LMFDB - Embedded newform 177.5.b.a.119.39

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			119.39
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.120344i q^{2} +(5.74463 + 6.92815i) q^{3} +15.9855 q^{4} -19.8202i q^{5} +(0.833764 - 0.691335i) q^{6} -29.4765 q^{7} -3.84928i q^{8} +(-14.9984 + 79.5993i) q^{9} +O(q^{10})$	\(q-0.120344i q^{2} +(5.74463 + 6.92815i) q^{3} +15.9855 q^{4} -19.8202i q^{5} +(0.833764 - 0.691335i) q^{6} -29.4765 q^{7} -3.84928i q^{8} +(-14.9984 + 79.5993i) q^{9} -2.38526 q^{10} +92.4333i q^{11} +(91.8309 + 110.750i) q^{12} +314.660 q^{13} +3.54733i q^{14} +(137.317 - 113.860i) q^{15} +255.305 q^{16} +150.847i q^{17} +(9.57933 + 1.80498i) q^{18} -29.2547 q^{19} -316.837i q^{20} +(-169.331 - 204.217i) q^{21} +11.1238 q^{22} -209.291i q^{23} +(26.6684 - 22.1127i) q^{24} +232.158 q^{25} -37.8676i q^{26} +(-637.636 + 353.357i) q^{27} -471.197 q^{28} +933.393i q^{29} +(-13.7024 - 16.5254i) q^{30} +1446.21 q^{31} -92.3130i q^{32} +(-640.391 + 530.995i) q^{33} +18.1536 q^{34} +584.230i q^{35} +(-239.758 + 1272.44i) q^{36} -753.498 q^{37} +3.52065i q^{38} +(1807.60 + 2180.01i) q^{39} -76.2936 q^{40} -3097.99i q^{41} +(-24.5764 + 20.3781i) q^{42} +441.582 q^{43} +1477.59i q^{44} +(1577.68 + 297.272i) q^{45} -25.1871 q^{46} -1614.41i q^{47} +(1466.63 + 1768.79i) q^{48} -1532.14 q^{49} -27.9390i q^{50} +(-1045.09 + 866.560i) q^{51} +5030.00 q^{52} +4434.77i q^{53} +(42.5246 + 76.7360i) q^{54} +1832.05 q^{55} +113.463i q^{56} +(-168.058 - 202.681i) q^{57} +112.329 q^{58} -453.188i q^{59} +(2195.09 - 1820.11i) q^{60} -1883.53 q^{61} -174.043i q^{62} +(442.101 - 2346.31i) q^{63} +4073.77 q^{64} -6236.63i q^{65} +(63.9023 + 77.0676i) q^{66} -1958.03 q^{67} +2411.37i q^{68} +(1450.00 - 1202.30i) q^{69} +70.3089 q^{70} +1688.08i q^{71} +(306.400 + 57.7331i) q^{72} -2752.02 q^{73} +90.6794i q^{74} +(1333.66 + 1608.43i) q^{75} -467.652 q^{76} -2724.61i q^{77} +(262.352 - 217.535i) q^{78} -9022.96 q^{79} -5060.21i q^{80} +(-6111.09 - 2387.73i) q^{81} -372.826 q^{82} +4221.20i q^{83} +(-2706.85 - 3264.52i) q^{84} +2989.82 q^{85} -53.1420i q^{86} +(-6466.68 + 5362.00i) q^{87} +355.802 q^{88} -1187.89i q^{89} +(35.7751 - 189.865i) q^{90} -9275.06 q^{91} -3345.63i q^{92} +(8307.94 + 10019.5i) q^{93} -194.285 q^{94} +579.836i q^{95} +(639.558 - 530.304i) q^{96} +610.655 q^{97} +184.384i q^{98} +(-7357.62 - 1386.35i) 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 $

$2$		−	0.120344i		−	0.0300861i	−0.999887	−	0.0150431i	$-0.995211\pi$
$2$		−	0.120344i		−	0.0300861i	0.999887	−	0.0150431i	$-0.00478853\pi$
$3$	5.74463	+	6.92815i	0.638292	+	0.769794i
$3$	5.74463	+	6.92815i	0.638292	+	0.769794i
$4$	15.9855			0.999095
$5$		−	19.8202i		−	0.792809i	−0.918076	−	0.396405i	$-0.870258\pi$
$5$		−	19.8202i		−	0.792809i	0.918076	−	0.396405i	$-0.129742\pi$
$6$	0.833764	−	0.691335i	0.0231601	−	0.0192037i
$7$	−29.4765			−0.601561			−0.300780	−	0.953693i	$-0.597247\pi$
$7$	−29.4765			−0.601561			−0.300780	+	0.953693i	$0.597247\pi$
$8$		−	3.84928i		−	0.0601450i
$9$	−14.9984	+	79.5993i	−0.185166	+	0.982707i
$10$	−2.38526			−0.0238526
$11$			92.4333i			0.763911i	0.924181	+	0.381956i	$0.124749\pi$
$11$			92.4333i			0.763911i	−0.924181	+	0.381956i	$0.875251\pi$
$12$	91.8309	+	110.750i	0.637715	+	0.769097i
$13$	314.660			1.86189			0.930946	−	0.365156i	$-0.118984\pi$
$13$	314.660			1.86189			0.930946	+	0.365156i	$0.118984\pi$
$14$			3.54733i			0.0180986i
$15$	137.317	−	113.860i	0.610300	−	0.506044i
$16$	255.305			0.997285
$17$			150.847i			0.521962i	0.965344	+	0.260981i	$0.0840459\pi$
$17$			150.847i			0.521962i	−0.965344	+	0.260981i	$0.915954\pi$
$18$	9.57933	+	1.80498i	0.0295658	+	0.00557092i
$19$	−29.2547			−0.0810380			−0.0405190	−	0.999179i	$-0.512901\pi$
$19$	−29.2547			−0.0810380			−0.0405190	+	0.999179i	$0.512901\pi$
$20$		−	316.837i		−	0.792092i
$21$	−169.331	−	204.217i	−0.383971	−	0.463078i
$22$	11.1238			0.0229831
$23$		−	209.291i		−	0.395636i	−0.980239	−	0.197818i	$-0.936615\pi$
$23$		−	209.291i		−	0.395636i	0.980239	−	0.197818i	$-0.0633855\pi$
$24$	26.6684	−	22.1127i	0.0462993	−	0.0383901i
$25$	232.158			0.371453
$26$		−	37.8676i		−	0.0560171i
$27$	−637.636	+	353.357i	−0.874672	+	0.484715i
$28$	−471.197			−0.601016
$29$			933.393i			1.10986i	0.831897	+	0.554930i	$0.187255\pi$
$29$			933.393i			1.10986i	−0.831897	+	0.554930i	$0.812745\pi$
$30$	−13.7024	−	16.5254i	−0.0152249	−	0.0183616i
$31$	1446.21			1.50490			0.752450	−	0.658650i	$-0.228872\pi$
$31$	1446.21			1.50490			0.752450	+	0.658650i	$0.228872\pi$
$32$		−	92.3130i		−	0.0901494i
$33$	−640.391	+	530.995i	−0.588054	+	0.487599i
$34$	18.1536			0.0157038
$35$			584.230i			0.476923i
$36$	−239.758	+	1272.44i	−0.184998	+	0.981818i
$37$	−753.498			−0.550401			−0.275200	−	0.961387i	$-0.588744\pi$
$37$	−753.498			−0.550401			−0.275200	+	0.961387i	$0.588744\pi$
$38$			3.52065i			0.00243812i
$39$	1807.60	+	2180.01i	1.18843	+	1.43327i
$40$	−76.2936			−0.0476835
$41$		−	3097.99i		−	1.84295i	−0.388443	−	0.921473i	$-0.626987\pi$
$41$		−	3097.99i		−	1.84295i	0.388443	−	0.921473i	$-0.373013\pi$
$42$	−24.5764	+	20.3781i	−0.0139322	+	0.0115522i
$43$	441.582			0.238822			0.119411	−	0.992845i	$-0.461899\pi$
$43$	441.582			0.238822			0.119411	+	0.992845i	$0.461899\pi$
$44$			1477.59i			0.763220i
$45$	1577.68	+	297.272i	0.779100	+	0.146801i
$46$	−25.1871			−0.0119031
$47$		−	1614.41i		−	0.730832i	−0.930844	−	0.365416i	$-0.880927\pi$
$47$		−	1614.41i		−	0.730832i	0.930844	−	0.365416i	$-0.119073\pi$
$48$	1466.63	+	1768.79i	0.636560	+	0.767704i
$49$	−1532.14			−0.638125
$50$		−	27.9390i		−	0.0111756i
$51$	−1045.09	+	866.560i	−0.401803	+	0.333164i
$52$	5030.00			1.86021
$53$			4434.77i			1.57877i	0.613897	+	0.789386i	$0.289601\pi$
$53$			4434.77i			1.57877i	−0.613897	+	0.789386i	$0.710399\pi$
$54$	42.5246	+	76.7360i	0.0145832	+	0.0263155i
$55$	1832.05			0.605636
$56$			113.463i			0.0361809i
$57$	−168.058	−	202.681i	−0.0517260	−	0.0623826i
$58$	112.329			0.0333914
$59$		−	453.188i		−	0.130189i
$59$		−	453.188i		−	0.130189i
$60$	2195.09	−	1820.11i	0.609747	−	0.505586i
$61$	−1883.53			−0.506190			−0.253095	−	0.967441i	$-0.581448\pi$
$61$	−1883.53			−0.506190			−0.253095	+	0.967441i	$0.581448\pi$
$62$		−	174.043i		−	0.0452766i
$63$	442.101	−	2346.31i	0.111388	−	0.591158i
$64$	4073.77			0.994573
$65$		−	6236.63i		−	1.47613i
$66$	63.9023	+	77.0676i	0.0146700	+	0.0176923i
$67$	−1958.03			−0.436184			−0.218092	−	0.975928i	$-0.569983\pi$
$67$	−1958.03			−0.436184			−0.218092	+	0.975928i	$0.569983\pi$
$68$			2411.37i			0.521489i
$69$	1450.00	−	1202.30i	0.304558	−	0.252531i
$70$	70.3089			0.0143488
$71$			1688.08i			0.334870i	0.985883	+	0.167435i	$0.0535484\pi$
$71$			1688.08i			0.334870i	−0.985883	+	0.167435i	$0.946452\pi$
$72$	306.400	+	57.7331i	0.0591049	+	0.0111368i
$73$	−2752.02			−0.516424			−0.258212	−	0.966088i	$-0.583133\pi$
$73$	−2752.02			−0.516424			−0.258212	+	0.966088i	$0.583133\pi$
$74$			90.6794i			0.0165594i
$75$	1333.66	+	1608.43i	0.237096	+	0.285943i
$76$	−467.652			−0.0809647
$77$		−	2724.61i		−	0.459539i
$78$	262.352	−	217.535i	0.0431216	−	0.0357553i
$79$	−9022.96			−1.44576			−0.722878	−	0.690976i	$-0.757181\pi$
