LMFDB - Embedded newform 35.5.i.a.24.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(19,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("35.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.i (of order $6$, degree $2$, 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:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			24.2
Character	$\chi$	$=$	35.24
Dual form			35.5.i.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.18283 + 2.99231i) q^{2} +(1.73039 - 2.99712i) q^{3} +(9.90784 - 17.1609i) q^{4} +(24.7118 - 3.78477i) q^{5} +20.7114i q^{6} +(-18.5361 + 45.3587i) q^{7} +22.8354i q^{8} +(34.5115 + 59.7757i) q^{9} +O(q^{10})$	\(q+(-5.18283 + 2.99231i) q^{2} +(1.73039 - 2.99712i) q^{3} +(9.90784 - 17.1609i) q^{4} +(24.7118 - 3.78477i) q^{5} +20.7114i q^{6} +(-18.5361 + 45.3587i) q^{7} +22.8354i q^{8} +(34.5115 + 59.7757i) q^{9} +(-116.752 + 93.5614i) q^{10} +(-90.7471 + 157.179i) q^{11} +(-34.2888 - 59.3899i) q^{12} +258.347 q^{13} +(-39.6579 - 290.552i) q^{14} +(31.4176 - 80.6134i) q^{15} +(90.1948 + 156.222i) q^{16} +(21.6502 - 37.4993i) q^{17} +(-357.735 - 206.538i) q^{18} +(161.952 - 93.5032i) q^{19} +(179.891 - 461.576i) q^{20} +(103.871 + 134.043i) q^{21} -1086.17i q^{22} +(-374.418 + 216.170i) q^{23} +(68.4405 + 39.5141i) q^{24} +(596.351 - 187.057i) q^{25} +(-1338.97 + 773.053i) q^{26} +519.196 q^{27} +(594.743 + 767.503i) q^{28} -647.009 q^{29} +(78.3880 + 511.817i) q^{30} +(540.761 + 312.209i) q^{31} +(-1251.35 - 722.465i) q^{32} +(314.055 + 543.960i) q^{33} +259.137i q^{34} +(-286.389 + 1191.05i) q^{35} +1367.74 q^{36} +(-282.150 + 162.899i) q^{37} +(-559.581 + 969.223i) q^{38} +(447.039 - 774.295i) q^{39} +(86.4269 + 564.306i) q^{40} -2880.05i q^{41} +(-939.443 - 383.909i) q^{42} -1291.07i q^{43} +(1798.22 + 3114.60i) q^{44} +(1079.08 + 1346.55i) q^{45} +(1293.70 - 2240.75i) q^{46} +(-177.475 - 307.395i) q^{47} +624.287 q^{48} +(-1713.83 - 1681.55i) q^{49} +(-2531.05 + 2753.95i) q^{50} +(-74.9265 - 129.777i) q^{51} +(2559.66 - 4433.46i) q^{52} +(796.722 + 459.987i) q^{53} +(-2690.91 + 1553.59i) q^{54} +(-1647.64 + 4227.63i) q^{55} +(-1035.79 - 423.280i) q^{56} -647.187i q^{57} +(3353.34 - 1936.05i) q^{58} +(-1859.01 - 1073.30i) q^{59} +(-1072.12 - 1337.86i) q^{60} +(-2374.90 + 1371.15i) q^{61} -3736.90 q^{62} +(-3351.06 + 457.390i) q^{63} +5761.13 q^{64} +(6384.22 - 977.782i) q^{65} +(-3255.39 - 1879.50i) q^{66} +(3446.74 + 1989.97i) q^{67} +(-429.014 - 743.074i) q^{68} +1496.23i q^{69} +(-2079.69 - 7029.99i) q^{70} +7721.08 q^{71} +(-1365.00 + 788.086i) q^{72} +(-931.137 + 1612.78i) q^{73} +(974.891 - 1688.56i) q^{74} +(471.285 - 2111.02i) q^{75} -3705.66i q^{76} +(-5447.32 - 7029.65i) q^{77} +5350.72i q^{78} +(-1994.52 - 3454.61i) q^{79} +(2820.14 + 3519.17i) q^{80} +(-1897.02 + 3285.74i) q^{81} +(8618.00 + 14926.8i) q^{82} -6817.31 q^{83} +(3329.43 - 454.439i) q^{84} +(393.091 - 1008.62i) q^{85} +(3863.29 + 6691.42i) q^{86} +(-1119.58 + 1939.16i) q^{87} +(-3589.24 - 2072.25i) q^{88} +(-1331.99 + 769.026i) q^{89} +(-9621.99 - 3750.00i) q^{90} +(-4788.73 + 11718.3i) q^{91} +8567.13i q^{92} +(1871.45 - 1080.48i) q^{93} +(1839.64 + 1062.12i) q^{94} +(3648.25 - 2923.59i) q^{95} +(-4330.63 + 2500.29i) q^{96} +12991.6 q^{97} +(13914.2 + 3586.88i) q^{98} -12527.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9}+O(q^{10}) $ 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9	$ 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9} + 390 q^{10} + 34 q^{11} - 258 q^{14} + 60 q^{15} - 206 q^{16} + 366 q^{19} - 1116 q^{21} - 288 q^{24} + 40 q^{25} + 474 q^{26} + 856 q^{29} - 1620 q^{30} - 5520 q^{31} - 2620 q^{35} + 11892 q^{36} + 1656 q^{39} + 6510 q^{40} - 1082 q^{44} + 7920 q^{45} - 5442 q^{46} + 8356 q^{49} - 15960 q^{50} - 2976 q^{51} + 4392 q^{54} + 11640 q^{56} - 13920 q^{59} - 5700 q^{60} - 24960 q^{61} - 45596 q^{64} + 5290 q^{65} + 10332 q^{66} - 26400 q^{70} + 38272 q^{71} + 31806 q^{74} + 41310 q^{75} + 22028 q^{79} + 48000 q^{80} - 29238 q^{81} + 62784 q^{84} - 33820 q^{85} - 21180 q^{86} - 12516 q^{89} + 4448 q^{91} - 89418 q^{94} - 28890 q^{95} - 27900 q^{96} - 3108 q^{99}+O(q^{100}) $ 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9 + 390 * q^10 + 34 * q^11 - 258 * q^14 + 60 * q^15 - 206 * q^16 + 366 * q^19 - 1116 * q^21 - 288 * q^24 + 40 * q^25 + 474 * q^26 + 856 * q^29 - 1620 * q^30 - 5520 * q^31 - 2620 * q^35 + 11892 * q^36 + 1656 * q^39 + 6510 * q^40 - 1082 * q^44 + 7920 * q^45 - 5442 * q^46 + 8356 * q^49 - 15960 * q^50 - 2976 * q^51 + 4392 * q^54 + 11640 * q^56 - 13920 * q^59 - 5700 * q^60 - 24960 * q^61 - 45596 * q^64 + 5290 * q^65 + 10332 * q^66 - 26400 * q^70 + 38272 * q^71 + 31806 * q^74 + 41310 * q^75 + 22028 * q^79 + 48000 * q^80 - 29238 * q^81 + 62784 * q^84 - 33820 * q^85 - 21180 * q^86 - 12516 * q^89 + 4448 * q^91 - 89418 * q^94 - 28890 * q^95 - 27900 * q^96 - 3108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−5.18283	+	2.99231i	−1.29571	+	0.748078i	−0.979660	−	0.200665i	$-0.935690\pi$
$2$	−5.18283	+	2.99231i	−1.29571	+	0.748078i	−0.316049	+	0.948743i	$0.602356\pi$
$3$	1.73039	−	2.99712i	0.192265	−	0.333013i	−0.753735	−	0.657178i	$-0.771750\pi$
$3$	1.73039	−	2.99712i	0.192265	−	0.333013i	0.946001	+	0.324165i	$0.105083\pi$
$4$	9.90784	−	17.1609i	0.619240	−	1.07256i
$5$	24.7118	−	3.78477i	0.988474	−	0.151391i
$5$	24.7118	−	3.78477i	0.988474	−	0.151391i
$6$			20.7114i			0.575317i
$7$	−18.5361	+	45.3587i	−0.378288	+	0.925688i
$7$	−18.5361	+	45.3587i	−0.378288	+	0.925688i
$8$			22.8354i			0.356804i
$9$	34.5115	+	59.7757i	0.426068	+	0.737972i
$10$	−116.752	+	93.5614i	−1.16752	+	0.935614i
$11$	−90.7471	+	157.179i	−0.749976	+	1.29900i	0.197857	+	0.980231i	$0.436602\pi$
$11$	−90.7471	+	157.179i	−0.749976	+	1.29900i	−0.947833	+	0.318766i	$0.896732\pi$
$12$	−34.2888	−	59.3899i	−0.238117	−	0.412430i
$13$	258.347			1.52868			0.764339	−	0.644815i	$-0.223066\pi$
$13$	258.347			1.52868			0.764339	+	0.644815i	$0.223066\pi$
$14$	−39.6579	−	290.552i	−0.202336	−	1.48241i
$15$	31.4176	−	80.6134i	0.139634	−	0.358282i
$16$	90.1948	+	156.222i	0.352323	+	0.610242i
$17$	21.6502	−	37.4993i	0.0749143	−	0.129755i	−0.826135	−	0.563473i	$-0.809465\pi$
$17$	21.6502	−	37.4993i	0.0749143	−	0.129755i	0.901049	+	0.433717i	$0.142798\pi$
$18$	−357.735	−	206.538i	−1.10412	−	0.637464i
$19$	161.952	−	93.5032i	0.448621	−	0.259012i	−0.258626	−	0.965977i	$-0.583270\pi$
$19$	161.952	−	93.5032i	0.448621	−	0.259012i	0.707248	+	0.706966i	$0.249937\pi$
$20$	179.891	−	461.576i	0.449728	−	1.15394i
$21$	103.871	+	134.043i	0.235535	+	0.303952i
$22$		−	1086.17i		−	2.24416i
$23$	−374.418	+	216.170i	−0.707785	+	0.408640i	−0.810240	−	0.586098i	$-0.800663\pi$
$23$	−374.418	+	216.170i	−0.707785	+	0.408640i	0.102455	+	0.994738i	$0.467330\pi$
$24$	68.4405	+	39.5141i	0.118820	+	0.0686009i
$25$	596.351	−	187.057i	0.954162	−	0.299292i
$26$	−1338.97	+	773.053i	−1.98072	+	1.14357i
$27$	519.196			0.712203
$28$	594.743	+	767.503i	0.758601	+	0.978958i
$29$	−647.009			−0.769333			−0.384666	−	0.923056i	$-0.625684\pi$
$29$	−647.009			−0.769333			−0.384666	+	0.923056i	$0.625684\pi$
$30$	78.3880	+	511.817i	0.0870977	+	0.568686i
$31$	540.761	+	312.209i	0.562707	+	0.324879i	0.754231	−	0.656609i	$-0.228010\pi$
$31$	540.761	+	312.209i	0.562707	+	0.324879i	−0.191524	+	0.981488i	$0.561343\pi$
$32$	−1251.35	−	722.465i	−1.22202	−	0.705532i
$33$	314.055	+	543.960i	0.288389	+	0.499504i
$34$			259.137i			0.224167i
$35$	−286.389	+	1191.05i	−0.233787	+	0.972288i
$36$	1367.74			1.05535
$37$	−282.150	+	162.899i	−0.206099	+	0.118992i	−0.599497	−	0.800377i	$-0.704633\pi$
$37$	−282.150	+	162.899i	−0.206099	+	0.118992i	0.393398	+	0.919368i	$0.371299\pi$
$38$	−559.581	+	969.223i	−0.387522	+	0.671207i
$39$	447.039	−	774.295i	0.293911	−	0.509070i
$40$	86.4269	+	564.306i	0.0540168	+	0.352691i
$41$		−	2880.05i		−	1.71330i	−0.515901	−	0.856648i	$-0.672543\pi$
$41$		−	2880.05i		−	1.71330i	0.515901	−	0.856648i	$-0.327457\pi$
$42$	−939.443	−	383.909i	−0.532564	−	0.217635i
$43$		−	1291.07i		−	0.698255i	−0.937075	−	0.349127i	$-0.886478\pi$
$43$		−	1291.07i		−	0.698255i	0.937075	−	0.349127i	$-0.113522\pi$
$44$	1798.22	+	3114.60i	0.928831	+	1.60878i
$45$	1079.08	+	1346.55i	0.532880	+	0.664963i
$46$	1293.70	−	2240.75i	0.611389	−	1.05896i
$47$	−177.475	−	307.395i	−0.0803416	−	0.139156i	0.823055	−	0.567962i	$-0.192268\pi$
$47$	−177.475	−	307.395i	−0.0803416	−	0.139156i	−0.903397	+	0.428806i	$0.858934\pi$
$48$	624.287			0.270958
$49$	−1713.83	−	1681.55i	−0.713797	−	0.700353i
$50$	−2531.05	+	2753.95i	−1.01242	+	1.10158i
$51$	−74.9265	−	129.777i	−0.0288068	−	0.0498949i
$52$	2559.66	−	4433.46i	0.946619	−	1.63959i
$53$	796.722	+	459.987i	0.283632	+	0.163755i	0.635066	−	0.772458i	$-0.280973\pi$
$53$	796.722	+	459.987i	0.283632	+	0.163755i	−0.351435	+	0.936212i	$0.614306\pi$
$54$	−2690.91	+	1553.59i	−0.922807	+	0.532783i
$55$	−1647.64	+	4227.63i	−0.544676	+	1.39756i
$56$	−1035.79	−	423.280i	−0.330289	−	0.134974i
$57$		−	647.187i		−	0.199196i
$58$	3353.34	−	1936.05i	0.996831	−	0.575521i
$59$	−1859.01	−	1073.30i	−0.534045	−	0.308331i	0.208617	−	0.977997i	$-0.433104\pi$
