LMFDB - Embedded newform 210.3.l.b.127.5

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			127.5
Root			$3.60306 + 3.60306i$ of defining polynomial
Character	$\chi$	$=$	210.127
Dual form			210.3.l.b.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.39814 + 2.37832i) q^{5} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.39814 + 2.37832i) q^{5} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(6.77646 + 2.01982i) q^{10} -14.7776 q^{11} +(2.44949 + 2.44949i) q^{12} +(-13.2827 + 13.2827i) q^{13} -3.74166i q^{14} +(-2.47376 + 8.29943i) q^{15} -4.00000 q^{16} +(1.17963 + 1.17963i) q^{17} +(-3.00000 + 3.00000i) q^{18} +15.1298i q^{19} +(-4.75664 - 8.79627i) q^{20} +4.58258 q^{21} +(14.7776 + 14.7776i) q^{22} +(-22.5070 + 22.5070i) q^{23} -4.89898i q^{24} +(13.6872 - 20.9203i) q^{25} +26.5654 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-3.74166 + 3.74166i) q^{28} -3.29748i q^{29} +(10.7732 - 5.82567i) q^{30} +50.0892 q^{31} +(4.00000 + 4.00000i) q^{32} +(-18.0988 + 18.0988i) q^{33} -2.35927i q^{34} +(-12.6776 - 3.77873i) q^{35} +6.00000 q^{36} +(6.15735 + 6.15735i) q^{37} +(15.1298 - 15.1298i) q^{38} +32.5359i q^{39} +(-4.03963 + 13.5529i) q^{40} -35.1369 q^{41} +(-4.58258 - 4.58258i) q^{42} +(-58.9417 + 58.9417i) q^{43} -29.5552i q^{44} +(7.13496 + 13.1944i) q^{45} +45.0141 q^{46} +(-20.1645 - 20.1645i) q^{47} +(-4.89898 + 4.89898i) q^{48} +7.00000i q^{49} +(-34.6075 + 7.23315i) q^{50} +2.88950 q^{51} +(-26.5654 - 26.5654i) q^{52} +(10.9028 - 10.9028i) q^{53} +7.34847i q^{54} +(64.9939 - 35.1459i) q^{55} +7.48331 q^{56} +(18.5302 + 18.5302i) q^{57} +(-3.29748 + 3.29748i) q^{58} -66.6774i q^{59} +(-16.5989 - 4.94752i) q^{60} -4.45593 q^{61} +(-50.0892 - 50.0892i) q^{62} +(5.61249 - 5.61249i) q^{63} -8.00000i q^{64} +(26.8286 - 90.0098i) q^{65} +36.1976 q^{66} +(-88.4424 - 88.4424i) q^{67} +(-2.35927 + 2.35927i) q^{68} +55.1307i q^{69} +(8.89886 + 16.4563i) q^{70} +69.3188 q^{71} +(-6.00000 - 6.00000i) q^{72} +(58.4166 - 58.4166i) q^{73} -12.3147i q^{74} +(-8.85877 - 42.3854i) q^{75} -30.2597 q^{76} +(-27.6464 - 27.6464i) q^{77} +(32.5359 - 32.5359i) q^{78} -52.8307i q^{79} +(17.5925 - 9.51328i) q^{80} -9.00000 q^{81} +(35.1369 + 35.1369i) q^{82} +(-53.4286 + 53.4286i) q^{83} +9.16515i q^{84} +(-7.99374 - 2.38264i) q^{85} +117.883 q^{86} +(-4.03857 - 4.03857i) q^{87} +(-29.5552 + 29.5552i) q^{88} -21.3553i q^{89} +(6.05945 - 20.3294i) q^{90} -49.6994 q^{91} +(-45.0141 - 45.0141i) q^{92} +(61.3464 - 61.3464i) q^{93} +40.3290i q^{94} +(-35.9836 - 66.5431i) q^{95} +9.79796 q^{96} +(90.3562 + 90.3562i) q^{97} +(7.00000 - 7.00000i) q^{98} +44.3328i 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
$5$	−4.39814	+	2.37832i	−0.879627	+	0.475664i
$5$	−4.39814	+	2.37832i	−0.879627	+	0.475664i
$6$	−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
$10$	6.77646	+	2.01982i	0.677646	+	0.201982i
$11$	−14.7776			−1.34342			−0.671710	−	0.740814i	$-0.734440\pi$
$11$	−14.7776			−1.34342			−0.671710	+	0.740814i	$0.734440\pi$
$12$	2.44949	+	2.44949i	0.204124	+	0.204124i
$13$	−13.2827	+	13.2827i	−1.02175	+	1.02175i	−0.0219895	+	0.999758i	$0.507000\pi$
$13$	−13.2827	+	13.2827i	−1.02175	+	1.02175i	−0.999758	+	0.0219895i	$0.993000\pi$
$14$		−	3.74166i		−	0.267261i
$15$	−2.47376	+	8.29943i	−0.164917	+	0.553295i
$16$	−4.00000			−0.250000
$17$	1.17963	+	1.17963i	0.0693902	+	0.0693902i	0.740950	−	0.671560i	$-0.234375\pi$
$17$	1.17963	+	1.17963i	0.0693902	+	0.0693902i	−0.671560	+	0.740950i	$0.734375\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$			15.1298i			0.796307i	0.917319	+	0.398154i	$0.130349\pi$
$19$			15.1298i			0.796307i	−0.917319	+	0.398154i	$0.869651\pi$
$20$	−4.75664	−	8.79627i	−0.237832	−	0.439814i
$21$	4.58258			0.218218
$22$	14.7776	+	14.7776i	0.671710	+	0.671710i
$23$	−22.5070	+	22.5070i	−0.978567	+	0.978567i	−0.999775	−	0.0212084i	$-0.993249\pi$
$23$	−22.5070	+	22.5070i	−0.978567	+	0.978567i	0.0212084	+	0.999775i	$0.493249\pi$
$24$		−	4.89898i		−	0.204124i
$25$	13.6872	−	20.9203i	0.547488	−	0.836814i
$26$	26.5654			1.02175
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	−3.74166	+	3.74166i	−0.133631	+	0.133631i
$29$		−	3.29748i		−	0.113706i	−0.998383	−	0.0568530i	$-0.981893\pi$
$29$		−	3.29748i		−	0.113706i	0.998383	−	0.0568530i	$-0.0181066\pi$
$30$	10.7732	−	5.82567i	0.359106	−	0.194189i
$31$	50.0892			1.61578			0.807890	−	0.589334i	$-0.200610\pi$
$31$	50.0892			1.61578			0.807890	+	0.589334i	$0.200610\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−18.0988	+	18.0988i	−0.548449	+	0.548449i
$34$		−	2.35927i		−	0.0693902i
$35$	−12.6776	−	3.77873i	−0.362217	−	0.107964i
$36$	6.00000			0.166667
$37$	6.15735	+	6.15735i	0.166415	+	0.166415i	0.785401	−	0.618987i	$-0.212457\pi$
$37$	6.15735	+	6.15735i	0.166415	+	0.166415i	−0.618987	+	0.785401i	$0.712457\pi$
$38$	15.1298	−	15.1298i	0.398154	−	0.398154i
$39$			32.5359i			0.834254i
$40$	−4.03963	+	13.5529i	−0.100991	+	0.338823i
$41$	−35.1369			−0.856998			−0.428499	−	0.903542i	$-0.640957\pi$
$41$	−35.1369			−0.856998			−0.428499	+	0.903542i	$0.640957\pi$
$42$	−4.58258	−	4.58258i	−0.109109	−	0.109109i
$43$	−58.9417	+	58.9417i	−1.37074	+	1.37074i	−0.511388	+	0.859350i	$0.670869\pi$
$43$	−58.9417	+	58.9417i	−1.37074	+	1.37074i	−0.859350	+	0.511388i	$0.829131\pi$
$44$		−	29.5552i		−	0.671710i
$45$	7.13496	+	13.1944i	0.158555	+	0.293209i
$46$	45.0141			0.978567
$47$	−20.1645	−	20.1645i	−0.429032	−	0.429032i	0.459266	−	0.888299i	$-0.348112\pi$
$47$	−20.1645	−	20.1645i	−0.429032	−	0.429032i	−0.888299	+	0.459266i	$0.848112\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$			7.00000i			0.142857i
$50$	−34.6075	+	7.23315i	−0.692151	+	0.144663i
$51$	2.88950			0.0566569
$52$	−26.5654	−	26.5654i	−0.510874	−	0.510874i
$53$	10.9028	−	10.9028i	0.205712	−	0.205712i	−0.596730	−	0.802442i	$-0.703534\pi$
$53$	10.9028	−	10.9028i	0.205712	−	0.205712i	0.802442	+	0.596730i	$0.203534\pi$
$54$			7.34847i			0.136083i
$55$	64.9939	−	35.1459i	1.18171	−	0.639016i
$56$	7.48331			0.133631
$57$	18.5302	+	18.5302i	0.325091	+	0.325091i
$58$	−3.29748	+	3.29748i	−0.0568530	+	0.0568530i
$59$		−	66.6774i		−	1.13013i	−0.825048	−	0.565063i	$-0.808852\pi$
$59$		−	66.6774i		−	1.13013i	0.825048	−	0.565063i	$-0.191148\pi$
$60$	−16.5989	−	4.94752i	−0.276648	−	0.0824586i
$61$	−4.45593			−0.0730481			−0.0365241	−	0.999333i	$-0.511629\pi$
$61$	−4.45593			−0.0730481			−0.0365241	+	0.999333i	$0.511629\pi$
$62$	−50.0892	−	50.0892i	−0.807890	−	0.807890i
$63$	5.61249	−	5.61249i	0.0890871	−	0.0890871i
$64$		−	8.00000i		−	0.125000i
$65$	26.8286	−	90.0098i	0.412748	−	1.38477i
$66$	36.1976			0.548449
$67$	−88.4424	−	88.4424i	−1.32004	−	1.32004i	−0.913743	−	0.406293i	$-0.866821\pi$
$67$	−88.4424	−	88.4424i	−1.32004	−	1.32004i	−0.406293	−	0.913743i	$-0.633179\pi$
$68$	−2.35927	+	2.35927i	−0.0346951	+	0.0346951i
$69$			55.1307i			0.798996i
$70$	8.89886	+	16.4563i	0.127127	+	0.235090i
$71$	69.3188			0.976321			0.488161	−	0.872754i	$-0.337668\pi$
$71$	69.3188			0.976321			0.488161	+	0.872754i	$0.337668\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	58.4166	−	58.4166i	0.800227	−	0.800227i	−0.182903	−	0.983131i	$-0.558550\pi$
$73$	58.4166	−	58.4166i	0.800227	−	0.800227i	0.983131	+	0.182903i	$0.0585496\pi$
$74$		−	12.3147i		−	0.166415i
$75$	−8.85877	−	42.3854i	−0.118117	−	0.565139i
$76$	−30.2597			−0.398154
$77$	−27.6464	−	27.6464i	−0.359044	−	0.359044i
$78$	32.5359	−	32.5359i	0.417127	−	0.417127i
$79$		−	52.8307i		−	0.668744i	−0.942441	−	0.334372i	$-0.891476\pi$
$79$		−	52.8307i		−	0.668744i	0.942441	−	0.334372i	$-0.108524\pi$
$80$	17.5925	−	9.51328i	0.219907	−	0.118916i
$81$	−9.00000			−0.111111
$82$	35.1369	+	35.1369i	0.428499	+	0.428499i
$83$	−53.4286	+	53.4286i	−0.643718	+	0.643718i	−0.951468	−	0.307749i	$-0.900424\pi$
$83$	−53.4286	+	53.4286i	−0.643718	+	0.643718i	0.307749	+	0.951468i	$0.400424\pi$
$84$			9.16515i			0.109109i
$85$	−7.99374	−	2.38264i	−0.0940440	−	0.0280311i
$86$	117.883			1.37074
$87$	−4.03857	−	4.03857i	−0.0464203	−	0.0464203i
