LMFDB - Embedded newform 177.6.d.b.176.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,6,Mod(176,177)]

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, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("177.176");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	177.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$28.3879361069$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			176.30
Character	$\chi$	$=$	177.176
Dual form			177.6.d.b.176.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.97069 q^{2} +(12.6885 + 9.05545i) q^{3} -7.29225 q^{4} +63.5291i q^{5} +(-63.0708 - 45.0118i) q^{6} -191.713 q^{7} +195.310 q^{8} +(78.9977 + 229.801i) q^{9} +O(q^{10})$	\(q-4.97069 q^{2} +(12.6885 + 9.05545i) q^{3} -7.29225 q^{4} +63.5291i q^{5} +(-63.0708 - 45.0118i) q^{6} -191.713 q^{7} +195.310 q^{8} +(78.9977 + 229.801i) q^{9} -315.783i q^{10} -473.280 q^{11} +(-92.5279 - 66.0346i) q^{12} +634.186i q^{13} +952.946 q^{14} +(-575.284 + 806.091i) q^{15} -737.471 q^{16} -1374.51i q^{17} +(-392.673 - 1142.27i) q^{18} -2066.47 q^{19} -463.270i q^{20} +(-2432.56 - 1736.05i) q^{21} +2352.53 q^{22} +3704.90 q^{23} +(2478.19 + 1768.62i) q^{24} -910.945 q^{25} -3152.34i q^{26} +(-1078.58 + 3631.19i) q^{27} +1398.02 q^{28} +2955.15i q^{29} +(2859.56 - 4006.83i) q^{30} +3136.19i q^{31} -2584.17 q^{32} +(-6005.23 - 4285.76i) q^{33} +6832.25i q^{34} -12179.4i q^{35} +(-576.071 - 1675.76i) q^{36} -6260.05i q^{37} +10271.8 q^{38} +(-5742.83 + 8046.88i) q^{39} +12407.8i q^{40} +12098.8i q^{41} +(12091.5 + 8629.35i) q^{42} -14820.9i q^{43} +3451.27 q^{44} +(-14599.0 + 5018.65i) q^{45} -18415.9 q^{46} +22473.8 q^{47} +(-9357.43 - 6678.13i) q^{48} +19946.9 q^{49} +4528.02 q^{50} +(12446.8 - 17440.5i) q^{51} -4624.64i q^{52} +3122.95i q^{53} +(5361.30 - 18049.5i) q^{54} -30067.0i q^{55} -37443.4 q^{56} +(-26220.5 - 18712.8i) q^{57} -14689.1i q^{58} +(-16336.6 - 21166.9i) q^{59} +(4195.12 - 5878.22i) q^{60} -35548.6i q^{61} -15589.0i q^{62} +(-15144.9 - 44055.8i) q^{63} +36444.2 q^{64} -40289.2 q^{65} +(29850.1 + 21303.2i) q^{66} -8881.53i q^{67} +10023.3i q^{68} +(47009.7 + 33549.5i) q^{69} +60539.8i q^{70} -38373.4i q^{71} +(15429.0 + 44882.3i) q^{72} -79866.2i q^{73} +31116.8i q^{74} +(-11558.6 - 8249.01i) q^{75} +15069.2 q^{76} +90733.9 q^{77} +(28545.8 - 39998.6i) q^{78} -98932.0 q^{79} -46850.9i q^{80} +(-46567.7 + 36307.5i) q^{81} -60139.2i q^{82} -10666.9 q^{83} +(17738.8 + 12659.7i) q^{84} +87321.3 q^{85} +73670.1i q^{86} +(-26760.2 + 37496.6i) q^{87} -92436.1 q^{88} +37859.7 q^{89} +(72567.2 - 24946.2i) q^{90} -121582. i q^{91} -27017.0 q^{92} +(-28399.6 + 39793.7i) q^{93} -111710. q^{94} -131281. i q^{95} +(-32789.3 - 23400.8i) q^{96} +164784. i q^{97} -99149.9 q^{98} +(-37388.0 - 108760. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9}+O(q^{10}) $ 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9	$ 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9} - 1244 q^{12} + 1116 q^{15} + 14724 q^{16} + 1784 q^{19} + 6388 q^{21} - 8140 q^{22} - 48208 q^{25} - 6458 q^{27} - 19092 q^{28} - 20832 q^{36} - 134984 q^{45} + 51180 q^{46} + 61720 q^{48} + 174556 q^{49} + 8332 q^{51} + 236784 q^{57} + 375208 q^{60} - 429890 q^{63} + 561472 q^{64} - 11596 q^{66} + 169948 q^{75} + 111488 q^{76} + 356264 q^{78} + 180260 q^{79} + 79554 q^{81} + 269308 q^{84} + 111028 q^{85} - 318764 q^{87} - 1242976 q^{88} - 513608 q^{94}+O(q^{100}) $ 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9 - 1244 * q^12 + 1116 * q^15 + 14724 * q^16 + 1784 * q^19 + 6388 * q^21 - 8140 * q^22 - 48208 * q^25 - 6458 * q^27 - 19092 * q^28 - 20832 * q^36 - 134984 * q^45 + 51180 * q^46 + 61720 * q^48 + 174556 * q^49 + 8332 * q^51 + 236784 * q^57 + 375208 * q^60 - 429890 * q^63 + 561472 * q^64 - 11596 * q^66 + 169948 * q^75 + 111488 * q^76 + 356264 * q^78 + 180260 * q^79 + 79554 * q^81 + 269308 * q^84 + 111028 * q^85 - 318764 * q^87 - 1242976 * q^88 - 513608 * q^94

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 $

$2$	−4.97069			−0.878702			−0.439351	−	0.898315i	$-0.644792\pi$
$2$	−4.97069			−0.878702			−0.439351	+	0.898315i	$0.644792\pi$
$3$	12.6885	+	9.05545i	0.813970	+	0.580907i
$3$	12.6885	+	9.05545i	0.813970	+	0.580907i
$4$	−7.29225			−0.227883
$5$			63.5291i			1.13644i	0.822876	+	0.568221i	$0.192368\pi$
$5$			63.5291i			1.13644i	−0.822876	+	0.568221i	$0.807632\pi$
$6$	−63.0708	−	45.0118i	−0.715237	−	0.510444i
$7$	−191.713			−1.47879			−0.739395	−	0.673272i	$-0.764888\pi$
$7$	−191.713			−1.47879			−0.739395	+	0.673272i	$0.764888\pi$
$8$	195.310			1.07894
$9$	78.9977	+	229.801i	0.325094	+	0.945682i
$10$		−	315.783i		−	0.998595i
$11$	−473.280			−1.17933			−0.589666	−	0.807647i	$-0.700741\pi$
$11$	−473.280			−1.17933			−0.589666	+	0.807647i	$0.700741\pi$
$12$	−92.5279	−	66.0346i	−0.185490	−	0.132379i
$13$			634.186i			1.04078i	0.853929	+	0.520389i	$0.174213\pi$
$13$			634.186i			1.04078i	−0.853929	+	0.520389i	$0.825787\pi$
$14$	952.946			1.29942
$15$	−575.284	+	806.091i	−0.660168	+	0.925030i
$16$	−737.471			−0.720187
$17$		−	1374.51i		−	1.15352i	−0.816914	−	0.576760i	$-0.804317\pi$
$17$		−	1374.51i		−	1.15352i	0.816914	−	0.576760i	$-0.195683\pi$
$18$	−392.673	−	1142.27i	−0.285660	−	0.830973i
$19$	−2066.47			−1.31324			−0.656622	−	0.754220i	$-0.728015\pi$
$19$	−2066.47			−1.31324			−0.656622	+	0.754220i	$0.728015\pi$
$20$		−	463.270i		−	0.258976i
$21$	−2432.56	−	1736.05i	−1.20369	−	0.859040i
$22$	2352.53			1.03628
$23$	3704.90			1.46035			0.730174	−	0.683261i	$-0.239439\pi$
$23$	3704.90			1.46035			0.730174	+	0.683261i	$0.239439\pi$
$24$	2478.19	+	1768.62i	0.878227	+	0.626766i
$25$	−910.945			−0.291502
$26$		−	3152.34i		−	0.914533i
$27$	−1078.58	+	3631.19i	−0.284737	+	0.958606i
$28$	1398.02			0.336991
$29$			2955.15i			0.652507i	0.945282	+	0.326253i	$0.105786\pi$
$29$			2955.15i			0.652507i	−0.945282	+	0.326253i	$0.894214\pi$
$30$	2859.56	−	4006.83i	0.580091	−	0.812826i
$31$			3136.19i			0.586136i	0.956092	+	0.293068i	$0.0946763\pi$
$31$			3136.19i			0.586136i	−0.956092	+	0.293068i	$0.905324\pi$
$32$	−2584.17			−0.446114
$33$	−6005.23	−	4285.76i	−0.959941	−	0.685083i
$34$			6832.25i			1.01360i
$35$		−	12179.4i		−	1.68056i
$36$	−576.071	−	1675.76i	−0.0740832	−	0.215505i
$37$		−	6260.05i		−	0.751750i	−0.926670	−	0.375875i	$-0.877342\pi$
$37$		−	6260.05i		−	0.751750i	0.926670	−	0.375875i	$-0.122658\pi$
$38$	10271.8			1.15395
$39$	−5742.83	+	8046.88i	−0.604595	+	0.847162i
$40$			12407.8i			1.22616i
$41$			12098.8i			1.12404i	0.827124	+	0.562020i	$0.189975\pi$
$41$			12098.8i			1.12404i	−0.827124	+	0.562020i	$0.810025\pi$
$42$	12091.5	+	8629.35i	1.05769	+	0.754840i
$43$		−	14820.9i		−	1.22237i	−0.791487	−	0.611186i	$-0.790693\pi$
$43$		−	14820.9i		−	1.22237i	0.791487	−	0.611186i	$-0.209307\pi$
$44$	3451.27			0.268750
$45$	−14599.0	+	5018.65i	−1.07471	+	0.369450i
$46$	−18415.9			−1.28321
$47$	22473.8			1.48399			0.741997	−	0.670403i	$-0.233879\pi$
$47$	22473.8			1.48399			0.741997	+	0.670403i	$0.233879\pi$
$48$	−9357.43	−	6678.13i	−0.586210	−	0.418362i
$49$	19946.9			1.18682
$50$	4528.02			0.256144
$51$	12446.8	−	17440.5i	0.670088	−	0.938930i
$52$		−	4624.64i		−	0.237175i
$53$			3122.95i			0.152713i	0.997081	+	0.0763563i	$0.0243286\pi$
$53$			3122.95i			0.152713i	−0.997081	+	0.0763563i	$0.975671\pi$
$54$	5361.30	−	18049.5i	0.250199	−	0.842329i
$55$		−	30067.0i		−	1.34024i
$56$	−37443.4			−1.59553
$57$	−26220.5	−	18712.8i	−1.06894	−	0.762873i
$58$		−	14689.1i		−	0.573359i
$59$	−16336.6	−	21166.9i	−0.610987	−	0.791641i
$59$	−16336.6	−	21166.9i	−0.610987	−	0.791641i
$60$	4195.12	−	5878.22i	0.150441	−	0.210798i
$61$		−	35548.6i		−	1.22320i	−0.791167	−	0.611601i	$-0.790526\pi$
$61$		−	35548.6i		−	1.22320i	0.791167	−	0.611601i	$-0.209474\pi$
