LMFDB - Embedded newform 125.3.f.c.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,3,Mod(7,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([17]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("125.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	125.f (of order $20$, degree $8$, not 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:	$3.40600330450$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.3
Character	$\chi$	$=$	125.7
Dual form			125.3.f.c.18.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61837 - 0.824603i) q^{2} +(-3.42034 + 0.541729i) q^{3} +(-0.411975 + 0.567034i) q^{4} +(-5.08868 + 3.69715i) q^{6} +(8.06323 + 8.06323i) q^{7} +(-1.33571 + 8.43332i) q^{8} +(2.84577 - 0.924645i) q^{9} +O(q^{10})$	\(q+(1.61837 - 0.824603i) q^{2} +(-3.42034 + 0.541729i) q^{3} +(-0.411975 + 0.567034i) q^{4} +(-5.08868 + 3.69715i) q^{6} +(8.06323 + 8.06323i) q^{7} +(-1.33571 + 8.43332i) q^{8} +(2.84577 - 0.924645i) q^{9} +(-1.43991 + 4.43160i) q^{11} +(1.10192 - 2.16263i) q^{12} +(7.37917 + 3.75988i) q^{13} +(19.6983 + 6.40037i) q^{14} +(3.92612 + 12.0833i) q^{16} +(-16.4746 - 2.60932i) q^{17} +(3.84305 - 3.84305i) q^{18} +(-2.60721 - 3.58851i) q^{19} +(-31.9471 - 23.2109i) q^{21} +(1.32399 + 8.35934i) q^{22} +(-1.57553 - 3.09215i) q^{23} -29.5684i q^{24} +15.0427 q^{26} +(18.5372 - 9.44519i) q^{27} +(-7.89398 + 1.25028i) q^{28} +(-14.6125 + 20.1124i) q^{29} +(39.2975 - 28.5513i) q^{31} +(-7.83247 - 7.83247i) q^{32} +(2.52427 - 15.9376i) q^{33} +(-28.8138 + 9.36216i) q^{34} +(-0.648078 + 1.99458i) q^{36} +(12.2064 - 23.9564i) q^{37} +(-7.17853 - 3.65765i) q^{38} +(-27.2761 - 8.86255i) q^{39} +(10.7638 + 33.1275i) q^{41} +(-70.8422 - 11.2203i) q^{42} +(13.5798 - 13.5798i) q^{43} +(-1.91966 - 2.64219i) q^{44} +(-5.09959 - 3.70507i) q^{46} +(8.94405 + 56.4705i) q^{47} +(-19.9746 - 39.2023i) q^{48} +81.0315i q^{49} +57.7624 q^{51} +(-5.17201 + 2.63527i) q^{52} +(15.9105 - 2.51997i) q^{53} +(22.2117 - 30.5717i) q^{54} +(-78.7699 + 57.2297i) q^{56} +(10.8615 + 10.8615i) q^{57} +(-7.06378 + 44.5989i) q^{58} +(50.4257 - 16.3843i) q^{59} +(25.1583 - 77.4292i) q^{61} +(40.0545 - 78.6115i) q^{62} +(30.4017 + 15.4904i) q^{63} +(-67.4679 - 21.9217i) q^{64} +(-9.05700 - 27.8746i) q^{66} +(-3.74472 - 0.593105i) q^{67} +(8.26671 - 8.26671i) q^{68} +(7.06395 + 9.72269i) q^{69} +(-23.0210 - 16.7257i) q^{71} +(3.99672 + 25.2343i) q^{72} +(19.4330 + 38.1394i) q^{73} -48.8358i q^{74} +3.10891 q^{76} +(-47.3434 + 24.1226i) q^{77} +(-51.4511 + 8.14905i) q^{78} +(46.6168 - 64.1625i) q^{79} +(-80.0737 + 58.1770i) q^{81} +(44.7368 + 44.7368i) q^{82} +(9.69615 - 61.2191i) q^{83} +(26.3228 - 8.55280i) q^{84} +(10.7792 - 33.1750i) q^{86} +(39.0843 - 76.7073i) q^{87} +(-35.4498 - 18.0626i) q^{88} +(91.0024 + 29.5685i) q^{89} +(29.1832 + 89.8167i) q^{91} +(2.40243 + 0.380508i) q^{92} +(-118.944 + 118.944i) q^{93} +(61.0406 + 84.0152i) q^{94} +(31.0328 + 22.5467i) q^{96} +(22.8066 + 143.995i) q^{97} +(66.8188 + 131.139i) q^{98} +13.9427i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} + 10 q^{3} - 10 q^{4} - 6 q^{6} + 10 q^{7} + 10 q^{8} - 10 q^{9}+O(q^{10}) $ 32 * q + 10 * q^2 + 10 * q^3 - 10 * q^4 - 6 * q^6 + 10 * q^7 + 10 * q^8 - 10 * q^9	$ 32 q + 10 q^{2} + 10 q^{3} - 10 q^{4} - 6 q^{6} + 10 q^{7} + 10 q^{8} - 10 q^{9} - 6 q^{11} + 10 q^{12} + 10 q^{13} - 10 q^{14} + 2 q^{16} - 60 q^{17} - 140 q^{18} + 90 q^{19} - 6 q^{21} - 70 q^{22} - 10 q^{23} + 4 q^{26} + 100 q^{27} + 250 q^{28} - 110 q^{29} - 6 q^{31} + 290 q^{32} + 190 q^{33} - 260 q^{34} - 58 q^{36} - 50 q^{37} - 320 q^{38} + 390 q^{39} - 86 q^{41} - 690 q^{42} - 230 q^{43} + 340 q^{44} - 6 q^{46} - 70 q^{47} - 160 q^{48} - 16 q^{51} + 320 q^{52} + 190 q^{53} - 660 q^{54} - 70 q^{56} + 650 q^{57} + 640 q^{58} - 260 q^{59} + 114 q^{61} - 60 q^{62} + 20 q^{63} + 340 q^{64} + 138 q^{66} - 270 q^{67} - 710 q^{68} + 340 q^{69} - 66 q^{71} - 360 q^{72} - 30 q^{73} - 80 q^{76} + 250 q^{77} + 500 q^{78} - 210 q^{79} + 62 q^{81} - 30 q^{82} - 10 q^{84} - 6 q^{86} - 300 q^{87} - 190 q^{88} - 10 q^{89} - 6 q^{91} + 30 q^{92} - 520 q^{93} + 790 q^{94} + 174 q^{96} - 270 q^{97} - 170 q^{98}+O(q^{100}) $ 32 * q + 10 * q^2 + 10 * q^3 - 10 * q^4 - 6 * q^6 + 10 * q^7 + 10 * q^8 - 10 * q^9 - 6 * q^11 + 10 * q^12 + 10 * q^13 - 10 * q^14 + 2 * q^16 - 60 * q^17 - 140 * q^18 + 90 * q^19 - 6 * q^21 - 70 * q^22 - 10 * q^23 + 4 * q^26 + 100 * q^27 + 250 * q^28 - 110 * q^29 - 6 * q^31 + 290 * q^32 + 190 * q^33 - 260 * q^34 - 58 * q^36 - 50 * q^37 - 320 * q^38 + 390 * q^39 - 86 * q^41 - 690 * q^42 - 230 * q^43 + 340 * q^44 - 6 * q^46 - 70 * q^47 - 160 * q^48 - 16 * q^51 + 320 * q^52 + 190 * q^53 - 660 * q^54 - 70 * q^56 + 650 * q^57 + 640 * q^58 - 260 * q^59 + 114 * q^61 - 60 * q^62 + 20 * q^63 + 340 * q^64 + 138 * q^66 - 270 * q^67 - 710 * q^68 + 340 * q^69 - 66 * q^71 - 360 * q^72 - 30 * q^73 - 80 * q^76 + 250 * q^77 + 500 * q^78 - 210 * q^79 + 62 * q^81 - 30 * q^82 - 10 * q^84 - 6 * q^86 - 300 * q^87 - 190 * q^88 - 10 * q^89 - 6 * q^91 + 30 * q^92 - 520 * q^93 + 790 * q^94 + 174 * q^96 - 270 * q^97 - 170 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{20}\right)$

Coefficient data

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

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

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

$2$	1.61837	−	0.824603i	0.809187	−	0.412302i	0.000107292	−	1.00000i	$-0.499966\pi$
$2$	1.61837	−	0.824603i	0.809187	−	0.412302i	0.809080	+	0.587698i	$0.199966\pi$
$3$	−3.42034	+	0.541729i	−1.14011	+	0.180576i	−0.697806	−	0.716287i	$-0.745840\pi$
$3$	−3.42034	+	0.541729i	−1.14011	+	0.180576i	−0.442308	+	0.896863i	$0.645840\pi$
$4$	−0.411975	+	0.567034i	−0.102994	+	0.141759i
$5$		0			0
$5$		0			0
$6$	−5.08868	+	3.69715i	−0.848114	+	0.616191i
$7$	8.06323	+	8.06323i	1.15189	+	1.15189i	0.986173	+	0.165717i	$0.0529939\pi$
$7$	8.06323	+	8.06323i	1.15189	+	1.15189i	0.165717	+	0.986173i	$0.447006\pi$
$8$	−1.33571	+	8.43332i	−0.166963	+	1.05416i
$9$	2.84577	−	0.924645i	0.316196	−	0.102738i
$10$		0			0
$11$	−1.43991	+	4.43160i	−0.130901	+	0.402872i	−0.994930	−	0.100570i	$-0.967933\pi$
$11$	−1.43991	+	4.43160i	−0.130901	+	0.402872i	0.864029	+	0.503442i	$0.167933\pi$
$12$	1.10192	−	2.16263i	0.0918263	−	0.180219i
$13$	7.37917	+	3.75988i	0.567629	+	0.289221i	0.714157	−	0.699985i	$-0.246810\pi$
$13$	7.37917	+	3.75988i	0.567629	+	0.289221i	−0.146529	+	0.989206i	$0.546810\pi$
$14$	19.6983	+	6.40037i	1.40702	+	0.457169i
$15$		0			0
$16$	3.92612	+	12.0833i	0.245382	+	0.755209i
$17$	−16.4746	−	2.60932i	−0.969096	−	0.153490i	−0.348232	−	0.937408i	$-0.613218\pi$
$17$	−16.4746	−	2.60932i	−0.969096	−	0.153490i	−0.620864	+	0.783919i	$0.713218\pi$
$18$	3.84305	−	3.84305i	0.213503	−	0.213503i
$19$	−2.60721	−	3.58851i	−0.137221	−	0.188869i	0.734876	−	0.678202i	$-0.237240\pi$
$19$	−2.60721	−	3.58851i	−0.137221	−	0.188869i	−0.872097	+	0.489333i	$0.837240\pi$
$20$		0			0
$21$	−31.9471	−	23.2109i	−1.52129	−	1.10528i
$22$	1.32399	+	8.35934i	0.0601813	+	0.379970i
$23$	−1.57553	−	3.09215i	−0.0685012	−	0.134441i	0.854217	−	0.519917i	$-0.174037\pi$
$23$	−1.57553	−	3.09215i	−0.0685012	−	0.134441i	−0.922718	+	0.385476i	$0.874037\pi$
$24$		−	29.5684i		−	1.23202i
$25$		0			0
$26$	15.0427			0.578564
$27$	18.5372	−	9.44519i	0.686564	−	0.349822i
$28$	−7.89398	+	1.25028i	−0.281928	+	0.0446530i
$29$	−14.6125	+	20.1124i	−0.503880	+	0.693531i	−0.982872	−	0.184288i	$-0.941002\pi$
$29$	−14.6125	+	20.1124i	−0.503880	+	0.693531i	0.478992	+	0.877819i	$0.341002\pi$
$30$		0			0
$31$	39.2975	−	28.5513i	1.26766	−	0.921009i	0.268553	−	0.963265i	$-0.413454\pi$
$31$	39.2975	−	28.5513i	1.26766	−	0.921009i	0.999107	+	0.0422559i	$0.0134545\pi$
$32$	−7.83247	−	7.83247i	−0.244765	−	0.244765i
$33$	2.52427	−	15.9376i	0.0764931	−	0.482958i
$34$	−28.8138	+	9.36216i	−0.847464	+	0.275358i
$35$		0			0
$36$	−0.648078	+	1.99458i	−0.0180022	+	0.0554049i
$37$	12.2064	−	23.9564i	0.329902	−	0.647469i	−0.665163	−	0.746699i	$-0.731638\pi$
$37$	12.2064	−	23.9564i	0.329902	−	0.647469i	0.995065	+	0.0992294i	$0.0316378\pi$
$38$	−7.17853	−	3.65765i	−0.188909	−	0.0962538i
$39$	−27.2761	−	8.86255i	−0.699388	−	0.227245i
$40$		0			0
$41$	10.7638	+	33.1275i	0.262531	+	0.807987i	0.992252	+	0.124242i	$0.0396500\pi$
$41$	10.7638	+	33.1275i	0.262531	+	0.807987i	−0.729721	+	0.683745i	$0.760350\pi$
$42$	−70.8422	−	11.2203i	−1.68672	−	0.267150i
$43$	13.5798	−	13.5798i	0.315808	−	0.315808i	−0.531346	−	0.847155i	$-0.678314\pi$
$43$	13.5798	−	13.5798i	0.315808	−	0.315808i	0.847155	+	0.531346i	$0.178314\pi$
$44$	−1.91966	−	2.64219i	−0.0436286	−	0.0600497i
$45$		0			0
$46$	−5.09959	−	3.70507i	−0.110861	−	0.0805449i
$47$	8.94405	+	56.4705i	0.190299	+	1.20150i	0.879131	+	0.476580i	$0.158124\pi$
