LMFDB - Embedded newform 201.3.c.a.68.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(68,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, 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("201.68");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.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:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			68.9
Character	$\chi$	$=$	201.68
Dual form			201.3.c.a.68.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.83332i q^{2} +(2.79666 - 1.08567i) q^{3} -4.02771 q^{4} -6.23827i q^{5} +(-3.07604 - 7.92385i) q^{6} +3.53484 q^{7} +0.0785029i q^{8} +(6.64266 - 6.07248i) q^{9} +O(q^{10})$	\(q-2.83332i q^{2} +(2.79666 - 1.08567i) q^{3} -4.02771 q^{4} -6.23827i q^{5} +(-3.07604 - 7.92385i) q^{6} +3.53484 q^{7} +0.0785029i q^{8} +(6.64266 - 6.07248i) q^{9} -17.6750 q^{10} +17.9707i q^{11} +(-11.2641 + 4.37274i) q^{12} +10.1653 q^{13} -10.0153i q^{14} +(-6.77267 - 17.4463i) q^{15} -15.8884 q^{16} +14.3944i q^{17} +(-17.2053 - 18.8208i) q^{18} -20.3937 q^{19} +25.1259i q^{20} +(9.88577 - 3.83766i) q^{21} +50.9167 q^{22} -17.7695i q^{23} +(0.0852279 + 0.219546i) q^{24} -13.9160 q^{25} -28.8016i q^{26} +(11.9846 - 24.1944i) q^{27} -14.2373 q^{28} +33.6742i q^{29} +(-49.4311 + 19.1891i) q^{30} -5.31967 q^{31} +45.3310i q^{32} +(19.5102 + 50.2580i) q^{33} +40.7840 q^{34} -22.0513i q^{35} +(-26.7547 + 24.4582i) q^{36} -4.65339 q^{37} +57.7818i q^{38} +(28.4290 - 11.0361i) q^{39} +0.489722 q^{40} +48.2667i q^{41} +(-10.8733 - 28.0096i) q^{42} +68.3054 q^{43} -72.3807i q^{44} +(-37.8818 - 41.4387i) q^{45} -50.3467 q^{46} -52.1409i q^{47} +(-44.4345 + 17.2495i) q^{48} -36.5049 q^{49} +39.4284i q^{50} +(15.6275 + 40.2563i) q^{51} -40.9430 q^{52} -54.0216i q^{53} +(-68.5505 - 33.9562i) q^{54} +112.106 q^{55} +0.277495i q^{56} +(-57.0342 + 22.1407i) q^{57} +95.4098 q^{58} +25.5885i q^{59} +(27.2783 + 70.2687i) q^{60} +76.4062 q^{61} +15.0723i q^{62} +(23.4808 - 21.4653i) q^{63} +64.8835 q^{64} -63.4141i q^{65} +(142.397 - 55.2785i) q^{66} -8.18535 q^{67} -57.9765i q^{68} +(-19.2917 - 49.6953i) q^{69} -62.4784 q^{70} -17.8693i q^{71} +(0.476707 + 0.521468i) q^{72} +126.603 q^{73} +13.1846i q^{74} +(-38.9183 + 15.1081i) q^{75} +82.1397 q^{76} +63.5236i q^{77} +(-31.2689 - 80.5485i) q^{78} -95.7714 q^{79} +99.1161i q^{80} +(7.24991 - 80.6749i) q^{81} +136.755 q^{82} -75.3364i q^{83} +(-39.8170 + 15.4570i) q^{84} +89.7962 q^{85} -193.531i q^{86} +(36.5589 + 94.1755i) q^{87} -1.41075 q^{88} +89.3445i q^{89} +(-117.409 + 107.331i) q^{90} +35.9329 q^{91} +71.5704i q^{92} +(-14.8773 + 5.77538i) q^{93} -147.732 q^{94} +127.221i q^{95} +(49.2142 + 126.775i) q^{96} -119.761 q^{97} +103.430i q^{98} +(109.127 + 119.373i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	2.83332i		−	1.41666i	−0.705881	−	0.708330i	$-0.749449\pi$
$2$		−	2.83332i		−	1.41666i	0.705881	−	0.708330i	$-0.250551\pi$
$3$	2.79666	−	1.08567i	0.932221	−	0.361888i
$3$	2.79666	−	1.08567i	0.932221	−	0.361888i
$4$	−4.02771			−1.00693
$5$		−	6.23827i		−	1.24765i	−0.781563	−	0.623827i	$-0.785577\pi$
$5$		−	6.23827i		−	1.24765i	0.781563	−	0.623827i	$-0.214423\pi$
$6$	−3.07604	−	7.92385i	−0.512673	−	1.32064i
$7$	3.53484			0.504978			0.252489	−	0.967600i	$-0.418751\pi$
$7$	3.53484			0.504978			0.252489	+	0.967600i	$0.418751\pi$
$8$			0.0785029i			0.00981286i
$9$	6.64266	−	6.07248i	0.738074	−	0.674720i
$10$	−17.6750			−1.76750
$11$			17.9707i			1.63370i	0.576851	+	0.816849i	$0.304281\pi$
$11$			17.9707i			1.63370i	−0.576851	+	0.816849i	$0.695719\pi$
$12$	−11.2641	+	4.37274i	−0.938679	+	0.364395i
$13$	10.1653			0.781949			0.390974	−	0.920402i	$-0.372138\pi$
$13$	10.1653			0.781949			0.390974	+	0.920402i	$0.372138\pi$
$14$		−	10.0153i		−	0.715382i
$15$	−6.77267	−	17.4463i	−0.451511	−	1.16309i
$16$	−15.8884			−0.993025
$17$			14.3944i			0.846730i	0.905959	+	0.423365i	$0.139151\pi$
$17$			14.3944i			0.846730i	−0.905959	+	0.423365i	$0.860849\pi$
$18$	−17.2053	−	18.8208i	−0.955850	−	1.04560i
$19$	−20.3937			−1.07335			−0.536675	−	0.843789i	$-0.680320\pi$
$19$	−20.3937			−1.07335			−0.536675	+	0.843789i	$0.680320\pi$
$20$			25.1259i			1.25630i
$21$	9.88577	−	3.83766i	0.470751	−	0.182746i
$22$	50.9167			2.31440
$23$		−	17.7695i		−	0.772587i	−0.922376	−	0.386294i	$-0.873755\pi$
$23$		−	17.7695i		−	0.772587i	0.922376	−	0.386294i	$-0.126245\pi$
$24$	0.0852279	+	0.219546i	0.00355116	+	0.00914776i
$25$	−13.9160			−0.556639
$26$		−	28.8016i		−	1.10776i
$27$	11.9846	−	24.1944i	0.443874	−	0.896089i
$28$	−14.2373			−0.508475
$29$			33.6742i			1.16118i	0.814196	+	0.580590i	$0.197178\pi$
$29$			33.6742i			1.16118i	−0.814196	+	0.580590i	$0.802822\pi$
$30$	−49.4311	+	19.1891i	−1.64770	+	0.639638i
$31$	−5.31967			−0.171602			−0.0858012	−	0.996312i	$-0.527345\pi$
$31$	−5.31967			−0.171602			−0.0858012	+	0.996312i	$0.527345\pi$
$32$			45.3310i			1.41659i
$33$	19.5102	+	50.2580i	0.591217	+	1.52297i
$34$	40.7840			1.19953
$35$		−	22.0513i		−	0.630037i
$36$	−26.7547	+	24.4582i	−0.743186	+	0.679394i
$37$	−4.65339			−0.125767			−0.0628837	−	0.998021i	$-0.520030\pi$
$37$	−4.65339			−0.125767			−0.0628837	+	0.998021i	$0.520030\pi$
$38$			57.7818i			1.52057i
$39$	28.4290	−	11.0361i	0.728949	−	0.282978i
$40$	0.489722			0.0122431
$41$			48.2667i			1.17724i	0.808411	+	0.588618i	$0.200328\pi$
$41$			48.2667i			1.17724i	−0.808411	+	0.588618i	$0.799672\pi$
$42$	−10.8733	−	28.0096i	−0.258888	−	0.666894i
$43$	68.3054			1.58850			0.794248	−	0.607593i	$-0.207865\pi$
$43$	68.3054			1.58850			0.794248	+	0.607593i	$0.207865\pi$
$44$		−	72.3807i		−	1.64502i
$45$	−37.8818	−	41.4387i	−0.841817	−	0.920860i
$46$	−50.3467			−1.09449
$47$		−	52.1409i		−	1.10938i	−0.832057	−	0.554691i	$-0.812837\pi$
$47$		−	52.1409i		−	1.10938i	0.832057	−	0.554691i	$-0.187163\pi$
$48$	−44.4345	+	17.2495i	−0.925719	+	0.359364i
$49$	−36.5049			−0.744998
$50$			39.4284i			0.788569i
$51$	15.6275	+	40.2563i	0.306422	+	0.789340i
$52$	−40.9430			−0.787365
$53$		−	54.0216i		−	1.01928i	−0.860389	−	0.509638i	$-0.829779\pi$
$53$		−	54.0216i		−	1.01928i	0.860389	−	0.509638i	$-0.170221\pi$
$54$	−68.5505	−	33.9562i	−1.26945	−	0.628819i
$55$	112.106			2.03829
$56$			0.277495i			0.00495527i
$57$	−57.0342	+	22.1407i	−1.00060	+	0.388433i
$58$	95.4098			1.64500
$59$			25.5885i			0.433703i	0.976205	+	0.216852i	$0.0695788\pi$
$59$			25.5885i			0.433703i	−0.976205	+	0.216852i	$0.930421\pi$
$60$	27.2783	+	70.2687i	0.454639	+	1.17115i
$61$	76.4062			1.25256			0.626280	−	0.779598i	$-0.284577\pi$
$61$	76.4062			1.25256			0.626280	+	0.779598i	$0.284577\pi$
$62$			15.0723i			0.243102i
$63$	23.4808	−	21.4653i	0.372711	−	0.340719i
$64$	64.8835			1.01381
$65$		−	63.4141i		−	0.975601i
$66$	142.397	−	55.2785i	2.15753	−	0.837553i
$67$	−8.18535			−0.122169
$67$	−8.18535			−0.122169
$68$		−	57.9765i		−	0.852595i
$69$	−19.2917	−	49.6953i	−0.279590	−	0.720222i
$70$	−62.4784			−0.892549
$71$		−	17.8693i		−	0.251680i	−0.992051	−	0.125840i	$-0.959837\pi$
$71$		−	17.8693i		−	0.251680i	0.992051	−	0.125840i	$-0.0401626\pi$
$72$	0.476707	+	0.521468i	0.00662094	+	0.00724261i
$73$	126.603			1.73429			0.867147	−	0.498053i	$-0.165952\pi$
