LMFDB - Embedded newform 230.3.f.a.93.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(47,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.f (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:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 52 x^{17} + 1020 x^{16} - 1316 x^{15} + 1352 x^{14} - 18724 x^{13} + 250686 x^{12} + \cdots + 88804 $ x^20 - 52x^17 + 1020x^16 - 1316x^15 + 1352x^14 - 18724x^13 + 250686x^12 - 439644x^11 + 460536x^10 - 1833716x^9 + 16970128x^8 - 36894604x^7 + 40544632x^6 - 4380588x^5 + 34721x^4 - 4419956x^3 + 9945800x^2 + 1329080*x + 88804
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			93.9
Root			$2.91022 + 2.91022i$ of defining polynomial
Character	$\chi$	$=$	230.93
Dual form			230.3.f.a.47.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(2.91022 + 2.91022i) q^{3} -2.00000i q^{4} +(-3.94243 + 3.07527i) q^{5} -5.82043 q^{6} +(-1.42062 + 1.42062i) q^{7} +(2.00000 + 2.00000i) q^{8} +7.93871i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(2.91022 + 2.91022i) q^{3} -2.00000i q^{4} +(-3.94243 + 3.07527i) q^{5} -5.82043 q^{6} +(-1.42062 + 1.42062i) q^{7} +(2.00000 + 2.00000i) q^{8} +7.93871i q^{9} +(0.867158 - 7.01769i) q^{10} -16.1752 q^{11} +(5.82043 - 5.82043i) q^{12} +(2.48563 + 2.48563i) q^{13} -2.84124i q^{14} +(-20.4230 - 2.52362i) q^{15} -4.00000 q^{16} +(-5.71130 + 5.71130i) q^{17} +(-7.93871 - 7.93871i) q^{18} +11.0577i q^{19} +(6.15054 + 7.88485i) q^{20} -8.26861 q^{21} +(16.1752 - 16.1752i) q^{22} +(3.39116 + 3.39116i) q^{23} +11.6409i q^{24} +(6.08545 - 24.2480i) q^{25} -4.97126 q^{26} +(3.08857 - 3.08857i) q^{27} +(2.84124 + 2.84124i) q^{28} +25.6960i q^{29} +(22.9466 - 17.8994i) q^{30} +5.93339 q^{31} +(4.00000 - 4.00000i) q^{32} +(-47.0732 - 47.0732i) q^{33} -11.4226i q^{34} +(1.23190 - 9.96946i) q^{35} +15.8774 q^{36} +(-1.76062 + 1.76062i) q^{37} +(-11.0577 - 11.0577i) q^{38} +14.4674i q^{39} +(-14.0354 - 1.73432i) q^{40} -45.0735 q^{41} +(8.26861 - 8.26861i) q^{42} +(19.3844 + 19.3844i) q^{43} +32.3503i q^{44} +(-24.4137 - 31.2978i) q^{45} -6.78233 q^{46} +(-8.98185 + 8.98185i) q^{47} +(-11.6409 - 11.6409i) q^{48} +44.9637i q^{49} +(18.1626 + 30.3335i) q^{50} -33.2422 q^{51} +(4.97126 - 4.97126i) q^{52} +(-42.4648 - 42.4648i) q^{53} +6.17715i q^{54} +(63.7694 - 49.7429i) q^{55} -5.68247 q^{56} +(-32.1802 + 32.1802i) q^{57} +(-25.6960 - 25.6960i) q^{58} +72.1819i q^{59} +(-5.04723 + 40.8460i) q^{60} +48.8017 q^{61} +(-5.93339 + 5.93339i) q^{62} +(-11.2779 - 11.2779i) q^{63} +8.00000i q^{64} +(-17.4434 - 2.15543i) q^{65} +94.1464 q^{66} +(20.4826 - 20.4826i) q^{67} +(11.4226 + 11.4226i) q^{68} +19.7380i q^{69} +(8.73756 + 11.2014i) q^{70} +94.7412 q^{71} +(-15.8774 + 15.8774i) q^{72} +(100.708 + 100.708i) q^{73} -3.52124i q^{74} +(88.2770 - 52.8571i) q^{75} +22.1153 q^{76} +(22.9787 - 22.9787i) q^{77} +(-14.4674 - 14.4674i) q^{78} -60.8590i q^{79} +(15.7697 - 12.3011i) q^{80} +89.4253 q^{81} +(45.0735 - 45.0735i) q^{82} +(85.2783 + 85.2783i) q^{83} +16.5372i q^{84} +(4.95260 - 40.0802i) q^{85} -38.7689 q^{86} +(-74.7809 + 74.7809i) q^{87} +(-32.3503 - 32.3503i) q^{88} +131.605i q^{89} +(55.7115 + 6.88412i) q^{90} -7.06226 q^{91} +(6.78233 - 6.78233i) q^{92} +(17.2674 + 17.2674i) q^{93} -17.9637i q^{94} +(-34.0053 - 43.5940i) q^{95} +23.2817 q^{96} +(-75.0875 + 75.0875i) q^{97} +(-44.9637 - 44.9637i) q^{98} -128.410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8	$ 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8} + 4 q^{10} + 56 q^{11} - 4 q^{13} - 48 q^{15} - 80 q^{16} - 72 q^{17} - 28 q^{18} - 16 q^{20} + 8 q^{21} - 56 q^{22} + 36 q^{25} + 8 q^{26} + 156 q^{27} - 16 q^{28} + 84 q^{30} - 212 q^{31} + 80 q^{32} - 100 q^{33} + 56 q^{36} + 72 q^{37} + 88 q^{38} + 24 q^{40} - 12 q^{41} - 8 q^{42} + 120 q^{43} - 32 q^{45} + 8 q^{47} - 28 q^{50} + 64 q^{51} - 8 q^{52} - 244 q^{53} + 68 q^{55} + 32 q^{56} - 384 q^{57} - 188 q^{58} - 72 q^{60} + 328 q^{61} + 212 q^{62} + 172 q^{63} + 20 q^{65} + 200 q^{66} + 56 q^{67} + 144 q^{68} - 28 q^{70} - 92 q^{71} - 56 q^{72} + 144 q^{73} - 124 q^{75} - 176 q^{76} + 292 q^{77} - 208 q^{78} - 16 q^{80} - 84 q^{81} + 12 q^{82} - 72 q^{83} - 20 q^{85} - 240 q^{86} - 208 q^{87} + 112 q^{88} - 56 q^{90} - 192 q^{91} + 256 q^{93} - 96 q^{95} - 276 q^{97} + 104 q^{98}+O(q^{100}) $ 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8 + 4 * q^10 + 56 * q^11 - 4 * q^13 - 48 * q^15 - 80 * q^16 - 72 * q^17 - 28 * q^18 - 16 * q^20 + 8 * q^21 - 56 * q^22 + 36 * q^25 + 8 * q^26 + 156 * q^27 - 16 * q^28 + 84 * q^30 - 212 * q^31 + 80 * q^32 - 100 * q^33 + 56 * q^36 + 72 * q^37 + 88 * q^38 + 24 * q^40 - 12 * q^41 - 8 * q^42 + 120 * q^43 - 32 * q^45 + 8 * q^47 - 28 * q^50 + 64 * q^51 - 8 * q^52 - 244 * q^53 + 68 * q^55 + 32 * q^56 - 384 * q^57 - 188 * q^58 - 72 * q^60 + 328 * q^61 + 212 * q^62 + 172 * q^63 + 20 * q^65 + 200 * q^66 + 56 * q^67 + 144 * q^68 - 28 * q^70 - 92 * q^71 - 56 * q^72 + 144 * q^73 - 124 * q^75 - 176 * q^76 + 292 * q^77 - 208 * q^78 - 16 * q^80 - 84 * q^81 + 12 * q^82 - 72 * q^83 - 20 * q^85 - 240 * q^86 - 208 * q^87 + 112 * q^88 - 56 * q^90 - 192 * q^91 + 256 * q^93 - 96 * q^95 - 276 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	2.91022	+	2.91022i	0.970072	+	0.970072i	0.999565	−	0.0294930i	$-0.00938928\pi$
$3$	2.91022	+	2.91022i	0.970072	+	0.970072i	−0.0294930	+	0.999565i	$0.509389\pi$
$4$		−	2.00000i		−	0.500000i
$5$	−3.94243	+	3.07527i	−0.788485	+	0.615054i
$5$	−3.94243	+	3.07527i	−0.788485	+	0.615054i
$6$	−5.82043			−0.970072
$7$	−1.42062	+	1.42062i	−0.202945	+	0.202945i	−0.801261	−	0.598315i	$-0.795837\pi$
$7$	−1.42062	+	1.42062i	−0.202945	+	0.202945i	0.598315	+	0.801261i	$0.295837\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			7.93871i			0.882079i
$10$	0.867158	−	7.01769i	0.0867158	−	0.701769i
$11$	−16.1752			−1.47047			−0.735234	−	0.677813i	$-0.762928\pi$
$11$	−16.1752			−1.47047			−0.735234	+	0.677813i	$0.762928\pi$
$12$	5.82043	−	5.82043i	0.485036	−	0.485036i
$13$	2.48563	+	2.48563i	0.191202	+	0.191202i	0.796215	−	0.605013i	$-0.206832\pi$
$13$	2.48563	+	2.48563i	0.191202	+	0.191202i	−0.605013	+	0.796215i	$0.706832\pi$
$14$		−	2.84124i		−	0.202945i
$15$	−20.4230	−	2.52362i	−1.36153	−	0.168241i
$16$	−4.00000			−0.250000
$17$	−5.71130	+	5.71130i	−0.335959	+	0.335959i	−0.854844	−	0.518885i	$-0.826347\pi$
$17$	−5.71130	+	5.71130i	−0.335959	+	0.335959i	0.518885	+	0.854844i	$0.326347\pi$
$18$	−7.93871	−	7.93871i	−0.441040	−	0.441040i
$19$			11.0577i			0.581982i	0.956726	+	0.290991i	$0.0939850\pi$
$19$			11.0577i			0.581982i	−0.956726	+	0.290991i	$0.906015\pi$
$20$	6.15054	+	7.88485i	0.307527	+	0.394243i
$21$	−8.26861			−0.393743
$22$	16.1752	−	16.1752i	0.735234	−	0.735234i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$24$			11.6409i			0.485036i
$25$	6.08545	−	24.2480i	0.243418	−	0.969922i
$26$	−4.97126			−0.191202
$27$	3.08857	−	3.08857i	0.114392	−	0.114392i
$28$	2.84124	+	2.84124i	0.101473	+	0.101473i
$29$			25.6960i			0.886069i	0.896505	+	0.443034i	$0.146098\pi$
$29$			25.6960i			0.886069i	−0.896505	+	0.443034i	$0.853902\pi$
$30$	22.9466	−	17.8994i	0.764887	−	0.596646i
$31$	5.93339			0.191400			0.0956999	−	0.995410i	$-0.469491\pi$
$31$	5.93339			0.191400			0.0956999	+	0.995410i	$0.469491\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−47.0732	−	47.0732i	−1.42646	−	1.42646i
$34$		−	11.4226i		−	0.335959i
$35$	1.23190	−	9.96946i	0.0351971	−	0.284842i
$36$	15.8774			0.441040
$37$	−1.76062	+	1.76062i	−0.0475843	+	0.0475843i	−0.730499	−	0.682914i	$-0.760712\pi$
$37$	−1.76062	+	1.76062i	−0.0475843	+	0.0475843i	0.682914	+	0.730499i	$0.260712\pi$
$38$	−11.0577	−	11.0577i	−0.290991	−	0.290991i
$39$			14.4674i			0.370960i
$40$	−14.0354	−	1.73432i	−0.350885	−	0.0433579i
$41$	−45.0735			−1.09935			−0.549676	−	0.835378i	$-0.685249\pi$
$41$	−45.0735			−1.09935			−0.549676	+	0.835378i	$0.685249\pi$
$42$	8.26861	−	8.26861i	0.196872	−	0.196872i
$43$	19.3844	+	19.3844i	0.450801	+	0.450801i	0.895620	−	0.444819i	$-0.146732\pi$
$43$	19.3844	+	19.3844i	0.450801	+	0.450801i	−0.444819	+	0.895620i	$0.646732\pi$
$44$			32.3503i			0.735234i
$45$	−24.4137	−	31.2978i	−0.542526	−	0.695506i
$46$	−6.78233			−0.147442
$47$	−8.98185	+	8.98185i	−0.191103	+	0.191103i	−0.796173	−	0.605070i	$-0.793145\pi$
$47$	−8.98185	+	8.98185i	−0.191103	+	0.191103i	0.605070	+	0.796173i	$0.293145\pi$
$48$	−11.6409	−	11.6409i	−0.242518	−	0.242518i
$49$			44.9637i			0.917626i
$50$	18.1626	+	30.3335i	0.363252	+	0.606670i
$51$	−33.2422			−0.651808
$52$	4.97126	−	4.97126i	0.0956012	−	0.0956012i
