LMFDB - Embedded newform 66.3.f.a.7.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [66,3,Mod(7,66)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("66.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(66, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 66 = 2 \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	66.f (of order $10$, degree $4$, 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:	$1.79836974478$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.6879707136000000000000.7
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 $ x^16 - 4x^14 + 15x^12 - 56x^10 + 209x^8 - 56x^6 + 15x^4 - 4*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			7.2
Root			$0.492303 - 0.159959i$ of defining polynomial
Character	$\chi$	$=$	66.7
Dual form			66.3.f.a.19.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.831254 + 1.14412i) q^{2} +(0.535233 - 1.64728i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(2.05461 - 1.49276i) q^{5} +(1.43977 + 1.98168i) q^{6} +(9.89425 - 3.21484i) q^{7} +(2.68999 + 0.874032i) q^{8} +(-2.42705 - 1.76336i) q^{9} +3.59159i q^{10} +(-4.04952 + 10.2275i) q^{11} -3.46410 q^{12} +(7.72450 - 10.6319i) q^{13} +(-4.54647 + 13.9926i) q^{14} +(-1.35930 - 4.18349i) q^{15} +(-3.23607 + 2.35114i) q^{16} +(6.07332 + 8.35921i) q^{17} +(4.03499 - 1.31105i) q^{18} +(-20.6212 - 6.70022i) q^{19} +(-4.10922 - 2.98552i) q^{20} -18.0193i q^{21} +(-8.33532 - 13.1348i) q^{22} -38.9614 q^{23} +(2.87955 - 3.96336i) q^{24} +(-5.73234 + 17.6423i) q^{25} +(5.74313 + 17.6755i) q^{26} +(-4.20378 + 3.05422i) q^{27} +(-12.2300 - 16.8331i) q^{28} +(10.8281 - 3.51825i) q^{29} +(5.91635 + 1.92234i) q^{30} +(13.6220 + 9.89698i) q^{31} -5.65685i q^{32} +(14.6801 + 12.1448i) q^{33} -14.6124 q^{34} +(15.5299 - 21.3750i) q^{35} +(-1.85410 + 5.70634i) q^{36} +(13.1643 + 40.5157i) q^{37} +(24.8073 - 18.0236i) q^{38} +(-13.3792 - 18.4149i) q^{39} +(6.83161 - 2.21973i) q^{40} +(19.9900 + 6.49515i) q^{41} +(20.6163 + 14.9786i) q^{42} +34.3891i q^{43} +(21.9566 + 1.38171i) q^{44} -7.61892 q^{45} +(32.3868 - 44.5767i) q^{46} +(-10.8979 + 33.5402i) q^{47} +(2.14093 + 6.58911i) q^{48} +(47.9192 - 34.8154i) q^{49} +(-15.4200 - 21.2237i) q^{50} +(17.0206 - 5.53032i) q^{51} +(-24.9970 - 8.12202i) q^{52} +(-20.4201 - 14.8361i) q^{53} -7.34847i q^{54} +(6.94702 + 27.0585i) q^{55} +29.4254 q^{56} +(-22.0743 + 30.3826i) q^{57} +(-4.97556 + 15.3132i) q^{58} +(-21.7474 - 66.9315i) q^{59} +(-7.11738 + 5.17108i) q^{60} +(-12.4580 - 17.1469i) q^{61} +(-22.6467 + 7.35836i) q^{62} +(-29.6828 - 9.64451i) q^{63} +(6.47214 + 4.70228i) q^{64} -33.3752i q^{65} +(-26.0980 + 6.70042i) q^{66} -128.308 q^{67} +(12.1466 - 16.7184i) q^{68} +(-20.8534 + 64.1803i) q^{69} +(11.5464 + 35.5361i) q^{70} +(83.3257 - 60.5397i) q^{71} +(-4.98752 - 6.86474i) q^{72} +(125.892 - 40.9047i) q^{73} +(-57.2978 - 18.6172i) q^{74} +(25.9937 + 18.8855i) q^{75} +43.3648i q^{76} +(-7.18725 + 114.212i) q^{77} +32.1905 q^{78} +(-74.4189 + 102.429i) q^{79} +(-3.13917 + 9.66136i) q^{80} +(2.78115 + 8.55951i) q^{81} +(-24.0480 + 17.4719i) q^{82} +(-71.0546 - 97.7983i) q^{83} +(-34.2747 + 11.1365i) q^{84} +(24.9566 + 8.10890i) q^{85} +(-39.3453 - 28.5860i) q^{86} -19.7199i q^{87} +(-19.8323 + 23.9725i) q^{88} -19.9962 q^{89} +(6.33325 - 8.71698i) q^{90} +(42.2484 - 130.027i) q^{91} +(24.0795 + 74.1090i) q^{92} +(23.5940 - 17.1421i) q^{93} +(-29.3152 - 40.3489i) q^{94} +(-52.3703 + 17.0161i) q^{95} +(-9.31841 - 3.02774i) q^{96} +(-8.82424 - 6.41119i) q^{97} +83.7659i q^{98} +(27.8631 - 17.6819i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 8 q^{5} + 60 q^{7} - 12 q^{9} - 4 q^{11} - 60 q^{13} - 32 q^{14} + 12 q^{15} - 16 q^{16} - 60 q^{17} - 16 q^{20} - 48 q^{22} - 8 q^{23} - 48 q^{25} + 48 q^{26} + 40 q^{28} - 160 q^{29}+ \cdots + 48 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 8 * q^5 + 60 * q^7 - 12 * q^9 - 4 * q^11 - 60 * q^13 - 32 * q^14 + 12 * q^15 - 16 * q^16 - 60 * q^17 - 16 * q^20 - 48 * q^22 - 8 * q^23 - 48 * q^25 + 48 * q^26 + 40 * q^28 - 160 * q^29 + 32 * q^31 + 36 * q^33 - 64 * q^34 + 160 * q^35 + 24 * q^36 - 84 * q^37 - 48 * q^38 - 80 * q^40 + 40 * q^41 + 96 * q^42 + 168 * q^44 + 24 * q^45 + 160 * q^46 + 372 * q^47 + 96 * q^49 + 160 * q^50 + 120 * q^51 + 40 * q^52 - 124 * q^53 + 32 * q^55 - 96 * q^56 - 120 * q^57 - 16 * q^58 - 172 * q^59 - 24 * q^60 + 100 * q^61 - 40 * q^62 - 180 * q^63 + 32 * q^64 - 216 * q^66 + 248 * q^67 - 120 * q^68 - 372 * q^69 + 8 * q^70 + 48 * q^71 + 160 * q^73 + 80 * q^74 + 192 * q^75 - 172 * q^77 - 460 * q^79 - 48 * q^80 - 36 * q^81 - 24 * q^82 - 420 * q^83 - 420 * q^85 - 456 * q^86 - 144 * q^88 - 360 * q^89 - 252 * q^91 - 64 * q^92 - 24 * q^93 - 280 * q^94 + 180 * q^95 + 324 * q^97 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$

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 $

$2$	−0.831254	+	1.14412i	−0.415627	+	0.572061i
$2$	−0.831254	+	1.14412i	−0.415627	+	0.572061i
$3$	0.535233	−	1.64728i	0.178411	−	0.549093i
$3$	0.535233	−	1.64728i	0.178411	−	0.549093i
$4$	−0.618034	−	1.90211i	−0.154508	−	0.475528i
$5$	2.05461	−	1.49276i	0.410922	−	0.298552i	−0.363053	−	0.931769i	$-0.618266\pi$
$5$	2.05461	−	1.49276i	0.410922	−	0.298552i	0.773975	+	0.633216i	$0.218266\pi$
$6$	1.43977	+	1.98168i	0.239962	+	0.330280i
$7$	9.89425	−	3.21484i	1.41346	−	0.459263i	0.499945	−	0.866057i	$-0.333353\pi$
$7$	9.89425	−	3.21484i	1.41346	−	0.459263i	0.913520	+	0.406794i	$0.133353\pi$
$8$	2.68999	+	0.874032i	0.336249	+	0.109254i
$9$	−2.42705	−	1.76336i	−0.269672	−	0.195928i
$10$			3.59159i			0.359159i
$11$	−4.04952	+	10.2275i	−0.368138	+	0.929771i
$11$	−4.04952	+	10.2275i	−0.368138	+	0.929771i
$12$	−3.46410			−0.288675
$13$	7.72450	−	10.6319i	0.594192	−	0.817835i	−0.400969	−	0.916092i	$-0.631327\pi$
$13$	7.72450	−	10.6319i	0.594192	−	0.817835i	0.995161	+	0.0982564i	$0.0313265\pi$
$14$	−4.54647	+	13.9926i	−0.324748	+	0.999471i
$15$	−1.35930	−	4.18349i	−0.0906199	−	0.278899i
$16$	−3.23607	+	2.35114i	−0.202254	+	0.146946i
$17$	6.07332	+	8.35921i	0.357254	+	0.491718i	0.949381	−	0.314126i	$-0.101712\pi$
$17$	6.07332	+	8.35921i	0.357254	+	0.491718i	−0.592127	+	0.805845i	$0.701712\pi$
$18$	4.03499	−	1.31105i	0.224166	−	0.0728360i
$19$	−20.6212	−	6.70022i	−1.08532	−	0.352643i	−0.288886	−	0.957363i	$-0.593285\pi$
$19$	−20.6212	−	6.70022i	−1.08532	−	0.352643i	−0.796438	+	0.604720i	$0.793285\pi$
$20$	−4.10922	−	2.98552i	−0.205461	−	0.149276i
$21$		−	18.0193i		−	0.858061i
$22$	−8.33532	−	13.1348i	−0.378878	−	0.597035i
$23$	−38.9614			−1.69398			−0.846988	−	0.531613i	$-0.821586\pi$
$23$	−38.9614			−1.69398			−0.846988	+	0.531613i	$0.821586\pi$
$24$	2.87955	−	3.96336i	0.119981	−	0.165140i
$25$	−5.73234	+	17.6423i	−0.229294	+	0.705693i
$26$	5.74313	+	17.6755i	0.220890	+	0.679829i
$27$	−4.20378	+	3.05422i	−0.155695	+	0.113119i
$28$	−12.2300	−	16.8331i	−0.436785	−	0.601183i
$29$	10.8281	−	3.51825i	0.373382	−	0.121319i	−0.116314	−	0.993213i	$-0.537108\pi$
$29$	10.8281	−	3.51825i	0.373382	−	0.121319i	0.489696	+	0.871893i	$0.337108\pi$
$30$	5.91635	+	1.92234i	0.197212	+	0.0640780i
$31$	13.6220	+	9.89698i	0.439420	+	0.319257i	0.785404	−	0.618983i	$-0.212455\pi$
$31$	13.6220	+	9.89698i	0.439420	+	0.319257i	−0.345984	+	0.938240i	$0.612455\pi$
$32$		−	5.65685i		−	0.176777i
$33$	14.6801	+	12.1448i	0.444851	+	0.368023i
$34$	−14.6124			−0.429778
$35$	15.5299	−	21.3750i	0.443710	−	0.610715i
$36$	−1.85410	+	5.70634i	−0.0515028	+	0.158509i
$37$	13.1643	+	40.5157i	0.355793	+	1.09502i	0.955548	+	0.294835i	$0.0952647\pi$
$37$	13.1643	+	40.5157i	0.355793	+	1.09502i	−0.599755	+	0.800184i	$0.704735\pi$
$38$	24.8073	−	18.0236i	0.652824	−	0.474304i
$39$	−13.3792	−	18.4149i	−0.343057	−	0.472177i
$40$	6.83161	−	2.21973i	0.170790	−	0.0554931i
$41$	19.9900	+	6.49515i	0.487562	+	0.158418i	0.542474	−	0.840073i	$-0.317488\pi$
$41$	19.9900	+	6.49515i	0.487562	+	0.158418i	−0.0549120	+	0.998491i	$0.517488\pi$
$42$	20.6163	+	14.9786i	0.490863	+	0.356633i
$43$			34.3891i			0.799745i	0.916571	+	0.399873i	$0.130946\pi$
$43$			34.3891i			0.799745i	−0.916571	+	0.399873i	$0.869054\pi$
$44$	21.9566	+	1.38171i	0.499013	+	0.0314024i
$45$	−7.61892			−0.169309
$46$	32.3868	−	44.5767i	0.704062	−	0.969058i
$47$	−10.8979	+	33.5402i	−0.231870	+	0.713621i	0.765652	+	0.643255i	$0.222417\pi$
$47$	−10.8979	+	33.5402i	−0.231870	+	0.713621i	−0.997521	+	0.0703657i	$0.977583\pi$
$48$	2.14093	+	6.58911i	0.0446028	+	0.137273i
$49$	47.9192	−	34.8154i	0.977944	−	0.710518i
$50$	−15.4200	−	21.2237i	−0.308399	−	0.424475i
$51$	17.0206	−	5.53032i	0.333737	−	0.108438i
$52$	−24.9970	−	8.12202i	−0.480711	−	0.156193i
$53$	−20.4201	−	14.8361i	−0.385284	−	0.279925i	0.378236	−	0.925709i	$-0.376531\pi$
$53$	−20.4201	−	14.8361i	−0.385284	−	0.279925i	−0.763520	+	0.645784i	$0.776531\pi$
$54$		−	7.34847i		−	0.136083i
$55$	6.94702	+	27.0585i	0.126309	+	0.491972i
$56$	29.4254			0.525453
$57$	−22.0743	+	30.3826i	−0.387268	+	0.533028i
$58$	−4.97556	+	15.3132i	−0.0857856	+	0.264021i
$59$	−21.7474	−	66.9315i	−0.368600	−	1.13443i	−0.947696	−	0.319174i	$-0.896595\pi$
$59$	−21.7474	−	66.9315i	−0.368600	−	1.13443i	0.579097	−	0.815259i	$-0.303405\pi$
$60$	−7.11738	+	5.17108i	−0.118623	+	0.0861847i
