LMFDB - Embedded newform 175.4.x.a.117.43

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			117.43
Character	$\chi$	$=$	175.117
Dual form			175.4.x.a.3.43

$q$-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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{20}\right)$

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	0.999990	−	0.00440625i	$-0.00140256\pi$
$2$	1.66660	+	2.56634i	0.589232	+	0.907338i	−0.410758	+	0.911744i	$0.634736\pi$
$3$	3.28687	+	8.56260i	0.632559	+	1.64787i	0.755257	+	0.655428i	$0.227512\pi$
$3$	3.28687	+	8.56260i	0.632559	+	1.64787i	−0.122698	+	0.992444i	$0.539155\pi$
$4$	−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	−0.939602	−	0.342269i	$-0.888805\pi$
$11$	−18.2776	+	20.2994i	−0.500993	+	0.556409i	0.438609	+	0.898678i	$0.355471\pi$
$12$	−12.4900	−	0.654575i	−0.300463	−	0.0157466i
$13$	−30.7491	+	15.6674i	−0.656020	+	0.334259i	−0.750118	−	0.661304i	$-0.770003\pi$
$13$	−30.7491	+	15.6674i	−0.656020	+	0.334259i	0.0940979	+	0.995563i	$0.470003\pi$
$14$	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	0.481772	−	0.876297i	$-0.339994\pi$
$17$	−33.3321	−	41.1617i	−0.475542	−	0.587246i	−0.957314	+	0.289051i	$0.906660\pi$
$18$	−168.837	−	45.2397i	−2.21084	−	0.592394i
$19$	17.3924	−	7.74361i	0.210005	−	0.0935003i	−0.299038	−	0.954241i	$-0.596666\pi$
$19$	17.3924	−	7.74361i	0.210005	−	0.0935003i	0.509044	+	0.860741i	$0.329999\pi$
$20$	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	−0.0566797	−	0.998392i	$-0.518051\pi$
$23$	91.8109	−	59.6227i	0.832343	−	0.540530i	0.889023	+	0.457862i	$0.151385\pi$
$24$	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	−0.966802	−	0.255528i	$-0.917751\pi$
$29$	−142.281	−	195.833i	−0.911065	−	1.25397i	0.0557366	−	0.998446i	$-0.482249\pi$
$30$	116.613	+	291.311i	0.709684	+	1.77286i
$31$	112.275	+	11.8006i	0.650491	+	0.0683693i	0.424026	−	0.905650i	$-0.360617\pi$
$31$	112.275	+	11.8006i	0.650491	+	0.0683693i	0.226465	+	0.974019i	$0.427283\pi$
$32$	−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	−0.899842	−	0.436216i	$-0.856318\pi$
$37$	9.15272	−	174.644i	0.0406675	−	0.775983i	0.940510	−	0.339767i	$-0.110348\pi$
$38$	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	−0.0782144	−	0.996937i	$-0.524922\pi$
$41$	−190.983	−	62.0541i	−0.727476	−	0.236371i	−0.649261	+	0.760565i	$0.724922\pi$
$42$	−453.260	+	254.423i	−1.66523	+	0.934723i
$43$	−131.557	+	131.557i	−0.466565	+	0.466565i	−0.900800	−	0.434235i	$-0.857019\pi$
$43$	−131.557	+	131.557i	−0.466565	+	0.466565i	0.434235	+	0.900800i	$0.357019\pi$
$44$	−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	0.983257	+	0.182223i	$0.0583291\pi$
$47$	440.124	+	356.405i	1.36593	+	1.10611i	0.382671	+	0.923885i	$0.375004\pi$
$48$	−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	−0.687708	−	0.725987i	$-0.741383\pi$
$53$	−275.106	+	105.603i	−0.712994	+	0.273693i	−0.0252861	+	0.999680i	$0.508050\pi$
$54$	−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	0.286510	−	0.958077i	$-0.407505\pi$
$59$	425.060	−	90.3494i	0.937935	−	0.199364i	0.651425	+	0.758713i	$0.274172\pi$
$60$	−80.5723	+	114.288i	−0.173364	+	0.245909i
$61$	14.1121	−	66.3922i	0.0296208	−	0.139355i	−0.960852	−	0.277061i	$-0.910640\pi$
$61$	14.1121	−	66.3922i	0.0296208	−	0.139355i	0.990473	+	0.137706i	$0.0439729\pi$
$62$	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	0.0910462	−	0.995847i	$-0.470979\pi$
$67$	594.519	−	481.432i	1.08406	−	0.877855i	0.993015	+	0.117992i	$0.0376456\pi$
$68$	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	−0.312738	+	0.949840i	$0.601246\pi$
$71$	−785.349	+	570.590i	−1.31273	+	0.953754i	−0.999992	+	0.00391469i	$0.998754\pi$
$72$	−730.001	+	901.477i	−1.19488	+	1.47556i
$73$	−540.459	+	28.3242i	−0.866519	+	0.0454123i	−0.480413	−	0.877042i	$-0.659513\pi$
$73$	−540.459	+	28.3242i	−0.866519	+	0.0454123i	−0.386106	+	0.922455i	$0.626180\pi$
$74$	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	−0.594503	−	0.804093i	$-0.702651\pi$
$79$	−708.371	+	74.4528i	−1.00883	+	0.106033i	−0.414332	+	0.910126i	$0.635985\pi$
$80$	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	−0.735176	−	0.677876i	$-0.762901\pi$
$83$	−185.606	−	1171.87i	−0.245457	−	1.54976i	0.489719	−	0.871880i	$-0.337099\pi$
$84$	−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	0.668430	−	0.743775i	$-0.266967\pi$
$89$	819.936	+	174.283i	0.976551	+	0.207572i	0.308121	+	0.951347i	$0.400300\pi$
$90$	−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	−0.539930	−	0.841710i	$-0.681549\pi$
$97$	223.240	−	1409.48i	0.233677	−	1.47538i	0.773607	−	0.633666i	$-0.218451\pi$
$98$	−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	0.549321	−	0.835611i	$-0.314886\pi$
$101$	1570.92	−	906.968i	1.54764	−	0.893532i	0.998321	−	0.0579208i	$-0.0184471\pi$
$102$	1484.47	−	77.7978i	1.44102	−	0.0755209i
$103$	−1185.60	+	1464.09i	−1.13418	+	1.40060i	−0.230136	+	0.973158i	$0.573917\pi$
$103$	−1185.60	+	1464.09i	−1.13418	+	1.40060i	−0.904044	+	0.427438i	$0.859416\pi$