$62$		−	15589.0i		−	0.515039i
$63$	−15144.9	−	44055.8i	−0.480745	−	1.39847i
$64$	36444.2			1.11219
$65$	−40289.2			−1.18278
$66$	29850.1	+	21303.2i	0.843502	+	0.601984i
$67$		−	8881.53i		−	0.241714i	−0.992670	−	0.120857i	$-0.961436\pi$
$67$		−	8881.53i		−	0.241714i	0.992670	−	0.120857i	$-0.0385642\pi$
$68$			10023.3i			0.262867i
$69$	47009.7	+	33549.5i	1.18868	+	0.848327i
$70$			60539.8i			1.47671i
$71$		−	38373.4i		−	0.903409i	−0.892168	−	0.451704i	$-0.850816\pi$
$71$		−	38373.4i		−	0.903409i	0.892168	−	0.451704i	$-0.149184\pi$
$72$	15429.0	+	44882.3i	0.350757	+	1.02034i
$73$		−	79866.2i		−	1.75411i	−0.480393	−	0.877053i	$-0.659506\pi$
$73$		−	79866.2i		−	1.75411i	0.480393	−	0.877053i	$-0.340494\pi$
$74$			31116.8i			0.660564i
$75$	−11558.6	−	8249.01i	−0.237274	−	0.169336i
$76$	15069.2			0.299266
$77$	90733.9			1.74399
$78$	28545.8	−	39998.6i	0.531259	−	0.744403i
$79$	−98932.0			−1.78348			−0.891742	−	0.452544i	$-0.850516\pi$
$79$	−98932.0			−1.78348			−0.891742	+	0.452544i	$0.850516\pi$
$80$		−	46850.9i		−	0.818451i
$81$	−46567.7	+	36307.5i	−0.788628	+	0.614870i
$82$		−	60139.2i		−	0.987695i
$83$	−10666.9			−0.169958			−0.0849792	−	0.996383i	$-0.527082\pi$
$83$	−10666.9			−0.169958			−0.0849792	+	0.996383i	$0.527082\pi$
$84$	17738.8	+	12659.7i	0.274300	+	0.195760i
$85$	87321.3			1.31091
$86$			73670.1i			1.07410i
$87$	−26760.2	+	37496.6i	−0.379046	+	0.531121i
$88$	−92436.1			−1.27243
$89$	37859.7			0.506643			0.253322	−	0.967382i	$-0.418477\pi$
$89$	37859.7			0.506643			0.253322	+	0.967382i	$0.418477\pi$
$90$	72567.2	−	24946.2i	0.944353	−	0.324637i
$91$		−	121582.i		−	1.53909i
$92$	−27017.0			−0.332788
$93$	−28399.6	+	39793.7i	−0.340491	+	0.477097i
$94$	−111710.			−1.30399
$95$		−	131281.i		−	1.49243i
$96$	−32789.3	−	23400.8i	−0.363123	−	0.259151i
$97$			164784.i			1.77822i	0.457693	+	0.889110i	$0.348676\pi$
$97$			164784.i			1.77822i	−0.457693	+	0.889110i	$0.651324\pi$
$98$	−99149.9			−1.04286
$99$	−37388.0	−	108760.i	−0.383393	−	1.11527i
$100$	6642.84			0.0664284
$101$	23143.2			0.225746			0.112873	−	0.993609i	$-0.463995\pi$
$101$	23143.2			0.225746			0.112873	+	0.993609i	$0.463995\pi$
$102$	−61869.1	+	86691.3i	−0.588808	+	0.825040i
$103$		−	162455.i		−	1.50883i	−0.656400	−	0.754413i	$-0.727921\pi$
$103$		−	162455.i		−	1.50883i	0.656400	−	0.754413i	$-0.272079\pi$
$104$			123862.i			1.12294i
$105$	110290.	−	154538.i	0.976250	−	1.36793i
$106$		−	15523.2i		−	0.134189i
$107$			60467.8i			0.510581i	0.966864	+	0.255290i	$0.0821711\pi$
$107$			60467.8i			0.510581i	−0.966864	+	0.255290i	$0.917829\pi$
$108$	7865.30	−	26479.6i	0.0648867	−	0.218450i
$109$			245142.i			1.97630i	0.153501	+	0.988149i	$0.450945\pi$
$109$			245142.i			1.97630i	−0.153501	+	0.988149i	$0.549055\pi$
$110$			149454.i			1.17768i
$111$	56687.6	−	79430.8i	0.436697	−	0.611902i
$112$	141383.			1.06501
$113$	−96345.4			−0.709798			−0.354899	−	0.934905i	$-0.615485\pi$
$113$	−96345.4			−0.709798			−0.354899	+	0.934905i	$0.615485\pi$
$114$	130334.	+	93015.6i	0.939280	+	0.670338i
$115$			235369.i			1.65960i
$116$		−	21549.7i		−	0.148695i
$117$	−145736.	+	50099.2i	−0.984245	+	0.338350i
$118$	81204.2	+	105214.i	0.536875	+	0.695616i
$119$			263511.i			1.70581i
$120$	−112359.	+	157437.i	−0.712284	+	0.998055i
$121$	62942.8			0.390826
$122$			176701.i			1.07483i
$123$	−109560.	+	153516.i	−0.652962	+	0.914934i
$124$		−	22869.9i		−	0.133570i
$125$			140657.i			0.805167i
$126$	75280.6	+	218988.i	0.422432	+	1.22883i
$127$	259836.			1.42952			0.714760	−	0.699370i	$-0.246536\pi$
$127$	259836.			1.42952			0.714760	+	0.699370i	$0.246536\pi$
$128$	−98459.3			−0.531168
$129$	134210.	−	188055.i	0.710085	−	0.994974i
$130$	200265.			1.03931
$131$	−124369.			−0.633189			−0.316595	−	0.948561i	$-0.602540\pi$
$131$	−124369.			−0.633189			−0.316595	+	0.948561i	$0.602540\pi$
$132$	43791.6	+	31252.8i	0.218754	+	0.156119i
$133$	396169.			1.94201
$134$			44147.3i			0.212394i
$135$	−230686.	−	68521.4i	−1.08940	−	0.323587i
$136$		−	268455.i		−	1.24458i
$137$		−	100289.i		−	0.456512i	−0.973601	−	0.228256i	$-0.926698\pi$
$137$		−	100289.i		−	0.456512i	0.973601	−	0.228256i	$-0.0733023\pi$
$138$	−233671.	−	166764.i	−1.04450	−	0.745427i
$139$	−192708.			−0.845985			−0.422992	−	0.906133i	$-0.639020\pi$
$139$	−192708.			−0.845985			−0.422992	+	0.906133i	$0.639020\pi$
$140$			88814.9i			0.382971i
$141$	285160.	+	203511.i	1.20793	+	0.862063i
$142$			190742.i			0.793827i
$143$		−	300147.i		−	1.22742i
$144$	−58258.5	−	169471.i	−0.234128	−	0.681067i
$145$	−187738.			−0.741537
$146$			396990.i			1.54134i
$147$	253097.	+	180628.i	0.966036	+	0.689433i
$148$			45649.8i			0.171311i
$149$	−37545.4			−0.138545			−0.0692725	−	0.997598i	$-0.522068\pi$
$149$	−37545.4			−0.138545			−0.0692725	+	0.997598i	$0.522068\pi$
$150$	57454.0	+	41003.3i	0.208493	+	0.148796i
$151$		−	7257.58i		−	0.0259030i	−0.999916	−	0.0129515i	$-0.995877\pi$
$151$		−	7257.58i		−	0.0259030i	0.999916	−	0.0129515i	$-0.00412270\pi$
$152$	−403601.			−1.41691
$153$	315863.	−	108583.i	1.09086	−	0.375002i
$154$	−451010.			−1.53244
$155$	−199239.			−0.666110
$156$	41878.2	−	58679.9i	0.137777	−	0.193054i
$157$		−	227383.i		−	0.736223i	−0.929782	−	0.368112i	$-0.880004\pi$
$157$		−	227383.i		−	0.736223i	0.929782	−	0.368112i	$-0.119996\pi$
$158$	491760.			1.56715
$159$	−28279.7	+	39625.6i	−0.0887118	+	0.124303i
$160$		−	164170.i		−	0.506983i
$161$	−710277.			−2.15955
$162$	231474.	−	180473.i	0.692969	−	0.540288i
$163$	17189.3			0.0506744			0.0253372	−	0.999679i	$-0.491934\pi$
$163$	17189.3			0.0506744			0.0253372	+	0.999679i	$0.491934\pi$
$164$		−	88227.2i		−	0.256149i
$165$	272270.	−	381507.i	0.778558	−	1.09092i
$166$	53021.8			0.149343
$167$			380723.i			1.05637i	0.849128	+	0.528187i	$0.177128\pi$
$167$			380723.i			1.05637i	−0.849128	+	0.528187i	$0.822872\pi$
$168$	−475102.	−	339067.i	−1.29871	−	0.926855i
$169$	−30898.3			−0.0832181
$170$	−434047.			−1.15190
$171$	−163246.	−	474876.i	−0.426927	−	1.24191i
$172$			108078.i			0.278558i
$173$	−530453.			−1.34751			−0.673755	−	0.738955i	$-0.735320\pi$
$173$	−530453.			−1.34751			−0.673755	+	0.738955i	$0.735320\pi$
$174$	133017.	−	186384.i	0.333068	−	0.466697i
$175$	174640.			0.431071
$176$	349030.			0.849340
$177$	−15611.4	−	416513.i	−0.0374549	−	0.999298i
$178$	−188189.			−0.445189
$179$	514078.			1.19921			0.599607	−	0.800295i	$-0.295324\pi$
$179$	514078.			1.19921			0.599607	+	0.800295i	$0.295324\pi$
$180$	106460.	−	36597.3i	0.244909	−	0.0841914i
$181$	−638440.			−1.44852			−0.724258	−	0.689529i	$-0.757818\pi$
$181$	−638440.			−1.44852			−0.724258	+	0.689529i	$0.757818\pi$
$182$			604345.i			1.35240i
$183$	321909.	−	451060.i	0.710566	−	0.995649i
$184$	723602.			1.57563
$185$	397695.			0.854321
$186$	141166.	−	197802.i	0.299190	−	0.419226i
$187$			650527.i			1.36038i
$188$	−163885.			−0.338177
$189$	206778.	−	696147.i	0.421067	−	1.41758i
$190$			652557.i			1.31140i
$191$	−447116.			−0.886823			−0.443411	−	0.896318i	$-0.646232\pi$
$191$	−447116.			−0.886823			−0.443411	+	0.896318i	$0.646232\pi$
$192$	462423.	+	330018.i	0.905287	+	0.646078i
$193$	−2950.65			−0.00570197			−0.00285098	−	0.999996i	$-0.500907\pi$
$193$	−2950.65			−0.00570197			−0.00285098	+	0.999996i	$0.500907\pi$
$194$		−	819090.i		−	1.56253i
$195$	−511211.	−	364837.i	−0.962751	−	0.687088i
$196$	−145458.			−0.270456
$197$			426889.i			0.783699i	0.920029	+	0.391849i	$0.128165\pi$
$197$			426889.i			0.783699i	−0.920029	+	0.391849i	$0.871835\pi$
$198$	185844.	+	540612.i	0.336889	+	0.979993i
$199$	−563700.			−1.00906			−0.504528	−	0.863395i	$-0.668334\pi$
$199$	−563700.			−1.00906			−0.504528	+	0.863395i	$0.668334\pi$
$200$	−177916.			−0.314514
$201$	80426.3	−	112694.i	0.140413	−	0.196747i