$47$	8.94405	+	56.4705i	0.190299	+	1.20150i	−0.688832	+	0.724921i	$0.741876\pi$
$48$	−19.9746	−	39.2023i	−0.416137	−	0.816714i
$49$			81.0315i			1.65370i
$50$		0			0
$51$	57.7624			1.13260
$52$	−5.17201	+	2.63527i	−0.0994617	+	0.0506783i
$53$	15.9105	−	2.51997i	0.300198	−	0.0475466i	−0.00451871	−	0.999990i	$-0.501438\pi$
$53$	15.9105	−	2.51997i	0.300198	−	0.0475466i	0.304716	+	0.952443i	$0.401438\pi$
$54$	22.2117	−	30.5717i	0.411327	−	0.566143i
$55$		0			0
$56$	−78.7699	+	57.2297i	−1.40661	+	1.02196i
$57$	10.8615	+	10.8615i	0.190553	+	0.190553i
$58$	−7.06378	+	44.5989i	−0.121789	+	0.768947i
$59$	50.4257	−	16.3843i	0.854672	−	0.277700i	0.151270	−	0.988492i	$-0.451664\pi$
$59$	50.4257	−	16.3843i	0.854672	−	0.277700i	0.703402	+	0.710793i	$0.251664\pi$
$60$		0			0
$61$	25.1583	−	77.4292i	0.412430	−	1.26933i	−0.502099	−	0.864810i	$-0.667439\pi$
$61$	25.1583	−	77.4292i	0.412430	−	1.26933i	0.914529	−	0.404520i	$-0.132561\pi$
$62$	40.0545	−	78.6115i	0.646041	−	1.26793i
$63$	30.4017	+	15.4904i	0.482567	+	0.245880i
$64$	−67.4679	−	21.9217i	−1.05419	−	0.342526i
$65$		0			0
$66$	−9.05700	−	27.8746i	−0.137227	−	0.422342i
$67$	−3.74472	−	0.593105i	−0.0558913	−	0.00885232i	0.128426	−	0.991719i	$-0.459007\pi$
$67$	−3.74472	−	0.593105i	−0.0558913	−	0.00885232i	−0.184318	+	0.982867i	$0.559007\pi$
$68$	8.26671	−	8.26671i	0.121569	−	0.121569i
$69$	7.06395	+	9.72269i	0.102376	+	0.140909i
$70$		0			0
$71$	−23.0210	−	16.7257i	−0.324239	−	0.235574i	0.413743	−	0.910394i	$-0.364221\pi$
$71$	−23.0210	−	16.7257i	−0.324239	−	0.235574i	−0.737982	+	0.674820i	$0.764221\pi$
$72$	3.99672	+	25.2343i	0.0555100	+	0.350476i
$73$	19.4330	+	38.1394i	0.266206	+	0.522458i	0.984955	−	0.172811i	$-0.0552851\pi$
$73$	19.4330	+	38.1394i	0.266206	+	0.522458i	−0.718749	+	0.695269i	$0.755285\pi$
$74$		−	48.8358i		−	0.659943i
$75$		0			0
$76$	3.10891			0.0409067
$77$	−47.3434	+	24.1226i	−0.614849	+	0.313281i
$78$	−51.4511	+	8.14905i	−0.659629	+	0.104475i
$79$	46.6168	−	64.1625i	0.590086	−	0.812184i	−0.404669	−	0.914463i	$-0.632613\pi$
$79$	46.6168	−	64.1625i	0.590086	−	0.812184i	0.994756	+	0.102279i	$0.0326134\pi$
$80$		0			0
$81$	−80.0737	+	58.1770i	−0.988565	+	0.718234i
$82$	44.7368	+	44.7368i	0.545571	+	0.545571i
$83$	9.69615	−	61.2191i	0.116821	−	0.737579i	−0.857844	−	0.513910i	$-0.828197\pi$
$83$	9.69615	−	61.2191i	0.116821	−	0.737579i	0.974665	−	0.223669i	$-0.0718035\pi$
$84$	26.3228	−	8.55280i	0.313367	−	0.101819i
$85$		0			0
$86$	10.7792	−	33.1750i	0.125340	−	0.385756i
$87$	39.0843	−	76.7073i	0.449245	−	0.881693i
$88$	−35.4498	−	18.0626i	−0.402838	−	0.205256i
$89$	91.0024	+	29.5685i	1.02250	+	0.332230i	0.771820	−	0.635841i	$-0.219346\pi$
$89$	91.0024	+	29.5685i	1.02250	+	0.332230i	0.250678	+	0.968070i	$0.419346\pi$
$90$		0			0
$91$	29.1832	+	89.8167i	0.320695	+	0.986997i
$92$	2.40243	+	0.380508i	0.0261134	+	0.00413595i
$93$	−118.944	+	118.944i	−1.27896	+	1.27896i
$94$	61.0406	+	84.0152i	0.649368	+	0.893778i
$95$		0			0
$96$	31.0328	+	22.5467i	0.323258	+	0.234861i
$97$	22.8066	+	143.995i	0.235119	+	1.48448i	0.769177	+	0.639036i	$0.220667\pi$
$97$	22.8066	+	143.995i	0.235119	+	1.48448i	−0.534058	+	0.845448i	$0.679333\pi$
$98$	66.8188	+	131.139i	0.681824	+	1.33816i
$99$			13.9427i			0.140835i
$100$		0			0
$101$	−114.662			−1.13526			−0.567632	−	0.823282i	$-0.692140\pi$
$101$	−114.662			−1.13526			−0.567632	+	0.823282i	$0.692140\pi$
$102$	93.4812	−	47.6311i	0.916483	−	0.466971i
$103$	157.550	−	24.9534i	1.52961	−	0.242266i	0.665818	−	0.746114i	$-0.268083\pi$
$103$	157.550	−	24.9534i	1.52961	−	0.242266i	0.863792	+	0.503848i	$0.168083\pi$
$104$	−41.5646	+	57.2088i	−0.399660	+	0.550085i
$105$		0			0
$106$	23.6711	−	17.1981i	0.223313	−	0.162246i
$107$	−35.0684	−	35.0684i	−0.327742	−	0.327742i	0.523985	−	0.851727i	$-0.324445\pi$
$107$	−35.0684	−	35.0684i	−0.327742	−	0.327742i	−0.851727	+	0.523985i	$0.824445\pi$
$108$	−2.28112	+	14.4024i	−0.0211215	+	0.133356i
$109$	−67.4721	+	21.9230i	−0.619010	+	0.201129i	−0.601701	−	0.798721i	$-0.705510\pi$
$109$	−67.4721	+	21.9230i	−0.619010	+	0.201129i	−0.0173095	+	0.999850i	$0.505510\pi$
$110$		0			0
$111$	−28.7721	+	88.5515i	−0.259208	+	0.797761i
$112$	−65.7736	+	129.088i	−0.587264	+	1.15257i
$113$	−99.6694	−	50.7841i	−0.882030	−	0.449417i	−0.0465362	−	0.998917i	$-0.514818\pi$
$113$	−99.6694	−	50.7841i	−0.882030	−	0.449417i	−0.835494	+	0.549500i	$0.814818\pi$
$114$	26.5345	+	8.62158i	0.232759	+	0.0756279i
$115$		0			0
$116$	−5.38444	−	16.5716i	−0.0464176	−	0.142859i
$117$	24.4759	+	3.87661i	0.209196	+	0.0331334i
$118$	68.0971	−	68.0971i	0.577094	−	0.577094i
$119$	−111.799	−	153.878i	−0.939489	−	1.29310i
$120$		0			0
$121$	80.3254	+	58.3598i	0.663846	+	0.482312i
$122$	−23.1328	−	146.055i	−0.189613	−	1.19717i
$123$	−54.7619	−	107.476i	−0.445219	−	0.873791i
$124$			34.0454i			0.274560i
$125$		0			0
$126$	61.9748			0.491864
$127$	3.65232	−	1.86095i	0.0287584	−	0.0146531i	−0.439552	−	0.898217i	$-0.644863\pi$
$127$	3.65232	−	1.86095i	0.0287584	−	0.0146531i	0.468311	+	0.883564i	$0.344863\pi$
$128$	−83.5034	+	13.2256i	−0.652370	+	0.103325i
$129$	−39.0909	+	53.8040i	−0.303030	+	0.417085i
$130$		0			0
$131$	72.3111	−	52.5371i	0.551993	−	0.401047i	−0.276527	−	0.961006i	$-0.589183\pi$
$131$	72.3111	−	52.5371i	0.551993	−	0.401047i	0.828520	+	0.559960i	$0.189183\pi$
$132$	7.99725	+	7.99725i	0.0605852	+	0.0605852i
$133$	7.91249	−	49.9575i	0.0594924	−	0.375620i
$134$	−6.54944	+	2.12804i	−0.0488764	+	0.0158809i
$135$		0			0
$136$	44.0105	−	135.450i	0.323607	−	0.995960i
$137$	−36.3518	+	71.3445i	−0.265342	+	0.520763i	−0.984783	−	0.173791i	$-0.944398\pi$
$137$	−36.3518	+	71.3445i	−0.265342	+	0.520763i	0.719441	+	0.694554i	$0.244398\pi$
$138$	19.4495	+	9.91001i	0.140938	+	0.0718116i
$139$	−34.6269	−	11.2510i	−0.249115	−	0.0809422i	0.181798	−	0.983336i	$-0.441808\pi$
$139$	−34.6269	−	11.2510i	−0.249115	−	0.0809422i	−0.430913	+	0.902394i	$0.641808\pi$
$140$		0			0
$141$	−61.1834	−	188.303i	−0.433925	−	1.33548i
$142$	−51.0487	−	8.08531i	−0.359498	−	0.0569388i
$143$	−27.2876	+	27.2876i	−0.190823	+	0.190823i
$144$	22.3456	+	30.7561i	0.155178	+	0.213584i
$145$		0			0
$146$	62.8998	+	45.6994i	0.430820	+	0.313009i
$147$	−43.8971	−	277.155i	−0.298620	−	1.88541i
$148$	8.55536	+	16.7908i	0.0578065	+	0.113452i
$149$		−	134.550i		−	0.903021i	−0.892266	−	0.451510i	$-0.850885\pi$
$149$		−	134.550i		−	0.903021i	0.892266	−	0.451510i	$-0.149115\pi$
$150$		0			0
$151$	4.03813			0.0267426			0.0133713	−	0.999911i	$-0.495744\pi$
$151$	4.03813			0.0267426			0.0133713	+	0.999911i	$0.495744\pi$
$152$	33.7455	−	17.1942i	0.222010	−	0.113120i
$153$	−49.2956	+	7.80766i	−0.322194	+	0.0510305i
$154$	−56.7277	+	78.0790i	−0.368362	+	0.507006i
$155$		0			0
$156$	16.2624	−	11.8154i	0.104246	−	0.0757395i
$157$	−110.437	−	110.437i	−0.703420	−	0.703420i	0.261723	−	0.965143i	$-0.415709\pi$
$157$	−110.437	−	110.437i	−0.703420	−	0.703420i	−0.965143	+	0.261723i	$0.915709\pi$
$158$	22.5348	−	142.279i	0.142626	−	0.900503i
$159$	−53.0541	+	17.2383i	−0.333674	+	0.108417i
$160$		0			0
$161$	12.2289	−	37.6365i	0.0759556	−	0.233767i
$162$	−81.6164	+	160.181i	−0.503805	+	0.988773i
$163$	159.166	+	81.0992i	0.976480	+	0.497541i	0.868004	−	0.496558i	$-0.165403\pi$
$163$	159.166	+	81.0992i	0.976480	+	0.497541i	0.108476	+	0.994099i	$0.465403\pi$
$164$	−23.2188	−	7.54425i	−0.141578	−	0.0460015i
$165$		0			0
$166$	−34.7894	−	107.071i	−0.209575	−	0.645005i
$167$	−31.9422	−	5.05914i	−0.191270	−	0.0302943i	0.0600642	−	0.998195i	$-0.480869\pi$
$167$	−31.9422	−	5.05914i	−0.191270	−	0.0302943i	−0.251335	+	0.967900i	$0.580869\pi$
$168$	238.417	−	238.417i	1.41915	−	1.41915i
$169$	−59.0202	−	81.2343i	−0.349232	−	0.480677i
$170$		0			0
$171$	−10.7376	−	7.80132i	−0.0627930	−	0.0456218i
$172$	2.10567	+	13.2947i	0.0122423	+	0.0772948i
$173$	−71.4907	−	140.308i	−0.413241	−	0.811031i	−0.999999	−	0.00126870i	$-0.999596\pi$
$173$	−71.4907	−	140.308i	−0.413241	−	0.811031i	0.586758	−	0.809762i	$-0.300404\pi$
$174$		−	156.370i		−	0.898680i
$175$		0			0
$176$	−59.2018			−0.336374
$177$	−163.597	+	83.3569i	−0.924278	+	0.470943i
$178$	171.658	−	27.1880i	0.964372	−	0.152741i
$179$	18.5657	−	25.5534i	0.103719	−	0.142757i	−0.754003	−	0.656871i	$-0.771879\pi$
$179$	18.5657	−	25.5534i	0.103719	−	0.142757i	0.857721	+	0.514115i	$0.171879\pi$
$180$		0			0
$181$	−17.5232	+	12.7314i	−0.0968135	+	0.0703391i	−0.635139	−	0.772398i	$-0.719057\pi$
$181$	−17.5232	+	12.7314i	−0.0968135	+	0.0703391i	0.538325	+	0.842737i	$0.319057\pi$
$182$	121.293	+	121.293i	0.666443	+	0.666443i
$183$	−44.1042	+	278.463i	−0.241007	+	1.52166i
$184$	28.1815	−	9.15673i	0.153160	−	0.0497648i
$185$		0			0
$186$	−94.4142	+	290.577i	−0.507603	+	1.56224i
$187$	35.2855	−	69.2517i	0.188693	−	0.370330i
$188$	−35.7054	−	18.1928i	−0.189923	−	0.0967704i
$189$	225.629	+	73.3113i	1.19380	+	0.387890i