$61$	−12.4580	−	17.1469i	−0.204229	−	0.281097i	0.694600	−	0.719396i	$-0.255581\pi$
$61$	−12.4580	−	17.1469i	−0.204229	−	0.281097i	−0.898829	+	0.438298i	$0.855581\pi$
$62$	−22.6467	+	7.35836i	−0.365270	+	0.118683i
$63$	−29.6828	−	9.64451i	−0.471155	−	0.153088i
$64$	6.47214	+	4.70228i	0.101127	+	0.0734732i
$65$		−	33.3752i		−	0.513464i
$66$	−26.0980	+	6.70042i	−0.395424	+	0.101522i
$67$	−128.308			−1.91505			−0.957525	−	0.288349i	$-0.906894\pi$
$67$	−128.308			−1.91505			−0.957525	+	0.288349i	$0.906894\pi$
$68$	12.1466	−	16.7184i	0.178627	−	0.245859i
$69$	−20.8534	+	64.1803i	−0.302224	+	0.930149i
$70$	11.5464	+	35.5361i	0.164948	+	0.507659i
$71$	83.3257	−	60.5397i	1.17360	−	0.852672i	0.182166	−	0.983268i	$-0.441689\pi$
$71$	83.3257	−	60.5397i	1.17360	−	0.852672i	0.991436	+	0.130596i	$0.0416891\pi$
$72$	−4.98752	−	6.86474i	−0.0692712	−	0.0953436i
$73$	125.892	−	40.9047i	1.72454	−	0.560338i	0.731901	−	0.681411i	$-0.238633\pi$
$73$	125.892	−	40.9047i	1.72454	−	0.560338i	0.992644	+	0.121073i	$0.0386335\pi$
$74$	−57.2978	−	18.6172i	−0.774295	−	0.251584i
$75$	25.9937	+	18.8855i	0.346582	+	0.251807i
$76$			43.3648i			0.570589i
$77$	−7.18725	+	114.212i	−0.0933408	+	1.48327i
$78$	32.1905			0.412698
$79$	−74.4189	+	102.429i	−0.942012	+	1.29657i	0.0129735	+	0.999916i	$0.495870\pi$
$79$	−74.4189	+	102.429i	−0.942012	+	1.29657i	−0.954986	+	0.296652i	$0.904130\pi$
$80$	−3.13917	+	9.66136i	−0.0392396	+	0.120767i
$81$	2.78115	+	8.55951i	0.0343352	+	0.105673i
$82$	−24.0480	+	17.4719i	−0.293269	+	0.213072i
$83$	−71.0546	−	97.7983i	−0.856080	−	1.17829i	−0.982490	−	0.186315i	$-0.940346\pi$
$83$	−71.0546	−	97.7983i	−0.856080	−	1.17829i	0.126410	−	0.991978i	$-0.459654\pi$
$84$	−34.2747	+	11.1365i	−0.408032	+	0.132578i
$85$	24.9566	+	8.10890i	0.293607	+	0.0953988i
$86$	−39.3453	−	28.5860i	−0.457503	−	0.332396i
$87$		−	19.7199i		−	0.226666i
$88$	−19.8323	+	23.9725i	−0.225367	+	0.272414i
$89$	−19.9962			−0.224677			−0.112338	−	0.993670i	$-0.535834\pi$
$89$	−19.9962			−0.224677			−0.112338	+	0.993670i	$0.535834\pi$
$90$	6.33325	−	8.71698i	0.0703695	−	0.0968553i
$91$	42.2484	−	130.027i	0.464268	−	1.42887i
$92$	24.0795	+	74.1090i	0.261734	+	0.805533i
$93$	23.5940	−	17.1421i	0.253699	−	0.184323i
$94$	−29.3152	−	40.3489i	−0.311864	−	0.429244i
$95$	−52.3703	+	17.0161i	−0.551266	+	0.179117i
$96$	−9.31841	−	3.02774i	−0.0970668	−	0.0315389i
$97$	−8.82424	−	6.41119i	−0.0909716	−	0.0660947i	0.541370	−	0.840785i	$-0.317906\pi$
$97$	−8.82424	−	6.41119i	−0.0909716	−	0.0660947i	−0.632341	+	0.774690i	$0.717906\pi$
$98$			83.7659i			0.854754i
$99$	27.8631	−	17.6819i	0.281445	−	0.178605i
$100$	37.1005			0.371005
$101$	18.4534	−	25.3989i	0.182706	−	0.251474i	−0.707833	−	0.706380i	$-0.750327\pi$
$101$	18.4534	−	25.3989i	0.182706	−	0.251474i	0.890540	+	0.454906i	$0.150327\pi$
$102$	−7.82106	+	24.0707i	−0.0766771	+	0.235988i
$103$	24.1492	+	74.3235i	0.234458	+	0.721587i	0.997193	+	0.0748760i	$0.0238561\pi$
$103$	24.1492	+	74.3235i	0.234458	+	0.721587i	−0.762735	+	0.646711i	$0.776144\pi$
$104$	30.0714	−	21.8482i	0.289148	−	0.210079i
$105$	−26.8985	−	37.0226i	−0.256176	−	0.352596i
$106$	33.9485	−	11.0305i	0.320269	−	0.104062i
$107$	133.996	+	43.5378i	1.25230	+	0.406896i	0.858743	−	0.512406i	$-0.171246\pi$
$107$	133.996	+	43.5378i	1.25230	+	0.406896i	0.393553	+	0.919302i	$0.371246\pi$
$108$	8.40755	+	6.10844i	0.0778477	+	0.0565597i
$109$		−	174.370i		−	1.59973i	−0.600181	−	0.799864i	$-0.704905\pi$
$109$		−	174.370i		−	1.59973i	0.600181	−	0.799864i	$-0.295095\pi$
$110$	−36.7329	−	14.5442i	−0.333936	−	0.132220i
$111$	73.7866			0.664744
$112$	−24.4599	+	33.6662i	−0.218392	+	0.300591i
$113$	24.2202	−	74.5422i	0.214338	−	0.659665i	−0.784862	−	0.619671i	$-0.787266\pi$
$113$	24.2202	−	74.5422i	0.214338	−	0.659665i	0.999200	−	0.0399943i	$-0.0127340\pi$
$114$	−16.4121	−	50.5113i	−0.143966	−	0.443082i
$115$	−80.0506	+	58.1601i	−0.696092	+	0.505740i
$116$	−13.3842	−	18.4218i	−0.115381	−	0.158809i
$117$	−37.4955	+	12.1830i	−0.320474	+	0.104128i
$118$	94.6555	+	30.7554i	0.802165	+	0.260639i
$119$	86.9645	+	63.1834i	0.730794	+	0.530953i
$120$		−	12.4416i		−	0.103680i
$121$	−88.2028	−	82.8327i	−0.728949	−	0.684568i
$122$	29.9740			0.245688
$123$	21.3986	−	29.4527i	0.173973	−	0.239453i
$124$	10.4063	−	32.0273i	0.0839218	−	0.258285i
$125$	34.1779	+	105.189i	0.273423	+	0.841509i
$126$	35.7084	−	25.9437i	0.283400	−	0.205902i
$127$	46.2429	+	63.6479i	0.364118	+	0.501165i	0.951290	−	0.308297i	$-0.0997590\pi$
$127$	46.2429	+	63.6479i	0.364118	+	0.501165i	−0.587173	+	0.809462i	$0.699759\pi$
$128$	−10.7600	+	3.49613i	−0.0840623	+	0.0273135i
$129$	56.6483	+	18.4062i	0.439134	+	0.142683i
$130$	38.1853	+	27.7432i	0.293733	+	0.213409i
$131$			73.3839i			0.560182i	0.959973	+	0.280091i	$0.0903647\pi$
$131$			73.3839i			0.560182i	−0.959973	+	0.280091i	$0.909635\pi$
$132$	14.0279	−	35.4290i	0.106272	−	0.268402i
$133$	−225.571			−1.69602
$134$	106.657	−	146.801i	0.795947	−	1.09553i
$135$	−4.07790	+	12.5505i	−0.0302066	+	0.0929665i
$136$	9.03098	+	27.7945i	0.0664043	+	0.204371i
$137$	−97.7509	+	71.0202i	−0.713511	+	0.518396i	−0.884304	−	0.466911i	$-0.845367\pi$
$137$	−97.7509	+	71.0202i	−0.713511	+	0.518396i	0.170794	+	0.985307i	$0.445367\pi$
$138$	−56.0956	−	77.2090i	−0.406490	−	0.559486i
$139$	188.880	−	61.3709i	1.35885	−	0.441518i	0.463192	−	0.886258i	$-0.346704\pi$
$139$	188.880	−	61.3709i	1.35885	−	0.441518i	0.895659	+	0.444741i	$0.146704\pi$
$140$	−50.2557	−	16.3291i	−0.358969	−	0.116636i
$141$	49.4171	+	35.9036i	0.350476	+	0.254636i
$142$			145.659i			1.02577i
$143$	77.4567	+	122.056i	0.541655	+	0.853539i
$144$	12.0000			0.0833333
$145$	16.9956	−	23.3924i	0.117211	−	0.161327i
$146$	−57.8480	+	178.038i	−0.396219	+	1.21944i
$147$	−31.7026	−	97.5707i	−0.215664	−	0.663746i
$148$	68.9294	−	50.0801i	0.465739	−	0.338379i
$149$	62.3005	+	85.7493i	0.418124	+	0.575498i	0.965176	−	0.261600i	$-0.0842501\pi$
$149$	62.3005	+	85.7493i	0.418124	+	0.575498i	−0.547052	+	0.837098i	$0.684250\pi$
$150$	−43.2147	+	14.0413i	−0.288098	+	0.0936087i
$151$	−10.6146	−	3.44889i	−0.0702952	−	0.0228403i	0.273658	−	0.961827i	$-0.411766\pi$
$151$	−10.6146	−	3.44889i	−0.0702952	−	0.0228403i	−0.343954	+	0.938987i	$0.611766\pi$
$152$	−49.6146	−	36.0471i	−0.326412	−	0.237152i
$153$		−	30.9977i		−	0.202599i
$154$	−124.698	−	103.162i	−0.809727	−	0.669884i
$155$	42.7618			0.275883
$156$	−26.7584	+	36.8298i	−0.171528	+	0.236089i
$157$	46.4799	−	143.050i	0.296050	−	0.911148i	−0.686817	−	0.726831i	$-0.740992\pi$
$157$	46.4799	−	143.050i	0.296050	−	0.911148i	0.982867	−	0.184318i	$-0.0590075\pi$
$158$	−55.3302	−	170.289i	−0.350191	−	1.07778i
$159$	−35.3686	+	25.6968i	−0.222444	+	0.161615i
$160$	−8.44434	−	11.6226i	−0.0527771	−	0.0726415i
$161$	−385.494	+	125.255i	−2.39437	+	0.777979i
$162$	−12.1050	−	3.93314i	−0.0747221	−	0.0242787i
$163$	−151.061	−	109.752i	−0.926756	−	0.673328i	0.0184403	−	0.999830i	$-0.494130\pi$
$163$	−151.061	−	109.752i	−0.926756	−	0.673328i	−0.945196	+	0.326502i	$0.894130\pi$
$164$		−	42.0375i		−	0.256326i
$165$	48.2911	+	3.03891i	0.292673	+	0.0184177i
$166$	170.958			1.02987
$167$	−137.309	+	188.990i	−0.822210	+	1.13167i	0.167113	+	0.985938i	$0.446555\pi$
$167$	−137.309	+	188.990i	−0.822210	+	1.13167i	−0.989323	+	0.145737i	$0.953445\pi$
$168$	15.7494	−	48.4717i	0.0937466	−	0.288522i
$169$	−1.14467	−	3.52292i	−0.00677318	−	0.0208457i
$170$	−30.0229	+	21.8129i	−0.176605	+	0.128311i
$171$	38.2337	+	52.6242i	0.223589	+	0.307744i
$172$	65.4119	−	21.2536i	0.380302	−	0.123567i
$173$	−77.7845	−	25.2737i	−0.449621	−	0.146091i	0.0754490	−	0.997150i	$-0.475961\pi$
$173$	−77.7845	−	25.2737i	−0.449621	−	0.146091i	−0.525070	+	0.851059i	$0.675961\pi$
$174$	22.5620	+	16.3923i	0.129667	+	0.0942085i
$175$			192.986i			1.10278i
$176$	−10.9417	−	42.6178i	−0.0621690	−	0.242147i
$177$	−121.895			−0.688671
$178$	16.6220	−	22.8782i	0.0933818	−	0.128529i
$179$	59.9705	−	184.570i	0.335031	−	1.03112i	−0.631676	−	0.775232i	$-0.717633\pi$
$179$	59.9705	−	184.570i	0.335031	−	1.03112i	0.966707	−	0.255886i	$-0.0823672\pi$
$180$	4.70875	+	14.4920i	0.0261597	+	0.0805113i
$181$	−107.188	+	77.8765i	−0.592198	+	0.430257i	−0.843101	−	0.537755i	$-0.819272\pi$
$181$	−107.188	+	77.8765i	−0.592198	+	0.430257i	0.250903	+	0.968012i	$0.419272\pi$
$182$	113.648	+	156.423i	0.624440	+	0.859468i
$183$	−34.9137	+	11.3442i	−0.190785	+	0.0619899i
$184$	−104.806	−	34.0535i	−0.569598	−	0.185074i
$185$	87.5279	+	63.5927i	0.473124	+	0.343745i
$186$			41.2439i			0.221741i
$187$	−110.088	+	28.2640i	−0.588704	+	0.151145i
$188$	70.5325			0.375173
$189$	−31.7744	+	43.7337i	−0.168118	+	0.231395i
$190$	24.0645	−	74.0628i	0.126655	−	0.389804i
$191$	−98.5311	−	303.248i	−0.515870	−	1.58768i	−0.781694	−	0.623662i	$-0.785644\pi$
$191$	−98.5311	−	303.248i	−0.515870	−	1.58768i	0.265824	−	0.964022i	$-0.414356\pi$
$192$	11.2101	−	8.14459i	0.0583858	−	0.0424197i
$193$	116.098	+	159.795i	0.601542	+	0.827952i	0.995848	−	0.0910273i	$-0.0290150\pi$
$193$	116.098	+	159.795i	0.601542	+	0.827952i	−0.394306	+	0.918979i	$0.629015\pi$
$194$	14.6704	−	4.76669i	0.0756205	−	0.0245706i
$195$	−54.9782	−	17.8635i	−0.281939	−	0.0916077i
$196$	−95.8385	−	69.6307i	−0.488972	−	0.355259i
