LMFDB - Embedded newform 177.5.b.a.119.42

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			119.42
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.04886i q^{2} +(6.16639 + 6.55558i) q^{3} +14.8999 q^{4} -21.6320i q^{5} +(-6.87585 + 6.46765i) q^{6} +65.3752 q^{7} +32.4095i q^{8} +(-4.95122 + 80.8485i) q^{9} +O(q^{10})$	\(q+1.04886i q^{2} +(6.16639 + 6.55558i) q^{3} +14.8999 q^{4} -21.6320i q^{5} +(-6.87585 + 6.46765i) q^{6} +65.3752 q^{7} +32.4095i q^{8} +(-4.95122 + 80.8485i) q^{9} +22.6889 q^{10} +53.0103i q^{11} +(91.8786 + 97.6775i) q^{12} -148.301 q^{13} +68.5691i q^{14} +(141.811 - 133.392i) q^{15} +204.406 q^{16} -477.905i q^{17} +(-84.7984 - 5.19312i) q^{18} +527.951 q^{19} -322.315i q^{20} +(403.129 + 428.572i) q^{21} -55.6001 q^{22} +216.329i q^{23} +(-212.463 + 199.850i) q^{24} +157.055 q^{25} -155.546i q^{26} +(-560.540 + 466.086i) q^{27} +974.084 q^{28} -154.009i q^{29} +(139.909 + 148.739i) q^{30} -1325.52 q^{31} +732.944i q^{32} +(-347.513 + 326.882i) q^{33} +501.253 q^{34} -1414.20i q^{35} +(-73.7728 + 1204.64i) q^{36} +1036.83 q^{37} +553.744i q^{38} +(-914.479 - 972.196i) q^{39} +701.084 q^{40} +2579.00i q^{41} +(-449.510 + 422.824i) q^{42} -2246.52 q^{43} +789.848i q^{44} +(1748.92 + 107.105i) q^{45} -226.898 q^{46} +2559.56i q^{47} +(1260.44 + 1340.00i) q^{48} +1872.91 q^{49} +164.727i q^{50} +(3132.95 - 2946.95i) q^{51} -2209.66 q^{52} -2821.55i q^{53} +(-488.856 - 587.925i) q^{54} +1146.72 q^{55} +2118.78i q^{56} +(3255.55 + 3461.03i) q^{57} +161.533 q^{58} -453.188i q^{59} +(2112.96 - 1987.52i) q^{60} +5202.66 q^{61} -1390.28i q^{62} +(-323.687 + 5285.49i) q^{63} +2501.74 q^{64} +3208.04i q^{65} +(-342.852 - 364.491i) q^{66} -6560.90 q^{67} -7120.74i q^{68} +(-1418.16 + 1333.97i) q^{69} +1483.29 q^{70} -4352.16i q^{71} +(-2620.26 - 160.467i) q^{72} -4814.33 q^{73} +1087.49i q^{74} +(968.460 + 1029.58i) q^{75} +7866.42 q^{76} +3465.56i q^{77} +(1019.69 - 959.156i) q^{78} -4650.16 q^{79} -4421.71i q^{80} +(-6511.97 - 800.598i) q^{81} -2704.99 q^{82} -10943.2i q^{83} +(6006.58 + 6385.68i) q^{84} -10338.1 q^{85} -2356.28i q^{86} +(1009.62 - 949.682i) q^{87} -1718.04 q^{88} -6020.37i q^{89} +(-112.338 + 1834.36i) q^{90} -9695.17 q^{91} +3223.28i q^{92} +(-8173.69 - 8689.56i) q^{93} -2684.61 q^{94} -11420.7i q^{95} +(-4804.87 + 4519.62i) q^{96} +9712.75 q^{97} +1964.42i q^{98} +(-4285.80 - 262.466i) 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 $

$2$			1.04886i			0.262214i	0.991368	+	0.131107i	$0.0418531\pi$
$2$			1.04886i			0.262214i	−0.991368	+	0.131107i	$0.958147\pi$
$3$	6.16639	+	6.55558i	0.685155	+	0.728398i
$3$	6.16639	+	6.55558i	0.685155	+	0.728398i
$4$	14.8999			0.931244
$5$		−	21.6320i		−	0.865282i	−0.901566	−	0.432641i	$-0.857582\pi$
$5$		−	21.6320i		−	0.865282i	0.901566	−	0.432641i	$-0.142418\pi$
$6$	−6.87585	+	6.46765i	−0.190996	+	0.179657i
$7$	65.3752			1.33419			0.667094	−	0.744974i	$-0.267538\pi$
$7$	65.3752			1.33419			0.667094	+	0.744974i	$0.267538\pi$
$8$			32.4095i			0.506399i
$9$	−4.95122	+	80.8485i	−0.0611262	+	0.998130i
$10$	22.6889			0.226889
$11$			53.0103i			0.438101i	0.975713	+	0.219051i	$0.0702960\pi$
$11$			53.0103i			0.438101i	−0.975713	+	0.219051i	$0.929704\pi$
$12$	91.8786	+	97.6775i	0.638046	+	0.678316i
$13$	−148.301			−0.877518			−0.438759	−	0.898605i	$-0.644582\pi$
$13$	−148.301			−0.877518			−0.438759	+	0.898605i	$0.644582\pi$
$14$			68.5691i			0.349842i
$15$	141.811	−	133.392i	0.630269	−	0.592852i
$16$	204.406			0.798459
$17$		−	477.905i		−	1.65365i	−0.562458	−	0.826826i	$-0.690144\pi$
$17$		−	477.905i		−	1.65365i	0.562458	−	0.826826i	$-0.309856\pi$
$18$	−84.7984	−	5.19312i	−0.261723	−	0.0160281i
$19$	527.951			1.46247			0.731234	−	0.682126i	$-0.238945\pi$
$19$	527.951			1.46247			0.731234	+	0.682126i	$0.238945\pi$
$20$		−	322.315i		−	0.805788i
$21$	403.129	+	428.572i	0.914125	+	0.971819i
$22$	−55.6001			−0.114876
$23$			216.329i			0.408939i	0.978873	+	0.204470i	$0.0655470\pi$
$23$			216.329i			0.408939i	−0.978873	+	0.204470i	$0.934453\pi$
$24$	−212.463	+	199.850i	−0.368860	+	0.346961i
$25$	157.055			0.251287
$26$		−	155.546i		−	0.230097i
$27$	−560.540	+	466.086i	−0.768916	+	0.639349i
$28$	974.084			1.24245
$29$		−	154.009i		−	0.183126i	−0.995799	−	0.0915632i	$-0.970814\pi$
$29$		−	154.009i		−	0.183126i	0.995799	−	0.0915632i	$-0.0291864\pi$
$30$	139.909	+	148.739i	0.155454	+	0.165265i
$31$	−1325.52			−1.37932			−0.689658	−	0.724136i	$-0.742239\pi$
$31$	−1325.52			−1.37932			−0.689658	+	0.724136i	$0.742239\pi$
$32$			732.944i			0.715766i
$33$	−347.513	+	326.882i	−0.319112	+	0.300167i
$34$	501.253			0.433610
$35$		−	1414.20i		−	1.15445i
$36$	−73.7728	+	1204.64i	−0.0569234	+	0.929503i
$37$	1036.83			0.757366			0.378683	−	0.925526i	$-0.376377\pi$
$37$	1036.83			0.757366			0.378683	+	0.925526i	$0.376377\pi$
$38$			553.744i			0.383480i
$39$	−914.479	−	972.196i	−0.601235	−	0.639182i
$40$	701.084			0.438178
$41$			2579.00i			1.53420i	0.641525	+	0.767102i	$0.278302\pi$
$41$			2579.00i			1.53420i	−0.641525	+	0.767102i	$0.721698\pi$
$42$	−449.510	+	422.824i	−0.254824	+	0.239696i
$43$	−2246.52			−1.21499			−0.607497	−	0.794322i	$-0.707826\pi$
$43$	−2246.52			−1.21499			−0.607497	+	0.794322i	$0.707826\pi$
$44$			789.848i			0.407979i
$45$	1748.92	+	107.105i	0.863664	+	0.0528914i
$46$	−226.898			−0.107230
$47$			2559.56i			1.15870i	0.815080	+	0.579349i	$0.196693\pi$
$47$			2559.56i			1.15870i	−0.815080	+	0.579349i	$0.803307\pi$
$48$	1260.44	+	1340.00i	0.547068	+	0.581596i
$49$	1872.91			0.780056
$50$			164.727i			0.0658910i
$51$	3132.95	−	2946.95i	1.20452	−	1.13301i
$52$	−2209.66			−0.817183
$53$		−	2821.55i		−	1.00447i	−0.864732	−	0.502233i	$-0.832512\pi$
$53$		−	2821.55i		−	1.00447i	0.864732	−	0.502233i	$-0.167488\pi$
$54$	−488.856	−	587.925i	−0.167646	−	0.201620i
$55$	1146.72			0.379081
$56$			2118.78i			0.675631i
$57$	3255.55	+	3461.03i	1.00202	+	1.06526i
$58$	161.533			0.0480183
$59$		−	453.188i		−	0.130189i
$59$		−	453.188i		−	0.130189i
$60$	2112.96	−	1987.52i	0.586934	−	0.552090i
$61$	5202.66			1.39819			0.699095	−	0.715029i	$-0.253587\pi$
$61$	5202.66			1.39819			0.699095	+	0.715029i	$0.253587\pi$
$62$		−	1390.28i		−	0.361675i
$63$	−323.687	+	5285.49i	−0.0815538	+	1.33169i
$64$	2501.74			0.610776
$65$			3208.04i			0.759300i
$66$	−342.852	−	364.491i	−0.0787080	−	0.0836756i
$67$	−6560.90			−1.46155			−0.730775	−	0.682619i	$-0.760841\pi$
$67$	−6560.90			−1.46155			−0.730775	+	0.682619i	$0.760841\pi$
$68$		−	7120.74i		−	1.53995i
$69$	−1418.16	+	1333.97i	−0.297870	+	0.280187i
$70$	1483.29			0.302712
$71$		−	4352.16i		−	0.863353i	−0.902028	−	0.431677i	$-0.857922\pi$
$71$		−	4352.16i		−	0.863353i	0.902028	−	0.431677i	$-0.142078\pi$
$72$	−2620.26	−	160.467i	−0.505452	−	0.0309542i
$73$	−4814.33			−0.903420			−0.451710	−	0.892165i	$-0.649186\pi$
$73$	−4814.33			−0.903420			−0.451710	+	0.892165i	$0.649186\pi$
$74$			1087.49i			0.198592i
$75$	968.460	+	1029.58i	0.172171	+	0.183037i
$76$	7866.42			1.36192
$77$			3465.56i			0.584509i
$78$	1019.69	−	959.156i	0.167602	−	0.157652i
$79$	−4650.16			−0.745099			−0.372549	−	0.928012i	$-0.621516\pi$
