LMFDB - Embedded newform 210.3.o.a.61.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(31,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("210.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.o (of order $6$, degree $2$, 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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			61.2
Root			$-1.72286 - 0.178197i$ of defining polynomial
Character	$\chi$	$=$	210.61
Dual form			210.3.o.a.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} +2.44949i q^{6} +(6.51658 + 2.55620i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} +2.44949i q^{6} +(6.51658 + 2.55620i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-2.73861 + 1.58114i) q^{10} +(-5.79240 - 10.0327i) q^{11} +(-3.00000 - 1.73205i) q^{12} +7.86371i q^{13} +(-7.73861 + 6.17364i) q^{14} +3.87298 q^{15} +(-2.00000 + 3.46410i) q^{16} +(23.9080 - 13.8033i) q^{17} +(2.12132 + 3.67423i) q^{18} +(27.2149 + 15.7125i) q^{19} -4.47214i q^{20} +(11.9886 - 1.80922i) q^{21} +16.3834 q^{22} +(-9.07959 + 15.7263i) q^{23} +(4.24264 - 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-9.63104 - 5.56049i) q^{26} -5.19615i q^{27} +(-2.08911 - 13.8433i) q^{28} -2.30331 q^{29} +(-2.73861 + 4.74342i) q^{30} +(-4.55860 + 2.63191i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-17.3772 - 10.0327i) q^{33} +39.0416i q^{34} +(9.76139 + 12.2358i) q^{35} -6.00000 q^{36} +(-0.993142 + 1.72017i) q^{37} +(-38.4876 + 22.2208i) q^{38} +(6.81018 + 11.7956i) q^{39} +(5.47723 + 3.16228i) q^{40} +22.1905i q^{41} +(-6.26139 + 15.9623i) q^{42} +49.8368 q^{43} +(-11.5848 + 20.0655i) q^{44} +(5.80948 - 3.35410i) q^{45} +(-12.8405 - 22.2404i) q^{46} +(-66.3956 - 38.3335i) q^{47} +6.92820i q^{48} +(35.9317 + 33.3154i) q^{49} -7.07107 q^{50} +(23.9080 - 41.4099i) q^{51} +(13.6204 - 7.86371i) q^{52} +(-28.5477 - 49.4461i) q^{53} +(6.36396 + 3.67423i) q^{54} -25.9044i q^{55} +(18.4317 + 7.23003i) q^{56} +54.4297 q^{57} +(1.62869 - 2.82097i) q^{58} +(-60.9245 + 35.1748i) q^{59} +(-3.87298 - 6.70820i) q^{60} +(-58.5590 - 33.8091i) q^{61} -7.44416i q^{62} +(16.4161 - 13.0963i) q^{63} +8.00000 q^{64} +(-8.79190 + 15.2280i) q^{65} +(24.5751 - 14.1884i) q^{66} +(-49.0823 - 85.0131i) q^{67} +(-47.8160 - 27.6066i) q^{68} +31.4526i q^{69} +(-21.8881 + 3.30318i) q^{70} -34.2597 q^{71} +(4.24264 - 7.34847i) q^{72} +(16.8801 - 9.74573i) q^{73} +(-1.40452 - 2.43269i) q^{74} +(7.50000 + 4.33013i) q^{75} -62.8501i q^{76} +(-12.1010 - 80.1856i) q^{77} -19.2621 q^{78} +(-45.2142 + 78.3134i) q^{79} +(-7.74597 + 4.47214i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-27.1777 - 15.6911i) q^{82} -133.803i q^{83} +(-15.1223 - 18.9557i) q^{84} +61.7302 q^{85} +(-35.2400 + 61.0374i) q^{86} +(-3.45496 + 1.99472i) q^{87} +(-16.3834 - 28.3768i) q^{88} +(-9.58232 - 5.53235i) q^{89} +9.48683i q^{90} +(-20.1012 + 51.2445i) q^{91} +36.3184 q^{92} +(-4.55860 + 7.89573i) q^{93} +(93.8975 - 54.2118i) q^{94} +(35.1342 + 60.8543i) q^{95} +(-8.48528 - 4.89898i) q^{96} +72.3112i q^{97} +(-66.2104 + 20.4496i) q^{98} -34.7544 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{3} - 8 q^{4} + 12 q^{9}+O(q^{10}) $ 8 * q + 12 * q^3 - 8 * q^4 + 12 * q^9	$ 8 q + 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} - 24 q^{12} - 40 q^{14} - 16 q^{16} + 84 q^{17} + 108 q^{19} - 48 q^{22} + 12 q^{23} + 20 q^{25} - 96 q^{26} + 72 q^{29} - 132 q^{31} - 12 q^{33} + 100 q^{35} - 48 q^{36} - 96 q^{37} - 168 q^{38} + 24 q^{39} - 72 q^{42} - 112 q^{43} - 8 q^{44} + 8 q^{46} - 24 q^{47} + 156 q^{49} + 84 q^{51} + 48 q^{52} + 32 q^{53} + 16 q^{56} + 216 q^{57} + 104 q^{58} + 132 q^{59} + 96 q^{61} + 64 q^{64} + 20 q^{65} - 72 q^{66} - 120 q^{67} - 168 q^{68} + 8 q^{71} + 24 q^{73} - 16 q^{74} + 60 q^{75} - 216 q^{77} - 192 q^{78} + 12 q^{79} - 36 q^{81} + 24 q^{82} + 120 q^{85} - 40 q^{86} + 108 q^{87} + 48 q^{88} + 492 q^{89} - 308 q^{91} - 48 q^{92} - 132 q^{93} + 480 q^{94} - 40 q^{95} - 24 q^{99}+O(q^{100}) $ 8 * q + 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 - 24 * q^12 - 40 * q^14 - 16 * q^16 + 84 * q^17 + 108 * q^19 - 48 * q^22 + 12 * q^23 + 20 * q^25 - 96 * q^26 + 72 * q^29 - 132 * q^31 - 12 * q^33 + 100 * q^35 - 48 * q^36 - 96 * q^37 - 168 * q^38 + 24 * q^39 - 72 * q^42 - 112 * q^43 - 8 * q^44 + 8 * q^46 - 24 * q^47 + 156 * q^49 + 84 * q^51 + 48 * q^52 + 32 * q^53 + 16 * q^56 + 216 * q^57 + 104 * q^58 + 132 * q^59 + 96 * q^61 + 64 * q^64 + 20 * q^65 - 72 * q^66 - 120 * q^67 - 168 * q^68 + 8 * q^71 + 24 * q^73 - 16 * q^74 + 60 * q^75 - 216 * q^77 - 192 * q^78 + 12 * q^79 - 36 * q^81 + 24 * q^82 + 120 * q^85 - 40 * q^86 + 108 * q^87 + 48 * q^88 + 492 * q^89 - 308 * q^91 - 48 * q^92 - 132 * q^93 + 480 * q^94 - 40 * q^95 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$6$			2.44949i			0.408248i
$7$	6.51658	+	2.55620i	0.930940	+	0.365172i
$7$	6.51658	+	2.55620i	0.930940	+	0.365172i
$8$	2.82843			0.353553
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$	−2.73861	+	1.58114i	−0.273861	+	0.158114i
$11$	−5.79240	−	10.0327i	−0.526582	−	0.912066i	−0.999520	−	0.0309707i	$-0.990140\pi$
$11$	−5.79240	−	10.0327i	−0.526582	−	0.912066i	0.472939	−	0.881095i	$-0.343193\pi$
$12$	−3.00000	−	1.73205i	−0.250000	−	0.144338i
$13$			7.86371i			0.604901i	0.953165	+	0.302451i	$0.0978047\pi$
$13$			7.86371i			0.604901i	−0.953165	+	0.302451i	$0.902195\pi$
$14$	−7.73861	+	6.17364i	−0.552758	+	0.440975i
$15$	3.87298			0.258199
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	23.9080	−	13.8033i	1.40635	−	0.811959i	0.411320	−	0.911491i	$-0.365068\pi$
$17$	23.9080	−	13.8033i	1.40635	−	0.811959i	0.995034	+	0.0995321i	$0.0317346\pi$
$18$	2.12132	+	3.67423i	0.117851	+	0.204124i
$19$	27.2149	+	15.7125i	1.43236	+	0.826974i	0.997301	−	0.0734266i	$-0.0233935\pi$
$19$	27.2149	+	15.7125i	1.43236	+	0.826974i	0.435061	+	0.900401i	$0.356727\pi$
$20$		−	4.47214i		−	0.223607i
$21$	11.9886	−	1.80922i	0.570886	−	0.0861535i
$22$	16.3834			0.744699
$23$	−9.07959	+	15.7263i	−0.394765	+	0.683753i	−0.993071	−	0.117515i	$-0.962507\pi$
$23$	−9.07959	+	15.7263i	−0.394765	+	0.683753i	0.598306	+	0.801268i	$0.295841\pi$
$24$	4.24264	−	2.44949i	0.176777	−	0.102062i
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$	−9.63104	−	5.56049i	−0.370425	−	0.213865i
$27$		−	5.19615i		−	0.192450i
$28$	−2.08911	−	13.8433i	−0.0746112	−	0.494402i
$29$	−2.30331			−0.0794244			−0.0397122	−	0.999211i	$-0.512644\pi$
$29$	−2.30331			−0.0794244			−0.0397122	+	0.999211i	$0.512644\pi$
$30$	−2.73861	+	4.74342i	−0.0912871	+	0.158114i
$31$	−4.55860	+	2.63191i	−0.147052	+	0.0849003i	−0.571721	−	0.820448i	$-0.693724\pi$
$31$	−4.55860	+	2.63191i	−0.147052	+	0.0849003i	0.424669	+	0.905349i	$0.360391\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$	−17.3772	−	10.0327i	−0.526582	−	0.304022i
$34$			39.0416i			1.14828i
$35$	9.76139	+	12.2358i	0.278897	+	0.349595i
$36$	−6.00000			−0.166667
$37$	−0.993142	+	1.72017i	−0.0268417	+	0.0464912i	−0.879134	−	0.476574i	$-0.841878\pi$
$37$	−0.993142	+	1.72017i	−0.0268417	+	0.0464912i	0.852293	+	0.523065i	$0.175212\pi$
$38$	−38.4876	+	22.2208i	−1.01283	+	0.584759i
$39$	6.81018	+	11.7956i	0.174620	+	0.302451i
$40$	5.47723	+	3.16228i	0.136931	+	0.0790569i
$41$			22.1905i			0.541233i	0.962687	+	0.270616i	$0.0872275\pi$
$41$			22.1905i			0.541233i	−0.962687	+	0.270616i	$0.912773\pi$
$42$	−6.26139	+	15.9623i	−0.149081	+	0.380055i
$43$	49.8368			1.15900			0.579498	−	0.814974i	$-0.303249\pi$
$43$	49.8368			1.15900			0.579498	+	0.814974i	$0.303249\pi$
$44$	−11.5848	+	20.0655i	−0.263291	+	0.456033i
$45$	5.80948	−	3.35410i	0.129099	−	0.0745356i
$46$	−12.8405	−	22.2404i	−0.279141	−	0.483486i
$47$	−66.3956	−	38.3335i	−1.41267	−	0.815606i	−0.417032	−	0.908892i	$-0.636930\pi$
$47$	−66.3956	−	38.3335i	−1.41267	−	0.815606i	−0.995639	+	0.0932854i	$0.970263\pi$
$48$			6.92820i			0.144338i
$49$	35.9317	+	33.3154i	0.733300	+	0.679906i
$50$	−7.07107			−0.141421
$51$	23.9080	−	41.4099i	0.468785	−	0.811959i
$52$	13.6204	−	7.86371i	0.261930	−	0.151225i
$53$	−28.5477	−	49.4461i	−0.538636	−	0.932945i	−0.998978	−	0.0452033i	$-0.985606\pi$
$53$	−28.5477	−	49.4461i	−0.538636	−	0.932945i	0.460342	−	0.887742i	$-0.347727\pi$
$54$	6.36396	+	3.67423i	0.117851	+	0.0680414i
$55$		−	25.9044i		−	0.470989i
$56$	18.4317	+	7.23003i	0.329137	+	0.129108i
$57$	54.4297			0.954908
$58$	1.62869	−	2.82097i	0.0280808	−	0.0486373i
$59$	−60.9245	+	35.1748i	−1.03262	+	0.596182i	−0.917734	−	0.397196i	$-0.869983\pi$
$59$	−60.9245	+	35.1748i	−1.03262	+	0.596182i	−0.114885	+	0.993379i	$0.536650\pi$
$60$	−3.87298	−	6.70820i	−0.0645497	−	0.111803i
$61$	−58.5590	−	33.8091i	−0.959984	−	0.554247i	−0.0638160	−	0.997962i	$-0.520327\pi$
$61$	−58.5590	−	33.8091i	−0.959984	−	0.554247i	−0.896168	+	0.443715i	$0.853660\pi$
$62$		−	7.44416i		−	0.120067i
$63$	16.4161	−	13.0963i	0.260573	−	0.207877i
$64$	8.00000			0.125000