$59$	−1859.01	−	1073.30i	−0.534045	−	0.308331i	−0.742662	+	0.669666i	$0.766437\pi$
$60$	−1072.12	−	1337.86i	−0.297810	−	0.371628i
$61$	−2374.90	+	1371.15i	−0.638242	+	0.368489i	−0.783937	−	0.620840i	$-0.786791\pi$
$61$	−2374.90	+	1371.15i	−0.638242	+	0.368489i	0.145695	+	0.989330i	$0.453458\pi$
$62$	−3736.90			−0.972139
$63$	−3351.06	+	457.390i	−0.844308	+	0.115241i
$64$	5761.13			1.40652
$65$	6384.22	−	977.782i	1.51106	−	0.231428i
$66$	−3255.39	−	1879.50i	−0.747335	−	0.431474i
$67$	3446.74	+	1989.97i	0.767818	+	0.443300i	0.832096	−	0.554632i	$-0.187141\pi$
$67$	3446.74	+	1989.97i	0.767818	+	0.443300i	−0.0642776	+	0.997932i	$0.520474\pi$
$68$	−429.014	−	743.074i	−0.0927799	−	0.160699i
$69$			1496.23i			0.314269i
$70$	−2079.69	−	7029.99i	−0.424427	−	1.43469i
$71$	7721.08			1.53166			0.765829	−	0.643045i	$-0.222329\pi$
$71$	7721.08			1.53166			0.765829	+	0.643045i	$0.222329\pi$
$72$	−1365.00	+	788.086i	−0.263311	+	0.152023i
$73$	−931.137	+	1612.78i	−0.174730	+	0.302642i	−0.940068	−	0.340987i	$-0.889239\pi$
$73$	−931.137	+	1612.78i	−0.174730	+	0.302642i	0.765338	+	0.643629i	$0.222572\pi$
$74$	974.891	−	1688.56i	0.178030	−	0.308357i
$75$	471.285	−	2111.02i	0.0837840	−	0.375292i
$76$		−	3705.66i		−	0.641562i
$77$	−5447.32	−	7029.65i	−0.918759	−	1.18564i
$78$			5350.72i			0.879474i
$79$	−1994.52	−	3454.61i	−0.319583	−	0.553535i	0.660818	−	0.750546i	$-0.270210\pi$
$79$	−1994.52	−	3454.61i	−0.319583	−	0.553535i	−0.980401	+	0.197012i	$0.936876\pi$
$80$	2820.14	+	3519.17i	0.440648	+	0.549870i
$81$	−1897.02	+	3285.74i	−0.289136	+	0.500799i
$82$	8618.00	+	14926.8i	1.28168	+	2.21993i
$83$	−6817.31			−0.989594			−0.494797	−	0.869009i	$-0.664758\pi$
$83$	−6817.31			−0.989594			−0.494797	+	0.869009i	$0.664758\pi$
$84$	3329.43	−	454.439i	0.471858	−	0.0644046i
$85$	393.091	−	1008.62i	0.0544070	−	0.139601i
$86$	3863.29	+	6691.42i	0.522349	+	0.904734i
$87$	−1119.58	+	1939.16i	−0.147916	+	0.256198i
$88$	−3589.24	−	2072.25i	−0.463487	−	0.267594i
$89$	−1331.99	+	769.026i	−0.168160	+	0.0970870i	−0.581718	−	0.813391i	$-0.697619\pi$
$89$	−1331.99	+	769.026i	−0.168160	+	0.0970870i	0.413558	+	0.910478i	$0.364286\pi$
$90$	−9621.99	−	3750.00i	−1.18790	−	0.462963i
$91$	−4788.73	+	11718.3i	−0.578280	+	1.41508i
$92$			8567.13i			1.01218i
$93$	1871.45	−	1080.48i	0.216378	−	0.124926i
$94$	1839.64	+	1062.12i	0.208198	+	0.120203i
$95$	3648.25	−	2923.59i	0.404239	−	0.323944i
$96$	−4330.63	+	2500.29i	−0.469903	+	0.271299i
$97$	12991.6			1.38076			0.690381	−	0.723446i	$-0.257443\pi$
$97$	12991.6			1.38076			0.690381	+	0.723446i	$0.257443\pi$
$98$	13914.2	+	3586.88i	1.44879	+	0.373477i
$99$	−12527.3			−1.27816
$100$	2698.48	−	12087.2i	0.269848	−	1.20872i
$101$	3671.74	+	2119.88i	0.359940	+	0.207811i	0.669054	−	0.743214i	$-0.266699\pi$
$101$	3671.74	+	2119.88i	0.359940	+	0.207811i	−0.309115	+	0.951025i	$0.600033\pi$
$102$	776.663	+	448.407i	0.0746505	+	0.0430995i
$103$	−5957.18	−	10318.1i	−0.561522	−	0.972584i	−0.997364	−	0.0725609i	$-0.976883\pi$
$103$	−5957.18	−	10318.1i	−0.561522	−	0.972584i	0.435842	−	0.900023i	$-0.356450\pi$
$104$			5899.46i			0.545438i
$105$	3074.16	+	2919.32i	0.278836	+	0.264791i
$106$	−5505.70			−0.490005
$107$	−16220.0	+	9364.61i	−1.41672	+	0.817942i	−0.996009	−	0.0892547i	$-0.971551\pi$
$107$	−16220.0	+	9364.61i	−1.41672	+	0.817942i	−0.420708	+	0.907196i	$0.638218\pi$
$108$	5144.11	−	8909.86i	0.441025	−	0.763877i
$109$	8697.68	−	15064.8i	0.732066	−	1.26798i	−0.223932	−	0.974605i	$-0.571890\pi$
$109$	8697.68	−	15064.8i	0.732066	−	1.26798i	0.955999	−	0.293371i	$-0.0947772\pi$
$110$	−4110.92	−	26841.4i	−0.339745	−	2.21830i
$111$			1127.52i			0.0915117i
$112$	−8757.89	+	1195.38i	−0.698173	+	0.0952946i
$113$		−	16482.8i		−	1.29085i	−0.763826	−	0.645423i	$-0.776681\pi$
$113$		−	16482.8i		−	1.29085i	0.763826	−	0.645423i	$-0.223319\pi$
$114$	1936.58	+	3354.26i	0.149014	+	0.258100i
$115$	−8434.41	+	6759.06i	−0.637763	+	0.511082i
$116$	−6410.46	+	11103.2i	−0.476402	+	0.825152i
$117$	8915.93	+	15442.8i	0.651321	+	1.12812i
$118$	12846.6			0.922622
$119$	1299.61	+	1677.12i	0.0917738	+	0.118432i
$120$	1840.84	+	717.436i	0.127836	+	0.0498219i
$121$	−9149.58	−	15847.5i	−0.624928	−	1.08241i
$122$	8205.80	−	14212.9i	0.551317	−	0.954909i
$123$	−8631.85	−	4983.60i	−0.570550	−	0.329407i
$124$	10715.6	−	6186.63i	0.696902	−	0.402356i
$125$	14029.0	−	6879.59i	0.897854	−	0.440294i
$126$	15999.3	−	12398.0i	1.00777	−	0.780926i
$127$		−	16081.9i		−	0.997078i	−0.866867	−	0.498539i	$-0.833870\pi$
$127$		−	16081.9i		−	0.997078i	0.866867	−	0.498539i	$-0.166130\pi$
$128$	−9837.42	+	5679.64i	−0.600428	+	0.346657i
$129$	−3869.50	−	2234.06i	−0.232528	−	0.134250i
$130$	−30162.5	+	24171.3i	−1.78476	+	1.43025i
$131$	15005.7	−	8663.57i	0.874410	−	0.504841i	0.00559877	−	0.999984i	$-0.498218\pi$
$131$	15005.7	−	8663.57i	0.874410	−	0.504841i	0.868811	+	0.495143i	$0.164885\pi$
$132$	12446.4			0.714327
$133$	1239.22	+	9079.14i	0.0700562	+	0.513264i
$134$	−23818.5			−1.32649
$135$	12830.3	−	1965.04i	0.703994	−	0.107821i
$136$	856.313	+	494.392i	0.0462972	+	0.0267297i
$137$	21030.0	+	12141.7i	1.12046	+	0.646900i	0.941519	−	0.336960i	$-0.109399\pi$
$137$	21030.0	+	12141.7i	1.12046	+	0.646900i	0.178944	+	0.983859i	$0.442732\pi$
$138$	−4477.20	−	7754.73i	−0.235097	−	0.407201i
$139$			20665.1i			1.06956i	0.844990	+	0.534782i	$0.179606\pi$
$139$			20665.1i			1.06956i	−0.844990	+	0.534782i	$0.820394\pi$
$140$	17602.0	+	16715.4i	0.898063	+	0.852829i
$141$	−1228.40			−0.0617875
$142$	−40017.1	+	23103.9i	−1.98458	+	1.14580i
$143$	−23444.2	+	40606.5i	−1.14647	+	1.98575i
$144$	−6225.52	+	10782.9i	−0.300228	+	0.520009i
$145$	−15988.8	+	2448.78i	−0.760466	+	0.116470i
$146$		−	11145.0i		−	0.522847i
$147$	−8005.38	+	2226.81i	−0.370465	+	0.103050i
$148$			6455.93i			0.294737i
$149$	−1793.25	−	3106.00i	−0.0807733	−	0.139903i	0.822809	−	0.568318i	$-0.192406\pi$
$149$	−1793.25	−	3106.00i	−0.0807733	−	0.139903i	−0.903582	+	0.428415i	$0.859072\pi$
$150$	3874.22	+	12351.3i	0.172188	+	0.548945i
$151$	−1154.74	+	2000.07i	−0.0506444	+	0.0877187i	−0.890236	−	0.455499i	$-0.849461\pi$
$151$	−1154.74	+	2000.07i	−0.0506444	+	0.0877187i	0.839592	+	0.543218i	$0.182794\pi$
$152$	2135.19	+	3698.25i	0.0924163	+	0.160070i
$153$	2988.73			0.127674
$154$	49267.5	+	20133.4i	2.07739	+	0.848938i
$155$	14544.9	+	5668.60i	0.605405	+	0.235946i
$156$	−8858.39	−	15343.2i	−0.364004	−	0.630473i
$157$	13423.8	−	23250.6i	0.544596	−	0.943269i	−0.454036	−	0.890983i	$-0.650016\pi$
$157$	13423.8	−	23250.6i	0.544596	−	0.943269i	0.998632	−	0.0522853i	$-0.0166505\pi$
$158$	20674.5	+	11936.4i	0.828174	+	0.478146i
$159$	2757.27	−	1591.91i	0.109065	−	0.0629687i
$160$	−33657.4	−	13117.4i	−1.31474	−	0.512398i
$161$	−2864.96	−	20990.1i	−0.110527	−	0.809771i
$162$		−	22705.9i		−	0.865186i
$163$	10481.8	−	6051.69i	0.394514	−	0.227773i	−0.289600	−	0.957148i	$-0.593522\pi$
$163$	10481.8	−	6051.69i	0.394514	−	0.227773i	0.684114	+	0.729375i	$0.260189\pi$
$164$	−49424.2	−	28535.1i	−1.83760	−	1.06094i
$165$	9819.65	+	12253.6i	0.360685	+	0.450087i
$166$	35333.0	−	20399.5i	1.28223	−	0.740293i
$167$	13334.9			0.478142			0.239071	−	0.971002i	$-0.423157\pi$
$167$	13334.9			0.478142			0.239071	+	0.971002i	$0.423157\pi$
$168$	−3060.93	+	2371.94i	−0.108451	+	0.0840397i
$169$	38181.9			1.33686
$170$	980.773	+	6403.75i	0.0339368	+	0.221583i
$171$	11178.4	+	6453.88i	0.382287	+	0.220713i
$172$	−22156.0	−	12791.7i	−0.748917	−	0.432387i
$173$	−13098.3	−	22686.9i	−0.437645	−	0.758024i	0.559862	−	0.828586i	$-0.310854\pi$
$173$	−13098.3	−	22686.9i	−0.437645	−	0.758024i	−0.997507	+	0.0705621i	$0.977521\pi$
$174$		−	13400.5i		−	0.442610i
$175$	−2569.33	+	30517.0i	−0.0838966	+	0.996474i
$176$	−32739.7			−1.05694
$177$	−6433.61	+	3714.45i	−0.205356	+	0.118563i
$178$	4602.33	−	7971.47i	0.145257	−	0.251593i
$179$	3158.23	−	5470.22i	0.0985684	−	0.170726i	−0.812524	−	0.582928i	$-0.801907\pi$
$179$	3158.23	−	5470.22i	0.0985684	−	0.170726i	0.911092	+	0.412202i	$0.135240\pi$
$180$	33799.4	−	5176.58i	1.04319	−	0.159771i
$181$			49922.9i			1.52385i	0.647664	+	0.761926i	$0.275746\pi$
$181$			49922.9i			1.52385i	−0.647664	+	0.761926i	$0.724254\pi$
$182$	−10245.5	−	75063.2i	−0.309307	−	2.26613i
$183$			9490.46i			0.283390i
$184$	−4936.35	−	8550.00i	−0.145804	−	0.252540i
$185$	−6355.91	+	5093.42i	−0.185710	+	0.148822i
$186$	−6466.29	+	11199.9i	−0.186908	+	0.323735i
$187$	3929.39	+	6805.90i	0.112368	+	0.194627i
$188$	−7033.56			−0.199003
$189$	−9623.86	+	23550.1i	−0.269417	+	0.659278i
$190$	−10160.0	+	26069.2i	−0.281441	+	0.722138i
$191$	−4868.68	−	8432.80i	−0.133458	−	0.231156i	0.791549	−	0.611105i	$-0.209275\pi$
$191$	−4868.68	−	8432.80i	−0.133458	−	0.231156i	−0.925007	+	0.379949i	$0.875941\pi$
$192$	9968.97	−	17266.8i	0.270426	−	0.468391i
$193$	−2643.18	−	1526.04i	−0.0709597	−	0.0409686i	0.464100	−	0.885783i	$-0.346378\pi$
$193$	−2643.18	−	1526.04i	−0.0709597	−	0.0409686i	−0.535060	+	0.844814i	$0.679711\pi$
$194$	−67333.2	+	38874.8i	−1.78906	+	1.03292i
$195$	8116.64	−	20826.2i	0.213455	−	0.547698i
$196$	−45837.2	+	12750.3i	−1.19318	+	0.331900i