$73$	126.603			1.73429			0.867147	+	0.498053i	$0.165952\pi$
$74$			13.1846i			0.178170i
$75$	−38.9183	+	15.1081i	−0.518911	+	0.201441i
$76$	82.1397			1.08079
$77$			63.5236i			0.824981i
$78$	−31.2689	−	80.5485i	−0.400884	−	1.03267i
$79$	−95.7714			−1.21230			−0.606148	−	0.795352i	$-0.707286\pi$
$79$	−95.7714			−1.21230			−0.606148	+	0.795352i	$0.707286\pi$
$80$			99.1161i			1.23895i
$81$	7.24991	−	80.6749i	0.0895051	−	0.995986i
$82$	136.755			1.66774
$83$		−	75.3364i		−	0.907667i	−0.891086	−	0.453834i	$-0.850056\pi$
$83$		−	75.3364i		−	0.907667i	0.891086	−	0.453834i	$-0.149944\pi$
$84$	−39.8170	+	15.4570i	−0.474012	+	0.184011i
$85$	89.7962			1.05643
$86$		−	193.531i		−	2.25036i
$87$	36.5589	+	94.1755i	0.420218	+	1.08248i
$88$	−1.41075			−0.0160313
$89$			89.3445i			1.00387i	0.864905	+	0.501935i	$0.167378\pi$
$89$			89.3445i			1.00387i	−0.864905	+	0.501935i	$0.832622\pi$
$90$	−117.409	+	107.331i	−1.30455	+	1.19257i
$91$	35.9329			0.394867
$92$			71.5704i			0.777939i
$93$	−14.8773	+	5.77538i	−0.159971	+	0.0621009i
$94$	−147.732			−1.57162
$95$			127.221i			1.33917i
$96$	49.2142	+	126.775i	0.512648	+	1.32058i
$97$	−119.761			−1.23465			−0.617326	−	0.786707i	$-0.711784\pi$
$97$	−119.761			−1.23465			−0.617326	+	0.786707i	$0.711784\pi$
$98$			103.430i			1.05541i
$99$	109.127	+	119.373i	1.10229	+	1.20579i
$100$	56.0495			0.560495
$101$		−	6.02709i		−	0.0596742i	−0.999555	−	0.0298371i	$-0.990501\pi$
$101$		−	6.02709i		−	0.0596742i	0.999555	−	0.0298371i	$-0.00949885\pi$
$102$	114.059	−	44.2778i	1.11823	−	0.434096i
$103$	4.69821			0.0456137			0.0228068	−	0.999740i	$-0.492740\pi$
$103$	4.69821			0.0456137			0.0228068	+	0.999740i	$0.492740\pi$
$104$			0.798008i			0.00767315i
$105$	−23.9403	−	61.6701i	−0.228003	−	0.587334i
$106$	−153.061			−1.44397
$107$		−	138.369i		−	1.29317i	−0.762843	−	0.646584i	$-0.776197\pi$
$107$		−	138.369i		−	1.29317i	0.762843	−	0.646584i	$-0.223803\pi$
$108$	−48.2705	+	97.4480i	−0.446949	+	0.902296i
$109$	−101.868			−0.934573			−0.467286	−	0.884106i	$-0.654768\pi$
$109$	−101.868			−0.934573			−0.467286	+	0.884106i	$0.654768\pi$
$110$		−	317.632i		−	2.88757i
$111$	−13.0140	+	5.05203i	−0.117243	+	0.0455138i
$112$	−56.1630			−0.501456
$113$			142.004i			1.25667i	0.777943	+	0.628335i	$0.216263\pi$
$113$			142.004i			1.25667i	−0.777943	+	0.628335i	$0.783737\pi$
$114$	62.7317	+	161.596i	0.550278	+	1.41751i
$115$	−110.851			−0.963921
$116$		−	135.630i		−	1.16922i
$117$	67.5249	−	61.7288i	0.577136	−	0.527597i
$118$	72.5004			0.614410
$119$			50.8820i			0.427580i
$120$	1.36959	−	0.531674i	0.0114132	−	0.00443062i
$121$	−201.946			−1.66897
$122$		−	216.483i		−	1.77445i
$123$	52.4014	+	134.986i	0.426028	+	1.09744i
$124$	21.4261			0.172791
$125$		−	69.1451i		−	0.553160i
$126$	−60.8180	−	66.5285i	−0.482683	−	0.528004i
$127$	−133.971			−1.05489			−0.527446	−	0.849589i	$-0.676850\pi$
$127$	−133.971			−1.05489			−0.527446	+	0.849589i	$0.676850\pi$
$128$		−	2.51203i		−	0.0196253i
$129$	191.027	−	74.1568i	1.48083	−	0.574859i
$130$	−179.672			−1.38210
$131$			40.5205i			0.309317i	0.987968	+	0.154659i	$0.0494277\pi$
$131$			40.5205i			0.309317i	−0.987968	+	0.154659i	$0.950572\pi$
$132$	−78.5812	−	202.424i	−0.595312	−	1.53352i
$133$	−72.0884			−0.542018
$134$			23.1917i			0.173073i
$135$	−150.931	−	74.7632i	−1.11801	−	0.553802i
$136$	−1.13000			−0.00830884
$137$			244.322i			1.78337i	0.452654	+	0.891686i	$0.350477\pi$
$137$			244.322i			1.78337i	−0.452654	+	0.891686i	$0.649523\pi$
$138$	−140.803	+	54.6597i	−1.02031	+	0.396085i
$139$	−244.534			−1.75924			−0.879619	−	0.475680i	$-0.842202\pi$
$139$	−244.534			−1.75924			−0.879619	+	0.475680i	$0.842202\pi$
$140$			88.8162i			0.634401i
$141$	−56.6076	−	145.821i	−0.401472	−	1.03419i
$142$	−50.6293			−0.356545
$143$			182.678i			1.27747i
$144$	−105.541	+	96.4821i	−0.732926	+	0.670014i
$145$	210.069			1.44875
$146$		−	358.708i		−	2.45690i
$147$	−102.092	+	39.6321i	−0.694503	+	0.269606i
$148$	18.7425			0.126639
$149$			88.7747i			0.595804i	0.954597	+	0.297902i	$0.0962868\pi$
$149$			88.7747i			0.595804i	−0.954597	+	0.297902i	$0.903713\pi$
$150$	42.8061	+	110.268i	0.285374	+	0.735121i
$151$	236.043			1.56320			0.781598	−	0.623783i	$-0.214405\pi$
$151$	236.043			1.56320			0.781598	+	0.623783i	$0.214405\pi$
$152$		−	1.60096i		−	0.0105326i
$153$	87.4098	+	95.6172i	0.571306	+	0.624949i
$154$	179.983			1.16872
$155$			33.1855i			0.214100i
$156$	−114.504	+	44.4504i	−0.733998	+	0.284938i
$157$	216.863			1.38129			0.690646	−	0.723193i	$-0.257326\pi$
$157$	216.863			1.38129			0.690646	+	0.723193i	$0.257326\pi$
$158$			271.351i			1.71741i
$159$	−58.6494	−	151.080i	−0.368864	−	0.950191i
$160$	282.787			1.76742
$161$		−	62.8124i		−	0.390139i
$162$	−228.578	−	20.5413i	−1.41097	−	0.126798i
$163$	58.6970			0.360104			0.180052	−	0.983657i	$-0.442373\pi$
$163$	58.6970			0.360104			0.180052	+	0.983657i	$0.442373\pi$
$164$		−	194.404i		−	1.18539i
$165$	313.523	−	121.710i	1.90014	−	0.737634i
$166$	−213.452			−1.28586
$167$			43.8528i			0.262591i	0.991343	+	0.131296i	$0.0419137\pi$
$167$			43.8528i			0.262591i	−0.991343	+	0.131296i	$0.958086\pi$
$168$	0.301267	+	0.776061i	0.00179326	+	0.00461941i
$169$	−65.6660			−0.388556
$170$		−	254.421i		−	1.49660i
$171$	−135.468	+	123.840i	−0.792211	+	0.724211i
$172$	−275.114			−1.59950
$173$		−	49.9147i		−	0.288524i	−0.989539	−	0.144262i	$-0.953919\pi$
$173$		−	49.9147i		−	0.288524i	0.989539	−	0.144262i	$-0.0460809\pi$
$174$	266.829	−	103.583i	1.53350	−	0.595306i
$175$	−49.1908			−0.281090
$176$		−	285.526i		−	1.62230i
$177$	27.7805	+	71.5624i	0.156952	+	0.404308i
$178$	253.142			1.42214
$179$			102.613i			0.573259i	0.958042	+	0.286629i	$0.0925348\pi$
$179$			102.613i			0.573259i	−0.958042	+	0.286629i	$0.907465\pi$
$180$	152.577	+	166.903i	0.847648	+	0.927239i
$181$	−225.962			−1.24841			−0.624204	−	0.781261i	$-0.714577\pi$
$181$	−225.962			−1.24841			−0.624204	+	0.781261i	$0.714577\pi$
$182$		−	101.809i		−	0.559392i
$183$	213.682	−	82.9516i	1.16766	−	0.453287i
$184$	1.39496			0.00758129
$185$			29.0291i			0.156914i
$186$	16.3635	+	42.1523i	0.0879759	+	0.226625i
$187$	−258.677			−1.38330
$188$			210.008i			1.11707i
$189$	42.3637	−	85.5234i	0.224147	−	0.452505i
$190$	360.458			1.89715
$191$		−	107.601i		−	0.563357i	−0.959509	−	0.281678i	$-0.909109\pi$
$191$		−	107.601i		−	0.563357i	0.959509	−	0.281678i	$-0.0908911\pi$
$192$	181.457	−	70.4418i	0.945091	−	0.366884i
$193$	−188.856			−0.978526			−0.489263	−	0.872136i	$-0.662734\pi$
$193$	−188.856			−0.978526			−0.489263	+	0.872136i	$0.662734\pi$
$194$			339.322i			1.74908i
$195$	−68.8464	−	177.348i	−0.353059	−	0.909476i
$196$	147.031			0.750158
$197$			334.638i			1.69867i	0.527854	+	0.849335i	$0.322997\pi$
$197$			334.638i			1.69867i	−0.527854	+	0.849335i	$0.677003\pi$
$198$	338.223	−	309.191i	1.70819	−	1.56157i
$199$	84.3528			0.423884			0.211942	−	0.977282i	$-0.432021\pi$
$199$	84.3528			0.423884			0.211942	+	0.977282i	$0.432021\pi$
$200$		−	1.09244i		−	0.00546222i
$201$	−22.8917	+	8.88655i	−0.113889	+	0.0442117i
$202$	−17.0767			−0.0845380
$203$			119.033i			0.586370i
$204$	−62.9430	−	162.141i	−0.308544	−	0.794807i
