LMFDB - Embedded newform 210.3.o.b.31.2

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + \cdots + 101626561 $ x^16 + 92x^14 - 112x^13 + 5846x^12 - 7728x^11 + 197216x^10 - 298200x^9 + 4836403x^8 - 6808704x^7 + 64376800x^6 - 91953512x^5 + 595763862x^4 - 630430976x^3 + 1087013404x^2 + 294123256x + 101626561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Root			$2.96377 + 5.13339i$ of defining polynomial
Character	$\chi$	$=$	210.31
Dual form			210.3.o.b.61.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +2.44949i q^{6} +(5.73733 + 4.01037i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(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} +(5.73733 + 4.01037i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(2.73861 + 1.58114i) q^{10} +(8.69259 - 15.0560i) q^{11} +(3.00000 - 1.73205i) q^{12} -7.22559i q^{13} +(0.854777 - 9.86252i) q^{14} +3.87298 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-2.29669 - 1.32600i) q^{17} +(2.12132 - 3.67423i) q^{18} +(2.20128 - 1.27091i) q^{19} -4.47214i q^{20} +(-5.13291 - 10.9842i) q^{21} -24.5864 q^{22} +(-20.0507 - 34.7289i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-8.84951 + 5.10926i) q^{26} -5.19615i q^{27} +(-12.6835 + 5.92697i) q^{28} +47.0080 q^{29} +(-2.73861 - 4.74342i) q^{30} +(34.9025 + 20.1510i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-26.0778 + 15.0560i) q^{33} +3.75049i q^{34} +(-15.5940 - 1.35152i) q^{35} -6.00000 q^{36} +(-16.2514 - 28.1482i) q^{37} +(-3.11308 - 1.79734i) q^{38} +(-6.25755 + 10.8384i) q^{39} +(-5.47723 + 3.16228i) q^{40} -70.6679i q^{41} +(-9.82336 + 14.0535i) q^{42} +37.3732 q^{43} +(17.3852 + 30.1120i) q^{44} +(-5.80948 - 3.35410i) q^{45} +(-28.3560 + 49.1141i) q^{46} +(-28.9672 + 16.7242i) q^{47} +6.92820i q^{48} +(16.8339 + 46.0176i) q^{49} -7.07107 q^{50} +(2.29669 + 3.97799i) q^{51} +(12.5151 + 7.22559i) q^{52} +(35.4442 - 61.3911i) q^{53} +(-6.36396 + 3.67423i) q^{54} +38.8745i q^{55} +(16.2276 + 11.3430i) q^{56} -4.40256 q^{57} +(-33.2397 - 57.5728i) q^{58} +(87.0863 + 50.2793i) q^{59} +(-3.87298 + 6.70820i) q^{60} +(-11.1621 + 6.44446i) q^{61} -56.9955i q^{62} +(-1.81326 + 20.9216i) q^{63} +8.00000 q^{64} +(8.07846 + 13.9923i) q^{65} +(36.8795 + 21.2924i) q^{66} +(-47.0361 + 81.4689i) q^{67} +(4.59339 - 2.65199i) q^{68} +69.4578i q^{69} +(9.37137 + 20.0544i) q^{70} -11.5793 q^{71} +(4.24264 + 7.34847i) q^{72} +(-19.6320 - 11.3345i) q^{73} +(-22.9829 + 39.8076i) q^{74} +(-7.50000 + 4.33013i) q^{75} +5.08364i q^{76} +(110.252 - 51.5208i) q^{77} +17.6990 q^{78} +(12.0542 + 20.8785i) q^{79} +(7.74597 + 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-86.5502 + 49.9698i) q^{82} +111.664i q^{83} +(24.1581 + 2.09377i) q^{84} +5.93004 q^{85} +(-26.4268 - 45.7726i) q^{86} +(-70.5120 - 40.7101i) q^{87} +(24.5864 - 42.5848i) q^{88} +(-110.770 + 63.9533i) q^{89} +9.48683i q^{90} +(28.9773 - 41.4556i) q^{91} +80.2029 q^{92} +(-34.9025 - 60.4529i) q^{93} +(40.9658 + 23.6516i) q^{94} +(-2.84184 + 4.92221i) q^{95} +(8.48528 - 4.89898i) q^{96} -7.48256i q^{97} +(44.4565 - 53.1566i) q^{98} +52.1556 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9}+O(q^{10}) $ 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9	$ 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} + 48 q^{12} + 8 q^{14} - 32 q^{16} + 12 q^{17} - 72 q^{19} - 24 q^{21} - 48 q^{22} - 12 q^{23} + 40 q^{25} + 32 q^{28} + 72 q^{29} + 120 q^{31} + 12 q^{33} - 20 q^{35} - 96 q^{36} + 44 q^{37} - 72 q^{38} + 36 q^{39} - 24 q^{42} - 56 q^{43} - 8 q^{44} + 8 q^{46} - 24 q^{47} - 40 q^{49} - 12 q^{51} - 72 q^{52} + 32 q^{53} + 16 q^{56} + 144 q^{57} - 88 q^{58} + 132 q^{59} + 96 q^{61} + 60 q^{63} + 128 q^{64} + 20 q^{65} + 72 q^{66} - 164 q^{67} - 24 q^{68} - 136 q^{71} - 348 q^{73} - 112 q^{74} - 120 q^{75} + 96 q^{77} + 280 q^{79} - 72 q^{81} + 264 q^{82} - 24 q^{84} + 120 q^{85} - 88 q^{86} - 108 q^{87} + 48 q^{88} - 300 q^{89} - 272 q^{91} + 48 q^{92} - 120 q^{93} + 200 q^{95} + 384 q^{98} - 24 q^{99}+O(q^{100}) $ 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 + 48 * q^12 + 8 * q^14 - 32 * q^16 + 12 * q^17 - 72 * q^19 - 24 * q^21 - 48 * q^22 - 12 * q^23 + 40 * q^25 + 32 * q^28 + 72 * q^29 + 120 * q^31 + 12 * q^33 - 20 * q^35 - 96 * q^36 + 44 * q^37 - 72 * q^38 + 36 * q^39 - 24 * q^42 - 56 * q^43 - 8 * q^44 + 8 * q^46 - 24 * q^47 - 40 * q^49 - 12 * q^51 - 72 * q^52 + 32 * q^53 + 16 * q^56 + 144 * q^57 - 88 * q^58 + 132 * q^59 + 96 * q^61 + 60 * q^63 + 128 * q^64 + 20 * q^65 + 72 * q^66 - 164 * q^67 - 24 * q^68 - 136 * q^71 - 348 * q^73 - 112 * q^74 - 120 * q^75 + 96 * q^77 + 280 * q^79 - 72 * q^81 + 264 * q^82 - 24 * q^84 + 120 * q^85 - 88 * q^86 - 108 * q^87 + 48 * q^88 - 300 * q^89 - 272 * q^91 + 48 * q^92 - 120 * q^93 + 200 * q^95 + 384 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	5.73733	+	4.01037i	0.819618	+	0.572910i
$7$	5.73733	+	4.01037i	0.819618	+	0.572910i
$8$	2.82843			0.353553
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	2.73861	+	1.58114i	0.273861	+	0.158114i
$11$	8.69259	−	15.0560i	0.790236	−	1.36873i	−0.135585	−	0.990766i	$-0.543291\pi$
$11$	8.69259	−	15.0560i	0.790236	−	1.36873i	0.925821	−	0.377963i	$-0.123375\pi$
$12$	3.00000	−	1.73205i	0.250000	−	0.144338i
$13$		−	7.22559i		−	0.555815i	−0.960608	−	0.277907i	$-0.910359\pi$
$13$		−	7.22559i		−	0.555815i	0.960608	−	0.277907i	$-0.0896408\pi$
$14$	0.854777	−	9.86252i	0.0610555	−	0.704466i
$15$	3.87298			0.258199
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−2.29669	−	1.32600i	−0.135100	−	0.0779998i	0.430927	−	0.902387i	$-0.358187\pi$
$17$	−2.29669	−	1.32600i	−0.135100	−	0.0779998i	−0.566027	+	0.824387i	$0.691520\pi$
$18$	2.12132	−	3.67423i	0.117851	−	0.204124i
$19$	2.20128	−	1.27091i	0.115857	−	0.0668900i	−0.440952	−	0.897531i	$-0.645359\pi$
$19$	2.20128	−	1.27091i	0.115857	−	0.0668900i	0.556809	+	0.830641i	$0.312026\pi$
$20$		−	4.47214i		−	0.223607i
$21$	−5.13291	−	10.9842i	−0.244424	−	0.523058i
$22$	−24.5864			−1.11756
$23$	−20.0507	−	34.7289i	−0.871771	−	1.50995i	−0.860163	−	0.510019i	$-0.829639\pi$
$23$	−20.0507	−	34.7289i	−0.871771	−	1.50995i	−0.0116074	−	0.999933i	$-0.503695\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	−8.84951	+	5.10926i	−0.340366	+	0.196510i
$27$		−	5.19615i		−	0.192450i
$28$	−12.6835	+	5.92697i	−0.452982	+	0.211678i
$29$	47.0080			1.62096			0.810482	−	0.585763i	$-0.199205\pi$
$29$	47.0080			1.62096			0.810482	+	0.585763i	$0.199205\pi$
$30$	−2.73861	−	4.74342i	−0.0912871	−	0.158114i
$31$	34.9025	+	20.1510i	1.12589	+	0.650031i	0.942897	−	0.333084i	$-0.108089\pi$
$31$	34.9025	+	20.1510i	1.12589	+	0.650031i	0.182990	+	0.983115i	$0.441422\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$	−26.0778	+	15.0560i	−0.790236	+	0.456243i
$34$			3.75049i			0.110308i
$35$	−15.5940	−	1.35152i	−0.445543	−	0.0386149i
$36$	−6.00000			−0.166667
$37$	−16.2514	−	28.1482i	−0.439226	−	0.760762i	0.558404	−	0.829569i	$-0.311414\pi$
$37$	−16.2514	−	28.1482i	−0.439226	−	0.760762i	−0.997630	+	0.0688071i	$0.978081\pi$
$38$	−3.11308	−	1.79734i	−0.0819232	−	0.0472984i
$39$	−6.25755	+	10.8384i	−0.160450	+	0.277907i
$40$	−5.47723	+	3.16228i	−0.136931	+	0.0790569i
$41$		−	70.6679i		−	1.72361i	−0.507241	−	0.861804i	$-0.669335\pi$
$41$		−	70.6679i		−	1.72361i	0.507241	−	0.861804i	$-0.330665\pi$
$42$	−9.82336	+	14.0535i	−0.233890	+	0.334608i
$43$	37.3732			0.869144			0.434572	−	0.900637i	$-0.356900\pi$
$43$	37.3732			0.869144			0.434572	+	0.900637i	$0.356900\pi$
$44$	17.3852	+	30.1120i	0.395118	+	0.684364i
$45$	−5.80948	−	3.35410i	−0.129099	−	0.0745356i
$46$	−28.3560	+	49.1141i	−0.616435	+	1.06770i
$47$	−28.9672	+	16.7242i	−0.616324	+	0.355835i	−0.775436	−	0.631426i	$-0.782470\pi$
$47$	−28.9672	+	16.7242i	−0.616324	+	0.355835i	0.159113	+	0.987260i	$0.449137\pi$
$48$			6.92820i			0.144338i
$49$	16.8339	+	46.0176i	0.343548	+	0.939135i
$50$	−7.07107			−0.141421
$51$	2.29669	+	3.97799i	0.0450332	+	0.0779998i
$52$	12.5151	+	7.22559i	0.240675	+	0.138954i
$53$	35.4442	−	61.3911i	0.668758	−	1.15832i	−0.309493	−	0.950902i	$-0.600159\pi$
$53$	35.4442	−	61.3911i	0.668758	−	1.15832i	0.978252	−	0.207422i	$-0.0665073\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$			38.8745i			0.706808i
$56$	16.2276	+	11.3430i	0.289779	+	0.202554i
$57$	−4.40256			−0.0772379
$58$	−33.2397	−	57.5728i	−0.573098	−	0.992634i
$59$	87.0863	+	50.2793i	1.47604	+	0.852192i	0.999635	−	0.0270340i	$-0.00860625\pi$
$59$	87.0863	+	50.2793i	1.47604	+	0.852192i	0.476405	+	0.879226i	$0.341940\pi$
$60$	−3.87298	+	6.70820i	−0.0645497	+	0.111803i
$61$	−11.1621	+	6.44446i	−0.182986	+	0.105647i	−0.588695	−	0.808355i	$-0.700358\pi$
$61$	−11.1621	+	6.44446i	−0.182986	+	0.105647i	0.405709	+	0.914002i	$0.367025\pi$
$62$		−	56.9955i		−	0.919283i
$63$	−1.81326	+	20.9216i	−0.0287819	+	0.332088i
$64$	8.00000			0.125000
$65$	8.07846	+	13.9923i	0.124284	+	0.215266i