$104$	−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	0.0409184	−	0.999162i	$-0.486972\pi$
$107$	637.456	−	170.806i	0.575936	−	0.154322i	0.535018	+	0.844841i	$0.320305\pi$
$108$	292.779	−	237.088i	0.260858	−	0.211239i
$109$	−37.4402	−	176.142i	−0.0329002	−	0.154783i	0.958631	−	0.284651i	$-0.0918779\pi$
$109$	−37.4402	−	176.142i	−0.0329002	−	0.154783i	−0.991531	+	0.129868i	$0.958545\pi$
$110$	−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	0.949143	−	0.314845i	$-0.101953\pi$
$113$	164.007	+	321.883i	0.136536	+	0.267966i	−0.812607	+	0.582811i	$0.801953\pi$
$114$	−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	−0.968640	−	0.248469i	$-0.920072\pi$
$127$	−283.770	+	556.929i	−0.198272	+	0.389130i	0.770368	+	0.637599i	$0.220072\pi$
$128$	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	0.862684	−	0.505742i	$-0.168781\pi$
$131$	−135.548	−	304.447i	−0.0904040	−	0.203051i	−0.953089	+	0.302692i	$0.902115\pi$
$132$	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	0.491315	−	0.870982i	$-0.336516\pi$
$137$	−167.619	−	108.853i	−0.104531	−	0.0678830i	−0.595846	+	0.803099i	$0.703183\pi$
$138$	−160.798	+	3068.20i	−0.0991884	+	1.89263i
$139$	504.857	+	1553.79i	0.308068	+	0.948136i	0.978515	+	0.206178i	$0.0661025\pi$
$139$	504.857	+	1553.79i	0.308068	+	0.948136i	−0.670447	+	0.741958i	$0.733897\pi$
$140$	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	0.179572	−	0.983745i	$-0.442529\pi$
$149$	−1059.60	−	611.762i	−0.582591	−	0.336359i	−0.762162	+	0.647386i	$0.775862\pi$
$150$	3450.95	+	631.322i	1.87846	+	0.343648i
$151$	−1089.16	−	1886.48i	−0.586984	−	1.01669i	−0.994625	−	0.103544i	$-0.966982\pi$
$151$	−1089.16	−	1886.48i	−0.586984	−	1.01669i	0.407641	−	0.913142i	$-0.366352\pi$
$152$	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	0.743207	−	0.669062i	$-0.233304\pi$
$157$	2070.11	+	554.685i	1.05231	+	0.281966i	0.309105	+	0.951028i	$0.399970\pi$
$158$	−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	−0.543229	−	0.839584i	$-0.682799\pi$
$163$	−2437.41	−	127.739i	−1.17124	−	0.0613823i	−0.628014	+	0.778202i	$0.716132\pi$
$164$	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	0.448547	−	0.893759i	$-0.351942\pi$
$167$	2484.70	−	393.537i	1.15133	−	0.182352i	0.702780	+	0.711407i	$0.251942\pi$
$168$	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	0.972934	+	0.231085i	$0.0742274\pi$
$173$	1793.77	+	2762.17i	0.788312	+	1.21389i	−0.184621	+	0.982810i	$0.559106\pi$
$174$	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	−0.930521	−	0.366238i	$-0.880646\pi$
$179$	−85.5285	+	192.100i	−0.0357134	+	0.0802136i	0.894808	+	0.446451i	$0.147312\pi$
$180$	−844.336	−	213.392i	−0.349628	−	0.0883629i
$181$	−1993.91	+	2744.38i	−0.818819	+	1.12701i	0.171083	+	0.985257i	$0.445273\pi$
$181$	−1993.91	+	2744.38i	−0.818819	+	1.12701i	−0.989902	+	0.141751i	$0.954727\pi$
$182$	−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	0.242759	−	0.970087i	$-0.421948\pi$
$191$	−1972.86	−	2191.08i	−0.747389	−	0.830059i	−0.990148	+	0.140027i	$0.955281\pi$
$192$	2294.42	+	2833.37i	0.862423	+	1.06500i
$193$	−3830.73	−	1026.44i	−1.42871	−	0.382823i	−0.540147	−	0.841571i	$-0.681631\pi$
$193$	−3830.73	−	1026.44i	−1.42871	−	0.382823i	−0.888566	+	0.458748i	$0.848298\pi$
$194$	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	−0.255840	−	0.966719i	$-0.582352\pi$
$197$	−2206.19	−	349.426i	−0.797890	−	0.126373i	−0.542051	+	0.840346i	$0.682352\pi$
$198$	4004.27	−	2600.41i	1.43723	−	0.933348i
$199$	1251.41	+	2167.51i	0.445781	+	0.772116i	0.998106	−	0.0615132i	$-0.0195926\pi$
$199$	1251.41	+	2167.51i	0.445781	+	0.772116i	−0.552325	+	0.833629i	$0.686259\pi$
$200$	−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	0.999943	−	0.0106464i	$-0.00338893\pi$
$211$	566.141	+	1742.40i	0.184714	+	0.568492i	−0.815229	+	0.579139i	$0.803389\pi$
$212$	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	−0.937856	−	0.347026i	$-0.887192\pi$
$223$	−352.484	+	691.789i	−0.105848	+	0.207738i	0.832008	+	0.554764i	$0.187192\pi$
$224$	−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	0.981477	+	0.191581i	$0.0613614\pi$
$227$	86.8784	+	1657.74i	0.0254023	+	0.484705i	−0.956075	+	0.293124i	$0.905305\pi$
$228$	−222.301	+	85.3333i	−0.0645712	+	0.0247866i
$229$	36.9237	+	351.305i	0.0106550	+	0.101375i	0.998557	−	0.0537051i	$-0.0171031\pi$
$229$	36.9237	+	351.305i	0.0106550	+	0.101375i	−0.987902	+	0.155080i	$0.950436\pi$
$230$	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	−0.613727	−	0.789518i	$-0.710330\pi$
$233$	1318.26	−	3434.18i	0.370652	−	0.965581i	0.984379	−	0.176063i	$-0.0563363\pi$
$234$	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	−0.529344	−	0.848407i	$-0.677562\pi$
$239$	−1695.61	+	550.937i	−0.458912	+	0.149109i	0.0704327	+	0.997517i	$0.477562\pi$
$240$	3837.45	+	6433.18i	1.03211	+	1.73025i
$241$	−518.048	−	2437.22i	−0.138466	−	0.651433i	−0.991557	−	0.129671i	$-0.958608\pi$
$241$	−518.048	−	2437.22i	−0.138466	−	0.651433i	0.853091	−	0.521763i	$-0.174725\pi$
$242$	−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	$0.322658\pi$
