LMFDB - Embedded newform 175.4.x.a.3.43

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(3,175)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			3.43
Character	$\chi$	$=$	175.3
Dual form			175.4.x.a.117.43

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.66660 - 2.56634i) q^{2} +(3.28687 - 8.56260i) q^{3} +(-0.554650 - 1.24576i) q^{4} +(5.95503 + 9.46244i) q^{5} +(-16.4966 - 22.7057i) q^{6} +(16.8267 - 7.73716i) q^{7} +(20.0573 + 3.17676i) q^{8} +(-42.4496 - 38.2218i) q^{9} +(34.2085 + 0.487482i) q^{10} +(-18.2776 - 20.2994i) q^{11} +(-12.4900 + 0.654575i) q^{12} +(-30.7491 - 15.6674i) q^{13} +(8.18715 - 56.0777i) q^{14} +(100.596 - 19.8887i) q^{15} +(48.8798 - 54.2865i) q^{16} +(-33.3321 + 41.1617i) q^{17} +(-168.837 + 45.2397i) q^{18} +(17.3924 + 7.74361i) q^{19} +(8.48500 - 12.6669i) q^{20} +(-10.9431 - 169.511i) q^{21} +(-82.5567 + 13.0757i) q^{22} +(91.8109 + 59.6227i) q^{23} +(93.1269 - 161.301i) q^{24} +(-54.0754 + 112.698i) q^{25} +(-91.4544 + 52.8012i) q^{26} +(-246.157 + 125.423i) q^{27} +(-18.9716 - 16.6706i) q^{28} +(-142.281 + 195.833i) q^{29} +(116.613 - 291.311i) q^{30} +(112.275 - 11.8006i) q^{31} +(-15.8073 - 58.9935i) q^{32} +(-233.892 + 89.7826i) q^{33} +(50.0836 + 154.141i) q^{34} +(173.416 + 113.146i) q^{35} +(-24.0707 + 74.0819i) q^{36} +(9.15272 + 174.644i) q^{37} +(48.8590 - 31.7294i) q^{38} +(-235.222 + 211.795i) q^{39} +(89.3816 + 208.708i) q^{40} +(-190.983 + 62.0541i) q^{41} +(-453.260 - 254.423i) q^{42} +(-131.557 - 131.557i) q^{43} +(-15.1505 + 34.0287i) q^{44} +(108.883 - 629.289i) q^{45} +(306.024 - 136.251i) q^{46} +(440.124 - 356.405i) q^{47} +(-304.172 - 596.971i) q^{48} +(223.273 - 260.381i) q^{49} +(199.100 + 326.598i) q^{50} +(242.893 + 420.702i) q^{51} +(-2.46296 + 46.9960i) q^{52} +(-275.106 - 105.603i) q^{53} +(-88.3668 + 840.754i) q^{54} +(83.2378 - 293.834i) q^{55} +(362.076 - 101.732i) q^{56} +(123.472 - 123.472i) q^{57} +(265.448 + 691.516i) q^{58} +(425.060 + 90.3494i) q^{59} +(-80.5723 - 114.288i) q^{60} +(14.1121 + 66.3922i) q^{61} +(156.833 - 307.803i) q^{62} +(-1010.01 - 314.706i) q^{63} +(378.053 + 122.837i) q^{64} +(-34.8594 - 384.261i) q^{65} +(-159.391 + 749.877i) q^{66} +(594.519 + 481.432i) q^{67} +(69.7653 + 18.6936i) q^{68} +(812.296 - 590.168i) q^{69} +(579.386 - 256.474i) q^{70} +(-785.349 - 570.590i) q^{71} +(-730.001 - 901.477i) q^{72} +(-540.459 - 28.3242i) q^{73} +(463.451 + 267.573i) q^{74} +(787.249 + 833.450i) q^{75} -25.9618i q^{76} +(-464.611 - 200.154i) q^{77} +(151.517 + 956.638i) q^{78} +(-708.371 - 74.4528i) q^{79} +(804.763 + 139.244i) q^{80} +(103.650 + 986.161i) q^{81} +(-159.040 + 593.546i) q^{82} +(-185.606 + 1171.87i) q^{83} +(-205.101 + 107.652i) q^{84} +(-587.983 - 70.2837i) q^{85} +(-556.874 + 118.367i) q^{86} +(1209.18 + 1861.97i) q^{87} +(-302.113 - 465.214i) q^{88} +(819.936 - 174.283i) q^{89} +(-1433.50 - 1328.20i) q^{90} +(-638.626 - 25.7202i) q^{91} +(23.3529 - 147.444i) q^{92} +(267.990 - 1000.15i) q^{93} +(-181.146 - 1723.49i) q^{94} +(30.2990 + 210.688i) q^{95} +(-557.094 - 58.5530i) q^{96} +(223.240 + 1409.48i) q^{97} +(-296.119 - 1006.95i) q^{98} +1560.31i 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	1.66660	−	2.56634i	0.589232	−	0.907338i	−0.410758	−	0.911744i	$-0.634736\pi$
$2$	1.66660	−	2.56634i	0.589232	−	0.907338i	0.999990	+	0.00440625i	$0.00140256\pi$
$3$	3.28687	−	8.56260i	0.632559	−	1.64787i	−0.122698	−	0.992444i	$-0.539155\pi$
$3$	3.28687	−	8.56260i	0.632559	−	1.64787i	0.755257	−	0.655428i	$-0.227512\pi$
$4$	−0.554650	−	1.24576i	−0.0693312	−	0.155720i
$5$	5.95503	+	9.46244i	0.532634	+	0.846346i
$5$	5.95503	+	9.46244i	0.532634	+	0.846346i
$6$	−16.4966	−	22.7057i	−1.12245	−	1.54492i
$7$	16.8267	−	7.73716i	0.908554	−	0.417767i
$7$	16.8267	−	7.73716i	0.908554	−	0.417767i
$8$	20.0573	+	3.17676i	0.886414	+	0.140394i
$9$	−42.4496	−	38.2218i	−1.57221	−	1.41562i
$10$	34.2085	+	0.487482i	1.08177	+	0.0154155i
$11$	−18.2776	−	20.2994i	−0.500993	−	0.556409i	0.438609	−	0.898678i	$-0.355471\pi$
$11$	−18.2776	−	20.2994i	−0.500993	−	0.556409i	−0.939602	+	0.342269i	$0.888805\pi$
$12$	−12.4900	+	0.654575i	−0.300463	+	0.0157466i
$13$	−30.7491	−	15.6674i	−0.656020	−	0.334259i	0.0940979	−	0.995563i	$-0.470003\pi$
$13$	−30.7491	−	15.6674i	−0.656020	−	0.334259i	−0.750118	+	0.661304i	$0.770003\pi$
$14$	8.18715	−	56.0777i	0.156293	−	1.07053i
$15$	100.596	−	19.8887i	1.73159	−	0.342349i
$16$	48.8798	−	54.2865i	0.763747	−	0.848227i
$17$	−33.3321	+	41.1617i	−0.475542	+	0.587246i	−0.957314	−	0.289051i	$-0.906660\pi$
$17$	−33.3321	+	41.1617i	−0.475542	+	0.587246i	0.481772	+	0.876297i	$0.339994\pi$
$18$	−168.837	+	45.2397i	−2.21084	+	0.592394i
$19$	17.3924	+	7.74361i	0.210005	+	0.0935003i	0.509044	−	0.860741i	$-0.329999\pi$
$19$	17.3924	+	7.74361i	0.210005	+	0.0935003i	−0.299038	+	0.954241i	$0.596666\pi$
$20$	8.48500	−	12.6669i	0.0948652	−	0.141620i
$21$	−10.9431	−	169.511i	−0.113713	−	1.76144i
$22$	−82.5567	+	13.0757i	−0.800052	+	0.126716i
$23$	91.8109	+	59.6227i	0.832343	+	0.540530i	0.889023	−	0.457862i	$-0.151385\pi$
$23$	91.8109	+	59.6227i	0.832343	+	0.540530i	−0.0566797	+	0.998392i	$0.518051\pi$
$24$	93.1269	−	161.301i	0.792061	−	1.37189i
$25$	−54.0754	+	112.698i	−0.432603	+	0.901585i
$26$	−91.4544	+	52.8012i	−0.689834	+	0.398276i
$27$	−246.157	+	125.423i	−1.75455	+	0.893990i
$28$	−18.9716	−	16.6706i	−0.128046	−	0.112516i
$29$	−142.281	+	195.833i	−0.911065	+	1.25397i	0.0557366	+	0.998446i	$0.482249\pi$
$29$	−142.281	+	195.833i	−0.911065	+	1.25397i	−0.966802	+	0.255528i	$0.917751\pi$
$30$	116.613	−	291.311i	0.709684	−	1.77286i
$31$	112.275	−	11.8006i	0.650491	−	0.0683693i	0.226465	−	0.974019i	$-0.427283\pi$
$31$	112.275	−	11.8006i	0.650491	−	0.0683693i	0.424026	+	0.905650i	$0.360617\pi$
$32$	−15.8073	−	58.9935i	−0.0873237	−	0.325896i
$33$	−233.892	+	89.7826i	−1.23380	+	0.473611i
$34$	50.0836	+	154.141i	0.252626	+	0.777501i
$35$	173.416	+	113.146i	0.837502	+	0.546434i
$36$	−24.0707	+	74.0819i	−0.111438	+	0.342972i
$37$	9.15272	+	174.644i	0.0406675	+	0.775983i	0.940510	+	0.339767i	$0.110348\pi$
$37$	9.15272	+	174.644i	0.0406675	+	0.775983i	−0.899842	+	0.436216i	$0.856318\pi$
$38$	48.8590	−	31.7294i	0.208578	−	0.135452i
$39$	−235.222	+	211.795i	−0.965788	+	0.869599i
$40$	89.3816	+	208.708i	0.353312	+	0.824991i
$41$	−190.983	+	62.0541i	−0.727476	+	0.236371i	−0.649261	−	0.760565i	$-0.724922\pi$
$41$	−190.983	+	62.0541i	−0.727476	+	0.236371i	−0.0782144	+	0.996937i	$0.524922\pi$
$42$	−453.260	−	254.423i	−1.66523	−	0.934723i
$43$	−131.557	−	131.557i	−0.466565	−	0.466565i	0.434235	−	0.900800i	$-0.357019\pi$
$43$	−131.557	−	131.557i	−0.466565	−	0.466565i	−0.900800	+	0.434235i	$0.857019\pi$
$44$	−15.1505	+	34.0287i	−0.0519098	+	0.116591i
$45$	108.883	−	629.289i	0.360695	−	2.08464i
$46$	306.024	−	136.251i	0.980887	−	0.436719i
$47$	440.124	−	356.405i	1.36593	−	1.10611i	0.382671	−	0.923885i	$-0.375004\pi$
$47$	440.124	−	356.405i	1.36593	−	1.10611i	0.983257	−	0.182223i	$-0.0583291\pi$
$48$	−304.172	−	596.971i	−0.914654	−	1.79511i
$49$	223.273	−	260.381i	0.650941	−	0.759128i
$50$	199.100	+	326.598i	0.563139	+	0.923760i
$51$	242.893	+	420.702i	0.666897	+	1.15510i
$52$	−2.46296	+	46.9960i	−0.00656828	+	0.125330i
$53$	−275.106	−	105.603i	−0.712994	−	0.273693i	−0.0252861	−	0.999680i	$-0.508050\pi$
