LMFDB - Embedded newform 230.3.f.a.93.3

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			93.3
Root			$-2.41818 - 2.41818i$ of defining polynomial
Character	$\chi$	$=$	230.93
Dual form			230.3.f.a.47.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-2.41818 - 2.41818i) q^{3} -2.00000i q^{4} +(-4.87518 - 1.11024i) q^{5} +4.83636 q^{6} +(3.71756 - 3.71756i) q^{7} +(2.00000 + 2.00000i) q^{8} +2.69521i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-2.41818 - 2.41818i) q^{3} -2.00000i q^{4} +(-4.87518 - 1.11024i) q^{5} +4.83636 q^{6} +(3.71756 - 3.71756i) q^{7} +(2.00000 + 2.00000i) q^{8} +2.69521i q^{9} +(5.98542 - 3.76494i) q^{10} +5.66411 q^{11} +(-4.83636 + 4.83636i) q^{12} +(-11.2692 - 11.2692i) q^{13} +7.43511i q^{14} +(9.10432 + 14.4738i) q^{15} -4.00000 q^{16} +(-19.5050 + 19.5050i) q^{17} +(-2.69521 - 2.69521i) q^{18} +21.5835i q^{19} +(-2.22047 + 9.75036i) q^{20} -17.9795 q^{21} +(-5.66411 + 5.66411i) q^{22} +(3.39116 + 3.39116i) q^{23} -9.67273i q^{24} +(22.5348 + 10.8252i) q^{25} +22.5384 q^{26} +(-15.2461 + 15.2461i) q^{27} +(-7.43511 - 7.43511i) q^{28} +38.9519i q^{29} +(-23.5781 - 5.36951i) q^{30} -39.9726 q^{31} +(4.00000 - 4.00000i) q^{32} +(-13.6968 - 13.6968i) q^{33} -39.0099i q^{34} +(-22.2511 + 13.9964i) q^{35} +5.39042 q^{36} +(34.6377 - 34.6377i) q^{37} +(-21.5835 - 21.5835i) q^{38} +54.5020i q^{39} +(-7.52989 - 11.9708i) q^{40} +65.8264 q^{41} +(17.9795 - 17.9795i) q^{42} +(-35.5529 - 35.5529i) q^{43} -11.3282i q^{44} +(2.99232 - 13.1396i) q^{45} -6.78233 q^{46} +(-45.5584 + 45.5584i) q^{47} +(9.67273 + 9.67273i) q^{48} +21.3596i q^{49} +(-33.3600 + 11.7095i) q^{50} +94.3331 q^{51} +(-22.5384 + 22.5384i) q^{52} +(-33.1565 - 33.1565i) q^{53} -30.4923i q^{54} +(-27.6135 - 6.28850i) q^{55} +14.8702 q^{56} +(52.1928 - 52.1928i) q^{57} +(-38.9519 - 38.9519i) q^{58} -32.5546i q^{59} +(28.9477 - 18.2086i) q^{60} -17.0786 q^{61} +(39.9726 - 39.9726i) q^{62} +(10.0196 + 10.0196i) q^{63} +8.00000i q^{64} +(42.4280 + 67.4510i) q^{65} +27.3937 q^{66} +(-15.3270 + 15.3270i) q^{67} +(39.0099 + 39.0099i) q^{68} -16.4009i q^{69} +(8.25473 - 36.2475i) q^{70} +38.4278 q^{71} +(-5.39042 + 5.39042i) q^{72} +(-14.7326 - 14.7326i) q^{73} +69.2754i q^{74} +(-28.3158 - 80.6704i) q^{75} +43.1669 q^{76} +(21.0566 - 21.0566i) q^{77} +(-54.5020 - 54.5020i) q^{78} +32.7703i q^{79} +(19.5007 + 4.44094i) q^{80} +97.9927 q^{81} +(-65.8264 + 65.8264i) q^{82} +(-1.79999 - 1.79999i) q^{83} +35.9589i q^{84} +(116.745 - 73.4350i) q^{85} +71.1058 q^{86} +(94.1928 - 94.1928i) q^{87} +(11.3282 + 11.3282i) q^{88} +130.635i q^{89} +(10.1473 + 16.1320i) q^{90} -83.7879 q^{91} +(6.78233 - 6.78233i) q^{92} +(96.6611 + 96.6611i) q^{93} -91.1167i q^{94} +(23.9627 - 105.223i) q^{95} -19.3455 q^{96} +(46.8143 - 46.8143i) q^{97} +(-21.3596 - 21.3596i) q^{98} +15.2660i 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
$3$	−2.41818	−	2.41818i	−0.806061	−	0.806061i	0.177974	−	0.984035i	$-0.443046\pi$
$3$	−2.41818	−	2.41818i	−0.806061	−	0.806061i	−0.984035	+	0.177974i	$0.943046\pi$
$4$		−	2.00000i		−	0.500000i
$5$	−4.87518	−	1.11024i	−0.975036	−	0.222047i
$5$	−4.87518	−	1.11024i	−0.975036	−	0.222047i
$6$	4.83636			0.806061
$7$	3.71756	−	3.71756i	0.531079	−	0.531079i	−0.389814	−	0.920894i	$-0.627461\pi$
$7$	3.71756	−	3.71756i	0.531079	−	0.531079i	0.920894	+	0.389814i	$0.127461\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			2.69521i			0.299468i
$10$	5.98542	−	3.76494i	0.598542	−	0.376494i
$11$	5.66411			0.514919			0.257459	−	0.966289i	$-0.417115\pi$
$11$	5.66411			0.514919			0.257459	+	0.966289i	$0.417115\pi$
$12$	−4.83636	+	4.83636i	−0.403030	+	0.403030i
$13$	−11.2692	−	11.2692i	−0.866863	−	0.866863i	0.125261	−	0.992124i	$-0.460023\pi$
$13$	−11.2692	−	11.2692i	−0.866863	−	0.866863i	−0.992124	+	0.125261i	$0.960023\pi$
$14$			7.43511i			0.531079i
$15$	9.10432	+	14.4738i	0.606955	+	0.964922i
$16$	−4.00000			−0.250000
$17$	−19.5050	+	19.5050i	−1.14735	+	1.14735i	−0.160278	+	0.987072i	$0.551239\pi$
$17$	−19.5050	+	19.5050i	−1.14735	+	1.14735i	−0.987072	+	0.160278i	$0.948761\pi$
$18$	−2.69521	−	2.69521i	−0.149734	−	0.149734i
$19$			21.5835i			1.13597i	0.823038	+	0.567986i	$0.192277\pi$
$19$			21.5835i			1.13597i	−0.823038	+	0.567986i	$0.807723\pi$
$20$	−2.22047	+	9.75036i	−0.111024	+	0.487518i
$21$	−17.9795			−0.856164
$22$	−5.66411	+	5.66411i	−0.257459	+	0.257459i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$24$		−	9.67273i		−	0.403030i
$25$	22.5348	+	10.8252i	0.901390	+	0.433008i
$26$	22.5384			0.866863
$27$	−15.2461	+	15.2461i	−0.564671	+	0.564671i
$28$	−7.43511	−	7.43511i	−0.265540	−	0.265540i
$29$			38.9519i			1.34317i	0.740928	+	0.671585i	$0.234386\pi$
$29$			38.9519i			1.34317i	−0.740928	+	0.671585i	$0.765614\pi$
$30$	−23.5781	−	5.36951i	−0.785938	−	0.178984i
$31$	−39.9726			−1.28944			−0.644720	−	0.764419i	$-0.723026\pi$
$31$	−39.9726			−1.28944			−0.644720	+	0.764419i	$0.723026\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−13.6968	−	13.6968i	−0.415056	−	0.415056i
$34$		−	39.0099i		−	1.14735i
$35$	−22.2511	+	13.9964i	−0.635746	+	0.399897i
$36$	5.39042			0.149734
$37$	34.6377	−	34.6377i	0.936154	−	0.936154i	−0.0619270	−	0.998081i	$-0.519725\pi$
$37$	34.6377	−	34.6377i	0.936154	−	0.936154i	0.998081	+	0.0619270i	$0.0197246\pi$
$38$	−21.5835	−	21.5835i	−0.567986	−	0.567986i
$39$			54.5020i			1.39749i
$40$	−7.52989	−	11.9708i	−0.188247	−	0.299271i
$41$	65.8264			1.60552			0.802761	−	0.596301i	$-0.203363\pi$
$41$	65.8264			1.60552			0.802761	+	0.596301i	$0.203363\pi$
$42$	17.9795	−	17.9795i	0.428082	−	0.428082i
$43$	−35.5529	−	35.5529i	−0.826812	−	0.826812i	0.160263	−	0.987074i	$-0.448766\pi$
$43$	−35.5529	−	35.5529i	−0.826812	−	0.826812i	−0.987074	+	0.160263i	$0.948766\pi$
$44$		−	11.3282i		−	0.257459i
$45$	2.99232	−	13.1396i	0.0664960	−	0.291992i
$46$	−6.78233			−0.147442
$47$	−45.5584	+	45.5584i	−0.969327	+	0.969327i	−0.999543	−	0.0302163i	$-0.990380\pi$
$47$	−45.5584	+	45.5584i	−0.969327	+	0.969327i	0.0302163	+	0.999543i	$0.490380\pi$
$48$	9.67273	+	9.67273i	0.201515	+	0.201515i
$49$			21.3596i			0.435910i
$50$	−33.3600	+	11.7095i	−0.667199	+	0.234191i
$51$	94.3331			1.84967
$52$	−22.5384	+	22.5384i	−0.433431	+	0.433431i
$53$	−33.1565	−	33.1565i	−0.625595	−	0.625595i	0.321361	−	0.946957i	$-0.395860\pi$
$53$	−33.1565	−	33.1565i	−0.625595	−	0.625595i	−0.946957	+	0.321361i	$0.895860\pi$
$54$		−	30.4923i		−	0.564671i
$55$	−27.6135	−	6.28850i	−0.502064	−	0.114336i
$56$	14.8702			0.265540
$57$	52.1928	−	52.1928i	0.915662	−	0.915662i
$58$	−38.9519	−	38.9519i	−0.671585	−	0.671585i
$59$		−	32.5546i		−	0.551773i	−0.961190	−	0.275886i	$-0.911029\pi$
$59$		−	32.5546i		−	0.551773i	0.961190	−	0.275886i	$-0.0889714\pi$
$60$	28.9477	−	18.2086i	0.482461	−	0.303477i
$61$	−17.0786			−0.279978			−0.139989	−	0.990153i	$-0.544707\pi$
$61$	−17.0786			−0.279978			−0.139989	+	0.990153i	$0.544707\pi$
$62$	39.9726	−	39.9726i	0.644720	−	0.644720i
$63$	10.0196	+	10.0196i	0.159041	+	0.159041i
$64$			8.00000i			0.125000i
$65$	42.4280	+	67.4510i	0.652738	+	1.03771i
$66$	27.3937			0.415056
$67$	−15.3270	+	15.3270i	−0.228761	+	0.228761i	−0.812175	−	0.583414i	$-0.801717\pi$
$67$	−15.3270	+	15.3270i	−0.228761	+	0.228761i	0.583414	+	0.812175i	$0.301717\pi$
$68$	39.0099	+	39.0099i	0.573675	+	0.573675i
$69$		−	16.4009i		−	0.237694i
$70$	8.25473	−	36.2475i	0.117925	−	0.517821i
$71$	38.4278			0.541237			0.270619	−	0.962687i	$-0.412772\pi$
$71$	38.4278			0.541237			0.270619	+	0.962687i	$0.412772\pi$
$72$	−5.39042	+	5.39042i	−0.0748670	+	0.0748670i
$73$	−14.7326	−	14.7326i	−0.201817	−	0.201817i	0.598961	−	0.800778i	$-0.295580\pi$
$73$	−14.7326	−	14.7326i	−0.201817	−	0.201817i	−0.800778	+	0.598961i	$0.795580\pi$
$74$			69.2754i			0.936154i
$75$	−28.3158	−	80.6704i	−0.377544	−	1.07561i
$76$	43.1669			0.567986
$77$	21.0566	−	21.0566i	0.273463	−	0.273463i
$78$	−54.5020	−	54.5020i	−0.698744	−	0.698744i
$79$			32.7703i			0.414814i	0.978255	+	0.207407i	$0.0665024\pi$