$65$	−8.79190	+	15.2280i	−0.135260	+	0.234277i
$66$	24.5751	−	14.1884i	0.372349	−	0.214976i
$67$	−49.0823	−	85.0131i	−0.732572	−	1.26885i	−0.955780	−	0.294081i	$-0.904986\pi$
$67$	−49.0823	−	85.0131i	−0.732572	−	1.26885i	0.223208	−	0.974771i	$-0.428347\pi$
$68$	−47.8160	−	27.6066i	−0.703177	−	0.405979i
$69$			31.4526i			0.455835i
$70$	−21.8881	+	3.30318i	−0.312687	+	0.0471882i
$71$	−34.2597			−0.482531			−0.241266	−	0.970459i	$-0.577563\pi$
$71$	−34.2597			−0.482531			−0.241266	+	0.970459i	$0.577563\pi$
$72$	4.24264	−	7.34847i	0.0589256	−	0.102062i
$73$	16.8801	−	9.74573i	0.231234	−	0.133503i	−0.379907	−	0.925025i	$-0.624044\pi$
$73$	16.8801	−	9.74573i	0.231234	−	0.133503i	0.611141	+	0.791521i	$0.290711\pi$
$74$	−1.40452	−	2.43269i	−0.0189799	−	0.0328742i
$75$	7.50000	+	4.33013i	0.100000	+	0.0577350i
$76$		−	62.8501i		−	0.826974i
$77$	−12.1010	−	80.1856i	−0.157155	−	1.04137i
$78$	−19.2621			−0.246950
$79$	−45.2142	+	78.3134i	−0.572332	+	0.991308i	0.423994	+	0.905665i	$0.360628\pi$
$79$	−45.2142	+	78.3134i	−0.572332	+	0.991308i	−0.996326	+	0.0856432i	$0.972705\pi$
$80$	−7.74597	+	4.47214i	−0.0968246	+	0.0559017i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−27.1777	−	15.6911i	−0.331436	−	0.191355i
$83$		−	133.803i		−	1.61209i	−0.591854	−	0.806045i	$-0.701604\pi$
$83$		−	133.803i		−	1.61209i	0.591854	−	0.806045i	$-0.298396\pi$
$84$	−15.1223	−	18.9557i	−0.180027	−	0.225663i
$85$	61.7302			0.726238
$86$	−35.2400	+	61.0374i	−0.409767	+	0.709737i
$87$	−3.45496	+	1.99472i	−0.0397122	+	0.0229279i
$88$	−16.3834	−	28.3768i	−0.186175	−	0.322464i
$89$	−9.58232	−	5.53235i	−0.107666	−	0.0621613i	0.445200	−	0.895431i	$-0.353133\pi$
$89$	−9.58232	−	5.53235i	−0.107666	−	0.0621613i	−0.552866	+	0.833270i	$0.686466\pi$
$90$			9.48683i			0.105409i
$91$	−20.1012	+	51.2445i	−0.220893	+	0.563127i
$92$	36.3184			0.394765
$93$	−4.55860	+	7.89573i	−0.0490172	+	0.0849003i
$94$	93.8975	−	54.2118i	0.998910	−	0.576721i
$95$	35.1342	+	60.8543i	0.369834	+	0.640572i
$96$	−8.48528	−	4.89898i	−0.0883883	−	0.0510310i
$97$			72.3112i			0.745476i	0.927937	+	0.372738i	$0.121581\pi$
$97$			72.3112i			0.745476i	−0.927937	+	0.372738i	$0.878419\pi$
$98$	−66.2104	+	20.4496i	−0.675616	+	0.208669i
$99$	−34.7544			−0.351054
$100$	5.00000	−	8.66025i	0.0500000	−	0.0866025i
$101$	43.8670	−	25.3266i	0.434327	−	0.250759i	−0.266861	−	0.963735i	$-0.585987\pi$
$101$	43.8670	−	25.3266i	0.434327	−	0.250759i	0.701188	+	0.712976i	$0.252653\pi$
$102$	33.8110	+	58.5625i	0.331481	+	0.574142i
$103$	−171.442	−	98.9823i	−1.66449	−	0.960993i	−0.970531	−	0.240978i	$-0.922532\pi$
$103$	−171.442	−	98.9823i	−1.66449	−	0.960993i	−0.693958	−	0.720015i	$-0.744135\pi$
$104$			22.2419i			0.213865i
$105$	25.2386	+	9.90012i	0.240368	+	0.0942869i
$106$	80.7451			0.761746
$107$	−73.9679	+	128.116i	−0.691289	+	1.19735i	0.280127	+	0.959963i	$0.409623\pi$
$107$	−73.9679	+	128.116i	−0.691289	+	1.19735i	−0.971416	+	0.237384i	$0.923710\pi$
$108$	−9.00000	+	5.19615i	−0.0833333	+	0.0481125i
$109$	27.1610	+	47.0442i	0.249183	+	0.431598i	0.963299	−	0.268429i	$-0.0865046\pi$
$109$	27.1610	+	47.0442i	0.249183	+	0.431598i	−0.714116	+	0.700027i	$0.753171\pi$
$110$	31.7263	+	18.3172i	0.288421	+	0.166520i
$111$			3.44035i			0.0309941i
$112$	−21.8881	+	17.4617i	−0.195429	+	0.155908i
$113$	47.7883			0.422906			0.211453	−	0.977388i	$-0.432181\pi$
$113$	47.7883			0.422906			0.211453	+	0.977388i	$0.432181\pi$
$114$	−38.4876	+	66.6625i	−0.337611	+	0.584759i
$115$	−35.1651	+	20.3026i	−0.305784	+	0.176544i
$116$	2.30331	+	3.98945i	0.0198561	+	0.0343918i
$117$	20.4305	+	11.7956i	0.174620	+	0.100817i
$118$		−	99.4892i		−	0.843129i
$119$	191.083	−	28.8367i	1.60574	−	0.242325i
$120$	10.9545			0.0912871
$121$	−6.60372	+	11.4380i	−0.0545762	+	0.0945288i
$122$	82.8150	−	47.8132i	0.678811	−	0.391912i
$123$	19.2176	+	33.2858i	0.156240	+	0.270616i
$124$	9.11720	+	5.26382i	0.0735258	+	0.0424501i
$125$			11.1803i			0.0894427i
$126$	4.43168	+	29.3660i	0.0351720	+	0.233063i
$127$	−101.973			−0.802940			−0.401470	−	0.915872i	$-0.631501\pi$
$127$	−101.973			−0.802940			−0.401470	+	0.915872i	$0.631501\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$	74.7552	−	43.1600i	0.579498	−	0.334573i
$130$	−12.4336	−	21.5357i	−0.0956433	−	0.165659i
$131$	−64.6037	−	37.2990i	−0.493158	−	0.284725i	0.232726	−	0.972542i	$-0.425236\pi$
$131$	−64.6037	−	37.2990i	−0.493158	−	0.284725i	−0.725884	+	0.687817i	$0.758569\pi$
$132$			40.1309i			0.304022i
$133$	137.184	+	171.959i	1.03146	+	1.29292i
$134$	138.826			1.03601
$135$	5.80948	−	10.0623i	0.0430331	−	0.0745356i
$136$	67.6221	−	39.0416i	0.497221	−	0.287071i
$137$	123.449	+	213.821i	0.901091	+	1.56074i	0.826080	+	0.563553i	$0.190566\pi$
$137$	123.449	+	213.821i	0.901091	+	1.56074i	0.0750109	+	0.997183i	$0.476101\pi$
$138$	−38.5215	−	22.2404i	−0.279141	−	0.161162i
$139$			155.917i			1.12170i	0.827916	+	0.560852i	$0.189526\pi$
$139$			155.917i			1.12170i	−0.827916	+	0.560852i	$0.810474\pi$
$140$	11.4317	−	29.1430i	0.0816548	−	0.208165i
$141$	−132.791			−0.941781
$142$	24.2253	−	41.9594i	0.170601	−	0.295489i
$143$	78.8945	−	45.5498i	0.551710	−	0.318530i
$144$	6.00000	+	10.3923i	0.0416667	+	0.0721688i
$145$	−4.46034	−	2.57518i	−0.0307609	−	0.0177598i
$146$			27.5651i			0.188802i
$147$	82.7495	+	18.8553i	0.562922	+	0.128268i
$148$	3.97257			0.0268417
$149$	−81.5452	+	141.240i	−0.547283	+	0.947922i	0.451176	+	0.892435i	$0.351005\pi$
$149$	−81.5452	+	141.240i	−0.547283	+	0.947922i	−0.998459	+	0.0554872i	$0.982329\pi$
$150$	−10.6066	+	6.12372i	−0.0707107	+	0.0408248i
$151$	37.5149	+	64.9778i	0.248443	+	0.430316i	0.963094	−	0.269165i	$-0.0867477\pi$
$151$	37.5149	+	64.9778i	0.248443	+	0.430316i	−0.714651	+	0.699481i	$0.753414\pi$
$152$	76.9753	+	44.4417i	0.506416	+	0.292380i
$153$		−	82.8198i		−	0.541306i
$154$	106.764	+	41.8792i	0.693270	+	0.271943i
$155$	−11.7703			−0.0759371
$156$	13.6204	−	23.5911i	0.0873100	−	0.151225i
$157$	−194.622	+	112.365i	−1.23963	+	0.715702i	−0.969019	−	0.246986i	$-0.920560\pi$
$157$	−194.622	+	112.365i	−1.23963	+	0.715702i	−0.270614	+	0.962688i	$0.587227\pi$
$158$	−63.9426	−	110.752i	−0.404700	−	0.700961i
$159$	−85.6431	−	49.4461i	−0.538636	−	0.310982i
$160$		−	12.6491i		−	0.0790569i
$161$	−99.3675	+	79.2726i	−0.617190	+	0.492376i
$162$	12.7279			0.0785674
$163$	115.059	−	199.288i	0.705882	−	1.22262i	−0.260491	−	0.965476i	$-0.583884\pi$
$163$	115.059	−	199.288i	0.705882	−	1.22262i	0.966372	−	0.257147i	$-0.0827823\pi$
$164$	38.4351	−	22.1905i	0.234361	−	0.135308i
$165$	−22.4339	−	38.8566i	−0.135963	−	0.235494i
$166$	163.875	+	94.6133i	0.987199	+	0.569960i
$167$		−	277.788i		−	1.66340i	−0.555223	−	0.831702i	$-0.687367\pi$
$167$		−	277.788i		−	1.66340i	0.555223	−	0.831702i	$-0.312633\pi$
$168$	33.9089	−	5.11726i	0.201839	−	0.0304599i
$169$	107.162			0.634095
$170$	−43.6499	+	75.6038i	−0.256764	+	0.444728i
$171$	81.6446	−	47.1375i	0.477454	−	0.275658i
$172$	−49.8368	−	86.3199i	−0.289749	−	0.501860i
$173$	109.176	+	63.0327i	0.631074	+	0.364351i	0.781168	−	0.624321i	$-0.214624\pi$
$173$	109.176	+	63.0327i	0.631074	+	0.364351i	−0.150094	+	0.988672i	$0.547958\pi$
$174$		−	5.64193i		−	0.0324249i
$175$	5.22278	+	34.6081i	0.0298445	+	0.197761i
$176$	46.3392			0.263291
$177$	−60.9245	+	105.524i	−0.344206	+	0.596182i
$178$	13.5514	−	7.82393i	0.0761317	−	0.0439547i
$179$	−38.5535	−	66.7766i	−0.215382	−	0.373053i	0.738008	−	0.674792i	$-0.235766\pi$
$179$	−38.5535	−	66.7766i	−0.215382	−	0.373053i	−0.953391	+	0.301738i	$0.902433\pi$
$180$	−11.6190	−	6.70820i	−0.0645497	−	0.0372678i
$181$		−	212.012i		−	1.17134i	−0.810551	−	0.585668i	$-0.800832\pi$
$181$		−	212.012i		−	1.17134i	0.810551	−	0.585668i	$-0.199168\pi$
$182$	−48.5478	−	60.8542i	−0.266746	−	0.334364i
$183$	−117.118			−0.639989
$184$	−25.6810	+	44.4807i	−0.139570	+	0.241743i
$185$	−3.84642	+	2.22073i	−0.0207915	+	0.0120040i
$186$	−6.44683	−	11.1662i	−0.0346604	−	0.0600336i
$187$	−276.969	−	159.908i	−1.48112	−	0.855125i
$188$			153.334i			0.815606i
$189$	13.2824	−	33.8612i	0.0702773	−	0.179160i
$190$	−99.3747			−0.523025
$191$	−82.8480	+	143.497i	−0.433759	+	0.751293i	−0.997193	−	0.0748682i	$-0.976146\pi$
$191$	−82.8480	+	143.497i	−0.433759	+	0.751293i	0.563434	+	0.826161i	$0.309480\pi$
$192$	12.0000	−	6.92820i	0.0625000	−	0.0360844i
$193$	52.6497	+	91.1920i	0.272796	+	0.472497i	0.969577	−	0.244787i	$-0.0787181\pi$
$193$	52.6497	+	91.1920i	0.272796	+	0.472497i	−0.696780	+	0.717285i	$0.745385\pi$
$194$	−88.5627	−	51.1317i	−0.456509	−	0.263566i
$195$			30.4560i			0.156185i
$196$	21.7723	−	95.5509i	0.111083	−	0.487504i
$197$	244.736			1.24231			0.621156	−	0.783687i	$-0.286663\pi$
$197$	244.736			1.24231			0.621156	+	0.783687i	$0.286663\pi$
$198$	24.5751	−	42.5653i	0.124116	−	0.214976i
$199$	84.8416	−	48.9833i	0.426340	−	0.246147i	−0.271446	−	0.962454i	$-0.587502\pi$
$199$	84.8416	−	48.9833i	0.426340	−	0.246147i	0.697786	+	0.716306i	$0.254169\pi$