$53$	−42.4648	−	42.4648i	−0.801223	−	0.801223i	0.182063	−	0.983287i	$-0.441722\pi$
$53$	−42.4648	−	42.4648i	−0.801223	−	0.801223i	−0.983287	+	0.182063i	$0.941722\pi$
$54$			6.17715i			0.114392i
$55$	63.7694	−	49.7429i	1.15944	−	0.904417i
$56$	−5.68247			−0.101473
$57$	−32.1802	+	32.1802i	−0.564564	+	0.564564i
$58$	−25.6960	−	25.6960i	−0.443034	−	0.443034i
$59$			72.1819i			1.22342i	0.791082	+	0.611711i	$0.209518\pi$
$59$			72.1819i			1.22342i	−0.791082	+	0.611711i	$0.790482\pi$
$60$	−5.04723	+	40.8460i	−0.0841205	+	0.680767i
$61$	48.8017			0.800028			0.400014	−	0.916509i	$-0.369005\pi$
$61$	48.8017			0.800028			0.400014	+	0.916509i	$0.369005\pi$
$62$	−5.93339	+	5.93339i	−0.0956999	+	0.0956999i
$63$	−11.2779	−	11.2779i	−0.179014	−	0.179014i
$64$			8.00000i			0.125000i
$65$	−17.4434	−	2.15543i	−0.268360	−	0.0331605i
$66$	94.1464			1.42646
$67$	20.4826	−	20.4826i	0.305710	−	0.305710i	−0.537533	−	0.843243i	$-0.680644\pi$
$67$	20.4826	−	20.4826i	0.305710	−	0.305710i	0.843243	+	0.537533i	$0.180644\pi$
$68$	11.4226	+	11.4226i	0.167979	+	0.167979i
$69$			19.7380i			0.286059i
$70$	8.73756	+	11.2014i	0.124822	+	0.160019i
$71$	94.7412			1.33438			0.667192	−	0.744886i	$-0.267496\pi$
$71$	94.7412			1.33438			0.667192	+	0.744886i	$0.267496\pi$
$72$	−15.8774	+	15.8774i	−0.220520	+	0.220520i
$73$	100.708	+	100.708i	1.37956	+	1.37956i	0.845360	+	0.534198i	$0.179386\pi$
$73$	100.708	+	100.708i	1.37956	+	1.37956i	0.534198	+	0.845360i	$0.320614\pi$
$74$		−	3.52124i		−	0.0475843i
$75$	88.2770	−	52.8571i	1.17703	−	0.704761i
$76$	22.1153			0.290991
$77$	22.9787	−	22.9787i	0.298425	−	0.298425i
$78$	−14.4674	−	14.4674i	−0.185480	−	0.185480i
$79$		−	60.8590i		−	0.770367i	−0.922840	−	0.385183i	$-0.874138\pi$
$79$		−	60.8590i		−	0.770367i	0.922840	−	0.385183i	$-0.125862\pi$
$80$	15.7697	−	12.3011i	0.197121	−	0.153763i
$81$	89.4253			1.10402
$82$	45.0735	−	45.0735i	0.549676	−	0.549676i
$83$	85.2783	+	85.2783i	1.02745	+	1.02745i	0.999612	+	0.0278375i	$0.00886210\pi$
$83$	85.2783	+	85.2783i	1.02745	+	1.02745i	0.0278375	+	0.999612i	$0.491138\pi$
$84$			16.5372i			0.196872i
$85$	4.95260	−	40.0802i	0.0582658	−	0.471531i
$86$	−38.7689			−0.450801
$87$	−74.7809	+	74.7809i	−0.859550	+	0.859550i
$88$	−32.3503	−	32.3503i	−0.367617	−	0.367617i
$89$			131.605i			1.47871i	0.673319	+	0.739353i	$0.264868\pi$
$89$			131.605i			1.47871i	−0.673319	+	0.739353i	$0.735132\pi$
$90$	55.7115	+	6.88412i	0.619016	+	0.0764902i
$91$	−7.06226			−0.0776072
$92$	6.78233	−	6.78233i	0.0737210	−	0.0737210i
$93$	17.2674	+	17.2674i	0.185671	+	0.185671i
$94$		−	17.9637i		−	0.191103i
$95$	−34.0053	−	43.5940i	−0.357950	−	0.458884i
$96$	23.2817			0.242518
$97$	−75.0875	+	75.0875i	−0.774098	+	0.774098i	−0.978820	−	0.204722i	$-0.934371\pi$
$97$	−75.0875	+	75.0875i	−0.774098	+	0.774098i	0.204722	+	0.978820i	$0.434371\pi$
$98$	−44.9637	−	44.9637i	−0.458813	−	0.458813i
$99$		−	128.410i		−	1.29707i
$100$	−48.4961	−	12.1709i	−0.484961	−	0.121709i
$101$	135.545			1.34203			0.671015	−	0.741444i	$-0.265859\pi$
$101$	135.545			1.34203			0.671015	+	0.741444i	$0.265859\pi$
$102$	33.2422	−	33.2422i	0.325904	−	0.325904i
$103$	−113.068	−	113.068i	−1.09775	−	1.09775i	−0.994673	−	0.103079i	$-0.967131\pi$
$103$	−113.068	−	113.068i	−1.09775	−	1.09775i	−0.103079	−	0.994673i	$-0.532869\pi$
$104$			9.94252i			0.0956012i
$105$	32.5984	−	25.4282i	0.310461	−	0.242173i
$106$	84.9297			0.801223
$107$	−34.5847	+	34.5847i	−0.323222	+	0.323222i	−0.850002	−	0.526780i	$-0.823399\pi$
$107$	−34.5847	+	34.5847i	−0.323222	+	0.323222i	0.526780	+	0.850002i	$0.323399\pi$
$108$	−6.17715	−	6.17715i	−0.0571958	−	0.0571958i
$109$			16.8511i			0.154598i	0.997008	+	0.0772988i	$0.0246295\pi$
$109$			16.8511i			0.154598i	−0.997008	+	0.0772988i	$0.975370\pi$
$110$	−14.0264	+	113.512i	−0.127513	+	1.03193i
$111$	−10.2476			−0.0923203
$112$	5.68247	−	5.68247i	0.0507363	−	0.0507363i
$113$	−71.9070	−	71.9070i	−0.636345	−	0.636345i	0.313307	−	0.949652i	$-0.398563\pi$
$113$	−71.9070	−	71.9070i	−0.636345	−	0.636345i	−0.949652	+	0.313307i	$0.898563\pi$
$114$		−	64.3603i		−	0.564564i
$115$	−23.7982	−	2.94067i	−0.206941	−	0.0255711i
$116$	51.3920			0.443034
$117$	−19.7327	+	19.7327i	−0.168656	+	0.168656i
$118$	−72.1819	−	72.1819i	−0.611711	−	0.611711i
$119$		−	16.2271i		−	0.136363i
$120$	−35.7988	−	45.8932i	−0.298323	−	0.382444i
$121$	140.636			1.16228
$122$	−48.8017	+	48.8017i	−0.400014	+	0.400014i
$123$	−131.173	−	131.173i	−1.06645	−	1.06645i
$124$		−	11.8668i		−	0.0956999i
$125$	50.5778	+	114.310i	0.404622	+	0.914484i
$126$	22.5558			0.179014
$127$	72.2014	−	72.2014i	0.568515	−	0.568515i	−0.363197	−	0.931712i	$-0.618315\pi$
$127$	72.2014	−	72.2014i	0.568515	−	0.568515i	0.931712	+	0.363197i	$0.118315\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			112.826i			0.874619i
$130$	19.5988	−	15.2880i	0.150760	−	0.117600i
$131$	−163.121			−1.24520			−0.622601	−	0.782539i	$-0.713924\pi$
$131$	−163.121			−1.24520			−0.622601	+	0.782539i	$0.713924\pi$
$132$	−94.1464	+	94.1464i	−0.713230	+	0.713230i
$133$	−15.7087	−	15.7087i	−0.118111	−	0.118111i
$134$			40.9652i			0.305710i
$135$	−2.67828	+	21.6747i	−0.0198391	+	0.160553i
$136$	−22.8452			−0.167979
$137$	−29.8936	+	29.8936i	−0.218201	+	0.218201i	−0.807740	−	0.589539i	$-0.799309\pi$
$137$	−29.8936	+	29.8936i	−0.218201	+	0.218201i	0.589539	+	0.807740i	$0.299309\pi$
$138$	−19.7380	−	19.7380i	−0.143029	−	0.143029i
$139$		−	37.2135i		−	0.267723i	−0.991000	−	0.133861i	$-0.957262\pi$
$139$		−	37.2135i		−	0.267723i	0.991000	−	0.133861i	$-0.0427377\pi$
$140$	−19.9389	−	2.46380i	−0.142421	−	0.0175986i
$141$	−52.2782			−0.370768
$142$	−94.7412	+	94.7412i	−0.667192	+	0.667192i
$143$	−40.2055	−	40.2055i	−0.281157	−	0.281157i
$144$		−	31.7549i		−	0.220520i
$145$	−79.0221	−	101.305i	−0.544980	−	0.698652i
$146$	−201.415			−1.37956
$147$	−130.854	+	130.854i	−0.890164	+	0.890164i
$148$	3.52124	+	3.52124i	0.0237921	+	0.0237921i
$149$			150.770i			1.01188i	0.862569	+	0.505939i	$0.168854\pi$
$149$			150.770i			1.01188i	−0.862569	+	0.505939i	$0.831146\pi$
$150$	−35.4199	+	141.134i	−0.236133	+	0.940894i
$151$	−154.121			−1.02067			−0.510334	−	0.859976i	$-0.670478\pi$
$151$	−154.121			−1.02067			−0.510334	+	0.859976i	$0.670478\pi$
$152$	−22.1153	+	22.1153i	−0.145495	+	0.145495i
$153$	−45.3404	−	45.3404i	−0.296342	−	0.296342i
$154$			45.9574i			0.298425i
$155$	−23.3920	+	18.2468i	−0.150916	+	0.117721i
$156$	28.9349			0.185480
$157$	72.9685	−	72.9685i	0.464768	−	0.464768i	−0.435447	−	0.900215i	$-0.643410\pi$
$157$	72.9685	−	72.9685i	0.464768	−	0.464768i	0.900215	+	0.435447i	$0.143410\pi$
$158$	60.8590	+	60.8590i	0.385183	+	0.385183i
$159$		−	247.164i		−	1.55449i
$160$	−3.46863	+	28.0708i	−0.0216789	+	0.175442i
$161$	−9.63510			−0.0598453
$162$	−89.4253	+	89.4253i	−0.552008	+	0.552008i
$163$	60.5388	+	60.5388i	0.371404	+	0.371404i	0.867988	−	0.496584i	$-0.165413\pi$
$163$	60.5388	+	60.5388i	0.371404	+	0.371404i	−0.496584	+	0.867988i	$0.665413\pi$
$164$			90.1469i			0.549676i
$165$	330.345	+	40.8199i	2.00209	+	0.247393i
$166$	−170.557			−1.02745
$167$	221.270	−	221.270i	1.32497	−	1.32497i	0.415270	−	0.909698i	$-0.363687\pi$
$167$	221.270	−	221.270i	1.32497	−	1.32497i	0.909698	−	0.415270i	$-0.136313\pi$
$168$	−16.5372	−	16.5372i	−0.0984358	−	0.0984358i
$169$		−	156.643i		−	0.926883i
$170$	35.1276	+	45.0328i	0.206633	+	0.264899i
$171$	−87.7836			−0.513354
$172$	38.7689	−	38.7689i	0.225401	−	0.225401i
$173$	−64.1445	−	64.1445i	−0.370777	−	0.370777i	0.496983	−	0.867760i	$-0.334441\pi$
$173$	−64.1445	−	64.1445i	−0.370777	−	0.370777i	−0.867760	+	0.496983i	$0.834441\pi$
$174$		−	149.562i		−	0.859550i
$175$	25.8021	+	43.0923i	0.147441	+	0.246242i
$176$	64.7006			0.367617
$177$	−210.065	+	210.065i	−1.18681	+	1.18681i
$178$	−131.605	−	131.605i	−0.739353	−	0.739353i
$179$		−	55.8012i		−	0.311739i	−0.987778	−	0.155869i	$-0.950182\pi$
$179$		−	55.8012i		−	0.311739i	0.987778	−	0.155869i	$-0.0498179\pi$
$180$	−62.5956	+	48.8273i	−0.347753	+	0.271263i
$181$	255.363			1.41085			0.705424	−	0.708786i	$-0.250757\pi$
$181$	255.363			1.41085			0.705424	+	0.708786i	$0.250757\pi$
$182$	7.06226	−	7.06226i	0.0388036	−	0.0388036i
$183$	142.023	+	142.023i	0.776085	+	0.776085i
$184$			13.5647i			0.0737210i
$185$	1.52673	−	12.3555i	0.00825261	−	0.0667864i
$186$	−34.5349			−0.185671
$187$	92.3812	−	92.3812i	0.494017	−	0.494017i
$188$	17.9637	+	17.9637i	0.0955516	+	0.0955516i
$189$			8.77536i			0.0464305i
$190$	77.5993	+	9.58873i	0.408417	+	0.0504670i
$191$	−304.733			−1.59546			−0.797731	−	0.603014i	$-0.793966\pi$
