LMFDB - Embedded newform 177.6.d.b.176.3

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			176.3
Character	$\chi$	$=$	177.176
Dual form			177.6.d.b.176.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.7490 q^{2} +(9.69295 + 12.2085i) q^{3} +83.5412 q^{4} +33.1454i q^{5} +(-104.190 - 131.229i) q^{6} -174.539 q^{7} -554.017 q^{8} +(-55.0934 + 236.672i) q^{9} +O(q^{10})$	\(q-10.7490 q^{2} +(9.69295 + 12.2085i) q^{3} +83.5412 q^{4} +33.1454i q^{5} +(-104.190 - 131.229i) q^{6} -174.539 q^{7} -554.017 q^{8} +(-55.0934 + 236.672i) q^{9} -356.281i q^{10} -67.7482 q^{11} +(809.761 + 1019.91i) q^{12} -762.395i q^{13} +1876.13 q^{14} +(-404.655 + 321.277i) q^{15} +3281.82 q^{16} -1054.79i q^{17} +(592.199 - 2543.99i) q^{18} +1517.46 q^{19} +2769.01i q^{20} +(-1691.80 - 2130.86i) q^{21} +728.226 q^{22} -1504.53 q^{23} +(-5370.06 - 6763.70i) q^{24} +2026.38 q^{25} +8194.99i q^{26} +(-3423.42 + 1621.45i) q^{27} -14581.2 q^{28} -4785.21i q^{29} +(4349.64 - 3453.41i) q^{30} +4004.32i q^{31} -17547.8 q^{32} +(-656.680 - 827.102i) q^{33} +11337.9i q^{34} -5785.18i q^{35} +(-4602.57 + 19771.9i) q^{36} -6219.64i q^{37} -16311.1 q^{38} +(9307.68 - 7389.86i) q^{39} -18363.2i q^{40} -14687.7i q^{41} +(18185.2 + 22904.6i) q^{42} +19978.1i q^{43} -5659.77 q^{44} +(-7844.60 - 1826.09i) q^{45} +16172.2 q^{46} +17461.3 q^{47} +(31810.5 + 40066.0i) q^{48} +13657.0 q^{49} -21781.6 q^{50} +(12877.4 - 10224.0i) q^{51} -63691.4i q^{52} +3262.05i q^{53} +(36798.4 - 17428.9i) q^{54} -2245.54i q^{55} +96697.9 q^{56} +(14708.6 + 18525.8i) q^{57} +51436.2i q^{58} +(-16303.5 + 21192.4i) q^{59} +(-33805.4 + 26839.9i) q^{60} -21833.5i q^{61} -43042.5i q^{62} +(9615.97 - 41308.6i) q^{63} +83602.8 q^{64} +25269.9 q^{65} +(7058.66 + 8890.53i) q^{66} -20335.2i q^{67} -88118.3i q^{68} +(-14583.3 - 18368.0i) q^{69} +62185.0i q^{70} +26490.5i q^{71} +(30522.7 - 131121. i) q^{72} +78490.3i q^{73} +66854.9i q^{74} +(19641.6 + 24739.0i) q^{75} +126770. q^{76} +11824.7 q^{77} +(-100048. + 79433.7i) q^{78} +78139.6 q^{79} +108777. i q^{80} +(-52978.4 - 26078.1i) q^{81} +157878. i q^{82} -36801.4 q^{83} +(-141335. - 178015. i) q^{84} +34961.4 q^{85} -214745. i q^{86} +(58420.0 - 46382.8i) q^{87} +37533.7 q^{88} +93253.5 q^{89} +(84321.7 + 19628.7i) q^{90} +133068. i q^{91} -125690. q^{92} +(-48886.7 + 38813.7i) q^{93} -187691. q^{94} +50296.7i q^{95} +(-170090. - 214231. i) q^{96} -42572.4i q^{97} -146799. q^{98} +(3732.48 - 16034.1i) 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 $

$2$	−10.7490			−1.90017			−0.950087	−	0.311984i	$-0.899006\pi$
$2$	−10.7490			−1.90017			−0.950087	+	0.311984i	$0.899006\pi$
$3$	9.69295	+	12.2085i	0.621803	+	0.783174i
$3$	9.69295	+	12.2085i	0.621803	+	0.783174i
$4$	83.5412			2.61066
$5$			33.1454i			0.592924i	0.955045	+	0.296462i	$0.0958068\pi$
$5$			33.1454i			0.592924i	−0.955045	+	0.296462i	$0.904193\pi$
$6$	−104.190	−	131.229i	−1.18153	−	1.48817i
$7$	−174.539			−1.34632			−0.673160	−	0.739497i	$-0.735063\pi$
$7$	−174.539			−1.34632			−0.673160	+	0.739497i	$0.735063\pi$
$8$	−554.017			−3.06054
$9$	−55.0934	+	236.672i	−0.226722	+	0.973960i
$10$		−	356.281i		−	1.12666i
$11$	−67.7482			−0.168817			−0.0844085	−	0.996431i	$-0.526900\pi$
$11$	−67.7482			−0.168817			−0.0844085	+	0.996431i	$0.526900\pi$
$12$	809.761	+	1019.91i	1.62332	+	2.04460i
$13$		−	762.395i		−	1.25119i	−0.780150	−	0.625593i	$-0.784857\pi$
$13$		−	762.395i		−	1.25119i	0.780150	−	0.625593i	$-0.215143\pi$
$14$	1876.13			2.55824
$15$	−404.655	+	321.277i	−0.464362	+	0.368682i
$16$	3281.82			3.20490
$17$		−	1054.79i		−	0.885203i	−0.896718	−	0.442602i	$-0.854056\pi$
$17$		−	1054.79i		−	0.885203i	0.896718	−	0.442602i	$-0.145944\pi$
$18$	592.199	−	2543.99i	0.430811	−	1.85069i
$19$	1517.46			0.964344			0.482172	−	0.876077i	$-0.339848\pi$
$19$	1517.46			0.964344			0.482172	+	0.876077i	$0.339848\pi$
$20$			2769.01i			1.54792i
$21$	−1691.80	−	2130.86i	−0.837146	−	1.05440i
$22$	728.226			0.320782
$23$	−1504.53			−0.593036			−0.296518	−	0.955027i	$-0.595826\pi$
$23$	−1504.53			−0.593036			−0.296518	+	0.955027i	$0.595826\pi$
$24$	−5370.06	−	6763.70i	−1.90306	−	2.39694i
$25$	2026.38			0.648442
$26$			8194.99i			2.37747i
$27$	−3423.42	+	1621.45i	−0.903756	+	0.428049i
$28$	−14581.2			−3.51479
$29$		−	4785.21i		−	1.05659i	−0.849061	−	0.528294i	$-0.822832\pi$
$29$		−	4785.21i		−	1.05659i	0.849061	−	0.528294i	$-0.177168\pi$
$30$	4349.64	−	3453.41i	0.882369	−	0.700560i
$31$			4004.32i			0.748385i	0.927351	+	0.374192i	$0.122080\pi$
$31$			4004.32i			0.748385i	−0.927351	+	0.374192i	$0.877920\pi$
$32$	−17547.8			−3.02933
$33$	−656.680	−	827.102i	−0.104971	−	0.132213i
$34$			11337.9i			1.68204i
$35$		−	5785.18i		−	0.798265i
$36$	−4602.57	+	19771.9i	−0.591894	+	2.54268i
$37$		−	6219.64i		−	0.746897i	−0.927651	−	0.373449i	$-0.878175\pi$
$37$		−	6219.64i		−	0.746897i	0.927651	−	0.373449i	$-0.121825\pi$
$38$	−16311.1			−1.83242
$39$	9307.68	−	7389.86i	0.979895	−	0.777991i
$40$		−	18363.2i		−	1.81467i
$41$		−	14687.7i		−	1.36457i	−0.731088	−	0.682283i	$-0.760987\pi$
$41$		−	14687.7i		−	1.36457i	0.731088	−	0.682283i	$-0.239013\pi$
$42$	18185.2	+	22904.6i	1.59072	+	2.00355i
$43$			19978.1i			1.64772i	0.566795	+	0.823859i	$0.308183\pi$
$43$			19978.1i			1.64772i	−0.566795	+	0.823859i	$0.691817\pi$
$44$	−5659.77			−0.440724
$45$	−7844.60	−	1826.09i	−0.577484	−	0.134429i
$46$	16172.2			1.12687
$47$	17461.3			1.15300			0.576502	−	0.817096i	$-0.304417\pi$
$47$	17461.3			1.15300			0.576502	+	0.817096i	$0.304417\pi$
$48$	31810.5	+	40066.0i	1.99282	+	2.50999i
$49$	13657.0			0.812578
$50$	−21781.6			−1.23215
$51$	12877.4	−	10224.0i	0.693268	−	0.550422i
$52$		−	63691.4i		−	3.26642i
$53$			3262.05i			0.159515i	0.996814	+	0.0797574i	$0.0254146\pi$
$53$			3262.05i			0.159515i	−0.996814	+	0.0797574i	$0.974585\pi$
$54$	36798.4	−	17428.9i	1.71729	−	0.813367i
$55$		−	2245.54i		−	0.100096i
$56$	96697.9			4.12047
$57$	14708.6	+	18525.8i	0.599632	+	0.755248i
$58$			51436.2i			2.00770i
$59$	−16303.5	+	21192.4i	−0.609749	+	0.792594i
$59$	−16303.5	+	21192.4i	−0.609749	+	0.792594i
$60$	−33805.4	+	26839.9i	−1.21229	+	0.962504i
$61$		−	21833.5i		−	0.751276i	−0.926766	−	0.375638i	$-0.877424\pi$
$61$		−	21833.5i		−	0.751276i	0.926766	−	0.375638i	$-0.122576\pi$
$62$		−	43042.5i		−	1.42206i
$63$	9615.97	−	41308.6i	0.305240	−	1.31126i
$64$	83602.8			2.55136
$65$	25269.9			0.741857
$66$	7058.66	+	8890.53i	0.199463	+	0.251228i
$67$		−	20335.2i		−	0.553427i	−0.960952	−	0.276714i	$-0.910755\pi$
$67$		−	20335.2i		−	0.553427i	0.960952	−	0.276714i	$-0.0892454\pi$
$68$		−	88118.3i		−	2.31097i
$69$	−14583.3	−	18368.0i	−0.368752	−	0.464450i
$70$			62185.0i			1.51684i
$71$			26490.5i			0.623655i	0.950139	+	0.311827i	$0.100941\pi$
$71$			26490.5i			0.623655i	−0.950139	+	0.311827i	$0.899059\pi$
$72$	30522.7	−	131121.i	0.693892	−	2.98085i
$73$			78490.3i			1.72389i	0.507003	+	0.861944i	$0.330753\pi$
$73$			78490.3i			1.72389i	−0.507003	+	0.861944i	$0.669247\pi$
$74$			66854.9i			1.41923i
$75$	19641.6	+	24739.0i	0.403203	+	0.507842i
$76$	126770.			2.51758
$77$	11824.7			0.227282
$78$	−100048.	+	79433.7i	−1.86197	+	1.47832i
$79$	78139.6			1.40865			0.704326	−	0.709877i	$-0.251249\pi$
$79$	78139.6			1.40865			0.704326	+	0.709877i	$0.251249\pi$
$80$			108777.i			1.90026i
$81$	−52978.4	−	26078.1i	−0.897194	−	0.441636i
$82$			157878.i			2.59291i
