LMFDB - Embedded newform 164.3.c.a.83.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [164,3,Mod(83,164)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(164, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("164.83");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 164 = 2^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	164.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.46867633551$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			83.23
Character	$\chi$	$=$	164.83
Dual form			164.3.c.a.83.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.384629 - 1.96267i) q^{2} -4.91252i q^{3} +(-3.70412 - 1.50980i) q^{4} +1.34854 q^{5} +(-9.64164 - 1.88950i) q^{6} -2.68078i q^{7} +(-4.38794 + 6.68924i) q^{8} -15.1329 q^{9} +O(q^{10})$	\(q+(0.384629 - 1.96267i) q^{2} -4.91252i q^{3} +(-3.70412 - 1.50980i) q^{4} +1.34854 q^{5} +(-9.64164 - 1.88950i) q^{6} -2.68078i q^{7} +(-4.38794 + 6.68924i) q^{8} -15.1329 q^{9} +(0.518686 - 2.64673i) q^{10} -4.05219i q^{11} +(-7.41692 + 18.1966i) q^{12} +18.6332 q^{13} +(-5.26147 - 1.03111i) q^{14} -6.62471i q^{15} +(11.4410 + 11.1850i) q^{16} -4.56320 q^{17} +(-5.82054 + 29.7007i) q^{18} +3.17732i q^{19} +(-4.99514 - 2.03602i) q^{20} -13.1694 q^{21} +(-7.95311 - 1.55859i) q^{22} +5.32782i q^{23} +(32.8610 + 21.5559i) q^{24} -23.1815 q^{25} +(7.16688 - 36.5708i) q^{26} +30.1278i q^{27} +(-4.04743 + 9.92992i) q^{28} +37.2786 q^{29} +(-13.0021 - 2.54806i) q^{30} -30.8219i q^{31} +(26.3529 - 18.1528i) q^{32} -19.9065 q^{33} +(-1.75514 + 8.95604i) q^{34} -3.61512i q^{35} +(56.0539 + 22.8476i) q^{36} -57.0093 q^{37} +(6.23603 + 1.22209i) q^{38} -91.5360i q^{39} +(-5.91730 + 9.02068i) q^{40} +6.40312 q^{41} +(-5.06533 + 25.8471i) q^{42} -50.7037i q^{43} +(-6.11800 + 15.0098i) q^{44} -20.4072 q^{45} +(10.4567 + 2.04924i) q^{46} +1.85824i q^{47} +(54.9463 - 56.2042i) q^{48} +41.8134 q^{49} +(-8.91627 + 45.4975i) q^{50} +22.4168i q^{51} +(-69.0196 - 28.1324i) q^{52} -33.3846 q^{53} +(59.1307 + 11.5880i) q^{54} -5.46453i q^{55} +(17.9324 + 11.7631i) q^{56} +15.6087 q^{57} +(14.3384 - 73.1655i) q^{58} -44.9156i q^{59} +(-10.0020 + 24.5387i) q^{60} +97.4235 q^{61} +(-60.4931 - 11.8550i) q^{62} +40.5678i q^{63} +(-25.4919 - 58.7040i) q^{64} +25.1275 q^{65} +(-7.65662 + 39.0698i) q^{66} +84.8144i q^{67} +(16.9026 + 6.88951i) q^{68} +26.1730 q^{69} +(-7.09528 - 1.39048i) q^{70} +81.7255i q^{71} +(66.4021 - 101.227i) q^{72} +88.4940 q^{73} +(-21.9275 + 111.890i) q^{74} +113.879i q^{75} +(4.79712 - 11.7692i) q^{76} -10.8630 q^{77} +(-179.655 - 35.2074i) q^{78} -136.840i q^{79} +(15.4286 + 15.0833i) q^{80} +11.8075 q^{81} +(2.46283 - 12.5672i) q^{82} +62.8608i q^{83} +(48.7809 + 19.8831i) q^{84} -6.15363 q^{85} +(-99.5145 - 19.5021i) q^{86} -183.132i q^{87} +(27.1061 + 17.7808i) q^{88} +151.228 q^{89} +(-7.84921 + 40.0525i) q^{90} -49.9515i q^{91} +(8.04394 - 19.7349i) q^{92} -151.413 q^{93} +(3.64711 + 0.714734i) q^{94} +4.28474i q^{95} +(-89.1762 - 129.459i) q^{96} +20.4652 q^{97} +(16.0827 - 82.0658i) q^{98} +61.3213i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} - 2 q^{4} + 12 q^{6} + 10 q^{8} - 120 q^{9}+O(q^{10}) $ 40 * q - 2 * q^2 - 2 * q^4 + 12 * q^6 + 10 * q^8 - 120 * q^9	$ 40 q - 2 q^{2} - 2 q^{4} + 12 q^{6} + 10 q^{8} - 120 q^{9} - 20 q^{10} + 10 q^{12} - 16 q^{13} + 36 q^{14} - 42 q^{16} - 34 q^{18} + 8 q^{20} + 48 q^{21} - 38 q^{22} + 52 q^{24} + 216 q^{25} + 54 q^{26} - 54 q^{28} - 32 q^{29} + 66 q^{30} - 2 q^{32} - 48 q^{33} - 124 q^{34} - 70 q^{36} + 16 q^{37} - 140 q^{38} + 16 q^{40} + 88 q^{42} + 100 q^{44} - 48 q^{45} + 196 q^{46} + 78 q^{48} - 152 q^{49} + 198 q^{50} + 26 q^{52} - 32 q^{53} - 74 q^{54} + 96 q^{56} - 112 q^{57} + 38 q^{58} - 102 q^{60} + 96 q^{61} - 112 q^{62} + 70 q^{64} - 96 q^{65} - 528 q^{66} - 148 q^{68} - 80 q^{69} - 82 q^{70} - 458 q^{72} + 128 q^{73} + 372 q^{74} - 50 q^{76} + 192 q^{77} + 144 q^{78} - 100 q^{80} + 520 q^{81} + 344 q^{84} - 176 q^{85} - 460 q^{86} + 66 q^{88} + 16 q^{89} + 80 q^{90} + 572 q^{92} + 32 q^{93} + 262 q^{94} - 304 q^{96} - 304 q^{97} + 174 q^{98}+O(q^{100}) $ 40 * q - 2 * q^2 - 2 * q^4 + 12 * q^6 + 10 * q^8 - 120 * q^9 - 20 * q^10 + 10 * q^12 - 16 * q^13 + 36 * q^14 - 42 * q^16 - 34 * q^18 + 8 * q^20 + 48 * q^21 - 38 * q^22 + 52 * q^24 + 216 * q^25 + 54 * q^26 - 54 * q^28 - 32 * q^29 + 66 * q^30 - 2 * q^32 - 48 * q^33 - 124 * q^34 - 70 * q^36 + 16 * q^37 - 140 * q^38 + 16 * q^40 + 88 * q^42 + 100 * q^44 - 48 * q^45 + 196 * q^46 + 78 * q^48 - 152 * q^49 + 198 * q^50 + 26 * q^52 - 32 * q^53 - 74 * q^54 + 96 * q^56 - 112 * q^57 + 38 * q^58 - 102 * q^60 + 96 * q^61 - 112 * q^62 + 70 * q^64 - 96 * q^65 - 528 * q^66 - 148 * q^68 - 80 * q^69 - 82 * q^70 - 458 * q^72 + 128 * q^73 + 372 * q^74 - 50 * q^76 + 192 * q^77 + 144 * q^78 - 100 * q^80 + 520 * q^81 + 344 * q^84 - 176 * q^85 - 460 * q^86 + 66 * q^88 + 16 * q^89 + 80 * q^90 + 572 * q^92 + 32 * q^93 + 262 * q^94 - 304 * q^96 - 304 * q^97 + 174 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/164\mathbb{Z}\right)^\times$.

$n$	$83$	$129$
$\chi(n)$	$-1$	$1$

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 $

$2$	0.384629	−	1.96267i	0.192315	−	0.981333i
$2$	0.384629	−	1.96267i	0.192315	−	0.981333i
$3$		−	4.91252i		−	1.63751i	−0.574145	−	0.818753i	$-0.694666\pi$
$3$		−	4.91252i		−	1.63751i	0.574145	−	0.818753i	$-0.305334\pi$
$4$	−3.70412	−	1.50980i	−0.926030	−	0.377450i
$5$	1.34854			0.269707			0.134854	−	0.990866i	$-0.456944\pi$
$5$	1.34854			0.269707			0.134854	+	0.990866i	$0.456944\pi$
$6$	−9.64164	−	1.88950i	−1.60694	−	0.314917i
$7$		−	2.68078i		−	0.382968i	−0.981496	−	0.191484i	$-0.938670\pi$
$7$		−	2.68078i		−	0.382968i	0.981496	−	0.191484i	$-0.0613300\pi$
$8$	−4.38794	+	6.68924i	−0.548493	+	0.836155i
$9$	−15.1329			−1.68143
$10$	0.518686	−	2.64673i	0.0518686	−	0.264673i
$11$		−	4.05219i		−	0.368381i	−0.982891	−	0.184191i	$-0.941034\pi$
$11$		−	4.05219i		−	0.368381i	0.982891	−	0.184191i	$-0.0589664\pi$
$12$	−7.41692	+	18.1966i	−0.618076	+	1.51638i
$13$	18.6332			1.43332			0.716661	−	0.697421i	$-0.245669\pi$
$13$	18.6332			1.43332			0.716661	+	0.697421i	$0.245669\pi$
$14$	−5.26147	−	1.03111i	−0.375819	−	0.0736504i
$15$		−	6.62471i		−	0.441647i
$16$	11.4410	+	11.1850i	0.715064	+	0.699059i
$17$	−4.56320			−0.268423			−0.134212	−	0.990953i	$-0.542850\pi$
$17$	−4.56320			−0.268423			−0.134212	+	0.990953i	$0.542850\pi$
$18$	−5.82054	+	29.7007i	−0.323363	+	1.65004i
$19$			3.17732i			0.167228i	0.996498	+	0.0836138i	$0.0266462\pi$
$19$			3.17732i			0.167228i	−0.996498	+	0.0836138i	$0.973354\pi$
$20$	−4.99514	−	2.03602i	−0.249757	−	0.101801i
$21$	−13.1694			−0.627113
$22$	−7.95311	−	1.55859i	−0.361505	−	0.0708451i
$23$			5.32782i			0.231645i	0.993270	+	0.115822i	$0.0369503\pi$
$23$			5.32782i			0.231645i	−0.993270	+	0.115822i	$0.963050\pi$
$24$	32.8610	+	21.5559i	1.36921	+	0.898161i
$25$	−23.1815			−0.927258
$26$	7.16688	−	36.5708i	0.275649	−	1.40657i
$27$			30.1278i			1.11584i
$28$	−4.04743	+	9.92992i	−0.144551	+	0.354640i
$29$	37.2786			1.28547			0.642734	−	0.766089i	$-0.277800\pi$
$29$	37.2786			1.28547			0.642734	+	0.766089i	$0.277800\pi$
$30$	−13.0021	−	2.54806i	−0.433403	−	0.0849353i
$31$		−	30.8219i		−	0.994255i	−0.867677	−	0.497128i	$-0.834388\pi$
$31$		−	30.8219i		−	0.994255i	0.867677	−	0.497128i	$-0.165612\pi$
$32$	26.3529	−	18.1528i	0.823528	−	0.567276i
$33$	−19.9065			−0.603227
$34$	−1.75514	+	8.95604i	−0.0516218	+	0.263413i
$35$		−	3.61512i		−	0.103289i
$36$	56.0539	+	22.8476i	1.55705	+	0.634654i
$37$	−57.0093			−1.54079			−0.770396	−	0.637565i	$-0.779942\pi$
$37$	−57.0093			−1.54079			−0.770396	+	0.637565i	$0.779942\pi$
$38$	6.23603	+	1.22209i	0.164106	+	0.0321603i
$39$		−	91.5360i		−	2.34708i
$40$	−5.91730	+	9.02068i	−0.147933	+	0.225517i
$41$	6.40312			0.156174
$41$	6.40312			0.156174
$42$	−5.06533	+	25.8471i	−0.120603	+	0.615407i
$43$		−	50.7037i		−	1.17916i	−0.807711	−	0.589578i	$-0.799294\pi$
$43$		−	50.7037i		−	1.17916i	0.807711	−	0.589578i	$-0.200706\pi$
$44$	−6.11800	+	15.0098i	−0.139045	+	0.341132i
$45$	−20.4072			−0.453493
$46$	10.4567	+	2.04924i	0.227320	+	0.0445486i
