LMFDB - Embedded newform 175.4.x.a.103.7

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			103.7
Character	$\chi$	$=$	175.103
Dual form			175.4.x.a.17.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.61688 - 0.241960i) q^{2} +(1.85463 + 2.29028i) q^{3} +(13.3008 + 1.39797i) q^{4} +(-10.3285 + 4.28033i) q^{5} +(-8.00844 - 11.0227i) q^{6} +(-16.5101 + 8.39150i) q^{7} +(-24.5397 - 3.88671i) q^{8} +(3.80790 - 17.9147i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22} + 296 q^{23} + 32 q^{25} - 48 q^{26} + 226 q^{28} - 200 q^{29} - 38 q^{30} - 18 q^{31} - 964 q^{32} - 1092 q^{33} + 288 q^{35} + 7400 q^{36} - 392 q^{37} + 5424 q^{38} + 2430 q^{39} + 2172 q^{40} - 2098 q^{42} + 1560 q^{43} - 10 q^{44} - 4224 q^{45} - 6 q^{46} + 96 q^{47} + 6232 q^{50} - 16 q^{51} - 8928 q^{52} - 2384 q^{53} - 30 q^{54} + 244 q^{56} + 1556 q^{57} + 640 q^{58} + 4890 q^{59} + 3676 q^{60} - 18 q^{61} + 224 q^{63} - 9700 q^{64} - 1116 q^{65} - 2610 q^{66} - 2404 q^{67} - 13614 q^{68} - 1700 q^{70} - 24 q^{71} - 518 q^{72} - 4200 q^{73} - 16104 q^{75} - 722 q^{77} - 356 q^{78} - 10 q^{79} + 6414 q^{80} - 6810 q^{81} + 1692 q^{82} + 20620 q^{84} + 2712 q^{85} - 6 q^{86} + 9102 q^{87} + 1650 q^{88} + 20370 q^{89} - 12 q^{91} + 1612 q^{92} - 4604 q^{93} - 30 q^{94} + 1652 q^{95} - 2610 q^{96} - 19478 q^{98}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−4.61688	−	0.241960i	−1.63231	−	0.0855459i	−0.785998	−	0.618229i	$-0.787850\pi$
$2$	−4.61688	−	0.241960i	−1.63231	−	0.0855459i	−0.846315	+	0.532683i	$0.821184\pi$
$3$	1.85463	+	2.29028i	0.356924	+	0.440764i	0.923705	−	0.383104i	$-0.125145\pi$
$3$	1.85463	+	2.29028i	0.356924	+	0.440764i	−0.566781	+	0.823868i	$0.691812\pi$
$4$	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	−0.0294412	−	0.999567i	$-0.509373\pi$
$11$	12.7772	−	2.71587i	0.350223	−	0.0744423i	0.379664	+	0.925124i	$0.376039\pi$
$12$	21.4664	+	33.0553i	0.516401	+	0.795188i
$13$	−54.2210	−	27.6270i	−1.15678	−	0.589411i	−0.233057	−	0.972463i	$-0.574873\pi$
$13$	−54.2210	−	27.6270i	−1.15678	−	0.589411i	−0.923727	+	0.383052i	$0.874873\pi$
$14$	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	0.978087	+	0.208196i	$0.0667593\pi$
$17$	27.3739	+	71.3113i	0.390537	+	1.01738i	−0.587550	+	0.809188i	$0.699907\pi$
$18$	−21.9153	+	81.7888i	−0.286971	+	1.07099i
$19$	3.44411	+	32.7686i	0.0415860	+	0.395664i	0.995440	+	0.0953927i	$0.0304107\pi$
$19$	3.44411	+	32.7686i	0.0415860	+	0.395664i	−0.953854	+	0.300272i	$0.902923\pi$
$20$	−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	−0.997714	−	0.0675826i	$-0.978471\pi$
$23$	0.176346	−	3.36488i	0.00159873	−	0.0305055i	0.999312	+	0.0370771i	$0.0118047\pi$
$24$	−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	−0.916279	−	0.400540i	$-0.868822\pi$
$29$	−39.3855	+	54.2095i	−0.252197	+	0.347119i	0.664082	+	0.747659i	$0.268822\pi$
$30$	129.896	+	79.5693i	0.790523	+	0.484244i
$31$	111.099	−	249.532i	0.643675	−	1.44572i	−0.236767	−	0.971566i	$-0.576088\pi$
$31$	111.099	−	249.532i	0.643675	−	1.44572i	0.880443	−	0.474152i	$-0.157245\pi$
$32$	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	−0.0147151	−	0.999892i	$-0.504684\pi$
$37$	200.923	−	130.481i	0.892746	−	0.579756i	0.907461	+	0.420136i	$0.138017\pi$
$38$	−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	0.458269	−	0.888813i	$-0.348470\pi$
$41$	354.793	−	115.279i	1.35145	−	0.439112i	0.893179	+	0.449701i	$0.148470\pi$