$205$	301.100			1.46878
$206$		−	13.3115i		−	0.0646191i
$207$	−107.905	−	118.037i	−0.521280	−	0.570226i
$208$	−161.511			−0.776495
$209$		−	366.488i		−	1.75353i
$210$	−174.731	+	67.8306i	−0.832053	+	0.323003i
$211$	−185.752			−0.880343			−0.440172	−	0.897914i	$-0.645082\pi$
$211$	−185.752			−0.880343			−0.440172	+	0.897914i	$0.645082\pi$
$212$			217.583i			1.02634i
$213$	−19.4000	−	49.9743i	−0.0910800	−	0.234621i
$214$	−392.044			−1.83198
$215$		−	426.107i		−	1.98189i
$216$	1.89933	+	0.940827i	0.00879320	+	0.00435568i
$217$	−18.8042			−0.0866553
$218$			288.626i			1.32397i
$219$	354.067	−	137.449i	1.61675	−	0.627621i
$220$	−451.530			−2.05241
$221$			146.324i			0.662099i
$222$	14.3140	+	36.8728i	0.0644775	+	0.166094i
$223$	−32.7839			−0.147013			−0.0735066	−	0.997295i	$-0.523419\pi$
$223$	−32.7839			−0.147013			−0.0735066	+	0.997295i	$0.523419\pi$
$224$			160.238i			0.715347i
$225$	−92.4392	+	84.5046i	−0.410841	+	0.375576i
$226$	402.342			1.78027
$227$			17.9255i			0.0789669i	0.999220	+	0.0394835i	$0.0125712\pi$
$227$			17.9255i			0.0789669i	−0.999220	+	0.0394835i	$0.987429\pi$
$228$	229.717	−	89.1762i	1.00753	−	0.391124i
$229$	81.2903			0.354980			0.177490	−	0.984123i	$-0.443202\pi$
$229$	81.2903			0.354980			0.177490	+	0.984123i	$0.443202\pi$
$230$			314.076i			1.36555i
$231$	68.9653	+	177.654i	0.298551	+	0.769065i
$232$	−2.64352			−0.0113945
$233$		−	207.739i		−	0.891582i	−0.895137	−	0.445791i	$-0.852922\pi$
$233$		−	207.739i		−	0.891582i	0.895137	−	0.445791i	$-0.147078\pi$
$234$	−174.897	−	191.320i	−0.747425	−	0.817605i
$235$	−325.269			−1.38412
$236$		−	103.063i		−	0.436708i
$237$	−267.841	+	103.976i	−1.13013	+	0.438716i
$238$	144.165			0.605735
$239$			103.158i			0.431622i	0.976435	+	0.215811i	$0.0692396\pi$
$239$			103.158i			0.431622i	−0.976435	+	0.215811i	$0.930760\pi$
$240$	107.607	+	277.195i	0.448362	+	1.15498i
$241$	408.161			1.69362			0.846808	−	0.531899i	$-0.178521\pi$
$241$	408.161			1.69362			0.846808	+	0.531899i	$0.178521\pi$
$242$			572.177i			2.36437i
$243$	−67.3104	−	233.492i	−0.276997	−	0.960871i
$244$	−307.742			−1.26124
$245$			227.727i			0.929499i
$246$	382.458	−	148.470i	1.55471	−	0.603537i
$247$	−207.308			−0.839305
$248$		−	0.417610i		−	0.00168391i
$249$	−81.7901	−	210.691i	−0.328474	−	0.846147i
$250$	−195.910			−0.783641
$251$		−	170.679i		−	0.679996i	−0.940426	−	0.339998i	$-0.889574\pi$
$251$		−	170.679i		−	0.679996i	0.940426	−	0.339998i	$-0.110426\pi$
$252$	−94.5737	+	86.4558i	−0.375292	+	0.343079i
$253$	319.330			1.26217
$254$			379.583i			1.49442i
$255$	251.130	−	97.4886i	0.984823	−	0.382308i
$256$	252.417			0.986003
$257$		−	164.728i		−	0.640966i	−0.947254	−	0.320483i	$-0.896155\pi$
$257$		−	164.728i		−	0.640966i	0.947254	−	0.320483i	$-0.103845\pi$
$258$	−210.110	−	541.241i	−0.814379	−	2.09783i
$259$	−16.4490			−0.0635097
$260$			255.413i			0.982359i
$261$	204.486	+	223.686i	0.783472	+	0.857036i
$262$	114.808			0.438197
$263$		−	338.140i		−	1.28570i	−0.765990	−	0.642852i	$-0.777751\pi$
$263$		−	338.140i		−	1.28570i	0.765990	−	0.642852i	$-0.222249\pi$
$264$	−3.94540	+	1.53160i	−0.0149447	+	0.00580153i
$265$	−337.001			−1.27170
$266$			204.250i			0.767855i
$267$	96.9982	+	249.867i	0.363289	+	0.935830i
$268$	32.9682			0.123016
$269$			121.209i			0.450590i	0.974291	+	0.225295i	$0.0723346\pi$
$269$			121.209i			0.450590i	−0.974291	+	0.225295i	$0.927665\pi$
$270$	−211.828	+	427.636i	−0.784549	+	1.58384i
$271$	240.793			0.888533			0.444267	−	0.895895i	$-0.353464\pi$
$271$	240.793			0.888533			0.444267	+	0.895895i	$0.353464\pi$
$272$		−	228.704i		−	0.840824i
$273$	100.492	−	39.0111i	0.368103	−	0.142898i
$274$	692.243			2.52643
$275$		−	250.080i		−	0.909381i
$276$	77.7014	+	200.158i	0.281527	+	0.725211i
$277$	−409.758			−1.47927			−0.739635	−	0.673008i	$-0.765002\pi$
$277$	−409.758			−1.47927			−0.739635	+	0.673008i	$0.765002\pi$
$278$			692.843i			2.49224i
$279$	−35.3368	+	32.3036i	−0.126655	+	0.115784i
$280$	1.73109			0.00618247
$281$		−	35.1244i		−	0.124998i	−0.998045	−	0.0624989i	$-0.980093\pi$
$281$		−	35.1244i		−	0.124998i	0.998045	−	0.0624989i	$-0.0199070\pi$
$282$	−413.157	+	160.387i	−1.46509	+	0.568750i
$283$	−404.699			−1.43003			−0.715015	−	0.699109i	$-0.753580\pi$
$283$	−404.699			−1.43003			−0.715015	+	0.699109i	$0.753580\pi$
$284$			71.9721i			0.253423i
$285$	138.120	+	355.795i	0.484630	+	1.24840i
$286$	517.585			1.80974
$287$			170.615i			0.594478i
$288$	275.271	+	301.118i	0.955804	+	1.04555i
$289$	81.8009			0.283048
$290$		−	595.192i		−	2.05239i
$291$	−334.932	+	130.021i	−1.15097	+	0.446807i
$292$	−509.921			−1.74631
$293$			311.974i			1.06476i	0.846506	+	0.532379i	$0.178702\pi$
$293$			311.974i			1.06476i	−0.846506	+	0.532379i	$0.821298\pi$
$294$	112.290	+	289.259i	0.381940	+	0.983875i
$295$	159.628			0.541112
$296$		−	0.365305i		−	0.00123414i
$297$	434.790	+	215.372i	1.46394	+	0.725157i
$298$	251.527			0.844051
$299$		−	180.633i		−	0.604123i
$300$	156.752	−	60.8510i	0.522506	−	0.202837i
$301$	241.449			0.802155
$302$		−	668.784i		−	2.21452i
$303$	−6.54340	−	16.8558i	−0.0215954	−	0.0556295i
$304$	324.023			1.06586
$305$		−	476.642i		−	1.56276i
$306$	270.914	−	247.660i	0.885341	−	0.809347i
$307$	−292.714			−0.953467			−0.476734	−	0.879048i	$-0.658179\pi$
$307$	−292.714			−0.953467			−0.476734	+	0.879048i	$0.658179\pi$
$308$		−	255.854i		−	0.830696i
$309$	13.1393	−	5.10068i	0.0425220	−	0.0165071i
$310$	94.0253			0.303307
$311$			382.666i			1.23044i	0.788357	+	0.615219i	$0.210932\pi$
$311$			382.666i			1.23044i	−0.788357	+	0.615219i	$0.789068\pi$
$312$	0.866369	+	2.23176i	0.00277683	+	0.00715308i
$313$	27.0823			0.0865249			0.0432625	−	0.999064i	$-0.486225\pi$
$313$	27.0823			0.0865249			0.0432625	+	0.999064i	$0.486225\pi$
$314$		−	614.442i		−	1.95682i
$315$	−133.906	−	146.479i	−0.425099	−	0.465014i
$316$	385.739			1.22069
$317$			129.365i			0.408091i	0.978961	+	0.204045i	$0.0654090\pi$
$317$			129.365i			0.408091i	−0.978961	+	0.204045i	$0.934591\pi$
$318$	−428.059	+	166.173i	−1.34610	+	0.522555i
$319$	−605.149			−1.89702
$320$		−	404.761i		−	1.26488i
$321$	−150.222	−	386.971i	−0.467982	−	1.20552i
$322$	−177.968			−0.552695
$323$		−	293.555i		−	0.908838i
$324$	−29.2005	+	324.935i	−0.0901251	+	1.00289i
$325$	−141.461			−0.435263
$326$		−	166.307i		−	0.510146i
$327$	−284.892	+	110.595i	−0.871229	+	0.338211i
$328$	−3.78907			−0.0115520
$329$		−	184.310i		−	0.560213i
$330$	−344.842	−	888.310i	−1.04498	−	2.69185i
$331$	−415.364			−1.25488			−0.627438	−	0.778667i	$-0.715896\pi$
$331$	−415.364			−1.25488			−0.627438	+	0.778667i	$0.715896\pi$
$332$			303.433i			0.913954i
$333$	−30.9109	+	28.2576i	−0.0928256	+	0.0848578i
$334$	124.249			0.372003
$335$			51.0624i			0.152425i
$336$	−157.069	+	60.9742i	−0.467468	+	0.181471i
$337$	75.3643			0.223633			0.111816	−	0.993729i	$-0.464333\pi$
$337$	75.3643			0.223633			0.111816	+	0.993729i	$0.464333\pi$
$338$			186.053i			0.550452i
$339$	154.168	+	397.136i	0.454774	+	1.17149i
$340$	−361.673			−1.06374
$341$		−	95.5982i		−	0.280347i
$342$	350.879	+	383.825i	1.02596	+	1.12229i
$343$	−302.246			−0.881185
$344$			5.36217i			0.0155877i