$47$			1.85824i			0.0395370i	0.999805	+	0.0197685i	$0.00629292\pi$
$47$			1.85824i			0.0395370i	−0.999805	+	0.0197685i	$0.993707\pi$
$48$	54.9463	−	56.2042i	1.14471	−	1.17092i
$49$	41.8134			0.853335
$50$	−8.91627	+	45.4975i	−0.178325	+	0.909949i
$51$			22.4168i			0.439545i
$52$	−69.0196	−	28.1324i	−1.32730	−	0.541007i
$53$	−33.3846			−0.629899			−0.314950	−	0.949108i	$-0.601988\pi$
$53$	−33.3846			−0.629899			−0.314950	+	0.949108i	$0.601988\pi$
$54$	59.1307	+	11.5880i	1.09501	+	0.214593i
$55$		−	5.46453i		−	0.0993551i
$56$	17.9324	+	11.7631i	0.320221	+	0.210055i
$57$	15.6087			0.273836
$58$	14.3384	−	73.1655i	0.247215	−	1.26147i
$59$		−	44.9156i		−	0.761282i	−0.924723	−	0.380641i	$-0.875703\pi$
$59$		−	44.9156i		−	0.761282i	0.924723	−	0.380641i	$-0.124297\pi$
$60$	−10.0020	+	24.5387i	−0.166700	+	0.408979i
$61$	97.4235			1.59711			0.798553	−	0.601924i	$-0.205599\pi$
$61$	97.4235			1.59711			0.798553	+	0.601924i	$0.205599\pi$
$62$	−60.4931	−	11.8550i	−0.975696	−	0.191210i
$63$			40.5678i			0.643933i
$64$	−25.4919	−	58.7040i	−0.398311	−	0.917251i
$65$	25.1275			0.386577
$66$	−7.65662	+	39.0698i	−0.116009	+	0.591967i
$67$			84.8144i			1.26589i	0.774198	+	0.632943i	$0.218153\pi$
$67$			84.8144i			1.26589i	−0.774198	+	0.632943i	$0.781847\pi$
$68$	16.9026	+	6.88951i	0.248568	+	0.101316i
$69$	26.1730			0.379319
$70$	−7.09528	−	1.39048i	−0.101361	−	0.0198640i
$71$			81.7255i			1.15106i	0.817780	+	0.575532i	$0.195205\pi$
$71$			81.7255i			1.15106i	−0.817780	+	0.575532i	$0.804795\pi$
$72$	66.4021	−	101.227i	0.922252	−	1.40593i
$73$	88.4940			1.21225			0.606123	−	0.795371i	$-0.292724\pi$
$73$	88.4940			1.21225			0.606123	+	0.795371i	$0.292724\pi$
$74$	−21.9275	+	111.890i	−0.296317	+	1.51203i
$75$			113.879i			1.51839i
$76$	4.79712	−	11.7692i	0.0631200	−	0.154858i
$77$	−10.8630			−0.141078
$78$	−179.655	−	35.2074i	−2.30326	−	0.451377i
$79$		−	136.840i		−	1.73215i	−0.499911	−	0.866077i	$-0.666634\pi$
$79$		−	136.840i		−	1.73215i	0.499911	−	0.866077i	$-0.333366\pi$
$80$	15.4286	+	15.0833i	0.192858	+	0.188541i
$81$	11.8075			0.145772
$82$	2.46283	−	12.5672i	0.0300345	−	0.153259i
$83$			62.8608i			0.757359i	0.925528	+	0.378679i	$0.123622\pi$
$83$			62.8608i			0.757359i	−0.925528	+	0.378679i	$0.876378\pi$
$84$	48.7809	+	19.8831i	0.580725	+	0.236704i
$85$	−6.15363			−0.0723957
$86$	−99.5145	−	19.5021i	−1.15715	−	0.226769i
$87$		−	183.132i		−	2.10496i
$88$	27.1061	+	17.7808i	0.308024	+	0.202055i
$89$	151.228			1.69920			0.849598	−	0.527430i	$-0.176844\pi$
$89$	151.228			1.69920			0.849598	+	0.527430i	$0.176844\pi$
$90$	−7.84921	+	40.0525i	−0.0872134	+	0.445028i
$91$		−	49.9515i		−	0.548917i
$92$	8.04394	−	19.7349i	0.0874341	−	0.214510i
$93$	−151.413			−1.62810
$94$	3.64711	+	0.714734i	0.0387990	+	0.00760355i
$95$			4.28474i			0.0451025i
$96$	−89.1762	−	129.459i	−0.928919	−	1.34853i
$97$	20.4652			0.210982			0.105491	−	0.994420i	$-0.466359\pi$
$97$	20.4652			0.210982			0.105491	+	0.994420i	$0.466359\pi$
$98$	16.0827	−	82.0658i	0.164109	−	0.837406i
$99$			61.3213i			0.619407i
$100$	85.8669	+	34.9993i	0.858669	+	0.349993i
$101$	−110.609			−1.09514			−0.547568	−	0.836761i	$-0.684446\pi$
$101$	−110.609			−1.09514			−0.547568	+	0.836761i	$0.684446\pi$
$102$	43.9967	+	8.62216i	0.431340	+	0.0845310i
$103$			106.441i			1.03341i	0.856164	+	0.516704i	$0.172841\pi$
$103$			106.441i			1.03341i	−0.856164	+	0.516704i	$0.827159\pi$
$104$	−81.7614	+	124.642i	−0.786168	+	1.19848i
$105$	−17.7594			−0.169137
$106$	−12.8407	+	65.5229i	−0.121139	+	0.618141i
$107$			180.767i			1.68941i	0.535234	+	0.844704i	$0.320223\pi$
$107$			180.767i			1.68941i	−0.535234	+	0.844704i	$0.679777\pi$
$108$	45.4868	−	111.597i	0.421174	−	1.03330i
$109$	11.6117			0.106529			0.0532645	−	0.998580i	$-0.483037\pi$
$109$	11.6117			0.106529			0.0532645	+	0.998580i	$0.483037\pi$
$110$	−10.7250	−	2.10182i	−0.0975004	−	0.0191074i
$111$			280.059i			2.52306i
$112$	29.9844	−	30.6708i	0.267718	−	0.273847i
$113$	18.3746			0.162607			0.0813035	−	0.996689i	$-0.474092\pi$
$113$	18.3746			0.162607			0.0813035	+	0.996689i	$0.474092\pi$
$114$	6.00355	−	30.6346i	0.0526627	−	0.268725i
$115$			7.18476i			0.0624762i
$116$	−138.084	−	56.2832i	−1.19038	−	0.485200i
$117$	−281.973			−2.41003
$118$	−88.1544	−	17.2759i	−0.747071	−	0.146406i
$119$			12.2329i			0.102798i
$120$	44.3143	+	29.0689i	0.369286	+	0.242240i
$121$	104.580			0.864295
$122$	37.4720	−	191.210i	0.307147	−	1.56729i
$123$		−	31.4555i		−	0.255736i
$124$	−46.5349	+	114.168i	−0.375281	+	0.920710i
$125$	−64.9744			−0.519795
$126$	79.6211	+	15.6036i	0.631913	+	0.123838i
$127$		−	170.624i		−	1.34350i	−0.740779	−	0.671749i	$-0.765544\pi$
$127$		−	170.624i		−	1.34350i	0.740779	−	0.671749i	$-0.234456\pi$
$128$	−125.021	+	27.4528i	−0.976730	+	0.214475i
$129$	−249.083			−1.93088
$130$	9.66479	−	49.3170i	0.0743445	−	0.379361i
$131$			223.278i			1.70442i	0.523203	+	0.852208i	$0.324737\pi$
$131$			223.278i			1.70442i	−0.523203	+	0.852208i	$0.675263\pi$
$132$	73.7360	+	30.0548i	0.558606	+	0.227688i
$133$	8.51770			0.0640429
$134$	166.462	+	32.6221i	1.24226	+	0.243448i
$135$			40.6284i			0.300951i
$136$	20.0231	−	30.5243i	0.147228	−	0.224444i
$137$	−93.9380			−0.685679			−0.342839	−	0.939394i	$-0.611389\pi$
$137$	−93.9380			−0.685679			−0.342839	+	0.939394i	$0.611389\pi$
$138$	10.0669	−	51.3690i	0.0729487	−	0.372239i
$139$			102.855i			0.739967i	0.929038	+	0.369983i	$0.120637\pi$
$139$			102.855i			0.739967i	−0.929038	+	0.369983i	$0.879363\pi$
$140$	−5.45811	+	13.3909i	−0.0389865	+	0.0956490i
$141$	9.12864			0.0647421
$142$	160.400	+	31.4340i	1.12958	+	0.221366i
$143$		−	75.5054i		−	0.528009i
$144$	−173.135	−	169.260i	−1.20233	−	1.17542i
$145$	50.2715			0.346700
$146$	34.0374	−	173.684i	0.233133	−	1.18962i
$147$		−	205.409i		−	1.39734i
$148$	211.169	+	86.0726i	1.42682	+	0.581572i
$149$	220.572			1.48035			0.740175	−	0.672414i	$-0.234742\pi$
$149$	220.572			1.48035			0.740175	+	0.672414i	$0.234742\pi$
$150$	223.507	+	43.8013i	1.49005	+	0.292009i
$151$		−	141.013i		−	0.933863i	−0.884294	−	0.466931i	$-0.845360\pi$
$151$		−	141.013i		−	0.933863i	0.884294	−	0.466931i	$-0.154640\pi$
$152$	−21.2539	−	13.9419i	−0.139828	−	0.0917232i
$153$	69.0542			0.451335
$154$	−4.17824	+	21.3205i	−0.0271314	+	0.138445i
$155$		−	41.5644i		−	0.268158i
$156$	−138.201	+	339.060i	−0.885903	+	2.17346i
$157$	68.6874			0.437500			0.218750	−	0.975781i	$-0.429802\pi$
$157$	68.6874			0.437500			0.218750	+	0.975781i	$0.429802\pi$
$158$	−268.572	−	52.6328i	−1.69982	−	0.333119i
$159$			164.003i			1.03146i
$160$	35.5378	−	24.4798i	0.222111	−	0.152998i
$161$	14.2827			0.0887125
$162$	4.54152	−	23.1743i	0.0280341	−	0.143051i
$163$		−	190.339i		−	1.16773i	−0.811852	−	0.583863i	$-0.801541\pi$
$163$		−	190.339i		−	1.16773i	0.811852	−	0.583863i	$-0.198459\pi$
$164$	−23.7179	−	9.66743i	−0.144622	−	0.0589477i
$165$	−26.8446			−0.162695
$166$	123.375	+	24.1781i	0.743221	+	0.145651i
$167$			35.5890i			0.213108i	0.994307	+	0.106554i	$0.0339817\pi$
$167$			35.5890i			0.213108i	−0.994307	+	0.106554i	$0.966018\pi$
$168$	57.7865	−	88.0931i	0.343967	−	0.524364i
$169$	178.196			1.05441
$170$	−2.36687	+	12.0775i	−0.0139228	+	0.0710443i
$171$		−	48.0820i		−	0.281181i
$172$	−76.5524	+	187.813i	−0.445072	+	1.09193i
$173$	120.254			0.695108			0.347554	−	0.937660i	$-0.387012\pi$
$173$	120.254			0.695108			0.347554	+	0.937660i	$0.387012\pi$
$174$	−359.427	−	70.4379i	−2.06567	−	0.404816i
$175$			62.1443i			0.355110i
$176$	45.3236	−	46.3612i	0.257520	−	0.263416i
$177$	−220.649			−1.24660
$178$	58.1669	−	296.811i	0.326780	−	1.66748i
$179$			61.4656i			0.343383i	0.985151	+	0.171692i	$0.0549233\pi$
$179$			61.4656i			0.343383i	−0.985151	+	0.171692i	$0.945077\pi$
$180$	75.5907	+	30.8107i	0.419948	+	0.171171i
$181$	−224.080			−1.23801			−0.619007	−	0.785386i	$-0.712465\pi$
$181$	−224.080			−1.23801			−0.619007	+	0.785386i	$0.712465\pi$
$182$	−98.0381	−	19.2128i	−0.538671	−	0.105565i
$183$		−	478.595i		−	2.61527i
$184$	−35.6391	−	23.3782i	−0.193691	−	0.127055i
$185$	−76.8791			−0.415563
$186$	−58.2380	+	297.174i	−0.313107	+	1.59771i
$187$			18.4910i			0.0988822i
