LMFDB - Embedded newform 230.3.f.a.47.4

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			47.4
Root			$-0.454110 + 0.454110i$ of defining polynomial
Character	$\chi$	$=$	230.47
Dual form			230.3.f.a.93.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-0.454110 + 0.454110i) q^{3} +2.00000i q^{4} +(4.61282 - 1.92922i) q^{5} +0.908220 q^{6} +(-8.21299 - 8.21299i) q^{7} +(2.00000 - 2.00000i) q^{8} +8.58757i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.454110 + 0.454110i) q^{3} +2.00000i q^{4} +(4.61282 - 1.92922i) q^{5} +0.908220 q^{6} +(-8.21299 - 8.21299i) q^{7} +(2.00000 - 2.00000i) q^{8} +8.58757i q^{9} +(-6.54204 - 2.68360i) q^{10} -1.80844 q^{11} +(-0.908220 - 0.908220i) q^{12} +(12.1431 - 12.1431i) q^{13} +16.4260i q^{14} +(-1.21865 + 2.97081i) q^{15} -4.00000 q^{16} +(-13.2264 - 13.2264i) q^{17} +(8.58757 - 8.58757i) q^{18} -13.8065i q^{19} +(3.85844 + 9.22564i) q^{20} +7.45921 q^{21} +(1.80844 + 1.80844i) q^{22} +(-3.39116 + 3.39116i) q^{23} +1.81644i q^{24} +(17.5562 - 17.7983i) q^{25} -24.2862 q^{26} +(-7.98669 - 7.98669i) q^{27} +(16.4260 - 16.4260i) q^{28} -47.4104i q^{29} +(4.18945 - 1.75216i) q^{30} -56.5594 q^{31} +(4.00000 + 4.00000i) q^{32} +(0.821229 - 0.821229i) q^{33} +26.4528i q^{34} +(-53.7297 - 22.0404i) q^{35} -17.1751 q^{36} +(3.64057 + 3.64057i) q^{37} +(-13.8065 + 13.8065i) q^{38} +11.0286i q^{39} +(5.36720 - 13.0841i) q^{40} -8.30147 q^{41} +(-7.45921 - 7.45921i) q^{42} +(17.7220 - 17.7220i) q^{43} -3.61687i q^{44} +(16.5673 + 39.6129i) q^{45} +6.78233 q^{46} +(8.93900 + 8.93900i) q^{47} +(1.81644 - 1.81644i) q^{48} +85.9066i q^{49} +(-35.3545 + 0.242091i) q^{50} +12.0125 q^{51} +(24.2862 + 24.2862i) q^{52} +(24.9637 - 24.9637i) q^{53} +15.9734i q^{54} +(-8.34199 + 3.48888i) q^{55} -32.8520 q^{56} +(6.26965 + 6.26965i) q^{57} +(-47.4104 + 47.4104i) q^{58} +6.35948i q^{59} +(-5.94161 - 2.43730i) q^{60} +98.9683 q^{61} +(56.5594 + 56.5594i) q^{62} +(70.5297 - 70.5297i) q^{63} -8.00000i q^{64} +(32.5872 - 79.4406i) q^{65} -1.64246 q^{66} +(-16.0688 - 16.0688i) q^{67} +(26.4528 - 26.4528i) q^{68} -3.07992i q^{69} +(31.6894 + 75.7701i) q^{70} +110.405 q^{71} +(17.1751 + 17.1751i) q^{72} +(-72.6670 + 72.6670i) q^{73} -7.28114i q^{74} +(0.109936 + 16.0548i) q^{75} +27.6129 q^{76} +(14.8527 + 14.8527i) q^{77} +(11.0286 - 11.0286i) q^{78} +81.2609i q^{79} +(-18.4513 + 7.71689i) q^{80} -70.0344 q^{81} +(8.30147 + 8.30147i) q^{82} +(70.5250 - 70.5250i) q^{83} +14.9184i q^{84} +(-86.5276 - 35.4943i) q^{85} -35.4441 q^{86} +(21.5295 + 21.5295i) q^{87} +(-3.61687 + 3.61687i) q^{88} +131.148i q^{89} +(23.0456 - 56.1802i) q^{90} -199.462 q^{91} +(-6.78233 - 6.78233i) q^{92} +(25.6842 - 25.6842i) q^{93} -17.8780i q^{94} +(-26.6357 - 63.6867i) q^{95} -3.63288 q^{96} +(79.5123 + 79.5123i) q^{97} +(85.9066 - 85.9066i) q^{98} -15.5301i 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

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

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
$3$	−0.454110	+	0.454110i	−0.151370	+	0.151370i	−0.778730	−	0.627360i	$-0.784136\pi$
$3$	−0.454110	+	0.454110i	−0.151370	+	0.151370i	0.627360	+	0.778730i	$0.284136\pi$
$4$			2.00000i			0.500000i
$5$	4.61282	−	1.92922i	0.922564	−	0.385844i
$5$	4.61282	−	1.92922i	0.922564	−	0.385844i
$6$	0.908220			0.151370
$7$	−8.21299	−	8.21299i	−1.17328	−	1.17328i	−0.981422	−	0.191863i	$-0.938547\pi$
$7$	−8.21299	−	8.21299i	−1.17328	−	1.17328i	−0.191863	−	0.981422i	$-0.561453\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$			8.58757i			0.954174i
$10$	−6.54204	−	2.68360i	−0.654204	−	0.268360i
$11$	−1.80844			−0.164403			−0.0822017	−	0.996616i	$-0.526195\pi$
$11$	−1.80844			−0.164403			−0.0822017	+	0.996616i	$0.526195\pi$
$12$	−0.908220	−	0.908220i	−0.0756850	−	0.0756850i
$13$	12.1431	−	12.1431i	0.934084	−	0.934084i	−0.0638744	−	0.997958i	$-0.520346\pi$
$13$	12.1431	−	12.1431i	0.934084	−	0.934084i	0.997958	+	0.0638744i	$0.0203457\pi$
$14$			16.4260i			1.17328i
$15$	−1.21865	+	2.97081i	−0.0812432	+	0.198054i
$16$	−4.00000			−0.250000
$17$	−13.2264	−	13.2264i	−0.778023	−	0.778023i	0.201471	−	0.979494i	$-0.435428\pi$
$17$	−13.2264	−	13.2264i	−0.778023	−	0.778023i	−0.979494	+	0.201471i	$0.935428\pi$
$18$	8.58757	−	8.58757i	0.477087	−	0.477087i
$19$		−	13.8065i		−	0.726656i	−0.931661	−	0.363328i	$-0.881640\pi$
$19$		−	13.8065i		−	0.726656i	0.931661	−	0.363328i	$-0.118360\pi$
$20$	3.85844	+	9.22564i	0.192922	+	0.461282i
$21$	7.45921			0.355200
$22$	1.80844	+	1.80844i	0.0822017	+	0.0822017i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$24$			1.81644i			0.0756850i
$25$	17.5562	−	17.7983i	0.702248	−	0.711932i
$26$	−24.2862			−0.934084
$27$	−7.98669	−	7.98669i	−0.295803	−	0.295803i
$28$	16.4260	−	16.4260i	0.586642	−	0.586642i
$29$		−	47.4104i		−	1.63484i	−0.576042	−	0.817420i	$-0.695403\pi$
$29$		−	47.4104i		−	1.63484i	0.576042	−	0.817420i	$-0.304597\pi$
$30$	4.18945	−	1.75216i	0.139648	−	0.0584052i
$31$	−56.5594			−1.82450			−0.912248	−	0.409637i	$-0.865655\pi$
$31$	−56.5594			−1.82450			−0.912248	+	0.409637i	$0.865655\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	0.821229	−	0.821229i	0.0248857	−	0.0248857i
$34$			26.4528i			0.778023i
$35$	−53.7297	−	22.0404i	−1.53514	−	0.629725i
$36$	−17.1751			−0.477087
$37$	3.64057	+	3.64057i	0.0983938	+	0.0983938i	0.754590	−	0.656196i	$-0.227836\pi$
$37$	3.64057	+	3.64057i	0.0983938	+	0.0983938i	−0.656196	+	0.754590i	$0.727836\pi$
$38$	−13.8065	+	13.8065i	−0.363328	+	0.363328i
$39$			11.0286i			0.282784i
$40$	5.36720	−	13.0841i	0.134180	−	0.327102i
$41$	−8.30147			−0.202475			−0.101237	−	0.994862i	$-0.532280\pi$
$41$	−8.30147			−0.202475			−0.101237	+	0.994862i	$0.532280\pi$
$42$	−7.45921	−	7.45921i	−0.177600	−	0.177600i
$43$	17.7220	−	17.7220i	0.412140	−	0.412140i	−0.470343	−	0.882484i	$-0.655870\pi$
$43$	17.7220	−	17.7220i	0.412140	−	0.412140i	0.882484	+	0.470343i	$0.155870\pi$
$44$		−	3.61687i		−	0.0822017i
$45$	16.5673	+	39.6129i	0.368163	+	0.880287i
$46$	6.78233			0.147442
$47$	8.93900	+	8.93900i	0.190191	+	0.190191i	0.795779	−	0.605587i	$-0.207062\pi$
$47$	8.93900	+	8.93900i	0.190191	+	0.190191i	−0.605587	+	0.795779i	$0.707062\pi$
$48$	1.81644	−	1.81644i	0.0378425	−	0.0378425i
$49$			85.9066i			1.75320i
$50$	−35.3545	+	0.242091i	−0.707090	+	0.00484182i
$51$	12.0125			0.235539
$52$	24.2862	+	24.2862i	0.467042	+	0.467042i
$53$	24.9637	−	24.9637i	0.471014	−	0.471014i	−0.431229	−	0.902243i	$-0.641920\pi$
$53$	24.9637	−	24.9637i	0.471014	−	0.471014i	0.902243	+	0.431229i	$0.141920\pi$
$54$			15.9734i			0.295803i
$55$	−8.34199	+	3.48888i	−0.151673	+	0.0634341i
$56$	−32.8520			−0.586642
$57$	6.26965	+	6.26965i	0.109994	+	0.109994i
$58$	−47.4104	+	47.4104i	−0.817420	+	0.817420i
$59$			6.35948i			0.107788i	0.998547	+	0.0538939i	$0.0171633\pi$
$59$			6.35948i			0.107788i	−0.998547	+	0.0538939i	$0.982837\pi$
$60$	−5.94161	−	2.43730i	−0.0990269	−	0.0406216i
$61$	98.9683			1.62243			0.811215	−	0.584748i	$-0.198806\pi$
$61$	98.9683			1.62243			0.811215	+	0.584748i	$0.198806\pi$
$62$	56.5594	+	56.5594i	0.912248	+	0.912248i
$63$	70.5297	−	70.5297i	1.11952	−	1.11952i
$64$		−	8.00000i		−	0.125000i
$65$	32.5872	−	79.4406i	0.501341	−	1.22216i
$66$	−1.64246			−0.0248857
$67$	−16.0688	−	16.0688i	−0.239833	−	0.239833i	0.576948	−	0.816781i	$-0.304244\pi$
$67$	−16.0688	−	16.0688i	−0.239833	−	0.239833i	−0.816781	+	0.576948i	$0.804244\pi$
$68$	26.4528	−	26.4528i	0.389012	−	0.389012i
$69$		−	3.07992i		−	0.0446366i
$70$	31.6894	+	75.7701i	0.452705	+	1.08243i
$71$	110.405			1.55500			0.777499	−	0.628884i	$-0.216488\pi$
$71$	110.405			1.55500			0.777499	+	0.628884i	$0.216488\pi$
$72$	17.1751	+	17.1751i	0.238544	+	0.238544i
$73$	−72.6670	+	72.6670i	−0.995438	+	0.995438i	−0.999990	−	0.00455142i	$-0.998551\pi$
$73$	−72.6670	+	72.6670i	−0.995438	+	0.995438i	0.00455142	+	0.999990i	$0.498551\pi$
$74$		−	7.28114i		−	0.0983938i
$75$	0.109936	+	16.0548i	0.00146581	+	0.214064i
$76$	27.6129			0.363328
$77$	14.8527	+	14.8527i	0.192892	+	0.192892i
$78$	11.0286	−	11.0286i	0.141392	−	0.141392i
$79$			81.2609i			1.02862i	0.857605	+	0.514310i	$0.171952\pi$
