LMFDB - Embedded newform 171.4.f.h.163.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,4,Mod(64,171)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("171.64");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	171.f (of order $3$, degree $2$, 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:	$10.0893266110$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 50x^{10} + 1797x^{8} + 29198x^{6} + 345409x^{4} + 2092128x^{2} + 8856576 $ x^12 + 50x^10 + 1797x^8 + 29198x^6 + 345409x^4 + 2092128*x^2 + 8856576
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.5
Root			$1.71809 - 2.97581i$ of defining polynomial
Character	$\chi$	$=$	171.163
Dual form			171.4.f.h.64.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71809 - 2.97581i) q^{2} +(-1.90364 - 3.29720i) q^{4} +(-6.83777 + 11.8434i) q^{5} -20.1525 q^{7} +14.4069 q^{8} +O(q^{10})$	\(q+(1.71809 - 2.97581i) q^{2} +(-1.90364 - 3.29720i) q^{4} +(-6.83777 + 11.8434i) q^{5} -20.1525 q^{7} +14.4069 q^{8} +(23.4957 + 40.6958i) q^{10} -48.0372 q^{11} +(34.8452 + 60.3537i) q^{13} +(-34.6237 + 59.9700i) q^{14} +(39.9814 - 69.2499i) q^{16} +(-58.9388 + 102.085i) q^{17} +(36.1083 + 74.5331i) q^{19} +52.0665 q^{20} +(-82.5321 + 142.950i) q^{22} +(-35.0585 - 60.7232i) q^{23} +(-31.0101 - 53.7110i) q^{25} +239.468 q^{26} +(38.3630 + 66.4467i) q^{28} +(-102.739 - 177.950i) q^{29} +264.207 q^{31} +(-79.7553 - 138.140i) q^{32} +(202.524 + 350.782i) q^{34} +(137.798 - 238.673i) q^{35} -385.101 q^{37} +(283.834 + 20.6027i) q^{38} +(-98.5112 + 170.626i) q^{40} +(-60.4708 + 104.738i) q^{41} +(156.011 - 270.219i) q^{43} +(91.4455 + 158.388i) q^{44} -240.934 q^{46} +(-57.5452 - 99.6712i) q^{47} +63.1222 q^{49} -213.112 q^{50} +(132.665 - 229.783i) q^{52} +(186.926 + 323.765i) q^{53} +(328.467 - 568.922i) q^{55} -290.335 q^{56} -706.060 q^{58} +(-131.683 + 228.082i) q^{59} +(143.638 + 248.788i) q^{61} +(453.930 - 786.229i) q^{62} +91.5968 q^{64} -953.053 q^{65} +(240.819 + 417.111i) q^{67} +448.793 q^{68} +(-473.497 - 820.121i) q^{70} +(17.3485 - 30.0484i) q^{71} +(352.438 - 610.440i) q^{73} +(-661.636 + 1145.99i) q^{74} +(177.013 - 260.940i) q^{76} +968.069 q^{77} +(-293.959 + 509.153i) q^{79} +(546.767 + 947.029i) q^{80} +(207.788 + 359.899i) q^{82} -898.559 q^{83} +(-806.020 - 1396.07i) q^{85} +(-536.081 - 928.520i) q^{86} -692.069 q^{88} +(100.471 + 174.020i) q^{89} +(-702.217 - 1216.28i) q^{91} +(-133.477 + 231.190i) q^{92} -395.470 q^{94} +(-1129.62 - 81.9960i) q^{95} +(-7.68349 + 13.3082i) q^{97} +(108.449 - 187.840i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 52 q^{4} - 60 q^{7}+O(q^{10}) $ 12 * q - 52 * q^4 - 60 * q^7	$ 12 q - 52 q^{4} - 60 q^{7} - 56 q^{10} + 178 q^{13} - 172 q^{16} + 296 q^{19} - 944 q^{22} - 458 q^{25} - 140 q^{28} + 196 q^{31} - 400 q^{34} + 628 q^{37} + 48 q^{40} + 642 q^{43} - 960 q^{46} - 2296 q^{49} - 300 q^{52} + 648 q^{55} - 2880 q^{58} + 3446 q^{61} + 9528 q^{64} + 2730 q^{67} - 1920 q^{70} + 1690 q^{73} - 4308 q^{76} - 2898 q^{79} - 1616 q^{82} - 4176 q^{85} + 11856 q^{88} - 3210 q^{91} - 5280 q^{94} - 1180 q^{97}+O(q^{100}) $ 12 * q - 52 * q^4 - 60 * q^7 - 56 * q^10 + 178 * q^13 - 172 * q^16 + 296 * q^19 - 944 * q^22 - 458 * q^25 - 140 * q^28 + 196 * q^31 - 400 * q^34 + 628 * q^37 + 48 * q^40 + 642 * q^43 - 960 * q^46 - 2296 * q^49 - 300 * q^52 + 648 * q^55 - 2880 * q^58 + 3446 * q^61 + 9528 * q^64 + 2730 * q^67 - 1920 * q^70 + 1690 * q^73 - 4308 * q^76 - 2898 * q^79 - 1616 * q^82 - 4176 * q^85 + 11856 * q^88 - 3210 * q^91 - 5280 * q^94 - 1180 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.71809	−	2.97581i	0.607435	−	1.05211i	−0.384227	−	0.923239i	$-0.625532\pi$
$2$	1.71809	−	2.97581i	0.607435	−	1.05211i	0.991662	−	0.128869i	$-0.0411348\pi$
$3$		0			0
$3$		0			0
$4$	−1.90364	−	3.29720i	−0.237955	−	0.412150i
$5$	−6.83777	+	11.8434i	−0.611588	+	1.05930i	0.379384	+	0.925239i	$0.376136\pi$
$5$	−6.83777	+	11.8434i	−0.611588	+	1.05930i	−0.990973	+	0.134063i	$0.957198\pi$
$6$		0			0
$7$	−20.1525			−1.08813			−0.544066	−	0.839043i	$-0.683116\pi$
$7$	−20.1525			−1.08813			−0.544066	+	0.839043i	$0.683116\pi$
$8$	14.4069			0.636702
$9$		0			0
$10$	23.4957	+	40.6958i	0.743000	+	1.28691i
$11$	−48.0372			−1.31671			−0.658353	−	0.752709i	$-0.728747\pi$
$11$	−48.0372			−1.31671			−0.658353	+	0.752709i	$0.728747\pi$
$12$		0			0
$13$	34.8452	+	60.3537i	0.743409	+	1.28762i	0.950934	+	0.309393i	$0.100126\pi$
$13$	34.8452	+	60.3537i	0.743409	+	1.28762i	−0.207525	+	0.978230i	$0.566541\pi$
$14$	−34.6237	+	59.9700i	−0.660969	+	1.14483i
$15$		0			0
$16$	39.9814	−	69.2499i	0.624710	−	1.08203i
$17$	−58.9388	+	102.085i	−0.840869	+	1.45643i	0.0482923	+	0.998833i	$0.484622\pi$
$17$	−58.9388	+	102.085i	−0.840869	+	1.45643i	−0.889161	+	0.457594i	$0.848711\pi$
$18$		0			0
$19$	36.1083	+	74.5331i	0.435991	+	0.899951i
$19$	36.1083	+	74.5331i	0.435991	+	0.899951i
$20$	52.0665			0.582121
$21$		0			0
$22$	−82.5321	+	142.950i	−0.799814	+	1.38532i
$23$	−35.0585	−	60.7232i	−0.317835	−	0.550507i	0.662201	−	0.749326i	$-0.269623\pi$
$23$	−35.0585	−	60.7232i	−0.317835	−	0.550507i	−0.980036	+	0.198820i	$0.936289\pi$
$24$		0			0
$25$	−31.0101	−	53.7110i	−0.248081	−	0.429688i
$26$	239.468			1.80629
$27$		0			0
$28$	38.3630	+	66.4467i	0.258926	+	0.448473i
$29$	−102.739	−	177.950i	−0.657870	−	1.13946i	−0.981166	−	0.193166i	$-0.938124\pi$
$29$	−102.739	−	177.950i	−0.657870	−	1.13946i	0.323296	−	0.946298i	$-0.395209\pi$
$30$		0			0
$31$	264.207			1.53074			0.765370	−	0.643591i	$-0.222556\pi$
$31$	264.207			1.53074			0.765370	+	0.643591i	$0.222556\pi$
$32$	−79.7553	−	138.140i	−0.440590	−	0.763125i
$33$		0			0
$34$	202.524	+	350.782i	1.02155	+	1.76937i
$35$	137.798	−	238.673i	0.665488	−	1.15266i
$36$		0			0
$37$	−385.101			−1.71108			−0.855542	−	0.517733i	$-0.826776\pi$
$37$	−385.101			−1.71108			−0.855542	+	0.517733i	$0.826776\pi$
$38$	283.834	+	20.6027i	1.21168	+	0.0879525i
$39$		0			0
$40$	−98.5112	+	170.626i	−0.389400	+	0.674460i
$41$	−60.4708	+	104.738i	−0.230340	+	0.398961i	−0.957908	−	0.287075i	$-0.907317\pi$
$41$	−60.4708	+	104.738i	−0.230340	+	0.398961i	0.727568	+	0.686036i	$0.240651\pi$
$42$		0			0
$43$	156.011	−	270.219i	0.553290	−	0.958327i	−0.444744	−	0.895658i	$-0.646705\pi$
$43$	156.011	−	270.219i	0.553290	−	0.958327i	0.998034	−	0.0626691i	$-0.0199613\pi$
$44$	91.4455	+	158.388i	0.313317	+	0.542680i
$45$		0			0
$46$	−240.934			−0.772257
$47$	−57.5452	−	99.6712i	−0.178592	−	0.309331i	0.762806	−	0.646627i	$-0.223821\pi$
$47$	−57.5452	−	99.6712i	−0.178592	−	0.309331i	−0.941399	+	0.337296i	$0.890488\pi$
$48$		0			0
$49$	63.1222			0.184030
$50$	−213.112			−0.602772
$51$		0			0
$52$	132.665	−	229.783i	0.353795	−	0.612792i
$53$	186.926	+	323.765i	0.484457	+	0.839104i	0.999841	−	0.0178557i	$-0.00568394\pi$
$53$	186.926	+	323.765i	0.484457	+	0.839104i	−0.515384	+	0.856960i	$0.672351\pi$
$54$		0			0
$55$	328.467	−	568.922i	0.805283	−	1.39479i
$56$	−290.335			−0.692816
$57$		0			0
$58$	−706.060			−1.59845
$59$	−131.683	+	228.082i	−0.290572	+	0.503285i	−0.973945	−	0.226784i	$-0.927179\pi$
$59$	−131.683	+	228.082i	−0.290572	+	0.503285i	0.683373	+	0.730069i	$0.260512\pi$
$60$		0			0