$188$	2.80557	−	6.88315i	0.0149232	−	0.0366125i
$189$	80.7658			0.427332
$190$	8.40951	+	1.64804i	0.0442606	+	0.00867387i
$191$			346.617i			1.81475i	0.420321	+	0.907375i	$0.361917\pi$
$191$			346.617i			1.81475i	−0.420321	+	0.907375i	$0.638083\pi$
$192$	−288.385	+	125.229i	−1.50200	+	0.652236i
$193$	314.384			1.62893			0.814467	−	0.580209i	$-0.197029\pi$
$193$	314.384			1.62893			0.814467	+	0.580209i	$0.197029\pi$
$194$	7.87153	−	40.1664i	0.0405749	−	0.207043i
$195$		−	123.440i		−	0.633023i
$196$	−154.882	−	63.1299i	−0.790214	−	0.322091i
$197$	−48.1257			−0.244293			−0.122146	−	0.992512i	$-0.538978\pi$
$197$	−48.1257			−0.244293			−0.122146	+	0.992512i	$0.538978\pi$
$198$	120.353	+	23.5860i	0.607844	+	0.119121i
$199$		−	135.437i		−	0.680589i	−0.940319	−	0.340294i	$-0.889473\pi$
$199$		−	135.437i		−	0.680589i	0.940319	−	0.340294i	$-0.110527\pi$
$200$	101.719	−	155.066i	0.508595	−	0.775332i
$201$	416.652			2.07290
$202$	−42.5434	+	217.088i	−0.210611	+	1.07469i
$203$		−	99.9356i		−	0.492294i
$204$	33.8449	−	83.0345i	0.165906	−	0.407032i
$205$	8.63484			0.0421212
$206$	208.908	+	40.9404i	1.01412	+	0.198740i
$207$		−	80.6252i		−	0.389494i
$208$	213.183	+	208.411i	1.02492	+	1.00198i
$209$	12.8751			0.0616035
$210$	−6.83078	+	34.8557i	−0.0325275	+	0.165980i
$211$			99.0044i			0.469215i	0.972090	+	0.234607i	$0.0753805\pi$
$211$			99.0044i			0.469215i	−0.972090	+	0.234607i	$0.924620\pi$
$212$	123.661	+	50.4041i	0.583305	+	0.237755i
$213$	401.478			1.88487
$214$	354.785	+	69.5282i	1.65787	+	0.324898i
$215$		−	68.3758i		−	0.318027i
$216$	−201.532	−	132.199i	−0.933018	−	0.612032i
$217$	−82.6267			−0.380768
$218$	4.46618	−	22.7898i	0.0204871	−	0.104540i
$219$		−	434.728i		−	1.98506i
$220$	−8.25034	+	20.2413i	−0.0375015	+	0.0920058i
$221$	−85.0270			−0.384737
$222$	549.663	+	107.719i	2.47596	+	0.485221i
$223$		−	50.0223i		−	0.224315i	−0.993690	−	0.112158i	$-0.964224\pi$
$223$		−	50.0223i		−	0.224315i	0.993690	−	0.112158i	$-0.0357762\pi$
$224$	−48.6637	−	70.6462i	−0.217249	−	0.315385i
$225$	350.801			1.55912
$226$	7.06741	−	36.0632i	0.0312717	−	0.159572i
$227$		−	56.6504i		−	0.249561i	−0.992184	−	0.124781i	$-0.960177\pi$
$227$		−	56.6504i		−	0.249561i	0.992184	−	0.124781i	$-0.0398227\pi$
$228$	−57.8164	−	23.5659i	−0.253581	−	0.103359i
$229$	−37.4166			−0.163391			−0.0816956	−	0.996657i	$-0.526034\pi$
$229$	−37.4166			−0.163391			−0.0816956	+	0.996657i	$0.526034\pi$
$230$	14.1013	+	2.76347i	0.0613100	+	0.0120151i
$231$			53.3649i			0.231017i
$232$	−163.576	+	249.366i	−0.705071	+	1.07485i
$233$	167.628			0.719436			0.359718	−	0.933061i	$-0.382873\pi$
$233$	167.628			0.719436			0.359718	+	0.933061i	$0.382873\pi$
$234$	−108.455	+	553.420i	−0.463484	+	2.36504i
$235$			2.50590i			0.0106634i
$236$	−67.8135	+	166.373i	−0.287345	+	0.704970i
$237$	−672.230			−2.83641
$238$	24.0091	+	4.70514i	0.100879	+	0.0197695i
$239$			315.372i			1.31955i	0.751465	+	0.659773i	$0.229348\pi$
$239$			315.372i			1.31955i	−0.751465	+	0.659773i	$0.770652\pi$
$240$	74.0970	−	75.7934i	0.308738	−	0.315806i
$241$	−207.049			−0.859124			−0.429562	−	0.903037i	$-0.641332\pi$
$241$	−207.049			−0.859124			−0.429562	+	0.903037i	$0.641332\pi$
$242$	40.2244	−	205.255i	0.166217	−	0.848162i
$243$			213.145i			0.877140i
$244$	−360.868	−	147.090i	−1.47897	−	0.602827i
$245$	56.3869			0.230151
$246$	−61.7366	−	12.0987i	−0.250962	−	0.0491817i
$247$			59.2037i			0.239691i
$248$	206.175	+	135.245i	0.831351	+	0.545342i
$249$	308.805			1.24018
$250$	−24.9911	+	127.523i	−0.0999643	+	0.510092i
$251$		−	337.540i		−	1.34478i	−0.740196	−	0.672391i	$-0.765267\pi$
$251$		−	337.540i		−	1.34478i	0.740196	−	0.672391i	$-0.234733\pi$
$252$	61.2492	−	150.268i	0.243052	−	0.596302i
$253$	21.5894			0.0853335
$254$	−334.878	−	65.6271i	−1.31842	−	0.258374i
$255$			30.2299i			0.118548i
$256$	5.79372	+	255.934i	0.0226317	+	0.999744i
$257$	−120.453			−0.468689			−0.234345	−	0.972154i	$-0.575294\pi$
$257$	−120.453			−0.468689			−0.234345	+	0.972154i	$0.575294\pi$
$258$	−95.8047	+	488.867i	−0.371336	+	1.89483i
$259$			152.829i			0.590074i
$260$	−93.0754	−	37.9375i	−0.357982	−	0.145914i
$261$	−564.132			−2.16142
$262$	438.221	+	85.8795i	1.67260	+	0.327784i
$263$		−	139.601i		−	0.530803i	−0.964138	−	0.265402i	$-0.914495\pi$
$263$		−	139.601i		−	0.530803i	0.964138	−	0.265402i	$-0.0855045\pi$
$264$	87.3486	−	133.159i	0.330866	−	0.504391i
$265$	−45.0204			−0.169888
$266$	3.27616	−	16.7174i	0.0123164	−	0.0628474i
$267$		−	742.913i		−	2.78245i
$268$	128.053	−	314.163i	0.477808	−	1.17225i
$269$	−142.803			−0.530866			−0.265433	−	0.964129i	$-0.585515\pi$
$269$	−142.803			−0.530866			−0.265433	+	0.964129i	$0.585515\pi$
$270$	79.7399	+	15.6269i	0.295333	+	0.0578773i
$271$			121.020i			0.446570i	0.974753	+	0.223285i	$0.0716780\pi$
$271$			121.020i			0.446570i	−0.974753	+	0.223285i	$0.928322\pi$
$272$	−52.2076	−	51.0391i	−0.191940	−	0.187644i
$273$	−245.388			−0.898855
$274$	−36.1313	+	184.369i	−0.131866	+	0.672880i
$275$			93.9358i			0.341585i
$276$	−96.9481	−	39.5160i	−0.351261	−	0.143174i
$277$	−318.020			−1.14809			−0.574043	−	0.818825i	$-0.694626\pi$
$277$	−318.020			−1.14809			−0.574043	+	0.818825i	$0.694626\pi$
$278$	201.871	+	39.5612i	0.726154	+	0.142307i
$279$			466.423i			1.67177i
$280$	24.1824	+	15.8630i	0.0863658	+	0.0566534i
$281$	−409.394			−1.45692			−0.728459	−	0.685089i	$-0.759763\pi$
$281$	−409.394			−1.45692			−0.728459	+	0.685089i	$0.759763\pi$
$282$	3.51114	−	17.9165i	0.0124509	−	0.0635336i
$283$		−	225.894i		−	0.798212i	−0.916905	−	0.399106i	$-0.869321\pi$
$283$		−	225.894i		−	0.798212i	0.916905	−	0.399106i	$-0.130679\pi$
$284$	123.389	−	302.721i	0.434468	−	1.06592i
$285$	21.0488			0.0738556
$286$	−148.192	−	29.0416i	−0.518153	−	0.101544i
$287$		−	17.1654i		−	0.0598096i
$288$	−398.794	+	274.704i	−1.38470	+	0.953834i
$289$	−268.177			−0.927949
$290$	19.3359	−	98.6662i	0.0666755	−	0.340228i
$291$		−	100.536i		−	0.345484i
$292$	−327.792	−	133.608i	−1.12258	−	0.457562i
$293$	−268.776			−0.917326			−0.458663	−	0.888610i	$-0.651671\pi$
$293$	−268.776			−0.917326			−0.458663	+	0.888610i	$0.651671\pi$
$294$	−403.150	−	79.0065i	−1.37126	−	0.268729i
$295$		−	60.5703i		−	0.205323i
$296$	250.154	−	381.349i	0.845114	−	1.28834i
$297$	122.084			0.411056
$298$	84.8386	−	432.910i	0.284693	−	1.45272i
$299$			99.2744i			0.332021i
$300$	171.935	−	421.823i	0.573116	−	1.40608i
$301$	−135.925			−0.451579
$302$	−276.762	−	54.2378i	−0.916431	−	0.179596i
$303$			543.368i			1.79329i
$304$	−35.5382	+	36.3518i	−0.116902	+	0.119578i
$305$	131.379			0.430751
$306$	26.5603	−	135.530i	0.0867983	−	0.442910i
$307$			161.518i			0.526116i	0.964780	+	0.263058i	$0.0847310\pi$
$307$			161.518i			0.526116i	−0.964780	+	0.263058i	$0.915269\pi$
$308$	40.2380	+	16.4010i	0.130643	+	0.0532500i
$309$	522.894			1.69221
$310$	−81.5771	−	15.9869i	−0.263152	−	0.0515707i
$311$		−	17.7020i		−	0.0569195i	−0.999595	−	0.0284598i	$-0.990940\pi$
$311$		−	17.7020i		−	0.0569195i	0.999595	−	0.0284598i	$-0.00906025\pi$
$312$	612.306	+	401.655i	1.96252	+	1.28735i
$313$	−251.791			−0.804444			−0.402222	−	0.915542i	$-0.631762\pi$
$313$	−251.791			−0.804444			−0.402222	+	0.915542i	$0.631762\pi$
$314$	26.4192	−	134.811i	0.0841376	−	0.429333i
$315$			54.7071i			0.173673i
$316$	−206.601	+	506.872i	−0.653801	+	1.60403i
$317$	−400.790			−1.26432			−0.632162	−	0.774837i	$-0.717832\pi$
$317$	−400.790			−1.26432			−0.632162	+	0.774837i	$0.717832\pi$
$318$	321.883	+	63.0803i	1.01221	+	0.198366i
$319$		−	151.060i		−	0.473543i
$320$	−34.3767	−	79.1645i	−0.107427	−	0.247389i
$321$	888.020			2.76642
$322$	5.49355	−	28.0322i	0.0170607	−	0.0870565i
$323$		−	14.4988i		−	0.0448878i
$324$	−43.7365	−	17.8270i	−0.134989	−	0.0550216i
$325$	−431.945			−1.32906
$326$	−373.572	−	73.2101i	−1.14593	−	0.224571i
$327$		−	57.0425i		−	0.174442i
$328$	−28.0966	+	42.8320i	−0.0856602	+	0.130585i
$329$	4.98153			0.0151414
$330$	−10.3252	+	52.6870i	−0.0312886	+	0.159658i
$331$		−	348.095i		−	1.05165i	−0.850594	−	0.525823i	$-0.823757\pi$
$331$		−	348.095i		−	1.05165i	0.850594	−	0.525823i	$-0.176243\pi$
$332$	94.9071	−	232.844i	0.285865	−	0.701337i