$79$			32.7703i			0.414814i	−0.978255	+	0.207407i	$0.933498\pi$
$80$	19.5007	+	4.44094i	0.243759	+	0.0555118i
$81$	97.9927			1.20979
$82$	−65.8264	+	65.8264i	−0.802761	+	0.802761i
$83$	−1.79999	−	1.79999i	−0.0216867	−	0.0216867i	0.696180	−	0.717867i	$-0.254881\pi$
$83$	−1.79999	−	1.79999i	−0.0216867	−	0.0216867i	−0.717867	+	0.696180i	$0.754881\pi$
$84$			35.9589i			0.428082i
$85$	116.745	−	73.4350i	1.37347	−	0.863942i
$86$	71.1058			0.826812
$87$	94.1928	−	94.1928i	1.08268	−	1.08268i
$88$	11.3282	+	11.3282i	0.128730	+	0.128730i
$89$			130.635i			1.46781i	0.679253	+	0.733904i	$0.262304\pi$
$89$			130.635i			1.46781i	−0.679253	+	0.733904i	$0.737696\pi$
$90$	10.1473	+	16.1320i	0.112748	+	0.179244i
$91$	−83.7879			−0.920746
$92$	6.78233	−	6.78233i	0.0737210	−	0.0737210i
$93$	96.6611	+	96.6611i	1.03937	+	1.03937i
$94$		−	91.1167i		−	0.969327i
$95$	23.9627	−	105.223i	0.252239	−	1.10761i
$96$	−19.3455			−0.201515
$97$	46.8143	−	46.8143i	0.482622	−	0.482622i	−0.423346	−	0.905968i	$-0.639145\pi$
$97$	46.8143	−	46.8143i	0.482622	−	0.482622i	0.905968	+	0.423346i	$0.139145\pi$
$98$	−21.3596	−	21.3596i	−0.217955	−	0.217955i
$99$			15.2660i			0.154202i
$100$	21.6504	−	45.0695i	0.216504	−	0.450695i
$101$	−153.927			−1.52403			−0.762016	−	0.647558i	$-0.775790\pi$
$101$	−153.927			−1.52403			−0.762016	+	0.647558i	$0.775790\pi$
$102$	−94.3331	+	94.3331i	−0.924834	+	0.924834i
$103$	12.7878	+	12.7878i	0.124153	+	0.124153i	0.766453	−	0.642300i	$-0.222020\pi$
$103$	12.7878	+	12.7878i	0.124153	+	0.124153i	−0.642300	+	0.766453i	$0.722020\pi$
$104$		−	45.0769i		−	0.433431i
$105$	87.6531	+	19.9614i	0.834791	+	0.190109i
$106$	66.3131			0.625595
$107$	−126.065	+	126.065i	−1.17817	+	1.17817i	−0.197965	+	0.980209i	$0.563433\pi$
$107$	−126.065	+	126.065i	−1.17817	+	1.17817i	−0.980209	+	0.197965i	$0.936567\pi$
$108$	30.4923	+	30.4923i	0.282336	+	0.282336i
$109$		−	169.079i		−	1.55119i	−0.631234	−	0.775593i	$-0.717451\pi$
$109$		−	169.079i		−	1.55119i	0.631234	−	0.775593i	$-0.282549\pi$
$110$	33.9020	−	21.3250i	0.308200	−	0.193864i
$111$	−167.520			−1.50919
$112$	−14.8702	+	14.8702i	−0.132770	+	0.132770i
$113$	−44.1668	−	44.1668i	−0.390857	−	0.390857i	0.484136	−	0.874993i	$-0.339134\pi$
$113$	−44.1668	−	44.1668i	−0.390857	−	0.390857i	−0.874993	+	0.484136i	$0.839134\pi$
$114$			104.386i			0.915662i
$115$	−12.7675	−	20.2975i	−0.111022	−	0.176500i
$116$	77.9038			0.671585
$117$	30.3729	−	30.3729i	0.259598	−	0.259598i
$118$	32.5546	+	32.5546i	0.275886	+	0.275886i
$119$			145.021i			1.21867i
$120$	−10.7390	+	47.1563i	−0.0894918	+	0.392969i
$121$	−88.9179			−0.734858
$122$	17.0786	−	17.0786i	0.139989	−	0.139989i
$123$	−159.180	−	159.180i	−1.29415	−	1.29415i
$124$			79.9452i			0.644720i
$125$	−97.8424	−	77.7937i	−0.782739	−	0.622350i
$126$	−20.0392			−0.159041
$127$	−85.3322	+	85.3322i	−0.671907	+	0.671907i	−0.958155	−	0.286248i	$-0.907592\pi$
$127$	−85.3322	+	85.3322i	−0.671907	+	0.671907i	0.286248	+	0.958155i	$0.407592\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			171.947i			1.33292i
$130$	−109.879	−	25.0230i	−0.845222	−	0.192485i
$131$	−134.789			−1.02892			−0.514460	−	0.857514i	$-0.672008\pi$
$131$	−134.789			−1.02892			−0.514460	+	0.857514i	$0.672008\pi$
$132$	−27.3937	+	27.3937i	−0.207528	+	0.207528i
$133$	80.2377	+	80.2377i	0.603291	+	0.603291i
$134$		−	30.6540i		−	0.228761i
$135$	91.2544	−	57.4008i	0.675959	−	0.425191i
$136$	−78.0198			−0.573675
$137$	−31.3211	+	31.3211i	−0.228621	+	0.228621i	−0.812116	−	0.583495i	$-0.801685\pi$
$137$	−31.3211	+	31.3211i	−0.228621	+	0.228621i	0.583495	+	0.812116i	$0.301685\pi$
$138$	16.4009	+	16.4009i	0.118847	+	0.118847i
$139$		−	47.8983i		−	0.344592i	−0.985045	−	0.172296i	$-0.944881\pi$
$139$		−	47.8983i		−	0.344592i	0.985045	−	0.172296i	$-0.0551186\pi$
$140$	27.9928	+	44.5022i	0.199948	+	0.317873i
$141$	220.337			1.56267
$142$	−38.4278	+	38.4278i	−0.270619	+	0.270619i
$143$	−63.8301	−	63.8301i	−0.446364	−	0.446364i
$144$		−	10.7808i		−	0.0748670i
$145$	43.2458	−	189.898i	0.298247	−	1.30964i
$146$	29.4653			0.201817
$147$	51.6513	−	51.6513i	0.351370	−	0.351370i
$148$	−69.2754	−	69.2754i	−0.468077	−	0.468077i
$149$		−	145.445i		−	0.976144i	−0.872803	−	0.488072i	$-0.837700\pi$
$149$		−	145.445i		−	0.976144i	0.872803	−	0.488072i	$-0.162300\pi$
$150$	108.986	+	52.3546i	0.726575	+	0.349031i
$151$	−146.442			−0.969812			−0.484906	−	0.874566i	$-0.661146\pi$
$151$	−146.442			−0.969812			−0.484906	+	0.874566i	$0.661146\pi$
$152$	−43.1669	+	43.1669i	−0.283993	+	0.283993i
$153$	−52.5700	−	52.5700i	−0.343595	−	0.343595i
$154$			42.1133i			0.273463i
$155$	194.874	+	44.3790i	1.25725	+	0.286316i
$156$	109.004			0.698744
$157$	57.8019	−	57.8019i	0.368165	−	0.368165i	−0.498643	−	0.866808i	$-0.666168\pi$
$157$	57.8019	−	57.8019i	0.368165	−	0.368165i	0.866808	+	0.498643i	$0.166168\pi$
$158$	−32.7703	−	32.7703i	−0.207407	−	0.207407i
$159$			160.357i			1.00854i
$160$	−23.9417	+	15.0598i	−0.149635	+	0.0941236i
$161$	25.2137			0.156607
$162$	−97.9927	+	97.9927i	−0.604893	+	0.604893i
$163$	−93.7188	−	93.7188i	−0.574962	−	0.574962i	0.358549	−	0.933511i	$-0.383272\pi$
$163$	−93.7188	−	93.7188i	−0.574962	−	0.574962i	−0.933511	+	0.358549i	$0.883272\pi$
$164$		−	131.653i		−	0.802761i
$165$	51.5679	+	81.9813i	0.312532	+	0.496857i
$166$	3.59999			0.0216867
$167$	−78.7266	+	78.7266i	−0.471417	+	0.471417i	−0.902373	−	0.430956i	$-0.858176\pi$
$167$	−78.7266	+	78.7266i	−0.471417	+	0.471417i	0.430956	+	0.902373i	$0.358176\pi$
$168$	−35.9589	−	35.9589i	−0.214041	−	0.214041i
$169$			84.9906i			0.502903i
$170$	−43.3102	+	190.180i	−0.254766	+	1.11871i
$171$	−58.1720			−0.340187
$172$	−71.1058	+	71.1058i	−0.413406	+	0.413406i
$173$	155.096	+	155.096i	0.896511	+	0.896511i	0.995126	−	0.0986144i	$-0.0314410\pi$
$173$	155.096	+	155.096i	0.896511	+	0.896511i	−0.0986144	+	0.995126i	$0.531441\pi$
$174$			188.386i			1.08268i
$175$	124.017	−	43.5309i	0.708671	−	0.248748i
$176$	−22.6564			−0.128730
$177$	−78.7229	+	78.7229i	−0.444762	+	0.444762i
$178$	−130.635	−	130.635i	−0.733904	−	0.733904i
$179$		−	168.381i		−	0.940677i	−0.882486	−	0.470338i	$-0.844132\pi$
$179$		−	168.381i		−	0.940677i	0.882486	−	0.470338i	$-0.155868\pi$
$180$	−26.2793	−	5.98464i	−0.145996	−	0.0332480i
$181$	−243.240			−1.34387			−0.671933	−	0.740612i	$-0.734536\pi$
$181$	−243.240			−1.34387			−0.671933	+	0.740612i	$0.734536\pi$
$182$	83.7879	−	83.7879i	0.460373	−	0.460373i
$183$	41.2993	+	41.2993i	0.225679	+	0.225679i
$184$			13.5647i			0.0737210i
$185$	−207.321	+	130.409i	−1.12065	+	0.704913i
$186$	−193.322			−1.03937
$187$	−110.478	+	110.478i	−0.590792	+	0.590792i
$188$	91.1167	+	91.1167i	0.484664	+	0.484664i
$189$			113.357i			0.599771i
$190$	81.2605	+	129.186i	0.427687	+	0.679926i
$191$	40.3889			0.211460			0.105730	−	0.994395i	$-0.466282\pi$
$191$	40.3889			0.211460			0.105730	+	0.994395i	$0.466282\pi$
$192$	19.3455	−	19.3455i	0.100758	−	0.100758i
$193$	10.5251	+	10.5251i	0.0545339	+	0.0545339i	0.733848	−	0.679314i	$-0.237723\pi$
$193$	10.5251	+	10.5251i	0.0545339	+	0.0545339i	−0.679314	+	0.733848i	$0.737723\pi$
$194$			93.6287i			0.482622i
$195$	60.5101	−	265.707i	0.310308	−	1.36260i
$196$	42.7191			0.217955
$197$	206.579	−	206.579i	1.04863	−	1.04863i	0.0498700	−	0.998756i	$-0.484119\pi$
$197$	206.579	−	206.579i	1.04863	−	1.04863i	0.998756	−	0.0498700i	$-0.0158807\pi$
$198$	−15.2660	−	15.2660i	−0.0771009	−	0.0771009i
$199$			53.8703i			0.270705i	0.990798	+	0.135353i	$0.0432167\pi$
$199$			53.8703i			0.270705i	−0.990798	+	0.135353i	$0.956783\pi$
$200$	23.4191	+	66.7199i	0.117095	+	0.333600i
$201$	74.1269			0.368791
$202$	153.927	−	153.927i	0.762016	−	0.762016i
$203$	144.806	+	144.806i	0.713330	+	0.713330i
$204$		−	188.666i		−	0.924834i
$205$	−320.916	−	73.0829i	−1.56544	−	0.356502i
$206$	−25.5756			−0.124153
$207$	−9.13991	+	9.13991i	−0.0441541	+	0.0441541i
$208$	45.0769	+	45.0769i	0.216716	+	0.216716i
$209$			122.251i			0.584933i
$210$	−107.614	+	67.6916i	−0.512450	+	0.322341i
$211$	141.933			0.672670			0.336335	−	0.941742i	$-0.390813\pi$