$88$	−29.5552	+	29.5552i	−0.335855	+	0.335855i
$89$		−	21.3553i		−	0.239947i	−0.992777	−	0.119973i	$-0.961719\pi$
$89$		−	21.3553i		−	0.239947i	0.992777	−	0.119973i	$-0.0382809\pi$
$90$	6.05945	−	20.3294i	0.0673272	−	0.225882i
$91$	−49.6994			−0.546147
$92$	−45.0141	−	45.0141i	−0.489283	−	0.489283i
$93$	61.3464	−	61.3464i	0.659639	−	0.659639i
$94$			40.3290i			0.429032i
$95$	−35.9836	−	66.5431i	−0.378775	−	0.700453i
$96$	9.79796			0.102062
$97$	90.3562	+	90.3562i	0.931507	+	0.931507i	0.997800	−	0.0662929i	$-0.0211172\pi$
$97$	90.3562	+	90.3562i	0.931507	+	0.931507i	−0.0662929	+	0.997800i	$0.521117\pi$
$98$	7.00000	−	7.00000i	0.0714286	−	0.0714286i
$99$			44.3328i			0.447806i
$100$	41.8407	+	27.3744i	0.418407	+	0.273744i
$101$	43.6109			0.431791			0.215896	−	0.976416i	$-0.430733\pi$
$101$	43.6109			0.431791			0.215896	+	0.976416i	$0.430733\pi$
$102$	−2.88950	−	2.88950i	−0.0283284	−	0.0283284i
$103$	−48.8638	+	48.8638i	−0.474405	+	0.474405i	−0.903337	−	0.428932i	$-0.858890\pi$
$103$	−48.8638	+	48.8638i	−0.474405	+	0.474405i	0.428932	+	0.903337i	$0.358890\pi$
$104$			53.1309i			0.510874i
$105$	−20.1548	+	10.8988i	−0.191950	+	0.103798i
$106$	−21.8055			−0.205712
$107$	23.1497	+	23.1497i	0.216352	+	0.216352i	0.806959	−	0.590607i	$-0.201112\pi$
$107$	23.1497	+	23.1497i	0.216352	+	0.216352i	−0.590607	+	0.806959i	$0.701112\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$			141.834i			1.30123i	0.759409	+	0.650613i	$0.225488\pi$
$109$			141.834i			1.30123i	−0.759409	+	0.650613i	$0.774512\pi$
$110$	−100.140	−	29.8481i	−0.910362	−	0.271346i
$111$	15.0824			0.135877
$112$	−7.48331	−	7.48331i	−0.0668153	−	0.0668153i
$113$	−113.746	+	113.746i	−1.00660	+	1.00660i	−0.00662298	+	0.999978i	$0.502108\pi$
$113$	−113.746	+	113.746i	−1.00660	+	1.00660i	−0.999978	+	0.00662298i	$0.997892\pi$
$114$		−	37.0604i		−	0.325091i
$115$	45.4601	−	152.518i	0.395305	−	1.32624i
$116$	6.59495			0.0568530
$117$	39.8482	+	39.8482i	0.340583	+	0.340583i
$118$	−66.6774	+	66.6774i	−0.565063	+	0.565063i
$119$			4.41379i			0.0370906i
$120$	11.6513	+	21.5464i	0.0970945	+	0.179553i
$121$	97.3779			0.804776
$122$	4.45593	+	4.45593i	0.0365241	+	0.0365241i
$123$	−43.0338	+	43.0338i	−0.349868	+	0.349868i
$124$			100.178i			0.807890i
$125$	−10.4429	+	124.563i	−0.0835428	+	0.996504i
$126$	−11.2250			−0.0890871
$127$	−172.678	−	172.678i	−1.35967	−	1.35967i	−0.874325	−	0.485341i	$-0.838695\pi$
$127$	−172.678	−	172.678i	−1.35967	−	1.35967i	−0.485341	−	0.874325i	$-0.661305\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$			144.377i			1.11920i
$130$	−116.838	+	63.1811i	−0.898757	+	0.486009i
$131$	147.540			1.12626			0.563129	−	0.826369i	$-0.309597\pi$
$131$	147.540			1.12626			0.563129	+	0.826369i	$0.309597\pi$
$132$	−36.1976	−	36.1976i	−0.274224	−	0.274224i
$133$	−28.3053	+	28.3053i	−0.212822	+	0.212822i
$134$			176.885i			1.32004i
$135$	24.8983	+	7.42128i	0.184432	+	0.0549724i
$136$	4.71854			0.0346951
$137$	96.5907	+	96.5907i	0.705042	+	0.705042i	0.965488	−	0.260447i	$-0.0838698\pi$
$137$	96.5907	+	96.5907i	0.705042	+	0.705042i	−0.260447	+	0.965488i	$0.583870\pi$
$138$	55.1307	−	55.1307i	0.399498	−	0.399498i
$139$		−	184.197i		−	1.32516i	−0.748993	−	0.662578i	$-0.769462\pi$
$139$		−	184.197i		−	1.32516i	0.748993	−	0.662578i	$-0.230538\pi$
$140$	7.55746	−	25.3552i	0.0539818	−	0.181108i
$141$	−49.3928			−0.350303
$142$	−69.3188	−	69.3188i	−0.488161	−	0.488161i
$143$	196.287	−	196.287i	1.37264	−	1.37264i
$144$			12.0000i			0.0833333i
$145$	7.84245	+	14.5027i	0.0540859	+	0.100019i
$146$	−116.833			−0.800227
$147$	8.57321	+	8.57321i	0.0583212	+	0.0583212i
$148$	−12.3147	+	12.3147i	−0.0832074	+	0.0832074i
$149$			206.358i			1.38495i	0.721442	+	0.692475i	$0.243480\pi$
$149$			206.358i			1.38495i	−0.721442	+	0.692475i	$0.756520\pi$
$150$	−33.5266	+	51.2442i	−0.223511	+	0.341628i
$151$	51.4825			0.340944			0.170472	−	0.985363i	$-0.445471\pi$
$151$	51.4825			0.340944			0.170472	+	0.985363i	$0.445471\pi$
$152$	30.2597	+	30.2597i	0.199077	+	0.199077i
$153$	3.53890	−	3.53890i	0.0231301	−	0.0231301i
$154$			55.2928i			0.359044i
$155$	−220.299	+	119.128i	−1.42128	+	0.768568i
$156$	−65.0718			−0.417127
$157$	91.7859	+	91.7859i	0.584624	+	0.584624i	0.936170	−	0.351547i	$-0.114344\pi$
$157$	91.7859	+	91.7859i	0.584624	+	0.584624i	−0.351547	+	0.936170i	$0.614344\pi$
$158$	−52.8307	+	52.8307i	−0.334372	+	0.334372i
$159$		−	26.7062i		−	0.167963i
$160$	−27.1058	−	8.07926i	−0.169411	−	0.0504954i
$161$	−84.2136			−0.523066
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	−11.1451	+	11.1451i	−0.0683748	+	0.0683748i	−0.740467	−	0.672092i	$-0.765396\pi$
$163$	−11.1451	+	11.1451i	−0.0683748	+	0.0683748i	0.672092	+	0.740467i	$0.265396\pi$
$164$		−	70.2739i		−	0.428499i
$165$	36.5563	−	122.646i	0.221553	−	0.743308i
$166$	106.857			0.643718
$167$	224.811	+	224.811i	1.34617	+	1.34617i	0.889776	+	0.456397i	$0.150860\pi$
$167$	224.811	+	224.811i	1.34617	+	1.34617i	0.456397	+	0.889776i	$0.349140\pi$
$168$	9.16515	−	9.16515i	0.0545545	−	0.0545545i
$169$		−	183.861i		−	1.08794i
$170$	5.61109	+	10.3764i	0.0330064	+	0.0610375i
$171$	45.3895			0.265436
$172$	−117.883	−	117.883i	−0.685369	−	0.685369i
$173$	43.4546	−	43.4546i	0.251183	−	0.251183i	−0.570273	−	0.821455i	$-0.693162\pi$
$173$	43.4546	−	43.4546i	0.251183	−	0.251183i	0.821455	+	0.570273i	$0.193162\pi$
$174$			8.07713i			0.0464203i
$175$	64.7448	−	13.5320i	0.369970	−	0.0773257i
$176$	59.1105			0.335855
$177$	−81.6628	−	81.6628i	−0.461372	−	0.461372i
$178$	−21.3553	+	21.3553i	−0.119973	+	0.119973i
$179$			167.373i			0.935046i	0.883981	+	0.467523i	$0.154854\pi$
$179$			167.373i			0.935046i	−0.883981	+	0.467523i	$0.845146\pi$
$180$	−26.3888	+	14.2699i	−0.146605	+	0.0792773i
$181$	225.762			1.24730			0.623652	−	0.781702i	$-0.285648\pi$
$181$	225.762			1.24730			0.623652	+	0.781702i	$0.285648\pi$
$182$	49.6994	+	49.6994i	0.273074	+	0.273074i
$183$	−5.45738	+	5.45738i	−0.0298218	+	0.0298218i
$184$			90.0281i			0.489283i
$185$	−41.7250	−	12.4367i	−0.225540	−	0.0672254i
$186$	−122.693			−0.659639
$187$	−17.4322	−	17.4322i	−0.0932202	−	0.0932202i
$188$	40.3290	−	40.3290i	0.214516	−	0.214516i
$189$		−	13.7477i		−	0.0727393i
$190$	−30.5595	+	102.527i	−0.160839	+	0.539614i
$191$	−148.626			−0.778145			−0.389073	−	0.921207i	$-0.627204\pi$
$191$	−148.626			−0.778145			−0.389073	+	0.921207i	$0.627204\pi$
$192$	−9.79796	−	9.79796i	−0.0510310	−	0.0510310i
$193$	−158.063	+	158.063i	−0.818979	+	0.818979i	−0.985960	−	0.166982i	$-0.946598\pi$
$193$	−158.063	+	158.063i	−0.818979	+	0.818979i	0.166982	+	0.985960i	$0.446598\pi$
$194$		−	180.712i		−	0.931507i
$195$	−77.3807	−	143.097i	−0.396824	−	0.733832i
$196$	−14.0000			−0.0714286
$197$	26.7707	+	26.7707i	0.135892	+	0.135892i	0.771781	−	0.635889i	$-0.219366\pi$
$197$	26.7707	+	26.7707i	0.135892	+	0.135892i	−0.635889	+	0.771781i	$0.719366\pi$
$198$	44.3328	−	44.3328i	0.223903	−	0.223903i
$199$		−	171.790i		−	0.863269i	−0.902049	−	0.431634i	$-0.857937\pi$
$199$		−	171.790i		−	0.863269i	0.902049	−	0.431634i	$-0.142063\pi$
$200$	−14.4663	−	69.2151i	−0.0723315	−	0.346075i
$201$	−216.639			−1.07780
$202$	−43.6109	−	43.6109i	−0.215896	−	0.215896i
$203$	6.16901	−	6.16901i	0.0303892	−	0.0303892i
$204$			5.77900i			0.0283284i
$205$	154.537	−	83.5668i	0.753839	−	0.407643i
$206$	97.7275			0.474405
$207$	67.5211	+	67.5211i	0.326189	+	0.326189i
$208$	53.1309	−	53.1309i	0.255437	−	0.255437i
$209$		−	223.583i		−	1.06977i
$210$	31.0536	+	9.25596i	0.147874	+	0.0440760i
$211$	−302.432			−1.43333			−0.716664	−	0.697419i	$-0.754332\pi$
$211$	−302.432			−1.43333			−0.716664	+	0.697419i	$0.754332\pi$
$212$	21.8055	+	21.8055i	0.102856	+	0.102856i
$213$	84.8978	−	84.8978i	0.398581	−	0.398581i
$214$		−	46.2994i		−	0.216352i
$215$	119.051	−	399.416i	0.553728	−	1.85775i
$216$	−14.6969			−0.0680414
$217$	93.7082	+	93.7082i	0.431835	+	0.431835i
$218$	141.834	−	141.834i	0.650613	−	0.650613i
$219$		−	143.091i		−	0.653383i
$220$	70.2918	+	129.988i	0.319508	+	0.590854i