$83$	−36801.4			−0.586366			−0.293183	−	0.956056i	$-0.594715\pi$
$83$	−36801.4			−0.586366			−0.293183	+	0.956056i	$0.594715\pi$
$84$	−141335.	−	178015.i	−2.18551	−	2.75269i
$85$	34961.4			0.524858
$86$		−	214745.i		−	3.13095i
$87$	58420.0	−	46382.8i	0.827492	−	0.656990i
$88$	37533.7			0.516671
$89$	93253.5			1.24793			0.623965	−	0.781453i	$-0.285521\pi$
$89$	93253.5			1.24793			0.623965	+	0.781453i	$0.285521\pi$
$90$	84321.7	+	19628.7i	1.09732	+	0.255438i
$91$			133068.i			1.68450i
$92$	−125690.			−1.54822
$93$	−48886.7	+	38813.7i	−0.586115	+	0.465348i
$94$	−187691.			−2.19091
$95$			50296.7i			0.571782i
$96$	−170090.	−	214231.i	−1.88365	−	2.37249i
$97$		−	42572.4i		−	0.459408i	−0.973261	−	0.229704i	$-0.926224\pi$
$97$		−	42572.4i		−	0.459408i	0.973261	−	0.229704i	$-0.0737759\pi$
$98$	−146799.			−1.54404
$99$	3732.48	−	16034.1i	0.0382745	−	0.164421i
$100$	169286.			1.69286
$101$	130012.			1.26817			0.634086	−	0.773262i	$-0.281376\pi$
$101$	130012.			1.26817			0.634086	+	0.773262i	$0.281376\pi$
$102$	−138419.	+	109898.i	−1.31733	+	1.04590i
$103$		−	183784.i		−	1.70693i	−0.521150	−	0.853465i	$-0.674497\pi$
$103$		−	183784.i		−	1.70693i	0.521150	−	0.853465i	$-0.325503\pi$
$104$			422380.i			3.82931i
$105$	70628.2	−	56075.5i	0.625180	−	0.496364i
$106$		−	35063.8i		−	0.303106i
$107$		−	142238.i		−	1.20104i	−0.799610	−	0.600519i	$-0.794961\pi$
$107$		−	142238.i		−	1.20104i	0.799610	−	0.600519i	$-0.205039\pi$
$108$	−285997.	+	135458.i	−2.35940	+	1.11749i
$109$			29378.8i			0.236847i	0.992963	+	0.118424i	$0.0377841\pi$
$109$			29378.8i			0.236847i	−0.992963	+	0.118424i	$0.962216\pi$
$110$			24137.4i			0.190199i
$111$	75932.2	−	60286.6i	0.584950	−	0.464423i
$112$	−572807.			−4.31482
$113$	−56037.4			−0.412840			−0.206420	−	0.978464i	$-0.566181\pi$
$113$	−56037.4			−0.412840			−0.206420	+	0.978464i	$0.566181\pi$
$114$	−158103.	−	199134.i	−1.13941	−	1.43510i
$115$		−	49868.3i		−	0.351625i
$116$		−	399762.i		−	2.75840i
$117$	180438.	+	42002.9i	1.21860	+	0.283671i
$118$	175247.	−	227798.i	1.15863	−	1.50607i
$119$			184102.i			1.19177i
$120$	224186.	−	177993.i	1.42120	−	1.12837i
$121$	−156461.			−0.971501
$122$			234689.i			1.42756i
$123$	179314.	−	142367.i	1.06869	−	0.848491i
$124$			334526.i			1.95378i
$125$			170745.i			0.977400i
$126$	−103362.	+	444027.i	−0.580009	+	2.49163i
$127$	339103.			1.86562			0.932808	−	0.360374i	$-0.117351\pi$
$127$	339103.			1.86562			0.932808	+	0.360374i	$0.117351\pi$
$128$	−337120.			−1.81869
$129$	−243902.	+	193647.i	−1.29045	+	1.02456i
$130$	−271627.			−1.40966
$131$	349637.			1.78008			0.890039	−	0.455884i	$-0.150677\pi$
$131$	349637.			1.78008			0.890039	+	0.455884i	$0.150677\pi$
$132$	−54859.9	−	69097.1i	−0.274044	−	0.345164i
$133$	−264856.			−1.29832
$134$			218583.i			1.05161i
$135$	−53743.5	−	113471.i	−0.253800	−	0.535858i
$136$			584371.i			2.70920i
$137$		−	120090.i		−	0.546643i	−0.961923	−	0.273322i	$-0.911878\pi$
$137$		−	120090.i		−	0.546643i	0.961923	−	0.273322i	$-0.0881223\pi$
$138$	156756.	+	197438.i	0.700693	+	0.882537i
$139$	20574.2			0.0903204			0.0451602	−	0.998980i	$-0.485620\pi$
$139$	20574.2			0.0903204			0.0451602	+	0.998980i	$0.485620\pi$
$140$		−	483301.i		−	2.08400i
$141$	169251.	+	213175.i	0.716942	+	0.903003i
$142$		−	284747.i		−	1.18505i
$143$			51650.9i			0.211221i
$144$	−180807.	+	776715.i	−0.726621	+	3.12145i
$145$	158608.			0.626476
$146$		−	843694.i		−	3.27569i
$147$	132377.	+	166731.i	0.505263	+	0.636389i
$148$		−	519596.i		−	1.94990i
$149$	−172905.			−0.638031			−0.319015	−	0.947750i	$-0.603352\pi$
$149$	−172905.			−0.638031			−0.319015	+	0.947750i	$0.603352\pi$
$150$	−211128.	−	265920.i	−0.766156	−	0.964989i
$151$			115365.i			0.411747i	0.978579	+	0.205873i	$0.0660035\pi$
$151$			115365.i			0.411747i	−0.978579	+	0.205873i	$0.933996\pi$
$152$	−840697.			−2.95142
$153$	249639.	+	58111.9i	0.862152	+	0.200695i
$154$	−127104.			−0.431875
$155$	−132725.			−0.443735
$156$	777575.	−	617358.i	2.55818	−	2.03107i
$157$		−	66650.4i		−	0.215801i	−0.994162	−	0.107901i	$-0.965587\pi$
$157$		−	66650.4i		−	0.215801i	0.994162	−	0.107901i	$-0.0344128\pi$
$158$	−839924.			−2.67668
$159$	−39824.7	+	31618.9i	−0.124928	+	0.0991868i
$160$		−	581628.i		−	1.79616i
$161$	262600.			0.798417
$162$	569466.	+	280314.i	1.70483	+	0.839185i
$163$	−416761.			−1.22862			−0.614311	−	0.789064i	$-0.710566\pi$
$163$	−416761.			−1.22862			−0.614311	+	0.789064i	$0.710566\pi$
$164$		−	1.22703e6i		−	3.56242i
$165$	27414.6	−	21765.9i	0.0783922	−	0.0622397i
$166$	395578.			1.11420
$167$		−	650842.i		−	1.80586i	−0.429785	−	0.902931i	$-0.641411\pi$
$167$		−	650842.i		−	1.80586i	0.429785	−	0.902931i	$-0.358589\pi$
$168$	937288.	+	1.18053e6i	2.56212	+	3.22704i
$169$	−209953.			−0.565465
$170$	−375801.			−0.997322
$171$	−83601.7	+	359139.i	−0.218638	+	0.939232i
$172$			1.66899e6i			4.30164i
$173$	203386.			0.516660			0.258330	−	0.966057i	$-0.416828\pi$
$173$	203386.			0.516660			0.258330	+	0.966057i	$0.416828\pi$
$174$	−627958.	+	498569.i	−1.57238	+	1.24840i
$175$	−353683.			−0.873010
$176$	−222337.			−0.541042
$177$	−416756.	+	6376.39i	−0.999883	+	0.0152983i
$178$	−1.00238e6			−2.37128
$179$	465710.			1.08638			0.543192	−	0.839609i	$-0.317216\pi$
$179$	465710.			1.08638			0.543192	+	0.839609i	$0.317216\pi$
$180$	−655348.	−	152554.i	−1.50762	−	0.350948i
$181$	863836.			1.95990			0.979952	−	0.199234i	$-0.0638455\pi$
$181$	863836.			1.95990			0.979952	+	0.199234i	$0.0638455\pi$
$182$		−	1.43035e6i		−	3.20084i
$183$	266554.	−	211631.i	0.588380	−	0.467146i
$184$	833536.			1.81501
$185$	206153.			0.442853
$186$	525483.	−	417209.i	1.11372	−	0.884243i
$187$			71460.0i			0.149437i
$188$	1.45874e6			3.01011
$189$	597522.	−	283006.i	1.21674	−	0.576290i
$190$		−	540640.i		−	1.08649i
$191$	560153.			1.11102			0.555512	−	0.831509i	$-0.312522\pi$
$191$	560153.			1.11102			0.555512	+	0.831509i	$0.312522\pi$
$192$	810358.	+	1.02066e6i	1.58644	+	1.99816i
$193$	27809.8			0.0537408			0.0268704	−	0.999639i	$-0.491446\pi$
$193$	27809.8			0.0537408			0.0268704	+	0.999639i	$0.491446\pi$
$194$			457611.i			0.872956i
$195$	244940.	+	308507.i	0.461289	+	0.581003i
$196$	1.14092e6			2.12137
$197$		−	151601.i		−	0.278316i	−0.990270	−	0.139158i	$-0.955560\pi$
$197$		−	151601.i		−	0.278316i	0.990270	−	0.139158i	$-0.0444395\pi$
$198$	−40120.4	+	172351.i	−0.0727282	+	0.312428i
$199$	72452.3			0.129694			0.0648469	−	0.997895i	$-0.479344\pi$
$199$	72452.3			0.129694			0.0648469	+	0.997895i	$0.479344\pi$
$200$	−1.12265e6			−1.98458
$201$	248261.	−	197108.i	0.433430	−	0.344123i
$202$	−1.39750e6			−2.40975
$203$			835207.i			1.42251i
$204$	1.07579e6	−	854127.i	1.80989	−	1.43697i
$205$	486831.			0.809083
$206$			1.97550e6i			3.24346i
$207$	82889.7	−	356080.i	0.134454	−	0.577594i
$208$		−	2.50204e6i		−	4.00993i
$209$	−102805.			−0.162798
$210$	−759184.	+	602756.i	−1.18795	+	0.943178i
$211$		−	923790.i		−	1.42846i	−0.699913	−	0.714228i	$-0.746778\pi$
$211$		−	923790.i		−	1.42846i	0.699913	−	0.714228i	$-0.253222\pi$
$212$			272516.i			0.416440i
$213$	−323408.	+	256771.i	−0.488430	+	0.387790i
$214$			1.52892e6i			2.28218i
$215$	−662182.			−0.976971
$216$	1.89664e6	−	898309.i	2.76598	−	1.31006i
$217$		−	698912.i		−	1.00757i
$218$		−	315793.i		−	0.450051i
$219$	−958247.	+	760803.i	−1.35010	+	1.07192i
$220$		−	187596.i		−	0.261316i
$221$	−804166.			−1.10755
