LMFDB - Embedded newform 177.4.d.c.176.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,4,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, 4, names="a")

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

chi := DirichletCharacter("177.176");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
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:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			176.4
Character	$\chi$	$=$	177.176
Dual form			177.4.d.c.176.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.02351 q^{2} +(4.35259 + 2.83813i) q^{3} +17.2357 q^{4} -15.7890i q^{5} +(-21.8653 - 14.2574i) q^{6} -18.9623 q^{7} -46.3956 q^{8} +(10.8900 + 24.7064i) q^{9} +O(q^{10})$	\(q-5.02351 q^{2} +(4.35259 + 2.83813i) q^{3} +17.2357 q^{4} -15.7890i q^{5} +(-21.8653 - 14.2574i) q^{6} -18.9623 q^{7} -46.3956 q^{8} +(10.8900 + 24.7064i) q^{9} +79.3161i q^{10} -36.5750 q^{11} +(75.0198 + 48.9172i) q^{12} +4.20455i q^{13} +95.2574 q^{14} +(44.8112 - 68.7228i) q^{15} +95.1835 q^{16} +97.3906i q^{17} +(-54.7061 - 124.113i) q^{18} -44.1528 q^{19} -272.134i q^{20} +(-82.5351 - 53.8175i) q^{21} +183.735 q^{22} +190.656 q^{23} +(-201.941 - 131.677i) q^{24} -124.291 q^{25} -21.1216i q^{26} +(-22.7204 + 138.444i) q^{27} -326.828 q^{28} +131.011i q^{29} +(-225.110 + 345.230i) q^{30} +206.913i q^{31} -106.991 q^{32} +(-159.196 - 103.805i) q^{33} -489.243i q^{34} +299.395i q^{35} +(187.697 + 425.832i) q^{36} +106.024i q^{37} +221.802 q^{38} +(-11.9331 + 18.3006i) q^{39} +732.539i q^{40} +214.440i q^{41} +(414.616 + 270.353i) q^{42} +213.227i q^{43} -630.396 q^{44} +(390.089 - 171.942i) q^{45} -957.762 q^{46} -444.240 q^{47} +(414.294 + 270.143i) q^{48} +16.5690 q^{49} +624.380 q^{50} +(-276.407 + 423.901i) q^{51} +72.4682i q^{52} -624.911i q^{53} +(114.136 - 695.476i) q^{54} +577.482i q^{55} +879.768 q^{56} +(-192.179 - 125.312i) q^{57} -658.135i q^{58} +(-389.685 - 231.353i) q^{59} +(772.352 - 1184.49i) q^{60} +437.873i q^{61} -1039.43i q^{62} +(-206.500 - 468.491i) q^{63} -223.999 q^{64} +66.3854 q^{65} +(799.723 + 521.465i) q^{66} -648.388i q^{67} +1678.59i q^{68} +(829.846 + 541.106i) q^{69} -1504.02i q^{70} +809.977i q^{71} +(-505.248 - 1146.27i) q^{72} -39.3227i q^{73} -532.613i q^{74} +(-540.989 - 352.756i) q^{75} -761.005 q^{76} +693.547 q^{77} +(59.9459 - 91.9335i) q^{78} +595.268 q^{79} -1502.85i q^{80} +(-491.816 + 538.106i) q^{81} -1077.24i q^{82} -642.266 q^{83} +(-1422.55 - 927.582i) q^{84} +1537.70 q^{85} -1071.15i q^{86} +(-371.826 + 570.236i) q^{87} +1696.92 q^{88} -258.723 q^{89} +(-1959.62 + 863.753i) q^{90} -79.7279i q^{91} +3286.08 q^{92} +(-587.246 + 900.605i) q^{93} +2231.65 q^{94} +697.128i q^{95} +(-465.685 - 303.653i) q^{96} +1812.27i q^{97} -83.2344 q^{98} +(-398.302 - 903.639i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9}+O(q^{10}) $ 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9	$ 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9} + 28 q^{12} + 114 q^{15} + 484 q^{16} - 184 q^{19} - 758 q^{21} - 60 q^{22} + 36 q^{25} + 742 q^{27} - 4 q^{28} - 888 q^{36} + 1402 q^{45} - 660 q^{46} - 488 q^{48} - 924 q^{49} - 1772 q^{51} - 630 q^{57} - 1880 q^{60} - 212 q^{63} + 7648 q^{64} + 1316 q^{66} - 1556 q^{75} - 5680 q^{76} + 3224 q^{78} - 1504 q^{79} - 276 q^{81} + 1228 q^{84} - 848 q^{85} + 3598 q^{87} + 5760 q^{88} + 888 q^{94}+O(q^{100}) $ 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9 + 28 * q^12 + 114 * q^15 + 484 * q^16 - 184 * q^19 - 758 * q^21 - 60 * q^22 + 36 * q^25 + 742 * q^27 - 4 * q^28 - 888 * q^36 + 1402 * q^45 - 660 * q^46 - 488 * q^48 - 924 * q^49 - 1772 * q^51 - 630 * q^57 - 1880 * q^60 - 212 * q^63 + 7648 * q^64 + 1316 * q^66 - 1556 * q^75 - 5680 * q^76 + 3224 * q^78 - 1504 * q^79 - 276 * q^81 + 1228 * q^84 - 848 * q^85 + 3598 * q^87 + 5760 * q^88 + 888 * 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 $

$2$	−5.02351			−1.77608			−0.888040	−	0.459766i	$-0.847933\pi$
$2$	−5.02351			−1.77608			−0.888040	+	0.459766i	$0.847933\pi$
$3$	4.35259	+	2.83813i	0.837656	+	0.546199i
$3$	4.35259	+	2.83813i	0.837656	+	0.546199i
$4$	17.2357			2.15446
$5$		−	15.7890i		−	1.41221i	−0.708108	−	0.706104i	$-0.750451\pi$
$5$		−	15.7890i		−	1.41221i	0.708108	−	0.706104i	$-0.249549\pi$
$6$	−21.8653	−	14.2574i	−1.48774	−	0.970093i
$7$	−18.9623			−1.02387			−0.511934	−	0.859025i	$-0.671071\pi$
$7$	−18.9623			−1.02387			−0.511934	+	0.859025i	$0.671071\pi$
$8$	−46.3956			−2.05042
$9$	10.8900	+	24.7064i	0.403334	+	0.915053i
$10$			79.3161i			2.50819i
$11$	−36.5750			−1.00253			−0.501263	−	0.865295i	$-0.667131\pi$
$11$	−36.5750			−1.00253			−0.501263	+	0.865295i	$0.667131\pi$
$12$	75.0198	+	48.9172i	1.80470	+	1.17676i
$13$			4.20455i			0.0897024i	0.998994	+	0.0448512i	$0.0142814\pi$
$13$			4.20455i			0.0897024i	−0.998994	+	0.0448512i	$0.985719\pi$
$14$	95.2574			1.81847
$15$	44.8112	−	68.7228i	0.771346	−	1.18294i
$16$	95.1835			1.48724
$17$			97.3906i			1.38945i	0.719274	+	0.694726i	$0.244474\pi$
$17$			97.3906i			1.38945i	−0.719274	+	0.694726i	$0.755526\pi$
$18$	−54.7061	−	124.113i	−0.716353	−	1.62521i
$19$	−44.1528			−0.533124			−0.266562	−	0.963818i	$-0.585888\pi$
$19$	−44.1528			−0.533124			−0.266562	+	0.963818i	$0.585888\pi$
$20$		−	272.134i		−	3.04255i
$21$	−82.5351	−	53.8175i	−0.857649	−	0.559236i
$22$	183.735			1.78057
$23$	190.656			1.72846			0.864228	−	0.503101i	$-0.167807\pi$
$23$	190.656			1.72846			0.864228	+	0.503101i	$0.167807\pi$
$24$	−201.941	−	131.677i	−1.71754	−	1.11993i
$25$	−124.291			−0.994331
$26$		−	21.1216i		−	0.159319i
$27$	−22.7204	+	138.444i	−0.161946	+	0.986800i
$28$	−326.828			−2.20588
$29$			131.011i			0.838900i	0.907778	+	0.419450i	$0.137777\pi$
$29$			131.011i			0.838900i	−0.907778	+	0.419450i	$0.862223\pi$
$30$	−225.110	+	345.230i	−1.36997	+	2.10100i
$31$			206.913i			1.19879i	0.800452	+	0.599397i	$0.204593\pi$
$31$			206.913i			1.19879i	−0.800452	+	0.599397i	$0.795407\pi$
$32$	−106.991			−0.591045
$33$	−159.196	−	103.805i	−0.839772	−	0.547579i
$34$		−	489.243i		−	2.46778i
$35$			299.395i			1.44591i
$36$	187.697	+	425.832i	0.868966	+	1.97145i
$37$			106.024i			0.471088i	0.971864	+	0.235544i	$0.0756871\pi$
$37$			106.024i			0.471088i	−0.971864	+	0.235544i	$0.924313\pi$
$38$	221.802			0.946871
$39$	−11.9331	+	18.3006i	−0.0489954	+	0.0751397i
$40$			732.539i			2.89561i
$41$			214.440i			0.816827i	0.912797	+	0.408413i	$0.133918\pi$
$41$			214.440i			0.816827i	−0.912797	+	0.408413i	$0.866082\pi$
$42$	414.616	+	270.353i	1.52325	+	0.993247i
$43$			213.227i			0.756206i	0.925763	+	0.378103i	$0.123424\pi$
$43$			213.227i			0.756206i	−0.925763	+	0.378103i	$0.876576\pi$
$44$	−630.396			−2.15990
$45$	390.089	−	171.942i	1.29225	−	0.569591i
$46$	−957.762			−3.06988
$47$	−444.240			−1.37870			−0.689352	−	0.724426i	$-0.742105\pi$
$47$	−444.240			−1.37870			−0.689352	+	0.724426i	$0.742105\pi$
$48$	414.294	+	270.143i	1.24580	+	0.812330i
$49$	16.5690			0.0483060
$50$	624.380			1.76601
$51$	−276.407	+	423.901i	−0.758917	+	1.16388i
$52$			72.4682i			0.193260i
$53$		−	624.911i		−	1.61959i	−0.586714	−	0.809794i	$-0.699579\pi$
$53$		−	624.911i		−	1.61959i	0.586714	−	0.809794i	$-0.300421\pi$
$54$	114.136	−	695.476i	0.287630	−	1.75264i
$55$			577.482i			1.41578i
$56$	879.768			2.09936
$57$	−192.179	−	125.312i	−0.446574	−	0.291192i
$58$		−	658.135i		−	1.48995i
$59$	−389.685	−	231.353i	−0.859876	−	0.510502i
