LMFDB - Embedded newform 177.6.d.b.176.17

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			176.17
Character	$\chi$	$=$	177.176
Dual form			177.6.d.b.176.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.56324 q^{2} +(11.2364 + 10.8048i) q^{3} +25.2027 q^{4} -51.3528i q^{5} +(-84.9838 - 81.7190i) q^{6} +90.7178 q^{7} +51.4099 q^{8} +(9.51431 + 242.814i) q^{9} +O(q^{10})$	\(q-7.56324 q^{2} +(11.2364 + 10.8048i) q^{3} +25.2027 q^{4} -51.3528i q^{5} +(-84.9838 - 81.7190i) q^{6} +90.7178 q^{7} +51.4099 q^{8} +(9.51431 + 242.814i) q^{9} +388.394i q^{10} -682.512 q^{11} +(283.188 + 272.309i) q^{12} +90.5395i q^{13} -686.121 q^{14} +(554.855 - 577.022i) q^{15} -1195.31 q^{16} +771.900i q^{17} +(-71.9590 - 1836.46i) q^{18} +2480.56 q^{19} -1294.23i q^{20} +(1019.34 + 980.185i) q^{21} +5162.01 q^{22} -440.319 q^{23} +(577.663 + 555.472i) q^{24} +487.887 q^{25} -684.772i q^{26} +(-2516.64 + 2831.16i) q^{27} +2286.33 q^{28} -6844.72i q^{29} +(-4196.50 + 4364.16i) q^{30} -1052.51i q^{31} +7395.31 q^{32} +(-7668.99 - 7374.38i) q^{33} -5838.07i q^{34} -4658.62i q^{35} +(239.786 + 6119.55i) q^{36} +10492.0i q^{37} -18761.1 q^{38} +(-978.258 + 1017.34i) q^{39} -2640.04i q^{40} +16643.5i q^{41} +(-7709.55 - 7413.38i) q^{42} -6372.48i q^{43} -17201.1 q^{44} +(12469.2 - 488.587i) q^{45} +3330.24 q^{46} +27748.5 q^{47} +(-13431.0 - 12915.0i) q^{48} -8577.27 q^{49} -3690.01 q^{50} +(-8340.20 + 8673.40i) q^{51} +2281.84i q^{52} +26135.8i q^{53} +(19033.9 - 21412.7i) q^{54} +35048.9i q^{55} +4663.80 q^{56} +(27872.6 + 26801.9i) q^{57} +51768.3i q^{58} +(13187.9 + 23259.5i) q^{59} +(13983.8 - 14542.5i) q^{60} -9403.19i q^{61} +7960.42i q^{62} +(863.118 + 22027.5i) q^{63} -17682.6 q^{64} +4649.46 q^{65} +(58002.5 + 55774.2i) q^{66} +73133.4i q^{67} +19453.9i q^{68} +(-4947.61 - 4757.54i) q^{69} +35234.3i q^{70} -43754.6i q^{71} +(489.130 + 12483.0i) q^{72} +37991.9i q^{73} -79353.6i q^{74} +(5482.10 + 5271.50i) q^{75} +62516.8 q^{76} -61916.0 q^{77} +(7398.80 - 7694.39i) q^{78} -18676.1 q^{79} +61382.6i q^{80} +(-58868.0 + 4620.41i) q^{81} -125879. i q^{82} +108851. q^{83} +(25690.2 + 24703.3i) q^{84} +39639.3 q^{85} +48196.6i q^{86} +(73955.5 - 76910.1i) q^{87} -35087.9 q^{88} -51749.3 q^{89} +(-94307.4 + 3695.30i) q^{90} +8213.55i q^{91} -11097.2 q^{92} +(11372.2 - 11826.5i) q^{93} -209869. q^{94} -127384. i q^{95} +(83096.8 + 79904.6i) q^{96} +90907.7i q^{97} +64872.0 q^{98} +(-6493.63 - 165723. 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 $

$2$	−7.56324			−1.33701			−0.668503	−	0.743710i	$-0.733064\pi$
$2$	−7.56324			−1.33701			−0.668503	+	0.743710i	$0.733064\pi$
$3$	11.2364	+	10.8048i	0.720817	+	0.693126i
$3$	11.2364	+	10.8048i	0.720817	+	0.693126i
$4$	25.2027			0.787583
$5$		−	51.3528i		−	0.918627i	−0.888274	−	0.459314i	$-0.848095\pi$
$5$		−	51.3528i		−	0.918627i	0.888274	−	0.459314i	$-0.151905\pi$
$6$	−84.9838	−	81.7190i	−0.963736	−	0.926713i
$7$	90.7178			0.699758			0.349879	−	0.936795i	$-0.386223\pi$
$7$	90.7178			0.699758			0.349879	+	0.936795i	$0.386223\pi$
$8$	51.4099			0.284002
$9$	9.51431	+	242.814i	0.0391535	+	0.999233i
$10$			388.394i			1.22821i
$11$	−682.512			−1.70070			−0.850352	−	0.526214i	$-0.823611\pi$
$11$	−682.512			−1.70070			−0.850352	+	0.526214i	$0.823611\pi$
$12$	283.188	+	272.309i	0.567703	+	0.545894i
$13$			90.5395i			0.148587i	0.997236	+	0.0742933i	$0.0236701\pi$
$13$			90.5395i			0.148587i	−0.997236	+	0.0742933i	$0.976330\pi$
$14$	−686.121			−0.935580
$15$	554.855	−	577.022i	0.636724	−	0.662162i
$16$	−1195.31			−1.16730
$17$			771.900i			0.647797i	0.946092	+	0.323899i	$0.104994\pi$
$17$			771.900i			0.647797i	−0.946092	+	0.323899i	$0.895006\pi$
$18$	−71.9590	−	1836.46i	−0.0523485	−	1.33598i
$19$	2480.56			1.57640			0.788199	−	0.615420i	$-0.211014\pi$
$19$	2480.56			1.57640			0.788199	+	0.615420i	$0.211014\pi$
$20$		−	1294.23i		−	0.723496i
$21$	1019.34	+	980.185i	0.504397	+	0.485020i
$22$	5162.01			2.27385
$23$	−440.319			−0.173559			−0.0867796	−	0.996228i	$-0.527658\pi$
$23$	−440.319			−0.173559			−0.0867796	+	0.996228i	$0.527658\pi$
$24$	577.663	+	555.472i	0.204714	+	0.196849i
$25$	487.887			0.156124
$26$		−	684.772i		−	0.198661i
$27$	−2516.64	+	2831.16i	−0.664372	+	0.747402i
$28$	2286.33			0.551117
$29$		−	6844.72i		−	1.51133i	−0.654956	−	0.755667i	$-0.727313\pi$
$29$		−	6844.72i		−	1.51133i	0.654956	−	0.755667i	$-0.272687\pi$
$30$	−4196.50	+	4364.16i	−0.851304	+	0.885314i
$31$		−	1052.51i		−	0.196709i	−0.995151	−	0.0983544i	$-0.968642\pi$
$31$		−	1052.51i		−	0.196709i	0.995151	−	0.0983544i	$-0.0313579\pi$
$32$	7395.31			1.27668
$33$	−7668.99	−	7374.38i	−1.22590	−	1.17880i
$34$		−	5838.07i		−	0.866108i
$35$		−	4658.62i		−	0.642816i
$36$	239.786	+	6119.55i	0.0308367	+	0.786979i
$37$			10492.0i			1.25995i	0.776614	+	0.629976i	$0.216935\pi$
$37$			10492.0i			1.25995i	−0.776614	+	0.629976i	$0.783065\pi$
$38$	−18761.1			−2.10765
$39$	−978.258	+	1017.34i	−0.102989	+	0.107104i
$40$		−	2640.04i		−	0.260892i
$41$			16643.5i			1.54627i	0.634242	+	0.773134i	$0.281312\pi$
$41$			16643.5i			1.54627i	−0.634242	+	0.773134i	$0.718688\pi$
$42$	−7709.55	−	7413.38i	−0.674381	−	0.648474i
$43$		−	6372.48i		−	0.525578i	−0.964853	−	0.262789i	$-0.915358\pi$
$43$		−	6372.48i		−	0.525578i	0.964853	−	0.262789i	$-0.0846423\pi$
$44$	−17201.1			−1.33945
$45$	12469.2	−	488.587i	0.917923	−	0.0359675i
$46$	3330.24			0.232049
$47$	27748.5			1.83229			0.916146	−	0.400845i	$-0.131284\pi$
$47$	27748.5			1.83229			0.916146	+	0.400845i	$0.131284\pi$
$48$	−13431.0	−	12915.0i	−0.841406	−	0.809083i
$49$	−8577.27			−0.510339
$50$	−3690.01			−0.208738
$51$	−8340.20	+	8673.40i	−0.449005	+	0.466943i
$52$			2281.84i			0.117024i
$53$			26135.8i			1.27805i	0.769187	+	0.639023i	$0.220661\pi$
$53$			26135.8i			1.27805i	−0.769187	+	0.639023i	$0.779339\pi$
$54$	19033.9	−	21412.7i	0.888269	−	0.999281i
$55$			35048.9i			1.56231i
$56$	4663.80			0.198733
$57$	27872.6	+	26801.9i	1.13629	+	1.09264i
$58$			51768.3i			2.02066i
$59$	13187.9	+	23259.5i	0.493225	+	0.869902i
$59$	13187.9	+	23259.5i	0.493225	+	0.869902i
$60$	13983.8	−	14542.5i	0.501473	−	0.521508i
$61$		−	9403.19i		−	0.323557i	−0.986827	−	0.161778i	$-0.948277\pi$
$61$		−	9403.19i		−	0.323557i	0.986827	−	0.161778i	$-0.0517230\pi$
$62$			7960.42i			0.263001i
$63$	863.118	+	22027.5i	0.0273980	+	0.699221i
$64$	−17682.6			−0.539630
$65$	4649.46			0.136496
$66$	58002.5	+	55774.2i	1.63903	+	1.57606i
$67$			73133.4i			1.99035i	0.0981376	+	0.995173i	$0.468711\pi$
$67$			73133.4i			1.99035i	−0.0981376	+	0.995173i	$0.531289\pi$
$68$			19453.9i			0.510194i
$69$	−4947.61	−	4757.54i	−0.125104	−	0.120298i
$70$			35234.3i			0.859449i
$71$		−	43754.6i		−	1.03010i	−0.857161	−	0.515048i	$-0.827774\pi$
$71$		−	43754.6i		−	1.03010i	0.857161	−	0.515048i	$-0.172226\pi$
$72$	489.130	+	12483.0i	0.0111197	+	0.283785i
$73$			37991.9i			0.834419i	0.908810	+	0.417210i	$0.136992\pi$
$73$			37991.9i			0.834419i	−0.908810	+	0.417210i	$0.863008\pi$
$74$		−	79353.6i		−	1.68456i
$75$	5482.10	+	5271.50i	0.112537	+	0.108213i
$76$	62516.8			1.24155
$77$	−61916.0			−1.19008
$78$	7398.80	−	7694.39i	0.137697	−	0.143198i
$79$	−18676.1			−0.336681			−0.168340	−	0.985729i	$-0.553841\pi$
$79$	−18676.1			−0.336681			−0.168340	+	0.985729i	$0.553841\pi$
$80$			61382.6i			1.07231i
$81$	−58868.0	+	4620.41i	−0.996934	+	0.0782470i
$82$		−	125879.i		−	2.06737i