$333$	862.714			2.59073
$334$	69.8494	+	13.6886i	0.209130	+	0.0409838i
$335$			114.375i			0.341418i
$336$	−150.671	−	147.299i	−0.448426	−	0.438389i
$337$	−72.9895			−0.216586			−0.108293	−	0.994119i	$-0.534538\pi$
$337$	−72.9895			−0.216586			−0.108293	+	0.994119i	$0.534538\pi$
$338$	68.5395	−	349.740i	0.202779	−	1.03473i
$339$		−	90.2656i		−	0.266270i
$340$	22.7938	+	9.29075i	0.0670406	+	0.0273257i
$341$	−124.896			−0.366265
$342$	−94.3689	−	18.4937i	−0.275932	−	0.0540753i
$343$		−	243.451i		−	0.709768i
$344$	339.169	+	222.485i	0.985957	+	0.646759i
$345$	35.2953			0.102305
$346$	46.2531	−	236.018i	0.133680	−	0.682133i
$347$			504.069i			1.45265i	0.687353	+	0.726324i	$0.258773\pi$
$347$			504.069i			1.45265i	−0.687353	+	0.726324i	$0.741227\pi$
$348$	−276.492	+	678.342i	−0.794518	+	1.94926i
$349$	372.732			1.06800			0.534000	−	0.845484i	$-0.320688\pi$
$349$	372.732			1.06800			0.534000	+	0.845484i	$0.320688\pi$
$350$	121.969	+	23.9025i	0.348482	+	0.0682929i
$351$			561.376i			1.59936i
$352$	−73.5588	−	106.787i	−0.208974	−	0.303372i
$353$	−449.434			−1.27318			−0.636592	−	0.771201i	$-0.719656\pi$
$353$	−449.434			−1.27318			−0.636592	+	0.771201i	$0.719656\pi$
$354$	−84.8680	+	433.060i	−0.239740	+	1.22333i
$355$			110.210i			0.310450i
$356$	−560.169	−	228.325i	−1.57351	−	0.641361i
$357$	60.0944			0.168332
$358$	120.637	+	23.6415i	0.336974	+	0.0660377i
$359$			69.0735i			0.192405i	0.995362	+	0.0962027i	$0.0306697\pi$
$359$			69.0735i			0.192405i	−0.995362	+	0.0962027i	$0.969330\pi$
$360$	89.5456	−	136.509i	0.248738	−	0.379191i
$361$	350.905			0.972035
$362$	−86.1879	+	439.795i	−0.238088	+	1.21490i
$363$		−	513.750i		−	1.41529i
$364$	−75.4166	+	185.026i	−0.207189	+	0.508314i
$365$	119.337			0.326951
$366$	−939.322	−	184.082i	−2.56645	−	0.502955i
$367$			578.712i			1.57687i	0.615118	+	0.788435i	$0.289109\pi$
$367$			578.712i			1.57687i	−0.615118	+	0.788435i	$0.710891\pi$
$368$	−59.5915	+	60.9557i	−0.161933	+	0.165641i
$369$	−96.8975			−0.262595
$370$	−29.5700	+	150.888i	−0.0799188	+	0.407806i
$371$			89.4968i			0.241231i
$372$	560.853	+	228.603i	1.50767	+	0.614525i
$373$	561.800			1.50617			0.753083	−	0.657926i	$-0.228566\pi$
$373$	561.800			1.50617			0.753083	+	0.657926i	$0.228566\pi$
$374$	36.2916	+	7.11217i	0.0970364	+	0.0190165i
$375$			319.188i			0.851168i
$376$	−12.4302	−	8.15386i	−0.0330591	−	0.0216858i
$377$	694.620			1.84249
$378$	31.0649	−	158.516i	0.0821823	−	0.419355i
$379$			381.055i			1.00542i	0.864454	+	0.502712i	$0.167664\pi$
$379$			381.055i			1.00542i	−0.864454	+	0.502712i	$0.832336\pi$
$380$	6.46909	−	15.8712i	0.0170239	−	0.0417663i
$381$	−838.195			−2.19999
$382$	680.294	+	133.319i	1.78088	+	0.349003i
$383$		−	407.272i		−	1.06337i	−0.846941	−	0.531686i	$-0.821559\pi$
$383$		−	407.272i		−	1.06337i	0.846941	−	0.531686i	$-0.178441\pi$
$384$	134.862	+	614.170i	0.351204	+	1.59940i
$385$	−14.6492			−0.0380498
$386$	120.921	−	617.032i	0.313268	−	1.59853i
$387$			767.292i			1.98267i
$388$	−75.8056	−	30.8984i	−0.195375	−	0.0796349i
$389$	499.193			1.28327			0.641636	−	0.767009i	$-0.278256\pi$
$389$	499.193			1.28327			0.641636	+	0.767009i	$0.278256\pi$
$390$	−242.271	−	47.4785i	−0.621207	−	0.121740i
$391$		−	24.3119i		−	0.0621788i
$392$	−183.475	+	279.700i	−0.468049	+	0.713521i
$393$	1096.86			2.79099
$394$	−18.5106	+	94.4547i	−0.0469811	+	0.239733i
$395$		−	184.534i		−	0.467174i
$396$	92.5828	−	227.141i	0.233795	−	0.573589i
$397$	−17.5804			−0.0442832			−0.0221416	−	0.999755i	$-0.507048\pi$
$397$	−17.5804			−0.0442832			−0.0221416	+	0.999755i	$0.507048\pi$
$398$	−265.818	−	52.0931i	−0.667884	−	0.130887i
$399$		−	41.8434i		−	0.104871i
$400$	−265.219	−	259.283i	−0.663048	−	0.648209i
$401$	108.903			0.271579			0.135790	−	0.990738i	$-0.456643\pi$
$401$	108.903			0.271579			0.135790	+	0.990738i	$0.456643\pi$
$402$	160.257	−	817.749i	0.398648	−	2.03420i
$403$		−	574.311i		−	1.42509i
$404$	409.708	+	166.997i	1.01413	+	0.413359i
$405$	15.9229			0.0393158
$406$	−196.140	−	38.4382i	−0.483104	−	0.0946753i
$407$			231.013i			0.567599i
$408$	−149.951	−	98.3637i	−0.367528	−	0.241087i
$409$	−192.706			−0.471163			−0.235581	−	0.971855i	$-0.575699\pi$
$409$	−192.706			−0.471163			−0.235581	+	0.971855i	$0.575699\pi$
$410$	3.32121	−	16.9473i	0.00810052	−	0.0413349i
$411$			461.472i			1.12280i
$412$	160.705	−	394.271i	0.390060	−	0.956968i
$413$	−120.409			−0.291547
$414$	−158.240	−	31.0108i	−0.382223	−	0.0749053i
$415$			84.7700i			0.204265i
$416$	491.038	−	338.245i	1.18038	−	0.813090i
$417$	505.279			1.21170
$418$	4.95216	−	25.2696i	0.0118473	−	0.0604536i
$419$			620.366i			1.48059i	0.672284	+	0.740293i	$0.265313\pi$
$419$			620.366i			1.48059i	−0.672284	+	0.740293i	$0.734687\pi$
$420$	65.7828	+	26.8131i	0.156626	+	0.0638406i
$421$	−145.555			−0.345736			−0.172868	−	0.984945i	$-0.555303\pi$
$421$	−145.555			−0.345736			−0.172868	+	0.984945i	$0.555303\pi$
$422$	194.313	+	38.0800i	0.460456	+	0.0902369i
$423$		−	28.1205i		−	0.0664787i
$424$	146.490	−	223.318i	0.345495	−	0.526693i
$425$	105.782			0.248898
$426$	154.420	−	787.968i	0.362489	−	1.84969i
$427$		−	261.171i		−	0.611641i
$428$	272.921	−	669.581i	0.637666	−	1.56444i
$429$	−370.922			−0.864619
$430$	−134.199	−	26.2993i	−0.312090	−	0.0611612i
$431$		−	126.553i		−	0.293626i	−0.989164	−	0.146813i	$-0.953098\pi$
$431$		−	126.553i		−	0.293626i	0.989164	−	0.146813i	$-0.0469015\pi$
$432$	−336.977	+	344.692i	−0.780040	+	0.797898i
$433$	−244.170			−0.563904			−0.281952	−	0.959429i	$-0.590982\pi$
$433$	−244.170			−0.563904			−0.281952	+	0.959429i	$0.590982\pi$
$434$	−31.7806	+	162.169i	−0.0732273	+	0.373660i
$435$		−	246.960i		−	0.567724i
$436$	−43.0110	−	17.5313i	−0.0986490	−	0.0402093i
$437$	−16.9282			−0.0387374
$438$	−853.227	−	167.209i	−1.94801	−	0.381756i
$439$		−	761.770i		−	1.73524i	−0.497228	−	0.867620i	$-0.665649\pi$
$439$		−	761.770i		−	1.73524i	0.497228	−	0.867620i	$-0.334351\pi$
$440$	36.5536	+	23.9781i	0.0830763	+	0.0544956i
$441$	−632.756			−1.43482
$442$	−32.7039	+	166.880i	−0.0739907	+	0.377556i
$443$			447.194i			1.00947i	0.863275	+	0.504734i	$0.168409\pi$
$443$			447.194i			1.00947i	−0.863275	+	0.504734i	$0.831591\pi$
$444$	422.833	−	1037.37i	0.952327	−	2.33643i
$445$	203.937			0.458285
$446$	−98.1771	−	19.2400i	−0.220128	−	0.0431391i
$447$		−	1083.57i		−	2.42408i
$448$	−157.372	+	68.3381i	−0.351278	+	0.152540i
$449$	706.271			1.57299			0.786493	−	0.617599i	$-0.211894\pi$
$449$	706.271			1.57299			0.786493	+	0.617599i	$0.211894\pi$
$450$	134.929	−	688.506i	0.299841	−	1.53001i
$451$		−	25.9467i		−	0.0575315i
$452$	−68.0617	−	27.7419i	−0.150579	−	0.0613760i
$453$	−692.730			−1.52921
$454$	−111.186	−	21.7894i	−0.244903	−	0.0479943i
$455$		−	67.3613i		−	0.148047i
$456$	−68.4900	+	104.410i	−0.150197	+	0.228970i
$457$	−831.696			−1.81990			−0.909952	−	0.414714i	$-0.863882\pi$
$457$	−831.696			−1.81990			−0.909952	+	0.414714i	$0.863882\pi$
$458$	−14.3915	+	73.4362i	−0.0314225	+	0.160341i
$459$		−	137.479i		−	0.299518i
$460$	10.8475	−	26.6132i	0.0235816	−	0.0578548i
$461$	115.935			0.251485			0.125743	−	0.992063i	$-0.459869\pi$
$461$	115.935			0.251485			0.125743	+	0.992063i	$0.459869\pi$
$462$	104.737	+	20.5257i	0.226704	+	0.0444279i
$463$			377.545i			0.815432i	0.913109	+	0.407716i	$0.133675\pi$
$463$			377.545i			0.815432i	−0.913109	+	0.407716i	$0.866325\pi$
$464$	426.505	+	416.959i	0.919192	+	0.898619i
$465$	−204.186			−0.439110
$466$	64.4748	−	328.999i	0.138358	−	0.706006i
$467$		−	97.7409i		−	0.209295i	−0.994509	−	0.104648i	$-0.966629\pi$
$467$		−	97.7409i		−	0.209295i	0.994509	−	0.104648i	$-0.0333715\pi$
$468$	1044.46	+	425.723i	2.23176	+	0.909665i
$469$	227.368			0.484794
$470$	4.91825	+	0.963844i	0.0104644	+	0.00205073i
$471$		−	337.428i		−	0.716409i
$472$	300.451	+	197.087i	0.636549	+	0.417558i
$473$	−205.461			−0.434379
$474$	−258.559	+	1319.36i	−0.545484	+	2.78347i
$475$		−	73.6550i		−	0.155063i
$476$	18.4692	−	45.3122i	0.0388009	−	0.0951937i
$477$	505.205			1.05913
$478$	618.969	+	121.301i	1.29491	+	0.253768i
$479$			82.7810i			0.172821i	0.996260	+	0.0864103i	$0.0275396\pi$