$53$	−275.106	−	105.603i	−0.712994	−	0.273693i	−0.687708	+	0.725987i	$0.741383\pi$
$54$	−88.3668	+	840.754i	−0.222689	+	2.11874i
$55$	83.2378	−	293.834i	0.204069	−	0.720375i
$56$	362.076	−	101.732i	0.864007	−	0.242759i
$57$	123.472	−	123.472i	0.286917	−	0.286917i
$58$	265.448	+	691.516i	0.600949	+	1.56553i
$59$	425.060	+	90.3494i	0.937935	+	0.199364i	0.651425	−	0.758713i	$-0.274172\pi$
$59$	425.060	+	90.3494i	0.937935	+	0.199364i	0.286510	+	0.958077i	$0.407505\pi$
$60$	−80.5723	−	114.288i	−0.173364	−	0.245909i
$61$	14.1121	+	66.3922i	0.0296208	+	0.139355i	0.990473	−	0.137706i	$-0.0439729\pi$
$61$	14.1121	+	66.3922i	0.0296208	+	0.139355i	−0.960852	+	0.277061i	$0.910640\pi$
$62$	156.833	−	307.803i	0.321256	−	0.630500i
$63$	−1010.01	−	314.706i	−2.01984	−	0.629353i
$64$	378.053	+	122.837i	0.738385	+	0.239916i
$65$	−34.8594	−	384.261i	−0.0665197	−	0.733258i
$66$	−159.391	+	749.877i	−0.297269	+	1.39854i
$67$	594.519	+	481.432i	1.08406	+	0.877855i	0.993015	−	0.117992i	$-0.0376456\pi$
$67$	594.519	+	481.432i	1.08406	+	0.877855i	0.0910462	+	0.995847i	$0.470979\pi$
$68$	69.7653	+	18.6936i	0.124416	+	0.0333372i
$69$	812.296	−	590.168i	1.41723	−	1.02968i
$70$	579.386	−	256.474i	0.989284	−	0.437921i
$71$	−785.349	−	570.590i	−1.31273	−	0.953754i	−0.999992	−	0.00391469i	$-0.998754\pi$
$71$	−785.349	−	570.590i	−1.31273	−	0.953754i	−0.312738	−	0.949840i	$-0.601246\pi$
$72$	−730.001	−	901.477i	−1.19488	−	1.47556i
$73$	−540.459	−	28.3242i	−0.866519	−	0.0454123i	−0.386106	−	0.922455i	$-0.626180\pi$
$73$	−540.459	−	28.3242i	−0.866519	−	0.0454123i	−0.480413	+	0.877042i	$0.659513\pi$
$74$	463.451	+	267.573i	0.728041	+	0.420335i
$75$	787.249	+	833.450i	1.21205	+	1.28318i
$76$		−	25.9618i		−	0.0391846i
$77$	−464.611	−	200.154i	−0.687628	−	0.296229i
$78$	151.517	+	956.638i	0.219947	+	1.38869i
$79$	−708.371	−	74.4528i	−1.00883	−	0.106033i	−0.414332	−	0.910126i	$-0.635985\pi$
$79$	−708.371	−	74.4528i	−1.00883	−	0.106033i	−0.594503	+	0.804093i	$0.702651\pi$
$80$	804.763	+	139.244i	1.12469	+	0.194600i
$81$	103.650	+	986.161i	0.142181	+	1.35276i
$82$	−159.040	+	593.546i	−0.214184	+	0.799344i
$83$	−185.606	+	1171.87i	−0.245457	+	1.54976i	0.489719	+	0.871880i	$0.337099\pi$
$83$	−185.606	+	1171.87i	−0.245457	+	1.54976i	−0.735176	+	0.677876i	$0.762901\pi$
$84$	−205.101	+	107.652i	−0.266409	+	0.139830i
$85$	−587.983	−	70.2837i	−0.750303	−	0.0896864i
$86$	−556.874	+	118.367i	−0.698247	+	0.148417i
$87$	1209.18	+	1861.97i	1.49009	+	2.29453i
$88$	−302.113	−	465.214i	−0.365970	−	0.563545i
$89$	819.936	−	174.283i	0.976551	−	0.207572i	0.308121	−	0.951347i	$-0.400300\pi$
$89$	819.936	−	174.283i	0.976551	−	0.207572i	0.668430	+	0.743775i	$0.266967\pi$
$90$	−1433.50	−	1328.20i	−1.67894	−	1.55561i
$91$	−638.626	−	25.7202i	−0.735672	−	0.0296287i
$92$	23.3529	−	147.444i	0.0264642	−	0.167088i
$93$	267.990	−	1000.15i	0.298810	−	1.11517i
$94$	−181.146	−	1723.49i	−0.198764	−	1.89111i
$95$	30.2990	+	210.688i	0.0327222	+	0.227538i
$96$	−557.094	−	58.5530i	−0.592273	−	0.0622504i
$97$	223.240	+	1409.48i	0.233677	+	1.47538i	0.773607	+	0.633666i	$0.218451\pi$
$97$	223.240	+	1409.48i	0.233677	+	1.47538i	−0.539930	+	0.841710i	$0.681549\pi$
$98$	−296.119	−	1006.95i	−0.305230	−	1.03793i
$99$			1560.31i			1.58401i
$100$	170.388	+	4.85715i	0.170388	+	0.00485715i
$101$	1570.92	+	906.968i	1.54764	+	0.893532i	0.998321	+	0.0579208i	$0.0184471\pi$
$101$	1570.92	+	906.968i	1.54764	+	0.893532i	0.549321	+	0.835611i	$0.314886\pi$
$102$	1484.47	+	77.7978i	1.44102	+	0.0755209i
$103$	−1185.60	−	1464.09i	−1.13418	−	1.40060i	−0.904044	−	0.427438i	$-0.859416\pi$
$103$	−1185.60	−	1464.09i	−1.13418	−	1.40060i	−0.230136	−	0.973158i	$-0.573917\pi$
$104$	−566.971	−	411.928i	−0.534577	−	0.388393i
$105$	1538.82	−	1112.99i	1.43022	−	1.03444i
$106$	−729.505	+	530.017i	−0.668451	+	0.485658i
$107$	637.456	+	170.806i	0.575936	+	0.154322i	0.535018	−	0.844841i	$-0.320305\pi$
$107$	637.456	+	170.806i	0.575936	+	0.154322i	0.0409184	+	0.999162i	$0.486972\pi$
$108$	292.779	+	237.088i	0.260858	+	0.211239i
$109$	−37.4402	+	176.142i	−0.0329002	+	0.154783i	−0.991531	−	0.129868i	$-0.958545\pi$
$109$	−37.4402	+	176.142i	−0.0329002	+	0.154783i	0.958631	+	0.284651i	$0.0918779\pi$
$110$	−615.355	−	703.321i	−0.533380	−	0.609627i
$111$	1525.49	+	495.663i	1.30444	+	0.423840i
$112$	402.460	−	1291.65i	0.339544	−	1.08973i
$113$	164.007	−	321.883i	0.136536	−	0.267966i	−0.812607	−	0.582811i	$-0.801953\pi$
$113$	164.007	−	321.883i	0.136536	−	0.267966i	0.949143	+	0.314845i	$0.101953\pi$
$114$	−111.093	−	522.650i	−0.0912701	−	0.429392i
$115$	−17.4397	+	1223.81i	−0.0141414	+	0.992355i
$116$	322.877	+	68.6297i	0.258434	+	0.0549319i
$117$	706.449	+	1840.36i	0.558216	+	1.45420i
$118$	940.273	−	940.273i	0.733552	−	0.733552i
$119$	−242.393	+	950.509i	−0.186724	+	0.732210i
$120$	2080.87	−	79.3414i	1.58297	−	0.0603571i
$121$	61.1348	−	581.659i	0.0459315	−	0.437009i
$122$	193.904	+	74.4329i	0.143896	+	0.0552363i
$123$	−96.3922	+	1839.27i	−0.0706617	+	1.34831i
$124$	−76.9741	−	133.323i	−0.0557458	−	0.0965545i
$125$	−1388.42	+	159.435i	−0.993471	+	0.114083i
$126$	−2490.93	+	2067.55i	−1.76119	+	1.46184i
$127$	−283.770	−	556.929i	−0.198272	−	0.389130i	0.770368	−	0.637599i	$-0.220072\pi$
$127$	−283.770	−	556.929i	−0.198272	−	0.389130i	−0.968640	+	0.248469i	$0.920072\pi$
$128$	1325.02	−	1072.98i	0.914969	−	0.740927i
$129$	−1558.88	+	694.059i	−1.06397	+	0.473709i
$130$	−1044.24	−	550.949i	−0.704508	−	0.371703i
$131$	−135.548	+	304.447i	−0.0904040	+	0.203051i	−0.953089	−	0.302692i	$-0.902115\pi$
$131$	−135.548	+	304.447i	−0.0904040	+	0.203051i	0.862684	+	0.505742i	$0.168781\pi$
$132$	241.576	+	241.576i	0.159291	+	0.159291i
$133$	352.570	−	4.26888i	0.229862	−	0.00278315i
$134$	2226.34	−	723.383i	1.43527	−	0.466349i
$135$	−2652.68	−	1582.35i	−1.69116	−	1.00879i
$136$	−799.310	+	719.702i	−0.503973	+	0.453779i
$137$	−167.619	+	108.853i	−0.104531	+	0.0678830i	−0.595846	−	0.803099i	$-0.703183\pi$
$137$	−167.619	+	108.853i	−0.104531	+	0.0678830i	0.491315	+	0.870982i	$0.336516\pi$
$138$	−160.798	−	3068.20i	−0.0991884	−	1.89263i
$139$	504.857	−	1553.79i	0.308068	−	0.948136i	−0.670447	−	0.741958i	$-0.733897\pi$
$139$	504.857	−	1553.79i	0.308068	−	0.948136i	0.978515	−	0.206178i	$-0.0661025\pi$
$140$	44.7686	−	278.791i	0.0270260	−	0.168301i
$141$	−1605.12	−	4940.06i	−0.958693	−	2.95055i
$142$	−2773.19	+	1064.53i	−1.63888	+	0.629107i
$143$	243.982	+	910.551i	0.142677	+	0.532476i
$144$	−4149.86	+	436.167i	−2.40154	+	0.252412i
$145$	−2700.34	−	180.134i	−1.54656	−	0.103168i
$146$	−973.418	+	1339.80i	−0.551785	+	0.759467i
$147$	−1495.67	−	2767.63i	−0.839188	−	1.55286i
$148$	212.489	−	108.269i	0.118017	−	0.0601326i
$149$	−1059.60	+	611.762i	−0.582591	+	0.336359i	−0.762162	−	0.647386i	$-0.775862\pi$
$149$	−1059.60	+	611.762i	−0.582591	+	0.336359i	0.179572	+	0.983745i	$0.442529\pi$
$150$	3450.95	−	631.322i	1.87846	−	0.343648i
$151$	−1089.16	+	1886.48i	−0.586984	+	1.01669i	0.407641	+	0.913142i	$0.366352\pi$
$151$	−1089.16	+	1886.48i	−0.586984	+	1.01669i	−0.994625	+	0.103544i	$0.966982\pi$
$152$	324.245	+	210.567i	0.173025	+	0.112363i
$153$	2988.21	−	473.286i	1.57897	−	0.250084i
$154$	−1287.98	+	858.774i	−0.673953	+	0.449363i
$155$	780.264	+	992.123i	0.404337	+	0.514124i
$156$	394.313	+	175.559i	0.202374	+	0.0901025i