$79$	−4650.16			−0.745099			−0.372549	+	0.928012i	$0.621516\pi$
$80$		−	4421.71i		−	0.690892i
$81$	−6511.97	−	800.598i	−0.992527	−	0.122024i
$82$	−2704.99			−0.402289
$83$		−	10943.2i		−	1.58850i	−0.607591	−	0.794250i	$-0.707864\pi$
$83$		−	10943.2i		−	1.58850i	0.607591	−	0.794250i	$-0.292136\pi$
$84$	6006.58	+	6385.68i	0.851273	+	0.905001i
$85$	−10338.1			−1.43087
$86$		−	2356.28i		−	0.318588i
$87$	1009.62	−	949.682i	0.133389	−	0.125470i
$88$	−1718.04			−0.221854
$89$		−	6020.37i		−	0.760052i	−0.924976	−	0.380026i	$-0.875915\pi$
$89$		−	6020.37i		−	0.760052i	0.924976	−	0.380026i	$-0.124085\pi$
$90$	−112.338	+	1834.36i	−0.0138689	+	0.226465i
$91$	−9695.17			−1.17077
$92$			3223.28i			0.380822i
$93$	−8173.69	−	8689.56i	−0.945044	−	1.00469i
$94$	−2684.61			−0.303826
$95$		−	11420.7i		−	1.26545i
$96$	−4804.87	+	4519.62i	−0.521362	+	0.490410i
$97$	9712.75			1.03228			0.516142	−	0.856503i	$-0.327368\pi$
$97$	9712.75			1.03228			0.516142	+	0.856503i	$0.327368\pi$
$98$			1964.42i			0.204541i
$99$	−4285.80	−	262.466i	−0.437282	−	0.0267795i
$100$	2340.10			0.234010
$101$			8182.01i			0.802079i	0.916061	+	0.401039i	$0.131351\pi$
$101$			8182.01i			0.802079i	−0.916061	+	0.401039i	$0.868649\pi$
$102$	3090.92	+	3286.01i	0.297090	+	0.315841i
$103$	−3868.26			−0.364620			−0.182310	−	0.983241i	$-0.558358\pi$
$103$	−3868.26			−0.364620			−0.182310	+	0.983241i	$0.558358\pi$
$104$		−	4806.35i		−	0.444374i
$105$	9270.89	−	8720.51i	0.840897	−	0.790976i
$106$	2959.39			0.263385
$107$			20088.1i			1.75457i	0.479970	+	0.877285i	$0.340648\pi$
$107$			20088.1i			1.75457i	−0.479970	+	0.877285i	$0.659352\pi$
$108$	−8351.99	+	6944.63i	−0.716049	+	0.595390i
$109$	−12218.5			−1.02841			−0.514204	−	0.857668i	$-0.671912\pi$
$109$	−12218.5			−1.02841			−0.514204	+	0.857668i	$0.671912\pi$
$110$			1202.74i			0.0994003i
$111$	6393.53	+	6797.05i	0.518913	+	0.551664i
$112$	13363.1			1.06529
$113$		−	9419.28i		−	0.737668i	−0.929495	−	0.368834i	$-0.879757\pi$
$113$		−	9419.28i		−	0.737668i	0.929495	−	0.368834i	$-0.120243\pi$
$114$	−3630.12	+	3414.61i	−0.279326	+	0.262743i
$115$	4679.64			0.353848
$116$		−	2294.72i		−	0.170535i
$117$	734.269	−	11989.9i	0.0536393	−	0.875877i
$118$	475.328			0.0341373
$119$		−	31243.1i		−	2.20628i
$120$	4323.16	+	4596.01i	0.300219	+	0.319168i
$121$	11830.9			0.808067
$122$			5456.84i			0.366625i
$123$	−16906.8	+	15903.1i	−1.11751	+	1.05117i
$124$	−19750.1			−1.28448
$125$		−	16917.4i		−	1.08272i
$126$	−5543.71	−	339.501i	−0.349188	−	0.0213845i
$127$	−9648.06			−0.598181			−0.299090	−	0.954225i	$-0.596683\pi$
$127$	−9648.06			−0.598181			−0.299090	+	0.954225i	$0.596683\pi$
$128$			14351.1i			0.875920i
$129$	−13852.9	−	14727.3i	−0.832458	−	0.884998i
$130$	−3364.77			−0.199099
$131$		−	24996.1i		−	1.45656i	−0.685277	−	0.728282i	$-0.740319\pi$
$131$		−	24996.1i		−	1.45656i	0.685277	−	0.728282i	$-0.259681\pi$
$132$	−5177.91	+	4870.51i	−0.297171	+	0.279529i
$133$	34514.9			1.95121
$134$		−	6881.43i		−	0.383238i
$135$	10082.4	+	12125.6i	0.553217	+	0.665329i
$136$	15488.7			0.837407
$137$		−	20444.0i		−	1.08925i	−0.838681	−	0.544623i	$-0.816673\pi$
$137$		−	20444.0i		−	1.08925i	0.838681	−	0.544623i	$-0.183327\pi$
$138$	−1399.14	−	1487.45i	−0.0734688	−	0.0781057i
$139$	−17984.9			−0.930846			−0.465423	−	0.885088i	$-0.654098\pi$
$139$	−17984.9			−0.930846			−0.465423	+	0.885088i	$0.654098\pi$
$140$		−	21071.4i		−	1.07507i
$141$	−16779.4	+	15783.3i	−0.843992	+	0.793887i
$142$	4564.79			0.226383
$143$		−	7861.45i		−	0.384442i
$144$	−1012.06	+	16525.9i	−0.0488068	+	0.796966i
$145$	−3331.54			−0.158456
$146$		−	5049.53i		−	0.236889i
$147$	11549.1	+	12278.0i	0.534459	+	0.568191i
$148$	15448.7			0.705293
$149$			16860.4i			0.759443i	0.925101	+	0.379721i	$0.123980\pi$
$149$			16860.4i			0.759443i	−0.925101	+	0.379721i	$0.876020\pi$
$150$	−1079.88	+	1015.77i	−0.0479948	+	0.0451455i
$151$	−37835.5			−1.65938			−0.829689	−	0.558226i	$-0.811482\pi$
$151$	−37835.5			−1.65938			−0.829689	+	0.558226i	$0.811482\pi$
$152$			17110.6i			0.740592i
$153$	38637.9	+	2366.22i	1.65056	+	0.101081i
$154$	−3634.87			−0.153266
$155$			28673.8i			1.19350i
$156$	−13625.6	−	14485.6i	−0.559897	−	0.595234i
$157$	12835.7			0.520740			0.260370	−	0.965509i	$-0.416155\pi$
$157$	12835.7			0.520740			0.260370	+	0.965509i	$0.416155\pi$
$158$		−	4877.35i		−	0.195375i
$159$	18496.9	−	17398.8i	0.731651	−	0.688215i
$160$	15855.1			0.619339
$161$			14142.5i			0.545602i
$162$	839.712	−	6830.11i	0.0319963	−	0.260254i
$163$	−16758.3			−0.630747			−0.315374	−	0.948968i	$-0.602130\pi$
$163$	−16758.3			−0.630747			−0.315374	+	0.948968i	$0.602130\pi$
$164$			38426.8i			1.42872i
$165$	7071.13	+	7517.42i	0.259729	+	0.276122i
$166$	11477.8			0.416527
$167$		−	8751.52i		−	0.313798i	−0.987615	−	0.156899i	$-0.949850\pi$
$167$		−	8751.52i		−	0.313798i	0.987615	−	0.156899i	$-0.0501498\pi$
$168$	−13889.8	+	13065.2i	−0.492128	+	0.462912i
$169$	−6567.96			−0.229963
$170$		−	10843.1i		−	0.375195i
$171$	−2614.01	+	42684.1i	−0.0893952	+	1.45973i
$172$	−33473.0			−1.13145
$173$		−	11049.0i		−	0.369173i	−0.982816	−	0.184586i	$-0.940905\pi$
$173$		−	11049.0i		−	0.369173i	0.982816	−	0.184586i	$-0.0590945\pi$
$174$	996.079	+	1058.95i	0.0328999	+	0.0349764i
$175$	10267.5			0.335264
$176$			10835.6i			0.349806i
$177$	2970.91	−	2794.53i	0.0948293	−	0.0891995i
$178$	6314.50			0.199296
$179$		−	34471.4i		−	1.07585i	−0.842992	−	0.537926i	$-0.819208\pi$
$179$		−	34471.4i		−	1.07585i	0.842992	−	0.537926i	$-0.180792\pi$
$180$	26058.7	+	1595.86i	0.804282	+	0.0492548i
$181$	6722.66			0.205203			0.102602	−	0.994723i	$-0.467283\pi$
$181$	6722.66			0.205203			0.102602	+	0.994723i	$0.467283\pi$
$182$		−	10168.8i		−	0.306993i
$183$	32081.7	+	34106.5i	0.957976	+	1.01844i
$184$	−7011.12			−0.207086
$185$		−	22428.8i		−	0.655335i
$186$	9114.09	−	8573.01i	0.263444	−	0.247804i
$187$	25333.9			0.724467
$188$			38137.2i			1.07903i
$189$	−36645.4	+	30470.4i	−1.02588	+	0.853012i
$190$	11978.6			0.331818
$191$			3444.51i			0.0944194i	0.998885	+	0.0472097i	$0.0150329\pi$
$191$			3444.51i			0.0944194i	−0.998885	+	0.0472097i	$0.984967\pi$
$192$	15426.7	+	16400.3i	0.418476	+	0.444887i
$193$	64450.0			1.73025			0.865124	−	0.501559i	$-0.167240\pi$
$193$	64450.0			1.73025			0.865124	+	0.501559i	$0.167240\pi$
$194$			10187.3i			0.270679i
$195$	−21030.6	+	19782.1i	−0.553072	+	0.520238i
$196$	27906.2			0.726423
$197$		−	20189.1i		−	0.520217i	−0.965579	−	0.260108i	$-0.916242\pi$
$197$		−	20189.1i		−	0.520217i	0.965579	−	0.260108i	$-0.0837583\pi$
$198$	275.289	−	4495.19i	0.00702195	−	0.114661i
$199$	−28262.5			−0.713683			−0.356841	−	0.934165i	$-0.616146\pi$
$199$	−28262.5			−0.713683			−0.356841	+	0.934165i	$0.616146\pi$
$200$			5090.06i			0.127252i
$201$	−40457.1	−	43010.5i	−1.00139	−	1.06459i
$202$	−8581.74			−0.210316
$203$		−	10068.4i		−	0.244325i
$204$	46680.6	−	43909.3i	1.12170	−	1.05511i
$205$	55789.0			1.32752
$206$		−	4057.24i		−	0.0956085i
$207$	−17489.9	−	1071.09i	−0.408175	−	0.0249969i
$208$	−30313.4			−0.700662
$209$			27986.8i			0.640710i
$210$	9146.55	+	9723.82i	0.207405	+	0.220495i
