LMFDB - Embedded newform 51.3.f.a.38.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,3,Mod(38,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.38"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	51.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.38964934824$
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} + 62 x^{18} + 1545 x^{16} + 20120 x^{14} + 149608 x^{12} + 655792 x^{10} + 1690896 x^{8} + \cdots + 36864 $ x^20 + 62x^18 + 1545x^16 + 20120x^14 + 149608x^12 + 655792x^10 + 1690896x^8 + 2476352x^6 + 1880640x^4 + 593152*x^2 + 36864
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			38.5
Root			$-1.20840i$ of defining polynomial
Character	$\chi$	$=$	51.38
Dual form			51.3.f.a.47.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.208400 q^{2} +(-2.91484 + 0.709732i) q^{3} -3.95657 q^{4} +(-5.25648 - 5.25648i) q^{5} +(0.607451 - 0.147908i) q^{6} +(2.40158 + 2.40158i) q^{7} +1.65815 q^{8} +(7.99256 - 4.13751i) q^{9} +(1.09545 + 1.09545i) q^{10} +(-11.4695 + 11.4695i) q^{11} +(11.5328 - 2.80810i) q^{12} -8.12160 q^{13} +(-0.500488 - 0.500488i) q^{14} +(19.0525 + 11.5911i) q^{15} +15.4807 q^{16} +(-13.5788 - 10.2282i) q^{17} +(-1.66565 + 0.862255i) q^{18} -24.0029i q^{19} +(20.7976 + 20.7976i) q^{20} +(-8.70468 - 5.29573i) q^{21} +(2.39024 - 2.39024i) q^{22} +(5.74247 - 5.74247i) q^{23} +(-4.83323 + 1.17684i) q^{24} +30.2612i q^{25} +1.69254 q^{26} +(-20.3605 + 17.7327i) q^{27} +(-9.50201 - 9.50201i) q^{28} +(-11.7489 - 11.7489i) q^{29} +(-3.97053 - 2.41558i) q^{30} +(5.33493 - 5.33493i) q^{31} -9.85876 q^{32} +(25.2915 - 41.5720i) q^{33} +(2.82983 + 2.13154i) q^{34} -25.2477i q^{35} +(-31.6231 + 16.3703i) q^{36} +(-42.7533 + 42.7533i) q^{37} +5.00220i q^{38} +(23.6731 - 5.76415i) q^{39} +(-8.71602 - 8.71602i) q^{40} +(-8.11856 + 8.11856i) q^{41} +(1.81405 + 1.10363i) q^{42} +2.45499i q^{43} +(45.3799 - 45.3799i) q^{44} +(-63.7615 - 20.2640i) q^{45} +(-1.19673 + 1.19673i) q^{46} +64.4496i q^{47} +(-45.1238 + 10.9872i) q^{48} -37.4649i q^{49} -6.30643i q^{50} +(46.8394 + 20.1761i) q^{51} +32.1337 q^{52} +9.84366 q^{53} +(4.24312 - 3.69550i) q^{54} +120.578 q^{55} +(3.98217 + 3.98217i) q^{56} +(17.0356 + 69.9646i) q^{57} +(2.44846 + 2.44846i) q^{58} +73.8881 q^{59} +(-75.3825 - 45.8610i) q^{60} +(-55.3702 - 55.3702i) q^{61} +(-1.11180 + 1.11180i) q^{62} +(29.1313 + 9.25821i) q^{63} -59.8683 q^{64} +(42.6910 + 42.6910i) q^{65} +(-5.27074 + 8.66359i) q^{66} +27.1997 q^{67} +(53.7256 + 40.4684i) q^{68} +(-12.6628 + 20.8140i) q^{69} +5.26161i q^{70} +(-6.71855 - 6.71855i) q^{71} +(13.2528 - 6.86059i) q^{72} +(-1.60189 + 1.60189i) q^{73} +(8.90977 - 8.90977i) q^{74} +(-21.4773 - 88.2065i) q^{75} +94.9692i q^{76} -55.0898 q^{77} +(-4.93347 + 1.20125i) q^{78} +(-64.8910 - 64.8910i) q^{79} +(-81.3741 - 81.3741i) q^{80} +(46.7621 - 66.1385i) q^{81} +(1.69190 - 1.69190i) q^{82} -64.2751 q^{83} +(34.4407 + 20.9529i) q^{84} +(17.6128 + 125.141i) q^{85} -0.511620i q^{86} +(42.5846 + 25.9075i) q^{87} +(-19.0181 + 19.0181i) q^{88} -142.221i q^{89} +(13.2879 + 4.22302i) q^{90} +(-19.5046 - 19.5046i) q^{91} +(-22.7205 + 22.7205i) q^{92} +(-11.7641 + 19.3368i) q^{93} -13.4313i q^{94} +(-126.171 + 126.171i) q^{95} +(28.7367 - 6.99708i) q^{96} +(48.5370 - 48.5370i) q^{97} +7.80767i q^{98} +(-44.2156 + 139.126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3} + 24 q^{4} - 2 q^{6} - 4 q^{7} - 16 q^{10} - 42 q^{12} - 12 q^{13} - 64 q^{16} - 4 q^{18} + 88 q^{21} - 40 q^{22} - 82 q^{24} + 54 q^{27} - 160 q^{28} + 48 q^{31} + 264 q^{33} + 152 q^{34}+ \cdots - 864 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 + 24 * q^4 - 2 * q^6 - 4 * q^7 - 16 * q^10 - 42 * q^12 - 12 * q^13 - 64 * q^16 - 4 * q^18 + 88 * q^21 - 40 * q^22 - 82 * q^24 + 54 * q^27 - 160 * q^28 + 48 * q^31 + 264 * q^33 + 152 * q^34 + 32 * q^37 + 56 * q^39 + 52 * q^40 + 64 * q^45 + 388 * q^46 - 230 * q^48 - 298 * q^51 + 64 * q^52 - 254 * q^54 - 204 * q^55 - 24 * q^57 + 396 * q^58 - 336 * q^61 - 400 * q^63 - 480 * q^64 - 408 * q^67 - 132 * q^69 + 276 * q^72 - 88 * q^73 - 358 * q^75 + 380 * q^78 - 172 * q^79 + 388 * q^81 + 372 * q^82 + 1320 * q^84 + 648 * q^85 - 156 * q^88 + 672 * q^90 - 124 * q^91 + 194 * q^96 + 688 * q^97 - 864 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.208400			−0.104200			−0.0520999	−	0.998642i	$-0.516591\pi$
$2$	−0.208400			−0.104200			−0.0520999	+	0.998642i	$0.516591\pi$
$3$	−2.91484	+	0.709732i	−0.971613	+	0.236577i
$3$	−2.91484	+	0.709732i	−0.971613	+	0.236577i
$4$	−3.95657			−0.989142
$5$	−5.25648	−	5.25648i	−1.05130	−	1.05130i	−0.998611	−	0.0526852i	$-0.983222\pi$
$5$	−5.25648	−	5.25648i	−1.05130	−	1.05130i	−0.0526852	−	0.998611i	$-0.516778\pi$
$6$	0.607451	−	0.147908i	0.101242	−	0.0246513i
$7$	2.40158	+	2.40158i	0.343082	+	0.343082i	0.857525	−	0.514442i	$-0.172001\pi$
$7$	2.40158	+	2.40158i	0.343082	+	0.343082i	−0.514442	+	0.857525i	$0.672001\pi$
$8$	1.65815			0.207268
$9$	7.99256	−	4.13751i	0.888062	−	0.459723i
$10$	1.09545	+	1.09545i	0.109545	+	0.109545i
$11$	−11.4695	+	11.4695i	−1.04268	+	1.04268i	−0.0436344	+	0.999048i	$0.513894\pi$
$11$	−11.4695	+	11.4695i	−1.04268	+	1.04268i	−0.999048	+	0.0436344i	$0.986106\pi$
$12$	11.5328	−	2.80810i	0.961063	−	0.234009i
$13$	−8.12160			−0.624738			−0.312369	−	0.949961i	$-0.601123\pi$
$13$	−8.12160			−0.624738			−0.312369	+	0.949961i	$0.601123\pi$
$14$	−0.500488	−	0.500488i	−0.0357491	−	0.0357491i
$15$	19.0525	+	11.5911i	1.27017	+	0.772740i
$16$	15.4807			0.967545
$17$	−13.5788	−	10.2282i	−0.798755	−	0.601656i
$17$	−13.5788	−	10.2282i	−0.798755	−	0.601656i
$18$	−1.66565	+	0.862255i	−0.0925360	+	0.0479031i
$19$		−	24.0029i		−	1.26331i	−0.775249	−	0.631656i	$-0.782376\pi$
$19$		−	24.0029i		−	1.26331i	0.775249	−	0.631656i	$-0.217624\pi$
$20$	20.7976	+	20.7976i	1.03988	+	1.03988i
$21$	−8.70468	−	5.29573i	−0.414509	−	0.252178i
$22$	2.39024	−	2.39024i	0.108647	−	0.108647i
$23$	5.74247	−	5.74247i	0.249673	−	0.249673i	−0.571164	−	0.820836i	$-0.693508\pi$
$23$	5.74247	−	5.74247i	0.249673	−	0.249673i	0.820836	+	0.571164i	$0.193508\pi$
$24$	−4.83323	+	1.17684i	−0.201385	+	0.0490350i
$25$			30.2612i			1.21045i
$26$	1.69254			0.0650976
$27$	−20.3605	+	17.7327i	−0.754093	+	0.656768i
$28$	−9.50201	−	9.50201i	−0.339357	−	0.339357i
$29$	−11.7489	−	11.7489i	−0.405133	−	0.405133i	0.474904	−	0.880037i	$-0.342483\pi$
$29$	−11.7489	−	11.7489i	−0.405133	−	0.405133i	−0.880037	+	0.474904i	$0.842483\pi$
$30$	−3.97053	−	2.41558i	−0.132351	−	0.0805194i
$31$	5.33493	−	5.33493i	0.172094	−	0.172094i	−0.615805	−	0.787899i	$-0.711169\pi$
$31$	5.33493	−	5.33493i	0.172094	−	0.172094i	0.787899	+	0.615805i	$0.211169\pi$
$32$	−9.85876			−0.308086
$33$	25.2915	−	41.5720i	0.766408	−	1.25976i
$34$	2.82983	+	2.13154i	0.0832302	+	0.0626925i
$35$		−	25.2477i		−	0.721363i
$36$	−31.6231	+	16.3703i	−0.878420	+	0.454731i
$37$	−42.7533	+	42.7533i	−1.15549	+	1.15549i	−0.170060	+	0.985434i	$0.554396\pi$
$37$	−42.7533	+	42.7533i	−1.15549	+	1.15549i	−0.985434	+	0.170060i	$0.945604\pi$
$38$			5.00220i			0.131637i
$39$	23.6731	−	5.76415i	0.607004	−	0.147799i
$40$	−8.71602	−	8.71602i	−0.217900	−	0.217900i
$41$	−8.11856	+	8.11856i	−0.198014	+	0.198014i	−0.799148	−	0.601134i	$-0.794716\pi$
$41$	−8.11856	+	8.11856i	−0.198014	+	0.198014i	0.601134	+	0.799148i	$0.294716\pi$
$42$	1.81405	+	1.10363i	0.0431917	+	0.0262769i
$43$			2.45499i			0.0570929i	0.999592	+	0.0285464i	$0.00908785\pi$
$43$			2.45499i			0.0570929i	−0.999592	+	0.0285464i	$0.990912\pi$
$44$	45.3799	−	45.3799i	1.03136	−	1.03136i
$45$	−63.7615	−	20.2640i	−1.41692	−	0.450312i
$46$	−1.19673	+	1.19673i	−0.0260158	+	0.0260158i
$47$			64.4496i			1.37127i	0.727947	+	0.685634i	$0.240475\pi$
$47$			64.4496i			1.37127i	−0.727947	+	0.685634i	$0.759525\pi$
$48$	−45.1238	+	10.9872i	−0.940079	+	0.228899i
$49$		−	37.4649i		−	0.764589i
$50$		−	6.30643i		−	0.126129i
$51$	46.8394	+	20.1761i	0.918419	+	0.395609i
$52$	32.1337			0.617955
$53$	9.84366			0.185729			0.0928647	−	0.995679i	$-0.470398\pi$
$53$	9.84366			0.185729			0.0928647	+	0.995679i	$0.470398\pi$
$54$	4.24312	−	3.69550i	0.0785764	−	0.0684351i
$55$	120.578			2.19234
$56$	3.98217	+	3.98217i	0.0711101	+	0.0711101i
$57$	17.0356	+	69.9646i	0.298871	+	1.22745i
$58$	2.44846	+	2.44846i	0.0422148	+	0.0422148i
$59$	73.8881			1.25234			0.626170	−	0.779686i	$-0.284622\pi$
$59$	73.8881			1.25234			0.626170	+	0.779686i	$0.284622\pi$
$60$	−75.3825	−	45.8610i	−1.25637	−	0.764350i
$61$	−55.3702	−	55.3702i	−0.907709	−	0.907709i	0.0883785	−	0.996087i	$-0.471832\pi$
$61$	−55.3702	−	55.3702i	−0.907709	−	0.907709i	−0.996087	+	0.0883785i	$0.971832\pi$
