LMFDB - Embedded newform 177.5.b.a.119.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,5,Mod(119,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, 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("177.119");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	177.b (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:	$18.2964834658$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.33
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.46

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.23974i q^{2} +(-7.10280 - 5.52723i) q^{3} +14.4630 q^{4} +12.0336i q^{5} +(-6.85234 + 8.80565i) q^{6} -19.7766 q^{7} -37.7663i q^{8} +(19.8995 + 78.5176i) q^{9} +O(q^{10})$	\(q-1.23974i q^{2} +(-7.10280 - 5.52723i) q^{3} +14.4630 q^{4} +12.0336i q^{5} +(-6.85234 + 8.80565i) q^{6} -19.7766 q^{7} -37.7663i q^{8} +(19.8995 + 78.5176i) q^{9} +14.9185 q^{10} -103.693i q^{11} +(-102.728 - 79.9405i) q^{12} +131.027 q^{13} +24.5179i q^{14} +(66.5122 - 85.4719i) q^{15} +184.588 q^{16} -328.287i q^{17} +(97.3416 - 24.6703i) q^{18} -310.416 q^{19} +174.042i q^{20} +(140.469 + 109.310i) q^{21} -128.553 q^{22} -158.312i q^{23} +(-208.743 + 268.247i) q^{24} +480.194 q^{25} -162.440i q^{26} +(292.642 - 667.684i) q^{27} -286.030 q^{28} -458.135i q^{29} +(-105.963 - 82.4580i) q^{30} -1611.19 q^{31} -833.103i q^{32} +(-573.134 + 736.510i) q^{33} -406.992 q^{34} -237.983i q^{35} +(287.807 + 1135.60i) q^{36} +82.1279 q^{37} +384.837i q^{38} +(-930.657 - 724.215i) q^{39} +454.463 q^{40} -2629.34i q^{41} +(135.516 - 174.146i) q^{42} -2937.80 q^{43} -1499.71i q^{44} +(-944.846 + 239.462i) q^{45} -196.266 q^{46} -1570.46i q^{47} +(-1311.09 - 1020.26i) q^{48} -2009.89 q^{49} -595.317i q^{50} +(-1814.52 + 2331.76i) q^{51} +1895.05 q^{52} -2263.99i q^{53} +(-827.756 - 362.801i) q^{54} +1247.79 q^{55} +746.890i q^{56} +(2204.83 + 1715.74i) q^{57} -567.970 q^{58} -453.188i q^{59} +(961.968 - 1236.18i) q^{60} +2420.99 q^{61} +1997.47i q^{62} +(-393.545 - 1552.81i) q^{63} +1920.57 q^{64} +1576.72i q^{65} +(913.083 + 710.539i) q^{66} +5202.79 q^{67} -4748.03i q^{68} +(-875.028 + 1124.46i) q^{69} -295.038 q^{70} +9128.68i q^{71} +(2965.32 - 751.532i) q^{72} +10406.9 q^{73} -101.818i q^{74} +(-3410.72 - 2654.14i) q^{75} -4489.56 q^{76} +2050.69i q^{77} +(-897.841 + 1153.78i) q^{78} -3852.54 q^{79} +2221.25i q^{80} +(-5769.02 + 3124.92i) q^{81} -3259.70 q^{82} +427.625i q^{83} +(2031.61 + 1580.95i) q^{84} +3950.46 q^{85} +3642.11i q^{86} +(-2532.22 + 3254.04i) q^{87} -3916.10 q^{88} -8238.58i q^{89} +(296.871 + 1171.37i) q^{90} -2591.27 q^{91} -2289.67i q^{92} +(11444.0 + 8905.44i) q^{93} -1946.97 q^{94} -3735.41i q^{95} +(-4604.75 + 5917.36i) q^{96} +7401.57 q^{97} +2491.74i q^{98} +(8141.71 - 2063.44i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	1.23974i		−	0.309936i	−0.987920	−	0.154968i	$-0.950473\pi$
$2$		−	1.23974i		−	0.309936i	0.987920	−	0.154968i	$-0.0495274\pi$
$3$	−7.10280	−	5.52723i	−0.789200	−	0.614136i
$3$	−7.10280	−	5.52723i	−0.789200	−	0.614136i
$4$	14.4630			0.903940
$5$			12.0336i			0.481342i	0.970607	+	0.240671i	$0.0773675\pi$
$5$			12.0336i			0.481342i	−0.970607	+	0.240671i	$0.922632\pi$
$6$	−6.85234	+	8.80565i	−0.190343	+	0.244601i
$7$	−19.7766			−0.403604			−0.201802	−	0.979426i	$-0.564680\pi$
$7$	−19.7766			−0.403604			−0.201802	+	0.979426i	$0.564680\pi$
$8$		−	37.7663i		−	0.590099i
$9$	19.8995	+	78.5176i	0.245673	+	0.969353i
$10$	14.9185			0.149185
$11$		−	103.693i		−	0.856966i	−0.903550	−	0.428483i	$-0.859048\pi$
$11$		−	103.693i		−	0.856966i	0.903550	−	0.428483i	$-0.140952\pi$
$12$	−102.728	−	79.9405i	−0.713389	−	0.555142i
$13$	131.027			0.775306			0.387653	−	0.921805i	$-0.373286\pi$
$13$	131.027			0.775306			0.387653	+	0.921805i	$0.373286\pi$
$14$			24.5179i			0.125091i
$15$	66.5122	−	85.4719i	0.295610	−	0.379875i
$16$	184.588			0.721047
$17$		−	328.287i		−	1.13594i	−0.823049	−	0.567971i	$-0.807729\pi$
$17$		−	328.287i		−	1.13594i	0.823049	−	0.567971i	$-0.192271\pi$
$18$	97.3416	−	24.6703i	0.300437	−	0.0761428i
$19$	−310.416			−0.859879			−0.429940	−	0.902858i	$-0.641465\pi$
$19$	−310.416			−0.859879			−0.429940	+	0.902858i	$0.641465\pi$
$20$			174.042i			0.435104i
$21$	140.469	+	109.310i	0.318524	+	0.247868i
$22$	−128.553			−0.265604
$23$		−	158.312i		−	0.299267i	−0.988742	−	0.149633i	$-0.952191\pi$
$23$		−	158.312i		−	0.299267i	0.988742	−	0.149633i	$-0.0478094\pi$
$24$	−208.743	+	268.247i	−0.362401	+	0.465706i
$25$	480.194			0.768310
$26$		−	162.440i		−	0.240295i
$27$	292.642	−	667.684i	0.401430	−	0.915890i
$28$	−286.030			−0.364834
$29$		−	458.135i		−	0.544751i	−0.962191	−	0.272375i	$-0.912191\pi$
$29$		−	458.135i		−	0.544751i	0.962191	−	0.272375i	$-0.0878092\pi$
$30$	−105.963	−	82.4580i	−0.117737	−	0.0916201i
$31$	−1611.19			−1.67658			−0.838290	−	0.545224i	$-0.816445\pi$
$31$	−1611.19			−1.67658			−0.838290	+	0.545224i	$0.816445\pi$
$32$		−	833.103i		−	0.813577i
$33$	−573.134	+	736.510i	−0.526294	+	0.676317i
$34$	−406.992			−0.352069
$35$		−	237.983i		−	0.194272i
$36$	287.807	+	1135.60i	0.222074	+	0.876237i
$37$	82.1279			0.0599912			0.0299956	−	0.999550i	$-0.490451\pi$
$37$	82.1279			0.0599912			0.0299956	+	0.999550i	$0.490451\pi$
$38$			384.837i			0.266507i
$39$	−930.657	−	724.215i	−0.611872	−	0.476144i
$40$	454.463			0.284040
$41$		−	2629.34i		−	1.56415i	−0.623184	−	0.782075i	$-0.714161\pi$
$41$		−	2629.34i		−	1.56415i	0.623184	−	0.782075i	$-0.285839\pi$
$42$	135.516	−	174.146i	0.0768232	−	0.0987221i
$43$	−2937.80			−1.58886			−0.794429	−	0.607358i	$-0.792230\pi$
$43$	−2937.80			−1.58886			−0.794429	+	0.607358i	$0.792230\pi$
$44$		−	1499.71i		−	0.774646i
$45$	−944.846	+	239.462i	−0.466590	+	0.118253i
$46$	−196.266			−0.0927535
$47$		−	1570.46i		−	0.710937i	−0.934688	−	0.355468i	$-0.884321\pi$
$47$		−	1570.46i		−	0.710937i	0.934688	−	0.355468i	$-0.115679\pi$
$48$	−1311.09	−	1020.26i	−0.569050	−	0.442821i
$49$	−2009.89			−0.837104
$50$		−	595.317i		−	0.238127i
$51$	−1814.52	+	2331.76i	−0.697623	+	0.896485i
$52$	1895.05			0.700830
$53$		−	2263.99i		−	0.805977i	−0.915205	−	0.402988i	$-0.867971\pi$
$53$		−	2263.99i		−	0.805977i	0.915205	−	0.402988i	$-0.132029\pi$
$54$	−827.756	−	362.801i	−0.283867	−	0.124417i
$55$	1247.79			0.412494
$56$			746.890i			0.238166i
$57$	2204.83	+	1715.74i	0.678617	+	0.528083i
$58$	−567.970			−0.168838
$59$		−	453.188i		−	0.130189i
$59$		−	453.188i		−	0.130189i
$60$	961.968	−	1236.18i	0.267213	−	0.343384i
$61$	2420.99			0.650628			0.325314	−	0.945606i	$-0.394530\pi$
$61$	2420.99			0.650628			0.325314	+	0.945606i	$0.394530\pi$
$62$			1997.47i			0.519632i
$63$	−393.545	−	1552.81i	−0.0991546	−	0.391235i
$64$	1920.57			0.468890
$65$			1576.72i			0.373188i
$66$	913.083	+	710.539i	0.209615	+	0.163117i
$67$	5202.79			1.15901			0.579505	−	0.814969i	$-0.303246\pi$
$67$	5202.79			1.15901			0.579505	+	0.814969i	$0.303246\pi$
$68$		−	4748.03i		−	1.02682i
$69$	−875.028	+	1124.46i	−0.183791	+	0.236181i
$70$	−295.038			−0.0602118
$71$			9128.68i			1.81089i	0.424468	+	0.905443i	$0.360461\pi$
$71$			9128.68i			1.81089i	−0.424468	+	0.905443i	$0.639539\pi$
$72$	2965.32	−	751.532i	0.572014	−	0.144971i
