LMFDB - Embedded newform 177.6.d.b.176.5

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			176.5
Character	$\chi$	$=$	177.176
Dual form			177.6.d.b.176.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.3821 q^{2} +(-12.6016 - 9.17604i) q^{3} +75.7873 q^{4} -9.35226i q^{5} +(130.831 + 95.2663i) q^{6} +67.1723 q^{7} -454.603 q^{8} +(74.6006 + 231.266i) q^{9} +O(q^{10})$	\(q-10.3821 q^{2} +(-12.6016 - 9.17604i) q^{3} +75.7873 q^{4} -9.35226i q^{5} +(130.831 + 95.2663i) q^{6} +67.1723 q^{7} -454.603 q^{8} +(74.6006 + 231.266i) q^{9} +97.0958i q^{10} -337.866 q^{11} +(-955.042 - 695.428i) q^{12} +682.151i q^{13} -697.388 q^{14} +(-85.8167 + 117.853i) q^{15} +2294.52 q^{16} -513.997i q^{17} +(-774.509 - 2401.01i) q^{18} +189.135 q^{19} -708.783i q^{20} +(-846.479 - 616.376i) q^{21} +3507.74 q^{22} +784.190 q^{23} +(5728.72 + 4171.45i) q^{24} +3037.54 q^{25} -7082.14i q^{26} +(1182.01 - 3598.85i) q^{27} +5090.81 q^{28} -4832.42i q^{29} +(890.955 - 1223.56i) q^{30} +4999.87i q^{31} -9274.61 q^{32} +(4257.65 + 3100.27i) q^{33} +5336.35i q^{34} -628.213i q^{35} +(5653.78 + 17527.0i) q^{36} -9261.10i q^{37} -1963.61 q^{38} +(6259.44 - 8596.19i) q^{39} +4251.56i q^{40} +4658.46i q^{41} +(8788.20 + 6399.26i) q^{42} -5287.94i q^{43} -25605.9 q^{44} +(2162.85 - 697.684i) q^{45} -8141.51 q^{46} -5081.19 q^{47} +(-28914.7 - 21054.6i) q^{48} -12294.9 q^{49} -31535.9 q^{50} +(-4716.46 + 6477.18i) q^{51} +51698.4i q^{52} -8728.92i q^{53} +(-12271.8 + 37363.5i) q^{54} +3159.81i q^{55} -30536.7 q^{56} +(-2383.41 - 1735.51i) q^{57} +50170.6i q^{58} +(-25651.4 + 7545.23i) q^{59} +(-6503.82 + 8931.79i) q^{60} -26624.9i q^{61} -51909.0i q^{62} +(5011.10 + 15534.6i) q^{63} +22864.9 q^{64} +6379.65 q^{65} +(-44203.2 - 32187.2i) q^{66} -36459.7i q^{67} -38954.4i q^{68} +(-9882.04 - 7195.75i) q^{69} +6522.15i q^{70} +83513.0i q^{71} +(-33913.7 - 105134. i) q^{72} +15824.8i q^{73} +96149.4i q^{74} +(-38277.8 - 27872.5i) q^{75} +14334.1 q^{76} -22695.2 q^{77} +(-64986.0 + 89246.3i) q^{78} -20068.7 q^{79} -21459.0i q^{80} +(-47918.5 + 34505.1i) q^{81} -48364.4i q^{82} +69484.9 q^{83} +(-64152.4 - 46713.5i) q^{84} -4807.03 q^{85} +54899.7i q^{86} +(-44342.5 + 60896.3i) q^{87} +153595. q^{88} -21384.8 q^{89} +(-22454.9 + 7243.40i) q^{90} +45821.7i q^{91} +59431.6 q^{92} +(45879.0 - 63006.4i) q^{93} +52753.3 q^{94} -1768.84i q^{95} +(116875. + 85104.2i) q^{96} -151770. i q^{97} +127646. q^{98} +(-25205.0 - 78136.7i) 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 $

$2$	−10.3821			−1.83531			−0.917654	−	0.397381i	$-0.869919\pi$
$2$	−10.3821			−1.83531			−0.917654	+	0.397381i	$0.869919\pi$
$3$	−12.6016	−	9.17604i	−0.808393	−	0.588643i
$3$	−12.6016	−	9.17604i	−0.808393	−	0.588643i
$4$	75.7873			2.36835
$5$		−	9.35226i		−	0.167298i	−0.996495	−	0.0836491i	$-0.973343\pi$
$5$		−	9.35226i		−	0.167298i	0.996495	−	0.0836491i	$-0.0266575\pi$
$6$	130.831	+	95.2663i	1.48365	+	1.08034i
$7$	67.1723			0.518138			0.259069	−	0.965859i	$-0.416584\pi$
$7$	67.1723			0.518138			0.259069	+	0.965859i	$0.416584\pi$
$8$	−454.603			−2.51135
$9$	74.6006	+	231.266i	0.306998	+	0.951710i
$10$			97.0958i			0.307044i
$11$	−337.866			−0.841903			−0.420952	−	0.907083i	$-0.638304\pi$
$11$	−337.866			−0.841903			−0.420952	+	0.907083i	$0.638304\pi$
$12$	−955.042	−	695.428i	−1.91456	−	1.39412i
$13$			682.151i			1.11949i	0.828663	+	0.559747i	$0.189102\pi$
$13$			682.151i			1.11949i	−0.828663	+	0.559747i	$0.810898\pi$
$14$	−697.388			−0.950942
$15$	−85.8167	+	117.853i	−0.0984790	+	0.135243i
$16$	2294.52			2.24075
$17$		−	513.997i		−	0.431358i	−0.976464	−	0.215679i	$-0.930803\pi$
$17$		−	513.997i		−	0.431358i	0.976464	−	0.215679i	$-0.0691965\pi$
$18$	−774.509	−	2401.01i	−0.563436	−	1.74668i
$19$	189.135			0.120196			0.0600978	−	0.998192i	$-0.480859\pi$
$19$	189.135			0.120196			0.0600978	+	0.998192i	$0.480859\pi$
$20$		−	708.783i		−	0.396221i
$21$	−846.479	−	616.376i	−0.418859	−	0.304998i
$22$	3507.74			1.54515
$23$	784.190			0.309102			0.154551	−	0.987985i	$-0.450607\pi$
$23$	784.190			0.309102			0.154551	+	0.987985i	$0.450607\pi$
$24$	5728.72	+	4171.45i	2.03016	+	1.47829i
$25$	3037.54			0.972011
$26$		−	7082.14i		−	2.05462i
$27$	1182.01	−	3598.85i	0.312042	−	0.950068i
$28$	5090.81			1.22713
$29$		−	4832.42i		−	1.06701i	−0.845796	−	0.533507i	$-0.820874\pi$
$29$		−	4832.42i		−	1.06701i	0.845796	−	0.533507i	$-0.179126\pi$
$30$	890.955	−	1223.56i	0.180739	−	0.248212i
$31$			4999.87i			0.934447i	0.884139	+	0.467223i	$0.154746\pi$
$31$			4999.87i			0.934447i	−0.884139	+	0.467223i	$0.845254\pi$
$32$	−9274.61			−1.60111
$33$	4257.65	+	3100.27i	0.680589	+	0.495581i
$34$			5336.35i			0.791675i
$35$		−	628.213i		−	0.0866835i
$36$	5653.78	+	17527.0i	0.727081	+	2.25399i
$37$		−	9261.10i		−	1.11214i	−0.831137	−	0.556068i	$-0.812309\pi$
$37$		−	9261.10i		−	1.11214i	0.831137	−	0.556068i	$-0.187691\pi$
$38$	−1963.61			−0.220596
$39$	6259.44	−	8596.19i	0.658983	−	0.904992i
$40$			4251.56i			0.420145i
$41$			4658.46i			0.432795i	0.976305	+	0.216398i	$0.0694307\pi$
$41$			4658.46i			0.432795i	−0.976305	+	0.216398i	$0.930569\pi$
$42$	8788.20	+	6399.26i	0.768735	+	0.559766i
$43$		−	5287.94i		−	0.436129i	−0.975934	−	0.218065i	$-0.930026\pi$
$43$		−	5287.94i		−	0.436129i	0.975934	−	0.218065i	$-0.0699744\pi$
$44$	−25605.9			−1.99392
$45$	2162.85	−	697.684i	0.159219	−	0.0513603i
$46$	−8141.51			−0.567297
$47$	−5081.19			−0.335522			−0.167761	−	0.985828i	$-0.553654\pi$
$47$	−5081.19			−0.335522			−0.167761	+	0.985828i	$0.553654\pi$
$48$	−28914.7	−	21054.6i	−1.81140	−	1.31900i
$49$	−12294.9			−0.731533
$50$	−31535.9			−1.78394
$51$	−4716.46	+	6477.18i	−0.253916	+	0.348707i
$52$			51698.4i			2.65136i
$53$		−	8728.92i		−	0.426846i	−0.976960	−	0.213423i	$-0.931539\pi$
$53$		−	8728.92i		−	0.426846i	0.976960	−	0.213423i	$-0.0684612\pi$
$54$	−12271.8	+	37363.5i	−0.572694	+	1.74367i
$55$			3159.81i			0.140849i
$56$	−30536.7			−1.30123
$57$	−2383.41	−	1735.51i	−0.0971652	−	0.0707523i
$58$			50170.6i			1.95830i
$59$	−25651.4	+	7545.23i	−0.959358	+	0.282191i
$59$	−25651.4	+	7545.23i	−0.959358	+	0.282191i
$60$	−6503.82	+	8931.79i	−0.233233	+	0.320303i
$61$		−	26624.9i		−	0.916143i	−0.888915	−	0.458071i	$-0.848540\pi$
$61$		−	26624.9i		−	0.916143i	0.888915	−	0.458071i	$-0.151460\pi$
$62$		−	51909.0i		−	1.71500i
$63$	5011.10	+	15534.6i	0.159067	+	0.493117i
$64$	22864.9			0.697781
$65$	6379.65			0.187290
$66$	−44203.2	−	32187.2i	−1.24909	−	0.909543i
$67$		−	36459.7i		−	0.992262i	−0.868248	−	0.496131i	$-0.834754\pi$
$67$		−	36459.7i		−	0.992262i	0.868248	−	0.496131i	$-0.165246\pi$
$68$		−	38954.4i		−	1.02161i
$69$	−9882.04	−	7195.75i	−0.249876	−	0.181951i
$70$			6522.15i			0.159091i
$71$			83513.0i			1.96611i	0.183305	+	0.983056i	$0.441320\pi$
$71$			83513.0i			1.96611i	−0.183305	+	0.983056i	$0.558680\pi$
$72$	−33913.7	−	105134.i	−0.770981	−	2.39008i
$73$			15824.8i			0.347561i	0.984784	+	0.173780i	$0.0555983\pi$
$73$			15824.8i			0.347561i	−0.984784	+	0.173780i	$0.944402\pi$
$74$			96149.4i			2.04111i
$75$	−38277.8	−	27872.5i	−0.785767	−	0.572168i
$76$	14334.1			0.284666
$77$	−22695.2			−0.436222
$78$	−64986.0	+	89246.3i	−1.20944	+	1.66094i
$79$	−20068.7			−0.361786			−0.180893	−	0.983503i	$-0.557899\pi$
$79$	−20068.7			−0.361786			−0.180893	+	0.983503i	$0.557899\pi$
$80$		−	21459.0i		−	0.374873i
$81$	−47918.5	+	34505.1i	−0.811504	+	0.584347i
