	−0.944868	+	1.04938i
$292$	−2958.13	+	3652.98i	−0.592847	+	0.732105i
$293$	−1938.99	+	1938.99i	−0.386612	+	0.386612i	−0.873477	−	0.486865i	$-0.838140\pi$
$293$	−1938.99	+	1938.99i	−0.386612	+	0.386612i	0.486865	+	0.873477i	$0.338140\pi$
$294$	−6814.27	−	2071.56i	−1.35176	−	0.410938i
$295$	3029.21	+	10.5559i	0.597856	+	0.00208335i
$296$	127.123	−	56.5987i	0.0249624	−	0.0111140i
$297$	−4432.00	+	3588.96i	−0.865895	+	0.701188i
$298$	2459.87	+	1597.46i	0.478177	+	0.310532i
$299$	395.307	−	684.692i	0.0764588	−	0.132431i
$300$	3427.11	−	1716.22i	0.659549	−	0.330287i
$301$	1645.13	−	3306.16i	0.315028	−	0.633102i
$302$	−137.358	−	269.579i	−0.0261723	−	0.0513661i
$303$	−2505.28	−	961.687i	−0.474999	−	0.182335i
$304$	−239.959	+	2283.06i	−0.0452717	+	0.430732i
$305$	−3057.23	−	332.103i	−0.573956	−	0.0623482i
$306$	1046.05	−	109.944i	0.195420	−	0.0205395i
$307$	4755.07	+	4755.07i	0.883994	+	0.883994i	0.993938	−	0.109944i	$-0.0350670\pi$
$307$	4755.07	+	4755.07i	0.883994	+	0.883994i	−0.109944	+	0.993938i	$0.535067\pi$
$308$	1915.40	+	4194.18i	0.354351	+	0.775927i
$309$	−351.996	+	114.371i	−0.0648038	+	0.0210560i
$310$	4870.29	−	1286.82i	0.892303	−	0.235762i
$311$	86.4570	+	406.748i	0.0157637	+	0.0741626i	0.985326	−	0.170681i	$-0.0545967\pi$
$311$	86.4570	+	406.748i	0.0157637	+	0.0741626i	−0.969563	+	0.244844i	$0.921263\pi$
$312$	−110.671	−	2111.73i	−0.0200818	−	0.383184i
$313$	948.181	−	615.756i	0.171228	−	0.111197i	−0.456180	−	0.889888i	$-0.650783\pi$
$313$	948.181	−	615.756i	0.171228	−	0.111197i	0.627408	+	0.778691i	$0.284116\pi$
$314$	−1072.15	+	3299.75i	−0.192692	+	0.593044i
$315$	798.211	+	710.040i	0.142775	+	0.127004i
$316$	−2054.26	−	6322.37i	−0.365700	−	1.12551i
$317$	8034.38	+	6506.11i	1.42352	+	1.15274i	0.964426	+	0.264355i	$0.0851590\pi$
$317$	8034.38	+	6506.11i	1.42352	+	1.15274i	0.459093	+	0.888388i	$0.348174\pi$
$318$	9720.71	+	2604.66i	1.71418	+	0.459314i
$319$	5066.32	−	11379.1i	0.889214	−	1.99721i
$320$	648.525	+	1470.38i	0.113293	+	0.256865i
$321$	−4398.31	+	6053.76i	−0.764766	+	1.05261i
$322$	−1332.52	+	296.517i	−0.230616	+	0.0513176i
$323$	1459.65	−	743.731i	0.251447	−	0.128119i
$324$	3941.26	+	2275.49i	0.675798	+	0.390172i
$325$	−2702.43	+	4098.55i	−0.461242	+	0.699528i
$326$	−1356.94	−	2350.30i	−0.230534	−	0.399297i
$327$	−287.303	+	5482.07i	−0.0485868	+	0.927092i
$328$	83.1916	−	13.1763i	0.0140045	−	0.00221810i
$329$	−24.4805	+	571.053i	−0.00410229	+	0.0956935i
$330$	37.2492	−	10689.3i	0.00621364	−	1.78311i
$331$	968.024	+	9210.13i	0.160747	+	1.52941i	0.716220	+	0.697874i	$0.245871\pi$
$331$	968.024	+	9210.13i	0.160747	+	1.52941i	−0.555473	+	0.831535i	$0.687463\pi$
$332$	−991.286	+	3699.53i	−0.163867	+	0.611561i
$333$	27.0987	+	70.5946i	0.00445946	+	0.0116173i
$334$	8789.80	+	1868.33i	1.43999	+	0.306079i
$335$	−3537.77	−	1818.14i	−0.576983	−	0.296525i
$336$	−5738.80	+	5849.09i	−0.931778	+	0.949684i
$337$	−5739.38	−	2924.36i	−0.927727	−	0.472701i	−0.0762481	−	0.997089i	$-0.524294\pi$
$337$	−5739.38	−	2924.36i	−0.927727	−	0.472701i	−0.851479	+	0.524388i	$0.824294\pi$
$338$	1305.26	+	2009.93i	0.210050	+	0.323449i
$339$	−11979.5	+	2546.33i	−1.91929	+	0.407957i
$340$	1842.96	−	2816.37i	0.293966	−	0.449232i
$341$	1178.00	−	5542.05i	0.187074	−	0.880114i
$342$	−549.006	−	86.9541i	−0.0868037	−	0.0137484i
$343$	−5243.74	−	3585.64i	−0.825467	−	0.564450i
$344$	−1112.77	−	1531.59i	−0.174408	−	0.240052i
$345$	1247.51	+	269.713i	0.194677	+	0.0420895i
$346$	13193.5	+	1386.69i	2.04996	+	0.215460i
$347$	−4271.33	−	5274.65i	−0.660798	−	0.816017i	0.331028	−	0.943621i	$-0.392605\pi$
$347$	−4271.33	−	5274.65i	−0.660798	−	0.816017i	−0.991825	+	0.127604i	$0.959271\pi$
$348$	−8283.50	−	434.120i	−1.27598	−	0.0668714i
$349$	−5857.65			−0.898433			−0.449216	−	0.893423i	$-0.648297\pi$
$349$	−5857.65			−0.898433			−0.449216	+	0.893423i	$0.648297\pi$
$350$	8368.85	−	1347.36i	1.27810	−	0.205770i
$351$	−4864.39			−0.739721
$352$	9643.24	+	505.381i	1.46019	+	0.0765253i
$353$	−3378.74	−	4172.40i	−0.509440	−	0.629106i	0.455922	−	0.890020i	$-0.349310\pi$
$353$	−3378.74	−	4172.40i	−0.509440	−	0.629106i	−0.965362	+	0.260914i	$0.915976\pi$
$354$	−5595.14	−	588.073i	−0.840052	−	0.0882930i
$355$	−786.182	−	7739.36i	−0.117539	−	1.15708i
$356$	−1749.92	−	2408.56i	−0.260521	−	0.358576i
$357$	5731.10	+	1161.29i	0.849641	+	0.172162i
$358$	−12094.8	−	1915.62i	−1.78555	−	0.282804i
$359$	−688.903	+	3241.03i	−0.101278	+	0.476477i	0.898052	+	0.439889i	$0.144982\pi$
$359$	−688.903	+	3241.03i	−0.101278	+	0.476477i	−0.999330	+	0.0365879i	$0.988351\pi$
$360$	511.980	−	194.486i	0.0749548	−	0.0284732i
$361$	5862.29	−	1246.07i	0.854686	−	0.181669i
$362$	86.2788	+	132.858i	0.0125268	+	0.0192896i
$363$	−3987.20	−	2031.58i	−0.576512	−	0.293748i
$364$	−981.707	+	3808.39i	−0.141361	+	0.548390i
$365$	9605.11	−	1487.01i	1.37741	−	0.213243i
$366$	5586.56	+	1187.46i	0.797854	+	0.169589i
$367$	267.393	+	696.583i	0.0380322	+	0.0990772i	0.951281	−	0.308324i	$-0.0997682\pi$
$367$	267.393	+	696.583i	0.0380322	+	0.0990772i	−0.913249	+	0.407402i	$0.866435\pi$
$368$	−406.499	+	1517.07i	−0.0575821	+	0.214899i
$369$	4.78432	+	45.5198i	0.000674965	+	0.00642186i
$370$	569.973	+	187.394i	0.0800851	+	0.0263301i
$371$	7574.08	+	4816.81i	1.05991	+	0.674060i
$372$	−3726.63	+	590.240i	−0.519400	+	0.0822649i
$373$	−246.856	+	4710.30i	−0.0342674	+	0.653861i	0.926464	+	0.376382i	$0.122832\pi$
$373$	−246.856	+	4710.30i	−0.0342674	+	0.653861i	−0.960732	+	0.277478i	$0.910501\pi$
$374$	−4693.41	−	8129.23i	−0.648905	−	1.12394i
$375$	−7633.45	−	2131.15i	−1.05117	−	0.293472i
$376$	253.764	+	146.511i	0.0348055	+	0.0200950i
$377$	9466.53	−	4823.44i	1.29324	−	0.658938i
$378$	5679.22	+	6187.96i	0.772772	+	0.841996i
$379$	−3441.45	+	4736.75i	−0.466426	+	0.641980i	−0.975826	−	0.218550i	$-0.929867\pi$
$379$	−3441.45	+	4736.75i	−0.466426	+	0.641980i	0.509400	+	0.860530i	$0.329867\pi$
$380$	−1325.98	+	1185.57i	−0.179003	+	0.160049i
$381$	5749.81	−	12914.3i	0.773154	−	1.73653i
$382$	7713.39	+	2066.80i	1.03312	+	0.276823i
$383$	−8518.92	−	6898.49i	−1.13654	−	0.920356i	−0.138993	−	0.990293i	$-0.544387\pi$
$383$	−8518.92	−	6898.49i	−1.13654	−	0.920356i	−0.997551	+	0.0699378i	$0.977720\pi$
$384$	2017.82	+	6210.22i	0.268155	+	0.825297i