$191$	−304.733			−1.59546			−0.797731	+	0.603014i	$0.793966\pi$
$192$	−23.2817	+	23.2817i	−0.121259	+	0.121259i
$193$	−163.945	−	163.945i	−0.849453	−	0.849453i	0.140611	−	0.990065i	$-0.455093\pi$
$193$	−163.945	−	163.945i	−0.849453	−	0.849453i	−0.990065	+	0.140611i	$0.955093\pi$
$194$		−	150.175i		−	0.774098i
$195$	−44.4913	−	57.0368i	−0.228160	−	0.292496i
$196$	89.9274			0.458813
$197$	133.539	−	133.539i	0.677865	−	0.677865i	−0.281652	−	0.959517i	$-0.590882\pi$
$197$	133.539	−	133.539i	0.677865	−	0.677865i	0.959517	+	0.281652i	$0.0908824\pi$
$198$	128.410	+	128.410i	0.648535	+	0.648535i
$199$		−	168.464i		−	0.846551i	−0.906001	−	0.423275i	$-0.860880\pi$
$199$		−	168.464i		−	0.846551i	0.906001	−	0.423275i	$-0.139120\pi$
$200$	60.6670	−	36.3252i	0.303335	−	0.181626i
$201$	119.218			0.593122
$202$	−135.545	+	135.545i	−0.671015	+	0.671015i
$203$	−36.5042	−	36.5042i	−0.179824	−	0.179824i
$204$			66.4845i			0.325904i
$205$	177.699	−	138.613i	0.866823	−	0.676161i
$206$	226.137			1.09775
$207$	−26.9215	+	26.9215i	−0.130055	+	0.130055i
$208$	−9.94252	−	9.94252i	−0.0478006	−	0.0478006i
$209$		−	178.859i		−	0.855786i
$210$	−7.17019	+	58.0266i	−0.0341437	+	0.276317i
$211$	−228.284			−1.08192			−0.540958	−	0.841049i	$-0.681938\pi$
$211$	−228.284			−1.08192			−0.540958	+	0.841049i	$0.681938\pi$
$212$	−84.9297	+	84.9297i	−0.400612	+	0.400612i
$213$	275.717	+	275.717i	1.29445	+	1.29445i
$214$		−	69.1694i		−	0.323222i
$215$	−136.034	−	16.8094i	−0.632717	−	0.0781831i
$216$	12.3543			0.0571958
$217$	−8.42908	+	8.42908i	−0.0388437	+	0.0388437i
$218$	−16.8511	−	16.8511i	−0.0772988	−	0.0772988i
$219$			586.162i			2.67654i
$220$	−99.4859	−	127.539i	−0.452209	−	0.579721i
$221$	−28.3924			−0.128472
$222$	10.2476	−	10.2476i	0.0461602	−	0.0461602i
$223$	−136.359	−	136.359i	−0.611475	−	0.611475i	0.331856	−	0.943330i	$-0.392325\pi$
$223$	−136.359	−	136.359i	−0.611475	−	0.611475i	−0.943330	+	0.331856i	$0.892325\pi$
$224$			11.3649i			0.0507363i
$225$	192.498	+	48.3106i	0.855548	+	0.214714i
$226$	143.814			0.636345
$227$	261.479	−	261.479i	1.15189	−	1.15189i	0.165715	−	0.986174i	$-0.447007\pi$
$227$	261.479	−	261.479i	1.15189	−	1.15189i	0.986174	−	0.165715i	$-0.0529933\pi$
$228$	64.3603	+	64.3603i	0.282282	+	0.282282i
$229$			314.702i			1.37425i	0.726541	+	0.687123i	$0.241127\pi$
$229$			314.702i			1.37425i	−0.726541	+	0.687123i	$0.758873\pi$
$230$	26.7388	−	20.8575i	0.116256	−	0.0906847i
$231$	133.746			0.578987
$232$	−51.3920	+	51.3920i	−0.221517	+	0.221517i
$233$	257.152	+	257.152i	1.10366	+	1.10366i	0.993966	+	0.109691i	$0.0349860\pi$
$233$	257.152	+	257.152i	1.10366	+	1.10366i	0.109691	+	0.993966i	$0.465014\pi$
$234$		−	39.4654i		−	0.168656i
$235$	7.78868	−	63.0319i	0.0331433	−	0.268221i
$236$	144.364			0.611711
$237$	177.113	−	177.113i	0.747311	−	0.747311i
$238$	16.2271	+	16.2271i	0.0681813	+	0.0681813i
$239$		−	202.382i		−	0.846787i	−0.905946	−	0.423393i	$-0.860839\pi$
$239$		−	202.382i		−	0.846787i	0.905946	−	0.423393i	$-0.139161\pi$
$240$	81.6920	+	10.0945i	0.340383	+	0.0420603i
$241$	−399.829			−1.65904			−0.829521	−	0.558476i	$-0.811386\pi$
$241$	−399.829			−1.65904			−0.829521	+	0.558476i	$0.811386\pi$
$242$	−140.636	+	140.636i	−0.581139	+	0.581139i
$243$	232.450	+	232.450i	0.956583	+	0.956583i
$244$		−	97.6034i		−	0.400014i
$245$	−138.275	−	177.266i	−0.564389	−	0.723535i
$246$	262.347			1.06645
$247$	−27.4852	+	27.4852i	−0.111276	+	0.111276i
$248$	11.8668	+	11.8668i	0.0478499	+	0.0478499i
$249$			496.357i			1.99340i
$250$	−164.888	−	63.7327i	−0.659553	−	0.254931i
$251$	−288.560			−1.14964			−0.574821	−	0.818279i	$-0.694928\pi$
$251$	−288.560			−1.14964			−0.574821	+	0.818279i	$0.694928\pi$
$252$	−22.5558	+	22.5558i	−0.0895069	+	0.0895069i
$253$	−54.8526	−	54.8526i	−0.216809	−	0.216809i
$254$			144.403i			0.568515i
$255$	131.055	−	102.229i	0.513941	−	0.400897i
$256$	16.0000			0.0625000
$257$	−36.9101	+	36.9101i	−0.143619	+	0.143619i	−0.775261	−	0.631641i	$-0.782382\pi$
$257$	−36.9101	+	36.9101i	−0.143619	+	0.143619i	0.631641	+	0.775261i	$0.282382\pi$
$258$	−112.826	−	112.826i	−0.437309	−	0.437309i
$259$		−	5.00233i		−	0.0193140i
$260$	−4.31087	+	34.8868i	−0.0165803	+	0.134180i
$261$	−203.993			−0.781583
$262$	163.121	−	163.121i	0.622601	−	0.622601i
$263$	−169.962	−	169.962i	−0.646242	−	0.646242i	0.305841	−	0.952083i	$-0.401062\pi$
$263$	−169.962	−	169.962i	−0.646242	−	0.646242i	−0.952083	+	0.305841i	$0.901062\pi$
$264$		−	188.293i		−	0.713230i
$265$	298.005	+	36.8237i	1.12455	+	0.138957i
$266$	31.4174			0.118111
$267$	−382.998	+	382.998i	−1.43445	+	1.43445i
$268$	−40.9652	−	40.9652i	−0.152855	−	0.152855i
$269$			406.494i			1.51113i	0.655074	+	0.755565i	$0.272637\pi$
$269$			406.494i			1.51113i	−0.655074	+	0.755565i	$0.727363\pi$
$270$	−18.9964	−	24.3529i	−0.0703570	−	0.0901961i
$271$	−91.9844			−0.339426			−0.169713	−	0.985494i	$-0.554284\pi$
$271$	−91.9844			−0.339426			−0.169713	+	0.985494i	$0.554284\pi$
$272$	22.8452	−	22.8452i	0.0839897	−	0.0839897i
$273$	−20.5527	−	20.5527i	−0.0752846	−	0.0752846i
$274$		−	59.7871i		−	0.218201i
$275$	−98.4331	+	392.216i	−0.357938	+	1.42624i
$276$	39.4761			0.143029
$277$	179.178	−	179.178i	0.646852	−	0.646852i	−0.305379	−	0.952231i	$-0.598783\pi$
$277$	179.178	−	179.178i	0.646852	−	0.646852i	0.952231	+	0.305379i	$0.0987831\pi$
$278$	37.2135	+	37.2135i	0.133861	+	0.133861i
$279$			47.1035i			0.168830i
$280$	22.4027	−	17.4751i	0.0800097	−	0.0624111i
$281$	−113.892			−0.405308			−0.202654	−	0.979250i	$-0.564957\pi$
$281$	−113.892			−0.405308			−0.202654	+	0.979250i	$0.564957\pi$
$282$	52.2782	−	52.2782i	0.185384	−	0.185384i
$283$	357.657	+	357.657i	1.26380	+	1.26380i	0.949234	+	0.314571i	$0.101861\pi$
$283$	357.657	+	357.657i	1.26380	+	1.26380i	0.314571	+	0.949234i	$0.398139\pi$
$284$		−	189.482i		−	0.667192i
$285$	27.9053	−	225.831i	0.0979133	−	0.792388i
$286$	80.4109			0.281157
$287$	64.0321	−	64.0321i	0.223108	−	0.223108i
$288$	31.7549	+	31.7549i	0.110260	+	0.110260i
$289$			223.762i			0.774263i
$290$	180.327	+	22.2825i	0.621816	+	0.0768361i
$291$	−437.042			−1.50186
$292$	201.415	−	201.415i	0.689779	−	0.689779i
$293$	76.7394	+	76.7394i	0.261909	+	0.261909i	0.825829	−	0.563920i	$-0.190707\pi$
$293$	76.7394	+	76.7394i	0.261909	+	0.261909i	−0.563920	+	0.825829i	$0.690707\pi$
$294$		−	261.708i		−	0.890164i
$295$	−221.979	−	284.572i	−0.752470	−	0.964650i
$296$	−7.04247			−0.0237921
$297$	−49.9582	+	49.9582i	−0.168209	+	0.168209i
$298$	−150.770	−	150.770i	−0.505939	−	0.505939i
$299$			16.8584i			0.0563825i
$300$	−105.714	−	176.554i	−0.352380	−	0.588513i
$301$	−55.0758			−0.182976
$302$	154.121	−	154.121i	0.510334	−	0.510334i
$303$	394.465	+	394.465i	1.30187	+	1.30187i
$304$		−	44.2306i		−	0.145495i
$305$	−192.397	+	150.078i	−0.630810	+	0.492060i
$306$	90.6807			0.296342
$307$	358.116	−	358.116i	1.16650	−	1.16650i	0.183479	−	0.983024i	$-0.441264\pi$
$307$	358.116	−	358.116i	1.16650	−	1.16650i	0.983024	−	0.183479i	$-0.0587360\pi$
$308$	−45.9574	−	45.9574i	−0.149212	−	0.149212i
$309$		−	658.107i		−	2.12980i
$310$	5.14519	−	41.6387i	0.0165974	−	0.134318i
$311$	591.335			1.90140			0.950700	−	0.310112i	$-0.100366\pi$
$311$	591.335			1.90140			0.950700	+	0.310112i	$0.100366\pi$
$312$	−28.9349	+	28.9349i	−0.0927400	+	0.0927400i
$313$	165.880	+	165.880i	0.529967	+	0.529967i	0.920562	−	0.390596i	$-0.127731\pi$
$313$	165.880	+	165.880i	0.529967	+	0.529967i	−0.390596	+	0.920562i	$0.627731\pi$
$314$			145.937i			0.464768i
$315$	79.1447	+	9.77970i	0.251253	+	0.0310467i
$316$	−121.718			−0.385183
$317$	57.4756	−	57.4756i	0.181311	−	0.181311i	−0.610616	−	0.791927i	$-0.709078\pi$
$317$	57.4756	−	57.4756i	0.181311	−	0.181311i	0.791927	+	0.610616i	$0.209078\pi$
$318$	247.164	+	247.164i	0.777244	+	0.777244i
$319$		−	415.637i		−	1.30294i
$320$	−24.6021	−	31.5394i	−0.0768817	−	0.0985607i
$321$	−201.298			−0.627096
$322$	9.63510	−	9.63510i	0.0299227	−	0.0299227i
$323$	−63.1536	−	63.1536i	−0.195522	−	0.195522i
$324$		−	178.851i		−	0.552008i
$325$	75.3978	−	45.1455i	0.231993	−	0.138909i
$326$	−121.078			−0.371404
$327$	−49.0405	+	49.0405i	−0.149971	+	0.149971i
$328$	−90.1469	−	90.1469i	−0.274838	−	0.274838i
$329$		−	25.5195i		−	0.0775670i
$330$	−371.165	+	289.525i	−1.12474	+	0.877350i
$331$	−224.233			−0.677442			−0.338721	−	0.940887i	$-0.609994\pi$
$331$	−224.233			−0.677442			−0.338721	+	0.940887i	$0.609994\pi$
$332$	170.557	−	170.557i	0.513725	−	0.513725i
$333$	−13.9770	−	13.9770i	−0.0419731	−	0.0419731i
$334$			442.539i			1.32497i