$61$	143.638	+	248.788i	0.301491	+	0.522197i	0.976474	−	0.215636i	$-0.0691824\pi$
$61$	143.638	+	248.788i	0.301491	+	0.522197i	−0.674983	+	0.737833i	$0.735849\pi$
$62$	453.930	−	786.229i	0.929825	−	1.61050i
$63$		0			0
$64$	91.5968			0.178900
$65$	−953.053			−1.81864
$66$		0			0
$67$	240.819	+	417.111i	0.439116	+	0.760571i	0.997622	−	0.0689299i	$-0.0219585\pi$
$67$	240.819	+	417.111i	0.439116	+	0.760571i	−0.558506	+	0.829501i	$0.688625\pi$
$68$	448.793			0.800355
$69$		0			0
$70$	−473.497	−	820.121i	−0.808482	−	1.40033i
$71$	17.3485	−	30.0484i	0.0289984	−	0.0502267i	−0.851162	−	0.524903i	$-0.824102\pi$
$71$	17.3485	−	30.0484i	0.0289984	−	0.0502267i	0.880160	+	0.474676i	$0.157435\pi$
$72$		0			0
$73$	352.438	−	610.440i	0.565065	−	0.978721i	−0.431979	−	0.901884i	$-0.642184\pi$
$73$	352.438	−	610.440i	0.565065	−	0.978721i	0.997044	−	0.0768374i	$-0.0244822\pi$
$74$	−661.636	+	1145.99i	−1.03937	+	1.80025i
$75$		0			0
$76$	177.013	−	260.940i	0.267168	−	0.393841i
$77$	968.069			1.43275
$78$		0			0
$79$	−293.959	+	509.153i	−0.418646	+	0.725116i	−0.995804	−	0.0915170i	$-0.970828\pi$
$79$	−293.959	+	509.153i	−0.418646	+	0.725116i	0.577158	+	0.816633i	$0.304162\pi$
$80$	546.767	+	947.029i	0.764131	+	1.32351i
$81$		0			0
$82$	207.788	+	359.899i	0.279833	+	0.484686i
$83$	−898.559			−1.18831			−0.594154	−	0.804351i	$-0.702513\pi$
$83$	−898.559			−1.18831			−0.594154	+	0.804351i	$0.702513\pi$
$84$		0			0
$85$	−806.020	−	1396.07i	−1.02853	−	1.78147i
$86$	−536.081	−	928.520i	−0.672176	−	1.16424i
$87$		0			0
$88$	−692.069			−0.838350
$89$	100.471	+	174.020i	0.119662	+	0.207260i	0.919634	−	0.392777i	$-0.128486\pi$
$89$	100.471	+	174.020i	0.119662	+	0.207260i	−0.799972	+	0.600037i	$0.795152\pi$
$90$		0			0
$91$	−702.217	−	1216.28i	−0.808927	−	1.40110i
$92$	−133.477	+	231.190i	−0.151261	+	0.261991i
$93$		0			0
$94$	−395.470			−0.433933
$95$	−1129.62	−	81.9960i	−1.21997	−	0.0885538i
$96$		0			0
$97$	−7.68349	+	13.3082i	−0.00804269	+	0.0139303i	−0.870019	−	0.493019i	$-0.835893\pi$
$97$	−7.68349	+	13.3082i	−0.00804269	+	0.0139303i	0.861976	+	0.506949i	$0.169227\pi$
$98$	108.449	−	187.840i	0.111786	−	0.193619i
$99$		0			0
$100$	−118.064	+	204.493i	−0.118064	+	0.204493i
$101$	150.572	+	260.798i	0.148341	+	0.256935i	0.930615	−	0.366001i	$-0.119273\pi$
$101$	150.572	+	260.798i	0.148341	+	0.256935i	−0.782273	+	0.622935i	$0.785940\pi$
$102$		0			0
$103$	899.433			0.860425			0.430212	−	0.902728i	$-0.358439\pi$
$103$	899.433			0.860425			0.430212	+	0.902728i	$0.358439\pi$
$104$	502.012	+	869.511i	0.473330	+	0.819832i
$105$		0			0
$106$	1284.62			1.17710
$107$	1137.79			1.02798			0.513991	−	0.857796i	$-0.328167\pi$
$107$	1137.79			1.02798			0.513991	+	0.857796i	$0.328167\pi$
$108$		0			0
$109$	124.787	−	216.138i	0.109655	−	0.189929i	−0.805975	−	0.591949i	$-0.798359\pi$
$109$	124.787	−	216.138i	0.109655	−	0.189929i	0.915631	+	0.402020i	$0.131692\pi$
$110$	−1128.67	−	1954.91i	−0.978314	−	1.69449i
$111$		0			0
$112$	−805.725	+	1395.56i	−0.679766	+	1.17739i
$113$	1120.78			0.933043			0.466521	−	0.884510i	$-0.345507\pi$
$113$	1120.78			0.933043			0.466521	+	0.884510i	$0.345507\pi$
$114$		0			0
$115$	958.888			0.777537
$116$	−391.157	+	677.504i	−0.313086	+	0.542281i
$117$		0			0
$118$	452.487	+	783.730i	0.353007	+	0.611426i
$119$	1187.76	−	2057.27i	0.914976	−	1.58478i
$120$		0			0
$121$	976.577			0.733717
$122$	987.128			0.732544
$123$		0			0
$124$	−502.954	−	871.141i	−0.364246	−	0.630893i
$125$	−861.283			−0.616284
$126$		0			0
$127$	759.128	+	1314.85i	0.530407	+	0.918693i	0.999371	+	0.0354749i	$0.0112944\pi$
$127$	759.128	+	1314.85i	0.530407	+	0.918693i	−0.468963	+	0.883218i	$0.655372\pi$
$128$	795.414	−	1377.70i	0.549260	−	0.951347i
$129$		0			0
$130$	−1637.43	+	2836.11i	−1.10471	+	1.91341i
$131$	140.689	−	243.681i	0.0938325	−	0.162523i	−0.815288	−	0.579055i	$-0.803422\pi$
$131$	140.689	−	243.681i	0.0938325	−	0.162523i	0.909121	+	0.416533i	$0.136755\pi$
$132$		0			0
$133$	−727.673	−	1502.03i	−0.474415	−	0.979265i
$134$	1654.99			1.06694
$135$		0			0
$136$	−849.127	+	1470.73i	−0.535383	+	0.927310i
$137$	1296.76	+	2246.05i	0.808681	+	1.40068i	0.913778	+	0.406215i	$0.133152\pi$
$137$	1296.76	+	2246.05i	0.808681	+	1.40068i	−0.105096	+	0.994462i	$0.533515\pi$
$138$		0			0
$139$	−229.801	−	398.026i	−0.140226	−	0.242879i	0.787356	−	0.616499i	$-0.211450\pi$
$139$	−229.801	−	398.026i	−0.140226	−	0.242879i	−0.927582	+	0.373620i	$0.878116\pi$
$140$	−1049.27			−0.633424
$141$		0			0
$142$	−59.6123	−	103.252i	−0.0352293	−	0.0610189i
$143$	−1673.87	−	2899.22i	−0.978852	−	1.69542i
$144$		0			0
$145$	2810.03			1.60938
$146$	−1211.04	−	2097.58i	−0.686481	−	1.18902i
$147$		0			0
$148$	733.092	+	1269.75i	0.407161	+	0.705223i
$149$	850.942	−	1473.87i	0.467865	−	0.810366i	−0.531461	−	0.847083i	$-0.678357\pi$
$149$	850.942	−	1473.87i	0.467865	−	0.810366i	0.999326	+	0.0367172i	$0.0116901\pi$
$150$		0			0
$151$	2188.78			1.17960			0.589802	−	0.807548i	$-0.299206\pi$
$151$	2188.78			1.17960			0.589802	+	0.807548i	$0.299206\pi$
$152$	520.210	+	1073.79i	0.277596	+	0.573001i
$153$		0			0
$154$	1663.23	−	2880.79i	0.870303	−	1.50741i
$155$	−1806.58	+	3129.09i	−0.936182	+	1.62152i
$156$		0			0
$157$	−1382.74	+	2394.98i	−0.702896	+	1.21745i	0.264549	+	0.964372i	$0.414777\pi$
$157$	−1382.74	+	2394.98i	−0.702896	+	1.21745i	−0.967445	+	0.253080i	$0.918557\pi$
$158$	1010.09	+	1749.54i	0.508600	+	0.880921i
$159$		0			0
$160$	2181.39			1.07784
$161$	706.516	+	1223.72i	0.345846	+	0.599024i
$162$		0			0
$163$	−3536.25			−1.69927			−0.849634	−	0.527372i	$-0.823177\pi$
$163$	−3536.25			−1.69927			−0.849634	+	0.527372i	$0.823177\pi$
$164$	460.458			0.219242
$165$		0			0
$166$	−1543.80	+	2673.94i	−0.721820	+	1.25023i
$167$	867.367	+	1502.32i	0.401909	+	0.696128i	0.993956	−	0.109776i	$-0.0350133\pi$
$167$	867.367	+	1502.32i	0.401909	+	0.696128i	−0.592047	+	0.805904i	$0.701680\pi$
$168$		0			0
$169$	−1329.88	+	2303.41i	−0.605315	+	1.04844i
$170$	−5539.25			−2.49906
$171$		0			0
$172$	−1187.95			−0.526632
$173$	−1761.89	+	3051.68i	−0.774300	+	1.34113i	0.160887	+	0.986973i	$0.448565\pi$
$173$	−1761.89	+	3051.68i	−0.774300	+	1.34113i	−0.935187	+	0.354154i	$0.884769\pi$
$174$		0			0
$175$	624.930	+	1082.41i	0.269944	+	0.467557i
$176$	−1920.60	+	3326.57i	−0.822560	+	1.42472i
$177$		0			0
$178$	690.470			0.290747
$179$	2266.85			0.946548			0.473274	−	0.880915i	$-0.343072\pi$
$179$	2266.85			0.946548			0.473274	+	0.880915i	$0.343072\pi$
$180$		0			0
$181$	515.892	+	893.552i	0.211856	+	0.366946i	0.952295	−	0.305178i	$-0.0987158\pi$
$181$	515.892	+	893.552i	0.211856	+	0.366946i	−0.740439	+	0.672123i	$0.765382\pi$
$182$	−4825.88			−1.96548
$183$		0			0
$184$	−505.086	−	874.834i	−0.202366	−	0.350509i
$185$	2633.23	−	4560.88i	1.04648	−	1.81256i
$186$		0			0
$187$	2831.26	−	4903.89i	1.10718	−	1.91769i
$188$	−219.090	+	379.476i	−0.0849937	+	0.147213i
$189$		0			0
$190$	−2184.79	+	3220.67i	−0.834219	+	1.22975i
$191$	2219.24			0.840724			0.420362	−	0.907357i	$-0.361903\pi$
$191$	2219.24			0.840724			0.420362	+	0.907357i	$0.361903\pi$
$192$		0			0
$193$	630.182	−	1091.51i	0.235034	−	0.407090i	−0.724249	−	0.689539i	$-0.757813\pi$
$193$	630.182	−	1091.51i	0.235034	−	0.407090i	0.959282	+	0.282449i	$0.0911467\pi$