$197$			13021.1i			0.335516i	0.985828	+	0.167758i	$0.0536528\pi$
$197$			13021.1i			0.335516i	−0.985828	+	0.167758i	$0.946347\pi$
$198$	64926.8	−	37485.5i	1.65613	−	0.956166i
$199$	2083.08	+	1202.67i	0.0526017	+	0.0303696i	0.526070	−	0.850441i	$-0.323665\pi$
$199$	2083.08	+	1202.67i	0.0526017	+	0.0303696i	−0.473469	+	0.880811i	$0.656998\pi$
$200$	4271.54	+	13617.9i	0.106788	+	0.340448i
$201$	11928.4	−	6886.85i	0.295249	−	0.170462i
$202$	−25373.4			−0.621836
$203$	11993.0	−	29347.5i	0.291029	−	0.712162i
$204$	−2969.44			−0.0713533
$205$	−10900.3	−	71171.4i	−0.259377	−	1.69355i
$206$	61750.2	+	35651.5i	1.45514	+	0.840123i
$207$	−25843.5	−	14920.7i	−0.603129	−	0.348217i
$208$	23301.5	+	40359.4i	0.538589	+	0.932863i
$209$			33940.6i			0.777010i
$210$	−24668.4	−	5931.52i	−0.559374	−	0.134501i
$211$	−41823.7			−0.939416			−0.469708	−	0.882822i	$-0.655641\pi$
$211$	−41823.7			−0.939416			−0.469708	+	0.882822i	$0.655641\pi$
$212$	15787.6	−	9114.97i	0.351272	−	0.202807i
$213$	13360.5	−	23141.0i	0.294484	−	0.510062i
$214$	56043.7	−	97070.5i	1.22377	−	2.11963i
$215$	−4886.42	−	31904.8i	−0.105709	−	0.690207i
$216$			11856.1i			0.254117i
$217$	−24185.0	+	18741.1i	−0.513602	+	0.397994i
$218$			104105.i			2.19057i
$219$	3222.46	+	5581.46i	0.0671891	+	0.116375i
$220$	56225.3	+	70161.7i	1.16168	+	1.44962i
$221$	5593.26	−	9687.81i	0.114520	−	0.198354i
$222$	−3373.88	−	5843.73i	−0.0684578	−	0.118572i
$223$	−87176.7			−1.75304			−0.876518	−	0.481369i	$-0.840140\pi$
$223$	−87176.7			−1.75304			−0.876518	+	0.481369i	$0.840140\pi$
$224$	55965.2	−	43367.8i	1.11538	−	0.864313i
$225$	31762.5	+	29191.7i	0.627407	+	0.576626i
$226$	49321.7	+	85427.7i	0.965653	+	1.67256i
$227$	21675.0	−	37542.1i	0.420636	−	0.728563i	−0.575366	−	0.817896i	$-0.695140\pi$
$227$	21675.0	−	37542.1i	0.420636	−	0.728563i	0.996002	+	0.0893331i	$0.0284736\pi$
$228$	−11106.3	−	6412.23i	−0.213648	−	0.123350i
$229$	12616.7	−	7284.25i	0.240588	−	0.138904i	−0.374859	−	0.927082i	$-0.622309\pi$
$229$	12616.7	−	7284.25i	0.240588	−	0.138904i	0.615447	+	0.788178i	$0.288975\pi$
$230$	23488.9	−	60269.5i	0.444025	−	1.13931i
$231$	−30494.7	+	4162.26i	−0.571478	+	0.0780019i
$232$		−	14774.7i		−	0.274501i
$233$	−82362.5	+	47552.0i	−1.51711	+	0.875905i	−0.517314	+	0.855795i	$0.673068\pi$
$233$	−82362.5	+	47552.0i	−1.51711	+	0.875905i	−0.999798	+	0.0201096i	$0.993598\pi$
$234$	−92419.6	−	53358.5i	−1.68784	−	0.974477i
$235$	−5549.14	−	6924.60i	−0.100482	−	0.125389i
$236$	−36837.6	+	21268.2i	−0.661404	+	0.381862i
$237$	−13805.2			−0.245779
$238$	−11754.1	−	4803.38i	−0.207508	−	0.0847995i
$239$	67047.6			1.17378			0.586891	−	0.809666i	$-0.300352\pi$
$239$	67047.6			1.17378			0.586891	+	0.809666i	$0.300352\pi$
$240$	15427.3	−	2362.78i	0.267835	−	0.0410206i
$241$	−42163.6	−	24343.2i	−0.725944	−	0.419124i	0.0909923	−	0.995852i	$-0.470996\pi$
$241$	−42163.6	−	24343.2i	−0.725944	−	0.419124i	−0.816937	+	0.576727i	$0.804329\pi$
$242$	94841.5	+	54756.7i	1.61945	+	0.934990i
$243$	27592.6	+	47791.8i	0.467283	+	0.809358i
$244$			54340.5i			0.912733i
$245$	−48716.1	−	35067.7i	−0.811597	−	0.584218i
$246$	59649.9			0.985688
$247$	41839.8	−	24156.2i	0.685798	−	0.395945i
$248$	−7129.42	+	12348.5i	−0.115918	+	0.200776i
$249$	−11796.6	+	20432.3i	−0.190264	+	0.329548i
$250$	−52123.9	+	77634.8i	−0.833983	+	1.24216i
$251$		−	20918.6i		−	0.332036i	−0.986123	−	0.166018i	$-0.946909\pi$
$251$		−	20918.6i		−	0.332036i	0.986123	−	0.166018i	$-0.0530910\pi$
$252$	−25352.5	+	62038.9i	−0.399227	+	0.976929i
$253$		−	78467.4i		−	1.22588i
$254$	48121.9	+	83349.6i	0.745891	+	1.29192i
$255$	−2342.75	−	2923.44i	−0.0360284	−	0.0449587i
$256$	−12098.5	+	20955.3i	−0.184609	+	0.319752i
$257$	2134.35	+	3696.81i	0.0323147	+	0.0559707i	0.881730	−	0.471754i	$-0.156379\pi$
$257$	2134.35	+	3696.81i	0.0323147	+	0.0559707i	−0.849416	+	0.527724i	$0.823045\pi$
$258$	26739.9			0.401718
$259$	−2158.95	−	15817.5i	−0.0321842	−	0.235797i
$260$	46474.2	−	119247.i	0.687489	−	1.76400i
$261$	−22329.3	−	38675.4i	−0.327788	−	0.567746i
$262$	−51848.2	+	89803.7i	−0.755320	+	1.30825i
$263$	1208.43	+	697.690i	0.0174708	+	0.0100867i	0.508710	−	0.860938i	$-0.330123\pi$
$263$	1208.43	+	697.690i	0.0174708	+	0.0100867i	−0.491239	+	0.871025i	$0.663456\pi$
$264$	−12421.6	+	7171.59i	−0.178225	+	0.102898i
$265$	21429.4	+	8351.73i	0.305154	+	0.118928i
$266$	−33590.3	−	43347.5i	−0.474734	−	0.612634i
$267$			5322.85i			0.0746658i
$268$	68299.4	−	39432.7i	0.950928	−	0.549018i
$269$	−30199.7	−	17435.8i	−0.417347	−	0.240956i	0.276594	−	0.960987i	$-0.410794\pi$
$269$	−30199.7	−	17435.8i	−0.417347	−	0.240956i	−0.693942	+	0.720031i	$0.744128\pi$
$270$	−60617.2	+	48576.7i	−0.831512	+	0.666347i
$271$	−16062.0	+	9273.37i	−0.218706	+	0.126270i	−0.605351	−	0.795959i	$-0.706967\pi$
$271$	−16062.0	+	9273.37i	−0.218706	+	0.126270i	0.386645	+	0.922229i	$0.373634\pi$
$272$	7810.95			0.105576
$273$	26834.7	+	34629.5i	0.360057	+	0.464645i
$274$	−145326.			−1.93572
$275$	−24715.7	+	110709.i	−0.326819	+	1.46391i
$276$	25676.7	+	14824.5i	0.337071	+	0.194608i
$277$	−126853.	−	73238.4i	−1.65326	−	0.954508i	−0.975721	−	0.219018i	$-0.929715\pi$
$277$	−126853.	−	73238.4i	−1.65326	−	0.954508i	−0.677535	−	0.735490i	$-0.736952\pi$
$278$	−61836.2	−	107104.i	−0.800117	−	1.38584i
$279$			43099.2i			0.553683i
$280$	−27198.2	−	6539.81i	−0.346916	−	0.0834160i
$281$	128070.			1.62194			0.810969	−	0.585089i	$-0.198940\pi$
$281$	128070.			1.62194			0.810969	+	0.585089i	$0.198940\pi$
$282$	6366.58	−	3675.75i	0.0800586	−	0.0462219i
$283$	45205.6	−	78298.4i	0.564442	−	0.977643i	−0.432659	−	0.901558i	$-0.642425\pi$
$283$	45205.6	−	78298.4i	0.564442	−	0.977643i	0.997101	−	0.0760850i	$-0.0242420\pi$
$284$	76499.3	−	132501.i	0.948464	−	1.64279i
$285$	−2449.45	−	15993.2i	−0.0301564	−	0.196900i
$286$		−	280609.i		−	3.43060i
$287$	130635.	+	53384.9i	1.58598	+	0.648119i
$288$		−	99733.5i		−	1.20242i
$289$	40823.0	+	70707.6i	0.488776	+	0.846584i
$290$	75539.7	−	60535.0i	0.898213	−	0.719798i
$291$	22480.5	−	38937.3i	0.265472	−	0.459811i
$292$	18451.1	+	31958.3i	0.216400	+	0.374816i
$293$	70381.3			0.819827			0.409913	−	0.912124i	$-0.365559\pi$
$293$	70381.3			0.819827			0.409913	+	0.912124i	$0.365559\pi$
$294$	34827.2	−	35495.8i	0.402925	−	0.410660i
$295$	−50001.8	−	19487.3i	−0.574568	−	0.223928i
$296$	−3719.88	−	6443.02i	−0.0424566	−	0.0735370i
$297$	−47115.5	+	81606.5i	−0.534135	+	0.925149i
$298$	18588.2	+	10731.9i	0.209317	+	0.120849i
$299$	−96729.6	+	55846.9i	−1.08197	+	0.624679i
$300$	−31557.5	−	29003.3i	−0.350639	−	0.322259i
$301$	58561.4	+	23931.4i	0.646366	+	0.264141i
$302$		−	13821.4i		−	0.151544i
$303$	12707.1	−	7336.43i	0.138408	−	0.0799097i
$304$	29214.5	+	16867.0i	0.316120	+	0.182512i
$305$	−53498.6	+	42872.0i	−0.575100	+	0.460866i
$306$	−15490.1	+	8943.20i	−0.165429	+	0.0955103i
$307$	94756.4			1.00538			0.502692	−	0.864466i	$-0.332343\pi$
$307$	94756.4			1.00538			0.502692	+	0.864466i	$0.332343\pi$
$308$	−174606.	+	23832.2i	−1.84060	+	0.251225i
$309$	−41232.9			−0.431844
$310$	−92345.8	+	14143.3i	−0.960934	+	0.147173i
$311$	−15872.8	−	9164.17i	−0.164109	−	0.0947485i	0.415696	−	0.909504i	$-0.363538\pi$
$311$	−15872.8	−	9164.17i	−0.164109	−	0.0947485i	−0.579805	+	0.814755i	$0.696871\pi$
$312$	17681.4	+	10208.3i	0.181638	+	0.104869i
$313$	35221.4	+	61005.3i	0.359516	+	0.622700i	0.987880	−	0.155219i	$-0.0496085\pi$
$313$	35221.4	+	61005.3i	0.359516	+	0.622700i	−0.628364	+	0.777919i	$0.716275\pi$
$314$			160672.i			1.62960i
$315$	−81079.7	+	23986.0i	−0.817130	+	0.241733i
$316$	−79045.6			−0.791596
$317$	−39046.6	+	22543.6i	−0.388566	+	0.224339i	−0.681539	−	0.731782i	$-0.738689\pi$
$317$	−39046.6	+	22543.6i	−0.388566	+	0.224339i	0.292973	+	0.956121i	$0.405355\pi$
$318$	−9526.99	+	16501.2i	−0.0942110	+	0.163178i
$319$	58714.2	−	101696.i	0.576981	−	0.999361i
$320$	142368.	−	21804.5i	1.39031	−	0.212935i
$321$			64817.6i			0.629047i
$322$	77657.5	+	100215.i	0.748982	+	0.966545i
$323$		−	8097.46i		−	0.0776147i
$324$	37590.8	+	65109.2i	0.358090	+	0.620230i
$325$	154065.	−	48325.6i	1.45861	−	0.457521i
$326$	−36217.1	+	62729.8i	−0.340783	+	0.590254i
$327$	−30100.7	−	52135.9i	−0.281502	−	0.487575i
$328$	65767.2			0.611310
$329$	17232.7	−	2352.12i	0.159207	−	0.0217304i
$330$	−87560.2	−	34125.0i	−0.804042	−	0.313361i
$331$	−22565.1	−	39083.9i	−0.205959	−	0.356732i	0.744479	−	0.667646i	$-0.232698\pi$
$331$	−22565.1	−	39083.9i	−0.205959	−	0.356732i	−0.950438	+	0.310914i	$0.899365\pi$
$332$	−67544.9	+	116991.i	−0.612796	+	1.06139i
$333$	−19474.9	−	11243.8i	−0.175625	−	0.101397i
$334$	−69112.5	+	39902.1i	−0.619532	+	0.357687i
$335$	92706.8	+	36130.8i	0.826080	+	0.321950i
$336$	−11571.8	+	28316.9i	−0.102500	+	0.250823i
$337$			207444.i			1.82659i	0.407298	+	0.913295i	$0.366471\pi$
$337$			207444.i			1.82659i	−0.407298	+	0.913295i	$0.633529\pi$
$338$	−197891.	+	114252.i	−1.73217	+	1.00007i
$339$	−49400.9	−	28521.6i	−0.429868	−	0.248185i
$340$	−13414.1	−	16739.0i	−0.116039	−	0.144801i
$341$	−98145.1	+	56664.1i	−0.844034	+	0.487303i
$342$	−77248.0			−0.660443
$343$	108040.	−	46567.7i	0.918329	−	0.395819i
