LMFDB - Embedded newform 197.2.d.a.36.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [197,2,Mod(36,197)] 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("197.36"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(197, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([12])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	197.d (of order $7$, degree $6$, 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:	$1.57305291982$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$15$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			36.12
Character	$\chi$	$=$	197.36
Dual form			197.2.d.a.104.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.52637 - 0.735059i) q^{2} +(-2.33495 - 1.12445i) q^{3} +(0.542502 - 0.680276i) q^{4} +(-1.58350 - 1.98564i) q^{5} -4.39053 q^{6} +(-1.94366 - 0.936020i) q^{7} +(-0.425949 + 1.86621i) q^{8} +(2.31713 + 2.90559i) q^{9} +(-3.87657 - 1.86686i) q^{10} +(2.00558 - 0.965835i) q^{11} +(-2.03165 + 0.978392i) q^{12} +(-0.992842 - 4.34992i) q^{13} -3.65477 q^{14} +(1.46463 + 6.41695i) q^{15} +(1.10885 + 4.85819i) q^{16} +(-3.39887 - 4.26205i) q^{17} +(5.67256 + 2.73176i) q^{18} +5.03154 q^{19} -2.20984 q^{20} +(3.48585 + 4.37112i) q^{21} +(2.35130 - 2.94844i) q^{22} +(3.56108 - 1.71492i) q^{23} +(3.09303 - 3.87854i) q^{24} +(-0.322712 + 1.41389i) q^{25} +(-4.71289 - 5.90978i) q^{26} +(-0.413127 - 1.81003i) q^{27} +(-1.69119 + 0.814436i) q^{28} +(5.00106 - 2.40838i) q^{29} +(6.95239 + 8.71803i) q^{30} +(-6.78243 + 3.26624i) q^{31} +(2.87660 + 3.60715i) q^{32} -5.76896 q^{33} +(-8.32078 - 4.00707i) q^{34} +(1.21919 + 5.34161i) q^{35} +3.23364 q^{36} +(1.29112 - 5.65676i) q^{37} +(7.67997 - 3.69848i) q^{38} +(-2.57305 + 11.2733i) q^{39} +(4.38011 - 2.10935i) q^{40} +(3.10818 + 3.89754i) q^{41} +(8.53371 + 4.10962i) q^{42} +(-5.13841 + 2.47453i) q^{43} +(0.430995 - 1.88831i) q^{44} +(2.10029 - 9.20198i) q^{45} +(4.17493 - 5.23520i) q^{46} +(-1.80672 + 7.91577i) q^{47} +(2.87369 - 12.5905i) q^{48} +(-1.46273 - 1.83420i) q^{49} +(0.546719 + 2.39533i) q^{50} +(3.14372 + 13.7735i) q^{51} +(-3.49777 - 1.68444i) q^{52} +(1.45734 - 1.82744i) q^{53} +(-1.96106 - 2.45909i) q^{54} +(-5.09363 - 2.45296i) q^{55} +(2.57471 - 3.22858i) q^{56} +(-11.7484 - 5.65773i) q^{57} +(5.86315 - 7.35215i) q^{58} +(11.6114 - 5.59174i) q^{59} +(5.15986 + 2.48486i) q^{60} +(-5.48985 + 2.64377i) q^{61} +(-7.95158 + 9.97097i) q^{62} +(-1.78403 - 7.81636i) q^{63} +(-1.93707 - 0.932845i) q^{64} +(-7.06524 + 8.85953i) q^{65} +(-8.80554 + 4.24052i) q^{66} +(-2.56062 + 11.2188i) q^{67} -4.74326 q^{68} -10.2433 q^{69} +(5.78733 + 7.25708i) q^{70} +(-5.64274 - 7.07577i) q^{71} +(-6.40940 + 3.08660i) q^{72} +(3.18436 - 13.9516i) q^{73} +(-2.18733 - 9.58333i) q^{74} +(2.34337 - 2.93850i) q^{75} +(2.72962 - 3.42283i) q^{76} -4.80221 q^{77} +(4.35910 + 19.0985i) q^{78} +(6.77200 - 8.49181i) q^{79} +(7.89078 - 9.89472i) q^{80} +(1.41026 - 6.17875i) q^{81} +(7.60914 + 3.66437i) q^{82} +2.26265 q^{83} +4.86465 q^{84} +(-3.08081 + 13.4979i) q^{85} +(-6.02417 + 7.55407i) q^{86} -14.3853 q^{87} +(0.948172 + 4.15421i) q^{88} +(4.95665 + 2.38699i) q^{89} +(-3.55819 - 15.5894i) q^{90} +(-2.14186 + 9.38411i) q^{91} +(0.765269 - 3.35286i) q^{92} +19.5094 q^{93} +(3.06084 + 13.4104i) q^{94} +(-7.96743 - 9.99085i) q^{95} +(-2.66066 - 11.6571i) q^{96} +(4.01289 + 5.03200i) q^{97} +(-3.58091 - 1.72447i) q^{98} +(7.45349 + 3.58941i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 2 q^{2} - 5 q^{3} - 26 q^{4} + q^{5} - 10 q^{6} - 11 q^{7} - 16 q^{9} + 9 q^{10} - 7 q^{11} + 15 q^{12} + 9 q^{13} - 40 q^{14} - 16 q^{15} - 10 q^{16} + 13 q^{17} + 15 q^{18} - 20 q^{19} + 26 q^{20}+ \cdots + 25 q^{99}+O(q^{100}) $ 90 * q - 2 * q^2 - 5 * q^3 - 26 * q^4 + q^5 - 10 * q^6 - 11 * q^7 - 16 * q^9 + 9 * q^10 - 7 * q^11 + 15 * q^12 + 9 * q^13 - 40 * q^14 - 16 * q^15 - 10 * q^16 + 13 * q^17 + 15 * q^18 - 20 * q^19 + 26 * q^20 + 13 * q^21 - 17 * q^22 + 25 * q^23 - 17 * q^24 + 16 * q^25 - 2 * q^26 - 41 * q^27 - 50 * q^28 - 33 * q^29 - 72 * q^30 - 15 * q^31 + 46 * q^32 - 32 * q^33 + 31 * q^34 + 45 * q^35 - 64 * q^36 - 27 * q^37 + 43 * q^38 + 14 * q^39 + 31 * q^40 + 35 * q^41 + 14 * q^42 + 16 * q^43 + 49 * q^44 - 8 * q^45 + 17 * q^46 - 4 * q^47 + 41 * q^48 - 48 * q^49 - 52 * q^50 + 51 * q^51 - 2 * q^52 + 41 * q^53 + 14 * q^54 + 53 * q^55 + 52 * q^56 - 104 * q^57 - 79 * q^58 - 17 * q^59 + 11 * q^60 + 21 * q^61 + 23 * q^62 + 48 * q^63 + 22 * q^64 + 5 * q^65 - 94 * q^66 - 5 * q^67 - 200 * q^68 + 54 * q^69 + 64 * q^70 - 94 * q^71 + 75 * q^72 + 31 * q^73 + 18 * q^74 + 36 * q^75 - 80 * q^76 + 22 * q^77 - 45 * q^78 - 25 * q^79 + 131 * q^80 + 6 * q^81 + 51 * q^82 - 130 * q^83 + 108 * q^84 - 129 * q^85 + 32 * q^86 + 98 * q^87 + 54 * q^88 + 17 * q^89 - 42 * q^90 - 119 * q^91 + 31 * q^92 + 60 * q^93 - 111 * q^94 - 77 * q^95 - 98 * q^96 + 49 * q^97 + 45 * q^98 + 25 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

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 $

$2$	1.52637	−	0.735059i	1.07930	−	0.519765i	0.192210	−	0.981354i	$-0.438435\pi$
$2$	1.52637	−	0.735059i	1.07930	−	0.519765i	0.887094	+	0.461589i	$0.152720\pi$
$3$	−2.33495	−	1.12445i	−1.34808	−	0.649203i	−0.386137	−	0.922441i	$-0.626191\pi$
$3$	−2.33495	−	1.12445i	−1.34808	−	0.649203i	−0.961946	+	0.273238i	$0.911905\pi$
$4$	0.542502	−	0.680276i	0.271251	−	0.340138i
$5$	−1.58350	−	1.98564i	−0.708162	−	0.888007i	0.289441	−	0.957196i	$-0.406530\pi$
$5$	−1.58350	−	1.98564i	−0.708162	−	0.888007i	−0.997604	+	0.0691884i	$0.977959\pi$
$6$	−4.39053			−1.79243
$7$	−1.94366	−	0.936020i	−0.734636	−	0.353782i	0.0288695	−	0.999583i	$-0.490809\pi$
$7$	−1.94366	−	0.936020i	−0.734636	−	0.353782i	−0.763506	+	0.645801i	$0.776524\pi$
$8$	−0.425949	+	1.86621i	−0.150596	+	0.659803i
$9$	2.31713	+	2.90559i	0.772376	+	0.968528i
$10$	−3.87657	−	1.86686i	−1.22588	−	0.590352i
$11$	2.00558	−	0.965835i	0.604704	−	0.291210i	−0.106371	−	0.994327i	$-0.533923\pi$
$11$	2.00558	−	0.965835i	0.604704	−	0.291210i	0.711075	+	0.703116i	$0.248209\pi$
$12$	−2.03165	+	0.978392i	−0.586487	+	0.282437i
$13$	−0.992842	−	4.34992i	−0.275365	−	1.20645i	−0.903582	−	0.428414i	$-0.859072\pi$
$13$	−0.992842	−	4.34992i	−0.275365	−	1.20645i	0.628218	−	0.778038i	$-0.283785\pi$
$14$	−3.65477			−0.976779
$15$	1.46463	+	6.41695i	0.378165	+	1.65685i
$16$	1.10885	+	4.85819i	0.277213	+	1.21455i
$17$	−3.39887	−	4.26205i	−0.824347	−	1.03370i	−0.998797	−	0.0490323i	$-0.984386\pi$
$17$	−3.39887	−	4.26205i	−0.824347	−	1.03370i	0.174450	−	0.984666i	$-0.444185\pi$
$18$	5.67256	+	2.73176i	1.33704	+	0.643882i
$19$	5.03154			1.15431			0.577157	−	0.816633i	$-0.304162\pi$
$19$	5.03154			1.15431			0.577157	+	0.816633i	$0.304162\pi$
$20$	−2.20984			−0.494135
$21$	3.48585	+	4.37112i	0.760675	+	0.953856i
$22$	2.35130	−	2.94844i	0.501299	−	0.628609i
$23$	3.56108	−	1.71492i	0.742536	−	0.357586i	−0.0240651	−	0.999710i	$-0.507661\pi$
$23$	3.56108	−	1.71492i	0.742536	−	0.357586i	0.766601	+	0.642124i	$0.221947\pi$
$24$	3.09303	−	3.87854i	0.631362	−	0.791703i
$25$	−0.322712	+	1.41389i	−0.0645424	+	0.282779i
$26$	−4.71289	−	5.90978i	−0.924274	−	1.15900i
$27$	−0.413127	−	1.81003i	−0.0795064	−	0.348340i
$28$	−1.69119	+	0.814436i	−0.319605	+	0.153914i
$29$	5.00106	−	2.40838i	0.928674	−	0.447226i	0.0925139	−	0.995711i	$-0.470510\pi$
$29$	5.00106	−	2.40838i	0.928674	−	0.447226i	0.836160	+	0.548486i	$0.184795\pi$
$30$	6.95239	+	8.71803i	1.26933	+	1.59169i
$31$	−6.78243	+	3.26624i	−1.21816	+	0.586635i	−0.928799	−	0.370585i	$-0.879157\pi$
$31$	−6.78243	+	3.26624i	−1.21816	+	0.586635i	−0.289361	+	0.957220i	$0.593443\pi$
$32$	2.87660	+	3.60715i	0.508516	+	0.637659i
$33$	−5.76896			−1.00425
$34$	−8.32078	−	4.00707i	−1.42700	−	0.687208i
$35$	1.21919	+	5.34161i	0.206080	+	0.902898i
$36$	3.23364			0.538941
$37$	1.29112	−	5.65676i	0.212258	−	0.929965i	−0.750770	−	0.660564i	$-0.770317\pi$
$37$	1.29112	−	5.65676i	0.212258	−	0.929965i	0.963028	−	0.269401i	$-0.0868257\pi$
$38$	7.67997	−	3.69848i	1.24586	−	0.599972i
$39$	−2.57305	+	11.2733i	−0.412017	+	1.80517i
$40$	4.38011	−	2.10935i	0.692556	−	0.333518i
$41$	3.10818	+	3.89754i	0.485416	+	0.608693i	0.962870	−	0.269964i	$-0.0870117\pi$
$41$	3.10818	+	3.89754i	0.485416	+	0.608693i	−0.477454	+	0.878657i	$0.658440\pi$
$42$	8.53371	+	4.10962i	1.31678	+	0.634128i
$43$	−5.13841	+	2.47453i	−0.783600	+	0.377362i	−0.782510	−	0.622637i	$-0.786061\pi$
$43$	−5.13841	+	2.47453i	−0.783600	+	0.377362i	−0.00108977	+	0.999999i	$0.500347\pi$
$44$	0.430995	−	1.88831i	0.0649749	−	0.284674i
$45$	2.10029	−	9.20198i	0.313093	−	1.37175i
$46$	4.17493	−	5.23520i	0.615560	−	0.771888i
$47$	−1.80672	+	7.91577i	−0.263538	+	1.15463i	0.653845	+	0.756628i	$0.273155\pi$
$47$	−1.80672	+	7.91577i	−0.263538	+	1.15463i	−0.917383	+	0.398006i	$0.869702\pi$
$48$	2.87369	−	12.5905i	0.414782	−	1.81728i
$49$	−1.46273	−	1.83420i	−0.208961	−	0.262029i
$50$	0.546719	+	2.39533i	0.0773177	+	0.338751i
$51$	3.14372	+	13.7735i	0.440209	+	1.92868i
$52$	−3.49777	−	1.68444i	−0.485053	−	0.233589i
$53$	1.45734	−	1.82744i	0.200180	−	0.251018i	−0.671601	−	0.740913i	$-0.734393\pi$
$53$	1.45734	−	1.82744i	0.200180	−	0.251018i	0.871782	+	0.489894i	$0.162965\pi$
$54$	−1.96106	−	2.45909i	−0.266867	−	0.334640i