$335$	−17.7616	+	143.741i	−0.0530198	+	0.429076i
$336$	33.0744			0.0984358
$337$	230.717	−	230.717i	0.684621	−	0.684621i	−0.276417	−	0.961038i	$-0.589147\pi$
$337$	230.717	−	230.717i	0.684621	−	0.684621i	0.961038	+	0.276417i	$0.0891471\pi$
$338$	156.643	+	156.643i	0.463442	+	0.463442i
$339$		−	418.530i		−	1.23460i
$340$	−80.1603	−	9.90519i	−0.235766	−	0.0291329i
$341$	−95.9735			−0.281447
$342$	87.7836	−	87.7836i	0.256677	−	0.256677i
$343$	−133.486	−	133.486i	−0.389173	−	0.389173i
$344$			77.5378i			0.225401i
$345$	−60.6998	−	77.8158i	−0.175941	−	0.225553i
$346$	128.289			0.370777
$347$	91.9955	−	91.9955i	0.265117	−	0.265117i	−0.562012	−	0.827129i	$-0.689973\pi$
$347$	91.9955	−	91.9955i	0.265117	−	0.265117i	0.827129	+	0.562012i	$0.189973\pi$
$348$	149.562	+	149.562i	0.429775	+	0.429775i
$349$			62.4595i			0.178967i	0.995988	+	0.0894835i	$0.0285216\pi$
$349$			62.4595i			0.178967i	−0.995988	+	0.0894835i	$0.971478\pi$
$350$	−68.8944	−	17.2902i	−0.196841	−	0.0494005i
$351$	15.3541			0.0437439
$352$	−64.7006	+	64.7006i	−0.183809	+	0.183809i
$353$	−277.111	−	277.111i	−0.785017	−	0.785017i	0.195655	−	0.980673i	$-0.437317\pi$
$353$	−277.111	−	277.111i	−0.785017	−	0.785017i	−0.980673	+	0.195655i	$0.937317\pi$
$354$		−	420.130i		−	1.18681i
$355$	−373.510	+	291.355i	−1.05214	+	0.820718i
$356$	263.209			0.739353
$357$	47.2245	−	47.2245i	0.132281	−	0.132281i
$358$	55.8012	+	55.8012i	0.155869	+	0.155869i
$359$		−	24.5700i		−	0.0684402i	−0.999414	−	0.0342201i	$-0.989105\pi$
$359$		−	24.5700i		−	0.0684402i	0.999414	−	0.0342201i	$-0.0108947\pi$
$360$	13.7682	−	111.423i	0.0382451	−	0.309508i
$361$	238.728			0.661297
$362$	−255.363	+	255.363i	−0.705424	+	0.705424i
$363$	409.280	+	409.280i	1.12749	+	1.12749i
$364$			14.1245i			0.0388036i
$365$	−706.736	−	87.3294i	−1.93626	−	0.239259i
$366$	−284.047			−0.776085
$367$	97.2838	−	97.2838i	0.265079	−	0.265079i	−0.562035	−	0.827113i	$-0.689981\pi$
$367$	97.2838	−	97.2838i	0.265079	−	0.265079i	0.827113	+	0.562035i	$0.189981\pi$
$368$	−13.5647	−	13.5647i	−0.0368605	−	0.0368605i
$369$		−	357.825i		−	0.969716i
$370$	10.8287	+	13.8822i	0.0292669	+	0.0375195i
$371$	120.653			0.325209
$372$	34.5349	−	34.5349i	0.0928357	−	0.0928357i
$373$	250.644	+	250.644i	0.671968	+	0.671968i	0.958170	−	0.286201i	$-0.0923926\pi$
$373$	250.644	+	250.644i	0.671968	+	0.671968i	−0.286201	+	0.958170i	$0.592393\pi$
$374$			184.762i			0.494017i
$375$	−185.476	+	479.860i	−0.494602	+	1.27963i
$376$	−35.9274			−0.0955516
$377$	−63.8707	+	63.8707i	−0.169418	+	0.169418i
$378$	−8.77536	−	8.77536i	−0.0232152	−	0.0232152i
$379$			408.259i			1.07720i	0.842562	+	0.538600i	$0.181047\pi$
$379$			408.259i			1.07720i	−0.842562	+	0.538600i	$0.818953\pi$
$380$	−87.1880	+	68.0105i	−0.229442	+	0.178975i
$381$	420.244			1.10300
$382$	304.733	−	304.733i	0.797731	−	0.797731i
$383$	−60.7142	−	60.7142i	−0.158523	−	0.158523i	0.623389	−	0.781912i	$-0.285755\pi$
$383$	−60.7142	−	60.7142i	−0.158523	−	0.158523i	−0.781912	+	0.623389i	$0.785755\pi$
$384$		−	46.5635i		−	0.121259i
$385$	−19.9262	+	161.258i	−0.0517563	+	0.418851i
$386$	327.889			0.849453
$387$	−153.888	+	153.888i	−0.397642	+	0.397642i
$388$	150.175	+	150.175i	0.387049	+	0.387049i
$389$			615.448i			1.58213i	0.611733	+	0.791064i	$0.290473\pi$
$389$			615.448i			1.58213i	−0.611733	+	0.791064i	$0.709527\pi$
$390$	101.528	+	12.5456i	0.260328	+	0.0321681i
$391$	−38.7359			−0.0990688
$392$	−89.9274	+	89.9274i	−0.229407	+	0.229407i
$393$	−474.719	−	474.719i	−1.20794	−	1.20794i
$394$			267.079i			0.677865i
$395$	187.158	+	239.932i	0.473817	+	0.607423i
$396$	−256.820			−0.648535
$397$	−454.386	+	454.386i	−1.14455	+	1.14455i	−0.156941	+	0.987608i	$0.550163\pi$
$397$	−454.386	+	454.386i	−1.14455	+	1.14455i	−0.987608	+	0.156941i	$0.949837\pi$
$398$	168.464	+	168.464i	0.423275	+	0.423275i
$399$		−	91.4314i		−	0.229151i
$400$	−24.3418	+	96.9922i	−0.0608545	+	0.242480i
$401$	−471.540			−1.17591			−0.587955	−	0.808894i	$-0.700067\pi$
$401$	−471.540			−1.17591			−0.587955	+	0.808894i	$0.700067\pi$
$402$	−119.218	+	119.218i	−0.296561	+	0.296561i
$403$	14.7482	+	14.7482i	0.0365961	+	0.0365961i
$404$		−	271.090i		−	0.671015i
$405$	−352.552	+	275.007i	−0.870500	+	0.679029i
$406$	73.0084			0.179824
$407$	28.4783	−	28.4783i	0.0699712	−	0.0699712i
$408$	−66.4845	−	66.4845i	−0.162952	−	0.162952i
$409$			99.5691i			0.243445i	0.992564	+	0.121723i	$0.0388418\pi$
$409$			99.5691i			0.243445i	−0.992564	+	0.121723i	$0.961158\pi$
$410$	−39.0858	+	316.312i	−0.0953312	+	0.771492i
$411$	−173.993			−0.423342
$412$	−226.137	+	226.137i	−0.548876	+	0.548876i
$413$	−102.543	−	102.543i	−0.248288	−	0.248288i
$414$		−	53.8430i		−	0.130055i
$415$	−598.457	−	73.9498i	−1.44207	−	0.178192i
$416$	19.8850			0.0478006
$417$	108.299	−	108.299i	0.259710	−	0.259710i
$418$	178.859	+	178.859i	0.427893	+	0.427893i
$419$		−	761.168i		−	1.81663i	−0.418287	−	0.908315i	$-0.637370\pi$
$419$		−	761.168i		−	1.81663i	0.418287	−	0.908315i	$-0.362630\pi$
$420$	−50.8564	−	65.1967i	−0.121087	−	0.155230i
$421$	−109.597			−0.260324			−0.130162	−	0.991493i	$-0.541550\pi$
$421$	−109.597			−0.260324			−0.130162	+	0.991493i	$0.541550\pi$
$422$	228.284	−	228.284i	0.540958	−	0.540958i
$423$	−71.3043	−	71.3043i	−0.168568	−	0.168568i
$424$		−	169.859i		−	0.400612i
$425$	103.732	+	173.244i	0.244075	+	0.407632i
$426$	−551.435			−1.29445
$427$	−69.3285	+	69.3285i	−0.162362	+	0.162362i
$428$	69.1694	+	69.1694i	0.161611	+	0.161611i
$429$		−	234.013i		−	0.545485i
$430$	152.843	−	119.225i	0.355450	−	0.277267i
$431$	516.446			1.19825			0.599125	−	0.800656i	$-0.295515\pi$
$431$	516.446			1.19825			0.599125	+	0.800656i	$0.295515\pi$
$432$	−12.3543	+	12.3543i	−0.0285979	+	0.0285979i
$433$	202.477	+	202.477i	0.467615	+	0.467615i	0.901141	−	0.433526i	$-0.142731\pi$
$433$	202.477	+	202.477i	0.467615	+	0.467615i	−0.433526	+	0.901141i	$0.642731\pi$
$434$		−	16.8582i		−	0.0388437i
$435$	64.8468	−	524.789i	0.149073	−	1.20641i
$436$	33.7023			0.0772988
$437$	−37.4983	+	37.4983i	−0.0858086	+	0.0858086i
$438$	−586.162	−	586.162i	−1.33827	−	1.33827i
$439$			20.4001i			0.0464695i	0.999730	+	0.0232348i	$0.00739652\pi$
$439$			20.4001i			0.0464695i	−0.999730	+	0.0232348i	$0.992603\pi$
$440$	227.025	+	28.0528i	0.515965	+	0.0637564i
$441$	−356.954			−0.809419
$442$	28.3924	−	28.3924i	0.0642361	−	0.0642361i
$443$	−225.032	−	225.032i	−0.507973	−	0.507973i	0.405931	−	0.913904i	$-0.366947\pi$
$443$	−225.032	−	225.032i	−0.507973	−	0.507973i	−0.913904	+	0.405931i	$0.866947\pi$
$444$			20.4951i			0.0461602i
$445$	−404.720	−	518.842i	−0.909483	−	1.16594i
$446$	272.718			0.611475
$447$	−438.773	+	438.773i	−0.981595	+	0.981595i
$448$	−11.3649	−	11.3649i	−0.0253682	−	0.0253682i
$449$			140.825i			0.313642i	0.987627	+	0.156821i	$0.0501245\pi$
$449$			140.825i			0.313642i	−0.987627	+	0.156821i	$0.949875\pi$
$450$	−240.809	+	144.188i	−0.535131	+	0.320417i
$451$	729.070			1.61656
$452$	−143.814	+	143.814i	−0.318172	+	0.318172i
$453$	−448.525	−	448.525i	−0.990121	−	0.990121i
$454$			522.958i			1.15189i
$455$	27.8424	−	21.7183i	0.0611922	−	0.0477326i
$456$	−128.721			−0.282282
$457$	−118.426	+	118.426i	−0.259139	+	0.259139i	−0.824704	−	0.565565i	$-0.808658\pi$
$457$	−118.426	+	118.426i	−0.259139	+	0.259139i	0.565565	+	0.824704i	$0.308658\pi$
$458$	−314.702	−	314.702i	−0.687123	−	0.687123i
$459$			35.2795i			0.0768617i
$460$	−5.88135	+	47.5963i	−0.0127855	+	0.103470i
$461$	−290.493			−0.630136			−0.315068	−	0.949069i	$-0.602027\pi$
$461$	−290.493			−0.630136			−0.315068	+	0.949069i	$0.602027\pi$
$462$	−133.746	+	133.746i	−0.289494	+	0.289494i
$463$	311.144	+	311.144i	0.672016	+	0.672016i	0.958181	−	0.286164i	$-0.0923803\pi$
$463$	311.144	+	311.144i	0.672016	+	0.672016i	−0.286164	+	0.958181i	$0.592380\pi$
$464$		−	102.784i		−	0.221517i
$465$	−121.178	−	14.9736i	−0.260597	−	0.0322013i
$466$	−514.304			−1.10366
$467$	409.704	−	409.704i	0.877311	−	0.877311i	−0.115945	−	0.993256i	$-0.536990\pi$
$467$	409.704	−	409.704i	0.877311	−	0.877311i	0.993256	+	0.115945i	$0.0369896\pi$
$468$	39.4654	+	39.4654i	0.0843278	+	0.0843278i
$469$			58.1959i			0.124085i
$470$	55.2432	+	70.8205i	0.117539	+	0.150682i
$471$	424.708			0.901716
$472$	−144.364	+	144.364i	−0.305855	+	0.305855i
$473$	−313.546	−	313.546i	−0.662889	−	0.662889i
$474$			354.226i			0.747311i
$475$	268.127	+	67.2908i	0.564477	+	0.141665i
$476$	−32.4543			−0.0681813
$477$	337.116	−	337.116i	0.706742	−	0.706742i
$478$	202.382	+	202.382i	0.423393	+	0.423393i
$479$		−	509.370i		−	1.06340i	−0.846932	−	0.531702i	$-0.821553\pi$