$211$	141.933			0.672670			0.336335	+	0.941742i	$0.390813\pi$
$212$	−66.3131	+	66.3131i	−0.312798	+	0.312798i
$213$	−92.9255	−	92.9255i	−0.436270	−	0.436270i
$214$		−	252.129i		−	1.17817i
$215$	133.855	+	212.799i	0.622580	+	0.989762i
$216$	−60.9845			−0.282336
$217$	−148.600	+	148.600i	−0.684794	+	0.684794i
$218$	169.079	+	169.079i	0.775593	+	0.775593i
$219$			71.2524i			0.325353i
$220$	−12.5770	+	55.2271i	−0.0571682	+	0.251032i
$221$	439.611			1.98919
$222$	167.520	−	167.520i	0.754597	−	0.754597i
$223$	97.6474	+	97.6474i	0.437881	+	0.437881i	0.891298	−	0.453418i	$-0.149795\pi$
$223$	97.6474	+	97.6474i	0.437881	+	0.437881i	−0.453418	+	0.891298i	$0.649795\pi$
$224$		−	29.7404i		−	0.132770i
$225$	−29.1762	+	60.7359i	−0.129672	+	0.269937i
$226$	88.3336			0.390857
$227$	−257.473	+	257.473i	−1.13424	+	1.13424i	−0.144781	+	0.989464i	$0.546248\pi$
$227$	−257.473	+	257.473i	−1.13424	+	1.13424i	−0.989464	+	0.144781i	$0.953752\pi$
$228$	−104.386	−	104.386i	−0.457831	−	0.457831i
$229$		−	83.2942i		−	0.363730i	−0.983323	−	0.181865i	$-0.941787\pi$
$229$		−	83.2942i		−	0.363730i	0.983323	−	0.181865i	$-0.0582134\pi$
$230$	33.0651	+	7.52999i	0.143761	+	0.0327391i
$231$	−101.838			−0.440855
$232$	−77.9038	+	77.9038i	−0.335792	+	0.335792i
$233$	240.294	+	240.294i	1.03130	+	1.03130i	0.999494	+	0.0318109i	$0.0101274\pi$
$233$	240.294	+	240.294i	1.03130	+	1.03130i	0.0318109	+	0.999494i	$0.489873\pi$
$234$			60.7459i			0.259598i
$235$	272.686	−	171.525i	1.16037	−	0.729892i
$236$	−65.1092			−0.275886
$237$	79.2445	−	79.2445i	0.334365	−	0.334365i
$238$	−145.021	−	145.021i	−0.609334	−	0.609334i
$239$		−	317.238i		−	1.32736i	−0.748018	−	0.663678i	$-0.768994\pi$
$239$		−	317.238i		−	1.32736i	0.748018	−	0.663678i	$-0.231006\pi$
$240$	−36.4173	−	57.8953i	−0.151739	−	0.241230i
$241$	−30.4932			−0.126528			−0.0632640	−	0.997997i	$-0.520151\pi$
$241$	−30.4932			−0.126528			−0.0632640	+	0.997997i	$0.520151\pi$
$242$	88.9179	−	88.9179i	0.367429	−	0.367429i
$243$	−99.7492	−	99.7492i	−0.410490	−	0.410490i
$244$			34.1573i			0.139989i
$245$	23.7142	−	104.132i	0.0967925	−	0.425027i
$246$	318.360			1.29415
$247$	243.229	−	243.229i	0.984732	−	0.984732i
$248$	−79.9452	−	79.9452i	−0.322360	−	0.322360i
$249$			8.70543i			0.0349616i
$250$	175.636	−	20.0487i	0.702545	−	0.0801949i
$251$	−117.061			−0.466377			−0.233188	−	0.972432i	$-0.574916\pi$
$251$	−117.061			−0.466377			−0.233188	+	0.972432i	$0.574916\pi$
$252$	20.0392	−	20.0392i	0.0795206	−	0.0795206i
$253$	19.2079	+	19.2079i	0.0759207	+	0.0759207i
$254$		−	170.664i		−	0.671907i
$255$	−459.891	−	104.732i	−1.80349	−	0.410714i
$256$	16.0000			0.0625000
$257$	147.733	−	147.733i	0.574837	−	0.574837i	−0.358639	−	0.933476i	$-0.616759\pi$
$257$	147.733	−	147.733i	0.574837	−	0.574837i	0.933476	+	0.358639i	$0.116759\pi$
$258$	−171.947	−	171.947i	−0.666460	−	0.666460i
$259$		−	257.535i		−	0.994344i
$260$	134.902	−	84.8559i	0.518854	−	0.326369i
$261$	−104.984			−0.402236
$262$	134.789	−	134.789i	0.514460	−	0.514460i
$263$	−118.051	−	118.051i	−0.448863	−	0.448863i	0.446113	−	0.894977i	$-0.352808\pi$
$263$	−118.051	−	118.051i	−0.448863	−	0.448863i	−0.894977	+	0.446113i	$0.852808\pi$
$264$		−	54.7874i		−	0.207528i
$265$	124.833	+	198.456i	0.471066	+	0.748890i
$266$	−160.475			−0.603291
$267$	315.899	−	315.899i	1.18314	−	1.18314i
$268$	30.6540	+	30.6540i	0.114381	+	0.114381i
$269$		−	359.618i		−	1.33687i	−0.743771	−	0.668435i	$-0.766965\pi$
$269$		−	359.618i		−	1.33687i	0.743771	−	0.668435i	$-0.233035\pi$
$270$	−33.8536	+	148.655i	−0.125384	+	0.550575i
$271$	355.547			1.31198			0.655992	−	0.754768i	$-0.272251\pi$
$271$	355.547			1.31198			0.655992	+	0.754768i	$0.272251\pi$
$272$	78.0198	−	78.0198i	0.286838	−	0.286838i
$273$	202.614	+	202.614i	0.742177	+	0.742177i
$274$		−	62.6422i		−	0.228621i
$275$	127.639	+	61.3151i	0.464143	+	0.222964i
$276$	−32.8018			−0.118847
$277$	−182.970	+	182.970i	−0.660543	+	0.660543i	−0.955508	−	0.294965i	$-0.904692\pi$
$277$	−182.970	+	182.970i	−0.660543	+	0.660543i	0.294965	+	0.955508i	$0.404692\pi$
$278$	47.8983	+	47.8983i	0.172296	+	0.172296i
$279$		−	107.735i		−	0.386146i
$280$	−72.4950	−	16.5095i	−0.258911	−	0.0589623i
$281$	−430.771			−1.53299			−0.766497	−	0.642248i	$-0.778002\pi$
$281$	−430.771			−1.53299			−0.766497	+	0.642248i	$0.778002\pi$
$282$	−220.337	+	220.337i	−0.781337	+	0.781337i
$283$	−175.608	−	175.608i	−0.620523	−	0.620523i	0.325142	−	0.945665i	$-0.394588\pi$
$283$	−175.608	−	175.608i	−0.620523	−	0.620523i	−0.945665	+	0.325142i	$0.894588\pi$
$284$		−	76.8557i		−	0.270619i
$285$	−312.395	+	196.503i	−1.09612	+	0.689483i
$286$	127.660			0.446364
$287$	244.713	−	244.713i	0.852659	−	0.852659i
$288$	10.7808	+	10.7808i	0.0374335	+	0.0374335i
$289$		−	471.886i		−	1.63282i
$290$	146.652	+	233.143i	0.505696	+	0.803943i
$291$	−226.411			−0.778045
$292$	−29.4653	+	29.4653i	−0.100908	+	0.100908i
$293$	206.915	+	206.915i	0.706194	+	0.706194i	0.965733	−	0.259539i	$-0.0835705\pi$
$293$	206.915	+	206.915i	0.706194	+	0.706194i	−0.259539	+	0.965733i	$0.583570\pi$
$294$			103.303i			0.351370i
$295$	−36.1433	+	158.709i	−0.122520	+	0.537998i
$296$	138.551			0.468077
$297$	−86.3557	+	86.3557i	−0.290760	+	0.290760i
$298$	145.445	+	145.445i	0.488072	+	0.488072i
$299$		−	76.4316i		−	0.255624i
$300$	−161.341	+	56.6317i	−0.537803	+	0.188772i
$301$	−264.340			−0.878205
$302$	146.442	−	146.442i	0.484906	−	0.484906i
$303$	372.224	+	372.224i	1.22846	+	1.22846i
$304$		−	86.3339i		−	0.283993i
$305$	83.2615	+	18.9613i	0.272988	+	0.0621683i
$306$	105.140			0.343595
$307$	−391.647	+	391.647i	−1.27572	+	1.27572i	−0.332684	+	0.943038i	$0.607954\pi$
$307$	−391.647	+	391.647i	−1.27572	+	1.27572i	−0.943038	+	0.332684i	$0.892046\pi$
$308$	−42.1133	−	42.1133i	−0.136731	−	0.136731i
$309$		−	61.8464i		−	0.200150i
$310$	−239.253	+	150.495i	−0.771783	+	0.485467i
$311$	214.460			0.689581			0.344791	−	0.938680i	$-0.387950\pi$
$311$	214.460			0.689581			0.344791	+	0.938680i	$0.387950\pi$
$312$	−109.004	+	109.004i	−0.349372	+	0.349372i
$313$	−37.5054	−	37.5054i	−0.119826	−	0.119826i	0.644651	−	0.764477i	$-0.277003\pi$
$313$	−37.5054	−	37.5054i	−0.119826	−	0.119826i	−0.764477	+	0.644651i	$0.777003\pi$
$314$			115.604i			0.368165i
$315$	−37.7232	−	59.9715i	−0.119756	−	0.190386i
$316$	65.5406			0.207407
$317$	−140.447	+	140.447i	−0.443052	+	0.443052i	−0.893036	−	0.449984i	$-0.851430\pi$
$317$	−140.447	+	140.447i	−0.443052	+	0.443052i	0.449984	+	0.893036i	$0.351430\pi$
$318$	−160.357	−	160.357i	−0.504268	−	0.504268i
$319$			220.628i			0.691624i
$320$	8.88189	−	39.0014i	0.0277559	−	0.121879i
$321$	609.695			1.89936
$322$	−25.2137	+	25.2137i	−0.0783034	+	0.0783034i
$323$	−420.984	−	420.984i	−1.30336	−	1.30336i
$324$		−	195.985i		−	0.604893i
$325$	−131.957	−	375.941i	−0.406023	−	1.15674i
$326$	187.438			0.574962
$327$	−408.864	+	408.864i	−1.25035	+	1.25035i
$328$	131.653	+	131.653i	0.401380	+	0.401380i
$329$			338.732i			1.02958i
$330$	−133.549	−	30.4135i	−0.404694	−	0.0921620i
$331$	−89.9646			−0.271796			−0.135898	−	0.990723i	$-0.543392\pi$
$331$	−89.9646			−0.271796			−0.135898	+	0.990723i	$0.543392\pi$
$332$	−3.59999	+	3.59999i	−0.0108433	+	0.0108433i
$333$	93.3559	+	93.3559i	0.280348	+	0.280348i
$334$		−	157.453i		−	0.471417i
$335$	91.7384	−	57.7053i	0.273846	−	0.172255i
$336$	71.9178			0.214041
$337$	285.730	−	285.730i	0.847862	−	0.847862i	−0.142004	−	0.989866i	$-0.545355\pi$
$337$	285.730	−	285.730i	0.847862	−	0.847862i	0.989866	+	0.142004i	$0.0453546\pi$
$338$	−84.9906	−	84.9906i	−0.251451	−	0.251451i
$339$			213.607i			0.630108i
$340$	−146.870	−	233.490i	−0.431971	−	0.686737i
$341$	−226.409			−0.663957
$342$	58.1720	−	58.1720i	0.170094	−	0.170094i
$343$	261.566	+	261.566i	0.762582	+	0.762582i
$344$		−	142.212i		−	0.413406i
$345$	−18.2089	+	79.9574i	−0.0527794	+	0.231761i
$346$	−310.193			−0.896511
$347$	−389.916	+	389.916i	−1.12368	+	1.12368i	−0.132493	+	0.991184i	$0.542298\pi$
$347$	−389.916	+	389.916i	−1.12368	+	1.12368i	−0.991184	+	0.132493i	$0.957702\pi$
