LMFDB - Embedded newform 210.3.l.b.127.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(43,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("210.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.l (of order $4$, 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 $\Q(i)$
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} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + \cdots + 2560000 $ x^16 - 8x^15 + 32x^14 + 152x^13 + 1954x^12 - 12664x^11 + 50336x^10 + 231896x^9 + 1093889x^8 - 4595248x^7 + 18837632x^6 + 86081152x^5 + 178889856x^4 + 70149120x^3 + 10035200x^2 - 7168000*x + 2560000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.8
Root			$-1.37832 - 1.37832i$ of defining polynomial
Character	$\chi$	$=$	210.127
Dual form			210.3.l.b.43.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.26896 - 2.60306i) q^{5} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.26896 - 2.60306i) q^{5} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-6.87203 - 1.66590i) q^{10} +11.5847 q^{11} +(2.44949 + 2.44949i) q^{12} +(-2.01552 + 2.01552i) q^{13} -3.74166i q^{14} +(2.04030 - 8.41648i) q^{15} -4.00000 q^{16} +(7.75862 + 7.75862i) q^{17} +(-3.00000 + 3.00000i) q^{18} -21.8455i q^{19} +(5.20613 + 8.53793i) q^{20} +4.58258 q^{21} +(-11.5847 - 11.5847i) q^{22} +(-7.41192 + 7.41192i) q^{23} -4.89898i q^{24} +(11.4481 - 22.2248i) q^{25} +4.03103 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-3.74166 + 3.74166i) q^{28} -31.0146i q^{29} +(-10.4568 + 6.37618i) q^{30} -11.5743 q^{31} +(4.00000 + 4.00000i) q^{32} +(14.1883 - 14.1883i) q^{33} -15.5172i q^{34} +(12.8564 + 3.11661i) q^{35} +6.00000 q^{36} +(-32.0546 - 32.0546i) q^{37} +(-21.8455 + 21.8455i) q^{38} +4.93699i q^{39} +(3.33180 - 13.7441i) q^{40} +39.6845 q^{41} +(-4.58258 - 4.58258i) q^{42} +(-19.3751 + 19.3751i) q^{43} +23.1694i q^{44} +(-7.80919 - 12.8069i) q^{45} +14.8238 q^{46} +(21.8753 + 21.8753i) q^{47} +(-4.89898 + 4.89898i) q^{48} +7.00000i q^{49} +(-33.6729 + 10.7767i) q^{50} +19.0047 q^{51} +(-4.03103 - 4.03103i) q^{52} +(-42.4043 + 42.4043i) q^{53} +7.34847i q^{54} +(49.4547 - 30.1557i) q^{55} +7.48331 q^{56} +(-26.7552 - 26.7552i) q^{57} +(-31.0146 + 31.0146i) q^{58} +89.0234i q^{59} +(16.8330 + 4.08060i) q^{60} +7.07420 q^{61} +(11.5743 + 11.5743i) q^{62} +(5.61249 - 5.61249i) q^{63} -8.00000i q^{64} +(-3.35765 + 13.8507i) q^{65} -28.3766 q^{66} +(15.6985 + 15.6985i) q^{67} +(-15.5172 + 15.5172i) q^{68} +18.1554i q^{69} +(-9.73978 - 15.9730i) q^{70} +133.620 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-92.3644 + 92.3644i) q^{73} +64.1091i q^{74} +(-13.1987 - 41.2407i) q^{75} +43.6910 q^{76} +(21.6730 + 21.6730i) q^{77} +(4.93699 - 4.93699i) q^{78} +126.569i q^{79} +(-17.0759 + 10.4123i) q^{80} -9.00000 q^{81} +(-39.6845 - 39.6845i) q^{82} +(-30.0489 + 30.0489i) q^{83} +9.16515i q^{84} +(53.3174 + 12.9251i) q^{85} +38.7501 q^{86} +(-37.9849 - 37.9849i) q^{87} +(23.1694 - 23.1694i) q^{88} +4.93527i q^{89} +(-4.99770 + 20.6161i) q^{90} -7.54137 q^{91} +(-14.8238 - 14.8238i) q^{92} +(-14.1755 + 14.1755i) q^{93} -43.7506i q^{94} +(-56.8652 - 93.2577i) q^{95} +9.79796 q^{96} +(-30.2346 - 30.2346i) q^{97} +(7.00000 - 7.00000i) q^{98} -34.7541i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8}+O(q^{10}) $ 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8	$ 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8} + 24 q^{10} + 8 q^{11} - 32 q^{13} - 12 q^{15} - 64 q^{16} + 56 q^{17} - 48 q^{18} - 16 q^{20} - 8 q^{22} + 24 q^{23} + 40 q^{25} + 64 q^{26} - 112 q^{31} + 64 q^{32} + 24 q^{33} + 28 q^{35} + 96 q^{36} - 152 q^{37} - 16 q^{40} + 24 q^{45} - 48 q^{46} + 80 q^{47} - 72 q^{50} - 72 q^{51} - 64 q^{52} + 48 q^{53} - 24 q^{55} + 24 q^{57} + 96 q^{58} + 24 q^{60} + 96 q^{61} + 112 q^{62} + 16 q^{65} - 48 q^{66} - 80 q^{67} - 112 q^{68} + 536 q^{71} - 96 q^{72} - 288 q^{75} - 168 q^{77} - 48 q^{78} + 64 q^{80} - 144 q^{81} - 256 q^{83} + 40 q^{85} - 144 q^{87} + 16 q^{88} + 24 q^{90} + 48 q^{92} + 192 q^{93} + 360 q^{95} + 688 q^{97} + 112 q^{98}+O(q^{100}) $ 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8 + 24 * q^10 + 8 * q^11 - 32 * q^13 - 12 * q^15 - 64 * q^16 + 56 * q^17 - 48 * q^18 - 16 * q^20 - 8 * q^22 + 24 * q^23 + 40 * q^25 + 64 * q^26 - 112 * q^31 + 64 * q^32 + 24 * q^33 + 28 * q^35 + 96 * q^36 - 152 * q^37 - 16 * q^40 + 24 * q^45 - 48 * q^46 + 80 * q^47 - 72 * q^50 - 72 * q^51 - 64 * q^52 + 48 * q^53 - 24 * q^55 + 24 * q^57 + 96 * q^58 + 24 * q^60 + 96 * q^61 + 112 * q^62 + 16 * q^65 - 48 * q^66 - 80 * q^67 - 112 * q^68 + 536 * q^71 - 96 * q^72 - 288 * q^75 - 168 * q^77 - 48 * q^78 + 64 * q^80 - 144 * q^81 - 256 * q^83 + 40 * q^85 - 144 * q^87 + 16 * q^88 + 24 * q^90 + 48 * q^92 + 192 * q^93 + 360 * q^95 + 688 * q^97 + 112 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$			2.00000i			0.500000i
$5$	4.26896	−	2.60306i	0.853793	−	0.520613i
$5$	4.26896	−	2.60306i	0.853793	−	0.520613i
$6$	−2.44949			−0.408248
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	−6.87203	−	1.66590i	−0.687203	−	0.166590i
$11$	11.5847			1.05316			0.526578	−	0.850127i	$-0.323475\pi$
$11$	11.5847			1.05316			0.526578	+	0.850127i	$0.323475\pi$
$12$	2.44949	+	2.44949i	0.204124	+	0.204124i
$13$	−2.01552	+	2.01552i	−0.155040	+	0.155040i	−0.780365	−	0.625325i	$-0.784966\pi$
$13$	−2.01552	+	2.01552i	−0.155040	+	0.155040i	0.625325	+	0.780365i	$0.284966\pi$
$14$		−	3.74166i		−	0.267261i
$15$	2.04030	−	8.41648i	0.136020	−	0.561099i
$16$	−4.00000			−0.250000
$17$	7.75862	+	7.75862i	0.456389	+	0.456389i	0.897468	−	0.441079i	$-0.145404\pi$
$17$	7.75862	+	7.75862i	0.456389	+	0.456389i	−0.441079	+	0.897468i	$0.645404\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$		−	21.8455i		−	1.14976i	−0.818237	−	0.574882i	$-0.805048\pi$
$19$		−	21.8455i		−	1.14976i	0.818237	−	0.574882i	$-0.194952\pi$
$20$	5.20613	+	8.53793i	0.260306	+	0.426896i
$21$	4.58258			0.218218
$22$	−11.5847	−	11.5847i	−0.526578	−	0.526578i
$23$	−7.41192	+	7.41192i	−0.322257	+	0.322257i	−0.849632	−	0.527375i	$-0.823176\pi$
$23$	−7.41192	+	7.41192i	−0.322257	+	0.322257i	0.527375	+	0.849632i	$0.323176\pi$
$24$		−	4.89898i		−	0.204124i
$25$	11.4481	−	22.2248i	0.457924	−	0.888991i
$26$	4.03103			0.155040
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	−3.74166	+	3.74166i	−0.133631	+	0.133631i
$29$		−	31.0146i		−	1.06947i	−0.845021	−	0.534734i	$-0.820412\pi$
$29$		−	31.0146i		−	1.06947i	0.845021	−	0.534734i	$-0.179588\pi$
$30$	−10.4568	+	6.37618i	−0.348559	+	0.212539i
$31$	−11.5743			−0.373364			−0.186682	−	0.982420i	$-0.559773\pi$
$31$	−11.5743			−0.373364			−0.186682	+	0.982420i	$0.559773\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	14.1883	−	14.1883i	0.429949	−	0.429949i
$34$		−	15.5172i		−	0.456389i
$35$	12.8564	+	3.11661i	0.367325	+	0.0890461i
$36$	6.00000			0.166667
$37$	−32.0546	−	32.0546i	−0.866340	−	0.866340i	0.125725	−	0.992065i	$-0.459874\pi$
$37$	−32.0546	−	32.0546i	−0.866340	−	0.866340i	−0.992065	+	0.125725i	$0.959874\pi$
$38$	−21.8455	+	21.8455i	−0.574882	+	0.574882i
$39$			4.93699i			0.126589i
$40$	3.33180	−	13.7441i	0.0832950	−	0.343601i
$41$	39.6845			0.967914			0.483957	−	0.875092i	$-0.339199\pi$
$41$	39.6845			0.967914			0.483957	+	0.875092i	$0.339199\pi$
$42$	−4.58258	−	4.58258i	−0.109109	−	0.109109i
$43$	−19.3751	+	19.3751i	−0.450583	+	0.450583i	−0.895548	−	0.444965i	$-0.853216\pi$
$43$	−19.3751	+	19.3751i	−0.450583	+	0.450583i	0.444965	+	0.895548i	$0.353216\pi$
$44$			23.1694i			0.526578i
$45$	−7.80919	−	12.8069i	−0.173538	−	0.284598i
$46$	14.8238			0.322257
$47$	21.8753	+	21.8753i	0.465432	+	0.465432i	0.900431	−	0.434999i	$-0.143251\pi$
$47$	21.8753	+	21.8753i	0.465432	+	0.465432i	−0.434999	+	0.900431i	$0.643251\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$			7.00000i			0.142857i
$50$	−33.6729	+	10.7767i	−0.673458	+	0.215533i
$51$	19.0047			0.372640
$52$	−4.03103	−	4.03103i	−0.0775199	−	0.0775199i
$53$	−42.4043	+	42.4043i	−0.800081	+	0.800081i	−0.983108	−	0.183027i	$-0.941410\pi$
$53$	−42.4043	+	42.4043i	−0.800081	+	0.800081i	0.183027	+	0.983108i	$0.441410\pi$
$54$			7.34847i			0.136083i
$55$	49.4547	−	30.1557i	0.899176	−	0.548286i
$56$	7.48331			0.133631
$57$	−26.7552	−	26.7552i	−0.469389	−	0.469389i
$58$	−31.0146	+	31.0146i	−0.534734	+	0.534734i
$59$			89.0234i			1.50887i	0.656374	+	0.754435i	$0.272089\pi$
$59$			89.0234i			1.50887i	−0.656374	+	0.754435i	$0.727911\pi$
$60$	16.8330	+	4.08060i	0.280549	+	0.0680101i