$79$			81.2609i			1.02862i	−0.857605	+	0.514310i	$0.828048\pi$
$80$	−18.4513	+	7.71689i	−0.230641	+	0.0964611i
$81$	−70.0344			−0.864623
$82$	8.30147	+	8.30147i	0.101237	+	0.101237i
$83$	70.5250	−	70.5250i	0.849699	−	0.849699i	−0.140396	−	0.990095i	$-0.544838\pi$
$83$	70.5250	−	70.5250i	0.849699	−	0.849699i	0.990095	+	0.140396i	$0.0448376\pi$
$84$			14.9184i			0.177600i
$85$	−86.5276	−	35.4943i	−1.01797	−	0.417580i
$86$	−35.4441			−0.412140
$87$	21.5295	+	21.5295i	0.247466	+	0.247466i
$88$	−3.61687	+	3.61687i	−0.0411008	+	0.0411008i
$89$			131.148i			1.47358i	0.676124	+	0.736788i	$0.263658\pi$
$89$			131.148i			1.47358i	−0.676124	+	0.736788i	$0.736342\pi$
$90$	23.0456	−	56.1802i	0.256062	−	0.624225i
$91$	−199.462			−2.19189
$92$	−6.78233	−	6.78233i	−0.0737210	−	0.0737210i
$93$	25.6842	−	25.6842i	0.276174	−	0.276174i
$94$		−	17.8780i		−	0.190191i
$95$	−26.6357	−	63.6867i	−0.280376	−	0.670387i
$96$	−3.63288			−0.0378425
$97$	79.5123	+	79.5123i	0.819715	+	0.819715i	0.986066	−	0.166352i	$-0.0531987\pi$
$97$	79.5123	+	79.5123i	0.819715	+	0.819715i	−0.166352	+	0.986066i	$0.553199\pi$
$98$	85.9066	−	85.9066i	0.876598	−	0.876598i
$99$		−	15.5301i		−	0.156869i
$100$	35.5966	+	35.1124i	0.355966	+	0.351124i
$101$	106.466			1.05412			0.527060	−	0.849828i	$-0.323294\pi$
$101$	106.466			1.05412			0.527060	+	0.849828i	$0.323294\pi$
$102$	−12.0125	−	12.0125i	−0.117769	−	0.117769i
$103$	−4.25928	+	4.25928i	−0.0413523	+	0.0413523i	−0.727481	−	0.686128i	$-0.759309\pi$
$103$	−4.25928	+	4.25928i	−0.0413523	+	0.0413523i	0.686128	+	0.727481i	$0.259309\pi$
$104$		−	48.5723i		−	0.467042i
$105$	34.4080	−	14.3905i	0.327695	−	0.137052i
$106$	−49.9274			−0.471014
$107$	−22.3097	−	22.3097i	−0.208502	−	0.208502i	0.595129	−	0.803631i	$-0.297101\pi$
$107$	−22.3097	−	22.3097i	−0.208502	−	0.208502i	−0.803631	+	0.595129i	$0.797101\pi$
$108$	15.9734	−	15.9734i	0.147902	−	0.147902i
$109$			151.792i			1.39258i	0.717759	+	0.696292i	$0.245168\pi$
$109$			151.792i			1.39258i	−0.717759	+	0.696292i	$0.754832\pi$
$110$	11.8309	+	4.85312i	0.107553	+	0.0441193i
$111$	−3.30644			−0.0297877
$112$	32.8520	+	32.8520i	0.293321	+	0.293321i
$113$	35.4658	−	35.4658i	0.313857	−	0.313857i	−0.532545	−	0.846402i	$-0.678764\pi$
$113$	35.4658	−	35.4658i	0.313857	−	0.313857i	0.846402	+	0.532545i	$0.178764\pi$
$114$		−	12.5393i		−	0.109994i
$115$	−9.10052	+	22.1851i	−0.0791350	+	0.192914i
$116$	94.8207			0.817420
$117$	104.280	+	104.280i	0.891278	+	0.891278i
$118$	6.35948	−	6.35948i	0.0538939	−	0.0538939i
$119$			217.257i			1.82569i
$120$	3.50431	+	8.37891i	0.0292026	+	0.0698242i
$121$	−117.730			−0.972972
$122$	−98.9683	−	98.9683i	−0.811215	−	0.811215i
$123$	3.76978	−	3.76978i	0.0306486	−	0.0306486i
$124$		−	113.119i		−	0.912248i
$125$	46.6468	−	115.970i	0.373174	−	0.927761i
$126$	−141.059			−1.11952
$127$	−0.468171	−	0.468171i	−0.00368639	−	0.00368639i	0.705261	−	0.708948i	$-0.250830\pi$
$127$	−0.468171	−	0.468171i	−0.00368639	−	0.00368639i	−0.708948	+	0.705261i	$0.750830\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$			16.0955i			0.124771i
$130$	−112.028	+	46.8534i	−0.861752	+	0.360411i
$131$	−57.9083			−0.442048			−0.221024	−	0.975268i	$-0.570940\pi$
$131$	−57.9083			−0.442048			−0.221024	+	0.975268i	$0.570940\pi$
$132$	1.64246	+	1.64246i	0.0124429	+	0.0124429i
$133$	−113.392	+	113.392i	−0.852575	+	0.852575i
$134$			32.1376i			0.239833i
$135$	−52.2493	−	21.4331i	−0.387032	−	0.158763i
$136$	−52.9056			−0.389012
$137$	−90.9859	−	90.9859i	−0.664131	−	0.664131i	0.292220	−	0.956351i	$-0.405606\pi$
$137$	−90.9859	−	90.9859i	−0.664131	−	0.664131i	−0.956351	+	0.292220i	$0.905606\pi$
$138$	−3.07992	+	3.07992i	−0.0223183	+	0.0223183i
$139$			15.9583i			0.114808i	0.998351	+	0.0574041i	$0.0182824\pi$
$139$			15.9583i			0.114808i	−0.998351	+	0.0574041i	$0.981718\pi$
$140$	44.0808	−	107.459i	0.314863	−	0.767568i
$141$	−8.11858			−0.0575785
$142$	−110.405	−	110.405i	−0.777499	−	0.777499i
$143$	−21.9600	+	21.9600i	−0.153566	+	0.153566i
$144$		−	34.3503i		−	0.238544i
$145$	−91.4651	−	218.695i	−0.630794	−	1.50824i
$146$	145.334			0.995438
$147$	−39.0110	−	39.0110i	−0.265381	−	0.265381i
$148$	−7.28114	+	7.28114i	−0.0491969	+	0.0491969i
$149$		−	273.895i		−	1.83822i	−0.394003	−	0.919109i	$-0.628910\pi$
$149$		−	273.895i		−	1.83822i	0.394003	−	0.919109i	$-0.371090\pi$
$150$	15.9449	−	16.1648i	0.106299	−	0.107765i
$151$	−67.1415			−0.444646			−0.222323	−	0.974973i	$-0.571364\pi$
$151$	−67.1415			−0.444646			−0.222323	+	0.974973i	$0.571364\pi$
$152$	−27.6129	−	27.6129i	−0.181664	−	0.181664i
$153$	113.583	−	113.583i	0.742370	−	0.742370i
$154$		−	29.7054i		−	0.192892i
$155$	−260.898	+	109.116i	−1.68322	+	0.703972i
$156$	−22.0572			−0.141392
$157$	20.7386	+	20.7386i	0.132093	+	0.132093i	0.770062	−	0.637969i	$-0.220225\pi$
$157$	20.7386	+	20.7386i	0.132093	+	0.132093i	−0.637969	+	0.770062i	$0.720225\pi$
$158$	81.2609	−	81.2609i	0.514310	−	0.514310i
$159$			22.6725i			0.142595i
$160$	26.1682	+	10.7344i	0.163551	+	0.0670900i
$161$	55.7032			0.345983
$162$	70.0344	+	70.0344i	0.432311	+	0.432311i
$163$	−5.13555	+	5.13555i	−0.0315064	+	0.0315064i	−0.722685	−	0.691178i	$-0.757092\pi$
$163$	−5.13555	+	5.13555i	−0.0315064	+	0.0315064i	0.691178	+	0.722685i	$0.257092\pi$
$164$		−	16.6029i		−	0.101237i
$165$	2.20385	−	5.37252i	0.0133567	−	0.0325607i
$166$	−141.050			−0.849699
$167$	−4.29668	−	4.29668i	−0.0257286	−	0.0257286i	0.694125	−	0.719854i	$-0.255791\pi$
$167$	−4.29668	−	4.29668i	−0.0257286	−	0.0257286i	−0.719854	+	0.694125i	$0.755791\pi$
$168$	14.9184	−	14.9184i	0.0888001	−	0.0888001i
$169$		−	125.909i		−	0.745024i
$170$	51.0333	+	122.022i	0.300196	+	0.717776i
$171$	118.564			0.693357
$172$	35.4441	+	35.4441i	0.206070	+	0.206070i
$173$	−59.7225	+	59.7225i	−0.345217	+	0.345217i	−0.858324	−	0.513107i	$-0.828494\pi$
$173$	−59.7225	+	59.7225i	−0.345217	+	0.345217i	0.513107	+	0.858324i	$0.328494\pi$
$174$		−	43.0590i		−	0.247466i
$175$	−290.366	+	1.98829i	−1.65924	+	0.0113617i
$176$	7.23375			0.0411008
$177$	−2.88790	−	2.88790i	−0.0163158	−	0.0163158i
$178$	131.148	−	131.148i	0.736788	−	0.736788i
$179$		−	186.219i		−	1.04033i	−0.854065	−	0.520166i	$-0.825870\pi$
$179$		−	186.219i		−	1.04033i	0.854065	−	0.520166i	$-0.174130\pi$
$180$	−79.2258	+	33.1346i	−0.440143	+	0.184081i
$181$	243.615			1.34594			0.672970	−	0.739670i	$-0.265018\pi$
$181$	243.615			1.34594			0.672970	+	0.739670i	$0.265018\pi$
$182$	199.462	+	199.462i	1.09595	+	1.09595i
$183$	−44.9425	+	44.9425i	−0.245587	+	0.245587i
$184$			13.5647i			0.0737210i
$185$	23.8168	+	9.76983i	0.128739	+	0.0528099i
$186$	−51.3684			−0.276174
$187$	23.9191	+	23.9191i	0.127910	+	0.127910i
$188$	−17.8780	+	17.8780i	−0.0950957	+	0.0950957i
$189$			131.189i			0.694123i
$190$	−37.0510	+	90.3225i	−0.195005	+	0.475381i
$191$	325.057			1.70187			0.850935	−	0.525271i	$-0.176036\pi$
$191$	325.057			1.70187			0.850935	+	0.525271i	$0.176036\pi$
$192$	3.63288	+	3.63288i	0.0189212	+	0.0189212i
$193$	189.666	−	189.666i	0.982725	−	0.982725i	−0.0171285	−	0.999853i	$-0.505452\pi$
$193$	189.666	−	189.666i	0.982725	−	0.982725i	0.999853	+	0.0171285i	$0.00545243\pi$
$194$		−	159.025i		−	0.819715i
$195$	21.2766	+	50.8729i	0.109111	+	0.260887i
$196$	−171.813			−0.876598
$197$	29.6698	+	29.6698i	0.150608	+	0.150608i	0.778390	−	0.627781i	$-0.216037\pi$
$197$	29.6698	+	29.6698i	0.150608	+	0.150608i	−0.627781	+	0.778390i	$0.716037\pi$
$198$	−15.5301	+	15.5301i	−0.0784347	+	0.0784347i
$199$		−	71.7477i		−	0.360541i	−0.983617	−	0.180271i	$-0.942303\pi$
$199$		−	71.7477i		−	0.360541i	0.983617	−	0.180271i	$-0.0576974\pi$
$200$	−0.484182	−	70.7090i	−0.00242091	−	0.353545i
$201$	14.5940			0.0726071
$202$	−106.466	−	106.466i	−0.527060	−	0.527060i
$203$	−389.381	+	389.381i	−1.91813	+	1.91813i
$204$			24.0250i			0.117769i
$205$	−38.2932	+	16.0154i	−0.186796	+	0.0781238i
$206$	8.51856			0.0413523
$207$	−29.1219	−	29.1219i	−0.140685	−	0.140685i
$208$	−48.5723	+	48.5723i	−0.233521	+	0.233521i
$209$			24.9681i			0.119465i
$210$	−48.7984	−	20.0175i	−0.232373	−	0.0953215i