$200$	7.07107	+	12.2474i	0.0353553	+	0.0612372i
$201$	−147.247	−	85.0131i	−0.732572	−	0.422951i
$202$			71.6346i			0.354627i
$203$	−15.0097	−	5.88772i	−0.0739394	−	0.0290035i
$204$	−95.6321			−0.468785
$205$	−24.8098	+	42.9718i	−0.121023	+	0.209619i
$206$	242.456	−	139.982i	1.17697	−	0.679525i
$207$	27.2388	+	47.1790i	0.131588	+	0.227918i
$208$	−27.2407	−	15.7274i	−0.130965	−	0.0756126i
$209$		−	364.052i		−	1.74188i
$210$	−29.9715	+	23.9104i	−0.142722	+	0.113859i
$211$	−388.914			−1.84319			−0.921597	−	0.388149i	$-0.873114\pi$
$211$	−388.914			−1.84319			−0.921597	+	0.388149i	$0.873114\pi$
$212$	−57.0954	+	98.8922i	−0.269318	+	0.466473i
$213$	−51.3896	+	29.6698i	−0.241266	+	0.139295i
$214$	−104.606	−	181.184i	−0.488815	−	0.846652i
$215$	96.5086	+	55.7193i	0.448877	+	0.259159i
$216$		−	14.6969i		−	0.0680414i
$217$	−36.4342	+	5.49835i	−0.167899	+	0.0253380i
$218$	−76.8228			−0.352398
$219$	16.8801	−	29.2372i	0.0770781	−	0.133503i
$220$	−44.8677	+	25.9044i	−0.203944	+	0.117747i
$221$	108.545	+	188.006i	0.491155	+	0.850705i
$222$	−4.21355	−	2.43269i	−0.0189799	−	0.0109581i
$223$			251.913i			1.12965i	0.825210	+	0.564827i	$0.191057\pi$
$223$			251.913i			1.12965i	−0.825210	+	0.564827i	$0.808943\pi$
$224$	−5.90890	−	39.1546i	−0.0263790	−	0.174797i
$225$	15.0000			0.0666667
$226$	−33.7915	+	58.5285i	−0.149520	+	0.258976i
$227$	231.941	−	133.911i	1.02176	−	0.589916i	0.107150	−	0.994243i	$-0.465827\pi$
$227$	231.941	−	133.911i	1.02176	−	0.589916i	0.914615	+	0.404327i	$0.132494\pi$
$228$	−54.4297	−	94.2751i	−0.238727	−	0.413487i
$229$	299.237	+	172.765i	1.30671	+	0.754431i	0.981546	−	0.191226i	$-0.0612463\pi$
$229$	299.237	+	172.765i	1.30671	+	0.754431i	0.325167	+	0.945657i	$0.394580\pi$
$230$		−	57.4244i		−	0.249671i
$231$	−87.5942	−	109.799i	−0.379196	−	0.475319i
$232$	−6.51474			−0.0280808
$233$	144.032	−	249.471i	0.618164	−	1.07069i	−0.371656	−	0.928370i	$-0.621210\pi$
$233$	144.032	−	249.471i	0.618164	−	1.07069i	0.989821	−	0.142321i	$-0.0454566\pi$
$234$	−28.8931	+	16.6815i	−0.123475	+	0.0712883i
$235$	−85.7163	−	148.465i	−0.364750	−	0.631766i
$236$	121.849	+	70.3495i	0.516309	+	0.298091i
$237$			156.627i			0.660872i
$238$	−99.7983	+	254.418i	−0.419320	+	1.06898i
$239$	−188.810			−0.789999			−0.395000	−	0.918681i	$-0.629255\pi$
$239$	−188.810			−0.789999			−0.395000	+	0.918681i	$0.629255\pi$
$240$	−7.74597	+	13.4164i	−0.0322749	+	0.0559017i
$241$	84.7389	−	48.9240i	0.351614	−	0.203004i	−0.313782	−	0.949495i	$-0.601596\pi$
$241$	84.7389	−	48.9240i	0.351614	−	0.203004i	0.665396	+	0.746491i	$0.268263\pi$
$242$	−9.33908	−	16.1758i	−0.0385912	−	0.0668420i
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$			135.236i			0.554247i
$245$	32.3337	+	104.688i	0.131974	+	0.427297i
$246$	−54.3555			−0.220957
$247$	−123.559	+	214.010i	−0.500238	+	0.866437i
$248$	−12.8937	+	7.44416i	−0.0519906	+	0.0300168i
$249$	−115.877	−	200.705i	−0.465370	−	0.806045i
$250$	−13.6931	−	7.90569i	−0.0547723	−	0.0316228i
$251$		−	241.345i		−	0.961533i	−0.876849	−	0.480767i	$-0.840358\pi$
$251$		−	241.345i		−	0.961533i	0.876849	−	0.480767i	$-0.159642\pi$
$252$	−39.0995	−	15.3372i	−0.155157	−	0.0608619i
$253$	210.370			0.831504
$254$	72.1061	−	124.891i	0.283882	−	0.491698i
$255$	92.5954	−	53.4600i	0.363119	−	0.209647i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−10.8807	−	6.28197i	−0.0423373	−	0.0244435i	0.478682	−	0.877988i	$-0.341115\pi$
$257$	−10.8807	−	6.28197i	−0.0423373	−	0.0244435i	−0.521019	+	0.853545i	$0.674448\pi$
$258$			122.075i			0.473158i
$259$	−10.8690	+	8.67098i	−0.0419653	+	0.0334787i
$260$	35.1676			0.135260
$261$	−3.45496	+	5.98417i	−0.0132374	+	0.0229279i
$262$	91.3635	−	52.7487i	0.348716	−	0.201331i
$263$	106.240	+	184.014i	0.403956	+	0.699672i	0.994199	−	0.107554i	$-0.0343017\pi$
$263$	106.240	+	184.014i	0.403956	+	0.699672i	−0.590244	+	0.807225i	$0.700968\pi$
$264$	−49.1501	−	28.3768i	−0.186175	−	0.107488i
$265$		−	127.669i		−	0.481771i
$266$	−307.609	+	46.4219i	−1.15642	+	0.174518i
$267$	−19.1646			−0.0717777
$268$	−98.1647	+	170.026i	−0.366286	+	0.634426i
$269$	−289.769	+	167.298i	−1.07721	+	0.621927i	−0.930142	−	0.367200i	$-0.880317\pi$
$269$	−289.769	+	167.298i	−1.07721	+	0.621927i	−0.147067	+	0.989127i	$0.546983\pi$
$270$	8.21584	+	14.2302i	0.0304290	+	0.0527046i
$271$	−157.920	−	91.1752i	−0.582731	−	0.336440i	0.179487	−	0.983760i	$-0.442556\pi$
$271$	−157.920	−	91.1752i	−0.582731	−	0.336440i	−0.762218	+	0.647321i	$0.775889\pi$
$272$			110.426i			0.405979i
$273$	14.2272	+	94.2750i	0.0521144	+	0.345330i
$274$	−349.168			−1.27434
$275$	28.9620	−	50.1636i	0.105316	−	0.182413i
$276$	54.4776	−	31.4526i	0.197382	−	0.113959i
$277$	−83.3807	−	144.420i	−0.301013	−	0.521370i	0.675353	−	0.737495i	$-0.263991\pi$
$277$	−83.3807	−	144.420i	−0.301013	−	0.521370i	−0.976366	+	0.216125i	$0.930658\pi$
$278$	−190.958	−	110.250i	−0.686900	−	0.396582i
$279$			15.7915i			0.0566002i
$280$	27.6094	+	34.6081i	0.0986049	+	0.123600i
$281$	38.3085			0.136329			0.0681647	−	0.997674i	$-0.478286\pi$
$281$	38.3085			0.136329			0.0681647	+	0.997674i	$0.478286\pi$
$282$	93.8975	−	162.635i	0.332970	−	0.576721i
$283$	−333.849	+	192.748i	−1.17968	+	0.681088i	−0.955940	−	0.293561i	$-0.905160\pi$
$283$	−333.849	+	192.748i	−1.17968	+	0.681088i	−0.223739	+	0.974649i	$0.571826\pi$
$284$	34.2597	+	59.3396i	0.120633	+	0.208942i
$285$	105.403	+	60.8543i	0.369834	+	0.213524i
$286$			128.834i			0.450469i
$287$	−56.7235	+	144.606i	−0.197643	+	0.503855i
$288$	−16.9706			−0.0589256
$289$	236.562	−	409.738i	0.818555	−	1.41778i
$290$	6.30787	−	3.64185i	0.0217513	−	0.0125581i
$291$	62.6233	+	108.467i	0.215200	+	0.372738i
$292$	−33.7602	−	19.4915i	−0.115617	−	0.0667516i
$293$			90.9844i			0.310527i	0.987873	+	0.155264i	$0.0496227\pi$
$293$			90.9844i			0.310527i	−0.987873	+	0.155264i	$0.950377\pi$
$294$	−81.6057	+	88.0143i	−0.277570	+	0.299368i
$295$	−157.306			−0.533242
$296$	−2.80903	+	4.86538i	−0.00948997	+	0.0164371i
$297$	−52.1316	+	30.0982i	−0.175527	+	0.101341i
$298$	−115.322	−	199.744i	−0.386988	−	0.670282i
$299$	−123.667	−	71.3993i	−0.413603	−	0.238794i
$300$		−	17.3205i		−	0.0577350i
$301$	324.766	+	127.393i	1.07896	+	0.423232i
$302$	−106.108			−0.351352
$303$	43.8670	−	75.9799i	0.144776	−	0.250759i
$304$	−108.859	+	62.8501i	−0.358090	+	0.206744i
$305$	−75.5994	−	130.942i	−0.247867	−	0.429318i
$306$	101.433	+	58.5625i	0.331481	+	0.191381i
$307$		−	508.077i		−	1.65497i	−0.561485	−	0.827487i	$-0.689770\pi$
$307$		−	508.077i		−	1.65497i	0.561485	−	0.827487i	$-0.310230\pi$
$308$	−126.785	+	101.145i	−0.411638	+	0.328393i
$309$	−342.885			−1.10966
$310$	8.32283	−	14.4156i	0.0268478	−	0.0465018i
$311$	90.3447	−	52.1605i	0.290497	−	0.167719i	−0.347669	−	0.937617i	$-0.613027\pi$
$311$	90.3447	−	52.1605i	0.290497	−	0.167719i	0.638166	+	0.769899i	$0.279693\pi$
$312$	19.2621	+	33.3629i	0.0617375	+	0.106932i
$313$	230.249	+	132.934i	0.735619	+	0.424710i	0.820474	−	0.571683i	$-0.193709\pi$
$313$	230.249	+	132.934i	0.735619	+	0.424710i	−0.0848550	+	0.996393i	$0.527043\pi$
$314$		−	317.817i		−	1.01216i
$315$	46.4317	−	7.00710i	0.147402	−	0.0222447i
$316$	180.857			0.572332
$317$	5.36113	−	9.28575i	0.0169121	−	0.0292926i	−0.857446	−	0.514575i	$-0.827950\pi$
$317$	5.36113	−	9.28575i	0.0169121	−	0.0292926i	0.874358	+	0.485282i	$0.161283\pi$
$318$	121.118	−	69.9273i	0.380873	−	0.219897i
$319$	13.3417	+	23.1085i	0.0418234	+	0.0724403i
$320$	15.4919	+	8.94427i	0.0484123	+	0.0279508i
$321$			256.232i			0.798231i
$322$	−26.8252	−	177.754i	−0.0833081	−	0.552031i
$323$	867.538			2.68588
$324$	−9.00000	+	15.5885i	−0.0277778	+	0.0481125i
$325$	−34.0509	+	19.6593i	−0.104772	+	0.0604901i
$326$	162.718	+	281.835i	0.499134	+	0.864525i
$327$	81.4829	+	47.0442i	0.249183	+	0.143866i
$328$			62.7643i			0.191355i
$329$	−334.684	−	419.524i	−1.01728	−	1.27515i
$330$	63.4525			0.192280
$331$	176.460	−	305.638i	0.533113	−	0.923379i	−0.466139	−	0.884711i	$-0.654355\pi$
$331$	176.460	−	305.638i	0.533113	−	0.923379i	0.999252	−	0.0386675i	$-0.0123113\pi$
$332$	−231.754	+	133.803i	−0.698055	+	0.403022i
$333$	2.97943	+	5.16052i	0.00894723	+	0.0154971i
$334$	340.220	+	196.426i	1.01862	+	0.588102i
$335$		−	219.503i		−	0.655233i
$336$	−17.7099	+	45.1482i	−0.0527080	+	0.134370i
$337$	220.634			0.654699			0.327349	−	0.944903i	$-0.393845\pi$
$337$	220.634			0.654699			0.327349	+	0.944903i	$0.393845\pi$
$338$	−75.7750	+	131.246i	−0.224186	+	0.388302i
$339$	71.6825	−	41.3859i	0.211453	−	0.122082i
$340$	−61.7302	−	106.920i	−0.181560	−	0.314470i
$341$	52.8104	+	30.4901i	0.154869	+	0.0894138i
$342$			133.325i			0.389839i
$343$	148.991	+	308.951i	0.434376	+	0.900732i
$344$	140.960			0.409767
$345$	−35.1651	+	60.9078i	−0.101928	+	0.176544i
$346$	−154.398	+	89.1417i	−0.446237	+	0.257635i
$347$	128.004	+	221.710i	0.368888	+	0.638933i	0.989392	−	0.145270i	$-0.0464051\pi$
