LMFDB - Embedded newform 175.4.x.a.17.7

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			17.7
Character	$\chi$	$=$	175.17
Dual form			175.4.x.a.103.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.61688 + 0.241960i) q^{2} +(1.85463 - 2.29028i) q^{3} +(13.3008 - 1.39797i) q^{4} +(-10.3285 - 4.28033i) q^{5} +(-8.00844 + 11.0227i) q^{6} +(-16.5101 - 8.39150i) q^{7} +(-24.5397 + 3.88671i) q^{8} +(3.80790 + 17.9147i) q^{9} +(48.7213 + 17.2627i) q^{10} +(12.7772 + 2.71587i) q^{11} +(21.4664 - 33.0553i) q^{12} +(-54.2210 + 27.6270i) q^{13} +(78.2554 + 34.7478i) q^{14} +(-28.9588 + 15.7168i) q^{15} +(7.70166 - 1.63704i) q^{16} +(27.3739 - 71.3113i) q^{17} +(-21.9153 - 81.7888i) q^{18} +(3.44411 - 32.7686i) q^{19} +(-143.362 - 42.4930i) q^{20} +(-49.8390 + 22.2495i) q^{21} +(-59.6477 - 9.44726i) q^{22} +(0.176346 + 3.36488i) q^{23} +(-36.6104 + 63.4112i) q^{24} +(88.3575 + 88.4192i) q^{25} +(243.647 - 140.670i) q^{26} +(118.989 + 60.6281i) q^{27} +(-231.329 - 88.5333i) q^{28} +(-39.3855 - 54.2095i) q^{29} +(129.896 - 79.5693i) q^{30} +(111.099 + 249.532i) q^{31} +(156.831 - 42.0226i) q^{32} +(29.9170 - 24.2263i) q^{33} +(-109.127 + 335.859i) q^{34} +(134.607 + 157.341i) q^{35} +(75.6926 + 232.958i) q^{36} +(200.923 + 130.481i) q^{37} +(-7.97236 + 152.122i) q^{38} +(-37.2864 + 175.419i) q^{39} +(270.096 + 64.8941i) q^{40} +(354.793 + 115.279i) q^{41} +(224.717 - 114.782i) q^{42} +(-251.156 + 251.156i) q^{43} +(173.743 + 18.2612i) q^{44} +(37.3511 - 201.332i) q^{45} +(-1.62834 - 15.4926i) q^{46} +(402.326 - 154.439i) q^{47} +(10.5345 - 20.6750i) q^{48} +(202.165 + 277.089i) q^{49} +(-429.330 - 386.842i) q^{50} +(-112.554 - 194.950i) q^{51} +(-682.562 + 443.261i) q^{52} +(-455.405 - 368.779i) q^{53} +(-564.029 - 251.122i) q^{54} +(-120.344 - 82.7414i) q^{55} +(437.768 + 141.755i) q^{56} +(-68.6615 - 68.6615i) q^{57} +(194.955 + 240.749i) q^{58} +(302.357 + 335.802i) q^{59} +(-363.204 + 249.530i) q^{60} +(320.873 + 288.915i) q^{61} +(-573.306 - 1125.18i) q^{62} +(87.4630 - 327.728i) q^{63} +(-773.806 + 251.425i) q^{64} +(678.276 - 53.2623i) q^{65} +(-132.261 + 119.089i) q^{66} +(43.9444 + 16.8687i) q^{67} +(264.404 - 986.768i) q^{68} +(8.03357 + 5.83673i) q^{69} +(-659.532 - 693.853i) q^{70} +(-87.7166 + 63.7298i) q^{71} +(-163.074 - 424.823i) q^{72} +(4.65598 + 7.16958i) q^{73} +(-959.210 - 553.800i) q^{74} +(366.375 - 38.3782i) q^{75} -440.664i q^{76} +(-188.162 - 152.059i) q^{77} +(129.702 - 818.909i) q^{78} +(-80.1143 + 179.940i) q^{79} +(-86.5539 - 16.0575i) q^{80} +(-92.2157 + 41.0571i) q^{81} +(-1665.93 - 446.384i) q^{82} +(76.1803 + 480.983i) q^{83} +(-631.795 + 365.611i) q^{84} +(-587.968 + 619.373i) q^{85} +(1098.79 - 1220.33i) q^{86} +(-197.200 - 10.3348i) q^{87} +(-324.103 - 16.9855i) q^{88} +(-103.149 + 114.559i) q^{89} +(-123.731 + 938.564i) q^{90} +(1127.02 - 1.12781i) q^{91} +(7.04957 + 44.5092i) q^{92} +(777.545 + 208.343i) q^{93} +(-1820.12 + 810.371i) q^{94} +(-175.833 + 323.709i) q^{95} +(194.619 - 437.122i) q^{96} +(48.3098 - 305.016i) q^{97} +(-1000.42 - 1230.37i) q^{98} +239.241i 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−4.61688	+	0.241960i	−1.63231	+	0.0855459i	−0.846315	−	0.532683i	$-0.821184\pi$
$2$	−4.61688	+	0.241960i	−1.63231	+	0.0855459i	−0.785998	+	0.618229i	$0.787850\pi$
$3$	1.85463	−	2.29028i	0.356924	−	0.440764i	−0.566781	−	0.823868i	$-0.691812\pi$
$3$	1.85463	−	2.29028i	0.356924	−	0.440764i	0.923705	+	0.383104i	$0.125145\pi$
$4$	13.3008	−	1.39797i	1.66260	−	0.174747i
$5$	−10.3285	−	4.28033i	−0.923813	−	0.382845i
$5$	−10.3285	−	4.28033i	−0.923813	−	0.382845i
$6$	−8.00844	+	11.0227i	−0.544906	+	0.749998i
$7$	−16.5101	−	8.39150i	−0.891460	−	0.453099i
$7$	−16.5101	−	8.39150i	−0.891460	−	0.453099i
$8$	−24.5397	+	3.88671i	−1.08451	+	0.171770i
$9$	3.80790	+	17.9147i	0.141033	+	0.663509i
$10$	48.7213	+	17.2627i	1.54070	+	0.545894i
$11$	12.7772	+	2.71587i	0.350223	+	0.0744423i	0.379664	−	0.925124i	$-0.376039\pi$
$11$	12.7772	+	2.71587i	0.350223	+	0.0744423i	−0.0294412	+	0.999567i	$0.509373\pi$
$12$	21.4664	−	33.0553i	0.516401	−	0.795188i
$13$	−54.2210	+	27.6270i	−1.15678	+	0.589411i	−0.923727	−	0.383052i	$-0.874873\pi$
$13$	−54.2210	+	27.6270i	−1.15678	+	0.589411i	−0.233057	+	0.972463i	$0.574873\pi$
$14$	78.2554	+	34.7478i	1.49390	+	0.663338i
$15$	−28.9588	+	15.7168i	−0.498475	+	0.270537i
$16$	7.70166	−	1.63704i	0.120338	−	0.0255787i
$17$	27.3739	−	71.3113i	0.390537	−	1.01738i	−0.587550	−	0.809188i	$-0.699907\pi$
$17$	27.3739	−	71.3113i	0.390537	−	1.01738i	0.978087	−	0.208196i	$-0.0667593\pi$
$18$	−21.9153	−	81.7888i	−0.286971	−	1.07099i
$19$	3.44411	−	32.7686i	0.0415860	−	0.395664i	−0.953854	−	0.300272i	$-0.902923\pi$
$19$	3.44411	−	32.7686i	0.0415860	−	0.395664i	0.995440	−	0.0953927i	$-0.0304107\pi$
$20$	−143.362	−	42.4930i	−1.60284	−	0.475086i
$21$	−49.8390	+	22.2495i	−0.517893	+	0.231202i
$22$	−59.6477	−	9.44726i	−0.578042	−	0.0915529i
$23$	0.176346	+	3.36488i	0.00159873	+	0.0305055i	0.999312	−	0.0370771i	$-0.0118047\pi$
$23$	0.176346	+	3.36488i	0.00159873	+	0.0305055i	−0.997714	+	0.0675826i	$0.978471\pi$
$24$	−36.6104	+	63.4112i	−0.311378	+	0.539323i
$25$	88.3575	+	88.4192i	0.706860	+	0.707354i
$26$	243.647	−	140.670i	1.83781	−	1.06106i
$27$	118.989	+	60.6281i	0.848130	+	0.432144i
$28$	−231.329	−	88.5333i	−1.56132	−	0.597544i
$29$	−39.3855	−	54.2095i	−0.252197	−	0.347119i	0.664082	−	0.747659i	$-0.268822\pi$
$29$	−39.3855	−	54.2095i	−0.252197	−	0.347119i	−0.916279	+	0.400540i	$0.868822\pi$
$30$	129.896	−	79.5693i	0.790523	−	0.484244i
$31$	111.099	+	249.532i	0.643675	+	1.44572i	0.880443	+	0.474152i	$0.157245\pi$
$31$	111.099	+	249.532i	0.643675	+	1.44572i	−0.236767	+	0.971566i	$0.576088\pi$
$32$	156.831	−	42.0226i	0.866375	−	0.232144i
$33$	29.9170	−	24.2263i	0.157814	−	0.127796i
$34$	−109.127	+	335.859i	−0.550446	+	1.69410i
$35$	134.607	+	157.341i	0.650076	+	0.759869i
$36$	75.6926	+	232.958i	0.350429	+	1.07851i
$37$	200.923	+	130.481i	0.892746	+	0.579756i	0.907461	−	0.420136i	$-0.138017\pi$
$37$	200.923	+	130.481i	0.892746	+	0.579756i	−0.0147151	+	0.999892i	$0.504684\pi$
$38$	−7.97236	+	152.122i	−0.0340339	+	0.649405i
$39$	−37.2864	+	175.419i	−0.153092	+	0.720244i
$40$	270.096	+	64.8941i	1.06765	+	0.256517i
$41$	354.793	+	115.279i	1.35145	+	0.439112i	0.893179	−	0.449701i	$-0.148470\pi$
$41$	354.793	+	115.279i	1.35145	+	0.439112i	0.458269	+	0.888813i	$0.348470\pi$
$42$	224.717	−	114.782i	0.825585	−	0.421698i
$43$	−251.156	+	251.156i	−0.890720	+	0.890720i	−0.994591	−	0.103871i	$-0.966877\pi$
$43$	−251.156	+	251.156i	−0.890720	+	0.890720i	0.103871	+	0.994591i	$0.466877\pi$
$44$	173.743	+	18.2612i	0.595291	+	0.0625676i
$45$	37.3511	−	201.332i	0.123733	−	0.666952i
$46$	−1.62834	−	15.4926i	−0.00521924	−	0.0496578i
$47$	402.326	−	154.439i	1.24862	−	0.479302i	0.357863	−	0.933774i	$-0.383505\pi$
$47$	402.326	−	154.439i	1.24862	−	0.479302i	0.890761	+	0.454472i	$0.150172\pi$
$48$	10.5345	−	20.6750i	0.0316774	−	0.0621705i
$49$	202.165	+	277.089i	0.589403	+	0.807839i
$50$	−429.330	−	386.842i	−1.21433	−	1.09415i
$51$	−112.554	−	194.950i	−0.309035	−	0.535263i
$52$	−682.562	+	443.261i	−1.82028	+	1.18210i
$53$	−455.405	−	368.779i	−1.18028	−	0.955769i	−0.180662	−	0.983545i	$-0.557824\pi$
$53$	−455.405	−	368.779i	−1.18028	−	0.955769i	−0.999614	+	0.0277768i	$0.991157\pi$
$54$	−564.029	−	251.122i	−1.42138	−	0.632840i
$55$	−120.344	−	82.7414i	−0.295041	−	0.202852i
$56$	437.768	+	141.755i	1.04463	+	0.338265i
$57$	−68.6615	−	68.6615i	−0.159552	−	0.159552i
$58$	194.955	+	240.749i	0.441358	+	0.545032i
$59$	302.357	+	335.802i	0.667179	+	0.740977i	0.977796	−	0.209558i	$-0.0672025\pi$
$59$	302.357	+	335.802i	0.667179	+	0.740977i	−0.310618	+	0.950535i	$0.600536\pi$
$60$	−363.204	+	249.530i	−0.781491	+	0.536903i
$61$	320.873	+	288.915i	0.673502	+	0.606424i	0.933239	−	0.359256i	$-0.116969\pi$
$61$	320.873	+	288.915i	0.673502	+	0.606424i	−0.259738	+	0.965679i	$0.583636\pi$
$62$	−573.306	−	1125.18i	−1.17435	−	2.30480i
$63$	87.4630	−	327.728i	0.174910	−	0.655394i
$64$	−773.806	+	251.425i	−1.51134	+	0.491064i
$65$	678.276	−	53.2623i	1.29430	−	0.101637i
$66$	−132.261	+	119.089i	−0.246670	+	0.222103i
$67$	43.9444	+	16.8687i	0.0801293	+	0.0307587i	0.398102	−	0.917341i	$-0.369669\pi$
$67$	43.9444	+	16.8687i	0.0801293	+	0.0307587i	−0.317973	+	0.948100i	$0.603002\pi$
$68$	264.404	−	986.768i	0.471524	−	1.75975i
$69$	8.03357	+	5.83673i	0.0140164	+	0.0101835i
$70$	−659.532	−	693.853i	−1.12613	−	1.18473i
$71$	−87.7166	+	63.7298i	−0.146620	+	0.106526i	−0.658677	−	0.752426i	$-0.728884\pi$
$71$	−87.7166	+	63.7298i	−0.146620	+	0.106526i	0.512057	+	0.858952i	$0.328884\pi$
$72$	−163.074	−	424.823i	−0.266923	−	0.695359i
$73$	4.65598	+	7.16958i	0.00746495	+	0.0114950i	0.842383	−	0.538879i	$-0.181152\pi$
$73$	4.65598	+	7.16958i	0.00746495	+	0.0114950i	−0.834918	+	0.550374i	$0.814485\pi$
$74$	−959.210	−	553.800i	−1.50684	−	0.869973i
$75$	366.375	−	38.3782i	0.564071	−	0.0590872i
$76$		−	440.664i		−	0.665100i
$77$	−188.162	−	152.059i	−0.278480	−	0.225048i
$78$	129.702	−	818.909i	0.188281	−	1.18876i
$79$	−80.1143	+	179.940i	−0.114096	+	0.256263i	−0.961563	−	0.274584i	$-0.911460\pi$
$79$	−80.1143	+	179.940i	−0.114096	+	0.256263i	0.847467	+	0.530848i	$0.178126\pi$