$211$	2198.92			0.0493905			0.0246953	−	0.999695i	$-0.492138\pi$
$211$	2198.92			0.0493905			0.0246953	+	0.999695i	$0.492138\pi$
$212$		−	42040.8i		−	0.935403i
$213$	28531.0	−	26837.1i	0.628864	−	0.591531i
$214$	−21069.5			−0.460072
$215$			48596.9i			1.05131i
$216$	−15105.6	−	18166.8i	−0.323766	−	0.389378i
$217$	−86656.2			−1.84027
$218$		−	12815.4i		−	0.269663i
$219$	−29687.0	−	31560.7i	−0.618983	−	0.658049i
$220$	17086.0			0.353017
$221$			70873.6i			1.45111i
$222$	−7129.12	+	6705.88i	−0.144654	+	0.136066i
$223$	−49839.2			−1.00222			−0.501108	−	0.865385i	$-0.667074\pi$
$223$	−49839.2			−1.00222			−0.501108	+	0.865385i	$0.667074\pi$
$224$			47916.4i			0.954966i
$225$	−777.612	+	12697.6i	−0.0153602	+	0.250817i
$226$	9879.46			0.193427
$227$		−	8748.35i		−	0.169775i	−0.996391	−	0.0848876i	$-0.972947\pi$
$227$		−	8748.35i		−	0.169775i	0.996391	−	0.0848876i	$-0.0270531\pi$
$228$	48507.4	+	51569.0i	0.933123	+	0.992016i
$229$	23787.1			0.453597			0.226798	−	0.973942i	$-0.427174\pi$
$229$	23787.1			0.453597			0.226798	+	0.973942i	$0.427174\pi$
$230$			4908.26i			0.0927838i
$231$	−22718.7	+	21370.0i	−0.425755	+	0.400479i
$232$	4991.37			0.0927350
$233$		−	373.812i		−	0.00688559i	−0.999994	−	0.00344279i	$-0.998904\pi$
$233$		−	373.812i		−	0.00688559i	0.999994	−	0.00344279i	$-0.00109588\pi$
$234$	12575.6	+	770.142i	0.229667	+	0.0140650i
$235$	55368.6			1.00260
$236$		−	6752.45i		−	0.121238i
$237$	−28674.7	−	30484.5i	−0.510508	−	0.542728i
$238$	32769.5			0.578517
$239$			77832.1i			1.36258i	0.732012	+	0.681291i	$0.238581\pi$
$239$			77832.1i			1.36258i	−0.732012	+	0.681291i	$0.761419\pi$
$240$	28986.9	−	27266.0i	0.503244	−	0.473368i
$241$	14396.1			0.247863			0.123931	−	0.992291i	$-0.460450\pi$
$241$	14396.1			0.247863			0.123931	+	0.992291i	$0.460450\pi$
$242$			12408.9i			0.211886i
$243$	−34907.0	−	47626.5i	−0.591153	−	0.806560i
$244$	77519.2			1.30206
$245$		−	40515.0i		−	0.674968i
$246$	−16680.0	−	17732.8i	−0.275630	−	0.293027i
$247$	−78295.4			−1.28334
$248$		−	42959.5i		−	0.698484i
$249$	71738.9	−	67479.9i	1.15706	−	1.08837i
$250$	17743.9			0.283903
$251$			96062.6i			1.52478i	0.647119	+	0.762389i	$0.275974\pi$
$251$			96062.6i			1.52478i	−0.647119	+	0.762389i	$0.724026\pi$
$252$	−4822.91	+	78753.3i	−0.0759465	+	1.24013i
$253$	−11467.7			−0.179157
$254$		−	10119.4i		−	0.156851i
$255$	−63748.6	−	67772.0i	−0.980370	−	1.04225i
$256$	24975.6			0.381097
$257$		−	33197.1i		−	0.502614i	−0.967907	−	0.251307i	$-0.919140\pi$
$257$		−	33197.1i		−	0.502614i	0.967907	−	0.251307i	$-0.0808603\pi$
$258$	15446.8	−	14529.7i	0.232059	−	0.218282i
$259$	67783.2			1.01047
$260$			47799.5i			0.707094i
$261$	12451.4	+	762.535i	0.182784	+	0.0111938i
$262$	26217.3			0.381931
$263$		−	30780.4i		−	0.445003i	−0.974932	−	0.222502i	$-0.928578\pi$
$263$		−	30780.4i		−	0.445003i	0.974932	−	0.222502i	$-0.0714223\pi$
$264$	−10594.1	−	11262.7i	−0.152004	−	0.161598i
$265$	−61035.8			−0.869146
$266$			36201.1i			0.511634i
$267$	39467.0	−	37124.0i	0.553620	−	0.520753i
$268$	−97756.7			−1.36106
$269$			50657.3i			0.700063i	0.936738	+	0.350032i	$0.113829\pi$
$269$			50657.3i			0.700063i	−0.936738	+	0.350032i	$0.886171\pi$
$270$	−12718.0	+	10575.0i	−0.174459	+	0.145061i
$271$	−178.577			−0.00243157			−0.00121578	−	0.999999i	$-0.500387\pi$
$271$	−178.577			−0.00243157			−0.00121578	+	0.999999i	$0.500387\pi$
$272$		−	97686.5i		−	1.32037i
$273$	−59784.2	−	63557.5i	−0.802161	−	0.852788i
$274$	21442.8			0.285615
$275$			8325.51i			0.110089i
$276$	−21130.5	+	19876.0i	−0.277390	+	0.260922i
$277$	−113783.			−1.48291			−0.741457	−	0.671000i	$-0.765865\pi$
$277$	−113783.			−1.48291			−0.741457	+	0.671000i	$0.765865\pi$
$278$		−	18863.5i		−	0.244081i
$279$	6562.96	−	107167.i	0.0843123	−	1.37674i
$280$	45833.5			0.584611
$281$		−	77118.8i		−	0.976669i	−0.872656	−	0.488335i	$-0.837605\pi$
$281$		−	77118.8i		−	0.976669i	0.872656	−	0.488335i	$-0.162395\pi$
$282$	−16554.4	−	17599.2i	−0.208168	−	0.221306i
$283$	104562.			1.30557			0.652787	−	0.757542i	$-0.273600\pi$
$283$	104562.			1.30557			0.652787	+	0.757542i	$0.273600\pi$
$284$		−	64846.8i		−	0.803993i
$285$	74869.1	−	70424.3i	0.921749	−	0.867027i
$286$	8245.52			0.100806
$287$			168602.i			2.04691i
$288$	−59257.5	−	3628.97i	−0.714427	−	0.0437521i
$289$	−144872.			−1.73456
$290$		−	3494.30i		−	0.0415493i
$291$	59892.6	+	63672.7i	0.707274	+	0.751913i
$292$	−71733.0			−0.841305
$293$			60118.6i			0.700283i	0.936697	+	0.350142i	$0.113867\pi$
$293$			60118.6i			0.700283i	−0.936697	+	0.350142i	$0.886133\pi$
$294$	−12877.9	+	12113.4i	−0.148988	+	0.140143i
$295$	−9803.38			−0.112650
$296$			33603.3i			0.383529i
$297$	−24707.3	−	29714.4i	−0.280100	−	0.336863i
$298$	−17684.1			−0.199136
$299$		−	32081.7i		−	0.358852i
$300$	14430.0	+	15340.7i	0.160333	+	0.170452i
$301$	−146867.			−1.62103
$302$		−	39683.9i		−	0.435112i
$303$	−53637.8	+	50453.5i	−0.584232	+	0.549548i
$304$	107916.			1.16772
$305$		−	112544.i		−	1.20983i
$306$	−2481.82	+	40525.6i	−0.0265049	+	0.432799i
$307$	33427.8			0.354675			0.177338	−	0.984150i	$-0.443252\pi$
$307$	33427.8			0.354675			0.177338	+	0.984150i	$0.443252\pi$
$308$			51636.5i			0.544321i
$309$	−23853.2	−	25358.7i	−0.249821	−	0.265589i
$310$	−30074.6			−0.312951
$311$			10376.1i			0.107278i	0.998560	+	0.0536391i	$0.0170821\pi$
$311$			10376.1i			0.107278i	−0.998560	+	0.0536391i	$0.982918\pi$
$312$	31508.4	−	29637.8i	0.323681	−	0.304465i
$313$	155557.			1.58782			0.793909	−	0.608037i	$-0.208043\pi$
$313$	155557.			1.58782			0.793909	+	0.608037i	$0.208043\pi$
$314$			13462.8i			0.136545i
$315$	114336.	+	7002.02i	1.15229	+	0.0705671i
$316$	−69287.0			−0.693869
$317$			151554.i			1.50817i	0.656778	+	0.754084i	$0.271919\pi$
$317$			151554.i			1.50817i	−0.656778	+	0.754084i	$0.728081\pi$
$318$	18248.8	+	19400.5i	0.180459	+	0.191849i
$319$	8164.08			0.0802280
$320$		−	54117.7i		−	0.528493i
$321$	−131689.	+	123871.i	−1.27802	+	1.20215i
$322$	−14833.5			−0.143064
$323$		−	252311.i		−	2.41841i
$324$	−97027.7	−	11928.8i	−0.924285	−	0.113634i
$325$	−23291.3			−0.220509
$326$		−	17577.1i		−	0.165391i
$327$	−75344.1	−	80099.4i	−0.704618	−	0.749089i
$328$	−83584.0			−0.776919
$329$			167332.i			1.54592i
$330$	−7884.68	+	7416.59i	−0.0724030	+	0.0681046i
$331$	−62442.7			−0.569935			−0.284968	−	0.958537i	$-0.591983\pi$
$331$	−62442.7			−0.569935			−0.284968	+	0.958537i	$0.591983\pi$
$332$		−	163052.i		−	1.47928i
$333$	−5133.60	+	83826.5i	−0.0462949	+	0.755950i
$334$	9179.08			0.0822822
$335$			141926.i			1.26465i
$336$	82401.8	+	87602.5i	0.729891	+	0.775958i
$337$	−127156.			−1.11964			−0.559818	−	0.828616i	$-0.689129\pi$
$337$	−127156.			−1.11964			−0.559818	+	0.828616i	$0.689129\pi$
$338$		−	6888.84i		−	0.0602993i
$339$	61748.9	−	58083.0i	0.537316	−	0.505417i
$340$	−154036.			−1.33249
$341$		−	70266.3i		−	0.604280i
$342$	−44769.4	−	2741.71i	−0.382762	−	0.0234407i
$343$	−34523.7			−0.293446
$344$		−	72808.7i		−	0.615271i
$345$	28856.5	+	30677.7i	0.242440	+	0.257742i
$346$	11588.8			0.0968022
$347$		−	32686.0i		−	0.271458i	−0.990746	−	0.135729i	$-0.956662\pi$
$347$		−	32686.0i		−	0.271458i	0.990746	−	0.135729i	$-0.0433377\pi$