$157$	2070.11	−	554.685i	1.05231	−	0.281966i	0.309105	−	0.951028i	$-0.399970\pi$
$157$	2070.11	−	554.685i	1.05231	−	0.281966i	0.743207	+	0.669062i	$0.233304\pi$
$158$	−1371.64	+	1693.84i	−0.690646	+	0.852876i
$159$	−1808.48	+	2008.52i	−0.902022	+	1.00180i
$160$	464.090	−	500.883i	0.229310	−	0.247489i
$161$	2006.18	+	292.896i	0.982045	+	0.143375i
$162$	2703.57	+	1377.54i	1.31119	+	0.668083i
$163$	−2437.41	+	127.739i	−1.17124	+	0.0613823i	−0.628014	−	0.778202i	$-0.716132\pi$
$163$	−2437.41	+	127.739i	−1.17124	+	0.0613823i	−0.543229	+	0.839584i	$0.682799\pi$
$164$	183.233	+	203.501i	0.0872446	+	0.0968949i
$165$	−2242.39	−	1678.53i	−1.05800	−	0.791959i
$166$	2698.09	+	2429.37i	1.26152	+	1.13588i
$167$	2484.70	+	393.537i	1.15133	+	0.182352i	0.702780	−	0.711407i	$-0.251942\pi$
$167$	2484.70	+	393.537i	1.15133	+	0.182352i	0.448547	+	0.893759i	$0.351942\pi$
$168$	319.007	−	3434.69i	0.146500	−	1.57733i
$169$	−591.327	−	813.891i	−0.269152	−	0.370456i
$170$	−1160.30	+	1391.83i	−0.523478	+	0.627932i
$171$	−442.327	−	993.483i	−0.197811	−	0.444290i
$172$	−90.9209	+	236.857i	−0.0403061	+	0.105001i
$173$	1793.77	−	2762.17i	0.788312	−	1.21389i	−0.184621	−	0.982810i	$-0.559106\pi$
$173$	1793.77	−	2762.17i	0.788312	−	1.21389i	0.972934	−	0.231085i	$-0.0742274\pi$
$174$	6793.67			2.95992
$175$	−37.9449	+	2314.72i	−0.0163907	+	0.999866i
$176$	−1995.39			−0.854592
$177$	2170.74	−	3342.65i	0.921826	−	1.41949i
$178$	919.237	−	2394.69i	0.387077	−	1.00837i
$179$	−85.5285	−	192.100i	−0.0357134	−	0.0802136i	0.894808	−	0.446451i	$-0.147312\pi$
$179$	−85.5285	−	192.100i	−0.0357134	−	0.0802136i	−0.930521	+	0.366238i	$0.880646\pi$
$180$	−844.336	+	213.392i	−0.349628	+	0.0883629i
$181$	−1993.91	−	2744.38i	−0.818819	−	1.12701i	−0.989902	−	0.141751i	$-0.954727\pi$
$181$	−1993.91	−	2744.38i	−0.818819	−	1.12701i	0.171083	−	0.985257i	$-0.445273\pi$
$182$	−1130.34	+	1596.07i	−0.460365	+	0.650045i
$183$	614.874	+	97.3865i	0.248376	+	0.0393389i
$184$	1652.07	+	1487.53i	0.661913	+	0.595990i
$185$	−1598.06	+	1126.62i	−0.635089	+	0.447733i
$186$	−2120.10	−	2354.61i	−0.835771	−	0.928218i
$187$	1444.79	−	75.7182i	0.564991	−	0.0296099i
$188$	−688.111	−	350.610i	−0.266945	−	0.136015i
$189$	−3171.58	+	4015.01i	−1.22063	+	1.54523i
$190$	591.194	+	273.376i	0.225735	+	0.104383i
$191$	−1972.86	+	2191.08i	−0.747389	+	0.830059i	−0.990148	−	0.140027i	$-0.955281\pi$
$191$	−1972.86	+	2191.08i	−0.747389	+	0.830059i	0.242759	+	0.970087i	$0.421948\pi$
$192$	2294.42	−	2833.37i	0.862423	−	1.06500i
$193$	−3830.73	+	1026.44i	−1.42871	+	0.382823i	−0.888566	−	0.458748i	$-0.848298\pi$
$193$	−3830.73	+	1026.44i	−1.42871	+	0.382823i	−0.540147	+	0.841571i	$0.681631\pi$
$194$	3989.27	+	1776.14i	1.47635	+	0.657315i
$195$	−3404.85	−	964.531i	−1.25039	−	0.354213i
$196$	−448.211	−	133.725i	−0.163342	−	0.0487336i
$197$	−2206.19	+	349.426i	−0.797890	+	0.126373i	−0.542051	−	0.840346i	$-0.682352\pi$
$197$	−2206.19	+	349.426i	−0.797890	+	0.126373i	−0.255840	+	0.966719i	$0.582352\pi$
$198$	4004.27	+	2600.41i	1.43723	+	0.933348i
$199$	1251.41	−	2167.51i	0.445781	−	0.772116i	−0.552325	−	0.833629i	$-0.686259\pi$
$199$	1251.41	−	2167.51i	0.445781	−	0.772116i	0.998106	+	0.0615132i	$0.0195926\pi$
$200$	−1442.62	+	2088.63i	−0.510042	+	0.738442i
$201$	6076.42	−	3508.22i	2.13233	−	1.23110i
$202$	4945.68	−	2519.95i	1.72266	−	0.877737i
$203$	−878.922	+	4396.06i	−0.303883	+	1.51992i
$204$	389.375	−	535.929i	0.133636	−	0.183934i
$205$	−1724.49	−	1437.63i	−0.587530	−	0.489797i
$206$	−5733.28	+	602.592i	−1.93911	+	0.203809i
$207$	−1618.45	−	6040.14i	−0.543430	−	2.02811i
$208$	−2353.54	+	903.439i	−0.784561	+	0.301165i
$209$	−160.702	−	494.591i	−0.0531866	−	0.163692i
$210$	−291.712	−	5804.04i	−0.0958573	−	1.90722i
$211$	566.141	−	1742.40i	0.184714	−	0.568492i	−0.815229	−	0.579139i	$-0.803389\pi$
$211$	566.141	−	1742.40i	0.184714	−	0.568492i	0.999943	+	0.0106464i	$0.00338893\pi$
$212$	21.0307	+	401.289i	0.00681318	+	0.130003i
$213$	−7467.07	+	4849.17i	−2.40204	+	1.55991i
$214$	1500.73	−	1351.26i	0.479382	−	0.431637i
$215$	461.425	−	2028.28i	0.146367	−	0.643383i
$216$	−5335.68	+	1733.67i	−1.68077	+	0.546116i
$217$	1797.91	−	1067.25i	0.562443	−	0.333871i
$218$	389.643	+	389.643i	0.121055	+	0.121055i
$219$	−2018.95	+	4534.63i	−0.622958	+	1.39919i
$220$	−412.216	+	59.2806i	−0.126325	+	0.0181668i
$221$	1669.83	−	743.456i	0.508257	−	0.226291i
$222$	3814.43	−	3088.86i	1.15319	−	0.933832i
$223$	−352.484	−	691.789i	−0.105848	−	0.207738i	0.832008	−	0.554764i	$-0.187192\pi$
$223$	−352.484	−	691.789i	−0.105848	−	0.207738i	−0.937856	+	0.347026i	$0.887192\pi$
$224$	−722.426	−	870.361i	−0.215487	−	0.259614i
$225$	6603.00	−	2717.13i	1.95644	−	0.805076i
$226$	−552.726	−	957.349i	−0.162685	−	0.281778i
$227$	86.8784	−	1657.74i	0.0254023	−	0.484705i	−0.956075	−	0.293124i	$-0.905305\pi$
$227$	86.8784	−	1657.74i	0.0254023	−	0.484705i	0.981477	−	0.191581i	$-0.0613614\pi$
$228$	−222.301	−	85.3333i	−0.0645712	−	0.0247866i
$229$	36.9237	−	351.305i	0.0106550	−	0.101375i	−0.987902	−	0.155080i	$-0.950436\pi$
$229$	36.9237	−	351.305i	0.0106550	−	0.101375i	0.998557	+	0.0537051i	$0.0171031\pi$
$230$	3111.65	+	2084.36i	0.892069	+	0.597559i
$231$	−3240.95	+	3320.40i	−0.923113	+	0.945741i
$232$	−3475.88	+	3475.88i	−0.983631	+	0.983631i
$233$	1318.26	+	3434.18i	0.370652	+	0.965581i	0.984379	+	0.176063i	$0.0563363\pi$
$233$	1318.26	+	3434.18i	0.370652	+	0.965581i	−0.613727	+	0.789518i	$0.710330\pi$
$234$	5900.36	+	1254.16i	1.64837	+	0.350372i
$235$	5993.41	+	2042.24i	1.66369	+	0.566898i
$236$	−123.206	−	579.637i	−0.0339831	−	0.159878i
$237$	−2965.83	+	5820.78i	−0.812876	+	1.59536i
$238$	2035.36	+	2206.18i	0.554339	+	0.600864i
$239$	−1695.61	−	550.937i	−0.458912	−	0.149109i	0.0704327	−	0.997517i	$-0.477562\pi$
$239$	−1695.61	−	550.937i	−0.458912	−	0.149109i	−0.529344	+	0.848407i	$0.677562\pi$
$240$	3837.45	−	6433.18i	1.03211	−	1.73025i
$241$	−518.048	+	2437.22i	−0.138466	+	0.651433i	0.853091	+	0.521763i	$0.174725\pi$
$241$	−518.048	+	2437.22i	−0.138466	+	0.651433i	−0.991557	+	0.129671i	$0.958608\pi$
$242$	−1390.85	−	1126.29i	−0.369450	−	0.299175i
$243$	1579.70	+	423.278i	0.417027	+	0.111742i
$244$	74.8817	−	54.4047i	0.0196468	−	0.0142742i
$245$	3793.43	+	562.130i	0.989198	+	0.146584i
$246$	4559.55	+	3312.71i	1.18173	+	0.858579i
$247$	−413.479	−	510.604i	−0.106514	−	0.131534i
$248$	2289.42	+	119.983i	0.586202	+	0.0307216i
$249$	9424.21	+	5441.07i	2.39853	+	1.38479i
$250$	−1904.77	+	3828.87i	−0.481874	+	0.968636i
$251$		−	6750.43i		−	1.69754i	−0.528759	−	0.848772i	$-0.677342\pi$
$251$		−	6750.43i		−	1.69754i	0.528759	−	0.848772i	$-0.322658\pi$
$252$	168.154	+	1432.79i	0.0420346	+	0.358164i
$253$	−467.783	−	2953.47i	−0.116242	−	0.733925i
$254$	−1902.20	−	199.929i	−0.469900	−	0.0493885i
$255$	−2534.44	+	4803.65i	−0.622402	+	1.17967i
$256$	−212.943	−	2026.02i	−0.0519880	−	0.494633i
$257$	−1866.88	+	6967.30i	−0.453124	+	1.69108i	0.240420	+	0.970669i	$0.422715\pi$
$257$	−1866.88	+	6967.30i	−0.453124	+	1.69108i	−0.693544	+	0.720414i	$0.743952\pi$
$258$	−816.843	+	5157.34i	−0.197110	+	1.24450i
$259$	1505.26	+	2867.86i	0.361129	+	0.688033i
$260$	−459.364	+	256.557i	−0.109571	+	0.0611961i
$261$	13524.8	−	2874.80i	3.20754	−	0.681783i
$262$	555.409	+	855.255i	0.130967	+	0.201671i