$344$	29482.2			0.249140
$345$	5662.90	+	36974.7i	0.0475774	+	0.310647i
$346$	135772.	+	78388.2i	1.13412	+	0.654785i
$347$	9697.58	+	5598.90i	0.0805387	+	0.0464990i	0.539728	−	0.841839i	$-0.318527\pi$
$347$	9697.58	+	5598.90i	0.0805387	+	0.0464990i	−0.459190	+	0.888338i	$0.651860\pi$
$348$	22185.2	+	38425.8i	0.183191	+	0.317296i
$349$		−	121107.i		−	0.994303i	−0.867664	−	0.497152i	$-0.834379\pi$
$349$		−	121107.i		−	0.994303i	0.867664	−	0.497152i	$-0.165621\pi$
$350$	−78000.0	−	165853.i	−0.636735	−	1.35390i
$351$	134132.			1.08873
$352$	227112.	−	131123.i	1.83297	−	1.05826i
$353$	−73625.0	+	127522.i	−0.590848	+	1.02338i	0.403270	+	0.915081i	$0.367873\pi$
$353$	−73625.0	+	127522.i	−0.590848	+	1.02338i	−0.994118	+	0.108298i	$0.965460\pi$
$354$	22229.6	−	38502.7i	0.177388	−	0.307245i
$355$	190802.	−	29222.5i	1.51400	−	0.231879i
$356$			30477.6i			0.240481i
$357$	7275.34	−	993.021i	0.0570843	−	0.00779152i
$358$			37801.6i			0.294947i
$359$	−119895.	−	207665.i	−0.930279	−	1.61129i	−0.782844	−	0.622219i	$-0.786232\pi$
$359$	−119895.	−	207665.i	−0.930279	−	1.61129i	−0.147435	−	0.989072i	$-0.547102\pi$
$360$	−30749.1	+	24641.3i	−0.237261	+	0.190133i
$361$	−47674.8	+	82575.2i	−0.365826	+	0.633629i
$362$	−149385.	−	258742.i	−1.13996	−	1.97447i
$363$	−63329.2			−0.480608
$364$	153650.	+	198282.i	1.15966	+	1.49651i
$365$	−16906.1	+	43378.9i	−0.126899	+	0.325606i
$366$	−28398.4	−	49187.5i	−0.211998	−	0.367191i
$367$	46183.7	−	79992.5i	0.342892	−	0.593906i	−0.642077	−	0.766640i	$-0.721927\pi$
$367$	46183.7	−	79992.5i	0.342892	−	0.593906i	0.984968	+	0.172735i	$0.0552603\pi$
$368$	−67541.1	−	38994.9i	−0.498738	−	0.287947i
$369$	172157.	−	99394.9i	1.26436	−	0.729981i
$370$	17700.5	−	45417.2i	0.129295	−	0.331755i
$371$	−35632.5	+	27611.9i	−0.258880	+	0.200608i
$372$		−	42821.1i		−	0.309436i
$373$	54164.7	−	31272.0i	0.389313	−	0.224770i	−0.292550	−	0.956250i	$-0.594504\pi$
$373$	54164.7	−	31272.0i	0.389313	−	0.224770i	0.681862	+	0.731481i	$0.261170\pi$
$374$	−40730.8	−	23515.9i	−0.291192	−	0.168120i
$375$	3656.61	−	53950.8i	0.0260026	−	0.383650i
$376$	7019.50	−	4052.71i	0.0496513	−	0.0286662i
$377$	−167153.			−1.17606
$378$	−20590.2	−	150854.i	−0.144104	−	1.05578i
$379$	−98575.0			−0.686260			−0.343130	−	0.939288i	$-0.611487\pi$
$379$	−98575.0			−0.686260			−0.343130	+	0.939288i	$0.611487\pi$
$380$	−14025.1	−	91573.7i	−0.0971266	−	0.634167i
$381$	−48199.2	−	27827.8i	−0.332040	−	0.191703i
$382$	50467.1	+	29137.2i	0.345845	+	0.199674i
$383$	120287.	+	208344.i	0.820016	+	1.42031i	0.905670	+	0.423984i	$0.139369\pi$
$383$	120287.	+	208344.i	0.820016	+	1.42031i	−0.0856543	+	0.996325i	$0.527298\pi$
$384$			39311.9i			0.266601i
$385$	−161219.	−	153099.i	−1.08766	−	1.03288i
$386$	18265.5			0.122591
$387$	77174.8	−	44556.9i	0.515292	−	0.297504i
$388$	128719.	−	222947.i	0.855023	−	1.48094i
$389$	−22305.2	+	38633.8i	−0.147403	+	0.255310i	−0.930267	−	0.366883i	$-0.880425\pi$
$389$	−22305.2	+	38633.8i	−0.147403	+	0.255310i	0.782864	+	0.622193i	$0.213758\pi$
$390$	20251.3	+	132226.i	0.133144	+	0.869337i
$391$			18720.6i			0.122452i
$392$	38398.9	−	39136.0i	0.249888	−	0.254685i
$393$		−	59965.3i		−	0.388253i
$394$	−38963.0	−	67486.0i	−0.250992	−	0.434731i
$395$	−62363.2	−	77821.0i	−0.399700	−	0.498773i
$396$	−124118.	+	214979.i	−0.791490	+	1.37090i
$397$	−102956.	−	178326.i	−0.653239	−	1.13144i	−0.982332	−	0.187145i	$-0.940077\pi$
$397$	−102956.	−	178326.i	−0.653239	−	1.13144i	0.329094	−	0.944297i	$-0.393257\pi$
$398$	−14395.0			−0.0908753
$399$	29355.6	+	11996.3i	0.184393	+	0.0753533i
$400$	83010.2	+	76291.5i	0.518814	+	0.476822i
$401$	63996.5	+	110845.i	0.397986	+	0.689332i	0.993477	−	0.114030i	$-0.0363760\pi$
$401$	63996.5	+	110845.i	0.397986	+	0.689332i	−0.595491	+	0.803362i	$0.703043\pi$
$402$	−41215.2	+	71386.8i	−0.255038	+	0.441739i
$403$	139704.	+	80658.0i	0.860198	+	0.496635i
$404$	72758.1	−	42006.9i	0.445778	−	0.257370i
$405$	−34443.2	+	88376.6i	−0.209987	+	0.538799i
$406$	25659.0	+	187990.i	0.155664	+	1.14047i
$407$		−	59130.6i		−	0.356963i
$408$	2963.50	−	1710.98i	0.0178027	−	0.0102784i
$409$	−238288.	−	137576.i	−1.42448	−	0.822422i	−0.427799	−	0.903874i	$-0.640711\pi$
$409$	−238288.	−	137576.i	−1.42448	−	0.822422i	−0.996677	+	0.0814519i	$0.974044\pi$
$410$	269461.	+	336252.i	1.60298	+	2.00031i
$411$	72780.0	−	42019.5i	0.430852	−	0.248753i
$412$	−236091.			−1.39087
$413$	83142.3	−	64427.5i	0.487441	−	0.377721i
$414$	178590.			1.04197
$415$	−168468.	+	25802.0i	−0.978188	+	0.149815i
$416$	−323281.	−	186646.i	−1.86807	−	1.07853i
$417$	61935.6	+	35758.5i	0.356179	+	0.205640i
$418$	−101561.	−	175908.i	−0.581264	−	1.00678i
$419$			97351.5i			0.554517i	0.960795	+	0.277258i	$0.0894258\pi$
$419$			97351.5i			0.554517i	−0.960795	+	0.277258i	$0.910574\pi$
$420$	80556.5	−	23831.2i	0.456669	−	0.135097i
$421$	−91328.5			−0.515279			−0.257639	−	0.966241i	$-0.582945\pi$
$421$	−91328.5			−0.515279			−0.257639	+	0.966241i	$0.582945\pi$
$422$	216765.	−	125150.i	1.21721	−	0.702756i
$423$	12249.8	−	21217.3i	0.0684620	−	0.118580i
$424$	−10504.0	+	18193.5i	−0.0584283	+	0.101201i
$425$	5896.61	−	26412.6i	0.0326456	−	0.146229i
$426$			159915.i			0.881189i
$427$	−18172.2	−	133138.i	−0.0996670	−	0.730208i
$428$			371132.i			2.02601i
$429$	81135.1	+	140530.i	0.440853	+	0.763580i
$430$	120795.	+	150736.i	0.653297	+	0.815228i
$431$	−46955.1	+	81328.5i	−0.252771	+	0.437813i	−0.964288	−	0.264857i	$-0.914675\pi$
$431$	−46955.1	+	81328.5i	−0.252771	+	0.437813i	0.711516	+	0.702669i	$0.248009\pi$
$432$	46828.7	+	81109.8i	0.250926	+	0.434616i
$433$	−36517.4			−0.194771			−0.0973854	−	0.995247i	$-0.531048\pi$
$433$	−36517.4			−0.194771			−0.0973854	+	0.995247i	$0.531048\pi$
$434$	69267.6	−	169501.i	0.367748	−	0.899898i
$435$	−20327.5	+	52157.6i	−0.107425	+	0.275638i
$436$	−172350.	−	298520.i	−0.906650	−	1.57036i
$437$	−40425.3	+	70018.6i	−0.211685	+	0.366649i
$438$	−33402.9	−	19285.2i	−0.174115	−	0.100525i
$439$	−112835.	+	65145.2i	−0.585483	+	0.338029i	−0.763309	−	0.646033i	$-0.776427\pi$
$439$	−112835.	+	65145.2i	−0.585483	+	0.338029i	0.177826	+	0.984062i	$0.443093\pi$
$440$	−96539.8	−	37624.7i	−0.498656	−	0.194342i
$441$	41368.9	−	160478.i	0.212714	−	0.825160i
$442$			66947.1i			0.342679i
$443$	−31137.4	+	17977.2i	−0.158663	+	0.0916038i	−0.577229	−	0.816582i	$-0.695866\pi$
$443$	−31137.4	+	17977.2i	−0.158663	+	0.0916038i	0.418567	+	0.908186i	$0.362533\pi$
$444$	19349.2	+	11171.2i	0.0981514	+	0.0566677i
$445$	−30005.4	+	24045.3i	−0.151523	+	0.121426i
$446$	451822.	−	260860.i	2.27142	−	1.31141i
$447$	−12412.1			−0.0621196
$448$	−106789.	+	261317.i	−0.532071	+	1.30200i
$449$	6593.60			0.0327062			0.0163531	−	0.999866i	$-0.494794\pi$
$449$	6593.60			0.0327062			0.0163531	+	0.999866i	$0.494794\pi$
$450$	−251970.	−	56252.4i	−1.24430	−	0.277790i
$451$	452682.	+	261356.i	2.22557	+	1.28493i
$452$	−282860.	−	163309.i	−1.38450	−	0.799344i
$453$	3996.30	+	6921.80i	0.0194743	+	0.0337305i
$454$			259433.i			1.25867i
$455$	−73987.5	+	307704.i	−0.357385	+	1.48631i
$456$	14778.8			0.0710738
$457$	−14865.3	+	8582.51i	−0.0711775	+	0.0410943i	−0.535166	−	0.844747i	$-0.679751\pi$
$457$	−14865.3	+	8582.51i	−0.0711775	+	0.0410943i	0.463989	+	0.885841i	$0.346418\pi$
$458$	−43593.5	+	75506.1i	−0.207822	+	0.359958i
$459$	11240.7	−	19469.5i	0.0533541	−	0.0924121i
$460$	32424.6	+	211710.i	0.153236	+	1.00052i
$461$		−	225801.i		−	1.06249i	−0.847219	−	0.531243i	$-0.821725\pi$
$461$		−	225801.i		−	1.06249i	0.847219	−	0.531243i	$-0.178275\pi$
$462$	145594.	−	112822.i	0.682118	−	0.528578i
$463$		−	129028.i		−	0.601895i	−0.953641	−	0.300947i	$-0.902697\pi$
$463$		−	129028.i		−	0.601895i	0.953641	−	0.300947i	$-0.0973029\pi$
$464$	−58356.8	−	101077.i	−0.271054	−	0.469479i
$465$	42157.7	−	33783.8i	0.194971	−	0.156244i
$466$	284581.	−	492908.i	1.31049	−	2.26984i
$467$	−121072.	−	209703.i	−0.555151	−	0.961549i	−0.997892	−	0.0648996i	$-0.979327\pi$
$467$	−121072.	−	209703.i	−0.555151	−	0.961549i	0.442741	−	0.896649i	$-0.354006\pi$
$468$	353351.			1.61330
$469$	−154152.	+	119453.i	−0.700814	+	0.543065i
$470$	49480.8	+	19284.3i	0.223996	+	0.0872986i
$471$	−46456.6	−	80465.2i	−0.209414	−	0.362715i
$472$	24509.3	−	42451.3i	0.110014	−	0.190549i
$473$	202929.	+	117161.i	0.907031	+	0.523674i
$474$	71549.9	−	41309.3i	0.318458	−	0.183862i
$475$	79090.0	−	86055.1i	0.350537	−	0.381408i
$476$	41657.1	−	5685.84i	0.183855	−	0.0250946i
$477$			63499.5i			0.279083i
$478$	−347496.	+	200627.i	−1.52088	+	0.878079i
$479$	324142.	+	187143.i	1.41275	+	0.815649i	0.995646	−	0.0932121i	$-0.0297135\pi$
$479$	324142.	+	187143.i	1.41275	+	0.815649i	0.417099	+	0.908861i	$0.363047\pi$
$480$	−97554.7	+	78177.2i	−0.423415	+	0.339311i
$481$	−72892.5	+	42084.5i	−0.315059	+	0.181900i
$482$	291369.			1.25415
$483$	−67867.2	−	27734.3i	−0.290915	−	0.118884i
$484$	−362610.			−1.54792
$485$	321046.	−	49170.2i	1.36485	−	0.209035i
$486$	−286016.	−	165131.i	−1.21093	−	0.699128i
$487$	−58644.9	−	33858.6i	−0.247270	−	0.142762i	0.371243	−	0.928536i	$-0.378932\pi$
$487$	−58644.9	−	33858.6i	−0.247270	−	0.142762i	−0.618514	+	0.785774i	$0.712265\pi$