$59$	−389.685	−	231.353i	−0.859876	−	0.510502i
$60$	772.352	−	1184.49i	1.66184	−	2.54861i
$61$			437.873i			0.919080i	0.888157	+	0.459540i	$0.151986\pi$
$61$			437.873i			0.919080i	−0.888157	+	0.459540i	$0.848014\pi$
$62$		−	1039.43i		−	2.12915i
$63$	−206.500	−	468.491i	−0.412960	−	0.936894i
$64$	−223.999			−0.437499
$65$	66.3854			0.126678
$66$	799.723	+	521.465i	1.49150	+	0.972544i
$67$		−	648.388i		−	1.18229i	−0.806567	−	0.591143i	$-0.798677\pi$
$67$		−	648.388i		−	1.18229i	0.806567	−	0.591143i	$-0.201323\pi$
$68$			1678.59i			2.99352i
$69$	829.846	+	541.106i	1.44785	+	0.944081i
$70$		−	1504.02i		−	2.56806i
$71$			809.977i			1.35390i	0.736031	+	0.676948i	$0.236698\pi$
$71$			809.977i			1.35390i	−0.736031	+	0.676948i	$0.763302\pi$
$72$	−505.248	−	1146.27i	−0.827001	−	1.87624i
$73$		−	39.3227i		−	0.0630463i	−0.999503	−	0.0315231i	$-0.989964\pi$
$73$		−	39.3227i		−	0.0630463i	0.999503	−	0.0315231i	$-0.0100358\pi$
$74$		−	532.613i		−	0.836689i
$75$	−540.989	−	352.756i	−0.832907	−	0.543103i
$76$	−761.005			−1.14859
$77$	693.547			1.02645
$78$	59.9459	−	91.9335i	0.0870197	−	0.133454i
$79$	595.268			0.847758			0.423879	−	0.905719i	$-0.360668\pi$
$79$	595.268			0.847758			0.423879	+	0.905719i	$0.360668\pi$
$80$		−	1502.85i		−	2.10029i
$81$	−491.816	+	538.106i	−0.674644	+	0.738143i
$82$		−	1077.24i		−	1.45075i
$83$	−642.266			−0.849372			−0.424686	−	0.905341i	$-0.639615\pi$
$83$	−642.266			−0.849372			−0.424686	+	0.905341i	$0.639615\pi$
$84$	−1422.55	−	927.582i	−1.84777	−	1.20485i
$85$	1537.70			1.96220
$86$		−	1071.15i		−	1.34308i
$87$	−371.826	+	570.236i	−0.458206	+	0.702709i
$88$	1696.92			2.05560
$89$	−258.723			−0.308141			−0.154070	−	0.988060i	$-0.549238\pi$
$89$	−258.723			−0.308141			−0.154070	+	0.988060i	$0.549238\pi$
$90$	−1959.62	+	863.753i	−2.29513	+	1.01164i
$91$		−	79.7279i		−	0.0918434i
$92$	3286.08			3.72389
$93$	−587.246	+	900.605i	−0.654780	+	1.00418i
$94$	2231.65			2.44869
$95$			697.128i			0.752882i
$96$	−465.685	−	303.653i	−0.495092	−	0.322828i
$97$			1812.27i			1.89699i	0.316796	+	0.948494i	$0.397393\pi$
$97$			1812.27i			1.89699i	−0.316796	+	0.948494i	$0.602607\pi$
$98$	−83.2344			−0.0857953
$99$	−398.302	−	903.639i	−0.404352	−	0.917365i
$100$	−2142.25			−2.14225
$101$	−614.895			−0.605785			−0.302893	−	0.953025i	$-0.597952\pi$
$101$	−614.895			−0.605785			−0.302893	+	0.953025i	$0.597952\pi$
$102$	1388.54	−	2129.47i	1.34790	−	2.06715i
$103$		−	1232.80i		−	1.17933i	−0.807648	−	0.589665i	$-0.799260\pi$
$103$		−	1232.80i		−	1.17933i	0.807648	−	0.589665i	$-0.200740\pi$
$104$		−	195.072i		−	0.183927i
$105$	−849.723	+	1303.14i	−0.789757	+	1.21118i
$106$			3139.25i			2.87652i
$107$			340.788i			0.307899i	0.988079	+	0.153950i	$0.0491994\pi$
$107$			340.788i			0.307899i	−0.988079	+	0.153950i	$0.950801\pi$
$108$	−391.602	+	2386.18i	−0.348907	+	2.12602i
$109$		−	1023.05i		−	0.898991i	−0.893283	−	0.449496i	$-0.851604\pi$
$109$		−	1023.05i		−	0.898991i	0.893283	−	0.449496i	$-0.148396\pi$
$110$		−	2900.99i		−	2.51453i
$111$	−300.910	+	461.479i	−0.257308	+	0.394609i
$112$	−1804.90			−1.52274
$113$	2261.94			1.88306			0.941529	−	0.336932i	$-0.109389\pi$
$113$	2261.94			1.88306			0.941529	+	0.336932i	$0.109389\pi$
$114$	965.414	+	629.505i	0.793152	+	0.517180i
$115$		−	3010.26i		−	2.44094i
$116$			2258.06i			1.80738i
$117$	−103.879	+	45.7875i	−0.0820825	+	0.0361800i
$118$	1957.59	+	1162.21i	1.52721	+	0.906693i
$119$		−	1846.75i		−	1.42262i
$120$	−2079.04	+	3188.44i	−1.58158	+	2.42553i
$121$	6.73330			0.00505883
$122$		−	2199.66i		−	1.63236i
$123$	−608.609	+	933.368i	−0.446150	+	0.684219i
$124$			3566.28i			2.58276i
$125$		−	11.1875i		−	0.00800513i
$126$	1037.35	+	2353.47i	0.733451	+	1.66400i
$127$	−781.993			−0.546383			−0.273192	−	0.961960i	$-0.588079\pi$
$127$	−781.993			−0.546383			−0.273192	+	0.961960i	$0.588079\pi$
$128$	1981.19			1.36808
$129$	−605.168	+	928.090i	−0.413039	+	0.633440i
$130$	−333.488			−0.224991
$131$	−1870.92			−1.24781			−0.623904	−	0.781501i	$-0.714454\pi$
$131$	−1870.92			−1.24781			−0.623904	+	0.781501i	$0.714454\pi$
$132$	−2743.85	−	1789.15i	−1.80926	−	1.17974i
$133$	837.239			0.545849
$134$			3257.19i			2.09984i
$135$	2185.89	+	358.732i	1.39357	+	0.228702i
$136$		−	4518.50i		−	2.84895i
$137$		−	2056.20i		−	1.28228i	−0.767422	−	0.641142i	$-0.778461\pi$
$137$		−	2056.20i		−	1.28228i	0.767422	−	0.641142i	$-0.221539\pi$
$138$	−4168.74	−	2718.26i	−2.57150	−	1.67676i
$139$	−2117.28			−1.29198			−0.645991	−	0.763345i	$-0.723556\pi$
$139$	−2117.28			−1.29198			−0.645991	+	0.763345i	$0.723556\pi$
$140$			5160.28i			3.11517i
$141$	−1933.59	−	1260.81i	−1.15488	−	0.753047i
$142$		−	4068.93i		−	2.40463i
$143$		−	153.781i		−	0.0899290i
$144$	1036.55	+	2351.64i	0.599854	+	1.36090i
$145$	2068.53			1.18470
$146$			197.538i			0.111975i
$147$	72.1178	+	47.0249i	0.0404638	+	0.0263847i
$148$			1827.40i			1.01494i
$149$	174.373			0.0958737			0.0479368	−	0.998850i	$-0.484735\pi$
$149$	174.373			0.0958737			0.0479368	+	0.998850i	$0.484735\pi$
$150$	2717.67	+	1772.07i	1.47931	+	0.964594i
$151$			2461.47i			1.32656i	0.748369	+	0.663282i	$0.230837\pi$
$151$			2461.47i			1.32656i	−0.748369	+	0.663282i	$0.769163\pi$
$152$	2048.50			1.09313
$153$	−2406.17	+	1060.58i	−1.27142	+	0.560413i
$154$	−3484.04			−1.82307
$155$	3266.94			1.69295
$156$	−205.674	+	315.424i	−0.105559	+	0.161886i
$157$			171.463i			0.0871606i	0.999050	+	0.0435803i	$0.0138764\pi$
$157$			171.463i			0.0871606i	−0.999050	+	0.0435803i	$0.986124\pi$
$158$	−2990.34			−1.50569
$159$	1773.58	−	2719.98i	0.884617	−	1.35666i
$160$			1689.27i			0.834678i
$161$	−3615.27			−1.76971
$162$	2470.64	−	2703.18i	1.19822	−	1.31100i
$163$	1926.75			0.925858			0.462929	−	0.886395i	$-0.346798\pi$
$163$	1926.75			0.925858			0.462929	+	0.886395i	$0.346798\pi$
$164$			3696.02i			1.75982i
$165$	−1638.97	+	2513.54i	−0.773295	+	1.18593i
$166$	3226.43			1.50855
$167$			1091.39i			0.505712i	0.967504	+	0.252856i	$0.0813700\pi$
$167$			1091.39i			0.505712i	−0.967504	+	0.252856i	$0.918630\pi$
$168$	3829.26	+	2496.90i	1.75854	+	1.14667i
$169$	2179.32			0.991953
$170$	−7724.64			−3.48502
$171$	−480.825	−	1090.86i	−0.215027	−	0.487837i
$172$			3675.12i			1.62922i
$173$	128.766			0.0565890			0.0282945	−	0.999600i	$-0.490992\pi$
$173$	128.766			0.0565890			0.0282945	+	0.999600i	$0.490992\pi$
$174$	1867.87	−	2864.59i	0.813811	−	1.24807i
$175$	2356.85			1.01806
$176$	−3481.34			−1.49100
$177$	−1039.53	−	2112.96i	−0.441444	−	0.897289i
$178$	1299.70			0.547283
$179$	−3323.70			−1.38785			−0.693924	−	0.720048i	$-0.744120\pi$
$179$	−3323.70			−1.38785			−0.693924	+	0.720048i	$0.744120\pi$
$180$	6723.45	−	2963.54i	2.78409	−	1.22716i
$181$	2547.84			1.04629			0.523147	−	0.852242i	$-0.324758\pi$
$181$	2547.84			1.04629			0.523147	+	0.852242i	$0.324758\pi$
$182$			400.514i			0.163121i
$183$	−1242.74	+	1905.88i	−0.502001	+	0.769873i
$184$	−8845.59			−3.54405
$185$	1674.01			0.665274
$186$	2950.04	−	4524.20i	1.16294	−	1.78350i
$187$		−	3562.06i		−	1.39296i
$188$	−7656.79			−2.97037
$189$	430.832	−	2625.22i	0.165812	−	1.01035i
$190$		−	3502.03i		−	1.33718i
$191$	677.105			0.256511			0.128255	−	0.991741i	$-0.459062\pi$
$191$	677.105			0.256511			0.128255	+	0.991741i	$0.459062\pi$
$192$	−974.976	−	635.740i	−0.366473	−	0.238961i
$193$	−133.205			−0.0496803			−0.0248402	−	0.999691i	$-0.507908\pi$
$193$	−133.205			−0.0496803			−0.0248402	+	0.999691i	$0.507908\pi$
$194$		−	9103.94i		−	3.36920i