$202$	−115038.			−0.198363
$203$		−	566542.i		−	0.964921i
$204$	−90765.1	+	127180.i	−0.152702	+	0.213966i
$205$	−768623.			−1.27741
$206$			807512.i			1.32581i
$207$	292678.	+	851388.i	0.474750	+	1.38103i
$208$		−	467694.i		−	0.749554i
$209$	978019.			1.54875
$210$	−548215.	+	768161.i	−0.857833	+	1.20200i
$211$		−	776064.i		−	1.20003i	−0.799990	−	0.600014i	$-0.795162\pi$
$211$		−	776064.i		−	1.20003i	0.799990	−	0.600014i	$-0.204838\pi$
$212$		−	22773.3i		−	0.0348006i
$213$	347488.	−	486902.i	0.524797	−	0.735347i
$214$		−	300566.i		−	0.448648i
$215$	941558.			1.38916
$216$	−210658.	+	709207.i	−0.307215	+	1.03428i
$217$		−	601249.i		−	0.866773i
$218$		−	1.21853e6i		−	1.73658i
$219$	723224.	−	1.01339e6i	1.01897	−	1.42779i
$220$			219256.i			0.305419i
$221$	871693.			1.20056
$222$	−281776.	+	394826.i	−0.383727	+	0.537679i
$223$	306742.			0.413059			0.206529	−	0.978440i	$-0.433783\pi$
$223$	306742.			0.413059			0.206529	+	0.978440i	$0.433783\pi$
$224$	495418.			0.659709
$225$	−71962.6	−	209336.i	−0.0947655	−	0.275668i
$226$	478903.			0.623701
$227$	−786256.			−1.01274			−0.506372	−	0.862315i	$-0.669014\pi$
$227$	−786256.			−1.01274			−0.506372	+	0.862315i	$0.669014\pi$
$228$	191206.	+	136459.i	0.243593	+	0.173846i
$229$			761586.i			0.959689i	0.877354	+	0.479845i	$0.159307\pi$
$229$			761586.i			0.959689i	−0.877354	+	0.479845i	$0.840693\pi$
$230$		−	1.16994e6i		−	1.45830i
$231$	1.15128e6	+	821636.i	1.41955	+	1.01309i
$232$			577170.i			0.704018i
$233$	−810979.			−0.978632			−0.489316	−	0.872106i	$-0.662754\pi$
$233$	−810979.			−0.978632			−0.489316	+	0.872106i	$0.662754\pi$
$234$	724410.	−	249028.i	0.864858	−	0.297309i
$235$			1.42774e6i			1.68647i
$236$	119131.	+	154355.i	0.139233	+	0.180401i
$237$	−1.25530e6	−	895874.i	−1.45170	−	1.03604i
$238$		−	1.30983e6i		−	1.49890i
$239$			363228.i			0.411324i	0.978623	+	0.205662i	$0.0659348\pi$
$239$			363228.i			0.411324i	−0.978623	+	0.205662i	$0.934065\pi$
$240$	424256.	−	594469.i	0.475444	−	0.666194i
$241$	9784.10			0.0108512			0.00542561	−	0.999985i	$-0.498273\pi$
$241$	9784.10			0.0108512			0.00542561	+	0.999985i	$0.498273\pi$
$242$	−312869.			−0.343419
$243$	−919656.	+	38997.0i	−0.999102	+	0.0423658i
$244$			259229.i			0.278747i
$245$			1.26721e6i			1.34875i
$246$	544587.	−	763078.i	0.573759	−	0.803954i
$247$		−	1.31053e6i		−	1.36679i
$248$			612528.i			0.632408i
$249$	−135347.	−	96593.4i	−0.138341	−	0.0987300i
$250$		−	699162.i		−	0.707502i
$251$		−	268655.i		−	0.269160i	−0.990903	−	0.134580i	$-0.957031\pi$
$251$		−	268655.i		−	0.269160i	0.990903	−	0.134580i	$-0.0429685\pi$
$252$	110440.	+	321266.i	0.109554	+	0.318686i
$253$	−1.75345e6			−1.72224
$254$	−1.29156e6			−1.25612
$255$	1.10798e6	+	790733.i	1.06704	+	0.761517i
$256$	−676803.			−0.645449
$257$		−	26997.6i		−	0.0254972i	−0.999919	−	0.0127486i	$-0.995942\pi$
$257$		−	26997.6i		−	0.0254972i	0.999919	−	0.0127486i	$-0.00405811\pi$
$258$	−667116.	+	934765.i	−0.623953	+	0.874285i
$259$			1.20013e6i			1.11168i
$260$	293799.			0.269536
$261$	−679096.	+	233450.i	−0.617064	+	0.212126i
$262$	618199.			0.556385
$263$		−	1.09506e6i		−	0.976225i	−0.872781	−	0.488112i	$-0.837686\pi$
$263$		−	1.09506e6i		−	0.976225i	0.872781	−	0.488112i	$-0.162314\pi$
$264$	−1.17288e6	−	837050.i	−1.03572	−	0.739165i
$265$	−198398.			−0.173549
$266$	−1.96924e6			−1.70645
$267$	480384.	+	342837.i	0.412392	+	0.294313i
$268$			64766.4i			0.0550824i
$269$	1.26480e6			1.06571			0.532856	−	0.846206i	$-0.321119\pi$
$269$	1.26480e6			1.06571			0.532856	+	0.846206i	$0.321119\pi$
$270$	1.14667e6	+	340598.i	0.957258	+	0.284337i
$271$	−736850.			−0.609475			−0.304737	−	0.952436i	$-0.598569\pi$
$271$	−736850.			−0.609475			−0.304737	+	0.952436i	$0.598569\pi$
$272$			1.01366e6i			0.830750i
$273$	1.10098e6	−	1.54269e6i	0.894070	−	1.25277i
$274$			498506.i			0.401138i
$275$	431132.			0.343778
$276$	−342807.	−	244651.i	−0.270880	−	0.193319i
$277$	−276562.			−0.216568			−0.108284	−	0.994120i	$-0.534536\pi$
$277$	−276562.			−0.216568			−0.108284	+	0.994120i	$0.534536\pi$
$278$	957891.			0.743369
$279$	−720699.	+	247752.i	−0.554298	+	0.190549i
$280$		−	2.37874e6i		−	1.81323i
$281$			1.56615e6i			1.18323i	0.806221	+	0.591614i	$0.201509\pi$
$281$			1.56615e6i			1.18323i	−0.806221	+	0.591614i	$0.798491\pi$
$282$	−1.41744e6	−	1.01159e6i	−1.06141	−	0.757497i
$283$		−	42674.3i		−	0.0316738i	−0.999875	−	0.0158369i	$-0.994959\pi$
$283$		−	42674.3i		−	0.0316738i	0.999875	−	0.0158369i	$-0.00504126\pi$
$284$			279828.i			0.205871i
$285$	1.18881e6	−	1.66576e6i	0.866961	−	1.21479i
$286$			1.49194e6i			1.07854i
$287$		−	2.31949e6i		−	1.66222i
$288$	−204143.	−	593843.i	−0.145029	−	0.421882i
$289$	−469416.			−0.330608
$290$	933188.			0.651590
$291$	−1.49219e6	+	2.09087e6i	−1.03298	+	1.44742i
$292$			582404.i			0.399731i
$293$		−	1.09650e6i		−	0.746170i	−0.927797	−	0.373085i	$-0.878300\pi$
$293$		−	1.09650e6i		−	0.746170i	0.927797	−	0.373085i	$-0.121700\pi$
$294$	−1.25807e6	−	897846.i	−0.848858	−	0.605806i
$295$	1.34472e6	−	1.03785e6i	0.899654	−	0.694352i
$296$		−	1.22265e6i		−	0.811095i
$297$	510472.	−	1.71857e6i	0.335800	−	1.13051i
$298$	186626.			0.121740
$299$			2.34959e6i			1.51990i
$300$	84287.9	+	60153.9i	0.0540707	+	0.0385887i
$301$			2.84136e6i			1.80763i
$302$			36075.2i			0.0227610i
$303$	293653.	+	209572.i	0.183750	+	0.131137i
$304$	1.52396e6			0.945780
$305$	2.25837e6			1.39010
$306$	−1.57006e6	+	539733.i	−0.958543	+	0.329515i
$307$	−1.26494e6			−0.765992			−0.382996	−	0.923750i	$-0.625108\pi$
$307$	−1.26494e6			−0.765992			−0.382996	+	0.923750i	$0.625108\pi$
$308$	−661655.			−0.397424
$309$	1.47110e6	−	2.06131e6i	0.876488	−	1.22814i
$310$	990357.			0.585312
$311$		−	1.56588e6i		−	0.918028i	−0.888429	−	0.459014i	$-0.848203\pi$
$311$		−	1.56588e6i		−	0.918028i	0.888429	−	0.459014i	$-0.151797\pi$
$312$	−1.12163e6	+	1.57163e6i	−0.652324	+	0.914039i
$313$		−	551327.i		−	0.318089i	−0.987271	−	0.159044i	$-0.949159\pi$
$313$		−	551327.i		−	0.318089i	0.987271	−	0.159044i	$-0.0508413\pi$
$314$			1.13025e6i			0.646921i
$315$	2.79882e6	−	962142.i	1.58928	−	0.546339i
$316$	721437.			0.406425
$317$		−	2.39218e6i		−	1.33704i	−0.743692	−	0.668522i	$-0.766927\pi$
$317$		−	2.39218e6i		−	1.33704i	0.743692	−	0.668522i	$-0.233073\pi$
$318$	140569.	−	196967.i	0.0779513	−	0.109226i
$319$		−	1.39861e6i		−	0.769523i
$320$			2.31526e6i			1.26394i
$321$	−547563.	+	767247.i	−0.296600	+	0.415597i
$322$	3.53057e6			1.89760
$323$			2.84038e6i			1.51485i
$324$	339583.	−	264763.i	0.179715	−	0.140118i
$325$		−	577708.i		−	0.303389i
$326$	−85442.6			−0.0445277
$327$	−2.21987e6	+	3.11050e6i	−1.14805	+	1.60865i
$328$			2.36300e6i			1.21277i
$329$	−4.30853e6			−2.19452
$330$	−1.35337e6	+	1.89635e6i	−0.684120	+	0.958592i
$331$	1.89522e6			0.950802			0.475401	−	0.879769i	$-0.342303\pi$
$331$	1.89522e6			0.950802			0.475401	+	0.879769i	$0.342303\pi$
$332$	77785.6			0.0387306
$333$	1.43856e6	−	494530.i	0.710916	−	0.244389i
$334$		−	1.89246e6i		−	0.928238i
$335$	564236.			0.274694
$336$	1.79394e6	+	1.28029e6i	0.866882	+	0.618669i
$337$		−	774928.i		−	0.371695i	−0.982579	−	0.185847i	$-0.940497\pi$
$337$		−	774928.i		−	0.371695i	0.982579	−	0.185847i	$-0.0595030\pi$
$338$	153586.			0.0731239
$339$	−1.22248e6	−	872451.i	−0.577754	−	0.412327i
$340$	−636768.			−0.298734
$341$		−	1.48430e6i		−	0.691250i
$342$	811448.	+	2.36046e6i	0.375142	+	1.09127i
$343$	−601960.			−0.276269
$344$		−	2.89466e6i		−	1.31887i
$345$	−2.13137e6	+	2.98648e6i	−0.964075	+	1.35087i
$346$	2.63672e6			1.18406
$347$	−1.88000e6			−0.838173			−0.419087	−	0.907946i	$-0.637650\pi$
$347$	−1.88000e6			−0.838173			−0.419087	+	0.907946i	$0.637650\pi$
$348$	195142.	−	273434.i	0.0863780	−	0.121033i