$80$	−86.5539	−	16.0575i	−0.120963	−	0.0224410i
$81$	−92.2157	+	41.0571i	−0.126496	+	0.0563197i
$82$	−1665.93	−	446.384i	−2.24355	−	0.601157i
$83$	76.1803	+	480.983i	0.100745	+	0.636082i	0.985455	+	0.169938i	$0.0543569\pi$
$83$	76.1803	+	480.983i	0.100745	+	0.636082i	−0.884709	+	0.466143i	$0.845643\pi$
$84$	−631.795	+	365.611i	−0.820649	+	0.474898i
$85$	−587.968	+	619.373i	−0.750284	+	0.790358i
$86$	1098.79	−	1220.33i	1.37774	−	1.53013i
$87$	−197.200	−	10.3348i	−0.243013	−	0.0127357i
$88$	−324.103	−	16.9855i	−0.392608	−	0.0205757i
$89$	−103.149	+	114.559i	−0.122851	+	0.136440i	−0.801433	−	0.598085i	$-0.795928\pi$
$89$	−103.149	+	114.559i	−0.122851	+	0.136440i	0.678581	+	0.734525i	$0.262595\pi$
$90$	−123.731	+	938.564i	−0.144915	+	1.09926i
$91$	1127.02	−	1.12781i	1.29829	−	0.00129920i
$92$	7.04957	+	44.5092i	0.00798879	+	0.0504392i
$93$	777.545	+	208.343i	0.866964	+	0.232302i
$94$	−1820.12	+	810.371i	−1.99714	+	0.889185i
$95$	−175.833	+	323.709i	−0.189896	+	0.349599i
$96$	194.619	−	437.122i	0.206909	−	0.464725i
$97$	48.3098	−	305.016i	0.0505683	−	0.319275i	−0.949418	−	0.314015i	$-0.898326\pi$
$97$	48.3098	−	305.016i	0.0505683	−	0.319275i	0.999986	−	0.00526010i	$-0.00167435\pi$
$98$	−1000.42	−	1230.37i	−1.03120	−	1.26822i
$99$			239.241i			0.242875i
$100$	1298.84	+	1052.53i	1.29884	+	1.05253i
$101$	−1089.84	−	629.222i	−1.07370	−	0.619900i	−0.144509	−	0.989503i	$-0.546160\pi$
$101$	−1089.84	−	629.222i	−1.07370	−	0.619900i	−0.929190	+	0.369603i	$0.879494\pi$
$102$	566.820	+	872.826i	0.550230	+	0.847281i
$103$	−557.845	−	1453.24i	−0.533652	−	1.39021i	−0.890044	−	0.455874i	$-0.849327\pi$
$103$	−557.845	−	1453.24i	−0.533652	−	1.39021i	0.356393	−	0.934336i	$-0.384007\pi$
$104$	1223.19	−	888.699i	1.15330	−	0.837924i
$105$	609.999	−	16.4777i	0.566951	−	0.0153148i
$106$	2191.78	+	1592.42i	2.00834	+	1.45915i
$107$	−390.847	+	1458.66i	−0.353127	+	1.31789i	0.529699	+	0.848186i	$0.322305\pi$
$107$	−390.847	+	1458.66i	−0.353127	+	1.31789i	−0.882826	+	0.469701i	$0.844362\pi$
$108$	1667.41	+	640.060i	1.48562	+	0.570276i
$109$	868.747	−	782.223i	0.763402	−	0.687370i	−0.192421	−	0.981312i	$-0.561634\pi$
$109$	868.747	−	782.223i	0.763402	−	0.687370i	0.955823	+	0.293942i	$0.0949673\pi$
$110$	575.636	+	352.888i	0.498952	+	0.305878i
$111$	671.477	−	218.176i	0.574178	−	0.186562i
$112$	−140.892	−	37.6009i	−0.118867	−	0.0317227i
$113$	971.566	+	1906.81i	0.808826	+	1.58741i	0.809290	+	0.587410i	$0.199852\pi$
$113$	971.566	+	1906.81i	0.808826	+	1.58741i	−0.000464277		1.00000i	$0.500148\pi$
$114$	333.615	+	300.388i	0.274087	+	0.246789i
$115$	12.5814	−	35.5092i	0.0102020	−	0.0287934i
$116$	−599.643	−	665.971i	−0.479961	−	0.533051i
$117$	−701.398	−	866.154i	−0.554224	−	0.684410i
$118$	−1477.20	−	1477.20i	−1.15243	−	1.15243i
$119$	−1050.35	+	947.648i	−0.809124	+	0.730006i
$120$	649.553	−	498.240i	0.494132	−	0.379024i
$121$	−1060.05	−	471.964i	−0.796431	−	0.354594i
$122$	−1551.34	−	1256.25i	−1.15124	−	0.932258i
$123$	922.032	−	598.774i	0.675909	−	0.438940i
$124$	1826.55	+	3163.67i	1.32281	+	2.29118i
$125$	−534.140	−	1291.44i	−0.382200	−	0.924080i
$126$	−324.509	+	1534.24i	−0.229441	+	1.08477i
$127$	−412.103	+	808.798i	−0.287939	+	0.565112i	−0.988987	−	0.148002i	$-0.952716\pi$
$127$	−412.103	+	808.798i	−0.287939	+	0.565112i	0.701048	+	0.713114i	$0.252716\pi$
$128$	2299.10	−	882.543i	1.58761	−	0.609426i
$129$	109.416	+	1041.02i	0.0746783	+	0.710517i
$130$	−3118.63	+	410.022i	−2.10401	+	0.276625i
$131$	909.530	+	95.5954i	0.606611	+	0.0637573i	0.402854	−	0.915264i	$-0.368018\pi$
$131$	909.530	+	95.5954i	0.606611	+	0.0637573i	0.203757	+	0.979022i	$0.434685\pi$
$132$	364.053	−	364.053i	0.240051	−	0.240051i
$133$	−331.840	+	512.110i	−0.216347	+	0.333877i
$134$	−206.967	−	67.2478i	−0.133427	−	0.0433532i
$135$	−969.478	−	1135.51i	−0.618069	−	0.723922i
$136$	−394.580	+	1856.35i	−0.248786	+	1.17045i
$137$	−41.5153	+	792.159i	−0.0258897	+	0.494005i	0.954656	+	0.297712i	$0.0962236\pi$
$137$	−41.5153	+	792.159i	−0.0258897	+	0.494005i	−0.980545	+	0.196293i	$0.937110\pi$
$138$	−38.5023	−	25.0037i	−0.0237502	−	0.0154236i
$139$	−253.295	−	779.563i	−0.154563	−	0.475695i	0.843554	−	0.537045i	$-0.180459\pi$
$139$	−253.295	−	779.563i	−0.154563	−	0.475695i	−0.998116	+	0.0613498i	$0.980459\pi$
$140$	2010.34	+	1904.59i	1.21360	+	1.14976i
$141$	392.459	−	1207.87i	0.234405	−	0.721423i
$142$	389.557	−	315.457i	0.230217	−	0.186426i
$143$	−767.821	+	205.737i	−0.449010	+	0.120312i
$144$	58.6542	+	131.740i	0.0339434	+	0.0762382i
$145$	174.760	+	728.488i	0.100090	+	0.417225i
$146$	−23.2308	−	31.9745i	−0.0131685	−	0.0181249i
$147$	1009.55	+	50.8825i	0.566438	+	0.0285491i
$148$	2854.86	+	1454.62i	1.58559	+	0.807901i
$149$	748.796	−	432.318i	0.411703	−	0.237697i	−0.279818	−	0.960053i	$-0.590274\pi$
$149$	748.796	−	432.318i	0.411703	−	0.237697i	0.691521	+	0.722356i	$0.256941\pi$
$150$	−1682.22	+	265.836i	−0.915686	+	0.144703i
$151$	393.087	−	680.847i	0.211848	−	0.366931i	−0.740445	−	0.672117i	$-0.765385\pi$
$151$	393.087	−	680.847i	0.211848	−	0.366931i	0.952293	+	0.305186i	$0.0987186\pi$
$152$	42.8443	+	817.517i	0.0228627	+	0.436246i
$153$	1381.76	+	218.849i	0.730123	+	0.115640i
$154$	905.511	+	656.509i	0.473819	+	0.343526i
$155$	−79.4082	−	3052.84i	−0.0411498	−	1.58200i
$156$	−250.710	+	2385.34i	−0.128672	+	1.22423i
$157$	673.396	+	2513.15i	0.342311	+	1.27752i	0.895722	+	0.444614i	$0.146659\pi$
$157$	673.396	+	2513.15i	0.342311	+	1.27752i	−0.553411	+	0.832908i	$0.686674\pi$
$158$	326.340	−	850.144i	0.164318	−	0.428062i
$159$	−1689.21	+	359.053i	−0.842537	+	0.179087i
$160$	−1799.70	−	237.255i	−0.889243	−	0.117229i
$161$	25.3250	−	57.0343i	0.0123968	−	0.0279188i
$162$	415.814	−	211.868i	0.201663	−	0.102753i
$163$	−1950.51	+	3003.53i	−0.937276	+	1.44328i	−0.0413141	+	0.999146i	$0.513154\pi$
$163$	−1950.51	+	3003.53i	−0.937276	+	1.44328i	−0.895962	+	0.444132i	$0.853512\pi$
$164$	4880.20	+	1037.32i	2.32366	+	0.493908i
$165$	−412.695	+	122.168i	−0.194717	+	0.0576408i
$166$	−468.094	−	2202.21i	−0.218862	−	1.02967i
$167$	3366.99	−	533.278i	1.56015	−	0.247104i	0.684124	−	0.729366i	$-0.260185\pi$
$167$	3366.99	−	533.278i	1.56015	−	0.247104i	0.876027	+	0.482262i	$0.160185\pi$
$168$	1136.56	−	739.706i	0.521948	−	0.339700i
$169$	885.300	−	1218.51i	0.402958	−	0.554625i
$170$	2564.71	−	3001.83i	1.15709	−	1.35429i
$171$	600.155	−	63.0789i	0.268392	−	0.0282091i
$172$	−2989.48	+	3691.70i	−1.32526	+	1.63657i
$173$	−1807.56	+	94.7302i	−0.794371	+	0.0416312i	−0.445204	−	0.895429i	$-0.646869\pi$
$173$	−1807.56	+	94.7302i	−0.794371	+	0.0416312i	−0.349167	+	0.937060i	$0.613536\pi$
$174$	912.950			0.397762
$175$	−716.819	−	2201.26i	−0.309637	−	0.950855i
$176$	102.851			0.0440494
$177$	1329.84	−	69.6939i	0.564728	−	0.0295961i
$178$	448.508	−	553.861i	0.188860	−	0.233223i
$179$	419.946	−	44.1381i	0.175353	−	0.0184304i	−0.0164448	−	0.999865i	$-0.505235\pi$
$179$	419.946	−	44.1381i	0.175353	−	0.0184304i	0.191798	+	0.981434i	$0.438568\pi$
$180$	215.343	−	2730.10i	0.0891708	−	1.13050i
$181$	−2034.34	+	2800.03i	−0.835423	+	1.14986i	0.151467	+	0.988462i	$0.451600\pi$
$181$	−2034.34	+	2800.03i	−0.835423	+	1.14986i	−0.986889	+	0.161398i	$0.948400\pi$
$182$	−5203.06	+	277.902i	−2.11910	+	0.113184i
$183$	1256.80	−	199.057i	0.507678	−	0.0804084i
$184$	−17.4058	−	81.8879i	−0.00697377	−	0.0328090i
$185$	−1516.74	−	2207.70i	−0.602774	−	0.877369i
$186$	−3640.24	−	773.757i	−1.43503	−	0.305025i
$187$	543.432	−	836.812i	0.212512	−	0.327239i
$188$	5135.37	−	2616.60i	1.99221	−	1.01508i
$189$	−1455.76	−	1999.47i	−0.560271	−	0.769526i
$190$	733.475	−	1537.07i	0.280062	−	0.586899i
$191$	−3139.06	+	667.228i	−1.18919	+	0.252769i	−0.759681	−	0.650295i	$-0.774645\pi$
$191$	−3139.06	+	667.228i	−1.18919	+	0.252769i	−0.429505	+	0.903065i	$0.641312\pi$
$192$	−859.292	+	2238.53i	−0.322990	+	0.841417i
$193$	−367.726	−	1372.37i	−0.137148	−	0.511841i	−0.999980	−	0.00635124i	$-0.997978\pi$
$193$	−367.726	−	1372.37i	−0.137148	−	0.511841i	0.862832	−	0.505490i	$-0.168688\pi$
$194$	−149.239	+	1419.91i	−0.0552305	+	0.525483i
$195$	1135.97	−	1652.22i	0.417170	−	0.606759i
$196$	3076.33	+	3402.89i	1.12111	+	1.24012i
$197$	−2199.84	−	348.421i	−0.795595	−	0.126010i	−0.254612	−	0.967043i	$-0.581948\pi$
$197$	−2199.84	−	348.421i	−0.795595	−	0.126010i	−0.540983	+	0.841034i	$0.681948\pi$
$198$	−57.8869	−	1104.55i	−0.0207770	−	0.396448i
$199$	−1262.51	+	2186.74i	−0.449734	+	0.778963i	−0.998368	−	0.0571000i	$-0.981815\pi$
$199$	−1262.51	+	2186.74i	−0.449734	+	0.778963i	0.548634	+	0.836062i	$0.315148\pi$
$200$	−2511.93	−	1826.36i	−0.888100	−	0.645716i
$201$	120.135	−	69.3597i	0.0421574	−	0.0243396i
$202$	5183.92	+	2641.34i	1.80564	+	0.920020i
$203$	195.358	+	1225.51i	0.0675442	+	0.423713i
$204$	−1769.60	−	2435.65i	−0.607338	−	0.835929i
$205$	−3171.06	−	2709.30i	−1.08037	−	0.923052i
$206$	2927.13	+	6574.44i	0.990013	+	2.22361i
$207$	−59.6095	+	15.9723i	−0.0200152	+	0.00536306i
$208$	−372.365	+	301.535i	−0.124129	+	0.100518i
$209$	133.001	−	409.335i	0.0440185	−	0.135475i
$210$	−2812.30	+	223.671i	−0.924131	+	0.0734989i
$211$	−260.419	−	801.487i	−0.0849667	−	0.261501i	0.899543	−	0.436833i	$-0.143900\pi$
