LMFDB - Embedded newform 77.5.d.a.34.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,5,Mod(34,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("77.34");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	77.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:	$7.95948715746$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.16
Character	$\chi$	$=$	77.34
Dual form			77.5.d.a.34.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.518092 q^{2} +16.0828i q^{3} -15.7316 q^{4} +43.3519i q^{5} -8.33238i q^{6} +(46.5272 - 15.3694i) q^{7} +16.4399 q^{8} -177.657 q^{9} +O(q^{10})$	\(q-0.518092 q^{2} +16.0828i q^{3} -15.7316 q^{4} +43.3519i q^{5} -8.33238i q^{6} +(46.5272 - 15.3694i) q^{7} +16.4399 q^{8} -177.657 q^{9} -22.4603i q^{10} +36.4829 q^{11} -253.008i q^{12} -15.1645i q^{13} +(-24.1054 + 7.96276i) q^{14} -697.221 q^{15} +243.188 q^{16} -377.577i q^{17} +92.0428 q^{18} +597.788i q^{19} -681.994i q^{20} +(247.183 + 748.289i) q^{21} -18.9015 q^{22} +438.616 q^{23} +264.400i q^{24} -1254.39 q^{25} +7.85661i q^{26} -1554.52i q^{27} +(-731.947 + 241.785i) q^{28} -558.459 q^{29} +361.224 q^{30} +523.369i q^{31} -389.032 q^{32} +586.748i q^{33} +195.620i q^{34} +(666.293 + 2017.04i) q^{35} +2794.83 q^{36} -3.57104 q^{37} -309.709i q^{38} +243.888 q^{39} +712.700i q^{40} -468.590i q^{41} +(-128.064 - 387.682i) q^{42} +1498.38 q^{43} -573.933 q^{44} -7701.78i q^{45} -227.243 q^{46} +1212.53i q^{47} +3911.15i q^{48} +(1928.56 - 1430.19i) q^{49} +649.887 q^{50} +6072.50 q^{51} +238.562i q^{52} +221.280 q^{53} +805.385i q^{54} +1581.60i q^{55} +(764.901 - 252.671i) q^{56} -9614.12 q^{57} +289.333 q^{58} -1596.34i q^{59} +10968.4 q^{60} +4561.91i q^{61} -271.153i q^{62} +(-8265.90 + 2730.49i) q^{63} -3689.45 q^{64} +657.410 q^{65} -303.989i q^{66} -4460.95 q^{67} +5939.88i q^{68} +7054.18i q^{69} +(-345.201 - 1045.01i) q^{70} -7623.18 q^{71} -2920.66 q^{72} +2849.97i q^{73} +1.85012 q^{74} -20174.1i q^{75} -9404.15i q^{76} +(1697.45 - 560.720i) q^{77} -126.356 q^{78} +605.940 q^{79} +10542.7i q^{80} +10610.9 q^{81} +242.773i q^{82} -5600.96i q^{83} +(-3888.59 - 11771.8i) q^{84} +16368.7 q^{85} -776.297 q^{86} -8981.59i q^{87} +599.774 q^{88} +4450.90i q^{89} +3990.23i q^{90} +(-233.069 - 705.562i) q^{91} -6900.12 q^{92} -8417.25 q^{93} -628.204i q^{94} -25915.2 q^{95} -6256.73i q^{96} +9419.50i q^{97} +(-999.173 + 740.970i) q^{98} -6481.45 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 256 q^{4} - 50 q^{7} + 180 q^{8} - 800 q^{9}+O(q^{10}) $ 28 * q + 256 * q^4 - 50 * q^7 + 180 * q^8 - 800 * q^9	$ 28 q + 256 q^{4} - 50 q^{7} + 180 q^{8} - 800 q^{9} + 360 q^{14} - 68 q^{15} + 2008 q^{16} - 1740 q^{18} + 1238 q^{21} + 300 q^{23} - 4008 q^{25} + 24 q^{28} - 2052 q^{29} + 1604 q^{30} - 780 q^{32} + 294 q^{35} - 2712 q^{36} + 1884 q^{37} + 7696 q^{39} + 7488 q^{42} + 1748 q^{43} - 2904 q^{44} - 9628 q^{46} - 9140 q^{49} + 8220 q^{50} + 15640 q^{51} - 4392 q^{53} + 5736 q^{56} - 11860 q^{57} - 9056 q^{58} + 19408 q^{60} - 14412 q^{63} + 8560 q^{64} - 7104 q^{65} - 9524 q^{67} - 22744 q^{70} - 8748 q^{71} - 67764 q^{72} + 13980 q^{74} - 726 q^{77} + 13880 q^{78} + 41624 q^{79} + 51188 q^{81} + 56956 q^{84} + 29584 q^{85} + 24 q^{86} - 7260 q^{88} + 9104 q^{91} - 32928 q^{92} + 18252 q^{93} - 56412 q^{95} - 15372 q^{98}+O(q^{100}) $ 28 * q + 256 * q^4 - 50 * q^7 + 180 * q^8 - 800 * q^9 + 360 * q^14 - 68 * q^15 + 2008 * q^16 - 1740 * q^18 + 1238 * q^21 + 300 * q^23 - 4008 * q^25 + 24 * q^28 - 2052 * q^29 + 1604 * q^30 - 780 * q^32 + 294 * q^35 - 2712 * q^36 + 1884 * q^37 + 7696 * q^39 + 7488 * q^42 + 1748 * q^43 - 2904 * q^44 - 9628 * q^46 - 9140 * q^49 + 8220 * q^50 + 15640 * q^51 - 4392 * q^53 + 5736 * q^56 - 11860 * q^57 - 9056 * q^58 + 19408 * q^60 - 14412 * q^63 + 8560 * q^64 - 7104 * q^65 - 9524 * q^67 - 22744 * q^70 - 8748 * q^71 - 67764 * q^72 + 13980 * q^74 - 726 * q^77 + 13880 * q^78 + 41624 * q^79 + 51188 * q^81 + 56956 * q^84 + 29584 * q^85 + 24 * q^86 - 7260 * q^88 + 9104 * q^91 - 32928 * q^92 + 18252 * q^93 - 56412 * q^95 - 15372 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.518092			−0.129523			−0.0647615	−	0.997901i	$-0.520629\pi$
$2$	−0.518092			−0.129523			−0.0647615	+	0.997901i	$0.520629\pi$
$3$			16.0828i			1.78698i	0.449082	+	0.893490i	$0.351751\pi$
$3$			16.0828i			1.78698i	−0.449082	+	0.893490i	$0.648249\pi$
$4$	−15.7316			−0.983224
$5$			43.3519i			1.73408i	0.498242	+	0.867038i	$0.333979\pi$
$5$			43.3519i			1.73408i	−0.498242	+	0.867038i	$0.666021\pi$
$6$		−	8.33238i		−	0.231455i
$7$	46.5272	−	15.3694i	0.949535	−	0.313661i
$7$	46.5272	−	15.3694i	0.949535	−	0.313661i
$8$	16.4399			0.256873
$9$	−177.657			−2.19330
$10$		−	22.4603i		−	0.224603i
$11$	36.4829			0.301511
$11$	36.4829			0.301511
$12$		−	253.008i		−	1.75700i
$13$		−	15.1645i		−	0.0897308i	−0.998993	−	0.0448654i	$-0.985714\pi$
$13$		−	15.1645i		−	0.0897308i	0.998993	−	0.0448654i	$-0.0142859\pi$
$14$	−24.1054	+	7.96276i	−0.122987	+	0.0406263i
$15$	−697.221			−3.09876
$16$	243.188			0.949953
$17$		−	377.577i		−	1.30649i	−0.757145	−	0.653247i	$-0.773406\pi$
$17$		−	377.577i		−	1.30649i	0.757145	−	0.653247i	$-0.226594\pi$
$18$	92.0428			0.284083
$19$			597.788i			1.65592i	0.560785	+	0.827961i	$0.310499\pi$
$19$			597.788i			1.65592i	−0.560785	+	0.827961i	$0.689501\pi$
$20$		−	681.994i		−	1.70498i
$21$	247.183	+	748.289i	0.560507	+	1.69680i
$22$	−18.9015			−0.0390526
$23$	438.616			0.829141			0.414571	−	0.910017i	$-0.363932\pi$
$23$	438.616			0.829141			0.414571	+	0.910017i	$0.363932\pi$
$24$			264.400i			0.459027i
$25$	−1254.39			−2.00702
$26$			7.85661i			0.0116222i
$27$		−	1554.52i		−	2.13240i
$28$	−731.947	+	241.785i	−0.933605	+	0.308399i
$29$	−558.459			−0.664041			−0.332021	−	0.943272i	$-0.607730\pi$
$29$	−558.459			−0.664041			−0.332021	+	0.943272i	$0.607730\pi$
$30$	361.224			0.401361
$31$			523.369i			0.544608i	0.962211	+	0.272304i	$0.0877857\pi$
$31$			523.369i			0.544608i	−0.962211	+	0.272304i	$0.912214\pi$
$32$	−389.032			−0.379914
$33$			586.748i			0.538795i
$34$			195.620i			0.169221i
$35$	666.293	+	2017.04i	0.543912	+	1.64657i
$36$	2794.83			2.15650
$37$	−3.57104			−0.00260850			−0.00130425	−	0.999999i	$-0.500415\pi$
$37$	−3.57104			−0.00260850			−0.00130425	+	0.999999i	$0.500415\pi$
$38$		−	309.709i		−	0.214480i
$39$	243.888			0.160347
$40$			712.700i			0.445437i
$41$		−	468.590i		−	0.278757i	−0.990239	−	0.139378i	$-0.955490\pi$
$41$		−	468.590i		−	0.278757i	0.990239	−	0.139378i	$-0.0445104\pi$
$42$	−128.064	−	387.682i	−0.0725985	−	0.219775i
$43$	1498.38			0.810372			0.405186	−	0.914234i	$-0.367207\pi$
$43$	1498.38			0.810372			0.405186	+	0.914234i	$0.367207\pi$
$44$	−573.933			−0.296453
$45$		−	7701.78i		−	3.80335i
$46$	−227.243			−0.107393
$47$			1212.53i			0.548906i	0.961600	+	0.274453i	$0.0884968\pi$
$47$			1212.53i			0.548906i	−0.961600	+	0.274453i	$0.911503\pi$
$48$			3911.15i			1.69755i
$49$	1928.56	−	1430.19i	0.803233	−	0.595665i
$50$	649.887			0.259955
$51$	6072.50			2.33468
$52$			238.562i			0.0882255i