$197$		−	200.593i		−	1.01824i	−0.860696	−	0.509118i	$-0.829972\pi$
$197$		−	200.593i		−	1.01824i	0.860696	−	0.509118i	$-0.170028\pi$
$198$	−2.93104	+	46.5769i	−0.0148032	+	0.235237i
$199$	211.354			1.06208			0.531040	−	0.847347i	$-0.321801\pi$
$199$	211.354			1.06208			0.531040	+	0.847347i	$0.321801\pi$
$200$	−30.8399	+	42.4475i	−0.154200	+	0.212237i
$201$	−68.6749	+	211.360i	−0.341666	+	1.05154i
$202$	13.7200	+	42.2258i	0.0679208	+	0.209039i
$203$	95.8251	−	69.6210i	0.472045	−	0.342961i
$204$	−21.0386	−	28.9572i	−0.103130	−	0.141947i
$205$	50.7674	−	16.4953i	0.247646	−	0.0804651i
$206$	−105.109	−	34.1521i	−0.510239	−	0.165787i
$207$	94.5614	+	68.7029i	0.456818	+	0.331898i
$208$			52.5668i			0.252725i
$209$	152.032	−	183.770i	0.727427	−	0.879282i
$210$	64.7179			0.308180
$211$	139.784	−	192.397i	0.662486	−	0.911833i	−0.337075	−	0.941478i	$-0.609438\pi$
$211$	139.784	−	192.397i	0.662486	−	0.911833i	0.999561	+	0.0296446i	$0.00943756\pi$
$212$	−15.5995	+	48.0105i	−0.0735828	+	0.226464i
$213$	−55.1270	−	169.664i	−0.258812	−	0.796542i
$214$	−161.197	+	117.117i	−0.753257	+	0.547273i
$215$	51.3347	+	70.6561i	0.238766	+	0.328633i
$216$	−13.9776	+	4.54160i	−0.0647112	+	0.0210259i
$217$	166.597	+	54.1306i	0.767728	+	0.249450i
$218$	199.501	+	144.946i	0.915143	+	0.664890i
$219$		−	229.272i		−	1.04691i
$220$	47.1748	−	29.9371i	0.214431	−	0.136078i
$221$	135.787			0.614422
$222$	−61.3354	+	84.4209i	−0.276286	+	0.380275i
$223$	−43.7397	+	134.617i	−0.196142	+	0.603664i	0.803819	+	0.594874i	$0.202798\pi$
$223$	−43.7397	+	134.617i	−0.196142	+	0.603664i	−0.999961	+	0.00878996i	$0.997202\pi$
$224$	−18.1859	−	55.9704i	−0.0811869	−	0.249868i
$225$	45.0224	−	32.7107i	0.200099	−	0.145381i
$226$	65.1523	+	89.6744i	0.288284	+	0.396789i
$227$	215.306	−	69.9573i	0.948486	−	0.308182i	0.206386	−	0.978471i	$-0.433830\pi$
$227$	215.306	−	69.9573i	0.948486	−	0.308182i	0.742100	+	0.670289i	$0.233830\pi$
$228$	71.4338	+	23.2103i	0.313306	+	0.101799i
$229$	−138.650	−	100.735i	−0.605457	−	0.439890i	0.242355	−	0.970188i	$-0.422080\pi$
$229$	−138.650	−	100.735i	−0.605457	−	0.439890i	−0.847812	+	0.530297i	$0.822080\pi$
$230$		−	139.934i		−	0.608407i
$231$	184.292	+	72.9694i	0.797800	+	0.315885i
$232$	32.2025			0.138804
$233$	−54.4065	+	74.8842i	−0.233504	+	0.321391i	−0.909649	−	0.415378i	$-0.863649\pi$
$233$	−54.4065	+	74.8842i	−0.233504	+	0.321391i	0.676145	+	0.736769i	$0.263649\pi$
$234$	17.2294	−	53.0266i	0.0736299	−	0.226610i
$235$	27.6766	+	85.1800i	0.117773	+	0.362468i
$236$	−113.871	+	82.7319i	−0.482503	+	0.350559i
$237$	128.897	+	177.412i	0.543871	+	0.748574i
$238$	−144.579	+	46.9766i	−0.607475	+	0.197381i
$239$	229.721	+	74.6409i	0.961176	+	0.312305i	0.747248	−	0.664545i	$-0.231374\pi$
$239$	229.721	+	74.6409i	0.961176	+	0.312305i	0.213927	+	0.976850i	$0.431374\pi$
$240$	14.2348	+	10.3422i	0.0593115	+	0.0430923i
$241$			110.134i			0.456988i	0.973545	+	0.228494i	$0.0733801\pi$
$241$			110.134i			0.456988i	−0.973545	+	0.228494i	$0.926620\pi$
$242$	168.090	−	32.0598i	0.694586	−	0.132479i
$243$	15.5885			0.0641500
$244$	−24.9160	+	34.2939i	−0.102115	+	0.140549i
$245$	46.4843	−	143.064i	0.189732	−	0.583935i
$246$	15.9098	+	48.9654i	0.0646740	+	0.199046i
$247$	−230.524	+	167.485i	−0.933295	+	0.678079i
$248$	27.9929	+	38.5289i	0.112875	+	0.155358i
$249$	−199.132	+	64.7018i	−0.799726	+	0.259847i
$250$	−148.759	−	48.3348i	−0.595037	−	0.193339i
$251$	−346.506	−	251.751i	−1.38050	−	1.00299i	−0.996833	−	0.0795227i	$-0.974660\pi$
$251$	−346.506	−	251.751i	−1.38050	−	1.00299i	−0.383669	−	0.923471i	$-0.625340\pi$
$252$			62.4206i			0.247701i
$253$	157.775	−	398.477i	0.623616	−	1.57501i
$254$	−111.261			−0.438034
$255$	26.7152	−	36.7704i	0.104766	−	0.144197i
$256$	4.94427	−	15.2169i	0.0193136	−	0.0594410i
$257$	11.5694	+	35.6070i	0.0450171	+	0.138549i	0.971039	−	0.238922i	$-0.0767940\pi$
$257$	11.5694	+	35.6070i	0.0450171	+	0.138549i	−0.926022	+	0.377470i	$0.876794\pi$
$258$	−68.1481	+	49.5125i	−0.264140	+	0.191909i
$259$	260.503	+	358.551i	1.00580	+	1.38437i
$260$	−63.4833	+	20.6270i	−0.244167	+	0.0793346i
$261$	−32.4842	−	10.5548i	−0.124461	−	0.0404397i
$262$	−83.9602	−	61.0007i	−0.320459	−	0.232827i
$263$		−	219.070i		−	0.832967i	−0.909143	−	0.416483i	$-0.863262\pi$
$263$		−	219.070i		−	0.832967i	0.909143	−	0.416483i	$-0.136738\pi$
$264$	28.8744	+	45.5002i	0.109373	+	0.172349i
$265$	−64.1020			−0.241894
$266$	187.507	−	258.081i	0.704913	−	0.970230i
$267$	−10.7027	+	32.9394i	−0.0400848	+	0.123368i
$268$	79.2990	+	244.057i	0.295892	+	0.910661i
$269$	−3.46229	+	2.51550i	−0.0128710	+	0.00935130i	−0.594202	−	0.804316i	$-0.702532\pi$
$269$	−3.46229	+	2.51550i	−0.0128710	+	0.00935130i	0.581331	+	0.813667i	$0.302532\pi$
$270$	−10.9695	−	15.0982i	−0.0406278	−	0.0559194i
$271$	19.2016	−	6.23898i	0.0708546	−	0.0230221i	−0.273375	−	0.961907i	$-0.588140\pi$
$271$	19.2016	−	6.23898i	0.0708546	−	0.0230221i	0.344230	+	0.938885i	$0.388140\pi$
$272$	−39.3074	−	12.7717i	−0.144512	−	0.0469549i
$273$	−191.578	−	139.190i	−0.701752	−	0.509853i
$274$		−	170.875i		−	0.623631i
$275$	−157.223	−	130.070i	−0.571721	−	0.472983i
$276$	134.966			0.489009
$277$	−114.896	+	158.140i	−0.414786	+	0.570903i	−0.964377	−	0.264530i	$-0.914783\pi$
$277$	−114.896	+	158.140i	−0.414786	+	0.570903i	0.549592	+	0.835433i	$0.314783\pi$
$278$	−86.7916	+	267.117i	−0.312200	+	0.960853i
$279$	−15.6094	−	48.0409i	−0.0559478	−	0.172190i
$280$	60.4577	−	43.9251i	0.215920	−	0.156875i
$281$	−204.185	−	281.037i	−0.726638	−	1.00013i	−0.999277	−	0.0380146i	$-0.987897\pi$
$281$	−204.185	−	281.037i	−0.726638	−	1.00013i	0.272640	−	0.962116i	$-0.412103\pi$
$282$	−82.1563	+	26.6942i	−0.291335	+	0.0946603i
$283$	−294.206	−	95.5933i	−1.03960	−	0.337785i	−0.261019	−	0.965334i	$-0.584059\pi$
$283$	−294.206	−	95.5933i	−1.03960	−	0.337785i	−0.778578	+	0.627548i	$0.784059\pi$
$284$	−166.651	−	121.079i	−0.586801	−	0.426336i
$285$			95.3761i			0.334653i
$286$	−204.033	−	12.8396i	−0.713403	−	0.0448938i
$287$	218.667			0.761907
$288$	−9.97505	+	13.7295i	−0.0346356	+	0.0476718i
$289$	56.3148	−	173.319i	0.194861	−	0.599720i
$290$	12.6361	+	38.8900i	0.0435729	+	0.134104i
$291$	−15.2840	+	11.1045i	−0.0525225	+	0.0381598i
$292$	−155.611	−	214.180i	−0.532914	−	0.733493i
$293$	−254.792	+	82.7869i	−0.869597	+	0.282549i	−0.709631	−	0.704574i	$-0.751138\pi$
$293$	−254.792	+	82.7869i	−0.869597	+	0.282549i	−0.159966	+	0.987123i	$0.551138\pi$
$294$	137.986	+	44.8343i	0.469339	+	0.152498i
$295$	−144.595	−	105.055i	−0.490153	−	0.356117i
$296$			120.493i			0.407071i
$297$	−14.2137	−	55.3622i	−0.0478577	−	0.186405i
$298$	−149.895			−0.503004
$299$	−300.957	+	414.232i	−1.00655	+	1.38539i
$300$	19.8574	−	61.1148i	0.0661913	−	0.203716i
$301$	110.555	+	340.254i	0.367293	+	1.13041i
$302$	12.7694	−	9.27748i	0.0422826	−	0.0307201i
$303$	−31.9621	−	43.9921i	−0.105486	−	0.145188i
$304$	82.4847	−	26.8009i	0.271331	−	0.0881608i
$305$	−51.1926	−	16.6335i	−0.167845	−	0.0545360i
$306$	35.4651	+	25.7669i	0.115899	+	0.0842056i
$307$			166.771i			0.543228i	0.962406	+	0.271614i	$0.0875575\pi$
$307$			166.771i			0.543228i	−0.962406	+	0.271614i	$0.912443\pi$
$308$	221.686	−	56.9159i	0.719759	−	0.184792i
$309$	135.357			0.438048
$310$	−35.5459	+	48.9247i	−0.114664	+	0.157822i
$311$	−118.949	+	366.088i	−0.382473	+	1.17713i	0.555824	+	0.831300i	$0.312403\pi$
$311$	−118.949	+	366.088i	−0.382473	+	1.17713i	−0.938297	+	0.345831i	$0.887597\pi$
$312$	−19.8948	−	61.2299i	−0.0637654	−	0.196250i
$313$	77.1325	−	56.0401i	0.246430	−	0.179042i	−0.457713	−	0.889100i	$-0.651331\pi$
$313$	77.1325	−	56.0401i	0.246430	−	0.179042i	0.704143	+	0.710058i	$0.251331\pi$
$314$	125.031	+	172.090i	0.398186	+	0.548057i
$315$	−75.3835	+	24.4936i	−0.239313	+	0.0777574i
$316$	240.825	+	78.2487i	0.762104	+	0.247623i
$317$	450.694	+	327.448i	1.42175	+	1.03296i	0.991480	+	0.130259i	$0.0415809\pi$
$317$	450.694	+	327.448i	1.42175	+	1.03296i	0.430268	+	0.902701i	$0.358419\pi$
$318$		−	61.8266i		−	0.194423i
$319$	−7.86558	+	124.991i	−0.0246570	+	0.391822i
$320$	20.3171			0.0634910
$321$	143.438	−	197.425i	0.446847	−	0.615032i
$322$	177.137	−	545.171i	0.550115	−	1.69308i
$323$	−69.2304	−	213.069i	−0.214336	−	0.659657i
$324$	14.5623	−	10.5801i	0.0449454	−	0.0326547i
$325$	143.291	+	197.223i	0.440896	+	0.606841i
$326$	251.141	−	81.6005i	0.770370	−	0.250308i
$327$	−287.236	−	93.3288i	−0.878399	−	0.285409i
$328$	48.0961	+	34.9438i	0.146634	+	0.106536i
$329$			366.890i			1.11517i
$330$	−43.6190	+	52.7248i	−0.132179	+	0.159772i
$331$	141.274			0.426808			0.213404	−	0.976964i	$-0.431545\pi$
$331$	141.274			0.426808			0.213404	+	0.976964i	$0.431545\pi$
$332$	−142.109	+	195.597i	−0.428040	+	0.589146i
$333$	39.4930	−	121.547i	0.118598	−	0.365006i
$334$	−102.089	−	314.197i	−0.305655	−	0.940709i
$335$	−263.624	+	191.534i	−0.786937	+	0.571743i
$336$	42.3659	+	58.3116i	0.126089	+	0.173546i
$337$	359.129	−	116.688i	1.06566	−	0.346255i	0.276866	−	0.960908i	$-0.410704\pi$
$337$	359.129	−	116.688i	1.06566	−	0.346255i	0.788797	+	0.614653i	$0.210704\pi$
$338$	4.98217	+	1.61880i	0.0147401	+	0.00478936i
$339$	−109.828	−	79.7949i	−0.323977	−	0.235383i
$340$		−	52.4819i		−	0.154359i