$55$	−5.09363	−	2.45296i	−0.686825	−	0.330758i
$56$	2.57471	−	3.22858i	0.344060	−	0.431437i
$57$	−11.7484	−	5.65773i	−1.55611	−	0.749384i
$58$	5.86315	−	7.35215i	0.769869	−	0.965385i
$59$	11.6114	−	5.59174i	1.51167	−	0.727982i	0.519688	−	0.854356i	$-0.326048\pi$
$59$	11.6114	−	5.59174i	1.51167	−	0.727982i	0.991983	+	0.126374i	$0.0403340\pi$
$60$	5.15986	+	2.48486i	0.666135	+	0.320794i
$61$	−5.48985	+	2.64377i	−0.702903	+	0.338500i	−0.750963	−	0.660344i	$-0.770410\pi$
$61$	−5.48985	+	2.64377i	−0.702903	+	0.338500i	0.0480601	+	0.998844i	$0.484696\pi$
$62$	−7.95158	+	9.97097i	−1.00985	+	1.26631i
$63$	−1.78403	−	7.81636i	−0.224767	−	0.984769i
$64$	−1.93707	−	0.932845i	−0.242134	−	0.116606i
$65$	−7.06524	+	8.85953i	−0.876335	+	1.09889i
$66$	−8.80554	+	4.24052i	−1.08389	+	0.521972i
$67$	−2.56062	+	11.2188i	−0.312829	+	1.37060i	0.537020	+	0.843570i	$0.319550\pi$
$67$	−2.56062	+	11.2188i	−0.312829	+	1.37060i	−0.849849	+	0.527026i	$0.823307\pi$
$68$	−4.74326			−0.575205
$69$	−10.2433			−1.23315
$70$	5.78733	+	7.25708i	0.691718	+	0.867387i
$71$	−5.64274	−	7.07577i	−0.669670	−	0.839740i	0.324687	−	0.945821i	$-0.394741\pi$
$71$	−5.64274	−	7.07577i	−0.669670	−	0.839740i	−0.994357	+	0.106082i	$0.966170\pi$
$72$	−6.40940	+	3.08660i	−0.755355	+	0.363760i
$73$	3.18436	−	13.9516i	0.372701	−	1.63291i	−0.346459	−	0.938065i	$-0.612616\pi$
$73$	3.18436	−	13.9516i	0.372701	−	1.63291i	0.719160	−	0.694844i	$-0.244527\pi$
$74$	−2.18733	−	9.58333i	−0.254272	−	1.11404i
$75$	2.34337	−	2.93850i	0.270589	−	0.339308i
$76$	2.72962	−	3.42283i	0.313109	−	0.392626i
$77$	−4.80221			−0.547263
$78$	4.35910	+	19.0985i	0.493571	+	2.16247i
$79$	6.77200	−	8.49181i	0.761909	−	0.955404i	−0.237965	−	0.971274i	$-0.576480\pi$
$79$	6.77200	−	8.49181i	0.761909	−	0.955404i	0.999874	+	0.0158700i	$0.00505179\pi$
$80$	7.89078	−	9.89472i	0.882216	−	1.10626i
$81$	1.41026	−	6.17875i	0.156695	−	0.686528i
$82$	7.60914	+	3.66437i	0.840289	+	0.404662i
$83$	2.26265			0.248358			0.124179	−	0.992260i	$-0.460370\pi$
$83$	2.26265			0.248358			0.124179	+	0.992260i	$0.460370\pi$
$84$	4.86465			0.530776
$85$	−3.08081	+	13.4979i	−0.334160	+	1.46405i
$86$	−6.02417	+	7.55407i	−0.649603	+	0.814576i
$87$	−14.3853			−1.54227
$88$	0.948172	+	4.15421i	0.101076	+	0.442841i
$89$	4.95665	+	2.38699i	0.525403	+	0.253021i	0.677732	−	0.735309i	$-0.262963\pi$
$89$	4.95665	+	2.38699i	0.525403	+	0.253021i	−0.152329	+	0.988330i	$0.548677\pi$
$90$	−3.55819	−	15.5894i	−0.375066	−	1.64327i
$91$	−2.14186	+	9.38411i	−0.224528	+	0.983722i
$92$	0.765269	−	3.35286i	0.0797848	−	0.349560i
$93$	19.5094			2.02303
$94$	3.06084	+	13.4104i	0.315702	+	1.38318i
$95$	−7.96743	−	9.99085i	−0.817442	−	1.02504i
$96$	−2.66066	−	11.6571i	−0.271552	−	1.18975i
$97$	4.01289	+	5.03200i	0.407447	+	0.510922i	0.942642	−	0.333806i	$-0.108333\pi$
$97$	4.01289	+	5.03200i	0.407447	+	0.510922i	−0.535195	+	0.844729i	$0.679762\pi$
$98$	−3.58091	−	1.72447i	−0.361726	−	0.174198i
$99$	7.45349	+	3.58941i	0.749104	+	0.360750i
$100$	0.786766	+	0.986573i	0.0786766	+	0.0986573i
$101$	2.79775	+	12.2578i	0.278387	+	1.21969i	0.899833	+	0.436236i	$0.143689\pi$
$101$	2.79775	+	12.2578i	0.278387	+	1.21969i	−0.621446	+	0.783457i	$0.713454\pi$
$102$	14.9228	+	18.7126i	1.47758	+	1.85283i
$103$	0.950034	+	4.16237i	0.0936096	+	0.410131i	0.999922	−	0.0124775i	$-0.00397182\pi$
$103$	0.950034	+	4.16237i	0.0936096	+	0.410131i	−0.906313	+	0.422608i	$0.861115\pi$
$104$	8.54075			0.837490
$105$	3.15965	−	13.8433i	0.308350	−	1.35097i
$106$	0.881150	−	3.86057i	0.0855849	−	0.374972i
$107$	1.31000	+	5.73947i	0.126642	+	0.554855i	0.997943	+	0.0641063i	$0.0204197\pi$
$107$	1.31000	+	5.73947i	0.126642	+	0.554855i	−0.871301	+	0.490749i	$0.836723\pi$
$108$	−1.45544	−	0.700903i	−0.140050	−	0.0674445i
$109$	−2.05776	−	9.01561i	−0.197097	−	0.863539i	−0.972654	−	0.232261i	$-0.925388\pi$
$109$	−2.05776	−	9.01561i	−0.197097	−	0.863539i	0.775556	−	0.631278i	$-0.217469\pi$
$110$	−9.57782			−0.913210
$111$	−9.37545	+	11.7564i	−0.889878	+	1.11587i
$112$	2.39213	−	10.4806i	0.226035	−	0.990323i
$113$	3.77361			0.354991			0.177496	−	0.984122i	$-0.443200\pi$
$113$	3.77361			0.354991			0.177496	+	0.984122i	$0.443200\pi$
$114$	−22.0911			−2.06902
$115$	−9.04419	−	4.35545i	−0.843375	−	0.406148i
$116$	1.07472	−	4.70865i	0.0997852	−	0.437188i
$117$	10.3385	−	12.9641i	0.955798	−	1.19853i
$118$	13.6129	−	17.0701i	1.25317	−	1.57143i
$119$	2.61690	+	11.4654i	0.239891	+	1.05103i
$120$	−12.5992			−1.15014
$121$	−3.76889	+	4.72603i	−0.342626	+	0.429639i
$122$	−6.43619	+	8.07073i	−0.582705	+	0.730689i
$123$	−2.87485	−	12.5956i	−0.259217	−	1.13570i
$124$	−1.45753	+	6.38586i	−0.130890	+	0.573468i
$125$	−8.12261	+	3.91164i	−0.726508	+	0.349868i
$126$	−8.46857	−	10.6193i	−0.754441	−	0.946039i
$127$	−11.7128	−	14.6874i	−1.03934	−	1.30329i	−0.951663	−	0.307145i	$-0.900627\pi$
$127$	−11.7128	−	14.6874i	−1.03934	−	1.30329i	−0.0876788	−	0.996149i	$-0.527945\pi$
$128$	−12.8698			−1.13754
$129$	14.7804			1.30134
$130$	−4.27186	+	18.7163i	−0.374667	+	1.64152i
$131$	11.2985	−	5.44108i	0.987156	−	0.475389i	0.130595	−	0.991436i	$-0.458311\pi$
$131$	11.2985	−	5.44108i	0.987156	−	0.475389i	0.856561	+	0.516047i	$0.172597\pi$
$132$	−3.12967	+	3.92448i	−0.272403	+	0.341582i
$133$	−9.77962	−	4.70962i	−0.848001	−	0.408376i
$134$	4.33804	+	19.0062i	0.374750	+	1.64189i
$135$	−2.93989	+	3.68650i	−0.253025	+	0.317284i
$136$	9.40160	−	4.52757i	0.806180	−	0.388236i
$137$	3.16124	+	1.52237i	0.270083	+	0.130065i	0.564024	−	0.825759i	$-0.309253\pi$
$137$	3.16124	+	1.52237i	0.270083	+	0.130065i	−0.293941	+	0.955824i	$0.594967\pi$
$138$	−15.6350	+	7.52942i	−1.33094	+	0.640947i
$139$	10.7007	−	13.4182i	0.907618	−	1.13812i	−0.0823188	−	0.996606i	$-0.526233\pi$
$139$	10.7007	−	13.4182i	0.907618	−	1.13812i	0.989937	−	0.141511i	$-0.0451960\pi$
$140$	4.29518	+	2.06845i	0.363009	+	0.174816i
$141$	13.1195	−	16.4514i	1.10486	−	1.38545i
$142$	−13.8140	−	6.65247i	−1.15925	−	0.558263i
$143$	−6.19253	−	7.76519i	−0.517845	−	0.649358i
$144$	−11.5465	+	14.4789i	−0.962212	+	1.20658i
$145$	−12.7014	−	6.11666i	−1.05479	−	0.507961i
$146$	−5.39474	−	23.6359i	−0.446472	−	1.95612i
$147$	1.35292	+	5.92754i	0.111587	+	0.488895i
$148$	−3.14772	−	3.94712i	−0.258741	−	0.324451i
$149$	−3.76929	+	16.5144i	−0.308793	+	1.35291i	0.547668	+	0.836696i	$0.315516\pi$
$149$	−3.76929	+	16.5144i	−0.308793	+	1.35291i	−0.856460	+	0.516213i	$0.827341\pi$
$150$	1.41688	−	6.20774i	0.115687	−	0.506860i
$151$	−4.29220	+	5.38225i	−0.349294	+	0.438001i	−0.925180	−	0.379529i	$-0.876086\pi$
$151$	−4.29220	+	5.38225i	−0.349294	+	0.438001i	0.575885	+	0.817530i	$0.304657\pi$
$152$	−2.14318	+	9.38988i	−0.173835	+	0.761620i
$153$	4.50813	−	19.7514i	0.364461	−	1.59681i
$154$	−7.32993	+	3.52991i	−0.590663	+	0.284448i
$155$	17.2256	+	8.29540i	1.38359	+	0.666302i
$156$	6.27304	+	7.86614i	0.502245	+	0.629796i
$157$	11.3666	−	5.47388i	0.907156	−	0.436864i	0.0786880	−	0.996899i	$-0.474927\pi$
$157$	11.3666	−	5.47388i	0.907156	−	0.436864i	0.828468	+	0.560036i	$0.189213\pi$
$158$	4.09456	−	17.9394i	0.325746	−	1.42718i
$159$	−5.45768	+	2.62828i	−0.432822	+	0.208436i
$160$	2.60741	−	11.4238i	0.206134	−	0.903132i
$161$	−8.52674			−0.672001
$162$	−2.38917	−	10.4677i	−0.187711	−	0.822417i
$163$	20.5138	+	9.87892i	1.60676	+	0.773777i	0.999781	−	0.0209375i	$-0.00666511\pi$
$163$	20.5138	+	9.87892i	1.60676	+	0.773777i	0.606984	+	0.794714i	$0.292379\pi$
$164$	4.33759			0.338709
$165$	9.13514	+	11.4551i	0.711169	+	0.891778i
$166$	3.45363	−	1.66318i	0.268054	−	0.129088i
$167$	4.03686	+	5.06206i	0.312382	+	0.391714i	0.913093	−	0.407752i	$-0.133687\pi$
$167$	4.03686	+	5.06206i	0.312382	+	0.391714i	−0.600711	+	0.799466i	$0.705116\pi$
$168$	−9.64220	+	4.64344i	−0.743912	+	0.358249i
$169$	−6.22351	+	2.99708i	−0.478732	+	0.230545i
$170$	5.21931	+	22.8673i	0.400303	+	1.75384i
$171$	11.6587	+	14.6196i	0.891564	+	1.11799i
$172$	−1.10424	+	4.83797i	−0.0841972	+	0.368892i
$173$	11.1477	−	13.9788i	0.847545	−	1.06279i	−0.149709	−	0.988730i	$-0.547834\pi$
$173$	11.1477	−	13.9788i	0.847545	−	1.06279i	0.997254	−	0.0740575i	$-0.0235948\pi$
$174$	−21.9573	+	10.5741i	−1.66458	+	0.801619i
$175$	1.95068	−	2.44607i	0.147457	−	0.184906i
$176$	6.91609	+	8.67251i	0.521320	+	0.653715i
$177$	−33.3996			−2.51047
$178$	9.32024			0.698581
$179$	4.12872	+	1.98828i	0.308595	+	0.148611i	0.581771	−	0.813353i	$-0.302360\pi$
$179$	4.12872	+	1.98828i	0.308595	+	0.148611i	−0.273176	+	0.961964i	$0.588074\pi$
$180$	−5.12047	−	6.42087i	−0.381658	−	0.478583i
$181$	−1.40628	−	6.16130i	−0.104528	−	0.457966i	−0.999920	−	0.0126868i	$-0.995962\pi$
$181$	−1.40628	−	6.16130i	−0.104528	−	0.457966i	0.895392	−	0.445279i	$-0.146896\pi$
$182$	3.62861	+	15.8980i	0.268971	+	1.17844i
$183$	15.7913			1.16733
$184$	1.68356	+	7.37617i	0.124114	+	0.543778i
$185$	−13.2768	+	6.39377i	−0.976129	+	0.470079i
$186$	29.7784	−	14.3405i	2.18346	−	1.05150i
$187$	−10.9331	−	5.26512i	−0.799509	−	0.385023i
$188$	4.40476	+	5.52339i	0.321250	+	0.402835i
$189$	−0.891242	+	3.90478i	−0.0648283	+	0.284031i
$190$	−19.5051	−	9.39315i	−1.41505	−	0.681451i
$191$	21.7023			1.57032			0.785162	−	0.619290i	$-0.212579\pi$
$191$	21.7023			1.57032			0.785162	+	0.619290i	$0.212579\pi$