$251$			6750.43i			1.69754i	−0.528759	+	0.848772i	$0.677342\pi$
$252$	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	−0.693544	−	0.720414i	$-0.743952\pi$
$257$	−1866.88	−	6967.30i	−0.453124	−	1.69108i	0.240420	−	0.970669i	$-0.422715\pi$
$258$	−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	−0.976964	−	0.213406i	$-0.931544\pi$
$263$	−1640.55	+	2526.22i	−0.384640	+	0.592294i	0.592323	+	0.805700i	$0.298211\pi$
$264$	−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	−0.577764	−	0.816204i	$-0.696075\pi$
$269$	692.994	−	6593.40i	0.157073	−	1.49445i	0.734837	−	0.678244i	$-0.237259\pi$
$270$	−8481.80	−	4170.54i	−1.91180	−	0.940042i
$271$	−2490.61	+	261.774i	−0.558280	+	0.0586776i	−0.379467	−	0.925205i	$-0.623893\pi$
$271$	−2490.61	+	261.774i	−0.558280	+	0.0586776i	−0.178814	+	0.983883i	$0.557226\pi$
$272$	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	−0.662801	−	0.748795i	$-0.730633\pi$
$277$	−5733.71	+	300.491i	−1.24370	+	0.0651796i	−0.580900	+	0.813975i	$0.697299\pi$
$278$	−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	0.663182	−	0.748458i	$-0.269206\pi$
$281$	736.192	+	534.875i	0.156290	+	0.113551i	−0.506892	+	0.862010i	$0.669206\pi$
$282$	−15353.0	+	4113.82i	−3.24204	+	0.868703i
$283$	1381.64	−	1118.83i	0.290212	−	0.235009i	−0.473147	−	0.880983i	$-0.656882\pi$
$283$	1381.64	−	1118.83i	0.290212	−	0.235009i	0.763359	+	0.645974i	$0.223549\pi$
$284$	−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	0.945847	−	0.324614i	$-0.105234\pi$
$293$	3115.70	+	3115.70i	0.621233	+	0.621233i	−0.324614	+	0.945847i	$0.605234\pi$
$294$	−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	−0.300840	+	0.953675i	$0.597267\pi$
$307$	−6748.13	+	6748.13i	−1.25451	+	1.25451i	−0.953675	+	0.300840i	$0.902733\pi$
$308$	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	0.291769	−	0.956489i	$-0.405756\pi$
$311$	−3449.68	−	3106.11i	−0.628982	−	0.566338i	−0.920751	+	0.390151i	$0.872423\pi$
$312$	−5390.74	−	3500.78i	−0.978174	−	0.635234i
$313$	−324.413	+	6190.17i	−0.0585844	+	1.11786i	0.798270	+	0.602299i	$0.205749\pi$
$313$	−324.413	+	6190.17i	−0.0585844	+	1.11786i	−0.856855	+	0.515558i	$0.827585\pi$
$314$	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	−0.104873	−	0.994486i	$-0.533444\pi$
$317$	−4787.54	−	1837.77i	−0.848250	−	0.325613i	−0.743377	+	0.668873i	$0.766777\pi$
$318$	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	0.0573456	−	0.998354i	$-0.481736\pi$
$331$	5044.28	−	2245.86i	0.837639	−	0.372941i	0.780294	+	0.625413i	$0.215070\pi$
$332$	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	−0.605813	−	0.795607i	$-0.707152\pi$
$337$	−1968.79	+	1003.15i	−0.318240	+	0.162152i	0.287572	+	0.957759i	$0.407152\pi$
$338$	−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	0.931430	−	0.363919i	$-0.118562\pi$
$347$	−27.5805	−	71.8497i	−0.00426686	−	0.0111155i	−0.935697	+	0.352804i	$0.885228\pi$
$348$	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	−0.980996	−	0.194027i	$-0.937845\pi$
$353$	−2532.22	−	6596.66i	−0.381803	−	0.994631i	0.599193	−	0.800604i	$-0.295488\pi$
$354$	−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	−0.924611	−	0.380913i	$-0.875610\pi$
$359$	−4369.88	+	3934.66i	−0.642433	+	0.578449i	0.282178	+	0.959362i	$0.408943\pi$
$360$	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	0.991309	−	0.131554i	$-0.0419966\pi$
$367$	4615.84	+	5700.09i	0.656525	+	0.810741i	−0.334784	+	0.942295i	$0.608663\pi$
$368$	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	−0.823046	−	0.567974i	$-0.807727\pi$
$373$	−4602.81	+	2989.10i	−0.638939	+	0.414932i	0.184107	+	0.982906i	$0.441061\pi$
$374$	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	0.997630	−	0.0688075i	$-0.0219194\pi$
$379$	4603.39	+	6336.02i	0.623905	+	0.858732i	−0.373724	+	0.927540i	$0.621919\pi$
$380$	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	0.0243137	−	0.999704i	$-0.492260\pi$
$383$	−4696.28	−	1802.73i	−0.626551	−	0.240510i	−0.650864	+	0.759194i	$0.725593\pi$
$384$	−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	0.967206	−	0.253995i	$-0.0817445\pi$
$389$	6258.30	+	5635.00i	0.815703	+	0.734462i	−0.151503	+	0.988457i	$0.548411\pi$
$390$	−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	0.128444	−	0.991717i	$-0.459002\pi$
$397$	−6445.97	−	5219.84i	−0.814896	−	0.659890i	−0.943340	+	0.331827i	$0.892335\pi$
$398$	−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	−0.0137742	−	0.999905i	$-0.504385\pi$
$401$	6898.24	−	11948.1i	0.859056	−	1.48793i	0.872830	−	0.488024i	$-0.162282\pi$
$402$	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	0.0224698	−	0.999748i	$-0.492847\pi$
$409$	3719.13	−	790.525i	0.449631	−	0.0955720i	0.427161	+	0.904176i	$0.359514\pi$
$410$	−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	0.218084	−	0.975930i	$-0.430019\pi$
$419$	−5512.16	−	4004.82i	−0.642689	−	0.466941i	−0.860773	+	0.508989i	$0.830019\pi$
$420$	−2240.03	+	1299.69i	−0.260243	+	0.150996i
$421$	3390.32	−	2463.21i	0.392479	−	0.285153i	−0.373991	−	0.927432i	$-0.622011\pi$