$61$	7.07420			0.115970			0.0579852	−	0.998317i	$-0.481532\pi$
$61$	7.07420			0.115970			0.0579852	+	0.998317i	$0.481532\pi$
$62$	11.5743	+	11.5743i	0.186682	+	0.186682i
$63$	5.61249	−	5.61249i	0.0890871	−	0.0890871i
$64$		−	8.00000i		−	0.125000i
$65$	−3.35765	+	13.8507i	−0.0516561	+	0.213088i
$66$	−28.3766			−0.429949
$67$	15.6985	+	15.6985i	0.234306	+	0.234306i	0.814487	−	0.580181i	$-0.197018\pi$
$67$	15.6985	+	15.6985i	0.234306	+	0.234306i	−0.580181	+	0.814487i	$0.697018\pi$
$68$	−15.5172	+	15.5172i	−0.228195	+	0.228195i
$69$			18.1554i			0.263122i
$70$	−9.73978	−	15.9730i	−0.139140	−	0.228186i
$71$	133.620			1.88197			0.940986	−	0.338447i	$-0.109901\pi$
$71$	133.620			1.88197			0.940986	+	0.338447i	$0.109901\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	−92.3644	+	92.3644i	−1.26527	+	1.26527i	−0.316760	+	0.948506i	$0.602595\pi$
$73$	−92.3644	+	92.3644i	−1.26527	+	1.26527i	−0.948506	+	0.316760i	$0.897405\pi$
$74$			64.1091i			0.866340i
$75$	−13.1987	−	41.2407i	−0.175982	−	0.549876i
$76$	43.6910			0.574882
$77$	21.6730	+	21.6730i	0.281468	+	0.281468i
$78$	4.93699	−	4.93699i	0.0632947	−	0.0632947i
$79$			126.569i			1.60214i	0.598569	+	0.801071i	$0.295736\pi$
$79$			126.569i			1.60214i	−0.598569	+	0.801071i	$0.704264\pi$
$80$	−17.0759	+	10.4123i	−0.213448	+	0.130153i
$81$	−9.00000			−0.111111
$82$	−39.6845	−	39.6845i	−0.483957	−	0.483957i
$83$	−30.0489	+	30.0489i	−0.362035	+	0.362035i	−0.864562	−	0.502527i	$-0.832404\pi$
$83$	−30.0489	+	30.0489i	−0.362035	+	0.362035i	0.502527	+	0.864562i	$0.332404\pi$
$84$			9.16515i			0.109109i
$85$	53.3174	+	12.9251i	0.627264	+	0.152060i
$86$	38.7501			0.450583
$87$	−37.9849	−	37.9849i	−0.436608	−	0.436608i
$88$	23.1694	−	23.1694i	0.263289	−	0.263289i
$89$			4.93527i			0.0554525i	0.999616	+	0.0277263i	$0.00882667\pi$
$89$			4.93527i			0.0554525i	−0.999616	+	0.0277263i	$0.991173\pi$
$90$	−4.99770	+	20.6161i	−0.0555300	+	0.229068i
$91$	−7.54137			−0.0828723
$92$	−14.8238	−	14.8238i	−0.161129	−	0.161129i
$93$	−14.1755	+	14.1755i	−0.152425	+	0.152425i
$94$		−	43.7506i		−	0.465432i
$95$	−56.8652	−	93.2577i	−0.598582	−	0.981659i
$96$	9.79796			0.102062
$97$	−30.2346	−	30.2346i	−0.311697	−	0.311697i	0.533870	−	0.845567i	$-0.320737\pi$
$97$	−30.2346	−	30.2346i	−0.311697	−	0.311697i	−0.845567	+	0.533870i	$0.820737\pi$
$98$	7.00000	−	7.00000i	0.0714286	−	0.0714286i
$99$		−	34.7541i		−	0.351052i
$100$	44.4496	+	22.8962i	0.444496	+	0.228962i
$101$	−176.319			−1.74573			−0.872867	−	0.487958i	$-0.837742\pi$
$101$	−176.319			−1.74573			−0.872867	+	0.487958i	$0.837742\pi$
$102$	−19.0047	−	19.0047i	−0.186320	−	0.186320i
$103$	−61.1510	+	61.1510i	−0.593699	+	0.593699i	−0.938629	−	0.344930i	$-0.887903\pi$
$103$	−61.1510	+	61.1510i	−0.593699	+	0.593699i	0.344930	+	0.938629i	$0.387903\pi$
$104$			8.06207i			0.0775199i
$105$	19.5629	−	11.9287i	0.186313	−	0.113607i
$106$	84.8086			0.800081
$107$	−0.766043	−	0.766043i	−0.00715928	−	0.00715928i	0.703518	−	0.710677i	$-0.251611\pi$
$107$	−0.766043	−	0.766043i	−0.00715928	−	0.00715928i	−0.710677	+	0.703518i	$0.751611\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$			26.6885i			0.244848i	0.992478	+	0.122424i	$0.0390668\pi$
$109$			26.6885i			0.244848i	−0.992478	+	0.122424i	$0.960933\pi$
$110$	−79.6104	−	19.2990i	−0.723731	−	0.175445i
$111$	−78.5173			−0.707363
$112$	−7.48331	−	7.48331i	−0.0668153	−	0.0668153i
$113$	133.108	−	133.108i	1.17795	−	1.17795i	0.197680	−	0.980267i	$-0.436659\pi$
$113$	133.108	−	133.108i	1.17795	−	1.17795i	0.980267	−	0.197680i	$-0.0633406\pi$
$114$			53.5103i			0.469389i
$115$	−12.3475	+	50.9349i	−0.107370	+	0.442912i
$116$	62.0291			0.534734
$117$	6.04655	+	6.04655i	0.0516799	+	0.0516799i
$118$	89.0234	−	89.0234i	0.754435	−	0.754435i
$119$			29.0301i			0.243950i
$120$	−12.7524	−	20.9136i	−0.106270	−	0.174280i
$121$	13.2054			0.109136
$122$	−7.07420	−	7.07420i	−0.0579852	−	0.0579852i
$123$	48.6034	−	48.6034i	0.395149	−	0.395149i
$124$		−	23.1486i		−	0.186682i
$125$	−8.98097	−	124.677i	−0.0718477	−	0.997416i
$126$	−11.2250			−0.0890871
$127$	59.4171	+	59.4171i	0.467851	+	0.467851i	0.901218	−	0.433367i	$-0.142675\pi$
$127$	59.4171	+	59.4171i	0.467851	+	0.467851i	−0.433367	+	0.901218i	$0.642675\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$			47.4590i			0.367899i
$130$	17.2083	−	10.4930i	0.132372	−	0.0807157i
$131$	51.2605			0.391302			0.195651	−	0.980674i	$-0.437318\pi$
$131$	51.2605			0.391302			0.195651	+	0.980674i	$0.437318\pi$
$132$	28.3766	+	28.3766i	0.214974	+	0.214974i
$133$	40.8692	−	40.8692i	0.307287	−	0.307287i
$134$		−	31.3970i		−	0.234306i
$135$	−25.2494	−	6.12091i	−0.187033	−	0.0453400i
$136$	31.0345			0.228195
$137$	−17.6526	−	17.6526i	−0.128851	−	0.128851i	0.639740	−	0.768591i	$-0.279042\pi$
$137$	−17.6526	−	17.6526i	−0.128851	−	0.128851i	−0.768591	+	0.639740i	$0.779042\pi$
$138$	18.1554	−	18.1554i	0.131561	−	0.131561i
$139$		−	206.210i		−	1.48353i	−0.670662	−	0.741763i	$-0.733990\pi$
$139$		−	206.210i		−	1.48353i	0.670662	−	0.741763i	$-0.266010\pi$
$140$	−6.23323	+	25.7128i	−0.0445230	+	0.183663i
$141$	53.5834			0.380024
$142$	−133.620	−	133.620i	−0.940986	−	0.940986i
$143$	−23.3492	+	23.3492i	−0.163281	+	0.163281i
$144$			12.0000i			0.0833333i
$145$	−80.7329	−	132.400i	−0.556779	−	0.913104i
$146$	184.729			1.26527
$147$	8.57321	+	8.57321i	0.0583212	+	0.0583212i
$148$	64.1091	−	64.1091i	0.433170	−	0.433170i
$149$		−	256.780i		−	1.72336i	−0.507456	−	0.861678i	$-0.669414\pi$
$149$		−	256.780i		−	1.72336i	0.507456	−	0.861678i	$-0.330586\pi$
$150$	−28.0420	+	54.4394i	−0.186947	+	0.362929i
$151$	255.541			1.69232			0.846161	−	0.532928i	$-0.178908\pi$
$151$	255.541			1.69232			0.846161	+	0.532928i	$0.178908\pi$
$152$	−43.6910	−	43.6910i	−0.287441	−	0.287441i
$153$	23.2759	−	23.2759i	0.152130	−	0.152130i
$154$		−	43.3460i		−	0.281468i
$155$	−49.4102	+	30.1286i	−0.318776	+	0.194378i
$156$	−9.87398			−0.0632947
$157$	−69.5363	−	69.5363i	−0.442906	−	0.442906i	0.450081	−	0.892988i	$-0.351395\pi$
$157$	−69.5363	−	69.5363i	−0.442906	−	0.442906i	−0.892988	+	0.450081i	$0.851395\pi$
$158$	126.569	−	126.569i	0.801071	−	0.801071i
$159$			103.869i			0.653263i
$160$	27.4881	+	6.66360i	0.171801	+	0.0416475i
$161$	−27.7328			−0.172254
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	−220.179	+	220.179i	−1.35079	+	1.35079i	−0.466020	+	0.884774i	$0.654313\pi$
$163$	−220.179	+	220.179i	−1.35079	+	1.35079i	−0.884774	+	0.466020i	$0.845687\pi$
$164$			79.3690i			0.483957i
$165$	23.6363	−	97.5025i	0.143250	−	0.590924i
$166$	60.0978			0.362035
$167$	27.6262	+	27.6262i	0.165426	+	0.165426i	0.784966	−	0.619539i	$-0.212681\pi$
$167$	27.6262	+	27.6262i	0.165426	+	0.165426i	−0.619539	+	0.784966i	$0.712681\pi$
$168$	9.16515	−	9.16515i	0.0545545	−	0.0545545i
$169$			160.875i			0.951925i
$170$	−40.3924	−	66.2425i	−0.237602	−	0.389662i
$171$	−65.5365			−0.383254
$172$	−38.7501	−	38.7501i	−0.225291	−	0.225291i
$173$	−128.172	+	128.172i	−0.740876	+	0.740876i	−0.972747	−	0.231870i	$-0.925516\pi$
$173$	−128.172	+	128.172i	−0.740876	+	0.740876i	0.231870	+	0.972747i	$0.425516\pi$
$174$			75.9698i			0.436608i
$175$	62.9962	−	20.1613i	0.359978	−	0.115207i
$176$	−46.3388			−0.263289
$177$	109.031	+	109.031i	0.615994	+	0.615994i
$178$	4.93527	−	4.93527i	0.0277263	−	0.0277263i
$179$			65.6591i			0.366811i	0.983037	+	0.183405i	$0.0587121\pi$
$179$			65.6591i			0.366811i	−0.983037	+	0.183405i	$0.941288\pi$
$180$	25.6138	−	15.6184i	0.142299	−	0.0867688i
$181$	−321.692			−1.77730			−0.888651	−	0.458584i	$-0.848357\pi$
$181$	−321.692			−1.77730			−0.888651	+	0.458584i	$0.848357\pi$
$182$	7.54137	+	7.54137i	0.0414361	+	0.0414361i
$183$	8.66409	−	8.66409i	0.0473447	−	0.0473447i
$184$			29.6477i			0.161129i
$185$	−220.280	−	53.3997i	−1.19070	−	0.288647i
$186$	28.3511			0.152425
$187$	89.8813	+	89.8813i	0.480649	+	0.480649i
$188$	−43.7506	+	43.7506i	−0.232716	+	0.232716i
$189$		−	13.7477i		−	0.0727393i
$190$	−36.3924	+	150.123i	−0.191539	+	0.790121i
$191$	−146.509			−0.767061			−0.383531	−	0.923528i	$-0.625292\pi$
$191$	−146.509			−0.767061			−0.383531	+	0.923528i	$0.625292\pi$
$192$	−9.79796	−	9.79796i	−0.0510310	−	0.0510310i
$193$	11.1318	−	11.1318i	0.0576775	−	0.0576775i	−0.677680	−	0.735357i	$-0.737014\pi$
$193$	11.1318	−	11.1318i	0.0576775	−	0.0576775i	0.735357	+	0.677680i	$0.237014\pi$
$194$			60.4692i			0.311697i
$195$	12.8513	+	21.0758i	0.0659041	+	0.108081i
$196$	−14.0000			−0.0714286