$192$	3.47403	+	4.35629i	0.250716	+	0.314388i
$193$	6.85306	−	8.59346i	0.493294	−	0.618571i	−0.471408	−	0.881915i	$-0.656254\pi$
$193$	6.85306	−	8.59346i	0.493294	−	0.618571i	0.964702	+	0.263344i	$0.0848255\pi$
$194$	9.82395	+	4.73097i	0.705319	+	0.339664i
$195$	26.4591	−	12.7420i	1.89478	−	0.912476i
$196$	−2.04130			−0.145807
$197$	13.9374	−	1.65780i	0.993000	−	0.118113i
$197$	13.9374	−	1.65780i	0.993000	−	0.118113i
$198$	14.0152			0.996016
$199$	−16.6289	+	8.00804i	−1.17879	+	0.567675i	−0.917558	−	0.397601i	$-0.869843\pi$
$199$	−16.6289	+	8.00804i	−1.17879	+	0.567675i	−0.261231	+	0.965276i	$0.584129\pi$
$200$	−2.50116	−	1.20449i	−0.176858	−	0.0851705i
$201$	18.5939	−	23.3161i	1.31151	−	1.64459i
$202$	13.2806	+	16.6533i	0.934418	+	1.17172i
$203$	−11.9747			−0.840458
$204$	11.0753	+	5.33357i	0.775424	+	0.373425i
$205$	2.81732	−	12.3435i	0.196770	−	0.862107i
$206$	4.50969	+	5.65497i	0.314205	+	0.394000i
$207$	13.2343	+	6.37331i	0.919849	+	0.442976i
$208$	20.0318	−	9.64683i	1.38896	−	0.668887i
$209$	10.0911	−	4.85964i	0.698018	−	0.336148i
$210$	−5.35288	−	23.4525i	−0.369384	−	1.61838i
$211$	−4.81726			−0.331634			−0.165817	−	0.986157i	$-0.553026\pi$
$211$	−4.81726			−0.331634			−0.165817	+	0.986157i	$0.553026\pi$
$212$	−0.452557	−	1.98278i	−0.0310817	−	0.136178i
$213$	5.21915	+	22.8666i	0.357610	+	1.56679i
$214$	6.21838	+	7.79760i	0.425080	+	0.533033i
$215$	13.0502	+	6.28465i	0.890016	+	0.428609i
$216$	3.55386			0.241809
$217$	16.2400			1.10245
$218$	−9.76790	−	12.2486i	−0.661565	−	0.829577i
$219$	−23.1232	+	28.9956i	−1.56252	+	1.95934i
$220$	−4.43200	+	2.13434i	−0.298805	+	0.143897i
$221$	−15.1650	+	19.0164i	−1.02011	+	1.27918i
$222$	−5.66869	+	24.8361i	−0.380457	+	1.66689i
$223$	−6.78560	−	8.50887i	−0.454397	−	0.569796i	0.500877	−	0.865519i	$-0.333011\pi$
$223$	−6.78560	−	8.50887i	−0.454397	−	0.569796i	−0.955274	+	0.295723i	$0.904440\pi$
$224$	−2.21479	−	9.70364i	−0.147982	−	0.648352i
$225$	−4.85595	+	2.33850i	−0.323730	+	0.155900i
$226$	5.75991	−	2.77382i	0.383143	−	0.184512i
$227$	−8.06502	−	10.1132i	−0.535294	−	0.671238i	0.438483	−	0.898739i	$-0.355516\pi$
$227$	−8.06502	−	10.1132i	−0.535294	−	0.671238i	−0.973778	+	0.227501i	$0.926944\pi$
$228$	−10.2223	+	4.92282i	−0.676991	+	0.326022i
$229$	−6.25702	−	7.84606i	−0.413476	−	0.518482i	0.530863	−	0.847458i	$-0.321868\pi$
$229$	−6.25702	−	7.84606i	−0.413476	−	0.518482i	−0.944338	+	0.328976i	$0.893297\pi$
$230$	−17.0063			−1.12136
$231$	11.2129	+	5.39986i	0.737756	+	0.355284i
$232$	2.36434	+	10.3589i	0.155227	+	0.680092i
$233$	−12.2780			−0.804358			−0.402179	−	0.915561i	$-0.631747\pi$
$233$	−12.2780			−0.804358			−0.402179	+	0.915561i	$0.631747\pi$
$234$	6.25100	−	27.3874i	0.408641	−	1.79037i
$235$	18.5789	−	8.94711i	1.21195	−	0.583645i
$236$	2.49526	−	10.9325i	0.162428	−	0.711642i
$237$	−25.3609	+	12.2132i	−1.64737	+	0.793331i
$238$	12.4221	+	15.5768i	0.805205	+	1.00970i
$239$	5.84245	+	2.81358i	0.377917	+	0.181995i	0.613192	−	0.789934i	$-0.289885\pi$
$239$	5.84245	+	2.81358i	0.377917	+	0.181995i	−0.235276	+	0.971929i	$0.575599\pi$
$240$	−29.5507	+	14.2309i	−1.90749	+	0.918599i
$241$	−4.15631	+	18.2100i	−0.267732	+	1.17301i	0.644913	+	0.764256i	$0.276893\pi$
$241$	−4.15631	+	18.2100i	−0.267732	+	1.17301i	−0.912645	+	0.408753i	$0.865964\pi$
$242$	−2.27879	+	9.98401i	−0.146486	+	0.641797i
$243$	−13.7133	+	17.1959i	−0.879706	+	1.10312i
$244$	−1.17976	+	5.16886i	−0.0755263	+	0.330902i
$245$	−1.32585	+	5.80892i	−0.0847053	+	0.371118i
$246$	−13.6466	−	17.1122i	−0.870073	−	1.09104i
$247$	−4.99552	−	21.8868i	−0.317857	−	1.39262i
$248$	−3.20651	−	14.0487i	−0.203614	−	0.892090i
$249$	−5.28318	−	2.54424i	−0.334808	−	0.161235i
$250$	−9.52278	+	11.9412i	−0.602274	+	0.755227i
$251$	5.56604	+	6.97959i	0.351325	+	0.440548i	0.925822	−	0.377959i	$-0.123374\pi$
$251$	5.56604	+	6.97959i	0.351325	+	0.440548i	−0.574497	+	0.818506i	$0.694802\pi$
$252$	−6.28512	−	3.02676i	−0.395925	−	0.190668i
$253$	5.48568	−	6.87882i	0.344882	−	0.432468i
$254$	−28.6741	−	13.8087i	−1.79917	−	0.866436i
$255$	22.3713	−	28.0527i	1.40094	−	1.75673i
$256$	−15.7699	+	7.59438i	−0.985618	+	0.474648i
$257$	11.8260	+	5.69512i	0.737688	+	0.355252i	0.764703	−	0.644383i	$-0.222886\pi$
$257$	11.8260	+	5.69512i	0.737688	+	0.355252i	−0.0270145	+	0.999635i	$0.508600\pi$
$258$	22.5603	−	10.8645i	1.40454	−	0.676393i
$259$	−7.80434	+	9.78633i	−0.484938	+	0.608093i
$260$	2.19402	+	9.61262i	0.136067	+	0.596150i
$261$	18.5859	+	8.95048i	1.15044	+	0.554021i
$262$	13.2462	−	16.6102i	0.818350	−	1.02618i
$263$	−15.4462	+	7.43850i	−0.952454	+	0.458678i	−0.844546	−	0.535483i	$-0.820129\pi$
$263$	−15.4462	+	7.43850i	−0.952454	+	0.458678i	−0.107908	+	0.994161i	$0.534415\pi$
$264$	2.45728	−	10.7661i	0.151235	−	0.662605i
$265$	−5.93634			−0.364666
$266$	−18.3891			−1.12751
$267$	−8.88945	−	11.1470i	−0.544026	−	0.682187i
$268$	6.24274	+	7.82815i	0.381336	+	0.478180i
$269$	−10.5696	+	5.09003i	−0.644437	+	0.310345i	−0.727406	−	0.686208i	$-0.759274\pi$
$269$	−10.5696	+	5.09003i	−0.644437	+	0.310345i	0.0829685	+	0.996552i	$0.473560\pi$
$270$	−1.77755	+	7.78794i	−0.108178	+	0.473959i
$271$	0.466042	+	2.04186i	0.0283100	+	0.124034i	0.987108	−	0.160053i	$-0.0511665\pi$
$271$	0.466042	+	2.04186i	0.0283100	+	0.124034i	−0.958798	+	0.284087i	$0.908309\pi$
$272$	16.9370	−	21.2383i	1.02696	−	1.28776i
$273$	15.5531	−	19.5030i	0.941318	−	1.18038i
$274$	5.94424			0.359105
$275$	0.718364	+	3.14736i	0.0433190	+	0.189793i
$276$	−5.55700	+	6.96826i	−0.334492	+	0.419440i
$277$	15.4560	−	19.3812i	0.928659	−	1.16450i	−0.0574416	−	0.998349i	$-0.518294\pi$
$277$	15.4560	−	19.3812i	0.928659	−	1.16450i	0.986100	−	0.166152i	$-0.0531343\pi$
$278$	6.46995	−	28.3467i	0.388042	−	1.70012i
$279$	−25.2061	−	12.1386i	−1.50905	−	0.726720i
$280$	−10.4879			−0.626770
$281$	−22.0974			−1.31822			−0.659110	−	0.752047i	$-0.729067\pi$
$281$	−22.0974			−1.31822			−0.659110	+	0.752047i	$0.729067\pi$
$282$	7.93247	−	34.7544i	0.472372	−	2.06960i
$283$	−16.7748	+	21.0350i	−0.997159	+	1.25040i	−0.0291264	+	0.999576i	$0.509273\pi$
$283$	−16.7748	+	21.0350i	−0.997159	+	1.25040i	−0.968033	+	0.250823i	$0.919299\pi$
$284$	−7.87468			−0.467276
$285$	7.36933	+	32.2871i	0.436521	+	1.91252i
$286$	−15.1599	−	7.30064i	−0.896426	−	0.431696i
$287$	−2.39309	−	10.4848i	−0.141260	−	0.618900i
$288$	−3.81542	+	16.7164i	−0.224825	+	0.985025i
$289$	−2.82988	+	12.3985i	−0.166463	+	0.729324i
$290$	−23.8830			−1.40246
$291$	−3.71164	−	16.2618i	−0.217580	−	0.953282i
$292$	−7.76340	−	9.73500i	−0.454319	−	0.569698i
$293$	3.73825	+	16.3784i	0.218391	+	0.956834i	0.958667	+	0.284531i	$0.0918378\pi$
$293$	3.73825	+	16.3784i	0.218391	+	0.956834i	−0.740276	+	0.672303i	$0.765305\pi$
$294$	6.42215	+	8.05312i	0.374547	+	0.469667i
$295$	−29.4898	−	14.2015i	−1.71696	−	0.826845i
$296$	10.0067	+	4.81898i	0.581629	+	0.280098i
$297$	−2.57675	−	3.23114i	−0.149518	−	0.187490i
$298$	6.38571	+	27.9776i	0.369914	+	1.62070i
$299$	−10.9954	−	13.7878i	−0.635879	−	0.797367i
$300$	−0.727704	−	3.18828i	−0.0420140	−	0.184075i
$301$	12.3036			0.709165
$302$	−2.59520	+	11.3703i	−0.149337	+	0.654287i
$303$	7.25066	−	31.7672i	0.416539	−	1.82498i
$304$	5.57922	+	24.4442i	0.319990	+	1.40197i
$305$	13.9428	+	6.71448i	0.798360	+	0.384470i
$306$	−7.63740	−	33.4616i	−0.436601	−	1.91287i
$307$	−14.0387			−0.801229			−0.400614	−	0.916247i	$-0.631203\pi$
$307$	−14.0387			−0.801229			−0.400614	+	0.916247i	$0.631203\pi$
$308$	−2.60521	+	3.26683i	−0.148445	+	0.186145i
$309$	2.46211	−	10.7872i	0.140064	−	0.613662i
$310$	32.3901			1.83964
$311$	−15.3585			−0.870903			−0.435452	−	0.900212i	$-0.643411\pi$
$311$	−15.3585			−0.870903			−0.435452	+	0.900212i	$0.643411\pi$
$312$	−19.9422	−	9.60367i	−1.12901	−	0.543701i
$313$	−3.91198	+	17.1395i	−0.221118	+	0.968781i	0.735520	+	0.677503i	$0.236938\pi$
$313$	−3.91198	+	17.1395i	−0.221118	+	0.968781i	−0.956638	+	0.291278i	$0.905919\pi$
$314$	13.3260	−	16.7103i	0.752031	−	0.943017i
$315$	−12.6955	+	15.9197i	−0.715310	+	0.896971i
$316$	−2.10296	−	9.21365i	−0.118300	−	0.518308i
$317$	23.2245			1.30442			0.652209	−	0.758039i	$-0.273842\pi$
$317$	23.2245			1.30442			0.652209	+	0.758039i	$0.273842\pi$
$318$	−6.39847	+	8.02343i	−0.358808	+	0.449932i
$319$	7.70391	−	9.66040i	0.431336	−	0.540879i
$320$	1.21505	+	5.32350i	0.0679235	+	0.297592i
$321$	3.39498	−	14.8744i	0.189490	−	0.830208i
$322$	−13.0149	+	6.26766i	−0.725293	+	0.349283i
$323$	−17.1015	−	21.4447i	−0.951555	−	1.19321i
$324$	−3.43818	−	4.31135i	−0.191010	−	0.239519i
$325$	6.47073			0.358932
$326$	38.5732			2.13637
$327$	−5.33287	+	23.3649i	−0.294909	+	1.29208i
$328$	−8.59753	+	4.14035i	−0.474719	+	0.228613i
$329$	10.9210	−	13.6945i	0.602093	−	0.755001i
$330$	22.3637	+	10.7698i	1.23108	+	0.592858i
$331$	−1.53008	−	6.70373i	−0.0841010	−	0.368471i	0.915311	−	0.402747i	$-0.131945\pi$
$331$	−1.53008	−	6.70373i	−0.0841010	−	0.368471i	−0.999412	+	0.0342763i	$0.989087\pi$
$332$	1.22749	−	1.53923i	0.0673674	−	0.0844761i
$333$	19.4279	−	9.35597i	1.06464	−	0.512704i
$334$	9.88264	+	4.75923i	0.540754	+	0.260413i
$335$	26.3313	−	12.6805i	1.43863	−	0.692809i
$336$	−17.3704	+	21.7818i	−0.947635	+	1.18830i
$337$	−30.4726	−	14.6748i	−1.65995	−	0.799390i	−0.998792	−	0.0491438i	$-0.984351\pi$