$221$	−31.3375			−0.141799
$222$	−15.0824	−	15.0824i	−0.0679385	−	0.0679385i
$223$	−170.784	+	170.784i	−0.765850	+	0.765850i	−0.977373	−	0.211523i	$-0.932158\pi$
$223$	−170.784	+	170.784i	−0.765850	+	0.765850i	0.211523	+	0.977373i	$0.432158\pi$
$224$			14.9666i			0.0668153i
$225$	−62.7610	−	41.0616i	−0.278938	−	0.182496i
$226$	227.492			1.00660
$227$	154.323	+	154.323i	0.679838	+	0.679838i	0.959963	−	0.280125i	$-0.0903760\pi$
$227$	154.323	+	154.323i	0.679838	+	0.679838i	−0.280125	+	0.959963i	$0.590376\pi$
$228$	−37.0604	+	37.0604i	−0.162546	+	0.162546i
$229$		−	33.7243i		−	0.147267i	−0.997285	−	0.0736337i	$-0.976540\pi$
$229$		−	33.7243i		−	0.147267i	0.997285	−	0.0736337i	$-0.0234596\pi$
$230$	−197.978	+	107.058i	−0.860774	+	0.465469i
$231$	−67.7195			−0.293158
$232$	−6.59495	−	6.59495i	−0.0284265	−	0.0284265i
$233$	−207.998	+	207.998i	−0.892697	+	0.892697i	−0.994776	−	0.102079i	$-0.967450\pi$
$233$	−207.998	+	207.998i	−0.892697	+	0.892697i	0.102079	+	0.994776i	$0.467450\pi$
$234$		−	79.6963i		−	0.340583i
$235$	136.644	+	40.7286i	0.581464	+	0.173313i
$236$	133.355			0.565063
$237$	−64.7042	−	64.7042i	−0.273013	−	0.273013i
$238$	4.41379	−	4.41379i	0.0185453	−	0.0185453i
$239$			49.7163i			0.208018i	0.994576	+	0.104009i	$0.0331670\pi$
$239$			49.7163i			0.208018i	−0.994576	+	0.104009i	$0.966833\pi$
$240$	9.89504	−	33.1977i	0.0412293	−	0.138324i
$241$	−49.9716			−0.207351			−0.103676	−	0.994611i	$-0.533060\pi$
$241$	−49.9716			−0.207351			−0.103676	+	0.994611i	$0.533060\pi$
$242$	−97.3779	−	97.3779i	−0.402388	−	0.402388i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$		−	8.91187i		−	0.0365241i
$245$	−16.6482	−	30.7869i	−0.0679520	−	0.125661i
$246$	86.0675			0.349868
$247$	−200.965	−	200.965i	−0.813625	−	0.813625i
$248$	100.178	−	100.178i	0.403945	−	0.403945i
$249$			130.873i			0.525594i
$250$	135.006	−	114.120i	0.540023	−	0.456481i
$251$	−315.486			−1.25692			−0.628459	−	0.777843i	$-0.716314\pi$
$251$	−315.486			−1.25692			−0.628459	+	0.777843i	$0.716314\pi$
$252$	11.2250	+	11.2250i	0.0445435	+	0.0445435i
$253$	332.600	−	332.600i	1.31463	−	1.31463i
$254$			345.355i			1.35967i
$255$	−12.7084	+	6.87216i	−0.0498369	+	0.0269496i
$256$	16.0000			0.0625000
$257$	275.744	+	275.744i	1.07293	+	1.07293i	0.997122	+	0.0758107i	$0.0241545\pi$
$257$	275.744	+	275.744i	1.07293	+	1.07293i	0.0758107	+	0.997122i	$0.475846\pi$
$258$	144.377	−	144.377i	0.559601	−	0.559601i
$259$			23.0387i			0.0889524i
$260$	180.020	+	53.6573i	0.692383	+	0.206374i
$261$	−9.89243			−0.0379020
$262$	−147.540	−	147.540i	−0.563129	−	0.563129i
$263$	122.744	−	122.744i	0.466708	−	0.466708i	−0.434138	−	0.900846i	$-0.642947\pi$
$263$	122.744	−	122.744i	0.466708	−	0.466708i	0.900846	+	0.434138i	$0.142947\pi$
$264$			72.3952i			0.274224i
$265$	−22.0216	+	73.8820i	−0.0831002	+	0.278800i
$266$	56.6107			0.212822
$267$	−26.1547	−	26.1547i	−0.0979578	−	0.0979578i
$268$	176.885	−	176.885i	0.660018	−	0.660018i
$269$			62.3232i			0.231685i	0.993268	+	0.115842i	$0.0369567\pi$
$269$			62.3232i			0.231685i	−0.993268	+	0.115842i	$0.963043\pi$
$270$	−17.4770	−	32.3196i	−0.0647297	−	0.119702i
$271$	127.663			0.471081			0.235541	−	0.971864i	$-0.424314\pi$
$271$	127.663			0.471081			0.235541	+	0.971864i	$0.424314\pi$
$272$	−4.71854	−	4.71854i	−0.0173476	−	0.0173476i
$273$	−60.8691	+	60.8691i	−0.222964	+	0.222964i
$274$		−	193.181i		−	0.705042i
$275$	−202.264	+	309.153i	−0.735506	+	1.12419i
$276$	−110.261			−0.399498
$277$	−57.6863	−	57.6863i	−0.208254	−	0.208254i	0.595271	−	0.803525i	$-0.297045\pi$
$277$	−57.6863	−	57.6863i	−0.208254	−	0.208254i	−0.803525	+	0.595271i	$0.797045\pi$
$278$	−184.197	+	184.197i	−0.662578	+	0.662578i
$279$		−	150.267i		−	0.538593i
$280$	−32.9126	+	17.7977i	−0.117545	+	0.0635633i
$281$	119.372			0.424812			0.212406	−	0.977182i	$-0.431870\pi$
$281$	119.372			0.424812			0.212406	+	0.977182i	$0.431870\pi$
$282$	49.3928	+	49.3928i	0.175152	+	0.175152i
$283$	−175.257	+	175.257i	−0.619282	+	0.619282i	−0.945347	−	0.326065i	$-0.894277\pi$
$283$	−175.257	+	175.257i	−0.619282	+	0.619282i	0.326065	+	0.945347i	$0.394277\pi$
$284$			138.638i			0.488161i
$285$	−125.569	−	37.4276i	−0.440593	−	0.131325i
$286$	−392.574			−1.37264
$287$	−65.7352	−	65.7352i	−0.229042	−	0.229042i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$		−	286.217i		−	0.990370i
$290$	6.66029	−	22.3452i	0.0229665	−	0.0770524i
$291$	221.327			0.760572
$292$	116.833	+	116.833i	0.400114	+	0.400114i
$293$	224.254	−	224.254i	0.765372	−	0.765372i	−0.211916	−	0.977288i	$-0.567970\pi$
$293$	224.254	−	224.254i	0.765372	−	0.765372i	0.977288	+	0.211916i	$0.0679703\pi$
$294$		−	17.1464i		−	0.0583212i
$295$	158.580	+	293.256i	0.537560	+	0.994089i
$296$	24.6294			0.0832074
$297$	54.2964	+	54.2964i	0.182816	+	0.182816i
$298$	206.358	−	206.358i	0.692475	−	0.692475i
$299$		−	597.909i		−	1.99970i
$300$	84.7708	−	17.7175i	0.282569	−	0.0590585i
$301$	−220.540			−0.732690
$302$	−51.4825	−	51.4825i	−0.170472	−	0.170472i
$303$	53.4123	−	53.4123i	0.176278	−	0.176278i
$304$		−	60.5194i		−	0.199077i
$305$	19.5978	−	10.5976i	0.0642551	−	0.0347464i
$306$	−7.07780			−0.0231301
$307$	202.366	+	202.366i	0.659172	+	0.659172i	0.955184	−	0.296012i	$-0.0956569\pi$
$307$	202.366	+	202.366i	0.659172	+	0.659172i	−0.296012	+	0.955184i	$0.595657\pi$
$308$	55.2928	−	55.2928i	0.179522	−	0.179522i
$309$			119.691i			0.387350i
$310$	339.427	+	101.171i	1.09493	+	0.326358i
$311$	−382.114			−1.22866			−0.614331	−	0.789049i	$-0.710574\pi$
$311$	−382.114			−1.22866			−0.614331	+	0.789049i	$0.710574\pi$
$312$	65.0718	+	65.0718i	0.208563	+	0.208563i
$313$	−235.445	+	235.445i	−0.752220	+	0.752220i	−0.974893	−	0.222674i	$-0.928522\pi$
$313$	−235.445	+	235.445i	−0.752220	+	0.752220i	0.222674	+	0.974893i	$0.428522\pi$
$314$		−	183.572i		−	0.584624i
$315$	−11.3362	+	38.0328i	−0.0359879	+	0.120739i
$316$	105.661			0.334372
$317$	297.704	+	297.704i	0.939129	+	0.939129i	0.998251	−	0.0591213i	$-0.0188299\pi$
$317$	297.704	+	297.704i	0.939129	+	0.939129i	−0.0591213	+	0.998251i	$0.518830\pi$
$318$	−26.7062	+	26.7062i	−0.0839817	+	0.0839817i
$319$			48.7288i			0.152755i
$320$	19.0266	+	35.1851i	0.0594580	+	0.109953i
$321$	56.7049			0.176651
$322$	84.2136	+	84.2136i	0.261533	+	0.261533i
$323$	−17.8477	+	17.8477i	−0.0552559	+	0.0552559i
$324$		−	18.0000i		−	0.0555556i
$325$	96.0760	+	459.682i	0.295618	+	1.41441i
$326$	22.2902			0.0683748
$327$	173.710	+	173.710i	0.531223	+	0.531223i
$328$	−70.2739	+	70.2739i	−0.214250	+	0.214250i
$329$		−	75.4487i		−	0.229327i
$330$	−159.202	+	86.0895i	−0.482430	+	0.260877i
$331$	−197.349			−0.596221			−0.298110	−	0.954531i	$-0.596356\pi$
$331$	−197.349			−0.596221			−0.298110	+	0.954531i	$0.596356\pi$
$332$	−106.857	−	106.857i	−0.321859	−	0.321859i
$333$	18.4720	−	18.4720i	0.0554716	−	0.0554716i
$334$		−	449.622i		−	1.34617i
$335$	599.326	+	178.637i	1.78903	+	0.533246i
$336$	−18.3303			−0.0545545
$337$	−259.060	−	259.060i	−0.768723	−	0.768723i	0.209159	−	0.977882i	$-0.432927\pi$
$337$	−259.060	−	259.060i	−0.768723	−	0.768723i	−0.977882	+	0.209159i	$0.932927\pi$
$338$	−183.861	+	183.861i	−0.543968	+	0.543968i
$339$			278.619i			0.821886i
$340$	4.76529	−	15.9875i	0.0140155	−	0.0470220i
$341$	−740.198			−2.17067
$342$	−45.3895	−	45.3895i	−0.132718	−	0.132718i
$343$	−13.0958	+	13.0958i	−0.0381802	+	0.0381802i
$344$			235.767i			0.685369i
$345$	−131.119	−	242.472i	−0.380054	−	0.702819i
$346$	−86.9092			−0.251183
$347$	−316.016	−	316.016i	−0.910710	−	0.910710i	0.0856183	−	0.996328i	$-0.472713\pi$
$347$	−316.016	−	316.016i	−0.910710	−	0.910710i	−0.996328	+	0.0856183i	$0.972713\pi$
$348$	8.07713	−	8.07713i	0.0232102	−	0.0232102i
$349$		−	64.9155i		−	0.186004i	−0.995666	−	0.0930022i	$-0.970354\pi$
$349$		−	64.9155i		−	0.186004i	0.995666	−	0.0930022i	$-0.0296464\pi$
$350$	−78.2768	−	51.2128i	−0.223648	−	0.146322i
$351$	97.6077			0.278085
$352$	−59.1105	−	59.1105i	−0.167927	−	0.167927i
$353$	328.571	−	328.571i	0.930796	−	0.930796i	−0.0669597	−	0.997756i	$-0.521330\pi$
