LMFDB - Embedded newform 210.3.l.b.43.8

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			43.8
Root			$-1.37832 + 1.37832i$ of defining polynomial
Character	$\chi$	$=$	210.43
Dual form			210.3.l.b.127.8

$q$-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 $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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	0.625325	−	0.780365i	$-0.284966\pi$
$13$	−2.01552	−	2.01552i	−0.155040	−	0.155040i	−0.780365	+	0.625325i	$0.784966\pi$
$14$			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	−0.441079	−	0.897468i	$-0.645404\pi$
$17$	7.75862	−	7.75862i	0.456389	−	0.456389i	0.897468	+	0.441079i	$0.145404\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$			21.8455i			1.14976i	0.818237	+	0.574882i	$0.194952\pi$
$19$			21.8455i			1.14976i	−0.818237	+	0.574882i	$0.805048\pi$
$20$	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	0.527375	−	0.849632i	$-0.323176\pi$
$23$	−7.41192	−	7.41192i	−0.322257	−	0.322257i	−0.849632	+	0.527375i	$0.823176\pi$
$24$			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	$0.179588\pi$
$29$			31.0146i			1.06947i	−0.845021	+	0.534734i	$0.820412\pi$
$30$	−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	−0.992065	−	0.125725i	$-0.959874\pi$
$37$	−32.0546	+	32.0546i	−0.866340	+	0.866340i	0.125725	+	0.992065i	$0.459874\pi$
$38$	−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	0.444965	−	0.895548i	$-0.353216\pi$
$43$	−19.3751	−	19.3751i	−0.450583	−	0.450583i	−0.895548	+	0.444965i	$0.853216\pi$
$44$		−	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	−0.434999	−	0.900431i	$-0.643251\pi$
$47$	21.8753	−	21.8753i	0.465432	−	0.465432i	0.900431	+	0.434999i	$0.143251\pi$
$48$	−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	0.183027	−	0.983108i	$-0.441410\pi$
$53$	−42.4043	−	42.4043i	−0.800081	−	0.800081i	−0.983108	+	0.183027i	$0.941410\pi$
$54$		−	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	$-0.727911\pi$
$59$		−	89.0234i		−	1.50887i	0.656374	−	0.754435i	$-0.272089\pi$
$60$	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	−0.580181	−	0.814487i	$-0.697018\pi$
$67$	15.6985	−	15.6985i	0.234306	−	0.234306i	0.814487	+	0.580181i	$0.197018\pi$
$68$	−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	−0.948506	−	0.316760i	$-0.897405\pi$
$73$	−92.3644	−	92.3644i	−1.26527	−	1.26527i	−0.316760	−	0.948506i	$-0.602595\pi$
$74$		−	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	$-0.704264\pi$
$79$		−	126.569i		−	1.60214i	0.598569	−	0.801071i	$-0.295736\pi$
$80$	−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	0.502527	−	0.864562i	$-0.332404\pi$
$83$	−30.0489	−	30.0489i	−0.362035	−	0.362035i	−0.864562	+	0.502527i	$0.832404\pi$
$84$		−	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	$-0.991173\pi$
$89$		−	4.93527i		−	0.0554525i	0.999616	−	0.0277263i	$-0.00882667\pi$
$90$	−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	−0.845567	−	0.533870i	$-0.820737\pi$
$97$	−30.2346	+	30.2346i	−0.311697	+	0.311697i	0.533870	+	0.845567i	$0.320737\pi$
$98$	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	0.344930	−	0.938629i	$-0.387903\pi$
$103$	−61.1510	−	61.1510i	−0.593699	−	0.593699i	−0.938629	+	0.344930i	$0.887903\pi$
$104$		−	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	−0.710677	−	0.703518i	$-0.751611\pi$
$107$	−0.766043	+	0.766043i	−0.00715928	+	0.00715928i	0.703518	+	0.710677i	$0.251611\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$		−	26.6885i		−	0.244848i	−0.992478	−	0.122424i	$-0.960933\pi$
$109$		−	26.6885i		−	0.244848i	0.992478	−	0.122424i	$-0.0390668\pi$
$110$	−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	0.980267	+	0.197680i	$0.0633406\pi$