$211$	−260.419	−	801.487i	−0.0849667	−	0.261501i	−0.984509	+	0.175332i	$0.943900\pi$
$212$	−6572.80	−	4268.43i	−2.12935	−	1.38282i
$213$	−16.7228	+	319.091i	−0.00537948	+	0.102647i
$214$	1451.55	−	6829.02i	0.463673	−	2.18141i
$215$	3669.11	−	1519.04i	1.16387	−	0.481851i
$216$	−3155.61	−	1025.32i	−0.994037	−	0.322982i
$217$	259.699	−	5052.08i	0.0812420	−	1.58045i
$218$	−3821.63	+	3821.63i	−1.18731	+	1.18731i
$219$	25.0555	+	2.63343i	0.00773101	+	0.000812562i
$220$	−1716.35	−	932.291i	−0.525984	−	0.285705i
$221$	485.878	+	4622.82i	0.147890	+	1.40708i
$222$	−3047.34	+	1169.76i	−0.921278	+	0.353646i
$223$	−2056.53	+	4036.17i	−0.617559	+	1.21203i	0.344397	+	0.938824i	$0.388083\pi$
$223$	−2056.53	+	4036.17i	−0.617559	+	1.21203i	−0.961956	+	0.273204i	$0.911917\pi$
$224$	−2941.92	−	622.248i	−0.877523	−	0.185606i
$225$	−1247.55	+	1919.59i	−0.369645	+	0.568768i
$226$	−4946.97	−	8568.41i	−1.45605	−	2.52196i
$227$	1502.58	−	975.788i	0.439338	−	0.285310i	−0.305955	−	0.952046i	$-0.598976\pi$
$227$	1502.58	−	975.788i	0.439338	−	0.285310i	0.745294	+	0.666736i	$0.232309\pi$
$228$	−1009.24	−	817.269i	−0.293152	−	0.237390i
$229$	5377.03	+	2394.01i	1.55163	+	0.690832i	0.990579	−	0.136945i	$-0.0437285\pi$
$229$	5377.03	+	2394.01i	1.55163	+	0.690832i	0.561056	+	0.827778i	$0.310395\pi$
$230$	−49.4951	+	166.986i	−0.0141896	+	0.0478726i
$231$	−697.227	+	148.929i	−0.198589	+	0.0424192i
$232$	1177.20	+	1177.20i	0.333135	+	0.333135i
$233$	3940.96	+	4866.68i	1.10807	+	1.36836i	0.922623	+	0.385702i	$0.126041\pi$
$233$	3940.96	+	4866.68i	1.10807	+	1.36836i	0.185449	+	0.982654i	$0.440626\pi$
$234$	3447.84	+	3829.22i	0.963216	+	1.06976i
$235$	−4816.49	−	126.966i	−1.33699	−	0.0352440i
$236$	4491.04	+	4043.75i	1.23874	+	1.11536i
$237$	263.529	+	517.206i	0.0722282	+	0.141756i
$238$	4620.06	−	4629.32i	1.25829	−	1.26082i
$239$	−3398.23	+	1104.15i	−0.919720	+	0.298835i	−0.730352	−	0.683071i	$-0.760644\pi$
$239$	−3398.23	+	1104.15i	−0.919720	+	0.298835i	−0.189368	+	0.981906i	$0.560644\pi$
$240$	−197.302	+	168.452i	−0.0530657	+	0.0453063i
$241$	4365.46	−	3930.68i	1.16682	−	1.05061i	0.168937	−	0.985627i	$-0.445967\pi$
$241$	4365.46	−	3930.68i	1.16682	−	1.05061i	0.997886	−	0.0649850i	$-0.0206999\pi$
$242$	5008.31	+	1922.51i	1.33036	+	0.510677i
$243$	−1010.22	+	3770.20i	−0.266690	+	0.995301i
$244$	4671.78	+	3394.24i	1.22574	+	0.890550i
$245$	−902.040	−	3727.26i	−0.235221	−	0.971942i
$246$	−4112.03	+	2987.56i	−1.06574	+	0.774309i
$247$	718.552	+	1871.89i	0.185103	+	0.482209i
$248$	−3696.19	−	5691.64i	−0.946405	−	1.45734i
$249$	1242.87	+	717.572i	0.316321	+	0.182628i
$250$	2778.54	+	5833.18i	0.702920	+	1.47569i
$251$			470.782i			0.118388i	0.998246	+	0.0591942i	$0.0188531\pi$
$251$			470.782i			0.118388i	−0.998246	+	0.0591942i	$0.981147\pi$
$252$	705.176	−	4481.33i	0.176277	−	1.12023i
$253$	−6.88538	+	43.4726i	−0.00171099	+	0.0108028i
$254$	1706.93	−	3833.83i	0.421663	−	0.947071i
$255$	328.072	+	2495.32i	0.0805672	+	0.612795i
$256$	−4454.85	+	1983.42i	−1.08761	+	0.484235i
$257$	1893.10	+	507.253i	0.459487	+	0.123119i	0.481135	−	0.876647i	$-0.340225\pi$
$257$	1893.10	+	507.253i	0.459487	+	0.123119i	−0.0216483	+	0.999766i	$0.506891\pi$
$258$	−757.043	−	4779.78i	−0.182680	−	1.15340i
$259$	−2222.33	−	3840.30i	−0.533161	−	0.921332i
$260$	8947.18	−	1656.65i	2.13416	−	0.395157i
$261$	821.173	−	912.005i	0.194748	−	0.216290i
$262$	−4222.32	−	221.282i	−0.995632	−	0.0521789i
$263$	−3533.85	−	185.201i	−0.828542	−	0.0434220i	−0.366651	−	0.930359i	$-0.619496\pi$
$263$	−3533.85	−	185.201i	−0.828542	−	0.0434220i	−0.461891	+	0.886937i	$0.652829\pi$
$264$	−639.993	+	710.785i	−0.149200	+	0.165704i
$265$	3125.17	+	5758.24i	0.724443	+	1.33481i
$266$	1408.15	−	2444.64i	0.324585	−	0.563498i
$267$	71.0677	+	448.704i	0.0162894	+	0.102847i
$268$	608.079	+	162.934i	0.138598	+	0.0371373i
$269$	1967.33	−	875.911i	0.445911	−	0.198532i	−0.171482	−	0.985187i	$-0.554856\pi$
$269$	1967.33	−	875.911i	0.445911	−	0.198532i	0.617393	+	0.786655i	$0.288189\pi$
$270$	4750.71	+	5007.95i	1.07081	+	1.12879i
$271$	1517.74	−	3408.90i	0.340207	−	0.764118i	−0.659713	−	0.751517i	$-0.729322\pi$
$271$	1517.74	−	3408.90i	0.340207	−	0.764118i	0.999921	−	0.0126006i	$-0.00401099\pi$
$272$	94.0847	−	594.027i	0.0209732	−	0.132420i
$273$	2087.63	−	2583.29i	0.462817	−	0.572703i
$274$		−	3667.34i		−	0.808585i
$275$	888.822	+	1369.71i	0.194902	+	0.300352i
$276$	115.013	+	66.4027i	0.0250832	+	0.0144818i
$277$	4524.38	+	6966.93i	0.981385	+	1.51120i	0.854611	+	0.519269i	$0.173796\pi$
$277$	4524.38	+	6966.93i	0.981385	+	1.51120i	0.126774	+	0.991932i	$0.459538\pi$
$278$	1358.06	+	3537.86i	0.292988	+	0.763261i
$279$	−4047.25	+	2940.50i	−0.868468	+	0.630979i
$280$	−3914.74	−	3337.92i	−0.835538	−	0.712424i
$281$	−2498.80	−	1815.49i	−0.530484	−	0.385419i	0.290055	−	0.957010i	$-0.406327\pi$
$281$	−2498.80	−	1815.49i	−0.530484	−	0.385419i	−0.820539	+	0.571591i	$0.806327\pi$
$282$	−1519.68	+	5671.53i	−0.320907	+	1.19764i
$283$	411.355	+	157.904i	0.0864046	+	0.0331676i	0.401186	−	0.915996i	$-0.368598\pi$
$283$	411.355	+	157.904i	0.0864046	+	0.0331676i	−0.314782	+	0.949164i	$0.601931\pi$
$284$	−1077.61	+	970.285i	−0.225156	+	0.202732i
$285$	415.279	+	1003.07i	0.0863123	+	0.208479i
$286$	3495.15	−	1135.64i	0.722632	−	0.234797i
$287$	−4890.30	−	4880.52i	−1.00580	−	1.00379i
$288$	1350.02	+	2649.56i	0.276218	+	0.542107i
$289$	−684.906	−	616.692i	−0.139407	−	0.125523i
$290$	−983.110	−	3321.05i	−0.199070	−	0.672479i
$291$	−608.975	−	676.336i	−0.122676	−	0.136246i
$292$	71.9513	+	88.8525i	0.0144200	+	0.0178072i
$293$	1667.78	+	1667.78i	0.332535	+	0.332535i	0.853548	−	0.521014i	$-0.174446\pi$
$293$	1667.78	+	1667.78i	0.332535	+	0.332535i	−0.521014	+	0.853548i	$0.674446\pi$
$294$	−4673.29	+	9.35314i	−0.927047	+	0.00185540i
$295$	−1685.56	−	4762.53i	−0.332669	−	0.939950i
$296$	−5437.75	−	2421.04i	−1.06778	−	0.475406i
$297$	1355.69	+	1097.81i	0.264865	+	0.214484i
$298$	−3352.50	+	2177.14i	−0.651694	+	0.423215i
$299$	−102.523	−	177.575i	−0.0198297	−	0.0343460i
$300$	4819.44	−	1022.65i	0.927502	−	0.196808i
$301$	6254.19	−	2039.03i	1.19763	−	0.390458i
$302$	−1650.10	+	3238.50i	−0.314412	+	0.617069i
$303$	−3462.35	+	1329.07i	−0.656458	+	0.251991i
$304$	−27.1180	−	258.010i	−0.00511619	−	0.0486773i
$305$	−2077.50	−	4357.52i	−0.390023	−	0.818068i
$306$	−6432.37	−	676.070i	−1.20168	−	0.126302i
$307$	−6008.04	+	6008.04i	−1.11693	+	1.11693i	−0.124738	+	0.992190i	$0.539809\pi$
$307$	−6008.04	+	6008.04i	−1.11693	+	1.11693i	−0.992190	+	0.124738i	$0.960191\pi$
$308$	−2715.28	−	1759.46i	−0.502329	−	0.325502i
$309$	−4362.91	−	1417.60i	−0.803228	−	0.260985i
$310$	1105.28	+	14075.4i	0.202503	+	2.57880i
$311$	1905.88	−	8966.44i	0.347499	−	1.63486i	−0.363451	−	0.931613i	$-0.618402\pi$
$311$	1905.88	−	8966.44i	0.347499	−	1.63486i	0.710950	−	0.703242i	$-0.248265\pi$
$312$	233.196	−	4449.65i	0.0423145	−	0.807410i
$313$	755.458	+	490.600i	0.136425	+	0.0885954i	0.611047	−	0.791594i	$-0.290749\pi$
$313$	755.458	+	490.600i	0.136425	+	0.0885954i	−0.474622	+	0.880190i	$0.657415\pi$
$314$	−3717.07	−	11440.0i	−0.668046	−	2.05603i
$315$	−2306.15	+	3010.58i	−0.412498	+	0.538498i
$316$	−814.036	+	2505.35i	−0.144915	+	0.446002i
$317$	968.684	−	784.425i	0.171630	−	0.138983i	−0.539657	−	0.841885i	$-0.681446\pi$
$317$	968.684	−	784.425i	0.171630	−	0.138983i	0.711287	+	0.702902i	$0.248113\pi$
$318$	7712.02	−	2066.43i	1.35996	−	0.364401i
$319$	−356.009	−	799.608i	−0.0624848	−	0.140343i
$320$	9068.47	+	715.297i	1.58420	+	0.124957i
$321$	2615.86	+	3600.42i	0.454838	+	0.626031i
$322$	−103.122	+	269.448i	−0.0178471	+	0.0466328i
$323$	−2242.49	−	1142.61i	−0.386302	−	0.196831i
$324$	−1169.15	+	675.009i	−0.200471	+	0.115742i
$325$	−7233.58	−	2353.13i	−1.23461	−	0.401624i
$326$	8278.54	−	14338.9i	1.40646	−	2.43606i
$327$	−180.304	−	3440.41i	−0.0304918	−	0.581819i
$328$	−9154.58	−	1449.94i	−1.54109	−	0.244084i
$329$	−7938.41	−	826.330i	−1.33027	−	0.138471i
$330$	1875.80	−	663.888i	0.312908	−	0.110745i
$331$	1245.95	−	11854.4i	0.206899	−	1.96851i	−0.0390738	−	0.999236i	$-0.512441\pi$
$331$	1245.95	−	11854.4i	0.206899	−	1.96851i	0.245973	−	0.969277i	$-0.420893\pi$
$332$	1685.66	+	6290.98i	0.278653	+	1.03995i
$333$	−1572.44	+	4096.35i	−0.258767	+	0.674110i
$334$	−15415.9	+	3276.76i	−2.52551	+	0.536815i
$335$	−381.678	−	362.325i	−0.0622486	−	0.0590924i
$336$	−347.419	+	252.946i	−0.0564085	+	0.0410695i
$337$	8330.07	−	4244.38i	1.34649	−	0.686072i	0.375868	−	0.926673i	$-0.377345\pi$
$337$	8330.07	−	4244.38i	1.34649	−	0.686072i	0.970624	+	0.240601i	$0.0773446\pi$
$338$	−3792.49	+	5839.92i	−0.610308	+	0.939792i
$339$	6169.01	+	1311.26i	0.988362	+	0.210083i
$340$	−6954.60	+	9060.14i	−1.10931	+	1.44516i
$341$	741.831	+	3490.04i	0.117808	+	0.554241i
$342$	−2755.58	+	436.441i	−0.435686	+	0.0690059i
$343$	−1012.57	−	6271.23i	−0.159399	−	0.987214i
$344$	5187.13	−	7139.47i	0.812998	−	1.11900i
$345$	−57.9919	−	94.6713i	−0.00904980	−	0.0147737i
$346$	8322.36	−	874.716i	1.29310	−	0.135910i
$347$	4757.29	−	5874.77i	0.735979	−	0.908859i	−0.262446	−	0.964947i	$-0.584529\pi$
$347$	4757.29	−	5874.77i	0.735979	−	0.908859i	0.998426	+	0.0560877i	$0.0178627\pi$
$348$	−2637.38	+	138.219i	−0.406259	+	0.0212911i
$349$	4696.87			0.720394			0.360197	−	0.932876i	$-0.382709\pi$