$222$	−816197.	+	648022.i	−1.11151	+	0.882485i
$223$	−290482.			−0.391162			−0.195581	−	0.980688i	$-0.562659\pi$
$223$	−290482.			−0.391162			−0.195581	+	0.980688i	$0.562659\pi$
$224$	3.06278e6			4.07845
$225$	−111640.	+	479588.i	−0.147016	+	0.631556i
$226$	602346.			0.784468
$227$	−1.29140e6			−1.66340			−0.831700	−	0.555225i	$-0.812632\pi$
$227$	−1.29140e6			−1.66340			−0.831700	+	0.555225i	$0.812632\pi$
$228$	1.22878e6	+	1.54767e6i	1.56544	+	1.97170i
$229$		−	1.12370e6i		−	1.41600i	−0.706214	−	0.707998i	$-0.749599\pi$
$229$		−	1.12370e6i		−	1.41600i	0.706214	−	0.707998i	$-0.250401\pi$
$230$			536035.i			0.668150i
$231$	114617.	+	144362.i	0.141324	+	0.178001i
$232$			2.65109e6i			3.23373i
$233$	−606409.			−0.731772			−0.365886	−	0.930660i	$-0.619234\pi$
$233$	−606409.			−0.731772			−0.365886	+	0.930660i	$0.619234\pi$
$234$	−1.93953e6	−	451490.i	−2.31556	−	0.539024i
$235$			578761.i			0.683644i
$236$	−1.36202e6	+	1.77044e6i	−1.59185	+	2.06920i
$237$	757404.	+	953965.i	0.875904	+	1.10322i
$238$		−	1.97892e6i		−	2.26457i
$239$			819859.i			0.928420i	0.885725	+	0.464210i	$0.153662\pi$
$239$			819859.i			0.928420i	−0.885725	+	0.464210i	$0.846338\pi$
$240$	−1.32800e6	+	1.05437e6i	−1.48824	+	1.18159i
$241$	−1.16362e6			−1.29053			−0.645266	−	0.763958i	$-0.723253\pi$
$241$	−1.16362e6			−1.29053			−0.645266	+	0.763958i	$0.723253\pi$
$242$	1.68180e6			1.84602
$243$	−195143.	−	899560.i	−0.212001	−	0.977269i
$244$		−	1.82400e6i		−	1.96133i
$245$			452667.i			0.481797i
$246$	−1.92745e6	+	1.53031e6i	−2.03070	+	1.61228i
$247$		−	1.15690e6i		−	1.20657i
$248$		−	2.21847e6i		−	2.29046i
$249$	−356714.	−	449288.i	−0.364604	−	0.459226i
$250$		−	1.83534e6i		−	1.85723i
$251$			1.79587e6i			1.79925i	0.436663	+	0.899625i	$0.356160\pi$
$251$			1.79587e6i			1.79925i	−0.436663	+	0.899625i	$0.643840\pi$
$252$	803330.	−	3.45097e6i	0.796879	−	3.42326i
$253$	101929.			0.100115
$254$	−3.64502e6			−3.54500
$255$	338879.	+	426825.i	0.326358	+	0.411055i
$256$	948411.			0.904476
$257$		−	1.48356e6i		−	1.40111i	−0.713599	−	0.700554i	$-0.752936\pi$
$257$		−	1.48356e6i		−	1.40111i	0.713599	−	0.700554i	$-0.247064\pi$
$258$	2.62170e6	−	2.08151e6i	2.45208	−	1.94684i
$259$			1.08557e6i			1.00556i
$260$	2.11108e6			1.93674
$261$	1.13253e6	+	263633.i	1.02907	+	0.239552i
$262$	−3.75825e6			−3.38246
$263$		−	485145.i		−	0.432496i	−0.976338	−	0.216248i	$-0.930618\pi$
$263$		−	485145.i		−	0.432496i	0.976338	−	0.216248i	$-0.0693820\pi$
$264$	363812.	+	458229.i	0.321268	+	0.404643i
$265$	−108122.			−0.0945801
$266$	2.84694e6			2.46703
$267$	903901.	+	1.13848e6i	0.775966	+	0.977345i
$268$		−	1.69882e6i		−	1.44481i
$269$	324626.			0.273528			0.136764	−	0.990604i	$-0.456330\pi$
$269$	324626.			0.273528			0.136764	+	0.990604i	$0.456330\pi$
$270$	577690.	+	1.21970e6i	0.482265	+	1.01822i
$271$	−1.01698e6			−0.841179			−0.420589	−	0.907251i	$-0.638177\pi$
$271$	−1.01698e6			−0.841179			−0.420589	+	0.907251i	$0.638177\pi$
$272$		−	3.46163e6i		−	2.83699i
$273$	−1.62456e6	+	1.28982e6i	−1.31925	+	1.04742i
$274$			1.29084e6i			1.03872i
$275$	−137284.			−0.109468
$276$	−1.21831e6	−	1.53449e6i	−0.962687	−	1.21252i
$277$	−49056.0			−0.0384143			−0.0192072	−	0.999816i	$-0.506114\pi$
$277$	−49056.0			−0.0384143			−0.0192072	+	0.999816i	$0.506114\pi$
$278$	−221152.			−0.171624
$279$	−947712.	−	220612.i	−0.728897	−	0.169675i
$280$			3.20509e6i			2.44312i
$281$		−	720981.i		−	0.544701i	−0.962198	−	0.272350i	$-0.912199\pi$
$281$		−	720981.i		−	0.544701i	0.962198	−	0.272350i	$-0.0878010\pi$
$282$	−1.81928e6	−	2.29142e6i	−1.36231	−	1.71586i
$283$		−	1.88644e6i		−	1.40016i	−0.714066	−	0.700079i	$-0.753148\pi$
$283$		−	1.88644e6i		−	1.40016i	0.714066	−	0.700079i	$-0.246852\pi$
$284$			2.21305e6i			1.62815i
$285$	−614046.	+	487524.i	−0.447805	+	0.355536i
$286$		−	555196.i		−	0.401357i
$287$			2.56358e6i			1.83714i
$288$	966766.	−	4.15307e6i	0.686815	−	2.95045i
$289$	307278.			0.216415
$290$	−1.70488e6			−1.19041
$291$	519744.	−	412652.i	0.359796	−	0.285661i
$292$			6.55718e6i			4.50049i
$293$			645578.i			0.439319i	0.975577	+	0.219659i	$0.0704946\pi$
$293$			645578.i			0.439319i	−0.975577	+	0.219659i	$0.929505\pi$
$294$	−1.42292e6	−	1.79219e6i	−0.960089	−	1.20925i
$295$	−702433.	−	540387.i	−0.469948	−	0.361535i
$296$			3.44579e6i			2.28591i
$297$	231931.	−	109850.i	0.152569	−	0.0722619i
$298$	1.85856e6			1.21237
$299$			1.14705e6i			0.741999i
$300$	1.64088e6	+	2.06673e6i	1.05263	+	1.32581i
$301$		−	3.48696e6i		−	2.21836i
$302$		−	1.24006e6i		−	0.782391i
$303$	1.26020e6	+	1.58724e6i	0.788554	+	0.993199i
$304$	4.98001e6			3.09063
$305$	723682.			0.445449
$306$	−2.68337e6	−	624645.i	−1.63824	−	0.381355i
$307$	−820548.			−0.496888			−0.248444	−	0.968646i	$-0.579919\pi$
$307$	−820548.			−0.496888			−0.248444	+	0.968646i	$0.579919\pi$
$308$	987852.			0.593356
$309$	2.24373e6	−	1.78141e6i	1.33682	−	1.06137i
$310$	1.42666e6			0.843174
$311$		−	1.29992e6i		−	0.762107i	−0.924553	−	0.381053i	$-0.875561\pi$
$311$		−	1.29992e6i		−	0.762107i	0.924553	−	0.381053i	$-0.124439\pi$
$312$	−5.15661e6	+	4.09411e6i	−2.99901	+	2.38107i
$313$			769798.i			0.444136i	0.975031	+	0.222068i	$0.0712807\pi$
$313$			769798.i			0.444136i	−0.975031	+	0.222068i	$0.928719\pi$
$314$			716426.i			0.410060i
$315$	1.36919e6	+	318725.i	0.777478	+	0.180984i
$316$	6.52788e6			3.67752
$317$		−	1.00921e6i		−	0.564068i	−0.959404	−	0.282034i	$-0.908991\pi$
$317$		−	1.00921e6i		−	0.564068i	0.959404	−	0.282034i	$-0.0910092\pi$
$318$	428076.	−	339872.i	0.237385	−	0.188472i
$319$			324189.i			0.178370i
$320$			2.77105e6i			1.51276i
$321$	1.73651e6	−	1.37871e6i	0.940622	−	0.746810i
$322$	−2.82269e6			−1.51713
$323$		−	1.60059e6i		−	0.853640i
$324$	−4.42588e6	−	2.17860e6i	−2.34227	−	1.15296i
$325$		−	1.54490e6i		−	0.811321i
$326$	4.47977e6			2.33460
$327$	−358670.	+	284767.i	−0.185492	+	0.147272i
$328$			8.13725e6i			4.17631i
$329$	−3.04768e6			−1.55231
$330$	−294680.	+	233962.i	−0.148959	+	0.118266i
$331$	1.87477e6			0.940539			0.470270	−	0.882523i	$-0.344157\pi$
$331$	1.87477e6			0.940539			0.470270	+	0.882523i	$0.344157\pi$
$332$	−3.07443e6			−1.53080
$333$	1.47202e6	+	342661.i	0.727447	+	0.169338i
$334$			6.99591e6i			3.43145i
$335$	674018.			0.328140
$336$	−5.55219e6	−	6.99309e6i	−2.68297	−	3.37926i
$337$			1.12324e6i			0.538763i	0.963034	+	0.269381i	$0.0868192\pi$
$337$			1.12324e6i			0.538763i	−0.963034	+	0.269381i	$0.913181\pi$
$338$	2.25679e6			1.07448
$339$	−543167.	−	684130.i	−0.256705	−	0.323325i
$340$	2.92072e6			1.37023
$341$		−	271286.i		−	0.126340i
$342$	898636.	−	3.86039e6i	0.415450	−	1.78470i
$343$	549800.			0.252330
$344$		−	1.10682e7i		−	5.04291i
$345$	608816.	−	483371.i	0.275384	−	0.218642i
$346$	−2.18620e6			−0.981745
$347$	827946.			0.369129			0.184565	−	0.982820i	$-0.440913\pi$
$347$	827946.			0.369129			0.184565	+	0.982820i	$0.440913\pi$
$348$	4.88048e6	−	3.87487e6i	2.16030	−	1.71518i
$349$		−	2.51515e6i		−	1.10535i	−0.833396	−	0.552676i	$-0.813607\pi$
$349$		−	2.51515e6i		−	1.10535i	0.833396	−	0.552676i	$-0.186393\pi$
$350$	3.80174e6			1.65887
$351$	1.23618e6	+	2.61000e6i	0.535568	+	1.13077i
$352$	1.18883e6			0.511402
$353$	3.47327e6			1.48355			0.741775	−	0.670649i	$-0.233984\pi$
$353$	3.47327e6			1.48355			0.741775	+	0.670649i	$0.233984\pi$
$354$	4.47972e6	−	68539.9i	1.89995	−	0.0290694i
$355$	−878039.			−0.369780
$356$	7.79051e6			3.25792