$211$	193.990			0.919385			0.459693	−	0.888078i	$-0.347960\pi$
$211$	193.990			0.919385			0.459693	+	0.888078i	$0.347960\pi$
$212$	49.9274	+	49.9274i	0.235507	+	0.235507i
$213$	−50.1360	+	50.1360i	−0.235380	+	0.235380i
$214$			44.6194i			0.208502i
$215$	47.5588	−	115.938i	0.221204	−	0.539248i
$216$	−31.9468			−0.147902
$217$	464.522	+	464.522i	2.14065	+	2.14065i
$218$	151.792	−	151.792i	0.696292	−	0.696292i
$219$		−	65.9976i		−	0.301359i
$220$	−6.97775	−	16.6840i	−0.0317171	−	0.0758363i
$221$	−321.219			−1.45348
$222$	3.30644	+	3.30644i	0.0148939	+	0.0148939i
$223$	−141.481	+	141.481i	−0.634445	+	0.634445i	−0.949180	−	0.314735i	$-0.898084\pi$
$223$	−141.481	+	141.481i	−0.634445	+	0.634445i	0.314735	+	0.949180i	$0.398084\pi$
$224$		−	65.7040i		−	0.293321i
$225$	152.844	+	150.765i	0.679307	+	0.670067i
$226$	−70.9316			−0.313857
$227$	−299.127	−	299.127i	−1.31774	−	1.31774i	−0.915561	−	0.402179i	$-0.868253\pi$
$227$	−299.127	−	299.127i	−1.31774	−	1.31774i	−0.402179	−	0.915561i	$-0.631747\pi$
$228$	−12.5393	+	12.5393i	−0.0549970	+	0.0549970i
$229$		−	30.5265i		−	0.133304i	−0.997776	−	0.0666518i	$-0.978768\pi$
$229$		−	30.5265i		−	0.133304i	0.997776	−	0.0666518i	$-0.0212317\pi$
$230$	31.2857	−	13.0846i	0.136025	−	0.0568896i
$231$	−13.4895			−0.0583961
$232$	−94.8207	−	94.8207i	−0.408710	−	0.408710i
$233$	−52.7346	+	52.7346i	−0.226329	+	0.226329i	−0.811157	−	0.584828i	$-0.801162\pi$
$233$	−52.7346	+	52.7346i	−0.226329	+	0.226329i	0.584828	+	0.811157i	$0.301162\pi$
$234$		−	208.559i		−	0.891278i
$235$	58.4793	+	23.9887i	0.248848	+	0.102079i
$236$	−12.7190			−0.0538939
$237$	−36.9014	−	36.9014i	−0.155702	−	0.155702i
$238$	217.257	−	217.257i	0.912843	−	0.912843i
$239$			128.388i			0.537190i	0.963253	+	0.268595i	$0.0865593\pi$
$239$			128.388i			0.537190i	−0.963253	+	0.268595i	$0.913441\pi$
$240$	4.87459	−	11.8832i	0.0203108	−	0.0495134i
$241$	148.698			0.617006			0.308503	−	0.951223i	$-0.400172\pi$
$241$	148.698			0.617006			0.308503	+	0.951223i	$0.400172\pi$
$242$	117.730	+	117.730i	0.486486	+	0.486486i
$243$	103.684	−	103.684i	0.426681	−	0.426681i
$244$			197.937i			0.811215i
$245$	165.733	+	396.271i	0.676460	+	1.61743i
$246$	−7.53956			−0.0306486
$247$	−167.653	−	167.653i	−0.678757	−	0.678757i
$248$	−113.119	+	113.119i	−0.456124	+	0.456124i
$249$			64.0522i			0.257238i
$250$	−162.617	+	69.3234i	−0.650468	+	0.277294i
$251$	410.299			1.63466			0.817329	−	0.576172i	$-0.195454\pi$
$251$	410.299			1.63466			0.817329	+	0.576172i	$0.195454\pi$
$252$	141.059	+	141.059i	0.559759	+	0.559759i
$253$	6.13271	−	6.13271i	0.0242400	−	0.0242400i
$254$			0.936342i			0.00368639i
$255$	55.4114	−	23.1747i	0.217300	−	0.0908813i
$256$	16.0000			0.0625000
$257$	−222.112	−	222.112i	−0.864250	−	0.864250i	0.127578	−	0.991829i	$-0.459280\pi$
$257$	−222.112	−	222.112i	−0.864250	−	0.864250i	−0.991829	+	0.127578i	$0.959280\pi$
$258$	16.0955	−	16.0955i	0.0623857	−	0.0623857i
$259$		−	59.8000i		−	0.230888i
$260$	158.881	+	65.1743i	0.611081	+	0.250670i
$261$	407.140			1.55992
$262$	57.9083	+	57.9083i	0.221024	+	0.221024i
$263$	191.483	−	191.483i	0.728071	−	0.728071i	−0.242165	−	0.970235i	$-0.577857\pi$
$263$	191.483	−	191.483i	0.728071	−	0.728071i	0.970235	+	0.242165i	$0.0778574\pi$
$264$		−	3.28492i		−	0.0124429i
$265$	66.9926	−	163.314i	0.252802	−	0.616278i
$266$	226.785			0.852575
$267$	−59.5557	−	59.5557i	−0.223055	−	0.223055i
$268$	32.1376	−	32.1376i	0.119917	−	0.119917i
$269$			448.520i			1.66736i	0.552249	+	0.833679i	$0.313770\pi$
$269$			448.520i			1.66736i	−0.552249	+	0.833679i	$0.686230\pi$
$270$	30.8162	+	73.6823i	0.114134	+	0.272897i
$271$	−355.709			−1.31258			−0.656289	−	0.754509i	$-0.727875\pi$
$271$	−355.709			−1.31258			−0.656289	+	0.754509i	$0.727875\pi$
$272$	52.9056	+	52.9056i	0.194506	+	0.194506i
$273$	90.5778	−	90.5778i	0.331787	−	0.331787i
$274$			181.972i			0.664131i
$275$	−31.7493	+	32.1871i	−0.115452	+	0.117044i
$276$	6.15985			0.0223183
$277$	−74.7381	−	74.7381i	−0.269813	−	0.269813i	0.559212	−	0.829025i	$-0.311104\pi$
$277$	−74.7381	−	74.7381i	−0.269813	−	0.269813i	−0.829025	+	0.559212i	$0.811104\pi$
$278$	15.9583	−	15.9583i	0.0574041	−	0.0574041i
$279$		−	485.708i		−	1.74089i
$280$	−151.540	+	63.3787i	−0.541215	+	0.226353i
$281$	−29.5344			−0.105105			−0.0525523	−	0.998618i	$-0.516736\pi$
$281$	−29.5344			−0.105105			−0.0525523	+	0.998618i	$0.516736\pi$
$282$	8.11858	+	8.11858i	0.0287893	+	0.0287893i
$283$	−337.330	+	337.330i	−1.19198	+	1.19198i	−0.215466	+	0.976511i	$0.569127\pi$
$283$	−337.330	+	337.330i	−1.19198	+	1.19198i	−0.976511	+	0.215466i	$0.930873\pi$
$284$			220.810i			0.777499i
$285$	41.0163	+	16.8252i	0.143917	+	0.0590359i
$286$	43.9200			0.153566
$287$	68.1800	+	68.1800i	0.237561	+	0.237561i
$288$	−34.3503	+	34.3503i	−0.119272	+	0.119272i
$289$			60.8752i			0.210641i
$290$	−127.230	+	310.161i	−0.438725	+	1.06952i
$291$	−72.2147			−0.248160
$292$	−145.334	−	145.334i	−0.497719	−	0.497719i
$293$	−0.725430	+	0.725430i	−0.00247587	+	0.00247587i	−0.708344	−	0.705868i	$-0.750557\pi$
$293$	−0.725430	+	0.725430i	−0.00247587	+	0.00247587i	0.705868	+	0.708344i	$0.250557\pi$
$294$			78.0220i			0.265381i
$295$	12.2688	+	29.3351i	0.0415893	+	0.0994412i
$296$	14.5623			0.0491969
$297$	14.4434	+	14.4434i	0.0486311	+	0.0486311i
$298$	−273.895	+	273.895i	−0.919109	+	0.919109i
$299$			82.3584i			0.275446i
$300$	−32.1097	+	0.219872i	−0.107032	+	0.000732907i
$301$	−291.102			−0.967116
$302$	67.1415	+	67.1415i	0.222323	+	0.222323i
$303$	−48.3473	+	48.3473i	−0.159562	+	0.159562i
$304$			55.2259i			0.181664i
$305$	456.523	−	190.932i	1.49680	−	0.626006i
$306$	−227.165			−0.742370
$307$	312.017	+	312.017i	1.01634	+	1.01634i	0.999864	+	0.0164770i	$0.00524503\pi$
$307$	312.017	+	312.017i	1.01634	+	1.01634i	0.0164770	+	0.999864i	$0.494755\pi$
$308$	−29.7054	+	29.7054i	−0.0964460	+	0.0964460i
$309$		−	3.86836i		−	0.0125190i
$310$	370.014	+	151.783i	1.19359	+	0.489622i
$311$	−442.383			−1.42245			−0.711227	−	0.702962i	$-0.751860\pi$
$311$	−442.383			−1.42245			−0.711227	+	0.702962i	$0.751860\pi$
$312$	22.0572	+	22.0572i	0.0706961	+	0.0706961i
$313$	−345.560	+	345.560i	−1.10403	+	1.10403i	−0.110107	+	0.993920i	$0.535119\pi$
$313$	−345.560	+	345.560i	−1.10403	+	1.10403i	−0.993920	+	0.110107i	$0.964881\pi$
$314$		−	41.4772i		−	0.132093i
$315$	189.273	−	461.408i	0.600867	−	1.46479i
$316$	−162.522			−0.514310
$317$	−446.526	−	446.526i	−1.40860	−	1.40860i	−0.767238	−	0.641363i	$-0.778369\pi$
$317$	−446.526	−	446.526i	−1.40860	−	1.40860i	−0.641363	−	0.767238i	$-0.721631\pi$
$318$	22.6725	−	22.6725i	0.0712973	−	0.0712973i
$319$			85.7387i			0.268773i
$320$	−15.4338	−	36.9026i	−0.0482305	−	0.115320i
$321$	20.2621			0.0631219
$322$	−55.7032	−	55.7032i	−0.172991	−	0.172991i
$323$	−182.610	+	182.610i	−0.565355	+	0.565355i
$324$		−	140.069i		−	0.432311i
$325$	−2.93973	−	429.313i	−0.00904533	−	1.32096i
$326$	10.2711			0.0315064
$327$	−68.9301	−	68.9301i	−0.210795	−	0.210795i
$328$	−16.6029	+	16.6029i	−0.0506187	+	0.0506187i
$329$		−	146.832i		−	0.446297i
$330$	−7.57637	+	3.16867i	−0.0229587	+	0.00960202i
$331$	541.509			1.63598			0.817989	−	0.575234i	$-0.195089\pi$
$331$	541.509			1.63598			0.817989	+	0.575234i	$0.195089\pi$
$332$	141.050	+	141.050i	0.424850	+	0.424850i
$333$	−31.2637	+	31.2637i	−0.0938848	+	0.0938848i
$334$			8.59336i			0.0257286i
$335$	−105.123	−	43.1223i	−0.313800	−	0.128723i
$336$	−29.8368			−0.0888001
$337$	50.2998	+	50.2998i	0.149258	+	0.149258i	0.777786	−	0.628529i	$-0.216343\pi$
$337$	50.2998	+	50.2998i	0.149258	+	0.149258i	−0.628529	+	0.777786i	$0.716343\pi$
$338$	−125.909	+	125.909i	−0.372512	+	0.372512i
$339$			32.2107i			0.0950169i
$340$	70.9887	−	173.055i	0.208790	−	0.508986i
$341$	102.284			0.299953
$342$	−118.564	−	118.564i	−0.346678	−	0.346678i
$343$	303.113	−	303.113i	0.883712	−	0.883712i
$344$		−	70.8881i		−	0.206070i
$345$	−5.94185	−	14.2071i	−0.0172228	−	0.0411801i
$346$	119.445			0.345217
$347$	286.439	+	286.439i	0.825472	+	0.825472i	0.986887	−	0.161414i	$-0.0516056\pi$
$347$	286.439	+	286.439i	0.825472	+	0.825472i	−0.161414	+	0.986887i	$0.551606\pi$