$347$	128.004	+	221.710i	0.368888	+	0.638933i	−0.620504	+	0.784204i	$0.713072\pi$
$348$	6.90993	+	3.98945i	0.0198561	+	0.0114639i
$349$		−	407.250i		−	1.16691i	−0.812147	−	0.583453i	$-0.801701\pi$
$349$		−	407.250i		−	1.16691i	0.812147	−	0.583453i	$-0.198299\pi$
$350$	−46.0792	−	18.0751i	−0.131655	−	0.0516431i
$351$	40.8611			0.116413
$352$	−32.7667	+	56.7537i	−0.0930873	+	0.161232i
$353$	−505.099	+	291.619i	−1.43087	+	0.826116i	−0.997187	−	0.0749482i	$-0.976121\pi$
$353$	−505.099	+	291.619i	−1.43087	+	0.826116i	−0.433687	+	0.901064i	$0.642788\pi$
$354$	−86.1602	−	149.234i	−0.243390	−	0.421565i
$355$	−66.3437	−	38.3035i	−0.186884	−	0.107897i
$356$			22.1294i			0.0621613i
$357$	261.651	−	208.737i	0.732915	−	0.584698i
$358$	109.046			0.304597
$359$	−345.764	+	598.881i	−0.963131	+	1.66819i	−0.248577	+	0.968612i	$0.579963\pi$
$359$	−345.764	+	598.881i	−0.963131	+	1.66819i	−0.714554	+	0.699580i	$0.753370\pi$
$360$	16.4317	−	9.48683i	0.0456435	−	0.0263523i
$361$	313.266	+	542.593i	0.867773	+	1.50303i
$362$	259.660	+	149.915i	0.717294	+	0.414130i
$363$			22.8760i			0.0630192i
$364$	108.859	−	16.4282i	0.299064	−	0.0451324i
$365$	43.5842			0.119409
$366$	82.8150	−	143.440i	0.226270	−	0.391912i
$367$	198.949	−	114.863i	0.542096	−	0.312980i	−0.203832	−	0.979006i	$-0.565340\pi$
$367$	198.949	−	114.863i	0.542096	−	0.312980i	0.745928	+	0.666026i	$0.232006\pi$
$368$	−36.3184	−	62.9053i	−0.0986912	−	0.170938i
$369$	57.6527	+	33.2858i	0.156240	+	0.0902054i
$370$		−	6.28118i		−	0.0169762i
$371$	−59.6394	−	395.193i	−0.160753	−	1.06521i
$372$	18.2344			0.0490172
$373$	202.304	−	350.401i	0.542371	−	0.939414i	−0.456397	−	0.889776i	$-0.650860\pi$
$373$	202.304	−	350.401i	0.542371	−	0.939414i	0.998767	−	0.0496372i	$-0.0158065\pi$
$374$	391.694	−	226.145i	1.04731	−	0.604665i
$375$	9.68246	+	16.7705i	0.0258199	+	0.0447214i
$376$	−187.795	−	108.424i	−0.499455	−	0.288360i
$377$		−	18.1126i		−	0.0480439i
$378$	32.0792	+	40.2110i	0.0848656	+	0.106378i
$379$	265.866			0.701493			0.350746	−	0.936471i	$-0.385928\pi$
$379$	265.866			0.701493			0.350746	+	0.936471i	$0.385928\pi$
$380$	70.2685	−	121.709i	0.184917	−	0.320286i
$381$	−152.960	+	88.3115i	−0.401470	+	0.231789i
$382$	−117.165	−	202.935i	−0.306714	−	0.531244i
$383$	265.353	+	153.202i	0.692829	+	0.400005i	0.804671	−	0.593721i	$-0.202342\pi$
$383$	265.353	+	153.202i	0.692829	+	0.400005i	−0.111842	+	0.993726i	$0.535675\pi$
$384$			19.5959i			0.0510310i
$385$	66.2168	−	168.808i	0.171992	−	0.438462i
$386$	−148.916			−0.385792
$387$	74.7552	−	129.480i	0.193166	−	0.334573i
$388$	125.247	−	72.3112i	0.322801	−	0.186369i
$389$	−53.1772	−	92.1056i	−0.136702	−	0.236775i	0.789544	−	0.613694i	$-0.210317\pi$
$389$	−53.1772	−	92.1056i	−0.136702	−	0.236775i	−0.926246	+	0.376918i	$0.876984\pi$
$390$	−37.3009	−	21.5357i	−0.0956433	−	0.0552197i
$391$			501.314i			1.28213i
$392$	101.630	+	94.2301i	0.259261	+	0.240383i
$393$	−129.207			−0.328772
$394$	−173.054	+	299.739i	−0.439224	+	0.760758i
$395$	−175.114	+	101.102i	−0.443327	+	0.255955i
$396$	34.7544	+	60.1964i	0.0877636	+	0.152011i
$397$	−188.643	−	108.913i	−0.475172	−	0.274341i	0.243230	−	0.969969i	$-0.421793\pi$
$397$	−188.643	−	108.913i	−0.475172	−	0.274341i	−0.718402	+	0.695628i	$0.755126\pi$
$398$			138.546i			0.348105i
$399$	354.696	+	139.133i	0.888962	+	0.348705i
$400$	−20.0000			−0.0500000
$401$	−30.9907	+	53.6775i	−0.0772836	+	0.133859i	−0.902077	−	0.431575i	$-0.857958\pi$
$401$	−30.9907	+	53.6775i	−0.0772836	+	0.133859i	0.824793	+	0.565434i	$0.191291\pi$
$402$	208.239	−	120.227i	0.518007	−	0.299071i
$403$	−20.6966	−	35.8475i	−0.0513563	−	0.0889517i
$404$	−87.7341	−	50.6533i	−0.217164	−	0.125379i
$405$		−	20.1246i		−	0.0496904i
$406$	17.8244	−	14.2198i	0.0439025	−	0.0350242i
$407$	23.0107			0.0565373
$408$	67.6221	−	117.125i	0.165740	−	0.287071i
$409$	−376.167	+	217.180i	−0.919724	+	0.531003i	−0.883547	−	0.468342i	$-0.844851\pi$
$409$	−376.167	+	217.180i	−0.919724	+	0.531003i	−0.0361772	+	0.999345i	$0.511518\pi$
$410$	−35.0863	−	60.7713i	−0.0855764	−	0.148223i
$411$	370.348	+	213.821i	0.901091	+	0.520245i
$412$			395.929i			0.960993i
$413$	−486.933	+	73.4840i	−1.17901	+	0.177927i
$414$	−77.0429			−0.186094
$415$	149.597	−	259.109i	0.360474	−	0.624360i
$416$	38.5242	−	22.2419i	0.0926062	−	0.0534662i
$417$	135.028	+	233.875i	0.323808	+	0.560852i
$418$	445.871	+	257.424i	1.06668	+	0.615847i
$419$			457.221i			1.09122i	0.838040	+	0.545609i	$0.183702\pi$
$419$			457.221i			1.09122i	−0.838040	+	0.545609i	$0.816298\pi$
$420$	−8.09110	−	53.6147i	−0.0192645	−	0.127654i
$421$	−653.149			−1.55142			−0.775712	−	0.631088i	$-0.782609\pi$
$421$	−653.149			−1.55142			−0.775712	+	0.631088i	$0.782609\pi$
$422$	275.004	−	476.320i	0.651667	−	1.12872i
$423$	−199.187	+	115.000i	−0.470891	+	0.271869i
$424$	−80.7451	−	139.855i	−0.190437	−	0.329846i
$425$	119.540	+	69.0165i	0.281271	+	0.162392i
$426$		−	83.9188i		−	0.196993i
$427$	−295.182	−	370.008i	−0.691293	−	0.866530i
$428$	295.872			0.691289
$429$	78.8945	−	136.649i	0.183903	−	0.318530i
$430$	−136.484	+	78.7989i	−0.317404	+	0.183253i
$431$	235.128	+	407.253i	0.545540	+	0.944904i	0.998573	+	0.0534095i	$0.0170089\pi$
$431$	235.128	+	407.253i	0.545540	+	0.944904i	−0.453032	+	0.891494i	$0.649658\pi$
$432$	18.0000	+	10.3923i	0.0416667	+	0.0240563i
$433$			32.0299i			0.0739719i	0.999316	+	0.0369860i	$0.0117757\pi$
$433$			32.0299i			0.0739719i	−0.999316	+	0.0369860i	$0.988224\pi$
$434$	19.0288	−	48.5105i	0.0438451	−	0.111775i
$435$	−8.92068			−0.0205073
$436$	54.3219	−	94.0883i	0.124592	−	0.215799i
$437$	−494.200	+	285.326i	−1.13089	+	0.652921i
$438$	23.8721	+	41.3476i	0.0545024	+	0.0944010i
$439$	331.028	+	191.119i	0.754051	+	0.435352i	0.827156	−	0.561973i	$-0.189957\pi$
$439$	331.028	+	191.119i	0.754051	+	0.435352i	−0.0731046	+	0.997324i	$0.523291\pi$
$440$		−	73.2687i		−	0.166520i
$441$	140.453	−	43.3802i	0.318488	−	0.0983677i
$442$	−307.012			−0.694598
$443$	−61.8708	+	107.163i	−0.139663	+	0.241904i	−0.927369	−	0.374148i	$-0.877935\pi$
$443$	−61.8708	+	107.163i	−0.139663	+	0.241904i	0.787706	+	0.616051i	$0.211269\pi$
$444$	5.95885	−	3.44035i	0.0134208	−	0.00774853i
$445$	−12.3707	−	21.4267i	−0.0277994	−	0.0481499i
$446$	−308.529	−	178.129i	−0.691769	−	0.399393i
$447$			282.481i			0.631948i
$448$	52.1327	+	20.4496i	0.116368	+	0.0456464i
$449$	−266.985			−0.594622			−0.297311	−	0.954781i	$-0.596090\pi$
$449$	−266.985			−0.594622			−0.297311	+	0.954781i	$0.596090\pi$
$450$	−10.6066	+	18.3712i	−0.0235702	+	0.0408248i
$451$	222.632	−	128.536i	0.493640	−	0.285003i
$452$	−47.7883	−	82.7718i	−0.105726	−	0.183124i
$453$	112.545	+	64.9778i	0.248443	+	0.143439i
$454$			378.757i			0.834267i
$455$	−96.2190	+	76.7608i	−0.211470	+	0.168705i
$456$	153.951			0.337611
$457$	224.670	−	389.140i	0.491619	−	0.851509i	−0.508334	−	0.861160i	$-0.669739\pi$
$457$	224.670	−	389.140i	0.491619	−	0.851509i	0.999953	+	0.00965069i	$0.00307196\pi$
$458$	−423.185	+	244.326i	−0.923985	+	0.533463i
$459$	−71.7241	−	124.230i	−0.156262	−	0.270653i
$460$	70.3302	+	40.6052i	0.152892	+	0.0882721i
$461$		−	105.528i		−	0.228912i	−0.993428	−	0.114456i	$-0.963487\pi$
$461$		−	105.528i		−	0.228912i	0.993428	−	0.114456i	$-0.0365125\pi$
$462$	196.414	−	29.6412i	0.425138	−	0.0641584i
$463$	588.555			1.27118			0.635588	−	0.772028i	$-0.280758\pi$
$463$	588.555			1.27118			0.635588	+	0.772028i	$0.280758\pi$
$464$	4.60662	−	7.97889i	0.00992805	−	0.0171959i
$465$	−17.6554	+	10.1933i	−0.0379686	+	0.0219212i
$466$	203.692	+	352.805i	0.437108	+	0.757093i
$467$	316.668	+	182.829i	0.678091	+	0.391496i	0.799135	−	0.601151i	$-0.205291\pi$
$467$	316.668	+	182.829i	0.678091	+	0.391496i	−0.121044	+	0.992647i	$0.538624\pi$
$468$		−	47.1823i		−	0.100817i
$469$	−102.539	−	679.459i	−0.218632	−	1.44874i
$470$	242.442			0.515835
$471$	−194.622	+	337.096i	−0.413211	+	0.715702i
$472$	−172.320	+	99.4892i	−0.365086	+	0.210782i
$473$	−288.675	−	499.999i	−0.610306	−	1.05708i
$474$	−191.828	−	110.752i	−0.404700	−	0.233654i
$475$			157.125i			0.330790i
$476$	−241.029	−	302.128i	−0.506364	−	0.634723i
$477$	−171.286			−0.359091
$478$	133.509	−	231.244i	0.279307	−	0.483774i
$479$	−421.907	+	243.588i	−0.880808	+	0.508535i	−0.870925	−	0.491416i	$-0.836479\pi$
$479$	−421.907	+	243.588i	−0.880808	+	0.508535i	−0.00988318	+	0.999951i	$0.503146\pi$
$480$	−10.9545	−	18.9737i	−0.0228218	−	0.0395285i
$481$	−13.5270	−	7.80979i	−0.0281226	−	0.0162366i
$482$			138.378i			0.287091i
$483$	−80.3992	+	204.964i	−0.166458	+	0.424355i
$484$	26.4149			0.0545762
$485$	−80.8463	+	140.030i	−0.166693	+	0.288722i
$486$	19.0919	−	11.0227i	0.0392837	−	0.0226805i
$487$	97.8870	+	169.545i	0.201000	+	0.348142i	0.948851	−	0.315725i	$-0.102248\pi$
$487$	97.8870	+	169.545i	0.201000	+	0.348142i	−0.747851	+	0.663867i	$0.768914\pi$
$488$	−165.630	−	95.6265i	−0.339406	−	0.195956i
$489$		−	398.575i		−	0.815082i
$490$	−151.079	−	34.4250i	−0.308325	−	0.0702550i