$79$	−9022.96			−1.44576			−0.722878	+	0.690976i	$0.757181\pi$
$80$		−	5060.21i		−	0.790657i
$81$	−6111.09	−	2387.73i	−0.931427	−	0.363927i
$82$	−372.826			−0.0554471
$83$			4221.20i			0.612746i	0.951912	+	0.306373i	$0.0991154\pi$
$83$			4221.20i			0.612746i	−0.951912	+	0.306373i	$0.900885\pi$
$84$	−2706.85	−	3264.52i	−0.383624	−	0.462659i
$85$	2989.82			0.413816
$86$		−	53.1420i		−	0.00718524i
$87$	−6466.68	+	5362.00i	−0.854364	+	0.708416i
$88$	355.802			0.0459455
$89$		−	1187.89i		−	0.149967i	−0.997185	−	0.0749835i	$-0.976110\pi$
$89$		−	1187.89i		−	0.149967i	0.997185	−	0.0749835i	$-0.0238904\pi$
$90$	35.7751	−	189.865i	0.00441668	−	0.0234401i
$91$	−9275.06			−1.12004
$92$		−	3345.63i		−	0.395278i
$93$	8307.94	+	10019.5i	0.960566	+	1.15846i
$94$	−194.285			−0.0219879
$95$			579.836i			0.0642477i
$96$	639.558	−	530.304i	0.0693965	−	0.0575417i
$97$	610.655			0.0649011			0.0324506	−	0.999473i	$-0.489669\pi$
$97$	610.655			0.0649011			0.0324506	+	0.999473i	$0.489669\pi$
$98$			184.384i			0.0191987i
$99$	−7357.62	−	1386.35i	−0.750701	−	0.141450i
$100$	3711.17			0.371117
$101$		−	14623.2i		−	1.43351i	−0.697327	−	0.716753i	$-0.745627\pi$
$101$		−	14623.2i		−	1.43351i	0.697327	−	0.716753i	$-0.254373\pi$
$102$	104.286	+	125.771i	0.0100236	+	0.0120887i
$103$	1718.83			0.162016			0.0810082	−	0.996713i	$-0.474186\pi$
$103$	1718.83			0.162016			0.0810082	+	0.996713i	$0.474186\pi$
$104$		−	1211.21i		−	0.111984i
$105$	−4047.63	+	3356.19i	−0.367132	+	0.304416i
$106$	533.700			0.0474991
$107$		−	8684.53i		−	0.758540i	−0.925286	−	0.379270i	$-0.876175\pi$
$107$		−	8684.53i		−	0.758540i	0.925286	−	0.379270i	$-0.123825\pi$
$108$	−10192.9	+	5648.60i	−0.873880	+	0.484276i
$109$	−13498.1			−1.13611			−0.568054	−	0.822991i	$-0.692304\pi$
$109$	−13498.1			−1.13611			−0.568054	+	0.822991i	$0.692304\pi$
$110$		−	220.477i		−	0.0182212i
$111$	−4328.57	−	5220.35i	−0.351316	−	0.423695i
$112$	−7525.49			−0.599927
$113$		−	17644.8i		−	1.38185i	−0.722928	−	0.690923i	$-0.757204\pi$
$113$		−	17644.8i		−	1.38185i	0.722928	−	0.690923i	$-0.242796\pi$
$114$	−24.3915	+	20.2248i	−0.00187685	+	0.00155623i
$115$	−4148.20			−0.313664
$116$			14920.8i			1.10886i
$117$	−4719.40	+	25046.7i	−0.344759	+	1.82970i
$118$	−54.5386			−0.00391688
$119$		−	4446.43i		−	0.313991i
$120$	−438.279	−	528.573i	−0.0304360	−	0.0367065i
$121$	6097.09			0.416439
$122$			226.673i			0.0152293i
$123$	21463.3	−	17796.8i	1.41869	−	1.17634i
$124$	23118.4			1.50354
$125$		−	16989.1i		−	1.08730i
$126$	−282.365	−	53.2044i	−0.0177856	−	0.00335124i
$127$	−17319.7			−1.07382			−0.536912	−	0.843638i	$-0.680409\pi$
$127$	−17319.7			−1.07382			−0.536912	+	0.843638i	$0.680409\pi$
$128$		−	1967.26i		−	0.120072i
$129$	2536.73	+	3059.35i	0.152438	+	0.183844i
$130$	−750.544			−0.0444109
$131$		−	13987.4i		−	0.815067i	−0.913190	−	0.407534i	$-0.866389\pi$
$131$		−	13987.4i		−	0.815067i	0.913190	−	0.407534i	$-0.133611\pi$
$132$	−10237.0	+	8488.23i	−0.587522	+	0.487157i
$133$	862.326			0.0487493
$134$			235.638i			0.0131231i
$135$	7003.62	+	12638.1i	0.384287	+	0.693448i
$136$	580.652			0.0313934
$137$		−	36812.6i		−	1.96135i	−0.195640	−	0.980676i	$-0.562678\pi$
$137$		−	36812.6i		−	1.96135i	0.195640	−	0.980676i	$-0.437322\pi$
$138$	−144.690	−	174.500i	−0.00759769	−	0.00916297i
$139$	7638.45			0.395345			0.197672	−	0.980268i	$-0.436662\pi$
$139$	7638.45			0.395345			0.197672	+	0.980268i	$0.436662\pi$
$140$			9339.23i			0.476491i
$141$	11184.9	−	9274.18i	0.562590	−	0.466484i
$142$	203.151			0.0100749
$143$			29085.0i			1.42232i
$144$	−3829.17	+	20322.1i	−0.184663	+	0.980040i
$145$	18500.1			0.879908
$146$			331.191i			0.0155372i
$147$	−8801.57	−	10614.9i	−0.407310	−	0.491225i
$148$	−12045.1			−0.549902
$149$		−	7723.33i		−	0.347882i	−0.984756	−	0.173941i	$-0.944350\pi$
$149$		−	7723.33i		−	0.347882i	0.984756	−	0.173941i	$-0.0556502\pi$
$150$	193.565	−	160.499i	0.00860290	−	0.00713329i
$151$	15554.6			0.682191			0.341095	−	0.940029i	$-0.389202\pi$
$151$	15554.6			0.682191			0.341095	+	0.940029i	$0.389202\pi$
$152$			112.610i			0.00487403i
$153$	−12007.3	−	2262.47i	−0.512935	−	0.0966494i
$154$	−327.891			−0.0138257
$155$		−	28664.2i		−	1.19310i
$156$	28895.5	+	34848.6i	1.18736	+	1.43198i
$157$	−31297.9			−1.26975			−0.634873	−	0.772617i	$-0.718947\pi$
$157$	−31297.9			−1.26975			−0.634873	+	0.772617i	$0.718947\pi$
$158$			1085.86i			0.0434972i
$159$	−30724.8	+	25476.1i	−1.21533	+	1.00772i
$160$	−1829.67			−0.0714713
$161$			6169.17i			0.237999i
$162$	−287.350	+	735.436i	−0.0109492	+	0.0280230i
$163$	−34813.9			−1.31032			−0.655161	−	0.755489i	$-0.727399\pi$
$163$	−34813.9			−1.31032			−0.655161	+	0.755489i	$0.727399\pi$
$164$		−	49523.0i		−	1.84128i
$165$	10524.4	+	12692.7i	0.386573	+	0.466215i
$166$	507.999			0.0184351
$167$			3353.17i			0.120233i	0.998191	+	0.0601163i	$0.0191472\pi$
$167$			3353.17i			0.120233i	−0.998191	+	0.0601163i	$0.980853\pi$
$168$	−786.089	+	651.804i	−0.0278518	+	0.0230940i
$169$	70449.8			2.46664
$170$		−	359.808i		−	0.0124501i
$171$	438.775	−	2328.66i	0.0150055	−	0.0796367i
$172$	7058.92			0.238606
$173$			3198.91i			0.106883i	0.998571	+	0.0534416i	$0.0170191\pi$
$173$			3198.91i			0.106883i	−0.998571	+	0.0534416i	$0.982981\pi$
$174$	645.287	+	778.230i	0.0213135	+	0.0257045i
$175$	−6843.21			−0.223452
$176$			23598.7i			0.761838i
$177$	3139.75	−	2603.40i	0.100219	−	0.0830986i
$178$	−142.956			−0.00451192
$179$			54559.7i			1.70281i	0.524510	+	0.851404i	$0.324249\pi$
$179$			54559.7i			1.70281i	−0.524510	+	0.851404i	$0.675751\pi$
$180$	25220.0	+	4752.05i	0.778394	+	0.146668i
$181$	31247.6			0.953806			0.476903	−	0.878956i	$-0.341759\pi$
$181$	31247.6			0.953806			0.476903	+	0.878956i	$0.341759\pi$
$182$			1116.20i			0.0336977i
$183$	−10820.2	−	13049.4i	−0.323097	−	0.389662i
$184$	−805.621			−0.0237955
$185$			14934.5i			0.436363i
$186$	1205.80	−	999.814i	0.0348537	−	0.0288997i
$187$	−13943.3			−0.398732
$188$		−	25807.1i		−	0.730170i
$189$	18795.3	−	10415.7i	0.526168	−	0.291585i
$190$	69.7800			0.00193296
$191$			72026.4i			1.97435i	0.159634	+	0.987176i	$0.448969\pi$
$191$			72026.4i			1.97435i	−0.159634	+	0.987176i	$0.551031\pi$
$192$	23402.3	+	28223.7i	0.634828	+	0.765616i
$193$	61614.6			1.65413			0.827063	−	0.562109i	$-0.190010\pi$
$193$	61614.6			1.65413			0.827063	+	0.562109i	$0.190010\pi$
$194$		−	73.4889i		−	0.00195262i
$195$	43208.3	−	35827.1i	1.13631	−	0.942200i
$196$	−24492.0			−0.637547
$197$		−	14506.5i		−	0.373792i	−0.982380	−	0.186896i	$-0.940157\pi$
$197$		−	14506.5i		−	0.373792i	0.982380	−	0.186896i	$-0.0598427\pi$
$198$	−166.840	+	885.449i	−0.00425569	+	0.0225857i
$199$	−42049.9			−1.06184			−0.530919	−	0.847423i	$-0.678153\pi$
$199$	−42049.9			−1.06184			−0.530919	+	0.847423i	$0.678153\pi$
$200$		−	893.643i		−	0.0223411i
$201$	−11248.2	−	13565.5i	−0.278413	−	0.335772i
$202$	−1759.82			−0.0431286
$203$		−	27513.1i		−	0.667648i
$204$	−16706.3	+	13852.4i	−0.401439	+	0.332862i
$205$	−61402.9			−1.46110
$206$		−	206.852i		−	0.00487444i
$207$	16659.4	+	3139.04i	0.388794	+	0.0732582i
$208$	80334.2			1.85684
$209$		−	2704.11i		−	0.0619059i
$210$	403.899	+	487.110i	0.00915870	+	0.0110456i