$385$	2891.45	−	9085.09i	0.382759	−	1.20265i
$386$	−585.865	+	1803.11i	−0.0772532	+	0.237761i
$387$	862.785	−	560.299i	0.113328	−	0.0735959i
$388$	−349.785	−	6674.29i	−0.0457671	−	0.873288i
$389$	2304.27	+	10840.7i	0.300337	+	1.41298i	0.826665	+	0.562694i	$0.190235\pi$
$389$	2304.27	+	10840.7i	0.300337	+	1.41298i	−0.526328	+	0.850282i	$0.676431\pi$
$390$	5762.59	−	7065.72i	0.748206	−	0.917402i
$391$	1065.95	−	346.347i	0.137870	−	0.0447968i
$392$	−2872.99	+	1533.43i	−0.370173	+	0.197576i
$393$	−11514.2	−	11514.2i	−1.47790	−	1.47790i
$394$	−13669.1	+	1436.68i	−1.74782	+	0.183703i
$395$	−5634.69	+	12537.9i	−0.717752	+	1.59710i
$396$	−134.266	+	1277.45i	−0.0170382	+	0.162107i
$397$	7134.62	+	2738.72i	0.901955	+	0.346228i	0.764759	−	0.644316i	$-0.222858\pi$
$397$	7134.62	+	2738.72i	0.901955	+	0.346228i	0.137195	+	0.990544i	$0.456191\pi$
$398$	−5465.72	−	10727.1i	−0.688371	−	1.35100i
$399$	−2766.67	−	1376.68i	−0.347135	−	0.172733i
$400$	3078.27	−	9254.00i	0.384784	−	1.15675i
$401$	1018.51	−	1764.12i	0.126838	−	0.219691i	−0.795612	−	0.605807i	$-0.792850\pi$
$401$	1018.51	−	1764.12i	0.126838	−	0.219691i	0.922450	+	0.386116i	$0.126184\pi$
$402$	6195.54	+	4023.43i	0.768671	+	0.499181i
$403$	3755.78	−	3041.37i	0.464240	−	0.375934i
$404$	2337.42	−	1040.68i	0.287848	−	0.128158i
$405$	−2876.74	−	8959.82i	−0.352954	−	1.09930i
$406$	−17188.1	−	6410.90i	−2.10107	−	0.783664i
$407$	477.184	−	477.184i	0.0581158	−	0.0581158i
$408$	1886.56	−	2329.71i	0.228919	−	0.282691i
$409$	8463.69	−	9399.87i	1.02323	−	1.13642i	0.0326549	−	0.999467i	$-0.489604\pi$
$409$	8463.69	−	9399.87i	1.02323	−	1.13642i	0.990578	−	0.136949i	$-0.0437295\pi$
$410$	303.888	+	198.856i	0.0366048	+	0.0239532i
$411$	−9649.31	+	8688.28i	−1.15807	+	1.04273i
$412$	160.206	−	314.423i	0.0191573	−	0.0375983i
$413$	−4603.32	−	1997.26i	−0.548461	−	0.237962i
$414$	−361.680	−	117.517i	−0.0429362	−	0.0139508i
$415$	6656.92	−	4290.15i	0.787410	−	0.507458i
$416$	6121.01	+	5511.38i	0.721412	+	0.649562i
$417$	−7285.86	+	2796.78i	−0.855612	+	0.328439i
$418$	1283.91	+	4791.62i	0.150235	+	0.560684i
$419$	−713.589	+	518.453i	−0.0832007	+	0.0604489i	−0.628608	−	0.777722i	$-0.716375\pi$
$419$	−713.589	+	518.453i	−0.0832007	+	0.0604489i	0.545407	+	0.838171i	$0.316375\pi$
$420$	−6338.26	+	370.526i	−0.736370	+	0.0430472i
$421$	8896.35	+	6463.57i	1.02988	+	0.748255i	0.968286	−	0.249846i	$-0.0803800\pi$
$421$	8896.35	+	6463.57i	1.02988	+	0.748255i	0.0615990	+	0.998101i	$0.480380\pi$
$422$	5399.63	−	14066.5i	0.622867	−	1.62262i
$423$	−86.7230	+	133.542i	−0.00996836	+	0.0153499i
$424$	3985.08	−	2300.78i	0.456444	−	0.263528i
$425$	−6734.85	+	1754.38i	−0.768678	+	0.200236i
$426$			14447.7i			1.64318i
$427$	4435.67	+	2504.95i	0.502710	+	0.283895i
$428$	−1116.09	−	7046.74i	−0.126048	−	0.795835i
$429$	−4171.14	−	9368.54i	−0.469428	−	1.05435i
$430$	881.519	−	8114.98i	0.0988620	−	0.910090i
$431$	−2382.36	−	1060.70i	−0.266252	−	0.118543i	0.269269	−	0.963065i	$-0.413218\pi$
$431$	−2382.36	−	1060.70i	−0.266252	−	0.118543i	−0.535521	+	0.844522i	$0.679885\pi$
$432$	9334.06	−	2501.05i	1.03955	−	0.278546i
$433$	−830.931	+	5246.29i	−0.0922217	+	0.582265i	0.897695	+	0.440617i	$0.145240\pi$
$433$	−830.931	+	5246.29i	−0.0922217	+	0.582265i	−0.989917	+	0.141648i	$0.954760\pi$
$434$	−8253.82	−	1226.87i	−0.912894	−	0.135695i
$435$	12085.8	+	12170.3i	1.33212	+	1.34143i
$436$	−3502.29	−	3889.69i	−0.384700	−	0.427253i
$437$	−591.499	+	30.9991i	−0.0647488	+	0.00339334i
$438$	−18026.6	+	944.734i	−1.96654	+	0.103062i
$439$	7520.46	+	8352.32i	0.817613	+	0.908051i	0.997130	−	0.0757034i	$-0.0241202\pi$
$439$	7520.46	+	8352.32i	0.817613	+	0.908051i	−0.179517	+	0.983755i	$0.557454\pi$
$440$	−3444.06	−	3468.15i	−0.373157	−	0.375767i
$441$	−750.428	−	1602.68i	−0.0810310	−	0.173057i
$442$	1252.51	−	7908.05i	0.134787	−	0.851013i
$443$	−10002.4	+	2680.14i	−1.07275	+	0.287443i	−0.751623	−	0.659593i	$-0.770729\pi$
$443$	−10002.4	+	2680.14i	−1.07275	+	0.287443i	−0.321128	+	0.947036i	$0.604062\pi$
$444$	−410.545	−	182.787i	−0.0438820	−	0.0195375i
$445$	−664.808	+	6120.01i	−0.0708201	+	0.651946i
$446$	−6161.08	−	13838.0i	−0.654116	−	1.46917i
$447$	710.628	+	4486.73i	0.0751936	+	0.474754i
$448$	−25.3348	−	2661.96i	−0.00267178	−	0.280727i
$449$			18171.0i			1.90989i	0.296776	+	0.954947i	$0.404088\pi$
$449$			18171.0i			1.90989i	−0.296776	+	0.954947i	$0.595912\pi$
$450$	2198.62	+	861.600i	0.230320	+	0.0902583i
$451$	353.751	−	204.238i	0.0369346	−	0.0213242i
$452$	6359.83	−	9793.28i	0.661817	−	1.01911i
$453$	167.928	−	437.468i	0.0174171	−	0.0453731i
$454$	4726.03	+	3433.66i	0.488554	+	0.354956i
$455$	6793.45	−	4470.21i	0.699960	−	0.460586i
$456$	−1281.67	+	931.190i	−0.131622	+	0.0956293i
$457$	−1762.60	−	6578.13i	−0.180418	−	0.673330i	−0.995565	−	0.0940755i	$-0.970010\pi$
$457$	−1762.60	−	6578.13i	−0.180418	−	0.673330i	0.815147	−	0.579254i	$-0.196656\pi$
$458$	14650.3	−	5623.71i	1.49468	−	0.573752i
$459$	−5124.68	−	4614.28i	−0.521132	−	0.469229i
$460$	−1022.91	+	659.226i	−0.103681	+	0.0668186i
$461$	13753.8	+	4468.88i	1.38954	+	0.451489i	0.905793	−	0.423720i	$-0.139276\pi$
$461$	13753.8	+	4468.88i	1.38954	+	0.451489i	0.483746	+	0.875208i	$0.339276\pi$
$462$	−7047.81	+	16244.0i	−0.709727	+	1.63579i
$463$	−2411.22	+	4732.28i	−0.242028	+	0.475006i	−0.979783	−	0.200062i	$-0.935886\pi$
$463$	−2411.22	+	4732.28i	−0.242028	+	0.475006i	0.737755	+	0.675068i	$0.235886\pi$
$464$	−15684.9	+	14122.8i	−1.56930	+	1.41300i
$465$	6528.32	+	4271.96i	0.651062	+	0.426037i
$466$	6000.57	−	6664.31i	0.596505	−	0.662486i
$467$	−1167.73	+	1442.03i	−0.115709	+	0.142889i	−0.831710	−	0.555211i	$-0.812638\pi$
$467$	−1167.73	+	1442.03i	−0.115709	+	0.142889i	0.716000	+	0.698100i	$0.245971\pi$
$468$	−774.724	+	774.724i	−0.0765206	+	0.0765206i
$469$	4195.10	+	5080.88i	0.413031	+	0.500241i
$470$	386.229	+	1202.94i	0.0379052	+	0.118058i
$471$	−4909.01	+	2185.63i	−0.480244	+	0.213819i
$472$	−1999.17	+	1618.90i	−0.194956	+	0.157873i
$473$	−7699.88	−	5000.36i	−0.748501	−	0.486082i
$474$	12764.6	−	22109.0i	1.23692	−	2.14240i
$475$	3677.85	+	25.6328i	0.355266	+	0.00247603i
$476$	−4646.82	+	3080.95i	−0.447451	+	0.296670i
$477$	1135.22	+	2227.99i	0.108969	+	0.213863i
$478$	−22151.6	−	8503.21i	−2.11965	−	0.813657i