$263$	−1640.55	−	2526.22i	−0.384640	−	0.592294i	0.592323	−	0.805700i	$-0.298211\pi$
$263$	−1640.55	−	2526.22i	−0.384640	−	0.592294i	−0.976964	+	0.213406i	$0.931544\pi$
$264$	−4976.44	+	1057.78i	−1.16015	+	0.246597i
$265$	−638.998	−	3232.04i	−0.148126	−	0.749218i
$266$	576.638	−	911.929i	0.132917	−	0.210203i
$267$	1202.71	−	7593.63i	0.275673	−	1.74053i
$268$	270.001	−	1007.66i	0.0615407	−	0.229673i
$269$	692.994	+	6593.40i	0.157073	+	1.49445i	0.734837	+	0.678244i	$0.237259\pi$
$269$	692.994	+	6593.40i	0.157073	+	1.49445i	−0.577764	+	0.816204i	$0.696075\pi$
$270$	−8481.80	+	4170.54i	−1.91180	+	0.940042i
$271$	−2490.61	−	261.774i	−0.558280	−	0.0586776i	−0.178814	−	0.983883i	$-0.557226\pi$
$271$	−2490.61	−	261.774i	−0.558280	−	0.0586776i	−0.379467	+	0.925205i	$0.623893\pi$
$272$	605.259	+	3821.46i	0.134924	+	0.851874i
$273$	−2319.31	+	5383.76i	−0.514180	+	1.19355i
$274$			611.583i			0.134843i
$275$	3276.07	−	962.159i	0.718380	−	0.210983i
$276$	−1185.75	−	684.592i	−0.258600	−	0.149303i
$277$	−5733.71	−	300.491i	−1.24370	−	0.0651796i	−0.580900	−	0.813975i	$-0.697299\pi$
$277$	−5733.71	−	300.491i	−1.24370	−	0.0651796i	−0.662801	+	0.748795i	$0.730633\pi$
$278$	−3146.16	−	3885.18i	−0.678756	−	0.838194i
$279$	−5217.08	−	3790.43i	−1.11949	−	0.813358i
$280$	3118.80	+	2820.30i	0.665657	+	0.601947i
$281$	736.192	−	534.875i	0.156290	−	0.113551i	−0.506892	−	0.862010i	$-0.669206\pi$
$281$	736.192	−	534.875i	0.156290	−	0.113551i	0.663182	+	0.748458i	$0.269206\pi$
$282$	−15353.0	−	4113.82i	−3.24204	−	0.868703i
$283$	1381.64	+	1118.83i	0.290212	+	0.235009i	0.763359	−	0.645974i	$-0.223549\pi$
$283$	1381.64	+	1118.83i	0.290212	+	0.235009i	−0.473147	+	0.880983i	$0.656882\pi$
$284$	−275.226	+	1294.84i	−0.0575059	+	0.270544i
$285$	1903.63	+	433.067i	0.395653	+	0.0900095i
$286$	2743.40	+	891.386i	0.567206	+	0.184296i
$287$	−2733.48	+	2521.83i	−0.562203	+	0.518671i
$288$	−1583.83	+	3108.44i	−0.324055	+	0.635994i
$289$	438.213	+	2061.63i	0.0891946	+	0.419628i
$290$	−4962.67	+	6629.78i	−1.00489	+	1.34246i
$291$	12802.6	+	2721.28i	2.57905	+	0.548193i
$292$	264.480	+	688.993i	0.0530052	+	0.138083i
$293$	3115.70	−	3115.70i	0.621233	−	0.621233i	−0.324614	−	0.945847i	$-0.605234\pi$
$293$	3115.70	−	3115.70i	0.621233	−	0.621233i	0.945847	+	0.324614i	$0.105234\pi$
$294$	−9595.37	−	774.150i	−1.90345	−	0.153569i
$295$	1676.32	+	4560.14i	0.330845	+	0.900005i
$296$	−371.224	+	3531.96i	−0.0728952	+	0.693551i
$297$	7045.19	+	2704.40i	1.37644	+	0.528367i
$298$	−195.945	+	3738.86i	−0.0380900	+	0.726800i
$299$	−1888.97	−	3271.79i	−0.365357	−	0.632817i
$300$	601.633	−	1443.00i	0.115784	−	0.277705i
$301$	−3231.55	−	1195.79i	−0.618814	−	0.228984i
$302$	3026.16	+	5939.17i	0.576608	+	1.13166i
$303$	12929.4	−	10470.0i	2.45140	−	1.98511i
$304$	1270.51	−	565.668i	0.239700	−	0.106721i
$305$	−544.194	+	528.902i	−0.102165	+	0.0992946i
$306$	3765.54	−	8457.53i	0.703469	−	1.58002i
$307$	−6748.13	−	6748.13i	−1.25451	−	1.25451i	−0.953675	−	0.300840i	$-0.902733\pi$
$307$	−6748.13	−	6748.13i	−1.25451	−	1.25451i	−0.300840	−	0.953675i	$-0.597267\pi$
$308$	8.35216	+	689.811i	0.00154516	+	0.127616i
$309$	−16433.4	+	5339.52i	−3.02544	+	0.983025i
$310$	3846.51	−	348.948i	0.704733	−	0.0639320i
$311$	−3449.68	+	3106.11i	−0.628982	+	0.566338i	−0.920751	−	0.390151i	$-0.872423\pi$
$311$	−3449.68	+	3106.11i	−0.628982	+	0.566338i	0.291769	+	0.956489i	$0.405756\pi$
$312$	−5390.74	+	3500.78i	−0.978174	+	0.635234i
$313$	−324.413	−	6190.17i	−0.0585844	−	1.11786i	−0.856855	−	0.515558i	$-0.827585\pi$
$313$	−324.413	−	6190.17i	−0.0585844	−	1.11786i	0.798270	−	0.602299i	$-0.205749\pi$
$314$	2026.54	−	6237.05i	0.364218	−	1.12095i
$315$	−3036.77	−	11431.3i	−0.543183	−	2.04469i
$316$	300.147	+	923.758i	0.0534322	+	0.164448i
$317$	−4787.54	+	1837.77i	−0.848250	+	0.325613i	−0.743377	−	0.668873i	$-0.766777\pi$
$317$	−4787.54	+	1837.77i	−0.848250	+	0.325613i	−0.104873	+	0.994486i	$0.533444\pi$
$318$	2140.53	+	7988.56i	0.377468	+	1.40873i
$319$	6575.84	−	691.149i	1.15416	−	0.121307i
$320$	1088.98	+	4308.80i	0.190237	+	0.752717i
$321$	3557.78	−	4896.86i	0.618616	−	0.851452i
$322$	4095.17	−	4660.40i	0.708742	−	0.806565i
$323$	−898.466	+	457.791i	−0.154774	+	0.0788612i
$324$	1171.03	−	676.097i	0.200795	−	0.115929i
$325$	3428.46	−	2618.14i	0.585159	−	0.446856i
$326$	−3734.37	+	6468.11i	−0.634440	+	1.09888i
$327$	1385.17	+	899.542i	0.234252	+	0.152125i
$328$	−4027.72	+	637.928i	−0.678030	+	0.107389i
$329$	4648.25	−	9402.41i	0.778925	−	1.57560i
$330$	−8044.85	+	2957.31i	−1.34198	+	0.493317i
$331$	5044.28	+	2245.86i	0.837639	+	0.372941i	0.780294	−	0.625413i	$-0.215070\pi$
$331$	5044.28	+	2245.86i	0.837639	+	0.372941i	0.0573456	+	0.998354i	$0.481736\pi$
$332$	1562.82	−	418.757i	0.258346	−	0.0692237i
$333$	6286.69	−	7763.42i	1.03456	−	1.27758i
$334$	5150.95	−	5720.71i	0.843855	−	0.937195i
$335$	−1015.14	+	8492.54i	−0.165562	+	1.38507i
$336$	−9737.05	−	7691.60i	−1.58095	−	1.24884i
$337$	−1968.79	−	1003.15i	−0.318240	−	0.162152i	0.287572	−	0.957759i	$-0.407152\pi$
$337$	−1968.79	−	1003.15i	−0.318240	−	0.162152i	−0.605813	+	0.795607i	$0.707152\pi$
$338$	−3074.23	+	161.113i	−0.494722	+	0.0259273i
$339$	−2217.08	−	2462.32i	−0.355207	−	0.394498i
$340$	238.568	+	771.470i	0.0380534	+	0.123055i
$341$	−2291.67	−	2063.43i	−0.363932	−	0.327686i
$342$	−3286.80	−	520.578i	−0.519678	−	0.0823088i
$343$	1742.33	−	6108.84i	0.274277	−	0.961651i
$344$	−2220.75	−	3056.60i	−0.348066	−	0.479072i
$345$	10421.7	+	4171.84i	1.62633	+	0.651026i
$346$	−4099.16	−	9206.86i	−0.636914	−	1.43053i
$347$	−27.5805	+	71.8497i	−0.00426686	+	0.0111155i	−0.935697	−	0.352804i	$-0.885228\pi$
$347$	−27.5805	+	71.8497i	−0.00426686	+	0.0111155i	0.931430	+	0.363919i	$0.118562\pi$
$348$	1648.90	−	2539.09i	0.253996	−	0.391119i
$349$	1764.87			0.270691			0.135346	−	0.990798i	$-0.456786\pi$
$349$	1764.87			0.270691			0.135346	+	0.990798i	$0.456786\pi$
$350$	5877.12	+	3955.10i	0.897558	+	0.604025i
$351$	9534.17			1.44985
$352$	−908.613	+	1399.14i	−0.137583	+	0.211859i
$353$	−2532.22	+	6596.66i	−0.381803	+	0.994631i	0.599193	+	0.800604i	$0.295488\pi$
$353$	−2532.22	+	6596.66i	−0.381803	+	0.994631i	−0.980996	+	0.194027i	$0.937845\pi$
$354$	−4960.62	−	11141.7i	−0.744785	−	1.67282i
$355$	722.393	−	10829.2i	0.108002	−	1.61903i
$356$	−671.892	−	924.781i	−0.100029	−	0.137678i
$357$	7342.11	+	5199.72i	1.08848	+	0.770863i
$358$	−635.536	−	100.659i	−0.0938244	−	0.0148603i
$359$	−4369.88	−	3934.66i	−0.642433	−	0.578449i	0.282178	−	0.959362i	$-0.408943\pi$
$359$	−4369.88	−	3934.66i	−0.642433	−	0.578449i	−0.924611	+	0.380913i	$0.875610\pi$
$360$	4182.99	−	12275.9i	0.612397	−	1.79721i
$361$	−4347.03	−	4827.87i	−0.633771	−	0.703874i
$362$	−10366.1	+	543.263i	−1.50505	+	0.0788764i
$363$	−4779.57	−	2435.31i	−0.691080	−	0.352123i
$364$	322.172	+	809.842i	0.0463912	+	0.116613i
$365$	−2950.43	−	5282.73i	−0.423103	−	0.757563i
$366$	1274.68	−	1415.67i	0.182045	−	0.202181i
$367$	4615.84	−	5700.09i	0.656525	−	0.810741i	−0.334784	−	0.942295i	$-0.608663\pi$
$367$	4615.84	−	5700.09i	0.656525	−	0.810741i	0.991309	+	0.131554i	$0.0419966\pi$
$368$	7724.41	−	2069.75i	1.09419	−	0.293188i
$369$	10479.0	+	4665.54i	1.47836	+	0.658206i
$370$	227.965	+	5978.78i	0.0320306	+	0.840059i
$371$	−5446.18	+	351.587i	−0.762134	+	0.0492008i