$348$	−43.0590	+	43.0590i	−0.123733	+	0.123733i
$349$			240.906i			0.690275i	0.938552	+	0.345137i	$0.112168\pi$
$349$			240.906i			0.690275i	−0.938552	+	0.345137i	$0.887832\pi$
$350$	292.355	+	288.378i	0.835299	+	0.823937i
$351$	−193.966			−0.552610
$352$	−7.23375	−	7.23375i	−0.0205504	−	0.0205504i
$353$	189.988	−	189.988i	0.538209	−	0.538209i	−0.384794	−	0.923003i	$-0.625727\pi$
$353$	189.988	−	189.988i	0.538209	−	0.538209i	0.923003	+	0.384794i	$0.125727\pi$
$354$			5.77581i			0.0163158i
$355$	509.278	−	212.995i	1.43459	−	0.599987i
$356$	−262.297			−0.736788
$357$	−98.6584	−	98.6584i	−0.276354	−	0.276354i
$358$	−186.219	+	186.219i	−0.520166	+	0.520166i
$359$		−	467.461i		−	1.30212i	−0.759026	−	0.651060i	$-0.774324\pi$
$359$		−	467.461i		−	1.30212i	0.759026	−	0.651060i	$-0.225676\pi$
$360$	112.360	+	46.0912i	0.312112	+	0.128031i
$361$	170.382			0.471971
$362$	−243.615	−	243.615i	−0.672970	−	0.672970i
$363$	53.4622	−	53.4622i	0.147279	−	0.147279i
$364$		−	398.924i		−	1.09595i
$365$	−195.009	+	475.390i	−0.534271	+	1.30244i
$366$	89.8850			0.245587
$367$	396.041	+	396.041i	1.07913	+	1.07913i	0.996587	+	0.0825436i	$0.0263044\pi$
$367$	396.041	+	396.041i	1.07913	+	1.07913i	0.0825436	+	0.996587i	$0.473696\pi$
$368$	13.5647	−	13.5647i	0.0368605	−	0.0368605i
$369$		−	71.2895i		−	0.193196i
$370$	−14.0469	−	33.5866i	−0.0379647	−	0.0907746i
$371$	−410.054			−1.10527
$372$	51.3684	+	51.3684i	0.138087	+	0.138087i
$373$	−61.2680	+	61.2680i	−0.164257	+	0.164257i	−0.784450	−	0.620192i	$-0.787055\pi$
$373$	−61.2680	+	61.2680i	−0.164257	+	0.164257i	0.620192	+	0.784450i	$0.287055\pi$
$374$		−	47.8382i		−	0.127910i
$375$	31.4804	+	73.8460i	0.0839479	+	0.196923i
$376$	35.7560			0.0950957
$377$	−575.708	−	575.708i	−1.52708	−	1.52708i
$378$	131.189	−	131.189i	0.347062	−	0.347062i
$379$		−	2.27599i		−	0.00600525i	−0.999995	−	0.00300262i	$-0.999044\pi$
$379$		−	2.27599i		−	0.00600525i	0.999995	−	0.00300262i	$-0.000955767\pi$
$380$	127.373	−	53.2715i	0.335193	−	0.140188i
$381$	0.425202			0.00111602
$382$	−325.057	−	325.057i	−0.850935	−	0.850935i
$383$	455.092	−	455.092i	1.18823	−	1.18823i	0.210673	−	0.977557i	$-0.432435\pi$
$383$	455.092	−	455.092i	1.18823	−	1.18823i	0.977557	−	0.210673i	$-0.0675655\pi$
$384$		−	7.26576i		−	0.0189212i
$385$	97.1669	+	39.8586i	0.252381	+	0.103529i
$386$	−379.332			−0.982725
$387$	152.189	+	152.189i	0.393254	+	0.393254i
$388$	−159.025	+	159.025i	−0.409857	+	0.409857i
$389$		−	94.4517i		−	0.242806i	−0.992603	−	0.121403i	$-0.961261\pi$
$389$		−	94.4517i		−	0.242806i	0.992603	−	0.121403i	$-0.0387394\pi$
$390$	29.5963	−	72.1495i	0.0758880	−	0.184999i
$391$	89.7058			0.229427
$392$	171.813	+	171.813i	0.438299	+	0.438299i
$393$	26.2967	−	26.2967i	0.0669128	−	0.0669128i
$394$		−	59.3397i		−	0.150608i
$395$	156.770	+	374.842i	0.396887	+	0.948967i
$396$	31.0602			0.0784347
$397$	−166.649	−	166.649i	−0.419771	−	0.419771i	0.465354	−	0.885125i	$-0.345927\pi$
$397$	−166.649	−	166.649i	−0.419771	−	0.419771i	−0.885125	+	0.465354i	$0.845927\pi$
$398$	−71.7477	+	71.7477i	−0.180271	+	0.180271i
$399$		−	102.985i		−	0.258108i
$400$	−70.2248	+	71.1932i	−0.175562	+	0.177983i
$401$	−56.3098			−0.140424			−0.0702118	−	0.997532i	$-0.522368\pi$
$401$	−56.3098			−0.140424			−0.0702118	+	0.997532i	$0.522368\pi$
$402$	−14.5940	−	14.5940i	−0.0363035	−	0.0363035i
$403$	−686.806	+	686.806i	−1.70423	+	1.70423i
$404$			212.932i			0.527060i
$405$	−323.056	+	135.112i	−0.797670	+	0.333610i
$406$	778.762			1.91813
$407$	−6.58374	−	6.58374i	−0.0161763	−	0.0161763i
$408$	24.0250	−	24.0250i	0.0588847	−	0.0588847i
$409$		−	617.869i		−	1.51068i	−0.655331	−	0.755342i	$-0.727471\pi$
$409$		−	617.869i		−	1.51068i	0.655331	−	0.755342i	$-0.272529\pi$
$410$	54.3086	+	22.2778i	0.132460	+	0.0543361i
$411$	82.6352			0.201059
$412$	−8.51856	−	8.51856i	−0.0206761	−	0.0206761i
$413$	52.2304	−	52.2304i	0.126466	−	0.126466i
$414$			58.2437i			0.140685i
$415$	189.261	−	461.378i	0.456050	−	1.11175i
$416$	97.1447			0.233521
$417$	−7.24684	−	7.24684i	−0.0173785	−	0.0173785i
$418$	24.9681	−	24.9681i	0.0597324	−	0.0597324i
$419$		−	327.397i		−	0.781377i	−0.920523	−	0.390688i	$-0.872237\pi$
$419$		−	327.397i		−	0.781377i	0.920523	−	0.390688i	$-0.127763\pi$
$420$	28.7809	+	68.8159i	0.0685260	+	0.163847i
$421$	271.135			0.644026			0.322013	−	0.946735i	$-0.395641\pi$
$421$	271.135			0.644026			0.322013	+	0.946735i	$0.395641\pi$
$422$	−193.990	−	193.990i	−0.459693	−	0.459693i
$423$	−76.7642	+	76.7642i	−0.181476	+	0.181476i
$424$		−	99.8549i		−	0.235507i
$425$	−467.613	+	3.20199i	−1.10027	+	0.00753410i
$426$	100.272			0.235380
$427$	−812.826	−	812.826i	−1.90357	−	1.90357i
$428$	44.6194	−	44.6194i	0.104251	−	0.104251i
$429$		−	19.9445i		−	0.0464907i
$430$	−163.497	+	68.3795i	−0.380226	+	0.159022i
$431$	148.281			0.344039			0.172019	−	0.985094i	$-0.444971\pi$
$431$	148.281			0.344039			0.172019	+	0.985094i	$0.444971\pi$
$432$	31.9468	+	31.9468i	0.0739508	+	0.0739508i
$433$	437.637	−	437.637i	1.01071	−	1.01071i	0.0107659	−	0.999942i	$-0.496573\pi$
$433$	437.637	−	437.637i	1.01071	−	1.01071i	0.999942	−	0.0107659i	$-0.00342697\pi$
$434$		−	929.044i		−	2.14065i
$435$	140.847	+	57.7766i	0.323786	+	0.132820i
$436$	−303.583			−0.696292
$437$	46.8200	+	46.8200i	0.107140	+	0.107140i
$438$	−65.9976	+	65.9976i	−0.150679	+	0.150679i
$439$			387.950i			0.883712i	0.897086	+	0.441856i	$0.145680\pi$
$439$			387.950i			0.883712i	−0.897086	+	0.441856i	$0.854320\pi$
$440$	−9.70624	+	23.6617i	−0.0220596	+	0.0537767i
$441$	−737.728			−1.67285
$442$	321.219	+	321.219i	0.726739	+	0.726739i
$443$	33.5070	−	33.5070i	0.0756366	−	0.0756366i	−0.668276	−	0.743913i	$-0.732968\pi$
$443$	33.5070	−	33.5070i	0.0756366	−	0.0756366i	0.743913	+	0.668276i	$0.232968\pi$
$444$		−	6.61288i		−	0.0148939i
$445$	253.014	+	604.963i	0.568571	+	1.35947i
$446$	282.962			0.634445
$447$	124.378	+	124.378i	0.278251	+	0.278251i
$448$	−65.7040	+	65.7040i	−0.146661	+	0.146661i
$449$			90.3725i			0.201275i	0.994923	+	0.100638i	$0.0320883\pi$
$449$			90.3725i			0.201275i	−0.994923	+	0.100638i	$0.967912\pi$
$450$	−2.07897	−	303.609i	−0.00461994	−	0.674687i
$451$	15.0127			0.0332876
$452$	70.9316	+	70.9316i	0.156928	+	0.156928i
$453$	30.4896	−	30.4896i	0.0673060	−	0.0673060i
$454$			598.254i			1.31774i
$455$	−920.083	+	384.807i	−2.02216	+	0.845729i
$456$	25.0786			0.0549970
$457$	−432.641	−	432.641i	−0.946698	−	0.946698i	0.0519513	−	0.998650i	$-0.483456\pi$
$457$	−432.641	−	432.641i	−0.946698	−	0.946698i	−0.998650	+	0.0519513i	$0.983456\pi$
$458$	−30.5265	+	30.5265i	−0.0666518	+	0.0666518i
$459$			211.270i			0.460284i
$460$	−44.3703	−	18.2010i	−0.0964571	−	0.0395675i
$461$	477.708			1.03624			0.518121	−	0.855307i	$-0.326632\pi$
$461$	477.708			1.03624			0.518121	+	0.855307i	$0.326632\pi$
$462$	13.4895	+	13.4895i	0.0291981	+	0.0291981i
$463$	−509.566	+	509.566i	−1.10058	+	1.10058i	−0.106234	+	0.994341i	$0.533879\pi$
$463$	−509.566	+	509.566i	−1.10058	+	1.10058i	−0.994341	+	0.106234i	$0.966121\pi$
$464$			189.641i			0.408710i
$465$	68.9260	−	168.027i	0.148228	−	0.361348i
$466$	105.469			0.226329
$467$	508.548	+	508.548i	1.08897	+	1.08897i	0.995635	+	0.0933331i	$0.0297522\pi$
$467$	508.548	+	508.548i	1.08897	+	1.08897i	0.0933331	+	0.995635i	$0.470248\pi$
$468$	−208.559	+	208.559i	−0.445639	+	0.445639i
$469$			263.946i			0.562785i
$470$	−34.4906	−	82.4680i	−0.0733843	−	0.175464i
$471$	−18.8352			−0.0399898
$472$	12.7190	+	12.7190i	0.0269470	+	0.0269470i
$473$	−32.0492	+	32.0492i	−0.0677573	+	0.0677573i
$474$			73.8028i			0.155702i
$475$	−245.732	−	242.389i	−0.517330	−	0.510293i
$476$	−434.513			−0.912843
$477$	214.378	+	214.378i	0.449429	+	0.449429i
$478$	128.388	−	128.388i	0.268595	−	0.268595i
$479$			213.247i			0.445192i	0.974911	+	0.222596i	$0.0714531\pi$
$479$			213.247i			0.445192i	−0.974911	+	0.222596i	$0.928547\pi$
$480$	−16.7578	+	7.00863i	−0.0349121	+	0.0146013i
$481$	88.4155			0.183816
$482$	−148.698	−	148.698i	−0.308503	−	0.308503i
$483$	−25.2954	+	25.2954i	−0.0523714	+	0.0523714i
$484$		−	235.459i		−	0.486486i
$485$	520.173	+	213.379i	1.07252	+	0.439957i