$62$	−1.11180	+	1.11180i	−0.0179322	+	0.0179322i
$63$	29.1313	+	9.25821i	0.462401	+	0.146956i
$64$	−59.8683			−0.935442
$65$	42.6910	+	42.6910i	0.656785	+	0.656785i
$66$	−5.27074	+	8.66359i	−0.0798596	+	0.131267i
$67$	27.1997			0.405965			0.202983	−	0.979182i	$-0.434937\pi$
$67$	27.1997			0.405965			0.202983	+	0.979182i	$0.434937\pi$
$68$	53.7256	+	40.4684i	0.790083	+	0.595124i
$69$	−12.6628	+	20.8140i	−0.183518	+	0.301652i
$70$			5.26161i			0.0751659i
$71$	−6.71855	−	6.71855i	−0.0946275	−	0.0946275i	0.658208	−	0.752836i	$-0.271315\pi$
$71$	−6.71855	−	6.71855i	−0.0946275	−	0.0946275i	−0.752836	+	0.658208i	$0.771315\pi$
$72$	13.2528	−	6.86059i	0.184067	−	0.0952860i
$73$	−1.60189	+	1.60189i	−0.0219437	+	0.0219437i	−0.717993	−	0.696050i	$-0.754939\pi$
$73$	−1.60189	+	1.60189i	−0.0219437	+	0.0219437i	0.696050	+	0.717993i	$0.254939\pi$
$74$	8.90977	−	8.90977i	0.120402	−	0.120402i
$75$	−21.4773	−	88.2065i	−0.286364	−	1.17609i
$76$			94.9692i			1.24959i
$77$	−55.0898			−0.715452
$78$	−4.93347	+	1.20125i	−0.0632497	+	0.0154006i
$79$	−64.8910	−	64.8910i	−0.821405	−	0.821405i	0.164904	−	0.986310i	$-0.447268\pi$
$79$	−64.8910	−	64.8910i	−0.821405	−	0.821405i	−0.986310	+	0.164904i	$0.947268\pi$
$80$	−81.3741	−	81.3741i	−1.01718	−	1.01718i
$81$	46.7621	−	66.1385i	0.577310	−	0.816525i
$82$	1.69190	−	1.69190i	0.0206330	−	0.0206330i
$83$	−64.2751			−0.774399			−0.387200	−	0.921996i	$-0.626558\pi$
$83$	−64.2751			−0.774399			−0.387200	+	0.921996i	$0.626558\pi$
$84$	34.4407	+	20.9529i	0.410008	+	0.249440i
$85$	17.6128	+	125.141i	0.207210	+	1.47225i
$86$		−	0.511620i		−	0.00594907i
$87$	42.5846	+	25.9075i	0.489478	+	0.297787i
$88$	−19.0181	+	19.0181i	−0.216115	+	0.216115i
$89$		−	142.221i		−	1.59799i	−0.601337	−	0.798996i	$-0.705365\pi$
$89$		−	142.221i		−	1.59799i	0.601337	−	0.798996i	$-0.294635\pi$
$90$	13.2879	+	4.22302i	0.147643	+	0.0469224i
$91$	−19.5046	−	19.5046i	−0.214337	−	0.214337i
$92$	−22.7205	+	22.7205i	−0.246962	+	0.246962i
$93$	−11.7641	+	19.3368i	−0.126495	+	0.207923i
$94$		−	13.4313i		−	0.142886i
$95$	−126.171	+	126.171i	−1.32811	+	1.32811i
$96$	28.7367	−	6.99708i	0.299341	−	0.0728862i
$97$	48.5370	−	48.5370i	0.500381	−	0.500381i	−0.411175	−	0.911556i	$-0.634881\pi$
$97$	48.5370	−	48.5370i	0.500381	−	0.500381i	0.911556	+	0.411175i	$0.134881\pi$
$98$			7.80767i			0.0796701i
$99$	−44.2156	+	139.126i	−0.446622	+	1.40531i
$100$		−	119.731i		−	1.19731i
$101$		−	41.2075i		−	0.407995i	−0.978971	−	0.203997i	$-0.934607\pi$
$101$		−	41.2075i		−	0.407995i	0.978971	−	0.203997i	$-0.0653934\pi$
$102$	−9.76131	−	4.20469i	−0.0956991	−	0.0412224i
$103$	−42.8144			−0.415674			−0.207837	−	0.978163i	$-0.566642\pi$
$103$	−42.8144			−0.415674			−0.207837	+	0.978163i	$0.566642\pi$
$104$	−13.4668			−0.129488
$105$	17.9191	+	73.5929i	0.170658	+	0.700885i
$106$	−2.05141			−0.0193530
$107$	−49.4125	−	49.4125i	−0.461799	−	0.461799i	0.437446	−	0.899245i	$-0.355883\pi$
$107$	−49.4125	−	49.4125i	−0.461799	−	0.461799i	−0.899245	+	0.437446i	$0.855883\pi$
$108$	80.5578	−	70.1608i	0.745905	−	0.649637i
$109$	99.6210	+	99.6210i	0.913954	+	0.913954i	0.996581	−	0.0826264i	$-0.0263308\pi$
$109$	99.6210	+	99.6210i	0.913954	+	0.913954i	−0.0826264	+	0.996581i	$0.526331\pi$
$110$	−25.1285			−0.228441
$111$	94.2755	−	154.962i	0.849329	−	1.39606i
$112$	37.1781	+	37.1781i	0.331948	+	0.331948i
$113$	−42.2935	+	42.2935i	−0.374279	+	0.374279i	−0.869033	−	0.494754i	$-0.835258\pi$
$113$	−42.2935	+	42.2935i	−0.374279	+	0.374279i	0.494754	+	0.869033i	$0.335258\pi$
$114$	−3.55022	−	14.5806i	−0.0311423	−	0.127900i
$115$	−60.3704			−0.524960
$116$	46.4852	+	46.4852i	0.400734	+	0.400734i
$117$	−64.9124	+	33.6032i	−0.554806	+	0.287206i
$118$	−15.3983			−0.130494
$119$	−8.04693	−	57.1743i	−0.0676212	−	0.480456i
$120$	31.5918	+	19.2197i	0.263265	+	0.160165i
$121$		−	142.099i		−	1.17437i
$122$	11.5391	+	11.5391i	0.0945831	+	0.0945831i
$123$	17.9023	−	29.4263i	0.145547	−	0.239238i
$124$	−21.1080	+	21.1080i	−0.170226	+	0.170226i
$125$	27.6554	−	27.6554i	0.221243	−	0.221243i
$126$	−6.07095	−	1.92941i	−0.0481822	−	0.0153128i
$127$			73.4454i			0.578310i	0.957282	+	0.289155i	$0.0933743\pi$
$127$			73.4454i			0.578310i	−0.957282	+	0.289155i	$0.906626\pi$
$128$	51.9116			0.405559
$129$	−1.74239	−	7.15591i	−0.0135069	−	0.0554722i
$130$	−8.89680	−	8.89680i	−0.0684369	−	0.0684369i
$131$	135.680	+	135.680i	1.03573	+	1.03573i	0.999338	+	0.0363881i	$0.0115852\pi$
$131$	135.680	+	135.680i	1.03573	+	1.03573i	0.0363881	+	0.999338i	$0.488415\pi$
$132$	−100.067	+	164.483i	−0.758087	+	1.24608i
$133$	57.6448	−	57.6448i	0.433420	−	0.433420i
$134$	−5.66840			−0.0423015
$135$	200.236	+	13.8128i	1.48323	+	0.102317i
$136$	−22.5157	−	16.9598i	−0.165557	−	0.124704i
$137$			187.183i			1.36630i	0.730279	+	0.683149i	$0.239390\pi$
$137$			187.183i			1.36630i	−0.730279	+	0.683149i	$0.760610\pi$
$138$	2.63891	−	4.33763i	0.0191226	−	0.0314321i
$139$	−10.4696	+	10.4696i	−0.0753212	+	0.0753212i	−0.743764	−	0.668443i	$-0.766961\pi$
$139$	−10.4696	+	10.4696i	−0.0753212	+	0.0753212i	0.668443	+	0.743764i	$0.266961\pi$
$140$			99.8942i			0.713530i
$141$	−45.7419	−	187.860i	−0.324411	−	1.33234i
$142$	1.40014	+	1.40014i	0.00986017	+	0.00986017i
$143$	93.1507	−	93.1507i	0.651403	−	0.651403i
$144$	123.731	−	64.0516i	0.859240	−	0.444803i
$145$			123.515i			0.851830i
$146$	0.333833	−	0.333833i	0.00228653	−	0.00228653i
$147$	26.5900	+	109.204i	0.180884	+	0.742884i
$148$	169.156	−	169.156i	1.14295	−	1.14295i
$149$		−	235.010i		−	1.57725i	−0.614875	−	0.788624i	$-0.710794\pi$
$149$		−	235.010i		−	1.57725i	0.614875	−	0.788624i	$-0.289206\pi$
$150$	4.47587	+	18.3822i	0.0298391	+	0.122548i
$151$			158.973i			1.05280i	0.850236	+	0.526402i	$0.176459\pi$
$151$			158.973i			1.05280i	−0.850236	+	0.526402i	$0.823541\pi$
$152$		−	39.8004i		−	0.261844i
$153$	−150.849	−	25.5666i	−0.985940	−	0.167102i
$154$	11.4807			0.0745500
$155$	−56.0859			−0.361844
$156$	−93.6644	+	22.8063i	−0.600413	+	0.146194i
$157$	−96.4573			−0.614377			−0.307189	−	0.951649i	$-0.599388\pi$
$157$	−96.4573			−0.614377			−0.307189	+	0.951649i	$0.599388\pi$
$158$	13.5233	+	13.5233i	0.0855903	+	0.0855903i
$159$	−28.6927	+	6.98635i	−0.180457	+	0.0439393i
$160$	51.8224	+	51.8224i	0.323890	+	0.323890i
$161$	27.5820			0.171317
$162$	−9.74521	+	13.7833i	−0.0601556	+	0.0850818i
$163$	−146.948	−	146.948i	−0.901524	−	0.901524i	0.0940437	−	0.995568i	$-0.470021\pi$
$163$	−146.948	−	146.948i	−0.901524	−	0.901524i	−0.995568	+	0.0940437i	$0.970021\pi$
$164$	32.1216	−	32.1216i	0.195864	−	0.195864i
$165$	−351.467	+	85.5783i	−2.13010	+	0.518657i
$166$	13.3949			0.0806923
$167$	−180.063	−	180.063i	−1.07822	−	1.07822i	−0.996669	−	0.0815525i	$-0.974012\pi$
$167$	−180.063	−	180.063i	−1.07822	−	1.07822i	−0.0815525	−	0.996669i	$-0.525988\pi$
$168$	−14.4336	−	8.78110i	−0.0859145	−	0.0522685i
$169$	−103.040			−0.609702
$170$	−3.67051	−	26.0794i	−0.0215912	−	0.153408i
$171$	−99.3122	−	191.845i	−0.580773	−	1.12190i
$172$		−	9.71336i		−	0.0564730i
$173$	58.9172	+	58.9172i	0.340562	+	0.340562i	0.856579	−	0.516017i	$-0.172586\pi$
$173$	58.9172	+	58.9172i	0.340562	+	0.340562i	−0.516017	+	0.856579i	$0.672586\pi$
$174$	−8.87461	−	5.39911i	−0.0510035	−	0.0310294i
$175$	−72.6746	+	72.6746i	−0.415283	+	0.415283i
$176$	−177.556	+	177.556i	−1.00884	+	1.00884i
$177$	−215.372	+	52.4407i	−1.21679	+	0.296275i
$178$			29.6389i			0.166511i
$179$	−98.2385			−0.548819			−0.274409	−	0.961613i	$-0.588482\pi$
$179$	−98.2385			−0.548819			−0.274409	+	0.961613i	$0.588482\pi$
$180$	252.277	+	80.1760i	1.40154	+	0.445422i
$181$	−36.6158	−	36.6158i	−0.202297	−	0.202297i	0.598686	−	0.800984i	$-0.295690\pi$
$181$	−36.6158	−	36.6158i	−0.202297	−	0.202297i	−0.800984	+	0.598686i	$0.795690\pi$
$182$	4.06476	+	4.06476i	0.0223338	+	0.0223338i
$183$	200.693	+	122.097i	1.09668	+	0.667198i
$184$	9.52186	−	9.52186i	0.0517492	−	0.0517492i
$185$	449.463			2.42953
$186$	2.45163	−	4.02979i	0.0131808	−	0.0216655i
$187$	273.054	−	38.4307i	1.46018	−	0.205512i
$188$		−	254.999i		−	1.35638i
$189$	−91.4838	−	6.31079i	−0.484041	−	0.0333904i
$190$	26.2940	−	26.2940i	0.138389	−	0.138389i
$191$			162.394i			0.850228i	0.905140	+	0.425114i	$0.139766\pi$
$191$			162.394i			0.850228i	−0.905140	+	0.425114i	$0.860234\pi$
$192$	174.506	−	42.4904i	0.908888	−	0.221304i
$193$	−30.4810	−	30.4810i	−0.157933	−	0.157933i	0.623717	−	0.781650i	$-0.285622\pi$
$193$	−30.4810	−	30.4810i	−0.157933	−	0.157933i	−0.781650	+	0.623717i	$0.785622\pi$
$194$	−10.1151	+	10.1151i	−0.0521397	+	0.0521397i
$195$	−154.737	−	94.1382i	−0.793521	−	0.482760i
$196$			148.232i			0.756287i