$83$	108851.			1.73436			0.867179	−	0.497996i	$-0.165931\pi$
$83$	108851.			1.73436			0.867179	+	0.497996i	$0.165931\pi$
$84$	25690.2	+	24703.3i	0.397255	+	0.381994i
$85$	39639.3			0.595084
$86$			48196.6i			0.702700i
$87$	73955.5	−	76910.1i	1.04754	−	1.08939i
$88$	−35087.9			−0.483004
$89$	−51749.3			−0.692516			−0.346258	−	0.938139i	$-0.612548\pi$
$89$	−51749.3			−0.692516			−0.346258	+	0.938139i	$0.612548\pi$
$90$	−94307.4	+	3695.30i	−1.22727	+	0.0480887i
$91$			8213.55i			0.103975i
$92$	−11097.2			−0.136692
$93$	11372.2	−	11826.5i	0.136344	−	0.141791i
$94$	−209869.			−2.44978
$95$		−	127384.i		−	1.44812i
$96$	83096.8	+	79904.6i	0.920251	+	0.884899i
$97$			90907.7i			0.981005i	0.871440	+	0.490503i	$0.163187\pi$
$97$			90907.7i			0.981005i	−0.871440	+	0.490503i	$0.836813\pi$
$98$	64872.0			0.682326
$99$	−6493.63	−	165723.i	−0.0665886	−	1.69940i
$100$	12296.0			0.122960
$101$	−73494.3			−0.716886			−0.358443	−	0.933552i	$-0.616692\pi$
$101$	−73494.3			−0.716886			−0.358443	+	0.933552i	$0.616692\pi$
$102$	63079.0	−	65599.0i	0.600322	−	0.624305i
$103$			105537.i			0.980193i	0.871668	+	0.490096i	$0.163038\pi$
$103$			105537.i			0.980193i	−0.871668	+	0.490096i	$0.836962\pi$
$104$			4654.63i			0.0421989i
$105$	50335.3	−	52346.2i	0.445553	−	0.463353i
$106$		−	197672.i		−	1.70875i
$107$			205373.i			1.73414i	0.498186	+	0.867070i	$0.334000\pi$
$107$			205373.i			1.73414i	−0.498186	+	0.867070i	$0.666000\pi$
$108$	−63426.0	+	71352.7i	−0.523248	+	0.588642i
$109$		−	15975.9i		−	0.128795i	−0.997924	−	0.0643976i	$-0.979487\pi$
$109$		−	15975.9i		−	0.128795i	0.997924	−	0.0643976i	$-0.0205126\pi$
$110$		−	265084.i		−	2.08882i
$111$	−113364.	+	117893.i	−0.873305	+	0.908195i
$112$	−108436.			−0.816824
$113$	187107.			1.37846			0.689229	−	0.724544i	$-0.257950\pi$
$113$	187107.			1.37846			0.689229	+	0.724544i	$0.257950\pi$
$114$	−210808.	−	202709.i	−1.51923	−	1.46087i
$115$			22611.6i			0.159436i
$116$		−	172505.i		−	1.19030i
$117$	−21984.2	+	861.421i	−0.148473	+	0.00581769i
$118$	−99743.2	−	175917.i	−0.659444	−	1.16306i
$119$			70025.1i			0.453301i
$120$	28525.0	−	29664.6i	0.180831	−	0.188056i
$121$	304772.			1.89239
$122$			71118.6i			0.432597i
$123$	−179829.	+	187013.i	−1.07176	+	1.11458i
$124$		−	26526.2i		−	0.154925i
$125$		−	185532.i		−	1.06205i
$126$	−6527.97	−	166600.i	−0.0366312	−	0.934862i
$127$	−160262.			−0.881703			−0.440851	−	0.897580i	$-0.645323\pi$
$127$	−160262.			−0.881703			−0.440851	+	0.897580i	$0.645323\pi$
$128$	−102912.			−0.555190
$129$	68853.1	−	71603.8i	0.364291	−	0.378845i
$130$	−35165.0			−0.182496
$131$	16913.4			0.0861098			0.0430549	−	0.999073i	$-0.486291\pi$
$131$	16913.4			0.0861098			0.0430549	+	0.999073i	$0.486291\pi$
$132$	−193279.	−	185854.i	−0.965495	−	0.928404i
$133$	225031.			1.10310
$134$		−	553125.i		−	2.66110i
$135$	145388.	+	129236.i	0.686584	+	0.610310i
$136$			39683.3i			0.183976i
$137$			125031.i			0.569135i	0.958656	+	0.284568i	$0.0918500\pi$
$137$			125031.i			0.569135i	−0.958656	+	0.284568i	$0.908150\pi$
$138$	37419.9	+	35982.4i	0.167265	+	0.160839i
$139$	−85153.3			−0.373822			−0.186911	−	0.982377i	$-0.559848\pi$
$139$	−85153.3			−0.373822			−0.186911	+	0.982377i	$0.559848\pi$
$140$		−	117410.i		−	0.506272i
$141$	311794.	+	299816.i	1.32075	+	1.27001i
$142$			330927.i			1.37724i
$143$		−	61794.3i		−	0.252702i
$144$	−11372.6	−	290238.i	−0.0457038	−	1.16640i
$145$	−351496.			−1.38835
$146$		−	287342.i		−	1.11562i
$147$	−96377.8	−	92675.4i	−0.367861	−	0.353729i
$148$			264426.i			0.992318i
$149$	160185.			0.591092			0.295546	−	0.955329i	$-0.404498\pi$
$149$	160185.			0.591092			0.295546	+	0.955329i	$0.404498\pi$
$150$	−41462.5	−	39869.6i	−0.150462	−	0.144682i
$151$		−	271823.i		−	0.970160i	−0.874470	−	0.485080i	$-0.838790\pi$
$151$		−	271823.i		−	0.970160i	0.874470	−	0.485080i	$-0.161210\pi$
$152$	127525.			0.447701
$153$	−187428.	+	7344.10i	−0.647300	+	0.0253635i
$154$	468286.			1.59114
$155$	−54049.6			−0.180702
$156$	−24654.7	+	25639.7i	−0.0811126	+	0.0843531i
$157$		−	116338.i		−	0.376681i	−0.982104	−	0.188340i	$-0.939689\pi$
$157$		−	116338.i		−	0.376681i	0.982104	−	0.188340i	$-0.0603108\pi$
$158$	141252.			0.450144
$159$	−282391.	+	293673.i	−0.885847	+	0.921237i
$160$		−	379770.i		−	1.17279i
$161$	−39944.8			−0.121449
$162$	445233.	−	34945.3i	1.33291	−	0.104617i
$163$	−157521.			−0.464377			−0.232188	−	0.972671i	$-0.574589\pi$
$163$	−157521.			−0.464377			−0.232188	+	0.972671i	$0.574589\pi$
$164$			419461.i			1.21782i
$165$	−378695.	+	393825.i	−1.08288	+	1.12614i
$166$	−823270.			−2.31885
$167$		−	284864.i		−	0.790399i	−0.918595	−	0.395199i	$-0.870676\pi$
$167$		−	284864.i		−	0.790399i	0.918595	−	0.395199i	$-0.129324\pi$
$168$	52404.4	+	50391.2i	0.143250	+	0.137747i
$169$	363096.			0.977922
$170$	−299802.			−0.795631
$171$	23600.8	+	602314.i	0.0617216	+	1.57519i
$172$		−	160603.i		−	0.413936i
$173$	331355.			0.841740			0.420870	−	0.907121i	$-0.361725\pi$
$173$	331355.			0.841740			0.420870	+	0.907121i	$0.361725\pi$
$174$	−559344.	+	581690.i	−1.40057	+	1.45653i
$175$	44260.0			0.109249
$176$	815814.			1.98522
$177$	−103129.	+	403845.i	−0.247426	+	0.968907i
$178$	391393.			0.925897
$179$	−284128.			−0.662799			−0.331399	−	0.943491i	$-0.607521\pi$
$179$	−284128.			−0.662799			−0.331399	+	0.943491i	$0.607521\pi$
$180$	314256.	−	12313.7i	0.722941	−	0.0283274i
$181$	353188.			0.801327			0.400663	−	0.916225i	$-0.368780\pi$
$181$	353188.			0.801327			0.400663	+	0.916225i	$0.368780\pi$
$182$		−	62121.1i		−	0.139015i
$183$	101599.	−	105658.i	0.224266	−	0.233225i
$184$	−22636.7			−0.0492912
$185$	538794.			1.15743
$186$	−86010.4	+	89446.6i	−0.182293	+	0.189575i
$187$		−	526831.i		−	1.10171i
$188$	699336.			1.44308
$189$	−228304.	+	256836.i	−0.464899	+	0.523000i
$190$			963435.i			1.93615i
$191$	409474.			0.812162			0.406081	−	0.913837i	$-0.366895\pi$
$191$	409474.			0.812162			0.406081	+	0.913837i	$0.366895\pi$
$192$	−198689.	−	191056.i	−0.388974	−	0.374032i
$193$	−77555.3			−0.149871			−0.0749356	−	0.997188i	$-0.523875\pi$
$193$	−77555.3			−0.149871			−0.0749356	+	0.997188i	$0.523875\pi$
$194$		−	687557.i		−	1.31161i
$195$	52243.3	+	50236.3i	0.0983884	+	0.0946087i
$196$	−216170.			−0.401935
$197$			666250.i			1.22313i	0.791195	+	0.611564i	$0.209459\pi$
$197$			666250.i			1.22313i	−0.791195	+	0.611564i	$0.790541\pi$
$198$	49112.9	+	1.25341e6i	0.0890293	+	2.27211i
$199$	−151342.			−0.270911			−0.135456	−	0.990783i	$-0.543250\pi$
$199$	−151342.			−0.270911			−0.135456	+	0.990783i	$0.543250\pi$
$200$	25082.2			0.0443395
$201$	−790188.	+	821757.i	−1.37956	+	1.43467i
$202$	555855.			0.958480
$203$		−	620938.i		−	1.05757i
$204$	−210195.	+	218593.i	−0.353629	+	0.367756i
$205$	854691.			1.42044
$206$		−	798202.i		−	1.31052i
$207$	−4189.33	−	106915.i	−0.00679545	−	0.173426i
$208$		−	108223.i		−	0.173445i
$209$	−1.69301e6			−2.68099
$210$	−380698.	+	395907.i	−0.595706	+	0.619505i
$211$			252243.i			0.390043i	0.980799	+	0.195021i	$0.0624776\pi$
$211$			252243.i			0.390043i	−0.980799	+	0.195021i	$0.937522\pi$
$212$			658693.i			1.00657i
$213$	472758.	−	491645.i	0.713986	−	0.742511i
$214$		−	1.55329e6i		−	2.31856i
$215$	−327245.			−0.482810
$216$	−129380.	+	145549.i	−0.188683	+	0.212264i
$217$		−	95481.8i		−	0.137648i
$218$			120830.i			0.172200i
$219$	−410494.	+	426893.i	−0.578357	+	0.601463i
$220$			883327.i			1.23045i
$221$	−69887.5			−0.0962540