$348$	15043.2	−	14150.2i	0.124218	−	0.116843i
$349$	−7485.86			−0.0614597			−0.0307299	−	0.999528i	$-0.509783\pi$
$349$	−7485.86			−0.0614597			−0.0307299	+	0.999528i	$0.509783\pi$
$350$			10769.1i			0.0879109i
$351$	83128.4	−	69120.7i	0.674738	−	0.561040i
$352$	−38853.6			−0.313578
$353$		−	27051.3i		−	0.217090i	−0.994092	−	0.108545i	$-0.965381\pi$
$353$		−	27051.3i		−	0.217090i	0.994092	−	0.108545i	$-0.0346191\pi$
$354$	2931.06	+	3116.05i	0.0233893	+	0.0248655i
$355$	−94146.2			−0.747044
$356$		−	89703.0i		−	0.707794i
$357$	204817.	−	192657.i	1.60705	−	1.51164i
$358$	36155.5			0.282103
$359$			133800.i			1.03817i	0.854722	+	0.519085i	$0.173727\pi$
$359$			133800.i			1.03817i	−0.854722	+	0.519085i	$0.826273\pi$
$360$	−3471.23	+	56681.6i	−0.0267841	+	0.437358i
$361$	148412.			1.13882
$362$			7051.09i			0.0538071i
$363$	72954.0	+	77558.5i	0.553651	+	0.588594i
$364$	−144457.			−1.09028
$365$			104144.i			0.781713i
$366$	−35772.7	+	33649.0i	−0.267048	+	0.251195i
$367$	184371.			1.36887			0.684433	−	0.729076i	$-0.260050\pi$
$367$	184371.			1.36887			0.684433	+	0.729076i	$0.260050\pi$
$368$			44218.8i			0.326521i
$369$	−208508.	−	12769.2i	−1.53133	−	0.0937801i
$370$	23524.6			0.171838
$371$		−	184459.i		−	1.34015i
$372$	−121787.	−	129474.i	−0.880067	−	0.935611i
$373$	12844.2			0.0923185			0.0461592	−	0.998934i	$-0.485302\pi$
$373$	12844.2			0.0923185			0.0461592	+	0.998934i	$0.485302\pi$
$374$			26571.6i			0.189965i
$375$	110904.	−	104320.i	0.788648	−	0.741828i
$376$	−82954.2			−0.586763
$377$			22839.7i			0.160697i
$378$	−31959.1	−	38435.7i	−0.223671	−	0.269000i
$379$	20625.0			0.143587			0.0717935	−	0.997420i	$-0.477128\pi$
$379$	20625.0			0.143587			0.0717935	+	0.997420i	$0.477128\pi$
$380$		−	170167.i		−	1.17844i
$381$	−59493.7	−	63248.6i	−0.409846	−	0.435714i
$382$	−3612.80			−0.0247581
$383$			177624.i			1.21089i	0.795889	+	0.605443i	$0.207004\pi$
$383$			177624.i			1.21089i	−0.795889	+	0.605443i	$0.792996\pi$
$384$	−94079.5	+	88494.3i	−0.638018	+	0.600140i
$385$	74967.1			0.505765
$386$			67598.7i			0.453695i
$387$	11123.0	−	181628.i	0.0742679	−	1.21272i
$388$	144719.			0.961308
$389$			275583.i			1.82118i	0.413312	+	0.910590i	$0.364372\pi$
$389$			275583.i			1.82118i	−0.413312	+	0.910590i	$0.635628\pi$
$390$	−20748.5	−	22058.0i	−0.136414	−	0.145023i
$391$	103385.			0.676243
$392$			60700.3i			0.395019i
$393$	163864.	−	154136.i	1.06096	−	0.997972i
$394$	21175.4			0.136408
$395$			100593.i			0.644720i
$396$	−63858.0	−	3910.71i	−0.407216	−	0.0249382i
$397$	279128.			1.77102			0.885508	−	0.464624i	$-0.153810\pi$
$397$	279128.			1.77102			0.885508	+	0.464624i	$0.153810\pi$
$398$		−	29643.3i		−	0.187137i
$399$	212832.	+	226265.i	1.33688	+	1.42126i
$400$	32102.8			0.200643
$401$		−	116689.i		−	0.725671i	−0.931853	−	0.362835i	$-0.881809\pi$
$401$		−	116689.i		−	0.725671i	0.931853	−	0.362835i	$-0.118191\pi$
$402$	45111.7	−	42433.6i	0.279150	−	0.262578i
$403$	196576.			1.21037
$404$			121911.i			0.746931i
$405$	−17318.6	+	140867.i	−0.105585	+	0.858816i
$406$	10560.3			0.0640654
$407$			54962.9i			0.331803i
$408$	95509.3	+	101537.i	0.573753	+	0.609965i
$409$	312760.			1.86967			0.934833	−	0.355087i	$-0.115549\pi$
$409$	312760.			1.86967			0.934833	+	0.355087i	$0.115549\pi$
$410$			58514.5i			0.348094i
$411$	134023.	−	126066.i	0.793404	−	0.746302i
$412$	−57636.7			−0.339551
$413$		−	29627.2i		−	0.173696i
$414$	1123.42	−	18344.3i	0.00655454	−	0.107029i
$415$	−236723.			−1.37450
$416$		−	108696.i		−	0.628097i
$417$	−110902.	−	117901.i	−0.637773	−	0.678026i
$418$	−29354.1			−0.168003
$419$			184121.i			1.04876i	0.851486	+	0.524378i	$0.175702\pi$
$419$			184121.i			1.04876i	−0.851486	+	0.524378i	$0.824298\pi$
$420$	138135.	−	129935.i	0.783081	−	0.736591i
$421$	76492.8			0.431575			0.215788	−	0.976440i	$-0.430768\pi$
$421$	76492.8			0.431575			0.215788	+	0.976440i	$0.430768\pi$
$422$			2306.34i			0.0129509i
$423$	−206937.	−	12673.0i	−1.15653	−	0.0708268i
$424$	91444.9			0.508660
$425$		−	75057.2i		−	0.415542i
$426$	28148.3	+	29924.8i	0.155107	+	0.164897i
$427$	340125.			1.86545
$428$			299310.i			1.63393i
$429$	51536.4	−	48476.8i	0.280026	−	0.263402i
$430$	−50971.1			−0.275668
$431$			232704.i			1.25271i	0.779539	+	0.626354i	$0.215454\pi$
$431$			232704.i			1.25271i	−0.779539	+	0.626354i	$0.784546\pi$
$432$	−114578.	+	95270.5i	−0.613948	+	0.510494i
$433$	66708.3			0.355799			0.177899	−	0.984049i	$-0.443070\pi$
$433$	66708.3			0.355799			0.177899	+	0.984049i	$0.443070\pi$
$434$		−	90889.8i		−	0.482543i
$435$	−20543.6	−	21840.2i	−0.108567	−	0.115419i
$436$	−182055.			−0.957698
$437$			114211.i			0.598061i
$438$	33102.6	−	31137.4i	0.172550	−	0.162306i
$439$	−23372.5			−0.121277			−0.0606383	−	0.998160i	$-0.519314\pi$
$439$	−23372.5			−0.121277			−0.0606383	+	0.998160i	$0.519314\pi$
$440$			37164.7i			0.191966i
$441$	−9273.22	+	151422.i	−0.0476819	+	0.778597i
$442$	−74336.1			−0.380501
$443$			55098.3i			0.280757i	0.990098	+	0.140379i	$0.0448319\pi$
$443$			55098.3i			0.280757i	−0.990098	+	0.140379i	$0.955168\pi$
$444$	95262.9	+	101275.i	0.483234	+	0.513733i
$445$	−130233.			−0.657659
$446$		−	52274.1i		−	0.262795i
$447$	−110530.	+	103968.i	−0.553176	+	0.520336i
$448$	163552.			0.814889
$449$			129152.i			0.640633i	0.947311	+	0.320316i	$0.103789\pi$
$449$			129152.i			0.640633i	−0.947311	+	0.320316i	$0.896211\pi$
$450$	−13318.0	−	815.603i	−0.0657678	−	0.00402767i
$451$	−136713.			−0.672137
$452$		−	140346.i		−	0.686949i
$453$	−233308.	−	248033.i	−1.13693	−	1.20869i
$454$	9175.75			0.0445174
$455$			209726.i			1.01305i
$456$	−112170.	+	105511.i	−0.539446	+	0.507420i
$457$	−28680.9			−0.137329			−0.0686643	−	0.997640i	$-0.521874\pi$
$457$	−28680.9			−0.137329			−0.0686643	+	0.997640i	$0.521874\pi$
$458$			24949.2i			0.118939i
$459$	222745.	+	267885.i	1.05726	+	1.27152i
$460$	69726.1			0.329519
$461$			335306.i			1.57776i	0.614549	+	0.788878i	$0.289338\pi$
$461$			335306.i			1.57776i	−0.614549	+	0.788878i	$0.710662\pi$
$462$	−22414.0	−	23828.7i	−0.105011	−	0.111639i
$463$	−59287.1			−0.276566			−0.138283	−	0.990393i	$-0.544158\pi$
$463$	−59287.1			−0.276566			−0.138283	+	0.990393i	$0.544158\pi$
$464$		−	31480.4i		−	0.146219i
$465$	−187973.	+	176814.i	−0.869340	+	0.817730i
$466$	392.074			0.00180550
$467$		−	9881.41i		−	0.0453091i	−0.999743	−	0.0226545i	$-0.992788\pi$
$467$		−	9881.41i		−	0.0453091i	0.999743	−	0.0226545i	$-0.00721178\pi$
$468$	10940.5	−	178648.i	0.0499513	−	0.815655i
$469$	−428920.			−1.94998
$470$			58073.6i			0.262895i
$471$	79150.1	+	84145.6i	0.356787	+	0.379306i
$472$	14687.6			0.0659275
$473$		−	119089.i		−	0.532290i
$474$	31973.8	−	30075.6i	0.142311	−	0.133862i
$475$	82917.2			0.367500
$476$		−	465520.i		−	2.05459i
$477$	228118.	+	13970.1i	1.00259	+	0.0613992i
$478$	−81634.6			−0.357288
$479$		−	412926.i		−	1.79971i	−0.436194	−	0.899853i	$-0.643674\pi$
$479$		−	412926.i		−	1.79971i	0.436194	−	0.899853i	$-0.356326\pi$
$480$	97768.6	+	103939.i	0.424343	+	0.451125i
$481$	−153763.			−0.664602
$482$			15099.4i			0.0649930i
$483$	−92712.6	+	87208.5i	−0.397415	+	0.373822i
$484$	176279.			0.752508