$349$		−	2.18175e6i		−	0.958828i	−0.877589	−	0.479414i	$-0.840849\pi$
$349$		−	2.18175e6i		−	0.958828i	0.877589	−	0.479414i	$-0.159151\pi$
$350$	−868081.			−0.378783
$351$	−2.30285e6	−	684022.i	−0.997695	−	0.296348i
$352$	1.22303e6			0.526116
$353$	−2.20284e6			−0.940907			−0.470454	−	0.882425i	$-0.655910\pi$
$353$	−2.20284e6			−0.940907			−0.470454	+	0.882425i	$0.655910\pi$
$354$	77599.5	+	2.07036e6i	0.0329117	+	0.878085i
$355$	2.43783e6			1.02667
$356$	−276083.			−0.115455
$357$	−2.38621e6	+	3.34357e6i	−0.990920	+	1.38848i
$358$	−2.55532e6			−1.05375
$359$			4.07491e6i			1.66871i	0.551226	+	0.834356i	$0.314160\pi$
$359$			4.07491e6i			1.66871i	−0.551226	+	0.834356i	$0.685840\pi$
$360$	−2.85133e6	+	980191.i	−1.15955	+	0.398616i
$361$	1.79420e6			0.724608
$362$	3.17349e6			1.27281
$363$	798652.	+	569976.i	0.318120	+	0.227033i
$364$			886604.i			0.350733i
$365$	5.07383e6			1.99344
$366$	−1.60011e6	+	2.24208e6i	−0.624376	+	0.874879i
$367$		−	59661.9i		−	0.0231223i	−0.999933	−	0.0115612i	$-0.996320\pi$
$367$		−	59661.9i		−	0.0231223i	0.999933	−	0.0115612i	$-0.00368012\pi$
$368$	−2.73225e6			−1.05172
$369$	−2.78030e6	+	955775.i	−1.06298	+	0.365418i
$370$	−1.97682e6			−0.750694
$371$		−	598709.i		−	0.225830i
$372$	207097.	−	290185.i	0.0775920	−	0.108722i
$373$	−2.58615e6			−0.962459			−0.481229	−	0.876595i	$-0.659810\pi$
$373$	−2.58615e6			−0.962459			−0.481229	+	0.876595i	$0.659810\pi$
$374$		−	3.23357e6i		−	1.19537i
$375$	−1.27371e6	+	1.78473e6i	−0.467727	+	0.655382i
$376$	4.38935e6			1.60115
$377$	−1.87412e6			−0.679115
$378$	−1.02783e6	+	3.46033e6i	−0.369992	+	1.24563i
$379$	−3.76227e6			−1.34540			−0.672701	−	0.739915i	$-0.734866\pi$
$379$	−3.76227e6			−1.34540			−0.672701	+	0.739915i	$0.734866\pi$
$380$			957334.i			0.340098i
$381$	3.29694e6	+	2.35293e6i	1.16359	+	0.830418i
$382$	2.22247e6			0.779253
$383$		−	1.79536e6i		−	0.625395i	−0.949853	−	0.312697i	$-0.898767\pi$
$383$		−	1.79536e6i		−	0.625395i	0.949853	−	0.312697i	$-0.101233\pi$
$384$	−1.24930e6	−	891593.i	−0.432355	−	0.308559i
$385$			5.76424e6i			1.98194i
$386$	14666.8			0.00501033
$387$	3.40585e6	−	1.17082e6i	1.15597	−	0.397385i
$388$		−	1.20165e6i		−	0.405226i
$389$		−	3.86435e6i		−	1.29480i	−0.762151	−	0.647399i	$-0.775857\pi$
$389$		−	3.86435e6i		−	1.29480i	0.762151	−	0.647399i	$-0.224143\pi$
$390$	2.54107e6	+	1.81349e6i	0.845971	+	0.603746i
$391$		−	5.09241e6i		−	1.68454i
$392$	3.89582e6			1.28051
$393$	−1.57806e6	−	1.12622e6i	−0.515397	−	0.367824i
$394$		−	2.12193e6i		−	0.688638i
$395$		−	6.28506e6i		−	2.02683i
$396$	272643.	+	793105.i	0.0873688	+	0.254152i
$397$		−	3.89788e6i		−	1.24123i	−0.784115	−	0.620615i	$-0.786883\pi$
$397$		−	3.89788e6i		−	1.24123i	0.784115	−	0.620615i	$-0.213117\pi$
$398$	2.80198e6			0.886660
$399$	5.02681e6	+	3.58749e6i	1.58074	+	1.12813i
$400$	671795.			0.209936
$401$	−1.28905e6			−0.400321			−0.200160	−	0.979763i	$-0.564146\pi$
$401$	−1.28905e6			−0.400321			−0.200160	+	0.979763i	$0.564146\pi$
$402$	−399774.	+	560165.i	−0.123381	+	0.172882i
$403$	−1.98893e6			−0.610037
$404$	−168766.			−0.0514436
$405$	−2.30658e6	−	2.95840e6i	−0.698765	−	0.896231i
$406$			2.81610e6i			0.847878i
$407$			2.96276e6i			0.886563i
$408$	2.43098e6	−	3.40630e6i	0.722987	−	1.01305i
$409$			2.48211e6i			0.733691i	0.930282	+	0.366845i	$0.119562\pi$
$409$			2.48211e6i			0.733691i	−0.930282	+	0.366845i	$0.880438\pi$
$410$	3.82059e6			1.12246
$411$	908162.	−	1.27252e6i	0.265191	−	0.371587i
$412$			1.18466e6i			0.343836i
$413$	3.13194e6	+	4.05798e6i	0.903521	+	1.17067i
$414$	−1.45481e6	−	4.23198e6i	−0.417164	−	1.21351i
$415$		−	677658.i		−	0.193148i
$416$		−	1.63884e6i		−	0.464305i
$417$	−2.44518e6	−	1.74506e6i	−0.688606	−	0.491439i
$418$	−4.86143e6			−1.36089
$419$	93927.3			0.0261371			0.0130685	−	0.999915i	$-0.495840\pi$
$419$	93927.3			0.0261371			0.0130685	+	0.999915i	$0.495840\pi$
$420$	−804259.	+	1.12693e6i	−0.222471	+	0.311727i
$421$		−	2.46967e6i		−	0.679099i	−0.940588	−	0.339550i	$-0.889725\pi$
$421$		−	2.46967e6i		−	0.679099i	0.940588	−	0.339550i	$-0.110275\pi$
$422$			3.85757e6i			1.05447i
$423$	1.77538e6	+	5.16450e6i	0.482437	+	1.40339i
$424$			609941.i			0.164768i
$425$			1.25210e6i			0.336254i
$426$	−1.72726e6	+	2.42024e6i	−0.461140	+	0.646151i
$427$			6.81513e6i			1.80886i
$428$		−	440946.i		−	0.116353i
$429$	2.71797e6	−	3.80843e6i	0.713019	−	0.999085i
$430$	−4.68019e6			−1.22065
$431$	2.81463e6			0.729841			0.364920	−	0.931039i	$-0.381096\pi$
$431$	2.81463e6			0.729841			0.364920	+	0.931039i	$0.381096\pi$
$432$	795424.	−	2.67790e6i	0.205064	−	0.690375i
$433$	5.95717e6			1.52693			0.763467	−	0.645847i	$-0.223496\pi$
$433$	5.95717e6			1.52693			0.763467	+	0.645847i	$0.223496\pi$
$434$			2.98862e6i			0.761635i
$435$	−2.38212e6	−	1.70005e6i	−0.603588	−	0.430764i
$436$		−	1.78764e6i		−	0.450364i
$437$	−7.65606e6			−1.91779
$438$	−3.59492e6	+	5.03722e6i	−0.895374	+	1.25460i
$439$	−5.10307e6			−1.26378			−0.631889	−	0.775059i	$-0.717720\pi$
$439$	−5.10307e6			−1.26378			−0.631889	+	0.775059i	$0.717720\pi$
$440$		−	5.87238e6i		−	1.44605i
$441$	1.57576e6	+	4.58381e6i	0.385828	+	1.12236i
$442$	−4.33292e6			−1.05493
$443$	1.54905e6			0.375021			0.187511	−	0.982263i	$-0.439958\pi$
$443$	1.54905e6			0.375021			0.187511	+	0.982263i	$0.439958\pi$
$444$	−413380.	+	579230.i	−0.0995157	+	0.139442i
$445$			2.40519e6i			0.575771i
$446$	−1.52472e6			−0.362955
$447$	−476396.	−	339990.i	−0.112771	−	0.0804817i
$448$	−6.98682e6			−1.64469
$449$			6.18756e6i			1.44845i	0.689564	+	0.724225i	$0.257802\pi$
$449$			6.18756e6i			1.44845i	−0.689564	+	0.724225i	$0.742198\pi$
$450$	357704.	+	1.04054e6i	0.0832707	+	0.242230i
$451$		−	5.72610e6i		−	1.32562i
$452$	702575.			0.161751
$453$	65720.6	−	92088.0i	0.0150472	−	0.0210842i
$454$	3.90824e6			0.889900
$455$	7.72397e6			1.74909
$456$	−5.12111e6	−	3.65479e6i	−1.15333	−	0.823096i
$457$			1.90651e6i			0.427021i	0.976941	+	0.213510i	$0.0684897\pi$
$457$			1.90651e6i			0.427021i	−0.976941	+	0.213510i	$0.931510\pi$
$458$		−	3.78561e6i		−	0.843281i
$459$	4.99111e6	+	1.48252e6i	1.10577	+	0.328450i
$460$		−	1.71637e6i		−	0.378195i
$461$			1.02228e6i			0.224035i	0.993706	+	0.112018i	$0.0357313\pi$
$461$			1.02228e6i			0.224035i	−0.993706	+	0.112018i	$0.964269\pi$
$462$	−5.72266e6	−	4.08410e6i	−1.24736	−	0.890208i
$463$			3.64013e6i			0.789159i	0.918862	+	0.394579i	$0.129110\pi$
$463$			3.64013e6i			0.789159i	−0.918862	+	0.394579i	$0.870890\pi$
$464$		−	2.17934e6i		−	0.469927i
$465$	−2.52806e6	−	1.80420e6i	−0.542194	−	0.386948i
$466$	4.03112e6			0.859926
$467$	2.01939e6			0.428477			0.214238	−	0.976781i	$-0.431273\pi$
$467$	2.01939e6			0.428477			0.214238	+	0.976781i	$0.431273\pi$
$468$	1.06275e6	−	365336.i	0.224292	−	0.0771042i
$469$			1.70271e6i			0.357444i
$470$		−	7.09686e6i		−	1.48191i
$471$	2.05906e6	−	2.88516e6i	0.427677	−	0.599263i
$472$	−3.19070e6	−	4.13411e6i	−0.659220	−	0.854135i
$473$			7.01443e6i			1.44158i
$474$	6.23972e6	+	4.45311e6i	1.27561	+	0.910369i
$475$	1.88244e6			0.382814
$476$		−	1.92159e6i		−	0.388726i
$477$	−717655.	+	246706.i	−0.144417	+	0.0496459i
$478$		−	1.80549e6i		−	0.361432i
$479$		−	9.57708e6i		−	1.90719i	−0.301088	−	0.953596i	$-0.597350\pi$
$479$		−	9.57708e6i		−	1.90719i	0.301088	−	0.953596i	$-0.402650\pi$
$480$	1.48663e6	−	2.08307e6i	0.294510	−	0.412669i
$481$	3.97003e6			0.782405
$482$	−48633.7			−0.00953498
$483$	−9.01238e6	−	6.43188e6i	−1.75781	−	1.25450i
$484$	−458995.			−0.0890624
$485$	−1.04686e7			−2.02085
$486$	4.57133e6	−	193842.i	0.877913	−	0.0372269i
$487$	7.51277e6			1.43542			0.717708	−	0.696344i	$-0.245191\pi$
$487$	7.51277e6			1.43542			0.717708	+	0.696344i	$0.245191\pi$
$488$		−	6.94298e6i		−	1.31976i
$489$	218107.	+	155657.i	0.0412475	+	0.0294371i
$490$		−	6.29890e6i		−	1.18515i