$349$	4696.87			0.720394			0.360197	+	0.932876i	$0.382709\pi$
$350$	3842.08	+	9989.51i	0.586765	+	1.52560i
$351$	−8126.69			−1.23581
$352$	2117.98	−	110.998i	0.320706	−	0.0168075i
$353$	3533.46	−	4363.46i	0.532768	−	0.657914i	−0.437706	−	0.899118i	$-0.644209\pi$
$353$	3533.46	−	4363.46i	0.532768	−	0.657914i	0.970474	+	0.241204i	$0.0775424\pi$
$354$	−6122.84	+	643.537i	−0.919281	+	0.0966203i
$355$	1178.77	−	282.780i	0.176233	−	0.0422772i
$356$	−1211.82	+	1667.92i	−0.180411	+	0.248314i
$357$	222.358	+	4163.14i	0.0329649	+	0.617189i
$358$	−1928.16	+	305.390i	−0.284655	+	0.0450849i
$359$	−240.966	−	1133.66i	−0.0354254	−	0.166663i	0.956879	−	0.290487i	$-0.0938174\pi$
$359$	−240.966	−	1133.66i	−0.0354254	−	0.166663i	−0.992304	+	0.123824i	$0.960484\pi$
$360$	−134.065	+	5085.81i	−0.0196274	+	0.744571i
$361$	5647.20	+	1200.35i	0.823327	+	0.175003i
$362$	8714.81	−	13419.6i	1.26530	−	1.94840i
$363$	−3046.93	+	1552.49i	−0.440557	+	0.224475i
$364$	14988.8	−	1590.55i	2.15831	−	0.229032i
$365$	−17.4013	−	93.9805i	−0.00249541	−	0.0134772i
$366$	−5754.32	+	1223.12i	−0.821811	+	0.174681i
$367$	86.2499	−	224.689i	0.0122676	−	0.0319582i	−0.927310	−	0.374295i	$-0.877885\pi$
$367$	86.2499	−	224.689i	0.0122676	−	0.0319582i	0.939577	+	0.342336i	$0.111218\pi$
$368$	6.86660	+	25.6265i	0.000972680	+	0.00363009i
$369$	−714.183	+	6795.00i	−0.100756	+	0.958628i
$370$	7536.79	+	9825.69i	1.05897	+	1.38058i
$371$	4424.15	+	9910.10i	0.619112	+	1.38681i
$372$	10633.3	+	1684.14i	1.48201	+	0.234728i
$373$	450.373	+	8593.63i	0.0625186	+	1.19293i	0.832192	+	0.554487i	$0.187086\pi$
$373$	450.373	+	8593.63i	0.0625186	+	1.19293i	−0.769673	+	0.638438i	$0.779581\pi$
$374$	−2306.48	+	3994.95i	−0.318891	+	0.552336i
$375$	−3948.39	−	1171.82i	−0.543717	−	0.161366i
$376$	−9272.71	+	5353.60i	−1.27182	+	0.734285i
$377$	3633.16	+	1851.19i	0.496333	+	0.252894i
$378$	7204.87	+	8879.09i	0.980367	+	1.20818i
$379$	2050.14	+	2821.78i	0.277860	+	0.382441i	0.925023	−	0.379910i	$-0.124045\pi$
$379$	2050.14	+	2821.78i	0.277860	+	0.382441i	−0.647164	+	0.762351i	$0.724045\pi$
$380$	−1886.19	+	4551.41i	−0.254630	+	0.614428i
$381$	1088.07	+	2443.85i	0.146309	+	0.328615i
$382$	14331.2	−	3840.04i	1.91950	−	0.514328i
$383$	−2440.15	+	1975.99i	−0.325550	+	0.263625i	−0.778136	−	0.628095i	$-0.783835\pi$
$383$	−2440.15	+	1975.99i	−0.325550	+	0.263625i	0.452586	+	0.891721i	$0.350501\pi$
$384$	2242.72	−	6902.38i	0.298042	−	0.917280i
$385$	1292.57	+	2375.94i	0.171105	+	0.314517i
$386$	2029.80	+	6247.09i	0.267654	+	0.823753i
$387$	−5455.78	−	3543.02i	−0.716622	−	0.465380i
$388$	216.156	−	4124.51i	0.0282827	−	0.539665i
$389$	−24.2451	+	114.064i	−0.00316010	+	0.0148671i	−0.979699	−	0.200472i	$-0.935752\pi$
$389$	−24.2451	+	114.064i	−0.00316010	+	0.0148671i	0.976539	+	0.215339i	$0.0690857\pi$
$390$	−4844.84	+	7902.97i	−0.629046	+	1.02611i
$391$	244.782	+	79.5344i	0.0316602	+	0.0102870i
$392$	−6038.04	−	6013.92i	−0.777977	−	0.774870i
$393$	1905.78	−	1905.78i	0.244616	−	0.244616i
$394$	10240.7	+	1076.34i	1.30944	+	0.137628i
$395$	1597.67	−	1515.60i	0.203512	−	0.193058i
$396$	334.453	+	3182.11i	0.0424416	+	0.403805i
$397$	−2119.80	+	813.716i	−0.267984	+	0.102870i	−0.488650	−	0.872480i	$-0.662510\pi$
$397$	−2119.80	+	813.716i	−0.267984	+	0.102870i	0.220665	+	0.975350i	$0.429177\pi$
$398$	5299.76	−	10401.4i	0.667470	−	1.30998i
$399$	557.434	+	1709.78i	0.0699413	+	0.214527i
$400$	825.244	+	536.330i	0.103156	+	0.0670412i
$401$	4713.79	+	8164.53i	0.587021	+	1.01675i	0.994620	+	0.103589i	$0.0330328\pi$
$401$	4713.79	+	8164.53i	0.587021	+	1.01675i	−0.407599	+	0.913161i	$0.633634\pi$
$402$	−537.864	+	349.293i	−0.0667319	+	0.0433362i
$403$	−12917.7	−	10460.5i	−1.59672	−	1.29299i
$404$	−15375.5	−	6845.60i	−1.89346	−	0.843023i
$405$	1128.19	−	29.3457i	0.138421	−	0.00360049i
$406$	−1198.47	−	5610.74i	−0.146500	−	0.685853i
$407$	2212.86	+	2212.86i	0.269502	+	0.269502i
$408$	3519.76	+	4346.55i	0.427094	+	0.527417i
$409$	5203.24	+	5778.78i	0.629056	+	0.698637i	0.970455	−	0.241281i	$-0.0775676\pi$
$409$	5203.24	+	5778.78i	0.629056	+	0.698637i	−0.341400	+	0.939918i	$0.610901\pi$
$410$	15295.9	+	11741.2i	1.84247	+	1.41429i
$411$	1737.27	+	1564.24i	0.208499	+	0.187733i
$412$	−9451.39	−	18549.4i	−1.13019	−	2.21812i
$413$	−2174.06	−	8081.34i	−0.259028	−	0.962849i
$414$	271.345	−	88.1654i	0.0322123	−	0.0104664i
$415$	1271.94	−	5293.93i	0.150451	−	0.626190i
$416$	−7342.55	+	6611.26i	−0.865380	+	0.779191i
$417$	−2255.18	−	865.684i	−0.264836	−	0.101661i
$418$	−515.007	+	1922.03i	−0.0602627	+	0.224903i
$419$	−4290.97	−	3117.57i	−0.500305	−	0.363493i	0.308829	−	0.951118i	$-0.400063\pi$
$419$	−4290.97	−	3117.57i	−0.500305	−	0.363493i	−0.809133	+	0.587625i	$0.800063\pi$
$420$	8090.46	−	1071.93i	0.939938	−	0.124535i
$421$	−9715.67	+	7058.85i	−1.12473	+	0.817167i	−0.984920	−	0.173011i	$-0.944650\pi$
$421$	−9715.67	+	7058.85i	−1.12473	+	0.817167i	−0.139814	+	0.990178i	$0.544650\pi$
$422$	1396.25	+	3637.36i	0.161063	+	0.419582i
$423$	4298.75	+	6619.49i	0.494119	+	0.760876i
$424$	12608.8	+	7279.71i	1.44420	+	0.833807i
$425$	8723.97	−	3880.51i	0.995706	−	0.442900i
$426$		−	1477.25i		−	0.168012i
$427$	−2873.21	−	7462.63i	−0.325630	−	0.845765i
$428$	−3159.42	+	19947.8i	−0.356814	+	2.25283i
$429$	−952.829	+	2140.09i	−0.107233	+	0.240849i
$430$	−16572.3	+	7901.02i	−1.85857	+	0.886095i
$431$	−3648.19	+	1624.28i	−0.407720	+	0.181528i	−0.600340	−	0.799745i	$-0.704968\pi$
$431$	−3648.19	+	1624.28i	−0.407720	+	0.181528i	0.192620	+	0.981273i	$0.438301\pi$
$432$	1015.67	+	272.147i	0.113116	+	0.0303094i
$433$	−118.142	−	745.917i	−0.0131121	−	0.0827864i	0.980265	−	0.197690i	$-0.0633440\pi$
$433$	−118.142	−	745.917i	−0.0131121	−	0.0827864i	−0.993377	+	0.114904i	$0.963344\pi$
$434$	23.4041	+	23387.7i	0.00258855	+	2.58674i
$435$	1992.55	+	950.827i	0.219622	+	0.104801i
$436$	10461.5	−	11618.7i	1.14912	−	1.27623i
$437$	110.870	+	5.81044i	0.0121364	+	0.000636043i
$438$	−116.315	−	6.09582i	−0.0126889	−	0.000664999i
$439$	1440.65	−	1600.00i	0.156625	−	0.173950i	−0.659725	−	0.751507i	$-0.729327\pi$
$439$	1440.65	−	1600.00i	0.156625	−	0.173950i	0.816350	+	0.577557i	$0.195994\pi$
$440$	3274.81	+	1562.71i	0.354819	+	0.169316i
$441$	−4194.15	+	4676.87i	−0.452883	+	0.505007i
$442$	−3361.78	−	21225.5i	−0.361773	−	2.28414i
$443$	−16695.9	−	4473.65i	−1.79062	−	0.479796i	−0.798170	−	0.602432i	$-0.794198\pi$
$443$	−16695.9	−	4473.65i	−1.79062	−	0.479796i	−0.992452	+	0.122637i	$0.960865\pi$
$444$	8626.20	−	3840.63i	0.922030	−	0.410514i
$445$	1555.73	−	741.711i	0.165727	−	0.0790123i
$446$	8518.17	−	19132.1i	0.904365	−	2.03124i
$447$	398.613	−	2516.74i	0.0421784	−	0.266304i
$448$	14885.4	+	2342.35i	1.56980	+	0.247022i
$449$		−	4468.40i		−	0.469659i	−0.972037	−	0.234830i	$-0.924547\pi$
$449$		−	4468.40i		−	0.469659i	0.972037	−	0.234830i	$-0.0754532\pi$
$450$	5295.33	−	9164.38i	0.554720	−	0.960029i
$451$	4220.16	+	2436.51i	0.440620	+	0.254392i
$452$	15588.3	+	24003.9i	1.62215	+	2.49789i
$453$	−830.298	−	2163.00i	−0.0861165	−	0.224341i
$454$	−6701.13	+	4868.66i	−0.692730	+	0.503298i
$455$	−11645.3	−	4812.39i	−1.19987	−	0.495843i
$456$	1951.80	+	1418.07i	0.200442	+	0.145630i
$457$	2652.58	−	9899.58i	0.271516	−	1.01331i	−0.686625	−	0.727012i	$-0.740908\pi$
$457$	2652.58	−	9899.58i	0.271516	−	1.01331i	0.958140	−	0.286298i	$-0.0924249\pi$
$458$	−25404.4	−	9751.82i	−2.59185	−	0.994918i
$459$	7580.67	−	6825.66i	0.770883	−	0.694106i
$460$	117.703	−	489.890i	0.0119302	−	0.0496549i
$461$	−994.127	+	323.012i	−0.100436	+	0.0326337i	−0.358804	−	0.933413i	$-0.616815\pi$
$461$	−994.127	+	323.012i	−0.100436	+	0.0326337i	0.258368	+	0.966047i	$0.416815\pi$
$462$	3182.97	−	856.290i	0.320531	−	0.0862299i
$463$	4014.05	+	7878.01i	0.402913	+	0.790761i	0.999934	−	0.0114644i	$-0.00364930\pi$
$463$	4014.05	+	7878.01i	0.402913	+	0.790761i	−0.597021	+	0.802225i	$0.703649\pi$
$464$	−392.076	−	353.027i	−0.0392278	−	0.0353209i
$465$	−7139.13	−	5480.03i	−0.711977	−	0.546516i
$466$	−19372.5	−	21515.3i	−1.92578	−	2.13879i
$467$	11375.5	+	14047.6i	1.12719	+	1.39196i	0.909379	+	0.415969i	$0.136557\pi$
$467$	11375.5	+	14047.6i	1.12719	+	1.39196i	0.217808	+	0.975992i	$0.430109\pi$
$468$	−10540.0	−	10540.0i	−1.04105	−	1.04105i
$469$	−583.972	−	647.263i	−0.0574953	−	0.0637267i
$470$	22267.9	−	579.215i	2.18541	−	0.0568451i
$471$	7004.71	+	3118.70i	0.685265	+	0.305100i
$472$	−8724.92	−	7065.30i	−0.850841	−	0.688997i
$473$	−3891.17	+	2526.95i	−0.378258	+	0.245644i
$474$	−1341.83	−	2324.11i	−0.130026	−	0.225211i
$475$	3201.68	−	2590.82i	0.309270	−	0.250263i
$476$	−12645.8	+	14072.9i	−1.21769	+	1.35510i
$477$	4872.45	−	9562.73i	0.467703	−	0.917919i
$478$	15422.0	−	5919.97i	1.47571	−	0.566471i
$479$	−378.000	−	3596.43i	−0.0360569	−	0.343059i	−0.997646	−	0.0685673i	$-0.978157\pi$
$479$	−378.000	−	3596.43i	−0.0360569	−	0.343059i	0.961590	−	0.274491i	$-0.0885095\pi$
$480$	−3881.16	+	3681.80i	−0.369062	+	0.350105i
$481$	−14499.1	−	1523.91i	−1.37443	−	0.144458i
$482$	−19203.7	+	19203.7i	−1.81474	+	1.81474i
$483$	−83.6560	−	163.779i	−0.00788091	−	0.0154290i
$484$	−14759.3	−	4795.60i	−1.38611	−	0.450375i
$485$	−1804.54	+	2943.59i	−0.168949	+	0.275591i
$486$	3751.83	−	17651.0i	0.350178	−	1.64746i