$211$	−25444.9			−0.571526			−0.285763	−	0.958300i	$-0.592247\pi$
$211$	−25444.9			−0.571526			−0.285763	+	0.958300i	$0.592247\pi$
$212$			70892.1i			1.57734i
$213$	−11695.3	+	9697.39i	−0.257781	+	0.213745i
$214$	−1045.13			−0.0228215
$215$		−	8752.27i		−	0.189341i
$216$	1360.17	+	2454.44i	0.0291532	+	0.0526072i
$217$	−42629.1			−0.905288
$218$			1624.42i			0.0341811i
$219$	−15809.4	−	19066.4i	−0.329629	−	0.397540i
$220$	29286.3			0.605088
$221$			47465.5i			0.971836i
$222$	−628.240	+	520.919i	−0.0127473	+	0.0105697i
$223$	46077.5			0.926572			0.463286	−	0.886209i	$-0.346670\pi$
$223$	46077.5			0.926572			0.463286	+	0.886209i	$0.346670\pi$
$224$			2721.06i			0.0542303i
$225$	−3482.01	+	18479.6i	−0.0687804	+	0.365030i
$226$	−2123.45			−0.0415744
$227$			10006.8i			0.194198i	0.995275	+	0.0970989i	$0.0309563\pi$
$227$			10006.8i			0.194198i	−0.995275	+	0.0970989i	$0.969044\pi$
$228$	−2686.49	−	3239.96i	−0.0516791	−	0.0623261i
$229$	−2538.38			−0.0484045			−0.0242022	−	0.999707i	$-0.507705\pi$
$229$	−2538.38			−0.0484045			−0.0242022	+	0.999707i	$0.507705\pi$
$230$			499.213i			0.00943693i
$231$	18876.5	−	15651.9i	0.353750	−	0.293320i
$232$	3592.89			0.0667526
$233$			39671.3i			0.730743i	0.930862	+	0.365372i	$0.119058\pi$
$233$			39671.3i			0.730743i	−0.930862	+	0.365372i	$0.880942\pi$
$234$	3014.23	+	567.954i	0.0550484	+	0.0103725i
$235$	−31997.9			−0.579410
$236$		−	7244.44i		−	0.130071i
$237$	−51833.6	−	62512.4i	−0.922815	−	1.11293i
$238$	−535.104			−0.00944678
$239$			15031.1i			0.263146i	0.991307	+	0.131573i	$0.0420027\pi$
$239$			15031.1i			0.263146i	−0.991307	+	0.131573i	$0.957997\pi$
$240$	35057.8	−	29069.0i	0.608643	−	0.504670i
$241$	19606.7			0.337575			0.168788	−	0.985652i	$-0.446015\pi$
$241$	19606.7			0.337575			0.168788	+	0.985652i	$0.446015\pi$
$242$		−	733.751i		−	0.0125290i
$243$	−18563.5	−	56055.2i	−0.314374	−	0.949299i
$244$	−30109.2			−0.505732
$245$			30367.3i			0.505911i
$246$	−2141.75	−	2582.99i	−0.0353914	−	0.0426828i
$247$	−9205.29			−0.150884
$248$		−	5566.86i		−	0.0905122i
$249$	−29245.1	+	24249.3i	−0.471688	+	0.391111i
$250$	−2044.54			−0.0327127
$251$			49541.7i			0.786364i	0.919461	+	0.393182i	$0.128626\pi$
$251$			49541.7i			0.786364i	−0.919461	+	0.393182i	$0.871374\pi$
$252$	7067.21	−	37506.9i	0.111288	−	0.590623i
$253$	19345.5			0.302231
$254$			2084.33i			0.0323072i
$255$	17175.4	+	20713.9i	0.264136	+	0.318553i
$256$	64943.6			0.990961
$257$		−	120518.i		−	1.82468i	−0.409433	−	0.912340i	$-0.634274\pi$
$257$		−	120518.i		−	1.82468i	0.409433	−	0.912340i	$-0.365726\pi$
$258$	368.176	−	305.281i	0.00553115	−	0.00458628i
$259$	22210.5			0.331099
$260$		−	99695.8i		−	1.47479i
$261$	−74297.4	−	13999.4i	−1.09067	−	0.205508i
$262$	−1683.30			−0.0245222
$263$		−	11226.4i		−	0.162304i	−0.996702	−	0.0811518i	$-0.974140\pi$
$263$		−	11226.4i		−	0.162304i	0.996702	−	0.0811518i	$-0.0258598\pi$
$264$	2043.95	+	2465.05i	0.0293266	+	0.0353685i
$265$	87898.2			1.25167
$266$		−	103.776i		−	0.00146668i
$267$	8229.86	−	6823.98i	0.115444	−	0.0957227i
$268$	−31300.1			−0.435789
$269$		−	93015.5i		−	1.28544i	−0.766102	−	0.642718i	$-0.777807\pi$
$269$		−	93015.5i		−	1.28544i	0.766102	−	0.642718i	$-0.222193\pi$
$270$	1520.92	−	842.847i	0.0208632	−	0.0115617i
$271$	−34122.2			−0.464620			−0.232310	−	0.972642i	$-0.574628\pi$
$271$	−34122.2			−0.464620			−0.232310	+	0.972642i	$0.574628\pi$
$272$			38512.0i			0.520545i
$273$	−53281.8	−	64259.0i	−0.714914	−	0.862201i
$274$	−4430.19			−0.0590095
$275$			21459.2i			0.283757i
$276$	23179.0	−	19219.4i	0.304282	−	0.252303i
$277$	−37488.9			−0.488589			−0.244295	−	0.969701i	$-0.578556\pi$
$277$	−37488.9			−0.488589			−0.244295	+	0.969701i	$0.578556\pi$
$278$		−	919.246i		−	0.0118944i
$279$	−21690.9	+	115117.i	−0.278656	+	1.47888i
$280$	2248.87			0.0286845
$281$			39905.3i			0.505380i	0.967547	+	0.252690i	$0.0813153\pi$
$281$			39905.3i			0.505380i	−0.967547	+	0.252690i	$0.918685\pi$
$282$	−1116.10	−	1346.04i	−0.0140347	−	0.0169261i
$283$	76270.6			0.952322			0.476161	−	0.879358i	$-0.342028\pi$
$283$	76270.6			0.952322			0.476161	+	0.879358i	$0.342028\pi$
$284$			26984.8i			0.334567i
$285$	−4017.19	+	3330.94i	−0.0494575	+	0.0410088i
$286$	3500.22			0.0427921
$287$			91317.8i			1.10864i
$288$	7348.05	+	1384.55i	0.0885905	+	0.0166926i
$289$	60766.2			0.727556
$290$		−	2226.38i		−	0.0264730i
$291$	3507.99	+	4230.71i	0.0414259	+	0.0499605i
$292$	−43992.5			−0.515956
$293$			41766.6i			0.486512i	0.969962	+	0.243256i	$0.0782156\pi$
$293$			41766.6i			0.486512i	−0.969962	+	0.243256i	$0.921784\pi$
$294$	−1277.44	+	1059.22i	−0.0147790	+	0.0122544i
$295$	−8982.28			−0.103215
$296$			2900.43i			0.0331038i
$297$	−32662.0	−	58938.8i	−0.370279	−	0.668172i
$298$	−929.460			−0.0104664
$299$		−	65855.6i		−	0.736631i
$300$	21319.3	+	25711.5i	0.236881	+	0.285684i
$301$	−13016.3			−0.143666
$302$		−	1871.91i		−	0.0205245i
$303$	101312.	−	84004.9i	1.10350	−	0.914996i
$304$	−7468.88			−0.0808181
$305$			37332.0i			0.401312i
$306$	−272.275	+	1445.01i	−0.00290781	+	0.0154322i
$307$	−158764.			−1.68452			−0.842260	−	0.539072i	$-0.818775\pi$
$307$	−158764.			−1.68452			−0.842260	+	0.539072i	$0.818775\pi$
$308$		−	43554.2i		−	0.459123i
$309$	9874.06	+	11908.3i	0.103414	+	0.124719i
$310$	−3449.58			−0.0358957
$311$			108444.i			1.12121i	0.828084	+	0.560603i	$0.189431\pi$
$311$			108444.i			1.12121i	−0.828084	+	0.560603i	$0.810569\pi$
$312$	8391.47	−	6957.98i	0.0862043	−	0.0714782i
$313$	−165217.			−1.68642			−0.843212	−	0.537582i	$-0.819338\pi$
$313$	−165217.			−1.68642			−0.843212	+	0.537582i	$0.819338\pi$
$314$			3766.53i			0.0382017i
$315$	−46504.3	−	8762.54i	−0.468675	−	0.0883098i
$316$	−144237.			−1.44445
$317$		−	130757.i		−	1.30120i	−0.759418	−	0.650602i	$-0.774516\pi$
$317$		−	130757.i		−	1.30120i	0.759418	−	0.650602i	$-0.225484\pi$
$318$	3065.91	+	3697.55i	0.0303183	+	0.0365646i
$319$	−86276.6			−0.847835
$320$		−	80743.1i		−	0.788507i
$321$	60167.7	−	49889.4i	0.583920	−	0.484171i
$322$	742.425			0.00716046
$323$		−	4412.99i		−	0.0422987i
$324$	−97689.0	−	38169.1i	−0.930584	−	0.363598i
$325$	73050.9			0.691606
$326$			4189.67i			0.0394225i
$327$	−77541.6	−	93516.8i	−0.725169	−	0.874569i
$328$	−11925.0			−0.110844
$329$			47587.0i			0.439640i
$330$	1527.50	−	1266.56i	0.0140266	−	0.0116305i
$331$	−146148.			−1.33395			−0.666973	−	0.745082i	$-0.732410\pi$
$331$	−146148.			−1.33395			−0.666973	+	0.745082i	$0.732410\pi$
$332$			67478.1i			0.612191i
$333$	11301.3	−	59977.9i	0.101915	−	0.540883i
$334$	403.535			0.00361733
$335$			38808.6i			0.345811i
$336$	−43231.2	−	52137.7i	−0.382929	−	0.461821i
$337$	59208.5			0.521344			0.260672	−	0.965427i	$-0.416056\pi$
$337$	59208.5			0.521344			0.260672	+	0.965427i	$0.416056\pi$
$338$		−	8478.24i		−	0.0742117i
$339$	122246.	−	101363.i	1.06374	−	0.882022i
$340$	47793.8			0.413441
$341$			133678.i			1.14961i
$342$	−280.241	−	52.8041i	−0.00239596	−	0.000451456i
$343$	115935.			0.985431
$344$		−	1699.77i		−	0.0143640i
$345$	−23829.9	−	28739.4i	−0.200209	−	0.241457i
$346$	384.971			0.00321570
$347$		−	154241.i		−	1.28098i	−0.767967	−	0.640489i	$-0.778732\pi$
$347$		−	154241.i		−	1.28098i	0.767967	−	0.640489i	$-0.221268\pi$