$195$	288.948	+	188.411i	0.106113	+	0.0691916i
$196$	285.577			0.104073
$197$			1551.34i			0.561059i	0.959845	+	0.280530i	$0.0905101\pi$
$197$			1551.34i			0.561059i	−0.959845	+	0.280530i	$0.909490\pi$
$198$	2000.88	+	4539.44i	0.718162	+	1.62931i
$199$	−1262.52			−0.449738			−0.224869	−	0.974389i	$-0.572195\pi$
$199$	−1262.52			−0.449738			−0.224869	+	0.974389i	$0.572195\pi$
$200$	5766.58			2.03879
$201$	1840.21	−	2822.16i	0.645763	−	0.990349i
$202$	3088.93			1.07592
$203$		−	2484.27i		−	0.858923i
$204$	−4764.07	+	7306.22i	−1.63506	+	2.50754i
$205$	3385.78			1.15353
$206$			6192.97i			2.09459i
$207$	2076.24	+	4710.42i	0.697144	+	1.58163i
$208$			400.203i			0.133409i
$209$	1614.89			0.534471
$210$	4268.60	−	6546.36i	1.40267	−	2.15115i
$211$		−	5221.63i		−	1.70366i	−0.523819	−	0.851830i	$-0.675493\pi$
$211$		−	5221.63i		−	1.70366i	0.523819	−	0.851830i	$-0.324507\pi$
$212$		−	10770.8i		−	3.48934i
$213$	−2298.82	+	3525.50i	−0.739496	+	1.13410i
$214$		−	1711.95i		−	0.546854i
$215$	3366.64			1.06792
$216$	1054.13	−	6423.20i	0.332057	−	2.02335i
$217$		−	3923.54i		−	1.22741i
$218$			5139.29i			1.59668i
$219$	111.603	−	171.156i	0.0344358	−	0.0528111i
$220$			9953.30i			3.05023i
$221$	−409.483			−0.124637
$222$	1511.63	−	2318.24i	0.456999	−	0.700858i
$223$	−2152.45			−0.646362			−0.323181	−	0.946337i	$-0.604752\pi$
$223$	−2152.45			−0.646362			−0.323181	+	0.946337i	$0.604752\pi$
$224$	2028.79			0.605152
$225$	−1353.53	−	3070.80i	−0.401047	−	0.909866i
$226$	−11362.9			−3.34446
$227$	−3014.43			−0.881386			−0.440693	−	0.897658i	$-0.645267\pi$
$227$	−3014.43			−0.881386			−0.440693	+	0.897658i	$0.645267\pi$
$228$	−3312.34	−	2159.83i	−0.962127	−	0.627361i
$229$			4895.24i			1.41261i	0.707910	+	0.706303i	$0.249638\pi$
$229$			4895.24i			1.41261i	−0.707910	+	0.706303i	$0.750362\pi$
$230$			15122.1i			4.33530i
$231$	3018.72	+	1968.38i	0.859815	+	0.560648i
$232$		−	6078.33i		−	1.72009i
$233$	6412.16			1.80289			0.901447	−	0.432889i	$-0.142506\pi$
$233$	6412.16			1.80289			0.901447	+	0.432889i	$0.142506\pi$
$234$	521.839	−	230.014i	0.145785	−	0.0642586i
$235$			7014.09i			1.94702i
$236$	−6716.49	−	3987.53i	−1.85257	−	1.09986i
$237$	2590.95	+	1689.45i	0.710129	+	0.463044i
$238$			9277.17i			2.52668i
$239$			2716.85i			0.735308i	0.929963	+	0.367654i	$0.119839\pi$
$239$			2716.85i			0.735308i	−0.929963	+	0.367654i	$0.880161\pi$
$240$	4265.28	−	6541.28i	1.14718	−	1.75932i
$241$	3203.55			0.856260			0.428130	−	0.903717i	$-0.359173\pi$
$241$	3203.55			0.856260			0.428130	+	0.903717i	$0.359173\pi$
$242$	−33.8248			−0.00898488
$243$	−3667.89	+	946.317i	−0.968292	+	0.249820i
$244$			7547.04i			1.98012i
$245$		−	261.607i		−	0.0682181i
$246$	3057.36	−	4688.79i	0.792398	−	1.21523i
$247$		−	185.643i		−	0.0478225i
$248$		−	9599.84i		−	2.45803i
$249$	−2795.52	−	1822.84i	−0.711481	−	0.463926i
$250$			56.2006i			0.0142178i
$251$			6998.29i			1.75987i	0.475091	+	0.879937i	$0.342415\pi$
$251$			6998.29i			1.75987i	−0.475091	+	0.879937i	$0.657585\pi$
$252$	−3559.16	−	8074.76i	−0.889707	−	2.01850i
$253$	−6973.24			−1.73282
$254$	3928.35			0.970421
$255$	6692.96	+	4364.19i	1.64364	+	1.07175i
$256$	−8160.53			−1.99232
$257$		−	4396.16i		−	1.06702i	−0.845793	−	0.533512i	$-0.820872\pi$
$257$		−	4396.16i		−	1.06702i	0.845793	−	0.533512i	$-0.179128\pi$
$258$	3040.07	−	4662.27i	0.733590	−	1.12504i
$259$		−	2010.46i		−	0.482332i
$260$	1144.20			0.272924
$261$	−3236.81	+	1426.71i	−0.767638	+	0.338357i
$262$	9398.58			2.21621
$263$		−	4541.15i		−	1.06471i	−0.846521	−	0.532356i	$-0.821307\pi$
$263$		−	4541.15i		−	1.06471i	0.846521	−	0.532356i	$-0.178693\pi$
$264$	7385.99	+	4816.09i	1.72188	+	1.12276i
$265$	−9866.71			−2.28720
$266$	−4205.88			−0.969471
$267$	−1126.11	−	734.289i	−0.258116	−	0.168306i
$268$		−	11175.4i		−	2.54719i
$269$	−1074.56			−0.243559			−0.121779	−	0.992557i	$-0.538860\pi$
$269$	−1074.56			−0.243559			−0.121779	+	0.992557i	$0.538860\pi$
$270$	−10980.8	−	1802.10i	−2.47509	−	0.406193i
$271$	−461.443			−0.103434			−0.0517171	−	0.998662i	$-0.516469\pi$
$271$	−461.443			−0.103434			−0.0517171	+	0.998662i	$0.516469\pi$
$272$			9269.97i			2.06645i
$273$	226.278	−	347.022i	0.0501648	−	0.0769332i
$274$			10329.3i			2.27744i
$275$	4545.96			0.996843
$276$	14303.0	+	9326.34i	3.11934	+	2.03398i
$277$	517.812			0.112319			0.0561594	−	0.998422i	$-0.482114\pi$
$277$	517.812			0.112319			0.0561594	+	0.998422i	$0.482114\pi$
$278$	10636.2			2.29466
$279$	−5112.07	+	2253.28i	−1.09696	+	0.483514i
$280$		−	13890.6i		−	2.96473i
$281$		−	4176.06i		−	0.886558i	−0.896384	−	0.443279i	$-0.853815\pi$
$281$		−	4176.06i		−	0.886558i	0.896384	−	0.443279i	$-0.146185\pi$
$282$	9713.44	+	6333.71i	2.05116	+	1.33747i
$283$		−	1172.22i		−	0.246224i	−0.992393	−	0.123112i	$-0.960712\pi$
$283$		−	1172.22i		−	0.246224i	0.992393	−	0.123112i	$-0.0392875\pi$
$284$			13960.5i			2.91692i
$285$	−1978.54	+	3034.31i	−0.411223	+	0.630656i
$286$			772.523i			0.159721i
$287$		−	4066.27i		−	0.836323i
$288$	−1165.13	−	2643.35i	−0.238388	−	0.540837i
$289$	−4571.93			−0.930578
$290$	−10391.3			−2.10413
$291$	−5143.45	+	7888.04i	−1.03613	+	1.58902i
$292$		−	677.755i		−	0.135831i
$293$			2489.88i			0.496451i	0.968702	+	0.248226i	$0.0798475\pi$
$293$			2489.88i			0.496451i	−0.968702	+	0.248226i	$0.920153\pi$
$294$	−362.285	−	236.230i	−0.0718669	−	0.0468613i
$295$	−3652.83	+	6152.73i	−0.720936	+	1.21432i
$296$		−	4919.05i		−	0.965925i
$297$	831.001	−	5063.60i	0.162355	−	0.989292i
$298$	−875.964			−0.170279
$299$			801.621i			0.155047i
$300$	−9324.32	−	6079.99i	−1.79447	−	1.17009i
$301$		−	4043.28i		−	0.774256i
$302$		−	12365.2i		−	2.35608i
$303$	−2676.38	−	1745.15i	−0.507439	−	0.330879i
$304$	−4202.62			−0.792884
$305$	6913.56			1.29793
$306$	12087.4	−	5327.86i	2.25815	−	0.995338i
$307$	4971.40			0.924210			0.462105	−	0.886825i	$-0.347094\pi$
$307$	4971.40			0.924210			0.462105	+	0.886825i	$0.347094\pi$
$308$	11953.8			2.21146
$309$	3498.84	−	5365.85i	0.644149	−	0.987873i
$310$	−16411.5			−3.00681
$311$			2050.81i			0.373925i	0.982367	+	0.186963i	$0.0598643\pi$
$311$			2050.81i			0.373925i	−0.982367	+	0.186963i	$0.940136\pi$
$312$	553.642	−	849.070i	0.100461	−	0.154068i
$313$		−	926.601i		−	0.167331i	−0.996494	−	0.0836655i	$-0.973337\pi$
$313$		−	926.601i		−	0.167331i	0.996494	−	0.0836655i	$-0.0266627\pi$
$314$		−	861.345i		−	0.154804i
$315$	−7396.99	+	3260.42i	−1.32309	+	0.583186i
$316$	10259.8			1.82646
$317$		−	302.700i		−	0.0536319i	−0.999640	−	0.0268160i	$-0.991463\pi$
$317$		−	302.700i		−	0.0536319i	0.999640	−	0.0268160i	$-0.00853681\pi$
$318$	−8909.61	+	13663.9i	−1.57115	+	2.40953i
$319$		−	4791.73i		−	0.841020i
$320$			3536.72i			0.617839i
$321$	−967.202	+	1483.31i	−0.168174	+	0.257914i
$322$	18161.4			3.14315
$323$		−	4300.07i		−	0.740750i
$324$	−8476.78	+	9274.63i	−1.45349	+	1.59030i
$325$		−	522.589i		−	0.0891939i
$326$	−9679.07			−1.64440
$327$	2903.54	−	4452.90i	0.491028	−	0.753045i
$328$		−	9949.07i		−	1.67483i
$329$	8423.82			1.41161
$330$	8233.39	−	12626.8i	1.37343	−	2.10631i
$331$	884.721			0.146914			0.0734572	−	0.997298i	$-0.476597\pi$
$331$	884.721			0.146914			0.0734572	+	0.997298i	$0.476597\pi$
$332$	−11069.9			−1.82994
$333$	−2619.48	+	1154.60i	−0.431070	+	0.190005i
$334$		−	5482.59i		−	0.898186i
$335$	−10237.4			−1.66963
$336$	−7855.97	−	5122.54i	−1.27553	−	0.831718i
$337$		−	1782.59i		−	0.288142i	−0.989567	−	0.144071i	$-0.953981\pi$