$222$	857397.	−	891650.i	1.16761	−	1.21426i
$223$	278083.			0.374466			0.187233	−	0.982315i	$-0.440048\pi$
$223$	278083.			0.374466			0.187233	+	0.982315i	$0.440048\pi$
$224$	670887.			0.893366
$225$	4641.91	+	118466.i	0.00611280	+	0.156004i
$226$	−1.41513e6			−1.84300
$227$	−1.13709e6			−1.46463			−0.732317	−	0.680964i	$-0.761561\pi$
$227$	−1.13709e6			−1.46463			−0.732317	+	0.680964i	$0.761561\pi$
$228$	702465.	+	675479.i	0.894927	+	0.860547i
$229$		−	556703.i		−	0.701511i	−0.936467	−	0.350756i	$-0.885925\pi$
$229$		−	556703.i		−	0.701511i	0.936467	−	0.350756i	$-0.114075\pi$
$230$		−	171017.i		−	0.213167i
$231$	−695715.	−	668988.i	−0.857830	−	0.824875i
$232$		−	351886.i		−	0.429222i
$233$	1.01799e6			1.22844			0.614218	−	0.789137i	$-0.289472\pi$
$233$	1.01799e6			1.22844			0.614218	+	0.789137i	$0.289472\pi$
$234$	166272.	−	6515.14i	0.198509	−	0.00777828i
$235$		−	1.42496e6i		−	1.68319i
$236$	332370.	+	586201.i	0.388456	+	0.685120i
$237$	−209852.	−	201791.i	−0.242685	−	0.233362i
$238$		−	529617.i		−	0.606066i
$239$		−	141346.i		−	0.160062i	−0.996792	−	0.0800311i	$-0.974498\pi$
$239$		−	141346.i		−	0.160062i	0.996792	−	0.0800311i	$-0.0255020\pi$
$240$	−663224.	+	689721.i	−0.743246	+	0.772939i
$241$	405397.			0.449612			0.224806	−	0.974403i	$-0.427825\pi$
$241$	405397.			0.449612			0.224806	+	0.974403i	$0.427825\pi$
$242$	−2.30506e6			−2.53014
$243$	−711388.	−	584137.i	−0.772842	−	0.634599i
$244$		−	236985.i		−	0.254828i
$245$			440467.i			0.468812i
$246$	1.36009e6	−	1.41443e6i	1.43295	−	1.49019i
$247$			224589.i			0.234232i
$248$		−	54109.6i		−	0.0558657i
$249$	1.22310e6	+	1.17611e6i	1.25015	+	1.20213i
$250$			1.40322e6i			1.41996i
$251$			1.09091e6i			1.09296i	0.837471	+	0.546482i	$0.184033\pi$
$251$			1.09091e6i			1.09296i	−0.837471	+	0.546482i	$0.815967\pi$
$252$	21752.9	+	555153.i	0.0215782	+	0.550695i
$253$	300523.			0.295173
$254$	1.21210e6			1.17884
$255$	445404.	+	428293.i	0.428947	+	0.412468i
$256$	1.34419e6			1.28192
$257$			4748.15i			0.00448427i	0.999997	+	0.00224213i	$0.000713694\pi$
$257$			4748.15i			0.00448427i	−0.999997	+	0.00224213i	$0.999286\pi$
$258$	−520753.	+	541557.i	−0.487060	+	0.506518i
$259$			951812.i			0.881661i
$260$	117179.			0.107502
$261$	1.66199e6	−	65122.7i	1.51018	−	0.0591741i
$262$	−127920.			−0.115129
$263$			500879.i			0.446522i	0.974759	+	0.223261i	$0.0716703\pi$
$263$			500879.i			0.446522i	−0.974759	+	0.223261i	$0.928330\pi$
$264$	−394262.	−	379116.i	−0.348157	−	0.334782i
$265$	1.34215e6			1.17405
$266$	−1.70197e6			−1.47485
$267$	−581477.	−	559139.i	−0.499177	−	0.480000i
$268$			1.84316e6i			1.56756i
$269$	−1.84500e6			−1.55459			−0.777293	−	0.629139i	$-0.783408\pi$
$269$	−1.84500e6			−1.55459			−0.777293	+	0.629139i	$0.783408\pi$
$270$	−1.09960e6	−	977447.i	−0.917967	−	0.815988i
$271$	417363.			0.345216			0.172608	−	0.984991i	$-0.444781\pi$
$271$	417363.			0.345216			0.172608	+	0.984991i	$0.444781\pi$
$272$		−	922661.i		−	0.756171i
$273$	−88745.4	+	92290.9i	−0.0720675	+	0.0749467i
$274$		−	945638.i		−	0.760937i
$275$	−332989.			−0.265520
$276$	−124693.	−	119903.i	−0.0985301	−	0.0947449i
$277$	50456.3			0.0395108			0.0197554	−	0.999805i	$-0.493711\pi$
$277$	50456.3			0.0395108			0.0197554	+	0.999805i	$0.493711\pi$
$278$	644035.			0.499802
$279$	255565.	−	10013.9i	0.196558	−	0.00770184i
$280$		−	239499.i		−	0.182561i
$281$			289552.i			0.218756i	0.994000	+	0.109378i	$0.0348859\pi$
$281$			289552.i			0.218756i	−0.994000	+	0.109378i	$0.965114\pi$
$282$	−2.35817e6	−	2.26758e6i	−1.76584	−	1.69801i
$283$		−	1.82269e6i		−	1.35284i	−0.736514	−	0.676422i	$-0.763530\pi$
$283$		−	1.82269e6i		−	1.35284i	0.736514	−	0.676422i	$-0.236470\pi$
$284$		−	1.10273e6i		−	0.811287i
$285$	1.37635e6	−	1.43134e6i	1.00373	−	1.04383i
$286$			467366.i			0.337864i
$287$			1.50986e6i			1.08201i
$288$	70361.3	+	1.79568e6i	0.0499865	+	1.27570i
$289$	824027.			0.580359
$290$	2.65845e6			1.85624
$291$	−982236.	+	1.02148e6i	−0.679960	+	0.707125i
$292$			957498.i			0.657175i
$293$		−	2.68342e6i		−	1.82608i	−0.407872	−	0.913039i	$-0.633729\pi$
$293$		−	2.68342e6i		−	1.82608i	0.407872	−	0.913039i	$-0.366271\pi$
$294$	728929.	+	700926.i	0.491832	+	0.472938i
$295$	1.19444e6	−	677235.i	0.799116	−	0.453090i
$296$			539393.i			0.357829i
$297$	1.71764e6	−	1.93230e6i	1.12990	−	1.27111i
$298$	−1.21151e6			−0.790293
$299$		−	39866.2i		−	0.0257886i
$300$	138164.	+	132856.i	0.0886320	+	0.0852271i
$301$		−	578097.i		−	0.367777i
$302$			2.05586e6i			1.29711i
$303$	−825813.	−	794088.i	−0.516743	−	0.496892i
$304$	−2.96504e6			−1.84012
$305$	−482880.			−0.297228
$306$	1.41756e6	−	55545.2i	0.865444	−	0.0339112i
$307$	509116.			0.308298			0.154149	−	0.988048i	$-0.450736\pi$
$307$	509116.			0.308298			0.154149	+	0.988048i	$0.450736\pi$
$308$	−1.56045e6			−0.937288
$309$	−1.14030e6	+	1.18586e6i	−0.679397	+	0.706539i
$310$	408790.			0.241600
$311$			1.38212e6i			0.810297i	0.914251	+	0.405148i	$0.132780\pi$
$311$			1.38212e6i			0.810297i	−0.914251	+	0.405148i	$0.867220\pi$
$312$	−50292.1	+	52301.4i	−0.0292492	+	0.0304177i
$313$			1.90212e6i			1.09743i	0.836009	+	0.548716i	$0.184883\pi$
$313$			1.90212e6i			1.09743i	−0.836009	+	0.548716i	$0.815117\pi$
$314$			879895.i			0.503624i
$315$	1.13118e6	−	44323.5i	0.642324	−	0.0251685i
$316$	−470687.			−0.265164
$317$		−	3.01161e6i		−	1.68326i	−0.540055	−	0.841630i	$-0.681597\pi$
$317$		−	3.01161e6i		−	1.68326i	0.540055	−	0.841630i	$-0.318403\pi$
$318$	2.13579e6	−	2.22112e6i	1.18438	−	1.23170i
$319$			4.67160e6i			2.57033i
$320$			908052.i			0.495719i
$321$	−2.21901e6	+	2.30766e6i	−1.20198	+	1.25000i
$322$	302112.			0.162378
$323$			1.91475e6i			1.02119i
$324$	−1.48363e6	+	116447.i	−0.785169	+	0.0616260i
$325$			44173.0i			0.0231979i
$326$	1.19137e6			0.620874
$327$	172616.	−	179512.i	0.0892712	−	0.0928377i
$328$			855641.i			0.439144i
$329$	2.51728e6			1.28216
$330$	2.86417e6	−	2.97859e6i	1.44782	−	1.50566i
$331$	−2.25633e6			−1.13196			−0.565981	−	0.824418i	$-0.691503\pi$
$331$	−2.25633e6			−1.13196			−0.565981	+	0.824418i	$0.691503\pi$
$332$	2.74335e6			1.36595
$333$	−2.54760e6	+	99824.2i	−1.25899	+	0.0493316i
$334$			2.15449e6i			1.05677i
$335$	3.75560e6			1.82839
$336$	−1.21843e6	−	1.17163e6i	−0.588781	−	0.566162i
$337$		−	893788.i		−	0.428706i	−0.976756	−	0.214353i	$-0.931236\pi$
$337$		−	893788.i		−	0.428706i	0.976756	−	0.214353i	$-0.0687643\pi$
$338$	−2.74618e6			−1.30749
$339$	2.10241e6	+	2.02164e6i	0.993615	+	0.955444i
$340$	999015.			0.468678
$341$			718354.i			0.334543i
$342$	−178499.	−	4.55545e6i	−0.0825221	−	2.10604i
$343$	−2.30281e6			−1.05687
$344$		−	327608.i		−	0.149265i
$345$	−244313.	+	254074.i	−0.110509	+	0.114924i
$346$	−2.50612e6			−1.12541
$347$	208504.			0.0929589			0.0464794	−	0.998919i	$-0.485200\pi$
$347$	208504.			0.0929589			0.0464794	+	0.998919i	$0.485200\pi$
$348$	1.86388e6	−	1.93834e6i	0.825029	−	0.857989i
$349$		−	3.61848e6i		−	1.59024i	−0.606454	−	0.795119i	$-0.707408\pi$
$349$		−	3.61848e6i		−	1.59024i	0.606454	−	0.795119i	$-0.292592\pi$
$350$	−334750.			−0.146066
$351$	−256332.	−	227855.i	−0.111054	−	0.0987168i
$352$	−5.04739e6			−2.17125
$353$	−920606.			−0.393221			−0.196611	−	0.980482i	$-0.562993\pi$
$353$	−920606.			−0.393221			−0.196611	+	0.980482i	$0.562993\pi$
$354$	779987.	−	3.05438e6i	0.330811	−	1.29543i
$355$	−2.24692e6			−0.946275
$356$	−1.30422e6			−0.545414
$357$	−756605.	+	786832.i	−0.314195	+	0.326747i