$421$	3390.32	−	2463.21i	0.392479	−	0.285153i	0.766471	+	0.642279i	$0.222011\pi$
$422$	−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	−0.824636	−	0.565664i	$-0.808620\pi$
$431$	891.091	−	8478.16i	0.0995878	−	0.947515i	0.924224	−	0.381851i	$-0.124713\pi$
$432$	−5223.32	−	19493.7i	−0.581729	−	2.17104i
$433$	835.023	+	5272.13i	0.0926759	+	0.585133i	0.989701	+	0.143152i	$0.0457239\pi$
$433$	835.023	+	5272.13i	0.0926759	+	0.585133i	−0.897025	+	0.441980i	$0.854276\pi$
$434$	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	−0.0824282	−	0.996597i	$-0.526268\pi$
$439$	−5179.27	−	1100.89i	−0.563083	−	0.119687i	−0.480654	+	0.876910i	$0.659601\pi$
$440$	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	0.998611	−	0.0526853i	$-0.0167780\pi$
$443$	1001.83	+	3738.89i	0.107446	+	0.400993i	−0.891165	+	0.453679i	$0.850111\pi$
$444$	−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	$0.135346\pi$
$449$			7849.27i			0.825011i	−0.910955	+	0.412506i	$0.864654\pi$
$450$	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	−0.468845	−	0.883280i	$-0.655330\pi$
$457$	−4232.53	+	1134.10i	−0.433237	+	0.116085i	0.0356084	+	0.999366i	$0.488663\pi$
$458$	−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	0.483446	−	0.875374i	$-0.339385\pi$
$461$	13749.4	−	4467.45i	1.38909	−	0.451344i	0.905648	+	0.424030i	$0.139385\pi$
$462$	3119.89	−	13851.2i	0.314179	−	1.39484i
$463$	1904.54	+	3737.88i	0.191170	+	0.375192i	0.966619	−	0.256218i	$-0.0824765\pi$
$463$	1904.54	+	3737.88i	0.191170	+	0.375192i	−0.775449	+	0.631410i	$0.782477\pi$
$464$	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	−0.697067	−	0.717006i	$-0.745512\pi$
$467$	3034.90	−	7906.19i	0.300725	−	0.783415i	0.997792	−	0.0664099i	$-0.0211545\pi$
$468$	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	0.728153	−	0.685415i	$-0.240379\pi$
$479$	7401.51	+	3295.37i	0.706020	+	0.314340i	−0.0221328	+	0.999755i	$0.507046\pi$
$480$	−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	0.338818	−	0.940852i	$-0.389973\pi$
$487$	−4114.91	−	2672.26i	−0.382884	−	0.248648i	−0.721702	+	0.692204i	$0.756640\pi$
$488$	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	−0.802126	−	0.597154i	$-0.796298\pi$
$491$	2152.10	−	6623.47i	0.197806	−	0.608785i	0.999932	−	0.0116301i	$-0.00370206\pi$
$492$	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	0.332533	−	0.943092i	$-0.392097\pi$
$499$	−3544.05	−	2046.16i	−0.317943	−	0.183564i	−0.650475	+	0.759528i	$0.725430\pi$
$500$	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	0.255673	−	0.966763i	$-0.417703\pi$
$503$	2257.20	+	357.506i	0.200087	+	0.0316907i	−0.0555864	+	0.998454i	$0.517703\pi$
$504$	−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	0.869386	+	0.494133i	$0.164515\pi$
$509$	14583.4	+	16196.5i	1.26994	+	1.41041i	0.400551	+	0.916275i	$0.368819\pi$
$510$	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	−0.976035	−	0.217614i	$-0.930173\pi$
$521$	−1917.25	+	4306.21i	−0.161221	+	0.362109i	0.814814	+	0.579723i	$0.196839\pi$
$522$	15162.8	+	39500.5i	1.27138	+	3.31205i
$523$	3854.41	+	5935.27i	0.322259	+	0.496236i	0.962257	−	0.272141i	$-0.0877316\pi$
$523$	3854.41	+	5935.27i	0.322259	+	0.496236i	−0.639998	+	0.768376i	$0.721065\pi$
$524$	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	0.960226	−	0.279223i	$-0.0900769\pi$
$541$	7325.54	+	8135.84i	0.582162	+	0.646556i	−0.378064	+	0.925779i	$0.623410\pi$
$542$	−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	0.115567	−	0.993300i	$-0.463132\pi$
$547$	−1042.25	−	165.077i	−0.0814690	−	0.0129034i	−0.197036	+	0.980396i	$0.563132\pi$
$548$	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	−0.882851	−	0.469654i	$-0.844379\pi$
$557$	1532.09	−	5717.86i	0.116547	−	0.434961i	0.999398	+	0.0346929i	$0.0110453\pi$
$558$	−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	0.808441	−	0.588577i	$-0.200312\pi$
$563$	8009.46	+	5201.40i	0.599571	+	0.389366i	−0.208870	+	0.977943i	$0.566978\pi$
$564$	−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	0.884354	+	0.466817i	$0.154599\pi$
$569$	8680.04	+	19495.7i	0.639518	+	1.43638i	−0.244835	+	0.969565i	$0.578734\pi$
$570$	4283.98	+	4163.60i	0.314801	+	0.305955i
$571$	13951.5	+	6211.62i	1.02251	+	0.455251i	0.848333	−	0.529463i	$-0.177607\pi$
$571$	13951.5	+	6211.62i	1.02251	+	0.455251i	0.174178	+	0.984714i	$0.444273\pi$
$572$	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	−0.996786	−	0.0801107i	$-0.974473\pi$
$577$	−191.744	−	3658.70i	−0.0138343	−	0.263975i	0.982952	−	0.183864i	$-0.0588607\pi$
$578$	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	0.976851	−	0.213923i	$-0.0686240\pi$
$587$	3265.42	+	6408.75i	0.229605	+	0.450626i	−0.747245	+	0.664548i	$0.768624\pi$
$588$	−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	0.188189	−	0.982133i	$-0.439738\pi$
$593$	12162.3	−	3258.87i	0.842233	−	0.225676i	0.654043	+	0.756457i	$0.273071\pi$
$594$	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	−0.0495765	−	0.998770i	$-0.515787\pi$