$197$	22.4067	+	22.4067i	0.113740	+	0.113740i	0.761686	−	0.647946i	$-0.224372\pi$
$197$	22.4067	+	22.4067i	0.113740	+	0.113740i	−0.647946	+	0.761686i	$0.724372\pi$
$198$	−34.7541	+	34.7541i	−0.175526	+	0.175526i
$199$			163.016i			0.819177i	0.912270	+	0.409589i	$0.134328\pi$
$199$			163.016i			0.819177i	−0.912270	+	0.409589i	$0.865672\pi$
$200$	−21.5533	−	67.3458i	−0.107767	−	0.336729i
$201$	38.4533			0.191310
$202$	176.319	+	176.319i	0.872867	+	0.872867i
$203$	58.0229	−	58.0229i	0.285827	−	0.285827i
$204$			38.0093i			0.186320i
$205$	169.412	−	103.301i	0.826398	−	0.503909i
$206$	122.302			0.593699
$207$	22.2357	+	22.2357i	0.107419	+	0.107419i
$208$	8.06207	−	8.06207i	0.0387599	−	0.0387599i
$209$		−	253.074i		−	1.21088i
$210$	−31.4916	−	7.63411i	−0.149960	−	0.0363529i
$211$	266.247			1.26184			0.630918	−	0.775850i	$-0.282678\pi$
$211$	266.247			1.26184			0.630918	+	0.775850i	$0.282678\pi$
$212$	−84.8086	−	84.8086i	−0.400040	−	0.400040i
$213$	163.650	−	163.650i	0.768312	−	0.768312i
$214$			1.53209i			0.00715928i
$215$	−32.2769	+	133.146i	−0.150125	+	0.619284i
$216$	−14.6969			−0.0680414
$217$	−21.6535	−	21.6535i	−0.0997857	−	0.0997857i
$218$	26.6885	−	26.6885i	0.122424	−	0.122424i
$219$			226.246i			1.03309i
$220$	60.3115	+	98.9094i	0.274143	+	0.449588i
$221$	−31.2753			−0.141517
$222$	78.5173	+	78.5173i	0.353682	+	0.353682i
$223$	−313.209	+	313.209i	−1.40453	+	1.40453i	−0.619635	+	0.784890i	$0.712719\pi$
$223$	−313.209	+	313.209i	−1.40453	+	1.40453i	−0.784890	+	0.619635i	$0.787281\pi$
$224$			14.9666i			0.0668153i
$225$	−66.6743	−	34.3443i	−0.296330	−	0.152641i
$226$	−266.216			−1.17795
$227$	100.753	+	100.753i	0.443847	+	0.443847i	0.893303	−	0.449455i	$-0.148382\pi$
$227$	100.753	+	100.753i	0.443847	+	0.443847i	−0.449455	+	0.893303i	$0.648382\pi$
$228$	53.5103	−	53.5103i	0.234694	−	0.234694i
$229$		−	120.710i		−	0.527119i	−0.964643	−	0.263559i	$-0.915104\pi$
$229$		−	120.710i		−	0.527119i	0.964643	−	0.263559i	$-0.0848965\pi$
$230$	63.2824	−	38.5874i	0.275141	−	0.167771i
$231$	53.0878			0.229817
$232$	−62.0291	−	62.0291i	−0.267367	−	0.267367i
$233$	200.874	−	200.874i	0.862119	−	0.862119i	−0.129465	−	0.991584i	$-0.541326\pi$
$233$	200.874	−	200.874i	0.862119	−	0.862119i	0.991584	+	0.129465i	$0.0413260\pi$
$234$		−	12.0931i		−	0.0516799i
$235$	150.328	+	36.4421i	0.639693	+	0.155073i
$236$	−178.047			−0.754435
$237$	155.015	+	155.015i	0.654072	+	0.654072i
$238$	29.0301	−	29.0301i	0.121975	−	0.121975i
$239$		−	288.534i		−	1.20725i	−0.797267	−	0.603627i	$-0.793722\pi$
$239$		−	288.534i		−	1.20725i	0.797267	−	0.603627i	$-0.206278\pi$
$240$	−8.16121	+	33.6659i	−0.0340050	+	0.140275i
$241$	−80.3054			−0.333218			−0.166609	−	0.986023i	$-0.553282\pi$
$241$	−80.3054			−0.333218			−0.166609	+	0.986023i	$0.553282\pi$
$242$	−13.2054	−	13.2054i	−0.0545679	−	0.0545679i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$			14.1484i			0.0579852i
$245$	18.2215	+	29.8827i	0.0743733	+	0.121970i
$246$	−97.2067			−0.395149
$247$	44.0300	+	44.0300i	0.178259	+	0.178259i
$248$	−23.1486	+	23.1486i	−0.0933410	+	0.0933410i
$249$			73.6045i			0.295600i
$250$	−115.696	+	133.658i	−0.462784	+	0.534632i
$251$	−238.919			−0.951868			−0.475934	−	0.879481i	$-0.657890\pi$
$251$	−238.919			−0.951868			−0.475934	+	0.879481i	$0.657890\pi$
$252$	11.2250	+	11.2250i	0.0445435	+	0.0445435i
$253$	−85.8649	+	85.8649i	−0.339387	+	0.339387i
$254$		−	118.834i		−	0.467851i
$255$	81.1302	−	49.4703i	0.318158	−	0.194001i
$256$	16.0000			0.0625000
$257$	357.876	+	357.876i	1.39251	+	1.39251i	0.819654	+	0.572859i	$0.194166\pi$
$257$	357.876	+	357.876i	1.39251	+	1.39251i	0.572859	+	0.819654i	$0.305834\pi$
$258$	47.4590	−	47.4590i	0.183950	−	0.183950i
$259$		−	119.937i		−	0.463078i
$260$	−27.7014	−	6.71530i	−0.106544	−	0.0258281i
$261$	−93.0437			−0.356489
$262$	−51.2605	−	51.2605i	−0.195651	−	0.195651i
$263$	−73.5388	+	73.5388i	−0.279615	+	0.279615i	−0.832955	−	0.553340i	$-0.813353\pi$
$263$	−73.5388	+	73.5388i	−0.279615	+	0.279615i	0.553340	+	0.832955i	$0.313353\pi$
$264$		−	56.7532i		−	0.214974i
$265$	−70.6413	+	291.403i	−0.266571	+	1.09964i
$266$	−81.7384			−0.307287
$267$	6.04445	+	6.04445i	0.0226384	+	0.0226384i
$268$	−31.3970	+	31.3970i	−0.117153	+	0.117153i
$269$			63.1334i			0.234697i	0.993091	+	0.117348i	$0.0374394\pi$
$269$			63.1334i			0.234697i	−0.993091	+	0.117348i	$0.962561\pi$
$270$	19.1285	+	31.3704i	0.0708464	+	0.116186i
$271$	−66.1173			−0.243975			−0.121988	−	0.992532i	$-0.538927\pi$
$271$	−66.1173			−0.243975			−0.121988	+	0.992532i	$0.538927\pi$
$272$	−31.0345	−	31.0345i	−0.114097	−	0.114097i
$273$	−9.23626	+	9.23626i	−0.0338325	+	0.0338325i
$274$			35.3053i			0.128851i
$275$	132.623	−	257.468i	0.482265	−	0.936246i
$276$	−36.3108			−0.131561
$277$	−268.807	−	268.807i	−0.970423	−	0.970423i	0.0291522	−	0.999575i	$-0.490719\pi$
$277$	−268.807	−	268.807i	−0.970423	−	0.970423i	−0.999575	+	0.0291522i	$0.990719\pi$
$278$	−206.210	+	206.210i	−0.741763	+	0.741763i
$279$			34.7229i			0.124455i
$280$	31.9460	−	19.4796i	0.114093	−	0.0695698i
$281$	−108.591			−0.386445			−0.193222	−	0.981155i	$-0.561894\pi$
$281$	−108.591			−0.386445			−0.193222	+	0.981155i	$0.561894\pi$
$282$	−53.5834	−	53.5834i	−0.190012	−	0.190012i
$283$	208.690	−	208.690i	0.737419	−	0.737419i	−0.234658	−	0.972078i	$-0.575397\pi$
$283$	208.690	−	208.690i	0.737419	−	0.737419i	0.972078	+	0.234658i	$0.0753972\pi$
$284$			267.240i			0.940986i
$285$	−183.862	−	44.5714i	−0.645131	−	0.156391i
$286$	46.6984			0.163281
$287$	74.2429	+	74.2429i	0.258686	+	0.258686i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$		−	168.608i		−	0.583418i
$290$	−51.6671	+	213.133i	−0.178163	+	0.734941i
$291$	−74.0593			−0.254499
$292$	−184.729	−	184.729i	−0.632633	−	0.632633i
$293$	315.640	−	315.640i	1.07727	−	1.07727i	0.0805153	−	0.996753i	$-0.474343\pi$
$293$	315.640	−	315.640i	1.07727	−	1.07727i	0.996753	−	0.0805153i	$-0.0256566\pi$
$294$		−	17.1464i		−	0.0583212i
$295$	231.734	+	380.038i	0.785538	+	1.28826i
$296$	−128.218			−0.433170
$297$	−42.5649	−	42.5649i	−0.143316	−	0.143316i
$298$	−256.780	+	256.780i	−0.861678	+	0.861678i
$299$		−	29.8777i		−	0.0999254i
$300$	82.4814	−	26.3973i	0.274938	−	0.0879911i
$301$	−72.4948			−0.240847
$302$	−255.541	−	255.541i	−0.846161	−	0.846161i
$303$	−215.946	+	215.946i	−0.712693	+	0.712693i
$304$			87.3820i			0.287441i
$305$	30.1995	−	18.4146i	0.0990147	−	0.0603757i
$306$	−46.5517			−0.152130
$307$	115.484	+	115.484i	0.376169	+	0.376169i	0.869718	−	0.493549i	$-0.164301\pi$
$307$	115.484	+	115.484i	0.376169	+	0.376169i	−0.493549	+	0.869718i	$0.664301\pi$
$308$	−43.3460	+	43.3460i	−0.140734	+	0.140734i
$309$			149.789i			0.484753i
$310$	79.5388	+	19.2816i	0.256577	+	0.0621987i
$311$	−489.397			−1.57362			−0.786812	−	0.617192i	$-0.788270\pi$
$311$	−489.397			−1.57362			−0.786812	+	0.617192i	$0.788270\pi$
$312$	9.87398	+	9.87398i	0.0316474	+	0.0316474i
$313$	95.5816	−	95.5816i	0.305372	−	0.305372i	−0.537739	−	0.843111i	$-0.680721\pi$
$313$	95.5816	−	95.5816i	0.305372	−	0.305372i	0.843111	+	0.537739i	$0.180721\pi$
$314$			139.073i			0.442906i
$315$	9.34984	−	38.5692i	0.0296820	−	0.122442i
$316$	−253.138			−0.801071
$317$	368.537	+	368.537i	1.16258	+	1.16258i	0.983909	+	0.178668i	$0.0571787\pi$
$317$	368.537	+	368.537i	1.16258	+	1.16258i	0.178668	+	0.983909i	$0.442821\pi$
$318$	103.869	−	103.869i	0.326632	−	0.326632i
$319$		−	359.295i		−	1.12632i
$320$	−20.8245	−	34.1517i	−0.0650766	−	0.106724i
$321$	−1.87641			−0.00584553
$322$	27.7328	+	27.7328i	0.0861269	+	0.0861269i
$323$	169.491	−	169.491i	0.524740	−	0.524740i
$324$		−	18.0000i		−	0.0555556i
$325$	21.7206	+	67.8683i	0.0668325	+	0.208825i
$326$	440.359			1.35079
$327$	32.6866	+	32.6866i	0.0999589	+	0.0999589i
$328$	79.3690	−	79.3690i	0.241979	−	0.241979i
$329$			81.8499i			0.248784i
$330$	−121.139	+	73.8662i	−0.367087	+	0.223837i
$331$	591.256			1.78627			0.893135	−	0.449788i	$-0.148501\pi$
$331$	591.256			1.78627			0.893135	+	0.449788i	$0.148501\pi$
$332$	−60.0978	−	60.0978i	−0.181017	−	0.181017i
$333$	−96.1637	+	96.1637i	−0.288780	+	0.288780i
$334$		−	55.2524i		−	0.165426i
$335$	107.881	+	26.1521i	0.322031	+	0.0780660i
$336$	−18.3303			−0.0545545
$337$	−148.222	−	148.222i	−0.439827	−	0.439827i	0.452127	−	0.891954i	$-0.350666\pi$
$337$	−148.222	−	148.222i	−0.439827	−	0.439827i	−0.891954	+	0.452127i	$0.850666\pi$
$338$	160.875	−	160.875i	0.475963	−	0.475963i
$339$		−	326.047i		−	0.961789i
$340$	−25.8502	+	106.635i	−0.0760299	+	0.313632i