$341$	−156.384	+	99.2410i	−0.458603	+	0.291029i
$342$	−91.9905			−0.268978
$343$	62.5652	−	86.1136i	0.182406	−	0.251060i
$344$	−30.0571	+	92.5063i	−0.0873754	+	0.268914i
$345$	52.9602	+	162.995i	0.153508	+	0.472449i
$346$	93.5749	−	67.9862i	0.270448	−	0.196492i
$347$	−1.81657	−	2.50029i	−0.00523507	−	0.00720546i	0.806391	−	0.591382i	$-0.201418\pi$
$347$	−1.81657	−	2.50029i	−0.00523507	−	0.00720546i	−0.811627	+	0.584177i	$0.801418\pi$
$348$	−37.5096	+	12.1876i	−0.107786	+	0.0350218i
$349$	−86.4085	−	28.0758i	−0.247589	−	0.0804465i	0.182594	−	0.983188i	$-0.441551\pi$
$349$	−86.4085	−	28.0758i	−0.247589	−	0.0804465i	−0.430182	+	0.902742i	$0.641551\pi$
$350$	−220.800	−	160.420i	−0.630857	−	0.458344i
$351$			68.2863i			0.194548i
$352$	57.8554	+	22.9075i	0.164362	+	0.0650782i
$353$	310.347			0.879169			0.439585	−	0.898201i	$-0.355126\pi$
$353$	310.347			0.879169			0.439585	+	0.898201i	$0.355126\pi$
$354$	101.326	−	139.463i	0.286230	−	0.393962i
$355$	80.8306	−	248.771i	0.227692	−	0.700763i
$356$	12.3584	+	38.0351i	0.0347145	+	0.106840i
$357$	150.627	−	109.437i	0.421924	−	0.306546i
$358$	161.320	+	222.038i	0.450615	+	0.620219i
$359$	80.4945	−	26.1542i	0.224219	−	0.0728531i	−0.194753	−	0.980852i	$-0.562391\pi$
$359$	80.4945	−	26.1542i	0.224219	−	0.0728531i	0.418972	+	0.907999i	$0.362391\pi$
$360$	−20.4948	−	6.65918i	−0.0569301	−	0.0184977i
$361$	88.2844	+	64.1424i	0.244555	+	0.177680i
$362$		−	187.371i		−	0.517600i
$363$	−183.658	+	100.960i	−0.505944	+	0.278126i
$364$	−273.438			−0.751202
$365$	197.598	−	271.970i	0.541363	−	0.745122i
$366$	16.0431	−	49.3755i	0.0438335	−	0.134906i
$367$	−190.835	−	587.330i	−0.519987	−	1.60035i	−0.774021	−	0.633160i	$-0.781758\pi$
$367$	−190.835	−	587.330i	−0.519987	−	1.60035i	0.254035	−	0.967195i	$-0.418242\pi$
$368$	126.082	−	91.6038i	0.342614	−	0.248923i
$369$	−37.0635	−	51.0136i	−0.100443	−	0.138248i
$370$	−145.516	+	47.2810i	−0.393286	+	0.127786i
$371$	−249.737	−	81.1444i	−0.673145	−	0.218718i
$372$	−47.1881	−	34.2841i	−0.126850	−	0.0921617i
$373$			84.5742i			0.226740i	0.993553	+	0.113370i	$0.0361646\pi$
$373$			84.5742i			0.226740i	−0.993553	+	0.113370i	$0.963835\pi$
$374$	59.1733	−	149.448i	0.158217	−	0.399595i
$375$	191.568			0.510848
$376$	−58.6304	+	80.6978i	−0.155932	+	0.214622i
$377$	46.2358	−	142.299i	0.122641	−	0.377452i
$378$	−23.6241	−	72.7076i	−0.0624977	−	0.192348i
$379$	192.558	−	139.901i	0.508067	−	0.369133i	−0.304023	−	0.952665i	$-0.598330\pi$
$379$	192.558	−	139.901i	0.508067	−	0.369133i	0.812090	+	0.583532i	$0.198330\pi$
$380$	64.7333	+	89.0977i	0.170351	+	0.234468i
$381$	129.597	−	42.1085i	0.340149	−	0.110521i
$382$	428.857	+	139.344i	1.12266	+	0.364775i
$383$	572.153	+	415.694i	1.49387	+	1.08536i	0.972744	+	0.231884i	$0.0744889\pi$
$383$	572.153	+	415.694i	1.49387	+	1.08536i	0.521129	+	0.853478i	$0.325511\pi$
$384$			19.5959i			0.0510310i
$385$	155.724	+	245.390i	0.404478	+	0.637376i
$386$	−279.331			−0.723656
$387$	60.6401	−	83.4640i	0.156693	−	0.215669i
$388$	−6.74112	+	20.7470i	−0.0173740	+	0.0534718i
$389$	104.504	+	321.629i	0.268647	+	0.826810i	0.990831	+	0.135109i	$0.0431384\pi$
$389$	104.504	+	321.629i	0.268647	+	0.826810i	−0.722184	+	0.691701i	$0.756862\pi$
$390$	66.1389	−	48.0527i	0.169587	−	0.123212i
$391$	−236.625	−	325.687i	−0.605180	−	0.832958i
$392$	159.332	−	51.7702i	0.406460	−	0.132067i
$393$	120.884	+	39.2775i	0.307592	+	0.0999427i
$394$	229.503	+	166.743i	0.582494	+	0.423207i
$395$			321.541i			0.814029i
$396$	−50.8533	−	42.0707i	−0.128417	−	0.106239i
$397$	−580.074			−1.46114			−0.730572	−	0.682836i	$-0.760747\pi$
$397$	−580.074			−1.46114			−0.730572	+	0.682836i	$0.760747\pi$
$398$	−175.689	+	241.815i	−0.441429	+	0.607575i
$399$	−120.733	+	371.579i	−0.302589	+	0.931274i
$400$	−22.9294	−	70.5693i	−0.0573234	−	0.176423i
$401$	−104.997	+	76.2847i	−0.261838	+	0.190236i	−0.710957	−	0.703236i	$-0.751738\pi$
$401$	−104.997	+	76.2847i	−0.261838	+	0.190236i	0.449119	+	0.893472i	$0.351738\pi$
$402$	−184.735	−	254.266i	−0.459540	−	0.632503i
$403$	210.447	−	68.3782i	0.522200	−	0.169673i
$404$	−59.7163	−	19.4030i	−0.147813	−	0.0480272i
$405$	18.4915	+	13.4349i	0.0456580	+	0.0331725i
$406$			167.508i			0.412582i
$407$	−467.683	−	29.4308i	−1.14910	−	0.0723116i
$408$	50.6190			0.124066
$409$	116.460	−	160.294i	0.284744	−	0.391917i	−0.642554	−	0.766241i	$-0.722125\pi$
$409$	116.460	−	160.294i	0.284744	−	0.391917i	0.927298	+	0.374324i	$0.122125\pi$
$410$	−23.3279	+	71.7960i	−0.0568974	+	0.175112i
$411$	64.6705	+	199.035i	0.157349	+	0.484271i
$412$	126.447	−	91.8689i	0.306909	−	0.222983i
$413$	−430.348	−	592.323i	−1.04201	−	1.43420i
$414$	−157.209	+	51.0803i	−0.379732	+	0.123382i
$415$	−291.979	−	94.8698i	−0.703564	−	0.228602i
$416$	−60.1429	−	43.6963i	−0.144574	−	0.105039i
$417$		−	343.986i		−	0.824907i
$418$	83.8781	+	326.703i	0.200665	+	0.781586i
$419$	6.28860			0.0150086			0.00750429	−	0.999972i	$-0.497611\pi$
$419$	6.28860			0.0150086			0.00750429	+	0.999972i	$0.497611\pi$
$420$	−53.7970	+	74.0452i	−0.128088	+	0.176298i
$421$	−68.1227	+	209.660i	−0.161812	+	0.498005i	−0.998787	−	0.0492351i	$-0.984322\pi$
$421$	−68.1227	+	209.660i	−0.161812	+	0.498005i	0.836975	+	0.547240i	$0.184322\pi$
$422$	103.929	+	319.861i	0.246278	+	0.757965i
$423$	85.5930	−	62.1869i	0.202347	−	0.147014i
$424$	−41.9627	−	57.7567i	−0.0989686	−	0.136219i
$425$	−182.290	+	59.2297i	−0.428918	+	0.139364i
$426$	239.940	+	77.9614i	0.563240	+	0.183008i
$427$	−178.387	−	129.606i	−0.417768	−	0.303527i
$428$		−	281.783i		−	0.658371i
$429$	242.518	−	62.2642i	0.565309	−	0.145138i
$430$	−123.511			−0.287236
$431$	−38.5539	+	53.0648i	−0.0894521	+	0.123120i	−0.851398	−	0.524521i	$-0.824244\pi$
$431$	−38.5539	+	53.0648i	−0.0894521	+	0.123120i	0.761945	+	0.647641i	$0.224244\pi$
$432$	6.42280	−	19.7673i	0.0148676	−	0.0457577i
$433$	142.450	+	438.415i	0.328983	+	1.01250i	0.969611	+	0.244653i	$0.0786742\pi$
$433$	142.450	+	438.415i	0.328983	+	1.01250i	−0.640628	+	0.767852i	$0.721326\pi$
$434$	−200.416	+	145.611i	−0.461789	+	0.335509i
$435$	−29.4372	−	40.5168i	−0.0676717	−	0.0931421i
$436$	−331.672	+	107.767i	−0.760716	+	0.247172i
$437$	803.430	+	261.050i	1.83851	+	0.597369i
$438$	262.316	+	190.583i	0.598894	+	0.435122i
$439$			2.92311i			0.00665856i	0.999994	+	0.00332928i	$0.00105974\pi$
$439$			2.92311i			0.00665856i	−0.999994	+	0.00332928i	$0.998940\pi$
$440$	−4.96252	+	78.8590i	−0.0112785	+	0.179225i
$441$	−177.694			−0.402935
$442$	−112.874	+	155.357i	−0.255370	+	0.351487i
$443$	93.6723	−	288.294i	0.211450	−	0.650776i	−0.787937	−	0.615756i	$-0.788851\pi$
$443$	93.6723	−	288.294i	0.211450	−	0.650776i	0.999387	−	0.0350198i	$-0.0111494\pi$
$444$	−45.6026	−	140.350i	−0.102709	−	0.316105i
$445$	−41.0845	+	29.8496i	−0.0923247	+	0.0670778i
$446$	−117.660	−	161.945i	−0.263811	−	0.363104i
$447$	174.598	−	56.7304i	0.390600	−	0.126914i
$448$	79.1540	+	25.7187i	0.176683	+	0.0574078i
$449$	275.746	+	200.341i	0.614133	+	0.446194i	0.850867	−	0.525380i	$-0.176077\pi$
$449$	275.746	+	200.341i	0.614133	+	0.446194i	−0.236734	+	0.971575i	$0.576077\pi$
$450$			78.7020i			0.174893i
$451$	−147.379	+	178.145i	−0.326783	+	0.395001i
$452$	−156.757			−0.346807
$453$	−11.3625	+	15.6392i	−0.0250829	+	0.0345236i
$454$	−98.9346	+	304.489i	−0.217918	+	0.670681i
$455$	−107.296	−	330.222i	−0.235815	−	0.725763i
$456$	−85.9350	+	62.4354i	−0.188454	+	0.136920i
$457$	−456.291	−	628.031i	−0.998449	−	1.37425i	−0.926272	−	0.376855i	$-0.877005\pi$
$457$	−456.291	−	628.031i	−0.998449	−	1.37425i	−0.0721770	−	0.997392i	$-0.522995\pi$
$458$	230.506	−	74.8960i	0.503289	−	0.163528i
$459$	−51.0618	−	16.5910i	−0.111246	−	0.0361459i
$460$	160.101	+	116.320i	0.348046	+	0.252870i
$461$		−	459.872i		−	0.997553i	−0.866731	−	0.498776i	$-0.833783\pi$
$461$		−	459.872i		−	0.997553i	0.866731	−	0.498776i	$-0.166217\pi$
$462$	−236.679	+	150.196i	−0.512293	+	0.325101i
$463$	−39.3897			−0.0850749			−0.0425375	−	0.999095i	$-0.513544\pi$
$463$	−39.3897			−0.0850749			−0.0425375	+	0.999095i	$0.513544\pi$
$464$	−26.7685	+	36.8436i	−0.0576907	+	0.0794044i
$465$	22.8875	−	70.4406i	0.0492205	−	0.151485i
$466$	−40.4511	−	124.496i	−0.0868048	−	0.267158i
$467$	296.268	−	215.251i	0.634406	−	0.460923i	−0.223518	−	0.974700i	$-0.571754\pi$
$467$	296.268	−	215.251i	0.634406	−	0.460923i	0.857924	+	0.513777i	$0.171754\pi$
$468$	46.3470	+	63.7911i	0.0990320	+	0.136306i
$469$	−1269.52	+	412.491i	−2.70686	+	0.879511i
$470$	−120.463	−	39.1407i	−0.256304	−	0.0832781i
$471$	−210.766	−	153.131i	−0.447486	−	0.325118i
$472$		−	199.053i		−	0.421723i
$473$	−351.713	−	139.259i	−0.743580	−	0.294417i
$474$	−310.128			−0.654278
$475$	236.415	−	325.397i	0.497716	−	0.685047i
$476$	66.4350	−	204.466i	0.139569	−	0.429550i
$477$	23.3993	+	72.0157i	0.0490552	+	0.150976i
$478$	−276.355	+	200.783i	−0.578148	+	0.420049i
$479$	−164.073	−	225.828i	−0.342533	−	0.471456i	0.602646	−	0.798009i	$-0.294113\pi$
$479$	−164.073	−	225.828i	−0.342533	−	0.471456i	−0.945179	+	0.326552i	$0.894113\pi$
$480$	−23.6654	+	7.68935i	−0.0493029	+	0.0160195i
$481$	532.445	+	173.002i	1.10695	+	0.359671i
$482$	−126.007	−	91.5494i	−0.261425	−	0.189936i
$483$			702.057i			1.45353i
$484$	−103.045	+	218.965i	−0.212903	+	0.452407i