$599$	11590.3	−	6691.66i	0.790596	−	0.456451i	0.840172	+	0.542320i	$0.182454\pi$
$600$	13142.4	−	19217.6i	0.894227	−	1.30759i
$601$		−	6732.60i		−	0.456953i	−0.973549	−	0.228476i	$-0.926626\pi$
$601$		−	6732.60i		−	0.456953i	0.973549	−	0.228476i	$-0.0733743\pi$
$602$	−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	0.998753	+	0.0499327i	$0.0159007\pi$
$607$	2374.44	+	8861.55i	0.158774	+	0.592552i	−0.839979	+	0.542619i	$0.817433\pi$
$608$	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	0.0855449	−	0.996334i	$-0.472737\pi$
$613$	14584.5	−	22458.1i	0.960947	−	1.47973i	0.875402	−	0.483395i	$-0.160596\pi$
$614$	−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	0.856504	+	0.516141i	$0.172632\pi$
$617$	3086.90	+	19489.9i	0.201417	+	1.27169i	−0.655087	+	0.755553i	$0.727368\pi$
$618$	−13684.8	−	51072.4i	−0.890751	−	3.32433i
$619$	−1038.21	+	9877.93i	−0.0674140	+	0.641402i	0.907688	+	0.419645i	$0.137846\pi$
$619$	−1038.21	+	9877.93i	−0.0674140	+	0.641402i	−0.975102	+	0.221756i	$0.928821\pi$
$620$	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	0.439426	−	0.898279i	$-0.355182\pi$
$631$	−4423.85	−	3214.12i	−0.279098	−	0.202777i	−0.718524	+	0.695502i	$0.755182\pi$
$632$	−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	−0.383105	−	0.923705i	$-0.625145\pi$
$641$	−5799.92	+	1232.81i	−0.357384	+	0.0759642i	0.0257211	+	0.999669i	$0.491812\pi$
$642$	−6637.61	+	17291.6i	−0.408046	+	1.06300i
$643$	−6638.15	−	6638.15i	−0.407128	−	0.407128i	0.473608	−	0.880736i	$-0.342951\pi$
$643$	−6638.15	−	6638.15i	−0.407128	−	0.407128i	−0.880736	+	0.473608i	$0.842951\pi$
$644$	−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	−0.784834	−	0.619706i	$-0.787252\pi$
$647$	−15690.6	+	6023.05i	−0.953416	+	0.365982i	−0.168581	+	0.985688i	$0.553919\pi$
$648$	−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	0.936120	−	0.351680i	$-0.114390\pi$
$653$	13128.3	+	10631.1i	0.786755	+	0.637102i	−0.149365	+	0.988782i	$0.547723\pi$
$654$	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	0.845460	−	0.534038i	$-0.179326\pi$
$659$	20563.7	+	6681.56i	1.21555	+	0.394957i	0.370092	+	0.928995i	$0.379326\pi$
$660$	−847.305	−	3724.49i	−0.0499717	−	0.219660i
$661$	16684.8	+	15023.1i	0.981793	+	0.884010i	0.993258	−	0.115924i	$-0.0369829\pi$
$661$	16684.8	+	15023.1i	0.981793	+	0.884010i	−0.0114653	+	0.999934i	$0.503650\pi$
$662$	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	−0.450473	−	0.892790i	$-0.648745\pi$
$673$	−25098.1	−	12788.1i	−1.43754	−	0.732462i	−0.987064	+	0.160328i	$0.948745\pi$
$674$	−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	−0.216093	−	0.976373i	$-0.569331\pi$
$677$	10357.2	−	6726.04i	0.587976	−	0.381836i	0.804068	+	0.594537i	$0.202665\pi$
$678$	−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	0.974447	+	0.224619i	$0.0721138\pi$
$683$	17699.0	+	21856.5i	0.991558	+	1.22447i	0.0171117	+	0.999854i	$0.494553\pi$
$684$	−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	−0.285952	−	0.958244i	$-0.592310\pi$
$691$	11573.4	−	10420.7i	0.637153	−	0.573695i	0.923105	+	0.384549i	$0.125643\pi$
$692$	−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	−0.619439	−	0.785045i	$-0.712640\pi$
$709$	1822.85	−	1641.30i	0.0965566	−	0.0869399i	0.715995	+	0.698105i	$0.245973\pi$
$710$	−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	−0.961028	−	0.276451i	$-0.910842\pi$
$719$	−26964.9	+	12005.5i	−1.39864	+	0.622714i	−0.437610	+	0.899165i	$0.644175\pi$
$720$	−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	0.326459	−	0.945211i	$-0.394144\pi$
$727$	−4828.87	−	2460.43i	−0.246345	−	0.125519i	−0.572804	+	0.819692i	$0.694144\pi$
$728$	−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	−0.206094	−	0.978532i	$-0.566075\pi$
$733$	−20123.4	−	7724.66i	−1.01402	−	0.389245i	−0.807924	+	0.589287i	$0.799409\pi$
$734$	−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	0.382424	−	0.923987i	$-0.375089\pi$
$739$	−9974.92	−	8981.46i	−0.496527	−	0.447075i	−0.878951	+	0.476912i	$0.841756\pi$
$740$	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	0.0644734	−	0.997919i	$-0.479463\pi$
$743$	21516.3	−	21516.3i	1.06239	−	1.06239i	0.997919	−	0.0644734i	$-0.0205368\pi$
$744$	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	−0.509209	−	0.860643i	$-0.670062\pi$
$751$	10099.6	−	17493.1i	0.490734	−	0.849976i	0.999943	+	0.0106666i	$0.00339534\pi$
$752$	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	0.501051	−	0.865418i	$-0.332947\pi$
$757$	−7588.97	−	7588.97i	−0.364367	−	0.364367i	−0.865418	+	0.501051i	$0.832947\pi$
$758$	−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	−0.968358	−	0.249566i	$-0.919712\pi$
$761$	373.440	−	1756.90i	0.0177887	−	0.0836891i	0.986146	+	0.165877i	$0.0530454\pi$
$762$	−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	−0.847978	+	0.227215i
$769$	−9918.00	−	7205.85i	−0.465088	−	0.337906i	0.330436	−	0.943828i	$-0.392804\pi$
$769$	−9918.00	−	7205.85i	−0.465088	−	0.337906i	−0.795524	+	0.605922i	$0.792804\pi$
$770$	−15796.1	+	7073.44i	−0.739287	+	0.331051i