$348$	−103373.	+	85714.3i	−0.853591	+	0.707774i
$349$	−15005.7			−0.123198			−0.0615992	−	0.998101i	$-0.519620\pi$
$349$	−15005.7			−0.123198			−0.0615992	+	0.998101i	$0.519620\pi$
$350$			823.542i			0.00672279i
$351$	−200638.	+	111187.i	−1.62855	+	0.902487i
$352$	8532.80			0.0688662
$353$			140777.i			1.12975i	0.825177	+	0.564874i	$0.191075\pi$
$353$			140777.i			1.12975i	−0.825177	+	0.564874i	$0.808925\pi$
$354$	−313.304	−	377.852i	−0.00250011	−	0.00301519i
$355$	33458.1			0.265488
$356$		−	18989.0i		−	0.149831i
$357$	30805.5	−	25543.1i	0.241709	−	0.200418i
$358$	6565.96			0.0512309
$359$			5640.99i			0.0437690i	0.999761	+	0.0218845i	$0.00696660\pi$
$359$			5640.99i			0.0437690i	−0.999761	+	0.0218845i	$0.993033\pi$
$360$	1144.28	−	6072.92i	0.00882935	−	0.0468589i
$361$	−129465.			−0.993433
$362$		−	3760.48i		−	0.0286963i
$363$	35025.5	+	42241.5i	0.265810	+	0.320573i
$364$	−148267.			−1.11903
$365$			54545.7i			0.409426i
$366$	−1570.42	+	1302.15i	−0.0117234	+	0.00972074i
$367$	212560.			1.57815			0.789076	−	0.614295i	$-0.210560\pi$
$367$	212560.			1.57815			0.789076	+	0.614295i	$0.210560\pi$
$368$		−	53433.1i		−	0.394562i
$369$	246598.	+	46465.0i	1.81108	+	0.341250i
$370$	1797.29			0.0131285
$371$		−	130721.i		−	0.949727i
$372$	132807.	+	160168.i	0.959697	+	1.15741i
$373$	−156245.			−1.12303			−0.561513	−	0.827468i	$-0.689780\pi$
$373$	−156245.			−1.12303			−0.561513	+	0.827468i	$0.689780\pi$
$374$			1678.00i			0.0119963i
$375$	117703.	−	97596.0i	0.836998	−	0.694016i
$376$	−6214.31			−0.0439559
$377$			293701.i			2.06644i
$378$	−1253.47	−	2261.90i	−0.00877267	−	0.0158304i
$379$	182195.			1.26840			0.634202	−	0.773168i	$-0.281329\pi$
$379$	182195.			1.26840			0.634202	+	0.773168i	$0.281329\pi$
$380$			9268.97i			0.0641896i
$381$	−99495.4	−	119994.i	−0.685414	−	0.826624i
$382$	8667.97			0.0594006
$383$		−	193663.i		−	1.32023i	−0.751167	−	0.660113i	$-0.770509\pi$
$383$		−	193663.i		−	1.32023i	0.751167	−	0.660113i	$-0.229491\pi$
$384$	13629.5	−	11301.2i	0.0924309	−	0.0766412i
$385$	−54002.3			−0.364327
$386$		−	7414.97i		−	0.0497663i
$387$	−6623.04	+	35149.6i	−0.0442217	+	0.234692i
$388$	9761.63			0.0648424
$389$		−	1576.79i		−	0.0104202i	−0.999986	−	0.00521010i	$-0.998342\pi$
$389$		−	1576.79i		−	0.0104202i	0.999986	−	0.00521010i	$-0.00165843\pi$
$390$	−4311.60	−	5199.88i	−0.0283471	−	0.0341872i
$391$	31570.9			0.206507
$392$			5897.63i			0.0383800i
$393$	96906.5	−	80352.3i	0.627434	−	0.520251i
$394$	−1745.78			−0.0112459
$395$			178837.i			1.14621i
$396$	−117615.	−	22161.6i	−0.750022	−	0.141322i
$397$	−32619.1			−0.206962			−0.103481	−	0.994631i	$-0.532998\pi$
$397$	−32619.1			−0.206962			−0.103481	+	0.994631i	$0.532998\pi$
$398$			5060.47i			0.0319466i
$399$	4953.75	+	5974.32i	0.0311163	+	0.0375269i
$400$	59271.2			0.370445
$401$			45477.1i			0.282816i	0.989951	+	0.141408i	$0.0451629\pi$
$401$			45477.1i			0.282816i	−0.989951	+	0.141408i	$0.954837\pi$
$402$	−1632.54	+	1353.65i	−0.0101021	+	0.00837636i
$403$	455064.			2.80196
$404$		−	233759.i		−	1.43221i
$405$	−47325.3	+	121123.i	−0.288525	+	0.738444i
$406$	−3311.05			−0.0200869
$407$		−	69648.3i		−	0.420457i
$408$	3335.63	+	4022.84i	0.0200382	+	0.0241664i
$409$	176282.			1.05381			0.526905	−	0.849924i	$-0.323352\pi$
$409$	176282.			1.05381			0.526905	+	0.849924i	$0.323352\pi$
$410$			7389.50i			0.0439590i
$411$	255043.	−	211475.i	1.50984	−	1.25192i
$412$	27476.4			0.161870
$413$			13358.4i			0.0783165i
$414$	377.766	−	2004.87i	0.00220406	−	0.0116973i
$415$	83665.2			0.485790
$416$		−	29047.2i		−	0.167849i
$417$	43880.1	+	52920.3i	0.252345	+	0.304334i
$418$	−325.425			−0.00186251
$419$			307206.i			1.74985i	0.484257	+	0.874926i	$0.339090\pi$
$419$			307206.i			1.74985i	−0.484257	+	0.874926i	$0.660910\pi$
$420$	−64703.5	+	53650.4i	−0.366800	+	0.304141i
$421$	242332.			1.36724			0.683622	−	0.729836i	$-0.260404\pi$
$421$	242332.			1.36724			0.683622	+	0.729836i	$0.260404\pi$
$422$			3062.15i			0.0171950i
$423$	128506.	+	24213.6i	0.718194	+	0.135325i
$424$	17070.7			0.0949553
$425$			35020.4i			0.193884i
$426$	1167.03	+	1407.46i	0.00643075	+	0.00775562i
$427$	55519.9			0.304504
$428$		−	138827.i		−	0.757854i
$429$	−201505.	+	167083.i	−1.09489	+	0.907857i
$430$	−1053.29			−0.00569652
$431$			322934.i			1.73844i	0.494427	+	0.869219i	$0.335378\pi$
$431$			322934.i			1.73844i	−0.494427	+	0.869219i	$0.664622\pi$
$432$	−162792.	+	90213.9i	−0.872298	+	0.483399i
$433$	−24717.5			−0.131834			−0.0659172	−	0.997825i	$-0.520997\pi$
$433$	−24717.5			−0.131834			−0.0659172	+	0.997825i	$0.520997\pi$
$434$			5130.18i			0.0272366i
$435$	106276.	+	128171.i	0.561639	+	0.677348i
$436$	−215774.			−1.13508
$437$			6122.76i			0.0320616i
$438$	−2294.54	+	1902.57i	−0.0119604	+	0.00991727i
$439$	−155905.			−0.808969			−0.404485	−	0.914545i	$-0.632549\pi$
$439$	−155905.			−0.808969			−0.404485	+	0.914545i	$0.632549\pi$
$440$		−	7052.07i		−	0.0364260i
$441$	22979.7	−	121957.i	0.118159	−	0.627090i
$442$	5712.20			0.0292388
$443$			327738.i			1.67001i	0.550240	+	0.835007i	$0.314536\pi$
$443$			327738.i			1.67001i	−0.550240	+	0.835007i	$0.685464\pi$
$444$	−69194.4	−	83449.9i	−0.350998	−	0.423312i
$445$	−23544.2			−0.118895
$446$		−	5545.17i		−	0.0278770i
$447$	53508.4	−	44367.7i	0.267798	−	0.222050i
$448$	−120080.			−0.598296
$449$		−	124454.i		−	0.617328i	−0.951171	−	0.308664i	$-0.900118\pi$
$449$		−	124454.i		−	0.617328i	0.951171	−	0.308664i	$-0.0998819\pi$
$450$	2223.92	+	419.041i	0.0109823	+	0.00206934i
$451$	286358.			1.40785
$452$		−	282061.i		−	1.38060i
$453$	89355.6	+	107765.i	0.435437	+	0.525146i
$454$	1204.27			0.00584266
$455$			183834.i			0.887979i
$456$	−780.176	+	646.901i	−0.00375200	+	0.00311106i
$457$	−237272.			−1.13609			−0.568046	−	0.822997i	$-0.692301\pi$
$457$	−237272.			−1.13609			−0.568046	+	0.822997i	$0.692301\pi$
$458$			305.480i			0.00145630i
$459$	−53302.8	−	96185.4i	−0.253003	−	0.456545i
$460$	−66311.2			−0.313380
$461$			121629.i			0.572316i	0.958182	+	0.286158i	$0.0923782\pi$
$461$			121629.i			0.572316i	−0.958182	+	0.286158i	$0.907622\pi$
$462$	−1883.61	−	2271.68i	−0.00882487	−	0.0106430i
$463$	115650.			0.539491			0.269745	−	0.962932i	$-0.413060\pi$
$463$	115650.			0.539491			0.269745	+	0.962932i	$0.413060\pi$
$464$			238300.i			1.10685i
$465$	198590.	−	164665.i	0.918440	−	0.761546i
$466$	4774.22			0.0219852
$467$			44342.0i			0.203320i	0.994819	+	0.101660i	$0.0324155\pi$
$467$			44342.0i			0.203320i	−0.994819	+	0.101660i	$0.967585\pi$
$468$	−75442.1	+	400384.i	−0.344447	+	1.82804i
$469$	57715.8			0.262391
$470$			3850.77i			0.0174322i
$471$	−179795.	−	216837.i	−0.810469	−	0.977442i
$472$	−1744.45			−0.00783021
$473$			40816.9i			0.182439i
$474$	−7523.02	+	6237.89i	−0.0334839	+	0.0277639i
$475$	−6791.73			−0.0301019
$476$		−	71078.5i		−	0.313707i
$477$	−353005.	−	66514.6i	−1.55147	−	0.292335i
$478$	1808.91			0.00791703
$479$			191518.i			0.834714i	0.908743	+	0.417357i	$0.137044\pi$
$479$			191518.i			0.834714i	−0.908743	+	0.417357i	$0.862956\pi$
$480$	−10510.8	−	12676.2i	−0.0456196	−	0.0550182i
$481$	−237096.			−1.02479
$482$		−	2359.56i		−	0.0101563i
$483$	−42740.9	+	35439.6i	−0.183210	+	0.151913i
$484$	97465.1			0.416062