$491$		−	6.53823e6i		−	1.22393i	−0.790885	−	0.611965i	$-0.790379\pi$
$491$		−	6.53823e6i		−	1.22393i	0.790885	−	0.611965i	$-0.209621\pi$
$492$	798937.	−	1.11947e6i	0.148799	−	0.208498i
$493$	4.06188e6			0.752680
$494$			6.51422e6i			1.20100i
$495$	6.90943e6	−	2.37523e6i	1.26744	−	0.435705i
$496$		−	2.31285e6i		−	0.422127i
$497$			7.35668e6i			1.33595i
$498$	672769.	+	480136.i	0.121560	+	0.0867543i
$499$	−3.95246e6			−0.710586			−0.355293	−	0.934755i	$-0.615619\pi$
$499$	−3.95246e6			−0.710586			−0.355293	+	0.934755i	$0.615619\pi$
$500$		−	1.02571e6i		−	0.183484i
$501$	−3.44762e6	+	4.83081e6i	−0.613655	+	0.859857i
$502$			1.33540e6i			0.236511i
$503$	−8.49350e6			−1.49681			−0.748405	−	0.663242i	$-0.769180\pi$
$503$	−8.49350e6			−1.49681			−0.748405	+	0.663242i	$0.769180\pi$
$504$	−2.95794e6	−	8.60452e6i	−0.518697	−	1.50886i
$505$			1.47026e6i			0.256547i
$506$	8.71587e6			1.51333
$507$	−392054.	−	279798.i	−0.0677370	−	0.0483420i
$508$	−1.89479e6			−0.325763
$509$	3.68438e6			0.630333			0.315167	−	0.949036i	$-0.397940\pi$
$509$	3.68438e6			0.630333			0.315167	+	0.949036i	$0.397940\pi$
$510$	−5.50742e6	−	3.93049e6i	−0.937611	−	0.669146i
$511$			1.53114e7i			2.59396i
$512$	6.51487e6			1.09833
$513$	2.22886e6	−	7.50375e6i	0.373929	−	1.25888i
$514$			134197.i			0.0224044i
$515$	1.03206e7			1.71470
$516$	−978692.	+	1.37135e6i	−0.161816	+	0.226737i
$517$	−1.06364e7			−1.75012
$518$		−	5.96549e6i		−	0.976836i
$519$	−6.73068e6	−	4.80349e6i	−1.09683	−	0.782778i
$520$	−7.86887e6			−1.27616
$521$		−	2.58088e6i		−	0.416556i	−0.978070	−	0.208278i	$-0.933214\pi$
$521$		−	2.58088e6i		−	0.416556i	0.978070	−	0.208278i	$-0.0667859\pi$
$522$	3.37558e6	−	1.16041e6i	0.542215	−	0.186395i
$523$	7.70706e6			1.23207			0.616033	−	0.787720i	$-0.288739\pi$
$523$	7.70706e6			1.23207			0.616033	+	0.787720i	$0.288739\pi$
$524$	906929.			0.144293
$525$	2.21593e6	+	1.58144e6i	0.350879	+	0.250412i
$526$			5.44322e6i			0.857811i
$527$	4.31072e6			0.676120
$528$	4.42868e6	+	3.16063e6i	0.691337	+	0.493388i
$529$	7.28992e6			1.13262
$530$	986174.			0.152498
$531$	3.57362e6	−	5.42630e6i	0.550012	−	0.835156i
$532$	−2.88897e6			−0.442551
$533$	−7.67286e6			−1.16987
$534$	−2.38784e6	−	1.70413e6i	−0.362370	−	0.258613i
$535$	−3.84146e6			−0.580246
$536$		−	1.73465e6i		−	0.260795i
$537$	6.52290e6	+	4.65521e6i	0.976124	+	0.696632i
$538$	−6.28691e6			−0.936444
$539$	−9.44047e6			−1.39966
$540$	1.68222e6	+	499675.i	0.248256	+	0.0737400i
$541$			713889.i			0.104867i	0.998624	+	0.0524334i	$0.0166977\pi$
$541$			713889.i			0.104867i	−0.998624	+	0.0524334i	$0.983302\pi$
$542$	3.66265e6			0.535547
$543$	−8.10086e6	−	5.78136e6i	−1.17905	−	0.841454i
$544$			3.55196e6i			0.514601i
$545$	−1.55737e7			−2.24595
$546$	−5.47261e6	+	7.66825e6i	−0.785621	+	1.10082i
$547$	−1.13138e7			−1.61675			−0.808373	−	0.588671i	$-0.799651\pi$
$547$	−1.13138e7			−1.61675			−0.808373	+	0.588671i	$0.799651\pi$
$548$			731333.i			0.104031i
$549$	8.16909e6	−	2.80826e6i	1.15676	−	0.397655i
$550$	−2.14302e6			−0.302079
$551$		−	6.10674e6i		−	0.856900i
$552$	9.18145e6	+	6.55254e6i	1.28252	+	0.915297i
$553$	1.89666e7			2.63740
$554$	1.37470e6			0.190298
$555$	5.04617e6	+	3.60131e6i	0.695391	+	0.496281i
$556$	1.40527e6			0.192785
$557$			1.86512e6i			0.254724i	0.991856	+	0.127362i	$0.0406510\pi$
$557$			1.86512e6i			0.254724i	−0.991856	+	0.127362i	$0.959349\pi$
$558$	3.58237e6	−	1.23150e6i	0.487063	−	0.167436i
$559$	9.39920e6			1.27222
$560$			8.98192e6i			1.21032i
$561$	−5.89081e6	+	8.25424e6i	−0.790257	+	1.10731i
$562$		−	7.78486e6i		−	1.03971i
$563$	9.27843e6			1.23368			0.616841	−	0.787088i	$-0.288412\pi$
$563$	9.27843e6			1.23368			0.616841	+	0.787088i	$0.288412\pi$
$564$	−2.07946e6	−	1.48405e6i	−0.275266	−	0.196449i
$565$		−	6.12074e6i		−	0.806645i
$566$			212121.i			0.0278319i
$567$	8.92764e6	−	6.96062e6i	1.16622	−	0.909264i
$568$		−	7.49469e6i		−	0.974726i
$569$	−2.28763e6			−0.296213			−0.148107	−	0.988971i	$-0.547318\pi$
$569$	−2.28763e6			−0.296213			−0.148107	+	0.988971i	$0.547318\pi$
$570$	−5.90920e6	+	8.27999e6i	−0.761800	+	1.06744i
$571$		−	8.80895e6i		−	1.13067i	−0.824863	−	0.565333i	$-0.808748\pi$
$571$		−	8.80895e6i		−	1.13067i	0.824863	−	0.565333i	$-0.191252\pi$
$572$			2.18875e6i			0.279709i
$573$	−5.67325e6	−	4.04884e6i	−0.721847	−	0.515162i
$574$			1.15295e7i			1.46059i
$575$	−3.37496e6			−0.425695
$576$	2.87901e6	+	8.37489e6i	0.361565	+	1.05178i
$577$	1.20450e7			1.50614			0.753072	−	0.657938i	$-0.228571\pi$
$577$	1.20450e7			1.50614			0.753072	+	0.657938i	$0.228571\pi$
$578$	2.33332e6			0.290506
$579$	−37439.4	−	26719.5i	−0.00464123	−	0.00331231i
$580$	1.36903e6			0.168983
$581$	2.04498e6			0.251333
$582$	7.41723e6	−	1.03930e7i	0.907683	−	1.27185i
$583$		−	1.47803e6i		−	0.180099i
$584$		−	1.55986e7i		−	1.89258i
$585$	−3.18276e6	−	9.25849e6i	−0.384516	−	1.11854i
$586$			5.45034e6i			0.655661i
$587$	5.64450e6			0.676130			0.338065	−	0.941123i	$-0.390228\pi$
$587$	5.64450e6			0.676130			0.338065	+	0.941123i	$0.390228\pi$
$588$	−1.84565e6	−	1.31719e6i	−0.220143	−	0.157110i
$589$		−	6.48085e6i		−	0.769739i
$590$	−6.68417e6	+	5.15883e6i	−0.790528	+	0.610128i
$591$	−3.86567e6	+	5.41659e6i	−0.455256	+	0.637907i
$592$			4.61661e6i			0.541400i
$593$			1.06417e7i			1.24272i	0.783524	+	0.621362i	$0.213420\pi$
$593$			1.06417e7i			1.24272i	−0.783524	+	0.621362i	$0.786580\pi$
$594$	−2.53740e6	+	8.54248e6i	−0.295068	+	0.993386i
$595$	−1.67406e7			−1.93856
$596$	273790.			0.0315720
$597$	−7.15253e6	−	5.10456e6i	−0.821342	−	0.586168i
$598$		−	1.16791e7i		−	1.33554i
$599$		−	6.19363e6i		−	0.705307i	−0.935754	−	0.352654i	$-0.885279\pi$
$599$		−	6.19363e6i		−	0.705307i	0.935754	−	0.352654i	$-0.114721\pi$
$600$	−2.25750e6	−	1.61111e6i	−0.256005	−	0.182704i
$601$			1.17981e7i			1.33238i	0.745783	+	0.666188i	$0.232075\pi$
$601$			1.17981e7i			1.33238i	−0.745783	+	0.666188i	$0.767925\pi$
$602$		−	1.41235e7i		−	1.58837i
$603$	2.04098e6	−	701621.i	0.228584	−	0.0785795i
$604$			52924.1i			0.00590284i
$605$			3.99870e6i			0.444151i
$606$	−1.45966e6	−	1.04172e6i	−0.161462	−	0.115231i
$607$	−8.78290e6			−0.967534			−0.483767	−	0.875197i	$-0.660732\pi$
$607$	−8.78290e6			−0.967534			−0.483767	+	0.875197i	$0.660732\pi$
$608$	5.34010e6			0.585856
$609$	5.13029e6	−	7.18858e6i	0.560530	−	0.785416i
$610$	−1.12257e7			−1.22148
$611$			1.42526e7i			1.54451i
$612$	−2.30335e6	+	791815.i	−0.248589	+	0.0854565i
$613$		−	1.11383e7i		−	1.19720i	−0.801047	−	0.598601i	$-0.795723\pi$
$613$		−	1.11383e7i		−	1.19720i	0.801047	−	0.598601i	$-0.204277\pi$
$614$	6.28763e6			0.673079
$615$	−9.75270e6	−	6.96023e6i	−1.03977	−	0.742054i
$616$	1.77212e7			1.88166
$617$			7.55364e6i			0.798810i	0.916775	+	0.399405i	$0.130783\pi$
$617$			7.55364e6i			0.798810i	−0.916775	+	0.399405i	$0.869217\pi$
$618$	−7.31238e6	+	1.02461e7i	−0.770172	+	1.07917i
$619$	−7.36417e6			−0.772498			−0.386249	−	0.922395i	$-0.626229\pi$
$619$	−7.36417e6			−0.772498			−0.386249	+	0.922395i	$0.626229\pi$
$620$	1.45290e6			0.151795
$621$	−3.99604e6	+	1.34532e7i	−0.415815	+	1.39990i
$622$			7.78348e6i			0.806673i
$623$	−7.25820e6			−0.749219
$624$	4.23517e6	−	5.93434e6i	0.435421	−	0.610114i
$625$	−1.17825e7			−1.20653
$626$			2.74048e6i			0.279505i
$627$	1.24096e7	+	8.85640e6i	1.26064	+	0.899681i
$628$			1.65814e6i			0.167773i
$629$	−8.60449e6			−0.867159
$630$	−1.39121e7	+	4.78251e6i	−1.39650	+	0.480070i
$631$	−8.82013e6			−0.881864			−0.440932	−	0.897541i	$-0.645352\pi$
$631$	−8.82013e6			−0.881864			−0.440932	+	0.897541i	$0.645352\pi$
$632$	−1.93224e7			−1.92428
$633$	7.02760e6	−	9.84711e6i	0.697105	−	0.976786i
$634$			1.18908e7i			1.17486i
$635$			1.65071e7i			1.62457i
$636$	206222.	−	288960.i	0.0202159	−	0.0283266i