$42$	224.717	+	114.782i	0.825585	+	0.421698i
$43$	−251.156	−	251.156i	−0.890720	−	0.890720i	0.103871	−	0.994591i	$-0.466877\pi$
$43$	−251.156	−	251.156i	−0.890720	−	0.890720i	−0.994591	+	0.103871i	$0.966877\pi$
$44$	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	0.890761	−	0.454472i	$-0.150172\pi$
$47$	402.326	+	154.439i	1.24862	+	0.479302i	0.357863	+	0.933774i	$0.383505\pi$
$48$	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	−0.999614	−	0.0277768i	$-0.991157\pi$
$53$	−455.405	+	368.779i	−1.18028	+	0.955769i	−0.180662	+	0.983545i	$0.557824\pi$
$54$	−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	−0.310618	−	0.950535i	$-0.600536\pi$
$59$	302.357	−	335.802i	0.667179	−	0.740977i	0.977796	+	0.209558i	$0.0672025\pi$
$60$	−363.204	−	249.530i	−0.781491	−	0.536903i
$61$	320.873	−	288.915i	0.673502	−	0.606424i	−0.259738	−	0.965679i	$-0.583636\pi$
$61$	320.873	−	288.915i	0.673502	−	0.606424i	0.933239	+	0.359256i	$0.116969\pi$
$62$	−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	−0.317973	−	0.948100i	$-0.603002\pi$
$67$	43.9444	−	16.8687i	0.0801293	−	0.0307587i	0.398102	+	0.917341i	$0.369669\pi$
$68$	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	0.512057	−	0.858952i	$-0.328884\pi$
$71$	−87.7166	−	63.7298i	−0.146620	−	0.106526i	−0.658677	+	0.752426i	$0.728884\pi$
$72$	−163.074	+	424.823i	−0.266923	+	0.695359i
$73$	4.65598	−	7.16958i	0.00746495	−	0.0114950i	−0.834918	−	0.550374i	$-0.814485\pi$
$73$	4.65598	−	7.16958i	0.00746495	−	0.0114950i	0.842383	+	0.538879i	$0.181152\pi$
$74$	−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	0.847467	−	0.530848i	$-0.178126\pi$
$79$	−80.1143	−	179.940i	−0.114096	−	0.256263i	−0.961563	+	0.274584i	$0.911460\pi$
$80$	−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	−0.884709	−	0.466143i	$-0.845643\pi$
$83$	76.1803	−	480.983i	0.100745	−	0.636082i	0.985455	−	0.169938i	$-0.0543569\pi$
$84$	−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	0.678581	−	0.734525i	$-0.262595\pi$
$89$	−103.149	−	114.559i	−0.122851	−	0.136440i	−0.801433	+	0.598085i	$0.795928\pi$
$90$	−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	0.999986	+	0.00526010i	$0.00167435\pi$
$97$	48.3098	+	305.016i	0.0505683	+	0.319275i	−0.949418	+	0.314015i	$0.898326\pi$
$98$	−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	−0.929190	−	0.369603i	$-0.879494\pi$
$101$	−1089.84	+	629.222i	−1.07370	+	0.619900i	−0.144509	+	0.989503i	$0.546160\pi$
$102$	566.820	−	872.826i	0.550230	−	0.847281i
$103$	−557.845	+	1453.24i	−0.533652	+	1.39021i	0.356393	+	0.934336i	$0.384007\pi$
$103$	−557.845	+	1453.24i	−0.533652	+	1.39021i	−0.890044	+	0.455874i	$0.849327\pi$
$104$	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	−0.882826	−	0.469701i	$-0.844362\pi$
$107$	−390.847	−	1458.66i	−0.353127	−	1.31789i	0.529699	−	0.848186i	$-0.322305\pi$
$108$	1667.41	−	640.060i	1.48562	−	0.570276i
$109$	868.747	+	782.223i	0.763402	+	0.687370i	0.955823	−	0.293942i	$-0.0949673\pi$
$109$	868.747	+	782.223i	0.763402	+	0.687370i	−0.192421	+	0.981312i	$0.561634\pi$
$110$	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	−0.000464277	−	1.00000i	$-0.500148\pi$
$113$	971.566	−	1906.81i	0.808826	−	1.58741i	0.809290	−	0.587410i	$-0.199852\pi$
$114$	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	0.701048	−	0.713114i	$-0.252716\pi$
$127$	−412.103	−	808.798i	−0.287939	−	0.565112i	−0.988987	+	0.148002i	$0.952716\pi$