$337$	−30.4726	−	14.6748i	−1.65995	−	0.799390i	−0.661159	−	0.750246i	$-0.729935\pi$
$338$	−7.29632	+	9.14930i	−0.396868	+	0.497656i
$339$	−8.81118	−	4.24324i	−0.478558	−	0.230461i
$340$	7.51095	+	9.41843i	0.407338	+	0.510786i
$341$	−10.4480	+	13.1014i	−0.565792	+	0.709481i
$342$	28.5417	+	13.7450i	1.54336	+	0.743242i
$343$	4.48652	+	19.6567i	0.242249	+	1.06136i
$344$	−2.42928	−	10.6434i	−0.130978	−	0.573851i
$345$	16.2202	+	20.3395i	0.873268	+	1.09504i
$346$	6.74025	−	29.5310i	0.362358	−	1.58760i
$347$	−0.0650207	+	0.284874i	−0.00349049	+	0.0152928i	−0.976643	−	0.214868i	$-0.931068\pi$
$347$	−0.0650207	+	0.284874i	−0.00349049	+	0.0152928i	0.973153	+	0.230161i	$0.0739251\pi$
$348$	−7.80407	+	9.78600i	−0.418342	+	0.524585i
$349$	2.74539	−	12.0283i	0.146957	−	0.643863i	−0.846763	−	0.531970i	$-0.821452\pi$
$349$	2.74539	−	12.0283i	0.146957	−	0.643863i	0.993720	−	0.111892i	$-0.0356911\pi$
$350$	1.17944	−	5.16746i	0.0630437	−	0.276212i
$351$	−7.46332	+	3.59414i	−0.398362	+	0.191841i
$352$	9.25315	+	4.45608i	0.493195	+	0.237510i
$353$	3.71682	+	4.66075i	0.197826	+	0.248067i	0.870843	−	0.491560i	$-0.163573\pi$
$353$	3.71682	+	4.66075i	0.197826	+	0.248067i	−0.673017	+	0.739627i	$0.735002\pi$
$354$	−50.9800	+	24.5507i	−2.70956	+	1.30485i
$355$	−5.11470	+	22.4090i	−0.271460	+	1.18934i
$356$	4.31280	−	2.07694i	0.228578	−	0.110077i
$357$	6.78196	−	29.7137i	0.358939	−	1.57262i
$358$	7.76344			0.410310
$359$	−3.73783	−	16.3765i	−0.197275	−	0.864318i	−0.972550	−	0.232694i	$-0.925246\pi$
$359$	−3.73783	−	16.3765i	−0.197275	−	0.864318i	0.775275	−	0.631624i	$-0.217611\pi$
$360$	16.2782	+	7.83915i	0.857935	+	0.413160i
$361$	6.31637			0.332441
$362$	−6.67542	−	8.37071i	−0.350852	−	0.439955i
$363$	14.1144	−	6.79712i	0.740812	−	0.356756i
$364$	5.22182	+	6.54796i	0.273698	+	0.343206i
$365$	−32.7453	+	15.7693i	−1.71397	+	0.825404i
$366$	24.1033	−	11.6075i	1.25990	−	0.606736i
$367$	6.41327	+	28.0984i	0.334770	+	1.46672i	0.809776	+	0.586740i	$0.199589\pi$
$367$	6.41327	+	28.0984i	0.334770	+	1.46672i	−0.475006	+	0.879983i	$0.657554\pi$
$368$	12.2801	+	15.3988i	0.640146	+	0.802717i
$369$	−4.12257	+	18.0622i	−0.214613	+	0.940279i
$370$	−15.5655	+	19.5185i	−0.809209	+	1.01472i
$371$	−4.54309	+	2.18784i	−0.235866	+	0.113587i
$372$	10.5839	−	13.2717i	0.548748	−	0.688108i
$373$	4.93532	+	6.18870i	0.255541	+	0.320439i	0.893009	−	0.450038i	$-0.148590\pi$
$373$	4.93532	+	6.18870i	0.255541	+	0.320439i	−0.637468	+	0.770477i	$0.720018\pi$
$374$	−20.5581			−1.06304
$375$	23.3643			1.20653
$376$	−14.0029	−	6.74343i	−0.722144	−	0.347766i
$377$	−15.4416	−	19.3631i	−0.795280	−	0.997250i
$378$	1.50989	+	6.61525i	0.0776602	+	0.340252i
$379$	−1.26643	−	5.54858i	−0.0650520	−	0.285011i	0.931931	−	0.362637i	$-0.118123\pi$
$379$	−1.26643	−	5.54858i	−0.0650520	−	0.285011i	−0.996983	+	0.0776253i	$0.975266\pi$
$380$	−11.1189			−0.570386
$381$	10.8335	+	47.4647i	0.555018	+	2.43169i
$382$	33.1257	−	15.9525i	1.69486	−	0.816200i
$383$	0.922204	−	0.444110i	0.0471224	−	0.0226930i	−0.410174	−	0.912007i	$-0.634532\pi$
$383$	0.922204	−	0.444110i	0.0471224	−	0.0226930i	0.457297	+	0.889314i	$0.348818\pi$
$384$	30.0503	+	14.4715i	1.53350	+	0.738495i
$385$	7.60429	+	9.53548i	0.387551	+	0.485973i
$386$	4.14357	−	18.1542i	0.210902	−	0.924023i
$387$	−19.0963	−	9.19629i	−0.970720	−	0.467474i
$388$	5.60015			0.284304
$389$	−5.56664	−	6.98035i	−0.282240	−	0.353918i	0.620422	−	0.784268i	$-0.286961\pi$
$389$	−5.56664	−	6.98035i	−0.282240	−	0.353918i	−0.902662	+	0.430350i	$0.858390\pi$
$390$	31.0201	−	38.8980i	1.57077	−	1.96968i
$391$	−19.4127	−	9.34867i	−0.981743	−	0.472783i
$392$	4.04605	−	1.94847i	0.204356	−	0.0984128i
$393$	−32.4997			−1.63939
$394$	20.0550	−	12.7752i	1.01036	−	0.643607i
$395$	−27.5852			−1.38796
$396$	6.48532	−	3.12317i	0.325900	−	0.156945i
$397$	−9.63162	−	4.63835i	−0.483397	−	0.232792i	0.176281	−	0.984340i	$-0.443593\pi$
$397$	−9.63162	−	4.63835i	−0.483397	−	0.232792i	−0.659678	+	0.751548i	$0.729308\pi$
$398$	−19.4954	+	24.4464i	−0.977214	+	1.22539i
$399$	17.5392	+	21.9934i	0.878058	+	1.10105i
$400$	−7.22680			−0.361340
$401$	3.47501	+	1.67348i	0.173534	+	0.0835695i	0.518634	−	0.854996i	$-0.326441\pi$
$401$	3.47501	+	1.67348i	0.173534	+	0.0835695i	−0.345100	+	0.938566i	$0.612155\pi$
$402$	11.2425	−	49.2565i	0.560723	−	2.45669i
$403$	20.9418	+	26.2602i	1.04319	+	1.30811i
$404$	9.85644	+	4.74661i	0.490376	+	0.236153i
$405$	−14.5019	+	6.98377i	−0.720607	+	0.347026i
$406$	−18.2778	+	8.80210i	−0.907110	+	0.436841i
$407$	−2.87406	−	12.5921i	−0.142462	−	0.624166i
$408$	−27.0433			−1.33884
$409$	6.28927	+	27.5551i	0.310984	+	1.36251i	0.852898	+	0.522078i	$0.174843\pi$
$409$	6.28927	+	27.5551i	0.310984	+	1.36251i	−0.541914	+	0.840434i	$0.682300\pi$
$410$	−4.77293	−	20.9116i	−0.235718	−	1.03275i
$411$	−5.66950	−	7.10933i	−0.279656	−	0.350677i
$412$	3.34695	+	1.61181i	0.164893	+	0.0794081i
$413$	−27.8026			−1.36807
$414$	24.8852			1.22304
$415$	−3.58291	−	4.49282i	−0.175878	−	0.220544i
$416$	12.8348	−	16.0943i	0.629278	−	0.789089i
$417$	−40.0736	+	19.2984i	−1.96241	+	0.945049i
$418$	11.8306	−	14.8352i	0.578656	−	0.725612i
$419$	0.216802	−	0.949873i	0.0105915	−	0.0464044i	−0.969356	−	0.245660i	$-0.920995\pi$
$419$	0.216802	−	0.949873i	0.0105915	−	0.0464044i	0.979948	+	0.199256i	$0.0638524\pi$
$420$	−7.70316	−	9.65946i	−0.375876	−	0.471333i
$421$	2.10313	+	9.21443i	0.102500	+	0.449084i	0.999968	+	0.00800327i	$0.00254755\pi$
$421$	2.10313	+	9.21443i	0.102500	+	0.449084i	−0.897468	+	0.441081i	$0.854595\pi$
$422$	−7.35291	+	3.54097i	−0.357934	+	0.172372i
$423$	−27.1864	+	13.0923i	−1.32185	+	0.636568i
$424$	2.78963	+	3.49808i	0.135476	+	0.169882i
$425$	7.12294	−	3.43022i	0.345513	−	0.166390i
$426$	24.7746	+	31.0664i	1.20033	+	1.50517i
$427$	13.1450			0.636133
$428$	4.61510	+	2.22251i	0.223079	+	0.107429i
$429$	5.72766	+	25.0945i	0.276534	+	1.21158i
$430$	24.5390			1.18337
$431$	7.66477	−	33.5815i	0.369199	−	1.61757i	−0.359786	−	0.933035i	$-0.617150\pi$
$431$	7.66477	−	33.5815i	0.369199	−	1.61757i	0.728984	−	0.684530i	$-0.239993\pi$
$432$	8.33537	−	4.01410i	0.401036	−	0.193129i
$433$	−0.497503	+	2.17970i	−0.0239085	+	0.104750i	−0.985474	−	0.169825i	$-0.945680\pi$
$433$	−0.497503	+	2.17970i	−0.0239085	+	0.104750i	0.961566	+	0.274575i	$0.0885370\pi$
$434$	24.7882	−	11.9374i	1.18987	−	0.573013i
$435$	22.7792	+	28.5642i	1.09218	+	1.36955i
$436$	−7.24944	−	3.49115i	−0.347185	−	0.167196i
$437$	17.9177	−	8.62870i	0.857119	−	0.412767i
$438$	−13.9810	+	61.2548i	−0.668039	+	2.92687i
$439$	2.96099	−	12.9730i	0.141320	−	0.619165i	−0.853809	−	0.520587i	$-0.825713\pi$
$439$	2.96099	−	12.9730i	0.141320	−	0.619165i	0.995129	−	0.0985785i	$-0.0314296\pi$
$440$	6.74736	−	8.46093i	0.321668	−	0.403359i
$441$	1.94011	−	8.50016i	0.0923860	−	0.404770i
$442$	−9.16926	+	40.1731i	−0.436137	+	1.91084i
$443$	20.6918	+	25.9467i	0.983097	+	1.23276i	0.972520	+	0.232820i	$0.0747954\pi$
$443$	20.6918	+	25.9467i	0.983097	+	1.23276i	0.0105770	+	0.999944i	$0.496633\pi$
$444$	2.91142	+	12.7558i	0.138170	+	0.605363i
$445$	−3.10912	−	13.6219i	−0.147386	−	0.645742i
$446$	−16.6118	−	7.99984i	−0.786593	−	0.378803i
$447$	27.3707	−	34.3218i	1.29459	−	1.62337i
$448$	2.89186	+	3.62627i	0.136627	+	0.171325i
$449$	20.2821	+	9.76734i	0.957171	+	0.460949i	0.846195	−	0.532874i	$-0.178888\pi$
$449$	20.2821	+	9.76734i	0.957171	+	0.460949i	0.110977	+	0.993823i	$0.464602\pi$
$450$	−5.69302	+	7.13882i	−0.268372	+	0.336527i
$451$	9.99808	+	4.81482i	0.470791	+	0.226721i
$452$	2.04719	−	2.56709i	0.0962917	−	0.120746i
$453$	16.0742	−	7.74091i	0.755230	−	0.363699i
$454$	−19.7440	−	9.50820i	−0.926631	−	0.446242i
$455$	22.0252	−	10.6068i	1.03256	−	0.497252i
$456$	15.5627	−	19.5150i	0.728790	−	0.913873i
$457$	5.17939	+	22.6924i	0.242282	+	1.06151i	0.938934	+	0.344097i	$0.111815\pi$
$457$	5.17939	+	22.6924i	0.242282	+	1.06151i	−0.696653	+	0.717409i	$0.745328\pi$
$458$	−15.3178	−	7.37668i	−0.715755	−	0.344689i
$459$	−6.31026	+	7.91282i	−0.294538	+	0.369339i
$460$	−7.86940	+	3.78970i	−0.366912	+	0.176696i
$461$	8.26245	−	36.2002i	0.384821	−	1.68601i	−0.297312	−	0.954780i	$-0.596090\pi$
$461$	8.26245	−	36.2002i	0.384821	−	1.68601i	0.682132	−	0.731229i	$-0.261053\pi$
$462$	21.0842			0.980927
$463$	15.2449			0.708492			0.354246	−	0.935152i	$-0.384738\pi$
$463$	15.2449			0.708492			0.354246	+	0.935152i	$0.384738\pi$
$464$	17.2458	+	21.6256i	0.800617	+	1.00394i
$465$	−30.8931	−	38.7387i	−1.43263	−	1.79646i
$466$	−18.7407	+	9.02505i	−0.868147	+	0.418077i
$467$	7.92640	−	34.7278i	0.366790	−	1.60701i	−0.368748	−	0.929529i	$-0.620213\pi$
$467$	7.92640	−	34.7278i	0.366790	−	1.60701i	0.735538	−	0.677483i	$-0.236929\pi$
$468$	−3.21050	−	14.0661i	−0.148405	−	0.650206i
$469$	15.4780	−	19.4088i	0.714708	−	0.896216i
$470$	21.7815	−	27.3131i	1.00471	−	1.25986i
$471$	−32.6956			−1.50654
$472$	5.48948	+	24.0510i	0.252674	+	1.10704i
$473$	−7.91549	+	9.92571i	−0.363955	+	0.456385i
$474$	−29.7326	+	37.2835i	−1.36566	+	1.71249i
$475$	−1.62374	+	7.11406i	−0.0745022	+	0.326415i
$476$	9.21931	+	4.43978i	0.422566	+	0.203497i
$477$	8.68662			0.397733
$478$	10.9859			0.502482
$479$	−7.62573	+	33.4105i	−0.348429	+	1.52657i	0.432320	+	0.901720i	$0.357695\pi$