$73$	10406.9			1.95288			0.976439	−	0.215792i	$-0.0692332\pi$
$73$	10406.9			1.95288			0.976439	+	0.215792i	$0.0692332\pi$
$74$		−	101.818i		−	0.0185934i
$75$	−3410.72	−	2654.14i	−0.606350	−	0.471847i
$76$	−4489.56			−0.777279
$77$			2050.69i			0.345875i
$78$	−897.841	+	1153.78i	−0.147574	+	0.189641i
$79$	−3852.54			−0.617296			−0.308648	−	0.951176i	$-0.599877\pi$
$79$	−3852.54			−0.617296			−0.308648	+	0.951176i	$0.599877\pi$
$80$			2221.25i			0.347070i
$81$	−5769.02	+	3124.92i	−0.879290	+	0.476287i
$82$	−3259.70			−0.484786
$83$			427.625i			0.0620736i	0.999518	+	0.0310368i	$0.00988091\pi$
$83$			427.625i			0.0620736i	−0.999518	+	0.0310368i	$0.990119\pi$
$84$	2031.61	+	1580.95i	0.287927	+	0.224058i
$85$	3950.46			0.546777
$86$			3642.11i			0.492444i
$87$	−2532.22	+	3254.04i	−0.334551	+	0.429917i
$88$	−3916.10			−0.505695
$89$		−	8238.58i		−	1.04009i	−0.854138	−	0.520046i	$-0.825915\pi$
$89$		−	8238.58i		−	1.04009i	0.854138	−	0.520046i	$-0.174085\pi$
$90$	296.871	+	1171.37i	0.0366508	+	0.144613i
$91$	−2591.27			−0.312917
$92$		−	2289.67i		−	0.270519i
$93$	11444.0	+	8905.44i	1.32316	+	1.02965i
$94$	−1946.97			−0.220345
$95$		−	3735.41i		−	0.413896i
$96$	−4604.75	+	5917.36i	−0.499648	+	0.642075i
$97$	7401.57			0.786648			0.393324	−	0.919400i	$-0.371325\pi$
$97$	7401.57			0.786648			0.393324	+	0.919400i	$0.371325\pi$
$98$			2491.74i			0.259448i
$99$	8141.71	−	2063.44i	0.830702	−	0.210533i
$100$	6945.06			0.694506
$101$		−	17815.7i		−	1.74646i	−0.487305	−	0.873232i	$-0.662020\pi$
$101$		−	17815.7i		−	1.74646i	0.487305	−	0.873232i	$-0.337980\pi$
$102$	2890.78	+	2249.54i	0.277853	+	0.216218i
$103$	−8891.13			−0.838074			−0.419037	−	0.907969i	$-0.637632\pi$
$103$	−8891.13			−0.838074			−0.419037	+	0.907969i	$0.637632\pi$
$104$		−	4948.40i		−	0.457508i
$105$	−1315.39	+	1690.34i	−0.119309	+	0.153319i
$106$	−2806.77			−0.249801
$107$			11993.3i			1.04754i	0.851859	+	0.523771i	$0.175475\pi$
$107$			11993.3i			1.04754i	−0.851859	+	0.523771i	$0.824525\pi$
$108$	4232.50	−	9656.73i	0.362868	−	0.827909i
$109$	7069.33			0.595011			0.297506	−	0.954720i	$-0.403845\pi$
$109$	7069.33			0.595011			0.297506	+	0.954720i	$0.403845\pi$
$110$		−	1546.94i		−	0.127847i
$111$	−583.338	−	453.940i	−0.0473450	−	0.0368428i
$112$	−3650.52			−0.291018
$113$			9931.74i			0.777801i	0.921280	+	0.388900i	$0.127145\pi$
$113$			9931.74i			0.777801i	−0.921280	+	0.388900i	$0.872855\pi$
$114$	2127.08	−	2733.42i	0.163672	−	0.210328i
$115$	1905.06			0.144050
$116$		−	6626.03i		−	0.492422i
$117$	2607.37	+	10287.9i	0.190472	+	0.751546i
$118$	−561.836			−0.0403502
$119$			6492.41i			0.458471i
$120$	−3227.96	−	2511.92i	−0.224164	−	0.174439i
$121$	3888.79			0.265609
$122$		−	3001.40i		−	0.201653i
$123$	−14532.9	+	18675.7i	−0.960602	+	1.23443i
$124$	−23302.8			−1.51553
$125$			13299.4i			0.851162i
$126$	−1925.09	+	487.894i	−0.121258	+	0.0307316i
$127$	17773.3			1.10195			0.550974	−	0.834522i	$-0.314256\pi$
$127$	17773.3			1.10195			0.550974	+	0.834522i	$0.314256\pi$
$128$		−	15710.7i		−	0.958903i
$129$	20866.6	+	16237.9i	1.25393	+	0.975775i
$130$	1954.73			0.115664
$131$		−	1583.03i		−	0.0922458i	−0.998936	−	0.0461229i	$-0.985313\pi$
$131$		−	1583.03i		−	0.0922458i	0.998936	−	0.0461229i	$-0.0146866\pi$
$132$	−8289.26	+	10652.2i	−0.475738	+	0.611350i
$133$	6138.98			0.347051
$134$		−	6450.13i		−	0.359219i
$135$	8034.61	+	3521.53i	0.440856	+	0.193225i
$136$	−12398.2			−0.670318
$137$		−	18965.1i		−	1.01045i	−0.862989	−	0.505223i	$-0.831410\pi$
$137$		−	18965.1i		−	1.01045i	0.862989	−	0.505223i	$-0.168590\pi$
$138$	1394.04	+	1084.81i	0.0732011	+	0.0569633i
$139$	16629.1			0.860675			0.430338	−	0.902668i	$-0.358395\pi$
$139$	16629.1			0.860675			0.430338	+	0.902668i	$0.358395\pi$
$140$		−	3441.95i		−	0.175610i
$141$	−8680.29	+	11154.7i	−0.436612	+	0.561071i
$142$	11317.2			0.561258
$143$		−	13586.5i		−	0.664411i
$144$	3673.21	+	14493.4i	0.177142	+	0.698949i
$145$	5513.00			0.262211
$146$		−	12901.9i		−	0.605267i
$147$	14275.8	+	11109.1i	0.660642	+	0.514096i
$148$	1187.82			0.0542284
$149$			30052.0i			1.35363i	0.736151	+	0.676817i	$0.236641\pi$
$149$			30052.0i			1.35363i	−0.736151	+	0.676817i	$0.763359\pi$
$150$	−3290.45	+	4228.41i	−0.146242	+	0.187930i
$151$	−13749.1			−0.603003			−0.301502	−	0.953466i	$-0.597488\pi$
$151$	−13749.1			−0.603003			−0.301502	+	0.953466i	$0.597488\pi$
$152$			11723.3i			0.507414i
$153$	25776.3	−	6532.75i	1.10113	−	0.279070i
$154$	2542.33			0.107199
$155$		−	19388.4i		−	0.807009i
$156$	−13460.1	−	10474.3i	−0.553095	−	0.430405i
$157$	153.350			0.00622134			0.00311067	−	0.999995i	$-0.499010\pi$
$157$	153.350			0.00622134			0.00311067	+	0.999995i	$0.499010\pi$
$158$			4776.17i			0.191322i
$159$	−12513.6	+	16080.7i	−0.494980	+	0.636077i
$160$	10025.2			0.391609
$161$			3130.88i			0.120785i
$162$	3874.10	+	7152.10i	0.147619	+	0.272523i
$163$	12363.4			0.465333			0.232666	−	0.972557i	$-0.425255\pi$
$163$	12363.4			0.465333			0.232666	+	0.972557i	$0.425255\pi$
$164$		−	38028.2i		−	1.41390i
$165$	−8862.83	−	6896.84i	−0.325540	−	0.253328i
$166$	530.145			0.0192388
$167$		−	7982.13i		−	0.286211i	−0.989707	−	0.143105i	$-0.954291\pi$
$167$		−	7982.13i		−	0.286211i	0.989707	−	0.143105i	$-0.0457088\pi$
$168$	4128.23	−	5305.01i	0.146267	−	0.187961i
$169$	−11393.0			−0.398900
$170$		−	4897.56i		−	0.169466i
$171$	−6177.13	−	24373.1i	−0.211249	−	0.833526i
$172$	−42489.5			−1.43623
$173$			23432.0i			0.782919i	0.920195	+	0.391459i	$0.128030\pi$
$173$			23432.0i			0.782919i	−0.920195	+	0.391459i	$0.871970\pi$
$174$	4034.18	+	3139.30i	0.133247	+	0.103689i
$175$	−9496.60			−0.310093
$176$		−	19140.5i		−	0.617913i
$177$	−2504.87	+	3218.90i	−0.0799538	+	0.102745i
$178$	−10213.7			−0.322362
$179$		−	22549.8i		−	0.703781i	−0.936041	−	0.351890i	$-0.885539\pi$
$179$		−	22549.8i		−	0.703781i	0.936041	−	0.351890i	$-0.114461\pi$
$180$	−13665.3	+	3463.34i	−0.421770	+	0.106893i
$181$	−50415.6			−1.53889			−0.769446	−	0.638712i	$-0.779468\pi$
$181$	−50415.6			−1.53889			−0.769446	+	0.638712i	$0.779468\pi$
$182$			3212.50i			0.0969842i
$183$	−17195.8	−	13381.4i	−0.513476	−	0.399575i
$184$	−5978.87			−0.176597
$185$			988.291i			0.0288763i
$186$	11040.5	−	14187.6i	0.319125	−	0.410094i
$187$	−34041.1			−0.973464
$188$		−	22713.6i		−	0.642644i
$189$	−5787.47	+	13204.5i	−0.162019	+	0.369657i
$190$	−4630.95			−0.128281
$191$			8742.33i			0.239641i	0.992796	+	0.119820i	$0.0382319\pi$
$191$			8742.33i			0.239641i	−0.992796	+	0.119820i	$0.961768\pi$
$192$	−13641.5	−	10615.5i	−0.370048	−	0.287963i
$193$	31505.3			0.845803			0.422901	−	0.906176i	$-0.361012\pi$
$193$	31505.3			0.845803			0.422901	+	0.906176i	$0.361012\pi$
$194$		−	9176.05i		−	0.243810i
$195$	8714.88	−	11199.1i	0.229188	−	0.294520i
$196$	−29069.1			−0.756691
$197$		−	28966.4i		−	0.746382i	−0.927754	−	0.373191i	$-0.878264\pi$
$197$		−	28966.4i		−	0.746382i	0.927754	−	0.373191i	$-0.121736\pi$
$198$	−2558.13	−	10093.6i	−0.0652518	−	0.257464i
$199$	39746.9			1.00368			0.501842	−	0.864959i	$-0.332656\pi$
$199$	39746.9			1.00368			0.501842	+	0.864959i	$0.332656\pi$
$200$		−	18135.2i		−	0.453379i
$201$	−36954.4	−	28757.0i	−0.914690	−	0.711790i
$202$	−22086.9			−0.541292