$485$		−	12103.3i		−	0.0514542i
$486$	−6745.93	+	2234.01i	−0.0285607	+	0.00945828i
$487$	−170064.			−0.717056			−0.358528	−	0.933519i	$-0.616721\pi$
$487$	−170064.			−0.717056			−0.358528	+	0.933519i	$0.616721\pi$
$488$			7250.24i			0.0304448i
$489$	−199993.	−	241196.i	−0.836369	−	1.00868i
$490$	3654.54			0.0152209
$491$		−	4785.36i		−	0.0198496i	−0.999951	−	0.00992479i	$-0.996841\pi$
$491$		−	4785.36i		−	0.0198496i	0.999951	−	0.00992479i	$-0.00315921\pi$
$492$	343103.	−	284491.i	1.41740	−	1.17527i
$493$	−140799.			−0.579305
$494$			1107.81i			0.00453952i
$495$	−27477.9	+	145830.i	−0.112143	+	0.595163i
$496$	369224.			1.50081
$497$		−	49758.6i		−	0.201444i
$498$	2918.26	+	3519.49i	0.0117670	+	0.0141913i
$499$	110455.			0.443592			0.221796	−	0.975093i	$-0.428808\pi$
$499$	110455.			0.443592			0.221796	+	0.975093i	$0.428808\pi$
$500$		−	271579.i		−	1.08632i
$501$	−23231.2	+	19262.7i	−0.0925544	+	0.0767436i
$502$	5962.07			0.0236586
$503$		−	309458.i		−	1.22311i	−0.791202	−	0.611555i	$-0.790544\pi$
$503$		−	309458.i		−	1.22311i	0.791202	−	0.611555i	$-0.209456\pi$
$504$	−9031.59	−	1701.77i	−0.0355552	−	0.00669946i
$505$	−289835.			−1.13650
$506$		−	2328.12i		−	0.00909295i
$507$	404708.	+	488087.i	1.57444	+	1.89881i
$508$	−276865.			−1.07285
$509$			41558.5i			0.160407i	0.996779	+	0.0802036i	$0.0255571\pi$
$509$			41558.5i			0.160407i	−0.996779	+	0.0802036i	$0.974443\pi$
$510$	2492.80	−	2066.97i	0.00958403	−	0.00794681i
$511$	81119.9			0.310660
$512$		−	39291.8i		−	0.149886i
$513$	18653.9	−	10337.4i	0.0708817	−	0.0392804i
$514$	−14503.7			−0.0548975
$515$		−	34067.6i		−	0.128448i
$516$	40550.9	+	48905.3i	0.152300	+	0.183678i
$517$	149225.			0.558291
$518$		−	2672.91i		−	0.00996149i
$519$	−22162.5	+	18376.5i	−0.0822780	+	0.0682227i
$520$	−24006.5			−0.0887816
$521$		−	408445.i		−	1.50473i	−0.658748	−	0.752364i	$-0.728914\pi$
$521$		−	408445.i		−	1.50473i	0.658748	−	0.752364i	$-0.271086\pi$
$522$	−1684.75	+	8941.28i	−0.00618294	+	0.0328140i
$523$	50942.3			0.186241			0.0931205	−	0.995655i	$-0.470316\pi$
$523$	50942.3			0.186241			0.0931205	+	0.995655i	$0.470316\pi$
$524$		−	223595.i		−	0.814330i
$525$	−39311.7	−	47410.7i	−0.142627	−	0.172012i
$526$	−1351.03			−0.00488308
$527$			218156.i			0.785500i
$528$	−163495.	+	135566.i	−0.586458	+	0.486275i
$529$	236038.			0.843472
$530$		−	10578.1i		−	0.0376578i
$531$	36073.4	+	6797.10i	0.127938	+	0.0241065i
$532$	13784.7			0.0487052
$533$		−	974814.i		−	3.43137i
$534$	−821.228	−	990.418i	−0.00287993	−	0.00347325i
$535$	−172129.			−0.601378
$536$			7537.01i			0.0262343i
$537$	−377998.	+	313425.i	−1.31081	+	1.08689i
$538$	−11193.9			−0.0386738
$539$		−	141621.i		−	0.487471i
$540$	111957.	+	202026.i	0.383939	+	0.692821i
$541$	−365190.			−1.24774			−0.623871	−	0.781528i	$-0.714441\pi$
$541$	−365190.			−1.24774			−0.623871	+	0.781528i	$0.714441\pi$
$542$			4106.42i			0.0139786i
$543$	179506.	+	216488.i	0.608807	+	0.734234i
$544$	13925.1			0.0470545
$545$			267535.i			0.900717i
$546$	−7733.21	+	6412.17i	−0.0259403	+	0.0215090i
$547$	120042.			0.401197			0.200598	−	0.979674i	$-0.435711\pi$
$547$	120042.			0.401197			0.200598	+	0.979674i	$0.435711\pi$
$548$		−	588469.i		−	1.95958i
$549$	28250.0	−	149928.i	0.0937290	−	0.497436i
$550$	2582.49			0.00853716
$551$		−	27306.2i		−	0.0899410i
$552$	−4628.00	−	5581.46i	−0.0151885	−	0.0183176i
$553$	265965.			0.869710
$554$			4511.59i			0.0146997i
$555$	−103468.	+	85793.3i	−0.335909	+	0.278527i
$556$	122105.			0.394987
$557$		−	205905.i		−	0.663675i	−0.943337	−	0.331838i	$-0.892331\pi$
$557$		−	205905.i		−	0.663675i	0.943337	−	0.331838i	$-0.107669\pi$
$558$	13853.7	+	2610.37i	0.0444936	+	0.00838367i
$559$	138948.			0.444661
$560$			149157.i			0.475628i
$561$	−80099.0	−	96601.0i	−0.254508	−	0.306942i
$562$	4802.38			0.0152049
$563$		−	259496.i		−	0.818680i	−0.912382	−	0.409340i	$-0.865759\pi$
$563$		−	259496.i		−	0.818680i	0.912382	−	0.409340i	$-0.134241\pi$
$564$	178796.	−	148252.i	0.562081	−	0.466062i
$565$	−349724.			−1.09554
$566$		−	9178.74i		−	0.0286517i
$567$	180133.	+	70381.8i	0.560310	+	0.218924i
$568$	6497.89			0.0201407
$569$			180025.i			0.556043i	0.960575	+	0.278021i	$0.0896786\pi$
$569$			180025.i			0.556043i	−0.960575	+	0.278021i	$0.910321\pi$
$570$	400.860	+	483.446i	0.00123380	+	0.00148798i
$571$	−430578.			−1.32063			−0.660313	−	0.750991i	$-0.729576\pi$
$571$	−430578.			−1.32063			−0.660313	+	0.750991i	$0.729576\pi$
$572$			464939.i			1.42103i
$573$	−499009.	+	413765.i	−1.51984	+	1.26021i
$574$	10989.6			0.0333548
$575$		−	48588.7i		−	0.146960i
$576$	−61100.2	+	324269.i	−0.184161	+	0.977374i
$577$	439306.			1.31952			0.659759	−	0.751477i	$-0.270658\pi$
$577$	439306.			1.31952			0.659759	+	0.751477i	$0.270658\pi$
$578$		−	7312.88i		−	0.0218893i
$579$	353953.	+	426875.i	1.05582	+	1.27334i
$580$	295733.			0.879112
$581$		−	124426.i		−	0.368604i
$582$	509.142	−	422.167i	0.00150312	−	0.00124634i
$583$	−409921.			−1.20604
$584$			10593.3i			0.0310603i
$585$	496431.	+	93539.6i	1.45060	+	0.273328i
$586$	5026.38			0.0146373
$587$			257010.i			0.745888i	0.927854	+	0.372944i	$0.121652\pi$
$587$			257010.i			0.745888i	−0.927854	+	0.372944i	$0.878348\pi$
$588$	−140698.	−	169684.i	−0.406942	−	0.490780i
$589$	−42308.5			−0.121954
$590$			1080.97i			0.00310534i
$591$	100503.	−	83334.4i	0.287743	−	0.238589i
$592$	−192372.			−0.548906
$593$		−	246274.i		−	0.700340i	−0.936686	−	0.350170i	$-0.886124\pi$
$593$		−	246274.i		−	0.700340i	0.936686	−	0.350170i	$-0.113876\pi$
$594$	−7092.96	+	3930.69i	−0.0201027	+	0.0111403i
$595$	−88129.3			−0.248935
$596$		−	123461.i		−	0.347567i
$597$	−241561.	−	291328.i	−0.677763	−	0.817397i
$598$	−7925.35			−0.0221624
$599$			275795.i			0.768658i	0.923196	+	0.384329i	$0.125567\pi$
$599$			275795.i			0.768658i	−0.923196	+	0.384329i	$0.874433\pi$
$600$	6191.29	−	5133.65i	0.0171980	−	0.0142601i
$601$	−310695.			−0.860171			−0.430085	−	0.902788i	$-0.641517\pi$
$601$	−310695.			−0.860171			−0.430085	+	0.902788i	$0.641517\pi$
$602$			1566.44i			0.00432235i
$603$	29367.4	−	155858.i	0.0807663	−	0.428641i
$604$	248649.			0.681573
$605$		−	120846.i		−	0.330157i
$606$	−10109.5	−	12192.3i	−0.0275287	−	0.0332002i
$607$	110153.			0.298963			0.149481	−	0.988765i	$-0.452240\pi$
$607$	110153.			0.298963			0.149481	+	0.988765i	$0.452240\pi$
$608$			2700.59i			0.00730553i
$609$	190615.	−	158053.i	0.513952	−	0.426155i
$610$	4492.71			0.0120739
$611$		−	507989.i		−	1.36073i
$612$	−191943.	−	36166.7i	−0.512471	−	0.0965619i
$613$	−395407.			−1.05226			−0.526130	−	0.850404i	$-0.676358\pi$
$613$	−395407.			−1.05226			−0.526130	+	0.850404i	$0.676358\pi$
$614$			19106.4i			0.0506806i
$615$	−352737.	−	425408.i	−0.932612	−	1.12475i
$616$	−10487.8			−0.0276390
$617$		−	336696.i		−	0.884439i	−0.896907	−	0.442219i	$-0.854191\pi$
$617$		−	336696.i		−	0.884439i	0.896907	−	0.442219i	$-0.145809\pi$
$618$	1433.10	−	1188.29i	0.00375232	−	0.00311132i
$619$	269325.			0.702904			0.351452	−	0.936206i	$-0.385688\pi$
$619$	269325.			0.702904			0.351452	+	0.936206i	$0.385688\pi$
$620$		−	458212.i		−	1.19202i
$621$	73954.6	+	133452.i	0.191771	+	0.346052i
$622$	13050.7			0.0337328
$623$			35014.7i			0.0902142i