$487$	493.365	−	9413.97i	0.0459066	−	0.875950i	−0.874509	−	0.485009i	$-0.838816\pi$
$487$	493.365	−	9413.97i	0.0459066	−	0.875950i	0.920416	−	0.390941i	$-0.127850\pi$
$488$	−8997.06	−	5842.76i	−0.834586	−	0.541986i
$489$	3261.43	+	10037.6i	0.301609	+	0.928258i
$490$	5066.46	+	16990.0i	0.467100	+	1.56639i
$491$	−4309.48	+	13263.2i	−0.396098	+	1.21906i	0.532005	+	0.846741i	$0.321439\pi$
$491$	−4309.48	+	13263.2i	−0.396098	+	1.21906i	−0.928103	+	0.372323i	$0.878561\pi$
$492$	11426.7	−	9253.17i	1.04707	−	0.847897i
$493$	−4943.88	+	1324.71i	−0.451646	+	0.121018i
$494$	−3770.39	−	8468.44i	−0.343397	−	0.771282i
$495$	1024.03	−	2471.01i	0.0929835	−	0.224371i
$496$	1264.14	+	1739.94i	0.114438	+	0.157511i
$497$	1983.00	−	316.110i	0.178973	−	0.0285301i
$498$	−5911.81	−	3012.22i	−0.531957	−	0.271046i
$499$	−3045.84	+	1758.52i	−0.273248	+	0.157760i	−0.630363	−	0.776301i	$-0.717094\pi$
$499$	−3045.84	+	1758.52i	−0.273248	+	0.157760i	0.357115	+	0.934060i	$0.383760\pi$
$500$	−8909.91	−	16430.5i	−0.796926	−	1.46959i
$501$	5023.16	−	8700.36i	0.447940	−	0.775856i
$502$	−113.910	−	2173.54i	−0.0101276	−	0.193247i
$503$	−10487.4	−	1661.05i	−0.929645	−	0.147241i	−0.326794	−	0.945096i	$-0.605968\pi$
$503$	−10487.4	−	1661.05i	−0.929645	−	0.147241i	−0.602850	+	0.797854i	$0.705968\pi$
$504$	−872.534	+	8382.29i	−0.0771146	+	0.740827i
$505$	8563.22	+	11163.8i	0.754571	+	0.983732i
$506$	21.2703	−	202.373i	0.00186874	−	0.0177798i
$507$	−1148.82	−	4287.47i	−0.100633	−	0.375568i
$508$	−4350.64	+	11333.8i	−0.379977	+	0.989874i
$509$	−4525.80	+	961.988i	−0.394111	+	0.0837709i	−0.400704	−	0.916207i	$-0.631235\pi$
$509$	−4525.80	+	961.988i	−0.394111	+	0.0837709i	0.00659344	+	0.999978i	$0.497901\pi$
$510$	−2118.43	−	11441.2i	−0.183933	−	0.993381i
$511$	−16.7070	−	157.441i	−0.00144633	−	0.0136297i
$512$	2533.50	−	1290.88i	0.218684	−	0.111425i
$513$	2396.51	−	3690.30i	0.206254	−	0.317604i
$514$	−8862.92	−	1883.87i	−0.760558	−	0.161662i
$515$	−458.611	+	17397.6i	−0.0392404	+	1.48860i
$516$	2910.64	+	13693.5i	0.248321	+	1.16826i
$517$	5560.02	−	880.621i	0.472977	−	0.0749123i
$518$	11189.4	+	17192.5i	0.949102	+	1.45829i
$519$	−3135.40	+	4315.50i	−0.265180	+	0.364990i
$520$	−16437.7	+	3943.30i	−1.38623	+	0.332549i
$521$	13856.4	−	1456.37i	1.16518	−	0.122466i	0.497875	−	0.867249i	$-0.334114\pi$
$521$	13856.4	−	1456.37i	1.16518	−	0.122466i	0.667307	+	0.744783i	$0.267447\pi$
$522$	−3570.59	+	4409.31i	−0.299388	+	0.369713i
$523$	11126.9	−	583.134i	0.930294	−	0.0487546i	0.418835	−	0.908062i	$-0.362439\pi$
$523$	11126.9	−	583.134i	0.930294	−	0.0487546i	0.511459	+	0.859308i	$0.329105\pi$
$524$	12231.1			1.01969
$525$	−6370.93	−	2440.81i	−0.529619	−	0.202906i
$526$	16360.2			1.35615
$527$	20835.7	−	1091.95i	1.72223	−	0.0902583i
$528$	190.751	−	235.558i	0.0157223	−	0.0194154i
$529$	12089.1	−	1270.61i	0.993594	−	0.104431i
$530$	−15821.8	−	25828.9i	−1.29670	−	2.11686i
$531$	−4864.46	+	6695.35i	−0.397551	+	0.547182i
$532$	−3697.83	+	7275.40i	−0.301356	+	0.592911i
$533$	−22422.0	+	3551.30i	−1.82215	+	0.288600i
$534$	−436.679	−	2054.41i	−0.0353876	−	0.166485i
$535$	10280.4	−	13392.9i	0.830769	−	1.08229i
$536$	−1143.95	−	243.153i	−0.0921846	−	0.0195944i
$537$	677.756	−	1043.65i	0.0544643	−	0.0838677i
$538$	−8870.97	+	4519.99i	−0.710883	+	0.362213i
$539$	1830.56	+	4089.46i	0.146285	+	0.326801i
$540$	−14482.3	−	13748.0i	−1.15411	−	1.09559i
$541$	−11418.0	+	2426.97i	−0.907388	+	0.192871i	−0.637888	−	0.770129i	$-0.720192\pi$
$541$	−11418.0	+	2426.97i	−0.907388	+	0.192871i	−0.269500	+	0.963000i	$0.586858\pi$
$542$	−6182.40	+	16105.7i	−0.489957	+	1.27638i
$543$	2639.90	+	9852.23i	0.208635	+	0.778637i
$544$	1296.37	−	12334.1i	0.102172	−	0.972097i
$545$	−12321.1	+	4360.70i	−0.968397	+	0.342737i
$546$	−9013.28	+	12431.9i	−0.706470	+	0.974422i
$547$	−12031.6	−	1905.62i	−0.940467	−	0.148955i	−0.332666	−	0.943045i	$-0.607948\pi$
$547$	−12031.6	−	1905.62i	−0.940467	−	0.148955i	−0.607801	+	0.794089i	$0.707948\pi$
$548$	555.229	+	10594.4i	0.0432814	+	0.825859i
$549$	−3954.00	+	6848.52i	−0.307382	+	0.532400i
$550$	−4435.00	−	6108.74i	−0.343834	−	0.473595i
$551$	−1912.01	+	1103.90i	−0.147830	+	0.0853499i
$552$	−219.827	−	112.008i	−0.0169501	−	0.00863652i
$553$	2832.66	−	2298.54i	0.217824	−	0.176752i
$554$	−22574.2	−	31070.8i	−1.73120	−	2.38280i
$555$	−7869.24	−	620.705i	−0.601857	−	0.0474729i
$556$	−4458.85	−	10014.7i	−0.340103	−	0.763883i
$557$	1877.95	−	503.196i	0.142857	−	0.0382784i	−0.186682	−	0.982420i	$-0.559773\pi$
$557$	1877.95	−	503.196i	0.142857	−	0.0382784i	0.329539	+	0.944142i	$0.393107\pi$
$558$	17974.2	−	14555.2i	1.36363	−	1.10425i
$559$	6679.25	−	20556.6i	0.505371	−	1.55537i
$560$	1294.27	+	991.427i	0.0976656	+	0.0748133i
$561$	−908.666	−	2796.59i	−0.0683849	−	0.210467i
$562$	11975.9	+	7777.27i	0.898887	+	0.583744i
$563$	879.401	−	16780.0i	0.0658301	−	1.25611i	−0.743491	−	0.668746i	$-0.766831\pi$
$563$	879.401	−	16780.0i	0.0658301	−	1.25611i	0.809321	−	0.587367i	$-0.199835\pi$
$564$	3531.47	−	16614.3i	0.263656	−	1.24040i
$565$	−1873.09	−	23853.2i	−0.139472	−	1.77612i
$566$	−1937.38	−	629.493i	−0.143877	−	0.0467483i
$567$	1867.02	+	95.9730i	0.138285	+	0.00710844i
$568$	1904.84	−	1904.84i	0.140714	−	0.140714i
$569$	−14184.9	−	1490.89i	−1.04510	−	0.109844i	−0.433611	−	0.901100i	$-0.642761\pi$
$569$	−14184.9	−	1490.89i	−1.04510	−	0.109844i	−0.611485	+	0.791256i	$0.709428\pi$
$570$	−2160.00	−	4530.56i	−0.158723	−	0.332920i
$571$	−2331.26	−	22180.5i	−0.170859	−	1.62561i	−0.658509	−	0.752573i	$-0.728813\pi$
$571$	−2331.26	−	22180.5i	−0.170859	−	1.62561i	0.487650	−	0.873039i	$-0.337854\pi$
$572$	−9925.04	+	3809.87i	−0.725501	+	0.278494i
$573$	−4293.66	+	8426.78i	−0.313037	+	0.614370i
$574$	23758.8	+	21349.5i	1.72765	+	1.55246i
$575$	−281.939	+	312.905i	−0.0204481	+	0.0226940i
$576$	−7450.79	−	12905.1i	−0.538975	−	0.933532i
$577$	−16923.0	+	10990.0i	−1.22100	+	0.792925i	−0.983928	−	0.178568i	$-0.942854\pi$
$577$	−16923.0	+	10990.0i	−1.22100	+	0.792925i	−0.237070	+	0.971493i	$0.576187\pi$
$578$	3311.34	+	2681.47i	0.238294	+	0.192966i
$579$	−3825.10	−	1703.05i	−0.274553	−	0.122239i
$580$	3342.86	+	9445.19i	0.239318	+	0.676190i
$581$	2778.43	−	8580.34i	0.198397	−	0.612689i
$582$	2975.21	+	2975.21i	0.211901	+	0.211901i
$583$	−4817.22	−	5948.77i	−0.342210	−	0.422595i
$584$	−142.123	−	157.843i	−0.0100703	−	0.0111842i
$585$	3536.99	+	11948.3i	0.249977	+	0.844449i
$586$	−8103.46	−	7296.39i	−0.571247	−	0.514353i
$587$	−2525.67	−	4956.91i	−0.177591	−	0.348541i	0.785002	−	0.619493i	$-0.212662\pi$
$587$	−2525.67	−	4956.91i	−0.177591	−	0.348541i	−0.962593	+	0.270952i	$0.912662\pi$
$588$	13499.0	−	734.548i	0.946752	−	0.0515174i
$589$	8559.44	−	2781.13i	0.598787	−	0.194558i
$590$	8934.39	+	21580.2i	0.623429	+	1.50583i
$591$	−4877.87	+	4392.05i	−0.339507	+	0.305694i
$592$	1761.05	+	676.002i	0.122261	+	0.0469316i
$593$	1511.37	−	5640.52i	0.104662	−	0.390605i	−0.893644	−	0.448776i	$-0.851860\pi$
$593$	1511.37	−	5640.52i	0.104662	−	0.390605i	0.998307	+	0.0581710i	$0.0185269\pi$
$594$	−6524.67	−	4740.45i	−0.450691	−	0.327446i
$595$	14904.9	−	5291.95i	1.02696	−	0.364620i
$596$	9355.24	−	6796.98i	0.642963	−	0.467140i
$597$	2666.74	+	6947.09i	0.182818	+	0.476257i
$598$	516.303	+	795.037i	0.0353064	+	0.0543670i
$599$	17009.7	+	9820.57i	1.16026	+	0.669879i	0.951367	−	0.308058i	$-0.0996793\pi$
$599$	17009.7	+	9820.57i	1.16026	+	0.669879i	0.208897	+	0.977938i	$0.433013\pi$
$600$	−8841.57	+	2365.78i	−0.601593	+	0.160971i
$601$			18645.0i			1.26547i	0.774370	+	0.632733i	$0.218067\pi$
$601$			18645.0i			1.26547i	−0.774370	+	0.632733i	$0.781933\pi$
$602$	−28381.4	+	10927.2i	−1.92150	+	0.739801i
$603$	−134.862	+	851.487i	−0.00910782	+	0.0575045i
$604$	4276.58	−	9605.36i	0.288099	−	0.647081i
$605$	8928.60	+	9412.07i	0.599999	+	0.632488i
$606$	15663.7	−	6973.91i	1.04999	−	0.467485i
$607$	3965.85	+	1062.64i	0.265187	+	0.0710567i	0.388963	−	0.921254i	$-0.372834\pi$
$607$	3965.85	+	1062.64i	0.265187	+	0.0710567i	−0.123775	+	0.992310i	$0.539500\pi$
$608$	−836.878	−	5283.84i	−0.0558222	−	0.352448i
$609$	3169.07	+	1825.44i	0.210865	+	0.121462i
$610$	10645.9	+	19615.5i	0.706622	+	1.30198i
$611$	−17547.9	+	19488.9i	−1.16188	+	1.29040i
$612$	18684.5	+	979.214i	1.23411	+	0.0646771i
$613$	5936.54	+	311.121i	0.391149	+	0.0204993i	0.246897	−	0.969042i	$-0.420589\pi$
$613$	5936.54	+	311.121i	0.391149	+	0.0204993i	0.144252	+	0.989541i	$0.453922\pi$
$614$	26284.7	−	29192.1i	1.72763	−	1.91872i
$615$	−12086.2	+	2237.86i	−0.792459	+	0.146731i
$616$	5208.44	+	3000.15i	0.340672	+	0.196233i
$617$	475.192	+	3000.24i	0.0310057	+	0.195762i	0.998329	−	0.0577833i	$-0.0184032\pi$
$617$	475.192	+	3000.24i	0.0310057	+	0.195762i	−0.967323	+	0.253545i	$0.918403\pi$
$618$	20486.0	+	5489.21i	1.33344	+	0.357295i
$619$	−9358.89	+	4166.85i	−0.607699	+	0.270565i	−0.687429	−	0.726251i	$-0.741261\pi$
$619$	−9358.89	+	4166.85i	−0.607699	+	0.270565i	0.0797302	+	0.996816i	$0.474594\pi$
$620$	−5323.99	−	40494.3i	−0.344865	−	2.62305i
$621$	−183.023	+	411.077i	−0.0118268	+	0.0265635i
$622$	−6629.67	+	41858.1i	−0.427372	+	2.69832i
$623$	2664.32	−	1025.80i	0.171338	−	0.0659673i
$624$			1412.05i			0.0905888i
$625$	−10.9109	+	15625.0i	−0.000698296	+	1.00000i
$626$	−3606.56	−	2082.25i	−0.230267	−	0.132945i