$345$	−310.013	+	120.347i	−0.898588	+	0.348832i
$346$	−141.424			−0.408741
$347$		−	557.637i		−	1.60702i	−0.595289	−	0.803512i	$-0.702962\pi$
$347$		−	557.637i		−	1.60702i	0.595289	−	0.803512i	$-0.297038\pi$
$348$	−147.249	−	379.311i	−0.423128	−	1.08997i
$349$	128.367			0.367815			0.183907	−	0.982944i	$-0.441125\pi$
$349$	128.367			0.367815			0.183907	+	0.982944i	$0.441125\pi$
$350$			139.373i			0.398210i
$351$	121.828	−	245.944i	0.347087	−	0.700696i
$352$	−814.628			−2.31429
$353$		−	613.881i		−	1.73904i	−0.493897	−	0.869521i	$-0.664428\pi$
$353$		−	613.881i		−	1.73904i	0.493897	−	0.869521i	$-0.335572\pi$
$354$	202.759	−	78.7112i	0.572767	−	0.222348i
$355$	−111.473			−0.314009
$356$		−	359.853i		−	1.01082i
$357$	55.2408	+	142.300i	0.154736	+	0.398599i
$358$	290.736			0.812113
$359$		−	574.491i		−	1.60025i	−0.599832	−	0.800126i	$-0.704766\pi$
$359$		−	574.491i		−	1.60025i	0.599832	−	0.800126i	$-0.295234\pi$
$360$	3.25306	−	2.97383i	0.00903627	−	0.00826063i
$361$	54.9012			0.152081
$362$			640.222i			1.76857i
$363$	−564.774	+	219.245i	−1.55585	+	0.603982i
$364$	−144.727			−0.397602
$365$		−	789.786i		−	2.16380i
$366$	−235.028	−	605.431i	−0.642154	−	1.65418i
$367$	247.876			0.675412			0.337706	−	0.941252i	$-0.390349\pi$
$367$	247.876			0.675412			0.337706	+	0.941252i	$0.390349\pi$
$368$			282.329i			0.767199i
$369$	293.098	+	320.619i	0.794305	+	0.868886i
$370$	82.2488			0.222294
$371$		−	190.958i		−	0.514712i
$372$	59.9216	−	23.2616i	0.161079	−	0.0625311i
$373$	702.843			1.88430			0.942149	−	0.335194i	$-0.108802\pi$
$373$	702.843			1.88430			0.942149	+	0.335194i	$0.108802\pi$
$374$			732.916i			1.95967i
$375$	−75.0684	−	193.376i	−0.200182	−	0.515668i
$376$	4.09321			0.0108862
$377$			342.310i			0.907983i
$378$	−242.315	−	120.030i	−0.641046	−	0.317540i
$379$	356.309			0.940129			0.470065	−	0.882632i	$-0.344231\pi$
$379$	356.309			0.940129			0.470065	+	0.882632i	$0.344231\pi$
$380$		−	512.409i		−	1.34845i
$381$	−374.672	+	145.448i	−0.983392	+	0.381753i
$382$	−304.869			−0.798085
$383$			325.572i			0.850058i	0.905180	+	0.425029i	$0.139736\pi$
$383$			325.572i			0.850058i	−0.905180	+	0.425029i	$0.860264\pi$
$384$	−2.72723	−	7.02531i	−0.00710215	−	0.0182951i
$385$	396.277			1.02929
$386$			535.088i			1.38624i
$387$	453.729	−	414.783i	1.17243	−	1.07179i
$388$	482.363			1.24320
$389$		−	38.2595i		−	0.0983535i	−0.998790	−	0.0491768i	$-0.984340\pi$
$389$		−	38.2595i		−	0.0983535i	0.998790	−	0.0491768i	$-0.0156598\pi$
$390$	−502.483	+	195.064i	−1.28842	+	0.500164i
$391$	255.782			0.654173
$392$		−	2.86574i		−	0.00731056i
$393$	43.9917	+	113.322i	0.111938	+	0.288352i
$394$	948.137			2.40644
$395$			597.448i			1.51253i
$396$	−439.530	−	480.800i	−1.10993	−	1.21414i
$397$	−715.605			−1.80253			−0.901266	−	0.433266i	$-0.857361\pi$
$397$	−715.605			−1.80253			−0.901266	+	0.433266i	$0.857361\pi$
$398$		−	238.999i		−	0.600499i
$399$	−201.607	+	78.2638i	−0.505281	+	0.196150i
$400$	221.103			0.552757
$401$		−	247.365i		−	0.616870i	−0.951245	−	0.308435i	$-0.900195\pi$
$401$		−	247.365i		−	0.616870i	0.951245	−	0.308435i	$-0.0998053\pi$
$402$	25.1785	+	64.8595i	0.0626330	+	0.161342i
$403$	−54.0762			−0.134184
$404$			24.2754i			0.0600875i
$405$	−503.272	−	45.2269i	−1.24265	−	0.111671i
$406$	337.259			0.830687
$407$		−	83.6247i		−	0.205466i
$408$	−3.16024	+	1.22680i	−0.00774568	+	0.00300687i
$409$	589.660			1.44171			0.720856	−	0.693085i	$-0.243749\pi$
$409$	589.660			1.44171			0.720856	+	0.693085i	$0.243749\pi$
$410$		−	853.114i		−	2.08077i
$411$	265.252	+	683.287i	0.645382	+	1.66250i
$412$	−18.9230			−0.0459296
$413$			90.4513i			0.219011i
$414$	−334.436	+	305.729i	−0.807817	+	0.738477i
$415$	−469.968			−1.13245
$416$			460.804i			1.10770i
$417$	−683.879	+	265.482i	−1.64000	+	0.636648i
$418$	−1038.38			−2.48416
$419$			534.064i			1.27462i	0.770609	+	0.637308i	$0.219952\pi$
$419$			534.064i			1.27462i	−0.770609	+	0.637308i	$0.780048\pi$
$420$	96.4246	+	248.389i	0.229582	+	0.591402i
$421$	549.717			1.30574			0.652870	−	0.757470i	$-0.273565\pi$
$421$	549.717			1.30574			0.652870	+	0.757470i	$0.273565\pi$
$422$			526.296i			1.24715i
$423$	−316.625	−	346.354i	−0.748522	−	0.818805i
$424$	4.24085			0.0100020
$425$		−	200.312i		−	0.471323i
$426$	−141.593	+	54.9665i	−0.332379	+	0.129029i
$427$	270.084			0.632515
$428$			557.310i			1.30213i
$429$	198.327	+	510.889i	0.462301	+	1.19088i
$430$	−1207.30			−2.80767
$431$		−	107.306i		−	0.248971i	−0.992221	−	0.124485i	$-0.960272\pi$
$431$		−	107.306i		−	0.248971i	0.992221	−	0.124485i	$-0.0397280\pi$
$432$	−190.416	+	384.410i	−0.440779	+	0.889839i
$433$	−93.6543			−0.216292			−0.108146	−	0.994135i	$-0.534491\pi$
$433$	−93.6543			−0.216292			−0.108146	+	0.994135i	$0.534491\pi$
$434$			53.2784i			0.122761i
$435$	587.492	−	228.064i	1.35056	−	0.524286i
$436$	410.296			0.941046
$437$			362.385i			0.829257i
$438$	−389.437	−	1003.19i	−0.889125	−	2.29038i
$439$	0.0658696			0.000150045			7.50223e−5	−	1.00000i	$-0.499976\pi$
$439$	0.0658696			0.000150045			7.50223e−5		1.00000i	$0.499976\pi$
$440$			8.80064i			0.0200015i
$441$	−242.490	+	221.675i	−0.549863	+	0.502665i
$442$	414.583			0.937970
$443$			136.436i			0.307982i	0.988072	+	0.153991i	$0.0492128\pi$
$443$			136.436i			0.307982i	−0.988072	+	0.153991i	$0.950787\pi$
$444$	52.4165	−	20.3481i	0.118055	−	0.0458290i
$445$	557.355			1.25248
$446$			92.8874i			0.208268i
$447$	96.3796	+	248.273i	0.215614	+	0.555421i
$448$	229.353			0.511949
$449$		−	357.072i		−	0.795261i	−0.917546	−	0.397630i	$-0.869833\pi$
$449$		−	357.072i		−	0.795261i	0.917546	−	0.397630i	$-0.130167\pi$
$450$	239.429	+	261.910i	0.532063	+	0.582022i
$451$	−867.385			−1.92325
$452$		−	571.949i		−	1.26537i
$453$	660.132	−	256.263i	1.45724	−	0.565703i
$454$	50.7887			0.111869
$455$		−	224.159i		−	0.492657i
$456$	−1.73811	−	4.47735i	−0.00381164	−	0.00981875i
$457$	133.415			0.291937			0.145968	−	0.989289i	$-0.453370\pi$
$457$	133.415			0.291937			0.145968	+	0.989289i	$0.453370\pi$
$458$		−	230.322i		−	0.502886i
$459$	348.264	+	172.511i	0.758745	+	0.375842i
$460$	446.475			0.970598
$461$			830.049i			1.80054i	0.435333	+	0.900270i	$0.356631\pi$
$461$			830.049i			1.80054i	−0.435333	+	0.900270i	$0.643369\pi$
$462$	503.351	−	195.401i	1.08950	−	0.422946i
$463$	−233.609			−0.504556			−0.252278	−	0.967655i	$-0.581180\pi$
$463$	−233.609			−0.504556			−0.252278	+	0.967655i	$0.581180\pi$
$464$		−	535.029i		−	1.15308i
$465$	36.0284	+	92.8088i	0.0774804	+	0.199589i
$466$	−588.590			−1.26307
$467$		−	305.573i		−	0.654332i	−0.944967	−	0.327166i	$-0.893906\pi$
$467$		−	305.573i		−	0.654332i	0.944967	−	0.327166i	$-0.106094\pi$
$468$	−271.970	+	248.626i	−0.581133	+	0.531251i
$469$	−28.9339			−0.0616928
$470$			921.591i			1.96083i
$471$	606.493	−	235.440i	1.28767	−	0.499874i
$472$	−2.00877			−0.00425587
$473$			1227.49i			2.59513i
$474$	294.597	+	758.878i	0.621512	+	1.60101i
$475$	283.798			0.597469
$476$		−	204.938i		−	0.430541i
$477$	−328.045	−	358.847i	−0.687726	−	0.752301i
$478$	292.279			0.611462
$479$			617.960i			1.29010i	0.764139	+	0.645052i	$0.223164\pi$
$479$			617.960i			1.29010i	−0.764139	+	0.645052i	$0.776836\pi$