$637$			1.26500e7i			1.23522i
$638$			6.95208e6i			0.676181i
$639$	8.81823e6	−	3.03141e6i	0.854337	−	0.293692i
$640$		−	6.25503e6i		−	0.603642i
$641$		−	6.36919e6i		−	0.612264i	−0.951989	−	0.306132i	$-0.900965\pi$
$641$		−	6.36919e6i		−	0.612264i	0.951989	−	0.306132i	$-0.0990349\pi$
$642$	2.72176e6	−	3.81375e6i	0.260623	−	0.365186i
$643$	−8.79943e6			−0.839319			−0.419660	−	0.907682i	$-0.637851\pi$
$643$	−8.79943e6			−0.839319			−0.419660	+	0.907682i	$0.637851\pi$
$644$	5.17952e6			0.492124
$645$	1.19470e7	+	8.52623e6i	1.13073	+	0.806971i
$646$		−	1.41187e7i		−	1.33110i
$647$			1.16792e7i			1.09686i	0.836196	+	0.548430i	$0.184774\pi$
$647$			1.16792e7i			1.09686i	−0.836196	+	0.548430i	$0.815226\pi$
$648$	−9.09512e6	+	7.09120e6i	−0.850885	+	0.663410i
$649$	7.73179e6	+	1.00179e7i	0.720557	+	0.933608i
$650$			2.87161e6i			0.266589i
$651$	5.44458e6	−	7.62897e6i	0.503514	−	0.705527i
$652$	−125349.			−0.0115478
$653$			1.28686e7i			1.18099i	0.807040	+	0.590497i	$0.201068\pi$
$653$			1.28686e7i			1.18099i	−0.807040	+	0.590497i	$0.798932\pi$
$654$	1.10343e7	−	1.54613e7i	1.00879	−	1.41352i
$655$		−	7.90104e6i		−	0.719584i
$656$		−	8.92249e6i		−	0.809518i
$657$	1.83533e7	−	6.30925e6i	1.65883	−	0.570249i
$658$	2.14163e7			1.92833
$659$	−1.70329e7			−1.52783			−0.763915	−	0.645317i	$-0.776725\pi$
$659$	−1.70329e7			−1.52783			−0.763915	+	0.645317i	$0.776725\pi$
$660$	−1.98546e6	+	2.78204e6i	−0.177420	+	0.248601i
$661$	−4.61679e6			−0.410995			−0.205497	−	0.978658i	$-0.565881\pi$
$661$	−4.61679e6			−0.410995			−0.205497	+	0.978658i	$0.565881\pi$
$662$	−9.42056e6			−0.835471
$663$	1.10605e7	+	7.89357e6i	0.977218	+	0.697413i
$664$	−2.08335e6			−0.183375
$665$			2.51683e7i			2.20699i
$666$	−7.15065e6	+	2.45815e6i	−0.624684	+	0.214745i
$667$			1.09485e7i			0.952887i
$668$		−	2.77633e6i		−	0.240730i
$669$	3.89211e6	+	2.77769e6i	0.336217	+	0.239949i
$670$	−2.80464e6			−0.241374
$671$			1.68244e7i			1.44256i
$672$	6.28613e6	+	4.48624e6i	0.536983	+	0.383229i
$673$			8.81060e6i			0.749838i	0.927058	+	0.374919i	$0.122330\pi$
$673$			8.81060e6i			0.749838i	−0.927058	+	0.374919i	$0.877670\pi$
$674$			3.85193e6i			0.326609i
$675$	982529.	−	3.30782e6i	0.0830015	−	0.279436i
$676$	225318.			0.0189640
$677$			4.50667e6i			0.377906i	0.981986	+	0.188953i	$0.0605094\pi$
$677$			4.50667e6i			0.377906i	−0.981986	+	0.188953i	$0.939491\pi$
$678$	6.07658e6	+	4.33668e6i	0.507674	+	0.362312i
$679$		−	3.15912e7i		−	2.62962i
$680$	1.70547e7			1.41440
$681$	−9.97644e6	−	7.11990e6i	−0.824343	−	0.588310i
$682$			7.37798e6i			0.607402i
$683$	−2.86358e6			−0.234886			−0.117443	−	0.993080i	$-0.537470\pi$
$683$	−2.86358e6			−0.234886			−0.117443	+	0.993080i	$0.537470\pi$
$684$	1.19043e6	+	3.46292e6i	0.0972893	+	0.283010i
$685$	6.37127e6			0.518800
$686$	2.99216e6			0.242758
$687$	−6.89651e6	+	9.66342e6i	−0.557490	+	0.781158i
$688$			1.09300e7i			0.880336i
$689$	−1.98053e6			−0.158940
$690$	1.05944e7	−	1.48449e7i	0.847135	−	1.18701i
$691$			7.55459e6i			0.601888i	0.953642	+	0.300944i	$0.0973017\pi$
$691$			7.55459e6i			0.601888i	−0.953642	+	0.300944i	$0.902698\pi$
$692$	3.86820e6			0.307074
$693$	7.16778e6	+	2.08507e7i	0.566959	+	1.64926i
$694$	9.34489e6			0.736504
$695$		−	1.22426e7i		−	0.961413i
$696$	−5.22653e6	+	7.32344e6i	−0.408969	+	0.573049i
$697$	1.66299e7			1.29660
$698$			1.08448e7i			0.842524i
$699$	−1.02901e7	−	7.34377e6i	−0.796577	−	0.568495i
$700$	−1.27352e6			−0.0982336
$701$	928630.			0.0713752			0.0356876	−	0.999363i	$-0.488638\pi$
$701$	928630.			0.0713752			0.0356876	+	0.999363i	$0.488638\pi$
$702$	1.14468e7	+	3.40006e6i	0.876677	+	0.260402i
$703$			1.29362e7i			0.987231i
$704$	−1.72483e7			−1.31164
$705$	−1.29288e7	+	1.81159e7i	−0.979685	+	1.37274i
$706$	1.09496e7			0.826777
$707$	−4.43685e6			−0.333831
$708$	113842.	+	3.03732e6i	0.00853533	+	0.227723i
$709$	−9.72670e6			−0.726691			−0.363346	−	0.931654i	$-0.618366\pi$
$709$	−9.72670e6			−0.726691			−0.363346	+	0.931654i	$0.618366\pi$
$710$	−1.21177e7			−0.902139
$711$	−7.81541e6	−	2.27347e7i	−0.579799	−	1.68661i
$712$	7.39437e6			0.546639
$713$			1.16193e7i			0.855963i
$714$	1.18611e7	−	1.66199e7i	0.870723	−	1.22006i
$715$	1.90681e7			1.39490
$716$	−3.74879e6			−0.273280
$717$	−3.28919e6	+	4.60883e6i	−0.238941	+	0.334806i
$718$		−	2.02551e7i		−	1.46630i
$719$	1.09593e7			0.790609			0.395305	−	0.918550i	$-0.370639\pi$
$719$	1.09593e7			0.790609			0.395305	+	0.918550i	$0.370639\pi$
$720$	1.07664e7	−	3.70111e6i	0.773994	−	0.266073i
$721$			3.11447e7i			2.23124i
$722$	−8.91842e6			−0.636715
$723$	124146.	+	88599.4i	0.00883256	+	0.00630355i
$724$	4.65566e6			0.330092
$725$		−	2.69198e6i		−	0.190207i
$726$	−3.96985e6	−	2.83317e6i	−0.279533	−	0.199495i
$727$	1.50214e7			1.05408			0.527041	−	0.849840i	$-0.323302\pi$
$727$	1.50214e7			1.05408			0.527041	+	0.849840i	$0.323302\pi$
$728$		−	2.37461e7i		−	1.66059i
$729$	−1.20222e7	−	7.83309e6i	−0.837850	−	0.545901i
$730$	−2.52204e7			−1.75164
$731$	−2.03714e7			−1.41003
$732$	−2.34744e6	+	3.28924e6i	−0.161926	+	0.226891i
$733$	2.19923e7			1.51186			0.755930	−	0.654653i	$-0.227185\pi$
$733$	2.19923e7			1.51186			0.755930	+	0.654653i	$0.227185\pi$
$734$			296561.i			0.0203176i
$735$	−1.14751e7	+	1.60790e7i	−0.783501	+	1.09785i
$736$	−9.57407e6			−0.651481
$737$			4.20345e6i			0.285061i
$738$	1.38200e7	−	4.75086e6i	0.934046	−	0.321093i
$739$		−	1.68831e6i		−	0.113721i	−0.998382	−	0.0568607i	$-0.981891\pi$
$739$		−	1.68831e6i		−	0.113721i	0.998382	−	0.0568607i	$-0.0181091\pi$
$740$	−2.90009e6			−0.194685
$741$	1.18674e7	−	1.66286e7i	0.793981	−	1.11253i
$742$			2.97600e6i			0.198437i
$743$		−	1.62922e7i		−	1.08270i	−0.840799	−	0.541348i	$-0.817914\pi$
$743$		−	1.62922e7i		−	1.08270i	0.840799	−	0.541348i	$-0.182086\pi$
$744$	−5.54672e6	+	7.77209e6i	−0.367370	+	0.514761i
$745$		−	2.38522e6i		−	0.157448i
$746$	1.28550e7			0.845714
$747$	−842660.	−	2.45126e6i	−0.0552524	−	0.160727i
$748$		−	4.74381e6i		−	0.310008i
$749$		−	1.15925e7i		−	0.755042i
$750$	6.33122e6	−	8.87134e6i	0.410993	−	0.575885i
$751$		−	1.99700e7i		−	1.29204i	−0.763319	−	0.646022i	$-0.776431\pi$
$751$		−	1.99700e7i		−	1.29204i	0.763319	−	0.646022i	$-0.223569\pi$
$752$	−1.65738e7			−1.06875
$753$	2.43279e6	−	3.40884e6i	0.156357	−	0.219088i
$754$	9.31565e6			0.596739
$755$	461067.			0.0294372
$756$	−1.50788e6	+	5.07648e6i	−0.0959538	+	0.323041i
$757$	−1.16636e7			−0.739764			−0.369882	−	0.929079i	$-0.620602\pi$
$757$	−1.16636e7			−0.739764			−0.369882	+	0.929079i	$0.620602\pi$
$758$	1.87011e7			1.18221
$759$	−2.22487e7	−	1.58783e7i	−1.40185	−	1.00046i
$760$		−	2.56404e7i		−	1.61024i
$761$		−	5.23863e6i		−	0.327911i	−0.986468	−	0.163955i	$-0.947575\pi$
$761$		−	5.23863e6i		−	0.327911i	0.986468	−	0.163955i	$-0.0524253\pi$
$762$	−1.63881e7	−	1.16957e7i	−1.02244	−	0.729690i
$763$		−	4.69970e7i		−	2.92253i
$764$	3.26048e6			0.202092
$765$	6.89818e6	+	2.00665e7i	0.426168	+	1.23970i
$766$			8.92417e6i			0.549536i
$767$	1.34238e7	−	1.03604e7i	0.823922	−	0.635901i
$768$	−8.58763e6	−	6.12875e6i	−0.525376	−	0.374946i
$769$		−	9.72052e6i		−	0.592753i	−0.955071	−	0.296376i	$-0.904222\pi$
$769$		−	9.72052e6i		−	0.592753i	0.955071	−	0.296376i	$-0.0957783\pi$
$770$		−	2.86523e7i		−	1.74153i
$771$	244475.	−	342560.i	0.0148115	−	0.0207539i
$772$	21516.9			0.00129938
$773$	−1.50929e7			−0.908498			−0.454249	−	0.890875i	$-0.650092\pi$
$773$	−1.50929e7			−0.908498			−0.454249	+	0.890875i	$0.650092\pi$
$774$	−1.69294e7	+	5.81977e6i	−1.01576	+	0.349183i
$775$		−	2.85690e6i		−	0.170860i
$776$			3.21839e7i			1.91860i
$777$	−1.08677e7	+	1.52279e7i	−0.645783	+	0.904875i
$778$			1.92085e7i			1.13774i
$779$		−	2.50017e7i		−	1.47614i
$780$	3.72788e6	+	2.66048e6i	0.219394	+	0.156576i
$781$			1.81614e7i			1.06542i