$479$	−7.62573	+	33.4105i	−0.348429	+	1.52657i	−0.780749	+	0.624845i	$0.785162\pi$
$480$	−18.9337	+	23.7421i	−0.864202	+	1.08368i
$481$	−25.8883			−1.18041
$482$	7.04137	+	30.8503i	0.320726	+	1.40519i
$483$	19.9095	+	9.58791i	0.905914	+	0.436265i
$484$	1.17038	+	5.12776i	0.0531990	+	0.233080i
$485$	3.63736	−	15.9363i	0.165164	−	0.723632i
$486$	−8.29146	+	36.3273i	−0.376108	+	1.64784i
$487$	−27.4012			−1.24167			−0.620835	−	0.783942i	$-0.713206\pi$
$487$	−27.4012			−1.24167			−0.620835	+	0.783942i	$0.713206\pi$
$488$	−2.59542	−	11.3713i	−0.117489	−	0.514754i
$489$	−36.7903	−	46.1336i	−1.66371	−	2.08623i
$490$	2.24617	+	9.84111i	0.101472	+	0.444576i
$491$	0.809212	+	1.01472i	0.0365192	+	0.0457936i	0.799756	−	0.600326i	$-0.204962\pi$
$491$	0.809212	+	1.01472i	0.0365192	+	0.0457936i	−0.763237	+	0.646119i	$0.776391\pi$
$492$	−10.1281	−	4.87742i	−0.456608	−	0.219891i
$493$	−27.2626	−	13.1290i	−1.22785	−	0.591299i
$494$	−23.7131	−	29.7353i	−1.06690	−	1.33785i
$495$	−4.67530	−	20.4838i	−0.210139	−	0.920679i
$496$	−23.3887	−	29.3285i	−1.05019	−	1.31689i
$497$	4.34454	+	19.0347i	0.194879	+	0.853821i
$498$	−9.93423			−0.445164
$499$	5.75605	−	25.2189i	0.257676	−	1.12895i	−0.666053	−	0.745905i	$-0.732017\pi$
$499$	5.75605	−	25.2189i	0.257676	−	1.12895i	0.923729	−	0.383048i	$-0.125125\pi$
$500$	−1.74553	+	7.64769i	−0.0780627	+	0.342015i
$501$	−3.73382	−	16.3589i	−0.166815	−	0.730863i
$502$	13.6262	+	6.56204i	0.608168	+	0.292878i
$503$	−5.82289	−	25.5117i	−0.259630	−	1.13751i	−0.921649	−	0.388025i	$-0.873157\pi$
$503$	−5.82289	−	25.5117i	−0.259630	−	1.13751i	0.662019	−	0.749487i	$-0.269700\pi$
$504$	15.3468			0.683603
$505$	19.9093	−	24.9655i	0.885953	−	1.11095i
$506$	3.31681	−	14.5319i	0.147450	−	0.646022i
$507$	17.9017			0.795041
$508$	−16.3457			−0.725222
$509$	10.3729	+	4.99530i	0.459769	+	0.221413i	0.649407	−	0.760441i	$-0.275017\pi$
$509$	10.3729	+	4.99530i	0.459769	+	0.221413i	−0.189638	+	0.981854i	$0.560731\pi$
$510$	13.5264	−	59.2629i	0.598957	−	2.62420i
$511$	−19.2483	+	24.1366i	−0.851494	+	1.06774i
$512$	−2.43992	+	3.05956i	−0.107830	+	0.135215i
$513$	−2.07867	−	9.10723i	−0.0917753	−	0.402094i
$514$	22.2371			0.980837
$515$	6.76061	−	8.47754i	0.297908	−	0.373565i
$516$	8.01840	−	10.0548i	0.352991	−	0.442636i
$517$	4.02181	+	17.6207i	0.176879	+	0.774957i
$518$	−4.71874	+	20.6742i	−0.207330	+	0.908371i
$519$	−41.7478	+	20.1047i	−1.83253	+	0.882498i
$520$	−13.5243	−	16.9589i	−0.593078	−	0.743697i
$521$	11.4004	+	14.2957i	0.499463	+	0.626306i	0.966108	−	0.258138i	$-0.0831090\pi$
$521$	11.4004	+	14.2957i	0.499463	+	0.626306i	−0.466645	+	0.884445i	$0.654538\pi$
$522$	34.9480			1.52963
$523$	16.6527			0.728170			0.364085	−	0.931366i	$-0.381382\pi$
$523$	16.6527			0.728170			0.364085	+	0.931366i	$0.381382\pi$
$524$	2.42803	−	10.6379i	0.106069	−	0.464719i
$525$	−7.30522	+	3.51801i	−0.318826	+	0.153538i
$526$	−18.1088	+	22.7077i	−0.789582	+	0.990105i
$527$	36.9735	+	17.8055i	1.61059	+	0.775619i
$528$	−6.39691	−	28.0267i	−0.278390	−	1.21970i
$529$	−4.59997	+	5.76818i	−0.199999	+	0.250790i
$530$	−9.06103	+	4.36356i	−0.393586	+	0.189541i
$531$	43.1523	+	20.7810i	1.87265	+	0.901820i
$532$	−8.50930	+	4.09786i	−0.368925	+	0.177665i
$533$	13.8681	−	17.3900i	0.600692	−	0.753244i
$534$	−21.7623	−	10.4802i	−0.941746	−	0.453521i
$535$	9.32217	−	11.6896i	0.403032	−	0.505387i
$536$	−19.8459	−	9.55728i	−0.857212	−	0.412812i
$537$	−7.40461	−	9.28509i	−0.319533	−	0.400681i
$538$	−12.3915	+	15.5385i	−0.534237	+	0.669912i
$539$	−4.70515	−	2.26588i	−0.202665	−	0.0975984i
$540$	0.912944	+	3.99987i	0.0392868	+	0.172127i
$541$	9.24257	+	40.4944i	0.397369	+	1.74099i	0.637688	+	0.770295i	$0.279891\pi$
$541$	9.24257	+	40.4944i	0.397369	+	1.74099i	−0.240319	+	0.970694i	$0.577252\pi$
$542$	2.21224	+	2.77406i	0.0950239	+	0.119156i
$543$	−3.64451	+	15.9676i	−0.156401	+	0.685236i
$544$	5.59663	−	24.5204i	0.239953	−	1.05130i
$545$	−14.6434	+	18.3622i	−0.627252	+	0.786550i
$546$	9.40391	−	41.2012i	0.402450	−	1.76325i
$547$	−4.09268	+	17.9312i	−0.174990	+	0.766682i	0.808905	+	0.587939i	$0.200060\pi$
$547$	−4.09268	+	17.9312i	−0.174990	+	0.766682i	−0.983896	+	0.178744i	$0.942797\pi$
$548$	2.75061	−	1.32462i	0.117500	−	0.0565851i
$549$	−20.4024	−	9.82527i	−0.870752	−	0.419332i
$550$	3.40998	+	4.27598i	0.145402	+	0.182328i
$551$	25.1630	−	12.1179i	1.07198	−	0.516239i
$552$	4.36312	−	19.1161i	0.185707	−	0.813634i
$553$	−21.1110	+	10.1665i	−0.897731	+	0.432324i
$554$	9.34515	−	40.9438i	0.397037	−	1.73953i
$555$	38.1901			1.62108
$556$	−3.32295	−	14.5588i	−0.140924	−	0.617430i
$557$	−6.57849	−	3.16803i	−0.278739	−	0.134234i	0.289291	−	0.957241i	$-0.406580\pi$
$557$	−6.57849	−	3.16803i	−0.278739	−	0.134234i	−0.568031	+	0.823007i	$0.692295\pi$
$558$	−47.3963			−2.00645
$559$	15.8656	+	19.8949i	0.671045	+	0.841464i
$560$	−24.5987	+	11.8461i	−1.03948	+	0.500589i
$561$	19.6079	+	24.5876i	0.827847	+	1.03809i
$562$	−33.7287	+	16.2429i	−1.42276	+	0.685165i
$563$	5.80572	−	2.79589i	0.244682	−	0.117833i	−0.307524	−	0.951540i	$-0.599500\pi$
$563$	5.80572	−	2.79589i	0.244682	−	0.117833i	0.552206	+	0.833708i	$0.313786\pi$
$564$	−4.07410	−	17.8498i	−0.171550	−	0.751611i
$565$	−5.97550	−	7.49304i	−0.251391	−	0.315235i
$566$	−10.1426	+	44.4375i	−0.426324	+	1.86785i
$567$	−8.52450	+	10.6894i	−0.357995	+	0.448912i
$568$	15.6084	−	7.51659i	0.654913	−	0.315389i
$569$	4.76702	−	5.97766i	0.199844	−	0.250596i	−0.671804	−	0.740729i	$-0.734480\pi$
$569$	4.76702	−	5.97766i	0.199844	−	0.250596i	0.871648	+	0.490133i	$0.163052\pi$
$570$	34.9812	+	43.8651i	1.46520	+	1.83731i
$571$	−25.3463			−1.06071			−0.530355	−	0.847776i	$-0.677941\pi$
$571$	−25.3463			−1.06071			−0.530355	+	0.847776i	$0.677941\pi$
$572$	−8.64193			−0.361337
$573$	−50.6738	−	24.4032i	−2.11693	−	1.01946i
$574$	−11.3597	−	14.2446i	−0.474145	−	0.594559i
$575$	1.27552	+	5.58841i	0.0531927	+	0.233053i
$576$	−1.77798	−	7.78985i	−0.0740826	−	0.324577i
$577$	22.1874			0.923675			0.461838	−	0.886964i	$-0.347190\pi$
$577$	22.1874			0.923675			0.461838	+	0.886964i	$0.347190\pi$
$578$	4.79421	+	21.0048i	0.199413	+	0.873684i
$579$	−25.6645	+	12.3594i	−1.06658	+	0.513638i
$580$	−11.0515	+	5.32214i	−0.458890	+	0.220990i
$581$	−4.39784	−	2.11789i	−0.182453	−	0.0878647i
$582$	−17.6187	−	22.0931i	−0.730318	−	0.915790i
$583$	1.15779	−	5.07262i	0.0479509	−	0.210086i
$584$	24.6801	+	11.8853i	1.02127	+	0.491819i
$585$	−42.1132			−1.74117
$586$	17.7450	+	22.2515i	0.733039	+	0.919202i
$587$	−10.4627	+	13.1198i	−0.431843	+	0.541514i	−0.949373	−	0.314151i	$-0.898280\pi$
$587$	−10.4627	+	13.1198i	−0.431843	+	0.541514i	0.517530	+	0.855665i	$0.326851\pi$
$588$	4.76633	+	2.29534i	0.196560	+	0.0946583i
$589$	−34.1260	+	16.4342i	−1.40614	+	0.677161i
$590$	−55.4512			−2.28289
$591$	−34.4073	−	11.8011i	−1.41533	−	0.485432i
$592$	28.9133			1.18833
$593$	31.0908	−	14.9726i	1.27675	−	0.614849i	0.332196	−	0.943211i	$-0.392211\pi$
$593$	31.0908	−	14.9726i	1.27675	−	0.614849i	0.944552	+	0.328361i	$0.106496\pi$
$594$	−6.30814	−	3.03784i	−0.258826	−	0.124644i
$595$	18.6223	−	23.3517i	0.763442	−	0.957326i
$596$	9.18947	+	11.5232i	0.376415	+	0.472010i
$597$	47.8322			1.95764
$598$	−26.9178	−	12.9629i	−1.10075	−	0.530093i
$599$	−0.294125	+	1.28865i	−0.0120176	+	0.0526527i	−0.980581	−	0.196113i	$-0.937168\pi$
$599$	−0.294125	+	1.28865i	−0.0120176	+	0.0526527i	0.968564	+	0.248766i	$0.0800251\pi$
$600$	4.48568	+	5.62486i	0.183127	+	0.229634i
$601$	20.6931	+	9.96525i	0.844087	+	0.406491i	0.805379	−	0.592760i	$-0.201962\pi$
$601$	20.6931	+	9.96525i	0.844087	+	0.406491i	0.0387078	+	0.999251i	$0.487676\pi$
$602$	18.7797	−	9.04384i	0.765405	−	0.368599i
$603$	−38.5305	+	18.5553i	−1.56908	+	0.755630i
$604$	1.33289	+	5.83976i	0.0542344	+	0.237616i
$605$	15.3523			0.624158
$606$	−12.2836	−	53.8180i	−0.498988	−	2.18621i
$607$	7.70022	+	33.7369i	0.312542	+	1.36934i	0.850327	+	0.526255i	$0.176404\pi$
$607$	7.70022	+	33.7369i	0.312542	+	1.36934i	−0.537785	+	0.843082i	$0.680739\pi$
$608$	14.4737	+	18.1495i	0.586987	+	0.736059i
$609$	27.9603	+	13.4650i	1.13301	+	0.545628i
$610$	26.2173			1.06151
$611$	36.2268			1.46558
$612$	−10.9907	−	13.7819i	−0.444274	−	0.557102i
$613$	14.5874	−	18.2921i	0.589181	−	0.738809i	−0.394467	−	0.918910i	$-0.629071\pi$
$613$	14.5874	−	18.2921i	0.589181	−	0.738809i	0.983648	+	0.180101i	$0.0576423\pi$
$614$	−21.4281	+	10.3192i	−0.864769	+	0.416451i
$615$	−20.4580	+	25.6535i	−0.824945	+	1.03445i
$616$	2.04550	−	8.96191i	0.0824154	−	0.361086i
$617$	−21.9761	−	27.5571i	−0.884723	−	1.10941i	−0.993328	−	0.115323i	$-0.963210\pi$
$617$	−21.9761	−	27.5571i	−0.884723	−	1.10941i	0.108605	−	0.994085i	$-0.465362\pi$
$618$	−4.17115	−	18.2750i	−0.167788	−	0.735128i
$619$	−7.26311	+	3.49773i	−0.291929	+	0.140586i	−0.574116	−	0.818774i	$-0.694654\pi$
$619$	−7.26311	+	3.49773i	−0.291929	+	0.140586i	0.282187	+	0.959359i	$0.408940\pi$
$620$	14.9881	−	7.21787i	0.601935	−	0.289877i
$621$	−4.57524	−	5.73717i	−0.183598	−	0.230225i
$622$	−23.4428	+	11.2894i	−0.939969	+	0.452665i
$623$	−7.39978	−	9.27903i	−0.296466	−	0.371757i
$624$	−57.6207			−2.30668
$625$	27.1624	+	13.0807i	1.08650	+	0.523230i
$626$	6.62743	+	29.0367i	0.264885	+	1.16054i