$480$	790.859	−	307.012i	1.64762	−	0.639608i
$481$	−47.3033			−0.0983436
$482$		−	1156.45i		−	2.39928i
$483$	−68.1933	−	175.665i	−0.141187	−	0.363696i
$484$	813.378			1.68053
$485$			747.103i			1.54042i
$486$	−661.557	+	190.712i	−1.36123	+	0.392411i
$487$	686.719			1.41010			0.705050	−	0.709158i	$-0.250925\pi$
$487$	686.719			1.41010			0.705050	+	0.709158i	$0.250925\pi$
$488$			5.99811i			0.0122912i
$489$	164.156	−	63.7253i	0.335697	−	0.130318i
$490$	645.224			1.31678
$491$			171.655i			0.349603i	0.984604	+	0.174802i	$0.0559284\pi$
$491$			171.655i			0.349603i	−0.984604	+	0.174802i	$0.944072\pi$
$492$	−211.058	−	543.683i	−0.428979	−	1.10505i
$493$	−484.720			−0.983206
$494$			587.371i			1.18901i
$495$	744.682	−	680.761i	1.50441	−	1.37528i
$496$	84.5211			0.170405
$497$		−	63.1650i		−	0.127093i
$498$	−596.954	+	231.738i	−1.19870	+	0.465336i
$499$	−725.320			−1.45355			−0.726774	−	0.686877i	$-0.758981\pi$
$499$	−725.320			−1.45355			−0.726774	+	0.686877i	$0.758981\pi$
$500$			278.496i			0.556992i
$501$	47.6094	+	122.641i	0.0950288	+	0.244793i
$502$	−483.589			−0.963324
$503$		−	378.288i		−	0.752063i	−0.926607	−	0.376032i	$-0.877288\pi$
$503$		−	378.288i		−	0.752063i	0.926607	−	0.376032i	$-0.122712\pi$
$504$	1.68509	+	1.84331i	0.00334342	+	0.00365736i
$505$	−37.5986			−0.0744527
$506$		−	904.765i		−	1.78807i
$507$	−183.646	+	71.2913i	−0.362221	+	0.140614i
$508$	539.597			1.06220
$509$			343.860i			0.675561i	0.941225	+	0.337780i	$0.109676\pi$
$509$			343.860i			0.675561i	−0.941225	+	0.337780i	$0.890324\pi$
$510$	−276.216	−	711.531i	−0.541601	−	1.39516i
$511$	447.523			0.875779
$512$		−	725.226i		−	1.41646i
$513$	−244.410	+	493.412i	−0.476433	+	0.961817i
$514$	−466.728			−0.908031
$515$		−	29.3087i		−	0.0569100i
$516$	−769.401	+	298.682i	−1.49109	+	0.578840i
$517$	937.008			1.81239
$518$			46.6053i			0.0899717i
$519$	−54.1907	−	139.595i	−0.104414	−	0.268969i
$520$	4.97819			0.00957344
$521$			38.8335i			0.0745364i	0.999305	+	0.0372682i	$0.0118656\pi$
$521$			38.8335i			0.0745364i	−0.999305	+	0.0372682i	$0.988134\pi$
$522$	633.775	−	579.375i	1.21413	−	1.10991i
$523$	411.278			0.786382			0.393191	−	0.919457i	$-0.371371\pi$
$523$	411.278			0.786382			0.393191	+	0.919457i	$0.371371\pi$
$524$		−	163.205i		−	0.311460i
$525$	−137.570	+	53.4048i	−0.262039	+	0.101723i
$526$	−958.060			−1.82141
$527$		−	76.5736i		−	0.145301i
$528$	−309.985	−	798.519i	−0.587093	−	1.51235i
$529$	213.245			0.403109
$530$			954.833i			1.80157i
$531$	155.386	+	169.976i	0.292628	+	0.320105i
$532$	290.351			0.545772
$533$			490.647i			0.920538i
$534$	707.952	−	274.827i	1.32575	−	0.514657i
$535$	−863.183			−1.61343
$536$		−	0.642574i		−	0.00119883i
$537$	111.404	+	286.975i	0.207456	+	0.534404i
$538$	343.423			0.638333
$539$		−	656.018i		−	1.21710i
$540$	607.906	+	301.124i	1.12575	+	0.557638i
$541$	14.4699			0.0267466			0.0133733	−	0.999911i	$-0.495743\pi$
$541$	14.4699			0.0267466			0.0133733	+	0.999911i	$0.495743\pi$
$542$		−	682.243i		−	1.25875i
$543$	−631.939	+	245.319i	−1.16379	+	0.451784i
$544$	−652.512			−1.19947
$545$			635.482i			1.16602i
$546$	−110.531	−	284.726i	−0.202437	−	0.521477i
$547$	−1060.23			−1.93827			−0.969135	−	0.246532i	$-0.920709\pi$
$547$	−1060.23			−1.93827			−0.969135	+	0.246532i	$0.920709\pi$
$548$		−	984.058i		−	1.79573i
$549$	507.541	−	463.975i	0.924482	−	0.845128i
$550$	−708.556			−1.28828
$551$		−	686.740i		−	1.24635i
$552$	3.90123	−	1.51446i	0.00706744	−	0.00274358i
$553$	−338.537			−0.612183
$554$			1160.98i			2.09562i
$555$	31.5159	+	81.1847i	0.0567854	+	0.146279i
$556$	984.911			1.77142
$557$		−	33.7191i		−	0.0605371i	−0.999542	−	0.0302685i	$-0.990364\pi$
$557$		−	33.7191i		−	0.0605371i	0.999542	−	0.0302685i	$-0.00963624\pi$
$558$	91.5265	+	100.120i	0.164026	+	0.179427i
$559$	694.347			1.24212
$560$			350.360i			0.625643i
$561$	−723.434	+	280.837i	−1.28954	+	0.500601i
$562$	−99.5186			−0.177079
$563$		−	113.416i		−	0.201449i	−0.994914	−	0.100724i	$-0.967884\pi$
$563$		−	113.416i		−	0.201449i	0.994914	−	0.100724i	$-0.0321160\pi$
$564$	227.999	+	587.323i	0.404253	+	1.04135i
$565$	885.857			1.56789
$566$			1146.64i			2.02587i
$567$	25.6273	−	285.173i	0.0451981	−	0.502951i
$568$	1.40279			0.00246970
$569$		−	916.059i		−	1.60995i	−0.593312	−	0.804973i	$-0.702180\pi$
$569$		−	916.059i		−	1.60995i	0.593312	−	0.804973i	$-0.297820\pi$
$570$	1008.08	−	391.337i	1.76856	−	0.686556i
$571$	−78.4791			−0.137442			−0.0687208	−	0.997636i	$-0.521892\pi$
$571$	−78.4791			−0.137442			−0.0687208	+	0.997636i	$0.521892\pi$
$572$		−	735.773i		−	1.28632i
$573$	−116.819	−	300.924i	−0.203872	−	0.525173i
$574$	483.407			0.842173
$575$			247.280i			0.430052i
$576$	430.999	−	394.004i	0.748263	−	0.684035i
$577$	428.410			0.742478			0.371239	−	0.928537i	$-0.378933\pi$
$577$	428.410			0.742478			0.371239	+	0.928537i	$0.378933\pi$
$578$		−	231.768i		−	0.400983i
$579$	−528.165	+	205.034i	−0.912203	+	0.354117i
$580$	−846.095			−1.45879
$581$		−	266.302i		−	0.458352i
$582$	368.390	+	948.970i	0.632973	+	1.63053i
$583$	970.806			1.66519
$584$			9.93873i			0.0170184i
$585$	−385.081	−	421.238i	−0.658258	−	0.720065i
$586$	883.923			1.50840
$587$			32.5302i			0.0554178i	0.999616	+	0.0277089i	$0.00882114\pi$
$587$			32.5302i			0.0554178i	−0.999616	+	0.0277089i	$0.991179\pi$
$588$	411.196	−	159.626i	0.699313	−	0.271474i
$589$	108.488			0.184189
$590$		−	452.277i		−	0.766571i
$591$	363.305	+	935.870i	0.614729	+	1.58354i
$592$	73.9350			0.124890
$593$			348.356i			0.587447i	0.955890	+	0.293724i	$0.0948945\pi$
$593$			348.356i			0.587447i	−0.955890	+	0.293724i	$0.905105\pi$
$594$	610.217	−	1231.90i	1.02730	−	2.07391i
$595$	317.415			0.533471
$596$		−	357.559i		−	0.599931i
$597$	235.907	−	91.5789i	0.395153	−	0.153399i
$598$	−511.791			−0.855838
$599$			818.953i			1.36720i	0.729856	+	0.683601i	$0.239587\pi$
$599$			818.953i			1.36720i	−0.729856	+	0.683601i	$0.760413\pi$
$600$	−1.18603	−	3.05520i	−0.00197672	−	0.00509200i
$601$	−71.7855			−0.119443			−0.0597217	−	0.998215i	$-0.519021\pi$
$601$	−71.7855			−0.119443			−0.0597217	+	0.998215i	$0.519021\pi$
$602$		−	684.102i		−	1.13638i
$603$	−54.3725	+	49.7054i	−0.0901700	+	0.0824302i
$604$	−950.710			−1.57402
$605$			1259.79i			2.08230i
$606$	−47.7577	+	18.5396i	−0.0788082	+	0.0305933i
$607$	−503.741			−0.829886			−0.414943	−	0.909847i	$-0.636199\pi$
$607$	−503.741			−0.829886			−0.414943	+	0.909847i	$0.636199\pi$
$608$		−	924.464i		−	1.52050i
$609$	129.230	+	332.896i	0.212200	+	0.546626i
$610$	−1350.48			−2.21390
$611$		−	530.030i		−	0.867479i
$612$	−352.061	−	385.118i	−0.575263	−	0.629278i
$613$	373.791			0.609773			0.304886	−	0.952389i	$-0.401382\pi$
$613$	373.791			0.609773			0.304886	+	0.952389i	$0.401382\pi$
$614$			829.354i			1.35074i
$615$	842.077	−	326.894i	1.36923	−	0.531535i
$616$	−4.98678			−0.00809543
$617$		−	653.182i		−	1.05864i	−0.848422	−	0.529321i	$-0.822447\pi$
$617$		−	653.182i		−	1.05864i	0.848422	−	0.529321i	$-0.177553\pi$
$618$	−14.4519	−	37.2279i	−0.0233849	−	0.0602393i
$619$	−325.525			−0.525889			−0.262944	−	0.964811i	$-0.584694\pi$
$619$	−325.525			−0.525889			−0.262944	+	0.964811i	$0.584694\pi$