$486$	−207.367			−0.426681
$487$	−444.728	−	444.728i	−0.913198	−	0.913198i	0.0833241	−	0.996523i	$-0.473446\pi$
$487$	−444.728	−	444.728i	−0.913198	−	0.913198i	−0.996523	+	0.0833241i	$0.973446\pi$
$488$	197.937	−	197.937i	0.405608	−	0.405608i
$489$		−	4.66421i		−	0.00953826i
$490$	230.539	−	562.004i	0.470487	−	1.14695i
$491$	488.473			0.994854			0.497427	−	0.867506i	$-0.334278\pi$
$491$	488.473			0.994854			0.497427	+	0.867506i	$0.334278\pi$
$492$	7.53956	+	7.53956i	0.0153243	+	0.0153243i
$493$	−627.068	+	627.068i	−1.27194	+	1.27194i
$494$			335.306i			0.678757i
$495$	−29.9610	−	71.6374i	−0.0605272	−	0.144722i
$496$	226.238			0.456124
$497$	−906.755	−	906.755i	−1.82446	−	1.82446i
$498$	64.0522	−	64.0522i	0.128619	−	0.128619i
$499$		−	727.731i		−	1.45838i	−0.684312	−	0.729189i	$-0.739897\pi$
$499$		−	727.731i		−	1.45838i	0.684312	−	0.729189i	$-0.260103\pi$
$500$	231.940	+	93.2935i	0.463881	+	0.186587i
$501$	3.90233			0.00778909
$502$	−410.299	−	410.299i	−0.817329	−	0.817329i
$503$	146.384	−	146.384i	0.291021	−	0.291021i	−0.546463	−	0.837484i	$-0.684026\pi$
$503$	146.384	−	146.384i	0.291021	−	0.291021i	0.837484	+	0.546463i	$0.184026\pi$
$504$		−	282.119i		−	0.559759i
$505$	491.109	−	205.397i	0.972493	−	0.406726i
$506$	−12.2654			−0.0242400
$507$	57.1766	+	57.1766i	0.112774	+	0.112774i
$508$	0.936342	−	0.936342i	0.00184319	−	0.00184319i
$509$			629.870i			1.23747i	0.785601	+	0.618733i	$0.212354\pi$
$509$			629.870i			1.23747i	−0.785601	+	0.618733i	$0.787646\pi$
$510$	−78.5861	−	32.2367i	−0.154090	−	0.0632091i
$511$	1193.63			2.33587
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−110.268	+	110.268i	−0.214947	+	0.214947i
$514$			444.225i			0.864250i
$515$	−11.4302	+	27.8644i	−0.0221946	+	0.0541056i
$516$	−32.1910			−0.0623857
$517$	−16.1656	−	16.1656i	−0.0312681	−	0.0312681i
$518$	−59.8000	+	59.8000i	−0.115444	+	0.115444i
$519$		−	54.2412i		−	0.104511i
$520$	−93.7068	−	224.055i	−0.180205	−	0.430876i
$521$	−299.772			−0.575379			−0.287690	−	0.957724i	$-0.592887\pi$
$521$	−299.772			−0.575379			−0.287690	+	0.957724i	$0.592887\pi$
$522$	−407.140	−	407.140i	−0.779961	−	0.779961i
$523$	189.039	−	189.039i	0.361451	−	0.361451i	−0.502896	−	0.864347i	$-0.667732\pi$
$523$	189.039	−	189.039i	0.361451	−	0.361451i	0.864347	+	0.502896i	$0.167732\pi$
$524$		−	115.817i		−	0.221024i
$525$	130.955	−	132.761i	0.249439	−	0.252878i
$526$	−382.965			−0.728071
$527$	748.077	+	748.077i	1.41950	+	1.41950i
$528$	−3.28492	+	3.28492i	−0.00622143	+	0.00622143i
$529$		−	23.0000i		−	0.0434783i
$530$	−230.306	+	96.3211i	−0.434540	+	0.181738i
$531$	−54.6125			−0.102848
$532$	−226.785	−	226.785i	−0.426287	−	0.426287i
$533$	−100.806	+	100.806i	−0.189129	+	0.189129i
$534$			119.111i			0.223055i
$535$	−145.951	−	59.8703i	−0.272806	−	0.111907i
$536$	−64.2753			−0.119917
$537$	84.5641	+	84.5641i	0.157475	+	0.157475i
$538$	448.520	−	448.520i	0.833679	−	0.833679i
$539$		−	155.357i		−	0.288231i
$540$	42.8661	−	104.499i	0.0793817	−	0.193516i
$541$	−428.185			−0.791470			−0.395735	−	0.918365i	$-0.629510\pi$
$541$	−428.185			−0.791470			−0.395735	+	0.918365i	$0.629510\pi$
$542$	355.709	+	355.709i	0.656289	+	0.656289i
$543$	−110.628	+	110.628i	−0.203735	+	0.203735i
$544$		−	105.811i		−	0.194506i
$545$	292.840	+	700.187i	0.537320	+	1.28475i
$546$	−181.156			−0.331787
$547$	402.240	+	402.240i	0.735356	+	0.735356i	0.971676	−	0.236319i	$-0.0759411\pi$
$547$	402.240	+	402.240i	0.735356	+	0.735356i	−0.236319	+	0.971676i	$0.575941\pi$
$548$	181.972	−	181.972i	0.332065	−	0.332065i
$549$			849.897i			1.54808i
$550$	63.9364	−	0.437807i	0.116248	−	0.000796012i
$551$	−654.570			−1.18797
$552$	−6.15985	−	6.15985i	−0.0111591	−	0.0111591i
$553$	667.395	−	667.395i	1.20686	−	1.20686i
$554$			149.476i			0.269813i
$555$	−15.2520	+	6.37885i	−0.0274811	+	0.0114934i
$556$	−31.9167			−0.0574041
$557$	−133.006	−	133.006i	−0.238789	−	0.238789i	0.577560	−	0.816349i	$-0.304005\pi$
$557$	−133.006	−	133.006i	−0.238789	−	0.238789i	−0.816349	+	0.577560i	$0.804005\pi$
$558$	−485.708	+	485.708i	−0.870444	+	0.870444i
$559$		−	430.400i		−	0.769947i
$560$	214.919	+	88.1615i	0.383784	+	0.157431i
$561$	−21.7238			−0.0387234
$562$	29.5344	+	29.5344i	0.0525523	+	0.0525523i
$563$	−490.785	+	490.785i	−0.871733	+	0.871733i	−0.992661	−	0.120929i	$-0.961413\pi$
$563$	−490.785	+	490.785i	−0.871733	+	0.871733i	0.120929	+	0.992661i	$0.461413\pi$
$564$		−	16.2372i		−	0.0287893i
$565$	95.1760	−	232.019i	0.168453	−	0.410653i
$566$	674.659			1.19198
$567$	575.192	+	575.192i	1.01445	+	1.01445i
$568$	220.810	−	220.810i	0.388750	−	0.388750i
$569$		−	258.800i		−	0.454834i	−0.973798	−	0.227417i	$-0.926972\pi$
$569$		−	258.800i		−	0.454834i	0.973798	−	0.227417i	$-0.0730280\pi$
$570$	−24.1911	−	57.8416i	−0.0424405	−	0.101476i
$571$	−122.892			−0.215223			−0.107612	−	0.994193i	$-0.534320\pi$
$571$	−122.892			−0.215223			−0.107612	+	0.994193i	$0.534320\pi$
$572$	−43.9200	−	43.9200i	−0.0767832	−	0.0767832i
$573$	−147.612	+	147.612i	−0.257612	+	0.257612i
$574$		−	136.360i		−	0.237561i
$575$	0.820971	+	119.893i	0.00142778	+	0.208510i
$576$	68.7005			0.119272
$577$	−86.1991	−	86.1991i	−0.149392	−	0.149392i	0.628454	−	0.777846i	$-0.283688\pi$
$577$	−86.1991	−	86.1991i	−0.149392	−	0.149392i	−0.777846	+	0.628454i	$0.783688\pi$
$578$	60.8752	−	60.8752i	0.105320	−	0.105320i
$579$			172.258i			0.297510i
$580$	437.391	−	182.930i	0.754122	−	0.315397i
$581$	−1158.44			−1.99388
$582$	72.2147	+	72.2147i	0.124080	+	0.124080i
$583$	−45.1453	+	45.1453i	−0.0774362	+	0.0774362i
$584$			290.668i			0.497719i
$585$	682.201	+	279.844i	1.16616	+	0.478367i
$586$	1.45086			0.00247587
$587$	41.7886	+	41.7886i	0.0711901	+	0.0711901i	0.741805	−	0.670615i	$-0.233970\pi$
$587$	41.7886	+	41.7886i	0.0711901	+	0.0711901i	−0.670615	+	0.741805i	$0.733970\pi$
$588$	78.0220	−	78.0220i	0.132691	−	0.132691i
$589$			780.885i			1.32578i
$590$	17.0663	−	41.6040i	0.0289259	−	0.0705152i
$591$	−26.9467			−0.0455952
$592$	−14.5623	−	14.5623i	−0.0245985	−	0.0245985i
$593$	0.797812	−	0.797812i	0.00134538	−	0.00134538i	−0.706434	−	0.707779i	$-0.749697\pi$
$593$	0.797812	−	0.797812i	0.00134538	−	0.00134538i	0.707779	+	0.706434i	$0.249697\pi$
$594$		−	28.8869i		−	0.0486311i
$595$	419.136	+	1002.17i	0.704431	+	1.68431i
$596$	547.789			0.919109
$597$	32.5814	+	32.5814i	0.0545752	+	0.0545752i
$598$	82.3584	−	82.3584i	0.137723	−	0.137723i
$599$			547.221i			0.913558i	0.889580	+	0.456779i	$0.150997\pi$
$599$			547.221i			0.913558i	−0.889580	+	0.456779i	$0.849003\pi$
$600$	32.3295	+	31.8898i	0.0538826	+	0.0531497i
$601$	−798.410			−1.32847			−0.664235	−	0.747524i	$-0.731243\pi$
$601$	−798.410			−1.32847			−0.664235	+	0.747524i	$0.731243\pi$
$602$	291.102	+	291.102i	0.483558	+	0.483558i
$603$	137.992	−	137.992i	0.228843	−	0.228843i
$604$		−	134.283i		−	0.222323i
$605$	−543.065	+	227.126i	−0.897628	+	0.375416i
$606$	96.6947			0.159562
$607$	431.327	+	431.327i	0.710588	+	0.710588i	0.966658	−	0.256070i	$-0.0824279\pi$
$607$	431.327	+	431.327i	0.710588	+	0.710588i	−0.256070	+	0.966658i	$0.582428\pi$
$608$	55.2259	−	55.2259i	0.0908320	−	0.0908320i
$609$		−	353.644i		−	0.580696i
$610$	−647.454	−	265.591i	−1.06140	−	0.435395i
$611$	217.094			0.355309
$612$	227.165	+	227.165i	0.371185	+	0.371185i
$613$	−538.393	+	538.393i	−0.878293	+	0.878293i	−0.993358	−	0.115065i	$-0.963292\pi$
$613$	−538.393	+	538.393i	−0.878293	+	0.878293i	0.115065	+	0.993358i	$0.463292\pi$
$614$		−	624.034i		−	1.01634i
$615$	10.1166	−	24.6621i	0.0164497	−	0.0401009i
$616$	59.4107			0.0964460
$617$	535.160	+	535.160i	0.867358	+	0.867358i	0.992179	−	0.124821i	$-0.0398358\pi$
$617$	535.160	+	535.160i	0.867358	+	0.867358i	−0.124821	+	0.992179i	$0.539836\pi$
$618$	−3.86836	+	3.86836i	−0.00625949	+	0.00625949i
$619$		−	103.368i		−	0.166991i	−0.996508	−	0.0834957i	$-0.973392\pi$
$619$		−	103.368i		−	0.166991i	0.996508	−	0.0834957i	$-0.0266085\pi$
$620$	−218.231	−	521.797i	−0.351986	−	0.841608i
$621$	54.1684			0.0872276
$622$	442.383	+	442.383i	0.711227	+	0.711227i
$623$	1077.12	−	1077.12i	1.72892	−	1.72892i
$624$		−	44.1144i		−	0.0706961i