$479$			82.7810i			0.172821i	−0.996260	+	0.0864103i	$0.972460\pi$
$480$	−120.257	−	174.580i	−0.250536	−	0.363709i
$481$	−1062.27			−2.20845
$482$	−79.6371	+	406.368i	−0.165222	+	0.843087i
$483$		−	70.1641i		−	0.145267i
$484$	−387.376	−	157.894i	−0.800363	−	0.326228i
$485$	27.5981			0.0569033
$486$	418.333	+	81.9819i	0.860767	+	0.168687i
$487$			55.3380i			0.113630i	0.998385	+	0.0568152i	$0.0180946\pi$
$487$			55.3380i			0.113630i	−0.998385	+	0.0568152i	$0.981905\pi$
$488$	−427.489	+	651.689i	−0.876002	+	1.33543i
$489$	−935.045			−1.91216
$490$	21.6881	−	110.669i	0.0442614	−	0.225854i
$491$			436.146i			0.888280i	0.895957	+	0.444140i	$0.146491\pi$
$491$			436.146i			0.888280i	−0.895957	+	0.444140i	$0.853509\pi$
$492$	−47.4914	+	116.515i	−0.0965273	+	0.236819i
$493$	−170.110			−0.345050
$494$	116.197	+	22.7715i	0.235217	+	0.0460961i
$495$			82.6939i			0.167058i
$496$	344.742	−	352.634i	0.695043	−	0.710956i
$497$	219.088			0.440821
$498$	118.775	−	606.081i	0.238505	−	1.21703i
$499$			316.633i			0.634535i	0.948336	+	0.317268i	$0.102765\pi$
$499$			316.633i			0.634535i	−0.948336	+	0.317268i	$0.897235\pi$
$500$	240.673	+	98.0983i	0.481346	+	0.196197i
$501$	174.832			0.348966
$502$	−662.479	−	129.828i	−1.31968	−	0.258622i
$503$			199.952i			0.397519i	0.980048	+	0.198760i	$0.0636913\pi$
$503$			199.952i			0.397519i	−0.980048	+	0.198760i	$0.936309\pi$
$504$	−271.368	−	178.009i	−0.538428	−	0.353193i
$505$	−149.160			−0.295366
$506$	8.30391	−	42.3728i	0.0164109	−	0.0837406i
$507$		−	875.392i		−	1.72661i
$508$	−257.608	+	632.012i	−0.507103	+	1.24412i
$509$	−249.339			−0.489860			−0.244930	−	0.969541i	$-0.578765\pi$
$509$	−249.339			−0.489860			−0.244930	+	0.969541i	$0.578765\pi$
$510$	59.3311	+	11.6273i	0.116336	+	0.0227986i
$511$		−	237.233i		−	0.464252i
$512$	504.542	+	87.0688i	0.985434	+	0.170056i
$513$	−95.7257			−0.186600
$514$	−46.3298	+	236.409i	−0.0901359	+	0.459941i
$515$			143.540i			0.278718i
$516$	922.634	+	376.065i	1.78805	+	0.728809i
$517$	7.52995			0.0145647
$518$	299.953	+	58.7826i	0.579060	+	0.113480i
$519$		−	590.749i		−	1.13824i
$520$	−110.258	+	168.084i	−0.212035	+	0.323239i
$521$	776.578			1.49055			0.745276	−	0.666756i	$-0.232318\pi$
$521$	776.578			1.49055			0.745276	+	0.666756i	$0.232318\pi$
$522$	−216.982	+	1107.20i	−0.415674	+	2.12108i
$523$			529.698i			1.01281i	0.862297	+	0.506403i	$0.169025\pi$
$523$			529.698i			1.01281i	−0.862297	+	0.506403i	$0.830975\pi$
$524$	337.106	−	827.050i	0.643331	−	1.57834i
$525$	305.285			0.581496
$526$	−273.991	−	53.6947i	−0.520895	−	0.102081i
$527$			140.646i			0.266881i
$528$	−227.750	−	222.653i	−0.431346	−	0.421691i
$529$	500.614			0.946341
$530$	−17.3162	+	88.3600i	−0.0326720	+	0.166717i
$531$			679.701i			1.28004i
$532$	−31.5506	−	12.8600i	−0.0593056	−	0.0241730i
$533$	119.311			0.223847
$534$	−1458.09	−	285.746i	−2.73051	−	0.535105i
$535$			243.770i			0.455645i
$536$	−567.344	−	372.161i	−1.05848	−	0.694330i
$537$	301.951			0.562293
$538$	−54.9262	+	280.274i	−0.102093	+	0.520956i
$539$		−	169.436i		−	0.314353i
$540$	61.3406	−	150.492i	0.113594	−	0.278689i
$541$	328.092			0.606455			0.303228	−	0.952918i	$-0.401936\pi$
$541$	328.092			0.606455			0.303228	+	0.952918i	$0.401936\pi$
$542$	237.523	+	46.5480i	0.438234	+	0.0858820i
$543$			1100.80i			2.02726i
$544$	−120.253	+	82.8350i	−0.221054	+	0.152270i
$545$	15.6587			0.0287316
$546$	−94.3833	+	481.614i	−0.172863	+	0.882077i
$547$			929.453i			1.69918i	0.527441	+	0.849592i	$0.323152\pi$
$547$			929.453i			1.69918i	−0.527441	+	0.849592i	$0.676848\pi$
$548$	347.958	+	141.827i	0.634959	+	0.258809i
$549$	−1474.30			−2.68542
$550$	184.365	+	36.1305i	0.335208	+	0.0656917i
$551$			118.446i			0.214966i
$552$	−114.846	+	175.078i	−0.208054	+	0.317170i
$553$	−366.838			−0.663360
$554$	−122.320	+	624.167i	−0.220794	+	1.12666i
$555$			377.670i			0.680487i
$556$	155.291	−	380.989i	0.279300	−	0.685232i
$557$	−71.6832			−0.128695			−0.0643476	−	0.997928i	$-0.520497\pi$
$557$	−71.6832			−0.128695			−0.0643476	+	0.997928i	$0.520497\pi$
$558$	915.434	+	179.400i	1.64056	+	0.321506i
$559$		−	944.772i		−	1.69011i
$560$	40.4350	−	41.3607i	0.0722053	−	0.0738584i
$561$	90.8372			0.161920
$562$	−157.465	+	803.504i	−0.280187	+	1.42972i
$563$		−	277.931i		−	0.493660i	−0.969059	−	0.246830i	$-0.920611\pi$
$563$		−	277.931i		−	0.493660i	0.969059	−	0.246830i	$-0.0793890\pi$
$564$	−33.8136	−	13.7824i	−0.0599532	−	0.0244369i
$565$	24.7788			0.0438563
$566$	−443.355	−	86.8855i	−0.783312	−	0.153508i
$567$		−	31.6534i		−	0.0558260i
$568$	−546.681	−	358.607i	−0.962467	−	0.631350i
$569$	−551.019			−0.968398			−0.484199	−	0.874958i	$-0.660889\pi$
$569$	−551.019			−0.968398			−0.484199	+	0.874958i	$0.660889\pi$
$570$	8.09601	−	41.3119i	0.0142035	−	0.0724770i
$571$		−	67.5153i		−	0.118241i	−0.998251	−	0.0591203i	$-0.981170\pi$
$571$		−	67.5153i		−	0.118241i	0.998251	−	0.0591203i	$-0.0188295\pi$
$572$	−113.998	+	279.681i	−0.199297	+	0.488953i
$573$	1702.76			2.97167
$574$	−33.6899	−	6.60230i	−0.0586931	−	0.0115023i
$575$		−	123.507i		−	0.214794i
$576$	385.765	+	888.360i	0.669731	+	1.54229i
$577$	−489.604			−0.848534			−0.424267	−	0.905537i	$-0.639468\pi$
$577$	−489.604			−0.848534			−0.424267	+	0.905537i	$0.639468\pi$
$578$	−103.149	+	526.342i	−0.178458	+	0.910627i
$579$		−	1544.42i		−	2.66739i
$580$	−186.212	−	75.8999i	−0.321055	−	0.130862i
$581$	168.516			0.290044
$582$	−197.318	−	38.6690i	−0.339035	−	0.0664416i
$583$			135.281i			0.232043i
$584$	−388.307	+	591.957i	−0.664909	+	1.01363i
$585$	−380.251			−0.650002
$586$	−103.379	+	527.519i	−0.176415	+	0.900202i
$587$		−	481.728i		−	0.820662i	−0.911937	−	0.410331i	$-0.865413\pi$
$587$		−	481.728i		−	0.820662i	0.911937	−	0.410331i	$-0.134587\pi$
$588$	−310.127	+	760.861i	−0.527426	+	1.29398i
$589$	97.9312			0.166267
$590$	−118.879	−	23.2971i	−0.201490	−	0.0394866i
$591$			236.419i			0.400031i
$592$	−652.245	−	637.646i	−1.10176	−	1.07711i
$593$	−191.048			−0.322171			−0.161086	−	0.986940i	$-0.551500\pi$
$593$	−191.048			−0.322171			−0.161086	+	0.986940i	$0.551500\pi$
$594$	46.9569	−	239.609i	0.0790520	−	0.403383i
$595$			16.4965i			0.0277253i
$596$	−817.026	−	333.020i	−1.37085	−	0.558758i
$597$	−665.338			−1.11447
$598$	194.843	+	38.1839i	0.325824	+	0.0638526i
$599$		−	880.192i		−	1.46944i	−0.678373	−	0.734718i	$-0.737314\pi$
$599$		−	880.192i		−	1.46944i	0.678373	−	0.734718i	$-0.262686\pi$
$600$	−761.766	−	499.696i	−1.26961	−	0.832827i
$601$	66.8193			0.111180			0.0555901	−	0.998454i	$-0.482296\pi$
$601$	66.8193			0.111180			0.0555901	+	0.998454i	$0.482296\pi$
$602$	−52.2809	+	266.776i	−0.0868453	+	0.443150i
$603$		−	1283.48i		−	2.12850i
$604$	−212.902	+	522.330i	−0.352486	+	0.864785i
$605$	141.029			0.233107
$606$	1066.45	+	208.995i	1.75982	+	0.344877i
$607$		−	1075.41i		−	1.77168i	−0.463995	−	0.885838i	$-0.653584\pi$
$607$		−	1075.41i		−	1.77168i	0.463995	−	0.885838i	$-0.346416\pi$
$608$	57.6775	+	83.7317i	0.0948642	+	0.137717i
$609$	−490.936			−0.806134
$610$	50.5323	−	257.853i	0.0828398	−	0.422710i
$611$			34.6250i			0.0566693i
$612$	−255.785	−	104.258i	−0.417949	−	0.170356i
$613$	32.8427			0.0535769			0.0267885	−	0.999641i	$-0.491472\pi$
$613$	32.8427			0.0535769			0.0267885	+	0.999641i	$0.491472\pi$
$614$	317.005	+	62.1244i	0.516295	+	0.101180i
$615$		−	42.4188i		−	0.0689737i
$616$	47.6664	−	72.6654i	0.0773805	−	0.117963i
$617$	809.710			1.31233			0.656167	−	0.754616i	$-0.272177\pi$
$617$	809.710			1.31233			0.656167	+	0.754616i	$0.272177\pi$
$618$	201.120	−	1026.27i	0.325438	−	1.66063i
$619$			1104.71i			1.78466i	0.451380	+	0.892332i	$0.350932\pi$
$619$			1104.71i			1.78466i	−0.451380	+	0.892332i	$0.649068\pi$
$620$	−62.7539	+	153.960i	−0.101216	+	0.248322i
$621$	−160.515			−0.258479
$622$	−34.7431	−	6.80870i	−0.0558570	−	0.0109465i
$623$		−	405.410i		−	0.650738i
$624$	1023.83	−	1047.26i	1.64075	−	1.67831i
$625$	491.916			0.787066
$626$	−96.8462	+	494.181i	−0.154706	+	0.789427i
$627$		−	63.2494i		−	0.100876i
$628$	−254.427	−	103.704i	−0.405138	−	0.165134i
$629$	260.145			0.413585
$630$	107.372	+	21.0420i	0.170432	+	0.0334000i
$631$		−	629.603i		−	0.997786i	−0.866664	−	0.498893i	$-0.833740\pi$