$372$	−1394.60	+	220.882i	−0.194372	+	0.0307855i
$373$	−4602.81	−	2989.10i	−0.638939	−	0.414932i	0.184107	−	0.982906i	$-0.441061\pi$
$373$	−4602.81	−	2989.10i	−0.638939	−	0.414932i	−0.823046	+	0.567974i	$0.807727\pi$
$374$	2213.57	−	3834.01i	0.306045	−	0.530085i
$375$	−3198.37	+	12412.5i	−0.440436	+	1.70928i
$376$	9959.89	−	5750.34i	1.36607	−	0.788700i
$377$	7443.20	−	3792.50i	1.01683	−	0.518100i
$378$	5018.12	+	14830.8i	0.682816	+	2.01802i
$379$	4603.39	−	6336.02i	0.623905	−	0.858732i	−0.373724	−	0.927540i	$-0.621919\pi$
$379$	4603.39	−	6336.02i	0.623905	−	0.858732i	0.997630	+	0.0688075i	$0.0219194\pi$
$380$	245.662	−	154.603i	0.0331637	−	0.0208710i
$381$	−5701.48	+	599.249i	−0.766655	+	0.0805787i
$382$	2335.10	+	8714.70i	0.312759	+	1.16723i
$383$	−4696.28	+	1802.73i	−0.626551	+	0.240510i	−0.650864	−	0.759194i	$-0.725593\pi$
$383$	−4696.28	+	1802.73i	−0.626551	+	0.240510i	0.0243137	+	0.999704i	$0.492260\pi$
$384$	−4832.31	−	14872.3i	−0.642182	−	1.97643i
$385$	−872.829	−	5588.27i	−0.115542	−	0.739753i
$386$	−3750.10	+	11541.6i	−0.494495	+	1.52190i
$387$	556.199	+	10612.9i	0.0730573	+	1.39402i
$388$	1632.06	−	1059.87i	0.213545	−	0.138678i
$389$	6258.30	−	5635.00i	0.815703	−	0.734462i	−0.151503	−	0.988457i	$-0.548411\pi$
$389$	6258.30	−	5635.00i	0.815703	−	0.734462i	0.967206	+	0.253995i	$0.0817445\pi$
$390$	−8149.84	+	7130.52i	−1.05816	+	0.925815i
$391$	−5514.42	+	1791.74i	−0.713238	+	0.231745i
$392$	5305.41	−	4513.24i	0.683580	−	0.581513i
$393$	2161.33	+	2161.33i	0.277416	+	0.277416i
$394$	−2780.09	+	6244.18i	−0.355479	+	0.798420i
$395$	−3513.86	−	7146.28i	−0.447599	−	0.910300i
$396$	1943.77	−	865.423i	0.246662	−	0.109821i
$397$	−6445.97	+	5219.84i	−0.814896	+	0.659890i	−0.943340	−	0.331827i	$-0.892335\pi$
$397$	−6445.97	+	5219.84i	−0.814896	+	0.659890i	0.128444	+	0.991717i	$0.459002\pi$
$398$	−3476.97	−	6823.94i	−0.437901	−	0.859430i
$399$	1122.30	−	3032.95i	0.140815	−	0.380544i
$400$	3474.79	+	8444.22i	0.434349	+	1.05553i
$401$	6898.24	+	11948.1i	0.859056	+	1.48793i	0.872830	+	0.488024i	$0.162282\pi$
$401$	6898.24	+	11948.1i	0.859056	+	1.48793i	−0.0137742	+	0.999905i	$0.504385\pi$
$402$	1123.67	−	21441.0i	0.139412	−	2.66014i
$403$	−3637.24	−	1396.21i	−0.449588	−	0.172581i
$404$	258.560	−	2460.04i	0.0318412	−	0.302949i
$405$	−8714.25	+	6853.39i	−1.06917	+	0.840859i
$406$	9816.97	+	9582.09i	1.20002	+	1.17131i
$407$	3377.88	−	3377.88i	0.411389	−	0.411389i
$408$	3535.29	+	9209.74i	0.428978	+	1.11753i
$409$	3719.13	+	790.525i	0.449631	+	0.0955720i	0.427161	−	0.904176i	$-0.359514\pi$
$409$	3719.13	+	790.525i	0.449631	+	0.0955720i	0.0224698	+	0.999748i	$0.492847\pi$
$410$	−6563.48	+	2029.67i	−0.790603	+	0.244484i
$411$	381.123	+	1793.04i	0.0457407	+	0.215193i
$412$	−1166.32	+	2289.04i	−0.139467	+	0.273720i
$413$	7851.39	−	1768.48i	0.935452	−	0.210705i
$414$	−18198.4	−	5913.01i	−2.16039	−	0.701953i
$415$	−12194.1	+	5222.24i	−1.44237	+	0.617710i
$416$	−438.219	+	2061.66i	−0.0516477	+	0.242983i
$417$	−11645.1	−	9430.00i	−1.36754	−	1.10741i
$418$	−1537.11	−	411.868i	−0.179863	−	0.0481941i
$419$	−5512.16	+	4004.82i	−0.642689	+	0.466941i	−0.860773	−	0.508989i	$-0.830019\pi$
$419$	−5512.16	+	4004.82i	−0.642689	+	0.466941i	0.218084	+	0.975930i	$0.430019\pi$
$420$	−2240.03	−	1299.69i	−0.260243	−	0.150996i
$421$	3390.32	+	2463.21i	0.392479	+	0.285153i	0.766471	−	0.642279i	$-0.222011\pi$
$421$	3390.32	+	2463.21i	0.392479	+	0.285153i	−0.373991	+	0.927432i	$0.622011\pi$
$422$	−3528.06	−	4356.80i	−0.406975	−	0.502572i
$423$	−32305.5	−	1693.06i	−3.71335	−	0.194609i
$424$	−5182.39	−	2992.05i	−0.593583	−	0.342705i
$425$	−2836.40	−	5982.29i	−0.323731	−	0.682785i
$426$			27244.7i			3.09861i
$427$	751.146	+	1007.97i	0.0851300	+	0.114237i
$428$	−140.781	−	888.856i	−0.0158993	−	0.100384i
$429$	8598.62	+	903.751i	0.967705	+	0.101710i
$430$	−4436.24	−	4564.50i	−0.497522	−	0.511906i
$431$	891.091	+	8478.16i	0.0995878	+	0.947515i	0.924224	+	0.381851i	$0.124713\pi$
$431$	891.091	+	8478.16i	0.0995878	+	0.947515i	−0.824636	+	0.565664i	$0.808620\pi$
$432$	−5223.32	+	19493.7i	−0.581729	+	2.17104i
$433$	835.023	−	5272.13i	0.0926759	−	0.585133i	−0.897025	−	0.441980i	$-0.854276\pi$
$433$	835.023	−	5272.13i	0.0926759	−	0.585133i	0.989701	−	0.143152i	$-0.0457239\pi$
$434$	257.463	−	6392.74i	0.0284761	−	0.707054i
$435$	−10418.1	+	22529.9i	−1.14830	+	2.48327i
$436$	240.198	−	51.0556i	0.0263839	−	0.00560807i
$437$	1135.12	+	1747.93i	0.124257	+	0.191338i
$438$	8272.62	+	12738.7i	0.902469	+	1.38968i
$439$	−5179.27	+	1100.89i	−0.563083	+	0.119687i	−0.480654	−	0.876910i	$-0.659601\pi$
$439$	−5179.27	+	1100.89i	−0.563083	+	0.119687i	−0.0824282	+	0.996597i	$0.526268\pi$
$440$	2602.96	−	5629.08i	0.282026	−	0.609900i
$441$	−19430.1	+	2519.18i	−2.09805	+	0.272020i
$442$	874.978	−	5524.39i	0.0941594	−	0.594499i
$443$	1001.83	−	3738.89i	0.107446	−	0.400993i	−0.891165	−	0.453679i	$-0.850111\pi$
$443$	1001.83	−	3738.89i	0.107446	−	0.400993i	0.998611	+	0.0526853i	$0.0167780\pi$
$444$	−228.636	−	2175.32i	−0.0244382	−	0.232514i
$445$	6531.88	+	6720.73i	0.695822	+	0.715940i
$446$	−2362.82	−	248.342i	−0.250858	−	0.0263662i
$447$	1755.49	+	11083.7i	0.185754	+	1.17280i
$448$	7311.78	−	858.122i	0.771092	−	0.0904965i
$449$		−	7849.27i		−	0.825011i	−0.910955	−	0.412506i	$-0.864654\pi$
$449$		−	7849.27i		−	0.825011i	0.910955	−	0.412506i	$-0.135346\pi$
$450$	4031.48	−	21473.9i	0.422324	−	2.24953i
$451$	4750.38	+	2742.63i	0.495979	+	0.286354i
$452$	−491.956	−	25.7823i	−0.0511940	−	0.00268296i
$453$	12573.2	+	15526.7i	1.30407	+	1.61039i
$454$	−4109.53	−	2985.75i	−0.424823	−	0.308652i
$455$	−3559.66	−	6196.12i	−0.366768	−	0.638414i
$456$	2868.75	−	2084.27i	0.294609	−	0.214046i
$457$	−4232.53	−	1134.10i	−0.433237	−	0.116085i	0.0356084	−	0.999366i	$-0.488663\pi$
$457$	−4232.53	−	1134.10i	−0.433237	−	0.116085i	−0.468845	+	0.883280i	$0.655330\pi$
$458$	−840.032	−	680.244i	−0.0857033	−	0.0694011i
$459$	3042.29	−	14312.9i	0.309373	−	1.45548i
$460$	1534.25	−	657.060i	0.155510	−	0.0665991i
$461$	13749.4	+	4467.45i	1.38909	+	0.451344i	0.905648	−	0.424030i	$-0.139385\pi$
$461$	13749.4	+	4467.45i	1.38909	+	0.451344i	0.483446	+	0.875374i	$0.339385\pi$
$462$	3119.89	+	13851.2i	0.314179	+	1.39484i
$463$	1904.54	−	3737.88i	0.191170	−	0.375192i	−0.775449	−	0.631410i	$-0.782477\pi$
$463$	1904.54	−	3737.88i	0.191170	−	0.375192i	0.966619	+	0.256218i	$0.0824765\pi$
$464$	3676.42	+	17296.2i	0.367831	+	1.73051i
$465$	11059.8	−	3420.10i	1.10298	−	0.341082i
$466$	11010.3	+	2340.31i	1.09451	+	0.232645i
$467$	3034.90	+	7906.19i	0.300725	+	0.783415i	0.997792	+	0.0664099i	$0.0211545\pi$
$467$	3034.90	+	7906.19i	0.300725	+	0.783415i	−0.697067	+	0.717006i	$0.745512\pi$
$468$	1900.82	−	1900.82i	0.187747	−	0.187747i
$469$	13728.7	+	3501.01i	1.35167	+	0.344694i
$470$	15229.7	−	11977.5i	1.49467	−	1.17549i
$471$	2054.65	−	19548.7i	0.201005	−	1.91244i
$472$	8238.53	+	3162.47i	0.803409	+	0.308400i
$473$	−265.974	+	5075.08i	−0.0258552	+	0.493346i
$474$	9995.23	+	17312.2i	0.968557	+	1.67759i
$475$	−1813.19	+	1541.36i	−0.175147	+	0.148889i
$476$	1318.55	−	225.235i	0.126966	−	0.0216883i
$477$	7641.79	+	14997.9i	0.733529	+	1.43963i
$478$	−4239.79	+	3433.32i	−0.405698	+	0.328528i
$479$	7401.51	−	3295.37i	0.706020	−	0.314340i	−0.0221328	−	0.999755i	$-0.507046\pi$