$624$	461491.	+	556567.i	1.18521	+	1.42938i
$625$	−191629.			−0.490569
$626$			19883.0i			0.0507379i
$627$	18734.5	−	15534.1i	0.0476548	−	0.0395141i
$628$	−500314.			−1.26860
$629$		−	113663.i		−	0.287288i
$630$	−1054.52	+	5596.54i	−0.00265690	+	0.0141006i
$631$	29483.1			0.0740483			0.0370241	−	0.999314i	$-0.488212\pi$
$631$	29483.1			0.0740483			0.0370241	+	0.999314i	$0.488212\pi$
$632$			34731.9i			0.0869550i
$633$	−146172.	−	176286.i	−0.364800	−	0.439957i
$634$	−15735.9			−0.0391482
$635$			343281.i			0.851338i
$636$	−491151.	+	407249.i	−1.21423	+	1.00681i
$637$	−482102.			−1.18812
$638$			10382.9i			0.0255081i
$639$	−134370.	−	25318.5i	−0.329079	−	0.0620064i
$640$	−38991.6			−0.0951944
$641$		−	18570.9i		−	0.0451978i	−0.999745	−	0.0225989i	$-0.992806\pi$
$641$		−	18570.9i		−	0.0451978i	0.999745	−	0.0225989i	$-0.00719406\pi$
$642$	−6003.92	−	7240.85i	−0.0145668	−	0.0175679i
$643$	107239.			0.259376			0.129688	−	0.991555i	$-0.458602\pi$
$643$	107239.			0.259376			0.129688	+	0.991555i	$0.458602\pi$
$644$			98617.4i			0.237783i
$645$	60637.0	−	50278.5i	0.145753	−	0.120855i
$646$	−531.078			−0.00127260
$647$			54077.1i			0.129183i	0.997912	+	0.0645915i	$0.0205744\pi$
$647$			54077.1i			0.129183i	−0.997912	+	0.0645915i	$0.979426\pi$
$648$	−9191.03	+	23523.3i	−0.0218884	+	0.0560207i
$649$	41889.6			0.0994528
$650$		−	8791.27i		−	0.0208077i
$651$	−244889.	−	295341.i	−0.577839	−	0.696886i
$652$	−556519.			−1.30914
$653$		−	717569.i		−	1.68282i	−0.540398	−	0.841410i	$-0.681726\pi$
$653$		−	717569.i		−	1.68282i	0.540398	−	0.841410i	$-0.318274\pi$
$654$	−11254.2	+	9331.70i	−0.0263124	+	0.0218175i
$655$	−277233.			−0.646193
$656$		−	790933.i		−	1.83794i
$657$	41276.0	−	219059.i	0.0956240	−	0.507494i
$658$	5726.84			0.0132270
$659$			482275.i			1.11051i	0.831679	+	0.555256i	$0.187380\pi$
$659$			482275.i			1.11051i	−0.831679	+	0.555256i	$0.812620\pi$
$660$	168239.	+	202899.i	0.386223	+	0.465793i
$661$	40317.6			0.0922767			0.0461384	−	0.998935i	$-0.485308\pi$
$661$	40317.6			0.0922767			0.0461384	+	0.998935i	$0.485308\pi$
$662$			17588.2i			0.0401332i
$663$	−328848.	+	272672.i	−0.748114	+	0.620316i
$664$	16248.6			0.0368536
$665$		−	17091.5i		−	0.0386489i
$666$	−7218.01	−	1360.05i	−0.0162731	−	0.00306624i
$667$	195351.			0.439101
$668$			53602.1i			0.120124i
$669$	264698.	+	319232.i	0.591424	+	0.713270i
$670$	4670.40			0.0104041
$671$		−	174101.i		−	0.386684i
$672$	−18851.9	+	15631.5i	−0.0417462	+	0.0346148i
$673$	−212954.			−0.470170			−0.235085	−	0.971975i	$-0.575537\pi$
$673$	−212954.			−0.470170			−0.235085	+	0.971975i	$0.575537\pi$
$674$		−	7125.42i		−	0.0156852i
$675$	−148033.	+	82034.8i	−0.324900	+	0.180049i
$676$	1.12618e6			2.46441
$677$		−	205371.i		−	0.448087i	−0.974579	−	0.224044i	$-0.928074\pi$
$677$		−	205371.i		−	0.448087i	0.974579	−	0.224044i	$-0.0719258\pi$
$678$	−12198.5	−	14711.6i	−0.0265366	−	0.0320037i
$679$	−17999.9			−0.0390420
$680$		−	11508.7i		−	0.0248890i
$681$	−69328.7	+	57485.5i	−0.149492	+	0.123955i
$682$	16087.4			0.0345873
$683$		−	183373.i		−	0.393091i	−0.980495	−	0.196546i	$-0.937028\pi$
$683$		−	183373.i		−	0.393091i	0.980495	−	0.196546i	$-0.0629724\pi$
$684$	7014.04	−	37224.8i	0.0149919	−	0.0795646i
$685$	−729635.			−1.55498
$686$		−	13952.1i		−	0.0296478i
$687$	−14582.1	−	17586.3i	−0.0308962	−	0.0372615i
$688$	112738.			0.238174
$689$			1.39544e6i			2.93951i
$690$	−3458.62	+	2867.80i	−0.00726449	+	0.00602352i
$691$	99813.7			0.209042			0.104521	−	0.994523i	$-0.466669\pi$
$691$	99813.7			0.209042			0.104521	+	0.994523i	$0.466669\pi$
$692$			51136.2i			0.106786i
$693$	216877.	+	40864.8i	0.451592	+	0.0850909i
$694$	−18562.1			−0.0385397
$695$		−	151396.i		−	0.313433i
$696$	20639.8	+	24892.1i	0.0426077	+	0.0513857i
$697$	467322.			0.961947
$698$			1805.85i			0.00370656i
$699$	−274849.	+	227897.i	−0.562522	+	0.466428i
$700$	−109392.			−0.223249
$701$		−	478522.i		−	0.973791i	−0.873460	−	0.486896i	$-0.838129\pi$
$701$		−	478522.i		−	0.973791i	0.873460	−	0.486896i	$-0.161871\pi$
$702$	13380.8	+	24145.7i	0.0271523	+	0.0489966i
$703$	22043.4			0.0446034
$704$			376552.i			0.759766i
$705$	−183816.	−	221686.i	−0.369833	−	0.446027i
$706$	16941.7			0.0339897
$707$			431040.i			0.862341i
$708$	50190.5	−	41616.6i	0.100128	−	0.0830234i
$709$	745394.			1.48284			0.741418	−	0.671043i	$-0.234154\pi$
$709$	745394.			1.48284			0.741418	+	0.671043i	$0.234154\pi$
$710$		−	4026.50i		−	0.00798750i
$711$	135330.	−	718222.i	0.267705	−	1.42076i
$712$	−4572.51			−0.00901976
$713$		−	302679.i		−	0.595392i
$714$	−3073.97	−	3707.28i	−0.00602981	−	0.00727208i
$715$	576472.			1.12763
$716$			872165.i			1.70127i
$717$	−104138.	+	86348.3i	−0.202568	+	0.167964i
$718$	678.862			0.00131684
$719$			234548.i			0.453705i	0.973929	+	0.226853i	$0.0728436\pi$
$719$			234548.i			0.453705i	−0.973929	+	0.226853i	$0.927156\pi$
$720$	402789.	+	75895.1i	0.776984	+	0.146403i
$721$	−50665.1			−0.0974627
$722$			15580.4i			0.0298885i
$723$	112633.	+	135838.i	0.215472	+	0.259863i
$724$	499510.			0.952943
$725$			216695.i			0.412262i
$726$	5083.53	−	4215.13i	0.00964478	−	0.00799719i
$727$	642599.			1.21583			0.607913	−	0.794004i	$-0.292007\pi$
$727$	642599.			1.21583			0.607913	+	0.794004i	$0.292007\pi$
$728$			35702.3i			0.0673649i
$729$	281718.	−	450627.i	0.530103	−	0.847933i
$730$	6564.28			0.0123180
$731$			66611.3i			0.124656i
$732$	−172966.	−	208601.i	−0.322805	−	0.389309i
$733$	171887.			0.319916			0.159958	−	0.987124i	$-0.448864\pi$
$733$	171887.			0.319916			0.159958	+	0.987124i	$0.448864\pi$
$734$		−	25580.4i		−	0.0474805i
$735$	−210389.	+	174449.i	−0.389448	+	0.322919i
$736$	−19320.3			−0.0356664
$737$		−	180987.i		−	0.333206i
$738$	5591.81	−	29676.7i	0.0102669	−	0.0544883i
$739$	894482.			1.63788			0.818941	−	0.573877i	$-0.194561\pi$
$739$	894482.			1.63788			0.818941	+	0.573877i	$0.194561\pi$
$740$			238736.i			0.435968i
$741$	−52881.0	−	63775.6i	−0.0963082	−	0.116150i
$742$	−15731.6			−0.0285736
$743$			789175.i			1.42954i	0.699361	+	0.714769i	$0.253468\pi$
$743$			789175.i			1.42954i	−0.699361	+	0.714769i	$0.746532\pi$
$744$	38568.0	−	31979.6i	0.0696758	−	0.0577732i
$745$	−153078.			−0.275804
$746$			18803.3i			0.0337875i
$747$	−336005.	−	63311.4i	−0.602149	−	0.113459i
$748$	−222890.			−0.398371
$749$			255989.i			0.456308i
$750$	−11745.1	−	14164.9i	−0.0208802	−	0.0251820i
$751$	−93909.3			−0.166506			−0.0832528	−	0.996528i	$-0.526531\pi$
$751$	−93909.3			−0.166506			−0.0832528	+	0.996528i	$0.526531\pi$
$752$		−	412166.i		−	0.728848i
$753$	−343232.	+	284599.i	−0.605338	+	0.501930i
$754$	35345.3			0.0621712
$755$		−	308296.i		−	0.540847i
$756$	300452.	−	166501.i	0.525692	−	0.291322i
$757$	539760.			0.941909			0.470955	−	0.882157i	$-0.343910\pi$
$757$	539760.			0.941909			0.470955	+	0.882157i	$0.343910\pi$
$758$		−	21926.1i		−	0.0381613i
$759$	111133.	+	134028.i	0.192912	+	0.232655i
$760$	2231.95			0.00386418
$761$			324451.i			0.560247i	0.959964	+	0.280123i	$0.0903754\pi$
$761$			324451.i			0.560247i	−0.959964	+	0.280123i	$0.909625\pi$
$762$	−14440.6	+	11973.7i	−0.0248699	+	0.0206215i
$763$	397876.			0.683438
$764$			1.15138e6i			1.97257i
$765$	−44842.6	+	237988.i	−0.0766245	+	0.406660i