$53$	221.280			0.0787752			0.0393876	−	0.999224i	$-0.487459\pi$
$53$	221.280			0.0787752			0.0393876	+	0.999224i	$0.487459\pi$
$54$			805.385i			0.276195i
$55$			1581.60i			0.522843i
$56$	764.901	−	252.671i	0.243910	−	0.0805711i
$57$	−9614.12			−2.95910
$58$	289.333			0.0860086
$59$		−	1596.34i		−	0.458585i	−0.973358	−	0.229293i	$-0.926359\pi$
$59$		−	1596.34i		−	0.458585i	0.973358	−	0.229293i	$-0.0736413\pi$
$60$	10968.4			3.04677
$61$			4561.91i			1.22599i	0.790087	+	0.612995i	$0.210035\pi$
$61$			4561.91i			1.22599i	−0.790087	+	0.612995i	$0.789965\pi$
$62$		−	271.153i		−	0.0705393i
$63$	−8265.90	+	2730.49i	−2.08261	+	0.687953i
$64$	−3689.45			−0.900745
$65$	657.410			0.155600
$66$		−	303.989i		−	0.0697863i
$67$	−4460.95			−0.993752			−0.496876	−	0.867822i	$-0.665520\pi$
$67$	−4460.95			−0.993752			−0.496876	+	0.867822i	$0.665520\pi$
$68$			5939.88i			1.28458i
$69$			7054.18i			1.48166i
$70$	−345.201	−	1045.01i	−0.0704491	−	0.213268i
$71$	−7623.18			−1.51223			−0.756117	−	0.654436i	$-0.772906\pi$
$71$	−7623.18			−1.51223			−0.756117	+	0.654436i	$0.772906\pi$
$72$	−2920.66			−0.563400
$73$			2849.97i			0.534805i	0.963585	+	0.267402i	$0.0861653\pi$
$73$			2849.97i			0.534805i	−0.963585	+	0.267402i	$0.913835\pi$
$74$	1.85012			0.000337861
$75$		−	20174.1i		−	3.58650i
$76$		−	9404.15i		−	1.62814i
$77$	1697.45	−	560.720i	0.286296	−	0.0945724i
$78$	−126.356			−0.0207687
$79$	605.940			0.0970903			0.0485451	−	0.998821i	$-0.484542\pi$
$79$	605.940			0.0970903			0.0485451	+	0.998821i	$0.484542\pi$
$80$			10542.7i			1.64729i
$81$	10610.9			1.61726
$82$			242.773i			0.0361054i
$83$		−	5600.96i		−	0.813030i	−0.913644	−	0.406515i	$-0.866744\pi$
$83$		−	5600.96i		−	0.813030i	0.913644	−	0.406515i	$-0.133256\pi$
$84$	−3888.59	−	11771.8i	−0.551103	−	1.66833i
$85$	16368.7			2.26556
$86$	−776.297			−0.104962
$87$		−	8981.59i		−	1.18663i
$88$	599.774			0.0774501
$89$			4450.90i			0.561911i	0.959721	+	0.280956i	$0.0906514\pi$
$89$			4450.90i			0.561911i	−0.959721	+	0.280956i	$0.909349\pi$
$90$			3990.23i			0.492621i
$91$	−233.069	−	705.562i	−0.0281451	−	0.0852026i
$92$	−6900.12			−0.815231
$93$	−8417.25			−0.973204
$94$		−	628.204i		−	0.0710960i
$95$	−25915.2			−2.87149
$96$		−	6256.73i		−	0.678898i
$97$			9419.50i			1.00112i	0.865703	+	0.500558i	$0.166872\pi$
$97$			9419.50i			1.00112i	−0.865703	+	0.500558i	$0.833128\pi$
$98$	−999.173	+	740.970i	−0.104037	+	0.0771523i
$99$	−6481.45			−0.661305
$100$	19733.5			1.97335
$101$			3815.33i			0.374015i	0.982358	+	0.187008i	$0.0598789\pi$
$101$			3815.33i			0.374015i	−0.982358	+	0.187008i	$0.940121\pi$
$102$	−3146.12			−0.302395
$103$		−	2424.59i		−	0.228541i	−0.993450	−	0.114270i	$-0.963547\pi$
$103$		−	2424.59i		−	0.228541i	0.993450	−	0.114270i	$-0.0364530\pi$
$104$		−	249.303i		−	0.0230494i
$105$	−32439.7	+	10715.9i	−2.94238	+	0.971961i
$106$	−114.643			−0.0102032
$107$	13674.2			1.19436			0.597180	−	0.802107i	$-0.296288\pi$
$107$	13674.2			1.19436			0.597180	+	0.802107i	$0.296288\pi$
$108$			24455.1i			2.09663i
$109$	20114.0			1.69296			0.846478	−	0.532423i	$-0.178718\pi$
$109$	20114.0			1.69296			0.846478	+	0.532423i	$0.178718\pi$
$110$		−	819.415i		−	0.0677202i
$111$		−	57.4324i		−	0.00466134i
$112$	11314.9	−	3737.65i	0.902013	−	0.297963i
$113$	−2160.51			−0.169200			−0.0845998	−	0.996415i	$-0.526961\pi$
$113$	−2160.51			−0.169200			−0.0845998	+	0.996415i	$0.526961\pi$
$114$	4981.00			0.383272
$115$			19014.8i			1.43779i
$116$	8785.44			0.652901
$117$			2694.09i			0.196807i
$118$			827.048i			0.0593973i
$119$	−5803.13	−	17567.6i	−0.409797	−	1.24056i
$120$	−11462.2			−0.795988
$121$	1331.00			0.0909091
$122$		−	2363.49i		−	0.158794i
$123$	7536.26			0.498133
$124$		−	8233.41i		−	0.535472i
$125$		−	27285.1i		−	1.74625i
$126$	4282.49	−	1414.64i	0.269746	−	0.0891057i
$127$	−1046.97			−0.0649121			−0.0324560	−	0.999473i	$-0.510333\pi$
$127$	−1046.97			−0.0649121			−0.0324560	+	0.999473i	$0.510333\pi$
$128$	8135.98			0.496581
$129$			24098.1i			1.44812i
$130$	−340.599			−0.0201538
$131$		−	9075.34i		−	0.528835i	−0.964408	−	0.264417i	$-0.914820\pi$
$131$		−	9075.34i		−	0.528835i	0.964408	−	0.264417i	$-0.0851797\pi$
$132$		−	9230.47i		−	0.529756i
$133$	9187.64	+	27813.4i	0.519399	+	1.57236i
$134$	2311.18			0.128714
$135$	67391.5			3.69775
$136$		−	6207.32i		−	0.335603i
$137$	22678.0			1.20827			0.604136	−	0.796881i	$-0.293518\pi$
$137$	22678.0			1.20827			0.604136	+	0.796881i	$0.293518\pi$
$138$		−	3654.71i		−	0.191909i
$139$		−	3948.34i		−	0.204355i	−0.994766	−	0.102177i	$-0.967419\pi$
$139$		−	3948.34i		−	0.204355i	0.994766	−	0.102177i	$-0.0325809\pi$
$140$	−10481.8	−	31731.3i	−0.534788	−	1.61894i
$141$	−19501.0			−0.980885
$142$	3949.51			0.195869
$143$		−	553.245i		−	0.0270549i
$144$	−43204.1			−2.08353
$145$		−	24210.2i		−	1.15150i
$146$		−	1476.55i		−	0.0692695i
$147$	23001.5	+	31016.7i	1.06444	+	1.43536i
$148$	56.1781			0.00256474
$149$	−35339.2			−1.59178			−0.795892	−	0.605438i	$-0.792998\pi$
$149$	−35339.2			−1.59178			−0.795892	+	0.605438i	$0.792998\pi$
$150$			10452.0i			0.464534i
$151$	13659.6			0.599078			0.299539	−	0.954084i	$-0.403167\pi$
$151$	13659.6			0.599078			0.299539	+	0.954084i	$0.403167\pi$
$152$			9827.56i			0.425362i
$153$			67079.3i			2.86553i
$154$	−879.433	+	290.504i	−0.0370818	+	0.0122493i
$155$	−22689.0			−0.944392
$156$	−3836.75			−0.157657
$157$		−	25757.6i		−	1.04498i	−0.852646	−	0.522489i	$-0.825004\pi$
$157$		−	25757.6i		−	1.04498i	0.852646	−	0.522489i	$-0.174996\pi$
$158$	−313.933			−0.0125754
$159$			3558.80i			0.140770i
$160$		−	16865.3i		−	0.658799i
$161$	20407.6	−	6741.26i	0.787299	−	0.260070i
$162$	−5497.41			−0.209473
$163$	5884.27			0.221471			0.110736	−	0.993850i	$-0.464679\pi$
$163$	5884.27			0.221471			0.110736	+	0.993850i	$0.464679\pi$
$164$			7371.67i			0.274080i
$165$	−25436.6			−0.934311
$166$			2901.81i			0.105306i
$167$		−	26671.3i		−	0.956339i	−0.878268	−	0.478169i	$-0.841300\pi$
$167$		−	26671.3i		−	0.956339i	0.878268	−	0.478169i	$-0.158700\pi$
$168$	4063.66	+	12301.8i	0.143979	+	0.435862i
$169$	28331.0			0.991948
$170$	−8480.48			−0.293442
$171$		−	106201.i		−	3.63193i
$172$	−23571.9			−0.796777
$173$			29137.7i			0.973560i	0.873525	+	0.486780i	$0.161829\pi$
$173$			29137.7i			0.973560i	−0.873525	+	0.486780i	$0.838171\pi$
$174$			4653.29i			0.153696i
$175$	−58363.1	+	19279.2i	−1.90573	+	0.629524i
$176$	8872.19			0.286422
$177$	25673.6			0.819483
$178$		−	2305.97i		−	0.0727804i
$179$	32276.4			1.00735			0.503674	−	0.863894i	$-0.331981\pi$
$179$	32276.4			1.00735			0.503674	+	0.863894i	$0.331981\pi$
$180$			121161.i			3.73954i
$181$			45286.7i			1.38233i	0.722695	+	0.691167i	$0.242903\pi$
$181$			45286.7i			1.38233i	−0.722695	+	0.691167i	$0.757097\pi$
$182$	120.751	+	365.546i	0.00364543	+	0.0110357i
$183$	−73368.4			−2.19082
$184$	7210.79			0.212984
$185$		−	154.811i		−	0.00452334i
$186$	4360.91			0.126052
$187$		−	13775.1i		−	0.393923i
$188$		−	19075.1i		−	0.539698i
$189$	−23892.1	−	72327.6i	−0.668853	−	2.02479i
$190$	13426.5			0.371924
$191$	12001.0			0.328967			0.164483	−	0.986380i	$-0.447404\pi$