$194$	26.4018	+	45.7293i	0.00977082	+	0.0169236i
$195$		0			0
$196$	−120.162	−	208.126i	−0.0437908	−	0.0758478i
$197$	1094.89			0.395977			0.197989	−	0.980204i	$-0.436559\pi$
$197$	1094.89			0.395977			0.197989	+	0.980204i	$0.436559\pi$
$198$		0			0
$199$	137.527	+	238.203i	0.0489900	+	0.0848531i	0.889481	−	0.456973i	$-0.151066\pi$
$199$	137.527	+	238.203i	0.0489900	+	0.0848531i	−0.840491	+	0.541826i	$0.817733\pi$
$200$	−446.760	−	773.811i	−0.157953	−	0.273583i
$201$		0			0
$202$	1034.78			0.360431
$203$	2070.45	+	3586.13i	0.715849	+	1.23989i
$204$		0			0
$205$	−826.970	−	1432.35i	−0.281747	−	0.488000i
$206$	1545.30	−	2676.54i	0.522652	−	0.905260i
$207$		0			0
$208$	5572.64			1.85766
$209$	−1734.55	−	3580.37i	−0.574072	−	1.18497i
$210$		0			0
$211$	−45.3420	+	78.5347i	−0.0147937	+	0.0256235i	−0.873327	−	0.487134i	$-0.838042\pi$
$211$	−45.3420	+	78.5347i	−0.0147937	+	0.0256235i	0.858534	+	0.512757i	$0.171376\pi$
$212$	711.677	−	1232.66i	0.230558	−	0.399337i
$213$		0			0
$214$	1954.82	−	3385.84i	0.624432	−	1.08155i
$215$	2133.54	+	3695.39i	0.676772	+	1.17220i
$216$		0			0
$217$	−5324.42			−1.66565
$218$	−428.790	−	742.686i	−0.133217	−	0.230739i
$219$		0			0
$220$	−2501.13			−0.766483
$221$	−8214.94			−2.50044
$222$		0			0
$223$	112.273	−	194.462i	0.0337145	−	0.0583952i	−0.848676	−	0.528913i	$-0.822600\pi$
$223$	112.273	−	194.462i	0.0337145	−	0.0583952i	0.882390	+	0.470518i	$0.155933\pi$
$224$	1607.27	+	2783.87i	0.479420	+	0.830380i
$225$		0			0
$226$	1925.59	−	3335.22i	0.566763	−	0.981662i
$227$	3900.61			1.14050			0.570248	−	0.821473i	$-0.306847\pi$
$227$	3900.61			1.14050			0.570248	+	0.821473i	$0.306847\pi$
$228$		0			0
$229$	−4006.56			−1.15616			−0.578081	−	0.815980i	$-0.696198\pi$
$229$	−4006.56			−1.15616			−0.578081	+	0.815980i	$0.696198\pi$
$230$	1647.45	−	2853.47i	0.472303	−	0.818053i
$231$		0			0
$232$	−1480.16	−	2563.71i	−0.418867	−	0.725499i
$233$	2459.07	−	4259.23i	0.691411	−	1.19756i	−0.279964	−	0.960010i	$-0.590323\pi$
$233$	2459.07	−	4259.23i	0.691411	−	1.19756i	0.971375	−	0.237549i	$-0.0763441\pi$
$234$		0			0
$235$	1573.92			0.436900
$236$	1002.71			0.276572
$237$		0			0
$238$	−4081.36	−	7069.12i	−1.11158	−	1.92531i
$239$	−4492.23			−1.21581			−0.607904	−	0.794010i	$-0.707990\pi$
$239$	−4492.23			−1.21581			−0.607904	+	0.794010i	$0.707990\pi$
$240$		0			0
$241$	−740.199	−	1282.06i	−0.197844	−	0.342676i	0.749985	−	0.661455i	$-0.230061\pi$
$241$	−740.199	−	1282.06i	−0.197844	−	0.342676i	−0.947829	+	0.318779i	$0.896727\pi$
$242$	1677.84	−	2906.11i	0.445685	−	0.771950i
$243$		0			0
$244$	546.869	−	947.204i	0.143482	−	0.248519i
$245$	−431.615	+	747.579i	−0.112551	+	0.194943i
$246$		0			0
$247$	−3240.14	+	4776.39i	−0.834678	+	1.23042i
$248$	3806.40			0.974625
$249$		0			0
$250$	−1479.76	+	2563.02i	−0.374352	+	0.648397i
$251$	−1986.80	−	3441.23i	−0.499624	−	0.865374i	0.500376	−	0.865808i	$-0.333195\pi$
$251$	−1986.80	−	3441.23i	−0.499624	−	0.865374i	−1.00000		0.000434399i	$0.999862\pi$
$252$		0			0
$253$	1684.12	+	2916.97i	0.418496	+	0.724856i
$254$	5216.99			1.28875
$255$		0			0
$256$	−2366.79	−	4099.40i	−0.577830	−	1.00083i
$257$	−2446.19	−	4236.92i	−0.593731	−	1.02837i	−0.993725	−	0.111855i	$-0.964321\pi$
$257$	−2446.19	−	4236.92i	−0.593731	−	1.02837i	0.399993	−	0.916518i	$-0.369013\pi$
$258$		0			0
$259$	7760.73			1.86189
$260$	1814.27	+	3142.40i	0.432754	+	0.749552i
$261$		0			0
$262$	−483.432	−	837.328i	−0.113994	−	0.197444i
$263$	−1207.94	+	2092.21i	−0.283212	+	0.490537i	−0.972174	−	0.234260i	$-0.924733\pi$
$263$	−1207.94	+	2092.21i	−0.283212	+	0.490537i	0.688962	+	0.724797i	$0.258067\pi$
$264$		0			0
$265$	−5112.62			−1.18515
$266$	−5719.95	−	415.195i	−1.31847	−	0.0957038i
$267$		0			0
$268$	916.865	−	1588.06i	0.208979	−	0.361963i
$269$	−1435.35	+	2486.10i	−0.325334	+	0.563496i	−0.981580	−	0.191052i	$-0.938810\pi$
$269$	−1435.35	+	2486.10i	−0.325334	+	0.563496i	0.656246	+	0.754547i	$0.272144\pi$
$270$		0			0
$271$	−922.683	+	1598.13i	−0.206823	+	0.358228i	−0.950712	−	0.310075i	$-0.899646\pi$
$271$	−922.683	+	1598.13i	−0.206823	+	0.358228i	0.743889	+	0.668303i	$0.232979\pi$
$272$	4712.92	+	8163.01i	1.05060	+	1.81969i
$273$		0			0
$274$	8911.75			1.96489
$275$	1489.64	+	2580.13i	0.326649	+	0.565774i
$276$		0			0
$277$	5123.32			1.11130			0.555651	−	0.831416i	$-0.312469\pi$
$277$	5123.32			1.11130			0.555651	+	0.831416i	$0.312469\pi$
$278$	−1579.27			−0.340713
$279$		0			0
$280$	1985.24	−	3438.54i	0.423718	−	0.733901i
$281$	−728.024	−	1260.98i	−0.154556	−	0.267699i	0.778341	−	0.627842i	$-0.216061\pi$
$281$	−728.024	−	1260.98i	−0.154556	−	0.267699i	−0.932897	+	0.360142i	$0.882728\pi$
$282$		0			0
$283$	−399.107	+	691.274i	−0.0838320	+	0.145201i	−0.904893	−	0.425639i	$-0.860049\pi$
$283$	−399.107	+	691.274i	−0.0838320	+	0.145201i	0.821061	+	0.570841i	$0.193383\pi$
$284$	−132.101			−0.0276012
$285$		0			0
$286$	−11503.4			−2.37836
$287$	1218.64	−	2110.74i	0.250640	−	0.434122i
$288$		0			0
$289$	−4491.07	−	7778.77i	−0.914121	−	1.58330i
$290$	4827.87	−	8362.12i	0.977595	−	1.69324i
$291$		0			0
$292$	−2683.66			−0.537839
$293$	170.658			0.0340272			0.0170136	−	0.999855i	$-0.494584\pi$
$293$	170.658			0.0340272			0.0170136	+	0.999855i	$0.494584\pi$
$294$		0			0
$295$	−1800.84	−	3119.15i	−0.355420	−	0.615606i
$296$	−5548.11			−1.08945
$297$		0			0
$298$	−2923.98	−	5064.48i	−0.568395	−	0.984489i
$299$	2443.24	−	4231.82i	0.472563	−	0.818503i
$300$		0			0
$301$	−3144.01	+	5445.59i	−0.602052	+	1.04279i
$302$	3760.51	−	6513.40i	0.716533	−	1.24107i
$303$		0			0
$304$	6605.07	+	479.443i	1.24614	+	0.0904537i
$305$	−3928.65			−0.737553
$306$		0			0
$307$	−2699.49	+	4675.65i	−0.501850	+	0.869229i	0.498148	+	0.867092i	$0.334014\pi$
$307$	−2699.49	+	4675.65i	−0.501850	+	0.869229i	−0.999998	+	0.00213696i	$0.999320\pi$
$308$	−1842.85	−	3191.91i	−0.340930	−	0.590507i
$309$		0			0
$310$	6207.73	+	10752.1i	1.13734	+	1.96993i
$311$	−2039.15			−0.371799			−0.185899	−	0.982569i	$-0.559520\pi$
$311$	−2039.15			−0.371799			−0.185899	+	0.982569i	$0.559520\pi$
$312$		0			0
$313$	−2081.83	−	3605.83i	−0.375949	−	0.651162i	0.614520	−	0.788901i	$-0.289350\pi$
$313$	−2081.83	−	3605.83i	−0.375949	−	0.651162i	−0.990469	+	0.137739i	$0.956016\pi$
$314$	4751.33	+	8229.55i	0.853927	+	1.47905i
$315$		0			0
$316$	2238.37			0.398475
$317$	3184.80	+	5516.23i	0.564278	+	0.977358i	0.997116	+	0.0758865i	$0.0241787\pi$
$317$	3184.80	+	5516.23i	0.564278	+	0.977358i	−0.432839	+	0.901471i	$0.642488\pi$
$318$		0			0
$319$	4935.32	+	8548.22i	0.866222	+	1.50034i
$320$	−626.317	+	1084.81i	−0.109413	+	0.189509i
$321$		0			0
$322$	4855.42			0.840317
$323$	−9736.90	−	706.773i	−1.67732	−	0.121752i
$324$		0			0
$325$	2161.11	−	3743.14i	0.368851	−	0.638868i
$326$	−6075.59	+	10523.2i	−1.03220	+	1.78782i
$327$		0			0
$328$	−871.198	+	1508.96i	−0.146658	+	0.254019i
$329$	1159.68	+	2008.62i	0.194332	+	0.336592i
$330$		0			0
$331$	4136.21			0.686848			0.343424	−	0.939180i	$-0.388413\pi$
$331$	4136.21			0.686848			0.343424	+	0.939180i	$0.388413\pi$
$332$	1710.53	+	2962.72i	0.282764	+	0.489761i
$333$		0			0
$334$	5960.84			0.976536
$335$	−6586.66			−1.07423
$336$		0			0