$771$	53522.0	−	38886.0i	2.50006	−	1.81640i
$772$	3403.41	−	4202.86i	0.158668	−	0.195938i
$773$	−11325.3	+	593.532i	−0.526961	+	0.0276169i	−0.313962	−	0.949435i	$-0.601657\pi$
$773$	−11325.3	+	593.532i	−0.526961	+	0.0276169i	−0.212999	+	0.977052i	$0.568323\pi$
$774$	28163.3	−	16260.1i	1.30789	−	0.755111i
$775$	−4741.41	−	13291.3i	−0.219763	−	0.616049i
$776$		−	28979.6i		−	1.34060i
$777$	29504.0	+	3462.63i	1.36223	+	0.159873i
$778$	−4031.24	+	25452.2i	−0.185767	+	1.17289i
$779$	−3802.18	+	399.625i	−0.174874	+	0.0183800i
$780$	686.923	−	4776.62i	0.0315331	−	0.219270i
$781$	2771.72	−	26371.1i	0.126991	−	1.20824i
$782$	−4592.11	−	17138.0i	−0.209992	−	0.783700i
$783$	10461.4	+	66051.0i	0.477473	+	3.01465i
$784$	−3221.64	+	24848.1i	−0.146758	+	1.13193i
$785$	17576.2	−	16285.1i	0.799138	−	0.740435i
$786$	9148.76	+	1944.63i	0.415172	+	0.0882476i
$787$	6454.62	−	9939.24i	0.292354	−	0.450185i	−0.661723	−	0.749749i	$-0.730174\pi$
$787$	6454.62	−	9939.24i	0.292354	−	0.450185i	0.954076	+	0.299564i	$0.0968411\pi$
$788$	1658.96	−	2554.58i	0.0749976	−	0.115486i
$789$	−27023.3	−	5743.97i	−1.21933	−	0.259177i
$790$	−24196.0	+	2892.23i	−1.08969	+	0.130254i
$791$	269.240	+	6685.16i	0.0121025	+	0.300502i
$792$	−4956.71	−	31295.4i	−0.222385	−	1.40408i
$793$	606.262	+	2262.60i	0.0271488	+	0.101321i
$794$	2653.03	−	25241.9i	0.118580	−	1.12821i
$795$	−29775.0	+	5151.82i	−1.32831	+	0.229832i
$796$	−3394.31	+	356.756i	−0.151141	+	0.0158855i
$797$	3064.71	−	19349.8i	0.136208	−	0.859983i	−0.821073	−	0.570823i	$-0.806624\pi$
$797$	3064.71	−	19349.8i	0.136208	−	0.859983i	0.957281	−	0.289160i	$-0.0933759\pi$
$798$	−5913.14	+	7934.91i	−0.262310	+	0.351996i
$799$		−	29996.0i		−	1.32814i
$800$	7503.24	−	1408.65i	0.331600	−	0.0622540i
$801$	−41467.4	+	23941.2i	−1.82919	+	1.05608i
$802$	42159.5	−	2209.48i	1.85624	−	0.0972813i
$803$	9303.35	−	11488.7i	0.408852	−	0.504890i
$804$	−7740.69	+	5623.94i	−0.339544	+	0.246693i
$805$	9175.35	−	20727.6i	0.401725	−	0.907516i
$806$	−9644.97	−	7007.48i	−0.421501	−	0.306238i
$807$	58734.4	−	15737.8i	2.56202	−	0.686490i
$808$	28627.0	−	23181.7i	1.24641	−	1.00932i
$809$	98.1840	+	461.919i	0.00426695	+	0.0200744i	0.980230	−	0.197864i	$-0.0634003\pi$
$809$	98.1840	+	461.919i	0.00426695	+	0.0200744i	−0.975963	+	0.217938i	$0.930067\pi$
$810$	3064.96	−	33785.6i	0.132953	−	1.46556i
$811$	−39464.3	+	12822.7i	−1.70873	+	0.555200i	−0.990121	−	0.140216i	$-0.955220\pi$
$811$	−39464.3	+	12822.7i	−1.70873	+	0.555200i	−0.718607	+	0.695416i	$0.755220\pi$
$812$	5963.94	+	1343.34i	0.257750	+	0.0580568i
$813$	−10427.8	−	20465.7i	−0.449838	−	0.882858i
$814$	−3039.21	+	14298.4i	−0.130865	+	0.615673i
$815$	−15723.6	+	22303.1i	−0.675794	+	0.958583i
$816$	34711.0	−	7378.05i	1.48913	−	0.316524i
$817$	−1269.37	+	3306.83i	−0.0543570	+	0.141605i
$818$	8227.06	+	8227.06i	0.351653	+	0.351653i
$819$	26126.3	−	25501.2i	1.11469	−	1.08802i
$820$	−834.458	−	2945.69i	−0.0355372	−	0.125449i
$821$	4086.66	+	38882.0i	0.173722	+	1.65285i	0.640118	+	0.768277i	$0.278885\pi$
$821$	4086.66	+	38882.0i	0.173722	+	1.65285i	−0.466396	+	0.884576i	$0.654448\pi$
$822$	5236.74	−	2010.20i	0.222205	−	0.0852964i
$823$	291.657	+	5565.15i	0.0123530	+	0.235709i	0.997827	+	0.0658845i	$0.0209869\pi$
$823$	291.657	+	5565.15i	0.0123530	+	0.235709i	−0.985474	+	0.169825i	$0.945680\pi$
$824$	−19128.8	+	33132.1i	−0.808718	+	1.40074i
$825$	2529.45	+	31214.2i	0.106744	+	1.31726i
$826$	8546.61	+	23096.7i	0.360018	+	0.972926i
$827$	10838.2	−	21271.2i	0.455721	−	0.894403i	−0.542791	−	0.839868i	$-0.682632\pi$
$827$	10838.2	−	21271.2i	0.455721	−	0.894403i	0.998512	−	0.0545351i	$-0.0173677\pi$
$828$	−6626.91	−	5366.37i	−0.278141	−	0.225234i
$829$	4372.51	+	1946.77i	0.183189	+	0.0815609i	0.496282	−	0.868162i	$-0.334698\pi$
$829$	4372.51	+	1946.77i	0.183189	+	0.0815609i	−0.313093	+	0.949723i	$0.601365\pi$
$830$	−6920.58	−	39997.5i	−0.289418	−	1.67269i
$831$	−21419.0	−	48107.8i	−0.894122	−	2.00823i
$832$	−9700.25	+	9700.25i	−0.404202	+	0.404202i
$833$	3275.57	−	17869.3i	0.136245	−	0.743260i
$834$	−43608.3	−	14169.2i	−1.81059	−	0.588296i
$835$	11072.6	−	25854.8i	0.458903	−	1.07155i
$836$	−527.009	−	474.521i	−0.0218026	−	0.0196312i
$837$	−26157.3	−	16986.7i	−1.08020	−	0.701490i
$838$	1091.16	−	20820.5i	0.0449802	−	0.858272i
$839$	11671.3	+	35920.5i	0.480258	+	1.47808i	0.838732	+	0.544544i	$0.183297\pi$
$839$	11671.3	+	35920.5i	0.480258	+	1.47808i	−0.358474	+	0.933540i	$0.616703\pi$
$840$	34400.2	+	17435.1i	1.41300	+	0.716151i
$841$	−10570.0	+	32531.2i	−0.433393	+	1.33385i
$842$	11971.7	+	4595.52i	0.489992	+	0.188090i
$843$	−2160.15	+	8061.78i	−0.0882555	+	0.329374i
$844$	−2484.63	−	261.145i	−0.101332	−	0.0106505i
$845$	4180.03	+	10442.1i	0.170174	+	0.425113i
$846$	−58185.4	−	80085.3i	−2.36460	−	3.25460i
$847$	−3471.69	+	10260.4i	−0.140837	+	0.416235i
$848$	−19179.9	−	9772.67i	−0.776700	−	0.395749i
$849$	14121.4	+	8152.97i	0.570841	+	0.329575i
$850$	−20079.7	+	2690.93i	−0.810270	+	0.108586i
$851$	−9572.45	−	16580.0i	−0.385593	−	0.667866i