$627$	−690.823	−	1063.77i	−0.0440013	−	0.0677561i
$628$	12470.0	+	32485.6i	0.792371	+	2.06420i
$629$	14804.8	−	10756.3i	0.938486	−	0.681850i
$630$	9918.77	−	14457.5i	0.627259	−	0.914285i
$631$	−5191.06	−	3771.52i	−0.327500	−	0.237943i	0.411869	−	0.911243i	$-0.364876\pi$
$631$	−5191.06	−	3771.52i	−0.327500	−	0.237943i	−0.739369	+	0.673300i	$0.764876\pi$
$632$	1266.61	−	4727.05i	0.0797199	−	0.297519i
$633$	−2318.61	−	890.030i	−0.145587	−	0.0558855i
$634$	−4282.49	+	3855.98i	−0.268264	+	0.241546i
$635$	7718.35	−	6589.76i	0.482352	−	0.411822i
$636$	−21966.0	+	7137.19i	−1.36951	+	0.444981i
$637$	−18616.7	−	9438.81i	−1.15796	−	0.587094i
$638$	1837.12	+	3605.55i	0.114001	+	0.223739i
$639$	−1475.72	−	1328.74i	−0.0913592	−	0.0822602i
$640$	−27524.0	−	725.548i	−1.69997	−	0.0448122i
$641$	16067.4	+	17844.7i	0.990055	+	1.09957i	0.995030	+	0.0995802i	$0.0317500\pi$
$641$	16067.4	+	17844.7i	0.990055	+	1.09957i	−0.00497419	+	0.999988i	$0.501583\pi$
$642$	−12948.3	−	15989.8i	−0.795992	−	0.982968i
$643$	19156.4	+	19156.4i	1.17489	+	1.17489i	0.981029	+	0.193859i	$0.0621003\pi$
$643$	19156.4	+	19156.4i	1.17489	+	1.17489i	0.193859	+	0.981029i	$0.437900\pi$
$644$	257.110	−	794.007i	0.0157323	−	0.0485843i
$645$	3325.81	−	11220.5i	0.203029	−	0.684974i
$646$	10629.8	+	4732.68i	0.647403	+	0.288243i
$647$	−10076.0	−	8159.35i	−0.612252	−	0.495792i	0.272313	−	0.962209i	$-0.412211\pi$
$647$	−10076.0	−	8159.35i	−0.612252	−	0.495792i	−0.884565	+	0.466417i	$0.845545\pi$
$648$	2103.37	−	1365.94i	0.127513	−	0.0828077i
$649$	2951.27	+	5111.75i	0.178501	+	0.309174i
$650$	33965.9	+	9113.85i	2.04962	+	0.549961i
$651$	−11089.0	−	9964.52i	−0.667608	−	0.599909i
$652$	−21744.6	+	42676.2i	−1.30611	+	2.56339i
$653$	30709.4	−	11788.2i	1.84036	−	0.706447i	0.859673	−	0.510844i	$-0.170667\pi$
$653$	30709.4	−	11788.2i	1.84036	−	0.706447i	0.980683	−	0.195602i	$-0.0626662\pi$
$654$	1664.88	+	15840.3i	0.0995444	+	0.947102i
$655$	−8984.94	−	4880.45i	−0.535985	−	0.291138i
$656$	2921.21	+	307.032i	0.173863	+	0.0182737i
$657$	−110.712	+	110.712i	−0.00657424	+	0.00657424i
$658$	36850.6	+	1894.28i	2.18326	+	0.112229i
$659$	−15103.9	−	4907.56i	−0.892816	−	0.290093i	−0.173547	−	0.984826i	$-0.555523\pi$
$659$	−15103.9	−	4907.56i	−0.892816	−	0.290093i	−0.719269	+	0.694732i	$0.755523\pi$
$660$	−5318.40	+	2201.87i	−0.313665	+	0.129860i
$661$	2221.23	−	10450.1i	0.130705	−	0.614918i	−0.863217	−	0.504833i	$-0.831554\pi$
$661$	2221.23	−	10450.1i	0.130705	−	0.614918i	0.993922	−	0.110085i	$-0.0351124\pi$
$662$	−2884.10	+	55031.9i	−0.169326	+	3.23093i
$663$	11488.7	+	7460.83i	0.672976	+	0.437036i
$664$	−3738.88	−	11507.1i	−0.218519	−	0.672533i
$665$	5619.43	−	3868.96i	0.327687	−	0.225612i
$666$	6268.62	−	19292.8i	0.364721	−	1.12250i
$667$	175.463	−	142.087i	0.0101858	−	0.00824834i
$668$	44038.2	−	11800.0i	2.55073	−	0.683467i
$669$	5429.85	+	12195.6i	0.313797	+	0.704799i
$670$	1849.83	+	1580.46i	0.106664	+	0.0911321i
$671$	3315.19	+	4562.97i	0.190732	+	0.262521i
$672$	−6881.29	+	5583.77i	−0.395017	+	0.320534i
$673$	7357.26	+	3748.71i	0.421399	+	0.214714i	0.651814	−	0.758379i	$-0.274008\pi$
$673$	7357.26	+	3748.71i	0.421399	+	0.214714i	−0.230415	+	0.973093i	$0.574008\pi$
$674$	−37431.9	+	21611.3i	−2.13921	+	1.23507i
$675$	5152.91	+	15877.9i	0.293831	+	0.905393i
$676$	10071.8	−	17444.8i	0.573042	−	0.992537i
$677$	1165.74	+	22243.7i	0.0661790	+	1.26277i	0.806791	+	0.590837i	$0.201202\pi$
$677$	1165.74	+	22243.7i	0.0661790	+	1.26277i	−0.740612	+	0.671933i	$0.765464\pi$
$678$	−28798.8	−	4561.29i	−1.63129	−	0.258371i
$679$	−3357.15	+	4630.45i	−0.189743	+	0.261709i
$680$	12021.2	−	17484.5i	0.677932	−	0.986028i
$681$	551.908	−	5251.05i	0.0310560	−	0.295478i
$682$	−4269.39	−	15933.6i	−0.239712	−	0.894617i
$683$	−2037.50	+	5307.87i	−0.114148	+	0.297365i	−0.978739	−	0.205112i	$-0.934244\pi$
$683$	−2037.50	+	5307.87i	−0.114148	+	0.297365i	0.864591	+	0.502476i	$0.167578\pi$
$684$	7894.38	−	1678.00i	0.441300	−	0.0938012i
$685$	3819.50	−	8004.14i	0.213044	−	0.446456i
$686$	6192.31	+	28708.5i	0.344641	+	1.59781i
$687$	15455.4	−	7874.90i	0.858309	−	0.437330i
$688$	−1523.17	+	2345.47i	−0.0844043	+	0.129971i
$689$	34880.7	+	7414.13i	1.92866	+	0.409950i
$690$	290.648	+	423.054i	0.0160359	+	0.0233412i
$691$	3926.85	+	18474.4i	0.216186	+	1.01707i	0.943654	+	0.330933i	$0.107363\pi$
$691$	3926.85	+	18474.4i	0.216186	+	1.01707i	−0.727469	+	0.686141i	$0.759303\pi$
$692$	−23909.6	+	3786.91i	−1.31345	+	0.208030i
$693$	2007.59	−	3949.89i	0.110046	−	0.216514i
$694$	−20542.4	+	28274.2i	−1.12360	+	1.54650i
$695$	−720.618	+	9135.93i	−0.0393304	+	0.498627i
$696$	4879.41	−	512.846i	0.265738	−	0.0279302i
$697$	17932.8	−	22145.1i	0.974537	−	1.20345i
$698$	−21684.9	+	1136.45i	−1.17591	+	0.0616267i
$699$	18455.1			0.998620
$700$	−12611.6	−	28276.5i	−0.680962	−	1.52679i
$701$	16828.3			0.906700			0.453350	−	0.891333i	$-0.350229\pi$
$701$	16828.3			0.906700			0.453350	+	0.891333i	$0.350229\pi$
$702$	37519.9	−	1966.34i	2.01723	−	0.105719i
$703$	4967.68	−	6134.58i	0.266515	−	0.329118i
$704$	−10569.9	+	1110.94i	−0.565863	+	0.0594745i
$705$	−9223.60	+	10795.6i	−0.492739	+	0.576719i
$706$	−15257.8	+	21000.5i	−0.813362	+	1.11950i
$707$	12713.3	+	19533.9i	0.676284	+	1.03911i
$708$	17590.5	−	2786.07i	0.933747	−	0.147891i
$709$	3109.40	+	14628.6i	0.164705	+	0.774877i	0.980497	+	0.196532i	$0.0629679\pi$
$709$	3109.40	+	14628.6i	0.164705	+	0.774877i	−0.815792	+	0.578345i	$0.803699\pi$
$710$	−5373.81	+	1590.77i	−0.284050	+	0.0840855i
$711$	−3528.64	−	750.036i	−0.186124	−	0.0395620i
$712$	2085.99	−	3212.15i	0.109798	−	0.169073i
$713$	−820.055	+	417.839i	−0.0430733	+	0.0219470i
$714$	−2033.92	−	19166.9i	−0.106607	−	1.00463i
$715$	8811.09	+	1161.57i	0.460862	+	0.0607554i
$716$	5523.93	−	1174.15i	0.288322	−	0.0612848i
$717$	−3773.64	+	9830.68i	−0.196554	+	0.512041i
$718$	1386.81	+	5175.65i	0.0720826	+	0.269016i
$719$	1533.01	−	14585.6i	0.0795154	−	0.756538i	−0.880017	−	0.474941i	$-0.842469\pi$
$719$	1533.01	−	14585.6i	0.0795154	−	0.756538i	0.959533	−	0.281597i	$-0.0908641\pi$
$720$	−41.9233	−	1611.74i	−0.00216998	−	0.0834248i
$721$	−2984.77	+	28674.2i	−0.154173	+	1.48111i
$722$	−26362.9	−	4175.47i	−1.35890	−	0.215228i
$723$	−906.030	−	17288.1i	−0.0466053	−	0.889282i
$724$	−23144.1	+	40086.7i	−1.18804	+	2.05775i
$725$	1313.16	−	8272.25i	0.0672681	−	0.423757i
$726$	13691.7	−	7904.88i	0.699924	−	0.404101i
$727$	−749.434	−	381.855i	−0.0382324	−	0.0194804i	0.434770	−	0.900542i	$-0.356830\pi$
$727$	−749.434	−	381.855i	−0.0382324	−	0.0194804i	−0.473002	+	0.881061i	$0.656830\pi$
$728$	−27652.5	+	4408.09i	−1.40779	+	0.224416i
$729$	5159.23	+	7101.07i	0.262116	+	0.360772i
$730$	103.079	+	429.686i	0.00522620	+	0.0217855i
$731$	11035.2	+	24785.4i	0.558345	+	1.25406i
$732$	16438.2	−	4404.60i	0.830017	−	0.222402i
$733$	12703.6	−	10287.2i	0.640134	−	0.518371i	−0.253402	−	0.967361i	$-0.581550\pi$
$733$	12703.6	−	10287.2i	0.640134	−	0.518371i	0.893537	+	0.448990i	$0.148216\pi$
$734$	−343.839	+	1058.23i	−0.0172907	+	0.0532152i
$735$	−10209.4	−	4846.76i	−0.512353	−	0.243232i
$736$	169.058	+	520.306i	0.00846678	+	0.0260581i
$737$	515.671	+	334.881i	0.0257734	+	0.0167374i
$738$	1653.18	−	31544.5i	0.0824584	−	1.57340i
$739$	1655.09	−	7786.59i	0.0823864	−	0.387597i	−0.917564	−	0.397589i	$-0.869847\pi$
$739$	1655.09	−	7786.59i	0.0823864	−	0.387597i	0.999950	+	0.00999138i	$0.00318041\pi$
$740$	−23260.2	−	27243.9i	−1.15549	−	1.35339i
$741$	5619.80	+	1825.99i	0.278608	+	0.0905253i
$742$	−22823.6	−	44683.3i	−1.12922	−	2.21075i
$743$	−13112.2	+	13112.2i	−0.647428	+	0.647428i	−0.952371	−	0.304943i	$-0.901363\pi$
$743$	−13112.2	+	13112.2i	−0.647428	+	0.647428i	0.304943	+	0.952371i	$0.401363\pi$
$744$	−19890.5	−	2090.58i	−0.980136	−	0.103016i
$745$	−9584.44	+	1260.11i	−0.471338	+	0.0619691i
$746$	−4158.63	−	39566.7i	−0.204100	−	1.94188i
$747$	−8326.61	+	3196.29i	−0.407838	+	0.156554i
$748$	6058.26	−	11890.0i	0.296139	−	0.581205i
$749$	18693.3	−	20802.8i	0.911931	−	1.01484i
$750$	18512.8	+	4454.78i	0.901321	+	0.216887i
$751$	13587.5	+	23534.3i	0.660208	+	1.14351i	0.980561	+	0.196215i	$0.0628652\pi$
$751$	13587.5	+	23534.3i	0.660208	+	1.14351i	−0.320353	+	0.947298i	$0.603801\pi$
$752$	2845.76	−	1848.06i	0.137997	−	0.0896166i
$753$	1078.22	+	873.126i	0.0521813	+	0.0422556i
$754$	−17221.8	−	7667.63i	−0.831804	−	0.370343i
$755$	−6974.27	+	5349.61i	−0.336185	+	0.257871i
$756$	−22158.1	−	24559.6i	−1.06598	−	1.18151i
$757$	−4319.52	−	4319.52i	−0.207392	−	0.207392i	0.595766	−	0.803158i	$-0.296849\pi$
$757$	−4319.52	−	4319.52i	−0.207392	−	0.207392i	−0.803158	+	0.595766i	$0.796849\pi$
$758$	−10148.0	−	12531.8i	−0.486270	−	0.600493i
$759$	86.7944	+	96.3949i	0.00415077	+	0.00460990i
$760$	3056.73	−	8627.15i	0.145894	−	0.411762i
$761$	−2602.12	−	2342.96i	−0.123951	−	0.111606i	0.604824	−	0.796359i	$-0.293243\pi$
$761$	−2602.12	−	2342.96i	−0.123951	−	0.111606i	−0.728775	+	0.684753i	$0.759910\pi$
$762$	−5614.81	−	11019.7i	−0.266933	−	0.523886i
$763$	−20907.1	+	5624.47i	−0.991989	+	0.266867i
$764$	−40819.4	+	13263.0i	−1.93297	+	0.628062i
$765$	−13334.8	−	8174.80i	−0.630224	−	0.386353i
$766$	10787.7	−	9713.33i	0.508847	−	0.458168i
$767$	−25671.3	−	9854.28i	−1.20852	−	0.463908i