$197$	91.4122	−	91.4122i	0.464021	−	0.464021i	−0.435950	−	0.899971i	$-0.643588\pi$
$197$	91.4122	−	91.4122i	0.464021	−	0.464021i	0.899971	+	0.435950i	$0.143588\pi$
$198$	9.21451	−	28.9938i	0.0465379	−	0.146433i
$199$	−33.8948	+	33.8948i	−0.170326	+	0.170326i	−0.787122	−	0.616797i	$-0.788430\pi$
$199$	−33.8948	+	33.8948i	−0.170326	+	0.170326i	0.616797	+	0.787122i	$0.288430\pi$
$200$			50.1775i			0.250888i
$201$	−79.2826	+	19.3045i	−0.394441	+	0.0960421i
$202$			8.58763i			0.0425130i
$203$		−	56.4316i		−	0.277988i
$204$	−185.323	−	79.8281i	−0.908447	−	0.391314i
$205$	85.3501			0.416342
$206$	8.92251			0.0433132
$207$	22.1375	−	69.6565i	0.106945	−	0.336505i
$208$	−125.728			−0.604462
$209$	275.301	+	275.301i	1.31723	+	1.31723i
$210$	−3.73433	−	15.3367i	−0.0177825	−	0.0730321i
$211$	46.7481	+	46.7481i	0.221555	+	0.221555i	0.809153	−	0.587598i	$-0.199926\pi$
$211$	46.7481	+	46.7481i	0.221555	+	0.221555i	−0.587598	+	0.809153i	$0.699926\pi$
$212$	−38.9471			−0.183713
$213$	24.3519	+	14.8151i	0.114328	+	0.0695545i
$214$	10.2975	+	10.2975i	0.0481194	+	0.0481194i
$215$	12.9046	−	12.9046i	0.0600216	−	0.0600216i
$216$	−33.7607	+	29.4035i	−0.156300	+	0.136127i
$217$	25.6245			0.118085
$218$	−20.7610	−	20.7610i	−0.0952339	−	0.0952339i
$219$	3.53233	−	5.80615i	0.0161294	−	0.0265121i
$220$	−477.077			−2.16853
$221$	110.282	+	83.0689i	0.499013	+	0.375878i
$222$	−19.6470	+	32.2941i	−0.0884999	+	0.145469i
$223$			174.588i			0.782907i	0.920198	+	0.391454i	$0.128028\pi$
$223$			174.588i			0.782907i	−0.920198	+	0.391454i	$0.871972\pi$
$224$	−23.6766	−	23.6766i	−0.105699	−	0.105699i
$225$	125.206	+	241.865i	0.556471	+	1.07495i
$226$	8.81395	−	8.81395i	0.0389998	−	0.0389998i
$227$	134.151	−	134.151i	0.590974	−	0.590974i	−0.346921	−	0.937895i	$-0.612773\pi$
$227$	134.151	−	134.151i	0.590974	−	0.590974i	0.937895	+	0.346921i	$0.112773\pi$
$228$	−67.4027	−	276.820i	−0.295626	−	1.21412i
$229$		−	304.733i		−	1.33071i	−0.746527	−	0.665355i	$-0.768280\pi$
$229$		−	304.733i		−	1.33071i	0.746527	−	0.665355i	$-0.231720\pi$
$230$	12.5812			0.0547007
$231$	160.578	−	39.0990i	0.695142	−	0.169260i
$232$	−19.4813	−	19.4813i	−0.0839713	−	0.0839713i
$233$	33.4180	+	33.4180i	0.143425	+	0.143425i	0.775173	−	0.631749i	$-0.217662\pi$
$233$	33.4180	+	33.4180i	0.143425	+	0.143425i	−0.631749	+	0.775173i	$0.717662\pi$
$234$	13.5277	−	7.00289i	0.0578108	−	0.0299269i
$235$	338.778	−	338.778i	1.44161	−	1.44161i
$236$	−292.343			−1.23874
$237$	235.202	+	143.092i	0.992414	+	0.603762i
$238$	1.67698	+	11.9151i	0.00704612	+	0.0500635i
$239$			107.386i			0.449314i	0.974438	+	0.224657i	$0.0721262\pi$
$239$			107.386i			0.449314i	−0.974438	+	0.224657i	$0.927874\pi$
$240$	294.946	+	179.439i	1.22894	+	0.747661i
$241$	311.851	−	311.851i	1.29399	−	1.29399i	0.361691	−	0.932298i	$-0.382200\pi$
$241$	311.851	−	311.851i	1.29399	−	1.29399i	0.932298	−	0.361691i	$-0.117800\pi$
$242$			29.6134i			0.122369i
$243$	−89.3633	+	225.972i	−0.367750	+	0.929925i
$244$	219.076	+	219.076i	0.897853	+	0.897853i
$245$	−196.933	+	196.933i	−0.803810	+	0.803810i
$246$	−3.73083	+	6.13243i	−0.0151660	+	0.0249286i
$247$			194.942i			0.789239i
$248$	8.84609	−	8.84609i	0.0356697	−	0.0356697i
$249$	187.352	−	45.6181i	0.752416	−	0.183205i
$250$	−5.76338	+	5.76338i	−0.0230535	+	0.0230535i
$251$			68.1607i			0.271557i	0.990739	+	0.135778i	$0.0433535\pi$
$251$			68.1607i			0.271557i	−0.990739	+	0.135778i	$0.956646\pi$
$252$	−115.260	−	36.6308i	−0.457381	−	0.145360i
$253$			131.727i			0.520658i
$254$		−	15.3060i		−	0.0602598i
$255$	−140.155	−	352.265i	−0.549628	−	1.38143i
$256$	228.655			0.893183
$257$	−96.8926			−0.377014			−0.188507	−	0.982072i	$-0.560365\pi$
$257$	−96.8926			−0.377014			−0.188507	+	0.982072i	$0.560365\pi$
$258$	0.363113	+	1.49129i	0.00140741	+	0.00578019i
$259$	−205.350			−0.792859
$260$	−168.910	−	168.910i	−0.649654	−	0.649654i
$261$	−142.514	−	45.2925i	−0.546033	−	0.173535i
$262$	−28.2757	−	28.2757i	−0.107922	−	0.107922i
$263$	−313.842			−1.19332			−0.596658	−	0.802496i	$-0.703505\pi$
$263$	−313.842			−1.19332			−0.596658	+	0.802496i	$0.703505\pi$
$264$	41.9370	−	68.9325i	0.158852	−	0.261108i
$265$	−51.7430	−	51.7430i	−0.195257	−	0.195257i
$266$	−12.0132	+	12.0132i	−0.0451623	+	0.0451623i
$267$	100.939	+	414.552i	0.378048	+	1.55263i
$268$	−107.617			−0.401557
$269$	−77.5856	−	77.5856i	−0.288422	−	0.288422i	0.548034	−	0.836456i	$-0.315377\pi$
$269$	−77.5856	−	77.5856i	−0.288422	−	0.288422i	−0.836456	+	0.548034i	$0.815377\pi$
$270$	−41.7292	−	2.87859i	−0.154553	−	0.0106614i
$271$	−428.668			−1.58180			−0.790900	−	0.611946i	$-0.790387\pi$
$271$	−428.668			−1.58180			−0.790900	+	0.611946i	$0.790387\pi$
$272$	−210.210	−	158.339i	−0.772832	−	0.582129i
$273$	70.6959	+	43.0098i	0.258959	+	0.157545i
$274$		−	39.0089i		−	0.142368i
$275$	−347.081	−	347.081i	−1.26211	−	1.26211i
$276$	50.1011	−	82.3520i	0.181526	−	0.298377i
$277$	−253.924	+	253.924i	−0.916694	+	0.916694i	−0.996787	−	0.0800938i	$-0.974478\pi$
$277$	−253.924	+	253.924i	−0.916694	+	0.916694i	0.0800938	+	0.996787i	$0.474478\pi$
$278$	2.18187	−	2.18187i	0.00784846	−	0.00784846i
$279$	20.5664	−	64.7130i	0.0737148	−	0.231946i
$280$		−	41.8644i		−	0.149516i
$281$	291.576			1.03764			0.518818	−	0.854885i	$-0.326372\pi$
$281$	291.576			1.03764			0.518818	+	0.854885i	$0.326372\pi$
$282$	9.53260	+	39.1500i	0.0338035	+	0.138830i
$283$	317.214	+	317.214i	1.12090	+	1.12090i	0.991607	+	0.129291i	$0.0412702\pi$
$283$	317.214	+	317.214i	1.12090	+	1.12090i	0.129291	+	0.991607i	$0.458730\pi$
$284$	26.5824	+	26.5824i	0.0936000	+	0.0936000i
$285$	278.220	−	457.315i	0.976211	−	1.60461i
$286$	−19.4126	+	19.4126i	−0.0678761	+	0.0678761i
$287$	−38.9947			−0.135870
$288$	−78.7968	+	40.7907i	−0.273600	+	0.141634i
$289$	79.7697	+	277.773i	0.276020	+	0.961152i
$290$		−	25.7406i		−	0.0887606i
$291$	−107.029	+	175.926i	−0.367798	+	0.604556i
$292$	6.33798	−	6.33798i	0.0217054	−	0.0217054i
$293$		−	322.630i		−	1.10113i	−0.834794	−	0.550563i	$-0.814413\pi$
$293$		−	322.630i		−	1.10113i	0.834794	−	0.550563i	$-0.185587\pi$
$294$	−5.54135	−	22.7581i	−0.0188481	−	0.0774084i
$295$	−388.391	−	388.391i	−1.31658	−	1.31658i
$296$	−70.8912	+	70.8912i	−0.239497	+	0.239497i
$297$	30.1392	−	436.910i	0.101479	−	1.47108i
$298$			48.9760i			0.164349i
$299$	−46.6380	+	46.6380i	−0.155980	+	0.155980i
$300$	84.9766	+	348.995i	0.283255	+	1.16332i
$301$	−5.89586	+	5.89586i	−0.0195876	+	0.0195876i
$302$		−	33.1300i		−	0.109702i
$303$	29.2463	+	120.113i	0.0965223	+	0.396413i
$304$		−	371.582i		−	1.22231i
$305$			582.105i			1.90854i
$306$	31.4368	+	5.32808i	0.102735	+	0.0174120i
$307$	−274.964			−0.895649			−0.447825	−	0.894121i	$-0.647801\pi$
$307$	−274.964			−0.895649			−0.447825	+	0.894121i	$0.647801\pi$
$308$	217.967			0.707684
$309$	124.797	−	30.3868i	0.403874	−	0.0983390i
$310$	11.6883			0.0377041
$311$	−192.999	−	192.999i	−0.620576	−	0.620576i	0.325103	−	0.945679i	$-0.394601\pi$
$311$	−192.999	−	192.999i	−0.620576	−	0.620576i	−0.945679	+	0.325103i	$0.894601\pi$
$312$	39.2535	−	9.55781i	0.125813	−	0.0306340i
$313$	187.331	+	187.331i	0.598501	+	0.598501i	0.939913	−	0.341413i	$-0.110905\pi$
$313$	187.331	+	187.331i	0.598501	+	0.598501i	−0.341413	+	0.939913i	$0.610905\pi$
$314$	20.1017			0.0640180
$315$	−104.462	−	201.794i	−0.331627	−	0.640615i
$316$	256.746	+	256.746i	0.812487	+	0.812487i
$317$	304.768	−	304.768i	0.961412	−	0.961412i	−0.0378706	−	0.999283i	$-0.512057\pi$
$317$	304.768	−	304.768i	0.961412	−	0.961412i	0.999283	+	0.0378706i	$0.0120575\pi$
$318$	5.97954	−	1.45595i	0.0188036	−	0.00457847i
$319$	269.507			0.844850
$320$	314.697	+	314.697i	0.983427	+	0.983427i
$321$	179.099	+	108.960i	0.557940	+	0.339438i
$322$	−5.74807			−0.0178512
$323$	−245.506	+	325.932i	−0.760079	+	1.00908i
$324$	−185.017	+	261.682i	−0.571042	+	0.807660i
$325$		−	245.769i		−	0.756213i
$326$	30.6240	+	30.6240i	0.0939387	+	0.0939387i
$327$	−361.083	−	219.675i	−1.10423	−	0.671789i
$328$	−13.4618	+	13.4618i	−0.0410419	+	0.0410419i
$329$	−154.781	+	154.781i	−0.470458	+	0.470458i
$330$	73.2455	−	17.8345i	0.221956	−	0.0540439i
$331$			311.214i			0.940223i	0.882607	+	0.470111i	$0.155786\pi$
$331$			311.214i			0.940223i	−0.882607	+	0.470111i	$0.844214\pi$
$332$	254.309			0.765991
$333$	−164.816	+	518.600i	−0.494944	+	1.55736i
$334$	37.5251	+	37.5251i	0.112351	+	0.112351i
$335$	−142.975	−	142.975i	−0.426790	−	0.426790i
$336$	−134.755	−	81.9818i	−0.401056	−	0.243993i
$337$	213.957	−	213.957i	0.634887	−	0.634887i	−0.314402	−	0.949290i	$-0.601804\pi$
$337$	213.957	−	213.957i	0.634887	−	0.634887i	0.949290	+	0.314402i	$0.101804\pi$
$338$	21.4734			0.0635309