$113$	133.108	+	133.108i	1.17795	+	1.17795i	0.197680	+	0.980267i	$0.436659\pi$
$114$		−	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	−0.433367	−	0.901218i	$-0.642675\pi$
$127$	59.4171	−	59.4171i	0.467851	−	0.467851i	0.901218	+	0.433367i	$0.142675\pi$
$128$	−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	−0.768591	−	0.639740i	$-0.779042\pi$
$137$	−17.6526	+	17.6526i	−0.128851	+	0.128851i	0.639740	+	0.768591i	$0.279042\pi$
$138$	18.1554	+	18.1554i	0.131561	+	0.131561i
$139$			206.210i			1.48353i	0.670662	+	0.741763i	$0.266010\pi$
$139$			206.210i			1.48353i	−0.670662	+	0.741763i	$0.733990\pi$
$140$	−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	$0.330586\pi$
$149$			256.780i			1.72336i	−0.507456	+	0.861678i	$0.669414\pi$
$150$	−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	−0.892988	−	0.450081i	$-0.851395\pi$
$157$	−69.5363	+	69.5363i	−0.442906	+	0.442906i	0.450081	+	0.892988i	$0.351395\pi$
$158$	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	−0.884774	−	0.466020i	$-0.845687\pi$
$163$	−220.179	−	220.179i	−1.35079	−	1.35079i	−0.466020	−	0.884774i	$-0.654313\pi$
$164$		−	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	−0.619539	−	0.784966i	$-0.712681\pi$
$167$	27.6262	−	27.6262i	0.165426	−	0.165426i	0.784966	+	0.619539i	$0.212681\pi$
$168$	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	0.231870	−	0.972747i	$-0.425516\pi$
$173$	−128.172	−	128.172i	−0.740876	−	0.740876i	−0.972747	+	0.231870i	$0.925516\pi$
$174$		−	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	$-0.941288\pi$
$179$		−	65.6591i		−	0.366811i	0.983037	−	0.183405i	$-0.0587121\pi$
$180$	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	0.735357	−	0.677680i	$-0.237014\pi$
$193$	11.1318	+	11.1318i	0.0576775	+	0.0576775i	−0.677680	+	0.735357i	$0.737014\pi$
$194$		−	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	−0.647946	−	0.761686i	$-0.724372\pi$
$197$	22.4067	−	22.4067i	0.113740	−	0.113740i	0.761686	+	0.647946i	$0.224372\pi$
$198$	−34.7541	−	34.7541i	−0.175526	−	0.175526i
$199$		−	163.016i		−	0.819177i	−0.912270	−	0.409589i	$-0.865672\pi$
$199$		−	163.016i		−	0.819177i	0.912270	−	0.409589i	$-0.134328\pi$
$200$	−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	−0.784890	−	0.619635i	$-0.787281\pi$
$223$	−313.209	−	313.209i	−1.40453	−	1.40453i	−0.619635	−	0.784890i	$-0.712719\pi$
$224$		−	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	−0.449455	−	0.893303i	$-0.648382\pi$
$227$	100.753	−	100.753i	0.443847	−	0.443847i	0.893303	+	0.449455i	$0.148382\pi$
$228$	53.5103	+	53.5103i	0.234694	+	0.234694i
$229$			120.710i			0.527119i	0.964643	+	0.263559i	$0.0848965\pi$
$229$			120.710i			0.527119i	−0.964643	+	0.263559i	$0.915104\pi$
$230$	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	0.991584	−	0.129465i	$-0.0413260\pi$
$233$	200.874	+	200.874i	0.862119	+	0.862119i	−0.129465	+	0.991584i	$0.541326\pi$
$234$			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	$0.206278\pi$
$239$			288.534i			1.20725i	−0.797267	+	0.603627i	$0.793722\pi$
$240$	−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	0.572859	−	0.819654i	$-0.305834\pi$
$257$	357.876	−	357.876i	1.39251	−	1.39251i	0.819654	−	0.572859i	$-0.194166\pi$
$258$	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	0.553340	−	0.832955i	$-0.313353\pi$
$263$	−73.5388	−	73.5388i	−0.279615	−	0.279615i	−0.832955	+	0.553340i	$0.813353\pi$
$264$			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	$-0.962561\pi$
$269$		−	63.1334i		−	0.234697i	0.993091	−	0.117348i	$-0.0374394\pi$
$270$	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	−0.999575	−	0.0291522i	$-0.990719\pi$
$277$	−268.807	+	268.807i	−0.970423	+	0.970423i	0.0291522	+	0.999575i	$0.490719\pi$