$488$	−31310.8	−	54231.8i	−0.131478	−	0.227727i
$489$		−	41887.0i		−	0.175171i
$490$	357421.	+	35976.3i	1.48863	+	0.149839i
$491$	−419122.			−1.73851			−0.869255	−	0.494364i	$-0.835401\pi$
$491$	−419122.			−1.73851			−0.869255	+	0.494364i	$0.835401\pi$
$492$	−171046.	+	98753.5i	−0.706615	+	0.407964i
$493$	−14007.9	+	24262.4i	−0.0576340	+	0.0998250i
$494$	−144566.	+	250395.i	−0.592396	+	1.02606i
$495$	−309572.	+	47412.9i	−1.26343	+	0.193502i
$496$			112638.i			0.457850i
$497$	−143119.	+	350218.i	−0.579407	+	1.41784i
$498$		−	141196.i		−	0.569330i
$499$	916.458	+	1587.35i	0.00368054	+	0.00637488i	0.867860	−	0.496809i	$-0.165495\pi$
$499$	916.458	+	1587.35i	0.00368054	+	0.00637488i	−0.864179	+	0.503184i	$0.832162\pi$
$500$	20937.0	−	308911.i	0.0837480	−	1.23565i
$501$	23074.5	−	39966.2i	0.0919300	−	0.159227i
$502$	62595.0	+	108418.i	0.248389	+	0.430222i
$503$	−194192.			−0.767530			−0.383765	−	0.923431i	$-0.625373\pi$
$503$	−194192.			−0.767530			−0.383765	+	0.923431i	$0.625373\pi$
$504$	−10444.7	−	76522.9i	−0.0411183	−	0.301252i
$505$	98758.8	+	38489.5i	0.387252	+	0.150924i
$506$	234799.	+	406683.i	0.917054	+	1.58838i
$507$	66069.5	−	114436.i	0.257031	−	0.445190i
$508$	−275979.	−	159337.i	−1.06942	−	0.617431i
$509$	18400.7	−	10623.7i	0.0710230	−	0.0410051i	−0.464068	−	0.885800i	$-0.653611\pi$
$509$	18400.7	−	10623.7i	0.0710230	−	0.0410051i	0.535091	+	0.844794i	$0.320277\pi$
$510$	20889.9	+	8141.47i	0.0803149	+	0.0313013i
$511$	−55893.9	−	72129.8i	−0.214053	−	0.276231i
$512$		−	326559.i		−	1.24572i
$513$	84085.0	−	48546.5i	0.319509	−	0.184469i
$514$	−22124.0	−	12773.3i	−0.0837409	−	0.0483478i
$515$	−186265.	−	232434.i	−0.702290	−	0.876365i
$516$	−76676.7	+	44269.3i	−0.287981	+	0.166266i
$517$	64421.2			0.241017
$518$	58520.3	+	75519.1i	0.218096	+	0.281448i
$519$	−90660.4			−0.336576
$520$	22328.1	+	145786.i	0.0825743	+	0.539151i
$521$	61999.2	+	35795.3i	0.228408	+	0.131871i	0.609837	−	0.792527i	$-0.291235\pi$
$521$	61999.2	+	35795.3i	0.228408	+	0.131871i	−0.381430	+	0.924398i	$0.624568\pi$
$522$	231458.	+	133632.i	0.849436	+	0.490422i
$523$	61746.7	+	106948.i	0.225741	+	0.390995i	0.956541	−	0.291596i	$-0.0941864\pi$
$523$	61746.7	+	106948.i	0.225741	+	0.390995i	−0.730801	+	0.682591i	$0.760853\pi$
$524$		−	343349.i		−	1.25047i
$525$	87017.2	+	60506.9i	0.315709	+	0.219526i
$526$	−8350.82			−0.0301827
$527$	23415.2	−	13518.8i	0.0843096	−	0.0486762i
$528$	−56652.3	+	98124.6i	−0.203212	+	0.351974i
$529$	−46461.2	+	80473.1i	−0.166027	+	0.287567i
$530$	−136056.	+	20837.8i	−0.484358	+	0.0741823i
$531$		−	148165.i		−	0.525480i
$532$	168084.	+	68688.5i	0.593886	+	0.242695i
$533$		−	744051.i		−	2.61908i
$534$	−15927.6	−	27587.4i	−0.0558558	−	0.0967451i
$535$	−365383.	+	292806.i	−1.27656	+	1.02299i
$536$	−45441.9	+	78707.7i	−0.158171	+	0.273960i
$537$	−10929.9	−	18931.2i	−0.0379026	−	0.0656492i
$538$	208693.			0.721014
$539$	419828.	−	116781.i	1.44509	−	0.401972i
$540$	93398.7	−	239648.i	0.320297	−	0.821839i
$541$	−30449.3	−	52739.7i	−0.104036	−	0.180195i	0.809308	−	0.587384i	$-0.199842\pi$
$541$	−30449.3	−	52739.7i	−0.104036	−	0.180195i	−0.913344	+	0.407189i	$0.866509\pi$
$542$	55497.6	−	96124.7i	0.188919	−	0.327217i
$543$	149625.	+	86385.9i	0.507462	+	0.292984i
$544$	−54183.8	+	31283.1i	−0.183093	+	0.105709i
$545$	157919.	−	405198.i	0.531668	−	1.36419i
$546$	−242702.	−	99181.5i	−0.814119	−	0.332694i
$547$			64769.2i			0.216468i	0.994125	+	0.108234i	$0.0345196\pi$
$547$			64769.2i			0.216468i	−0.994125	+	0.108234i	$0.965480\pi$
$548$	416723.	−	240595.i	1.38767	−	0.801173i
$549$	−163923.	−	94640.8i	−0.543869	−	0.314003i
$550$	−203177.	−	647741.i	−0.671659	−	2.14129i
$551$	−104785.	+	60497.4i	−0.345139	+	0.199266i
$552$	−34167.2			−0.112132
$553$	193667.	−	26433.9i	0.633295	−	0.0864393i
$554$	876609.			2.85618
$555$	4267.39	+	27863.0i	0.0138540	+	0.0904569i
$556$	354631.	+	204746.i	1.14717	+	0.662317i
$557$	106067.	+	61237.6i	0.341876	+	0.197382i	0.661101	−	0.750297i	$-0.270089\pi$
$557$	106067.	+	61237.6i	0.341876	+	0.197382i	−0.319225	+	0.947679i	$0.603423\pi$
$558$	−128966.	−	223376.i	−0.414198	−	0.717411i
$559$		−	333544.i		−	1.06741i
$560$	−211899.	+	62686.5i	−0.675699	+	0.199893i
$561$	27197.5			0.0864177
$562$	−663765.	+	383225.i	−2.10156	+	1.21334i
$563$	−204736.	+	354614.i	−0.645919	+	1.11876i	0.338169	+	0.941085i	$0.390192\pi$
$563$	−204736.	+	354614.i	−0.645919	+	1.11876i	−0.984088	+	0.177680i	$0.943141\pi$
$564$	−12170.8	+	21080.4i	−0.0382613	+	0.0662706i
$565$	−62383.7	−	407321.i	−0.195422	−	1.27597i
$566$			541077.i			1.68899i
$567$	−113874.	−	146951.i	−0.354207	−	0.457096i
$568$			176314.i			0.546501i
$569$	124356.	+	215390.i	0.384097	+	0.665276i	0.991643	−	0.129009i	$-0.0411795\pi$
$569$	124356.	+	215390.i	0.384097	+	0.665276i	−0.607546	+	0.794284i	$0.707846\pi$
$570$	60551.7	+	75560.5i	0.186370	+	0.232565i
$571$	−19724.2	+	34163.3i	−0.0604960	+	0.104782i	−0.894687	−	0.446693i	$-0.852602\pi$
$571$	−19724.2	+	34163.3i	−0.0604960	+	0.104782i	0.834191	+	0.551475i	$0.185935\pi$
$572$	464563.	+	804647.i	1.41988	+	2.45931i
$573$	−33698.8			−0.102637
$574$	−836806.	+	114217.i	−2.53981	+	0.346662i
$575$	−182848.	+	198951.i	−0.553039	+	0.601743i
$576$	198825.	+	344375.i	0.599276	+	1.03798i
$577$	−189957.	+	329015.i	−0.570563	+	0.988244i	0.425946	+	0.904749i	$0.359942\pi$
$577$	−189957.	+	329015.i	−0.570563	+	0.988244i	−0.996508	+	0.0834948i	$0.973392\pi$
$578$	−423158.	−	244310.i	−1.26662	−	0.731284i
$579$	−9147.45	+	5281.28i	−0.0272862	+	0.0157537i
$580$	−116391.	+	298644.i	−0.345990	+	0.887764i
$581$	126366.	−	309225.i	0.374351	−	0.916055i
$582$			269074.i			0.794375i
$583$	−144600.	+	83485.1i	−0.425434	+	0.245624i
$584$	−36828.5	−	21262.9i	−0.107984	−	0.0623444i
$585$	278777.	+	347877.i	0.814601	+	1.01651i
$586$	−364775.	+	210603.i	−1.06226	+	0.613294i
$587$	400505.			1.16234			0.581168	−	0.813784i	$-0.302596\pi$
$587$	400505.			1.16234			0.581168	+	0.813784i	$0.302596\pi$
$588$	−41101.9	+	159442.i	−0.118880	+	0.461157i
$589$	116770.			0.336590
$590$	317463.	−	48621.4i	0.911988	−	0.139677i
$591$	39025.6	+	22531.5i	0.111731	+	0.0645081i
$592$	−50896.9	−	29385.3i	−0.145227	−	0.0838470i
$593$	124531.	+	215695.i	0.354135	+	0.613381i	0.986970	−	0.160907i	$-0.0514419\pi$
$593$	124531.	+	215695.i	0.354135	+	0.613381i	−0.632834	+	0.774287i	$0.718109\pi$
$594$		−	563937.i		−	1.59830i
$595$	38463.2	+	36525.9i	0.108646	+	0.103173i
$596$	−71068.9			−0.200072
$597$	7209.06	−	4162.16i	0.0202269	−	0.0116780i
$598$	334222.	−	578890.i	0.934616	−	1.61880i
$599$	−21439.9	+	37135.0i	−0.0597542	+	0.103497i	−0.894355	−	0.447358i	$-0.852365\pi$
$599$	−21439.9	+	37135.0i	−0.0597542	+	0.103497i	0.834601	+	0.550855i	$0.185698\pi$
$600$	48206.0	+	10762.0i	0.133905	+	0.0298944i
$601$			586850.i			1.62472i	0.583157	+	0.812359i	$0.301817\pi$
$601$			586850.i			1.62472i	−0.583157	+	0.812359i	$0.698183\pi$
$602$	−375124.	+	51201.2i	−1.03510	+	0.141282i
$603$			274708.i			0.755504i
$604$	22882.0	+	39632.8i	0.0627221	+	0.108638i
$605$	−286082.	−	356993.i	−0.781592	−	0.975323i
$606$	−43905.8	+	76047.0i	−0.119557	+	0.207079i
$607$	272798.	+	472501.i	0.740396	+	1.28240i	0.952315	+	0.305117i	$0.0986955\pi$
$607$	272798.	+	472501.i	0.740396	+	1.28240i	−0.211919	+	0.977287i	$0.567971\pi$
$608$	−270211.			−0.730964
$609$	−67205.3	−	86727.0i	−0.181205	−	0.233840i
$610$	148988.	−	382283.i	0.400398	−	1.02737i
$611$	−45849.9	−	79414.4i	−0.122816	−	0.212724i
$612$	29611.9	−	51289.2i	0.0790611	−	0.136938i
$613$	233424.	+	134768.i	0.621191	+	0.358645i	0.777333	−	0.629090i	$-0.216572\pi$
$613$	233424.	+	134768.i	0.621191	+	0.358645i	−0.156142	+	0.987735i	$0.549906\pi$
$614$	−491107.	+	283541.i	−1.30268	+	0.752105i
$615$	−232171.	−	90484.4i	−0.613843	−	0.239234i
$616$	160525.	−	124392.i	0.423040	−	0.327817i
$617$			44994.2i			0.118192i	0.998252	+	0.0590958i	$0.0188217\pi$
$617$			44994.2i			0.118192i	−0.998252	+	0.0590958i	$0.981178\pi$
$618$	213703.	−	123382.i	0.559544	−	0.323053i
$619$	521998.	+	301376.i	1.36235	+	0.786552i	0.989936	−	0.141516i	$-0.0451977\pi$
$619$	521998.	+	301376.i	1.36235	+	0.786552i	0.372411	+	0.928068i	$0.378531\pi$
$620$	241386.	−	193439.i	0.627956	−	0.503223i
$621$	−194396.	+	112235.i	−0.504086	+	0.291034i
$622$	109688.			0.283517
$623$	−10192.1	−	74672.2i	−0.0262596	−	0.192390i
$624$	161282.			0.414207
$625$	320644.	−	223104.i	0.820849	−	0.571146i
$626$	−365094.	−	210787.i	−0.931656	−	0.537892i
$627$	101724.	+	58730.3i	0.258755	+	0.149392i
$628$	−266001.	−	460727.i	−0.674472	−	1.16822i
$629$			14107.2i			0.0356566i
$630$	348449.	−	366931.i	0.877927	−	0.924492i
$631$	121034.			0.303981			0.151991	−	0.988382i	$-0.451432\pi$
$631$	121034.			0.303981			0.151991	+	0.988382i	$0.451432\pi$
$632$	78887.5	−	45545.7i	0.197503	−	0.114029i
$633$	−72371.2	+	125351.i	−0.180617	+	0.312838i
$634$	134915.	−	233679.i	0.335645	−	0.581355i
$635$	−60866.2	−	397413.i	−0.150948	−	0.985585i
$636$		−	63089.7i		−	0.155971i
$637$	−442761.	−	434422.i	−1.09117	−	1.07061i
$638$			702764.i			1.72651i
$639$	266466.	+	461533.i	0.652590	+	1.13032i