$768$	−3719.50	+	13881.4i	−0.174760	+	0.652214i
$769$	19050.5	+	13841.0i	0.893339	+	0.649049i	0.936747	−	0.350009i	$-0.113821\pi$
$769$	19050.5	+	13841.0i	0.893339	+	0.649049i	−0.0434073	+	0.999057i	$0.513821\pi$
$770$	−6542.53	−	10656.7i	−0.306203	−	0.498753i
$771$	4672.74	−	3394.95i	0.218268	−	0.158581i
$772$	−6809.60	−	17739.6i	−0.317465	−	0.827024i
$773$	−6437.97	−	9913.61i	−0.299557	−	0.461278i	0.656555	−	0.754278i	$-0.272013\pi$
$773$	−6437.97	−	9913.61i	−0.299557	−	0.461278i	−0.956112	+	0.293000i	$0.905346\pi$
$774$	26045.9	+	15037.6i	1.20956	+	0.698341i
$775$	−12247.0	+	31871.3i	−0.567646	+	1.47723i
$776$			7672.78i			0.354944i
$777$	−12917.0	−	2032.60i	−0.596388	−	0.0938469i
$778$	84.3378	−	532.488i	0.00388645	−	0.0245381i
$779$	4999.48	−	11229.0i	0.229942	−	0.516459i
$780$	12799.5	−	23564.0i	0.587560	−	1.08170i
$781$	−1293.85	+	576.059i	−0.0592799	+	0.0263931i
$782$	−1149.37	−	307.973i	−0.0525593	−	0.0140832i
$783$	−1399.84	−	8838.22i	−0.0638903	−	0.403387i
$784$	2010.61	+	1803.09i	0.0915913	+	0.0821378i
$785$	3801.92	−	28839.5i	0.172861	−	1.31124i
$786$	−8337.64	+	9259.88i	−0.378363	+	0.420215i
$787$	4534.82	+	237.660i	0.205399	+	0.0107645i	0.154758	−	0.987952i	$-0.450540\pi$
$787$	4534.82	+	237.660i	0.205399	+	0.0107645i	0.0506409	+	0.998717i	$0.483874\pi$
$788$	−29746.8	−	1558.96i	−1.34478	−	0.0704769i
$789$	−6978.15	+	7750.02i	−0.314865	+	0.349693i
$790$	−7009.51	+	7383.90i	−0.315680	+	0.332541i
$791$	−39.6622	−	39634.4i	−0.00178284	−	1.78159i
$792$	−929.861	−	5870.91i	−0.0417186	−	0.263401i
$793$	−25379.9	−	6800.53i	−1.13653	−	0.304532i
$794$	9589.98	−	4269.73i	0.428634	−	0.190840i
$795$	18984.0	+	3521.90i	0.846909	+	0.157118i
$796$	−13735.5	+	30850.4i	−0.611609	+	1.37370i
$797$	3139.32	−	19820.9i	0.139524	−	0.880917i	−0.814277	−	0.580476i	$-0.802866\pi$
$797$	3139.32	−	19820.9i	0.139524	−	0.880917i	0.953801	−	0.300440i	$-0.0971337\pi$
$798$	−2987.30	−	7758.97i	−0.132518	−	0.344191i
$799$		−	32918.0i		−	1.45752i
$800$	17572.8	+	10153.8i	0.776614	+	0.448740i
$801$	−2445.07	−	1411.66i	−0.107856	−	0.0622704i
$802$	−23738.5	−	36554.1i	−1.04518	−	1.60944i
$803$	40.0185	+	104.252i	0.00175868	+	0.00458153i
$804$	1500.93	−	1090.49i	0.0658378	−	0.0478340i
$805$	−505.696	+	480.682i	−0.0221409	+	0.0210457i
$806$	62170.5	+	45169.5i	2.71695	+	1.97398i
$807$	1642.59	−	6130.22i	0.0716503	−	0.267402i
$808$	29190.1	+	11205.0i	1.27092	+	0.487860i
$809$	−25233.2	+	22720.0i	−1.09660	+	0.987384i	−0.999969	−	0.00793603i	$-0.997474\pi$
$809$	−25233.2	+	22720.0i	−1.09660	+	0.987384i	−0.0966326	+	0.995320i	$0.530807\pi$
$810$	−5201.62	+	408.463i	−0.225638	+	0.0177184i
$811$	−17332.0	+	5631.50i	−0.750442	+	0.243833i	−0.659171	−	0.751993i	$-0.729093\pi$
$811$	−17332.0	+	5631.50i	−0.750442	+	0.243833i	−0.0912704	+	0.995826i	$0.529093\pi$
$812$	4311.66	+	16027.1i	0.186342	+	0.692663i
$813$	−4992.48	−	9798.29i	−0.215368	−	0.422683i
$814$	−10751.9	−	9681.08i	−0.462967	−	0.416857i
$815$	33002.0	−	22673.2i	1.41842	−	0.974487i
$816$	−1185.99	−	1317.18i	−0.0508801	−	0.0565080i
$817$	7365.02	+	9095.04i	0.315385	+	0.389468i
$818$	−25421.0	−	25421.0i	−1.08658	−	1.08658i
$819$	4311.80	+	20186.1i	0.183964	+	0.861243i
$820$	−45965.3	−	31602.9i	−1.95753	−	1.34588i
$821$	−35588.0	−	15844.8i	−1.51283	−	0.673554i	−0.528344	−	0.849031i	$-0.677187\pi$
$821$	−35588.0	−	15844.8i	−1.51283	−	0.673554i	−0.984484	+	0.175476i	$0.943853\pi$
$822$	−8399.23	−	6801.57i	−0.356395	−	0.288603i
$823$	−11876.0	+	7712.38i	−0.503004	+	0.326654i	−0.771075	−	0.636745i	$-0.780280\pi$
$823$	−11876.0	+	7712.38i	−0.503004	+	0.326654i	0.268071	+	0.963399i	$0.413614\pi$
$824$	19337.7	+	33493.8i	0.817548	+	1.41603i
$825$	4785.46	+	504.661i	0.201949	+	0.0212970i
$826$	11992.7	+	36784.5i	0.505182	+	1.54951i
$827$	−677.613	+	1329.89i	−0.0284920	+	0.0559187i	−0.904814	−	0.425808i	$-0.859990\pi$
$827$	−677.613	+	1329.89i	−0.0284920	+	0.0559187i	0.876322	+	0.481726i	$0.159990\pi$
$828$	−770.528	+	295.778i	−0.0323402	+	0.0124142i
$829$	1681.75	+	16000.8i	0.0704579	+	0.670362i	0.971566	+	0.236768i	$0.0760881\pi$
$829$	1681.75	+	16000.8i	0.0704579	+	0.670362i	−0.901108	+	0.433594i	$0.857245\pi$
$830$	−4591.46	+	24749.2i	−0.192014	+	1.03501i
$831$	24347.3	+	2559.00i	1.01636	+	0.106824i
$832$	35010.4	−	35010.4i	1.45886	−	1.45886i
$833$	25293.6	−	6831.69i	1.05207	−	0.284158i
$834$	10621.4	+	3451.09i	0.440993	+	0.143287i
$835$	−37058.7	−	8903.84i	−1.53589	−	0.369018i
$836$	1196.78	−	5630.43i	0.0495116	−	0.232934i
$837$	−1909.08	+	36427.4i	−0.0788380	+	1.50432i
$838$	20565.2	+	13355.2i	0.847749	+	0.550535i
$839$	2485.70	+	7650.18i	0.102283	+	0.314796i	0.989083	−	0.147358i	$-0.0470769\pi$
$839$	2485.70	+	7650.18i	0.102283	+	0.314796i	−0.886800	+	0.462154i	$0.847077\pi$
$840$	−14905.2	+	2775.25i	−0.612234	+	0.113994i
$841$	6149.16	−	18925.2i	0.252129	−	0.775972i
$842$	43148.1	−	34940.6i	1.76601	−	1.43009i
$843$	−8792.32	+	2355.90i	−0.359221	+	0.0962531i
$844$	−4584.25	−	10296.4i	−0.186962	−	0.419924i
$845$	−14359.5	+	8796.06i	−0.584593	+	0.358099i
$846$	−21448.4	−	29521.2i	−0.871646	−	1.19972i
$847$	13541.0	+	16687.6i	0.549321	+	0.676968i
$848$	−4111.07	−	2094.70i	−0.166480	−	0.0848257i
$849$	1124.56	−	649.262i	0.0454589	−	0.0262457i
$850$	−39338.6	+	20026.7i	−1.58741	+	0.808130i
$851$	−403.622	+	699.094i	−0.0162585	+	0.0281606i
$852$	223.653	+	4267.55i	0.00899321	+	0.171601i
$853$	29168.4	+	4619.82i	1.17082	+	0.185439i	0.711404	−	0.702783i	$-0.248060\pi$
$853$	29168.4	+	4619.82i	1.17082	+	0.185439i	0.459414	+	0.888223i	$0.348060\pi$
$854$	15070.9	+	33758.8i	0.603882	+	1.35270i
$855$	−6468.73	−	1917.35i	−0.258744	−	0.0766925i
$856$	3921.88	−	37314.2i	0.156597	−	1.48992i
$857$	−11625.6	−	43387.3i	−0.463387	−	1.72939i	−0.662181	−	0.749344i	$-0.730369\pi$
$857$	−11625.6	−	43387.3i	−0.463387	−	1.72939i	0.198794	−	0.980041i	$-0.436298\pi$
$858$	3881.28	−	10111.1i	0.154434	−	0.402315i
$859$	−35451.5	+	7535.46i	−1.40814	+	0.299309i	−0.848398	−	0.529359i	$-0.822433\pi$
$859$	−35451.5	+	7535.46i	−1.40814	+	0.299309i	−0.559740	+	0.828668i	$0.689099\pi$
$860$	46678.6	−	25333.9i	1.85085	−	1.00451i
$861$	−20247.4	+	2148.58i	−0.801429	+	0.0850445i
$862$	16450.2	−	8381.81i	0.649997	−	0.331190i
$863$	−25984.9	+	40013.3i	−1.02496	+	1.57829i	−0.228549	+	0.973532i	$0.573398\pi$
$863$	−25984.9	+	40013.3i	−1.02496	+	1.57829i	−0.796407	+	0.604761i	$0.793269\pi$
$864$	21208.9	+	4508.10i	0.835118	+	0.177510i
$865$	19074.9	+	6758.54i	0.749789	+	0.265661i
$866$	725.928	+	3415.22i	0.0284850	+	0.134012i
$867$	−2682.64	+	424.889i	−0.105083	+	0.0166436i
$868$	−3608.46	−	67559.9i	−0.141105	−	2.64186i
$869$	−1512.33	+	2081.54i	−0.0590358	+	0.0812558i
$870$	−9429.44	−	3907.73i	−0.367457	−	0.152281i
$871$	−2848.74	+	299.414i	−0.110822	+	0.0116478i
$872$	−18278.5	+	22572.1i	−0.709849	+	0.876591i
$873$	5648.25	−	296.012i	0.218974	−	0.0114759i
$874$	−513.278			−0.0198649
$875$	−2018.44	+	25804.0i	−0.0779836	+	0.996955i
$876$	336.940			0.0129956
$877$	−26824.8	+	1405.83i	−1.03285	+	0.0541294i	−0.561220	−	0.827667i	$-0.689668\pi$
$877$	−26824.8	+	1405.83i	−1.03285	+	0.0541294i	−0.471631	+	0.881796i	$0.656335\pi$
$878$	−6264.16	+	7735.59i	−0.240780	+	0.297339i
$879$	6912.79	−	726.563i	0.265259	−	0.0278798i
$880$	−1062.30	−	440.237i	−0.0406934	−	0.0168641i
$881$	27633.2	−	38033.8i	1.05674	−	1.45447i	0.173918	−	0.984760i	$-0.444357\pi$
$881$	27633.2	−	38033.8i	1.05674	−	1.45447i	0.882819	−	0.469713i	$-0.155643\pi$
$882$	18232.3	−	22607.3i	0.696046	−	0.863071i
$883$	−19115.4	+	3027.58i	−0.728522	+	0.115387i	−0.509668	−	0.860371i	$-0.670232\pi$
$883$	−19115.4	+	3027.58i	−0.728522	+	0.115387i	−0.218854	+	0.975758i	$0.570232\pi$
$884$	12925.2	+	60808.2i	0.491766	+	2.31357i
$885$	−14033.6	−	4972.32i	−0.533034	−	0.188862i
$886$	78165.3	+	16614.5i	2.96390	+	0.629996i
$887$	−20349.3	+	31335.2i	−0.770308	+	1.18617i	0.207821	+	0.978167i	$0.433363\pi$
$887$	−20349.3	+	31335.2i	−0.770308	+	1.18617i	−0.978128	+	0.208003i	$0.933304\pi$
$888$	−15629.9	+	7963.81i	−0.590657	+	0.300955i
$889$	13590.9	−	9895.15i	0.512738	−	0.373310i
$890$	−7003.14	+	3800.81i	−0.263759	+	0.143150i
$891$	−1289.76	+	274.147i	−0.0484945	+	0.0103078i
$892$	−21711.1	+	56559.4i	−0.814958	+	2.12304i
$893$	−3675.07	−	13715.6i	−0.137717	−	0.513968i
$894$	−1231.39	+	11715.9i	−0.0460671	+	0.438299i
$895$	−4526.35	−	1341.63i	−0.169050	−	0.0501069i
$896$	−45364.2	−	4722.08i	−1.69142	−	0.176064i
$897$	−596.839	−	94.5301i	−0.0222162	−	0.00351869i
$898$	1081.18	+	20630.1i	0.0401774	+	0.766630i
$899$	9151.32	−	15850.6i	0.339503	−	0.588037i
$900$	−13909.9	+	27276.2i	−0.515183	+	1.01023i
$901$	−38764.3	+	22380.6i	−1.43333	+	0.827531i
$902$	−20073.5	−	10228.0i	−0.740992	−	0.377554i
$903$	6929.26	−	18105.5i	0.255361	−	0.667234i
$904$	−31253.2	−	43016.3i	−1.14985	−	1.58263i
$905$	32996.9	−	20212.6i	1.21199	−	0.742419i
$906$	4356.74	+	9785.40i	0.159761	+	0.358828i
$907$	39385.0	−	10553.2i	1.44185	−	0.386342i	0.548668	−	0.836040i	$-0.315135\pi$
$907$	39385.0	−	10553.2i	1.44185	−	0.386342i	0.893181	+	0.449698i	$0.148468\pi$
$908$	18621.5	−	15079.4i	0.680589	−	0.551130i
$909$	7122.34	−	21920.3i	0.259882	−	0.799836i
$910$	54929.5	+	19400.5i	2.00098	+	0.706726i