$278$	−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	0.972078	−	0.234658i	$-0.0753972\pi$
$283$	208.690	+	208.690i	0.737419	+	0.737419i	−0.234658	+	0.972078i	$0.575397\pi$
$284$		−	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	0.996753	+	0.0805153i	$0.0256566\pi$
$293$	315.640	+	315.640i	1.07727	+	1.07727i	0.0805153	+	0.996753i	$0.474343\pi$
$294$			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	−0.493549	−	0.869718i	$-0.664301\pi$
$307$	115.484	−	115.484i	0.376169	−	0.376169i	0.869718	+	0.493549i	$0.164301\pi$
$308$	−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	0.843111	−	0.537739i	$-0.180721\pi$
$313$	95.5816	+	95.5816i	0.305372	+	0.305372i	−0.537739	+	0.843111i	$0.680721\pi$
$314$		−	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	0.178668	−	0.983909i	$-0.442821\pi$
$317$	368.537	−	368.537i	1.16258	−	1.16258i	0.983909	−	0.178668i	$-0.0571787\pi$
$318$	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	−0.891954	−	0.452127i	$-0.850666\pi$
$337$	−148.222	+	148.222i	−0.439827	+	0.439827i	0.452127	+	0.891954i	$0.350666\pi$
$338$	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	−0.991829	−	0.127577i	$-0.959280\pi$
$347$	−299.896	+	299.896i	−0.864252	+	0.864252i	0.127577	+	0.991829i	$0.459280\pi$
$348$	75.9698	+	75.9698i	0.218304	+	0.218304i
$349$			421.152i			1.20674i	0.797462	+	0.603369i	$0.206176\pi$
$349$			421.152i			1.20674i	−0.797462	+	0.603369i	$0.793824\pi$
$350$	−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	0.993519	−	0.113662i	$-0.0362581\pi$
$353$	310.590	+	310.590i	0.879858	+	0.879858i	−0.113662	+	0.993519i	$0.536258\pi$
$354$			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	$0.100669\pi$
$359$			223.309i			0.622030i	−0.950405	+	0.311015i	$0.899331\pi$
$360$	−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	−0.967401	−	0.253251i	$-0.918500\pi$
$367$	−262.093	+	262.093i	−0.714149	+	0.714149i	0.253251	+	0.967401i	$0.418500\pi$
$368$	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	0.778461	−	0.627694i	$-0.216001\pi$
$373$	56.2361	+	56.2361i	0.150767	+	0.150767i	−0.627694	+	0.778461i	$0.716001\pi$
$374$			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	$0.0761979\pi$
$379$			179.724i			0.474206i	−0.971485	+	0.237103i	$0.923802\pi$
$380$	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	0.227761	−	0.973717i	$-0.426859\pi$
$383$	−285.701	−	285.701i	−0.745956	−	0.745956i	−0.973717	+	0.227761i	$0.926859\pi$
$384$		−	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	$-0.613727\pi$
$389$		−	728.870i		−	1.87370i	0.349730	−	0.936851i	$-0.386273\pi$
$390$	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	−0.681919	−	0.731428i	$-0.738854\pi$
$397$	19.6549	−	19.6549i	0.0495086	−	0.0495086i	0.731428	+	0.681919i	$0.238854\pi$
$398$	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	$0.172010\pi$
$409$			420.833i			1.02893i	−0.857511	+	0.514466i	$0.827990\pi$
$410$	−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	$0.0753850\pi$
$419$			196.613i			0.469243i	−0.972087	+	0.234621i	$0.924615\pi$
$420$	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	0.167776	−	0.985825i	$-0.446342\pi$
$433$	−354.216	−	354.216i	−0.818050	−	0.818050i	−0.985825	+	0.167776i	$0.946342\pi$
$434$		−	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	$0.195748\pi$
$439$			506.541i			1.15385i	−0.816797	+	0.576926i	$0.804252\pi$
$440$	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	1.00000		0.000312670i	$9.95260e-5\pi$
$443$	443.138	+	443.138i	1.00031	+	1.00031i	0.000312670		1.00000i	$0.499900\pi$
$444$			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	$-0.868438\pi$
$449$		−	360.679i		−	0.803294i	0.915795	−	0.401647i	$-0.131562\pi$