$337$		−	1782.59i		−	0.288142i	0.989567	−	0.144071i	$-0.0460194\pi$
$338$	−10947.9			−1.76179
$339$	9845.29	+	6419.69i	1.57735	+	1.02852i
$340$	26503.3			4.22747
$341$		−	7567.84i		−	1.20182i
$342$	2415.43	+	5479.94i	0.381905	+	0.866437i
$343$	6189.88			0.974409
$344$		−	9892.81i		−	1.55054i
$345$	8543.51	−	13102.4i	1.33324	−	2.04467i
$346$	−646.858			−0.100507
$347$	−2878.22			−0.445277			−0.222638	−	0.974901i	$-0.571467\pi$
$347$	−2878.22			−0.445277			−0.222638	+	0.974901i	$0.571467\pi$
$348$	−6408.68	+	9828.41i	−0.987188	+	1.51396i
$349$		−	1591.36i		−	0.244079i	−0.992525	−	0.122040i	$-0.961056\pi$
$349$		−	1591.36i		−	0.244079i	0.992525	−	0.122040i	$-0.0389435\pi$
$350$	−11839.7			−1.80816
$351$	−582.095	−	95.5291i	−0.0885183	−	0.0145270i
$352$	3913.18			0.592538
$353$	8834.08			1.33198			0.665992	−	0.745959i	$-0.268008\pi$
$353$	8834.08			1.33198			0.665992	+	0.745959i	$0.268008\pi$
$354$	5222.08	+	10614.5i	0.784041	+	1.59366i
$355$	12788.7			1.91198
$356$	−4459.26			−0.663878
$357$	5241.32	−	8038.14i	0.777031	−	1.19166i
$358$	16696.6			2.46493
$359$		−	2254.31i		−	0.331414i	−0.986175	−	0.165707i	$-0.947009\pi$
$359$		−	2254.31i		−	0.331414i	0.986175	−	0.165707i	$-0.0529906\pi$
$360$	−18098.4	+	7977.35i	−2.64964	+	1.16790i
$361$	−4909.53			−0.715779
$362$	−12799.1			−1.85830
$363$	29.3073	+	19.1100i	0.00423755	+	0.00276313i
$364$		−	1374.16i		−	0.197873i
$365$	−620.865			−0.0890345
$366$	6242.93	−	9574.22i	0.891594	−	1.36736i
$367$			7324.96i			1.04185i	0.853602	+	0.520926i	$0.174413\pi$
$367$			7324.96i			1.04185i	−0.853602	+	0.520926i	$0.825587\pi$
$368$	18147.3			2.57063
$369$	−5298.04	+	2335.25i	−0.747440	+	0.329454i
$370$	−8409.41			−1.18158
$371$			11849.8i			1.65825i
$372$	−10121.6	+	15522.6i	−1.41070	+	2.16346i
$373$	−12190.8			−1.69226			−0.846131	−	0.532975i	$-0.821074\pi$
$373$	−12190.8			−1.69226			−0.846131	+	0.532975i	$0.821074\pi$
$374$			17894.1i			2.47401i
$375$	31.7516	−	48.6946i	0.00437239	−	0.00670554i
$376$	20610.8			2.82692
$377$	−550.841			−0.0752514
$378$	−2164.29	+	13187.8i	−0.294495	+	1.79447i
$379$	−12783.7			−1.73260			−0.866298	−	0.499528i	$-0.833507\pi$
$379$	−12783.7			−1.73260			−0.866298	+	0.499528i	$0.833507\pi$
$380$			12015.5i			1.62205i
$381$	−3403.69	−	2219.40i	−0.457681	−	0.298434i
$382$	−3401.45			−0.455584
$383$			8079.16i			1.07787i	0.842346	+	0.538937i	$0.181174\pi$
$383$			8079.16i			1.07787i	−0.842346	+	0.538937i	$0.818826\pi$
$384$	8623.29	+	5622.87i	1.14598	+	0.747242i
$385$		−	10950.4i		−	1.44957i
$386$	669.157			0.0882362
$387$	−5268.09	+	2322.05i	−0.691969	+	0.305003i
$388$			31235.7i			4.08699i
$389$		−	4699.78i		−	0.612566i	−0.951940	−	0.306283i	$-0.900915\pi$
$389$		−	4699.78i		−	0.612566i	0.951940	−	0.306283i	$-0.0990855\pi$
$390$	−1451.54	−	946.483i	−0.188465	−	0.122890i
$391$			18568.1i			2.40161i
$392$	−768.727			−0.0990474
$393$	−8143.33	−	5309.91i	−1.04523	−	0.681551i
$394$		−	7793.20i		−	0.996486i
$395$		−	9398.66i		−	1.19721i
$396$	−6865.02	−	15574.8i	−0.871162	−	1.97643i
$397$			3284.57i			0.415234i	0.978210	+	0.207617i	$0.0665708\pi$
$397$			3284.57i			0.415234i	−0.978210	+	0.207617i	$0.933429\pi$
$398$	6342.30			0.798770
$399$	3644.16	+	2376.20i	0.457233	+	0.298142i
$400$	−11830.5			−1.47881
$401$	10745.7			1.33819			0.669097	−	0.743175i	$-0.266681\pi$
$401$	10745.7			1.33819			0.669097	+	0.743175i	$0.266681\pi$
$402$	−9244.32	+	14177.2i	−1.14693	+	1.75894i
$403$	−869.974			−0.107535
$404$	−10598.1			−1.30514
$405$	8496.14	+	7765.26i	1.04241	+	0.952738i
$406$			12479.8i			1.52552i
$407$		−	3877.83i		−	0.472278i
$408$	12824.1	−	19667.1i	1.55610	−	2.38644i
$409$		−	608.438i		−	0.0735583i	−0.999323	−	0.0367791i	$-0.988290\pi$
$409$		−	608.438i		−	0.0735583i	0.999323	−	0.0367791i	$-0.0117098\pi$
$410$	−17008.5			−2.04876
$411$	5835.77	−	8949.78i	0.700382	−	1.07411i
$412$		−	21248.1i		−	2.54082i
$413$	7389.33	+	4386.99i	0.880400	+	0.522687i
$414$	−10430.0	−	23662.9i	−1.23818	−	2.80910i
$415$			10140.7i			1.19949i
$416$		−	449.847i		−	0.0530181i
$417$	−9215.65	−	6009.12i	−1.08224	−	0.705679i
$418$	−8112.43			−0.949263
$419$	2140.32			0.249551			0.124775	−	0.992185i	$-0.460179\pi$
$419$	2140.32			0.249551			0.124775	+	0.992185i	$0.460179\pi$
$420$	−14645.6	+	22460.6i	−1.70150	+	2.60944i
$421$		−	6114.20i		−	0.707809i	−0.935281	−	0.353905i	$-0.884854\pi$
$421$		−	6114.20i		−	0.707809i	0.935281	−	0.353905i	$-0.115146\pi$
$422$			26230.9i			3.02584i
$423$	−4837.78	−	10975.6i	−0.556078	−	1.26159i
$424$			28993.1i			3.32083i
$425$		−	12104.8i		−	1.38158i
$426$	11548.2	−	17710.4i	1.31340	−	2.01425i
$427$		−	8303.08i		−	0.941017i
$428$			5873.72i			0.663357i
$429$	436.452	−	669.347i	0.0491191	−	0.0753295i
$430$	−16912.4			−1.89671
$431$	5957.62			0.665820			0.332910	−	0.942959i	$-0.391969\pi$
$431$	5957.62			0.665820			0.332910	+	0.942959i	$0.391969\pi$
$432$	−2162.61	+	13177.6i	−0.240853	+	1.46761i
$433$	5929.89			0.658135			0.329067	−	0.944306i	$-0.393266\pi$
$433$	5929.89			0.658135			0.329067	+	0.944306i	$0.393266\pi$
$434$			19710.0i			2.17997i
$435$	9003.44	+	5870.75i	0.992372	+	0.647083i
$436$		−	17632.9i		−	1.93684i
$437$	−8417.99			−0.921481
$438$	−560.640	+	859.803i	−0.0611608	+	0.0937967i
$439$	2601.68			0.282851			0.141425	−	0.989949i	$-0.454831\pi$
$439$	2601.68			0.282851			0.141425	+	0.989949i	$0.454831\pi$
$440$		−	26792.6i		−	2.90293i
$441$	180.436	+	409.360i	0.0194834	+	0.0442025i
$442$	2057.04			0.221366
$443$	−4968.72			−0.532892			−0.266446	−	0.963850i	$-0.585849\pi$
$443$	−4968.72			−0.532892			−0.266446	+	0.963850i	$0.585849\pi$
$444$	−5186.40	+	7953.90i	−0.554359	+	0.850170i
$445$			4084.96i			0.435159i
$446$	10812.9			1.14799
$447$	758.972	+	494.893i	0.0803091	+	0.0523661i
$448$	4247.54			0.447941
$449$			10888.3i			1.14443i	0.820102	+	0.572217i	$0.193916\pi$
$449$			10888.3i			1.14443i	−0.820102	+	0.572217i	$0.806084\pi$
$450$	6799.50	+	15426.2i	0.712292	+	1.61600i
$451$		−	7843.15i		−	0.818890i
$452$	38986.1			4.05697
$453$	−6985.97	+	10713.7i	−0.724568	+	1.11120i
$454$	15143.0			1.56541
$455$	−1258.82			−0.129702
$456$	8916.26	+	5813.91i	0.915663	+	0.597064i
$457$			11335.6i			1.16030i	0.814511	+	0.580149i	$0.197006\pi$
$457$			11335.6i			1.16030i	−0.814511	+	0.580149i	$0.802994\pi$
$458$		−	24591.3i		−	2.50890i
$459$	−13483.2	−	2212.76i	−1.37111	−	0.225017i
$460$		−	51883.9i		−	5.25891i
$461$		−	2047.70i		−	0.206878i	−0.994636	−	0.103439i	$-0.967015\pi$
$461$		−	2047.70i		−	0.206878i	0.994636	−	0.103439i	$-0.0329846\pi$
$462$	−15164.6	−	9888.17i	−1.52710	−	0.995757i
$463$		−	8560.90i		−	0.859306i	−0.902994	−	0.429653i	$-0.858636\pi$
$463$		−	8560.90i		−	0.859306i	0.902994	−	0.429653i	$-0.141364\pi$
$464$			12470.1i			1.24765i
$465$	14219.6	+	9272.00i	1.41811	+	0.924686i
$466$	−32211.6			−3.20209
$467$	−12235.6			−1.21241			−0.606204	−	0.795309i	$-0.707308\pi$
$467$	−12235.6			−1.21241			−0.606204	+	0.795309i	$0.707308\pi$
$468$	−1790.43	+	789.180i	−0.176843	+	0.0779484i
$469$			12294.9i			1.21051i
$470$		−	35235.4i		−	3.45806i
$471$	−486.634	+	746.306i	−0.0476070	+	0.0730105i
$472$	18079.7	+	10733.8i	1.76310	+	1.04674i
$473$		−	7798.80i		−	0.758117i
$474$	−13015.7	−	8486.97i	−1.26125	−	0.822404i
$475$	5487.82			0.530102
$476$		−	31830.0i		−	3.06497i
$477$	15439.3	−	6805.29i	1.48201	−	0.653234i
$478$		−	13648.2i		−	1.30597i
$479$			20219.0i			1.92866i	0.264701	+	0.964331i	$0.414727\pi$