$203$			9060.36i			0.219864i
$204$	−26243.4	+	33724.3i	−0.630610	+	0.810369i
$205$	31640.3			0.752892
$206$			11022.7i			0.259749i
$207$	12430.3	−	3150.33i	0.290095	−	0.0735218i
$208$	24186.0			0.559032
$209$			32188.0i			0.736887i
$210$	2095.59	+	1630.74i	0.0475191	+	0.0369782i
$211$	−15923.6			−0.357664			−0.178832	−	0.983880i	$-0.557232\pi$
$211$	−15923.6			−0.357664			−0.178832	+	0.983880i	$0.557232\pi$
$212$		−	32744.2i		−	0.728555i
$213$	50456.3	−	64839.1i	1.11213	−	1.42915i
$214$	14868.6			0.324671
$215$		−	35352.1i		−	0.764784i
$216$	−25216.0	−	11052.0i	−0.540466	−	0.236883i
$217$	31863.9			0.676675
$218$		−	8764.15i		−	0.184415i
$219$	−73918.1	−	57521.3i	−1.54121	−	1.19933i
$220$	18046.9			0.372870
$221$		−	43014.4i		−	0.880703i
$222$	−562.769	+	723.190i	−0.0114189	+	0.0146739i
$223$	−31176.3			−0.626923			−0.313462	−	0.949601i	$-0.601489\pi$
$223$	−31176.3			−0.626923			−0.313462	+	0.949601i	$0.601489\pi$
$224$			16476.0i			0.328363i
$225$	9555.62	+	37703.6i	0.188753	+	0.744763i
$226$	12312.8			0.241068
$227$			57660.9i			1.11900i	0.828831	+	0.559500i	$0.189007\pi$
$227$			57660.9i			1.11900i	−0.828831	+	0.559500i	$0.810993\pi$
$228$	31888.5	+	24814.8i	0.613429	+	0.477355i
$229$	−90613.4			−1.72791			−0.863956	−	0.503567i	$-0.832021\pi$
$229$	−90613.4			−1.72791			−0.863956	+	0.503567i	$0.832021\pi$
$230$		−	2361.78i		−	0.0446462i
$231$	11334.6	−	14565.7i	0.212414	−	0.272965i
$232$	−17302.1			−0.321457
$233$			105233.i			1.93839i	0.246294	+	0.969195i	$0.420787\pi$
$233$			105233.i			1.93839i	−0.246294	+	0.969195i	$0.579213\pi$
$234$	12754.4	−	3232.47i	0.232931	−	0.0590340i
$235$	18898.2			0.342204
$236$		−	6554.47i		−	0.117683i
$237$	27363.8	+	21293.9i	0.487170	+	0.379104i
$238$	8048.92			0.142097
$239$			14533.4i			0.254431i	0.991875	+	0.127216i	$0.0406040\pi$
$239$			14533.4i			0.254431i	−0.991875	+	0.127216i	$0.959396\pi$
$240$	12277.4	−	15777.1i	0.213149	−	0.273908i
$241$	41772.5			0.719212			0.359606	−	0.933104i	$-0.382911\pi$
$241$	41772.5			0.719212			0.359606	+	0.933104i	$0.382911\pi$
$242$		−	4821.10i		−	0.0823219i
$243$	58248.3	+	9690.99i	0.986441	+	0.164118i
$244$	35014.8			0.588129
$245$		−	24186.1i		−	0.402933i
$246$	23153.0	+	18017.1i	0.382593	+	0.297725i
$247$	−40672.9			−0.666670
$248$			60848.9i			0.989349i
$249$	2363.58	−	3037.34i	0.0381217	−	0.0489885i
$250$	16487.9			0.263806
$251$			101350.i			1.60870i	0.594156	+	0.804350i	$0.297486\pi$
$251$			101350.i			1.60870i	−0.594156	+	0.804350i	$0.702514\pi$
$252$	−5691.85	−	22458.4i	−0.0896298	−	0.353653i
$253$	−16415.8			−0.256462
$254$		−	22034.4i		−	0.341533i
$255$	−28059.3	−	21835.1i	−0.431516	−	0.335796i
$256$	11252.0			0.171692
$257$			30919.7i			0.468133i	0.972221	+	0.234067i	$0.0752034\pi$
$257$			30919.7i			0.468133i	−0.972221	+	0.234067i	$0.924797\pi$
$258$	20130.8	−	25869.2i	0.302428	−	0.388637i
$259$	−1624.21			−0.0242127
$260$			22804.1i			0.337339i
$261$	35971.7	−	9116.67i	0.528056	−	0.133830i
$262$	−1962.55			−0.0285903
$263$			30242.3i			0.437224i	0.975812	+	0.218612i	$0.0701529\pi$
$263$			30242.3i			0.437224i	−0.975812	+	0.218612i	$0.929847\pi$
$264$	27815.3	+	21645.2i	0.399094	+	0.310566i
$265$	27243.8			0.387951
$266$		−	7610.76i		−	0.107563i
$267$	−45536.5	+	58516.9i	−0.638759	+	0.820841i
$268$	75248.2			1.04767
$269$			28773.4i			0.397636i	0.980036	+	0.198818i	$0.0637103\pi$
$269$			28773.4i			0.397636i	−0.980036	+	0.198818i	$0.936290\pi$
$270$	4365.79	−	9960.85i	0.0598874	−	0.136637i
$271$	−9601.35			−0.130736			−0.0653678	−	0.997861i	$-0.520822\pi$
$271$	−9601.35			−0.130736			−0.0653678	+	0.997861i	$0.520822\pi$
$272$		−	60597.9i		−	0.819068i
$273$	18405.2	+	14322.5i	0.246954	+	0.192174i
$274$	−23511.8			−0.313173
$275$		−	49792.7i		−	0.658415i
$276$	−12655.6	+	16263.1i	−0.166136	+	0.213494i
$277$	45379.4			0.591425			0.295712	−	0.955277i	$-0.404443\pi$
$277$	45379.4			0.591425			0.295712	+	0.955277i	$0.404443\pi$
$278$		−	20615.8i		−	0.266754i
$279$	−32062.0	−	126507.i	−0.411890	−	1.62520i
$280$	−8987.74			−0.114640
$281$		−	25663.2i		−	0.325011i	−0.986708	−	0.162505i	$-0.948043\pi$
$281$		−	25663.2i		−	0.325011i	0.986708	−	0.162505i	$-0.0519575\pi$
$282$	13828.9	+	10761.3i	0.173896	+	0.135322i
$283$	−22433.1			−0.280102			−0.140051	−	0.990144i	$-0.544727\pi$
$283$	−22433.1			−0.280102			−0.140051	+	0.990144i	$0.544727\pi$
$284$			132028.i			1.63693i
$285$	−20646.5	+	26531.9i	−0.254189	+	0.326647i
$286$	−16843.8			−0.205925
$287$			51999.4i			0.631298i
$288$	65413.2	−	16578.3i	0.788644	−	0.199874i
$289$	−24251.5			−0.290364
$290$		−	6834.70i		−	0.0812687i
$291$	−52571.9	−	40910.2i	−0.620822	−	0.483109i
$292$	150515.			1.76528
$293$			11812.1i			0.137592i	0.997631	+	0.0687960i	$0.0219158\pi$
$293$			11812.1i			0.137592i	−0.997631	+	0.0687960i	$0.978084\pi$
$294$	13772.4	−	17698.3i	0.159337	−	0.204757i
$295$	5453.46			0.0626654
$296$		−	3101.67i		−	0.0354007i
$297$	−69234.0	−	30344.9i	−0.784886	−	0.344012i
$298$	37256.8			0.419540
$299$		−	20743.1i		−	0.232024i
$300$	−49329.3	−	38386.9i	−0.548104	−	0.426521i
$301$	58099.6			0.641269
$302$			17045.3i			0.186892i
$303$	−98471.3	+	126541.i	−1.07257	+	1.37831i
$304$	−57299.1			−0.620013
$305$			29133.1i			0.313175i
$306$	−8098.94	−	31956.0i	−0.0864939	−	0.341279i
$307$	−33184.0			−0.352089			−0.176045	−	0.984382i	$-0.556330\pi$
$307$	−33184.0			−0.352089			−0.176045	+	0.984382i	$0.556330\pi$
$308$			29659.2i			0.312650i
$309$	63151.9	+	49143.3i	0.661408	+	0.514692i
$310$	−24036.6			−0.250121
$311$		−	40356.1i		−	0.417242i	−0.977997	−	0.208621i	$-0.933102\pi$
$311$		−	40356.1i		−	0.417242i	0.977997	−	0.208621i	$-0.0668975\pi$
$312$	−27351.0	+	35147.5i	−0.280972	+	0.361065i
$313$	38161.1			0.389522			0.194761	−	0.980851i	$-0.437607\pi$
$313$	38161.1			0.389522			0.194761	+	0.980851i	$0.437607\pi$
$314$		−	190.115i		−	0.00192822i
$315$	18685.8	−	4735.74i	0.188318	−	0.0477273i
$316$	−55719.5			−0.557998
$317$			51035.0i			0.507866i	0.967222	+	0.253933i	$0.0817243\pi$
$317$			51035.0i			0.507866i	−0.967222	+	0.253933i	$0.918276\pi$
$318$	19935.9	+	15513.6i	0.197143	+	0.153412i
$319$	−47505.4			−0.466833
$320$			23111.3i			0.225697i
$321$	66289.8	−	85186.1i	0.643334	−	0.826720i
$322$	3881.48			0.0374357
$323$			101906.i			0.976773i
$324$	−83437.5	+	45195.9i	−0.794825	+	0.430535i
$325$	62918.2			0.595676
$326$		−	15327.5i		−	0.144223i
$327$	−50212.0	−	39073.8i	−0.469583	−	0.365418i
$328$	−99300.5			−0.923004
$329$			31058.3i			0.286937i
$330$	−8550.31	+	10987.6i	−0.0785153	+	0.100897i
$331$	26515.7			0.242017			0.121009	−	0.992651i	$-0.461387\pi$
$331$	26515.7			0.242017			0.121009	+	0.992651i	$0.461387\pi$
$332$			6184.76i			0.0561108i
$333$	1634.31	+	6448.49i	0.0147382	+	0.0581526i
$334$	−9895.79			−0.0887069
$335$			62608.1i			0.557880i
$336$	25928.9	+	20177.3i	0.229671	+	0.178724i
$337$	112632.			0.991747			0.495873	−	0.868395i	$-0.334848\pi$
$337$	112632.			0.991747			0.495873	+	0.868395i	$0.334848\pi$
$338$			14124.4i			0.123633i
$339$	54895.0	−	70543.1i	0.477676	−	0.613840i
$340$	57135.7			0.494253
$341$			167069.i			1.43677i
$342$	−30216.4	+	7658.06i	−0.258340	+	0.0654736i
$343$	87232.3			0.741463
$344$			110950.i			0.937583i