$625$	−8.55901	−	624.941i	−0.0136944	−	0.999906i
$626$	691.121			1.10403
$627$	−11.3383	−	11.3383i	−0.0180834	−	0.0180834i
$628$	−41.4772	+	41.4772i	−0.0660465	+	0.0660465i
$629$		−	96.3033i		−	0.153105i
$630$	−650.681	+	272.135i	−1.03283	+	0.431960i
$631$	914.802			1.44977			0.724883	−	0.688872i	$-0.241894\pi$
$631$	914.802			1.44977			0.724883	+	0.688872i	$0.241894\pi$
$632$	162.522	+	162.522i	0.257155	+	0.257155i
$633$	−88.0929	+	88.0929i	−0.139167	+	0.139167i
$634$			893.053i			1.40860i
$635$	−3.06279	−	1.25638i	−0.00482330	−	0.00197856i
$636$	−45.3451			−0.0712973
$637$	1043.17	+	1043.17i	1.63763	+	1.63763i
$638$	85.7387	−	85.7387i	0.134387	−	0.134387i
$639$			948.110i			1.48374i
$640$	−21.4688	+	52.3363i	−0.0335450	+	0.0817755i
$641$	629.609			0.982230			0.491115	−	0.871095i	$-0.336590\pi$
$641$	629.609			0.982230			0.491115	+	0.871095i	$0.336590\pi$
$642$	−20.2621	−	20.2621i	−0.0315610	−	0.0315610i
$643$	469.588	−	469.588i	0.730307	−	0.730307i	−0.240373	−	0.970681i	$-0.577270\pi$
$643$	469.588	−	469.588i	0.730307	−	0.730307i	0.970681	+	0.240373i	$0.0772698\pi$
$644$			111.406i			0.172991i
$645$	31.0518	+	74.2457i	0.0481423	+	0.115110i
$646$	365.220			0.565355
$647$	−102.877	−	102.877i	−0.159007	−	0.159007i	0.623120	−	0.782126i	$-0.285865\pi$
$647$	−102.877	−	102.877i	−0.159007	−	0.159007i	−0.782126	+	0.623120i	$0.785865\pi$
$648$	−140.069	+	140.069i	−0.216156	+	0.216156i
$649$		−	11.5007i		−	0.0177207i
$650$	−426.373	+	432.253i	−0.655959	+	0.665004i
$651$	−421.888			−0.648062
$652$	−10.2711	−	10.2711i	−0.0157532	−	0.0157532i
$653$	108.889	−	108.889i	0.166752	−	0.166752i	−0.618798	−	0.785550i	$-0.712380\pi$
$653$	108.889	−	108.889i	0.166752	−	0.166752i	0.785550	+	0.618798i	$0.212380\pi$
$654$			137.860i			0.210795i
$655$	−267.120	+	111.718i	−0.407817	+	0.170562i
$656$	33.2059			0.0506187
$657$	−624.033	−	624.033i	−0.949822	−	0.949822i
$658$	−146.832	+	146.832i	−0.223149	+	0.223149i
$659$		−	534.158i		−	0.810558i	−0.914193	−	0.405279i	$-0.867174\pi$
$659$		−	534.158i		−	0.810558i	0.914193	−	0.405279i	$-0.132826\pi$
$660$	10.7450	+	4.40770i	0.0162804	+	0.00667833i
$661$	−596.050			−0.901740			−0.450870	−	0.892590i	$-0.648886\pi$
$661$	−596.050			−0.901740			−0.450870	+	0.892590i	$0.648886\pi$
$662$	−541.509	−	541.509i	−0.817989	−	0.817989i
$663$	145.869	−	145.869i	0.220013	−	0.220013i
$664$		−	282.100i		−	0.424850i
$665$	−304.300	+	741.818i	−0.457594	+	1.11552i
$666$	62.5273			0.0938848
$667$	160.776	+	160.776i	0.241044	+	0.241044i
$668$	8.59336	−	8.59336i	0.0128643	−	0.0128643i
$669$		−	128.496i		−	0.192072i
$670$	62.0006	+	148.245i	0.0925382	+	0.221261i
$671$	−178.978			−0.266733
$672$	29.8368	+	29.8368i	0.0444000	+	0.0444000i
$673$	159.122	−	159.122i	0.236437	−	0.236437i	−0.578936	−	0.815373i	$-0.696532\pi$
$673$	159.122	−	159.122i	0.236437	−	0.236437i	0.815373	+	0.578936i	$0.196532\pi$
$674$		−	100.600i		−	0.149258i
$675$	−282.366	+	1.93351i	−0.418319	+	0.00286445i
$676$	251.818			0.372512
$677$	−209.613	−	209.613i	−0.309621	−	0.309621i	0.535142	−	0.844762i	$-0.320258\pi$
$677$	−209.613	−	209.613i	−0.309621	−	0.309621i	−0.844762	+	0.535142i	$0.820258\pi$
$678$	32.2107	−	32.2107i	0.0475085	−	0.0475085i
$679$		−	1306.07i		−	1.92352i
$680$	−244.044	+	102.067i	−0.358888	+	0.150098i
$681$	271.673			0.398933
$682$	−102.284	−	102.284i	−0.149977	−	0.149977i
$683$	17.8410	−	17.8410i	0.0261215	−	0.0261215i	−0.693925	−	0.720047i	$-0.744120\pi$
$683$	17.8410	−	17.8410i	0.0261215	−	0.0261215i	0.720047	+	0.693925i	$0.244120\pi$
$684$			237.128i			0.346678i
$685$	−595.234	−	244.170i	−0.868954	−	0.356452i
$686$	−606.227			−0.883712
$687$	13.8624	+	13.8624i	0.0201782	+	0.0201782i
$688$	−70.8881	+	70.8881i	−0.103035	+	0.103035i
$689$		−	606.273i		−	0.879932i
$690$	−8.26528	+	20.1490i	−0.0119787	+	0.0292014i
$691$	1004.98			1.45438			0.727190	−	0.686436i	$-0.240826\pi$
$691$	1004.98			1.45438			0.727190	+	0.686436i	$0.240826\pi$
$692$	−119.445	−	119.445i	−0.172608	−	0.172608i
$693$	−127.548	+	127.548i	−0.184053	+	0.184053i
$694$		−	572.878i		−	0.825472i
$695$	30.7872	+	73.6130i	0.0442981	+	0.105918i
$696$	86.1181			0.123733
$697$	109.799	+	109.799i	0.157530	+	0.157530i
$698$	240.906	−	240.906i	0.345137	−	0.345137i
$699$		−	47.8946i		−	0.0685188i
$700$	−3.97659	−	580.733i	−0.00568084	−	0.829618i
$701$	−243.834			−0.347838			−0.173919	−	0.984760i	$-0.555643\pi$
$701$	−243.834			−0.347838			−0.173919	+	0.984760i	$0.555643\pi$
$702$	193.966	+	193.966i	0.276305	+	0.276305i
$703$	50.2634	−	50.2634i	0.0714985	−	0.0714985i
$704$			14.4675i			0.0205504i
$705$	−37.4495	+	15.6625i	−0.0531199	+	0.0222164i
$706$	−379.976			−0.538209
$707$	−874.406	−	874.406i	−1.23678	−	1.23678i
$708$	5.77581	−	5.77581i	0.00815792	−	0.00815792i
$709$		−	57.7605i		−	0.0814675i	−0.999170	−	0.0407338i	$-0.987030\pi$
$709$		−	57.7605i		−	0.0814675i	0.999170	−	0.0407338i	$-0.0129695\pi$
$710$	−722.273	−	296.282i	−1.01729	−	0.417299i
$711$	−697.834			−0.981482
$712$	262.297	+	262.297i	0.368394	+	0.368394i
$713$	191.802	−	191.802i	0.269007	−	0.269007i
$714$			197.317i			0.276354i
$715$	−58.9318	+	143.663i	−0.0824221	+	0.200928i
$716$	372.439			0.520166
$717$	−58.3024	−	58.3024i	−0.0813144	−	0.0813144i
$718$	−467.461	+	467.461i	−0.651060	+	0.651060i
$719$		−	24.2148i		−	0.0336784i	−0.999858	−	0.0168392i	$-0.994640\pi$
$719$		−	24.2148i		−	0.0336784i	0.999858	−	0.0168392i	$-0.00536033\pi$
$720$	−66.2693	−	158.452i	−0.0920407	−	0.220072i
$721$	69.9629			0.0970359
$722$	−170.382	−	170.382i	−0.235985	−	0.235985i
$723$	−67.5255	+	67.5255i	−0.0933962	+	0.0933962i
$724$			487.230i			0.672970i
$725$	−843.824	−	832.346i	−1.16390	−	1.14806i
$726$	−106.924			−0.147279
$727$	554.026	+	554.026i	0.762072	+	0.762072i	0.976697	−	0.214625i	$-0.0688529\pi$
$727$	554.026	+	554.026i	0.762072	+	0.762072i	−0.214625	+	0.976697i	$0.568853\pi$
$728$	−398.924	+	398.924i	−0.547973	+	0.547973i
$729$		−	536.143i		−	0.735449i
$730$	670.399	−	280.381i	0.918355	−	0.384084i
$731$	−468.797			−0.641310
$732$	−89.8850	−	89.8850i	−0.122794	−	0.122794i
$733$	259.853	−	259.853i	0.354507	−	0.354507i	−0.507277	−	0.861783i	$-0.669348\pi$
$733$	259.853	−	259.853i	0.354507	−	0.354507i	0.861783	+	0.507277i	$0.169348\pi$
$734$		−	792.082i		−	1.07913i
$735$	−255.212	−	104.690i	−0.347227	−	0.142435i
$736$	−27.1293			−0.0368605
$737$	29.0594	+	29.0594i	0.0394294	+	0.0394294i
$738$	−71.2895	+	71.2895i	−0.0965982	+	0.0965982i
$739$		−	1082.77i		−	1.46518i	−0.680668	−	0.732592i	$-0.738310\pi$
$739$		−	1082.77i		−	1.46518i	0.680668	−	0.732592i	$-0.261690\pi$
$740$	−19.5397	+	47.6335i	−0.0264049	+	0.0643696i
$741$	152.266			0.205487
$742$	410.054	+	410.054i	0.552633	+	0.552633i
$743$	−477.140	+	477.140i	−0.642181	+	0.642181i	−0.951091	−	0.308910i	$-0.900036\pi$
$743$	−477.140	+	477.140i	−0.642181	+	0.642181i	0.308910	+	0.951091i	$0.400036\pi$
$744$		−	102.737i		−	0.138087i
$745$	−528.403	−	1263.43i	−0.709266	−	1.69587i
$746$	122.536			0.164257
$747$	605.639	+	605.639i	0.810761	+	0.810761i
$748$	−47.8382	+	47.8382i	−0.0639548	+	0.0639548i
$749$			366.459i			0.489265i
$750$	42.3655	−	105.326i	0.0564874	−	0.140435i
$751$	904.489			1.20438			0.602190	−	0.798353i	$-0.294295\pi$
$751$	904.489			1.20438			0.602190	+	0.798353i	$0.294295\pi$
$752$	−35.7560	−	35.7560i	−0.0475479	−	0.0475479i
$753$	−186.321	+	186.321i	−0.247438	+	0.247438i
$754$			1151.42i			1.52708i
$755$	−309.712	+	129.531i	−0.410214	+	0.171564i
$756$	−262.379			−0.347062
$757$	290.718	+	290.718i	0.384040	+	0.384040i	0.872555	−	0.488515i	$-0.162461\pi$
$757$	290.718	+	290.718i	0.384040	+	0.384040i	−0.488515	+	0.872555i	$0.662461\pi$
$758$	−2.27599	+	2.27599i	−0.00300262	+	0.00300262i
$759$			5.56985i			0.00733840i
$760$	−180.645	−	74.1020i	−0.237691	−	0.0975026i
$761$	−492.010			−0.646531			−0.323266	−	0.946308i	$-0.604781\pi$
$761$	−492.010			−0.646531			−0.323266	+	0.946308i	$0.604781\pi$
$762$	−0.425202	−	0.425202i	−0.000558008	−	0.000558008i
$763$	1246.66	−	1246.66i	1.63390	−	1.63390i
$764$			650.114i			0.850935i
$765$	304.810	−	743.062i	0.398445	−	0.971323i
$766$	−910.184			−1.18823