$479$	1800.78	−	17133.3i	0.171774	−	1.63432i	−0.480967	−	0.876739i	$-0.659714\pi$
$479$	1800.78	−	17133.3i	0.171774	−	1.63432i	0.652741	−	0.757581i	$-0.273619\pi$
$480$	−5450.62	+	12128.4i	−0.518303	+	1.15329i
$481$	572.461	−	60.1681i	0.0542661	−	0.00570360i
$482$	9771.38	+	9771.38i	0.923391	+	0.923391i
$483$	−1722.21	−	1226.39i	−0.162243	−	0.115533i
$484$	4057.84	−	1318.47i	0.381090	−	0.123823i
$485$	−8734.43	+	10709.6i	−0.817753	+	1.00268i
$486$	1087.87	+	5118.02i	0.101537	+	0.477692i
$487$	−400.435	−	7640.75i	−0.0372596	−	0.710956i	−0.951848	−	0.306570i	$-0.900819\pi$
$487$	−400.435	−	7640.75i	−0.0372596	−	0.710956i	0.914588	−	0.404386i	$-0.132515\pi$
$488$	2190.20	−	1422.33i	0.203167	−	0.131938i
$489$	1298.86	−	3997.48i	0.120116	−	0.369678i
$490$	−13618.0	−	3422.89i	−1.25550	−	0.315572i
$491$	−2772.50	−	8532.86i	−0.254829	−	0.784282i	−0.993863	−	0.110615i	$-0.964718\pi$
$491$	−2772.50	−	8532.86i	−0.254829	−	0.784282i	0.739035	−	0.673668i	$-0.235282\pi$
$492$	−211.398	−	171.186i	−0.0193710	−	0.0156863i
$493$	14548.5	+	3898.26i	1.32907	+	0.356124i
$494$	−1721.01	+	3865.45i	−0.156745	+	0.352054i
$495$	1979.99	−	1770.33i	0.179785	−	0.160749i
$496$	−5643.06	+	7767.01i	−0.510848	+	0.703123i
$497$	−3865.25	+	12292.9i	−0.348854	+	1.10948i
$498$	−13105.3	+	6677.50i	−1.17925	+	0.600855i
$499$	14142.1	+	8164.94i	1.26871	+	0.732490i	0.974744	−	0.223325i	$-0.0716912\pi$
$499$	14142.1	+	8164.94i	1.26871	+	0.732490i	0.293967	+	0.955816i	$0.405025\pi$
$500$	6583.25	−	3709.63i	0.588824	−	0.331799i
$501$	6958.78	+	12053.0i	0.620550	+	1.07482i
$502$	−1121.17	+	21393.3i	−0.0996821	+	1.90205i
$503$	−4695.86	+	743.751i	−0.416259	+	0.0659289i	−0.361051	−	0.932546i	$-0.617582\pi$
$503$	−4695.86	+	743.751i	−0.416259	+	0.0659289i	−0.0552075	+	0.998475i	$0.517582\pi$
$504$	−906.393	−	38.8562i	−0.0801071	−	0.00343411i
$505$	−5025.94	−	1652.41i	−0.442874	−	0.145607i
$506$	354.759	+	3375.31i	0.0311679	+	0.296543i
$507$	−960.669	+	3585.27i	−0.0841515	+	0.314058i
$508$	4830.26	+	12583.3i	0.421867	+	1.09900i
$509$	11741.6	+	2495.75i	1.02247	+	0.217332i	0.688487	−	0.725248i	$-0.258275\pi$
$509$	11741.6	+	2495.75i	1.02247	+	0.217332i	0.333979	+	0.942580i	$0.391608\pi$
$510$	12773.4	−	1977.50i	1.10905	−	0.171697i
$511$	−15590.8	−	4018.90i	−1.34970	−	0.347917i
$512$	−9298.85	−	4738.00i	−0.802647	−	0.408969i
$513$	1984.83	+	3056.36i	0.170823	+	0.263044i
$514$	−21428.9	+	4554.85i	−1.83889	+	0.390868i
$515$	−682.123	+	259.119i	−0.0583649	+	0.0221711i
$516$	−1271.16	+	5980.36i	−0.108449	+	0.510214i
$517$	1403.55	+	222.300i	0.119396	+	0.0189105i
$518$	−744.894	−	657.978i	−0.0631829	−	0.0558106i
$519$	12076.8	+	16622.3i	1.02141	+	1.40585i
$520$	−421.332	−	4147.69i	−0.0355320	−	0.349785i
$521$	5191.14	+	545.611i	0.436522	+	0.0458804i	0.320241	−	0.947336i	$-0.396236\pi$
$521$	5191.14	+	545.611i	0.436522	+	0.0458804i	0.116281	+	0.993216i	$0.462903\pi$
$522$	−3216.14	−	3971.60i	−0.269668	−	0.333012i
$523$	22807.0	+	1195.26i	1.90684	+	0.0999334i	0.968990	−	0.247100i	$-0.0794776\pi$
$523$	22807.0	+	1195.26i	1.90684	+	0.0999334i	0.937853	+	0.347033i	$0.112811\pi$
$524$	15525.7			1.29436
$525$	10223.7	+	8235.93i	0.849901	+	0.684658i
$526$	14850.3			1.23100
$527$	6841.74	+	358.561i	0.565524	+	0.0296378i
$528$	12820.7	+	15832.3i	1.05672	+	1.30494i
$529$	11697.3	+	1229.44i	0.961398	+	0.101047i
$530$	19392.6	+	4192.70i	1.58936	+	0.343621i
$531$	−821.662	−	1130.92i	−0.0671508	−	0.0924252i
$532$	2793.43	−	937.125i	0.227652	−	0.0763713i
$533$	344.126	+	54.5043i	0.0279658	+	0.00442935i
$534$	2377.07	−	11183.2i	0.192633	−	0.906267i
$535$	−8077.91	+	12344.5i	−0.652782	+	0.997569i
$536$	3304.03	−	702.293i	0.266254	−	0.0565941i
$537$	−10329.4	−	15905.9i	−0.830067	−	1.27819i
$538$	27178.4	+	13848.1i	2.17796	+	1.10973i
$539$	−10342.5	+	11935.7i	−0.826497	+	0.953817i
$540$	6659.40	+	3422.42i	0.530695	+	0.272736i
$541$	−9100.23	−	1934.31i	−0.723196	−	0.153720i	−0.168415	−	0.985716i	$-0.553865\pi$
$541$	−9100.23	−	1934.31i	−0.723196	−	0.153720i	−0.554782	+	0.831996i	$0.687198\pi$
$542$	−2111.06	−	5499.50i	−0.167302	−	0.435837i
$543$	−63.5009	+	236.989i	−0.00501857	+	0.0187296i
$544$	1220.53	+	11612.6i	0.0961947	+	0.915231i
$545$	−37.7142	+	10822.8i	−0.00296422	+	0.850636i
$546$	−13391.4	+	6984.58i	−1.04963	+	0.547459i
$547$	4362.44	−	690.942i	0.340995	−	0.0540083i	0.0164116	−	0.999865i	$-0.494776\pi$
$547$	4362.44	−	690.942i	0.340995	−	0.0540083i	0.324584	+	0.945857i	$0.394776\pi$
$548$	647.924	−	12363.1i	0.0505072	−	0.963735i
$549$	709.559	+	1228.99i	0.0551607	+	0.0955412i
$550$	−956.246	−	21052.6i	−0.0741354	−	1.63216i
$551$	−6893.28	−	3979.84i	−0.532965	−	0.307707i
$552$	−965.741	+	492.070i	−0.0744650	+	0.0379418i
$553$	16775.7	−	15396.5i	1.29001	−	1.18396i
$554$	−10965.3	+	15092.5i	−0.840925	+	1.15743i
$555$	374.998	+	850.221i	0.0286807	+	0.0650268i
$556$	3026.52	−	6797.68i	0.230851	−	0.518499i
$557$	−11270.3	−	3019.87i	−0.857341	−	0.229724i	−0.196735	−	0.980457i	$-0.563034\pi$
$557$	−11270.3	−	3019.87i	−0.857341	−	0.229724i	−0.660606	+	0.750733i	$0.729701\pi$
$558$	−1806.56	−	1462.93i	−0.137057	−	0.110987i
$559$	−2419.95	−	7447.83i	−0.183100	−	0.563524i
$560$	−10737.3	+	12070.6i	−0.810236	+	0.910849i
$561$	4492.51	−	13826.5i	0.338100	−	1.04056i
$562$	−14476.5	+	9401.13i	−1.08657	+	0.705628i
$563$	−499.107	−	9523.52i	−0.0373621	−	0.712910i	−0.951526	−	0.307567i	$-0.900485\pi$
$563$	−499.107	−	9523.52i	−0.0373621	−	0.712910i	0.914164	−	0.405344i	$-0.132848\pi$
$564$	−196.750	−	925.638i	−0.0146892	−	0.0691071i
$565$	−23344.4	+	6168.01i	−1.73824	+	0.459275i
$566$	−5171.79	+	1680.42i	−0.384076	+	0.124794i
$567$	−1481.80	+	15517.6i	−0.109753	+	1.14935i
$568$	4671.27	+	4671.27i	0.345074	+	0.345074i
$569$	−8550.06	+	898.647i	−0.629942	+	0.0662096i	−0.414119	−	0.910223i	$-0.635910\pi$
$569$	−8550.06	+	898.647i	−0.629942	+	0.0662096i	−0.215823	+	0.976432i	$0.569244\pi$
$570$	−6790.81	−	737.677i	−0.499010	−	0.0542068i
$571$	422.626	−	4021.02i	0.0309743	−	0.294701i	−0.968058	−	0.250725i	$-0.919331\pi$
$571$	422.626	−	4021.02i	0.0309743	−	0.294701i	0.999033	−	0.0439758i	$-0.0140024\pi$
$572$	9128.40	+	3504.07i	0.667269	+	0.256140i
$573$	5614.83	+	11019.7i	0.409359	+	0.803413i
$574$	−332.437	−	501.395i	−0.0241736	−	0.0364596i