$357$	−2.24760e6	+	1.78449e6i	−0.933360	+	0.741044i
$358$	−5.00592e6			−2.06432
$359$		−	1.49142e6i		−	0.610751i	−0.952232	−	0.305376i	$-0.901218\pi$
$359$		−	1.49142e6i		−	0.610751i	0.952232	−	0.305376i	$-0.0987820\pi$
$360$	4.34605e6	+	1.01169e6i	1.76741	+	0.411425i
$361$	−173429.			−0.0700413
$362$	−9.28538e6			−3.72416
$363$	−1.51657e6	−	1.91015e6i	−0.604082	−	0.760854i
$364$			1.11167e7i			4.39765i
$365$	−2.60160e6			−1.02213
$366$	−2.86519e6	+	2.27483e6i	−1.11802	+	0.887659i
$367$		−	3.83867e6i		−	1.48770i	−0.668346	−	0.743850i	$-0.732997\pi$
$367$		−	3.83867e6i		−	1.48770i	0.668346	−	0.743850i	$-0.267003\pi$
$368$	−4.93760e6			−1.90062
$369$	3.47617e6	+	809196.i	1.32903	+	0.309377i
$370$	−2.21594e6			−0.841498
$371$		−	569356.i		−	0.214758i
$372$	−4.08405e6	+	3.24255e6i	−1.53015	+	1.21487i
$373$	2.13313e6			0.793862			0.396931	−	0.917848i	$-0.370075\pi$
$373$	2.13313e6			0.793862			0.396931	+	0.917848i	$0.370075\pi$
$374$		−	768125.i		−	0.283957i
$375$	−2.08453e6	+	1.65502e6i	−0.765474	+	0.607750i
$376$	−9.67384e6			−3.52882
$377$	−3.64822e6			−1.32199
$378$	−6.42277e6	+	3.04204e6i	−2.31203	+	1.09505i
$379$	−341863.			−0.122252			−0.0611258	−	0.998130i	$-0.519469\pi$
$379$	−341863.			−0.122252			−0.0611258	+	0.998130i	$0.519469\pi$
$380$			4.20185e6i			1.49273i
$381$	3.28691e6	+	4.13993e6i	1.16005	+	1.46110i
$382$	−6.02109e6			−2.11114
$383$		−	2.17138e6i		−	0.756378i	−0.925728	−	0.378189i	$-0.876547\pi$
$383$		−	2.17138e6i		−	0.756378i	0.925728	−	0.378189i	$-0.123453\pi$
$384$	−3.26768e6	−	4.11571e6i	−1.13087	−	1.42435i
$385$			391936.i			0.134761i
$386$	−298928.			−0.102117
$387$	−4.72826e6	−	1.10066e6i	−1.60481	−	0.373573i
$388$		−	3.55655e6i		−	1.19936i
$389$			1.49102e6i			0.499586i	0.968299	+	0.249793i	$0.0803625\pi$
$389$			1.49102e6i			0.499586i	−0.968299	+	0.249793i	$0.919638\pi$
$390$	−2.63286e6	−	3.31615e6i	−0.876530	−	1.10401i
$391$			1.58696e6i			0.524958i
$392$	−7.56621e6			−2.48693
$393$	3.38902e6	+	4.26853e6i	1.10686	+	1.39411i
$394$			1.62957e6i			0.528848i
$395$			2.58997e6i			0.835223i
$396$	311816.	−	1.33951e6i	0.0999218	−	0.429248i
$397$			89427.3i			0.0284770i	0.999899	+	0.0142385i	$0.00453240\pi$
$397$			89427.3i			0.0284770i	−0.999899	+	0.0142385i	$0.995468\pi$
$398$	−778790.			−0.246441
$399$	−2.56723e6	−	3.23348e6i	−0.807296	−	1.01681i
$400$	6.65021e6			2.07819
$401$	−1.56878e6			−0.487194			−0.243597	−	0.969877i	$-0.578327\pi$
$401$	−1.56878e6			−0.487194			−0.243597	+	0.969877i	$0.578327\pi$
$402$	−2.66856e6	+	2.11871e6i	−0.823592	+	0.653894i
$403$	3.05288e6			0.936368
$404$	1.08613e7			3.31077
$405$	864372.	−	1.75599e6i	0.261856	−	0.531968i
$406$		−	8.97765e6i		−	2.70301i
$407$			421369.i			0.126089i
$408$	−7.13428e6	+	5.66428e6i	−2.12178	+	1.68459i
$409$		−	5.10075e6i		−	1.50774i	−0.657025	−	0.753869i	$-0.728185\pi$
$409$		−	5.10075e6i		−	1.50774i	0.657025	−	0.753869i	$-0.271815\pi$
$410$	−5.23295e6			−1.53740
$411$	1.46611e6	−	1.16402e6i	0.428117	−	0.339904i
$412$		−	1.53536e7i		−	4.45622i
$413$	2.84561e6	−	3.69892e6i	0.820918	−	1.06709i
$414$	−890982.	+	3.82751e6i	−0.255487	+	1.09753i
$415$		−	1.21980e6i		−	0.347670i
$416$			1.33783e7i			3.79026i
$417$	199425.	+	251179.i	0.0561615	+	0.0707365i
$418$	1.10505e6			0.309344
$419$	1.49547e6			0.416143			0.208071	−	0.978114i	$-0.433281\pi$
$419$	1.49547e6			0.416143			0.208071	+	0.978114i	$0.433281\pi$
$420$	5.90037e6	−	4.68462e6i	1.63214	−	1.29584i
$421$			4.23420e6i			1.16430i	0.813080	+	0.582151i	$0.197789\pi$
$421$			4.23420e6i			1.16430i	−0.813080	+	0.582151i	$0.802211\pi$
$422$			9.92983e6i			2.71432i
$423$	−962000.	+	4.13259e6i	−0.261411	+	1.12298i
$424$		−	1.80723e6i		−	0.488202i
$425$		−	2.13740e6i		−	0.574003i
$426$	3.47632e6	−	2.76003e6i	0.928102	−	0.736870i
$427$			3.81081e6i			1.01146i
$428$		−	1.18828e7i		−	3.13551i
$429$	−630578.	+	500650.i	−0.165423	+	0.131338i
$430$	7.11781e6			1.85641
$431$	2.91462e6			0.755769			0.377885	−	0.925853i	$-0.376652\pi$
$431$	2.91462e6			0.755769			0.377885	+	0.925853i	$0.376652\pi$
$432$	−1.12351e7	+	5.32129e6i	−2.89645	+	1.37185i
$433$	−2.84121e6			−0.728256			−0.364128	−	0.931349i	$-0.618633\pi$
$433$	−2.84121e6			−0.728256			−0.364128	+	0.931349i	$0.618633\pi$
$434$			7.51262e6i			1.91455i
$435$	1.53738e6	+	1.93636e6i	0.389545	+	0.490640i
$436$			2.45434e6i			0.618328i
$437$	−2.28306e6			−0.571891
$438$	1.03002e7	−	8.17788e6i	2.56543	−	2.03683i
$439$	−6.42656e6			−1.59154			−0.795769	−	0.605600i	$-0.792933\pi$
$439$	−6.42656e6			−1.59154			−0.795769	+	0.605600i	$0.792933\pi$
$440$			1.24407e6i			0.306347i
$441$	−752410.	+	3.23223e6i	−0.184229	+	0.791418i
$442$	8.64398e6			2.10455
$443$	5.11084e6			1.23732			0.618662	−	0.785657i	$-0.287675\pi$
$443$	5.11084e6			1.23732			0.618662	+	0.785657i	$0.287675\pi$
$444$	6.34347e6	−	5.03642e6i	1.52711	−	1.21245i
$445$			3.09093e6i			0.739927i
$446$	3.12239e6			0.743277
$447$	−1.67596e6	−	2.11090e6i	−0.396729	−	0.499689i
$448$	−1.45920e7			−3.43494
$449$		−	3.61586e6i		−	0.846438i	−0.906027	−	0.423219i	$-0.860900\pi$
$449$		−	3.61586e6i		−	0.846438i	0.906027	−	0.423219i	$-0.139100\pi$
$450$	1.20002e6	−	5.15509e6i	0.279356	−	1.20007i
$451$			995066.i			0.230362i
$452$	−4.68143e6			−1.07779
$453$	−1.40843e6	+	1.11822e6i	−0.322469	+	0.256026i
$454$	1.38813e7			3.16075
$455$	−4.41060e6			−0.998778
$456$	−8.14883e6	−	1.02636e7i	−1.83520	−	2.31147i
$457$			7.99940e6i			1.79171i	0.444350	+	0.895853i	$0.353435\pi$
$457$			7.99940e6i			1.79171i	−0.444350	+	0.895853i	$0.646565\pi$
$458$			1.20787e7i			2.69064i
$459$	1.71028e6	+	3.61099e6i	0.378910	+	0.800008i
$460$		−	4.16606e6i		−	0.917976i
$461$		−	2.33966e6i		−	0.512743i	−0.966578	−	0.256372i	$-0.917473\pi$
$461$		−	2.33966e6i		−	0.512743i	0.966578	−	0.256372i	$-0.0825271\pi$
$462$	−1.23201e6	−	1.55175e6i	−0.268541	−	0.338233i
$463$			6.12417e6i			1.32768i	0.747873	+	0.663842i	$0.231075\pi$
$463$			6.12417e6i			1.32768i	−0.747873	+	0.663842i	$0.768925\pi$
$464$		−	1.57042e7i		−	3.38626i
$465$	−1.28650e6	−	1.62037e6i	−0.275916	−	0.347522i
$466$	6.51829e6			1.39049
$467$	2.76756e6			0.587225			0.293612	−	0.955925i	$-0.405142\pi$
$467$	2.76756e6			0.587225			0.293612	+	0.955925i	$0.405142\pi$
$468$	1.50740e7	+	3.50898e6i	3.18137	+	0.740570i
$469$			3.54929e6i			0.745090i
$470$		−	6.22111e6i		−	1.29904i
$471$	813700.	−	646040.i	0.169010	−	0.134186i
$472$	9.03243e6	−	1.17410e7i	1.86616	−	2.42577i
$473$		−	1.35348e6i		−	0.278163i
$474$	−8.14134e6	−	1.02542e7i	−1.66437	−	2.09631i
$475$	3.07494e6			0.625320
$476$			1.53801e7i			3.11130i
$477$	−772037.	−	179717.i	−0.155361	−	0.0361655i
$478$		−	8.81268e6i		−	1.76416i
$479$		−	3.22713e6i		−	0.642656i	−0.946968	−	0.321328i	$-0.895871\pi$
$479$		−	3.22713e6i		−	0.642656i	0.946968	−	0.321328i	$-0.104129\pi$
$480$	7.10079e6	−	5.63769e6i	1.40671	−	1.11686i
$481$	−4.74182e6			−0.934507
$482$	1.25078e7			2.45223
$483$	2.54537e6	+	3.20594e6i	0.496458	+	0.625299i
$484$	−1.30710e7			−2.53626
$485$	1.41108e6			0.272394
$486$	2.09760e6	+	9.66938e6i	0.402839	+	1.85698i
$487$	1.97410e6			0.377178			0.188589	−	0.982056i	$-0.439609\pi$
$487$	1.97410e6			0.377178			0.188589	+	0.982056i	$0.439609\pi$
$488$			1.20962e7i			2.29931i
$489$	−4.03965e6	−	5.08802e6i	−0.763961	−	0.962225i
$490$		−	4.86572e6i		−	0.915498i
$491$			8.54422e6i			1.59944i	0.600371	+	0.799722i	$0.295020\pi$