$479$		−	509.370i		−	1.06340i	0.846932	−	0.531702i	$-0.178447\pi$
$480$	−91.7865	+	71.5976i	−0.191222	+	0.149162i
$481$	−8.75249			−0.0181964
$482$	399.829	−	399.829i	0.829521	−	0.829521i
$483$	−28.0402	−	28.0402i	−0.0580543	−	0.0580543i
$484$		−	281.271i		−	0.581139i
$485$	65.1127	−	526.941i	0.134253	−	1.08648i
$486$	−464.899			−0.956583
$487$	−434.483	+	434.483i	−0.892162	+	0.892162i	−0.994726	−	0.102564i	$-0.967295\pi$
$487$	−434.483	+	434.483i	−0.892162	+	0.892162i	0.102564	+	0.994726i	$0.467295\pi$
$488$	97.6034	+	97.6034i	0.200007	+	0.200007i
$489$			352.362i			0.720577i
$490$	315.541	+	38.9906i	0.643962	+	0.0795727i
$491$	483.200			0.984114			0.492057	−	0.870563i	$-0.336245\pi$
$491$	483.200			0.984114			0.492057	+	0.870563i	$0.336245\pi$
$492$	−262.347	+	262.347i	−0.533226	+	0.533226i
$493$	−146.758	−	146.758i	−0.297683	−	0.297683i
$494$		−	54.9705i		−	0.111276i
$495$	394.895	+	506.247i	0.797768	+	1.02272i
$496$	−23.7336			−0.0478499
$497$	−134.591	+	134.591i	−0.270807	+	0.270807i
$498$	−496.357	−	496.357i	−0.996700	−	0.996700i
$499$			521.499i			1.04509i	0.852612	+	0.522544i	$0.175017\pi$
$499$			521.499i			1.04509i	−0.852612	+	0.522544i	$0.824983\pi$
$500$	228.621	−	101.156i	0.457242	−	0.202311i
$501$	1287.89			2.57063
$502$	288.560	−	288.560i	0.574821	−	0.574821i
$503$	61.3183	+	61.3183i	0.121905	+	0.121905i	0.765427	−	0.643522i	$-0.222528\pi$
$503$	61.3183	+	61.3183i	0.121905	+	0.121905i	−0.643522	+	0.765427i	$0.722528\pi$
$504$		−	45.1115i		−	0.0895069i
$505$	−534.376	+	416.837i	−1.05817	+	0.825420i
$506$	109.705			0.216809
$507$	455.866	−	455.866i	0.899144	−	0.899144i
$508$	−144.403	−	144.403i	−0.284258	−	0.284258i
$509$		−	453.399i		−	0.890765i	−0.895340	−	0.445383i	$-0.853068\pi$
$509$		−	453.399i		−	0.890765i	0.895340	−	0.445383i	$-0.146932\pi$
$510$	−28.8263	+	233.284i	−0.0565221	+	0.457419i
$511$	−286.134			−0.559950
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	34.1524	+	34.1524i	0.0665739	+	0.0665739i
$514$		−	73.8203i		−	0.143619i
$515$	793.480	+	98.0482i	1.54074	+	0.190385i
$516$	225.652			0.437309
$517$	145.283	−	145.283i	0.281011	−	0.281011i
$518$	5.00233	+	5.00233i	0.00965700	+	0.00965700i
$519$		−	373.349i		−	0.719362i
$520$	−30.5759	−	39.1977i	−0.0587998	−	0.0753801i
$521$	20.7328			0.0397942			0.0198971	−	0.999802i	$-0.493666\pi$
$521$	20.7328			0.0397942			0.0198971	+	0.999802i	$0.493666\pi$
$522$	203.993	−	203.993i	0.390791	−	0.390791i
$523$	241.331	+	241.331i	0.461435	+	0.461435i	0.899126	−	0.437690i	$-0.144203\pi$
$523$	241.331	+	241.331i	0.461435	+	0.461435i	−0.437690	+	0.899126i	$0.644203\pi$
$524$			326.243i			0.622601i
$525$	−50.3182	+	200.498i	−0.0958441	+	0.381900i
$526$	339.923			0.646242
$527$	−33.8874	+	33.8874i	−0.0643024	+	0.0643024i
$528$	188.293	+	188.293i	0.356615	+	0.356615i
$529$			23.0000i			0.0434783i
$530$	−334.829	+	261.182i	−0.631753	+	0.492795i
$531$	−573.031			−1.07915
$532$	−31.4174	+	31.4174i	−0.0590553	+	0.0590553i
$533$	−112.036	−	112.036i	−0.210199	−	0.210199i
$534$		−	765.996i		−	1.43445i
$535$	29.9904	−	242.705i	0.0560568	−	0.453654i
$536$	81.9304			0.152855
$537$	162.394	−	162.394i	0.302409	−	0.302409i
$538$	−406.494	−	406.494i	−0.755565	−	0.755565i
$539$		−	727.295i		−	1.34934i
$540$	43.3493	+	5.35656i	0.0802765	+	0.00991956i
$541$	440.058			0.813417			0.406708	−	0.913558i	$-0.366677\pi$
$541$	440.058			0.813417			0.406708	+	0.913558i	$0.366677\pi$
$542$	91.9844	−	91.9844i	0.169713	−	0.169713i
$543$	743.163	+	743.163i	1.36862	+	1.36862i
$544$			45.6904i			0.0839897i
$545$	−51.8218	−	66.4344i	−0.0950859	−	0.121898i
$546$	41.1054			0.0752846
$547$	−44.9813	+	44.9813i	−0.0822327	+	0.0822327i	−0.747027	−	0.664794i	$-0.768519\pi$
$547$	−44.9813	+	44.9813i	−0.0822327	+	0.0822327i	0.664794	+	0.747027i	$0.268519\pi$
$548$	59.7871	+	59.7871i	0.109101	+	0.109101i
$549$			387.423i			0.705688i
$550$	−293.783	−	490.649i	−0.534150	−	0.892089i
$551$	−284.138			−0.515676
$552$	−39.4761	+	39.4761i	−0.0715147	+	0.0715147i
$553$	86.4573	+	86.4573i	0.156342	+	0.156342i
$554$			358.356i			0.646852i
$555$	40.4002	−	31.5140i	0.0727932	−	0.0567819i
$556$	−74.4270			−0.133861
$557$	718.417	−	718.417i	1.28980	−	1.28980i	0.354889	−	0.934908i	$-0.384519\pi$
$557$	718.417	−	718.417i	1.28980	−	1.28980i	0.934908	−	0.354889i	$-0.115481\pi$
$558$	−47.1035	−	47.1035i	−0.0844149	−	0.0844149i
$559$			96.3651i			0.172388i
$560$	−4.92760	+	39.8778i	−0.00879928	+	0.0712104i
$561$	537.698			0.958464
$562$	113.892	−	113.892i	0.202654	−	0.202654i
$563$	273.569	+	273.569i	0.485914	+	0.485914i	0.907014	−	0.421100i	$-0.138356\pi$
$563$	273.569	+	273.569i	0.485914	+	0.485914i	−0.421100	+	0.907014i	$0.638356\pi$
$564$			104.556i			0.185384i
$565$	504.621	+	62.3547i	0.893135	+	0.110362i
$566$	−715.314			−1.26380
$567$	−127.039	+	127.039i	−0.224055	+	0.224055i
$568$	189.482	+	189.482i	0.333596	+	0.333596i
$569$			600.751i			1.05580i	0.849306	+	0.527901i	$0.177021\pi$
$569$			600.751i			1.05580i	−0.849306	+	0.527901i	$0.822979\pi$
$570$	197.925	+	253.736i	0.347237	+	0.445151i
$571$	−569.434			−0.997257			−0.498628	−	0.866816i	$-0.666163\pi$
$571$	−569.434			−0.997257			−0.498628	+	0.866816i	$0.666163\pi$
$572$	−80.4109	+	80.4109i	−0.140579	+	0.140579i
$573$	−886.839	−	886.839i	−1.54771	−	1.54771i
$574$			128.064i			0.223108i
$575$	102.866	−	61.5923i	0.178897	−	0.107117i
$576$	−63.5097			−0.110260
$577$	−717.007	+	717.007i	−1.24265	+	1.24265i	−0.283747	+	0.958899i	$0.591578\pi$
$577$	−717.007	+	717.007i	−1.24265	+	1.24265i	−0.958899	+	0.283747i	$0.908422\pi$
$578$	−223.762	−	223.762i	−0.387132	−	0.387132i
$579$		−	954.228i		−	1.64806i
$580$	−202.609	+	158.044i	−0.349326	+	0.272490i
$581$	−242.296			−0.417032
$582$	437.042	−	437.042i	0.750931	−	0.750931i
$583$	686.875	+	686.875i	1.17817	+	1.17817i
$584$			402.831i			0.689779i
$585$	17.1114	−	138.478i	0.0292502	−	0.236715i
$586$	−153.479			−0.261909
$587$	−121.299	+	121.299i	−0.206642	+	0.206642i	−0.802838	−	0.596197i	$-0.796678\pi$
$587$	−121.299	+	121.299i	−0.206642	+	0.206642i	0.596197	+	0.802838i	$0.296678\pi$
$588$	261.708	+	261.708i	0.445082	+	0.445082i
$589$			65.6094i			0.111391i
$590$	506.550	+	62.5931i	0.858560	+	0.106090i
$591$	777.256			1.31515
$592$	7.04247	−	7.04247i	0.0118961	−	0.0118961i
$593$	794.085	+	794.085i	1.33910	+	1.33910i	0.896934	+	0.442164i	$0.145789\pi$
$593$	794.085	+	794.085i	1.33910	+	1.33910i	0.442164	+	0.896934i	$0.354211\pi$
$594$		−	99.9163i		−	0.168209i
$595$	49.9028	+	63.9743i	0.0838703	+	0.107520i
$596$	301.540			0.505939
$597$	490.266	−	490.266i	0.821215	−	0.821215i
$598$	−16.8584	−	16.8584i	−0.0281912	−	0.0281912i
$599$			60.9458i			0.101746i	0.998705	+	0.0508730i	$0.0162004\pi$
$599$			60.9458i			0.101746i	−0.998705	+	0.0508730i	$0.983800\pi$
$600$	282.268	+	70.8399i	0.470447	+	0.118066i
$601$	752.118			1.25144			0.625722	−	0.780046i	$-0.284804\pi$
$601$	752.118			1.25144			0.625722	+	0.780046i	$0.284804\pi$
$602$	55.0758	−	55.0758i	0.0914880	−	0.0914880i
$603$	162.605	+	162.605i	0.269661	+	0.269661i
$604$			308.242i			0.510334i
$605$	−554.446	+	432.492i	−0.916439	+	0.714864i
$606$	−788.930			−1.30187
$607$	−613.418	+	613.418i	−1.01057	+	1.01057i	−0.0106304	+	0.999943i	$0.503384\pi$
$607$	−613.418	+	613.418i	−1.01057	+	1.01057i	−0.999943	+	0.0106304i	$0.996616\pi$
$608$	44.2306	+	44.2306i	0.0727477	+	0.0727477i
$609$		−	212.470i		−	0.348884i
$610$	42.3188	−	342.475i	0.0693750	−	0.561435i
$611$	−44.6511			−0.0730787
$612$	−90.6807	+	90.6807i	−0.148171	+	0.148171i
$613$	147.819	+	147.819i	0.241140	+	0.241140i	0.817321	−	0.576182i	$-0.195458\pi$
$613$	147.819	+	147.819i	0.241140	+	0.241140i	−0.576182	+	0.817321i	$0.695458\pi$
$614$			716.233i			1.16650i
$615$	920.535	+	113.748i	1.49681	+	0.184956i
$616$	91.9148			0.149212
$617$	562.325	−	562.325i	0.911386	−	0.911386i	−0.0849950	−	0.996381i	$-0.527087\pi$
$617$	562.325	−	562.325i	0.911386	−	0.911386i	0.996381	+	0.0849950i	$0.0270874\pi$
$618$	658.107	+	658.107i	1.06490	+	1.06490i
$619$			90.9583i			0.146944i	0.997297	+	0.0734719i	$0.0234079\pi$
$619$			90.9583i			0.146944i	−0.997297	+	0.0734719i	$0.976592\pi$
$620$	36.4935	+	46.7839i	0.0588606	+	0.0754579i
$621$	20.9477			0.0337322
$622$	−591.335	+	591.335i	−0.950700	+	0.950700i
$623$	−186.960	−	186.960i	−0.300096	−	0.300096i
$624$		−	57.8698i		−	0.0927400i
$625$	−550.935	−	295.120i	−0.881495	−	0.472193i
$626$	−331.759			−0.529967
$627$	520.519	−	520.519i	0.830174	−	0.830174i
$628$	−145.937	−	145.937i	−0.232384	−	0.232384i
$629$		−	20.1108i		−	0.0319727i