$575$	2482.53	+	410.950i	0.180050	+	0.0298049i
$576$	370.801	−	642.246i	0.0268230	−	0.0464588i
$577$	1304.67	+	847.266i	0.0941323	+	0.0611302i	0.590847	−	0.806784i	$-0.298794\pi$
$577$	1304.67	+	847.266i	0.0941323	+	0.0611302i	−0.496715	+	0.867914i	$0.665460\pi$
$578$	−5159.26	+	4177.89i	−0.371275	+	0.300652i
$579$	−2682.46	+	1194.31i	−0.192538	+	0.0857233i
$580$	−16353.4	−	56.9868i	−1.17075	−	0.00407974i
$581$	−12937.2	+	2175.46i	−0.923796	+	0.155341i
$582$	18148.9	−	18148.9i	1.29260	−	1.29260i
$583$	14043.8	−	17342.7i	0.997660	−	1.23201i
$584$	−5522.96	+	6133.87i	−0.391339	+	0.434626i
$585$	2262.78	−	110.682i	0.159922	−	0.00782246i
$586$	7461.58	−	6718.43i	0.525998	−	0.473611i
$587$	−7022.00	+	13781.5i	−0.493746	+	0.969032i	0.500881	+	0.865516i	$0.333009\pi$
$587$	−7022.00	+	13781.5i	−0.493746	+	0.969032i	−0.994628	+	0.103516i	$0.966991\pi$
$588$	9888.67	+	3581.49i	0.693541	+	0.251187i
$589$	−3443.41	−	1118.83i	−0.240888	−	0.0782694i
$590$	−11074.4	−	619.089i	−0.772755	−	0.0431991i
$591$	−15819.3	−	14243.8i	−1.10105	−	0.991388i
$592$	−1067.54	+	409.788i	−0.0741139	+	0.0284497i
$593$	1032.73	+	3854.22i	0.0715166	+	0.266903i	0.992421	−	0.122885i	$-0.0392147\pi$
$593$	1032.73	+	3854.22i	0.0715166	+	0.266903i	−0.920904	+	0.389789i	$0.872548\pi$
$594$	16893.5	−	12273.9i	1.16692	−	0.847816i
$595$	11397.3	+	1734.75i	0.785286	+	0.119526i
$596$	−3504.04	−	2545.83i	−0.240824	−	0.174969i
$597$	6682.18	−	17407.7i	0.458096	−	1.19338i
$598$	−1576.66	+	2427.85i	−0.107817	+	0.166024i
$599$	343.689	−	198.429i	0.0234437	−	0.0135352i	−0.488232	−	0.872714i	$-0.662358\pi$
$599$	343.689	−	198.429i	0.0234437	−	0.0135352i	0.511676	+	0.859178i	$0.329025\pi$
$600$	6167.37	−	2694.54i	0.419636	−	0.183341i
$601$		−	8246.41i		−	0.559697i	−0.960044	−	0.279849i	$-0.909716\pi$
$601$		−	8246.41i		−	0.559697i	0.960044	−	0.279849i	$-0.0902843\pi$
$602$	−6649.03	+	11773.8i	−0.450156	+	0.797118i
$603$	287.143	+	1812.95i	0.0193920	+	0.122436i
$604$	181.722	+	408.155i	0.0122420	+	0.0274960i
$605$	−8047.15	−	3616.47i	−0.540765	−	0.243026i
$606$	8976.36	+	3996.53i	0.601716	+	0.267901i
$607$	−23799.2	+	6376.99i	−1.59140	+	0.426415i	−0.942432	−	0.334398i	$-0.891467\pi$
$607$	−23799.2	+	6376.99i	−1.59140	+	0.426415i	−0.648971	+	0.760813i	$0.724800\pi$
$608$	965.311	−	6094.73i	0.0643890	−	0.406536i
$609$	−10433.9	−	26426.8i	−0.694259	−	1.75840i
$610$	11115.2	+	1800.21i	0.737776	+	0.119489i
$611$	811.052	+	900.764i	0.0537015	+	0.0596416i
$612$	−1551.07	+	81.2881i	−0.102448	+	0.00536908i
$613$	−17969.2	+	941.725i	−1.18396	+	0.0620488i	−0.634130	−	0.773226i	$-0.718642\pi$
$613$	−17969.2	+	941.725i	−1.18396	+	0.0620488i	−0.549832	+	0.835275i	$0.685308\pi$
$614$	−16475.9	−	18298.3i	−1.08292	−	1.20270i
$615$	86.0529	+	555.846i	0.00564225	+	0.0364453i
$616$	2973.33	+	7530.76i	0.194478	+	0.492570i
$617$	2634.93	−	16636.3i	0.171926	−	1.08550i	−0.739235	−	0.673448i	$-0.764813\pi$
$617$	2634.93	−	16636.3i	0.171926	−	1.08550i	0.911161	−	0.412051i	$-0.135187\pi$
$618$	1309.00	−	350.747i	0.0852037	−	0.0228303i
$619$	24078.4	+	10720.4i	1.56348	+	0.696105i	0.992201	−	0.124651i	$-0.0397813\pi$
$619$	24078.4	+	10720.4i	1.56348	+	0.696105i	0.571278	+	0.820757i	$0.306448\pi$
$620$	−7281.50	+	1521.23i	−0.471665	+	0.0985389i
$621$	1014.11	+	2277.74i	0.0655314	+	0.147186i
$622$	−238.188	−	1503.86i	−0.0153544	−	0.0969440i
$623$	5014.44	−	8879.37i	0.322471	−	0.571018i
$624$			17376.9i			1.11479i
$625$	−15236.8	−	3461.33i	−0.975155	−	0.221525i
$626$	−3585.06	+	2069.83i	−0.228894	+	0.132152i
$627$	−4184.42	+	6443.45i	−0.266523	+	0.410409i
$628$	1836.09	−	4783.18i	0.116669	−	0.303932i
$629$	660.168	+	479.640i	0.0418484	+	0.0304046i
$630$	−2782.62	−	2749.25i	−0.175972	−	0.173862i
$631$	−5818.38	+	4227.30i	−0.367078	+	0.266698i	−0.755998	−	0.654574i	$-0.772848\pi$
$631$	−5818.38	+	4227.30i	−0.367078	+	0.266698i	0.388920	+	0.921271i	$0.372848\pi$
$632$	−3021.24	−	11275.4i	−0.190156	−	0.709672i
$633$	21785.9	−	8362.82i	1.36795	−	0.525106i
$634$	−28131.2	−	25329.5i	−1.76220	−	1.58669i
$635$	10078.4	−	25984.2i	0.629843	−	1.62386i
$636$	−14133.5	−	4592.26i	−0.881180	−	0.286313i
$637$	−13262.7	+	2360.20i	−0.824944	+	0.146805i
$638$	−20705.8	+	40637.4i	−1.28487	+	2.52171i
$639$	−2667.78	+	2402.08i	−0.165158	+	0.148709i
$640$	4571.60	+	12034.6i	0.282357	+	0.743295i
$641$	2257.04	−	2506.69i	0.139076	−	0.154459i	−0.669583	−	0.742737i	$-0.733527\pi$
$641$	2257.04	−	2506.69i	0.139076	−	0.154459i	0.808659	+	0.588278i	$0.200194\pi$
$642$	17242.7	−	21292.9i	1.05999	−	1.30898i
$643$	−6544.77	+	6544.77i	−0.401401	+	0.401401i	−0.878726	−	0.477326i	$-0.841606\pi$
$643$	−6544.77	+	6544.77i	−0.401401	+	0.401401i	0.477326	+	0.878726i	$0.341606\pi$
$644$	1987.93	−	334.282i	0.121639	−	0.0204543i
$645$	10253.6	−	7395.22i	0.625945	−	0.451452i
$646$	−5479.80	+	2439.77i	−0.333746	+	0.148593i
$647$	3056.58	−	2475.17i	0.185729	−	0.150400i	−0.531947	−	0.846778i	$-0.678539\pi$
$647$	3056.58	−	2475.17i	0.185729	−	0.150400i	0.717676	+	0.696377i	$0.245206\pi$
$648$	6702.11	+	4352.40i	0.406302	+	0.263856i
$649$	−6237.72	+	10804.0i	−0.377275	+	0.653460i
$650$	10666.9	−	14468.6i	0.643679	−	0.873087i
$651$	−7141.61	−	10771.3i	−0.429957	−	0.648480i
$652$	1819.40	+	3570.78i	0.109284	+	0.214482i
$653$	−16097.8	−	6179.38i	−0.964712	−	0.370318i	−0.175527	−	0.984475i	$-0.556163\pi$
$653$	−16097.8	−	6179.38i	−0.964712	−	0.370318i	−0.789184	+	0.614156i	$0.789496\pi$
$654$	2101.07	−	19990.3i	0.125624	−	1.19523i
$655$	−23782.5	−	21564.4i	−1.41872	−	1.28640i
$656$	−688.353	+	72.3488i	−0.0409690	+	0.00430601i
$657$	−3171.56	−	3171.56i	−0.188332	−	0.188332i
$658$	198.945	−	2083.38i	0.0117868	−	0.123433i
$659$	6615.94	−	2149.65i	0.391078	−	0.127069i	−0.106876	−	0.994272i	$-0.534085\pi$
$659$	6615.94	−	2149.65i	0.391078	−	0.127069i	0.497954	+	0.867203i	$0.334085\pi$
$660$	−881.044	+	15760.3i	−0.0519615	+	0.929499i
$661$	−3589.14	−	16885.6i	−0.211197	−	0.993606i	−0.948190	−	0.317705i	$-0.897088\pi$
$661$	−3589.14	−	16885.6i	−0.211197	−	0.993606i	0.736992	−	0.675901i	$-0.236245\pi$
$662$	−1774.67	−	33862.7i	−0.104191	−	1.98808i
$663$	10399.9	−	6753.78i	0.609199	−	0.395618i
$664$	−2078.27	+	6396.25i	−0.121464	+	0.373829i
$665$	−5580.64	−	2444.43i	−0.325425	−	0.142543i