$485$	−27.7008			−0.0571150
$486$	−12.9580	+	17.8351i	−0.0266625	+	0.0366978i
$487$	−141.465	+	435.383i	−0.290482	+	0.894011i	0.694220	+	0.719763i	$0.255749\pi$
$487$	−141.465	+	435.383i	−0.290482	+	0.894011i	−0.984702	+	0.174248i	$0.944251\pi$
$488$	−18.5249	−	57.0139i	−0.0379609	−	0.116832i
$489$	−261.646	+	190.097i	−0.535063	+	0.388746i
$490$	125.043	+	172.106i	0.255189	+	0.351237i
$491$	156.302	−	50.7856i	0.318334	−	0.103433i	−0.145492	−	0.989359i	$-0.546476\pi$
$491$	156.302	−	50.7856i	0.318334	−	0.103433i	0.463826	+	0.885927i	$0.346476\pi$
$492$	−69.2475	−	22.4999i	−0.140747	−	0.0457314i
$493$	95.1722	+	69.1467i	0.193047	+	0.140257i
$494$		−	402.971i		−	0.815730i
$495$	30.8529	−	77.9223i	0.0623291	−	0.157419i
$496$	−67.3510			−0.135788
$497$	629.821	−	866.874i	1.26724	−	1.74421i
$498$	91.5022	−	281.615i	0.183739	−	0.565492i
$499$	40.2278	+	123.808i	0.0806168	+	0.248113i	0.983239	−	0.182320i	$-0.0583608\pi$
$499$	40.2278	+	123.808i	0.0806168	+	0.248113i	−0.902622	+	0.430433i	$0.858361\pi$
$500$	178.958	−	130.020i	0.357915	−	0.260041i
$501$	237.826	+	327.340i	0.474703	+	0.653373i
$502$	576.069	−	187.176i	1.14755	−	0.372861i
$503$	−301.238	−	97.8781i	−0.598883	−	0.194589i	−0.00614061	−	0.999981i	$-0.501955\pi$
$503$	−301.238	−	97.8781i	−0.598883	−	0.194589i	−0.592742	+	0.805392i	$0.701955\pi$
$504$	−71.4168	−	51.8874i	−0.141700	−	0.102951i
$505$		−	79.7312i		−	0.157884i
$506$	324.756	+	511.750i	0.641810	+	1.01136i
$507$	−6.41590			−0.0126546
$508$	92.4859	−	127.296i	0.182059	−	0.250582i
$509$	−141.338	+	434.993i	−0.277677	+	0.854602i	0.710822	+	0.703372i	$0.248323\pi$
$509$	−141.338	+	434.993i	−0.277677	+	0.854602i	−0.988499	+	0.151230i	$0.951677\pi$
$510$	19.8627	+	61.1310i	0.0389464	+	0.119865i
$511$	1114.10	−	809.443i	2.18024	−	1.58404i
$512$	13.3001	+	18.3060i	0.0259767	+	0.0357538i
$513$	107.151	−	34.8154i	0.208871	−	0.0678662i
$514$	−50.3559	−	16.3616i	−0.0979686	−	0.0318319i
$515$	160.564	+	116.657i	0.311776	+	0.226518i
$516$		−	119.127i		−	0.230867i
$517$	−298.901	−	247.279i	−0.578144	−	0.478297i
$518$	−626.771			−1.20998
$519$	−83.2657	+	114.605i	−0.160435	+	0.220820i
$520$	29.1710	−	89.7790i	0.0560980	−	0.172652i
$521$	130.177	+	400.643i	0.249859	+	0.768988i	0.994799	+	0.101856i	$0.0324783\pi$
$521$	130.177	+	400.643i	0.249859	+	0.768988i	−0.744940	+	0.667132i	$0.767522\pi$
$522$	39.0786	−	28.3923i	0.0748632	−	0.0543913i
$523$	−149.432	−	205.675i	−0.285720	−	0.393260i	0.641898	−	0.766790i	$-0.278147\pi$
$523$	−149.432	−	205.675i	−0.285720	−	0.393260i	−0.927618	+	0.373530i	$0.878147\pi$
$524$	139.584	−	45.3537i	0.266383	−	0.0865529i
$525$	317.902	+	103.293i	0.605527	+	0.196748i
$526$	250.643	+	182.103i	0.476508	+	0.346203i
$527$			173.977i			0.330127i
$528$	−76.0598	−	4.78637i	−0.144053	−	0.00906510i
$529$	988.993			1.86955
$530$	53.2850	−	73.3406i	0.100538	−	0.138378i
$531$	−65.2421	+	200.795i	−0.122867	+	0.378144i
$532$	139.411	+	429.062i	0.262050	+	0.806507i
$533$	223.468	−	162.359i	0.419265	−	0.304614i
$534$	−28.7901	−	39.6261i	−0.0539140	−	0.0742062i
$535$	340.301	−	110.570i	0.636076	−	0.206674i
$536$	−345.149	−	112.146i	−0.643934	−	0.209227i
$537$	−271.940	−	197.576i	−0.506406	−	0.367926i
$538$		−	6.05230i		−	0.0112496i
$539$	162.024	+	631.079i	0.300601	+	1.17083i
$540$	26.3927			0.0488754
$541$	117.474	−	161.689i	0.217142	−	0.298870i	−0.686525	−	0.727106i	$-0.740865\pi$
$541$	117.474	−	161.689i	0.217142	−	0.298870i	0.903667	+	0.428236i	$0.140865\pi$
$542$	−8.82325	+	27.1552i	−0.0162791	+	0.0501018i
$543$	70.9138	+	218.250i	0.130596	+	0.401934i
$544$	47.2868	−	34.3559i	0.0869243	−	0.0631542i
$545$	−260.293	−	358.263i	−0.477603	−	0.657364i
$546$	318.501	−	103.487i	0.583334	−	0.189537i
$547$	−616.280	−	200.242i	−1.12665	−	0.366072i	−0.314351	−	0.949307i	$-0.601787\pi$
$547$	−616.280	−	200.242i	−1.12665	−	0.366072i	−0.812304	+	0.583235i	$0.801787\pi$
$548$	195.502	+	142.040i	0.356755	+	0.259198i
$549$			63.5844i			0.115819i
$550$	279.509	−	71.7614i	0.508198	−	0.130475i
$551$	−246.861			−0.448023
$552$	−112.191	+	154.418i	−0.203245	+	0.279743i
$553$	−407.028	+	1252.70i	−0.736036	+	2.26528i
$554$	−85.4244	−	262.909i	−0.154196	−	0.474566i
$555$	151.603	−	110.146i	0.273158	−	0.198461i
$556$	−233.469	−	321.342i	−0.419908	−	0.577954i
$557$	721.950	−	234.576i	1.29614	−	0.421141i	0.421903	−	0.906641i	$-0.361362\pi$
$557$	721.950	−	234.576i	1.29614	−	0.421141i	0.874237	+	0.485500i	$0.161362\pi$
$558$	67.9402	+	22.0751i	0.121757	+	0.0395611i
$559$	365.619	+	265.638i	0.654060	+	0.475202i
$560$			105.684i			0.188721i
$561$	−12.3639	+	196.473i	−0.0220390	+	0.350219i
$562$	491.270			0.874146
$563$	−279.523	+	384.731i	−0.496489	+	0.683359i	−0.981568	−	0.191111i	$-0.938791\pi$
$563$	−279.523	+	384.731i	−0.496489	+	0.683359i	0.485079	+	0.874470i	$0.338791\pi$
$564$	37.7513	−	116.187i	0.0669350	−	0.206005i
$565$	−61.5106	−	189.310i	−0.108868	−	0.335062i
$566$	353.930	−	257.145i	0.625318	−	0.454320i
$567$	55.0349	+	75.7490i	0.0970633	+	0.133596i
$568$	277.059	−	90.0220i	0.487781	−	0.158490i
$569$	−181.060	−	58.8299i	−0.318207	−	0.103392i	0.145559	−	0.989350i	$-0.453502\pi$
$569$	−181.060	−	58.8299i	−0.318207	−	0.103392i	−0.463766	+	0.885958i	$0.653502\pi$
$570$	−109.122	−	79.2817i	−0.191442	−	0.139091i
$571$			221.036i			0.387104i	0.981090	+	0.193552i	$0.0620008\pi$
$571$			221.036i			0.387104i	−0.981090	+	0.193552i	$0.937999\pi$
$572$	184.294	−	222.766i	0.322191	−	0.389451i
$573$	−552.270			−0.963822
$574$	−181.768	+	250.182i	−0.316669	+	0.435857i
$575$	223.340	−	687.370i	0.388418	−	1.19543i
$576$	−7.41641	−	22.8254i	−0.0128757	−	0.0396274i
$577$	−672.664	+	488.719i	−1.16580	+	0.847000i	−0.990500	−	0.137516i	$-0.956088\pi$
$577$	−672.664	+	488.719i	−1.16580	+	0.847000i	−0.175296	+	0.984516i	$0.556088\pi$
$578$	151.486	+	208.503i	0.262087	+	0.360732i
$579$	325.366	−	105.718i	0.561944	−	0.182587i
$580$	−54.9988	−	17.8702i	−0.0948255	−	0.0308107i
$581$	−1017.44	−	739.212i	−1.75118	−	1.27231i
$582$		−	26.7175i		−	0.0459063i
$583$	234.427	−	148.767i	0.402104	−	0.255175i
$584$	374.400			0.641096
$585$	−58.8523	+	81.0032i	−0.100602	+	0.138467i
$586$	117.078	−	360.330i	0.199792	−	0.614898i
$587$	234.125	+	720.562i	0.398850	+	1.22753i	0.925923	+	0.377713i	$0.123289\pi$
$587$	234.125	+	720.562i	0.398850	+	1.22753i	−0.527073	+	0.849820i	$0.676711\pi$
$588$	−165.997	+	120.604i	−0.282308	+	0.205109i
$589$	−214.590	−	295.358i	−0.364329	−	0.501456i
$590$	240.391	−	78.1077i	0.407442	−	0.132386i
$591$	−330.432	−	107.364i	−0.559106	−	0.181665i
$592$	−137.859	−	100.160i	−0.232870	−	0.169190i
$593$			770.248i			1.29890i	0.760404	+	0.649450i	$0.225001\pi$
$593$			770.248i			1.29890i	−0.760404	+	0.649450i	$0.774999\pi$
$594$	75.1563	+	29.7577i	0.126526	+	0.0500972i
$595$	272.996			0.458817
$596$	124.601	−	171.499i	0.209062	−	0.287749i
$597$	113.124	−	348.159i	0.189487	−	0.583180i
$598$	−223.761	−	688.664i	−0.374182	−	1.15161i
$599$	123.174	−	89.4914i	0.205633	−	0.149401i	−0.480203	−	0.877158i	$-0.659437\pi$
$599$	123.174	−	89.4914i	0.205633	−	0.149401i	0.685836	+	0.727756i	$0.259437\pi$
$600$	53.4163	+	73.5212i	0.0890272	+	0.122535i
$601$	−75.3361	+	24.4782i	−0.125351	+	0.0407291i	−0.371021	−	0.928625i	$-0.620992\pi$
$601$	−75.3361	+	24.4782i	−0.125351	+	0.0407291i	0.245670	+	0.969354i	$0.420992\pi$
$602$	−481.192	−	156.349i	−0.799322	−	0.259715i
$603$	311.411	+	226.253i	0.516436	+	0.375213i
$604$			22.3217i			0.0369564i
$605$	−304.872	−	38.5232i	−0.503921	−	0.0636747i
$606$	76.9010			0.126899
$607$	−113.294	+	155.936i	−0.186646	+	0.256896i	−0.892078	−	0.451882i	$-0.850753\pi$
$607$	−113.294	+	155.936i	−0.186646	+	0.256896i	0.705432	+	0.708777i	$0.250753\pi$
$608$	−37.9022	+	116.651i	−0.0623391	+	0.191860i
$609$	−63.3964	−	195.114i	−0.104099	−	0.320384i
$610$	61.5848	−	44.7440i	0.100959	−	0.0733508i
$611$	272.414	+	374.946i	0.445849	+	0.613659i
$612$	−58.9610	+	19.1576i	−0.0963416	+	0.0313033i
$613$	−343.466	−	111.599i	−0.560304	−	0.182054i	0.0151539	−	0.999885i	$-0.495176\pi$
$613$	−343.466	−	111.599i	−0.560304	−	0.182054i	−0.575458	+	0.817831i	$0.695176\pi$
$614$	−190.807	−	138.629i	−0.310760	−	0.225780i
$615$		−	92.4570i		−	0.150337i
$616$	−119.158	+	300.947i	−0.193439	+	0.488551i
$617$	−928.141			−1.50428			−0.752140	−	0.659003i	$-0.770978\pi$
$617$	−928.141			−1.50428			−0.752140	+	0.659003i	$0.770978\pi$
$618$	−112.516	+	154.865i	−0.182065	+	0.250590i
$619$	−248.587	+	765.072i	−0.401594	+	1.23598i	0.522111	+	0.852877i	$0.325145\pi$
$619$	−248.587	+	765.072i	−0.401594	+	1.23598i	−0.923706	+	0.383103i	$0.874855\pi$
$620$	−26.4282	−	81.3378i	−0.0426262	−	0.131190i
$621$	163.785	−	118.997i	0.263744	−	0.191621i
$622$	−319.973	−	440.404i	−0.514425	−	0.708046i
$623$	−197.848	+	64.2847i	−0.317573	+	0.103186i
$624$	86.5921	+	28.1355i	0.138769	+	0.0450889i
$625$	−147.943	−	107.487i	−0.236708	−	0.171979i
$626$			134.833i			0.215388i
$627$	−221.348	−	348.799i	−0.353026	−	0.556298i
$628$	−300.824			−0.479019
$629$	−258.728	+	356.108i	−0.411332	+	0.566150i
$630$	34.6392	−	106.608i	0.0549828	−	0.169220i
$631$	4.37296	+	13.4586i	0.00693020	+	0.0213290i	0.954462	−	0.298333i	$-0.0964306\pi$