$341$	−134.085			−0.393210
$342$	65.5365	+	65.5365i	0.191627	+	0.191627i
$343$	−13.0958	+	13.0958i	−0.0381802	+	0.0381802i
$344$			77.5002i			0.225291i
$345$	47.2597	+	77.5048i	0.136985	+	0.224652i
$346$	256.343			0.740876
$347$	−299.896	−	299.896i	−0.864252	−	0.864252i	0.127577	−	0.991829i	$-0.459280\pi$
$347$	−299.896	−	299.896i	−0.864252	−	0.864252i	−0.991829	+	0.127577i	$0.959280\pi$
$348$	75.9698	−	75.9698i	0.218304	−	0.218304i
$349$		−	421.152i		−	1.20674i	−0.797462	−	0.603369i	$-0.793824\pi$
$349$		−	421.152i		−	1.20674i	0.797462	−	0.603369i	$-0.206176\pi$
$350$	−83.1575	−	42.8349i	−0.237593	−	0.122385i
$351$	14.8110			0.0421965
$352$	46.3388	+	46.3388i	0.131644	+	0.131644i
$353$	310.590	−	310.590i	0.879858	−	0.879858i	−0.113662	−	0.993519i	$-0.536258\pi$
$353$	310.590	−	310.590i	0.879858	−	0.879858i	0.993519	+	0.113662i	$0.0362581\pi$
$354$		−	218.062i		−	0.615994i
$355$	570.419	−	347.821i	1.60681	−	0.979779i
$356$	−9.87055			−0.0277263
$357$	35.5545	+	35.5545i	0.0995923	+	0.0995923i
$358$	65.6591	−	65.6591i	0.183405	−	0.183405i
$359$		−	223.309i		−	0.622030i	−0.950405	−	0.311015i	$-0.899331\pi$
$359$		−	223.309i		−	0.622030i	0.950405	−	0.311015i	$-0.100669\pi$
$360$	−41.2322	−	9.99540i	−0.114534	−	0.0277650i
$361$	−116.226			−0.321955
$362$	321.692	+	321.692i	0.888651	+	0.888651i
$363$	16.1733	−	16.1733i	0.0445545	−	0.0445545i
$364$		−	15.0827i		−	0.0414361i
$365$	−153.870	+	634.731i	−0.421561	+	1.73899i
$366$	−17.3282			−0.0473447
$367$	−262.093	−	262.093i	−0.714149	−	0.714149i	0.253251	−	0.967401i	$-0.418500\pi$
$367$	−262.093	−	262.093i	−0.714149	−	0.714149i	−0.967401	+	0.253251i	$0.918500\pi$
$368$	29.6477	−	29.6477i	0.0805643	−	0.0805643i
$369$		−	119.053i		−	0.322638i
$370$	166.880	+	273.680i	0.451028	+	0.739675i
$371$	−158.662			−0.427661
$372$	−28.3511	−	28.3511i	−0.0762126	−	0.0762126i
$373$	56.2361	−	56.2361i	0.150767	−	0.150767i	−0.627694	−	0.778461i	$-0.716001\pi$
$373$	56.2361	−	56.2361i	0.150767	−	0.150767i	0.778461	+	0.627694i	$0.216001\pi$
$374$		−	179.763i		−	0.480649i
$375$	−163.697	−	141.698i	−0.436525	−	0.377862i
$376$	87.5012			0.232716
$377$	62.5104	+	62.5104i	0.165810	+	0.165810i
$378$	−13.7477	+	13.7477i	−0.0363696	+	0.0363696i
$379$		−	179.724i		−	0.474206i	−0.971485	−	0.237103i	$-0.923802\pi$
$379$		−	179.724i		−	0.474206i	0.971485	−	0.237103i	$-0.0761979\pi$
$380$	186.515	−	113.730i	0.490830	−	0.299291i
$381$	145.541			0.381999
$382$	146.509	+	146.509i	0.383531	+	0.383531i
$383$	−285.701	+	285.701i	−0.745956	+	0.745956i	−0.973717	−	0.227761i	$-0.926859\pi$
$383$	−285.701	+	285.701i	−0.745956	+	0.745956i	0.227761	+	0.973717i	$0.426859\pi$
$384$			19.5959i			0.0510310i
$385$	148.937	+	36.1050i	0.386851	+	0.0937793i
$386$	−22.2635			−0.0576775
$387$	58.1252	+	58.1252i	0.150194	+	0.150194i
$388$	60.4692	−	60.4692i	0.155848	−	0.155848i
$389$			728.870i			1.87370i	0.349730	+	0.936851i	$0.386273\pi$
$389$			728.870i			1.87370i	−0.349730	+	0.936851i	$0.613727\pi$
$390$	8.22453	−	33.9271i	0.0210885	−	0.0869926i
$391$	−115.012			−0.294149
$392$	14.0000	+	14.0000i	0.0357143	+	0.0357143i
$393$	62.7811	−	62.7811i	0.159748	−	0.159748i
$394$		−	44.8135i		−	0.113740i
$395$	329.468	+	540.319i	0.834096	+	1.36790i
$396$	69.5082			0.175526
$397$	19.6549	+	19.6549i	0.0495086	+	0.0495086i	0.731428	−	0.681919i	$-0.238854\pi$
$397$	19.6549	+	19.6549i	0.0495086	+	0.0495086i	−0.681919	+	0.731428i	$0.738854\pi$
$398$	163.016	−	163.016i	0.409589	−	0.409589i
$399$		−	100.109i		−	0.250899i
$400$	−45.7924	+	88.8991i	−0.114481	+	0.222248i
$401$	230.054			0.573701			0.286851	−	0.957975i	$-0.407392\pi$
$401$	230.054			0.573701			0.286851	+	0.957975i	$0.407392\pi$
$402$	−38.4533	−	38.4533i	−0.0956550	−	0.0956550i
$403$	23.3282	−	23.3282i	0.0578863	−	0.0578863i
$404$		−	352.638i		−	0.872867i
$405$	−38.4207	+	23.4276i	−0.0948659	+	0.0578459i
$406$	−116.046			−0.285827
$407$	−371.343	−	371.343i	−0.912390	−	0.912390i
$408$	38.0093	−	38.0093i	0.0931601	−	0.0931601i
$409$		−	420.833i		−	1.02893i	−0.857511	−	0.514466i	$-0.827990\pi$
$409$		−	420.833i		−	1.02893i	0.857511	−	0.514466i	$-0.172010\pi$
$410$	−272.713	−	66.1103i	−0.665153	−	0.161245i
$411$	−43.2400			−0.105207
$412$	−122.302	−	122.302i	−0.296849	−	0.296849i
$413$	−166.547	+	166.547i	−0.403263	+	0.403263i
$414$		−	44.4715i		−	0.107419i
$415$	−50.0584	+	206.497i	−0.120623	+	0.497583i
$416$	−16.1241			−0.0387599
$417$	−252.555	−	252.555i	−0.605647	−	0.605647i
$418$	−253.074	+	253.074i	−0.605439	+	0.605439i
$419$		−	196.613i		−	0.469243i	−0.972087	−	0.234621i	$-0.924615\pi$
$419$		−	196.613i		−	0.469243i	0.972087	−	0.234621i	$-0.0753850\pi$
$420$	23.8575	+	39.1257i	0.0568035	+	0.0931564i
$421$	−169.718			−0.403132			−0.201566	−	0.979475i	$-0.564603\pi$
$421$	−169.718			−0.403132			−0.201566	+	0.979475i	$0.564603\pi$
$422$	−266.247	−	266.247i	−0.630918	−	0.630918i
$423$	65.6259	−	65.6259i	0.155144	−	0.155144i
$424$			169.617i			0.400040i
$425$	261.255	−	83.6121i	0.614718	−	0.196734i
$426$	−327.301			−0.768312
$427$	13.2346	+	13.2346i	0.0309944	+	0.0309944i
$428$	1.53209	−	1.53209i	0.00357964	−	0.00357964i
$429$			57.1936i			0.133318i
$430$	165.423	−	100.869i	0.384704	−	0.234579i
$431$	−279.559			−0.648628			−0.324314	−	0.945949i	$-0.605133\pi$
$431$	−279.559			−0.648628			−0.324314	+	0.945949i	$0.605133\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	−354.216	+	354.216i	−0.818050	+	0.818050i	−0.985825	−	0.167776i	$-0.946342\pi$
$433$	−354.216	+	354.216i	−0.818050	+	0.818050i	0.167776	+	0.985825i	$0.446342\pi$
$434$			43.3070i			0.0997857i
$435$	−261.033	−	63.2791i	−0.600077	−	0.145469i
$436$	−53.3770			−0.122424
$437$	161.917	+	161.917i	0.370519	+	0.370519i
$438$	226.246	−	226.246i	0.516543	−	0.516543i
$439$		−	506.541i		−	1.15385i	−0.816797	−	0.576926i	$-0.804252\pi$
$439$		−	506.541i		−	1.15385i	0.816797	−	0.576926i	$-0.195748\pi$
$440$	38.5979	−	159.221i	0.0877225	−	0.361866i
$441$	21.0000			0.0476190
$442$	31.2753	+	31.2753i	0.0707585	+	0.0707585i
$443$	443.138	−	443.138i	1.00031	−	1.00031i	0.000312670	−	1.00000i	$-0.499900\pi$
$443$	443.138	−	443.138i	1.00031	−	1.00031i	1.00000		0.000312670i	$-9.95260e-5\pi$
$444$		−	157.035i		−	0.353682i
$445$	12.8468	+	21.0685i	0.0288693	+	0.0473450i
$446$	626.418			1.40453
$447$	−314.490	−	314.490i	−0.703557	−	0.703557i
$448$	14.9666	−	14.9666i	0.0334077	−	0.0334077i
$449$			360.679i			0.803294i	0.915795	+	0.401647i	$0.131562\pi$
$449$			360.679i			0.803294i	−0.915795	+	0.401647i	$0.868438\pi$
$450$	32.3300	+	101.019i	0.0718445	+	0.224486i
$451$	459.733			1.01936
$452$	266.216	+	266.216i	0.588973	+	0.588973i
$453$	312.972	−	312.972i	0.690887	−	0.690887i
$454$		−	201.507i		−	0.443847i
$455$	−32.1939	+	19.6307i	−0.0707557	+	0.0431444i
$456$	−107.021			−0.234694
$457$	206.799	+	206.799i	0.452514	+	0.452514i	0.896188	−	0.443674i	$-0.146325\pi$
$457$	206.799	+	206.799i	0.452514	+	0.452514i	−0.443674	+	0.896188i	$0.646325\pi$
$458$	−120.710	+	120.710i	−0.263559	+	0.263559i
$459$		−	57.0140i		−	0.124213i
$460$	−101.870	−	24.6950i	−0.221456	−	0.0536848i
$461$	−649.704			−1.40934			−0.704668	−	0.709537i	$-0.748904\pi$
$461$	−649.704			−1.40934			−0.704668	+	0.709537i	$0.748904\pi$
$462$	−53.0878	−	53.0878i	−0.114909	−	0.114909i
$463$	199.904	−	199.904i	0.431759	−	0.431759i	−0.457467	−	0.889226i	$-0.651243\pi$
$463$	199.904	−	199.904i	0.431759	−	0.431759i	0.889226	+	0.457467i	$0.151243\pi$
$464$			124.058i			0.267367i
$465$	−23.6150	+	97.4148i	−0.0507850	+	0.209494i
$466$	−401.747			−0.862119
$467$	−120.654	−	120.654i	−0.258359	−	0.258359i	0.566027	−	0.824386i	$-0.308480\pi$
$467$	−120.654	−	120.654i	−0.258359	−	0.258359i	−0.824386	+	0.566027i	$0.808480\pi$
$468$	−12.0931	+	12.0931i	−0.0258400	+	0.0258400i
$469$			58.7384i			0.125242i
$470$	−113.886	−	186.770i	−0.242310	−	0.397383i
$471$	−170.328			−0.361632
$472$	178.047	+	178.047i	0.377218	+	0.377218i
$473$	−224.454	+	224.454i	−0.474534	+	0.474534i
$474$		−	310.030i		−	0.654072i
$475$	−485.511	−	250.090i	−1.02213	−	0.526505i
$476$	−58.0602			−0.121975
$477$	127.213	+	127.213i	0.266694	+	0.266694i
$478$	−288.534	+	288.534i	−0.603627	+	0.603627i
$479$			527.483i			1.10122i	0.834764	+	0.550609i	$0.185604\pi$
$479$			527.483i			1.10122i	−0.834764	+	0.550609i	$0.814396\pi$
$480$	41.8271	−	25.5047i	0.0871399	−	0.0531348i
$481$	129.213			0.268634
$482$	80.3054	+	80.3054i	0.166609	+	0.166609i
$483$	−33.9657	+	33.9657i	−0.0703223	+	0.0703223i
$484$			26.4109i			0.0545679i