$353$	328.571	−	328.571i	0.930796	−	0.930796i	0.997756	+	0.0669597i	$0.0213299\pi$
$354$			163.326i			0.461372i
$355$	−304.873	+	164.862i	−0.858798	+	0.464401i
$356$	42.7105			0.119973
$357$	5.40576	+	5.40576i	0.0151422	+	0.0151422i
$358$	167.373	−	167.373i	0.467523	−	0.467523i
$359$		−	110.889i		−	0.308883i	−0.988002	−	0.154442i	$-0.950642\pi$
$359$		−	110.889i		−	0.308883i	0.988002	−	0.154442i	$-0.0493579\pi$
$360$	40.6587	+	12.1189i	0.112941	+	0.0336636i
$361$	132.088			0.365895
$362$	−225.762	−	225.762i	−0.623652	−	0.623652i
$363$	119.263	−	119.263i	0.328548	−	0.328548i
$364$		−	99.3988i		−	0.273074i
$365$	−117.991	+	395.857i	−0.323262	+	1.08454i
$366$	10.9148			0.0298218
$367$	−347.342	−	347.342i	−0.946436	−	0.946436i	0.0522011	−	0.998637i	$-0.483376\pi$
$367$	−347.342	−	347.342i	−0.946436	−	0.946436i	−0.998637	+	0.0522011i	$0.983376\pi$
$368$	90.0281	−	90.0281i	0.244642	−	0.244642i
$369$			105.411i			0.285666i
$370$	29.2883	+	54.1617i	0.0791575	+	0.146383i
$371$	40.7944			0.109958
$372$	122.693	+	122.693i	0.329820	+	0.329820i
$373$	−433.660	+	433.660i	−1.16263	+	1.16263i	−0.178728	+	0.983899i	$0.557198\pi$
$373$	−433.660	+	433.660i	−1.16263	+	1.16263i	−0.983899	+	0.178728i	$0.942802\pi$
$374$			34.8644i			0.0932202i
$375$	139.768	+	165.348i	0.372715	+	0.440927i
$376$	−80.6581			−0.214516
$377$	43.7995	+	43.7995i	0.116179	+	0.116179i
$378$	−13.7477	+	13.7477i	−0.0363696	+	0.0363696i
$379$			5.82662i			0.0153737i	0.999970	+	0.00768684i	$0.00244682\pi$
$379$			5.82662i			0.0153737i	−0.999970	+	0.00768684i	$0.997553\pi$
$380$	133.086	−	71.9672i	0.350227	−	0.189387i
$381$	−422.972			−1.11016
$382$	148.626	+	148.626i	0.389073	+	0.389073i
$383$	−84.7856	+	84.7856i	−0.221372	+	0.221372i	−0.809076	−	0.587704i	$-0.800032\pi$
$383$	−84.7856	+	84.7856i	−0.221372	+	0.221372i	0.587704	+	0.809076i	$0.300032\pi$
$384$			19.5959i			0.0510310i
$385$	187.344	+	55.8406i	0.486609	+	0.145041i
$386$	316.126			0.818979
$387$	176.825	+	176.825i	0.456913	+	0.456913i
$388$	−180.712	+	180.712i	−0.465754	+	0.465754i
$389$		−	287.140i		−	0.738150i	−0.929400	−	0.369075i	$-0.879675\pi$
$389$		−	287.140i		−	0.738150i	0.929400	−	0.369075i	$-0.120325\pi$
$390$	−65.7165	+	220.478i	−0.168504	+	0.565328i
$391$	−53.1001			−0.135806
$392$	14.0000	+	14.0000i	0.0357143	+	0.0357143i
$393$	180.699	−	180.699i	0.459793	−	0.459793i
$394$		−	53.5413i		−	0.135892i
$395$	125.648	+	232.357i	0.318097	+	0.588245i
$396$	−88.6657			−0.223903
$397$	89.5514	+	89.5514i	0.225570	+	0.225570i	0.810839	−	0.585269i	$-0.199011\pi$
$397$	89.5514	+	89.5514i	0.225570	+	0.225570i	−0.585269	+	0.810839i	$0.699011\pi$
$398$	−171.790	+	171.790i	−0.431634	+	0.431634i
$399$			69.3336i			0.173768i
$400$	−54.7488	+	83.6814i	−0.136872	+	0.209203i
$401$	−649.944			−1.62081			−0.810405	−	0.585871i	$-0.800753\pi$
$401$	−649.944			−1.62081			−0.810405	+	0.585871i	$0.800753\pi$
$402$	216.639	+	216.639i	0.538902	+	0.538902i
$403$	−665.320	+	665.320i	−1.65092	+	1.65092i
$404$			87.2218i			0.215896i
$405$	39.5832	−	21.4049i	0.0977363	−	0.0528515i
$406$	−12.3380			−0.0303892
$407$	−90.9909	−	90.9909i	−0.223565	−	0.223565i
$408$	5.77900	−	5.77900i	0.0141642	−	0.0141642i
$409$			717.337i			1.75388i	0.480600	+	0.876940i	$0.340419\pi$
$409$			717.337i			1.75388i	−0.480600	+	0.876940i	$0.659581\pi$
$410$	−238.104	−	70.9701i	−0.580741	−	0.173098i
$411$	236.598			0.575664
$412$	−97.7275	−	97.7275i	−0.237203	−	0.237203i
$413$	124.742	−	124.742i	0.302039	−	0.302039i
$414$		−	135.042i		−	0.326189i
$415$	107.916	−	362.057i	0.260038	−	0.872426i
$416$	−106.262			−0.255437
$417$	−225.594	−	225.594i	−0.540992	−	0.540992i
$418$	−223.583	+	223.583i	−0.534887	+	0.534887i
$419$			680.885i			1.62502i	0.582945	+	0.812511i	$0.301900\pi$
$419$			680.885i			1.62502i	−0.582945	+	0.812511i	$0.698100\pi$
$420$	−21.7977	−	40.3096i	−0.0518992	−	0.0959752i
$421$	710.333			1.68725			0.843626	−	0.536931i	$-0.180416\pi$
$421$	710.333			1.68725			0.843626	+	0.536931i	$0.180416\pi$
$422$	302.432	+	302.432i	0.716664	+	0.716664i
$423$	−60.4936	+	60.4936i	−0.143011	+	0.143011i
$424$		−	43.6110i		−	0.102856i
$425$	40.8242	−	8.53247i	0.0960570	−	0.0200764i
$426$	−169.796			−0.398581
$427$	−8.33629	−	8.33629i	−0.0195229	−	0.0195229i
$428$	−46.2994	+	46.2994i	−0.108176	+	0.108176i
$429$		−	480.803i		−	1.12075i
$430$	−518.467	+	280.365i	−1.20574	+	0.652011i
$431$	785.543			1.82261			0.911303	−	0.411737i	$-0.135078\pi$
$431$	785.543			1.82261			0.911303	+	0.411737i	$0.135078\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	484.429	−	484.429i	1.11877	−	1.11877i	0.126852	−	0.991922i	$-0.459513\pi$
$433$	484.429	−	484.429i	1.11877	−	1.11877i	0.991922	−	0.126852i	$-0.0404874\pi$
$434$		−	187.416i		−	0.431835i
$435$	27.3672	+	8.15716i	0.0629130	+	0.0187521i
$436$	−283.667			−0.650613
$437$	−340.528	−	340.528i	−0.779240	−	0.779240i
$438$	−143.091	+	143.091i	−0.326691	+	0.326691i
$439$			558.366i			1.27190i	0.771728	+	0.635952i	$0.219392\pi$
$439$			558.366i			1.27190i	−0.771728	+	0.635952i	$0.780608\pi$
$440$	59.6961	−	200.280i	0.135673	−	0.455181i
$441$	21.0000			0.0476190
$442$	31.3375	+	31.3375i	0.0708993	+	0.0708993i
$443$	94.3596	−	94.3596i	0.213001	−	0.213001i	−0.592540	−	0.805541i	$-0.701875\pi$
$443$	94.3596	−	94.3596i	0.213001	−	0.213001i	0.805541	+	0.592540i	$0.201875\pi$
$444$			30.1647i			0.0679385i
$445$	50.7896	+	93.9233i	0.114134	+	0.211064i
$446$	341.569			0.765850
$447$	252.735	+	252.735i	0.565404	+	0.565404i
$448$	14.9666	−	14.9666i	0.0334077	−	0.0334077i
$449$		−	642.007i		−	1.42986i	−0.699197	−	0.714929i	$-0.746459\pi$
$449$		−	642.007i		−	1.42986i	0.699197	−	0.714929i	$-0.253541\pi$
$450$	21.6995	+	103.823i	0.0482210	+	0.230717i
$451$	519.240			1.15131
$452$	−227.492	−	227.492i	−0.503301	−	0.503301i
$453$	63.0529	−	63.0529i	0.139190	−	0.139190i
$454$		−	308.647i		−	0.679838i
$455$	218.585	−	118.201i	0.480406	−	0.259782i
$456$	74.1208			0.162546
$457$	320.594	+	320.594i	0.701519	+	0.701519i	0.964736	−	0.263218i	$-0.0847838\pi$
$457$	320.594	+	320.594i	0.701519	+	0.701519i	−0.263218	+	0.964736i	$0.584784\pi$
$458$	−33.7243	+	33.7243i	−0.0736337	+	0.0736337i
$459$		−	8.66850i		−	0.0188856i
$460$	305.036	+	90.9201i	0.663121	+	0.197652i
$461$	−300.193			−0.651177			−0.325589	−	0.945512i	$-0.605562\pi$
$461$	−300.193			−0.651177			−0.325589	+	0.945512i	$0.605562\pi$
$462$	67.7195	+	67.7195i	0.146579	+	0.146579i
$463$	58.9154	−	58.9154i	0.127247	−	0.127247i	−0.640615	−	0.767862i	$-0.721321\pi$
$463$	58.9154	−	58.9154i	0.127247	−	0.127247i	0.767862	+	0.640615i	$0.221321\pi$
$464$			13.1899i			0.0284265i
$465$	−123.908	+	415.711i	−0.266470	+	0.894003i
$466$	415.997			0.892697
$467$	−362.497	−	362.497i	−0.776226	−	0.776226i	0.202961	−	0.979187i	$-0.434943\pi$
$467$	−362.497	−	362.497i	−0.776226	−	0.776226i	−0.979187	+	0.202961i	$0.934943\pi$
$468$	−79.6963	+	79.6963i	−0.170291	+	0.170291i
$469$		−	330.921i		−	0.705589i
$470$	−95.9153	−	177.373i	−0.204075	−	0.377388i
$471$	224.829			0.477343
$472$	−133.355	−	133.355i	−0.282531	−	0.282531i
$473$	871.018	−	871.018i	1.84148	−	1.84148i
$474$			129.408i			0.273013i
$475$	316.521	+	207.085i	0.666361	+	0.435968i
$476$	−8.82757			−0.0185453
$477$	−32.7083	−	32.7083i	−0.0685708	−	0.0685708i
$478$	49.7163	−	49.7163i	0.104009	−	0.104009i
$479$		−	233.704i		−	0.487900i	−0.969788	−	0.243950i	$-0.921557\pi$
$479$		−	233.704i		−	0.487900i	0.969788	−	0.243950i	$-0.0784433\pi$
$480$	−43.0928	+	23.3027i	−0.0897766	+	0.0485472i
$481$	−163.573			−0.340068
$482$	49.9716	+	49.9716i	0.103676	+	0.103676i
$483$	−103.140	+	103.140i	−0.213541	+	0.213541i
$484$			194.756i			0.402388i
$485$	−612.295	−	182.503i	−1.26246	−	0.376295i
$486$	22.0454			0.0453609
$487$	234.027	+	234.027i	0.480549	+	0.480549i	0.905307	−	0.424758i	$-0.139641\pi$
$487$	234.027	+	234.027i	0.480549	+	0.480549i	−0.424758	+	0.905307i	$0.639641\pi$
$488$	−8.91187	+	8.91187i	−0.0182620	+	0.0182620i
$489$			27.2998i			0.0558278i
$490$	−14.1387	+	47.4352i	−0.0288545	+	0.0968065i