$345$	−13531.2	−	10529.7i	−0.113684	−	0.0884662i
$346$	29049.6			0.242654
$347$		−	110313.i		−	0.916150i	−0.888914	−	0.458075i	$-0.848539\pi$
$347$		−	110313.i		−	0.916150i	0.888914	−	0.458075i	$-0.151461\pi$
$348$	−36623.6	+	47063.3i	−0.302414	+	0.388619i
$349$	−153099.			−1.25696			−0.628480	−	0.777825i	$-0.716323\pi$
$349$	−153099.			−1.25696			−0.628480	+	0.777825i	$0.716323\pi$
$350$			11773.3i			0.0961089i
$351$	38344.0	−	87484.5i	0.311231	−	0.710095i
$352$	−86386.9			−0.697208
$353$		−	133847.i		−	1.07414i	−0.843538	−	0.537069i	$-0.819531\pi$
$353$		−	133847.i		−	1.07414i	0.843538	−	0.537069i	$-0.180469\pi$
$354$	3990.61	+	3105.40i	0.0318444	+	0.0247805i
$355$	−109850.			−0.871656
$356$		−	119155.i		−	0.940181i
$357$	35885.0	−	46114.3i	0.281564	−	0.361825i
$358$	−27956.0			−0.218127
$359$		−	63767.5i		−	0.494778i	−0.968916	−	0.247389i	$-0.920427\pi$
$359$		−	63767.5i		−	0.494778i	0.968916	−	0.247389i	$-0.0795725\pi$
$360$	9043.60	+	35683.4i	0.0697808	+	0.275335i
$361$	−33962.7			−0.260608
$362$			62502.4i			0.476958i
$363$	−27621.3	−	21494.2i	−0.209619	−	0.163120i
$364$	−37477.6			−0.282858
$365$			125232.i			0.940003i
$366$	−16589.4	+	21318.4i	−0.123842	+	0.159145i
$367$	186792.			1.38684			0.693419	−	0.720535i	$-0.256104\pi$
$367$	186792.			1.38684			0.693419	+	0.720535i	$0.256104\pi$
$368$		−	29222.5i		−	0.215785i
$369$	206449.	−	52322.5i	1.51621	−	0.384269i
$370$	1225.23			0.00894980
$371$			44774.0i			0.325296i
$372$	165515.	+	128800.i	1.19605	+	0.930741i
$373$	124262.			0.893142			0.446571	−	0.894748i	$-0.352645\pi$
$373$	124262.			0.893142			0.446571	+	0.894748i	$0.352645\pi$
$374$			42202.2i			0.301711i
$375$	73508.9	−	94463.0i	0.522730	−	0.671737i
$376$	−59310.5			−0.419523
$377$		−	60028.0i		−	0.422349i
$378$	16370.2	+	7174.98i	0.114570	+	0.0502154i
$379$	203837.			1.41907			0.709536	−	0.704669i	$-0.248904\pi$
$379$	203837.			1.41907			0.709536	+	0.704669i	$0.248904\pi$
$380$		−	54025.4i		−	0.374137i
$381$	−126240.	−	98237.3i	−0.869658	−	0.676747i
$382$	10838.2			0.0742732
$383$		−	21395.4i		−	0.145856i	−0.997337	−	0.0729278i	$-0.976766\pi$
$383$		−	21395.4i		−	0.145856i	0.997337	−	0.0729278i	$-0.0232343\pi$
$384$	−86836.5	+	111590.i	−0.588897	+	0.756766i
$385$	−24677.1			−0.166484
$386$		−	39058.5i		−	0.262145i
$387$	−58460.7	−	230669.i	−0.390339	−	1.54016i
$388$	107049.			0.711082
$389$			169974.i			1.12327i	0.827387	+	0.561633i	$0.189827\pi$
$389$			169974.i			1.12327i	−0.827387	+	0.561633i	$0.810173\pi$
$390$	−13884.0	−	10804.2i	−0.0912822	−	0.0710336i
$391$	−51971.9			−0.339950
$392$			75906.0i			0.493974i
$393$	−8749.77	+	11243.9i	−0.0566515	+	0.0728004i
$394$	−35910.8			−0.231331
$395$		−	46359.8i		−	0.297131i
$396$	117754.	−	29843.6i	0.750905	−	0.190309i
$397$	79161.1			0.502263			0.251131	−	0.967953i	$-0.419197\pi$
$397$	79161.1			0.502263			0.251131	+	0.967953i	$0.419197\pi$
$398$		−	49276.0i		−	0.311078i
$399$	−43604.0	−	33931.6i	−0.273892	−	0.213137i
$400$	88638.0			0.553987
$401$			74109.0i			0.460874i	0.973087	+	0.230437i	$0.0740156\pi$
$401$			74109.0i			0.460874i	−0.973087	+	0.230437i	$0.925984\pi$
$402$	−35651.3	+	45814.0i	−0.220609	+	0.283495i
$403$	−211110.			−1.29986
$404$		−	257669.i		−	1.57870i
$405$	−37603.9	−	69421.8i	−0.229257	−	0.423239i
$406$	11232.5			0.0681436
$407$		−	8516.08i		−	0.0514104i
$408$	88062.0	+	68527.7i	0.529015	+	0.411667i
$409$	65068.5			0.388977			0.194489	−	0.980905i	$-0.437695\pi$
$409$	65068.5			0.388977			0.194489	+	0.980905i	$0.437695\pi$
$410$		−	39225.8i		−	0.233348i
$411$	−104824.	+	134705.i	−0.620551	+	0.797443i
$412$	−128593.			−0.757568
$413$			8962.51i			0.0525448i
$414$	−3905.61	−	15410.4i	−0.0227870	−	0.0899109i
$415$	−5145.85			−0.0298787
$416$		−	109159.i		−	0.630772i
$417$	−118113.	−	91912.9i	−0.679245	−	0.528572i
$418$	39904.8			0.228388
$419$		−	178259.i		−	1.01537i	−0.861544	−	0.507683i	$-0.830502\pi$
$419$		−	178259.i		−	1.01537i	0.861544	−	0.507683i	$-0.169498\pi$
$420$	−19024.5	+	24447.5i	−0.107848	+	0.138591i
$421$	−312819.			−1.76494			−0.882469	−	0.470371i	$-0.844120\pi$
$421$	−312819.			−1.76494			−0.882469	+	0.470371i	$0.844120\pi$
$422$			19741.2i			0.110853i
$423$	123309.	−	31251.4i	0.689148	−	0.174658i
$424$	−85502.6			−0.475606
$425$		−	157641.i		−	0.872755i
$426$	−80383.9	−	62552.8i	−0.442945	−	0.344689i
$427$	−47878.9			−0.262596
$428$			173460.i			0.946915i
$429$	−75095.9	+	96502.5i	−0.408039	+	0.524353i
$430$	−43827.6			−0.237034
$431$			17810.0i			0.0958761i	0.998850	+	0.0479380i	$0.0152650\pi$
$431$			17810.0i			0.0958761i	−0.998850	+	0.0479380i	$0.984735\pi$
$432$	54018.3	−	123246.i	0.289450	−	0.660400i
$433$	−202203.			−1.07848			−0.539241	−	0.842152i	$-0.681289\pi$
$433$	−202203.			−1.07848			−0.539241	+	0.842152i	$0.681289\pi$
$434$		−	39503.1i		−	0.209726i
$435$	−39157.7	−	30471.6i	−0.206937	−	0.161034i
$436$	102244.			0.537854
$437$			49142.7i			0.257333i
$438$	−71311.6	+	91639.4i	−0.371717	+	0.477677i
$439$	46459.4			0.241071			0.120535	−	0.992709i	$-0.461539\pi$
$439$	46459.4			0.241071			0.120535	+	0.992709i	$0.461539\pi$
$440$		−	47124.6i		−	0.243412i
$441$	−39995.7	−	157811.i	−0.205654	−	0.811449i
$442$	−53326.8			−0.272961
$443$		−	159073.i		−	0.810565i	−0.914191	−	0.405283i	$-0.867173\pi$
$443$		−	159073.i		−	0.810565i	0.914191	−	0.405283i	$-0.132827\pi$
$444$	−8436.84	−	6565.35i	−0.0427971	−	0.0333036i
$445$	99139.3			0.500641
$446$			38650.6i			0.194306i
$447$	166104.	−	213454.i	0.831316	−	1.06829i
$448$	−37982.4			−0.189246
$449$		−	338279.i		−	1.67796i	−0.544162	−	0.838980i	$-0.683152\pi$
$449$		−	338279.i		−	1.67796i	0.544162	−	0.838980i	$-0.316848\pi$
$450$	46742.8	−	11846.5i	0.230829	−	0.0585013i
$451$	−272644.			−1.34042
$452$			143643.i			0.703085i
$453$	97657.0	+	75994.3i	0.475890	+	0.370326i
$454$	71484.7			0.346818
$455$		−	31182.1i		−	0.150620i
$456$	64797.3	−	83268.2i	0.311621	−	0.400451i
$457$	−151498.			−0.725394			−0.362697	−	0.931907i	$-0.618144\pi$
$457$	−151498.			−0.725394			−0.362697	+	0.931907i	$0.618144\pi$
$458$			112337.i			0.535542i
$459$	−219192.	−	96070.7i	−1.04040	−	0.456001i
$460$	27552.9			0.130212
$461$			345460.i			1.62553i	0.582590	+	0.812766i	$0.302039\pi$
$461$			345460.i			1.62553i	−0.582590	+	0.812766i	$0.697961\pi$
$462$	−18057.7	−	14052.1i	−0.0846015	−	0.0658348i
$463$	144569.			0.674394			0.337197	−	0.941434i	$-0.390521\pi$
$463$	144569.			0.674394			0.337197	+	0.941434i	$0.390521\pi$
$464$		−	84566.3i		−	0.392791i
$465$	−107164.	+	137712.i	−0.495614	+	0.636891i
$466$	130462.			0.600777
$467$			138749.i			0.636202i	0.948057	+	0.318101i	$0.103045\pi$
$467$			138749.i			0.636202i	−0.948057	+	0.318101i	$0.896955\pi$
$468$	37710.5	+	148794.i	0.172175	+	0.679352i
$469$	−102894.			−0.467781
$470$		−	23428.9i		−	0.106061i
$471$	−1089.21	−	847.600i	−0.00490988	−	0.00382075i
$472$	−17115.2			−0.0768244
$473$			304629.i			1.36160i
$474$	26399.0	−	33924.1i	0.117498	−	0.150991i
$475$	−149060.			−0.660654
$476$			93899.9i			0.414430i
$477$	177763.	−	45052.3i	0.781276	−	0.198007i
$478$	18017.6			0.0788573
$479$		−	435884.i		−	1.89977i	−0.312606	−	0.949883i	$-0.601202\pi$