$479$			20219.0i			1.92866i	−0.264701	+	0.964331i	$0.585273\pi$
$480$	−4794.37	+	7352.69i	−0.455900	+	0.699173i
$481$	−445.783			−0.0422577
$482$	−16093.1			−1.52079
$483$	−15735.8	−	10260.6i	−1.48241	−	0.966614i
$484$	116.053			0.0108990
$485$	28613.8			2.67894
$486$	18425.7	−	4753.83i	1.71976	−	0.443700i
$487$	3590.52			0.334091			0.167045	−	0.985949i	$-0.446577\pi$
$487$	3590.52			0.334091			0.167045	+	0.985949i	$0.446577\pi$
$488$		−	20315.4i		−	1.88450i
$489$	8386.35	+	5468.38i	0.775550	+	0.505703i
$490$			1314.18i			0.121161i
$491$			11912.8i			1.09494i	0.836824	+	0.547472i	$0.184410\pi$
$491$			11912.8i			1.09494i	−0.836824	+	0.547472i	$0.815590\pi$
$492$	−10489.8	+	16087.2i	−0.961212	+	1.47412i
$493$	−12759.2			−1.16561
$494$			932.578i			0.0849366i
$495$	−14267.5	+	6288.78i	−1.29551	+	0.571030i
$496$			19694.7i			1.78290i
$497$		−	15359.0i		−	1.38621i
$498$	14043.3	+	9157.04i	1.26365	+	0.823969i
$499$	−12240.9			−1.09815			−0.549074	−	0.835773i	$-0.685020\pi$
$499$	−12240.9			−1.09815			−0.549074	+	0.835773i	$0.685020\pi$
$500$		−	192.825i		−	0.0172467i
$501$	−3097.50	+	4750.35i	−0.276220	+	0.423613i
$502$		−	35156.0i		−	3.12568i
$503$	21730.3			1.92626			0.963128	−	0.269044i	$-0.0867078\pi$
$503$	21730.3			1.92626			0.963128	+	0.269044i	$0.0867078\pi$
$504$	9580.67	+	21735.9i	0.846740	+	1.92102i
$505$			9708.55i			0.855495i
$506$	35030.2			3.07763
$507$	9485.69	+	6185.20i	0.830915	+	0.541804i
$508$	−13478.2			−1.17716
$509$	8351.63			0.727268			0.363634	−	0.931542i	$-0.381536\pi$
$509$	8351.63			0.727268			0.363634	+	0.931542i	$0.381536\pi$
$510$	−33622.2	−	21923.6i	−2.91924	−	1.90351i
$511$			745.650i			0.0645511i
$512$	25145.0			2.17044
$513$	1003.17	−	6112.70i	0.0863375	−	0.526086i
$514$			22084.2i			1.89512i
$515$	−19464.6			−1.66546
$516$	−10430.5	+	15996.3i	−0.889876	+	1.36472i
$517$	16248.1			1.38219
$518$			10099.6i			0.856660i
$519$	560.465	+	365.455i	0.0474021	+	0.0309088i
$520$	−3079.99			−0.259743
$521$			1641.69i			0.138050i	0.997615	+	0.0690248i	$0.0219887\pi$
$521$			1641.69i			0.138050i	−0.997615	+	0.0690248i	$0.978011\pi$
$522$	16260.2	−	7167.09i	1.36339	−	0.600949i
$523$	2499.37			0.208967			0.104483	−	0.994527i	$-0.466681\pi$
$523$	2499.37			0.208967			0.104483	+	0.994527i	$0.466681\pi$
$524$	−32246.5			−2.68835
$525$	10258.4	+	6689.06i	0.852787	+	0.556066i
$526$			22812.5i			1.89101i
$527$	−20151.4			−1.66567
$528$	−15152.8	−	9880.50i	−1.24894	−	0.814382i
$529$	24182.6			1.98756
$530$	49565.5			4.06224
$531$	1472.24	−	12147.2i	0.120320	−	0.992735i
$532$	14430.4			1.17601
$533$	−901.622			−0.0732713
$534$	5657.04	+	3688.71i	0.458435	+	0.298925i
$535$	5380.69			0.434818
$536$			30082.3i			2.42418i
$537$	−14466.7	−	9433.09i	−1.16254	−	0.758041i
$538$	5398.09			0.432580
$539$	−606.010			−0.0484280
$540$	37675.3	+	6183.00i	3.00238	+	0.492729i
$541$		−	8763.50i		−	0.696437i	−0.937413	−	0.348218i	$-0.886787\pi$
$541$		−	8763.50i		−	0.696437i	0.937413	−	0.348218i	$-0.113213\pi$
$542$	2318.06			0.183707
$543$	11089.7	+	7231.10i	0.876434	+	0.571485i
$544$		−	10419.9i		−	0.821228i
$545$	−16152.8			−1.26956
$546$	−1136.71	+	1743.27i	−0.0890967	+	0.136639i
$547$	−8486.37			−0.663348			−0.331674	−	0.943394i	$-0.607613\pi$
$547$	−8486.37			−0.663348			−0.331674	+	0.943394i	$0.607613\pi$
$548$		−	35440.0i		−	2.76263i
$549$	−10818.3	+	4768.44i	−0.841007	+	0.370696i
$550$	−22836.7			−1.77047
$551$		−	5784.50i		−	0.447238i
$552$	−38501.2	−	25105.0i	−2.96870	−	1.93576i
$553$	−11287.6			−0.867992
$554$	−2601.24			−0.199487
$555$	7286.27	+	4751.06i	0.557270	+	0.363372i
$556$	−36492.8			−2.78352
$557$		−	4363.80i		−	0.331958i	−0.986129	−	0.165979i	$-0.946922\pi$
$557$		−	4363.80i		−	0.331958i	0.986129	−	0.165979i	$-0.0530783\pi$
$558$	25680.6	−	11319.4i	1.94829	−	0.858760i
$559$	−896.524			−0.0678335
$560$			28497.5i			2.15042i
$561$	10109.6	−	15504.2i	0.760834	−	1.16682i
$562$			20978.5i			1.57460i
$563$	−14160.7			−1.06004			−0.530020	−	0.847985i	$-0.677816\pi$
$563$	−14160.7			−1.06004			−0.530020	+	0.847985i	$0.677816\pi$
$564$	−33326.8	−	21731.0i	−2.48814	−	1.62241i
$565$		−	35713.7i		−	2.65927i
$566$			5888.68i			0.437314i
$567$	9325.95	−	10203.7i	0.690747	−	0.755761i
$568$		−	37579.4i		−	2.77605i
$569$	−23427.8			−1.72609			−0.863044	−	0.505129i	$-0.831445\pi$
$569$	−23427.8			−1.72609			−0.863044	+	0.505129i	$0.831445\pi$
$570$	9939.23	−	15242.9i	0.730365	−	1.12010i
$571$			3642.83i			0.266983i	0.991050	+	0.133492i	$0.0426190\pi$
$571$			3642.83i			0.266983i	−0.991050	+	0.133492i	$0.957381\pi$
$572$		−	2650.53i		−	0.193749i
$573$	2947.16	+	1921.71i	0.214868	+	0.140106i
$574$			20427.0i			1.48538i
$575$	−23696.9			−1.71866
$576$	−2439.35	−	5534.22i	−0.176458	−	0.400335i
$577$	−1937.25			−0.139773			−0.0698863	−	0.997555i	$-0.522264\pi$
$577$	−1937.25			−0.139773			−0.0698863	+	0.997555i	$0.522264\pi$
$578$	22967.1			1.65278
$579$	−579.786	−	378.053i	−0.0416150	−	0.0271353i
$580$	35652.5			2.55239
$581$	12178.8			0.869644
$582$	25838.2	−	39625.7i	1.84025	−	2.82223i
$583$			22856.2i			1.62368i
$584$			1824.40i			0.129271i
$585$	722.938	+	1640.15i	0.0510937	+	0.115918i
$586$		−	12507.9i		−	0.881737i
$587$	7040.82			0.495070			0.247535	−	0.968879i	$-0.420380\pi$
$587$	7040.82			0.495070			0.247535	+	0.968879i	$0.420380\pi$
$588$	1243.00	+	810.506i	0.0871777	+	0.0568448i
$589$		−	9135.78i		−	0.639106i
$590$	18350.0	−	30908.3i	1.28044	−	2.15674i
$591$	−4402.92	+	6752.36i	−0.306450	+	0.469974i
$592$			10091.7i			0.700621i
$593$		−	20860.2i		−	1.44457i	−0.691598	−	0.722283i	$-0.743093\pi$
$593$		−	20860.2i		−	1.44457i	0.691598	−	0.722283i	$-0.256907\pi$
$594$	−4174.54	+	25437.1i	−0.288356	+	1.75706i
$595$	−29158.3			−2.00903
$596$	3005.43			0.206556
$597$	−5495.24	−	3583.21i	−0.376725	−	0.245646i
$598$		−	4026.95i		−	0.275375i
$599$		−	25414.9i		−	1.73359i	−0.498661	−	0.866797i	$-0.666175\pi$
$599$		−	25414.9i		−	1.73359i	0.498661	−	0.866797i	$-0.333825\pi$
$600$	25099.5	+	16366.3i	1.70781	+	1.11359i
$601$		−	11780.0i		−	0.799527i	−0.916618	−	0.399763i	$-0.869092\pi$
$601$		−	11780.0i		−	0.799527i	0.916618	−	0.399763i	$-0.130908\pi$
$602$			20311.5i			1.37514i
$603$	16019.3	−	7060.95i	1.08185	−	0.476856i
$604$			42425.0i			2.85803i
$605$		−	106.312i		−	0.00714412i
$606$	13444.8	+	8766.80i	0.901253	+	0.587668i
$607$	−10681.0			−0.714214			−0.357107	−	0.934064i	$-0.616237\pi$
$607$	−10681.0			−0.714214			−0.357107	+	0.934064i	$0.616237\pi$
$608$	4723.93			0.315100
$609$	7050.68	−	10813.0i	0.469143	−	0.719482i
$610$	−34730.4			−2.30523
$611$		−	1867.83i		−	0.123673i
$612$	−41472.1	+	18279.9i	−2.73923	+	1.20739i
$613$			20194.4i			1.33058i	0.746585	+	0.665290i	$0.231692\pi$
$613$			20194.4i			1.33058i	−0.746585	+	0.665290i	$0.768308\pi$
$614$	−24973.9			−1.64147
$615$	14736.9	+	9609.30i	0.966260	+	0.630056i
$616$	−32177.5			−2.10466
$617$			15263.6i			0.995929i	0.867197	+	0.497964i	$0.165919\pi$
$617$			15263.6i			0.995929i	−0.867197	+	0.497964i	$0.834081\pi$
$618$	−17576.5	+	26955.4i	−1.14406	+	1.75454i
$619$	23507.2			1.52639			0.763194	−	0.646169i	$-0.223630\pi$
$619$	23507.2			1.52639			0.763194	+	0.646169i	$0.223630\pi$
$620$	56307.9			3.64739
$621$	−4331.78	+	26395.2i	−0.279917	+	1.70564i
$622$		−	10302.3i		−	0.664121i
$623$	4905.98			0.315496
$624$	−1135.83	+	1741.92i	−0.0728679	+	0.111751i
$625$	−15713.1			−1.00564
$626$			4654.79i			0.297193i
$627$	7028.95	+	4583.28i	0.447702	+	0.291927i