$66$	36.8795	+	21.2924i	0.558781	+	0.322612i
$67$	−47.0361	+	81.4689i	−0.702031	+	1.21595i	0.265721	+	0.964050i	$0.414390\pi$
$67$	−47.0361	+	81.4689i	−0.702031	+	1.21595i	−0.967752	+	0.251904i	$0.918943\pi$
$68$	4.59339	−	2.65199i	0.0675498	−	0.0389999i
$69$			69.4578i			1.00663i
$70$	9.37137	+	20.0544i	0.133877	+	0.286491i
$71$	−11.5793			−0.163088			−0.0815440	−	0.996670i	$-0.525985\pi$
$71$	−11.5793			−0.163088			−0.0815440	+	0.996670i	$0.525985\pi$
$72$	4.24264	+	7.34847i	0.0589256	+	0.102062i
$73$	−19.6320	−	11.3345i	−0.268931	−	0.155267i	0.359471	−	0.933156i	$-0.382957\pi$
$73$	−19.6320	−	11.3345i	−0.268931	−	0.155267i	−0.628402	+	0.777889i	$0.716291\pi$
$74$	−22.9829	+	39.8076i	−0.310580	+	0.537940i
$75$	−7.50000	+	4.33013i	−0.100000	+	0.0577350i
$76$			5.08364i			0.0668900i
$77$	110.252	−	51.5208i	1.43185	−	0.669101i
$78$	17.6990			0.226910
$79$	12.0542	+	20.8785i	0.152585	+	0.264285i	0.932177	−	0.362003i	$-0.117907\pi$
$79$	12.0542	+	20.8785i	0.152585	+	0.264285i	−0.779592	+	0.626287i	$0.784574\pi$
$80$	7.74597	+	4.47214i	0.0968246	+	0.0559017i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−86.5502	+	49.9698i	−1.05549	+	0.609388i
$83$			111.664i			1.34535i	0.739937	+	0.672676i	$0.234855\pi$
$83$			111.664i			1.34535i	−0.739937	+	0.672676i	$0.765145\pi$
$84$	24.1581	+	2.09377i	0.287597	+	0.0249258i
$85$	5.93004			0.0697652
$86$	−26.4268	−	45.7726i	−0.307289	−	0.532240i
$87$	−70.5120	−	40.7101i	−0.810482	−	0.467932i
$88$	24.5864	−	42.5848i	0.279390	−	0.483919i
$89$	−110.770	+	63.9533i	−1.24461	+	0.718577i	−0.970030	−	0.242987i	$-0.921873\pi$
$89$	−110.770	+	63.9533i	−1.24461	+	0.718577i	−0.274582	+	0.961564i	$0.588540\pi$
$90$			9.48683i			0.105409i
$91$	28.9773	−	41.4556i	0.318432	−	0.455556i
$92$	80.2029			0.871771
$93$	−34.9025	−	60.4529i	−0.375296	−	0.650031i
$94$	40.9658	+	23.6516i	0.435807	+	0.251613i
$95$	−2.84184	+	4.92221i	−0.0299141	+	0.0518128i
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$		−	7.48256i		−	0.0771398i	−0.999256	−	0.0385699i	$-0.987720\pi$
$97$		−	7.48256i		−	0.0771398i	0.999256	−	0.0385699i	$-0.0122802\pi$
$98$	44.4565	−	53.1566i	0.453638	−	0.542414i
$99$	52.1556			0.526824
$100$	5.00000	+	8.66025i	0.0500000	+	0.0866025i
$101$	−81.9228	−	47.2982i	−0.811117	−	0.468299i	0.0362267	−	0.999344i	$-0.488466\pi$
$101$	−81.9228	−	47.2982i	−0.811117	−	0.468299i	−0.847344	+	0.531045i	$0.821799\pi$
$102$	3.24802	−	5.62573i	0.0318433	−	0.0551542i
$103$	−51.8072	+	29.9109i	−0.502982	+	0.290397i	−0.729944	−	0.683507i	$-0.760454\pi$
$103$	−51.8072	+	29.9109i	−0.502982	+	0.290397i	0.226962	+	0.973904i	$0.427121\pi$
$104$		−	20.4371i		−	0.196510i
$105$	22.2206	+	15.5321i	0.211625	+	0.147925i
$106$	−100.251			−0.945767
$107$	−3.23081	−	5.59592i	−0.0301945	−	0.0522983i	0.850533	−	0.525921i	$-0.176279\pi$
$107$	−3.23081	−	5.59592i	−0.0301945	−	0.0522983i	−0.880728	+	0.473623i	$0.842946\pi$
$108$	9.00000	+	5.19615i	0.0833333	+	0.0481125i
$109$	81.9201	−	141.890i	0.751560	−	1.30174i	−0.195506	−	0.980703i	$-0.562635\pi$
$109$	81.9201	−	141.890i	0.751560	−	1.30174i	0.947066	−	0.321038i	$-0.104032\pi$
$110$	47.6113	−	27.4884i	0.432830	−	0.249894i
$111$			56.2964i			0.507175i
$112$	2.41768	−	27.8954i	0.0215864	−	0.249066i
$113$	−105.434			−0.933040			−0.466520	−	0.884511i	$-0.654492\pi$
$113$	−105.434			−0.933040			−0.466520	+	0.884511i	$0.654492\pi$
$114$	3.11308	+	5.39202i	0.0273077	+	0.0472984i
$115$	77.6561	+	44.8348i	0.675271	+	0.389868i
$116$	−47.0080	+	81.4202i	−0.405241	+	0.701898i
$117$	18.7726	−	10.8384i	0.160450	−	0.0926358i
$118$		−	142.211i		−	1.20518i
$119$	−7.85915	−	16.8183i	−0.0660433	−	0.141330i
$120$	10.9545			0.0912871
$121$	−90.6223	−	156.962i	−0.748945	−	1.29721i
$122$	15.7856	+	9.11384i	0.129391	+	0.0747036i
$123$	−61.2002	+	106.002i	−0.497563	+	0.861804i
$124$	−69.8050	+	40.3019i	−0.562944	+	0.325016i
$125$			11.1803i			0.0894427i
$126$	26.9058	−	12.5730i	0.213538	−	0.0997858i
$127$	53.7033			0.422860			0.211430	−	0.977393i	$-0.432188\pi$
$127$	53.7033			0.422860			0.211430	+	0.977393i	$0.432188\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$	−56.0598	−	32.3661i	−0.434572	−	0.250900i
$130$	11.4247	−	19.7881i	0.0878820	−	0.152216i
$131$	−50.6489	+	29.2421i	−0.386632	+	0.223222i	−0.680700	−	0.732562i	$-0.738324\pi$
$131$	−50.6489	+	29.2421i	−0.386632	+	0.223222i	0.294068	+	0.955785i	$0.404991\pi$
$132$		−	60.2240i		−	0.456243i
$133$	17.7263	+	1.53632i	0.133280	+	0.0115513i
$134$	133.038			0.992822
$135$	5.80948	+	10.0623i	0.0430331	+	0.0745356i
$136$	−6.49603	−	3.75049i	−0.0477650	−	0.0275771i
$137$	6.05848	−	10.4936i	0.0442225	−	0.0765956i	−0.843067	−	0.537809i	$-0.819252\pi$
$137$	6.05848	−	10.4936i	0.0442225	−	0.0765956i	0.887289	+	0.461213i	$0.152586\pi$
$138$	85.0680	−	49.1141i	0.616435	−	0.355899i
$139$			45.2562i			0.325584i	0.986660	+	0.162792i	$0.0520500\pi$
$139$			45.2562i			0.325584i	−0.986660	+	0.162792i	$0.947950\pi$
$140$	17.9349	−	25.6581i	0.128107	−	0.183272i
$141$	57.9344			0.410882
$142$	8.18777	+	14.1816i	0.0576603	+	0.0998706i
$143$	−108.789	−	62.8091i	−0.760759	−	0.439225i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$	−91.0306	+	52.5565i	−0.627797	+	0.362459i
$146$			32.0589i			0.219581i
$147$	14.6016	−	83.6050i	0.0993309	−	0.568741i
$148$	65.0055			0.439226
$149$	25.4474	+	44.0762i	0.170788	+	0.295814i	0.938696	−	0.344747i	$-0.112035\pi$
$149$	25.4474	+	44.0762i	0.170788	+	0.295814i	−0.767908	+	0.640561i	$0.778702\pi$
$150$	10.6066	+	6.12372i	0.0707107	+	0.0408248i
$151$	78.8476	−	136.568i	0.522169	−	0.904424i	−0.477498	−	0.878633i	$-0.658456\pi$
$151$	78.8476	−	136.568i	0.522169	−	0.904424i	0.999667	−	0.0257911i	$-0.00821047\pi$
$152$	6.22616	−	3.59468i	0.0409616	−	0.0236492i
$153$		−	7.95598i		−	0.0519999i
$154$	−141.060	−	98.6004i	−0.915974	−	0.640263i
$155$	−90.1179			−0.581406
$156$	−12.5151	−	21.6768i	−0.0802249	−	0.138954i
$157$	145.359	+	83.9231i	0.925854	+	0.534542i	0.885498	−	0.464643i	$-0.153817\pi$
$157$	145.359	+	83.9231i	0.925854	+	0.534542i	0.0403562	+	0.999185i	$0.487151\pi$
$158$	17.0472	−	29.5266i	0.107894	−	0.186877i
$159$	−106.333	+	61.3911i	−0.668758	+	0.386108i
$160$		−	12.6491i		−	0.0790569i
$161$	24.2381	−	279.662i	0.150547	−	1.73703i
$162$	12.7279			0.0785674
$163$	−138.285	−	239.517i	−0.848374	−	1.46943i	−0.882658	−	0.470015i	$-0.844248\pi$
$163$	−138.285	−	239.517i	−0.848374	−	1.46943i	0.0342839	−	0.999412i	$-0.489085\pi$
$164$	122.400	+	70.6679i	0.746344	+	0.430902i
$165$	33.6663	−	58.3117i	0.204038	−	0.353404i
$166$	136.760	−	78.9586i	0.823857	−	0.475654i
$167$		−	48.4258i		−	0.289975i	−0.989433	−	0.144987i	$-0.953686\pi$
$167$		−	48.4258i		−	0.289975i	0.989433	−	0.144987i	$-0.0463142\pi$
$168$	−14.5181	−	31.0681i	−0.0864170	−	0.184929i
$169$	116.791			0.691070
$170$	−4.19317	−	7.26279i	−0.0246657	−	0.0427223i
$171$	6.60384	+	3.81273i	0.0386190	+	0.0222967i
$172$	−37.3732	+	64.7323i	−0.217286	+	0.376351i
$173$	−97.8337	+	56.4843i	−0.565513	+	0.326499i	−0.755355	−	0.655316i	$-0.772536\pi$
$173$	−97.8337	+	56.4843i	−0.565513	+	0.326499i	0.189842	+	0.981815i	$0.439202\pi$
$174$			115.146i			0.661756i
$175$	31.7087	−	14.8174i	0.181193	−	0.0846710i
$176$	−69.5407			−0.395118
$177$	−87.0863	−	150.838i	−0.492013	−	0.852192i
$178$	156.653	+	90.4437i	0.880073	+	0.508111i
$179$	−165.708	+	287.015i	−0.925744	+	1.60344i	−0.135384	+	0.990793i	$0.543227\pi$
$179$	−165.708	+	287.015i	−0.925744	+	1.60344i	−0.790360	+	0.612642i	$0.790107\pi$
$180$	11.6190	−	6.70820i	0.0645497	−	0.0372678i
$181$			213.328i			1.17861i	0.807912	+	0.589303i	$0.200598\pi$
$181$			213.328i			1.17861i	−0.807912	+	0.589303i	$0.799402\pi$
$182$	−71.2626	−	6.17627i	−0.391553	−	0.0339356i
$183$	22.3243			0.121991
$184$	−56.7120	−	98.2281i	−0.308218	−	0.533848i
$185$	62.9413	+	36.3392i	0.340223	+	0.196428i
$186$	−49.3596	+	85.4933i	−0.265374	+	0.459642i
$187$	−39.9285	+	23.0527i	−0.213521	+	0.123277i
$188$		−	66.8969i		−	0.355835i
$189$	20.8385	−	29.8120i	0.110257	−	0.157736i
$190$	8.03794			0.0423050
$191$	33.4517	+	57.9400i	0.175140	+	0.303351i	0.940210	−	0.340596i	$-0.110629\pi$
$191$	33.4517	+	57.9400i	0.175140	+	0.303351i	−0.765070	+	0.643947i	$0.777296\pi$
$192$	−12.0000	−	6.92820i	−0.0625000	−	0.0360844i
$193$	56.3020	−	97.5179i	0.291720	−	0.505274i	−0.682497	−	0.730889i	$-0.739106\pi$
$193$	56.3020	−	97.5179i	0.291720	−	0.505274i	0.974217	+	0.225615i	$0.0724391\pi$
$194$	−9.16422	+	5.29097i	−0.0472383	+	0.0272730i
$195$		−	27.9846i		−	0.143511i
$196$	−96.5387	−	16.8605i	−0.492544	−	0.0860231i
$197$	−61.0211			−0.309752			−0.154876	−	0.987934i	$-0.549498\pi$
$197$	−61.0211			−0.309752			−0.154876	+	0.987934i	$0.549498\pi$
$198$	−36.8795	−	63.8772i	−0.186260	−	0.322612i
$199$	−165.554	−	95.5826i	−0.831929	−	0.480314i	0.0225837	−	0.999745i	$-0.492811\pi$
$199$	−165.554	−	95.5826i	−0.831929	−	0.480314i	−0.854513	+	0.519431i	$0.826144\pi$