$339$	93.2616	−	153.296i	0.275108	−	0.452200i
$340$	−69.6863	−	495.129i	−0.204960	−	1.45626i
$341$			122.378i			0.358879i
$342$	20.6966	+	39.9804i	0.0605165	+	0.116902i
$343$	207.652	−	207.652i	0.605399	−	0.605399i
$344$			4.07074i			0.0118336i
$345$	175.970	−	42.8468i	0.510058	−	0.124194i
$346$	−12.2783	−	12.2783i	−0.0354865	−	0.0354865i
$347$	435.384	−	435.384i	1.25471	−	1.25471i	0.301124	−	0.953585i	$-0.402638\pi$
$347$	435.384	−	435.384i	1.25471	−	1.25471i	0.953585	−	0.301124i	$-0.0973617\pi$
$348$	−168.489	−	102.505i	−0.484163	−	0.294554i
$349$			120.847i			0.346267i	0.984898	+	0.173133i	$0.0553892\pi$
$349$			120.847i			0.346267i	−0.984898	+	0.173133i	$0.944611\pi$
$350$	15.1454	−	15.1454i	0.0432725	−	0.0432725i
$351$	165.360	−	144.018i	0.471111	−	0.410308i
$352$	113.075	−	113.075i	0.321236	−	0.321236i
$353$			25.6098i			0.0725491i	0.999342	+	0.0362745i	$0.0115491\pi$
$353$			25.6098i			0.0725491i	−0.999342	+	0.0362745i	$0.988451\pi$
$354$	44.8834	−	10.9286i	0.126789	−	0.0308718i
$355$			70.6319i			0.198963i
$356$			562.708i			1.58064i
$357$	64.0339	+	160.943i	0.179367	+	0.450820i
$358$	20.4729			0.0571868
$359$	326.176			0.908568			0.454284	−	0.890857i	$-0.349895\pi$
$359$	326.176			0.908568			0.454284	+	0.890857i	$0.349895\pi$
$360$	−105.726	−	33.6007i	−0.293683	−	0.0933354i
$361$	−215.140			−0.595955
$362$	7.63072	+	7.63072i	0.0210793	+	0.0210793i
$363$	100.852	+	414.195i	0.277829	+	1.14103i
$364$	77.1714	+	77.1714i	0.212009	+	0.212009i
$365$	16.8406			0.0461386
$366$	−41.8244	−	25.4450i	−0.114274	−	0.0695219i
$367$	−291.432	−	291.432i	−0.794092	−	0.794092i	0.188065	−	0.982157i	$-0.439778\pi$
$367$	−291.432	−	291.432i	−0.794092	−	0.794092i	−0.982157	+	0.188065i	$0.939778\pi$
$368$	88.8976	−	88.8976i	0.241569	−	0.241569i
$369$	−31.2975	+	98.4786i	−0.0848170	+	0.266880i
$370$	−93.6681			−0.253157
$371$	23.6403	+	23.6403i	0.0637205	+	0.0637205i
$372$	46.5454	−	76.5074i	0.125122	−	0.205665i
$373$	−151.514			−0.406204			−0.203102	−	0.979158i	$-0.565102\pi$
$373$	−151.514			−0.406204			−0.203102	+	0.979158i	$0.565102\pi$
$374$	−56.9044	+	8.00894i	−0.152151	+	0.0214143i
$375$	−60.9831	+	100.239i	−0.162622	+	0.267304i
$376$			106.867i			0.284220i
$377$	95.4195	+	95.4195i	0.253102	+	0.253102i
$378$	19.0652	+	1.31517i	0.0504370	+	0.00347928i
$379$	19.0727	−	19.0727i	0.0503238	−	0.0503238i	−0.681497	−	0.731821i	$-0.738671\pi$
$379$	19.0727	−	19.0727i	0.0503238	−	0.0503238i	0.731821	+	0.681497i	$0.238671\pi$
$380$	499.204	−	499.204i	1.31369	−	1.31369i
$381$	−52.1265	−	214.081i	−0.136815	−	0.561893i
$382$		−	33.8428i		−	0.0885937i
$383$	−375.569			−0.980597			−0.490299	−	0.871555i	$-0.663112\pi$
$383$	−375.569			−0.980597			−0.490299	+	0.871555i	$0.663112\pi$
$384$	−151.314	+	36.8433i	−0.394047	+	0.0959461i
$385$	289.578	+	289.578i	0.752152	+	0.752152i
$386$	6.35223	+	6.35223i	0.0164565	+	0.0164565i
$387$	10.1576	+	19.6217i	0.0262469	+	0.0507021i
$388$	−192.040	+	192.040i	−0.494949	+	0.494949i
$389$	−699.064			−1.79708			−0.898540	−	0.438891i	$-0.855371\pi$
$389$	−699.064			−1.79708			−0.898540	+	0.438891i	$0.855371\pi$
$390$	32.2471	+	19.6184i	0.0826848	+	0.0503035i
$391$	−136.711	+	19.2412i	−0.349644	+	0.0492103i
$392$		−	62.1222i		−	0.158475i
$393$	−491.782	−	299.189i	−1.25135	−	0.761295i
$394$	−19.0503	+	19.0503i	−0.0483509	+	0.0483509i
$395$			682.197i			1.72708i
$396$	174.942	−	550.461i	0.441773	−	1.39005i
$397$	77.1209	+	77.1209i	0.194259	+	0.194259i	0.797534	−	0.603274i	$-0.206138\pi$
$397$	77.1209	+	77.1209i	0.194259	+	0.194259i	−0.603274	+	0.797534i	$0.706138\pi$
$398$	7.06367	−	7.06367i	0.0177479	−	0.0177479i
$399$	−127.113	+	208.938i	−0.318579	+	0.523654i
$400$			468.465i			1.17116i
$401$	414.092	−	414.092i	1.03265	−	1.03265i	0.0332009	−	0.999449i	$-0.489430\pi$
$401$	414.092	−	414.092i	1.03265	−	1.03265i	0.999449	−	0.0332009i	$-0.0105701\pi$
$402$	16.5225	−	4.02304i	0.0411007	−	0.0100076i
$403$	−43.3281	+	43.3281i	−0.107514	+	0.107514i
$404$			163.040i			0.403565i
$405$	−593.460	+	101.852i	−1.46533	+	0.251486i
$406$			11.7603i			0.0289663i
$407$		−	980.717i		−	2.40962i
$408$	77.6665	+	33.4549i	0.190359	+	0.0819973i
$409$	−187.440			−0.458289			−0.229144	−	0.973392i	$-0.573593\pi$
$409$	−187.440			−0.458289			−0.229144	+	0.973392i	$0.573593\pi$
$410$	−17.7869			−0.0433828
$411$	−132.850	−	545.608i	−0.323235	−	1.32751i
$412$	169.398			0.411161
$413$	177.448	+	177.448i	0.429656	+	0.429656i
$414$	−4.61346	+	14.5164i	−0.0111436	+	0.0350638i
$415$	337.861	+	337.861i	0.814123	+	0.814123i
$416$	80.0689			0.192473
$417$	23.0867	−	37.9480i	0.0553638	−	0.0910023i
$418$	−57.3727	−	57.3727i	−0.137255	−	0.137255i
$419$	−136.575	+	136.575i	−0.325955	+	0.325955i	−0.851046	−	0.525091i	$-0.824031\pi$
$419$	−136.575	+	136.575i	−0.325955	+	0.325955i	0.525091	+	0.851046i	$0.324031\pi$
$420$	−70.8981	−	291.176i	−0.168805	−	0.693275i
$421$	−43.5185			−0.103369			−0.0516846	−	0.998663i	$-0.516459\pi$
$421$	−43.5185			−0.103369			−0.0516846	+	0.998663i	$0.516459\pi$
$422$	−9.74228	−	9.74228i	−0.0230860	−	0.0230860i
$423$	266.660	+	515.117i	0.630403	+	1.21777i
$424$	16.3222			0.0384958
$425$	309.516	−	410.912i	0.728273	−	0.966852i
$426$	−5.07492	−	3.08747i	−0.0119130	−	0.00724757i
$427$		−	265.952i		−	0.622838i
$428$	195.504	+	195.504i	0.456785	+	0.456785i
$429$	−205.407	+	337.631i	−0.478804	+	0.787019i
$430$	−2.68932	+	2.68932i	−0.00625424	+	0.00625424i
$431$	−383.047	+	383.047i	−0.888741	+	0.888741i	−0.994402	−	0.105661i	$-0.966304\pi$
$431$	−383.047	+	383.047i	−0.888741	+	0.888741i	0.105661	+	0.994402i	$0.466304\pi$
$432$	−315.195	+	274.516i	−0.729619	+	0.635453i
$433$		−	546.173i		−	1.26137i	−0.776039	−	0.630685i	$-0.782774\pi$
$433$		−	546.173i		−	1.26137i	0.776039	−	0.630685i	$-0.217226\pi$
$434$	−5.34013			−0.0123045
$435$	−87.6628	−	360.027i	−0.201524	−	0.827649i
$436$	−394.157	−	394.157i	−0.904031	−	0.904031i
$437$	−137.836	−	137.836i	−0.315414	−	0.315414i
$438$	−0.736137	+	1.21000i	−0.00168068	+	0.00276256i
$439$	176.803	−	176.803i	0.402740	−	0.402740i	−0.476458	−	0.879197i	$-0.658079\pi$
$439$	176.803	−	176.803i	0.402740	−	0.402740i	0.879197	+	0.476458i	$0.158079\pi$
$440$	199.937			0.454402
$441$	−155.011	−	299.440i	−0.351499	−	0.679003i
$442$	−22.9827	−	17.3115i	−0.0519971	−	0.0391664i
$443$		−	44.3558i		−	0.100126i	−0.998746	−	0.0500630i	$-0.984058\pi$
$443$		−	44.3558i		−	0.100126i	0.998746	−	0.0500630i	$-0.0159422\pi$
$444$	−373.008	+	613.119i	−0.840107	+	1.38090i
$445$	−747.583	+	747.583i	−1.67996	+	1.67996i
$446$		−	36.3842i		−	0.0815788i
$447$	166.794	+	685.016i	0.373141	+	1.53247i
$448$	−143.778	−	143.778i	−0.320934	−	0.320934i
$449$	−104.094	+	104.094i	−0.231835	+	0.231835i	−0.813458	−	0.581623i	$-0.802418\pi$
$449$	−104.094	+	104.094i	−0.231835	+	0.231835i	0.581623	+	0.813458i	$0.302418\pi$
$450$	−26.0929	−	50.4045i	−0.0579842	−	0.112010i
$451$		−	186.232i		−	0.412930i
$452$	167.337	−	167.337i	0.370215	−	0.370215i
$453$	−112.828	−	463.382i	−0.249069	−	1.02292i
$454$	−27.9570	+	27.9570i	−0.0615794	+	0.0615794i
$455$			205.052i			0.450663i
$456$	28.2476	+	116.012i	0.0619464	+	0.254411i
$457$		−	52.3160i		−	0.114477i	−0.998361	−	0.0572385i	$-0.981770\pi$
$457$		−	52.3160i		−	0.114477i	0.998361	−	0.0572385i	$-0.0182295\pi$
$458$			63.5062i			0.138660i
$459$	457.845	−	32.5396i	0.997484	−	0.0708923i
$460$	238.860			0.519260
$461$	−291.344			−0.631983			−0.315991	−	0.948762i	$-0.602337\pi$
$461$	−291.344			−0.631983			−0.315991	+	0.948762i	$0.602337\pi$
$462$	−33.4644	+	8.14821i	−0.0724337	+	0.0176368i
$463$	711.561			1.53685			0.768425	−	0.639940i	$-0.221041\pi$
$463$	711.561			1.53685			0.768425	+	0.639940i	$0.221041\pi$
$464$	−181.881	−	181.881i	−0.391985	−	0.391985i
$465$	163.481	−	39.8059i	0.351573	−	0.0856041i
$466$	−6.96430	−	6.96430i	−0.0149449	−	0.0149449i
$467$	378.114			0.809666			0.404833	−	0.914391i	$-0.367330\pi$
$467$	378.114			0.809666			0.404833	+	0.914391i	$0.367330\pi$
$468$	256.830	−	132.953i	0.548783	−	0.284088i
$469$	65.3221	+	65.3221i	0.139279	+	0.139279i
$470$	−70.6012	+	70.6012i	−0.150215	+	0.150215i
$471$	281.157	−	68.4588i	0.596937	−	0.145348i
$472$	122.517			0.259571
$473$	−28.1576	−	28.1576i	−0.0595297	−	0.0595297i
$474$	−49.0160	−	29.8202i	−0.103409	−	0.0629119i
$475$	726.357			1.52917
$476$	31.8382	+	226.214i	0.0668870	+	0.475240i
$477$	78.6760	−	40.7282i	0.164939	−	0.0853840i
$478$		−	22.3792i		−	0.0468185i
$479$	152.051	+	152.051i	0.317434	+	0.317434i	0.847781	−	0.530347i	$-0.177938\pi$
$479$	152.051	+	152.051i	0.317434	+	0.317434i	−0.530347	+	0.847781i	$0.677938\pi$
$480$	−187.834	−	114.274i	−0.391321	−	0.238071i