$666$	−85.5594	−	263.325i	−0.00497802	−	0.0153208i
$667$	−4232.12	−	3427.10i	−0.245680	−	0.198947i
$668$	−12817.6	−	3434.48i	−0.742409	−	0.198928i
$669$	9542.13	−	21432.0i	0.551450	−	1.23858i
$670$	12587.6	+	7326.05i	0.725822	+	0.422433i
$671$	7444.20	−	10246.1i	0.428287	−	0.589486i
$672$	16227.7	−	14893.6i	0.931544	−	0.854958i
$673$	491.355	−	250.358i	0.0281431	−	0.0143397i	−0.439862	−	0.898065i	$-0.644973\pi$
$673$	491.355	−	250.358i	0.0281431	−	0.0143397i	0.468005	+	0.883726i	$0.344973\pi$
$674$	20425.9	+	11792.9i	1.16732	+	0.673954i
$675$	−5447.41	−	14492.1i	−0.310623	−	0.826370i
$676$	−1769.49	−	3064.85i	−0.100677	−	0.174377i
$677$	1322.21	−	25229.4i	0.0750618	−	1.43226i	−0.658469	−	0.752608i	$-0.728796\pi$
$677$	1322.21	−	25229.4i	0.0750618	−	1.43226i	0.733531	−	0.679656i	$-0.237871\pi$
$678$	44291.6	−	7015.09i	2.50886	−	0.397364i
$679$	20297.5	−	10586.6i	1.14720	−	0.598346i
$680$	3490.56	−	4769.30i	0.196848	−	0.268962i
$681$	945.719	+	8997.91i	0.0532159	+	0.506315i
$682$	−5369.43	+	20039.0i	−0.301475	+	1.12512i
$683$	4997.35	+	13018.5i	0.279968	+	0.729342i	0.999395	+	0.0347740i	$0.0110711\pi$
$683$	4997.35	+	13018.5i	0.279968	+	0.729342i	−0.719427	+	0.694568i	$0.755596\pi$
$684$	802.881	+	170.658i	0.0448815	+	0.00953985i
$685$	−18164.2	+	18038.1i	−1.01317	+	1.00613i
$686$	18486.8	+	14115.9i	1.02891	+	0.785638i
$687$	21655.2	+	11033.9i	1.20262	+	0.612764i
$688$	8472.88	+	13047.1i	0.469514	+	0.722988i
$689$	18618.7	−	3957.52i	1.02949	−	0.218824i
$690$	−4509.88	−	1225.28i	−0.248823	−	0.0676022i
$691$	−776.577	+	3653.51i	−0.0427531	+	0.201137i	−0.994340	−	0.106241i	$-0.966118\pi$
$691$	−776.577	+	3653.51i	−0.0427531	+	0.201137i	0.951587	+	0.307379i	$0.0994518\pi$
$692$	−19348.8	−	3064.55i	−1.06291	−	0.168348i
$693$	−4171.23	+	1399.34i	−0.228647	+	0.0767051i
$694$	14607.5	+	20105.5i	0.798980	+	1.09970i
$695$	−14077.7	+	6209.10i	−0.768341	+	0.338884i
$696$	−14485.7	−	1522.51i	−0.788907	−	0.0829175i
$697$	310.839	+	383.854i	0.0168922	+	0.0208601i
$698$	21418.7	+	1122.51i	1.16148	+	0.0608704i
$699$	13889.0			0.751544
$700$	−12445.4	+	1340.13i	−0.671988	+	0.0723602i
$701$	−19010.7			−1.02429			−0.512143	−	0.858900i	$-0.671148\pi$
$701$	−19010.7			−1.02429			−0.512143	+	0.858900i	$0.671148\pi$
$702$	17786.8	+	932.168i	0.956297	+	0.0501174i
$703$	−271.387	−	335.135i	−0.0145598	−	0.0179799i
$704$	−6582.13	−	691.810i	−0.352377	−	0.0370363i
$705$	−984.278	+	1691.18i	−0.0525816	+	0.0903455i
$706$	11554.9	+	15904.0i	0.615971	+	0.847812i
$707$	6568.37	+	5801.95i	0.349404	+	0.308635i
$708$	8205.51	+	1299.63i	0.435568	+	0.0689872i
$709$	1507.38	−	7091.67i	0.0798460	−	0.375646i	−0.920022	−	0.391866i	$-0.871830\pi$
$709$	1507.38	−	7091.67i	0.0798460	−	0.375646i	0.999868	+	0.0162196i	$0.00516310\pi$
$710$	1391.60	+	28449.9i	0.0735577	+	1.50381i
$711$	6204.69	−	1318.85i	0.327277	−	0.0695649i
$712$	−2847.24	−	4384.36i	−0.149866	−	0.230774i
$713$	−2207.11	−	1124.58i	−0.115928	−	0.0590684i
$714$	−20733.4	−	5344.55i	−1.08674	−	0.280133i
$715$	−9116.05	−	18046.4i	−0.476813	−	0.943915i
$716$	17687.7	+	3759.64i	0.923213	+	0.196235i
$717$	−13169.6	−	34307.9i	−0.685950	−	1.78696i
$718$	3140.08	−	11718.9i	0.163213	−	0.609119i
$719$	2737.43	+	26044.9i	0.141987	+	1.35092i	0.800945	+	0.598738i	$0.204331\pi$
$719$	2737.43	+	26044.9i	0.141987	+	1.35092i	−0.658958	+	0.752180i	$0.729003\pi$
$720$	−4285.05	+	1375.81i	−0.221798	+	0.0712129i
$721$	1207.61	+	51.7690i	0.0623768	+	0.00267403i
$722$	−21674.5	+	3432.90i	−1.11723	+	0.176952i
$723$	−1120.11	+	21372.9i	−0.0576172	+	1.09940i
$724$	−116.965	−	202.589i	−0.00600409	−	0.0103994i
$725$	24971.2	+	22801.3i	1.27918	+	1.16803i
$726$	14190.0	+	8192.63i	0.725402	+	0.418811i
$727$	−16650.6	+	8483.88i	−0.849429	+	0.432806i	−0.823810	−	0.566866i	$-0.808156\pi$
$727$	−16650.6	+	8483.88i	−0.849429	+	0.432806i	−0.0256190	+	0.999672i	$0.508156\pi$
$728$	−2071.47	+	6588.02i	−0.105459	+	0.335396i
$729$	8594.43	−	11829.2i	0.436642	−	0.600986i
$730$	−35406.4	+	3596.66i	−1.79514	+	0.182354i
$731$	4515.46	−	10141.9i	0.228468	−	0.513148i
$732$	−8146.55	−	2182.86i	−0.411346	−	0.110220i
$733$	−20554.3	−	16644.5i	−1.03573	−	0.838716i	−0.0486274	−	0.998817i	$-0.515485\pi$
$733$	−20554.3	−	16644.5i	−1.03573	−	0.838716i	−0.987101	+	0.160101i	$0.948818\pi$
$734$	−844.246	−	2598.32i	−0.0424546	−	0.130662i
$735$	−10173.1	−	19221.0i	−0.510532	−	0.964596i
$736$	1304.60	−	4015.15i	0.0653372	−	0.201087i
$737$	13738.5	−	8921.87i	0.686653	−	0.445918i
$738$	−8.77105	−	167.362i	−0.000437489	−	0.00834779i
$739$	21.8487	+	102.790i	0.00108757	+	0.00511663i	0.978688	−	0.205353i	$-0.0658341\pi$
$739$	21.8487	+	102.790i	0.00108757	+	0.00511663i	−0.977600	+	0.210469i	$0.932501\pi$
$740$	−826.038	−	320.393i	−0.0410348	−	0.0159161i
$741$	−6232.53	+	2025.07i	−0.308985	+	0.100395i
$742$	−26771.8	−	19064.3i	−1.32456	−	0.943222i
$743$	−1133.40	−	1133.40i	−0.0559631	−	0.0559631i	0.678571	−	0.734534i	$-0.262599\pi$
$743$	−1133.40	−	1133.40i	−0.0559631	−	0.0559631i	−0.734534	+	0.678571i	$0.762599\pi$
$744$	−6589.11	+	692.544i	−0.324689	+	0.0341262i
$745$	1831.51	+	8766.66i	0.0900687	+	0.431122i
$746$	1805.28	−	17176.1i	0.0886004	−	0.842977i
$747$	−3411.91	−	1309.71i	−0.167115	−	0.0641495i
$748$	6292.96	+	12350.6i	0.307611	+	0.603721i
$749$	20367.6	−	13504.2i	0.993613	−	0.658788i
$750$	27503.6	+	9255.43i	1.33905	+	0.450614i
$751$	819.087	−	1418.70i	0.0397988	−	0.0689336i	−0.845440	−	0.534071i	$-0.820662\pi$
$751$	819.087	−	1418.70i	0.0397988	−	0.0689336i	0.885239	+	0.465137i	$0.153995\pi$
$752$	−2019.42	−	1311.43i	−0.0979266	−	0.0635943i
$753$	−25784.8	+	20880.1i	−1.24788	+	1.01051i
$754$	−35539.0	+	15823.0i	−1.71652	+	0.764244i
$755$	288.541	−	877.621i	0.0139087	−	0.0423045i
$756$	−7896.73	−	9564.09i	−0.379896	−	0.460109i
$757$	−26296.9	+	26296.9i	−1.26258	+	1.26258i	−0.312748	+	0.949836i	$0.601250\pi$
$757$	−26296.9	+	26296.9i	−1.26258	+	1.26258i	−0.949836	+	0.312748i	$0.898750\pi$
$758$	13491.5	−	16660.6i	0.646482	−	0.798338i
$759$	−3517.21	+	3906.26i	−0.168204	+	0.186809i
$760$	−2434.13	+	1957.12i	−0.116178	+	0.0934107i
$761$	56.3544	−	50.7417i	0.00268442	−	0.00241706i	−0.667787	−	0.744352i	$-0.732758\pi$
$761$	56.3544	−	50.7417i	0.00268442	−	0.00241706i	0.670472	+	0.741935i	$0.266092\pi$