$491$	29.6268			0.0603398			0.0301699	−	0.999545i	$-0.490395\pi$
$491$	29.6268			0.0603398			0.0301699	+	0.999545i	$0.490395\pi$
$492$	−86.0675	−	86.0675i	−0.174934	−	0.174934i
$493$	3.88981	−	3.88981i	0.00789009	−	0.00789009i
$494$			401.931i			0.813625i
$495$	−105.438	−	194.982i	−0.213005	−	0.393903i
$496$	−200.357			−0.403945
$497$	129.684	+	129.684i	0.260933	+	0.260933i
$498$	130.873	−	130.873i	0.262797	−	0.262797i
$499$		−	322.566i		−	0.646426i	−0.946326	−	0.323213i	$-0.895237\pi$
$499$		−	322.566i		−	0.646426i	0.946326	−	0.323213i	$-0.104763\pi$
$500$	−249.126	−	20.8857i	−0.498252	−	0.0417714i
$501$	550.672			1.09915
$502$	315.486	+	315.486i	0.628459	+	0.628459i
$503$	−350.402	+	350.402i	−0.696625	+	0.696625i	−0.963681	−	0.267056i	$-0.913949\pi$
$503$	−350.402	+	350.402i	−0.696625	+	0.696625i	0.267056	+	0.963681i	$0.413949\pi$
$504$		−	22.4499i		−	0.0445435i
$505$	−191.807	+	103.721i	−0.379815	+	0.205388i
$506$	−665.200			−1.31463
$507$	−225.183	−	225.183i	−0.444148	−	0.444148i
$508$	345.355	−	345.355i	0.679833	−	0.679833i
$509$			66.4967i			0.130642i	0.997864	+	0.0653210i	$0.0208071\pi$
$509$			66.4967i			0.130642i	−0.997864	+	0.0653210i	$0.979193\pi$
$510$	19.5806	+	5.83626i	0.0383933	+	0.0114436i
$511$	218.575			0.427740
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	55.5906	−	55.5906i	0.108364	−	0.108364i
$514$		−	551.488i		−	1.07293i
$515$	98.6958	−	331.123i	0.191642	−	0.642957i
$516$	−288.754			−0.559601
$517$	297.983	+	297.983i	0.576370	+	0.576370i
$518$	23.0387	−	23.0387i	0.0444762	−	0.0444762i
$519$		−	106.442i		−	0.205090i
$520$	−126.362	−	233.677i	−0.243004	−	0.449378i
$521$	−603.618			−1.15858			−0.579288	−	0.815123i	$-0.696669\pi$
$521$	−603.618			−1.15858			−0.579288	+	0.815123i	$0.696669\pi$
$522$	9.89243	+	9.89243i	0.0189510	+	0.0189510i
$523$	−294.450	+	294.450i	−0.563002	+	0.563002i	−0.930159	−	0.367157i	$-0.880331\pi$
$523$	−294.450	+	294.450i	−0.563002	+	0.563002i	0.367157	+	0.930159i	$0.380331\pi$
$524$			295.080i			0.563129i
$525$	62.7226	−	95.8691i	0.119472	−	0.182608i
$526$	−245.488			−0.466708
$527$	59.0869	+	59.0869i	0.112119	+	0.112119i
$528$	72.3952	−	72.3952i	0.137112	−	0.137112i
$529$		−	484.133i		−	0.915185i
$530$	95.9036	−	51.8605i	0.180950	−	0.0978499i
$531$	−200.032			−0.376709
$532$	−56.6107	−	56.6107i	−0.106411	−	0.106411i
$533$	466.714	−	466.714i	0.875636	−	0.875636i
$534$			52.3095i			0.0979578i
$535$	−156.873	−	46.7581i	−0.293220	−	0.0873983i
$536$	−353.770			−0.660018
$537$	204.990	+	204.990i	0.381731	+	0.381731i
$538$	62.3232	−	62.3232i	0.115842	−	0.115842i
$539$		−	103.443i		−	0.191917i
$540$	−14.8426	+	49.7966i	−0.0274862	+	0.0922159i
$541$	−248.513			−0.459358			−0.229679	−	0.973266i	$-0.573768\pi$
$541$	−248.513			−0.459358			−0.229679	+	0.973266i	$0.573768\pi$
$542$	−127.663	−	127.663i	−0.235541	−	0.235541i
$543$	276.501	−	276.501i	0.509209	−	0.509209i
$544$			9.43707i			0.0173476i
$545$	−337.326	−	623.804i	−0.618946	−	1.14459i
$546$	121.738			0.222964
$547$	−246.861	−	246.861i	−0.451299	−	0.451299i	0.444487	−	0.895786i	$-0.353386\pi$
$547$	−246.861	−	246.861i	−0.451299	−	0.451299i	−0.895786	+	0.444487i	$0.853386\pi$
$548$	−193.181	+	193.181i	−0.352521	+	0.352521i
$549$			13.3678i			0.0243494i
$550$	511.417	−	106.889i	0.929849	−	0.194343i
$551$	49.8903			0.0905450
$552$	110.261	+	110.261i	0.199749	+	0.199749i
$553$	98.8373	−	98.8373i	0.178729	−	0.178729i
$554$			115.373i			0.208254i
$555$	−66.3343	+	35.8707i	−0.119521	+	0.0646318i
$556$	368.393			0.662578
$557$	−333.317	−	333.317i	−0.598416	−	0.598416i	0.341475	−	0.939891i	$-0.389073\pi$
$557$	−333.317	−	333.317i	−0.598416	−	0.598416i	−0.939891	+	0.341475i	$0.889073\pi$
$558$	−150.267	+	150.267i	−0.269297	+	0.269297i
$559$		−	1565.81i		−	2.80110i
$560$	50.7103	+	15.1149i	0.0905542	+	0.0269909i
$561$	−42.6999			−0.0761140
$562$	−119.372	−	119.372i	−0.212406	−	0.212406i
$563$	499.267	−	499.267i	0.886798	−	0.886798i	−0.107416	−	0.994214i	$-0.534258\pi$
$563$	499.267	−	499.267i	0.886798	−	0.886798i	0.994214	+	0.107416i	$0.0342577\pi$
$564$		−	98.7856i		−	0.175152i
$565$	229.746	−	770.794i	0.406630	−	1.36424i
$566$	350.514			0.619282
$567$	−16.8375	−	16.8375i	−0.0296957	−	0.0296957i
$568$	138.638	−	138.638i	0.244080	−	0.244080i
$569$			990.818i			1.74133i	0.491874	+	0.870666i	$0.336312\pi$
$569$			990.818i			1.74133i	−0.491874	+	0.870666i	$0.663688\pi$
$570$	88.1414	+	162.997i	0.154634	+	0.285959i
$571$	−172.474			−0.302057			−0.151028	−	0.988529i	$-0.548258\pi$
$571$	−172.474			−0.302057			−0.151028	+	0.988529i	$0.548258\pi$
$572$	392.574	+	392.574i	0.686318	+	0.686318i
$573$	−182.029	+	182.029i	−0.317676	+	0.317676i
$574$			131.470i			0.229042i
$575$	162.797	+	778.913i	0.283125	+	1.35463i
$576$	−24.0000			−0.0416667
$577$	−75.2134	−	75.2134i	−0.130352	−	0.130352i	0.638920	−	0.769273i	$-0.279381\pi$
$577$	−75.2134	−	75.2134i	−0.130352	−	0.130352i	−0.769273	+	0.638920i	$0.779381\pi$
$578$	−286.217	+	286.217i	−0.495185	+	0.495185i
$579$			387.173i			0.668693i
$580$	−29.0055	+	15.6849i	−0.0500095	+	0.0270429i
$581$	−199.912			−0.344082
$582$	−221.327	−	221.327i	−0.380286	−	0.380286i
$583$	−161.117	+	161.117i	−0.276358	+	0.276358i
$584$		−	233.666i		−	0.400114i
$585$	−270.029	−	80.4859i	−0.461588	−	0.137583i
$586$	−448.508			−0.765372
$587$	371.013	+	371.013i	0.632050	+	0.632050i	0.948582	−	0.316532i	$-0.102519\pi$
$587$	371.013	+	371.013i	0.632050	+	0.632050i	−0.316532	+	0.948582i	$0.602519\pi$
$588$	−17.1464	+	17.1464i	−0.0291606	+	0.0291606i
$589$			757.841i			1.28666i
$590$	134.676	−	451.836i	0.228265	−	0.765824i
$591$	65.5745			0.110955
$592$	−24.6294	−	24.6294i	−0.0416037	−	0.0416037i
$593$	106.940	−	106.940i	0.180337	−	0.180337i	−0.611166	−	0.791503i	$-0.709299\pi$
$593$	106.940	−	106.940i	0.180337	−	0.180337i	0.791503	+	0.611166i	$0.209299\pi$
$594$		−	108.593i		−	0.182816i
$595$	−10.4974	−	19.4124i	−0.0176427	−	0.0326259i
$596$	−412.715			−0.692475
$597$	−210.399	−	210.399i	−0.352428	−	0.352428i
$598$	−597.909	+	597.909i	−0.999848	+	0.999848i
$599$			382.077i			0.637859i	0.947778	+	0.318929i	$0.103323\pi$
$599$			382.077i			0.637859i	−0.947778	+	0.318929i	$0.896677\pi$
$600$	−102.488	−	67.0533i	−0.170814	−	0.111755i
$601$	618.446			1.02903			0.514514	−	0.857482i	$-0.327972\pi$
$601$	618.446			1.02903			0.514514	+	0.857482i	$0.327972\pi$
$602$	220.540	+	220.540i	0.366345	+	0.366345i
$603$	−265.327	+	265.327i	−0.440012	+	0.440012i
$604$			102.965i			0.170472i
$605$	−428.281	+	231.596i	−0.707903	+	0.382803i
$606$	−106.825			−0.176278
$607$	222.670	+	222.670i	0.366837	+	0.366837i	0.866322	−	0.499485i	$-0.166477\pi$
$607$	222.670	+	222.670i	0.366837	+	0.366837i	−0.499485	+	0.866322i	$0.666477\pi$
$608$	−60.5194	+	60.5194i	−0.0995384	+	0.0995384i
$609$		−	15.1109i		−	0.0248127i
$610$	−30.1954	−	9.00017i	−0.0495007	−	0.0147544i
$611$	535.679			0.876725
$612$	7.07780	+	7.07780i	0.0115650	+	0.0115650i
$613$	422.055	−	422.055i	0.688508	−	0.688508i	−0.273394	−	0.961902i	$-0.588146\pi$
$613$	422.055	−	422.055i	0.688508	−	0.688508i	0.961902	+	0.273394i	$0.0881464\pi$
$614$		−	404.731i		−	0.659172i
$615$	86.9203	−	291.616i	0.141334	−	0.474173i
$616$	−110.586			−0.179522
$617$	−651.882	−	651.882i	−1.05653	−	1.05653i	−0.998303	−	0.0582314i	$-0.981454\pi$
$617$	−651.882	−	651.882i	−1.05653	−	1.05653i	−0.0582314	−	0.998303i	$-0.518546\pi$
$618$	119.691	−	119.691i	0.193675	−	0.193675i
$619$			687.434i			1.11056i	0.831665	+	0.555278i	$0.187388\pi$
$619$			687.434i			1.11056i	−0.831665	+	0.555278i	$0.812612\pi$
$620$	−238.256	−	440.598i	−0.384284	−	0.710642i
$621$	165.392			0.266332
$622$	382.114	+	382.114i	0.614331	+	0.614331i
$623$	39.9520	−	39.9520i	0.0641284	−	0.0641284i
$624$		−	130.144i		−	0.208563i
$625$	−250.322	−	572.681i	−0.400515	−	0.916290i
$626$	470.889			0.752220
$627$	−273.832	−	273.832i	−0.436734	−	0.436734i
$628$	−183.572	+	183.572i	−0.292312	+	0.292312i
$629$			14.5268i			0.0230951i
$630$	49.3689	−	26.6966i	0.0783634	−	0.0423755i