$852$	10182.5	−	6612.61i	0.409446	−	0.265897i
$853$	12622.4	+	1999.20i	0.506664	+	0.0802477i	0.404533	−	0.914523i	$-0.367434\pi$
$853$	12622.4	+	1999.20i	0.506664	+	0.0802477i	0.102131	+	0.994771i	$0.467434\pi$
$854$	3838.66	+	247.811i	0.153813	+	0.00992964i
$855$	6766.70	+	10101.7i	0.270662	+	0.404060i
$856$	12243.0	−	5450.93i	0.488852	−	0.217651i
$857$	1842.67	+	493.742i	0.0734475	+	0.0196802i	0.295356	−	0.955387i	$-0.404562\pi$
$857$	1842.67	+	493.742i	0.0734475	+	0.0196802i	−0.221908	+	0.975068i	$0.571229\pi$
$858$	16649.8	+	20560.8i	0.662488	+	0.818105i
$859$	219.820	+	244.135i	0.00873127	+	0.00969706i	0.747495	−	0.664268i	$-0.231257\pi$
$859$	219.820	+	244.135i	0.00873127	+	0.00969706i	−0.738763	+	0.673965i	$0.764590\pi$
$860$	−2782.68	−	550.157i	−0.110336	−	0.0218142i
$861$	12608.8	−	31694.6i	0.499078	−	1.25453i
$862$	23242.9	−	11842.9i	0.918397	−	0.467946i
$863$	−47514.4	−	2490.12i	−1.87417	−	0.0982211i	−0.918996	−	0.394266i	$-0.870999\pi$
$863$	−47514.4	−	2490.12i	−1.87417	−	0.0982211i	−0.955174	+	0.296045i	$0.904332\pi$
$864$	11290.2	−	12539.1i	0.444562	−	0.493736i
$865$	36818.8	−	524.680i	1.44726	−	0.0206239i
$866$	−12138.4	+	10929.5i	−0.476305	+	0.428867i
$867$	19093.3	−	3024.08i	0.747914	−	0.118458i
$868$	−2326.76	+	1647.82i	−0.0909854	+	0.0644363i
$869$	11436.0	−	15740.3i	0.446421	−	0.614446i
$870$	40456.5	−	64284.6i	1.57655	−	2.50512i
$871$	−10738.1	+	24118.2i	−0.417735	+	0.938248i
$872$	−1310.51	−	3413.99i	−0.0508938	−	0.132583i
$873$	44396.6	+	68364.7i	1.72119	+	2.65040i
$874$	6377.58			0.246825
$875$	−22128.9	−	13425.2i	−0.854962	−	0.518690i
$876$	6768.88			0.261072
$877$	−19137.3	−	29468.8i	−0.736853	−	1.13465i	−0.986090	−	0.166212i	$-0.946846\pi$
$877$	−19137.3	−	29468.8i	−0.736853	−	1.13465i	0.249237	−	0.968443i	$-0.419820\pi$
$878$	−5806.53	−	15126.5i	−0.223190	−	0.581430i
$879$	−16437.6	+	36919.4i	−0.630746	+	1.41668i
$880$	−11882.6	+	18881.2i	−0.455184	+	0.723280i
$881$	−1757.80	+	2419.40i	−0.0672210	+	0.0925218i	−0.841304	−	0.540563i	$-0.818211\pi$
$881$	−1757.80	+	2419.40i	−0.0672210	+	0.0925218i	0.774083	+	0.633084i	$0.218211\pi$
$882$	−25917.1	−	54062.6i	−0.989427	−	2.06393i
$883$	−11837.4	+	1874.87i	−0.451145	+	0.0714544i	−0.377873	−	0.925858i	$-0.623344\pi$
$883$	−11837.4	+	1874.87i	−0.451145	+	0.0714544i	−0.0732726	+	0.997312i	$0.523344\pi$
$884$	−1852.34	+	1667.85i	−0.0704762	+	0.0634570i
$885$	44556.5	−	634.944i	1.69237	−	0.0241169i
$886$	−7925.61	+	8802.28i	−0.300526	+	0.333768i
$887$	−6956.91	−	364.596i	−0.263349	−	0.0138015i	−0.0797953	−	0.996811i	$-0.525427\pi$
$887$	−6956.91	−	364.596i	−0.263349	−	0.0138015i	−0.183553	+	0.983010i	$0.558760\pi$
$888$	29022.6	−	14787.8i	1.09677	−	0.558834i
$889$	−9083.94	+	7175.69i	−0.342706	+	0.270714i
$890$	28133.7	+	5562.25i	1.05960	+	0.209491i
$891$	18124.0	+	20128.7i	0.681455	+	0.756832i
$892$	−666.300	−	822.813i	−0.0250105	−	0.0308854i
$893$	10414.7	+	2790.61i	0.390273	+	0.104573i
$894$	31370.3	−	13967.0i	1.17358	−	0.522511i
$895$	1308.41	+	1953.27i	0.0488663	+	0.0729504i
$896$	13993.8	+	28306.5i	0.521764	+	1.05542i
$897$	−34223.8	−	5420.51i	−1.27391	−	0.201768i
$898$	−20143.9	+	13081.6i	−0.748564	+	0.486123i
$899$	−13663.7	−	23666.1i	−0.506906	−	0.877987i
$900$	−7047.26	+	6718.72i	−0.261009	+	0.248841i
$901$	13516.7	+	7803.84i	0.499783	+	0.288550i
$902$	14955.5	+	7620.21i	0.552066	+	0.281292i
$903$	−20860.7	−	23740.0i	−0.768773	−	0.874882i
$904$	4312.08	+	5935.07i	0.158648	+	0.218360i
$905$	14094.8	+	35210.1i	0.517708	+	1.29329i
$906$	60801.3	+	6390.47i	2.22957	+	0.234337i
$907$	−2751.33	+	10268.1i	−0.100724	+	0.375906i	−0.997825	−	0.0659191i	$-0.979002\pi$
$907$	−2751.33	+	10268.1i	−0.100724	+	0.375906i	0.897101	+	0.441825i	$0.145669\pi$
$908$	−2113.34	−	811.234i	−0.0772396	−	0.0296495i
$909$	−32018.8	+	98543.7i	−1.16831	+	3.59570i
$910$	−21833.9	+	1191.17i	−0.795369	+	0.0433921i
$911$	−998.375	−	3072.68i	−0.0363092	−	0.111748i	0.931259	−	0.364357i	$-0.118711\pi$
$911$	−998.375	−	3072.68i	−0.0363092	−	0.111748i	−0.967568	+	0.252609i	$0.918711\pi$
$912$	−667.579	+	12738.2i	−0.0242388	+	0.462503i
$913$	27180.7	+	17651.4i	0.985270	+	0.639842i
$914$	−9964.42	−	8972.00i	−0.360606	−	0.324691i
$915$	2740.08	−	6398.15i	0.0989991	−	0.231165i
$916$	−458.123	−	148.853i	−0.0165249	−	0.00536926i
$917$	74.7250	−	6171.58i	0.00269099	−	0.222250i
$918$	−31661.4	+	31661.4i	−1.13832	+	1.13832i
$919$	17554.1	+	39427.1i	0.630093	+	1.41521i	0.892852	+	0.450350i	$0.148701\pi$
$919$	17554.1	+	39427.1i	0.630093	+	1.41521i	−0.262760	+	0.964861i	$0.584633\pi$
$920$	−4237.54	−	24490.9i	−0.151856	−	0.877652i
$921$	−79961.7	−	35601.3i	−2.86083	−	1.27373i
$922$	34379.7	+	27840.1i	1.22802	+	0.994432i
$923$	15209.1	−	29849.5i	0.542376	−	1.06447i
$924$	5934.02	−	2195.80i	0.211272	−	0.0781782i
$925$	−20177.0	+	8412.46i	−0.717207	+	0.299027i
$926$	−6418.55	+	11117.2i	−0.227782	+	0.394531i
$927$	−5632.05	−	107466.i	−0.199548	−	3.80760i
$928$	13801.9	−	5298.07i	0.488223	−	0.187411i
$929$	−4486.05	−	42681.9i	−0.158431	−	1.50737i	−0.728084	−	0.685487i	$-0.759589\pi$
