LMFDB - Embedded newform 201.4.d.b.200.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(200,201)]

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, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("201.200");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.d (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:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			200.4
Character	$\chi$	$=$	201.200
Dual form			201.4.d.b.200.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.08650 q^{2} +(-0.0109234 + 5.19614i) q^{3} +17.8725 q^{4} -16.6834 q^{5} +(0.0555619 - 26.4302i) q^{6} +1.72249i q^{7} -50.2166 q^{8} +(-26.9998 - 0.113519i) q^{9} +O(q^{10})$	\(q-5.08650 q^{2} +(-0.0109234 + 5.19614i) q^{3} +17.8725 q^{4} -16.6834 q^{5} +(0.0555619 - 26.4302i) q^{6} +1.72249i q^{7} -50.2166 q^{8} +(-26.9998 - 0.113519i) q^{9} +84.8599 q^{10} +45.8008 q^{11} +(-0.195229 + 92.8681i) q^{12} -73.5018i q^{13} -8.76143i q^{14} +(0.182239 - 86.6891i) q^{15} +112.447 q^{16} +36.5463i q^{17} +(137.334 + 0.577415i) q^{18} -61.7440 q^{19} -298.173 q^{20} +(-8.95028 - 0.0188154i) q^{21} -232.966 q^{22} -170.730i q^{23} +(0.548536 - 260.932i) q^{24} +153.334 q^{25} +373.867i q^{26} +(0.884791 - 140.293i) q^{27} +30.7851i q^{28} +109.942i q^{29} +(-0.926960 + 440.944i) q^{30} +162.512i q^{31} -170.228 q^{32} +(-0.500301 + 237.987i) q^{33} -185.893i q^{34} -28.7368i q^{35} +(-482.554 - 2.02887i) q^{36} +193.660 q^{37} +314.061 q^{38} +(381.926 + 0.802890i) q^{39} +837.781 q^{40} +7.08888 q^{41} +(45.5256 + 0.0957047i) q^{42} +287.886i q^{43} +818.575 q^{44} +(450.447 + 1.89388i) q^{45} +868.420i q^{46} +7.00839i q^{47} +(-1.22830 + 584.288i) q^{48} +340.033 q^{49} -779.935 q^{50} +(-189.900 - 0.399211i) q^{51} -1313.66i q^{52} +280.031 q^{53} +(-4.50049 + 713.602i) q^{54} -764.111 q^{55} -86.4973i q^{56} +(0.674455 - 320.830i) q^{57} -559.222i q^{58} +852.014i q^{59} +(3.25707 - 1549.35i) q^{60} +381.012i q^{61} -826.619i q^{62} +(0.195535 - 46.5067i) q^{63} -33.7101 q^{64} +1226.26i q^{65} +(2.54478 - 1210.52i) q^{66} +(-372.829 - 402.196i) q^{67} +653.175i q^{68} +(887.138 + 1.86496i) q^{69} +146.170i q^{70} +520.949i q^{71} +(1355.84 + 5.70054i) q^{72} +450.510 q^{73} -985.053 q^{74} +(-1.67493 + 796.747i) q^{75} -1103.52 q^{76} +78.8912i q^{77} +(-1942.67 - 4.08390i) q^{78} -650.095i q^{79} -1875.99 q^{80} +(728.974 + 6.12998i) q^{81} -36.0576 q^{82} -1141.43i q^{83} +(-159.964 - 0.336279i) q^{84} -609.715i q^{85} -1464.33i q^{86} +(-571.276 - 1.20094i) q^{87} -2299.96 q^{88} -542.610i q^{89} +(-2291.20 - 9.63323i) q^{90} +126.606 q^{91} -3051.38i q^{92} +(-844.436 - 1.77519i) q^{93} -35.6482i q^{94} +1030.10 q^{95} +(1.85946 - 884.526i) q^{96} +1322.50i q^{97} -1729.58 q^{98} +(-1236.61 - 5.19927i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 268 q^{4} - 46 q^{6} + 22 q^{9}+O(q^{10}) $ 64 * q + 268 * q^4 - 46 * q^6 + 22 * q^9	$ 64 q + 268 q^{4} - 46 q^{6} + 22 q^{9} - 36 q^{10} + 20 q^{15} + 556 q^{16} + 128 q^{19} + 96 q^{22} - 904 q^{24} + 2080 q^{25} - 236 q^{33} - 1574 q^{36} + 1004 q^{37} - 176 q^{39} - 648 q^{40} - 1220 q^{49} + 2188 q^{54} - 1344 q^{55} + 550 q^{60} + 4336 q^{64} - 3512 q^{67} + 3968 q^{73} - 3316 q^{76} - 1170 q^{81} + 4020 q^{82} - 9270 q^{84} + 2436 q^{88} + 746 q^{90} - 3408 q^{91} - 1412 q^{93} - 7032 q^{96}+O(q^{100}) $ 64 * q + 268 * q^4 - 46 * q^6 + 22 * q^9 - 36 * q^10 + 20 * q^15 + 556 * q^16 + 128 * q^19 + 96 * q^22 - 904 * q^24 + 2080 * q^25 - 236 * q^33 - 1574 * q^36 + 1004 * q^37 - 176 * q^39 - 648 * q^40 - 1220 * q^49 + 2188 * q^54 - 1344 * q^55 + 550 * q^60 + 4336 * q^64 - 3512 * q^67 + 3968 * q^73 - 3316 * q^76 - 1170 * q^81 + 4020 * q^82 - 9270 * q^84 + 2436 * q^88 + 746 * q^90 - 3408 * q^91 - 1412 * q^93 - 7032 * q^96

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 $

$2$	−5.08650			−1.79835			−0.899175	−	0.437589i	$-0.855833\pi$
$2$	−5.08650			−1.79835			−0.899175	+	0.437589i	$0.855833\pi$
$3$	−0.0109234	+	5.19614i	−0.00210221	+	0.999998i
$3$	−0.0109234	+	5.19614i	−0.00210221	+	0.999998i
$4$	17.8725			2.23406
$5$	−16.6834			−1.49220			−0.746102	−	0.665831i	$-0.768077\pi$
$5$	−16.6834			−1.49220			−0.746102	+	0.665831i	$0.768077\pi$
$6$	0.0555619	−	26.4302i	0.00378051	−	1.79835i
$7$			1.72249i			0.0930055i	0.998918	+	0.0465027i	$0.0148076\pi$
$7$			1.72249i			0.0930055i	−0.998918	+	0.0465027i	$0.985192\pi$
$8$	−50.2166			−2.21928
$9$	−26.9998	−	0.113519i	−0.999991	−	0.00420441i
$10$	84.8599			2.68351
$11$	45.8008			1.25541			0.627703	−	0.778453i	$-0.283995\pi$
$11$	45.8008			1.25541			0.627703	+	0.778453i	$0.283995\pi$
$12$	−0.195229	+	92.8681i	−0.00469647	+	2.23406i
$13$		−	73.5018i		−	1.56813i	−0.620677	−	0.784066i	$-0.713142\pi$
$13$		−	73.5018i		−	1.56813i	0.620677	−	0.784066i	$-0.286858\pi$
$14$		−	8.76143i		−	0.167256i
$15$	0.182239	−	86.6891i	0.00313693	−	1.49220i
$16$	112.447			1.75698
$17$			36.5463i			0.521399i	0.965420	+	0.260700i	$0.0839532\pi$
$17$			36.5463i			0.521399i	−0.965420	+	0.260700i	$0.916047\pi$
$18$	137.334	+	0.577415i	1.79833	+	0.00756101i
$19$	−61.7440			−0.745528			−0.372764	−	0.927926i	$-0.621590\pi$
$19$	−61.7440			−0.745528			−0.372764	+	0.927926i	$0.621590\pi$
$20$	−298.173			−3.33368
$21$	−8.95028	−	0.0188154i	−0.0930053	−	0.000195517i
$22$	−232.966			−2.25766
$23$		−	170.730i		−	1.54781i	−0.633300	−	0.773907i	$-0.718300\pi$
$23$		−	170.730i		−	1.54781i	0.633300	−	0.773907i	$-0.281700\pi$
$24$	0.548536	−	260.932i	0.00466539	−	2.21927i
$25$	153.334			1.22667
$26$			373.867i			2.82005i
$27$	0.884791	−	140.293i	0.00630660	−	0.999980i
$28$			30.7851i			0.207780i
$29$			109.942i			0.703992i	0.936001	+	0.351996i	$0.114497\pi$
$29$			109.942i			0.703992i	−0.936001	+	0.351996i	$0.885503\pi$
$30$	−0.926960	+	440.944i	−0.00564130	+	2.68350i
$31$			162.512i			0.941550i	0.882253	+	0.470775i	$0.156026\pi$
$31$			162.512i			0.941550i	−0.882253	+	0.470775i	$0.843974\pi$
$32$	−170.228			−0.940383
$33$	−0.500301	+	237.987i	−0.00263913	+	1.25540i
$34$		−	185.893i		−	0.937659i
$35$		−	28.7368i		−	0.138783i
$36$	−482.554	−	2.02887i	−2.23404	−	0.00939293i
$37$	193.660			0.860474			0.430237	−	0.902716i	$-0.358430\pi$
$37$	193.660			0.860474			0.430237	+	0.902716i	$0.358430\pi$
$38$	314.061			1.34072
$39$	381.926	+	0.802890i	1.56813	+	0.00329655i
$40$	837.781			3.31162
$41$	7.08888			0.0270024			0.0135012	−	0.999909i	$-0.495702\pi$
$41$	7.08888			0.0270024			0.0135012	+	0.999909i	$0.495702\pi$
$42$	45.5256	+	0.0957047i	0.167256	+	0.000351608i
$43$			287.886i			1.02098i	0.859883	+	0.510491i	$0.170536\pi$
$43$			287.886i			1.02098i	−0.859883	+	0.510491i	$0.829464\pi$
$44$	818.575			2.80466
$45$	450.447	+	1.89388i	1.49219	+	0.00627384i
$46$			868.420i			2.78351i
$47$			7.00839i			0.0217506i	0.999941	+	0.0108753i	$0.00346179\pi$
$47$			7.00839i			0.0217506i	−0.999941	+	0.0108753i	$0.996538\pi$
$48$	−1.22830	+	584.288i	−0.00369354	+	1.75697i
$49$	340.033			0.991350
$50$	−779.935			−2.20599
$51$	−189.900	−	0.399211i	−0.521398	−	0.00109609i
$52$		−	1313.66i		−	3.50331i
$53$	280.031			0.725758			0.362879	−	0.931836i	$-0.381794\pi$
$53$	280.031			0.725758			0.362879	+	0.931836i	$0.381794\pi$
$54$	−4.50049	+	713.602i	−0.0113415	+	1.79831i
$55$	−764.111			−1.87332
$56$		−	86.4973i		−	0.206405i
$57$	0.674455	−	320.830i	0.00156726	−	0.745527i
$58$		−	559.222i		−	1.26602i
$59$			852.014i			1.88005i	0.341108	+	0.940024i	$0.389198\pi$
$59$			852.014i			1.88005i	−0.341108	+	0.940024i	$0.610802\pi$