$348$	−188.386	−	188.386i	−0.541338	−	0.541338i
$349$			459.513i			1.31666i	0.752731	+	0.658329i	$0.228736\pi$
$349$			459.513i			1.31666i	−0.752731	+	0.658329i	$0.771264\pi$
$350$	−80.4866	+	167.548i	−0.229962	+	0.478710i
$351$	343.624			0.978985
$352$	22.6564	−	22.6564i	0.0643649	−	0.0643649i
$353$	−40.4868	−	40.4868i	−0.114694	−	0.114694i	0.647431	−	0.762124i	$-0.275844\pi$
$353$	−40.4868	−	40.4868i	−0.114694	−	0.114694i	−0.762124	+	0.647431i	$0.775844\pi$
$354$		−	157.446i		−	0.444762i
$355$	−187.343	−	42.6640i	−0.527726	−	0.120180i
$356$	261.270			0.733904
$357$	350.688	−	350.688i	0.982320	−	0.982320i
$358$	168.381	+	168.381i	0.470338	+	0.470338i
$359$			433.495i			1.20751i	0.797171	+	0.603753i	$0.206329\pi$
$359$			433.495i			1.20751i	−0.797171	+	0.603753i	$0.793671\pi$
$360$	32.2639	−	20.2946i	0.0896220	−	0.0563740i
$361$	−104.846			−0.290432
$362$	243.240	−	243.240i	0.671933	−	0.671933i
$363$	215.020	+	215.020i	0.592341	+	0.592341i
$364$			167.576i			0.460373i
$365$	55.4675	+	88.1809i	0.151966	+	0.241592i
$366$	−82.5986			−0.225679
$367$	−23.7488	+	23.7488i	−0.0647106	+	0.0647106i	−0.738721	−	0.674011i	$-0.764570\pi$
$367$	−23.7488	+	23.7488i	−0.0647106	+	0.0647106i	0.674011	+	0.738721i	$0.264570\pi$
$368$	−13.5647	−	13.5647i	−0.0368605	−	0.0368605i
$369$			177.416i			0.480802i
$370$	76.9120	−	337.730i	0.207870	−	0.912783i
$371$	−246.523			−0.664481
$372$	193.322	−	193.322i	0.519683	−	0.519683i
$373$	66.5228	+	66.5228i	0.178345	+	0.178345i	0.790634	−	0.612289i	$-0.209751\pi$
$373$	66.5228	+	66.5228i	0.178345	+	0.178345i	−0.612289	+	0.790634i	$0.709751\pi$
$374$		−	220.956i		−	0.590792i
$375$	48.4815	+	424.720i	0.129284	+	1.13259i
$376$	−182.233			−0.484664
$377$	438.958	−	438.958i	1.16434	−	1.16434i
$378$	−113.357	−	113.357i	−0.299885	−	0.299885i
$379$			323.563i			0.853728i	0.904316	+	0.426864i	$0.140382\pi$
$379$			323.563i			0.853728i	−0.904316	+	0.426864i	$0.859618\pi$
$380$	−210.447	−	47.9255i	−0.553807	−	0.126120i
$381$	412.698			1.08320
$382$	−40.3889	+	40.3889i	−0.105730	+	0.105730i
$383$	−299.857	−	299.857i	−0.782917	−	0.782917i	0.197405	−	0.980322i	$-0.436749\pi$
$383$	−299.857	−	299.857i	−0.782917	−	0.782917i	−0.980322	+	0.197405i	$0.936749\pi$
$384$			38.6909i			0.100758i
$385$	−126.033	+	79.2770i	−0.327358	+	0.205914i
$386$	−21.0501			−0.0545339
$387$	95.8226	−	95.8226i	0.247604	−	0.247604i
$388$	−93.6287	−	93.6287i	−0.241311	−	0.241311i
$389$			64.2288i			0.165113i	0.996586	+	0.0825563i	$0.0263084\pi$
$389$			64.2288i			0.165113i	−0.996586	+	0.0825563i	$0.973692\pi$
$390$	205.197	+	326.217i	0.526146	+	0.836455i
$391$	−132.289			−0.338335
$392$	−42.7191	+	42.7191i	−0.108977	+	0.108977i
$393$	325.943	+	325.943i	0.829372	+	0.829372i
$394$			413.159i			1.04863i
$395$	36.3827	−	159.761i	0.0921082	−	0.404458i
$396$	30.5319			0.0771009
$397$	489.291	−	489.291i	1.23247	−	1.23247i	0.269460	−	0.963012i	$-0.413155\pi$
$397$	489.291	−	489.291i	1.23247	−	1.23247i	0.963012	−	0.269460i	$-0.0868450\pi$
$398$	−53.8703	−	53.8703i	−0.135353	−	0.135353i
$399$		−	388.059i		−	0.972579i
$400$	−90.1390	−	43.3008i	−0.225348	−	0.108252i
$401$	−615.748			−1.53553			−0.767765	−	0.640731i	$-0.778631\pi$
$401$	−615.748			−1.53553			−0.767765	+	0.640731i	$0.778631\pi$
$402$	−74.1269	+	74.1269i	−0.184395	+	0.184395i
$403$	450.460	+	450.460i	1.11777	+	1.11777i
$404$			307.855i			0.762016i
$405$	−477.732	−	108.795i	−1.17959	−	0.268630i
$406$	−289.612			−0.713330
$407$	196.192	−	196.192i	0.482043	−	0.482043i
$408$	188.666	+	188.666i	0.462417	+	0.462417i
$409$		−	43.1536i		−	0.105510i	−0.998607	−	0.0527551i	$-0.983200\pi$
$409$		−	43.1536i		−	0.105510i	0.998607	−	0.0527551i	$-0.0168003\pi$
$410$	393.998	−	247.833i	0.960972	−	0.604470i
$411$	151.480			0.368565
$412$	25.5756	−	25.5756i	0.0620767	−	0.0620767i
$413$	−121.023	−	121.023i	−0.293035	−	0.293035i
$414$		−	18.2798i		−	0.0441541i
$415$	6.77688	+	10.7737i	0.0163298	+	0.0259608i
$416$	−90.1537			−0.216716
$417$	−115.827	+	115.827i	−0.277762	+	0.277762i
$418$	−122.251	−	122.251i	−0.292467	−	0.292467i
$419$		−	49.6628i		−	0.118527i	−0.998242	−	0.0592635i	$-0.981125\pi$
$419$		−	49.6628i		−	0.118527i	0.998242	−	0.0592635i	$-0.0188752\pi$
$420$	39.9229	−	175.306i	0.0950545	−	0.417396i
$421$	−95.0400			−0.225748			−0.112874	−	0.993609i	$-0.536006\pi$
$421$	−95.0400			−0.225748			−0.112874	+	0.993609i	$0.536006\pi$
$422$	−141.933	+	141.933i	−0.336335	+	0.336335i
$423$	−122.789	−	122.789i	−0.290282	−	0.290282i
$424$		−	132.626i		−	0.312798i
$425$	−650.684	+	228.394i	−1.53102	+	0.537398i
$426$	185.851			0.436270
$427$	−63.4908	+	63.4908i	−0.148690	+	0.148690i
$428$	252.129	+	252.129i	0.589087	+	0.589087i
$429$			308.706i			0.719593i
$430$	−346.654	−	78.9442i	−0.806171	−	0.183591i
$431$	−697.801			−1.61903			−0.809514	−	0.587100i	$-0.800270\pi$
$431$	−697.801			−1.61903			−0.809514	+	0.587100i	$0.800270\pi$
$432$	60.9845	−	60.9845i	0.141168	−	0.141168i
$433$	387.368	+	387.368i	0.894614	+	0.894614i	0.994953	−	0.100340i	$-0.0319930\pi$
$433$	387.368	+	387.368i	0.894614	+	0.894614i	−0.100340	+	0.994953i	$0.531993\pi$
$434$		−	297.201i		−	0.684794i
$435$	−563.783	+	354.631i	−1.29605	+	0.815243i
$436$	−338.158			−0.775593
$437$	−73.1931	+	73.1931i	−0.167490	+	0.167490i
$438$	−71.2524	−	71.2524i	−0.162677	−	0.162677i
$439$		−	186.351i		−	0.424490i	−0.977216	−	0.212245i	$-0.931923\pi$
$439$		−	186.351i		−	0.424490i	0.977216	−	0.212245i	$-0.0680775\pi$
$440$	−42.6501	−	67.8041i	−0.0969320	−	0.154100i
$441$	−57.5686			−0.130541
$442$	−439.611	+	439.611i	−0.994595	+	0.994595i
$443$	344.391	+	344.391i	0.777407	+	0.777407i	0.979389	−	0.201982i	$-0.0647383\pi$
$443$	344.391	+	344.391i	0.777407	+	0.777407i	−0.201982	+	0.979389i	$0.564738\pi$
$444$			335.041i			0.754597i
$445$	145.036	−	636.869i	0.325923	−	1.43117i
$446$	−195.295			−0.437881
$447$	−351.714	+	351.714i	−0.786831	+	0.786831i
$448$	29.7404	+	29.7404i	0.0663849	+	0.0663849i
$449$			85.4403i			0.190290i	0.995463	+	0.0951451i	$0.0303315\pi$
$449$			85.4403i			0.190290i	−0.995463	+	0.0951451i	$0.969668\pi$
$450$	−31.5597	−	89.9121i	−0.0701327	−	0.199805i
$451$	372.848			0.826714
$452$	−88.3336	+	88.3336i	−0.195428	+	0.195428i
$453$	354.123	+	354.123i	0.781728	+	0.781728i
$454$		−	514.947i		−	1.13424i
$455$	408.481	+	93.0243i	0.897760	+	0.204449i
$456$	208.771			0.457831
$457$	238.455	−	238.455i	0.521784	−	0.521784i	−0.396326	−	0.918110i	$-0.629715\pi$
$457$	238.455	−	238.455i	0.521784	−	0.521784i	0.918110	+	0.396326i	$0.129715\pi$
$458$	83.2942	+	83.2942i	0.181865	+	0.181865i
$459$		−	594.750i		−	1.29575i
$460$	−40.5951	+	25.5351i	−0.0882501	+	0.0555111i
$461$	278.593			0.604323			0.302161	−	0.953257i	$-0.402292\pi$
$461$	278.593			0.604323			0.302161	+	0.953257i	$0.402292\pi$
$462$	101.838	−	101.838i	0.220428	−	0.220428i
$463$	317.977	+	317.977i	0.686775	+	0.686775i	0.961518	−	0.274743i	$-0.0885927\pi$
$463$	317.977	+	317.977i	0.686775	+	0.686775i	−0.274743	+	0.961518i	$0.588593\pi$
$464$		−	155.808i		−	0.335792i
$465$	−363.923	−	578.557i	−0.782631	−	1.24421i
$466$	−480.588			−1.03130
$467$	164.319	−	164.319i	0.351861	−	0.351861i	−0.508940	−	0.860802i	$-0.669963\pi$
$467$	164.319	−	164.319i	0.351861	−	0.351861i	0.860802	+	0.508940i	$0.169963\pi$
$468$	−60.7459	−	60.7459i	−0.129799	−	0.129799i
$469$			113.958i			0.242981i
$470$	−101.161	+	444.210i	−0.215236	+	0.945129i
$471$	−279.551			−0.593527
$472$	65.1092	−	65.1092i	0.137943	−	0.137943i
$473$	−201.375	−	201.375i	−0.425741	−	0.425741i
$474$			158.489i			0.334365i
$475$	−233.645	+	486.378i	−0.491885	+	1.02395i
$476$	290.043			0.609334
$477$	89.3639	−	89.3639i	0.187346	−	0.187346i
$478$	317.238	+	317.238i	0.663678	+	0.663678i
$479$		−	55.2512i		−	0.115347i	−0.998335	−	0.0576735i	$-0.981632\pi$
$479$		−	55.2512i		−	0.115347i	0.998335	−	0.0576735i	$-0.0183682\pi$
$480$	94.3126	+	21.4780i	0.196485	+	0.0447459i
$481$	−780.679			−1.62303
$482$	30.4932	−	30.4932i	0.0632640	−	0.0632640i
$483$	−60.9713	−	60.9713i	−0.126235	−	0.126235i