$200$	7.07107	−	12.2474i	0.0353553	−	0.0612372i
$201$	141.108	−	81.4689i	0.702031	−	0.405318i
$202$			133.779i			0.662274i
$203$	269.700	+	188.519i	1.32857	+	0.928667i
$204$	−9.18678			−0.0450332
$205$	79.0092	+	136.848i	0.385410	+	0.667551i
$206$	73.2664	+	42.3004i	0.355662	+	0.205342i
$207$	60.1522	−	104.187i	0.290590	−	0.503317i
$208$	−25.0302	+	14.4512i	−0.120337	+	0.0694768i
$209$		−	44.1900i		−	0.211435i
$210$	3.31054	−	38.1974i	0.0157645	−	0.181892i
$211$	280.115			1.32756			0.663781	−	0.747927i	$-0.268951\pi$
$211$	280.115			1.32756			0.663781	+	0.747927i	$0.268951\pi$
$212$	70.8884	+	122.782i	0.334379	+	0.579162i
$213$	17.3689	+	10.0279i	0.0815440	+	0.0470795i
$214$	−4.56905	+	7.91383i	−0.0213507	+	0.0369805i
$215$	−72.3729	+	41.7845i	−0.336618	+	0.194347i
$216$		−	14.6969i		−	0.0680414i
$217$	119.434	+	255.585i	0.550388	+	1.17781i
$218$	−231.705			−1.06287
$219$	19.6320	+	34.0036i	0.0896437	+	0.155267i
$220$	−67.3325	−	38.8745i	−0.306057	−	0.176702i
$221$	−9.58111	+	16.5950i	−0.0433535	+	0.0750904i
$222$	68.9487	−	39.8076i	0.310580	−	0.179313i
$223$			272.759i			1.22313i	0.791192	+	0.611567i	$0.209461\pi$
$223$			272.759i			1.22313i	−0.791192	+	0.611567i	$0.790539\pi$
$224$	−35.8743	+	16.7640i	−0.160153	+	0.0748393i
$225$	15.0000			0.0666667
$226$	74.5528	+	129.129i	0.329879	+	0.571368i
$227$	13.9191	+	8.03620i	0.0613176	+	0.0354018i	0.530345	−	0.847782i	$-0.322062\pi$
$227$	13.9191	+	8.03620i	0.0613176	+	0.0354018i	−0.469028	+	0.883183i	$0.655396\pi$
$228$	4.40256	−	7.62546i	0.0193095	−	0.0334450i
$229$	128.261	−	74.0517i	0.560093	−	0.323370i	−0.193090	−	0.981181i	$-0.561851\pi$
$229$	128.261	−	74.0517i	0.560093	−	0.323370i	0.753183	+	0.657811i	$0.228518\pi$
$230$		−	126.812i		−	0.551356i
$231$	−209.997	−	18.2003i	−0.909078	−	0.0787891i
$232$	132.959			0.573098
$233$	149.559	+	259.044i	0.641885	+	1.11178i	0.985012	+	0.172488i	$0.0551806\pi$
$233$	149.559	+	259.044i	0.641885	+	1.11178i	−0.343127	+	0.939289i	$0.611486\pi$
$234$	−26.5485	−	15.3278i	−0.113455	−	0.0655034i
$235$	37.3965	−	64.7727i	0.159134	−	0.275628i
$236$	−174.173	+	100.559i	−0.738020	+	0.426096i
$237$		−	41.7570i		−	0.176190i
$238$	−15.0408	+	21.5178i	−0.0631968	+	0.0904108i
$239$	−114.253			−0.478046			−0.239023	−	0.971014i	$-0.576827\pi$
$239$	−114.253			−0.478046			−0.239023	+	0.971014i	$0.576827\pi$
$240$	−7.74597	−	13.4164i	−0.0322749	−	0.0559017i
$241$	−118.162	−	68.2209i	−0.490299	−	0.283074i	0.234399	−	0.972140i	$-0.424688\pi$
$241$	−118.162	−	68.2209i	−0.490299	−	0.283074i	−0.724699	+	0.689066i	$0.758021\pi$
$242$	−128.159	+	221.978i	−0.529584	+	0.917266i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		−	25.7778i		−	0.105647i
$245$	−84.0479	−	70.2919i	−0.343053	−	0.286906i
$246$	173.100			0.703660
$247$	−9.18308	−	15.9056i	−0.0371785	−	0.0643950i
$248$	98.7192	+	56.9955i	0.398061	+	0.229821i
$249$	96.7041	−	167.496i	0.388370	−	0.672676i
$250$	13.6931	−	7.90569i	0.0547723	−	0.0316228i
$251$			457.024i			1.82081i	0.413717	+	0.910406i	$0.364230\pi$
$251$			457.024i			1.82081i	−0.413717	+	0.910406i	$0.635770\pi$
$252$	−34.4240	−	24.0622i	−0.136603	−	0.0954850i
$253$	−697.171			−2.75562
$254$	−37.9739	−	65.7728i	−0.149504	−	0.258948i
$255$	−8.89506	−	5.13557i	−0.0348826	−	0.0201395i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	43.2997	−	24.9991i	0.168481	−	0.0972726i	−0.413388	−	0.910555i	$-0.635655\pi$
$257$	43.2997	−	24.9991i	0.168481	−	0.0972726i	0.581869	+	0.813282i	$0.302321\pi$
$258$			91.5453i			0.354827i
$259$	19.6453	−	226.669i	0.0758505	−	0.875172i
$260$	−32.3138			−0.124284
$261$	70.5120	+	122.130i	0.270161	+	0.467932i
$262$	71.6283	+	41.3546i	0.273390	+	0.157842i
$263$	−91.1388	+	157.857i	−0.346535	+	0.600217i	−0.985631	−	0.168910i	$-0.945975\pi$
$263$	−91.1388	+	157.857i	−0.346535	+	0.600217i	0.639096	+	0.769127i	$0.279309\pi$
$264$	−73.7591	+	42.5848i	−0.279390	+	0.161306i
$265$			158.511i			0.598156i
$266$	−10.6528	−	22.7965i	−0.0400480	−	0.0857012i
$267$	221.541			0.829741
$268$	−94.0722	−	162.938i	−0.351016	−	0.607977i
$269$	−32.5814	−	18.8109i	−0.121120	−	0.0699289i	0.438216	−	0.898870i	$-0.355611\pi$
$269$	−32.5814	−	18.8109i	−0.121120	−	0.0699289i	−0.559336	+	0.828941i	$0.688944\pi$
$270$	8.21584	−	14.2302i	0.0304290	−	0.0527046i
$271$	175.576	−	101.369i	0.647880	−	0.374054i	−0.139763	−	0.990185i	$-0.544634\pi$
$271$	175.576	−	101.369i	0.647880	−	0.374054i	0.787644	+	0.616131i	$0.211301\pi$
$272$			10.6080i			0.0389999i
$273$	−79.3675	+	37.0883i	−0.290724	+	0.135855i
$274$	−17.1360			−0.0625401
$275$	−43.4630	−	75.2801i	−0.158047	−	0.273746i
$276$	−120.304	−	69.4578i	−0.435885	−	0.251659i
$277$	−128.121	+	221.912i	−0.462530	+	0.801126i	−0.999086	−	0.0427390i	$-0.986392\pi$
$277$	−128.121	+	221.912i	−0.462530	+	0.801126i	0.536556	+	0.843865i	$0.319725\pi$
$278$	55.4273	−	32.0010i	0.199379	−	0.115111i
$279$			120.906i			0.433354i
$280$	−44.1065	−	3.82268i	−0.157523	−	0.0136524i
$281$	−141.462			−0.503423			−0.251711	−	0.967802i	$-0.580993\pi$
$281$	−141.462			−0.503423			−0.251711	+	0.967802i	$0.580993\pi$
$282$	−40.9658	−	70.9549i	−0.145269	−	0.251613i
$283$	470.571	+	271.684i	1.66279	+	0.960014i	0.971372	+	0.237562i	$0.0763483\pi$
$283$	470.571	+	271.684i	1.66279	+	0.960014i	0.691421	+	0.722452i	$0.256985\pi$
$284$	11.5793	−	20.0559i	0.0407720	−	0.0706192i
$285$	8.52553	−	4.92221i	0.0299141	−	0.0172709i
$286$			177.651i			0.621157i
$287$	283.405	−	405.445i	0.987472	−	1.41270i
$288$	−16.9706			−0.0589256
$289$	−140.983	−	244.191i	−0.487832	−	0.844950i
$290$	128.737	+	74.3261i	0.443920	+	0.256297i
$291$	−6.48008	+	11.2238i	−0.0222683	+	0.0385699i
$292$	39.2639	−	22.6690i	0.134466	−	0.0776337i
$293$		−	375.289i		−	1.28085i	−0.768021	−	0.640424i	$-0.778759\pi$
$293$		−	375.289i		−	1.28085i	0.768021	−	0.640424i	$-0.221241\pi$
$294$	−112.720	+	41.2344i	−0.383400	+	0.140253i
$295$	−224.856			−0.762224
$296$	−45.9658	−	79.6151i	−0.155290	−	0.268970i
$297$	−78.2333	−	45.1680i	−0.263412	−	0.152081i
$298$	35.9881	−	62.3332i	0.120765	−	0.209172i
$299$	−250.937	+	144.878i	−0.839253	+	0.484543i
$300$		−	17.3205i		−	0.0577350i
$301$	214.422	+	149.880i	0.712367	+	0.497942i
$302$	−223.015			−0.738459
$303$	81.9228	+	141.894i	0.270372	+	0.468299i
$304$	−8.80512	−	5.08364i	−0.0289642	−	0.0167225i
$305$	14.4103	−	24.9593i	0.0472467	−	0.0818337i
$306$	−9.74405	+	5.62573i	−0.0318433	+	0.0183847i
$307$			41.3436i			0.134670i	0.997730	+	0.0673349i	$0.0214496\pi$
$307$			41.3436i			0.134670i	−0.997730	+	0.0673349i	$0.978550\pi$
$308$	−21.0159	+	242.484i	−0.0682333	+	0.787284i
$309$	103.614			0.335321
$310$	63.7230	+	110.371i	0.205558	+	0.356037i
$311$	−126.924	−	73.2794i	−0.408115	−	0.235625i	0.281865	−	0.959454i	$-0.409047\pi$
$311$	−126.924	−	73.2794i	−0.408115	−	0.235625i	−0.689979	+	0.723829i	$0.742380\pi$
$312$	−17.6990	+	30.6556i	−0.0567276	+	0.0982551i
$313$	194.744	−	112.435i	0.622184	−	0.359218i	−0.155535	−	0.987830i	$-0.549710\pi$
$313$	194.744	−	112.435i	0.622184	−	0.359218i	0.777719	+	0.628612i	$0.216377\pi$
$314$		−	237.370i		−	0.755957i
$315$	−19.8797	−	42.5417i	−0.0631101	−	0.135053i
$316$	−48.2168			−0.152585
$317$	113.113	+	195.918i	0.356825	+	0.618038i	0.987428	−	0.158067i	$-0.0505261\pi$
$317$	113.113	+	195.918i	0.356825	+	0.618038i	−0.630604	+	0.776105i	$0.717193\pi$
$318$	150.377	+	86.8202i	0.472884	+	0.273019i
$319$	408.621	−	707.753i	1.28094	−	2.21866i
$320$	−15.4919	+	8.94427i	−0.0484123	+	0.0279508i
$321$			11.1918i			0.0348656i
$322$	−359.653	+	168.065i	−1.11694	+	0.521942i
$323$	−6.74089			−0.0208696
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$	−31.2877	−	18.0640i	−0.0962699	−	0.0555815i
$326$	−195.565	+	338.728i	−0.599891	+	1.03904i
$327$	−245.760	+	141.890i	−0.751560	+	0.433914i
$328$		−	199.879i		−	0.609388i
$329$	−233.265	−	20.2169i	−0.709011	−	0.0614495i
$330$	−95.2226			−0.288553
$331$	−69.9082	−	121.085i	−0.211203	−	0.365814i	0.740888	−	0.671628i	$-0.234405\pi$
$331$	−69.9082	−	121.085i	−0.211203	−	0.365814i	−0.952091	+	0.305814i	$0.901071\pi$
$332$	−193.408	−	111.664i	−0.582555	−	0.336338i
$333$	48.7541	−	84.4446i	0.146409	−	0.253587i
$334$	−59.3093	+	34.2422i	−0.177573	+	0.102522i
$335$		−	210.352i		−	0.627916i
$336$	−27.7847	+	39.7494i	−0.0826924	+	0.118302i
$337$	30.1128			0.0893556			0.0446778	−	0.999001i	$-0.485774\pi$
$337$	30.1128			0.0893556			0.0446778	+	0.999001i	$0.485774\pi$
$338$	−82.5836	−	143.039i	−0.244330	−	0.423192i
$339$	158.150	+	91.3081i	0.466520	+	0.269345i
$340$	−5.93004	+	10.2711i	−0.0174413	+	0.0302092i
$341$	606.786	−	350.328i	1.77943	−	1.02736i
$342$		−	10.7840i		−	0.0315323i
$343$	−87.9664	+	331.528i	−0.256462	+	0.966554i
$344$	105.707			0.307289
$345$	−77.6561	−	134.504i	−0.225090	−	0.389868i
$346$	138.358	+	79.8809i	0.399878	+	0.230870i
$347$	207.954	−	360.186i	0.599290	−	1.03800i	−0.393636	−	0.919266i	$-0.628783\pi$