$627$	−29.0267			−1.15922
$628$	2.44267	−	10.7020i	0.0974732	−	0.427058i
$629$	−28.4977	+	13.7238i	−1.13628	+	0.547203i
$630$	−7.67609	+	33.6312i	−0.305823	+	1.33990i
$631$	14.8916	−	7.17141i	0.592825	−	0.285489i	−0.113318	−	0.993559i	$-0.536148\pi$
$631$	14.8916	−	7.17141i	0.592825	−	0.285489i	0.706143	+	0.708069i	$0.250434\pi$
$632$	12.9629	+	16.2550i	0.515638	+	0.646590i
$633$	11.2481	+	5.41678i	0.447071	+	0.215298i
$634$	35.4491	−	17.0714i	1.40786	−	0.677991i
$635$	−10.6167	+	46.5149i	−0.421311	+	1.84589i
$636$	−1.17285	+	5.13857i	−0.0465063	+	0.203758i
$637$	−6.52639	+	8.18383i	−0.258585	+	0.324255i
$638$	4.65802	−	20.4081i	0.184413	−	0.807966i
$639$	7.48432	−	32.7909i	0.296075	−	1.29719i
$640$	20.3793	+	25.5549i	0.805563	+	1.01014i
$641$	8.29410	+	36.3388i	0.327597	+	1.43530i	0.823696	+	0.567032i	$0.191908\pi$
$641$	8.29410	+	36.3388i	0.327597	+	1.43530i	−0.496099	+	0.868266i	$0.665235\pi$
$642$	−5.75157	−	25.1993i	−0.226996	−	0.994537i
$643$	41.3024	+	19.8902i	1.62881	+	0.784392i	0.999977	+	0.00685067i	$0.00218065\pi$
$643$	41.3024	+	19.8902i	1.62881	+	0.784392i	0.628831	+	0.777542i	$0.283534\pi$
$644$	−4.62577	+	5.80053i	−0.182281	+	0.228573i
$645$	−23.4048	−	29.3487i	−0.921562	−	1.15560i
$646$	−41.8663	−	20.1617i	−1.64721	−	0.793253i
$647$	−5.66225	+	7.10024i	−0.222606	+	0.279139i	−0.880576	−	0.473905i	$-0.842844\pi$
$647$	−5.66225	+	7.10024i	−0.222606	+	0.279139i	0.657970	+	0.753044i	$0.271415\pi$
$648$	10.9301	+	5.26367i	0.429375	+	0.206776i
$649$	17.8868	−	22.4293i	0.702118	−	0.880428i
$650$	9.87670	−	4.75637i	0.387396	−	0.186560i
$651$	−37.9197	−	18.2611i	−1.48619	−	0.715711i
$652$	17.8492	−	8.59570i	0.699027	−	0.336634i
$653$	−22.8206	+	28.6162i	−0.893040	+	1.11984i	0.0991460	+	0.995073i	$0.468389\pi$
$653$	−22.8206	+	28.6162i	−0.893040	+	1.11984i	−0.992186	+	0.124764i	$0.960183\pi$
$654$	9.03463	+	39.5833i	0.353282	+	1.54783i
$655$	−28.6952	−	13.8189i	−1.12122	−	0.539949i
$656$	−15.4885	+	19.4219i	−0.604723	+	0.758299i
$657$	47.9161	−	23.0752i	1.86938	−	0.900248i
$658$	6.60317	−	28.9304i	0.257418	−	1.12782i
$659$	20.3453			0.792541			0.396270	−	0.918134i	$-0.370304\pi$
$659$	20.3453			0.792541			0.396270	+	0.918134i	$0.370304\pi$
$660$	12.7485			0.496233
$661$	−19.8091	−	24.8398i	−0.770485	−	0.966158i	0.229489	−	0.973311i	$-0.426294\pi$
$661$	−19.8091	−	24.8398i	−0.770485	−	0.966158i	−0.999974	+	0.00715341i	$0.997723\pi$
$662$	−7.26311	−	9.10765i	−0.282289	−	0.353979i
$663$	56.7926	−	27.3499i	2.20564	−	1.06218i
$664$	−0.963775	+	4.22257i	−0.0374017	+	0.163868i
$665$	6.13439	+	26.8765i	0.237882	+	1.04223i
$666$	22.7769	−	28.5613i	0.882585	−	1.10673i
$667$	13.6790	−	17.1529i	0.529652	−	0.664162i
$668$	5.63360			0.217971
$669$	6.27621	+	27.4979i	0.242652	+	1.06313i
$670$	30.8703	−	38.7101i	1.19262	−	1.49550i
$671$	−8.45686	+	10.6046i	−0.326474	+	0.409385i
$672$	−5.73985	+	25.1479i	−0.221420	+	0.970103i
$673$	19.0839	+	9.19032i	0.735630	+	0.354261i	0.763896	−	0.645339i	$-0.223284\pi$
$673$	19.0839	+	9.19032i	0.735630	+	0.354261i	−0.0282654	+	0.999600i	$0.508998\pi$
$674$	−57.2993			−2.20709
$675$	2.69251			0.103635
$676$	−1.33742	+	5.85963i	−0.0514393	+	0.225370i
$677$	11.5091	−	14.4320i	0.442331	−	0.554665i	−0.509825	−	0.860278i	$-0.670290\pi$
$677$	11.5091	−	14.4320i	0.442331	−	0.554665i	0.952156	+	0.305613i	$0.0988613\pi$
$678$	−16.5681			−0.636295
$679$	−3.08966	−	13.5367i	−0.118570	−	0.519489i
$680$	−23.8776	−	11.4988i	−0.915663	−	0.440960i
$681$	7.45959	+	32.6826i	0.285852	+	1.25240i
$682$	−6.31720	+	27.6775i	−0.241898	+	1.05982i
$683$	9.81939	−	43.0216i	0.375728	−	1.64617i	−0.334642	−	0.942345i	$-0.608615\pi$
$683$	9.81939	−	43.0216i	0.375728	−	1.64617i	0.710370	−	0.703828i	$-0.248528\pi$
$684$	16.2702			0.622107
$685$	−1.98293	−	8.68777i	−0.0757638	−	0.331943i
$686$	21.2969	+	26.7055i	0.813121	+	1.01962i
$687$	5.78731	+	25.3559i	0.220800	+	0.967387i
$688$	−17.7195	−	22.2195i	−0.675548	−	0.847110i
$689$	−9.39613	−	4.52494i	−0.357964	−	0.172386i
$690$	39.7087	+	19.1227i	1.51169	+	0.727990i
$691$	−24.8575	−	31.1703i	−0.945622	−	1.18577i	−0.982464	−	0.186452i	$-0.940301\pi$
$691$	−24.8575	−	31.1703i	−0.945622	−	1.18577i	0.0368417	−	0.999321i	$-0.488270\pi$
$692$	−3.46178	−	15.1670i	−0.131597	−	0.576564i
$693$	−11.1273	−	13.9532i	−0.422692	−	0.530039i
$694$	0.110154	+	0.482616i	0.00418139	+	0.0183199i
$695$	−43.5883			−1.65340
$696$	6.12742	−	26.8460i	0.232259	−	1.01759i
$697$	6.04718	−	26.4944i	0.229053	−	1.00355i
$698$	−4.65107	−	20.3777i	−0.176046	−	0.771307i
$699$	28.6685	+	13.8060i	1.08434	+	0.522192i
$700$	−0.605757	−	2.65399i	−0.0228955	−	0.100312i
$701$	19.2920			0.728649			0.364324	−	0.931272i	$-0.381300\pi$
$701$	19.2920			0.728649			0.364324	+	0.931272i	$0.381300\pi$
$702$	−8.74985	+	10.9720i	−0.330242	+	0.414110i
$703$	6.49631	−	28.4622i	0.245013	−	1.07347i
$704$	−4.78592			−0.180376
$705$	−53.4413			−2.01272
$706$	9.09916	+	4.38192i	0.342451	+	0.164916i
$707$	6.03561	−	26.4437i	0.226992	−	0.994519i
$708$	−18.1193	+	22.7209i	−0.680966	+	0.853905i
$709$	−10.8438	+	13.5977i	−0.407247	+	0.510672i	−0.942585	−	0.333966i	$-0.891613\pi$
$709$	−10.8438	+	13.5977i	−0.407247	+	0.510672i	0.535338	+	0.844638i	$0.320184\pi$
$710$	8.66501	+	37.9639i	0.325192	+	1.42476i
$711$	40.3653			1.51382
$712$	−6.56590	+	8.23338i	−0.246068	+	0.308559i
$713$	−18.5514	+	23.2627i	−0.694754	+	0.871194i
$714$	−11.4896	−	50.3391i	−0.429987	−	1.88390i
$715$	−5.61304	+	24.5923i	−0.209916	+	0.919701i
$716$	3.59242	−	1.73002i	0.134255	−	0.0646538i
$717$	−10.4781	−	13.1391i	−0.391312	−	0.490689i
$718$	−17.7430	−	22.2490i	−0.662162	−	0.830325i
$719$	−2.42502			−0.0904379			−0.0452189	−	0.998977i	$-0.514399\pi$
$719$	−2.42502			−0.0904379			−0.0452189	+	0.998977i	$0.514399\pi$
$720$	47.0339			1.75285
$721$	2.04951	−	8.97950i	0.0763279	−	0.334414i
$722$	9.64110	−	4.64291i	0.358805	−	0.172791i
$723$	30.1811	−	37.8458i	1.12245	−	1.40750i
$724$	−4.95429	−	2.38586i	−0.184125	−	0.0886698i
$725$	1.79130	+	7.84818i	0.0665271	+	0.291474i
$726$	16.5474	−	20.7498i	0.614131	−	0.770097i
$727$	4.48600	−	2.16034i	0.166376	−	0.0801226i	−0.348842	−	0.937181i	$-0.613425\pi$
$727$	4.48600	−	2.16034i	0.166376	−	0.0801226i	0.515218	+	0.857059i	$0.327711\pi$
$728$	−16.6004	−	7.99431i	−0.615250	−	0.296289i
$729$	34.2257	−	16.4822i	1.26762	−	0.610452i
$730$	−38.3900	+	48.1395i	−1.42088	+	1.78172i
$731$	28.0113	+	13.4896i	1.03604	+	0.498929i
$732$	8.56682	−	10.7424i	0.316639	−	0.397052i
$733$	−2.26986	−	1.09311i	−0.0838393	−	0.0403749i	0.391494	−	0.920181i	$-0.371958\pi$
$733$	−2.26986	−	1.09311i	−0.0838393	−	0.0403749i	−0.475334	+	0.879806i	$0.657673\pi$
$734$	30.4430	+	38.1743i	1.12367	+	1.40904i
$735$	9.62764	−	12.0727i	0.355121	−	0.445307i
$736$	16.4298	+	7.91216i	0.605610	+	0.291646i
$737$	5.70000	+	24.9733i	0.209962	+	0.919904i
$738$	6.98421	+	30.5998i	0.257092	+	1.12640i
$739$	1.79523	+	2.25115i	0.0660386	+	0.0828098i	0.813754	−	0.581210i	$-0.197420\pi$
$739$	1.79523	+	2.25115i	0.0660386	+	0.0828098i	−0.747715	+	0.664020i	$0.768849\pi$
$740$	−2.85316	+	12.5005i	−0.104884	+	0.459528i
$741$	−12.9464	+	56.7218i	−0.475597	+	2.08373i
$742$	−5.32623	+	6.67888i	−0.195532	+	0.245190i
$743$	−6.15929	+	26.9856i	−0.225963	+	0.990007i	0.726933	+	0.686708i	$0.240945\pi$
$743$	−6.15929	+	26.9856i	−0.225963	+	0.990007i	−0.952896	+	0.303298i	$0.901912\pi$
$744$	−8.31000	+	36.4085i	−0.304659	+	1.33480i
$745$	38.7603	−	18.6660i	1.42007	−	0.683869i
$746$	12.0822	+	5.81847i	0.442360	+	0.213029i
$747$	5.24285	+	6.57433i	0.191826	+	0.240542i
$748$	−9.51297	+	4.58121i	−0.347829	+	0.167505i
$749$	2.82606	−	12.3818i	0.103262	−	0.452421i
$750$	35.6625	−	17.1742i	1.30221	−	0.627112i
$751$	−1.26833	+	5.55691i	−0.0462820	+	0.202775i	−0.992783	−	0.119927i	$-0.961734\pi$
$751$	−1.26833	+	5.55691i	−0.0462820	+	0.202775i	0.946501	+	0.322702i	$0.104591\pi$
$752$	−40.4597			−1.47541
$753$	−5.14820	−	22.5557i	−0.187611	−	0.821977i
$754$	−37.8025	−	18.2047i	−1.37669	−	0.662977i
$755$	17.4839			0.636305
$756$	2.17283	+	2.72464i	0.0790251	+	0.0990943i
$757$	22.7850	−	10.9727i	0.828136	−	0.398809i	0.0287200	−	0.999587i	$-0.490857\pi$
$757$	22.7850	−	10.9727i	0.828136	−	0.398809i	0.799416	+	0.600778i	$0.205143\pi$
$758$	−6.01156	−	7.53826i	−0.218350	−	0.273802i
$759$	−20.5437	+	9.89332i	−0.745689	+	0.359105i
$760$	22.0387	−	10.6133i	0.799427	−	0.384984i
$761$	−7.99231	−	35.0166i	−0.289721	−	1.26935i	−0.884909	−	0.465765i	$-0.845779\pi$
$761$	−7.99231	−	35.0166i	−0.289721	−	1.26935i	0.595188	−	0.803587i	$-0.297078\pi$
$762$	51.4253	+	64.4853i	1.86294	+	2.33606i
$763$	−4.43921	+	19.4494i	−0.160710	+	0.704117i
$764$	11.7735	−	14.7636i	0.425952	−	0.534127i
$765$	−46.3579	+	22.3248i	−1.67607	+	0.807154i
$766$	1.08117	−	1.35575i	0.0390644	−	0.0489852i
$767$	−35.8519	−	44.9568i	−1.29454	−	1.62330i
$768$	45.3614			1.63684
$769$	33.0583			1.19211			0.596056	−	0.802943i	$-0.296734\pi$
$769$	33.0583			1.19211			0.596056	+	0.802943i	$0.296734\pi$
$770$	18.6161	+	8.96503i	0.670877	+	0.323077i
$771$	−21.2093	−	26.5956i	−0.763835	−	0.957819i
$772$	−2.12813	−	9.32394i	−0.0765930	−	0.335576i
$773$	−6.60393	−	28.9337i	−0.237527	−	1.04067i	−0.943223	−	0.332159i	$-0.892223\pi$