$481$	347.225	−	347.225i	0.721881	−	0.721881i
$482$	−64.9897	+	64.9897i	−0.134833	+	0.134833i
$483$	−80.3970	+	19.5758i	−0.166453	+	0.0405296i
$484$			562.224i			1.16162i
$485$	−510.268			−1.05210
$486$	18.6233	−	47.0924i	0.0383195	−	0.0968980i
$487$	−329.746	−	329.746i	−0.677097	−	0.677097i	0.282245	−	0.959342i	$-0.408921\pi$
$487$	−329.746	−	329.746i	−0.677097	−	0.677097i	−0.959342	+	0.282245i	$0.908921\pi$
$488$	−91.8120	−	91.8120i	−0.188139	−	0.188139i
$489$	532.625	+	324.037i	1.08921	+	0.662652i
$490$	41.0409	−	41.0409i	0.0837568	−	0.0837568i
$491$	432.522			0.880900			0.440450	−	0.897777i	$-0.354819\pi$
$491$	432.522			0.880900			0.440450	+	0.897777i	$0.354819\pi$
$492$	−70.8316	+	116.427i	−0.143967	+	0.236640i
$493$	39.3667	+	279.705i	0.0798514	+	0.567353i
$494$		−	40.6259i		−	0.0822386i
$495$	963.731	−	498.894i	1.94693	−	1.00787i
$496$	82.5885	−	82.5885i	0.166509	−	0.166509i
$497$		−	32.2702i		−	0.0649300i
$498$	−39.0440	+	9.50680i	−0.0784016	+	0.0190900i
$499$	29.1588	+	29.1588i	0.0584344	+	0.0584344i	0.735720	−	0.677286i	$-0.236844\pi$
$499$	29.1588	+	29.1588i	0.0584344	+	0.0584344i	−0.677286	+	0.735720i	$0.736844\pi$
$500$	−109.421	+	109.421i	−0.218841	+	0.218841i
$501$	652.651	+	397.058i	1.30270	+	0.792531i
$502$		−	14.2047i		−	0.0282962i
$503$	−537.457	+	537.457i	−1.06850	+	1.06850i	−0.0710294	+	0.997474i	$0.522628\pi$
$503$	−537.457	+	537.457i	−1.06850	+	1.06850i	−0.997474	+	0.0710294i	$0.977372\pi$
$504$	48.3040	+	15.3515i	0.0958412	+	0.0304593i
$505$	−216.606	+	216.606i	−0.428924	+	0.428924i
$506$		−	27.4518i		−	0.0542525i
$507$	300.344	−	73.1305i	0.592394	−	0.144242i
$508$		−	290.592i		−	0.572031i
$509$			56.9404i			0.111867i	0.998434	+	0.0559336i	$0.0178135\pi$
$509$			56.9404i			0.111867i	−0.998434	+	0.0559336i	$0.982186\pi$
$510$	29.2083	+	73.4120i	0.0572711	+	0.143945i
$511$	−7.69411			−0.0150570
$512$	−255.298			−0.498629
$513$	425.637	+	488.711i	0.829702	+	0.952654i
$514$	20.1924			0.0392848
$515$	225.053	+	225.053i	0.436997	+	0.436997i
$516$	6.89388	+	28.3129i	0.0133602	+	0.0548699i
$517$	−739.204	−	739.204i	−1.42980	−	1.42980i
$518$	42.7950			0.0826158
$519$	−213.550	−	129.919i	−0.411463	−	0.250325i
$520$	70.7880	+	70.7880i	0.136131	+	0.136131i
$521$	−526.193	+	526.193i	−1.00997	+	1.00997i	−0.0100166	+	0.999950i	$0.503188\pi$
$521$	−526.193	+	526.193i	−1.00997	+	1.00997i	−0.999950	+	0.0100166i	$0.996812\pi$
$522$	29.7000	+	9.43895i	0.0568965	+	0.0180823i
$523$	−917.253			−1.75383			−0.876915	−	0.480645i	$-0.840403\pi$
$523$	−917.253			−1.75383			−0.876915	+	0.480645i	$0.840403\pi$
$524$	−536.828	−	536.828i	−1.02448	−	1.02448i
$525$	160.255	−	263.414i	0.305248	−	0.501741i
$526$	65.4046			0.124343
$527$	−127.009	+	17.8757i	−0.241003	+	0.0339197i
$528$	391.530	−	643.565i	0.741534	−	1.21887i
$529$			463.048i			0.875327i
$530$	10.7832	+	10.7832i	0.0203457	+	0.0203457i
$531$	590.555	−	305.712i	1.11216	−	0.575730i
$532$	−228.076	+	228.076i	−0.428714	+	0.428714i
$533$	65.9356	−	65.9356i	0.123707	−	0.123707i
$534$	−21.0356	−	86.3925i	−0.0393926	−	0.161784i
$535$			519.471i			0.970974i
$536$	45.1010			0.0841437
$537$	286.349	−	69.7230i	0.533239	−	0.129838i
$538$	16.1688	+	16.1688i	0.0300536	+	0.0300536i
$539$	429.703	+	429.703i	0.797223	+	0.797223i
$540$	−792.249	−	54.6514i	−1.46713	−	0.101206i
$541$	118.414	−	118.414i	0.218879	−	0.218879i	−0.589147	−	0.808026i	$-0.700536\pi$
$541$	118.414	−	118.414i	0.218879	−	0.218879i	0.808026	+	0.589147i	$0.200536\pi$
$542$	89.3342			0.164823
$543$	132.716	+	80.7417i	0.244413	+	0.148696i
$544$	133.871	+	100.837i	0.246086	+	0.185362i
$545$		−	1047.31i		−	1.92167i
$546$	−14.7330	−	8.96323i	−0.0269835	−	0.0164162i
$547$	50.1729	−	50.1729i	0.0917238	−	0.0917238i	−0.659756	−	0.751480i	$-0.729340\pi$
$547$	50.1729	−	50.1729i	0.0917238	−	0.0917238i	0.751480	+	0.659756i	$0.229340\pi$
$548$		−	740.602i		−	1.35146i
$549$	−671.645	−	213.455i	−1.22340	−	0.388807i
$550$	72.3316	+	72.3316i	0.131512	+	0.131512i
$551$	−282.007	+	282.007i	−0.511809	+	0.511809i
$552$	−20.9967	+	34.5126i	−0.0380375	+	0.0625229i
$553$		−	311.682i		−	0.563619i
$554$	52.9177	−	52.9177i	0.0955193	−	0.0955193i
$555$	−1310.11	+	318.998i	−2.36056	+	0.574772i
$556$	41.4239	−	41.4239i	0.0745034	−	0.0745034i
$557$		−	423.368i		−	0.760085i	−0.924969	−	0.380043i	$-0.875909\pi$
$557$		−	423.368i		−	0.760085i	0.924969	−	0.380043i	$-0.124091\pi$
$558$	−4.28604	+	13.4862i	−0.00768107	+	0.0241688i
$559$		−	19.9385i		−	0.0356681i
$560$		−	390.852i		−	0.697951i
$561$	−768.634	+	305.815i	−1.37011	+	0.545124i
$562$	−60.7643			−0.108121
$563$	48.4445			0.0860471			0.0430236	−	0.999074i	$-0.486301\pi$
$563$	48.4445			0.0860471			0.0430236	+	0.999074i	$0.486301\pi$
$564$	180.981	+	743.281i	0.320888	+	1.31787i
$565$	444.630			0.786955
$566$	−66.1073	−	66.1073i	−0.116797	−	0.116797i
$567$	271.140	−	46.5340i	0.478200	−	0.0820706i
$568$	−11.1403	−	11.1403i	−0.0196133	−	0.0196133i
$569$	−732.102			−1.28665			−0.643323	−	0.765595i	$-0.722445\pi$
$569$	−732.102			−1.28665			−0.643323	+	0.765595i	$0.722445\pi$
$570$	−57.9810	+	95.3043i	−0.101721	+	0.167201i
$571$	309.245	+	309.245i	0.541584	+	0.541584i	0.923993	−	0.382409i	$-0.124905\pi$
$571$	309.245	+	309.245i	0.541584	+	0.541584i	−0.382409	+	0.923993i	$0.624905\pi$
$572$	−368.557	+	368.557i	−0.644330	+	0.644330i
$573$	−115.256	−	473.351i	−0.201145	−	0.826093i
$574$	8.12648			0.0141576
$575$	173.774	+	173.774i	0.302216	+	0.302216i
$576$	−478.501	+	247.706i	−0.830731	+	0.430044i
$577$	791.867			1.37239			0.686193	−	0.727419i	$-0.259281\pi$
$577$	791.867			1.37239			0.686193	+	0.727419i	$0.259281\pi$
$578$	−16.6240	−	57.8878i	−0.0287612	−	0.100152i
$579$	110.480	+	67.2138i	0.190813	+	0.116086i
$580$		−	488.697i		−	0.842581i
$581$	−154.362	−	154.362i	−0.265683	−	0.265683i
$582$	22.3049	−	36.6629i	0.0383245	−	0.0629946i
$583$	−112.902	+	112.902i	−0.193657	+	0.193657i
$584$	−2.65616	+	2.65616i	−0.00454823	+	0.00454823i
$585$	517.845	+	164.576i	0.885205	+	0.281327i
$586$			67.2360i			0.114737i
$587$	914.776			1.55839			0.779196	−	0.626780i	$-0.215628\pi$
$587$	914.776			1.55839			0.779196	+	0.626780i	$0.215628\pi$
$588$	−105.205	−	432.073i	−0.178920	−	0.734818i
$589$	−128.054	−	128.054i	−0.217409	−	0.217409i
$590$	80.9406	+	80.9406i	0.137188	+	0.137188i
$591$	−201.574	+	331.330i	−0.341072	+	0.560626i
$592$	−661.851	+	661.851i	−1.11799	+	1.11799i
$593$	476.612			0.803730			0.401865	−	0.915699i	$-0.368362\pi$
$593$	476.612			0.803730			0.401865	+	0.915699i	$0.368362\pi$
$594$	−6.28100	+	91.0520i	−0.0105741	+	0.153286i
$595$	−258.237	+	342.834i	−0.434012	+	0.576192i
$596$			929.833i			1.56012i
$597$	74.7417	−	122.854i	0.125195	−	0.205786i
$598$	9.71935	−	9.71935i	0.0162531	−	0.0162531i
$599$		−	338.504i		−	0.565116i	−0.959250	−	0.282558i	$-0.908817\pi$
$599$		−	338.504i		−	0.565116i	0.959250	−	0.282558i	$-0.0911829\pi$
$600$	−35.6126	−	146.259i	−0.0593543	−	0.243766i
$601$	−475.300	−	475.300i	−0.790848	−	0.790848i	0.190784	−	0.981632i	$-0.438897\pi$
$601$	−475.300	−	475.300i	−0.790848	−	0.790848i	−0.981632	+	0.190784i	$0.938897\pi$
$602$	1.22870	−	1.22870i	0.00204102	−	0.00204102i
$603$	217.395	−	112.539i	0.360522	−	0.186631i
$604$		−	628.989i		−	1.04137i
$605$	−746.940	+	746.940i	−1.23461	+	1.23461i
$606$	−6.09491	−	25.0315i	−0.0100576	−	0.0413062i
$607$	39.2266	−	39.2266i	0.0646237	−	0.0646237i	−0.674056	−	0.738680i	$-0.735449\pi$
$607$	39.2266	−	39.2266i	0.0646237	−	0.0646237i	0.738680	+	0.674056i	$0.235449\pi$
$608$			236.639i			0.389209i
$609$	40.0513	+	164.489i	0.0657657	+	0.270097i
$610$		−	121.311i		−	0.198870i
$611$		−	523.433i		−	0.856683i
$612$	596.844	+	101.156i	0.975235	+	0.165288i
$613$	610.766			0.996355			0.498178	−	0.867075i	$-0.334003\pi$
$613$	610.766			0.996355			0.498178	+	0.867075i	$0.334003\pi$
$614$	57.3025			0.0933265
$615$	−248.782	+	60.5757i	−0.404523	+	0.0984970i
$616$	−91.3469			−0.148290
$617$	−489.618	−	489.618i	−0.793546	−	0.793546i	0.188523	−	0.982069i	$-0.439630\pi$
$617$	−489.618	−	489.618i	−0.793546	−	0.793546i	−0.982069	+	0.188523i	$0.939630\pi$
$618$	−26.0077	+	6.33259i	−0.0420836	+	0.0102469i
$619$	−144.357	−	144.357i	−0.233209	−	0.233209i	0.580822	−	0.814031i	$-0.302731\pi$
$619$	−144.357	−	144.357i	−0.233209	−	0.233209i	−0.814031	+	0.580822i	$0.802731\pi$
$620$	221.908			0.357916
$621$	−15.0899	+	218.749i	−0.0242993	+	0.352253i
$622$	40.2210	+	40.2210i	0.0646639	+	0.0646639i
$623$	341.555	−	341.555i	0.548243	−	0.548243i
$624$	366.477	−	89.2333i	0.587303	−	0.143002i
$625$	465.790			0.745264
$626$	−39.0397	−	39.0397i	−0.0623637	−	0.0623637i