$485$	−207.773	−	50.3678i	−0.428398	−	0.103851i
$486$	22.0454			0.0453609
$487$	−361.051	−	361.051i	−0.741378	−	0.741378i	0.231465	−	0.972843i	$-0.425648\pi$
$487$	−361.051	−	361.051i	−0.741378	−	0.741378i	−0.972843	+	0.231465i	$0.925648\pi$
$488$	14.1484	−	14.1484i	0.0289926	−	0.0289926i
$489$			539.327i			1.10292i
$490$	11.6613	−	48.1042i	0.0237986	−	0.0981718i
$491$	579.301			1.17984			0.589920	−	0.807462i	$-0.299159\pi$
$491$	579.301			1.17984			0.589920	+	0.807462i	$0.299159\pi$
$492$	97.2067	+	97.2067i	0.197575	+	0.197575i
$493$	240.630	−	240.630i	0.488093	−	0.488093i
$494$		−	88.0600i		−	0.178259i
$495$	−90.4672	−	148.364i	−0.182762	−	0.299725i
$496$	46.2971			0.0933410
$497$	249.980	+	249.980i	0.502978	+	0.502978i
$498$	73.6045	−	73.6045i	0.147800	−	0.147800i
$499$			269.123i			0.539324i	0.962955	+	0.269662i	$0.0869120\pi$
$499$			269.123i			0.539324i	−0.962955	+	0.269662i	$0.913088\pi$
$500$	249.354	−	17.9619i	0.498708	−	0.0359239i
$501$	67.6701			0.135070
$502$	238.919	+	238.919i	0.475934	+	0.475934i
$503$	−297.017	+	297.017i	−0.590492	+	0.590492i	−0.937764	−	0.347273i	$-0.887108\pi$
$503$	−297.017	+	297.017i	−0.590492	+	0.590492i	0.347273	+	0.937764i	$0.387108\pi$
$504$		−	22.4499i		−	0.0445435i
$505$	−752.700	+	458.970i	−1.49050	+	0.908852i
$506$	171.730			0.339387
$507$	197.031	+	197.031i	0.388622	+	0.388622i
$508$	−118.834	+	118.834i	−0.233925	+	0.233925i
$509$			518.564i			1.01879i	0.860533	+	0.509395i	$0.170131\pi$
$509$			518.564i			1.01879i	−0.860533	+	0.509395i	$0.829869\pi$
$510$	−130.601	−	31.6598i	−0.256079	−	0.0620781i
$511$	−345.596			−0.676313
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−80.2655	+	80.2655i	−0.156463	+	0.156463i
$514$		−	715.752i		−	1.39251i
$515$	−101.871	+	420.231i	−0.197809	+	0.815983i
$516$	−94.9180			−0.183950
$517$	253.419	+	253.419i	0.490172	+	0.490172i
$518$	−119.937	+	119.937i	−0.231539	+	0.231539i
$519$			313.955i			0.604923i
$520$	20.9861	+	34.4167i	0.0403579	+	0.0661859i
$521$	583.187			1.11936			0.559680	−	0.828709i	$-0.310924\pi$
$521$	583.187			1.11936			0.559680	+	0.828709i	$0.310924\pi$
$522$	93.0437	+	93.0437i	0.178245	+	0.178245i
$523$	−135.776	+	135.776i	−0.259610	+	0.259610i	−0.824895	−	0.565286i	$-0.808766\pi$
$523$	−135.776	+	135.776i	−0.259610	+	0.259610i	0.565286	+	0.824895i	$0.308766\pi$
$524$			102.521i			0.195651i
$525$	52.4618	−	101.847i	0.0999273	−	0.193994i
$526$	147.078			0.279615
$527$	−89.8004	−	89.8004i	−0.170399	−	0.170399i
$528$	−56.7532	+	56.7532i	−0.107487	+	0.107487i
$529$			419.127i			0.792301i
$530$	362.045	−	220.762i	0.683103	−	0.416532i
$531$	267.070			0.502957
$532$	81.7384	+	81.7384i	0.153644	+	0.153644i
$533$	−79.9847	+	79.9847i	−0.150065	+	0.150065i
$534$		−	12.0889i		−	0.0226384i
$535$	−5.26427	−	1.27615i	−0.00983976	−	0.00238533i
$536$	62.7940			0.117153
$537$	80.4157	+	80.4157i	0.149750	+	0.149750i
$538$	63.1334	−	63.1334i	0.117348	−	0.117348i
$539$			81.0929i			0.150451i
$540$	12.2418	−	50.4989i	0.0226700	−	0.0935165i
$541$	−631.949			−1.16811			−0.584057	−	0.811713i	$-0.698535\pi$
$541$	−631.949			−1.16811			−0.584057	+	0.811713i	$0.698535\pi$
$542$	66.1173	+	66.1173i	0.121988	+	0.121988i
$543$	−393.990	+	393.990i	−0.725581	+	0.725581i
$544$			62.0689i			0.114097i
$545$	69.4718	+	113.932i	0.127471	+	0.209050i
$546$	18.4725			0.0338325
$547$	−465.158	−	465.158i	−0.850381	−	0.850381i	0.139799	−	0.990180i	$-0.455354\pi$
$547$	−465.158	−	465.158i	−0.850381	−	0.850381i	−0.990180	+	0.139799i	$0.955354\pi$
$548$	35.3053	−	35.3053i	0.0644257	−	0.0644257i
$549$		−	21.2226i		−	0.0386568i
$550$	−390.091	+	124.845i	−0.709256	+	0.226990i
$551$	−677.529			−1.22963
$552$	36.3108	+	36.3108i	0.0657805	+	0.0657805i
$553$	−236.789	+	236.789i	−0.428190	+	0.428190i
$554$			537.614i			0.970423i
$555$	−335.188	+	204.386i	−0.603942	+	0.368263i
$556$	412.421			0.741763
$557$	432.756	+	432.756i	0.776941	+	0.776941i	0.979309	−	0.202368i	$-0.0648639\pi$
$557$	432.756	+	432.756i	0.776941	+	0.776941i	−0.202368	+	0.979309i	$0.564864\pi$
$558$	34.7229	−	34.7229i	0.0622273	−	0.0622273i
$559$		−	78.1015i		−	0.139717i
$560$	−51.4256	−	12.4665i	−0.0918313	−	0.0222615i
$561$	220.163			0.392448
$562$	108.591	+	108.591i	0.193222	+	0.193222i
$563$	382.111	−	382.111i	0.678706	−	0.678706i	−0.281002	−	0.959707i	$-0.590667\pi$
$563$	382.111	−	382.111i	0.678706	−	0.678706i	0.959707	+	0.281002i	$0.0906666\pi$
$564$			107.167i			0.190012i
$565$	221.744	−	914.722i	0.392468	−	1.61898i
$566$	−417.379			−0.737419
$567$	−16.8375	−	16.8375i	−0.0296957	−	0.0296957i
$568$	267.240	−	267.240i	0.470493	−	0.470493i
$569$		−	298.102i		−	0.523905i	−0.965081	−	0.261952i	$-0.915634\pi$
$569$		−	298.102i		−	0.523905i	0.965081	−	0.261952i	$-0.0843663\pi$
$570$	139.291	+	228.434i	0.244370	+	0.400761i
$571$	769.585			1.34778			0.673892	−	0.738830i	$-0.264621\pi$
$571$	769.585			1.34778			0.673892	+	0.738830i	$0.264621\pi$
$572$	−46.6984	−	46.6984i	−0.0816405	−	0.0816405i
$573$	−179.436	+	179.436i	−0.313151	+	0.313151i
$574$		−	148.486i		−	0.258686i
$575$	79.8758	+	249.581i	0.138914	+	0.434053i
$576$	−24.0000			−0.0416667
$577$	−357.027	−	357.027i	−0.618765	−	0.618765i	0.326450	−	0.945215i	$-0.394148\pi$
$577$	−357.027	−	357.027i	−0.618765	−	0.618765i	−0.945215	+	0.326450i	$0.894148\pi$
$578$	−168.608	+	168.608i	−0.291709	+	0.291709i
$579$		−	27.2671i		−	0.0470935i
$580$	264.800	−	161.466i	0.456552	−	0.278389i
$581$	−112.433			−0.193516
$582$	74.0593	+	74.0593i	0.127250	+	0.127250i
$583$	−491.241	+	491.241i	−0.842609	+	0.842609i
$584$			369.458i			0.632633i
$585$	41.5521	+	10.0729i	0.0710292	+	0.0172187i
$586$	−631.279			−1.07727
$587$	−107.406	−	107.406i	−0.182974	−	0.182974i	0.609677	−	0.792650i	$-0.291299\pi$
$587$	−107.406	−	107.406i	−0.182974	−	0.182974i	−0.792650	+	0.609677i	$0.791299\pi$
$588$	−17.1464	+	17.1464i	−0.0291606	+	0.0291606i
$589$			252.846i			0.429280i
$590$	148.304	−	611.771i	0.251363	−	1.03690i
$591$	54.8851			0.0928682
$592$	128.218	+	128.218i	0.216585	+	0.216585i
$593$	108.955	−	108.955i	0.183735	−	0.183735i	−0.609246	−	0.792981i	$-0.708528\pi$
$593$	108.955	−	108.955i	0.183735	−	0.183735i	0.792981	+	0.609246i	$0.208528\pi$
$594$			85.1299i			0.143316i
$595$	75.5672	+	123.928i	0.127004	+	0.208283i
$596$	513.560			0.861678
$597$	199.653	+	199.653i	0.334428	+	0.334428i
$598$	−29.8777	+	29.8777i	−0.0499627	+	0.0499627i
$599$			641.351i			1.07070i	0.844629	+	0.535352i	$0.179821\pi$
$599$			641.351i			1.07070i	−0.844629	+	0.535352i	$0.820179\pi$
$600$	−108.879	−	56.0841i	−0.181465	−	0.0934734i
$601$	52.4826			0.0873255			0.0436627	−	0.999046i	$-0.486097\pi$
$601$	52.4826			0.0873255			0.0436627	+	0.999046i	$0.486097\pi$
$602$	72.4948	+	72.4948i	0.120423	+	0.120423i
$603$	47.0955	−	47.0955i	0.0781020	−	0.0781020i
$604$			511.081i			0.846161i
$605$	56.3735	−	34.3746i	0.0931794	−	0.0568175i
$606$	431.892			0.712693
$607$	318.678	+	318.678i	0.525005	+	0.525005i	0.919079	−	0.394074i	$-0.128935\pi$
$607$	318.678	+	318.678i	0.525005	+	0.525005i	−0.394074	+	0.919079i	$0.628935\pi$
$608$	87.3820	−	87.3820i	0.143720	−	0.143720i
$609$		−	142.127i		−	0.233377i
$610$	−48.6141	−	11.7849i	−0.0796952	−	0.0193195i
$611$	−88.1801			−0.144321
$612$	46.5517	+	46.5517i	0.0760649	+	0.0760649i
$613$	102.852	−	102.852i	0.167784	−	0.167784i	−0.618220	−	0.786005i	$-0.712146\pi$
$613$	102.852	−	102.852i	0.167784	−	0.167784i	0.786005	+	0.618220i	$0.212146\pi$
$614$		−	230.968i		−	0.376169i
$615$	80.9683	−	334.004i	0.131656	−	0.543095i
$616$	86.6920			0.140734
$617$	−433.993	−	433.993i	−0.703392	−	0.703392i	0.261745	−	0.965137i	$-0.415702\pi$
$617$	−433.993	−	433.993i	−0.703392	−	0.703392i	−0.965137	+	0.261745i	$0.915702\pi$
$618$	149.789	−	149.789i	0.242377	−	0.242377i
$619$			642.310i			1.03766i	0.854878	+	0.518828i	$0.173632\pi$
$619$			642.310i			1.03766i	−0.854878	+	0.518828i	$0.826368\pi$
$620$	−60.2572	−	98.8204i	−0.0971891	−	0.159388i
$621$	54.4662			0.0877073
$622$	489.397	+	489.397i	0.786812	+	0.786812i
$623$	−9.23305	+	9.23305i	−0.0148203	+	0.0148203i
$624$		−	19.7480i		−	0.0316474i
$625$	−362.882	−	508.863i	−0.580611	−	0.814181i
$626$	−191.163			−0.305372
$627$	−309.951	−	309.951i	−0.494339	−	0.494339i
$628$	139.073	−	139.073i	0.221453	−	0.221453i
$629$		−	497.398i		−	0.790776i
$630$	−47.9190	+	29.2193i	−0.0760619	+	0.0463799i
$631$	−571.788			−0.906162			−0.453081	−	0.891469i	$-0.649675\pi$
$631$	−571.788			−0.906162			−0.453081	+	0.891469i	$0.649675\pi$