$767$	77.2237	+	77.2237i	0.100683	+	0.100683i
$768$	−7.26576	+	7.26576i	−0.00946062	+	0.00946062i
$769$			1181.65i			1.53661i	0.640086	+	0.768304i	$0.278899\pi$
$769$			1181.65i			1.53661i	−0.640086	+	0.768304i	$0.721101\pi$
$770$	−57.3082	−	137.026i	−0.0744263	−	0.177955i
$771$	201.727			0.261643
$772$	379.332	+	379.332i	0.491362	+	0.491362i
$773$	60.7545	−	60.7545i	0.0785957	−	0.0785957i	−0.666716	−	0.745312i	$-0.732301\pi$
$773$	60.7545	−	60.7545i	0.0785957	−	0.0785957i	0.745312	+	0.666716i	$0.232301\pi$
$774$		−	304.378i		−	0.393254i
$775$	−992.969	+	1006.66i	−1.28125	+	1.29892i
$776$	318.049			0.409857
$777$	27.1558	+	27.1558i	0.0349495	+	0.0349495i
$778$	−94.4517	+	94.4517i	−0.121403	+	0.121403i
$779$			114.614i			0.147130i
$780$	−101.746	+	42.5532i	−0.130443	+	0.0545554i
$781$	−199.660			−0.255647
$782$	−89.7058	−	89.7058i	−0.114713	−	0.114713i
$783$	−378.652	+	378.652i	−0.483591	+	0.483591i
$784$		−	343.626i		−	0.438299i
$785$	135.673	+	55.6541i	0.172832	+	0.0708969i
$786$	−52.5934			−0.0669128
$787$	−364.615	−	364.615i	−0.463297	−	0.463297i	0.436437	−	0.899735i	$-0.356240\pi$
$787$	−364.615	−	364.615i	−0.463297	−	0.463297i	−0.899735	+	0.436437i	$0.856240\pi$
$788$	−59.3397	+	59.3397i	−0.0753042	+	0.0753042i
$789$			173.908i			0.220416i
$790$	218.072	−	531.612i	0.276040	−	0.672927i
$791$	−582.561			−0.736487
$792$	−31.0602	−	31.0602i	−0.0392174	−	0.0392174i
$793$	1201.78	−	1201.78i	1.51549	−	1.51549i
$794$			333.298i			0.419771i
$795$	43.7404	+	104.584i	0.0550193	+	0.131553i
$796$	143.495			0.180271
$797$	130.697	+	130.697i	0.163986	+	0.163986i	0.784330	−	0.620344i	$-0.213007\pi$
$797$	130.697	+	130.697i	0.163986	+	0.163986i	−0.620344	+	0.784330i	$0.713007\pi$
$798$	−102.985	+	102.985i	−0.129054	+	0.129054i
$799$		−	236.461i		−	0.295947i
$800$	141.418	−	0.968365i	0.176773	−	0.00121046i
$801$	−1126.24			−1.40605
$802$	56.3098	+	56.3098i	0.0702118	+	0.0702118i
$803$	131.414	−	131.414i	0.163653	−	0.163653i
$804$			29.1880i			0.0363035i
$805$	256.949	−	107.464i	0.319191	−	0.133496i
$806$	1373.61			1.70423
$807$	−203.677	−	203.677i	−0.252388	−	0.252388i
$808$	212.932	−	212.932i	0.263530	−	0.263530i
$809$			183.753i			0.227135i	0.993530	+	0.113568i	$0.0362279\pi$
$809$			183.753i			0.227135i	−0.993530	+	0.113568i	$0.963772\pi$
$810$	458.168	+	187.944i	0.565640	+	0.232030i
$811$	−1246.28			−1.53672			−0.768360	−	0.640018i	$-0.778927\pi$
$811$	−1246.28			−1.53672			−0.768360	+	0.640018i	$0.778927\pi$
$812$	−778.762	−	778.762i	−0.959067	−	0.959067i
$813$	161.531	−	161.531i	0.198685	−	0.198685i
$814$			13.1675i			0.0161763i
$815$	−13.7818	+	33.5970i	−0.0169101	+	0.0412233i
$816$	−48.0499			−0.0588847
$817$	−244.679	−	244.679i	−0.299484	−	0.299484i
$818$	−617.869	+	617.869i	−0.755342	+	0.755342i
$819$		−	1712.90i		−	2.09145i
$820$	−32.0308	−	76.5864i	−0.0390619	−	0.0933981i
$821$	−50.3398			−0.0613152			−0.0306576	−	0.999530i	$-0.509760\pi$
$821$	−50.3398			−0.0613152			−0.0306576	+	0.999530i	$0.509760\pi$
$822$	−82.6352	−	82.6352i	−0.100529	−	0.100529i
$823$	−43.2603	+	43.2603i	−0.0525642	+	0.0525642i	−0.732900	−	0.680336i	$-0.761834\pi$
$823$	−43.2603	+	43.2603i	−0.0525642	+	0.0525642i	0.680336	+	0.732900i	$0.261834\pi$
$824$			17.0371i			0.0206761i
$825$	−0.198812	−	29.0342i	−0.000240985	−	0.0351929i
$826$	−104.461			−0.126466
$827$	−412.757	−	412.757i	−0.499102	−	0.499102i	0.412057	−	0.911158i	$-0.364811\pi$
$827$	−412.757	−	412.757i	−0.499102	−	0.499102i	−0.911158	+	0.412057i	$0.864811\pi$
$828$	58.2437	−	58.2437i	0.0703427	−	0.0703427i
$829$		−	375.863i		−	0.453393i	−0.973965	−	0.226697i	$-0.927207\pi$
$829$		−	375.863i		−	0.453393i	0.973965	−	0.226697i	$-0.0727926\pi$
$830$	−650.639	+	272.117i	−0.783902	+	0.327852i
$831$	67.8787			0.0816831
$832$	−97.1447	−	97.1447i	−0.116760	−	0.116760i
$833$	1136.23	−	1136.23i	1.36403	−	1.36403i
$834$			14.4937i			0.0173785i
$835$	−28.1091	−	11.5306i	−0.0336636	−	0.0138091i
$836$	−49.9362			−0.0597324
$837$	451.722	+	451.722i	0.539692	+	0.539692i
$838$	−327.397	+	327.397i	−0.390688	+	0.390688i
$839$		−	21.1937i		−	0.0252607i	−0.999920	−	0.0126304i	$-0.995980\pi$
$839$		−	21.1937i		−	0.0252607i	0.999920	−	0.0126304i	$-0.00402047\pi$
$840$	40.0350	−	97.5969i	0.0476607	−	0.116187i
$841$	−1406.74			−1.67270
$842$	−271.135	−	271.135i	−0.322013	−	0.322013i
$843$	13.4119	−	13.4119i	0.0159097	−	0.0159097i
$844$			387.981i			0.459693i
$845$	−242.906	−	580.796i	−0.287463	−	0.687332i
$846$	153.528			0.181476
$847$	966.912	+	966.912i	1.14157	+	1.14157i
$848$	−99.8549	+	99.8549i	−0.117753	+	0.117753i
$849$		−	306.370i		−	0.360859i
$850$	470.815	+	464.411i	0.553900	+	0.546366i
$851$	−24.6916			−0.0290148
$852$	−100.272	−	100.272i	−0.117690	−	0.117690i
$853$	−53.9548	+	53.9548i	−0.0632530	+	0.0632530i	−0.738026	−	0.674773i	$-0.764242\pi$
$853$	−53.9548	+	53.9548i	−0.0632530	+	0.0632530i	0.674773	+	0.738026i	$0.264242\pi$
$854$			1625.65i			1.90357i
$855$	546.914	−	228.736i	0.639666	−	0.267528i
$856$	−89.2389			−0.104251
$857$	−568.035	−	568.035i	−0.662818	−	0.662818i	0.293225	−	0.956043i	$-0.405271\pi$
$857$	−568.035	−	568.035i	−0.662818	−	0.662818i	−0.956043	+	0.293225i	$0.905271\pi$
$858$	−19.9445	+	19.9445i	−0.0232454	+	0.0232454i
$859$		−	1184.25i		−	1.37864i	−0.724457	−	0.689320i	$-0.757909\pi$
$859$		−	1184.25i		−	1.37864i	0.724457	−	0.689320i	$-0.242091\pi$
$860$	231.877	+	95.1176i	0.269624	+	0.110602i
$861$	−61.9224			−0.0719192
$862$	−148.281	−	148.281i	−0.172019	−	0.172019i
$863$	781.788	−	781.788i	0.905896	−	0.905896i	−0.0900420	−	0.995938i	$-0.528700\pi$
$863$	781.788	−	781.788i	0.905896	−	0.905896i	0.995938	+	0.0900420i	$0.0287001\pi$
$864$		−	63.8935i		−	0.0739508i
$865$	−160.271	+	390.707i	−0.185285	+	0.451685i
$866$	−875.273			−1.01071
$867$	−27.6440	−	27.6440i	−0.0318847	−	0.0318847i
$868$	−929.044	+	929.044i	−1.07033	+	1.07033i
$869$		−	146.955i		−	0.169108i
$870$	−83.0704	−	198.624i	−0.0954833	−	0.228303i
$871$	−390.250			−0.448048
$872$	303.583	+	303.583i	0.348146	+	0.348146i
$873$	−682.818	+	682.818i	−0.782151	+	0.782151i
$874$		−	93.6400i		−	0.107140i
$875$	−1335.57	+	569.353i	−1.52637	+	0.650689i
$876$	131.995			0.150679
$877$	−314.824	−	314.824i	−0.358978	−	0.358978i	0.504458	−	0.863436i	$-0.331692\pi$
$877$	−314.824	−	314.824i	−0.358978	−	0.358978i	−0.863436	+	0.504458i	$0.831692\pi$
$878$	387.950	−	387.950i	0.441856	−	0.441856i
$879$		−	0.658850i		−	0.000749545i
$880$	33.3680	−	13.9555i	0.0379182	−	0.0158585i
$881$	−654.884			−0.743342			−0.371671	−	0.928365i	$-0.621215\pi$
$881$	−654.884			−0.743342			−0.371671	+	0.928365i	$0.621215\pi$
$882$	737.728	+	737.728i	0.836427	+	0.836427i
$883$	−899.338	+	899.338i	−1.01850	+	1.01850i	−0.0186775	+	0.999826i	$0.505946\pi$
$883$	−899.338	+	899.338i	−1.01850	+	1.01850i	−0.999826	+	0.0186775i	$0.994054\pi$
$884$		−	642.437i		−	0.726739i
$885$	−18.8928	−	7.74997i	−0.0213478	−	0.00875703i
$886$	−67.0140			−0.0756366
$887$	−79.8383	−	79.8383i	−0.0900094	−	0.0900094i	0.660668	−	0.750678i	$-0.270273\pi$
$887$	−79.8383	−	79.8383i	−0.0900094	−	0.0900094i	−0.750678	+	0.660668i	$0.770273\pi$
$888$	−6.61288	+	6.61288i	−0.00744693	+	0.00744693i
$889$			7.69017i			0.00865036i
$890$	351.949	−	857.977i	0.395449	−	0.964019i
$891$	126.653			0.142147
$892$	−282.962	−	282.962i	−0.317222	−	0.317222i
$893$	123.416	−	123.416i	0.138204	−	0.138204i
$894$		−	248.756i		−	0.278251i
$895$	−359.258	−	858.996i	−0.401406	−	0.959772i
$896$	131.408			0.146661
$897$	−37.3998	−	37.3998i	−0.0416943	−	0.0416943i
$898$	90.3725	−	90.3725i	0.100638	−	0.100638i
$899$			2681.50i			2.98276i
$900$	−301.530	+	305.688i	−0.335034	+	0.339654i
$901$	−660.360			−0.732919
$902$	−15.0127	−	15.0127i	−0.0166438	−	0.0166438i
$903$	132.192	−	132.192i	0.146392	−	0.146392i
$904$		−	141.863i		−	0.156928i
$905$	1123.75	−	469.987i	1.24172	−	0.519323i
$906$	−60.9792			−0.0673060
$907$	399.844	+	399.844i	0.440842	+	0.440842i	0.892295	−	0.451453i	$-0.149094\pi$
$907$	399.844	+	399.844i	0.440842	+	0.440842i	−0.451453	+	0.892295i	$0.649094\pi$
$908$	598.254	−	598.254i	0.658870	−	0.658870i