$358$	2.14893e6			0.886166
$359$		−	3.37657e6i		−	1.38274i	−0.722503	−	0.691368i	$-0.757008\pi$
$359$		−	3.37657e6i		−	1.38274i	0.722503	−	0.691368i	$-0.242992\pi$
$360$	641039.	−	25118.2i	0.260692	−	0.0102149i
$361$	3.67709e6			1.48503
$362$	−2.67125e6			−1.07138
$363$	3.42455e6	+	3.29299e6i	1.36407	+	1.31167i
$364$			207003.i			0.0818887i
$365$	1.95099e6			0.766520
$366$	−768420.	+	799119.i	−0.299844	+	0.311823i
$367$			752319.i			0.291566i	0.989317	+	0.145783i	$0.0465701\pi$
$367$			752319.i			0.291566i	−0.989317	+	0.145783i	$0.953430\pi$
$368$	526318.			0.202595
$369$	−4.04127e6	+	158351.i	−1.54508	+	0.0605419i
$370$	−4.07503e6			−1.54749
$371$			2.37099e6i			0.894323i
$372$	286609.	−	298059.i	0.107382	−	0.111672i
$373$	−3.35113e6			−1.24715			−0.623576	−	0.781763i	$-0.714321\pi$
$373$	−3.35113e6			−1.24715			−0.623576	+	0.781763i	$0.714321\pi$
$374$			3.98456e6i			1.47299i
$375$	2.00463e6	−	2.08472e6i	0.736132	−	0.765541i
$376$	1.42655e6			0.520375
$377$	619717.			0.224564
$378$	1.72672e6	−	1.94252e6i	0.621573	−	0.699254i
$379$	−1.39388e6			−0.498456			−0.249228	−	0.968445i	$-0.580177\pi$
$379$	−1.39388e6			−0.498456			−0.249228	+	0.968445i	$0.580177\pi$
$380$		−	3.21041e6i		−	1.14052i
$381$	−1.80078e6	−	1.73160e6i	−0.635546	−	0.611131i
$382$	−3.09695e6			−1.08587
$383$		−	5.08435e6i		−	1.77108i	−0.464560	−	0.885541i	$-0.653788\pi$
$383$		−	5.08435e6i		−	1.77108i	0.464560	−	0.885541i	$-0.346212\pi$
$384$	−1.15636e6	−	1.11194e6i	−0.400190	−	0.384817i
$385$			3.17956e6i			1.09324i
$386$	586569.			0.200379
$387$	1.54732e6	−	60629.7i	0.525175	−	0.0205782i
$388$			2.29112e6i			0.772623i
$389$		−	133568.i		−	0.0447536i	−0.999750	−	0.0223768i	$-0.992877\pi$
$389$		−	133568.i		−	0.0447536i	0.999750	−	0.0223768i	$-0.00712335\pi$
$390$	−395129.	−	379949.i	−0.131546	−	0.126492i
$391$		−	339882.i		−	0.112431i
$392$	−440957.			−0.144938
$393$	190046.	+	182745.i	0.0620694	+	0.0596849i
$394$		−	5.03901e6i		−	1.63533i
$395$			959070.i			0.309284i
$396$	−163657.	−	4.17667e6i	−0.0524440	−	1.33842i
$397$		−	4.15269e6i		−	1.32237i	−0.750223	−	0.661185i	$-0.770054\pi$
$397$		−	4.15269e6i		−	1.32237i	0.750223	−	0.661185i	$-0.229946\pi$
$398$	1.14464e6			0.362210
$399$	2.52855e6	+	2.43141e6i	0.795131	+	0.764585i
$400$	−583177.			−0.182243
$401$	−2.86291e6			−0.889092			−0.444546	−	0.895756i	$-0.646635\pi$
$401$	−2.86291e6			−0.889092			−0.444546	+	0.895756i	$0.646635\pi$
$402$	5.97639e6	−	6.21515e6i	1.84448	−	1.91817i
$403$	95294.1			0.0292283
$404$	−1.85225e6			−0.564607
$405$	237271.	+	3.02304e6i	0.0718798	+	0.915811i
$406$			4.69631e6i			1.41397i
$407$		−	7.16092e6i		−	2.14281i
$408$	−428769.	+	445899.i	−0.127518	+	0.132613i
$409$			1.11852e6i			0.330625i	0.986241	+	0.165313i	$0.0528633\pi$
$409$			1.11852e6i			0.330625i	−0.986241	+	0.165313i	$0.947137\pi$
$410$	−6.46423e6			−1.89914
$411$	−1.35093e6	+	1.40490e6i	−0.394482	+	0.410242i
$412$			2.65981e6i			0.771983i
$413$	1.19638e6	+	2.11005e6i	0.345138	+	0.608720i
$414$	31684.9	+	808627.i	0.00908556	+	0.231872i
$415$		−	5.58983e6i		−	1.59323i
$416$			669568.i			0.189697i
$417$	−956818.	−	920061.i	−0.269457	−	0.259105i
$418$	1.28047e7			3.58449
$419$	2.23799e6			0.622764			0.311382	−	0.950285i	$-0.399208\pi$
$419$	2.23799e6			0.622764			0.311382	+	0.950285i	$0.399208\pi$
$420$	1.26858e6	−	1.31926e6i	0.350910	−	0.364929i
$421$		−	5.55658e6i		−	1.52793i	−0.645260	−	0.763963i	$-0.723251\pi$
$421$		−	5.55658e6i		−	1.52793i	0.645260	−	0.763963i	$-0.276749\pi$
$422$		−	1.90777e6i		−	0.521489i
$423$	264008.	+	6.73771e6i	0.0717407	+	1.83089i
$424$			1.34364e6i			0.362968i
$425$			376600.i			0.101137i
$426$	−3.57559e6	+	3.71843e6i	−0.954604	+	0.992741i
$427$		−	853037.i		−	0.226411i
$428$			5.17595e6i			1.36578i
$429$	667673.	−	694347.i	0.175154	−	0.182152i
$430$	2.47503e6			0.645520
$431$	−4.62303e6			−1.19876			−0.599381	−	0.800464i	$-0.704587\pi$
$431$	−4.62303e6			−1.19876			−0.599381	+	0.800464i	$0.704587\pi$
$432$	3.00816e6	−	3.38411e6i	0.775518	−	0.872440i
$433$	1.20291e6			0.308328			0.154164	−	0.988045i	$-0.450732\pi$
$433$	1.20291e6			0.308328			0.154164	+	0.988045i	$0.450732\pi$
$434$			722152.i			0.184037i
$435$	−3.94955e6	−	3.79783e6i	−1.00075	−	0.962303i
$436$		−	402636.i		−	0.101437i
$437$	−1.09224e6			−0.273598
$438$	3.10466e6	−	3.22870e6i	0.773267	−	0.804160i
$439$	1.81269e6			0.448912			0.224456	−	0.974484i	$-0.427939\pi$
$439$	1.81269e6			0.448912			0.224456	+	0.974484i	$0.427939\pi$
$440$			1.80186e6i			0.443700i
$441$	−81606.8	−	2.08268e6i	−0.0199816	−	0.509948i
$442$	528576.			0.128692
$443$	−4.60126e6			−1.11395			−0.556977	−	0.830528i	$-0.688039\pi$
$443$	−4.60126e6			−1.11395			−0.556977	+	0.830528i	$0.688039\pi$
$444$	−2.85706e6	+	2.97121e6i	−0.687801	+	0.715279i
$445$			2.65747e6i			0.636164i
$446$	−2.10321e6			−0.500664
$447$	1.79990e6	+	1.73076e6i	0.426069	+	0.409701i
$448$	−1.60413e6			−0.377610
$449$			3.94651e6i			0.923840i	0.886921	+	0.461920i	$0.152839\pi$
$449$			3.94651e6i			0.923840i	−0.886921	+	0.461920i	$0.847161\pi$
$450$	−35107.9	−	895984.i	−0.00817284	−	0.208578i
$451$		−	1.13594e7i		−	2.62975i
$452$	4.71559e6			1.08565
$453$	2.93698e6	−	3.05432e6i	0.672443	−	0.699308i
$454$	8.60007e6			1.95822
$455$	421789.			0.0955139
$456$	1.43293e6	+	1.37788e6i	0.322710	+	0.310313i
$457$			1.48061e6i			0.331626i	0.986157	+	0.165813i	$0.0530248\pi$
$457$			1.48061e6i			0.331626i	−0.986157	+	0.165813i	$0.946975\pi$
$458$			4.21048e6i			0.937924i
$459$	−2.18537e6	−	1.94259e6i	−0.484165	−	0.430378i
$460$			569873.i			0.125569i
$461$		−	1.08421e6i		−	0.237608i	−0.992918	−	0.118804i	$-0.962094\pi$
$461$		−	1.08421e6i		−	0.237608i	0.992918	−	0.118804i	$-0.0379060\pi$
$462$	5.26186e6	+	5.05972e6i	1.14692	+	1.10286i
$463$			5.94024e6i			1.28781i	0.765106	+	0.643904i	$0.222687\pi$
$463$			5.94024e6i			1.28781i	−0.765106	+	0.643904i	$0.777313\pi$
$464$			8.18157e6i			1.76417i
$465$	−607324.	−	583993.i	−0.130253	−	0.125249i
$466$	−7.69928e6			−1.64242
$467$	−4.27370e6			−0.906800			−0.453400	−	0.891307i	$-0.649789\pi$
$467$	−4.27370e6			−0.906800			−0.453400	+	0.891307i	$0.649789\pi$
$468$	−554061.	+	21710.1i	−0.116935	+	0.00458192i
$469$			6.63450e6i			1.39276i
$470$			1.07773e7i			2.25044i
$471$	1.25701e6	−	1.30723e6i	0.261087	−	0.271518i
$472$	677988.	+	1.19577e6i	0.140077	+	0.247054i
$473$			4.34929e6i			0.893852i
$474$	1.58716e6	+	1.52619e6i	0.324471	+	0.312006i
$475$	1.21023e6			0.246113
$476$			1.76482e6i			0.357012i
$477$	−6.34614e6	+	248664.i	−1.27707	+	0.0500400i
$478$			1.06903e6i			0.214004i
$479$			8.56691e6i			1.70602i	0.521891	+	0.853012i	$0.325227\pi$
$479$			8.56691e6i			1.70602i	−0.521891	+	0.853012i	$0.674773\pi$
$480$	4.10333e6	−	4.26726e6i	0.812892	−	0.845368i
$481$	−949941.			−0.187212
$482$	−3.06612e6			−0.601134
$483$	−448836.	−	431594.i	−0.0875427	−	0.0841796i
$484$	7.68106e6			1.49042
$485$	4.66837e6			0.901178
$486$	5.38040e6	+	4.41797e6i	1.03329	+	0.848462i
$487$	6.39670e6			1.22217			0.611087	−	0.791563i	$-0.290732\pi$
$487$	6.39670e6			1.22217			0.611087	+	0.791563i	$0.290732\pi$
$488$		−	483417.i		−	0.0918909i
$489$	−1.76998e6	−	1.70198e6i	−0.334731	−	0.321872i
$490$		−	3.33136e6i		−	0.626804i
$491$		−	355606.i		−	0.0665681i	−0.999446	−	0.0332840i	$-0.989403\pi$
$491$		−	355606.i		−	0.0665681i	0.999446	−	0.0332840i	$-0.0105966\pi$
$492$	−4.53217e6	+	4.71323e6i	−0.844099	+	0.877822i