$479$	7401.51	−	3295.37i	0.706020	−	0.314340i	0.728153	+	0.685415i	$0.240379\pi$
$480$	−2763.46	−	5620.15i	−0.262779	−	0.534424i
$481$	2454.79	−	5513.55i	0.232700	−	0.522654i
$482$	5391.37	+	5391.37i	0.509482	+	0.509482i
$483$	9102.01	−	16215.4i	0.857465	−	1.52759i
$484$	−758.517	+	246.457i	−0.0712357	+	0.0231459i
$485$	−12007.8	+	10505.9i	−1.12421	+	0.983606i
$486$	3719.00	−	3348.60i	0.347114	−	0.312542i
$487$	−4114.91	+	2672.26i	−0.382884	+	0.248648i	−0.721702	−	0.692204i	$-0.756640\pi$
$487$	−4114.91	+	2672.26i	−0.382884	+	0.248648i	0.338818	+	0.940852i	$0.389973\pi$
$488$	72.1381	+	1376.48i	0.00669167	+	0.127685i
$489$	−6917.68	+	21290.4i	−0.639730	+	1.96889i
$490$	7764.75	−	8798.39i	0.715869	−	0.811165i
$491$	2152.10	+	6623.47i	0.197806	+	0.608785i	0.999932	+	0.0116301i	$0.00370206\pi$
$491$	2152.10	+	6623.47i	0.197806	+	0.608785i	−0.802126	+	0.597154i	$0.796298\pi$
$492$	2344.76	−	900.070i	0.214858	−	0.0824762i
$493$	−3318.29	−	12384.0i	−0.303141	−	1.13134i
$494$	−1999.49	+	210.155i	−0.182108	+	0.0191403i
$495$	−14764.3	+	9291.66i	−1.34062	+	0.843695i
$496$	4847.37	−	6671.84i	0.438817	−	0.603980i
$497$	−17629.5	−	3524.75i	−1.59113	−	0.318122i
$498$	29670.0	−	15117.6i	2.66977	−	1.36032i
$499$	−3544.05	+	2046.16i	−0.317943	+	0.183564i	−0.650475	−	0.759528i	$-0.725430\pi$
$499$	−3544.05	+	2046.16i	−0.317943	+	0.183564i	0.332533	+	0.943092i	$0.392097\pi$
$500$	968.704	+	1641.21i	0.0866435	+	0.146794i
$501$	11536.6	−	19982.0i	1.02878	−	1.78189i
$502$	−17323.9	−	11250.3i	−1.54025	−	1.00025i
$503$	2257.20	−	357.506i	0.200087	−	0.0316907i	−0.0555864	−	0.998454i	$-0.517703\pi$
$503$	2257.20	−	357.506i	0.200087	−	0.0316907i	0.255673	+	0.966763i	$0.417703\pi$
$504$	−19258.3	−	9520.70i	−1.70205	−	0.841440i
$505$	772.711	+	20265.7i	0.0680894	+	1.78577i
$506$	−8359.21	−	3721.76i	−0.734411	−	0.326981i
$507$	−8912.64	+	2388.13i	−0.780718	+	0.209193i
$508$	−536.409	+	662.410i	−0.0468491	+	0.0578538i
$509$	14583.4	−	16196.5i	1.26994	−	1.41041i	0.400551	−	0.916275i	$-0.368819\pi$
$509$	14583.4	−	16196.5i	1.26994	−	1.41041i	0.869386	−	0.494133i	$-0.164515\pi$
$510$	8103.90	+	14510.0i	0.703621	+	1.25983i
$511$	−9313.26	+	3705.01i	−0.806251	+	0.320744i
$512$	6598.83	+	3362.27i	0.569589	+	0.290220i
$513$	−5252.50	+	275.272i	−0.452054	+	0.0236911i
$514$	14769.1	+	16402.8i	1.26739	+	1.40758i
$515$	6793.62	−	19937.4i	0.581286	−	1.70591i
$516$	1729.27	+	1557.04i	0.147532	+	0.132839i
$517$	−15279.2	−	2419.99i	−1.29977	−	0.205863i
$518$	9868.58	+	916.576i	0.837067	+	0.0777452i
$519$	−17755.4	−	24438.2i	−1.50169	−	2.06690i
$520$	521.520	−	7817.96i	0.0439811	−	0.659309i
$521$	−1917.25	−	4306.21i	−0.161221	−	0.362109i	0.814814	−	0.579723i	$-0.196839\pi$
$521$	−1917.25	−	4306.21i	−0.161221	−	0.362109i	−0.976035	+	0.217614i	$0.930173\pi$
$522$	15162.8	−	39500.5i	1.27138	−	3.31205i
$523$	3854.41	−	5935.27i	0.322259	−	0.496236i	−0.639998	−	0.768376i	$-0.721065\pi$
$523$	3854.41	−	5935.27i	0.322259	−	0.496236i	0.962257	+	0.272141i	$0.0877316\pi$
$524$	454.451			0.0378870
$525$	19695.3	+	7933.10i	1.63728	+	0.659484i
$526$	−9217.27			−0.764054
$527$	−3256.63	+	5014.77i	−0.269186	+	0.414510i
$528$	−6558.59	+	17085.7i	−0.540580	+	1.40826i
$529$	−74.3878	−	167.078i	−0.00611390	−	0.0137320i
$530$	−9359.47	−	3746.63i	−0.767074	−	0.307063i
$531$	−14590.3	−	20081.9i	−1.19240	−	1.64120i
$532$	−200.871	−	436.851i	−0.0163700	−	0.0356013i
$533$	6844.78	+	1084.11i	0.556248	+	0.0881010i
$534$	−17483.4	−	15742.1i	−1.41682	−	1.27571i
$535$	2179.83	+	7049.03i	0.176153	+	0.569638i
$536$	10395.0	+	11544.8i	0.837681	+	0.930339i
$537$	−1926.00	+	100.937i	−0.154773	+	0.00811129i
$538$	18075.8	+	9210.10i	1.44852	+	0.738059i
$539$	−9366.48	+	226.850i	−0.748502	+	0.0181282i
$540$	−499.921	+	4182.26i	−0.0398392	+	0.333289i
$541$	7325.54	−	8135.84i	0.582162	−	0.646556i	−0.378064	−	0.925779i	$-0.623410\pi$
$541$	7325.54	−	8135.84i	0.582162	−	0.646556i	0.960226	+	0.279223i	$0.0900769\pi$
$542$	−4822.66	+	5955.49i	−0.382197	+	0.471974i
$543$	−30052.8	+	8052.62i	−2.37512	+	0.636411i
$544$	2955.16	+	1315.72i	0.232907	+	0.103697i
$545$	−1889.69	+	694.656i	−0.148524	+	0.0545978i
$546$	9951.18	+	14924.7i	0.779984	+	1.16981i
$547$	−1042.25	+	165.077i	−0.0814690	+	0.0129034i	−0.197036	−	0.980396i	$-0.563132\pi$
$547$	−1042.25	+	165.077i	−0.0814690	+	0.0129034i	0.115567	+	0.993300i	$0.463132\pi$
$548$	228.575	+	148.439i	0.0178180	+	0.0115711i
$549$	1938.58	−	3357.71i	0.150704	−	0.261027i
$550$	2990.68	−	10011.0i	0.231860	−	0.776132i
$551$	−3991.06	+	2304.24i	−0.308575	+	0.178156i
$552$	18167.2	−	9256.67i	1.40081	−	0.713750i
$553$	−12495.6	+	4227.98i	−0.960878	+	0.325121i
$554$	−10327.0	+	14213.9i	−0.791969	+	1.09005i
$555$	4394.17	+	17386.6i	0.336076	+	1.32976i
$556$	−2215.67	+	232.877i	−0.169003	+	0.0177629i
$557$	1532.09	+	5717.86i	0.116547	+	0.434961i	0.999398	−	0.0346929i	$-0.0110453\pi$
$557$	1532.09	+	5717.86i	0.116547	+	0.434961i	−0.882851	+	0.469654i	$0.844379\pi$
$558$	−18422.3	+	7071.66i	−1.39763	+	0.536501i
$559$	1984.10	+	6106.43i	0.150122	+	0.462029i
$560$	14618.8	−	3883.56i	1.10314	−	0.293054i
$561$	4100.49	−	12620.0i	0.308597	−	0.949764i
$562$	−145.732	−	2780.74i	−0.0109383	−	0.208716i
$563$	8009.46	−	5201.40i	0.599571	−	0.389366i	−0.208870	−	0.977943i	$-0.566978\pi$
$563$	8009.46	−	5201.40i	0.599571	−	0.389366i	0.808441	+	0.588577i	$0.200312\pi$
$564$	−5263.86	+	4739.60i	−0.392994	+	0.353853i
$565$	4022.46	−	364.910i	0.299516	−	0.0271715i
$566$	5173.94	−	1681.12i	0.384235	−	0.124845i
$567$	9374.16	+	15791.8i	0.694317	+	1.16966i
$568$	−13939.3	−	13939.3i	−1.02972	−	1.02972i
$569$	8680.04	−	19495.7i	0.639518	−	1.43638i	−0.244835	−	0.969565i	$-0.578734\pi$
$569$	8680.04	−	19495.7i	0.639518	−	1.43638i	0.884354	−	0.466817i	$-0.154599\pi$
$570$	4283.98	−	4163.60i	0.314801	−	0.305955i
$571$	13951.5	−	6211.62i	1.02251	−	0.455251i	0.174178	−	0.984714i	$-0.444273\pi$
$571$	13951.5	−	6211.62i	1.02251	−	0.455251i	0.848333	+	0.529463i	$0.177607\pi$
$572$	999.007	−	808.980i	0.0730255	−	0.0591349i
$573$	12276.8	+	24094.6i	0.895064	+	1.75666i
$574$	1916.24	+	11217.9i	0.139342	+	0.815726i
$575$	−11684.1	+	7122.79i	−0.847408	+	0.516593i
$576$	−11353.2	−	19664.3i	−0.821265	−	1.42247i
$577$	−191.744	+	3658.70i	−0.0138343	+	0.263975i	0.982952	+	0.183864i	$0.0588607\pi$
$577$	−191.744	+	3658.70i	−0.0138343	+	0.263975i	−0.996786	+	0.0801107i	$0.974473\pi$
$578$	6021.17	+	2311.31i	0.433301	+	0.166329i
$579$	−3802.12	+	36174.7i	−0.272903	+	2.59650i
$580$	1273.34	+	3463.90i	0.0911595	+	0.247984i
$581$	5943.83	+	21154.8i	0.424426	+	1.51058i
$582$	28320.6	−	28320.6i	2.01705	−	2.01705i
$583$	2884.61	+	7514.66i	0.204920	+	0.533834i
$584$	−10750.1	−	2285.01i	−0.761719	−	0.161908i
$585$	−13207.4	+	17644.1i	−0.933433	+	1.24700i
$586$	−2803.32	−	13188.6i	−0.197618	−	0.929719i
$587$	3265.42	−	6408.75i	0.229605	−	0.450626i	−0.747245	−	0.664548i	$-0.768624\pi$
$587$	3265.42	−	6408.75i	0.229605	−	0.450626i	0.976851	+	0.213923i	$0.0686240\pi$
$588$	−2618.25	+	3398.31i	−0.183630	+	0.238340i
$589$	2044.12	+	664.174i	0.142999	+	0.0464632i
$590$	14496.6	+	3297.92i	1.01155	+	0.230124i
$591$	−4259.47	+	20039.2i	−0.296465	+	1.39476i
$592$	9928.21	+	8039.71i	0.689269	+	0.558159i
$593$	12162.3	+	3258.87i	0.842233	+	0.225676i	0.654043	−	0.756457i	$-0.273071\pi$