$347$	207.954	−	360.186i	0.599290	−	1.03800i	0.992926	−	0.118734i	$-0.0378836\pi$
$348$	141.024	−	81.4202i	0.405241	−	0.233966i
$349$		−	594.950i		−	1.70473i	−0.522950	−	0.852363i	$-0.675169\pi$
$349$		−	594.950i		−	1.70473i	0.522950	−	0.852363i	$-0.324831\pi$
$350$	−40.5690	−	28.3576i	−0.115912	−	0.0810217i
$351$	−37.5453			−0.106967
$352$	49.1727	+	85.1697i	0.139695	+	0.241959i
$353$	315.509	+	182.159i	0.893793	+	0.516031i	0.875181	−	0.483795i	$-0.160742\pi$
$353$	315.509	+	182.159i	0.893793	+	0.516031i	0.0186116	+	0.999827i	$0.494075\pi$
$354$	−123.159	+	213.317i	−0.347906	+	0.602591i
$355$	22.4231	−	12.9460i	0.0631637	−	0.0364676i
$356$		−	255.813i		−	0.718577i
$357$	−2.77633	+	32.0336i	−0.00777684	+	0.0897301i
$358$	468.693			1.30920
$359$	306.381	+	530.668i	0.853430	+	1.47818i	0.878094	+	0.478488i	$0.158815\pi$
$359$	306.381	+	530.668i	0.853430	+	1.47818i	−0.0246647	+	0.999696i	$0.507852\pi$
$360$	−16.4317	−	9.48683i	−0.0456435	−	0.0263523i
$361$	−177.270	+	307.040i	−0.491051	+	0.850526i
$362$	261.272	−	150.846i	0.721746	−	0.416700i
$363$			313.925i			0.864807i
$364$	42.8259	+	91.6457i	0.117654	+	0.251774i
$365$	50.6895			0.138875
$366$	−15.7856	−	27.3415i	−0.0431302	−	0.0747036i
$367$	−426.967	−	246.509i	−1.16340	−	0.671687i	−0.211281	−	0.977425i	$-0.567764\pi$
$367$	−426.967	−	246.509i	−1.16340	−	0.671687i	−0.952116	+	0.305738i	$0.901097\pi$
$368$	−80.2029	+	138.916i	−0.217943	+	0.377488i
$369$	183.601	−	106.002i	0.497563	−	0.287268i
$370$		−	102.783i		−	0.277791i
$371$	449.556	−	210.077i	1.21174	−	0.566245i
$372$	139.610			0.375296
$373$	−82.7013	−	143.243i	−0.221719	−	0.384029i	0.733611	−	0.679570i	$-0.237834\pi$
$373$	−82.7013	−	143.243i	−0.221719	−	0.384029i	−0.955330	+	0.295541i	$0.904500\pi$
$374$	56.4674	+	32.6015i	0.150982	+	0.0871697i
$375$	9.68246	−	16.7705i	0.0258199	−	0.0447214i
$376$	−81.9317	+	47.3033i	−0.217903	+	0.125807i
$377$		−	339.660i		−	0.900956i
$378$	−51.2472	−	4.44155i	−0.135575	−	0.0117501i
$379$	−179.349			−0.473215			−0.236608	−	0.971605i	$-0.576036\pi$
$379$	−179.349			−0.473215			−0.236608	+	0.971605i	$0.576036\pi$
$380$	−5.68368	−	9.84443i	−0.0149571	−	0.0259064i
$381$	−80.5549	−	46.5084i	−0.211430	−	0.122069i
$382$	47.3078	−	81.9395i	0.123842	−	0.214501i
$383$	233.108	−	134.585i	0.608636	−	0.351396i	−0.163795	−	0.986494i	$-0.552374\pi$
$383$	233.108	−	134.585i	0.608636	−	0.351396i	0.772432	+	0.635098i	$0.219040\pi$
$384$			19.5959i			0.0510310i
$385$	−155.901	+	223.035i	−0.404938	+	0.579313i
$386$	−159.246			−0.412554
$387$	56.0598	+	97.0984i	0.144857	+	0.250900i
$388$	12.9602	+	7.48256i	0.0334025	+	0.0192849i
$389$	236.874	−	410.277i	0.608930	−	1.05470i	−0.382487	−	0.923961i	$-0.624932\pi$
$389$	236.874	−	410.277i	0.608930	−	1.05470i	0.991417	−	0.130737i	$-0.0417344\pi$
$390$	−34.2740	+	19.7881i	−0.0878820	+	0.0507387i
$391$			106.349i			0.271992i
$392$	47.6133	+	130.157i	0.121463	+	0.332034i
$393$	101.298			0.257755
$394$	43.1484	+	74.7353i	0.109514	+	0.189683i
$395$	−46.6857	−	26.9540i	−0.118192	−	0.0682380i
$396$	−52.1556	+	90.3361i	−0.131706	+	0.228121i
$397$	−445.080	+	256.967i	−1.12111	+	0.647271i	−0.941683	−	0.336500i	$-0.890757\pi$
$397$	−445.080	+	256.967i	−1.12111	+	0.647271i	−0.179424	+	0.983772i	$0.557423\pi$
$398$			270.348i			0.679267i
$399$	−25.2589	−	17.6559i	−0.0633056	−	0.0442504i
$400$	−20.0000			−0.0500000
$401$	203.367	+	352.242i	0.507150	+	0.878410i	0.999966	+	0.00827591i	$0.00263433\pi$
$401$	203.367	+	352.242i	0.507150	+	0.878410i	−0.492816	+	0.870134i	$0.664032\pi$
$402$	−199.557	−	115.214i	−0.496411	−	0.286603i
$403$	145.603	−	252.191i	0.361297	−	0.625785i
$404$	163.846	−	94.5963i	0.405558	−	0.234149i
$405$		−	20.1246i		−	0.0496904i
$406$	40.1814	−	463.617i	0.0989689	−	1.14191i
$407$	−565.066			−1.38837
$408$	6.49603	+	11.2515i	0.0159217	+	0.0275771i
$409$	−422.173	−	243.742i	−1.03221	−	0.595946i	−0.114592	−	0.993413i	$-0.536556\pi$
$409$	−422.173	−	243.742i	−1.03221	−	0.595946i	−0.917617	+	0.397467i	$0.869889\pi$
$410$	111.736	−	193.532i	0.272526	−	0.472030i
$411$	−18.1755	+	10.4936i	−0.0442225	+	0.0255319i
$412$		−	119.643i		−	0.290397i
$413$	298.004	+	637.717i	0.721560	+	1.54411i
$414$	−170.136			−0.410957
$415$	−124.844	−	216.237i	−0.300830	−	0.521053i
$416$	35.3980	+	20.4371i	0.0850914	+	0.0491275i
$417$	39.1930	−	67.8843i	0.0939881	−	0.162792i
$418$	−54.1215	+	31.2471i	−0.129477	+	0.0747537i
$419$		−	552.257i		−	1.31804i	−0.752127	−	0.659018i	$-0.770972\pi$
$419$		−	552.257i		−	1.31804i	0.752127	−	0.659018i	$-0.229028\pi$
$420$	−49.1230	+	22.9551i	−0.116959	+	0.0546549i
$421$	−74.6870			−0.177404			−0.0887019	−	0.996058i	$-0.528272\pi$
$421$	−74.6870			−0.177404			−0.0887019	+	0.996058i	$0.528272\pi$
$422$	−198.072	−	343.070i	−0.469364	−	0.812962i
$423$	−86.9016	−	50.1727i	−0.205441	−	0.118612i
$424$	100.251	−	173.640i	0.236442	−	0.409529i
$425$	−11.4835	+	6.62999i	−0.0270199	+	0.0156000i
$426$		−	28.3633i		−	0.0665804i
$427$	−89.8855	−	7.79031i	−0.210505	−	0.0182443i
$428$	12.9232			0.0301945
$429$	108.789	+	188.427i	0.253586	+	0.439225i
$430$	102.351	+	59.0922i	0.238025	+	0.137424i
$431$	−242.339	+	419.743i	−0.562271	+	0.973881i	0.435027	+	0.900417i	$0.356739\pi$
$431$	−242.339	+	419.743i	−0.562271	+	0.973881i	−0.997298	+	0.0734641i	$0.976595\pi$
$432$	−18.0000	+	10.3923i	−0.0416667	+	0.0240563i
$433$			458.196i			1.05819i	0.848563	+	0.529094i	$0.177468\pi$
$433$			458.196i			1.05819i	−0.848563	+	0.529094i	$0.822532\pi$
$434$	228.573	−	327.002i	0.526667	−	0.753461i
$435$	182.061			0.418531
$436$	163.840	+	283.779i	0.375780	+	0.650870i
$437$	−88.2746	−	50.9653i	−0.202001	−	0.116626i
$438$	27.7638	−	48.0883i	0.0633877	−	0.109791i
$439$	121.167	−	69.9559i	0.276007	−	0.159353i	−0.355607	−	0.934635i	$-0.615726\pi$
$439$	121.167	−	69.9559i	0.276007	−	0.159353i	0.631614	+	0.775283i	$0.282393\pi$
$440$			109.954i			0.249894i
$441$	−94.3065	+	112.762i	−0.213847	+	0.255696i
$442$	27.0995			0.0613110
$443$	8.04616	+	13.9364i	0.0181629	+	0.0314591i	0.874964	−	0.484188i	$-0.160885\pi$
$443$	8.04616	+	13.9364i	0.0181629	+	0.0314591i	−0.856801	+	0.515647i	$0.827552\pi$
$444$	−97.5082	−	56.2964i	−0.219613	−	0.126794i
$445$	143.004	−	247.690i	0.321357	−	0.556607i
$446$	334.060	−	192.870i	0.749014	−	0.432444i
$447$		−	88.1524i		−	0.197209i
$448$	45.8986	+	32.0830i	0.102452	+	0.0716138i
$449$	−329.314			−0.733439			−0.366720	−	0.930332i	$-0.619519\pi$
$449$	−329.314			−0.733439			−0.366720	+	0.930332i	$0.619519\pi$
$450$	−10.6066	−	18.3712i	−0.0235702	−	0.0408248i
$451$	−1063.98	−	614.288i	−2.35915	−	1.36206i
$452$	105.434	−	182.616i	0.233260	−	0.404018i
$453$	−236.543	+	136.568i	−0.522169	+	0.301475i
$454$		−	22.7298i		−	0.0500657i
$455$	−9.76554	+	112.676i	−0.0214627	+	0.247640i
$456$	−12.4523			−0.0273077
$457$	445.459	+	771.557i	0.974745	+	1.68831i	0.680773	+	0.732494i	$0.261644\pi$
$457$	445.459	+	771.557i	0.974745	+	1.68831i	0.293972	+	0.955814i	$0.405023\pi$
$458$	−181.389	−	104.725i	−0.396046	−	0.228657i
$459$	−6.89008	+	11.9340i	−0.0150111	+	0.0259999i
$460$	−155.312	+	89.6696i	−0.337635	+	0.194934i
$461$		−	534.019i		−	1.15839i	−0.815188	−	0.579196i	$-0.803367\pi$
$461$		−	534.019i		−	1.15839i	0.815188	−	0.579196i	$-0.196633\pi$
$462$	126.200	+	270.062i	0.273159	+	0.584550i
$463$	158.679			0.342719			0.171359	−	0.985209i	$-0.445184\pi$
$463$	158.679			0.342719			0.171359	+	0.985209i	$0.445184\pi$
$464$	−94.0160	−	162.840i	−0.202621	−	0.350949i
$465$	135.177	+	78.0444i	0.290703	+	0.167837i
$466$	211.509	−	366.344i	0.453881	−	0.786145i
$467$	−97.1671	+	56.0995i	−0.208067	+	0.120127i	−0.600413	−	0.799690i	$-0.704997\pi$
$467$	−97.1671	+	56.0995i	−0.208067	+	0.120127i	0.392346	+	0.919818i	$0.371664\pi$
$468$			43.3535i			0.0926358i
$469$	−596.582	+	278.782i	−1.27203	+	0.594417i
$470$	−105.773			−0.225050
$471$	−145.359	−	251.769i	−0.308618	−	0.534542i
$472$	246.317	+	142.211i	0.521859	+	0.301295i
$473$	324.870	−	562.691i	0.686829	−	1.18962i
$474$	−51.1416	+	29.5266i	−0.107894	+	0.0622925i
$475$		−	12.7091i		−	0.0267560i
$476$	36.9893	+	3.20583i	0.0777085	+	0.00673494i
$477$	212.665			0.445839
$478$	80.7891	+	139.931i	0.169015	+	0.292742i
$479$	−598.669	−	345.642i	−1.24983	−	0.721590i	−0.278755	−	0.960362i	$-0.589922\pi$
$479$	−598.669	−	345.642i	−1.24983	−	0.721590i	−0.971076	+	0.238772i	$0.923255\pi$
$480$	−10.9545	+	18.9737i	−0.0228218	+	0.0395285i
$481$	−203.387	+	117.426i	−0.422843	+	0.244128i
$482$			192.958i			0.400328i
$483$	−278.551	+	398.502i	−0.576711	+	0.825056i
$484$	362.489			0.748945
$485$	8.36575	+	14.4899i	0.0172490	+	0.0298761i
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	−360.410	+	624.248i	−0.740062	+	1.28182i	0.212405	+	0.977182i	$0.431870\pi$
$487$	−360.410	+	624.248i	−0.740062	+	1.28182i	−0.952467	+	0.304643i	$0.901463\pi$
$488$	−31.5713	+	18.2277i	−0.0646953	+	0.0373518i
$489$			479.033i			0.979618i
$490$	−26.6588	+	152.641i	−0.0544058	+	0.311512i