$640$	−221605.	+	177587.i	−0.541027	+	0.433561i
$641$	167682.	−	290434.i	0.408104	−	0.706857i	−0.586573	−	0.809896i	$-0.699523\pi$
$641$	167682.	−	290434.i	0.408104	−	0.706857i	0.994677	+	0.103039i	$0.0328567\pi$
$642$	−193954.	−	335939.i	−0.470576	−	0.815061i
$643$	−742309.			−1.79541			−0.897704	−	0.440600i	$-0.854766\pi$
$643$	−742309.			−1.79541			−0.897704	+	0.440600i	$0.854766\pi$
$644$	−388594.	−	158801.i	−0.936967	−	0.382897i
$645$	−104078.	−	40562.5i	−0.250172	−	0.0975001i
$646$	24230.1	+	41967.8i	0.0580618	+	0.100566i
$647$	338110.	−	585624.i	0.807699	−	1.39898i	−0.106755	−	0.994285i	$-0.534046\pi$
$647$	338110.	−	585624.i	0.807699	−	1.39898i	0.914454	−	0.404690i	$-0.132621\pi$
$648$	−75031.4	−	43319.4i	−0.178687	−	0.103165i
$649$	337400.	−	194798.i	0.801042	−	0.462482i
$650$	−653889.	+	711475.i	−1.54767	+	1.68396i
$651$	14319.9	+	104915.i	0.0337893	+	0.247556i
$652$		−	239837.i		−	0.564184i
$653$	422445.	−	243899.i	0.990704	−	0.571983i	0.0852197	−	0.996362i	$-0.472841\pi$
$653$	422445.	−	243899.i	0.990704	−	0.571983i	0.905485	+	0.424379i	$0.139507\pi$
$654$	312014.	+	180141.i	0.729488	+	0.421170i
$655$	338030.	−	270886.i	0.787903	−	0.631400i
$656$	449927.	−	259766.i	1.04553	−	0.603634i
$657$	−128540.			−0.297788
$658$	−82276.1	+	63756.3i	−0.190030	+	0.147255i
$659$	−555967.			−1.28020			−0.640101	−	0.768291i	$-0.721107\pi$
$659$	−555967.			−1.28020			−0.640101	+	0.768291i	$0.721107\pi$
$660$	307574.	−	47106.9i	0.706094	−	0.108143i
$661$	−244319.	−	141058.i	−0.559183	−	0.322845i	0.193634	−	0.981074i	$-0.437972\pi$
$661$	−244319.	−	141058.i	−0.559183	−	0.322845i	−0.752818	+	0.658229i	$0.771306\pi$
$662$	233903.	+	135044.i	0.533727	+	0.308147i
$663$	−19357.0	−	33527.3i	−0.0440363	−	0.0762732i
$664$		−	155676.i		−	0.353091i
$665$	64985.9	+	219672.i	0.146952	+	0.496743i
$666$	134580.			0.303411
$667$	242252.	−	139864.i	0.544522	−	0.314380i
$668$	132120.	−	228839.i	0.296085	−	0.512834i
$669$	−150849.	+	261279.i	−0.337048	+	0.583784i
$670$	−588599.	+	90147.5i	−1.31120	+	0.200819i
$671$		−	497711.i		−	1.10543i
$672$	−33137.0	−	242777.i	−0.0733794	−	0.537612i
$673$			410717.i			0.906802i	0.891307	+	0.453401i	$0.149789\pi$
$673$			410717.i			0.906802i	−0.891307	+	0.453401i	$0.850211\pi$
$674$	−620737.	−	1.07515e6i	−1.36643	−	2.36673i
$675$	309623.	−	97119.4i	0.679556	−	0.213156i
$676$	378300.	−	655236.i	0.827834	−	1.43385i
$677$	421978.	+	730887.i	0.920688	+	1.59468i	0.798353	+	0.602190i	$0.205705\pi$
$677$	421978.	+	730887.i	0.920688	+	1.59468i	0.122335	+	0.992489i	$0.460962\pi$
$678$	341382.			0.742646
$679$	−240813.	+	589281.i	−0.522325	+	1.27815i
$680$	23032.2	+	8976.40i	0.0498102	+	0.0194126i
$681$	−75012.1	−	129925.i	−0.161747	−	0.280155i
$682$	339113.	−	587361.i	0.729081	−	1.26281i
$683$	−677710.	−	391276.i	−1.45279	−	0.838768i	−0.454150	−	0.890925i	$-0.650057\pi$
$683$	−677710.	−	391276.i	−1.45279	−	0.838768i	−0.998639	+	0.0521574i	$0.983390\pi$
$684$	221509.	−	127888.i	0.473455	−	0.273349i
$685$	565643.	+	220449.i	1.20548	+	0.469816i
$686$	−420611.	+	564643.i	−0.893783	+	1.19985i
$687$		−	50418.3i		−	0.106825i
$688$	201694.	−	116448.i	0.426104	−	0.246011i
$689$	205830.	+	118836.i	0.433581	+	0.250328i
$690$	−139990.	−	174689.i	−0.294034	−	0.366916i
$691$	−654499.	+	377875.i	−1.37073	+	0.791393i	−0.991020	−	0.133711i	$-0.957311\pi$
$691$	−654499.	+	377875.i	−1.37073	+	0.791393i	−0.379713	+	0.925104i	$0.623977\pi$
$692$	−519103.			−1.08403
$693$	232207.	−	568222.i	0.483514	−	1.18318i
$694$	−67014.6			−0.139139
$695$	78212.5	+	510672.i	0.161922	+	1.05724i
$696$	−44281.6	−	25566.0i	−0.0914124	−	0.0527769i
$697$	−108000.	−	62353.7i	−0.222309	−	0.128350i
$698$	362390.	+	627678.i	0.743816	+	1.28833i
$699$			329133.i			0.673624i
$700$	498243.	+	346450.i	1.01682	+	0.707041i
$701$	434772.			0.884761			0.442380	−	0.896828i	$-0.354134\pi$
$701$	434772.			0.884761			0.442380	+	0.896828i	$0.354134\pi$
$702$	−695186.	+	401366.i	−1.41067	+	0.814453i
$703$	−30463.2	+	52763.9i	−0.0616404	+	0.106764i
$704$	−522806.	+	905526.i	−1.05486	+	1.82707i
$705$	−30356.0	+	4649.21i	−0.0610754	+	0.00935407i
$706$		−	881235.i		−	1.76800i
$707$	−164215.	+	127251.i	−0.328529	+	0.254579i
$708$			147209.i			0.293675i
$709$	19217.0	+	33284.9i	0.0382291	+	0.0662147i	0.884507	−	0.466527i	$-0.154495\pi$
$709$	19217.0	+	33284.9i	0.0382291	+	0.0662147i	−0.846278	+	0.532742i	$0.821162\pi$
$710$	−901453.	+	722395.i	−1.78824	+	1.43304i
$711$	137668.	−	238448.i	0.272329	−	0.471687i
$712$	−17561.0	−	30416.6i	−0.0346410	−	0.0600000i
$713$	−269961.			−0.531034
$714$	−34735.5	+	26916.7i	−0.0681360	+	0.0527990i
$715$	−425663.	+	1.09219e6i	−0.832633	+	2.13642i
$716$	−62582.5	−	108396.i	−0.122075	−	0.211440i
$717$	116018.	−	200949.i	0.225677	−	0.390884i
$718$	1.24279e6	+	717528.i	2.41074	+	1.39184i
$719$	76175.2	−	43979.8i	0.147352	−	0.0850737i	−0.424511	−	0.905423i	$-0.639554\pi$
$719$	76175.2	−	43979.8i	0.147352	−	0.0850737i	0.571863	+	0.820349i	$0.306221\pi$
$720$	−113033.	+	290028.i	−0.218042	+	0.559467i
$721$	578441.	−	78952.1i	1.11273	−	0.151877i
$722$		−	570631.i		−	1.09466i
$723$	−145919.	+	84246.1i	−0.279148	+	0.161166i
$724$	856721.	+	494628.i	1.63442	+	0.943630i
$725$	−385844.	+	121028.i	−0.734068	+	0.230255i
$726$	328225.	−	189501.i	0.622728	−	0.359532i
$727$	121358.			0.229615			0.114807	−	0.993388i	$-0.463375\pi$
$727$	121358.			0.229615			0.114807	+	0.993388i	$0.463375\pi$
$728$	−267592.	−	109353.i	−0.504905	−	0.206332i
$729$	−116334.			−0.218904
$730$	−42181.3	−	275414.i	−0.0791543	−	0.516821i
$731$	−48414.3	−	27952.0i	−0.0906023	−	0.0523092i
$732$	162865.	+	94030.0i	0.303952	+	0.175487i
$733$	−295020.	−	510989.i	−0.549090	−	0.951051i	−0.998337	−	0.0576440i	$-0.981641\pi$
$733$	−295020.	−	510989.i	−0.549090	−	0.951051i	0.449247	−	0.893407i	$-0.351692\pi$
$734$			552784.i			1.02604i
$735$	−189400.	+	85327.2i	−0.350594	+	0.157948i
$736$	624702.			1.15323
$737$	−625563.	+	361169.i	−1.15169	+	0.664929i
$738$	−594841.	+	1.03029e6i	−1.09216	+	1.89168i
$739$	263193.	−	455864.i	0.481932	−	0.834730i	−0.517853	−	0.855469i	$-0.673269\pi$
$739$	263193.	−	455864.i	0.481932	−	0.834730i	0.999785	+	0.0207394i	$0.00660202\pi$
$740$	24434.2	+	159538.i	0.0446205	+	0.291340i
$741$		−	167198.i		−	0.304506i
$742$	102054.	−	249732.i	0.185363	−	0.453592i
$743$		−	763557.i		−	1.38313i	−0.722313	−	0.691566i	$-0.756921\pi$
$743$		−	763557.i		−	1.38313i	0.722313	−	0.691566i	$-0.243079\pi$
$744$	24673.3	+	42735.4i	0.0445740	+	0.0772044i
$745$	−56070.0	−	69967.9i	−0.101022	−	0.126063i
$746$	−187151.	+	324155.i	−0.336290	+	0.582472i
$747$	−235276.	−	407510.i	−0.421634	−	0.730292i
$748$	155727.			0.278331
$749$	−124112.	−	909301.i	−0.221233	−	1.62085i
$750$	142486.	+	290560.i	0.253308	+	0.516551i
$751$	−100488.	−	174050.i	−0.178170	−	0.308599i	0.763084	−	0.646300i	$-0.223684\pi$
$751$	−100488.	−	174050.i	−0.178170	−	0.308599i	−0.941254	+	0.337700i	$0.890351\pi$
$752$	32014.6	−	55450.8i	0.0566124	−	0.0980556i
$753$	−62695.5	−	36197.3i	−0.110572	−	0.0638390i
$754$	866324.	−	500172.i	1.52383	−	0.879786i
$755$	−20966.0	+	53795.9i	−0.0367809	+	0.0943747i
$756$	308788.	+	398484.i	0.540278	+	0.697216i
$757$		−	91627.6i		−	0.159895i	−0.996799	−	0.0799474i	$-0.974525\pi$
$757$		−	91627.6i		−	0.159895i	0.996799	−	0.0799474i	$-0.0254752\pi$
$758$	510898.	−	294967.i	0.889192	−	0.513375i
$759$	−235176.	−	135779.i	−0.408234	−	0.235694i
$760$	66761.5	+	83309.5i	0.115584	+	0.144234i
$761$	98668.1	−	56966.0i	0.170376	−	0.0983664i	−0.412387	−	0.911009i	$-0.635305\pi$
$761$	98668.1	−	56966.0i	0.170376	−	0.0983664i	0.582763	+	0.812642i	$0.301972\pi$
$762$	333078.			0.573636
$763$	522100.	+	673758.i	0.896819	+	1.15732i
$764$	−192952.			−0.330570
$765$	73857.0	−	11311.7i	0.126203	−	0.0193287i
$766$	−1.24686e6	−	719874.i	−2.12500	−	1.22687i
$767$	−480269.	−	277283.i	−0.816383	−	0.471339i
$768$	41870.3	+	72521.5i	0.0709878	+	0.122954i
$769$		−	667207.i		−	1.12826i	−0.825687	−	0.564128i	$-0.809212\pi$
$769$		−	667207.i		−	1.12826i	0.825687	−	0.564128i	$-0.190788\pi$
$770$	1.29369e6	+	311068.i	2.18197	+	0.524655i
$771$	14773.0			0.0248520
$772$	−52376.4	+	30239.5i	−0.0878823	+	0.0507388i
$773$	−81777.7	+	141643.i	−0.136860	+	0.237048i	−0.926306	−	0.376771i	$-0.877034\pi$
$773$	−81777.7	+	141643.i	−0.136860	+	0.237048i	0.789447	+	0.613819i	$0.210368\pi$
$774$	−266656.	+	461862.i	−0.445112	+	0.770957i
$775$	380885.	+	85032.6i	0.634147	+	0.141574i
$776$			296668.i			0.492661i
$777$	−51142.7	−	20899.7i	−0.0847113	−	0.0346177i
$778$		−	266977.i		−	0.441077i
$779$	−269294.	−	466431.i	−0.443764	−	0.768621i
$780$	−276978.	−	345631.i	−0.455256	−	0.568099i
$781$	−700666.	+	1.21359e6i	−1.14871	+	1.98962i
$782$	−56017.7	−	97025.5i	−0.0916035	−	0.158662i
$783$	−335924.			−0.547921
$784$	108116.	−	419404.i	0.175897	−	0.682339i
$785$	243728.	−	625372.i	0.395517	−	1.01484i
$786$	179435.	+	310790.i	0.290444	+	0.503063i
$787$	189785.	−	328717.i	0.306416	−	0.530728i	−0.671159	−	0.741313i	$-0.734203\pi$
$787$	189785.	−	328717.i	0.306416	−	0.530728i	0.977576	+	0.210585i	$0.0675367\pi$