$631$	4.37296	+	13.4586i	0.00693020	+	0.0213290i	−0.947532	+	0.319662i	$0.896431\pi$
$632$	−289.713	+	210.489i	−0.458406	+	0.333052i
$633$	−242.114	−	333.241i	−0.382486	−	0.526447i
$634$	−749.282	+	243.457i	−1.18183	+	0.384001i
$635$	190.022	+	61.7421i	0.299248	+	0.0972316i
$636$	70.7372	+	51.3936i	0.111222	+	0.0808075i
$637$		−	778.402i		−	1.22198i
$638$	−136.467	−	112.899i	−0.213898	−	0.176957i
$639$	−308.989			−0.483551
$640$	−16.8887	+	23.2453i	−0.0263886	+	0.0363207i
$641$	162.989	−	501.628i	0.254273	−	0.782571i	−0.739699	−	0.672937i	$-0.765032\pi$
$641$	162.989	−	501.628i	0.254273	−	0.782571i	0.993972	−	0.109633i	$-0.0349677\pi$
$642$	106.645	+	328.221i	0.166114	+	0.511248i
$643$	348.552	−	253.238i	0.542072	−	0.393839i	−0.282782	−	0.959184i	$-0.591257\pi$
$643$	348.552	−	253.238i	0.542072	−	0.393839i	0.824854	+	0.565346i	$0.191257\pi$
$644$	476.497	+	655.842i	0.739902	+	1.01839i
$645$	143.866	−	46.7450i	0.223049	−	0.0724729i
$646$	301.325	+	97.9066i	0.466448	+	0.151558i
$647$	40.3167	+	29.2918i	0.0623133	+	0.0452732i	0.618506	−	0.785780i	$-0.287738\pi$
$647$	40.3167	+	29.2918i	0.0623133	+	0.0452732i	−0.556193	+	0.831053i	$0.687738\pi$
$648$			25.4558i			0.0392837i
$649$	772.608	+	48.6195i	1.19046	+	0.0749144i
$650$	−344.759			−0.530399
$651$	178.336	−	245.459i	0.273942	−	0.377049i
$652$	−115.401	+	355.166i	−0.176995	+	0.544734i
$653$	225.607	+	694.347i	0.345493	+	1.06332i	0.961319	+	0.275436i	$0.0888222\pi$
$653$	225.607	+	694.347i	0.345493	+	1.06332i	−0.615826	+	0.787882i	$0.711178\pi$
$654$	345.546	−	251.054i	0.528358	−	0.383874i
$655$	109.545	+	150.775i	0.167244	+	0.230191i
$656$	−79.9601	+	25.9806i	−0.121890	+	0.0396046i
$657$	−377.675	−	122.714i	−0.574848	−	0.186779i
$658$	−419.767	−	304.979i	−0.637944	−	0.463494i
$659$			536.209i			0.813671i	0.913501	+	0.406836i	$0.133368\pi$
$659$			536.209i			0.813671i	−0.913501	+	0.406836i	$0.866632\pi$
$660$	−24.0652	−	93.7333i	−0.0364624	−	0.142020i
$661$	−636.800			−0.963389			−0.481694	−	0.876339i	$-0.659978\pi$
$661$	−636.800			−0.963389			−0.481694	+	0.876339i	$0.659978\pi$
$662$	−117.434	+	161.634i	−0.177393	+	0.244161i
$663$	72.6779	−	223.679i	0.109620	−	0.337375i
$664$	−105.658	−	325.181i	−0.159123	−	0.489730i
$665$	−463.461	+	336.724i	−0.696934	+	0.506352i
$666$	106.236	+	146.221i	0.159514	+	0.219552i
$667$	−421.877	+	137.076i	−0.632500	+	0.205512i
$668$	444.341	+	144.375i	0.665182	+	0.216131i
$669$	198.341	+	144.103i	0.296473	+	0.215401i
$670$		−	460.831i		−	0.687808i
$671$	225.819	−	57.9770i	0.336541	−	0.0864039i
$672$	−101.932			−0.151685
$673$	294.827	−	405.795i	0.438079	−	0.602965i	−0.531705	−	0.846930i	$-0.678448\pi$
$673$	294.827	−	405.795i	0.438079	−	0.602965i	0.969784	+	0.243965i	$0.0784483\pi$
$674$	−165.022	+	507.885i	−0.244839	+	0.753538i
$675$	−29.7861	−	91.6722i	−0.0441276	−	0.135811i
$676$	−5.99356	+	4.35457i	−0.00886621	+	0.00644168i
$677$	130.318	+	179.367i	0.192493	+	0.264944i	0.894344	−	0.447380i	$-0.147643\pi$
$677$	130.318	+	179.367i	0.192493	+	0.264944i	−0.701851	+	0.712324i	$0.747643\pi$
$678$	182.590	−	59.3272i	0.269307	−	0.0875032i
$679$	−107.920	−	35.0654i	−0.158940	−	0.0516427i
$680$	60.0457	+	43.6258i	0.0883026	+	0.0641556i
$681$		−	392.113i		−	0.575790i
$682$	16.4507	−	261.417i	0.0241213	−	0.383309i
$683$	247.703			0.362669			0.181335	−	0.983421i	$-0.441958\pi$
$683$	247.703			0.362669			0.181335	+	0.983421i	$0.441958\pi$
$684$	76.4675	−	105.248i	0.111795	−	0.153872i
$685$	−94.8239	+	291.838i	−0.138429	+	0.426041i
$686$	46.5170	+	143.164i	0.0678090	+	0.208695i
$687$	−240.148	+	174.478i	−0.349561	+	0.253971i
$688$	−80.8535	−	111.285i	−0.117520	−	0.161752i
$689$	−315.470	+	102.502i	−0.457866	+	0.148770i
$690$	−230.509	−	74.8971i	−0.334072	−	0.108546i
$691$	343.704	+	249.715i	0.497401	+	0.361383i	0.808023	−	0.589151i	$-0.200538\pi$
$691$	343.704	+	249.715i	0.497401	+	0.361383i	−0.310623	+	0.950533i	$0.600538\pi$
$692$			163.575i			0.236380i
$693$	218.840	−	264.524i	0.315786	−	0.381709i
$694$	4.37067			0.00629780
$695$	296.463	−	408.047i	0.426566	−	0.587118i
$696$	17.2359	−	53.0465i	0.0247642	−	0.0762163i
$697$	67.1115	+	206.548i	0.0962862	+	0.296339i
$698$	103.950	−	75.5238i	0.148925	−	0.108200i
$699$	94.2349	+	129.703i	0.134814	+	0.185555i
$700$	367.081	−	119.272i	0.524402	−	0.170389i
$701$	326.685	+	106.146i	0.466027	+	0.151421i	0.532612	−	0.846359i	$-0.321210\pi$
$701$	326.685	+	106.146i	0.466027	+	0.151421i	−0.0665852	+	0.997781i	$0.521210\pi$
$702$	−78.1279	−	56.7632i	−0.111293	−	0.0808593i
$703$		−	923.685i		−	1.31392i
$704$	−74.3015	+	47.1517i	−0.105542	+	0.0669768i
$705$	155.129			0.220040
$706$	−257.977	+	355.075i	−0.365407	+	0.502939i
$707$	100.929	−	310.627i	0.142757	−	0.439360i
$708$	75.3351	+	231.858i	0.106406	+	0.327483i
$709$	−185.730	+	134.940i	−0.261960	+	0.190325i	−0.711011	−	0.703181i	$-0.751762\pi$
$709$	−185.730	+	134.940i	−0.261960	+	0.190325i	0.449051	+	0.893506i	$0.351762\pi$
$710$	217.434	+	299.272i	0.306245	+	0.421510i
$711$	361.237	−	117.373i	0.508069	−	0.165082i
$712$	−53.7898	−	17.4774i	−0.0755474	−	0.0245468i
$713$	−530.733	−	385.600i	−0.744367	−	0.540814i
$714$			263.306i			0.368775i
$715$	341.344	+	135.153i	0.477404	+	0.189026i
$716$	−388.137			−0.542091
$717$	245.909	−	338.464i	0.342969	−	0.472056i
$718$	−36.9877	+	113.836i	−0.0515149	+	0.158547i
$719$	−119.186	−	366.816i	−0.165766	−	0.510175i	0.833326	−	0.552782i	$-0.186434\pi$
$719$	−119.186	−	366.816i	−0.165766	−	0.510175i	−0.999092	+	0.0426067i	$0.986434\pi$
$720$	24.6553	−	17.9131i	0.0342435	−	0.0248794i
$721$	477.876	+	657.740i	0.662796	+	0.912261i
$722$	−146.774	+	47.6896i	−0.203287	+	0.0660521i
$723$	181.421	+	58.9474i	0.250929	+	0.0815317i
$724$	214.376	+	155.753i	0.296099	+	0.215128i
$725$			211.200i			0.291311i
$726$	37.1557	−	294.050i	0.0511787	−	0.405028i
$727$	1278.70			1.75887			0.879434	−	0.476022i	$-0.157922\pi$
$727$	1278.70			1.75887			0.879434	+	0.476022i	$0.157922\pi$
$728$	227.296	−	312.846i	0.312220	−	0.429734i
$729$	8.34346	−	25.6785i	0.0114451	−	0.0352243i
$730$	146.913	+	452.152i	0.201251	+	0.619386i
$731$	−287.465	+	208.856i	−0.393249	+	0.285712i
$732$	43.1557	+	59.3988i	0.0589559	+	0.0811459i
$733$	−205.424	+	66.7463i	−0.280251	+	0.0910591i	−0.445770	−	0.895148i	$-0.647070\pi$
$733$	−205.424	+	66.7463i	−0.280251	+	0.0910591i	0.165519	+	0.986207i	$0.447070\pi$
$734$	830.610	+	269.882i	1.13162	+	0.367686i
$735$	−210.786	−	153.145i	−0.286784	−	0.208361i
$736$			220.399i			0.299455i
$737$	519.587	−	1312.27i	0.705003	−	1.78056i
$738$	89.1750			0.120833
$739$	−104.632	+	144.014i	−0.141586	+	0.194876i	−0.873921	−	0.486068i	$-0.838431\pi$
$739$	−104.632	+	144.014i	−0.141586	+	0.194876i	0.732335	+	0.680945i	$0.238431\pi$
$740$	66.8654	−	205.790i	0.0903586	−	0.278095i
$741$	152.511	+	469.381i	0.205818	+	0.633442i
$742$	300.434	−	218.278i	0.404898	−	0.294175i
$743$	291.220	+	400.829i	0.391951	+	0.539474i	0.958701	−	0.284415i	$-0.0917995\pi$
$743$	291.220	+	400.829i	0.391951	+	0.539474i	−0.566750	+	0.823890i	$0.691799\pi$
$744$	78.4505	−	25.4901i	0.105444	−	0.0342609i
$745$	256.007	+	83.1816i	0.343633	+	0.111653i
$746$	−96.7632	−	70.3026i	−0.129709	−	0.0942394i
$747$			362.656i			0.485483i
$748$	121.799	+	191.931i	0.162833	+	0.256592i
$749$	1465.75			1.95695
$750$	−159.242	+	219.177i	−0.212322	+	0.292236i
$751$	238.869	−	735.163i	0.318068	−	0.978912i	−0.656406	−	0.754408i	$-0.727924\pi$
$751$	238.869	−	735.163i	0.318068	−	0.978912i	0.974473	−	0.224504i	$-0.0720760\pi$
$752$	−43.5915	−	134.161i	−0.0579674	−	0.178405i
$753$	−600.166	+	436.046i	−0.797033	+	0.579078i
$754$	124.374	+	171.186i	0.164952	+	0.227038i
$755$	−26.9572	+	8.75892i	−0.0357049	+	0.0116012i
$756$	102.824	+	33.4096i	0.136011	+	0.0441926i
$757$	577.842	+	419.827i	0.763332	+	0.554593i	0.899931	−	0.436033i	$-0.143617\pi$
$757$	577.842	+	419.827i	0.763332	+	0.554593i	−0.136598	+	0.990627i	$0.543617\pi$
$758$			336.603i			0.444067i
$759$	−571.957	−	473.178i	−0.753566	−	0.623422i
$760$	−155.748			−0.204932
$761$	−69.9198	+	96.2364i	−0.0918789	+	0.126460i	−0.852482	−	0.522757i	$-0.824903\pi$
$761$	−69.9198	+	96.2364i	−0.0918789	+	0.126460i	0.760603	+	0.649217i	$0.224903\pi$
$762$	−59.5504	+	183.277i	−0.0781501	+	0.240521i
$763$	−560.572	−	1725.26i	−0.734695	−	2.26116i
$764$	−515.916	+	374.835i	−0.675282	+	0.490621i
$765$	−46.2721	−	63.6881i	−0.0604864	−	0.0832524i
$766$	−951.209	+	309.067i	−1.24179	+	0.403481i
$767$	−879.594	−	285.797i	−1.14680	−	0.372617i
$768$	−22.4201	−	16.2892i	−0.0291929	−	0.0212099i
$769$		−	1110.58i		−	1.44419i	−0.691792	−	0.722097i	$-0.743179\pi$
$769$		−	1110.58i		−	1.44419i	0.691792	−	0.722097i	$-0.256821\pi$
$770$	−410.202	−	25.8136i	−0.532730	−	0.0335242i
$771$	64.8469			0.0841075
$772$	232.195	−	319.589i	0.300771	−	0.413976i
$773$	−146.414	+	450.617i	−0.189411	+	0.582946i	−0.999996	−	0.00267413i	$-0.999149\pi$
$773$	−146.414	+	450.617i	−0.189411	+	0.582946i	0.810586	+	0.585620i	$0.199149\pi$
$774$	45.0857	+	138.760i	0.0582503	+	0.179276i
$775$	−252.692	+	183.591i	−0.326054	+	0.236892i
$776$	−18.1336	−	24.9587i	−0.0233680	−	0.0321633i
$777$	730.063	−	237.212i	0.939593	−	0.305292i
$778$	−454.852	−	147.790i	−0.584643	−	0.189962i