$628$			2955.28i			0.187784i
$629$	−10325.7			−0.654554
$630$	37158.9	−	16378.7i	2.34991	−	1.03579i
$631$	1583.44			0.0998982			0.0499491	−	0.998752i	$-0.484094\pi$
$631$	1583.44			0.0998982			0.0499491	+	0.998752i	$0.484094\pi$
$632$	−27617.8			−1.73826
$633$	14819.7	−	22727.6i	0.930537	−	1.42708i
$634$			1520.62i			0.0952546i
$635$			12346.9i			0.771607i
$636$	30568.9	−	46880.7i	1.90587	−	2.92287i
$637$			69.6649i			0.00433316i
$638$			24071.3i			1.49372i
$639$	−20011.6	+	8820.66i	−1.23889	+	0.546072i
$640$		−	31280.9i		−	1.93201i
$641$			20497.2i			1.26301i	0.775371	+	0.631506i	$0.217563\pi$
$641$			20497.2i			1.26301i	−0.775371	+	0.631506i	$0.782437\pi$
$642$	4858.75	−	7451.43i	0.298691	−	0.458075i
$643$	−4515.90			−0.276967			−0.138483	−	0.990365i	$-0.544223\pi$
$643$	−4515.90			−0.276967			−0.138483	+	0.990365i	$0.544223\pi$
$644$	−62311.7			−3.81277
$645$	14653.6	+	9554.97i	0.894550	+	0.583297i
$646$			21601.5i			1.31563i
$647$			7206.18i			0.437873i	0.975739	+	0.218937i	$0.0702588\pi$
$647$			7206.18i			0.437873i	−0.975739	+	0.218937i	$0.929741\pi$
$648$	22818.1	−	24965.8i	1.38330	−	1.51350i
$649$	14252.8	+	8461.76i	0.862049	+	0.511792i
$650$			2625.23i			0.158416i
$651$	11135.5	−	17077.6i	0.670408	−	1.02814i
$652$	33208.9			1.99473
$653$			1838.01i			0.110148i	0.998482	+	0.0550742i	$0.0175395\pi$
$653$			1838.01i			0.110148i	−0.998482	+	0.0550742i	$0.982460\pi$
$654$	−14586.0	+	22369.2i	−0.872105	+	1.33747i
$655$			29539.8i			1.76216i
$656$			20411.1i			1.21482i
$657$	971.525	−	428.225i	0.0576907	−	0.0254287i
$658$	−42317.2			−2.50714
$659$	−5231.00			−0.309212			−0.154606	−	0.987976i	$-0.549411\pi$
$659$	−5231.00			−0.309212			−0.154606	+	0.987976i	$0.549411\pi$
$660$	−28248.8	+	43322.6i	−1.66603	+	2.55504i
$661$	−1527.63			−0.0898910			−0.0449455	−	0.998989i	$-0.514311\pi$
$661$	−1527.63			−0.0898910			−0.0449455	+	0.998989i	$0.514311\pi$
$662$	−4444.41			−0.260932
$663$	−1782.31	−	1162.17i	−0.104403	−	0.0680767i
$664$	29798.3			1.74156
$665$		−	13219.1i		−	0.770852i
$666$	13159.0	−	5800.16i	0.765615	−	0.337465i
$667$			24978.0i			1.45000i
$668$			18810.8i			1.08954i
$669$	−9368.72	−	6108.94i	−0.541429	−	0.353042i
$670$	51427.6			2.96540
$671$		−	16015.2i		−	0.921402i
$672$	8830.47	+	5757.96i	0.506909	+	0.330533i
$673$		−	13657.3i		−	0.782242i	−0.920339	−	0.391121i	$-0.872087\pi$
$673$		−	13657.3i		−	0.782242i	0.920339	−	0.391121i	$-0.127913\pi$
$674$			8954.88i			0.511764i
$675$	2823.96	−	17207.4i	0.161028	−	0.981206i
$676$	37562.1			2.13713
$677$			11537.8i			0.655000i	0.944851	+	0.327500i	$0.106206\pi$
$677$			11537.8i			0.655000i	−0.944851	+	0.327500i	$0.893794\pi$
$678$	−49458.0	−	32249.4i	−2.80151	−	1.82674i
$679$		−	34364.7i		−	1.94226i
$680$	−71342.4			−4.02332
$681$	−13120.6	−	8555.35i	−0.738298	−	0.481412i
$682$			38017.1i			2.13453i
$683$	20558.2			1.15174			0.575869	−	0.817542i	$-0.304664\pi$
$683$	20558.2			1.15174			0.575869	+	0.817542i	$0.304664\pi$
$684$	−8287.34	−	18801.7i	−0.463267	−	1.05103i
$685$	−32465.3			−1.81085
$686$	−31095.0			−1.73063
$687$	−13893.3	+	21307.0i	−0.771563	+	1.18328i
$688$			20295.7i			1.12466i
$689$	2627.47			0.145281
$690$	−42918.4	+	65820.1i	−2.36794	+	3.63149i
$691$			10360.1i			0.570358i	0.958474	+	0.285179i	$0.0920531\pi$
$691$			10360.1i			0.570358i	−0.958474	+	0.285179i	$0.907947\pi$
$692$	2219.37			0.121919
$693$	7552.73	+	17135.1i	0.414004	+	0.939260i
$694$	14458.8			0.790847
$695$			33429.7i			1.82455i
$696$	17251.1	−	26456.4i	0.939514	−	1.44085i
$697$	−20884.4			−1.13494
$698$			7994.23i			0.433505i
$699$	27909.5	+	18198.6i	1.51020	+	0.984739i
$700$	40622.0			2.19338
$701$	−15053.3			−0.811064			−0.405532	−	0.914081i	$-0.632914\pi$
$701$	−15053.3			−0.811064			−0.405532	+	0.914081i	$0.632914\pi$
$702$	2924.16	+	479.892i	0.157216	+	0.0258011i
$703$		−	4681.26i		−	0.251148i
$704$	8192.78			0.438604
$705$	−19906.9	+	30529.5i	−1.06346	+	1.63093i
$706$	−44378.1			−2.36571
$707$	11659.8			0.620244
$708$	−17917.0	−	36418.4i	−0.951075	−	1.93317i
$709$	6457.43			0.342051			0.171025	−	0.985267i	$-0.445292\pi$
$709$	6457.43			0.342051			0.171025	+	0.985267i	$0.445292\pi$
$710$	−64244.2			−3.39583
$711$	6482.47	+	14706.9i	0.341929	+	0.775743i
$712$	12003.6			0.631817
$713$			39449.1i			2.07206i
$714$	−26329.8	+	40379.7i	−1.38007	+	2.11649i
$715$	−2428.05			−0.126998
$716$	−57286.2			−2.99006
$717$	−7710.79	+	11825.3i	−0.401625	+	0.615935i
$718$			11324.5i			0.588618i
$719$	3504.48			0.181773			0.0908866	−	0.995861i	$-0.471030\pi$
$719$	3504.48			0.181773			0.0908866	+	0.995861i	$0.471030\pi$
$720$	37130.0	−	16366.0i	1.92188	−	0.847119i
$721$			23376.7i			1.20748i
$722$	24663.1			1.27128
$723$	13943.7	+	9092.09i	0.717251	+	0.467688i
$724$	43913.7			2.25420
$725$		−	16283.5i		−	0.834145i
$726$	−147.225	−	95.9993i	−0.00752624	−	0.00490753i
$727$	21316.2			1.08745			0.543723	−	0.839265i	$-0.317014\pi$
$727$	21316.2			1.08745			0.543723	+	0.839265i	$0.317014\pi$
$728$			3699.02i			0.188317i
$729$	−18650.6	−	6291.02i	−0.947547	−	0.319617i
$730$	3118.93			0.158132
$731$	−20766.3			−1.05071
$732$	−21419.5	+	32849.2i	−1.08154	+	1.65866i
$733$	503.085			0.0253504			0.0126752	−	0.999920i	$-0.495965\pi$
$733$	503.085			0.0253504			0.0126752	+	0.999920i	$0.495965\pi$
$734$		−	36797.1i		−	1.85041i
$735$	742.474	−	1138.67i	0.0372607	−	0.0571433i
$736$	−20398.4			−1.02159
$737$			23714.8i			1.18527i
$738$	26614.8	−	11731.2i	1.32751	−	0.585136i
$739$		−	12261.2i		−	0.610332i	−0.952299	−	0.305166i	$-0.901288\pi$
$739$		−	12261.2i		−	0.610332i	0.952299	−	0.305166i	$-0.0987119\pi$
$740$	28852.7			1.43331
$741$	526.878	−	808.025i	0.0261206	−	0.0400588i
$742$		−	59527.4i		−	2.94518i
$743$			10092.6i			0.498335i	0.968460	+	0.249168i	$0.0801570\pi$
$743$			10092.6i			0.498335i	−0.968460	+	0.249168i	$0.919843\pi$
$744$	27245.6	−	41784.1i	1.34257	−	2.05898i
$745$		−	2753.17i		−	0.135394i
$746$	61240.5			3.00559
$747$	−6994.28	−	15868.1i	−0.342580	−	0.777220i
$748$		−	61394.6i		−	3.00108i
$749$		−	6462.13i		−	0.315248i
$750$	−159.505	+	244.618i	−0.00776572	+	0.0119096i
$751$			12579.2i			0.611213i	0.952158	+	0.305606i	$0.0988591\pi$
$751$			12579.2i			0.611213i	−0.952158	+	0.305606i	$0.901141\pi$
$752$	−42284.3			−2.05047
$753$	−19862.1	+	30460.7i	−0.961241	+	1.47417i
$754$	2767.16			0.133652
$755$	38864.0			1.87338
$756$	7425.68	−	45247.5i	0.357235	−	2.17677i
$757$	25539.6			1.22623			0.613114	−	0.789995i	$-0.289917\pi$
$757$	25539.6			1.22623			0.613114	+	0.789995i	$0.289917\pi$
$758$	64219.0			3.07723
$759$	−30351.6	−	19791.0i	−1.45151	−	0.946466i
$760$		−	32343.7i		−	1.54372i
$761$			1308.83i			0.0623457i	0.999514	+	0.0311729i	$0.00992424\pi$
$761$			1308.83i			0.0623457i	−0.999514	+	0.0311729i	$0.990076\pi$
$762$	17098.5	+	11149.2i	0.812878	+	0.530043i
$763$			19399.3i			0.920449i
$764$	11670.4			0.552643
$765$	16745.5	+	37991.0i	0.791419	+	1.79551i
$766$		−	40585.8i		−	1.91439i
$767$	972.736	−	1638.45i	0.0457933	−	0.0771330i
$768$	−35519.4	−	23160.7i	−1.66888	−	1.08820i
$769$		−	36500.3i		−	1.71162i	−0.517293	−	0.855808i	$-0.673060\pi$
$769$		−	36500.3i		−	1.71162i	0.517293	−	0.855808i	$-0.326940\pi$
$770$			55009.4i			2.57455i
$771$	12476.9	−	19134.7i	0.582807	−	0.893798i
$772$	−2295.88			−0.107034
$773$	−8733.49			−0.406367			−0.203184	−	0.979141i	$-0.565129\pi$
$773$	−8733.49			−0.406367			−0.203184	+	0.979141i	$0.565129\pi$