$620$		−	133.662i		−	0.215583i
$621$	−429.923	−	212.961i	−0.692307	−	0.342932i
$622$	1084.22			1.74311
$623$			315.819i			0.506932i
$624$	−451.692	+	175.347i	−0.723865	+	0.281004i
$625$	−779.245			−1.24679
$626$		−	76.7328i		−	0.122576i
$627$	−397.883	−	1024.94i	−0.634583	−	1.63468i
$628$	−873.460			−1.39086
$629$		−	66.9829i		−	0.106491i
$630$	−415.023	+	379.399i	−0.658767	+	0.602221i
$631$	464.988			0.736906			0.368453	−	0.929646i	$-0.379887\pi$
$631$	464.988			0.736906			0.368453	+	0.929646i	$0.379887\pi$
$632$		−	7.51833i		−	0.0118961i
$633$	−519.487	+	201.665i	−0.820675	+	0.318586i
$634$	366.532			0.578126
$635$			835.748i			1.31614i
$636$	236.223	+	608.507i	0.371419	+	0.956773i
$637$	−371.084			−0.582550
$638$			1714.58i			2.68743i
$639$	−108.511	−	118.699i	−0.169813	−	0.185758i
$640$	−15.6707			−0.0244855
$641$		−	749.409i		−	1.16913i	−0.811349	−	0.584563i	$-0.801266\pi$
$641$		−	749.409i		−	1.16913i	0.811349	−	0.584563i	$-0.198734\pi$
$642$	−1096.41	+	425.628i	−1.70781	+	0.662972i
$643$	392.280			0.610078			0.305039	−	0.952340i	$-0.401330\pi$
$643$	392.280			0.610078			0.305039	+	0.952340i	$0.401330\pi$
$644$			252.990i			0.392842i
$645$	−462.610	−	1191.68i	−0.717224	−	1.84756i
$646$	−831.735			−1.28751
$647$		−	1220.76i		−	1.88679i	−0.331667	−	0.943397i	$-0.607611\pi$
$647$		−	1220.76i		−	1.88679i	0.331667	−	0.943397i	$-0.392389\pi$
$648$	6.33321	+	0.569139i	0.00977348	+	0.000878301i
$649$	−459.843			−0.708541
$650$			400.803i			0.616620i
$651$	−52.5891	+	20.4151i	−0.0807820	+	0.0313596i
$652$	−236.414			−0.362599
$653$		−	356.372i		−	0.545746i	−0.962050	−	0.272873i	$-0.912026\pi$
$653$		−	356.372i		−	0.545746i	0.962050	−	0.272873i	$-0.0879739\pi$
$654$	313.351	+	807.190i	0.479130	+	1.23423i
$655$	252.778			0.385920
$656$		−	766.880i		−	1.16902i
$657$	840.984	−	768.797i	1.28004	−	1.17016i
$658$	−522.209			−0.793631
$659$			283.026i			0.429478i	0.976671	+	0.214739i	$0.0688901\pi$
$659$			283.026i			0.429478i	−0.976671	+	0.214739i	$0.931110\pi$
$660$	−1262.78	+	490.210i	−1.91330	+	0.742743i
$661$	−962.852			−1.45666			−0.728330	−	0.685227i	$-0.759703\pi$
$661$	−962.852			−1.45666			−0.728330	+	0.685227i	$0.759703\pi$
$662$			1176.86i			1.77773i
$663$	158.859	+	409.219i	0.239606	+	0.617223i
$664$	5.91412			0.00890681
$665$			449.707i			0.676251i
$666$	80.0630	+	87.5805i	0.120215	+	0.131502i
$667$	598.374			0.897112
$668$		−	176.626i		−	0.264410i
$669$	−91.6856	+	35.5924i	−0.137049	+	0.0532023i
$670$	144.676			0.215935
$671$			1373.07i			2.04631i
$672$	173.965	+	448.131i	0.258876	+	0.666862i
$673$	981.136			1.45785			0.728927	−	0.684591i	$-0.240019\pi$
$673$	981.136			1.45785			0.728927	+	0.684591i	$0.240019\pi$
$674$		−	213.531i		−	0.316812i
$675$	−166.778	+	336.689i	−0.247078	+	0.498798i
$676$	264.484			0.391248
$677$		−	998.086i		−	1.47428i	−0.675741	−	0.737139i	$-0.736176\pi$
$677$		−	998.086i		−	1.47428i	0.675741	−	0.737139i	$-0.263824\pi$
$678$	1125.21	−	436.809i	1.65961	−	0.644260i
$679$	−423.337			−0.623472
$680$			7.04926i			0.0103666i
$681$	19.4611	+	50.1316i	0.0285772	+	0.0736147i
$682$	−270.860			−0.397156
$683$			424.571i			0.621626i	0.950471	+	0.310813i	$0.100601\pi$
$683$			424.571i			0.621626i	−0.950471	+	0.310813i	$0.899399\pi$
$684$	545.626	−	498.792i	0.797699	−	0.729228i
$685$	1524.15			2.22503
$686$			856.361i			1.24834i
$687$	227.342	−	88.2541i	0.330920	−	0.128463i
$688$	−1085.26			−1.57742
$689$		−	549.148i		−	0.797021i
$690$	340.982	+	878.366i	0.494176	+	1.27299i
$691$	96.5569			0.139735			0.0698675	−	0.997556i	$-0.477742\pi$
$691$	96.5569			0.139735			0.0698675	+	0.997556i	$0.477742\pi$
$692$			201.042i			0.290523i
$693$	385.746	+	421.966i	0.556632	+	0.608897i
$694$	−1579.96			−2.27661
$695$			1525.47i			2.19492i
$696$	−7.39305	+	2.86998i	−0.0106222	+	0.00412354i
$697$	−694.770			−0.996801
$698$		−	363.706i		−	0.521069i
$699$	−225.535	−	580.975i	−0.322653	−	0.831152i
$700$	198.126			0.283037
$701$		−	1248.44i		−	1.78093i	−0.455047	−	0.890467i	$-0.650378\pi$
$701$		−	1248.44i		−	1.78093i	0.455047	−	0.890467i	$-0.349622\pi$
$702$	−696.839	−	345.177i	−0.992648	−	0.491704i
$703$	94.8997			0.134992
$704$			1166.00i			1.65625i
$705$	−909.668	+	353.133i	−1.29031	+	0.500898i
$706$	−1739.32			−2.46363
$707$		−	21.3048i		−	0.0301341i
$708$	−111.892	−	288.233i	−0.158039	−	0.407108i
$709$	−395.593			−0.557959			−0.278980	−	0.960297i	$-0.589996\pi$
$709$	−395.593			−0.557959			−0.278980	+	0.960297i	$0.589996\pi$
$710$			315.839i			0.444844i
$711$	−636.177	+	581.570i	−0.894764	+	0.817961i
$712$	−7.01380			−0.00985084
$713$			94.5279i			0.132578i
$714$	403.181	−	156.515i	0.564679	−	0.219209i
$715$	1139.59			1.59384
$716$		−	413.296i		−	0.577229i
$717$	111.995	+	288.498i	0.156199	+	0.402368i
$718$	−1627.72			−2.26701
$719$		−	557.854i		−	0.775875i	−0.921686	−	0.387938i	$-0.873188\pi$
$719$		−	557.854i		−	0.775875i	0.921686	−	0.387938i	$-0.126812\pi$
$720$	601.881	+	658.395i	0.835946	+	0.914437i
$721$	16.6074			0.0230339
$722$		−	155.553i		−	0.215447i
$723$	1141.49	−	443.127i	1.57882	−	0.612900i
$724$	910.108			1.25706
$725$		−	468.610i		−	0.646358i
$726$	621.192	+	1600.19i	0.855637	+	2.20411i
$727$	−670.423			−0.922177			−0.461088	−	0.887354i	$-0.652541\pi$
$727$	−670.423			−0.922177			−0.461088	+	0.887354i	$0.652541\pi$
$728$			2.82083i			0.00387477i
$729$	−441.738	−	579.921i	−0.605951	−	0.795502i
$730$	−2237.72			−3.06537
$731$			983.215i			1.34503i
$732$	−860.651	+	334.105i	−1.17575	+	0.456427i
$733$	−498.707			−0.680364			−0.340182	−	0.940360i	$-0.610489\pi$
$733$	−498.707			−0.680364			−0.340182	+	0.940360i	$0.610489\pi$
$734$		−	702.313i		−	0.956830i
$735$	247.236	+	636.877i	0.336375	+	0.866499i
$736$	805.509			1.09444
$737$		−	147.096i		−	0.199588i
$738$	908.417	−	830.442i	1.23092	−	1.12526i
$739$	−869.914			−1.17715			−0.588575	−	0.808443i	$-0.700311\pi$
$739$	−869.914			−1.17715			−0.588575	+	0.808443i	$0.700311\pi$
$740$		−	116.921i		−	0.158001i
$741$	−579.772	+	225.067i	−0.782418	+	0.303735i
$742$	−541.045			−0.729171
$743$		−	47.4077i		−	0.0638058i	−0.999491	−	0.0319029i	$-0.989843\pi$
$743$		−	47.4077i		−	0.0638058i	0.999491	−	0.0319029i	$-0.0101567\pi$
$744$	−0.453384	−	1.16791i	−0.000609388	−	0.00156978i
$745$	553.801			0.743356
$746$		−	1991.38i		−	2.66941i
$747$	−457.479	−	500.434i	−0.612421	−	0.669925i
$748$	1041.88			1.39288
$749$		−	489.113i		−	0.653021i
$750$	−547.895	+	212.693i	−0.730526	+	0.283590i
$751$	−105.078			−0.139918			−0.0699589	−	0.997550i	$-0.522287\pi$
$751$	−105.078			−0.139918			−0.0699589	+	0.997550i	$0.522287\pi$
$752$			828.436i			1.10164i
$753$	−185.300	−	477.332i	−0.246083	−	0.633907i
$754$	969.873			1.28630
$755$		−	1472.50i		−	1.95033i
$756$	−170.629	+	344.463i	−0.225699	+	0.455639i
$757$	−654.026			−0.863971			−0.431986	−	0.901880i	$-0.642187\pi$
$757$	−654.026			−0.863971			−0.431986	+	0.901880i	$0.642187\pi$
$758$		−	1009.54i		−	1.33184i
$759$	893.059	−	346.686i	1.17663	−	0.456766i
$760$	−9.98722			−0.0131411
$761$		−	489.454i		−	0.643172i	−0.946880	−	0.321586i	$-0.895784\pi$
$761$		−	489.454i		−	0.643172i	0.946880	−	0.321586i	$-0.104216\pi$