$191$	12001.0			0.328967			0.164483	+	0.986380i	$0.447404\pi$
$192$		−	59336.8i		−	1.60961i
$193$	24068.0			0.646137			0.323068	−	0.946376i	$-0.395286\pi$
$193$	24068.0			0.646137			0.323068	+	0.946376i	$0.395286\pi$
$194$		−	4880.17i		−	0.129667i
$195$			10573.0i			0.278054i
$196$	−30339.3	+	22499.2i	−0.789758	+	0.585672i
$197$	31839.1			0.820406			0.410203	−	0.911994i	$-0.365458\pi$
$197$	31839.1			0.820406			0.410203	+	0.911994i	$0.365458\pi$
$198$	3357.99			0.0856542
$199$			30783.8i			0.777349i	0.921375	+	0.388674i	$0.127067\pi$
$199$			30783.8i			0.777349i	−0.921375	+	0.388674i	$0.872933\pi$
$200$	−20622.0			−0.515549
$201$		−	71744.7i		−	1.77582i
$202$		−	1976.69i		−	0.0484436i
$203$	−25983.5	+	8583.18i	−0.630530	+	0.208284i
$204$	−95530.1			−2.29551
$205$	20314.3			0.483386
$206$			1256.16i			0.0296013i
$207$	−77923.3			−1.81856
$208$		−	3687.83i		−	0.0852401i
$209$			21809.0i			0.499279i
$210$	16806.8	−	5551.80i	0.381106	−	0.125891i
$211$	73424.8			1.64922			0.824609	−	0.565703i	$-0.191395\pi$
$211$	73424.8			1.64922			0.824609	+	0.565703i	$0.191395\pi$
$212$	−3481.08			−0.0774537
$213$		−	122602.i		−	2.70233i
$214$	−7084.51			−0.154697
$215$			64957.5i			1.40525i
$216$		−	25556.2i		−	0.547757i
$217$	8043.86	+	24350.9i	0.170823	+	0.517125i
$218$	−10420.9			−0.219277
$219$	−45835.7			−0.955686
$220$		−	24881.1i		−	0.514072i
$221$	−5725.77			−0.117233
$222$			29.7552i			0.000603750i
$223$			9395.63i			0.188937i	0.995528	+	0.0944683i	$0.0301151\pi$
$223$			9395.63i			0.188937i	−0.995528	+	0.0944683i	$0.969885\pi$
$224$	−18100.6	+	5979.18i	−0.360741	+	0.119164i
$225$	222851.			4.40199
$226$	1119.34			0.0219152
$227$			31573.8i			0.612739i	0.951913	+	0.306370i	$0.0991144\pi$
$227$			31573.8i			0.612739i	−0.951913	+	0.306370i	$0.900886\pi$
$228$	151245.			2.90946
$229$		−	81408.4i		−	1.55238i	−0.630499	−	0.776190i	$-0.717150\pi$
$229$		−	81408.4i		−	1.55238i	0.630499	−	0.776190i	$-0.282850\pi$
$230$		−	9851.42i		−	0.186227i
$231$	9017.96	+	27299.7i	0.168999	+	0.511605i
$232$	−9180.99			−0.170574
$233$	−76396.1			−1.40721			−0.703606	−	0.710591i	$-0.748428\pi$
$233$	−76396.1			−1.40721			−0.703606	+	0.710591i	$0.748428\pi$
$234$		−	1395.78i		−	0.0254910i
$235$	−52565.6			−0.951845
$236$			25112.9i			0.450892i
$237$			9745.23i			0.173498i
$238$	3006.56	+	9101.63i	0.0530781	+	0.160681i
$239$	−75427.3			−1.32048			−0.660241	−	0.751053i	$-0.729546\pi$
$239$	−75427.3			−1.32048			−0.660241	+	0.751053i	$0.729546\pi$
$240$	−169556.			−2.94368
$241$			92838.5i			1.59843i	0.601044	+	0.799216i	$0.294752\pi$
$241$			92838.5i			1.59843i	−0.601044	+	0.799216i	$0.705248\pi$
$242$	−689.580			−0.0117748
$243$			44736.5i			0.757617i
$244$		−	71766.0i		−	1.20542i
$245$	62001.5	+	83606.8i	1.03293	+	1.39287i
$246$	−3904.47			−0.0645197
$247$	9065.16			0.148587
$248$			8604.11i			0.139895i
$249$	90079.3			1.45287
$250$			14136.2i			0.226179i
$251$		−	38562.1i		−	0.612087i	−0.952017	−	0.306044i	$-0.900995\pi$
$251$		−	38562.1i		−	0.612087i	0.952017	−	0.306044i	$-0.0990054\pi$
$252$	130036.	−	42954.9i	2.04768	−	0.676412i
$253$	16002.0			0.249996
$254$	542.425			0.00840760
$255$			263255.i			4.04851i
$256$	54816.1			0.836427
$257$			59777.1i			0.905042i	0.891754	+	0.452521i	$0.149475\pi$
$257$			59777.1i			0.905042i	−0.891754	+	0.452521i	$0.850525\pi$
$258$		−	12485.1i		−	0.187565i
$259$	−166.150	+	54.8847i	−0.00247686	+	0.000818185i
$260$	−10342.1			−0.152990
$261$	99214.3			1.45644
$262$			4701.86i			0.0684963i
$263$	64336.6			0.930136			0.465068	−	0.885275i	$-0.346030\pi$
$263$	64336.6			0.930136			0.465068	+	0.885275i	$0.346030\pi$
$264$			9646.06i			0.138402i
$265$			9592.89i			0.136602i
$266$	−4760.04	−	14409.9i	−0.0672741	−	0.203656i
$267$	−71583.0			−1.00412
$268$	70177.8			0.977081
$269$			31981.1i			0.441965i	0.975278	+	0.220983i	$0.0709264\pi$
$269$			31981.1i			0.441965i	−0.975278	+	0.220983i	$0.929074\pi$
$270$	−34915.0			−0.478943
$271$			37712.0i			0.513501i	0.966478	+	0.256751i	$0.0826519\pi$
$271$			37712.0i			0.513501i	−0.966478	+	0.256751i	$0.917348\pi$
$272$		−	91822.2i		−	1.24111i
$273$	11347.4	−	3748.42i	0.152255	−	0.0502947i
$274$	−11749.3			−0.156499
$275$	−45763.6			−0.605139
$276$		−	110973.i		−	1.45680i
$277$	−75581.1			−0.985040			−0.492520	−	0.870301i	$-0.663924\pi$
$277$	−75581.1			−0.985040			−0.492520	+	0.870301i	$0.663924\pi$
$278$			2045.60i			0.0264686i
$279$		−	92980.2i		−	1.19449i
$280$	10953.8	+	33159.9i	0.139716	+	0.422958i
$281$	−60874.5			−0.770944			−0.385472	−	0.922719i	$-0.625961\pi$
$281$	−60874.5			−0.770944			−0.385472	+	0.922719i	$0.625961\pi$
$282$	10103.3			0.127047
$283$		−	40140.8i		−	0.501202i	−0.968090	−	0.250601i	$-0.919372\pi$
$283$		−	40140.8i		−	0.501202i	0.968090	−	0.250601i	$-0.0806283\pi$
$284$	119925.			1.48687
$285$		−	416790.i		−	5.13131i
$286$			286.632i			0.00350423i
$287$	−7201.95	−	21802.2i	−0.0874352	−	0.264689i
$288$	69114.3			0.833265
$289$	−59043.4			−0.706928
$290$			12543.1i			0.149145i
$291$	−151492.			−1.78897
$292$		−	44834.6i		−	0.525833i
$293$		−	33843.6i		−	0.394222i	−0.980381	−	0.197111i	$-0.936844\pi$
$293$		−	33843.6i		−	0.394222i	0.980381	−	0.197111i	$-0.0631560\pi$
$294$	−11916.9	−	16069.5i	−0.137870	−	0.185912i
$295$	69204.2			0.795222
$296$	−58.7074			−0.000670053
$297$		−	56713.4i		−	0.642944i
$298$	18309.0			0.206173
$299$		−	6651.39i		−	0.0743995i
$300$			317370.i			3.52633i
$301$	69715.3	−	23029.2i	0.769477	−	0.254182i
$302$	−7076.92			−0.0775944
$303$	−61361.3			−0.668358
$304$			145375.i			1.57305i
$305$	−197767.			−2.12596
$306$		−	34753.2i		−	0.371153i
$307$			83845.4i			0.889616i	0.895626	+	0.444808i	$0.146728\pi$
$307$			83845.4i			0.889616i	−0.895626	+	0.444808i	$0.853272\pi$
$308$	−26703.5	+	8821.01i	−0.281493	+	0.0929859i
$309$	38994.3			0.408398
$310$	11755.0			0.122320
$311$			100673.i			1.04086i	0.853903	+	0.520432i	$0.174229\pi$
$311$			100673.i			1.04086i	−0.853903	+	0.520432i	$0.825771\pi$
$312$	4009.49			0.0411889
$313$			78606.2i			0.802358i	0.916000	+	0.401179i	$0.131399\pi$
$313$			78606.2i			0.802358i	−0.916000	+	0.401179i	$0.868601\pi$
$314$			13344.8i			0.135349i
$315$	−118372.	−	358342.i	−1.19296	−	3.61141i
$316$	−9532.40			−0.0954615
$317$	165673.			1.64867			0.824336	−	0.566101i	$-0.191549\pi$
$317$	165673.			1.64867			0.824336	+	0.566101i	$0.191549\pi$
$318$		−	1843.79i		−	0.0182329i
$319$	−20374.2			−0.200216
$320$		−	159945.i		−	1.56196i
$321$			219920.i			2.13430i
$322$	−10573.0	+	3492.59i	−0.101973	+	0.0336850i
$323$	225711.			2.16345
$324$	−166926.			−1.59013
$325$			19022.2i			0.180091i
$326$	−3048.59			−0.0286856
$327$			323490.i			3.02528i
$328$		−	7703.57i		−	0.0716051i
$329$	18635.9	+	56415.8i	0.172171	+	0.521206i
$330$	13178.5			0.121015
$331$	−205856.			−1.87892			−0.939458	−	0.342665i	$-0.888671\pi$
$331$	−205856.			−1.87892			−0.939458	+	0.342665i	$0.888671\pi$
$332$			88112.0i			0.799390i
$333$	634.421			0.00572122
$334$			13818.2i			0.123868i
$335$		−	193391.i		−	1.72324i
$336$	60112.0	+	181975.i	0.532455	+	1.61188i