$484$			177.836i			0.367429i
$485$	−280.203	+	176.253i	−0.577739	+	0.363409i
$486$	199.498			0.410490
$487$	353.979	−	353.979i	0.726857	−	0.726857i	−0.243136	−	0.969992i	$-0.578176\pi$
$487$	353.979	−	353.979i	0.726857	−	0.726857i	0.969992	+	0.243136i	$0.0781760\pi$
$488$	−34.1573	−	34.1573i	−0.0699945	−	0.0699945i
$489$			453.258i			0.926908i
$490$	80.4176	+	127.846i	0.164117	+	0.260910i
$491$	−698.356			−1.42231			−0.711157	−	0.703034i	$-0.751828\pi$
$491$	−698.356			−1.42231			−0.711157	+	0.703034i	$0.751828\pi$
$492$	−318.360	+	318.360i	−0.647074	+	0.647074i
$493$	−759.755	−	759.755i	−1.54109	−	1.54109i
$494$			486.458i			0.984732i
$495$	16.9488	−	74.4244i	0.0342401	−	0.150352i
$496$	159.890			0.322360
$497$	142.858	−	142.858i	0.287440	−	0.287440i
$498$	−8.70543	−	8.70543i	−0.0174808	−	0.0174808i
$499$		−	27.0217i		−	0.0541518i	−0.999633	−	0.0270759i	$-0.991380\pi$
$499$		−	27.0217i		−	0.0541518i	0.999633	−	0.0270759i	$-0.00861958\pi$
$500$	−155.587	+	195.685i	−0.311175	+	0.391370i
$501$	380.751			0.759981
$502$	117.061	−	117.061i	0.233188	−	0.233188i
$503$	−673.941	−	673.941i	−1.33984	−	1.33984i	−0.896208	−	0.443634i	$-0.853689\pi$
$503$	−673.941	−	673.941i	−1.33984	−	1.33984i	−0.443634	−	0.896208i	$-0.646311\pi$
$504$			40.0784i			0.0795206i
$505$	750.423	+	170.896i	1.48599	+	0.338407i
$506$	−38.4159			−0.0759207
$507$	205.523	−	205.523i	0.405370	−	0.405370i
$508$	170.664	+	170.664i	0.335954	+	0.335954i
$509$		−	809.386i		−	1.59015i	−0.606512	−	0.795074i	$-0.707432\pi$
$509$		−	809.386i		−	1.59015i	0.606512	−	0.795074i	$-0.292568\pi$
$510$	564.623	−	355.159i	1.10710	−	0.696389i
$511$	−109.539			−0.214361
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−329.064	−	329.064i	−0.641451	−	0.641451i
$514$			295.466i			0.574837i
$515$	−48.1453	−	76.5403i	−0.0934861	−	0.148622i
$516$	343.894			0.666460
$517$	−258.048	+	258.048i	−0.499125	+	0.499125i
$518$	257.535	+	257.535i	0.497172	+	0.497172i
$519$		−	750.103i		−	1.44529i
$520$	−50.0460	+	219.758i	−0.0962423	+	0.422611i
$521$	−310.331			−0.595645			−0.297822	−	0.954621i	$-0.596260\pi$
$521$	−310.331			−0.595645			−0.297822	+	0.954621i	$0.596260\pi$
$522$	104.984	−	104.984i	0.201118	−	0.201118i
$523$	464.606	+	464.606i	0.888347	+	0.888347i	0.994364	−	0.106017i	$-0.0338098\pi$
$523$	464.606	+	464.606i	0.888347	+	0.888347i	−0.106017	+	0.994364i	$0.533810\pi$
$524$			269.577i			0.514460i
$525$	−405.162	−	194.631i	−0.771738	−	0.370726i
$526$	236.102			0.448863
$527$	779.664	−	779.664i	1.47944	−	1.47944i
$528$	54.7874	+	54.7874i	0.103764	+	0.103764i
$529$			23.0000i			0.0434783i
$530$	−323.288	−	73.6232i	−0.609978	−	0.138912i
$531$	87.7415			0.165238
$532$	160.475	−	160.475i	0.301646	−	0.301646i
$533$	−741.812	−	741.812i	−1.39177	−	1.39177i
$534$			631.798i			1.18314i
$535$	754.549	−	474.626i	1.41037	−	0.887152i
$536$	−61.3080			−0.114381
$537$	−407.176	+	407.176i	−0.758243	+	0.758243i
$538$	359.618	+	359.618i	0.668435	+	0.668435i
$539$			120.983i			0.224458i
$540$	−114.802	−	182.509i	−0.212596	−	0.337979i
$541$	807.280			1.49220			0.746100	−	0.665834i	$-0.231924\pi$
$541$	807.280			1.49220			0.746100	+	0.665834i	$0.231924\pi$
$542$	−355.547	+	355.547i	−0.655992	+	0.655992i
$543$	588.198	+	588.198i	1.08324	+	1.08324i
$544$			156.040i			0.286838i
$545$	−187.718	+	824.291i	−0.344436	+	1.51246i
$546$	−405.229			−0.742177
$547$	−419.482	+	419.482i	−0.766877	+	0.766877i	−0.977555	−	0.210678i	$-0.932433\pi$
$547$	−419.482	+	419.482i	−0.766877	+	0.766877i	0.210678	+	0.977555i	$0.432433\pi$
$548$	62.6422	+	62.6422i	0.114311	+	0.114311i
$549$		−	46.0306i		−	0.0838444i
$550$	−188.954	+	66.3242i	−0.343553	+	0.120589i
$551$	−840.717			−1.52580
$552$	32.8018	−	32.8018i	0.0594236	−	0.0594236i
$553$	121.825	+	121.825i	0.220299	+	0.220299i
$554$		−	365.941i		−	0.660543i
$555$	816.692	+	185.987i	1.47152	+	0.335112i
$556$	−95.7966			−0.172296
$557$	193.565	−	193.565i	0.347514	−	0.347514i	−0.511669	−	0.859183i	$-0.670973\pi$
$557$	193.565	−	193.565i	0.347514	−	0.347514i	0.859183	+	0.511669i	$0.170973\pi$
$558$	107.735	+	107.735i	0.193073	+	0.193073i
$559$			801.307i			1.43346i
$560$	89.0045	−	55.9855i	0.158937	−	0.0999742i
$561$	534.313			0.952429
$562$	430.771	−	430.771i	0.766497	−	0.766497i
$563$	−180.193	−	180.193i	−0.320058	−	0.320058i	0.528731	−	0.848789i	$-0.322668\pi$
$563$	−180.193	−	180.193i	−0.320058	−	0.320058i	−0.848789	+	0.528731i	$0.822668\pi$
$564$		−	440.674i		−	0.781337i
$565$	166.286	+	264.357i	0.294311	+	0.467888i
$566$	351.216			0.620523
$567$	364.293	−	364.293i	0.642493	−	0.642493i
$568$	76.8557	+	76.8557i	0.135309	+	0.135309i
$569$		−	26.7672i		−	0.0470425i	−0.999723	−	0.0235213i	$-0.992512\pi$
$569$		−	26.7672i		−	0.0470425i	0.999723	−	0.0235213i	$-0.00748774\pi$
$570$	115.893	−	508.898i	0.203320	−	0.892804i
$571$	687.381			1.20382			0.601910	−	0.798564i	$-0.294407\pi$
$571$	687.381			1.20382			0.601910	+	0.798564i	$0.294407\pi$
$572$	−127.660	+	127.660i	−0.223182	+	0.223182i
$573$	−97.6678	−	97.6678i	−0.170450	−	0.170450i
$574$			489.427i			0.852659i
$575$	39.7090	+	113.129i	0.0690592	+	0.196746i
$576$	−21.5617			−0.0374335
$577$	−153.323	+	153.323i	−0.265725	+	0.265725i	−0.827375	−	0.561650i	$-0.810167\pi$
$577$	−153.323	+	153.323i	−0.265725	+	0.265725i	0.561650	+	0.827375i	$0.310167\pi$
$578$	471.886	+	471.886i	0.816412	+	0.816412i
$579$		−	50.9030i		−	0.0879153i
$580$	−379.795	−	86.4917i	−0.654819	−	0.149124i
$581$	−13.3832			−0.0230347
$582$	226.411	−	226.411i	0.389023	−	0.389023i
$583$	−187.802	−	187.802i	−0.322131	−	0.322131i
$584$		−	58.9305i		−	0.100908i
$585$	−181.795	+	114.352i	−0.310760	+	0.195474i
$586$	−413.830			−0.706194
$587$	588.851	−	588.851i	1.00315	−	1.00315i	0.00315852	−	0.999995i	$-0.498995\pi$
$587$	588.851	−	588.851i	1.00315	−	1.00315i	0.999995	−	0.00315852i	$-0.00100539\pi$
$588$	−103.303	−	103.303i	−0.175685	−	0.175685i
$589$		−	862.748i		−	1.46477i
$590$	−122.566	−	194.853i	−0.207739	−	0.330259i
$591$	−999.093			−1.69051
$592$	−138.551	+	138.551i	−0.234038	+	0.234038i
$593$	−465.426	−	465.426i	−0.784866	−	0.784866i	0.195781	−	0.980648i	$-0.437276\pi$
$593$	−465.426	−	465.426i	−0.784866	−	0.784866i	−0.980648	+	0.195781i	$0.937276\pi$
$594$		−	172.711i		−	0.290760i
$595$	161.008	−	707.006i	0.270602	−	1.18824i
$596$	−290.891			−0.488072
$597$	130.268	−	130.268i	0.218205	−	0.218205i
$598$	76.4316	+	76.4316i	0.127812	+	0.127812i
$599$		−	552.633i		−	0.922592i	−0.887246	−	0.461296i	$-0.847385\pi$
$599$		−	552.633i		−	0.922592i	0.887246	−	0.461296i	$-0.152615\pi$
$600$	104.709	−	217.973i	0.174515	−	0.363288i
$601$	597.140			0.993577			0.496788	−	0.867872i	$-0.334512\pi$
$601$	597.140			0.993577			0.496788	+	0.867872i	$0.334512\pi$
$602$	264.340	−	264.340i	0.439102	−	0.439102i
$603$	−41.3095	−	41.3095i	−0.0685066	−	0.0685066i
$604$			292.883i			0.484906i
$605$	433.491	+	98.7198i	0.716513	+	0.163173i
$606$	−744.448			−1.22846
$607$	−535.238	+	535.238i	−0.881776	+	0.881776i	−0.993715	−	0.111939i	$-0.964294\pi$
$607$	−535.238	+	535.238i	−0.881776	+	0.881776i	0.111939	+	0.993715i	$0.464294\pi$
$608$	86.3339	+	86.3339i	0.141996	+	0.141996i
$609$		−	700.334i		−	1.14997i
$610$	−102.223	+	64.3001i	−0.167578	+	0.105410i
$611$	1026.81			1.68055
$612$	−105.140	+	105.140i	−0.171797	+	0.171797i
$613$	−697.916	−	697.916i	−1.13853	−	1.13853i	−0.988715	−	0.149811i	$-0.952134\pi$
$613$	−697.916	−	697.916i	−1.13853	−	1.13853i	−0.149811	−	0.988715i	$-0.547866\pi$
$614$		−	783.293i		−	1.27572i
$615$	599.305	+	952.760i	0.974479	+	1.54920i
$616$	84.2265			0.136731
$617$	−758.632	+	758.632i	−1.22955	+	1.22955i	−0.265416	+	0.964134i	$0.585509\pi$
$617$	−758.632	+	758.632i	−1.22955	+	1.22955i	−0.964134	+	0.265416i	$0.914491\pi$
$618$	61.8464	+	61.8464i	0.100075	+	0.100075i
$619$		−	550.862i		−	0.889923i	−0.895550	−	0.444961i	$-0.853217\pi$
$619$		−	550.862i		−	0.889923i	0.895550	−	0.444961i	$-0.146783\pi$
$620$	88.7581	−	389.747i	0.143158	−	0.628625i
$621$	−103.404			−0.166513
$622$	−214.460	+	214.460i	−0.344791	+	0.344791i