$337$	−1545.96	+	2677.68i	−0.249892	+	0.432826i	−0.963496	−	0.267724i	$-0.913728\pi$
$337$	−1545.96	+	2677.68i	−0.249892	+	0.432826i	0.713604	+	0.700550i	$0.247062\pi$
$338$	4569.68	+	7914.92i	0.735378	+	1.27371i
$339$		0			0
$340$	−3068.74	+	5315.21i	−0.489488	+	0.847817i
$341$	−12691.8			−2.01553
$342$		0			0
$343$	5640.23			0.887883
$344$	2247.64	−	3893.03i	0.352281	−	0.610169i
$345$		0			0
$346$	6054.15	+	10486.1i	0.940674	+	1.62930i
$347$	−4129.64	+	7152.74i	−0.638877	+	1.10657i	0.346802	+	0.937938i	$0.387268\pi$
$347$	−4129.64	+	7152.74i	−0.638877	+	1.10657i	−0.985679	+	0.168630i	$0.946066\pi$
$348$		0			0
$349$	−12685.4			−1.94566			−0.972829	−	0.231525i	$-0.925628\pi$
$349$	−12685.4			−1.94566			−0.972829	+	0.231525i	$0.925628\pi$
$350$	4294.73			0.655895
$351$		0			0
$352$	3831.23	+	6635.88i	0.580128	+	1.00481i
$353$	10158.2			1.53163			0.765813	−	0.643064i	$-0.222337\pi$
$353$	10158.2			1.53163			0.765813	+	0.643064i	$0.222337\pi$
$354$		0			0
$355$	237.250	+	410.928i	0.0354701	+	0.0614361i
$356$	382.520	−	662.544i	0.0569481	−	0.0986369i
$357$		0			0
$358$	3894.64	−	6745.71i	0.574966	−	0.995871i
$359$	−2770.03	+	4797.83i	−0.407232	+	0.705347i	−0.994578	−	0.103989i	$-0.966839\pi$
$359$	−2770.03	+	4797.83i	−0.407232	+	0.705347i	0.587346	+	0.809336i	$0.300173\pi$
$360$		0			0
$361$	−4251.37	+	5382.54i	−0.619824	+	0.784741i
$362$	3545.39			0.514756
$363$		0			0
$364$	−2673.53	+	4630.69i	−0.384976	+	0.666798i
$365$	4819.78	+	8348.10i	0.691174	+	1.19715i
$366$		0			0
$367$	3060.24	+	5300.50i	0.435268	+	0.753907i	0.997317	−	0.0731971i	$-0.0233202\pi$
$367$	3060.24	+	5300.50i	0.435268	+	0.753907i	−0.562049	+	0.827104i	$0.689987\pi$
$368$	−5606.76			−0.794219
$369$		0			0
$370$	−9048.22	−	15672.0i	−1.27134	−	2.20202i
$371$	−3767.01	−	6524.66i	−0.527153	−	0.913055i
$372$		0			0
$373$	−528.331			−0.0733403			−0.0366702	−	0.999327i	$-0.511675\pi$
$373$	−528.331			−0.0733403			−0.0366702	+	0.999327i	$0.511675\pi$
$374$	−9728.69	−	16850.6i	−1.34508	−	2.32974i
$375$		0			0
$376$	−829.050	−	1435.96i	−0.113710	−	0.196952i
$377$	7159.95	−	12401.4i	0.978133	−	1.69418i
$378$		0			0
$379$	−3642.88			−0.493726			−0.246863	−	0.969050i	$-0.579400\pi$
$379$	−3642.88			−0.493726			−0.246863	+	0.969050i	$0.579400\pi$
$380$	1880.04	+	3880.68i	0.253799	+	0.523881i
$381$		0			0
$382$	3812.84	−	6604.03i	0.510685	−	0.884533i
$383$	−137.925	+	238.893i	−0.0184011	+	0.0318717i	−0.875079	−	0.483979i	$-0.839191\pi$
$383$	−137.925	+	238.893i	−0.0184011	+	0.0318717i	0.856678	+	0.515851i	$0.172524\pi$
$384$		0			0
$385$	−6619.43	+	11465.2i	−0.876253	+	1.51772i
$386$	−2165.41	−	3750.60i	−0.285535	−	0.494562i
$387$		0			0
$388$	58.5063			0.00765518
$389$	3120.51	+	5404.88i	0.406725	+	0.704469i	0.994521	−	0.104541i	$-0.0333373\pi$
$389$	3120.51	+	5404.88i	0.406725	+	0.704469i	−0.587795	+	0.809010i	$0.700004\pi$
$390$		0			0
$391$	8265.24			1.06903
$392$	909.397			0.117172
$393$		0			0
$394$	1881.11	−	3258.18i	0.240531	−	0.416611i
$395$	−4020.05	−	6962.93i	−0.512078	−	0.886945i
$396$		0			0
$397$	−5264.38	+	9118.17i	−0.665521	+	1.15272i	0.313623	+	0.949547i	$0.398457\pi$
$397$	−5264.38	+	9118.17i	−0.665521	+	1.15272i	−0.979144	+	0.203168i	$0.934876\pi$
$398$	945.130			0.119033
$399$		0			0
$400$	−4959.31			−0.619914
$401$	74.0088	−	128.187i	0.00921651	−	0.0159635i	−0.861380	−	0.507960i	$-0.830400\pi$
$401$	74.0088	−	128.187i	0.00921651	−	0.0159635i	0.870597	+	0.491997i	$0.163733\pi$
$402$		0			0
$403$	9206.33	+	15945.8i	1.13797	+	1.97101i
$404$	573.269	−	992.931i	0.0705970	−	0.122278i
$405$		0			0
$406$	14228.9			1.73933
$407$	18499.2			2.25300
$408$		0			0
$409$	−5886.65	−	10196.0i	−0.711677	−	1.23266i	−0.964227	−	0.265077i	$-0.914603\pi$
$409$	−5886.65	−	10196.0i	−0.711677	−	1.23266i	0.252550	−	0.967584i	$-0.418731\pi$
$410$	−5683.22			−0.684572
$411$		0			0
$412$	−1712.19	−	2965.61i	−0.204742	−	0.354624i
$413$	2653.75	−	4596.43i	0.316180	−	0.547640i
$414$		0			0
$415$	6144.13	−	10642.0i	0.726756	−	1.25878i
$416$	5558.18	−	9627.05i	0.655078	−	1.13463i
$417$		0			0
$418$	−13634.6	−	989.695i	−1.59543	−	0.115808i
$419$	14181.6			1.65350			0.826748	−	0.562572i	$-0.190188\pi$
$419$	14181.6			1.65350			0.826748	+	0.562572i	$0.190188\pi$
$420$		0			0
$421$	1297.61	−	2247.52i	0.150217	−	0.260184i	−0.781090	−	0.624419i	$-0.785336\pi$
$421$	1297.61	−	2247.52i	0.150217	−	0.260184i	0.931307	+	0.364234i	$0.118669\pi$
$422$	155.803	+	269.859i	0.0179724	+	0.0311292i
$423$		0			0
$424$	2693.02	+	4664.45i	0.308455	+	0.534259i
$425$	7310.79			0.834413
$426$		0			0
$427$	−2894.66	−	5013.69i	−0.328062	−	0.568219i
$428$	−2165.93	−	3751.51i	−0.244613	−	0.423682i
$429$		0			0
$430$	14662.4			1.64438
$431$	77.1243	+	133.583i	0.00861937	+	0.0149292i	0.870303	−	0.492517i	$-0.163923\pi$
$431$	77.1243	+	133.583i	0.00861937	+	0.0149292i	−0.861684	+	0.507446i	$0.830590\pi$
$432$		0			0
$433$	6168.73	+	10684.6i	0.684642	+	1.18584i	0.973549	+	0.228478i	$0.0733750\pi$
$433$	6168.73	+	10684.6i	0.684642	+	1.18584i	−0.288907	+	0.957357i	$0.593292\pi$
$434$	−9147.81	+	15844.5i	−1.01177	+	1.75244i
$435$		0			0
$436$	−950.198			−0.104372
$437$	3259.98	−	4805.63i	0.356856	−	0.526052i
$438$		0			0
$439$	6179.21	−	10702.7i	0.671795	−	1.16358i	−0.305600	−	0.952160i	$-0.598857\pi$
$439$	6179.21	−	10702.7i	0.671795	−	1.16358i	0.977395	−	0.211422i	$-0.0678096\pi$
$440$	4732.21	−	8196.42i	0.512725	−	0.888066i
$441$		0			0
$442$	−14114.0	+	24446.1i	−1.51885	+	2.63073i
$443$	−6098.89	−	10563.6i	−0.654102	−	1.13294i	−0.982118	−	0.188265i	$-0.939714\pi$
$443$	−6098.89	−	10563.6i	−0.654102	−	1.13294i	0.328017	−	0.944672i	$-0.393620\pi$
$444$		0			0
$445$	−2747.98			−0.292735
$446$	−385.788	−	668.204i	−0.0409587	−	0.0709425i
$447$		0			0
$448$	−1845.90			−0.194667
$449$	−296.946			−0.0312111			−0.0156055	−	0.999878i	$-0.504968\pi$
$449$	−296.946			−0.0312111			−0.0156055	+	0.999878i	$0.504968\pi$
$450$		0			0
$451$	2904.85	−	5031.35i	0.303291	−	0.525315i
$452$	−2133.55	−	3695.42i	−0.222022	−	0.384553i
$453$		0			0
$454$	6701.58	−	11607.5i	0.692777	−	1.19992i
$455$	19206.4			1.97892
$456$		0			0
$457$	−11551.4			−1.18239			−0.591194	−	0.806530i	$-0.701343\pi$
$457$	−11551.4			−1.18239			−0.591194	+	0.806530i	$0.701343\pi$
$458$	−6883.61	+	11922.8i	−0.702293	+	1.21641i
$459$		0			0
$460$	−1825.38	−	3161.64i	−0.185019	−	0.320462i
$461$	−7182.15	+	12439.9i	−0.725610	+	1.25679i	0.233113	+	0.972450i	$0.425109\pi$
$461$	−7182.15	+	12439.9i	−0.725610	+	1.25679i	−0.958722	+	0.284343i	$0.908224\pi$
$462$		0			0
$463$	6329.23			0.635300			0.317650	−	0.948208i	$-0.397106\pi$
$463$	6329.23			0.635300			0.317650	+	0.948208i	$0.397106\pi$
$464$	−16430.7			−1.64391
$465$		0			0
$466$	−8449.78	−	14635.4i	−0.839975	−	1.45488i
$467$	−4857.69			−0.481343			−0.240671	−	0.970607i	$-0.577368\pi$
$467$	−4857.69			−0.481343			−0.240671	+	0.970607i	$0.577368\pi$
$468$		0			0
$469$	−4853.10	−	8405.82i	−0.477816	−	0.827601i
$470$	2704.13	−	4683.70i	0.265388	−	0.459666i
$471$		0			0
$472$	−1897.15	+	3285.97i	−0.185008	+	0.320443i
$473$	−7494.35	+	12980.6i	−0.728521	+	1.26184i
$474$		0			0
$475$	2883.53	−	4250.70i	0.278538	−	0.410601i
$476$	−9044.28			−0.870891
$477$		0			0