$491$			8.54422e6i			1.59944i	−0.600371	+	0.799722i	$0.704980\pi$
$492$	1.49801e7	−	1.18935e7i	2.78999	−	2.21513i
$493$	−5.04738e6			−0.935295
$494$			1.24355e7i			2.29270i
$495$	531458.	+	123715.i	0.0974890	+	0.0226938i
$496$			1.31415e7i			2.39850i
$497$		−	4.62363e6i		−	0.839639i
$498$	3.83432e6	+	4.82941e6i	0.692812	+	0.872610i
$499$	−5.53151e6			−0.994472			−0.497236	−	0.867615i	$-0.665652\pi$
$499$	−5.53151e6			−0.994472			−0.497236	+	0.867615i	$0.665652\pi$
$500$			1.42642e7i			2.55166i
$501$	7.94579e6	−	6.30858e6i	1.41430	−	1.12289i
$502$		−	1.93039e7i		−	3.41889i
$503$	2.37831e6			0.419130			0.209565	−	0.977795i	$-0.432795\pi$
$503$	2.37831e6			0.419130			0.209565	+	0.977795i	$0.432795\pi$
$504$	−5.32741e6	+	2.28857e7i	−0.934200	+	4.01317i
$505$			4.30929e6i			0.751930i
$506$	−1.09564e6			−0.190235
$507$	−2.03507e6	−	2.56321e6i	−0.351608	−	0.442857i
$508$	2.83291e7			4.87050
$509$	−9.30835e6			−1.59250			−0.796248	−	0.604971i	$-0.793185\pi$
$509$	−9.30835e6			−1.59250			−0.796248	+	0.604971i	$0.793185\pi$
$510$	−3.64262e6	−	4.58795e6i	−0.620138	−	0.781076i
$511$		−	1.36997e7i		−	2.32090i
$512$	593343.			0.100030
$513$	−5.19489e6	+	2.46047e6i	−0.871531	+	0.412786i
$514$			1.59468e7i			2.66235i
$515$	6.09162e6			1.01208
$516$	−2.03759e7	+	1.61775e7i	−3.36893	+	2.67477i
$517$	−1.18297e6			−0.194647
$518$		−	1.16688e7i		−	1.91074i
$519$	1.97141e6	+	2.48303e6i	0.321261	+	0.404635i
$520$	−1.40000e7			−2.27049
$521$		−	7.87657e6i		−	1.27129i	−0.771983	−	0.635643i	$-0.780735\pi$
$521$		−	7.87657e6i		−	1.27129i	0.771983	−	0.635643i	$-0.219265\pi$
$522$	−1.21735e7	−	2.83380e6i	−1.95542	−	0.455190i
$523$	−715534.			−0.114387			−0.0571934	−	0.998363i	$-0.518215\pi$
$523$	−715534.			−0.114387			−0.0571934	+	0.998363i	$0.518215\pi$
$524$	2.92091e7			4.64719
$525$	−3.42823e6	−	4.31793e6i	−0.542840	−	0.683718i
$526$			5.21483e6i			0.821818i
$527$	4.22372e6			0.662473
$528$	−2.15511e6	−	2.71440e6i	−0.336421	−	0.423730i
$529$	−4.17273e6			−0.648308
$530$	1.16221e6			0.179719
$531$	−4.11745e6	−	5.02615e6i	−0.633712	−	0.773569i
$532$	−2.21264e7			−3.38946
$533$	−1.11978e7			−1.70732
$534$	−9.71605e6	−	1.22376e7i	−1.47447	−	1.85713i
$535$	4.71455e6			0.712124
$536$			1.12660e7i			1.69379i
$537$	4.51411e6	+	5.68561e6i	0.675517	+	0.850827i
$538$	−3.48941e6			−0.519752
$539$	−925237.			−0.137177
$540$	−4.48980e6	−	9.47949e6i	−0.662587	−	1.39895i
$541$			5.55517e6i			0.816027i	0.912976	+	0.408013i	$0.133778\pi$
$541$			5.55517e6i			0.816027i	−0.912976	+	0.408013i	$0.866222\pi$
$542$	1.09315e7			1.59839
$543$	8.37312e6	+	1.05461e7i	1.21867	+	1.53494i
$544$			1.85092e7i			2.68157i
$545$	−973774.			−0.140432
$546$	1.74624e7	−	1.38643e7i	2.50681	−	1.99029i
$547$	−2.56306e6			−0.366261			−0.183131	−	0.983089i	$-0.558623\pi$
$547$	−2.56306e6			−0.366261			−0.183131	+	0.983089i	$0.558623\pi$
$548$		−	1.00324e7i		−	1.42710i
$549$	5.16739e6	+	1.20288e6i	0.731712	+	0.170331i
$550$	1.47566e6			0.208008
$551$		−	7.26134e6i		−	1.01891i
$552$	8.07942e6	+	1.01762e7i	1.12858	+	1.42147i
$553$	−1.36384e7			−1.89650
$554$	527304.			0.0729939
$555$	1.99823e6	+	2.51681e6i	0.275367	+	0.346831i
$556$	1.71879e6			0.235796
$557$		−	7.81111e6i		−	1.06678i	−0.845870	−	0.533390i	$-0.820918\pi$
$557$		−	7.81111e6i		−	1.06678i	0.845870	−	0.533390i	$-0.179082\pi$
$558$	1.01870e7	+	2.37136e6i	1.38503	+	0.322412i
$559$	1.52312e7			2.06160
$560$		−	1.89859e7i		−	2.55836i
$561$	−872417.	+	692658.i	−0.117035	+	0.0929206i
$562$			7.74984e6i			1.03503i
$563$	2.06962e6			0.275182			0.137591	−	0.990489i	$-0.456064\pi$
$563$	2.06962e6			0.275182			0.137591	+	0.990489i	$0.456064\pi$
$564$	1.41395e7	+	1.78089e7i	1.87169	+	2.35744i
$565$		−	1.85738e6i		−	0.244782i
$566$			2.02774e7i			2.66054i
$567$	9.24682e6	+	4.55166e6i	1.20791	+	0.594583i
$568$		−	1.46762e7i		−	1.90872i
$569$	−4.95942e6			−0.642170			−0.321085	−	0.947050i	$-0.604047\pi$
$569$	−4.95942e6			−0.642170			−0.321085	+	0.947050i	$0.604047\pi$
$570$	6.60039e6	−	5.24040e6i	0.850907	−	0.675580i
$571$		−	1.32636e7i		−	1.70244i	−0.524809	−	0.851220i	$-0.675863\pi$
$571$		−	1.32636e7i		−	1.70244i	0.524809	−	0.851220i	$-0.324137\pi$
$572$			4.31498e6i			0.551428i
$573$	5.42954e6	+	6.83861e6i	0.690838	+	0.870124i
$574$		−	2.75560e7i		−	3.49089i
$575$	−3.04875e6			−0.384549
$576$	−4.60596e6	+	1.97865e7i	−0.578448	+	2.48492i
$577$	−5.63487e6			−0.704603			−0.352302	−	0.935887i	$-0.614601\pi$
$577$	−5.63487e6			−0.704603			−0.352302	+	0.935887i	$0.614601\pi$
$578$	−3.30294e6			−0.411226
$579$	269559.	+	339515.i	0.0334162	+	0.0420884i
$580$	1.32503e7			1.63552
$581$	6.42329e6			0.789436
$582$	−5.58673e6	+	4.43560e6i	−0.683676	+	0.542807i
$583$		−	220998.i		−	0.0269288i
$584$		−	4.34850e7i		−	5.27603i
$585$	−1.39221e6	+	5.98069e6i	−0.168195	+	0.722539i
$586$		−	6.93933e6i		−	0.834783i
$587$	−2.95346e6			−0.353782			−0.176891	−	0.984230i	$-0.556604\pi$
$587$	−2.95346e6			−0.353782			−0.176891	+	0.984230i	$0.556604\pi$
$588$	1.10589e7	+	1.39289e7i	1.31907	+	1.66140i
$589$			6.07638e6i			0.721700i
$590$	7.55046e6	+	5.80863e6i	0.892983	+	0.686979i
$591$	1.85082e6	−	1.46947e6i	0.217970	−	0.173058i
$592$		−	2.04117e7i		−	2.39373i
$593$			2.61462e6i			0.305331i	0.988278	+	0.152666i	$0.0487858\pi$
$593$			2.61462e6i			0.305331i	−0.988278	+	0.152666i	$0.951214\pi$
$594$	−2.49303e6	+	1.18078e6i	−0.289908	+	0.137310i
$595$	−6.10215e6			−0.706627
$596$	−1.44447e7			−1.66568
$597$	702276.	+	884531.i	0.0806440	+	0.101573i
$598$		−	1.23296e7i		−	1.40993i
$599$		−	5.62418e6i		−	0.640460i	−0.947340	−	0.320230i	$-0.896240\pi$
$599$		−	5.62418e6i		−	0.640460i	0.947340	−	0.320230i	$-0.103760\pi$
$600$	−1.08818e7	−	1.37058e7i	−1.23402	−	1.55427i
$601$			9.21924e6i			1.04114i	0.853819	+	0.520570i	$0.174280\pi$
$601$			9.21924e6i			1.04114i	−0.853819	+	0.520570i	$0.825720\pi$
$602$			3.74814e7i			4.21526i
$603$	4.81277e6	+	1.12033e6i	0.539016	+	0.125474i
$604$			9.63771e6i			1.07493i
$605$		−	5.18597e6i		−	0.576026i
$606$	−1.35459e7	−	1.70613e7i	−1.49839	−	1.88725i
$607$	6.39908e6			0.704930			0.352465	−	0.935825i	$-0.385344\pi$
$607$	6.39908e6			0.704930			0.352465	+	0.935825i	$0.385344\pi$
$608$	−2.66279e7			−2.92132
$609$	−1.01966e7	+	8.09562e6i	−1.11407	+	0.884518i
$610$	−7.77887e6			−0.846432
$611$		−	1.33124e7i		−	1.44262i
$612$	2.08552e7	+	4.85474e6i	2.25079	+	0.523947i
$613$		−	1.13754e7i		−	1.22269i	−0.791366	−	0.611343i	$-0.790630\pi$
$613$		−	1.13754e7i		−	1.22269i	0.791366	−	0.611343i	$-0.209370\pi$
$614$	8.82008e6			0.944173
$615$	4.71882e6	+	5.94346e6i	0.503090	+	0.633653i
$616$	−6.55111e6			−0.695605
$617$			4.96198e6i			0.524737i	0.964968	+	0.262369i	$0.0845036\pi$
$617$			4.96198e6i			0.524737i	−0.964968	+	0.262369i	$0.915496\pi$
$618$	−2.41178e7	+	1.91484e7i	−2.54020	+	2.01680i
$619$	7.34946e6			0.770955			0.385477	−	0.922717i	$-0.374037\pi$
$619$	7.34946e6			0.770955			0.385477	+	0.922717i	$0.374037\pi$
$620$	−1.10880e7			−1.15844
$621$	5.15064e6	−	2.43951e6i	0.535960	−	0.253848i
$622$			1.39729e7i			1.44814i
$623$	−1.62764e7			−1.68011
$624$	3.05461e7	−	2.42522e7i	3.14047	−	2.49339i
$625$	673027.			0.0689180
$626$		−	8.27457e6i		−	0.843936i
$627$	−996482.	−	1.25509e6i	−0.101228	−	0.127499i
$628$		−	5.56806e6i		−	0.563384i
$629$	−6.56040e6			−0.661156
$630$	−1.47175e7	−	3.42598e6i	−1.47734	−	0.343901i
$631$	−5.08043e6			−0.507957			−0.253979	−	0.967210i	$-0.581739\pi$