$485$		−	210107.i		−	0.893216i
$486$	49953.3	−	36612.4i	0.211491	−	0.155008i
$487$	117496.			0.495411			0.247706	−	0.968835i	$-0.420323\pi$
$487$	117496.			0.495411			0.247706	+	0.968835i	$0.420323\pi$
$488$			168616.i			0.708041i
$489$	−103338.	−	109861.i	−0.432159	−	0.459435i
$490$	42494.3			0.176986
$491$		−	293598.i		−	1.21784i	−0.793232	−	0.608920i	$-0.791603\pi$
$491$		−	293598.i		−	1.21784i	0.793232	−	0.608920i	$-0.208397\pi$
$492$	−251910.	+	236955.i	−1.04067	+	0.978893i
$493$	−73601.9			−0.302827
$494$		−	82120.6i		−	0.336510i
$495$	−5677.67	+	92710.7i	−0.0231718	+	0.378372i
$496$	−270944.			−1.10133
$497$		−	284524.i		−	1.15188i
$498$	70776.6	+	75243.7i	0.285385	+	0.303397i
$499$	201642.			0.809804			0.404902	−	0.914360i	$-0.367306\pi$
$499$	201642.			0.809804			0.404902	+	0.914360i	$0.367306\pi$
$500$		−	252068.i		−	1.00827i
$501$	57371.3	−	53965.3i	0.228570	−	0.215000i
$502$	−100756.			−0.399818
$503$		−	419143.i		−	1.65663i	−0.560262	−	0.828316i	$-0.689299\pi$
$503$		−	419143.i		−	1.65663i	0.560262	−	0.828316i	$-0.310701\pi$
$504$	−171300.	−	10490.5i	−0.674367	−	0.0412988i
$505$	176994.			0.694024
$506$		−	12027.9i		−	0.0469774i
$507$	−40500.6	−	43056.8i	−0.157560	−	0.167504i
$508$	−143755.			−0.557052
$509$			241722.i			0.932999i	0.884521	+	0.466500i	$0.154485\pi$
$509$			241722.i			0.932999i	−0.884521	+	0.466500i	$0.845515\pi$
$510$	71083.0	−	66863.0i	0.273291	−	0.257067i
$511$	−314737.			−1.20533
$512$			255813.i			0.975849i
$513$	−295938.	+	246070.i	−1.12452	+	0.935028i
$514$	34819.0			0.131792
$515$			83678.3i			0.315499i
$516$	−206407.	−	219435.i	−0.775222	−	0.824149i
$517$	−135683.			−0.507627
$518$			71094.8i			0.264959i
$519$	72432.4	−	68132.3i	0.268905	−	0.252940i
$520$	−103971.			−0.384509
$521$			353570.i			1.30257i	0.758834	+	0.651284i	$0.225769\pi$
$521$			353570.i			1.30257i	−0.758834	+	0.651284i	$0.774231\pi$
$522$	−799.788	+	13059.7i	−0.00293518	+	0.0479285i
$523$	−54526.6			−0.199345			−0.0996725	−	0.995020i	$-0.531779\pi$
$523$	−54526.6			−0.199345			−0.0996725	+	0.995020i	$0.531779\pi$
$524$		−	372440.i		−	1.35642i
$525$	63313.3	+	67309.2i	0.229708	+	0.244206i
$526$	32284.2			0.116686
$527$			633474.i			2.28091i
$528$	−71033.6	+	66816.5i	−0.254798	+	0.239671i
$529$	233043.			0.832769
$530$		−	64017.7i		−	0.227902i
$531$	36639.6	+	2243.83i	0.129945	+	0.00795796i
$532$	514269.			1.81705
$533$		−	382466.i		−	1.34629i
$534$	38937.7	+	41395.2i	0.136549	+	0.145167i
$535$	434546.			1.51820
$536$		−	212635.i		−	0.740127i
$537$	225980.	−	212564.i	0.783649	−	0.737125i
$538$	−53132.2			−0.183566
$539$			99283.7i			0.341744i
$540$	150227.	+	180671.i	0.515180	+	0.619584i
$541$	385900.			1.31850			0.659251	−	0.751923i	$-0.270874\pi$
$541$	385900.			1.31850			0.659251	+	0.751923i	$0.270874\pi$
$542$		−	187.301i		−	0.000637591i
$543$	41454.5	+	44070.9i	0.140596	+	0.149469i
$544$	350278.			1.18363
$545$			264311.i			0.889862i
$546$	66662.6	−	62705.0i	0.223613	−	0.210338i
$547$	−186158.			−0.622167			−0.311083	−	0.950383i	$-0.600692\pi$
$547$	−186158.			−0.622167			−0.311083	+	0.950383i	$0.600692\pi$
$548$		−	304614.i		−	1.01435i
$549$	−25759.6	+	420628.i	−0.0854661	+	1.39558i
$550$	−8732.25			−0.0288669
$551$		−	81309.4i		−	0.267817i
$552$	−43233.3	−	45961.9i	−0.141886	−	0.150841i
$553$	−304005.			−0.994101
$554$		−	119341.i		−	0.388840i
$555$	147034.	−	138305.i	0.477345	−	0.449006i
$556$	−267973.			−0.866845
$557$		−	546742.i		−	1.76227i	−0.472865	−	0.881135i	$-0.656780\pi$
$557$		−	546742.i		−	1.76227i	0.472865	−	0.881135i	$-0.343220\pi$
$558$	112402.	+	6883.59i	0.360999	+	0.0221079i
$559$	333160.			1.06618
$560$		−	289070.i		−	0.921780i
$561$	156219.	+	166078.i	0.496372	+	0.527700i
$562$	80886.4			0.256096
$563$			145468.i			0.458933i	0.973317	+	0.229467i	$0.0736981\pi$
$563$			145468.i			0.458933i	−0.973317	+	0.229467i	$0.926302\pi$
$564$	−250012.	+	235169.i	−0.785963	+	0.739302i
$565$	−203758.			−0.638291
$566$			109670.i			0.342339i
$567$	−425721.	−	52339.3i	−1.32422	−	0.162803i
$568$	141052.			0.437201
$569$		−	94623.0i		−	0.292262i	−0.989265	−	0.146131i	$-0.953318\pi$
$569$		−	94623.0i		−	0.292262i	0.989265	−	0.146131i	$-0.0466821\pi$
$570$	73864.9	+	78526.8i	0.227347	+	0.241695i
$571$	39348.7			0.120686			0.0603432	−	0.998178i	$-0.480780\pi$
$571$	39348.7			0.120686			0.0603432	+	0.998178i	$0.480780\pi$
$572$		−	117135.i		−	0.358009i
$573$	−22580.8	+	21240.2i	−0.0687748	+	0.0646919i
$574$	−176839.			−0.536729
$575$			33975.4i			0.102761i
$576$	−12386.7	+	202262.i	−0.0373344	+	0.609633i
$577$	−268300.			−0.805877			−0.402938	−	0.915227i	$-0.632011\pi$
$577$	−268300.			−0.805877			−0.402938	+	0.915227i	$0.632011\pi$
$578$		−	151950.i		−	0.454826i
$579$	397424.	+	422507.i	1.18549	+	1.26031i
$580$	−49639.6			−0.147561
$581$		−	715412.i		−	2.11936i
$582$	−66783.5	+	62818.7i	−0.197162	+	0.185457i
$583$	149571.			0.440058
$584$		−	156030.i		−	0.457491i
$585$	−259366.	−	15883.7i	−0.757880	−	0.0464132i
$586$	−63055.7			−0.183624
$587$			634807.i			1.84232i	0.389183	+	0.921161i	$0.372757\pi$
$587$			634807.i			1.84232i	−0.389183	+	0.921161i	$0.627243\pi$
$588$	172081.	+	182942.i	0.497712	+	0.529124i
$589$	−699811.			−2.01721
$590$		−	10282.3i		−	0.0295384i
$591$	132351.	−	124494.i	0.378924	−	0.356429i
$592$	211935.			0.604726
$593$		−	647832.i		−	1.84227i	−0.389244	−	0.921135i	$-0.627264\pi$
$593$		−	647832.i		−	1.84227i	0.389244	−	0.921135i	$-0.372736\pi$
$594$	31166.1	−	25914.4i	0.0883302	−	0.0734460i
$595$	−675853.			−1.90905
$596$			251218.i			0.707226i
$597$	−174278.	−	185277.i	−0.488983	−	0.519845i
$598$	33649.0			0.0940958
$599$		−	101382.i		−	0.282557i	−0.989970	−	0.141279i	$-0.954879\pi$
$599$		−	101382.i		−	0.282557i	0.989970	−	0.141279i	$-0.0451214\pi$
$600$	−33368.3	+	31387.3i	−0.0926898	+	0.0871870i
$601$	−400069.			−1.10761			−0.553804	−	0.832647i	$-0.686824\pi$
$601$	−400069.			−1.10761			−0.553804	+	0.832647i	$0.686824\pi$
$602$		−	154042.i		−	0.425056i
$603$	32484.5	−	530439.i	0.0893390	−	1.45882i
$604$	−563745.			−1.54529
$605$		−	255927.i		−	0.699206i
$606$	−52918.4	−	56258.3i	−0.144099	−	0.153194i
$607$	−372970.			−1.01227			−0.506135	−	0.862454i	$-0.668926\pi$
$607$	−372970.			−1.01227			−0.506135	+	0.862454i	$0.668926\pi$
$608$			386959.i			1.04679i
$609$	66004.1	−	62085.6i	0.177966	−	0.167400i
$610$	118043.			0.317234
$611$		−	379584.i		−	1.01678i
$612$	575701.	+	35256.4i	1.53707	+	0.0941315i
$613$	−13952.2			−0.0371298			−0.0185649	−	0.999828i	$-0.505910\pi$
$613$	−13952.2			−0.0371298			−0.0185649	+	0.999828i	$0.505910\pi$
$614$			35060.9i			0.0930007i
$615$	344017.	+	365729.i	0.909555	+	0.966961i
$616$	−112317.			−0.295995
$617$		−	90806.5i		−	0.238532i	−0.992862	−	0.119266i	$-0.961946\pi$
$617$		−	90806.5i		−	0.238532i	0.992862	−	0.119266i	$-0.0380541\pi$
$618$	26597.6	−	25018.5i	0.0696410	−	0.0655066i
$619$	328774.			0.858056			0.429028	−	0.903291i	$-0.358856\pi$
$619$	328774.			0.858056			0.429028	+	0.903291i	$0.358856\pi$
$620$			427236.i			1.11144i
$621$	−100828.	−	121261.i	−0.261455	−	0.314440i
$622$	−10883.0			−0.0281298
$623$		−	393583.i		−	1.01405i