$491$	−349.221			−0.711244			−0.355622	−	0.934630i	$-0.615731\pi$
$491$	−349.221			−0.711244			−0.355622	+	0.934630i	$0.615731\pi$
$492$	38.4351	−	66.5716i	0.0781202	−	0.135308i
$493$	−55.0675	+	31.7933i	−0.111699	+	0.0644894i
$494$	−174.738	−	302.656i	−0.353722	−	0.612664i
$495$	−67.3016	−	38.8566i	−0.135963	−	0.0784981i
$496$		−	21.0553i		−	0.0424501i
$497$	−223.256	−	87.5747i	−0.449208	−	0.176207i
$498$	327.750			0.658133
$499$	167.719	−	290.498i	0.336111	−	0.582161i	−0.647587	−	0.761992i	$-0.724222\pi$
$499$	167.719	−	290.498i	0.336111	−	0.582161i	0.983698	+	0.179831i	$0.0575550\pi$
$500$	19.3649	−	11.1803i	0.0387298	−	0.0223607i
$501$	−240.572	−	416.683i	−0.480183	−	0.831702i
$502$	295.586	+	170.657i	0.588817	+	0.339953i
$503$		−	523.663i		−	1.04108i	−0.853837	−	0.520540i	$-0.825731\pi$
$503$		−	523.663i		−	1.04108i	0.853837	−	0.520540i	$-0.174269\pi$
$504$	46.4317	−	37.0419i	0.0921263	−	0.0734958i
$505$	113.264			0.224286
$506$	−148.754	+	257.650i	−0.293981	+	0.509190i
$507$	160.743	−	92.8050i	0.317047	−	0.183047i
$508$	101.973	+	176.623i	0.200735	+	0.347683i
$509$	−417.731	−	241.177i	−0.820690	−	0.473825i	0.0299645	−	0.999551i	$-0.490461\pi$
$509$	−417.731	−	241.177i	−0.820690	−	0.473825i	−0.850654	+	0.525726i	$0.823794\pi$
$510$			151.208i			0.296485i
$511$	134.913	−	20.3599i	0.264017	−	0.0398433i
$512$	22.6274			0.0441942
$513$	81.6446	−	141.413i	0.159151	−	0.275658i
$514$	15.3876	−	8.88405i	0.0299370	−	0.0172841i
$515$	−221.331	−	383.357i	−0.429769	−	0.744382i
$516$	−149.510	−	86.3199i	−0.289749	−	0.167287i
$517$			888.171i			1.71793i
$518$	−2.93419	−	19.4431i	−0.00566446	−	0.0375349i
$519$	218.352			0.420716
$520$	−24.8673	+	43.0713i	−0.0478216	+	0.0828295i
$521$	−61.7509	+	35.6519i	−0.118524	+	0.0684298i	−0.558090	−	0.829780i	$-0.688466\pi$
$521$	−61.7509	+	35.6519i	−0.118524	+	0.0684298i	0.439566	+	0.898210i	$0.355132\pi$
$522$	−4.88606	−	8.46290i	−0.00936026	−	0.0162124i
$523$	−521.458	−	301.064i	−0.997052	−	0.575648i	−0.0896773	−	0.995971i	$-0.528584\pi$
$523$	−521.458	−	301.064i	−0.997052	−	0.575648i	−0.907375	+	0.420323i	$0.861917\pi$
$524$			149.196i			0.284725i
$525$	37.8057	+	47.3891i	0.0720108	+	0.0902650i
$526$	−300.493			−0.571279
$527$	−72.6581	+	125.847i	−0.137871	+	0.238800i
$528$	69.5088	−	40.1309i	0.131645	−	0.0760055i
$529$	99.6220	+	172.550i	0.188321	+	0.326182i
$530$	156.362	+	90.2758i	0.295023	+	0.170332i
$531$			211.049i			0.397455i
$532$	160.657	−	409.568i	0.301987	−	0.769864i
$533$	−174.500			−0.327392
$534$	13.5514	−	23.4718i	0.0253772	−	0.0439547i
$535$	−286.476	+	165.397i	−0.535470	+	0.309154i
$536$	−138.826	−	240.453i	−0.259003	−	0.448607i
$537$	−115.660	−	66.7766i	−0.215382	−	0.124351i
$538$		−	473.191i		−	0.879537i
$539$	126.114	−	553.469i	0.233977	−	1.02684i
$540$	−23.2379			−0.0430331
$541$	301.657	−	522.485i	0.557591	−	0.965776i	−0.440106	−	0.897946i	$-0.645059\pi$
$541$	301.657	−	522.485i	0.557591	−	0.965776i	0.997697	−	0.0678303i	$-0.0216077\pi$
$542$	223.333	−	128.941i	0.412053	−	0.237899i
$543$	−183.608	−	318.018i	−0.338136	−	0.585668i
$544$	−135.244	−	78.0833i	−0.248611	−	0.143535i
$545$			121.468i			0.222876i
$546$	−125.523	−	49.2378i	−0.229896	−	0.0901791i
$547$	−879.935			−1.60866			−0.804328	−	0.594185i	$-0.797475\pi$
$547$	−879.935			−1.60866			−0.804328	+	0.594185i	$0.797475\pi$
$548$	246.899	−	427.642i	0.450546	−	0.780368i
$549$	−175.677	+	101.427i	−0.319995	+	0.184749i
$550$	40.9584	+	70.9421i	0.0744699	+	0.128986i
$551$	−62.6842	−	36.1908i	−0.113765	−	0.0656820i
$552$			88.9615i			0.161162i
$553$	−494.827	+	394.759i	−0.894805	+	0.713849i
$554$	235.836			0.425697
$555$	−3.84642	+	6.66220i	−0.00693049	+	0.0120040i
$556$	270.056	−	155.917i	0.485712	−	0.280426i
$557$	441.404	+	764.533i	0.792466	+	1.37259i	0.924436	+	0.381338i	$0.124536\pi$
$557$	441.404	+	764.533i	0.792466	+	1.37259i	−0.131970	+	0.991254i	$0.542130\pi$
$558$	−19.3405	−	11.1662i	−0.0346604	−	0.0200112i
$559$			391.903i			0.701078i
$560$	−61.9089	+	9.34279i	−0.110552	+	0.0166836i
$561$	−553.939			−0.987414
$562$	−27.0882	+	46.9182i	−0.0481997	+	0.0834843i
$563$	−451.334	+	260.578i	−0.801659	+	0.462838i	−0.844051	−	0.536263i	$-0.819835\pi$
$563$	−451.334	+	260.578i	−0.801659	+	0.462838i	0.0423920	+	0.999101i	$0.486502\pi$
$564$	132.791	+	230.001i	0.235445	+	0.407803i
$565$	92.5417	+	53.4290i	0.163791	+	0.0945646i
$566$		−	545.174i		−	0.963204i
$567$	−9.40101	−	62.2946i	−0.0165803	−	0.109867i
$568$	−96.9011			−0.170601
$569$	−122.400	+	212.004i	−0.215115	+	0.372590i	−0.953308	−	0.301999i	$-0.902346\pi$
$569$	−122.400	+	212.004i	−0.215115	+	0.372590i	0.738193	+	0.674589i	$0.235679\pi$
$570$	−149.062	+	86.0610i	−0.261512	+	0.150984i
$571$	208.126	+	360.486i	0.364495	+	0.631323i	0.988695	−	0.149941i	$-0.0479084\pi$
$571$	208.126	+	360.486i	0.364495	+	0.631323i	−0.624200	+	0.781264i	$0.714575\pi$
$572$	−157.789	−	91.0995i	−0.275855	−	0.159265i
$573$			286.994i			0.500862i
$574$	−136.996	−	171.724i	−0.238670	−	0.299171i
$575$	−90.7959			−0.157906
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	669.929	−	386.784i	1.16106	−	0.670336i	0.209499	−	0.977809i	$-0.432817\pi$
$577$	669.929	−	386.784i	1.16106	−	0.670336i	0.951557	+	0.307473i	$0.0994833\pi$
$578$	334.550	+	579.457i	0.578806	+	1.00252i
$579$	157.949	+	91.1920i	0.272796	+	0.157499i
$580$			10.3007i			0.0177598i
$581$	342.028	−	871.941i	0.588689	−	1.50076i
$582$	−177.125			−0.304339
$583$	−330.719	+	572.823i	−0.567272	+	0.982543i
$584$	47.7441	−	27.5651i	0.0817537	−	0.0472005i
$585$	26.3757	+	45.6841i	0.0450867	+	0.0780924i
$586$	−111.433	−	64.3357i	−0.190158	−	0.109788i
$587$		−	633.860i		−	1.07983i	−0.841720	−	0.539915i	$-0.818456\pi$
$587$		−	633.860i		−	1.07983i	0.841720	−	0.539915i	$-0.181544\pi$
$588$	−50.0911	−	162.182i	−0.0851889	−	0.275819i
$589$	−165.416			−0.280841
$590$	111.232	−	192.660i	0.188529	−	0.326543i
$591$	367.103	−	211.947i	0.621156	−	0.358625i
$592$	−3.97257	−	6.88069i	−0.00671042	−	0.0116228i
$593$	80.4028	+	46.4206i	0.135587	+	0.0782809i	0.566259	−	0.824227i	$-0.308390\pi$
$593$	80.4028	+	46.4206i	0.135587	+	0.0782809i	−0.430672	+	0.902508i	$0.641724\pi$
$594$		−	85.1305i		−	0.143317i
$595$	402.270	+	157.795i	0.676084	+	0.265201i
$596$	326.181			0.547283
$597$	84.8416	−	146.950i	0.142113	−	0.246147i
$598$	174.892	−	100.974i	0.292461	−	0.168853i
$599$	307.680	+	532.918i	0.513657	+	0.889679i	0.999875	+	0.0158418i	$0.00504280\pi$
$599$	307.680	+	532.918i	0.513657	+	0.889679i	−0.486218	+	0.873838i	$0.661624\pi$
$600$	21.2132	+	12.2474i	0.0353553	+	0.0204124i
$601$			821.399i			1.36672i	0.730081	+	0.683360i	$0.239482\pi$
$601$			821.399i			1.36672i	−0.730081	+	0.683360i	$0.760518\pi$
$602$	−385.668	+	307.675i	−0.640644	+	0.511088i
$603$	−294.494			−0.488381
$604$	75.0299	−	129.956i	0.124222	−	0.215158i
$605$	−25.5761	+	14.7664i	−0.0422746	+	0.0244072i
$606$	62.0374	+	107.452i	0.102372	+	0.177313i
$607$	−869.979	−	502.282i	−1.43324	−	0.827483i	−0.435876	−	0.900006i	$-0.643562\pi$
$607$	−869.979	−	502.282i	−1.43324	−	0.827483i	−0.997367	+	0.0725231i	$0.976895\pi$
$608$		−	177.767i		−	0.292380i
$609$	−27.6135	+	4.16720i	−0.0453423	+	0.00684270i
$610$	213.827			0.350537
$611$	301.444	−	522.116i	0.493361	−	0.854527i
$612$	−143.448	+	82.8198i	−0.234392	+	0.135326i
$613$	−556.873	−	964.532i	−0.908438	−	1.57346i	−0.816234	−	0.577721i	$-0.803942\pi$
$613$	−556.873	−	964.532i	−0.908438	−	1.57346i	−0.0922038	−	0.995740i	$-0.529391\pi$
$614$	622.264	+	359.265i	1.01346	+	0.585121i
$615$			85.9436i			0.139746i
$616$	−34.2267	−	226.799i	−0.0555628	−	0.368180i
$617$	−463.256			−0.750820			−0.375410	−	0.926859i	$-0.622498\pi$
$617$	−463.256			−0.750820			−0.375410	+	0.926859i	$0.622498\pi$
$618$	242.456	−	419.946i	0.392324	−	0.679525i
$619$	486.109	−	280.655i	0.785314	−	0.453401i	−0.0529963	−	0.998595i	$-0.516877\pi$
$619$	486.109	−	280.655i	0.785314	−	0.453401i	0.838310	+	0.545193i	$0.183544\pi$
$620$	11.7703	+	20.3867i	0.0189843	+	0.0328817i
$621$	81.7163	+	47.1790i	0.131588	+	0.0759725i
$622$			147.532i			0.237190i
$623$	−48.3021	−	60.5464i	−0.0775315	−	0.0971852i
$624$	−54.4814			−0.0873100
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$	−325.621	+	187.997i	−0.520161	+	0.300315i
$627$	−315.279	−	546.079i	−0.502837	−	0.870939i
$628$	389.245	+	224.731i	0.619816	+	0.357851i
$629$			54.8346i			0.0871774i
$630$	−24.2502	+	61.8217i	−0.0384925	+	0.0981297i
$631$	244.533			0.387533			0.193767	−	0.981048i	$-0.437930\pi$
$631$	244.533			0.387533			0.193767	+	0.981048i	$0.437930\pi$
$632$	−127.885	+	221.504i	−0.202350	+	0.350480i
$633$	−583.371	+	336.809i	−0.921597	+	0.532084i
$634$	7.58178	+	13.1320i	0.0119587	+	0.0207130i
$635$	−197.471	−	114.010i	−0.310977	−	0.179543i
$636$			197.784i			0.310982i
$637$	−261.983	+	282.556i	−0.411276	+	0.443574i
$638$	−37.7360			−0.0591473
$639$	−51.3896	+	89.0094i	−0.0804219	+	0.139295i