$493$	5.28344e6			0.979038
$494$		−	1.69862e6i		−	0.313169i
$495$	−8.51036e6	+	333466.i	−1.56112	+	0.0611701i
$496$			1.25808e6i			0.229617i
$497$		−	3.96932e6i		−	0.720818i
$498$	−9.25061e6	−	8.89523e6i	−1.67146	−	1.60725i
$499$	−6.30405e6			−1.13336			−0.566681	−	0.823937i	$-0.691773\pi$
$499$	−6.30405e6			−1.13336			−0.566681	+	0.823937i	$0.691773\pi$
$500$		−	4.67590e6i		−	0.836450i
$501$	3.07789e6	−	3.20085e6i	0.547846	−	0.569733i
$502$		−	8.25085e6i		−	1.46130i
$503$	8.08256e6			1.42439			0.712195	−	0.701982i	$-0.247701\pi$
$503$	8.08256e6			1.42439			0.712195	+	0.701982i	$0.247701\pi$
$504$	44372.8	+	1.13243e6i	0.00778109	+	0.198580i
$505$			3.77414e6i			0.658551i
$506$	−2.27293e6			−0.394647
$507$	4.07989e6	+	3.92316e6i	0.704903	+	0.677823i
$508$	−4.03904e6			−0.694414
$509$	1.08452e6			0.185542			0.0927709	−	0.995687i	$-0.470428\pi$
$509$	1.08452e6			0.185542			0.0927709	+	0.995687i	$0.470428\pi$
$510$	−3.36870e6	−	3.23928e6i	−0.573504	−	0.551472i
$511$			3.44655e6i			0.583891i
$512$	−6.87327e6			−1.15875
$513$	−6.24267e6	+	7.02286e6i	−1.04731	+	1.17820i
$514$		−	35911.4i		−	0.00599549i
$515$	5.41962e6			0.900432
$516$	1.73528e6	−	1.80461e6i	0.286910	−	0.298372i
$517$	−1.89387e7			−3.11619
$518$		−	7.19879e6i		−	1.17879i
$519$	3.72324e6	+	3.58021e6i	0.606740	+	0.583432i
$520$	239028.			0.0387651
$521$		−	2.94176e6i		−	0.474802i	−0.971412	−	0.237401i	$-0.923704\pi$
$521$		−	2.94176e6i		−	0.474802i	0.971412	−	0.237401i	$-0.0762956\pi$
$522$	−1.25700e7	+	492539.i	−2.01911	+	0.0791160i
$523$	−7.68801e6			−1.22902			−0.614511	−	0.788908i	$-0.710647\pi$
$523$	−7.68801e6			−1.22902			−0.614511	+	0.788908i	$0.710647\pi$
$524$	426263.			0.0678186
$525$	497325.	+	478219.i	0.0787484	+	0.0757232i
$526$		−	3.78827e6i		−	0.597003i
$527$	812436.			0.127427
$528$	9.16683e6	+	8.81468e6i	1.43098	+	1.37601i
$529$	−6.24246e6			−0.969877
$530$	−1.01510e7			−1.56971
$531$	−5.52225e6	+	3.42350e6i	−0.849923	+	0.526906i
$532$	5.67139e6			0.868781
$533$	−1.50689e6			−0.229755
$534$	4.39785e6	+	4.22890e6i	0.667402	+	0.641763i
$535$	1.05465e7			1.59303
$536$			3.75978e6i			0.565263i
$537$	−3.19258e6	−	3.06994e6i	−0.477757	−	0.459403i
$538$	1.39542e7			2.07849
$539$	5.85409e6			0.867936
$540$	3.66416e6	+	3.25710e6i	0.540742	+	0.480670i
$541$			5.59453e6i			0.821809i	0.911678	+	0.410904i	$0.134787\pi$
$541$			5.59453e6i			0.821809i	−0.911678	+	0.410904i	$0.865213\pi$
$542$	−3.15662e6			−0.461556
$543$	3.96857e6	+	3.81611e6i	0.577610	+	0.555420i
$544$			5.70844e6i			0.827029i
$545$	−820409.			−0.118315
$546$	671203.	−	698019.i	0.0963546	−	0.100204i
$547$	8.95135e6			1.27915			0.639573	−	0.768730i	$-0.279111\pi$
$547$	8.95135e6			1.27915			0.639573	+	0.768730i	$0.279111\pi$
$548$			3.15111e6i			0.448241i
$549$	2.28322e6	−	89464.9i	0.323309	−	0.0126684i
$550$	2.51848e6			0.355002
$551$		−	1.69787e7i		−	2.38247i
$552$	−254356.	−	244585.i	−0.0355299	−	0.0341650i
$553$	−1.69425e6			−0.235595
$554$	−381613.			−0.0528261
$555$	6.05412e6	+	5.82154e6i	0.834293	+	0.802242i
$556$	−2.14609e6			−0.294416
$557$		−	3.54159e6i		−	0.483683i	−0.970316	−	0.241841i	$-0.922249\pi$
$557$		−	3.54159e6i		−	0.483683i	0.970316	−	0.241841i	$-0.0777513\pi$
$558$	−1.93290e6	+	75737.9i	−0.262799	+	0.0102974i
$559$	576961.			0.0780938
$560$			5.56850e6i			0.750357i
$561$	5.69229e6	−	5.91970e6i	0.763624	−	0.794132i
$562$		−	2.18995e6i		−	0.292478i
$563$	5.89504e6			0.783818			0.391909	−	0.920004i	$-0.371815\pi$
$563$	5.89504e6			0.783818			0.391909	+	0.920004i	$0.371815\pi$
$564$	7.85803e6	+	7.55615e6i	1.04020	+	1.00024i
$565$		−	9.60846e6i		−	1.26629i
$566$			1.37855e7i			1.80876i
$567$	−5.34037e6	+	419153.i	−0.697612	+	0.0547539i
$568$		−	2.24942e6i		−	0.292550i
$569$	1.23342e7			1.59710			0.798548	−	0.601931i	$-0.205602\pi$
$569$	1.23342e7			1.59710			0.798548	+	0.601931i	$0.205602\pi$
$570$	−1.04097e7	+	1.08256e7i	−1.34199	+	1.39561i
$571$			1.24034e7i			1.59203i	0.605276	+	0.796015i	$0.293063\pi$
$571$			1.24034e7i			1.59203i	−0.605276	+	0.796015i	$0.706937\pi$
$572$		−	1.55738e6i		−	0.199024i
$573$	4.60102e6	+	4.42427e6i	0.585420	+	0.562930i
$574$		−	1.14195e7i		−	1.44666i
$575$	−214826.			−0.0270967
$576$	−168238.	−	4.29358e6i	−0.0211284	−	0.539216i
$577$	9.28511e6			1.16104			0.580520	−	0.814246i	$-0.302849\pi$
$577$	9.28511e6			1.16104			0.580520	+	0.814246i	$0.302849\pi$
$578$	−6.23231e6			−0.775943
$579$	−871444.	−	837966.i	−0.108030	−	0.103880i
$580$	−8.85863e6			−1.09344
$581$	9.87476e6			1.21363
$582$	7.42889e6	−	7.72568e6i	0.909110	−	0.945430i
$583$		−	1.78380e7i		−	2.17358i
$584$			1.95316e6i			0.236977i
$585$	44236.4	+	1.12895e6i	0.00534429	+	0.136391i
$586$			2.02954e7i			2.44148i
$587$	−2.94212e6			−0.352423			−0.176212	−	0.984352i	$-0.556384\pi$
$587$	−2.94212e6			−0.352423			−0.176212	+	0.984352i	$0.556384\pi$
$588$	−2.42898e6	−	2.33567e6i	−0.289721	−	0.278591i
$589$		−	2.61083e6i		−	0.310091i
$590$	−9.03385e6	+	5.12209e6i	−1.06842	+	0.605784i
$591$	−7.19868e6	+	7.48627e6i	−0.847781	+	0.881651i
$592$		−	1.25412e7i		−	1.47074i
$593$		−	185695.i		−	0.0216852i	−0.999941	−	0.0108426i	$-0.996549\pi$
$593$		−	185695.i		−	0.0216852i	0.999941	−	0.0108426i	$-0.00345137\pi$
$594$	−1.29909e7	+	1.46144e7i	−1.51068	+	1.69948i
$595$	3.59599e6			0.416415
$596$	4.03708e6			0.465534
$597$	−1.70054e6	−	1.63521e6i	−0.195277	−	0.187775i
$598$			301518.i			0.0344795i
$599$		−	7.69736e6i		−	0.876547i	−0.898842	−	0.438273i	$-0.855590\pi$
$599$		−	7.69736e6i		−	0.876547i	0.898842	−	0.438273i	$-0.144410\pi$
$600$	281834.	+	271007.i	0.0319607	+	0.0307329i
$601$		−	4.64907e6i		−	0.525025i	−0.964929	−	0.262513i	$-0.915449\pi$
$601$		−	4.64907e6i		−	0.525025i	0.964929	−	0.262513i	$-0.0845511\pi$
$602$			4.37229e6i			0.491720i
$603$	−1.77578e7	+	695813.i	−1.98882	+	0.0779291i
$604$		−	6.85066e6i		−	0.764082i
$605$		−	1.56509e7i		−	1.73840i
$606$	6.24582e6	+	6.00588e6i	0.690889	+	0.664347i
$607$	4.50819e6			0.496628			0.248314	−	0.968680i	$-0.420124\pi$
$607$	4.50819e6			0.496628			0.248314	+	0.968680i	$0.420124\pi$
$608$	1.83445e7			2.01255
$609$	6.70909e6	−	6.97712e6i	0.733027	−	0.762312i
$610$	3.65214e6			0.397396
$611$			2.51233e6i			0.272254i
$612$	−4.72368e6	+	185091.i	−0.509803	+	0.0199759i
$613$			1.23655e7i			1.32911i	0.747240	+	0.664554i	$0.231379\pi$
$613$			1.23655e7i			1.32911i	−0.747240	+	0.664554i	$0.768621\pi$
$614$	−3.85057e6			−0.412196
$615$	9.60366e6	+	9.23473e6i	1.02388	+	0.984547i
$616$	−3.18310e6			−0.337986
$617$			8.93156e6i			0.944527i	0.881457	+	0.472264i	$0.156563\pi$
$617$			8.93156e6i			0.944527i	−0.881457	+	0.472264i	$0.843437\pi$
$618$	8.62438e6	−	8.96893e6i	0.908357	−	0.944647i
$619$	9.58850e6			1.00583			0.502914	−	0.864336i	$-0.332261\pi$
$619$	9.58850e6			1.00583			0.502914	+	0.864336i	$0.332261\pi$
$620$	−1.36219e6			−0.142318
$621$	1.10812e6	−	1.24661e6i	0.115308	−	0.129719i
$622$		−	1.04533e7i		−	1.08337i
$623$	−4.69459e6			−0.484593
$624$	1.16932e6	−	1.21604e6i	0.120219	−	0.125022i
$625$	−8.00294e6			−0.819502
$626$		−	1.43862e7i		−	1.46727i
$627$	−1.90234e7	−	1.82926e7i	−1.93250	−	1.85826i
$628$		−	2.93203e6i		−	0.296668i
$629$	−8.09878e6			−0.816194
$630$	−8.55536e6	+	335230.i	−0.858790	+	0.0336505i
$631$	−1.05488e7			−1.05470			−0.527350	−	0.849648i	$-0.676814\pi$
$631$	−1.05488e7			−1.05470			−0.527350	+	0.849648i	$0.676814\pi$
$632$	−960135.			−0.0956180