$624$	−186925.	−	198722.i	−0.480062	−	0.510361i
$625$	−267800.			−0.685567
$626$			163157.i			0.416348i
$627$	−183470.	+	172578.i	−0.466691	+	0.438985i
$628$	191251.			0.484936
$629$		−	495508.i		−	1.25242i
$630$	−7344.10	+	119922.i	−0.0185037	+	0.302146i
$631$	630118.			1.58257			0.791286	−	0.611446i	$-0.209412\pi$
$631$	630118.			1.58257			0.791286	+	0.611446i	$0.209412\pi$
$632$		−	150710.i		−	0.377317i
$633$	13559.4	+	14415.2i	0.0338401	+	0.0359759i
$634$	−158959.			−0.395463
$635$			208707.i			0.517595i
$636$	275601.	−	259240.i	0.681345	−	0.640896i
$637$	−277754.			−0.684513
$638$			8562.93i			0.0210369i
$639$	351866.	+	21548.5i	0.861739	+	0.0527735i
$640$	310443.			0.757917
$641$		−	51710.5i		−	0.125853i	−0.998018	−	0.0629263i	$-0.979957\pi$
$641$		−	51710.5i		−	0.125853i	0.998018	−	0.0629263i	$-0.0200433\pi$
$642$	−129923.	−	138123.i	−0.315221	−	0.335116i
$643$	−57992.1			−0.140264			−0.0701321	−	0.997538i	$-0.522342\pi$
$643$	−57992.1			−0.140264			−0.0701321	+	0.997538i	$0.522342\pi$
$644$			210723.i			0.508088i
$645$	−318581.	+	299667.i	−0.765773	+	0.720311i
$646$	264637.			0.634141
$647$			117396.i			0.280444i	0.990120	+	0.140222i	$0.0447816\pi$
$647$			117396.i			0.280444i	−0.990120	+	0.140222i	$0.955218\pi$
$648$	25947.0	−	211050.i	0.0617927	−	0.502615i
$649$	24023.6			0.0570359
$650$		−	24429.2i		−	0.0578205i
$651$	−534356.	−	568082.i	−1.26087	−	1.34044i
$652$	−249697.			−0.587380
$653$			275742.i			0.646662i	0.946286	+	0.323331i	$0.104803\pi$
$653$			275742.i			0.646662i	−0.946286	+	0.323331i	$0.895197\pi$
$654$	84012.6	−	79025.0i	0.196422	−	0.184761i
$655$	−540717.			−1.26034
$656$			527161.i			1.22500i
$657$	23836.8	−	389231.i	0.0552227	−	0.901731i
$658$	−175507.			−0.405361
$659$			594127.i			1.36807i	0.729449	+	0.684035i	$0.239777\pi$
$659$			594127.i			1.36807i	−0.729449	+	0.684035i	$0.760223\pi$
$660$	105359.	+	112009.i	0.241871	+	0.257137i
$661$	109649.			0.250959			0.125480	−	0.992096i	$-0.459953\pi$
$661$	109649.			0.250959			0.125480	+	0.992096i	$0.459953\pi$
$662$		−	65493.3i		−	0.149445i
$663$	−464617.	+	437034.i	−1.05698	+	0.994234i
$664$	354663.			0.804414
$665$		−	746628.i		−	1.68834i
$666$	−87921.9	−	5384.40i	−0.198220	−	0.0121392i
$667$	33316.7			0.0748876
$668$		−	130397.i		−	0.292223i
$669$	−307328.	−	326725.i	−0.686673	−	0.730012i
$670$	−148859.			−0.331609
$671$			275795.i			0.612549i
$672$	−314119.	+	295471.i	−0.695595	+	0.654299i
$673$	141202.			0.311754			0.155877	−	0.987776i	$-0.450180\pi$
$673$	141202.			0.311754			0.155877	+	0.987776i	$0.450180\pi$
$674$		−	133368.i		−	0.293584i
$675$	−88035.4	+	73200.9i	−0.193219	+	0.160660i
$676$	−97862.0			−0.214151
$677$			493166.i			1.07601i	0.842942	+	0.538004i	$0.180822\pi$
$677$			493166.i			1.07601i	−0.842942	+	0.538004i	$0.819178\pi$
$678$	60920.6	+	64765.6i	0.132527	+	0.140892i
$679$	634973.			1.37726
$680$		−	335052.i		−	0.724593i
$681$	57350.5	−	53945.7i	0.123664	−	0.116322i
$682$	73699.1			0.158451
$683$		−	360162.i		−	0.772070i	−0.922484	−	0.386035i	$-0.873844\pi$
$683$		−	360162.i		−	0.772070i	0.922484	−	0.386035i	$-0.126156\pi$
$684$	−38948.4	+	635989.i	−0.0832487	+	1.35937i
$685$	−442247.			−0.942504
$686$		−	36210.3i		−	0.0769457i
$687$	146680.	+	155938.i	0.310784	+	0.330399i
$688$	−459202.			−0.970122
$689$			418437.i			0.881437i
$690$	−32176.5	+	30266.3i	−0.0675835	+	0.0635712i
$691$	−388560.			−0.813770			−0.406885	−	0.913479i	$-0.633385\pi$
$691$	−388560.			−0.813770			−0.406885	+	0.913479i	$0.633385\pi$
$692$		−	164629.i		−	0.343790i
$693$	−280185.	−	17158.7i	−0.583416	−	0.0357289i
$694$	34282.9			0.0711802
$695$			389050.i			0.805444i
$696$	30778.7	+	32721.3i	0.0635378	+	0.0675480i
$697$	1.23252e6			2.53704
$698$		−	7851.58i		−	0.0161156i
$699$	2450.55	−	2305.07i	0.00501545	−	0.00471769i
$700$	152984.			0.312213
$701$		−	884057.i		−	1.79905i	−0.436866	−	0.899527i	$-0.643912\pi$
$701$		−	884057.i		−	1.79905i	0.436866	−	0.899527i	$-0.356088\pi$
$702$	72497.6	+	87189.6i	0.147112	+	0.176926i
$703$	547398.			1.10762
$704$			132618.i			0.267582i
$705$	341424.	+	362973.i	0.686936	+	0.730291i
$706$	28372.9			0.0569239
$707$			534900.i			1.07012i
$708$	44266.2	−	41638.3i	0.0883092	−	0.0830665i
$709$	−122786.			−0.244263			−0.122131	−	0.992514i	$-0.538973\pi$
$709$	−122786.			−0.244263			−0.122131	+	0.992514i	$0.538973\pi$
$710$		−	98745.7i		−	0.195885i
$711$	23024.0	−	375959.i	0.0455451	−	0.743705i
$712$	195117.			0.384889
$713$		−	286749.i		−	0.564056i
$714$	202070.	+	214823.i	0.396374	+	0.421391i
$715$	−170059.			−0.332651
$716$		−	513620.i		−	1.00188i
$717$	−510234.	+	479943.i	−0.992502	+	0.933580i
$718$	−140337.			−0.272223
$719$		−	189873.i		−	0.367287i	−0.982993	−	0.183644i	$-0.941211\pi$
$719$		−	189873.i		−	0.367287i	0.982993	−	0.183644i	$-0.0587893\pi$
$720$	357489.	+	21892.9i	0.689600	+	0.0422316i
$721$	−252888.			−0.486472
$722$			155662.i			0.298613i
$723$	88772.1	+	94374.9i	0.169824	+	0.180543i
$724$	100167.			0.191094
$725$		−	24187.9i		−	0.0460174i
$726$	−81347.6	+	76518.2i	−0.154338	+	0.145175i
$727$	420618.			0.795828			0.397914	−	0.917423i	$-0.369734\pi$
$727$	420618.			0.795828			0.397914	+	0.917423i	$0.369734\pi$
$728$		−	314216.i		−	0.592878i
$729$	96969.4	−	522519.i	0.182465	−	0.983212i
$730$	−109232.			−0.204976
$731$			1.07362e6i			2.00917i
$732$	478014.	+	508183.i	0.892109	+	0.948414i
$733$	−106369.			−0.197974			−0.0989870	−	0.995089i	$-0.531560\pi$
$733$	−106369.			−0.197974			−0.0989870	+	0.995089i	$0.531560\pi$
$734$			193379.i			0.358935i
$735$	265599.	−	249831.i	0.491645	−	0.462458i
$736$	−158557.			−0.292705
$737$		−	347795.i		−	0.640307i
$738$	13393.0	−	218695.i	0.0245904	−	0.401537i
$739$	632534.			1.15823			0.579115	−	0.815246i	$-0.303398\pi$
$739$	632534.			1.15823			0.579115	+	0.815246i	$0.303398\pi$
$740$		−	334188.i		−	0.610277i
$741$	−482800.	−	513272.i	−0.879288	−	0.934784i
$742$	193471.			0.351405
$743$		−	142520.i		−	0.258165i	−0.991634	−	0.129083i	$-0.958797\pi$
$743$		−	142520.i		−	0.258165i	0.991634	−	0.129083i	$-0.0412032\pi$
$744$	281625.	−	264905.i	0.508774	−	0.478569i
$745$	364725.			0.657132
$746$			13471.7i			0.0242072i
$747$	884740.	+	54182.1i	1.58553	+	0.0970990i
$748$	377472.			0.674655
$749$			1.31326e6i			2.34092i
$750$	109416.	+	116322.i	0.194518	+	0.206794i
$751$	−189379.			−0.335778			−0.167889	−	0.985806i	$-0.553695\pi$
$751$	−189379.			−0.335778			−0.167889	+	0.985806i	$0.553695\pi$
$752$			523189.i			0.925172i
$753$	−629746.	+	592359.i	−1.11064	+	1.04471i
$754$	−23955.5			−0.0421369
$755$			818459.i			1.43583i
$756$	−546013.	+	454006.i	−0.955343	+	0.794362i
$757$	264680.			0.461880			0.230940	−	0.972968i	$-0.425820\pi$
$757$	264680.			0.461880			0.230940	+	0.972968i	$0.425820\pi$
$758$			21632.6i			0.0376505i
$759$	−70714.1	−	75177.1i	−0.122750	−	0.130497i
$760$	370138.			0.640821
$761$			338777.i			0.584986i	0.956268	+	0.292493i	$0.0944848\pi$
$761$			338777.i			0.584986i	−0.956268	+	0.292493i	$0.905515\pi$
$762$	66338.6	−	62400.3i	0.114250	−	0.107467i
$763$	−798787.			−1.37209
$764$			51322.9i			0.0879275i
$765$	51186.1	−	835818.i	0.0874639	−	1.42820i