$491$	589.995			1.20162			0.600809	−	0.799392i	$-0.294845\pi$
$491$	589.995			1.20162			0.600809	+	0.799392i	$0.294845\pi$
$492$	−122.400	−	212.004i	−0.248781	−	0.430902i
$493$	−107.963	−	62.3325i	−0.218992	−	0.126435i
$494$	−12.9868	+	22.4939i	−0.0262891	+	0.0455341i
$495$	−100.999	+	58.3117i	−0.204038	+	0.117801i
$496$		−	161.208i		−	0.325016i
$497$	−66.4340	−	46.4371i	−0.133670	−	0.0934348i
$498$	−273.521			−0.549238
$499$	437.845	+	758.370i	0.877445	+	1.51978i	0.854135	+	0.520052i	$0.174087\pi$
$499$	437.845	+	758.370i	0.877445	+	1.51978i	0.0233104	+	0.999728i	$0.492579\pi$
$500$	−19.3649	−	11.1803i	−0.0387298	−	0.0223607i
$501$	−41.9380	+	72.6387i	−0.0837085	+	0.144987i
$502$	559.737	−	323.165i	1.11501	−	0.643754i
$503$		−	817.809i		−	1.62586i	−0.582360	−	0.812931i	$-0.697871\pi$
$503$		−	817.809i		−	1.62586i	0.582360	−	0.812931i	$-0.302129\pi$
$504$	−5.12866	+	59.1751i	−0.0101759	+	0.117411i
$505$	211.524			0.418859
$506$	492.974	+	853.857i	0.974258	+	1.68746i
$507$	−175.186	−	101.144i	−0.345535	−	0.199495i
$508$	−53.7033	+	93.0168i	−0.105715	+	0.183104i
$509$	−657.585	+	379.657i	−1.29191	+	0.745887i	−0.978993	−	0.203892i	$-0.934641\pi$
$509$	−657.585	+	379.657i	−1.29191	+	0.745887i	−0.312921	+	0.949779i	$0.601308\pi$
$510$			14.5256i			0.0284815i
$511$	−67.1794	−	143.761i	−0.131467	−	0.281333i
$512$	22.6274			0.0441942
$513$	−6.60384	−	11.4382i	−0.0128730	−	0.0222967i
$514$	−61.2350	−	35.3540i	−0.119134	−	0.0687821i
$515$	66.8827	−	115.844i	0.129869	−	0.224940i
$516$	112.120	−	64.7323i	0.217286	−	0.125450i
$517$			581.508i			1.12477i
$518$	−291.504	+	136.219i	−0.562748	+	0.262971i
$519$	195.667			0.377009
$520$	22.8493	+	39.5762i	0.0439410	+	0.0761081i
$521$	−153.671	−	88.7220i	−0.294954	−	0.170292i	0.345220	−	0.938522i	$-0.387804\pi$
$521$	−153.671	−	88.7220i	−0.294954	−	0.170292i	−0.640174	+	0.768230i	$0.721138\pi$
$522$	99.7190	−	172.718i	0.191033	−	0.330878i
$523$	91.1221	−	52.6094i	0.174230	−	0.100592i	−0.410349	−	0.911929i	$-0.634593\pi$
$523$	91.1221	−	52.6094i	0.174230	−	0.100592i	0.584579	+	0.811337i	$0.301260\pi$
$524$		−	116.969i		−	0.223222i
$525$	−60.3954	−	5.23442i	−0.115039	−	0.00997033i
$526$	257.780			0.490075
$527$	−53.4403	−	92.5612i	−0.101405	−	0.175638i
$528$	104.311	+	60.2240i	0.197559	+	0.114061i
$529$	−539.563	+	934.551i	−1.01997	+	1.76664i
$530$	194.136	−	112.084i	0.366294	−	0.211480i
$531$			301.676i			0.568128i
$532$	−20.3873	+	29.1665i	−0.0383220	+	0.0548243i
$533$	−510.618			−0.958007
$534$	−156.653	−	271.331i	−0.293358	−	0.508111i
$535$	12.5129	+	7.22430i	0.0233885	+	0.0135034i
$536$	−133.038	+	230.429i	−0.248206	+	0.429905i
$537$	497.125	−	287.015i	0.925744	−	0.534479i
$538$			53.2051i			0.0988943i
$539$	839.172	+	146.562i	1.55690	+	0.271914i
$540$	−23.2379			−0.0430331
$541$	138.181	+	239.337i	0.255419	+	0.442398i	0.965009	−	0.262216i	$-0.0844534\pi$
$541$	138.181	+	239.337i	0.255419	+	0.442398i	−0.709591	+	0.704614i	$0.751120\pi$
$542$	−248.301	−	143.357i	−0.458121	−	0.264496i
$543$	184.747	−	319.992i	0.340234	−	0.589303i
$544$	12.9921	−	7.50097i	0.0238825	−	0.0137886i
$545$			366.358i			0.672216i
$546$	101.545	+	70.9796i	0.185980	+	0.129999i
$547$	918.409			1.67899			0.839496	−	0.543366i	$-0.182850\pi$
$547$	918.409			1.67899			0.839496	+	0.543366i	$0.182850\pi$
$548$	12.1170	+	20.9872i	0.0221113	+	0.0382978i
$549$	−33.4864	−	19.3334i	−0.0609953	−	0.0352156i
$550$	−61.4659	+	106.462i	−0.111756	+	0.193567i
$551$	103.478	−	59.7429i	0.187800	−	0.108426i
$552$			196.456i			0.355899i
$553$	−14.5716	+	168.128i	−0.0263500	+	0.304030i
$554$	362.380			0.654116
$555$	−62.9413	−	109.018i	−0.113408	−	0.196428i
$556$	−78.3861	−	45.2562i	−0.140982	−	0.0813961i
$557$	−367.505	+	636.538i	−0.659794	+	1.14280i	0.320875	+	0.947122i	$0.396023\pi$
$557$	−367.505	+	636.538i	−0.659794	+	1.14280i	−0.980669	+	0.195675i	$0.937310\pi$
$558$	148.079	−	85.4933i	0.265374	−	0.153214i
$559$		−	270.044i		−	0.483083i
$560$	26.5062	+	56.7223i	0.0473325	+	0.101290i
$561$	79.8569			0.142347
$562$	100.029	+	173.255i	0.177987	+	0.308282i
$563$	715.827	+	413.283i	1.27145	+	0.734073i	0.975261	−	0.221056i	$-0.0709502\pi$
$563$	715.827	+	413.283i	1.27145	+	0.734073i	0.296191	+	0.955129i	$0.404284\pi$
$564$	−57.9344	+	100.345i	−0.102721	+	0.177917i
$565$	204.171	−	117.878i	0.361365	−	0.208634i
$566$		−	768.438i		−	1.35767i
$567$	−57.0757	+	26.6714i	−0.100663	+	0.0470395i
$568$	−32.7511			−0.0576603
$569$	216.546	+	375.069i	0.380573	+	0.659172i	0.991144	−	0.132790i	$-0.0423935\pi$
$569$	216.546	+	375.069i	0.380573	+	0.659172i	−0.610571	+	0.791961i	$0.709060\pi$
$570$	−12.0569	−	6.96106i	−0.0211525	−	0.0122124i
$571$	−240.036	+	415.754i	−0.420378	+	0.728116i	−0.995976	−	0.0896166i	$-0.971436\pi$
$571$	−240.036	+	415.754i	−0.420378	+	0.728116i	0.575598	+	0.817733i	$0.304769\pi$
$572$	217.577	−	125.618i	0.380380	−	0.219612i
$573$		−	115.880i		−	0.202234i
$574$	−696.964	−	60.4054i	−1.21422	−	0.105236i
$575$	−200.507			−0.348708
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−75.4646	−	43.5695i	−0.130788	−	0.0755104i	0.433179	−	0.901308i	$-0.357392\pi$
$577$	−75.4646	−	43.5695i	−0.130788	−	0.0755104i	−0.563966	+	0.825798i	$0.690725\pi$
$578$	−199.381	+	345.338i	−0.344949	+	0.597470i
$579$	−168.906	+	97.5179i	−0.291720	+	0.168425i
$580$		−	210.226i		−	0.362459i
$581$	−447.815	+	640.655i	−0.770766	+	1.10268i
$582$	18.3284			0.0314922
$583$	−616.204	−	1067.30i	−1.05695	−	1.83070i
$584$	−55.5276	−	32.0589i	−0.0950815	−	0.0548953i
$585$	−24.2354	+	41.9769i	−0.0414280	+	0.0717554i
$586$	−459.633	+	265.369i	−0.784356	+	0.452848i
$587$			104.332i			0.177737i	0.996043	+	0.0888687i	$0.0283252\pi$
$587$			104.332i			0.177737i	−0.996043	+	0.0888687i	$0.971675\pi$
$588$	130.206	+	108.896i	0.221439	+	0.185197i
$589$	102.440			0.173922
$590$	158.997	+	275.391i	0.269487	+	0.466765i
$591$	91.5316	+	52.8458i	0.154876	+	0.0894176i
$592$	−65.0055	+	112.593i	−0.109807	+	0.190191i
$593$	252.421	−	145.735i	0.425668	−	0.245760i	−0.271831	−	0.962345i	$-0.587629\pi$
$593$	252.421	−	145.735i	0.425668	−	0.245760i	0.697499	+	0.716585i	$0.254296\pi$
$594$			127.754i			0.215075i
$595$	34.0226	+	23.7817i	0.0571808	+	0.0399692i
$596$	−101.790			−0.170788
$597$	165.554	+	286.748i	0.277310	+	0.480314i
$598$	354.878	+	204.889i	0.593442	+	0.342624i
$599$	−298.839	+	517.604i	−0.498896	+	0.864114i	−0.999999	−	0.00127378i	$-0.999595\pi$
$599$	−298.839	+	517.604i	−0.498896	+	0.864114i	0.501103	+	0.865388i	$0.332928\pi$
$600$	−21.2132	+	12.2474i	−0.0353553	+	0.0204124i
$601$			447.444i			0.744499i	0.928133	+	0.372250i	$0.121413\pi$
$601$			447.444i			0.744499i	−0.928133	+	0.372250i	$0.878587\pi$
$602$	31.9458	−	368.594i	0.0530661	−	0.612283i
$603$	−282.217			−0.468021
$604$	157.695	+	273.136i	0.261085	+	0.452212i
$605$	350.979	+	202.638i	0.580130	+	0.334938i
$606$	115.856	−	200.669i	0.191182	−	0.331137i
$607$	533.739	−	308.155i	0.879307	−	0.507668i	0.00887709	−	0.999961i	$-0.497174\pi$
$607$	533.739	−	308.155i	0.879307	−	0.507668i	0.870430	+	0.492293i	$0.163841\pi$
$608$			14.3787i			0.0236492i
$609$	−241.288	−	516.346i	−0.396203	−	0.847859i
$610$	−40.7584			−0.0668170
$611$	120.842	+	209.305i	0.197778	+	0.342562i
$612$	13.7802	+	7.95598i	0.0225166	+	0.0130000i
$613$	63.5384	−	110.052i	0.103651	−	0.179530i	−0.809535	−	0.587072i	$-0.800281\pi$
$613$	63.5384	−	110.052i	0.103651	−	0.179530i	0.913186	+	0.407542i	$0.133614\pi$
$614$	50.6354	−	29.2344i	0.0824681	−	0.0476130i
$615$		−	273.696i		−	0.445034i
$616$	311.841	−	145.723i	0.506235	−	0.236563i
$617$	68.5630			0.111123			0.0555616	−	0.998455i	$-0.482305\pi$
$617$	68.5630			0.111123			0.0555616	+	0.998455i	$0.482305\pi$
$618$	−73.2664	−	126.901i	−0.118554	−	0.205342i
$619$	833.529	+	481.238i	1.34657	+	0.777445i	0.987763	−	0.155965i	$-0.0498487\pi$
$619$	833.529	+	481.238i	1.34657	+	0.777445i	0.358812	+	0.933410i	$0.383182\pi$
$620$	90.1179	−	156.089i	0.145351	−	0.251756i
$621$	−180.457	+	104.187i	−0.290590	+	0.167772i
$622$			207.265i			0.333224i
$623$	−892.003	−	77.3092i	−1.43179	−	0.124092i
$624$	50.0604			0.0802249
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−275.409	−	159.008i	−0.439951	−	0.254006i
$627$	−38.2697	+	66.2850i	−0.0610362	+	0.105718i
$628$	−290.718	+	167.846i	−0.462927	+	0.267271i
$629$			86.1971i			0.137038i
$630$	−38.0457	+	54.4291i	−0.0603900	+	0.0863953i
$631$	412.586			0.653860			0.326930	−	0.945048i	$-0.393986\pi$
$631$	412.586			0.653860			0.326930	+	0.945048i	$0.393986\pi$
$632$	34.0944	+	59.0533i	0.0539469	+	0.0934387i
$633$	−420.173	−	242.587i	−0.663781	−	0.383234i
$634$	159.966	−	277.070i	0.252313	−	0.437019i
$635$	−103.996	+	60.0421i	−0.163773	+	0.0945545i
$636$		−	245.565i		−	0.386108i
$637$	332.504	−	121.635i	0.521985	−	0.190949i
$638$	−1155.76			−1.81153
$639$	−17.3689	−	30.0838i	−0.0271813	−	0.0470795i
$640$	21.9089	+	12.6491i	0.0342327	+	0.0197642i