$779$	−368.699	−	267.875i	−0.473297	−	0.343871i
$780$			115.615i			0.148224i
$781$	281.740	+	1097.37i	0.360742	+	1.40508i
$782$	569.321			0.728032
$783$	−34.7733	+	47.8613i	−0.0444103	+	0.0611255i
$784$	−73.2141	+	225.330i	−0.0933853	+	0.287410i
$785$	−118.042	−	363.296i	−0.150372	−	0.462798i
$786$	−145.423	+	105.656i	−0.185017	+	0.134423i
$787$	479.922	+	660.556i	0.609812	+	0.839334i	0.996562	−	0.0828505i	$-0.0264024\pi$
$787$	479.922	+	660.556i	0.609812	+	0.839334i	−0.386750	+	0.922185i	$0.626402\pi$
$788$	−381.550	+	123.973i	−0.484200	+	0.157326i
$789$	−360.870	−	117.254i	−0.457376	−	0.148610i
$790$	−367.883	−	267.282i	−0.465674	−	0.338332i
$791$		−	815.403i		−	1.03085i
$792$	90.4060	−	23.2109i	0.114149	−	0.0293067i
$793$	−278.536			−0.351243
$794$	482.189	−	663.676i	0.607291	−	0.835864i
$795$	−34.3095	+	105.594i	−0.0431566	+	0.132822i
$796$	−130.624	−	402.019i	−0.164100	−	0.505049i
$797$	669.042	−	486.088i	0.839451	−	0.609897i	−0.0827665	−	0.996569i	$-0.526376\pi$
$797$	669.042	−	486.088i	0.839451	−	0.609897i	0.922217	+	0.386672i	$0.126376\pi$
$798$	−324.772	−	447.010i	−0.406982	−	0.560162i
$799$	−346.556	+	112.603i	−0.433737	+	0.140930i
$800$	99.8000	+	32.4270i	0.124750	+	0.0405338i
$801$	48.5319	+	35.2605i	0.0605891	+	0.0440206i
$802$		−	183.541i		−	0.228854i
$803$	−91.4485	+	1453.20i	−0.113884	+	1.80971i
$804$	444.473			0.552828
$805$	−605.065	+	832.801i	−0.751634	+	1.03454i
$806$	−96.7014	+	297.616i	−0.119977	+	0.369251i
$807$	2.29060	+	7.04973i	0.00283841	+	0.00873572i
$808$	71.8388	−	52.1940i	0.0889094	−	0.0645965i
$809$	−280.739	−	386.404i	−0.347020	−	0.477632i	0.599455	−	0.800408i	$-0.295384\pi$
$809$	−280.739	−	386.404i	−0.347020	−	0.477632i	−0.946475	+	0.322776i	$0.895384\pi$
$810$	−30.7423	+	9.98877i	−0.0379534	+	0.0123318i
$811$	1096.93	+	356.415i	1.35257	+	0.439477i	0.893556	−	0.448953i	$-0.148203\pi$
$811$	1096.93	+	356.415i	1.35257	+	0.439477i	0.459014	+	0.888429i	$0.348203\pi$
$812$	−191.650	−	139.242i	−0.236022	−	0.171480i
$813$		−	34.9697i		−	0.0430132i
$814$	422.436	−	510.622i	0.518963	−	0.627300i
$815$	−474.206			−0.581848
$816$	−42.0772	+	57.9143i	−0.0515652	+	0.0709734i
$817$	230.414	−	709.142i	0.282025	−	0.867983i
$818$	86.5878	+	266.490i	0.105853	+	0.325782i
$819$	−331.823	+	241.084i	−0.405157	+	0.294364i
$820$	−62.7520	−	86.3707i	−0.0765268	−	0.105330i
$821$	−1006.94	+	327.176i	−1.22648	+	0.398509i	−0.849440	−	0.527686i	$-0.823060\pi$
$821$	−1006.94	+	327.176i	−1.22648	+	0.398509i	−0.377045	+	0.926195i	$0.623060\pi$
$822$	−281.479	−	91.4579i	−0.342431	−	0.111263i
$823$	340.139	+	247.126i	0.413292	+	0.300274i	0.774933	−	0.632043i	$-0.217784\pi$
$823$	340.139	+	247.126i	0.413292	+	0.300274i	−0.361641	+	0.932317i	$0.617784\pi$
$824$			221.037i			0.268249i
$825$	−298.413	+	189.373i	−0.361713	+	0.229543i
$826$	1035.42			1.25353
$827$	−362.950	+	499.558i	−0.438875	+	0.604060i	−0.969962	−	0.243258i	$-0.921784\pi$
$827$	−362.950	+	499.558i	−0.438875	+	0.604060i	0.531086	+	0.847318i	$0.321784\pi$
$828$	72.2385	−	222.327i	0.0872445	−	0.268511i
$829$	−258.162	−	794.542i	−0.311414	−	0.958435i	−0.977205	−	0.212296i	$-0.931906\pi$
$829$	−258.162	−	794.542i	−0.311414	−	0.958435i	0.665791	−	0.746138i	$-0.268094\pi$
$830$	351.251	−	255.199i	0.423195	−	0.307469i
$831$	199.005	+	273.907i	0.239477	+	0.329611i
$832$	99.9880	−	32.4881i	0.120178	−	0.0390482i
$833$	582.058	+	189.122i	0.698749	+	0.227037i
$834$	393.562	+	285.940i	0.471897	+	0.342854i
$835$			593.270i			0.710503i
$836$	−443.512	−	175.606i	−0.530517	−	0.210055i
$837$	−87.4915			−0.104530
$838$	−5.22742	+	7.19493i	−0.00623797	+	0.00858583i
$839$	334.351	−	1029.03i	0.398511	−	1.22649i	−0.527682	−	0.849442i	$-0.676939\pi$
$839$	334.351	−	1029.03i	0.398511	−	1.22649i	0.926193	−	0.377049i	$-0.123061\pi$
$840$	−39.9979	−	123.101i	−0.0476165	−	0.146548i
$841$	−575.514	+	418.136i	−0.684321	+	0.497189i
$842$	−183.250	−	252.222i	−0.217636	−	0.299551i
$843$	−572.232	+	185.930i	−0.678805	+	0.220557i
$844$	−452.352	−	146.978i	−0.535962	−	0.174145i
$845$	−7.61074	−	5.52952i	−0.00900679	−	0.00654381i
$846$			149.622i			0.176858i
$847$	−1139.00	−	536.010i	−1.34474	−	0.632834i
$848$	100.962			0.119059
$849$	−314.937	+	433.474i	−0.370951	+	0.510570i
$850$	83.7634	−	257.797i	0.0985452	−	0.303291i
$851$	−512.902	−	1578.55i	−0.602705	−	1.85493i
$852$	−288.649	+	209.716i	−0.338790	+	0.246145i
$853$	240.453	+	330.955i	0.281891	+	0.387989i	0.926359	−	0.376642i	$-0.122921\pi$
$853$	240.453	+	330.955i	0.281891	+	0.387989i	−0.644468	+	0.764631i	$0.722921\pi$
$854$	296.570	−	96.3614i	0.347272	−	0.112835i
$855$	157.111	+	51.0484i	0.183755	+	0.0597058i
$856$	322.394	+	234.233i	0.376629	+	0.273637i
$857$			1699.98i			1.98364i	0.127639	+	0.991821i	$0.459260\pi$
$857$			1699.98i			1.98364i	−0.127639	+	0.991821i	$0.540740\pi$
$858$	−130.356	+	329.227i	−0.151930	+	0.383715i
$859$	554.842			0.645916			0.322958	−	0.946413i	$-0.395323\pi$
$859$	554.842			0.645916			0.322958	+	0.946413i	$0.395323\pi$
$860$	102.669	−	141.312i	0.119383	−	0.164317i
$861$	117.038	−	360.206i	0.135933	−	0.418358i
$862$	−28.6646	−	88.2207i	−0.0332536	−	0.102344i
$863$	−118.151	+	85.8417i	−0.136907	+	0.0994690i	−0.654131	−	0.756381i	$-0.726966\pi$
$863$	−118.151	+	85.8417i	−0.136907	+	0.0994690i	0.517224	+	0.855850i	$0.326966\pi$
$864$	17.2773	+	23.7801i	0.0199969	+	0.0275233i
$865$	−197.545	+	64.1861i	−0.228375	+	0.0742036i
$866$	−620.012	−	201.454i	−0.715949	−	0.232626i
$867$	−255.363	−	185.532i	−0.294536	−	0.213993i
$868$		−	350.341i		−	0.403618i
$869$	−746.229	−	1175.91i	−0.858722	−	1.35317i
$870$	70.8260			0.0814091
$871$	−991.118	+	1364.16i	−1.13791	+	1.56620i
$872$	152.405	−	469.055i	0.174777	−	0.537907i
$873$	10.1117	+	31.1206i	0.0115827	+	0.0356478i
$874$	−966.528	+	702.224i	−1.10587	+	0.803460i
$875$	676.329	+	930.887i	0.772947	+	1.06387i
$876$	−436.102	+	141.698i	−0.497833	+	0.161756i
$877$	119.880	+	38.9512i	0.136693	+	0.0444142i	0.376564	−	0.926390i	$-0.377105\pi$
$877$	119.880	+	38.9512i	0.136693	+	0.0444142i	−0.239872	+	0.970805i	$0.577105\pi$
$878$	−3.34439	−	2.42984i	−0.00380910	−	0.00276748i
$879$			464.023i			0.527899i
$880$	−86.0993	−	71.2296i	−0.0978401	−	0.0809427i
$881$	−146.295			−0.166055			−0.0830276	−	0.996547i	$-0.526459\pi$
$881$	−146.295			−0.166055			−0.0830276	+	0.996547i	$0.526459\pi$
$882$	147.709	−	203.304i	0.167471	−	0.230504i
$883$	−470.836	+	1449.08i	−0.533223	+	1.64109i	0.214235	+	0.976782i	$0.431274\pi$
$883$	−470.836	+	1449.08i	−0.533223	+	1.64109i	−0.747458	+	0.664309i	$0.768726\pi$
$884$	−83.9212	−	258.283i	−0.0949334	−	0.292175i
$885$	−250.446	+	181.960i	−0.282990	+	0.205604i
$886$	251.978	+	346.818i	0.284400	+	0.391442i
$887$	1530.10	−	497.161i	1.72503	−	0.560497i	0.732314	−	0.680967i	$-0.238440\pi$
$887$	1530.10	−	497.161i	1.72503	−	0.560497i	0.992717	+	0.120470i	$0.0384401\pi$
$888$	198.486	+	64.4919i	0.223520	+	0.0726260i
$889$	662.157	+	481.085i	0.744834	+	0.541153i
$890$		−	71.8183i		−	0.0806948i
$891$	−98.8046	−	6.21768i	−0.110892	−	0.00697831i
$892$	283.089			0.317365
$893$	449.454	−	618.620i	0.503307	−	0.692743i
$894$	−80.2289	+	246.919i	−0.0897415	+	0.276196i
$895$	−152.303	−	468.741i	−0.170171	−	0.523733i
$896$	−95.2225	+	69.1832i	−0.106275	+	0.0772134i
$897$	521.274	+	717.471i	0.581130	+	0.799857i
$898$	−458.430	+	148.953i	−0.510501	+	0.165872i
$899$	182.320	+	59.2395i	0.202804	+	0.0658949i
$900$	−90.0447	−	65.4213i	−0.100050	−	0.0726904i
$901$		−	260.800i		−	0.289456i
$902$	−81.3109	−	316.704i	−0.0901451	−	0.351113i
$903$	619.666			0.686230
$904$	130.305	−	179.349i	0.144142	−	0.198395i
$905$	−103.978	+	320.012i	−0.114893	+	0.353604i
$906$	−8.44801	−	26.0003i	−0.00932451	−	0.0286979i
$907$	−951.857	+	691.564i	−1.04946	+	0.762474i	−0.972109	−	0.234530i	$-0.924645\pi$
$907$	−951.857	+	691.564i	−1.04946	+	0.762474i	−0.0773471	+	0.997004i	$0.524645\pi$
$908$	−266.133	−	366.301i	−0.293098	−	0.403415i
$909$	−89.5744	+	29.1045i	−0.0985417	+	0.0320182i
$910$	467.005	+	151.739i	0.513192	+	0.166746i
$911$	−840.113	−	610.378i	−0.922187	−	0.670008i	0.0218802	−	0.999761i	$-0.493035\pi$
$911$	−840.113	−	610.378i	−0.922187	−	0.670008i	−0.944067	+	0.329752i	$0.893035\pi$
$912$		−	150.220i		−	0.164715i
$913$	1287.97	−	330.674i	1.41070	−	0.362184i
$914$	1097.84			1.20114
$915$	−54.8000	+	75.4257i	−0.0598907	+	0.0824325i
$916$	−105.919	+	325.985i	−0.115632	+	0.355879i
$917$	235.917	+	726.079i	0.257271	+	0.791798i
$918$	61.4274	−	44.6296i	0.0669144	−	0.0486161i
$919$	−757.545	−	1042.67i	−0.824315	−	1.13457i	−0.988955	−	0.148218i	$-0.952646\pi$
$919$	−757.545	−	1042.67i	−0.824315	−	1.13457i	0.164640	−	0.986354i	$-0.447354\pi$
$920$	−266.169	+	86.4837i	−0.289315	+	0.0940040i
$921$	274.718	+	89.2614i	0.298283	+	0.0969180i
$922$	526.150	+	382.270i	0.570662	+	0.414610i
$923$		−	1353.55i		−	1.46646i
$924$	24.8973	−	395.641i	0.0269452	−	0.428183i
$925$	−790.253			−0.854328
$926$	32.7428	−	45.0666i	0.0353594	−	0.0486681i
$927$	72.4475	−	222.970i	0.0781526	−	0.240529i
$928$	−19.9023	−	61.2528i	−0.0214464	−	0.0660052i
$929$	73.5639	−	53.4473i	0.0791862	−	0.0575321i	−0.547488	−	0.836814i	$-0.684416\pi$
$929$	73.5639	−	53.4473i	0.0791862	−	0.0575321i	0.626674	+	0.779282i	$0.284416\pi$