$82$		−	48364.4i		−	0.794312i
$83$	69484.9			1.10712			0.553561	−	0.832809i	$-0.313269\pi$
$83$	69484.9			1.10712			0.553561	+	0.832809i	$0.313269\pi$
$84$	−64152.4	−	46713.5i	−0.992006	−	0.722344i
$85$	−4807.03			−0.0721655
$86$			54899.7i			0.800431i
$87$	−44342.5	+	60896.3i	−0.628090	+	0.862566i
$88$	153595.			2.11431
$89$	−21384.8			−0.286174			−0.143087	−	0.989710i	$-0.545703\pi$
$89$	−21384.8			−0.286174			−0.143087	+	0.989710i	$0.545703\pi$
$90$	−22454.9	+	7243.40i	−0.292217	+	0.0942619i
$91$			45821.7i			0.580053i
$92$	59431.6			0.732062
$93$	45879.0	−	63006.4i	0.550056	−	0.755400i
$94$	52753.3			0.615786
$95$		−	1768.84i		−	0.0201085i
$96$	116875.	+	85104.2i	1.29433	+	0.942482i
$97$		−	151770.i		−	1.63779i	−0.573944	−	0.818894i	$-0.694587\pi$
$97$		−	151770.i		−	1.63779i	0.573944	−	0.818894i	$-0.305413\pi$
$98$	127646.			1.34259
$99$	−25205.0	−	78136.7i	−0.258463	−	0.801248i
$100$	230207.			2.30207
$101$	22547.4			0.219934			0.109967	−	0.993935i	$-0.464925\pi$
$101$	22547.4			0.219934			0.109967	+	0.993935i	$0.464925\pi$
$102$	48966.6	−	67246.5i	0.466014	−	0.639985i
$103$			91170.0i			0.846757i	0.905953	+	0.423379i	$0.139156\pi$
$103$			91170.0i			0.846757i	−0.905953	+	0.423379i	$0.860844\pi$
$104$		−	310108.i		−	2.81144i
$105$	−5764.51	+	7916.49i	−0.0510257	+	0.0700744i
$106$			90624.2i			0.783393i
$107$			112334.i			0.948529i	0.880383	+	0.474264i	$0.157286\pi$
$107$			112334.i			0.948529i	−0.880383	+	0.474264i	$0.842714\pi$
$108$	89581.7	−	272748.i	0.739027	−	2.25010i
$109$			102382.i			0.825383i	0.910871	+	0.412692i	$0.135411\pi$
$109$			102382.i			0.825383i	−0.910871	+	0.412692i	$0.864589\pi$
$110$		−	32805.3i		−	0.258501i
$111$	−84980.2	+	116705.i	−0.654652	+	0.899044i
$112$	154129.			1.16102
$113$	−84179.3			−0.620168			−0.310084	−	0.950709i	$-0.600357\pi$
$113$	−84179.3			−0.620168			−0.310084	+	0.950709i	$0.600357\pi$
$114$	24744.7	+	18018.2i	0.178328	+	0.129852i
$115$		−	7333.94i		−	0.0517122i
$116$		−	366237.i		−	2.52707i
$117$	−157758.	+	50888.9i	−1.06543	+	0.343683i
$118$	266314.	−	78335.1i	1.76072	−	0.517907i
$119$		−	34526.4i		−	0.223503i
$120$	39012.5	−	53576.5i	0.247315	−	0.339642i
$121$	−46897.9			−0.291199
$122$			276421.i			1.68140i
$123$	42746.2	−	58704.0i	0.254762	−	0.349869i
$124$			378927.i			2.21310i
$125$		−	57633.6i		−	0.329914i
$126$	−52025.5	−	161282.i	−0.291938	−	0.905021i
$127$	−293804.			−1.61640			−0.808200	−	0.588909i	$-0.799558\pi$
$127$	−293804.			−1.61640			−0.808200	+	0.588909i	$0.799558\pi$
$128$	59402.9			0.320467
$129$	−48522.3	+	66636.5i	−0.256725	+	0.352564i
$130$	−66234.0			−0.343734
$131$	−142504.			−0.725517			−0.362758	−	0.931883i	$-0.618165\pi$
$131$	−142504.			−0.725517			−0.362758	+	0.931883i	$0.618165\pi$
$132$	322676.	+	234961.i	1.61187	+	1.17371i
$133$	12704.7			0.0622779
$134$			378527.i			1.82111i
$135$	−33657.4	−	11054.5i	−0.158945	−	0.0522041i
$136$			233665.i			1.08329i
$137$			240224.i			1.09349i	0.837299	+	0.546746i	$0.184134\pi$
$137$			240224.i			1.09349i	−0.837299	+	0.546746i	$0.815866\pi$
$138$	102596.	+	74706.8i	0.458599	+	0.333935i
$139$	−433932.			−1.90495			−0.952477	−	0.304610i	$-0.901474\pi$
$139$	−433932.			−1.90495			−0.952477	+	0.304610i	$0.901474\pi$
$140$		−	47610.6i		−	0.205297i
$141$	64031.1	+	46625.2i	0.271234	+	0.197503i
$142$		−	867038.i		−	3.60842i
$143$		−	230475.i		−	0.942506i
$144$	171173.	+	530644.i	0.687906	+	2.13254i
$145$	−45194.1			−0.178510
$146$		−	164294.i		−	0.637881i
$147$	154935.	+	112818.i	0.591366	+	0.430612i
$148$		−	701874.i		−	2.63393i
$149$	−194855.			−0.719027			−0.359513	−	0.933140i	$-0.617057\pi$
$149$	−194855.			−0.719027			−0.359513	+	0.933140i	$0.617057\pi$
$150$	397403.	+	289375.i	1.44212	+	1.05010i
$151$			257172.i			0.917870i	0.888470	+	0.458935i	$0.151769\pi$
$151$			257172.i			0.917870i	−0.888470	+	0.458935i	$0.848231\pi$
$152$	−85981.4			−0.301853
$153$	118870.	−	38344.5i	0.410528	−	0.132426i
$154$	235623.			0.800601
$155$	46760.1			0.156331
$156$	474387.	−	651482.i	1.56071	−	2.14334i
$157$		−	294763.i		−	0.954384i	−0.878799	−	0.477192i	$-0.841655\pi$
$157$		−	294763.i		−	0.954384i	0.878799	−	0.477192i	$-0.158345\pi$
$158$	208355.			0.663988
$159$	−80096.9	+	109998.i	−0.251260	+	0.345059i
$160$			86738.6i			0.267863i
$161$	52675.8			0.160157
$162$	497493.	−	358234.i	1.48936	−	1.07246i
$163$	466677.			1.37578			0.687888	−	0.725817i	$-0.258538\pi$
$163$	466677.			1.37578			0.687888	+	0.725817i	$0.258538\pi$
$164$			353052.i			1.02501i
$165$	28994.5	−	39818.6i	0.0829098	−	0.113861i
$166$	−721397.			−2.03191
$167$		−	483482.i		−	1.34150i	−0.741686	−	0.670748i	$-0.765973\pi$
$167$		−	483482.i		−	1.34150i	0.741686	−	0.670748i	$-0.234027\pi$
$168$	384812.	+	280206.i	1.05190	+	0.765958i
$169$	−94036.9			−0.253269
$170$	49906.9			0.132446
$171$	14109.6	+	43740.5i	0.0368998	+	0.114391i
$172$		−	400759.i		−	1.03291i
$173$	−422426.			−1.07309			−0.536545	−	0.843872i	$-0.680271\pi$
$173$	−422426.			−1.07309			−0.536545	+	0.843872i	$0.680271\pi$
$174$	460367.	−	632229.i	1.15274	−	1.58307i
$175$	204038.			0.503636
$176$	−775241.			−1.88649
$177$	392484.	+	140296.i	0.941648	+	0.336599i
$178$	222018.			0.525217
$179$	183578.			0.428242			0.214121	−	0.976807i	$-0.431311\pi$
$179$	183578.			0.428242			0.214121	+	0.976807i	$0.431311\pi$
$180$	163917.	−	52875.6i	0.377088	−	0.121639i
$181$	−452441.			−1.02652			−0.513258	−	0.858234i	$-0.671562\pi$
$181$	−452441.			−1.02652			−0.513258	+	0.858234i	$0.671562\pi$
$182$		−	475724.i		−	1.06458i
$183$	−244311.	+	335516.i	−0.539281	+	0.740603i
$184$	−356495.			−0.776263
$185$	−86612.2			−0.186059
$186$	−476319.	+	654136.i	−1.00952	+	1.38639i
$187$			173662.i			0.363162i
$188$	−385090.			−0.794635
$189$	79398.7	−	241743.i	0.161681	−	0.492266i
$190$			18364.2i			0.0369053i
$191$	−612167.			−1.21419			−0.607095	−	0.794629i	$-0.707665\pi$
$191$	−612167.			−1.21419			−0.607095	+	0.794629i	$0.707665\pi$
$192$	−288134.	−	209809.i	−0.564081	−	0.410744i
$193$	−545872.			−1.05487			−0.527433	−	0.849596i	$-0.676846\pi$
$193$	−545872.			−1.05487			−0.527433	+	0.849596i	$0.676846\pi$
$194$			1.57569e6i			3.00585i
$195$	−80393.8	−	58539.9i	−0.151404	−	0.110247i
$196$	−931796.			−1.73253
$197$			788573.i			1.44769i	0.689962	+	0.723846i	$0.257627\pi$
$197$			788573.i			1.44769i	−0.689962	+	0.723846i	$0.742373\pi$
$198$	261680.	+	811220.i	0.474359	+	1.47054i
$199$	−305544.			−0.546942			−0.273471	−	0.961880i	$-0.588172\pi$
$199$	−305544.			−0.546942			−0.273471	+	0.961880i	$0.588172\pi$
$200$	−1.38087e6			−2.44106
$201$	−334556.	+	459451.i	−0.584088	+	0.802137i
$202$	−234088.			−0.403647
$203$		−	324605.i		−	0.552860i
$204$	−357448.	+	490888.i	−0.601363	+	0.825862i
$205$	43567.1			0.0724059
$206$		−	946533.i		−	1.55406i
$207$	58501.0	+	181356.i	0.0948937	+	0.294175i
$208$			1.56521e6i			2.50850i
$209$	−63902.3			−0.101193
$210$	59847.5	−	82189.5i	0.0936478	−	0.128608i
$211$			406972.i			0.629301i	0.949208	+	0.314651i	$0.101887\pi$
$211$			406972.i			0.629301i	−0.949208	+	0.314651i	$0.898113\pi$
$212$		−	661541.i		−	1.01092i
$213$	766319.	−	1.05240e6i	1.15734	−	1.58939i
$214$		−	1.16626e6i		−	1.74084i
$215$	−49454.2			−0.0729637
$216$	−537347.	+	1.63605e6i	−0.783648	+	2.38595i
$217$			335853.i			0.484172i
$218$		−	1.06293e6i		−	1.51483i
$219$	145209.	−	199418.i	0.204589	−	0.280966i
$220$			239473.i			0.333580i
$221$	350623.			0.482903