$478$	−7718.04	+	13368.0i	−0.738525	+	1.27916i
$479$	−3942.68	−	6828.91i	−0.376086	−	0.651401i	0.614403	−	0.788993i	$-0.289397\pi$
$479$	−3942.68	−	6828.91i	−0.376086	−	0.651401i	−0.990489	+	0.137592i	$0.956064\pi$
$480$		0			0
$481$	−13418.9	−	23242.2i	−1.27204	−	2.20323i
$482$	−5086.90			−0.480710
$483$		0			0
$484$	−1859.05	−	3219.97i	−0.174591	−	0.302401i
$485$	−105.076	−	181.997i	−0.00983763	−	0.0170393i
$486$		0			0
$487$	−6718.11			−0.625106			−0.312553	−	0.949900i	$-0.601184\pi$
$487$	−6718.11			−0.625106			−0.312553	+	0.949900i	$0.601184\pi$
$488$	2069.38	+	3584.27i	0.191960	+	0.332484i
$489$		0			0
$490$	1483.10	+	2568.81i	0.136734	+	0.236831i
$491$	1291.08	−	2236.21i	0.118667	−	0.205537i	−0.800573	−	0.599236i	$-0.795471\pi$
$491$	1291.08	−	2236.21i	0.118667	−	0.205537i	0.919240	+	0.393698i	$0.128805\pi$
$492$		0			0
$493$	24221.4			2.21273
$494$	8646.80	+	17848.3i	0.787526	+	1.62557i
$495$		0			0
$496$	10563.4	−	18296.3i	0.956268	−	1.65630i
$497$	−349.615	+	605.550i	−0.0315540	+	0.0546532i
$498$		0			0
$499$	9391.32	−	16266.2i	0.842511	−	1.45927i	−0.0452537	−	0.998976i	$-0.514410\pi$
$499$	9391.32	−	16266.2i	0.842511	−	1.45927i	0.887765	−	0.460297i	$-0.152257\pi$
$500$	1639.57	+	2839.82i	0.146648	+	0.254001i
$501$		0			0
$502$	−13654.0			−1.21396
$503$	−2427.45	−	4204.46i	−0.215178	−	0.372699i	0.738150	−	0.674637i	$-0.235700\pi$
$503$	−2427.45	−	4204.46i	−0.215178	−	0.372699i	−0.953328	+	0.301938i	$0.902367\pi$
$504$		0			0
$505$	−4118.30			−0.362895
$506$	11573.8			1.01684
$507$		0			0
$508$	2890.21	−	5005.99i	0.252426	−	0.437214i
$509$	901.675	+	1561.75i	0.0785187	+	0.135998i	0.902611	−	0.430457i	$-0.141648\pi$
$509$	901.675	+	1561.75i	0.0785187	+	0.135998i	−0.824092	+	0.566456i	$0.808314\pi$
$510$		0			0
$511$	−7102.50	+	12301.9i	−0.614865	+	1.06498i
$512$	−3538.78			−0.305456
$513$		0			0
$514$	−16811.0			−1.44261
$515$	−6150.11	+	10652.3i	−0.526226	+	0.911450i
$516$		0			0
$517$	2764.31	+	4787.93i	0.235154	+	0.407298i
$518$	13333.6	−	23094.5i	1.13097	−	1.95890i
$519$		0			0
$520$	−13730.6			−1.15793
$521$	−3359.86			−0.282530			−0.141265	−	0.989972i	$-0.545117\pi$
$521$	−3359.86			−0.282530			−0.141265	+	0.989972i	$0.545117\pi$
$522$		0			0
$523$	−4378.41	−	7583.62i	−0.366070	−	0.634051i	0.622878	−	0.782319i	$-0.285963\pi$
$523$	−4378.41	−	7583.62i	−0.366070	−	0.634051i	−0.988947	+	0.148268i	$0.952630\pi$
$524$	−1071.28			−0.0893115
$525$		0			0
$526$	4150.69	+	7189.20i	0.344066	+	0.595939i
$527$	−15572.0	+	26971.6i	−1.28715	+	2.22941i
$528$		0			0
$529$	3625.30	−	6279.20i	0.297962	−	0.516085i
$530$	−8783.91	+	15214.2i	−0.719903	+	1.24691i
$531$		0			0
$532$	−3567.25	+	5258.59i	−0.290714	+	0.428551i
$533$	−8428.47			−0.684948
$534$		0			0
$535$	−7779.92	+	13475.2i	−0.628702	+	1.08894i
$536$	3469.46	+	6009.29i	0.279586	+	0.484257i
$537$		0			0
$538$	4932.11	+	8542.67i	0.395239	+	0.684574i
$539$	−3032.22			−0.242313
$540$		0			0
$541$	−6221.44	−	10775.9i	−0.494419	−	0.856359i	0.505560	−	0.862791i	$-0.331286\pi$
$541$	−6221.44	−	10775.9i	−0.494419	−	0.856359i	−0.999979	+	0.00643258i	$0.997952\pi$
$542$	3170.50	+	5491.46i	0.251263	+	0.435200i
$543$		0			0
$544$	18802.8			1.48191
$545$	1706.53	+	2955.80i	0.134128	+	0.232316i
$546$		0			0
$547$	−4266.57	−	7389.92i	−0.333502	−	0.577642i	0.649694	−	0.760196i	$-0.274897\pi$
$547$	−4266.57	−	7389.92i	−0.333502	−	0.577642i	−0.983196	+	0.182554i	$0.941564\pi$
$548$	4937.10	−	8551.32i	0.384859	−	0.666595i
$549$		0			0
$550$	10237.3			0.793673
$551$	9553.41	−	14083.0i	0.738637	−	1.08885i
$552$		0			0
$553$	5924.01	−	10260.7i	0.455542	−	0.789021i
$554$	8802.30	−	15246.0i	0.675043	−	1.16921i
$555$		0			0
$556$	−874.914	+	1515.40i	−0.0667349	+	0.115588i
$557$	−6672.82	−	11557.7i	−0.507606	−	0.879199i	−0.999961	−	0.00880454i	$-0.997197\pi$
$557$	−6672.82	−	11557.7i	−0.507606	−	0.879199i	0.492356	−	0.870394i	$-0.336136\pi$
$558$		0			0
$559$	21745.0			1.64528
$560$	−11018.7	−	19085.0i	−0.831474	−	1.44016i
$561$		0			0
$562$	−5003.23			−0.375531
$563$	20502.4			1.53477			0.767384	−	0.641188i	$-0.221558\pi$
$563$	20502.4			1.53477			0.767384	+	0.641188i	$0.221558\pi$
$564$		0			0
$565$	−7663.61	+	13273.8i	−0.570638	+	0.988374i
$566$	1371.40	+	2375.34i	0.101845	+	0.176401i
$567$		0			0
$568$	249.938	−	432.905i	0.0184633	−	0.0319794i
$569$	508.261			0.0374471			0.0187236	−	0.999825i	$-0.494040\pi$
$569$	508.261			0.0374471			0.0187236	+	0.999825i	$0.494040\pi$
$570$		0			0
$571$	−4594.65			−0.336743			−0.168371	−	0.985724i	$-0.553851\pi$
$571$	−4594.65			−0.336743			−0.168371	+	0.985724i	$0.553851\pi$
$572$	−6372.87	+	11038.1i	−0.465845	+	0.806867i
$573$		0			0
$574$	−4187.44	−	7252.86i	−0.304496	−	0.527402i
$575$	−2174.34	+	3766.06i	−0.157698	+	0.273140i
$576$		0			0
$577$	−2104.42			−0.151834			−0.0759170	−	0.997114i	$-0.524188\pi$
$577$	−2104.42			−0.151834			−0.0759170	+	0.997114i	$0.524188\pi$
$578$	−30864.2			−2.22108
$579$		0			0
$580$	−5349.28	−	9265.22i	−0.382960	−	0.663306i
$581$	18108.2			1.29304
$582$		0			0
$583$	−8979.39	−	15552.8i	−0.637888	−	1.10485i
$584$	5077.55	−	8794.57i	0.359778	−	0.623154i
$585$		0			0
$586$	293.206	−	507.848i	0.0206693	−	0.0358003i
$587$	4334.65	−	7507.84i	0.304787	−	0.527907i	−0.672427	−	0.740164i	$-0.734748\pi$
$587$	4334.65	−	7507.84i	0.304787	−	0.527907i	0.977214	+	0.212257i	$0.0680813\pi$
$588$		0			0
$589$	9540.06	+	19692.1i	0.667388	+	1.37759i
$590$	−12376.0			−0.863579
$591$		0			0
$592$	−15396.9	+	26668.2i	−1.06893	+	1.85144i
$593$	9878.50	+	17110.1i	0.684084	+	1.18487i	0.973724	+	0.227732i	$0.0731310\pi$
$593$	9878.50	+	17110.1i	0.684084	+	1.18487i	−0.289640	+	0.957136i	$0.593536\pi$
$594$		0			0
$595$	16243.3	+	28134.2i	1.11918	+	1.93847i
$596$	−6479.54			−0.445322
$597$		0			0
$598$	−8395.40	−	14541.3i	−0.574103	−	0.994375i
$599$	−297.408	−	515.125i	−0.0202867	−	0.0351376i	0.855704	−	0.517466i	$-0.173125\pi$
$599$	−297.408	−	515.125i	−0.0202867	−	0.0351376i	−0.875991	+	0.482328i	$0.839791\pi$
$600$		0			0
$601$	15851.2			1.07585			0.537923	−	0.842994i	$-0.319209\pi$
$601$	15851.2			1.07585			0.537923	+	0.842994i	$0.319209\pi$
$602$	10803.4	+	18712.0i	0.731416	+	1.26685i
$603$		0			0
$604$	−4166.64	−	7216.84i	−0.280692	−	0.486174i
$605$	−6677.61	+	11566.0i	−0.448733	+	0.777228i
$606$		0			0
$607$	9350.34			0.625237			0.312618	−	0.949879i	$-0.398794\pi$
$607$	9350.34			0.625237			0.312618	+	0.949879i	$0.398794\pi$
$608$	7416.20	−	10932.4i	0.494682	−	0.729225i
$609$		0			0
$610$	−6749.75	+	11690.9i	−0.448016	+	0.775986i
$611$	4010.35	−	6946.13i	0.265534	−	0.459919i
$612$		0			0
$613$	5438.10	−	9419.06i	0.358308	−	0.620607i	−0.629370	−	0.777105i	$-0.716687\pi$
$613$	5438.10	−	9419.06i	0.358308	−	0.620607i	0.987678	+	0.156498i	$0.0500205\pi$
$614$	9275.90	+	16066.3i	0.609682	+	1.05600i
$615$		0			0
$616$	13946.9			0.912235
$617$	−9676.84	−	16760.8i	−0.631402	−	1.09362i	−0.987265	−	0.159082i	$-0.949147\pi$
$617$	−9676.84	−	16760.8i	−0.631402	−	1.09362i	0.355864	−	0.934538i	$-0.384187\pi$
$618$		0			0
$619$	−9439.93			−0.612961			−0.306480	−	0.951877i	$-0.599151\pi$
$619$	−9439.93			−0.612961			−0.306480	+	0.951877i	$0.599151\pi$
$620$	13756.3			0.891076