$632$	253.138	+	253.138i	0.400535	+	0.400535i
$633$	326.085	−	326.085i	0.515142	−	0.515142i
$634$		−	737.074i		−	1.16258i
$635$	408.316	+	98.9828i	0.643017	+	0.155878i
$636$	−207.738			−0.326632
$637$	−14.1086	−	14.1086i	−0.0221485	−	0.0221485i
$638$	−359.295	+	359.295i	−0.563158	+	0.563158i
$639$		−	400.860i		−	0.627324i
$640$	−13.3272	+	54.9762i	−0.0208237	+	0.0859004i
$641$	−530.212			−0.827164			−0.413582	−	0.910467i	$-0.635722\pi$
$641$	−530.212			−0.827164			−0.413582	+	0.910467i	$0.635722\pi$
$642$	1.87641	+	1.87641i	0.00292276	+	0.00292276i
$643$	314.561	−	314.561i	0.489208	−	0.489208i	−0.418848	−	0.908056i	$-0.637566\pi$
$643$	314.561	−	314.561i	0.489208	−	0.489208i	0.908056	+	0.418848i	$0.137566\pi$
$644$		−	55.4657i		−	0.0861269i
$645$	123.539	+	202.601i	0.191533	+	0.314110i
$646$	−338.982			−0.524740
$647$	−62.4615	−	62.4615i	−0.0965401	−	0.0965401i	0.657187	−	0.753727i	$-0.271746\pi$
$647$	−62.4615	−	62.4615i	−0.0965401	−	0.0965401i	−0.753727	+	0.657187i	$0.771746\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$			1031.31i			1.58907i
$650$	46.1477	−	89.5888i	0.0709965	−	0.137829i
$651$	−53.0400			−0.0814747
$652$	−440.359	−	440.359i	−0.675397	−	0.675397i
$653$	666.847	−	666.847i	1.02121	−	1.02121i	0.0214354	−	0.999770i	$-0.493176\pi$
$653$	666.847	−	666.847i	1.02121	−	1.02121i	0.999770	−	0.0214354i	$-0.00682362\pi$
$654$		−	65.3731i		−	0.0999589i
$655$	218.829	−	133.435i	0.334091	−	0.203717i
$656$	−158.738			−0.241979
$657$	277.093	+	277.093i	0.421755	+	0.421755i
$658$	81.8499	−	81.8499i	0.124392	−	0.124392i
$659$		−	594.414i		−	0.901994i	−0.892525	−	0.450997i	$-0.851068\pi$
$659$		−	594.414i		−	0.901994i	0.892525	−	0.450997i	$-0.148932\pi$
$660$	195.005	+	47.2726i	0.295462	+	0.0716252i
$661$	1114.18			1.68560			0.842799	−	0.538228i	$-0.180906\pi$
$661$	1114.18			1.68560			0.842799	+	0.538228i	$0.180906\pi$
$662$	−591.256	−	591.256i	−0.893135	−	0.893135i
$663$	−38.3042	+	38.3042i	−0.0577741	+	0.0577741i
$664$			120.196i			0.181017i
$665$	68.0840	−	280.854i	0.102382	−	0.422337i
$666$	192.327			0.288780
$667$	229.877	+	229.877i	0.344644	+	0.344644i
$668$	−55.2524	+	55.2524i	−0.0827132	+	0.0827132i
$669$			767.202i			1.14679i
$670$	−81.7284	−	134.033i	−0.121983	−	0.200049i
$671$	81.9525			0.122135
$672$	18.3303	+	18.3303i	0.0272772	+	0.0272772i
$673$	171.862	−	171.862i	0.255367	−	0.255367i	−0.567800	−	0.823167i	$-0.692205\pi$
$673$	171.862	−	171.862i	0.255367	−	0.255367i	0.823167	+	0.567800i	$0.192205\pi$
$674$			296.444i			0.439827i
$675$	−123.722	+	39.5960i	−0.183292	+	0.0586608i
$676$	−321.751			−0.475963
$677$	−920.701	−	920.701i	−1.35997	−	1.35997i	−0.873943	−	0.486029i	$-0.838445\pi$
$677$	−920.701	−	920.701i	−1.35997	−	1.35997i	−0.486029	−	0.873943i	$-0.661555\pi$
$678$	−326.047	+	326.047i	−0.480895	+	0.480895i
$679$		−	113.127i		−	0.166609i
$680$	132.485	−	80.7847i	0.194831	−	0.118801i
$681$	246.794			0.362400
$682$	134.085	+	134.085i	0.196605	+	0.196605i
$683$	272.628	−	272.628i	0.399162	−	0.399162i	−0.478775	−	0.877937i	$-0.658919\pi$
$683$	272.628	−	272.628i	0.399162	−	0.399162i	0.877937	+	0.478775i	$0.158919\pi$
$684$		−	131.073i		−	0.191627i
$685$	−121.309	−	29.4075i	−0.177094	−	0.0429307i
$686$	26.1916			0.0381802
$687$	−147.839	−	147.839i	−0.215195	−	0.215195i
$688$	77.5002	−	77.5002i	0.112646	−	0.112646i
$689$		−	170.933i		−	0.248089i
$690$	30.2451	−	124.764i	0.0438335	−	0.180818i
$691$	418.117			0.605090			0.302545	−	0.953135i	$-0.402164\pi$
$691$	418.117			0.605090			0.302545	+	0.953135i	$0.402164\pi$
$692$	−256.343	−	256.343i	−0.370438	−	0.370438i
$693$	65.0190	−	65.0190i	0.0938225	−	0.0938225i
$694$			599.791i			0.864252i
$695$	−536.779	−	880.304i	−0.772343	−	1.26662i
$696$	−151.940			−0.218304
$697$	307.897	+	307.897i	0.441746	+	0.441746i
$698$	−421.152	+	421.152i	−0.603369	+	0.603369i
$699$		−	492.038i		−	0.703917i
$700$	40.3226	+	125.992i	0.0576037	+	0.179989i
$701$	1093.07			1.55930			0.779651	−	0.626214i	$-0.215396\pi$
$701$	1093.07			1.55930			0.779651	+	0.626214i	$0.215396\pi$
$702$	−14.8110	−	14.8110i	−0.0210982	−	0.0210982i
$703$	−700.248	+	700.248i	−0.996085	+	0.996085i
$704$		−	92.6777i		−	0.131644i
$705$	228.745	−	139.481i	0.324462	−	0.197845i
$706$	−621.179			−0.879858
$707$	−329.863	−	329.863i	−0.466567	−	0.466567i
$708$	−218.062	+	218.062i	−0.307997	+	0.307997i
$709$			80.7065i			0.113831i	0.998379	+	0.0569157i	$0.0181266\pi$
$709$			80.7065i			0.113831i	−0.998379	+	0.0569157i	$0.981873\pi$
$710$	−918.240	−	222.597i	−1.29330	−	0.313518i
$711$	379.708			0.534047
$712$	9.87055	+	9.87055i	0.0138631	+	0.0138631i
$713$	85.7876	−	85.7876i	0.120319	−	0.120319i
$714$		−	71.1089i		−	0.0995923i
$715$	−38.8974	+	160.456i	−0.0544019	+	0.224414i
$716$	−131.318			−0.183405
$717$	−353.380	−	353.380i	−0.492860	−	0.492860i
$718$	−223.309	+	223.309i	−0.311015	+	0.311015i
$719$		−	266.201i		−	0.370238i	−0.982716	−	0.185119i	$-0.940733\pi$
$719$		−	266.201i		−	0.370238i	0.982716	−	0.185119i	$-0.0592670\pi$
$720$	31.2368	+	51.2276i	0.0433844	+	0.0711494i
$721$	−228.806			−0.317345
$722$	116.226	+	116.226i	0.160978	+	0.160978i
$723$	−98.3537	+	98.3537i	−0.136035	+	0.136035i
$724$		−	643.383i		−	0.888651i
$725$	−689.292	−	355.058i	−0.950747	−	0.489735i
$726$	−32.3466			−0.0445545
$727$	551.246	+	551.246i	0.758248	+	0.758248i	0.976003	−	0.217756i	$-0.0698736\pi$
$727$	551.246	+	551.246i	0.758248	+	0.758248i	−0.217756	+	0.976003i	$0.569874\pi$
$728$	−15.0827	+	15.0827i	−0.0207181	+	0.0207181i
$729$			27.0000i			0.0370370i
$730$	788.601	−	480.861i	1.08028	−	0.658714i
$731$	−300.647			−0.411282
$732$	17.3282	+	17.3282i	0.0236724	+	0.0236724i
$733$	439.355	−	439.355i	0.599393	−	0.599393i	−0.340758	−	0.940151i	$-0.610684\pi$
$733$	439.355	−	439.355i	0.599393	−	0.599393i	0.940151	+	0.340758i	$0.110684\pi$
$734$			524.186i			0.714149i
$735$	58.9154	+	14.2821i	0.0801570	+	0.0194314i
$736$	−59.2953			−0.0805643
$737$	181.862	+	181.862i	0.246761	+	0.246761i
$738$	−119.053	+	119.053i	−0.161319	+	0.161319i
$739$		−	1138.45i		−	1.54053i	−0.637722	−	0.770267i	$-0.720123\pi$
$739$		−	1138.45i		−	1.54053i	0.637722	−	0.770267i	$-0.279877\pi$
$740$	106.799	−	440.560i	0.144323	−	0.595351i
$741$	107.851			0.145548
$742$	158.662	+	158.662i	0.213831	+	0.213831i
$743$	334.460	−	334.460i	0.450148	−	0.450148i	−0.445256	−	0.895404i	$-0.646887\pi$
$743$	334.460	−	334.460i	0.450148	−	0.450148i	0.895404	+	0.445256i	$0.146887\pi$
$744$			56.7022i			0.0762126i
$745$	−668.415	−	1096.18i	−0.897201	−	1.47139i
$746$	−112.472			−0.150767
$747$	90.1467	+	90.1467i	0.120678	+	0.120678i
$748$	−179.763	+	179.763i	−0.240324	+	0.240324i
$749$		−	2.86627i		−	0.00382680i
$750$	21.9988	+	305.395i	0.0293317	+	0.407193i
$751$	1204.09			1.60331			0.801656	−	0.597785i	$-0.203953\pi$
$751$	1204.09			1.60331			0.801656	+	0.597785i	$0.203953\pi$
$752$	−87.5012	−	87.5012i	−0.116358	−	0.116358i
$753$	−292.615	+	292.615i	−0.388599	+	0.388599i
$754$		−	125.021i		−	0.165810i
$755$	1090.89	−	665.189i	1.44489	−	0.881045i
$756$	27.4955			0.0363696
$757$	−343.214	−	343.214i	−0.453387	−	0.453387i	0.443090	−	0.896477i	$-0.353882\pi$
$757$	−343.214	−	343.214i	−0.453387	−	0.453387i	−0.896477	+	0.443090i	$0.853882\pi$
$758$	−179.724	+	179.724i	−0.237103	+	0.237103i
$759$			210.325i			0.277108i
$760$	−300.246	−	72.7848i	−0.395060	−	0.0957695i
$761$	−210.154			−0.276155			−0.138078	−	0.990421i	$-0.544092\pi$
$761$	−210.154			−0.276155			−0.138078	+	0.990421i	$0.544092\pi$
$762$	−145.541	−	145.541i	−0.190999	−	0.190999i
$763$	−49.9296	+	49.9296i	−0.0654385	+	0.0654385i
$764$		−	293.017i		−	0.383531i
$765$	38.7752	−	159.952i	0.0506866	−	0.209088i
$766$	571.402			0.745956
$767$	−179.428	−	179.428i	−0.233935	−	0.233935i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$			1250.27i			1.62583i	0.582381	+	0.812916i	$0.302121\pi$
$769$			1250.27i			1.62583i	−0.582381	+	0.812916i	$0.697879\pi$
$770$	−112.832	−	185.043i	−0.146536	−	0.240315i
$771$	876.613			1.13698
$772$	22.2635	+	22.2635i	0.0288388	+	0.0288388i
$773$	734.887	−	734.887i	0.950695	−	0.950695i	−0.0481453	−	0.998840i	$-0.515331\pi$
$773$	734.887	−	734.887i	0.950695	−	0.950695i	0.998840	+	0.0481453i	$0.0153310\pi$
$774$		−	116.250i		−	0.150194i
$775$	−132.504	+	257.236i	−0.170972	+	0.331917i
$776$	−120.938			−0.155848
$777$	−146.892	−	146.892i	−0.189051	−	0.189051i
$778$	728.870	−	728.870i	0.936851	−	0.936851i
$779$		−	866.927i		−	1.11287i
$780$	−42.1517	+	25.7026i	−0.0540406	+	0.0329521i
$781$	1547.95			1.98201