$222$	882270.	−	1.21164e6i	1.20149	−	1.65002i
$223$	−234388.			−0.315627			−0.157813	−	0.987469i	$-0.550444\pi$
$223$	−234388.			−0.315627			−0.157813	+	0.987469i	$0.550444\pi$
$224$	−622997.			−0.829595
$225$	226602.	+	702477.i	0.298406	+	0.925073i
$226$	873956.			1.13820
$227$	−1.11450e6			−1.43554			−0.717768	−	0.696283i	$-0.754836\pi$
$227$	−1.11450e6			−1.43554			−0.717768	+	0.696283i	$0.754836\pi$
$228$	−180632.	−	131530.i	−0.230122	−	0.167566i
$229$			255462.i			0.321912i	0.986962	+	0.160956i	$0.0514578\pi$
$229$			255462.i			0.321912i	−0.986962	+	0.160956i	$0.948542\pi$
$230$			76141.5i			0.0949078i
$231$	285996.	+	208252.i	0.352639	+	0.256779i
$232$			2.19683e6i			2.67965i
$233$	783301.			0.945233			0.472617	−	0.881268i	$-0.343310\pi$
$233$	783301.			0.945233			0.472617	+	0.881268i	$0.343310\pi$
$234$	1.63785e6	−	528332.i	1.95540	−	0.630764i
$235$			47520.6i			0.0561322i
$236$	−1.94405e6	+	571833.i	−2.27210	+	0.668327i
$237$	252898.	+	184151.i	0.292465	+	0.212963i
$238$			358455.i			0.410197i
$239$		−	1.01079e6i		−	1.14463i	−0.820032	−	0.572317i	$-0.806044\pi$
$239$		−	1.01079e6i		−	1.14463i	0.820032	−	0.572317i	$-0.193956\pi$
$240$	−196908.	+	270417.i	−0.220666	+	0.303045i
$241$	−354547.			−0.393216			−0.196608	−	0.980482i	$-0.562993\pi$
$241$	−354547.			−0.393216			−0.196608	+	0.980482i	$0.562993\pi$
$242$	486897.			0.534440
$243$	920470.	+	4882.62i	0.999986	+	0.00530442i
$244$		−	2.01783e6i		−	2.16975i
$245$			114985.i			0.122384i
$246$	−443794.	+	609469.i	−0.467567	+	0.642116i
$247$			129019.i			0.134558i
$248$		−	2.27296e6i		−	2.34672i
$249$	−875621.	−	637597.i	−0.894990	−	0.651700i
$250$			598356.i			0.605494i
$251$			1.03607e6i			1.03802i	0.854768	+	0.519010i	$0.173699\pi$
$251$			1.03607e6i			1.03802i	−0.854768	+	0.519010i	$0.826301\pi$
$252$	379778.	+	1.17733e6i	0.376728	+	1.16788i
$253$	−264951.			−0.260234
$254$	3.05029e6			2.96659
$255$	60576.3	+	44109.5i	0.0583381	+	0.0424797i
$256$	−1.34840e6			−1.28594
$257$			303483.i			0.286617i	0.989678	+	0.143308i	$0.0457741\pi$
$257$			303483.i			0.286617i	−0.989678	+	0.143308i	$0.954226\pi$
$258$	503762.	−	691824.i	0.471168	−	0.647063i
$259$		−	622090.i		−	0.576240i
$260$	483497.			0.443568
$261$	1.11757e6	−	360502.i	1.01549	−	0.327572i
$262$	1.47948e6			1.33155
$263$		−	531107.i		−	0.473470i	−0.971574	−	0.236735i	$-0.923923\pi$
$263$		−	531107.i		−	0.473470i	0.971574	−	0.236735i	$-0.0760773\pi$
$264$	−1.93554e6	−	1.40939e6i	−1.70920	−	1.24458i
$265$	−81635.1			−0.0714105
$266$	−131901.			−0.114299
$267$	269482.	+	196228.i	0.231341	+	0.168454i
$268$		−	2.76318e6i		−	2.35003i
$269$	1.65340e6			1.39315			0.696576	−	0.717483i	$-0.254706\pi$
$269$	1.65340e6			1.39315			0.696576	+	0.717483i	$0.254706\pi$
$270$	349433.	+	114769.i	0.291713	+	0.0958106i
$271$	436144.			0.360751			0.180375	−	0.983598i	$-0.442269\pi$
$271$	436144.			0.360751			0.180375	+	0.983598i	$0.442269\pi$
$272$		−	1.17938e6i		−	0.966565i
$273$	420461.	−	577426.i	0.341444	−	0.468910i
$274$		−	2.49402e6i		−	2.00689i
$275$	−1.02628e6			−0.818339
$276$	−748934.	−	545347.i	−0.591794	−	0.430924i
$277$	546800.			0.428182			0.214091	−	0.976814i	$-0.431321\pi$
$277$	546800.			0.428182			0.214091	+	0.976814i	$0.431321\pi$
$278$	4.50511e6			3.49618
$279$	−1.15630e6	+	372993.i	−0.889322	+	0.286874i
$280$			285587.i			0.217693i
$281$		−	1.70601e6i		−	1.28889i	−0.764652	−	0.644443i	$-0.777089\pi$
$281$		−	1.70601e6i		−	1.28889i	0.764652	−	0.644443i	$-0.222911\pi$
$282$	−664776.	−	484066.i	−0.497797	−	0.362478i
$283$			1.13239e6i			0.840482i	0.907412	+	0.420241i	$0.138055\pi$
$283$			1.13239e6i			0.840482i	−0.907412	+	0.420241i	$0.861945\pi$
$284$			6.32923e6i			4.65645i
$285$	−16231.0	+	22290.2i	−0.0118367	+	0.0162556i
$286$			2.39281e6i			1.72979i
$287$			312919.i			0.224248i
$288$	−691892.	−	2.14490e6i	−0.491538	−	1.52379i
$289$	1.15566e6			0.813930
$290$	469208.			0.327620
$291$	−1.39265e6	+	1.91255e6i	−0.964073	+	1.32398i
$292$			1.19932e6i			0.823147i
$293$		−	745834.i		−	0.507543i	−0.967264	−	0.253772i	$-0.918329\pi$
$293$		−	745834.i		−	0.507543i	0.967264	−	0.253772i	$-0.0816712\pi$
$294$	−1.60855e6	−	1.17129e6i	−1.08534	−	0.790306i
$295$	70565.0	+	239898.i	0.0472100	+	0.160499i
$296$			4.21012e6i			2.79297i
$297$	−399362.	+	1.21593e6i	−0.262709	+	0.799866i
$298$	2.02299e6			1.31964
$299$			534936.i			0.346038i
$300$	−2.90097e6	−	2.11239e6i	−1.86097	−	1.35510i
$301$		−	355203.i		−	0.225975i
$302$		−	2.66998e6i		−	1.68457i
$303$	−284133.	−	206896.i	−0.177793	−	0.129463i
$304$	433975.			0.269328
$305$	−249003.			−0.153269
$306$	−1.23411e6	+	398095.i	−0.753445	+	0.243043i
$307$	1.41643e6			0.857726			0.428863	−	0.903369i	$-0.358914\pi$
$307$	1.41643e6			0.857726			0.428863	+	0.903369i	$0.358914\pi$
$308$	−1.72001e6			−1.03313
$309$	836580.	−	1.14889e6i	0.498438	−	0.684513i
$310$	−485466.			−0.286916
$311$		−	2.54619e6i		−	1.49276i	−0.665521	−	0.746379i	$-0.731791\pi$
$311$		−	2.54619e6i		−	1.49276i	0.665521	−	0.746379i	$-0.268209\pi$
$312$	−2.84556e6	+	3.90786e6i	−1.65494	+	2.27275i
$313$		−	3.07369e6i		−	1.77337i	−0.462375	−	0.886684i	$-0.653003\pi$
$313$		−	3.07369e6i		−	1.77337i	0.462375	−	0.886684i	$-0.346997\pi$
$314$			3.06025e6i			1.75159i
$315$	145284.	−	46865.1i	0.0824976	−	0.0266117i
$316$	−1.52095e6			−0.856837
$317$			175287.i			0.0979719i	0.998799	+	0.0489860i	$0.0155990\pi$
$317$			175287.i			0.0979719i	−0.998799	+	0.0489860i	$0.984401\pi$
$318$	831572.	−	1.14201e6i	0.461139	−	0.633289i
$319$			1.63271e6i			0.898322i
$320$		−	213838.i		−	0.116737i
$321$	1.03078e6	−	1.41558e6i	0.558345	−	0.766784i
$322$	−546884.			−0.293938
$323$		−	97214.9i		−	0.0518474i
$324$	−3.63162e6	+	2.61505e6i	−1.92193	+	1.38394i
$325$			2.07206e6i			1.08816i
$326$	−4.84507e6			−2.52497
$327$	939457.	−	1.29017e6i	0.485856	−	0.667234i
$328$		−	2.11775e6i		−	1.08690i
$329$	−341315.			−0.173847
$330$	−301023.	+	413399.i	−0.152165	+	0.208971i
$331$	−1.28354e6			−0.643929			−0.321965	−	0.946752i	$-0.604343\pi$
$331$	−1.28354e6			−0.643929			−0.321965	+	0.946752i	$0.604343\pi$
$332$	5.26608e6			2.62206
$333$	2.14177e6	−	690884.i	1.05843	−	0.341424i
$334$			5.01954e6i			2.46206i
$335$	−340981.			−0.166004
$336$	−1.94227e6	−	1.41429e6i	−0.938557	−	0.683424i
$337$		−	3.76381e6i		−	1.80532i	−0.430358	−	0.902659i	$-0.641613\pi$
$337$		−	3.76381e6i		−	1.80532i	0.430358	−	0.902659i	$-0.358387\pi$
$338$	976298.			0.464826
$339$	1.06079e6	+	772433.i	0.501340	+	0.365058i
$340$	−364312.			−0.170913
$341$		−	1.68928e6i		−	0.786714i
$342$	−146487.	−	454116.i	−0.0677226	−	0.209943i
$343$	−1.95484e6			−0.897173
$344$			2.40391e6i			1.09527i
$345$	−67296.5	+	92419.4i	−0.0304400	+	0.0418038i
$346$	4.38566e6			1.96945
$347$	−3.62674e6			−1.61694			−0.808469	−	0.588539i	$-0.799703\pi$
$347$	−3.62674e6			−1.61694			−0.808469	+	0.588539i	$0.799703\pi$
$348$	−3.36060e6	+	4.61517e6i	−1.48754	+	2.04286i
$349$		−	1.91448e6i		−	0.841370i	−0.907207	−	0.420685i	$-0.861790\pi$
$349$		−	1.91448e6i		−	0.841370i	0.907207	−	0.420685i	$-0.138210\pi$
$350$	−2.11834e6			−0.924327
$351$	2.45496e6	+	806313.i	1.06360	+	0.349330i
$352$	3.13357e6			1.34798
$353$	−1.73817e6			−0.742428			−0.371214	−	0.928547i	$-0.621058\pi$
$353$	−1.73817e6			−0.742428			−0.371214	+	0.928547i	$0.621058\pi$
$354$	−4.07479e6	−	1.45656e6i	−1.72821	−	0.617762i
$355$	781035.			0.328927
$356$	−1.62069e6			−0.677760