$929$	−4486.05	−	42681.9i	−0.158431	−	1.50737i	0.569653	−	0.821885i	$-0.307078\pi$
$930$	9655.10	+	34083.1i	0.340433	+	1.20175i
$931$	5899.55	+	2799.72i	0.207680	+	0.0985576i
$932$	3547.00	+	3547.00i	0.124663	+	0.124663i
$933$	15257.7	−	39747.6i	0.535384	−	1.39472i
$934$	25348.0	−	5387.87i	0.888020	−	0.188754i
$935$	9320.23	−	13220.3i	0.325994	−	0.462407i
$936$	8323.04	−	39156.8i	0.290649	−	1.36739i
$937$	−4357.77	−	8552.61i	−0.151934	−	0.298187i	0.802477	−	0.596683i	$-0.203515\pi$
$937$	−4357.77	−	8552.61i	−0.151934	−	0.298187i	−0.954411	+	0.298496i	$0.903515\pi$
$938$	31865.0	+	29397.7i	1.10920	+	1.02331i
$939$	−54070.2	+	17568.5i	−1.87914	+	0.610571i
$940$	−780.093	+	8599.10i	−0.0270679	+	0.298374i
$941$	−3730.64	−	17551.3i	−0.129241	−	0.608029i	−0.994323	−	0.106400i	$-0.966068\pi$
$941$	−3730.64	−	17551.3i	−0.129241	−	0.608029i	0.865083	−	0.501629i	$-0.167266\pi$
$942$	−46744.4	+	37852.8i	−1.61679	+	1.30925i
$943$	−21234.1	+	5689.67i	−0.733275	+	0.196481i
$944$	25681.6	+	18658.8i	0.885451	+	0.643318i
$945$	−56878.6	+	6101.40i	−1.95795	+	0.210030i
$946$	12581.1	−	9140.72i	0.432397	−	0.314155i
$947$	31130.3	−	38442.7i	1.06821	−	1.31914i	0.123101	−	0.992394i	$-0.460716\pi$
$947$	31130.3	−	38442.7i	1.06821	−	1.31914i	0.945114	−	0.326741i	$-0.105950\pi$
$948$	8896.31	−	466.236i	0.304788	−	0.0159732i
$949$	16174.8	−	9338.55i	0.553274	−	0.319433i
$950$	933.775	−	7222.09i	0.0318902	−	0.246648i
$951$		−	47034.3i		−	1.60378i
$952$	−7881.27	−	18294.6i	−0.268313	−	0.622826i
$953$	4009.11	−	25312.5i	0.136273	−	0.860391i	−0.820942	−	0.571012i	$-0.806551\pi$
$953$	4009.11	−	25312.5i	0.136273	−	0.860391i	0.957215	−	0.289379i	$-0.0934489\pi$
$954$	51225.4	−	5384.01i	1.73845	−	0.182719i
$955$	−32481.4	+	5620.11i	−1.10060	+	0.190432i
$956$	254.132	−	2417.90i	0.00859751	−	0.0817998i
$957$	15695.9	+	58578.0i	0.530175	+	1.97864i
$958$	3878.34	+	24486.9i	0.130797	+	0.825819i
$959$	−1978.26	−	3128.53i	−0.0666124	−	0.105345i
$960$	40473.9	−	4837.99i	1.36072	−	0.162651i
$961$	−16673.5	−	3544.07i	−0.559684	−	0.118964i
$962$	−10058.5	+	15488.7i	−0.337109	+	0.519102i
$963$	−20531.2	+	31615.3i	−0.687030	+	1.05793i
$964$	3323.54	+	706.440i	0.111042	+	0.0236026i
$965$	−32524.7	+	30135.5i	−1.08498	+	1.00528i
$966$	−26444.8	+	50383.5i	−0.880796	+	1.67812i
$967$	−2334.45	−	14739.1i	−0.0776328	−	0.490154i	−0.995616	−	0.0935348i	$-0.970183\pi$
$967$	−2334.45	−	14739.1i	−0.0776328	−	0.490154i	0.917983	−	0.396619i	$-0.129817\pi$
$968$	3073.98	+	11472.3i	0.102068	+	0.380922i
$969$	966.738	−	9197.90i	0.0320497	−	0.304932i
$970$	6949.62	−	48325.1i	0.230040	−	1.59962i
$971$	44203.2	−	4645.95i	1.46092	−	0.153548i	0.659522	−	0.751685i	$-0.270759\pi$
$971$	44203.2	−	4645.95i	1.46092	−	0.153548i	0.801394	+	0.598137i	$0.204092\pi$
$972$	−348.873	+	2202.70i	−0.0115125	+	0.0726868i
$973$	−3526.86	+	30051.3i	−0.116204	+	0.990133i
$974$		−	15013.8i		−	0.493917i
$975$	−11149.2	+	37962.0i	−0.366215	+	1.24693i
$976$	4294.00	−	2479.14i	0.140827	−	0.0813067i
$977$	4638.44	−	243.090i	0.151890	−	0.00796023i	0.0237608	−	0.999718i	$-0.492436\pi$
$977$	4638.44	−	243.090i	0.151890	−	0.00796023i	0.128130	+	0.991757i	$0.459103\pi$
$978$	43109.4	−	53235.7i	1.40950	−	1.74058i
$979$	−18524.3	+	13458.7i	−0.604740	+	0.439369i
$980$	−1403.75	+	5037.50i	−0.0457561	+	0.164201i
$981$	8321.80	+	6046.14i	0.270840	+	0.196777i
$982$	20584.8	−	5515.67i	0.668927	−	0.179238i
$983$	35867.2	−	29044.7i	1.16377	−	0.942403i	0.164736	−	0.986338i	$-0.447323\pi$
$983$	35867.2	−	29044.7i	1.16377	−	0.942403i	0.999034	+	0.0439349i	$0.0139894\pi$
$984$	−7776.28	−	36584.5i	−0.251930	−	1.18524i
$985$	−16444.3	+	18795.1i	−0.531939	+	0.607981i
$986$	−37311.9	+	12123.4i	−1.20512	+	0.391569i
$987$	−65230.9	+	70705.6i	−2.10367	+	2.28023i
$988$	−406.756	−	798.303i	−0.0130978	−	0.0257059i
$989$	−4234.59	+	19922.2i	−0.136150	+	0.640534i
$990$	−760.620	−	53375.7i	−0.0244183	−	1.71353i
$991$	36233.8	−	7701.73i	1.16146	−	0.246875i	0.413425	−	0.910538i	$-0.364332\pi$
$991$	36233.8	−	7701.73i	1.16146	−	0.246875i	0.748032	+	0.663663i	$0.230999\pi$
$992$	−2470.92	+	6436.97i	−0.0790845	+	0.206022i
$993$	35810.3	+	35810.3i	1.14442	+	1.14442i
$994$	−38427.1	−	39369.1i	−1.22619	−	1.25625i
$995$	27962.2	+	1066.17i	0.890915	+	0.0339697i
$996$	1551.15	+	14758.2i	0.0493475	+	0.469510i
$997$	−11360.6	+	4360.93i	−0.360877	+	0.138528i	−0.532049	−	0.846713i	$-0.678578\pi$
$997$	−11360.6	+	4360.93i	−0.360877	+	0.138528i	0.171172	+	0.985241i	$0.445245\pi$
$998$	−655.378	−	12505.4i	−0.0207872	−	0.396643i
$999$	−24157.5	+	41842.0i	−0.765074	+	1.32515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.x.a.117.43	yes	928
7.3	odd	6	inner	175.4.x.a.17.16	yes	928
25.3	odd	20	inner	175.4.x.a.103.16	yes	928
175.3	even	60	inner	175.4.x.a.3.43	✓	928

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.4.x.a.3.43	✓	928	175.3	even	60	inner
175.4.x.a.17.16	yes	928	7.3	odd	6	inner
175.4.x.a.103.16	yes	928	25.3	odd	20	inner
175.4.x.a.117.43	yes	928	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more