$930$	61.5673	+	84.7401i	0.0662014	+	0.0911184i
$931$	−1221.42	+	396.864i	−1.31195	+	0.426277i
$932$	176.063	+	57.2064i	0.188909	+	0.0613803i
$933$	539.383	+	391.885i	0.578117	+	0.420026i
$934$			517.895i			0.554491i
$935$	−183.996	+	222.406i	−0.196787	+	0.237868i
$936$	−111.511			−0.119136
$937$	−13.4725	+	18.5432i	−0.0143783	+	0.0197900i	−0.816146	−	0.577846i	$-0.803893\pi$
$937$	−13.4725	+	18.5432i	−0.0143783	+	0.0197900i	0.801767	+	0.597636i	$0.203893\pi$
$938$	583.350	−	1795.37i	0.621908	−	1.91404i
$939$	−51.0297	−	157.053i	−0.0543447	−	0.167256i
$940$	144.917	−	105.288i	0.154167	−	0.112009i
$941$	877.872	+	1208.29i	0.932914	+	1.28405i	0.958712	+	0.284379i	$0.0917873\pi$
$941$	877.872	+	1208.29i	0.932914	+	1.28405i	−0.0257980	+	0.999667i	$0.508213\pi$
$942$	350.400	−	113.852i	0.371975	−	0.120862i
$943$	−778.840	−	253.060i	−0.825917	−	0.268357i
$944$	227.741	+	165.464i	0.241252	+	0.175280i
$945$			137.287i			0.145278i
$946$	451.693	−	286.644i	0.477476	−	0.303006i
$947$	−667.556			−0.704917			−0.352458	−	0.935827i	$-0.614654\pi$
$947$	−667.556			−0.704917			−0.352458	+	0.935827i	$0.614654\pi$
$948$	257.795	−	354.824i	0.271935	−	0.374287i
$949$	537.557	−	1654.43i	0.566446	−	1.74334i
$950$	175.774	+	540.976i	0.185025	+	0.569448i
$951$	780.625	−	567.157i	0.820846	−	0.596380i
$952$	178.710	+	245.973i	0.187720	+	0.258375i
$953$	−536.830	+	174.427i	−0.563305	+	0.183029i	−0.576808	−	0.816880i	$-0.695702\pi$
$953$	−536.830	+	174.427i	−0.563305	+	0.183029i	0.0135027	+	0.999909i	$0.495702\pi$
$954$	−101.846	−	33.0916i	−0.106756	−	0.0346872i
$955$	−655.120	−	475.972i	−0.685989	−	0.498400i
$956$		−	483.086i		−	0.505320i
$957$	201.685	+	79.8562i	0.210747	+	0.0834443i
$958$	394.761			0.412068
$959$	−738.854	+	1016.95i	−0.770442	+	1.06042i
$960$	10.8744	−	33.4679i	0.0113275	−	0.0348624i
$961$	−209.356	−	644.332i	−0.217852	−	0.670480i
$962$	−640.532	+	465.374i	−0.665834	+	0.483757i
$963$	−248.442	−	341.951i	−0.257987	−	0.355089i
$964$	209.487	−	68.0666i	0.217311	−	0.0706085i
$965$	477.071	+	155.010i	0.494374	+	0.160632i
$966$	−803.239	−	583.587i	−0.831511	−	0.604128i
$967$			1283.73i			1.32754i	0.747936	+	0.663771i	$0.231045\pi$
$967$			1283.73i			1.32754i	−0.747936	+	0.663771i	$0.768955\pi$
$968$	−164.867	−	299.912i	−0.170317	−	0.309826i
$969$	−388.039			−0.400453
$970$	23.0264	−	31.6931i	0.0237385	−	0.0326733i
$971$	378.309	−	1164.31i	0.389607	−	1.19909i	−0.543475	−	0.839425i	$-0.682892\pi$
$971$	378.309	−	1164.31i	0.389607	−	1.19909i	0.933083	−	0.359662i	$-0.117108\pi$
$972$	−9.63420	−	29.6510i	−0.00991172	−	0.0305052i
$973$	1671.53	−	1214.44i	1.71792	−	1.24814i
$974$	−380.539	−	523.767i	−0.390697	−	0.537748i
$975$	401.576	−	130.480i	0.411873	−	0.133826i
$976$	80.6298	+	26.1982i	0.0826125	+	0.0268424i
$977$	−122.385	−	88.9181i	−0.125266	−	0.0910113i	0.523388	−	0.852095i	$-0.324668\pi$
$977$	−122.385	−	88.9181i	−0.125266	−	0.0910113i	−0.648654	+	0.761083i	$0.724668\pi$
$978$		−	457.374i		−	0.467662i
$979$	80.9751	−	204.511i	0.0827121	−	0.208898i
$980$	−300.853			−0.306993
$981$	−307.477	+	423.206i	−0.313432	+	0.431402i
$982$	−71.8217	+	221.044i	−0.0731381	+	0.225096i
$983$	410.105	+	1262.17i	0.417197	+	1.28400i	0.910271	+	0.414013i	$0.135873\pi$
$983$	410.105	+	1262.17i	0.417197	+	1.28400i	−0.493074	+	0.869987i	$0.664127\pi$
$984$	83.3049	−	60.5245i	0.0846594	−	0.0615087i
$985$	−299.437	−	412.140i	−0.303997	−	0.418416i
$986$	−158.225	+	51.4103i	−0.160471	+	0.0521402i
$987$	604.370	+	196.372i	0.612330	+	0.198958i
$988$	461.048	+	334.971i	0.466648	+	0.339039i
$989$		−	1339.85i		−	1.35475i
$990$	63.5061	+	100.073i	0.0641476	+	0.101084i
$991$	−255.463			−0.257783			−0.128892	−	0.991659i	$-0.541142\pi$
$991$	−255.463			−0.257783			−0.128892	+	0.991659i	$0.541142\pi$
$992$	55.9858	−	77.0578i	0.0564373	−	0.0776792i
$993$	75.6143	−	232.717i	0.0761473	−	0.234357i
$994$	468.269	+	1441.18i	0.471096	+	1.44988i
$995$	434.250	−	315.501i	0.436432	−	0.317087i
$996$	246.140	+	338.783i	0.247129	+	0.340144i
$997$	397.110	−	129.029i	0.398305	−	0.129417i	−0.103014	−	0.994680i	$-0.532849\pi$
$997$	397.110	−	129.029i	0.398305	−	0.129417i	0.501318	+	0.865263i	$0.332849\pi$
$998$	−175.091	−	56.8907i	−0.175442	−	0.0570047i
$999$	−179.084	−	130.112i	−0.179263	−	0.130242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	66.3.f.a.7.2	✓	16
3.2	odd	2		198.3.j.b.73.3		16
4.3	odd	2		528.3.bf.c.337.2		16
11.5	even	5		726.3.d.e.241.6		16
11.6	odd	10		726.3.d.e.241.14		16
11.8	odd	10	inner	66.3.f.a.19.2	yes	16
33.5	odd	10		2178.3.d.m.1693.14		16
33.8	even	10		198.3.j.b.19.3		16
33.17	even	10		2178.3.d.m.1693.6		16
44.19	even	10		528.3.bf.c.481.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.3.f.a.7.2	✓	16	1.1	even	1	trivial
66.3.f.a.19.2	yes	16	11.8	odd	10	inner
198.3.j.b.19.3		16	33.8	even	10
198.3.j.b.73.3		16	3.2	odd	2
528.3.bf.c.337.2		16	4.3	odd	2
528.3.bf.c.481.2		16	44.19	even	10
726.3.d.e.241.6		16	11.5	even	5
726.3.d.e.241.14		16	11.6	odd	10
2178.3.d.m.1693.6		16	33.17	even	10
2178.3.d.m.1693.14		16	33.5	odd	10

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:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	66.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.831254 + 1.14412i) q^{2} +(0.535233 - 1.64728i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(2.05461 - 1.49276i) q^{5} +(1.43977 + 1.98168i) q^{6} +(9.89425 - 3.21484i) q^{7} +(2.68999 + 0.874032i) q^{8} +(-2.42705 - 1.76336i) q^{9} +3.59159i q^{10} +(-4.04952 + 10.2275i) q^{11} -3.46410 q^{12} +(7.72450 - 10.6319i) q^{13} +(-4.54647 + 13.9926i) q^{14} +(-1.35930 - 4.18349i) q^{15} +(-3.23607 + 2.35114i) q^{16} +(6.07332 + 8.35921i) q^{17} +(4.03499 - 1.31105i) q^{18} +(-20.6212 - 6.70022i) q^{19} +(-4.10922 - 2.98552i) q^{20} -18.0193i q^{21} +(-8.33532 - 13.1348i) q^{22} -38.9614 q^{23} +(2.87955 - 3.96336i) q^{24} +(-5.73234 + 17.6423i) q^{25} +(5.74313 + 17.6755i) q^{26} +(-4.20378 + 3.05422i) q^{27} +(-12.2300 - 16.8331i) q^{28} +(10.8281 - 3.51825i) q^{29} +(5.91635 + 1.92234i) q^{30} +(13.6220 + 9.89698i) q^{31} -5.65685i q^{32} +(14.6801 + 12.1448i) q^{33} -14.6124 q^{34} +(15.5299 - 21.3750i) q^{35} +(-1.85410 + 5.70634i) q^{36} +(13.1643 + 40.5157i) q^{37} +(24.8073 - 18.0236i) q^{38} +(-13.3792 - 18.4149i) q^{39} +(6.83161 - 2.21973i) q^{40} +(19.9900 + 6.49515i) q^{41} +(20.6163 + 14.9786i) q^{42} +34.3891i q^{43} +(21.9566 + 1.38171i) q^{44} -7.61892 q^{45} +(32.3868 - 44.5767i) q^{46} +(-10.8979 + 33.5402i) q^{47} +(2.14093 + 6.58911i) q^{48} +(47.9192 - 34.8154i) q^{49} +(-15.4200 - 21.2237i) q^{50} +(17.0206 - 5.53032i) q^{51} +(-24.9970 - 8.12202i) q^{52} +(-20.4201 - 14.8361i) q^{53} -7.34847i q^{54} +(6.94702 + 27.0585i) q^{55} +29.4254 q^{56} +(-22.0743 + 30.3826i) q^{57} +(-4.97556 + 15.3132i) q^{58} +(-21.7474 - 66.9315i) q^{59} +(-7.11738 + 5.17108i) q^{60} +(-12.4580 - 17.1469i) q^{61} +(-22.6467 + 7.35836i) q^{62} +(-29.6828 - 9.64451i) q^{63} +(6.47214 + 4.70228i) q^{64} -33.3752i q^{65} +(-26.0980 + 6.70042i) q^{66} -128.308 q^{67} +(12.1466 - 16.7184i) q^{68} +(-20.8534 + 64.1803i) q^{69} +(11.5464 + 35.5361i) q^{70} +(83.3257 - 60.5397i) q^{71} +(-4.98752 - 6.86474i) q^{72} +(125.892 - 40.9047i) q^{73} +(-57.2978 - 18.6172i) q^{74} +(25.9937 + 18.8855i) q^{75} +43.3648i q^{76} +(-7.18725 + 114.212i) q^{77} +32.1905 q^{78} +(-74.4189 + 102.429i) q^{79} +(-3.13917 + 9.66136i) q^{80} +(2.78115 + 8.55951i) q^{81} +(-24.0480 + 17.4719i) q^{82} +(-71.0546 - 97.7983i) q^{83} +(-34.2747 + 11.1365i) q^{84} +(24.9566 + 8.10890i) q^{85} +(-39.3453 - 28.5860i) q^{86} -19.7199i q^{87} +(-19.8323 + 23.9725i) q^{88} -19.9962 q^{89} +(6.33325 - 8.71698i) q^{90} +(42.2484 - 130.027i) q^{91} +(24.0795 + 74.1090i) q^{92} +(23.5940 - 17.1421i) q^{93} +(-29.3152 - 40.3489i) q^{94} +(-52.3703 + 17.0161i) q^{95} +(-9.31841 - 3.02774i) q^{96} +(-8.82424 - 6.41119i) q^{97} +83.7659i q^{98} +(27.8631 - 17.6819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 8 q^{5} + 60 q^{7} - 12 q^{9} - 4 q^{11} - 60 q^{13} - 32 q^{14} + 12 q^{15} - 16 q^{16} - 60 q^{17} - 16 q^{20} - 48 q^{22} - 8 q^{23} - 48 q^{25} + 48 q^{26} + 40 q^{28} - 160 q^{29}+ \cdots + 48 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 8 * q^5 + 60 * q^7 - 12 * q^9 - 4 * q^11 - 60 * q^13 - 32 * q^14 + 12 * q^15 - 16 * q^16 - 60 * q^17 - 16 * q^20 - 48 * q^22 - 8 * q^23 - 48 * q^25 + 48 * q^26 + 40 * q^28 - 160 * q^29 + 32 * q^31 + 36 * q^33 - 64 * q^34 + 160 * q^35 + 24 * q^36 - 84 * q^37 - 48 * q^38 - 80 * q^40 + 40 * q^41 + 96 * q^42 + 168 * q^44 + 24 * q^45 + 160 * q^46 + 372 * q^47 + 96 * q^49 + 160 * q^50 + 120 * q^51 + 40 * q^52 - 124 * q^53 + 32 * q^55 - 96 * q^56 - 120 * q^57 - 16 * q^58 - 172 * q^59 - 24 * q^60 + 100 * q^61 - 40 * q^62 - 180 * q^63 + 32 * q^64 - 216 * q^66 + 248 * q^67 - 120 * q^68 - 372 * q^69 + 8 * q^70 + 48 * q^71 + 160 * q^73 + 80 * q^74 + 192 * q^75 - 172 * q^77 - 460 * q^79 - 48 * q^80 - 36 * q^81 - 24 * q^82 - 420 * q^83 - 420 * q^85 - 456 * q^86 - 144 * q^88 - 360 * q^89 - 252 * q^91 - 64 * q^92 - 24 * q^93 - 280 * q^94 + 180 * q^95 + 324 * q^97 + 48 * q^99

Introduction

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