$357$	−316815.	+	435087.i	−0.131564	+	0.180678i
$358$	−1.90592e6			−0.785955
$359$		−	2.34856e6i		−	0.961759i	−0.876787	−	0.480880i	$-0.840317\pi$
$359$		−	2.34856e6i		−	0.961759i	0.876787	−	0.480880i	$-0.159683\pi$
$360$	−983240.	+	317169.i	−0.399856	+	0.128984i
$361$	−2.44033e6			−0.985553
$362$	4.69728e6			1.88397
$363$	590988.	+	430337.i	0.235403	+	0.171412i
$364$			3.47270e6i			1.37377i
$365$	147997.			0.0581463
$366$	2.53645e6	−	3.48335e6i	0.989747	−	1.35923i
$367$			4.90872e6i			1.90240i	0.308567	+	0.951202i	$0.400150\pi$
$367$			4.90872e6i			1.90240i	−0.308567	+	0.951202i	$0.599850\pi$
$368$	1.79934e6			0.692619
$369$	−1.07734e6	+	347524.i	−0.411896	+	0.132867i
$370$	899213.			0.341475
$371$		−	586342.i		−	0.221165i
$372$	3.47705e6	−	4.77508e6i	1.30273	−	1.78906i
$373$	1.54029e6			0.573232			0.286616	−	0.958045i	$-0.407470\pi$
$373$	1.54029e6			0.573232			0.286616	+	0.958045i	$0.407470\pi$
$374$		−	1.80297e6i		−	0.666514i
$375$	−528848.	+	726276.i	−0.194202	+	0.266700i
$376$	2.30992e6			0.842613
$377$	3.29644e6			1.19452
$378$	−824322.	+	2.50980e6i	−0.296734	+	0.903460i
$379$	−3.31374e6			−1.18501			−0.592503	−	0.805568i	$-0.701860\pi$
$379$	−3.31374e6			−1.18501			−0.592503	+	0.805568i	$0.701860\pi$
$380$		−	134056.i		−	0.0476241i
$381$	3.70240e6	+	2.69596e6i	1.30669	+	0.951482i
$382$	6.35556e6			2.22841
$383$			4.60560e6i			1.60431i	0.597113	+	0.802157i	$0.296314\pi$
$383$			4.60560e6i			1.60431i	−0.597113	+	0.802157i	$0.703686\pi$
$384$	−748572.	−	545084.i	−0.259063	−	0.188641i
$385$			212251.i			0.0729792i
$386$	5.66728e6			1.93600
$387$	1.22292e6	−	394483.i	0.415069	−	0.133891i
$388$		−	1.15023e7i		−	3.87886i
$389$			1.85129e6i			0.620298i	0.950688	+	0.310149i	$0.100379\pi$
$389$			1.85129e6i			0.620298i	−0.950688	+	0.310149i	$0.899621\pi$
$390$	834654.	+	607765.i	0.277872	+	0.202337i
$391$		−	403071.i		−	0.133334i
$392$	5.58929e6			1.83714
$393$	1.79577e6	+	1.30762e6i	0.586503	+	0.427071i
$394$		−	8.18701e6i		−	2.65696i
$395$			187688.i			0.0605261i
$396$	−1.91022e6	−	5.92177e6i	−0.612132	−	1.89764i
$397$		−	4.77548e6i		−	1.52069i	−0.649520	−	0.760345i	$-0.725030\pi$
$397$		−	4.77548e6i		−	1.52069i	0.649520	−	0.760345i	$-0.274970\pi$
$398$	3.17218e6			1.00381
$399$	−160099.	−	116578.i	−0.0503450	−	0.0366594i
$400$	6.96970e6			2.17803
$401$	−2.40174e6			−0.745872			−0.372936	−	0.927857i	$-0.621649\pi$
$401$	−2.40174e6			−0.745872			−0.372936	+	0.927857i	$0.621649\pi$
$402$	3.47338e6	−	4.77005e6i	1.07198	−	1.47217i
$403$	−3.41067e6			−1.04611
$404$	1.70881e6			0.520882
$405$	322701.	+	448146.i	0.0977602	+	0.135763i
$406$			3.37007e6i			1.01467i
$407$			3.12901e6i			0.936312i
$408$	2.14411e6	−	2.94455e6i	0.637672	−	0.875726i
$409$			4.44463e6i			1.31379i	0.753980	+	0.656897i	$0.228131\pi$
$409$			4.44463e6i			1.31379i	−0.753980	+	0.656897i	$0.771869\pi$
$410$	−452316.			−0.132887
$411$	2.20431e6	−	3.02721e6i	0.643676	−	0.883971i
$412$			6.90953e6i			2.00542i
$413$	−1.72306e6	+	506831.i	−0.497080	+	0.146214i
$414$	−607361.	−	1.88285e6i	−0.174159	−	0.539902i
$415$		−	649841.i		−	0.185220i
$416$		−	6.32669e6i		−	1.79243i
$417$	5.46824e6	+	3.98178e6i	1.53995	+	1.12134i
$418$	663438.			0.185720
$419$	−4.40819e6			−1.22666			−0.613331	−	0.789826i	$-0.710171\pi$
$419$	−4.40819e6			−1.22666			−0.613331	+	0.789826i	$0.710171\pi$
$420$	−436876.	+	599969.i	−0.120847	+	0.165961i
$421$		−	1.52637e6i		−	0.419715i	−0.977732	−	0.209857i	$-0.932700\pi$
$421$		−	1.52637e6i		−	0.419715i	0.977732	−	0.209857i	$-0.0673000\pi$
$422$		−	4.22521e6i		−	1.15496i
$423$	−379060.	−	1.17510e6i	−0.103005	−	0.319320i
$424$			3.96819e6i			1.07196i
$425$		−	1.56128e6i		−	0.419285i
$426$	−7.95597e6	+	1.09261e7i	−2.12407	+	2.91702i
$427$		−	1.78846e6i		−	0.474688i
$428$			8.51347e6i			2.24645i
$429$	−2.11485e6	+	2.90436e6i	−0.554800	+	0.761916i
$430$	513436.			0.133911
$431$	−311908.			−0.0808785			−0.0404393	−	0.999182i	$-0.512876\pi$
$431$	−311908.			−0.0808785			−0.0404393	+	0.999182i	$0.512876\pi$
$432$	2.71216e6	−	8.25766e6i	0.699208	−	2.12886i
$433$	−6.61265e6			−1.69494			−0.847472	−	0.530840i	$-0.821877\pi$
$433$	−6.61265e6			−1.69494			−0.847472	+	0.530840i	$0.821877\pi$
$434$		−	3.48685e6i		−	0.888605i
$435$	569518.	+	414703.i	0.144306	+	0.105078i
$436$			7.75923e6i			1.95480i
$437$	148318.			0.0371527
$438$	−1.50757e6	+	2.07037e6i	−0.375484	+	0.515658i
$439$	−3.66105e6			−0.906659			−0.453329	−	0.891343i	$-0.649764\pi$
$439$	−3.66105e6			−0.906659			−0.453329	+	0.891343i	$0.649764\pi$
$440$		−	1.43646e6i		−	0.353721i
$441$	−917205.	−	2.84338e6i	−0.224580	−	0.696208i
$442$	−3.64020e6			−0.886276
$443$	−1.92663e6			−0.466433			−0.233217	−	0.972425i	$-0.574925\pi$
$443$	−1.92663e6			−0.466433			−0.233217	+	0.972425i	$0.574925\pi$
$444$	−6.44042e6	+	8.84473e6i	−1.55045	+	2.12925i
$445$			199996.i			0.0478763i
$446$	2.43344e6			0.579272
$447$	2.45548e6	+	1.78799e6i	0.581256	+	0.423250i
$448$	1.53589e6			0.361547
$449$			6.86780e6i			1.60769i	0.594841	+	0.803844i	$0.297215\pi$
$449$			6.86780e6i			1.60769i	−0.594841	+	0.803844i	$0.702785\pi$
$450$	−2.35260e6	−	7.29317e6i	−0.547667	−	1.69779i
$451$		−	1.57393e6i		−	0.364372i
$452$	−6.37973e6			−1.46878
$453$	2.35982e6	−	3.24078e6i	0.540298	−	0.742000i
$454$	1.15708e7			2.63465
$455$	428536.			0.0970418
$456$	1.08350e6	+	788969.i	0.244016	+	0.177684i
$457$		−	925489.i		−	0.207291i	−0.994614	−	0.103646i	$-0.966949\pi$
$457$		−	925489.i		−	0.207291i	0.994614	−	0.103646i	$-0.0330508\pi$
$458$		−	2.65222e6i		−	0.590808i
$459$	−1.84980e6	−	607552.i	−0.409820	−	0.134602i
$460$		−	555820.i		−	0.122473i
$461$		−	6.86778e6i		−	1.50510i	−0.658537	−	0.752548i	$-0.728825\pi$
$461$		−	6.86778e6i		−	1.50510i	0.658537	−	0.752548i	$-0.271175\pi$
$462$	−2.96923e6	−	2.16209e6i	−0.647201	−	0.471269i
$463$			2.05018e6i			0.444467i	0.974993	+	0.222233i	$0.0713347\pi$
$463$			2.05018e6i			0.444467i	−0.974993	+	0.222233i	$0.928665\pi$
$464$		−	1.10881e7i		−	2.39091i
$465$	−589252.	−	429072.i	−0.126377	−	0.0920234i
$466$	−8.13228e6			−1.73479
$467$	7.22686e6			1.53341			0.766704	−	0.642001i	$-0.221896\pi$
$467$	7.22686e6			1.53341			0.766704	+	0.642001i	$0.221896\pi$
$468$	−1.19561e7	+	3.85673e6i	−2.52333	+	0.813963i
$469$		−	2.44908e6i		−	0.514128i
$470$		−	493362.i		−	0.103020i
$471$	−2.70475e6	+	3.71448e6i	−0.561792	+	0.771517i
$472$	1.16612e7	−	3.43009e6i	2.40929	−	0.708680i
$473$			1.78661e6i			0.367179i
$474$	−2.62560e6	−	1.91187e6i	−0.536763	−	0.390852i
$475$	574505.			0.116831
$476$		−	2.61666e6i		−	0.529334i
$477$	2.01870e6	−	651183.i	0.406233	−	0.131041i
$478$			1.04941e7i			2.10076i
$479$			2.56610e6i			0.511017i	0.966807	+	0.255508i	$0.0822429\pi$
$479$			2.56610e6i			0.511017i	−0.966807	+	0.255508i	$0.917757\pi$
$480$	795916.	−	1.09304e6i	0.157676	−	0.216538i
$481$	6.31747e6			1.24503
$482$	3.68093e6			0.721672
$483$	−663800.	−	483356.i	−0.129470	−	0.0942755i
$484$	−3.55426e6			−0.689662
$485$	−1.41940e6			−0.273999
$486$	−9.55638e6	−	50691.7i	−1.83528	−	0.00973524i
$487$	−7.24144e6			−1.38357			−0.691787	−	0.722101i	$-0.743177\pi$
$487$	−7.24144e6			−1.38357			−0.691787	+	0.722101i	$0.743177\pi$
$488$			1.21038e7i			2.30076i
$489$	−5.88088e6	−	4.28225e6i	−1.11217	−	0.809841i
$490$		−	1.19378e6i		−	0.224613i
$491$		−	3.59515e6i		−	0.672997i	−0.941684	−	0.336498i	$-0.890757\pi$
$491$		−	3.59515e6i		−	0.672997i	0.941684	−	0.336498i	$-0.109243\pi$