$766$	−186302.			−0.317511
$767$			67207.9i			0.114243i
$768$	154009.	+	163730.i	0.261111	+	0.277590i
$769$	338021.			0.571598			0.285799	−	0.958290i	$-0.407741\pi$
$769$	338021.			0.571598			0.285799	+	0.958290i	$0.407741\pi$
$770$			78629.6i			0.132619i
$771$	217626.	−	204707.i	0.366103	−	0.344368i
$772$	960298.			1.61128
$773$			321410.i			0.537898i	0.963154	+	0.268949i	$0.0866763\pi$
$773$			321410.i			0.537898i	−0.963154	+	0.268949i	$0.913324\pi$
$774$	190501.	+	11666.5i	0.317992	+	0.0194741i
$775$	−208179.			−0.346604
$776$			314786.i			0.522747i
$777$	417978.	+	444358.i	0.692327	+	0.736023i
$778$	−289046.			−0.477538
$779$			1.36158e6i			2.24372i
$780$	−313354.	+	294751.i	−0.515045	+	0.484469i
$781$	230709.			0.378236
$782$			108436.i			0.177320i
$783$	71781.5	+	86328.4i	0.117082	+	0.140809i
$784$	382834.			0.622843
$785$		−	277663.i		−	0.450587i
$786$	161666.	+	171870.i	0.261682	+	0.278198i
$787$	696771.			1.12497			0.562484	−	0.826808i	$-0.309846\pi$
$787$	696771.			1.12497			0.562484	+	0.826808i	$0.309846\pi$
$788$		−	300815.i		−	0.484448i
$789$	201784.	−	189804.i	0.324139	−	0.304896i
$790$	−105507.			−0.169055
$791$		−	615787.i		−	0.984188i
$792$	8506.39	−	138901.i	0.0135611	−	0.221439i
$793$	−771558.			−1.22694
$794$			292765.i			0.464385i
$795$	−376371.	−	400125.i	−0.595500	−	0.633084i
$796$	−421109.			−0.664613
$797$		−	583667.i		−	0.918858i	−0.888214	−	0.459429i	$-0.848054\pi$
$797$		−	583667.i		−	0.918858i	0.888214	−	0.459429i	$-0.151946\pi$
$798$	−237319.	+	223230.i	−0.372673	+	0.350548i
$799$	1.22323e6			1.91608
$800$			115112.i			0.179863i
$801$	486738.	+	29808.2i	0.758631	+	0.0464591i
$802$	122389.			0.190281
$803$		−	255209.i		−	0.395790i
$804$	−602806.	−	640852.i	−0.932536	−	0.991392i
$805$	305932.			0.472099
$806$			206179.i			0.317377i
$807$	−332088.	+	312373.i	−0.509925	+	0.479652i
$808$	−265175.			−0.406172
$809$		−	41032.7i		−	0.0626951i	−0.999509	−	0.0313475i	$-0.990020\pi$
$809$		−	41032.7i		−	0.0626951i	0.999509	−	0.0313475i	$-0.00997986\pi$
$810$	−147749.	−	18164.7i	−0.225193	−	0.0276858i
$811$	1.15677e6			1.75876			0.879378	−	0.476124i	$-0.157958\pi$
$811$	1.15677e6			1.75876			0.879378	+	0.476124i	$0.157958\pi$
$812$		−	150018.i		−	0.227526i
$813$	−1101.17	−	1170.67i	−0.00166600	−	0.00177115i
$814$	−57648.1			−0.0870034
$815$			362517.i			0.545774i
$816$	640391.	−	602373.i	0.961757	−	0.904660i
$817$	−1.18605e6			−1.77689
$818$			328040.i			0.490252i
$819$	48003.0	−	783841.i	0.0715649	−	1.16858i
$820$	831250.			1.23624
$821$		−	622525.i		−	0.923571i	−0.886992	−	0.461786i	$-0.847209\pi$
$821$		−	622525.i		−	0.923571i	0.886992	−	0.461786i	$-0.152791\pi$
$822$	132225.	+	140570.i	0.195691	+	0.208041i
$823$	−1.17475e6			−1.73438			−0.867192	−	0.497974i	$-0.834078\pi$
$823$	−1.17475e6			−1.73438			−0.867192	+	0.497974i	$0.834078\pi$
$824$		−	125368.i		−	0.184643i
$825$	−54578.5	+	51338.3i	−0.0801888	+	0.0754282i
$826$	31074.7			0.0455456
$827$			102605.i			0.150023i	0.997183	+	0.0750116i	$0.0238994\pi$
$827$			102605.i			0.150023i	−0.997183	+	0.0750116i	$0.976101\pi$
$828$	−260597.	−	15959.2i	−0.380110	−	0.0232782i
$829$	−1.20338e6			−1.75103			−0.875513	−	0.483195i	$-0.839476\pi$
$829$	−1.20338e6			−1.75103			−0.875513	+	0.483195i	$0.839476\pi$
$830$		−	248288.i		−	0.360413i
$831$	−701628.	−	745910.i	−1.01603	−	1.08015i
$832$	−371009.			−0.535966
$833$		−	895076.i		−	1.28994i
$834$	123661.	−	116320.i	0.177788	−	0.167233i
$835$	−189313.			−0.271524
$836$			417001.i			0.596657i
$837$	743008.	−	617807.i	1.06058	−	0.881864i
$838$	−193116.			−0.274998
$839$			686709.i			0.975548i	0.872970	+	0.487774i	$0.162191\pi$
$839$			686709.i			0.975548i	−0.872970	+	0.487774i	$0.837809\pi$
$840$	282627.	+	300465.i	0.400549	+	0.425829i
$841$	683562.			0.966465
$842$			80229.9i			0.113165i
$843$	505558.	−	475545.i	0.711403	−	0.669169i
$844$	32763.6			0.0459946
$845$			142078.i			0.198982i
$846$	13292.1	−	217047.i	0.0185718	−	0.303258i
$847$	773448.			1.07811
$848$		−	576740.i		−	0.802025i
$849$	644771.	+	685465.i	0.894520	+	0.950976i
$850$	78724.1			0.108961
$851$			224297.i			0.309717i
$852$	425108.	−	399871.i	0.585626	−	0.550859i
$853$	−291970.			−0.401273			−0.200636	−	0.979666i	$-0.564301\pi$
$853$	−291970.			−0.401273			−0.200636	+	0.979666i	$0.564301\pi$
$854$			356742.i			0.489146i
$855$	923344.	+	56546.3i	1.26308	+	0.0773520i
$856$	−651045.			−0.888512
$857$			526332.i			0.716635i	0.933600	+	0.358318i	$0.116649\pi$
$857$			526332.i			0.716635i	−0.933600	+	0.358318i	$0.883351\pi$
$858$	50845.1	+	54054.2i	0.0690677	+	0.0734268i
$859$	241016.			0.326632			0.163316	−	0.986574i	$-0.447781\pi$
$859$	241016.			0.326632			0.163316	+	0.986574i	$0.447781\pi$
$860$			724089.i			0.979027i
$861$	−1.10529e6	+	1.03967e6i	−1.49097	+	1.40245i
$862$	−244073.			−0.328477
$863$		−	1.21542e6i		−	1.63195i	−0.578090	−	0.815973i	$-0.696202\pi$
$863$		−	1.21542e6i		−	1.63195i	0.578090	−	0.815973i	$-0.303798\pi$
$864$	−341615.	−	410845.i	−0.457624	−	0.550364i
$865$	−239012.			−0.319438
$866$			69967.4i			0.0932953i
$867$	−893340.	−	949722.i	−1.18844	−	1.26345i
$868$	−1.29117e6			−1.71374
$869$		−	246506.i		−	0.326429i
$870$	22907.2	−	21547.2i	0.0302644	−	0.0284677i
$871$	972984.			1.28254
$872$		−	395996.i		−	0.520784i
$873$	−48090.0	+	785262.i	−0.0630996	+	1.03035i
$874$	−119791.			−0.156820
$875$		−	1.10598e6i		−	1.44455i
$876$	−442334.	−	470251.i	−0.576424	−	0.612804i
$877$	−468635.			−0.609307			−0.304653	−	0.952463i	$-0.598541\pi$
$877$	−468635.			−0.609307			−0.304653	+	0.952463i	$0.598541\pi$
$878$		−	24514.4i		−	0.0318004i
$879$	−394112.	+	370715.i	−0.510085	+	0.479802i
$880$	234396.			0.302681
$881$			52745.3i			0.0679566i	0.999423	+	0.0339783i	$0.0108177\pi$
$881$			52745.3i			0.0679566i	−0.999423	+	0.0339783i	$0.989182\pi$
$882$	−158820.	−	9726.26i	−0.204159	−	0.0125028i
$883$	−22265.6			−0.0285570			−0.0142785	−	0.999898i	$-0.504545\pi$
$883$	−22265.6			−0.0285570			−0.0142785	+	0.999898i	$0.504545\pi$
$884$			1.05601e6i			1.35134i
$885$	−60451.5	−	64266.8i	−0.0771827	−	0.0820541i
$886$	−57790.1			−0.0736184
$887$		−	729375.i		−	0.927051i	−0.886084	−	0.463526i	$-0.846584\pi$
$887$		−	729375.i		−	0.927051i	0.886084	−	0.463526i	$-0.153416\pi$
$888$	−220289.	+	207211.i	−0.279362	+	0.262777i
$889$	−630744.			−0.798085
$890$		−	136596.i		−	0.172447i
$891$	42439.9	−	345201.i	0.0534588	−	0.434828i
$892$	−742599.			−0.933307
$893$			1.35132e6i			1.69456i
$894$	−109047.	−	115930.i	−0.136439	−	0.145050i
$895$	−745687.			−0.930916
$896$			938204.i			1.16864i
$897$	210314.	−	197828.i	0.261387	−	0.245869i
$898$	−135462.			−0.167983
$899$			204143.i			0.252589i
$900$	−11586.3	+	189193.i	−0.0143041	+	0.233572i
$901$	−1.34843e6			−1.66104
$902$		−	143392.i		−	0.176244i
$903$	−905638.	−	962797.i	−1.11066	−	1.18075i
$904$	305274.			0.373554
$905$		−	145425.i		−	0.177559i
$906$	260151.	−	244707.i	0.316934	−	0.298119i
$907$	133592.			0.162393			0.0811964	−	0.996698i	$-0.474126\pi$
$907$	133592.			0.162393			0.0811964	+	0.996698i	$0.474126\pi$
$908$		−	130350.i		−	0.158102i
$909$	−661503.	−	40511.0i	−0.800579	−	0.0490281i