$621$		0			0
$622$	−3503.43	+	6068.12i	−0.225844	+	0.391173i
$623$	−2024.73	−	3506.94i	−0.130208	−	0.225526i
$624$		0			0
$625$	9765.51	−	16914.4i	0.624993	−	1.08252i
$626$	−14307.0			−0.913458
$627$		0			0
$628$	10528.9			0.669030
$629$	22697.4	−	39313.0i	1.43880	−	2.49207i
$630$		0			0
$631$	−1928.16	−	3339.68i	−0.121646	−	0.210698i	0.798771	−	0.601636i	$-0.205484\pi$
$631$	−1928.16	−	3339.68i	−0.121646	−	0.210698i	−0.920417	+	0.390938i	$0.872151\pi$
$632$	−4235.05	+	7335.32i	−0.266553	+	0.461683i
$633$		0			0
$634$	21887.0			1.37105
$635$	−20763.0			−1.29756
$636$		0			0
$637$	2199.51	+	3809.66i	0.136809	+	0.236961i
$638$	33917.2			2.10469
$639$		0			0
$640$	10877.7	+	18840.7i	0.671842	+	1.16367i
$641$	−13098.6	+	22687.4i	−0.807117	+	1.39797i	0.107735	+	0.994180i	$0.465640\pi$
$641$	−13098.6	+	22687.4i	−0.807117	+	1.39797i	−0.914852	+	0.403788i	$0.867693\pi$
$642$		0			0
$643$	−7522.53	+	13029.4i	−0.461368	+	0.799113i	−0.999029	−	0.0440482i	$-0.985974\pi$
$643$	−7522.53	+	13029.4i	−0.461368	+	0.799113i	0.537662	+	0.843161i	$0.319308\pi$
$644$	2689.90	−	4659.04i	0.164592	−	0.285081i
$645$		0			0
$646$	−18832.1	+	27760.9i	−1.14696	+	1.69077i
$647$	−4217.62			−0.256278			−0.128139	−	0.991756i	$-0.540900\pi$
$647$	−4217.62			−0.256278			−0.128139	+	0.991756i	$0.540900\pi$
$648$		0			0
$649$	6325.71	−	10956.5i	0.382598	−	0.662679i
$650$	−7425.93	−	12862.1i	−0.448106	−	0.776142i
$651$		0			0
$652$	6731.75	+	11659.7i	0.404349	+	0.700353i
$653$	9871.02			0.591551			0.295776	−	0.955257i	$-0.404422\pi$
$653$	9871.02			0.591551			0.295776	+	0.955257i	$0.404422\pi$
$654$		0			0
$655$	1924.00	+	3332.46i	0.114774	+	0.198794i
$656$	4835.42	+	8375.19i	0.287792	+	0.498470i
$657$		0			0
$658$	7969.71			0.472176
$659$	−13580.8	−	23522.6i	−0.802781	−	1.39046i	−0.917779	−	0.397092i	$-0.870019\pi$
$659$	−13580.8	−	23522.6i	−0.802781	−	1.39046i	0.114998	−	0.993366i	$-0.463314\pi$
$660$		0			0
$661$	−2406.19	−	4167.65i	−0.141589	−	0.245239i	0.786506	−	0.617582i	$-0.211888\pi$
$661$	−2406.19	−	4167.65i	−0.141589	−	0.245239i	−0.928095	+	0.372343i	$0.878554\pi$
$662$	7106.36	−	12308.6i	0.417216	−	0.722638i
$663$		0			0
$664$	−12945.5			−0.756599
$665$	22764.7	+	1652.42i	1.32748	+	0.0963582i
$666$		0			0
$667$	−7203.78	+	12477.3i	−0.418188	+	0.724323i
$668$	3302.30	−	5719.76i	0.191272	−	0.331294i
$669$		0			0
$670$	−11316.4	+	19600.7i	−0.652526	+	1.13021i
$671$	−6899.96	−	11951.1i	−0.396975	−	0.687581i
$672$		0			0
$673$	−1181.18			−0.0676540			−0.0338270	−	0.999428i	$-0.510770\pi$
$673$	−1181.18			−0.0676540			−0.0338270	+	0.999428i	$0.510770\pi$
$674$	5312.17	+	9200.95i	0.303586	+	0.525827i
$675$		0			0
$676$	10126.4			0.576150
$677$	−10321.0			−0.585919			−0.292959	−	0.956125i	$-0.594640\pi$
$677$	−10321.0			−0.585919			−0.292959	+	0.956125i	$0.594640\pi$
$678$		0			0
$679$	154.841	−	268.193i	0.00875150	−	0.0151580i
$680$	−11612.3	−	20113.0i	−0.654868	−	1.13426i
$681$		0			0
$682$	−21805.5	+	37768.3i	−1.22431	+	2.12056i
$683$	29335.0			1.64344			0.821721	−	0.569889i	$-0.193014\pi$
$683$	29335.0			1.64344			0.821721	+	0.569889i	$0.193014\pi$
$684$		0			0
$685$	−35467.6			−1.97832
$686$	9690.40	−	16784.3i	0.539331	−	0.934149i
$687$		0			0
$688$	−12475.1	−	21607.5i	−0.691292	−	1.19735i
$689$	−13026.9	+	22563.3i	−0.720299	+	1.24760i
$690$		0			0
$691$	22205.1			1.22247			0.611233	−	0.791451i	$-0.290674\pi$
$691$	22205.1			1.22247			0.611233	+	0.791451i	$0.290674\pi$
$692$	13416.0			0.736993
$693$		0			0
$694$	14190.1	+	24578.0i	0.776153	+	1.34434i
$695$	6285.29			0.343043
$696$		0			0
$697$	−7128.16	−	12346.3i	−0.387372	−	0.670948i
$698$	−21794.6	+	37749.4i	−1.18186	+	2.04704i
$699$		0			0
$700$	2379.28	−	4121.03i	0.128469	−	0.222515i
$701$	2076.36	−	3596.37i	0.111873	−	0.193770i	−0.804652	−	0.593746i	$-0.797648\pi$
$701$	2076.36	−	3596.37i	0.111873	−	0.193770i	0.916526	+	0.399976i	$0.130982\pi$
$702$		0			0
$703$	−13905.3	−	28702.7i	−0.746017	−	1.53989i
$704$	−4400.06			−0.235559
$705$		0			0
$706$	17452.6	−	30228.7i	0.930363	−	1.61144i
$707$	−3034.40	−	5255.73i	−0.161415	−	0.279579i
$708$		0			0
$709$	11645.4	+	20170.5i	0.616859	+	1.06843i	0.990055	+	0.140679i	$0.0449286\pi$
$709$	11645.4	+	20170.5i	0.616859	+	1.06843i	−0.373196	+	0.927753i	$0.621738\pi$
$710$	1630.46			0.0861832
$711$		0			0
$712$	1447.47	+	2507.10i	0.0761888	+	0.131963i
$713$	−9262.70	−	16043.5i	−0.486523	−	0.842682i
$714$		0			0
$715$	45782.1			2.39462
$716$	−4315.25	−	7474.24i	−0.225235	−	0.390119i
$717$		0			0
$718$	9518.29	+	16486.2i	0.494735	+	0.856905i
$719$	−13084.6	+	22663.1i	−0.678682	+	1.17551i	0.296696	+	0.954972i	$0.404115\pi$
$719$	−13084.6	+	22663.1i	−0.678682	+	1.17551i	−0.975378	+	0.220540i	$0.929218\pi$
$720$		0			0
$721$	−18125.8			−0.936255
$722$	8713.19	+	21898.9i	0.449129	+	1.12880i
$723$		0			0
$724$	1964.14	−	3402.00i	0.100824	−	0.174633i
$725$	−6371.91	+	11036.5i	−0.326410	+	0.565358i
$726$		0			0
$727$	15166.3	−	26268.8i	0.773708	−	1.34010i	−0.161809	−	0.986822i	$-0.551733\pi$
$727$	15166.3	−	26268.8i	0.773708	−	1.34010i	0.935518	−	0.353280i	$-0.114934\pi$
$728$	−10116.8	−	17522.8i	−0.515045	−	0.892085i
$729$		0			0
$730$	33123.2			1.67937
$731$	18390.2	+	31852.8i	0.930489	+	1.61165i
$732$		0			0
$733$	14731.3			0.742308			0.371154	−	0.928571i	$-0.378962\pi$
$733$	14731.3			0.742308			0.371154	+	0.928571i	$0.378962\pi$
$734$	21031.0			1.05759
$735$		0			0
$736$	−5592.21	+	9685.99i	−0.280070	+	0.485096i
$737$	−11568.3	−	20036.9i	−0.578187	−	1.00145i
$738$		0			0
$739$	−6622.38	+	11470.3i	−0.329646	+	0.570963i	−0.982442	−	0.186571i	$-0.940263\pi$
$739$	−6622.38	+	11470.3i	−0.329646	+	0.570963i	0.652796	+	0.757534i	$0.273596\pi$
$740$	−20050.8			−0.996059
$741$		0			0
$742$	−25888.2			−1.28084
$743$	−11120.8	+	19261.8i	−0.549102	+	0.951072i	0.449234	+	0.893414i	$0.351697\pi$
$743$	−11120.8	+	19261.8i	−0.549102	+	0.951072i	−0.998336	+	0.0576585i	$0.981637\pi$
$744$		0			0
$745$	11637.1	+	20156.0i	0.572281	+	0.991220i
$746$	−907.718	+	1572.21i	−0.0445495	+	0.0771619i
$747$		0			0
$748$	−21558.8			−1.05383
$749$	−22929.2			−1.11858
$750$		0			0
$751$	−7341.12	−	12715.2i	−0.356699	−	0.617821i	0.630708	−	0.776020i	$-0.282765\pi$
$751$	−7341.12	−	12715.2i	−0.356699	−	0.617821i	−0.987407	+	0.158199i	$0.949431\pi$
$752$	−9202.96			−0.446273
$753$		0			0
$754$	−24602.8	−	42613.3i	−1.18830	−	2.05820i
$755$	−14966.4	+	25922.5i	−0.721433	+	1.24956i
$756$		0			0
$757$	−348.860	+	604.243i	−0.0167497	+	0.0290113i	−0.874279	−	0.485424i	$-0.838665\pi$
$757$	−348.860	+	604.243i	−0.0167497	+	0.0290113i	0.857529	+	0.514436i	$0.171999\pi$
$758$	−6258.78	+	10840.5i	−0.299907	+	0.519453i
$759$		0			0
$760$	−16274.4	−	1181.31i	−0.776756	−	0.0563824i
$761$	−8661.54			−0.412589			−0.206295	−	0.978490i	$-0.566141\pi$
$761$	−8661.54			−0.412589			−0.206295	+	0.978490i	$0.566141\pi$
$762$		0			0
$763$	−2514.77	+	4355.71i	−0.119319	+	0.206667i
$764$	−4224.62	−	7317.26i	−0.200054	−	0.346504i
$765$		0			0
$766$	473.933	+	820.877i	0.0223550	+	0.0387200i
$767$	−18354.1			−0.864055
$768$		0			0
$769$	−7896.13	−	13676.5i	−0.370275	−	0.641336i	0.619332	−	0.785129i	$-0.287403\pi$
$769$	−7896.13	−	13676.5i	−0.370275	−	0.641336i	−0.989608	+	0.143793i	$0.954070\pi$