$337$	60500.0			0.532716			0.266358	−	0.963874i	$-0.414180\pi$
$337$	60500.0			0.532716			0.266358	+	0.963874i	$0.414180\pi$
$338$	−14678.1			−0.128480
$339$		−	34747.1i		−	0.302356i
$340$	−257505.			−2.22755
$341$			19094.0i			0.164206i
$342$			55022.1i			0.470419i
$343$	67749.5	−	96183.7i	0.575861	−	0.817548i
$344$	24633.1			0.208163
$345$	−305812.			−2.56931
$346$		−	15096.0i		−	0.126098i
$347$	−145408.			−1.20762			−0.603808	−	0.797130i	$-0.706351\pi$
$347$	−145408.			−1.20762			−0.603808	+	0.797130i	$0.706351\pi$
$348$			141295.i			1.16672i
$349$		−	140759.i		−	1.15565i	−0.816162	−	0.577824i	$-0.803902\pi$
$349$		−	140759.i		−	1.15565i	0.816162	−	0.577824i	$-0.196098\pi$
$350$	30237.4	−	9988.38i	0.246836	−	0.0815378i
$351$	−23573.6			−0.191342
$352$	−14193.0			−0.114548
$353$		−	97595.3i		−	0.783212i	−0.920133	−	0.391606i	$-0.871920\pi$
$353$		−	97595.3i		−	0.783212i	0.920133	−	0.391606i	$-0.128080\pi$
$354$	−13301.3			−0.106142
$355$		−	330479.i		−	2.62233i
$356$		−	70019.7i		−	0.552485i
$357$	282537.	−	93330.8i	2.21686	−	0.732299i
$358$	−16722.1			−0.130475
$359$	−70400.7			−0.546246			−0.273123	−	0.961979i	$-0.588057\pi$
$359$	−70400.7			−0.546246			−0.273123	+	0.961979i	$0.588057\pi$
$360$		−	126616.i		−	0.976977i
$361$	−227029.			−1.74208
$362$		−	23462.7i		−	0.179044i
$363$			21406.2i			0.162453i
$364$	3666.55	+	11099.6i	0.0276729	+	0.0837732i
$365$	−123552.			−0.927392
$366$	38011.6			0.283762
$367$			36880.8i			0.273822i	0.990583	+	0.136911i	$0.0437174\pi$
$367$			36880.8i			0.273822i	−0.990583	+	0.136911i	$0.956283\pi$
$368$	106666.			0.787645
$369$			83248.5i			0.611397i
$370$			80.2064i			0.000585876i
$371$	10295.5	−	3400.93i	0.0747998	−	0.0247087i
$372$	132417.			0.956878
$373$	161945.			1.16399			0.581997	−	0.813191i	$-0.302271\pi$
$373$	161945.			1.16399			0.581997	+	0.813191i	$0.302271\pi$
$374$			7136.76i			0.0510221i
$375$	438821.			3.12051
$376$			19933.9i			0.140999i
$377$			8468.75i			0.0595850i
$378$	12378.3	+	37472.3i	0.0866318	+	0.262257i
$379$	−132496.			−0.922408			−0.461204	−	0.887294i	$-0.652582\pi$
$379$	−132496.			−0.922408			−0.461204	+	0.887294i	$0.652582\pi$
$380$	407688.			2.82332
$381$		−	16838.2i		−	0.115997i
$382$	−6217.64			−0.0426088
$383$		−	176305.i		−	1.20190i	−0.799288	−	0.600949i	$-0.794790\pi$
$383$		−	176305.i		−	1.20190i	0.799288	−	0.600949i	$-0.205210\pi$
$384$			130850.i			0.887380i
$385$	24308.3	+	73587.5i	0.163996	+	0.496458i
$386$	−12469.4			−0.0836896
$387$	−266198.			−1.77739
$388$		−	148184.i		−	0.984321i
$389$	158097.			1.04478			0.522391	−	0.852706i	$-0.325040\pi$
$389$	158097.			1.04478			0.522391	+	0.852706i	$0.325040\pi$
$390$		−	5477.79i		−	0.0360144i
$391$		−	165611.i		−	1.08327i
$392$	31705.3	−	23512.2i	0.206329	−	0.153010i
$393$	145957.			0.945018
$394$	−16495.6			−0.106261
$395$			26268.7i			0.168362i
$396$	101963.			0.650211
$397$			186450.i			1.18299i	0.806308	+	0.591496i	$0.201462\pi$
$397$			186450.i			1.18299i	−0.806308	+	0.591496i	$0.798538\pi$
$398$		−	15948.8i		−	0.100685i
$399$	−447318.	+	147763.i	−2.80977	+	0.928156i
$400$	−305052.			−1.90657
$401$	−170271.			−1.05889			−0.529445	−	0.848344i	$-0.677600\pi$
$401$	−170271.			−1.05889			−0.529445	+	0.848344i	$0.677600\pi$
$402$			37170.4i			0.230009i
$403$	7936.63			0.0488682
$404$		−	60021.2i		−	0.367741i
$405$			460001.i			2.80446i
$406$	13461.9	−	4446.87i	0.0816682	−	0.0269776i
$407$	−130.282			−0.000786492
$408$	99831.2			0.599716
$409$		−	205917.i		−	1.23096i	−0.788152	−	0.615481i	$-0.788962\pi$
$409$		−	205917.i		−	1.23096i	0.788152	−	0.615481i	$-0.211038\pi$
$410$	−10524.7			−0.0626095
$411$			364727.i			2.15916i
$412$			38142.6i			0.224707i
$413$	−24534.7	−	74273.0i	−0.143840	−	0.435443i
$414$	40371.4			0.235545
$415$	242812.			1.40985
$416$			5899.47i			0.0340900i
$417$	63500.4			0.365178
$418$		−	11299.1i		−	0.0646681i
$419$		−	91240.8i		−	0.519710i	−0.965648	−	0.259855i	$-0.916325\pi$
$419$		−	91240.8i		−	0.519710i	0.965648	−	0.259855i	$-0.0836747\pi$
$420$	510328.	−	168578.i	2.89302	−	0.955655i
$421$	162130.			0.914741			0.457370	−	0.889276i	$-0.348791\pi$
$421$	162130.			0.914741			0.457370	+	0.889276i	$0.348791\pi$
$422$	−38040.8			−0.213612
$423$		−	215416.i		−	1.20392i
$424$	3637.81			0.0202352
$425$			473627.i			2.62216i
$426$			63519.2i			0.350014i
$427$	70113.8	+	212253.i	0.384546	+	1.16412i
$428$	−215117.			−1.17432
$429$	8897.74			0.0483465
$430$		−	33654.0i		−	0.182012i
$431$	357989.			1.92715			0.963573	−	0.267445i	$-0.0861795\pi$
$431$	357989.			1.92715			0.963573	+	0.267445i	$0.0861795\pi$
$432$		−	378041.i		−	2.02568i
$433$		−	135183.i		−	0.721020i	−0.932755	−	0.360510i	$-0.882603\pi$
$433$		−	135183.i		−	0.721020i	0.932755	−	0.360510i	$-0.117397\pi$
$434$	−4167.46	−	12616.0i	−0.0221254	−	0.0669795i
$435$	389369.			2.05770
$436$	−316425.			−1.66456
$437$			262199.i			1.37299i
$438$	23747.1			0.123783
$439$			227170.i			1.17875i	0.807860	+	0.589375i	$0.200626\pi$
$439$			227170.i			1.17875i	−0.807860	+	0.589375i	$0.799374\pi$
$440$			26001.3i			0.134304i
$441$	−342623.	+	254084.i	−1.76173	+	1.30647i
$442$	2966.47			0.0151843
$443$	62002.7			0.315939			0.157969	−	0.987444i	$-0.449505\pi$
$443$	62002.7			0.315939			0.157969	+	0.987444i	$0.449505\pi$
$444$			903.502i			0.00458314i
$445$	−192955.			−0.974397
$446$		−	4867.80i		−	0.0244716i
$447$		−	568354.i		−	2.84449i
$448$	−171660.	+	56704.7i	−0.855289	+	0.282529i
$449$	81326.1			0.403401			0.201701	−	0.979447i	$-0.435353\pi$
$449$	81326.1			0.403401			0.201701	+	0.979447i	$0.435353\pi$
$450$	−115457.			−0.570159
$451$		−	17095.5i		−	0.0840484i
$452$	33988.2			0.166361
$453$			219685.i			1.07054i
$454$		−	16358.2i		−	0.0793638i
$455$	30587.5	−	10104.0i	0.147748	−	0.0488057i
$456$	−158055.			−0.760113
$457$	110375.			0.528494			0.264247	−	0.964455i	$-0.414877\pi$
$457$	110375.			0.528494			0.264247	+	0.964455i	$0.414877\pi$
$458$			42177.0i			0.201069i
$459$	−586952.			−2.78597
$460$		−	299133.i		−	1.41367i
$461$			259668.i			1.22185i	0.791689	+	0.610924i	$0.209202\pi$
$461$			259668.i			1.22185i	−0.791689	+	0.610924i	$0.790798\pi$
$462$	−4672.13	−	14143.8i	−0.0218893	−	0.0662645i
$463$	292324.			1.36365			0.681825	−	0.731515i	$-0.261187\pi$
$463$	292324.			1.36365			0.681825	+	0.731515i	$0.261187\pi$
$464$	−135810.			−0.630808
$465$		−	364903.i		−	1.68761i
$466$	39580.2			0.182266
$467$			41447.6i			0.190049i	0.995475	+	0.0950245i	$0.0302930\pi$
$467$			41447.6i			0.190049i	−0.995475	+	0.0950245i	$0.969707\pi$
$468$		−	42382.2i		−	0.193505i
$469$	−207556.	+	68562.2i	−0.943602	+	0.311702i
$470$	27233.8			0.123286
$471$	414256.			1.86735
$472$		−	26243.5i		−	0.117798i
$473$	54665.1			0.244336
$474$		−	5048.93i		−	0.0224720i
$475$		−	749857.i		−	3.32347i
$476$	91292.5	+	276366.i	0.402922	+	1.21975i
$477$	−39311.9			−0.172778
$478$	39078.3			0.171033
$479$		−	406781.i		−	1.77292i	−0.462805	−	0.886460i	$-0.653157\pi$
$479$		−	406781.i		−	1.77292i	0.462805	−	0.886460i	$-0.346843\pi$
$480$	271241.			1.17726