$909$			914.285i			1.00581i
$910$	1304.89	+	535.276i	1.43394	+	0.588216i
$911$	375.905			0.412629			0.206315	−	0.978486i	$-0.433853\pi$
$911$	375.905			0.412629			0.206315	+	0.978486i	$0.433853\pi$
$912$	−25.0786	−	25.0786i	−0.0274985	−	0.0274985i
$913$	−127.540	+	127.540i	−0.139693	+	0.139693i
$914$			865.282i			0.946698i
$915$	−120.608	+	294.016i	−0.131812	+	0.321328i
$916$	61.0530			0.0666518
$917$	475.600	+	475.600i	0.518648	+	0.518648i
$918$	211.270	−	211.270i	0.230142	−	0.230142i
$919$			218.112i			0.237336i	0.992934	+	0.118668i	$0.0378624\pi$
$919$			218.112i			0.237336i	−0.992934	+	0.118668i	$0.962138\pi$
$920$	26.1692	+	62.5713i	0.0284448	+	0.0680123i
$921$	−283.380			−0.307687
$922$	−477.708	−	477.708i	−0.518121	−	0.518121i
$923$	1340.66	−	1340.66i	1.45250	−	1.45250i
$924$		−	26.9790i		−	0.0291981i
$925$	128.711	−	0.881350i	0.139147	−	0.000952811i
$926$	1019.13			1.10058
$927$	−36.5769	−	36.5769i	−0.0394573	−	0.0394573i
$928$	189.641	−	189.641i	0.204355	−	0.204355i
$929$			1273.70i			1.37104i	0.728052	+	0.685522i	$0.240426\pi$
$929$			1273.70i			1.37104i	−0.728052	+	0.685522i	$0.759574\pi$
$930$	−236.953	+	99.1010i	−0.254788	+	0.106560i
$931$	1186.07			1.27397
$932$	−105.469	−	105.469i	−0.113164	−	0.113164i
$933$	200.891	−	200.891i	0.215317	−	0.215317i
$934$		−	1017.10i		−	1.08897i
$935$	156.480	+	64.1893i	0.167358	+	0.0686516i
$936$	417.118			0.445639
$937$	636.364	+	636.364i	0.679151	+	0.679151i	0.959808	−	0.280657i	$-0.0905525\pi$
$937$	636.364	+	636.364i	0.679151	+	0.679151i	−0.280657	+	0.959808i	$0.590552\pi$
$938$	263.946	−	263.946i	0.281393	−	0.281393i
$939$		−	313.845i		−	0.334233i
$940$	−47.9774	+	116.959i	−0.0510397	+	0.124424i
$941$	1561.91			1.65984			0.829921	−	0.557881i	$-0.188386\pi$
$941$	1561.91			1.65984			0.829921	+	0.557881i	$0.188386\pi$
$942$	18.8352	+	18.8352i	0.0199949	+	0.0199949i
$943$	28.1517	−	28.1517i	0.0298533	−	0.0298533i
$944$		−	25.4379i		−	0.0269470i
$945$	253.093	+	605.152i	0.267823	+	0.640373i
$946$	64.0984			0.0677573
$947$	689.902	+	689.902i	0.728513	+	0.728513i	0.970324	−	0.241810i	$-0.0777411\pi$
$947$	689.902	+	689.902i	0.728513	+	0.728513i	−0.241810	+	0.970324i	$0.577741\pi$
$948$	73.8028	−	73.8028i	0.0778510	−	0.0778510i
$949$			1764.80i			1.85964i
$950$	3.34242	+	488.121i	0.00351834	+	0.513811i
$951$	405.544			0.426440
$952$	434.513	+	434.513i	0.456422	+	0.456422i
$953$	1126.44	−	1126.44i	1.18200	−	1.18200i	0.202771	−	0.979226i	$-0.435005\pi$
$953$	1126.44	−	1126.44i	1.18200	−	1.18200i	0.979226	−	0.202771i	$-0.0649946\pi$
$954$		−	428.755i		−	0.449429i
$955$	1499.43	−	627.107i	1.57008	−	0.656657i
$956$	−256.777			−0.268595
$957$	−38.9348	−	38.9348i	−0.0406842	−	0.0406842i
$958$	213.247	−	213.247i	0.222596	−	0.222596i
$959$			1494.53i			1.55843i
$960$	23.7664	+	9.74919i	0.0247567	+	0.0101554i
$961$	2237.97			2.32879
$962$	−88.4155	−	88.4155i	−0.0919080	−	0.0919080i
$963$	191.586	−	191.586i	0.198947	−	0.198947i
$964$			297.397i			0.308503i
$965$	508.987	−	1240.80i	0.527448	−	1.28581i
$966$	50.5908			0.0523714
$967$	−823.547	−	823.547i	−0.851651	−	0.851651i	0.138685	−	0.990337i	$-0.455712\pi$
$967$	−823.547	−	823.547i	−0.851651	−	0.851651i	−0.990337	+	0.138685i	$0.955712\pi$
$968$	−235.459	+	235.459i	−0.243243	+	0.243243i
$969$		−	165.850i		−	0.171156i
$970$	−306.794	−	733.552i	−0.316282	−	0.756239i
$971$	−1767.79			−1.82059			−0.910294	−	0.413963i	$-0.864144\pi$
$971$	−1767.79			−1.82059			−0.910294	+	0.413963i	$0.864144\pi$
$972$	207.367	+	207.367i	0.213341	+	0.213341i
$973$	131.066	−	131.066i	0.134703	−	0.134703i
$974$			889.455i			0.913198i
$975$	196.290	+	193.620i	0.201323	+	0.198585i
$976$	−395.873			−0.405608
$977$	−355.445	−	355.445i	−0.363813	−	0.363813i	0.501402	−	0.865215i	$-0.332818\pi$
$977$	−355.445	−	355.445i	−0.363813	−	0.363813i	−0.865215	+	0.501402i	$0.832818\pi$
$978$	−4.66421	+	4.66421i	−0.00476913	+	0.00476913i
$979$		−	237.173i		−	0.242261i
$980$	−792.543	+	331.466i	−0.808717	+	0.338230i
$981$	−1303.52			−1.32877
$982$	−488.473	−	488.473i	−0.497427	−	0.497427i
$983$	−874.521	+	874.521i	−0.889644	+	0.889644i	−0.994489	−	0.104844i	$-0.966566\pi$
$983$	−874.521	+	874.521i	−0.889644	+	0.889644i	0.104844	+	0.994489i	$0.466566\pi$
$984$		−	15.0791i		−	0.0153243i
$985$	194.101	+	79.6219i	0.197057	+	0.0808344i
$986$	1254.14			1.27194
$987$	66.6778	+	66.6778i	0.0675560	+	0.0675560i
$988$	335.306	−	335.306i	0.339379	−	0.339379i
$989$			120.197i			0.121534i
$990$	−41.6765	+	101.598i	−0.0420975	+	0.102625i
$991$	1547.23			1.56128			0.780639	−	0.624982i	$-0.214894\pi$
$991$	1547.23			1.56128			0.780639	+	0.624982i	$0.214894\pi$
$992$	−226.238	−	226.238i	−0.228062	−	0.228062i
$993$	−245.905	+	245.905i	−0.247638	+	0.247638i
$994$			1813.51i			1.82446i
$995$	−138.417	−	330.959i	−0.139113	−	0.332623i
$996$	−128.104			−0.128619
$997$	58.7774	+	58.7774i	0.0589543	+	0.0589543i	0.735969	−	0.677015i	$-0.236727\pi$
$997$	58.7774	+	58.7774i	0.0589543	+	0.0589543i	−0.677015	+	0.735969i	$0.736727\pi$
$998$	−727.731	+	727.731i	−0.729189	+	0.729189i
$999$		−	58.1522i		−	0.0582104i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.a.47.4	✓	20
5.3	odd	4	inner	230.3.f.a.93.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.a.47.4	✓	20	1.1	even	1	trivial
230.3.f.a.93.4	yes	20	5.3	odd	4	inner

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)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.454110 + 0.454110i) q^{3} +2.00000i q^{4} +(4.61282 - 1.92922i) q^{5} +0.908220 q^{6} +(-8.21299 - 8.21299i) q^{7} +(2.00000 - 2.00000i) q^{8} +8.58757i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.454110 + 0.454110i) q^{3} +2.00000i q^{4} +(4.61282 - 1.92922i) q^{5} +0.908220 q^{6} +(-8.21299 - 8.21299i) q^{7} +(2.00000 - 2.00000i) q^{8} +8.58757i q^{9} +(-6.54204 - 2.68360i) q^{10} -1.80844 q^{11} +(-0.908220 - 0.908220i) q^{12} +(12.1431 - 12.1431i) q^{13} +16.4260i q^{14} +(-1.21865 + 2.97081i) q^{15} -4.00000 q^{16} +(-13.2264 - 13.2264i) q^{17} +(8.58757 - 8.58757i) q^{18} -13.8065i q^{19} +(3.85844 + 9.22564i) q^{20} +7.45921 q^{21} +(1.80844 + 1.80844i) q^{22} +(-3.39116 + 3.39116i) q^{23} +1.81644i q^{24} +(17.5562 - 17.7983i) q^{25} -24.2862 q^{26} +(-7.98669 - 7.98669i) q^{27} +(16.4260 - 16.4260i) q^{28} -47.4104i q^{29} +(4.18945 - 1.75216i) q^{30} -56.5594 q^{31} +(4.00000 + 4.00000i) q^{32} +(0.821229 - 0.821229i) q^{33} +26.4528i q^{34} +(-53.7297 - 22.0404i) q^{35} -17.1751 q^{36} +(3.64057 + 3.64057i) q^{37} +(-13.8065 + 13.8065i) q^{38} +11.0286i q^{39} +(5.36720 - 13.0841i) q^{40} -8.30147 q^{41} +(-7.45921 - 7.45921i) q^{42} +(17.7220 - 17.7220i) q^{43} -3.61687i q^{44} +(16.5673 + 39.6129i) q^{45} +6.78233 q^{46} +(8.93900 + 8.93900i) q^{47} +(1.81644 - 1.81644i) q^{48} +85.9066i q^{49} +(-35.3545 + 0.242091i) q^{50} +12.0125 q^{51} +(24.2862 + 24.2862i) q^{52} +(24.9637 - 24.9637i) q^{53} +15.9734i q^{54} +(-8.34199 + 3.48888i) q^{55} -32.8520 q^{56} +(6.26965 + 6.26965i) q^{57} +(-47.4104 + 47.4104i) q^{58} +6.35948i q^{59} +(-5.94161 - 2.43730i) q^{60} +98.9683 q^{61} +(56.5594 + 56.5594i) q^{62} +(70.5297 - 70.5297i) q^{63} -8.00000i q^{64} +(32.5872 - 79.4406i) q^{65} -1.64246 q^{66} +(-16.0688 - 16.0688i) q^{67} +(26.4528 - 26.4528i) q^{68} -3.07992i q^{69} +(31.6894 + 75.7701i) q^{70} +110.405 q^{71} +(17.1751 + 17.1751i) q^{72} +(-72.6670 + 72.6670i) q^{73} -7.28114i q^{74} +(0.109936 + 16.0548i) q^{75} +27.6129 q^{76} +(14.8527 + 14.8527i) q^{77} +(11.0286 - 11.0286i) q^{78} +81.2609i q^{79} +(-18.4513 + 7.71689i) q^{80} -70.0344 q^{81} +(8.30147 + 8.30147i) q^{82} +(70.5250 - 70.5250i) q^{83} +14.9184i q^{84} +(-86.5276 - 35.4943i) q^{85} -35.4441 q^{86} +(21.5295 + 21.5295i) q^{87} +(-3.61687 + 3.61687i) q^{88} +131.148i q^{89} +(23.0456 - 56.1802i) q^{90} -199.462 q^{91} +(-6.78233 - 6.78233i) q^{92} +(25.6842 - 25.6842i) q^{93} -17.8780i q^{94} +(-26.6357 - 63.6867i) q^{95} -3.63288 q^{96} +(79.5123 + 79.5123i) q^{97} +(85.9066 - 85.9066i) q^{98} -15.5301i 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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