$641$	71.3374	−	123.560i	0.111291	−	0.192761i	−0.805000	−	0.593275i	$-0.797835\pi$
$641$	71.3374	−	123.560i	0.111291	−	0.192761i	0.916291	+	0.400513i	$0.131168\pi$
$642$	13.7072	−	7.91383i	0.0213507	−	0.0123268i
$643$		−	239.942i		−	0.373160i	−0.982440	−	0.186580i	$-0.940260\pi$
$643$		−	239.942i		−	0.373160i	0.982440	−	0.186580i	$-0.0597403\pi$
$644$	460.150	+	321.643i	0.714519	+	0.499446i
$645$	144.746			0.224412
$646$	4.76653	+	8.25588i	0.00737853	+	0.0127800i
$647$	−128.817	−	74.3724i	−0.199098	−	0.114950i	0.397136	−	0.917760i	$-0.370004\pi$
$647$	−128.817	−	74.3724i	−0.199098	−	0.114950i	−0.596235	+	0.802810i	$0.703337\pi$
$648$	−12.7279	+	22.0454i	−0.0196419	+	0.0340207i
$649$	1514.01	−	874.115i	2.33284	−	1.34686i
$650$			51.0926i			0.0786041i
$651$	42.1915	−	486.810i	0.0648102	−	0.747788i
$652$	553.140			0.848374
$653$	−144.011	−	249.434i	−0.220537	−	0.381982i	0.734434	−	0.678680i	$-0.237448\pi$
$653$	−144.011	−	249.434i	−0.220537	−	0.381982i	−0.954971	+	0.296698i	$0.904114\pi$
$654$	347.557	+	200.662i	0.531433	+	0.306823i
$655$	65.3874	−	113.254i	0.0998281	−	0.172907i
$656$	−244.801	+	141.336i	−0.373172	+	0.215451i
$657$		−	68.0071i		−	0.103512i
$658$	140.183	+	299.985i	0.213043	+	0.455905i
$659$	−175.647			−0.266536			−0.133268	−	0.991080i	$-0.542547\pi$
$659$	−175.647			−0.266536			−0.133268	+	0.991080i	$0.542547\pi$
$660$	67.3325	+	116.623i	0.102019	+	0.176702i
$661$	−615.015	−	355.079i	−0.930432	−	0.537185i	−0.0434835	−	0.999054i	$-0.513846\pi$
$661$	−615.015	−	355.079i	−0.930432	−	0.537185i	−0.886948	+	0.461869i	$0.847179\pi$
$662$	−98.8651	+	171.239i	−0.149343	+	0.258670i
$663$	28.7433	−	16.5950i	0.0433535	−	0.0250301i
$664$			315.834i			0.475654i
$665$	−36.0445	+	16.8435i	−0.0542022	+	0.0253286i
$666$	−137.897			−0.207053
$667$	−942.544	−	1632.53i	−1.41311	−	2.44758i
$668$	83.8760	+	48.4258i	0.125563	+	0.0724937i
$669$	236.216	−	409.139i	0.353089	−	0.611567i
$670$	−257.627	+	148.741i	−0.384518	+	0.222002i
$671$			224.076i			0.333944i
$672$	68.3296	+	5.92207i	0.101681	+	0.00881261i
$673$	−1173.04			−1.74301			−0.871504	−	0.490389i	$-0.836855\pi$
$673$	−1173.04			−1.74301			−0.871504	+	0.490389i	$0.836855\pi$
$674$	−21.2930	−	36.8806i	−0.0315920	−	0.0547189i
$675$	−22.5000	−	12.9904i	−0.0333333	−	0.0192450i
$676$	−116.791	+	202.288i	−0.172768	+	0.299242i
$677$	586.699	−	338.731i	0.866616	−	0.500341i	0.000393478	−	1.00000i	$-0.499875\pi$
$677$	586.699	−	338.731i	0.866616	−	0.500341i	0.866222	+	0.499659i	$0.166541\pi$
$678$		−	258.258i		−	0.380912i
$679$	30.0078	−	42.9299i	0.0441941	−	0.0632252i
$680$	16.7727			0.0246657
$681$	−13.9191	−	24.1086i	−0.0204392	−	0.0354018i
$682$	−858.126	−	495.439i	−1.25825	−	0.726450i
$683$	415.514	−	719.691i	0.608366	−	1.05372i	−0.383144	−	0.923689i	$-0.625159\pi$
$683$	415.514	−	719.691i	0.608366	−	1.05372i	0.991510	−	0.130032i	$-0.0415079\pi$
$684$	−13.2077	+	7.62546i	−0.0193095	+	0.0111483i
$685$			27.0944i			0.0395538i
$686$	468.239	−	126.689i	0.682564	−	0.184679i
$687$	−256.523			−0.373395
$688$	−74.7464	−	129.465i	−0.108643	−	0.188175i
$689$	−443.587	−	256.105i	−0.643813	−	0.371706i
$690$	−109.822	+	190.218i	−0.159163	+	0.275678i
$691$	541.436	−	312.598i	0.783554	−	0.452385i	−0.0541345	−	0.998534i	$-0.517240\pi$
$691$	541.436	−	312.598i	0.783554	−	0.452385i	0.837688	+	0.546149i	$0.183907\pi$
$692$		−	225.937i		−	0.326499i
$693$	299.233	+	209.163i	0.431794	+	0.301823i
$694$	−588.181			−0.847524
$695$	−50.5980	−	87.6383i	−0.0728029	−	0.126098i
$696$	−199.438	−	115.146i	−0.286549	−	0.165439i
$697$	−93.7055	+	162.303i	−0.134441	+	0.232859i
$698$	−728.661	+	420.693i	−1.04393	+	0.602712i
$699$		−	518.088i		−	0.741185i
$700$	−6.04419	+	69.7386i	−0.00863456	+	0.0996265i
$701$	1030.02			1.46936			0.734678	−	0.678416i	$-0.237333\pi$
$701$	1030.02			1.46936			0.734678	+	0.678416i	$0.237333\pi$
$702$	26.5485	+	45.9834i	0.0378184	+	0.0655034i
$703$	−71.5477	−	41.3081i	−0.101775	−	0.0587597i
$704$	69.5407	−	120.448i	0.0987795	−	0.171091i
$705$	−112.190	+	64.7727i	−0.159134	+	0.0918761i
$706$		−	515.224i		−	0.729779i
$707$	−280.335	−	599.906i	−0.396513	−	0.848523i
$708$	348.345			0.492013
$709$	329.126	+	570.062i	0.464211	+	0.804037i	0.999166	−	0.0408438i	$-0.0130046\pi$
$709$	329.126	+	570.062i	0.464211	+	0.804037i	−0.534955	+	0.844881i	$0.679671\pi$
$710$	−31.7111	−	18.3084i	−0.0446635	−	0.0257865i
$711$	−36.1626	+	62.6354i	−0.0508616	+	0.0880949i
$712$	−313.306	+	180.887i	−0.440037	+	0.254055i
$713$		−	1616.17i		−	2.26671i
$714$	41.1962	−	19.2509i	0.0576978	−	0.0269621i
$715$	280.891			0.392854
$716$	−331.416	−	574.030i	−0.462872	−	0.801718i
$717$	171.380	+	98.9461i	0.239023	+	0.138000i
$718$	433.288	−	750.478i	0.603466	−	1.04523i
$719$	−1166.99	+	673.760i	−1.62307	+	0.937079i	−0.636975	+	0.770884i	$0.719815\pi$
$719$	−1166.99	+	673.760i	−1.62307	+	0.937079i	−0.986093	+	0.166195i	$0.946852\pi$
$720$			26.8328i			0.0372678i
$721$	−417.188	−	36.1574i	−0.578625	−	0.0501490i
$722$	501.394			0.694452
$723$	118.162	+	204.663i	0.163433	+	0.283074i
$724$	−369.495	−	213.328i	−0.510352	−	0.294652i
$725$	117.520	−	203.551i	0.162096	−	0.280759i
$726$	384.478	−	221.978i	0.529584	−	0.305755i
$727$		−	1126.18i		−	1.54907i	−0.632530	−	0.774536i	$-0.717983\pi$
$727$		−	1126.18i		−	1.54907i	0.632530	−	0.774536i	$-0.282017\pi$
$728$	81.9602	−	117.254i	0.112583	−	0.161063i
$729$	−27.0000			−0.0370370
$730$	−35.8429	−	62.0817i	−0.0490999	−	0.0850435i
$731$	−85.8348	−	49.5568i	−0.117421	−	0.0677931i
$732$	−22.3243	+	38.6668i	−0.0304976	+	0.0528235i
$733$	525.395	−	303.337i	0.716773	−	0.413829i	−0.0967907	−	0.995305i	$-0.530858\pi$
$733$	525.395	−	303.337i	0.716773	−	0.413829i	0.813564	+	0.581476i	$0.197524\pi$
$734$			697.233i			0.949909i
$735$	65.1972	+	178.225i	0.0887037	+	0.242484i
$736$	226.848			0.308218
$737$	817.731	+	1416.35i	1.10954	+	1.92178i
$738$	−259.651	−	149.909i	−0.351830	−	0.203129i
$739$	−461.084	+	798.622i	−0.623930	+	1.08068i	0.364817	+	0.931079i	$0.381132\pi$
$739$	−461.084	+	798.622i	−0.623930	+	1.08068i	−0.988747	+	0.149599i	$0.952202\pi$
$740$	−125.883	+	72.6783i	−0.170112	+	0.0982140i
$741$			31.8111i			0.0429300i
$742$	−575.175	−	402.045i	−0.775168	−	0.541840i
$743$	13.3994			0.0180342			0.00901712	−	0.999959i	$-0.497130\pi$
$743$	13.3994			0.0180342			0.00901712	+	0.999959i	$0.497130\pi$
$744$	−98.7192	−	170.987i	−0.132687	−	0.229821i
$745$	−98.5574	−	56.9022i	−0.132292	−	0.0763787i
$746$	−116.957	+	202.576i	−0.156779	+	0.271550i
$747$	−290.112	+	167.496i	−0.388370	+	0.224225i
$748$		−	92.2108i		−	0.123277i
$749$	3.90552	−	45.0624i	0.00521431	−	0.0601634i
$750$	−27.3861			−0.0365148
$751$	−538.071	−	931.967i	−0.716473	−	1.24097i	−0.962389	−	0.271676i	$-0.912422\pi$
$751$	−538.071	−	931.967i	−0.716473	−	1.24097i	0.245916	−	0.969291i	$-0.420911\pi$
$752$	115.869	+	66.8969i	0.154081	+	0.0889587i
$753$	395.794	−	685.536i	0.525623	−	0.910406i
$754$	−415.997	+	240.176i	−0.551721	+	0.318536i
$755$			352.617i			0.467043i
$756$	30.7975	+	65.9054i	0.0407374	+	0.0871764i
$757$	−254.117			−0.335690			−0.167845	−	0.985813i	$-0.553681\pi$
$757$	−254.117			−0.335690			−0.167845	+	0.985813i	$0.553681\pi$
$758$	126.819	+	219.656i	0.167307	+	0.289784i
$759$	1045.76	+	603.768i	1.37781	+	0.795478i
$760$	−8.03794	+	13.9221i	−0.0105762	+	0.0183186i
$761$	−685.095	+	395.540i	−0.900256	+	0.519763i	−0.877283	−	0.479973i	$-0.840646\pi$
$761$	−685.095	+	395.540i	−0.900256	+	0.519763i	−0.0229729	+	0.999736i	$0.507313\pi$
$762$			131.546i			0.172632i
$763$	1039.03	−	485.538i	1.36177	−	0.636354i
$764$	−133.807			−0.175140
$765$	8.89506	+	15.4067i	0.0116275	+	0.0201395i
$766$	−329.664	−	190.332i	−0.430371	−	0.248475i
$767$	363.298	−	629.250i	0.473661	−	0.820405i
$768$	24.0000	−	13.8564i	0.0312500	−	0.0180422i
$769$			464.403i			0.603905i	0.953323	+	0.301952i	$0.0976384\pi$
$769$			464.403i			0.603905i	−0.953323	+	0.301952i	$0.902362\pi$
$770$	383.400	+	33.2290i	0.497922	+	0.0431546i
$771$	−86.5993			−0.112321
$772$	112.604	+	195.036i	0.145860	+	0.252637i
$773$	675.608	+	390.063i	0.874008	+	0.504609i	0.868678	−	0.495377i	$-0.164970\pi$
$773$	675.608	+	390.063i	0.874008	+	0.504609i	0.00533002	+	0.999986i	$0.498303\pi$
$774$	79.2805	−	137.318i	0.102430	−	0.177413i
$775$	174.513	−	100.755i	0.225177	−	0.130006i
$776$		−	21.1639i		−	0.0272730i
$777$	−225.769	+	322.991i	−0.290566	+	0.415690i
$778$	−669.980			−0.861157
$779$	−89.8126	−	155.560i	−0.115292	−	0.199692i
$780$	48.4707	+	27.9846i	0.0621420	+	0.0358777i
$781$	−100.654	+	174.337i	−0.128878	+	0.223223i
$782$	130.250	−	75.2000i	0.166560	−	0.0961637i
$783$		−	244.261i		−	0.311955i
$784$	125.742	−	150.349i	0.160385	−	0.191772i
$785$	−375.316			−0.478109
$786$	−71.6283	−	124.064i	−0.0911302	−	0.157842i
$787$	998.358	+	576.402i	1.26856	+	0.732404i	0.974716	−	0.223449i	$-0.0717316\pi$
$787$	998.358	+	576.402i	1.26856	+	0.732404i	0.293845	+	0.955853i	$0.405065\pi$