$60$	3.25707	−	1549.35i	0.00700810	−	3.33367i
$61$			381.012i			0.799730i	0.916574	+	0.399865i	$0.130943\pi$
$61$			381.012i			0.799730i	−0.916574	+	0.399865i	$0.869057\pi$
$62$		−	826.619i		−	1.69324i
$63$	0.195535	−	46.5067i	0.000391033	−	0.0930047i
$64$	−33.7101			−0.0658401
$65$			1226.26i			2.33998i
$66$	2.54478	−	1210.52i	0.00474607	−	2.25765i
$67$	−372.829	−	402.196i	−0.679826	−	0.733374i
$67$	−372.829	−	402.196i	−0.679826	−	0.733374i
$68$			653.175i			1.16484i
$69$	887.138	+	1.86496i	1.54781	+	0.00325383i
$70$			146.170i			0.249581i
$71$			520.949i			0.870779i	0.900242	+	0.435389i	$0.143389\pi$
$71$			520.949i			0.870779i	−0.900242	+	0.435389i	$0.856611\pi$
$72$	1355.84	+	5.70054i	2.21926	+	0.00933077i
$73$	450.510			0.722304			0.361152	−	0.932507i	$-0.382384\pi$
$73$	450.510			0.722304			0.361152	+	0.932507i	$0.382384\pi$
$74$	−985.053			−1.54743
$75$	−1.67493	+	796.747i	−0.00257873	+	1.22667i
$76$	−1103.52			−1.66556
$77$			78.8912i			0.116760i
$78$	−1942.67	−	4.08390i	−2.82005	−	0.00592835i
$79$		−	650.095i		−	0.925841i	−0.886400	−	0.462920i	$-0.846802\pi$
$79$		−	650.095i		−	0.925841i	0.886400	−	0.462920i	$-0.153198\pi$
$80$	−1875.99			−2.62177
$81$	728.974	+	6.12998i	0.999965	+	0.00840875i
$82$	−36.0576			−0.0485597
$83$		−	1141.43i		−	1.50949i	−0.656018	−	0.754745i	$-0.727760\pi$
$83$		−	1141.43i		−	1.50949i	0.656018	−	0.754745i	$-0.272240\pi$
$84$	−159.964	−	0.336279i	−0.207780	−	0.000436798i
$85$		−	609.715i		−	0.778034i
$86$		−	1464.33i		−	1.83608i
$87$	−571.276	−	1.20094i	−0.703991	−	0.00147994i
$88$	−2299.96			−2.78609
$89$		−	542.610i		−	0.646253i	−0.946356	−	0.323126i	$-0.895266\pi$
$89$		−	542.610i		−	0.646253i	0.946356	−	0.323126i	$-0.104734\pi$
$90$	−2291.20	−	9.63323i	−2.68348	−	0.0112826i
$91$	126.606			0.145845
$92$		−	3051.38i		−	3.45791i
$93$	−844.436	−	1.77519i	−0.941548	−	0.00197934i
$94$		−	35.6482i		−	0.0391152i
$95$	1030.10			1.11248
$96$	1.85946	−	884.526i	0.00197688	−	0.940381i
$97$			1322.50i			1.38432i	0.721743	+	0.692162i	$0.243341\pi$
$97$			1322.50i			1.38432i	−0.721743	+	0.692162i	$0.756659\pi$
$98$	−1729.58			−1.78279
$99$	−1236.61	−	5.19927i	−1.25539	−	0.00527824i
$100$	2740.47			2.74047
$101$	1470.63			1.44884			0.724422	−	0.689357i	$-0.242107\pi$
$101$	1470.63			1.44884			0.724422	+	0.689357i	$0.242107\pi$
$102$	965.926	+	2.03059i	0.937657	+	0.00197116i
$103$	1623.18			1.55279			0.776393	−	0.630249i	$-0.217047\pi$
$103$	1623.18			1.55279			0.776393	+	0.630249i	$0.217047\pi$
$104$			3691.01i			3.48013i
$105$	149.321	+	0.313904i	0.138783	+	0.000291752i
$106$	−1424.38			−1.30517
$107$		−	1509.81i		−	1.36410i	−0.731304	−	0.682052i	$-0.761088\pi$
$107$		−	1509.81i		−	1.36410i	0.731304	−	0.682052i	$-0.238912\pi$
$108$	15.8134	−	2507.39i	0.0140893	−	2.23402i
$109$		−	902.368i		−	0.792946i	−0.918046	−	0.396473i	$-0.870234\pi$
$109$		−	902.368i		−	0.792946i	0.918046	−	0.396473i	$-0.129766\pi$
$110$	3886.65			3.36889
$111$	−2.11543	+	1006.29i	−0.00180890	+	0.860472i
$112$			193.688i			0.163409i
$113$	−1374.10			−1.14393			−0.571966	−	0.820278i	$-0.693819\pi$
$113$	−1374.10			−1.14393			−0.571966	+	0.820278i	$0.693819\pi$
$114$	−3.43061	+	1631.90i	−0.00281848	+	1.34072i
$115$			2848.35i			2.30965i
$116$			1964.95i			1.57276i
$117$	−8.34386	+	1984.53i	−0.00659308	+	1.56812i
$118$		−	4333.77i		−	3.38098i
$119$	−62.9505			−0.0484930
$120$	−9.15142	+	4353.23i	−0.00696172	+	3.31161i
$121$	766.712			0.576042
$122$		−	1938.02i		−	1.43820i
$123$	−0.0774348	+	36.8348i	−5.67647e−5	+	0.0270023i
$124$			2904.50i			2.10348i
$125$	−472.711			−0.338245
$126$	−0.994590	+	236.556i	−0.000703215	+	0.167255i
$127$	2641.40			1.84556			0.922782	−	0.385323i	$-0.125910\pi$
$127$	2641.40			1.84556			0.922782	+	0.385323i	$0.125910\pi$
$128$	1533.29			1.05879
$129$	−1495.90	−	3.14470i	−1.02098	−	0.00214632i
$130$		−	6237.36i		−	4.20810i
$131$			1640.51i			1.09414i	0.837087	+	0.547069i	$0.184257\pi$
$131$			1640.51i			1.09414i	−0.837087	+	0.547069i	$0.815743\pi$
$132$	−8.94163	+	4253.43i	−0.00589598	+	2.80465i
$133$		−	106.353i		−	0.0693382i
$134$	1896.40	+	2045.77i	1.22256	+	1.31886i
$135$	−14.7613	+	2340.56i	−0.00941073	+	1.49217i
$136$		−	1835.23i		−	1.15713i
$137$	226.841			0.141462			0.0707310	−	0.997495i	$-0.477467\pi$
$137$	226.841			0.141462			0.0707310	+	0.997495i	$0.477467\pi$
$138$	−4512.43	−	9.48610i	−2.78350	−	0.00585153i
$139$			115.363i			0.0703955i	0.999380	+	0.0351977i	$0.0112061\pi$
$139$			115.363i			0.0703955i	−0.999380	+	0.0351977i	$0.988794\pi$
$140$		−	513.600i		−	0.310051i
$141$	−36.4166	−	0.0765555i	−0.0217506	−	4.57244e-5i
$142$		−	2649.81i		−	1.56597i
$143$		−	3366.44i		−	1.96864i
$144$	−3036.03	−	12.7648i	−1.75696	−	0.00738706i
$145$		−	1834.21i		−	1.05050i
$146$	−2291.52			−1.29896
$147$	−3.71432	+	1766.86i	−0.00208403	+	0.991348i
$148$	3461.19			1.92235
$149$		−	2205.97i		−	1.21288i	−0.795128	−	0.606442i	$-0.792596\pi$
$149$		−	2205.97i		−	1.21288i	0.795128	−	0.606442i	$-0.207404\pi$
$150$	8.51955	−	4052.65i	0.00463746	−	2.20599i
$151$	−1785.31			−0.962162			−0.481081	−	0.876676i	$-0.659756\pi$
$151$	−1785.31			−0.962162			−0.481081	+	0.876676i	$0.659756\pi$
$152$	3100.57			1.65454
$153$	4.14871	−	986.742i	0.00219218	−	0.521395i
$154$		−	401.280i		−	0.209975i
$155$		−	2711.25i		−	1.40499i
$156$	6825.97	+	14.3497i	3.50330	+	0.00736470i
$157$	469.358			0.238591			0.119296	−	0.992859i	$-0.461936\pi$
$157$	469.358			0.238591			0.119296	+	0.992859i	$0.461936\pi$
$158$			3306.71i			1.66499i
$159$	−3.05889	+	1455.08i	−0.00152570	+	0.725756i
$160$	2839.97			1.40324
$161$	294.080			0.143955
$162$	−3707.93	−	31.1802i	−1.79829	−	0.0151219i
$163$	−2642.84			−1.26996			−0.634979	−	0.772529i	$-0.718991\pi$
$163$	−2642.84			−1.26996			−0.634979	+	0.772529i	$0.718991\pi$
$164$	126.696			0.0603250
$165$	8.34669	−	3970.43i	0.00393812	−	1.87332i
$166$			5805.87i			2.71459i
$167$		−	1527.23i		−	0.707667i	−0.935308	−	0.353833i	$-0.884878\pi$
$167$		−	1527.23i		−	0.707667i	0.935308	−	0.353833i	$-0.115122\pi$
$168$	449.452	+	0.944845i	0.206405	+	0.000433907i
$169$	−3205.51			−1.45904
$170$			3101.32i			1.39918i
$171$	1667.07	+	7.00912i	0.745522	+	0.00313451i
$172$			5145.25i			2.28094i
$173$			2523.06i			1.10882i	0.832245	+	0.554408i	$0.187055\pi$
$173$			2523.06i			1.10882i	−0.832245	+	0.554408i	$0.812945\pi$
$174$	2905.80	+	6.10861i	1.26602	+	0.00266145i
$175$			264.116i			0.114087i
$176$	5150.14			2.20572
$177$	−4427.19	−	9.30690i	−1.88004	−	0.00395226i
$178$			2759.98i			1.16219i
$179$	−179.275			−0.0748583			−0.0374291	−	0.999299i	$-0.511917\pi$
$179$	−179.275			−0.0748583			−0.0374291	+	0.999299i	$0.511917\pi$
$180$	8050.61	+	33.8484i	3.33365	+	0.0140162i
$181$	3959.72			1.62610			0.813050	−	0.582194i	$-0.197806\pi$
$181$	3959.72			1.62610			0.813050	+	0.582194i	$0.197806\pi$
$182$	−643.981			−0.262280
$183$	−1979.79	−	4.16195i	−0.799729	−	0.00168120i
$184$			8573.49i			3.43503i
$185$	−3230.90			−1.28400
$186$	4295.23	+	9.02950i	1.69323	+	0.00355954i
$187$			1673.85i			0.654567i
$188$			125.258i			0.0485923i
$189$	241.653	+	1.52404i	0.0930036	+	0.000586548i
$190$	−5239.59			−2.00063
$191$	2518.48			0.954089			0.477044	−	0.878879i	$-0.341708\pi$
$191$	2518.48			0.954089			0.477044	+	0.878879i	$0.341708\pi$
$192$	0.368229	−	175.163i	0.000138410	−	0.0658399i
$193$	1629.19			0.607624			0.303812	−	0.952732i	$-0.401741\pi$
$193$	1629.19			0.607624			0.303812	+	0.952732i	$0.401741\pi$
$194$		−	6726.89i		−	2.48950i
$195$	−6371.80	−	13.3949i	−2.33997	−	0.00491912i