$623$	485.643	+	485.643i	0.779523	+	0.779523i
$624$		−	218.008i		−	0.349372i
$625$	390.630	+	487.886i	0.625008	+	0.780618i
$626$	75.0109			0.119826
$627$	295.625	−	295.625i	0.471492	−	0.471492i
$628$	−115.604	−	115.604i	−0.184083	−	0.184083i
$629$			1351.21i			2.14819i
$630$	97.6947	+	22.2482i	0.155071	+	0.0353147i
$631$	676.596			1.07226			0.536130	−	0.844136i	$-0.319886\pi$
$631$	676.596			1.07226			0.536130	+	0.844136i	$0.319886\pi$
$632$	−65.5406	+	65.5406i	−0.103703	+	0.103703i
$633$	−343.221	−	343.221i	−0.542213	−	0.542213i
$634$		−	280.895i		−	0.443052i
$635$	510.749	−	321.271i	0.804329	−	0.505938i
$636$	320.714			0.504268
$637$	240.706	−	240.706i	0.377874	−	0.377874i
$638$	−220.628	−	220.628i	−0.345812	−	0.345812i
$639$			103.571i			0.162083i
$640$	30.1195	+	47.8833i	0.0470618	+	0.0748177i
$641$	786.673			1.22726			0.613630	−	0.789594i	$-0.289709\pi$
$641$	786.673			1.22726			0.613630	+	0.789594i	$0.289709\pi$
$642$	−609.695	+	609.695i	−0.949680	+	0.949680i
$643$	−632.234	−	632.234i	−0.983256	−	0.983256i	0.0166059	−	0.999862i	$-0.494714\pi$
$643$	−632.234	−	632.234i	−0.983256	−	0.983256i	−0.999862	+	0.0166059i	$0.994714\pi$
$644$		−	50.4274i		−	0.0783034i
$645$	190.902	−	838.271i	0.295971	−	1.29965i
$646$	841.969			1.30336
$647$	387.458	−	387.458i	0.598853	−	0.598853i	−0.341154	−	0.940007i	$-0.610818\pi$
$647$	387.458	−	387.458i	0.598853	−	0.598853i	0.940007	+	0.341154i	$0.110818\pi$
$648$	195.985	+	195.985i	0.302447	+	0.302447i
$649$		−	184.393i		−	0.284118i
$650$	507.898	+	243.983i	0.781382	+	0.375359i
$651$	718.686			1.10397
$652$	−187.438	+	187.438i	−0.287481	+	0.287481i
$653$	15.7216	+	15.7216i	0.0240760	+	0.0240760i	0.719042	−	0.694966i	$-0.244581\pi$
$653$	15.7216	+	15.7216i	0.0240760	+	0.0240760i	−0.694966	+	0.719042i	$0.744581\pi$
$654$		−	817.729i		−	1.25035i
$655$	657.119	+	149.647i	1.00323	+	0.228469i
$656$	−263.306			−0.401380
$657$	39.7076	−	39.7076i	0.0604377	−	0.0604377i
$658$	−338.732	−	338.732i	−0.514790	−	0.514790i
$659$			387.603i			0.588169i	0.955779	+	0.294084i	$0.0950147\pi$
$659$			387.603i			0.588169i	−0.955779	+	0.294084i	$0.904985\pi$
$660$	163.963	−	103.136i	0.248428	−	0.156266i
$661$	−1281.37			−1.93853			−0.969266	−	0.246017i	$-0.920878\pi$
$661$	−1281.37			−1.93853			−0.969266	+	0.246017i	$0.920878\pi$
$662$	89.9646	−	89.9646i	0.135898	−	0.135898i
$663$	−1063.06	−	1063.06i	−1.60341	−	1.60341i
$664$		−	7.19998i		−	0.0108433i
$665$	−302.090	−	480.256i	−0.454271	−	0.722190i
$666$	−186.712			−0.280348
$667$	−132.092	+	132.092i	−0.198040	+	0.198040i
$668$	157.453	+	157.453i	0.235708	+	0.235708i
$669$		−	472.258i		−	0.705917i
$670$	−34.0332	+	149.444i	−0.0507958	+	0.223050i
$671$	−96.7353			−0.144166
$672$	−71.9178	+	71.9178i	−0.107021	+	0.107021i
$673$	−44.9321	−	44.9321i	−0.0667639	−	0.0667639i	0.672936	−	0.739700i	$-0.265033\pi$
$673$	−44.9321	−	44.9321i	−0.0667639	−	0.0667639i	−0.739700	+	0.672936i	$0.765033\pi$
$674$			571.459i			0.847862i
$675$	−508.610	+	178.525i	−0.753496	+	0.264482i
$676$	169.981			0.251451
$677$	−480.166	+	480.166i	−0.709255	+	0.709255i	−0.966379	−	0.257124i	$-0.917225\pi$
$677$	−480.166	+	480.166i	−0.709255	+	0.709255i	0.257124	+	0.966379i	$0.417225\pi$
$678$	−213.607	−	213.607i	−0.315054	−	0.315054i
$679$		−	348.070i		−	0.512621i
$680$	380.361	+	86.6204i	0.559354	+	0.127383i
$681$	1245.24			1.82854
$682$	226.409	−	226.409i	0.331978	−	0.331978i
$683$	895.860	+	895.860i	1.31165	+	1.31165i	0.920196	+	0.391459i	$0.128029\pi$
$683$	895.860	+	895.860i	1.31165	+	1.31165i	0.391459	+	0.920196i	$0.371971\pi$
$684$			116.344i			0.170094i
$685$	187.470	−	117.922i	0.273678	−	0.172149i
$686$	−523.131			−0.762582
$687$	−201.421	+	201.421i	−0.293189	+	0.293189i
$688$	142.212	+	142.212i	0.206703	+	0.206703i
$689$			747.297i			1.08461i
$690$	−61.7485	−	98.1663i	−0.0894906	−	0.142270i
$691$	1025.93			1.48470			0.742350	−	0.670012i	$-0.233711\pi$
$691$	1025.93			1.48470			0.742350	+	0.670012i	$0.233711\pi$
$692$	310.193	−	310.193i	0.448256	−	0.448256i
$693$	56.7521	+	56.7521i	0.0818934	+	0.0818934i
$694$		−	779.832i		−	1.12368i
$695$	−53.1784	+	233.513i	−0.0765157	+	0.335990i
$696$	376.771			0.541338
$697$	−1283.94	+	1283.94i	−1.84210	+	1.84210i
$698$	−459.513	−	459.513i	−0.658329	−	0.658329i
$699$		−	1162.15i		−	1.66259i
$700$	−87.0618	−	248.035i	−0.124374	−	0.354336i
$701$	289.331			0.412740			0.206370	−	0.978474i	$-0.433835\pi$
$701$	289.331			0.412740			0.206370	+	0.978474i	$0.433835\pi$
$702$	−343.624	+	343.624i	−0.489493	+	0.489493i
$703$	747.601	+	747.601i	1.06344	+	1.06344i
$704$			45.3129i			0.0643649i
$705$	−1074.18	−	244.626i	−1.52366	−	0.346987i
$706$	80.9737			0.114694
$707$	−572.233	+	572.233i	−0.809382	+	0.809382i
$708$	157.446	+	157.446i	0.222381	+	0.222381i
$709$			741.084i			1.04525i	0.852562	+	0.522626i	$0.175048\pi$
$709$			741.084i			1.04525i	−0.852562	+	0.522626i	$0.824952\pi$
$710$	230.007	−	144.679i	0.323953	−	0.203773i
$711$	−88.3228			−0.124223
$712$	−261.270	+	261.270i	−0.366952	+	0.366952i
$713$	−135.554	−	135.554i	−0.190117	−	0.190117i
$714$			701.377i			0.982320i
$715$	240.317	+	382.050i	0.336107	+	0.534335i
$716$	−336.762			−0.470338
$717$	−767.140	+	767.140i	−1.06993	+	1.06993i
$718$	−433.495	−	433.495i	−0.603753	−	0.603753i
$719$		−	894.494i		−	1.24408i	−0.782985	−	0.622040i	$-0.786304\pi$
$719$		−	894.494i		−	1.24408i	0.782985	−	0.622040i	$-0.213696\pi$
$720$	−11.9693	+	52.5586i	−0.0166240	+	0.0729980i
$721$	95.0787			0.131871
$722$	104.846	−	104.846i	0.145216	−	0.145216i
$723$	73.7382	+	73.7382i	0.101989	+	0.101989i
$724$			486.480i			0.671933i
$725$	−421.662	+	877.772i	−0.581603	+	1.21072i
$726$	−430.039			−0.592341
$727$	−91.2326	+	91.2326i	−0.125492	+	0.125492i	−0.767063	−	0.641571i	$-0.778283\pi$
$727$	−91.2326	+	91.2326i	−0.125492	+	0.125492i	0.641571	+	0.767063i	$0.278283\pi$
$728$	−167.576	−	167.576i	−0.230186	−	0.230186i
$729$		−	399.511i		−	0.548026i
$730$	−143.648	−	32.7134i	−0.196779	−	0.0448129i
$731$	1386.92			1.89728
$732$	82.5986	−	82.5986i	0.112840	−	0.112840i
$733$	830.074	+	830.074i	1.13243	+	1.13243i	0.989771	+	0.142663i	$0.0455666\pi$
$733$	830.074	+	830.074i	1.13243	+	1.13243i	0.142663	+	0.989771i	$0.454433\pi$
$734$		−	47.4976i		−	0.0647106i
$735$	−309.155	+	194.464i	−0.420619	+	0.264577i
$736$	27.1293			0.0368605
$737$	−86.8138	+	86.8138i	−0.117793	+	0.117793i
$738$	−177.416	−	177.416i	−0.240401	−	0.240401i
$739$			980.834i			1.32725i	0.748067	+	0.663623i	$0.230982\pi$
$739$			980.834i			1.32725i	−0.748067	+	0.663623i	$0.769018\pi$
$740$	260.818	+	414.642i	0.352457	+	0.560327i
$741$	−1176.34			−1.58751
$742$	246.523	−	246.523i	0.332241	−	0.332241i
$743$	−752.792	−	752.792i	−1.01318	−	1.01318i	−0.999912	−	0.0132664i	$-0.995777\pi$
$743$	−752.792	−	752.792i	−1.01318	−	1.01318i	−0.0132664	−	0.999912i	$-0.504223\pi$
$744$			386.644i			0.519683i
$745$	−161.479	+	709.073i	−0.216750	+	0.951775i
$746$	−133.046			−0.178345
$747$	4.85137	−	4.85137i	0.00649446	−	0.00649446i
$748$	220.956	+	220.956i	0.295396	+	0.295396i
$749$			937.304i			1.25141i
$750$	−473.202	−	376.239i	−0.630936	−	0.501652i
$751$	−121.843			−0.162241			−0.0811207	−	0.996704i	$-0.525850\pi$
$751$	−121.843			−0.162241			−0.0811207	+	0.996704i	$0.525850\pi$
$752$	182.233	−	182.233i	0.242332	−	0.242332i
$753$	283.074	+	283.074i	0.375928	+	0.375928i
$754$			877.915i			1.16434i
$755$	713.929	+	162.585i	0.945602	+	0.215344i
$756$	226.713			0.299885
$757$	257.331	−	257.331i	0.339936	−	0.339936i	−0.516407	−	0.856343i	$-0.672731\pi$
$757$	257.331	−	257.331i	0.339936	−	0.339936i	0.856343	+	0.516407i	$0.172731\pi$
$758$	−323.563	−	323.563i	−0.426864	−	0.426864i
$759$		−	92.8965i		−	0.122393i
$760$	258.372	−	162.521i	0.339963	−	0.213843i
$761$	−232.530			−0.305558			−0.152779	−	0.988260i	$-0.548822\pi$
$761$	−232.530			−0.305558			−0.152779	+	0.988260i	$0.548822\pi$
$762$	−412.698	+	412.698i	−0.541598	+	0.541598i
$763$	−628.561	−	628.561i	−0.823802	−	0.823802i
$764$		−	80.7778i		−	0.105730i