$492$	3.23962e6	−	4.44902e6i	0.603366	−	0.828613i
$493$	−2.48385e6			−0.460265
$494$		−	1.33948e6i		−	0.246956i
$495$	−730754.	+	235723.i	−0.134047	+	0.0432404i
$496$			1.14723e7i			2.09386i
$497$			5.60976e6i			1.01872i
$498$	9.09076e6	+	6.61957e6i	1.64258	+	1.19607i
$499$	2.28721e6			0.411202			0.205601	−	0.978636i	$-0.434085\pi$
$499$	2.28721e6			0.411202			0.205601	+	0.978636i	$0.434085\pi$
$500$		−	4.36790e6i		−	0.781353i
$501$	−4.43645e6	+	6.09265e6i	−0.789662	+	1.08446i
$502$		−	1.07566e7i		−	1.90509i
$503$	−7.76929e6			−1.36918			−0.684591	−	0.728927i	$-0.740019\pi$
$503$	−7.76929e6			−1.36918			−0.684591	+	0.728927i	$0.740019\pi$
$504$	−2.27806e6	−	7.06210e6i	−0.399474	−	1.23839i
$505$		−	210869.i		−	0.0367946i
$506$	2.75074e6			0.477609
$507$	1.18502e6	+	862887.i	0.204741	+	0.149085i
$508$	−2.22666e7			−3.82821
$509$	1.00260e7			1.71527			0.857635	−	0.514259i	$-0.171933\pi$
$509$	1.00260e7			1.71527			0.857635	+	0.514259i	$0.171933\pi$
$510$	−628907.	−	457948.i	−0.107068	−	0.0779634i
$511$			1.06299e6i			0.180084i
$512$	1.20983e7			2.03962
$513$	223561.	−	680670.i	0.0375061	−	0.114194i
$514$		−	3.15078e6i		−	0.526030i
$515$	852645.			0.141661
$516$	−3.67738e6	+	5.05020e6i	−0.608015	+	0.834996i
$517$	1.71676e6			0.282477
$518$			6.45858e6i			1.05758i
$519$	5.32325e6	+	3.87620e6i	0.867478	+	0.631667i
$520$	−2.90021e6			−0.470350
$521$			9.90696e6i			1.59899i	0.600672	+	0.799496i	$0.294900\pi$
$521$			9.90696e6i			1.59899i	−0.600672	+	0.799496i	$0.705100\pi$
$522$	−1.16027e7	+	3.74275e6i	−1.86373	+	0.601194i
$523$	−418873.			−0.0669619			−0.0334810	−	0.999439i	$-0.510659\pi$
$523$	−418873.			−0.0669619			−0.0334810	+	0.999439i	$0.510659\pi$
$524$	−1.08000e7			−1.71828
$525$	−2.57121e6	−	1.87226e6i	−0.407136	−	0.296462i
$526$			5.51399e6i			0.868963i
$527$	2.56992e6			0.403081
$528$	9.76927e6	+	7.11364e6i	1.52503	+	1.11047i
$529$	−5.82139e6			−0.904456
$530$	847541.			0.131060
$531$	−3.65856e6	−	5.36940e6i	−0.563085	−	0.826399i
$532$	962852.			0.147496
$533$	−3.17777e6			−0.484512
$534$	−2.79778e6	−	2.03725e6i	−0.424581	−	0.309165i
$535$	1.05057e6			0.158687
$536$			1.65747e7i			2.49192i
$537$	−2.31338e6	−	1.68452e6i	−0.346187	−	0.252081i
$538$	−1.71658e7			−2.55686
$539$	4.15402e6			0.615880
$540$	−2.55080e6	−	837791.i	−0.376437	−	0.123638i
$541$		−	1.21275e7i		−	1.78147i	−0.454518	−	0.890737i	$-0.650189\pi$
$541$		−	1.21275e7i		−	1.78147i	0.454518	−	0.890737i	$-0.349811\pi$
$542$	−4.52808e6			−0.662088
$543$	5.70148e6	+	4.15162e6i	0.829829	+	0.604252i
$544$			4.76712e6i			0.690652i
$545$	957499.			0.138085
$546$	−4.36526e6	+	5.99488e6i	−0.626655	+	0.860595i
$547$	−2.13534e6			−0.305139			−0.152570	−	0.988293i	$-0.548755\pi$
$547$	−2.13534e6			−0.305139			−0.152570	+	0.988293i	$0.548755\pi$
$548$			1.82059e7i			2.58977i
$549$	6.15742e6	−	1.98623e6i	0.871902	−	0.281254i
$550$	1.06549e7			1.50190
$551$		−	913982.i		−	0.128250i
$552$	4.49241e6	+	3.27121e6i	0.627525	+	0.456942i
$553$	−1.34806e6			−0.187455
$554$	−5.67691e6			−0.785846
$555$	1.09145e6	+	794757.i	0.150408	+	0.109522i
$556$	−3.28865e7			−4.51161
$557$		−	2.87203e6i		−	0.392240i	−0.980580	−	0.196120i	$-0.937166\pi$
$557$		−	2.87203e6i		−	0.392240i	0.980580	−	0.196120i	$-0.0628342\pi$
$558$	1.20048e7	−	3.87244e6i	1.63218	−	0.526501i
$559$	3.60717e6			0.488244
$560$		−	1.44145e6i		−	0.194236i
$561$	1.59353e6	−	2.18842e6i	0.213773	−	0.293578i
$562$			1.77119e7i			2.36550i
$563$	−8.75269e6			−1.16378			−0.581890	−	0.813268i	$-0.697686\pi$
$563$	−8.75269e6			−1.16378			−0.581890	+	0.813268i	$0.697686\pi$
$564$	4.85275e6	+	3.53360e6i	0.642377	+	0.467756i
$565$			787267.i			0.103753i
$566$		−	1.17565e7i		−	1.54254i
$567$	−3.21880e6	+	2.31779e6i	−0.420471	+	0.302772i
$568$		−	3.79653e7i		−	4.93760i
$569$	3.22905e6			0.418114			0.209057	−	0.977904i	$-0.432961\pi$
$569$	3.22905e6			0.418114			0.209057	+	0.977904i	$0.432961\pi$
$570$	168511.	−	231419.i	0.0217241	−	0.0298340i
$571$		−	9.79432e6i		−	1.25714i	−0.777752	−	0.628571i	$-0.783640\pi$
$571$		−	9.79432e6i		−	1.25714i	0.777752	−	0.628571i	$-0.216360\pi$
$572$		−	1.74671e7i		−	2.23219i
$573$	7.71428e6	+	5.61727e6i	0.981542	+	0.714724i
$574$		−	3.24875e6i		−	0.411563i
$575$	2.38200e6			0.300450
$576$	1.70573e6	+	5.28786e6i	0.214218	+	0.664085i
$577$	2.28516e6			0.285744			0.142872	−	0.989741i	$-0.454366\pi$
$577$	2.28516e6			0.285744			0.142872	+	0.989741i	$0.454366\pi$
$578$	−1.19982e7			−1.49381
$579$	6.87886e6	+	5.00894e6i	0.852747	+	0.620940i
$580$	−3.42514e6			−0.422774
$581$	4.66747e6			0.573642
$582$	1.44586e7	−	1.98562e7i	1.76937	−	2.42990i
$583$			2.94920e6i			0.359363i
$584$		−	7.19400e6i		−	0.872847i
$585$	475926.	+	1.47539e6i	0.0574976	+	0.178245i
$586$			7.74330e6i			0.931498i
$587$	−5.57604e6			−0.667929			−0.333965	−	0.942586i	$-0.608387\pi$
$587$	−5.57604e6			−0.667929			−0.333965	+	0.942586i	$0.608387\pi$
$588$	1.17421e7	+	8.55020e6i	1.40056	+	1.01984i
$589$			945652.i			0.112316i
$590$	−732610.	−	2.49064e6i	−0.0866449	−	0.294565i
$591$	7.23597e6	−	9.93728e6i	0.852174	−	1.17030i
$592$		−	2.12498e7i		−	2.49202i
$593$		−	1.15688e7i		−	1.35099i	−0.737363	−	0.675496i	$-0.763929\pi$
$593$		−	1.15688e7i		−	1.35099i	0.737363	−	0.675496i	$-0.236071\pi$
$594$	4.14620e6	−	1.26239e7i	0.482153	−	1.46800i
$595$	−322899.			−0.0373917
$596$	−1.47675e7			−1.70291
$597$	3.85035e6	+	2.80369e6i	0.442144	+	0.321954i
$598$		−	5.55374e6i		−	0.635086i
$599$		−	8.72307e6i		−	0.993350i	−0.867937	−	0.496675i	$-0.834554\pi$
$599$		−	8.72307e6i		−	0.993350i	0.867937	−	0.496675i	$-0.165446\pi$
$600$	1.74012e7	+	1.26709e7i	1.97334	+	1.43691i
$601$			1.67437e7i			1.89089i	0.325788	+	0.945443i	$0.394370\pi$
$601$			1.67437e7i			1.89089i	−0.325788	+	0.945443i	$0.605630\pi$
$602$			3.68774e6i			0.414734i
$603$	8.43188e6	−	2.71992e6i	0.944345	−	0.304623i
$604$			1.94904e7i			2.17384i
$605$			438601.i			0.0487171i
$606$	2.94989e6	+	2.14800e6i	0.326305	+	0.237604i
$607$	4.23190e6			0.466191			0.233096	−	0.972454i	$-0.425114\pi$
$607$	4.23190e6			0.466191			0.233096	+	0.972454i	$0.425114\pi$
$608$	−1.75416e6			−0.192446
$609$	−2.97859e6	+	4.09054e6i	−0.325437	+	0.446928i
$610$	2.58516e6			0.281296
$611$		−	3.46614e6i		−	0.375615i
$612$	9.00882e6	−	2.90603e6i	0.972276	−	0.313632i
$613$			7.26766e6i			0.781166i	0.920568	+	0.390583i	$0.127727\pi$
$613$			7.26766e6i			0.781166i	−0.920568	+	0.390583i	$0.872273\pi$
$614$	−1.47055e7			−1.57419
$615$	−549015.	−	399773.i	−0.0585324	−	0.0426212i
$616$	1.03173e7			1.09551
$617$		−	1.38840e7i		−	1.46826i	−0.679009	−	0.734130i	$-0.737590\pi$
$617$		−	1.38840e7i		−	1.46826i	0.679009	−	0.734130i	$-0.262410\pi$
$618$	−8.68543e6	+	1.19278e7i	−0.914787	+	1.25629i
$619$	−5.18447e6			−0.543849			−0.271924	−	0.962319i	$-0.587660\pi$
$619$	−5.18447e6			−0.543849			−0.271924	+	0.962319i	$0.587660\pi$
$620$	3.54382e6			0.370248
$621$	926924.	−	2.82218e6i	0.0964528	−	0.293668i
$622$			2.64347e7i			2.73967i
$623$	−1.43646e6			−0.148277
$624$	1.43624e7	−	1.97242e7i	1.47661	−	2.02786i
$625$	8.95329e6			0.916817
$626$			3.19112e7i			3.25468i
$627$	805271.	+	586370.i	0.0818037	+	0.0595666i
$628$		−	2.23393e7i		−	2.26032i
$629$	−4.76018e6			−0.479729
$630$	−1.50835e6	+	486556.i	−0.151408	+	0.0488407i
$631$	1.48363e7			1.48338			0.741689	−	0.670744i	$-0.234025\pi$
$631$	1.48363e7			1.48338			0.741689	+	0.670744i	$0.234025\pi$