$770$	22745.5	+	39396.4i	1.06453	+	1.84383i
$771$		0			0
$772$	−4798.55			−0.223709
$773$	12645.3	+	21902.3i	0.588384	+	1.01911i	0.994444	+	0.105264i	$0.0335689\pi$
$773$	12645.3	+	21902.3i	0.588384	+	1.01911i	−0.406061	+	0.913846i	$0.633098\pi$
$774$		0			0
$775$	−8193.07	−	14190.8i	−0.379747	−	0.657741i
$776$	−110.695	+	191.730i	−0.00512079	+	0.00886948i
$777$		0			0
$778$	21445.2			0.988236
$779$	−9989.99	−	725.144i	−0.459472	−	0.0333517i
$780$		0			0
$781$	−833.373	+	1443.44i	−0.0381824	+	0.0661338i
$782$	14200.4	−	24595.8i	0.649367	−	1.12474i
$783$		0			0
$784$	2523.72	−	4371.21i	0.114965	−	0.199126i
$785$	−18909.7	−	32752.6i	−0.859766	−	1.48916i
$786$		0			0
$787$	5864.90			0.265643			0.132822	−	0.991140i	$-0.457596\pi$
$787$	5864.90			0.265643			0.132822	+	0.991140i	$0.457596\pi$
$788$	−2084.27	−	3610.06i	−0.0942247	−	0.163202i
$789$		0			0
$790$	−27627.2			−1.24422
$791$	−22586.4			−1.01527
$792$		0			0
$793$	−10010.2	+	17338.1i	−0.448262	+	0.776413i
$794$	18089.3	+	31331.6i	0.808521	+	1.40040i
$795$		0			0
$796$	523.601	−	906.904i	0.0233148	−	0.0403824i
$797$	24968.0			1.10967			0.554837	−	0.831959i	$-0.312781\pi$
$797$	24968.0			1.10967			0.554837	+	0.831959i	$0.312781\pi$
$798$		0			0
$799$	13566.6			0.600690
$800$	−4946.44	+	8567.49i	−0.218604	+	0.378633i
$801$		0			0
$802$	−254.307	−	440.472i	−0.0111969	−	0.0193935i
$803$	−16930.1	+	29323.9i	−0.744025	+	1.28869i
$804$		0			0
$805$	−19324.0			−0.846063
$806$	63269.1			2.76496
$807$		0			0
$808$	2169.28	+	3757.30i	0.0944492	+	0.163591i
$809$	−6447.62			−0.280206			−0.140103	−	0.990137i	$-0.544743\pi$
$809$	−6447.62			−0.280206			−0.140103	+	0.990137i	$0.544743\pi$
$810$		0			0
$811$	14130.1	+	24474.0i	0.611806	+	1.05968i	0.990936	+	0.134336i	$0.0428901\pi$
$811$	14130.1	+	24474.0i	0.611806	+	1.05968i	−0.379130	+	0.925344i	$0.623777\pi$
$812$	7882.78	−	13653.4i	0.340679	−	0.590073i
$813$		0			0
$814$	31783.2	−	55050.0i	1.36855	−	2.37040i
$815$	24180.1	−	41881.1i	1.03925	−	1.80004i
$816$		0			0
$817$	25773.6	+	1870.83i	1.10368	+	0.0801127i
$818$	−40455.1			−1.72919
$819$		0			0
$820$	−3148.50	+	5453.37i	−0.134086	+	0.232244i
$821$	−16719.7	−	28959.4i	−0.710745	−	1.23105i	−0.964578	−	0.263798i	$-0.915025\pi$
$821$	−16719.7	−	28959.4i	−0.710745	−	1.23105i	0.253833	−	0.967248i	$-0.418309\pi$
$822$		0			0
$823$	−12853.8	−	22263.4i	−0.544417	−	0.942958i	−0.998643	−	0.0520717i	$-0.983418\pi$
$823$	−12853.8	−	22263.4i	−0.544417	−	0.942958i	0.454226	−	0.890886i	$-0.349916\pi$
$824$	12958.1			0.547834
$825$		0			0
$826$	−9118.73	−	15794.1i	−0.384118	−	0.665312i
$827$	18188.6	+	31503.5i	0.764786	+	1.32465i	0.940360	+	0.340182i	$0.110489\pi$
$827$	18188.6	+	31503.5i	0.764786	+	1.32465i	−0.175574	+	0.984466i	$0.556178\pi$
$828$		0			0
$829$	−7507.51			−0.314532			−0.157266	−	0.987556i	$-0.550268\pi$
$829$	−7507.51			−0.314532			−0.157266	+	0.987556i	$0.550268\pi$
$830$	−21112.3	−	36567.6i	−0.882914	−	1.52925i
$831$		0			0
$832$	3191.71	+	5528.20i	0.132996	+	0.230356i
$833$	−3720.35	+	6443.84i	−0.154745	+	0.268026i
$834$		0			0
$835$	−23723.4			−0.983213
$836$	−8503.23	+	12534.9i	−0.351783	+	0.518573i
$837$		0			0
$838$	24365.1	−	42201.7i	1.00439	−	1.73966i
$839$	11882.5	−	20581.1i	0.488951	−	0.846888i	−0.510968	−	0.859600i	$-0.670713\pi$
$839$	11882.5	−	20581.1i	0.488951	−	0.846888i	0.999919	+	0.0127114i	$0.00404627\pi$
$840$		0			0
$841$	−8916.26	+	15443.4i	−0.365585	+	0.633212i
$842$	−4458.80	−	7722.87i	−0.182495	−	0.316090i
$843$		0			0
$844$	345.259			0.0140809
$845$	−18186.8	−	31500.4i	−0.740407	−	1.28242i
$846$		0			0
$847$	−19680.4			−0.798380
$848$	29894.2			1.21058
$849$		0			0
$850$	12560.6	−	21755.5i	0.506852	−	0.877893i
$851$	13501.1	+	23384.5i	0.543843	+	0.941964i
$852$		0			0
$853$	1044.10	−	1808.43i	0.0419101	−	0.0725904i	−0.844309	−	0.535856i	$-0.819989\pi$
$853$	1044.10	−	1808.43i	0.0419101	−	0.0725904i	0.886220	+	0.463265i	$0.153322\pi$
$854$	−19893.1			−0.797104
$855$		0			0
$856$	16392.0			0.654518
$857$	11006.9	−	19064.4i	0.438725	−	0.759894i	−0.558867	−	0.829258i	$-0.688764\pi$
$857$	11006.9	−	19064.4i	0.438725	−	0.759894i	0.997591	+	0.0693638i	$0.0220969\pi$
$858$		0			0
$859$	−882.757	−	1528.98i	−0.0350632	−	0.0607312i	0.847961	−	0.530058i	$-0.177830\pi$
$859$	−882.757	−	1528.98i	−0.0350632	−	0.0607312i	−0.883024	+	0.469327i	$0.844497\pi$
$860$	8122.96	−	14069.4i	0.322082	−	0.557862i
$861$		0			0
$862$	530.025			0.0209428
$863$	−1230.83			−0.0485492			−0.0242746	−	0.999705i	$-0.507728\pi$
$863$	−1230.83			−0.0485492			−0.0242746	+	0.999705i	$0.507728\pi$
$864$		0			0
$865$	−24094.8	−	41733.4i	−0.947106	−	1.64044i
$866$	42393.6			1.66350
$867$		0			0
$868$	10135.8	+	17555.6i	0.396348	+	0.686495i
$869$	14121.0	−	24458.3i	0.551234	−	0.954765i
$870$		0			0
$871$	−16782.8	+	29068.6i	−0.652885	+	1.13083i
$872$	1797.80	−	3113.88i	0.0698178	−	0.120928i
$873$		0			0
$874$	−8699.74	−	17957.6i	−0.336697	−	0.694993i
$875$	17357.0			0.670598
$876$		0			0
$877$	−16694.1	+	28915.1i	−0.642783	+	1.11333i	0.342026	+	0.939690i	$0.388887\pi$
$877$	−16694.1	+	28915.1i	−0.642783	+	1.11333i	−0.984809	+	0.173642i	$0.944446\pi$
$878$	−21232.8	−	36776.4i	−0.816143	−	1.41360i
$879$		0			0
$880$	−26265.2	−	45492.7i	−1.00614	−	1.74268i
$881$	37508.8			1.43440			0.717198	−	0.696869i	$-0.245424\pi$
$881$	37508.8			1.43440			0.717198	+	0.696869i	$0.245424\pi$
$882$		0			0
$883$	−6307.84	−	10925.5i	−0.240403	−	0.416390i	0.720426	−	0.693532i	$-0.243946\pi$
$883$	−6307.84	−	10925.5i	−0.240403	−	0.416390i	−0.960829	+	0.277142i	$0.910613\pi$
$884$	15638.3	+	27086.3i	0.594991	+	1.03055i
$885$		0			0
$886$	−41913.7			−1.58930
$887$	−7532.37	−	13046.4i	−0.285132	−	0.493863i	0.687509	−	0.726176i	$-0.258704\pi$
$887$	−7532.37	−	13046.4i	−0.285132	−	0.493863i	−0.972641	+	0.232312i	$0.925371\pi$
$888$		0			0
$889$	−15298.3	−	26497.5i	−0.577153	−	0.999658i
$890$	−4721.27	+	8177.48i	−0.177817	+	0.307988i
$891$		0			0
$892$	−854.905			−0.0320901
$893$	5350.95	−	7887.99i	0.200518	−	0.295590i
$894$		0			0
$895$	−15500.2	+	26847.1i	−0.578898	+	1.00268i
$896$	−16029.6	+	27764.0i	−0.597667	+	1.03519i
$897$		0			0
$898$	−510.179	+	883.656i	−0.0189587	+	0.0328374i
$899$	−27144.4	−	47015.5i	−1.00703	−	1.74422i
$900$		0			0
$901$	−44068.7			−1.62946
$902$	−9981.56	−	17288.6i	−0.368459	−	0.638189i
$903$		0			0
$904$	16146.9			0.594070
$905$	−14110.2			−0.518275
$906$		0			0
$907$	12114.7	−	20983.3i	0.443509	−	0.768180i	−0.554438	−	0.832225i	$-0.687067\pi$
$907$	12114.7	−	20983.3i	0.443509	−	0.768180i	0.997947	+	0.0640453i	$0.0204002\pi$
$908$	−7425.34	−	12861.1i	−0.271386	−	0.470055i
$909$		0			0
$910$	32998.2	−	57154.6i	1.20207	−	2.08204i
$911$	48867.9			1.77724			0.888619	−	0.458645i	$-0.151665\pi$
$911$	48867.9			1.77724			0.888619	+	0.458645i	$0.151665\pi$
$912$		0			0
$913$	43164.3			1.56465
$914$	−19846.3	+	34374.8i	−0.718224	+	1.24400i
$915$		0			0
$916$	7627.04	+	13210.4i	0.275114	+	0.476511i
$917$	−2835.23	+	4910.77i	−0.102102	+	0.176846i
$918$		0			0
$919$	26159.2			0.938969			0.469484	−	0.882941i	$-0.344440\pi$
$919$	26159.2			0.938969			0.469484	+	0.882941i	$0.344440\pi$
$920$	13814.6			0.495060