$633$	−2.72542e6	+	2.83430e6i	−0.270349	+	0.281149i
$634$			2.27776e7i			2.25053i
$635$			8.22993e6i			0.809956i
$636$	−7.11701e6	+	7.40135e6i	−0.697678	+	0.725551i
$637$		−	776582.i		−	0.0758296i
$638$		−	3.53325e7i		−	3.43655i
$639$	1.06242e7	−	416295.i	1.02931	−	0.0403319i
$640$			5.28483e6i			0.510013i
$641$		−	1.11258e7i		−	1.06952i	−0.845005	−	0.534758i	$-0.820403\pi$
$641$		−	1.11258e7i		−	1.06952i	0.845005	−	0.534758i	$-0.179597\pi$
$642$	1.67829e7	−	1.74534e7i	1.60705	−	1.67125i
$643$	−909665.			−0.0867669			−0.0433834	−	0.999058i	$-0.513814\pi$
$643$	−909665.			−0.0867669			−0.0433834	+	0.999058i	$0.513814\pi$
$644$	−1.00671e6			−0.0956515
$645$	−3.67706e6	−	3.53580e6i	−0.348018	−	0.334648i
$646$		−	1.44817e7i		−	1.36533i
$647$			557807.i			0.0523869i	0.999657	+	0.0261935i	$0.00833859\pi$
$647$			557807.i			0.0523869i	−0.999657	+	0.0261935i	$0.991661\pi$
$648$	−3.02640e6	+	237535.i	−0.283132	+	0.0222223i
$649$	−9.00089e6	−	1.58749e7i	−0.838830	−	1.47945i
$650$		−	334091.i		−	0.0310157i
$651$	1.03166e6	−	1.07287e6i	0.0954077	−	0.0992193i
$652$	−3.96996e6			−0.365736
$653$		−	5.96299e6i		−	0.547244i	−0.961837	−	0.273622i	$-0.911778\pi$
$653$		−	5.96299e6i		−	0.547244i	0.961837	−	0.273622i	$-0.0882217\pi$
$654$	−1.30554e6	+	1.35769e6i	−0.119356	+	0.124125i
$655$		−	868551.i		−	0.0791028i
$656$		−	1.98942e7i		−	1.80495i
$657$	−9.22496e6	+	361467.i	−0.833779	+	0.0326705i
$658$	−1.90388e7			−1.71425
$659$	−92952.4			−0.00833772			−0.00416886	−	0.999991i	$-0.501327\pi$
$659$	−92952.4			−0.00833772			−0.00416886	+	0.999991i	$0.501327\pi$
$660$	−9.54413e6	+	9.92543e6i	−0.852858	+	0.886930i
$661$	934288.			0.0831720			0.0415860	−	0.999135i	$-0.486759\pi$
$661$	934288.			0.0831720			0.0415860	+	0.999135i	$0.486759\pi$
$662$	1.70652e7			1.51344
$663$	−785285.	−	755118.i	−0.0693815	−	0.0667161i
$664$	5.59604e6			0.492562
$665$		−	1.15560e7i		−	1.01334i
$666$	1.92681e7	−	754995.i	1.68327	−	0.0659566i
$667$			3.01386e6i			0.262306i
$668$		−	7.17933e6i		−	0.622505i
$669$	3.12466e6	+	3.00462e6i	0.269922	+	0.259552i
$670$	−2.84046e7			−2.44456
$671$			6.41779e6i			0.550275i
$672$	7.53837e6	+	7.24877e6i	0.643953	+	0.619215i
$673$		−	8.53811e6i		−	0.726648i	−0.931663	−	0.363324i	$-0.881642\pi$
$673$		−	8.53811e6i		−	0.726648i	0.931663	−	0.363324i	$-0.118358\pi$
$674$			6.75994e6i			0.573183i
$675$	−1.22783e6	+	1.38128e6i	−0.103724	+	0.116687i
$676$	9.15098e6			0.770195
$677$		−	1.23950e7i		−	1.03938i	−0.854356	−	0.519689i	$-0.826048\pi$
$677$		−	1.23950e7i		−	1.03938i	0.854356	−	0.519689i	$-0.173952\pi$
$678$	−1.59010e7	−	1.52902e7i	−1.32847	−	1.27743i
$679$			8.24695e6i			0.686466i
$680$	2.03785e6			0.169005
$681$	−1.27768e7	−	1.22860e7i	−1.05573	−	1.01518i
$682$		−	5.43308e6i		−	0.447286i
$683$	−2.08318e7			−1.70874			−0.854369	−	0.519667i	$-0.826056\pi$
$683$	−2.08318e7			−1.70874			−0.854369	+	0.519667i	$0.826056\pi$
$684$	594804.	+	1.51799e7i	0.0486109	+	1.24059i
$685$	6.42068e6			0.522823
$686$	1.74167e7			1.41304
$687$	6.01504e6	−	6.25535e6i	0.486235	−	0.505661i
$688$			7.61709e6i			0.613505i
$689$	−2.36633e6			−0.189901
$690$	1.84780e6	−	1.92162e6i	0.147752	−	0.153654i
$691$		−	2.11131e7i		−	1.68212i	−0.540945	−	0.841058i	$-0.681933\pi$
$691$		−	2.11131e7i		−	1.68212i	0.540945	−	0.841058i	$-0.318067\pi$
$692$	8.35102e6			0.662940
$693$	−589088.	−	1.50341e7i	−0.0465959	−	1.18917i
$694$	−1.57697e6			−0.124287
$695$			4.37286e6i			0.343403i
$696$	3.80205e6	−	3.95394e6i	0.297505	−	0.309391i
$697$	−1.28471e7			−1.00167
$698$			2.73674e7i			2.12616i
$699$	1.14385e7	+	1.09991e7i	0.885477	+	0.851460i
$700$	1.11547e6			0.0860425
$701$	4.36551e6			0.335537			0.167768	−	0.985826i	$-0.446344\pi$
$701$	4.36551e6			0.335537			0.167768	+	0.985826i	$0.446344\pi$
$702$	1.93870e6	+	1.72332e6i	0.148480	+	0.131985i
$703$			2.60261e7i			1.98619i
$704$	1.20686e7			0.917751
$705$	1.53964e7	−	1.60115e7i	1.16666	−	1.21327i
$706$	6.96277e6			0.525739
$707$	−6.66724e6			−0.501646
$708$	−2.59912e6	+	1.01780e7i	−0.194869	+	0.763095i
$709$	−1.32319e7			−0.988567			−0.494284	−	0.869301i	$-0.664570\pi$
$709$	−1.32319e7			−0.988567			−0.494284	+	0.869301i	$0.664570\pi$
$710$	1.69940e7			1.26517
$711$	−177690.	−	4.53481e6i	−0.0131822	−	0.336422i
$712$	−2.66043e6			−0.196676
$713$			463442.i			0.0341406i
$714$	5.72239e6	−	5.95100e6i	0.420080	−	0.436862i
$715$	−3.17331e6			−0.232139
$716$	−7.16079e6			−0.522009
$717$	1.52721e6	−	1.58822e6i	0.110943	−	0.115376i
$718$			2.55378e7i			1.84872i
$719$	9.06635e6			0.654049			0.327024	−	0.945016i	$-0.393954\pi$
$719$	9.06635e6			0.654049			0.327024	+	0.945016i	$0.393954\pi$
$720$	−1.49045e7	+	584013.i	−1.07149	+	0.0419847i
$721$			9.57408e6i			0.685897i
$722$	−2.78107e7			−1.98550
$723$	4.55522e6	+	4.38022e6i	0.324088	+	0.311638i
$724$	8.90128e6			0.631112
$725$		−	3.33945e6i		−	0.235955i
$726$	−2.59007e7	−	2.49057e7i	−1.82377	−	1.75371i
$727$	−8.46504e6			−0.594009			−0.297004	−	0.954876i	$-0.595988\pi$
$727$	−8.46504e6			−0.594009			−0.297004	+	0.954876i	$0.595988\pi$
$728$			422258.i			0.0295290i
$729$	−1.68199e6	−	1.42500e7i	−0.117221	−	0.993106i
$730$	−1.47558e7			−1.02484
$731$	4.91892e6			0.340468
$732$	2.56057e6	−	2.66287e6i	0.176628	−	0.183684i
$733$	1.86428e7			1.28159			0.640797	−	0.767710i	$-0.278604\pi$
$733$	1.86428e7			1.28159			0.640797	+	0.767710i	$0.278604\pi$
$734$		−	5.68997e6i		−	0.389825i
$735$	−4.75914e6	+	4.94927e6i	−0.324945	+	0.337927i
$736$	−3.25629e6			−0.221579
$737$		−	4.99144e7i		−	3.38499i
$738$	3.05651e7	−	1.19765e6i	2.06578	−	0.0809448i
$739$			1.79550e7i			1.20941i	0.796449	+	0.604705i	$0.206709\pi$
$739$			1.79550e7i			1.20941i	−0.796449	+	0.604705i	$0.793291\pi$
$740$	1.35790e7			0.911570
$741$	−2.42663e6	+	2.52358e6i	−0.162352	+	0.168838i
$742$		−	1.79323e7i		−	1.19571i
$743$			6.34797e6i			0.421854i	0.977502	+	0.210927i	$0.0676483\pi$
$743$			6.34797e6i			0.421854i	−0.977502	+	0.210927i	$0.932352\pi$
$744$	584642.	−	607999.i	0.0387220	−	0.0402690i
$745$		−	8.22593e6i		−	0.542993i
$746$	2.53454e7			1.66745
$747$	1.03565e6	+	2.64306e7i	0.0679062	+	1.73303i
$748$		−	1.32776e7i		−	0.867689i
$749$			1.86310e7i			1.21348i
$750$	−1.51615e7	+	1.57672e7i	−0.984212	+	1.02353i
$751$		−	1.02347e7i		−	0.662177i	−0.943600	−	0.331089i	$-0.892584\pi$
$751$		−	1.02347e7i		−	0.662177i	0.943600	−	0.331089i	$-0.107416\pi$
$752$	−3.31681e7			−2.13883
$753$	−1.17871e7	+	1.22580e7i	−0.757562	+	0.787827i
$754$	−4.68707e6			−0.300243
$755$	−1.39589e7			−0.891216
$756$	−5.75387e6	+	6.47296e6i	−0.366147	+	0.411906i
$757$	6.04589e6			0.383460			0.191730	−	0.981448i	$-0.438590\pi$
$757$	6.04589e6			0.383460			0.191730	+	0.981448i	$0.438590\pi$
$758$	1.05423e7			0.666439
$759$	3.37680e6	+	3.24708e6i	0.212765	+	0.204592i
$760$		−	6.54879e6i		−	0.411270i
$761$		−	3.64475e6i		−	0.228142i	−0.993473	−	0.114071i	$-0.963611\pi$
$761$		−	3.64475e6i		−	0.228142i	0.993473	−	0.114071i	$-0.0363892\pi$
$762$	1.36197e7	+	1.30965e7i	0.849729	+	0.817085i
$763$		−	1.44930e6i		−	0.0901254i
$764$	1.03198e7			0.639645
$765$	377140.	+	9.62496e6i	0.0232996	+	0.594628i
$766$			3.84542e7i			2.36795i
$767$	−2.10590e6	+	1.19402e6i	−0.129256	+	0.0732866i
$768$	1.51039e7	+	1.45237e7i	0.924031	+	0.888533i
$769$			1.02131e7i			0.622790i	0.950281	+	0.311395i	$0.100796\pi$
$769$			1.02131e7i			0.622790i	−0.950281	+	0.311395i	$0.899204\pi$
$770$		−	2.40478e7i		−	1.46167i