$766$	−23306.2			−0.0397205
$767$		−	142600.i		−	0.242398i
$768$	373077.	+	449939.i	0.632523	+	0.762836i
$769$	−447415.			−0.756585			−0.378292	−	0.925686i	$-0.623489\pi$
$769$	−447415.			−0.756585			−0.378292	+	0.925686i	$0.623489\pi$
$770$			6498.88i			0.0109612i
$771$	834968.	−	692333.i	1.40463	−	1.16468i
$772$	984941.			1.65263
$773$			529335.i			0.885874i	0.896553	+	0.442937i	$0.146063\pi$
$773$			529335.i			0.885874i	−0.896553	+	0.442937i	$0.853937\pi$
$774$	4230.07	+	797.046i	0.00706098	+	0.00133046i
$775$	335749.			0.559000
$776$		−	2350.58i		−	0.00390348i
$777$	127591.	+	153877.i	0.211338	+	0.254878i
$778$	−189.758			−0.000313503
$779$			90630.9i			0.149349i
$780$	690707.	−	572715.i	1.13528	−	0.941347i
$781$	−156035.			−0.255811
$782$		−	3799.39i		−	0.00621298i
$783$	−329821.	−	595165.i	−0.537966	−	0.970764i
$784$	−391163.			−0.636393
$785$			620333.i			1.00667i
$786$	−9669.95	−	11662.2i	−0.0156523	−	0.0188771i
$787$	−932833.			−1.50610			−0.753051	−	0.657962i	$-0.771419\pi$
$787$	−932833.			−1.50610			−0.753051	+	0.657962i	$0.771419\pi$
$788$		−	231894.i		−	0.373454i
$789$	77778.0	−	64491.4i	0.124940	−	0.103597i
$790$	21522.1			0.0344850
$791$			520106.i			0.831264i
$792$	−5336.46	+	28321.6i	−0.00850752	+	0.0451509i
$793$	−592672.			−0.942471
$794$			3925.53i			0.00622669i
$795$	504943.	+	608972.i	0.798929	+	0.963525i
$796$	−672189.			−1.06088
$797$			1.09595e6i			1.72535i	0.505763	+	0.862673i	$0.331211\pi$
$797$			1.09595e6i			1.72535i	−0.505763	+	0.862673i	$0.668789\pi$
$798$	718.977	−	596.156i	0.00112904	−	0.000936169i
$799$	243528.			0.381466
$800$		−	21431.2i		−	0.0334863i
$801$	94555.0	+	17816.5i	0.147374	+	0.0277687i
$802$	5472.92			0.00850883
$803$		−	254378.i		−	0.394502i
$804$	−179808.	−	216852.i	−0.278161	−	0.335468i
$805$	122274.			0.188688
$806$		−	54764.4i		−	0.0843001i
$807$	644425.	−	534340.i	0.989522	−	0.820485i
$808$	−56288.8			−0.0862183
$809$		−	1.26930e6i		−	1.93940i	−0.244309	−	0.969698i	$-0.578561\pi$
$809$		−	1.26930e6i		−	1.93940i	0.244309	−	0.969698i	$-0.421439\pi$
$810$	14576.5	+	5695.34i	0.0222169	+	0.00868060i
$811$	−870258.			−1.32314			−0.661571	−	0.749883i	$-0.730110\pi$
$811$	−870258.			−1.32314			−0.661571	+	0.749883i	$0.730110\pi$
$812$		−	439812.i		−	0.667044i
$813$	−196019.	−	236403.i	−0.296564	−	0.357662i
$814$	−8381.79			−0.0126499
$815$			690021.i			1.03884i
$816$	−266817.	+	221237.i	−0.400712	+	0.332260i
$817$	−12918.4			−0.0193537
$818$		−	21214.6i		−	0.0317051i
$819$	139111.	−	738288.i	0.207393	−	1.10067i
$820$	−981557.			−1.45978
$821$			855386.i			1.26904i	0.772906	+	0.634521i	$0.218803\pi$
$821$			855386.i			1.26904i	−0.772906	+	0.634521i	$0.781197\pi$
$822$	−25449.8	−	30693.0i	−0.0376653	−	0.0454251i
$823$	850277.			1.25534			0.627669	−	0.778480i	$-0.284009\pi$
$823$	850277.			1.25534			0.627669	+	0.778480i	$0.284009\pi$
$824$		−	6616.27i		−	0.00974448i
$825$	−148672.	+	123275.i	−0.218435	+	0.181120i
$826$	1607.61			0.00235624
$827$		−	873092.i		−	1.27658i	−0.769795	−	0.638291i	$-0.779642\pi$
$827$		−	873092.i		−	1.27658i	0.769795	−	0.638291i	$-0.220358\pi$
$828$	266310.	+	50179.2i	0.388442	+	0.0731919i
$829$	869790.			1.26563			0.632813	−	0.774305i	$-0.281900\pi$
$829$	869790.			1.26563			0.632813	+	0.774305i	$0.281900\pi$
$830$		−	10068.6i		−	0.0146155i
$831$	−215360.	−	259729.i	−0.311863	−	0.376113i
$832$	1.28185e6			1.85179
$833$		−	231118.i		−	0.333077i
$834$	6368.67	−	5280.73i	0.00915623	−	0.00759210i
$835$	66460.6			0.0953216
$836$		−	43226.6i		−	0.0618499i
$837$	−922155.	+	511028.i	−1.31629	+	0.729448i
$838$	36970.5			0.0526462
$839$		−	1.30761e6i		−	1.85761i	−0.370567	−	0.928806i	$-0.620837\pi$
$839$		−	1.30761e6i		−	1.85761i	0.370567	−	0.928806i	$-0.379163\pi$
$840$	12918.9	+	15580.5i	0.0183091	+	0.0220812i
$841$	−163941.			−0.231791
$842$		−	29163.3i		−	0.0411351i
$843$	−276470.	+	229241.i	−0.389039	+	0.322580i
$844$	−406750.			−0.571008
$845$		−	1.39633e6i		−	1.95558i
$846$	2913.97	−	15464.9i	0.00407140	−	0.0216077i
$847$	−179721.			−0.250513
$848$			1.13222e6i			1.57449i
$849$	438146.	+	528414.i	0.607860	+	0.733092i
$850$	4214.51			0.00583323
$851$			157701.i			0.217758i
$852$	−186955.	+	155018.i	−0.257547	+	0.213551i
$853$	−926932.			−1.27394			−0.636971	−	0.770887i	$-0.719813\pi$
$853$	−926932.			−1.27394			−0.636971	+	0.770887i	$0.719813\pi$
$854$		−	6681.51i		−	0.00916134i
$855$	−46154.5	−	8696.62i	−0.0631367	−	0.0118965i
$856$	−33429.2			−0.0456224
$857$		−	1.38132e6i		−	1.88076i	−0.340122	−	0.940381i	$-0.610469\pi$
$857$		−	1.38132e6i		−	1.88076i	0.340122	−	0.940381i	$-0.389531\pi$
$858$	20107.5	+	24250.1i	0.0273139	+	0.0329411i
$859$	−149840.			−0.203068			−0.101534	−	0.994832i	$-0.532375\pi$
$859$	−149840.			−0.203068			−0.101534	+	0.994832i	$0.532375\pi$
$860$		−	139910.i		−	0.189169i
$861$	−632663.	+	524587.i	−0.853427	+	0.707639i
$862$	38863.3			0.0523029
$863$		−	543811.i		−	0.730174i	−0.930973	−	0.365087i	$-0.881039\pi$
$863$		−	543811.i		−	0.730174i	0.930973	−	0.365087i	$-0.118961\pi$
$864$	32619.5	+	58862.1i	0.0436968	+	0.0788512i
$865$	63403.1			0.0847380
$866$			2974.61i			0.00396638i
$867$	349080.	+	420997.i	0.464394	+	0.560068i
$868$	−681449.			−0.904469
$869$		−	834022.i		−	1.10443i
$870$	15424.7	−	12789.7i	0.0203788	−	0.0168975i
$871$	−616113.			−0.812128
$872$			51958.0i			0.0683312i
$873$	−9158.86	+	48607.7i	−0.0120175	+	0.0637788i
$874$	736.841			0.000964608
$875$			500778.i			0.654077i
$876$	−252721.	−	304787.i	−0.329331	−	0.397180i
$877$	−278285.			−0.361819			−0.180909	−	0.983500i	$-0.557904\pi$
$877$	−278285.			−0.361819			−0.180909	+	0.983500i	$0.557904\pi$
$878$			18762.3i			0.0243387i
$879$	−289365.	+	239934.i	−0.374514	+	0.310537i
$880$	467731.			0.603992
$881$			529913.i			0.682737i	0.939930	+	0.341368i	$0.110890\pi$
$881$			529913.i			0.682737i	−0.939930	+	0.341368i	$0.889110\pi$
$882$	−14676.9	−	2765.47i	−0.0188667	−	0.00355494i
$883$	−1.02911e6			−1.31990			−0.659948	−	0.751311i	$-0.729422\pi$
$883$	−1.02911e6			−1.31990			−0.659948	+	0.751311i	$0.729422\pi$
$884$			758760.i			0.970957i
$885$	−51599.9	−	62230.6i	−0.0658813	−	0.0794543i
$886$	39441.5			0.0502442
$887$			1.09147e6i			1.38728i	0.720324	+	0.693638i	$0.243993\pi$
$887$			1.09147e6i			1.38728i	−0.720324	+	0.693638i	$0.756007\pi$
$888$	−20094.6	+	16661.9i	−0.0254831	+	0.0211299i
$889$	510524.			0.645971
$890$			2833.42i			0.00357709i
$891$	220706.	−	564869.i	0.278008	−	0.711528i
$892$	736573.			0.925733
$893$			47229.1i			0.0592252i
$894$	−5339.41	−	6439.44i	−0.00668064	−	0.00805699i
$895$	1.08139e6			1.35000
$896$			57988.0i			0.0722307i
$897$	456257.	−	378316.i	0.567054	−	0.470186i
$898$	−14977.3			−0.0185730
$899$			1.34988e6i			1.67023i
$900$	−55661.7	+	295407.i	−0.0687182	+	0.364700i
$901$	−668972.			−0.824059
$902$		−	34461.5i		−	0.0423567i
$903$	−74773.8	−	90178.8i	−0.0917009	−	0.110593i
$904$	−67919.7			−0.0831111
$905$		−	619335.i		−	0.756186i
$906$	12968.9	−	10753.5i	0.0157996	−	0.0131006i
$907$	−1.39914e6			−1.70077			−0.850386	−	0.526159i	$-0.823632\pi$
$907$	−1.39914e6			−1.70077			−0.850386	+	0.526159i	$0.823632\pi$
$908$			159964.i			0.194022i
$909$	1.16400e6	+	219325.i	1.40872	+	0.265436i