$788$	61.0211	−	105.692i	0.0774379	−	0.134126i
$789$	273.416	−	157.857i	0.346535	−	0.200072i
$790$			76.2374i			0.0965031i
$791$	−604.907	−	422.827i	−0.764737	−	0.534548i
$792$	147.518			0.186260
$793$	46.5650	+	80.6530i	0.0587201	+	0.101706i
$794$	629.437	+	363.406i	0.792742	+	0.457690i
$795$	137.275	−	237.767i	0.172673	−	0.299078i
$796$	331.108	−	191.165i	0.415964	−	0.240157i
$797$			1475.63i			1.85148i	0.378156	+	0.925742i	$0.376558\pi$
$797$			1475.63i			1.85148i	−0.378156	+	0.925742i	$0.623442\pi$
$798$	−3.76321	+	43.4204i	−0.00471580	+	0.0544115i
$799$	88.7051			0.111020
$800$	14.1421	+	24.4949i	0.0176777	+	0.0306186i
$801$	−332.311	−	191.860i	−0.414871	−	0.239526i
$802$	287.605	−	498.146i	0.358609	−	0.621129i
$803$	−341.305	+	197.053i	−0.425038	+	0.245396i
$804$			325.876i			0.405318i
$805$	265.735	+	568.662i	0.330105	+	0.706412i
$806$	−411.827			−0.510951
$807$	32.5814	+	56.4326i	0.0403734	+	0.0699289i
$808$	−231.713	−	133.779i	−0.286773	−	0.165569i
$809$	6.88050	−	11.9174i	0.00850495	−	0.0147310i	−0.861742	−	0.507347i	$-0.830626\pi$
$809$	6.88050	−	11.9174i	0.00850495	−	0.0147310i	0.870247	+	0.492616i	$0.163959\pi$
$810$	−24.6475	+	14.2302i	−0.0304290	+	0.0175682i
$811$			1274.65i			1.57170i	0.618416	+	0.785851i	$0.287775\pi$
$811$			1274.65i			1.57170i	−0.618416	+	0.785851i	$0.712225\pi$
$812$	−596.225	+	278.615i	−0.734268	+	0.343122i
$813$	−351.151			−0.431920
$814$	399.562	+	692.062i	0.490863	+	0.850199i
$815$	535.576	+	309.215i	0.657148	+	0.379405i
$816$	9.18678	−	15.9120i	0.0112583	−	0.0195000i
$817$	82.2689	−	47.4980i	0.100696	−	0.0581371i
$818$			689.406i			0.842795i
$819$	151.171	+	13.1019i	0.184580	+	0.0159974i
$820$	−316.037			−0.385410
$821$	−292.249	−	506.190i	−0.355967	−	0.616553i	0.631316	−	0.775526i	$-0.282515\pi$
$821$	−292.249	−	506.190i	−0.355967	−	0.616553i	−0.987283	+	0.158973i	$0.949182\pi$
$822$	25.7040	+	14.8402i	0.0312700	+	0.0180538i
$823$	40.4835	−	70.1196i	0.0491902	−	0.0851999i	−0.840382	−	0.541995i	$-0.817669\pi$
$823$	40.4835	−	70.1196i	0.0491902	−	0.0851999i	0.889572	+	0.456795i	$0.151003\pi$
$824$	−146.533	+	84.6007i	−0.177831	+	0.102671i
$825$			150.560i			0.182497i
$826$	570.320	−	815.913i	0.690461	−	0.987789i
$827$	−1628.46			−1.96911			−0.984556	−	0.175072i	$-0.943984\pi$
$827$	−1628.46			−1.96911			−0.984556	+	0.175072i	$0.943984\pi$
$828$	120.304	+	208.373i	0.145295	+	0.251659i
$829$	−761.982	−	439.931i	−0.919158	−	0.530676i	−0.0357920	−	0.999359i	$-0.511395\pi$
$829$	−761.982	−	439.931i	−0.919158	−	0.530676i	−0.883366	+	0.468683i	$0.844729\pi$
$830$	−176.557	+	305.805i	−0.212719	+	0.368440i
$831$	384.362	−	221.912i	0.462530	−	0.267042i
$832$		−	57.8047i		−	0.0694768i
$833$	22.3570	−	128.010i	0.0268391	−	0.153674i
$834$	−110.855			−0.132919
$835$	54.1417	+	93.7762i	0.0648404	+	0.112307i
$836$	76.5394	+	44.1900i	0.0915543	+	0.0528589i
$837$	104.708	−	181.359i	0.125099	−	0.216677i
$838$	−676.374	+	390.505i	−0.807129	+	0.465996i
$839$			647.389i			0.771619i	0.922578	+	0.385810i	$0.126078\pi$
$839$			647.389i			0.771619i	−0.922578	+	0.385810i	$0.873922\pi$
$840$	62.8493	+	43.9314i	0.0748206	+	0.0522993i
$841$	1368.75			1.62753
$842$	52.8117	+	91.4725i	0.0627217	+	0.108637i
$843$	212.193	+	122.510i	0.251711	+	0.145326i
$844$	−280.115	+	485.174i	−0.331890	+	0.574851i
$845$	−226.164	+	130.576i	−0.267650	+	0.154528i
$846$			141.910i			0.167742i
$847$	109.548	−	1263.97i	0.129336	−	1.49230i
$848$	−283.554			−0.334379
$849$	−470.571	−	815.052i	−0.554264	−	0.960014i
$850$	16.2401	+	9.37622i	0.0191060	+	0.0110308i
$851$	−651.704	+	1128.78i	−0.765809	+	1.32642i
$852$	−34.7378	+	20.0559i	−0.0407720	+	0.0235397i
$853$		−	569.518i		−	0.667665i	−0.942632	−	0.333833i	$-0.891658\pi$
$853$		−	569.518i		−	0.667665i	0.942632	−	0.333833i	$-0.108342\pi$
$854$	54.0175	+	115.595i	0.0632524	+	0.135358i
$855$	−17.0511			−0.0199427
$856$	−9.13810	−	15.8277i	−0.0106754	−	0.0184903i
$857$	553.041	+	319.299i	0.645322	+	0.372577i	0.786662	−	0.617384i	$-0.211808\pi$
$857$	553.041	+	319.299i	0.645322	+	0.372577i	−0.141339	+	0.989961i	$0.545141\pi$
$858$	153.850	−	266.477i	0.179313	−	0.310579i
$859$	1097.36	−	633.562i	1.27749	−	0.737558i	0.301102	−	0.953592i	$-0.402645\pi$
$859$	1097.36	−	633.562i	1.27749	−	0.737558i	0.976386	+	0.216034i	$0.0693122\pi$
$860$		−	167.138i		−	0.194347i
$861$	−776.233	+	362.732i	−0.901548	+	0.421292i
$862$	685.437			0.795171
$863$	103.017	+	178.430i	0.119371	+	0.206756i	0.919518	−	0.393047i	$-0.128579\pi$
$863$	103.017	+	178.430i	0.119371	+	0.206756i	−0.800148	+	0.599803i	$0.795246\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$	126.303	−	218.763i	0.146015	−	0.252905i
$866$	561.173	−	323.993i	0.648006	−	0.374126i
$867$			488.381i			0.563300i
$868$	−562.120	−	48.7185i	−0.647604	−	0.0561273i
$869$	419.129			0.482312
$870$	−128.737	−	222.978i	−0.147973	−	0.256297i
$871$	588.661	+	339.864i	0.675845	+	0.390199i
$872$	231.705	−	401.325i	0.265717	−	0.460235i
$873$	19.4403	−	11.2238i	0.0222683	−	0.0128566i
$874$			144.152i			0.164933i
$875$	−44.8373	+	64.1453i	−0.0512426	+	0.0733089i
$876$	−78.5279			−0.0896437
$877$	−412.272	−	714.076i	−0.470093	−	0.814226i	0.529322	−	0.848421i	$-0.322446\pi$
$877$	−412.272	−	714.076i	−0.470093	−	0.814226i	−0.999415	+	0.0341955i	$0.989113\pi$
$878$	−171.356	−	98.9325i	−0.195167	−	0.112679i
$879$	−325.009	+	562.933i	−0.369749	+	0.640424i
$880$	134.665	−	77.7489i	0.153028	−	0.0883510i
$881$		−	416.337i		−	0.472574i	−0.971683	−	0.236287i	$-0.924070\pi$
$881$		−	416.337i		−	0.472574i	0.971683	−	0.236287i	$-0.0759305\pi$
$882$	204.790	+	35.7666i	0.232188	+	0.0405517i
$883$	650.529			0.736726			0.368363	−	0.929682i	$-0.379918\pi$
$883$	650.529			0.736726			0.368363	+	0.929682i	$0.379918\pi$
$884$	−19.1622	−	33.1900i	−0.0216767	−	0.0375452i
$885$	337.284	+	194.731i	0.381112	+	0.220035i
$886$	11.3790	−	19.7090i	0.0128431	−	0.0222449i
$887$	−299.987	+	173.198i	−0.338204	+	0.195262i	−0.659478	−	0.751724i	$-0.729223\pi$
$887$	−299.987	+	173.198i	−0.338204	+	0.195262i	0.321273	+	0.946987i	$0.395889\pi$
$888$			159.230i			0.179313i
$889$	308.113	+	215.370i	0.346584	+	0.242261i
$890$	−404.476			−0.454468
$891$	78.2333	+	135.504i	0.0878040	+	0.152081i
$892$	−472.433	−	272.759i	−0.529633	−	0.305784i
$893$	−42.5100	+	73.6295i	−0.0476036	+	0.0824518i
$894$	−107.964	+	62.3332i	−0.120765	+	0.0697239i
$895$		−	741.069i		−	0.828011i
$896$	6.83822	−	78.9002i	0.00763194	−	0.0880582i
$897$	501.873			0.559502
$898$	232.860	+	403.326i	0.259310	+	0.449138i
$899$	1640.70	+	947.256i	1.82502	+	1.05368i
$900$	−15.0000	+	25.9808i	−0.0166667	+	0.0288675i
$901$	−162.809	+	93.9978i	−0.180698	+	0.104326i
$902$			1737.47i			1.92624i
$903$	−191.833	−	410.516i	−0.212440	−	0.454613i
$904$	−298.211			−0.329879
$905$	−238.508	−	413.107i	−0.263544	−	0.456472i
$906$	334.522	+	193.136i	0.369230	+	0.213175i
$907$	−210.091	+	363.888i	−0.231633	+	0.401199i	−0.958289	−	0.285802i	$-0.907740\pi$
$907$	−210.091	+	363.888i	−0.231633	+	0.401199i	0.726656	+	0.687001i	$0.241073\pi$
$908$	−27.8382	+	16.0724i	−0.0306588	+	0.0177009i
$909$		−	283.789i		−	0.312199i
$910$	144.905	−	67.7137i	0.159236	−	0.0744106i
$911$	717.087			0.787142			0.393571	−	0.919294i	$-0.371239\pi$
$911$	717.087			0.787142			0.393571	+	0.919294i	$0.371239\pi$
$912$	8.80512	+	15.2509i	0.00965474	+	0.0167225i
$913$	1681.22	+	970.652i	1.84142	+	1.06315i
$914$	629.974	−	1091.15i	0.689249	−	1.19381i
$915$	−43.2308	+	24.9593i	−0.0472467	+	0.0272779i
$916$			296.207i			0.323370i
$917$	−407.861	−	35.3490i	−0.444777	−	0.0385485i
$918$	19.4881			0.0212289
$919$	59.5137	+	103.081i	0.0647592	+	0.112166i	0.896587	−	0.442867i	$-0.146039\pi$
$919$	59.5137	+	103.081i	0.0647592	+	0.112166i	−0.831828	+	0.555034i	$0.812705\pi$
$920$	219.645	+	126.812i	0.238744	+	0.137839i
$921$	35.8046	−	62.0154i	0.0388758	−	0.0673349i
$922$	−654.037	+	377.608i	−0.709367	+	0.409553i
$923$			83.6669i			0.0906467i
$924$	241.521	−	345.525i	0.261386	−	0.373945i
$925$	−162.514			−0.175691
$926$	−112.203	−	194.341i	−0.121169	−	0.209872i
$927$	−155.421	−	89.7326i	−0.167661	−	0.0967989i
$928$	−132.959	+	230.291i	−0.143274	+	0.248159i
$929$	328.049	−	189.399i	0.353121	−	0.203874i	−0.312938	−	0.949773i	$-0.601313\pi$
$929$	328.049	−	189.399i	0.353121	−	0.203874i	0.666059	+	0.745899i	$0.267980\pi$
$930$		−	220.743i		−	0.237358i
$931$	95.5403	+	79.9034i	0.102621	+	0.0858253i
$932$	−598.237			−0.641885
$933$	126.924	+	219.838i	0.136038	+	0.235625i
$934$	137.415	+	79.3366i	0.147125	+	0.0849429i
$935$	51.5474	−	89.2827i	0.0551309	−	0.0954896i
$936$	53.0970	−	30.6556i	0.0567276	−	0.0327517i
$937$		−	365.585i		−	0.390165i	−0.980787	−	0.195083i	$-0.937503\pi$
$937$		−	365.585i		−	0.390165i	0.980787	−	0.195083i	$-0.0624975\pi$
$938$	763.284	+	533.532i	0.813735	+	0.568798i
$939$	−389.487			−0.414790
$940$	74.7930	+	129.545i	0.0795670	+	0.137814i