$190$		0			0
$191$	34.1484	+	105.098i	0.178788	+	0.550252i	0.999786	−	0.0206784i	$-0.00658262\pi$
$191$	34.1484	+	105.098i	0.178788	+	0.550252i	−0.820998	+	0.570930i	$0.806583\pi$
$192$	242.639	+	38.4302i	1.26374	+	0.200158i
$193$	−202.877	+	202.877i	−1.05118	+	1.05118i	−0.0525601	+	0.998618i	$0.516738\pi$
$193$	−202.877	+	202.877i	−1.05118	+	1.05118i	−0.998618	+	0.0525601i	$0.983262\pi$
$194$	155.648	+	214.231i	0.802311	+	1.10429i
$195$		0			0
$196$	−45.9476	−	33.3829i	−0.234427	−	0.170321i
$197$	−18.4724	−	116.630i	−0.0937684	−	0.592030i	−0.989170	−	0.146772i	$-0.953112\pi$
$197$	−18.4724	−	116.630i	−0.0937684	−	0.592030i	0.895402	−	0.445259i	$-0.146888\pi$
$198$	11.4972	+	22.5645i	0.0580666	+	0.113962i
$199$			304.416i			1.52973i	0.644192	+	0.764864i	$0.277194\pi$
$199$			304.416i			1.52973i	−0.644192	+	0.764864i	$0.722806\pi$
$200$		0			0
$201$	13.1295			0.0653210
$202$	−185.566	+	94.5504i	−0.918641	+	0.468071i
$203$	−279.995	+	44.3469i	−1.37929	+	0.218457i
$204$	−23.7967	+	32.7533i	−0.116650	+	0.160555i
$205$		0			0
$206$	234.398	−	170.300i	1.13785	−	0.826700i
$207$	−7.34272	−	7.34272i	−0.0354721	−	0.0354721i
$208$	−16.4604	+	103.927i	−0.0791364	+	0.499648i
$209$	19.6570	−	6.38694i	0.0940526	−	0.0305595i
$210$		0			0
$211$	−100.154	+	308.242i	−0.474663	+	1.46086i	0.371748	+	0.928334i	$0.378759\pi$
$211$	−100.154	+	308.242i	−0.474663	+	1.46086i	−0.846411	+	0.532530i	$0.821241\pi$
$212$	−5.12580	+	10.0599i	−0.0241783	+	0.0474526i
$213$	87.8005	+	44.7366i	0.412209	+	0.210031i
$214$	−85.6714	−	27.8363i	−0.400334	−	0.130076i
$215$		0			0
$216$	54.8940	+	168.946i	0.254139	+	0.782159i
$217$	547.080	+	86.6490i	2.52111	+	0.399304i
$218$	−91.1174	+	91.1174i	−0.417970	+	0.417970i
$219$	−87.1288	−	119.922i	−0.397848	−	0.547591i
$220$		0			0
$221$	−111.758	−	81.1972i	−0.505694	−	0.367408i
$222$	26.4558	+	167.035i	0.119170	+	0.752410i
$223$	−17.0342	−	33.4316i	−0.0763868	−	0.149917i	0.849654	−	0.527340i	$-0.176811\pi$
$223$	−17.0342	−	33.4316i	−0.0763868	−	0.149917i	−0.926041	+	0.377422i	$0.876811\pi$
$224$		−	126.310i		−	0.563884i
$225$		0			0
$226$	−203.179			−0.899023
$227$	259.847	−	132.399i	1.14470	−	0.583254i	0.224413	−	0.974494i	$-0.427954\pi$
$227$	259.847	−	132.399i	1.14470	−	0.583254i	0.920289	+	0.391240i	$0.127954\pi$
$228$	−10.6335	+	1.68419i	−0.0466384	+	0.00738679i
$229$	205.786	−	283.240i	0.898627	−	1.23685i	−0.0722771	−	0.997385i	$-0.523027\pi$
$229$	205.786	−	283.240i	0.898627	−	1.23685i	0.970904	−	0.239469i	$-0.0769734\pi$
$230$		0			0
$231$	148.863	−	108.155i	0.644427	−	0.468203i
$232$	−150.096	−	150.096i	−0.646967	−	0.646967i
$233$	12.3861	−	78.2025i	0.0531590	−	0.335633i	−0.946748	−	0.321976i	$-0.895653\pi$
$233$	12.3861	−	78.2025i	0.0531590	−	0.335633i	0.999907	−	0.0136566i	$-0.00434717\pi$
$234$	42.8079	−	13.9091i	0.182940	−	0.0594407i
$235$		0			0
$236$	−11.4836	+	35.3430i	−0.0486595	+	0.149758i
$237$	−124.687	+	244.712i	−0.526105	+	1.03254i
$238$	−307.822	−	156.843i	−1.29337	−	0.659004i
$239$	−375.540	−	122.021i	−1.57130	−	0.510546i	−0.611503	−	0.791242i	$-0.709435\pi$
$239$	−375.540	−	122.021i	−1.57130	−	0.510546i	−0.959797	+	0.280696i	$0.909435\pi$
$240$		0			0
$241$	−9.67765	−	29.7847i	−0.0401562	−	0.123588i	0.928969	−	0.370158i	$-0.120696\pi$
$241$	−9.67765	−	29.7847i	−0.0401562	−	0.123588i	−0.969125	+	0.246570i	$0.920696\pi$
$242$	178.120	+	28.2115i	0.736034	+	0.116576i
$243$	109.962	−	109.962i	0.452520	−	0.452520i
$244$	33.5404	+	46.1644i	0.137461	+	0.189199i
$245$		0			0
$246$	−177.251	−	128.780i	−0.720531	−	0.523496i
$247$	−5.74666	−	36.2830i	−0.0232658	−	0.146895i
$248$	188.292	+	369.544i	0.759243	+	1.49010i
$249$			214.643i			0.862020i
$250$		0			0
$251$	−155.694			−0.620295			−0.310147	−	0.950689i	$-0.600378\pi$
$251$	−155.694			−0.620295			−0.310147	+	0.950689i	$0.600378\pi$
$252$	−21.3083	+	10.8571i	−0.0845569	+	0.0430839i
$253$	15.9718	−	2.52968i	0.0631295	−	0.00999874i
$254$	4.37627	−	6.02342i	0.0172294	−	0.0237143i
$255$		0			0
$256$	105.333	−	76.5287i	0.411456	−	0.298940i
$257$	49.8494	+	49.8494i	0.193967	+	0.193967i	0.797408	−	0.603441i	$-0.206204\pi$
$257$	49.8494	+	49.8494i	0.193967	+	0.193967i	−0.603441	+	0.797408i	$0.706204\pi$
$258$	−18.8968	+	119.309i	−0.0732432	+	0.462440i
$259$	291.589	−	94.7429i	1.12582	−	0.365803i
$260$		0			0
$261$	−22.9870	+	70.7466i	−0.0880726	+	0.271060i
$262$	73.7042	−	144.653i	0.281314	−	0.552109i
$263$	419.056	+	213.520i	1.59337	+	0.811863i	0.999976	+	0.00695066i	$0.00221248\pi$
$263$	419.056	+	213.520i	1.59337	+	0.811863i	0.593394	+	0.804912i	$0.297788\pi$
$264$	131.035	+	42.5760i	0.496346	+	0.161273i
$265$		0			0
$266$	−28.3897	−	87.3747i	−0.106728	−	0.328476i
$267$	−327.277	−	51.8356i	−1.22576	−	0.194141i
$268$	1.87904	−	1.87904i	0.00701135	−	0.00701135i
$269$	219.028	+	301.467i	0.814232	+	1.12069i	0.990657	+	0.136380i	$0.0435467\pi$
$269$	219.028	+	301.467i	0.814232	+	1.12069i	−0.176425	+	0.984314i	$0.556453\pi$
$270$		0			0
$271$	269.883	+	196.082i	0.995878	+	0.723548i	0.961201	−	0.275850i	$-0.0889595\pi$
$271$	269.883	+	196.082i	0.995878	+	0.723548i	0.0346779	+	0.999399i	$0.488959\pi$
$272$	−33.1519	−	209.313i	−0.121882	−	0.769533i
$273$	−148.473	−	291.395i	−0.543857	−	1.06738i
$274$			145.438i			0.530796i
$275$		0			0
$276$	−8.42327			−0.0305191
$277$	−255.508	+	130.188i	−0.922413	+	0.469993i	−0.849644	−	0.527356i	$-0.823183\pi$
$277$	−255.508	+	130.188i	−0.922413	+	0.469993i	−0.0727686	+	0.997349i	$0.523183\pi$
$278$	−65.3169	+	10.3452i	−0.234953	+	0.0372129i
$279$	85.4316	−	117.586i	0.306206	−	0.421457i
$280$		0			0
$281$	−162.496	+	118.060i	−0.578278	+	0.420143i	−0.838103	−	0.545512i	$-0.816335\pi$
$281$	−162.496	+	118.060i	−0.578278	+	0.420143i	0.259825	+	0.965656i	$0.416335\pi$
$282$	−254.293	−	254.293i	−0.901749	−	0.901749i
$283$	25.4422	−	160.636i	0.0899019	−	0.567618i	−0.901083	−	0.433646i	$-0.857227\pi$
$283$	25.4422	−	160.636i	0.0899019	−	0.567618i	0.990985	−	0.133972i	$-0.0427733\pi$
$284$	18.9681	−	6.16312i	0.0667892	−	0.0217011i
$285$		0			0
$286$	−21.6601	+	66.6630i	−0.0757347	+	0.233088i
$287$	−180.324	+	353.905i	−0.628306	+	1.23312i
$288$	−29.5316	−	15.0471i	−0.102540	−	0.0522469i
$289$	−10.2505	−	3.33060i	−0.0354690	−	0.0115246i
$290$		0			0
$291$	−156.013	−	480.157i	−0.536126	−	1.65002i
$292$	−29.6323	−	4.69329i	−0.101480	−	0.0160729i
$293$	269.435	−	269.435i	0.919573	−	0.919573i	−0.0774250	−	0.996998i	$-0.524670\pi$
$293$	269.435	−	269.435i	0.919573	−	0.919573i	0.996998	+	0.0774250i	$0.0246698\pi$
$294$	−299.585	−	412.344i	−1.01900	−	1.40253i
$295$		0			0
$296$	185.727	+	134.939i	0.627458	+	0.455875i
$297$	15.1653	+	95.7498i	0.0510616	+	0.322390i
$298$	−110.950	−	217.752i	−0.372317	−	0.730713i
$299$		−	28.7413i		−	0.0961246i
$300$		0			0
$301$	218.993			0.727553
$302$	6.53520	−	3.32985i	0.0216397	−	0.0110260i
$303$	392.182	−	62.1156i	1.29433	−	0.205002i
$304$	33.1250	−	45.5927i	0.108964	−	0.149976i
$305$		0			0
$306$	−73.3406	+	53.2850i	−0.239675	+	0.174134i
$307$	−15.5293	−	15.5293i	−0.0505840	−	0.0505840i	0.681362	−	0.731946i	$-0.261388\pi$
$307$	−15.5293	−	15.5293i	−0.0505840	−	0.0505840i	−0.731946	+	0.681362i	$0.761388\pi$
$308$	5.82589	−	36.7832i	0.0189152	−	0.119426i
$309$	−525.357	+	170.699i	−1.70018	+	0.552423i
$310$		0			0
$311$	133.569	−	411.082i	0.429481	−	1.32181i	−0.469157	−	0.883115i	$-0.655442\pi$
$311$	133.569	−	411.082i	0.429481	−	1.32181i	0.898638	−	0.438691i	$-0.144558\pi$
$312$	111.174	−	218.191i	0.356326	−	0.699329i
$313$	−83.8100	−	42.7034i	−0.267764	−	0.136432i	0.314954	−	0.949107i	$-0.398011\pi$
$313$	−83.8100	−	42.7034i	−0.267764	−	0.136432i	−0.582718	+	0.812674i	$0.698011\pi$
$314$	−269.795	−	87.6617i	−0.859220	−	0.279177i
$315$		0			0
$316$	17.1774	+	52.8667i	0.0543589	+	0.167300i
$317$	−190.794	−	30.2188i	−0.601874	−	0.0953274i	−0.151940	−	0.988390i	$-0.548552\pi$
$317$	−190.794	−	30.2188i	−0.601874	−	0.0953274i	−0.449933	+	0.893062i	$0.648552\pi$
$318$	−71.6467	+	71.6467i	−0.225304	+	0.225304i
$319$	−68.0893	−	93.7169i	−0.213446	−	0.293783i
$320$		0			0
$321$	138.944	+	100.948i	0.432846	+	0.314481i
$322$	−11.2443	−	70.9940i	−0.0349203	−	0.220478i
$323$	33.5892	+	65.9224i	0.103991	+	0.204094i
$324$		−	69.3720i		−	0.214111i
$325$		0			0
$326$	324.465			0.995292
$327$	218.902	−	111.536i	0.669424	−	0.341088i
$328$	−293.752	+	46.5257i	−0.895585	+	0.141847i
$329$	−383.217	+	527.453i	−1.16479	+	1.60320i
$330$		0			0
$331$	−220.979	+	160.551i	−0.667611	+	0.485048i	−0.869225	−	0.494417i	$-0.835382\pi$
$331$	−220.979	+	160.551i	−0.667611	+	0.485048i	0.201613	+	0.979465i	$0.435382\pi$
$332$	30.7187	+	30.7187i	0.0925264	+	0.0925264i
$333$	12.5853	−	79.4608i	0.0377938	−	0.238621i
$334$	−55.8662	+	18.1520i	−0.167264	+	0.0543474i
$335$		0			0
$336$	155.038	−	477.157i	0.461421	−	1.42011i