$479$		−	435884.i		−	1.89977i	0.312606	−	0.949883i	$-0.398798\pi$
$480$	−71206.9	−	55411.5i	−0.309058	−	0.240501i
$481$	10761.0			0.0465116
$482$		−	51787.2i		−	0.222910i
$483$	17305.1	−	22238.0i	0.0741787	−	0.0953238i
$484$	56243.7			0.240095
$485$			89067.2i			0.378647i
$486$	12014.3	−	72213.0i	0.0508660	−	0.305733i
$487$	−243644.			−1.02730			−0.513650	−	0.858000i	$-0.671707\pi$
$487$	−243644.			−1.02730			−0.513650	+	0.858000i	$0.671707\pi$
$488$		−	91431.9i		−	0.383935i
$489$	−87814.9	−	68335.4i	−0.367240	−	0.285778i
$490$	−29984.5			−0.124883
$491$			14883.5i			0.0617365i	0.999523	+	0.0308682i	$0.00982723\pi$
$491$			14883.5i			0.0617365i	−0.999523	+	0.0308682i	$0.990173\pi$
$492$	−210191.	+	270107.i	−0.868326	+	1.11585i
$493$	−150400.			−0.618805
$494$			50423.9i			0.206625i
$495$	24830.5	+	97973.8i	0.101339	+	0.399852i
$496$	−297407.			−1.20889
$497$		−	180534.i		−	0.730881i
$498$	−3765.52	−	2930.23i	−0.0151833	−	0.0118153i
$499$	−26782.3			−0.107559			−0.0537794	−	0.998553i	$-0.517127\pi$
$499$	−26782.3			−0.107559			−0.0537794	+	0.998553i	$0.517127\pi$
$500$			192350.i			0.769399i
$501$	−44119.1	+	56695.5i	−0.175772	+	0.225877i
$502$	125648.			0.498594
$503$		−	71023.3i		−	0.280714i	−0.990101	−	0.140357i	$-0.955175\pi$
$503$		−	71023.3i		−	0.280714i	0.990101	−	0.140357i	$-0.0448251\pi$
$504$	−58644.0	+	14862.7i	−0.230867	+	0.0585111i
$505$	214386.			0.840646
$506$			20351.4i			0.0794866i
$507$	80922.0	+	62971.6i	0.314812	+	0.244979i
$508$	257056.			0.996095
$509$		−	323203.i		−	1.24750i	−0.781625	−	0.623748i	$-0.785609\pi$
$509$		−	323203.i		−	1.24750i	0.781625	−	0.623748i	$-0.214391\pi$
$510$	−27069.9	+	34786.4i	−0.104075	+	0.133742i
$511$	−205813.			−0.788190
$512$		−	265320.i		−	1.01212i
$513$	−90841.0	+	207260.i	−0.345181	+	0.787555i
$514$	38332.5			0.145091
$515$		−	106992.i		−	0.403400i
$516$	301794.	+	234849.i	1.13347	+	0.882042i
$517$	−162845.			−0.609249
$518$			2013.61i			0.00750438i
$519$	129514.	−	166433.i	0.480819	−	0.617879i
$520$	59546.9			0.220218
$521$			345707.i			1.27360i	0.771029	+	0.636800i	$0.219742\pi$
$521$			345707.i			1.27360i	−0.771029	+	0.636800i	$0.780258\pi$
$522$	−11302.3	−	44595.6i	−0.0414789	−	0.163663i
$523$	351547.			1.28523			0.642614	−	0.766190i	$-0.277850\pi$
$523$	351547.			1.28523			0.642614	+	0.766190i	$0.277850\pi$
$524$		−	22895.4i		−	0.0833847i
$525$	67452.4	+	52489.9i	0.244725	+	0.190439i
$526$	37492.7			0.135511
$527$			528934.i			1.90450i
$528$	−105794.	+	135951.i	−0.379483	+	0.487657i
$529$	254778.			0.910439
$530$		−	33775.4i		−	0.120240i
$531$	35583.2	−	9018.21i	0.126199	−	0.0319839i
$532$	88788.3			0.313713
$533$		−	344514.i		−	1.21270i
$534$	72546.0	+	56453.5i	0.254408	+	0.197974i
$535$	−144322.			−0.504226
$536$		−	196491.i		−	0.683931i
$537$	−124638.	+	160167.i	−0.432217	+	0.555424i
$538$	35671.6			0.123242
$539$			208411.i			0.717369i
$540$	116205.	+	50932.0i	0.398508	+	0.174664i
$541$	54991.5			0.187889			0.0939445	−	0.995577i	$-0.470052\pi$
$541$	54991.5			0.187889			0.0939445	+	0.995577i	$0.470052\pi$
$542$			11903.2i			0.0405196i
$543$	358092.	+	278659.i	1.21449	+	0.945090i
$544$	−273497.			−0.924177
$545$			85069.1i			0.286404i
$546$	17756.2	−	22817.8i	0.0595615	−	0.0765399i
$547$	484167.			1.61816			0.809078	−	0.587702i	$-0.199967\pi$
$547$	484167.			1.61816			0.809078	+	0.587702i	$0.199967\pi$
$548$		−	274292.i		−	0.913382i
$549$	48176.5	+	190090.i	0.159842	+	0.630688i
$550$	−61730.1			−0.204066
$551$			142213.i			0.468420i
$552$	42466.7	+	33046.6i	0.139370	+	0.108455i
$553$	76190.2			0.249143
$554$		−	56258.8i		−	0.183304i
$555$	5462.51	−	7019.63i	0.0177340	−	0.0227892i
$556$	240507.			0.777999
$557$		−	539693.i		−	1.73955i	−0.493450	−	0.869774i	$-0.664264\pi$
$557$		−	539693.i		−	1.73955i	0.493450	−	0.869774i	$-0.335736\pi$
$558$	−156836.	+	39748.6i	−0.503707	+	0.127660i
$559$	−384930.			−1.23185
$560$		−	43928.8i		−	0.140079i
$561$	241787.	+	188153.i	0.768257	+	0.597839i
$562$	−31815.7			−0.100732
$563$		−	303295.i		−	0.956860i	−0.878126	−	0.478430i	$-0.841206\pi$
$563$		−	303295.i		−	0.956860i	0.878126	−	0.478430i	$-0.158794\pi$
$564$	−125543.	+	161330.i	−0.394671	+	0.507175i
$565$	−119514.			−0.374388
$566$			27811.3i			0.0868136i
$567$	114092.	−	61800.3i	0.354885	−	0.192232i
$568$	344757.			1.06860
$569$			555992.i			1.71729i	0.512570	+	0.858645i	$0.328693\pi$
$569$			555992.i			1.71729i	−0.512570	+	0.858645i	$0.671307\pi$
$570$	32892.7	+	25596.3i	0.101240	+	0.0787822i
$571$	120473.			0.369503			0.184751	−	0.982785i	$-0.440852\pi$
$571$	120473.			0.369503			0.184751	+	0.982785i	$0.440852\pi$
$572$		−	196503.i		−	0.600588i
$573$	48320.9	−	62095.0i	0.147172	−	0.189124i
$574$	64465.9			0.195662
$575$		−	76020.5i		−	0.229930i
$576$	38218.5	+	150799.i	0.115194	+	0.454520i
$577$	373462.			1.12175			0.560873	−	0.827902i	$-0.310466\pi$
$577$	373462.			1.12175			0.560873	+	0.827902i	$0.310466\pi$
$578$			30065.7i			0.0899943i
$579$	−223776.	−	174137.i	−0.667507	−	0.519438i
$580$	79734.7			0.237023
$581$		−	8456.97i		−	0.0250532i
$582$	−50718.1	+	65175.6i	−0.149733	+	0.192415i
$583$	−234760.			−0.690695
$584$		−	393030.i		−	1.15239i
$585$	−123800.	+	31375.9i	−0.361751	+	0.0916821i
$586$	14644.0			0.0426447
$587$		−	651887.i		−	1.89189i	−0.324325	−	0.945946i	$-0.605137\pi$
$587$		−	651887.i		−	1.89189i	0.324325	−	0.945946i	$-0.394863\pi$
$588$	206472.	+	160671.i	0.597181	+	0.464712i
$589$	500141.			1.44166
$590$		−	6760.89i		−	0.0194223i
$591$	−160104.	+	205742.i	−0.458381	+	0.589045i
$592$	15159.8			0.0432565
$593$		−	391087.i		−	1.11215i	−0.831132	−	0.556075i	$-0.812307\pi$
$593$		−	391087.i		−	1.11215i	0.831132	−	0.556075i	$-0.187693\pi$
$594$	−37619.9	+	85832.4i	−0.106622	+	0.243264i
$595$	−78126.7			−0.220681
$596$			434644.i			1.22360i
$597$	−282314.	−	219690.i	−0.792108	−	0.616399i
$598$	−25716.2			−0.0719124
$599$			647307.i			1.80408i	0.431649	+	0.902041i	$0.357932\pi$
$599$			647307.i			1.80408i	−0.431649	+	0.902041i	$0.642068\pi$
$600$	−100237.	+	128810.i	−0.278436	+	0.357807i
$601$	358812.			0.993387			0.496694	−	0.867926i	$-0.334547\pi$
$601$	358812.			0.993387			0.496694	+	0.867926i	$0.334547\pi$
$602$		−	72028.6i		−	0.198752i
$603$	103533.	+	408511.i	0.284737	+	1.12349i
$604$	−198853.			−0.545079
$605$			46795.9i			0.127849i
$606$	156879.	+	122079.i	0.427187	+	0.332427i
$607$	−246639.			−0.669397			−0.334698	−	0.942325i	$-0.608634\pi$
$607$	−246639.			−0.669397			−0.334698	+	0.942325i	$0.608634\pi$
$608$			258609.i			0.699578i
$609$	50078.7	−	64353.9i	0.135026	−	0.173516i
$610$	36117.6			0.0970641
$611$		−	205772.i		−	0.551194i
$612$	372804.	−	94483.5i	0.995354	−	0.252263i
$613$	−95172.2			−0.253273			−0.126637	−	0.991949i	$-0.540418\pi$
$613$	−95172.2			−0.253273			−0.126637	+	0.991949i	$0.540418\pi$
$614$			41139.7i			0.109125i
$615$	−224734.	−	174883.i	−0.594182	−	0.462378i
$616$	77447.2			0.204101
$617$			745016.i			1.95702i	0.206196	+	0.978511i	$0.433891\pi$
$617$			745016.i			1.95702i	−0.206196	+	0.978511i	$0.566109\pi$
$618$	60925.0	−	78292.1i	0.159521	−	0.204994i
$619$	−321740.			−0.839699			−0.419849	−	0.907594i	$-0.637917\pi$
$619$	−321740.			−0.839699			−0.419849	+	0.907594i	$0.637917\pi$