$762$	412.100	+	1061.57i	0.540814	+	1.39313i
$763$	−360.089			−0.471938
$764$			433.386i			0.567259i
$765$	596.486	−	545.286i	0.779720	−	0.712792i
$766$	922.450			1.20424
$767$			260.116i			0.339134i
$768$	705.925	−	274.040i	0.919173	−	0.356823i
$769$	655.864			0.852878			0.426439	−	0.904516i	$-0.359768\pi$
$769$	655.864			0.852878			0.426439	+	0.904516i	$0.359768\pi$
$770$		−	1122.78i		−	1.45816i
$771$	−178.840	−	460.690i	−0.231958	−	0.597522i
$772$	760.655			0.985304
$773$			839.375i			1.08587i	0.839776	+	0.542934i	$0.182686\pi$
$773$			839.375i			1.08587i	−0.839776	+	0.542934i	$0.817314\pi$
$774$	−1175.21	−	1285.56i	−1.51836	−	1.66093i
$775$	74.0285			0.0955206
$776$		−	9.40161i		−	0.0121155i
$777$	−46.0024	+	17.8581i	−0.0592051	+	0.0229834i
$778$	−108.402			−0.139334
$779$		−	984.334i		−	1.26359i
$780$	277.293	+	714.305i	0.355504	+	0.915776i
$781$	321.123			0.411169
$782$		−	724.711i		−	0.926741i
$783$	814.727	+	403.572i	1.04052	+	0.515418i
$784$	580.004			0.739801
$785$		−	1352.85i		−	1.72337i
$786$	321.078	−	124.643i	0.408497	−	0.158578i
$787$	269.380			0.342287			0.171143	−	0.985246i	$-0.445254\pi$
$787$	269.380			0.342287			0.171143	+	0.985246i	$0.445254\pi$
$788$		−	1347.82i		−	1.71044i
$789$	−367.107	−	945.665i	−0.465282	−	1.19856i
$790$	1692.76			2.14274
$791$			501.961i			0.634590i
$792$	−9.37114	+	8.56676i	−0.0118322	+	0.0108166i
$793$	776.694			0.979438
$794$			2027.54i			2.55358i
$795$	−942.480	+	365.871i	−1.18551	+	0.460215i
$796$	−339.748			−0.426820
$797$		−	799.444i		−	1.00307i	−0.865138	−	0.501533i	$-0.832769\pi$
$797$		−	799.444i		−	1.00307i	0.865138	−	0.501533i	$-0.167231\pi$
$798$	221.747	+	571.217i	0.277878	+	0.715811i
$799$	750.538			0.939346
$800$		−	630.825i		−	0.788531i
$801$	542.543	+	593.485i	0.677332	+	0.740930i
$802$	−700.864			−0.873896
$803$			2275.15i			2.83331i
$804$	92.2010	−	35.7924i	0.114678	−	0.0445180i
$805$	−391.841			−0.486759
$806$			153.215i			0.190093i
$807$	131.592	+	338.980i	0.163063	+	0.420050i
$808$	0.473144			0.000585574
$809$		−	971.101i		−	1.20037i	−0.799860	−	0.600186i	$-0.795093\pi$
$809$		−	971.101i		−	1.20037i	0.799860	−	0.600186i	$-0.204907\pi$
$810$	−128.142	+	1425.93i	−0.158200	+	1.76041i
$811$	99.7798			0.123033			0.0615165	−	0.998106i	$-0.480406\pi$
$811$	99.7798			0.123033			0.0615165	+	0.998106i	$0.480406\pi$
$812$		−	479.430i		−	0.590431i
$813$	673.416	−	261.420i	0.828310	−	0.321550i
$814$	−236.936			−0.291076
$815$		−	366.168i		−	0.449286i
$816$	−248.296	−	639.609i	−0.304285	−	0.783834i
$817$	−1393.00			−1.70501
$818$		−	1670.70i		−	2.04242i
$819$	238.690	−	218.202i	0.291441	−	0.266424i
$820$	−1212.74			−1.47896
$821$		−	339.059i		−	0.412983i	−0.978448	−	0.206491i	$-0.933795\pi$
$821$		−	339.059i		−	0.412983i	0.978448	−	0.206491i	$-0.0662045\pi$
$822$	1935.97	−	751.544i	2.35520	−	0.914287i
$823$	−1199.62			−1.45762			−0.728809	−	0.684717i	$-0.759926\pi$
$823$	−1199.62			−1.45762			−0.728809	+	0.684717i	$0.759926\pi$
$824$			0.368823i			0.000447600i
$825$	−271.503	−	699.389i	−0.329095	−	0.847745i
$826$	256.278			0.310264
$827$		−	1305.50i		−	1.57860i	−0.614006	−	0.789302i	$-0.710443\pi$
$827$		−	1305.50i		−	1.57860i	0.614006	−	0.789302i	$-0.289557\pi$
$828$	434.610	+	475.418i	0.524891	+	0.574176i
$829$	307.440			0.370856			0.185428	−	0.982658i	$-0.440633\pi$
$829$	307.440			0.370856			0.185428	+	0.982658i	$0.440633\pi$
$830$			1331.57i			1.60430i
$831$	−1145.96	+	444.860i	−1.37901	+	0.535331i
$832$	659.563			0.792744
$833$		−	525.466i		−	0.630812i
$834$	752.196	+	1937.65i	0.901913	+	2.32332i
$835$	273.565			0.327623
$836$			1476.11i			1.76568i
$837$	−63.7542	+	128.706i	−0.0761699	+	0.153771i
$838$	1513.18			1.80570
$839$		−	270.293i		−	0.322161i	−0.986941	−	0.161081i	$-0.948502\pi$
$839$		−	270.293i		−	0.322161i	0.986941	−	0.161081i	$-0.0514980\pi$
$840$	4.84128	−	1.87938i	0.00576343	−	0.00223736i
$841$	−292.953			−0.348338
$842$		−	1557.52i		−	1.84979i
$843$	−38.1333	−	98.2311i	−0.0452352	−	0.116526i
$844$	748.156			0.886441
$845$			409.642i			0.484784i
$846$	−981.333	+	897.100i	−1.15997	+	1.06040i
$847$	−713.846			−0.842793
$848$			858.317i			1.01217i
$849$	−1131.81	+	439.367i	−1.33311	+	0.517512i
$850$	−567.549			−0.667705
$851$			82.6885i			0.0971663i
$852$	78.1377	+	201.282i	0.0917109	+	0.236246i
$853$	−263.837			−0.309304			−0.154652	−	0.987969i	$-0.549426\pi$
$853$	−263.837			−0.309304			−0.154652	+	0.987969i	$0.549426\pi$
$854$		−	765.234i		−	0.896059i
$855$	772.548	+	845.087i	0.903565	+	0.988405i
$856$	10.8624			0.0126897
$857$			1024.58i			1.19554i	0.801668	+	0.597770i	$0.203946\pi$
$857$			1024.58i			1.19554i	−0.801668	+	0.597770i	$0.796054\pi$
$858$	1447.51	−	561.924i	1.68708	−	0.654924i
$859$	1211.21			1.41002			0.705009	−	0.709199i	$-0.250943\pi$
$859$	1211.21			1.41002			0.705009	+	0.709199i	$0.250943\pi$
$860$			1716.23i			1.99562i
$861$	185.231	+	477.153i	0.215135	+	0.554185i
$862$	−304.033			−0.352707
$863$			548.781i			0.635899i	0.948108	+	0.317949i	$0.102994\pi$
$863$			548.781i			0.635899i	−0.948108	+	0.317949i	$0.897006\pi$
$864$	1096.76	+	543.274i	1.26939	+	0.628789i
$865$	−311.381			−0.359978
$866$			265.353i			0.306412i
$867$	228.770	−	88.8084i	0.263864	−	0.102432i
$868$	75.7378			0.0872556
$869$		−	1721.08i		−	1.98053i
$870$	−646.179	−	1664.55i	−0.742735	−	1.91328i
$871$	−83.2068			−0.0955302
$872$		−	7.99696i		−	0.00917083i
$873$	−795.534	+	727.249i	−0.911265	+	0.833045i
$874$	1026.75			1.17478
$875$		−	244.417i		−	0.279334i
$876$	−1426.08	+	553.604i	−1.62794	+	0.631968i
$877$	−1656.91			−1.88929			−0.944646	−	0.328090i	$-0.893595\pi$
$877$	−1656.91			−1.88929			−0.944646	+	0.328090i	$0.893595\pi$
$878$		−	0.186630i		−	0.000212562i
$879$	338.700	+	872.487i	0.385324	+	0.992591i
$880$	−1781.18			−2.02407
$881$			998.350i			1.13320i	0.823993	+	0.566601i	$0.191742\pi$
$881$			998.350i			1.13320i	−0.823993	+	0.566601i	$0.808258\pi$
$882$	628.077	+	687.051i	0.712106	+	0.778969i
$883$	−953.181			−1.07948			−0.539740	−	0.841832i	$-0.681477\pi$
$883$	−953.181			−1.07948			−0.539740	+	0.841832i	$0.681477\pi$
$884$		−	589.350i		−	0.666686i
$885$	446.426	−	173.302i	0.504436	−	0.195822i
$886$	386.568			0.436307
$887$			1230.43i			1.38718i	0.720371	+	0.693589i	$0.243972\pi$
$887$			1230.43i			1.38718i	−0.720371	+	0.693589i	$0.756028\pi$
$888$	−0.396599	−	1.02163i	−0.000446620	−	0.00115049i
$889$	−473.567			−0.532696
$890$		−	1579.17i		−	1.77434i
$891$	1449.78	+	130.286i	1.62714	+	0.146224i
$892$	132.044			0.148031
$893$			1063.34i			1.19075i
$894$	703.437	−	273.074i	0.786843	−	0.305452i
$895$	640.129			0.715228
$896$		−	8.87964i		−	0.00991031i
$897$	−196.107	−	505.170i	−0.218625	−	0.563177i
$898$	−1011.70			−1.12661
$899$		−	179.136i		−	0.199261i
$900$	372.318	−	340.360i	0.413687	−	0.378177i
$901$	777.609			0.863052
$902$			2457.58i			2.72459i
$903$	675.251	−	262.132i	0.747786	−	0.290291i
$904$	−11.1477			−0.0123315
$905$			1409.61i			1.55758i
$906$	−726.076	−	1870.37i	−0.801408	−	2.06442i
$907$	779.728			0.859679			0.429839	−	0.902905i	$-0.358570\pi$
$907$	779.728			0.859679			0.429839	+	0.902905i	$0.358570\pi$
$908$		−	72.1986i		−	0.0795139i