$196$	6077.25			2.21474
$197$	3036.91			1.09833			0.549166	−	0.835714i	$-0.314946\pi$
$197$	3036.91			1.09833			0.549166	+	0.835714i	$0.314946\pi$
$198$	6290.02	+	26.4461i	2.25764	+	0.00949213i
$199$	1510.03			0.537904			0.268952	−	0.963154i	$-0.413323\pi$
$199$	1510.03			0.537904			0.268952	+	0.963154i	$0.413323\pi$
$200$	−7699.92			−2.72233
$201$	2093.94	−	1932.88i	0.734801	−	0.678283i
$202$	−7480.37			−2.60553
$203$	−189.374			−0.0654751
$204$	−3393.99	−	7.13490i	−1.16484	−	0.00244874i
$205$	−118.266			−0.0402931
$206$	−8256.32			−2.79245
$207$	−19.3811	+	4609.68i	−0.00650765	+	1.54780i
$208$		−	8265.03i		−	2.75518i
$209$	−2827.92			−0.935940
$210$	−759.520	−	1.59667i	−0.249580	−	0.000524672i
$211$	5437.85			1.77420			0.887102	−	0.461574i	$-0.152715\pi$
$211$	5437.85			1.77420			0.887102	+	0.461574i	$0.152715\pi$
$212$	5004.85			1.62139
$213$	−2706.93	−	5.69054i	−0.870777	−	0.00183056i
$214$			7679.67i			2.45314i
$215$		−	4802.91i		−	1.52351i
$216$	−44.4312	+	7045.05i	−0.0139961	+	2.21924i
$217$	−279.925			−0.0875693
$218$			4589.90i			1.42600i
$219$	−4.92110	+	2340.91i	−0.00151844	+	0.722303i
$220$	−13656.6			−4.18512
$221$	2686.22			0.817623
$222$	10.7601	−	5118.47i	0.00325303	−	1.54743i
$223$	−4225.43			−1.26886			−0.634430	−	0.772981i	$-0.718765\pi$
$223$	−4225.43			−1.26886			−0.634430	+	0.772981i	$0.718765\pi$
$224$		−	293.214i		−	0.0874608i
$225$	−4139.99	−	17.4064i	−1.22666	−	0.00515745i
$226$	6989.35			2.05719
$227$		−	1070.49i		−	0.313001i	−0.987678	−	0.156500i	$-0.949979\pi$
$227$		−	1070.49i		−	0.313001i	0.987678	−	0.156500i	$-0.0500212\pi$
$228$	12.0542	−	5734.04i	0.00350135	−	1.66555i
$229$		−	1857.33i		−	0.535965i	−0.963424	−	0.267982i	$-0.913643\pi$
$229$		−	1857.33i		−	0.535965i	0.963424	−	0.267982i	$-0.0863569\pi$
$230$		−	14488.2i		−	4.15357i
$231$	−409.930	−	0.861761i	−0.116759	−	0.000245453i
$232$		−	5520.93i		−	1.56236i
$233$	3509.69			0.986814			0.493407	−	0.869799i	$-0.335751\pi$
$233$	3509.69			0.986814			0.493407	+	0.869799i	$0.335751\pi$
$234$	42.4411	−	10094.3i	0.0118567	−	2.82003i
$235$		−	116.923i		−	0.0324564i
$236$			15227.6i			4.20015i
$237$	3377.99	+	7.10125i	0.925839	+	0.00194631i
$238$	320.198			0.0872074
$239$	−393.959			−0.106624			−0.0533119	−	0.998578i	$-0.516978\pi$
$239$	−393.959			−0.106624			−0.0533119	+	0.998578i	$0.516978\pi$
$240$	20.4922	−	9747.89i	0.00551152	−	2.62177i
$241$	612.613			0.163742			0.0818711	−	0.996643i	$-0.473910\pi$
$241$	612.613			0.163742			0.0818711	+	0.996643i	$0.473910\pi$
$242$	−3899.88			−1.03592
$243$	−39.8151	+	3787.79i	−0.0105109	+	0.999945i
$244$			6809.64i			1.78665i
$245$	−5672.89			−1.47930
$246$	0.393872	−	187.361i	0.000102083	−	0.0485596i
$247$			4538.29i			1.16909i
$248$		−	8160.81i		−	2.08956i
$249$	5931.01	+	12.4683i	1.50949	+	0.00317327i
$250$	2404.45			0.608282
$251$	5073.71			1.27590			0.637948	−	0.770080i	$-0.279784\pi$
$251$	5073.71			1.27590			0.637948	+	0.770080i	$0.279784\pi$
$252$	3.49470	−	831.192i	0.000873594	−	0.207778i
$253$		−	7819.58i		−	1.94313i
$254$	−13435.5			−3.31897
$255$	3168.17	+	6.66017i	0.778033	+	0.00163559i
$256$	−7529.39			−1.83823
$257$		−	1864.90i		−	0.452642i	−0.974053	−	0.226321i	$-0.927330\pi$
$257$		−	1864.90i		−	0.452642i	0.974053	−	0.226321i	$-0.0726698\pi$
$258$	7608.88	+	15.9955i	1.83608	+	0.00385983i
$259$			333.577i			0.0800288i
$260$			21916.3i			5.22765i
$261$	12.4806	−	2968.42i	0.00295987	−	0.703986i
$262$		−	8344.47i		−	1.96765i
$263$			5326.46i			1.24884i	0.781091	+	0.624418i	$0.214664\pi$
$263$			5326.46i			1.24884i	−0.781091	+	0.624418i	$0.785336\pi$
$264$	25.1234	−	11950.9i	0.00585696	−	2.78609i
$265$	−4671.85			−1.08298
$266$			540.965i			0.124694i
$267$	2819.48	+	5.92715i	0.646251	+	0.00135856i
$268$	−6663.39	−	7188.25i	−1.51877	−	1.63840i
$269$		−	2031.69i		−	0.460500i	−0.973132	−	0.230250i	$-0.926046\pi$
$269$		−	2031.69i		−	0.460500i	0.973132	−	0.230250i	$-0.0739544\pi$
$270$	75.0833	−	11905.3i	0.0169238	−	2.68345i
$271$		−	171.676i		−	0.0384818i	−0.999815	−	0.0192409i	$-0.993875\pi$
$271$		−	171.676i		−	0.0384818i	0.999815	−	0.0192409i	$-0.00612495\pi$
$272$			4109.51i			0.916087i
$273$	−1.38297	+	657.861i	−0.000306597	+	0.145845i
$274$	−1153.83			−0.254398
$275$	7022.83			1.53997
$276$	15855.4	+	33.3314i	3.45791	+	0.00726927i
$277$	−3321.75			−0.720521			−0.360261	−	0.932852i	$-0.617312\pi$
$277$	−3321.75			−0.720521			−0.360261	+	0.932852i	$0.617312\pi$
$278$		−	586.795i		−	0.126596i
$279$	18.4482	−	4387.79i	0.00395867	−	0.941542i
$280$			1443.07i			0.307999i
$281$	849.769			0.180402			0.0902010	−	0.995924i	$-0.471249\pi$
$281$	849.769			0.180402			0.0902010	+	0.995924i	$0.471249\pi$
$282$	185.233	+	0.389400i	0.0391152	+	8.22285e-5i
$283$	2709.01			0.569025			0.284512	−	0.958672i	$-0.408168\pi$
$283$	2709.01			0.569025			0.284512	+	0.958672i	$0.408168\pi$
$284$			9310.67i			1.94538i
$285$	−11.2522	+	5352.53i	−0.00233867	+	1.11248i
$286$			17123.4i			3.54031i
$287$			12.2105i			0.00251137i
$288$	4596.10	+	19.3241i	0.940375	+	0.00395376i
$289$	3577.37			0.728143
$290$			9329.70i			1.88917i
$291$	−6871.89	−	14.4462i	−1.38432	−	0.00291014i
$292$	8051.75			1.61367
$293$			4762.23i			0.949532i	0.880112	+	0.474766i	$0.157467\pi$
$293$			4762.23i			0.949532i	−0.880112	+	0.474766i	$0.842533\pi$
$294$	18.8929	−	8987.14i	0.00374781	−	1.78279i
$295$		−	14214.5i		−	2.80542i
$296$	−9724.95			−1.90963
$297$	40.5241	−	6425.54i	0.00791733	−	1.25538i
$298$			11220.7i			2.18119i
$299$	−12549.0			−2.42718
$300$	−29.9353	+	14239.9i	−0.00576104	+	2.74046i
$301$	−495.880			−0.0949569
$302$	9080.98			1.73030
$303$	−16.0643	+	7641.60i	−0.00304577	+	1.44884i
$304$	−6942.90			−1.30988
$305$		−	6356.55i		−	1.19336i
$306$	−21.1024	+	5019.07i	−0.00394230	+	0.937650i
$307$	5088.55			0.945990			0.472995	−	0.881065i	$-0.343173\pi$
$307$	5088.55			0.945990			0.472995	+	0.881065i	$0.343173\pi$
$308$			1409.98i			0.260848i
$309$	−17.7307	+	8434.28i	−0.00326428	+	1.55278i
$310$			13790.8i			2.52666i
$311$	8662.94			1.57952			0.789759	−	0.613417i	$-0.210206\pi$
$311$	8662.94			1.57952			0.789759	+	0.613417i	$0.210206\pi$
$312$	−19179.0	−	40.3184i	−3.48012	−	0.00731596i
$313$			5315.82i			0.959962i	0.877279	+	0.479981i	$0.159356\pi$
$313$			5315.82i			0.959962i	−0.877279	+	0.479981i	$0.840644\pi$
$314$	−2387.39			−0.429071
$315$	−3.26218	+	775.888i	−0.000583502	+	0.138782i
$316$		−	11618.8i		−	2.06839i
$317$			254.550i			0.0451008i	0.999746	+	0.0225504i	$0.00717863\pi$
$317$			254.550i			0.0451008i	−0.999746	+	0.0225504i	$0.992821\pi$
$318$	15.5590	−	7401.26i	0.00274374	−	1.30516i
$319$			5035.44i			0.883795i
$320$	562.398			0.0982469
$321$	7845.20	+	16.4923i	1.36410	+	0.00286763i
$322$	−1495.84			−0.258882
$323$		−	2256.52i		−	0.388718i
$324$	13028.6	+	109.558i	2.23399	+	0.0187857i
$325$		−	11270.3i		−	1.92359i
$326$	13442.8			2.28383
$327$	4688.83	+	9.85693i	0.792945	+	0.00166694i
$328$	−355.979			−0.0599258
$329$	−12.0719			−0.00202293
$330$	−42.4555	+	20195.6i	−0.00708211	+	3.36888i
$331$			4265.47i			0.708312i	0.935186	+	0.354156i	$0.115232\pi$
$331$			4265.47i			0.708312i	−0.935186	+	0.354156i	$0.884768\pi$
$332$		−	20400.1i		−	3.37230i
$333$	−5228.78	−	21.9841i	−0.860466	−	0.00361779i
$334$			7768.24i			1.27263i
$335$	6220.04	+	6709.97i	1.01444	+	1.09434i
$336$	−1006.43	−	2.11573i	−0.163408	−	0.000343519i
$337$		−	5702.86i		−	0.921823i	−0.887446	−	0.460912i	$-0.847522\pi$
$337$		−	5702.86i		−	0.921823i	0.887446	−	0.460912i	$-0.152478\pi$
$338$	16304.9			2.62387