$128$	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	0.203757	−	0.979022i	$-0.434685\pi$
$131$	909.530	−	95.5954i	0.606611	−	0.0637573i	0.402854	+	0.915264i	$0.368018\pi$
$132$	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	−0.980545	−	0.196293i	$-0.937110\pi$
$137$	−41.5153	−	792.159i	−0.0258897	−	0.494005i	0.954656	−	0.297712i	$-0.0962236\pi$
$138$	−38.5023	+	25.0037i	−0.0237502	+	0.0154236i
$139$	−253.295	+	779.563i	−0.154563	+	0.475695i	−0.998116	−	0.0613498i	$-0.980459\pi$
$139$	−253.295	+	779.563i	−0.154563	+	0.475695i	0.843554	+	0.537045i	$0.180459\pi$
$140$	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	0.691521	−	0.722356i	$-0.256941\pi$
$149$	748.796	+	432.318i	0.411703	+	0.237697i	−0.279818	+	0.960053i	$0.590274\pi$
$150$	−1682.22	−	265.836i	−0.915686	−	0.144703i
$151$	393.087	+	680.847i	0.211848	+	0.366931i	0.952293	−	0.305186i	$-0.0987186\pi$
$151$	393.087	+	680.847i	0.211848	+	0.366931i	−0.740445	+	0.672117i	$0.765385\pi$
$152$	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	−0.553411	−	0.832908i	$-0.686674\pi$
$157$	673.396	−	2513.15i	0.342311	−	1.27752i	0.895722	−	0.444614i	$-0.146659\pi$
$158$	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	−0.895962	−	0.444132i	$-0.853512\pi$
$163$	−1950.51	−	3003.53i	−0.937276	−	1.44328i	−0.0413141	−	0.999146i	$-0.513154\pi$
$164$	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	0.876027	−	0.482262i	$-0.160185\pi$
$167$	3366.99	+	533.278i	1.56015	+	0.247104i	0.684124	+	0.729366i	$0.260185\pi$
$168$	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	−0.349167	−	0.937060i	$-0.613536\pi$
$173$	−1807.56	−	94.7302i	−0.794371	−	0.0416312i	−0.445204	+	0.895429i	$0.646869\pi$
$174$	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	0.191798	−	0.981434i	$-0.438568\pi$
$179$	419.946	+	44.1381i	0.175353	+	0.0184304i	−0.0164448	+	0.999865i	$0.505235\pi$
$180$	215.343	+	2730.10i	0.0891708	+	1.13050i
$181$	−2034.34	−	2800.03i	−0.835423	−	1.14986i	−0.986889	−	0.161398i	$-0.948400\pi$
$181$	−2034.34	−	2800.03i	−0.835423	−	1.14986i	0.151467	−	0.988462i	$-0.451600\pi$
$182$	−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	−0.429505	−	0.903065i	$-0.641312\pi$
$191$	−3139.06	−	667.228i	−1.18919	−	0.252769i	−0.759681	+	0.650295i	$0.774645\pi$
$192$	−859.292	−	2238.53i	−0.322990	−	0.841417i
$193$	−367.726	+	1372.37i	−0.137148	+	0.511841i	0.862832	+	0.505490i	$0.168688\pi$
$193$	−367.726	+	1372.37i	−0.137148	+	0.511841i	−0.999980	+	0.00635124i	$0.997978\pi$
$194$	−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	−0.540983	−	0.841034i	$-0.681948\pi$
$197$	−2199.84	+	348.421i	−0.795595	+	0.126010i	−0.254612	+	0.967043i	$0.581948\pi$
$198$	−57.8869	+	1104.55i	−0.0207770	+	0.396448i
$199$	−1262.51	−	2186.74i	−0.449734	−	0.778963i	0.548634	−	0.836062i	$-0.315148\pi$
$199$	−1262.51	−	2186.74i	−0.449734	−	0.778963i	−0.998368	+	0.0571000i	$0.981815\pi$
$200$	−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	−0.984509	−	0.175332i	$-0.943900\pi$
$211$	−260.419	+	801.487i	−0.0849667	+	0.261501i	0.899543	+	0.436833i	$0.143900\pi$
$212$	−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	−0.961956	−	0.273204i	$-0.911917\pi$
$223$	−2056.53	−	4036.17i	−0.617559	−	1.21203i	0.344397	−	0.938824i	$-0.388083\pi$
$224$	−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	0.745294	−	0.666736i	$-0.232309\pi$