$481$			54.1530i			0.000234063i
$482$		−	48098.9i		−	0.207034i
$483$	108419.	+	328211.i	0.464739	+	1.40689i
$484$	−20938.7			−0.0893840
$485$	−408353.			−1.73601
$486$		−	23177.6i		−	0.0981288i
$487$	−327399.			−1.38045			−0.690224	−	0.723596i	$-0.742488\pi$
$487$	−327399.			−1.38045			−0.690224	+	0.723596i	$0.742488\pi$
$488$			74997.2i			0.314924i
$489$			94635.7i			0.395765i
$490$	−32122.5	−	43316.0i	−0.133788	−	0.180408i
$491$	396591.			1.64505			0.822527	−	0.568726i	$-0.192564\pi$
$491$	396591.			1.64505			0.822527	+	0.568726i	$0.192564\pi$
$492$	−118557.			−0.489776
$493$			210861.i			0.867566i
$494$	−4696.59			−0.0192455
$495$		−	280983.i		−	1.14675i
$496$			127277.i			0.517352i
$497$	−354685.	+	117164.i	−1.43592	+	0.474330i
$498$	−46669.3			−0.188180
$499$	−221929.			−0.891278			−0.445639	−	0.895213i	$-0.647023\pi$
$499$	−221929.			−0.891278			−0.445639	+	0.895213i	$0.647023\pi$
$500$			429238.i			1.71695i
$501$	428950.			1.70896
$502$			19978.7i			0.0792794i
$503$		−	320431.i		−	1.26648i	−0.773955	−	0.633240i	$-0.781724\pi$
$503$		−	320431.i		−	1.26648i	0.773955	−	0.633240i	$-0.218276\pi$
$504$	−135890.	+	44888.9i	−0.534968	+	0.176717i
$505$	−165402.			−0.648571
$506$	−8290.49			−0.0323802
$507$			455643.i			1.77259i
$508$	16470.4			0.0638231
$509$		−	393695.i		−	1.51958i	−0.650168	−	0.759790i	$-0.725301\pi$
$509$		−	393695.i		−	1.51958i	0.650168	−	0.759790i	$-0.274699\pi$
$510$		−	136390.i		−	0.524375i
$511$	43802.4	+	132601.i	0.167748	+	0.507816i
$512$	−158575.			−0.604917
$513$	929275.			3.53110
$514$		−	30970.0i		−	0.117224i
$515$	105111.			0.396307
$516$		−	379102.i		−	1.42383i
$517$			44236.7i			0.165501i
$518$	86.0812	−	28.4353i	0.000320810	−	0.000105974i
$519$	−468616.			−1.73973
$520$	10807.7			0.0399694
$521$		−	270910.i		−	0.998043i	−0.866590	−	0.499021i	$-0.833693\pi$
$521$		−	270910.i		−	0.998043i	0.866590	−	0.499021i	$-0.166307\pi$
$522$	−51402.1			−0.188643
$523$			189254.i			0.691899i	0.938253	+	0.345949i	$0.112443\pi$
$523$			189254.i			0.691899i	−0.938253	+	0.345949i	$0.887557\pi$
$524$			142769.i			0.519963i
$525$	−310064.	−	938644.i	−1.12495	−	3.40551i
$526$	−33332.3			−0.120474
$527$	197612.			0.711528
$528$			142690.i			0.511830i
$529$	−87457.2			−0.312525
$530$		−	4970.00i		−	0.0176931i
$531$			283601.i			1.00582i
$532$	−144536.	−	437549.i	−0.510685	−	1.54598i
$533$	−7105.94			−0.0250131
$534$	37086.6			0.130057
$535$			592804.i			2.07111i
$536$	−73337.5			−0.255268
$537$			519096.i			1.80011i
$538$		−	16569.1i		−	0.0572447i
$539$	70359.5	−	52177.5i	0.242184	−	0.179600i
$540$	−1.06017e6			−3.63572
$541$	502242.			1.71600			0.858002	−	0.513647i	$-0.171706\pi$
$541$	502242.			1.71600			0.858002	+	0.513647i	$0.171706\pi$
$542$		−	19538.3i		−	0.0665102i
$543$	−728338.			−2.47021
$544$			146889.i			0.496355i
$545$			871981.i			2.93572i
$546$	−5879.01	+	1942.02i	−0.0197206	+	0.00651432i
$547$	−207191.			−0.692463			−0.346231	−	0.938149i	$-0.612539\pi$
$547$	−207191.			−0.692463			−0.346231	+	0.938149i	$0.612539\pi$
$548$	−356762.			−1.18800
$549$		−	810456.i		−	2.68896i
$550$	23709.8			0.0783794
$551$		−	333840.i		−	1.09960i
$552$			115970.i			0.380598i
$553$	28192.7	−	9312.94i	0.0921906	−	0.0304535i
$554$	39158.0			0.127585
$555$	2489.80			0.00808311
$556$			62113.6i			0.200926i
$557$	−86409.3			−0.278516			−0.139258	−	0.990256i	$-0.544472\pi$
$557$	−86409.3			−0.278516			−0.139258	+	0.990256i	$0.544472\pi$
$558$			48172.3i			0.154714i
$559$		−	22722.2i		−	0.0727153i
$560$	162034.	+	490520.i	0.516691	+	1.56416i
$561$	221542.			0.703933
$562$	31538.6			0.0998550
$563$		−	287174.i		−	0.905999i	−0.891511	−	0.453000i	$-0.850354\pi$
$563$		−	287174.i		−	0.905999i	0.891511	−	0.453000i	$-0.149646\pi$
$564$	306781.			0.964430
$565$		−	93662.1i		−	0.293405i
$566$			20796.6i			0.0649172i
$567$	493694.	−	163083.i	1.53565	−	0.507273i
$568$	−125324.			−0.388452
$569$	348202.			1.07549			0.537745	−	0.843107i	$-0.319276\pi$
$569$	348202.			1.07549			0.537745	+	0.843107i	$0.319276\pi$
$570$			215936.i			0.664622i
$571$	250265.			0.767589			0.383794	−	0.923419i	$-0.374617\pi$
$571$	250265.			0.767589			0.383794	+	0.923419i	$0.374617\pi$
$572$			8703.42i			0.0266010i
$573$			193011.i			0.587857i
$574$	3731.27	+	11295.5i	0.0113249	+	0.0342834i
$575$	−550194.			−1.66410
$576$	655458.			1.97560
$577$			209935.i			0.630569i	0.948997	+	0.315284i	$0.102100\pi$
$577$			209935.i			0.630569i	−0.948997	+	0.315284i	$0.897900\pi$
$578$	30589.9			0.0915635
$579$			387081.i			1.15463i
$580$			380865.i			1.13218i
$581$	−86083.4	−	260597.i	−0.255016	−	0.772000i
$582$	78486.9			0.231713
$583$	8072.91			0.0237516
$584$			46853.2i			0.137377i
$585$	−116794.			−0.341278
$586$			17534.1i			0.0510608i
$587$			118389.i			0.343586i	0.985133	+	0.171793i	$0.0549560\pi$
$587$			118389.i			0.343586i	−0.985133	+	0.171793i	$0.945044\pi$
$588$	−361850.	−	487942.i	−1.04658	−	1.41128i
$589$	−312863.			−0.901829
$590$	−35854.1			−0.102999
$591$			512063.i			1.46605i
$592$	−868.433			−0.00247795
$593$		−	632489.i		−	1.79864i	−0.437295	−	0.899318i	$-0.644063\pi$
$593$		−	632489.i		−	1.79864i	0.437295	−	0.899318i	$-0.355937\pi$
$594$			29382.8i			0.0832760i
$595$	761589.	−	251577.i	2.15123	−	0.710619i
$596$	555942.			1.56508
$597$	−495090.			−1.38911
$598$			3446.03i			0.00963645i
$599$	109614.			0.305502			0.152751	−	0.988265i	$-0.451187\pi$
$599$	109614.			0.305502			0.152751	+	0.988265i	$0.451187\pi$
$600$		−	331659.i		−	0.921276i
$601$		−	463782.i		−	1.28400i	−0.766705	−	0.642000i	$-0.778105\pi$
$601$		−	463782.i		−	1.28400i	0.766705	−	0.642000i	$-0.221895\pi$
$602$	−36118.9	+	11931.2i	−0.0996649	+	0.0329224i
$603$	792521.			2.17960
$604$	−214887.			−0.589028
$605$			57701.4i			0.157643i
$606$	31790.8			0.0865678
$607$			494571.i			1.34230i	0.741320	+	0.671152i	$0.234200\pi$
$607$			494571.i			1.34230i	−0.741320	+	0.671152i	$0.765800\pi$
$608$		−	232558.i		−	0.629108i
$609$	−138042.	−	417889.i	−0.372200	−	1.12675i
$610$	102462.			0.275361
$611$	18387.5			0.0492538
$612$		−	1.05526e6i		−	2.81746i
$613$	716483.			1.90671			0.953355	−	0.301851i	$-0.0976045\pi$
$613$	716483.			1.90671			0.953355	+	0.301851i	$0.0976045\pi$
$614$		−	43439.6i		−	0.115226i
$615$			326711.i			0.863801i
$616$	27905.8	−	9218.16i	0.0735416	−	0.0242931i
$617$	389770.			1.02385			0.511927	−	0.859029i	$-0.328932\pi$
$617$	389770.			1.02385			0.511927	+	0.859029i	$0.328932\pi$
$618$	−20202.6			−0.0528969
$619$			294798.i			0.769385i	0.923045	+	0.384692i	$0.125693\pi$
$619$			294798.i			0.769385i	−0.923045	+	0.384692i	$0.874307\pi$
$620$	356934.			0.928549
$621$		−	681838.i		−	1.76806i
$622$		−	52158.1i		−	0.134816i
$623$	68407.7	+	207088.i	0.176250	+	0.533554i
$624$	59310.7			0.152322
$625$	398869.			1.02110
$626$		−	40725.2i		−	0.103924i
$627$	−350751.			−0.892203
$628$			405209.i			1.02745i
$629$			1348.34i			0.00340799i
$630$	61327.4	+	185654.i	0.154516	+	0.467761i
$631$	−261785.			−0.657485			−0.328742	−	0.944420i	$-0.606625\pi$
$631$	−261785.			−0.657485			−0.328742	+	0.944420i	$0.606625\pi$