$788$	223453.	+	129011.i	0.359860	+	0.207765i
$789$	4182.12	−	2414.55i	0.00671804	−	0.00387866i
$790$	556083.	+	216723.i	0.891015	+	0.347257i
$791$	747639.	+	305527.i	1.19492	+	0.488311i
$792$		−	286066.i		−	0.456054i
$793$	−613546.	+	354231.i	−0.975666	+	0.563301i
$794$	1.06721e6	+	616154.i	1.69281	+	0.977346i
$795$	62112.3	−	49774.7i	0.0982750	−	0.0787544i
$796$	41277.6	−	23831.7i	0.0651462	−	0.0376121i
$797$	513623.			0.808589			0.404294	−	0.914629i	$-0.367517\pi$
$797$	513623.			0.808589			0.404294	+	0.914629i	$0.367517\pi$
$798$	−188042.	+	25666.1i	−0.295290	+	0.0403045i
$799$	−15369.5			−0.0240749
$800$	−881384.	−	196769.i	−1.37716	−	0.307452i
$801$	−91938.2	−	53080.5i	−0.143295	−	0.0827314i
$802$	−663367.	−	382995.i	−1.03135	−	0.595449i
$803$	−168996.	−	292710.i	−0.262087	−	0.453948i
$804$		−	272935.i		−	0.422228i
$805$	−150241.	−	507861.i	−0.231845	−	0.783705i
$806$	−965416.			−1.48609
$807$	−104514.	+	60341.3i	−0.160483	+	0.0926548i
$808$	−48408.4	+	83845.9i	−0.0741478	+	0.128428i
$809$	−524794.	+	908970.i	−0.801848	+	1.38884i	0.116551	+	0.993185i	$0.462816\pi$
$809$	−524794.	+	908970.i	−0.801848	+	1.38884i	−0.918399	+	0.395656i	$0.870517\pi$
$810$	−85936.8	−	561106.i	−0.130981	−	0.855214i
$811$			574256.i			0.873100i	0.899680	+	0.436550i	$0.143800\pi$
$811$			574256.i			0.873100i	−0.899680	+	0.436550i	$0.856200\pi$
$812$	−384804.	−	496581.i	−0.583617	−	0.753144i
$813$			64186.1i			0.0971091i
$814$	176937.	+	306464.i	0.267036	+	0.462520i
$815$	236121.	−	189220.i	0.355484	−	0.284873i
$816$	13516.0	−	23410.3i	0.0202986	−	0.0351582i
$817$	−120719.	−	209092.i	−0.180856	−	0.313252i
$818$	1.64668e6			2.46094
$819$	−865734.	+	118165.i	−1.29067	+	0.176166i
$820$	−1.32936e6	−	518095.i	−1.97704	−	0.770517i
$821$	1036.00	+	1794.40i	0.00153700	+	0.00266216i	0.866793	−	0.498668i	$-0.166177\pi$
$821$	1036.00	+	1794.40i	0.00153700	+	0.00266216i	−0.865256	+	0.501330i	$0.832844\pi$
$822$	−251471.	+	435560.i	−0.372172	+	0.644622i
$823$	−66882.1	−	38614.4i	−0.0987439	−	0.0570098i	0.449815	−	0.893122i	$-0.351490\pi$
$823$	−66882.1	−	38614.4i	−0.0987439	−	0.0570098i	−0.548559	+	0.836112i	$0.684823\pi$
$824$	235619.	−	136035.i	0.347022	−	0.200353i
$825$	289039.	+	265644.i	0.424667	+	0.390295i
$826$	−238126.	+	582705.i	−0.349016	+	0.854060i
$827$			74490.6i			0.108916i	0.998516	+	0.0544579i	$0.0173431\pi$
$827$			74490.6i			0.108916i	−0.998516	+	0.0544579i	$0.982657\pi$
$828$	−512106.	+	295665.i	−0.746964	+	0.431260i
$829$	−686420.	−	396305.i	−0.998805	−	0.576660i	−0.0909103	−	0.995859i	$-0.528978\pi$
$829$	−686420.	−	396305.i	−0.998805	−	0.576660i	−0.907894	+	0.419199i	$0.862311\pi$
$830$	795936.	−	637837.i	1.15537	−	0.925877i
$831$	−439008.	+	253462.i	−0.635727	+	0.367037i
$832$	1.48837e6			2.15012
$833$	−100162.	+	27861.4i	−0.144348	+	0.0401526i
$834$	−428002.			−0.615339
$835$	329530.	−	50469.5i	0.472631	−	0.0723863i
$836$	582451.	+	336278.i	0.833387	+	0.481156i
$837$	280761.	+	162097.i	0.400761	+	0.231380i
$838$	−291306.	−	504557.i	−0.414822	−	0.718492i
$839$		−	602242.i		−	0.855554i	−0.903884	−	0.427777i	$-0.859297\pi$
$839$		−	602242.i		−	0.855554i	0.903884	−	0.427777i	$-0.140703\pi$
$840$	−66664.0	+	70199.8i	−0.0944785	+	0.0994895i
$841$	−288660.			−0.408127
$842$	473340.	−	273283.i	0.667651	−	0.385468i
$843$	221610.	−	383840.i	0.311842	−	0.540126i
$844$	−414383.	+	717732.i	−0.581724	+	1.00758i
$845$	943546.	−	144510.i	1.32145	−	0.202388i
$846$			146621.i			0.204859i
$847$	888421.	−	121262.i	1.23837	−	0.169027i
$848$			165954.i			0.230779i
$849$	−156446.	−	270973.i	−0.217045	−	0.375933i
$850$	48473.4	+	154536.i	0.0670913	+	0.213891i
$851$	70428.1	−	121985.i	0.0972493	−	0.168441i
$852$	−264747.	−	458555.i	−0.364713	−	0.631702i
$853$	−1.14242e6			−1.57010			−0.785049	−	0.619434i	$-0.787362\pi$
$853$	−1.14242e6			−1.57010			−0.785049	+	0.619434i	$0.787362\pi$
$854$	492574.	+	635655.i	0.675391	+	0.871578i
$855$	300666.	+	117179.i	0.411294	+	0.160295i
$856$	−213845.	−	370390.i	−0.291845	−	0.505490i
$857$	−212306.	+	367726.i	−0.289069	+	0.500682i	−0.973588	−	0.228313i	$-0.926679\pi$
$857$	−212306.	+	367726.i	−0.289069	+	0.500682i	0.684519	+	0.728995i	$0.260012\pi$
$858$	−841019.	−	485563.i	−1.14243	−	0.659585i
$859$	893686.	−	515970.i	1.21115	−	0.699259i	0.248142	−	0.968724i	$-0.420180\pi$
$859$	893686.	−	515970.i	1.21115	−	0.699259i	0.963010	+	0.269465i	$0.0868467\pi$
$860$	−595929.	−	232253.i	−0.805744	−	0.314025i
$861$	386050.	−	299153.i	0.520760	−	0.403541i
$862$		−	562016.i		−	0.756370i
$863$	−319161.	+	184268.i	−0.428538	+	0.247416i	−0.698723	−	0.715392i	$-0.746248\pi$
$863$	−319161.	+	184268.i	−0.428538	+	0.247416i	0.270186	+	0.962808i	$0.412915\pi$
$864$	−649694.	−	375101.i	−0.870324	−	0.502482i
$865$	−409547.	−	511061.i	−0.547359	−	0.683031i
$866$	189264.	−	109271.i	0.252366	−	0.145704i
$867$	282559.			0.375898
$868$	81993.1	+	600720.i	0.108827	+	0.797320i
$869$	723988.			0.958720
$870$	−50717.7	−	331150.i	−0.0670072	−	0.437509i
$871$	890452.	+	514103.i	1.17375	+	0.677663i
$872$	344012.	+	198615.i	0.452418	+	0.261204i
$873$	448359.	+	776581.i	0.588298	+	1.01896i
$874$		−	483860.i		−	0.633427i
$875$	52007.0	+	763857.i	0.0679275	+	0.997690i
$876$	127710.			0.166425
$877$	−460418.	+	265823.i	−0.598623	+	0.345615i	−0.768500	−	0.639850i	$-0.778996\pi$
$877$	−460418.	+	265823.i	−0.598623	+	0.345615i	0.169877	+	0.985465i	$0.445663\pi$
$878$	389869.	−	675274.i	0.505743	−	0.875973i
$879$	121787.	−	210941.i	0.157624	−	0.273013i
$880$	−809058.	+	123912.i	−1.04475	+	0.160010i
$881$			713931.i			0.919823i	0.887965	+	0.459912i	$0.152119\pi$
$881$			713931.i			0.919823i	−0.887965	+	0.459912i	$0.847881\pi$
$882$	265792.	+	955519.i	0.341668	+	1.22829i
$883$			242866.i			0.311491i	0.987797	+	0.155745i	$0.0497780\pi$
$883$			242866.i			0.311491i	−0.987797	+	0.155745i	$0.950222\pi$
$884$	−110834.	−	191971.i	−0.141830	−	0.245658i
$885$	−144928.	+	116141.i	−0.185040	+	0.148285i
$886$	107587.	−	186345.i	0.137054	−	0.237384i
$887$	−117855.	−	204131.i	−0.149796	−	0.259454i	0.781356	−	0.624086i	$-0.214528\pi$
$887$	−117855.	−	204131.i	−0.149796	−	0.259454i	−0.931152	+	0.364631i	$0.881195\pi$
$888$	−25747.3			−0.0326517
$889$	729453.	+	298095.i	0.922983	+	0.377182i
$890$	83561.9	−	214409.i	0.105494	−	0.270684i
$891$	−344299.	−	596343.i	−0.433691	−	0.751175i
$892$	−863733.	+	1.49603e6i	−1.08555	+	1.88023i
$893$	−57484.8	−	33188.9i	−0.0720859	−	0.0416188i
$894$	64329.6	−	37140.7i	0.0804889	−	0.0464703i
$895$	57342.2	−	147132.i	0.0715861	−	0.183680i
$896$	−75273.7	−	551491.i	−0.0937621	−	0.686946i
$897$			386547.i			0.480416i
$898$	−34173.5	+	19730.1i	−0.0423777	+	0.0244668i
$899$	−349878.	−	202002.i	−0.432909	−	0.249940i
$900$	815653.	−	255846.i	1.00698	−	0.315859i
$901$	34498.4	−	19917.7i	0.0424961	−	0.0245352i
$902$	−3.12824e6			−3.84491
$903$	173059.	−	134105.i	0.212236	−	0.164463i
$904$	376392.			0.460578
$905$	188947.	+	1.23369e6i	0.230697	+	1.50629i
$906$	−41424.3	−	23916.4i	−0.0504660	−	0.0291366i
$907$	840698.	+	485377.i	1.02194	+	0.590017i	0.914665	−	0.404212i	$-0.132454\pi$
$907$	840698.	+	485377.i	1.02194	+	0.590017i	0.107275	+	0.994229i	$0.465788\pi$
$908$	−429504.	−	743923.i	−0.520950	−	0.902311i
$909$			292641.i			0.354167i
$910$	−537282.	−	1.81617e6i	−0.648813	−	2.19318i
$911$	123274.			0.148537			0.0742685	−	0.997238i	$-0.476338\pi$
$911$	123274.			0.148537			0.0742685	+	0.997238i	$0.476338\pi$
$912$	101105.	−	58372.9i	0.121558	−	0.0701813i
$913$	618651.	−	1.07154e6i	0.742172	−	1.28548i
$914$	51363.1	−	88963.4i	0.0614835	−	0.106493i
$915$	35919.2	+	234527.i	0.0429027	+	0.280124i
$916$		−	288685.i		−	0.344059i
$917$	114821.	+	841230.i	0.136547	+	1.00041i
$918$			134543.i			0.159652i
$919$	−58146.1	−	100712.i	−0.0688477	−	0.119248i	0.829547	−	0.558437i	$-0.188599\pi$
$919$	−58146.1	−	100712.i	−0.0688477	−	0.119248i	−0.898394	+	0.439190i	$0.855266\pi$
$920$	−154346.	−	192603.i	−0.182356	−	0.227556i
$921$	163965.	−	283996.i	0.193300	−	0.334806i
$922$	675665.	+	1.17029e6i	0.794822	+	1.37667i
$923$	1.99471e6			2.34141
$924$	−230708.	+	564554.i	−0.270221	+	0.661244i
$925$	−137789.	+	149923.i	−0.161039	+	0.175221i
$926$	386091.	+	668729.i	0.450264	+	0.779880i
$927$	411183.	−	712190.i	0.478493	−	0.828774i
$928$	809632.	+	467441.i	0.940138	+	0.542789i
$929$	−1.04959e6	+	605984.i	−1.21616	+	0.702150i	−0.964094	−	0.265561i	$-0.914443\pi$
$929$	−1.04959e6	+	605984.i	−1.21616	+	0.702150i	−0.252065	+	0.967710i	$0.581110\pi$
$930$	−117405.	+	301245.i	−0.135744	+	0.348300i
$931$	−434788.	−	112082.i	−0.501624	−	0.129311i
$932$			1.88455e6i			2.16958i
$933$	−54932.2	+	31715.1i	−0.0631050	+	0.0364337i
$934$	1.25499e6	+	724571.i	1.43863	+	0.830591i
$935$	122861.	+	153315.i	0.140537	+	0.175372i
$936$	−352644.	+	203599.i	−0.402518	+	0.232394i
$937$	−1.04032e6			−1.18491			−0.592456	−	0.805603i	$-0.701842\pi$
$937$	−1.04032e6			−1.18491			−0.592456	+	0.805603i	$0.701842\pi$
$938$	441501.	−	1.08038e6i	0.501795	−	1.22792i
$939$	243787.			0.276490
$940$	−173812.	+	26620.4i	−0.196709	+	0.0301272i
$941$	−176350.	−	101816.i	−0.199157	−	0.114983i	0.397105	−	0.917773i	$-0.370015\pi$