$627$	−997.849	−	607.069i	−1.59147	−	0.968212i
$628$	381.640			0.607707
$629$	1017.83	−	143.253i	1.61817	−	0.227747i
$630$	21.7699	+	42.0538i	0.0345555	+	0.0667520i
$631$			138.795i			0.219960i	0.993934	+	0.109980i	$0.0350787\pi$
$631$			138.795i			0.219960i	−0.993934	+	0.109980i	$0.964921\pi$
$632$	−107.599	−	107.599i	−0.170251	−	0.170251i
$633$	−169.442	−	103.084i	−0.267680	−	0.162851i
$634$	−63.5135	+	63.5135i	−0.100179	+	0.100179i
$635$	386.064	−	386.064i	0.607975	−	0.607975i
$636$	113.525	−	27.6420i	0.178498	−	0.0434623i
$637$			304.274i			0.477668i
$638$	−56.1652			−0.0880333
$639$	−81.4965	−	25.9004i	−0.127538	−	0.0405327i
$640$	−272.872	−	272.872i	−0.426363	−	0.426363i
$641$	222.717	+	222.717i	0.347453	+	0.347453i	0.859160	−	0.511707i	$-0.170987\pi$
$641$	222.717	+	222.717i	0.347453	+	0.347453i	−0.511707	+	0.859160i	$0.670987\pi$
$642$	−37.3242	−	22.7072i	−0.0581373	−	0.0353694i
$643$	−417.674	+	417.674i	−0.649570	+	0.649570i	−0.952889	−	0.303319i	$-0.901905\pi$
$643$	−417.674	+	417.674i	−0.649570	+	0.649570i	0.303319	+	0.952889i	$0.401905\pi$
$644$	−109.130			−0.169456
$645$	−28.4561	+	46.7737i	−0.0441180	+	0.0725174i
$646$	51.1633	−	67.9241i	0.0792001	−	0.105146i
$647$			790.271i			1.22144i	0.791847	+	0.610720i	$0.209120\pi$
$647$			790.271i			1.22144i	−0.791847	+	0.610720i	$0.790880\pi$
$648$	77.5384	−	109.667i	0.119658	−	0.169240i
$649$	−847.459	+	847.459i	−1.30579	+	1.30579i
$650$			51.2182i			0.0787973i
$651$	−74.6912	+	18.1865i	−0.114733	+	0.0279362i
$652$	581.412	+	581.412i	0.891736	+	0.891736i
$653$	−263.332	+	263.332i	−0.403265	+	0.403265i	−0.879382	−	0.476117i	$-0.842044\pi$
$653$	−263.332	+	263.332i	−0.403265	+	0.403265i	0.476117	+	0.879382i	$0.342044\pi$
$654$	75.2497	+	45.7802i	0.115061	+	0.0700003i
$655$		−	1426.40i		−	2.17771i
$656$	−125.681	+	125.681i	−0.191587	+	0.191587i
$657$	−6.17537	+	19.4310i	−0.00939934	+	0.0295753i
$658$	32.2562	−	32.2562i	0.0490216	−	0.0490216i
$659$		−	237.290i		−	0.360076i	−0.983660	−	0.180038i	$-0.942378\pi$
$659$		−	237.290i		−	0.360076i	0.983660	−	0.180038i	$-0.0576221\pi$
$660$	1390.60	−	338.597i	2.10697	−	0.513025i
$661$			808.638i			1.22336i	0.791107	+	0.611678i	$0.209505\pi$
$661$			808.638i			1.22336i	−0.791107	+	0.611678i	$0.790495\pi$
$662$		−	64.8568i		−	0.0979711i
$663$	−380.410	−	163.862i	−0.573771	−	0.247152i
$664$	−106.578			−0.160508
$665$	−606.018			−0.911305
$666$	34.3476	−	108.076i	0.0515730	−	0.162276i
$667$	−134.935			−0.202301
$668$	712.432	+	712.432i	1.06651	+	1.06651i
$669$	−123.911	−	508.897i	−0.185218	−	0.760683i
$670$	29.7958	+	29.7958i	0.0444714	+	0.0444714i
$671$	1270.14			1.89290
$672$	85.8174	+	52.2094i	0.127704	+	0.0776925i
$673$	−761.037	−	761.037i	−1.13081	−	1.13081i	−0.990042	−	0.140771i	$-0.955042\pi$
$673$	−761.037	−	761.037i	−1.13081	−	1.13081i	−0.140771	−	0.990042i	$-0.544958\pi$
$674$	−44.5886	+	44.5886i	−0.0661552	+	0.0661552i
$675$	−536.614	−	616.133i	−0.794983	−	0.912790i
$676$	407.684			0.603082
$677$	674.888	+	674.888i	0.996880	+	0.996880i	0.999995	−	0.00311505i	$-0.000991552\pi$
$677$	674.888	+	674.888i	0.996880	+	0.996880i	−0.00311505	+	0.999995i	$0.500992\pi$
$678$	−19.4357	+	31.9468i	−0.0286662	+	0.0471191i
$679$	233.131			0.343344
$680$	29.2046	+	207.502i	0.0429480	+	0.305150i
$681$	−295.817	+	486.240i	−0.434387	+	0.714009i
$682$		−	25.5035i		−	0.0373952i
$683$	281.976	+	281.976i	0.412849	+	0.412849i	0.882730	−	0.469881i	$-0.155703\pi$
$683$	281.976	+	281.976i	0.412849	+	0.412849i	−0.469881	+	0.882730i	$0.655703\pi$
$684$	392.936	+	759.047i	0.574467	+	1.10972i
$685$	983.923	−	983.923i	1.43638	−	1.43638i
$686$	−43.2746	+	43.2746i	−0.0630825	+	0.0630825i
$687$	216.279	+	888.247i	0.314816	+	1.29294i
$688$			38.0051i			0.0552400i
$689$	−79.9462			−0.116032
$690$	−36.6721	+	8.92925i	−0.0531479	+	0.0129409i
$691$	−83.8802	−	83.8802i	−0.121390	−	0.121390i	0.643802	−	0.765192i	$-0.277356\pi$
$691$	−83.8802	−	83.8802i	−0.121390	−	0.121390i	−0.765192	+	0.643802i	$0.777356\pi$
$692$	−233.110	−	233.110i	−0.336864	−	0.336864i
$693$	−440.308	+	227.934i	−0.635366	+	0.328909i
$694$	−90.7339	+	90.7339i	−0.130740	+	0.130740i
$695$	110.067			0.158370
$696$	70.6115	+	42.9584i	0.101453	+	0.0617219i
$697$	193.278	−	27.2027i	0.277300	−	0.0390283i
$698$		−	25.1845i		−	0.0360810i
$699$	−121.126	−	73.6902i	−0.173284	−	0.105422i
$700$	287.542	−	287.542i	0.410774	−	0.410774i
$701$		−	439.507i		−	0.626972i	−0.949593	−	0.313486i	$-0.898503\pi$
$701$		−	439.507i		−	0.626972i	0.949593	−	0.313486i	$-0.101497\pi$
$702$	−34.4609	+	30.0133i	−0.0490896	+	0.0427540i
$703$	1026.20	+	1026.20i	1.45975	+	1.45975i
$704$	686.660	−	686.660i	0.975369	−	0.975369i
$705$	−747.041	+	1227.92i	−1.05963	+	1.74174i
$706$		−	5.33708i		−	0.00755960i
$707$	98.9629	−	98.9629i	0.139976	−	0.139976i
$708$	852.133	−	207.485i	1.20358	−	0.293058i
$709$	542.109	−	542.109i	0.764611	−	0.764611i	−0.212541	−	0.977152i	$-0.568174\pi$
$709$	542.109	−	542.109i	0.764611	−	0.764611i	0.977152	+	0.212541i	$0.0681740\pi$
$710$		−	14.7197i		−	0.0207319i
$711$	−787.132	−	250.158i	−1.10708	−	0.351840i
$712$		−	235.824i		−	0.331213i
$713$		−	61.2713i		−	0.0859345i
$714$	−13.3446	−	33.5404i	−0.0186900	−	0.0469754i
$715$	−979.289			−1.36964
$716$	388.688			0.542860
$717$	−76.2153	−	313.013i	−0.106298	−	0.436559i
$718$	−67.9750			−0.0946726
$719$	−93.0554	−	93.0554i	−0.129423	−	0.129423i	0.639428	−	0.768851i	$-0.279171\pi$
$719$	−93.0554	−	93.0554i	−0.129423	−	0.129423i	−0.768851	+	0.639428i	$0.779171\pi$
$720$	−987.074	−	313.702i	−1.37094	−	0.435697i
$721$	−102.822	−	102.822i	−0.142610	−	0.142610i
$722$	44.8351			0.0620985
$723$	−687.665	+	1130.33i	−0.951128	+	1.56338i
$724$	144.873	+	144.873i	0.200101	+	0.200101i
$725$	355.535	−	355.535i	0.490393	−	0.490393i
$726$	−21.0176	−	86.3182i	−0.0289498	−	0.118896i
$727$	−331.684			−0.456236			−0.228118	−	0.973634i	$-0.573257\pi$
$727$	−331.684			−0.456236			−0.228118	+	0.973634i	$0.573257\pi$
$728$	−32.3415	−	32.3415i	−0.0444252	−	0.0444252i
$729$	100.100	−	722.095i	0.137312	−	0.990528i
$730$	−3.50957			−0.00480763
$731$	25.1101	−	33.3360i	0.0343503	−	0.0456033i
$732$	−794.057	−	483.086i	−1.08478	−	0.659954i
$733$			288.501i			0.393589i	0.980445	+	0.196795i	$0.0630533\pi$
$733$			288.501i			0.393589i	−0.980445	+	0.196795i	$0.936947\pi$
$734$	60.7343	+	60.7343i	0.0827442	+	0.0827442i
$735$	434.259	−	713.799i	0.590829	−	0.971155i
$736$	−56.6137	+	56.6137i	−0.0769207	+	0.0769207i
$737$	−311.967	+	311.967i	−0.423292	+	0.423292i
$738$	6.52239	−	20.5229i	0.00883792	−	0.0278088i
$739$		−	778.144i		−	1.05297i	−0.850185	−	0.526484i	$-0.823510\pi$
$739$		−	778.144i		−	1.05297i	0.850185	−	0.526484i	$-0.176490\pi$
$740$	−1778.33			−2.40315
$741$	−138.356	−	568.224i	−0.186716	−	0.766834i
$742$	−4.92663	−	4.92663i	−0.00663966	−	0.00663966i
$743$	−757.612	−	757.612i	−1.01967	−	1.01967i	−0.999803	−	0.0198633i	$-0.993677\pi$
$743$	−757.612	−	757.612i	−1.01967	−	1.01967i	−0.0198633	−	0.999803i	$-0.506323\pi$
$744$	−19.5066	+	32.0633i	−0.0262185	+	0.0430958i
$745$	−1235.33	+	1235.33i	−1.65816	+	1.65816i
$746$	31.5755			0.0423264
$747$	−513.723	+	265.939i	−0.687715	+	0.356009i
$748$	−1080.36	+	152.054i	−1.44433	+	0.203280i
$749$		−	237.336i		−	0.316870i
$750$	12.7089	−	20.8898i	0.0169452	−	0.0278530i
$751$	421.711	−	421.711i	0.561533	−	0.561533i	−0.368210	−	0.929743i	$-0.620029\pi$
$751$	421.711	−	421.711i	0.561533	−	0.561533i	0.929743	+	0.368210i	$0.120029\pi$
$752$			997.726i			1.32676i
$753$	−48.3758	−	198.678i	−0.0642441	−	0.263848i
$754$	−19.8854	−	19.8854i	−0.0263732	−	0.0263732i
$755$	835.641	−	835.641i	1.10681	−	1.10681i
$756$	361.962	+	24.9691i	0.478786	+	0.0330279i
$757$			797.793i			1.05389i	0.849900	+	0.526944i	$0.176662\pi$
$757$			797.793i			1.05389i	−0.849900	+	0.526944i	$0.823338\pi$
$758$	−3.97475	+	3.97475i	−0.00524374	+	0.00524374i
$759$	−93.4905	−	383.962i	−0.123176	−	0.505878i
$760$	−209.210	+	209.210i	−0.275276	+	0.275276i
$761$			81.3949i			0.106958i	0.998569	+	0.0534789i	$0.0170310\pi$
$761$			81.3949i			0.106958i	−0.998569	+	0.0534789i	$0.982969\pi$
$762$	10.8632	+	44.6145i	0.0142561	+	0.0585492i
$763$			478.495i			0.627123i
$764$		−	642.522i		−	0.840997i
$765$	658.543	+	927.324i	0.860841	+	1.21219i
$766$	78.2684			0.102178
$767$	−600.089			−0.782385
$768$	−666.492	+	162.284i	−0.867828	+	0.211307i
$769$	−412.662			−0.536621			−0.268310	−	0.963332i	$-0.586465\pi$
$769$	−412.662			−0.536621			−0.268310	+	0.963332i	$0.586465\pi$
$770$	−60.3481	−	60.3481i	−0.0783741	−	0.0783741i
$771$	282.426	−	68.7678i	0.366312	−	0.0891929i
$772$	120.600	+	120.600i	0.156218	+	0.156218i