$782$	115.012	+	115.012i	0.147075	+	0.147075i
$783$	−113.955	+	113.955i	−0.145536	+	0.145536i
$784$		−	28.0000i		−	0.0357143i
$785$	−477.855	−	115.841i	−0.608733	−	0.147568i
$786$	−125.562			−0.159748
$787$	−787.788	−	787.788i	−1.00100	−	1.00100i	−0.999999	−	0.00100239i	$-0.999681\pi$
$787$	−787.788	−	787.788i	−1.00100	−	1.00100i	−0.00100239	−	0.999999i	$-0.500319\pi$
$788$	−44.8135	+	44.8135i	−0.0568699	+	0.0568699i
$789$			180.132i			0.228305i
$790$	210.852	−	869.787i	0.266901	−	1.10100i
$791$	498.044			0.629639
$792$	−69.5082	−	69.5082i	−0.0877629	−	0.0877629i
$793$	−14.2582	+	14.2582i	−0.0179800	+	0.0179800i
$794$		−	39.3098i		−	0.0495086i
$795$	270.377	+	443.412i	0.340097	+	0.557751i
$796$	−326.032			−0.409589
$797$	603.311	+	603.311i	0.756977	+	0.756977i	0.975771	−	0.218794i	$-0.0702123\pi$
$797$	603.311	+	603.311i	0.756977	+	0.756977i	−0.218794	+	0.975771i	$0.570212\pi$
$798$	−100.109	+	100.109i	−0.125449	+	0.125449i
$799$			339.444i			0.424836i
$800$	134.692	−	43.1067i	0.168364	−	0.0538833i
$801$	14.8058			0.0184842
$802$	−230.054	−	230.054i	−0.286851	−	0.286851i
$803$	−1070.01	+	1070.01i	−1.33252	+	1.33252i
$804$			76.9066i			0.0956550i
$805$	−118.391	+	72.1904i	−0.147069	+	0.0896775i
$806$	−46.6563			−0.0578863
$807$	77.3223	+	77.3223i	0.0958145	+	0.0958145i
$808$	−352.638	+	352.638i	−0.436434	+	0.436434i
$809$		−	637.421i		−	0.787912i	−0.919129	−	0.393956i	$-0.871106\pi$
$809$		−	637.421i		−	0.787912i	0.919129	−	0.393956i	$-0.128894\pi$
$810$	61.8483	+	14.9931i	0.0763559	+	0.0185100i
$811$	262.276			0.323399			0.161699	−	0.986840i	$-0.448303\pi$
$811$	262.276			0.323399			0.161699	+	0.986840i	$0.448303\pi$
$812$	116.046	+	116.046i	0.142914	+	0.142914i
$813$	−80.9768	+	80.9768i	−0.0996025	+	0.0996025i
$814$			742.686i			0.912390i
$815$	−366.797	+	1513.08i	−0.450057	+	1.85654i
$816$	−76.0186			−0.0931601
$817$	423.258	+	423.258i	0.518064	+	0.518064i
$818$	−420.833	+	420.833i	−0.514466	+	0.514466i
$819$			22.6241i			0.0276241i
$820$	206.603	+	338.823i	0.251954	+	0.413199i
$821$	0.899179			0.00109522			0.000547612	−	1.00000i	$-0.499826\pi$
$821$	0.899179			0.00109522			0.000547612		1.00000i	$0.499826\pi$
$822$	43.2400	+	43.2400i	0.0526034	+	0.0526034i
$823$	805.679	−	805.679i	0.978954	−	0.978954i	−0.0208291	−	0.999783i	$-0.506631\pi$
$823$	805.679	−	805.679i	0.978954	−	0.978954i	0.999783	+	0.0208291i	$0.00663060\pi$
$824$			244.604i			0.296849i
$825$	−152.903	−	477.761i	−0.185337	−	0.579105i
$826$	333.095			0.403263
$827$	−1086.99	−	1086.99i	−1.31438	−	1.31438i	−0.918150	−	0.396232i	$-0.870317\pi$
$827$	−1086.99	−	1086.99i	−1.31438	−	1.31438i	−0.396232	−	0.918150i	$-0.629683\pi$
$828$	−44.4715	+	44.4715i	−0.0537095	+	0.0537095i
$829$			1385.23i			1.67097i	0.549514	+	0.835485i	$0.314813\pi$
$829$			1385.23i			1.67097i	−0.549514	+	0.835485i	$0.685187\pi$
$830$	256.555	−	156.438i	0.309103	−	0.188480i
$831$	−658.440			−0.792347
$832$	16.1241	+	16.1241i	0.0193800	+	0.0193800i
$833$	−54.3103	+	54.3103i	−0.0651985	+	0.0651985i
$834$			505.110i			0.605647i
$835$	189.848	+	46.0225i	0.227363	+	0.0551167i
$836$	506.147			0.605439
$837$	42.5266	+	42.5266i	0.0508084	+	0.0508084i
$838$	−196.613	+	196.613i	−0.234621	+	0.234621i
$839$		−	1077.27i		−	1.28399i	−0.766707	−	0.641997i	$-0.778106\pi$
$839$		−	1077.27i		−	1.28399i	0.766707	−	0.641997i	$-0.221894\pi$
$840$	15.2682	−	62.9832i	0.0181765	−	0.0749800i
$841$	−120.903			−0.143761
$842$	169.718	+	169.718i	0.201566	+	0.201566i
$843$	−132.996	+	132.996i	−0.157765	+	0.157765i
$844$			532.495i			0.630918i
$845$	418.769	+	686.771i	0.495585	+	0.812747i
$846$	−131.252			−0.155144
$847$	24.7051	+	24.7051i	0.0291678	+	0.0291678i
$848$	169.617	−	169.617i	0.200020	−	0.200020i
$849$		−	511.183i		−	0.602100i
$850$	−344.867	−	177.643i	−0.405726	−	0.208992i
$851$	475.171			0.558368
$852$	327.301	+	327.301i	0.384156	+	0.384156i
$853$	−447.775	+	447.775i	−0.524942	+	0.524942i	−0.919060	−	0.394118i	$-0.871050\pi$
$853$	−447.775	+	447.775i	−0.524942	+	0.524942i	0.394118	+	0.919060i	$0.371050\pi$
$854$		−	26.4692i		−	0.0309944i
$855$	−279.773	+	170.596i	−0.327220	+	0.199527i
$856$	−3.06417			−0.00357964
$857$	−223.510	−	223.510i	−0.260805	−	0.260805i	0.564576	−	0.825381i	$-0.309040\pi$
$857$	−223.510	−	223.510i	−0.260805	−	0.260805i	−0.825381	+	0.564576i	$0.809040\pi$
$858$	57.1936	−	57.1936i	0.0666592	−	0.0666592i
$859$			1389.27i			1.61731i	0.588280	+	0.808657i	$0.299805\pi$
$859$			1389.27i			1.61731i	−0.588280	+	0.808657i	$0.700195\pi$
$860$	−266.292	−	64.5538i	−0.309642	−	0.0750626i
$861$	181.857			0.211216
$862$	279.559	+	279.559i	0.324314	+	0.324314i
$863$	−1076.82	+	1076.82i	−1.24776	+	1.24776i	−0.291051	+	0.956707i	$0.594005\pi$
$863$	−1076.82	+	1076.82i	−1.24776	+	1.24776i	−0.956707	+	0.291051i	$0.905995\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−213.521	+	880.799i	−0.246845	+	1.01826i
$866$	708.431			0.818050
$867$	−206.501	−	206.501i	−0.238179	−	0.238179i
$868$	43.3070	−	43.3070i	0.0498929	−	0.0498929i
$869$			1466.27i			1.68730i
$870$	197.754	+	324.313i	0.227304	+	0.372773i
$871$	−63.2812			−0.0726535
$872$	53.3770	+	53.3770i	0.0612121	+	0.0612121i
$873$	−90.7038	+	90.7038i	−0.103899	+	0.103899i
$874$		−	323.834i		−	0.370519i
$875$	216.447	−	250.051i	0.247368	−	0.285773i
$876$	−452.491			−0.516543
$877$	−114.375	−	114.375i	−0.130417	−	0.130417i	0.638885	−	0.769302i	$-0.279396\pi$
$877$	−114.375	−	114.375i	−0.130417	−	0.130417i	−0.769302	+	0.638885i	$0.779396\pi$
$878$	−506.541	+	506.541i	−0.576926	+	0.576926i
$879$		−	773.156i		−	0.879586i
$880$	−197.819	+	120.623i	−0.224794	+	0.137072i
$881$	909.307			1.03213			0.516065	−	0.856549i	$-0.327396\pi$
$881$	909.307			1.03213			0.516065	+	0.856549i	$0.327396\pi$
$882$	−21.0000	−	21.0000i	−0.0238095	−	0.0238095i
$883$	745.228	−	745.228i	0.843973	−	0.843973i	−0.145400	−	0.989373i	$-0.546447\pi$
$883$	745.228	−	745.228i	0.843973	−	0.843973i	0.989373	+	0.145400i	$0.0464469\pi$
$884$		−	62.5505i		−	0.0707585i
$885$	749.264	+	181.635i	0.846625	+	0.205237i
$886$	−886.277			−1.00031
$887$	−138.997	−	138.997i	−0.156704	−	0.156704i	0.624400	−	0.781105i	$-0.285343\pi$
$887$	−138.997	−	138.997i	−0.156704	−	0.156704i	−0.781105	+	0.624400i	$0.785343\pi$
$888$	−157.035	+	157.035i	−0.176841	+	0.176841i
$889$			222.318i			0.250077i
$890$	8.22167	−	33.9153i	0.00923783	−	0.0381071i
$891$	−104.262			−0.117017
$892$	−626.418	−	626.418i	−0.702263	−	0.702263i
$893$	477.877	−	477.877i	0.535137	−	0.535137i
$894$			628.980i			0.703557i
$895$	170.915	+	280.296i	0.190966	+	0.313180i
$896$	−29.9333			−0.0334077
$897$	−36.5925	−	36.5925i	−0.0407944	−	0.0407944i
$898$	360.679	−	360.679i	0.401647	−	0.401647i
$899$			358.971i			0.399301i
$900$	68.6887	−	133.349i	0.0763207	−	0.148165i
$901$	−657.997			−0.730296
$902$	−459.733	−	459.733i	−0.509682	−	0.509682i
$903$	−88.7877	+	88.7877i	−0.0983252	+	0.0983252i
$904$		−	532.432i		−	0.588973i
$905$	−1373.29	+	837.384i	−1.51745	+	0.925287i
$906$	−625.944			−0.690887
$907$	475.689	+	475.689i	0.524464	+	0.524464i	0.918916	−	0.394452i	$-0.129066\pi$
$907$	475.689	+	475.689i	0.524464	+	0.524464i	−0.394452	+	0.918916i	$0.629066\pi$
$908$	−201.507	+	201.507i	−0.221924	+	0.221924i
$909$			528.958i			0.581912i
$910$	51.8245	+	12.5632i	0.0569500	+	0.0138057i
$911$	197.368			0.216650			0.108325	−	0.994116i	$-0.465451\pi$
$911$	197.368			0.216650			0.108325	+	0.994116i	$0.465451\pi$
$912$	107.021	+	107.021i	0.117347	+	0.117347i
$913$	−348.108	+	348.108i	−0.381279	+	0.381279i
$914$		−	413.598i		−	0.452514i
$915$	14.4335	−	59.5399i	0.0157743	−	0.0650709i
$916$	241.420			0.263559
$917$	95.8997	+	95.8997i	0.104580	+	0.104580i
$918$	−57.0140	+	57.0140i	−0.0621067	+	0.0621067i
$919$		−	227.388i		−	0.247430i	−0.992318	−	0.123715i	$-0.960519\pi$
$919$		−	227.388i		−	0.247430i	0.992318	−	0.123715i	$-0.0394809\pi$
$920$	77.1748	+	126.565i	0.0838856	+	0.137570i
$921$	282.876			0.307140
$922$	649.704	+	649.704i	0.704668	+	0.704668i
$923$	−269.313	+	269.313i	−0.291780	+	0.291780i
$924$			106.176i			0.114909i
$925$	−1079.37	+	345.441i	−1.16689	+	0.373450i
$926$	−399.809			−0.431759
$927$	183.453	+	183.453i	0.197900	+	0.197900i
$928$	124.058	−	124.058i	0.133683	−	0.133683i
$929$		−	1423.69i		−	1.53250i	−0.642542	−	0.766250i	$-0.722120\pi$
$929$		−	1423.69i		−	1.53250i	0.642542	−	0.766250i	$-0.277880\pi$
$930$	121.030	−	73.7997i	0.130140	−	0.0793545i
$931$	152.918			0.164252
$932$	401.747	+	401.747i	0.431060	+	0.431060i