$227$	1502.58	+	975.788i	0.439338	+	0.285310i	−0.305955	+	0.952046i	$0.598976\pi$
$228$	−1009.24	+	817.269i	−0.293152	+	0.237390i
$229$	5377.03	−	2394.01i	1.55163	−	0.690832i	0.561056	−	0.827778i	$-0.310395\pi$
$229$	5377.03	−	2394.01i	1.55163	−	0.690832i	0.990579	+	0.136945i	$0.0437285\pi$
$230$	−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	0.185449	−	0.982654i	$-0.440626\pi$
$233$	3940.96	−	4866.68i	1.10807	−	1.36836i	0.922623	−	0.385702i	$-0.126041\pi$
$234$	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	−0.189368	−	0.981906i	$-0.560644\pi$
$239$	−3398.23	−	1104.15i	−0.919720	−	0.298835i	−0.730352	+	0.683071i	$0.760644\pi$
$240$	−197.302	−	168.452i	−0.0530657	−	0.0453063i
$241$	4365.46	+	3930.68i	1.16682	+	1.05061i	0.997886	+	0.0649850i	$0.0206999\pi$
$241$	4365.46	+	3930.68i	1.16682	+	1.05061i	0.168937	+	0.985627i	$0.445967\pi$
$242$	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	$-0.981147\pi$
$251$		−	470.782i		−	0.118388i	0.998246	−	0.0591942i	$-0.0188531\pi$
$252$	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	−0.0216483	−	0.999766i	$-0.506891\pi$
$257$	1893.10	−	507.253i	0.459487	−	0.123119i	0.481135	+	0.876647i	$0.340225\pi$
$258$	−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	−0.461891	−	0.886937i	$-0.652829\pi$
$263$	−3533.85	+	185.201i	−0.828542	+	0.0434220i	−0.366651	+	0.930359i	$0.619496\pi$
$264$	−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	0.617393	−	0.786655i	$-0.288189\pi$
$269$	1967.33	+	875.911i	0.445911	+	0.198532i	−0.171482	+	0.985187i	$0.554856\pi$
$270$	4750.71	−	5007.95i	1.07081	−	1.12879i
$271$	1517.74	+	3408.90i	0.340207	+	0.764118i	0.999921	+	0.0126006i	$0.00401099\pi$
$271$	1517.74	+	3408.90i	0.340207	+	0.764118i	−0.659713	+	0.751517i	$0.729322\pi$
$272$	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	0.126774	−	0.991932i	$-0.459538\pi$
$277$	4524.38	−	6966.93i	0.981385	−	1.51120i	0.854611	−	0.519269i	$-0.173796\pi$
$278$	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	−0.820539	−	0.571591i	$-0.806327\pi$
$281$	−2498.80	+	1815.49i	−0.530484	+	0.385419i	0.290055	+	0.957010i	$0.406327\pi$
$282$	−1519.68	−	5671.53i	−0.320907	−	1.19764i
$283$	411.355	−	157.904i	0.0864046	−	0.0331676i	−0.314782	−	0.949164i	$-0.601931\pi$
$283$	411.355	−	157.904i	0.0864046	−	0.0331676i	0.401186	+	0.915996i	$0.368598\pi$
$284$	−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	−0.521014	−	0.853548i	$-0.674446\pi$
$293$	1667.78	−	1667.78i	0.332535	−	0.332535i	0.853548	+	0.521014i	$0.174446\pi$
$294$	−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	−0.992190	−	0.124738i	$-0.960191\pi$
$307$	−6008.04	−	6008.04i	−1.11693	−	1.11693i	−0.124738	−	0.992190i	$-0.539809\pi$
$308$	−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	0.710950	+	0.703242i	$0.248265\pi$
$311$	1905.88	+	8966.44i	0.347499	+	1.63486i	−0.363451	+	0.931613i	$0.618402\pi$
$312$	233.196	+	4449.65i	0.0423145	+	0.807410i
$313$	755.458	−	490.600i	0.136425	−	0.0885954i	−0.474622	−	0.880190i	$-0.657415\pi$
$313$	755.458	−	490.600i	0.136425	−	0.0885954i	0.611047	+	0.791594i	$0.290749\pi$
$314$	−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	0.711287	−	0.702902i	$-0.248113\pi$
$317$	968.684	+	784.425i	0.171630	+	0.138983i	−0.539657	+	0.841885i	$0.681446\pi$
$318$	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	0.245973	+	0.969277i	$0.420893\pi$
$331$	1245.95	+	11854.4i	0.206899	+	1.96851i	−0.0390738	+	0.999236i	$0.512441\pi$