$337$	258.565	−	507.462i	0.767254	−	1.50582i	−0.0928377	−	0.995681i	$-0.529594\pi$
$337$	258.565	−	507.462i	0.767254	−	1.50582i	0.860092	−	0.510140i	$-0.170406\pi$
$338$	−162.503	−	82.7994i	−0.480778	−	0.244969i
$339$	368.415	+	119.705i	1.08677	+	0.353113i
$340$		0			0
$341$	69.9428	+	215.262i	0.205111	+	0.631267i
$342$	−23.8105	−	3.77121i	−0.0696212	−	0.0110269i
$343$	−258.277	+	258.277i	−0.752995	+	0.752995i
$344$	96.3838	+	132.661i	0.280185	+	0.385642i
$345$		0			0
$346$	−231.397	−	168.120i	−0.668778	−	0.485896i
$347$	52.3196	+	330.333i	0.150777	+	0.951968i	0.940817	+	0.338914i	$0.110059\pi$
$347$	52.3196	+	330.333i	0.150777	+	0.951968i	−0.790040	+	0.613055i	$0.789941\pi$
$348$	27.3939	+	53.7636i	0.0787182	+	0.154493i
$349$		−	502.965i		−	1.44116i	−0.693372	−	0.720580i	$-0.743876\pi$
$349$		−	502.965i		−	1.44116i	0.693372	−	0.720580i	$-0.256124\pi$
$350$		0			0
$351$	172.302			0.490889
$352$	45.9884	−	23.4323i	0.130649	−	0.0665690i
$353$	−173.477	+	27.4761i	−0.491437	+	0.0778360i	−0.397235	−	0.917717i	$-0.630030\pi$
$353$	−173.477	+	27.4761i	−0.491437	+	0.0778360i	−0.0942023	+	0.995553i	$0.530030\pi$
$354$	−196.025	+	269.805i	−0.553743	+	0.762162i
$355$		0			0
$356$	−54.2570	+	39.4200i	−0.152407	+	0.110730i
$357$	465.752	+	465.752i	1.30463	+	1.30463i
$358$	8.97475	−	56.6643i	0.0250691	−	0.158280i
$359$	−129.730	+	42.1519i	−0.361366	+	0.117415i	−0.484072	−	0.875028i	$-0.660843\pi$
$359$	−129.730	+	42.1519i	−0.361366	+	0.117415i	0.122706	+	0.992443i	$0.460843\pi$
$360$		0			0
$361$	105.475	−	324.619i	0.292175	−	0.899223i
$362$	−17.8608	+	35.0539i	−0.0493393	+	0.0968339i
$363$	−306.355	−	156.096i	−0.843954	−	0.430016i
$364$	−62.9519	−	20.4543i	−0.172945	−	0.0561932i
$365$		0			0
$366$	158.244	+	487.026i	0.432362	+	1.33067i
$367$	−330.443	−	52.3370i	−0.900389	−	0.142608i	−0.310955	−	0.950425i	$-0.600649\pi$
$367$	−330.443	−	52.3370i	−0.900389	−	0.142608i	−0.589433	+	0.807817i	$0.700649\pi$
$368$	31.1778	−	31.1778i	0.0847222	−	0.0847222i
$369$	61.2623	+	84.3204i	0.166023	+	0.228510i
$370$		0			0
$371$	148.609	+	107.971i	0.400563	+	0.291026i
$372$	−18.4434	−	116.447i	−0.0495790	−	0.313030i
$373$	83.7541	+	164.377i	0.224542	+	0.440688i	0.975602	−	0.219545i	$-0.0704574\pi$
$373$	83.7541	+	164.377i	0.224542	+	0.440688i	−0.751060	+	0.660233i	$0.770457\pi$
$374$		−	141.172i		−	0.377465i
$375$		0			0
$376$	−488.180			−1.29835
$377$	−183.448	+	93.4716i	−0.486600	+	0.247935i
$378$	425.605	−	67.4092i	1.12594	−	0.178331i
$379$	143.236	−	197.147i	0.377931	−	0.520178i	−0.577104	−	0.816671i	$-0.695817\pi$
$379$	143.236	−	197.147i	0.377931	−	0.520178i	0.955035	+	0.296493i	$0.0958171\pi$
$380$		0			0
$381$	−11.4840	+	8.34365i	−0.0301418	+	0.0218993i
$382$	141.929	+	141.929i	0.371542	+	0.371542i
$383$	101.123	−	638.468i	0.264030	−	1.66702i	−0.397882	−	0.917437i	$-0.630255\pi$
$383$	101.123	−	638.468i	0.264030	−	1.66702i	0.661912	−	0.749582i	$-0.269745\pi$
$384$	278.445	−	90.4724i	0.725118	−	0.235605i
$385$		0			0
$386$	−161.038	+	495.625i	−0.417198	+	1.28400i
$387$	26.0883	−	51.2012i	0.0674117	−	0.132303i
$388$	−91.0458	−	46.3902i	−0.234654	−	0.119562i
$389$	698.667	+	227.011i	1.79606	+	0.583575i	0.999772	−	0.0213423i	$-0.00679398\pi$
$389$	698.667	+	227.011i	1.79606	+	0.583575i	0.796288	+	0.604918i	$0.206794\pi$
$390$		0			0
$391$	17.8878	+	55.0530i	0.0457489	+	0.140801i
$392$	−683.364	−	108.234i	−1.74328	−	0.276108i
$393$	−218.868	+	218.868i	−0.556916	+	0.556916i
$394$	−126.069	−	173.519i	−0.319971	−	0.440402i
$395$		0			0
$396$	−7.90599	−	5.74404i	−0.0199646	−	0.0145051i
$397$	−29.3710	−	185.441i	−0.0739823	−	0.467106i	−0.996669	−	0.0815548i	$-0.974011\pi$
$397$	−29.3710	−	185.441i	−0.0739823	−	0.467106i	0.922687	−	0.385551i	$-0.125989\pi$
$398$	251.022	+	492.659i	0.630709	+	1.23784i
$399$			175.158i			0.438993i
$400$		0			0
$401$	88.3502			0.220325			0.110162	−	0.993914i	$-0.464863\pi$
$401$	88.3502			0.220325			0.110162	+	0.993914i	$0.464863\pi$
$402$	21.2485	−	10.8267i	0.0528570	−	0.0269320i
$403$	397.332	−	62.9312i	0.985935	−	0.156157i
$404$	47.2377	−	65.0171i	0.116925	−	0.160933i
$405$		0			0
$406$	−416.568	+	302.655i	−1.02603	+	0.745455i
$407$	88.5888	+	88.5888i	0.217663	+	0.217663i
$408$	−77.1536	+	487.129i	−0.189102	+	1.19394i
$409$	−172.391	+	56.0134i	−0.421495	+	0.136952i	−0.512082	−	0.858936i	$-0.671126\pi$
$409$	−172.391	+	56.0134i	−0.421495	+	0.136952i	0.0905870	+	0.995889i	$0.471126\pi$
$410$		0			0
$411$	85.6864	−	263.715i	0.208483	−	0.641644i
$412$	−50.7571	+	99.6164i	−0.123197	+	0.241787i
$413$	538.704	+	274.483i	1.30437	+	0.664609i
$414$	−17.9381	−	5.82844i	−0.0433288	−	0.0140784i
$415$		0			0
$416$	−28.3480	−	87.2463i	−0.0681443	−	0.209727i
$417$	124.531	+	19.7238i	0.298635	+	0.0472992i
$418$	26.5457	−	26.5457i	0.0635064	−	0.0635064i
$419$	113.418	+	156.106i	0.270687	+	0.372569i	0.922622	−	0.385706i	$-0.126042\pi$
$419$	113.418	+	156.106i	0.270687	+	0.372569i	−0.651934	+	0.758275i	$0.726042\pi$
$420$		0			0
$421$	−659.764	−	479.346i	−1.56713	−	1.13859i	−0.929837	−	0.367972i	$-0.880052\pi$
$421$	−659.764	−	479.346i	−1.56713	−	1.13859i	−0.637298	−	0.770617i	$-0.719948\pi$
$422$	92.0908	+	581.439i	0.218225	+	1.37782i
$423$	77.6679	+	152.432i	0.183612	+	0.360359i
$424$			137.544i			0.324396i
$425$		0			0
$426$	178.984			0.420150
$427$	827.186	−	421.472i	1.93720	−	0.987055i
$428$	34.3323	−	5.43771i	0.0802157	−	0.0127049i
$429$	78.5505	−	108.116i	0.183101	−	0.252017i
$430$		0			0
$431$	−199.776	+	145.146i	−0.463518	+	0.336765i	−0.794910	−	0.606728i	$-0.792482\pi$
$431$	−199.776	+	145.146i	−0.463518	+	0.336765i	0.331392	+	0.943493i	$0.392482\pi$
$432$	186.909	+	186.909i	0.432659	+	0.432659i
$433$	−120.729	+	762.250i	−0.278819	+	1.76039i	0.308679	+	0.951166i	$0.400113\pi$
$433$	−120.729	+	762.250i	−0.278819	+	1.76039i	−0.587498	+	0.809226i	$0.699887\pi$
$434$	956.832	−	310.894i	2.20468	−	0.716345i
$435$		0			0
$436$	15.3657	−	47.2908i	0.0352424	−	0.108465i
$437$	−6.98848	+	13.7157i	−0.0159919	+	0.0313860i
$438$	−239.895	−	122.233i	−0.547707	−	0.279070i
$439$	−16.9661	−	5.51263i	−0.0386472	−	0.0125572i	0.289630	−	0.957139i	$-0.406468\pi$
$439$	−16.9661	−	5.51263i	−0.0386472	−	0.0125572i	−0.328277	+	0.944582i	$0.606468\pi$
$440$		0			0
$441$	74.9254	+	230.597i	0.169899	+	0.522895i
$442$	−247.822	−	39.2512i	−0.560684	−	0.0888036i
$443$	−184.814	+	184.814i	−0.417187	+	0.417187i	−0.884233	−	0.467046i	$-0.845318\pi$
$443$	−184.814	+	184.814i	−0.417187	+	0.417187i	0.467046	+	0.884233i	$0.345318\pi$
$444$	−38.3584	−	52.7958i	−0.0863927	−	0.118909i
$445$		0			0
$446$	−55.1356	−	40.0583i	−0.123622	−	0.0898169i
$447$	72.8897	+	460.207i	0.163064	+	1.02955i
$448$	−367.250	−	720.769i	−0.819755	−	1.60886i
$449$		−	266.342i		−	0.593189i	−0.955004	−	0.296594i	$-0.904149\pi$
$449$		−	266.342i		−	0.593189i	0.955004	−	0.296594i	$-0.0958509\pi$
$450$		0			0
$451$	−162.307			−0.359881
$452$	69.8576	−	35.5942i	0.154552	−	0.0787483i
$453$	−13.8118	+	2.18757i	−0.0304896	+	0.00482907i
$454$	311.354	−	428.542i	0.685801	−	0.943924i
$455$		0			0
$456$	−106.107	+	77.0910i	−0.232690	+	0.169059i
$457$	−473.310	−	473.310i	−1.03569	−	1.03569i	−0.999339	−	0.0363511i	$-0.988427\pi$
$457$	−473.310	−	473.310i	−1.03569	−	1.03569i	−0.0363511	−	0.999339i	$-0.511573\pi$
$458$	99.4779	−	628.079i	0.217201	−	1.37135i
$459$	−330.040	+	107.236i	−0.719041	+	0.233630i
$460$		0			0
$461$	14.4681	−	44.5284i	0.0313843	−	0.0965909i	−0.934137	−	0.356914i	$-0.883829\pi$
$461$	14.4681	−	44.5284i	0.0313843	−	0.0965909i	0.965522	+	0.260323i	$0.0838290\pi$
$462$	151.730	−	297.788i	0.328421	−	0.644562i
$463$	−308.662	−	157.271i	−0.666657	−	0.339679i	0.0876962	−	0.996147i	$-0.472050\pi$
$463$	−308.662	−	157.271i	−0.666657	−	0.339679i	−0.754354	+	0.656468i	$0.772050\pi$
$464$	−300.395	−	97.6044i	−0.647404	−	0.210354i
$465$		0			0
$466$	−44.4407	−	136.775i	−0.0953664	−	0.293508i
$467$	106.477	+	16.8643i	0.228002	+	0.0361120i	0.269390	−	0.963031i	$-0.413178\pi$
$467$	106.477	+	16.8643i	0.228002	+	0.0361120i	−0.0413877	+	0.999143i	$0.513178\pi$
$468$	−12.2816	+	12.2816i	−0.0262428	+	0.0262428i
$469$	−25.4122	−	34.9769i	−0.0541838	−	0.0745776i
$470$		0			0
$471$	437.559	+	317.905i	0.929000	+	0.674958i
$472$	70.8201	+	447.140i	0.150042	+	0.947331i
$473$	40.6263	+	79.7337i	0.0858908	+	0.168570i
$474$			498.852i			1.05243i
$475$		0			0
$476$	133.313			0.280069
$477$	42.9474	−	21.8828i	0.0900365	−	0.0458759i
$478$	−708.384	+	112.197i	−1.48197	+	0.234722i
$479$	−214.282	+	294.934i	−0.447353	+	0.615729i	−0.971826	−	0.235698i	$-0.924262\pi$
$479$	−214.282	+	294.934i	−0.447353	+	0.615729i	0.524473	+	0.851427i	$0.324262\pi$
$480$		0			0
$481$	180.146	−	130.884i	0.374524	−	0.272107i
$482$	−40.2227	−	40.2227i	−0.0834495	−	0.0834495i
$483$	−21.4381	+	135.355i	−0.0443852	+	0.280237i