$631$		−	629.603i		−	0.997786i	0.866664	−	0.498893i	$-0.166260\pi$
$632$	915.357	+	600.447i	1.44835	+	0.950075i
$633$	486.361			0.768343
$634$	−154.156	+	786.618i	−0.243148	+	1.24072i
$635$		−	230.093i		−	0.362351i
$636$	247.611	−	607.486i	0.389326	−	0.955167i
$637$	779.118			1.22311
$638$	−296.481	−	58.1022i	−0.464703	−	0.0910692i
$639$		−	1236.74i		−	1.93543i
$640$	−168.596	+	37.0210i	−0.263431	+	0.0578454i
$641$	525.908			0.820449			0.410224	−	0.911985i	$-0.365450\pi$
$641$	525.908			0.820449			0.410224	+	0.911985i	$0.365450\pi$
$642$	341.558	−	1742.89i	0.532023	−	2.71478i
$643$			927.585i			1.44259i	0.692628	+	0.721295i	$0.256453\pi$
$643$			927.585i			1.44259i	−0.692628	+	0.721295i	$0.743547\pi$
$644$	−52.9049	−	21.5640i	−0.0821504	−	0.0334845i
$645$	−335.897			−0.520771
$646$	−28.4562	−	5.57665i	−0.0440499	−	0.00863258i
$647$		−	466.550i		−	0.721098i	−0.932740	−	0.360549i	$-0.882589\pi$
$647$		−	466.550i		−	0.721098i	0.932740	−	0.360549i	$-0.117411\pi$
$648$	−51.8108	+	78.9834i	−0.0799550	+	0.121888i
$649$	−182.007			−0.280442
$650$	−166.139	+	847.763i	−0.255598	+	1.30425i
$651$			405.905i			0.623510i
$652$	−287.374	+	705.040i	−0.440758	+	1.08135i
$653$	339.180			0.519419			0.259709	−	0.965687i	$-0.416373\pi$
$653$	339.180			0.519419			0.259709	+	0.965687i	$0.416373\pi$
$654$	−111.955	−	21.9402i	−0.171186	−	0.0335477i
$655$			301.099i			0.459693i
$656$	73.2583	+	71.6186i	0.111674	+	0.109175i
$657$	−1339.17			−2.03830
$658$	1.91604	−	9.77708i	0.00291192	−	0.0148588i
$659$			134.332i			0.203842i	0.994793	+	0.101921i	$0.0324988\pi$
$659$			134.332i			0.203842i	−0.994793	+	0.101921i	$0.967501\pi$
$660$	99.4357	+	40.5300i	0.150660	+	0.0614090i
$661$	722.694			1.09333			0.546667	−	0.837350i	$-0.315896\pi$
$661$	722.694			1.09333			0.546667	+	0.837350i	$0.315896\pi$
$662$	−683.194	−	133.888i	−1.03202	−	0.202247i
$663$			417.697i			0.630010i
$664$	−420.491	−	275.830i	−0.633269	−	0.415406i
$665$	11.4864			0.0172728
$666$	331.825	−	1693.22i	0.498236	−	2.54237i
$667$			198.614i			0.297772i
$668$	53.7323	−	131.826i	0.0804375	−	0.197344i
$669$	−245.736			−0.367318
$670$	224.480	+	43.9921i	0.335045	+	0.0656598i
$671$		−	394.779i		−	0.588344i
$672$	−347.051	+	239.061i	−0.516445	+	0.355746i
$673$	−238.313			−0.354106			−0.177053	−	0.984201i	$-0.556656\pi$
$673$	−238.313			−0.354106			−0.177053	+	0.984201i	$0.556656\pi$
$674$	−28.0739	+	143.254i	−0.0416527	+	0.212543i
$675$		−	698.405i		−	1.03467i
$676$	−660.060	−	269.040i	−0.976420	−	0.397988i
$677$	−659.538			−0.974207			−0.487104	−	0.873344i	$-0.661947\pi$
$677$	−659.538			−0.974207			−0.487104	+	0.873344i	$0.661947\pi$
$678$	−177.161	−	34.7188i	−0.261300	−	0.0512077i
$679$		−	54.8627i		−	0.0807993i
$680$	27.0018	−	41.1631i	0.0397085	−	0.0605340i
$681$	−278.296			−0.408658
$682$	−48.0388	+	245.130i	−0.0704381	+	0.359428i
$683$			950.270i			1.39132i	0.718373	+	0.695659i	$0.244887\pi$
$683$			950.270i			1.39132i	−0.718373	+	0.695659i	$0.755113\pi$
$684$	−72.5941	+	178.101i	−0.106132	+	0.260382i
$685$	−126.679			−0.184933
$686$	−477.812	−	93.6383i	−0.696519	−	0.136499i
$687$			183.810i			0.267554i
$688$	567.119	−	580.102i	0.824300	−	0.843172i
$689$	−622.063			−0.902849
$690$	13.5756	−	69.2729i	0.0196748	−	0.100395i
$691$			823.429i			1.19165i	0.803115	+	0.595824i	$0.203175\pi$
$691$			823.429i			1.19165i	−0.803115	+	0.595824i	$0.796825\pi$
$692$	−445.434	−	181.559i	−0.643691	−	0.262368i
$693$	164.389			0.237213
$694$	989.319	+	193.880i	1.42553	+	0.279366i
$695$			138.704i			0.199574i
$696$	1225.01	+	803.573i	1.76008	+	1.15456i
$697$	−29.2187			−0.0419207
$698$	143.364	−	731.549i	0.205392	−	1.04806i
$699$		−	823.478i		−	1.17808i
$700$	93.8254	−	230.190i	0.134036	−	0.328843i
$701$	211.054			0.301076			0.150538	−	0.988604i	$-0.451899\pi$
$701$	211.054			0.301076			0.150538	+	0.988604i	$0.451899\pi$
$702$	1101.79	+	215.922i	1.56951	+	0.307581i
$703$		−	181.137i		−	0.257663i
$704$	−237.880	+	103.298i	−0.337898	+	0.146730i
$705$	12.3103			0.0174614
$706$	−172.865	+	882.089i	−0.244852	+	1.24942i
$707$			296.517i			0.419402i
$708$	817.310	+	333.135i	1.15439	+	0.470530i
$709$	−697.407			−0.983649			−0.491824	−	0.870694i	$-0.663670\pi$
$709$	−697.407			−0.983649			−0.491824	+	0.870694i	$0.663670\pi$
$710$	216.305	+	42.3899i	0.304655	+	0.0597041i
$711$			2070.78i			2.91249i
$712$	−663.582	+	1011.60i	−0.931998	+	1.42079i
$713$	164.214			0.230314
$714$	23.1141	−	117.945i	0.0323727	−	0.165190i
$715$		−	101.822i		−	0.142408i
$716$	92.8007	−	227.676i	0.129610	−	0.317983i
$717$	1549.27			2.16077
$718$	135.568	+	26.5677i	0.188814	+	0.0370024i
$719$			473.775i			0.658936i	0.944167	+	0.329468i	$0.106869\pi$
$719$			473.775i			0.658936i	−0.944167	+	0.329468i	$0.893131\pi$
$720$	−233.479	−	228.253i	−0.324276	−	0.317019i
$721$	285.345			0.395763
$722$	134.968	−	688.709i	0.186937	−	0.953890i
$723$			1017.13i			1.40682i
$724$	830.021	+	338.316i	1.14644	+	0.467288i
$725$	−864.172			−1.19196
$726$	−1008.32	−	197.603i	−1.38887	−	0.272181i
$727$		−	329.602i		−	0.453373i	−0.973968	−	0.226686i	$-0.927211\pi$
$727$		−	329.602i		−	0.453373i	0.973968	−	0.226686i	$-0.0727892\pi$
$728$	334.137	+	219.184i	0.458980	+	0.301077i
$729$	1153.35			1.58209
$730$	45.9006	−	234.219i	0.0628776	−	0.320848i
$731$			231.371i			0.316513i
$732$	−722.582	+	1772.77i	−0.987134	+	2.42182i
$733$	209.047			0.285193			0.142597	−	0.989781i	$-0.454455\pi$
$733$	209.047			0.285193			0.142597	+	0.989781i	$0.454455\pi$
$734$	1135.82	+	222.589i	1.54744	+	0.303255i
$735$		−	277.002i		−	0.376873i
$736$	96.7151	+	140.404i	0.131406	+	0.190766i
$737$	343.684			0.466329
$738$	−37.2696	+	190.178i	−0.0505009	+	0.257693i
$739$		−	1078.14i		−	1.45891i	−0.684027	−	0.729457i	$-0.739773\pi$
$739$		−	1078.14i		−	1.45891i	0.684027	−	0.729457i	$-0.260227\pi$
$740$	284.769	+	116.072i	0.384824	+	0.156854i
$741$	290.839			0.392496
$742$	175.652	+	34.4231i	0.236728	+	0.0463923i
$743$		−	714.862i		−	0.962129i	−0.876685	−	0.481064i	$-0.840250\pi$
$743$		−	714.862i		−	0.962129i	0.876685	−	0.481064i	$-0.159750\pi$
$744$	664.393	−	1012.84i	0.893001	−	1.36134i
$745$	297.450			0.399261
$746$	216.085	−	1102.63i	0.289658	−	1.47805i
$747$		−	951.263i		−	1.27344i
$748$	27.9176	−	68.4928i	0.0373230	−	0.0915679i
$749$	484.595			0.646989
$750$	626.460	+	122.769i	0.835280	+	0.163692i
$751$			1062.70i			1.41505i	0.706689	+	0.707524i	$0.250188\pi$
$751$			1062.70i			1.41505i	−0.706689	+	0.707524i	$0.749812\pi$
$752$	−20.7843	+	21.2602i	−0.0276387	+	0.0282715i
$753$	−1658.17			−2.20209
$754$	267.171	−	1363.31i	0.354338	−	1.80810i
$755$		−	190.161i		−	0.251869i
$756$	−299.166	−	121.940i	−0.395723	−	0.161296i
$757$	−436.463			−0.576570			−0.288285	−	0.957545i	$-0.593085\pi$
$757$	−436.463			−0.576570			−0.288285	+	0.957545i	$0.593085\pi$
$758$	747.885	+	146.565i	0.986655	+	0.193358i
$759$		−	106.058i		−	0.139734i
$760$	−28.6616	−	18.8012i	−0.0377127	−	0.0247384i
$761$	−372.604			−0.489625			−0.244812	−	0.969570i	$-0.578726\pi$
$761$	−372.604			−0.489625			−0.244812	+	0.969570i	$0.578726\pi$
$762$	−322.394	+	1645.10i	−0.423090	+	2.15892i
$763$		−	31.1283i		−	0.0407972i
$764$	523.322	−	1283.91i	0.684977	−	1.68051i
$765$	93.1220			0.121728
$766$	−799.338	−	156.649i	−1.04352	−	0.204502i
$767$		−	836.922i		−	1.09116i
$768$	1257.28	−	28.4618i	1.63709	−	0.0370596i
$769$	−561.838			−0.730608			−0.365304	−	0.930888i	$-0.619035\pi$
$769$	−561.838			−0.730608			−0.365304	+	0.930888i	$0.619035\pi$
$770$	−5.63451	+	28.7515i	−0.00731754	+	0.0373396i
$771$			591.729i			0.767482i
$772$	−1164.52	−	474.657i	−1.50844	−	0.614841i
$773$	−569.441			−0.736663			−0.368332	−	0.929695i	$-0.620071\pi$
$773$	−569.441			−0.736663			−0.368332	+	0.929695i	$0.620071\pi$
$774$	1505.94	+	295.123i	1.94566	+	0.381296i
$775$			714.497i			0.921931i
$776$	−89.8003	+	136.897i	−0.115722	+	0.176413i
$777$	750.777			0.966251
$778$	192.004	−	979.749i	0.246792	−	1.25932i
$779$			20.3448i			0.0261166i
$780$	−186.369	+	457.235i	−0.238934	+	0.586198i
$781$	331.168			0.424030
$782$	−47.7162	−	9.35108i	−0.0610181	−	0.0119579i
$783$			1123.12i			1.43438i