$773$	−6.60393	−	28.9337i	−0.237527	−	1.04067i	0.705697	−	0.708514i	$-0.250634\pi$
$774$	−35.9078			−1.29068
$775$	−2.42935	−	10.6437i	−0.0872649	−	0.382332i
$776$	−11.1000	+	5.34549i	−0.398468	+	0.191892i
$777$	29.2270	−	14.0750i	1.04851	−	0.504937i
$778$	−13.6277	−	6.56276i	−0.488577	−	0.235286i
$779$	15.6389	+	19.6106i	0.560323	+	0.702623i
$780$	5.68602	−	24.9121i	0.203592	−	0.891995i
$781$	−18.1510	−	8.74105i	−0.649493	−	0.312779i
$782$	−36.5027			−1.30534
$783$	−6.42532	−	8.05710i	−0.229622	−	0.287937i
$784$	7.28896	−	9.14007i	0.260320	−	0.326431i
$785$	−28.8682	−	13.9022i	−1.03035	−	0.496191i
$786$	−49.6064	+	23.8892i	−1.76940	+	0.852100i
$787$	13.5928			0.484532			0.242266	−	0.970210i	$-0.422109\pi$
$787$	13.5928			0.484532			0.242266	+	0.970210i	$0.422109\pi$
$788$	6.43332	−	10.3806i	0.229177	−	0.369795i
$789$	44.4304			1.58176
$790$	−42.1051	+	20.2767i	−1.49803	+	0.721414i
$791$	−7.33463	−	3.53217i	−0.260789	−	0.125590i
$792$	−9.87339	+	12.3808i	−0.350836	+	0.439934i
$793$	16.9508	+	21.2556i	0.601939	+	0.754808i
$794$	−18.1108			−0.642730
$795$	13.8611	+	6.67513i	0.491601	+	0.236742i
$796$	−3.57352	+	15.6566i	−0.126660	+	0.554933i
$797$	−3.97101	−	4.97949i	−0.140660	−	0.176382i	0.706511	−	0.707702i	$-0.250268\pi$
$797$	−3.97101	−	4.97949i	−0.140660	−	0.176382i	−0.847172	+	0.531319i	$0.821696\pi$
$798$	42.9377	+	20.6777i	1.51998	+	0.731983i
$799$	39.8782	−	19.2043i	1.41079	−	0.679401i
$800$	−6.02843	+	2.90314i	−0.213137	+	0.102641i
$801$	4.54956	+	19.9329i	0.160751	+	0.704295i
$802$	6.53425			0.230732
$803$	−7.08845	−	31.0565i	−0.250146	−	1.09596i
$804$	−5.77410	−	25.2980i	−0.203637	−	0.892192i
$805$	13.5021	+	16.9311i	0.475886	+	0.596742i
$806$	51.2676	+	24.6892i	1.80583	+	0.869640i
$807$	30.4029			1.07023
$808$	−24.0672			−0.846681
$809$	5.09445	+	6.38824i	0.179111	+	0.224599i	0.863280	−	0.504725i	$-0.168406\pi$
$809$	5.09445	+	6.38824i	0.179111	+	0.224599i	−0.684169	+	0.729324i	$0.739835\pi$
$810$	−17.0018	+	21.3196i	−0.597382	+	0.749093i
$811$	−34.5876	+	16.6565i	−1.21453	+	0.584888i	−0.927784	−	0.373117i	$-0.878289\pi$
$811$	−34.5876	+	16.6565i	−1.21453	+	0.584888i	−0.286749	+	0.958006i	$0.592575\pi$
$812$	−6.49629	+	8.14609i	−0.227975	+	0.285872i
$813$	1.20779	−	5.29169i	0.0423592	−	0.185588i
$814$	−13.6428	−	17.1075i	−0.478179	−	0.599618i
$815$	−12.8675	−	56.3764i	−0.450730	−	1.97478i
$816$	−63.4285	+	30.5456i	−2.22044	+	1.06931i
$817$	−25.8541	+	12.4507i	−0.904521	+	0.435594i
$818$	29.8544	+	37.4362i	1.04383	+	1.30893i
$819$	−32.2293	+	15.5208i	−1.12618	+	0.542341i
$820$	−6.86858	−	8.61292i	−0.239861	−	0.300776i
$821$	−19.9881			−0.697590			−0.348795	−	0.937199i	$-0.613409\pi$
$821$	−19.9881			−0.697590			−0.348795	+	0.937199i	$0.613409\pi$
$822$	−13.8795	−	6.68402i	−0.484103	−	0.233132i
$823$	−10.7495	−	47.0966i	−0.374704	−	1.64169i	−0.713376	−	0.700781i	$-0.752835\pi$
$823$	−10.7495	−	47.0966i	−0.374704	−	1.64169i	0.338672	−	0.940904i	$-0.390022\pi$
$824$	−8.17250			−0.284703
$825$	1.86171	−	8.15669i	0.0648165	−	0.283979i
$826$	−42.4369	+	20.4365i	−1.47657	+	0.711078i
$827$	−2.28359	+	10.0051i	−0.0794082	+	0.347910i	−0.998987	−	0.0449951i	$-0.985673\pi$
$827$	−2.28359	+	10.0051i	−0.0794082	+	0.347910i	0.919579	+	0.392905i	$0.128530\pi$
$828$	11.5153	−	5.54545i	0.400183	−	0.192718i
$829$	−14.5147	−	18.2008i	−0.504115	−	0.632140i	0.463037	−	0.886339i	$-0.346760\pi$
$829$	−14.5147	−	18.2008i	−0.504115	−	0.632140i	−0.967152	+	0.254199i	$0.918188\pi$
$830$	−8.77132	−	4.22404i	−0.304457	−	0.146619i
$831$	−57.8821	+	27.8745i	−2.00791	+	0.966957i
$832$	−2.13460	+	9.35228i	−0.0740039	+	0.324232i
$833$	−2.84584	+	12.4684i	−0.0986025	+	0.432006i
$834$	−46.9815	+	58.9130i	−1.62684	+	2.03999i
$835$	3.65910	−	16.0315i	0.126628	−	0.554794i
$836$	2.16857	−	9.50112i	0.0750015	−	0.328603i
$837$	8.71400	+	10.9270i	0.301200	+	0.377693i
$838$	−0.367293	−	1.60922i	−0.0126879	−	0.0555895i
$839$	2.27308	+	9.95903i	0.0784755	+	0.343824i	0.998889	−	0.0471223i	$-0.0150050\pi$
$839$	2.27308	+	9.95903i	0.0784755	+	0.343824i	−0.920414	+	0.390946i	$0.872148\pi$
$840$	24.4886	+	11.7931i	0.844938	+	0.406901i
$841$	1.12910	−	1.41585i	0.0389345	−	0.0488223i
$842$	9.98330	+	12.5187i	0.344047	+	0.431422i
$843$	51.5963	+	24.8475i	1.77707	+	0.855792i
$844$	−2.61337	+	3.27707i	−0.0899561	+	0.112801i
$845$	15.8061	+	7.61180i	0.543745	+	0.261854i
$846$	−31.8728	+	39.9672i	−1.09581	+	1.37410i
$847$	11.7491	−	5.65807i	0.403704	−	0.194414i
$848$	10.4940	+	5.05366i	0.360366	+	0.173543i
$849$	62.8212	−	30.2531i	2.15602	−	1.03828i
$850$	8.35079	−	10.4716i	0.286430	−	0.359171i
$851$	−5.10314	−	22.3583i	−0.174933	−	0.766433i
$852$	18.3870	+	8.85470i	0.629927	+	0.303357i
$853$	−3.95278	+	4.95663i	−0.135341	+	0.169712i	−0.844883	−	0.534951i	$-0.820330\pi$
$853$	−3.95278	+	4.95663i	−0.135341	+	0.169712i	0.709543	+	0.704663i	$0.248902\pi$
$854$	20.0642	−	9.66239i	0.686581	−	0.330640i
$855$	10.5677	−	46.3001i	0.361408	−	1.58343i
$856$	−11.2690			−0.385167
$857$	−20.8305			−0.711555			−0.355778	−	0.934571i	$-0.615784\pi$
$857$	−20.8305			−0.711555			−0.355778	+	0.934571i	$0.615784\pi$
$858$	27.1885	+	34.0933i	0.928199	+	1.16392i
$859$	2.70274	+	3.38913i	0.0922164	+	0.115636i	0.825799	−	0.563965i	$-0.190725\pi$
$859$	2.70274	+	3.38913i	0.0922164	+	0.115636i	−0.733582	+	0.679600i	$0.762153\pi$
$860$	11.3550	−	5.46830i	0.387204	−	0.186468i
$861$	−6.20194	+	27.1725i	−0.211361	+	0.926035i
$862$	−12.9852	−	56.8918i	−0.442277	−	1.93774i
$863$	3.54383	−	4.44382i	0.120633	−	0.151269i	−0.717848	−	0.696200i	$-0.754873\pi$
$863$	3.54383	−	4.44382i	0.120633	−	0.151269i	0.838481	+	0.544931i	$0.183444\pi$
$864$	5.34063	−	6.69694i	0.181692	−	0.227835i
$865$	−45.4093			−1.54396
$866$	0.842839	+	3.69272i	0.0286408	+	0.125484i
$867$	20.5492	−	25.7678i	0.697886	−	0.875121i
$868$	8.81025	−	11.0477i	0.299039	−	0.374983i
$869$	5.38007	−	23.5716i	0.182506	−	0.799612i
$870$	55.7657	+	26.8554i	1.89063	+	0.910482i
$871$	51.3433			1.73970
$872$	17.7015			0.599448
$873$	−5.32254	+	23.3196i	−0.180141	+	0.789248i
$874$	21.0063	−	26.3411i	0.710550	−	0.891002i
$875$	19.4490			0.657496
$876$	7.18061	+	31.4603i	0.242610	+	1.06295i
$877$	4.82653	+	2.32433i	0.162980	+	0.0784872i	0.513596	−	0.858032i	$-0.328313\pi$
$877$	4.82653	+	2.32433i	0.162980	+	0.0784872i	−0.350615	+	0.936520i	$0.614027\pi$
$878$	−5.01633	−	21.9780i	−0.169293	−	0.741721i
$879$	9.68805	−	42.4461i	0.326770	−	1.43167i
$880$	6.26889	−	27.4658i	0.211324	−	0.925872i
$881$	25.5158			0.859650			0.429825	−	0.902912i	$-0.358575\pi$
$881$	25.5158			0.859650			0.429825	+	0.902912i	$0.358575\pi$
$882$	−3.28681	−	14.4005i	−0.110673	−	0.484889i
$883$	15.2409	+	19.1115i	0.512897	+	0.643153i	0.969084	−	0.246731i	$-0.0793565\pi$
$883$	15.2409	+	19.1115i	0.512897	+	0.643153i	−0.456187	+	0.889884i	$0.650785\pi$
$884$	4.70931	+	20.6328i	0.158391	+	0.693957i
$885$	52.8882	+	66.3197i	1.77782	+	2.22931i
$886$	50.6556	+	24.3945i	1.70181	+	0.819548i
$887$	−34.3104	−	16.5230i	−1.15203	−	0.554789i	−0.242388	−	0.970179i	$-0.577931\pi$
$887$	−34.3104	−	16.5230i	−1.15203	−	0.554789i	−0.909643	+	0.415390i	$0.863645\pi$
$888$	−17.9465	−	22.5042i	−0.602244	−	0.755190i
$889$	9.01806	+	39.5107i	0.302456	+	1.32515i
$890$	−14.7586	−	18.5067i	−0.494709	−	0.620345i
$891$	−3.13927	−	13.7540i	−0.105169	−	0.460777i
$892$	−9.46958			−0.317065
$893$	−9.09060	+	39.8285i	−0.304205	+	1.33281i
$894$	16.5492	−	72.5067i	0.553488	−	2.42499i
$895$	−2.58979	−	11.3466i	−0.0865671	−	0.379275i
$896$	25.0146	+	12.0464i	0.835678	+	0.402442i
$897$	10.1700	+	44.5575i	0.339565	+	1.48773i
$898$	38.1375			1.27266
$899$	−26.0530	+	32.6694i	−0.868915	+	1.08959i
$900$	−1.04354	+	4.57203i	−0.0347845	+	0.152401i
$901$	−12.7419			−0.424495
$902$	18.7999			0.625968
$903$	−28.7282	−	13.8348i	−0.956014	−	0.460392i
$904$	−1.60736	+	7.04233i	−0.0534602	+	0.234224i
$905$	−10.0073	+	12.5488i	−0.332655	+	0.417136i
$906$	18.8450	−	23.6309i	0.626084	−	0.785084i
$907$	−0.655169	−	2.87048i	−0.0217545	−	0.0953129i	0.962885	−	0.269911i	$-0.0869944\pi$
$907$	−0.655169	−	2.87048i	−0.0217545	−	0.0953129i	−0.984640	+	0.174598i	$0.944137\pi$
$908$	−11.2551			−0.373512
$909$	−29.1332	+	36.5319i	−0.966288	+	1.21169i
$910$	25.8219	−	32.3796i	0.855986	−	1.07337i
$911$	4.90671	+	21.4977i	0.162567	+	0.712251i	0.988840	+	0.148981i	$0.0475995\pi$
$911$	4.90671	+	21.4977i	0.162567	+	0.712251i	−0.826273	+	0.563269i	$0.809543\pi$
$912$	14.4591	−	63.3495i	0.478789	−	2.09771i
$913$	4.53792	−	2.18535i	0.150183	−	0.0723245i
$914$	24.5859	+	30.8297i	0.813229	+	1.01976i
$915$	−25.0055	−	31.3559i	−0.826657	−	1.03660i
$916$	−8.73193			−0.288511
$917$	−27.0535			−0.893385
$918$	−3.81538	+	16.7163i	−0.125926	+	0.551719i
$919$	2.89054	−	1.39201i	0.0953502	−	0.0459182i	−0.385601	−	0.922666i	$-0.626006\pi$
$919$	2.89054	−	1.39201i	0.0953502	−	0.0459182i	0.480951	+	0.876747i	$0.340292\pi$
$920$	11.9805	−	15.0231i	0.394986	−	0.495297i
$921$	32.7796	+	15.7858i	1.08012	+	0.520160i
$922$	−13.9977	−	61.3281i	−0.460991	−	2.01973i
$923$	−25.1767	+	31.5706i	−0.828702	+	1.03916i
$924$	9.75642	−	4.69844i	0.320963	−	0.154567i
$925$	7.58139	+	3.65101i	0.249275	+	0.120044i
$926$	23.2693	−	11.2059i	0.764678	−	0.368249i
$927$	−9.89277	+	12.4051i	−0.324921	+	0.407438i