$630$	−88.9244	+	69.3650i	−0.141150	+	0.110103i
$631$	−946.747			−1.50039			−0.750195	−	0.661216i	$-0.770041\pi$
$631$	−946.747			−1.50039			−0.750195	+	0.661216i	$0.770041\pi$
$632$	121.718	−	121.718i	0.192592	−	0.192592i
$633$	−664.357	−	664.357i	−1.04954	−	1.04954i
$634$			114.951i			0.181311i
$635$	−62.6100	+	506.688i	−0.0985985	+	0.797933i
$636$	−494.327			−0.777244
$637$	−111.763	+	111.763i	−0.175452	+	0.175452i
$638$	415.637	+	415.637i	0.651468	+	0.651468i
$639$			752.124i			1.17703i
$640$	56.1416	+	6.93726i	0.0877212	+	0.0108395i
$641$	−796.641			−1.24281			−0.621405	−	0.783489i	$-0.713438\pi$
$641$	−796.641			−1.24281			−0.621405	+	0.783489i	$0.713438\pi$
$642$	201.298	−	201.298i	0.313548	−	0.313548i
$643$	187.226	+	187.226i	0.291175	+	0.291175i	0.837544	−	0.546369i	$-0.183990\pi$
$643$	187.226	+	187.226i	0.291175	+	0.291175i	−0.546369	+	0.837544i	$0.683990\pi$
$644$			19.2702i			0.0299227i
$645$	−346.970	−	444.808i	−0.537938	−	0.689624i
$646$	126.307			0.195522
$647$	−497.770	+	497.770i	−0.769350	+	0.769350i	−0.977992	−	0.208642i	$-0.933096\pi$
$647$	−497.770	+	497.770i	−0.769350	+	0.769350i	0.208642	+	0.977992i	$0.433096\pi$
$648$	178.851	+	178.851i	0.276004	+	0.276004i
$649$		−	1167.55i		−	1.79900i
$650$	−30.2523	+	120.543i	−0.0465421	+	0.185451i
$651$	−49.0609			−0.0753623
$652$	121.078	−	121.078i	0.185702	−	0.185702i
$653$	−646.860	−	646.860i	−0.990598	−	0.990598i	0.00935823	−	0.999956i	$-0.497021\pi$
$653$	−646.860	−	646.860i	−0.990598	−	0.990598i	−0.999956	+	0.00935823i	$0.997021\pi$
$654$		−	98.0809i		−	0.149971i
$655$	643.094	−	501.642i	0.981823	−	0.765866i
$656$	180.294			0.274838
$657$	−799.489	+	799.489i	−1.21688	+	1.21688i
$658$	25.5195	+	25.5195i	0.0387835	+	0.0387835i
$659$		−	2.45884i		−	0.00373117i	−0.999998	−	0.00186559i	$-0.999406\pi$
$659$		−	2.45884i		−	0.00373117i	0.999998	−	0.00186559i	$-0.000593835\pi$
$660$	81.6398	−	660.691i	0.123697	−	1.00105i
$661$	855.665			1.29450			0.647250	−	0.762277i	$-0.275919\pi$
$661$	855.665			1.29450			0.647250	+	0.762277i	$0.275919\pi$
$662$	224.233	−	224.233i	0.338721	−	0.338721i
$663$	−82.6279	−	82.6279i	−0.124627	−	0.124627i
$664$			341.113i			0.513725i
$665$	110.239	+	13.6219i	0.165773	+	0.0204841i
$666$	27.9541			0.0419731
$667$	−87.1394	+	87.1394i	−0.130644	+	0.130644i
$668$	−442.539	−	442.539i	−0.662484	−	0.662484i
$669$		−	793.667i		−	1.18635i
$670$	−125.979	−	161.502i	−0.188028	−	0.241048i
$671$	−789.375			−1.17642
$672$	−33.0744	+	33.0744i	−0.0492179	+	0.0492179i
$673$	656.444	+	656.444i	0.975399	+	0.975399i	0.999705	−	0.0243053i	$-0.00773736\pi$
$673$	656.444	+	656.444i	0.975399	+	0.975399i	−0.0243053	+	0.999705i	$0.507737\pi$
$674$			461.434i			0.684621i
$675$	−56.0965	−	93.6872i	−0.0831059	−	0.138796i
$676$	−313.287			−0.463442
$677$	−65.8751	+	65.8751i	−0.0973044	+	0.0973044i	−0.754083	−	0.656779i	$-0.771918\pi$
$677$	−65.8751	+	65.8751i	−0.0973044	+	0.0973044i	0.656779	+	0.754083i	$0.271918\pi$
$678$	418.530	+	418.530i	0.617300	+	0.617300i
$679$		−	213.341i		−	0.314199i
$680$	90.0655	−	70.2551i	0.132449	−	0.103316i
$681$	1521.92			2.23483
$682$	95.9735	−	95.9735i	0.140724	−	0.140724i
$683$	−638.547	−	638.547i	−0.934914	−	0.934914i	0.0630932	−	0.998008i	$-0.479903\pi$
$683$	−638.547	−	638.547i	−0.934914	−	0.934914i	−0.998008	+	0.0630932i	$0.979903\pi$
$684$			175.567i			0.256677i
$685$	25.9224	−	209.784i	0.0378430	−	0.306254i
$686$	266.973			0.389173
$687$	−915.852	+	915.852i	−1.33312	+	1.33312i
$688$	−77.5378	−	77.5378i	−0.112700	−	0.112700i
$689$		−	211.104i		−	0.306392i
$690$	138.516	+	17.1160i	0.200747	+	0.0248058i
$691$	188.696			0.273077			0.136539	−	0.990635i	$-0.456402\pi$
$691$	188.696			0.273077			0.136539	+	0.990635i	$0.456402\pi$
$692$	−128.289	+	128.289i	−0.185389	+	0.185389i
$693$	182.421	+	182.421i	0.263234	+	0.263234i
$694$			183.991i			0.265117i
$695$	114.441	+	146.711i	0.164664	+	0.211096i
$696$	−299.124			−0.429775
$697$	257.428	−	257.428i	0.369337	−	0.369337i
$698$	−62.4595	−	62.4595i	−0.0894835	−	0.0894835i
$699$			1496.74i			2.14125i
$700$	86.1846	−	51.6042i	0.123121	−	0.0737203i
$701$	361.600			0.515834			0.257917	−	0.966167i	$-0.416964\pi$
$701$	361.600			0.515834			0.257917	+	0.966167i	$0.416964\pi$
$702$	−15.3541	+	15.3541i	−0.0218719	+	0.0218719i
$703$	−19.4683	−	19.4683i	−0.0276932	−	0.0276932i
$704$		−	129.401i		−	0.183809i
$705$	206.103	−	160.770i	0.292345	−	0.228042i
$706$	554.222			0.785017
$707$	−192.558	+	192.558i	−0.272359	+	0.272359i
$708$	420.130	+	420.130i	0.593403	+	0.593403i
$709$		−	239.107i		−	0.337245i	−0.985681	−	0.168622i	$-0.946068\pi$
$709$		−	239.107i		−	0.337245i	0.985681	−	0.168622i	$-0.0539319\pi$
$710$	82.1556	−	664.865i	0.115712	−	0.936430i
$711$	483.142			0.679525
$712$	−263.209	+	263.209i	−0.369676	+	0.369676i
$713$	20.1211	+	20.1211i	0.0282203	+	0.0282203i
$714$			94.4490i			0.132281i
$715$	282.150	+	34.8645i	0.394615	+	0.0487615i
$716$	−111.602			−0.155869
$717$	588.975	−	588.975i	0.821444	−	0.821444i
$718$	24.5700	+	24.5700i	0.0342201	+	0.0342201i
$719$		−	320.210i		−	0.445355i	−0.974892	−	0.222677i	$-0.928520\pi$
$719$		−	320.210i		−	0.445355i	0.974892	−	0.222677i	$-0.0714796\pi$
$720$	97.6547	+	125.191i	0.135632	+	0.173877i
$721$	321.254			0.445567
$722$	−238.728	+	238.728i	−0.330648	+	0.330648i
$723$	−1163.59	−	1163.59i	−1.60939	−	1.60939i
$724$		−	510.727i		−	0.705424i
$725$	623.077	+	156.372i	0.859417	+	0.215685i
$726$	−818.560			−1.12749
$727$	−154.348	+	154.348i	−0.212309	+	0.212309i	−0.805248	−	0.592939i	$-0.797968\pi$
$727$	−154.348	+	154.348i	−0.212309	+	0.212309i	0.592939	+	0.805248i	$0.297968\pi$
$728$	−14.1245	−	14.1245i	−0.0194018	−	0.0194018i
$729$			548.130i			0.751893i
$730$	794.065	−	619.406i	1.08776	−	0.848502i
$731$	−221.421			−0.302901
$732$	284.047	−	284.047i	0.388042	−	0.388042i
$733$	598.281	+	598.281i	0.816208	+	0.816208i	0.985556	−	0.169348i	$-0.0541662\pi$
$733$	598.281	+	598.281i	0.816208	+	0.816208i	−0.169348	+	0.985556i	$0.554166\pi$
$734$			194.568i			0.265079i
$735$	113.471	−	918.294i	0.154382	−	1.24938i
$736$	27.1293			0.0368605
$737$	−331.309	+	331.309i	−0.449537	+	0.449537i
$738$	357.825	+	357.825i	0.484858	+	0.484858i
$739$			892.374i			1.20754i	0.797157	+	0.603772i	$0.206336\pi$
$739$			892.374i			1.20754i	−0.797157	+	0.603772i	$0.793664\pi$
$740$	−24.7110	−	3.05347i	−0.0333932	−	0.00412631i
$741$	−159.976			−0.215892
$742$	−120.653	+	120.653i	−0.162605	+	0.162605i
$743$	618.674	+	618.674i	0.832671	+	0.832671i	0.987881	−	0.155211i	$-0.0496057\pi$
$743$	618.674	+	618.674i	0.832671	+	0.832671i	−0.155211	+	0.987881i	$0.549606\pi$
$744$			69.0698i			0.0928357i
$745$	−463.658	−	594.399i	−0.622360	−	0.797852i
$746$	−501.288			−0.671968
$747$	−677.000	+	677.000i	−0.906292	+	0.906292i
$748$	−184.762	−	184.762i	−0.247008	−	0.247008i
$749$		−	98.2633i		−	0.131193i
$750$	−294.385	−	665.336i	−0.392513	−	0.887115i
$751$	−239.106			−0.318384			−0.159192	−	0.987248i	$-0.550889\pi$
$751$	−239.106			−0.318384			−0.159192	+	0.987248i	$0.550889\pi$
$752$	35.9274	−	35.9274i	0.0477758	−	0.0477758i
$753$	−839.773	−	839.773i	−1.11524	−	1.11524i
$754$		−	127.741i		−	0.169418i
$755$	607.610	−	473.963i	0.804781	−	0.627765i
$756$	17.5507			0.0232152
$757$	428.943	−	428.943i	0.566636	−	0.566636i	−0.364549	−	0.931184i	$-0.618777\pi$
$757$	428.943	−	428.943i	0.566636	−	0.566636i	0.931184	+	0.364549i	$0.118777\pi$
$758$	−408.259	−	408.259i	−0.538600	−	0.538600i
$759$		−	319.266i		−	0.420640i
$760$	19.1775	−	155.199i	0.0252335	−	0.204209i
$761$	−1254.77			−1.64885			−0.824424	−	0.565972i	$-0.808501\pi$
$761$	−1254.77			−1.64885			−0.824424	+	0.565972i	$0.808501\pi$
$762$	−420.244	+	420.244i	−0.551501	+	0.551501i
$763$	−23.9390	−	23.9390i	−0.0313749	−	0.0313749i
$764$			609.466i			0.797731i
$765$	318.185	+	39.3172i	0.415928	+	0.0513951i
$766$	121.428			0.158523
$767$	−179.417	+	179.417i	−0.233921	+	0.233921i
$768$	46.5635	+	46.5635i	0.0606295	+	0.0606295i
$769$		−	393.539i		−	0.511754i	−0.966709	−	0.255877i	$-0.917636\pi$
$769$		−	393.539i		−	0.511754i	0.966709	−	0.255877i	$-0.0823642\pi$
$770$	−141.331	−	181.184i	−0.183547	−	0.235304i
$771$	−214.833			−0.278642
$772$	−327.889	+	327.889i	−0.424727	+	0.424727i
$773$	−484.217	−	484.217i	−0.626413	−	0.626413i	0.320751	−	0.947164i	$-0.396065\pi$
$773$	−484.217	−	484.217i	−0.626413	−	0.626413i	−0.947164	+	0.320751i	$0.896065\pi$
$774$		−	307.775i		−	0.397642i
$775$	36.1073	−	143.873i	0.0465901	−	0.185643i
$776$	−300.350			−0.387049
$777$	14.5579	−	14.5579i	0.0187360	−	0.0187360i