$784$	478.388	+	467.681i	0.610189	+	0.596532i
$785$	92.6275			0.117997
$786$	421.885	−	2152.77i	0.536749	−	2.73889i
$787$		−	871.782i		−	1.10773i	−0.832607	−	0.553864i	$-0.813153\pi$
$787$		−	871.782i		−	1.10773i	0.832607	−	0.553864i	$-0.186847\pi$
$788$	178.263	+	72.6601i	0.226223	+	0.0922083i
$789$	−685.794			−0.869193
$790$	−362.178	−	70.9771i	−0.458454	−	0.0898445i
$791$		−	49.2582i		−	0.0622733i
$792$	−410.193	−	269.074i	−0.517920	−	0.339740i
$793$	1815.31			2.28917
$794$	−6.76195	+	34.5045i	−0.00851631	+	0.0434566i
$795$			221.164i			0.278193i
$796$	−204.483	+	501.675i	−0.256888	+	0.630245i
$797$	−770.352			−0.966564			−0.483282	−	0.875465i	$-0.660555\pi$
$797$	−770.352			−0.966564			−0.483282	+	0.875465i	$0.660555\pi$
$798$	−82.1246	−	16.0942i	−0.102913	−	0.0201682i
$799$		−	8.47952i		−	0.0106127i
$800$	−610.898	+	420.809i	−0.763623	+	0.526011i
$801$	−2288.52			−2.85708
$802$	41.8874	−	213.741i	0.0522287	−	0.266510i
$803$		−	358.595i		−	0.446569i
$804$	−1543.33	−	629.061i	−1.91956	−	0.782414i
$805$	19.2607			0.0239264
$806$	−1127.18	−	220.897i	−1.39849	−	0.274065i
$807$			701.522i			0.869296i
$808$	485.345	−	739.889i	0.600675	−	0.915704i
$809$	−135.358			−0.167315			−0.0836574	−	0.996495i	$-0.526660\pi$
$809$	−135.358			−0.167315			−0.0836574	+	0.996495i	$0.526660\pi$
$810$	6.12441	−	31.2513i	0.00756100	−	0.0385819i
$811$			196.306i			0.242054i	0.992649	+	0.121027i	$0.0386187\pi$
$811$			196.306i			0.242054i	−0.992649	+	0.121027i	$0.961381\pi$
$812$	−150.883	+	370.174i	−0.185816	+	0.455879i
$813$	594.515			0.731261
$814$	453.401	+	88.8543i	0.557004	+	0.109158i
$815$		−	256.679i		−	0.314944i
$816$	−250.731	+	256.471i	−0.307268	+	0.314303i
$817$	161.102			0.197187
$818$	−74.1202	+	378.217i	−0.0906115	+	0.462368i
$819$			755.908i			0.922965i
$820$	−31.9845	−	13.0369i	−0.0390055	−	0.0158986i
$821$	1404.37			1.71056			0.855282	−	0.518162i	$-0.173384\pi$
$821$	1404.37			1.71056			0.855282	+	0.518162i	$0.173384\pi$
$822$	905.716	+	177.496i	1.10184	+	0.215932i
$823$		−	1366.93i		−	1.66092i	−0.557080	−	0.830459i	$-0.688078\pi$
$823$		−	1366.93i		−	1.66092i	0.557080	−	0.830459i	$-0.311922\pi$
$824$	−712.010	−	467.058i	−0.864090	−	0.566818i
$825$	461.461			0.559347
$826$	−46.3127	+	236.322i	−0.0560687	+	0.286104i
$827$			525.580i			0.635526i	0.948170	+	0.317763i	$0.102932\pi$
$827$			525.580i			0.635526i	−0.948170	+	0.317763i	$0.897068\pi$
$828$	−121.728	+	298.645i	−0.147014	+	0.360683i
$829$	1157.93			1.39678			0.698392	−	0.715715i	$-0.253899\pi$
$829$	1157.93			1.39678			0.698392	+	0.715715i	$0.253899\pi$
$830$	166.375	+	32.6050i	0.200452	+	0.0392832i
$831$			1562.28i			1.88000i
$832$	−474.995	−	1093.84i	−0.570908	−	1.31472i
$833$	−190.803			−0.229055
$834$	194.345	−	991.695i	0.233028	−	1.18908i
$835$			47.9931i			0.0574768i
$836$	−47.6911	−	19.4389i	−0.0570467	−	0.0232522i
$837$	928.595			1.10943
$838$	1217.57	+	238.611i	1.45295	+	0.284739i
$839$		−	180.527i		−	0.215170i	−0.994196	−	0.107585i	$-0.965688\pi$
$839$		−	180.527i		−	0.215170i	0.994196	−	0.107585i	$-0.0343117\pi$
$840$	77.9271	−	118.797i	0.0927704	−	0.141425i
$841$	548.694			0.652430
$842$	−55.9846	+	285.675i	−0.0664901	+	0.339282i
$843$			2011.16i			2.38571i
$844$	149.477	−	366.724i	0.177105	−	0.434507i
$845$	240.304			0.284383
$846$	−55.1911	−	10.8160i	−0.0652377	−	0.0127848i
$847$		−	280.355i		−	0.330998i
$848$	−381.954	−	373.406i	−0.450418	−	0.440337i
$849$	−1109.71			−1.30708
$850$	40.6867	−	207.614i	0.0478667	−	0.244252i
$851$		−	303.736i		−	0.356916i
$852$	−1487.12	−	606.151i	−1.74545	−	0.711445i
$853$	−1162.45			−1.36277			−0.681387	−	0.731923i	$-0.738623\pi$
$853$	−1162.45			−1.36277			−0.681387	+	0.731923i	$0.738623\pi$
$854$	−512.591	−	100.454i	−0.600224	−	0.117628i
$855$		−	64.8403i		−	0.0758366i
$856$	−1209.19	−	793.194i	−1.41261	−	0.926628i
$857$	430.041			0.501798			0.250899	−	0.968013i	$-0.419274\pi$
$857$	430.041			0.501798			0.250899	+	0.968013i	$0.419274\pi$
$858$	−142.667	+	727.995i	−0.166279	+	0.848479i
$859$			751.862i			0.875276i	0.899151	+	0.437638i	$0.144185\pi$
$859$			751.862i			0.875276i	−0.899151	+	0.437638i	$0.855815\pi$
$860$	−103.234	+	253.272i	−0.120039	+	0.294502i
$861$	−84.3251			−0.0979386
$862$	−248.381	−	48.6759i	−0.288145	−	0.0564685i
$863$		−	1630.21i		−	1.88900i	−0.328507	−	0.944502i	$-0.606545\pi$
$863$		−	1630.21i		−	1.88900i	0.328507	−	0.944502i	$-0.393455\pi$
$864$	546.904	+	793.953i	0.632991	+	0.918927i
$865$	162.166			0.187476
$866$	−93.9151	+	479.225i	−0.108447	+	0.553378i
$867$			1317.43i			1.51952i
$868$	306.059	+	124.750i	0.352603	+	0.143721i
$869$	−554.503			−0.638093
$870$	−484.700	−	94.9880i	−0.557126	−	0.109182i
$871$			1580.36i			1.81442i
$872$	−50.9513	+	77.6731i	−0.0584304	+	0.0890747i
$873$	−309.697			−0.354750
$874$	−6.51109	+	33.2245i	−0.00744976	+	0.0380143i
$875$			174.182i			0.199065i
$876$	−656.352	+	1610.29i	−0.749261	+	1.83823i
$877$	135.893			0.154952			0.0774760	−	0.996994i	$-0.475314\pi$
$877$	135.893			0.154952			0.0774760	+	0.996994i	$0.475314\pi$
$878$	−1495.10	−	292.999i	−1.70285	−	0.333712i
$879$			1320.37i			1.50213i
$880$	61.1205	−	62.5198i	0.0694551	−	0.0710452i
$881$	−526.553			−0.597676			−0.298838	−	0.954304i	$-0.596599\pi$
$881$	−526.553			−0.597676			−0.298838	+	0.954304i	$0.596599\pi$
$882$	−243.377	+	1241.89i	−0.275937	+	1.40804i
$883$		−	1661.72i		−	1.88190i	−0.338546	−	0.940950i	$-0.609935\pi$
$883$		−	1661.72i		−	1.88190i	0.338546	−	0.940950i	$-0.390065\pi$
$884$	314.950	+	128.374i	0.356278	+	0.145219i
$885$	−297.553			−0.336218
$886$	877.693	+	172.004i	0.990624	+	0.194135i
$887$			238.919i			0.269356i	0.990889	+	0.134678i	$0.0430001\pi$
$887$			238.919i			0.269356i	−0.990889	+	0.134678i	$0.957000\pi$
$888$	−1873.38	−	1228.89i	−2.10967	−	1.38388i
$889$	−457.405			−0.514517
$890$	78.4402	−	400.260i	0.0881350	−	0.449731i
$891$		−	47.8464i		−	0.0536997i
$892$	−75.5236	+	185.289i	−0.0846677	+	0.207723i
$893$	−5.90423			−0.00661168
$894$	−2126.68	−	416.771i	−2.37883	−	0.466187i
$895$			82.8886i			0.0926130i
$896$	73.5947	+	335.154i	0.0821370	+	0.374056i
$897$	487.687			0.543687
$898$	271.653	−	1386.17i	0.302508	−	1.54362i
$899$		−	1149.00i		−	1.27808i
$900$	−1299.41	−	529.640i	−1.44379	−	0.588488i
$901$	152.341			0.169080
$902$	−50.9247	−	9.97987i	−0.0564576	−	0.0110642i
$903$			667.736i			0.739464i
$904$	−80.6267	+	122.912i	−0.0891889	+	0.135965i
$905$	−302.181			−0.333901
$906$	−266.444	+	1359.60i	−0.294089	+	1.50066i
$907$			87.3382i			0.0962935i	0.998840	+	0.0481468i	$0.0153315\pi$
$907$			87.3382i			0.0962935i	−0.998840	+	0.0481468i	$0.984668\pi$
$908$	−85.5307	+	209.840i	−0.0941968	+	0.231101i
$909$	1673.83			1.84139
$910$	−132.208	−	25.9091i	−0.145283	−	0.0284716i
$911$		−	1353.13i		−	1.48532i	−0.669668	−	0.742660i	$-0.733564\pi$
$911$		−	1353.13i		−	1.48532i	0.669668	−	0.742660i	$-0.266436\pi$
$912$	178.579	+	174.582i	0.195810	+	0.191428i
$913$	254.724			0.278997
$914$	−319.895	+	1632.34i	−0.349994	+	1.78593i
$915$		−	645.402i		−	0.705358i
$916$	138.595	+	56.4915i	0.151305	+	0.0616719i
$917$	598.560			0.652737
$918$	−269.825	−	52.8784i	−0.293927	−	0.0576018i
$919$			818.696i			0.890855i	0.895318	+	0.445428i	$0.146948\pi$
$919$			818.696i			0.890855i	−0.895318	+	0.445428i	$0.853052\pi$
$920$	−48.0606	−	31.5263i	−0.0522398	−	0.0342678i
$921$	793.458			0.861518
$922$	44.5919	−	227.541i	0.0483643	−	0.246791i
$923$			1522.81i			1.64985i
$924$	80.5702	−	197.670i	0.0871972	−	0.213928i
$925$	1321.56			1.42871
$926$	740.995	+	145.215i	0.800211	+	0.156820i
$927$		−	1610.76i		−	1.73760i
$928$	982.399	−	676.712i	1.05862	−	0.729216i
$929$	−1712.20			−1.84305			−0.921527	−	0.388313i	$-0.873058\pi$
$929$	−1712.20			−1.84305			−0.921527	+	0.388313i	$0.873058\pi$
$930$	−78.5360	+	400.749i	−0.0844473	+	0.430913i
$931$			132.855i			0.142701i
$932$	−620.916	−	253.085i	−0.666219	−	0.271551i
$933$	−86.9613			−0.0932061
$934$	−191.833	−	37.5940i	−0.205389	−	0.0402506i
$935$			24.9357i			0.0266692i
$936$	1237.28	−	1886.19i	1.32188	−	2.01516i
$937$	−1758.31			−1.87653			−0.938263	−	0.345922i	$-0.887566\pi$