$332$	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	0.970624	−	0.240601i	$-0.0773446\pi$
$337$	8330.07	+	4244.38i	1.34649	+	0.686072i	0.375868	+	0.926673i	$0.377345\pi$
$338$	−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	0.998426	−	0.0560877i	$-0.0178627\pi$
$347$	4757.29	+	5874.77i	0.735979	+	0.908859i	−0.262446	+	0.964947i	$0.584529\pi$
$348$	−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	0.970474	−	0.241204i	$-0.0775424\pi$
$353$	3533.46	+	4363.46i	0.532768	+	0.657914i	−0.437706	+	0.899118i	$0.644209\pi$
$354$	−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	−0.992304	−	0.123824i	$-0.960484\pi$
$359$	−240.966	+	1133.66i	−0.0354254	+	0.166663i	0.956879	+	0.290487i	$0.0938174\pi$
$360$	−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	0.939577	−	0.342336i	$-0.111218\pi$
$367$	86.2499	+	224.689i	0.0122676	+	0.0319582i	−0.927310	+	0.374295i	$0.877885\pi$
$368$	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	−0.769673	−	0.638438i	$-0.779581\pi$
$373$	450.373	−	8593.63i	0.0625186	−	1.19293i	0.832192	−	0.554487i	$-0.187086\pi$
$374$	−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	−0.647164	−	0.762351i	$-0.724045\pi$
$379$	2050.14	−	2821.78i	0.277860	−	0.382441i	0.925023	+	0.379910i	$0.124045\pi$
$380$	−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	0.452586	−	0.891721i	$-0.350501\pi$
$383$	−2440.15	−	1975.99i	−0.325550	−	0.263625i	−0.778136	+	0.628095i	$0.783835\pi$
$384$	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	0.976539	−	0.215339i	$-0.0690857\pi$
$389$	−24.2451	−	114.064i	−0.00316010	−	0.0148671i	−0.979699	+	0.200472i	$0.935752\pi$
$390$	−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	0.220665	−	0.975350i	$-0.429177\pi$
$397$	−2119.80	−	813.716i	−0.267984	−	0.102870i	−0.488650	+	0.872480i	$0.662510\pi$
$398$	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	−0.407599	−	0.913161i	$-0.633634\pi$
$401$	4713.79	−	8164.53i	0.587021	−	1.01675i	0.994620	−	0.103589i	$-0.0330328\pi$
$402$	−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	−0.341400	−	0.939918i	$-0.610901\pi$
$409$	5203.24	−	5778.78i	0.629056	−	0.698637i	0.970455	+	0.241281i	$0.0775676\pi$
$410$	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	−0.809133	−	0.587625i	$-0.800063\pi$
$419$	−4290.97	+	3117.57i	−0.500305	+	0.363493i	0.308829	+	0.951118i	$0.400063\pi$
$420$	8090.46	+	1071.93i	0.939938	+	0.124535i
$421$	−9715.67	−	7058.85i	−1.12473	−	0.817167i	−0.139814	−	0.990178i	$-0.544650\pi$
$421$	−9715.67	−	7058.85i	−1.12473	−	0.817167i	−0.984920	+	0.173011i	$0.944650\pi$
$422$	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	0.192620	−	0.981273i	$-0.438301\pi$
$431$	−3648.19	−	1624.28i	−0.407720	−	0.181528i	−0.600340	+	0.799745i	$0.704968\pi$
$432$	1015.67	−	272.147i	0.113116	−	0.0303094i
$433$	−118.142	+	745.917i	−0.0131121	+	0.0827864i	−0.993377	−	0.114904i	$-0.963344\pi$
$433$	−118.142	+	745.917i	−0.0131121	+	0.0827864i	0.980265	+	0.197690i	$0.0633440\pi$
$434$	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	0.816350	−	0.577557i	$-0.195994\pi$
$439$	1440.65	+	1600.00i	0.156625	+	0.173950i	−0.659725	+	0.751507i	$0.729327\pi$
$440$	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	−0.992452	−	0.122637i	$-0.960865\pi$
$443$	−16695.9	+	4473.65i	−1.79062	+	0.479796i	−0.798170	+	0.602432i	$0.794198\pi$
$444$	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	$0.0754532\pi$