$620$		−	280415.i		−	0.729488i
$621$	−105702.	−	46328.8i	−0.274095	−	0.120135i
$622$	−50031.2			−0.129318
$623$			162931.i			0.419786i
$624$	−171788.	−	133681.i	−0.441188	−	0.343322i
$625$	140082.			0.358609
$626$		−	47310.0i		−	0.120727i
$627$	177910.	−	228625.i	0.452549	−	0.581551i
$628$	2217.91			0.00562372
$629$		−	26961.6i		−	0.0681465i
$630$	−5871.10	−	23165.6i	−0.0147924	−	0.0583664i
$631$	421549.			1.05874			0.529370	−	0.848391i	$-0.322428\pi$
$631$	421549.			1.05874			0.529370	+	0.848391i	$0.322428\pi$
$632$			145497.i			0.364266i
$633$	113102.	+	88013.3i	0.282269	+	0.219655i
$634$	63270.3			0.157406
$635$			213876.i			0.530414i
$636$	−180984.	+	232575.i	−0.447432	+	0.574975i
$637$	−263349.			−0.649012
$638$			58894.5i			0.144688i
$639$	−716761.	+	181656.i	−1.75539	+	0.444886i
$640$	189055.			0.461561
$641$			651134.i			1.58473i	0.610050	+	0.792363i	$0.291149\pi$
$641$			651134.i			1.58473i	−0.610050	+	0.792363i	$0.708851\pi$
$642$	−105609.	−	82182.3i	−0.256230	−	0.199392i
$643$	359517.			0.869555			0.434777	−	0.900538i	$-0.356827\pi$
$643$	359517.			0.869555			0.434777	+	0.900538i	$0.356827\pi$
$644$			45282.0i			0.109183i
$645$	−195399.	+	251099.i	−0.469682	+	0.603567i
$646$	126337.			0.302737
$647$		−	591053.i		−	1.41194i	−0.708239	−	0.705972i	$-0.750510\pi$
$647$		−	591053.i		−	1.41194i	0.708239	−	0.705972i	$-0.249490\pi$
$648$	118017.	+	217875.i	0.281057	+	0.518868i
$649$	−46992.3			−0.111567
$650$		−	78002.4i		−	0.184621i
$651$	−226323.	−	176119.i	−0.534032	−	0.415571i
$652$	178813.			0.420633
$653$			305439.i			0.716305i	0.933663	+	0.358152i	$0.116593\pi$
$653$			305439.i			0.716305i	−0.933663	+	0.358152i	$0.883407\pi$
$654$	−48441.4	+	62250.0i	−0.113256	+	0.145540i
$655$	19049.5			0.0444018
$656$		−	485344.i		−	1.12783i
$657$	207092.	+	817124.i	0.479769	+	1.89303i
$658$	38504.4			0.0889321
$659$		−	369904.i		−	0.851761i	−0.904779	−	0.425880i	$-0.859964\pi$
$659$		−	369904.i		−	0.851761i	0.904779	−	0.425880i	$-0.140036\pi$
$660$	−128183.	−	99749.3i	−0.294269	−	0.228993i
$661$	−611896.			−1.40047			−0.700236	−	0.713911i	$-0.746922\pi$
$661$	−611896.			−1.40047			−0.700236	+	0.713911i	$0.746922\pi$
$662$		−	32872.6i		−	0.0750098i
$663$	−237751.	+	305523.i	−0.540872	+	0.695051i
$664$	16149.8			0.0366296
$665$			73873.8i			0.167050i
$666$	7994.47	−	2026.12i	0.0180236	−	0.00456790i
$667$	−72528.4			−0.163026
$668$		−	115446.i		−	0.258717i
$669$	221439.	+	172318.i	0.494768	+	0.385016i
$670$	77618.0			0.172907
$671$		−	251039.i		−	0.557566i
$672$	91066.3	−	117025.i	0.201660	−	0.259144i
$673$	507199.			1.11982			0.559910	−	0.828553i	$-0.310836\pi$
$673$	507199.			1.11982			0.559910	+	0.828553i	$0.310836\pi$
$674$		−	139634.i		−	0.307378i
$675$	140525.	−	320617.i	0.308422	−	0.703687i
$676$	−164777.			−0.360581
$677$		−	735950.i		−	1.60572i	−0.596165	−	0.802862i	$-0.703310\pi$
$677$		−	735950.i		−	1.60572i	0.596165	−	0.802862i	$-0.296690\pi$
$678$	−87455.4	−	68055.7i	−0.190251	−	0.148049i
$679$	−146378.			−0.317494
$680$		−	149195.i		−	0.322653i
$681$	318705.	−	409554.i	0.687218	−	0.883114i
$682$	207123.			0.445307
$683$		−	125399.i		−	0.268814i	−0.990926	−	0.134407i	$-0.957087\pi$
$683$		−	125399.i		−	0.268814i	0.990926	−	0.134407i	$-0.0429129\pi$
$684$	−89340.1	−	352510.i	−0.190956	−	0.753458i
$685$	228217.			0.486370
$686$		−	108146.i		−	0.229806i
$687$	643609.	+	500841.i	1.36367	+	1.06117i
$688$	−542282.			−1.14564
$689$		−	296643.i		−	0.624879i
$690$	−13054.1	+	16775.3i	−0.0274188	+	0.0352348i
$691$	463614.			0.970957			0.485478	−	0.874249i	$-0.338645\pi$
$691$	463614.			0.970957			0.485478	+	0.874249i	$0.338645\pi$
$692$			338897.i			0.707711i
$693$	−161015.	+	40807.8i	−0.335275	+	0.0849721i
$694$	−136759.			−0.283948
$695$			200107.i			0.414279i
$696$	122893.	+	95632.6i	0.253694	+	0.197418i
$697$	−863178.			−1.77678
$698$			189804.i			0.389577i
$699$	581648.	−	747451.i	1.19044	−	1.52978i
$700$	−137350.			−0.280305
$701$			95005.4i			0.193336i	0.995317	+	0.0966679i	$0.0308185\pi$
$701$			95005.4i			0.193336i	−0.995317	+	0.0966679i	$0.969182\pi$
$702$	−108458.	−	47536.7i	−0.220084	−	0.0964617i
$703$	−25493.9			−0.0515852
$704$		−	199150.i		−	0.401823i
$705$	−134230.	−	104455.i	−0.270067	−	0.210160i
$706$	−165936.			−0.332914
$707$			352334.i			0.704880i
$708$	−36228.0	+	46555.1i	−0.0722734	+	0.0928754i
$709$	−480418.			−0.955711			−0.477855	−	0.878439i	$-0.658586\pi$
$709$	−480418.			−0.955711			−0.477855	+	0.878439i	$0.658586\pi$
$710$			136186.i			0.270157i
$711$	−76663.7	−	302492.i	−0.151653	−	0.598378i
$712$	−311141.			−0.613758
$713$			255072.i			0.501745i
$714$	−57169.8	−	44488.2i	−0.112143	−	0.0872667i
$715$	163494.			0.319809
$716$		−	326139.i		−	0.636176i
$717$	80329.2	−	103228.i	0.156255	−	0.200797i
$718$	−79055.3			−0.153349
$719$		−	67823.7i		−	0.131197i	−0.997846	−	0.0655984i	$-0.979104\pi$
$719$		−	67823.7i		−	0.131197i	0.997846	−	0.0655984i	$-0.0208956\pi$
$720$	−174407.	+	44201.8i	−0.336434	+	0.0852658i
$721$	175836.			0.338250
$722$			42105.0i			0.0807717i
$723$	−296702.	−	230886.i	−0.567602	−	0.441694i
$724$	−729163.			−1.39107
$725$		−	219994.i		−	0.418537i
$726$	−26647.3	+	34243.3i	−0.0505568	+	0.0649684i
$727$	−594536.			−1.12489			−0.562444	−	0.826835i	$-0.690139\pi$
$727$	−594536.			−1.12489			−0.562444	+	0.826835i	$0.690139\pi$
$728$			97862.6i			0.184652i
$729$	−360162.	−	390785.i	−0.677708	−	0.735331i
$730$	155255.			0.291341
$731$			964441.i			1.80485i
$732$	−248703.	−	193535.i	−0.464151	−	0.361191i
$733$	95693.6			0.178105			0.0890523	−	0.996027i	$-0.471616\pi$
$733$	95693.6			0.178105			0.0890523	+	0.996027i	$0.471616\pi$
$734$		−	231574.i		−	0.429831i
$735$	−133682.	+	171789.i	−0.247456	+	0.317995i
$736$	−131890.			−0.243477
$737$		−	539493.i		−	0.993232i
$738$	−64866.5	−	255944.i	−0.119099	−	0.469929i
$739$	273743.			0.501249			0.250625	−	0.968084i	$-0.419364\pi$
$739$	273743.			0.501249			0.250625	+	0.968084i	$0.419364\pi$
$740$			14293.7i			0.0261024i
$741$	288891.	+	224808.i	0.526136	+	0.409426i
$742$	55508.3			0.100821
$743$			1.03592e6i			1.87649i	0.345965	+	0.938247i	$0.387551\pi$
$743$			1.03592e6i			1.87649i	−0.345965	+	0.938247i	$0.612449\pi$
$744$	336326.	−	432198.i	0.607595	−	0.780794i
$745$	−361633.			−0.651561
$746$		−	154053.i		−	0.276817i
$747$	−33576.1	+	8509.53i	−0.0601712	+	0.0152498i
$748$	−492337.			−0.879953
$749$		−	237187.i		−	0.422792i
$750$	−117110.	−	91132.1i	−0.208195	−	0.162013i
$751$	384578.			0.681875			0.340938	−	0.940086i	$-0.389256\pi$
$751$	384578.			0.681875			0.340938	+	0.940086i	$0.389256\pi$
$752$		−	289888.i		−	0.512619i
$753$	560183.	−	719866.i	0.987961	−	1.26959i
$754$	−74419.3			−0.130901
$755$		−	165450.i		−	0.290251i
$756$	−83704.4	+	190977.i	−0.146455	+	0.334148i
$757$	361144.			0.630214			0.315107	−	0.949056i	$-0.397960\pi$
$757$	361144.			0.630214			0.315107	+	0.949056i	$0.397960\pi$
$758$		−	252706.i		−	0.439821i
$759$	116598.	+	90734.1i	0.202399	+	0.157502i
$760$	−141073.			−0.244240
$761$			1.11964e6i			1.93335i	0.256005	+	0.966675i	$0.417594\pi$
$761$			1.11964e6i			1.93335i	−0.256005	+	0.966675i	$0.582406\pi$
$762$	−121789.	+	156506.i	−0.209748	+	0.269538i