$631$	589.381			0.934043			0.467021	−	0.884246i	$-0.345327\pi$
$631$	589.381			0.934043			0.467021	+	0.884246i	$0.345327\pi$
$632$	−105.661	−	105.661i	−0.167186	−	0.167186i
$633$	−370.402	+	370.402i	−0.585154	+	0.585154i
$634$		−	595.408i		−	0.939129i
$635$	1170.14	+	348.777i	1.84274	+	0.549255i
$636$	53.4124			0.0839817
$637$	−92.9790	−	92.9790i	−0.145964	−	0.145964i
$638$	48.7288	−	48.7288i	0.0763775	−	0.0763775i
$639$		−	207.956i		−	0.325440i
$640$	16.1585	−	54.2116i	0.0252477	−	0.0847057i
$641$	410.799			0.640872			0.320436	−	0.947270i	$-0.396171\pi$
$641$	410.799			0.640872			0.320436	+	0.947270i	$0.396171\pi$
$642$	−56.7049	−	56.7049i	−0.0883254	−	0.0883254i
$643$	216.800	−	216.800i	0.337169	−	0.337169i	−0.518132	−	0.855301i	$-0.673372\pi$
$643$	216.800	−	216.800i	0.337169	−	0.337169i	0.855301	+	0.518132i	$0.173372\pi$
$644$		−	168.427i		−	0.261533i
$645$	−343.375	−	634.990i	−0.532364	−	0.984481i
$646$	35.6953			0.0552559
$647$	−411.008	−	411.008i	−0.635252	−	0.635252i	0.314129	−	0.949380i	$-0.398288\pi$
$647$	−411.008	−	411.008i	−0.635252	−	0.635252i	−0.949380	+	0.314129i	$0.898288\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$			985.333i			1.51823i
$650$	363.606	−	555.758i	0.559394	−	0.855013i
$651$	229.537			0.352592
$652$	−22.2902	−	22.2902i	−0.0341874	−	0.0341874i
$653$	−46.1020	+	46.1020i	−0.0706003	+	0.0706003i	−0.741525	−	0.670925i	$-0.765897\pi$
$653$	−46.1020	+	46.1020i	−0.0706003	+	0.0706003i	0.670925	+	0.741525i	$0.265897\pi$
$654$		−	347.420i		−	0.531223i
$655$	−648.900	+	350.897i	−0.990687	+	0.535720i
$656$	140.548			0.214250
$657$	−175.250	−	175.250i	−0.266742	−	0.266742i
$658$	−75.4487	+	75.4487i	−0.114664	+	0.114664i
$659$			911.116i			1.38257i	0.722580	+	0.691287i	$0.242956\pi$
$659$			911.116i			1.38257i	−0.722580	+	0.691287i	$0.757044\pi$
$660$	245.292	+	73.1125i	0.371654	+	0.110777i
$661$	24.2084			0.0366239			0.0183120	−	0.999832i	$-0.494171\pi$
$661$	24.2084			0.0366239			0.0183120	+	0.999832i	$0.494171\pi$
$662$	197.349	+	197.349i	0.298110	+	0.298110i
$663$	−38.3804	+	38.3804i	−0.0578890	+	0.0578890i
$664$			213.714i			0.321859i
$665$	57.1716	−	191.810i	0.0859723	−	0.288436i
$666$	−36.9441			−0.0554716
$667$	74.2164	+	74.2164i	0.111269	+	0.111269i
$668$	−449.622	+	449.622i	−0.673087	+	0.673087i
$669$			418.335i			0.625314i
$670$	−420.689	−	777.963i	−0.627894	−	1.16114i
$671$	65.8481			0.0981343
$672$	18.3303	+	18.3303i	0.0272772	+	0.0272772i
$673$	522.406	−	522.406i	0.776235	−	0.776235i	−0.202954	−	0.979188i	$-0.565054\pi$
$673$	522.406	−	522.406i	0.776235	−	0.776235i	0.979188	+	0.202954i	$0.0650541\pi$
$674$			518.119i			0.768723i
$675$	−127.156	+	26.5763i	−0.188380	+	0.0393723i
$676$	367.723			0.543968
$677$	−283.980	−	283.980i	−0.419468	−	0.419468i	0.465552	−	0.885020i	$-0.345856\pi$
$677$	−283.980	−	283.980i	−0.419468	−	0.419468i	−0.885020	+	0.465552i	$0.845856\pi$
$678$	278.619	−	278.619i	0.410943	−	0.410943i
$679$			338.082i			0.497912i
$680$	−20.7528	+	11.2222i	−0.0305188	+	0.0165032i
$681$	378.013			0.555086
$682$	740.198	+	740.198i	1.08533	+	1.08533i
$683$	−549.911	+	549.911i	−0.805141	+	0.805141i	−0.983894	−	0.178753i	$-0.942794\pi$
$683$	−549.911	+	549.911i	−0.805141	+	0.805141i	0.178753	+	0.983894i	$0.442794\pi$
$684$			90.7790i			0.132718i
$685$	−654.542	−	195.095i	−0.955536	−	0.284811i
$686$	26.1916			0.0381802
$687$	−41.3036	−	41.3036i	−0.0601217	−	0.0601217i
$688$	235.767	−	235.767i	0.342685	−	0.342685i
$689$			289.636i			0.420372i
$690$	−111.354	+	373.591i	−0.161383	+	0.541436i
$691$	−1119.58			−1.62023			−0.810117	−	0.586268i	$-0.800597\pi$
$691$	−1119.58			−1.62023			−0.810117	+	0.586268i	$0.800597\pi$
$692$	86.9092	+	86.9092i	0.125591	+	0.125591i
$693$	−82.9392	+	82.9392i	−0.119681	+	0.119681i
$694$			632.033i			0.910710i
$695$	438.078	+	810.122i	0.630329	+	1.16564i
$696$	−16.1543			−0.0232102
$697$	−41.4487	−	41.4487i	−0.0594673	−	0.0594673i
$698$	−64.9155	+	64.9155i	−0.0930022	+	0.0930022i
$699$			509.490i			0.728884i
$700$	27.0640	+	129.490i	0.0386628	+	0.184985i
$701$	693.405			0.989166			0.494583	−	0.869130i	$-0.335321\pi$
$701$	693.405			0.989166			0.494583	+	0.869130i	$0.335321\pi$
$702$	−97.6077	−	97.6077i	−0.139042	−	0.139042i
$703$	−93.1597	+	93.1597i	−0.132517	+	0.132517i
$704$			118.221i			0.167927i
$705$	217.236	−	117.472i	0.308136	−	0.166627i
$706$	−657.142			−0.930796
$707$	81.5886	+	81.5886i	0.115401	+	0.115401i
$708$	163.326	−	163.326i	0.230686	−	0.230686i
$709$			774.547i			1.09245i	0.837638	+	0.546225i	$0.183936\pi$
$709$			774.547i			1.09245i	−0.837638	+	0.546225i	$0.816064\pi$
$710$	469.736	+	140.011i	0.661600	+	0.197199i
$711$	−158.492			−0.222915
$712$	−42.7105	−	42.7105i	−0.0599867	−	0.0599867i
$713$	−1127.36	+	1127.36i	−1.58115	+	1.58115i
$714$		−	10.8115i		−	0.0151422i
$715$	−396.463	+	1330.13i	−0.554494	+	1.86032i
$716$	−334.747			−0.467523
$717$	60.8897	+	60.8897i	0.0849229	+	0.0849229i
$718$	−110.889	+	110.889i	−0.154442	+	0.154442i
$719$		−	8.61314i		−	0.0119793i	−0.999982	−	0.00598966i	$-0.998093\pi$
$719$		−	8.61314i		−	0.0119793i	0.999982	−	0.00598966i	$-0.00190658\pi$
$720$	−28.5398	−	52.7776i	−0.0396387	−	0.0733023i
$721$	−182.831			−0.253580
$722$	−132.088	−	132.088i	−0.182947	−	0.182947i
$723$	−61.2025	+	61.2025i	−0.0846507	+	0.0846507i
$724$			451.524i			0.623652i
$725$	−68.9843	−	45.1332i	−0.0951508	−	0.0622527i
$726$	−238.526			−0.328548
$727$	−305.108	−	305.108i	−0.419681	−	0.419681i	0.465413	−	0.885094i	$-0.345906\pi$
$727$	−305.108	−	305.108i	−0.419681	−	0.419681i	−0.885094	+	0.465413i	$0.845906\pi$
$728$	−99.3988	+	99.3988i	−0.136537	+	0.136537i
$729$			27.0000i			0.0370370i
$730$	513.848	−	277.867i	0.703902	−	0.380639i
$731$	−139.059			−0.190232
$732$	−10.9148	−	10.9148i	−0.0149109	−	0.0149109i
$733$	−73.0619	+	73.0619i	−0.0996751	+	0.0996751i	−0.755186	−	0.655511i	$-0.772453\pi$
$733$	−73.0619	+	73.0619i	−0.0996751	+	0.0996751i	0.655511	+	0.755186i	$0.272453\pi$
$734$			694.684i			0.946436i
$735$	−58.0960	−	17.3163i	−0.0790422	−	0.0235596i
$736$	−180.056			−0.244642
$737$	1306.97	+	1306.97i	1.77336	+	1.77336i
$738$	105.411	−	105.411i	0.142833	−	0.142833i
$739$			81.9526i			0.110897i	0.998462	+	0.0554483i	$0.0176588\pi$
$739$			81.9526i			0.110897i	−0.998462	+	0.0554483i	$0.982341\pi$
$740$	24.8734	−	83.4500i	0.0336127	−	0.112770i
$741$	−492.263			−0.664322
$742$	−40.7944	−	40.7944i	−0.0549789	−	0.0549789i
$743$	225.872	−	225.872i	0.304000	−	0.304000i	−0.538577	−	0.842577i	$-0.681038\pi$
$743$	225.872	−	225.872i	0.304000	−	0.304000i	0.842577	+	0.538577i	$0.181038\pi$
$744$		−	245.386i		−	0.329820i
$745$	−490.784	−	907.589i	−0.658771	−	1.21824i
$746$	867.319			1.16263
$747$	160.286	+	160.286i	0.214573	+	0.214573i
$748$	34.8644	−	34.8644i	0.0466101	−	0.0466101i
$749$			86.6182i			0.115645i
$750$	25.5797	−	305.116i	0.0341062	−	0.406821i
$751$	795.157			1.05880			0.529399	−	0.848373i	$-0.322417\pi$
$751$	795.157			1.05880			0.529399	+	0.848373i	$0.322417\pi$
$752$	80.6581	+	80.6581i	0.107258	+	0.107258i
$753$	−386.390	+	386.390i	−0.513134	+	0.513134i
$754$		−	87.5989i		−	0.116179i
$755$	−226.427	+	122.442i	−0.299903	+	0.162175i
$756$	27.4955			0.0363696
$757$	−43.3607	−	43.3607i	−0.0572796	−	0.0572796i	0.677887	−	0.735166i	$-0.262896\pi$
$757$	−43.3607	−	43.3607i	−0.0572796	−	0.0572796i	−0.735166	+	0.677887i	$0.762896\pi$
$758$	5.82662	−	5.82662i	0.00768684	−	0.00768684i
$759$		−	814.701i		−	1.07339i
$760$	−205.053	−	61.1190i	−0.269807	−	0.0804197i
$761$	448.207			0.588972			0.294486	−	0.955656i	$-0.404852\pi$
$761$	448.207			0.588972			0.294486	+	0.955656i	$0.404852\pi$
$762$	422.972	+	422.972i	0.555081	+	0.555081i
$763$	−265.346	+	265.346i	−0.347767	+	0.347767i
$764$		−	297.251i		−	0.389073i
$765$	−7.14793	+	23.9812i	−0.00934370	+	0.0313480i
$766$	169.571			0.221372
$767$	885.657	+	885.657i	1.15470	+	1.15470i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$			126.308i			0.164249i	0.996622	+	0.0821245i	$0.0261705\pi$