$632$	9.12329e6			0.908571
$633$	3.73439e6	−	5.12850e6i	0.370434	−	0.508723i
$634$		−	1.81984e6i		−	0.179809i
$635$			2.74773e6i			0.270421i
$636$	−6.07033e6	+	8.33648e6i	−0.595072	+	0.817222i
$637$		−	8.38696e6i		−	0.818948i
$638$		−	1.69509e7i		−	1.64870i
$639$	−1.93137e7	+	6.23012e6i	−1.87117	+	0.603593i
$640$		−	555552.i		−	0.0536135i
$641$		−	6.98516e6i		−	0.671478i	−0.941955	−	0.335739i	$-0.891014\pi$
$641$		−	6.98516e6i		−	0.671478i	0.941955	−	0.335739i	$-0.108986\pi$
$642$	−1.07016e7	+	1.46967e7i	−1.02473	+	1.40728i
$643$	9.85148e6			0.939667			0.469834	−	0.882755i	$-0.344314\pi$
$643$	9.85148e6			0.939667			0.469834	+	0.882755i	$0.344314\pi$
$644$	3.99216e6			0.379309
$645$	623201.	+	453793.i	0.0589833	+	0.0429496i
$646$			1.00929e6i			0.0951558i
$647$			782301.i			0.0734705i	0.999325	+	0.0367353i	$0.0116958\pi$
$647$			782301.i			0.0734705i	−0.999325	+	0.0367353i	$0.988304\pi$
$648$	2.17839e7	−	1.56861e7i	2.03797	−	1.46750i
$649$	8.66672e6	−	2.54927e6i	0.807687	−	0.237577i
$650$		−	2.15122e7i		−	1.99711i
$651$	3.08180e6	−	4.23228e6i	0.285005	−	0.391401i
$652$	3.53682e7			3.25832
$653$		−	1.18437e6i		−	0.108694i	−0.998522	−	0.0543468i	$-0.982692\pi$
$653$		−	1.18437e6i		−	0.108694i	0.998522	−	0.0543468i	$-0.0173077\pi$
$654$	−9.75351e6	+	1.33946e7i	−0.891695	+	1.22458i
$655$			1.33273e6i			0.121378i
$656$			1.06889e7i			0.969784i
$657$	−3.65973e6	+	1.18054e6i	−0.330777	+	0.106701i
$658$	3.54356e6			0.319062
$659$	−5.36643e6			−0.481362			−0.240681	−	0.970604i	$-0.577371\pi$
$659$	−5.36643e6			−0.481362			−0.240681	+	0.970604i	$0.577371\pi$
$660$	2.19742e6	−	3.01775e6i	0.196360	−	0.269664i
$661$	1.31364e6			0.116943			0.0584715	−	0.998289i	$-0.481377\pi$
$661$	1.31364e6			0.116943			0.0584715	+	0.998289i	$0.481377\pi$
$662$	1.33258e7			1.18181
$663$	−4.41842e6	−	3.21733e6i	−0.390376	−	0.284258i
$664$	−3.15881e7			−2.78037
$665$		−	118817.i		−	0.0104190i
$666$	−2.22360e7	+	7.17280e6i	−1.94255	+	0.626618i
$667$		−	3.78954e6i		−	0.329816i
$668$		−	3.66418e7i		−	3.17714i
$669$	2.95367e6	+	2.15076e6i	0.255151	+	0.185792i
$670$	3.54008e6			0.304668
$671$			8.99563e6i			0.771303i
$672$	7.85076e6	+	5.71665e6i	0.670639	+	0.488335i
$673$		−	997261.i		−	0.0848733i	−0.999099	−	0.0424367i	$-0.986488\pi$
$673$		−	997261.i		−	0.0848733i	0.999099	−	0.0424367i	$-0.0135121\pi$
$674$			3.90762e7i			3.31331i
$675$	3.59041e6	−	1.09316e7i	0.303309	−	0.923477i
$676$	−7.12681e6			−0.599830
$677$			1.00182e7i			0.840071i	0.907508	+	0.420036i	$0.137982\pi$
$677$			1.00182e7i			0.840071i	−0.907508	+	0.420036i	$0.862018\pi$
$678$	−1.10132e7	−	8.01945e6i	−0.920112	−	0.669993i
$679$		−	1.01948e7i		−	0.848600i
$680$	2.18529e6			0.181233
$681$	1.40444e7	+	1.02267e7i	1.16048	+	0.845018i
$682$			1.75383e7i			1.44386i
$683$	−1.44372e6			−0.118421			−0.0592107	−	0.998246i	$-0.518858\pi$
$683$	−1.44372e6			−0.118421			−0.0592107	+	0.998246i	$0.518858\pi$
$684$	1.06933e6	+	3.31497e6i	0.0873919	+	0.270919i
$685$	2.24664e6			0.182939
$686$	2.02953e7			1.64659
$687$	2.34413e6	−	3.21923e6i	0.189492	−	0.260232i
$688$		−	1.21333e7i		−	0.977255i
$689$	5.95444e6			0.477851
$690$	698677.	−	959504.i	0.0558668	−	0.0767228i
$691$		−	8.99999e6i		−	0.717046i	−0.933521	−	0.358523i	$-0.883280\pi$
$691$		−	8.99999e6i		−	0.717046i	0.933521	−	0.358523i	$-0.116720\pi$
$692$	−3.20146e7			−2.54146
$693$	−1.69308e6	−	5.24862e6i	−0.133919	−	0.415157i
$694$	3.76531e7			2.96758
$695$			4.05824e6i			0.318696i
$696$	2.01582e7	−	2.76836e7i	1.57736	−	2.16621i
$697$	2.39443e6			0.186690
$698$			1.98762e7i			1.54417i
$699$	−9.87085e6	−	7.18760e6i	−0.764120	−	0.556405i
$700$	1.54635e7			1.19279
$701$	1.53156e7			1.17717			0.588584	−	0.808436i	$-0.299686\pi$
$701$	1.53156e7			1.17717			0.588584	+	0.808436i	$0.299686\pi$
$702$	−2.54876e7	−	8.37119e6i	−1.95203	−	0.641128i
$703$		−	1.75160e6i		−	0.133674i
$704$	−7.72525e6			−0.587464
$705$	436051.	−	598836.i	0.0330419	−	0.0453769i
$706$	1.80458e7			1.36258
$707$	1.51456e6			0.113956
$708$	2.97453e7	+	1.06327e7i	2.23016	+	0.797185i
$709$	2.03520e7			1.52051			0.760257	−	0.649622i	$-0.225073\pi$
$709$	2.03520e7			1.52051			0.760257	+	0.649622i	$0.225073\pi$
$710$	−8.10876e6			−0.603682
$711$	−1.49714e6	−	4.64120e6i	−0.111068	−	0.344315i
$712$	9.72158e6			0.718682
$713$			3.92085e6i			0.288839i
$714$	3.28920e6	−	4.51711e6i	0.241460	−	0.331600i
$715$	−2.15546e6			−0.157680
$716$	1.39129e7			1.01423
$717$	−9.27507e6	+	1.27376e7i	−0.673782	+	0.925315i
$718$			2.43830e7i			1.76512i
$719$	−1.83467e7			−1.32353			−0.661767	−	0.749710i	$-0.730193\pi$
$719$	−1.83467e7			−1.32353			−0.661767	+	0.749710i	$0.730193\pi$
$720$	4.96272e6	−	1.60085e6i	0.356770	−	0.115085i
$721$			6.12410e6i			0.438737i
$722$	2.53356e7			1.80879
$723$	4.46786e6	+	3.25333e6i	0.317873	+	0.231464i
$724$	−3.42893e7			−2.43115
$725$		−	1.46787e7i		−	1.03715i
$726$	−6.13568e6	−	4.46778e6i	−0.432037	−	0.314594i
$727$	2.11091e7			1.48127			0.740636	−	0.671907i	$-0.234524\pi$
$727$	2.11091e7			1.48127			0.740636	+	0.671907i	$0.234524\pi$
$728$		−	2.08307e7i		−	1.45672i
$729$	−1.15546e7	−	8.50780e6i	−0.805259	−	0.592923i
$730$	−1.53652e6			−0.106716
$731$	−2.71798e6			−0.188128
$732$	−1.85157e7	+	2.54279e7i	−1.27721	+	1.75401i
$733$	−1.29047e7			−0.887132			−0.443566	−	0.896242i	$-0.646287\pi$
$733$	−1.29047e7			−0.887132			−0.443566	+	0.896242i	$0.646287\pi$
$734$		−	5.09626e7i		−	3.49150i
$735$	1.05511e6	−	1.44899e6i	0.0720406	−	0.0989345i
$736$	−7.27305e6			−0.494906
$737$			1.23185e7i			0.835388i
$738$	1.11850e7	−	3.60801e6i	0.755955	−	0.243853i
$739$			6.93935e6i			0.467420i	0.972306	+	0.233710i	$0.0750867\pi$
$739$			6.93935e6i			0.467420i	−0.972306	+	0.233710i	$0.924913\pi$
$740$	−6.56411e6			−0.440653
$741$	1.18388e6	−	1.62584e6i	0.0792068	−	0.108776i
$742$			6.08744e6i			0.405906i
$743$			4.29355e6i			0.285328i	0.989771	+	0.142664i	$0.0455668\pi$
$743$			4.29355e6i			0.285328i	−0.989771	+	0.142664i	$0.954433\pi$
$744$	−2.08567e7	+	2.86429e7i	−1.38138	+	1.89707i
$745$			1.82233e6i			0.120292i
$746$	−1.59914e7			−1.05206
$747$	5.18362e6	+	1.60695e7i	0.339885	+	1.05366i
$748$			1.31614e7i			0.860096i
$749$			7.54571e6i			0.491468i
$750$	5.49054e6	−	7.54024e6i	0.356420	−	0.489477i
$751$		−	1.38957e6i		−	0.0899045i	−0.998989	−	0.0449522i	$-0.985686\pi$
$751$		−	1.38957e6i		−	0.0899045i	0.998989	−	0.0449522i	$-0.0143136\pi$
$752$	−1.16589e7			−0.751820
$753$	9.50705e6	−	1.30562e7i	0.611024	−	0.839129i
$754$	−3.42239e7			−2.19231
$755$	2.40514e6			0.153558
$756$	6.01741e6	−	1.83211e7i	0.382918	−	1.16586i
$757$	3.31380e6			0.210178			0.105089	−	0.994463i	$-0.466487\pi$
$757$	3.31380e6			0.210178			0.105089	+	0.994463i	$0.466487\pi$
$758$	3.44035e7			2.17485
$759$	3.33880e6	+	2.43120e6i	0.210371	+	0.153185i
$760$			804120.i			0.0504995i
$761$			2.79825e6i			0.175156i	0.996158	+	0.0875779i	$0.0279127\pi$
$761$			2.79825e6i			0.175156i	−0.996158	+	0.0875779i	$0.972087\pi$
$762$	−3.84386e7	−	2.79896e7i	−2.39817	−	1.74626i
$763$			6.87721e6i			0.427662i
$764$	−4.63945e7			−2.87563
$765$	−358607.	−	1.11170e6i	−0.0221547	−	0.0686806i
$766$		−	4.78157e7i		−	2.94441i
$767$	−5.14699e6	−	1.74981e7i	−0.315911	−	1.07400i
$768$	1.69920e7	+	1.23730e7i	1.03954	+	0.756957i
$769$			1.98174e7i			1.20846i	0.796811	+	0.604229i	$0.206519\pi$
$769$			1.98174e7i			1.20846i	−0.796811	+	0.604229i	$0.793481\pi$
$770$		−	2.20361e6i		−	0.133939i