$339$	15.0098	−	7140.00i	0.00240478	−	1.14393i
$340$		−	10897.1i		−	1.73818i
$341$			7443.19i			1.18203i
$342$	−8479.57	−	35.6519i	−1.34071	−	0.00563694i
$343$			1176.51i			0.185206i
$344$		−	14456.7i		−	2.26584i
$345$	−14800.4	−	31.1137i	−2.30965	−	0.00485538i
$346$		−	12833.6i		−	1.99404i
$347$	−6405.01			−0.990890			−0.495445	−	0.868639i	$-0.664995\pi$
$347$	−6405.01			−0.990890			−0.495445	+	0.868639i	$0.664995\pi$
$348$	−10210.1	−	21.4639i	−1.57276	−	0.00330628i
$349$	−3349.46			−0.513733			−0.256866	−	0.966447i	$-0.582690\pi$
$349$	−3349.46			−0.513733			−0.256866	+	0.966447i	$0.582690\pi$
$350$		−	1343.43i		−	0.205169i
$351$	−10311.8	−	65.0337i	−1.56810	−	0.00988958i
$352$	−7796.55			−1.18056
$353$	−5788.20			−0.872733			−0.436366	−	0.899769i	$-0.643735\pi$
$353$	−5788.20			−0.872733			−0.436366	+	0.899769i	$0.643735\pi$
$354$	22518.9	+	47.3396i	3.38098	+	0.00710754i
$355$		−	8691.18i		−	1.29938i
$356$		−	9697.80i		−	1.44377i
$357$	0.687634	−	327.100i	0.000101942	−	0.0484929i
$358$	911.882			0.134621
$359$			6572.55i			0.966256i	0.875550	+	0.483128i	$0.160500\pi$
$359$			6572.55i			0.966256i	−0.875550	+	0.483128i	$0.839500\pi$
$360$	−22619.9	−	95.1041i	−3.31159	−	0.0139234i
$361$	−3046.68			−0.444188
$362$	−20141.2			−2.92430
$363$	−8.37510	+	3983.94i	−0.00121096	+	0.576040i
$364$	2262.76			0.325827
$365$	−7516.02			−1.07783
$366$	10070.2	+	21.1698i	1.43819	+	0.00302339i
$367$			9803.56i			1.39439i	0.716881	+	0.697196i	$0.245569\pi$
$367$			9803.56i			1.39439i	−0.716881	+	0.697196i	$0.754431\pi$
$368$		−	19198.0i		−	2.71947i
$369$	−191.398	−	0.804724i	−0.0270021	−	0.000113529i
$370$	16434.0			2.30909
$371$			482.349i			0.0674994i
$372$	−15092.2	−	31.7271i	−2.10348	−	0.00442197i
$373$		−	12099.8i		−	1.67963i	−0.542870	−	0.839817i	$-0.682662\pi$
$373$		−	12099.8i		−	1.67963i	0.542870	−	0.839817i	$-0.317338\pi$
$374$		−	8514.05i		−	1.17714i
$375$	5.16362	−	2456.27i	0.000711061	−	0.338244i
$376$		−	351.937i		−	0.0482707i
$377$	8080.96			1.10395
$378$	−1229.17	−	7.75203i	−0.167253	−	0.00105482i
$379$		−	7772.70i		−	1.05345i	−0.850036	−	0.526724i	$-0.823420\pi$
$379$		−	7772.70i		−	1.05345i	0.850036	−	0.526724i	$-0.176580\pi$
$380$	18410.4			2.48535
$381$	−28.8531	+	13725.1i	−0.00387976	+	1.84556i
$382$	−12810.3			−1.71579
$383$	1981.96			0.264422			0.132211	−	0.991222i	$-0.457792\pi$
$383$	1981.96			0.264422			0.132211	+	0.991222i	$0.457792\pi$
$384$	−16.7487	+	7967.17i	−0.00222579	+	1.05878i
$385$		−	1316.17i		−	0.174229i
$386$	−8286.86			−1.09272
$387$	32.6806	−	7772.86i	0.00429263	−	1.02097i
$388$			23636.4i			3.09267i
$389$		−	11595.3i		−	1.51132i	−0.654964	−	0.755660i	$-0.727316\pi$
$389$		−	11595.3i		−	1.51132i	0.654964	−	0.755660i	$-0.272684\pi$
$390$	32410.2	+	68.1332i	4.20809	+	0.00884630i
$391$	6239.56			0.807029
$392$	−17075.3			−2.20008
$393$	−8524.33	−	17.9200i	−1.09414	−	0.00230011i
$394$	−15447.3			−1.97518
$395$			10845.8i			1.38154i
$396$	−22101.3	−	92.9239i	−2.80463	−	0.0117919i
$397$	−9457.14			−1.19557			−0.597783	−	0.801658i	$-0.703952\pi$
$397$	−9457.14			−1.19557			−0.597783	+	0.801658i	$0.703952\pi$
$398$	−7680.75			−0.967339
$399$	552.626	+	1.16174i	0.0693381	+	0.000145764i
$400$	17241.9			2.15524
$401$	−4150.52			−0.516875			−0.258437	−	0.966028i	$-0.583208\pi$
$401$	−4150.52			−0.516875			−0.258437	+	0.966028i	$0.583208\pi$
$402$	−10650.8	+	9831.60i	−1.32143	+	1.21979i
$403$	11944.9			1.47648
$404$	26283.9			3.23681
$405$	−12161.7	−	102.269i	−1.49215	−	0.0125476i
$406$	963.252			0.117747
$407$	8869.78			1.08024
$408$	9536.12	+	20.0470i	1.15713	+	0.00243253i
$409$			10345.7i			1.25076i	0.780319	+	0.625382i	$0.215057\pi$
$409$			10345.7i			1.25076i	−0.780319	+	0.625382i	$0.784943\pi$
$410$	601.562			0.0724611
$411$	−2.47787	+	1178.70i	−0.000297383	+	0.141462i
$412$	29010.3			3.46902
$413$	−1467.58			−0.174855
$414$	98.5823	−	23447.1i	0.0117030	−	2.78349i
$415$			19042.8i			2.25247i
$416$			12512.0i			1.47465i
$417$	−599.443	−	1.26016i	−0.0703953	−	0.000147986i
$418$	14384.2			1.68315
$419$		−	7292.75i		−	0.850296i	−0.905124	−	0.425148i	$-0.860222\pi$
$419$		−	7292.75i		−	0.850296i	0.905124	−	0.425148i	$-0.139778\pi$
$420$	2668.74	+	5.61026i	0.310050	+	0.000651792i
$421$	−2641.55			−0.305799			−0.152899	−	0.988242i	$-0.548861\pi$
$421$	−2641.55			−0.305799			−0.152899	+	0.988242i	$0.548861\pi$
$422$	−27659.6			−3.19064
$423$	0.795587	−	189.225i	9.14486e−5	−	0.0217504i
$424$	−14062.2			−1.61066
$425$			5603.81i			0.639587i
$426$	13768.8	+	28.9450i	1.56596	+	0.00329199i
$427$	−656.287			−0.0743793
$428$		−	26984.1i		−	3.04750i
$429$	17492.5	+	36.7730i	1.96864	+	0.00413850i
$430$			24430.0i			2.73981i
$431$			2828.33i			0.316093i	0.987432	+	0.158047i	$0.0505196\pi$
$431$			2828.33i			0.316093i	−0.987432	+	0.158047i	$0.949480\pi$
$432$	99.4917	−	15775.5i	0.0110806	−	1.75694i
$433$		−	9318.93i		−	1.03427i	−0.855904	−	0.517135i	$-0.826998\pi$
$433$		−	9318.93i		−	1.03427i	0.855904	−	0.517135i	$-0.173002\pi$
$434$	1423.84			0.157480
$435$	9530.80	+	20.0358i	1.05050	+	0.00220837i
$436$		−	16127.6i		−	1.77149i
$437$			10541.6i			1.15394i
$438$	25.0312	−	11907.1i	0.00273068	−	1.29895i
$439$	1841.99			0.200258			0.100129	−	0.994974i	$-0.468074\pi$
$439$	1841.99			0.200258			0.100129	+	0.994974i	$0.468074\pi$
$440$	38371.0			4.15742
$441$	−9180.81	−	38.6003i	−0.991341	−	0.00416804i
$442$	−13663.5			−1.47037
$443$	52.9367			0.00567743			0.00283871	−	0.999996i	$-0.499096\pi$
$443$	52.9367			0.00567743			0.00283871	+	0.999996i	$0.499096\pi$
$444$	−37.8080	+	17984.8i	−0.00404119	+	1.92235i
$445$			9052.55i			0.964341i
$446$	21492.7			2.28185
$447$	11462.5	+	24.0967i	1.21288	+	0.00254974i
$448$		−	58.0652i		−	0.00612349i
$449$			7815.00i			0.821409i	0.911769	+	0.410704i	$0.134717\pi$
$449$			7815.00i			0.821409i	−0.911769	+	0.410704i	$0.865283\pi$
$450$	21058.1	+	88.5376i	2.20597	+	0.00927489i
$451$	324.676			0.0338989
$452$	−24558.6			−2.55562
$453$	19.5017	−	9276.72i	0.00202267	−	0.962160i
$454$			5445.07i			0.562885i
$455$	−2112.21			−0.217631
$456$	−33.8688	+	16111.0i	−0.00347818	+	1.65453i
$457$	4501.48			0.460767			0.230383	−	0.973100i	$-0.426002\pi$
$457$	4501.48			0.460767			0.230383	+	0.973100i	$0.426002\pi$
$458$			9447.32i			0.963853i
$459$	5127.21	+	32.3359i	0.521389	+	0.00328825i
$460$			50907.2i			5.15992i
$461$			7465.62i			0.754248i	0.926163	+	0.377124i	$0.123087\pi$
$461$			7465.62i			0.754248i	−0.926163	+	0.377124i	$0.876913\pi$
$462$	2085.11	+	4.38335i	0.209974	+	0.000441411i
$463$		−	8359.64i		−	0.839104i	−0.907731	−	0.419552i	$-0.862187\pi$
$463$		−	8359.64i		−	0.839104i	0.907731	−	0.419552i	$-0.137813\pi$
$464$			12362.6i			1.23690i
$465$	14088.0	+	29.6161i	1.40498	+	0.00295358i
$466$	−17852.1			−1.77464
$467$		−	4743.52i		−	0.470030i	−0.971992	−	0.235015i	$-0.924486\pi$
$467$		−	4743.52i		−	0.470030i	0.971992	−	0.235015i	$-0.0755139\pi$
$468$	−149.126	+	35468.6i	−0.0147294	+	3.50328i
$469$	692.776	−	642.193i	0.0682078	−	0.0632275i
$470$			594.732i			0.0583679i
$471$	−5.12699	+	2438.85i	−0.000501569	+	0.238591i
$472$		−	42785.2i		−	4.17235i
$473$			13185.4i			1.28175i
$474$	−17182.1	−	36.1206i	−1.66498	−	0.00350015i
$475$	−9467.47			−0.914520
$476$	−1125.08			−0.108336
$477$	−7560.76	−	31.7888i	−0.725751	−	0.00305138i
$478$	2003.87			0.191747
$479$			5767.46i			0.550150i	0.961423	+	0.275075i	$0.0887027\pi$
$479$			5767.46i			0.550150i	−0.961423	+	0.275075i	$0.911297\pi$
$480$	−31.0221	+	14756.9i	−0.00294991	+	1.40324i