$484$	−66.1840	+	21.5045i	−0.136744	+	0.0444308i
$485$		0			0
$486$	87.2850	−	268.636i	0.179599	−	0.552748i
$487$	171.861	−	337.296i	0.352897	−	0.692599i	−0.644508	−	0.764598i	$-0.722938\pi$
$487$	171.861	−	337.296i	0.352897	−	0.692599i	0.997405	+	0.0719988i	$0.0229378\pi$
$488$	619.381	+	315.590i	1.26922	+	0.646701i
$489$	−588.337	−	191.162i	−1.20314	−	0.390925i
$490$		0			0
$491$	−80.8943	−	248.967i	−0.164754	−	0.507061i	0.834264	−	0.551365i	$-0.185893\pi$
$491$	−80.8943	−	248.967i	−0.164754	−	0.507061i	−0.999018	+	0.0443043i	$0.985893\pi$
$492$	83.5033	+	13.2256i	0.169722	+	0.0268813i
$493$	293.216	−	293.216i	0.594758	−	0.594758i
$494$	−39.2193	−	53.9808i	−0.0793914	−	0.109273i
$495$		0			0
$496$	499.281	+	362.749i	1.00662	+	0.731349i
$497$	−50.7602	−	320.487i	−0.102133	−	0.644843i
$498$	176.995	+	347.373i	0.355412	+	0.697535i
$499$			75.2156i			0.150733i	0.997156	+	0.0753664i	$0.0240126\pi$
$499$			75.2156i			0.150733i	−0.997156	+	0.0753664i	$0.975987\pi$
$500$		0			0
$501$	111.994			0.223541
$502$	−251.971	+	128.386i	−0.501935	+	0.255748i
$503$	−778.940	+	123.372i	−1.54859	+	0.245272i	−0.871413	−	0.490549i	$-0.836796\pi$
$503$	−778.940	+	123.372i	−1.54859	+	0.245272i	−0.677175	+	0.735822i	$0.736796\pi$
$504$	−171.244	+	235.697i	−0.339769	+	0.467652i
$505$		0			0
$506$	23.7623	−	17.2643i	0.0469611	−	0.0341193i
$507$	245.876	+	245.876i	0.484963	+	0.484963i
$508$	−0.449440	+	2.83765i	−0.000884724	+	0.00558593i
$509$	−193.504	+	62.8734i	−0.380166	+	0.123523i	−0.492865	−	0.870106i	$-0.664050\pi$
$509$	−193.504	+	62.8734i	−0.380166	+	0.123523i	0.112699	+	0.993629i	$0.464050\pi$
$510$		0			0
$511$	−150.834	+	464.220i	−0.295175	+	0.908454i
$512$	260.891	−	512.028i	0.509553	−	1.00005i
$513$	−82.2246	−	41.8955i	−0.160282	−	0.0816677i
$514$	121.781	+	39.5690i	0.236928	+	0.0769826i
$515$		0			0
$516$	−14.4043	−	44.3317i	−0.0279152	−	0.0859142i
$517$	−263.133	−	41.6762i	−0.508962	−	0.0806116i
$518$	393.774	−	393.774i	0.760182	−	0.760182i
$519$	320.532	+	441.174i	0.617595	+	0.850046i
$520$		0			0
$521$	−626.036	−	454.842i	−1.20160	−	0.873016i	−0.207163	−	0.978307i	$-0.566423\pi$
$521$	−626.036	−	454.842i	−1.20160	−	0.873016i	−0.994442	+	0.105290i	$0.966423\pi$
$522$	21.1363	+	133.450i	0.0404911	+	0.255651i
$523$	−328.674	−	645.059i	−0.628440	−	1.23338i	−0.957325	−	0.289013i	$-0.906673\pi$
$523$	−328.674	−	645.059i	−0.628440	−	1.23338i	0.328885	−	0.944370i	$-0.393327\pi$
$524$			62.6468i			0.119555i
$525$		0			0
$526$	854.259			1.62407
$527$	−721.911	+	367.832i	−1.36985	+	0.697973i
$528$	202.490	−	32.0713i	0.383504	−	0.0607411i
$529$	303.859	−	418.226i	0.574403	−	0.790598i
$530$		0			0
$531$	128.350	−	93.2517i	0.241714	−	0.175615i
$532$	25.0679	+	25.0679i	0.0471201	+	0.0471201i
$533$	−45.1275	+	284.924i	−0.0846670	+	0.534566i
$534$	−572.401	+	185.984i	−1.07191	+	0.348286i
$535$		0			0
$536$	10.0037	−	30.7882i	0.0186636	−	0.0574407i
$537$	−49.6579	+	97.4590i	−0.0924727	+	0.181488i
$538$	603.060	+	307.275i	1.12093	+	0.571142i
$539$	−359.099	−	116.678i	−0.666232	−	0.216472i
$540$		0			0
$541$	283.746	+	873.280i	0.524484	+	1.61420i	0.765334	+	0.643633i	$0.222574\pi$
$541$	283.746	+	873.280i	0.524484	+	1.61420i	−0.240850	+	0.970562i	$0.577426\pi$
$542$	598.461	+	94.7870i	1.10417	+	0.174884i
$543$	53.0385	−	53.0385i	0.0976768	−	0.0976768i
$544$	108.600	+	149.475i	0.199632	+	0.274769i
$545$		0			0
$546$	−480.570	−	349.154i	−0.880164	−	0.639477i
$547$	55.9587	+	353.309i	0.102301	+	0.645903i	0.984548	+	0.175116i	$0.0560301\pi$
$547$	55.9587	+	353.309i	0.102301	+	0.645903i	−0.882247	+	0.470787i	$0.843970\pi$
$548$	−25.4788	−	50.0049i	−0.0464941	−	0.0912498i
$549$		−	243.608i		−	0.443730i
$550$		0			0
$551$	110.271			0.200130
$552$	−91.4299	+	46.5859i	−0.165634	+	0.0843947i
$553$	893.240	−	141.475i	1.61526	−	0.255832i
$554$	−306.155	+	421.386i	−0.552626	+	0.760625i
$555$		0			0
$556$	20.6451	−	14.9995i	0.0371315	−	0.0269776i
$557$	−404.198	−	404.198i	−0.725670	−	0.725670i	0.244084	−	0.969754i	$-0.421513\pi$
$557$	−404.198	−	404.198i	−0.725670	−	0.725670i	−0.969754	+	0.244084i	$0.921513\pi$
$558$	41.2981	−	260.746i	0.0740110	−	0.467287i
$559$	151.265	−	49.1491i	0.270600	−	0.0879233i
$560$		0			0
$561$	−83.1729	+	255.980i	−0.148258	+	0.456292i
$562$	−165.627	+	325.060i	−0.294709	+	0.578399i
$563$	−872.036	−	444.324i	−1.54891	−	0.789208i	−0.549966	−	0.835187i	$-0.685359\pi$
$563$	−872.036	−	444.324i	−1.54891	−	0.789208i	−0.998942	+	0.0459785i	$0.985359\pi$
$564$	131.980	+	42.8830i	0.234008	+	0.0760338i
$565$		0			0
$566$	−91.2859	−	280.949i	−0.161282	−	0.496376i
$567$	−1114.75	−	176.559i	−1.96605	−	0.311391i
$568$	171.803	−	171.803i	0.302469	−	0.302469i
$569$	−431.512	−	593.925i	−0.758369	−	1.04381i	−0.997348	−	0.0727807i	$-0.976813\pi$
$569$	−431.512	−	593.925i	−0.758369	−	1.04381i	0.238979	−	0.971025i	$-0.423187\pi$
$570$		0			0
$571$	−612.726	−	445.171i	−1.07308	−	0.779635i	−0.0966128	−	0.995322i	$-0.530801\pi$
$571$	−612.726	−	445.171i	−1.07308	−	0.779635i	−0.976463	+	0.215687i	$0.930801\pi$
$572$	−4.23121	−	26.7148i	−0.00739723	−	0.0467042i
$573$	−173.734	−	340.972i	−0.303201	−	0.595065i
$574$			721.447i			1.25688i
$575$		0			0
$576$	−212.268			−0.368520
$577$	−367.699	+	187.352i	−0.637261	+	0.324700i	−0.742599	−	0.669736i	$-0.766407\pi$
$577$	−367.699	+	187.352i	−0.637261	+	0.324700i	0.105339	+	0.994436i	$0.466407\pi$
$578$	−19.3356	+	3.06246i	−0.0334527	+	0.00529838i
$579$	584.005	−	803.815i	1.00865	−	1.38828i
$580$		0			0
$581$	571.806	−	415.441i	0.984175	−	0.715045i
$582$	−648.426	−	648.426i	−1.11413	−	1.11413i
$583$	−11.7422	+	74.1373i	−0.0201410	+	0.127165i
$584$	−347.599	+	112.942i	−0.595203	+	0.193393i
$585$		0			0
$586$	213.870	−	658.224i	0.364966	−	1.12325i
$587$	199.151	−	390.856i	0.339269	−	0.665853i	−0.656835	−	0.754034i	$-0.728105\pi$
$587$	199.151	−	390.856i	0.339269	−	0.665853i	0.996104	+	0.0881807i	$0.0281053\pi$
$588$	175.241	+	89.2898i	0.298029	+	0.151853i
$589$	−204.913	−	66.5803i	−0.347900	−	0.113040i
$590$		0			0
$591$	126.364	+	388.907i	0.213813	+	0.658050i
$592$	337.397	+	53.4384i	0.569927	+	0.0902675i
$593$	279.182	−	279.182i	0.470796	−	0.470796i	−0.431376	−	0.902172i	$-0.641972\pi$
$593$	279.182	−	279.182i	0.470796	−	0.470796i	0.902172	+	0.431376i	$0.141972\pi$
$594$	103.499	+	142.454i	0.174240	+	0.239821i
$595$		0			0
$596$	76.2945	+	55.4312i	0.128011	+	0.0930054i
$597$	−164.911	−	1041.21i	−0.276233	−	1.74406i
$598$	−23.7001	−	46.5141i	−0.0396323	−	0.0777828i
$599$		−	65.2707i		−	0.108966i	−0.998515	−	0.0544831i	$-0.982649\pi$
$599$		−	65.2707i		−	0.108966i	0.998515	−	0.0544831i	$-0.0173511\pi$
$600$		0			0
$601$	192.168			0.319747			0.159873	−	0.987138i	$-0.448891\pi$
$601$	192.168			0.319747			0.159873	+	0.987138i	$0.448891\pi$
$602$	354.413	−	180.583i	0.588727	−	0.299971i
$603$	−11.2050	+	1.77470i	−0.0185821	+	0.00294312i
$604$	−1.66361	+	2.28976i	−0.00275431	+	0.00379099i
$605$		0			0
$606$	583.477	−	423.921i	0.962833	−	0.699539i
$607$	510.986	+	510.986i	0.841822	+	0.841822i	0.989096	−	0.147274i	$-0.0470499\pi$
$607$	510.986	+	510.986i	0.841822	+	0.841822i	−0.147274	+	0.989096i	$0.547050\pi$
$608$	−7.68605	+	48.5278i	−0.0126415	+	0.0798154i
$609$	933.655	−	303.363i	1.53310	−	0.498133i
$610$		0			0
$611$	−146.322	+	450.334i	−0.239480	+	0.737044i
$612$	15.8813	−	31.1689i	0.0259499	−	0.0509295i
$613$	104.510	+	53.2504i	0.170489	+	0.0868686i	0.537153	−	0.843485i	$-0.319500\pi$
$613$	104.510	+	53.2504i	0.170489	+	0.0868686i	−0.366663	+	0.930354i	$0.619500\pi$
$614$	−37.9377	−	12.3267i	−0.0617877	−	0.0200761i
$615$		0			0
$616$	−140.197	−	431.482i	−0.227593	−	0.700458i
$617$	667.508	+	105.723i	1.08186	+	0.171350i	0.671818	−	0.740716i	$-0.265514\pi$
$617$	667.508	+	105.723i	1.08186	+	0.171350i	0.410043	+	0.912066i	$0.365514\pi$
$618$	−709.465	+	709.465i	−1.14800	+	1.14800i
$619$	−239.653	−	329.853i	−0.387161	−	0.532881i	0.570303	−	0.821434i	$-0.306826\pi$
$619$	−239.653	−	329.853i	−0.387161	−	0.532881i	−0.957464	+	0.288553i	$0.906826\pi$
$620$		0			0
$621$	−58.4119	−	42.4387i	−0.0940610	−	0.0683393i
$622$	−122.815	−	775.425i	−0.197452	−	1.24666i
$623$	495.356	+	972.191i	0.795114	+	1.56050i
$624$		−	364.382i		−	0.583946i
$625$		0			0
$626$	−170.849			−0.272922
$627$	−63.7736	+	32.4943i	−0.101712	+	0.0518250i
$628$	108.119	−	17.1243i	0.172164	−	0.0272680i
$629$	−263.605	+	362.822i	−0.419087	+	0.576823i
$630$		0			0
$631$	620.336	−	450.700i	0.983099	−	0.714263i	0.0247001	−	0.999695i	$-0.492137\pi$
$631$	620.336	−	450.700i	0.983099	−	0.714263i	0.958399	+	0.285431i	$0.0921369\pi$
$632$	478.837	+	478.837i	0.757653	+	0.757653i
$633$	175.577	−	1108.55i	0.277373	−	1.75126i
$634$	−333.695	+	108.424i	−0.526332	+	0.171016i
$635$		0			0
$636$	12.0822	−	37.1853i	0.0189972	−	0.0584674i