$928$	23.0735	+	11.1116i	0.757423	+	0.364756i
$929$	20.5290	−	25.7425i	0.673534	−	0.844585i	−0.321207	−	0.947009i	$-0.604088\pi$
$929$	20.5290	−	25.7425i	0.673534	−	0.844585i	0.994741	+	0.102424i	$0.0326598\pi$
$930$	−75.6293	−	36.4212i	−2.47998	−	1.19430i
$931$	−7.35977	−	9.22886i	−0.241207	−	0.302464i
$932$	−6.66083	+	8.35242i	−0.218183	+	0.273593i
$933$	35.8614	+	17.2700i	1.17405	+	0.565393i
$934$	−13.4284	−	58.8338i	−0.439391	−	1.92510i
$935$	6.85794	+	30.0466i	0.224279	+	0.982629i
$936$	19.7900	+	24.8159i	0.646856	+	0.811132i
$937$	−1.60020	+	7.01096i	−0.0522764	+	0.229038i	−0.994317	−	0.106461i	$-0.966048\pi$
$937$	−1.60020	+	7.01096i	−0.0522764	+	0.229038i	0.942040	+	0.335499i	$0.108905\pi$
$938$	9.35849	−	41.0022i	0.305565	−	1.33877i
$939$	28.4068	−	35.6210i	0.927021	−	1.16245i
$940$	3.99256	−	17.4926i	0.130223	−	0.570545i
$941$	4.58006	−	20.0665i	0.149306	−	0.654150i	−0.843773	−	0.536700i	$-0.819671\pi$
$941$	4.58006	−	20.0665i	0.149306	−	0.654150i	0.993079	−	0.117450i	$-0.0374721\pi$
$942$	−49.9055	+	24.0332i	−1.62601	+	0.783045i
$943$	17.7524	+	8.54913i	0.578099	+	0.278398i
$944$	40.0410	+	50.2098i	1.30322	+	1.63419i
$945$	9.16479	−	4.41353i	0.298131	−	0.143572i
$946$	−4.78595	+	20.9686i	−0.155605	+	0.681749i
$947$	19.5479	−	9.41379i	0.635222	−	0.305907i	−0.0884188	−	0.996083i	$-0.528181\pi$
$947$	19.5479	−	9.41379i	0.635222	−	0.305907i	0.723641	+	0.690176i	$0.242467\pi$
$948$	−5.45002	+	23.8781i	−0.177008	+	0.775524i
$949$	−63.8499			−2.07266
$950$	2.75084	+	12.0522i	0.0892489	+	0.391025i
$951$	−54.2281	−	26.1149i	−1.75847	−	0.846832i
$952$	−22.5115			−0.729600
$953$	4.35401	+	5.45976i	0.141040	+	0.176859i	0.847335	−	0.531059i	$-0.178206\pi$
$953$	4.35401	+	5.45976i	0.141040	+	0.176859i	−0.706294	+	0.707918i	$0.749634\pi$
$954$	13.2590	−	6.38518i	0.429275	−	0.206728i
$955$	−34.3656	−	43.0931i	−1.11204	−	1.39446i
$956$	5.08355	−	2.44811i	0.164414	−	0.0791775i
$957$	−28.8509	+	13.8939i	−0.932617	+	0.449125i
$958$	12.9190	+	56.6020i	0.417395	+	1.82873i
$959$	−4.71942	−	5.91796i	−0.152398	−	0.191101i
$960$	3.14893	−	13.7964i	0.101631	−	0.445276i
$961$	16.0048	−	20.0694i	0.516283	−	0.647399i
$962$	−39.5151	+	19.0295i	−1.27402	+	0.613534i
$963$	−13.6411	+	17.1054i	−0.439578	+	0.551213i
$964$	10.1330	+	12.7064i	0.326362	+	0.409245i
$965$	−27.9154			−0.898628
$966$	37.4369			1.20451
$967$	−28.2614	−	13.6100i	−0.908826	−	0.437668i	−0.0797574	−	0.996814i	$-0.525415\pi$
$967$	−28.2614	−	13.6100i	−0.908826	−	0.437668i	−0.829069	+	0.559147i	$0.811129\pi$
$968$	−7.21439	−	9.04656i	−0.231879	−	0.290768i
$969$	15.8177	+	69.3020i	0.508139	+	2.22630i
$970$	−6.16220	−	26.9984i	−0.197856	−	0.866865i
$971$	0.307756			0.00987637			0.00493818	−	0.999988i	$-0.498428\pi$
$971$	0.307756			0.00987637			0.00493818	+	0.999988i	$0.498428\pi$
$972$	4.25848	+	18.6576i	0.136591	+	0.598443i
$973$	−33.3582	+	16.0645i	−1.06941	+	0.515003i
$974$	−41.8243	+	20.1415i	−1.34014	+	0.645377i
$975$	−15.1088	−	7.27603i	−0.483870	−	0.233019i
$976$	−18.9314	−	23.7392i	−0.605978	−	0.759873i
$977$	−11.7565	+	51.5084i	−0.376122	+	1.64790i	0.333084	+	0.942897i	$0.391911\pi$
$977$	−11.7565	+	51.5084i	−0.376122	+	1.64790i	−0.709206	+	0.705002i	$0.750946\pi$
$978$	−90.0664	−	43.3737i	−2.88000	−	1.38694i
$979$	12.2464			0.391396
$980$	3.23239	+	4.05329i	0.103255	+	0.129478i
$981$	21.4276	−	26.8693i	0.684129	−	0.857871i
$982$	1.98103	+	0.954015i	0.0632173	+	0.0304438i
$983$	−26.6212	+	12.8201i	−0.849084	+	0.408897i	−0.807237	−	0.590227i	$-0.799038\pi$
$983$	−26.6212	+	12.8201i	−0.849084	+	0.408897i	−0.0418464	+	0.999124i	$0.513324\pi$
$984$	24.7304			0.788377
$985$	−25.3617	−	25.0496i	−0.808091	−	0.798148i
$986$	−51.2633			−1.63256
$987$	−40.8987	+	19.6958i	−1.30182	+	0.626924i
$988$	−17.5991	−	8.47530i	−0.559903	−	0.269635i
$989$	−14.0546	+	17.6240i	−0.446912	+	0.560409i
$990$	−22.1930	−	27.8292i	−0.705341	−	0.884470i
$991$	−19.1025			−0.606810			−0.303405	−	0.952862i	$-0.598123\pi$
$991$	−19.1025			−0.606810			−0.303405	+	0.952862i	$0.598123\pi$
$992$	−31.2922	−	15.0695i	−0.993527	−	0.478458i
$993$	−3.96536	+	17.3734i	−0.125837	+	0.551328i
$994$	20.6229	+	25.8604i	0.654120	+	0.820241i
$995$	42.2329	+	20.3383i	1.33887	+	0.644768i
$996$	−4.59692	+	2.21376i	−0.145659	+	0.0701457i
$997$	1.11712	−	0.537976i	0.0353795	−	0.0170379i	−0.416110	−	0.909314i	$-0.636607\pi$
$997$	1.11712	−	0.537976i	0.0353795	−	0.0170379i	0.451490	+	0.892276i	$0.350893\pi$
$998$	−9.75154	−	42.7243i	−0.308680	−	1.35241i
$999$	−10.7723			−0.340820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.2.d.a.36.12	✓	90
197.104	even	7	inner	197.2.d.a.104.12	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.2.d.a.36.12	✓	90	1.1	even	1	trivial
197.2.d.a.104.12	yes	90	197.104	even	7	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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	197.d (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.52637 - 0.735059i) q^{2} +(-2.33495 - 1.12445i) q^{3} +(0.542502 - 0.680276i) q^{4} +(-1.58350 - 1.98564i) q^{5} -4.39053 q^{6} +(-1.94366 - 0.936020i) q^{7} +(-0.425949 + 1.86621i) q^{8} +(2.31713 + 2.90559i) q^{9} +(-3.87657 - 1.86686i) q^{10} +(2.00558 - 0.965835i) q^{11} +(-2.03165 + 0.978392i) q^{12} +(-0.992842 - 4.34992i) q^{13} -3.65477 q^{14} +(1.46463 + 6.41695i) q^{15} +(1.10885 + 4.85819i) q^{16} +(-3.39887 - 4.26205i) q^{17} +(5.67256 + 2.73176i) q^{18} +5.03154 q^{19} -2.20984 q^{20} +(3.48585 + 4.37112i) q^{21} +(2.35130 - 2.94844i) q^{22} +(3.56108 - 1.71492i) q^{23} +(3.09303 - 3.87854i) q^{24} +(-0.322712 + 1.41389i) q^{25} +(-4.71289 - 5.90978i) q^{26} +(-0.413127 - 1.81003i) q^{27} +(-1.69119 + 0.814436i) q^{28} +(5.00106 - 2.40838i) q^{29} +(6.95239 + 8.71803i) q^{30} +(-6.78243 + 3.26624i) q^{31} +(2.87660 + 3.60715i) q^{32} -5.76896 q^{33} +(-8.32078 - 4.00707i) q^{34} +(1.21919 + 5.34161i) q^{35} +3.23364 q^{36} +(1.29112 - 5.65676i) q^{37} +(7.67997 - 3.69848i) q^{38} +(-2.57305 + 11.2733i) q^{39} +(4.38011 - 2.10935i) q^{40} +(3.10818 + 3.89754i) q^{41} +(8.53371 + 4.10962i) q^{42} +(-5.13841 + 2.47453i) q^{43} +(0.430995 - 1.88831i) q^{44} +(2.10029 - 9.20198i) q^{45} +(4.17493 - 5.23520i) q^{46} +(-1.80672 + 7.91577i) q^{47} +(2.87369 - 12.5905i) q^{48} +(-1.46273 - 1.83420i) q^{49} +(0.546719 + 2.39533i) q^{50} +(3.14372 + 13.7735i) q^{51} +(-3.49777 - 1.68444i) q^{52} +(1.45734 - 1.82744i) q^{53} +(-1.96106 - 2.45909i) q^{54} +(-5.09363 - 2.45296i) q^{55} +(2.57471 - 3.22858i) q^{56} +(-11.7484 - 5.65773i) q^{57} +(5.86315 - 7.35215i) q^{58} +(11.6114 - 5.59174i) q^{59} +(5.15986 + 2.48486i) q^{60} +(-5.48985 + 2.64377i) q^{61} +(-7.95158 + 9.97097i) q^{62} +(-1.78403 - 7.81636i) q^{63} +(-1.93707 - 0.932845i) q^{64} +(-7.06524 + 8.85953i) q^{65} +(-8.80554 + 4.24052i) q^{66} +(-2.56062 + 11.2188i) q^{67} -4.74326 q^{68} -10.2433 q^{69} +(5.78733 + 7.25708i) q^{70} +(-5.64274 - 7.07577i) q^{71} +(-6.40940 + 3.08660i) q^{72} +(3.18436 - 13.9516i) q^{73} +(-2.18733 - 9.58333i) q^{74} +(2.34337 - 2.93850i) q^{75} +(2.72962 - 3.42283i) q^{76} -4.80221 q^{77} +(4.35910 + 19.0985i) q^{78} +(6.77200 - 8.49181i) q^{79} +(7.89078 - 9.89472i) q^{80} +(1.41026 - 6.17875i) q^{81} +(7.60914 + 3.66437i) q^{82} +2.26265 q^{83} +4.86465 q^{84} +(-3.08081 + 13.4979i) q^{85} +(-6.02417 + 7.55407i) q^{86} -14.3853 q^{87} +(0.948172 + 4.15421i) q^{88} +(4.95665 + 2.38699i) q^{89} +(-3.55819 - 15.5894i) q^{90} +(-2.14186 + 9.38411i) q^{91} +(0.765269 - 3.35286i) q^{92} +19.5094 q^{93} +(3.06084 + 13.4104i) q^{94} +(-7.96743 - 9.99085i) q^{95} +(-2.66066 - 11.6571i) q^{96} +(4.01289 + 5.03200i) q^{97} +(-3.58091 - 1.72447i) q^{98} +(7.45349 + 3.58941i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 2 q^{2} - 5 q^{3} - 26 q^{4} + q^{5} - 10 q^{6} - 11 q^{7} - 16 q^{9} + 9 q^{10} - 7 q^{11} + 15 q^{12} + 9 q^{13} - 40 q^{14} - 16 q^{15} - 10 q^{16} + 13 q^{17} + 15 q^{18} - 20 q^{19} + 26 q^{20}+ \cdots + 25 q^{99}+O(q^{100}) \) 90 * q - 2 * q^2 - 5 * q^3 - 26 * q^4 + q^5 - 10 * q^6 - 11 * q^7 - 16 * q^9 + 9 * q^10 - 7 * q^11 + 15 * q^12 + 9 * q^13 - 40 * q^14 - 16 * q^15 - 10 * q^16 + 13 * q^17 + 15 * q^18 - 20 * q^19 + 26 * q^20 + 13 * q^21 - 17 * q^22 + 25 * q^23 - 17 * q^24 + 16 * q^25 - 2 * q^26 - 41 * q^27 - 50 * q^28 - 33 * q^29 - 72 * q^30 - 15 * q^31 + 46 * q^32 - 32 * q^33 + 31 * q^34 + 45 * q^35 - 64 * q^36 - 27 * q^37 + 43 * q^38 + 14 * q^39 + 31 * q^40 + 35 * q^41 + 14 * q^42 + 16 * q^43 + 49 * q^44 - 8 * q^45 + 17 * q^46 - 4 * q^47 + 41 * q^48 - 48 * q^49 - 52 * q^50 + 51 * q^51 - 2 * q^52 + 41 * q^53 + 14 * q^54 + 53 * q^55 + 52 * q^56 - 104 * q^57 - 79 * q^58 - 17 * q^59 + 11 * q^60 + 21 * q^61 + 23 * q^62 + 48 * q^63 + 22 * q^64 + 5 * q^65 - 94 * q^66 - 5 * q^67 - 200 * q^68 + 54 * q^69 + 64 * q^70 - 94 * q^71 + 75 * q^72 + 31 * q^73 + 18 * q^74 + 36 * q^75 - 80 * q^76 + 22 * q^77 - 45 * q^78 - 25 * q^79 + 131 * q^80 + 6 * q^81 + 51 * q^82 - 130 * q^83 + 108 * q^84 - 129 * q^85 + 32 * q^86 + 98 * q^87 + 54 * q^88 + 17 * q^89 - 42 * q^90 - 119 * q^91 + 31 * q^92 + 60 * q^93 - 111 * q^94 - 77 * q^95 - 98 * q^96 + 49 * q^97 + 45 * q^98 + 25 * q^99

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