$769$			126.308i			0.164249i	−0.996622	+	0.0821245i	$0.973829\pi$
$770$	−131.504	−	243.185i	−0.170784	−	0.315825i
$771$	675.432			0.876046
$772$	−316.126	−	316.126i	−0.409489	−	0.409489i
$773$	−534.661	+	534.661i	−0.691670	+	0.691670i	−0.962599	−	0.270929i	$-0.912669\pi$
$773$	−534.661	+	534.661i	−0.691670	+	0.691670i	0.270929	+	0.962599i	$0.412669\pi$
$774$		−	353.650i		−	0.456913i
$775$	685.580	−	1047.88i	0.884619	−	1.35211i
$776$	361.425			0.465754
$777$	28.2165	+	28.2165i	0.0363147	+	0.0363147i
$778$	−287.140	+	287.140i	−0.369075	+	0.369075i
$779$		−	531.616i		−	0.682434i
$780$	286.194	−	154.761i	0.366916	−	0.198412i
$781$	−1024.37			−1.31161
$782$	53.1001	+	53.1001i	0.0679030	+	0.0679030i
$783$	−12.1157	+	12.1157i	−0.0154734	+	0.0154734i
$784$		−	28.0000i		−	0.0357143i
$785$	−621.983	−	185.391i	−0.792335	−	0.236166i
$786$	−361.397			−0.459793
$787$	−1038.23	−	1038.23i	−1.31922	−	1.31922i	−0.914394	−	0.404825i	$-0.867332\pi$
$787$	−1038.23	−	1038.23i	−1.31922	−	1.31922i	−0.404825	−	0.914394i	$-0.632668\pi$
$788$	−53.5413	+	53.5413i	−0.0679458	+	0.0679458i
$789$		−	300.661i		−	0.381065i
$790$	106.708	−	358.005i	0.135074	−	0.453171i
$791$	−425.598			−0.538051
$792$	88.6657	+	88.6657i	0.111952	+	0.111952i
$793$	59.1869	−	59.1869i	0.0746367	−	0.0746367i
$794$		−	179.103i		−	0.225570i
$795$	63.5158	+	117.457i	0.0798941	+	0.147745i
$796$	343.581			0.431634
$797$	−294.158	−	294.158i	−0.369081	−	0.369081i	0.498061	−	0.867142i	$-0.334046\pi$
$797$	−294.158	−	294.158i	−0.369081	−	0.369081i	−0.867142	+	0.498061i	$0.834046\pi$
$798$	69.3336	−	69.3336i	0.0868842	−	0.0868842i
$799$		−	47.5735i		−	0.0595413i
$800$	138.430	−	28.9326i	0.173038	−	0.0361658i
$801$	−64.0658			−0.0799822
$802$	649.944	+	649.944i	0.810405	+	0.810405i
$803$	−863.258	+	863.258i	−1.07504	+	1.07504i
$804$		−	433.278i		−	0.538902i
$805$	370.383	−	200.287i	0.460103	−	0.248804i
$806$	1330.64			1.65092
$807$	76.3300	+	76.3300i	0.0945849	+	0.0945849i
$808$	87.2218	−	87.2218i	0.107948	−	0.107948i
$809$		−	22.0860i		−	0.0273004i	−0.999907	−	0.0136502i	$-0.995655\pi$
$809$		−	22.0860i		−	0.0273004i	0.999907	−	0.0136502i	$-0.00434513\pi$
$810$	−60.9881	−	18.1783i	−0.0752939	−	0.0224424i
$811$	−242.865			−0.299464			−0.149732	−	0.988727i	$-0.547841\pi$
$811$	−242.865			−0.299464			−0.149732	+	0.988727i	$0.547841\pi$
$812$	12.3380	+	12.3380i	0.0151946	+	0.0151946i
$813$	156.355	−	156.355i	0.192318	−	0.192318i
$814$			181.982i			0.223565i
$815$	22.5110	−	75.5242i	0.0276209	−	0.0926677i
$816$	−11.5580			−0.0141642
$817$	−891.779	−	891.779i	−1.09153	−	1.09153i
$818$	717.337	−	717.337i	0.876940	−	0.876940i
$819$			149.098i			0.182049i
$820$	167.134	+	309.074i	0.203822	+	0.376919i
$821$	228.561			0.278394			0.139197	−	0.990265i	$-0.455548\pi$
$821$	228.561			0.278394			0.139197	+	0.990265i	$0.455548\pi$
$822$	−236.598	−	236.598i	−0.287832	−	0.287832i
$823$	−641.691	+	641.691i	−0.779698	+	0.779698i	−0.979779	−	0.200081i	$-0.935879\pi$
$823$	−641.691	+	641.691i	−0.779698	+	0.779698i	0.200081	+	0.979779i	$0.435879\pi$
$824$			195.455i			0.237203i
$825$	130.911	+	626.355i	0.158681	+	0.759218i
$826$	−249.484			−0.302039
$827$	−1075.03	−	1075.03i	−1.29992	−	1.29992i	−0.928441	−	0.371479i	$-0.878851\pi$
$827$	−1075.03	−	1075.03i	−1.29992	−	1.29992i	−0.371479	−	0.928441i	$-0.621149\pi$
$828$	−135.042	+	135.042i	−0.163094	+	0.163094i
$829$			530.478i			0.639901i	0.947434	+	0.319950i	$0.103666\pi$
$829$			530.478i			0.639901i	−0.947434	+	0.319950i	$0.896334\pi$
$830$	−469.973	+	254.141i	−0.566232	+	0.306194i
$831$	−141.302			−0.170039
$832$	106.262	+	106.262i	0.127718	+	0.127718i
$833$	−8.25744	+	8.25744i	−0.00991289	+	0.00991289i
$834$			451.188i			0.540992i
$835$	−1523.42	−	454.077i	−1.82446	−	0.543804i
$836$	447.166			0.534887
$837$	−184.039	−	184.039i	−0.219880	−	0.219880i
$838$	680.885	−	680.885i	0.812511	−	0.812511i
$839$		−	618.719i		−	0.737448i	−0.929539	−	0.368724i	$-0.879795\pi$
$839$		−	618.719i		−	0.737448i	0.929539	−	0.368724i	$-0.120205\pi$
$840$	−18.5119	+	62.1072i	−0.0220380	+	0.0739372i
$841$	830.127			0.987071
$842$	−710.333	−	710.333i	−0.843626	−	0.843626i
$843$	146.200	−	146.200i	0.173429	−	0.173429i
$844$		−	604.864i		−	0.716664i
$845$	437.281	+	808.647i	0.517492	+	0.956979i
$846$	120.987			0.143011
$847$	182.177	+	182.177i	0.215085	+	0.215085i
$848$	−43.6110	+	43.6110i	−0.0514281	+	0.0514281i
$849$			429.290i			0.505642i
$850$	−49.3567	−	32.2918i	−0.0580667	−	0.0379903i
$851$	−277.167			−0.325696
$852$	169.796	+	169.796i	0.199291	+	0.199291i
$853$	164.001	−	164.001i	0.192264	−	0.192264i	−0.604410	−	0.796674i	$-0.706591\pi$
$853$	164.001	−	164.001i	0.192264	−	0.192264i	0.796674	+	0.604410i	$0.206591\pi$
$854$			16.6726i			0.0195229i
$855$	−199.629	+	107.951i	−0.233484	+	0.126258i
$856$	92.5987			0.108176
$857$	889.068	+	889.068i	1.03742	+	1.03742i	0.999272	+	0.0381473i	$0.0121456\pi$
$857$	889.068	+	889.068i	1.03742	+	1.03742i	0.0381473	+	0.999272i	$0.487854\pi$
$858$	−480.803	+	480.803i	−0.560376	+	0.560376i
$859$		−	1203.95i		−	1.40157i	−0.713374	−	0.700783i	$-0.752834\pi$
$859$		−	1203.95i		−	1.40157i	0.713374	−	0.700783i	$-0.247166\pi$
$860$	798.832	+	238.103i	0.928875	+	0.276864i
$861$	−161.018			−0.187012
$862$	−785.543	−	785.543i	−0.911303	−	0.911303i
$863$	813.145	−	813.145i	0.942230	−	0.942230i	−0.0561900	−	0.998420i	$-0.517895\pi$
$863$	813.145	−	813.145i	0.942230	−	0.942230i	0.998420	+	0.0561900i	$0.0178953\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−87.7703	+	294.468i	−0.101469	+	0.340426i
$866$	−968.858			−1.11877
$867$	−350.543	−	350.543i	−0.404317	−	0.404317i
$868$	−187.416	+	187.416i	−0.215918	+	0.215918i
$869$			780.712i			0.898403i
$870$	−19.2100	−	35.5243i	−0.0220805	−	0.0408326i
$871$	2349.51			2.69749
$872$	283.667	+	283.667i	0.325307	+	0.325307i
$873$	271.069	−	271.069i	0.310502	−	0.310502i
$874$			681.056i			0.779240i
$875$	−252.573	+	213.499i	−0.288655	+	0.243999i
$876$	286.182			0.326691
$877$	−233.930	−	233.930i	−0.266739	−	0.266739i	0.561046	−	0.827785i	$-0.310399\pi$
$877$	−233.930	−	233.930i	−0.266739	−	0.266739i	−0.827785	+	0.561046i	$0.810399\pi$
$878$	558.366	−	558.366i	0.635952	−	0.635952i
$879$		−	549.308i		−	0.624923i
$880$	−259.976	+	140.584i	−0.295427	+	0.159754i
$881$	34.2672			0.0388957			0.0194479	−	0.999811i	$-0.493809\pi$
$881$	34.2672			0.0388957			0.0194479	+	0.999811i	$0.493809\pi$
$882$	−21.0000	−	21.0000i	−0.0238095	−	0.0238095i
$883$	1030.29	−	1030.29i	1.16680	−	1.16680i	0.183846	−	0.982955i	$-0.441145\pi$
$883$	1030.29	−	1030.29i	1.16680	−	1.16680i	0.982955	−	0.183846i	$-0.0588547\pi$
$884$		−	62.6750i		−	0.0708993i
$885$	553.384	+	164.944i	0.625293	+	0.186377i
$886$	−188.719			−0.213001
$887$	−129.771	−	129.771i	−0.146303	−	0.146303i	0.630161	−	0.776464i	$-0.282989\pi$
$887$	−129.771	−	129.771i	−0.146303	−	0.146303i	−0.776464	+	0.630161i	$0.782989\pi$
$888$	30.1647	−	30.1647i	0.0339693	−	0.0339693i
$889$		−	646.100i		−	0.726772i
$890$	43.1337	−	144.713i	0.0484648	−	0.162599i
$891$	132.999			0.149269
$892$	−341.569	−	341.569i	−0.382925	−	0.382925i
$893$	305.086	−	305.086i	0.341642	−	0.341642i
$894$		−	505.471i		−	0.565404i
$895$	−398.067	−	736.130i	−0.444768	−	0.822492i
$896$	−29.9333			−0.0334077
$897$	−732.286	−	732.286i	−0.816373	−	0.816373i
$898$	−642.007	+	642.007i	−0.714929	+	0.714929i
$899$		−	165.168i		−	0.183724i
$900$	82.1231	−	125.522i	0.0912479	−	0.139469i
$901$	25.7225			0.0285489
$902$	−519.240	−	519.240i	−0.575654	−	0.575654i
$903$	−270.105	+	270.105i	−0.299120	+	0.299120i
$904$			454.984i			0.503301i
$905$	−992.931	+	536.934i	−1.09716	+	0.593297i
$906$	−126.106			−0.139190
$907$	−914.642	−	914.642i	−1.00843	−	1.00843i	−0.999964	−	0.00846121i	$-0.997307\pi$
$907$	−914.642	−	914.642i	−1.00843	−	1.00843i	−0.00846121	−	0.999964i	$-0.502693\pi$
$908$	−308.647	+	308.647i	−0.339919	+	0.339919i
$909$		−	130.833i		−	0.143930i
$910$	−336.786	−	100.384i	−0.370094	−	0.110312i
$911$	75.4264			0.0827952			0.0413976	−	0.999143i	$-0.486819\pi$