$778$	−615.448	−	615.448i	−0.791064	−	0.791064i
$779$		−	498.407i		−	0.639803i
$780$	−114.074	+	88.9825i	−0.146248	+	0.114080i
$781$	−1532.45			−1.96217
$782$	38.7359	−	38.7359i	0.0495344	−	0.0495344i
$783$	79.3640	+	79.3640i	0.101359	+	0.101359i
$784$		−	179.855i		−	0.229407i
$785$	−63.2752	+	512.071i	−0.0806054	+	0.652320i
$786$	949.437			1.20794
$787$	−295.962	+	295.962i	−0.376064	+	0.376064i	−0.869680	−	0.493616i	$-0.835675\pi$
$787$	−295.962	+	295.962i	−0.376064	+	0.376064i	0.493616	+	0.869680i	$0.335675\pi$
$788$	−267.079	−	267.079i	−0.338932	−	0.338932i
$789$		−	989.250i		−	1.25380i
$790$	−427.090	−	52.7743i	−0.540620	−	0.0668030i
$791$	204.305			0.258286
$792$	256.820	−	256.820i	0.324267	−	0.324267i
$793$	121.303	+	121.303i	0.152967	+	0.152967i
$794$		−	908.772i		−	1.14455i
$795$	760.095	+	974.425i	0.956094	+	1.22569i
$796$	−336.927			−0.423275
$797$	−238.478	+	238.478i	−0.299219	+	0.299219i	−0.840708	−	0.541489i	$-0.817861\pi$
$797$	−238.478	+	238.478i	−0.299219	+	0.299219i	0.541489	+	0.840708i	$0.317861\pi$
$798$	91.4314	+	91.4314i	0.114576	+	0.114576i
$799$		−	102.596i		−	0.128406i
$800$	−72.6504	−	121.334i	−0.0908130	−	0.151667i
$801$	−1044.77			−1.30434
$802$	471.540	−	471.540i	0.587955	−	0.587955i
$803$	−1628.96	−	1628.96i	−2.02860	−	2.02860i
$804$		−	238.435i		−	0.296561i
$805$	37.9857	−	29.6305i	0.0471872	−	0.0368081i
$806$	−29.4964			−0.0365961
$807$	−1182.98	+	1182.98i	−1.46590	+	1.46590i
$808$	271.090	+	271.090i	0.335507	+	0.335507i
$809$			243.958i			0.301554i	0.988568	+	0.150777i	$0.0481776\pi$
$809$			243.958i			0.301554i	−0.988568	+	0.150777i	$0.951822\pi$
$810$	77.5458	−	627.559i	0.0957355	−	0.774764i
$811$	−245.731			−0.302998			−0.151499	−	0.988457i	$-0.548410\pi$
$811$	−245.731			−0.302998			−0.151499	+	0.988457i	$0.548410\pi$
$812$	−73.0084	+	73.0084i	−0.0899118	+	0.0899118i
$813$	−267.694	−	267.694i	−0.329267	−	0.329267i
$814$			56.9565i			0.0699712i
$815$	−424.843	−	52.4967i	−0.521280	−	0.0644131i
$816$	132.969			0.162952
$817$	−214.347	+	214.347i	−0.262358	+	0.262358i
$818$	−99.5691	−	99.5691i	−0.121723	−	0.121723i
$819$		−	56.0652i		−	0.0684557i
$820$	−277.226	−	355.398i	−0.338080	−	0.433412i
$821$	−332.884			−0.405462			−0.202731	−	0.979234i	$-0.564982\pi$
$821$	−332.884			−0.405462			−0.202731	+	0.979234i	$0.564982\pi$
$822$	173.993	−	173.993i	0.211671	−	0.211671i
$823$	−229.794	−	229.794i	−0.279215	−	0.279215i	0.553581	−	0.832795i	$-0.313261\pi$
$823$	−229.794	−	229.794i	−0.279215	−	0.279215i	−0.832795	+	0.553581i	$0.813261\pi$
$824$		−	452.274i		−	0.548876i
$825$	−1427.89	+	854.971i	−1.73078	+	1.03633i
$826$	205.086			0.248288
$827$	1095.92	−	1095.92i	1.32518	−	1.32518i	0.415661	−	0.909520i	$-0.363550\pi$
$827$	1095.92	−	1095.92i	1.32518	−	1.32518i	0.909520	−	0.415661i	$-0.136450\pi$
$828$	53.8430	+	53.8430i	0.0650277	+	0.0650277i
$829$			1299.89i			1.56802i	0.620745	+	0.784012i	$0.286830\pi$
$829$			1299.89i			1.56802i	−0.620745	+	0.784012i	$0.713170\pi$
$830$	672.407	−	524.508i	0.810129	−	0.631937i
$831$	1042.89			1.25499
$832$	−19.8850	+	19.8850i	−0.0239003	+	0.0239003i
$833$	−256.801	−	256.801i	−0.308285	−	0.308285i
$834$			216.599i			0.259710i
$835$	−191.876	+	1552.80i	−0.229791	+	1.85964i
$836$	−357.719			−0.427893
$837$	18.3257	−	18.3257i	0.0218945	−	0.0218945i
$838$	761.168	+	761.168i	0.908315	+	0.908315i
$839$			1354.86i			1.61485i	0.589972	+	0.807424i	$0.299139\pi$
$839$			1354.86i			1.61485i	−0.589972	+	0.807424i	$0.700861\pi$
$840$	116.053	+	14.3404i	0.138158	+	0.0170719i
$841$	180.716			0.214882
$842$	109.597	−	109.597i	0.130162	−	0.130162i
$843$	−331.449	−	331.449i	−0.393178	−	0.393178i
$844$			456.569i			0.540958i
$845$	481.720	+	617.555i	0.570083	+	0.730834i
$846$	142.609			0.168568
$847$	−199.789	+	199.789i	−0.235879	+	0.235879i
$848$	169.859	+	169.859i	0.200306	+	0.200306i
$849$			2081.72i			2.45196i
$850$	−276.976	−	69.5116i	−0.325854	−	0.0817784i
$851$	−11.9411			−0.0140318
$852$	551.435	−	551.435i	0.647224	−	0.647224i
$853$	171.936	+	171.936i	0.201566	+	0.201566i	0.800671	−	0.599105i	$-0.204477\pi$
$853$	171.936	+	171.936i	0.201566	+	0.201566i	−0.599105	+	0.800671i	$0.704477\pi$
$854$		−	138.657i		−	0.162362i
$855$	346.080	−	269.958i	0.404772	−	0.315740i
$856$	−138.339			−0.161611
$857$	−194.003	+	194.003i	−0.226374	+	0.226374i	−0.811176	−	0.584802i	$-0.801172\pi$
$857$	−194.003	+	194.003i	−0.226374	+	0.226374i	0.584802	+	0.811176i	$0.301172\pi$
$858$	234.013	+	234.013i	0.272743	+	0.272743i
$859$		−	1314.56i		−	1.53034i	−0.643828	−	0.765170i	$-0.722655\pi$
$859$		−	1314.56i		−	1.53034i	0.643828	−	0.765170i	$-0.277345\pi$
$860$	−33.6187	+	272.068i	−0.0390916	+	0.316358i
$861$	372.695			0.432863
$862$	−516.446	+	516.446i	−0.599125	+	0.599125i
$863$	−390.385	−	390.385i	−0.452358	−	0.452358i	0.443779	−	0.896136i	$-0.353638\pi$
$863$	−390.385	−	390.385i	−0.452358	−	0.452358i	−0.896136	+	0.443779i	$0.853638\pi$
$864$		−	24.7086i		−	0.0285979i
$865$	450.146	+	55.6234i	0.520401	+	0.0643045i
$866$	−404.954			−0.467615
$867$	−651.196	+	651.196i	−0.751091	+	0.751091i
$868$	16.8582	+	16.8582i	0.0194218	+	0.0194218i
$869$			984.404i			1.13280i
$870$	459.943	+	589.636i	0.528670	+	0.677743i
$871$	101.824			0.116905
$872$	−33.7023	+	33.7023i	−0.0386494	+	0.0386494i
$873$	−596.098	−	596.098i	−0.682816	−	0.682816i
$874$		−	74.9967i		−	0.0858086i
$875$	−234.243	−	90.5398i	−0.267706	−	0.103474i
$876$	1172.32			1.33827
$877$	−909.317	+	909.317i	−1.03685	+	1.03685i	−0.0375554	+	0.999295i	$0.511957\pi$
$877$	−909.317	+	909.317i	−1.03685	+	1.03685i	−0.999295	+	0.0375554i	$0.988043\pi$
$878$	−20.4001	−	20.4001i	−0.0232348	−	0.0232348i
$879$			446.657i			0.508142i
$880$	−255.077	+	198.972i	−0.289861	+	0.226104i
$881$	547.786			0.621778			0.310889	−	0.950446i	$-0.399373\pi$
$881$	547.786			0.621778			0.310889	+	0.950446i	$0.399373\pi$
$882$	356.954	−	356.954i	0.404710	−	0.404710i
$883$	49.1207	+	49.1207i	0.0556294	+	0.0556294i	0.734374	−	0.678745i	$-0.237476\pi$
$883$	49.1207	+	49.1207i	0.0556294	+	0.0556294i	−0.678745	+	0.734374i	$0.737476\pi$
$884$			56.7847i			0.0642361i
$885$	182.159	−	1474.17i	0.205830	−	1.66573i
$886$	450.064			0.507973
$887$	567.690	−	567.690i	0.640012	−	0.640012i	−0.310546	−	0.950558i	$-0.600512\pi$
$887$	567.690	−	567.690i	0.640012	−	0.640012i	0.950558	+	0.310546i	$0.100512\pi$
$888$	−20.4951	−	20.4951i	−0.0230801	−	0.0230801i
$889$			205.141i			0.230755i
$890$	923.562	+	114.122i	1.03771	+	0.128227i
$891$	−1446.47			−1.62342
$892$	−272.718	+	272.718i	−0.305737	+	0.305737i
$893$	−99.3182	−	99.3182i	−0.111219	−	0.111219i
$894$		−	877.546i		−	0.981595i
$895$	171.604	+	219.992i	0.191736	+	0.245801i
$896$	22.7299			0.0253682
$897$	−49.0615	+	49.0615i	−0.0546951	+	0.0546951i
$898$	−140.825	−	140.825i	−0.156821	−	0.156821i
$899$			152.464i			0.169593i
$900$	96.6212	−	384.996i	0.107357	−	0.427774i
$901$	485.059			0.538356
$902$	−729.070	+	729.070i	−0.808282	+	0.808282i
$903$	−160.282	−	160.282i	−0.177500	−	0.177500i
$904$		−	287.628i		−	0.318172i
$905$	−1006.75	+	785.311i	−1.11243	+	0.867747i
$906$	897.049			0.990121
$907$	530.271	−	530.271i	0.584643	−	0.584643i	−0.351533	−	0.936176i	$-0.614339\pi$
$907$	530.271	−	530.271i	0.584643	−	0.584643i	0.936176	+	0.351533i	$0.114339\pi$
$908$	−522.958	−	522.958i	−0.575944	−	0.575944i
$909$			1076.05i			1.18378i
$910$	−6.12409	+	49.5608i	−0.00672977	+	0.0544624i
$911$	898.508			0.986287			0.493144	−	0.869948i	$-0.335848\pi$
$911$	898.508			0.986287			0.493144	+	0.869948i	$0.335848\pi$
$912$	128.721	−	128.721i	0.141141	−	0.141141i
$913$	−1379.39	−	1379.39i	−1.51083	−	1.51083i
$914$		−	236.853i		−	0.259139i
$915$	−996.677	−	123.157i	−1.08926	−	0.134598i
$916$	629.405			0.687123
$917$	231.733	−	231.733i	0.252708	−	0.252708i
$918$	−35.2795	−	35.2795i	−0.0384309	−	0.0384309i
$919$		−	144.224i		−	0.156936i	−0.996917	−	0.0784679i	$-0.974997\pi$
$919$		−	144.224i		−	0.156936i	0.996917	−	0.0784679i	$-0.0250028\pi$
$920$	−41.7150	−	53.4777i	−0.0453424	−	0.0581279i
$921$	2084.39			2.26318
$922$	290.493	−	290.493i	0.315068	−	0.315068i
$923$	235.492	+	235.492i	0.255137	+	0.255137i
$924$		−	267.492i		−	0.289494i
$925$	31.9774	+	53.4057i	0.0345701	+	0.0577359i
$926$	−622.287			−0.672016
$927$	897.618	−	897.618i	0.968304	−	0.968304i
$928$	102.784	+	102.784i	0.110759	+	0.110759i
$929$			119.872i			0.129034i	0.997917	+	0.0645168i	$0.0205506\pi$
$929$			119.872i			0.129034i	−0.997917	+	0.0645168i	$0.979449\pi$
$930$	136.151	−	106.204i	0.146399	−	0.114198i
$931$	−497.193			−0.534042
$932$	514.304	−	514.304i	0.551828	−	0.551828i