$763$	−139807.			−0.240149
$764$			126441.i			0.216621i
$765$	78612.3	+	310181.i	0.134328	+	0.530020i
$766$	−26524.8			−0.0452059
$767$		−	59379.7i		−	0.100936i
$768$	−79920.6	−	62192.3i	−0.135499	−	0.105442i
$769$	215885.			0.365065			0.182532	−	0.983200i	$-0.441571\pi$
$769$	215885.			0.365065			0.182532	+	0.983200i	$0.441571\pi$
$770$			30593.3i			0.0515994i
$771$	170900.	−	219617.i	0.287498	−	0.369451i
$772$	455662.			0.764555
$773$		−	57812.8i		−	0.0967531i	−0.998829	−	0.0483765i	$-0.984595\pi$
$773$		−	57812.8i		−	0.0967531i	0.998829	−	0.0483765i	$-0.0154047\pi$
$774$	−285970.	+	72476.3i	−0.477352	+	0.120980i
$775$	−773685.			−1.28813
$776$		−	279530.i		−	0.464200i
$777$	11536.4	+	8977.39i	0.0191087	+	0.0148699i
$778$	210724.			0.348140
$779$			816189.i			1.34498i
$780$	126044.	−	161973.i	0.207172	−	0.266228i
$781$	946579.			1.55187
$782$			64431.8i			0.105363i
$783$	−305889.	−	134070.i	−0.498932	−	0.218679i
$784$	−371001.			−0.603591
$785$			1845.34i			0.00299460i
$786$	13939.6	+	10847.5i	0.0225634	+	0.0175583i
$787$	−415931.			−0.671539			−0.335770	−	0.941944i	$-0.608996\pi$
$787$	−415931.			−0.671539			−0.335770	+	0.941944i	$0.608996\pi$
$788$		−	418941.i		−	0.674685i
$789$	167156.	−	214805.i	0.268515	−	0.345057i
$790$	−57474.3			−0.0920914
$791$		−	196416.i		−	0.313924i
$792$	−77928.5	−	307483.i	−0.124236	−	0.490197i
$793$	317214.			0.504436
$794$		−	98139.5i		−	0.155669i
$795$	−193508.	−	150583.i	−0.306171	−	0.238255i
$796$	574861.			0.907271
$797$		−	311252.i		−	0.489999i	−0.969523	−	0.244999i	$-0.921212\pi$
$797$		−	311252.i		−	0.489999i	0.969523	−	0.244999i	$-0.0787878\pi$
$798$	−42066.4	+	54057.7i	−0.0660587	+	0.0848891i
$799$	−515562.			−0.807583
$800$		−	400051.i		−	0.625079i
$801$	646873.	−	163944.i	1.00822	−	0.255523i
$802$	91876.2			0.142841
$803$		−	1.07912e6i		−	1.67355i
$804$	−534473.	−	415914.i	−0.826825	−	0.643415i
$805$	−37675.6			−0.0581391
$806$			261722.i			0.402874i
$807$	159037.	−	204371.i	0.244203	−	0.313815i
$808$	−672833.			−1.03059
$809$		−	783698.i		−	1.19743i	−0.800961	−	0.598717i	$-0.795677\pi$
$809$		−	783698.i		−	1.19743i	0.800961	−	0.598717i	$-0.204323\pi$
$810$	−86065.2	+	46619.2i	−0.131177	+	0.0710550i
$811$	846897.			1.28762			0.643811	−	0.765184i	$-0.277352\pi$
$811$	846897.			1.28762			0.643811	+	0.765184i	$0.277352\pi$
$812$			131040.i			0.198743i
$813$	68196.4	+	53068.8i	0.103176	+	0.0802894i
$814$	−10557.8			−0.0159339
$815$			148776.i			0.223984i
$816$	−334938.	+	430415.i	−0.503019	+	0.646408i
$817$	911940.			1.36623
$818$		−	80668.2i		−	0.120558i
$819$	−51564.9	−	203460.i	−0.0768752	−	0.303327i
$820$	457614.			0.680569
$821$			258263.i			0.383156i	0.981477	+	0.191578i	$0.0613605\pi$
$821$			258263.i			0.383156i	−0.981477	+	0.191578i	$0.938639\pi$
$822$	167000.	+	129955.i	0.247156	+	0.192331i
$823$	275275.			0.406412			0.203206	−	0.979136i	$-0.434864\pi$
$823$	275275.			0.406412			0.203206	+	0.979136i	$0.434864\pi$
$824$			335785.i			0.494547i
$825$	−275215.	+	353667.i	−0.404357	+	0.519621i
$826$	11111.2			0.0162855
$827$			167434.i			0.244813i	0.992480	+	0.122406i	$0.0390611\pi$
$827$			167434.i			0.244813i	−0.992480	+	0.122406i	$0.960939\pi$
$828$	179780.	−	45563.4i	0.262229	−	0.0664593i
$829$	−482607.			−0.702239			−0.351119	−	0.936331i	$-0.614199\pi$
$829$	−482607.			−0.702239			−0.351119	+	0.936331i	$0.614199\pi$
$830$			6379.53i			0.00926046i
$831$	−322321.	−	250822.i	−0.466752	−	0.363215i
$832$	251647.			0.363534
$833$			659820.i			0.950901i
$834$	−113948.	+	146430.i	−0.163823	+	0.210522i
$835$	96053.4			0.137765
$836$			465536.i			0.666102i
$837$	−471504.	+	1.07577e6i	−0.673029	+	1.53556i
$838$	−220995.			−0.314698
$839$		−	214773.i		−	0.305109i	−0.988295	−	0.152555i	$-0.951250\pi$
$839$		−	214773.i		−	0.305109i	0.988295	−	0.152555i	$-0.0487500\pi$
$840$	63838.1	+	49677.3i	0.0904735	+	0.0704043i
$841$	497393.			0.703247
$842$			387816.i			0.547017i
$843$	−141846.	+	182280.i	−0.199601	+	0.256498i
$844$	−230303.			−0.323307
$845$		−	137098.i		−	0.192007i
$846$	−38743.7	−	152871.i	−0.0541327	−	0.213592i
$847$	−76907.0			−0.107201
$848$		−	417905.i		−	0.581147i
$849$	159338.	+	123993.i	0.221056	+	0.172021i
$850$	−195435.			−0.270498
$851$		−	13001.9i		−	0.0179534i
$852$	729751.	−	937771.i	1.00530	−	1.29187i
$853$	79692.2			0.109526			0.0547630	−	0.998499i	$-0.482560\pi$
$853$	79692.2			0.109526			0.0547630	+	0.998499i	$0.482560\pi$
$854$			59357.6i			0.0813880i
$855$	293296.	−	74332.9i	0.401211	−	0.101683i
$856$	452944.			0.618154
$857$			1.38019e6i			1.87922i	0.342248	+	0.939610i	$0.388812\pi$
$857$			1.38019e6i			1.87922i	−0.342248	+	0.939610i	$0.611188\pi$
$858$	119638.	+	93099.7i	0.162516	+	0.126466i
$859$	−1.03198e6			−1.39857			−0.699287	−	0.714841i	$-0.746499\pi$
$859$	−1.03198e6			−1.39857			−0.699287	+	0.714841i	$0.746499\pi$
$860$		−	511299.i		−	0.691319i
$861$	287412.	−	369341.i	0.387703	−	0.498220i
$862$	22079.9			0.0297154
$863$		−	1.18152e6i		−	1.58643i	−0.608944	−	0.793214i	$-0.708406\pi$
$863$		−	1.18152e6i		−	1.58643i	0.608944	−	0.793214i	$-0.291594\pi$
$864$	−556249.	−	243801.i	−0.745147	−	0.326594i
$865$	−281970.			−0.376852
$866$			250680.i			0.334260i
$867$	172254.	+	134044.i	0.229156	+	0.178323i
$868$	460849.			0.611673
$869$			399481.i			0.529002i
$870$	−37776.9	+	48545.5i	−0.0499101	+	0.0641373i
$871$	681705.			0.898588
$872$		−	266983.i		−	0.351115i
$873$	147288.	+	581153.i	0.193258	+	0.762539i
$874$	60924.3			0.0797568
$875$		−	263017.i		−	0.343533i
$876$	−1.06908e6	−	831932.i	−1.39316	−	1.08413i
$877$	−1.28447e6			−1.67004			−0.835018	−	0.550223i	$-0.814543\pi$
$877$	−1.28447e6			−1.67004			−0.835018	+	0.550223i	$0.814543\pi$
$878$		−	57597.7i		−	0.0747165i
$879$	65288.4	−	83899.2i	0.0845002	−	0.108588i
$880$	230328.			0.297427
$881$			199735.i			0.257337i	0.991688	+	0.128668i	$0.0410703\pi$
$881$			199735.i			0.257337i	−0.991688	+	0.128668i	$0.958930\pi$
$882$	−195646.	+	49584.4i	−0.251497	+	0.0637394i
$883$	23082.9			0.0296053			0.0148027	−	0.999890i	$-0.495288\pi$
$883$	23082.9			0.0296053			0.0148027	+	0.999890i	$0.495288\pi$
$884$		−	622119.i		−	0.796103i
$885$	−38734.8	−	30142.5i	−0.0494555	−	0.0384851i
$886$	−197209.			−0.251223
$887$		−	7396.20i		−	0.00940073i	−0.999989	−	0.00470036i	$-0.998504\pi$
$887$		−	7396.20i		−	0.00940073i	0.999989	−	0.00470036i	$-0.00149618\pi$
$888$	−17143.6	+	22030.6i	−0.0217409	+	0.0279383i
$889$	−351496.			−0.444751
$890$		−	122907.i		−	0.155166i
$891$	324032.	+	598206.i	0.408162	+	0.753521i
$892$	−450904.			−0.566701
$893$			487496.i			0.611320i
$894$	−264628.	−	205927.i	−0.331101	−	0.257655i
$895$	271355.			0.338759
$896$			310704.i			0.387017i
$897$	−114652.	+	147334.i	−0.142494	+	0.183113i
$898$	−419379.			−0.520060
$899$			738145.i			0.913318i
$900$	138203.	+	545309.i	0.170621	+	0.673221i
$901$	−743239.			−0.915543
$902$			338008.i			0.415445i
$903$	−412670.	−	321130.i	−0.506090	−	0.393827i
$904$	375085.			0.458979
$905$		−	606679.i		−	0.740734i
$906$	94213.4	−	121070.i	0.114777	−	0.147495i
$907$	−296243.			−0.360109			−0.180054	−	0.983657i	$-0.557627\pi$
$907$	−296243.			−0.360109			−0.180054	+	0.983657i	$0.557627\pi$