$765$	197.923	+	314.653i	0.258723	+	0.411311i
$766$	599.714			0.782917
$767$	−366.865	+	366.865i	−0.478311	+	0.478311i
$768$	−38.6909	−	38.6909i	−0.0503788	−	0.0503788i
$769$			949.124i			1.23423i	0.786872	+	0.617116i	$0.211699\pi$
$769$			949.124i			1.23423i	−0.786872	+	0.617116i	$0.788301\pi$
$770$	46.7557	−	205.310i	0.0607217	−	0.266636i
$771$	−714.492			−0.926708
$772$	21.0501	−	21.0501i	0.0272670	−	0.0272670i
$773$	−502.010	−	502.010i	−0.649431	−	0.649431i	0.303425	−	0.952855i	$-0.401870\pi$
$773$	−502.010	−	502.010i	−0.649431	−	0.649431i	−0.952855	+	0.303425i	$0.901870\pi$
$774$			191.645i			0.247604i
$775$	−900.773	−	432.712i	−1.16229	−	0.558338i
$776$	187.257			0.241311
$777$	−622.767	+	622.767i	−0.801501	+	0.801501i
$778$	−64.2288	−	64.2288i	−0.0825563	−	0.0825563i
$779$			1420.76i			1.82383i
$780$	−531.415	−	121.020i	−0.681301	−	0.155154i
$781$	217.659			0.278693
$782$	132.289	−	132.289i	0.169168	−	0.169168i
$783$	−593.866	−	593.866i	−0.758450	−	0.758450i
$784$		−	85.4383i		−	0.108977i
$785$	−345.969	+	217.621i	−0.440724	+	0.277224i
$786$	−651.887			−0.829372
$787$	−846.737	+	846.737i	−1.07591	+	1.07591i	−0.0790333	+	0.996872i	$0.525183\pi$
$787$	−846.737	+	846.737i	−1.07591	+	1.07591i	−0.996872	+	0.0790333i	$0.974817\pi$
$788$	−413.159	−	413.159i	−0.524313	−	0.524313i
$789$			570.938i			0.723623i
$790$	123.378	+	196.144i	0.156175	+	0.248283i
$791$	−328.385			−0.415152
$792$	−30.5319	+	30.5319i	−0.0385504	+	0.0385504i
$793$	192.463	+	192.463i	0.242702	+	0.242702i
$794$			978.582i			1.23247i
$795$	178.034	−	781.770i	0.223943	−	0.983358i
$796$	107.741			0.135353
$797$	119.516	−	119.516i	0.149957	−	0.149957i	−0.628142	−	0.778099i	$-0.716184\pi$
$797$	119.516	−	119.516i	0.149957	−	0.149957i	0.778099	+	0.628142i	$0.216184\pi$
$798$	388.059	+	388.059i	0.486289	+	0.486289i
$799$		−	1777.23i		−	2.22431i
$800$	133.440	−	46.8382i	0.166800	−	0.0585477i
$801$	−352.089			−0.439562
$802$	615.748	−	615.748i	0.767765	−	0.767765i
$803$	−83.4472	−	83.4472i	−0.103919	−	0.103919i
$804$		−	148.254i		−	0.184395i
$805$	−122.921	−	27.9931i	−0.152697	−	0.0347741i
$806$	−900.920			−1.11777
$807$	−869.622	+	869.622i	−1.07760	+	1.07760i
$808$	−307.855	−	307.855i	−0.381008	−	0.381008i
$809$		−	305.296i		−	0.377374i	−0.982037	−	0.188687i	$-0.939577\pi$
$809$		−	305.296i		−	0.377374i	0.982037	−	0.188687i	$-0.0604232\pi$
$810$	586.527	−	368.937i	0.724108	−	0.455478i
$811$	−499.487			−0.615890			−0.307945	−	0.951404i	$-0.599641\pi$
$811$	−499.487			−0.615890			−0.307945	+	0.951404i	$0.599641\pi$
$812$	289.612	−	289.612i	0.356665	−	0.356665i
$813$	−859.779	−	859.779i	−1.05754	−	1.05754i
$814$			392.383i			0.482043i
$815$	352.846	+	560.946i	0.432940	+	0.688277i
$816$	−377.332			−0.462417
$817$	767.355	−	767.355i	0.939235	−	0.939235i
$818$	43.1536	+	43.1536i	0.0527551	+	0.0527551i
$819$		−	225.826i		−	0.275734i
$820$	−146.166	+	641.831i	−0.178251	+	0.782721i
$821$	202.465			0.246608			0.123304	−	0.992369i	$-0.460651\pi$
$821$	202.465			0.246608			0.123304	+	0.992369i	$0.460651\pi$
$822$	−151.480	+	151.480i	−0.184282	+	0.184282i
$823$	740.027	+	740.027i	0.899182	+	0.899182i	0.995364	−	0.0961816i	$-0.0306630\pi$
$823$	740.027	+	740.027i	0.899182	+	0.899182i	−0.0961816	+	0.995364i	$0.530663\pi$
$824$			51.1512i			0.0620767i
$825$	−160.384	−	456.926i	−0.194405	−	0.553850i
$826$	242.047			0.293035
$827$	544.959	−	544.959i	0.658959	−	0.658959i	−0.296175	−	0.955134i	$-0.595711\pi$
$827$	544.959	−	544.959i	0.658959	−	0.658959i	0.955134	+	0.296175i	$0.0957111\pi$
$828$	18.2798	+	18.2798i	0.0220771	+	0.0220771i
$829$		−	736.438i		−	0.888345i	−0.895941	−	0.444173i	$-0.853498\pi$
$829$		−	736.438i		−	0.888345i	0.895941	−	0.444173i	$-0.146502\pi$
$830$	−17.5506	−	3.99684i	−0.0211453	−	0.00481547i
$831$	884.911			1.06487
$832$	90.1537	−	90.1537i	0.108358	−	0.108358i
$833$	−416.617	−	416.617i	−0.500141	−	0.500141i
$834$		−	231.654i		−	0.277762i
$835$	471.212	−	296.401i	0.564325	−	0.354972i
$836$	244.502			0.292467
$837$	609.428	−	609.428i	0.728109	−	0.728109i
$838$	49.6628	+	49.6628i	0.0592635	+	0.0592635i
$839$			1022.72i			1.21897i	0.792797	+	0.609485i	$0.208624\pi$
$839$			1022.72i			1.21897i	−0.792797	+	0.609485i	$0.791376\pi$
$840$	135.383	+	215.229i	0.161171	+	0.256225i
$841$	−676.252			−0.804105
$842$	95.0400	−	95.0400i	0.112874	−	0.112874i
$843$	1041.68	+	1041.68i	1.23569	+	1.23569i
$844$		−	283.867i		−	0.336335i
$845$	94.3596	−	414.344i	0.111668	−	0.490348i
$846$	245.579			0.290282
$847$	−330.557	+	330.557i	−0.390268	+	0.390268i
$848$	132.626	+	132.626i	0.156399	+	0.156399i
$849$			849.304i			1.00036i
$850$	422.290	−	879.078i	0.496812	−	1.03421i
$851$	234.924			0.276057
$852$	−185.851	+	185.851i	−0.218135	+	0.218135i
$853$	393.306	+	393.306i	0.461085	+	0.461085i	0.899011	−	0.437926i	$-0.144287\pi$
$853$	393.306	+	393.306i	0.461085	+	0.461085i	−0.437926	+	0.899011i	$0.644287\pi$
$854$		−	126.982i		−	0.148690i
$855$	283.599	+	64.5847i	0.331695	+	0.0755376i
$856$	−504.259			−0.589087
$857$	−280.421	+	280.421i	−0.327213	+	0.327213i	−0.851526	−	0.524313i	$-0.824322\pi$
$857$	−280.421	+	280.421i	−0.327213	+	0.327213i	0.524313	+	0.851526i	$0.324322\pi$
$858$	−308.706	−	308.706i	−0.359797	−	0.359797i
$859$		−	777.697i		−	0.905351i	−0.891675	−	0.452676i	$-0.850470\pi$
$859$		−	777.697i		−	0.905351i	0.891675	−	0.452676i	$-0.149530\pi$
$860$	425.598	−	267.709i	0.494881	−	0.311290i
$861$	−1183.52			−1.37459
$862$	697.801	−	697.801i	0.809514	−	0.809514i
$863$	−641.227	−	641.227i	−0.743021	−	0.743021i	0.230137	−	0.973158i	$-0.426083\pi$
$863$	−641.227	−	641.227i	−0.743021	−	0.743021i	−0.973158	+	0.230137i	$0.926083\pi$
$864$			121.969i			0.141168i
$865$	−583.929	−	928.317i	−0.675063	−	1.07320i
$866$	−774.735			−0.894614
$867$	−1141.11	+	1141.11i	−1.31616	+	1.31616i
$868$	297.201	+	297.201i	0.342397	+	0.342397i
$869$			185.614i			0.213595i
$870$	209.153	−	918.414i	0.240405	−	1.05565i
$871$	345.447			0.396609
$872$	338.158	−	338.158i	0.387796	−	0.387796i
$873$	126.175	+	126.175i	0.144530	+	0.144530i
$874$		−	146.386i		−	0.167490i
$875$	−652.937	+	74.5323i	−0.746214	+	0.0851797i
$876$	142.505			0.162677
$877$	661.294	−	661.294i	0.754041	−	0.754041i	−0.221190	−	0.975231i	$-0.570994\pi$
$877$	661.294	−	661.294i	0.754041	−	0.754041i	0.975231	+	0.221190i	$0.0709941\pi$
$878$	186.351	+	186.351i	0.212245	+	0.212245i
$879$		−	1000.72i		−	1.13847i
$880$	110.454	+	25.1540i	0.125516	+	0.0285841i
$881$	486.151			0.551817			0.275909	−	0.961184i	$-0.411021\pi$
$881$	486.151			0.551817			0.275909	+	0.961184i	$0.411021\pi$
$882$	57.5686	−	57.5686i	0.0652705	−	0.0652705i
$883$	756.733	+	756.733i	0.857003	+	0.857003i	0.990984	−	0.133981i	$-0.0427761\pi$
$883$	756.733	+	756.733i	0.857003	+	0.857003i	−0.133981	+	0.990984i	$0.542776\pi$
$884$		−	879.222i		−	0.994595i
$885$	471.190	−	296.387i	0.532418	−	0.334901i
$886$	−688.783			−0.777407
$887$	545.935	−	545.935i	0.615485	−	0.615485i	−0.328885	−	0.944370i	$-0.606673\pi$
$887$	545.935	−	545.935i	0.615485	−	0.615485i	0.944370	+	0.328885i	$0.106673\pi$
$888$	−335.041	−	335.041i	−0.377298	−	0.377298i
$889$			634.454i			0.713672i
$890$	491.833	+	781.905i	0.552622	+	0.878545i
$891$	555.042			0.622942
$892$	195.295	−	195.295i	0.218940	−	0.218940i
$893$	−983.308	−	983.308i	−1.10113	−	1.10113i
$894$		−	703.427i		−	0.786831i
$895$	−186.943	+	820.888i	−0.208875	+	0.917194i
$896$	−59.4809			−0.0663849
$897$	−184.825	+	184.825i	−0.206048	+	0.206048i
$898$	−85.4403	−	85.4403i	−0.0951451	−	0.0951451i
$899$		−	1557.01i		−	1.73194i
$900$	121.472	+	58.3524i	0.134969	+	0.0648360i
$901$	1293.43			1.43555
$902$	−372.848	+	372.848i	−0.413357	+	0.413357i
$903$	639.222	+	639.222i	0.707887	+	0.707887i
$904$		−	176.667i		−	0.195428i
$905$	1185.84	+	270.054i	1.31032	+	0.298402i
$906$	−708.245			−0.781728
$907$	−591.187	+	591.187i	−0.651805	+	0.651805i	−0.953427	−	0.301623i	$-0.902472\pi$
$907$	−591.187	+	591.187i	−0.651805	+	0.651805i	0.301623	+	0.953427i	$0.402472\pi$
$908$	514.947	+	514.947i	0.567122	+	0.567122i