$637$	−304.668	+	597.945i	−0.478286	+	0.938689i
$638$	−187.473	−	95.5224i	−0.293845	−	0.149722i
$639$	−80.9777	−	26.3112i	−0.126726	−	0.0411757i
$640$		0			0
$641$	8.23463	+	25.3436i	0.0128465	+	0.0395376i	0.957274	−	0.289181i	$-0.0933831\pi$
$641$	8.23463	+	25.3436i	0.0128465	+	0.0395376i	−0.944428	+	0.328719i	$0.893383\pi$
$642$	308.105	+	48.7991i	0.479915	+	0.0760111i
$643$	−16.0826	+	16.0826i	−0.0250118	+	0.0250118i	−0.719502	−	0.694490i	$-0.755630\pi$
$643$	−16.0826	+	16.0826i	−0.0250118	+	0.0250118i	0.694490	+	0.719502i	$0.255630\pi$
$644$	16.3032	+	22.4395i	0.0253156	+	0.0348439i
$645$		0			0
$646$	108.720	+	78.9895i	0.168297	+	0.122275i
$647$	79.1197	+	499.542i	0.122287	+	0.772090i	0.970263	+	0.242054i	$0.0778213\pi$
$647$	79.1197	+	499.542i	0.122287	+	0.772090i	−0.847976	+	0.530035i	$0.822179\pi$
$648$	−383.670	−	752.995i	−0.592083	−	1.16203i
$649$			247.058i			0.380675i
$650$		0			0
$651$	−1918.14			−2.94646
$652$	−111.558	+	56.8419i	−0.171102	+	0.0871808i
$653$	−1110.46	+	175.880i	−1.70055	+	0.269341i	−0.929873	−	0.367881i	$-0.880083\pi$
$653$	−1110.46	+	175.880i	−1.70055	+	0.269341i	−0.770680	+	0.637222i	$0.780083\pi$
$654$	262.292	−	361.014i	0.401058	−	0.552009i
$655$		0			0
$656$	−358.031	+	260.125i	−0.545779	+	0.396531i
$657$	90.5672	+	90.5672i	0.137850	+	0.137850i
$658$	−185.249	+	1169.62i	−0.281534	+	1.77754i
$659$	837.920	−	272.257i	1.27150	−	0.413136i	0.405923	−	0.913907i	$-0.366950\pi$
$659$	837.920	−	272.257i	1.27150	−	0.413136i	0.865580	+	0.500771i	$0.166950\pi$
$660$		0			0
$661$	−406.010	+	1249.57i	−0.614235	+	1.89042i	−0.201834	+	0.979420i	$0.564690\pi$
$661$	−406.010	+	1249.57i	−0.614235	+	1.89042i	−0.412401	+	0.911002i	$0.635310\pi$
$662$	−225.237	+	442.052i	−0.340237	+	0.667752i
$663$	426.239	+	217.180i	0.642894	+	0.327571i
$664$	503.329	+	163.541i	0.758025	+	0.246297i
$665$		0			0
$666$	−45.1558	−	138.975i	−0.0678015	−	0.208671i
$667$	85.2129	+	13.4964i	0.127756	+	0.0202345i
$668$	16.0281	−	16.0281i	0.0239941	−	0.0239941i
$669$	76.3738	+	105.120i	0.114161	+	0.157129i
$670$		0			0
$671$	306.909	+	222.983i	0.457391	+	0.332314i
$672$	68.4258	+	432.024i	0.101824	+	0.642893i
$673$	533.613	+	1047.27i	0.792887	+	1.55613i	0.830620	+	0.556840i	$0.187986\pi$
$673$	533.613	+	1047.27i	0.792887	+	1.55613i	−0.0377336	+	0.999288i	$0.512014\pi$
$674$		−	1034.48i		−	1.53483i
$675$		0			0
$676$	70.3775			0.104109
$677$	1025.90	−	522.720i	1.51536	−	0.772112i	0.518789	−	0.854902i	$-0.326383\pi$
$677$	1025.90	−	522.720i	1.51536	−	0.772112i	0.996567	+	0.0827899i	$0.0263830\pi$
$678$	694.942	−	110.068i	1.02499	−	0.162342i
$679$	−977.170	+	1344.96i	−1.43913	+	1.98079i
$680$		0			0
$681$	−817.042	+	593.616i	−1.19977	+	0.871683i
$682$	290.699	+	290.699i	0.426245	+	0.426245i
$683$	−99.8898	+	630.679i	−0.146252	+	0.923396i	0.800008	+	0.599989i	$0.204828\pi$
$683$	−99.8898	+	630.679i	−0.146252	+	0.923396i	−0.946260	+	0.323407i	$0.895172\pi$
$684$	8.84724	−	2.87464i	0.0129346	−	0.00420269i
$685$		0			0
$686$	−205.013	+	630.965i	−0.298853	+	0.919775i
$687$	−550.418	+	1080.26i	−0.801191	+	1.57243i
$688$	217.404	+	110.773i	0.315995	+	0.161007i
$689$	126.881	+	41.2261i	0.184152	+	0.0598347i
$690$		0			0
$691$	−230.779	−	710.264i	−0.333978	−	1.02788i	−0.967223	−	0.253928i	$-0.918277\pi$
$691$	−230.779	−	710.264i	−0.333978	−	1.02788i	0.633245	−	0.773951i	$-0.281723\pi$
$692$	109.012	+	17.2658i	0.157532	+	0.0249506i
$693$	−112.423	+	112.423i	−0.162227	+	0.162227i
$694$	357.066	+	491.460i	0.514505	+	0.708155i
$695$		0			0
$696$	594.692	+	432.069i	0.854443	+	0.620789i
$697$	−90.8888	−	573.849i	−0.130400	−	0.823313i
$698$	−414.746	−	813.985i	−0.594192	−	1.16617i
$699$			274.189i			0.392259i
$700$		0			0
$701$	1200.51			1.71256			0.856282	−	0.516508i	$-0.172768\pi$
$701$	1200.51			1.71256			0.856282	+	0.516508i	$0.172768\pi$
$702$	278.849	−	142.081i	0.397222	−	0.202394i
$703$	−117.792	+	18.6565i	−0.167557	+	0.0265383i
$704$	194.296	−	267.425i	0.275988	−	0.379866i
$705$		0			0
$706$	−258.094	+	187.516i	−0.365573	+	0.265604i
$707$	−924.544	−	924.544i	−1.30770	−	1.30770i
$708$	20.1316	−	127.106i	0.0284345	−	0.179528i
$709$	−428.385	+	139.191i	−0.604210	+	0.196320i	−0.595117	−	0.803639i	$-0.702894\pi$
$709$	−428.385	+	139.191i	−0.604210	+	0.196320i	−0.00909262	+	0.999959i	$0.502894\pi$
$710$		0			0
$711$	73.3329	−	225.696i	0.103141	−	0.317434i
$712$	−370.913	+	727.957i	−0.520945	+	1.02241i
$713$	−150.199	−	76.5302i	−0.210658	−	0.107335i
$714$	1137.82	+	369.701i	1.59359	+	0.517788i
$715$		0			0
$716$	6.84110	+	21.0547i	0.00955460	+	0.0294060i
$717$	1350.58	+	213.911i	1.88365	+	0.298341i
$718$	−175.194	+	175.194i	−0.244002	+	0.244002i
$719$	571.568	+	786.696i	0.794949	+	1.09415i	0.993474	+	0.114057i	$0.0363847\pi$
$719$	571.568	+	786.696i	0.794949	+	1.09415i	−0.198526	+	0.980096i	$0.563615\pi$
$720$		0			0
$721$	1471.57	+	1069.16i	2.04101	+	1.48288i
$722$	−96.9837	−	612.331i	−0.134326	−	0.848104i
$723$	49.2361	+	96.6314i	0.0680998	+	0.133653i
$724$		−	15.1813i		−	0.0209686i
$725$		0			0
$726$	−624.515			−0.860214
$727$	247.938	−	126.331i	0.341043	−	0.173770i	−0.275077	−	0.961422i	$-0.588703\pi$
$727$	247.938	−	126.331i	0.341043	−	0.173770i	0.616120	+	0.787652i	$0.288703\pi$
$728$	−796.433	+	126.143i	−1.09400	+	0.173273i
$729$	207.054	−	284.985i	0.284024	−	0.390926i
$730$		0			0
$731$	−259.155	+	188.287i	−0.354522	+	0.257575i
$732$	−139.728	−	139.728i	−0.190886	−	0.190886i
$733$	−17.0101	+	107.397i	−0.0232061	+	0.146518i	−0.996571	−	0.0827448i	$-0.973631\pi$
$733$	−17.0101	+	107.397i	−0.0232061	+	0.146518i	0.973365	+	0.229262i	$0.0736314\pi$
$734$	−577.937	+	187.783i	−0.787380	+	0.255835i
$735$		0			0
$736$	−11.8789	+	36.5594i	−0.0161398	+	0.0496731i
$737$	8.02048	−	15.7411i	0.0108826	−	0.0213583i
$738$	168.676	+	85.9448i	0.228559	+	0.116456i
$739$	1097.79	+	356.694i	1.48551	+	0.482671i	0.935754	−	0.352654i	$-0.114721\pi$
$739$	1097.79	+	356.694i	1.48551	+	0.482671i	0.549755	+	0.835326i	$0.314721\pi$
$740$		0			0
$741$	39.3111	+	120.987i	0.0530515	+	0.163276i
$742$	329.538	+	52.1937i	0.444121	+	0.0703419i
$743$	8.69864	−	8.69864i	0.0117075	−	0.0117075i	−0.701229	−	0.712936i	$-0.747365\pi$
$743$	8.69864	−	8.69864i	0.0117075	−	0.0117075i	0.712936	+	0.701229i	$0.247365\pi$
$744$	−844.216	−	1161.96i	−1.13470	−	1.56178i
$745$		0			0
$746$	271.091	+	196.959i	0.363393	+	0.264020i
$747$	−29.0130	−	183.181i	−0.0388393	−	0.245222i
$748$	24.7314	+	48.5380i	0.0330633	+	0.0648904i
$749$		−	565.530i		−	0.755047i
$750$		0			0
$751$	−452.240			−0.602183			−0.301092	−	0.953595i	$-0.597351\pi$
$751$	−452.240			−0.602183			−0.301092	+	0.953595i	$0.597351\pi$
$752$	−647.237	+	329.784i	−0.860688	+	0.438542i
$753$	532.527	−	84.3439i	0.707207	−	0.112011i
$754$	−219.811	+	302.544i	−0.291527	+	0.401252i
$755$		0			0
$756$	−134.523	+	97.7370i	−0.177941	+	0.129282i
$757$	706.820	+	706.820i	0.933712	+	0.933712i	0.997936	−	0.0642239i	$-0.0204572\pi$
$757$	706.820	+	706.820i	0.933712	+	0.933712i	−0.0642239	+	0.997936i	$0.520457\pi$
$758$	69.2411	−	437.171i	0.0913471	−	0.576743i
$759$	−53.2585	+	17.3047i	−0.0701693	+	0.0227994i
$760$		0			0
$761$	449.482	−	1383.36i	0.590646	−	1.81782i	0.0153439	−	0.999882i	$-0.495116\pi$
$761$	449.482	−	1383.36i	0.590646	−	1.81782i	0.575303	−	0.817941i	$-0.304884\pi$
$762$	−11.7053	+	22.9729i	−0.0153613	+	0.0301482i
$763$	−720.814	−	367.273i	−0.944710	−	0.481354i
$764$	−73.6625	−	23.9344i	−0.0964169	−	0.0313278i
$765$		0			0
$766$	−362.827	−	1116.67i	−0.473665	−	1.45779i
$767$	433.702	+	68.6917i	0.565453	+	0.0895590i
$768$	−318.816	+	318.816i	−0.415125	+	0.415125i
$769$	−181.101	−	249.264i	−0.235502	−	0.324141i	0.674866	−	0.737940i	$-0.264201\pi$
$769$	−181.101	−	249.264i	−0.235502	−	0.324141i	−0.910368	+	0.413800i	$0.864201\pi$
$770$		0			0
$771$	−197.507	−	143.497i	−0.256170	−	0.186118i
$772$	−31.4581	−	198.619i	−0.0407489	−	0.257278i
$773$	1.75392	+	3.44225i	0.00226897	+	0.00445311i	0.892138	−	0.451763i	$-0.149205\pi$
$773$	1.75392	+	3.44225i	0.00226897	+	0.00445311i	−0.889869	+	0.456216i	$0.849205\pi$
$774$		−	104.375i		−	0.134852i
$775$		0			0
$776$	−1244.82			−1.60415
$777$	−946.008	+	482.015i	−1.21751	+	0.620354i
$778$	1317.90	−	208.735i	1.69396	−	0.268297i
$779$	90.8150	−	124.996i	0.116579	−	0.160457i
$780$		0			0
$781$	107.270	−	77.9361i	0.137349	−	0.0997902i
$782$	74.3461	+	74.3461i	0.0950717	+	0.0950717i
$783$	−80.9101	+	510.846i	−0.103333	+	0.652422i
$784$	−979.131	+	318.139i	−1.24889	+	0.405789i
$785$		0			0
$786$	−173.731	+	534.689i	−0.221032	+	0.680266i
$787$	−60.1800	+	118.110i	−0.0764676	+	0.150076i	−0.926075	−	0.377340i	$-0.876839\pi$
$787$	−60.1800	+	118.110i	−0.0764676	+	0.150076i	0.849607	+	0.527416i	$0.176839\pi$
$788$	73.7433	+	37.5741i	0.0935829	+	0.0476829i
$789$	−1548.99	−	503.296i	−1.96323	−	0.637891i