$771$	2.78477e6	−	3.82437e6i	0.168715	−	0.231699i
$772$	−4.13702e7			−2.49830
$773$	−1.17719e7			−0.708594			−0.354297	−	0.935133i	$-0.615280\pi$
$773$	−1.17719e7			−0.708594			−0.354297	+	0.935133i	$0.615280\pi$
$774$	−1.26964e7	+	4.09555e6i	−0.761779	+	0.245731i
$775$			1.51873e7i			0.908293i
$776$			6.89953e7i			4.11306i
$777$	−5.70832e6	+	7.83932e6i	−0.339200	+	0.465828i
$778$		−	1.92202e7i		−	1.13844i
$779$			881078.i			0.0520201i
$780$	−6.09283e6	−	4.43658e6i	−0.358577	−	0.261103i
$781$		−	2.82162e7i		−	1.65528i
$782$			4.18471e6i			0.244708i
$783$	−1.73912e7	−	5.71200e6i	−1.01374	−	0.332953i
$784$	−2.82109e7			−1.63918
$785$	−2.75670e6			−0.159667
$786$	−1.86438e7	−	1.35758e7i	−1.07641	−	0.783806i
$787$	−3.14376e7			−1.80931			−0.904654	−	0.426148i	$-0.859870\pi$
$787$	−3.14376e7			−1.80931			−0.904654	+	0.426148i	$0.859870\pi$
$788$			5.97638e7i			3.42865i
$789$	−4.87346e6	+	6.69280e6i	−0.278705	+	0.382750i
$790$		−	1.94859e6i		−	0.111084i
$791$	−5.65452e6			−0.321333
$792$	1.14583e7	+	3.55212e7i	0.649091	+	2.01221i
$793$	1.81622e7			1.02562
$794$			4.95793e7i			2.79093i
$795$	1.02873e6	+	749087.i	0.0577278	+	0.0420353i
$796$	−2.31564e7			−1.29535
$797$	1.05297e7			0.587181			0.293590	−	0.955931i	$-0.405150\pi$
$797$	1.05297e7			0.587181			0.293590	+	0.955931i	$0.405150\pi$
$798$	1.66216e6	+	1.21032e6i	0.0923985	+	0.0672813i
$799$			2.61172e6i			0.144730i
$800$	−2.81720e7			−1.55630
$801$	−1.59532e6	−	4.94556e6i	−0.0878548	−	0.272354i
$802$	2.49350e7			1.36890
$803$		−	5.34665e6i		−	0.292613i
$804$	−2.53551e7	+	3.48205e7i	−1.38333	+	1.89975i
$805$		−	492638.i		−	0.0267940i
$806$	3.54098e7			1.91993
$807$	−2.08355e7	−	1.51717e7i	−1.12621	−	0.820069i
$808$	−1.02501e7			−0.552332
$809$	−3.24657e7			−1.74403			−0.872015	−	0.489480i	$-0.837187\pi$
$809$	−3.24657e7			−1.74403			−0.872015	+	0.489480i	$0.837187\pi$
$810$	−3.35030e6	−	4.65268e6i	−0.179420	−	0.249167i
$811$			3.49979e7i			1.86849i	0.356635	+	0.934244i	$0.383924\pi$
$811$			3.49979e7i			1.86849i	−0.356635	+	0.934244i	$0.616076\pi$
$812$		−	2.46010e7i		−	1.30937i
$813$	−5.49612e6	−	4.00208e6i	−0.291628	−	0.212353i
$814$		−	3.24856e7i		−	1.71842i
$815$		−	4.36448e6i		−	0.230165i
$816$	−1.08220e7	+	1.48621e7i	−0.568962	+	0.781364i
$817$		−	1.00014e6i		−	0.0524208i
$818$		−	4.61444e7i		−	2.41122i
$819$	−1.05970e7	+	3.41832e6i	−0.552042	+	0.178075i
$820$	3.30183e6			0.171483
$821$	2.41658e7			1.25125			0.625623	−	0.780126i	$-0.284845\pi$
$821$	2.41658e7			1.25125			0.625623	+	0.780126i	$0.284845\pi$
$822$	−2.28853e7	+	3.14287e7i	−1.18134	+	1.62236i
$823$			1.97850e7i			1.01821i	0.860705	+	0.509104i	$0.170023\pi$
$823$			1.97850e7i			1.01821i	−0.860705	+	0.509104i	$0.829977\pi$
$824$		−	4.14462e7i		−	2.12650i
$825$	1.29328e7	+	9.41717e6i	0.661540	+	0.481710i
$826$	1.78890e7	−	5.26195e6i	0.912294	−	0.268347i
$827$		−	3.23922e7i		−	1.64693i	−0.567365	−	0.823467i	$-0.692037\pi$
$827$		−	3.23922e7i		−	1.64693i	0.567365	−	0.823467i	$-0.307963\pi$
$828$	4.43364e6	+	1.37445e7i	0.224742	+	0.696711i
$829$	2.35718e7			1.19126			0.595629	−	0.803260i	$-0.296903\pi$
$829$	2.35718e7			1.19126			0.595629	+	0.803260i	$0.296903\pi$
$830$			6.74669e6i			0.339935i
$831$	−6.89055e6	−	5.01746e6i	−0.346140	−	0.252047i
$832$			1.55973e7i			0.781162i
$833$			6.31953e6i			0.315553i
$834$	−5.67716e7	−	4.13391e7i	−2.82629	−	2.05800i
$835$	−4.52165e6			−0.224430
$836$	−4.84298e6			−0.239661
$837$	1.79938e7	+	5.90992e6i	0.887788	+	0.291587i
$838$	4.57661e7			2.25130
$839$	7.60591e6			0.373032			0.186516	−	0.982452i	$-0.440280\pi$
$839$	7.60591e6			0.373032			0.186516	+	0.982452i	$0.440280\pi$
$840$	2.62056e6	−	3.59886e6i	0.128143	−	0.175981i
$841$	−2.84117e6			−0.138518
$842$			1.58469e7i			0.770306i
$843$	−1.56544e7	+	2.14984e7i	−0.758694	+	1.04193i
$844$			3.08433e7i			1.49041i
$845$			879458.i			0.0423714i
$846$	3.93543e6	+	1.22000e7i	0.189045	+	0.586050i
$847$	−3.15024e6			−0.150881
$848$		−	2.00287e7i		−	0.956453i
$849$	1.03908e7	−	1.42699e7i	0.494744	−	0.679440i
$850$			1.62094e7i			0.769517i
$851$		−	7.26246e6i		−	0.343763i
$852$	5.80772e7	−	7.97584e7i	2.74099	−	3.76424i
$853$	−2.30014e6			−0.108239			−0.0541193	−	0.998534i	$-0.517235\pi$
$853$	−2.30014e6			−0.108239			−0.0541193	+	0.998534i	$0.517235\pi$
$854$			1.85679e7i			0.871199i
$855$	409072.	−	131957.i	0.0191375	−	0.00617328i
$856$		−	5.10672e7i		−	2.38209i
$857$	−1.15421e7			−0.536827			−0.268414	−	0.963304i	$-0.586499\pi$
$857$	−1.15421e7			−0.536827			−0.268414	+	0.963304i	$0.586499\pi$
$858$	2.19565e7	−	3.01532e7i	1.01823	−	1.39835i
$859$			1.38374e7i			0.639839i	0.947445	+	0.319919i	$0.103656\pi$
$859$			1.38374e7i			0.639839i	−0.947445	+	0.319919i	$0.896344\pi$
$860$	−3.74800e6			−0.172804
$861$	2.87136e6	−	3.94328e6i	0.132002	−	0.181280i
$862$	3.23825e6			0.148437
$863$	−3.33675e7			−1.52509			−0.762546	−	0.646934i	$-0.776051\pi$
$863$	−3.33675e7			−1.52509			−0.762546	+	0.646934i	$0.776051\pi$
$864$	−1.09627e7	+	3.33780e7i	−0.499614	+	1.52116i
$865$			3.95064e6i			0.179526i
$866$	6.86529e7			3.11074
$867$	−1.45632e7	−	1.06044e7i	−0.657975	−	0.479114i
$868$			2.54534e7i			1.14669i
$869$	6.78052e6			0.304589
$870$	−5.91277e6	−	4.30547e6i	−0.264846	−	0.192851i
$871$	2.48710e7			1.11083
$872$		−	4.65430e7i		−	2.07283i
$873$	3.50993e7	−	1.13222e7i	1.55870	−	0.502798i
$874$	−1.53985e6			−0.0681866
$875$		−	3.87138e6i		−	0.170941i
$876$	1.10050e7	−	1.51133e7i	0.484540	−	0.665426i
$877$	3.69788e7			1.62351			0.811753	−	0.584001i	$-0.198513\pi$
$877$	3.69788e7			1.62351			0.811753	+	0.584001i	$0.198513\pi$
$878$	3.80092e7			1.66400
$879$	−6.84380e6	+	9.39870e6i	−0.298762	+	0.410295i
$880$			7.25025e6i			0.315607i
$881$	1.13565e7			0.492952			0.246476	−	0.969149i	$-0.420727\pi$
$881$	1.13565e7			0.492952			0.246476	+	0.969149i	$0.420727\pi$
$882$	9.52249e6	+	2.95202e7i	0.412172	+	1.27775i
$883$	3.95740e7			1.70808			0.854040	−	0.520208i	$-0.174145\pi$
$883$	3.95740e7			1.70808			0.854040	+	0.520208i	$0.174145\pi$
$884$	2.65728e7			1.14369
$885$	1.31209e6	−	3.67061e6i	0.0563124	−	0.157536i
$886$	2.00024e7			0.856048
$887$	−5.58672e6			−0.238423			−0.119212	−	0.992869i	$-0.538037\pi$
$887$	−5.58672e6			−0.238423			−0.119212	+	0.992869i	$0.538037\pi$
$888$	3.86323e7	−	5.30543e7i	1.64406	−	2.25781i
$889$	−1.97355e7			−0.837518
$890$		−	2.07637e6i		−	0.0878678i
$891$	1.61900e7	−	1.16581e7i	0.683208	−	0.491964i
$892$	−1.77637e7			−0.747516
$893$	−961032.			−0.0403282
$894$	−2.54930e7	−	1.85631e7i	−1.06678	−	0.776794i
$895$		−	1.71687e6i		−	0.0716441i
$896$	3.99023e6			0.166046
$897$	4.90859e6	−	6.74104e6i	0.203693	−	0.279735i
$898$		−	7.13019e7i		−	2.95060i
$899$	2.41615e7			0.997068
$900$	1.71736e7	+	5.32389e7i	0.706731	+	2.19090i
$901$	−4.48664e6			−0.184123
$902$			1.63407e7i			0.668734i
$903$	−3.25936e6	+	4.47613e6i	−0.133019	+	0.182677i
$904$	3.82682e7			1.55746
$905$			4.23135e6i			0.171734i
$906$	−2.44998e7	+	3.36460e7i	−0.991613	+	1.36180i
$907$	−1.94320e7			−0.784329			−0.392164	−	0.919895i	$-0.628274\pi$
$907$	−1.94320e7			−0.784329			−0.392164	+	0.919895i	$0.628274\pi$
$908$	−8.44647e7			−3.39986
$909$	1.68205e6	+	5.21443e6i	0.0675194	+	0.209313i
$910$	−4.44909e6			−0.178102
$911$			2.24584e6i			0.0896566i	0.998995	+	0.0448283i	$0.0142741\pi$
$911$			2.24584e6i			0.0896566i	−0.998995	+	0.0448283i	$0.985726\pi$
$912$	−5.46878e6	−	3.98218e6i	−0.217723	−	0.158538i