$909$		−	414.867i		−	0.456399i
$910$	−501.505	+	315.457i	−0.551105	+	0.346656i
$911$	−1015.60			−1.11482			−0.557409	−	0.830238i	$-0.688204\pi$
$911$	−1015.60			−1.11482			−0.557409	+	0.830238i	$0.688204\pi$
$912$	−208.771	+	208.771i	−0.228916	+	0.228916i
$913$	−10.1954	−	10.1954i	−0.0111669	−	0.0111669i
$914$			476.910i			0.521784i
$915$	−155.489	−	247.193i	−0.169934	−	0.270157i
$916$	−166.588			−0.181865
$917$	−501.084	+	501.084i	−0.546438	+	0.546438i
$918$	594.750	+	594.750i	0.647876	+	0.647876i
$919$			621.488i			0.676266i	0.941098	+	0.338133i	$0.109795\pi$
$919$			621.488i			0.676266i	−0.941098	+	0.338133i	$0.890205\pi$
$920$	15.0600	−	66.1302i	0.0163695	−	0.0718806i
$921$	1894.15			2.05662
$922$	−278.593	+	278.593i	−0.302161	+	0.302161i
$923$	−433.052	−	433.052i	−0.469178	−	0.469178i
$924$			203.675i			0.220428i
$925$	1155.51	−	405.592i	1.24920	−	0.438478i
$926$	−635.954			−0.686775
$927$	−34.4658	+	34.4658i	−0.0371800	+	0.0371800i
$928$	155.808	+	155.808i	0.167896	+	0.167896i
$929$			812.510i			0.874607i	0.899314	+	0.437304i	$0.144067\pi$
$929$			812.510i			0.874607i	−0.899314	+	0.437304i	$0.855933\pi$
$930$	942.480	+	214.633i	1.01342	+	0.230788i
$931$	−461.013			−0.495181
$932$	480.588	−	480.588i	0.515652	−	0.515652i
$933$	−518.603	−	518.603i	−0.555844	−	0.555844i
$934$			328.639i			0.351861i
$935$	661.258	−	415.944i	0.707228	−	0.444860i
$936$	121.492			0.129799
$937$	443.029	−	443.029i	0.472816	−	0.472816i	−0.430008	−	0.902825i	$-0.641489\pi$
$937$	443.029	−	443.029i	0.472816	−	0.472816i	0.902825	+	0.430008i	$0.141489\pi$
$938$	−113.958	−	113.958i	−0.121490	−	0.121490i
$939$			181.390i			0.193174i
$940$	−343.049	−	545.372i	−0.364946	−	0.580183i
$941$	−751.943			−0.799090			−0.399545	−	0.916714i	$-0.630832\pi$
$941$	−751.943			−0.799090			−0.399545	+	0.916714i	$0.630832\pi$
$942$	279.551	−	279.551i	0.296763	−	0.296763i
$943$	223.228	+	223.228i	0.236721	+	0.236721i
$944$			130.218i			0.137943i
$945$	125.853	−	552.634i	0.133177	−	0.584798i
$946$	402.751			0.425741
$947$	−1086.68	+	1086.68i	−1.14750	+	1.14750i	−0.160460	+	0.987042i	$0.551298\pi$
$947$	−1086.68	+	1086.68i	−1.14750	+	1.14750i	−0.987042	+	0.160460i	$0.948702\pi$
$948$	−158.489	−	158.489i	−0.167183	−	0.167183i
$949$			332.050i			0.349895i
$950$	−252.733	−	720.023i	−0.266034	−	0.757919i
$951$	679.255			0.714254
$952$	−290.043	+	290.043i	−0.304667	+	0.304667i
$953$	−58.8145	−	58.8145i	−0.0617151	−	0.0617151i	0.675576	−	0.737291i	$-0.263895\pi$
$953$	−58.8145	−	58.8145i	−0.0617151	−	0.0617151i	−0.737291	+	0.675576i	$0.763895\pi$
$954$			178.728i			0.187346i
$955$	−196.903	−	44.8412i	−0.206181	−	0.0469542i
$956$	−634.476			−0.663678
$957$	533.519	−	533.519i	0.557491	−	0.557491i
$958$	55.2512	+	55.2512i	0.0576735	+	0.0576735i
$959$			232.876i			0.242832i
$960$	−115.791	+	72.8346i	−0.120615	+	0.0758693i
$961$	636.810			0.662654
$962$	780.679	−	780.679i	0.811517	−	0.811517i
$963$	−339.771	−	339.771i	−0.352825	−	0.352825i
$964$			60.9865i			0.0632640i
$965$	−39.6262	−	62.9968i	−0.0410634	−	0.0652817i
$966$	121.943			0.126235
$967$	−280.533	+	280.533i	−0.290107	+	0.290107i	−0.837122	−	0.547016i	$-0.815764\pi$
$967$	−280.533	+	280.533i	−0.290107	+	0.290107i	0.547016	+	0.837122i	$0.315764\pi$
$968$	−177.836	−	177.836i	−0.183715	−	0.183715i
$969$			2036.03i			2.10117i
$970$	103.950	−	456.457i	0.107165	−	0.470574i
$971$	1572.33			1.61929			0.809644	−	0.586922i	$-0.199660\pi$
$971$	1572.33			1.61929			0.809644	+	0.586922i	$0.199660\pi$
$972$	−199.498	+	199.498i	−0.205245	+	0.205245i
$973$	−178.065	−	178.065i	−0.183006	−	0.183006i
$974$			707.958i			0.726857i
$975$	−589.996	+	1228.19i	−0.605124	+	1.25968i
$976$	68.3146			0.0699945
$977$	411.650	−	411.650i	0.421341	−	0.421341i	−0.464324	−	0.885665i	$-0.653703\pi$
$977$	411.650	−	411.650i	0.421341	−	0.421341i	0.885665	+	0.464324i	$0.153703\pi$
$978$	−453.258	−	453.258i	−0.463454	−	0.463454i
$979$			739.931i			0.755803i
$980$	−208.263	−	47.4283i	−0.212514	−	0.0483963i
$981$	455.704			0.464530
$982$	698.356	−	698.356i	0.711157	−	0.711157i
$983$	583.376	+	583.376i	0.593465	+	0.593465i	0.938566	−	0.345100i	$-0.112155\pi$
$983$	583.376	+	583.376i	0.593465	+	0.593465i	−0.345100	+	0.938566i	$0.612155\pi$
$984$		−	636.721i		−	0.647074i
$985$	−1236.46	+	777.759i	−1.25529	+	0.789603i
$986$	1519.51			1.54109
$987$	819.115	−	819.115i	0.829903	−	0.829903i
$988$	−486.458	−	486.458i	−0.492366	−	0.492366i
$989$		−	241.131i		−	0.243813i
$990$	57.4755	+	91.3732i	0.0580561	+	0.0922962i
$991$	−1102.34			−1.11235			−0.556174	−	0.831066i	$-0.687731\pi$
$991$	−1102.34			−1.11235			−0.556174	+	0.831066i	$0.687731\pi$
$992$	−159.890	+	159.890i	−0.161180	+	0.161180i
$993$	217.551	+	217.551i	0.219084	+	0.219084i
$994$			285.715i			0.287440i
$995$	59.8088	−	262.627i	0.0601093	−	0.263947i
$996$	17.4109			0.0174808
$997$	1326.04	−	1326.04i	1.33003	−	1.33003i	0.424696	−	0.905336i	$-0.360381\pi$
$997$	1326.04	−	1326.04i	1.33003	−	1.33003i	0.905336	−	0.424696i	$-0.139619\pi$
$998$	27.0217	+	27.0217i	0.0270759	+	0.0270759i
$999$			1056.18i			1.05724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.a.93.3	yes	20
5.2	odd	4	inner	230.3.f.a.47.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.a.47.3	✓	20	5.2	odd	4	inner
230.3.f.a.93.3	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-2.41818 - 2.41818i) q^{3} -2.00000i q^{4} +(-4.87518 - 1.11024i) q^{5} +4.83636 q^{6} +(3.71756 - 3.71756i) q^{7} +(2.00000 + 2.00000i) q^{8} +2.69521i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-2.41818 - 2.41818i) q^{3} -2.00000i q^{4} +(-4.87518 - 1.11024i) q^{5} +4.83636 q^{6} +(3.71756 - 3.71756i) q^{7} +(2.00000 + 2.00000i) q^{8} +2.69521i q^{9} +(5.98542 - 3.76494i) q^{10} +5.66411 q^{11} +(-4.83636 + 4.83636i) q^{12} +(-11.2692 - 11.2692i) q^{13} +7.43511i q^{14} +(9.10432 + 14.4738i) q^{15} -4.00000 q^{16} +(-19.5050 + 19.5050i) q^{17} +(-2.69521 - 2.69521i) q^{18} +21.5835i q^{19} +(-2.22047 + 9.75036i) q^{20} -17.9795 q^{21} +(-5.66411 + 5.66411i) q^{22} +(3.39116 + 3.39116i) q^{23} -9.67273i q^{24} +(22.5348 + 10.8252i) q^{25} +22.5384 q^{26} +(-15.2461 + 15.2461i) q^{27} +(-7.43511 - 7.43511i) q^{28} +38.9519i q^{29} +(-23.5781 - 5.36951i) q^{30} -39.9726 q^{31} +(4.00000 - 4.00000i) q^{32} +(-13.6968 - 13.6968i) q^{33} -39.0099i q^{34} +(-22.2511 + 13.9964i) q^{35} +5.39042 q^{36} +(34.6377 - 34.6377i) q^{37} +(-21.5835 - 21.5835i) q^{38} +54.5020i q^{39} +(-7.52989 - 11.9708i) q^{40} +65.8264 q^{41} +(17.9795 - 17.9795i) q^{42} +(-35.5529 - 35.5529i) q^{43} -11.3282i q^{44} +(2.99232 - 13.1396i) q^{45} -6.78233 q^{46} +(-45.5584 + 45.5584i) q^{47} +(9.67273 + 9.67273i) q^{48} +21.3596i q^{49} +(-33.3600 + 11.7095i) q^{50} +94.3331 q^{51} +(-22.5384 + 22.5384i) q^{52} +(-33.1565 - 33.1565i) q^{53} -30.4923i q^{54} +(-27.6135 - 6.28850i) q^{55} +14.8702 q^{56} +(52.1928 - 52.1928i) q^{57} +(-38.9519 - 38.9519i) q^{58} -32.5546i q^{59} +(28.9477 - 18.2086i) q^{60} -17.0786 q^{61} +(39.9726 - 39.9726i) q^{62} +(10.0196 + 10.0196i) q^{63} +8.00000i q^{64} +(42.4280 + 67.4510i) q^{65} +27.3937 q^{66} +(-15.3270 + 15.3270i) q^{67} +(39.0099 + 39.0099i) q^{68} -16.4009i q^{69} +(8.25473 - 36.2475i) q^{70} +38.4278 q^{71} +(-5.39042 + 5.39042i) q^{72} +(-14.7326 - 14.7326i) q^{73} +69.2754i q^{74} +(-28.3158 - 80.6704i) q^{75} +43.1669 q^{76} +(21.0566 - 21.0566i) q^{77} +(-54.5020 - 54.5020i) q^{78} +32.7703i q^{79} +(19.5007 + 4.44094i) q^{80} +97.9927 q^{81} +(-65.8264 + 65.8264i) q^{82} +(-1.79999 - 1.79999i) q^{83} +35.9589i q^{84} +(116.745 - 73.4350i) q^{85} +71.1058 q^{86} +(94.1928 - 94.1928i) q^{87} +(11.3282 + 11.3282i) q^{88} +130.635i q^{89} +(10.1473 + 16.1320i) q^{90} -83.7879 q^{91} +(6.78233 - 6.78233i) q^{92} +(96.6611 + 96.6611i) q^{93} -91.1167i q^{94} +(23.9627 - 105.223i) q^{95} -19.3455 q^{96} +(46.8143 - 46.8143i) q^{97} +(-21.3596 - 21.3596i) q^{98} +15.2660i 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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