$790$		0			0
$791$	−394.174	−	1213.14i	−0.498323	−	1.53368i
$792$	−117.583	−	18.6233i	−0.148464	−	0.0235143i
$793$	476.771	−	476.771i	0.601225	−	0.601225i
$794$	−200.448	−	275.894i	−0.252454	−	0.347473i
$795$		0			0
$796$	−172.614	−	125.412i	−0.216852	−	0.157552i
$797$	−149.295	−	942.614i	−0.187322	−	1.18270i	−0.884756	−	0.466054i	$-0.845675\pi$
$797$	−149.295	−	942.614i	−0.187322	−	1.18270i	0.697435	−	0.716648i	$-0.254325\pi$
$798$	144.436	+	283.472i	0.180998	+	0.355228i
$799$		−	953.669i		−	1.19358i
$800$		0			0
$801$	286.312			0.357443
$802$	142.984	−	72.8539i	0.178284	−	0.0908402i
$803$	−197.000	+	31.2018i	−0.245331	+	0.0388565i
$804$	−5.40903	+	7.44490i	−0.00672765	+	0.00925982i
$805$		0			0
$806$	591.139	−	429.487i	0.733423	−	0.532863i
$807$	−912.465	−	912.465i	−1.13069	−	1.13069i
$808$	153.154	−	966.978i	0.189547	−	1.19676i
$809$	1278.62	−	415.449i	1.58049	−	0.513534i	0.618310	−	0.785934i	$-0.287818\pi$
$809$	1278.62	−	415.449i	1.58049	−	0.513534i	0.962184	+	0.272400i	$0.0878175\pi$
$810$		0			0
$811$	168.798	−	519.506i	0.208135	−	0.640574i	−0.791435	−	0.611253i	$-0.790666\pi$
$811$	168.798	−	519.506i	0.208135	−	0.640574i	0.999570	−	0.0293206i	$-0.00933438\pi$
$812$	90.2047	−	177.037i	0.111090	−	0.218025i
$813$	−1029.32	−	524.463i	−1.26607	−	0.645095i
$814$	216.421	+	70.3193i	0.265873	+	0.0863873i
$815$		0			0
$816$	226.782	+	697.963i	0.277919	+	0.855347i
$817$	−84.1363	−	13.3259i	−0.102982	−	0.0163108i
$818$	−232.805	+	232.805i	−0.284603	+	0.284603i
$819$	166.097	+	228.613i	0.202805	+	0.279137i
$820$		0			0
$821$	124.274	+	90.2905i	0.151369	+	0.109976i	0.660892	−	0.750481i	$-0.270178\pi$
$821$	124.274	+	90.2905i	0.151369	+	0.109976i	−0.509523	+	0.860457i	$0.670178\pi$
$822$	−78.7880	−	497.448i	−0.0958491	−	0.605168i
$823$	112.681	+	221.149i	0.136915	+	0.268711i	0.949276	−	0.314444i	$-0.101818\pi$
$823$	112.681	+	221.149i	0.136915	+	0.268711i	−0.812361	+	0.583155i	$0.801818\pi$
$824$			1362.00i			1.65291i
$825$		0			0
$826$	1098.17			1.32950
$827$	−8.58569	+	4.37463i	−0.0103817	+	0.00528976i	−0.459174	−	0.888347i	$-0.651854\pi$
$827$	−8.58569	+	4.37463i	−0.0103817	+	0.00528976i	0.448792	+	0.893636i	$0.351854\pi$
$828$	7.18859	−	1.13856i	0.00868187	−	0.00137507i
$829$	−360.443	+	496.107i	−0.434792	+	0.598440i	−0.969045	−	0.246885i	$-0.920593\pi$
$829$	−360.443	+	496.107i	−0.434792	+	0.598440i	0.534253	+	0.845325i	$0.320593\pi$
$830$		0			0
$831$	803.400	−	583.704i	0.966787	−	0.702412i
$832$	−415.435	−	415.435i	−0.499320	−	0.499320i
$833$	211.437	−	1334.96i	0.253826	−	1.60260i
$834$	217.802	−	70.7682i	0.261153	−	0.0848539i
$835$		0			0
$836$	−4.47656	+	13.7774i	−0.00535474	+	0.0164802i
$837$	458.794	−	900.434i	0.548141	−	1.07579i
$838$	312.279	+	159.114i	0.372647	+	0.189873i
$839$	−1114.35	−	362.075i	−1.32819	−	0.431555i	−0.442890	−	0.896576i	$-0.646047\pi$
$839$	−1114.35	−	362.075i	−1.32819	−	0.431555i	−0.885300	+	0.465021i	$0.846047\pi$
$840$		0			0
$841$	68.9002	+	212.053i	0.0819265	+	0.252144i
$842$	−1463.02	−	231.719i	−1.73755	−	0.275201i
$843$	491.835	−	491.835i	0.583435	−	0.583435i
$844$	−133.523	−	183.779i	−0.158203	−	0.217747i
$845$		0			0
$846$	251.391	+	182.647i	0.297153	+	0.215894i
$847$	177.114	+	1118.25i	0.209107	+	1.32025i
$848$	92.9160	+	182.358i	0.109571	+	0.215045i
$849$			563.213i			0.663384i
$850$		0			0
$851$	−93.3081			−0.109645
$852$	−61.5387	+	31.3556i	−0.0722286	+	0.0368023i
$853$	488.140	−	77.3137i	0.572262	−	0.0906374i	0.136405	−	0.990653i	$-0.456445\pi$
$853$	488.140	−	77.3137i	0.572262	−	0.0906374i	0.435857	+	0.900016i	$0.356445\pi$
$854$	991.150	−	1364.20i	1.16060	−	1.59742i
$855$		0			0
$856$	342.584	−	248.902i	0.400216	−	0.290774i
$857$	127.840	+	127.840i	0.149171	+	0.149171i	0.777748	−	0.628577i	$-0.216362\pi$
$857$	127.840	+	127.840i	0.149171	+	0.149171i	−0.628577	+	0.777748i	$0.716362\pi$
$858$	37.9718	−	239.744i	0.0442562	−	0.279422i
$859$	−242.766	+	78.8793i	−0.282614	+	0.0918269i	−0.446894	−	0.894587i	$-0.647470\pi$
$859$	−242.766	+	78.8793i	−0.282614	+	0.0918269i	0.164280	+	0.986414i	$0.447470\pi$
$860$		0			0
$861$	425.048	−	1308.16i	0.493668	−	1.51935i
$862$	−203.625	+	399.636i	−0.236224	+	0.463615i
$863$	725.309	+	369.564i	0.840451	+	0.428231i	0.820553	−	0.571571i	$-0.193666\pi$
$863$	725.309	+	369.564i	0.840451	+	0.428231i	0.0198983	+	0.999802i	$0.493666\pi$
$864$	−219.172	−	71.2132i	−0.253671	−	0.0824226i
$865$		0			0
$866$	433.170	+	1333.16i	0.500196	+	1.53944i
$867$	36.8646	+	5.83878i	0.0425198	+	0.00673447i
$868$	−274.516	+	274.516i	−0.316263	+	0.316263i
$869$	217.218	+	298.975i	0.249964	+	0.344045i
$870$		0			0
$871$	−25.4029	−	18.4563i	−0.0291652	−	0.0211898i
$872$	−94.7609	−	598.297i	−0.108671	−	0.686120i
$873$	198.046	+	388.688i	0.226857	+	0.445232i
$874$			27.9598i			0.0319906i
$875$		0			0
$876$	103.895			0.118602
$877$	−1141.28	+	581.509i	−1.30134	+	0.663067i	−0.960821	−	0.277170i	$-0.910603\pi$
$877$	−1141.28	+	581.509i	−1.30134	+	0.663067i	−0.340521	+	0.940237i	$0.610603\pi$
$878$	−32.0033	+	5.06882i	−0.0364502	+	0.00577315i
$879$	−775.599	+	1067.52i	−0.882365	+	1.21447i
$880$		0			0
$881$	−1038.70	+	754.660i	−1.17900	+	0.856595i	−0.992059	−	0.125776i	$-0.959858\pi$
$881$	−1038.70	+	754.660i	−1.17900	+	0.856595i	−0.186943	+	0.982371i	$0.559858\pi$
$882$	311.408	+	311.408i	0.353070	+	0.353070i
$883$	101.079	−	638.190i	0.114473	−	0.722752i	−0.861968	−	0.506963i	$-0.830768\pi$
$883$	101.079	−	638.190i	0.114473	−	0.722752i	0.976440	−	0.215788i	$-0.0692321\pi$
$884$	92.0832	−	29.9197i	0.104167	−	0.0338458i
$885$		0			0
$886$	−146.700	+	451.497i	−0.165576	+	0.509590i
$887$	−8.37810	+	16.4430i	−0.00944544	+	0.0185377i	−0.895681	−	0.444697i	$-0.853311\pi$
$887$	−8.37810	+	16.4430i	−0.00944544	+	0.0185377i	0.886236	+	0.463235i	$0.153311\pi$
$888$	−708.352	−	360.923i	−0.797694	−	0.406445i
$889$	44.4547	+	14.4442i	0.0500053	+	0.0162477i
$890$		0			0
$891$	−142.518	−	438.624i	−0.159953	−	0.492283i
$892$	25.9745	+	4.11396i	0.0291194	+	0.00461207i
$893$	179.326	−	179.326i	0.200813	−	0.200813i
$894$	497.451	+	684.683i	0.556433	+	0.765865i
$895$		0			0
$896$	−779.949	−	566.666i	−0.870478	−	0.632440i
$897$	15.5700	+	98.3050i	0.0173578	+	0.109593i
$898$	−219.626	−	431.041i	−0.244573	−	0.480001i
$899$			1207.57i			1.34324i
$900$		0			0
$901$	−268.695			−0.298218
$902$	−262.673	+	133.838i	−0.291211	+	0.148380i
$903$	−749.033	+	118.635i	−0.829493	+	0.131379i
$904$	561.407	−	772.711i	0.621026	−	0.854769i
$905$		0			0
$906$	−20.5488	+	14.9295i	−0.0226807	+	0.0164785i
$907$	17.1888	+	17.1888i	0.0189512	+	0.0189512i	0.716519	−	0.697568i	$-0.245734\pi$
$907$	17.1888	+	17.1888i	0.0189512	+	0.0189512i	−0.697568	+	0.716519i	$0.745734\pi$
$908$	−31.9758	+	201.887i	−0.0352156	+	0.222343i
$909$	−326.300	+	106.021i	−0.358966	+	0.116635i
$910$		0			0
$911$	−541.240	+	1665.77i	−0.594116	+	1.82850i	−0.0350398	+	0.999386i	$0.511156\pi$
$911$	−541.240	+	1665.77i	−0.594116	+	1.82850i	−0.559077	+	0.829116i	$0.688844\pi$
$912$	−88.6000	+	173.887i	−0.0971492	+	0.190666i
$913$	257.337	+	131.120i	0.281858	+	0.143614i
$914$	−1156.29	−	375.700i	−1.26508	−	0.411051i
$915$		0			0
$916$	75.8281	+	233.375i	0.0827818	+	0.254776i
$917$	1006.68	+	159.442i	1.09780	+	0.173874i
$918$	−445.700	+	445.700i	−0.485512	+	0.485512i
$919$	−374.893	−	515.995i	−0.407935	−	0.561475i	0.554778	−	0.831998i	$-0.312803\pi$
$919$	−374.893	−	515.995i	−0.407935	−	0.561475i	−0.962713	+	0.270524i	$0.912803\pi$
$920$		0			0
$921$	61.5281	+	44.7028i	0.0668058	+	0.0485372i
$922$	−13.3034	−	83.9941i	−0.0144288	−	0.0910999i
$923$	−106.989	−	209.978i	−0.115915	−	0.227495i
$924$			128.967i			0.139575i
$925$		0			0
$926$	−629.218			−0.679501
$927$	425.277	−	216.689i	0.458767	−	0.233753i
$928$	271.982	−	43.0777i	0.293084	−	0.0464199i
$929$	394.294	−	542.700i	0.424429	−	0.584176i	−0.542234	−	0.840227i	$-0.682422\pi$
$929$	394.294	−	542.700i	0.424429	−	0.584176i	0.966663	+	0.256051i	$0.0824215\pi$
$930$		0			0
$931$	290.782	−	211.266i	0.312333	−	0.226923i
$932$	39.2408	+	39.2408i	0.0421038	+	0.0421038i
$933$	−234.155	+	1478.40i	−0.250970	+	1.58456i
$934$	186.226	−	60.5086i	0.199386	−	0.0647844i
$935$		0			0
$936$	−65.3853	+	201.235i	−0.0698561	+	0.214995i
$937$	−58.1616	+	114.149i	−0.0620721	+	0.121823i	−0.919958	−	0.392017i	$-0.871778\pi$
$937$	−58.1616	+	114.149i	−0.0620721	+	0.121823i	0.857886	+	0.513840i	$0.171778\pi$
$938$	−69.9685	−	35.6507i	−0.0745933	−	0.0380072i
$939$	309.793	+	100.658i	0.329918	+	0.107197i
$940$		0			0
$941$	−46.4634	−	143.000i	−0.0493766	−	0.151966i	0.923328	−	0.384012i	$-0.125458\pi$
$941$	−46.4634	−	143.000i	−0.0493766	−	0.151966i	−0.972705	+	0.232046i	$0.925458\pi$
$942$	970.280	+	153.677i	1.03002	+	0.163139i
$943$	85.4764	−	85.4764i	0.0906431	−	0.0906431i