$631$	−5.08043e6			−0.507957			−0.253979	+	0.967210i	$0.581739\pi$
$632$	−4.32907e7			−4.31124
$633$	1.12781e7	−	8.95425e6i	1.11873	−	0.888219i
$634$			1.08480e7i			1.07183i
$635$			1.12397e7i			1.10617i
$636$	−3.32700e6	+	2.64148e6i	−0.326145	+	0.258944i
$637$		−	1.04120e7i		−	1.01669i
$638$		−	3.48471e6i		−	0.338934i
$639$	−6.26956e6	−	1.45945e6i	−0.607414	−	0.141396i
$640$		−	1.11740e7i		−	1.07835i
$641$		−	398727.i		−	0.0383292i	−0.999816	−	0.0191646i	$-0.993899\pi$
$641$		−	398727.i		−	0.0383292i	0.999816	−	0.0191646i	$-0.00610066\pi$
$642$	−1.86658e7	+	1.48198e7i	−1.78735	+	1.41907i
$643$	1.90598e7			1.81799			0.908994	−	0.416810i	$-0.136852\pi$
$643$	1.90598e7			1.81799			0.908994	+	0.416810i	$0.136852\pi$
$644$	2.19379e7			2.08440
$645$	−6.41850e6	−	8.08423e6i	−0.607483	−	0.765138i
$646$			1.72048e7i			1.62207i
$647$			1.69729e7i			1.59403i	0.603963	+	0.797013i	$0.293588\pi$
$647$			1.69729e7i			1.59403i	−0.603963	+	0.797013i	$0.706412\pi$
$648$	2.93510e7	+	1.44477e7i	2.74590	+	1.35164i
$649$	1.10453e6	−	1.43575e6i	0.102936	−	0.133803i
$650$			1.66062e7i			1.54165i
$651$	8.53265e6	−	6.77452e6i	0.789099	−	0.626507i
$652$	−3.48168e7			−3.20752
$653$			5.01672e6i			0.460402i	0.973143	+	0.230201i	$0.0739384\pi$
$653$			5.01672e6i			0.460402i	−0.973143	+	0.230201i	$0.926062\pi$
$654$	3.85535e6	−	3.06097e6i	0.352468	−	0.279843i
$655$			1.15889e7i			1.05545i
$656$		−	4.82024e7i		−	4.37330i
$657$	−1.85765e7	−	4.32430e6i	−1.67900	−	0.390843i
$658$	3.27595e7			2.94967
$659$	1.03472e6			0.0928127			0.0464063	−	0.998923i	$-0.485223\pi$
$659$	1.03472e6			0.0928127			0.0464063	+	0.998923i	$0.485223\pi$
$660$	2.29025e6	−	1.81835e6i	0.204656	−	0.162487i
$661$	2.39787e6			0.213463			0.106731	−	0.994288i	$-0.465961\pi$
$661$	2.39787e6			0.213463			0.106731	+	0.994288i	$0.465961\pi$
$662$	−2.01519e7			−1.78719
$663$	−7.79474e6	−	9.81763e6i	−0.688680	−	0.867407i
$664$	2.03886e7			1.79460
$665$		−	8.77876e6i		−	0.769802i
$666$	−1.58227e7	−	3.68327e6i	−1.38228	−	0.321771i
$667$			7.19949e6i			0.626595i
$668$		−	5.43722e7i		−	4.71450i
$669$	−2.81563e6	−	3.54634e6i	−0.243226	−	0.306348i
$670$	−7.24503e6			−0.623524
$671$			1.47918e6i			0.126828i
$672$	2.96873e7	+	3.73918e7i	2.53599	+	3.19413i
$673$			4.67594e6i			0.397952i	0.980004	+	0.198976i	$0.0637617\pi$
$673$			4.67594e6i			0.397952i	−0.980004	+	0.198976i	$0.936238\pi$
$674$		−	1.20737e7i		−	1.02374i
$675$	−6.93715e6	+	3.28567e6i	−0.586033	+	0.277564i
$676$	−1.75398e7			−1.47624
$677$			5.07682e6i			0.425716i	0.977083	+	0.212858i	$0.0682772\pi$
$677$			5.07682e6i			0.425716i	−0.977083	+	0.212858i	$0.931723\pi$
$678$	5.83851e6	+	7.35372e6i	0.487785	+	0.614374i
$679$			7.43056e6i			0.618511i
$680$	−1.93692e7			−1.60635
$681$	−1.25175e7	−	1.57660e7i	−1.03431	−	1.30273i
$682$			2.91605e6i			0.240068i
$683$	−2.30885e7			−1.89384			−0.946921	−	0.321467i	$-0.895824\pi$
$683$	−2.30885e7			−1.89384			−0.946921	+	0.321467i	$0.895824\pi$
$684$	−6.98419e6	+	3.00030e7i	−0.570790	+	2.45202i
$685$	3.98042e6			0.324118
$686$	−5.90981e6			−0.479472
$687$	1.37187e7	−	1.08920e7i	1.10897	−	0.880471i
$688$			6.55645e7i			5.28077i
$689$	2.48697e6			0.199583
$690$	−6.54417e6	+	5.19576e6i	−0.523277	+	0.415457i
$691$		−	1.33115e7i		−	1.06055i	−0.847825	−	0.530277i	$-0.822088\pi$
$691$		−	1.33115e7i		−	1.06055i	0.847825	−	0.530277i	$-0.177912\pi$
$692$	1.69911e7			1.34883
$693$	−651464.	+	2.79858e6i	−0.0515297	+	0.221363i
$694$	−8.89960e6			−0.701410
$695$			681940.i			0.0535531i
$696$	−3.23657e7	+	2.56969e7i	−2.53257	+	2.01075i
$697$	−1.54924e7			−1.20792
$698$			2.70354e7i			2.10036i
$699$	−5.87789e6	−	7.40332e6i	−0.455018	−	0.573104i
$700$	−2.95471e7			−2.27914
$701$	−9.60518e6			−0.738262			−0.369131	−	0.929377i	$-0.620345\pi$
$701$	−9.60518e6			−0.738262			−0.369131	+	0.929377i	$0.620345\pi$
$702$	−1.32877e7	−	2.80549e7i	−1.01767	−	2.14865i
$703$		−	9.43802e6i		−	0.720265i
$704$	−5.66394e6			−0.430712
$705$	−7.06579e6	+	5.60990e6i	−0.535412	+	0.425092i
$706$	−3.73342e7			−2.81900
$707$	−2.26921e7			−1.70737
$708$	−3.48164e7	+	532692.i	−2.61036	+	0.0399386i
$709$	576086.			0.0430400			0.0215200	−	0.999768i	$-0.493149\pi$
$709$	576086.			0.0430400			0.0215200	+	0.999768i	$0.493149\pi$
$710$	9.43805e6			0.702646
$711$	−4.30498e6	+	1.84935e7i	−0.319372	+	1.37197i
$712$	−5.16640e7			−3.81934
$713$		−	6.02463e6i		−	0.443820i
$714$	2.41595e7	−	1.91815e7i	1.77355	−	1.40811i
$715$	−1.71199e6			−0.125238
$716$	3.89060e7			2.83618
$717$	−1.00092e7	+	7.94686e6i	−0.727114	+	0.577295i
$718$			1.60313e7i			1.16053i
$719$	−4.40017e6			−0.317430			−0.158715	−	0.987324i	$-0.550735\pi$
$719$	−4.40017e6			−0.317430			−0.158715	+	0.987324i	$0.550735\pi$
$720$	−2.57446e7	−	5.99291e6i	−1.85078	−	0.430831i
$721$			3.20776e7i			2.29807i
$722$	1.86419e6			0.133091
$723$	−1.12789e7	−	1.42060e7i	−0.802456	−	1.01071i
$724$	7.21659e7			5.11665
$725$		−	9.69665e6i		−	0.685136i
$726$	1.63016e7	+	2.05322e7i	1.14786	+	1.44576i
$727$	8.07553e6			0.566677			0.283338	−	0.959020i	$-0.408558\pi$
$727$	8.07553e6			0.566677			0.283338	+	0.959020i	$0.408558\pi$
$728$		−	7.37220e7i		−	5.15547i
$729$	9.09073e6	−	1.11018e7i	0.633549	−	0.773703i
$730$	2.79646e7			1.94223
$731$	2.10727e7			1.45857
$732$	2.22683e7	−	1.76800e7i	1.53606	−	1.21956i
$733$	−1.12591e7			−0.774005			−0.387002	−	0.922079i	$-0.626489\pi$
$733$	−1.12591e7			−0.774005			−0.387002	+	0.922079i	$0.626489\pi$
$734$			4.12619e7i			2.82689i
$735$	−5.52637e6	+	4.38768e6i	−0.377330	+	0.299583i
$736$	2.64011e7			1.79650
$737$			1.37767e6i			0.0934279i
$738$	−3.73654e7	−	8.69805e6i	−2.52539	−	0.587870i
$739$			5.14515e6i			0.346567i	0.984872	+	0.173283i	$0.0554377\pi$
$739$			5.14515e6i			0.346567i	−0.984872	+	0.173283i	$0.944562\pi$
$740$	1.72222e7			1.15614
$741$	1.41240e7	−	1.12138e7i	0.944956	−	0.750251i
$742$			6.12002e6i			0.408078i
$743$		−	4.93562e6i		−	0.327997i	−0.986461	−	0.163998i	$-0.947561\pi$
$743$		−	4.93562e6i		−	0.327997i	0.986461	−	0.163998i	$-0.0524392\pi$
$744$	2.70841e7	−	2.15035e7i	1.79383	−	1.42422i
$745$		−	5.73101e6i		−	0.378303i
$746$	−2.29290e7			−1.50848
$747$	2.02751e6	−	8.70986e6i	0.132942	−	0.571097i
$748$			5.96986e6i			0.390131i
$749$			2.48262e7i			1.61698i
$750$	2.24067e7	−	1.77898e7i	1.45453	−	1.15483i
$751$		−	8.39631e6i		−	0.543236i	−0.962405	−	0.271618i	$-0.912441\pi$
$751$		−	8.39631e6i		−	0.543236i	0.962405	−	0.271618i	$-0.0875588\pi$
$752$	5.73047e7			3.69527
$753$	−2.19249e7	+	1.74073e7i	−1.40913	+	1.11878i
$754$	3.92147e7			2.51201
$755$	−3.82381e6			−0.244134
$756$	4.99177e7	−	2.36427e7i	3.17651	−	1.50450i
$757$	2.42372e7			1.53725			0.768623	−	0.639703i	$-0.220942\pi$
$757$	2.42372e7			1.53725			0.768623	+	0.639703i	$0.220942\pi$
$758$	3.67469e6			0.232299
$759$	987995.	+	1.24440e6i	0.0622516	+	0.0784071i
$760$		−	2.78653e7i		−	1.74996i
$761$			6.17608e6i			0.386591i	0.981141	+	0.193295i	$0.0619175\pi$
$761$			6.17608e6i			0.386591i	−0.981141	+	0.193295i	$0.938082\pi$
$762$	−3.53310e7	−	4.45001e7i	−2.20429	−	2.77635i
$763$		−	5.12776e6i		−	0.318872i
$764$	4.67959e7			2.90051
$765$	−1.92614e6	+	8.27440e6i	−0.118997	+	0.511190i
$766$			2.33402e7i			1.43725i
$767$	1.61570e7	+	1.24297e7i	0.991683	+	0.762909i
$768$	9.19291e6	+	1.15787e7i	0.562406	+	0.708361i
$769$			1.75329e7i			1.06915i	0.845121	+	0.534575i	$0.179528\pi$