$910$	22123.4			0.0267158
$911$		−	890497.i		−	1.07299i	−0.843903	−	0.536495i	$-0.819748\pi$
$911$		−	890497.i		−	1.07299i	0.843903	−	0.536495i	$-0.180252\pi$
$912$	−42906.0	−	51745.5i	−0.0515855	−	0.0622133i
$913$	−390180.			−0.468083
$914$			28554.4i			0.0341806i
$915$	−258642.	+	214459.i	−0.308928	+	0.256154i
$916$	−40577.3			−0.0483607
$917$			412298.i			0.490312i
$918$	−11575.4	+	6414.70i	−0.0137357	+	0.00761187i
$919$	−724824.			−0.858226			−0.429113	−	0.903251i	$-0.641174\pi$
$919$	−724824.			−0.858226			−0.429113	+	0.903251i	$0.641174\pi$
$920$			15967.6i			0.0188653i
$921$	−912042.	−	1.09994e6i	−1.07522	−	1.29673i
$922$	14637.4			0.0172188
$923$			531170.i			0.623491i
$924$	301750.	−	250203.i	0.353430	−	0.293055i
$925$	−174931.			−0.204448
$926$		−	13917.8i		−	0.0162312i
$927$	−25779.8	+	136818.i	−0.0299999	+	0.159215i
$928$	86164.3			0.100053
$929$			434448.i			0.503392i	0.967806	+	0.251696i	$0.0809883\pi$
$929$			434448.i			0.503392i	−0.967806	+	0.251696i	$0.919012\pi$
$930$	−19816.5	−	23899.2i	−0.0229120	−	0.0276323i
$931$	44822.3			0.0517124
$932$			634167.i			0.730082i
$933$	−751317.	+	622972.i	−0.863098	+	0.715658i
$934$	5336.31			0.00611712
$935$			276359.i			0.316119i
$936$	96411.8	+	18166.3i	0.110047	+	0.0207355i
$937$	629337.			0.716810			0.358405	−	0.933566i	$-0.383321\pi$
$937$	629337.			0.716810			0.358405	+	0.933566i	$0.383321\pi$
$938$		−	6945.78i		−	0.00789433i
$939$	−949112.	−	1.14465e6i	−1.07643	−	1.29820i
$940$	−511504.			−0.578886
$941$			530659.i			0.599289i	0.954051	+	0.299644i	$0.0968681\pi$
$941$			530659.i			0.599289i	−0.954051	+	0.299644i	$0.903132\pi$
$942$	−26095.1	+	21637.4i	−0.0294074	+	0.0243839i
$943$	−648383.			−0.729135
$944$		−	115701.i		−	0.129835i
$945$	−206442.	−	372526.i	−0.231172	−	0.417151i
$946$	4912.09			0.00548888
$947$		−	1.06526e6i		−	1.18784i	−0.804526	−	0.593918i	$-0.797580\pi$
$947$		−	1.06526e6i		−	1.18784i	0.804526	−	0.593918i	$-0.202420\pi$
$948$	−828587.	−	999293.i	−0.921980	−	1.11193i
$949$	−865951.			−0.961526
$950$			817.347i			0.000905648i
$951$	905902.	−	751149.i	1.00166	−	0.830549i
$952$	−17115.6			−0.0188850
$953$		−	1.54583e6i		−	1.70206i	−0.525115	−	0.851031i	$-0.675978\pi$
$953$		−	1.54583e6i		−	1.70206i	0.525115	−	0.851031i	$-0.324022\pi$
$954$	−8004.67	+	42482.2i	−0.00879522	+	0.0466778i
$955$	1.42758e6			1.56529
$956$			240280.i			0.262907i
$957$	−495627.	−	597737.i	−0.541167	−	0.652659i
$958$	23048.1			0.0251133
$959$			1.08511e6i			1.17987i
$960$	559400.	−	463839.i	0.606988	−	0.503298i
$961$	1.16800e6			1.26472
$962$			28533.1i			0.0308318i
$963$	691282.	+	130254.i	0.745423	+	0.140456i
$964$	313423.			0.337270
$965$		−	1.22122e6i		−	1.31141i
$966$	4264.96	+	5143.63i	0.00457047	+	0.00551208i
$967$	899007.			0.961413			0.480707	−	0.876881i	$-0.340380\pi$
$967$	899007.			0.961413			0.480707	+	0.876881i	$0.340380\pi$
$968$		−	23469.4i		−	0.0250467i
$969$	30573.8	−	25351.0i	0.0325613	−	0.0269990i
$970$	−1456.57			−0.00154806
$971$			759451.i			0.805492i	0.915312	+	0.402746i	$0.131944\pi$
$971$			759451.i			0.805492i	−0.915312	+	0.402746i	$0.868056\pi$
$972$	−296746.	−	896071.i	−0.314089	−	0.948440i
$973$	−225155.			−0.237824
$974$			20466.2i			0.0215734i
$975$	419651.	+	506107.i	0.441447	+	0.532394i
$976$	−480875.			−0.504816
$977$			939537.i			0.984294i	0.870512	+	0.492147i	$0.163788\pi$
$977$			939537.i			0.984294i	−0.870512	+	0.492147i	$0.836212\pi$
$978$	−29026.6	+	24068.1i	−0.0303472	+	0.0251631i
$979$	109800.			0.114561
$980$			485438.i			0.505453i
$981$	202450.	−	1.07444e6i	0.210368	−	1.11646i
$982$	−575.891			−0.000597197
$983$		−	61823.8i		−	0.0639807i	−0.999488	−	0.0319903i	$-0.989815\pi$
$983$		−	61823.8i		−	0.0639807i	0.999488	−	0.0319903i	$-0.0101846\pi$
$984$	−68504.9	−	82618.4i	−0.0707509	−	0.0853270i
$985$	−287522.			−0.296346
$986$			16944.4i			0.0174290i
$987$	−329690.	+	273370.i	−0.338432	+	0.280619i
$988$	−147151.			−0.150748
$989$		−	92419.4i		−	0.0944867i
$990$	17549.8	+	3306.81i	0.0179061	+	0.00337395i
$991$	948474.			0.965780			0.482890	−	0.875681i	$-0.339587\pi$
$991$	948474.			0.965780			0.482890	+	0.875681i	$0.339587\pi$
$992$		−	133504.i		−	0.135666i
$993$	−839569.	−	1.01254e6i	−0.851447	−	1.02686i
$994$	−5988.17			−0.00606068
$995$			833438.i			0.841835i
$996$	−467498.	+	387637.i	−0.471261	+	0.390757i
$997$	1.13621e6			1.14306			0.571529	−	0.820582i	$-0.306350\pi$
$997$	1.13621e6			1.14306			0.571529	+	0.820582i	$0.306350\pi$
$998$		−	13292.6i		−	0.0133460i
$999$	480458.	−	266254.i	0.481420	−	0.266787i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.39	✓	78
3.2	odd	2	inner	177.5.b.a.119.40	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.39	✓	78	1.1	even	1	trivial
177.5.b.a.119.40	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)

\(f(q)\)	\(=\)	\(q-0.120344i q^{2} +(5.74463 + 6.92815i) q^{3} +15.9855 q^{4} -19.8202i q^{5} +(0.833764 - 0.691335i) q^{6} -29.4765 q^{7} -3.84928i q^{8} +(-14.9984 + 79.5993i) q^{9} +O(q^{10})\)	\(q-0.120344i q^{2} +(5.74463 + 6.92815i) q^{3} +15.9855 q^{4} -19.8202i q^{5} +(0.833764 - 0.691335i) q^{6} -29.4765 q^{7} -3.84928i q^{8} +(-14.9984 + 79.5993i) q^{9} -2.38526 q^{10} +92.4333i q^{11} +(91.8309 + 110.750i) q^{12} +314.660 q^{13} +3.54733i q^{14} +(137.317 - 113.860i) q^{15} +255.305 q^{16} +150.847i q^{17} +(9.57933 + 1.80498i) q^{18} -29.2547 q^{19} -316.837i q^{20} +(-169.331 - 204.217i) q^{21} +11.1238 q^{22} -209.291i q^{23} +(26.6684 - 22.1127i) q^{24} +232.158 q^{25} -37.8676i q^{26} +(-637.636 + 353.357i) q^{27} -471.197 q^{28} +933.393i q^{29} +(-13.7024 - 16.5254i) q^{30} +1446.21 q^{31} -92.3130i q^{32} +(-640.391 + 530.995i) q^{33} +18.1536 q^{34} +584.230i q^{35} +(-239.758 + 1272.44i) q^{36} -753.498 q^{37} +3.52065i q^{38} +(1807.60 + 2180.01i) q^{39} -76.2936 q^{40} -3097.99i q^{41} +(-24.5764 + 20.3781i) q^{42} +441.582 q^{43} +1477.59i q^{44} +(1577.68 + 297.272i) q^{45} -25.1871 q^{46} -1614.41i q^{47} +(1466.63 + 1768.79i) q^{48} -1532.14 q^{49} -27.9390i q^{50} +(-1045.09 + 866.560i) q^{51} +5030.00 q^{52} +4434.77i q^{53} +(42.5246 + 76.7360i) q^{54} +1832.05 q^{55} +113.463i q^{56} +(-168.058 - 202.681i) q^{57} +112.329 q^{58} -453.188i q^{59} +(2195.09 - 1820.11i) q^{60} -1883.53 q^{61} -174.043i q^{62} +(442.101 - 2346.31i) q^{63} +4073.77 q^{64} -6236.63i q^{65} +(63.9023 + 77.0676i) q^{66} -1958.03 q^{67} +2411.37i q^{68} +(1450.00 - 1202.30i) q^{69} +70.3089 q^{70} +1688.08i q^{71} +(306.400 + 57.7331i) q^{72} -2752.02 q^{73} +90.6794i q^{74} +(1333.66 + 1608.43i) q^{75} -467.652 q^{76} -2724.61i q^{77} +(262.352 - 217.535i) q^{78} -9022.96 q^{79} -5060.21i q^{80} +(-6111.09 - 2387.73i) q^{81} -372.826 q^{82} +4221.20i q^{83} +(-2706.85 - 3264.52i) q^{84} +2989.82 q^{85} -53.1420i q^{86} +(-6466.68 + 5362.00i) q^{87} +355.802 q^{88} -1187.89i q^{89} +(35.7751 - 189.865i) q^{90} -9275.06 q^{91} -3345.63i q^{92} +(8307.94 + 10019.5i) q^{93} -194.285 q^{94} +579.836i q^{95} +(639.558 - 530.304i) q^{96} +610.655 q^{97} +184.384i q^{98} +(-7357.62 - 1386.35i) 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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