$933$	−599.387	+	599.387i	−0.642430	+	0.642430i
$934$			241.307i			0.258359i
$935$	617.667	+	149.733i	0.660606	+	0.160142i
$936$	24.1862			0.0258400
$937$	333.167	+	333.167i	0.355567	+	0.355567i	0.862176	−	0.506609i	$-0.169101\pi$
$937$	333.167	+	333.167i	0.355567	+	0.355567i	−0.506609	+	0.862176i	$0.669101\pi$
$938$	58.7384	−	58.7384i	0.0626209	−	0.0626209i
$939$		−	234.126i		−	0.249336i
$940$	−72.8841	+	300.656i	−0.0775363	+	0.319846i
$941$	−703.676			−0.747796			−0.373898	−	0.927470i	$-0.621979\pi$
$941$	−703.676			−0.747796			−0.373898	+	0.927470i	$0.621979\pi$
$942$	170.328	+	170.328i	0.180816	+	0.180816i
$943$	−294.138	+	294.138i	−0.311917	+	0.311917i
$944$		−	356.093i		−	0.377218i
$945$	−35.7862	−	58.6886i	−0.0378690	−	0.0621043i
$946$	448.909			0.474534
$947$	457.028	+	457.028i	0.482606	+	0.482606i	0.905963	−	0.423357i	$-0.139148\pi$
$947$	457.028	+	457.028i	0.482606	+	0.482606i	−0.423357	+	0.905963i	$0.639148\pi$
$948$	−310.030	+	310.030i	−0.327036	+	0.327036i
$949$		−	372.324i		−	0.392333i
$950$	235.422	+	735.601i	0.247812	+	0.774317i
$951$	902.727			0.949240
$952$	58.0602	+	58.0602i	0.0609876	+	0.0609876i
$953$	−705.067	+	705.067i	−0.739839	+	0.739839i	−0.972547	−	0.232707i	$-0.925242\pi$
$953$	−705.067	+	705.067i	−0.739839	+	0.739839i	0.232707	+	0.972547i	$0.425242\pi$
$954$		−	254.426i		−	0.266694i
$955$	−625.440	+	381.372i	−0.654911	+	0.399342i
$956$	577.068			0.603627
$957$	−440.044	−	440.044i	−0.459816	−	0.459816i
$958$	527.483	−	527.483i	0.550609	−	0.550609i
$959$		−	66.0501i		−	0.0688740i
$960$	−67.3319	−	16.3224i	−0.0701373	−	0.0170025i
$961$	−827.036			−0.860599
$962$	−129.213	−	129.213i	−0.134317	−	0.134317i
$963$	−2.29813	+	2.29813i	−0.00238643	+	0.00238643i
$964$		−	160.611i		−	0.166609i
$965$	18.5444	−	76.4978i	0.0192170	−	0.0792723i
$966$	67.9313			0.0703223
$967$	−509.515	−	509.515i	−0.526902	−	0.526902i	0.392745	−	0.919647i	$-0.371525\pi$
$967$	−509.515	−	509.515i	−0.526902	−	0.526902i	−0.919647	+	0.392745i	$0.871525\pi$
$968$	26.4109	−	26.4109i	0.0272840	−	0.0272840i
$969$		−	415.166i		−	0.428448i
$970$	157.405	+	258.141i	0.162273	+	0.266124i
$971$	68.3318			0.0703727			0.0351863	−	0.999381i	$-0.488798\pi$
$971$	68.3318			0.0703727			0.0351863	+	0.999381i	$0.488798\pi$
$972$	−22.0454	−	22.0454i	−0.0226805	−	0.0226805i
$973$	385.784	−	385.784i	0.396489	−	0.396489i
$974$			722.102i			0.741378i
$975$	109.723	+	56.5192i	0.112537	+	0.0579684i
$976$	−28.2968			−0.0289926
$977$	−69.5422	−	69.5422i	−0.0711793	−	0.0711793i	0.670621	−	0.741800i	$-0.266028\pi$
$977$	−69.5422	−	69.5422i	−0.0711793	−	0.0711793i	−0.741800	+	0.670621i	$0.766028\pi$
$978$	539.327	−	539.327i	0.551459	−	0.551459i
$979$			57.1737i			0.0584001i
$980$	−59.7655	+	36.4429i	−0.0609852	+	0.0371866i
$981$	80.0654			0.0816161
$982$	−579.301	−	579.301i	−0.589920	−	0.589920i
$983$	−554.809	+	554.809i	−0.564403	+	0.564403i	−0.930555	−	0.366152i	$-0.880675\pi$
$983$	−554.809	+	554.809i	−0.564403	+	0.564403i	0.366152	+	0.930555i	$0.380675\pi$
$984$		−	194.413i		−	0.197575i
$985$	153.980	+	37.3274i	0.156325	+	0.0378958i
$986$	−481.260			−0.488093
$987$	100.245	+	100.245i	0.101566	+	0.101566i
$988$	−88.0600	+	88.0600i	−0.0891295	+	0.0891295i
$989$		−	287.213i		−	0.290407i
$990$	−57.8969	+	238.831i	−0.0584817	+	0.241244i
$991$	−1286.89			−1.29858			−0.649291	−	0.760540i	$-0.724934\pi$
$991$	−1286.89			−1.29858			−0.649291	+	0.760540i	$0.724934\pi$
$992$	−46.2971	−	46.2971i	−0.0466705	−	0.0466705i
$993$	724.137	−	724.137i	0.729242	−	0.729242i
$994$		−	499.960i		−	0.502978i
$995$	424.342	+	695.910i	0.426474	+	0.699408i
$996$	−147.209			−0.147800
$997$	−637.153	−	637.153i	−0.639071	−	0.639071i	0.311256	−	0.950326i	$-0.399250\pi$
$997$	−637.153	−	637.153i	−0.639071	−	0.639071i	−0.950326	+	0.311256i	$0.899250\pi$
$998$	269.123	−	269.123i	0.269662	−	0.269662i
$999$			235.552i			0.235788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.l.b.127.8	yes	16
3.2	odd	2		630.3.o.f.127.2		16
5.2	odd	4		1050.3.l.h.43.2		16
5.3	odd	4	inner	210.3.l.b.43.8	✓	16
5.4	even	2		1050.3.l.h.757.2		16
15.8	even	4		630.3.o.f.253.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.8	✓	16	5.3	odd	4	inner
210.3.l.b.127.8	yes	16	1.1	even	1	trivial
630.3.o.f.127.2		16	3.2	odd	2
630.3.o.f.253.2		16	15.8	even	4
1050.3.l.h.43.2		16	5.2	odd	4
1050.3.l.h.757.2		16	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.26896 - 2.60306i) q^{5} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.26896 - 2.60306i) q^{5} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-6.87203 - 1.66590i) q^{10} +11.5847 q^{11} +(2.44949 + 2.44949i) q^{12} +(-2.01552 + 2.01552i) q^{13} -3.74166i q^{14} +(2.04030 - 8.41648i) q^{15} -4.00000 q^{16} +(7.75862 + 7.75862i) q^{17} +(-3.00000 + 3.00000i) q^{18} -21.8455i q^{19} +(5.20613 + 8.53793i) q^{20} +4.58258 q^{21} +(-11.5847 - 11.5847i) q^{22} +(-7.41192 + 7.41192i) q^{23} -4.89898i q^{24} +(11.4481 - 22.2248i) q^{25} +4.03103 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-3.74166 + 3.74166i) q^{28} -31.0146i q^{29} +(-10.4568 + 6.37618i) q^{30} -11.5743 q^{31} +(4.00000 + 4.00000i) q^{32} +(14.1883 - 14.1883i) q^{33} -15.5172i q^{34} +(12.8564 + 3.11661i) q^{35} +6.00000 q^{36} +(-32.0546 - 32.0546i) q^{37} +(-21.8455 + 21.8455i) q^{38} +4.93699i q^{39} +(3.33180 - 13.7441i) q^{40} +39.6845 q^{41} +(-4.58258 - 4.58258i) q^{42} +(-19.3751 + 19.3751i) q^{43} +23.1694i q^{44} +(-7.80919 - 12.8069i) q^{45} +14.8238 q^{46} +(21.8753 + 21.8753i) q^{47} +(-4.89898 + 4.89898i) q^{48} +7.00000i q^{49} +(-33.6729 + 10.7767i) q^{50} +19.0047 q^{51} +(-4.03103 - 4.03103i) q^{52} +(-42.4043 + 42.4043i) q^{53} +7.34847i q^{54} +(49.4547 - 30.1557i) q^{55} +7.48331 q^{56} +(-26.7552 - 26.7552i) q^{57} +(-31.0146 + 31.0146i) q^{58} +89.0234i q^{59} +(16.8330 + 4.08060i) q^{60} +7.07420 q^{61} +(11.5743 + 11.5743i) q^{62} +(5.61249 - 5.61249i) q^{63} -8.00000i q^{64} +(-3.35765 + 13.8507i) q^{65} -28.3766 q^{66} +(15.6985 + 15.6985i) q^{67} +(-15.5172 + 15.5172i) q^{68} +18.1554i q^{69} +(-9.73978 - 15.9730i) q^{70} +133.620 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-92.3644 + 92.3644i) q^{73} +64.1091i q^{74} +(-13.1987 - 41.2407i) q^{75} +43.6910 q^{76} +(21.6730 + 21.6730i) q^{77} +(4.93699 - 4.93699i) q^{78} +126.569i q^{79} +(-17.0759 + 10.4123i) q^{80} -9.00000 q^{81} +(-39.6845 - 39.6845i) q^{82} +(-30.0489 + 30.0489i) q^{83} +9.16515i q^{84} +(53.3174 + 12.9251i) q^{85} +38.7501 q^{86} +(-37.9849 - 37.9849i) q^{87} +(23.1694 - 23.1694i) q^{88} +4.93527i q^{89} +(-4.99770 + 20.6161i) q^{90} -7.54137 q^{91} +(-14.8238 - 14.8238i) q^{92} +(-14.1755 + 14.1755i) q^{93} -43.7506i q^{94} +(-56.8652 - 93.2577i) q^{95} +9.79796 q^{96} +(-30.2346 - 30.2346i) q^{97} +(7.00000 - 7.00000i) q^{98} -34.7541i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8}+O(q^{10}) \) 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8	\( 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8} + 24 q^{10} + 8 q^{11} - 32 q^{13} - 12 q^{15} - 64 q^{16} + 56 q^{17} - 48 q^{18} - 16 q^{20} - 8 q^{22} + 24 q^{23} + 40 q^{25} + 64 q^{26} - 112 q^{31} + 64 q^{32} + 24 q^{33} + 28 q^{35} + 96 q^{36} - 152 q^{37} - 16 q^{40} + 24 q^{45} - 48 q^{46} + 80 q^{47} - 72 q^{50} - 72 q^{51} - 64 q^{52} + 48 q^{53} - 24 q^{55} + 24 q^{57} + 96 q^{58} + 24 q^{60} + 96 q^{61} + 112 q^{62} + 16 q^{65} - 48 q^{66} - 80 q^{67} - 112 q^{68} + 536 q^{71} - 96 q^{72} - 288 q^{75} - 168 q^{77} - 48 q^{78} + 64 q^{80} - 144 q^{81} - 256 q^{83} + 40 q^{85} - 144 q^{87} + 16 q^{88} + 24 q^{90} + 48 q^{92} + 192 q^{93} + 360 q^{95} + 688 q^{97} + 112 q^{98}+O(q^{100}) \) 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8 + 24 * q^10 + 8 * q^11 - 32 * q^13 - 12 * q^15 - 64 * q^16 + 56 * q^17 - 48 * q^18 - 16 * q^20 - 8 * q^22 + 24 * q^23 + 40 * q^25 + 64 * q^26 - 112 * q^31 + 64 * q^32 + 24 * q^33 + 28 * q^35 + 96 * q^36 - 152 * q^37 - 16 * q^40 + 24 * q^45 - 48 * q^46 + 80 * q^47 - 72 * q^50 - 72 * q^51 - 64 * q^52 + 48 * q^53 - 24 * q^55 + 24 * q^57 + 96 * q^58 + 24 * q^60 + 96 * q^61 + 112 * q^62 + 16 * q^65 - 48 * q^66 - 80 * q^67 - 112 * q^68 + 536 * q^71 - 96 * q^72 - 288 * q^75 - 168 * q^77 - 48 * q^78 + 64 * q^80 - 144 * q^81 - 256 * q^83 + 40 * q^85 - 144 * q^87 + 16 * q^88 + 24 * q^90 + 48 * q^92 + 192 * q^93 + 360 * q^95 + 688 * q^97 + 112 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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