$769$			1.75329e7i			1.06915i	−0.845121	+	0.534575i	$0.820472\pi$
$770$		−	4.21292e6i		−	0.256069i
$771$	1.81120e7	−	1.43801e7i	1.09731	−	0.871213i
$772$	2.32326e6			0.140299
$773$	−1.85958e7			−1.11935			−0.559674	−	0.828713i	$-0.689074\pi$
$773$	−1.85958e7			−1.11935			−0.559674	+	0.828713i	$0.689074\pi$
$774$	5.08241e7	+	1.18310e7i	3.04942	+	0.709855i
$775$			8.11428e6i			0.485284i
$776$			2.35859e7i			1.40604i
$777$	−1.32532e7	+	1.05224e7i	−0.787530	+	0.625262i
$778$		−	1.60270e7i		−	0.949300i
$779$		−	2.22879e7i		−	1.31591i
$780$	2.04626e7	+	2.57731e7i	1.20427	+	1.51680i
$781$		−	1.79468e6i		−	0.105283i
$782$		−	1.70583e7i		−	0.997512i
$783$	7.75895e6	+	1.63818e7i	0.452271	+	0.954898i
$784$	4.48198e7			2.60423
$785$	2.20916e6			0.127954
$786$	−3.64286e7	−	4.58825e7i	−2.10322	−	2.64905i
$787$	2.03674e7			1.17219			0.586096	−	0.810242i	$-0.300664\pi$
$787$	2.03674e7			1.17219			0.586096	+	0.810242i	$0.300664\pi$
$788$		−	1.26650e7i		−	0.726589i
$789$	5.92288e6	−	4.70249e6i	0.338720	−	0.268928i
$790$		−	2.78396e7i		−	1.58707i
$791$	9.78073e6			0.555815
$792$	−2.06786e6	+	8.88318e6i	−0.117141	+	0.503217i
$793$	−1.66458e7			−0.939986
$794$		−	961255.i		−	0.0541112i
$795$	−1.04802e6	−	1.32001e6i	−0.0588102	−	0.0740727i
$796$	6.05275e6			0.338587
$797$	1.94611e7			1.08523			0.542615	−	0.839982i	$-0.317434\pi$
$797$	1.94611e7			1.08523			0.542615	+	0.839982i	$0.317434\pi$
$798$	2.75952e7	+	3.47567e7i	1.53400	+	1.93211i
$799$		−	1.84179e7i		−	1.02064i
$800$	−3.55584e7			−1.96434
$801$	−5.13765e6	+	2.20705e7i	−0.282933	+	1.21543i
$802$	1.68629e7			0.925753
$803$		−	5.31758e6i		−	0.291022i
$804$	2.07400e7	−	1.64666e7i	1.13154	−	0.898389i
$805$			8.70399e6i			0.473400i
$806$	−3.28154e7			−1.77926
$807$	3.14658e6	+	3.96319e6i	0.170081	+	0.214220i
$808$	−7.20287e7			−3.88130
$809$	3.54946e6			0.190674			0.0953369	−	0.995445i	$-0.469607\pi$
$809$	3.54946e6			0.190674			0.0953369	+	0.995445i	$0.469607\pi$
$810$	−9.29114e6	+	1.88752e7i	−0.497573	+	1.01083i
$811$		−	1.40304e7i		−	0.749064i	−0.927214	−	0.374532i	$-0.877803\pi$
$811$		−	1.40304e7i		−	0.749064i	0.927214	−	0.374532i	$-0.122197\pi$
$812$			6.97742e7i			3.71368i
$813$	−9.85752e6	−	1.24157e7i	−0.523047	−	0.658789i
$814$		−	4.52930e6i		−	0.239591i
$815$		−	1.38137e7i		−	0.728479i
$816$	4.22611e7	−	3.35534e7i	2.22186	−	1.76405i
$817$			3.03158e7i			1.58897i
$818$			5.48280e7i			2.86497i
$819$	−3.14935e7	−	7.33116e6i	−1.64063	−	0.381912i
$820$	4.06704e7			2.11224
$821$	3.27873e7			1.69765			0.848825	−	0.528674i	$-0.177311\pi$
$821$	3.27873e7			1.69765			0.848825	+	0.528674i	$0.177311\pi$
$822$	−1.57592e7	+	1.25121e7i	−0.813496	+	0.645878i
$823$		−	2.33932e6i		−	0.120390i	−0.998187	−	0.0601950i	$-0.980828\pi$
$823$		−	2.33932e6i		−	0.120390i	0.998187	−	0.0601950i	$-0.0191723\pi$
$824$			1.01820e8i			5.22413i
$825$	−1.33068e6	−	1.67602e6i	−0.0680675	−	0.0857324i
$826$	−3.05874e7	+	3.97597e7i	−1.55989	+	2.02765i
$827$			1.57681e7i			0.801709i	0.916142	+	0.400855i	$0.131287\pi$
$827$			1.57681e7i			0.801709i	−0.916142	+	0.400855i	$0.868713\pi$
$828$	6.92471e6	−	2.97474e7i	0.351015	−	1.50790i
$829$	−154501.			−0.00780811			−0.00390405	−	0.999992i	$-0.501243\pi$
$829$	−154501.			−0.00780811			−0.00390405	+	0.999992i	$0.501243\pi$
$830$			1.31116e7i			0.660634i
$831$	−475498.	−	598899.i	−0.0238861	−	0.0300851i
$832$		−	6.37384e7i		−	3.19222i
$833$		−	1.44052e7i		−	0.719296i
$834$	−2.14362e6	−	2.69993e6i	−0.106717	−	0.134412i
$835$	2.15725e7			1.07074
$836$	−8.58844e6			−0.425010
$837$	−6.49280e6	−	1.37085e7i	−0.320345	−	0.676357i
$838$	−1.60748e7			−0.790744
$839$	2.75824e7			1.35278			0.676390	−	0.736543i	$-0.263543\pi$
$839$	2.75824e7			1.35278			0.676390	+	0.736543i	$0.263543\pi$
$840$	−3.91293e7	+	3.10668e7i	−1.91339	+	1.51914i
$841$	−2.38705e6			−0.116378
$842$		−	4.55134e7i		−	2.21238i
$843$	8.80208e6	−	6.98844e6i	0.426595	−	0.338697i
$844$		−	7.71745e7i		−	3.72922i
$845$		−	6.95899e6i		−	0.335278i
$846$	1.03405e7	−	4.44213e7i	0.496727	−	2.13386i
$847$	2.73086e7			1.30795
$848$			1.07055e7i			0.511230i
$849$	2.30305e7	−	1.82852e7i	1.09657	−	0.870622i
$850$			2.29750e7i			1.09071i
$851$			9.35763e6i			0.442937i
$852$	−2.70179e7	+	2.14510e7i	−1.27513	+	1.01239i
$853$	1.51712e7			0.713915			0.356958	−	0.934121i	$-0.383814\pi$
$853$	1.51712e7			0.713915			0.356958	+	0.934121i	$0.383814\pi$
$854$		−	4.09625e7i		−	1.92195i
$855$	−1.19038e7	−	2.77102e6i	−0.556893	−	0.129635i
$856$			7.88025e7i			3.67583i
$857$	−2.18772e7			−1.01751			−0.508757	−	0.860910i	$-0.669895\pi$
$857$	−2.18772e7			−1.01751			−0.508757	+	0.860910i	$0.669895\pi$
$858$	6.77809e6	−	5.38149e6i	0.314333	−	0.249565i
$859$		−	4.13582e7i		−	1.91240i	−0.292711	−	0.956201i	$-0.594557\pi$
$859$		−	4.13582e7i		−	1.91240i	0.292711	−	0.956201i	$-0.405443\pi$
$860$	−5.53195e7			−2.55054
$861$	−3.12974e7	+	2.48487e7i	−1.43880	+	1.14234i
$862$	−3.13293e7			−1.43609
$863$	7.13489e6			0.326107			0.163054	−	0.986617i	$-0.447866\pi$
$863$	7.13489e6			0.326107			0.163054	+	0.986617i	$0.447866\pi$
$864$	6.00734e7	−	2.84527e7i	2.73778	−	1.29670i
$865$			6.74131e6i			0.306340i
$866$	3.05402e7			1.38381
$867$	2.97843e6	+	3.75140e6i	0.134568	+	0.169491i
$868$		−	5.83880e7i		−	2.63042i
$869$	−5.29382e6			−0.237804
$870$	−1.65253e7	−	2.08139e7i	−0.740203	−	0.932301i
$871$	−1.55034e7			−0.692440
$872$		−	1.62764e7i		−	0.724881i
$873$	1.00757e7	+	2.34546e6i	0.447445	+	0.104158i
$874$	2.45406e7			1.08669
$875$		−	2.98017e7i		−	1.31589i
$876$	−8.00531e7	+	6.35584e7i	−3.52467	+	2.79842i
$877$	1.06884e6			0.0469262			0.0234631	−	0.999725i	$-0.492531\pi$
$877$	1.06884e6			0.0469262			0.0234631	+	0.999725i	$0.492531\pi$
$878$	6.90791e7			3.02420
$879$	−7.88152e6	+	6.25756e6i	−0.344063	+	0.273170i
$880$		−	7.36947e6i		−	0.320796i
$881$	−6.75682e6			−0.293294			−0.146647	−	0.989189i	$-0.546848\pi$
$881$	−6.75682e6			−0.293294			−0.146647	+	0.989189i	$0.546848\pi$
$882$	8.08766e6	−	3.47433e7i	0.350067	−	1.50383i
$883$	−1.26215e7			−0.544766			−0.272383	−	0.962189i	$-0.587812\pi$
$883$	−1.26215e7			−0.544766			−0.272383	+	0.962189i	$0.587812\pi$
$884$	−6.71810e7			−2.89145
$885$	−211348.	−	1.38136e7i	−0.00907070	−	0.592854i
$886$	−5.49365e7			−2.35113
$887$	−4.16969e7			−1.77949			−0.889744	−	0.456459i	$-0.849117\pi$
$887$	−4.16969e7			−1.77949			−0.889744	+	0.456459i	$0.849117\pi$
$888$	−4.20678e7	+	3.33998e7i	−1.79026	+	1.42139i
$889$	−5.91868e7			−2.51172
$890$		−	3.32244e7i		−	1.40599i
$891$	3.58919e6	+	1.76675e6i	0.151462	+	0.0745556i
$892$	−2.42672e7			−1.02119
$893$	2.64967e7			1.11189
$894$	1.80149e7	+	2.26901e7i	0.753855	+	0.949496i
$895$			1.54362e7i			0.644143i
$896$	5.88406e7			2.44854
$897$	−1.40037e7	+	1.11183e7i	−0.581114	+	0.461377i
$898$			3.88669e7i			1.60838i
$899$	1.91615e7			0.790735
$900$	−9.32656e6	+	4.00654e7i	−0.383809	+	1.64878i
$901$	3.44077e6			0.141203
$902$		−	1.06960e7i		−	0.437728i
$903$	4.25705e7	−	3.37990e7i	1.73736	−	1.37938i
$904$	3.10457e7			1.26351
$905$			2.86322e7i			1.16207i
$906$	1.51392e7	−	1.20198e7i	0.612748	−	0.486493i
$907$	1.97646e7			0.797757			0.398879	−	0.917004i	$-0.369399\pi$
$907$	1.97646e7			0.797757			0.398879	+	0.917004i	$0.369399\pi$
$908$	−1.07885e8			−4.34258
$909$	−7.16278e6	+	3.07701e7i	−0.287522	+	1.23515i
$910$	4.74095e7			1.89785
$911$			2.84690e7i			1.13652i	0.822849	+	0.568259i	$0.192383\pi$