$941$	−1193.22	−	688.903i	−1.26803	−	0.732097i	−0.293414	−	0.955985i	$-0.594791\pi$
$941$	−1193.22	−	688.903i	−1.26803	−	0.732097i	−0.974615	+	0.223889i	$0.928125\pi$
$942$	−205.569	+	356.056i	−0.218226	+	0.377978i
$943$	−2454.22	+	1416.94i	−2.60256	+	1.50259i
$944$		−	402.235i		−	0.426096i
$945$	−7.02271	+	81.0289i	−0.00743144	+	0.0857449i
$946$	−918.871			−0.971323
$947$	−237.417	−	411.218i	−0.250704	−	0.434232i	0.713016	−	0.701148i	$-0.247329\pi$
$947$	−237.417	−	411.218i	−0.250704	−	0.434232i	−0.963720	+	0.266916i	$0.913995\pi$
$948$	72.3252	+	41.7570i	0.0762924	+	0.0440474i
$949$	−81.8986	+	141.853i	−0.0862999	+	0.149476i
$950$	−15.5654	+	8.98669i	−0.0163846	+	0.00945968i
$951$		−	391.836i		−	0.412025i
$952$	−22.2290	−	47.5693i	−0.0233498	−	0.0499677i
$953$	−172.839			−0.181363			−0.0906813	−	0.995880i	$-0.528904\pi$
$953$	−172.839			−0.181363			−0.0906813	+	0.995880i	$0.528904\pi$
$954$	−150.377	−	260.461i	−0.157628	−	0.273019i
$955$	−129.558	−	74.8002i	−0.135663	−	0.0783248i
$956$	114.253	−	197.892i	0.119512	−	0.207000i
$957$	−1225.86	+	707.753i	−1.28094	+	0.739554i
$958$			977.622i			1.02048i
$959$	76.8427	−	35.9085i	0.0801280	−	0.0374437i
$960$	30.9839			0.0322749
$961$	331.623	+	574.388i	0.345081	+	0.597698i
$962$	287.633	+	166.065i	0.298995	+	0.172625i
$963$	9.69242	−	16.7878i	0.0100648	−	0.0174328i
$964$	236.324	−	136.442i	0.245150	−	0.141537i
$965$			251.790i			0.260922i
$966$	685.029	+	59.3709i	0.709139	+	0.0614606i
$967$	−1209.88			−1.25117			−0.625583	−	0.780158i	$-0.715139\pi$
$967$	−1209.88			−1.25117			−0.625583	+	0.780158i	$0.715139\pi$
$968$	−256.319	−	443.957i	−0.264792	−	0.458633i
$969$	10.1113	+	5.83779i	0.0104348	+	0.00602455i
$970$	11.8310	−	20.4918i	0.0121969	−	0.0211256i
$971$	−675.990	+	390.283i	−0.696180	+	0.401939i	−0.805923	−	0.592020i	$-0.798330\pi$
$971$	−675.990	+	390.283i	−0.696180	+	0.401939i	0.109743	+	0.993960i	$0.464997\pi$
$972$			31.1769i			0.0320750i
$973$	−181.494	+	259.650i	−0.186531	+	0.266855i
$974$	1019.39			1.04661
$975$	31.2877	+	54.1919i	0.0320900	+	0.0555815i
$976$	44.6485	+	25.7778i	0.0457465	+	0.0264117i
$977$	−794.931	+	1376.86i	−0.813644	+	1.40927i	0.0966527	+	0.995318i	$0.469186\pi$
$977$	−794.931	+	1376.86i	−0.813644	+	1.40927i	−0.910297	+	0.413955i	$0.864147\pi$
$978$	586.694	−	338.728i	0.599891	−	0.346347i
$979$			2223.68i			2.27138i
$980$	205.797	−	75.2833i	0.209997	−	0.0768197i
$981$	491.520			0.501040
$982$	−417.189	−	722.593i	−0.424836	−	0.735838i
$983$	607.577	+	350.785i	0.618084	+	0.356851i	0.776123	−	0.630582i	$-0.217184\pi$
$983$	607.577	+	350.785i	0.618084	+	0.356851i	−0.158039	+	0.987433i	$0.550517\pi$
$984$	−173.100	+	299.819i	−0.175915	+	0.304694i
$985$	118.167	−	68.2237i	0.119966	−	0.0692626i
$986$			176.303i			0.178806i
$987$	332.389	+	232.339i	0.336767	+	0.235399i
$988$	36.7323			0.0371785
$989$	−749.360	−	1297.93i	−0.757695	−	1.31237i
$990$	142.834	+	82.4652i	0.144277	+	0.0832982i
$991$	−203.359	+	352.228i	−0.205206	+	0.355427i	−0.950198	−	0.311646i	$-0.899120\pi$
$991$	−203.359	+	352.228i	−0.205206	+	0.355427i	0.744992	+	0.667073i	$0.232453\pi$
$992$	−197.438	+	113.991i	−0.199031	+	0.114910i
$993$			242.169i			0.243876i
$994$	−9.89768	+	114.201i	−0.00995743	+	0.114890i
$995$	427.458			0.429606
$996$	193.408	+	334.993i	0.194185	+	0.336338i
$997$	−655.372	−	378.379i	−0.657344	−	0.379518i	0.133920	−	0.990992i	$-0.457243\pi$
$997$	−655.372	−	378.379i	−0.657344	−	0.379518i	−0.791264	+	0.611474i	$0.790577\pi$
$998$	619.207	−	1072.50i	0.620448	−	1.07465i
$999$	−146.262	+	84.4446i	−0.146409	+	0.0845291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.o.b.31.2	✓	16
3.2	odd	2		630.3.v.c.451.8		16
5.2	odd	4		1050.3.q.e.199.15		32
5.3	odd	4		1050.3.q.e.199.2		32
5.4	even	2		1050.3.p.i.451.5		16
7.3	odd	6		1470.3.f.d.391.11		16
7.4	even	3		1470.3.f.d.391.13		16
7.5	odd	6	inner	210.3.o.b.61.2	yes	16
21.5	even	6		630.3.v.c.271.8		16
35.12	even	12		1050.3.q.e.649.2		32
35.19	odd	6		1050.3.p.i.901.5		16
35.33	even	12		1050.3.q.e.649.15		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.2	✓	16	1.1	even	1	trivial
210.3.o.b.61.2	yes	16	7.5	odd	6	inner
630.3.v.c.271.8		16	21.5	even	6
630.3.v.c.451.8		16	3.2	odd	2
1050.3.p.i.451.5		16	5.4	even	2
1050.3.p.i.901.5		16	35.19	odd	6
1050.3.q.e.199.2		32	5.3	odd	4
1050.3.q.e.199.15		32	5.2	odd	4
1050.3.q.e.649.2		32	35.12	even	12
1050.3.q.e.649.15		32	35.33	even	12
1470.3.f.d.391.11		16	7.3	odd	6
1470.3.f.d.391.13		16	7.4	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +2.44949i q^{6} +(5.73733 + 4.01037i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(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} +(5.73733 + 4.01037i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(2.73861 + 1.58114i) q^{10} +(8.69259 - 15.0560i) q^{11} +(3.00000 - 1.73205i) q^{12} -7.22559i q^{13} +(0.854777 - 9.86252i) q^{14} +3.87298 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-2.29669 - 1.32600i) q^{17} +(2.12132 - 3.67423i) q^{18} +(2.20128 - 1.27091i) q^{19} -4.47214i q^{20} +(-5.13291 - 10.9842i) q^{21} -24.5864 q^{22} +(-20.0507 - 34.7289i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-8.84951 + 5.10926i) q^{26} -5.19615i q^{27} +(-12.6835 + 5.92697i) q^{28} +47.0080 q^{29} +(-2.73861 - 4.74342i) q^{30} +(34.9025 + 20.1510i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-26.0778 + 15.0560i) q^{33} +3.75049i q^{34} +(-15.5940 - 1.35152i) q^{35} -6.00000 q^{36} +(-16.2514 - 28.1482i) q^{37} +(-3.11308 - 1.79734i) q^{38} +(-6.25755 + 10.8384i) q^{39} +(-5.47723 + 3.16228i) q^{40} -70.6679i q^{41} +(-9.82336 + 14.0535i) q^{42} +37.3732 q^{43} +(17.3852 + 30.1120i) q^{44} +(-5.80948 - 3.35410i) q^{45} +(-28.3560 + 49.1141i) q^{46} +(-28.9672 + 16.7242i) q^{47} +6.92820i q^{48} +(16.8339 + 46.0176i) q^{49} -7.07107 q^{50} +(2.29669 + 3.97799i) q^{51} +(12.5151 + 7.22559i) q^{52} +(35.4442 - 61.3911i) q^{53} +(-6.36396 + 3.67423i) q^{54} +38.8745i q^{55} +(16.2276 + 11.3430i) q^{56} -4.40256 q^{57} +(-33.2397 - 57.5728i) q^{58} +(87.0863 + 50.2793i) q^{59} +(-3.87298 + 6.70820i) q^{60} +(-11.1621 + 6.44446i) q^{61} -56.9955i q^{62} +(-1.81326 + 20.9216i) q^{63} +8.00000 q^{64} +(8.07846 + 13.9923i) q^{65} +(36.8795 + 21.2924i) q^{66} +(-47.0361 + 81.4689i) q^{67} +(4.59339 - 2.65199i) q^{68} +69.4578i q^{69} +(9.37137 + 20.0544i) q^{70} -11.5793 q^{71} +(4.24264 + 7.34847i) q^{72} +(-19.6320 - 11.3345i) q^{73} +(-22.9829 + 39.8076i) q^{74} +(-7.50000 + 4.33013i) q^{75} +5.08364i q^{76} +(110.252 - 51.5208i) q^{77} +17.6990 q^{78} +(12.0542 + 20.8785i) q^{79} +(7.74597 + 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-86.5502 + 49.9698i) q^{82} +111.664i q^{83} +(24.1581 + 2.09377i) q^{84} +5.93004 q^{85} +(-26.4268 - 45.7726i) q^{86} +(-70.5120 - 40.7101i) q^{87} +(24.5864 - 42.5848i) q^{88} +(-110.770 + 63.9533i) q^{89} +9.48683i q^{90} +(28.9773 - 41.4556i) q^{91} +80.2029 q^{92} +(-34.9025 - 60.4529i) q^{93} +(40.9658 + 23.6516i) q^{94} +(-2.84184 + 4.92221i) q^{95} +(8.48528 - 4.89898i) q^{96} -7.48256i q^{97} +(44.4565 - 53.1566i) q^{98} +52.1556 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9}+O(q^{10}) \) 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9	\( 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} + 48 q^{12} + 8 q^{14} - 32 q^{16} + 12 q^{17} - 72 q^{19} - 24 q^{21} - 48 q^{22} - 12 q^{23} + 40 q^{25} + 32 q^{28} + 72 q^{29} + 120 q^{31} + 12 q^{33} - 20 q^{35} - 96 q^{36} + 44 q^{37} - 72 q^{38} + 36 q^{39} - 24 q^{42} - 56 q^{43} - 8 q^{44} + 8 q^{46} - 24 q^{47} - 40 q^{49} - 12 q^{51} - 72 q^{52} + 32 q^{53} + 16 q^{56} + 144 q^{57} - 88 q^{58} + 132 q^{59} + 96 q^{61} + 60 q^{63} + 128 q^{64} + 20 q^{65} + 72 q^{66} - 164 q^{67} - 24 q^{68} - 136 q^{71} - 348 q^{73} - 112 q^{74} - 120 q^{75} + 96 q^{77} + 280 q^{79} - 72 q^{81} + 264 q^{82} - 24 q^{84} + 120 q^{85} - 88 q^{86} - 108 q^{87} + 48 q^{88} - 300 q^{89} - 272 q^{91} + 48 q^{92} - 120 q^{93} + 200 q^{95} + 384 q^{98} - 24 q^{99}+O(q^{100}) \) 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 + 48 * q^12 + 8 * q^14 - 32 * q^16 + 12 * q^17 - 72 * q^19 - 24 * q^21 - 48 * q^22 - 12 * q^23 + 40 * q^25 + 32 * q^28 + 72 * q^29 + 120 * q^31 + 12 * q^33 - 20 * q^35 - 96 * q^36 + 44 * q^37 - 72 * q^38 + 36 * q^39 - 24 * q^42 - 56 * q^43 - 8 * q^44 + 8 * q^46 - 24 * q^47 - 40 * q^49 - 12 * q^51 - 72 * q^52 + 32 * q^53 + 16 * q^56 + 144 * q^57 - 88 * q^58 + 132 * q^59 + 96 * q^61 + 60 * q^63 + 128 * q^64 + 20 * q^65 + 72 * q^66 - 164 * q^67 - 24 * q^68 - 136 * q^71 - 348 * q^73 - 112 * q^74 - 120 * q^75 + 96 * q^77 + 280 * q^79 - 72 * q^81 + 264 * q^82 - 24 * q^84 + 120 * q^85 - 88 * q^86 - 108 * q^87 + 48 * q^88 - 300 * q^89 - 272 * q^91 + 48 * q^92 - 120 * q^93 + 200 * q^95 + 384 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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