$911$	10035.3	+	30885.6i	0.364968	+	1.12326i	0.950001	+	0.312246i	$0.101081\pi$
$911$	10035.3	+	30885.6i	0.364968	+	1.12326i	−0.585033	+	0.811009i	$0.698919\pi$
$912$	−641.209	−	416.406i	−0.0232813	−	0.0151191i
$913$	−332.920	+	6352.49i	−0.0120680	+	0.230270i
$914$	−9851.35	+	46347.0i	−0.356514	+	1.67727i
$915$	−13832.9	−	3323.54i	−0.499784	−	0.120080i
$916$	74865.8	+	24325.4i	2.70048	+	0.877438i
$917$	−14214.2	−	9210.61i	−0.511881	−	0.331692i
$918$	−33347.5	+	33347.5i	−1.19894	+	1.19894i
$919$	20369.5	+	2140.92i	0.731152	+	0.0768472i	0.462786	−	0.886470i	$-0.346850\pi$
$919$	20369.5	+	2140.92i	0.731152	+	0.0768472i	0.268366	+	0.963317i	$0.413516\pi$
$920$	−170.731	+	920.285i	−0.00611829	+	0.0329792i
$921$	2617.39	+	24902.8i	0.0936436	+	0.890960i
$922$	4511.61	−	1731.84i	0.161152	−	0.0618603i
$923$	2995.42	−	5878.83i	0.106820	−	0.209647i
$924$	−9065.50	+	2955.59i	−0.322763	+	0.105229i
$925$	6216.05	+	29294.5i	0.220954	+	1.04129i
$926$	−20438.5	−	35400.6i	−0.725326	−	1.25630i
$927$	23910.2	−	15527.4i	0.847155	−	0.550149i
$928$	−8454.87	−	6846.62i	−0.299078	−	0.242189i
$929$	−1967.15	−	875.831i	−0.0694726	−	0.0309312i	0.371706	−	0.928350i	$-0.378773\pi$
$929$	−1967.15	−	875.831i	−0.0694726	−	0.0309312i	−0.441179	+	0.897419i	$0.645440\pi$
$930$	34286.4	+	23573.2i	1.20892	+	0.831179i
$931$	9776.08	−	5670.34i	0.344144	−	0.199611i
$932$	59221.6	+	59221.6i	2.08140	+	2.08140i
$933$	−17000.9	−	20994.4i	−0.596555	−	0.736684i
$934$	−55918.4	−	62103.6i	−1.95900	−	2.17569i
$935$	−9194.69	+	6316.97i	−0.321603	+	0.220949i
$936$	20578.6	+	18529.0i	0.718624	+	0.647052i
$937$	−25164.8	−	49388.7i	−0.877373	−	1.72194i	−0.668082	−	0.744088i	$-0.732884\pi$
$937$	−25164.8	−	49388.7i	−0.877373	−	1.72194i	−0.209291	−	0.977853i	$-0.567116\pi$
$938$	2852.74	+	2847.03i	0.0993019	+	0.0991034i
$939$	2524.71	−	820.327i	0.0877430	−	0.0285094i
$940$	−64240.9	+	5044.58i	−2.22905	+	0.175038i
$941$	−3215.75	+	2895.48i	−0.111403	+	0.100308i	−0.722950	−	0.690900i	$-0.757214\pi$
$941$	−3215.75	+	2895.48i	−0.111403	+	0.100308i	0.611547	+	0.791208i	$0.290548\pi$
$942$	−33094.5	−	12703.8i	−1.14467	−	0.439396i
$943$	−325.335	+	1214.17i	−0.0112347	+	0.0419286i
$944$	2878.37	+	2091.26i	0.0992404	+	0.0721024i
$945$	6477.48	+	26882.8i	0.222976	+	0.925394i
$946$	17353.6	−	12608.1i	0.596422	−	0.433326i
$947$	−10226.9	−	26641.9i	−0.350928	−	0.914198i	−0.989487	−	0.144625i	$-0.953802\pi$
$947$	−10226.9	−	26641.9i	−0.350928	−	0.914198i	0.638559	−	0.769573i	$-0.279531\pi$
$948$	4228.20	+	6510.86i	0.144858	+	0.223062i
$949$	−450.526	−	260.111i	−0.0154106	−	0.00889733i
$950$	−14154.9	+	12736.2i	−0.483416	+	0.434965i
$951$		−	3673.37i		−	0.125255i
$952$	22092.1	−	27337.4i	0.752112	−	0.930684i
$953$	7473.39	−	47185.2i	0.254026	−	1.60386i	−0.449561	−	0.893250i	$-0.648420\pi$
$953$	7473.39	−	47185.2i	0.254026	−	1.60386i	0.703587	−	0.710609i	$-0.251580\pi$
$954$	−20181.7	+	45328.9i	−0.684913	+	1.53834i
$955$	35277.9	+	6544.74i	1.19536	+	0.221762i
$956$	−43655.7	+	19436.8i	−1.47691	+	0.657563i
$957$	−2491.59	−	667.619i	−0.0841606	−	0.0225508i
$958$	2615.37	+	16512.8i	0.0882034	+	0.556894i
$959$	7332.82	−	12730.2i	0.246913	−	0.428655i
$960$	18456.9	−	19442.7i	0.620514	−	0.653657i
$961$	−29989.2	+	33306.4i	−1.00665	+	1.11800i
$962$	67309.1	+	3527.52i	2.25586	+	0.118224i
$963$	−27619.8	−	1447.49i	−0.924233	−	0.0484370i
$964$	52569.3	−	58384.1i	1.75637	−	1.95065i
$965$	−2076.14	+	15748.6i	−0.0692572	+	0.525352i
$966$	425.857	+	735.905i	0.0141840	+	0.0245107i
$967$	−847.893	−	5353.39i	−0.0281969	−	0.178028i	0.969571	−	0.244812i	$-0.0787262\pi$
$967$	−847.893	−	5353.39i	−0.0281969	−	0.178028i	−0.997767	+	0.0667838i	$0.978726\pi$
$968$	27847.7	+	7461.77i	0.924647	+	0.247759i
$969$	−6775.88	+	3016.81i	−0.224636	+	0.100014i
$970$	7619.12	−	14026.8i	0.252201	−	0.464303i
$971$	−1106.25	+	2484.69i	−0.0365616	+	0.0821188i	−0.930903	−	0.365266i	$-0.880978\pi$
$971$	−1106.25	+	2484.69i	−0.0365616	+	0.0821188i	0.894341	+	0.447385i	$0.147645\pi$
$972$	−8166.14	+	51559.0i	−0.269474	+	1.70139i
$973$	−2359.78	+	14996.2i	−0.0777503	+	0.494096i
$974$			43582.5i			1.43375i
$975$	−18804.9	+	12202.7i	−0.617682	+	0.400821i
$976$	2944.22	+	1699.85i	0.0965596	+	0.0557487i
$977$	−23602.1	−	36344.1i	−0.772875	−	1.19012i	−0.977428	−	0.211268i	$-0.932241\pi$
$977$	−23602.1	−	36344.1i	−0.772875	−	1.19012i	0.204553	−	0.978856i	$-0.434426\pi$
$978$	−17486.3	−	45553.4i	−0.571729	−	1.48941i
$979$	−1629.08	+	1183.59i	−0.0531824	+	0.0386392i
$980$	−17208.5	−	48314.6i	−0.560924	−	1.57485i
$981$	17321.4	+	12584.8i	0.563742	+	0.409582i
$982$	16687.2	−	62277.4i	0.542270	−	2.02378i
$983$	8573.91	+	3291.21i	0.278194	+	0.106789i	0.493465	−	0.869766i	$-0.335730\pi$
$983$	8573.91	+	3291.21i	0.278194	+	0.106789i	−0.215271	+	0.976554i	$0.569063\pi$
$984$	−20299.1	+	18277.4i	−0.657635	+	0.592137i
$985$	21229.8	+	13014.7i	0.686738	+	0.420999i
$986$	22504.8	−	7312.24i	0.726874	−	0.236176i
$987$	−16615.3	+	16648.6i	−0.535838	+	0.536912i
$988$	12174.2	+	23893.2i	0.392017	+	0.769377i
$989$	−889.402	−	800.821i	−0.0285959	−	0.0257479i
$990$	−4129.94	+	11656.1i	−0.132584	+	0.374198i
$991$	−20165.3	−	22395.8i	−0.646390	−	0.717889i	0.327515	−	0.944846i	$-0.393789\pi$
$991$	−20165.3	−	22395.8i	−0.646390	−	0.717889i	−0.973905	+	0.226957i	$0.927122\pi$
$992$	27909.7	+	34465.6i	0.893280	+	1.10311i
$993$	−24839.1	−	24839.1i	−0.793803	−	0.793803i
$994$	−9078.76	+	1939.25i	−0.289699	+	0.0618805i
$995$	22399.9	−	17181.8i	0.713692	−	0.547437i
$996$	17534.4	+	7806.81i	0.557829	+	0.248362i
$997$	−18233.3	−	14765.0i	−0.579191	−	0.469019i	0.294399	−	0.955683i	$-0.404881\pi$
$997$	−18233.3	−	14765.0i	−0.579191	−	0.469019i	−0.873590	+	0.486663i	$0.838214\pi$
$998$	13636.8	−	8855.83i	0.432530	−	0.280888i
$999$	15996.9	+	27707.5i	0.506627	+	0.877504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.x.a.17.7	yes	928
7.5	odd	6	inner	175.4.x.a.117.52	yes	928
25.3	odd	20	inner	175.4.x.a.3.52	✓	928
175.103	even	60	inner	175.4.x.a.103.7	yes	928

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.4.x.a.3.52	✓	928	25.3	odd	20	inner
175.4.x.a.17.7	yes	928	1.1	even	1	trivial
175.4.x.a.103.7	yes	928	175.103	even	60	inner
175.4.x.a.117.52	yes	928	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-4.61688 + 0.241960i) q^{2} +(1.85463 - 2.29028i) q^{3} +(13.3008 - 1.39797i) q^{4} +(-10.3285 - 4.28033i) q^{5} +(-8.00844 + 11.0227i) q^{6} +(-16.5101 - 8.39150i) q^{7} +(-24.5397 + 3.88671i) q^{8} +(3.80790 + 17.9147i) q^{9} +(48.7213 + 17.2627i) q^{10} +(12.7772 + 2.71587i) q^{11} +(21.4664 - 33.0553i) q^{12} +(-54.2210 + 27.6270i) q^{13} +(78.2554 + 34.7478i) q^{14} +(-28.9588 + 15.7168i) q^{15} +(7.70166 - 1.63704i) q^{16} +(27.3739 - 71.3113i) q^{17} +(-21.9153 - 81.7888i) q^{18} +(3.44411 - 32.7686i) q^{19} +(-143.362 - 42.4930i) q^{20} +(-49.8390 + 22.2495i) q^{21} +(-59.6477 - 9.44726i) q^{22} +(0.176346 + 3.36488i) q^{23} +(-36.6104 + 63.4112i) q^{24} +(88.3575 + 88.4192i) q^{25} +(243.647 - 140.670i) q^{26} +(118.989 + 60.6281i) q^{27} +(-231.329 - 88.5333i) q^{28} +(-39.3855 - 54.2095i) q^{29} +(129.896 - 79.5693i) q^{30} +(111.099 + 249.532i) q^{31} +(156.831 - 42.0226i) q^{32} +(29.9170 - 24.2263i) q^{33} +(-109.127 + 335.859i) q^{34} +(134.607 + 157.341i) q^{35} +(75.6926 + 232.958i) q^{36} +(200.923 + 130.481i) q^{37} +(-7.97236 + 152.122i) q^{38} +(-37.2864 + 175.419i) q^{39} +(270.096 + 64.8941i) q^{40} +(354.793 + 115.279i) q^{41} +(224.717 - 114.782i) q^{42} +(-251.156 + 251.156i) q^{43} +(173.743 + 18.2612i) q^{44} +(37.3511 - 201.332i) q^{45} +(-1.62834 - 15.4926i) q^{46} +(402.326 - 154.439i) q^{47} +(10.5345 - 20.6750i) q^{48} +(202.165 + 277.089i) q^{49} +(-429.330 - 386.842i) q^{50} +(-112.554 - 194.950i) q^{51} +(-682.562 + 443.261i) q^{52} +(-455.405 - 368.779i) q^{53} +(-564.029 - 251.122i) q^{54} +(-120.344 - 82.7414i) q^{55} +(437.768 + 141.755i) q^{56} +(-68.6615 - 68.6615i) q^{57} +(194.955 + 240.749i) q^{58} +(302.357 + 335.802i) q^{59} +(-363.204 + 249.530i) q^{60} +(320.873 + 288.915i) q^{61} +(-573.306 - 1125.18i) q^{62} +(87.4630 - 327.728i) q^{63} +(-773.806 + 251.425i) q^{64} +(678.276 - 53.2623i) q^{65} +(-132.261 + 119.089i) q^{66} +(43.9444 + 16.8687i) q^{67} +(264.404 - 986.768i) q^{68} +(8.03357 + 5.83673i) q^{69} +(-659.532 - 693.853i) q^{70} +(-87.7166 + 63.7298i) q^{71} +(-163.074 - 424.823i) q^{72} +(4.65598 + 7.16958i) q^{73} +(-959.210 - 553.800i) q^{74} +(366.375 - 38.3782i) q^{75} -440.664i q^{76} +(-188.162 - 152.059i) q^{77} +(129.702 - 818.909i) q^{78} +(-80.1143 + 179.940i) q^{79} +(-86.5539 - 16.0575i) q^{80} +(-92.2157 + 41.0571i) q^{81} +(-1665.93 - 446.384i) q^{82} +(76.1803 + 480.983i) q^{83} +(-631.795 + 365.611i) q^{84} +(-587.968 + 619.373i) q^{85} +(1098.79 - 1220.33i) q^{86} +(-197.200 - 10.3348i) q^{87} +(-324.103 - 16.9855i) q^{88} +(-103.149 + 114.559i) q^{89} +(-123.731 + 938.564i) q^{90} +(1127.02 - 1.12781i) q^{91} +(7.04957 + 44.5092i) q^{92} +(777.545 + 208.343i) q^{93} +(-1820.12 + 810.371i) q^{94} +(-175.833 + 323.709i) q^{95} +(194.619 - 437.122i) q^{96} +(48.3098 - 305.016i) q^{97} +(-1000.42 - 1230.37i) q^{98} +239.241i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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