$909$	−36.5994	−	40.0359i	−0.0402634	−	0.0440439i
$910$	−635.114			−0.697927
$911$		−	412.766i		−	0.453091i	−0.974001	−	0.226546i	$-0.927257\pi$
$911$		−	412.766i		−	0.453091i	0.974001	−	0.226546i	$-0.0727433\pi$
$912$	906.183	−	351.780i	0.993621	−	0.385724i
$913$	1353.85			1.48285
$914$		−	378.008i		−	0.413575i
$915$	−517.474	−	1333.01i	−0.565545	−	1.45684i
$916$	−327.414			−0.357438
$917$			143.234i			0.156198i
$918$	488.780	−	986.744i	0.532440	−	1.07488i
$919$	1643.89			1.78878			0.894390	−	0.447287i	$-0.147610\pi$
$919$	1643.89			1.78878			0.894390	+	0.447287i	$0.147610\pi$
$920$		−	8.70212i		−	0.00945882i
$921$	−818.624	+	317.790i	−0.888843	+	0.345049i
$922$	2351.79			2.55075
$923$		−	181.647i		−	0.196801i
$924$	−277.772	−	715.539i	−0.300619	−	0.774392i
$925$	64.7565			0.0700071
$926$			661.890i			0.714784i
$927$	31.2086	−	28.5298i	0.0336662	−	0.0307765i
$928$	−1526.48			−1.64492
$929$			775.977i			0.835282i	0.908612	+	0.417641i	$0.137143\pi$
$929$			775.977i			0.835282i	−0.908612	+	0.417641i	$0.862857\pi$
$930$	262.957	−	102.080i	0.282750	−	0.109763i
$931$	744.468			0.799643
$932$			836.710i			0.897758i
$933$	415.447	+	1070.19i	0.445281	+	1.14704i
$934$	−865.787			−0.926966
$935$			1613.70i			1.72588i
$936$	4.84589	+	5.30090i	0.00517723	+	0.00566335i
$937$	9.91942			0.0105864			0.00529318	−	0.999986i	$-0.498315\pi$
$937$	9.91942			0.0105864			0.00529318	+	0.999986i	$0.498315\pi$
$938$			81.9791i			0.0873978i
$939$	75.7401	−	29.4023i	0.0806604	−	0.0313124i
$940$	1310.09			1.39371
$941$			7.03586i			0.00747701i	0.999993	+	0.00373850i	$0.00119001\pi$
$941$			7.03586i			0.00747701i	−0.999993	+	0.00373850i	$0.998810\pi$
$942$	−667.078	−	1718.39i	−0.708151	−	1.82419i
$943$	857.674			0.909517
$944$		−	406.560i		−	0.430678i
$945$	−533.518	−	264.276i	−0.564569	−	0.279657i
$946$	3477.88			3.67641
$947$		−	94.5271i		−	0.0998175i	−0.998754	−	0.0499087i	$-0.984107\pi$
$947$		−	94.5271i		−	0.0998175i	0.998754	−	0.0499087i	$-0.0158930\pi$
$948$	1078.78	−	418.784i	1.13796	−	0.441755i
$949$	1286.97			1.35613
$950$		−	804.090i		−	0.846411i
$951$	140.447	+	361.790i	0.147683	+	0.380431i
$952$	−3.99438			−0.00419578
$953$			1162.21i			1.21952i	0.792584	+	0.609762i	$0.208735\pi$
$953$			1162.21i			1.21952i	−0.792584	+	0.609762i	$0.791265\pi$
$954$	−1016.73	+	929.458i	−1.06575	+	0.974274i
$955$	−671.245			−0.702874
$956$		−	415.489i		−	0.434612i
$957$	−1692.40	+	656.989i	−1.76844	+	0.686509i
$958$	1750.88			1.82764
$959$			863.640i			0.900563i
$960$	−439.435	−	1131.98i	−0.457745	−	1.17915i
$961$	−932.701			−0.970553
$962$			134.025i			0.139320i
$963$	−840.243	−	919.138i	−0.872527	−	0.954453i
$964$	−1643.95			−1.70535
$965$			1178.13i			1.22086i
$966$	−497.716	+	193.213i	−0.515234	+	0.200014i
$967$	−1467.23			−1.51730			−0.758649	−	0.651499i	$-0.774140\pi$
$967$	−1467.23			−1.51730			−0.758649	+	0.651499i	$0.774140\pi$
$968$		−	15.8533i		−	0.0163774i
$969$	−318.702	−	820.974i	−0.328898	−	0.847238i
$970$	2116.78			2.18225
$971$			1029.20i			1.05994i	0.848017	+	0.529968i	$0.177796\pi$
$971$			1029.20i			1.05994i	−0.848017	+	0.529968i	$0.822204\pi$
$972$	271.106	+	940.436i	0.278916	+	0.967526i
$973$	−864.389			−0.888375
$974$		−	1945.69i		−	1.99763i
$975$	−395.618	+	153.579i	−0.405762	+	0.157517i
$976$	−1213.97			−1.24382
$977$		−	583.260i		−	0.596991i	−0.954411	−	0.298495i	$-0.903515\pi$
$977$		−	583.260i		−	0.596991i	0.954411	−	0.298495i	$-0.0964848\pi$
$978$	−180.554	−	465.106i	−0.184616	−	0.475569i
$979$	−1605.58			−1.64002
$980$		−	917.219i		−	0.935937i
$981$	−676.677	+	618.594i	−0.689783	+	0.630575i
$982$	486.354			0.495269
$983$			1107.56i			1.12671i	0.826215	+	0.563355i	$0.190490\pi$
$983$			1107.56i			1.12671i	−0.826215	+	0.563355i	$0.809510\pi$
$984$	−10.5968	+	4.11366i	−0.0107691	+	0.00418055i
$985$	2087.56			2.11935
$986$			1373.37i			1.39287i
$987$	−200.099	−	515.453i	−0.202734	−	0.522242i
$988$	834.977			0.845118
$989$		−	1213.75i		−	1.22725i
$990$	−1928.82	−	2109.92i	−1.94830	−	2.13124i
$991$	1220.76			1.23184			0.615921	−	0.787808i	$-0.288784\pi$
$991$	1220.76			1.23184			0.615921	+	0.787808i	$0.288784\pi$
$992$		−	241.146i		−	0.243091i
$993$	−1161.63	+	450.946i	−1.16982	+	0.454125i
$994$	−178.967			−0.180047
$995$		−	526.215i		−	0.528860i
$996$	329.426	+	848.600i	0.330749	+	0.852008i
$997$	−1195.16			−1.19876			−0.599378	−	0.800466i	$-0.704585\pi$
$997$	−1195.16			−1.19876			−0.599378	+	0.800466i	$0.704585\pi$
$998$			2055.06i			2.05918i
$999$	−55.7691	+	112.586i	−0.0558249	+	0.112699i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.c.a.68.9	✓	44
3.2	odd	2	inner	201.3.c.a.68.36	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.c.a.68.9	✓	44	1.1	even	1	trivial
201.3.c.a.68.36	yes	44	3.2	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.83332i q^{2} +(2.79666 - 1.08567i) q^{3} -4.02771 q^{4} -6.23827i q^{5} +(-3.07604 - 7.92385i) q^{6} +3.53484 q^{7} +0.0785029i q^{8} +(6.64266 - 6.07248i) q^{9} +O(q^{10})\)	\(q-2.83332i q^{2} +(2.79666 - 1.08567i) q^{3} -4.02771 q^{4} -6.23827i q^{5} +(-3.07604 - 7.92385i) q^{6} +3.53484 q^{7} +0.0785029i q^{8} +(6.64266 - 6.07248i) q^{9} -17.6750 q^{10} +17.9707i q^{11} +(-11.2641 + 4.37274i) q^{12} +10.1653 q^{13} -10.0153i q^{14} +(-6.77267 - 17.4463i) q^{15} -15.8884 q^{16} +14.3944i q^{17} +(-17.2053 - 18.8208i) q^{18} -20.3937 q^{19} +25.1259i q^{20} +(9.88577 - 3.83766i) q^{21} +50.9167 q^{22} -17.7695i q^{23} +(0.0852279 + 0.219546i) q^{24} -13.9160 q^{25} -28.8016i q^{26} +(11.9846 - 24.1944i) q^{27} -14.2373 q^{28} +33.6742i q^{29} +(-49.4311 + 19.1891i) q^{30} -5.31967 q^{31} +45.3310i q^{32} +(19.5102 + 50.2580i) q^{33} +40.7840 q^{34} -22.0513i q^{35} +(-26.7547 + 24.4582i) q^{36} -4.65339 q^{37} +57.7818i q^{38} +(28.4290 - 11.0361i) q^{39} +0.489722 q^{40} +48.2667i q^{41} +(-10.8733 - 28.0096i) q^{42} +68.3054 q^{43} -72.3807i q^{44} +(-37.8818 - 41.4387i) q^{45} -50.3467 q^{46} -52.1409i q^{47} +(-44.4345 + 17.2495i) q^{48} -36.5049 q^{49} +39.4284i q^{50} +(15.6275 + 40.2563i) q^{51} -40.9430 q^{52} -54.0216i q^{53} +(-68.5505 - 33.9562i) q^{54} +112.106 q^{55} +0.277495i q^{56} +(-57.0342 + 22.1407i) q^{57} +95.4098 q^{58} +25.5885i q^{59} +(27.2783 + 70.2687i) q^{60} +76.4062 q^{61} +15.0723i q^{62} +(23.4808 - 21.4653i) q^{63} +64.8835 q^{64} -63.4141i q^{65} +(142.397 - 55.2785i) q^{66} -8.18535 q^{67} -57.9765i q^{68} +(-19.2917 - 49.6953i) q^{69} -62.4784 q^{70} -17.8693i q^{71} +(0.476707 + 0.521468i) q^{72} +126.603 q^{73} +13.1846i q^{74} +(-38.9183 + 15.1081i) q^{75} +82.1397 q^{76} +63.5236i q^{77} +(-31.2689 - 80.5485i) q^{78} -95.7714 q^{79} +99.1161i q^{80} +(7.24991 - 80.6749i) q^{81} +136.755 q^{82} -75.3364i q^{83} +(-39.8170 + 15.4570i) q^{84} +89.7962 q^{85} -193.531i q^{86} +(36.5589 + 94.1755i) q^{87} -1.41075 q^{88} +89.3445i q^{89} +(-117.409 + 107.331i) q^{90} +35.9329 q^{91} +71.5704i q^{92} +(-14.8773 + 5.77538i) q^{93} -147.732 q^{94} +127.221i q^{95} +(49.2142 + 126.775i) q^{96} -119.761 q^{97} +103.430i q^{98} +(109.127 + 119.373i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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