$908$			833952.i			1.01151i
$909$	1.39884e6	−	354523.i	1.69294	−	0.429059i
$910$	−38657.8			−0.0466826
$911$		−	53030.5i		−	0.0638983i	−0.999489	−	0.0319491i	$-0.989829\pi$
$911$		−	53030.5i		−	0.0638983i	0.999489	−	0.0319491i	$-0.0101715\pi$
$912$	406984.	+	316705.i	0.489314	+	0.380773i
$913$	44341.7			0.0531950
$914$			187818.i			0.224826i
$915$	161025.	−	206926.i	0.192332	−	0.247158i
$916$	−1.31055e6			−1.56193
$917$			31307.0i			0.0372308i
$918$	−119103.	+	271742.i	−0.141331	+	0.322457i
$919$	−369645.			−0.437677			−0.218838	−	0.975761i	$-0.570227\pi$
$919$	−369645.			−0.437677			−0.218838	+	0.975761i	$0.570227\pi$
$920$		−	71947.1i		−	0.0850036i
$921$	235700.	+	183416.i	0.277869	+	0.216231i
$922$	428281.			0.503811
$923$			1.19610e6i			1.40399i
$924$	163933.	−	210664.i	0.192010	−	0.246744i
$925$	39437.3			0.0460918
$926$		−	179229.i		−	0.209019i
$927$	−176929.	−	698110.i	−0.205892	−	0.812389i
$928$	−381674.			−0.443197
$929$		−	957471.i		−	1.10942i	−0.832045	−	0.554708i	$-0.812830\pi$
$929$		−	957471.i		−	1.10942i	0.832045	−	0.554708i	$-0.187170\pi$
$930$	170727.	+	132856.i	0.197395	+	0.153608i
$931$	623902.			0.719808
$932$			1.52199e6i			1.75219i
$933$	−223057.	+	286641.i	−0.256244	+	0.329287i
$934$	172013.			0.197182
$935$		−	409635.i		−	0.468569i
$936$	388537.	−	98470.8i	0.443486	−	0.112397i
$937$	1.28478e6			1.46336			0.731680	−	0.681648i	$-0.238737\pi$
$937$	1.28478e6			1.46336			0.731680	+	0.681648i	$0.238737\pi$
$938$			127562.i			0.144982i
$939$	−271051.	−	210925.i	−0.307411	−	0.239220i
$940$	273325.			0.309332
$941$			393769.i			0.444695i	0.974967	+	0.222348i	$0.0713720\pi$
$941$			393769.i			0.444695i	−0.974967	+	0.222348i	$0.928628\pi$
$942$	−1050.81	+	1350.35i	−0.00118419	+	0.00152175i
$943$	−416256.			−0.468098
$944$		−	83653.0i		−	0.0938723i
$945$	−158897.	−	69643.9i	−0.177931	−	0.0779865i
$946$	377661.			0.422007
$947$		−	976398.i		−	1.08875i	−0.838843	−	0.544373i	$-0.816768\pi$
$947$		−	976398.i		−	1.08875i	0.838843	−	0.544373i	$-0.183232\pi$
$948$	395764.	+	307974.i	0.440372	+	0.342687i
$949$	1.36358e6			1.51408
$950$			184796.i			0.204760i
$951$	282082.	−	362491.i	0.311899	−	0.400808i
$952$	245194.			0.270543
$953$			1.70287e6i			1.87498i	0.348015	+	0.937489i	$0.386856\pi$
$953$			1.70287e6i			1.87498i	−0.348015	+	0.937489i	$0.613144\pi$
$954$	−55853.2	−	220380.i	−0.0613694	−	0.242145i
$955$	−105201.			−0.115349
$956$			210197.i			0.229990i
$957$	337421.	+	262573.i	0.368424	+	0.286699i
$958$	−540384.			−0.588805
$959$			375064.i			0.407820i
$960$	127742.	−	164155.i	0.138609	−	0.178120i
$961$	1.67243e6			1.81092
$962$		−	13340.8i		−	0.0144156i
$963$	−941686.	+	238661.i	−1.01544	+	0.257353i
$964$	604158.			0.650124
$965$			379121.i			0.407121i
$966$	−27569.4	−	21453.8i	−0.0295443	−	0.0229906i
$967$	494765.			0.529110			0.264555	−	0.964371i	$-0.414775\pi$
$967$	494765.			0.529110			0.264555	+	0.964371i	$0.414775\pi$
$968$		−	146865.i		−	0.156736i
$969$	563256.	−	723816.i	0.599872	−	0.770869i
$970$	110420.			0.117356
$971$		−	750250.i		−	0.795734i	−0.917443	−	0.397867i	$-0.869751\pi$
$971$		−	750250.i		−	0.795734i	0.917443	−	0.397867i	$-0.130249\pi$
$972$	842448.	+	140161.i	0.891683	+	0.148353i
$973$	−328867.			−0.347372
$974$			302056.i			0.318397i
$975$	−446896.	−	347763.i	−0.470107	−	0.365826i
$976$	446885.			0.469134
$977$			62851.3i			0.0658453i	0.999458	+	0.0329227i	$0.0104815\pi$
$977$			62851.3i			0.0658453i	−0.999458	+	0.0329227i	$0.989518\pi$
$978$	−84718.4	+	108868.i	−0.0885727	+	0.113821i
$979$	−854282.			−0.891324
$980$		−	349804.i		−	0.364227i
$981$	140676.	+	555066.i	0.146178	+	0.576776i
$982$	18451.7			0.0191344
$983$			805340.i			0.833436i	0.909036	+	0.416718i	$0.136820\pi$
$983$			805340.i			0.833436i	−0.909036	+	0.416718i	$0.863180\pi$
$984$	705311.	+	548856.i	0.728435	+	0.566850i
$985$	348568.			0.359265
$986$			186457.i			0.191790i
$987$	171667.	−	220601.i	0.176218	−	0.226451i
$988$	−588253.			−0.602630
$989$			465089.i			0.475492i
$990$	121462.	−	30783.4i	0.123928	−	0.0314085i
$991$	974373.			0.992151			0.496075	−	0.868279i	$-0.334774\pi$
$991$	974373.			0.992151			0.496075	+	0.868279i	$0.334774\pi$
$992$			1.34229e6i			1.36403i
$993$	−188335.	−	146558.i	−0.191000	−	0.148632i
$994$	−223816.			−0.226526
$995$			478297.i			0.483116i
$996$	34184.6	−	43929.1i	0.0344597	−	0.0442826i
$997$	−1.77189e6			−1.78257			−0.891287	−	0.453440i	$-0.850197\pi$
$997$	−1.77189e6			−1.78257			−0.891287	+	0.453440i	$0.850197\pi$
$998$			33203.1i			0.0333364i
$999$	24034.1	−	54835.5i	0.0240823	−	0.0549453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.33	✓	78
3.2	odd	2	inner	177.5.b.a.119.46	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.33	✓	78	1.1	even	1	trivial
177.5.b.a.119.46	yes	78	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.23974i q^{2} +(-7.10280 - 5.52723i) q^{3} +14.4630 q^{4} +12.0336i q^{5} +(-6.85234 + 8.80565i) q^{6} -19.7766 q^{7} -37.7663i q^{8} +(19.8995 + 78.5176i) q^{9} +O(q^{10})\)	\(q-1.23974i q^{2} +(-7.10280 - 5.52723i) q^{3} +14.4630 q^{4} +12.0336i q^{5} +(-6.85234 + 8.80565i) q^{6} -19.7766 q^{7} -37.7663i q^{8} +(19.8995 + 78.5176i) q^{9} +14.9185 q^{10} -103.693i q^{11} +(-102.728 - 79.9405i) q^{12} +131.027 q^{13} +24.5179i q^{14} +(66.5122 - 85.4719i) q^{15} +184.588 q^{16} -328.287i q^{17} +(97.3416 - 24.6703i) q^{18} -310.416 q^{19} +174.042i q^{20} +(140.469 + 109.310i) q^{21} -128.553 q^{22} -158.312i q^{23} +(-208.743 + 268.247i) q^{24} +480.194 q^{25} -162.440i q^{26} +(292.642 - 667.684i) q^{27} -286.030 q^{28} -458.135i q^{29} +(-105.963 - 82.4580i) q^{30} -1611.19 q^{31} -833.103i q^{32} +(-573.134 + 736.510i) q^{33} -406.992 q^{34} -237.983i q^{35} +(287.807 + 1135.60i) q^{36} +82.1279 q^{37} +384.837i q^{38} +(-930.657 - 724.215i) q^{39} +454.463 q^{40} -2629.34i q^{41} +(135.516 - 174.146i) q^{42} -2937.80 q^{43} -1499.71i q^{44} +(-944.846 + 239.462i) q^{45} -196.266 q^{46} -1570.46i q^{47} +(-1311.09 - 1020.26i) q^{48} -2009.89 q^{49} -595.317i q^{50} +(-1814.52 + 2331.76i) q^{51} +1895.05 q^{52} -2263.99i q^{53} +(-827.756 - 362.801i) q^{54} +1247.79 q^{55} +746.890i q^{56} +(2204.83 + 1715.74i) q^{57} -567.970 q^{58} -453.188i q^{59} +(961.968 - 1236.18i) q^{60} +2420.99 q^{61} +1997.47i q^{62} +(-393.545 - 1552.81i) q^{63} +1920.57 q^{64} +1576.72i q^{65} +(913.083 + 710.539i) q^{66} +5202.79 q^{67} -4748.03i q^{68} +(-875.028 + 1124.46i) q^{69} -295.038 q^{70} +9128.68i q^{71} +(2965.32 - 751.532i) q^{72} +10406.9 q^{73} -101.818i q^{74} +(-3410.72 - 2654.14i) q^{75} -4489.56 q^{76} +2050.69i q^{77} +(-897.841 + 1153.78i) q^{78} -3852.54 q^{79} +2221.25i q^{80} +(-5769.02 + 3124.92i) q^{81} -3259.70 q^{82} +427.625i q^{83} +(2031.61 + 1580.95i) q^{84} +3950.46 q^{85} +3642.11i q^{86} +(-2532.22 + 3254.04i) q^{87} -3916.10 q^{88} -8238.58i q^{89} +(296.871 + 1171.37i) q^{90} -2591.27 q^{91} -2289.67i q^{92} +(11444.0 + 8905.44i) q^{93} -1946.97 q^{94} -3735.41i q^{95} +(-4604.75 + 5917.36i) q^{96} +7401.57 q^{97} +2491.74i q^{98} +(8141.71 - 2063.44i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

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