$911$			2.84690e7i			1.13652i	−0.822849	+	0.568259i	$0.807617\pi$
$912$	4.82710e7	+	6.07983e7i	1.92176	+	2.42050i
$913$	2.49323e6			0.0989885
$914$		−	8.59856e7i		−	3.40456i
$915$	7.01462e6	+	8.83505e6i	0.276982	+	0.348864i
$916$		−	9.38754e7i		−	3.69669i
$917$	−6.10254e7			−2.39656
$918$	−1.83838e7	−	3.88145e7i	−0.719995	−	1.52015i
$919$			3.60778e7i			1.40913i	0.709640	+	0.704564i	$0.248858\pi$
$919$			3.60778e7i			1.40913i	−0.709640	+	0.704564i	$0.751142\pi$
$920$			2.76279e7i			1.07616i
$921$	−7.95353e6	−	1.00176e7i	−0.308966	−	0.389149i
$922$			2.51490e7i			0.974302i
$923$	2.01962e7			0.780308
$924$	9.57521e6	+	1.20602e7i	0.368951	+	0.464701i
$925$		−	1.26033e7i		−	0.484319i
$926$		−	6.58288e7i		−	2.52283i
$927$	4.34967e7	+	1.01253e7i	1.66248	+	0.386998i
$928$			8.39697e7i			3.20076i
$929$	2.80879e7			1.06778			0.533889	−	0.845555i	$-0.320730\pi$
$929$	2.80879e7			1.06778			0.533889	+	0.845555i	$0.320730\pi$
$930$	1.38286e7	+	1.74174e7i	0.524288	+	0.660352i
$931$	2.07239e7			0.783604
$932$	−5.06601e7			−1.91041
$933$	1.58700e7	−	1.26001e7i	0.596862	−	0.473880i
$934$	−2.97485e7			−1.11583
$935$	−2.36857e6			−0.0886049
$936$	−9.99656e7	−	2.32704e7i	−3.72959	−	0.868187i
$937$		−	9.24927e6i		−	0.344159i	−0.985083	−	0.172079i	$-0.944951\pi$
$937$		−	9.24927e6i		−	0.344159i	0.985083	−	0.172079i	$-0.0550485\pi$
$938$		−	3.81513e7i		−	1.41580i
$939$	−9.39806e6	+	7.46162e6i	−0.347836	+	0.276165i
$940$			4.83504e7i			1.78476i
$941$	3.26318e7			1.20134			0.600671	−	0.799496i	$-0.294900\pi$
$941$	3.26318e7			1.20134			0.600671	+	0.799496i	$0.294900\pi$
$942$	−8.74647e6	+	6.94429e6i	−0.321148	+	0.254977i
$943$			2.20981e7i			0.809237i
$944$	−5.35052e7	+	6.95498e7i	−1.95419	+	2.54019i
$945$	9.38036e6	+	1.98051e7i	0.341696	+	0.721437i
$946$			1.45486e7i			0.528558i
$947$			4.99180e7i			1.80876i	0.426723	+	0.904382i	$0.359668\pi$
$947$			4.99180e7i			1.80876i	−0.426723	+	0.904382i	$0.640332\pi$
$948$	6.32745e7	+	7.96955e7i	2.28669	+	2.88013i
$949$	5.98406e7			2.15690
$950$	−3.30526e7			−1.18822
$951$	1.23209e7	−	9.78219e6i	0.441763	−	0.350739i
$952$		−	1.01996e8i		−	3.64745i
$953$		−	3.80787e7i		−	1.35816i	−0.734066	−	0.679078i	$-0.762380\pi$
$953$		−	3.80787e7i		−	1.35816i	0.734066	−	0.679078i	$-0.237620\pi$
$954$	8.29863e6	+	1.93179e6i	0.295213	+	0.0687208i
$955$			1.85665e7i			0.658752i
$956$			6.84921e7i			2.42379i
$957$	−3.95785e6	+	3.14235e6i	−0.139695	+	0.110911i
$958$			3.46885e7i			1.22116i
$959$			2.09604e7i			0.735957i
$960$	−3.38303e7	+	2.68597e7i	−1.18475	+	0.940639i
$961$	1.25945e7			0.439920
$962$	5.09699e7			1.77573
$963$	3.36638e7	+	7.83639e6i	1.16976	+	0.272302i
$964$	−9.72102e7			−3.36914
$965$			921767.i			0.0318642i
$966$	−2.73602e7	−	3.44607e7i	−0.943357	−	1.18818i
$967$		−	2.13883e7i		−	0.735547i	−0.929915	−	0.367774i	$-0.880120\pi$
$967$		−	2.13883e7i		−	0.735547i	0.929915	−	0.367774i	$-0.119880\pi$
$968$	8.66822e7			2.97332
$969$	1.95408e7	−	1.55145e7i	0.668548	−	0.530796i
$970$	−1.51677e7			−0.517596
$971$		−	2.63021e7i		−	0.895245i	−0.894223	−	0.447623i	$-0.852271\pi$
$971$		−	2.63021e7i		−	0.895245i	0.894223	−	0.447623i	$-0.147729\pi$
$972$	−1.63025e7	−	7.51503e7i	−0.553463	−	2.55132i
$973$	−3.59101e6			−0.121600
$974$	−2.12196e7			−0.716704
$975$	1.88609e7	−	1.49747e7i	0.635405	−	0.504482i
$976$		−	7.16537e7i		−	2.40777i
$977$	4.11612e7			1.37960			0.689798	−	0.724002i	$-0.257699\pi$
$977$	4.11612e7			1.37960			0.689798	+	0.724002i	$0.257699\pi$
$978$	4.34222e7	+	5.46912e7i	1.45166	+	1.82840i
$979$	−6.31775e6			−0.210672
$980$			3.78164e7i			1.25781i
$981$	−6.95315e6	−	1.61858e6i	−0.230679	−	0.0536984i
$982$		−	9.18420e7i		−	3.03922i
$983$	−4.94781e7			−1.63316			−0.816581	−	0.577230i	$-0.804133\pi$
$983$	−4.94781e7			−1.63316			−0.816581	+	0.577230i	$0.804133\pi$
$984$	−9.93433e7	+	7.88739e7i	−3.27078	+	2.59684i
$985$	5.02490e6			0.165020
$986$	5.42544e7			1.77722
$987$	−2.95410e7	−	3.72075e7i	−0.965233	−	1.21573i
$988$		−	9.66489e7i		−	3.14996i
$989$		−	3.00576e7i		−	0.977157i
$990$	−5.71265e6	−	1.32981e6i	−0.185246	−	0.0431223i
$991$			1.23029e7i			0.397944i	0.980005	+	0.198972i	$0.0637603\pi$
$991$			1.23029e7i			0.397944i	−0.980005	+	0.198972i	$0.936240\pi$
$992$		−	7.02669e7i		−	2.26711i
$993$	1.81720e7	+	2.28880e7i	0.584830	+	0.736606i
$994$			4.96995e7i			1.59546i
$995$			2.40146e6i			0.0768985i
$996$	−2.98003e7	−	3.75341e7i	−0.951859	−	1.19889i
$997$	−9.61030e6			−0.306196			−0.153098	−	0.988211i	$-0.548925\pi$
$997$	−9.61030e6			−0.306196			−0.153098	+	0.988211i	$0.548925\pi$
$998$	5.94583e7			1.88967
$999$	1.00848e7	+	2.12924e7i	0.319708	+	0.675012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.d.b.176.3	✓	92
3.2	odd	2	inner	177.6.d.b.176.90	yes	92
59.58	odd	2	inner	177.6.d.b.176.89	yes	92
177.176	even	2	inner	177.6.d.b.176.4	yes	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.d.b.176.3	✓	92	1.1	even	1	trivial
177.6.d.b.176.4	yes	92	177.176	even	2	inner
177.6.d.b.176.89	yes	92	59.58	odd	2	inner
177.6.d.b.176.90	yes	92	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-10.7490 q^{2} +(9.69295 + 12.2085i) q^{3} +83.5412 q^{4} +33.1454i q^{5} +(-104.190 - 131.229i) q^{6} -174.539 q^{7} -554.017 q^{8} +(-55.0934 + 236.672i) q^{9} +O(q^{10})\)	\(q-10.7490 q^{2} +(9.69295 + 12.2085i) q^{3} +83.5412 q^{4} +33.1454i q^{5} +(-104.190 - 131.229i) q^{6} -174.539 q^{7} -554.017 q^{8} +(-55.0934 + 236.672i) q^{9} -356.281i q^{10} -67.7482 q^{11} +(809.761 + 1019.91i) q^{12} -762.395i q^{13} +1876.13 q^{14} +(-404.655 + 321.277i) q^{15} +3281.82 q^{16} -1054.79i q^{17} +(592.199 - 2543.99i) q^{18} +1517.46 q^{19} +2769.01i q^{20} +(-1691.80 - 2130.86i) q^{21} +728.226 q^{22} -1504.53 q^{23} +(-5370.06 - 6763.70i) q^{24} +2026.38 q^{25} +8194.99i q^{26} +(-3423.42 + 1621.45i) q^{27} -14581.2 q^{28} -4785.21i q^{29} +(4349.64 - 3453.41i) q^{30} +4004.32i q^{31} -17547.8 q^{32} +(-656.680 - 827.102i) q^{33} +11337.9i q^{34} -5785.18i q^{35} +(-4602.57 + 19771.9i) q^{36} -6219.64i q^{37} -16311.1 q^{38} +(9307.68 - 7389.86i) q^{39} -18363.2i q^{40} -14687.7i q^{41} +(18185.2 + 22904.6i) q^{42} +19978.1i q^{43} -5659.77 q^{44} +(-7844.60 - 1826.09i) q^{45} +16172.2 q^{46} +17461.3 q^{47} +(31810.5 + 40066.0i) q^{48} +13657.0 q^{49} -21781.6 q^{50} +(12877.4 - 10224.0i) q^{51} -63691.4i q^{52} +3262.05i q^{53} +(36798.4 - 17428.9i) q^{54} -2245.54i q^{55} +96697.9 q^{56} +(14708.6 + 18525.8i) q^{57} +51436.2i q^{58} +(-16303.5 + 21192.4i) q^{59} +(-33805.4 + 26839.9i) q^{60} -21833.5i q^{61} -43042.5i q^{62} +(9615.97 - 41308.6i) q^{63} +83602.8 q^{64} +25269.9 q^{65} +(7058.66 + 8890.53i) q^{66} -20335.2i q^{67} -88118.3i q^{68} +(-14583.3 - 18368.0i) q^{69} +62185.0i q^{70} +26490.5i q^{71} +(30522.7 - 131121. i) q^{72} +78490.3i q^{73} +66854.9i q^{74} +(19641.6 + 24739.0i) q^{75} +126770. q^{76} +11824.7 q^{77} +(-100048. + 79433.7i) q^{78} +78139.6 q^{79} +108777. i q^{80} +(-52978.4 - 26078.1i) q^{81} +157878. i q^{82} -36801.4 q^{83} +(-141335. - 178015. i) q^{84} +34961.4 q^{85} -214745. i q^{86} +(58420.0 - 46382.8i) q^{87} +37533.7 q^{88} +93253.5 q^{89} +(84321.7 + 19628.7i) q^{90} +133068. i q^{91} -125690. q^{92} +(-48886.7 + 38813.7i) q^{93} -187691. q^{94} +50296.7i q^{95} +(-170090. - 214231. i) q^{96} -42572.4i q^{97} -146799. q^{98} +(3732.48 - 16034.1i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more