$911$	75.4264			0.0827952			0.0413976	+	0.999143i	$0.486819\pi$
$912$	−74.1208	−	74.1208i	−0.0812728	−	0.0812728i
$913$	789.548	−	789.548i	0.864784	−	0.864784i
$914$		−	641.188i		−	0.701519i
$915$	11.0229	−	36.9817i	0.0120469	−	0.0404172i
$916$	67.4485			0.0736337
$917$	276.022	+	276.022i	0.301005	+	0.301005i
$918$	−8.66850	+	8.66850i	−0.00944281	+	0.00944281i
$919$		−	1008.57i		−	1.09747i	−0.835998	−	0.548733i	$-0.815111\pi$
$919$		−	1008.57i		−	1.09747i	0.835998	−	0.548733i	$-0.184889\pi$
$920$	−214.116	−	395.956i	−0.232734	−	0.430387i
$921$	495.693			0.538212
$922$	300.193	+	300.193i	0.325589	+	0.325589i
$923$	−920.742	+	920.742i	−0.997554	+	0.997554i
$924$		−	135.439i		−	0.146579i
$925$	213.091	−	44.5370i	0.230368	−	0.0481481i
$926$	−117.831			−0.127247
$927$	146.591	+	146.591i	0.158135	+	0.158135i
$928$	13.1899	−	13.1899i	0.0142133	−	0.0142133i
$929$		−	1240.03i		−	1.33480i	−0.744699	−	0.667400i	$-0.767407\pi$
$929$		−	1240.03i		−	1.33480i	0.744699	−	0.667400i	$-0.232593\pi$
$930$	539.620	−	291.803i	0.580236	−	0.313767i
$931$	−105.909			−0.113758
$932$	−415.997	−	415.997i	−0.446348	−	0.446348i
$933$	−467.992	+	467.992i	−0.501599	+	0.501599i
$934$			724.995i			0.776226i
$935$	118.128	+	35.2098i	0.126340	+	0.0376575i
$936$	159.393			0.170291
$937$	239.199	+	239.199i	0.255282	+	0.255282i	0.823132	−	0.567850i	$-0.192225\pi$
$937$	239.199	+	239.199i	0.255282	+	0.255282i	−0.567850	+	0.823132i	$0.692225\pi$
$938$	−330.921	+	330.921i	−0.352794	+	0.352794i
$939$			576.719i			0.614185i
$940$	−81.4572	+	273.288i	−0.0866566	+	0.290732i
$941$	1412.22			1.50077			0.750384	−	0.661003i	$-0.229869\pi$
$941$	1412.22			1.50077			0.750384	+	0.661003i	$0.229869\pi$
$942$	−224.829	−	224.829i	−0.238672	−	0.238672i
$943$	790.828	−	790.828i	0.838630	−	0.838630i
$944$			266.710i			0.282531i
$945$	32.6965	+	60.4644i	0.0345995	+	0.0639835i
$946$	−1742.04			−1.84148
$947$	13.0937	+	13.0937i	0.0138265	+	0.0138265i	0.713986	−	0.700160i	$-0.246888\pi$
$947$	13.0937	+	13.0937i	0.0138265	+	0.0138265i	−0.700160	+	0.713986i	$0.746888\pi$
$948$	129.408	−	129.408i	0.136507	−	0.136507i
$949$			1551.86i			1.63526i
$950$	−109.436	−	523.606i	−0.115196	−	0.551165i
$951$	729.223			0.766796
$952$	8.82757	+	8.82757i	0.00927266	+	0.00927266i
$953$	−1186.29	+	1186.29i	−1.24480	+	1.24480i	−0.286809	+	0.957988i	$0.592594\pi$
$953$	−1186.29	+	1186.29i	−1.24480	+	1.24480i	−0.957988	+	0.286809i	$0.907406\pi$
$954$			65.4165i			0.0685708i
$955$	653.676	−	353.479i	0.684477	−	0.370136i
$956$	−99.4325			−0.104009
$957$	59.6804	+	59.6804i	0.0623619	+	0.0623619i
$958$	−233.704	+	233.704i	−0.243950	+	0.243950i
$959$			361.409i			0.376861i
$960$	66.3954	+	19.7901i	0.0691619	+	0.0206147i
$961$	1547.92			1.61074
$962$	163.573	+	163.573i	0.170034	+	0.170034i
$963$	69.4491	−	69.4491i	0.0721174	−	0.0721174i
$964$		−	99.9432i		−	0.103676i
$965$	319.258	−	1071.11i	0.330837	−	1.10995i
$966$	206.280			0.213541
$967$	989.527	+	989.527i	1.02330	+	1.02330i	0.999722	+	0.0235735i	$0.00750437\pi$
$967$	989.527	+	989.527i	1.02330	+	1.02330i	0.0235735	+	0.999722i	$0.492496\pi$
$968$	194.756	−	194.756i	0.201194	−	0.201194i
$969$			43.7177i			0.0451163i
$970$	429.792	+	794.798i	0.443084	+	0.819379i
$971$	104.077			0.107185			0.0535927	−	0.998563i	$-0.482933\pi$
$971$	104.077			0.107185			0.0535927	+	0.998563i	$0.482933\pi$
$972$	−22.0454	−	22.0454i	−0.0226805	−	0.0226805i
$973$	344.600	−	344.600i	0.354163	−	0.354163i
$974$		−	468.055i		−	0.480549i
$975$	680.662	+	445.325i	0.698115	+	0.456743i
$976$	17.8237			0.0182620
$977$	−635.859	−	635.859i	−0.650828	−	0.650828i	0.302364	−	0.953192i	$-0.402224\pi$
$977$	−635.859	−	635.859i	−0.650828	−	0.650828i	−0.953192	+	0.302364i	$0.902224\pi$
$978$	27.2998	−	27.2998i	0.0279139	−	0.0279139i
$979$			315.580i			0.322349i
$980$	61.5739	−	33.2965i	0.0628305	−	0.0339760i
$981$	425.501			0.433742
$982$	−29.6268	−	29.6268i	−0.0301699	−	0.0301699i
$983$	1166.39	−	1166.39i	1.18656	−	1.18656i	0.208553	−	0.978011i	$-0.433125\pi$
$983$	1166.39	−	1166.39i	1.18656	−	1.18656i	0.978011	−	0.208553i	$-0.0668752\pi$
$984$			172.135i			0.174934i
$985$	−181.410	−	54.0718i	−0.184173	−	0.0548952i
$986$	−7.77963			−0.00789009
$987$	−92.4054	−	92.4054i	−0.0936225	−	0.0936225i
$988$	401.931	−	401.931i	0.406813	−	0.406813i
$989$		−	2653.21i		−	2.68272i
$990$	−89.5442	+	300.420i	−0.0904487	+	0.303454i
$991$	−978.880			−0.987770			−0.493885	−	0.869527i	$-0.664424\pi$
$991$	−978.880			−0.987770			−0.493885	+	0.869527i	$0.664424\pi$
$992$	200.357	+	200.357i	0.201972	+	0.201972i
$993$	−241.702	+	241.702i	−0.243406	+	0.243406i
$994$		−	259.367i		−	0.260933i
$995$	408.573	+	755.558i	0.410626	+	0.759354i
$996$	−261.746			−0.262797
$997$	646.604	+	646.604i	0.648550	+	0.648550i	0.952642	−	0.304093i	$-0.0983532\pi$
$997$	646.604	+	646.604i	0.648550	+	0.648550i	−0.304093	+	0.952642i	$0.598353\pi$
$998$	−322.566	+	322.566i	−0.323213	+	0.323213i
$999$		−	45.2471i		−	0.0452924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.l.b.127.5	yes	16
3.2	odd	2		630.3.o.f.127.7		16
5.2	odd	4		1050.3.l.h.43.1		16
5.3	odd	4	inner	210.3.l.b.43.5	✓	16
5.4	even	2		1050.3.l.h.757.1		16
15.8	even	4		630.3.o.f.253.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.5	✓	16	5.3	odd	4	inner
210.3.l.b.127.5	yes	16	1.1	even	1	trivial
630.3.o.f.127.7		16	3.2	odd	2
630.3.o.f.253.7		16	15.8	even	4
1050.3.l.h.43.1		16	5.2	odd	4
1050.3.l.h.757.1		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)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.39814 + 2.37832i) q^{5} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.39814 + 2.37832i) q^{5} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(6.77646 + 2.01982i) q^{10} -14.7776 q^{11} +(2.44949 + 2.44949i) q^{12} +(-13.2827 + 13.2827i) q^{13} -3.74166i q^{14} +(-2.47376 + 8.29943i) q^{15} -4.00000 q^{16} +(1.17963 + 1.17963i) q^{17} +(-3.00000 + 3.00000i) q^{18} +15.1298i q^{19} +(-4.75664 - 8.79627i) q^{20} +4.58258 q^{21} +(14.7776 + 14.7776i) q^{22} +(-22.5070 + 22.5070i) q^{23} -4.89898i q^{24} +(13.6872 - 20.9203i) q^{25} +26.5654 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-3.74166 + 3.74166i) q^{28} -3.29748i q^{29} +(10.7732 - 5.82567i) q^{30} +50.0892 q^{31} +(4.00000 + 4.00000i) q^{32} +(-18.0988 + 18.0988i) q^{33} -2.35927i q^{34} +(-12.6776 - 3.77873i) q^{35} +6.00000 q^{36} +(6.15735 + 6.15735i) q^{37} +(15.1298 - 15.1298i) q^{38} +32.5359i q^{39} +(-4.03963 + 13.5529i) q^{40} -35.1369 q^{41} +(-4.58258 - 4.58258i) q^{42} +(-58.9417 + 58.9417i) q^{43} -29.5552i q^{44} +(7.13496 + 13.1944i) q^{45} +45.0141 q^{46} +(-20.1645 - 20.1645i) q^{47} +(-4.89898 + 4.89898i) q^{48} +7.00000i q^{49} +(-34.6075 + 7.23315i) q^{50} +2.88950 q^{51} +(-26.5654 - 26.5654i) q^{52} +(10.9028 - 10.9028i) q^{53} +7.34847i q^{54} +(64.9939 - 35.1459i) q^{55} +7.48331 q^{56} +(18.5302 + 18.5302i) q^{57} +(-3.29748 + 3.29748i) q^{58} -66.6774i q^{59} +(-16.5989 - 4.94752i) q^{60} -4.45593 q^{61} +(-50.0892 - 50.0892i) q^{62} +(5.61249 - 5.61249i) q^{63} -8.00000i q^{64} +(26.8286 - 90.0098i) q^{65} +36.1976 q^{66} +(-88.4424 - 88.4424i) q^{67} +(-2.35927 + 2.35927i) q^{68} +55.1307i q^{69} +(8.89886 + 16.4563i) q^{70} +69.3188 q^{71} +(-6.00000 - 6.00000i) q^{72} +(58.4166 - 58.4166i) q^{73} -12.3147i q^{74} +(-8.85877 - 42.3854i) q^{75} -30.2597 q^{76} +(-27.6464 - 27.6464i) q^{77} +(32.5359 - 32.5359i) q^{78} -52.8307i q^{79} +(17.5925 - 9.51328i) q^{80} -9.00000 q^{81} +(35.1369 + 35.1369i) q^{82} +(-53.4286 + 53.4286i) q^{83} +9.16515i q^{84} +(-7.99374 - 2.38264i) q^{85} +117.883 q^{86} +(-4.03857 - 4.03857i) q^{87} +(-29.5552 + 29.5552i) q^{88} -21.3553i q^{89} +(6.05945 - 20.3294i) q^{90} -49.6994 q^{91} +(-45.0141 - 45.0141i) q^{92} +(61.3464 - 61.3464i) q^{93} +40.3290i q^{94} +(-35.9836 - 66.5431i) q^{95} +9.79796 q^{96} +(90.3562 + 90.3562i) q^{97} +(7.00000 - 7.00000i) q^{98} +44.3328i 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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