$481$		−	14234.4i		−	1.34934i
$482$	−3116.06			−0.294466
$483$	−3.21236	+	1528.08i	−0.000302624	+	0.143955i
$484$	13703.1			1.28691
$485$		−	22063.7i		−	2.06569i
$486$	202.520	−	19266.6i	0.0189022	−	1.79825i
$487$			1562.99i			0.145433i	0.997353	+	0.0727163i	$0.0231668\pi$
$487$			1562.99i			0.145433i	−0.997353	+	0.0727163i	$0.976833\pi$
$488$		−	19133.1i		−	1.77483i
$489$	28.8688	−	13732.6i	0.00266972	−	1.26996i
$490$	28855.2			2.66029
$491$		−	5847.20i		−	0.537435i	−0.963219	−	0.268717i	$-0.913400\pi$
$491$		−	5847.20i		−	0.537435i	0.963219	−	0.268717i	$-0.0865997\pi$
$492$	−1.38395	+	658.331i	−0.000126816	+	0.0603249i
$493$	−4017.99			−0.367061
$494$		−	23084.0i		−	2.10243i
$495$	20630.8	+	86.7412i	1.87330	+	0.00787621i
$496$			18273.9i			1.65428i
$497$	−897.327			−0.0809872
$498$	−30168.1	−	63.4198i	−2.71459	−	0.00570665i
$499$		−	3981.41i		−	0.357179i	−0.983924	−	0.178589i	$-0.942847\pi$
$499$		−	3981.41i		−	0.357179i	0.983924	−	0.178589i	$-0.0571534\pi$
$500$	−8448.54			−0.755660
$501$	7935.69	+	16.6825i	0.707665	+	0.00148766i
$502$	−25807.4			−2.29451
$503$	1951.59			0.172996			0.0864980	−	0.996252i	$-0.472432\pi$
$503$	1951.59			0.172996			0.0864980	+	0.996252i	$0.472432\pi$
$504$	−9.81910	+	2335.41i	−0.000867813	+	0.206403i
$505$	−24535.0			−2.16197
$506$			39774.3i			3.49443i
$507$	35.0151	−	16656.3i	0.00306721	−	1.45904i
$508$	47208.5			4.12311
$509$		−	10606.2i		−	0.923602i	−0.886983	−	0.461801i	$-0.847203\pi$
$509$		−	10606.2i		−	0.923602i	0.886983	−	0.461801i	$-0.152797\pi$
$510$	−16114.9	−	33.8770i	−1.39918	−	0.00294137i
$511$			775.997i			0.0671782i
$512$	26032.0			2.24699
$513$	−54.6305	+	8662.27i	−0.00470175	+	0.745513i
$514$			9485.80i			0.814009i
$515$	−27080.1			−2.31707
$516$	−26735.4	−	56.2036i	−2.28093	−	0.00479501i
$517$			320.990i			0.0273058i
$518$		−	1696.74i		−	0.143920i
$519$	−13110.2	−	27.5605i	−1.10881	−	0.00233096i
$520$		−	61578.4i		−	5.19306i
$521$	5057.71			0.425302			0.212651	−	0.977128i	$-0.431790\pi$
$521$	5057.71			0.425302			0.212651	+	0.977128i	$0.431790\pi$
$522$	−63.4824	+	15098.9i	−0.00532289	+	1.26601i
$523$	−3028.51			−0.253208			−0.126604	−	0.991953i	$-0.540408\pi$
$523$	−3028.51			−0.253208			−0.126604	+	0.991953i	$0.540408\pi$
$524$			29320.1i			2.44438i
$525$	−1372.38	−	2.88505i	−0.114087	−	0.000239836i
$526$		−	27093.1i		−	2.24584i
$527$	−5939.23			−0.490924
$528$	−56.2571	+	26760.9i	−0.00463689	+	2.20571i
$529$	−16981.8			−1.39573
$530$	23763.4			1.94758
$531$	96.7199	−	23004.2i	0.00790450	−	1.88003i
$532$		−	1900.80i		−	0.154906i
$533$		−	521.046i		−	0.0423433i
$534$	−14341.3	−	30.1484i	−1.16219	−	0.00244317i
$535$			25188.7i			2.03552i
$536$	18722.2	+	20196.9i	1.50872	+	1.62756i
$537$	1.95829	−	931.537i	0.000157368	−	0.0748581i
$538$			10334.2i			0.828140i
$539$	15573.8			1.24455
$540$	−263.821	+	41831.7i	−0.0210242	+	3.33361i
$541$		−	17988.4i		−	1.42954i	−0.699359	−	0.714770i	$-0.746531\pi$
$541$		−	17988.4i		−	1.42954i	0.699359	−	0.714770i	$-0.253469\pi$
$542$			873.230i			0.0692038i
$543$	−43.2537	+	20575.3i	−0.00341840	+	1.62610i
$544$		−	6221.19i		−	0.490315i
$545$			15054.5i			1.18324i
$546$	7.03446	−	3346.21i	0.000551369	−	0.262280i
$547$		−	8353.11i		−	0.652931i	−0.945209	−	0.326465i	$-0.894142\pi$
$547$		−	8353.11i		−	0.652931i	0.945209	−	0.326465i	$-0.105858\pi$
$548$	4054.21			0.316035
$549$	43.2521	−	10287.2i	0.00336240	−	0.799723i
$550$	−35721.6			−2.76941
$551$		−	6788.27i		−	0.524846i
$552$	−44549.0	−	93.6517i	−3.43502	−	0.00722116i
$553$	1119.78			0.0861083
$554$	16896.1			1.29575
$555$	35.2924	−	16788.2i	0.00269924	−	1.28400i
$556$			2061.83i			0.157268i
$557$		−	17004.1i		−	1.29352i	−0.762695	−	0.646758i	$-0.776124\pi$
$557$		−	17004.1i		−	1.29352i	0.762695	−	0.646758i	$-0.223876\pi$
$558$	−93.8371	+	22318.5i	−0.00711907	+	1.69322i
$559$	21160.1			1.60104
$560$		−	3231.36i		−	0.243839i
$561$	−8697.56	−	18.2842i	−0.654566	−	0.00137604i
$562$	−4322.35			−0.324426
$563$	−18492.6			−1.38432			−0.692159	−	0.721745i	$-0.743340\pi$
$563$	−18492.6			−1.38432			−0.692159	+	0.721745i	$0.743340\pi$
$564$	−650.856	−	1.36824i	−0.0485922	−	0.000102151i
$565$	22924.6			1.70698
$566$	−13779.4			−1.02331
$567$	−10.5588	+	1255.65i	−0.000782060	+	0.0930022i
$568$		−	26160.3i		−	1.93250i
$569$			11920.9i			0.878296i	0.898415	+	0.439148i	$0.144720\pi$
$569$			11920.9i			0.878296i	−0.898415	+	0.439148i	$0.855280\pi$
$570$	57.2342	−	27225.6i	0.00420575	−	2.00063i
$571$	−2784.57			−0.204081			−0.102041	−	0.994780i	$-0.532537\pi$
$571$	−2784.57			−0.204081			−0.102041	+	0.994780i	$0.532537\pi$
$572$		−	60166.7i		−	4.39807i
$573$	−27.5104	+	13086.4i	−0.00200570	+	0.954087i
$574$		−	62.1087i		−	0.00451632i
$575$		−	26178.8i		−	1.89866i
$576$	910.165	+	3.82674i	0.0658395	+	0.000276819i
$577$			19032.1i			1.37317i	0.727051	+	0.686583i	$0.240890\pi$
$577$			19032.1i			1.37317i	−0.727051	+	0.686583i	$0.759110\pi$
$578$	−18196.3			−1.30946
$579$	−17.7963	+	8465.48i	−0.00127735	+	0.607622i
$580$		−	32781.9i		−	2.34689i
$581$	1966.09			0.140391
$582$	34953.9	+	73.4806i	2.48949	+	0.00523345i
$583$	12825.6			0.911120
$584$	−22623.1			−1.60299
$585$	139.204	−	33108.6i	0.00983822	−	2.33995i
$586$		−	24223.1i		−	1.70759i
$587$	9321.25			0.655416			0.327708	−	0.944779i	$-0.393724\pi$
$587$	9321.25			0.655416			0.327708	+	0.944779i	$0.393724\pi$
$588$	−66.3842	+	31578.2i	−0.00465585	+	2.21473i
$589$		−	10034.1i		−	0.701952i
$590$			72301.9i			5.04512i
$591$	−33.1735	+	15780.2i	−0.00230892	+	1.09833i
$592$	21776.4			1.51183
$593$	−3086.89			−0.213766			−0.106883	−	0.994272i	$-0.534087\pi$
$593$	−3086.89			−0.213766			−0.106883	+	0.994272i	$0.534087\pi$
$594$	−206.126	+	32683.5i	−0.0142381	+	2.25761i
$595$	1050.23			0.0723615
$596$		−	39426.1i		−	2.70966i
$597$	−16.4946	+	7846.30i	−0.00113079	+	0.537903i
$598$	63830.4			4.36492
$599$	−21083.8			−1.43817			−0.719084	−	0.694923i	$-0.755438\pi$
$599$	−21083.8			−1.43817			−0.719084	+	0.694923i	$0.755438\pi$
$600$	84.1094	−	40009.9i	0.00572292	−	2.72233i
$601$	25997.7			1.76451			0.882253	−	0.470775i	$-0.156026\pi$
$601$	25997.7			1.76451			0.882253	+	0.470775i	$0.156026\pi$
$602$	2522.29			0.170766
$603$	10020.6	+	10901.5i	0.676736	+	0.736225i
$604$	−31908.0			−2.14953
$605$	−12791.3			−0.859572
$606$	81.7111	−	38869.0i	0.00547737	−	2.60552i
$607$	18793.5			1.25668			0.628339	−	0.777939i	$-0.283735\pi$
$607$	18793.5			1.25668			0.628339	+	0.777939i	$0.283735\pi$
$608$	10510.5			0.701082
$609$	2.06861	−	984.014i	0.000137643	−	0.0654750i
$610$			32332.6i			2.14608i
$611$	515.129			0.0341079
$612$	74.1478	−	17635.6i	0.00489747	−	1.16483i
$613$	9620.29			0.633866			0.316933	−	0.948448i	$-0.397347\pi$
$613$	9620.29			0.633866			0.316933	+	0.948448i	$0.397347\pi$
$614$	−25882.9			−1.70122
$615$	1.29187	−	614.529i	8.47045e−5	−	0.0402930i
$616$		−	3961.64i		−	0.259122i
$617$			19959.4i			1.30233i	0.758937	+	0.651164i	$0.225719\pi$
$617$			19959.4i			1.30233i	−0.758937	+	0.651164i	$0.774281\pi$
$618$	90.1872	−	42901.0i	0.00587032	−	2.79245i
$619$	15489.1			1.00575			0.502875	−	0.864359i	$-0.332275\pi$
$619$	15489.1			1.00575			0.502875	+	0.864359i	$0.332275\pi$
$620$		−	48456.8i		−	3.13883i
$621$	−23952.3	−	151.061i	−1.54778	−	0.00976143i
$622$	−44064.1			−2.84053
$623$	934.637			0.0601050
$624$	42946.2	+	90.2823i	2.75517	+	0.00579196i
$625$	−11280.4			−0.721944
$626$		−	27038.9i		−	1.72635i
$627$	30.8905	−	14694.3i	0.00196754	−	0.935938i
$628$	8388.60			0.533028
$629$			7077.57i			0.448650i