$450$	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	−0.443674	−	0.896188i	$-0.646325\pi$
$457$	206.799	−	206.799i	0.452514	−	0.452514i	0.896188	+	0.443674i	$0.146325\pi$
$458$	−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	0.889226	−	0.457467i	$-0.151243\pi$
$463$	199.904	+	199.904i	0.431759	+	0.431759i	−0.457467	+	0.889226i	$0.651243\pi$
$464$		−	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	−0.824386	−	0.566027i	$-0.808480\pi$
$467$	−120.654	+	120.654i	−0.258359	+	0.258359i	0.566027	+	0.824386i	$0.308480\pi$
$468$	−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	$-0.814396\pi$
$479$		−	527.483i		−	1.10122i	0.834764	−	0.550609i	$-0.185604\pi$
$480$	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	−0.972843	−	0.231465i	$-0.925648\pi$
$487$	−361.051	+	361.051i	−0.741378	+	0.741378i	0.231465	+	0.972843i	$0.425648\pi$
$488$	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	$-0.913088\pi$
$499$		−	269.123i		−	0.539324i	0.962955	−	0.269662i	$-0.0869120\pi$
$500$	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	0.347273	−	0.937764i	$-0.387108\pi$
$503$	−297.017	−	297.017i	−0.590492	−	0.590492i	−0.937764	+	0.347273i	$0.887108\pi$
$504$			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	$-0.829869\pi$
$509$		−	518.564i		−	1.01879i	0.860533	−	0.509395i	$-0.170131\pi$
$510$	−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	0.565286	−	0.824895i	$-0.308766\pi$
$523$	−135.776	−	135.776i	−0.259610	−	0.259610i	−0.824895	+	0.565286i	$0.808766\pi$
$524$		−	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	−0.990180	−	0.139799i	$-0.955354\pi$
$547$	−465.158	+	465.158i	−0.850381	+	0.850381i	0.139799	+	0.990180i	$0.455354\pi$
$548$	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	−0.202368	−	0.979309i	$-0.564864\pi$
$557$	432.756	−	432.756i	0.776941	−	0.776941i	0.979309	+	0.202368i	$0.0648639\pi$
$558$	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	0.959707	−	0.281002i	$-0.0906666\pi$
$563$	382.111	+	382.111i	0.678706	+	0.678706i	−0.281002	+	0.959707i	$0.590667\pi$
$564$		−	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	$0.0843663\pi$
$569$			298.102i			0.523905i	−0.965081	+	0.261952i	$0.915634\pi$
$570$	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	−0.945215	−	0.326450i	$-0.894148\pi$
$577$	−357.027	+	357.027i	−0.618765	+	0.618765i	0.326450	+	0.945215i	$0.394148\pi$
$578$	−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	−0.792650	−	0.609677i	$-0.791299\pi$
$587$	−107.406	+	107.406i	−0.182974	+	0.182974i	0.609677	+	0.792650i	$0.291299\pi$
$588$	−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	0.792981	−	0.609246i	$-0.208528\pi$
$593$	108.955	+	108.955i	0.183735	+	0.183735i	−0.609246	+	0.792981i	$0.708528\pi$
$594$		−	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	$-0.820179\pi$
$599$		−	641.351i		−	1.07070i	0.844629	−	0.535352i	$-0.179821\pi$
$600$	−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	−0.394074	−	0.919079i	$-0.628935\pi$
$607$	318.678	−	318.678i	0.525005	−	0.525005i	0.919079	+	0.394074i	$0.128935\pi$
$608$	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	0.786005	−	0.618220i	$-0.212146\pi$
$613$	102.852	+	102.852i	0.167784	+	0.167784i	−0.618220	+	0.786005i	$0.712146\pi$
$614$			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	−0.965137	−	0.261745i	$-0.915702\pi$
$617$	−433.993	+	433.993i	−0.703392	+	0.703392i	0.261745	+	0.965137i	$0.415702\pi$
$618$	149.789	+	149.789i	0.242377	+	0.242377i
$619$		−	642.310i		−	1.03766i	−0.854878	−	0.518828i	$-0.826368\pi$
$619$		−	642.310i		−	1.03766i	0.854878	−	0.518828i	$-0.173632\pi$
$620$	−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	0.908056	−	0.418848i	$-0.137566\pi$