$640$	−21.9089	+	12.6491i	−0.0342327	+	0.0197642i
$641$	−325.885	−	564.449i	−0.508400	−	0.880575i	−0.999953	−	0.00972698i	$-0.996904\pi$
$641$	−325.885	−	564.449i	−0.508400	−	0.880575i	0.491553	−	0.870848i	$-0.336430\pi$
$642$	−313.819	−	181.184i	−0.488815	−	0.282217i
$643$		−	76.4894i		−	0.118957i	−0.998230	−	0.0594786i	$-0.981056\pi$
$643$		−	76.4894i		−	0.118957i	0.998230	−	0.0594786i	$-0.0189438\pi$
$644$	236.672	+	92.8371i	0.367503	+	0.144157i
$645$	193.017			0.299251
$646$	−613.442	+	1062.51i	−0.949601	+	1.64476i
$647$	141.933	−	81.9453i	0.219372	−	0.126654i	−0.386288	−	0.922378i	$-0.626243\pi$
$647$	141.933	−	81.9453i	0.219372	−	0.126654i	0.605659	+	0.795724i	$0.292909\pi$
$648$	−12.7279	−	22.0454i	−0.0196419	−	0.0340207i
$649$	705.797	+	407.492i	1.08752	+	0.627877i
$650$		−	55.6049i		−	0.0855459i
$651$	−49.8895	+	39.8004i	−0.0766352	+	0.0611374i
$652$	−460.235			−0.705882
$653$	557.431	−	965.499i	0.853647	−	1.47856i	−0.0242480	−	0.999706i	$-0.507719\pi$
$653$	557.431	−	965.499i	0.853647	−	1.47856i	0.877895	−	0.478854i	$-0.158948\pi$
$654$	−115.234	+	66.5305i	−0.176199	+	0.101729i
$655$	−83.4031	−	144.458i	−0.127333	−	0.220547i
$656$	−76.8703	−	44.3811i	−0.117180	−	0.0676541i
$657$		−	58.4744i		−	0.0890021i
$658$	750.467	−	113.254i	1.14053	−	0.172119i
$659$	1164.66			1.76732			0.883660	−	0.468130i	$-0.155072\pi$
$659$	1164.66			1.76732			0.883660	+	0.468130i	$0.155072\pi$
$660$	−44.8677	+	77.7132i	−0.0679814	+	0.117747i
$661$	542.087	−	312.974i	0.820101	−	0.473485i	−0.0303505	−	0.999539i	$-0.509662\pi$
$661$	542.087	−	312.974i	0.820101	−	0.473485i	0.850451	+	0.526054i	$0.176329\pi$
$662$	249.553	+	432.238i	0.376968	+	0.652928i
$663$	325.636	+	188.006i	0.491155	+	0.283568i
$664$		−	378.453i		−	0.569960i
$665$	73.3994	+	486.372i	0.110375	+	0.731387i
$666$	−8.42709			−0.0126533
$667$	20.9131	−	36.2226i	0.0313540	−	0.0543067i
$668$	−481.144	+	277.788i	−0.720275	+	0.415851i
$669$	218.163	+	377.869i	0.326103	+	0.564827i
$670$	268.835	+	155.212i	0.401246	+	0.231660i
$671$			783.342i			1.16743i
$672$	−42.7723	−	53.6147i	−0.0636492	−	0.0797838i
$673$	−38.0207			−0.0564943			−0.0282471	−	0.999601i	$-0.508993\pi$
$673$	−38.0207			−0.0564943			−0.0282471	+	0.999601i	$0.508993\pi$
$674$	−156.011	+	270.220i	−0.231471	+	0.400920i
$675$	22.5000	−	12.9904i	0.0333333	−	0.0192450i
$676$	−107.162	−	185.610i	−0.158524	−	0.274571i
$677$	676.984	+	390.857i	0.999976	+	0.577336i	0.908241	−	0.418447i	$-0.137426\pi$
$677$	676.984	+	390.857i	0.999976	+	0.577336i	0.0917347	+	0.995783i	$0.470759\pi$
$678$			117.057i			0.172651i
$679$	−184.842	+	471.222i	−0.272227	+	0.693994i
$680$	174.599			0.256764
$681$	231.941	−	401.733i	0.340588	−	0.589916i
$682$	−74.6852	+	43.1195i	−0.109509	+	0.0632251i
$683$	67.2190	+	116.427i	0.0984172	+	0.170464i	0.911030	−	0.412341i	$-0.135289\pi$
$683$	67.2190	+	116.427i	0.0984172	+	0.170464i	−0.812612	+	0.582804i	$0.801955\pi$
$684$	−163.289	−	94.2751i	−0.238727	−	0.137829i
$685$			552.083i			0.805960i
$686$	−483.739	−	35.9855i	−0.705158	−	0.0524570i
$687$	598.474			0.871142
$688$	−99.6736	+	172.640i	−0.144874	+	0.250930i
$689$	388.830	−	224.491i	0.564340	−	0.325822i
$690$	−49.7310	−	86.1366i	−0.0720739	−	0.124836i
$691$	−393.253	−	227.045i	−0.569107	−	0.328574i	0.187686	−	0.982229i	$-0.439901\pi$
$691$	−393.253	−	227.045i	−0.569107	−	0.328574i	−0.756792	+	0.653655i	$0.773235\pi$
$692$		−	252.131i		−	0.364351i
$693$	−226.480	−	88.8392i	−0.326811	−	0.128195i
$694$	−362.051			−0.521687
$695$	−174.320	+	301.932i	−0.250821	+	0.434434i
$696$	−9.77211	+	5.64193i	−0.0140404	+	0.00810622i
$697$	306.303	+	530.532i	0.439459	+	0.761165i
$698$	498.778	+	287.969i	0.714581	+	0.412564i
$699$		−	498.942i		−	0.713794i
$700$	54.7203	−	43.6543i	0.0781718	−	0.0623632i
$701$	982.015			1.40088			0.700439	−	0.713713i	$-0.252988\pi$
$701$	982.015			1.40088			0.700439	+	0.713713i	$0.252988\pi$
$702$	−28.8931	+	50.0444i	−0.0411583	+	0.0712883i
$703$	−54.0565	+	31.2095i	−0.0768940	+	0.0443948i
$704$	−46.3392	−	80.2618i	−0.0658227	−	0.114008i
$705$	−257.149	−	148.465i	−0.364750	−	0.210589i
$706$		−	824.822i		−	1.16830i
$707$	350.603	−	52.9102i	0.495903	−	0.0748376i
$708$	243.698			0.344206
$709$	166.536	−	288.449i	0.234889	−	0.406839i	−0.724352	−	0.689431i	$-0.757861\pi$
$709$	166.536	−	288.449i	0.234889	−	0.406839i	0.959240	+	0.282591i	$0.0911940\pi$
$710$	93.8241	−	54.1694i	0.132147	−	0.0762949i
$711$	135.643	+	234.940i	0.190777	+	0.330436i
$712$	−27.1029	−	15.6479i	−0.0380658	−	0.0219773i
$713$		−	95.5866i		−	0.134063i
$714$	70.6351	+	468.055i	0.0989287	+	0.655539i
$715$	203.705			0.284902
$716$	−77.1069	+	133.553i	−0.107691	+	0.186527i
$717$	−283.215	+	163.514i	−0.395000	+	0.228053i
$718$	−488.984	−	846.946i	−0.681037	−	1.17959i
$719$	1055.73	+	609.523i	1.46832	+	0.847737i	0.999370	−	0.0354852i	$-0.0112977\pi$
$719$	1055.73	+	609.523i	1.46832	+	0.847737i	0.468954	+	0.883223i	$0.344631\pi$
$720$			26.8328i			0.0372678i
$721$	−864.200	−	1083.27i	−1.19861	−	1.50245i
$722$	−886.051			−1.22722
$723$	84.7389	−	146.772i	0.117205	−	0.203004i
$724$	−367.215	+	212.012i	−0.507203	+	0.292834i
$725$	−5.75827	−	9.97362i	−0.00794244	−	0.0137567i
$726$	−28.0172	−	16.1758i	−0.0385912	−	0.0222807i
$727$			215.108i			0.295885i	0.988996	+	0.147942i	$0.0472650\pi$
$727$			215.108i			0.295885i	−0.988996	+	0.147942i	$0.952735\pi$
$728$	−56.8549	+	144.941i	−0.0780974	+	0.199095i
$729$	−27.0000			−0.0370370
$730$	−30.8187	+	53.3796i	−0.0422174	+	0.0731227i
$731$	1191.50	−	687.913i	1.62996	−	0.941057i
$732$	117.118	+	202.854i	0.159997	+	0.277124i
$733$	−649.047	−	374.728i	−0.885467	−	0.511225i	−0.0130099	−	0.999915i	$-0.504141\pi$
$733$	−649.047	−	374.728i	−0.885467	−	0.511225i	−0.872457	+	0.488691i	$0.837475\pi$
$734$			324.883i			0.442620i
$735$	139.163	+	129.030i	0.189337	+	0.175551i
$736$	102.724			0.139570
$737$	−568.609	+	984.859i	−0.771518	+	1.33631i
$738$	−81.5332	+	47.0732i	−0.110479	+	0.0637849i
$739$	467.102	+	809.045i	0.632073	+	1.09478i	0.987127	+	0.159937i	$0.0511291\pi$
$739$	467.102	+	809.045i	0.632073	+	1.09478i	−0.355054	+	0.934846i	$0.615538\pi$
$740$	7.69285	+	4.44147i	0.0103957	+	0.00600198i
$741$			428.020i			0.577625i
$742$	526.182	+	206.401i	0.709140	+	0.278168i
$743$	1232.47			1.65878			0.829389	−	0.558671i	$-0.188689\pi$
$743$	1232.47			1.65878			0.829389	+	0.558671i	$0.188689\pi$
$744$	−12.8937	+	22.3325i	−0.0173302	+	0.0300168i
$745$	−315.823	+	182.341i	−0.423924	+	0.244752i
$746$	286.101	+	495.542i	0.383514	+	0.664266i
$747$	−347.632	−	200.705i	−0.465370	−	0.268682i
$748$			639.634i			0.855125i
$749$	−809.508	+	645.803i	−1.08079	+	0.862220i
$750$	−27.3861			−0.0365148
$751$	−393.353	+	681.307i	−0.523772	+	0.907200i	0.475845	+	0.879529i	$0.342142\pi$
$751$	−393.353	+	681.307i	−0.523772	+	0.907200i	−0.999617	+	0.0276709i	$0.991191\pi$
$752$	265.582	−	153.334i	0.353168	−	0.203902i
$753$	−209.011	−	362.017i	−0.277571	−	0.480767i
$754$	22.1833	+	12.8075i	0.0294208	+	0.0169861i
$755$			167.772i			0.222214i
$756$	−71.9316	+	10.8553i	−0.0951477	+	0.0143589i
$757$	1303.18			1.72151			0.860753	−	0.509023i	$-0.169993\pi$
$757$	1303.18			1.72151			0.860753	+	0.509023i	$0.169993\pi$
$758$	−187.995	+	325.618i	−0.248015	+	0.429575i
$759$	315.556	−	182.186i	0.415752	−	0.240034i
$760$	99.3747	+	172.122i	0.130756	+	0.226476i
$761$	601.784	+	347.440i	0.790780	+	0.456557i	0.840237	−	0.542219i	$-0.182416\pi$
$761$	601.784	+	347.440i	0.790780	+	0.456557i	−0.0494571	+	0.998776i	$0.515749\pi$
$762$		−	249.783i		−	0.327799i
$763$	56.7423	+	375.996i	0.0743674	+	0.492786i
$764$	331.392			0.433759
$765$	92.5954	−	160.380i	0.121040	−	0.209647i
$766$	−375.266	+	216.660i	−0.489904	+	0.282846i
$767$	−276.604	−	479.093i	−0.360631	−	0.624632i
$768$	−24.0000	−	13.8564i	−0.0312500	−	0.0180422i
$769$			263.988i			0.343287i	0.985159	+	0.171644i	$0.0549077\pi$
$769$			263.988i			0.343287i	−0.985159	+	0.171644i	$0.945092\pi$
$770$	159.924	+	200.464i	0.207694	+	0.260343i
$771$	−21.7614			−0.0282249
$772$	105.299	−	182.384i	0.136398	−	0.236249i
$773$	−136.278	+	78.6802i	−0.176298	+	0.101786i	−0.585552	−	0.810635i	$-0.699122\pi$
$773$	−136.278	+	78.6802i	−0.176298	+	0.101786i	0.409254	+	0.912420i	$0.365789\pi$
$774$	105.720	+	183.112i	0.136589	+	0.236579i
$775$	−22.7930	−	13.1595i	−0.0294103	−	0.0169801i
$776$			204.527i			0.263566i
$777$	−8.79422	+	22.4193i	−0.0113182	+	0.0288537i
$778$	150.408			0.193326
$779$	−348.669	+	603.913i	−0.447586	+	0.775241i
$780$	52.7514	−	30.4560i	0.0676300	−	0.0390462i
$781$	198.446	+	343.718i	0.254092	+	0.440100i
$782$	−613.981	−	354.482i	−0.785142	−	0.453302i
$783$			11.9683i			0.0152852i
$784$	−187.271	+	57.8402i	−0.238866	+	0.0737758i
$785$	−502.513			−0.640144
$786$	91.3635	−	158.246i	0.116239	−	0.201331i
$787$	850.660	−	491.129i	1.08089	−	0.624052i	0.149754	−	0.988723i	$-0.452152\pi$