$630$	16.5931	−	3946.56i	0.00104934	−	0.249579i
$631$			17753.3i			1.12004i	0.828478	+	0.560021i	$0.189207\pi$
$631$			17753.3i			1.12004i	−0.828478	+	0.560021i	$0.810793\pi$
$632$			32645.5i			2.05470i
$633$	−59.3998	+	28255.8i	−0.00372975	+	1.77420i
$634$		−	1294.77i		−	0.0811071i
$635$	−44067.5			−2.75396
$636$	−54.6700	+	26005.9i	−0.00340850	+	1.62139i
$637$		−	24993.0i		−	1.55457i
$638$		−	25612.8i		−	1.58937i
$639$	59.1377	−	14065.5i	0.00366111	−	0.870771i
$640$	−25580.4			−1.57993
$641$	564.484			0.0347828			0.0173914	−	0.999849i	$-0.494464\pi$
$641$	564.484			0.0347828			0.0173914	+	0.999849i	$0.494464\pi$
$642$	−39904.6	−	83.8881i	−2.45313	−	0.00515701i
$643$	−28370.7			−1.74002			−0.870009	−	0.493036i	$-0.835887\pi$
$643$	−28370.7			−1.74002			−0.870009	+	0.493036i	$0.835887\pi$
$644$	5255.95			0.321605
$645$	24956.6	+	52.4641i	1.52351	+	0.00320275i
$646$			11477.8i			0.699051i
$647$	−19171.9			−1.16495			−0.582477	−	0.812847i	$-0.697916\pi$
$647$	−19171.9			−1.16495			−0.582477	+	0.812847i	$0.697916\pi$
$648$	−36606.6	−	307.827i	−2.21920	−	0.0186614i
$649$			39022.9i			2.36022i
$650$			57326.6i			3.45929i
$651$	3.05773	−	1454.53i	0.000184089	−	0.0875691i
$652$	−47234.2			−2.83717
$653$	21212.0			1.27120			0.635598	−	0.772020i	$-0.280753\pi$
$653$	21212.0			1.27120			0.635598	+	0.772020i	$0.280753\pi$
$654$	−23849.7	−	50.1373i	−1.42599	−	0.00299774i
$655$		−	27369.2i		−	1.63268i
$656$	797.121			0.0474426
$657$	−12163.7	−	51.1415i	−0.722298	−	0.00303686i
$658$	61.4035			0.00363793
$659$			20626.8i			1.21928i	0.792678	+	0.609641i	$0.208686\pi$
$659$			20626.8i			1.21928i	−0.792678	+	0.609641i	$0.791314\pi$
$660$	149.176	−	70961.5i	0.00879800	−	4.18511i
$661$		−	15243.9i		−	0.897002i	−0.893782	−	0.448501i	$-0.851958\pi$
$661$		−	15243.9i		−	0.897002i	0.893782	−	0.448501i	$-0.148042\pi$
$662$		−	21696.3i		−	1.27379i
$663$	−29.3427	+	13958.0i	−0.00171882	+	0.817622i
$664$			57318.5i			3.34998i
$665$			1774.33i			0.103467i
$666$	26596.2	+	111.822i	1.54742	+	0.00650605i
$667$	18770.5			1.08965
$668$		−	27295.4i		−	1.58097i
$669$	46.1561	−	21955.9i	0.00266741	−	1.26886i
$670$	−31638.3	−	34130.3i	−1.82432	−	1.96801i
$671$			17450.6i			1.00399i
$672$	1523.58	+	3.20290i	0.0874606	+	0.000183861i
$673$		−	5661.22i		−	0.324256i	−0.986770	−	0.162128i	$-0.948164\pi$
$673$		−	5661.22i		−	0.324256i	0.986770	−	0.162128i	$-0.0518357\pi$
$674$			29007.6i			1.65776i
$675$	135.669	−	21511.8i	0.00773614	−	1.22665i
$676$	−57290.6			−3.25959
$677$	−14037.5			−0.796907			−0.398453	−	0.917189i	$-0.630453\pi$
$677$	−14037.5			−0.796907			−0.398453	+	0.917189i	$0.630453\pi$
$678$	−76.3475	+	36317.7i	−0.00432465	+	2.05718i
$679$	−2277.98			−0.128750
$680$			30617.8i			1.72668i
$681$	5562.43	+	11.6934i	0.313000	+	0.000657993i
$682$		−	37859.8i		−	2.12570i
$683$	2133.21			0.119509			0.0597547	−	0.998213i	$-0.480968\pi$
$683$	2133.21			0.119509			0.0597547	+	0.998213i	$0.480968\pi$
$684$	29794.8	+	125.271i	1.66554	+	0.00700269i
$685$	−3784.46			−0.211090
$686$		−	5984.35i		−	0.333066i
$687$	9650.96	+	20.2884i	0.535964	+	0.00112671i
$688$			32371.8i			1.79384i
$689$		−	20582.7i		−	1.13808i
$690$	75282.5	+	158.260i	4.15356	+	0.00873168i
$691$	−11738.2			−0.646224			−0.323112	−	0.946361i	$-0.604729\pi$
$691$	−11738.2			−0.646224			−0.323112	+	0.946361i	$0.604729\pi$
$692$			45093.5i			2.47716i
$693$	8.95566	−	2130.04i	0.000490905	−	0.116759i
$694$	32579.1			1.78197
$695$		−	1924.64i		−	0.105044i
$696$	28687.5	+	60.3073i	1.56235	+	0.00328440i
$697$			259.073i			0.0140790i
$698$	17037.1			0.923871
$699$	−38.3378	+	18236.9i	−0.00207449	+	0.986812i
$700$			4720.42i			0.254879i
$701$	10588.3			0.570493			0.285246	−	0.958454i	$-0.407925\pi$
$701$	10588.3			0.570493			0.285246	+	0.958454i	$0.407925\pi$
$702$	52451.1	+	330.794i	2.82000	+	0.0177849i
$703$	−11957.3			−0.641507
$704$	−1543.95			−0.0826560
$705$	607.551	+	1.27720i	0.0324563	+	6.82301e-5i
$706$	29441.7			1.56948
$707$			2533.14i			0.134750i
$708$	−79125.0	−	166.338i	−4.20014	−	0.00882960i
$709$	7665.99			0.406068			0.203034	−	0.979172i	$-0.434920\pi$
$709$	7665.99			0.406068			0.203034	+	0.979172i	$0.434920\pi$
$710$			44207.7i			2.33674i
$711$	−73.7982	+	17552.4i	−0.00389262	+	0.925833i
$712$			27248.0i			1.43422i
$713$	27745.7			1.45734
$714$	−3.49765	+	1663.79i	−0.000183328	+	0.0872072i
$715$			56163.5i			2.93762i
$716$	−3204.09			−0.167238
$717$	4.30338	−	2047.07i	0.000224146	−	0.106624i
$718$		−	33431.3i		−	1.73767i
$719$		−	23062.6i		−	1.19623i	−0.801410	−	0.598115i	$-0.795917\pi$
$719$		−	23062.6i		−	1.19623i	0.801410	−	0.598115i	$-0.204083\pi$
$720$	50651.2	+	212.960i	2.62175	+	0.0110230i
$721$			2795.91i			0.144418i
$722$	15497.0			0.798805
$723$	−6.69182	+	3183.22i	−0.000344221	+	0.163742i
$724$	70770.2			3.63281
$725$			16857.9i			0.863569i
$726$	42.6000	−	20264.3i	0.00217773	−	1.03592i
$727$		−	25813.9i		−	1.31690i	−0.752626	−	0.658448i	$-0.771213\pi$
$727$		−	25813.9i		−	1.31690i	0.752626	−	0.658448i	$-0.228787\pi$
$728$	−6357.71			−0.323671
$729$	−19681.4	−	248.260i	−0.999920	−	0.0126129i
$730$	38230.2			1.93831
$731$	−10521.2			−0.532339
$732$	−35383.8	−	74.3844i	−1.78664	−	0.00375591i
$733$		−	1462.57i		−	0.0736988i	−0.999321	−	0.0368494i	$-0.988268\pi$
$733$		−	1462.57i		−	0.0736988i	0.999321	−	0.0368494i	$-0.0117322\pi$
$734$		−	49865.8i		−	2.50760i
$735$	61.9673	−	29477.1i	0.00310979	−	1.47929i
$736$			29063.0i			1.45554i
$737$	−17075.9	−	18420.9i	−0.853457	−	0.920681i
$738$	973.547	+	4.09323i	0.0485593	+	0.000204165i
$739$		−	37794.4i		−	1.88131i	−0.339362	−	0.940656i	$-0.610211\pi$
$739$		−	37794.4i		−	1.88131i	0.339362	−	0.940656i	$-0.389789\pi$
$740$	−57744.3			−2.86854
$741$	−23581.6	−	49.5736i	−1.16908	−	0.00245767i
$742$		−	2453.47i		−	0.121388i
$743$			5188.27i			0.256177i	0.991763	+	0.128088i	$0.0408841\pi$
$743$			5188.27i			0.256177i	−0.991763	+	0.128088i	$0.959116\pi$
$744$	42404.7	+	89.1438i	2.08956	+	0.00439270i
$745$			36802.9i			1.80987i
$746$			61545.6i			3.02057i
$747$	−129.574	+	30818.2i	−0.00634652	+	1.50948i
$748$			29915.9i			1.46235i
$749$	2600.63			0.126869
$750$	−26.2648	+	12493.8i	−0.00127874	+	0.608281i
$751$	−10280.6			−0.499525			−0.249762	−	0.968307i	$-0.580352\pi$
$751$	−10280.6			−0.499525			−0.249762	+	0.968307i	$0.580352\pi$
$752$			788.070i			0.0382154i
$753$	−55.4222	+	26363.7i	−0.00268220	+	1.27589i
$754$	−41103.8			−1.98530
$755$	29785.0			1.43574
$756$	4318.95	+	27.2384i	0.207776	+	0.00131039i
$757$			1243.30i			0.0596944i	0.999554	+	0.0298472i	$0.00950207\pi$
$757$			1243.30i			0.0596944i	−0.999554	+	0.0298472i	$0.990498\pi$
$758$			39535.9i			1.89447i
$759$	40631.6	+	85.4164i	1.94313	+	0.00408488i
$760$	−51727.9			−2.46891
$761$			4801.38i			0.228712i	0.993440	+	0.114356i	$0.0364805\pi$
$761$			4801.38i			0.228712i	−0.993440	+	0.114356i	$0.963520\pi$
$762$	146.761	−	69812.8i	0.00697717	−	3.31896i
$763$	1554.32			0.0737484
$764$	45011.6			2.13150
$765$	−69.2144	+	16462.2i	−0.00327118	+	0.778027i
$766$	−10081.2			−0.475523
$767$	62624.6			2.94817
$768$	82.2466	−	39123.8i	0.00386435	−	1.83823i
$769$		−	3840.08i		−	0.180074i	−0.995938	−	0.0900370i	$-0.971301\pi$
$769$		−	3840.08i		−	0.180074i	0.995938	−	0.0900370i	$-0.0286985\pi$
$770$			6694.70i			0.313325i
$771$	9690.26	+	20.3710i	0.452641	+	0.000951549i
$772$	29117.6			1.35747
$773$		−	24658.5i		−	1.14735i	−0.819081	−	0.573677i	$-0.805516\pi$
$773$		−	24658.5i		−	1.14735i	0.819081	−	0.573677i	$-0.194484\pi$
$774$	−166.230	+	39536.7i	−0.00771965	+	1.83607i