$774$	26464.3	−	11664.8i	1.22899	−	0.541710i
$775$		−	25717.5i		−	1.19200i
$776$		−	84081.2i		−	3.88961i
$777$	5705.95	−	8750.70i	0.263449	−	0.404028i
$778$			23609.4i			1.08797i
$779$		−	9468.13i		−	0.435470i
$780$	4980.22	+	3247.39i	0.228616	+	0.149071i
$781$		−	29624.9i		−	1.35732i
$782$		−	93277.0i		−	4.26545i
$783$	−18137.7	−	2976.62i	−0.827826	−	0.135857i
$784$	1577.09			0.0718427
$785$	2707.22			0.123089
$786$	40908.1	+	26674.4i	1.85642	+	1.21049i
$787$	40134.6			1.81785			0.908923	−	0.416964i	$-0.136906\pi$
$787$	40134.6			1.81785			0.908923	+	0.416964i	$0.136906\pi$
$788$			26738.5i			1.20878i
$789$	12888.4	−	19765.7i	0.581545	−	0.891862i
$790$			47214.3i			2.12634i
$791$	−42891.6			−1.92800
$792$	18479.5	+	41924.9i	0.829091	+	1.88098i
$793$	−1841.06			−0.0824437
$794$		−	16500.1i		−	0.737489i
$795$	−42945.7	−	28003.0i	−1.91588	−	1.24926i
$796$	−21760.4			−0.968943
$797$	22982.0			1.02141			0.510706	−	0.859755i	$-0.329384\pi$
$797$	22982.0			1.02141			0.510706	+	0.859755i	$0.329384\pi$
$798$	−18306.5	−	11936.9i	−0.812083	−	0.529524i
$799$		−	43264.8i		−	1.91564i
$800$	13298.0			0.587694
$801$	−2817.49	−	6392.11i	−0.124284	−	0.281965i
$802$	−53981.3			−2.37674
$803$			1438.23i			0.0632056i
$804$	31717.3	−	48641.9i	1.39127	−	2.13367i
$805$			57081.4i			2.49920i
$806$	4370.33			0.190990
$807$	−4677.13	−	3049.75i	−0.204018	−	0.133032i
$808$	28528.4			1.24211
$809$	3742.78			0.162656			0.0813282	−	0.996687i	$-0.474084\pi$
$809$	3742.78			0.162656			0.0813282	+	0.996687i	$0.474084\pi$
$810$	−42680.5	−	39008.9i	−1.85141	−	1.69214i
$811$			33946.8i			1.46983i	0.678159	+	0.734915i	$0.262778\pi$
$811$			33946.8i			1.46983i	−0.678159	+	0.734915i	$0.737222\pi$
$812$		−	42818.1i		−	1.85052i
$813$	−2008.47	−	1309.64i	−0.0866422	−	0.0564956i
$814$			19480.3i			0.838803i
$815$		−	30421.4i		−	1.30750i
$816$	−26309.4	+	40348.4i	−1.12869	+	1.73097i
$817$		−	9414.59i		−	0.403152i
$818$			3056.50i			0.130645i
$819$	1969.79	−	868.237i	0.0840416	−	0.0370435i
$820$	58356.3			2.48523
$821$	21275.6			0.904415			0.452208	−	0.891913i	$-0.350637\pi$
$821$	21275.6			0.904415			0.452208	+	0.891913i	$0.350637\pi$
$822$	−29316.1	+	44959.4i	−1.24394	+	1.90771i
$823$		−	4449.77i		−	0.188468i	−0.995550	−	0.0942341i	$-0.969960\pi$
$823$		−	4449.77i		−	0.188468i	0.995550	−	0.0942341i	$-0.0300402\pi$
$824$			57196.3i			2.41812i
$825$	19786.7	+	12902.0i	0.835011	+	0.544475i
$826$	−37120.4	−	22038.1i	−1.56366	−	0.928334i
$827$			25812.8i			1.08537i	0.839936	+	0.542685i	$0.182592\pi$
$827$			25812.8i			1.08537i	−0.839936	+	0.542685i	$0.817408\pi$
$828$	35785.5	+	81187.4i	1.50197	+	3.40756i
$829$	−23156.4			−0.970151			−0.485076	−	0.874472i	$-0.661208\pi$
$829$	−23156.4			−0.970151			−0.485076	+	0.874472i	$0.661208\pi$
$830$		−	50942.0i		−	2.13039i
$831$	2253.82	+	1469.62i	0.0940845	+	0.0613484i
$832$		−	941.816i		−	0.0392447i
$833$			1613.66i			0.0671189i
$834$	46294.9	+	30186.9i	1.92214	+	1.25334i
$835$	17231.9			0.714171
$836$	27833.8			1.15150
$837$	−28645.9	−	4701.15i	−1.18297	−	0.194140i
$838$	−10751.9			−0.443222
$839$	13669.6			0.562488			0.281244	−	0.959636i	$-0.409253\pi$
$839$	13669.6			0.562488			0.281244	+	0.959636i	$0.409253\pi$
$840$	39423.4	−	60460.1i	1.61933	−	2.48342i
$841$	7225.15			0.296246
$842$			30714.8i			1.25713i
$843$	11852.2	−	18176.7i	0.484237	−	0.742630i
$844$		−	89998.5i		−	3.67047i
$845$		−	34409.2i		−	1.40084i
$846$	24302.7	+	55136.0i	0.987639	+	2.24068i
$847$	−127.679			−0.00517957
$848$		−	59481.2i		−	2.40872i
$849$	3326.93	−	5102.21i	0.134487	−	0.206251i
$850$			60808.7i			2.45379i
$851$			20214.1i			0.814254i
$852$	−39621.8	+	60764.3i	−1.59322	+	2.44337i
$853$	−22695.9			−0.911010			−0.455505	−	0.890233i	$-0.650541\pi$
$853$	−22695.9			−0.911010			−0.455505	+	0.890233i	$0.650541\pi$
$854$			41710.7i			1.67132i
$855$	−17223.5	+	7591.72i	−0.688927	+	0.303663i
$856$		−	15811.1i		−	0.631322i
$857$	834.550			0.0332645			0.0166323	−	0.999862i	$-0.494706\pi$
$857$	834.550			0.0332645			0.0166323	+	0.999862i	$0.494706\pi$
$858$	−2192.52	+	3362.47i	−0.0872395	+	0.133791i
$859$		−	5061.06i		−	0.201026i	−0.994936	−	0.100513i	$-0.967952\pi$
$859$		−	5061.06i		−	0.201026i	0.994936	−	0.100513i	$-0.0320484\pi$
$860$	58026.4			2.30079
$861$	11540.6	−	17698.8i	0.456798	−	0.700550i
$862$	−29928.2			−1.18255
$863$	−9567.81			−0.377395			−0.188698	−	0.982035i	$-0.560427\pi$
$863$	−9567.81			−0.377395			−0.188698	+	0.982035i	$0.560427\pi$
$864$	2430.87	−	14812.2i	0.0957175	−	0.583243i
$865$		−	2033.08i		−	0.0799154i
$866$	−29788.9			−1.16890
$867$	−19899.7	−	12975.7i	−0.779503	−	0.508280i
$868$		−	67624.9i		−	2.64440i
$869$	−21771.9			−0.849899
$870$	−45228.9	−	29491.8i	−1.76253	−	1.14927i
$871$	2726.18			0.106054
$872$			47464.8i			1.84331i
$873$	−44774.6	+	19735.6i	−1.73584	+	0.765119i
$874$	42287.9			1.63662
$875$			212.141i			0.00819620i
$876$	1923.56	−	2949.98i	0.0741906	−	0.113779i
$877$	−21272.9			−0.819080			−0.409540	−	0.912292i	$-0.634311\pi$
$877$	−21272.9			−0.819080			−0.409540	+	0.912292i	$0.634311\pi$
$878$	−13069.6			−0.502365
$879$	−7066.60	+	10837.4i	−0.271161	+	0.415855i
$880$			54966.7i			2.10560i
$881$	−34872.2			−1.33357			−0.666784	−	0.745251i	$-0.732330\pi$
$881$	−34872.2			−1.33357			−0.666784	+	0.745251i	$0.732330\pi$
$882$	−906.423	−	2056.42i	−0.0346041	−	0.0785073i
$883$	−38286.3			−1.45916			−0.729580	−	0.683896i	$-0.760284\pi$
$883$	−38286.3			−1.45916			−0.729580	+	0.683896i	$0.760284\pi$
$884$	−7057.73			−0.268526
$885$	−33361.5	+	16413.1i	−1.26716	+	0.623411i
$886$	24960.4			0.946458
$887$	3876.39			0.146738			0.0733690	−	0.997305i	$-0.476625\pi$
$887$	3876.39			0.146738			0.0733690	+	0.997305i	$0.476625\pi$
$888$	13960.9	−	21410.6i	0.527587	−	0.809113i
$889$	14828.4			0.559425
$890$		−	20520.9i		−	0.772877i
$891$	17988.2	−	19681.3i	0.676348	−	0.740008i
$892$	−37099.0			−1.39256
$893$	19614.5			0.735020
$894$	−3812.71	−	2486.10i	−0.142635	−	0.0930064i
$895$			52477.7i			1.95993i
$896$	−37567.9			−1.40073
$897$	−2275.11	+	3489.12i	−0.0846863	+	0.129876i
$898$		−	54697.5i		−	2.03261i
$899$	−27107.8			−1.00567
$900$	−23329.1	−	52927.3i	−0.864041	−	1.96027i
$901$	60860.5			2.25034
$902$			39400.2i			1.45441i
$903$	11475.4	−	17598.7i	0.422897	−	0.648559i
$904$	−104944.			−3.86105
$905$		−	40227.7i		−	1.47759i
$906$	35094.1	−	53820.6i	1.28689	−	1.97359i
$907$	2599.47			0.0951643			0.0475822	−	0.998867i	$-0.484848\pi$
$907$	2599.47			0.0951643			0.0475822	+	0.998867i	$0.484848\pi$
$908$	−51955.7			−1.89891
$909$	−6696.21	−	15191.9i	−0.244334	−	0.554326i
$910$	6323.70			0.230361
$911$			52075.0i			1.89388i	0.321413	+	0.946939i	$0.395842\pi$
$911$			52075.0i			1.89388i	−0.321413	+	0.946939i	$0.604158\pi$
$912$	−18292.3	−	11927.6i	−0.664164	−	0.433072i
$913$	23490.9			0.851517
$914$		−	56944.4i		−	2.06078i
$915$	30091.9	+	19621.6i	1.08722	+	0.708929i
$916$			84372.8i			3.04340i
$917$	35476.9			1.27759
$918$	67732.8	+	11115.8i	2.43520	+	0.399648i
$919$		−	53145.8i		−	1.90764i	−0.300385	−	0.953818i	$-0.597115\pi$
$919$		−	53145.8i		−	1.90764i	0.300385	−	0.953818i	$-0.402885\pi$
$920$			139663.i			5.00494i
$921$	21638.4	+	14109.5i	0.774170	+	0.504803i
$922$			10286.6i			0.367432i
$923$	−3405.59			−0.121448
$924$	52029.8	+	33926.4i	1.85244	+	1.20790i
$925$		−	13177.9i		−	0.468417i
$926$			43005.8i			1.52620i
$927$	30458.0	−	13425.2i	1.07915	−	0.475664i
$928$		−	14016.9i		−	0.495828i