$921$		0			0
$922$	24679.1	+	42745.5i	0.881522	+	1.52684i
$923$	2418.04			0.0862306
$924$		0			0
$925$	11942.0	+	20684.1i	0.424487	+	0.735233i
$926$	10874.2	−	18834.6i	0.385904	−	0.668405i
$927$		0			0
$928$	−16388.0	+	28384.9i	−0.579702	+	1.00407i
$929$	−20608.9	+	35695.6i	−0.727831	+	1.26064i	0.229968	+	0.973198i	$0.426138\pi$
$929$	−20608.9	+	35695.6i	−0.727831	+	1.26064i	−0.957798	+	0.287441i	$0.907195\pi$
$930$		0			0
$931$	2279.24	+	4704.70i	0.0802353	+	0.165618i
$932$	−18724.7			−0.658098
$933$		0			0
$934$	−8345.93	+	14455.6i	−0.292385	+	0.506425i
$935$	38719.0	+	67063.2i	1.35427	+	2.34567i
$936$		0			0
$937$	−765.118	−	1325.22i	−0.0266759	−	0.0462040i	0.852379	−	0.522924i	$-0.175159\pi$
$937$	−765.118	−	1325.22i	−0.0266759	−	0.0462040i	−0.879055	+	0.476720i	$0.841826\pi$
$938$	−33352.2			−1.16097
$939$		0			0
$940$	−2996.18	−	5189.53i	−0.103962	−	0.180068i
$941$	28011.5	+	48517.3i	0.970402	+	1.68079i	0.694342	+	0.719645i	$0.255696\pi$
$941$	28011.5	+	48517.3i	0.970402	+	1.68079i	0.276060	+	0.961140i	$0.410971\pi$
$942$		0			0
$943$	8480.07			0.292841
$944$	10529.8	+	18238.1i	0.363046	+	0.628814i
$945$		0			0
$946$	25751.9	+	44603.5i	0.885058	+	1.53297i
$947$	−13508.1	+	23396.7i	−0.463520	+	0.802840i	−0.999133	−	0.0416230i	$-0.986747\pi$
$947$	−13508.1	+	23396.7i	−0.463520	+	0.802840i	0.535613	+	0.844463i	$0.320081\pi$
$948$		0			0
$949$	49123.1			1.68030
$950$	−7695.12	−	15883.9i	−0.262803	−	0.542465i
$951$		0			0
$952$	17112.0	−	29638.9i	0.582567	−	1.00904i
$953$	3150.12	−	5456.17i	0.107075	−	0.185459i	−0.807509	−	0.589855i	$-0.799185\pi$
$953$	3150.12	−	5456.17i	0.107075	−	0.185459i	0.914584	+	0.404396i	$0.132518\pi$
$954$		0			0
$955$	−15174.6	+	26283.2i	−0.514177	+	0.890580i
$956$	8551.58	+	14811.8i	0.289307	+	0.501095i
$957$		0			0
$958$	−27095.4			−0.913792
$959$	−26132.8	−	45263.4i	−0.879951	−	1.52412i
$960$		0			0
$961$	40014.1			1.34316
$962$	−92219.3			−3.09072
$963$		0			0
$964$	−2818.14	+	4881.16i	−0.0941558	+	0.163083i
$965$	8618.07	+	14926.9i	0.287488	+	0.497943i
$966$		0			0
$967$	−17965.7	+	31117.4i	−0.597453	+	1.03482i	0.395743	+	0.918361i	$0.370487\pi$
$967$	−17965.7	+	31117.4i	−0.597453	+	1.03482i	−0.993196	+	0.116457i	$0.962846\pi$
$968$	14069.5			0.467159
$969$		0			0
$970$	−722.117			−0.0239029
$971$	27922.0	−	48362.3i	0.922820	−	1.59837i	0.127791	−	0.991801i	$-0.459211\pi$
$971$	27922.0	−	48362.3i	0.922820	−	1.59837i	0.795030	−	0.606571i	$-0.207455\pi$
$972$		0			0
$973$	4631.05	+	8021.21i	0.152584	+	0.264284i
$974$	−11542.3	+	19991.8i	−0.379711	+	0.657679i
$975$		0			0
$976$	22971.4			0.753377
$977$	−23155.4			−0.758247			−0.379124	−	0.925346i	$-0.623774\pi$
$977$	−23155.4			−0.758247			−0.379124	+	0.925346i	$0.623774\pi$
$978$		0			0
$979$	−4826.34	−	8359.46i	−0.157559	−	0.272901i
$980$	3286.55			0.107128
$981$		0			0
$982$	−4436.36	−	7684.01i	−0.144165	−	0.249701i
$983$	22002.7	−	38109.8i	0.713914	−	1.23654i	−0.249463	−	0.968384i	$-0.580254\pi$
$983$	22002.7	−	38109.8i	0.713914	−	1.23654i	0.963377	−	0.268151i	$-0.0864126\pi$
$984$		0			0
$985$	−7486.59	+	12967.2i	−0.242175	+	0.419460i
$986$	41614.4	−	72078.2i	1.34409	−	2.32803i
$987$		0			0
$988$	21916.8	+	1590.87i	0.705734	+	0.0512272i
$989$	−21878.1			−0.703420
$990$		0			0
$991$	−22980.8	+	39803.9i	−0.736639	+	1.27590i	0.217362	+	0.976091i	$0.430255\pi$
$991$	−22980.8	+	39803.9i	−0.736639	+	1.27590i	−0.954001	+	0.299805i	$0.903078\pi$
$992$	−21071.9	−	36497.6i	−0.674429	−	1.16814i
$993$		0			0
$994$	1201.34	+	2080.77i	0.0383341	+	0.0663965i
$995$	−3761.50			−0.119847
$996$		0			0
$997$	19751.6	+	34210.7i	0.627420	+	1.08672i	0.988067	+	0.154022i	$0.0492225\pi$
$997$	19751.6	+	34210.7i	0.627420	+	1.08672i	−0.360647	+	0.932702i	$0.617444\pi$
$998$	−32270.2	−	55893.6i	−1.02354	−	1.77283i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.4.f.h.163.5	yes	12
3.2	odd	2	inner	171.4.f.h.163.2	yes	12
19.7	even	3	inner	171.4.f.h.64.5	yes	12
57.26	odd	6	inner	171.4.f.h.64.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.4.f.h.64.2	✓	12	57.26	odd	6	inner
171.4.f.h.64.5	yes	12	19.7	even	3	inner
171.4.f.h.163.2	yes	12	3.2	odd	2	inner
171.4.f.h.163.5	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	171.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.71809 - 2.97581i) q^{2} +(-1.90364 - 3.29720i) q^{4} +(-6.83777 + 11.8434i) q^{5} -20.1525 q^{7} +14.4069 q^{8} +O(q^{10})\)	\(q+(1.71809 - 2.97581i) q^{2} +(-1.90364 - 3.29720i) q^{4} +(-6.83777 + 11.8434i) q^{5} -20.1525 q^{7} +14.4069 q^{8} +(23.4957 + 40.6958i) q^{10} -48.0372 q^{11} +(34.8452 + 60.3537i) q^{13} +(-34.6237 + 59.9700i) q^{14} +(39.9814 - 69.2499i) q^{16} +(-58.9388 + 102.085i) q^{17} +(36.1083 + 74.5331i) q^{19} +52.0665 q^{20} +(-82.5321 + 142.950i) q^{22} +(-35.0585 - 60.7232i) q^{23} +(-31.0101 - 53.7110i) q^{25} +239.468 q^{26} +(38.3630 + 66.4467i) q^{28} +(-102.739 - 177.950i) q^{29} +264.207 q^{31} +(-79.7553 - 138.140i) q^{32} +(202.524 + 350.782i) q^{34} +(137.798 - 238.673i) q^{35} -385.101 q^{37} +(283.834 + 20.6027i) q^{38} +(-98.5112 + 170.626i) q^{40} +(-60.4708 + 104.738i) q^{41} +(156.011 - 270.219i) q^{43} +(91.4455 + 158.388i) q^{44} -240.934 q^{46} +(-57.5452 - 99.6712i) q^{47} +63.1222 q^{49} -213.112 q^{50} +(132.665 - 229.783i) q^{52} +(186.926 + 323.765i) q^{53} +(328.467 - 568.922i) q^{55} -290.335 q^{56} -706.060 q^{58} +(-131.683 + 228.082i) q^{59} +(143.638 + 248.788i) q^{61} +(453.930 - 786.229i) q^{62} +91.5968 q^{64} -953.053 q^{65} +(240.819 + 417.111i) q^{67} +448.793 q^{68} +(-473.497 - 820.121i) q^{70} +(17.3485 - 30.0484i) q^{71} +(352.438 - 610.440i) q^{73} +(-661.636 + 1145.99i) q^{74} +(177.013 - 260.940i) q^{76} +968.069 q^{77} +(-293.959 + 509.153i) q^{79} +(546.767 + 947.029i) q^{80} +(207.788 + 359.899i) q^{82} -898.559 q^{83} +(-806.020 - 1396.07i) q^{85} +(-536.081 - 928.520i) q^{86} -692.069 q^{88} +(100.471 + 174.020i) q^{89} +(-702.217 - 1216.28i) q^{91} +(-133.477 + 231.190i) q^{92} -395.470 q^{94} +(-1129.62 - 81.9960i) q^{95} +(-7.68349 + 13.3082i) q^{97} +(108.449 - 187.840i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 52 q^{4} - 60 q^{7}+O(q^{10}) \) 12 * q - 52 * q^4 - 60 * q^7	\( 12 q - 52 q^{4} - 60 q^{7} - 56 q^{10} + 178 q^{13} - 172 q^{16} + 296 q^{19} - 944 q^{22} - 458 q^{25} - 140 q^{28} + 196 q^{31} - 400 q^{34} + 628 q^{37} + 48 q^{40} + 642 q^{43} - 960 q^{46} - 2296 q^{49} - 300 q^{52} + 648 q^{55} - 2880 q^{58} + 3446 q^{61} + 9528 q^{64} + 2730 q^{67} - 1920 q^{70} + 1690 q^{73} - 4308 q^{76} - 2898 q^{79} - 1616 q^{82} - 4176 q^{85} + 11856 q^{88} - 3210 q^{91} - 5280 q^{94} - 1180 q^{97}+O(q^{100}) \) 12 * q - 52 * q^4 - 60 * q^7 - 56 * q^10 + 178 * q^13 - 172 * q^16 + 296 * q^19 - 944 * q^22 - 458 * q^25 - 140 * q^28 + 196 * q^31 - 400 * q^34 + 628 * q^37 + 48 * q^40 + 642 * q^43 - 960 * q^46 - 2296 * q^49 - 300 * q^52 + 648 * q^55 - 2880 * q^58 + 3446 * q^61 + 9528 * q^64 + 2730 * q^67 - 1920 * q^70 + 1690 * q^73 - 4308 * q^76 - 2898 * q^79 - 1616 * q^82 - 4176 * q^85 + 11856 * q^88 - 3210 * q^91 - 5280 * q^94 - 1180 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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