$775$			24918.7i			1.15498i
$776$		−	66411.3i		−	3.07220i
$777$	−1733.31	−	3.64379i	−0.0800286	−	0.000168237i
$778$			58979.4i			2.71788i
$779$	−437.696			−0.0201310
$780$	−113880.	−	239.401i	−5.22764	−	0.0109896i
$781$			23859.9i			1.09318i
$782$	−31737.6			−1.45132
$783$	15424.2	+	97.2759i	0.703978	+	0.00443979i
$784$	38235.6			1.74178
$785$	−7830.46			−0.356027
$786$	43359.0	+	91.1500i	1.96764	+	0.00413641i
$787$			8861.99i			0.401392i	0.979654	+	0.200696i	$0.0643204\pi$
$787$			8861.99i			0.401392i	−0.979654	+	0.200696i	$0.935680\pi$
$788$	54277.3			2.45374
$789$	−27677.0	−	58.1831i	−1.24883	−	0.00262532i
$790$		−	55167.0i		−	2.48450i
$791$		−	2366.86i		−	0.106392i
$792$	62098.3	+	261.089i	2.78607	+	0.0117139i
$793$	28005.0			1.25408
$794$	48103.7			2.15005
$795$	51.0325	−	24275.6i	0.00227665	−	1.08298i
$796$	26987.9			1.20171
$797$			39193.2i			1.74190i	0.491373	+	0.870949i	$0.336495\pi$
$797$			39193.2i			1.74190i	−0.491373	+	0.870949i	$0.663505\pi$
$798$	−2810.93	−	5.90918i	−0.124694	−	0.000262134i
$799$	−256.131			−0.0113408
$800$	−26101.7			−1.15354
$801$	−61.5966	+	14650.3i	−0.00271711	+	0.646247i
$802$	21111.6			0.929522
$803$	20633.7			0.906784
$804$	37423.9	−	34545.4i	1.64159	−	1.51533i
$805$	−4906.25			−0.214811
$806$	−60758.0			−2.65522
$807$	10557.0	+	22.1930i	0.460499	+	0.000968068i
$808$	−73850.0			−3.21539
$809$	−12194.2			−0.529947			−0.264973	−	0.964256i	$-0.585363\pi$
$809$	−12194.2			−0.529947			−0.264973	+	0.964256i	$0.585363\pi$
$810$	61860.7	+	520.190i	2.68341	+	0.0225649i
$811$			29267.5i			1.26723i	0.773649	+	0.633614i	$0.218429\pi$
$811$			29267.5i			1.26723i	−0.773649	+	0.633614i	$0.781571\pi$
$812$	−3384.59			−0.146276
$813$	892.053	+	1.87529i	0.0384817	+	8.08969e-5i
$814$	−45116.2			−1.94266
$815$	44091.5			1.89504
$816$	−21353.6	−	44.8899i	−0.916085	−	0.00192581i
$817$		−	17775.2i		−	0.761171i
$818$		−	52623.5i		−	2.24931i
$819$	−3418.33	−	14.3722i	−0.145844	−	0.000613192i
$820$	−2113.72			−0.0900173
$821$		−	31427.6i		−	1.33597i	−0.744175	−	0.667985i	$-0.767157\pi$
$821$		−	31427.6i		−	1.33597i	0.744175	−	0.667985i	$-0.232843\pi$
$822$	12.6037	−	5995.44i	0.000534799	−	0.254398i
$823$	14699.4			0.622587			0.311293	−	0.950314i	$-0.399238\pi$
$823$	14699.4			0.622587			0.311293	+	0.950314i	$0.399238\pi$
$824$	−81510.6			−3.44607
$825$	−76.7132	+	36491.6i	−0.00323735	+	1.53997i
$826$	7464.86			0.314450
$827$			32680.8i			1.37415i	0.726586	+	0.687076i	$0.241106\pi$
$827$			32680.8i			1.37415i	−0.726586	+	0.687076i	$0.758894\pi$
$828$	−346.390	+	82386.5i	−0.0145385	+	3.45788i
$829$	−28063.4			−1.17573			−0.587866	−	0.808958i	$-0.700032\pi$
$829$	−28063.4			−1.17573			−0.587866	+	0.808958i	$0.700032\pi$
$830$		−	96861.3i		−	4.05073i
$831$	36.2848	−	17260.3i	0.00151469	−	0.720519i
$832$			2477.75i			0.103246i
$833$			12427.0i			0.516889i
$834$	3049.07	+	6.40980i	0.126595	+	0.000266131i
$835$			25479.3i			1.05598i
$836$	−50542.1			−2.09095
$837$	22799.4	+	143.789i	0.941531	+	0.00593798i
$838$			37094.6i			1.52913i
$839$			7106.59i			0.292428i	0.989253	+	0.146214i	$0.0467088\pi$
$839$			7106.59i			0.292428i	−0.989253	+	0.146214i	$0.953291\pi$
$840$	−7498.37	−	15.7632i	−0.307998	−	0.000647478i
$841$	12301.7			0.504395
$842$	13436.2			0.549933
$843$	−9.28238	+	4415.52i	−0.000379243	+	0.180402i
$844$	97188.0			3.96368
$845$	53478.7			2.17719
$846$	−4.04675	+	962.493i	−0.000164457	+	0.0391149i
$847$			1320.65i			0.0535750i
$848$	31488.5			1.27514
$849$	−29.5916	+	14076.4i	−0.00119621	+	0.569023i
$850$		−	28503.8i		−	1.15020i
$851$		−	33063.6i		−	1.33185i
$852$	−48379.6	−	101.704i	−1.94537	−	0.00408959i
$853$	−100.524			−0.00403501			−0.00201750	−	0.999998i	$-0.500642\pi$
$853$	−100.524			−0.00403501			−0.00201750	+	0.999998i	$0.500642\pi$
$854$	3338.21			0.133760
$855$	−27812.4	−	116.936i	−1.11247	−	0.00467733i
$856$			75817.6i			3.02733i
$857$	1971.88			0.0785976			0.0392988	−	0.999228i	$-0.487488\pi$
$857$	1971.88			0.0785976			0.0392988	+	0.999228i	$0.487488\pi$
$858$	−88975.6	−	187.046i	−3.54030	−	0.00744247i
$859$	−42816.4			−1.70067			−0.850337	−	0.526239i	$-0.823602\pi$
$859$	−42816.4			−1.70067			−0.850337	+	0.526239i	$0.823602\pi$
$860$		−	85840.0i		−	3.40363i
$861$	−63.4475	−	0.133380i	−0.00251136	−	5.27943e-6i
$862$		−	14386.3i		−	0.568446i
$863$			30031.5i			1.18457i	0.805729	+	0.592285i	$0.201774\pi$
$863$			30031.5i			1.18457i	−0.805729	+	0.592285i	$0.798226\pi$
$864$	−150.616	+	23881.8i	−0.00593062	+	0.940364i
$865$		−	42093.2i		−	1.65458i
$866$			47400.7i			1.85998i
$867$	−39.0770	+	18588.5i	−0.00153071	+	0.728141i
$868$	−5002.96			−0.195636
$869$		−	29774.9i		−	1.16231i
$870$	−48478.4	−	101.912i	−1.88916	−	0.00397143i
$871$	−29562.1	+	27403.6i	−1.15003	+	1.06606i
$872$			45313.8i			1.75977i
$873$	150.129	−	35707.1i	0.00582027	−	1.38431i
$874$		−	53619.7i		−	2.07519i
$875$		−	814.238i		−	0.0314586i
$876$	−87.9525	+	41838.0i	−0.00339228	+	1.61367i
$877$	26292.8			1.01237			0.506183	−	0.862426i	$-0.331056\pi$
$877$	26292.8			1.01237			0.506183	+	0.862426i	$0.331056\pi$
$878$	−9369.28			−0.360134
$879$	−24745.2	−	52.0198i	−0.949529	−	0.00199612i
$880$	−85921.7			−3.29138
$881$		−	14360.3i		−	0.549159i	−0.961564	−	0.274580i	$-0.911461\pi$
$881$		−	14360.3i		−	0.549159i	0.961564	−	0.274580i	$-0.0885387\pi$
$882$	46698.2	+	196.340i	1.78278	+	0.00749560i
$883$		−	6188.65i		−	0.235860i	−0.993022	−	0.117930i	$-0.962374\pi$
$883$		−	6188.65i		−	0.235860i	0.993022	−	0.117930i	$-0.0376259\pi$
$884$	48009.5			1.82662
$885$	73860.3	+	155.270i	2.80541	+	0.00589758i
$886$	−269.263			−0.0102100
$887$			11748.0i			0.444711i	0.974966	+	0.222355i	$0.0713745\pi$
$887$			11748.0i			0.444711i	−0.974966	+	0.222355i	$0.928625\pi$
$888$	106.230	−	50532.2i	0.00401445	−	1.90963i
$889$			4549.78i			0.171648i
$890$		−	46045.8i		−	1.73422i
$891$	33387.6	+	280.758i	1.25536	+	0.0105564i
$892$	−75519.0			−2.83471
$893$		−	432.726i		−	0.0162157i
$894$	−58304.1	−	122.568i	−2.18119	−	0.00458532i
$895$	2990.91			0.111704
$896$			2641.06i			0.0984730i
$897$	137.078	−	65206.3i	0.00510244	−	2.42717i
$898$		−	39751.0i		−	1.47718i
$899$	−17867.0			−0.662844
$900$	−73992.0	−	311.096i	−2.74045	−	0.0115221i
$901$			10234.1i			0.378410i
$902$	−1651.47			−0.0609621
$903$	5.41670	−	2576.66i	0.000199619	−	0.0949567i
$904$	69002.5			2.53870
$905$	−66061.5			−2.42647
$906$	−99.1953	+	47186.1i	−0.00363746	+	1.73030i
$907$	−7234.70			−0.264856			−0.132428	−	0.991193i	$-0.542277\pi$
$907$	−7234.70			−0.264856			−0.132428	+	0.991193i	$0.542277\pi$
$908$		−	19132.4i		−	0.699263i
$909$	−39706.7	−	166.945i	−1.44883	−	0.00609154i
$910$	10743.8			0.391376
$911$			39342.8i			1.43083i	0.698700	+	0.715414i	$0.253762\pi$
$911$			39342.8i			1.43083i	−0.698700	+	0.715414i	$0.746238\pi$
$912$	75.8401	−	36076.3i	0.00275364	−	1.30987i
$913$		−	52278.2i		−	1.89502i
$914$	−22896.8			−0.828620
$915$	33029.5	+	69.4352i	1.19336	+	0.00250870i
$916$		−	33195.2i		−	1.19738i
$917$	−2825.76			−0.101761
$918$	−26079.6	−	164.476i	−0.937640	−	0.00591343i
$919$			19759.2i			0.709246i	0.935009	+	0.354623i	$0.115391\pi$
$919$			19759.2i			0.709246i	−0.935009	+	0.354623i	$0.884609\pi$
$920$		−	143034.i		−	5.12577i
$921$	−55.5843	+	26440.8i	−0.00198867	+	0.945988i
$922$		−	37973.9i		−	1.35640i
$923$	38290.7			1.36550
$924$	−7326.47	−	15.4018i	−0.260848	−	0.000548358i
$925$	29694.7			1.05552
$926$			42521.3i			1.50900i
$927$	−43825.5	−	184.262i	−1.55277	−	0.00652855i
$928$		−	18715.2i		−	0.662022i