$771$	−51302.6	+	53352.2i	−0.00310816	+	0.00323234i
$772$	−1.95460e6			−0.118036
$773$	1.74197e7			1.04856			0.524278	−	0.851547i	$-0.324335\pi$
$773$	1.74197e7			1.04856			0.524278	+	0.851547i	$0.324335\pi$
$774$	−1.17028e7	+	458557.i	−0.702162	+	0.0275132i
$775$		−	513508.i		−	0.0307109i
$776$			4.67356e6i			0.278608i
$777$	−1.02841e7	+	1.06950e7i	−0.611102	+	0.635516i
$778$			1.01021e6i			0.0598358i
$779$			4.12852e7i			2.43754i
$780$	1.31667e6	+	1.26609e6i	0.0774891	+	0.0745122i
$781$			2.98631e7i			1.75189i
$782$			2.57061e6i			0.150321i
$783$	1.93785e7	+	1.72257e7i	1.12957	+	1.00409i
$784$	1.02525e7			0.595717
$785$	−5.97430e6			−0.346029
$786$	−1.43736e6	−	1.38215e6i	−0.0829871	−	0.0797991i
$787$	3.39441e7			1.95356			0.976781	−	0.214240i	$-0.0687274\pi$
$787$	3.39441e7			1.95356			0.976781	+	0.214240i	$0.0687274\pi$
$788$			1.67913e7i			0.963315i
$789$	−5.41187e6	+	5.62808e6i	−0.309496	+	0.321861i
$790$		−	7.25368e6i		−	0.413514i
$791$	1.69739e7			0.964586
$792$	−333837.	−	8.51982e6i	−0.0189113	−	0.482633i
$793$	851360.			0.0480762
$794$			3.14078e7i			1.76802i
$795$	1.50809e7	+	1.45016e7i	0.846274	+	0.813763i
$796$	−3.81422e6			−0.213365
$797$	−1.74467e7			−0.972899			−0.486450	−	0.873709i	$-0.661708\pi$
$797$	−1.74467e7			−0.972899			−0.486450	+	0.873709i	$0.661708\pi$
$798$	−1.91240e7	−	1.83893e7i	−1.06309	−	1.02225i
$799$			2.14191e7i			1.18695i
$800$	3.60808e6			0.199320
$801$	−492359.	−	1.25654e7i	−0.0271144	−	0.691985i
$802$	2.16529e7			1.18872
$803$		−	2.59300e7i		−	1.41910i
$804$	−1.99149e7	+	2.07105e7i	−1.08652	+	1.12993i
$805$			2.05128e6i			0.111567i
$806$	−720733.			−0.0390784
$807$	−2.07312e7	−	1.99347e7i	−1.12057	−	1.07752i
$808$	−3.77833e6			−0.203597
$809$	2.11906e7			1.13834			0.569171	−	0.822219i	$-0.307264\pi$
$809$	2.11906e7			1.13834			0.569171	+	0.822219i	$0.307264\pi$
$810$	−1.79454e6	−	2.28640e7i	−0.0961037	−	1.22444i
$811$		−	5.25984e6i		−	0.280815i	−0.990094	−	0.140407i	$-0.955159\pi$
$811$		−	5.25984e6i		−	0.280815i	0.990094	−	0.140407i	$-0.0448412\pi$
$812$		−	1.56493e7i		−	0.832923i
$813$	4.68967e6	+	4.50951e6i	0.248838	+	0.239278i
$814$			5.41598e7i			2.86494i
$815$			8.08917e6i			0.426589i
$816$	9.96913e6	−	1.03674e7i	0.524121	−	0.545061i
$817$		−	1.58073e7i		−	0.828520i
$818$		−	8.45965e6i		−	0.442048i
$819$	−1.99436e6	+	78146.2i	−0.103895	+	0.00407097i
$820$	2.15405e7			1.11872
$821$	−6.62750e6			−0.343156			−0.171578	−	0.985171i	$-0.554887\pi$
$821$	−6.62750e6			−0.343156			−0.171578	+	0.985171i	$0.554887\pi$
$822$	1.02174e7	−	1.06256e7i	0.527425	−	0.548496i
$823$			2.39642e7i			1.23328i	0.787244	+	0.616642i	$0.211507\pi$
$823$			2.39642e7i			1.23328i	−0.787244	+	0.616642i	$0.788493\pi$
$824$			5.42564e6i			0.278377i
$825$	−3.74160e6	−	3.59786e6i	−0.191392	−	0.184039i
$826$	−9.04849e6	−	1.59588e7i	−0.461451	−	0.813862i
$827$			1.92579e7i			0.979142i	0.871963	+	0.489571i	$0.162847\pi$
$827$			1.92579e7i			0.979142i	−0.871963	+	0.489571i	$0.837153\pi$
$828$	−105582.	−	2.69455e6i	−0.00535199	−	0.136587i
$829$	−1.23458e7			−0.623925			−0.311962	−	0.950094i	$-0.600986\pi$
$829$	−1.23458e7			−0.623925			−0.311962	+	0.950094i	$0.600986\pi$
$830$			4.22772e7i			2.13016i
$831$	566948.	+	545168.i	0.0284800	+	0.0273859i
$832$		−	1.60097e6i		−	0.0801818i
$833$		−	6.62080e6i		−	0.330596i
$834$	7.23665e6	+	6.95865e6i	0.360265	+	0.346425i
$835$	−1.46286e7			−0.726082
$836$	−4.26685e7			−2.11150
$837$	2.97983e6	+	2.64880e6i	0.147021	+	0.130688i
$838$	−1.69265e7			−0.832638
$839$	−1.97118e7			−0.966768			−0.483384	−	0.875408i	$-0.660592\pi$
$839$	−1.97118e7			−0.966768			−0.483384	+	0.875408i	$0.660592\pi$
$840$	2.58773e6	−	2.69111e6i	0.126538	−	0.131593i
$841$	−2.63390e7			−1.28413
$842$			4.20258e7i			2.04285i
$843$	−3.12854e6	+	3.25353e6i	−0.151626	+	0.157683i
$844$			6.35719e6i			0.307191i
$845$		−	1.86460e7i		−	0.898346i
$846$	−1.99675e6	−	5.09589e7i	−0.0959177	−	2.44790i
$847$	2.76483e7			1.32422
$848$		−	3.12404e7i		−	1.49186i
$849$	1.96938e7	−	2.04806e7i	0.937691	−	0.975152i
$850$		−	2.84832e6i		−	0.135220i
$851$		−	4.61983e6i		−	0.218676i
$852$	1.19148e7	−	1.23908e7i	0.562324	−	0.584789i
$853$	1.73670e7			0.817247			0.408623	−	0.912703i	$-0.366009\pi$
$853$	1.73670e7			0.817247			0.408623	+	0.912703i	$0.366009\pi$
$854$			6.45173e6i			0.302713i
$855$	3.09305e7	−	1.21197e6i	1.44701	−	0.0566991i
$856$			1.05582e7i			0.492500i
$857$	−1.02414e7			−0.476328			−0.238164	−	0.971225i	$-0.576546\pi$
$857$	−1.02414e7			−0.476328			−0.238164	+	0.971225i	$0.576546\pi$
$858$	−5.04977e6	+	5.25152e6i	−0.234182	+	0.243538i
$859$		−	7.65375e6i		−	0.353909i	−0.984219	−	0.176954i	$-0.943375\pi$
$859$		−	7.65375e6i		−	0.353909i	0.984219	−	0.176954i	$-0.0566245\pi$
$860$	−8.24744e6			−0.380253
$861$	−1.63137e7	+	1.69654e7i	−0.749971	+	0.779933i
$862$	3.49651e7			1.60275
$863$	4.64967e6			0.212518			0.106259	−	0.994339i	$-0.466113\pi$
$863$	4.64967e6			0.212518			0.106259	+	0.994339i	$0.466113\pi$
$864$	−1.86113e7	+	2.09373e7i	−0.848189	+	0.954193i
$865$		−	1.70160e7i		−	0.773245i
$866$	−9.09789e6			−0.412236
$867$	9.25911e6	+	8.90341e6i	0.418332	+	0.402262i
$868$		−	2.40640e6i		−	0.108410i
$869$	1.27467e7			0.572594
$870$	2.98714e7	+	2.87239e7i	1.33801	+	1.28660i
$871$	−6.62146e6			−0.295739
$872$		−	821320.i		−	0.0365781i
$873$	−2.20736e7	+	864924.i	−0.980253	+	0.0384098i
$874$	8.26086e6			0.365803
$875$		−	1.68311e7i		−	0.743175i
$876$	−1.03455e7	+	1.07589e7i	−0.455505	+	0.473702i
$877$	−1.47835e7			−0.649049			−0.324525	−	0.945877i	$-0.605204\pi$
$877$	−1.47835e7			−0.649049			−0.324525	+	0.945877i	$0.605204\pi$
$878$	−1.37098e7			−0.600198
$879$	2.89937e7	−	3.01520e7i	1.26570	−	1.31627i
$880$		−	4.18944e7i		−	1.82368i
$881$	4.18565e7			1.81687			0.908434	−	0.418028i	$-0.137278\pi$
$881$	4.18565e7			1.81687			0.908434	+	0.418028i	$0.137278\pi$
$882$	617212.	+	1.57518e7i	0.0267155	+	0.681803i
$883$	1.06724e7			0.460639			0.230320	−	0.973115i	$-0.426023\pi$
$883$	1.06724e7			0.460639			0.230320	+	0.973115i	$0.426023\pi$
$884$	−1.76135e6			−0.0758080
$885$	2.07386e7	+	5.29595e6i	0.890064	+	0.227293i
$886$	3.48005e7			1.48936
$887$	−2.45260e7			−1.04669			−0.523345	−	0.852121i	$-0.675316\pi$
$887$	−2.45260e7			−1.04669			−0.523345	+	0.852121i	$0.675316\pi$
$888$	−5.82801e6	+	6.06085e6i	−0.248021	+	0.257929i
$889$	−1.45387e7			−0.616978
$890$		−	2.00991e7i		−	0.850554i
$891$	4.01781e7	−	3.15348e6i	1.69549	−	0.133075i
$892$	7.00844e6			0.294923
$893$	6.88318e7			2.88842
$894$	−1.36131e7	−	1.30901e7i	−0.569656	−	0.547772i
$895$			1.45908e7i			0.608865i
$896$	−9.33597e6			−0.388499
$897$	430745.	−	447954.i	0.0178747	−	0.0185888i
$898$		−	2.98484e7i		−	1.23518i
$899$	−7.20416e6			−0.297293
$900$	116988.	+	2.98565e6i	0.00481434	+	0.122866i
$901$	−2.01743e7			−0.827915
$902$			8.59138e7i			3.51598i
$903$	6.24620e6	−	6.49574e6i	0.254916	−	0.265100i
$904$	9.61914e6			0.391485
$905$		−	1.81372e7i		−	0.736121i
$906$	−2.22131e7	+	2.31005e7i	−0.899060	+	0.934978i
$907$	2.48597e7			1.00341			0.501704	−	0.865039i	$-0.332707\pi$
$907$	2.48597e7			1.00341			0.501704	+	0.865039i	$0.332707\pi$
$908$	−2.86576e7			−1.15352
$909$	−699247.	−	1.78454e7i	−0.0280686	−	0.716336i
$910$	−3.19009e6			−0.127703
$911$			2.17026e7i			0.866394i	0.901299	+	0.433197i	$0.142615\pi$
$911$			2.17026e7i			0.866394i	−0.901299	+	0.433197i	$0.857385\pi$
$912$	−3.33165e7	−	3.20366e7i	−1.32639	−	1.27544i