$632$	9961.58			0.0249399
$633$			1.18088e6i			2.94712i
$634$	−85834.0			−0.213541
$635$		−	45388.0i		−	0.112562i
$636$		−	55985.6i		−	0.138408i
$637$	−21688.1	−	29245.7i	−0.0534495	−	0.0720748i
$638$	10555.7			0.0259326
$639$	1.35431e6			3.31678
$640$			352710.i			0.861109i
$641$	−330538.			−0.804461			−0.402230	−	0.915538i	$-0.631765\pi$
$641$	−330538.			−0.804461			−0.402230	+	0.915538i	$0.631765\pi$
$642$		−	113939.i		−	0.276441i
$643$			551577.i			1.33409i	0.745019	+	0.667044i	$0.232441\pi$
$643$			551577.i			1.33409i	−0.745019	+	0.667044i	$0.767559\pi$
$644$	−321043.	+	106051.i	−0.774091	+	0.255707i
$645$	−1.04470e6			−2.51115
$646$	−116939.			−0.280217
$647$		−	597288.i		−	1.42684i	−0.700736	−	0.713420i	$-0.747145\pi$
$647$		−	597288.i		−	1.42684i	0.700736	−	0.713420i	$-0.252855\pi$
$648$	174441.			0.415432
$649$		−	58238.9i		−	0.138269i
$650$		−	9855.22i		−	0.0233260i
$651$	−391631.	+	129368.i	−0.924092	+	0.305257i
$652$	−92568.9			−0.217756
$653$	264649.			0.620645			0.310323	−	0.950631i	$-0.399563\pi$
$653$	264649.			0.620645			0.310323	+	0.950631i	$0.399563\pi$
$654$		−	167598.i		−	0.391843i
$655$	393433.			0.917040
$656$		−	113956.i		−	0.264806i
$657$		−	506319.i		−	1.17299i
$658$	−9655.12	−	29228.6i	−0.0223001	−	0.0675081i
$659$	−516250.			−1.18875			−0.594374	−	0.804189i	$-0.702600\pi$
$659$	−516250.			−1.18875			−0.594374	+	0.804189i	$0.702600\pi$
$660$	400158.			0.918637
$661$		−	502130.i		−	1.14925i	−0.818418	−	0.574623i	$-0.805149\pi$
$661$		−	502130.i		−	1.14925i	0.818418	−	0.574623i	$-0.194851\pi$
$662$	106652.			0.243363
$663$		−	92086.6i		−	0.209493i
$664$		−	92079.1i		−	0.208845i
$665$	−1.20576e6	+	398302.i	−2.72658	+	0.900677i
$666$	−328.688			−0.000741030
$667$	−244949.			−0.550584
$668$			419582.i			0.940295i
$669$	−151108.			−0.337626
$670$			100194.i			0.223199i
$671$			166432.i			0.369650i
$672$	−96162.2	−	291108.i	−0.212944	−	0.644638i
$673$	−250914.			−0.553981			−0.276990	−	0.960873i	$-0.589337\pi$
$673$	−250914.			−0.553981			−0.276990	+	0.960873i	$0.589337\pi$
$674$	−31344.6			−0.0689989
$675$			1.94997e6i			4.27977i
$676$	−445692.			−0.975307
$677$		−	233424.i		−	0.509293i	−0.967034	−	0.254647i	$-0.918041\pi$
$677$		−	233424.i		−	0.509293i	0.967034	−	0.254647i	$-0.0819592\pi$
$678$			18002.2i			0.0391621i
$679$	144772.	+	438263.i	0.314011	+	0.950595i
$680$	269099.			0.581961
$681$	−507797.			−1.09495
$682$		−	9892.44i		−	0.0212684i
$683$	−524048.			−1.12339			−0.561694	−	0.827345i	$-0.689850\pi$
$683$	−524048.			−1.12339			−0.561694	+	0.827345i	$0.689850\pi$
$684$			1.67072e6i			3.57100i
$685$			983136.i			2.09523i
$686$	−35100.4	+	49832.0i	−0.0745872	+	0.105891i
$687$	1.30928e6			2.77407
$688$	364387.			0.769815
$689$		−	3355.60i		−	0.00706856i
$690$	158439.			0.332785
$691$		−	930604.i		−	1.94899i	−0.224417	−	0.974493i	$-0.572048\pi$
$691$		−	930604.i		−	1.94899i	0.224417	−	0.974493i	$-0.427952\pi$
$692$		−	458382.i		−	0.957227i
$693$	−301564.	+	99616.0i	−0.627932	+	0.207426i
$694$	75334.6			0.156414
$695$	171168.			0.354367
$696$		−	147656.i		−	0.304813i
$697$	−176929.			−0.364194
$698$			72926.1i			0.149683i
$699$		−	1.22867e6i		−	2.51466i
$700$	918144.	−	303292.i	1.87376	−	0.618963i
$701$	−162287.			−0.330254			−0.165127	−	0.986272i	$-0.552803\pi$
$701$	−162287.			−0.330254			−0.165127	+	0.986272i	$0.552803\pi$
$702$	12213.3			0.0247832
$703$		−	2134.72i		−	0.00431947i
$704$	−134602.			−0.271585
$705$		−	845404.i		−	1.70093i
$706$			50563.3i			0.101444i
$707$	58639.4	+	177517.i	0.117314	+	0.355141i
$708$	−403886.			−0.805735
$709$	510782.			1.01611			0.508057	−	0.861323i	$-0.330364\pi$
$709$	510782.			1.01611			0.508057	+	0.861323i	$0.330364\pi$
$710$			171219.i			0.339652i
$711$	−107650.			−0.212948
$712$			73172.2i			0.144340i
$713$			229558.i			0.451557i
$714$	−146380.	+	48353.9i	−0.287134	+	0.0948495i
$715$	23984.2			0.0469152
$716$	−507759.			−0.990448
$717$		−	1.21308e6i		−	2.35968i
$718$	36474.0			0.0707514
$719$		−	186411.i		−	0.360591i	−0.983613	−	0.180295i	$-0.942295\pi$
$719$		−	186411.i		−	0.360591i	0.983613	−	0.180295i	$-0.0577053\pi$
$720$		−	1.87298e6i		−	3.61300i
$721$	−37264.5	−	112809.i	−0.0716844	−	0.217008i
$722$	117622.			0.225639
$723$	−1.49311e6			−2.85637
$724$		−	712431.i		−	1.35914i
$725$	700523.			1.33274
$726$		−	11090.4i		−	0.0210414i
$727$		−	909519.i		−	1.72085i	−0.509577	−	0.860425i	$-0.670198\pi$
$727$		−	909519.i		−	1.72085i	0.509577	−	0.860425i	$-0.329802\pi$
$728$	−3831.63	−	11599.4i	−0.00722971	−	0.0218862i
$729$	139991.			0.263418
$730$	64011.2			0.120119
$731$		−	565753.i		−	1.05875i
$732$	1.15420e6			2.15407
$733$			627905.i			1.16865i	0.811518	+	0.584327i	$0.198642\pi$
$733$			627905.i			1.16865i	−0.811518	+	0.584327i	$0.801358\pi$
$734$		−	19107.6i		−	0.0354662i
$735$	−1.34463e6	+	997159.i	−2.48903	+	1.84582i
$736$	−170635.			−0.315002
$737$	−162748.			−0.299628
$738$		−	43130.4i		−	0.0791900i
$739$	−464434.			−0.850422			−0.425211	−	0.905094i	$-0.639800\pi$
$739$	−464434.			−0.850422			−0.425211	+	0.905094i	$0.639800\pi$
$740$			2435.42i			0.00444745i
$741$			145793.i			0.265523i
$742$	−5334.03	+	1762.00i	−0.00968829	+	0.00320035i
$743$	−446611.			−0.809006			−0.404503	−	0.914537i	$-0.632555\pi$
$743$	−446611.			−0.809006			−0.404503	+	0.914537i	$0.632555\pi$
$744$	−138378.			−0.249990
$745$		−	1.53202e6i		−	2.76027i
$746$	−83902.6			−0.150764
$747$			995051.i			1.78322i
$748$			216704.i			0.387314i
$749$	636224.	−	210165.i	1.13409	−	0.374624i
$750$	−227350.			−0.404177
$751$	420821.			0.746135			0.373068	−	0.927804i	$-0.378306\pi$
$751$	420821.			0.746135			0.373068	+	0.927804i	$0.378306\pi$
$752$			294874.i			0.521435i
$753$	620188.			1.09379
$754$		−	4387.59i		−	0.00771762i
$755$			592169.i			1.03885i
$756$	375860.	+	1.13783e6i	0.657632	+	1.99082i
$757$	491386.			0.857494			0.428747	−	0.903425i	$-0.358955\pi$
$757$	491386.			0.857494			0.428747	+	0.903425i	$0.358955\pi$
$758$	68644.9			0.119473
$759$			257357.i			0.446737i
$760$	−426043.			−0.737609
$761$		−	618117.i		−	1.06734i	−0.845694	−	0.533668i	$-0.820813\pi$
$761$		−	618117.i		−	1.06734i	0.845694	−	0.533668i	$-0.179187\pi$
$762$			8723.73i			0.0150242i
$763$	935849.	−	309140.i	1.60752	−	0.531015i
$764$	−188795.			−0.323448
$765$	−2.90801e6			−4.96905
$766$			91342.2i			0.155673i
$767$	−24207.6			−0.0411492
$768$			881597.i			1.49468i
$769$		−	334483.i		−	0.565616i	−0.959177	−	0.282808i	$-0.908734\pi$
$769$		−	334483.i		−	0.565616i	0.959177	−	0.282808i	$-0.0912660\pi$
$770$	−12593.9	−	38125.1i	−0.0212412	−	0.0643027i
$771$	−961385.			−1.61729
$772$	−378627.			−0.635297
$773$		−	98856.1i		−	0.165442i	−0.996573	−	0.0827208i	$-0.973639\pi$
$773$		−	98856.1i		−	0.165442i	0.996573	−	0.0827208i	$-0.0263610\pi$
$774$	137915.			0.230213
$775$		−	656506.i		−	1.09304i
$776$			154855.i			0.257160i
$777$	−882.701	−	2672.17i	−0.00146208	−	0.00442610i
$778$	−81908.9			−0.135323
$779$	280118.			0.461600
$780$		−	166330.i		−	0.273390i
$781$	−278115.			−0.455956
$782$			85801.8i			0.140308i
$783$			868137.i			1.41600i