$762$	−23499.2	+	46119.7i	−1.11717	+	2.19257i
$763$	7135.80	−	16446.8i	0.338576	−	0.780357i
$764$	−11215.0	−	3643.96i	−0.531077	−	0.172557i
$765$	2488.86	+	2029.84i	0.117627	+	0.0959332i
$766$	29827.8	+	26857.1i	1.40695	+	1.26682i
$767$	−9934.33	+	3813.43i	−0.467676	+	0.179524i
$768$	−7875.94	−	29393.4i	−0.370050	−	1.38105i
$769$	17086.5	−	12414.1i	0.801244	−	0.582138i	−0.110035	−	0.993928i	$-0.535096\pi$
$769$	17086.5	−	12414.1i	0.801244	−	0.582138i	0.911279	+	0.411790i	$0.135096\pi$
$770$	−12313.7	+	32665.9i	−0.576305	+	1.52883i
$771$	−27449.9	−	19943.5i	−1.28221	−	0.931581i
$772$	1003.31	−	2613.70i	0.0467744	−	0.121851i
$773$	−4752.10	+	7317.60i	−0.221114	+	0.340486i	−0.931767	−	0.363057i	$-0.881733\pi$
$773$	−4752.10	+	7317.60i	−0.221114	+	0.340486i	0.710653	+	0.703543i	$0.248400\pi$
$774$	−3262.18	+	1883.42i	−0.151494	+	0.0874652i
$775$	13266.8	+	7783.38i	0.614914	+	0.360758i
$776$		−	11735.9i		−	0.542905i
$777$	−14.6494	−	1539.23i	−0.000676376	−	0.0710677i
$778$	−6348.23	−	40081.2i	−0.292539	−	1.84702i
$779$	−106.169	−	238.459i	−0.00488304	−	0.0109675i
$780$	−9043.97	+	9974.23i	−0.415162	+	0.457865i
$781$	29267.7	+	13030.8i	1.34095	+	0.597028i
$782$	−3964.05	+	1062.16i	−0.181271	+	0.0485715i
$783$	−5241.45	+	33093.2i	−0.239226	+	1.51042i
$784$	24235.8	−	11348.0i	1.10404	−	0.516947i
$785$	−9456.13	+	4776.71i	−0.429941	+	0.217182i
$786$	39895.7	+	44308.7i	1.81048	+	2.01074i
$787$	34628.2	−	1814.79i	1.56844	−	0.0821984i	0.751818	−	0.659371i	$-0.229177\pi$
$787$	34628.2	−	1814.79i	1.56844	−	0.0821984i	0.816622	+	0.577173i	$0.195844\pi$
$788$	20268.4	−	1062.22i	0.916284	−	0.0480204i
$789$	15389.9	+	17092.2i	0.694416	+	0.771227i
$790$	23006.1	−	44765.7i	1.03610	−	2.01607i
$791$	39562.4	+	5880.68i	1.77835	+	0.264340i
$792$	−352.841	+	2227.75i	−0.0158304	+	0.0999491i
$793$	10434.6	−	2795.93i	0.467266	−	0.125204i
$794$	−25563.2	−	11381.5i	−1.14257	−	0.508706i
$795$	15271.5	+	26665.2i	0.681289	+	1.18958i
$796$	7231.08	+	16241.3i	0.321983	+	0.723187i
$797$	−3692.63	−	23314.4i	−0.164115	−	1.03618i	−0.922956	−	0.384906i	$-0.874234\pi$
$797$	−3692.63	−	23314.4i	−0.164115	−	1.03618i	0.758841	−	0.651276i	$-0.225766\pi$
$798$	9852.62	+	5564.07i	0.437067	+	0.246824i
$799$			1718.31i			0.0760821i
$800$	−9564.96	+	24407.8i	−0.422716	+	1.07868i
$801$	2460.21	−	1420.40i	0.108523	−	0.0626560i
$802$	−4062.30	+	6255.39i	−0.178859	+	0.275418i
$803$	−14344.9	+	37369.8i	−0.630412	+	1.64228i
$804$	−8825.42	−	6412.04i	−0.387125	−	0.281263i
$805$	−3509.45	−	2249.08i	−0.153654	−	0.0984716i
$806$	−14316.0	+	10401.2i	−0.625631	+	0.454547i
$807$	12227.2	+	45632.6i	0.533356	+	1.99051i
$808$	4194.44	−	1610.09i	0.182623	−	0.0701026i
$809$	−769.914	−	693.233i	−0.0334595	−	0.0301271i	0.652231	−	0.758020i	$-0.273833\pi$
$809$	−769.914	−	693.233i	−0.0334595	−	0.0301271i	−0.685691	+	0.727893i	$0.740500\pi$
$810$	8801.93	+	33313.2i	0.381813	+	1.44507i
$811$	−35331.9	−	11480.0i	−1.52980	−	0.497063i	−0.581263	−	0.813716i	$-0.697441\pi$
$811$	−35331.9	−	11480.0i	−1.52980	−	0.497063i	−0.948542	+	0.316653i	$0.897441\pi$
$812$	24851.3	+	10782.3i	1.07403	+	0.465991i
$813$	4141.97	−	8129.07i	0.178678	−	0.350675i
$814$	−1836.28	+	1653.40i	−0.0790684	+	0.0711935i
$815$	2172.64	−	7996.82i	0.0933793	−	0.343701i
$816$	−16483.4	+	18306.7i	−0.707151	+	0.785371i
$817$	−3692.16	+	4559.44i	−0.158106	+	0.195244i
$818$	−32749.1	+	32749.1i	−1.39981	+	1.39981i
$819$	−3516.17	−	1311.48i	−0.150018	−	0.0559544i
$820$	−432.765	−	316.732i	−0.0184303	−	0.0134888i
$821$	27088.4	−	12060.5i	1.15151	−	0.512687i	0.259968	−	0.965617i	$-0.416288\pi$
$821$	27088.4	−	12060.5i	1.15151	−	0.512687i	0.891546	+	0.452931i	$0.149621\pi$
$822$	36948.0	−	29919.9i	1.56777	−	1.26956i
$823$	−19839.3	−	12883.8i	−0.840287	−	0.545689i	0.0512243	−	0.998687i	$-0.483688\pi$
$823$	−19839.3	−	12883.8i	−0.840287	−	0.545689i	−0.891511	+	0.452998i	$0.850354\pi$
$824$	309.827	−	536.636i	0.0130987	−	0.0226876i
$825$	23239.8	−	22918.1i	0.980736	−	0.967160i
$826$	16449.5	+	8185.17i	0.692918	+	0.344793i
$827$	−10328.3	−	20270.4i	−0.434279	−	0.852321i	−0.999623	−	0.0274654i	$-0.991256\pi$
$827$	−10328.3	−	20270.4i	−0.434279	−	0.852321i	0.565344	−	0.824856i	$-0.308744\pi$
$828$	524.275	+	201.250i	0.0220046	+	0.00844677i
$829$	742.848	−	7067.73i	0.0311220	−	0.296106i	−0.967879	−	0.251417i	$-0.919103\pi$
$829$	742.848	−	7067.73i	0.0311220	−	0.296106i	0.999001	−	0.0446895i	$-0.0142299\pi$
$830$	−25163.4	+	14411.4i	−1.05233	+	0.602684i
$831$	−28734.7	+	3020.13i	−1.19951	+	0.126074i
$832$	−3991.79	−	3991.79i	−0.166335	−	0.166335i
$833$	−16211.3	−	10094.3i	−0.674295	−	0.419866i
$834$	27177.0	−	8830.33i	1.12837	−	0.366630i
$835$	14863.9	+	23064.0i	0.616033	+	0.955884i
$836$	−1523.02	−	7165.27i	−0.0630083	−	0.296431i
$837$	797.640	+	15219.9i	0.0329396	+	0.628525i
$838$	2708.62	−	1759.00i	0.111656	−	0.0725101i
$839$	4127.35	−	12702.7i	0.169835	−	0.522699i	−0.829525	−	0.558470i	$-0.811389\pi$
$839$	4127.35	−	12702.7i	0.169835	−	0.522699i	0.999360	+	0.0357707i	$0.0113886\pi$
$840$	−11148.6	+	67.2531i	−0.457931	+	0.00276244i
$841$	−15077.7	−	46404.4i	−0.618217	−	1.90268i
$842$	−31291.2	−	25339.1i	−1.28072	−	1.03711i
$843$	−25822.8	−	6919.20i	−1.05502	−	0.282693i
$844$	−9049.78	+	20326.1i	−0.369083	+	0.828974i
$845$	−1546.38	+	7152.52i	−0.0629553	+	0.291188i
$846$	342.696	−	471.681i	0.0139269	−	0.0191687i
$847$	9881.86	+	10767.1i	0.400879	+	0.436789i
$848$	−33691.8	+	17166.8i	−1.36436	+	0.695178i
$849$	−7293.80	−	4211.08i	−0.294844	−	0.170228i
$850$	24962.4	−	5124.36i	1.00730	−	0.206781i
$851$	−147.519	−	255.510i	−0.00594228	−	0.0102923i
$852$	1116.58	−	21305.5i	0.0448982	−	0.856709i
$853$	−23658.6	+	3747.16i	−0.949656	+	0.150411i	−0.611999	−	0.790859i	$-0.709634\pi$
$853$	−23658.6	+	3747.16i	−0.949656	+	0.150411i	−0.337657	+	0.941269i	$0.609634\pi$
$854$	−15739.2	−	10009.5i	−0.630659	−	0.401074i
$855$	−992.830	−	1376.58i	−0.0397124	−	0.0550619i
$856$	−1309.54	−	12459.5i	−0.0522888	−	0.497495i
$857$	−4523.61	+	16882.3i	−0.180308	+	0.672917i	0.815279	+	0.579069i	$0.196584\pi$
$857$	−4523.61	+	16882.3i	−0.180308	+	0.672917i	−0.995586	+	0.0938486i	$0.970083\pi$
$858$	13456.6	+	35055.7i	0.535434	+	1.39485i