$787$	850.660	−	491.129i	1.08089	−	0.624052i	0.931136	+	0.364671i	$0.118819\pi$
$788$	−244.736	−	423.894i	−0.310578	−	0.537937i
$789$	318.721	+	184.014i	0.403956	+	0.233224i
$790$		−	285.960i		−	0.361975i
$791$	311.417	+	122.157i	0.393700	+	0.154433i
$792$	−98.3002			−0.124116
$793$	265.865	−	460.492i	0.335265	−	0.580695i
$794$	266.782	−	154.027i	0.335998	−	0.193988i
$795$	−110.565	−	191.504i	−0.139075	−	0.240885i
$796$	−169.683	−	97.9667i	−0.213170	−	0.123074i
$797$		−	946.927i		−	1.18811i	−0.804423	−	0.594057i	$-0.797525\pi$
$797$		−	946.927i		−	1.18811i	0.804423	−	0.594057i	$-0.202475\pi$
$798$	−421.211	+	336.030i	−0.527833	+	0.421090i
$799$	−2116.52			−2.64896
$800$	14.1421	−	24.4949i	0.0176777	−	0.0306186i
$801$	−28.7470	+	16.5971i	−0.0358888	+	0.0207204i
$802$	−43.8275	−	75.9114i	−0.0546477	−	0.0946526i
$803$	−195.553	−	112.902i	−0.243527	−	0.140601i
$804$			340.052i			0.422951i
$805$	−281.054	+	42.4144i	−0.349135	+	0.0526887i
$806$	58.5388			0.0726287
$807$	−289.769	+	501.895i	−0.359070	+	0.621927i
$808$	124.075	−	71.6346i	0.153558	−	0.0886567i
$809$	−214.568	−	371.642i	−0.265226	−	0.459385i	0.702397	−	0.711786i	$-0.252113\pi$
$809$	−214.568	−	371.642i	−0.265226	−	0.459385i	−0.967623	+	0.252401i	$0.918780\pi$
$810$	24.6475	+	14.2302i	0.0304290	+	0.0175682i
$811$		−	948.404i		−	1.16943i	−0.811241	−	0.584713i	$-0.801207\pi$
$811$		−	948.404i		−	1.16943i	0.811241	−	0.584713i	$-0.198793\pi$
$812$	4.81187	+	31.8853i	0.00592595	+	0.0392676i
$813$	−315.840			−0.388487
$814$	−16.2710	+	28.1822i	−0.0199890	+	0.0346219i
$815$	445.620	−	257.279i	0.546774	−	0.315680i
$816$	95.6321	+	165.640i	0.117196	+	0.202990i
$817$	1356.30	+	783.062i	1.66010	+	0.958460i
$818$		−	614.278i		−	0.750952i
$819$	102.985	+	129.091i	0.125745	+	0.157621i
$820$	99.2391			0.121023
$821$	201.884	−	349.673i	0.245900	−	0.425911i	−0.716484	−	0.697603i	$-0.754250\pi$
$821$	201.884	−	349.673i	0.245900	−	0.425911i	0.962384	+	0.271692i	$0.0875832\pi$
$822$	−523.752	+	302.388i	−0.637168	+	0.367869i
$823$	−433.014	−	750.003i	−0.526141	−	0.911303i	−0.999536	−	0.0304530i	$-0.990305\pi$
$823$	−433.014	−	750.003i	−0.526141	−	0.911303i	0.473395	−	0.880850i	$-0.343028\pi$
$824$	−484.912	−	279.964i	−0.588486	−	0.339762i
$825$		−	100.327i		−	0.121609i
$826$	254.314	−	648.330i	0.307887	−	0.784903i
$827$	−363.528			−0.439574			−0.219787	−	0.975548i	$-0.570536\pi$
$827$	−363.528			−0.439574			−0.219787	+	0.975548i	$0.570536\pi$
$828$	54.4776	−	94.3579i	0.0657942	−	0.113959i
$829$	208.617	−	120.445i	0.251649	−	0.145290i	−0.368870	−	0.929481i	$-0.620255\pi$
$829$	208.617	−	120.445i	0.251649	−	0.145290i	0.620519	+	0.784191i	$0.286922\pi$
$830$	211.562	+	366.436i	0.254894	+	0.441489i
$831$	−250.142	−	144.420i	−0.301013	−	0.173790i
$832$			62.9097i			0.0756126i
$833$	1318.92	+	300.529i	1.58333	+	0.360779i
$834$	−381.917			−0.457934
$835$	310.577	−	537.935i	0.371948	−	0.644233i
$836$	−630.557	+	364.052i	−0.754255	+	0.435469i
$837$	13.6758	+	23.6872i	0.0163391	+	0.0283001i
$838$	−559.979	−	323.304i	−0.668232	−	0.385804i
$839$		−	214.638i		−	0.255826i	−0.991785	−	0.127913i	$-0.959172\pi$
$839$		−	214.638i		−	0.255826i	0.991785	−	0.127913i	$-0.0408278\pi$
$840$	71.3856	+	28.0018i	0.0849828	+	0.0333354i
$841$	−835.695			−0.993692
$842$	461.846	−	799.941i	0.548511	−	0.950049i
$843$	57.4628	−	33.1762i	0.0681647	−	0.0393549i
$844$	388.914	+	673.618i	0.460798	+	0.798126i
$845$	207.518	+	119.811i	0.245584	+	0.141788i
$846$		−	325.271i		−	0.384481i
$847$	−72.2715	+	57.6561i	−0.0853264	+	0.0680710i
$848$	228.382			0.269318
$849$	−333.849	+	578.244i	−0.393226	+	0.681088i
$850$	−169.055	+	97.6041i	−0.198889	+	0.114828i
$851$	−18.0347	−	31.2369i	−0.0211923	−	0.0367062i
$852$	102.779	+	59.3396i	0.120633	+	0.0696474i
$853$		−	1388.39i		−	1.62765i	−0.581110	−	0.813825i	$-0.697382\pi$
$853$		−	1388.39i		−	1.62765i	0.581110	−	0.813825i	$-0.302618\pi$
$854$	661.891	−	99.8873i	0.775048	−	0.116964i
$855$	210.805			0.246556
$856$	−209.213	+	362.367i	−0.244407	+	0.423326i
$857$	950.012	−	548.489i	1.10853	−	0.640011i	0.170083	−	0.985430i	$-0.445596\pi$
$857$	950.012	−	548.489i	1.10853	−	0.640011i	0.938449	+	0.345419i	$0.112263\pi$
$858$	111.574	+	193.251i	0.130039	+	0.225235i
$859$	−234.305	−	135.276i	−0.272764	−	0.157481i	0.357379	−	0.933959i	$-0.383670\pi$
$859$	−234.305	−	135.276i	−0.272764	−	0.157481i	−0.630143	+	0.776479i	$0.717004\pi$
$860$		−	222.877i		−	0.259159i
$861$	40.1477	+	266.034i	0.0466291	+	0.308982i
$862$	−665.042			−0.771511
$863$	−134.107	+	232.280i	−0.155396	+	0.269154i	−0.933203	−	0.359349i	$-0.882999\pi$
$863$	−134.107	+	232.280i	−0.155396	+	0.269154i	0.777807	+	0.628503i	$0.216332\pi$
$864$	−25.4558	+	14.6969i	−0.0294628	+	0.0170103i
$865$	140.945	+	244.125i	0.162943	+	0.282225i
$866$	−39.2284	−	22.6485i	−0.0452984	−	0.0261530i
$867$		−	819.476i		−	0.945186i
$868$	45.9576	+	57.6075i	0.0529465	+	0.0663681i
$869$	1047.60			1.20552
$870$	6.30787	−	10.9256i	0.00725043	−	0.0125581i
$871$	668.519	−	385.970i	0.767530	−	0.443134i
$872$	76.8228	+	133.061i	0.0880995	+	0.152593i
$873$	187.870	+	108.467i	0.215200	+	0.124246i
$874$		−	807.025i		−	0.923370i
$875$	−28.5792	+	72.8576i	−0.0326619	+	0.0832658i
$876$	−67.5204			−0.0770781
$877$	−253.705	+	439.430i	−0.289288	+	0.501061i	−0.973640	−	0.228091i	$-0.926752\pi$
$877$	−253.705	+	439.430i	−0.289288	+	0.501061i	0.684352	+	0.729152i	$0.260085\pi$
$878$	−468.145	+	270.284i	−0.533195	+	0.307840i
$879$	78.7948	+	136.477i	0.0896414	+	0.155264i
$880$	89.7354	+	51.8088i	0.101972	+	0.0588736i
$881$			833.545i			0.946135i	0.881026	+	0.473067i	$0.156853\pi$
$881$			833.545i			0.946135i	−0.881026	+	0.473067i	$0.843147\pi$
$882$	−46.1859	+	202.694i	−0.0523650	+	0.229812i
$883$	−1350.99			−1.53000			−0.765002	−	0.644028i	$-0.777262\pi$
$883$	−1350.99			−1.53000			−0.765002	+	0.644028i	$0.777262\pi$
$884$	217.090	−	376.012i	0.245577	−	0.425353i
$885$	−235.959	+	136.231i	−0.266621	+	0.153934i
$886$	−87.4985	−	151.552i	−0.0987568	−	0.171052i
$887$	324.005	+	187.065i	0.365282	+	0.210896i	0.671395	−	0.741099i	$-0.265695\pi$
$887$	324.005	+	187.065i	0.365282	+	0.210896i	−0.306113	+	0.951995i	$0.599029\pi$
$888$			9.73077i			0.0109581i
$889$	−664.518	−	260.664i	−0.747489	−	0.293211i
$890$	34.9897			0.0393142
$891$	−52.1316	+	90.2945i	−0.0585091	+	0.101341i
$892$	436.326	−	251.913i	0.489154	−	0.282413i
$893$	−1204.63	−	2086.48i	−1.34897	−	2.33649i
$894$	−345.967	−	199.744i	−0.386988	−	0.223427i
$895$		−	172.416i		−	0.192644i
$896$	−61.9089	+	49.3891i	−0.0690948	+	0.0551218i
$897$	−247.335			−0.275735
$898$	188.787	−	326.989i	0.210230	−	0.364130i
$899$	10.4999	−	6.06210i	0.0116795	−	0.00674316i
$900$	−15.0000	−	25.9808i	−0.0166667	−	0.0288675i
$901$	−1365.04	−	788.105i	−1.51503	−	0.874701i
$902$			363.556i			0.403055i
$903$	597.474	−	90.1660i	0.661655	−	0.0998516i
$904$	135.166			0.149520
$905$	237.036	−	410.559i	0.261919	−	0.453657i
$906$	−159.162	+	91.8925i	−0.175676	+	0.101427i
$907$	178.758	+	309.618i	0.197087	+	0.341365i	0.947583	−	0.319510i	$-0.103518\pi$
$907$	178.758	+	309.618i	0.197087	+	0.341365i	−0.750496	+	0.660875i	$0.770185\pi$
$908$	−463.881	−	267.822i	−0.510882	−	0.294958i
$909$		−	151.960i		−	0.167173i
$910$	−25.9752	−	172.122i	−0.0285442	−	0.189145i
$911$	−1503.55			−1.65044			−0.825219	−	0.564813i	$-0.808948\pi$
$911$	−1503.55			−1.65044			−0.825219	+	0.564813i	$0.808948\pi$
$912$	−108.859	+	188.550i	−0.119363	+	0.206744i
$913$	−1342.41	+	775.043i	−1.47033	+	0.848897i
$914$	317.731	+	550.327i	0.347627	+	0.602108i
$915$	−226.798	−	130.942i	−0.247867	−	0.143106i
$916$		−	691.059i		−	0.754431i
$917$	−325.652	−	408.202i	−0.355127	−	0.445149i
$918$	202.866			0.220987
$919$	312.499	−	541.265i	0.340043	−	0.588971i	−0.644398	−	0.764691i	$-0.722892\pi$
$919$	312.499	−	541.265i	0.340043	−	0.588971i	0.984440	+	0.175719i	$0.0562251\pi$
$920$	−99.4620	+	57.4244i	−0.108111	+	0.0624178i
$921$	−440.007	−	762.115i	−0.477750	−	0.827487i
$922$	129.245	+	74.6199i	0.140179	+	0.0809327i
$923$		−	269.409i		−	0.291884i
$924$	−102.583	+	261.516i	−0.111020	+	0.283026i
$925$	−9.93142			−0.0107367
$926$	−416.171	+	720.829i	−0.449429	+	0.778433i
$927$	−514.327	+	296.947i	−0.554830	+	0.320331i
$928$	6.51474	+	11.2839i	0.00702019	+	0.0121593i
$929$	−942.883	−	544.374i	−1.01494	−	0.585978i	−0.102309	−	0.994753i	$-0.532623\pi$
$929$	−942.883	−	544.374i	−1.01494	−	0.585978i	−0.912636	+	0.408774i	$0.865956\pi$
$930$		−	28.8311i		−	0.0310012i
$931$	454.408	+	1471.25i	0.488086	+	1.58029i
$932$	−576.129			−0.618164
$933$	90.3447	−	156.482i	0.0968325	−	0.167719i
$934$	−447.837	+	258.559i	−0.479483	+	0.276829i
$935$	−357.566	−	619.323i	−0.382424	−	0.662377i
$936$	57.7863	+	33.3629i	0.0617375	+	0.0356441i
$937$			252.836i			0.269835i	0.990857	+	0.134918i	$0.0430770\pi$
$937$			252.836i			0.269835i	−0.990857	+	0.134918i	$0.956923\pi$
$938$	904.670	+	354.867i	0.964467	+	0.378323i
$939$	460.498			0.490413