$913$	−2.34766e7			−0.932090
$914$			9.60849e6i			0.380443i
$915$	3.13783e6	+	2.28486e6i	0.123902	+	0.0902208i
$916$			1.93608e7i			0.762402i
$917$	−9.57230e6			−0.375918
$918$	1.92047e7	+	6.30764e6i	0.752145	+	0.247036i
$919$			1.35695e7i			0.530000i	0.964248	+	0.265000i	$0.0853719\pi$
$919$			1.35695e7i			0.530000i	−0.964248	+	0.265000i	$0.914628\pi$
$920$			3.33403e6i			0.129867i
$921$	−1.78493e7	−	1.29972e7i	−0.693380	−	0.504895i
$922$			7.13018e7i			2.76231i
$923$	−5.69685e7			−2.20105
$924$	2.16749e7	+	1.57829e7i	0.835173	+	0.608144i
$925$		−	2.81309e7i		−	1.08101i
$926$		−	2.12851e7i		−	0.815734i
$927$	−2.10845e7	+	6.80134e6i	−0.805868	+	0.259953i
$928$			4.48189e7i			1.70841i
$929$	−1.11778e7			−0.424931			−0.212466	−	0.977169i	$-0.568149\pi$
$929$	−1.11778e7			−0.424931			−0.212466	+	0.977169i	$0.568149\pi$
$930$	6.11765e6	+	4.45466e6i	0.231941	+	0.168891i
$931$	−2.32539e6			−0.0879270
$932$	5.93643e7			2.23865
$933$	−2.33639e7	+	3.20860e7i	−0.878702	+	1.20674i
$934$	−7.50298e7			−2.81427
$935$	1.62413e6			0.0607564
$936$	7.17173e7	−	2.31342e7i	2.67568	−	0.863109i
$937$			5.84439e6i			0.217465i	0.994071	+	0.108733i	$0.0346792\pi$
$937$			5.84439e6i			0.217465i	−0.994071	+	0.108733i	$0.965321\pi$
$938$			2.54266e7i			0.943584i
$939$	−2.82043e7	+	3.87334e7i	−1.04388	+	1.43358i
$940$			3.60146e6i			0.132941i
$941$	−4.25055e7			−1.56485			−0.782423	−	0.622748i	$-0.786016\pi$
$941$	−4.25055e7			−1.56485			−0.782423	+	0.622748i	$0.786016\pi$
$942$	2.80809e7	−	3.85640e7i	1.03106	−	1.41597i
$943$			3.65311e6i			0.133778i
$944$	−5.88577e7	+	1.73127e7i	−2.14968	+	0.632318i
$945$	−2.26085e6	−	742557.i	−0.0823553	−	0.0270489i
$946$		−	1.85487e7i		−	0.673886i
$947$		−	5.97667e6i		−	0.216563i	−0.994120	−	0.108282i	$-0.965465\pi$
$947$		−	5.97667e6i		−	0.216563i	0.994120	−	0.108282i	$-0.0345348\pi$
$948$	1.91664e7	+	1.39563e7i	0.692661	+	0.504371i
$949$	−1.07949e7			−0.389093
$950$	−5.96455e6			−0.214422
$951$	1.60844e6	−	2.20890e6i	0.0576705	−	0.0791998i
$952$			1.56958e7i			0.561294i
$953$			1.70093e7i			0.606671i	0.952884	+	0.303335i	$0.0981002\pi$
$953$			1.70093e7i			0.606671i	−0.952884	+	0.303335i	$0.901900\pi$
$954$	−2.09583e7	+	6.76062e6i	−0.745563	+	0.240500i
$955$			5.72514e6i			0.203132i
$956$		−	7.66052e7i		−	2.71090i
$957$	1.49818e7	−	2.05748e7i	0.528791	−	0.726198i
$958$		−	2.66415e7i		−	0.937873i
$959$			1.61364e7i			0.566579i
$960$	−1.96219e6	+	2.69470e6i	−0.0687167	+	0.0943698i
$961$	3.63044e6			0.126809
$962$	−6.55884e7			−2.28502
$963$	−2.59789e7	+	8.38016e6i	−0.902724	+	0.291197i
$964$	−2.68701e7			−0.931274
$965$			5.10513e6i			0.176477i
$966$	6.89161e6	+	5.01823e6i	0.237617	+	0.173025i
$967$		−	1.65763e6i		−	0.0570062i	−0.999594	−	0.0285031i	$-0.990926\pi$
$967$		−	1.65763e6i		−	0.0570062i	0.999594	−	0.0285031i	$-0.00907404\pi$
$968$	2.13199e7			0.731302
$969$	−892048.	+	1.22506e6i	−0.0305196	+	0.0419130i
$970$	1.47363e7			0.502873
$971$		−	1.41344e7i		−	0.481093i	−0.970638	−	0.240546i	$-0.922673\pi$
$971$		−	1.41344e7i		−	0.481093i	0.970638	−	0.240546i	$-0.0773266\pi$
$972$	6.97600e7	+	370041.i	2.36832	+	0.0125627i
$973$	−2.91482e7			−0.987029
$974$	7.51811e7			2.53929
$975$	1.90133e7	−	2.61112e7i	0.640539	−	0.879662i
$976$		−	6.10914e7i		−	2.05284i
$977$	−2.18258e7			−0.731534			−0.365767	−	0.930706i	$-0.619193\pi$
$977$	−2.18258e7			−0.731534			−0.365767	+	0.930706i	$0.619193\pi$
$978$	6.10557e7	+	4.44586e7i	2.04117	+	1.48631i
$979$	7.22518e6			0.240931
$980$			8.71440e6i			0.289849i
$981$	−2.36773e7	+	7.63773e6i	−0.785525	+	0.253391i
$982$			3.73250e7i			1.23516i
$983$	5.12487e6			0.169161			0.0845803	−	0.996417i	$-0.473045\pi$
$983$	5.12487e6			0.169161			0.0845803	+	0.996417i	$0.473045\pi$
$984$	−1.94325e7	+	2.66870e7i	−0.639797	+	0.878643i
$985$	7.37493e6			0.242196
$986$	2.57875e7			0.844728
$987$	4.30112e6	+	3.13192e6i	0.140536	+	0.102334i
$988$			9.77799e6i			0.318682i
$989$		−	4.14675e6i		−	0.134808i
$990$	7.58674e6	−	2.44730e6i	0.246018	−	0.0793594i
$991$		−	1.16632e7i		−	0.377253i	−0.982049	−	0.188627i	$-0.939596\pi$
$991$		−	1.16632e7i		−	0.377253i	0.982049	−	0.188627i	$-0.0604036\pi$
$992$		−	4.63719e7i		−	1.49615i
$993$	1.61746e7	+	1.17778e7i	0.520548	+	0.379045i
$994$		−	5.82409e7i		−	1.86966i
$995$			2.85753e6i			0.0915025i
$996$	−6.63610e7	−	4.83217e7i	−2.11965	−	1.54346i
$997$	−4.37934e7			−1.39531			−0.697655	−	0.716434i	$-0.745773\pi$
$997$	−4.37934e7			−1.39531			−0.697655	+	0.716434i	$0.745773\pi$
$998$	−2.37460e7			−0.754682
$999$	−3.33293e7	−	1.09468e7i	−1.05661	−	0.347034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.d.b.176.5	✓	92
3.2	odd	2	inner	177.6.d.b.176.88	yes	92
59.58	odd	2	inner	177.6.d.b.176.87	yes	92
177.176	even	2	inner	177.6.d.b.176.6	yes	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.d.b.176.5	✓	92	1.1	even	1	trivial
177.6.d.b.176.6	yes	92	177.176	even	2	inner
177.6.d.b.176.87	yes	92	59.58	odd	2	inner
177.6.d.b.176.88	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)

\(f(q)\)	\(=\)	\(q-10.3821 q^{2} +(-12.6016 - 9.17604i) q^{3} +75.7873 q^{4} -9.35226i q^{5} +(130.831 + 95.2663i) q^{6} +67.1723 q^{7} -454.603 q^{8} +(74.6006 + 231.266i) q^{9} +O(q^{10})\)	\(q-10.3821 q^{2} +(-12.6016 - 9.17604i) q^{3} +75.7873 q^{4} -9.35226i q^{5} +(130.831 + 95.2663i) q^{6} +67.1723 q^{7} -454.603 q^{8} +(74.6006 + 231.266i) q^{9} +97.0958i q^{10} -337.866 q^{11} +(-955.042 - 695.428i) q^{12} +682.151i q^{13} -697.388 q^{14} +(-85.8167 + 117.853i) q^{15} +2294.52 q^{16} -513.997i q^{17} +(-774.509 - 2401.01i) q^{18} +189.135 q^{19} -708.783i q^{20} +(-846.479 - 616.376i) q^{21} +3507.74 q^{22} +784.190 q^{23} +(5728.72 + 4171.45i) q^{24} +3037.54 q^{25} -7082.14i q^{26} +(1182.01 - 3598.85i) q^{27} +5090.81 q^{28} -4832.42i q^{29} +(890.955 - 1223.56i) q^{30} +4999.87i q^{31} -9274.61 q^{32} +(4257.65 + 3100.27i) q^{33} +5336.35i q^{34} -628.213i q^{35} +(5653.78 + 17527.0i) q^{36} -9261.10i q^{37} -1963.61 q^{38} +(6259.44 - 8596.19i) q^{39} +4251.56i q^{40} +4658.46i q^{41} +(8788.20 + 6399.26i) q^{42} -5287.94i q^{43} -25605.9 q^{44} +(2162.85 - 697.684i) q^{45} -8141.51 q^{46} -5081.19 q^{47} +(-28914.7 - 21054.6i) q^{48} -12294.9 q^{49} -31535.9 q^{50} +(-4716.46 + 6477.18i) q^{51} +51698.4i q^{52} -8728.92i q^{53} +(-12271.8 + 37363.5i) q^{54} +3159.81i q^{55} -30536.7 q^{56} +(-2383.41 - 1735.51i) q^{57} +50170.6i q^{58} +(-25651.4 + 7545.23i) q^{59} +(-6503.82 + 8931.79i) q^{60} -26624.9i q^{61} -51909.0i q^{62} +(5011.10 + 15534.6i) q^{63} +22864.9 q^{64} +6379.65 q^{65} +(-44203.2 - 32187.2i) q^{66} -36459.7i q^{67} -38954.4i q^{68} +(-9882.04 - 7195.75i) q^{69} +6522.15i q^{70} +83513.0i q^{71} +(-33913.7 - 105134. i) q^{72} +15824.8i q^{73} +96149.4i q^{74} +(-38277.8 - 27872.5i) q^{75} +14334.1 q^{76} -22695.2 q^{77} +(-64986.0 + 89246.3i) q^{78} -20068.7 q^{79} -21459.0i q^{80} +(-47918.5 + 34505.1i) q^{81} -48364.4i q^{82} +69484.9 q^{83} +(-64152.4 - 46713.5i) q^{84} -4807.03 q^{85} +54899.7i q^{86} +(-44342.5 + 60896.3i) q^{87} +153595. q^{88} -21384.8 q^{89} +(-22454.9 + 7243.40i) q^{90} +45821.7i q^{91} +59431.6 q^{92} +(45879.0 - 63006.4i) q^{93} +52753.3 q^{94} -1768.84i q^{95} +(116875. + 85104.2i) q^{96} -151770. i q^{97} +127646. q^{98} +(-25205.0 - 78136.7i) 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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