$913$	−7.42924e7			−2.94963
$914$		−	1.11982e7i		−	0.443386i
$915$	−5.42585e6	−	5.21741e6i	−0.214247	−	0.206017i
$916$		−	1.40304e7i		−	0.552498i
$917$	1.53435e6			0.0602560
$918$	1.65285e7	+	1.46923e7i	0.647331	+	0.575418i
$919$			3.10147e7i			1.21138i	0.795702	+	0.605688i	$0.207102\pi$
$919$			3.10147e7i			1.21138i	−0.795702	+	0.605688i	$0.792898\pi$
$920$			1.16246e6i			0.0452802i
$921$	5.72065e6	+	5.50088e6i	0.222227	+	0.213689i
$922$			8.20013e6i			0.317683i
$923$	3.96152e6			0.153059
$924$	−1.75339e7	−	1.68603e7i	−0.675613	−	0.649658i
$925$			5.11891e6i			0.196709i
$926$		−	4.49275e7i		−	1.72181i
$927$	−2.56258e7	+	1.00411e6i	−0.979441	+	0.0383780i
$928$		−	5.06188e7i		−	1.92949i
$929$	−4.97769e7			−1.89229			−0.946147	−	0.323738i	$-0.895060\pi$
$929$	−4.97769e7			−1.89229			−0.946147	+	0.323738i	$0.895060\pi$
$930$	4.59334e6	+	4.41688e6i	0.174149	+	0.167459i
$931$	−2.12765e7			−0.804498
$932$	2.56560e7			0.967495
$933$	−1.49334e7	+	1.55301e7i	−0.561637	+	0.584075i
$934$	3.23230e7			1.21240
$935$	−2.70543e7			−1.01206
$936$	−1.13021e6	+	44285.6i	−0.0421666	+	0.00165224i
$937$		−	4.77907e7i		−	1.77826i	−0.457659	−	0.889128i	$-0.651312\pi$
$937$		−	4.77907e7i		−	1.77826i	0.457659	−	0.889128i	$-0.348688\pi$
$938$		−	5.01784e7i		−	1.86213i
$939$	−2.05520e7	+	2.13730e7i	−0.760658	+	0.791047i
$940$		−	3.59129e7i		−	1.32565i
$941$	−2.53175e7			−0.932068			−0.466034	−	0.884767i	$-0.654318\pi$
$941$	−2.53175e7			−0.932068			−0.466034	+	0.884767i	$0.654318\pi$
$942$	−9.50705e6	+	9.88687e6i	−0.349075	+	0.363021i
$943$		−	7.32844e6i		−	0.268369i
$944$	−1.57636e7	−	2.78023e7i	−0.575739	−	1.01543i
$945$	1.31893e7	+	1.17240e7i	0.480443	+	0.427069i
$946$		−	3.28948e7i		−	1.19509i
$947$			2.19876e7i			0.796713i	0.917231	+	0.398357i	$0.130419\pi$
$947$			2.19876e7i			0.796713i	−0.917231	+	0.398357i	$0.869581\pi$
$948$	−5.28884e6	−	5.08566e6i	−0.191135	−	0.183792i
$949$	−3.43977e6			−0.123984
$950$	−9.15329e6			−0.329055
$951$	3.25398e7	−	3.38398e7i	1.16671	−	1.21332i
$952$			3.59999e6i			0.128739i
$953$			1.62711e7i			0.580343i	0.956975	+	0.290171i	$0.0937123\pi$
$953$			1.62711e7i			0.580343i	−0.956975	+	0.290171i	$0.906288\pi$
$954$	4.79974e7	−	1.88071e6i	1.70744	−	0.0669038i
$955$		−	2.10276e7i		−	0.746074i
$956$		−	3.56230e6i		−	0.126062i
$957$	−5.04756e7	+	5.24921e7i	−1.78156	+	1.85274i
$958$		−	6.47936e7i		−	2.28096i
$959$			1.13425e7i			0.398257i
$960$	−9.81128e6	+	1.02032e7i	−0.343596	+	0.357323i
$961$	2.75214e7			0.961306
$962$	7.18464e6			0.250304
$963$	−4.98674e7	+	1.95398e6i	−1.73281	+	0.0678977i
$964$	1.02171e7			0.354107
$965$			3.98268e6i			0.137676i
$966$	3.39466e6	+	3.26425e6i	0.117045	+	0.112549i
$967$			1.46175e7i			0.502697i	0.967897	+	0.251348i	$0.0808740\pi$
$967$			1.46175e7i			0.502697i	−0.967897	+	0.251348i	$0.919126\pi$
$968$	1.56683e7			0.537444
$969$	−2.06884e7	+	2.15149e7i	−0.707811	+	0.736088i
$970$	−3.53080e7			−1.20488
$971$		−	4.75451e6i		−	0.161830i	−0.996721	−	0.0809148i	$-0.974216\pi$
$971$		−	4.75451e6i		−	0.161830i	0.996721	−	0.0809148i	$-0.0257842\pi$
$972$	−1.79289e7	−	1.47218e7i	−0.608677	−	0.499799i
$973$	−7.72492e6			−0.261585
$974$	−4.83798e7			−1.63405
$975$	−477279.	+	496347.i	−0.0160791	+	0.0167214i
$976$			1.12397e7i			0.377687i
$977$	−7.34779e6			−0.246275			−0.123137	−	0.992390i	$-0.539296\pi$
$977$	−7.34779e6			−0.246275			−0.123137	+	0.992390i	$0.539296\pi$
$978$	1.33868e7	+	1.28725e7i	0.447537	+	0.430344i
$979$	3.53195e7			1.17776
$980$			1.11009e7i			0.369228i
$981$	3.87917e6	−	152000.i	0.128696	−	0.00504279i
$982$			2.68954e6i			0.0890019i
$983$	−1.79483e6			−0.0592433			−0.0296217	−	0.999561i	$-0.509430\pi$
$983$	−1.79483e6			−0.0592433			−0.0296217	+	0.999561i	$0.509430\pi$
$984$	−9.24499e6	+	9.61434e6i	−0.304382	+	0.316542i
$985$	3.42138e7			1.12360
$986$	−3.99600e7			−1.30898
$987$	2.82852e7	+	2.71986e7i	0.924202	+	0.888698i
$988$			5.66024e6i			0.184477i
$989$			2.80592e6i			0.0912188i
$990$	6.43659e7	−	2.52209e6i	2.08722	−	0.0817847i
$991$			2.51297e7i			0.812835i	0.913687	+	0.406418i	$0.133222\pi$
$991$			2.51297e7i			0.812835i	−0.913687	+	0.406418i	$0.866778\pi$
$992$		−	7.78367e6i		−	0.251134i
$993$	−2.53530e7	−	2.43791e7i	−0.815938	−	0.784592i
$994$			3.00210e7i			0.963738i
$995$			7.77184e6i			0.248866i
$996$	3.08254e7	+	2.96412e7i	0.984601	+	0.946776i
$997$	5.76794e7			1.83774			0.918868	−	0.394565i	$-0.129105\pi$
$997$	5.76794e7			1.83774			0.918868	+	0.394565i	$0.129105\pi$
$998$	4.76791e7			1.51531
$999$	−2.97045e7	−	2.64046e7i	−0.941691	−	0.837077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.d.b.176.17	✓	92
3.2	odd	2	inner	177.6.d.b.176.76	yes	92
59.58	odd	2	inner	177.6.d.b.176.75	yes	92
177.176	even	2	inner	177.6.d.b.176.18	yes	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.d.b.176.17	✓	92	1.1	even	1	trivial
177.6.d.b.176.18	yes	92	177.176	even	2	inner
177.6.d.b.176.75	yes	92	59.58	odd	2	inner
177.6.d.b.176.76	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)

\(f(q)\)	\(=\)	\(q-7.56324 q^{2} +(11.2364 + 10.8048i) q^{3} +25.2027 q^{4} -51.3528i q^{5} +(-84.9838 - 81.7190i) q^{6} +90.7178 q^{7} +51.4099 q^{8} +(9.51431 + 242.814i) q^{9} +O(q^{10})\)	\(q-7.56324 q^{2} +(11.2364 + 10.8048i) q^{3} +25.2027 q^{4} -51.3528i q^{5} +(-84.9838 - 81.7190i) q^{6} +90.7178 q^{7} +51.4099 q^{8} +(9.51431 + 242.814i) q^{9} +388.394i q^{10} -682.512 q^{11} +(283.188 + 272.309i) q^{12} +90.5395i q^{13} -686.121 q^{14} +(554.855 - 577.022i) q^{15} -1195.31 q^{16} +771.900i q^{17} +(-71.9590 - 1836.46i) q^{18} +2480.56 q^{19} -1294.23i q^{20} +(1019.34 + 980.185i) q^{21} +5162.01 q^{22} -440.319 q^{23} +(577.663 + 555.472i) q^{24} +487.887 q^{25} -684.772i q^{26} +(-2516.64 + 2831.16i) q^{27} +2286.33 q^{28} -6844.72i q^{29} +(-4196.50 + 4364.16i) q^{30} -1052.51i q^{31} +7395.31 q^{32} +(-7668.99 - 7374.38i) q^{33} -5838.07i q^{34} -4658.62i q^{35} +(239.786 + 6119.55i) q^{36} +10492.0i q^{37} -18761.1 q^{38} +(-978.258 + 1017.34i) q^{39} -2640.04i q^{40} +16643.5i q^{41} +(-7709.55 - 7413.38i) q^{42} -6372.48i q^{43} -17201.1 q^{44} +(12469.2 - 488.587i) q^{45} +3330.24 q^{46} +27748.5 q^{47} +(-13431.0 - 12915.0i) q^{48} -8577.27 q^{49} -3690.01 q^{50} +(-8340.20 + 8673.40i) q^{51} +2281.84i q^{52} +26135.8i q^{53} +(19033.9 - 21412.7i) q^{54} +35048.9i q^{55} +4663.80 q^{56} +(27872.6 + 26801.9i) q^{57} +51768.3i q^{58} +(13187.9 + 23259.5i) q^{59} +(13983.8 - 14542.5i) q^{60} -9403.19i q^{61} +7960.42i q^{62} +(863.118 + 22027.5i) q^{63} -17682.6 q^{64} +4649.46 q^{65} +(58002.5 + 55774.2i) q^{66} +73133.4i q^{67} +19453.9i q^{68} +(-4947.61 - 4757.54i) q^{69} +35234.3i q^{70} -43754.6i q^{71} +(489.130 + 12483.0i) q^{72} +37991.9i q^{73} -79353.6i q^{74} +(5482.10 + 5271.50i) q^{75} +62516.8 q^{76} -61916.0 q^{77} +(7398.80 - 7694.39i) q^{78} -18676.1 q^{79} +61382.6i q^{80} +(-58868.0 + 4620.41i) q^{81} -125879. i q^{82} +108851. q^{83} +(25690.2 + 24703.3i) q^{84} +39639.3 q^{85} +48196.6i q^{86} +(73955.5 - 76910.1i) q^{87} -35087.9 q^{88} -51749.3 q^{89} +(-94307.4 + 3695.30i) q^{90} +8213.55i q^{91} -11097.2 q^{92} +(11372.2 - 11826.5i) q^{93} -209869. q^{94} -127384. i q^{95} +(83096.8 + 79904.6i) q^{96} +90907.7i q^{97} +64872.0 q^{98} +(-6493.63 - 165723. 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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