$859$	−25620.6	−	5445.83i	−1.01765	−	0.216309i	−0.331260	−	0.943540i	$-0.607474\pi$
$859$	−25620.6	−	5445.83i	−1.01765	−	0.216309i	−0.686393	+	0.727231i	$0.740807\pi$
$860$	−1927.11	+	11898.8i	−0.0764113	+	0.471796i
$861$	232.573	−	902.235i	0.00920566	−	0.0357121i
$862$	8507.94	+	4335.01i	0.336174	+	0.171289i
$863$	25940.9	+	39945.4i	1.02322	+	1.57562i	0.799229	+	0.601027i	$0.205241\pi$
$863$	25940.9	+	39945.4i	1.02322	+	1.57562i	0.223989	+	0.974592i	$0.428092\pi$
$864$	−25407.6	+	5400.55i	−1.00044	+	0.212651i
$865$	25382.3	+	31568.8i	0.997716	+	1.24089i
$866$	4043.68	−	19024.0i	0.158672	−	0.746492i
$867$	−10155.3	−	1608.44i	−0.397800	−	0.0630053i
$868$	12076.8	+	2447.12i	0.472251	+	0.0956918i
$869$	−33274.8	−	45798.8i	−1.29893	−	1.78782i
$870$	−41860.0	−	46817.3i	−1.63125	−	1.82443i
$871$	13896.1	+	1460.54i	0.540587	+	0.0568180i
$872$	−5784.01	−	7142.66i	−0.224623	−	0.277386i
$873$	6368.65	+	333.767i	0.246903	+	0.0129396i
$874$	2168.78			0.0839359
$875$	20925.4	+	15233.2i	0.808466	+	0.588543i
$876$	26656.2			1.02812
$877$	21342.5	+	1118.51i	0.821760	+	0.0430666i	0.458581	−	0.888653i	$-0.348358\pi$
$877$	21342.5	+	1118.51i	0.821760	+	0.0430666i	0.363179	+	0.931719i	$0.381691\pi$
$878$	−25898.3	−	31981.7i	−0.995473	−	1.22931i
$879$	15465.3	+	1625.47i	0.593439	+	0.0623730i
$880$	26771.1	+	29941.5i	1.02551	+	1.14696i
$881$	4337.67	+	5970.29i	0.165879	+	0.228313i	0.883862	−	0.467747i	$-0.154934\pi$
$881$	4337.67	+	5970.29i	0.165879	+	0.228313i	−0.717983	+	0.696061i	$0.754934\pi$
$882$	2436.84	+	6004.06i	0.0930304	+	0.229214i
$883$	22451.1	+	3555.91i	0.855652	+	0.135522i	0.568823	−	0.822460i	$-0.307399\pi$
$883$	22451.1	+	3555.91i	0.855652	+	0.135522i	0.286829	+	0.957982i	$0.407399\pi$
$884$	−2458.20	+	11564.9i	−0.0935276	+	0.440013i
$885$	−10764.2	−	13387.8i	−0.408853	−	0.508504i
$886$	37087.8	−	7883.25i	1.40631	−	0.298920i
$887$	20300.9	+	31260.7i	0.768476	+	1.18335i	0.978620	+	0.205679i	$0.0659402\pi$
$887$	20300.9	+	31260.7i	0.768476	+	1.18335i	−0.210143	+	0.977671i	$0.567393\pi$
$888$	−703.118	−	358.256i	−0.0265710	−	0.0135386i
$889$	−32333.0	+	32954.3i	−1.21981	+	1.24325i
$890$	3603.68	−	22250.6i	0.135725	−	0.838026i
$891$	37908.1	+	8057.61i	1.42533	+	0.302963i
$892$	8016.08	+	20882.6i	0.300895	+	0.783858i
$893$	235.028	−	877.135i	0.00880728	−	0.0328692i
$894$	−1738.64	−	16542.1i	−0.0650434	−	0.618847i
$895$	−21872.3	−	30326.4i	−0.816885	−	1.13262i
$896$	913.353	−	21305.7i	0.0340547	−	0.794389i
$897$	−4428.31	+	701.376i	−0.164835	+	0.0261073i
$898$	3482.13	−	66442.9i	0.129399	−	2.46907i
$899$	−16644.0	−	28828.3i	−0.617474	−	1.06950i
$900$	−3175.65	−	1440.49i	−0.117617	−	0.0533515i
$901$	23369.0	+	13492.1i	0.864078	+	0.498876i
$902$	−1332.64	+	679.015i	−0.0491930	+	0.0250651i
$903$	−20441.9	+	4548.80i	−0.753336	+	0.167635i
$904$	12052.3	−	16588.6i	0.443423	−	0.610320i
$905$	−102.217	+	472.786i	−0.00375448	+	0.0173657i
$906$	−697.867	+	1567.44i	−0.0255906	+	0.0574775i
$907$	1667.38	+	446.773i	0.0610412	+	0.0163559i	0.289210	−	0.957266i	$-0.406607\pi$
$907$	1667.38	+	446.773i	0.0610412	+	0.0163559i	−0.228169	+	0.973621i	$0.573274\pi$
$908$	−6703.96	−	5428.76i	−0.245020	−	0.198414i
$909$	754.450	+	2321.96i	0.0275286	+	0.0847244i
$910$	−25697.1	+	15043.7i	−0.936101	+	0.548014i
$911$	9474.19	−	29158.6i	0.344560	−	1.06045i	−0.617259	−	0.786760i	$-0.711757\pi$
$911$	9474.19	−	29158.6i	0.344560	−	1.06045i	0.961819	−	0.273686i	$-0.0882429\pi$
$912$	10918.1	−	7090.31i	0.396420	−	0.257438i
$913$	1706.97	+	32571.0i	0.0618757	+	1.18066i
$914$	5184.45	+	24390.9i	0.187622	+	0.882692i
$915$	9447.12	+	14658.9i	0.341325	+	0.529625i
$916$	−22038.9	+	7160.86i	−0.794962	+	0.258299i
$917$	22091.4	+	48373.7i	0.795552	+	1.74203i
$918$	17854.3	+	17854.3i	0.641919	+	0.641919i
$919$	−5766.67	+	606.101i	−0.206991	+	0.0217556i	−0.207456	−	0.978244i	$-0.566519\pi$
$919$	−5766.67	+	606.101i	−0.206991	+	0.0217556i	0.000465359		1.00000i	$0.499852\pi$
$920$	−1854.31	+	1061.99i	−0.0664508	+	0.0380572i
$921$	3986.21	−	37926.3i	0.142617	−	1.35691i
$922$	−49434.9	−	18976.3i	−1.76578	−	0.677820i
$923$	12406.1	+	24348.4i	0.442418	+	0.868295i
$924$	11648.6	−	23409.7i	0.414729	−	0.833467i
$925$	820.327	+	1638.11i	0.0291591	+	0.0582277i
$926$	9723.57	−	16841.7i	0.345071	−	0.597681i
$927$	282.401	+	183.394i	0.0100057	+	0.00649777i
$928$	44090.3	−	35703.6i	1.55963	−	1.26296i
$929$	−29024.8	+	12922.7i	−1.02505	+	0.456383i	−0.849221	−	0.528038i	$-0.822928\pi$
$929$	−29024.8	+	12922.7i	−1.02505	+	0.456383i	−0.175831	+	0.984420i	$0.556261\pi$
$930$	−23052.4	−	16871.6i	−0.812815	−	0.594883i
$931$	6894.57	+	7370.13i	0.242707	+	0.259448i
$932$	−9363.89	+	9363.89i	−0.329103	+	0.329103i
$933$	1484.04	−	1832.64i	0.0520744	−	0.0643065i
$934$	4546.19	−	5049.06i	0.159268	−	0.176885i
$935$	7514.73	−	27659.4i	0.262843	−	0.967445i
$936$	−1429.72	+	1287.33i	−0.0499272	+	0.0449547i
$937$	−12643.4	+	24814.1i	−0.440814	+	0.865146i	0.558549	+	0.829471i	$0.311358\pi$
$937$	−12643.4	+	24814.1i	−0.440814	+	0.865146i	−0.999363	+	0.0356751i	$0.988642\pi$
$938$	−14365.9	−	19382.3i	−0.500067	−	0.674686i
$939$	−6097.61	−	1981.23i	−0.211915	−	0.0688553i
$940$	−476.592	−	1803.78i	−0.0165369	−	0.0625882i
$941$	11452.7	+	10312.1i	0.396756	+	0.357241i	0.843227	−	0.537557i	$-0.180653\pi$
$941$	11452.7	+	10312.1i	0.396756	+	0.357241i	−0.446471	+	0.894798i	$0.647319\pi$
$942$	18368.8	−	7051.12i	0.635337	−	0.243883i
$943$	−46.2210	−	172.499i	−0.00159614	−	0.00595689i
$944$	17101.8	−	12425.2i	0.589637	−	0.428397i
$945$	−1187.69	+	25618.6i	−0.0408843	+	0.881875i
$946$	27196.7	+	19759.5i	0.934715	+	0.679110i
$947$	7855.69	−	20464.8i	0.269563	−	0.702234i	−0.730256	−	0.683174i	$-0.760599\pi$
$947$	7855.69	−	20464.8i	0.269563	−	0.702234i	0.999818	−	0.0190606i	$-0.00606753\pi$
$948$	−20532.2	+	31616.8i	−0.703434	+	1.08319i
$949$	−29568.6	+	17071.4i	−1.01142	+	0.583943i
$950$	−13443.3	−	798.517i	−0.459113	−	0.0272709i
$951$		−	58627.8i		−	1.99909i
$952$	−8431.61	+	4975.58i	−0.287048	+	0.169390i
$953$	3789.18	+	23924.0i	0.128797	+	0.813193i	0.964514	+	0.264032i	$0.0850526\pi$
$953$	3789.18	+	23924.0i	0.128797	+	0.813193i	−0.835717	+	0.549161i	$0.814947\pi$
$954$	−3724.01	−	8364.27i	−0.126383	−	0.283861i
$955$	12118.0	+	21158.8i	0.410605	+	0.716947i
$956$	32009.1	+	14251.4i	1.08290	+	0.482136i