$941$	−176350.	−	101816.i	−0.199157	−	0.114983i	−0.596262	+	0.802790i	$0.703348\pi$
$942$	481553.	+	278025.i	0.542679	+	0.313316i
$943$	622582.	+	1.07834e6i	0.700121	+	1.21265i
$944$		−	387224.i		−	0.434529i
$945$	−148692.	+	618389.i	−0.166504	+	0.692466i
$946$	−1.40233e6			−1.56700
$947$	807088.	−	465972.i	0.899955	−	0.519589i	0.0227695	−	0.999741i	$-0.492752\pi$
$947$	807088.	−	465972.i	0.899955	−	0.519589i	0.877186	+	0.480151i	$0.159418\pi$
$948$	−136779.	+	236909.i	−0.152196	+	0.263612i
$949$	−240556.	+	416655.i	−0.267106	+	0.462641i
$950$	−152407.	+	682671.i	−0.168872	+	0.756422i
$951$			156036.i			0.172530i
$952$	−38297.7	+	29677.1i	−0.0422570	+	0.0327452i
$953$		−	336208.i		−	0.370188i	−0.982721	−	0.185094i	$-0.940741\pi$
$953$		−	336208.i		−	0.370188i	0.982721	−	0.185094i	$-0.0592590\pi$
$954$	−190010.	−	329107.i	−0.208776	−	0.361610i
$955$	−152230.	−	189963.i	−0.166915	−	0.208287i
$956$	664297.	−	1.15060e6i	0.726853	−	1.25895i
$957$	−203197.	−	351947.i	−0.221867	−	0.384285i
$958$	−2.23996e6			−2.44067
$959$	−940544.	+	728834.i	−1.02268	+	0.792485i
$960$	181001.	−	464424.i	0.196399	−	0.503932i
$961$	−266812.	−	462132.i	−0.288907	−	0.500402i
$962$	251860.	−	436234.i	0.272150	−	0.471378i
$963$	−1.11955e6	−	646374.i	−1.20724	−	0.696998i
$964$	−835500.	+	482376.i	−0.899068	+	0.519077i
$965$	−71093.6	−	27707.5i	−0.0763441	−	0.0297538i
$966$	434734.	−	59337.5i	0.465875	−	0.0635879i
$967$			849675.i			0.908656i	0.890834	+	0.454328i	$0.150121\pi$
$967$			849675.i			0.908656i	−0.890834	+	0.454328i	$0.849879\pi$
$968$	361885.	−	208935.i	0.386207	−	0.222977i
$969$	−24269.0	−	14011.7i	−0.0258467	−	0.0149226i
$970$	−1.51680e6	+	1.21551e6i	−1.61207	+	1.29186i
$971$	543840.	−	313986.i	0.576809	−	0.333021i	−0.183055	−	0.983103i	$-0.558599\pi$
$971$	543840.	−	313986.i	0.576809	−	0.333021i	0.759864	+	0.650082i	$0.225265\pi$
$972$	1.09353e6			1.15744
$973$	−937340.	−	383049.i	−0.990083	−	0.404603i
$974$	405262.			0.427187
$975$	121755.	−	545374.i	0.128079	−	0.573700i
$976$	−428407.	−	247341.i	−0.449735	−	0.259655i
$977$	−7902.87	−	4562.72i	−0.00827934	−	0.00478008i	0.495855	−	0.868406i	$-0.334855\pi$
$977$	−7902.87	−	4562.72i	−0.00827934	−	0.00478008i	−0.504134	+	0.863625i	$0.668188\pi$
$978$	125339.	+	217094.i	0.131041	+	0.226970i
$979$		−	279148.i		−	0.291252i
$980$	−1.08446e6	+	488566.i	−1.12918	+	0.508711i
$981$	1.20068e6			1.24764
$982$	2.17224e6	−	1.25414e6i	2.25260	−	1.30054i
$983$	−311158.	+	538941.i	−0.322013	+	0.557743i	−0.980903	−	0.194496i	$-0.937693\pi$
$983$	−311158.	+	538941.i	−0.322013	+	0.557743i	0.658890	+	0.752239i	$0.271026\pi$
$984$	113803.	−	197112.i	0.117534	−	0.203574i
$985$	49281.7	+	321774.i	0.0507941	+	0.331649i
$986$		−	167664.i		−	0.172459i
$987$	22769.7	−	55718.6i	0.0233735	−	0.0571960i
$988$		−	957345.i		−	0.980741i
$989$	279092.	+	483401.i	0.285335	+	0.494214i
$990$	1.46259e6	−	1.17207e6i	1.49228	−	1.19587i
$991$	585886.	−	1.01478e6i	0.596576	−	1.03330i	−0.396747	−	0.917928i	$-0.629861\pi$
$991$	585886.	−	1.01478e6i	0.596576	−	1.03330i	0.993322	−	0.115371i	$-0.0368058\pi$
$992$	−451120.	−	781362.i	−0.458425	−	0.794016i
$993$	−156186.			−0.158395
$994$	−306202.	−	2.24338e6i	−0.309910	−	2.27054i
$995$	56028.6	+	21836.1i	0.0565931	+	0.0220561i
$996$	233757.	+	404880.i	0.235639	+	0.408138i
$997$	−691910.	+	1.19842e6i	−0.696080	+	1.20565i	0.273735	+	0.961805i	$0.411741\pi$
$997$	−691910.	+	1.19842e6i	−0.696080	+	1.20565i	−0.969815	+	0.243841i	$0.921592\pi$
$998$	−9499.70	−	5484.66i	−0.00953782	−	0.00550666i
$999$	−146491.	+	84576.7i	−0.146784	+	0.0847461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.i.a.24.2	yes	28
5.2	odd	4		175.5.i.e.101.2		28
5.3	odd	4		175.5.i.e.101.13		28
5.4	even	2	inner	35.5.i.a.24.13	yes	28
7.3	odd	6		245.5.c.a.244.9		28
7.4	even	3		245.5.c.a.244.19		28
7.5	odd	6	inner	35.5.i.a.19.13	yes	28
35.4	even	6		245.5.c.a.244.10		28
35.12	even	12		175.5.i.e.26.2		28
35.19	odd	6	inner	35.5.i.a.19.2	✓	28
35.24	odd	6		245.5.c.a.244.20		28
35.33	even	12		175.5.i.e.26.13		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.i.a.19.2	✓	28	35.19	odd	6	inner
35.5.i.a.19.13	yes	28	7.5	odd	6	inner
35.5.i.a.24.2	yes	28	1.1	even	1	trivial
35.5.i.a.24.13	yes	28	5.4	even	2	inner
175.5.i.e.26.2		28	35.12	even	12
175.5.i.e.26.13		28	35.33	even	12
175.5.i.e.101.2		28	5.2	odd	4
175.5.i.e.101.13		28	5.3	odd	4
245.5.c.a.244.9		28	7.3	odd	6
245.5.c.a.244.10		28	35.4	even	6
245.5.c.a.244.19		28	7.4	even	3
245.5.c.a.244.20		28	35.24	odd	6

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.18283 + 2.99231i) q^{2} +(1.73039 - 2.99712i) q^{3} +(9.90784 - 17.1609i) q^{4} +(24.7118 - 3.78477i) q^{5} +20.7114i q^{6} +(-18.5361 + 45.3587i) q^{7} +22.8354i q^{8} +(34.5115 + 59.7757i) q^{9} +O(q^{10})\)	\(q+(-5.18283 + 2.99231i) q^{2} +(1.73039 - 2.99712i) q^{3} +(9.90784 - 17.1609i) q^{4} +(24.7118 - 3.78477i) q^{5} +20.7114i q^{6} +(-18.5361 + 45.3587i) q^{7} +22.8354i q^{8} +(34.5115 + 59.7757i) q^{9} +(-116.752 + 93.5614i) q^{10} +(-90.7471 + 157.179i) q^{11} +(-34.2888 - 59.3899i) q^{12} +258.347 q^{13} +(-39.6579 - 290.552i) q^{14} +(31.4176 - 80.6134i) q^{15} +(90.1948 + 156.222i) q^{16} +(21.6502 - 37.4993i) q^{17} +(-357.735 - 206.538i) q^{18} +(161.952 - 93.5032i) q^{19} +(179.891 - 461.576i) q^{20} +(103.871 + 134.043i) q^{21} -1086.17i q^{22} +(-374.418 + 216.170i) q^{23} +(68.4405 + 39.5141i) q^{24} +(596.351 - 187.057i) q^{25} +(-1338.97 + 773.053i) q^{26} +519.196 q^{27} +(594.743 + 767.503i) q^{28} -647.009 q^{29} +(78.3880 + 511.817i) q^{30} +(540.761 + 312.209i) q^{31} +(-1251.35 - 722.465i) q^{32} +(314.055 + 543.960i) q^{33} +259.137i q^{34} +(-286.389 + 1191.05i) q^{35} +1367.74 q^{36} +(-282.150 + 162.899i) q^{37} +(-559.581 + 969.223i) q^{38} +(447.039 - 774.295i) q^{39} +(86.4269 + 564.306i) q^{40} -2880.05i q^{41} +(-939.443 - 383.909i) q^{42} -1291.07i q^{43} +(1798.22 + 3114.60i) q^{44} +(1079.08 + 1346.55i) q^{45} +(1293.70 - 2240.75i) q^{46} +(-177.475 - 307.395i) q^{47} +624.287 q^{48} +(-1713.83 - 1681.55i) q^{49} +(-2531.05 + 2753.95i) q^{50} +(-74.9265 - 129.777i) q^{51} +(2559.66 - 4433.46i) q^{52} +(796.722 + 459.987i) q^{53} +(-2690.91 + 1553.59i) q^{54} +(-1647.64 + 4227.63i) q^{55} +(-1035.79 - 423.280i) q^{56} -647.187i q^{57} +(3353.34 - 1936.05i) q^{58} +(-1859.01 - 1073.30i) q^{59} +(-1072.12 - 1337.86i) q^{60} +(-2374.90 + 1371.15i) q^{61} -3736.90 q^{62} +(-3351.06 + 457.390i) q^{63} +5761.13 q^{64} +(6384.22 - 977.782i) q^{65} +(-3255.39 - 1879.50i) q^{66} +(3446.74 + 1989.97i) q^{67} +(-429.014 - 743.074i) q^{68} +1496.23i q^{69} +(-2079.69 - 7029.99i) q^{70} +7721.08 q^{71} +(-1365.00 + 788.086i) q^{72} +(-931.137 + 1612.78i) q^{73} +(974.891 - 1688.56i) q^{74} +(471.285 - 2111.02i) q^{75} -3705.66i q^{76} +(-5447.32 - 7029.65i) q^{77} +5350.72i q^{78} +(-1994.52 - 3454.61i) q^{79} +(2820.14 + 3519.17i) q^{80} +(-1897.02 + 3285.74i) q^{81} +(8618.00 + 14926.8i) q^{82} -6817.31 q^{83} +(3329.43 - 454.439i) q^{84} +(393.091 - 1008.62i) q^{85} +(3863.29 + 6691.42i) q^{86} +(-1119.58 + 1939.16i) q^{87} +(-3589.24 - 2072.25i) q^{88} +(-1331.99 + 769.026i) q^{89} +(-9621.99 - 3750.00i) q^{90} +(-4788.73 + 11718.3i) q^{91} +8567.13i q^{92} +(1871.45 - 1080.48i) q^{93} +(1839.64 + 1062.12i) q^{94} +(3648.25 - 2923.59i) q^{95} +(-4330.63 + 2500.29i) q^{96} +12991.6 q^{97} +(13914.2 + 3586.88i) q^{98} -12527.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9}+O(q^{10}) \) 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9	\( 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9} + 390 q^{10} + 34 q^{11} - 258 q^{14} + 60 q^{15} - 206 q^{16} + 366 q^{19} - 1116 q^{21} - 288 q^{24} + 40 q^{25} + 474 q^{26} + 856 q^{29} - 1620 q^{30} - 5520 q^{31} - 2620 q^{35} + 11892 q^{36} + 1656 q^{39} + 6510 q^{40} - 1082 q^{44} + 7920 q^{45} - 5442 q^{46} + 8356 q^{49} - 15960 q^{50} - 2976 q^{51} + 4392 q^{54} + 11640 q^{56} - 13920 q^{59} - 5700 q^{60} - 24960 q^{61} - 45596 q^{64} + 5290 q^{65} + 10332 q^{66} - 26400 q^{70} + 38272 q^{71} + 31806 q^{74} + 41310 q^{75} + 22028 q^{79} + 48000 q^{80} - 29238 q^{81} + 62784 q^{84} - 33820 q^{85} - 21180 q^{86} - 12516 q^{89} + 4448 q^{91} - 89418 q^{94} - 28890 q^{95} - 27900 q^{96} - 3108 q^{99}+O(q^{100}) \) 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9 + 390 * q^10 + 34 * q^11 - 258 * q^14 + 60 * q^15 - 206 * q^16 + 366 * q^19 - 1116 * q^21 - 288 * q^24 + 40 * q^25 + 474 * q^26 + 856 * q^29 - 1620 * q^30 - 5520 * q^31 - 2620 * q^35 + 11892 * q^36 + 1656 * q^39 + 6510 * q^40 - 1082 * q^44 + 7920 * q^45 - 5442 * q^46 + 8356 * q^49 - 15960 * q^50 - 2976 * q^51 + 4392 * q^54 + 11640 * q^56 - 13920 * q^59 - 5700 * q^60 - 24960 * q^61 - 45596 * q^64 + 5290 * q^65 + 10332 * q^66 - 26400 * q^70 + 38272 * q^71 + 31806 * q^74 + 41310 * q^75 + 22028 * q^79 + 48000 * q^80 - 29238 * q^81 + 62784 * q^84 - 33820 * q^85 - 21180 * q^86 - 12516 * q^89 + 4448 * q^91 - 89418 * q^94 - 28890 * q^95 - 27900 * q^96 - 3108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more