$593$	12162.3	+	3258.87i	0.842233	+	0.225676i	0.188189	+	0.982133i	$0.439738\pi$
$594$	18681.9	−	13573.2i	1.29045	−	0.937568i
$595$	−10437.6	+	3366.68i	−0.719158	+	0.231967i
$596$	1349.82	+	980.700i	0.0927696	+	0.0674011i
$597$	−14446.3	−	17839.7i	−0.990365	−	1.22300i
$598$	−11544.7	−	605.030i	−0.789459	−	0.0413738i
$599$	11590.3	+	6691.66i	0.790596	+	0.456451i	0.840172	−	0.542320i	$-0.182454\pi$
$599$	11590.3	+	6691.66i	0.790596	+	0.456451i	−0.0495765	+	0.998770i	$0.515787\pi$
$600$	13142.4	+	19217.6i	0.894227	+	1.30759i
$601$			6732.60i			0.456953i	0.973549	+	0.228476i	$0.0733743\pi$
$601$			6732.60i			0.456953i	−0.973549	+	0.228476i	$0.926626\pi$
$602$	−8454.50	+	6300.34i	−0.572391	+	0.426549i
$603$	−6835.90	−	43160.2i	−0.461658	−	2.91479i
$604$	2954.21	+	310.500i	0.199015	+	0.0209173i
$605$	5867.97	−	2885.31i	0.394325	−	0.193892i
$606$	−5321.49	−	50630.6i	−0.356717	−	3.39394i
$607$	2374.44	−	8861.55i	0.158774	−	0.592552i	−0.839979	−	0.542619i	$-0.817433\pi$
$607$	2374.44	−	8861.55i	0.158774	−	0.592552i	0.998753	−	0.0499327i	$-0.0159007\pi$
$608$	181.896	−	1148.45i	0.0121330	−	0.0766047i
$609$	34752.8	+	21975.1i	2.31240	+	1.46220i
$610$	450.388	+	2278.06i	0.0298946	+	0.151206i
$611$	−19117.4	+	4063.52i	−1.26580	+	0.269055i
$612$	−2247.01	−	3460.09i	−0.148415	−	0.228539i
$613$	14584.5	+	22458.1i	0.960947	+	1.47973i	0.875402	+	0.483395i	$0.160596\pi$
$613$	14584.5	+	22458.1i	0.960947	+	1.47973i	0.0855449	+	0.996334i	$0.472737\pi$
$614$	−28564.4	+	6071.56i	−1.87747	+	0.399068i
$615$	−17978.0	+	10040.8i	−1.17877	+	0.658349i
$616$	−8682.99	−	5490.49i	−0.567934	−	0.359121i
$617$	3086.90	−	19489.9i	0.201417	−	1.27169i	−0.655087	−	0.755553i	$-0.727368\pi$
$617$	3086.90	−	19489.9i	0.201417	−	1.27169i	0.856504	−	0.516141i	$-0.172632\pi$
$618$	−13684.8	+	51072.4i	−0.890751	+	3.32433i
$619$	−1038.21	−	9877.93i	−0.0674140	−	0.641402i	−0.975102	−	0.221756i	$-0.928821\pi$
$619$	−1038.21	−	9877.93i	−0.0674140	−	0.641402i	0.907688	−	0.419645i	$-0.137846\pi$
$620$	803.178	−	1522.30i	0.0520265	−	0.0986084i
$621$	−30078.0	−	3161.32i	−1.94362	−	0.204283i
$622$	2222.08	+	14029.7i	0.143243	+	0.904404i
$623$	12448.3	−	9276.57i	0.800533	−	0.596562i
$624$			23121.9i			1.48336i
$625$	−9776.71	−	12188.4i	−0.625710	−	0.780056i
$626$	−16426.8	−	9483.99i	−1.04879	−	0.605521i
$627$	−4763.19	−	249.628i	−0.303387	−	0.0158998i
$628$	−1839.19	−	2271.21i	−0.116866	−	0.144317i
$629$	−7493.73	−	5444.52i	−0.475031	−	0.345131i
$630$	−34397.6	−	11258.0i	−2.17529	−	0.711950i
$631$	−4423.85	+	3214.12i	−0.279098	+	0.202777i	−0.718524	−	0.695502i	$-0.755182\pi$
$631$	−4423.85	+	3214.12i	−0.279098	+	0.202777i	0.439426	+	0.898279i	$0.355182\pi$
$632$	−13971.5	−	3743.64i	−0.879359	−	0.235623i
$633$	−13058.7	−	10574.7i	−0.819960	−	0.663991i
$634$	−3262.59	+	15349.3i	−0.204376	+	0.961511i
$635$	3580.05	−	6001.68i	0.223732	−	0.375070i
$636$	3505.20	+	1138.91i	0.218538	+	0.0710074i
$637$	−10944.9	+	4508.36i	−0.680776	+	0.280420i
$638$	9185.58	−	18027.7i	0.570001	−	1.11869i
$639$	11528.8	+	54238.8i	0.713729	+	3.35783i
$640$	18043.5	+	6148.28i	1.11442	+	0.379737i
$641$	−5799.92	−	1232.81i	−0.357384	−	0.0759642i	0.0257211	−	0.999669i	$-0.491812\pi$
$641$	−5799.92	−	1232.81i	−0.357384	−	0.0759642i	−0.383105	+	0.923705i	$0.625145\pi$
$642$	−6637.61	−	17291.6i	−0.408046	−	1.06300i
$643$	−6638.15	+	6638.15i	−0.407128	+	0.407128i	−0.880736	−	0.473608i	$-0.842951\pi$
$643$	−6638.15	+	6638.15i	−0.407128	+	0.407128i	0.473608	+	0.880736i	$0.342951\pi$
$644$	−747.849	−	2661.68i	−0.0457599	−	0.162865i
$645$	−15850.7	−	10617.7i	−0.967627	−	0.648172i
$646$	−322.536	+	3068.72i	−0.0196440	+	0.186900i
$647$	−15690.6	−	6023.05i	−0.953416	−	0.365982i	−0.168581	−	0.985688i	$-0.553919\pi$
$647$	−15690.6	−	6023.05i	−0.953416	−	0.365982i	−0.784834	+	0.619706i	$0.787252\pi$
$648$	−1053.87	+	20109.0i	−0.0638885	+	1.21907i
$649$	−5935.07	−	10279.8i	−0.358970	−	0.621755i
$650$	−1005.17	−	13162.0i	−0.0606552	−	0.794239i
$651$	−3228.96	−	18902.7i	−0.194398	−	1.13803i
$652$	1511.04	+	2965.58i	0.0907622	+	0.178131i
$653$	13128.3	−	10631.1i	0.786755	−	0.637102i	−0.149365	−	0.988782i	$-0.547723\pi$
$653$	13128.3	−	10631.1i	0.786755	−	0.637102i	0.936120	+	0.351680i	$0.114390\pi$
$654$	4617.06	−	2055.65i	0.276057	−	0.122909i
$655$	−3688.00	+	530.370i	−0.220003	+	0.0316386i
$656$	−5966.50	+	13401.0i	−0.355111	+	0.797592i
$657$	21859.7	+	21859.7i	1.29806	+	1.29806i
$658$	−16383.0	−	27599.1i	−0.970633	−	1.63514i
$659$	20563.7	−	6681.56i	1.21555	−	0.394957i	0.370092	−	0.928995i	$-0.379326\pi$
$659$	20563.7	−	6681.56i	1.21555	−	0.394957i	0.845460	+	0.534038i	$0.179326\pi$
$660$	−847.305	+	3724.49i	−0.0499717	+	0.219660i
$661$	16684.8	−	15023.1i	0.981793	−	0.884010i	−0.0114653	−	0.999934i	$-0.503650\pi$
$661$	16684.8	−	15023.1i	0.981793	−	0.884010i	0.993258	+	0.115924i	$0.0369829\pi$
$662$	14170.4	−	9202.38i	0.831948	−	0.540273i
$663$	−877.396	−	16741.7i	−0.0513955	−	0.980685i
$664$	−7445.51	+	22914.9i	−0.435153	+	1.33926i
$665$	2139.96	+	3310.75i	0.124788	+	0.193061i
$666$	−9446.17	−	29072.3i	−0.549597	−	1.69149i
$667$	−24739.0	+	9496.42i	−1.43613	+	0.551278i
$668$	−887.882	−	3313.62i	−0.0514269	−	0.191928i
$669$	−7082.08	+	744.357i	−0.409281	+	0.0430172i
$670$	20102.9	+	16758.9i	1.15917	+	0.966346i
$671$	1089.79	−	1499.96i	0.0626985	−	0.0862971i
$672$	−9827.07	+	3325.07i	−0.564118	+	0.190874i
$673$	−25098.1	+	12788.1i	−1.43754	+	0.732462i	−0.987064	−	0.160328i	$-0.948745\pi$
$673$	−25098.1	+	12788.1i	−1.43754	+	0.732462i	−0.450473	+	0.892790i	$0.648745\pi$
$674$	−5855.61	+	3380.74i	−0.334644	+	0.193207i
$675$	−823.933	−	34523.8i	−0.0469825	−	1.96862i
$676$	−685.937	+	1188.08i	−0.0390269	+	0.0675966i
$677$	10357.2	+	6726.04i	0.587976	+	0.381836i	0.804068	−	0.594537i	$-0.202665\pi$
$677$	10357.2	+	6726.04i	0.587976	+	0.381836i	−0.216093	+	0.976373i	$0.569331\pi$
$678$	−10014.1	+	1586.08i	−0.567242	+	0.0898424i
$679$	14661.8	+	21989.7i	0.828671	+	1.24284i
$680$	−11570.1	−	3277.58i	−0.652487	−	0.184837i
$681$	−13909.0	−	6192.68i	−0.782663	−	0.348464i
$682$	−9114.76	+	2442.29i	−0.511763	+	0.137126i
$683$	17699.0	−	21856.5i	0.991558	−	1.22447i	0.0171117	−	0.999854i	$-0.494553\pi$
$683$	17699.0	−	21856.5i	0.991558	−	1.22447i	0.974447	−	0.224619i	$-0.0721138\pi$
$684$	−992.308	+	1102.07i	−0.0554706	+	0.0616063i
$685$	−2028.19	−	937.863i	−0.113129	−	0.0523123i
$686$	−12773.6	−	14652.4i	−0.710930	−	0.815497i
$687$	−2886.72	−	1470.86i	−0.160313	−	0.0816838i
$688$	−13572.3	+	711.292i	−0.752090	+	0.0394153i
$689$	6804.72	+	7557.41i	0.376254	+	0.417873i
$690$	28075.1	−	19792.8i	1.54899	−	1.09202i
$691$	11573.4	+	10420.7i	0.637153	+	0.573695i	0.923105	−	0.384549i	$-0.125643\pi$
$691$	11573.4	+	10420.7i	0.637153	+	0.573695i	−0.285952	+	0.958244i	$0.592310\pi$
$692$	−4435.92	−	702.581i	−0.243683	−	0.0385956i
$693$	12072.3	+	26254.7i	0.661746	+	1.43916i
$694$	138.425	+	190.526i	0.00757138	+	0.0104211i
$695$	17709.1	−	4475.69i	0.966538	−	0.244277i
$696$	18337.8	+	41187.3i	0.998694	+	2.24310i
$697$	3811.60	−	9929.56i	0.207137	−	0.539611i
$698$	2941.33	−	4529.25i	0.159500	−	0.245608i
$699$	33738.4			1.82561
$700$	2904.64	−	1236.59i	0.156836	−	0.0667695i
$701$	660.516			0.0355882			0.0177941	−	0.999842i	$-0.494336\pi$
$701$	660.516			0.0355882			0.0177941	+	0.999842i	$0.494336\pi$