$940$	−171.433	+	296.930i	−0.182375	+	0.315883i
$941$	−332.262	+	191.832i	−0.353095	+	0.203859i	−0.666048	−	0.745909i	$-0.732015\pi$
$941$	−332.262	+	191.832i	−0.353095	+	0.203859i	0.312953	+	0.949769i	$0.398682\pi$
$942$	−275.238	−	476.726i	−0.292184	−	0.506078i
$943$	−348.975	−	201.481i	−0.370069	−	0.213660i
$944$		−	281.398i		−	0.298091i
$945$	63.5792	−	50.7217i	0.0672796	−	0.0536737i
$946$	816.495			0.863103
$947$	140.892	−	244.032i	0.148777	−	0.257690i	−0.781999	−	0.623280i	$-0.785800\pi$
$947$	140.892	−	244.032i	0.148777	−	0.257690i	0.930776	+	0.365591i	$0.119133\pi$
$948$	271.285	−	156.627i	0.286166	−	0.165218i
$949$	76.6377	+	132.740i	0.0807562	+	0.139874i
$950$	−192.438	−	111.104i	−0.202567	−	0.116952i
$951$		−	18.5715i		−	0.0195284i
$952$	540.463	−	81.5624i	0.567713	−	0.0856748i
$953$	−332.322			−0.348711			−0.174356	−	0.984683i	$-0.555784\pi$
$953$	−332.322			−0.348711			−0.174356	+	0.984683i	$0.555784\pi$
$954$	121.118	−	209.782i	0.126958	−	0.219897i
$955$	−320.869	+	185.254i	−0.335988	+	0.193983i
$956$	188.810	+	327.028i	0.197500	+	0.342080i
$957$	40.0250	+	23.1085i	0.0418234	+	0.0241468i
$958$		−	688.971i		−	0.719177i
$959$	257.900	+	1708.94i	0.268926	+	1.78200i
$960$	30.9839			0.0322749
$961$	−466.646	+	808.255i	−0.485584	+	0.841056i
$962$	19.1300	−	11.0447i	0.0198857	−	0.0114810i
$963$	221.904	+	384.348i	0.230430	+	0.399116i
$964$	−169.478	−	97.8480i	−0.175807	−	0.101502i
$965$			235.457i			0.243997i
$966$	−194.177	−	243.400i	−0.201012	−	0.251967i
$967$	1155.53			1.19496			0.597482	−	0.801882i	$-0.296168\pi$
$967$	1155.53			1.19496			0.597482	+	0.801882i	$0.296168\pi$
$968$	−18.6782	+	32.3515i	−0.0192956	+	0.0334210i
$969$	1301.31	−	751.310i	1.34294	−	0.775346i
$970$	−114.334	−	198.032i	−0.117870	−	0.204157i
$971$	−1307.94	−	755.140i	−1.34700	−	0.777693i	−0.359179	−	0.933269i	$-0.616943\pi$
$971$	−1307.94	−	755.140i	−1.34700	−	0.777693i	−0.987824	+	0.155576i	$0.950277\pi$
$972$			31.1769i			0.0320750i
$973$	−398.555	+	1016.04i	−0.409614	+	1.04424i
$974$	−276.866			−0.284257
$975$	−34.0509	+	58.9779i	−0.0349240	+	0.0604901i
$976$	234.236	−	135.236i	0.239996	−	0.138562i
$977$	−400.808	−	694.220i	−0.410244	−	0.710563i	0.584672	−	0.811269i	$-0.301223\pi$
$977$	−400.808	−	694.220i	−0.410244	−	0.710563i	−0.994916	+	0.100706i	$0.967890\pi$
$978$	488.153	+	281.835i	0.499134	+	0.288175i
$979$			128.182i			0.130932i
$980$	148.991	−	160.691i	0.152032	−	0.163971i
$981$	162.966			0.166122
$982$	246.937	−	427.707i	0.251463	−	0.435547i
$983$	−948.116	+	547.395i	−0.964513	+	0.556862i	−0.897559	−	0.440894i	$-0.854661\pi$
$983$	−948.116	+	547.395i	−0.964513	+	0.556862i	−0.0669540	+	0.997756i	$0.521328\pi$
$984$	54.3555	+	94.1465i	0.0552393	+	0.0956773i
$985$	473.928	+	273.623i	0.481146	+	0.277790i
$986$		−	89.9249i		−	0.0912018i
$987$	−865.344	−	339.441i	−0.876742	−	0.343912i
$988$	494.235			0.500238
$989$	−452.498	+	783.750i	−0.457531	+	0.792467i
$990$	95.1788	−	54.9515i	0.0961402	−	0.0555066i
$991$	−21.9962	−	38.0986i	−0.0221960	−	0.0384446i	0.854714	−	0.519099i	$-0.173732\pi$
$991$	−21.9962	−	38.0986i	−0.0221960	−	0.0384446i	−0.876910	+	0.480655i	$0.840399\pi$
$992$	25.7873	+	14.8883i	0.0259953	+	0.0150084i
$993$		−	611.277i		−	0.615586i
$994$	265.123	−	211.507i	0.266723	−	0.212784i
$995$	219.060			0.220161
$996$	−231.754	+	401.410i	−0.232685	+	0.403022i
$997$	10.6141	−	6.12803i	0.0106460	−	0.00614647i	−0.494668	−	0.869082i	$-0.664710\pi$
$997$	10.6141	−	6.12803i	0.0106460	−	0.00614647i	0.505314	+	0.862936i	$0.331377\pi$
$998$	237.191	+	410.827i	0.237666	+	0.411650i
$999$	8.93828	+	5.16052i	0.00894723	+	0.00516569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.o.a.61.2	yes	8
3.2	odd	2		630.3.v.b.271.3		8
5.2	odd	4		1050.3.q.c.649.2		16
5.3	odd	4		1050.3.q.c.649.7		16
5.4	even	2		1050.3.p.b.901.3		8
7.2	even	3		1470.3.f.a.391.7		8
7.3	odd	6	inner	210.3.o.a.31.2	✓	8
7.5	odd	6		1470.3.f.a.391.6		8
21.17	even	6		630.3.v.b.451.3		8
35.3	even	12		1050.3.q.c.199.2		16
35.17	even	12		1050.3.q.c.199.7		16
35.24	odd	6		1050.3.p.b.451.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.a.31.2	✓	8	7.3	odd	6	inner
210.3.o.a.61.2	yes	8	1.1	even	1	trivial
630.3.v.b.271.3		8	3.2	odd	2
630.3.v.b.451.3		8	21.17	even	6
1050.3.p.b.451.3		8	35.24	odd	6
1050.3.p.b.901.3		8	5.4	even	2
1050.3.q.c.199.2		16	35.3	even	12
1050.3.q.c.199.7		16	35.17	even	12
1050.3.q.c.649.2		16	5.2	odd	4
1050.3.q.c.649.7		16	5.3	odd	4
1470.3.f.a.391.6		8	7.5	odd	6
1470.3.f.a.391.7		8	7.2	even	3

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} +2.44949i q^{6} +(6.51658 + 2.55620i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} +2.44949i q^{6} +(6.51658 + 2.55620i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-2.73861 + 1.58114i) q^{10} +(-5.79240 - 10.0327i) q^{11} +(-3.00000 - 1.73205i) q^{12} +7.86371i q^{13} +(-7.73861 + 6.17364i) q^{14} +3.87298 q^{15} +(-2.00000 + 3.46410i) q^{16} +(23.9080 - 13.8033i) q^{17} +(2.12132 + 3.67423i) q^{18} +(27.2149 + 15.7125i) q^{19} -4.47214i q^{20} +(11.9886 - 1.80922i) q^{21} +16.3834 q^{22} +(-9.07959 + 15.7263i) q^{23} +(4.24264 - 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-9.63104 - 5.56049i) q^{26} -5.19615i q^{27} +(-2.08911 - 13.8433i) q^{28} -2.30331 q^{29} +(-2.73861 + 4.74342i) q^{30} +(-4.55860 + 2.63191i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-17.3772 - 10.0327i) q^{33} +39.0416i q^{34} +(9.76139 + 12.2358i) q^{35} -6.00000 q^{36} +(-0.993142 + 1.72017i) q^{37} +(-38.4876 + 22.2208i) q^{38} +(6.81018 + 11.7956i) q^{39} +(5.47723 + 3.16228i) q^{40} +22.1905i q^{41} +(-6.26139 + 15.9623i) q^{42} +49.8368 q^{43} +(-11.5848 + 20.0655i) q^{44} +(5.80948 - 3.35410i) q^{45} +(-12.8405 - 22.2404i) q^{46} +(-66.3956 - 38.3335i) q^{47} +6.92820i q^{48} +(35.9317 + 33.3154i) q^{49} -7.07107 q^{50} +(23.9080 - 41.4099i) q^{51} +(13.6204 - 7.86371i) q^{52} +(-28.5477 - 49.4461i) q^{53} +(6.36396 + 3.67423i) q^{54} -25.9044i q^{55} +(18.4317 + 7.23003i) q^{56} +54.4297 q^{57} +(1.62869 - 2.82097i) q^{58} +(-60.9245 + 35.1748i) q^{59} +(-3.87298 - 6.70820i) q^{60} +(-58.5590 - 33.8091i) q^{61} -7.44416i q^{62} +(16.4161 - 13.0963i) q^{63} +8.00000 q^{64} +(-8.79190 + 15.2280i) q^{65} +(24.5751 - 14.1884i) q^{66} +(-49.0823 - 85.0131i) q^{67} +(-47.8160 - 27.6066i) q^{68} +31.4526i q^{69} +(-21.8881 + 3.30318i) q^{70} -34.2597 q^{71} +(4.24264 - 7.34847i) q^{72} +(16.8801 - 9.74573i) q^{73} +(-1.40452 - 2.43269i) q^{74} +(7.50000 + 4.33013i) q^{75} -62.8501i q^{76} +(-12.1010 - 80.1856i) q^{77} -19.2621 q^{78} +(-45.2142 + 78.3134i) q^{79} +(-7.74597 + 4.47214i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-27.1777 - 15.6911i) q^{82} -133.803i q^{83} +(-15.1223 - 18.9557i) q^{84} +61.7302 q^{85} +(-35.2400 + 61.0374i) q^{86} +(-3.45496 + 1.99472i) q^{87} +(-16.3834 - 28.3768i) q^{88} +(-9.58232 - 5.53235i) q^{89} +9.48683i q^{90} +(-20.1012 + 51.2445i) q^{91} +36.3184 q^{92} +(-4.55860 + 7.89573i) q^{93} +(93.8975 - 54.2118i) q^{94} +(35.1342 + 60.8543i) q^{95} +(-8.48528 - 4.89898i) q^{96} +72.3112i q^{97} +(-66.2104 + 20.4496i) q^{98} -34.7544 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{3} - 8 q^{4} + 12 q^{9}+O(q^{10}) \) 8 * q + 12 * q^3 - 8 * q^4 + 12 * q^9	\( 8 q + 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} - 24 q^{12} - 40 q^{14} - 16 q^{16} + 84 q^{17} + 108 q^{19} - 48 q^{22} + 12 q^{23} + 20 q^{25} - 96 q^{26} + 72 q^{29} - 132 q^{31} - 12 q^{33} + 100 q^{35} - 48 q^{36} - 96 q^{37} - 168 q^{38} + 24 q^{39} - 72 q^{42} - 112 q^{43} - 8 q^{44} + 8 q^{46} - 24 q^{47} + 156 q^{49} + 84 q^{51} + 48 q^{52} + 32 q^{53} + 16 q^{56} + 216 q^{57} + 104 q^{58} + 132 q^{59} + 96 q^{61} + 64 q^{64} + 20 q^{65} - 72 q^{66} - 120 q^{67} - 168 q^{68} + 8 q^{71} + 24 q^{73} - 16 q^{74} + 60 q^{75} - 216 q^{77} - 192 q^{78} + 12 q^{79} - 36 q^{81} + 24 q^{82} + 120 q^{85} - 40 q^{86} + 108 q^{87} + 48 q^{88} + 492 q^{89} - 308 q^{91} - 48 q^{92} - 132 q^{93} + 480 q^{94} - 40 q^{95} - 24 q^{99}+O(q^{100}) \) 8 * q + 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 - 24 * q^12 - 40 * q^14 - 16 * q^16 + 84 * q^17 + 108 * q^19 - 48 * q^22 + 12 * q^23 + 20 * q^25 - 96 * q^26 + 72 * q^29 - 132 * q^31 - 12 * q^33 + 100 * q^35 - 48 * q^36 - 96 * q^37 - 168 * q^38 + 24 * q^39 - 72 * q^42 - 112 * q^43 - 8 * q^44 + 8 * q^46 - 24 * q^47 + 156 * q^49 + 84 * q^51 + 48 * q^52 + 32 * q^53 + 16 * q^56 + 216 * q^57 + 104 * q^58 + 132 * q^59 + 96 * q^61 + 64 * q^64 + 20 * q^65 - 72 * q^66 - 120 * q^67 - 168 * q^68 + 8 * q^71 + 24 * q^73 - 16 * q^74 + 60 * q^75 - 216 * q^77 - 192 * q^78 + 12 * q^79 - 36 * q^81 + 24 * q^82 + 120 * q^85 - 40 * q^86 + 108 * q^87 + 48 * q^88 + 492 * q^89 - 308 * q^91 - 48 * q^92 - 132 * q^93 + 480 * q^94 - 40 * q^95 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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