$929$	−23366.0			−0.825204			−0.412602	−	0.910911i	$-0.635380\pi$
$929$	−23366.0			−0.825204			−0.412602	+	0.910911i	$0.635380\pi$
$930$	−71658.8	−	150.642i	−2.52665	−	0.00531156i
$931$	−20995.0			−0.739079
$932$	62727.0			2.20461
$933$	−94.6288	+	45013.8i	−0.00332048	+	1.57951i
$934$			24127.9i			0.845278i
$935$		−	27925.4i		−	0.976748i
$936$	419.000	−	99656.3i	0.0146319	−	3.48009i
$937$		−	15861.3i		−	0.553005i	−0.961013	−	0.276502i	$-0.910825\pi$
$937$		−	15861.3i		−	0.553005i	0.961013	−	0.276502i	$-0.0891754\pi$
$938$	−3523.81	+	3266.52i	−0.122661	+	0.113705i
$939$	−27621.8	−	58.0669i	−0.959960	−	0.00201804i
$940$		−	2089.72i		−	0.0725096i
$941$	25765.1			0.892579			0.446290	−	0.894889i	$-0.352745\pi$
$941$	25765.1			0.892579			0.446290	+	0.894889i	$0.352745\pi$
$942$	26.0784	−	12405.2i	0.000901997	−	0.429070i
$943$		−	1210.29i		−	0.0417946i
$944$			95806.1i			3.30320i
$945$	−4031.59	−	25.4261i	−0.138780	−	0.000875250i
$946$		−	67067.6i		−	2.30503i
$947$		−	5228.86i		−	0.179425i	−0.995968	−	0.0897123i	$-0.971405\pi$
$947$		−	5228.86i		−	0.179425i	0.995968	−	0.0897123i	$-0.0285947\pi$
$948$	60373.1	+	126.917i	2.06838	+	0.00434819i
$949$		−	33113.3i		−	1.13267i
$950$	48156.3			1.64463
$951$	−1322.68	−	2.78056i	−0.0451007	−	9.48115e-5i
$952$	3161.16			0.107620
$953$			742.004i			0.0252213i	0.999920	+	0.0126106i	$0.00401420\pi$
$953$			742.004i			0.0252213i	−0.999920	+	0.0126106i	$0.995986\pi$
$954$	38457.8	+	161.694i	1.30516	+	0.00548746i
$955$	−42016.7			−1.42370
$956$	−7041.04			−0.238204
$957$	−26164.9	−	55.0042i	−0.883793	−	0.00185792i
$958$		−	29336.2i		−	0.989362i
$959$			390.730i			0.0131567i
$960$	−6.14330	+	2922.30i	−0.000206536	+	0.0982466i
$961$	3380.78			0.113483
$962$			72403.1i			2.42658i
$963$	−171.393	+	40764.6i	−0.00573526	+	1.36409i
$964$	10948.9			0.365811
$965$	−27180.3			−0.906699
$966$	16.3397	−	7772.60i	0.000544224	−	0.258881i
$967$	56532.1			1.87999			0.939994	−	0.341190i	$-0.110830\pi$
$967$	56532.1			1.87999			0.939994	+	0.341190i	$0.110830\pi$
$968$	−38501.6			−1.27840
$969$	11725.2	+	24.6488i	0.388717	+	0.000817167i
$970$			112227.i			3.71484i
$971$			6865.73i			0.226912i	0.993543	+	0.113456i	$0.0361921\pi$
$971$			6865.73i			0.226912i	−0.993543	+	0.113456i	$0.963808\pi$
$972$	−711.596	+	67697.3i	−0.0234820	+	2.23394i
$973$	−198.711			−0.00654716
$974$		−	7950.13i		−	0.261539i
$975$	58562.3	+	123.111i	1.92358	+	0.00404379i
$976$			42843.5i			1.40511i
$977$		−	50753.7i		−	1.66198i	−0.556286	−	0.830991i	$-0.687774\pi$
$977$		−	50753.7i		−	1.66198i	0.556286	−	0.830991i	$-0.312226\pi$
$978$	−146.841	+	69850.8i	−0.00480109	+	2.28383i
$979$		−	24851.9i		−	0.811309i
$980$	−101389.			−3.30484
$981$	−102.436	+	24363.7i	−0.00333387	+	0.792939i
$982$			29741.8i			0.966496i
$983$	4753.73			0.154242			0.0771212	−	0.997022i	$-0.475427\pi$
$983$	4753.73			0.154242			0.0771212	+	0.997022i	$0.475427\pi$
$984$	3.88851	−	1849.72i	0.000125977	−	0.0599257i
$985$	−50665.9			−1.63893
$986$	20437.5			0.660104
$987$	0.131866	−	62.7271i	4.25262e−6	−	0.00202292i
$988$			81110.7i			2.61182i
$989$	49150.9			1.58029
$990$	−104939.	−	441.209i	−3.36886	−	0.0141642i
$991$			58722.0i			1.88231i	0.337978	+	0.941154i	$0.390257\pi$
$991$			58722.0i			1.88231i	−0.337978	+	0.941154i	$0.609743\pi$
$992$		−	27664.1i		−	0.885418i
$993$	−22164.0	−	46.5935i	−0.708311	−	0.00148902i
$994$	4564.26			0.145643
$995$	−25192.3			−0.802662
$996$	106002.	+	222.839i	3.37229	+	0.00708928i
$997$	49256.5			1.56466			0.782332	−	0.622861i	$-0.214030\pi$
$997$	49256.5			1.56466			0.782332	+	0.622861i	$0.214030\pi$
$998$			20251.4i			0.642333i
$999$	171.349	−	27169.2i	0.00542666	−	0.860457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.d.b.200.4	yes	64
3.2	odd	2	inner	201.4.d.b.200.62	yes	64
67.66	odd	2	inner	201.4.d.b.200.61	yes	64
201.200	even	2	inner	201.4.d.b.200.3	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.d.b.200.3	✓	64	201.200	even	2	inner
201.4.d.b.200.4	yes	64	1.1	even	1	trivial
201.4.d.b.200.61	yes	64	67.66	odd	2	inner
201.4.d.b.200.62	yes	64	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.08650 q^{2} +(-0.0109234 + 5.19614i) q^{3} +17.8725 q^{4} -16.6834 q^{5} +(0.0555619 - 26.4302i) q^{6} +1.72249i q^{7} -50.2166 q^{8} +(-26.9998 - 0.113519i) q^{9} +O(q^{10})\)	\(q-5.08650 q^{2} +(-0.0109234 + 5.19614i) q^{3} +17.8725 q^{4} -16.6834 q^{5} +(0.0555619 - 26.4302i) q^{6} +1.72249i q^{7} -50.2166 q^{8} +(-26.9998 - 0.113519i) q^{9} +84.8599 q^{10} +45.8008 q^{11} +(-0.195229 + 92.8681i) q^{12} -73.5018i q^{13} -8.76143i q^{14} +(0.182239 - 86.6891i) q^{15} +112.447 q^{16} +36.5463i q^{17} +(137.334 + 0.577415i) q^{18} -61.7440 q^{19} -298.173 q^{20} +(-8.95028 - 0.0188154i) q^{21} -232.966 q^{22} -170.730i q^{23} +(0.548536 - 260.932i) q^{24} +153.334 q^{25} +373.867i q^{26} +(0.884791 - 140.293i) q^{27} +30.7851i q^{28} +109.942i q^{29} +(-0.926960 + 440.944i) q^{30} +162.512i q^{31} -170.228 q^{32} +(-0.500301 + 237.987i) q^{33} -185.893i q^{34} -28.7368i q^{35} +(-482.554 - 2.02887i) q^{36} +193.660 q^{37} +314.061 q^{38} +(381.926 + 0.802890i) q^{39} +837.781 q^{40} +7.08888 q^{41} +(45.5256 + 0.0957047i) q^{42} +287.886i q^{43} +818.575 q^{44} +(450.447 + 1.89388i) q^{45} +868.420i q^{46} +7.00839i q^{47} +(-1.22830 + 584.288i) q^{48} +340.033 q^{49} -779.935 q^{50} +(-189.900 - 0.399211i) q^{51} -1313.66i q^{52} +280.031 q^{53} +(-4.50049 + 713.602i) q^{54} -764.111 q^{55} -86.4973i q^{56} +(0.674455 - 320.830i) q^{57} -559.222i q^{58} +852.014i q^{59} +(3.25707 - 1549.35i) q^{60} +381.012i q^{61} -826.619i q^{62} +(0.195535 - 46.5067i) q^{63} -33.7101 q^{64} +1226.26i q^{65} +(2.54478 - 1210.52i) q^{66} +(-372.829 - 402.196i) q^{67} +653.175i q^{68} +(887.138 + 1.86496i) q^{69} +146.170i q^{70} +520.949i q^{71} +(1355.84 + 5.70054i) q^{72} +450.510 q^{73} -985.053 q^{74} +(-1.67493 + 796.747i) q^{75} -1103.52 q^{76} +78.8912i q^{77} +(-1942.67 - 4.08390i) q^{78} -650.095i q^{79} -1875.99 q^{80} +(728.974 + 6.12998i) q^{81} -36.0576 q^{82} -1141.43i q^{83} +(-159.964 - 0.336279i) q^{84} -609.715i q^{85} -1464.33i q^{86} +(-571.276 - 1.20094i) q^{87} -2299.96 q^{88} -542.610i q^{89} +(-2291.20 - 9.63323i) q^{90} +126.606 q^{91} -3051.38i q^{92} +(-844.436 - 1.77519i) q^{93} -35.6482i q^{94} +1030.10 q^{95} +(1.85946 - 884.526i) q^{96} +1322.50i q^{97} -1729.58 q^{98} +(-1236.61 - 5.19927i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 268 q^{4} - 46 q^{6} + 22 q^{9}+O(q^{10}) \) 64 * q + 268 * q^4 - 46 * q^6 + 22 * q^9	\( 64 q + 268 q^{4} - 46 q^{6} + 22 q^{9} - 36 q^{10} + 20 q^{15} + 556 q^{16} + 128 q^{19} + 96 q^{22} - 904 q^{24} + 2080 q^{25} - 236 q^{33} - 1574 q^{36} + 1004 q^{37} - 176 q^{39} - 648 q^{40} - 1220 q^{49} + 2188 q^{54} - 1344 q^{55} + 550 q^{60} + 4336 q^{64} - 3512 q^{67} + 3968 q^{73} - 3316 q^{76} - 1170 q^{81} + 4020 q^{82} - 9270 q^{84} + 2436 q^{88} + 746 q^{90} - 3408 q^{91} - 1412 q^{93} - 7032 q^{96}+O(q^{100}) \) 64 * q + 268 * q^4 - 46 * q^6 + 22 * q^9 - 36 * q^10 + 20 * q^15 + 556 * q^16 + 128 * q^19 + 96 * q^22 - 904 * q^24 + 2080 * q^25 - 236 * q^33 - 1574 * q^36 + 1004 * q^37 - 176 * q^39 - 648 * q^40 - 1220 * q^49 + 2188 * q^54 - 1344 * q^55 + 550 * q^60 + 4336 * q^64 - 3512 * q^67 + 3968 * q^73 - 3316 * q^76 - 1170 * q^81 + 4020 * q^82 - 9270 * q^84 + 2436 * q^88 + 746 * q^90 - 3408 * q^91 - 1412 * q^93 - 7032 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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