$702$	15889.7	−	24467.9i	0.854297	−	1.31550i
$703$	−1193.19	+	3108.37i	−0.0640142	+	0.166763i
$704$	−4416.41	−	9919.42i	−0.236434	−	0.531040i
$705$	37186.5	−	44606.6i	1.98656	−	2.38295i
$706$	12709.1	+	17492.5i	0.677496	+	0.932493i
$707$	33450.6	+	3106.83i	1.77941	+	0.165268i
$708$	−5368.16	−	850.233i	−0.284954	−	0.0451323i
$709$	1822.85	+	1641.30i	0.0965566	+	0.0869399i	0.715995	−	0.698105i	$-0.245973\pi$
$709$	1822.85	+	1641.30i	0.0965566	+	0.0869399i	−0.619439	+	0.785045i	$0.712640\pi$
$710$	−26587.5	−	19901.8i	−1.40537	−	1.05198i
$711$	27224.3	+	30235.7i	1.43600	+	1.59483i
$712$	16999.3	−	890.897i	0.894770	−	0.0468929i
$713$	11011.7	+	5610.72i	0.578387	+	0.294703i
$714$	25580.6	−	10176.5i	1.34080	−	0.533398i
$715$	−7163.12	+	7731.02i	−0.374665	+	0.404369i
$716$	−191.873	+	213.097i	−0.0100148	+	0.0111226i
$717$	−10290.7	+	12708.0i	−0.536002	+	0.661907i
$718$	−17380.5	+	4657.09i	−0.903391	+	0.242063i
$719$	−26964.9	−	12005.5i	−1.39864	−	0.622714i	−0.437610	−	0.899165i	$-0.644175\pi$
$719$	−26964.9	−	12005.5i	−1.39864	−	0.622714i	−0.961028	+	0.276451i	$0.910842\pi$
$720$	−28839.7	−	36670.4i	−1.49277	−	1.89809i
$721$	−31277.6	−	15462.6i	−1.61559	−	0.798694i
$722$	−19634.7	+	3109.83i	−1.01209	+	0.160299i
$723$	19166.2	+	12446.7i	0.985891	+	0.640245i
$724$	−2312.93	+	4006.11i	−0.118728	+	0.205644i
$725$	−14376.1	−	26624.5i	−0.736434	−	1.36387i
$726$	−14215.5	+	8207.30i	−0.726702	+	0.419561i
$727$	−4828.87	+	2460.43i	−0.246345	+	0.125519i	−0.572804	−	0.819692i	$-0.694144\pi$
$727$	−4828.87	+	2460.43i	−0.246345	+	0.125519i	0.326459	+	0.945211i	$0.394144\pi$
$728$	−12727.4	−	2544.64i	−0.647950	−	0.129547i
$729$	−6920.16	+	9524.78i	−0.351581	+	0.483909i
$730$	−18474.5	−	1232.39i	−0.936672	−	0.0624834i
$731$	9800.18	−	1030.04i	0.495859	−	0.0521169i
$732$	−219.719	−	820.003i	−0.0110943	−	0.0414046i
$733$	−20123.4	+	7724.66i	−1.01402	+	0.389245i	−0.807924	−	0.589287i	$-0.799409\pi$
$733$	−20123.4	+	7724.66i	−1.01402	+	0.389245i	−0.206094	+	0.978532i	$0.566075\pi$
$734$	−6935.60	−	21345.6i	−0.348771	−	1.07341i
$735$	17281.8	−	30634.0i	0.867278	−	1.53735i
$736$	2066.07	−	6358.72i	0.103474	−	0.318459i
$737$	−1093.64	−	20867.8i	−0.0546602	−	1.04298i
$738$	29437.6	−	19117.0i	1.46831	−	0.953532i
$739$	−9974.92	+	8981.46i	−0.496527	+	0.447075i	−0.878951	−	0.476912i	$-0.841756\pi$
$739$	−9974.92	+	8981.46i	−0.496527	+	0.447075i	0.382424	+	0.923987i	$0.375089\pi$
$740$	2289.86	+	1365.92i	0.113753	+	0.0678544i
$741$	−5731.15	+	1862.16i	−0.284128	+	0.0923188i
$742$	−8174.31	+	14562.7i	−0.404432	+	0.720504i
$743$	21516.3	+	21516.3i	1.06239	+	1.06239i	0.997919	+	0.0644734i	$0.0205368\pi$
$743$	21516.3	+	21516.3i	1.06239	+	1.06239i	0.0644734	+	0.997919i	$0.479463\pi$
$744$	8552.40	−	19209.0i	0.421433	−	0.946554i
$745$	−12098.7	−	6383.36i	−0.594983	−	0.313917i
$746$	−15342.1	+	6830.73i	−0.752967	+	0.335243i
$747$	52670.0	−	42651.3i	2.57978	−	2.08906i
$748$	−895.678	−	1757.87i	−0.0437824	−	0.0859278i
$749$	12047.8	−	2058.00i	0.587740	−	0.100398i
$750$	26524.3	+	28894.8i	1.29137	+	1.40679i
$751$	10099.6	+	17493.1i	0.490734	+	0.849976i	0.999943	−	0.0106666i	$-0.00339534\pi$
$751$	10099.6	+	17493.1i	0.490734	+	0.849976i	−0.509209	+	0.860643i	$0.670062\pi$
$752$	2165.16	−	41313.8i	0.104994	−	2.00340i
$753$	−57801.2	−	22187.8i	−2.79734	−	1.07380i
$754$	2672.00	−	25422.4i	0.129056	−	1.22789i
$755$	−24336.7	+	927.933i	−1.17312	+	0.0447297i
$756$	6760.87	+	1724.12i	0.325252	+	0.0829438i
$757$	−7588.97	+	7588.97i	−0.364367	+	0.364367i	−0.865418	−	0.501051i	$-0.832947\pi$
$757$	−7588.97	+	7588.97i	−0.364367	+	0.364367i	0.501051	+	0.865418i	$0.332947\pi$
$758$	−8588.37	−	22373.5i	−0.411535	−	1.07209i
$759$	−26826.9	−	5702.23i	−1.28294	−	0.272698i
$760$	−61.5910	+	4322.08i	−0.00293966	+	0.206287i
$761$	373.440	+	1756.90i	0.0177887	+	0.0836891i	0.986146	−	0.165877i	$-0.0530454\pi$
$761$	373.440	+	1756.90i	0.0177887	+	0.0836891i	−0.968358	+	0.249566i	$0.919712\pi$
$762$	−7964.21	+	15630.6i	−0.378626	+	0.743095i
$763$	732.847	+	3253.57i	0.0347717	+	0.154374i
$764$	3823.82	+	1242.43i	0.181075	+	0.0588347i
$765$	22273.3	+	25457.3i	1.05267	+	1.20315i
$766$	−3200.40	+	15056.7i	−0.150960	+	0.710210i
$767$	−11654.7	−	9437.77i	−0.548665	−	0.444300i
$768$	−18047.9	−	4835.92i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.66660 - 2.56634i) q^{2} +(3.28687 - 8.56260i) q^{3} +(-0.554650 - 1.24576i) q^{4} +(5.95503 + 9.46244i) q^{5} +(-16.4966 - 22.7057i) q^{6} +(16.8267 - 7.73716i) q^{7} +(20.0573 + 3.17676i) q^{8} +(-42.4496 - 38.2218i) q^{9} +(34.2085 + 0.487482i) q^{10} +(-18.2776 - 20.2994i) q^{11} +(-12.4900 + 0.654575i) q^{12} +(-30.7491 - 15.6674i) q^{13} +(8.18715 - 56.0777i) q^{14} +(100.596 - 19.8887i) q^{15} +(48.8798 - 54.2865i) q^{16} +(-33.3321 + 41.1617i) q^{17} +(-168.837 + 45.2397i) q^{18} +(17.3924 + 7.74361i) q^{19} +(8.48500 - 12.6669i) q^{20} +(-10.9431 - 169.511i) q^{21} +(-82.5567 + 13.0757i) q^{22} +(91.8109 + 59.6227i) q^{23} +(93.1269 - 161.301i) q^{24} +(-54.0754 + 112.698i) q^{25} +(-91.4544 + 52.8012i) q^{26} +(-246.157 + 125.423i) q^{27} +(-18.9716 - 16.6706i) q^{28} +(-142.281 + 195.833i) q^{29} +(116.613 - 291.311i) q^{30} +(112.275 - 11.8006i) q^{31} +(-15.8073 - 58.9935i) q^{32} +(-233.892 + 89.7826i) q^{33} +(50.0836 + 154.141i) q^{34} +(173.416 + 113.146i) q^{35} +(-24.0707 + 74.0819i) q^{36} +(9.15272 + 174.644i) q^{37} +(48.8590 - 31.7294i) q^{38} +(-235.222 + 211.795i) q^{39} +(89.3816 + 208.708i) q^{40} +(-190.983 + 62.0541i) q^{41} +(-453.260 - 254.423i) q^{42} +(-131.557 - 131.557i) q^{43} +(-15.1505 + 34.0287i) q^{44} +(108.883 - 629.289i) q^{45} +(306.024 - 136.251i) q^{46} +(440.124 - 356.405i) q^{47} +(-304.172 - 596.971i) q^{48} +(223.273 - 260.381i) q^{49} +(199.100 + 326.598i) q^{50} +(242.893 + 420.702i) q^{51} +(-2.46296 + 46.9960i) q^{52} +(-275.106 - 105.603i) q^{53} +(-88.3668 + 840.754i) q^{54} +(83.2378 - 293.834i) q^{55} +(362.076 - 101.732i) q^{56} +(123.472 - 123.472i) q^{57} +(265.448 + 691.516i) q^{58} +(425.060 + 90.3494i) q^{59} +(-80.5723 - 114.288i) q^{60} +(14.1121 + 66.3922i) q^{61} +(156.833 - 307.803i) q^{62} +(-1010.01 - 314.706i) q^{63} +(378.053 + 122.837i) q^{64} +(-34.8594 - 384.261i) q^{65} +(-159.391 + 749.877i) q^{66} +(594.519 + 481.432i) q^{67} +(69.7653 + 18.6936i) q^{68} +(812.296 - 590.168i) q^{69} +(579.386 - 256.474i) q^{70} +(-785.349 - 570.590i) q^{71} +(-730.001 - 901.477i) q^{72} +(-540.459 - 28.3242i) q^{73} +(463.451 + 267.573i) q^{74} +(787.249 + 833.450i) q^{75} -25.9618i q^{76} +(-464.611 - 200.154i) q^{77} +(151.517 + 956.638i) q^{78} +(-708.371 - 74.4528i) q^{79} +(804.763 + 139.244i) q^{80} +(103.650 + 986.161i) q^{81} +(-159.040 + 593.546i) q^{82} +(-185.606 + 1171.87i) q^{83} +(-205.101 + 107.652i) q^{84} +(-587.983 - 70.2837i) q^{85} +(-556.874 + 118.367i) q^{86} +(1209.18 + 1861.97i) q^{87} +(-302.113 - 465.214i) q^{88} +(819.936 - 174.283i) q^{89} +(-1433.50 - 1328.20i) q^{90} +(-638.626 - 25.7202i) q^{91} +(23.3529 - 147.444i) q^{92} +(267.990 - 1000.15i) q^{93} +(-181.146 - 1723.49i) q^{94} +(30.2990 + 210.688i) q^{95} +(-557.094 - 58.5530i) q^{96} +(223.240 + 1409.48i) q^{97} +(-296.119 - 1006.95i) q^{98} +1560.31i 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

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