$929$	35880.3			1.26716			0.633581	−	0.773676i	$-0.281584\pi$
$929$	35880.3			1.26716			0.633581	+	0.773676i	$0.281584\pi$
$930$	−71432.5	−	46578.0i	−2.51867	−	1.64232i
$931$	−731.566			−0.0257531
$932$	110518.			3.88427
$933$	−5820.47	+	8926.32i	−0.204237	+	0.313220i
$934$	61465.5			2.15333
$935$	−56241.3			−1.96715
$936$	4819.54	−	2124.34i	0.168303	−	0.0741840i
$937$			15090.6i			0.526135i	0.964777	+	0.263068i	$0.0847342\pi$
$937$			15090.6i			0.526135i	−0.964777	+	0.263068i	$0.915266\pi$
$938$		−	61763.7i		−	2.14995i
$939$	2629.82	−	4033.11i	0.0913960	−	0.140166i
$940$			120893.i			4.19477i
$941$	−29849.4			−1.03407			−0.517037	−	0.855963i	$-0.672965\pi$
$941$	−29849.4			−1.03407			−0.517037	+	0.855963i	$0.672965\pi$
$942$	2444.61	−	3749.08i	0.0845539	−	0.129673i
$943$			40884.2i			1.41185i
$944$	−37091.6	−	22021.0i	−1.27884	−	0.759240i
$945$	−41449.5	−	6802.39i	−1.42683	−	0.234161i
$946$			39177.4i			1.34648i
$947$		−	23364.4i		−	0.801732i	−0.916137	−	0.400866i	$-0.868709\pi$
$947$		−	23364.4i		−	0.801732i	0.916137	−	0.400866i	$-0.131291\pi$
$948$	44656.9	+	29118.8i	1.52994	+	0.997611i
$949$	165.334			0.00565540
$950$	−27568.1			−0.941504
$951$	859.103	−	1317.53i	0.0292937	−	0.0449251i
$952$			85681.1i			2.91695i
$953$		−	17639.4i		−	0.599577i	−0.954006	−	0.299788i	$-0.903084\pi$
$953$		−	17639.4i		−	0.599577i	0.954006	−	0.299788i	$-0.0969161\pi$
$954$	−77559.7	+	34186.5i	−2.63217	+	1.16020i
$955$		−	10690.8i		−	0.362247i
$956$			46826.9i			1.58419i
$957$	13599.6	−	20856.4i	0.459364	−	0.704485i
$958$		−	101570.i		−	3.42546i
$959$			38990.3i			1.31289i
$960$	−10037.7	+	15393.9i	−0.337463	+	0.517536i
$961$	−13021.9			−0.437108
$962$	2239.40			0.0750531
$963$	−8419.66	+	3711.19i	−0.281744	+	0.124186i
$964$	55215.3			1.84478
$965$			2103.17i			0.0701589i
$966$	79048.9	+	51544.4i	2.63288	+	1.71678i
$967$		−	39637.7i		−	1.31816i	−0.752072	−	0.659081i	$-0.770945\pi$
$967$		−	39637.7i		−	1.31816i	0.752072	−	0.659081i	$-0.229055\pi$
$968$	−312.396			−0.0103727
$969$	12204.2	−	18716.4i	0.404597	−	0.620494i
$970$	−143742.			−4.75801
$971$		−	34016.1i		−	1.12423i	−0.827059	−	0.562115i	$-0.809988\pi$
$971$		−	34016.1i		−	1.12423i	0.827059	−	0.562115i	$-0.190012\pi$
$972$	−63218.6	+	16310.4i	−2.08615	+	0.538227i
$973$	40148.5			1.32282
$974$	−18037.0			−0.593372
$975$	1483.18	−	2274.61i	0.0487176	−	0.0747138i
$976$			41678.3i			1.36689i
$977$	31648.1			1.03635			0.518174	−	0.855275i	$-0.326612\pi$
$977$	31648.1			1.03635			0.518174	+	0.855275i	$0.326612\pi$
$978$	−42129.0	−	27470.5i	−1.37744	−	0.898168i
$979$	9462.79			0.308919
$980$		−	4508.97i		−	0.146973i
$981$	25275.8	−	11141.0i	0.822625	−	0.362593i
$982$		−	59844.2i		−	1.94471i
$983$	42525.0			1.37979			0.689897	−	0.723908i	$-0.257656\pi$
$983$	42525.0			1.37979			0.689897	+	0.723908i	$0.257656\pi$
$984$	28236.8	−	43304.2i	0.914792	−	1.40293i
$985$	24494.1			0.792332
$986$	64096.2			2.07022
$987$	36665.4	+	23907.9i	1.18244	+	0.771021i
$988$		−	3199.68i		−	0.103032i
$989$			40653.0i			1.30707i
$990$	71673.1	−	31591.8i	2.30093	−	1.01419i
$991$		−	8077.18i		−	0.258910i	−0.991585	−	0.129455i	$-0.958677\pi$
$991$		−	8077.18i		−	0.258910i	0.991585	−	0.129455i	$-0.0413228\pi$
$992$		−	22137.7i		−	0.708541i
$993$	3850.83	+	2510.96i	0.123064	+	0.0802445i
$994$			77156.3i			2.46202i
$995$			19933.9i			0.635123i
$996$	−48182.7	−	31417.8i	−1.53286	−	0.999510i
$997$	28050.2			0.891031			0.445515	−	0.895274i	$-0.353020\pi$
$997$	28050.2			0.891031			0.445515	+	0.895274i	$0.353020\pi$
$998$	61492.1			1.95040
$999$	−14678.4	−	2408.91i	−0.464869	−	0.0762909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.d.c.176.4	yes	52
3.2	odd	2	inner	177.4.d.c.176.49	yes	52
59.58	odd	2	inner	177.4.d.c.176.50	yes	52
177.176	even	2	inner	177.4.d.c.176.3	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.d.c.176.3	✓	52	177.176	even	2	inner
177.4.d.c.176.4	yes	52	1.1	even	1	trivial
177.4.d.c.176.49	yes	52	3.2	odd	2	inner
177.4.d.c.176.50	yes	52	59.58	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.02351 q^{2} +(4.35259 + 2.83813i) q^{3} +17.2357 q^{4} -15.7890i q^{5} +(-21.8653 - 14.2574i) q^{6} -18.9623 q^{7} -46.3956 q^{8} +(10.8900 + 24.7064i) q^{9} +O(q^{10})\)	\(q-5.02351 q^{2} +(4.35259 + 2.83813i) q^{3} +17.2357 q^{4} -15.7890i q^{5} +(-21.8653 - 14.2574i) q^{6} -18.9623 q^{7} -46.3956 q^{8} +(10.8900 + 24.7064i) q^{9} +79.3161i q^{10} -36.5750 q^{11} +(75.0198 + 48.9172i) q^{12} +4.20455i q^{13} +95.2574 q^{14} +(44.8112 - 68.7228i) q^{15} +95.1835 q^{16} +97.3906i q^{17} +(-54.7061 - 124.113i) q^{18} -44.1528 q^{19} -272.134i q^{20} +(-82.5351 - 53.8175i) q^{21} +183.735 q^{22} +190.656 q^{23} +(-201.941 - 131.677i) q^{24} -124.291 q^{25} -21.1216i q^{26} +(-22.7204 + 138.444i) q^{27} -326.828 q^{28} +131.011i q^{29} +(-225.110 + 345.230i) q^{30} +206.913i q^{31} -106.991 q^{32} +(-159.196 - 103.805i) q^{33} -489.243i q^{34} +299.395i q^{35} +(187.697 + 425.832i) q^{36} +106.024i q^{37} +221.802 q^{38} +(-11.9331 + 18.3006i) q^{39} +732.539i q^{40} +214.440i q^{41} +(414.616 + 270.353i) q^{42} +213.227i q^{43} -630.396 q^{44} +(390.089 - 171.942i) q^{45} -957.762 q^{46} -444.240 q^{47} +(414.294 + 270.143i) q^{48} +16.5690 q^{49} +624.380 q^{50} +(-276.407 + 423.901i) q^{51} +72.4682i q^{52} -624.911i q^{53} +(114.136 - 695.476i) q^{54} +577.482i q^{55} +879.768 q^{56} +(-192.179 - 125.312i) q^{57} -658.135i q^{58} +(-389.685 - 231.353i) q^{59} +(772.352 - 1184.49i) q^{60} +437.873i q^{61} -1039.43i q^{62} +(-206.500 - 468.491i) q^{63} -223.999 q^{64} +66.3854 q^{65} +(799.723 + 521.465i) q^{66} -648.388i q^{67} +1678.59i q^{68} +(829.846 + 541.106i) q^{69} -1504.02i q^{70} +809.977i q^{71} +(-505.248 - 1146.27i) q^{72} -39.3227i q^{73} -532.613i q^{74} +(-540.989 - 352.756i) q^{75} -761.005 q^{76} +693.547 q^{77} +(59.9459 - 91.9335i) q^{78} +595.268 q^{79} -1502.85i q^{80} +(-491.816 + 538.106i) q^{81} -1077.24i q^{82} -642.266 q^{83} +(-1422.55 - 927.582i) q^{84} +1537.70 q^{85} -1071.15i q^{86} +(-371.826 + 570.236i) q^{87} +1696.92 q^{88} -258.723 q^{89} +(-1959.62 + 863.753i) q^{90} -79.7279i q^{91} +3286.08 q^{92} +(-587.246 + 900.605i) q^{93} +2231.65 q^{94} +697.128i q^{95} +(-465.685 - 303.653i) q^{96} +1812.27i q^{97} -83.2344 q^{98} +(-398.302 - 903.639i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9}+O(q^{10}) \) 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9	\( 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9} + 28 q^{12} + 114 q^{15} + 484 q^{16} - 184 q^{19} - 758 q^{21} - 60 q^{22} + 36 q^{25} + 742 q^{27} - 4 q^{28} - 888 q^{36} + 1402 q^{45} - 660 q^{46} - 488 q^{48} - 924 q^{49} - 1772 q^{51} - 630 q^{57} - 1880 q^{60} - 212 q^{63} + 7648 q^{64} + 1316 q^{66} - 1556 q^{75} - 5680 q^{76} + 3224 q^{78} - 1504 q^{79} - 276 q^{81} + 1228 q^{84} - 848 q^{85} + 3598 q^{87} + 5760 q^{88} + 888 q^{94}+O(q^{100}) \) 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9 + 28 * q^12 + 114 * q^15 + 484 * q^16 - 184 * q^19 - 758 * q^21 - 60 * q^22 + 36 * q^25 + 742 * q^27 - 4 * q^28 - 888 * q^36 + 1402 * q^45 - 660 * q^46 - 488 * q^48 - 924 * q^49 - 1772 * q^51 - 630 * q^57 - 1880 * q^60 - 212 * q^63 + 7648 * q^64 + 1316 * q^66 - 1556 * q^75 - 5680 * q^76 + 3224 * q^78 - 1504 * q^79 - 276 * q^81 + 1228 * q^84 - 848 * q^85 + 3598 * q^87 + 5760 * q^88 + 888 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more