$784$	469003.	−	347805.i	0.763034	−	0.565853i
$785$	1.11664e6			1.81207
$786$	−75619.2			−0.122402
$787$			480315.i			0.775491i	0.921766	+	0.387746i	$0.126746\pi$
$787$			480315.i			0.775491i	−0.921766	+	0.387746i	$0.873254\pi$
$788$	−500880.			−0.806642
$789$			1.03471e6i			1.66214i
$790$		−	13609.6i		−	0.0218067i
$791$	−100522.	+	33205.7i	−0.160661	+	0.0530713i
$792$	−106554.			−0.169871
$793$	69179.1			0.110009
$794$		−	96598.3i		−	0.153225i
$795$	−154281.			−0.244105
$796$		−	484278.i		−	0.764308i
$797$			790121.i			1.24388i	0.783067	+	0.621938i	$0.213654\pi$
$797$			790121.i			1.24388i	−0.783067	+	0.621938i	$0.786346\pi$
$798$	231752.	−	76555.0i	0.363930	−	0.120217i
$799$	457825.			0.717143
$800$	487996.			0.762494
$801$		−	790735.i		−	1.23244i
$802$	88215.8			0.137151
$803$			103975.i			0.161250i
$804$			1.12866e6i			1.74602i
$805$	292246.	+	884707.i	0.450980	+	1.36524i
$806$	−4111.90			−0.00632955
$807$	−514346.			−0.789784
$808$			62723.6i			0.0960745i
$809$	−115602.			−0.176631			−0.0883157	−	0.996093i	$-0.528148\pi$
$809$	−115602.			−0.176631			−0.0883157	+	0.996093i	$0.528148\pi$
$810$		−	238323.i		−	0.363242i
$811$			14364.2i			0.0218394i	0.999940	+	0.0109197i	$0.00347591\pi$
$811$			14364.2i			0.0218394i	−0.999940	+	0.0109197i	$0.996524\pi$
$812$	408762.	−	135027.i	0.619952	−	0.204790i
$813$	−606516.			−0.917617
$814$	67.4979			0.000101869
$815$			255094.i			0.384048i
$816$	1.47676e6			2.21784
$817$			895712.i			1.34191i
$818$			106684.i			0.159438i
$819$	41406.5	+	125348.i	0.0617306	+	0.186875i
$820$	−319576.			−0.475276
$821$	−302115.			−0.448215			−0.224108	−	0.974564i	$-0.571947\pi$
$821$	−302115.			−0.448215			−0.224108	+	0.974564i	$0.571947\pi$
$822$		−	188962.i		−	0.279661i
$823$	−47053.7			−0.0694695			−0.0347347	−	0.999397i	$-0.511059\pi$
$823$	−47053.7			−0.0694695			−0.0347347	+	0.999397i	$0.511059\pi$
$824$		−	39860.0i		−	0.0587060i
$825$		−	736008.i		−	1.08137i
$826$	12711.2	+	38480.3i	0.0186306	+	0.0563998i
$827$	−569569.			−0.832789			−0.416394	−	0.909184i	$-0.636706\pi$
$827$	−569569.			−0.832789			−0.416394	+	0.909184i	$0.636706\pi$
$828$	1.22586e6			1.78805
$829$		−	63135.3i		−	0.0918678i	−0.998944	−	0.0459339i	$-0.985374\pi$
$829$		−	63135.3i		−	0.0918678i	0.998944	−	0.0459339i	$-0.0146264\pi$
$830$	−125799.			−0.182609
$831$		−	1.21556e6i		−	1.76025i
$832$			55948.7i			0.0808246i
$833$	−540007.	−	728181.i	−0.778233	−	1.04942i
$834$	−32899.1			−0.0472989
$835$	1.15625e6			1.65836
$836$		−	343090.i		−	0.490903i
$837$	813588.			1.16132
$838$			47271.1i			0.0673144i
$839$		−	1.37295e6i		−	1.95043i	−0.221261	−	0.975215i	$-0.571017\pi$
$839$		−	1.37295e6i		−	1.95043i	0.221261	−	0.975215i	$-0.428983\pi$
$840$	−533305.	+	176168.i	−0.755818	+	0.249671i
$841$	−395405.			−0.559049
$842$	−83998.0			−0.118480
$843$		−	979035.i		−	1.37766i
$844$	−1.15509e6			−1.62155
$845$			1.22820e6i			1.72011i
$846$			111605.i			0.155935i
$847$	61927.7	−	20456.7i	0.0863214	−	0.0285147i
$848$	53812.5			0.0748327
$849$	645578.			0.895639
$850$		−	245382.i		−	0.339630i
$851$	−1566.31			−0.00216282
$852$			1.92873e6i			2.65700i
$853$			1.03006e6i			1.41567i	0.706375	+	0.707837i	$0.250329\pi$
$853$			1.03006e6i			1.41567i	−0.706375	+	0.707837i	$0.749671\pi$
$854$	−36325.4	−	109966.i	−0.0498075	−	0.150780i
$855$	4.60403e6			6.29805
$856$	224803.			0.306799
$857$			851480.i			1.15934i	0.814850	+	0.579672i	$0.196819\pi$
$857$			851480.i			1.15934i	−0.814850	+	0.579672i	$0.803181\pi$
$858$	−4609.85			−0.00626198
$859$		−	312562.i		−	0.423594i	−0.977314	−	0.211797i	$-0.932068\pi$
$859$		−	312562.i		−	0.423594i	0.977314	−	0.211797i	$-0.0679316\pi$
$860$		−	1.02188e6i		−	1.38167i
$861$	350641.	−	115828.i	0.472995	−	0.156245i
$862$	−185471.			−0.249610
$863$	367581.			0.493550			0.246775	−	0.969073i	$-0.420629\pi$
$863$	367581.			0.493550			0.246775	+	0.969073i	$0.420629\pi$
$864$			604758.i			0.810129i
$865$	−1.26317e6			−1.68823
$866$			70037.3i			0.0933886i
$867$		−	949584.i		−	1.26327i
$868$	−126543.	−	383078.i	−0.167957	−	0.508449i
$869$	22106.4			0.0292738
$870$	−201729.			−0.266520
$871$			67648.2i			0.0891702i
$872$	330672.			0.434875
$873$		−	1.67344e6i		−	2.19575i
$874$		−	135843.i		−	0.177834i
$875$	−419355.	−	1.26950e6i	−0.547730	−	1.65812i
$876$	721067.			0.939653
$877$	338117.			0.439610			0.219805	−	0.975544i	$-0.429458\pi$
$877$	338117.			0.439610			0.219805	+	0.975544i	$0.429458\pi$
$878$		−	117695.i		−	0.152675i
$879$	544300.			0.704468
$880$			384626.i			0.496677i
$881$			1.02777e6i			1.32417i	0.749429	+	0.662085i	$0.230328\pi$
$881$			1.02777e6i			1.32417i	−0.749429	+	0.662085i	$0.769672\pi$
$882$	177510.	−	131639.i	0.228185	−	0.169218i
$883$	911206.			1.16868			0.584340	−	0.811509i	$-0.301354\pi$
$883$	911206.			1.16868			0.584340	+	0.811509i	$0.301354\pi$
$884$	90075.4			0.115266
$885$			1.11300e6i			1.42105i
$886$	−32123.1			−0.0409213
$887$			486584.i			0.618459i	0.950987	+	0.309229i	$0.100071\pi$
$887$			486584.i			0.618459i	−0.950987	+	0.309229i	$0.899929\pi$
$888$		−	944.181i		−	0.00119737i
$889$	−48712.4	+	16091.3i	−0.0616363	+	0.0203604i
$890$	99968.4			0.126207
$891$	387115.			0.487624
$892$		−	147808.i		−	0.185767i
$893$	−724838.			−0.908946
$894$			294460.i			0.368427i
$895$			1.39924e6i			1.74682i
$896$	378545.	−	125045.i	0.471521	−	0.155758i
$897$	106973.			0.132951
$898$	−42134.4			−0.0522497
$899$		−	292280.i		−	0.361642i
$900$	−3.50580e6			−4.32814
$901$		−	83550.1i		−	0.102919i
$902$			8857.05i			0.0108862i
$903$	370374.	+	1.12122e6i	0.454219	+	1.37504i
$904$	−35518.5			−0.0434628
$905$	−1.96326e6			−2.39707
$906$		−	113817.i		−	0.138660i
$907$	1.33681e6			1.62501			0.812505	−	0.582954i	$-0.198103\pi$
$907$	1.33681e6			1.62501			0.812505	+	0.582954i	$0.198103\pi$
$908$		−	496707.i		−	0.602460i
$909$		−	677821.i		−	0.820328i
$910$	−15847.1	+	5234.80i	−0.0191367	+	0.00632146i
$911$	−909975.			−1.09646			−0.548230	−	0.836328i	$-0.684698\pi$
$911$	−909975.			−1.09646			−0.548230	+	0.836328i	$0.684698\pi$
$912$	−2.33804e6			−2.81101
$913$		−	204339.i		−	0.245138i
$914$	−57184.6			−0.0684521
$915$		−	3.18066e6i		−	3.79905i
$916$			1.28068e6i			1.52634i
$917$	−139483.	−	422250.i	−0.165875	−	0.502147i
$918$	304095.			0.360848
$919$	677188.			0.801823			0.400911	−	0.916117i	$-0.368693\pi$
$919$	677188.			0.801823			0.400911	+	0.916117i	$0.368693\pi$
$920$			312601.i			0.369330i
$921$	−1.34847e6			−1.58973
$922$		−	134532.i		−	0.158257i
$923$			115602.i			0.135694i
$924$	−141867.	−	429468.i	−0.166164	−	0.503022i
$925$	4479.46			0.00523531
$926$	−151451.			−0.176624
$927$			430746.i			0.501259i
$928$	217258.			0.252278
$929$			764095.i			0.885352i	0.896682	+	0.442676i	$0.145971\pi$
$929$			764095.i			0.885352i	−0.896682	+	0.442676i	$0.854029\pi$
$930$			189054.i			0.218584i
$931$	854951.	+	1.15287e6i	0.986375	+	1.33009i
$932$	1.20183e6			1.38360
$933$	−1.61911e6			−1.86001
$934$		−	21473.7i		−	0.0246157i
$935$	597176.			0.683092
$936$			44290.4i			0.0505543i
$937$		−	155536.i		−	0.177155i	−0.996069	−	0.0885773i	$-0.971768\pi$