$773$	−915.455			−1.18429			−0.592144	−	0.805832i	$-0.701718\pi$
$773$	−915.455			−1.18429			−0.592144	+	0.805832i	$0.701718\pi$
$774$	−2.11683	−	4.08916i	−0.00273492	−	0.00528315i
$775$	161.441	+	161.441i	0.208311	+	0.208311i
$776$	80.4815	−	80.4815i	0.103713	−	0.103713i
$777$	598.563	−	145.744i	0.770352	−	0.187572i
$778$	145.685			0.187256
$779$	194.869	+	194.869i	0.250153	+	0.250153i
$780$	612.226	+	372.465i	0.784905	+	0.477519i
$781$	154.117			0.197333
$782$	28.4905	−	4.00986i	0.0364329	−	0.00512770i
$783$	447.552	+	30.8733i	0.571586	+	0.0394295i
$784$		−	579.983i		−	0.739774i
$785$	507.026	+	507.026i	0.645893	+	0.645893i
$786$	102.487	+	62.3509i	0.130391	+	0.0793268i
$787$	603.765	−	603.765i	0.767172	−	0.767172i	−0.210435	−	0.977608i	$-0.567488\pi$
$787$	603.765	−	603.765i	0.767172	−	0.767172i	0.977608	+	0.210435i	$0.0674881\pi$
$788$	−361.679	+	361.679i	−0.458983	+	0.458983i
$789$	914.798	−	222.744i	1.15944	−	0.282311i
$790$		−	142.170i		−	0.179962i
$791$	−203.142			−0.256817
$792$	−73.3159	+	230.691i	−0.0925706	+	0.291277i
$793$	449.695	+	449.695i	0.567080	+	0.567080i
$794$	−16.0720	−	16.0720i	−0.0202418	−	0.0202418i
$795$	187.546	+	114.099i	0.235907	+	0.143521i
$796$	134.107	−	134.107i	0.168476	−	0.168476i
$797$	−1418.96			−1.78037			−0.890187	−	0.455595i	$-0.849427\pi$
$797$	−1418.96			−1.78037			−0.890187	+	0.455595i	$0.849427\pi$
$798$	26.4903	−	43.5426i	0.0331959	−	0.0545646i
$799$	659.200	−	875.150i	0.825031	−	1.09531i
$800$		−	298.338i		−	0.372923i
$801$	−588.441	−	1136.71i	−0.734633	−	1.41912i
$802$	−86.2968	+	86.2968i	−0.107602	+	0.107602i
$803$		−	36.7457i		−	0.0457605i
$804$	313.687	−	76.3794i	0.390158	−	0.0949993i
$805$	−144.984	−	144.984i	−0.180104	−	0.180104i
$806$	9.02957	−	9.02957i	0.0112029	−	0.0112029i
$807$	281.215	+	171.085i	0.348469	+	0.212001i
$808$		−	68.3281i		−	0.0845644i
$809$	831.666	−	831.666i	1.02802	−	1.02802i	0.0284212	−	0.999596i	$-0.490952\pi$
$809$	831.666	−	831.666i	1.02802	−	1.02802i	0.999596	−	0.0284212i	$-0.00904797\pi$
$810$	123.677	−	21.2259i	0.152688	−	0.0262048i
$811$	−987.345	+	987.345i	−1.21744	+	1.21744i	−0.248916	+	0.968525i	$0.580074\pi$
$811$	−987.345	+	987.345i	−1.21744	+	1.21744i	−0.968525	+	0.248916i	$0.919926\pi$
$812$			223.276i			0.274970i
$813$	1249.50	−	304.239i	1.53690	−	0.374218i
$814$			204.381i			0.251083i
$815$			1544.86i			1.89554i
$816$	725.107	+	312.340i	0.888612	+	0.382770i
$817$	58.9270			0.0721261
$818$	39.0625			0.0477536
$819$	−236.593	−	75.1915i	−0.288880	−	0.0918089i
$820$	−337.694			−0.411821
$821$	−382.463	−	382.463i	−0.465850	−	0.465850i	0.434717	−	0.900567i	$-0.356848\pi$
$821$	−382.463	−	382.463i	−0.465850	−	0.465850i	−0.900567	+	0.434717i	$0.856848\pi$
$822$	27.6858	+	113.704i	0.0336810	+	0.138327i
$823$	−423.539	−	423.539i	−0.514629	−	0.514629i	0.401313	−	0.915941i	$-0.368554\pi$
$823$	−423.539	−	423.539i	−0.514629	−	0.514629i	−0.915941	+	0.401313i	$0.868554\pi$
$824$	−70.9926			−0.0861561
$825$	1258.02	+	765.350i	1.52487	+	0.927697i
$826$	−36.9801	−	36.9801i	−0.0447701	−	0.0447701i
$827$	200.991	−	200.991i	0.243036	−	0.243036i	−0.575069	−	0.818105i	$-0.695025\pi$
$827$	200.991	−	200.991i	0.243036	−	0.243036i	0.818105	+	0.575069i	$0.195025\pi$
$828$	−87.5887	+	275.601i	−0.105783	+	0.332851i
$829$	11.6848			0.0140950			0.00704751	−	0.999975i	$-0.497757\pi$
$829$	11.6848			0.0140950			0.00704751	+	0.999975i	$0.497757\pi$
$830$	−70.4102	−	70.4102i	−0.0848315	−	0.0848315i
$831$	559.930	−	920.366i	0.673802	−	1.10754i
$832$	486.226			0.584407
$833$	−383.196	+	508.729i	−0.460020	+	0.610719i
$834$	−4.81126	+	7.90835i	−0.00576890	+	0.00948243i
$835$			1893.00i			2.26706i
$836$	−1089.25	−	1089.25i	−1.30293	−	1.30293i
$837$	−14.0190	+	203.225i	−0.0167491	+	0.242801i
$838$	28.4622	−	28.4622i	0.0339645	−	0.0339645i
$839$	−153.284	+	153.284i	−0.182699	+	0.182699i	−0.792531	−	0.609832i	$-0.791237\pi$
$839$	−153.284	+	153.284i	−0.182699	+	0.182699i	0.609832	+	0.792531i	$0.291237\pi$
$840$	29.7125	+	122.028i	0.0353720	+	0.145271i
$841$		−	564.928i		−	0.671734i
$842$	9.06923			0.0107711
$843$	−849.896	+	206.940i	−1.00818	+	0.245481i
$844$	−184.962	−	184.962i	−0.219149	−	0.219149i
$845$	541.626	+	541.626i	0.640978	+	0.640978i
$846$	−55.5719	−	107.350i	−0.0656879	−	0.126892i
$847$	341.261	−	341.261i	0.402906	−	0.402906i
$848$	152.387			0.179702
$849$	−1149.76	−	699.491i	−1.35426	−	0.823900i
$850$	−64.5031	+	85.6339i	−0.0758860	+	0.100746i
$851$			491.019i			0.576990i
$852$	−96.3498	−	58.6170i	−0.113087	−	0.0687994i
$853$	311.919	−	311.919i	0.365673	−	0.365673i	−0.500223	−	0.865896i	$-0.666749\pi$
$853$	311.919	−	311.919i	0.365673	−	0.365673i	0.865896	+	0.500223i	$0.166749\pi$
$854$			55.4242i			0.0648996i
$855$	−486.396	+	1530.46i	−0.568884	+	1.79001i
$856$	−81.9331	−	81.9331i	−0.0957162	−	0.0957162i
$857$	−803.544	+	803.544i	−0.937625	+	0.937625i	−0.998166	−	0.0605412i	$-0.980717\pi$
$857$	−803.544	+	803.544i	−0.937625	+	0.937625i	0.0605412	+	0.998166i	$0.480717\pi$
$858$	42.8068	−	70.3622i	0.0498914	−	0.0820072i
$859$		−	1489.02i		−	1.73344i	−0.498796	−	0.866720i	$-0.666224\pi$
$859$		−	1489.02i		−	1.73344i	0.498796	−	0.866720i	$-0.333776\pi$
$860$	−51.0581	+	51.0581i	−0.0593699	+	0.0593699i
$861$	113.663	−	27.6758i	0.132013	−	0.0321437i
$862$	79.8270	−	79.8270i	0.0926067	−	0.0926067i
$863$		−	340.663i		−	0.394743i	−0.980329	−	0.197372i	$-0.936759\pi$
$863$		−	340.663i		−	0.394743i	0.980329	−	0.197372i	$-0.0632406\pi$
$864$	200.729	−	174.823i	0.232326	−	0.202341i
$865$		−	619.394i		−	0.716063i
$866$			113.822i			0.131435i
$867$	−429.660	−	753.048i	−0.495571	−	0.868567i
$868$	−101.385			−0.116803
$869$	1488.54			1.71293
$870$	18.2689	+	75.0296i	0.0209987	+	0.0862409i
$871$	−220.905			−0.253622
$872$	165.186	+	165.186i	0.189434	+	0.189434i
$873$	187.113	−	588.757i	0.214333	−	0.674407i
$874$	28.7250	+	28.7250i	0.0328661	+	0.0328661i
$875$	132.833			0.151809
$876$	−13.9759	+	22.9724i	−0.0159542	+	0.0262243i
$877$	586.686	+	586.686i	0.668969	+	0.668969i	0.957477	−	0.288508i	$-0.0931593\pi$
$877$	586.686	+	586.686i	0.668969	+	0.668969i	−0.288508	+	0.957477i	$0.593159\pi$
$878$	−36.8456	+	36.8456i	−0.0419654	+	0.0419654i
$879$	228.981	+	940.414i	0.260501	+	1.06987i
$880$	1866.64			2.12118
$881$	−552.994	−	552.994i	−0.627689	−	0.627689i	0.319797	−	0.947486i	$-0.396385\pi$
$881$	−552.994	−	552.994i	−0.627689	−	0.627689i	−0.947486	+	0.319797i	$0.896385\pi$
$882$	32.3043	+	62.4032i	0.0366261	+	0.0707520i
$883$	61.7667			0.0699510			0.0349755	−	0.999388i	$-0.488865\pi$
$883$	61.7667			0.0699510			0.0349755	+	0.999388i	$0.488865\pi$
$884$	−436.338	−	328.668i	−0.493595	−	0.371796i
$885$	1407.75	+	856.444i	1.59068	+	0.967734i
$886$			9.24374i			0.0104331i
$887$	278.018	+	278.018i	0.313436	+	0.313436i	0.846239	−	0.532803i	$-0.178861\pi$
$887$	278.018	+	278.018i	0.313436	+	0.313436i	−0.532803	+	0.846239i	$0.678861\pi$
$888$	156.323	−	256.950i	0.176039	−	0.289358i
$889$	−176.385	+	176.385i	−0.198408	+	0.198408i
$890$	155.796	−	155.796i	0.175052	−	0.175052i
$891$	222.238	+	1294.91i	0.249426	+	1.45333i
$892$		−	690.771i		−	0.774407i
$893$	1546.98			1.73234
$894$	−34.7598	−	142.757i	−0.0388812	−	0.159684i
$895$	516.389	+	516.389i	0.576971	+	0.576971i
$896$	124.670	+	124.670i	0.139140	+	0.139140i
$897$	102.842	−	169.043i	0.114651	−	0.188453i
$898$	21.6931	−	21.6931i	0.0241571	−	0.0241571i
$899$	−125.359			−0.139442
$900$	−495.386	−	956.954i	−0.550429	−	1.06328i
$901$	−133.665	−	100.682i	−0.148352	−	0.111745i
$902$			38.8106i			0.0430273i
$903$	13.0010	−	21.3699i	0.0143976	−	0.0236655i
$904$	−70.1288	+	70.1288i	−0.0775761	+	0.0775761i
$905$			384.940i			0.425349i
$906$	23.5134	+	96.5686i	0.0259530	+	0.106588i
$907$	−134.894	−	134.894i	−0.148726	−	0.148726i	0.628823	−	0.777549i	$-0.283537\pi$
$907$	−134.894	−	134.894i	−0.148726	−	0.148726i	−0.777549	+	0.628823i	$0.783537\pi$
$908$	−530.778	+	530.778i	−0.584557	+	0.584557i
$909$	−170.496	−	329.353i	−0.187565	−	0.362325i
$910$		−	42.7327i		−	0.0469590i
$911$	529.607	−	529.607i	0.581347	−	0.581347i	−0.353926	−	0.935273i	$-0.615154\pi$
$911$	529.607	−	529.607i	0.581347	−	0.581347i	0.935273	+	0.353926i	$0.115154\pi$
$912$	263.724	+	1083.10i	0.289171	+	1.18761i
$913$	737.204	−	737.204i	0.807452	−	0.807452i
$914$			10.9026i			0.0119285i
$915$	−413.138	−	1696.74i	−0.451517	−	1.85436i
$916$			1205.70i			1.31626i
$917$			651.692i			0.710679i
$918$	−95.4148	+	6.78124i	−0.103938	+	0.00738697i
$919$	−427.922			−0.465639			−0.232820	−	0.972520i	$-0.574795\pi$
$919$	−427.922			−0.465639			−0.232820	+	0.972520i	$0.574795\pi$
$920$	−100.103			−0.108808