$782$			2.53128e7i			1.48021i
$783$	−1.07307e7	−	3.18738e6i	−0.625497	−	0.185793i
$784$	−1.47103e7			−0.854733
$785$	1.44455e7			0.836676
$786$	7.84404e6	+	5.59807e6i	0.452880	+	0.323208i
$787$	−1.78805e7			−1.02906			−0.514532	−	0.857471i	$-0.672034\pi$
$787$	−1.78805e7			−1.02906			−0.514532	+	0.857471i	$0.672034\pi$
$788$		−	3.11298e6i		−	0.178591i
$789$	9.91629e6	−	1.38947e7i	0.567096	−	0.794618i
$790$			3.12411e7i			1.78098i
$791$	1.84707e7			1.04964
$792$	−7.30224e6	−	2.12419e7i	−0.413660	−	1.20332i
$793$	2.25444e7			1.27308
$794$			1.93752e7i			1.09067i
$795$	−2.51738e6	−	1.79658e6i	−0.141264	−	0.100816i
$796$	4.11064e6			0.229947
$797$	−8.67178e6			−0.483574			−0.241787	−	0.970329i	$-0.577733\pi$
$797$	−8.67178e6			−0.483574			−0.241787	+	0.970329i	$0.577733\pi$
$798$	−2.49867e7	−	1.78323e7i	−1.38900	−	0.991289i
$799$		−	3.08905e7i		−	1.71182i
$800$	2.35403e6			0.130043
$801$	2.99083e6	+	8.70019e6i	0.164707	+	0.479124i
$802$	6.40745e6			0.351762
$803$			3.77991e7i			2.06867i
$804$	−586488.	+	821790.i	−0.0319977	+	0.0448354i
$805$		−	4.51233e7i		−	2.45420i
$806$	9.88634e6			0.536041
$807$	1.60484e7	+	1.14533e7i	0.867458	+	0.619080i
$808$	4.52008e6			0.243567
$809$	−4.10393e6			−0.220459			−0.110230	−	0.993906i	$-0.535159\pi$
$809$	−4.10393e6			−0.220459			−0.110230	+	0.993906i	$0.535159\pi$
$810$	1.14653e7	+	1.47053e7i	0.614006	+	0.787520i
$811$		−	1.40772e7i		−	0.751563i	−0.926708	−	0.375781i	$-0.877374\pi$
$811$		−	1.40772e7i		−	0.751563i	0.926708	−	0.375781i	$-0.122626\pi$
$812$			4.13136e6i			0.219889i
$813$	−9.34954e6	−	6.67251e6i	−0.496094	−	0.354048i
$814$		−	1.47269e7i		−	0.779025i
$815$			1.09202e6i			0.0575886i
$816$	−9.17915e6	+	1.28619e7i	−0.482588	+	0.676205i
$817$			3.06269e7i			1.60527i
$818$		−	1.23378e7i		−	0.644696i
$819$	2.79395e7	−	9.60468e6i	1.45549	−	0.500349i
$820$	5.60499e6			0.291099
$821$	−2.06195e7			−1.06763			−0.533813	−	0.845602i	$-0.679241\pi$
$821$	−2.06195e7			−1.06763			−0.533813	+	0.845602i	$0.679241\pi$
$822$	−4.51419e6	+	6.32531e6i	−0.233024	+	0.326514i
$823$			1.31596e7i			0.677240i	0.940923	+	0.338620i	$0.109960\pi$
$823$			1.31596e7i			0.677240i	−0.940923	+	0.338620i	$0.890040\pi$
$824$		−	3.17290e7i		−	1.62794i
$825$	5.47043e6	+	3.90409e6i	0.279825	+	0.199703i
$826$	−1.55679e7	−	2.01710e7i	−0.793926	−	1.02867i
$827$			1.53526e7i			0.780583i	0.920691	+	0.390291i	$0.127626\pi$
$827$			1.53526e7i			0.780583i	−0.920691	+	0.390291i	$0.872374\pi$
$828$	−2.13428e6	−	6.20853e6i	−0.108187	−	0.314712i
$829$	−1.04557e7			−0.528405			−0.264202	−	0.964467i	$-0.585109\pi$
$829$	−1.04557e7			−0.528405			−0.264202	+	0.964467i	$0.585109\pi$
$830$			3.36843e6i			0.169719i
$831$	−3.50917e6	−	2.50439e6i	−0.176279	−	0.125806i
$832$			2.31124e7i			1.15754i
$833$		−	2.74172e7i		−	1.36902i
$834$	1.21542e7	+	8.67413e6i	0.605080	+	0.431828i
$835$	−2.41870e7			−1.20051
$836$	−7.13196e6			−0.352934
$837$	−1.13881e7	−	3.38264e6i	−0.561873	−	0.166895i
$838$	−466883.			−0.0229667
$839$	1.52990e7			0.750338			0.375169	−	0.926956i	$-0.377585\pi$
$839$	1.52990e7			0.750338			0.375169	+	0.926956i	$0.377585\pi$
$840$	2.15406e7	−	3.01828e7i	1.05332	−	1.47591i
$841$	1.17782e7			0.574235
$842$			1.22759e7i			0.596726i
$843$	−1.41822e7	+	1.98722e7i	−0.687346	+	0.963112i
$844$			5.65925e6i			0.273466i
$845$		−	1.96294e6i		−	0.0945726i
$846$	−8.82487e6	−	2.56711e7i	−0.423918	−	1.23316i
$847$	−1.20670e7			−0.577949
$848$		−	2.30308e6i		−	0.109982i
$849$	386435.	−	541475.i	0.0183996	−	0.0257815i
$850$		−	6.22381e6i		−	0.295467i
$851$		−	2.31928e7i		−	1.09782i
$852$	−2.53397e6	+	3.55061e6i	−0.119592	+	0.167573i
$853$	3.63743e6			0.171168			0.0855840	−	0.996331i	$-0.472724\pi$
$853$	3.63743e6			0.171168			0.0855840	+	0.996331i	$0.472724\pi$
$854$		−	3.38759e7i		−	1.58945i
$855$	3.01685e7	−	1.03709e7i	1.41136	−	0.485178i
$856$			1.18099e7i			0.550887i
$857$	3.41664e7			1.58909			0.794543	−	0.607208i	$-0.207710\pi$
$857$	3.41664e7			1.58909			0.794543	+	0.607208i	$0.207710\pi$
$858$	−1.35102e7	+	1.89305e7i	−0.626531	+	0.877898i
$859$		−	418809.i		−	0.0193657i	−0.999953	−	0.00968285i	$-0.996918\pi$
$859$		−	418809.i		−	0.0193657i	0.999953	−	0.00968285i	$-0.00308219\pi$
$860$	−6.86608e6			−0.316565
$861$	2.10040e7	−	2.94309e7i	0.965595	−	1.35300i
$862$	−1.39907e7			−0.641313
$863$	−3.73889e7			−1.70890			−0.854448	−	0.519536i	$-0.826105\pi$
$863$	−3.73889e7			−1.70890			−0.854448	+	0.519536i	$0.826105\pi$
$864$	2.78724e6	−	9.38361e6i	0.127025	−	0.427647i
$865$		−	3.36992e7i		−	1.53137i
$866$	−2.96112e7			−1.34172
$867$	−5.95620e6	−	4.25077e6i	−0.269105	−	0.192053i
$868$			4.38446e6i			0.197523i
$869$	4.68225e7			2.10332
$870$	1.18408e7	+	8.45044e6i	0.530374	+	0.378513i
$871$	5.63254e6			0.251570
$872$			4.78787e7i			2.13231i
$873$	−3.78675e7	+	1.30176e7i	−1.68163	+	0.578088i
$874$	3.80559e7			1.68517
$875$		−	2.69658e7i		−	1.19067i
$876$	−5.27393e6	+	7.38986e6i	−0.232206	+	0.325369i
$877$	1.08416e7			0.475985			0.237992	−	0.971267i	$-0.423511\pi$
$877$	1.08416e7			0.475985			0.237992	+	0.971267i	$0.423511\pi$
$878$	2.53658e7			1.11048
$879$	9.92926e6	−	1.39129e7i	0.433456	−	0.607360i
$880$			2.21736e7i			0.965226i
$881$	2.18813e7			0.949803			0.474902	−	0.880039i	$-0.342484\pi$
$881$	2.18813e7			0.949803			0.474902	+	0.880039i	$0.342484\pi$
$882$	−7.83261e6	−	2.27847e7i	−0.339028	−	0.986216i
$883$	3.55544e6			0.153459			0.0767294	−	0.997052i	$-0.475552\pi$
$883$	3.55544e6			0.153459			0.0767294	+	0.997052i	$0.475552\pi$
$884$	−6.35661e6			−0.273586
$885$	2.64607e7	−	991778.i	1.13565	−	0.0425654i
$886$	−7.69985e6			−0.329532
$887$	3.20026e7			1.36576			0.682882	−	0.730529i	$-0.260726\pi$
$887$	3.20026e7			1.36576			0.682882	+	0.730529i	$0.260726\pi$
$888$	1.10716e7	−	1.55136e7i	0.471171	−	0.660207i
$889$	−4.98140e7			−2.11396
$890$		−	1.19555e7i		−	0.505931i
$891$	2.20396e7	−	1.71836e7i	0.930055	−	0.725136i
$892$	−2.23684e6			−0.0941290
$893$	−4.64415e7			−1.94885
$894$	2.36801e6	+	1.68998e6i	0.0990924	+	0.0707195i
$895$			3.26589e7i			1.36284i
$896$	1.88759e7			0.785486
$897$	−2.12766e7	+	2.98129e7i	−0.882920	+	1.23715i
$898$		−	3.07564e7i		−	1.27276i
$899$	−9.26793e6			−0.382458
$900$	524769.	+	1.52653e6i	0.0215954	+	0.0628201i
$901$	4.29251e6			0.176157
$902$			2.84627e7i			1.16482i
$903$	−2.57298e7	+	3.60527e7i	−1.05007	+	1.47136i
$904$	−1.88172e7			−0.765832
$905$		−	4.05595e7i		−	1.64616i
$906$	−326677.	+	457741.i	−0.0132220	+	0.0185268i
$907$	−2.22872e7			−0.899575			−0.449787	−	0.893136i	$-0.648500\pi$
$907$	−2.22872e7			−0.899575			−0.449787	+	0.893136i	$0.648500\pi$
$908$	5.73358e6			0.230787
$909$	1.82826e6	+	5.31832e6i	0.0733885	+	0.213484i
$910$	−3.83935e7			−1.53693
$911$		−	8.47511e6i		−	0.338337i	−0.985587	−	0.169169i	$-0.945892\pi$
$911$		−	8.47511e6i		−	0.338337i	0.985587	−	0.169169i	$-0.0541082\pi$
$912$	1.93368e7	+	1.38002e7i	0.769837	+	0.549411i
$913$	5.04842e6			0.200437
$914$		−	9.47668e6i		−	0.375224i
$915$	2.86554e7	+	2.04506e7i	1.13150	+	0.807518i
$916$		−	5.55368e6i		−	0.218697i
$917$	2.38431e7			0.936354
$918$	−2.48092e7	−	7.36915e6i	−0.971643	−	0.288610i
$919$			3.30291e7i			1.29005i	0.764160	+	0.645027i	$0.223154\pi$
$919$			3.30291e7i			1.29005i	−0.764160	+	0.645027i	$0.776846\pi$
$920$			4.59698e7i			1.79062i
$921$	−1.60502e7	−	1.14546e7i	−0.623494	−	0.444970i
$922$		−	5.08142e6i		−	0.196860i
$923$	2.43358e7			0.940248
$924$	−8.39543e6	−	5.99158e6i	−0.323491	−	0.230867i
$925$			5.70256e6i			0.219137i
$926$		−	1.80940e7i		−	0.693436i
$927$	3.73322e7	−	1.28336e7i	1.42687	−	0.490510i
$928$		−	7.63661e6i		−	0.291092i
$929$	−6.01346e6			−0.228605			−0.114302	−	0.993446i	$-0.536463\pi$
$929$	−6.01346e6			−0.228605			−0.114302	+	0.993446i	$0.536463\pi$