$937$		−	155536.i		−	0.177155i	0.996069	−	0.0885773i	$-0.0282320\pi$
$938$	107533.	−	35521.5i	0.122218	−	0.0403725i
$939$	−1.26421e6			−1.43380
$940$	826941.			0.935877
$941$		−	1.71472e6i		−	1.93648i	−0.250021	−	0.968240i	$-0.580438\pi$
$941$		−	1.71472e6i		−	1.93648i	0.250021	−	0.968240i	$-0.419562\pi$
$942$	−214623.			−0.241865
$943$		−	205531.i		−	0.231129i
$944$		−	388209.i		−	0.435634i
$945$	3.13554e6	−	1.03577e6i	3.51114	−	1.15984i
$946$	−28321.6			−0.0316472
$947$	−1.66054e6			−1.85161			−0.925804	−	0.378004i	$-0.876610\pi$
$947$	−1.66054e6			−1.85161			−0.925804	+	0.378004i	$0.876610\pi$
$948$		−	153308.i		−	0.170588i
$949$	43218.5			0.0479885
$950$			388495.i			0.430465i
$951$			2.66450e6i			2.94614i
$952$	−95402.8	−	288809.i	−0.105266	−	0.318667i
$953$	625410.			0.688619			0.344309	−	0.938856i	$-0.388113\pi$
$953$	625410.			0.688619			0.344309	+	0.938856i	$0.388113\pi$
$954$	20367.2			0.0223787
$955$			520268.i			0.570453i
$956$	1.18659e6			1.29833
$957$		−	327674.i		−	0.357782i
$958$			210750.i			0.229634i
$959$	1.05515e6	−	348548.i	1.14730	−	0.378988i
$960$	2.57236e6			2.79119
$961$	649606.			0.703402
$962$		−	28.0562i		−	3.03165e-5i
$963$	−2.42933e6			−2.61959
$964$		−	1.46050e6i		−	1.57162i
$965$			1.04339e6i			1.12045i
$966$	−56170.8	−	170044.i	−0.0601944	−	0.182224i
$967$	−1.02318e6			−1.09420			−0.547101	−	0.837067i	$-0.684269\pi$
$967$	−1.02318e6			−1.09420			−0.547101	+	0.837067i	$0.684269\pi$
$968$	21881.5			0.0233521
$969$			3.63007e6i			3.86605i
$970$	211564.			0.224853
$971$			468180.i			0.496563i	0.968688	+	0.248281i	$0.0798658\pi$
$971$			468180.i			0.496563i	−0.968688	+	0.248281i	$0.920134\pi$
$972$		−	703776.i		−	0.744907i
$973$	−60683.6	−	183705.i	−0.0640982	−	0.194042i
$974$	169623.			0.178800
$975$	−305930.			−0.321820
$976$			1.10940e6i			1.16463i
$977$	147783.			0.154823			0.0774113	−	0.996999i	$-0.475335\pi$
$977$	147783.			0.154823			0.0774113	+	0.996999i	$0.475335\pi$
$978$		−	49030.0i		−	0.0512607i
$979$			162382.i			0.169423i
$980$	−975381.	−	1.31527e6i	−1.01560	−	1.36950i
$981$	−3.57340e6			−3.71316
$982$	−205471.			−0.213072
$983$		−	1.04635e6i		−	1.08285i	−0.840748	−	0.541426i	$-0.817884\pi$
$983$		−	1.04635e6i		−	1.08285i	0.840748	−	0.541426i	$-0.182116\pi$
$984$	123895.			0.127957
$985$			1.38029e6i			1.42265i
$986$		−	109245.i		−	0.112370i
$987$	−907326.	+	299718.i	−0.931385	+	0.307666i
$988$	−142609.			−0.146095
$989$	657212.			0.671913
$990$			145575.i			0.148531i
$991$	441123.			0.449172			0.224586	−	0.974454i	$-0.427897\pi$
$991$	441123.			0.449172			0.224586	+	0.974454i	$0.427897\pi$
$992$		−	203607.i		−	0.206904i
$993$		−	3.31074e6i		−	3.35759i
$994$	183759.	−	60701.5i	0.185985	−	0.0614366i
$995$	−1.33454e6			−1.34798
$996$	−1.41709e6			−1.42849
$997$			1.21745e6i			1.22479i	0.790552	+	0.612395i	$0.209794\pi$
$997$			1.21745e6i			1.22479i	−0.790552	+	0.612395i	$0.790206\pi$
$998$	114980.			0.115441
$999$			5551.26i			0.00556238i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.5.d.a.34.16	yes	28
7.6	odd	2	inner	77.5.d.a.34.15	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.5.d.a.34.15	✓	28	7.6	odd	2	inner
77.5.d.a.34.16	yes	28	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	77.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.518092 q^{2} +16.0828i q^{3} -15.7316 q^{4} +43.3519i q^{5} -8.33238i q^{6} +(46.5272 - 15.3694i) q^{7} +16.4399 q^{8} -177.657 q^{9} +O(q^{10})\)	\(q-0.518092 q^{2} +16.0828i q^{3} -15.7316 q^{4} +43.3519i q^{5} -8.33238i q^{6} +(46.5272 - 15.3694i) q^{7} +16.4399 q^{8} -177.657 q^{9} -22.4603i q^{10} +36.4829 q^{11} -253.008i q^{12} -15.1645i q^{13} +(-24.1054 + 7.96276i) q^{14} -697.221 q^{15} +243.188 q^{16} -377.577i q^{17} +92.0428 q^{18} +597.788i q^{19} -681.994i q^{20} +(247.183 + 748.289i) q^{21} -18.9015 q^{22} +438.616 q^{23} +264.400i q^{24} -1254.39 q^{25} +7.85661i q^{26} -1554.52i q^{27} +(-731.947 + 241.785i) q^{28} -558.459 q^{29} +361.224 q^{30} +523.369i q^{31} -389.032 q^{32} +586.748i q^{33} +195.620i q^{34} +(666.293 + 2017.04i) q^{35} +2794.83 q^{36} -3.57104 q^{37} -309.709i q^{38} +243.888 q^{39} +712.700i q^{40} -468.590i q^{41} +(-128.064 - 387.682i) q^{42} +1498.38 q^{43} -573.933 q^{44} -7701.78i q^{45} -227.243 q^{46} +1212.53i q^{47} +3911.15i q^{48} +(1928.56 - 1430.19i) q^{49} +649.887 q^{50} +6072.50 q^{51} +238.562i q^{52} +221.280 q^{53} +805.385i q^{54} +1581.60i q^{55} +(764.901 - 252.671i) q^{56} -9614.12 q^{57} +289.333 q^{58} -1596.34i q^{59} +10968.4 q^{60} +4561.91i q^{61} -271.153i q^{62} +(-8265.90 + 2730.49i) q^{63} -3689.45 q^{64} +657.410 q^{65} -303.989i q^{66} -4460.95 q^{67} +5939.88i q^{68} +7054.18i q^{69} +(-345.201 - 1045.01i) q^{70} -7623.18 q^{71} -2920.66 q^{72} +2849.97i q^{73} +1.85012 q^{74} -20174.1i q^{75} -9404.15i q^{76} +(1697.45 - 560.720i) q^{77} -126.356 q^{78} +605.940 q^{79} +10542.7i q^{80} +10610.9 q^{81} +242.773i q^{82} -5600.96i q^{83} +(-3888.59 - 11771.8i) q^{84} +16368.7 q^{85} -776.297 q^{86} -8981.59i q^{87} +599.774 q^{88} +4450.90i q^{89} +3990.23i q^{90} +(-233.069 - 705.562i) q^{91} -6900.12 q^{92} -8417.25 q^{93} -628.204i q^{94} -25915.2 q^{95} -6256.73i q^{96} +9419.50i q^{97} +(-999.173 + 740.970i) q^{98} -6481.45 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 256 q^{4} - 50 q^{7} + 180 q^{8} - 800 q^{9}+O(q^{10}) \) 28 * q + 256 * q^4 - 50 * q^7 + 180 * q^8 - 800 * q^9	\( 28 q + 256 q^{4} - 50 q^{7} + 180 q^{8} - 800 q^{9} + 360 q^{14} - 68 q^{15} + 2008 q^{16} - 1740 q^{18} + 1238 q^{21} + 300 q^{23} - 4008 q^{25} + 24 q^{28} - 2052 q^{29} + 1604 q^{30} - 780 q^{32} + 294 q^{35} - 2712 q^{36} + 1884 q^{37} + 7696 q^{39} + 7488 q^{42} + 1748 q^{43} - 2904 q^{44} - 9628 q^{46} - 9140 q^{49} + 8220 q^{50} + 15640 q^{51} - 4392 q^{53} + 5736 q^{56} - 11860 q^{57} - 9056 q^{58} + 19408 q^{60} - 14412 q^{63} + 8560 q^{64} - 7104 q^{65} - 9524 q^{67} - 22744 q^{70} - 8748 q^{71} - 67764 q^{72} + 13980 q^{74} - 726 q^{77} + 13880 q^{78} + 41624 q^{79} + 51188 q^{81} + 56956 q^{84} + 29584 q^{85} + 24 q^{86} - 7260 q^{88} + 9104 q^{91} - 32928 q^{92} + 18252 q^{93} - 56412 q^{95} - 15372 q^{98}+O(q^{100}) \) 28 * q + 256 * q^4 - 50 * q^7 + 180 * q^8 - 800 * q^9 + 360 * q^14 - 68 * q^15 + 2008 * q^16 - 1740 * q^18 + 1238 * q^21 + 300 * q^23 - 4008 * q^25 + 24 * q^28 - 2052 * q^29 + 1604 * q^30 - 780 * q^32 + 294 * q^35 - 2712 * q^36 + 1884 * q^37 + 7696 * q^39 + 7488 * q^42 + 1748 * q^43 - 2904 * q^44 - 9628 * q^46 - 9140 * q^49 + 8220 * q^50 + 15640 * q^51 - 4392 * q^53 + 5736 * q^56 - 11860 * q^57 - 9056 * q^58 + 19408 * q^60 - 14412 * q^63 + 8560 * q^64 - 7104 * q^65 - 9524 * q^67 - 22744 * q^70 - 8748 * q^71 - 67764 * q^72 + 13980 * q^74 - 726 * q^77 + 13880 * q^78 + 41624 * q^79 + 51188 * q^81 + 56956 * q^84 + 29584 * q^85 + 24 * q^86 - 7260 * q^88 + 9104 * q^91 - 32928 * q^92 + 18252 * q^93 - 56412 * q^95 - 15372 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

Properties

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