$449$			4468.40i			0.469659i	−0.972037	+	0.234830i	$0.924547\pi$
$450$	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	0.958140	+	0.286298i	$0.0924249\pi$
$457$	2652.58	+	9899.58i	0.271516	+	1.01331i	−0.686625	+	0.727012i	$0.740908\pi$
$458$	−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	0.258368	−	0.966047i	$-0.416815\pi$
$461$	−994.127	−	323.012i	−0.100436	−	0.0326337i	−0.358804	+	0.933413i	$0.616815\pi$
$462$	3182.97	+	856.290i	0.320531	+	0.0862299i
$463$	4014.05	−	7878.01i	0.402913	−	0.790761i	−0.597021	−	0.802225i	$-0.703649\pi$
$463$	4014.05	−	7878.01i	0.402913	−	0.790761i	0.999934	+	0.0114644i	$0.00364930\pi$
$464$	−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	0.217808	−	0.975992i	$-0.430109\pi$
$467$	11375.5	−	14047.6i	1.12719	−	1.39196i	0.909379	−	0.415969i	$-0.136557\pi$
$468$	−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	0.961590	+	0.274491i	$0.0885095\pi$
$479$	−378.000	+	3596.43i	−0.0360569	+	0.343059i	−0.997646	+	0.0685673i	$0.978157\pi$
$480$	−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	0.920416	+	0.390941i	$0.127850\pi$
$487$	493.365	+	9413.97i	0.0459066	+	0.875950i	−0.874509	+	0.485009i	$0.838816\pi$
$488$	−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	−0.928103	−	0.372323i	$-0.878561\pi$
$491$	−4309.48	−	13263.2i	−0.396098	−	1.21906i	0.532005	−	0.846741i	$-0.321439\pi$
$492$	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	0.357115	−	0.934060i	$-0.383760\pi$
$499$	−3045.84	−	1758.52i	−0.273248	−	0.157760i	−0.630363	+	0.776301i	$0.717094\pi$
$500$	−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	−0.602850	−	0.797854i	$-0.705968\pi$
$503$	−10487.4	+	1661.05i	−0.929645	+	0.147241i	−0.326794	+	0.945096i	$0.605968\pi$
$504$	−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	0.00659344	−	0.999978i	$-0.497901\pi$
$509$	−4525.80	−	961.988i	−0.394111	−	0.0837709i	−0.400704	+	0.916207i	$0.631235\pi$
$510$	−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	0.667307	−	0.744783i	$-0.267447\pi$
$521$	13856.4	+	1456.37i	1.16518	+	0.122466i	0.497875	+	0.867249i	$0.334114\pi$
$522$	−3570.59	−	4409.31i	−0.299388	−	0.369713i
$523$	11126.9	+	583.134i	0.930294	+	0.0487546i	0.511459	−	0.859308i	$-0.329105\pi$
$523$	11126.9	+	583.134i	0.930294	+	0.0487546i	0.418835	+	0.908062i	$0.362439\pi$
$524$	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	−0.269500	−	0.963000i	$-0.586858\pi$
$541$	−11418.0	−	2426.97i	−0.907388	−	0.192871i	−0.637888	+	0.770129i	$0.720192\pi$
$542$	−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	−0.607801	−	0.794089i	$-0.707948\pi$
$547$	−12031.6	+	1905.62i	−0.940467	+	0.148955i	−0.332666	+	0.943045i	$0.607948\pi$
$548$	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	0.329539	−	0.944142i	$-0.393107\pi$
$557$	1877.95	+	503.196i	0.142857	+	0.0382784i	−0.186682	+	0.982420i	$0.559773\pi$
$558$	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	0.809321	+	0.587367i	$0.199835\pi$
$563$	879.401	+	16780.0i	0.0658301	+	1.25611i	−0.743491	+	0.668746i	$0.766831\pi$
$564$	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	−0.611485	−	0.791256i	$-0.709428\pi$
$569$	−14184.9	+	1490.89i	−1.04510	+	0.109844i	−0.433611	+	0.901100i	$0.642761\pi$
$570$	−2160.00	+	4530.56i	−0.158723	+	0.332920i
$571$	−2331.26	+	22180.5i	−0.170859	+	1.62561i	0.487650	+	0.873039i	$0.337854\pi$