$643$	314.561	+	314.561i	0.489208	+	0.489208i	−0.418848	+	0.908056i	$0.637566\pi$
$644$			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	−0.753727	−	0.657187i	$-0.771746\pi$
$647$	−62.4615	+	62.4615i	−0.0965401	+	0.0965401i	0.657187	+	0.753727i	$0.271746\pi$
$648$	−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	0.999770	+	0.0214354i	$0.00682362\pi$
$653$	666.847	+	666.847i	1.02121	+	1.02121i	0.0214354	+	0.999770i	$0.493176\pi$
$654$			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	$0.148932\pi$
$659$			594.414i			0.901994i	−0.892525	+	0.450997i	$0.851068\pi$
$660$	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	0.823167	−	0.567800i	$-0.192205\pi$
$673$	171.862	+	171.862i	0.255367	+	0.255367i	−0.567800	+	0.823167i	$0.692205\pi$
$674$		−	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	−0.486029	+	0.873943i	$0.661555\pi$
$677$	−920.701	+	920.701i	−1.35997	+	1.35997i	−0.873943	+	0.486029i	$0.838445\pi$
$678$	−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	0.877937	−	0.478775i	$-0.158919\pi$
$683$	272.628	+	272.628i	0.399162	+	0.399162i	−0.478775	+	0.877937i	$0.658919\pi$
$684$			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	$-0.981873\pi$
$709$		−	80.7065i		−	0.113831i	0.998379	−	0.0569157i	$-0.0181266\pi$
$710$	−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	$0.0592670\pi$
$719$			266.201i			0.370238i	−0.982716	+	0.185119i	$0.940733\pi$
$720$	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	−0.217756	−	0.976003i	$-0.569874\pi$
$727$	551.246	−	551.246i	0.758248	−	0.758248i	0.976003	+	0.217756i	$0.0698736\pi$
$728$	−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	0.940151	−	0.340758i	$-0.110684\pi$
$733$	439.355	+	439.355i	0.599393	+	0.599393i	−0.340758	+	0.940151i	$0.610684\pi$
$734$		−	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	$0.279877\pi$
$739$			1138.45i			1.54053i	−0.637722	+	0.770267i	$0.720123\pi$
$740$	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	0.895404	−	0.445256i	$-0.146887\pi$
$743$	334.460	+	334.460i	0.450148	+	0.450148i	−0.445256	+	0.895404i	$0.646887\pi$
$744$		−	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	−0.896477	−	0.443090i	$-0.853882\pi$
$757$	−343.214	+	343.214i	−0.453387	+	0.453387i	0.443090	+	0.896477i	$0.353882\pi$
$758$	−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	$-0.697879\pi$
$769$		−	1250.27i		−	1.62583i	0.582381	−	0.812916i	$-0.302121\pi$
$770$	−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	0.998840	−	0.0481453i	$-0.0153310\pi$
$773$	734.887	+	734.887i	0.950695	+	0.950695i	−0.0481453	+	0.998840i	$0.515331\pi$
$774$			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	−0.00100239	+	0.999999i	$0.500319\pi$
$787$	−787.788	+	787.788i	−1.00100	+	1.00100i	−0.999999	+	0.00100239i	$0.999681\pi$
$788$	−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	−0.218794	−	0.975771i	$-0.570212\pi$
$797$	603.311	−	603.311i	0.756977	−	0.756977i	0.975771	+	0.218794i	$0.0702123\pi$
$798$	−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	$0.128894\pi$
$809$			637.421i			0.787912i	−0.919129	+	0.393956i	$0.871106\pi$
$810$	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	0.999783	−	0.0208291i	$-0.00663060\pi$
$823$	805.679	+	805.679i	0.978954	+	0.978954i	−0.0208291	+	0.999783i	$0.506631\pi$
$824$		−	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	−0.396232	+	0.918150i	$0.629683\pi$
$827$	−1086.99	+	1086.99i	−1.31438	+	1.31438i	−0.918150	+	0.396232i	$0.870317\pi$
$828$	−44.4715	−	44.4715i	−0.0537095	−	0.0537095i
$829$		−	1385.23i		−	1.67097i	−0.549514	−	0.835485i	$-0.685187\pi$
$829$		−	1385.23i		−	1.67097i	0.549514	−	0.835485i	$-0.314813\pi$