$910$	−219973.			−0.265635
$911$			409102.i			0.492941i	0.969150	+	0.246471i	$0.0792709\pi$
$911$			409102.i			0.492941i	−0.969150	+	0.246471i	$0.920729\pi$
$912$	665453.	+	707453.i	0.800070	+	0.850566i
$913$	580101.			0.695924
$914$		−	30082.1i		−	0.0360094i
$915$	737793.	−	693992.i	0.881236	−	0.828919i
$916$	354425.			0.422409
$917$		−	1.63413e6i		−	1.94333i
$918$	−280973.	+	233627.i	−0.333410	+	0.277228i
$919$	−826279.			−0.978353			−0.489177	−	0.872185i	$-0.662703\pi$
$919$	−826279.			−0.978353			−0.489177	+	0.872185i	$0.662703\pi$
$920$			151665.i			0.179188i
$921$	206129.	+	219138.i	0.243007	+	0.258345i
$922$	−351688.			−0.413710
$923$			645428.i			0.757608i
$924$	−338507.	+	318411.i	−0.396482	+	0.372944i
$925$	162840.			0.190316
$926$		−	62183.6i		−	0.0725194i
$927$	19152.6	−	312743.i	0.0222879	−	0.363939i
$928$	112880.			0.131076
$929$		−	689216.i		−	0.798590i	−0.916822	−	0.399295i	$-0.869255\pi$
$929$		−	689216.i		−	0.798590i	0.916822	−	0.399295i	$-0.130745\pi$
$930$	−185452.	−	197156.i	−0.214420	−	0.227953i
$931$	988808.			1.14081
$932$		−	5569.76i		−	0.00641216i
$933$	−68021.1	+	63982.8i	−0.0781412	+	0.0735022i
$934$	10364.2			0.0118807
$935$		−	548024.i		−	0.626868i
$936$	388586.	+	23797.3i	0.443543	+	0.0271629i
$937$	554911.			0.632039			0.316019	−	0.948753i	$-0.397654\pi$
$937$	554911.			0.632039			0.316019	+	0.948753i	$0.397654\pi$
$938$		−	449875.i		−	0.511312i
$939$	959225.	+	1.01977e6i	1.08790	+	1.15656i
$940$	824986.			0.933665
$941$			1.51365e6i			1.70941i	0.519113	+	0.854706i	$0.326262\pi$
$941$			1.51365e6i			1.70941i	−0.519113	+	0.854706i	$0.673738\pi$
$942$	−88256.5	+	83017.0i	−0.0994592	+	0.0935546i
$943$	−557911.			−0.627396
$944$		−	92634.1i		−	0.103951i
$945$	659138.	+	792715.i	0.738096	+	0.887674i
$946$	124907.			0.139574
$947$			1.37848e6i			1.53709i	0.639796	+	0.768545i	$0.279019\pi$
$947$			1.37848e6i			1.53709i	−0.639796	+	0.768545i	$0.720981\pi$
$948$	−427251.	−	454216.i	−0.475407	−	0.505412i
$949$	713967.			0.792767
$950$			86968.1i			0.0963635i
$951$	−993527.	+	934544.i	−1.09855	+	1.03333i
$952$	1.01258e6			1.11726
$953$			437585.i			0.481810i	0.970549	+	0.240905i	$0.0774443\pi$
$953$			437585.i			0.481810i	−0.970549	+	0.240905i	$0.922556\pi$
$954$	−14652.6	+	239263.i	−0.0160997	+	0.262892i
$955$	74511.9			0.0816994
$956$			1.15969e6i			1.26890i
$957$	50342.9	+	53520.3i	0.0549686	+	0.0584379i
$958$	433100.			0.471907
$959$		−	1.33653e6i		−	1.45326i
$960$	354773.	−	333711.i	0.384953	−	0.362099i
$961$	833488.			0.902511
$962$		−	161275.i		−	0.174268i
$963$	−1.62409e6	−	99460.5i	−1.75129	−	0.107250i
$964$	214501.			0.230821
$965$		−	1.39418e6i		−	1.49715i
$966$	−91469.0	−	97242.0i	−0.0980212	−	0.104208i
$967$	−603107.			−0.644973			−0.322486	−	0.946574i	$-0.604519\pi$
$967$	−603107.			−0.644973			−0.322486	+	0.946574i	$0.604519\pi$
$968$			383434.i			0.409204i
$969$	1.65404e6	−	1.55585e6i	1.76157	−	1.65699i
$970$	220372.			0.234214
$971$		−	95731.5i		−	0.101535i	−0.998710	−	0.0507676i	$-0.983833\pi$
$971$		−	95731.5i		−	0.101535i	0.998710	−	0.0507676i	$-0.0161668\pi$
$972$	−520111.	−	709631.i	−0.550507	−	0.751104i
$973$	−1.17576e6			−1.24192
$974$			123236.i			0.129904i
$975$	−143623.	−	152688.i	−0.151083	−	0.160618i
$976$	1.06345e6			1.11640
$977$			1.13157e6i			1.18547i	0.805397	+	0.592736i	$0.201952\pi$
$977$			1.13157e6i			1.18547i	−0.805397	+	0.592736i	$0.798048\pi$
$978$	115228.	−	108387.i	0.120470	−	0.113318i
$979$	319142.			0.332980
$980$		−	603669.i		−	0.628560i
$981$	60496.6	−	987848.i	0.0628626	−	1.02648i
$982$	307942.			0.319335
$983$		−	1.60157e6i		−	1.65745i	−0.559659	−	0.828723i	$-0.689068\pi$
$983$		−	1.60157e6i		−	1.65745i	0.559659	−	0.828723i	$-0.310932\pi$
$984$	−515412.	−	547942.i	−0.532309	−	0.565906i
$985$	−436731.			−0.450134
$986$		−	77197.7i		−	0.0794055i
$987$	−1.09696e6	+	1.03183e6i	−1.12604	+	1.05919i
$988$	−1.16659e6			−1.19510
$989$		−	485988.i		−	0.496858i
$990$	−97240.1	−	5955.05i	−0.0992144	−	0.00607597i
$991$	−1.79647e6			−1.82925			−0.914624	−	0.404305i	$-0.867513\pi$
$991$	−1.79647e6			−1.82925			−0.914624	+	0.404305i	$0.867513\pi$
$992$		−	971534.i		−	0.987267i
$993$	−385046.	−	409348.i	−0.390494	−	0.415140i
$994$	298424.			0.302038
$995$			611377.i			0.617537i
$996$	1.06890e6	−	1.00544e6i	1.07750	−	1.01354i
$997$	−281149.			−0.282843			−0.141422	−	0.989949i	$-0.545167\pi$
$997$	−281149.			−0.282843			−0.141422	+	0.989949i	$0.545167\pi$
$998$			211493.i			0.212342i
$999$	−581187.	+	483253.i	−0.582351	+	0.484221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.42	yes	78
3.2	odd	2	inner	177.5.b.a.119.37	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.37	✓	78	3.2	odd	2	inner
177.5.b.a.119.42	yes	78	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.04886i q^{2} +(6.16639 + 6.55558i) q^{3} +14.8999 q^{4} -21.6320i q^{5} +(-6.87585 + 6.46765i) q^{6} +65.3752 q^{7} +32.4095i q^{8} +(-4.95122 + 80.8485i) q^{9} +O(q^{10})\)	\(q+1.04886i q^{2} +(6.16639 + 6.55558i) q^{3} +14.8999 q^{4} -21.6320i q^{5} +(-6.87585 + 6.46765i) q^{6} +65.3752 q^{7} +32.4095i q^{8} +(-4.95122 + 80.8485i) q^{9} +22.6889 q^{10} +53.0103i q^{11} +(91.8786 + 97.6775i) q^{12} -148.301 q^{13} +68.5691i q^{14} +(141.811 - 133.392i) q^{15} +204.406 q^{16} -477.905i q^{17} +(-84.7984 - 5.19312i) q^{18} +527.951 q^{19} -322.315i q^{20} +(403.129 + 428.572i) q^{21} -55.6001 q^{22} +216.329i q^{23} +(-212.463 + 199.850i) q^{24} +157.055 q^{25} -155.546i q^{26} +(-560.540 + 466.086i) q^{27} +974.084 q^{28} -154.009i q^{29} +(139.909 + 148.739i) q^{30} -1325.52 q^{31} +732.944i q^{32} +(-347.513 + 326.882i) q^{33} +501.253 q^{34} -1414.20i q^{35} +(-73.7728 + 1204.64i) q^{36} +1036.83 q^{37} +553.744i q^{38} +(-914.479 - 972.196i) q^{39} +701.084 q^{40} +2579.00i q^{41} +(-449.510 + 422.824i) q^{42} -2246.52 q^{43} +789.848i q^{44} +(1748.92 + 107.105i) q^{45} -226.898 q^{46} +2559.56i q^{47} +(1260.44 + 1340.00i) q^{48} +1872.91 q^{49} +164.727i q^{50} +(3132.95 - 2946.95i) q^{51} -2209.66 q^{52} -2821.55i q^{53} +(-488.856 - 587.925i) q^{54} +1146.72 q^{55} +2118.78i q^{56} +(3255.55 + 3461.03i) q^{57} +161.533 q^{58} -453.188i q^{59} +(2112.96 - 1987.52i) q^{60} +5202.66 q^{61} -1390.28i q^{62} +(-323.687 + 5285.49i) q^{63} +2501.74 q^{64} +3208.04i q^{65} +(-342.852 - 364.491i) q^{66} -6560.90 q^{67} -7120.74i q^{68} +(-1418.16 + 1333.97i) q^{69} +1483.29 q^{70} -4352.16i q^{71} +(-2620.26 - 160.467i) q^{72} -4814.33 q^{73} +1087.49i q^{74} +(968.460 + 1029.58i) q^{75} +7866.42 q^{76} +3465.56i q^{77} +(1019.69 - 959.156i) q^{78} -4650.16 q^{79} -4421.71i q^{80} +(-6511.97 - 800.598i) q^{81} -2704.99 q^{82} -10943.2i q^{83} +(6006.58 + 6385.68i) q^{84} -10338.1 q^{85} -2356.28i q^{86} +(1009.62 - 949.682i) q^{87} -1718.04 q^{88} -6020.37i q^{89} +(-112.338 + 1834.36i) q^{90} -9695.17 q^{91} +3223.28i q^{92} +(-8173.69 - 8689.56i) q^{93} -2684.61 q^{94} -11420.7i q^{95} +(-4804.87 + 4519.62i) q^{96} +9712.75 q^{97} +1964.42i q^{98} +(-4285.80 - 262.466i) 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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