$571$	−2331.26	+	22180.5i	−0.170859	+	1.62561i	−0.658509	+	0.752573i	$0.728813\pi$
$572$	−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	−0.237070	−	0.971493i	$-0.576187\pi$
$577$	−16923.0	−	10990.0i	−1.22100	−	0.792925i	−0.983928	+	0.178568i	$0.942854\pi$
$578$	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	−0.962593	−	0.270952i	$-0.912662\pi$
$587$	−2525.67	+	4956.91i	−0.177591	+	0.348541i	0.785002	+	0.619493i	$0.212662\pi$
$588$	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	0.998307	−	0.0581710i	$-0.0185269\pi$
$593$	1511.37	+	5640.52i	0.104662	+	0.390605i	−0.893644	+	0.448776i	$0.851860\pi$
$594$	−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	0.208897	−	0.977938i	$-0.433013\pi$
$599$	17009.7	−	9820.57i	1.16026	−	0.669879i	0.951367	+	0.308058i	$0.0996793\pi$
$600$	−8841.57	−	2365.78i	−0.601593	−	0.160971i
$601$		−	18645.0i		−	1.26547i	−0.774370	−	0.632733i	$-0.781933\pi$
$601$		−	18645.0i		−	1.26547i	0.774370	−	0.632733i	$-0.218067\pi$
$602$	−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	−0.123775	−	0.992310i	$-0.539500\pi$
$607$	3965.85	−	1062.64i	0.265187	−	0.0710567i	0.388963	+	0.921254i	$0.372834\pi$
$608$	−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	0.144252	−	0.989541i	$-0.453922\pi$
$613$	5936.54	−	311.121i	0.391149	−	0.0204993i	0.246897	+	0.969042i	$0.420589\pi$
$614$	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	−0.967323	−	0.253545i	$-0.918403\pi$
$617$	475.192	−	3000.24i	0.0310057	−	0.195762i	0.998329	+	0.0577833i	$0.0184032\pi$
$618$	20486.0	−	5489.21i	1.33344	−	0.357295i
$619$	−9358.89	−	4166.85i	−0.607699	−	0.270565i	0.0797302	−	0.996816i	$-0.474594\pi$
$619$	−9358.89	−	4166.85i	−0.607699	−	0.270565i	−0.687429	+	0.726251i	$0.741261\pi$
$620$	−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	−0.739369	−	0.673300i	$-0.764876\pi$
$631$	−5191.06	+	3771.52i	−0.327500	+	0.237943i	0.411869	+	0.911243i	$0.364876\pi$
$632$	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	−0.00497419	−	0.999988i	$-0.501583\pi$
$641$	16067.4	−	17844.7i	0.990055	−	1.09957i	0.995030	−	0.0995802i	$-0.0317500\pi$
$642$	−12948.3	+	15989.8i	−0.795992	+	0.982968i
$643$	19156.4	−	19156.4i	1.17489	−	1.17489i	0.193859	−	0.981029i	$-0.437900\pi$
$643$	19156.4	−	19156.4i	1.17489	−	1.17489i	0.981029	−	0.193859i	$-0.0621003\pi$
$644$	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	−0.884565	−	0.466417i	$-0.845545\pi$
$647$	−10076.0	+	8159.35i	−0.612252	+	0.495792i	0.272313	+	0.962209i	$0.412211\pi$
$648$	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	0.980683	+	0.195602i	$0.0626662\pi$
$653$	30709.4	+	11788.2i	1.84036	+	0.706447i	0.859673	+	0.510844i	$0.170667\pi$
$654$	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	−0.719269	−	0.694732i	$-0.755523\pi$
$659$	−15103.9	+	4907.56i	−0.892816	+	0.290093i	−0.173547	+	0.984826i	$0.555523\pi$
$660$	−5318.40	−	2201.87i	−0.313665	−	0.129860i
$661$	2221.23	+	10450.1i	0.130705	+	0.614918i	0.993922	+	0.110085i	$0.0351124\pi$
$661$	2221.23	+	10450.1i	0.130705	+	0.614918i	−0.863217	+	0.504833i	$0.831554\pi$
$662$	−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	−0.230415	−	0.973093i	$-0.574008\pi$
$673$	7357.26	−	3748.71i	0.421399	−	0.214714i	0.651814	+	0.758379i	$0.274008\pi$
$674$	−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	−0.740612	−	0.671933i	$-0.765464\pi$
$677$	1165.74	−	22243.7i	0.0661790	−	1.26277i	0.806791	−	0.590837i	$-0.201202\pi$