$944$	395.954	+	544.984i	0.419443	+	0.577313i
$945$		0			0
$946$	131.497	+	95.5383i	0.139003	+	0.100992i
$947$	238.481	+	1505.71i	0.251828	+	1.58998i	0.712019	+	0.702160i	$0.247781\pi$
$947$	238.481	+	1505.71i	0.251828	+	1.58998i	−0.460191	+	0.887820i	$0.652219\pi$
$948$	−87.3921	−	171.517i	−0.0921858	−	0.180925i
$949$			354.503i			0.373554i
$950$		0			0
$951$	668.951			0.703419
$952$	1447.04	−	737.302i	1.52000	−	0.774477i
$953$	608.849	−	96.4322i	0.638876	−	0.101188i	0.171411	−	0.985200i	$-0.445167\pi$
$953$	608.849	−	96.4322i	0.638876	−	0.101188i	0.467465	+	0.884012i	$0.345167\pi$
$954$	51.4604	−	70.8291i	0.0539417	−	0.0742443i
$955$		0			0
$956$	223.903	−	162.675i	0.234208	−	0.170162i
$957$	283.658	+	283.658i	0.296403	+	0.296403i
$958$	−103.585	+	654.012i	−0.108127	+	0.682685i
$959$	−868.381	+	282.154i	−0.905506	+	0.294217i
$960$		0			0
$961$	432.150	−	1330.02i	0.449688	−	1.38400i
$962$	183.616	−	360.368i	0.190870	−	0.374603i
$963$	−132.222	−	67.3707i	−0.137303	−	0.0699592i
$964$	20.8759	+	6.78300i	0.0216555	+	0.00703630i
$965$		0			0
$966$	76.9190	+	236.732i	0.0796263	+	0.245065i
$967$	136.090	+	21.5545i	0.140734	+	0.0222901i	0.226404	−	0.974033i	$-0.427303\pi$
$967$	136.090	+	21.5545i	0.140734	+	0.0222901i	−0.0856700	+	0.996324i	$0.527303\pi$
$968$	−599.458	+	599.458i	−0.619275	+	0.619275i
$969$	−150.599	−	207.281i	−0.155416	−	0.213912i
$970$		0			0
$971$	596.601	+	433.456i	0.614419	+	0.446401i	0.850968	−	0.525218i	$-0.176016\pi$
$971$	596.601	+	433.456i	0.614419	+	0.446401i	−0.236549	+	0.971620i	$0.576016\pi$
$972$	17.0507	+	107.654i	0.0175419	+	0.110755i
$973$	−188.486	−	369.924i	−0.193716	−	0.380189i
$974$		−	687.587i		−	0.705942i
$975$		0			0
$976$	1034.38			1.05981
$977$	−443.170	+	225.806i	−0.453603	+	0.231122i	−0.665838	−	0.746096i	$-0.731926\pi$
$977$	−443.170	+	225.806i	−0.453603	+	0.231122i	0.212235	+	0.977219i	$0.431926\pi$
$978$	−1109.78	+	175.772i	−1.13475	+	0.179726i
$979$	−262.071	+	360.710i	−0.267693	+	0.368447i
$980$		0			0
$981$	−171.739	+	124.776i	−0.175065	+	0.127192i
$982$	−336.216	−	336.216i	−0.342379	−	0.342379i
$983$	−117.421	+	741.369i	−0.119452	+	0.754190i	0.853142	+	0.521679i	$0.174694\pi$
$983$	−117.421	+	741.369i	−0.119452	+	0.754190i	−0.972594	+	0.232511i	$0.925306\pi$
$984$	979.527	−	318.268i	0.995455	−	0.323443i
$985$		0			0
$986$	232.746	−	716.319i	0.236051	−	0.726490i
$987$	1025.00	−	2011.67i	1.03850	−	2.03817i
$988$	22.9412	+	11.6891i	0.0232198	+	0.0118311i
$989$	−63.3859	−	20.5953i	−0.0640909	−	0.0208244i
$990$		0			0
$991$	−40.9055	−	125.894i	−0.0412770	−	0.127038i	0.928294	−	0.371846i	$-0.121275\pi$
$991$	−40.9055	−	125.894i	−0.0412770	−	0.127038i	−0.969572	+	0.244808i	$0.921275\pi$
$992$	−531.423	−	84.1692i	−0.535709	−	0.0848480i
$993$	668.850	−	668.850i	0.673565	−	0.673565i
$994$	−346.424	−	476.811i	−0.348515	−	0.479689i
$995$		0			0
$996$	−121.710	−	88.4274i	−0.122199	−	0.0887825i
$997$	78.2443	+	494.015i	0.0784797	+	0.495501i	0.995351	+	0.0963177i	$0.0307065\pi$
$997$	78.2443	+	494.015i	0.0784797	+	0.495501i	−0.916871	+	0.399184i	$0.869294\pi$
$998$	62.0230	+	121.727i	0.0621473	+	0.121971i
$999$		−	559.376i		−	0.559936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.3.f.c.7.3		32
5.2	odd	4		125.3.f.a.118.3		32
5.3	odd	4		125.3.f.b.118.2		32
5.4	even	2		25.3.f.a.22.2	yes	32
15.14	odd	2		225.3.r.a.172.3		32
20.19	odd	2		400.3.bg.c.97.1		32
25.6	even	5		125.3.f.b.107.2		32
25.8	odd	20	inner	125.3.f.c.18.3		32
25.17	odd	20		25.3.f.a.8.2	✓	32
25.19	even	10		125.3.f.a.107.3		32
75.17	even	20		225.3.r.a.208.3		32
100.67	even	20		400.3.bg.c.33.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.8.2	✓	32	25.17	odd	20
25.3.f.a.22.2	yes	32	5.4	even	2
125.3.f.a.107.3		32	25.19	even	10
125.3.f.a.118.3		32	5.2	odd	4
125.3.f.b.107.2		32	25.6	even	5
125.3.f.b.118.2		32	5.3	odd	4
125.3.f.c.7.3		32	1.1	even	1	trivial
125.3.f.c.18.3		32	25.8	odd	20	inner
225.3.r.a.172.3		32	15.14	odd	2
225.3.r.a.208.3		32	75.17	even	20
400.3.bg.c.33.1		32	100.67	even	20
400.3.bg.c.97.1		32	20.19	odd	2

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	125.f (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.61837 - 0.824603i) q^{2} +(-3.42034 + 0.541729i) q^{3} +(-0.411975 + 0.567034i) q^{4} +(-5.08868 + 3.69715i) q^{6} +(8.06323 + 8.06323i) q^{7} +(-1.33571 + 8.43332i) q^{8} +(2.84577 - 0.924645i) q^{9} +O(q^{10})\)	\(q+(1.61837 - 0.824603i) q^{2} +(-3.42034 + 0.541729i) q^{3} +(-0.411975 + 0.567034i) q^{4} +(-5.08868 + 3.69715i) q^{6} +(8.06323 + 8.06323i) q^{7} +(-1.33571 + 8.43332i) q^{8} +(2.84577 - 0.924645i) q^{9} +(-1.43991 + 4.43160i) q^{11} +(1.10192 - 2.16263i) q^{12} +(7.37917 + 3.75988i) q^{13} +(19.6983 + 6.40037i) q^{14} +(3.92612 + 12.0833i) q^{16} +(-16.4746 - 2.60932i) q^{17} +(3.84305 - 3.84305i) q^{18} +(-2.60721 - 3.58851i) q^{19} +(-31.9471 - 23.2109i) q^{21} +(1.32399 + 8.35934i) q^{22} +(-1.57553 - 3.09215i) q^{23} -29.5684i q^{24} +15.0427 q^{26} +(18.5372 - 9.44519i) q^{27} +(-7.89398 + 1.25028i) q^{28} +(-14.6125 + 20.1124i) q^{29} +(39.2975 - 28.5513i) q^{31} +(-7.83247 - 7.83247i) q^{32} +(2.52427 - 15.9376i) q^{33} +(-28.8138 + 9.36216i) q^{34} +(-0.648078 + 1.99458i) q^{36} +(12.2064 - 23.9564i) q^{37} +(-7.17853 - 3.65765i) q^{38} +(-27.2761 - 8.86255i) q^{39} +(10.7638 + 33.1275i) q^{41} +(-70.8422 - 11.2203i) q^{42} +(13.5798 - 13.5798i) q^{43} +(-1.91966 - 2.64219i) q^{44} +(-5.09959 - 3.70507i) q^{46} +(8.94405 + 56.4705i) q^{47} +(-19.9746 - 39.2023i) q^{48} +81.0315i q^{49} +57.7624 q^{51} +(-5.17201 + 2.63527i) q^{52} +(15.9105 - 2.51997i) q^{53} +(22.2117 - 30.5717i) q^{54} +(-78.7699 + 57.2297i) q^{56} +(10.8615 + 10.8615i) q^{57} +(-7.06378 + 44.5989i) q^{58} +(50.4257 - 16.3843i) q^{59} +(25.1583 - 77.4292i) q^{61} +(40.0545 - 78.6115i) q^{62} +(30.4017 + 15.4904i) q^{63} +(-67.4679 - 21.9217i) q^{64} +(-9.05700 - 27.8746i) q^{66} +(-3.74472 - 0.593105i) q^{67} +(8.26671 - 8.26671i) q^{68} +(7.06395 + 9.72269i) q^{69} +(-23.0210 - 16.7257i) q^{71} +(3.99672 + 25.2343i) q^{72} +(19.4330 + 38.1394i) q^{73} -48.8358i q^{74} +3.10891 q^{76} +(-47.3434 + 24.1226i) q^{77} +(-51.4511 + 8.14905i) q^{78} +(46.6168 - 64.1625i) q^{79} +(-80.0737 + 58.1770i) q^{81} +(44.7368 + 44.7368i) q^{82} +(9.69615 - 61.2191i) q^{83} +(26.3228 - 8.55280i) q^{84} +(10.7792 - 33.1750i) q^{86} +(39.0843 - 76.7073i) q^{87} +(-35.4498 - 18.0626i) q^{88} +(91.0024 + 29.5685i) q^{89} +(29.1832 + 89.8167i) q^{91} +(2.40243 + 0.380508i) q^{92} +(-118.944 + 118.944i) q^{93} +(61.0406 + 84.0152i) q^{94} +(31.0328 + 22.5467i) q^{96} +(22.8066 + 143.995i) q^{97} +(66.8188 + 131.139i) q^{98} +13.9427i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} + 10 q^{3} - 10 q^{4} - 6 q^{6} + 10 q^{7} + 10 q^{8} - 10 q^{9}+O(q^{10}) \) 32 * q + 10 * q^2 + 10 * q^3 - 10 * q^4 - 6 * q^6 + 10 * q^7 + 10 * q^8 - 10 * q^9	\( 32 q + 10 q^{2} + 10 q^{3} - 10 q^{4} - 6 q^{6} + 10 q^{7} + 10 q^{8} - 10 q^{9} - 6 q^{11} + 10 q^{12} + 10 q^{13} - 10 q^{14} + 2 q^{16} - 60 q^{17} - 140 q^{18} + 90 q^{19} - 6 q^{21} - 70 q^{22} - 10 q^{23} + 4 q^{26} + 100 q^{27} + 250 q^{28} - 110 q^{29} - 6 q^{31} + 290 q^{32} + 190 q^{33} - 260 q^{34} - 58 q^{36} - 50 q^{37} - 320 q^{38} + 390 q^{39} - 86 q^{41} - 690 q^{42} - 230 q^{43} + 340 q^{44} - 6 q^{46} - 70 q^{47} - 160 q^{48} - 16 q^{51} + 320 q^{52} + 190 q^{53} - 660 q^{54} - 70 q^{56} + 650 q^{57} + 640 q^{58} - 260 q^{59} + 114 q^{61} - 60 q^{62} + 20 q^{63} + 340 q^{64} + 138 q^{66} - 270 q^{67} - 710 q^{68} + 340 q^{69} - 66 q^{71} - 360 q^{72} - 30 q^{73} - 80 q^{76} + 250 q^{77} + 500 q^{78} - 210 q^{79} + 62 q^{81} - 30 q^{82} - 10 q^{84} - 6 q^{86} - 300 q^{87} - 190 q^{88} - 10 q^{89} - 6 q^{91} + 30 q^{92} - 520 q^{93} + 790 q^{94} + 174 q^{96} - 270 q^{97} - 170 q^{98}+O(q^{100}) \) 32 * q + 10 * q^2 + 10 * q^3 - 10 * q^4 - 6 * q^6 + 10 * q^7 + 10 * q^8 - 10 * q^9 - 6 * q^11 + 10 * q^12 + 10 * q^13 - 10 * q^14 + 2 * q^16 - 60 * q^17 - 140 * q^18 + 90 * q^19 - 6 * q^21 - 70 * q^22 - 10 * q^23 + 4 * q^26 + 100 * q^27 + 250 * q^28 - 110 * q^29 - 6 * q^31 + 290 * q^32 + 190 * q^33 - 260 * q^34 - 58 * q^36 - 50 * q^37 - 320 * q^38 + 390 * q^39 - 86 * q^41 - 690 * q^42 - 230 * q^43 + 340 * q^44 - 6 * q^46 - 70 * q^47 - 160 * q^48 - 16 * q^51 + 320 * q^52 + 190 * q^53 - 660 * q^54 - 70 * q^56 + 650 * q^57 + 640 * q^58 - 260 * q^59 + 114 * q^61 - 60 * q^62 + 20 * q^63 + 340 * q^64 + 138 * q^66 - 270 * q^67 - 710 * q^68 + 340 * q^69 - 66 * q^71 - 360 * q^72 - 30 * q^73 - 80 * q^76 + 250 * q^77 + 500 * q^78 - 210 * q^79 + 62 * q^81 - 30 * q^82 - 10 * q^84 - 6 * q^86 - 300 * q^87 - 190 * q^88 - 10 * q^89 - 6 * q^91 + 30 * q^92 - 520 * q^93 + 790 * q^94 + 174 * q^96 - 270 * q^97 - 170 * q^98

Introduction

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