$921$	801.477	−	195.151i	0.870224	−	0.211890i
$922$	60.7160			0.0658525
$923$	54.5654	+	54.5654i	0.0591174	+	0.0591174i
$924$	−635.337	+	154.698i	−0.687594	+	0.167422i
$925$	−1293.77	−	1293.77i	−1.39866	−	1.39866i
$926$	−148.289			−0.160139
$927$	−342.197	+	177.145i	−0.369144	+	0.191095i
$928$	115.829	+	115.829i	0.124816	+	0.124816i
$929$	−872.431	+	872.431i	−0.939107	+	0.939107i	−0.998250	−	0.0591421i	$-0.981163\pi$
$929$	−872.431	+	872.431i	−0.939107	+	0.939107i	0.0591421	+	0.998250i	$0.481163\pi$
$930$	−34.0694	+	8.29554i	−0.0366338	+	0.00891994i
$931$	−899.266			−0.965914
$932$	−132.221	−	132.221i	−0.141868	−	0.141868i
$933$	699.539	+	425.584i	0.749774	+	0.456145i
$934$	−78.7989			−0.0843671
$935$	−1637.32	−	1233.29i	−1.75114	−	1.31903i
$936$	−107.634	+	55.7190i	−0.114994	+	0.0595288i
$937$			855.452i			0.912969i	0.889731	+	0.456485i	$0.150892\pi$
$937$			855.452i			0.912969i	−0.889731	+	0.456485i	$0.849108\pi$
$938$	−13.6131	−	13.6131i	−0.0145129	−	0.0145129i
$939$	−678.993	−	413.084i	−0.723102	−	0.439919i
$940$	−1340.40	+	1340.40i	−1.42596	+	1.42596i
$941$	701.925	−	701.925i	0.745936	−	0.745936i	−0.227778	−	0.973713i	$-0.573146\pi$
$941$	701.925	−	701.925i	0.745936	−	0.745936i	0.973713	+	0.227778i	$0.0731459\pi$
$942$	−58.5931	+	14.2668i	−0.0622007	+	0.0151452i
$943$			93.2411i			0.0988771i
$944$	1143.84			1.21170
$945$	447.711	+	514.056i	0.473768	+	0.543974i
$946$	5.86803	+	5.86803i	0.00620299	+	0.00620299i
$947$	−392.939	−	392.939i	−0.414930	−	0.414930i	0.468522	−	0.883452i	$-0.344787\pi$
$947$	−392.939	−	392.939i	−0.414930	−	0.414930i	−0.883452	+	0.468522i	$0.844787\pi$
$948$	−930.593	−	566.152i	−0.981638	−	0.597207i
$949$	13.0099	−	13.0099i	0.0137090	−	0.0137090i
$950$	−151.373			−0.159340
$951$	−672.045	+	1104.65i	−0.706672	+	1.16157i
$952$	−13.3430	−	94.8034i	−0.0140157	−	0.0995834i
$953$		−	1366.13i		−	1.43350i	−0.697328	−	0.716752i	$-0.745628\pi$
$953$		−	1366.13i		−	1.43350i	0.697328	−	0.716752i	$-0.254372\pi$
$954$	−16.3961	+	8.48774i	−0.0171866	+	0.00889700i
$955$	853.619	−	853.619i	0.893842	−	0.893842i
$956$		−	424.881i		−	0.444436i
$957$	−785.570	+	191.278i	−0.820867	+	0.199872i
$958$	−31.6874	−	31.6874i	−0.0330766	−	0.0330766i
$959$	−449.534	+	449.534i	−0.468753	+	0.468753i
$960$	−1140.64	−	693.940i	−1.18817	−	0.722854i
$961$			904.077i			0.940767i
$962$	−72.3615	+	72.3615i	−0.0752199	+	0.0752199i
$963$	−599.376	−	190.488i	−0.622405	−	0.197807i
$964$	−1233.86	+	1233.86i	−1.27994	+	1.27994i
$965$			320.445i			0.332068i
$966$	16.7547	−	4.07959i	0.0173444	−	0.00422318i
$967$			332.446i			0.343791i	0.985115	+	0.171896i	$0.0549892\pi$
$967$			332.446i			0.343791i	−0.985115	+	0.171896i	$0.945011\pi$
$968$		−	235.621i		−	0.243410i
$969$	484.285	−	1124.28i	0.499778	−	1.16025i
$970$	106.340			0.109629
$971$	284.514			0.293011			0.146506	−	0.989210i	$-0.453197\pi$
$971$	284.514			0.293011			0.146506	+	0.989210i	$0.453197\pi$
$972$	353.572	−	894.073i	0.363757	−	0.919828i
$973$	−50.2873			−0.0516828
$974$	68.7190	+	68.7190i	0.0705534	+	0.0705534i
$975$	174.430	+	716.378i	0.178903	+	0.734746i
$976$	−857.171	−	857.171i	−0.878249	−	0.878249i
$977$	−843.372			−0.863226			−0.431613	−	0.902059i	$-0.642055\pi$
$977$	−843.372			−0.863226			−0.431613	+	0.902059i	$0.642055\pi$
$978$	−110.999	−	67.5292i	−0.113496	−	0.0690483i
$979$	1631.21	+	1631.21i	1.66620	+	1.66620i
$980$	779.180	−	779.180i	0.795082	−	0.795082i
$981$	1208.41	+	384.045i	1.23181	+	0.391483i
$982$	−90.1374			−0.0917896
$983$	84.6921	+	84.6921i	0.0861568	+	0.0861568i	0.748872	−	0.662715i	$-0.230596\pi$
$983$	84.6921	+	84.6921i	0.0861568	+	0.0861568i	−0.662715	+	0.748872i	$0.730596\pi$
$984$	29.6846	−	48.7931i	0.0301673	−	0.0495865i
$985$	−961.013			−0.975647
$986$	−8.20402	−	58.2905i	−0.00832050	−	0.0591181i
$987$	341.308	−	561.013i	0.345803	−	0.568402i
$988$		−	771.301i		−	0.780670i
$989$	14.0977	+	14.0977i	0.0142545	+	0.0142545i
$990$	−200.841	+	103.969i	−0.202870	+	0.105020i
$991$	581.980	−	581.980i	0.587265	−	0.587265i	−0.349625	−	0.936890i	$-0.613691\pi$
$991$	581.980	−	581.980i	0.587265	−	0.587265i	0.936890	+	0.349625i	$0.113691\pi$
$992$	−52.5958	+	52.5958i	−0.0530199	+	0.0530199i
$993$	−220.878	−	907.137i	−0.222435	−	0.913532i
$994$			6.72511i			0.00676570i
$995$	356.335			0.358126
$996$	−741.270	+	180.491i	−0.744247	+	0.181216i
$997$	829.581	+	829.581i	0.832078	+	0.832078i	0.987801	−	0.155723i	$-0.0497707\pi$
$997$	829.581	+	829.581i	0.832078	+	0.832078i	−0.155723	+	0.987801i	$0.549771\pi$
$998$	−6.07668	−	6.07668i	−0.00608885	−	0.00608885i
$999$	112.346	−	1628.61i	0.112458	−	1.63024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.3.f.a.38.5	✓	20
3.2	odd	2	inner	51.3.f.a.38.6	yes	20
17.13	even	4	inner	51.3.f.a.47.6	yes	20
51.47	odd	4	inner	51.3.f.a.47.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.3.f.a.38.5	✓	20	1.1	even	1	trivial
51.3.f.a.38.6	yes	20	3.2	odd	2	inner
51.3.f.a.47.5	yes	20	51.47	odd	4	inner
51.3.f.a.47.6	yes	20	17.13	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	51.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.208400 q^{2} +(-2.91484 + 0.709732i) q^{3} -3.95657 q^{4} +(-5.25648 - 5.25648i) q^{5} +(0.607451 - 0.147908i) q^{6} +(2.40158 + 2.40158i) q^{7} +1.65815 q^{8} +(7.99256 - 4.13751i) q^{9} +(1.09545 + 1.09545i) q^{10} +(-11.4695 + 11.4695i) q^{11} +(11.5328 - 2.80810i) q^{12} -8.12160 q^{13} +(-0.500488 - 0.500488i) q^{14} +(19.0525 + 11.5911i) q^{15} +15.4807 q^{16} +(-13.5788 - 10.2282i) q^{17} +(-1.66565 + 0.862255i) q^{18} -24.0029i q^{19} +(20.7976 + 20.7976i) q^{20} +(-8.70468 - 5.29573i) q^{21} +(2.39024 - 2.39024i) q^{22} +(5.74247 - 5.74247i) q^{23} +(-4.83323 + 1.17684i) q^{24} +30.2612i q^{25} +1.69254 q^{26} +(-20.3605 + 17.7327i) q^{27} +(-9.50201 - 9.50201i) q^{28} +(-11.7489 - 11.7489i) q^{29} +(-3.97053 - 2.41558i) q^{30} +(5.33493 - 5.33493i) q^{31} -9.85876 q^{32} +(25.2915 - 41.5720i) q^{33} +(2.82983 + 2.13154i) q^{34} -25.2477i q^{35} +(-31.6231 + 16.3703i) q^{36} +(-42.7533 + 42.7533i) q^{37} +5.00220i q^{38} +(23.6731 - 5.76415i) q^{39} +(-8.71602 - 8.71602i) q^{40} +(-8.11856 + 8.11856i) q^{41} +(1.81405 + 1.10363i) q^{42} +2.45499i q^{43} +(45.3799 - 45.3799i) q^{44} +(-63.7615 - 20.2640i) q^{45} +(-1.19673 + 1.19673i) q^{46} +64.4496i q^{47} +(-45.1238 + 10.9872i) q^{48} -37.4649i q^{49} -6.30643i q^{50} +(46.8394 + 20.1761i) q^{51} +32.1337 q^{52} +9.84366 q^{53} +(4.24312 - 3.69550i) q^{54} +120.578 q^{55} +(3.98217 + 3.98217i) q^{56} +(17.0356 + 69.9646i) q^{57} +(2.44846 + 2.44846i) q^{58} +73.8881 q^{59} +(-75.3825 - 45.8610i) q^{60} +(-55.3702 - 55.3702i) q^{61} +(-1.11180 + 1.11180i) q^{62} +(29.1313 + 9.25821i) q^{63} -59.8683 q^{64} +(42.6910 + 42.6910i) q^{65} +(-5.27074 + 8.66359i) q^{66} +27.1997 q^{67} +(53.7256 + 40.4684i) q^{68} +(-12.6628 + 20.8140i) q^{69} +5.26161i q^{70} +(-6.71855 - 6.71855i) q^{71} +(13.2528 - 6.86059i) q^{72} +(-1.60189 + 1.60189i) q^{73} +(8.90977 - 8.90977i) q^{74} +(-21.4773 - 88.2065i) q^{75} +94.9692i q^{76} -55.0898 q^{77} +(-4.93347 + 1.20125i) q^{78} +(-64.8910 - 64.8910i) q^{79} +(-81.3741 - 81.3741i) q^{80} +(46.7621 - 66.1385i) q^{81} +(1.69190 - 1.69190i) q^{82} -64.2751 q^{83} +(34.4407 + 20.9529i) q^{84} +(17.6128 + 125.141i) q^{85} -0.511620i q^{86} +(42.5846 + 25.9075i) q^{87} +(-19.0181 + 19.0181i) q^{88} -142.221i q^{89} +(13.2879 + 4.22302i) q^{90} +(-19.5046 - 19.5046i) q^{91} +(-22.7205 + 22.7205i) q^{92} +(-11.7641 + 19.3368i) q^{93} -13.4313i q^{94} +(-126.171 + 126.171i) q^{95} +(28.7367 - 6.99708i) q^{96} +(48.5370 - 48.5370i) q^{97} +7.80767i q^{98} +(-44.2156 + 139.126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} + 24 q^{4} - 2 q^{6} - 4 q^{7} - 16 q^{10} - 42 q^{12} - 12 q^{13} - 64 q^{16} - 4 q^{18} + 88 q^{21} - 40 q^{22} - 82 q^{24} + 54 q^{27} - 160 q^{28} + 48 q^{31} + 264 q^{33} + 152 q^{34}+ \cdots - 864 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 + 24 * q^4 - 2 * q^6 - 4 * q^7 - 16 * q^10 - 42 * q^12 - 12 * q^13 - 64 * q^16 - 4 * q^18 + 88 * q^21 - 40 * q^22 - 82 * q^24 + 54 * q^27 - 160 * q^28 + 48 * q^31 + 264 * q^33 + 152 * q^34 + 32 * q^37 + 56 * q^39 + 52 * q^40 + 64 * q^45 + 388 * q^46 - 230 * q^48 - 298 * q^51 + 64 * q^52 - 254 * q^54 - 204 * q^55 - 24 * q^57 + 396 * q^58 - 336 * q^61 - 400 * q^63 - 480 * q^64 - 408 * q^67 - 132 * q^69 + 276 * q^72 - 88 * q^73 - 358 * q^75 + 380 * q^78 - 172 * q^79 + 388 * q^81 + 372 * q^82 + 1320 * q^84 + 648 * q^85 - 156 * q^88 + 672 * q^90 - 124 * q^91 + 194 * q^96 + 688 * q^97 - 864 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more