$937$	−1758.31			−1.87653			−0.938263	+	0.345922i	$0.887566\pi$
$938$	87.4526	−	446.248i	0.0932330	−	0.475745i
$939$			1236.93i			1.31728i
$940$	3.78341	−	9.28217i	0.00402490	−	0.00987465i
$941$	−1652.00			−1.75558			−0.877791	−	0.479044i	$-0.840984\pi$
$941$	−1652.00			−1.75558			−0.877791	+	0.479044i	$0.840984\pi$
$942$	−662.259	−	129.785i	−0.703036	−	0.137776i
$943$			34.1147i			0.0361768i
$944$	502.379	−	513.880i	0.532181	−	0.544365i
$945$	108.916			0.115255
$946$	−79.0265	+	403.252i	−0.0835375	+	0.426271i
$947$		−	1487.16i		−	1.57039i	−0.619251	−	0.785193i	$-0.712564\pi$
$947$		−	1487.16i		−	1.57039i	0.619251	−	0.785193i	$-0.287436\pi$
$948$	2490.02	+	1014.93i	2.62660	+	1.07060i
$949$	1648.93			1.73754
$950$	−144.560	−	28.3299i	−0.152169	−	0.0298209i
$951$			1968.89i			2.07034i
$952$	−81.8289	−	53.6774i	−0.0859547	−	0.0563838i
$953$	212.707			0.223197			0.111599	−	0.993753i	$-0.464403\pi$
$953$	212.707			0.223197			0.111599	+	0.993753i	$0.464403\pi$
$954$	194.317	−	991.549i	0.203686	−	1.03936i
$955$			467.426i			0.489451i
$956$	476.148	−	1168.17i	0.498062	−	1.22194i
$957$	−742.086			−0.775429
$958$	162.472	+	31.8400i	0.169595	+	0.0332359i
$959$			251.827i			0.262593i
$960$	−388.897	+	168.876i	−0.405101	+	0.175913i
$961$	11.0100			0.0114568
$962$	−408.579	+	2084.87i	−0.424718	+	2.16723i
$963$		−	2735.51i		−	2.84062i
$964$	766.934	+	312.602i	0.795575	+	0.324276i
$965$	423.959			0.439335
$966$	−137.709	−	26.9872i	−0.142556	−	0.0279370i
$967$		−	291.755i		−	0.301711i	−0.988556	−	0.150856i	$-0.951797\pi$
$967$		−	291.755i		−	0.301711i	0.988556	−	0.150856i	$-0.0482028\pi$
$968$	−458.890	+	699.559i	−0.474060	+	0.722685i
$969$	−71.2254			−0.0735041
$970$	10.6150	−	54.1658i	0.0109433	−	0.0558411i
$971$		−	1893.74i		−	1.95029i	−0.221557	−	0.975147i	$-0.571114\pi$
$971$		−	1893.74i		−	1.95029i	0.221557	−	0.975147i	$-0.428886\pi$
$972$	321.806	−	789.515i	0.331076	−	0.812258i
$973$	275.732			0.283384
$974$	108.610	+	21.2846i	0.111509	+	0.0218528i
$975$			2121.94i			2.17635i
$976$	1114.62	+	1089.68i	1.14203	+	1.11647i
$977$	201.277			0.206016			0.103008	−	0.994681i	$-0.467153\pi$
$977$	201.277			0.206016			0.103008	+	0.994681i	$0.467153\pi$
$978$	−359.646	+	1835.18i	−0.367736	+	1.87646i
$979$		−	612.807i		−	0.625952i
$980$	−208.864	−	85.1329i	−0.213126	−	0.0868703i
$981$	−175.717			−0.179121
$982$	856.009	+	167.754i	0.871699	+	0.170829i
$983$		−	618.732i		−	0.629432i	−0.949186	−	0.314716i	$-0.898091\pi$
$983$		−	618.732i		−	0.629432i	0.949186	−	0.314716i	$-0.101909\pi$
$984$	210.413	+	138.025i	0.213835	+	0.140269i
$985$	−64.8993			−0.0658876
$986$	−65.4292	+	333.868i	−0.0663582	+	0.338609i
$987$		−	24.4719i		−	0.0247942i
$988$	89.3857	−	219.298i	0.0904713	−	0.221961i
$989$	270.140			0.273145
$990$	162.301	+	31.8065i	0.163940	+	0.0321278i
$991$			352.818i			0.356022i	0.984028	+	0.178011i	$0.0569663\pi$
$991$			352.818i			0.356022i	−0.984028	+	0.178011i	$0.943034\pi$
$992$	−559.505	−	812.246i	−0.564017	−	0.818796i
$993$	−1710.02			−1.72208
$994$	84.2676	−	429.996i	0.0847763	−	0.432592i
$995$		−	182.642i		−	0.183560i
$996$	−1143.85	−	466.233i	−1.14844	−	0.468105i
$997$	971.069			0.973991			0.486996	−	0.873404i	$-0.338093\pi$
$997$	971.069			0.973991			0.486996	+	0.873404i	$0.338093\pi$
$998$	621.445	+	121.786i	0.622691	+	0.122030i
$999$		−	1717.56i		−	1.71928i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	164.3.c.a.83.23	✓	40
4.3	odd	2	inner	164.3.c.a.83.24	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.3.c.a.83.23	✓	40	1.1	even	1	trivial
164.3.c.a.83.24	yes	40	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	164.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.384629 - 1.96267i) q^{2} -4.91252i q^{3} +(-3.70412 - 1.50980i) q^{4} +1.34854 q^{5} +(-9.64164 - 1.88950i) q^{6} -2.68078i q^{7} +(-4.38794 + 6.68924i) q^{8} -15.1329 q^{9} +O(q^{10})\)	\(q+(0.384629 - 1.96267i) q^{2} -4.91252i q^{3} +(-3.70412 - 1.50980i) q^{4} +1.34854 q^{5} +(-9.64164 - 1.88950i) q^{6} -2.68078i q^{7} +(-4.38794 + 6.68924i) q^{8} -15.1329 q^{9} +(0.518686 - 2.64673i) q^{10} -4.05219i q^{11} +(-7.41692 + 18.1966i) q^{12} +18.6332 q^{13} +(-5.26147 - 1.03111i) q^{14} -6.62471i q^{15} +(11.4410 + 11.1850i) q^{16} -4.56320 q^{17} +(-5.82054 + 29.7007i) q^{18} +3.17732i q^{19} +(-4.99514 - 2.03602i) q^{20} -13.1694 q^{21} +(-7.95311 - 1.55859i) q^{22} +5.32782i q^{23} +(32.8610 + 21.5559i) q^{24} -23.1815 q^{25} +(7.16688 - 36.5708i) q^{26} +30.1278i q^{27} +(-4.04743 + 9.92992i) q^{28} +37.2786 q^{29} +(-13.0021 - 2.54806i) q^{30} -30.8219i q^{31} +(26.3529 - 18.1528i) q^{32} -19.9065 q^{33} +(-1.75514 + 8.95604i) q^{34} -3.61512i q^{35} +(56.0539 + 22.8476i) q^{36} -57.0093 q^{37} +(6.23603 + 1.22209i) q^{38} -91.5360i q^{39} +(-5.91730 + 9.02068i) q^{40} +6.40312 q^{41} +(-5.06533 + 25.8471i) q^{42} -50.7037i q^{43} +(-6.11800 + 15.0098i) q^{44} -20.4072 q^{45} +(10.4567 + 2.04924i) q^{46} +1.85824i q^{47} +(54.9463 - 56.2042i) q^{48} +41.8134 q^{49} +(-8.91627 + 45.4975i) q^{50} +22.4168i q^{51} +(-69.0196 - 28.1324i) q^{52} -33.3846 q^{53} +(59.1307 + 11.5880i) q^{54} -5.46453i q^{55} +(17.9324 + 11.7631i) q^{56} +15.6087 q^{57} +(14.3384 - 73.1655i) q^{58} -44.9156i q^{59} +(-10.0020 + 24.5387i) q^{60} +97.4235 q^{61} +(-60.4931 - 11.8550i) q^{62} +40.5678i q^{63} +(-25.4919 - 58.7040i) q^{64} +25.1275 q^{65} +(-7.65662 + 39.0698i) q^{66} +84.8144i q^{67} +(16.9026 + 6.88951i) q^{68} +26.1730 q^{69} +(-7.09528 - 1.39048i) q^{70} +81.7255i q^{71} +(66.4021 - 101.227i) q^{72} +88.4940 q^{73} +(-21.9275 + 111.890i) q^{74} +113.879i q^{75} +(4.79712 - 11.7692i) q^{76} -10.8630 q^{77} +(-179.655 - 35.2074i) q^{78} -136.840i q^{79} +(15.4286 + 15.0833i) q^{80} +11.8075 q^{81} +(2.46283 - 12.5672i) q^{82} +62.8608i q^{83} +(48.7809 + 19.8831i) q^{84} -6.15363 q^{85} +(-99.5145 - 19.5021i) q^{86} -183.132i q^{87} +(27.1061 + 17.7808i) q^{88} +151.228 q^{89} +(-7.84921 + 40.0525i) q^{90} -49.9515i q^{91} +(8.04394 - 19.7349i) q^{92} -151.413 q^{93} +(3.64711 + 0.714734i) q^{94} +4.28474i q^{95} +(-89.1762 - 129.459i) q^{96} +20.4652 q^{97} +(16.0827 - 82.0658i) q^{98} +61.3213i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - 2 q^{4} + 12 q^{6} + 10 q^{8} - 120 q^{9}+O(q^{10}) \) 40 * q - 2 * q^2 - 2 * q^4 + 12 * q^6 + 10 * q^8 - 120 * q^9	\( 40 q - 2 q^{2} - 2 q^{4} + 12 q^{6} + 10 q^{8} - 120 q^{9} - 20 q^{10} + 10 q^{12} - 16 q^{13} + 36 q^{14} - 42 q^{16} - 34 q^{18} + 8 q^{20} + 48 q^{21} - 38 q^{22} + 52 q^{24} + 216 q^{25} + 54 q^{26} - 54 q^{28} - 32 q^{29} + 66 q^{30} - 2 q^{32} - 48 q^{33} - 124 q^{34} - 70 q^{36} + 16 q^{37} - 140 q^{38} + 16 q^{40} + 88 q^{42} + 100 q^{44} - 48 q^{45} + 196 q^{46} + 78 q^{48} - 152 q^{49} + 198 q^{50} + 26 q^{52} - 32 q^{53} - 74 q^{54} + 96 q^{56} - 112 q^{57} + 38 q^{58} - 102 q^{60} + 96 q^{61} - 112 q^{62} + 70 q^{64} - 96 q^{65} - 528 q^{66} - 148 q^{68} - 80 q^{69} - 82 q^{70} - 458 q^{72} + 128 q^{73} + 372 q^{74} - 50 q^{76} + 192 q^{77} + 144 q^{78} - 100 q^{80} + 520 q^{81} + 344 q^{84} - 176 q^{85} - 460 q^{86} + 66 q^{88} + 16 q^{89} + 80 q^{90} + 572 q^{92} + 32 q^{93} + 262 q^{94} - 304 q^{96} - 304 q^{97} + 174 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 - 2 * q^4 + 12 * q^6 + 10 * q^8 - 120 * q^9 - 20 * q^10 + 10 * q^12 - 16 * q^13 + 36 * q^14 - 42 * q^16 - 34 * q^18 + 8 * q^20 + 48 * q^21 - 38 * q^22 + 52 * q^24 + 216 * q^25 + 54 * q^26 - 54 * q^28 - 32 * q^29 + 66 * q^30 - 2 * q^32 - 48 * q^33 - 124 * q^34 - 70 * q^36 + 16 * q^37 - 140 * q^38 + 16 * q^40 + 88 * q^42 + 100 * q^44 - 48 * q^45 + 196 * q^46 + 78 * q^48 - 152 * q^49 + 198 * q^50 + 26 * q^52 - 32 * q^53 - 74 * q^54 + 96 * q^56 - 112 * q^57 + 38 * q^58 - 102 * q^60 + 96 * q^61 - 112 * q^62 + 70 * q^64 - 96 * q^65 - 528 * q^66 - 148 * q^68 - 80 * q^69 - 82 * q^70 - 458 * q^72 + 128 * q^73 + 372 * q^74 - 50 * q^76 + 192 * q^77 + 144 * q^78 - 100 * q^80 + 520 * q^81 + 344 * q^84 - 176 * q^85 - 460 * q^86 + 66 * q^88 + 16 * q^89 + 80 * q^90 + 572 * q^92 + 32 * q^93 + 262 * q^94 - 304 * q^96 - 304 * q^97 + 174 * q^98

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