$830$	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	$0.221894\pi$
$839$			1077.27i			1.28399i	−0.766707	+	0.641997i	$0.778106\pi$
$840$	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	0.394118	−	0.919060i	$-0.371050\pi$
$853$	−447.775	−	447.775i	−0.524942	−	0.524942i	−0.919060	+	0.394118i	$0.871050\pi$
$854$			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	−0.825381	−	0.564576i	$-0.809040\pi$
$857$	−223.510	+	223.510i	−0.260805	+	0.260805i	0.564576	+	0.825381i	$0.309040\pi$
$858$	57.1936	+	57.1936i	0.0666592	+	0.0666592i
$859$		−	1389.27i		−	1.61731i	−0.588280	−	0.808657i	$-0.700195\pi$
$859$		−	1389.27i		−	1.61731i	0.588280	−	0.808657i	$-0.299805\pi$
$860$	−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	−0.956707	−	0.291051i	$-0.905995\pi$
$863$	−1076.82	−	1076.82i	−1.24776	−	1.24776i	−0.291051	−	0.956707i	$-0.594005\pi$
$864$			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	−0.769302	−	0.638885i	$-0.779396\pi$
$877$	−114.375	+	114.375i	−0.130417	+	0.130417i	0.638885	+	0.769302i	$0.279396\pi$
$878$	−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	0.989373	−	0.145400i	$-0.0464469\pi$
$883$	745.228	+	745.228i	0.843973	+	0.843973i	−0.145400	+	0.989373i	$0.546447\pi$
$884$			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	−0.781105	−	0.624400i	$-0.785343\pi$
$887$	−138.997	+	138.997i	−0.156704	+	0.156704i	0.624400	+	0.781105i	$0.285343\pi$
$888$	−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	−0.394452	−	0.918916i	$-0.629066\pi$
$907$	475.689	−	475.689i	0.524464	−	0.524464i	0.918916	+	0.394452i	$0.129066\pi$
$908$	−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	$0.0394809\pi$
$919$			227.388i			0.247430i	−0.992318	+	0.123715i	$0.960519\pi$
$920$	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	$0.277880\pi$
$929$			1423.69i			1.53250i	−0.642542	+	0.766250i	$0.722120\pi$
$930$	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	−0.506609	−	0.862176i	$-0.669101\pi$
$937$	333.167	−	333.167i	0.355567	−	0.355567i	0.862176	+	0.506609i	$0.169101\pi$
$938$	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	−0.423357	−	0.905963i	$-0.639148\pi$
$947$	457.028	−	457.028i	0.482606	−	0.482606i	0.905963	+	0.423357i	$0.139148\pi$
$948$	−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	0.232707	−	0.972547i	$-0.425242\pi$
$953$	−705.067	−	705.067i	−0.739839	−	0.739839i	−0.972547	+	0.232707i	$0.925242\pi$
$954$			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	−0.919647	−	0.392745i	$-0.871525\pi$
$967$	−509.515	+	509.515i	−0.526902	+	0.526902i	0.392745	+	0.919647i	$0.371525\pi$
$968$	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	−0.741800	−	0.670621i	$-0.766028\pi$
$977$	−69.5422	+	69.5422i	−0.0711793	+	0.0711793i	0.670621	+	0.741800i	$0.266028\pi$
$978$	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	0.366152	−	0.930555i	$-0.380675\pi$
$983$	−554.809	−	554.809i	−0.564403	−	0.564403i	−0.930555	+	0.366152i	$0.880675\pi$
$984$			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	−0.950326	−	0.311256i	$-0.899250\pi$
$997$	−637.153	+	637.153i	−0.639071	+	0.639071i	0.311256	+	0.950326i	$0.399250\pi$
$998$	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.43.8	✓	16
3.2	odd	2		630.3.o.f.253.2		16
5.2	odd	4	inner	210.3.l.b.127.8	yes	16
5.3	odd	4		1050.3.l.h.757.2		16
5.4	even	2		1050.3.l.h.43.2		16
15.2	even	4		630.3.o.f.127.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.8	✓	16	1.1	even	1	trivial
210.3.l.b.127.8	yes	16	5.2	odd	4	inner
630.3.o.f.127.2		16	15.2	even	4
630.3.o.f.253.2		16	3.2	odd	2
1050.3.l.h.43.2		16	5.4	even	2
1050.3.l.h.757.2		16	5.3	odd	4

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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