$678$	−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	0.864591	−	0.502476i	$-0.167578\pi$
$683$	−2037.50	−	5307.87i	−0.114148	−	0.297365i	−0.978739	+	0.205112i	$0.934244\pi$
$684$	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	−0.727469	−	0.686141i	$-0.759303\pi$
$691$	3926.85	−	18474.4i	0.216186	−	1.01707i	0.943654	−	0.330933i	$-0.107363\pi$
$692$	−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	−0.815792	−	0.578345i	$-0.803699\pi$
$709$	3109.40	−	14628.6i	0.164705	−	0.774877i	0.980497	−	0.196532i	$-0.0629679\pi$
$710$	−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	0.959533	+	0.281597i	$0.0908641\pi$
$719$	1533.01	+	14585.6i	0.0795154	+	0.756538i	−0.880017	+	0.474941i	$0.842469\pi$
$720$	−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	−0.473002	−	0.881061i	$-0.656830\pi$
$727$	−749.434	+	381.855i	−0.0382324	+	0.0194804i	0.434770	+	0.900542i	$0.356830\pi$
$728$	−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	0.893537	−	0.448990i	$-0.148216\pi$
$733$	12703.6	+	10287.2i	0.640134	+	0.518371i	−0.253402	+	0.967361i	$0.581550\pi$
$734$	−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	0.999950	−	0.00999138i	$-0.00318041\pi$
$739$	1655.09	+	7786.59i	0.0823864	+	0.387597i	−0.917564	+	0.397589i	$0.869847\pi$
$740$	−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	0.304943	−	0.952371i	$-0.401363\pi$
$743$	−13112.2	−	13112.2i	−0.647428	−	0.647428i	−0.952371	+	0.304943i	$0.901363\pi$
$744$	−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	−0.320353	−	0.947298i	$-0.603801\pi$
$751$	13587.5	−	23534.3i	0.660208	−	1.14351i	0.980561	−	0.196215i	$-0.0628652\pi$
$752$	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	−0.803158	−	0.595766i	$-0.796849\pi$
$757$	−4319.52	+	4319.52i	−0.207392	+	0.207392i	0.595766	+	0.803158i	$0.296849\pi$
$758$	−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	−0.728775	−	0.684753i	$-0.759910\pi$
$761$	−2602.12	+	2342.96i	−0.123951	+	0.111606i	0.604824	+	0.796359i	$0.293243\pi$
$762$	−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

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)

\(f(q)\)	\(=\)	\(q+(-4.61688 - 0.241960i) q^{2} +(1.85463 + 2.29028i) q^{3} +(13.3008 + 1.39797i) q^{4} +(-10.3285 + 4.28033i) q^{5} +(-8.00844 - 11.0227i) q^{6} +(-16.5101 + 8.39150i) q^{7} +(-24.5397 - 3.88671i) q^{8} +(3.80790 - 17.9147i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9}+O(q^{10}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22} + 296 q^{23} + 32 q^{25} - 48 q^{26} + 226 q^{28} - 200 q^{29} - 38 q^{30} - 18 q^{31} - 964 q^{32} - 1092 q^{33} + 288 q^{35} + 7400 q^{36} - 392 q^{37} + 5424 q^{38} + 2430 q^{39} + 2172 q^{40} - 2098 q^{42} + 1560 q^{43} - 10 q^{44} - 4224 q^{45} - 6 q^{46} + 96 q^{47} + 6232 q^{50} - 16 q^{51} - 8928 q^{52} - 2384 q^{53} - 30 q^{54} + 244 q^{56} + 1556 q^{57} + 640 q^{58} + 4890 q^{59} + 3676 q^{60} - 18 q^{61} + 224 q^{63} - 9700 q^{64} - 1116 q^{65} - 2610 q^{66} - 2404 q^{67} - 13614 q^{68} - 1700 q^{70} - 24 q^{71} - 518 q^{72} - 4200 q^{73} - 16104 q^{75} - 722 q^{77} - 356 q^{78} - 10 q^{79} + 6414 q^{80} - 6810 q^{81} + 1692 q^{82} + 20620 q^{84} + 2712 q^{85} - 6 q^{86} + 9102 q^{87} + 1650 q^{88} + 20370 q^{89} - 12 q^{91} + 1612 q^{92} - 4604 q^{93} - 30 q^{94} + 1652 q^{95} - 2610 q^{96} - 19478 q^{98}+O(q^{100}) \) 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