$957$	−68230.2	+	18282.2i	−2.30467	+	0.617534i
$958$	−9867.88	+	62303.4i	−0.332794	+	2.10118i
$959$	39442.0	−	15572.6i	1.32810	−	0.524365i
$960$	4165.69	−	8105.67i	0.140049	−	0.272510i
$961$	9802.27	+	10886.5i	0.329035	+	0.365430i
$962$	−2104.76	+	110.306i	−0.0705406	+	0.00369688i
$963$	6798.54	−	356.296i	0.227497	−	0.0119226i
$964$	−13654.4	−	15164.7i	−0.456201	−	0.506662i
$965$	−5167.18	+	2610.17i	−0.172370	+	0.0870718i
$966$	6062.32	+	4814.36i	0.201917	+	0.160352i
$967$	−4246.69	+	26812.5i	−0.141225	+	0.891658i	0.810730	+	0.585420i	$0.199070\pi$
$967$	−4246.69	+	26812.5i	−0.141225	+	0.891658i	−0.951955	+	0.306238i	$0.900930\pi$
$968$	7236.83	−	1939.10i	0.240290	−	0.0643855i
$969$	−8486.98	−	3778.65i	−0.281363	−	0.125271i
$970$	33990.1	−	37486.3i	1.12511	−	1.24084i
$971$	14848.8	+	33351.0i	0.490753	+	1.10225i	0.973955	+	0.226741i	$0.0728070\pi$
$971$	14848.8	+	33351.0i	0.490753	+	1.10225i	−0.483202	+	0.875509i	$0.660526\pi$
$972$	−1208.70	−	7631.45i	−0.0398860	−	0.251830i
$973$	25486.1	−	242.560i	0.839718	−	0.00799190i
$974$			28015.4i			0.921635i
$975$	27707.4	−	2717.06i	0.910098	−	0.0892469i
$976$	−18584.9	+	10730.0i	−0.609516	+	0.351904i
$977$	17714.8	−	27278.4i	0.580089	−	0.893258i	−0.419808	−	0.907613i	$-0.637903\pi$
$977$	17714.8	−	27278.4i	0.580089	−	0.893258i	0.999897	+	0.0143547i	$0.00456941\pi$
$978$	−5515.38	+	14368.0i	−0.180330	+	0.469775i
$979$	−20510.7	−	14901.9i	−0.669586	−	0.486483i
$980$	19817.4	+	6100.07i	0.645963	+	0.198836i
$981$	4040.56	−	2935.64i	0.131504	−	0.0955430i
$982$	8502.57	+	31732.0i	0.276301	+	1.03117i
$983$	−25388.0	+	9745.52i	−0.823754	+	0.316209i	−0.733483	−	0.679708i	$-0.762107\pi$
$983$	−25388.0	+	9745.52i	−0.823754	+	0.316209i	−0.0902707	+	0.995917i	$0.528773\pi$
$984$	−354.966	−	319.613i	−0.0114999	−	0.0103546i
$985$	−32522.8	−	26524.6i	−1.05204	−	0.858015i
$986$	−52450.2	−	17042.1i	−1.69407	−	0.550437i
$987$	2604.07	−	1930.10i	0.0839803	−	0.0622450i
$988$	2836.65	−	5567.24i	0.0913420	−	0.179269i
$989$	−2982.93	+	2685.84i	−0.0959065	+	0.0863546i
$990$	−7579.14	+	6093.86i	−0.243314	+	0.195632i
$991$	−16394.1	+	18207.5i	−0.525505	+	0.583633i	−0.946205	−	0.323567i	$-0.895118\pi$
$991$	−16394.1	+	18207.5i	−0.525505	+	0.583633i	0.420700	+	0.907200i	$0.361785\pi$
$992$	16240.5	−	20055.4i	0.519795	−	0.641894i
$993$	37135.6	−	37135.6i	1.18677	−	1.18677i
$994$	16489.1	−	44208.7i	0.526161	−	1.41068i
$995$	11481.6	−	34922.2i	0.365820	−	1.11267i
$996$	19842.1	−	8834.26i	0.631245	−	0.281048i
$997$	−19690.7	+	15945.2i	−0.625488	+	0.506510i	−0.888857	−	0.458185i	$-0.848500\pi$
$997$	−19690.7	+	15945.2i	−0.625488	+	0.506510i	0.263369	+	0.964695i	$0.415166\pi$
$998$	−50146.4	−	32565.4i	−1.59054	−	1.03291i
$999$	−907.635	+	1572.07i	−0.0287450	+	0.0497879i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.x.a.103.12	yes	928
7.3	odd	6	inner	175.4.x.a.3.47	✓	928
25.17	odd	20	inner	175.4.x.a.117.47	yes	928
175.17	even	60	inner	175.4.x.a.17.12	yes	928

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.4.x.a.3.47	✓	928	7.3	odd	6	inner
175.4.x.a.17.12	yes	928	175.17	even	60	inner
175.4.x.a.103.12	yes	928	1.1	even	1	trivial
175.4.x.a.117.47	yes	928	25.17	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.65654 - 0.191631i) q^{2} +(-3.56883 - 4.40714i) q^{3} +(5.37736 + 0.565184i) q^{4} +(-7.45211 - 8.33463i) q^{5} +(12.2050 + 16.7988i) q^{6} +(5.89045 + 17.5585i) q^{7} +(9.37758 + 1.48526i) q^{8} +(-1.07270 + 5.04663i) q^{9} +(25.6517 + 31.9039i) q^{10} +(45.0384 - 9.57321i) q^{11} +(-16.7000 - 25.7158i) q^{12} +(34.9937 + 17.8302i) q^{13} +(-18.1739 - 65.3323i) q^{14} +(-10.1366 + 62.5873i) q^{15} +(-76.3155 - 16.2214i) q^{16} +(19.9528 + 51.9788i) q^{17} +(4.88944 - 18.2476i) q^{18} +(-3.07560 - 29.2623i) q^{19} +(-35.3621 - 49.0301i) q^{20} +(56.3609 - 88.6234i) q^{21} +(-166.519 + 26.3740i) q^{22} +(1.05355 - 20.1029i) q^{23} +(-26.9212 - 46.6289i) q^{24} +(-13.9321 + 124.221i) q^{25} +(-124.539 - 71.9027i) q^{26} +(-110.357 + 56.2297i) q^{27} +(21.7513 + 97.7479i) q^{28} +(159.008 - 218.856i) q^{29} +(49.0583 - 226.910i) q^{30} +(50.0497 - 112.413i) q^{31} +(202.574 + 54.2796i) q^{32} +(-202.925 - 164.325i) q^{33} +(-62.9974 - 193.886i) q^{34} +(102.448 - 179.943i) q^{35} +(-8.62054 + 26.5313i) q^{36} +(12.2917 - 7.98236i) q^{37} +(5.63846 + 107.588i) q^{38} +(-46.3065 - 217.855i) q^{39} +(-57.5036 - 89.2270i) q^{40} +(8.43713 - 2.74139i) q^{41} +(-223.069 + 313.254i) q^{42} +(-140.993 - 140.993i) q^{43} +(247.598 - 26.0236i) q^{44} +(50.0557 - 28.6675i) q^{45} +(-7.70469 + 73.3052i) q^{46} +(28.8124 + 11.0601i) q^{47} +(200.867 + 394.224i) q^{48} +(-273.605 + 206.855i) q^{49} +(74.7480 - 451.549i) q^{50} +(157.870 - 273.438i) q^{51} +(178.097 + 115.657i) q^{52} +(376.650 - 305.005i) q^{53} +(414.300 - 184.458i) q^{54} +(-415.420 - 304.038i) q^{55} +(29.1591 + 173.406i) q^{56} +(-117.987 + 117.987i) q^{57} +(-623.358 + 769.784i) q^{58} +(-181.296 + 201.350i) q^{59} +(-89.8812 + 330.826i) q^{60} +(204.406 - 184.048i) q^{61} +(-204.550 + 401.453i) q^{62} +(-94.9302 + 10.8919i) q^{63} +(-136.704 - 44.4177i) q^{64} +(-112.169 - 424.533i) q^{65} +(710.512 + 639.748i) q^{66} +(332.139 - 127.496i) q^{67} +(77.9158 + 290.786i) q^{68} +(-92.3563 + 67.1008i) q^{69} +(-409.087 + 638.336i) q^{70} +(562.908 + 408.976i) q^{71} +(-17.5549 + 45.7320i) q^{72} +(-473.477 + 729.091i) q^{73} +(-46.4749 + 26.8323i) q^{74} +(597.181 - 381.923i) q^{75} -159.092i q^{76} +(433.388 + 734.418i) q^{77} +(127.574 + 805.469i) q^{78} +(-500.071 - 1123.18i) q^{79} +(433.512 + 756.945i) q^{80} +(768.917 + 342.344i) q^{81} +(-31.3760 + 8.40718i) q^{82} +(-110.810 + 699.629i) q^{83} +(353.162 - 444.706i) q^{84} +(284.534 - 553.651i) q^{85} +(488.529 + 542.567i) q^{86} +(-1532.00 + 80.2887i) q^{87} +(436.570 - 22.8797i) q^{88} +(-368.430 - 409.183i) q^{89} +(-188.524 + 95.2317i) q^{90} +(-106.944 + 719.467i) q^{91} +(17.0272 - 107.505i) q^{92} +(-674.040 + 180.608i) q^{93} +(-103.234 - 45.9628i) q^{94} +(-220.971 + 243.700i) q^{95} +(-483.735 - 1086.49i) q^{96} +(-193.365 - 1220.86i) q^{97} +(1040.09 - 703.943i) q^{98} +237.561i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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