$933$	1720.91	+	1720.91i	1.84450	+	1.84450i
$934$			819.408i			0.877311i
$935$	−80.1090	+	648.303i	−0.0856781	+	0.693372i
$936$	−78.9308			−0.0843278
$937$	−739.304	+	739.304i	−0.789012	+	0.789012i	−0.981332	−	0.192320i	$-0.938399\pi$
$937$	−739.304	+	739.304i	−0.789012	+	0.789012i	0.192320	+	0.981332i	$0.438399\pi$
$938$	−58.1959	−	58.1959i	−0.0620425	−	0.0620425i
$939$			965.490i			1.02821i
$940$	−126.064	−	15.5774i	−0.134110	−	0.0165717i
$941$	1638.48			1.74121			0.870604	−	0.491984i	$-0.163728\pi$
$941$	1638.48			1.74121			0.870604	+	0.491984i	$0.163728\pi$
$942$	−424.708	+	424.708i	−0.450858	+	0.450858i
$943$	−152.852	−	152.852i	−0.162091	−	0.162091i
$944$		−	288.727i		−	0.305855i
$945$	−26.9866	−	34.5962i	−0.0285572	−	0.0366098i
$946$	627.093			0.662889
$947$	−664.414	+	664.414i	−0.701599	+	0.701599i	−0.964754	−	0.263155i	$-0.915237\pi$
$947$	−664.414	+	664.414i	−0.701599	+	0.701599i	0.263155	+	0.964754i	$0.415237\pi$
$948$	−354.226	−	354.226i	−0.373656	−	0.373656i
$949$			500.644i			0.527549i
$950$	−335.417	+	200.836i	−0.353071	+	0.211406i
$951$	334.533			0.351769
$952$	32.4543	−	32.4543i	0.0340906	−	0.0340906i
$953$	544.995	+	544.995i	0.571874	+	0.571874i	0.932652	−	0.360778i	$-0.117489\pi$
$953$	544.995	+	544.995i	0.571874	+	0.571874i	−0.360778	+	0.932652i	$0.617489\pi$
$954$			674.232i			0.706742i
$955$	1201.39	−	937.136i	1.25800	−	0.981294i
$956$	−404.764			−0.423393
$957$	1209.59	−	1209.59i	1.26394	−	1.26394i
$958$	509.370	+	509.370i	0.531702	+	0.531702i
$959$		−	84.9346i		−	0.0885658i
$960$	20.1889	−	163.384i	0.0210301	−	0.170192i
$961$	−925.795			−0.963366
$962$	8.75249	−	8.75249i	0.00909822	−	0.00909822i
$963$	−274.558	−	274.558i	−0.285107	−	0.285107i
$964$			799.658i			0.829521i
$965$	1150.51	+	142.166i	1.19224	+	0.147322i
$966$	56.0804			0.0580543
$967$	−23.1667	+	23.1667i	−0.0239573	+	0.0239573i	−0.718984	−	0.695027i	$-0.755393\pi$
$967$	−23.1667	+	23.1667i	−0.0239573	+	0.0239573i	0.695027	+	0.718984i	$0.255393\pi$
$968$	281.271	+	281.271i	0.290570	+	0.290570i
$969$		−	367.581i		−	0.379341i
$970$	461.828	+	592.054i	0.476112	+	0.610365i
$971$	1292.57			1.33117			0.665587	−	0.746320i	$-0.268181\pi$
$971$	1292.57			1.33117			0.665587	+	0.746320i	$0.268181\pi$
$972$	464.899	−	464.899i	0.478291	−	0.478291i
$973$	52.8661	+	52.8661i	0.0543331	+	0.0543331i
$974$		−	868.966i		−	0.892162i
$975$	350.807	+	88.0408i	0.359802	+	0.0902983i
$976$	−195.207			−0.200007
$977$	819.775	−	819.775i	0.839074	−	0.839074i	−0.149663	−	0.988737i	$-0.547819\pi$
$977$	819.775	−	819.775i	0.839074	−	0.839074i	0.988737	+	0.149663i	$0.0478190\pi$
$978$	−352.362	−	352.362i	−0.360289	−	0.360289i
$979$		−	2128.73i		−	2.17439i
$980$	−354.532	+	276.551i	−0.361767	+	0.282195i
$981$	−133.776			−0.136367
$982$	−483.200	+	483.200i	−0.492057	+	0.492057i
$983$	−1173.04	−	1173.04i	−1.19333	−	1.19333i	−0.976127	−	0.217203i	$-0.930307\pi$
$983$	−1173.04	−	1173.04i	−1.19333	−	1.19333i	−0.217203	−	0.976127i	$-0.569693\pi$
$984$		−	524.694i		−	0.533226i
$985$	−115.800	+	937.138i	−0.117563	+	0.951409i
$986$	293.515			0.297683
$987$	74.2674	−	74.2674i	0.0752456	−	0.0752456i
$988$	54.9705	+	54.9705i	0.0556381	+	0.0556381i
$989$			131.472i			0.132934i
$990$	−901.142	−	111.352i	−0.910244	−	0.112476i
$991$	1579.70			1.59405			0.797024	−	0.603947i	$-0.206406\pi$
$991$	1579.70			1.59405			0.797024	+	0.603947i	$0.206406\pi$
$992$	23.7336	−	23.7336i	0.0239250	−	0.0239250i
$993$	−652.567	−	652.567i	−0.657167	−	0.657167i
$994$		−	269.182i		−	0.270807i
$995$	518.071	+	664.155i	0.520674	+	0.667493i
$996$	992.714			0.996700
$997$	407.478	−	407.478i	0.408704	−	0.408704i	−0.472582	−	0.881286i	$-0.656678\pi$
$997$	407.478	−	407.478i	0.408704	−	0.408704i	0.881286	+	0.472582i	$0.156678\pi$
$998$	−521.499	−	521.499i	−0.522544	−	0.522544i
$999$			10.8756i			0.0108865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.a.93.9	yes	20
5.2	odd	4	inner	230.3.f.a.47.9	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.a.47.9	✓	20	5.2	odd	4	inner
230.3.f.a.93.9	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(2.91022 + 2.91022i) q^{3} -2.00000i q^{4} +(-3.94243 + 3.07527i) q^{5} -5.82043 q^{6} +(-1.42062 + 1.42062i) q^{7} +(2.00000 + 2.00000i) q^{8} +7.93871i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(2.91022 + 2.91022i) q^{3} -2.00000i q^{4} +(-3.94243 + 3.07527i) q^{5} -5.82043 q^{6} +(-1.42062 + 1.42062i) q^{7} +(2.00000 + 2.00000i) q^{8} +7.93871i q^{9} +(0.867158 - 7.01769i) q^{10} -16.1752 q^{11} +(5.82043 - 5.82043i) q^{12} +(2.48563 + 2.48563i) q^{13} -2.84124i q^{14} +(-20.4230 - 2.52362i) q^{15} -4.00000 q^{16} +(-5.71130 + 5.71130i) q^{17} +(-7.93871 - 7.93871i) q^{18} +11.0577i q^{19} +(6.15054 + 7.88485i) q^{20} -8.26861 q^{21} +(16.1752 - 16.1752i) q^{22} +(3.39116 + 3.39116i) q^{23} +11.6409i q^{24} +(6.08545 - 24.2480i) q^{25} -4.97126 q^{26} +(3.08857 - 3.08857i) q^{27} +(2.84124 + 2.84124i) q^{28} +25.6960i q^{29} +(22.9466 - 17.8994i) q^{30} +5.93339 q^{31} +(4.00000 - 4.00000i) q^{32} +(-47.0732 - 47.0732i) q^{33} -11.4226i q^{34} +(1.23190 - 9.96946i) q^{35} +15.8774 q^{36} +(-1.76062 + 1.76062i) q^{37} +(-11.0577 - 11.0577i) q^{38} +14.4674i q^{39} +(-14.0354 - 1.73432i) q^{40} -45.0735 q^{41} +(8.26861 - 8.26861i) q^{42} +(19.3844 + 19.3844i) q^{43} +32.3503i q^{44} +(-24.4137 - 31.2978i) q^{45} -6.78233 q^{46} +(-8.98185 + 8.98185i) q^{47} +(-11.6409 - 11.6409i) q^{48} +44.9637i q^{49} +(18.1626 + 30.3335i) q^{50} -33.2422 q^{51} +(4.97126 - 4.97126i) q^{52} +(-42.4648 - 42.4648i) q^{53} +6.17715i q^{54} +(63.7694 - 49.7429i) q^{55} -5.68247 q^{56} +(-32.1802 + 32.1802i) q^{57} +(-25.6960 - 25.6960i) q^{58} +72.1819i q^{59} +(-5.04723 + 40.8460i) q^{60} +48.8017 q^{61} +(-5.93339 + 5.93339i) q^{62} +(-11.2779 - 11.2779i) q^{63} +8.00000i q^{64} +(-17.4434 - 2.15543i) q^{65} +94.1464 q^{66} +(20.4826 - 20.4826i) q^{67} +(11.4226 + 11.4226i) q^{68} +19.7380i q^{69} +(8.73756 + 11.2014i) q^{70} +94.7412 q^{71} +(-15.8774 + 15.8774i) q^{72} +(100.708 + 100.708i) q^{73} -3.52124i q^{74} +(88.2770 - 52.8571i) q^{75} +22.1153 q^{76} +(22.9787 - 22.9787i) q^{77} +(-14.4674 - 14.4674i) q^{78} -60.8590i q^{79} +(15.7697 - 12.3011i) q^{80} +89.4253 q^{81} +(45.0735 - 45.0735i) q^{82} +(85.2783 + 85.2783i) q^{83} +16.5372i q^{84} +(4.95260 - 40.0802i) q^{85} -38.7689 q^{86} +(-74.7809 + 74.7809i) q^{87} +(-32.3503 - 32.3503i) q^{88} +131.605i q^{89} +(55.7115 + 6.88412i) q^{90} -7.06226 q^{91} +(6.78233 - 6.78233i) q^{92} +(17.2674 + 17.2674i) q^{93} -17.9637i q^{94} +(-34.0053 - 43.5940i) q^{95} +23.2817 q^{96} +(-75.0875 + 75.0875i) q^{97} +(-44.9637 - 44.9637i) q^{98} -128.410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8	\( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8} + 4 q^{10} + 56 q^{11} - 4 q^{13} - 48 q^{15} - 80 q^{16} - 72 q^{17} - 28 q^{18} - 16 q^{20} + 8 q^{21} - 56 q^{22} + 36 q^{25} + 8 q^{26} + 156 q^{27} - 16 q^{28} + 84 q^{30} - 212 q^{31} + 80 q^{32} - 100 q^{33} + 56 q^{36} + 72 q^{37} + 88 q^{38} + 24 q^{40} - 12 q^{41} - 8 q^{42} + 120 q^{43} - 32 q^{45} + 8 q^{47} - 28 q^{50} + 64 q^{51} - 8 q^{52} - 244 q^{53} + 68 q^{55} + 32 q^{56} - 384 q^{57} - 188 q^{58} - 72 q^{60} + 328 q^{61} + 212 q^{62} + 172 q^{63} + 20 q^{65} + 200 q^{66} + 56 q^{67} + 144 q^{68} - 28 q^{70} - 92 q^{71} - 56 q^{72} + 144 q^{73} - 124 q^{75} - 176 q^{76} + 292 q^{77} - 208 q^{78} - 16 q^{80} - 84 q^{81} + 12 q^{82} - 72 q^{83} - 20 q^{85} - 240 q^{86} - 208 q^{87} + 112 q^{88} - 56 q^{90} - 192 q^{91} + 256 q^{93} - 96 q^{95} - 276 q^{97} + 104 q^{98}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8 + 4 * q^10 + 56 * q^11 - 4 * q^13 - 48 * q^15 - 80 * q^16 - 72 * q^17 - 28 * q^18 - 16 * q^20 + 8 * q^21 - 56 * q^22 + 36 * q^25 + 8 * q^26 + 156 * q^27 - 16 * q^28 + 84 * q^30 - 212 * q^31 + 80 * q^32 - 100 * q^33 + 56 * q^36 + 72 * q^37 + 88 * q^38 + 24 * q^40 - 12 * q^41 - 8 * q^42 + 120 * q^43 - 32 * q^45 + 8 * q^47 - 28 * q^50 + 64 * q^51 - 8 * q^52 - 244 * q^53 + 68 * q^55 + 32 * q^56 - 384 * q^57 - 188 * q^58 - 72 * q^60 + 328 * q^61 + 212 * q^62 + 172 * q^63 + 20 * q^65 + 200 * q^66 + 56 * q^67 + 144 * q^68 - 28 * q^70 - 92 * q^71 - 56 * q^72 + 144 * q^73 - 124 * q^75 - 176 * q^76 + 292 * q^77 - 208 * q^78 - 16 * q^80 - 84 * q^81 + 12 * q^82 - 72 * q^83 - 20 * q^85 - 240 * q^86 - 208 * q^87 + 112 * q^88 - 56 * q^90 - 192 * q^91 + 256 * q^93 - 96 * q^95 - 276 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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