$930$	1.25662e7	+	8.96813e6i	0.476427	+	0.340012i
$931$	−4.12197e7			−1.55858
$932$	5.91386e6			0.223014
$933$	1.41797e7	−	1.98687e7i	0.533289	−	0.747247i
$934$	−1.00377e7			−0.376504
$935$	−4.13274e7			−1.54600
$936$	−2.84637e7	+	9.78486e6i	−1.06194	+	0.365060i
$937$			3.15171e7i			1.17273i	0.810047	+	0.586365i	$0.199441\pi$
$937$			3.15171e7i			1.17273i	−0.810047	+	0.586365i	$0.800559\pi$
$938$		−	8.46362e6i		−	0.314086i
$939$	4.99251e6	−	6.99553e6i	0.184780	−	0.258915i
$940$		−	1.04114e7i		−	0.384319i
$941$	3.65094e7			1.34410			0.672049	−	0.740506i	$-0.265414\pi$
$941$	3.65094e7			1.34410			0.672049	+	0.740506i	$0.265414\pi$
$942$	−1.02349e7	+	1.43412e7i	−0.375801	+	0.526574i
$943$			4.48247e7i			1.64149i
$944$	1.20478e7	+	1.56100e7i	0.440025	+	0.570129i
$945$	4.42256e7	+	1.31364e7i	1.61100	+	0.478518i
$946$		−	3.48666e7i		−	1.26672i
$947$			1.06042e6i			0.0384240i	0.999815	+	0.0192120i	$0.00611575\pi$
$947$			1.06042e6i			0.0384240i	−0.999815	+	0.0192120i	$0.993884\pi$
$948$	9.15398e6	+	6.53294e6i	0.330818	+	0.236095i
$949$	5.06500e7			1.82563
$950$	−9.35703e6			−0.336379
$951$	2.16623e7	−	3.03533e7i	0.776698	−	1.08831i
$952$			5.14663e7i			1.84048i
$953$			4.00099e7i			1.42704i	0.700637	+	0.713518i	$0.252899\pi$
$953$			4.00099e7i			1.42704i	−0.700637	+	0.713518i	$0.747101\pi$
$954$	3.56724e6	−	1.22630e6i	0.126900	−	0.0436239i
$955$		−	2.84049e7i		−	1.00782i
$956$		−	2.64875e6i		−	0.0937337i
$957$	1.26651e7	−	1.77464e7i	0.447021	−	0.626368i
$958$			4.76047e7i			1.67585i
$959$			1.92267e7i			0.675086i
$960$	−2.09658e7	+	2.93773e7i	−0.734231	+	1.02881i
$961$	1.87934e7			0.656444
$962$	−1.97338e7			−0.687501
$963$	−1.38955e7	+	4.77682e6i	−0.482847	+	0.165986i
$964$	−71348.1			−0.00247280
$965$		−	187452.i		−	0.00647996i
$966$	4.47977e7	+	3.19709e7i	1.54459	+	1.10233i
$967$		−	1.77979e7i		−	0.612071i	−0.952020	−	0.306036i	$-0.900997\pi$
$967$		−	1.77979e7i		−	0.612071i	0.952020	−	0.306036i	$-0.0990026\pi$
$968$	1.22933e7			0.421679
$969$	−2.57209e7	+	3.60403e7i	−0.879989	+	1.23304i
$970$	5.20360e7			1.77572
$971$			1.46117e7i			0.497340i	0.968588	+	0.248670i	$0.0799934\pi$
$971$			1.46117e7i			0.497340i	−0.968588	+	0.248670i	$0.920007\pi$
$972$	6.70636e6	−	284376.i	0.227678	−	0.00965443i
$973$	3.69446e7			1.25103
$974$	−3.73436e7			−1.26130
$975$	5.23140e6	−	7.33027e6i	0.176241	−	0.246950i
$976$			2.62161e7i			0.880933i
$977$	−4.46371e7			−1.49610			−0.748049	−	0.663644i	$-0.769009\pi$
$977$	−4.46371e7			−1.49610			−0.748049	+	0.663644i	$0.769009\pi$
$978$	−1.08414e6	−	773721.i	−0.0362442	−	0.0258665i
$979$	−1.79182e7			−0.597501
$980$		−	9.24080e6i		−	0.307358i
$981$	−5.63339e7	+	1.93657e7i	−1.86895	+	0.642481i
$982$			3.24995e7i			1.07547i
$983$	−2.69898e6			−0.0890872			−0.0445436	−	0.999007i	$-0.514183\pi$
$983$	−2.69898e6			−0.0890872			−0.0445436	+	0.999007i	$0.514183\pi$
$984$	−2.13981e7	+	2.99831e7i	−0.704509	+	0.987161i
$985$	−2.71199e7			−0.890629
$986$	−2.01904e7			−0.661381
$987$	−5.46689e7	−	3.90156e7i	−1.78627	−	1.27481i
$988$			9.55668e6i			0.311469i
$989$		−	5.49099e7i		−	1.78509i
$990$	−3.43446e7	+	1.18065e7i	−1.11371	+	0.382855i
$991$		−	5.71967e7i		−	1.85006i	−0.379888	−	0.925032i	$-0.624038\pi$
$991$		−	5.71967e7i		−	1.85006i	0.379888	−	0.925032i	$-0.375962\pi$
$992$		−	8.10444e6i		−	0.261483i
$993$	2.40476e7	+	1.71621e7i	0.773924	+	0.552328i
$994$		−	3.65678e7i		−	1.17390i
$995$		−	3.58114e7i		−	1.14674i
$996$	986985.	+	704384.i	0.0315255	+	0.0224989i
$997$	−5.54076e7			−1.76535			−0.882676	−	0.469983i	$-0.844260\pi$
$997$	−5.54076e7			−1.76535			−0.882676	+	0.469983i	$0.844260\pi$
$998$	1.96465e7			0.624393
$999$	2.27315e7	+	6.75198e6i	0.720632	+	0.214051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.d.b.176.30	yes	92
3.2	odd	2	inner	177.6.d.b.176.63	yes	92
59.58	odd	2	inner	177.6.d.b.176.64	yes	92
177.176	even	2	inner	177.6.d.b.176.29	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.d.b.176.29	✓	92	177.176	even	2	inner
177.6.d.b.176.30	yes	92	1.1	even	1	trivial
177.6.d.b.176.63	yes	92	3.2	odd	2	inner
177.6.d.b.176.64	yes	92	59.58	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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	177.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.97069 q^{2} +(12.6885 + 9.05545i) q^{3} -7.29225 q^{4} +63.5291i q^{5} +(-63.0708 - 45.0118i) q^{6} -191.713 q^{7} +195.310 q^{8} +(78.9977 + 229.801i) q^{9} +O(q^{10})\)	\(q-4.97069 q^{2} +(12.6885 + 9.05545i) q^{3} -7.29225 q^{4} +63.5291i q^{5} +(-63.0708 - 45.0118i) q^{6} -191.713 q^{7} +195.310 q^{8} +(78.9977 + 229.801i) q^{9} -315.783i q^{10} -473.280 q^{11} +(-92.5279 - 66.0346i) q^{12} +634.186i q^{13} +952.946 q^{14} +(-575.284 + 806.091i) q^{15} -737.471 q^{16} -1374.51i q^{17} +(-392.673 - 1142.27i) q^{18} -2066.47 q^{19} -463.270i q^{20} +(-2432.56 - 1736.05i) q^{21} +2352.53 q^{22} +3704.90 q^{23} +(2478.19 + 1768.62i) q^{24} -910.945 q^{25} -3152.34i q^{26} +(-1078.58 + 3631.19i) q^{27} +1398.02 q^{28} +2955.15i q^{29} +(2859.56 - 4006.83i) q^{30} +3136.19i q^{31} -2584.17 q^{32} +(-6005.23 - 4285.76i) q^{33} +6832.25i q^{34} -12179.4i q^{35} +(-576.071 - 1675.76i) q^{36} -6260.05i q^{37} +10271.8 q^{38} +(-5742.83 + 8046.88i) q^{39} +12407.8i q^{40} +12098.8i q^{41} +(12091.5 + 8629.35i) q^{42} -14820.9i q^{43} +3451.27 q^{44} +(-14599.0 + 5018.65i) q^{45} -18415.9 q^{46} +22473.8 q^{47} +(-9357.43 - 6678.13i) q^{48} +19946.9 q^{49} +4528.02 q^{50} +(12446.8 - 17440.5i) q^{51} -4624.64i q^{52} +3122.95i q^{53} +(5361.30 - 18049.5i) q^{54} -30067.0i q^{55} -37443.4 q^{56} +(-26220.5 - 18712.8i) q^{57} -14689.1i q^{58} +(-16336.6 - 21166.9i) q^{59} +(4195.12 - 5878.22i) q^{60} -35548.6i q^{61} -15589.0i q^{62} +(-15144.9 - 44055.8i) q^{63} +36444.2 q^{64} -40289.2 q^{65} +(29850.1 + 21303.2i) q^{66} -8881.53i q^{67} +10023.3i q^{68} +(47009.7 + 33549.5i) q^{69} +60539.8i q^{70} -38373.4i q^{71} +(15429.0 + 44882.3i) q^{72} -79866.2i q^{73} +31116.8i q^{74} +(-11558.6 - 8249.01i) q^{75} +15069.2 q^{76} +90733.9 q^{77} +(28545.8 - 39998.6i) q^{78} -98932.0 q^{79} -46850.9i q^{80} +(-46567.7 + 36307.5i) q^{81} -60139.2i q^{82} -10666.9 q^{83} +(17738.8 + 12659.7i) q^{84} +87321.3 q^{85} +73670.1i q^{86} +(-26760.2 + 37496.6i) q^{87} -92436.1 q^{88} +37859.7 q^{89} +(72567.2 - 24946.2i) q^{90} -121582. i q^{91} -27017.0 q^{92} +(-28399.6 + 39793.7i) q^{93} -111710. q^{94} -131281. i q^{95} +(-32789.3 - 23400.8i) q^{96} +164784. i q^{97} -99149.9 q^{98} +(-37388.0 - 108760. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9}+O(q^{10}) \) 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9	\( 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9} - 1244 q^{12} + 1116 q^{15} + 14724 q^{16} + 1784 q^{19} + 6388 q^{21} - 8140 q^{22} - 48208 q^{25} - 6458 q^{27} - 19092 q^{28} - 20832 q^{36} - 134984 q^{45} + 51180 q^{46} + 61720 q^{48} + 174556 q^{49} + 8332 q^{51} + 236784 q^{57} + 375208 q^{60} - 429890 q^{63} + 561472 q^{64} - 11596 q^{66} + 169948 q^{75} + 111488 q^{76} + 356264 q^{78} + 180260 q^{79} + 79554 q^{81} + 269308 q^{84} + 111028 q^{85} - 318764 q^{87} - 1242976 q^{88} - 513608 q^{94}+O(q^{100}) \) 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9 - 1244 * q^12 + 1116 * q^15 + 14724 * q^16 + 1784 * q^19 + 6388 * q^21 - 8140 * q^22 - 48208 * q^25 - 6458 * q^27 - 19092 * q^28 - 20832 * q^36 - 134984 * q^45 + 51180 * q^46 + 61720 * q^48 + 174556 * q^49 + 8332 * q^51 + 236784 * q^57 + 375208 * q^60 - 429890 * q^63 + 561472 * q^64 - 11596 * q^66 + 169948 * q^75 + 111488 * q^76 + 356264 * q^78 + 180260 * q^79 + 79554 * q^81 + 269308 * q^84 + 111028 * q^85 - 318764 * q^87 - 1242976 * q^88 - 513608 * q^94

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